LMFDB - Embedded newform 273.2.bz.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	273.73
Dual form			273.2.bz.b.187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.677708 + 2.52924i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-4.20573 - 2.42818i) q^{4} +(3.92082 + 1.05058i) q^{5} +(1.85153 - 1.85153i) q^{6} +(1.12389 + 2.39518i) q^{7} +(5.28864 - 5.28864i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.677708 + 2.52924i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-4.20573 - 2.42818i) q^{4} +(3.92082 + 1.05058i) q^{5} +(1.85153 - 1.85153i) q^{6} +(1.12389 + 2.39518i) q^{7} +(5.28864 - 5.28864i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-5.31435 + 9.20472i) q^{10} +(-0.150292 - 0.560897i) q^{11} +(2.42818 + 4.20573i) q^{12} +(2.59678 + 2.50134i) q^{13} +(-6.81965 + 1.21935i) q^{14} +(-2.87024 - 2.87024i) q^{15} +(4.93574 + 8.54896i) q^{16} +(-0.229516 + 0.397534i) q^{17} +(-2.52924 + 0.677708i) q^{18} +(-7.44023 - 1.99360i) q^{19} +(-13.9389 - 13.9389i) q^{20} +(0.224276 - 2.63623i) q^{21} +1.52050 q^{22} +(0.0405237 - 0.0233964i) q^{23} +(-7.22442 + 1.93578i) q^{24} +(9.93900 + 5.73828i) q^{25} +(-8.08636 + 4.87272i) q^{26} -1.00000i q^{27} +(1.08917 - 12.8025i) q^{28} -1.08136 q^{29} +(9.20472 - 5.31435i) q^{30} +(1.31025 + 4.88993i) q^{31} +(-10.5185 + 2.81843i) q^{32} +(-0.150292 + 0.560897i) q^{33} +(-0.849915 - 0.849915i) q^{34} +(1.89022 + 10.5718i) q^{35} -4.85636i q^{36} +(-4.23261 - 1.13412i) q^{37} +(10.0846 - 17.4671i) q^{38} +(-0.998211 - 3.46462i) q^{39} +(26.2920 - 15.1797i) q^{40} +(4.50540 - 4.50540i) q^{41} +(6.51567 + 2.35384i) q^{42} +0.884530i q^{43} +(-0.729872 + 2.72392i) q^{44} +(1.05058 + 3.92082i) q^{45} +(0.0317118 + 0.118350i) q^{46} +(0.852236 - 3.18059i) q^{47} -9.87148i q^{48} +(-4.47376 + 5.38381i) q^{49} +(-21.2493 + 21.2493i) q^{50} +(0.397534 - 0.229516i) q^{51} +(-4.84767 - 16.8254i) q^{52} +(0.253079 - 0.438345i) q^{53} +(2.52924 + 0.677708i) q^{54} -2.35707i q^{55} +(18.6111 + 6.72342i) q^{56} +(5.44662 + 5.44662i) q^{57} +(0.732844 - 2.73501i) q^{58} +(2.15568 - 0.577611i) q^{59} +(5.10200 + 19.0409i) q^{60} +(0.165995 - 0.0958371i) q^{61} -13.2558 q^{62} +(-1.51234 + 2.17090i) q^{63} -8.77105i q^{64} +(7.55367 + 12.5354i) q^{65} +(-1.31679 - 0.760250i) q^{66} +(8.62657 - 2.31148i) q^{67} +(1.93057 - 1.11461i) q^{68} -0.0467928 q^{69} +(-28.0197 - 2.38377i) q^{70} +(-4.23807 - 4.23807i) q^{71} +(7.22442 + 1.93578i) q^{72} +(-6.99707 + 1.87486i) q^{73} +(5.73695 - 9.93669i) q^{74} +(-5.73828 - 9.93900i) q^{75} +(26.4507 + 26.4507i) q^{76} +(1.17454 - 0.990361i) q^{77} +(9.43935 - 0.176717i) q^{78} +(2.92382 + 5.06421i) q^{79} +(10.3708 + 38.7043i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.34191 + 14.4486i) q^{82} +(9.67812 - 9.67812i) q^{83} +(-7.34448 + 10.5427i) q^{84} +(-1.31754 + 1.31754i) q^{85} +(-2.23719 - 0.599453i) q^{86} +(0.936481 + 0.540678i) q^{87} +(-3.76123 - 2.17154i) q^{88} +(4.88190 - 18.2195i) q^{89} -10.6287 q^{90} +(-3.07267 + 9.03098i) q^{91} -0.227242 q^{92} +(1.31025 - 4.88993i) q^{93} +(7.46691 + 4.31102i) q^{94} +(-27.0774 - 15.6331i) q^{95} +(10.5185 + 2.81843i) q^{96} +(5.63729 - 5.63729i) q^{97} +(-10.5851 - 14.9639i) q^{98} +(0.410605 - 0.410605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.677708	+	2.52924i	−0.479212	+	1.78844i	0.125605	+	0.992080i	$0.459913\pi$
$2$	−0.677708	+	2.52924i	−0.479212	+	1.78844i	−0.604817	+	0.796364i	$0.706754\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−4.20573	−	2.42818i	−2.10286	−	1.21409i
$5$	3.92082	+	1.05058i	1.75344	+	0.469834i	0.985356	−	0.170509i	$-0.0545412\pi$
$5$	3.92082	+	1.05058i	1.75344	+	0.469834i	0.768089	+	0.640343i	$0.221208\pi$
$6$	1.85153	−	1.85153i	0.755886	−	0.755886i
$7$	1.12389	+	2.39518i	0.424789	+	0.905293i
$7$	1.12389	+	2.39518i	0.424789	+	0.905293i
$8$	5.28864	−	5.28864i	1.86982	−	1.86982i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−5.31435	+	9.20472i	−1.68054	+	2.91079i
$11$	−0.150292	−	0.560897i	−0.0453148	−	0.169117i	0.939560	−	0.342384i	$-0.111234\pi$
$11$	−0.150292	−	0.560897i	−0.0453148	−	0.169117i	−0.984875	+	0.173267i	$0.944568\pi$
$12$	2.42818	+	4.20573i	0.700955	+	1.21409i
$13$	2.59678	+	2.50134i	0.720219	+	0.693747i
$13$	2.59678	+	2.50134i	0.720219	+	0.693747i
$14$	−6.81965	+	1.21935i	−1.82263	+	0.325884i
$15$	−2.87024	−	2.87024i	−0.741093	−	0.741093i
$16$	4.93574	+	8.54896i	1.23394	+	2.13724i
$17$	−0.229516	+	0.397534i	−0.0556659	+	0.0964162i	−0.892516	−	0.451017i	$-0.851062\pi$
$17$	−0.229516	+	0.397534i	−0.0556659	+	0.0964162i	0.836850	+	0.547433i	$0.184395\pi$
$18$	−2.52924	+	0.677708i	−0.596148	+	0.159737i
$19$	−7.44023	−	1.99360i	−1.70691	−	0.457364i	−0.732243	−	0.681044i	$-0.761526\pi$
$19$	−7.44023	−	1.99360i	−1.70691	−	0.457364i	−0.974663	+	0.223680i	$0.928193\pi$
$20$	−13.9389	−	13.9389i	−3.11684	−	3.11684i
$21$	0.224276	−	2.63623i	0.0489411	−	0.575272i
$22$	1.52050			0.324172
$23$	0.0405237	−	0.0233964i	0.00844978	−	0.00487848i	−0.495769	−	0.868454i	$-0.665114\pi$
$23$	0.0405237	−	0.0233964i	0.00844978	−	0.00487848i	0.504219	+	0.863576i	$0.331780\pi$
$24$	−7.22442	+	1.93578i	−1.47468	+	0.395139i
$25$	9.93900	+	5.73828i	1.98780	+	1.14766i
$26$	−8.08636	+	4.87272i	−1.58587	+	0.955619i
$27$		−	1.00000i		−	0.192450i
$28$	1.08917	−	12.8025i	0.205833	−	2.41944i
$29$	−1.08136			−0.200803			−0.100401	−	0.994947i	$-0.532013\pi$
$29$	−1.08136			−0.200803			−0.100401	+	0.994947i	$0.532013\pi$
$30$	9.20472	−	5.31435i	1.68054	−	0.970263i
$31$	1.31025	+	4.88993i	0.235328	+	0.878258i	0.978001	+	0.208602i	$0.0668914\pi$
$31$	1.31025	+	4.88993i	0.235328	+	0.878258i	−0.742672	+	0.669655i	$0.766442\pi$
$32$	−10.5185	+	2.81843i	−1.85943	+	0.498234i
$33$	−0.150292	+	0.560897i	−0.0261625	+	0.0976397i
$34$	−0.849915	−	0.849915i	−0.145759	−	0.145759i
$35$	1.89022	+	10.5718i	0.319506	+	1.78696i
$36$		−	4.85636i		−	0.809393i
$37$	−4.23261	−	1.13412i	−0.695836	−	0.186449i	−0.106471	−	0.994316i	$-0.533955\pi$
$37$	−4.23261	−	1.13412i	−0.695836	−	0.186449i	−0.589365	+	0.807867i	$0.700622\pi$
$38$	10.0846	−	17.4671i	1.63594	−	2.83353i
$39$	−0.998211	−	3.46462i	−0.159842	−	0.554783i
$40$	26.2920	−	15.1797i	4.15712	−	2.40012i
$41$	4.50540	−	4.50540i	0.703626	−	0.703626i	−0.261561	−	0.965187i	$-0.584237\pi$
$41$	4.50540	−	4.50540i	0.703626	−	0.703626i	0.965187	+	0.261561i	$0.0842373\pi$
$42$	6.51567	+	2.35384i	1.00539	+	0.363206i
$43$			0.884530i			0.134890i	0.997723	+	0.0674448i	$0.0214846\pi$
$43$			0.884530i			0.134890i	−0.997723	+	0.0674448i	$0.978515\pi$
$44$	−0.729872	+	2.72392i	−0.110032	+	0.410646i
$45$	1.05058	+	3.92082i	0.156611	+	0.584482i
$46$	0.0317118	+	0.118350i	0.00467566	+	0.0174498i
$47$	0.852236	−	3.18059i	0.124311	−	0.463936i	−0.875503	−	0.483213i	$-0.839470\pi$
$47$	0.852236	−	3.18059i	0.124311	−	0.463936i	0.999814	+	0.0192766i	$0.00613631\pi$
$48$		−	9.87148i		−	1.42483i
$49$	−4.47376	+	5.38381i	−0.639109	+	0.769116i
$50$	−21.2493	+	21.2493i	−3.00510	+	3.00510i
$51$	0.397534	−	0.229516i	0.0556659	−	0.0321387i
$52$	−4.84767	−	16.8254i	−0.672251	−	2.33327i
$53$	0.253079	−	0.438345i	0.0347630	−	0.0602113i	−0.848120	−	0.529803i	$-0.822266\pi$
$53$	0.253079	−	0.438345i	0.0347630	−	0.0602113i	0.882883	+	0.469592i	$0.155599\pi$
$54$	2.52924	+	0.677708i	0.344186	+	0.0922244i
$55$		−	2.35707i		−	0.317828i
$56$	18.6111	+	6.72342i	2.48701	+	0.898454i
$57$	5.44662	+	5.44662i	0.721423	+	0.721423i
$58$	0.732844	−	2.73501i	0.0962271	−	0.359124i
$59$	2.15568	−	0.577611i	0.280645	−	0.0751986i	−0.115751	−	0.993278i	$-0.536927\pi$
$59$	2.15568	−	0.577611i	0.280645	−	0.0751986i	0.396396	+	0.918080i	$0.370261\pi$
$60$	5.10200	+	19.0409i	0.658665	+	2.45817i
$61$	0.165995	−	0.0958371i	0.0212535	−	0.0122707i	−0.489336	−	0.872096i	$-0.662761\pi$
$61$	0.165995	−	0.0958371i	0.0212535	−	0.0122707i	0.510589	+	0.859825i	$0.329427\pi$
$62$	−13.2558			−1.68349
$63$	−1.51234	+	2.17090i	−0.190537	+	0.273508i
$64$		−	8.77105i		−	1.09638i
$65$	7.55367	+	12.5354i	0.936917	+	1.55483i
$66$	−1.31679	−	0.760250i	−0.162086	−	0.0935803i
$67$	8.62657	−	2.31148i	1.05390	−	0.282392i	0.310039	−	0.950724i	$-0.399658\pi$
$67$	8.62657	−	2.31148i	1.05390	−	0.282392i	0.743864	+	0.668331i	$0.232991\pi$
$68$	1.93057	−	1.11461i	0.234116	−	0.135167i
$69$	−0.0467928			−0.00563319
$70$	−28.0197	−	2.38377i	−3.34899	−	0.284914i
$71$	−4.23807	−	4.23807i	−0.502966	−	0.502966i	0.409392	−	0.912358i	$-0.365741\pi$
$71$	−4.23807	−	4.23807i	−0.502966	−	0.502966i	−0.912358	+	0.409392i	$0.865741\pi$
$72$	7.22442	+	1.93578i	0.851406	+	0.228133i
$73$	−6.99707	+	1.87486i	−0.818945	+	0.219436i	−0.643885	−	0.765122i	$-0.722678\pi$
$73$	−6.99707	+	1.87486i	−0.818945	+	0.219436i	−0.175060	+	0.984558i	$0.556012\pi$
$74$	5.73695	−	9.93669i	0.666907	−	1.15512i
$75$	−5.73828	−	9.93900i	−0.662600	−	1.14766i
$76$	26.4507	+	26.4507i	3.03411	+	3.03411i
$77$	1.17454	−	0.990361i	0.133851	−	0.112862i
$78$	9.43935	−	0.176717i	1.06880	−	0.0200093i
$79$	2.92382	+	5.06421i	0.328956	+	0.569768i	0.982305	−	0.187289i	$-0.0599699\pi$
