LMFDB - Embedded newform 546.2.bi.e.257.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.10
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.e.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.787258 - 1.54280i) q^{3} +1.00000 q^{4} +(-3.27919 - 1.89324i) q^{5} +(-0.787258 + 1.54280i) q^{6} +(0.475130 + 2.60274i) q^{7} -1.00000 q^{8} +(-1.76045 - 2.42916i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.787258 - 1.54280i) q^{3} +1.00000 q^{4} +(-3.27919 - 1.89324i) q^{5} +(-0.787258 + 1.54280i) q^{6} +(0.475130 + 2.60274i) q^{7} -1.00000 q^{8} +(-1.76045 - 2.42916i) q^{9} +(3.27919 + 1.89324i) q^{10} +(-2.90419 + 5.03020i) q^{11} +(0.787258 - 1.54280i) q^{12} +(-0.879475 + 3.49664i) q^{13} +(-0.475130 - 2.60274i) q^{14} +(-5.50246 + 3.56866i) q^{15} +1.00000 q^{16} +4.53944 q^{17} +(1.76045 + 2.42916i) q^{18} +(-1.42838 - 2.47403i) q^{19} +(-3.27919 - 1.89324i) q^{20} +(4.38955 + 1.31600i) q^{21} +(2.90419 - 5.03020i) q^{22} +4.84897i q^{23} +(-0.787258 + 1.54280i) q^{24} +(4.66874 + 8.08650i) q^{25} +(0.879475 - 3.49664i) q^{26} +(-5.13363 + 0.803642i) q^{27} +(0.475130 + 2.60274i) q^{28} +(2.20269 - 1.27172i) q^{29} +(5.50246 - 3.56866i) q^{30} +(-0.824954 - 1.42886i) q^{31} -1.00000 q^{32} +(5.47423 + 8.44064i) q^{33} -4.53944 q^{34} +(3.36958 - 9.43442i) q^{35} +(-1.76045 - 2.42916i) q^{36} +0.999410i q^{37} +(1.42838 + 2.47403i) q^{38} +(4.70224 + 4.10961i) q^{39} +(3.27919 + 1.89324i) q^{40} +(3.48711 - 2.01328i) q^{41} +(-4.38955 - 1.31600i) q^{42} +(-0.445979 + 0.772459i) q^{43} +(-2.90419 + 5.03020i) q^{44} +(1.17386 + 11.2986i) q^{45} -4.84897i q^{46} +(-6.23486 - 3.59970i) q^{47} +(0.787258 - 1.54280i) q^{48} +(-6.54850 + 2.47328i) q^{49} +(-4.66874 - 8.08650i) q^{50} +(3.57371 - 7.00344i) q^{51} +(-0.879475 + 3.49664i) q^{52} +(-5.41458 + 3.12611i) q^{53} +(5.13363 - 0.803642i) q^{54} +(19.0468 - 10.9967i) q^{55} +(-0.475130 - 2.60274i) q^{56} +(-4.94143 + 0.256004i) q^{57} +(-2.20269 + 1.27172i) q^{58} +10.0175i q^{59} +(-5.50246 + 3.56866i) q^{60} +(-3.15624 + 1.82226i) q^{61} +(0.824954 + 1.42886i) q^{62} +(5.48603 - 5.73616i) q^{63} +1.00000 q^{64} +(9.50397 - 9.80111i) q^{65} +(-5.47423 - 8.44064i) q^{66} +(-9.24567 - 5.33799i) q^{67} +4.53944 q^{68} +(7.48098 + 3.81739i) q^{69} +(-3.36958 + 9.43442i) q^{70} +(-6.77969 + 11.7428i) q^{71} +(1.76045 + 2.42916i) q^{72} +(2.19097 + 3.79486i) q^{73} -0.999410i q^{74} +(16.1513 - 0.836763i) q^{75} +(-1.42838 - 2.47403i) q^{76} +(-14.4722 - 5.16884i) q^{77} +(-4.70224 - 4.10961i) q^{78} +(-8.40177 + 14.5523i) q^{79} +(-3.27919 - 1.89324i) q^{80} +(-2.80163 + 8.55283i) q^{81} +(-3.48711 + 2.01328i) q^{82} +11.9716i q^{83} +(4.38955 + 1.31600i) q^{84} +(-14.8857 - 8.59427i) q^{85} +(0.445979 - 0.772459i) q^{86} +(-0.227927 - 4.39948i) q^{87} +(2.90419 - 5.03020i) q^{88} -2.18827i q^{89} +(-1.17386 - 11.2986i) q^{90} +(-9.51872 - 0.627686i) q^{91} +4.84897i q^{92} +(-2.85390 + 0.147854i) q^{93} +(6.23486 + 3.59970i) q^{94} +10.8171i q^{95} +(-0.787258 + 1.54280i) q^{96} +(6.30970 - 10.9287i) q^{97} +(6.54850 - 2.47328i) q^{98} +(17.3318 - 1.80068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.787258	−	1.54280i	0.454524	−	0.890735i
$3$	0.787258	−	1.54280i	0.454524	−	0.890735i
$4$	1.00000			0.500000
$5$	−3.27919	−	1.89324i	−1.46650	−	0.846684i	−0.467202	−	0.884151i	$-0.654738\pi$
$5$	−3.27919	−	1.89324i	−1.46650	−	0.846684i	−0.999298	+	0.0374664i	$0.988071\pi$
$6$	−0.787258	+	1.54280i	−0.321397	+	0.629845i
$7$	0.475130	+	2.60274i	0.179582	+	0.983743i
$7$	0.475130	+	2.60274i	0.179582	+	0.983743i
$8$	−1.00000			−0.353553
$9$	−1.76045	−	2.42916i	−0.586817	−	0.809720i
$10$	3.27919	+	1.89324i	1.03697	+	0.598696i
$11$	−2.90419	+	5.03020i	−0.875645	+	1.51666i	−0.0195712	+	0.999808i	$0.506230\pi$
$11$	−2.90419	+	5.03020i	−0.875645	+	1.51666i	−0.856074	+	0.516853i	$0.827103\pi$
$12$	0.787258	−	1.54280i	0.227262	−	0.445367i
$13$	−0.879475	+	3.49664i	−0.243923	+	0.969795i
$13$	−0.879475	+	3.49664i	−0.243923	+	0.969795i
$14$	−0.475130	−	2.60274i	−0.126984	−	0.695611i
$15$	−5.50246	+	3.56866i	−1.42073	+	0.921424i
$16$	1.00000			0.250000
$17$	4.53944			1.10098			0.550488	−	0.834843i	$-0.314442\pi$
$17$	4.53944			1.10098			0.550488	+	0.834843i	$0.314442\pi$
$18$	1.76045	+	2.42916i	0.414942	+	0.572558i
$19$	−1.42838	−	2.47403i	−0.327693	−	0.567582i	0.654360	−	0.756183i	$-0.272938\pi$
$19$	−1.42838	−	2.47403i	−0.327693	−	0.567582i	−0.982054	+	0.188601i	$0.939605\pi$
$20$	−3.27919	−	1.89324i	−0.733250	−	0.423342i
$21$	4.38955	+	1.31600i	0.957878	+	0.287174i
$22$	2.90419	−	5.03020i	0.619175	−	1.07244i
$23$			4.84897i			1.01108i	0.862803	+	0.505540i	$0.168707\pi$
$23$			4.84897i			1.01108i	−0.862803	+	0.505540i	$0.831293\pi$
$24$	−0.787258	+	1.54280i	−0.160698	+	0.314922i
$25$	4.66874	+	8.08650i	0.933748	+	1.61730i
$26$	0.879475	−	3.49664i	0.172479	−	0.685748i
$27$	−5.13363	+	0.803642i	−0.987968	+	0.154661i
$28$	0.475130	+	2.60274i	0.0897911	+	0.491871i
$29$	2.20269	−	1.27172i	0.409029	−	0.236153i	−0.281344	−	0.959607i	$-0.590780\pi$
$29$	2.20269	−	1.27172i	0.409029	−	0.236153i	0.690372	+	0.723454i	$0.257447\pi$
$30$	5.50246	−	3.56866i	1.00461	−	0.651545i
$31$	−0.824954	−	1.42886i	−0.148166	−	0.256631i	0.782384	−	0.622797i	$-0.214004\pi$
$31$	−0.824954	−	1.42886i	−0.148166	−	0.256631i	−0.930550	+	0.366166i	$0.880670\pi$
$32$	−1.00000			−0.176777
$33$	5.47423	+	8.44064i	0.952942	+	1.46933i
$34$	−4.53944			−0.778508
$35$	3.36958	−	9.43442i	0.569562	−	1.59471i
$36$	−1.76045	−	2.42916i	−0.293408	−	0.404860i
$37$			0.999410i			0.164302i	0.996620	+	0.0821510i	$0.0261790\pi$
$37$			0.999410i			0.164302i	−0.996620	+	0.0821510i	$0.973821\pi$
$38$	1.42838	+	2.47403i	0.231714	+	0.401341i
$39$	4.70224	+	4.10961i	0.752961	+	0.658065i
$40$	3.27919	+	1.89324i	0.518486	+	0.299348i
$41$	3.48711	−	2.01328i	0.544595	−	0.314422i	−0.202344	−	0.979314i	$-0.564856\pi$
$41$	3.48711	−	2.01328i	0.544595	−	0.314422i	0.746939	+	0.664893i	$0.231523\pi$
$42$	−4.38955	−	1.31600i	−0.677322	−	0.203063i
$43$	−0.445979	+	0.772459i	−0.0680112	+	0.117799i	−0.898026	−	0.439943i	$-0.854999\pi$
$43$	−0.445979	+	0.772459i	−0.0680112	+	0.117799i	0.830015	+	0.557742i	$0.188332\pi$
$44$	−2.90419	+	5.03020i	−0.437823	+	0.758331i
$45$	1.17386	+	11.2986i	0.174989	+	1.68430i
$46$		−	4.84897i		−	0.714941i
$47$	−6.23486	−	3.59970i	−0.909448	−	0.525070i	−0.0291943	−	0.999574i	$-0.509294\pi$
$47$	−6.23486	−	3.59970i	−0.909448	−	0.525070i	−0.880253	+	0.474504i	$0.842627\pi$
$48$	0.787258	−	1.54280i	0.113631	−	0.222684i
$49$	−6.54850	+	2.47328i	−0.935501	+	0.353325i
$50$	−4.66874	−	8.08650i	−0.660260	−	1.14360i
$51$	3.57371	−	7.00344i	0.500420	−	0.980678i
$52$	−0.879475	+	3.49664i	−0.121961	+	0.484897i
$53$	−5.41458	+	3.12611i	−0.743749	+	0.429404i	−0.823431	−	0.567417i	$-0.807943\pi$
$53$	−5.41458	+	3.12611i	−0.743749	+	0.429404i	0.0796817	+	0.996820i	$0.474610\pi$
$54$	5.13363	−	0.803642i	0.698599	−	0.109362i
$55$	19.0468	−	10.9967i	2.56827	−	1.48279i
$56$	−0.475130	−	2.60274i	−0.0634919	−	0.347806i
$57$	−4.94143	+	0.256004i	−0.654509	+	0.0339086i
$58$	−2.20269	+	1.27172i	−0.289227	+	0.166985i
$59$			10.0175i			1.30417i	0.758144	+	0.652087i	$0.226106\pi$
$59$			10.0175i			1.30417i	−0.758144	+	0.652087i	$0.773894\pi$
$60$	−5.50246	+	3.56866i	−0.710365	+	0.460712i
$61$	−3.15624	+	1.82226i	−0.404115	+	0.233316i	−0.688258	−	0.725466i	$-0.741624\pi$
$61$	−3.15624	+	1.82226i	−0.404115	+	0.233316i	0.284143	+	0.958782i	$0.408291\pi$
$62$	0.824954	+	1.42886i	0.104769	+	0.181466i
$63$	5.48603	−	5.73616i	0.691175	−	0.722688i
$64$	1.00000			0.125000
$65$	9.50397	−	9.80111i	1.17882	−	1.21568i
$66$	−5.47423	−	8.44064i	−0.673832	−	1.03897i
$67$	−9.24567	−	5.33799i	−1.12954	−	0.652139i	−0.185720	−	0.982603i	$-0.559462\pi$
$67$	−9.24567	−	5.33799i	−1.12954	−	0.652139i	−0.943819	+	0.330464i	$0.892795\pi$
