LMFDB - Embedded newform 570.2.q.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, degree $2$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$2.34324 - 0.627868i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.c.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.384547 + 2.20275i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.51805i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.384547 + 2.20275i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.51805i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.768349 - 2.09991i) q^{10} +2.88497 q^{11} +1.00000i q^{12} +(-4.03244 + 2.32813i) q^{13} +(1.25902 - 2.18069i) q^{14} +(-0.768349 + 2.09991i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.31158 - 3.64399i) q^{17} -1.00000i q^{18} +(4.11420 + 1.43993i) q^{19} +(-1.71537 + 1.43440i) q^{20} +(-1.25902 + 2.18069i) q^{21} +(-2.49846 - 1.44248i) q^{22} +(1.48237 - 0.855848i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.70425 + 1.69412i) q^{25} +4.65626 q^{26} +1.00000i q^{27} +(-2.18069 + 1.25902i) q^{28} +(2.20959 + 3.82712i) q^{29} +(1.71537 - 1.43440i) q^{30} -9.22060 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.49846 + 1.44248i) q^{33} +(3.64399 + 6.31158i) q^{34} +(-5.54663 + 0.968307i) q^{35} +(-0.500000 + 0.866025i) q^{36} +3.26480i q^{37} +(-2.84303 - 3.30411i) q^{38} -4.65626 q^{39} +(2.20275 - 0.384547i) q^{40} +(4.48368 - 7.76596i) q^{41} +(2.18069 - 1.25902i) q^{42} +(5.84894 + 3.37689i) q^{43} +(1.44248 + 2.49846i) q^{44} +(-1.71537 + 1.43440i) q^{45} -1.71170 q^{46} +(-3.98083 + 2.29833i) q^{47} +(-0.866025 + 0.500000i) q^{48} +0.659446 q^{49} +(4.92106 + 0.884968i) q^{50} +(-3.64399 - 6.31158i) q^{51} +(-4.03244 - 2.32813i) q^{52} +(9.38113 - 5.41620i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.10941 + 6.35487i) q^{55} +2.51805 q^{56} +(2.84303 + 3.30411i) q^{57} -4.41917i q^{58} +(4.73274 - 8.19734i) q^{59} +(-2.20275 + 0.384547i) q^{60} +(7.50173 + 12.9934i) q^{61} +(7.98528 + 4.61030i) q^{62} +(-2.18069 + 1.25902i) q^{63} -1.00000 q^{64} +(-6.67896 - 7.98719i) q^{65} +(-1.44248 - 2.49846i) q^{66} +(-9.23107 + 5.32956i) q^{67} -7.28798i q^{68} +1.71170 q^{69} +(5.28768 + 1.93474i) q^{70} +(-5.38040 + 9.31912i) q^{71} +(0.866025 - 0.500000i) q^{72} +(12.2689 + 7.08348i) q^{73} +(1.63240 - 2.82740i) q^{74} +(-4.92106 - 0.884968i) q^{75} +(0.810083 + 4.28296i) q^{76} +7.26448i q^{77} +(4.03244 + 2.32813i) q^{78} +(4.11998 - 7.13601i) q^{79} +(-2.09991 - 0.768349i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.76596 + 4.48368i) q^{82} +7.14523i q^{83} -2.51805 q^{84} +(5.59972 - 15.3041i) q^{85} +(-3.37689 - 5.84894i) q^{86} +4.41917i q^{87} -2.88497i q^{88} +(2.37111 + 4.10688i) q^{89} +(2.20275 - 0.384547i) q^{90} +(-5.86233 - 10.1539i) q^{91} +(1.48237 + 0.855848i) q^{92} +(-7.98528 - 4.61030i) q^{93} +4.59667 q^{94} +(-1.58971 + 9.61628i) q^{95} +1.00000 q^{96} +(1.98898 + 1.14834i) q^{97} +(-0.571097 - 0.329723i) q^{98} +(1.44248 + 2.49846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.384547	+	2.20275i	0.171975	+	0.985101i
$5$	0.384547	+	2.20275i	0.171975	+	0.985101i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$			2.51805i			0.951732i	0.879518	+	0.475866i	$0.157865\pi$
$7$			2.51805i			0.951732i	−0.879518	+	0.475866i	$0.842135\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.768349	−	2.09991i	0.242973	−	0.664051i
$11$	2.88497			0.869851			0.434925	−	0.900467i	$-0.356775\pi$
$11$	2.88497			0.869851			0.434925	+	0.900467i	$0.356775\pi$
$12$			1.00000i			0.288675i
$13$	−4.03244	+	2.32813i	−1.11840	+	0.645707i	−0.940991	−	0.338431i	$-0.890104\pi$
$13$	−4.03244	+	2.32813i	−1.11840	+	0.645707i	−0.177406	+	0.984138i	$0.556770\pi$
$14$	1.25902	−	2.18069i	0.336488	−	0.582814i
$15$	−0.768349	+	2.09991i	−0.198387	+	0.542195i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.31158	−	3.64399i	−1.53078	−	0.883798i	−0.999326	−	0.0367122i	$-0.988312\pi$
$17$	−6.31158	−	3.64399i	−1.53078	−	0.883798i	−0.531457	−	0.847085i	$-0.678355\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.11420	+	1.43993i	0.943861	+	0.330342i
$19$	4.11420	+	1.43993i	0.943861	+	0.330342i
$20$	−1.71537	+	1.43440i	−0.383568	+	0.320743i
$21$	−1.25902	+	2.18069i	−0.274741	+	0.475866i
$22$	−2.49846	−	1.44248i	−0.532673	−	0.307539i
$23$	1.48237	−	0.855848i	0.309096	−	0.178457i	−0.337426	−	0.941352i	$-0.609556\pi$
$23$	1.48237	−	0.855848i	0.309096	−	0.178457i	0.646522	+	0.762895i	$0.276223\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.70425	+	1.69412i	−0.940849	+	0.338825i
$26$	4.65626			0.913167
$27$			1.00000i			0.192450i
$28$	−2.18069	+	1.25902i	−0.412112	+	0.237933i
$29$	2.20959	+	3.82712i	0.410310	+	0.710678i	0.994923	−	0.100634i	$-0.0320872\pi$
$29$	2.20959	+	3.82712i	0.410310	+	0.710678i	−0.584613	+	0.811312i	$0.698754\pi$
$30$	1.71537	−	1.43440i	0.313182	−	0.261885i
$31$	−9.22060			−1.65607			−0.828035	−	0.560677i	$-0.810541\pi$
$31$	−9.22060			−1.65607			−0.828035	+	0.560677i	$0.810541\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.49846	+	1.44248i	0.434925	+	0.251104i
$34$	3.64399	+	6.31158i	0.624939	+	1.08243i
$35$	−5.54663	+	0.968307i	−0.937552	+	0.163674i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$			3.26480i			0.536730i	0.963317	+	0.268365i	$0.0864834\pi$
$37$			3.26480i			0.536730i	−0.963317	+	0.268365i	$0.913517\pi$
$38$	−2.84303	−	3.30411i	−0.461201	−	0.535998i
$39$	−4.65626			−0.745598
$40$	2.20275	−	0.384547i	0.348286	−	0.0608022i
$41$	4.48368	−	7.76596i	0.700233	−	1.21284i	−0.268151	−	0.963377i	$-0.586413\pi$
$41$	4.48368	−	7.76596i	0.700233	−	1.21284i	0.968384	−	0.249463i	$-0.0802540\pi$
$42$	2.18069	−	1.25902i	0.336488	−	0.194271i
$43$	5.84894	+	3.37689i	0.891955	+	0.514971i	0.874582	−	0.484878i	$-0.161136\pi$
$43$	5.84894	+	3.37689i	0.891955	+	0.514971i	0.0173738	+	0.999849i	$0.494469\pi$
$44$	1.44248	+	2.49846i	0.217463	+	0.376656i
$45$	−1.71537	+	1.43440i	−0.255712	+	0.213828i
$46$	−1.71170			−0.252376
$47$	−3.98083	+	2.29833i	−0.580664	+	0.335246i	−0.761397	−	0.648286i	$-0.775486\pi$
$47$	−3.98083	+	2.29833i	−0.580664	+	0.335246i	0.180733	+	0.983532i	$0.442153\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	0.659446			0.0942065
$50$	4.92106	+	0.884968i	0.695943	+	0.125153i
$51$	−3.64399	−	6.31158i	−0.510261	−	0.883798i
$52$	−4.03244	−	2.32813i	−0.559198	−	0.322853i
$53$	9.38113	−	5.41620i	1.28860	−	0.743972i	0.310193	−	0.950673i	$-0.399606\pi$
$53$	9.38113	−	5.41620i	1.28860	−	0.743972i	0.978404	+	0.206701i	$0.0662729\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	1.10941	+	6.35487i	0.149592	+	0.856891i
$56$	2.51805			0.336488
$57$	2.84303	+	3.30411i	0.376569	+	0.437640i
$58$		−	4.41917i		−	0.580266i
$59$	4.73274	−	8.19734i	0.616150	−	1.06720i	−0.374032	−	0.927416i	$-0.622025\pi$
$59$	4.73274	−	8.19734i	0.616150	−	1.06720i	0.990182	−	0.139787i	$-0.0446418\pi$
$60$	−2.20275	+	0.384547i	−0.284374	+	0.0496448i
$61$	7.50173	+	12.9934i	0.960498	+	1.66363i	0.721254	+	0.692671i	$0.243566\pi$
$61$	7.50173	+	12.9934i	0.960498	+	1.66363i	0.239244	+	0.970959i	$0.423100\pi$
$62$	7.98528	+	4.61030i	1.01413	+	0.585509i
$63$	−2.18069	+	1.25902i	−0.274741	+	0.158622i
$64$	−1.00000			−0.125000
$65$	−6.67896	−	7.98719i	−0.828422	−	0.990689i
$66$	−1.44248	−	2.49846i	−0.177558	−	0.307539i
$67$	−9.23107	+	5.32956i	−1.12776	+	0.651110i	−0.943369	−	0.331744i	$-0.892363\pi$
$67$	−9.23107	+	5.32956i	−1.12776	+	0.651110i	−0.184386	+	0.982854i	$0.559030\pi$
$68$		−	7.28798i		−	0.883798i
$69$	1.71170			0.206064
$70$	5.28768	+	1.93474i	0.631999	+	0.231246i
$71$	−5.38040	+	9.31912i	−0.638536	+	1.10598i	0.347218	+	0.937784i	$0.387126\pi$
$71$	−5.38040	+	9.31912i	−0.638536	+	1.10598i	−0.985754	+	0.168192i	$0.946207\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	12.2689	+	7.08348i	1.43597	+	0.829059i	0.997567	−	0.0697187i	$-0.0222102\pi$
$73$	12.2689	+	7.08348i	1.43597	+	0.829059i	0.438405	+	0.898777i	$0.355543\pi$
$74$	1.63240	−	2.82740i	0.189763	−	0.328679i
$75$	−4.92106	−	0.884968i	−0.568235	−	0.102187i
$76$	0.810083	+	4.28296i	0.0929229	+	0.491289i
$77$			7.26448i			0.827865i
$78$	4.03244	+	2.32813i	0.456584	+	0.263609i
$79$	4.11998	−	7.13601i	0.463533	−	0.802864i	−0.535601	−	0.844471i	$-0.679915\pi$
$79$	4.11998	−	7.13601i	0.463533	−	0.802864i	0.999134	+	0.0416079i	$0.0132480\pi$
$80$	−2.09991	−	0.768349i	−0.234778	−	0.0859041i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.76596	+	4.48368i	−0.857607	+	0.495140i
$83$			7.14523i			0.784291i	0.919903	+	0.392146i	$0.128267\pi$