$79$	2.92382	+	5.06421i	0.328956	+	0.569768i	−0.653349	+	0.757057i	$0.726637\pi$
$80$	10.3708	+	38.7043i	1.15949	+	4.32728i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.34191	+	14.4486i	0.921210	+	1.59558i
$83$	9.67812	−	9.67812i	1.06231	−	1.06231i	0.0643872	−	0.997925i	$-0.479491\pi$
$83$	9.67812	−	9.67812i	1.06231	−	1.06231i	0.997925	−	0.0643872i	$-0.0205093\pi$
$84$	−7.34448	+	10.5427i	−0.801348	+	1.15030i
$85$	−1.31754	+	1.31754i	−0.142907	+	0.142907i
$86$	−2.23719	−	0.599453i	−0.241242	−	0.0646407i
$87$	0.936481	+	0.540678i	0.100401	+	0.0579667i
$88$	−3.76123	−	2.17154i	−0.400948	−	0.231487i
$89$	4.88190	−	18.2195i	0.517481	−	1.93126i	0.234913	−	0.972016i	$-0.424520\pi$
$89$	4.88190	−	18.2195i	0.517481	−	1.93126i	0.282568	−	0.959247i	$-0.408814\pi$
$90$	−10.6287			−1.12036
$91$	−3.07267	+	9.03098i	−0.322104	+	0.946704i
$92$	−0.227242			−0.0236916
$93$	1.31025	−	4.88993i	0.135867	−	0.507062i
$94$	7.46691	+	4.31102i	0.770153	+	0.444648i
$95$	−27.0774	−	15.6331i	−2.77808	−	1.60392i
$96$	10.5185	+	2.81843i	1.07354	+	0.287655i
$97$	5.63729	−	5.63729i	0.572380	−	0.572380i	−0.360413	−	0.932793i	$-0.617364\pi$
$97$	5.63729	−	5.63729i	0.572380	−	0.572380i	0.932793	+	0.360413i	$0.117364\pi$
$98$	−10.5851	−	14.9639i	−1.06925	−	1.51158i
$99$	0.410605	−	0.410605i	0.0412674	−	0.0412674i
$100$	−27.8671	−	48.2673i	−2.78671	−	4.82673i
$101$	3.16376	−	5.47980i	0.314806	−	0.545261i	−0.664590	−	0.747208i	$-0.731394\pi$
$101$	3.16376	−	5.47980i	0.314806	−	0.545261i	0.979396	+	0.201948i	$0.0647271\pi$
$102$	0.311091	+	1.16101i	0.0308026	+	0.114957i
$103$	−8.07204	−	13.9812i	−0.795361	−	1.37761i	−0.922609	−	0.385736i	$-0.873948\pi$
$103$	−8.07204	−	13.9812i	−0.795361	−	1.37761i	0.127248	−	0.991871i	$-0.459386\pi$
$104$	26.9622	−	0.504767i	2.64386	−	0.0494965i
$105$	3.64892	−	10.1006i	0.356098	−	0.985714i
$106$	0.937167	+	0.937167i	0.0910257	+	0.0910257i
$107$	0.476396	+	0.825143i	0.0460550	+	0.0797695i	0.888134	−	0.459585i	$-0.152002\pi$
$107$	0.476396	+	0.825143i	0.0460550	+	0.0797695i	−0.842079	+	0.539354i	$0.818668\pi$
$108$	−2.42818	+	4.20573i	−0.233652	+	0.404696i
$109$	−6.84849	+	1.83505i	−0.655967	+	0.175766i	−0.571425	−	0.820654i	$-0.693609\pi$
$109$	−6.84849	+	1.83505i	−0.655967	+	0.175766i	−0.0845416	+	0.996420i	$0.526943\pi$
$110$	5.96161	+	1.59741i	0.568417	+	0.152307i
$111$	3.09848	+	3.09848i	0.294095	+	0.294095i
$112$	−14.9291	+	21.4300i	−1.41066	+	2.02495i
$113$	18.2692			1.71862			0.859309	−	0.511457i	$-0.170894\pi$
$113$	18.2692			1.71862			0.859309	+	0.511457i	$0.170894\pi$
$114$	−17.4671	+	10.0846i	−1.63594	+	0.944510i
$115$	0.183466	−	0.0491596i	0.0171083	−	0.00458415i
$116$	4.54789	+	2.62572i	0.422261	+	0.243792i
$117$	−0.867833	+	3.49955i	−0.0802312	+	0.323534i
$118$			5.84368i			0.537954i
$119$	−1.21012	−	0.102950i	−0.110931	−	0.00943743i
$120$	−30.3593			−2.77142
$121$	9.23426	−	5.33140i	0.839478	−	0.484673i
$122$	0.129899	+	0.484791i	0.0117605	+	0.0438909i
$123$	−6.15450	+	1.64909i	−0.554932	+	0.148694i
$124$	6.36306	−	23.7472i	0.571419	−	2.13257i
$125$	18.5893	+	18.5893i	1.66268	+	1.66268i
$126$	−4.46581	−	5.29632i	−0.397846	−	0.471834i
$127$		−	5.46783i		−	0.485192i	−0.970127	−	0.242596i	$-0.922001\pi$
$127$		−	5.46783i		−	0.485192i	0.970127	−	0.242596i	$-0.0779989\pi$
$128$	1.14703	+	0.307346i	0.101384	+	0.0271658i
$129$	0.442265	−	0.766025i	0.0389392	−	0.0674448i
$130$	−36.8244	+	10.6097i	−3.22971	+	0.930531i
$131$	−5.30476	+	3.06270i	−0.463479	+	0.267590i	−0.713506	−	0.700649i	$-0.752894\pi$
$131$	−5.30476	+	3.06270i	−0.463479	+	0.267590i	0.250027	+	0.968239i	$0.419560\pi$
$132$	1.99405	−	1.99405i	0.173559	−	0.173559i
$133$	−3.58693	−	20.0613i	−0.311026	−	1.73953i
$134$			23.3852i			2.02017i
$135$	1.05058	−	3.92082i	0.0904196	−	0.337451i
$136$	0.888585	+	3.31625i	0.0761956	+	0.284366i
$137$	1.01061	+	3.77164i	0.0863420	+	0.322233i	0.995565	−	0.0940768i	$-0.0299899\pi$
$137$	1.01061	+	3.77164i	0.0863420	+	0.322233i	−0.909223	+	0.416310i	$0.863323\pi$
$138$	0.0317118	−	0.118350i	0.00269949	−	0.0100746i
$139$			8.41346i			0.713620i	0.934177	+	0.356810i	$0.116136\pi$
$139$			8.41346i			0.713620i	−0.934177	+	0.356810i	$0.883864\pi$
$140$	17.7205	−	49.0519i	1.49765	−	4.14564i
$141$	−2.32835	+	2.32835i	−0.196083	+	0.196083i
$142$	13.5913	−	7.84692i	1.14055	−	0.658499i
$143$	1.01272	−	1.83246i	0.0846879	−	0.153238i
$144$	−4.93574	+	8.54896i	−0.411312	+	0.712413i
$145$	−4.23980	−	1.13605i	−0.352096	−	0.0943439i
$146$		−	18.9679i		−	1.56979i
$147$	6.56630	−	2.42564i	0.541579	−	0.200063i
$148$	15.0473	+	15.0473i	1.23688	+	1.23688i
$149$	−3.72585	+	13.9051i	−0.305234	+	1.13915i	0.627511	+	0.778608i	$0.284074\pi$
$149$	−3.72585	+	13.9051i	−0.305234	+	1.13915i	−0.932744	+	0.360539i	$0.882593\pi$
$150$	29.0270	−	7.77777i	2.37005	−	0.635052i
$151$	−1.92772	−	7.19436i	−0.156876	−	0.585469i	−0.998937	−	0.0460873i	$-0.985325\pi$
$151$	−1.92772	−	7.19436i	−0.156876	−	0.585469i	0.842062	−	0.539381i	$-0.181342\pi$
$152$	−49.8921	+	28.8052i	−4.04679	+	2.33641i
$153$	−0.459033			−0.0371106
$154$	1.70887	+	3.64187i	0.137704	+	0.293470i
$155$			20.5491i			1.65054i
$156$	−4.21450	+	16.9951i	−0.337430	+	1.36069i
$157$	−18.1293	−	10.4670i	−1.44688	−	0.835355i	−0.448584	−	0.893741i	$-0.648071\pi$
$157$	−18.1293	−	10.4670i	−1.44688	−	0.835355i	−0.998294	+	0.0583857i	$0.981405\pi$
$158$	−14.7901	+	3.96300i	−1.17664	+	0.315279i
$159$	−0.438345	+	0.253079i	−0.0347630	+	0.0200704i
$160$	−44.2023			−3.49450
$161$	0.101583	+	0.0707667i	0.00800582	+	0.00557720i
$162$	−1.85153	−	1.85153i	−0.145470	−	0.145470i
$163$	−10.9079	−	2.92277i	−0.854375	−	0.228929i	−0.195055	−	0.980792i	$-0.562489\pi$
$163$	−10.9079	−	2.92277i	−0.854375	−	0.228929i	−0.659319	+	0.751863i	$0.729155\pi$
$164$	−29.8884	+	8.00858i	−2.33389	+	0.625365i
$165$	−1.17854	+	2.04129i	−0.0917490	+	0.158914i
$166$	17.9194	+	31.0373i	1.39081	+	2.40896i
$167$	−9.38835	−	9.38835i	−0.726492	−	0.726492i	0.243427	−	0.969919i	$-0.421728\pi$
$167$	−9.38835	−	9.38835i	−0.726492	−	0.726492i	−0.969919	+	0.243427i	$0.921728\pi$
$168$	−12.7559	−	15.1282i	−0.984143	−	1.16716i
$169$	0.486584	+	12.9909i	0.0374295	+	0.999299i
$170$	−2.43946	−	4.22527i	−0.187098	−	0.324063i
$171$	−1.99360	−	7.44023i	−0.152455	−	0.568968i
$172$	2.14780	−	3.72009i	0.163768	−	0.283654i
$173$	3.19038	+	5.52590i	0.242560	+	0.420127i	0.961443	−	0.275005i	$-0.0886795\pi$
$173$	3.19038	+	5.52590i	0.242560	+	0.420127i	−0.718883	+	0.695131i	$0.755346\pi$
$174$	−2.00217	+	2.00217i	−0.151784	+	0.151784i
$175$	−2.57392	+	30.2548i	−0.194570	+	2.28705i
$176$	4.05329	−	4.05329i	0.305528	−	0.305528i
$177$	−2.15568	−	0.577611i	−0.162030	−	0.0434159i
$178$	42.7730	+	24.6950i	3.20598	+	1.85097i
$179$	16.2954	+	9.40817i	1.21798	+	0.703200i	0.964485	−	0.264137i	$-0.0850872\pi$
$179$	16.2954	+	9.40817i	1.21798	+	0.703200i	0.253493	+	0.967337i	$0.418421\pi$
$180$	5.10200	−	19.0409i	0.380280	−	1.41923i
$181$	−15.0820			−1.12104			−0.560519	−	0.828141i	$-0.689398\pi$
$181$	−15.0820			−1.12104			−0.560519	+	0.828141i	$0.689398\pi$
$182$	−20.7592	−	13.8919i	−1.53877	−	1.02974i
$183$	−0.191674			−0.0141690
$184$	0.0905803	−	0.338050i	0.00667767	−	0.0249214i
$185$	−15.4038	−	8.89339i	−1.13251	−	0.653855i
$186$	11.4799	+	6.62790i	0.841744	+	0.485981i
$187$	0.257470	+	0.0689890i	0.0188281	+	0.00504497i
$188$	−11.3073	+	11.3073i	−0.824670	+	0.824670i
$189$	2.39518	−	1.12389i	0.174224	−	0.0817506i
$190$	57.8905	−	57.8905i	4.19982	−	4.19982i
$191$	0.485364	+	0.840675i	0.0351197	+	0.0608291i	0.883051	−	0.469277i	$-0.155485\pi$
$191$	0.485364	+	0.840675i	0.0351197	+	0.0608291i	−0.847931	+	0.530106i	$0.822152\pi$
$192$	−4.38552	+	7.59595i	−0.316498	+	0.548191i
$193$	3.14492	+	11.7370i	0.226376	+	0.844847i	0.981849	+	0.189667i	$0.0607408\pi$
$193$	3.14492	+	11.7370i	0.226376	+	0.844847i	−0.755472	+	0.655181i	$0.772593\pi$
$194$	10.4376	+	18.0785i	0.749378	+	1.29796i
$195$	−0.273946	−	14.6329i	−0.0196177	−	1.04788i
$196$	31.8883	−	11.7798i	2.27773	−	0.841411i
$197$	−5.15273	−	5.15273i	−0.367117	−	0.367117i	0.499308	−	0.866425i	$-0.333588\pi$
$197$	−5.15273	−	5.15273i	−0.367117	−	0.367117i	−0.866425	+	0.499308i	$0.833588\pi$
$198$	0.760250	+	1.31679i	0.0540286	+	0.0935803i
$199$	−0.108027	+	0.187109i	−0.00765787	+	0.0132638i	−0.869829	−	0.493353i	$-0.835771\pi$
$199$	−0.108027	+	0.187109i	−0.00765787	+	0.0132638i	0.862171	+	0.506617i	$0.169104\pi$
$200$	82.9115	−	22.2161i	5.86273	−	1.57091i
$201$	−8.62657	−	2.31148i	−0.608471	−	0.163039i
$202$	11.7156	+	11.7156i	0.824309	+	0.824309i
$203$	−1.21532	−	2.59004i	−0.0852987	−	0.181785i
$204$	−2.22923			−0.156077
$205$	22.3982	−	12.9316i	1.56436	−	0.903182i
$206$	40.8323	−	10.9410i	2.84492	−	0.762294i
$207$	0.0405237	+	0.0233964i	0.00281659	+	0.00162616i
$208$	−8.56680	+	34.5458i	−0.594000	+	2.39532i
$209$			4.47283i			0.309392i
$210$	23.0739	+	16.0742i	1.59225	+	1.10923i
$211$	−0.835450			−0.0575147			−0.0287574	−	0.999586i	$-0.509155\pi$
$211$	−0.835450			−0.0575147			−0.0287574	+	0.999586i	$0.509155\pi$
