LMFDB - Embedded newform 570.2.q.c.49.6

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			49.6
Root			$-0.627868 - 2.34324i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.c.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09991 + 0.768349i) q^{5} +(-0.500000 - 0.866025i) q^{6} -2.51805i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09991 + 0.768349i) q^{5} +(-0.500000 - 0.866025i) q^{6} -2.51805i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.20275 - 0.384547i) q^{10} +2.88497 q^{11} -1.00000i q^{12} +(4.03244 - 2.32813i) q^{13} +(1.25902 - 2.18069i) q^{14} +(2.20275 + 0.384547i) 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} +(3.81928 - 3.22694i) 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} +(1.93474 + 5.28768i) q^{35} +(-0.500000 + 0.866025i) q^{36} -3.26480i q^{37} +(2.84303 + 3.30411i) q^{38} -4.65626 q^{39} +(-0.768349 - 2.09991i) 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} +(-6.05819 + 2.21666i) q^{55} +2.51805 q^{56} +(-2.84303 - 3.30411i) q^{57} +4.41917i q^{58} +(4.73274 - 8.19734i) q^{59} +(0.768349 + 2.09991i) 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} +(-0.968307 + 5.54663i) 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} +(0.384547 - 2.20275i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.76596 - 4.48368i) q^{82} -7.14523i q^{83} -2.51805 q^{84} +(-16.0536 - 2.80257i) q^{85} +(-3.37689 - 5.84894i) q^{86} -4.41917i q^{87} +2.88497i q^{88} +(2.37111 + 4.10688i) q^{89} +(-0.768349 - 2.09991i) q^{90} +(-5.86233 - 10.1539i) q^{91} +(-1.48237 - 0.855848i) q^{92} +(7.98528 + 4.61030i) q^{93} +4.59667 q^{94} +(-9.74583 + 0.137412i) 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
$5$	−2.09991	+	0.768349i	−0.939110	+	0.343616i
$5$	−2.09991	+	0.768349i	−0.939110	+	0.343616i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$		−	2.51805i		−	0.951732i	−0.879518	−	0.475866i	$-0.842135\pi$
$7$		−	2.51805i		−	0.951732i	0.879518	−	0.475866i	$-0.157865\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.20275	−	0.384547i	−0.696572	−	0.121604i
$11$	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	0.177406	−	0.984138i	$-0.443230\pi$
$13$	4.03244	−	2.32813i	1.11840	−	0.645707i	0.940991	+	0.338431i	$0.109896\pi$
$14$	1.25902	−	2.18069i	0.336488	−	0.582814i
$15$	2.20275	+	0.384547i	0.568749	+	0.0992896i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.31158	+	3.64399i	1.53078	+	0.883798i	0.999326	+	0.0367122i	$0.0116885\pi$
$17$	6.31158	+	3.64399i	1.53078	+	0.883798i	0.531457	+	0.847085i	$0.321645\pi$
$18$			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	−0.646522	−	0.762895i	$-0.723777\pi$
$23$	−1.48237	+	0.855848i	−0.309096	+	0.178457i	0.337426	+	0.941352i	$0.390444\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	3.81928	−	3.22694i	0.763856	−	0.645387i
$26$	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
$35$	1.93474	+	5.28768i	0.327031	+	0.893781i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$		−	3.26480i		−	0.536730i	−0.963317	−	0.268365i	$-0.913517\pi$
$37$		−	3.26480i		−	0.536730i	0.963317	−	0.268365i	$-0.0864834\pi$
$38$	2.84303	+	3.30411i	0.461201	+	0.535998i
$39$	−4.65626			−0.745598
$40$	−0.768349	−	2.09991i	−0.121487	−	0.332026i
$41$	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	−0.0173738	−	0.999849i	$-0.505531\pi$
$43$	−5.84894	−	3.37689i	−0.891955	−	0.514971i	−0.874582	+	0.484878i	$0.838864\pi$
$44$	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	−0.180733	−	0.983532i	$-0.557847\pi$
$47$	3.98083	−	2.29833i	0.580664	−	0.335246i	0.761397	+	0.648286i	$0.224514\pi$
$48$	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	−0.978404	−	0.206701i	$-0.933727\pi$
$53$	−9.38113	+	5.41620i	−1.28860	+	0.743972i	−0.310193	+	0.950673i	$0.600394\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−6.05819	+	2.21666i	−0.816886	+	0.298895i
$56$	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	$-0.0446418\pi$
$60$	0.768349	+	2.09991i	0.0991935	+	0.271098i
$61$	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	0.184386	−	0.982854i	$-0.440970\pi$
$67$	9.23107	−	5.32956i	1.12776	−	0.651110i	0.943369	+	0.331744i	$0.107637\pi$
$68$			7.28798i			0.883798i
$69$	1.71170			0.206064
$70$	−0.968307	+	5.54663i	−0.115735	+	0.662950i
$71$	−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	−0.438405	−	0.898777i	$-0.644457\pi$