$68$	4.53944			0.550488
$69$	7.48098	+	3.81739i	0.900604	+	0.459560i
$70$	−3.36958	+	9.43442i	−0.402741	+	1.12763i
$71$	−6.77969	+	11.7428i	−0.804602	+	1.39361i	0.111958	+	0.993713i	$0.464288\pi$
$71$	−6.77969	+	11.7428i	−0.804602	+	1.39361i	−0.916560	+	0.399898i	$0.869046\pi$
$72$	1.76045	+	2.42916i	0.207471	+	0.286279i
$73$	2.19097	+	3.79486i	0.256433	+	0.444155i	0.965284	−	0.261203i	$-0.0841193\pi$
$73$	2.19097	+	3.79486i	0.256433	+	0.444155i	−0.708851	+	0.705359i	$0.750786\pi$
$74$		−	0.999410i		−	0.116179i
$75$	16.1513	−	0.836763i	1.86500	−	0.0966211i
$76$	−1.42838	−	2.47403i	−0.163847	−	0.283791i
$77$	−14.4722	−	5.16884i	−1.64926	−	0.589044i
$78$	−4.70224	−	4.10961i	−0.532424	−	0.465322i
$79$	−8.40177	+	14.5523i	−0.945273	+	1.63726i	−0.190071	+	0.981770i	$0.560872\pi$
$79$	−8.40177	+	14.5523i	−0.945273	+	1.63726i	−0.755203	+	0.655491i	$0.772462\pi$
$80$	−3.27919	−	1.89324i	−0.366625	−	0.211671i
$81$	−2.80163	+	8.55283i	−0.311293	+	0.950314i
$82$	−3.48711	+	2.01328i	−0.385087	+	0.222330i
$83$			11.9716i			1.31405i	0.753867	+	0.657027i	$0.228186\pi$
$83$			11.9716i			1.31405i	−0.753867	+	0.657027i	$0.771814\pi$
$84$	4.38955	+	1.31600i	0.478939	+	0.143587i
$85$	−14.8857	−	8.59427i	−1.61458	−	0.932180i
$86$	0.445979	−	0.772459i	0.0480912	−	0.0832963i
$87$	−0.227927	−	4.39948i	−0.0244363	−	0.471673i
$88$	2.90419	−	5.03020i	0.309587	−	0.536221i
$89$		−	2.18827i		−	0.231956i	−0.993252	−	0.115978i	$-0.963000\pi$
$89$		−	2.18827i		−	0.231956i	0.993252	−	0.115978i	$-0.0370003\pi$
$90$	−1.17386	−	11.2986i	−0.123736	−	1.19098i
$91$	−9.51872	−	0.627686i	−0.997833	−	0.0657994i
$92$			4.84897i			0.505540i
$93$	−2.85390	+	0.147854i	−0.295935	+	0.0153317i
$94$	6.23486	+	3.59970i	0.643077	+	0.371280i
$95$			10.8171i			1.10981i
$96$	−0.787258	+	1.54280i	−0.0803492	+	0.157461i
$97$	6.30970	−	10.9287i	0.640653	−	1.10964i	−0.344634	−	0.938737i	$-0.611997\pi$
$97$	6.30970	−	10.9287i	0.640653	−	1.10964i	0.985287	−	0.170907i	$-0.0546697\pi$
$98$	6.54850	−	2.47328i	0.661499	−	0.249839i
$99$	17.3318	−	1.80068i	1.74191	−	0.180975i
$100$	4.66874	+	8.08650i	0.466874	+	0.808650i
$101$	−4.84579	+	8.39315i	−0.482174	+	0.835150i	−0.999791	−	0.0204629i	$-0.993486\pi$
$101$	−4.84579	+	8.39315i	−0.482174	+	0.835150i	0.517617	+	0.855613i	$0.326819\pi$
$102$	−3.57371	+	7.00344i	−0.353850	+	0.693444i
$103$	2.94432	+	1.69990i	0.290112	+	0.167496i	0.637992	−	0.770043i	$-0.279765\pi$
$103$	2.94432	+	1.69990i	0.290112	+	0.167496i	−0.347880	+	0.937539i	$0.613098\pi$
$104$	0.879475	−	3.49664i	0.0862397	−	0.342874i
$105$	−11.9027	−	12.6259i	−1.16158	−	1.23216i
$106$	5.41458	−	3.12611i	0.525910	−	0.303634i
$107$		−	8.84801i		−	0.855369i	−0.903928	−	0.427684i	$-0.859329\pi$
$107$		−	8.84801i		−	0.855369i	0.903928	−	0.427684i	$-0.140671\pi$
$108$	−5.13363	+	0.803642i	−0.493984	+	0.0773305i
$109$	2.56093	−	1.47855i	0.245292	−	0.141620i	−0.372314	−	0.928107i	$-0.621436\pi$
$109$	2.56093	−	1.47855i	0.245292	−	0.141620i	0.617607	+	0.786487i	$0.288102\pi$
$110$	−19.0468	+	10.9967i	−1.81604	+	1.04849i
$111$	1.54189	+	0.786794i	0.146349	+	0.0746791i
$112$	0.475130	+	2.60274i	0.0448955	+	0.245936i
$113$	−8.71628	−	5.03235i	−0.819959	−	0.473403i	0.0304434	−	0.999536i	$-0.490308\pi$
$113$	−8.71628	−	5.03235i	−0.819959	−	0.473403i	−0.850402	+	0.526133i	$0.823641\pi$
$114$	4.94143	−	0.256004i	0.462808	−	0.0239770i
$115$	9.18028	−	15.9007i	0.856065	−	1.48275i
$116$	2.20269	−	1.27172i	0.204514	−	0.118076i
$117$	10.0422	−	4.01928i	0.928400	−	0.371583i
$118$		−	10.0175i		−	0.922190i
$119$	2.15682	+	11.8150i	0.197716	+	1.08308i
$120$	5.50246	−	3.56866i	0.502304	−	0.325773i
$121$	−11.3686	−	19.6910i	−1.03351	−	1.79009i
$122$	3.15624	−	1.82226i	0.285753	−	0.164979i
$123$	−0.360834	−	6.96487i	−0.0325353	−	0.628002i
$124$	−0.824954	−	1.42886i	−0.0740830	−	0.128316i
$125$		−	16.4238i		−	1.46899i
$126$	−5.48603	+	5.73616i	−0.488734	+	0.511017i
$127$	−0.534780	−	0.926266i	−0.0474540	−	0.0821928i	0.841323	−	0.540533i	$-0.181777\pi$
$127$	−0.534780	−	0.926266i	−0.0474540	−	0.0821928i	−0.888777	+	0.458340i	$0.848444\pi$
$128$	−1.00000			−0.0883883
$129$	0.840647	+	1.29618i	0.0740148	+	0.114122i
$130$	−9.50397	+	9.80111i	−0.833553	+	0.859615i
$131$	6.27140	−	10.8624i	0.547935	−	0.949051i	−0.450481	−	0.892786i	$-0.648747\pi$
$131$	6.27140	−	10.8624i	0.547935	−	0.949051i	0.998416	−	0.0562650i	$-0.0179192\pi$
$132$	5.47423	+	8.44064i	0.476471	+	0.734663i
$133$	5.76059	−	4.89319i	0.499507	−	0.424294i
$134$	9.24567	+	5.33799i	0.798704	+	0.461132i
$135$	18.3557	+	7.08391i	1.57980	+	0.609686i
$136$	−4.53944			−0.389254
$137$	15.5523			1.32872			0.664360	−	0.747413i	$-0.268704\pi$
$137$	15.5523			1.32872			0.664360	+	0.747413i	$0.268704\pi$
$138$	−7.48098	−	3.81739i	−0.636823	−	0.324958i
$139$	−7.60046	−	4.38812i	−0.644662	−	0.372196i	0.141746	−	0.989903i	$-0.454728\pi$
$139$	−7.60046	−	4.38812i	−0.644662	−	0.372196i	−0.786408	+	0.617707i	$0.788062\pi$
$140$	3.36958	−	9.43442i	0.284781	−	0.797354i
$141$	−10.4620	+	6.78524i	−0.881063	+	0.571420i
$142$	6.77969	−	11.7428i	0.568939	−	0.985432i
$143$	−15.0347	−	14.5788i	−1.25726	−	1.21914i
$144$	−1.76045	−	2.42916i	−0.146704	−	0.202430i
$145$	−9.63072			−0.799788
$146$	−2.19097	−	3.79486i	−0.181326	−	0.314065i
$147$	−1.33960	+	12.0501i	−0.110488	+	0.993877i
$148$			0.999410i			0.0821510i
$149$	−1.53689	−	2.66197i	−0.125907	−	0.218077i	0.796180	−	0.605060i	$-0.206851\pi$
$149$	−1.53689	−	2.66197i	−0.125907	−	0.218077i	−0.922087	+	0.386982i	$0.873517\pi$
$150$	−16.1513	+	0.836763i	−1.31875	+	0.0683214i
$151$	10.9434	−	6.31820i	0.890564	−	0.514167i	0.0164372	−	0.999865i	$-0.494768\pi$
$151$	10.9434	−	6.31820i	0.890564	−	0.514167i	0.874127	+	0.485697i	$0.161434\pi$
$152$	1.42838	+	2.47403i	0.115857	+	0.200670i
$153$	−7.99146	−	11.0270i	−0.646071	−	0.891483i
$154$	14.4722	+	5.16884i	1.16620	+	0.416517i
$155$			6.24735i			0.501799i
$156$	4.70224	+	4.10961i	0.376481	+	0.329032i
$157$	8.31434	−	4.80029i	0.663556	−	0.383104i	−0.130074	−	0.991504i	$-0.541522\pi$
$157$	8.31434	−	4.80029i	0.663556	−	0.383104i	0.793631	+	0.608400i	$0.208188\pi$
$158$	8.40177	−	14.5523i	0.668409	−	1.15772i
$159$	0.560282	+	10.8146i	0.0444333	+	0.857657i
$160$	3.27919	+	1.89324i	0.259243	+	0.149674i
$161$	−12.6206	+	2.30389i	−0.994643	+	0.181572i
$162$	2.80163	−	8.55283i	0.220117	−	0.671974i
$163$	5.52266	−	3.18851i	0.432568	−	0.249743i	−0.267872	−	0.963454i	$-0.586320\pi$
$163$	5.52266	−	3.18851i	0.432568	−	0.249743i	0.700440	+	0.713711i	$0.252987\pi$
$164$	3.48711	−	2.01328i	0.272297	−	0.157211i
$165$	−1.97090	−	38.0425i	−0.153434	−	2.96161i
$166$		−	11.9716i		−	0.929177i
$167$	6.39087	−	3.68977i	0.494540	−	0.285523i	−0.231916	−	0.972736i	$-0.574499\pi$
$167$	6.39087	−	3.68977i	0.494540	−	0.285523i	0.726456	+	0.687213i	$0.241166\pi$
$168$	−4.38955	−	1.31600i	−0.338661	−	0.101531i
$169$	−11.4530	−	6.15043i	−0.881004	−	0.473110i
$170$	14.8857	+	8.59427i	1.14168	+	0.659151i
$171$	−3.49522	+	7.82518i	−0.267286	+	0.598406i
$172$	−0.445979	+	0.772459i	−0.0340056	+	0.0588994i
$173$	−2.54914	−	4.41523i	−0.193807	−	0.335684i	0.752702	−	0.658362i	$-0.228750\pi$
$173$	−2.54914	−	4.41523i	−0.193807	−	0.335684i	−0.946509	+	0.322678i	$0.895417\pi$
$174$	0.227927	+	4.39948i	0.0172791	+	0.333523i
$175$	−18.8288	+	15.9936i	−1.42332	+	1.20901i
$176$	−2.90419	+	5.03020i	−0.218911	+	0.379165i
$177$	15.4550	+	7.88639i	1.16167	+	0.592778i
$178$			2.18827i			0.164018i
$179$	−7.44227	−	4.29680i	−0.556261	−	0.321158i	0.195382	−	0.980727i	$-0.437405\pi$
$179$	−7.44227	−	4.29680i	−0.556261	−	0.321158i	−0.751643	+	0.659570i	$0.770739\pi$
$180$	1.17386	+	11.2986i	0.0874947	+	0.842151i
$181$		−	2.78775i		−	0.207211i	−0.994618	−	0.103606i	$-0.966962\pi$
$181$		−	2.78775i		−	0.207211i	0.994618	−	0.103606i	$-0.0330380\pi$
$182$	9.51872	+	0.627686i	0.705574	+	0.0465272i