$212$	−2.12876	+	1.22904i	−0.146204	+	0.0844108i
$213$	1.55124	+	5.78931i	0.106289	+	0.396677i
$214$	−2.40984	+	0.645716i	−0.164734	+	0.0441402i
$215$	−0.929270	+	3.46808i	−0.0633757	+	0.236521i
$216$	−5.28864	−	5.28864i	−0.359846	−	0.359846i
$217$	−10.2397	+	8.63401i	−0.695115	+	0.586115i
$218$		−	18.5651i		−	1.25739i
$219$	6.99707	+	1.87486i	0.472818	+	0.126691i
$220$	−5.72339	+	9.91321i	−0.385871	+	0.668348i
$221$	−1.59037	+	0.458212i	−0.106980	+	0.0308227i
$222$	−9.93669	+	5.73695i	−0.666907	+	0.385039i
$223$	0.345071	−	0.345071i	0.0231077	−	0.0231077i	−0.695459	−	0.718566i	$-0.744799\pi$
$223$	0.345071	−	0.345071i	0.0231077	−	0.0231077i	0.718566	+	0.695459i	$0.244799\pi$
$224$	−18.5723	−	22.0262i	−1.24091	−	1.47169i
$225$			11.4766i			0.765104i
$226$	−12.3812	+	46.2071i	−0.823583	+	3.07365i
$227$	−0.287231	−	1.07196i	−0.0190642	−	0.0711485i	0.955738	−	0.294218i	$-0.0950591\pi$
$227$	−0.287231	−	1.07196i	−0.0190642	−	0.0711485i	−0.974803	+	0.223069i	$0.928392\pi$
$228$	−9.68165	−	36.1324i	−0.641183	−	2.39293i
$229$	2.77889	−	10.3710i	0.183634	−	0.685332i	−0.811285	−	0.584651i	$-0.801231\pi$
$229$	2.77889	−	10.3710i	0.183634	−	0.685332i	0.994919	−	0.100681i	$-0.0321020\pi$
$230$			0.497346i			0.0327940i
$231$	−1.51236	+	0.270408i	−0.0995060	+	0.0177915i
$232$	−5.71890	+	5.71890i	−0.375464	+	0.375464i
$233$	9.10406	−	5.25623i	0.596427	−	0.344347i	−0.171208	−	0.985235i	$-0.554767\pi$
$233$	9.10406	−	5.25623i	0.596427	−	0.344347i	0.767635	+	0.640888i	$0.221434\pi$
$234$	−8.26308	−	4.56664i	−0.540174	−	0.298530i
$235$	6.68293	−	11.5752i	0.435946	−	0.755081i
$236$	−10.4687	−	2.80509i	−0.681456	−	0.182596i
$237$		−	5.84765i		−	0.379845i
$238$	1.08049	−	2.99091i	0.0700379	−	0.193872i
$239$	11.4260	+	11.4260i	0.739090	+	0.739090i	0.972402	−	0.233312i	$-0.0749564\pi$
$239$	11.4260	+	11.4260i	0.739090	+	0.739090i	−0.233312	+	0.972402i	$0.574956\pi$
$240$	10.3708	−	38.7043i	0.669432	−	2.49835i
$241$	−9.42517	+	2.52547i	−0.607128	+	0.162680i	−0.549270	−	0.835645i	$-0.685094\pi$
$241$	−9.42517	+	2.52547i	−0.607128	+	0.162680i	−0.0578588	+	0.998325i	$0.518427\pi$
$242$	7.22627	+	26.9688i	0.464523	+	1.73362i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−0.930838			−0.0595908
$245$	−23.1970	+	16.4089i	−1.48200	+	1.04833i
$246$		−	16.6838i		−	1.06372i
$247$	−14.3340	−	23.7875i	−0.912050	−	1.51356i
$248$	32.7905	+	18.9316i	2.08220	+	1.20216i
$249$	−13.2206	+	3.54244i	−0.837819	+	0.224493i
$250$	−59.6150	+	34.4187i	−3.77038	+	2.17683i
$251$	−15.5951			−0.984355			−0.492177	−	0.870495i	$-0.663799\pi$
$251$	−15.5951			−0.984355			−0.492177	+	0.870495i	$0.663799\pi$
$252$	11.6318	−	5.45799i	0.732737	−	0.343821i
$253$	−0.0192134	−	0.0192134i	−0.00120793	−	0.00120793i
$254$	13.8295	+	3.70560i	0.867738	+	0.232510i
$255$	1.79979	−	0.482251i	0.112707	−	0.0301998i
$256$	7.21635	−	12.4991i	0.451022	−	0.781192i
$257$	−7.55731	−	13.0896i	−0.471412	−	0.816509i	0.528053	−	0.849211i	$-0.322922\pi$
$257$	−7.55731	−	13.0896i	−0.471412	−	0.816509i	−0.999465	+	0.0327020i	$0.989589\pi$
$258$	1.63774	+	1.63774i	0.101961	+	0.101961i
$259$	−2.04054	−	11.4125i	−0.126793	−	0.709137i
$260$	−1.33038	−	71.0623i	−0.0825067	−	4.40710i
$261$	−0.540678	−	0.936481i	−0.0334671	−	0.0579667i
$262$	−4.15124	−	15.4926i	−0.256464	−	0.957138i
$263$	−13.1981	+	22.8598i	−0.813832	+	1.40960i	0.0963317	+	0.995349i	$0.469289\pi$
$263$	−13.1981	+	22.8598i	−0.813832	+	1.40960i	−0.910164	+	0.414249i	$0.864044\pi$
$264$	2.17154	+	3.76123i	0.133649	+	0.231487i
$265$	1.45279	−	1.45279i	0.0892443	−	0.0892443i
$266$	53.1707	+	4.52348i	3.26010	+	0.277352i
$267$	−13.3376	+	13.3376i	−0.816248	+	0.816248i
$268$	−41.8937	−	11.2254i	−2.55906	−	0.685699i
$269$	−11.5339	−	6.65909i	−0.703234	−	0.406012i	0.105317	−	0.994439i	$-0.466414\pi$
$269$	−11.5339	−	6.65909i	−0.703234	−	0.406012i	−0.808551	+	0.588427i	$0.799748\pi$
$270$	9.20472	+	5.31435i	0.560182	+	0.323421i
$271$	−5.21791	+	19.4735i	−0.316965	+	1.18293i	0.605180	+	0.796089i	$0.293101\pi$
$271$	−5.21791	+	19.4735i	−0.316965	+	1.18293i	−0.922146	+	0.386843i	$0.873566\pi$
$272$	−4.53134			−0.274753
$273$	7.17650	−	6.28473i	0.434342	−	0.380369i
$274$	−10.2243			−0.617671
$275$	1.72484	−	6.43718i	0.104012	−	0.388176i
$276$	0.196798	+	0.113621i	0.0118458	+	0.00683919i
$277$	3.53497	+	2.04092i	0.212396	+	0.122627i	0.602424	−	0.798176i	$-0.294202\pi$
$277$	3.53497	+	2.04092i	0.212396	+	0.122627i	−0.390029	+	0.920803i	$0.627535\pi$
$278$	−21.2797	−	5.70187i	−1.27627	−	0.341976i
$279$	−3.57968	+	3.57968i	−0.214310	+	0.214310i
$280$	65.9072	+	45.9138i	3.93871	+	2.74387i
$281$	0.558878	−	0.558878i	0.0333399	−	0.0333399i	−0.690240	−	0.723580i	$-0.742495\pi$
$281$	0.558878	−	0.558878i	0.0333399	−	0.0333399i	0.723580	+	0.690240i	$0.242495\pi$
$282$	−4.31102	−	7.46691i	−0.256718	−	0.444648i
$283$	11.3665	−	19.6873i	0.675667	−	1.17029i	−0.300607	−	0.953748i	$-0.597189\pi$
$283$	11.3665	−	19.6873i	0.675667	−	1.17029i	0.976274	−	0.216541i	$-0.0694774\pi$
$284$	7.53337	+	28.1149i	0.447024	+	1.66831i
$285$	15.6331	+	27.0774i	0.926026	+	1.60392i
$286$	3.94841	+	3.80329i	0.233474	+	0.224893i
$287$	15.8548	+	5.72769i	0.935880	+	0.338095i
$288$	−7.70011	−	7.70011i	−0.453733	−	0.453733i
$289$	8.39464	+	14.5400i	0.493803	+	0.855291i
$290$	5.74670	−	9.95357i	0.337458	−	0.584494i
$291$	−7.70068	+	2.06339i	−0.451422	+	0.120958i
$292$	33.9802	+	9.10498i	1.98854	+	0.532829i
$293$	−7.07914	−	7.07914i	−0.413568	−	0.413568i	0.469412	−	0.882979i	$-0.344466\pi$
$293$	−7.07914	−	7.07914i	−0.413568	−	0.413568i	−0.882979	+	0.469412i	$0.844466\pi$
$294$	1.68499	+	18.2516i	0.0982703	+	1.06446i
$295$	9.05885			0.527426
$296$	−28.3827	+	16.3868i	−1.64971	+	0.952461i
$297$	−0.560897	+	0.150292i	−0.0325466	+	0.00872083i
$298$	−32.6442	−	18.8472i	−1.89103	−	1.09179i
$299$	0.163754	+	0.0406083i	0.00947012	+	0.00234844i
$300$			55.7343i			3.21782i
$301$	−2.11861	+	0.994110i	−0.122114	+	0.0572995i
$302$	19.5027			1.12226
$303$	−5.47980	+	3.16376i	−0.314806	+	0.181754i
$304$	−19.6798	−	73.4461i	−1.12872	−	4.21242i
$305$	0.751521	−	0.201369i	0.0430319	−	0.0115304i
$306$	0.311091	−	1.16101i	0.0177839	−	0.0663703i
$307$	12.9630	+	12.9630i	0.739837	+	0.739837i	0.972546	−	0.232709i	$-0.0747590\pi$
$307$	12.9630	+	12.9630i	0.739837	+	0.739837i	−0.232709	+	0.972546i	$0.574759\pi$
$308$	−7.34456	+	1.31320i	−0.418495	+	0.0748264i
$309$			16.1441i			0.918404i
$310$	−51.9736	−	13.9263i	−2.95190	−	0.790960i
$311$	3.35745	−	5.81527i	0.190383	−	0.329753i	−0.754994	−	0.655732i	$-0.772360\pi$
$311$	3.35745	−	5.81527i	0.190383	−	0.329753i	0.945377	+	0.325978i	$0.105694\pi$
$312$	−23.6023	−	13.0439i	−1.33622	−	0.738468i
$313$	0.880023	−	0.508082i	0.0497418	−	0.0287185i	−0.474923	−	0.880027i	$-0.657524\pi$
$313$	0.880023	−	0.508082i	0.0497418	−	0.0287185i	0.524665	+	0.851309i	$0.324191\pi$
$314$	38.7599	−	38.7599i	2.18735	−	2.18735i
$315$	−8.21034	+	6.92288i	−0.462600	+	0.390060i
$316$		−	28.3983i		−	1.59753i
$317$	6.12568	−	22.8613i	0.344052	−	1.28402i	−0.549663	−	0.835387i	$-0.685244\pi$
$317$	6.12568	−	22.8613i	0.344052	−	1.28402i	0.893715	−	0.448634i	$-0.148089\pi$
$318$	−0.343027	−	1.28019i	−0.0192360	−	0.0717897i
$319$	0.162519	+	0.606529i	0.00909932	+	0.0339591i
$320$	9.21470	−	34.3897i	0.515117	−	1.92244i
$321$		−	0.952793i		−	0.0531797i
$322$	−0.247829	+	0.208968i	−0.0138110	+	0.0116453i
$323$	2.50018	−	2.50018i	0.139114	−	0.139114i
$324$	4.20573	−	2.42818i	0.233652	−	0.134899i
$325$	11.4560	+	39.7619i	0.635467	+	2.20559i
$326$	14.7848	−	25.6080i	0.818854	−	1.41830i
$327$	6.84849	+	1.83505i	0.378723	+	0.101478i
$328$		−	47.6549i		−	2.63130i
$329$	8.57589	−	1.53336i	0.472804	−	0.0845368i
$330$	−4.36420	−	4.36420i	−0.240241	−	0.240241i
$331$	4.18120	−	15.6044i	0.229819	−	0.857698i	−0.750597	−	0.660761i	$-0.770234\pi$
$331$	4.18120	−	15.6044i	0.229819	−	0.857698i	0.980416	−	0.196937i	$-0.0630995\pi$
$332$	−64.2038	+	17.2033i	−3.52364	+	0.944156i
$333$	−1.13412	−	4.23261i	−0.0621496	−	0.231945i
$334$	30.1080	−	17.3828i	1.64743	−	0.951147i
$335$	36.2516			1.98064
$336$	23.6440	−	11.0944i	1.28988	−	0.605250i
$337$			9.93413i			0.541147i	0.962699	+	0.270573i	$0.0872132\pi$
$337$			9.93413i			0.541147i	−0.962699	+	0.270573i	$0.912787\pi$
$338$	−33.1869	−	7.57335i	−1.80513	−	0.411936i
$339$	−15.8216	−	9.13458i	−0.859309	−	0.496122i
$340$	8.74040	−	2.34198i	0.474015	−	0.127012i
$341$	2.54583	−	1.46984i	0.137864	−	0.0795961i
$342$	20.1692			1.09063
$343$	−17.9232	−	4.66468i	−0.967761	−	0.251869i
$344$	4.67796	+	4.67796i	0.252219	+	0.252219i
$345$	−0.183466	−	0.0491596i	−0.00987748	−	0.00264666i
$346$	−16.1385	+	4.32430i	−0.867611	+	0.232476i
$347$	5.33134	−	9.23415i	0.286201	−	0.495715i	−0.686698	−	0.726942i	$-0.740941\pi$
$347$	5.33134	−	9.23415i	0.286201	−	0.495715i	0.972900	+	0.231227i	$0.0742740\pi$
$348$	−2.62572	−	4.54789i	−0.140754	−	0.243792i
$349$	−14.7539	−	14.7539i	−0.789757	−	0.789757i	0.191697	−	0.981454i	$-0.438601\pi$
$349$	−14.7539	−	14.7539i	−0.789757	−	0.789757i	−0.981454	+	0.191697i	$0.938601\pi$