$73$	−12.2689	−	7.08348i	−1.43597	−	0.829059i	−0.997567	+	0.0697187i	$0.977790\pi$
$74$	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	$0.0132480\pi$
$80$	0.384547	−	2.20275i	0.0429937	−	0.246275i
$81$	−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	$-0.871733\pi$
$83$		−	7.14523i		−	0.784291i	0.919903	−	0.392146i	$-0.128267\pi$
$84$	−2.51805			−0.274741
$85$	−16.0536	−	2.80257i	−1.74126	−	0.303982i
$86$	−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	$0.752463\pi$
$90$	−0.768349	−	2.09991i	−0.0809911	−	0.221350i
$91$	−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
$95$	−9.74583	+	0.137412i	−0.999901	+	0.0140982i
$96$	1.00000			0.102062
$97$	−1.98898	−	1.14834i	−0.201950	−	0.116596i	0.395615	−	0.918417i	$-0.370532\pi$
$97$	−1.98898	−	1.14834i	−0.201950	−	0.116596i	−0.597565	+	0.801821i	$0.703865\pi$
$98$	0.571097	+	0.329723i	0.0576895	+	0.0333070i
$99$	1.44248	+	2.49846i	0.144975	+	0.251104i
$100$	4.70425	+	1.69412i	0.470425	+	0.169412i
$101$	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	$0.182070\pi$
$103$			10.9873i			1.08261i	−0.840826	+	0.541305i	$0.817930\pi$
$104$	2.32813	+	4.03244i	0.228292	+	0.395413i
$105$	0.968307	−	5.54663i	0.0944971	−	0.541296i
$106$	−10.8324			−1.05214
$107$			3.35775i			0.324605i	0.986741	+	0.162303i	$0.0518921\pi$
$107$			3.35775i			0.324605i	−0.986741	+	0.162303i	$0.948108\pi$
$108$	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	$0.101688\pi$
$110$	−6.35487	−	1.10941i	−0.605914	−	0.105778i
$111$	−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	$0.345292\pi$
$113$			18.7982i			1.76839i	−0.467118	+	0.884195i	$0.654708\pi$
$114$	−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
$120$	−0.384547	+	2.20275i	−0.0351042	+	0.201083i
$121$	−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	−0.962962	−	0.269637i	$-0.913096\pi$
$127$	−13.6465	+	7.87880i	−1.21093	+	0.699131i	−0.247968	+	0.968768i	$0.579763\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.37689	+	5.84894i	0.297318	+	0.514971i
$130$	−9.77774	+	3.57763i	−0.857565	+	0.313779i
$131$	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
$135$	0.768349	+	2.09991i	0.0661290	+	0.180732i
$136$	−3.64399	+	6.31158i	−0.312470	+	0.541213i
$137$	−12.5023	+	7.21818i	−1.06814	+	0.616691i	−0.927673	−	0.373394i	$-0.878194\pi$
$137$	−12.5023	+	7.21818i	−1.06814	+	0.616691i	−0.140467	+	0.990085i	$0.544861\pi$
$138$	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	$0.330075\pi$
$150$	−4.70425	−	1.69412i	−0.384100	−	0.138325i
$151$	−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
$155$	19.3625	−	7.08464i	1.55523	−	0.569052i
$156$	−2.32813	−	4.03244i	−0.186399	−	0.322853i
$157$	10.6341	+	6.13962i	0.848696	+	0.489995i	0.860211	−	0.509939i	$-0.170332\pi$
$157$	10.6341	+	6.13962i	0.848696	+	0.489995i	−0.0115149	+	0.999934i	$0.503665\pi$
$158$	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	$0.0432403\pi$
$163$			3.45801i			0.270852i	−0.990787	+	0.135426i	$0.956760\pi$
$164$	8.96736			0.700233
$165$	6.35487	+	1.10941i	0.494726	+	0.0863671i
$166$	3.57262	−	6.18795i	0.277289	−	0.480278i
$167$	5.37144	−	3.10120i	0.415654	−	0.239978i	−0.277562	−	0.960708i	$-0.589526\pi$
$167$	5.37144	−	3.10120i	0.415654	−	0.239978i	0.693216	+	0.720730i	$0.256193\pi$
$168$	−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	−0.0556571	−	0.998450i	$-0.517725\pi$
$173$	−12.4712	−	7.20026i	−0.948169	−	0.547425i	−0.892512	+	0.451025i	$0.851059\pi$
$174$	2.20959	−	3.82712i	0.167508	−	0.290133i
$175$	−8.12557	−	9.61712i	−0.614235	−	0.726986i
$176$	−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	$0.523119\pi$
$180$	0.384547	−	2.20275i	0.0286624	−	0.164184i
$181$	−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
$185$	2.50851	+	6.85581i	0.184429	+	0.504049i
$186$	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
$190$	−8.50884	−	4.75391i	−0.617296	−	0.344885i
$191$	−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	$-0.974946\pi$
$193$	−21.7202	−	12.5401i	−1.56345	−	0.902659i	−0.566547	−	0.824030i	$-0.691721\pi$
$194$	−1.14834	−	1.98898i	−0.0824458	−	0.142800i
$195$	9.77774	−	3.57763i	0.700198	−	0.256200i
$196$	0.329723	+	0.571097i	0.0235516	+	0.0407926i
$197$			3.62439i			0.258227i	0.991630	+	0.129113i	$0.0412131\pi$
$197$			3.62439i			0.258227i	−0.991630	+	0.129113i	$0.958787\pi$