$83$			7.14523i			0.784291i	−0.919903	+	0.392146i	$0.871733\pi$
$84$	−2.51805			−0.274741
$85$	5.59972	−	15.3041i	0.607375	−	1.65997i
$86$	−3.37689	−	5.84894i	−0.364139	−	0.630708i
$87$			4.41917i			0.473785i
$88$		−	2.88497i		−	0.307539i
$89$	2.37111	+	4.10688i	0.251337	+	0.435328i	0.963894	−	0.266286i	$-0.0857964\pi$
$89$	2.37111	+	4.10688i	0.251337	+	0.435328i	−0.712557	+	0.701614i	$0.752463\pi$
$90$	2.20275	−	0.384547i	0.232191	−	0.0405348i
$91$	−5.86233	−	10.1539i	−0.614540	−	1.06441i
$92$	1.48237	+	0.855848i	0.154548	+	0.0892284i
$93$	−7.98528	−	4.61030i	−0.828035	−	0.478066i
$94$	4.59667			0.474110
$95$	−1.58971	+	9.61628i	−0.163100	+	0.986609i
$96$	1.00000			0.102062
$97$	1.98898	+	1.14834i	0.201950	+	0.116596i	0.597565	−	0.801821i	$-0.296135\pi$
$97$	1.98898	+	1.14834i	0.201950	+	0.116596i	−0.395615	+	0.918417i	$0.629468\pi$
$98$	−0.571097	−	0.329723i	−0.0576895	−	0.0333070i
$99$	1.44248	+	2.49846i	0.144975	+	0.251104i
$100$	−3.81928	−	3.22694i	−0.381928	−	0.322694i
$101$	1.68398	+	2.91673i	0.167562	+	0.290226i	0.937562	−	0.347818i	$-0.113077\pi$
$101$	1.68398	+	2.91673i	0.167562	+	0.290226i	−0.770000	+	0.638044i	$0.779744\pi$
$102$			7.28798i			0.721618i
$103$		−	10.9873i		−	1.08261i	−0.840826	−	0.541305i	$-0.817930\pi$
$103$		−	10.9873i		−	1.08261i	0.840826	−	0.541305i	$-0.182070\pi$
$104$	2.32813	+	4.03244i	0.228292	+	0.395413i
$105$	−5.28768	−	1.93474i	−0.516025	−	0.188811i
$106$	−10.8324			−1.05214
$107$		−	3.35775i		−	0.324605i	−0.986741	−	0.162303i	$-0.948108\pi$
$107$		−	3.35775i		−	0.324605i	0.986741	−	0.162303i	$-0.0518921\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	2.11647	−	3.66583i	0.202721	−	0.351122i	−0.746683	−	0.665180i	$-0.768355\pi$
$109$	2.11647	−	3.66583i	0.202721	−	0.351122i	0.949404	+	0.314057i	$0.101688\pi$
$110$	2.21666	−	6.05819i	0.211351	−	0.577625i
$111$	−1.63240	+	2.82740i	−0.154941	+	0.268365i
$112$	−2.18069	−	1.25902i	−0.206056	−	0.118966i
$113$		−	18.7982i		−	1.76839i	−0.467118	−	0.884195i	$-0.654708\pi$
$113$		−	18.7982i		−	1.76839i	0.467118	−	0.884195i	$-0.345292\pi$
$114$	−0.810083	−	4.28296i	−0.0758712	−	0.401136i
$115$	2.45527	+	2.93619i	0.228955	+	0.273801i
$116$	−2.20959	+	3.82712i	−0.205155	+	0.355339i
$117$	−4.03244	−	2.32813i	−0.372799	−	0.215236i
$118$	−8.19734	+	4.73274i	−0.754626	+	0.435684i
$119$	9.17574	−	15.8928i	0.841138	−	1.45689i
$120$	2.09991	+	0.768349i	0.191695	+	0.0701404i
$121$	−2.67696			−0.243360
$122$		−	15.0035i		−	1.35835i
$123$	7.76596	−	4.48368i	0.700233	−	0.404280i
$124$	−4.61030	−	7.98528i	−0.414017	−	0.717099i
$125$	−5.54074	−	9.71083i	−0.495579	−	0.868563i
$126$	2.51805			0.224325
$127$	13.6465	−	7.87880i	1.21093	−	0.699131i	0.247968	−	0.968768i	$-0.420237\pi$
$127$	13.6465	−	7.87880i	1.21093	−	0.699131i	0.962962	+	0.269637i	$0.0869038\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.37689	+	5.84894i	0.297318	+	0.514971i
$130$	1.79055	+	10.2566i	0.157042	+	0.899562i
$131$	3.28357	−	5.68732i	0.286887	−	0.496903i	−0.686178	−	0.727434i	$-0.740713\pi$
$131$	3.28357	−	5.68732i	0.286887	−	0.496903i	0.973065	+	0.230531i	$0.0740462\pi$
$132$			2.88497i			0.251104i
$133$	−3.62581	+	10.3597i	−0.314397	+	0.898303i
$134$	10.6591			0.920808
$135$	−2.20275	+	0.384547i	−0.189583	+	0.0330965i
$136$	−3.64399	+	6.31158i	−0.312470	+	0.541213i
$137$	12.5023	−	7.21818i	1.06814	−	0.616691i	0.140467	−	0.990085i	$-0.455139\pi$
$137$	12.5023	−	7.21818i	1.06814	−	0.616691i	0.927673	+	0.373394i	$0.121806\pi$
$138$	−1.48237	−	0.855848i	−0.126188	−	0.0728547i
$139$	−3.09728	−	5.36464i	−0.262708	−	0.455023i	0.704253	−	0.709949i	$-0.251282\pi$
$139$	−3.09728	−	5.36464i	−0.262708	−	0.455023i	−0.966960	+	0.254926i	$0.917949\pi$
$140$	−3.61190	−	4.31937i	−0.305261	−	0.365054i
$141$	−4.59667			−0.387109
$142$	9.31912	−	5.38040i	0.782043	−	0.451513i
$143$	−11.6335	+	6.71658i	−0.972838	+	0.561668i
$144$	−1.00000			−0.0833333
$145$	−7.58051	+	6.33888i	−0.629527	+	0.526416i
$146$	−7.08348	−	12.2689i	−0.586233	−	1.01539i
$147$	0.571097	+	0.329723i	0.0471033	+	0.0271951i
$148$	−2.82740	+	1.63240i	−0.232411	+	0.134183i
$149$	−5.99475	+	10.3832i	−0.491109	+	0.850626i	−0.999948	−	0.0102357i	$-0.996742\pi$
$149$	−5.99475	+	10.3832i	−0.491109	+	0.850626i	0.508838	+	0.860862i	$0.330075\pi$
$150$	3.81928	+	3.22694i	0.311843	+	0.263478i
$151$	−5.51534			−0.448832			−0.224416	−	0.974493i	$-0.572047\pi$
$151$	−5.51534			−0.448832			−0.224416	+	0.974493i	$0.572047\pi$
$152$	1.43993	−	4.11420i	0.116794	−	0.333705i
$153$		−	7.28798i		−	0.589198i
$154$	3.63224	−	6.29123i	0.292694	−	0.506961i
$155$	−3.54576	−	20.3107i	−0.284802	−	1.63140i
$156$	−2.32813	−	4.03244i	−0.186399	−	0.322853i
$157$	−10.6341	−	6.13962i	−0.848696	−	0.489995i	0.0115149	−	0.999934i	$-0.496335\pi$
$157$	−10.6341	−	6.13962i	−0.848696	−	0.489995i	−0.860211	+	0.509939i	$0.829668\pi$
$158$	−7.13601	+	4.11998i	−0.567710	+	0.327768i
$159$	10.8324			0.859065
$160$	1.43440	+	1.71537i	0.113400	+	0.135612i
$161$	2.15507	+	3.73268i	0.169843	+	0.294177i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	3.45801i		−	0.270852i	−0.990787	−	0.135426i	$-0.956760\pi$
$163$		−	3.45801i		−	0.270852i	0.990787	−	0.135426i	$-0.0432403\pi$
$164$	8.96736			0.700233
$165$	−2.21666	+	6.05819i	−0.172567	+	0.471629i
$166$	3.57262	−	6.18795i	0.277289	−	0.480278i
$167$	−5.37144	+	3.10120i	−0.415654	+	0.239978i	−0.693216	−	0.720730i	$-0.743807\pi$
$167$	−5.37144	+	3.10120i	−0.415654	+	0.239978i	0.277562	+	0.960708i	$0.410474\pi$
$168$	2.18069	+	1.25902i	0.168244	+	0.0971357i
$169$	4.34036	−	7.51773i	0.333874	−	0.578287i
$170$	−12.5016	+	10.4539i	−0.958826	+	0.801779i
$171$	0.810083	+	4.28296i	0.0619486	+	0.327526i
$172$			6.75378i			0.514971i
$173$	12.4712	+	7.20026i	0.948169	+	0.547425i	0.892512	−	0.451025i	$-0.148941\pi$
$173$	12.4712	+	7.20026i	0.948169	+	0.547425i	0.0556571	+	0.998450i	$0.482275\pi$
$174$	2.20959	−	3.82712i	0.167508	−	0.290133i
$175$	−4.26588	−	11.8455i	−0.322471	−	0.895436i
$176$	−1.44248	+	2.49846i	−0.108731	+	0.188328i
$177$	8.19734	−	4.73274i	0.616150	−	0.355734i
$178$		−	4.74222i		−	0.355444i
$179$	−1.94176			−0.145134			−0.0725670	−	0.997364i	$-0.523119\pi$
$179$	−1.94176			−0.145134			−0.0725670	+	0.997364i	$0.523119\pi$
$180$	−2.09991	−	0.768349i	−0.156518	−	0.0572694i
$181$	−8.81480	−	15.2677i	−0.655199	−	1.13484i	−0.981844	−	0.189691i	$-0.939251\pi$
$181$	−8.81480	−	15.2677i	−0.655199	−	1.13484i	0.326645	−	0.945147i	$-0.394082\pi$
$182$			11.7247i			0.869090i
$183$			15.0035i			1.10909i
$184$	−0.855848	−	1.48237i	−0.0630940	−	0.109282i
$185$	−7.19156	+	1.25547i	−0.528734	+	0.0923040i
$186$	4.61030	+	7.98528i	0.338044	+	0.585509i
$187$	−18.2087	−	10.5128i	−1.33155	−	0.768772i
$188$	−3.98083	−	2.29833i	−0.290332	−	0.167623i
$189$	−2.51805			−0.183161
$190$	6.18487	−	7.53309i	0.448697	−	0.546508i
$191$	−4.61377			−0.333840			−0.166920	−	0.985970i	$-0.553382\pi$
$191$	−4.61377			−0.333840			−0.166920	+	0.985970i	$0.553382\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	21.7202	+	12.5401i	1.56345	+	0.902659i	0.996904	+	0.0786292i	$0.0250543\pi$
$193$	21.7202	+	12.5401i	1.56345	+	0.902659i	0.566547	+	0.824030i	$0.308279\pi$
$194$	−1.14834	−	1.98898i	−0.0824458	−	0.142800i
$195$	−1.79055	−	10.2566i	−0.128224	−	0.734489i
$196$	0.329723	+	0.571097i	0.0235516	+	0.0407926i
$197$		−	3.62439i		−	0.258227i	−0.991630	−	0.129113i	$-0.958787\pi$
$197$		−	3.62439i		−	0.258227i	0.991630	−	0.129113i	$-0.0412131\pi$
$198$		−	2.88497i		−	0.205026i
$199$	0.298493	+	0.517005i	0.0211596	+	0.0366495i	0.876411	−	0.481563i	$-0.159931\pi$
$199$	0.298493	+	0.517005i	0.0211596	+	0.0366495i	−0.855252	+	0.518213i	$0.826598\pi$
$200$	1.69412	+	4.70425i	0.119793	+	0.332641i
$201$	−10.6591			−0.751837
$202$		−	3.36795i		−	0.236968i
$203$	−9.63686	+	5.56384i	−0.676375	+	0.390505i
$204$	3.64399	−	6.31158i	0.255130	−	0.441899i
$205$	18.8307	+	6.89006i	1.31519	+	0.481223i
$206$	−5.49365	+	9.51527i	−0.382760	+	0.662961i
$207$	1.48237	+	0.855848i	0.103032	+	0.0594856i
$208$		−	4.65626i		−	0.322853i
$209$	11.8693	+	4.15415i	0.821018	+	0.287349i
$210$	3.61190	+	4.31937i	0.249244	+	0.298065i
$211$	11.4644	−	19.8569i	0.789242	−	1.36701i	−0.137191	−	0.990545i	$-0.543807\pi$
$211$	11.4644	−	19.8569i	0.789242	−	1.36701i	0.926432	−	0.376462i	$-0.122859\pi$
$212$	9.38113	+	5.41620i	0.644299	+	0.371986i
$213$	−9.31912	+	5.38040i	−0.638536	+	0.368659i
$214$	−1.67887	+	2.90789i	−0.114765	+	0.198779i
$215$	−5.18926	+	14.1824i	−0.353905	+	0.967228i
$216$	1.00000			0.0680414