$350$	−74.7775	−	27.0140i	−3.99702	−	1.44396i
$351$	2.50134	−	2.59678i	0.133512	−	0.138606i
$352$	3.16171	+	5.47623i	0.168519	+	0.291884i
$353$	7.55771	+	28.2057i	0.402256	+	1.50124i	0.809061	+	0.587725i	$0.199976\pi$
$353$	7.55771	+	28.2057i	0.402256	+	1.50124i	−0.406805	+	0.913515i	$0.633357\pi$
$354$	2.92184	−	5.06077i	0.155294	−	0.268977i
$355$	−12.1643	−	21.0691i	−0.645613	−	1.11823i
$356$	−64.7722	+	64.7722i	−3.43292	+	3.43292i
$357$	0.996516	+	0.694215i	0.0527412	+	0.0367418i
$358$	−34.8391	+	34.8391i	−1.84130	+	1.84130i
$359$	18.3744	+	4.92341i	0.969764	+	0.259847i	0.708728	−	0.705482i	$-0.249269\pi$
$359$	18.3744	+	4.92341i	0.969764	+	0.259847i	0.261036	+	0.965329i	$0.415936\pi$
$360$	26.2920	+	15.1797i	1.38571	+	0.800039i
$361$	34.9280	+	20.1657i	1.83832	+	1.06135i
$362$	10.2212	−	38.1461i	0.537215	−	2.00492i
$363$	−10.6628			−0.559652
$364$	34.8517	−	30.5209i	1.82672	−	1.59973i
$365$	−29.4039			−1.53907
$366$	0.129899	−	0.484791i	0.00678994	−	0.0253404i
$367$	21.7369	+	12.5498i	1.13466	+	0.655094i	0.945102	−	0.326776i	$-0.105962\pi$
$367$	21.7369	+	12.5498i	1.13466	+	0.655094i	0.189555	+	0.981870i	$0.439296\pi$
$368$	0.400029	+	0.230957i	0.0208530	+	0.0120395i
$369$	6.15450	+	1.64909i	0.320390	+	0.0858483i
$370$	32.9328	−	32.9328i	1.71210	−	1.71210i
$371$	1.33435	+	0.113519i	0.0692758	+	0.00589361i
$372$	−17.3842	+	17.3842i	−0.901328	+	0.901328i
$373$	16.6168	+	28.7811i	0.860383	+	1.49023i	0.871560	+	0.490289i	$0.163109\pi$
$373$	16.6168	+	28.7811i	0.860383	+	1.49023i	−0.0111767	+	0.999938i	$0.503558\pi$
$374$	−0.348980	+	0.604451i	−0.0180453	+	0.0312554i
$375$	−6.80416	−	25.3935i	−0.351365	−	1.31131i
$376$	−12.3138	−	21.3282i	−0.635037	−	1.09992i
$377$	−2.80805	−	2.70484i	−0.144622	−	0.139306i
$378$	1.21935	+	6.81965i	0.0627163	+	0.350765i
$379$	−21.2082	−	21.2082i	−1.08939	−	1.08939i	−0.995591	−	0.0938026i	$-0.970098\pi$
$379$	−21.2082	−	21.2082i	−1.08939	−	1.08939i	−0.0938026	−	0.995591i	$-0.529902\pi$
$380$	75.9200	+	131.497i	3.89462	+	6.74567i
$381$	−2.73392	+	4.73528i	−0.140063	+	0.242596i
$382$	−2.45521	+	0.657870i	−0.125619	+	0.0336596i
$383$	19.2811	+	5.16636i	0.985220	+	0.263989i	0.715241	−	0.698878i	$-0.246317\pi$
$383$	19.2811	+	5.16636i	0.985220	+	0.263989i	0.269978	+	0.962866i	$0.412983\pi$
$384$	−0.839684	−	0.839684i	−0.0428499	−	0.0428499i
$385$	5.64561	−	2.64908i	0.287727	−	0.135010i
$386$	−31.8170			−1.61944
$387$	−0.766025	+	0.442265i	−0.0389392	+	0.0224816i
$388$	−37.3972	+	10.0206i	−1.89856	+	0.508717i
$389$	−16.9603	−	9.79204i	−0.859922	−	0.496476i	0.00406416	−	0.999992i	$-0.498706\pi$
$389$	−16.9603	−	9.79204i	−0.859922	−	0.496476i	−0.863986	+	0.503516i	$0.832040\pi$
$390$	37.1957	+	9.22393i	1.88348	+	0.467072i
$391$			0.0214794i			0.00108626i
$392$	4.81292	+	52.1332i	0.243089	+	2.63312i
$393$	6.12540			0.308986
$394$	16.5246	−	9.54046i	0.832495	−	0.480641i
$395$	6.14343	+	22.9276i	0.309109	+	1.15361i
$396$	−2.72392	+	0.729872i	−0.136882	+	0.0366774i
$397$	6.28296	−	23.4483i	0.315333	−	1.17684i	−0.608347	−	0.793671i	$-0.708167\pi$
$397$	6.28296	−	23.4483i	0.315333	−	1.17684i	0.923679	−	0.383166i	$-0.125166\pi$
$398$	−0.400033	−	0.400033i	−0.0200518	−	0.0200518i
$399$	−6.92426	+	19.1670i	−0.346647	+	0.959551i
$400$			113.291i			5.66454i
$401$	−24.7535	−	6.63267i	−1.23613	−	0.331220i	−0.419166	−	0.907910i	$-0.637677\pi$
$401$	−24.7535	−	6.63267i	−1.23613	−	0.331220i	−0.816963	+	0.576690i	$0.804344\pi$
$402$	11.6926	−	20.2522i	0.583174	−	1.01009i
$403$	−8.82894	+	15.9755i	−0.439801	+	0.795796i
$404$	−26.6119	+	15.3644i	−1.32399	+	0.764406i
$405$	−2.87024	+	2.87024i	−0.142623	+	0.142623i
$406$	7.37447	−	1.31855i	0.365989	−	0.0654383i
$407$			2.54451i			0.126127i
$408$	0.888585	−	3.31625i	0.0439915	−	0.164179i
$409$	−2.63676	−	9.84051i	−0.130379	−	0.486582i	0.869595	−	0.493766i	$-0.164380\pi$
$409$	−2.63676	−	9.84051i	−0.130379	−	0.486582i	−0.999974	+	0.00718375i	$0.997713\pi$
$410$	17.5277	+	65.4143i	0.865632	+	3.23058i
$411$	1.01061	−	3.77164i	0.0498496	−	0.186041i
$412$			78.4014i			3.86256i
$413$	3.80621	+	4.51406i	0.187292	+	0.222122i
$414$	−0.0866384	+	0.0866384i	−0.00425804	+	0.00425804i
$415$	48.1139	−	27.7785i	2.36182	−	1.36360i
$416$	−34.3643	−	18.9916i	−1.68485	−	0.931139i
$417$	4.20673	−	7.28627i	0.206004	−	0.356810i
$418$	−11.3129	−	3.03127i	−0.553330	−	0.148264i
$419$			20.6163i			1.00717i	0.863945	+	0.503586i	$0.167986\pi$
$419$			20.6163i			1.00717i	−0.863945	+	0.503586i	$0.832014\pi$
$420$	−39.8723	+	33.6200i	−1.94557	+	1.64049i
$421$	−10.3833	−	10.3833i	−0.506050	−	0.506050i	0.407262	−	0.913311i	$-0.366484\pi$
$421$	−10.3833	−	10.3833i	−0.506050	−	0.506050i	−0.913311	+	0.407262i	$0.866484\pi$
$422$	0.566191	−	2.11306i	0.0275618	−	0.102862i
$423$	3.18059	−	0.852236i	0.154645	−	0.0414371i
$424$	−0.979807	−	3.65669i	−0.0475836	−	0.177585i
$425$	−4.56233	+	2.63406i	−0.221305	+	0.127771i
$426$	−15.6938			−0.760369
$427$	0.416106	+	0.289877i	0.0201368	+	0.0140281i
$428$		−	4.62710i		−	0.223659i
$429$	−1.79327	+	1.08060i	−0.0865800	+	0.0521718i
$430$	−8.14185	−	4.70070i	−0.392635	−	0.226688i
$431$	−4.72385	+	1.26575i	−0.227540	+	0.0609691i	−0.370787	−	0.928718i	$-0.620912\pi$
$431$	−4.72385	+	1.26575i	−0.227540	+	0.0609691i	0.143248	+	0.989687i	$0.454245\pi$
$432$	8.54896	−	4.93574i	0.411312	−	0.237471i
$433$	24.5015			1.17747			0.588733	−	0.808328i	$-0.299627\pi$
$433$	24.5015			1.17747			0.588733	+	0.808328i	$0.299627\pi$
$434$	−14.8980	−	31.7500i	−0.715126	−	1.52405i
$435$	3.10375	+	3.10375i	0.148813	+	0.148813i
$436$	33.2587	+	8.91165i	1.59280	+	0.426791i
$437$	−0.348149	+	0.0932862i	−0.0166542	+	0.00446248i
$438$	−9.48394	+	16.4267i	−0.453160	+	0.784897i
$439$	−16.1929	−	28.0470i	−0.772846	−	1.33861i	−0.935997	−	0.352008i	$-0.885499\pi$
$439$	−16.1929	−	28.0470i	−0.772846	−	1.33861i	0.163151	−	0.986601i	$-0.447834\pi$
$440$	−12.4657	−	12.4657i	−0.594280	−	0.594280i
$441$	−6.89940	−	1.18249i	−0.328543	−	0.0563089i
$442$	−0.0811190	−	4.33297i	−0.00385844	−	0.206099i
$443$	−17.6889	−	30.6380i	−0.840423	−	1.45566i	−0.889538	−	0.456862i	$-0.848973\pi$
$443$	−17.6889	−	30.6380i	−0.840423	−	1.45566i	0.0491148	−	0.998793i	$-0.484360\pi$
$444$	−5.50771	−	20.5550i	−0.261384	−	0.975499i
$445$	38.2821	−	66.3066i	1.81475	−	3.14323i
$446$	0.638911	+	1.10663i	0.0302533	+	0.0524003i
$447$	10.1792	−	10.1792i	0.481460	−	0.481460i
$448$	21.0082	−	9.85765i	0.992546	−	0.465730i
$449$	15.3334	−	15.3334i	0.723628	−	0.723628i	−0.245714	−	0.969342i	$-0.579022\pi$
$449$	15.3334	−	15.3334i	0.723628	−	0.723628i	0.969342	+	0.245714i	$0.0790225\pi$
$450$	−29.0270	−	7.77777i	−1.36835	−	0.366647i
$451$	−3.20420	−	1.84994i	−0.150880	−	0.0871104i
$452$	−76.8351	−	44.3608i	−3.61402	−	2.08656i
$453$	−1.92772	+	7.19436i	−0.0905723	+	0.338021i
$454$	2.90591			0.136381
$455$	−21.5352	+	32.1808i	−1.00958	+	1.50866i
$456$	57.6105			2.69786
$457$	−8.39516	+	31.3312i	−0.392709	+	1.46561i	0.432938	+	0.901424i	$0.357477\pi$
$457$	−8.39516	+	31.3312i	−0.392709	+	1.46561i	−0.825647	+	0.564187i	$0.809190\pi$
$458$	24.3474	+	14.0570i	1.13768	+	0.656839i
$459$	0.397534	+	0.229516i	0.0185553	+	0.0107129i
$460$	−0.890977	−	0.238736i	−0.0415420	−	0.0111311i
$461$	−16.4874	+	16.4874i	−0.767896	+	0.767896i	−0.977736	−	0.209840i	$-0.932706\pi$
$461$	−16.4874	+	16.4874i	−0.767896	+	0.767896i	0.209840	+	0.977736i	$0.432706\pi$
$462$	0.341012	−	4.00839i	0.0158653	−	0.186487i
$463$	−19.8546	+	19.8546i	−0.922722	+	0.922722i	−0.997221	−	0.0744988i	$-0.976264\pi$
$463$	−19.8546	+	19.8546i	−0.922722	+	0.922722i	0.0744988	+	0.997221i	$0.476264\pi$
$464$	−5.33729	−	9.24446i	−0.247777	−	0.429163i
$465$	10.2745	−	17.7960i	0.476470	−	0.825271i
$466$	7.12439	+	26.5886i	0.330031	+	1.23169i
$467$	−3.59024	−	6.21849i	−0.166137	−	0.287757i	0.770922	−	0.636930i	$-0.219796\pi$
$467$	−3.59024	−	6.21849i	−0.166137	−	0.287757i	−0.937058	+	0.349173i	$0.886463\pi$
$468$	12.1474	−	12.6109i	0.561514	−	0.582940i
$469$	15.2317	+	18.0643i	0.703334	+	0.834133i
$470$	24.7474	+	24.7474i	1.14151	+	1.14151i
$471$	10.4670	+	18.1293i	0.482293	+	0.835355i
$472$	8.34581	−	14.4554i	0.384147	−	0.665362i
$473$	0.496130	−	0.132938i	0.0228121	−	0.00611248i
$474$	14.7901	+	3.96300i	0.679333	+	0.182027i
$475$	−62.5085	−	62.5085i	−2.86809	−	2.86809i
$476$	4.83944	+	3.37136i	0.221815	+	0.154526i
$477$	0.506157			0.0231753
$478$	−36.6428	+	21.1557i	−1.67600	+	0.967640i
$479$	−27.8499	+	7.46237i	−1.27250	+	0.340964i	−0.830987	−	0.556292i	$-0.812223\pi$
$479$	−27.8499	+	7.46237i	−1.27250	+	0.340964i	−0.441509	+	0.897257i	$0.645557\pi$
$480$	38.2803	+	22.1012i	1.74725	+	1.00878i
$481$	−8.15434	−	13.5323i	−0.371806	−	0.617018i
$482$		−	25.5501i		−	1.16377i
$483$	−0.0525897	−	0.112077i	−0.00239291	−	0.00509968i
$484$	−51.7824			−2.35374
$485$	28.0252	−	16.1804i	1.27256	−	0.734713i
$486$	0.677708	+	2.52924i	0.0307415	+	0.114729i
$487$	0.0670152	−	0.0179567i	0.00303675	−	0.000813694i	−0.257300	−	0.966331i	$-0.582833\pi$