$198$			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	$0.826598\pi$
$200$	3.22694	+	3.81928i	0.228179	+	0.270064i
$201$	−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
$205$	−3.44837	+	19.7529i	−0.240845	+	1.37960i
$206$	−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
$215$	14.8769	+	2.59715i	1.01460	+	0.177124i
$216$	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	0.137068	−	0.990562i	$-0.456232\pi$
$223$	−9.74016	−	5.62349i	−0.652250	−	0.376576i	−0.789318	+	0.613985i	$0.789565\pi$
$224$	1.25902	+	2.18069i	0.0841220	+	0.145704i
$225$	4.70425	+	1.69412i	0.313616	+	0.112942i
$226$	−9.39912	+	16.2798i	−0.625220	+	1.08291i
$227$		−	8.82814i		−	0.585944i	−0.956121	−	0.292972i	$-0.905356\pi$
$227$		−	8.82814i		−	0.585944i	0.956121	−	0.292972i	$-0.0946443\pi$
$228$	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	$0.236615\pi$
$230$	3.59442	−	1.31518i	0.237009	−	0.0867205i
$231$	−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	0.664993	−	0.746850i	$-0.268435\pi$
$233$	5.35318	+	3.09066i	0.350699	+	0.202476i	−0.314294	+	0.949326i	$0.601768\pi$
$234$	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
$245$	−1.38478	+	0.506685i	−0.0884703	+	0.0323709i
$246$	−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
$250$	−9.65384	+	5.63945i	−0.610562	+	0.356670i
$251$	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	−0.334577	−	0.942368i	$-0.608594\pi$
$257$	5.03779	−	2.90857i	0.314249	−	0.181432i	0.648826	+	0.760937i	$0.275260\pi$
$258$			6.75378i			0.420472i
$259$	−8.22092			−0.510823
$260$	−10.2566	−	1.79055i	−0.636087	−	0.111045i
$261$	−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	−0.0380737	−	0.999275i	$-0.512122\pi$
$263$	−14.9606	−	8.63749i	−0.922508	−	0.532610i	−0.884434	+	0.466665i	$0.845456\pi$
$264$	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	$0.261764\pi$
$270$	−0.384547	+	2.20275i	−0.0234028	+	0.134055i
$271$	−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
$275$	11.0185	−	9.30961i	0.664440	−	0.561390i
$276$	0.855848	+	1.48237i	0.0515160	+	0.0892284i
$277$			11.1309i			0.668791i	0.942433	+	0.334396i	$0.108532\pi$
$277$			11.1309i			0.668791i	−0.942433	+	0.334396i	$0.891468\pi$
$278$		−	6.19455i		−	0.371525i
$279$	−4.61030	−	7.98528i	−0.276012	−	0.478066i
$280$	−5.28768	+	1.93474i	−0.315999	+	0.115623i
$281$	−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	0.673985	−	0.738745i	$-0.264581\pi$
$283$	6.24466	+	3.60536i	0.371207	+	0.214316i	−0.302779	+	0.953061i	$0.597914\pi$
$284$	−10.7608			−0.638536
$285$	8.50884	+	4.75391i	0.504020	+	0.281597i
$286$	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
$290$	−3.39547	−	9.27989i	−0.199389	−	0.544934i
$291$	1.14834	+	1.98898i	0.0673167	+	0.116596i
$292$		−	14.1670i		−	0.829059i
$293$		−	9.26719i		−	0.541395i	−0.962664	−	0.270697i	$-0.912746\pi$
$293$		−	9.26719i		−	0.541395i	0.962664	−	0.270697i	$-0.0872543\pi$
$294$	−0.329723	−	0.571097i	−0.0192298	−	0.0333070i
$295$	−3.63992	+	20.8501i	−0.211924	+	1.21394i
$296$	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
$300$	−3.22694	−	3.81928i	−0.186307	−	0.220506i
$301$	−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	0.731897	−	0.681415i	$-0.238635\pi$
$307$	8.89602	+	5.13612i	0.507722	+	0.293134i	−0.224175	+	0.974549i	$0.571969\pi$
$308$	6.29123	−	3.63224i	0.358476	−	0.206966i
$309$	5.49365	−	9.51527i	0.312523	−	0.541305i
$310$	20.3107	+	3.54576i	1.15357	+	0.201385i
$311$	−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	−0.399973	−	0.916527i	$-0.630981\pi$
$313$	3.42825	−	1.97930i	0.193776	−	0.111877i	0.593749	+	0.804650i	$0.297647\pi$
$314$	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	−0.927480	−	0.373872i	$-0.878030\pi$
$317$	−19.0052	+	10.9727i	−1.06744	+	0.616286i	−0.139958	+	0.990157i	$0.544697\pi$
$318$	9.38113	+	5.41620i	0.526068	+	0.303725i
$319$	6.37459	+	11.0411i	0.356908	+	0.618184i
$320$	2.09991	−	0.768349i	0.117389	−	0.0429520i
$321$	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
$325$	7.88828	−	21.9042i	0.437563	−	1.21503i
$326$	−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	0.385699	−	0.922625i	$-0.373960\pi$
$337$	−4.04725	−	2.33668i	−0.220468	−	0.127287i	−0.606167	+	0.795338i	$0.707294\pi$
$338$	7.51773	−	4.34036i	0.408911	−	0.236085i
$339$	9.39912	−	16.2798i	0.510490	−	0.884195i