$183$	0.326597	+	6.30402i	0.0241427	+	0.466007i
$184$		−	4.84897i		−	0.357471i
$185$	1.89213	−	3.27726i	0.139112	−	0.240949i
$186$	2.85390	−	0.147854i	0.209258	−	0.0108412i
$187$	−13.1834	+	22.8343i	−0.964065	+	1.66981i
$188$	−6.23486	−	3.59970i	−0.454724	−	0.262535i
$189$	−4.53081	−	12.9797i	−0.329568	−	0.944132i
$190$		−	10.8171i		−	0.784755i
$191$	−16.9062	+	9.76080i	−1.22329	+	0.706267i	−0.965618	−	0.259966i	$-0.916289\pi$
$191$	−16.9062	+	9.76080i	−1.22329	+	0.706267i	−0.257672	+	0.966232i	$0.582955\pi$
$192$	0.787258	−	1.54280i	0.0568155	−	0.111342i
$193$	5.49481	+	3.17243i	0.395525	+	0.228357i	0.684551	−	0.728965i	$-0.259998\pi$
$193$	5.49481	+	3.17243i	0.395525	+	0.228357i	−0.289026	+	0.957321i	$0.593331\pi$
$194$	−6.30970	+	10.9287i	−0.453010	+	0.784637i
$195$	−7.63906	−	22.3787i	−0.547044	−	1.60257i
$196$	−6.54850	+	2.47328i	−0.467750	+	0.176663i
$197$	−4.25750	−	7.37421i	−0.303334	−	0.525391i	0.673555	−	0.739137i	$-0.264767\pi$
$197$	−4.25750	−	7.37421i	−0.303334	−	0.525391i	−0.976889	+	0.213747i	$0.931433\pi$
$198$	−17.3318	+	1.80068i	−1.23172	+	0.127969i
$199$			1.69156i			0.119912i	0.998201	+	0.0599559i	$0.0190960\pi$
$199$			1.69156i			0.119912i	−0.998201	+	0.0599559i	$0.980904\pi$
$200$	−4.66874	−	8.08650i	−0.330130	−	0.571802i
$201$	−15.5142	+	10.0618i	−1.09428	+	0.709706i
$202$	4.84579	−	8.39315i	0.340948	−	0.590540i
$203$	4.35652	+	5.12879i	0.305768	+	0.359970i
$204$	3.57371	−	7.00344i	0.250210	−	0.490339i
$205$	−15.2465			−1.06486
$206$	−2.94432	−	1.69990i	−0.205140	−	0.118438i
$207$	11.7789	−	8.53636i	0.818691	−	0.593318i
$208$	−0.879475	+	3.49664i	−0.0609807	+	0.242449i
$209$	16.5932			1.14777
$210$	11.9027	+	12.6259i	0.821363	+	0.871270i
$211$	11.5387	+	19.9857i	0.794360	+	1.37587i	0.923245	+	0.384213i	$0.125527\pi$
$211$	11.5387	+	19.9857i	0.794360	+	1.37587i	−0.128885	+	0.991660i	$0.541140\pi$
$212$	−5.41458	+	3.12611i	−0.371875	+	0.214702i
$213$	12.7794	+	19.7043i	0.875627	+	1.35012i
$214$			8.84801i			0.604837i
$215$	2.92490	−	1.68869i	0.199477	−	0.115168i
$216$	5.13363	−	0.803642i	0.349299	−	0.0546809i
$217$	3.32699	−	2.82603i	0.225851	−	0.191844i
$218$	−2.56093	+	1.47855i	−0.173448	+	0.100140i
$219$	7.57956	−	0.392680i	0.512179	−	0.0265348i
$220$	19.0468	−	10.9967i	1.28413	−	0.741395i
$221$	−3.99233	+	15.8728i	−0.268553	+	1.06772i
$222$	−1.54189	−	0.786794i	−0.103485	−	0.0528061i
$223$	8.68120	+	15.0363i	0.581336	+	1.00690i	0.995321	+	0.0966199i	$0.0308031\pi$
$223$	8.68120	+	15.0363i	0.581336	+	1.00690i	−0.413985	+	0.910284i	$0.635864\pi$
$224$	−0.475130	−	2.60274i	−0.0317459	−	0.173903i
$225$	11.4243	−	25.5770i	0.761621	−	1.70513i
$226$	8.71628	+	5.03235i	0.579798	+	0.334747i
$227$		−	19.1522i		−	1.27118i	−0.772027	−	0.635589i	$-0.780757\pi$
$227$		−	19.1522i		−	1.27118i	0.772027	−	0.635589i	$-0.219243\pi$
$228$	−4.94143	+	0.256004i	−0.327254	+	0.0169543i
$229$	−8.79153	+	15.2274i	−0.580960	+	1.00625i	0.414405	+	0.910092i	$0.363990\pi$
$229$	−8.79153	+	15.2274i	−0.580960	+	1.00625i	−0.995366	+	0.0961607i	$0.969344\pi$
$230$	−9.18028	+	15.9007i	−0.605330	+	1.04846i
$231$	−19.3678	+	18.2584i	−1.27431	+	1.20131i
$232$	−2.20269	+	1.27172i	−0.144614	+	0.0834927i
$233$	−1.22176	−	0.705386i	−0.0800405	−	0.0462114i	0.459446	−	0.888206i	$-0.348048\pi$
$233$	−1.22176	−	0.705386i	−0.0800405	−	0.0462114i	−0.539486	+	0.841995i	$0.681381\pi$
$234$	−10.0422	+	4.01928i	−0.656478	+	0.262749i
$235$	13.6302	+	23.6082i	0.889137	+	1.54003i
$236$			10.0175i			0.652087i
$237$	15.8369	+	24.4187i	1.02872	+	1.58616i
$238$	−2.15682	−	11.8150i	−0.139806	−	0.765852i
$239$	22.2321			1.43807			0.719037	−	0.694972i	$-0.244583\pi$
$239$	22.2321			1.43807			0.719037	+	0.694972i	$0.244583\pi$
$240$	−5.50246	+	3.56866i	−0.355182	+	0.230356i
$241$	12.1874			0.785057			0.392528	−	0.919740i	$-0.371600\pi$
$241$	12.1874			0.785057			0.392528	+	0.919740i	$0.371600\pi$
$242$	11.3686	+	19.6910i	0.730801	+	1.26578i
$243$	10.9897	+	11.0556i	0.704988	+	0.709219i
$244$	−3.15624	+	1.82226i	−0.202058	+	0.116658i
$245$	26.1563	+	4.28756i	1.67107	+	0.273922i
$246$	0.360834	+	6.96487i	0.0230059	+	0.444064i
$247$	9.90703	−	2.81870i	0.630369	−	0.179349i
$248$	0.824954	+	1.42886i	0.0523846	+	0.0907328i
$249$	18.4698	+	9.42475i	1.17047	+	0.597269i
$250$			16.4238i			1.03873i
$251$	4.15920	−	7.20395i	0.262527	−	0.454709i	−0.704386	−	0.709817i	$-0.748778\pi$
$251$	4.15920	−	7.20395i	0.262527	−	0.454709i	0.966913	+	0.255108i	$0.0821109\pi$
$252$	5.48603	−	5.73616i	0.345587	−	0.361344i
$253$	−24.3913	−	14.0823i	−1.53347	−	0.885347i
$254$	0.534780	+	0.926266i	0.0335551	+	0.0581191i
$255$	−24.9781	+	16.1997i	−1.56419	+	1.01447i
$256$	1.00000			0.0625000
$257$	22.0410			1.37488			0.687438	−	0.726243i	$-0.258735\pi$
$257$	22.0410			1.37488			0.687438	+	0.726243i	$0.258735\pi$
$258$	−0.840647	−	1.29618i	−0.0523364	−	0.0806966i
$259$	−2.60120	+	0.474849i	−0.161631	+	0.0295057i
$260$	9.50397	−	9.80111i	0.589411	−	0.607839i
$261$	−6.96694	−	3.11188i	−0.431243	−	0.192620i
$262$	−6.27140	+	10.8624i	−0.387448	+	0.671080i
$263$	14.9822	+	8.64996i	0.923840	+	0.533379i	0.884858	−	0.465861i	$-0.154255\pi$
$263$	14.9822	+	8.64996i	0.923840	+	0.533379i	0.0389820	+	0.999240i	$0.487588\pi$
$264$	−5.47423	−	8.44064i	−0.336916	−	0.519485i
$265$	23.6739			1.45428
$266$	−5.76059	+	4.89319i	−0.353204	+	0.300021i
$267$	−3.37606	−	1.72273i	−0.206611	−	0.105430i
$268$	−9.24567	−	5.33799i	−0.564769	−	0.326070i
$269$	7.57009			0.461557			0.230778	−	0.973006i	$-0.425873\pi$
$269$	7.57009			0.461557			0.230778	+	0.973006i	$0.425873\pi$
$270$	−18.3557	−	7.08391i	−1.11709	−	0.431113i
$271$	−2.07387			−0.125979			−0.0629893	−	0.998014i	$-0.520063\pi$
$271$	−2.07387			−0.125979			−0.0629893	+	0.998014i	$0.520063\pi$
$272$	4.53944			0.275244
$273$	−8.46208	+	14.1913i	−0.512148	+	0.858897i
$274$	−15.5523			−0.939547
$275$	−54.2356			−3.27053
$276$	7.48098	+	3.81739i	0.450302	+	0.229780i
$277$	−23.6718			−1.42230			−0.711150	−	0.703040i	$-0.751825\pi$
$277$	−23.6718			−1.42230			−0.711150	+	0.703040i	$0.751825\pi$
$278$	7.60046	+	4.38812i	0.455845	+	0.263182i
$279$	−2.01864	+	4.51938i	−0.120853	+	0.270568i
$280$	−3.36958	+	9.43442i	−0.201371	+	0.563815i
$281$	−25.8285			−1.54080			−0.770400	−	0.637561i	$-0.779944\pi$
$281$	−25.8285			−1.54080			−0.770400	+	0.637561i	$0.779944\pi$
$282$	10.4620	−	6.78524i	0.623006	−	0.404055i
$283$	−14.5695	−	8.41173i	−0.866070	−	0.500026i	−2.94496e−5	−	1.00000i	$-0.500009\pi$
$283$	−14.5695	−	8.41173i	−0.866070	−	0.500026i	−0.866040	+	0.499974i	$0.833343\pi$
$284$	−6.77969	+	11.7428i	−0.402301	+	0.696805i
$285$	16.6886	+	8.51585i	0.988547	+	0.504435i
$286$	15.0347	+	14.5788i	0.889018	+	0.862065i
$287$	6.89688	+	8.11946i	0.407110	+	0.479277i
$288$	1.76045	+	2.42916i	0.103735	+	0.143140i
$289$	3.60655			0.212150
$290$	9.63072			0.565535
$291$	−11.8934	−	18.3383i	−0.697206	−	1.07501i
$292$	2.19097	+	3.79486i	0.128217	+	0.222078i
$293$	−23.6154	−	13.6344i	−1.37963	−	0.796529i	−0.387514	−	0.921864i	$-0.626666\pi$
$293$	−23.6154	−	13.6344i	−1.37963	−	0.796529i	−0.992115	+	0.125335i	$0.960000\pi$
$294$	1.33960	−	12.0501i	0.0781268	−	0.702777i
$295$	18.9657	−	32.8495i	1.10422	−	1.91257i
$296$		−	0.999410i		−	0.0580895i
$297$	10.8665	−	28.1571i	0.630541	−	1.63384i
$298$	1.53689	+	2.66197i	0.0890297	+	0.154204i
$299$	−16.9551	−	4.26455i	−0.980540	−	0.246625i
$300$	16.1513	−	0.836763i	0.932498	−	0.0483106i
$301$	−2.22241	−	0.793749i	−0.128097	−	0.0457510i
$302$	−10.9434	+	6.31820i	−0.629724	+	0.363571i
$303$	9.13405	+	14.0836i	0.524737	+	0.809084i
$304$	−1.42838	−	2.47403i	−0.0819233	−	0.141895i
$305$	13.7999			0.790180
$306$	7.99146	+	11.0270i	0.456841	+	0.630374i
$307$	−22.9818			−1.31164			−0.655821	−	0.754917i	$-0.727677\pi$
$307$	−22.9818			−1.31164			−0.655821	+	0.754917i	$0.727677\pi$
$308$	−14.4722	−	5.16884i	−0.824628	−	0.294522i