$487$	0.0670152	−	0.0179567i	0.00303675	−	0.000813694i	0.260337	+	0.965518i	$0.416166\pi$
$488$	0.371039	−	1.38473i	0.0167961	−	0.0626840i
$489$	7.98516	+	7.98516i	0.361101	+	0.361101i
$490$	−25.7814	−	69.7912i	−1.16468	−	3.15285i
$491$			29.0806i			1.31239i	0.754592	+	0.656195i	$0.227835\pi$
$491$			29.0806i			1.31239i	−0.754592	+	0.656195i	$0.772165\pi$
$492$	29.8884	+	8.00858i	1.34747	+	0.361055i
$493$	0.248189	−	0.429876i	0.0111779	−	0.0193606i
$494$	69.8786	−	20.1331i	3.14399	−	0.905833i
$495$	2.04129	−	1.17854i	0.0917490	−	0.0529713i
$496$	−35.3367	+	35.3367i	−1.58667	+	1.58667i
$497$	5.38783	−	14.9140i	0.241677	−	0.668986i
$498$		−	35.8388i		−	1.60597i
$499$	−5.21725	+	19.4710i	−0.233556	+	0.871644i	0.745238	+	0.666798i	$0.232336\pi$
$499$	−5.21725	+	19.4710i	−0.233556	+	0.871644i	−0.978794	+	0.204845i	$0.934331\pi$
$500$	−33.0434	−	123.320i	−1.47775	−	5.51502i
$501$	3.43637	+	12.8247i	0.153526	+	0.572966i
$502$	10.5689	−	39.4438i	0.471715	−	1.76046i
$503$			34.9296i			1.55743i	0.627376	+	0.778716i	$0.284129\pi$
$503$			34.9296i			1.55743i	−0.627376	+	0.778716i	$0.715871\pi$
$504$	3.48288	+	19.4794i	0.155140	+	0.867680i
$505$	18.1615	−	18.1615i	0.808178	−	0.808178i
$506$	0.0616163	−	0.0355742i	0.00273918	−	0.00158147i
$507$	6.07405	−	11.4937i	0.269758	−	0.510455i
$508$	−13.2769	+	22.9962i	−0.589066	+	1.02029i
$509$	−24.2168	−	6.48888i	−1.07339	−	0.287615i	−0.321506	−	0.946907i	$-0.604189\pi$
$509$	−24.2168	−	6.48888i	−1.07339	−	0.287615i	−0.751886	+	0.659293i	$0.770856\pi$
$510$			4.87892i			0.216042i
$511$	−12.3545	−	14.6521i	−0.546532	−	0.648171i
$512$	28.4020	+	28.4020i	1.25520	+	1.25520i
$513$	−1.99360	+	7.44023i	−0.0880197	+	0.328494i
$514$	38.2285	−	10.2433i	1.68619	−	0.451813i
$515$	−16.9607	−	63.2980i	−0.747376	−	2.78925i
$516$	−3.72009	+	2.14780i	−0.163768	+	0.0945514i
$517$	−1.91207			−0.0840927
$518$	30.2478	+	2.57332i	1.32901	+	0.113065i
$519$		−	6.38076i		−	0.280084i
$520$	106.244	+	26.3468i	4.65911	+	1.15538i
$521$	−3.25185	−	1.87746i	−0.142466	−	0.0822528i	0.427073	−	0.904217i	$-0.359545\pi$
$521$	−3.25185	−	1.87746i	−0.142466	−	0.0822528i	−0.569539	+	0.821964i	$0.692878\pi$
$522$	2.73501	−	0.732844i	0.119708	−	0.0320757i
$523$	−0.279523	+	0.161383i	−0.0122227	+	0.00705678i	−0.506099	−	0.862475i	$-0.668913\pi$
$523$	−0.279523	+	0.161383i	−0.0122227	+	0.00705678i	0.493876	+	0.869532i	$0.335580\pi$
$524$	29.7471			1.29951
$525$	17.3565	−	24.9145i	0.757500	−	1.08736i
$526$	−48.8736	−	48.8736i	−2.13099	−	2.13099i
$527$	−2.24464	−	0.601449i	−0.0977780	−	0.0261995i
$528$	−5.53689	+	1.48361i	−0.240962	+	0.0645656i
$529$	−11.4989	+	19.9167i	−0.499952	+	0.865943i
$530$	2.68990	+	4.65903i	0.116842	+	0.202376i
$531$	1.57806	+	1.57806i	0.0684821	+	0.0684821i
$532$	−33.6267	+	93.0819i	−1.45790	+	4.03561i
$533$	22.9691	−	0.430012i	0.994903	−	0.0186259i
$534$	−24.6950	−	42.7730i	−1.06866	−	1.85097i
$535$	1.00099	+	3.73573i	0.0432764	+	0.161510i
$536$	33.3982	−	57.8474i	1.44258	−	2.49863i
$537$	−9.40817	−	16.2954i	−0.405993	−	0.703200i
$538$	24.6591	−	24.6591i	1.06313	−	1.06313i
$539$	3.69214	+	1.70018i	0.159032	+	0.0732319i
$540$	−13.9389	+	13.9389i	−0.599835	+	0.599835i
$541$	−23.9468	−	6.41652i	−1.02955	−	0.275868i	−0.295775	−	0.955258i	$-0.595578\pi$
$541$	−23.9468	−	6.41652i	−1.02955	−	0.275868i	−0.733777	+	0.679390i	$0.762244\pi$
$542$	−45.7170	−	26.3947i	−1.96371	−	1.13375i
$543$	13.0614	+	7.54102i	0.560519	+	0.323616i
$544$	1.29375	−	4.82836i	0.0554693	−	0.207014i
$545$	−28.7796			−1.23278
$546$	11.0320	+	22.4103i	0.472127	+	0.959074i
$547$	−2.96777			−0.126893			−0.0634464	−	0.997985i	$-0.520209\pi$
$547$	−2.96777			−0.126893			−0.0634464	+	0.997985i	$0.520209\pi$
$548$	4.90787	−	18.3164i	0.209654	−	0.782438i
$549$	0.165995	+	0.0958371i	0.00708448	+	0.00409023i
$550$	15.1122	+	8.72506i	0.644388	+	0.372038i
$551$	8.04553	+	2.15579i	0.342751	+	0.0918399i
$552$	−0.247470	+	0.247470i	−0.0105330	+	0.0105330i
$553$	−8.84365	+	12.6947i	−0.376070	+	0.539832i
$554$	−7.55765	+	7.55765i	−0.321094	+	0.321094i
$555$	8.89339	+	15.4038i	0.377504	+	0.653855i
$556$	20.4294	−	35.3847i	0.866399	−	1.50065i
$557$	1.60734	+	5.99869i	0.0681054	+	0.254173i	0.991582	−	0.129483i	$-0.0413317\pi$
$557$	1.60734	+	5.99869i	0.0681054	+	0.254173i	−0.923476	+	0.383656i	$0.874665\pi$
$558$	−6.62790	−	11.4799i	−0.280581	−	0.485981i
$559$	−2.21251	+	2.29693i	−0.0935792	+	0.0971499i
$560$	−81.0482	+	68.3391i	−3.42491	+	2.88786i
$561$	−0.188481	−	0.188481i	−0.00795769	−	0.00795769i
$562$	1.03478	+	1.79230i	0.0436497	+	0.0756034i
$563$	−9.09381	+	15.7509i	−0.383259	+	0.663823i	−0.991526	−	0.129909i	$-0.958532\pi$
$563$	−9.09381	+	15.7509i	−0.383259	+	0.663823i	0.608267	+	0.793732i	$0.291865\pi$
$564$	15.4461	−	4.13876i	0.650397	−	0.174273i
$565$	71.6301	+	19.1932i	3.01350	+	0.807465i
$566$	42.0908	+	42.0908i	1.76921	+	1.76921i
$567$	−2.63623	−	0.224276i	−0.110711	−	0.00941872i
$568$	−44.8272			−1.88091
$569$	−26.1342	+	15.0886i	−1.09560	+	0.632547i	−0.935063	−	0.354482i	$-0.884657\pi$
$569$	−26.1342	+	15.0886i	−1.09560	+	0.632547i	−0.160541	+	0.987029i	$0.551324\pi$
$570$	−79.0799	+	21.1894i	−3.31229	+	0.887526i
$571$	34.6783	+	20.0215i	1.45124	+	0.837876i	0.998552	−	0.0537918i	$-0.0171307\pi$
$571$	34.6783	+	20.0215i	1.45124	+	0.837876i	0.452691	+	0.891667i	$0.350464\pi$
$572$	−8.70877	+	5.24777i	−0.364132	+	0.219420i
$573$		−	0.970728i		−	0.0405527i
$574$	−25.2317	+	36.2189i	−1.05315	+	1.51175i
$575$	0.537020			0.0223953
$576$	7.59595	−	4.38552i	0.316498	−	0.182730i
$577$	−0.730637	−	2.72677i	−0.0304168	−	0.113517i	0.949048	−	0.315130i	$-0.102048\pi$
$577$	−0.730637	−	2.72677i	−0.0304168	−	0.113517i	−0.979465	+	0.201613i	$0.935382\pi$
$578$	−42.4642	+	11.3782i	−1.76628	+	0.473273i
$579$	3.14492	−	11.7370i	0.130698	−	0.487773i
$580$	15.0729	+	15.0729i	0.625869	+	0.625869i
$581$	34.0579	+	12.3037i	1.41296	+	0.510445i
$582$		−	20.8753i		−	0.865307i
$583$	−0.283902	−	0.0760714i	−0.0117580	−	0.00315055i
$584$	−27.0895	+	46.9204i	−1.12097	+	1.94158i
$585$	−7.07918	+	12.8094i	−0.292688	+	0.529603i
$586$	22.7024	−	13.1073i	0.937829	−	0.541456i
$587$	24.8081	−	24.8081i	1.02394	−	1.02394i	0.0242353	−	0.999706i	$-0.492285\pi$
$587$	24.8081	−	24.8081i	1.02394	−	1.02394i	0.999706	−	0.0242353i	$-0.00771510\pi$
$588$	−33.5059	−	5.74258i	−1.38176	−	0.236820i
$589$		−	38.9943i		−	1.60673i
$590$	−6.13926	+	22.9120i	−0.252749	+	0.943273i
$591$	1.88603	+	7.03876i	0.0775809	+	0.289536i
$592$	−11.1955	−	41.7821i	−0.460132	−	1.71723i
$593$	3.77472	−	14.0874i	0.155009	−	0.578501i	−0.844096	−	0.536193i	$-0.819862\pi$
$593$	3.77472	−	14.0874i	0.155009	−	0.578501i	0.999105	−	0.0423087i	$-0.0134713\pi$
$594$		−	1.52050i		−	0.0623869i
$595$	−4.63649	−	1.67497i	−0.190078	−	0.0686672i
$596$	49.4339	−	49.4339i	2.02489	−	2.02489i
$597$	0.187109	−	0.108027i	0.00765787	−	0.00442127i
$598$	−0.213685	+	0.386652i	−0.00873825	+	0.0158114i
$599$	−14.5135	+	25.1381i	−0.593006	+	1.02712i	0.400819	+	0.916157i	$0.368726\pi$
$599$	−14.5135	+	25.1381i	−0.593006	+	1.02712i	−0.993825	+	0.110959i	$0.964608\pi$
$600$	−82.9115	−	22.2161i	−3.38485	−	0.906967i
$601$			4.85980i			0.198235i	0.995076	+	0.0991176i	$0.0316020\pi$
$601$			4.85980i			0.198235i	−0.995076	+	0.0991176i	$0.968398\pi$
$602$	−1.07855	−	6.03219i	−0.0439583	−	0.245854i
$603$	6.31508	+	6.31508i	0.257170	+	0.257170i
$604$	−9.36171	+	34.9384i	−0.380923	+	1.42162i
$605$	41.8070	−	11.2021i	1.69969	−	0.455432i
$606$	−4.28822	−	16.0039i	−0.174197	−	0.650112i
$607$	−27.0785	+	15.6338i	−1.09908	+	0.634557i	−0.935980	−	0.352052i	$-0.885484\pi$
$607$	−27.0785	+	15.6338i	−1.09908	+	0.634557i	−0.163104	+	0.986609i	$0.552151\pi$
$608$	83.8792			3.40175
$609$	−0.242522	+	2.85070i	−0.00982750	+	0.115516i
$610$			2.03725i			0.0824857i
$611$	10.1688	−	6.12757i	0.411386	−	0.247895i
$612$	1.93057	+	1.11461i	0.0780386	+	0.0450556i
$613$	−32.0396	+	8.58499i	−1.29407	+	0.346744i	−0.839204	−	0.543817i	$-0.816979\pi$
$613$	−32.0396	+	8.58499i	−1.29407	+	0.346744i	−0.454864	+	0.890561i	$0.650312\pi$
$614$	−41.5717	+	24.0014i	−1.67770	+	0.968619i
$615$	−25.8632			−1.04290
$616$	0.974052	−	11.4494i	0.0392457	−	0.461309i
$617$	−13.6876	−	13.6876i	−0.551042	−	0.551042i	0.375700	−	0.926741i	$-0.377402\pi$
$617$	−13.6876	−	13.6876i	−0.551042	−	0.551042i	−0.926741	+	0.375700i	$0.877402\pi$
$618$	−40.8323	−	10.9410i	−1.64252	−	0.440111i
$619$	−11.6936	+	3.13330i	−0.470007	+	0.125938i	−0.486046	−	0.873933i	$-0.661561\pi$
$619$	−11.6936	+	3.13330i	−0.470007	+	0.125938i	0.0160389	+	0.999871i	$0.494894\pi$
$620$	49.8968	−	86.4238i	2.00390	−	3.47086i
$621$	−0.0233964	−	0.0405237i	−0.000938864	−	0.00162616i
$622$	12.4328	+	12.4328i	0.498512	+	0.498512i
$623$	49.1257	−	8.78360i	1.96818	−	0.351908i
$624$	24.6919	−	25.6341i	0.988469	−	1.02619i
$625$	24.6644	+	42.7199i	0.986575	+	1.70880i
$626$	0.688662	+	2.57012i	0.0275245	+	0.102723i
$627$	2.23641	−	3.87358i	0.0893138	−	0.154696i
$628$	50.8313	+	88.0425i	2.02839	+	3.51328i
$629$	1.42231	−	1.42231i	0.0567111	−	0.0567111i
$630$	−11.9454	−	25.4576i	−0.475918	−	1.01426i