$217$		−	23.2179i		−	1.57613i
$218$	−3.66583	+	2.11647i	−0.248281	+	0.143345i
$219$	7.08348	+	12.2689i	0.478657	+	0.829059i
$220$	−4.94878	+	4.13821i	−0.333647	+	0.278998i
$221$	33.9347			2.28270
$222$	2.82740	−	1.63240i	0.189763	−	0.109560i
$223$	9.74016	+	5.62349i	0.652250	+	0.376576i	0.789318	−	0.613985i	$-0.210435\pi$
$223$	9.74016	+	5.62349i	0.652250	+	0.376576i	−0.137068	+	0.990562i	$0.543768\pi$
$224$	1.25902	+	2.18069i	0.0841220	+	0.145704i
$225$	−3.81928	−	3.22694i	−0.254619	−	0.215129i
$226$	−9.39912	+	16.2798i	−0.625220	+	1.08291i
$227$			8.82814i			0.585944i	0.956121	+	0.292972i	$0.0946443\pi$
$227$			8.82814i			0.585944i	−0.956121	+	0.292972i	$0.905356\pi$
$228$	−1.43993	+	4.11420i	−0.0953616	+	0.272469i
$229$	22.2817			1.47241			0.736207	−	0.676756i	$-0.236615\pi$
$229$	22.2817			1.47241			0.736207	+	0.676756i	$0.236615\pi$
$230$	−0.658228	−	3.77045i	−0.0434023	−	0.248616i
$231$	−3.63224	+	6.29123i	−0.238984	+	0.413932i
$232$	3.82712	−	2.20959i	0.251263	−	0.145066i
$233$	−5.35318	−	3.09066i	−0.350699	−	0.202476i	0.314294	−	0.949326i	$-0.398232\pi$
$233$	−5.35318	−	3.09066i	−0.350699	−	0.202476i	−0.664993	+	0.746850i	$0.731565\pi$
$234$	2.32813	+	4.03244i	0.152195	+	0.263609i
$235$	−6.59348	−	7.88497i	−0.430111	−	0.514359i
$236$	9.46547			0.616150
$237$	7.13601	−	4.11998i	0.463533	−	0.267621i
$238$	−15.8928	+	9.17574i	−1.03018	+	0.594775i
$239$	−18.1898			−1.17660			−0.588299	−	0.808644i	$-0.700202\pi$
$239$	−18.1898			−1.17660			−0.588299	+	0.808644i	$0.700202\pi$
$240$	−1.43440	−	1.71537i	−0.0925904	−	0.110726i
$241$	−1.24768	−	2.16104i	−0.0803699	−	0.139205i	0.823039	−	0.567985i	$-0.192277\pi$
$241$	−1.24768	−	2.16104i	−0.0803699	−	0.139205i	−0.903409	+	0.428780i	$0.858943\pi$
$242$	2.31831	+	1.33848i	0.149027	+	0.0860407i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−7.50173	+	12.9934i	−0.480249	+	0.831815i
$245$	0.253588	+	1.45260i	0.0162011	+	0.0928030i
$246$	−8.96736			−0.571738
$247$	−19.9426	+	3.77195i	−1.26892	+	0.240004i
$248$			9.22060i			0.585509i
$249$	−3.57262	+	6.18795i	−0.226405	+	0.392146i
$250$	−0.0569884	+	11.1802i	−0.00360426	+	0.707098i
$251$	10.6317	+	18.4147i	0.671069	+	1.16232i	0.977601	+	0.210465i	$0.0674977\pi$
$251$	10.6317	+	18.4147i	0.671069	+	1.16232i	−0.306533	+	0.951860i	$0.599169\pi$
$252$	−2.18069	−	1.25902i	−0.137371	−	0.0793110i
$253$	4.27660	−	2.46910i	0.268867	−	0.155231i
$254$	−15.7576			−0.988720
$255$	12.5016	−	10.4539i	0.782878	−	0.654649i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.03779	+	2.90857i	−0.314249	+	0.181432i	−0.648826	−	0.760937i	$-0.724740\pi$
$257$	−5.03779	+	2.90857i	−0.314249	+	0.181432i	0.334577	+	0.942368i	$0.391406\pi$
$258$		−	6.75378i		−	0.420472i
$259$	−8.22092			−0.510823
$260$	3.57763	−	9.77774i	0.221875	−	0.606390i
$261$	−2.20959	+	3.82712i	−0.136770	+	0.236893i
$262$	−5.68732	+	3.28357i	−0.351364	+	0.202860i
$263$	14.9606	+	8.63749i	0.922508	+	0.532610i	0.884434	−	0.466665i	$-0.154544\pi$
$263$	14.9606	+	8.63749i	0.922508	+	0.532610i	0.0380737	+	0.999275i	$0.487878\pi$
$264$	1.44248	−	2.49846i	0.0887788	−	0.153769i
$265$	15.5380	+	18.5815i	0.954494	+	1.14145i
$266$	8.31991	−	7.15889i	0.510126	−	0.438940i
$267$			4.74222i			0.290219i
$268$	−9.23107	−	5.32956i	−0.563878	−	0.325555i
$269$	−4.82743	+	8.36136i	−0.294334	+	0.509801i	−0.974830	−	0.222951i	$-0.928431\pi$
$269$	−4.82743	+	8.36136i	−0.294334	+	0.509801i	0.680496	+	0.732752i	$0.261764\pi$
$270$	2.09991	+	0.768349i	0.127797	+	0.0467602i
$271$	−3.21818	+	5.57406i	−0.195491	+	0.338600i	−0.947061	−	0.321053i	$-0.895963\pi$
$271$	−3.21818	+	5.57406i	−0.195491	+	0.338600i	0.751571	+	0.659653i	$0.229297\pi$
$272$	6.31158	−	3.64399i	0.382696	−	0.220949i
$273$		−	11.7247i		−	0.709609i
$274$	−14.4364			−0.872133
$275$	−13.5716	+	4.88750i	−0.818399	+	0.294727i
$276$	0.855848	+	1.48237i	0.0515160	+	0.0892284i
$277$		−	11.1309i		−	0.668791i	−0.942433	−	0.334396i	$-0.891468\pi$
$277$		−	11.1309i		−	0.668791i	0.942433	−	0.334396i	$-0.108532\pi$
$278$			6.19455i			0.371525i
$279$	−4.61030	−	7.98528i	−0.276012	−	0.478066i
$280$	0.968307	+	5.54663i	0.0578674	+	0.331475i
$281$	−2.84358	−	4.92523i	−0.169634	−	0.293815i	0.768657	−	0.639661i	$-0.220925\pi$
$281$	−2.84358	−	4.92523i	−0.169634	−	0.293815i	−0.938291	+	0.345846i	$0.887592\pi$
$282$	3.98083	+	2.29833i	0.237055	+	0.136864i
$283$	−6.24466	−	3.60536i	−0.371207	−	0.214316i	0.302779	−	0.953061i	$-0.402086\pi$
$283$	−6.24466	−	3.60536i	−0.371207	−	0.214316i	−0.673985	+	0.738745i	$0.735419\pi$
$284$	−10.7608			−0.638536
$285$	−6.18487	+	7.53309i	−0.366360	+	0.446222i
$286$	13.4332			0.794319
$287$	19.5550	+	11.2901i	1.15430	+	0.666434i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	18.0573	+	31.2762i	1.06220	+	1.83978i
$290$	9.73435	−	1.69938i	0.571621	−	0.0997910i
$291$	1.14834	+	1.98898i	0.0673167	+	0.116596i
$292$			14.1670i			0.829059i
$293$			9.26719i			0.541395i	0.962664	+	0.270697i	$0.0872543\pi$
$293$			9.26719i			0.541395i	−0.962664	+	0.270697i	$0.912746\pi$
$294$	−0.329723	−	0.571097i	−0.0192298	−	0.0333070i
$295$	19.8767	+	7.27279i	1.15727	+	0.423438i
$296$	3.26480			0.189763
$297$			2.88497i			0.167403i
$298$	10.3832	−	5.99475i	0.601484	−	0.347267i
$299$	−3.98505	+	6.90231i	−0.230461	+	0.399171i
$300$	−1.69412	−	4.70425i	−0.0978103	−	0.271600i
$301$	−8.50316	+	14.7279i	−0.490114	+	0.848902i
$302$	4.77643	+	2.75767i	0.274852	+	0.158686i
$303$			3.36795i			0.193484i
$304$	−3.30411	+	2.84303i	−0.189504	+	0.163059i
$305$	−25.7364	+	21.5210i	−1.47366	+	1.23229i
$306$	−3.64399	+	6.31158i	−0.208313	+	0.360809i
$307$	−8.89602	−	5.13612i	−0.507722	−	0.293134i	0.224175	−	0.974549i	$-0.428031\pi$
$307$	−8.89602	−	5.13612i	−0.507722	−	0.293134i	−0.731897	+	0.681415i	$0.761365\pi$
$308$	−6.29123	+	3.63224i	−0.358476	+	0.206966i
$309$	5.49365	−	9.51527i	0.312523	−	0.541305i
$310$	−7.08464	+	19.3625i	−0.402381	+	1.09971i
$311$	−11.4317			−0.648232			−0.324116	−	0.946017i	$-0.605067\pi$
$311$	−11.4317			−0.648232			−0.324116	+	0.946017i	$0.605067\pi$
$312$			4.65626i			0.263609i
$313$	−3.42825	+	1.97930i	−0.193776	+	0.111877i	−0.593749	−	0.804650i	$-0.702353\pi$
$313$	−3.42825	+	1.97930i	−0.193776	+	0.111877i	0.399973	+	0.916527i	$0.369019\pi$
$314$	6.13962	+	10.6341i	0.346479	+	0.600118i
$315$	−3.61190	−	4.31937i	−0.203507	−	0.243369i
$316$	8.23995			0.463533
$317$	19.0052	−	10.9727i	1.06744	−	0.616286i	0.139958	−	0.990157i	$-0.455303\pi$
$317$	19.0052	−	10.9727i	1.06744	−	0.616286i	0.927480	+	0.373872i	$0.121970\pi$
$318$	−9.38113	−	5.41620i	−0.526068	−	0.303725i
$319$	6.37459	+	11.0411i	0.356908	+	0.618184i
$320$	−0.384547	−	2.20275i	−0.0214968	−	0.123138i
$321$	1.67887	−	2.90789i	0.0937055	−	0.162303i
$322$		−	4.31013i		−	0.240194i
$323$	−20.7200	−	24.0803i	−1.15289	−	1.33986i
$324$	−1.00000			−0.0555556
$325$	15.0254	−	17.7835i	0.833461	−	0.986453i
$326$	−1.72900	+	2.99472i	−0.0957606	+	0.165862i
$327$	3.66583	−	2.11647i	0.202721	−	0.117041i
$328$	−7.76596	−	4.48368i	−0.428803	−	0.247570i
$329$	−5.78731	−	10.0239i	−0.319065	−	0.552636i
$330$	4.94878	−	4.13821i	0.272421	−	0.227801i
$331$	7.44789			0.409373			0.204687	−	0.978828i	$-0.434382\pi$
$331$	7.44789			0.409373			0.204687	+	0.978828i	$0.434382\pi$
$332$	−6.18795	+	3.57262i	−0.339608	+	0.196073i
$333$	−2.82740	+	1.63240i	−0.154941	+	0.0894551i
$334$	6.20240			0.339380
$335$	−15.2895	−	18.2843i	−0.835354	−	0.998979i
$336$	−1.25902	−	2.18069i	−0.0686853	−	0.118966i
$337$	4.04725	+	2.33668i	0.220468	+	0.127287i	0.606167	−	0.795338i	$-0.292706\pi$
$337$	4.04725	+	2.33668i	0.220468	+	0.127287i	−0.385699	+	0.922625i	$0.626040\pi$
$338$	−7.51773	+	4.34036i	−0.408911	+	0.236085i
$339$	9.39912	−	16.2798i	0.510490	−	0.884195i
$340$	16.0536	−	2.80257i	0.870630	−	0.151991i
$341$	−26.6011			−1.44053
$342$	1.43993	−	4.11420i	0.0778624	−	0.222470i
$343$			19.2868i			1.04139i
$344$	3.37689	−	5.84894i	0.182070	−	0.315354i
$345$	0.658228	+	3.77045i	0.0354378	+	0.202994i
$346$	−7.20026	−	12.4712i	−0.387088	−	0.670456i
$347$	11.8564	+	6.84531i	0.636486	+	0.367475i	0.783260	−	0.621695i	$-0.213556\pi$
$347$	11.8564	+	6.84531i	0.636486	+	0.367475i	−0.146774	+	0.989170i	$0.546889\pi$
$348$	−3.82712	+	2.20959i	−0.205155	+	0.118446i
$349$	34.7901			1.86227			0.931137	−	0.364671i	$-0.118818\pi$
$349$	34.7901			1.86227			0.931137	+	0.364671i	$0.118818\pi$
$350$	−2.22839	+	12.3915i	−0.119113	+	0.662351i
$351$	−2.32813	−	4.03244i	−0.124266	−	0.215236i
$352$	2.49846	−	1.44248i	0.133168	−	0.0768847i