$340$	−5.59972	−	15.3041i	−0.303687	−	0.829983i
$341$	−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
$345$	−3.59442	+	1.31518i	−0.193517	+	0.0708070i
$346$	−7.20026	−	12.4712i	−0.387088	−	0.670456i
$347$	−11.8564	−	6.84531i	−0.636486	−	0.367475i	0.146774	−	0.989170i	$-0.453111\pi$
$347$	−11.8564	−	6.84531i	−0.636486	−	0.367475i	−0.783260	+	0.621695i	$0.786444\pi$
$348$	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	$0.0259394\pi$
$353$			3.05876i			0.162802i	−0.996681	+	0.0814008i	$0.974061\pi$
$354$	−9.46547			−0.503084
$355$	4.13803	−	23.7034i	0.219624	−	1.25805i
$356$	−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
$365$	31.2063	+	5.44786i	1.63341	+	0.285154i
$366$	7.50173	−	12.9934i	0.392121	−	0.679174i
$367$	−4.66821	+	2.69519i	−0.243679	+	0.140688i	−0.616866	−	0.787068i	$-0.711598\pi$
$367$	−4.66821	+	2.69519i	−0.243679	+	0.140688i	0.373188	+	0.927756i	$0.378265\pi$
$368$		−	1.71170i		−	0.0892284i
$369$	8.96736			0.466822
$370$	−1.25547	+	7.19156i	−0.0652688	+	0.373871i
$371$	13.6382	+	23.6221i	0.708062	+	1.22640i
$372$			9.22060i			0.478066i
$373$		−	3.85586i		−	0.199649i	−0.995005	−	0.0998244i	$-0.968172\pi$
$373$		−	3.85586i		−	0.199649i	0.995005	−	0.0998244i	$-0.0318281\pi$
$374$	10.5128	+	18.2087i	0.543604	+	0.941550i
$375$	9.65384	−	5.63945i	0.498522	−	0.291220i
$376$	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	$0.614072\pi$
$380$	−4.99192	−	8.37143i	−0.256080	−	0.429445i
$381$	15.7576			0.807287
$382$	−3.99564	−	2.30688i	−0.204435	−	0.118030i
$383$	6.30771	+	3.64176i	0.322309	+	0.186085i	0.652421	−	0.757857i	$-0.273753\pi$
$383$	6.30771	+	3.64176i	0.322309	+	0.186085i	−0.330112	+	0.943942i	$0.607087\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	5.58166	+	15.2548i	0.284468	+	0.777456i
$386$	−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	$0.999101\pi$
$390$	10.2566	+	1.79055i	0.519362	+	0.0906680i
$391$	−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
$395$	−3.16865	+	18.1506i	−0.159432	+	0.913255i
$396$	−1.44248	+	2.49846i	−0.0724876	+	0.125552i
$397$	10.0280	+	5.78964i	0.503288	+	0.290574i	0.730071	−	0.683372i	$-0.239487\pi$
$397$	10.0280	+	5.78964i	0.503288	+	0.290574i	−0.226782	+	0.973946i	$0.572821\pi$
$398$			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
$405$	0.384547	−	2.20275i	0.0191083	−	0.109456i
$406$	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
$415$	5.49003	+	15.0044i	0.269495	+	0.736536i
$416$	−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	$0.718592\pi$
$420$	5.28768	−	1.93474i	0.258012	−	0.0944056i
$421$	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	−0.246925	−	0.969035i	$-0.579420\pi$
$433$	9.75555	−	5.63237i	0.468822	−	0.270674i	0.715746	+	0.698360i	$0.246087\pi$
$434$	−11.6089	+	20.1073i	−0.557247	+	0.965181i
$435$	3.39547	+	9.27989i	0.162800	+	0.444936i
$436$	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	$0.289693\pi$
$440$	−2.21666	−	6.05819i	−0.105675	−	0.288813i
$441$	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	−0.348194	−	0.937423i	$-0.613205\pi$
$443$	6.09413	−	3.51845i	0.289541	−	0.167167i	0.637735	+	0.770256i	$0.279872\pi$
$444$	−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	$0.626393\pi$
$450$	3.22694	+	3.81928i	0.152119	+	0.180043i
$451$	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	$0.0874383\pi$
$457$			11.5975i			0.542508i	−0.962508	+	0.271254i	$0.912562\pi$
$458$	19.2965	+	11.1408i	0.901666	+	0.520577i
$459$	3.64399	−	6.31158i	0.170087	−	0.294599i
$460$	3.77045	+	0.658228i	0.175798	+	0.0306900i
$461$	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	$0.0911527\pi$
$463$			12.1559i			0.564934i	−0.959277	+	0.282467i	$0.908847\pi$
$464$	−4.41917			−0.205155
$465$	−20.3107	−	3.54576i	−0.941887	−	0.164430i
$466$	3.09066	+	5.35318i	0.143172	+	0.247981i
$467$			1.60463i			0.0742533i	0.999311	+	0.0371266i	$0.0118205\pi$
$467$			1.60463i			0.0742533i	−0.999311	+	0.0371266i	$0.988180\pi$
$468$			4.65626i			0.215236i
$469$	−13.4201	−	23.2443i	−0.619682	−	1.07332i
$470$	−9.65260	+	3.53184i	−0.445241	+	0.162912i
$471$	−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
$475$	20.3598	−	7.77675i	0.934172	−	0.356822i
$476$	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	$-0.456682\pi$
$480$	−2.09991	+	0.768349i	−0.0958475	+	0.0350702i