$631$	19.1930	−	19.1930i	0.764060	−	0.764060i	−0.212993	−	0.977054i	$-0.568321\pi$
$631$	19.1930	−	19.1930i	0.764060	−	0.764060i	0.977054	+	0.212993i	$0.0683212\pi$
$632$	42.2458	+	11.3197i	1.68045	+	0.450275i
$633$	0.723521	+	0.417725i	0.0287574	+	0.0166031i
$634$	53.6705	+	30.9867i	2.13153	+	1.23064i
$635$	5.74440	−	21.4384i	0.227960	−	0.850757i
$636$	2.45808			0.0974692
$637$	−25.0842	+	2.79019i	−0.993870	+	0.110551i
$638$	−1.64420			−0.0650945
$639$	1.55124	−	5.78931i	0.0613661	−	0.229021i
$640$	4.17441	+	2.41010i	0.165008	+	0.0952674i
$641$	−11.0951	−	6.40575i	−0.438229	−	0.253012i	0.264617	−	0.964354i	$-0.414754\pi$
$641$	−11.0951	−	6.40575i	−0.438229	−	0.253012i	−0.702846	+	0.711342i	$0.748088\pi$
$642$	2.40984	+	0.645716i	0.0951089	+	0.0254844i
$643$	−3.85306	+	3.85306i	−0.151950	+	0.151950i	−0.778988	−	0.627038i	$-0.784267\pi$
$643$	−3.85306	+	3.85306i	−0.151950	+	0.151950i	0.627038	+	0.778988i	$0.284267\pi$
$644$	−0.255394	−	0.544286i	−0.0100639	−	0.0214479i
$645$	2.53881	−	2.53881i	0.0999657	−	0.0999657i
$646$	4.62917	+	8.01796i	0.182132	+	0.315462i
$647$	12.4892	−	21.6319i	0.491001	−	0.850438i	−0.508945	−	0.860799i	$-0.669965\pi$
$647$	12.4892	−	21.6319i	0.491001	−	0.850438i	0.999946	+	0.0103604i	$0.00329786\pi$
$648$	1.93578	+	7.22442i	0.0760445	+	0.283802i
$649$	−0.647962	−	1.12230i	−0.0254347	−	0.0440542i
$650$	−108.331	+	2.02811i	−4.24911	+	0.0795489i
$651$	13.1848	−	2.35743i	0.516754	−	0.0923950i
$652$	38.7788	+	38.7788i	1.51869	+	1.51869i
$653$	−15.4392	−	26.7415i	−0.604183	−	1.04648i	−0.992180	−	0.124815i	$-0.960166\pi$
$653$	−15.4392	−	26.7415i	−0.604183	−	1.04648i	0.387997	−	0.921660i	$-0.373167\pi$
$654$	−9.28256	+	16.0779i	−0.362977	+	0.628695i
$655$	−24.0166	+	6.43523i	−0.938407	+	0.251445i
$656$	60.7540	+	16.2790i	2.37205	+	0.635588i
$657$	−5.12221	−	5.12221i	−0.199836	−	0.199836i
$658$	−1.93372	+	22.7297i	−0.0753843	+	0.886095i
$659$	14.7700			0.575357			0.287678	−	0.957727i	$-0.407117\pi$
$659$	14.7700			0.575357			0.287678	+	0.957727i	$0.407117\pi$
$660$	9.91321	−	5.72339i	0.385871	−	0.222783i
$661$	−27.4334	+	7.35076i	−1.06704	+	0.285912i	−0.749275	−	0.662259i	$-0.769598\pi$
$661$	−27.4334	+	7.35076i	−1.06704	+	0.285912i	−0.317762	+	0.948171i	$0.602931\pi$
$662$	36.6338	+	21.1505i	1.42381	+	0.822038i
$663$	1.60641	+	0.398364i	0.0623878	+	0.0154712i
$664$		−	102.368i		−	3.97266i
$665$	7.01228	−	82.4250i	0.271925	−	3.19630i
$666$	11.4739			0.444604
$667$	−0.0438205	+	0.0252998i	−0.00169674	+	0.000979612i
$668$	16.6883	+	62.2814i	0.645688	+	2.40974i
$669$	−0.471376	+	0.126305i	−0.0182245	+	0.00488323i
$670$	−24.5680	+	91.6892i	−0.949146	+	3.54226i
$671$	−0.0787025	−	0.0787025i	−0.00303828	−	0.00303828i
$672$	5.07098	+	28.3614i	0.195617	+	1.09406i
$673$			25.3723i			0.978030i	0.872275	+	0.489015i	$0.162644\pi$
$673$			25.3723i			0.978030i	−0.872275	+	0.489015i	$0.837356\pi$
$674$	−25.1258	−	6.73244i	−0.967811	−	0.259324i
$675$	5.73828	−	9.93900i	0.220867	−	0.382552i
$676$	29.4978	−	55.8177i	1.13453	−	2.14683i
$677$	−27.0806	+	15.6350i	−1.04079	+	0.600902i	−0.920058	−	0.391783i	$-0.871858\pi$
$677$	−27.0806	+	15.6350i	−1.04079	+	0.600902i	−0.120735	+	0.992685i	$0.538525\pi$
$678$	33.8260	−	33.8260i	1.29908	−	1.29908i
$679$	19.8380	+	7.16665i	0.761311	+	0.275031i
$680$			13.9359i			0.534419i
$681$	−0.287231	+	1.07196i	−0.0110067	+	0.0410776i
$682$	1.99224	+	7.43514i	0.0762868	+	0.284706i
$683$	0.222715	+	0.831182i	0.00852193	+	0.0318043i	0.970056	−	0.242882i	$-0.0780927\pi$
$683$	0.222715	+	0.831182i	0.00852193	+	0.0318043i	−0.961534	+	0.274686i	$0.911426\pi$
$684$	−9.68165	+	36.1324i	−0.370187	+	1.38156i
$685$			15.8496i			0.605584i
$686$	23.9448	−	42.1708i	0.914217	−	1.61009i
$687$	−7.59207	+	7.59207i	−0.289655	+	0.289655i
$688$	−7.56180	+	4.36581i	−0.288291	+	0.166445i
$689$	1.75364	−	0.505252i	0.0668084	−	0.0192486i
$690$	0.248673	−	0.430714i	0.00946682	−	0.0163970i
$691$	32.5456	+	8.72057i	1.23809	+	0.331746i	0.817726	−	0.575608i	$-0.195234\pi$
$691$	32.5456	+	8.72057i	1.23809	+	0.331746i	0.420368	+	0.907354i	$0.361901\pi$
$692$		−	30.9873i		−	1.17796i
$693$	1.44495	+	0.522000i	0.0548890	+	0.0198291i
$694$	19.7423	+	19.7423i	0.749408	+	0.749408i
$695$	−8.83902	+	32.9877i	−0.335283	+	1.25129i
$696$	7.81216	−	2.09326i	0.296119	−	0.0793449i
$697$	0.756988	+	2.82512i	0.0286730	+	0.107009i
$698$	47.3149	−	27.3173i	1.79090	−	1.03397i
$699$	−10.5125			−0.397618
$700$	84.2894	−	120.994i	3.18584	−	4.57313i
$701$		−	4.56454i		−	0.172400i	−0.996278	−	0.0862002i	$-0.972528\pi$
$701$		−	4.56454i		−	0.172400i	0.996278	−	0.0862002i	$-0.0274725\pi$
$702$	4.87272	+	8.08636i	0.183909	+	0.305200i
$703$	29.2306	+	16.8763i	1.10245	+	0.636501i
$704$	−4.91966	+	1.31822i	−0.185417	+	0.0496822i
$705$	−11.5752	+	6.68293i	−0.435946	+	0.251694i
$706$	−76.4611			−2.87765
$707$	16.6808	+	1.41911i	0.627346	+	0.0533713i
$708$	7.66364	+	7.66364i	0.288017	+	0.288017i
$709$	25.8466	+	6.92558i	0.970690	+	0.260096i	0.709119	−	0.705089i	$-0.249093\pi$
$709$	25.8466	+	6.92558i	0.970690	+	0.260096i	0.261571	+	0.965184i	$0.415760\pi$
$710$	61.5328	−	16.4877i	2.30928	−	0.618771i
$711$	−2.92382	+	5.06421i	−0.109652	+	0.189923i
$712$	−70.5378	−	122.175i	−2.64352	−	4.57870i
$713$	0.167503	+	0.167503i	0.00627304	+	0.00627304i
$714$	−2.43119	+	2.04995i	−0.0909849	+	0.0767176i
$715$	5.89584	−	6.12081i	0.220492	−	0.228905i
$716$	−45.6894	−	79.1364i	−1.70749	−	2.95747i
$717$	−4.18222	−	15.6083i	−0.156188	−	0.582902i
$718$	−24.9050	+	43.1367i	−0.929445	+	1.60985i
$719$	12.4067	+	21.4890i	0.462690	+	0.801403i	0.999094	−	0.0425584i	$-0.0135509\pi$
$719$	12.4067	+	21.4890i	0.462690	+	0.801403i	−0.536404	+	0.843962i	$0.680218\pi$
$720$	−28.3335	+	28.3335i	−1.05593	+	1.05593i
$721$	24.4154	−	35.0472i	0.909276	−	1.30523i
$722$	−74.6750	+	74.6750i	−2.77912	+	2.77912i
$723$	9.42517	+	2.52547i	0.350526	+	0.0939231i
$724$	63.4309	+	36.6219i	2.35739	+	1.36104i
$725$	−10.7476	−	6.20512i	−0.399155	−	0.230452i
$726$	7.22627	−	26.9688i	0.268192	−	1.00091i
$727$	15.9619			0.591993			0.295997	−	0.955189i	$-0.404348\pi$
$727$	15.9619			0.591993			0.295997	+	0.955189i	$0.404348\pi$
$728$	31.5114	+	64.0119i	1.16789	+	2.37244i
$729$	−1.00000			−0.0370370
$730$	19.9273	−	74.3697i	0.737542	−	2.75255i
$731$	−0.351631	−	0.203014i	−0.0130055	−	0.00750875i
$732$	0.806130	+	0.465419i	0.0297954	+	0.0172024i
$733$	28.4602	+	7.62589i	1.05120	+	0.281669i	0.742748	−	0.669571i	$-0.233522\pi$
$733$	28.4602	+	7.62589i	1.05120	+	0.281669i	0.308453	+	0.951240i	$0.400189\pi$
$734$	−46.4728	+	46.4728i	−1.71534	+	1.71534i
$735$	28.2936	−	2.61206i	1.04363	−	0.0963472i
$736$	−0.360309	+	0.360309i	−0.0132812	+	0.0132812i
$737$	−2.59301	−	4.49122i	−0.0955147	−	0.165436i
$738$	−8.34191	+	14.4486i	−0.307070	+	0.531861i
$739$	−1.94879	−	7.27300i	−0.0716876	−	0.267542i	0.920774	−	0.390096i	$-0.127558\pi$
$739$	−1.94879	−	7.27300i	−0.0716876	−	0.267542i	−0.992462	+	0.122554i	$0.960891\pi$
$740$	43.1895	+	74.8064i	1.58768	+	2.74994i
$741$	0.519846	+	27.7676i	0.0190970	+	1.02007i
$742$	−1.19141	+	3.29795i	−0.0437382	+	0.121072i
$743$	16.2100	+	16.2100i	0.594686	+	0.594686i	0.938894	−	0.344207i	$-0.111852\pi$
$743$	16.2100	+	16.2100i	0.594686	+	0.594686i	−0.344207	+	0.938894i	$0.611852\pi$
$744$	−18.9316	−	32.7905i	−0.694067	−	1.20216i
$745$	−29.2168	+	50.6050i	−1.07042	+	1.85402i
$746$	−84.0556	+	22.5226i	−3.07749	+	0.824612i
$747$	13.2206	+	3.54244i	0.483715	+	0.129611i
$748$	−0.915333	−	0.915333i	−0.0334679	−	0.0334679i
$749$	−1.44095	+	2.06842i	−0.0526511	+	0.0755784i
$750$	68.8375			2.51359
$751$	−0.625628	+	0.361207i	−0.0228295	+	0.0131806i	−0.511371	−	0.859360i	$-0.670862\pi$
$751$	−0.625628	+	0.361207i	−0.0228295	+	0.0131806i	0.488542	+	0.872540i	$0.337529\pi$
$752$	31.3971	−	8.41283i	1.14494	−	0.306785i
$753$	13.5058	+	7.79756i	0.492177	+	0.284159i
$754$	8.74423	−	5.26914i	0.318446	−	0.191891i
$755$		−	30.2330i		−	1.10029i
$756$	−12.8025	−	1.08917i	−0.465621	−	0.0396126i
$757$	−16.2792			−0.591679			−0.295839	−	0.955238i	$-0.595599\pi$
$757$	−16.2792			−0.591679			−0.295839	+	0.955238i	$0.595599\pi$
$758$	68.0137	−	39.2678i	2.47037	−	1.42627i
$759$	0.00703258	+	0.0262459i	0.000255266	+	0.000952667i
$760$	−225.880	+	60.5245i	−8.19354	+	2.19545i
$761$	0.338495	−	1.26328i	0.0122704	−	0.0457939i	−0.959519	−	0.281643i	$-0.909121\pi$
$761$	0.338495	−	1.26328i	0.0122704	−	0.0457939i	0.971790	+	0.235849i	$0.0757872\pi$
$762$	−10.1239	−	10.1239i	−0.366749	−	0.366749i
$763$	−12.0922	−	14.3410i	−0.437767	−	0.519178i
$764$		−	4.71420i		−	0.170554i
$765$	−1.79979	−	0.482251i	−0.0650714	−	0.0174358i
$766$	−26.1340	+	45.2654i	−0.944259	+	1.63550i
$767$	7.04263	+	3.89215i	0.254295	+	0.140537i
$768$	−12.4991	+	7.21635i	−0.451022	+	0.260397i
$769$	−20.7983	+	20.7983i	−0.750007	+	0.750007i	−0.974480	−	0.224473i	$-0.927934\pi$
$769$	−20.7983	+	20.7983i	−0.750007	+	0.750007i	0.224473	+	0.974480i	$0.427934\pi$
$770$	2.87409	+	16.0744i	0.103575	+	0.579282i
$771$			15.1146i			0.544339i