$353$		−	3.05876i		−	0.162802i	−0.996681	−	0.0814008i	$-0.974061\pi$
$353$		−	3.05876i		−	0.162802i	0.996681	−	0.0814008i	$-0.0259394\pi$
$354$	−9.46547			−0.503084
$355$	−22.5967	−	8.26805i	−1.19931	−	0.438823i
$356$	−2.37111	+	4.10688i	−0.125668	+	0.217664i
$357$	15.8928	−	9.17574i	0.841138	−	0.485631i
$358$	1.68161	+	0.970880i	0.0888760	+	0.0513126i
$359$	8.49408	−	14.7122i	0.448300	−	0.776479i	−0.549975	−	0.835181i	$-0.685363\pi$
$359$	8.49408	−	14.7122i	0.448300	−	0.776479i	0.998276	+	0.0587020i	$0.0186962\pi$
$360$	1.43440	+	1.71537i	0.0755997	+	0.0904078i
$361$	14.8532	+	11.8483i	0.781748	+	0.623595i
$362$			17.6296i			0.926592i
$363$	−2.31831	−	1.33848i	−0.121680	−	0.0702519i
$364$	5.86233	−	10.1539i	0.307270	−	0.532207i
$365$	−10.8852	+	29.7494i	−0.569756	+	1.55715i
$366$	7.50173	−	12.9934i	0.392121	−	0.679174i
$367$	4.66821	−	2.69519i	0.243679	−	0.140688i	−0.373188	−	0.927756i	$-0.621735\pi$
$367$	4.66821	−	2.69519i	0.243679	−	0.140688i	0.616866	+	0.787068i	$0.288402\pi$
$368$			1.71170i			0.0892284i
$369$	8.96736			0.466822
$370$	6.85581	+	2.50851i	0.356416	+	0.130411i
$371$	13.6382	+	23.6221i	0.708062	+	1.22640i
$372$		−	9.22060i		−	0.478066i
$373$			3.85586i			0.199649i	0.995005	+	0.0998244i	$0.0318281\pi$
$373$			3.85586i			0.199649i	−0.995005	+	0.0998244i	$0.968172\pi$
$374$	10.5128	+	18.2087i	0.543604	+	0.941550i
$375$	0.0569884	−	11.1802i	0.00294287	−	0.577343i
$376$	2.29833	+	3.98083i	0.118527	+	0.205296i
$377$	−17.8200	−	10.2884i	−0.917779	−	0.529880i
$378$	2.18069	+	1.25902i	0.112163	+	0.0647571i
$379$	−13.6566			−0.701495			−0.350747	−	0.936470i	$-0.614072\pi$
$379$	−13.6566			−0.701495			−0.350747	+	0.936470i	$0.614072\pi$
$380$	−9.12280	+	3.43141i	−0.467990	+	0.176028i
$381$	15.7576			0.807287
$382$	3.99564	+	2.30688i	0.204435	+	0.118030i
$383$	−6.30771	−	3.64176i	−0.322309	−	0.186085i	0.330112	−	0.943942i	$-0.392913\pi$
$383$	−6.30771	−	3.64176i	−0.322309	−	0.186085i	−0.652421	+	0.757857i	$0.726247\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−16.0019	+	2.79354i	−0.815531	+	0.142372i
$386$	−12.5401	−	21.7202i	−0.638276	−	1.10553i
$387$			6.75378i			0.343314i
$388$			2.29667i			0.116596i
$389$	−9.81327	−	16.9971i	−0.497553	−	0.861786i	0.502443	−	0.864610i	$-0.332435\pi$
$389$	−9.81327	−	16.9971i	−0.497553	−	0.861786i	−0.999996	+	0.00282365i	$0.999101\pi$
$390$	−3.57763	+	9.77774i	−0.181160	+	0.495115i
$391$	−12.4748			−0.630879
$392$		−	0.659446i		−	0.0333070i
$393$	5.68732	−	3.28357i	0.286887	−	0.165634i
$394$	−1.81219	+	3.13881i	−0.0912969	+	0.158131i
$395$	17.3032	+	6.33116i	0.870618	+	0.318555i
$396$	−1.44248	+	2.49846i	−0.0724876	+	0.125552i
$397$	−10.0280	−	5.78964i	−0.503288	−	0.290574i	0.226782	−	0.973946i	$-0.427179\pi$
$397$	−10.0280	−	5.78964i	−0.503288	−	0.290574i	−0.730071	+	0.683372i	$0.760513\pi$
$398$		−	0.596986i		−	0.0299242i
$399$	−8.31991	+	7.15889i	−0.416516	+	0.358393i
$400$	0.884968	−	4.92106i	0.0442484	−	0.246053i
$401$	0.738065	−	1.27837i	0.0368572	−	0.0638386i	−0.847008	−	0.531580i	$-0.821599\pi$
$401$	0.738065	−	1.27837i	0.0368572	−	0.0638386i	0.883866	+	0.467741i	$0.154932\pi$
$402$	9.23107	+	5.32956i	0.460404	+	0.265814i
$403$	37.1815	−	21.4667i	1.85214	−	1.06933i
$404$	−1.68398	+	2.91673i	−0.0837810	+	0.145113i
$405$	−2.09991	−	0.768349i	−0.104346	−	0.0381796i
$406$	11.1277			0.552258
$407$			9.41885i			0.466875i
$408$	−6.31158	+	3.64399i	−0.312470	+	0.180404i
$409$	0.325761	+	0.564235i	0.0161078	+	0.0278996i	0.873967	−	0.485985i	$-0.161539\pi$
$409$	0.325761	+	0.564235i	0.0161078	+	0.0278996i	−0.857859	+	0.513885i	$0.828206\pi$
$410$	−12.8628	−	15.3823i	−0.635249	−	0.759678i
$411$	14.4364			0.712093
$412$	9.51527	−	5.49365i	0.468784	−	0.270653i
$413$	20.6413	+	11.9172i	1.01569	+	0.586409i
$414$	−0.855848	−	1.48237i	−0.0420627	−	0.0728547i
$415$	−15.7392	+	2.74768i	−0.772606	+	0.134878i
$416$	−2.32813	+	4.03244i	−0.114146	+	0.197706i
$417$		−	6.19455i		−	0.303349i
$418$	−8.20206	−	9.53226i	−0.401176	−	0.466238i
$419$	−25.9557			−1.26802			−0.634010	−	0.773325i	$-0.718592\pi$
$419$	−25.9557			−1.26802			−0.634010	+	0.773325i	$0.718592\pi$
$420$	−0.968307	−	5.54663i	−0.0472485	−	0.270648i
$421$	14.9470	−	25.8890i	0.728473	−	1.26175i	−0.229055	−	0.973414i	$-0.573564\pi$
$421$	14.9470	−	25.8890i	0.728473	−	1.26175i	0.957528	−	0.288339i	$-0.0931032\pi$
$422$	−19.8569	+	11.4644i	−0.966620	+	0.558078i
$423$	−3.98083	−	2.29833i	−0.193555	−	0.111749i
$424$	−5.41620	−	9.38113i	−0.263034	−	0.455588i
$425$	35.8646	+	6.44963i	1.73969	+	0.312853i
$426$	10.7608			0.521362
$427$	−32.7179	+	18.8897i	−1.58333	+	0.914136i
$428$	2.90789	−	1.67887i	0.140558	−	0.0811514i
$429$	−13.4332			−0.648559
$430$	11.5852	−	9.68765i	0.558688	−	0.467180i
$431$	−13.7123	−	23.7503i	−0.660496	−	1.14401i	−0.980485	−	0.196592i	$-0.937013\pi$
$431$	−13.7123	−	23.7503i	−0.660496	−	1.14401i	0.319989	−	0.947421i	$-0.396321\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−9.75555	+	5.63237i	−0.468822	+	0.270674i	−0.715746	−	0.698360i	$-0.753913\pi$
$433$	−9.75555	+	5.63237i	−0.468822	+	0.270674i	0.246925	+	0.969035i	$0.420580\pi$
$434$	−11.6089	+	20.1073i	−0.557247	+	0.965181i
$435$	−9.73435	+	1.69938i	−0.466726	+	0.0814790i
$436$	4.23293			0.202721
$437$	7.33113	−	1.38662i	0.350696	−	0.0663308i
$438$		−	14.1670i		−	0.676924i
$439$	−7.89796	+	13.6797i	−0.376949	+	0.652895i	−0.990617	−	0.136670i	$-0.956360\pi$
$439$	−7.89796	+	13.6797i	−0.376949	+	0.652895i	0.613668	+	0.789564i	$0.289693\pi$
$440$	6.35487	−	1.10941i	0.302957	−	0.0528889i
$441$	0.329723	+	0.571097i	0.0157011	+	0.0271951i
$442$	−29.3883	−	16.9674i	−1.39786	−	0.807055i
$443$	−6.09413	+	3.51845i	−0.289541	+	0.167167i	−0.637735	−	0.770256i	$-0.720128\pi$
$443$	−6.09413	+	3.51845i	−0.289541	+	0.167167i	0.348194	+	0.937423i	$0.386795\pi$
$444$	−3.26480			−0.154941
$445$	−8.13464	+	6.80226i	−0.385619	+	0.322458i
$446$	−5.62349	−	9.74016i	−0.266280	−	0.461210i
$447$	−10.3832	+	5.99475i	−0.491109	+	0.283542i
$448$		−	2.51805i		−	0.118966i
$449$	−16.3890			−0.773444			−0.386722	−	0.922196i	$-0.626393\pi$
$449$	−16.3890			−0.773444			−0.386722	+	0.922196i	$0.626393\pi$
$450$	1.69412	+	4.70425i	0.0798618	+	0.221760i
$451$	12.9353	−	22.4046i	0.609098	−	1.05499i
$452$	16.2798	−	9.39912i	0.765735	−	0.442097i
$453$	−4.77643	−	2.75767i	−0.224416	−	0.129567i
$454$	4.41407	−	7.64539i	0.207163	−	0.358816i
$455$	20.1121	−	16.8179i	0.942870	−	0.788436i
$456$	3.30411	−	2.84303i	0.154729	−	0.133137i
$457$		−	11.5975i		−	0.542508i	−0.962508	−	0.271254i	$-0.912562\pi$
$457$		−	11.5975i		−	0.542508i	0.962508	−	0.271254i	$-0.0874383\pi$
$458$	−19.2965	−	11.1408i	−0.901666	−	0.520577i
$459$	3.64399	−	6.31158i	0.170087	−	0.294599i
$460$	−1.31518	+	3.59442i	−0.0613206	+	0.167591i
$461$	2.39232	−	4.14363i	0.111422	−	0.192988i	−0.804922	−	0.593381i	$-0.797793\pi$
$461$	2.39232	−	4.14363i	0.111422	−	0.192988i	0.916344	+	0.400393i	$0.131126\pi$
$462$	6.29123	−	3.63224i	0.292694	−	0.168987i
$463$		−	12.1559i		−	0.564934i	−0.959277	−	0.282467i	$-0.908847\pi$
$463$		−	12.1559i		−	0.564934i	0.959277	−	0.282467i	$-0.0911527\pi$
$464$	−4.41917			−0.205155
$465$	7.08464	−	19.3625i	0.328542	−	0.897913i
$466$	3.09066	+	5.35318i	0.143172	+	0.247981i
$467$		−	1.60463i		−	0.0742533i	−0.999311	−	0.0371266i	$-0.988180\pi$
$467$		−	1.60463i		−	0.0742533i	0.999311	−	0.0371266i	$-0.0118205\pi$
$468$		−	4.65626i		−	0.215236i
$469$	−13.4201	−	23.2443i	−0.619682	−	1.07332i
$470$	1.76763	+	10.1253i	0.0815349	+	0.467046i
$471$	−6.13962	−	10.6341i	−0.282899	−	0.489995i
$472$	−8.19734	−	4.73274i	−0.377313	−	0.217842i
$473$	16.8740	+	9.74222i	0.775868	+	0.447948i
$474$	−8.23995			−0.378473
$475$	−21.7936	+	0.196179i	−0.999959	+	0.00900132i
$476$	18.3515			0.841138
$477$	9.38113	+	5.41620i	0.429532	+	0.247991i
$478$	15.7528	+	9.09488i	0.720516	+	0.415990i
$479$	−17.2940	−	29.9541i	−0.790184	−	1.36864i	−0.925853	−	0.377884i	$-0.876652\pi$
$479$	−17.2940	−	29.9541i	−0.790184	−	1.36864i	0.135669	−	0.990754i	$-0.456682\pi$
$480$	0.384547	+	2.20275i	0.0175521	+	0.100541i
$481$	−7.60088	−	13.1651i	−0.346570	−	0.600277i
$482$			2.49535i			0.113660i
$483$			4.31013i			0.196118i
$484$	−1.33848	−	2.31831i	−0.0608399	−	0.105378i
$485$	−1.76465	+	4.82282i	−0.0801286	+	0.218993i
$486$	1.00000			0.0453609
$487$			24.3737i			1.10448i	0.833687	+	0.552238i	$0.186226\pi$
$487$			24.3737i			1.10448i	−0.833687	+	0.552238i	$0.813774\pi$
$488$	12.9934	−	7.50173i	0.588182	−	0.339587i
$489$	1.72900	−	2.99472i	0.0781882	−	0.135426i
$490$	0.506685	−	1.38478i	0.0228897	−	0.0625579i