$481$	−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
$485$	5.05901	+	0.883179i	0.229718	+	0.0401031i
$486$	1.00000			0.0453609
$487$		−	24.3737i		−	1.10448i	−0.833687	−	0.552238i	$-0.813774\pi$
$487$		−	24.3737i		−	1.10448i	0.833687	−	0.552238i	$-0.186226\pi$
$488$	−12.9934	+	7.50173i	−0.588182	+	0.339587i
$489$	1.72900	−	2.99472i	0.0781882	−	0.135426i
$490$	−1.45260	−	0.253588i	−0.0656216	−	0.0114559i
$491$	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	$0.246557\pi$
$500$	−11.1802	+	0.0569884i	−0.499994	+	0.00254860i
$501$	−6.20240			−0.277103
$502$			21.2635i			0.949034i
$503$	−17.0870	+	9.86519i	−0.761872	+	0.439867i	−0.829967	−	0.557812i	$-0.811641\pi$
$503$	−17.0870	+	9.86519i	−0.761872	+	0.439867i	0.0680955	+	0.997679i	$0.478308\pi$
$504$	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	$-0.431677\pi$
$510$	5.59972	+	15.3041i	0.247960	+	0.677679i
$511$	−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
$515$	−8.44208	−	23.0724i	−0.372002	−	1.01669i
$516$	−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	−0.311753	−	0.950163i	$-0.600916\pi$
$523$	8.12396	−	4.69037i	0.355236	−	0.205096i	0.666989	+	0.745068i	$0.267583\pi$
$524$	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
$530$	22.7471	−	8.32306i	0.988071	−	0.361531i
$531$	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
$535$	−2.57992	−	7.05098i	−0.111540	−	0.304840i
$536$	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
$545$	−1.62776	+	9.32410i	−0.0697256	+	0.399401i
$546$	−5.86233	+	10.1539i	−0.250885	+	0.434545i
$547$	−5.07734	+	2.93141i	−0.217092	+	0.125338i	−0.604603	−	0.796527i	$-0.706668\pi$
$547$	−5.07734	+	2.93141i	−0.217092	+	0.125338i	0.387511	+	0.921865i	$0.373335\pi$
$548$	−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
$555$	1.25547	−	7.19156i	0.0532917	−	0.305265i
$556$	3.09728	−	5.36464i	0.131354	−	0.227511i
$557$	18.3570	−	10.5984i	0.777809	−	0.449068i	−0.0578442	−	0.998326i	$-0.518423\pi$
$557$	18.3570	−	10.5984i	0.777809	−	0.449068i	0.835653	+	0.549257i	$0.185089\pi$
$558$		−	9.22060i		−	0.390339i
$559$	−31.4473			−1.33008
$560$	−5.54663	−	0.968307i	−0.234388	−	0.0409184i
$561$	−10.5128	−	18.2087i	−0.443851	−	0.768772i
$562$		−	5.68717i		−	0.239899i
$563$		−	26.4882i		−	1.11634i	−0.829725	−	0.558172i	$-0.811503\pi$
$563$		−	26.4882i		−	1.11634i	0.829725	−	0.558172i	$-0.188497\pi$
$564$	−2.29833	−	3.98083i	−0.0967773	−	0.167623i
$565$	−14.4436	−	39.4747i	−0.607647	−	1.66071i
$566$	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	$0.651705\pi$
$570$	4.99192	+	8.37143i	0.209088	+	0.350640i
$571$	−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
$575$	−2.89983	+	8.05225i	−0.120931	+	0.335802i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			27.9608i			1.16402i	0.813180	+	0.582012i	$0.197734\pi$
$577$			27.9608i			1.16402i	−0.813180	+	0.582012i	$0.802266\pi$
$578$			36.1147i			1.50217i
$579$	12.5401	+	21.7202i	0.521150	+	0.902659i
$580$	1.69938	−	9.73435i	0.0705629	−	0.404197i
$581$	−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
$585$	−10.2566	−	1.79055i	−0.424058	−	0.0740301i
$586$	4.63359	−	8.02562i	0.191412	−	0.331535i
$587$	9.03637	+	5.21715i	0.372971	+	0.215335i	0.674756	−	0.738041i	$-0.264249\pi$
$587$	9.03637	+	5.21715i	0.372971	+	0.215335i	−0.301785	+	0.953376i	$0.597582\pi$
$588$		−	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	−0.398708	−	0.917078i	$-0.630541\pi$
$593$	4.77660	−	2.75777i	0.196152	−	0.113248i	0.594859	+	0.803830i	$0.297208\pi$
$594$	1.44248	−	2.49846i	0.0591858	−	0.102513i
$595$	−7.05700	+	40.4238i	−0.289309	+	1.65721i
$596$	−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
$605$	5.62138	−	2.05684i	0.228542	−	0.0836224i
$606$	1.68398	−	2.91673i	0.0684069	−	0.118484i
$607$			6.78955i			0.275579i	0.990462	+	0.137790i	$0.0439998\pi$
$607$			6.78955i			0.275579i	−0.990462	+	0.137790i	$0.956000\pi$
$608$	−4.28296	+	0.810083i	−0.173697	+	0.0328532i
$609$	−11.1277			−0.450916
$610$	−11.5279	−	31.5060i	−0.466751	−	1.27564i
$611$	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	0.0149366	−	0.999888i	$-0.495245\pi$
$613$	−20.8847	−	12.0578i	−0.843524	−	0.487009i	−0.858460	+	0.512880i	$0.828579\pi$
$614$	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	−0.988730	−	0.149711i	$-0.952166\pi$
$617$	−33.6188	+	19.4098i	−1.35344	+	0.781410i	−0.364712	+	0.931121i	$0.618832\pi$