$772$	15.2728	−	56.9990i	0.549682	−	2.05144i
$773$	−2.85866	−	10.6687i	−0.102819	−	0.383725i	0.895270	−	0.445524i	$-0.146983\pi$
$773$	−2.85866	−	10.6687i	−0.102819	−	0.383725i	−0.998089	+	0.0617995i	$0.980316\pi$
$774$	−0.599453	−	2.23719i	−0.0215469	−	0.0804141i
$775$	−15.0372	+	56.1196i	−0.540152	+	2.01588i
$776$		−	59.6272i		−	2.14049i
$777$	−3.93908	+	10.9038i	−0.141314	+	0.391170i
$778$	36.2606	−	36.2606i	1.30001	−	1.30001i
$779$	−42.5032	+	24.5392i	−1.52284	+	0.879210i
$780$	−34.3790	+	62.2070i	−1.23097	+	2.22737i
$781$	−1.74017	+	3.01407i	−0.0622683	+	0.107852i
$782$	−0.0543267	−	0.0145568i	−0.00194272	−	0.000520549i
$783$			1.08136i			0.0386445i
$784$	−68.1073	−	11.6729i	−2.43240	−	0.416889i
$785$	−60.0855	−	60.0855i	−2.14454	−	2.14454i
$786$	−4.15124	+	15.4926i	−0.148070	+	0.552604i
$787$	−37.9988	+	10.1818i	−1.35451	+	0.362940i	−0.861798	−	0.507251i	$-0.830662\pi$
$787$	−37.9988	+	10.1818i	−1.35451	+	0.362940i	−0.492714	+	0.870192i	$0.663995\pi$
$788$	9.15923	+	34.1827i	0.326284	+	1.21771i
$789$	22.8598	−	13.1981i	0.813832	−	0.469866i
$790$	−62.1529			−2.21130
$791$	20.5324	+	43.7579i	0.730049	+	1.55585i
$792$		−	4.34309i		−	0.154325i
$793$	0.670774	+	0.166341i	0.0238199	+	0.00590695i
$794$	55.0485	+	31.7822i	1.95360	+	1.12791i
$795$	−1.98455	+	0.531759i	−0.0703848	+	0.0188595i
$796$	0.908668	−	0.524620i	0.0322069	−	0.0185947i
$797$	35.8509			1.26990			0.634952	−	0.772552i	$-0.281020\pi$
$797$	35.8509			1.26990			0.634952	+	0.772552i	$0.281020\pi$
$798$	−43.7854	−	30.5028i	−1.54999	−	1.07979i
$799$	1.06879	+	1.06879i	0.0378111	+	0.0378111i
$800$	−120.717	−	32.3460i	−4.26798	−	1.14360i
$801$	18.2195	−	4.88190i	0.643755	−	0.172494i
$802$	33.5513	−	58.1125i	1.18474	−	2.05202i
$803$	2.10321	+	3.64286i	0.0742205	+	0.128554i
$804$	30.6683	+	30.6683i	1.08159	+	1.08159i
$805$	0.323941	+	0.384184i	0.0114174	+	0.0135407i
$806$	−34.4224	−	33.1573i	−1.21248	−	1.16791i
$807$	6.65909	+	11.5339i	0.234411	+	0.406012i
$808$	−12.2487	−	45.7127i	−0.430907	−	1.60817i
$809$	19.4427	−	33.6758i	0.683570	−	1.18398i	−0.290315	−	0.956931i	$-0.593760\pi$
$809$	19.4427	−	33.6758i	0.683570	−	1.18398i	0.973884	−	0.227046i	$-0.0729067\pi$
$810$	−5.31435	−	9.20472i	−0.186727	−	0.323421i
$811$	25.4440	−	25.4440i	0.893460	−	0.893460i	−0.101387	−	0.994847i	$-0.532328\pi$
$811$	25.4440	−	25.4440i	0.893460	−	0.893460i	0.994847	+	0.101387i	$0.0323282\pi$
$812$	−1.17778	+	13.8440i	−0.0413318	+	0.485830i
$813$	14.2556	−	14.2556i	0.499966	−	0.499966i
$814$	−6.43568	−	1.72444i	−0.225570	−	0.0604414i
$815$	−39.6974	−	22.9193i	−1.39054	−	0.802829i
$816$	3.92425	+	2.26567i	0.137376	+	0.0793143i
$817$	1.76340	−	6.58110i	0.0616936	−	0.230244i
$818$	26.6760			0.932704
$819$	−9.35740	+	1.85448i	−0.326974	+	0.0648008i
$820$	−125.601			−4.38617
$821$	−12.8034	+	47.7830i	−0.446842	+	1.66764i	0.264184	+	0.964472i	$0.414897\pi$
$821$	−12.8034	+	47.7830i	−0.446842	+	1.66764i	−0.711027	+	0.703165i	$0.751769\pi$
$822$	8.85449	+	5.11214i	0.308836	+	0.178306i
$823$	45.1357	+	26.0591i	1.57333	+	0.908363i	0.995757	+	0.0920243i	$0.0293337\pi$
$823$	45.1357	+	26.0591i	1.57333	+	0.908363i	0.577574	+	0.816338i	$0.304000\pi$
$824$	−116.632	−	31.2513i	−4.06305	−	1.08869i
$825$	−4.71234	+	4.71234i	−0.164063	+	0.164063i
$826$	−13.9967	+	6.56762i	−0.487006	+	0.228517i
$827$	23.0612	−	23.0612i	0.801917	−	0.801917i	−0.181478	−	0.983395i	$-0.558088\pi$
$827$	23.0612	−	23.0612i	0.801917	−	0.801917i	0.983395	+	0.181478i	$0.0580881\pi$
$828$	−0.113621	−	0.196798i	−0.00394861	−	0.00683919i
$829$	−11.2371	+	19.4633i	−0.390282	+	0.675989i	−0.992487	−	0.122353i	$-0.960956\pi$
$829$	−11.2371	+	19.4633i	−0.390282	+	0.675989i	0.602204	+	0.798342i	$0.294289\pi$
$830$	37.6515	+	140.517i	1.30690	+	4.87743i
$831$	−2.04092	−	3.53497i	−0.0707986	−	0.122627i
$832$	21.9394	−	22.7765i	0.760611	−	0.789634i
$833$	−1.11345	−	3.01415i	−0.0385787	−	0.104434i
$834$	15.5778	+	15.5778i	0.539415	+	0.539415i
$835$	−26.9468	−	46.6733i	−0.932533	−	1.61519i
$836$	10.8608	−	18.8115i	0.375629	−	0.650609i
$837$	4.88993	−	1.31025i	0.169021	−	0.0452890i
$838$	−52.1436	−	13.9718i	−1.80127	−	0.482649i
$839$	−2.56768	−	2.56768i	−0.0886463	−	0.0886463i	0.661393	−	0.750039i	$-0.269966\pi$
$839$	−2.56768	−	2.56768i	−0.0886463	−	0.0886463i	−0.750039	+	0.661393i	$0.769966\pi$
$840$	−34.1204	−	72.7161i	−1.17727	−	2.50894i
$841$	−27.8307			−0.959678
$842$	33.2986	−	19.2250i	1.14755	−	0.662536i
$843$	−0.763442	+	0.204564i	−0.0262943	+	0.00704555i
$844$	3.51367	+	2.02862i	0.120946	+	0.0698280i
$845$	−11.7402	+	51.4462i	−0.403874	+	1.76980i
$846$			8.62205i			0.296432i
$847$	23.1479	+	16.1258i	0.795372	+	0.554090i
$848$	4.99652			0.171581
$849$	−19.6873	+	11.3665i	−0.675667	+	0.390096i
$850$	−3.57025	−	13.3244i	−0.122459	−	0.457022i
$851$	−0.198055	+	0.0530688i	−0.00678925	+	0.00181917i
$852$	7.53337	−	28.1149i	0.258089	−	0.963202i
$853$	1.75869	+	1.75869i	0.0602165	+	0.0602165i	0.736574	−	0.676357i	$-0.236442\pi$
$853$	1.75869	+	1.75869i	0.0602165	+	0.0602165i	−0.676357	+	0.736574i	$0.736442\pi$
$854$	−1.01517	+	0.855981i	−0.0347383	+	0.0292911i
$855$		−	31.2662i		−	1.06928i
$856$	6.88337	+	1.84439i	0.235269	+	0.0630401i
$857$	5.72312	−	9.91273i	0.195498	−	0.338613i	−0.751566	−	0.659658i	$-0.770701\pi$
$857$	5.72312	−	9.91273i	0.195498	−	0.338613i	0.947064	+	0.321046i	$0.104034\pi$
$858$	−1.51778	−	5.26795i	−0.0518162	−	0.179845i
$859$	−35.5016	+	20.4969i	−1.21130	+	0.699344i	−0.963042	−	0.269351i	$-0.913191\pi$
$859$	−35.5016	+	20.4969i	−1.21130	+	0.699344i	−0.248257	+	0.968694i	$0.579858\pi$
$860$	12.3294	−	12.3294i	0.420428	−	0.420428i
$861$	−10.8668	−	12.8877i	−0.370340	−	0.439213i
$862$		−	12.8056i		−	0.436159i
$863$	−9.64858	+	36.0090i	−0.328441	+	1.22576i	0.582365	+	0.812927i	$0.302127\pi$
$863$	−9.64858	+	36.0090i	−0.328441	+	1.22576i	−0.910807	+	0.412833i	$0.864539\pi$
$864$	2.81843	+	10.5185i	0.0958851	+	0.357848i
$865$	6.70351	+	25.0178i	0.227926	+	0.850632i
$866$	−16.6049	+	61.9702i	−0.564256	+	2.10583i
$867$		−	16.7893i		−	0.570194i
$868$	64.0303	−	11.4485i	2.17333	−	0.388588i
$869$	2.40108	−	2.40108i	0.0814509	−	0.0814509i
$870$	−9.95357	+	5.74670i	−0.337458	+	0.194831i
$871$	28.1831	+	15.5756i	0.954949	+	0.527758i
$872$	−26.5143	+	45.9241i	−0.897888	+	1.55519i
$873$	7.70068	+	2.06339i	0.260628	+	0.0698352i
$874$		−	0.943773i		−	0.0319236i
$875$	−23.6325	+	65.4170i	−0.798923	+	2.21150i
$876$	−24.8753	−	24.8753i	−0.840457	−	0.840457i
$877$	9.42472	−	35.1735i	0.318250	−	1.18773i	−0.602675	−	0.797986i	$-0.705899\pi$
$877$	9.42472	−	35.1735i	0.318250	−	1.18773i	0.920925	−	0.389739i	$-0.127435\pi$
$878$	81.9117	−	21.9482i	2.76438	−	0.740715i
$879$	2.59114	+	9.67028i	0.0873971	+	0.326170i
$880$	20.1505	−	11.6339i	0.679274	−	0.392179i
$881$	−44.0473			−1.48399			−0.741995	−	0.670406i	$-0.766120\pi$
$881$	−44.0473			−1.48399			−0.741995	+	0.670406i	$0.766120\pi$
$882$	7.66658	−	16.6489i	0.258147	−	0.560597i
$883$			4.14168i			0.139379i	0.997569	+	0.0696894i	$0.0222008\pi$
$883$			4.14168i			0.139379i	−0.997569	+	0.0696894i	$0.977799\pi$
$884$	7.80130	+	1.93460i	0.262386	+	0.0650675i
$885$	−7.84519	−	4.52942i	−0.263713	−	0.152255i
$886$	89.4788	−	23.9758i	3.00610	−	0.805482i
$887$	43.3054	−	25.0024i	1.45405	−	0.839497i	0.455344	−	0.890316i	$-0.349516\pi$
$887$	43.3054	−	25.0024i	1.45405	−	0.839497i	0.998708	+	0.0508183i	$0.0161829\pi$
$888$	32.7735			1.09981
$889$	13.0964	−	6.14522i	0.439240	−	0.206104i
$890$	141.761	+	141.761i	4.75185	+	4.75185i
$891$	0.560897	+	0.150292i	0.0187908	+	0.00503497i
$892$	−2.28917	+	0.613381i	−0.0766471	+	0.0205375i
$893$	−12.6817	+	21.9653i	−0.424376	+	0.735040i
$894$	18.8472	+	32.6442i	0.630343	+	1.09179i
$895$	54.0075	+	54.0075i	1.80527	+	1.80527i
$896$	0.552982	+	3.09276i	0.0184738	+	0.103322i
$897$	−0.121511	−	0.117045i	−0.00405712	−	0.00390801i
$898$	28.3903	+	49.1735i	0.947397	+	1.64094i
$899$	−1.41685	−	5.28775i	−0.0472546	−	0.176356i
$900$	27.8671	−	48.2673i	0.928905	−	1.60891i
$901$	0.116171	+	0.201215i	0.00387023	+	0.00670343i
$902$	6.85047	−	6.85047i	0.228096	−	0.228096i
$903$	2.33182	+	0.198379i	0.0775982	+	0.00660164i
$904$	96.6190	−	96.6190i	3.21350	−	3.21350i
$905$	−59.1340	−	15.8449i	−1.96568	−	0.526702i
$906$	−16.8898	−	9.75136i	−0.561128	−	0.323967i
$907$	−18.9852	−	10.9611i	−0.630393	−	0.363958i	0.150511	−	0.988608i	$-0.451908\pi$
$907$	−18.9852	−	10.9611i	−0.630393	−	0.363958i	−0.780904	+	0.624651i	$0.785241\pi$
$908$	−1.39490	+	5.20582i	−0.0462912	+	0.172761i
$909$	6.32753			0.209871
$910$	−66.7985	−	76.2769i	−2.21435	−	2.52855i
$911$	18.0264			0.597240			0.298620	−	0.954372i	$-0.403474\pi$
$911$	18.0264			0.597240			0.298620	+	0.954372i	$0.403474\pi$
$912$	−19.6798	+	73.4461i	−0.651664	+	2.43204i
$913$	−6.88298	−	3.97389i	−0.227793	−	0.131517i
$914$	−73.5547	−	42.4668i	−2.43297	−	1.40468i
$915$	−0.751521	−	0.201369i	−0.0248445	−	0.00665706i
$916$	−36.8698	+	36.8698i	−1.21821	+	1.21821i
$917$	−13.2977	−	9.26371i	−0.439127	−	0.305915i
$918$	−0.849915	+	0.849915i	−0.0280514	+	0.0280514i