$491$	5.45453	−	9.44752i	0.246159	−	0.426360i	−0.716298	−	0.697795i	$-0.754165\pi$
$491$	5.45453	−	9.44752i	0.246159	−	0.426360i	0.962457	+	0.271434i	$0.0874980\pi$
$492$	7.76596	+	4.48368i	0.350117	+	0.202140i
$493$		−	32.2069i		−	1.45052i
$494$	19.1568	+	6.70468i	0.861903	+	0.301658i
$495$	−4.94878	+	4.13821i	−0.222431	+	0.185999i
$496$	4.61030	−	7.98528i	0.207009	−	0.358549i
$497$	−23.4660	−	13.5481i	−1.05259	−	0.607715i
$498$	6.18795	−	3.57262i	0.277289	−	0.160093i
$499$	−5.54788	+	9.60920i	−0.248357	+	0.430167i	−0.963070	−	0.269251i	$-0.913224\pi$
$499$	−5.54788	+	9.60920i	−0.248357	+	0.430167i	0.714713	+	0.699418i	$0.246557\pi$
$500$	5.63945	−	9.65384i	0.252204	−	0.431733i
$501$	−6.20240			−0.277103
$502$		−	21.2635i		−	0.949034i
$503$	17.0870	−	9.86519i	0.761872	−	0.439867i	−0.0680955	−	0.997679i	$-0.521692\pi$
$503$	17.0870	−	9.86519i	0.761872	−	0.439867i	0.829967	+	0.557812i	$0.188359\pi$
$504$	1.25902	+	2.18069i	0.0560813	+	0.0971357i
$505$	−5.77728	+	4.83101i	−0.257085	+	0.214977i
$506$	−4.93819			−0.219529
$507$	7.51773	−	4.34036i	0.333874	−	0.192762i
$508$	13.6465	+	7.87880i	0.605465	+	0.349565i
$509$	−16.6873	−	28.9033i	−0.739653	−	1.28112i	−0.952652	−	0.304064i	$-0.901656\pi$
$509$	−16.6873	−	28.9033i	−0.739653	−	1.28112i	0.212999	−	0.977052i	$-0.431677\pi$
$510$	−16.0536	+	2.80257i	−0.710867	+	0.124100i
$511$	−17.8365	+	30.8938i	−0.789042	+	1.36666i
$512$			1.00000i			0.0441942i
$513$	−1.43993	+	4.11420i	−0.0635744	+	0.181646i
$514$	5.81714			0.256583
$515$	24.2023	−	4.22513i	1.06648	−	0.186181i
$516$	−3.37689	+	5.84894i	−0.148659	+	0.257485i
$517$	−11.4846	+	6.63062i	−0.505091	+	0.291614i
$518$	7.11953	+	4.11046i	0.312814	+	0.180603i
$519$	7.20026	+	12.4712i	0.316056	+	0.547425i
$520$	−7.98719	+	6.67896i	−0.350261	+	0.292892i
$521$	−32.4955			−1.42366			−0.711828	−	0.702354i	$-0.752132\pi$
$521$	−32.4955			−1.42366			−0.711828	+	0.702354i	$0.752132\pi$
$522$	3.82712	−	2.20959i	0.167508	−	0.0967110i
$523$	−8.12396	+	4.69037i	−0.355236	+	0.205096i	−0.666989	−	0.745068i	$-0.732417\pi$
$523$	−8.12396	+	4.69037i	−0.355236	+	0.205096i	0.311753	+	0.950163i	$0.399084\pi$
$524$	6.56715			0.286887
$525$	2.22839	−	12.3915i	0.0972550	−	0.540807i
$526$	−8.63749	−	14.9606i	−0.376612	−	0.652312i
$527$	58.1966	+	33.5998i	2.53508	+	1.46363i
$528$	−2.49846	+	1.44248i	−0.108731	+	0.0627761i
$529$	−10.0350	+	17.3812i	−0.436306	+	0.755705i
$530$	−4.16557	−	23.8611i	−0.180941	−	1.03646i
$531$	9.46547			0.410767
$532$	−10.7847	+	2.03983i	−0.467576	+	0.0884376i
$533$			41.7543i			1.80858i
$534$	2.37111	−	4.10688i	0.102608	−	0.177722i
$535$	7.39629	−	1.29121i	0.319769	−	0.0558239i
$536$	5.32956	+	9.23107i	0.230202	+	0.398722i
$537$	−1.68161	−	0.970880i	−0.0725670	−	0.0418966i
$538$	8.36136	−	4.82743i	0.360484	−	0.208125i
$539$	1.90248			0.0819456
$540$	−1.43440	−	1.71537i	−0.0617269	−	0.0738176i
$541$	18.8739	+	32.6906i	0.811453	+	1.40548i	0.911847	+	0.410530i	$0.134656\pi$
$541$	18.8739	+	32.6906i	0.811453	+	1.40548i	−0.100394	+	0.994948i	$0.532010\pi$
$542$	5.57406	−	3.21818i	0.239426	−	0.138233i
$543$		−	17.6296i		−	0.756559i
$544$	−7.28798			−0.312470
$545$	8.88879	+	3.25237i	0.380754	+	0.139316i
$546$	−5.86233	+	10.1539i	−0.250885	+	0.434545i
$547$	5.07734	−	2.93141i	0.217092	−	0.125338i	−0.387511	−	0.921865i	$-0.626665\pi$
$547$	5.07734	−	2.93141i	0.217092	−	0.125338i	0.604603	+	0.796527i	$0.293332\pi$
$548$	12.5023	+	7.21818i	0.534070	+	0.308345i
$549$	−7.50173	+	12.9934i	−0.320166	+	0.554544i
$550$	14.1971	+	2.55311i	0.605366	+	0.108865i
$551$	3.57990	+	18.9272i	0.152509	+	0.806324i
$552$		−	1.71170i		−	0.0728547i
$553$	17.9688	+	10.3743i	0.764111	+	0.441160i
$554$	−5.56545	+	9.63965i	−0.236453	+	0.409549i
$555$	−6.85581	−	2.50851i	−0.291013	−	0.106480i
$556$	3.09728	−	5.36464i	0.131354	−	0.227511i
$557$	−18.3570	+	10.5984i	−0.777809	+	0.449068i	−0.835653	−	0.549257i	$-0.814911\pi$
$557$	−18.3570	+	10.5984i	−0.777809	+	0.449068i	0.0578442	+	0.998326i	$0.481577\pi$
$558$			9.22060i			0.390339i
$559$	−31.4473			−1.33008
$560$	1.93474	−	5.28768i	0.0817576	−	0.223445i
$561$	−10.5128	−	18.2087i	−0.443851	−	0.768772i
$562$			5.68717i			0.239899i
$563$			26.4882i			1.11634i	0.829725	+	0.558172i	$0.188497\pi$
$563$			26.4882i			1.11634i	−0.829725	+	0.558172i	$0.811503\pi$
$564$	−2.29833	−	3.98083i	−0.0967773	−	0.167623i
$565$	41.4079	−	7.22881i	1.74204	−	0.304118i
$566$	3.60536	+	6.24466i	0.151544	+	0.262483i
$567$	−2.18069	−	1.25902i	−0.0915804	−	0.0528740i
$568$	9.31912	+	5.38040i	0.391022	+	0.225757i
$569$	−21.8861			−0.917514			−0.458757	−	0.888562i	$-0.651705\pi$
$569$	−21.8861			−0.917514			−0.458757	+	0.888562i	$0.651705\pi$
$570$	9.12280	−	3.43141i	0.382112	−	0.143726i
$571$	−14.0325			−0.587242			−0.293621	−	0.955922i	$-0.594860\pi$
$571$	−14.0325			−0.587242			−0.293621	+	0.955922i	$0.594860\pi$
$572$	−11.6335	−	6.71658i	−0.486419	−	0.280834i
$573$	−3.99564	−	2.30688i	−0.166920	−	0.0963714i
$574$	−11.2901	−	19.5550i	−0.471240	−	0.816212i
$575$	−5.52353	+	6.53745i	−0.230347	+	0.272630i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	27.9608i		−	1.16402i	−0.813180	−	0.582012i	$-0.802266\pi$
$577$		−	27.9608i		−	1.16402i	0.813180	−	0.582012i	$-0.197734\pi$
$578$		−	36.1147i		−	1.50217i
$579$	12.5401	+	21.7202i	0.521150	+	0.902659i
$580$	−9.27989	−	3.39547i	−0.385326	−	0.140989i
$581$	−17.9920			−0.746435
$582$		−	2.29667i		−	0.0952002i
$583$	27.0643	−	15.6256i	1.12089	−	0.647145i
$584$	7.08348	−	12.2689i	0.293117	−	0.507693i
$585$	3.57763	−	9.77774i	0.147917	−	0.404260i
$586$	4.63359	−	8.02562i	0.191412	−	0.331535i
$587$	−9.03637	−	5.21715i	−0.372971	−	0.215335i	0.301785	−	0.953376i	$-0.402418\pi$
$587$	−9.03637	−	5.21715i	−0.372971	−	0.215335i	−0.674756	+	0.738041i	$0.735751\pi$
$588$			0.659446i			0.0271951i
$589$	−37.9354	−	13.2770i	−1.56310	−	0.547070i
$590$	−13.5773	−	16.2368i	−0.558969	−	0.668457i
$591$	1.81219	−	3.13881i	0.0745436	−	0.129113i
$592$	−2.82740	−	1.63240i	−0.116206	−	0.0670913i
$593$	−4.77660	+	2.75777i	−0.196152	+	0.113248i	−0.594859	−	0.803830i	$-0.702792\pi$
$593$	−4.77660	+	2.75777i	−0.196152	+	0.113248i	0.398708	+	0.917078i	$0.369459\pi$
$594$	1.44248	−	2.49846i	0.0591858	−	0.102513i
$595$	38.5365	+	14.1003i	1.57984	+	0.578058i
$596$	−11.9895			−0.491109
$597$			0.596986i			0.0244330i
$598$	6.90231	−	3.98505i	0.282256	−	0.162961i
$599$	22.5946	+	39.1349i	0.923189	+	1.59901i	0.794448	+	0.607332i	$0.207760\pi$
$599$	22.5946	+	39.1349i	0.923189	+	1.59901i	0.128741	+	0.991678i	$0.458907\pi$
$600$	−0.884968	+	4.92106i	−0.0361287	+	0.200901i
$601$	−10.2025			−0.416167			−0.208083	−	0.978111i	$-0.566723\pi$
$601$	−10.2025			−0.416167			−0.208083	+	0.978111i	$0.566723\pi$
$602$	14.7279	−	8.50316i	0.600265	−	0.346563i
$603$	−9.23107	−	5.32956i	−0.375918	−	0.217037i
$604$	−2.75767	−	4.77643i	−0.112208	−	0.194350i
$605$	−1.02942	−	5.89668i	−0.0418517	−	0.239734i
$606$	1.68398	−	2.91673i	0.0684069	−	0.118484i
$607$		−	6.78955i		−	0.275579i	−0.990462	−	0.137790i	$-0.956000\pi$
$607$		−	6.78955i		−	0.275579i	0.990462	−	0.137790i	$-0.0439998\pi$
$608$	4.28296	−	0.810083i	0.173697	−	0.0328532i
$609$	−11.1277			−0.450916
$610$	33.0489	−	5.76953i	1.33811	−	0.233602i
$611$	10.7016	−	18.5358i	0.432942	−	0.749877i
$612$	6.31158	−	3.64399i	0.255130	−	0.147300i
$613$	20.8847	+	12.0578i	0.843524	+	0.487009i	0.858460	−	0.512880i	$-0.171421\pi$
$613$	20.8847	+	12.0578i	0.843524	+	0.487009i	−0.0149366	+	0.999888i	$0.504755\pi$
$614$	5.13612	+	8.89602i	0.207277	+	0.359014i
$615$	12.8628	+	15.3823i	0.518679	+	0.620275i
$616$	7.26448			0.292694
$617$	33.6188	−	19.4098i	1.35344	−	0.781410i	0.364712	−	0.931121i	$-0.381168\pi$
$617$	33.6188	−	19.4098i	1.35344	−	0.781410i	0.988730	+	0.149711i	$0.0478343\pi$
$618$	−9.51527	+	5.49365i	−0.382760	+	0.220987i
$619$	−43.0532			−1.73046			−0.865228	−	0.501379i	$-0.832826\pi$
$619$	−43.0532			−1.73046			−0.865228	+	0.501379i	$0.832826\pi$
$620$	15.8167	−	13.2261i	0.635215	−	0.531172i
$621$	0.855848	+	1.48237i	0.0343440	+	0.0594856i
$622$	9.90014	+	5.71585i	0.396959	+	0.229185i
$623$	−10.3413	+	5.97056i	−0.414316	+	0.239205i
$624$	2.32813	−	4.03244i	0.0931997	−	0.161427i
$625$	19.2599	−	15.9392i	0.770395	−	0.637567i
$626$	3.95860			0.158217
$627$	8.20206	+	9.53226i	0.327559	+	0.380682i
$628$		−	12.2792i		−	0.489995i
$629$	11.8969	−	20.6061i	0.474361	−	0.821617i
$630$	0.968307	+	5.54663i	0.0385783	+	0.220983i
$631$	20.9642	+	36.3110i	0.834571	+	1.44552i	0.894379	+	0.447310i	$0.147618\pi$