$309$	4.94054	−	3.20422i	0.281058	−	0.182282i
$310$		−	6.24735i		−	0.354826i
$311$	15.9662	+	27.6543i	0.905360	+	1.56813i	0.820434	+	0.571742i	$0.193732\pi$
$311$	15.9662	+	27.6543i	0.905360	+	1.56813i	0.0849258	+	0.996387i	$0.472935\pi$
$312$	−4.70224	−	4.10961i	−0.266212	−	0.232661i
$313$	−5.32050	−	3.07179i	−0.300732	−	0.173628i	0.342039	−	0.939686i	$-0.388882\pi$
$313$	−5.32050	−	3.07179i	−0.300732	−	0.173628i	−0.642772	+	0.766058i	$0.722216\pi$
$314$	−8.31434	+	4.80029i	−0.469205	+	0.270896i
$315$	−28.8497	+	8.42358i	−1.62550	+	0.474615i
$316$	−8.40177	+	14.5523i	−0.472637	+	0.818631i
$317$	7.01958	−	12.1583i	0.394259	−	0.682877i	−0.598747	−	0.800938i	$-0.704335\pi$
$317$	7.01958	−	12.1583i	0.394259	−	0.682877i	0.993006	+	0.118061i	$0.0376679\pi$
$318$	−0.560282	−	10.8146i	−0.0314191	−	0.606455i
$319$			14.7733i			0.827145i
$320$	−3.27919	−	1.89324i	−0.183313	−	0.105836i
$321$	−13.6507	−	6.96566i	−0.761907	−	0.388785i
$322$	12.6206	−	2.30389i	0.703319	−	0.128391i
$323$	−6.48406	−	11.2307i	−0.360783	−	0.624894i
$324$	−2.80163	+	8.55283i	−0.155646	+	0.475157i
$325$	−32.3816	+	9.21305i	−1.79621	+	0.511048i
$326$	−5.52266	+	3.18851i	−0.305872	+	0.176595i
$327$	−0.264996	−	5.11499i	−0.0146543	−	0.282860i
$328$	−3.48711	+	2.01328i	−0.192543	+	0.111165i
$329$	6.40671	−	17.9380i	0.353213	−	0.988956i
$330$	1.97090	+	38.0425i	0.108494	+	2.09417i
$331$	−7.16125	+	4.13455i	−0.393618	+	0.227256i	−0.683727	−	0.729738i	$-0.739642\pi$
$331$	−7.16125	+	4.13455i	−0.393618	+	0.227256i	0.290108	+	0.956994i	$0.406309\pi$
$332$			11.9716i			0.657027i
$333$	2.42773	−	1.75941i	0.133039	−	0.0964151i
$334$	−6.39087	+	3.68977i	−0.349693	+	0.201895i
$335$	20.2122	+	35.0086i	1.10431	+	1.91272i
$336$	4.38955	+	1.31600i	0.239470	+	0.0717936i
$337$	8.78687			0.478651			0.239326	−	0.970939i	$-0.423074\pi$
$337$	8.78687			0.478651			0.239326	+	0.970939i	$0.423074\pi$
$338$	11.4530	+	6.15043i	0.622964	+	0.334539i
$339$	−14.6259	+	9.48570i	−0.794368	+	0.515193i
$340$	−14.8857	−	8.59427i	−0.807291	−	0.466090i
$341$	9.58328			0.518964
$342$	3.49522	−	7.82518i	0.189000	−	0.423137i
$343$	−9.54868	−	15.8689i	−0.515580	−	0.856841i
$344$	0.445979	−	0.772459i	0.0240456	−	0.0416482i
$345$	−17.3043	−	26.6813i	−0.931634	−	1.43647i
$346$	2.54914	+	4.41523i	0.137042	+	0.237364i
$347$		−	16.4055i		−	0.880693i	−0.897828	−	0.440347i	$-0.854856\pi$
$347$		−	16.4055i		−	0.880693i	0.897828	−	0.440347i	$-0.145144\pi$
$348$	−0.227927	−	4.39948i	−0.0122182	−	0.235837i
$349$	4.38530	+	7.59556i	0.234740	+	0.406581i	0.959197	−	0.282739i	$-0.0912429\pi$
$349$	4.38530	+	7.59556i	0.234740	+	0.406581i	−0.724457	+	0.689320i	$0.757910\pi$
$350$	18.8288	−	15.9936i	1.00644	−	0.854897i
$351$	1.70485	−	18.6573i	0.0909983	−	0.995851i
$352$	2.90419	−	5.03020i	0.154794	−	0.268110i
$353$	16.9161	+	9.76652i	0.900353	+	0.519819i	0.877315	−	0.479915i	$-0.159333\pi$
$353$	16.9161	+	9.76652i	0.900353	+	0.519819i	0.0230385	+	0.999735i	$0.492666\pi$
$354$	−15.4550	−	7.88639i	−0.821427	−	0.419157i
$355$	44.4639	−	25.6712i	2.35990	−	1.36249i
$356$		−	2.18827i		−	0.115978i
$357$	19.9261	+	5.97390i	1.05460	+	0.316172i
$358$	7.44227	+	4.29680i	0.393336	+	0.227093i
$359$	1.54798	−	2.68118i	0.0816994	−	0.141507i	−0.822281	−	0.569082i	$-0.807299\pi$
$359$	1.54798	−	2.68118i	0.0816994	−	0.141507i	0.903980	+	0.427575i	$0.140632\pi$
$360$	−1.17386	−	11.2986i	−0.0618681	−	0.595491i
$361$	5.41945	−	9.38676i	0.285234	−	0.494040i
$362$			2.78775i			0.146521i
$363$	−39.3292	+	2.03756i	−2.06425	+	0.106944i
$364$	−9.51872	−	0.627686i	−0.498916	−	0.0328997i
$365$		−	16.5921i		−	0.868472i
$366$	−0.326597	−	6.30402i	−0.0170715	−	0.329517i
$367$	7.02340	+	4.05496i	0.366619	+	0.211667i	0.671980	−	0.740569i	$-0.265444\pi$
$367$	7.02340	+	4.05496i	0.366619	+	0.211667i	−0.305362	+	0.952236i	$0.598777\pi$
$368$			4.84897i			0.252770i
$369$	−11.0295	−	4.92646i	−0.574171	−	0.256461i
$370$	−1.89213	+	3.27726i	−0.0983670	+	0.170377i
$371$	−10.7091	−	12.6074i	−0.555987	−	0.654545i
$372$	−2.85390	+	0.147854i	−0.147968	+	0.00766586i
$373$	10.1944	+	17.6572i	0.527845	+	0.914255i	0.999473	+	0.0324572i	$0.0103333\pi$
$373$	10.1944	+	17.6572i	0.527845	+	0.914255i	−0.471628	+	0.881798i	$0.656333\pi$
$374$	13.1834	−	22.8343i	0.681697	−	1.18073i
$375$	−25.3386	−	12.9298i	−1.30848	−	0.667691i
$376$	6.23486	+	3.59970i	0.321538	+	0.185640i
$377$	2.50955	+	8.82046i	0.129248	+	0.454277i
$378$	4.53081	+	12.9797i	0.233040	+	0.667602i
$379$	−16.2771	+	9.39758i	−0.836098	+	0.482721i	−0.855936	−	0.517082i	$-0.827018\pi$
$379$	−16.2771	+	9.39758i	−0.836098	+	0.482721i	0.0198382	+	0.999803i	$0.493685\pi$
$380$			10.8171i			0.554906i
$381$	−1.85005	+	0.0958468i	−0.0947809	+	0.00491038i
$382$	16.9062	−	9.76080i	0.864997	−	0.499406i
$383$	21.4155	−	12.3643i	1.09428	−	0.631785i	0.159570	−	0.987187i	$-0.448989\pi$
$383$	21.4155	−	12.3643i	1.09428	−	0.631785i	0.934714	+	0.355402i	$0.115656\pi$
$384$	−0.787258	+	1.54280i	−0.0401746	+	0.0787306i
$385$	37.6711	+	44.3490i	1.91990	+	2.26023i
$386$	−5.49481	−	3.17243i	−0.279679	−	0.161472i
$387$	2.66155	−	0.276520i	0.135294	−	0.0140563i
$388$	6.30970	−	10.9287i	0.320327	−	0.554822i
$389$	−7.93751	+	4.58272i	−0.402448	+	0.232353i	−0.687540	−	0.726147i	$-0.741309\pi$
$389$	−7.93751	+	4.58272i	−0.402448	+	0.232353i	0.285092	+	0.958500i	$0.407976\pi$
$390$	7.63906	+	22.3787i	0.386819	+	1.13319i
$391$			22.0116i			1.11318i
$392$	6.54850	−	2.47328i	0.330749	−	0.124919i
$393$	−11.8213	−	18.2270i	−0.596303	−	0.919431i
$394$	4.25750	+	7.37421i	0.214490	+	0.371507i
$395$	55.1021	−	31.8132i	2.77249	−	1.60070i
$396$	17.3318	−	1.80068i	0.870957	−	0.0904874i
$397$	1.69223	+	2.93103i	0.0849306	+	0.147104i	0.905362	−	0.424641i	$-0.139600\pi$
$397$	1.69223	+	2.93103i	0.0849306	+	0.147104i	−0.820431	+	0.571746i	$0.806266\pi$
$398$		−	1.69156i		−	0.0847905i
$399$	−3.01413	−	12.7396i	−0.150895	−	0.637779i
$400$	4.66874	+	8.08650i	0.233437	+	0.404325i
$401$	7.25130			0.362112			0.181056	−	0.983473i	$-0.442048\pi$
$401$	7.25130			0.362112			0.181056	+	0.983473i	$0.442048\pi$
$402$	15.5142	−	10.0618i	0.773776	−	0.501838i
$403$	5.72175	−	1.62792i	0.285021	−	0.0810925i
$404$	−4.84579	+	8.39315i	−0.241087	+	0.417575i
$405$	25.3797	−	22.7422i	1.26113	−	1.13007i
$406$	−4.35652	−	5.12879i	−0.216211	−	0.254538i
$407$	−5.02723	−	2.90247i	−0.249191	−	0.143870i
$408$	−3.57371	+	7.00344i	−0.176925	+	0.346722i
$409$	1.57460			0.0778592			0.0389296	−	0.999242i	$-0.487605\pi$
$409$	1.57460			0.0778592			0.0389296	+	0.999242i	$0.487605\pi$
$410$	15.2465			0.752973
$411$	12.2437	−	23.9940i	0.603935	−	1.18354i
$412$	2.94432	+	1.69990i	0.145056	+	0.0837482i
$413$	−26.0731	+	4.75963i	−1.28297	+	0.234206i
$414$	−11.7789	+	8.53636i	−0.578902	+	0.419539i
$415$	22.6652	−	39.2572i	1.11259	−	1.92706i
$416$	0.879475	−	3.49664i	0.0431198	−	0.171437i
$417$	−12.7535	+	8.27138i	−0.624542	+	0.405051i
$418$	−16.5932			−0.811598
$419$	13.4922	+	23.3691i	0.659136	+	1.14166i	0.980840	+	0.194817i	$0.0624112\pi$
$419$	13.4922	+	23.3691i	0.659136	+	1.14166i	−0.321704	+	0.946840i	$0.604255\pi$
$420$	−11.9027	−	12.6259i	−0.580791	−	0.616081i
$421$			13.0461i			0.635827i	0.948120	+	0.317913i	$0.102982\pi$
$421$			13.0461i			0.635827i	−0.948120	+	0.317913i	$0.897018\pi$
$422$	−11.5387	−	19.9857i	−0.561697	−	0.972889i
$423$	2.23191	+	21.4826i	0.108519	+	1.04452i
$424$	5.41458	−	3.12611i	0.262955	−	0.151817i
$425$	21.1935	+	36.7082i	1.02804	+	1.78061i
$426$	−12.7794	−	19.7043i	−0.619162	−	0.954676i
$427$	−6.24248	−	7.34906i	−0.302095	−	0.355646i
$428$		−	8.84801i		−	0.427684i
$429$	−34.3284	+	11.7181i	−1.65739	+	0.565756i
$430$	−2.92490	+	1.68869i	−0.141051	+	0.0814361i
$431$	−18.2521	+	31.6136i	−0.879173	+	1.52277i	−0.0269232	+	0.999638i	$0.508571\pi$
$431$	−18.2521	+	31.6136i	−0.879173	+	1.52277i	−0.852250	+	0.523135i	$0.824762\pi$
$432$	−5.13363	+	0.803642i	−0.246992	+	0.0386652i