$919$	−9.95304	−	17.2392i	−0.328321	−	0.568668i	0.653858	−	0.756617i	$-0.273149\pi$
$919$	−9.95304	−	17.2392i	−0.328321	−	0.568668i	−0.982179	+	0.187949i	$0.939816\pi$
$920$	0.710299	−	1.23027i	0.0234179	−	0.0405609i
$921$	−4.74479	−	17.7078i	−0.156346	−	0.583491i
$922$	−30.5270	−	52.8744i	−1.00535	−	1.74133i
$923$	−0.404497	−	21.6062i	−0.0133142	−	0.711177i
$924$	7.01718	+	2.53502i	0.230848	+	0.0833960i
$925$	−35.5600	−	35.5600i	−1.16920	−	1.16920i
$926$	−36.7615	−	63.6728i	−1.20806	−	2.09242i
$927$	8.07204	−	13.9812i	0.265120	−	0.459202i
$928$	11.3743	−	3.04773i	0.373379	−	0.100047i
$929$	−48.0085	−	12.8638i	−1.57511	−	0.422049i	−0.637700	−	0.770285i	$-0.720114\pi$
$929$	−48.0085	−	12.8638i	−1.57511	−	0.422049i	−0.937407	+	0.348236i	$0.886781\pi$
$930$	38.0473	+	38.0473i	1.24762	+	1.24762i
$931$	44.0190	−	31.1379i	1.44266	−	1.02050i
$932$	−51.0523			−1.67227
$933$	−5.81527	+	3.35745i	−0.190383	+	0.109918i
$934$	18.1612	−	4.86628i	0.594252	−	0.159229i
$935$	0.937017	+	0.540987i	0.0306437	+	0.0176922i
$936$	13.9182	+	23.0975i	0.454931	+	0.754966i
$937$			7.64256i			0.249672i	0.992177	+	0.124836i	$0.0398404\pi$
$937$			7.64256i			0.249672i	−0.992177	+	0.124836i	$0.960160\pi$
$938$	−56.0117	+	26.2823i	−1.82885	+	0.858146i
$939$	−1.01616			−0.0331612
$940$	−56.2132	+	32.4547i	−1.83347	+	1.05856i
$941$	−4.20355	−	15.6879i	−0.137032	−	0.511410i	−0.999981	−	0.00611953i	$-0.998052\pi$
$941$	−4.20355	−	15.6879i	−0.137032	−	0.511410i	0.862949	−	0.505290i	$-0.168615\pi$
$942$	−52.9470	+	14.1871i	−1.72511	+	0.462241i
$943$	0.0771656	−	0.287986i	0.00251286	−	0.00937811i
$944$	15.5778	+	15.5778i	0.507015	+	0.507015i
$945$	10.5718	−	1.89022i	0.343901	−	0.0614890i
$946$			1.34493i			0.0437274i
$947$	−18.1395	−	4.86048i	−0.589456	−	0.157944i	−0.0482515	−	0.998835i	$-0.515365\pi$
$947$	−18.1395	−	4.86048i	−0.589456	−	0.157944i	−0.541205	+	0.840891i	$0.682032\pi$
$948$	−14.1991	+	24.5936i	−0.461166	+	0.798763i
$949$	−22.8595	−	12.6334i	−0.742052	−	0.410099i
$950$	200.462	−	115.737i	6.50384	−	3.75499i
$951$	−16.7357	+	16.7357i	−0.542691	+	0.542691i
$952$	−6.94433	+	5.85540i	−0.225067	+	0.189775i
$953$		−	37.5539i		−	1.21649i	−0.793749	−	0.608246i	$-0.791874\pi$
$953$		−	37.5539i		−	1.21649i	0.793749	−	0.608246i	$-0.208126\pi$
$954$	−0.343027	+	1.28019i	−0.0111059	+	0.0414478i
$955$	1.01983	+	3.80605i	0.0330009	+	0.123161i
$956$	−20.3104	−	75.7993i	−0.656884	−	2.45153i
$957$	0.162519	−	0.606529i	0.00525350	−	0.0196063i
$958$		−	75.4965i		−	2.43918i
$959$	−7.89794	+	6.65947i	−0.255038	+	0.215046i
$960$	−25.1750	+	25.1750i	−0.812520	+	0.812520i
$961$	4.65212	−	2.68590i	0.150068	−	0.0866421i
$962$	39.7527	−	11.4534i	1.28168	−	0.369271i
$963$	−0.476396	+	0.825143i	−0.0153517	+	0.0265898i
$964$	45.7720	+	12.2646i	1.47422	+	0.395015i
$965$			49.3227i			1.58775i
$966$	0.319110	−	0.0570565i	0.0102672	−	0.00183576i
$967$	6.79849	+	6.79849i	0.218625	+	0.218625i	0.807919	−	0.589294i	$-0.200594\pi$
$967$	6.79849	+	6.79849i	0.218625	+	0.218625i	−0.589294	+	0.807919i	$0.700594\pi$
$968$	20.6408	−	77.0326i	0.663421	−	2.47592i
$969$	−3.41531	+	0.915129i	−0.109716	+	0.0293982i
$970$	21.9311	+	81.8482i	0.704167	+	2.62799i
$971$	9.79864	−	5.65725i	0.314453	−	0.181550i	−0.334464	−	0.942408i	$-0.608555\pi$
$971$	9.79864	−	5.65725i	0.314453	−	0.181550i	0.648918	+	0.760859i	$0.275222\pi$
$972$	−4.85636			−0.155768
$973$	−20.1517	+	9.45576i	−0.646035	+	0.303138i
$974$			0.181667i			0.00582099i
$975$	9.95974	−	40.1628i	0.318967	−	1.28624i
$976$	1.63861	+	0.946055i	0.0524508	+	0.0302825i
$977$	32.9347	−	8.82482i	1.05367	−	0.282331i	0.309904	−	0.950768i	$-0.399703\pi$
$977$	32.9347	−	8.82482i	1.05367	−	0.282331i	0.743769	+	0.668437i	$0.233036\pi$
$978$	−25.6080	+	14.7848i	−0.818854	+	0.472765i
$979$	−10.9530			−0.350059
$980$	137.404	−	12.6851i	4.38921	−	0.405210i
$981$	−5.01344	−	5.01344i	−0.160067	−	0.160067i
$982$	−73.5519	−	19.7082i	−2.34714	−	0.628913i
$983$	−42.8226	+	11.4743i	−1.36583	+	0.365973i	−0.865954	−	0.500124i	$-0.833288\pi$
$983$	−42.8226	+	11.4743i	−1.36583	+	0.365973i	−0.499876	+	0.866097i	$0.666621\pi$
$984$	−23.8275	+	41.2704i	−0.759592	+	1.31565i
$985$	−14.7896	−	25.6163i	−0.471235	−	0.816203i
$986$	0.919060	+	0.919060i	0.0292688	+	0.0292688i
$987$	−8.19362	−	2.96002i	−0.260806	−	0.0942185i
$988$	2.52456	+	134.849i	0.0803168	+	4.29013i
$989$	0.0206948	+	0.0358444i	0.000658056	+	0.00113979i
$990$	1.59741	+	5.96161i	0.0507690	+	0.189472i
$991$	−9.99638	+	17.3142i	−0.317546	+	0.550005i	−0.979975	−	0.199119i	$-0.936192\pi$
$991$	−9.99638	+	17.3142i	−0.317546	+	0.550005i	0.662430	+	0.749124i	$0.269525\pi$
$992$	−27.5639	−	47.7421i	−0.875155	−	1.51581i
$993$	−11.4232	+	11.4232i	−0.362506	+	0.362506i
$994$	34.0698	+	23.7345i	1.08063	+	0.752812i
$995$	−0.620130	+	0.620130i	−0.0196594	+	0.0196594i
$996$	64.2038	+	17.2033i	2.03437	+	0.545109i
$997$	5.32624	+	3.07511i	0.168684	+	0.0973897i	0.581965	−	0.813214i	$-0.302284\pi$
$997$	5.32624	+	3.07511i	0.168684	+	0.0973897i	−0.413281	+	0.910603i	$0.635617\pi$
$998$	−45.7112	−	26.3914i	−1.44696	−	0.835405i
$999$	−1.13412	+	4.23261i	−0.0358821	+	0.133914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.73.1	yes	36
3.2	odd	2		819.2.fn.g.73.9		36
7.5	odd	6		273.2.bz.a.229.9	yes	36
13.5	odd	4		273.2.bz.a.31.9	✓	36
21.5	even	6		819.2.fn.f.775.1		36
39.5	even	4		819.2.fn.f.577.1		36
91.5	even	12	inner	273.2.bz.b.187.1	yes	36
273.5	odd	12		819.2.fn.g.460.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.31.9	✓	36	13.5	odd	4
273.2.bz.a.229.9	yes	36	7.5	odd	6
273.2.bz.b.73.1	yes	36	1.1	even	1	trivial
273.2.bz.b.187.1	yes	36	91.5	even	12	inner
819.2.fn.f.577.1		36	39.5	even	4
819.2.fn.f.775.1		36	21.5	even	6
819.2.fn.g.73.9		36	3.2	odd	2
819.2.fn.g.460.9		36	273.5	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.677708 + 2.52924i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-4.20573 - 2.42818i) q^{4} +(3.92082 + 1.05058i) q^{5} +(1.85153 - 1.85153i) q^{6} +(1.12389 + 2.39518i) q^{7} +(5.28864 - 5.28864i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.677708 + 2.52924i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-4.20573 - 2.42818i) q^{4} +(3.92082 + 1.05058i) q^{5} +(1.85153 - 1.85153i) q^{6} +(1.12389 + 2.39518i) q^{7} +(5.28864 - 5.28864i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-5.31435 + 9.20472i) q^{10} +(-0.150292 - 0.560897i) q^{11} +(2.42818 + 4.20573i) q^{12} +(2.59678 + 2.50134i) q^{13} +(-6.81965 + 1.21935i) q^{14} +(-2.87024 - 2.87024i) q^{15} +(4.93574 + 8.54896i) q^{16} +(-0.229516 + 0.397534i) q^{17} +(-2.52924 + 0.677708i) q^{18} +(-7.44023 - 1.99360i) q^{19} +(-13.9389 - 13.9389i) q^{20} +(0.224276 - 2.63623i) q^{21} +1.52050 q^{22} +(0.0405237 - 0.0233964i) q^{23} +(-7.22442 + 1.93578i) q^{24} +(9.93900 + 5.73828i) q^{25} +(-8.08636 + 4.87272i) q^{26} -1.00000i q^{27} +(1.08917 - 12.8025i) q^{28} -1.08136 q^{29} +(9.20472 - 5.31435i) q^{30} +(1.31025 + 4.88993i) q^{31} +(-10.5185 + 2.81843i) q^{32} +(-0.150292 + 0.560897i) q^{33} +(-0.849915 - 0.849915i) q^{34} +(1.89022 + 10.5718i) q^{35} -4.85636i q^{36} +(-4.23261 - 1.13412i) q^{37} +(10.0846 - 17.4671i) q^{38} +(-0.998211 - 3.46462i) q^{39} +(26.2920 - 15.1797i) q^{40} +(4.50540 - 4.50540i) q^{41} +(6.51567 + 2.35384i) q^{42} +0.884530i q^{43} +(-0.729872 + 2.72392i) q^{44} +(1.05058 + 3.92082i) q^{45} +(0.0317118 + 0.118350i) q^{46} +(0.852236 - 3.18059i) q^{47} -9.87148i q^{48} +(-4.47376 + 5.38381i) q^{49} +(-21.2493 + 21.2493i) q^{50} +(0.397534 - 0.229516i) q^{51} +(-4.84767 - 16.8254i) q^{52} +(0.253079 - 0.438345i) q^{53} +(2.52924 + 0.677708i) q^{54} -2.35707i q^{55} +(18.6111 + 6.72342i) q^{56} +(5.44662 + 5.44662i) q^{57} +(0.732844 - 2.73501i) q^{58} +(2.15568 - 0.577611i) q^{59} +(5.10200 + 19.0409i) q^{60} +(0.165995 - 0.0958371i) q^{61} -13.2558 q^{62} +(-1.51234 + 2.17090i) q^{63} -8.77105i q^{64} +(7.55367 + 12.5354i) q^{65} +(-1.31679 - 0.760250i) q^{66} +(8.62657 - 2.31148i) q^{67} +(1.93057 - 1.11461i) q^{68} -0.0467928 q^{69} +(-28.0197 - 2.38377i) q^{70} +(-4.23807 - 4.23807i) q^{71} +(7.22442 + 1.93578i) q^{72} +(-6.99707 + 1.87486i) q^{73} +(5.73695 - 9.93669i) q^{74} +(-5.73828 - 9.93900i) q^{75} +(26.4507 + 26.4507i) q^{76} +(1.17454 - 0.990361i) q^{77} +(9.43935 - 0.176717i) q^{78} +(2.92382 + 5.06421i) q^{79} +(10.3708 + 38.7043i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.34191 + 14.4486i) q^{82} +(9.67812 - 9.67812i) q^{83} +(-7.34448 + 10.5427i) q^{84} +(-1.31754 + 1.31754i) q^{85} +(-2.23719 - 0.599453i) q^{86} +(0.936481 + 0.540678i) q^{87} +(-3.76123 - 2.17154i) q^{88} +(4.88190 - 18.2195i) q^{89} -10.6287 q^{90} +(-3.07267 + 9.03098i) q^{91} -0.227242 q^{92} +(1.31025 - 4.88993i) q^{93} +(7.46691 + 4.31102i) q^{94} +(-27.0774 - 15.6331i) q^{95} +(10.5185 + 2.81843i) q^{96} +(5.63729 - 5.63729i) q^{97} +(-10.5851 - 14.9639i) q^{98} +(0.410605 - 0.410605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

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