$631$	20.9642	+	36.3110i	0.834571	+	1.44552i	−0.0598078	+	0.998210i	$0.519049\pi$
$632$	−7.13601	−	4.11998i	−0.283855	−	0.163884i
$633$	19.8569	−	11.4644i	0.789242	−	0.455669i
$634$	−21.9453			−0.871560
$635$	22.6028	+	27.0301i	0.896964	+	1.07266i
$636$	5.41620	+	9.38113i	0.214766	+	0.371986i
$637$	−2.65917	+	1.53527i	−0.105360	+	0.0608298i
$638$		−	12.7492i		−	0.504745i
$639$	−10.7608			−0.425691
$640$	−0.768349	+	2.09991i	−0.0303717	+	0.0830064i
$641$	0.126170	−	0.218532i	0.00498340	−	0.00863150i	−0.863523	−	0.504310i	$-0.831747\pi$
$641$	0.126170	−	0.218532i	0.00498340	−	0.00863150i	0.868506	+	0.495678i	$0.165080\pi$
$642$	−2.90789	+	1.67887i	−0.114765	+	0.0662598i
$643$	−35.9135	−	20.7347i	−1.41629	−	0.817696i	−0.420320	−	0.907376i	$-0.638082\pi$
$643$	−35.9135	−	20.7347i	−1.41629	−	0.817696i	−0.995971	+	0.0896801i	$0.971416\pi$
$644$	−2.15507	+	3.73268i	−0.0849215	+	0.147088i
$645$	−11.5852	+	9.68765i	−0.456167	+	0.381451i
$646$	5.90387	+	31.2142i	0.232285	+	1.22810i
$647$		−	11.3601i		−	0.446612i	−0.974748	−	0.223306i	$-0.928315\pi$
$647$		−	11.3601i		−	0.446612i	0.974748	−	0.223306i	$-0.0716848\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	13.6538	−	23.6491i	0.535958	−	0.928307i
$650$	−21.9042	+	7.88828i	−0.859153	+	0.309404i
$651$	11.6089	−	20.1073i	0.454991	−	0.788067i
$652$	2.99472	−	1.72900i	0.117282	−	0.0677130i
$653$		−	14.1285i		−	0.552889i	−0.961030	−	0.276444i	$-0.910844\pi$
$653$		−	14.1285i		−	0.552889i	0.961030	−	0.276444i	$-0.0891562\pi$
$654$	−4.23293			−0.165521
$655$	13.7904	+	5.04586i	0.538837	+	0.197158i
$656$	4.48368	+	7.76596i	0.175058	+	0.303210i
$657$			14.1670i			0.552706i
$658$			11.5746i			0.451225i
$659$	−14.6536	−	25.3808i	−0.570823	−	0.988695i	−0.996482	−	0.0838112i	$-0.973291\pi$
$659$	−14.6536	−	25.3808i	−0.570823	−	0.988695i	0.425658	−	0.904884i	$-0.360043\pi$
$660$	−6.35487	+	1.10941i	−0.247363	+	0.0431836i
$661$	0.0305882	+	0.0529803i	0.00118974	+	0.00206070i	0.866620	−	0.498969i	$-0.166288\pi$
$661$	0.0305882	+	0.0529803i	0.00118974	+	0.00206070i	−0.865430	+	0.501030i	$0.832955\pi$
$662$	−6.45007	−	3.72395i	−0.250689	−	0.144735i
$663$	29.3883	+	16.9674i	1.14135	+	0.658958i
$664$	7.14523			0.277289
$665$	−24.2142	−	4.00295i	−0.938988	−	0.155228i
$666$	3.26480			0.126509
$667$	6.55086	+	3.78214i	0.253650	+	0.146445i
$668$	−5.37144	−	3.10120i	−0.207827	−	0.119989i
$669$	5.62349	+	9.74016i	0.217417	+	0.376576i
$670$	4.09894	+	23.4794i	0.158356	+	0.907089i
$671$	21.6422	+	37.4855i	0.835489	+	1.44711i
$672$			2.51805i			0.0971357i
$673$			29.7678i			1.14747i	0.819042	+	0.573733i	$0.194505\pi$
$673$			29.7678i			1.14747i	−0.819042	+	0.573733i	$0.805495\pi$
$674$	−2.33668	−	4.04725i	−0.0900055	−	0.155894i
$675$	−1.69412	−	4.70425i	−0.0652069	−	0.181067i
$676$	8.68073			0.333874
$677$		−	14.3460i		−	0.551360i	−0.961249	−	0.275680i	$-0.911097\pi$
$677$		−	14.3460i		−	0.551360i	0.961249	−	0.275680i	$-0.0889031\pi$
$678$	−16.2798	+	9.39912i	−0.625220	+	0.360971i
$679$	−2.89157	+	5.00834i	−0.110968	+	0.192202i
$680$	−15.3041	−	5.59972i	−0.586887	−	0.214739i
$681$	−4.41407	+	7.64539i	−0.169148	+	0.292972i
$682$	23.0373	+	13.3006i	0.882143	+	0.509305i
$683$		−	39.5539i		−	1.51349i	−0.653712	−	0.756744i	$-0.726789\pi$
$683$		−	39.5539i		−	1.51349i	0.653712	−	0.756744i	$-0.273211\pi$
$684$	−3.30411	+	2.84303i	−0.126336	+	0.108706i
$685$	20.7076	+	24.7637i	0.791196	+	0.946171i
$686$	9.64342	−	16.7029i	0.368187	−	0.637719i
$687$	19.2965	+	11.1408i	0.736207	+	0.425049i
$688$	−5.84894	+	3.37689i	−0.222989	+	0.128743i
$689$	−25.2192	+	43.6810i	−0.960775	+	1.66411i
$690$	1.31518	−	3.59442i	0.0500681	−	0.136837i
$691$	−32.4212			−1.23336			−0.616681	−	0.787213i	$-0.711523\pi$
$691$	−32.4212			−1.23336			−0.616681	+	0.787213i	$0.711523\pi$
$692$			14.4005i			0.547425i
$693$	−6.29123	+	3.63224i	−0.238984	+	0.137977i
$694$	−6.84531	−	11.8564i	−0.259844	−	0.450064i
$695$	10.6259	−	8.88550i	0.403065	−	0.337046i
$696$	4.41917			0.167508
$697$	−56.5982	+	32.6770i	−2.14381	+	1.23773i
$698$	−30.1291	−	17.3951i	−1.14040	−	0.658413i
$699$	−3.09066	−	5.35318i	−0.116900	−	0.202476i
$700$	8.12557	−	9.61712i	0.307118	−	0.363493i
$701$	10.1662	−	17.6084i	0.383972	−	0.665059i	−0.607654	−	0.794202i	$-0.707889\pi$
$701$	10.1662	−	17.6084i	0.383972	−	0.665059i	0.991626	+	0.129143i	$0.0412226\pi$
$702$			4.65626i			0.175739i
$703$	−4.70108	+	13.4320i	−0.177305	+	0.506599i
$704$	−2.88497			−0.108731
$705$	−1.76763	−	10.1253i	−0.0665730	−	0.381342i
$706$	−1.52938	+	2.64897i	−0.0575590	+	0.0996952i
$707$	−7.34447	+	4.24033i	−0.276217	+	0.159474i
$708$	8.19734	+	4.73274i	0.308075	+	0.177867i
$709$	20.1591	+	34.9165i	0.757089	+	1.31132i	0.944329	+	0.329003i	$0.106712\pi$
$709$	20.1591	+	34.9165i	0.757089	+	1.31132i	−0.187240	+	0.982314i	$0.559954\pi$
$710$	15.4353	+	18.4587i	0.579278	+	0.692743i
$711$	8.23995			0.309022
$712$	4.10688	−	2.37111i	0.153912	−	0.0888610i
$713$	−13.6684	+	7.89144i	−0.511885	+	0.295537i
$714$	−18.3515			−0.686787
$715$	−19.2686	−	23.0428i	−0.720604	−	0.861752i
$716$	−0.970880	−	1.68161i	−0.0362835	−	0.0628448i
$717$	−15.7528	−	9.09488i	−0.588299	−	0.339655i
$718$	−14.7122	+	8.49408i	−0.549054	+	0.316996i
$719$	−14.5708	+	25.2374i	−0.543401	+	0.941198i	0.455305	+	0.890336i	$0.349530\pi$
$719$	−14.5708	+	25.2374i	−0.543401	+	0.941198i	−0.998706	+	0.0508623i	$0.983803\pi$
$720$	−0.384547	−	2.20275i	−0.0143312	−	0.0820918i
$721$	27.6665			1.03035
$722$	−6.93911	−	17.6875i	−0.258247	−	0.658262i
$723$		−	2.49535i		−	0.0928031i
$724$	8.81480	−	15.2677i	0.327600	−	0.567419i
$725$	−16.8781	−	14.2604i	−0.626835	−	0.529618i
$726$	1.33848	+	2.31831i	0.0496756	+	0.0860407i
$727$	−15.6863	−	9.05647i	−0.581771	−	0.335886i	0.180066	−	0.983655i	$-0.442369\pi$
$727$	−15.6863	−	9.05647i	−0.581771	−	0.335886i	−0.761837	+	0.647769i	$0.775702\pi$
$728$	−10.1539	+	5.86233i	−0.376327	+	0.217273i
$729$	−1.00000			−0.0370370
$730$	24.3015	−	20.3212i	0.899440	−	0.752120i
$731$	−24.6107	−	42.6270i	−0.910260	−	1.57662i
$732$	−12.9934	+	7.50173i	−0.480249	+	0.277272i
$733$			8.31171i			0.307000i	0.988149	+	0.153500i	$0.0490545\pi$
$733$			8.31171i			0.307000i	−0.988149	+	0.153500i	$0.950946\pi$
$734$	−5.39039			−0.198963
$735$	−0.506685	+	1.38478i	−0.0186893	+	0.0510784i
$736$	0.855848	−	1.48237i	0.0315470	−	0.0546410i
$737$	−26.6314	+	15.3756i	−0.980979	+	0.566368i
$738$	−7.76596	−	4.48368i	−0.285869	−	0.165047i
$739$	7.63311	−	13.2209i	0.280788	−	0.486340i	−0.690791	−	0.723055i	$-0.742737\pi$
$739$	7.63311	−	13.2209i	0.280788	−	0.486340i	0.971579	+	0.236715i	$0.0760708\pi$
$740$	−4.68305	−	5.60034i	−0.172152	−	0.205872i
$741$	−19.1568	−	6.70468i	−0.703741	−	0.246303i
$742$		−	27.2765i		−	1.00135i
$743$	−29.0049	−	16.7460i	−1.06409	−	0.614351i	−0.137528	−	0.990498i	$-0.543916\pi$
$743$	−29.0049	−	16.7460i	−1.06409	−	0.614351i	−0.926560	+	0.376147i	$0.877249\pi$
$744$	−4.61030	+	7.98528i	−0.169022	+	0.292754i
$745$	−25.1769	−	9.21213i	−0.922412	−	0.337506i
$746$	1.92793	−	3.33927i	0.0705865	−	0.122259i
$747$	−6.18795	+	3.57262i	−0.226405	+	0.130715i
$748$		−	21.0256i		−	0.768772i
$749$	8.45496			0.308937
$750$	−5.63945	+	9.65384i	−0.205924	+	0.352508i
$751$	−10.0737	−	17.4481i	−0.367594	−	0.636691i	0.621595	−	0.783339i	$-0.286485\pi$
$751$	−10.0737	−	17.4481i	−0.367594	−	0.636691i	−0.989189	+	0.146648i	$0.953152\pi$
$752$		−	4.59667i		−	0.167623i
$753$			21.2635i			0.774883i
$754$	10.2884	+	17.8200i	0.374682	+	0.648968i
$755$	−2.12091	−	12.1489i	−0.0771878	−	0.442145i
$756$	−1.25902	−	2.18069i	−0.0457902	−	0.0793110i
$757$	−26.9406	−	15.5542i	−0.979174	−	0.565327i	−0.0771537	−	0.997019i	$-0.524583\pi$
$757$	−26.9406	−	15.5542i	−0.979174	−	0.565327i	−0.902021	+	0.431693i	$0.857917\pi$
$758$	11.8270	+	6.82832i	0.429576	+	0.248016i
$759$	4.93819			0.179245
$760$	9.61628	+	1.58971i	0.348819	+	0.0576647i
$761$	2.73496			0.0991421			0.0495710	−	0.998771i	$-0.484215\pi$
$761$	2.73496			0.0991421			0.0495710	+	0.998771i	$0.484215\pi$
$762$	−13.6465	−	7.87880i	−0.494360	−	0.285419i
$763$	9.23072	+	5.32936i	0.334174	+	0.192936i
$764$	−2.30688	−	3.99564i	−0.0834601	−	0.144557i
$765$	16.0536	−	2.80257i	0.580420	−	0.101327i
$766$	3.64176	+	6.30771i	0.131582	+	0.227907i
$767$			44.0737i			1.59141i
$768$		−	1.00000i		−	0.0360844i
$769$	11.3522	+	19.6626i	0.409371	+	0.709052i	0.994819	−	0.101658i	$-0.0324147\pi$
$769$	11.3522	+	19.6626i	0.409371	+	0.709052i	−0.585448	+	0.810710i	$0.699081\pi$
$770$	15.2548	+	5.58166i	0.549744	+	0.201149i
$771$	−5.81714			−0.209499
$772$			25.0803i			0.902659i