$618$	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
$625$	4.17378	−	24.6491i	0.166951	−	0.985965i
$626$	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
$630$	−5.28768	+	1.93474i	−0.210666	+	0.0770818i
$631$	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
$640$	2.20275	+	0.384547i	0.0870715	+	0.0152006i
$641$	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	0.995971	−	0.0896801i	$-0.0285845\pi$
$643$	35.9135	+	20.7347i	1.41629	+	0.817696i	0.420320	+	0.907376i	$0.361918\pi$
$644$	−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	$0.0716848\pi$
$647$			11.3601i			0.446612i	−0.974748	+	0.223306i	$0.928315\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	13.6538	−	23.6491i	0.535958	−	0.928307i
$650$	17.7835	−	15.0254i	0.697528	−	0.589346i
$651$	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	$0.0891562\pi$
$653$			14.1285i			0.552889i	−0.961030	+	0.276444i	$0.910844\pi$
$654$	−4.23293			−0.165521
$655$	−2.52538	+	14.4658i	−0.0986746	+	0.565226i
$656$	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	$-0.360043\pi$
$660$	2.21666	+	6.05819i	0.0862835	+	0.235815i
$661$	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
$665$	0.346010	+	24.5404i	0.0134177	+	0.951637i
$666$	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
$670$	−22.3832	+	8.18993i	−0.864740	+	0.316405i
$671$	21.6422	+	37.4855i	0.835489	+	1.44711i
$672$		−	2.51805i		−	0.0971357i
$673$		−	29.7678i		−	1.14747i	−0.819042	−	0.573733i	$-0.805495\pi$
$673$		−	29.7678i		−	1.14747i	0.819042	−	0.573733i	$-0.194505\pi$
$674$	−2.33668	−	4.04725i	−0.0900055	−	0.155894i
$675$	−3.22694	−	3.81928i	−0.124205	−	0.147004i
$676$	8.68073			0.333874
$677$			14.3460i			0.551360i	0.961249	+	0.275680i	$0.0889031\pi$
$677$			14.3460i			0.551360i	−0.961249	+	0.275680i	$0.911097\pi$
$678$	16.2798	−	9.39912i	0.625220	−	0.360971i
$679$	−2.89157	+	5.00834i	−0.110968	+	0.192202i
$680$	2.80257	−	16.0536i	0.107474	−	0.615629i
$681$	−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	$0.273211\pi$
$683$			39.5539i			1.51349i	−0.653712	+	0.756744i	$0.726789\pi$
$684$	−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
$690$	−3.77045	−	0.658228i	−0.143538	−	0.0250583i
$691$	−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
$700$	4.26588	−	11.8455i	0.161235	−	0.447718i
$701$	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
$705$	9.65260	−	3.53184i	0.363538	−	0.133017i
$706$	−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	$0.983803\pi$
$720$	2.09991	−	0.768349i	0.0782592	−	0.0286347i
$721$	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
$725$	20.7889	+	7.48663i	0.772080	+	0.278047i
$726$	1.33848	+	2.31831i	0.0496756	+	0.0860407i
$727$	15.6863	+	9.05647i	0.581771	+	0.335886i	0.761837	−	0.647769i	$-0.224298\pi$
$727$	15.6863	+	9.05647i	0.581771	+	0.335886i	−0.180066	+	0.983655i	$0.557631\pi$
$728$	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	$-0.950946\pi$
$733$		−	8.31171i		−	0.307000i	0.988149	−	0.153500i	$-0.0490545\pi$
$734$	−5.39039			−0.198963
$735$	1.45260	+	0.253588i	0.0535798	+	0.00935373i
$736$	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	0.926560	−	0.376147i	$-0.122751\pi$
$743$	29.0049	+	16.7460i	1.06409	+	0.614351i	0.137528	+	0.990498i	$0.456084\pi$
$744$	−4.61030	+	7.98528i	−0.169022	+	0.292754i
$745$	4.61053	−	26.4099i	0.168917	−	0.967585i
$746$	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
$750$	11.1802	−	0.0569884i	0.408243	−	0.00208092i
$751$	−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
$755$	11.5817	−	4.23771i	0.421503	−	0.154226i
$756$	−1.25902	−	2.18069i	−0.0457902	−	0.0793110i
$757$	26.9406	+	15.5542i	0.979174	+	0.565327i	0.902021	−	0.431693i	$-0.142083\pi$
$757$	26.9406	+	15.5542i	0.979174	+	0.565327i	0.0771537	+	0.997019i	$0.475417\pi$
$758$	−11.8270	−	6.82832i	−0.429576	−	0.248016i
$759$	4.93819			0.179245
$760$	−0.137412	−	9.74583i	−0.00498446	−	0.353518i
$761$	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
$765$	−5.59972	−	15.3041i	−0.202458	−	0.553322i
$766$	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	$0.699081\pi$
$770$	−2.79354	+	16.0019i	−0.100672	+	0.576667i
$771$	−5.81714			−0.209499
$772$		−	25.0803i		−	0.902659i
$773$	−11.9910	+	6.92302i	−0.431287	+	0.249004i	−0.699895	−	0.714246i	$-0.746770\pi$
$773$	−11.9910	+	6.92302i	−0.431287	+	0.249004i	0.268608	+	0.963250i	$0.413437\pi$