$433$	−23.6502	−	13.6545i	−1.13656	−	0.656192i	−0.190982	−	0.981594i	$-0.561167\pi$
$433$	−23.6502	−	13.6545i	−1.13656	−	0.656192i	−0.945576	+	0.325402i	$0.894501\pi$
$434$	−3.32699	+	2.82603i	−0.159701	+	0.135654i
$435$	−7.58186	+	14.8583i	−0.363522	+	0.712399i
$436$	2.56093	−	1.47855i	0.122646	−	0.0708098i
$437$	11.9965	−	6.92618i	0.573870	−	0.331324i
$438$	−7.57956	+	0.392680i	−0.362166	+	0.0187630i
$439$			0.455718i			0.0217502i	0.999941	+	0.0108751i	$0.00346172\pi$
$439$			0.455718i			0.0217502i	−0.999941	+	0.0108751i	$0.996538\pi$
$440$	−19.0468	+	10.9967i	−0.908020	+	0.524245i
$441$	17.5363	+	11.5533i	0.835062	+	0.550156i
$442$	3.99233	−	15.8728i	0.189896	−	0.754993i
$443$	23.2231	+	13.4079i	1.10337	+	0.637028i	0.937103	−	0.349053i	$-0.113497\pi$
$443$	23.2231	+	13.4079i	1.10337	+	0.637028i	0.166262	+	0.986082i	$0.446830\pi$
$444$	1.54189	+	0.786794i	0.0731747	+	0.0373396i
$445$	−4.14293	+	7.17576i	−0.196394	+	0.340164i
$446$	−8.68120	−	15.0363i	−0.411067	−	0.711988i
$447$	−5.31681	+	0.275452i	−0.251477	+	0.0130284i
$448$	0.475130	+	2.60274i	0.0224478	+	0.122968i
$449$	0.402024	−	0.696326i	0.0189727	−	0.0328616i	−0.856383	−	0.516341i	$-0.827294\pi$
$449$	0.402024	−	0.696326i	0.0189727	−	0.0328616i	0.875356	+	0.483479i	$0.160627\pi$
$450$	−11.4243	+	25.5770i	−0.538547	+	1.20571i
$451$			23.3878i			1.10129i
$452$	−8.71628	−	5.03235i	−0.409979	−	0.236702i
$453$	−1.13239	−	21.8576i	−0.0532043	−	1.02696i
$454$			19.1522i			0.898859i
$455$	30.0254	+	20.0796i	1.40761	+	0.941344i
$456$	4.94143	−	0.256004i	0.231404	−	0.0119885i
$457$		−	15.2345i		−	0.712641i	−0.934364	−	0.356321i	$-0.884031\pi$
$457$		−	15.2345i		−	0.712641i	0.934364	−	0.356321i	$-0.115969\pi$
$458$	8.79153	−	15.2274i	0.410801	−	0.711528i
$459$	−23.3038	+	3.64809i	−1.08773	+	0.170278i
$460$	9.18028	−	15.9007i	0.428033	−	0.741374i
$461$	11.4420	+	6.60603i	0.532906	+	0.307673i	0.742199	−	0.670180i	$-0.233783\pi$
$461$	11.4420	+	6.60603i	0.532906	+	0.307673i	−0.209293	+	0.977853i	$0.567116\pi$
$462$	19.3678	−	18.2584i	0.901072	−	0.849458i
$463$			15.4572i			0.718355i	0.933269	+	0.359177i	$0.116943\pi$
$463$			15.4572i			0.718355i	−0.933269	+	0.359177i	$0.883057\pi$
$464$	2.20269	−	1.27172i	0.102257	−	0.0590382i
$465$	9.63840	+	4.91828i	0.446970	+	0.228080i
$466$	1.22176	+	0.705386i	0.0565972	+	0.0326764i
$467$	0.665574	−	1.15281i	0.0307991	−	0.0533456i	−0.850215	−	0.526436i	$-0.823528\pi$
$467$	0.665574	−	1.15281i	0.0307991	−	0.0533456i	0.881014	+	0.473090i	$0.156861\pi$
$468$	10.0422	−	4.01928i	0.464200	−	0.185791i
$469$	9.50050	−	26.6003i	0.438693	−	1.22829i
$470$	−13.6302	−	23.6082i	−0.628715	−	1.08897i
$471$	−0.860340	−	16.6064i	−0.0396424	−	0.765183i
$472$		−	10.0175i		−	0.461095i
$473$	−2.59041	−	4.48673i	−0.119107	−	0.206300i
$474$	−15.8369	−	24.4187i	−0.727412	−	1.12159i
$475$	13.3375	−	23.1012i	0.611966	−	1.05996i
$476$	2.15682	+	11.8150i	0.0988579	+	0.541539i
$477$	17.1259	+	7.64952i	0.784141	+	0.350247i
$478$	−22.2321			−1.01687
$479$	12.4718	+	7.20059i	0.569851	+	0.329003i	0.757090	−	0.653311i	$-0.226621\pi$
$479$	12.4718	+	7.20059i	0.569851	+	0.329003i	−0.187239	+	0.982314i	$0.559954\pi$
$480$	5.50246	−	3.56866i	0.251152	−	0.162886i
$481$	−3.49458	−	0.878957i	−0.159339	−	0.0400770i
$482$	−12.1874			−0.555119
$483$	−6.38124	+	21.2848i	−0.290356	+	0.968491i
$484$	−11.3686	−	19.6910i	−0.516754	−	0.895045i
$485$	−41.3815	+	23.8916i	−1.87904	+	1.08486i
$486$	−10.9897	−	11.0556i	−0.498502	−	0.501494i
$487$		−	30.5356i		−	1.38370i	−0.722042	−	0.691849i	$-0.756796\pi$
$487$		−	30.5356i		−	1.38370i	0.722042	−	0.691849i	$-0.243204\pi$
$488$	3.15624	−	1.82226i	0.142876	−	0.0824896i
$489$	−0.571466	−	11.0305i	−0.0258426	−	0.498817i
$490$	−26.1563	−	4.28756i	−1.18162	−	0.193692i
$491$	2.79101	−	1.61139i	0.125957	−	0.0727211i	−0.435698	−	0.900093i	$-0.643498\pi$
$491$	2.79101	−	1.61139i	0.125957	−	0.0727211i	0.561655	+	0.827372i	$0.310165\pi$
$492$	−0.360834	−	6.96487i	−0.0162677	−	0.314001i
$493$	9.99898	−	5.77291i	0.450331	−	0.259999i
$494$	−9.90703	+	2.81870i	−0.445738	+	0.126819i
$495$	−60.2435	−	26.9086i	−2.70775	−	1.20945i
$496$	−0.824954	−	1.42886i	−0.0370415	−	0.0641578i
$497$	−33.7846	−	12.0664i	−1.51545	−	0.541254i
$498$	−18.4698	−	9.42475i	−0.827650	−	0.422333i
$499$	15.8562	+	9.15459i	0.709821	+	0.409816i	0.810995	−	0.585053i	$-0.198926\pi$
$499$	15.8562	+	9.15459i	0.709821	+	0.409816i	−0.101173	+	0.994869i	$0.532260\pi$
$500$		−	16.4238i		−	0.734495i
$501$	−0.661306	−	12.7646i	−0.0295450	−	0.570281i
$502$	−4.15920	+	7.20395i	−0.185634	+	0.321528i
$503$	−4.84489	+	8.39159i	−0.216023	+	0.374162i	−0.953588	−	0.301113i	$-0.902642\pi$
$503$	−4.84489	+	8.39159i	−0.216023	+	0.374162i	0.737566	+	0.675275i	$0.235975\pi$
$504$	−5.48603	+	5.73616i	−0.244367	+	0.255509i
$505$	31.7806	−	18.3485i	1.41422	−	0.816498i
$506$	24.3913	+	14.0823i	1.08432	+	0.626035i
$507$	−18.5054	+	12.8278i	−0.821852	+	0.569701i
$508$	−0.534780	−	0.926266i	−0.0237270	−	0.0410964i
$509$		−	32.4912i		−	1.44015i	−0.693897	−	0.720074i	$-0.744108\pi$
$509$		−	32.4912i		−	1.44015i	0.693897	−	0.720074i	$-0.255892\pi$
$510$	24.9781	−	16.1997i	1.10605	−	0.717336i
$511$	−8.83605	+	7.50556i	−0.390884	+	0.332027i
$512$	−1.00000			−0.0441942
$513$	9.32102	+	11.5529i	0.411533	+	0.510071i
$514$	−22.0410			−0.972185
$515$	−6.43666	−	11.1486i	−0.283633	−	0.491267i
$516$	0.840647	+	1.29618i	0.0370074	+	0.0570611i
$517$	36.2144	−	20.9084i	1.59271	−	0.919550i
$518$	2.60120	−	0.474849i	0.114290	−	0.0208637i
$519$	−8.81864	+	0.456874i	−0.387095	+	0.0200545i
$520$	−9.50397	+	9.80111i	−0.416777	+	0.429807i
$521$	−21.3684	−	37.0111i	−0.936166	−	1.62149i	−0.772542	−	0.634964i	$-0.781015\pi$
$521$	−21.3684	−	37.0111i	−0.936166	−	1.62149i	−0.163624	−	0.986523i	$-0.552318\pi$
$522$	6.96694	+	3.11188i	0.304935	+	0.136203i
$523$			0.499654i			0.0218484i	0.999940	+	0.0109242i	$0.00347734\pi$
$523$			0.499654i			0.0218484i	−0.999940	+	0.0109242i	$0.996523\pi$
$524$	6.27140	−	10.8624i	0.273967	−	0.474526i
$525$	9.85185	+	41.6401i	0.429970	+	1.81732i
$526$	−14.9822	−	8.64996i	−0.653254	−	0.377156i
$527$	−3.74483	−	6.48624i	−0.163127	−	0.282545i
$528$	5.47423	+	8.44064i	0.238235	+	0.367332i
$529$	−0.512495			−0.0222824
$530$	−23.6739			−1.02833
$531$	24.3342	−	17.6354i	1.05602	−	0.765311i
$532$	5.76059	−	4.89319i	0.249753	−	0.212147i
$533$	3.97291	+	13.9638i	0.172086	+	0.604840i
$534$	3.37606	+	1.72273i	0.146096	+	0.0745500i
$535$	−16.7514	+	29.0143i	−0.724227	+	1.25440i
$536$	9.24567	+	5.33799i	0.399352	+	0.230566i
$537$	−12.4881	+	8.09923i	−0.538900	+	0.349507i
$538$	−7.57009			−0.326370
$539$	6.57700	−	40.1231i	0.283291	−	1.72823i
$540$	18.3557	+	7.08391i	0.789902	+	0.304843i
$541$	−14.9336	−	8.62192i	−0.642046	−	0.370685i	0.143356	−	0.989671i	$-0.454210\pi$
$541$	−14.9336	−	8.62192i	−0.642046	−	0.370685i	−0.785402	+	0.618986i	$0.787544\pi$
$542$	2.07387			0.0890803
$543$	−4.30093	−	2.19467i	−0.184570	−	0.0941825i
$544$	−4.53944			−0.194627
$545$	−11.1970			−0.479628
$546$	8.46208	−	14.1913i	0.362144	−	0.607332i
$547$	22.0489			0.942741			0.471370	−	0.881935i	$-0.343759\pi$
$547$	22.0489			0.942741			0.471370	+	0.881935i	$0.343759\pi$
$548$	15.5523			0.664360
$549$	9.98295	+	4.45902i	0.426062	+	0.190306i
$550$	54.2356			2.31261
$551$	−6.29256	−	3.63301i	−0.268072	−	0.154771i
$552$	−7.48098	−	3.81739i	−0.318412	−	0.162479i
$553$	−41.8678	−	14.9534i	−1.78040	−	0.635883i
$554$	23.6718			1.00572
$555$	−3.56656	−	5.49922i	−0.151392	−	0.233429i
$556$	−7.60046	−	4.38812i	−0.322331	−	0.186098i
$557$	−7.59729	+	13.1589i	−0.321908	+	0.557560i	−0.980882	−	0.194605i	$-0.937657\pi$
$557$	−7.59729	+	13.1589i	−0.321908	+	0.557560i	0.658974	+	0.752166i	$0.270991\pi$
$558$	2.01864	−	4.51938i	0.0854560	−	0.191321i
$559$	−2.30879	−	2.23879i	−0.0976512	−	0.0946907i
$560$	3.36958	−	9.43442i	0.142391	−	0.398677i