$773$	11.9910	−	6.92302i	0.431287	−	0.249004i	−0.268608	−	0.963250i	$-0.586563\pi$
$773$	11.9910	−	6.92302i	0.431287	−	0.249004i	0.699895	+	0.714246i	$0.253230\pi$
$774$	3.37689	−	5.84894i	0.121380	−	0.210236i
$775$	43.3760	−	15.6209i	1.55811	−	0.561118i
$776$	1.14834	−	1.98898i	0.0412229	−	0.0714002i
$777$	−7.11953	−	4.11046i	−0.255412	−	0.147462i
$778$			19.6265i			0.703646i
$779$	29.6292	−	25.4945i	1.06158	−	0.913435i
$780$	7.98719	−	6.67896i	0.285987	−	0.239145i
$781$	−15.5223	+	26.8854i	−0.555431	+	0.962034i
$782$	10.8035	+	6.23741i	0.386333	+	0.223049i
$783$	−3.82712	+	2.20959i	−0.136770	+	0.0789642i
$784$	−0.329723	+	0.571097i	−0.0117758	+	0.0203963i
$785$	9.43474	−	25.7853i	0.336740	−	0.920318i
$786$	−6.56715			−0.234242
$787$			0.272719i			0.00972137i	0.999988	+	0.00486069i	$0.00154721\pi$
$787$			0.272719i			0.00972137i	−0.999988	+	0.00486069i	$0.998453\pi$
$788$	3.13881	−	1.81219i	0.111815	−	0.0645567i
$789$	8.63749	+	14.9606i	0.307503	+	0.532610i
$790$	−11.8194	−	14.1345i	−0.420516	−	0.502884i
$791$	47.3348			1.68303
$792$	2.49846	−	1.44248i	0.0887788	−	0.0512564i
$793$	−60.5005	−	34.9300i	−2.14843	−	1.24040i
$794$	5.78964	+	10.0280i	0.205467	+	0.355879i
$795$	4.16557	+	23.8611i	0.147737	+	0.846266i
$796$	−0.298493	+	0.517005i	−0.0105798	+	0.0183248i
$797$		−	2.18853i		−	0.0775216i	−0.999249	−	0.0387608i	$-0.987659\pi$
$797$		−	2.18853i		−	0.0775216i	0.999249	−	0.0387608i	$-0.0123410\pi$
$798$	10.7847	−	2.03983i	0.381774	−	0.0722090i
$799$	33.5004			1.18516
$800$	−3.22694	+	3.81928i	−0.114089	+	0.135032i
$801$	−2.37111	+	4.10688i	−0.0837790	+	0.145109i
$802$	−1.27837	+	0.738065i	−0.0451407	+	0.0260620i
$803$	35.3955	+	20.4356i	1.24908	+	0.721157i
$804$	−5.32956	−	9.23107i	−0.187959	−	0.325555i
$805$	−7.39346	+	6.18247i	−0.260585	+	0.217903i
$806$	−42.9335			−1.51227
$807$	−8.36136	+	4.82743i	−0.294334	+	0.169934i
$808$	2.91673	−	1.68398i	0.102610	−	0.0592421i
$809$	8.89531			0.312743			0.156371	−	0.987698i	$-0.450020\pi$
$809$	8.89531			0.312743			0.156371	+	0.987698i	$0.450020\pi$
$810$	1.43440	+	1.71537i	0.0503998	+	0.0602719i
$811$	6.06868	+	10.5113i	0.213100	+	0.369101i	0.952683	−	0.303965i	$-0.0983106\pi$
$811$	6.06868	+	10.5113i	0.213100	+	0.369101i	−0.739583	+	0.673065i	$0.764977\pi$
$812$	−9.63686	−	5.56384i	−0.338187	−	0.195253i
$813$	−5.57406	+	3.21818i	−0.195491	+	0.112867i
$814$	4.70943	−	8.15697i	0.165065	−	0.285902i
$815$	7.61714	−	1.32977i	0.266817	−	0.0465797i
$816$	7.28798			0.255130
$817$	19.2012	+	22.3152i	0.671765	+	0.780711i
$818$		−	0.651522i		−	0.0227799i
$819$	5.86233	−	10.1539i	0.204847	−	0.354805i
$820$	3.44837	+	19.7529i	0.120422	+	0.689801i
$821$	21.4432	+	37.1408i	0.748374	+	1.29622i	0.948602	+	0.316472i	$0.102498\pi$
$821$	21.4432	+	37.1408i	0.748374	+	1.29622i	−0.200228	+	0.979749i	$0.564168\pi$
$822$	−12.5023	−	7.21818i	−0.436066	−	0.251763i
$823$	−27.1468	+	15.6732i	−0.946278	+	0.546334i	−0.891923	−	0.452188i	$-0.850644\pi$
$823$	−27.1468	+	15.6732i	−0.946278	+	0.546334i	−0.0543553	+	0.998522i	$0.517310\pi$
$824$	−10.9873			−0.382760
$825$	−14.1971	−	2.55311i	−0.494280	−	0.0888877i
$826$	−11.9172	−	20.6413i	−0.414654	−	0.718202i
$827$	28.4166	−	16.4063i	0.988143	−	0.570505i	0.0834244	−	0.996514i	$-0.473414\pi$
$827$	28.4166	−	16.4063i	0.988143	−	0.570505i	0.904719	+	0.426009i	$0.140081\pi$
$828$			1.71170i			0.0594856i
$829$	−51.8181			−1.79972			−0.899858	−	0.436182i	$-0.856330\pi$
$829$	−51.8181			−1.79972			−0.899858	+	0.436182i	$0.856330\pi$
$830$	15.0044	+	5.49003i	0.520809	+	0.190562i
$831$	5.56545	−	9.63965i	0.193063	−	0.334396i
$832$	4.03244	−	2.32813i	0.139800	−	0.0807133i
$833$	−4.16214	−	2.40301i	−0.144210	−	0.0832595i
$834$	−3.09728	+	5.36464i	−0.107250	+	0.185762i
$835$	−8.89675	−	10.6394i	−0.307885	−	0.368192i
$836$	2.33706	+	12.3562i	0.0808290	+	0.427348i
$837$		−	9.22060i		−	0.318711i
$838$	22.4783	+	12.9779i	0.776500	+	0.448313i
$839$	0.433475	−	0.750801i	0.0149652	−	0.0259205i	−0.858446	−	0.512904i	$-0.828570\pi$
$839$	0.433475	−	0.750801i	0.0149652	−	0.0259205i	0.873411	+	0.486984i	$0.161903\pi$
$840$	−1.93474	+	5.28768i	−0.0667548	+	0.182442i
$841$	4.73545	−	8.20204i	0.163291	−	0.282829i
$842$	−25.8890	+	14.9470i	−0.892194	+	0.515109i
$843$		−	5.68717i		−	0.195876i
$844$	22.9288			0.789242
$845$	18.2288	+	6.66983i	0.627089	+	0.229449i
$846$	2.29833	+	3.98083i	0.0790183	+	0.136864i
$847$		−	6.74070i		−	0.231613i
$848$			10.8324i			0.371986i
$849$	−3.60536	−	6.24466i	−0.123736	−	0.214316i
$850$	−27.8348	−	23.5178i	−0.954727	−	0.806656i
$851$	2.79418	+	4.83966i	0.0957831	+	0.165901i
$852$	−9.31912	−	5.38040i	−0.319268	−	0.184329i
$853$	−1.05924	−	0.611551i	−0.0362676	−	0.0209391i	0.481757	−	0.876305i	$-0.339999\pi$
$853$	−1.05924	−	0.611551i	−0.0362676	−	0.0209391i	−0.518024	+	0.855366i	$0.673332\pi$
$854$	37.7794			1.29278
$855$	−9.12280	+	3.43141i	−0.311993	+	0.117352i
$856$	−3.35775			−0.114765
$857$	14.7442	+	8.51258i	0.503653	+	0.290784i	0.730221	−	0.683211i	$-0.239417\pi$
$857$	14.7442	+	8.51258i	0.503653	+	0.290784i	−0.226568	+	0.973995i	$0.572751\pi$
$858$	11.6335	+	6.71658i	0.397160	+	0.229300i
$859$	−4.21282	−	7.29683i	−0.143740	−	0.248964i	0.785162	−	0.619290i	$-0.212579\pi$
$859$	−4.21282	−	7.29683i	−0.143740	−	0.248964i	−0.928902	+	0.370326i	$0.879246\pi$
$860$	−14.8769	+	2.59715i	−0.507298	+	0.0885619i
$861$	11.2901	+	19.5550i	0.384766	+	0.666434i
$862$			27.4245i			0.934083i
$863$		−	6.06986i		−	0.206620i	−0.994649	−	0.103310i	$-0.967057\pi$
$863$		−	6.06986i		−	0.206620i	0.994649	−	0.103310i	$-0.0329434\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−11.0646	+	30.2398i	−0.376209	+	1.02819i
$866$	11.2647			0.382791
$867$			36.1147i			1.22652i
$868$	20.1073	−	11.6089i	0.682486	−	0.394033i
$869$	11.8860	−	20.5872i	0.403205	−	0.698371i
$870$	9.27989	+	3.39547i	0.314618	+	0.115117i
$871$	24.8158	−	42.9822i	0.840852	−	1.45640i
$872$	−3.66583	−	2.11647i	−0.124141	−	0.0716726i
$873$			2.29667i			0.0777307i
$874$	−7.04226	−	2.46472i	−0.238208	−	0.0833705i
$875$	24.4523	−	13.9518i	0.826639	−	0.471659i
$876$	−7.08348	+	12.2689i	−0.239329	+	0.414529i
$877$	29.4618	+	17.0098i	0.994855	+	0.574380i	0.906722	−	0.421729i	$-0.138577\pi$
$877$	29.4618	+	17.0098i	0.994855	+	0.574380i	0.0881333	+	0.996109i	$0.471910\pi$
$878$	13.6797	−	7.89796i	0.461666	−	0.266543i
$879$	−4.63359	+	8.02562i	−0.156287	+	0.270697i
$880$	−6.05819	−	2.21666i	−0.204221	−	0.0747237i
$881$	37.8182			1.27413			0.637064	−	0.770811i	$-0.280149\pi$
$881$	37.8182			1.27413			0.637064	+	0.770811i	$0.280149\pi$
$882$		−	0.659446i		−	0.0222047i
$883$	39.0605	−	22.5516i	1.31449	−	0.758921i	0.331653	−	0.943401i	$-0.392394\pi$
$883$	39.0605	−	22.5516i	1.31449	−	0.758921i	0.982836	+	0.184480i	$0.0590602\pi$
$884$	16.9674	+	29.3883i	0.570674	+	0.988436i
$885$	13.5773	+	16.2368i	0.456397	+	0.545793i
$886$	7.03690			0.236409
$887$	−37.0666	+	21.4004i	−1.24457	+	0.718555i	−0.970022	−	0.243017i	$-0.921863\pi$
$887$	−37.0666	+	21.4004i	−1.24457	+	0.718555i	−0.274552	+	0.961572i	$0.588529\pi$
$888$	2.82740	+	1.63240i	0.0948814	+	0.0547798i
$889$	19.8392	+	34.3625i	0.665385	+	1.15248i
$890$	10.4459	−	1.82361i	0.350149	−	0.0611274i
$891$	−1.44248	+	2.49846i	−0.0483250	+	0.0837014i
$892$			11.2470i			0.376576i
$893$	−19.6873	+	3.72368i	−0.658812	+	0.124608i
$894$	11.9895			0.400989
$895$	−0.746698	−	4.27722i	−0.0249594	−	0.142972i
$896$	−1.25902	+	2.18069i	−0.0420610	+	0.0728518i
$897$	−6.90231	+	3.98505i	−0.230461	+	0.133057i
$898$	14.1933	+	8.19449i	0.473635	+	0.273454i
$899$	−20.3737	−	35.2883i	−0.679502	−	1.17693i
$900$	0.884968	−	4.92106i	0.0294989	−	0.164035i
$901$	−78.9463			−2.63008
$902$	−22.4046	+	12.9353i	−0.745990	+	0.430698i
$903$	−14.7279	+	8.50316i	−0.490114	+	0.282967i
$904$	−18.7982			−0.625220
$905$	30.2412	−	25.2880i	1.00525	−	0.840601i
$906$	2.75767	+	4.77643i	0.0916175	+	0.158686i
$907$	−26.2663	−	15.1648i	−0.872157	−	0.503540i	−0.00409285	−	0.999992i	$-0.501303\pi$
$907$	−26.2663	−	15.1648i	−0.872157	−	0.503540i	−0.868065	+	0.496451i	$0.834636\pi$
$908$	−7.64539	+	4.41407i	−0.253721	+	0.146486i
$909$	−1.68398	+	2.91673i	−0.0558540	+	0.0967419i
$910$	−25.8266	+	4.50869i	−0.856142	+	0.149462i
$911$	35.4194			1.17350			0.586748	−	0.809770i	$-0.300408\pi$
$911$	35.4194			1.17350			0.586748	+	0.809770i	$0.300408\pi$
$912$	−4.28296	+	0.810083i	−0.141823	+	0.0268245i
$913$			20.6138i			0.682216i
$914$	−5.79875	+	10.0437i	−0.191805	+	0.332217i
$915$	−33.0489	+	5.76953i	−1.09256	+	0.190735i
$916$	11.1408	+	19.2965i	0.368104	+	0.637574i