$774$	3.37689	−	5.84894i	0.121380	−	0.210236i
$775$	−35.2161	+	29.7543i	−1.26500	+	1.06881i
$776$	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
$785$	−27.0481	−	4.72194i	−0.965389	−	0.168533i
$786$	−6.56715			−0.234242
$787$		−	0.272719i		−	0.00972137i	−0.999988	−	0.00486069i	$-0.998453\pi$
$787$		−	0.272719i		−	0.00972137i	0.999988	−	0.00486069i	$-0.00154721\pi$
$788$	−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
$795$	−22.7471	+	8.32306i	−0.806757	+	0.295189i
$796$	−0.298493	+	0.517005i	−0.0105798	+	0.0183248i
$797$			2.18853i			0.0775216i	0.999249	+	0.0387608i	$0.0123410\pi$
$797$			2.18853i			0.0775216i	−0.999249	+	0.0387608i	$0.987659\pi$
$798$	−10.7847	+	2.03983i	−0.381774	+	0.0722090i
$799$	33.5004			1.18516
$800$	−1.69412	+	4.70425i	−0.0598964	+	0.166320i
$801$	−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
$815$	−2.65696	−	7.26152i	−0.0930691	−	0.254360i
$816$	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
$820$	−18.8307	+	6.89006i	−0.657596	+	0.240611i
$821$	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	0.0543553	−	0.998522i	$-0.482690\pi$
$823$	27.1468	−	15.6732i	0.946278	−	0.546334i	0.891923	+	0.452188i	$0.149356\pi$
$824$	−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	−0.904719	−	0.426009i	$-0.859919\pi$
$827$	−28.4166	+	16.4063i	−0.988143	+	0.570505i	−0.0834244	+	0.996514i	$0.526586\pi$
$828$		−	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	$0.856330\pi$
$830$	−2.74768	+	15.7392i	−0.0953733	+	0.546315i
$831$	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	$0.161903\pi$
$840$	5.54663	+	0.968307i	0.191377	+	0.0334098i
$841$	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
$845$	−3.33815	+	19.1215i	−0.114836	+	0.657800i
$846$	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
$850$	34.2845	+	12.3468i	1.17595	+	0.423490i
$851$	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	0.518024	−	0.855366i	$-0.326668\pi$
$853$	1.05924	+	0.611551i	0.0362676	+	0.0209391i	−0.481757	+	0.876305i	$0.660001\pi$
$854$	37.7794			1.29278
$855$	−4.99192	−	8.37143i	−0.170720	−	0.286297i
$856$	−3.35775			−0.114765
$857$	−14.7442	−	8.51258i	−0.503653	−	0.290784i	0.226568	−	0.973995i	$-0.427249\pi$
$857$	−14.7442	−	8.51258i	−0.503653	−	0.290784i	−0.730221	+	0.683211i	$0.760583\pi$
$858$	−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	$0.879246\pi$
$860$	5.18926	+	14.1824i	0.176952	+	0.483614i
$861$	11.2901	+	19.5550i	0.384766	+	0.666434i
$862$		−	27.4245i		−	0.934083i
$863$			6.06986i			0.206620i	0.994649	+	0.103310i	$0.0329434\pi$
$863$			6.06986i			0.206620i	−0.994649	+	0.103310i	$0.967057\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	31.7208	+	5.53768i	1.07854	+	0.188287i
$866$	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
$870$	−1.69938	+	9.73435i	−0.0576144	+	0.330025i
$871$	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	−0.0881333	−	0.996109i	$-0.528090\pi$
$877$	−29.4618	−	17.0098i	−0.994855	−	0.574380i	−0.906722	+	0.421729i	$0.861423\pi$
$878$	−13.6797	+	7.89796i	−0.461666	+	0.266543i
$879$	−4.63359	+	8.02562i	−0.156287	+	0.270697i
$880$	1.10941	−	6.35487i	0.0373981	−	0.214223i
$881$	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	−0.982836	−	0.184480i	$-0.940940\pi$
$883$	−39.0605	+	22.5516i	−1.31449	+	0.758921i	−0.331653	+	0.943401i	$0.607606\pi$
$884$	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	0.274552	−	0.961572i	$-0.411471\pi$
$887$	37.0666	−	21.4004i	1.24457	−	0.718555i	0.970022	+	0.243017i	$0.0781372\pi$
$888$	−2.82740	−	1.63240i	−0.0948814	−	0.0547798i
$889$	19.8392	+	34.3625i	0.665385	+	1.15248i
$890$	−3.64368	−	9.95825i	−0.122136	−	0.333801i
$891$	−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
$895$	4.07753	−	1.49195i	0.136297	−	0.0498704i
$896$	−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	0.868065	−	0.496451i	$-0.165364\pi$
$907$	26.2663	+	15.1648i	0.872157	+	0.503540i	0.00409285	+	0.999992i	$0.498697\pi$
$908$	7.64539	−	4.41407i	0.253721	−	0.146486i
$909$	−1.68398	+	2.91673i	−0.0558540	+	0.0967419i
$910$	9.00864	+	24.6208i	0.298634	+	0.816171i
$911$	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
$915$	11.5279	+	31.5060i	0.381100	+	1.04155i
$916$	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
$925$	−10.5353	−	12.4692i	−0.346399	−	0.409985i