$561$	24.8500	+	38.3158i	1.04917	+	1.61769i
$562$	25.8285			1.08951
$563$	2.63574			0.111083			0.0555416	−	0.998456i	$-0.482311\pi$
$563$	2.63574			0.111083			0.0555416	+	0.998456i	$0.482311\pi$
$564$	−10.4620	+	6.78524i	−0.440532	+	0.285710i
$565$	19.0549	+	33.0041i	0.801646	+	1.38849i
$566$	14.5695	+	8.41173i	0.612404	+	0.353571i
$567$	−23.5919	−	3.22822i	−0.990767	−	0.135573i
$568$	6.77969	−	11.7428i	0.284470	−	0.492716i
$569$			44.2841i			1.85649i	0.371973	+	0.928244i	$0.378681\pi$
$569$			44.2841i			1.85649i	−0.371973	+	0.928244i	$0.621319\pi$
$570$	−16.6886	−	8.51585i	−0.699008	−	0.356690i
$571$	−1.88780	−	3.26977i	−0.0790021	−	0.136836i	0.823818	−	0.566855i	$-0.191840\pi$
$571$	−1.88780	−	3.26977i	−0.0790021	−	0.136836i	−0.902820	+	0.430019i	$0.858507\pi$
$572$	−15.0347	−	14.5788i	−0.628630	−	0.609572i
$573$	1.74940	+	33.7671i	0.0730821	+	1.41064i
$574$	−6.89688	−	8.11946i	−0.287870	−	0.338900i
$575$	−39.2112	+	22.6386i	−1.63522	+	0.944094i
$576$	−1.76045	−	2.42916i	−0.0733521	−	0.101215i
$577$	11.1370	+	19.2899i	0.463640	+	0.803048i	0.999139	−	0.0414882i	$-0.0132099\pi$
$577$	11.1370	+	19.2899i	0.463640	+	0.803048i	−0.535499	+	0.844536i	$0.679877\pi$
$578$	−3.60655			−0.150013
$579$	9.22025	−	5.97986i	0.383181	−	0.248515i
$580$	−9.63072			−0.399894
$581$	−31.1590	+	5.68807i	−1.29269	+	0.235981i
$582$	11.8934	+	18.3383i	0.492999	+	0.760148i
$583$		−	36.3152i		−	1.50402i
$584$	−2.19097	−	3.79486i	−0.0906628	−	0.157033i
$585$	−40.5397	−	5.83230i	−1.67611	−	0.241136i
$586$	23.6154	+	13.6344i	0.975545	+	0.563231i
$587$	−18.7811	+	10.8433i	−0.775179	+	0.447550i	−0.834719	−	0.550676i	$-0.814370\pi$
$587$	−18.7811	+	10.8433i	−0.775179	+	0.447550i	0.0595402	+	0.998226i	$0.481037\pi$
$588$	−1.33960	+	12.0501i	−0.0552440	+	0.496939i
$589$	−2.35670	+	4.08192i	−0.0971061	+	0.168193i
$590$	−18.9657	+	32.8495i	−0.780804	+	1.35239i
$591$	−14.7287	+	0.763058i	−0.605856	+	0.0313880i
$592$			0.999410i			0.0410755i
$593$	−2.83216	−	1.63515i	−0.116303	−	0.0671475i	0.440720	−	0.897645i	$-0.354723\pi$
$593$	−2.83216	−	1.63515i	−0.116303	−	0.0671475i	−0.557023	+	0.830497i	$0.688056\pi$
$594$	−10.8665	+	28.1571i	−0.445860	+	1.15530i
$595$	15.2960	−	42.8270i	0.627075	−	1.75574i
$596$	−1.53689	−	2.66197i	−0.0629535	−	0.109039i
$597$	2.60974	+	1.33170i	0.106810	+	0.0545028i
$598$	16.9551	+	4.26455i	0.693346	+	0.174390i
$599$	17.7669	−	10.2577i	0.725935	−	0.419119i	−0.0909981	−	0.995851i	$-0.529006\pi$
$599$	17.7669	−	10.2577i	0.725935	−	0.419119i	0.816933	+	0.576732i	$0.195672\pi$
$600$	−16.1513	+	0.836763i	−0.659375	+	0.0341607i
$601$	−25.4328	+	14.6836i	−1.03743	+	0.598958i	−0.919103	−	0.394017i	$-0.871085\pi$
$601$	−25.4328	+	14.6836i	−1.03743	+	0.598958i	−0.118322	+	0.992975i	$0.537752\pi$
$602$	2.22241	+	0.793749i	0.0905785	+	0.0323508i
$603$	3.30970	+	31.8565i	0.134782	+	1.29730i
$604$	10.9434	−	6.31820i	0.445282	−	0.257084i
$605$			86.0941i			3.50022i
$606$	−9.13405	−	14.0836i	−0.371045	−	0.572109i
$607$	6.35329	−	3.66808i	0.257872	−	0.148883i	−0.365491	−	0.930815i	$-0.619099\pi$
$607$	6.35329	−	3.66808i	0.257872	−	0.148883i	0.623364	+	0.781932i	$0.285766\pi$
$608$	1.42838	+	2.47403i	0.0579286	+	0.100335i
$609$	11.3424	−	2.68355i	0.459617	−	0.108743i
$610$	−13.7999			−0.558741
$611$	18.0703	−	18.6352i	0.731045	−	0.753901i
$612$	−7.99146	−	11.0270i	−0.323036	−	0.445741i
$613$	8.59919	+	4.96474i	0.347318	+	0.200524i	0.663503	−	0.748173i	$-0.269069\pi$
$613$	8.59919	+	4.96474i	0.347318	+	0.200524i	−0.316185	+	0.948697i	$0.602402\pi$
$614$	22.9818			0.927470
$615$	−12.0030	+	23.5223i	−0.484006	+	0.948512i
$616$	14.4722	+	5.16884i	0.583100	+	0.208259i
$617$	9.05420	−	15.6823i	0.364508	−	0.631347i	−0.624189	−	0.781273i	$-0.714570\pi$
$617$	9.05420	−	15.6823i	0.364508	−	0.631347i	0.988697	+	0.149927i	$0.0479038\pi$
$618$	−4.94054	+	3.20422i	−0.198738	+	0.128893i
$619$	−24.1824	−	41.8852i	−0.971973	−	1.68351i	−0.689582	−	0.724208i	$-0.742206\pi$
$619$	−24.1824	−	41.8852i	−0.971973	−	1.68351i	−0.282392	−	0.959299i	$-0.591128\pi$
$620$			6.24735i			0.250900i
$621$	−3.89683	−	24.8928i	−0.156375	−	0.998914i
$622$	−15.9662	−	27.6543i	−0.640186	−	1.10883i
$623$	5.69550	−	1.03971i	0.228185	−	0.0416552i
$624$	4.70224	+	4.10961i	0.188240	+	0.164516i
$625$	−7.75058	+	13.4244i	−0.310023	+	0.536976i
$626$	5.32050	+	3.07179i	0.212650	+	0.122773i
$627$	13.0631	−	25.5999i	0.521690	−	1.02236i
$628$	8.31434	−	4.80029i	0.331778	−	0.191552i
$629$			4.53677i			0.180893i
$630$	28.8497	−	8.42358i	1.14940	−	0.335604i
$631$	12.4784	+	7.20438i	0.496756	+	0.286802i	0.727373	−	0.686243i	$-0.240741\pi$
$631$	12.4784	+	7.20438i	0.496756	+	0.286802i	−0.230617	+	0.973045i	$0.574075\pi$
$632$	8.40177	−	14.5523i	0.334205	−	0.578859i
$633$	39.9179	−	2.06805i	1.58659	−	0.0821977i
$634$	−7.01958	+	12.1583i	−0.278783	+	0.482867i
$635$			4.04987i			0.160714i
$636$	0.560282	+	10.8146i	0.0222166	+	0.428829i
$637$	−2.88892	−	25.0730i	−0.114463	−	0.993427i
$638$		−	14.7733i		−	0.584880i
$639$	40.4604	−	4.20360i	1.60059	−	0.166292i
$640$	3.27919	+	1.89324i	0.129622	+	0.0748370i
$641$			8.01456i			0.316556i	0.987395	+	0.158278i	$0.0505942\pi$
$641$			8.01456i			0.316556i	−0.987395	+	0.158278i	$0.949406\pi$
$642$	13.6507	+	6.96566i	0.538749	+	0.274913i
$643$	−13.5619	+	23.4899i	−0.534830	+	0.926353i	0.464342	+	0.885656i	$0.346291\pi$
$643$	−13.5619	+	23.4899i	−0.534830	+	0.926353i	−0.999172	+	0.0406964i	$0.987042\pi$
$644$	−12.6206	+	2.30389i	−0.497321	+	0.0907859i
$645$	−0.302659	−	5.84197i	−0.0119172	−	0.230027i
$646$	6.48406	+	11.2307i	0.255112	+	0.441867i
$647$	−7.96876	+	13.8023i	−0.313284	+	0.542624i	−0.979071	−	0.203518i	$-0.934763\pi$
$647$	−7.96876	+	13.8023i	−0.313284	+	0.542624i	0.665787	+	0.746142i	$0.268096\pi$
$648$	2.80163	−	8.55283i	0.110059	−	0.335987i
$649$	−50.3902	−	29.0928i	−1.97799	−	1.14199i
$650$	32.3816	−	9.21305i	1.27011	−	0.361366i
$651$	−1.74080	−	7.35770i	−0.0682272	−	0.288371i
$652$	5.52266	−	3.18851i	0.216284	−	0.124872i
$653$		−	42.3070i		−	1.65560i	−0.561022	−	0.827801i	$-0.689592\pi$
$653$		−	42.3070i		−	1.65560i	0.561022	−	0.827801i	$-0.310408\pi$
$654$	0.264996	+	5.11499i	0.0103622	+	0.200012i
$655$	−41.1303	+	23.7466i	−1.60709	+	0.927856i
$656$	3.48711	−	2.01328i	0.136149	−	0.0786055i
$657$	5.36125	−	12.0029i	0.209162	−	0.468277i
$658$	−6.40671	+	17.9380i	−0.249760	+	0.699298i
$659$	32.3775	+	18.6932i	1.26125	+	0.728182i	0.973316	−	0.229469i	$-0.0736989\pi$
$659$	32.3775	+	18.6932i	1.26125	+	0.728182i	0.287932	+	0.957651i	$0.407032\pi$
$660$	−1.97090	−	38.0425i	−0.0767170	−	1.48080i
$661$	−10.4632	+	18.1227i	−0.406970	+	0.704892i	−0.994549	−	0.104275i	$-0.966748\pi$
$661$	−10.4632	+	18.1227i	−0.406970	+	0.704892i	0.587579	+	0.809167i	$0.300081\pi$
$662$	7.16125	−	4.13455i	0.278330	−	0.160694i
$663$	21.3456	+	18.6554i	0.828993	+	0.724514i
$664$		−	11.9716i		−	0.464589i
$665$	−28.1541	+	5.13953i	−1.09177	+	0.199302i
$666$	−2.42773	+	1.75941i	−0.0940725	+	0.0681758i
$667$	6.16654	+	10.6808i	0.238769	+	0.413561i
$668$	6.39087	−	3.68977i	0.247270	−	0.142761i
$669$	30.0323	−	1.55590i	1.16111	−	0.0601547i
$670$	−20.2122	−	35.0086i	−0.780867	−	1.35250i
$671$		−	21.1687i		−	0.817208i
$672$	−4.38955	−	1.31600i	−0.169331	−	0.0507657i
$673$	10.6922	+	18.5194i	0.412152	+	0.713869i	0.995125	−	0.0986232i	$-0.0314439\pi$
$673$	10.6922	+	18.5194i	0.412152	+	0.713869i	−0.582973	+	0.812492i	$0.698111\pi$
$674$	−8.78687			−0.338458
$675$	−30.4662	−	37.7611i	−1.17265	−	1.45342i
$676$	−11.4530	−	6.15043i	−0.440502	−	0.236555i
$677$	−12.4515	+	21.5666i	−0.478550	+	0.828873i	−0.999698	−	0.0245935i	$-0.992171\pi$
$677$	−12.4515	+	21.5666i	−0.478550	+	0.828873i	0.521147	+	0.853467i	$0.325504\pi$
$678$	14.6259	−	9.48570i	0.561703	−	0.364296i
$679$	31.4425	+	11.2299i	1.20665	+	0.430966i
$680$	14.8857	+	8.59427i	0.570841	+	0.329575i