$917$	14.3209	+	8.26819i	0.472918	+	0.273040i
$918$	−6.31158	+	3.64399i	−0.208313	+	0.120270i
$919$	−17.0531			−0.562531			−0.281265	−	0.959630i	$-0.590754\pi$
$919$	−17.0531			−0.562531			−0.281265	+	0.959630i	$0.590754\pi$
$920$	2.93619	−	2.45527i	0.0968033	−	0.0809477i
$921$	−5.13612	−	8.89602i	−0.169241	−	0.293134i
$922$	−4.14363	+	2.39232i	−0.136463	+	0.0787870i
$923$		−	50.1050i		−	1.64923i
$924$	−7.26448			−0.238984
$925$	−5.53098	−	15.3584i	−0.181858	−	0.504982i
$926$	−6.07796	+	10.5273i	−0.199734	+	0.345950i
$927$	9.51527	−	5.49365i	0.312523	−	0.180435i
$928$	3.82712	+	2.20959i	0.125631	+	0.0725332i
$929$	−16.0271	+	27.7598i	−0.525834	+	0.910771i	0.473714	+	0.880679i	$0.342913\pi$
$929$	−16.0271	+	27.7598i	−0.525834	+	0.910771i	−0.999547	+	0.0300916i	$0.990420\pi$
$930$	−15.8167	+	13.2261i	−0.518651	+	0.433700i
$931$	2.71309	+	0.949555i	0.0889179	+	0.0311204i
$932$		−	6.18132i		−	0.202476i
$933$	−9.90014	−	5.71585i	−0.324116	−	0.187128i
$934$	−0.802313	+	1.38965i	−0.0262525	+	0.0454706i
$935$	16.1550	−	44.1520i	0.528325	−	1.44392i
$936$	−2.32813	+	4.03244i	−0.0760973	+	0.131804i
$937$	22.9312	−	13.2393i	0.749128	−	0.432509i	−0.0762506	−	0.997089i	$-0.524295\pi$
$937$	22.9312	−	13.2393i	0.749128	−	0.432509i	0.825379	+	0.564579i	$0.190962\pi$
$938$			26.8402i			0.876362i
$939$	−3.95860			−0.129184
$940$	3.53184	−	9.65260i	0.115196	−	0.314833i
$941$	−7.18502	−	12.4448i	−0.234225	−	0.405689i	0.724822	−	0.688936i	$-0.241922\pi$
$941$	−7.18502	−	12.4448i	−0.234225	−	0.405689i	−0.959047	+	0.283247i	$0.908589\pi$
$942$			12.2792i			0.400079i
$943$		−	15.3494i		−	0.499845i
$944$	4.73274	+	8.19734i	0.154037	+	0.266801i
$945$	−0.968307	−	5.54663i	−0.0314990	−	0.180432i
$946$	−9.74222	−	16.8740i	−0.316747	−	0.548622i
$947$	−39.4692	−	22.7875i	−1.28258	−	0.740495i	−0.305257	−	0.952270i	$-0.598742\pi$
$947$	−39.4692	−	22.7875i	−1.28258	−	0.740495i	−0.977318	+	0.211775i	$0.932076\pi$
$948$	7.13601	+	4.11998i	0.231767	+	0.133811i
$949$	−65.9650			−2.14132
$950$	18.9719	+	10.7269i	0.615530	+	0.348027i
$951$	21.9453			0.711625
$952$	−15.8928	−	9.17574i	−0.515090	−	0.297387i
$953$	−46.7123	−	26.9694i	−1.51316	−	0.873623i	−0.999881	−	0.0154010i	$-0.995098\pi$
$953$	−46.7123	−	26.9694i	−1.51316	−	0.873623i	−0.513278	−	0.858222i	$-0.671569\pi$
$954$	−5.41620	−	9.38113i	−0.175356	−	0.303725i
$955$	−1.77421	−	10.1630i	−0.0574121	−	0.328867i
$956$	−9.09488	−	15.7528i	−0.294149	−	0.509482i
$957$			12.7492i			0.412122i
$958$			34.5880i			1.11749i
$959$	18.1757	+	31.4813i	0.586924	+	1.01658i
$960$	0.768349	−	2.09991i	0.0247984	−	0.0677744i
$961$	54.0195			1.74257
$962$			15.2018i			0.490124i
$963$	2.90789	−	1.67887i	0.0937055	−	0.0541009i
$964$	1.24768	−	2.16104i	0.0401849	−	0.0696023i
$965$	−19.2704	+	52.6664i	−0.620336	+	1.69539i
$966$	2.15507	−	3.73268i	0.0693381	−	0.120097i
$967$	19.5534	+	11.2892i	0.628795	+	0.363035i	0.780285	−	0.625424i	$-0.215074\pi$
$967$	19.5534	+	11.2892i	0.628795	+	0.363035i	−0.151490	+	0.988459i	$0.548407\pi$
$968$			2.67696i			0.0860407i
$969$	−5.90387	−	31.2142i	−0.189660	−	1.00274i
$970$	3.93964	−	3.29436i	0.126494	−	0.105776i
$971$	−29.4664	+	51.0372i	−0.945621	+	1.63786i	−0.191117	+	0.981567i	$0.561211\pi$
$971$	−29.4664	+	51.0372i	−0.945621	+	1.63786i	−0.754504	+	0.656296i	$0.772122\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	13.5084	−	7.79909i	0.433060	−	0.250027i
$974$	12.1868	−	21.1082i	0.390491	−	0.676350i
$975$	21.9042	−	7.88828i	0.701495	−	0.252627i
$976$	−15.0035			−0.480249
$977$			1.86548i			0.0596821i	0.999555	+	0.0298411i	$0.00950012\pi$
$977$			1.86548i			0.0596821i	−0.999555	+	0.0298411i	$0.990500\pi$
$978$	−2.99472	+	1.72900i	−0.0957606	+	0.0552874i
$979$	6.84057	+	11.8482i	0.218626	+	0.378671i
$980$	−1.13119	+	0.945912i	−0.0361346	+	0.0302160i
$981$	4.23293			0.135147
$982$	−9.44752	+	5.45453i	−0.301482	+	0.174061i
$983$	38.1239	+	22.0109i	1.21597	+	0.702038i	0.964052	−	0.265712i	$-0.0856071\pi$
$983$	38.1239	+	22.0109i	1.21597	+	0.702038i	0.251913	+	0.967750i	$0.418940\pi$
$984$	−4.48368	−	7.76596i	−0.142934	−	0.247570i
$985$	7.98363	−	1.39375i	0.254380	−	0.0444085i
$986$	−16.1034	+	27.8920i	−0.512838	+	0.888261i
$987$		−	11.5746i		−	0.368424i
$988$	−13.2379	−	15.3848i	−0.421154	−	0.489456i
$989$	11.5604			0.367600
$990$	6.35487	−	1.10941i	0.201971	−	0.0352592i
$991$	16.2964	−	28.2263i	0.517674	−	0.896637i	−0.482116	−	0.876108i	$-0.660132\pi$
$991$	16.2964	−	28.2263i	0.517674	−	0.896637i	0.999789	−	0.0205293i	$-0.00653513\pi$
$992$	−7.98528	+	4.61030i	−0.253533	+	0.146377i
$993$	6.45007	+	3.72395i	0.204687	+	0.118176i
$994$	13.5481	+	23.4660i	0.429719	+	0.744296i
$995$	−1.02405	+	0.856319i	−0.0324646	+	0.0271471i
$996$	−7.14523			−0.226405
$997$	−16.4589	+	9.50256i	−0.521259	+	0.300949i	−0.737450	−	0.675402i	$-0.763970\pi$
$997$	−16.4589	+	9.50256i	−0.521259	+	0.300949i	0.216190	+	0.976351i	$0.430637\pi$
$998$	9.60920	−	5.54788i	0.304174	−	0.175615i
$999$	−3.26480			−0.103294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.c.49.3	✓	20
3.2	odd	2		1710.2.t.c.1189.8		20
5.4	even	2	inner	570.2.q.c.49.6	yes	20
15.14	odd	2		1710.2.t.c.1189.5		20
19.7	even	3	inner	570.2.q.c.349.6	yes	20
57.26	odd	6		1710.2.t.c.919.5		20
95.64	even	6	inner	570.2.q.c.349.3	yes	20
285.254	odd	6		1710.2.t.c.919.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.3	✓	20	1.1	even	1	trivial
570.2.q.c.49.6	yes	20	5.4	even	2	inner
570.2.q.c.349.3	yes	20	95.64	even	6	inner
570.2.q.c.349.6	yes	20	19.7	even	3	inner
1710.2.t.c.919.5		20	57.26	odd	6
1710.2.t.c.919.8		20	285.254	odd	6
1710.2.t.c.1189.5		20	15.14	odd	2
1710.2.t.c.1189.8		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.384547 + 2.20275i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.51805i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.384547 + 2.20275i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.51805i q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.768349 - 2.09991i) q^{10} +2.88497 q^{11} +1.00000i q^{12} +(-4.03244 + 2.32813i) q^{13} +(1.25902 - 2.18069i) q^{14} +(-0.768349 + 2.09991i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.31158 - 3.64399i) q^{17} -1.00000i q^{18} +(4.11420 + 1.43993i) q^{19} +(-1.71537 + 1.43440i) q^{20} +(-1.25902 + 2.18069i) q^{21} +(-2.49846 - 1.44248i) q^{22} +(1.48237 - 0.855848i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.70425 + 1.69412i) q^{25} +4.65626 q^{26} +1.00000i q^{27} +(-2.18069 + 1.25902i) q^{28} +(2.20959 + 3.82712i) q^{29} +(1.71537 - 1.43440i) q^{30} -9.22060 q^{31} +(0.866025 - 0.500000i) q^{32} +(2.49846 + 1.44248i) q^{33} +(3.64399 + 6.31158i) q^{34} +(-5.54663 + 0.968307i) q^{35} +(-0.500000 + 0.866025i) q^{36} +3.26480i q^{37} +(-2.84303 - 3.30411i) q^{38} -4.65626 q^{39} +(2.20275 - 0.384547i) q^{40} +(4.48368 - 7.76596i) q^{41} +(2.18069 - 1.25902i) q^{42} +(5.84894 + 3.37689i) q^{43} +(1.44248 + 2.49846i) q^{44} +(-1.71537 + 1.43440i) q^{45} -1.71170 q^{46} +(-3.98083 + 2.29833i) q^{47} +(-0.866025 + 0.500000i) q^{48} +0.659446 q^{49} +(4.92106 + 0.884968i) q^{50} +(-3.64399 - 6.31158i) q^{51} +(-4.03244 - 2.32813i) q^{52} +(9.38113 - 5.41620i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.10941 + 6.35487i) q^{55} +2.51805 q^{56} +(2.84303 + 3.30411i) q^{57} -4.41917i q^{58} +(4.73274 - 8.19734i) q^{59} +(-2.20275 + 0.384547i) q^{60} +(7.50173 + 12.9934i) q^{61} +(7.98528 + 4.61030i) q^{62} +(-2.18069 + 1.25902i) q^{63} -1.00000 q^{64} +(-6.67896 - 7.98719i) q^{65} +(-1.44248 - 2.49846i) q^{66} +(-9.23107 + 5.32956i) q^{67} -7.28798i q^{68} +1.71170 q^{69} +(5.28768 + 1.93474i) q^{70} +(-5.38040 + 9.31912i) q^{71} +(0.866025 - 0.500000i) q^{72} +(12.2689 + 7.08348i) q^{73} +(1.63240 - 2.82740i) q^{74} +(-4.92106 - 0.884968i) q^{75} +(0.810083 + 4.28296i) q^{76} +7.26448i q^{77} +(4.03244 + 2.32813i) q^{78} +(4.11998 - 7.13601i) q^{79} +(-2.09991 - 0.768349i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.76596 + 4.48368i) q^{82} +7.14523i q^{83} -2.51805 q^{84} +(5.59972 - 15.3041i) q^{85} +(-3.37689 - 5.84894i) q^{86} +4.41917i q^{87} -2.88497i q^{88} +(2.37111 + 4.10688i) q^{89} +(2.20275 - 0.384547i) q^{90} +(-5.86233 - 10.1539i) q^{91} +(1.48237 + 0.855848i) q^{92} +(-7.98528 - 4.61030i) q^{93} +4.59667 q^{94} +(-1.58971 + 9.61628i) q^{95} +1.00000 q^{96} +(1.98898 + 1.14834i) q^{97} +(-0.571097 - 0.329723i) q^{98} +(1.44248 + 2.49846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

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