$926$	−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
$935$	−46.3142	−	8.08533i	−1.51464	−	0.264419i
$936$	−2.32813	+	4.03244i	−0.0760973	+	0.131804i
$937$	−22.9312	+	13.2393i	−0.749128	+	0.432509i	−0.825379	−	0.564579i	$-0.809038\pi$
$937$	−22.9312	+	13.2393i	−0.749128	+	0.432509i	0.0762506	+	0.997089i	$0.475705\pi$
$938$		−	26.8402i		−	0.876362i
$939$	−3.95860			−0.129184
$940$	−10.1253	−	1.76763i	−0.330252	−	0.0576539i
$941$	−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
$945$	5.28768	−	1.93474i	0.172008	−	0.0629371i
$946$	−9.74222	−	16.8740i	−0.316747	−	0.548622i
$947$	39.4692	+	22.7875i	1.28258	+	0.740495i	0.977318	−	0.211775i	$-0.0679243\pi$
$947$	39.4692	+	22.7875i	1.28258	+	0.740495i	0.305257	+	0.952270i	$0.401258\pi$
$948$	−7.13601	−	4.11998i	−0.231767	−	0.133811i
$949$	−65.9650			−2.14132
$950$	21.5205	+	3.44504i	0.698217	+	0.111772i
$951$	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	$0.00490249\pi$
$953$	46.7123	+	26.9694i	1.51316	+	0.873623i	0.513278	+	0.858222i	$0.328431\pi$
$954$	−5.41620	−	9.38113i	−0.175356	−	0.303725i
$955$	9.68851	−	3.54498i	0.313513	−	0.114713i
$956$	−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
$960$	−2.20275	−	0.384547i	−0.0710936	−	0.0124112i
$961$	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
$965$	55.2457	+	9.64454i	1.77842	+	0.310469i
$966$	2.15507	−	3.73268i	0.0693381	−	0.120097i
$967$	−19.5534	−	11.2892i	−0.628795	−	0.363035i	0.151490	−	0.988459i	$-0.451593\pi$
$967$	−19.5534	−	11.2892i	−0.628795	−	0.363035i	−0.780285	+	0.625424i	$0.784926\pi$
$968$		−	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
$975$	−17.7835	+	15.0254i	−0.569529	+	0.481199i
$976$	−15.0035			−0.480249
$977$		−	1.86548i		−	0.0596821i	−0.999555	−	0.0298411i	$-0.990500\pi$
$977$		−	1.86548i		−	0.0596821i	0.999555	−	0.0298411i	$-0.00950012\pi$
$978$	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	−0.251913	−	0.967750i	$-0.581060\pi$
$983$	−38.1239	−	22.0109i	−1.21597	−	0.702038i	−0.964052	+	0.265712i	$0.914393\pi$
$984$	−4.48368	−	7.76596i	−0.142934	−	0.247570i
$985$	−2.78479	−	7.61090i	−0.0887309	−	0.242503i
$986$	−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
$990$	−2.21666	−	6.05819i	−0.0704502	−	0.192542i
$991$	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	−0.216190	−	0.976351i	$-0.569363\pi$
$997$	16.4589	−	9.50256i	0.521259	−	0.300949i	0.737450	+	0.675402i	$0.236030\pi$
$998$	−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.49.6	yes	20
3.2	odd	2		1710.2.t.c.1189.5		20
5.4	even	2	inner	570.2.q.c.49.3	✓	20
15.14	odd	2		1710.2.t.c.1189.8		20
19.7	even	3	inner	570.2.q.c.349.3	yes	20
57.26	odd	6		1710.2.t.c.919.8		20
95.64	even	6	inner	570.2.q.c.349.6	yes	20
285.254	odd	6		1710.2.t.c.919.5		20

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09991 + 0.768349i) q^{5} +(-0.500000 - 0.866025i) q^{6} -2.51805i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.09991 + 0.768349i) q^{5} +(-0.500000 - 0.866025i) q^{6} -2.51805i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.20275 - 0.384547i) q^{10} +2.88497 q^{11} -1.00000i q^{12} +(4.03244 - 2.32813i) q^{13} +(1.25902 - 2.18069i) q^{14} +(2.20275 + 0.384547i) 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} +(3.81928 - 3.22694i) 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} +(1.93474 + 5.28768i) q^{35} +(-0.500000 + 0.866025i) q^{36} -3.26480i q^{37} +(2.84303 + 3.30411i) q^{38} -4.65626 q^{39} +(-0.768349 - 2.09991i) 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} +(-6.05819 + 2.21666i) q^{55} +2.51805 q^{56} +(-2.84303 - 3.30411i) q^{57} +4.41917i q^{58} +(4.73274 - 8.19734i) q^{59} +(0.768349 + 2.09991i) 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} +(-0.968307 + 5.54663i) 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} +(0.384547 - 2.20275i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.76596 - 4.48368i) q^{82} -7.14523i q^{83} -2.51805 q^{84} +(-16.0536 - 2.80257i) q^{85} +(-3.37689 - 5.84894i) q^{86} -4.41917i q^{87} +2.88497i q^{88} +(2.37111 + 4.10688i) q^{89} +(-0.768349 - 2.09991i) q^{90} +(-5.86233 - 10.1539i) q^{91} +(-1.48237 - 0.855848i) q^{92} +(7.98528 + 4.61030i) q^{93} +4.59667 q^{94} +(-9.74583 + 0.137412i) 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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