$681$	−29.5480	−	15.0778i	−1.13228	−	0.577781i
$682$	−9.58328			−0.366963
$683$	17.9767			0.687860			0.343930	−	0.938995i	$-0.388242\pi$
$683$	17.9767			0.687860			0.343930	+	0.938995i	$0.388242\pi$
$684$	−3.49522	+	7.82518i	−0.133643	+	0.299203i
$685$	−50.9989	−	29.4442i	−1.94857	−	1.12501i
$686$	9.54868	+	15.8689i	0.364570	+	0.605878i
$687$	16.5716	+	25.5514i	0.632244	+	0.974847i
$688$	−0.445979	+	0.772459i	−0.0170028	+	0.0294497i
$689$	−6.16890	−	21.6822i	−0.235016	−	0.826025i
$690$	17.3043	+	26.6813i	0.658764	+	1.01574i
$691$	21.1436			0.804341			0.402170	−	0.915565i	$-0.368256\pi$
$691$	21.1436			0.804341			0.402170	+	0.915565i	$0.368256\pi$
$692$	−2.54914	−	4.41523i	−0.0969036	−	0.167842i
$693$	12.9216	+	44.2547i	0.490849	+	1.68110i
$694$			16.4055i			0.622744i
$695$	16.6156	+	28.7790i	0.630265	+	1.09165i
$696$	0.227927	+	4.39948i	0.00863954	+	0.166762i
$697$	15.8295	−	9.13918i	0.599586	−	0.346171i
$698$	−4.38530	−	7.59556i	−0.165986	−	0.287496i
$699$	−2.05011	+	1.32962i	−0.0775424	+	0.0502907i
$700$	−18.8288	+	15.9936i	−0.711661	+	0.604503i
$701$			22.8317i			0.862342i	0.902270	+	0.431171i	$0.141900\pi$
$701$			22.8317i			0.862342i	−0.902270	+	0.431171i	$0.858100\pi$
$702$	−1.70485	+	18.6573i	−0.0643455	+	0.704173i
$703$	2.47257	−	1.42754i	0.0932548	−	0.0538407i
$704$	−2.90419	+	5.03020i	−0.109456	+	0.189583i
$705$	47.1532	−	2.44290i	1.77589	−	0.0920049i
$706$	−16.9161	−	9.76652i	−0.636646	−	0.367568i
$707$	−24.1476	−	8.62449i	−0.908163	−	0.324357i
$708$	15.4550	+	7.88639i	0.580836	+	0.296389i
$709$	−42.6427	+	24.6198i	−1.60148	+	0.924615i	−0.610289	+	0.792179i	$0.708947\pi$
$709$	−42.6427	+	24.6198i	−1.60148	+	0.924615i	−0.991191	+	0.132437i	$0.957720\pi$
$710$	−44.4639	+	25.6712i	−1.66870	+	0.963424i
$711$	50.1408	−	5.20934i	1.88043	−	0.195365i
$712$			2.18827i			0.0820089i
$713$	6.92851	−	4.00017i	0.259475	−	0.149808i
$714$	−19.9261	−	5.97390i	−0.745716	−	0.223568i
$715$	21.7002	+	76.2711i	0.811543	+	2.85238i
$716$	−7.44227	−	4.29680i	−0.278131	−	0.160579i
$717$	17.5024	−	34.2996i	0.653638	−	1.28094i
$718$	−1.54798	+	2.68118i	−0.0577702	+	0.100061i
$719$	−24.8204	−	42.9901i	−0.925643	−	1.60326i	−0.790524	−	0.612431i	$-0.790192\pi$
$719$	−24.8204	−	42.9901i	−0.925643	−	1.60326i	−0.135119	−	0.990829i	$-0.543142\pi$
$720$	1.17386	+	11.2986i	0.0437473	+	0.421076i
$721$	−3.02547	+	8.47096i	−0.112674	+	0.315475i
$722$	−5.41945	+	9.38676i	−0.201691	+	0.349339i
$723$	9.59460	−	18.8026i	0.356827	−	0.699277i
$724$		−	2.78775i		−	0.103606i
$725$	20.5676	+	11.8747i	0.763860	+	0.441015i
$726$	39.3292	−	2.03756i	1.45964	−	0.0756208i
$727$			24.4519i			0.906870i	0.891289	+	0.453435i	$0.149802\pi$
$727$			24.4519i			0.906870i	−0.891289	+	0.453435i	$0.850198\pi$
$728$	9.51872	+	0.627686i	0.352787	+	0.0232636i
$729$	25.7083	−	8.25120i	0.952160	−	0.305600i
$730$			16.5921i			0.614102i
$731$	−2.02450	+	3.50653i	−0.0748787	+	0.129694i
$732$	0.326597	+	6.30402i	0.0120714	+	0.233003i
$733$	1.21258	−	2.10024i	0.0447875	−	0.0775743i	−0.842763	−	0.538285i	$-0.819072\pi$
$733$	1.21258	−	2.10024i	0.0447875	−	0.0775743i	0.887550	+	0.460711i	$0.152406\pi$
$734$	−7.02340	−	4.05496i	−0.259239	−	0.149671i
$735$	27.2066	−	36.9785i	1.00353	−	1.36397i
$736$		−	4.84897i		−	0.178735i
$737$	53.7023	−	31.0050i	1.97815	−	1.14209i
$738$	11.0295	+	4.92646i	0.406000	+	0.181345i
$739$	40.5440	+	23.4081i	1.49144	+	0.861081i	0.999952	−	0.00980593i	$-0.00312138\pi$
$739$	40.5440	+	23.4081i	1.49144	+	0.861081i	0.491484	+	0.870887i	$0.336455\pi$
$740$	1.89213	−	3.27726i	0.0695560	−	0.120474i
$741$	3.45071	−	17.5036i	0.126765	−	0.643010i
$742$	10.7091	+	12.6074i	0.393142	+	0.462833i
$743$	−3.32899	−	5.76598i	−0.122129	−	0.211533i	0.798478	−	0.602024i	$-0.205639\pi$
$743$	−3.32899	−	5.76598i	−0.122129	−	0.211533i	−0.920607	+	0.390490i	$0.872305\pi$
$744$	2.85390	−	0.147854i	0.104629	−	0.00542058i
$745$			11.6388i			0.426414i
$746$	−10.1944	−	17.6572i	−0.373243	−	0.646476i
$747$	29.0810	−	21.0754i	1.06402	−	0.771109i
$748$	−13.1834	+	22.8343i	−0.482032	+	0.834905i
$749$	23.0291	−	4.20395i	0.841463	−	0.153609i
$750$	25.3386	+	12.9298i	0.925236	+	0.472129i
$751$	−5.99014			−0.218583			−0.109292	−	0.994010i	$-0.534858\pi$
$751$	−5.99014			−0.218583			−0.109292	+	0.994010i	$0.534858\pi$
$752$	−6.23486	−	3.59970i	−0.227362	−	0.131267i
$753$	−7.83987	−	12.0882i	−0.285701	−	0.440518i
$754$	−2.50955	−	8.82046i	−0.0913925	−	0.321222i
$755$	−47.8475			−1.74135
$756$	−4.53081	−	12.9797i	−0.164784	−	0.472066i
$757$	25.0828	+	43.4447i	0.911651	+	1.57903i	0.811732	+	0.584030i	$0.198525\pi$
$757$	25.0828	+	43.4447i	0.911651	+	1.57903i	0.0999189	+	0.994996i	$0.468142\pi$
$758$	16.2771	−	9.39758i	0.591210	−	0.341335i
$759$	−40.9284	+	26.5444i	−1.48561	+	0.963500i
$760$		−	10.8171i		−	0.392378i
$761$	7.23145	−	4.17508i	0.262140	−	0.151347i	−0.363170	−	0.931723i	$-0.618306\pi$
$761$	7.23145	−	4.17508i	0.262140	−	0.151347i	0.625310	+	0.780376i	$0.284972\pi$
$762$	1.85005	−	0.0958468i	0.0670202	−	0.00347216i
$763$	5.06506	+	5.96292i	0.183367	+	0.215872i
$764$	−16.9062	+	9.76080i	−0.611645	+	0.353133i
$765$	5.32869	+	51.2896i	0.192659	+	1.85438i
$766$	−21.4155	+	12.3643i	−0.773775	+	0.446739i
$767$	−35.0278	−	8.81019i	−1.26478	−	0.318117i
$768$	0.787258	−	1.54280i	0.0284077	−	0.0556709i
$769$	23.1255	+	40.0545i	0.833926	+	1.44440i	0.894902	+	0.446263i	$0.147245\pi$
$769$	23.1255	+	40.0545i	0.833926	+	1.44440i	−0.0609760	+	0.998139i	$0.519421\pi$
$770$	−37.6711	−	44.3490i	−1.35757	−	1.59823i
$771$	17.3519	−	34.0047i	0.624914	−	1.22465i
$772$	5.49481	+	3.17243i	0.197763	+	0.114178i
$773$		−	0.668313i		−	0.0240375i	−0.999928	−	0.0120188i	$-0.996174\pi$
$773$		−	0.668313i		−	0.0240375i	0.999928	−	0.0120188i	$-0.00382578\pi$
$774$	−2.66155	+	0.276520i	−0.0956674	+	0.00993929i
$775$	7.70299	−	13.3420i	0.276700	−	0.479258i
$776$	−6.30970	+	10.9287i	−0.226505	+	0.392318i
$777$	−1.31522	+	4.38696i	−0.0471833	+	0.157381i
$778$	7.93751	−	4.58272i	0.284574	−	0.164299i
$779$	−9.96185	−	5.75147i	−0.356920	−	0.206068i
$780$	−7.63906	−	22.3787i	−0.273522	−	0.801286i
$781$	−39.3790	−	68.2064i	−1.40909	−	2.44062i
$782$		−	22.0116i		−	0.787134i
$783$	−10.2858	+	8.29872i	−0.367584	+	0.296572i
$784$	−6.54850	+	2.47328i	−0.233875	+	0.0883313i
$785$	−36.3524			−1.29747
$786$	11.8213	+	18.2270i	0.421650	+	0.650136i
$787$	3.24383			0.115630			0.0578150	−	0.998327i	$-0.481587\pi$
$787$	3.24383			0.115630			0.0578150	+	0.998327i	$0.481587\pi$
$788$	−4.25750	−	7.37421i	−0.151667	−	0.262695i
$789$	25.1400	−	16.3047i	0.895007	−	0.580463i
$790$	−55.1021	+	31.8132i	−1.96044	+	1.13186i
$791$	8.95653	−	25.0772i	0.318457	−	0.891644i
$792$	−17.3318	+	1.80068i	−0.615860	+	0.0639843i
$793$	−3.59595	−	12.6389i	−0.127696	−	0.448820i
$794$	−1.69223	−	2.93103i	−0.0600550	−	0.104018i
$795$	18.6375	−	36.5241i	0.661004	−	1.29538i
$796$			1.69156i			0.0599559i
$797$	22.9206	−	39.6996i	0.811889	−	1.40623i	−0.0996520	−	0.995022i	$-0.531773\pi$
$797$	22.9206	−	39.6996i	0.811889	−	1.40623i	0.911541	−	0.411210i	$-0.134894\pi$
$798$	3.01413	+	12.7396i	0.106699	+	0.450978i
$799$	−28.3028	−	16.3406i	−1.00128	−	0.578090i
$800$	−4.66874	−	8.08650i	−0.165065	−	0.285901i
$801$	−5.31566	+	3.85234i	−0.187820	+	0.136116i
$802$	−7.25130			−0.256052
$803$	−25.4519			−0.898178
$804$	−15.5142	+	10.0618i	−0.547142	+	0.354853i
$805$	45.7472	+	16.3390i	1.61238	+	0.575873i
$806$	−5.72175	+	1.62792i	−0.201540	+	0.0573411i
$807$	5.95962	−	11.6791i	0.209788	−	0.411124i
$808$	4.84579	−	8.39315i	0.170474	−	0.295270i
$809$	−7.44117	−	4.29616i	−0.261618	−	0.151045i	0.363455	−	0.931612i	$-0.381597\pi$
$809$	−7.44117	−	4.29616i	−0.261618	−	0.151045i	−0.625072	+	0.780567i	$0.714931\pi$
$810$	−25.3797	+	22.7422i	−0.891751	+	0.799079i
$811$	37.1687			1.30517			0.652585	−	0.757716i	$-0.273685\pi$
$811$	37.1687			1.30517			0.652585	+	0.757716i	$0.273685\pi$
$812$	4.35652	+	5.12879i	0.152884	+	0.179985i
$813$	−1.63267	+	3.19956i	−0.0572602	+	0.112213i
$814$	5.02723	+	2.90247i	0.176204	+	0.101732i
$815$	−24.1465			−0.845814
$816$	3.57371	−	7.00344i	0.125105	−	0.245170i
$817$	2.54811			0.0891473
$818$	−1.57460			−0.0550547
$819$	15.2325	+	24.2275i	0.532266	+	0.846577i
$820$	−15.2465			−0.532432
$821$	4.63795			0.161866			0.0809328	−	0.996720i	$-0.474210\pi$
$821$	4.63795			0.161866			0.0809328	+	0.996720i	$0.474210\pi$
$822$	−12.2437	+	23.9940i	−0.427046	+	0.836887i
$823$	−35.0288			−1.22103			−0.610514	−	0.792006i	$-0.709037\pi$
$823$	−35.0288			−1.22103			−0.610514	+	0.792006i	$0.709037\pi$
$824$	−2.94432	−	1.69990i	−0.102570	−	0.0592189i
$825$	−42.6974	+	83.6745i	−1.48653	+	2.91317i
$826$	26.0731	−	4.75963i	0.907198	−	0.165609i
$827$	21.1109			0.734098			0.367049	−	0.930202i	$-0.380368\pi$
$827$	21.1109			0.734098			0.367049	+	0.930202i	$0.380368\pi$
$828$	11.7789	−	8.53636i	0.409346	−	0.296659i
$829$	−44.9376	−	25.9448i	−1.56075	−	0.901099i	−0.997181	−	0.0750287i	$-0.976095\pi$
$829$	−44.9376	−	25.9448i	−1.56075	−	0.901099i	−0.563567	−	0.826070i	$-0.690572\pi$
$830$	−22.6652	+	39.2572i	−0.786720	+	1.36264i
$831$	−18.6358	+	36.5208i	−0.646469	+	1.26689i
$832$	−0.879475	+	3.49664i	−0.0304903	+	0.121224i
$833$	−29.7266	+	11.2273i	−1.02996	+	0.389003i
$834$	12.7535	−	8.27138i	0.441618	−	0.286414i
$835$	−27.9425			−0.966991
$836$	16.5932			0.573886
$837$	5.38330	+	6.67228i	0.186074	+	0.230628i
$838$	−13.4922	−	23.3691i	−0.466080	−	0.807274i
$839$	−38.8948	−	22.4560i	−1.34280	−	0.775266i	−0.355582	−	0.934645i	$-0.615717\pi$
$839$	−38.8948	−	22.4560i	−1.34280	−	0.775266i	−0.987217	+	0.159380i	$0.949051\pi$
$840$	11.9027	+	12.6259i	0.410681	+	0.435635i
$841$	−11.2654	+	19.5123i	−0.388464	+	0.672839i
$842$		−	13.0461i		−	0.449597i
$843$	−20.3337	+	39.8482i	−0.700330	+	1.37244i
$844$	11.5387	+	19.9857i	0.397180	+	0.687936i
$845$	25.9125	+	41.8518i	0.891417	+	1.43975i
$846$	−2.23191	−	21.4826i	−0.0767348	−	0.738586i
$847$	45.8489	−	38.9453i	1.57539	−	1.33818i
$848$	−5.41458	+	3.12611i	−0.185937	+	0.107351i
$849$	−24.4476	+	15.8557i	−0.839039	+	0.544165i
$850$	−21.1935	−	36.7082i	−0.726931	−	1.25908i
$851$	−4.84611			−0.166122
$852$	12.7794	+	19.7043i	0.437813	+	0.675058i
$853$	26.1545			0.895513			0.447756	−	0.894156i	$-0.352223\pi$
$853$	26.1545			0.895513			0.447756	+	0.894156i	$0.352223\pi$
$854$	6.24248	+	7.34906i	0.213613	+	0.251480i
$855$	26.2765	−	19.0430i	0.898636	−	0.651256i
$856$			8.84801i			0.302419i
$857$	−10.1488	−	17.5783i	−0.346678	−	0.600464i	0.638979	−	0.769224i	$-0.279357\pi$
$857$	−10.1488	−	17.5783i	−0.346678	−	0.600464i	−0.985657	+	0.168760i	$0.946024\pi$
$858$	34.3284	−	11.7181i	1.17195	−	0.400050i
$859$	38.0174	+	21.9494i	1.29714	+	0.748903i	0.979909	−	0.199446i	$-0.0639143\pi$
$859$	38.0174	+	21.9494i	1.29714	+	0.748903i	0.317229	+	0.948349i	$0.397248\pi$
$860$	2.92490	−	1.68869i	0.0997384	−	0.0575840i
$861$	17.9563	−	4.24838i	0.611949	−	0.144784i
$862$	18.2521	−	31.6136i	0.621669	−	1.07676i
$863$	−9.06101	+	15.6941i	−0.308440	+	0.534234i	−0.978021	−	0.208505i	$-0.933140\pi$
$863$	−9.06101	+	15.6941i	−0.308440	+	0.534234i	0.669581	+	0.742739i	$0.266474\pi$
$864$	5.13363	−	0.803642i	0.174650	−	0.0273405i
$865$			19.3045i			0.656374i
$866$	23.6502	+	13.6545i	0.803668	+	0.463998i
$867$	2.83928	−	5.56417i	0.0964271	−	0.188969i
$868$	3.32699	−	2.82603i	0.112926	−	0.0959219i
$869$	−48.8006	−	84.5252i	−1.65545	−	2.86732i
$870$	7.58186	−	14.8583i	0.257049	−	0.503742i
$871$	26.7964	−	27.6342i	0.907961	−	0.936349i
$872$	−2.56093	+	1.47855i	−0.0867239	+	0.0500701i
$873$	−37.6555	+	3.91219i	−1.27445	+	0.132408i
$874$	−11.9965	+	6.92618i	−0.405788	+	0.234282i
$875$	42.7469	−	7.80344i	1.44511	−	0.263805i
$876$	7.57956	−	0.392680i	0.256090	−	0.0132674i
$877$	31.6001	−	18.2443i	1.06706	−	0.616068i	0.139684	−	0.990196i	$-0.455391\pi$
$877$	31.6001	−	18.2443i	1.06706	−	0.616068i	0.927377	+	0.374128i	$0.122058\pi$
$878$		−	0.455718i		−	0.0153797i
$879$	−39.6265	+	25.7001i	−1.33657	+	0.866842i
$880$	19.0468	−	10.9967i	0.642067	−	0.370697i
$881$	26.9414	+	46.6639i	0.907679	+	1.57215i	0.817280	+	0.576241i	$0.195481\pi$
$881$	26.9414	+	46.6639i	0.907679	+	1.57215i	0.0903999	+	0.995906i	$0.471185\pi$
$882$	−17.5363	−	11.5533i	−0.590478	−	0.389019i
$883$	14.2182			0.478482			0.239241	−	0.970960i	$-0.423101\pi$
$883$	14.2182			0.478482			0.239241	+	0.970960i	$0.423101\pi$
$884$	−3.99233	+	15.8728i	−0.134277	+	0.533861i
$885$	−35.7492	−	55.1212i	−1.20170	−	1.85288i
$886$	−23.2231	−	13.4079i	−0.780197	−	0.450447i
$887$	−6.50075			−0.218274			−0.109137	−	0.994027i	$-0.534809\pi$
$887$	−6.50075			−0.218274			−0.109137	+	0.994027i	$0.534809\pi$
$888$	−1.54189	−	0.786794i	−0.0517424	−	0.0264031i
$889$	2.15674	−	1.83199i	0.0723347	−	0.0614429i
$890$	4.14293	−	7.17576i	0.138871	−	0.240532i
$891$	−34.8859	−	38.9318i	−1.16872	−	1.30426i
$892$	8.68120	+	15.0363i	0.290668	+	0.503452i
$893$			20.5670i			0.688248i
$894$	5.31681	−	0.275452i	0.177821	−	0.00921249i
$895$	16.2698	+	28.1800i	0.543838	+	0.941955i
$896$	−0.475130	−	2.60274i	−0.0158730	−	0.0869514i
$897$	−19.9274	+	22.8010i	−0.665356	+	0.761304i
$898$	−0.402024	+	0.696326i	−0.0134157	+	0.0232367i
$899$	−3.63423	−	2.09822i	−0.121208	−	0.0699797i
$900$	11.4243	−	25.5770i	0.380810	−	0.852566i
$901$	−24.5792	+	14.1908i	−0.818851	+	0.472764i
$902$		−	23.3878i		−	0.778728i
$903$	−2.97420	+	2.80384i	−0.0989752	+	0.0933059i
$904$	8.71628	+	5.03235i	0.289899	+	0.167373i
$905$	−5.27788	+	9.14156i	−0.175443	+	0.303876i
$906$	1.13239	+	21.8576i	0.0376211	+	0.726169i
$907$	−11.8262	+	20.4836i	−0.392683	+	0.680147i	−0.992802	−	0.119763i	$-0.961786\pi$
$907$	−11.8262	+	20.4836i	−0.392683	+	0.680147i	0.600119	+	0.799911i	$0.295120\pi$
$908$		−	19.1522i		−	0.635589i
$909$	28.9191	−	3.00453i	0.959185	−	0.0996538i
$910$	−30.0254	−	20.0796i	−0.995331	−	0.665631i
$911$			55.8572i			1.85063i	0.379197	+	0.925316i	$0.376200\pi$
$911$			55.8572i			1.85063i	−0.379197	+	0.925316i	$0.623800\pi$
$912$	−4.94143	+	0.256004i	−0.163627	+	0.00847715i
$913$	−60.2196	−	34.7678i	−1.99298	−	1.15065i
$914$			15.2345i			0.503914i
$915$	10.8641	−	21.2904i	0.359155	−	0.703840i
$916$	−8.79153	+	15.2274i	−0.290480	+	0.503127i
$917$	31.2517	+	11.1618i	1.03202	+	0.368594i
$918$	23.3038	−	3.64809i	0.769141	−	0.120405i
$919$	11.7813	+	20.4058i	0.388630	+	0.673126i	0.992265	−	0.124134i	$-0.0396152\pi$
$919$	11.7813	+	20.4058i	0.388630	+	0.673126i	−0.603636	+	0.797260i	$0.706282\pi$
$920$	−9.18028	+	15.9007i	−0.302665	+	0.524231i
$921$	−18.0926	+	35.4563i	−0.596172	+	1.16832i
$922$	−11.4420	−	6.60603i	−0.376821	−	0.217558i
$923$	−35.0977	−	34.0337i	−1.15526	−	1.12023i
$924$	−19.3678	+	18.2584i	−0.637154	+	0.600657i
$925$	−8.08173	+	4.66599i	−0.265726	+	0.153417i
$926$		−	15.4572i		−	0.507954i
$927$	−1.05399	−	10.1448i	−0.0346175	−	0.333199i
$928$	−2.20269	+	1.27172i	−0.0723068	+	0.0417463i
$929$	−20.6071	+	11.8975i	−0.676098	+	0.390345i	−0.798383	−	0.602150i	$-0.794311\pi$
$929$	−20.6071	+	11.8975i	−0.676098	+	0.390345i	0.122285	+	0.992495i	$0.460978\pi$
$930$	−9.63840	−	4.91828i	−0.316056	−	0.161277i
$931$	15.4727	+	12.6684i	0.507098	+	0.415190i
$932$	−1.22176	−	0.705386i	−0.0400202	−	0.0231057i
$933$	55.2344	−	2.86157i	1.80829	−	0.0936836i
$934$	−0.665574	+	1.15281i	−0.0217782	+	0.0377210i
$935$	86.4618	−	49.9187i	2.82760	−	1.63252i
$936$	−10.0422	+	4.01928i	−0.328239	+	0.131374i
$937$		−	8.86156i		−	0.289495i	−0.989469	−	0.144747i	$-0.953763\pi$
$937$		−	8.86156i		−	0.289495i	0.989469	−	0.144747i	$-0.0462369\pi$
$938$	−9.50050	+	26.6003i	−0.310202	+	0.868531i
$939$	−8.92776	+	5.79016i	−0.291346	+	0.188955i
$940$	13.6302	+	23.6082i	0.444568	+	0.770015i
$941$	11.5201	−	6.65114i	0.375545	−	0.216821i	−0.300333	−	0.953834i	$-0.597098\pi$
$941$	11.5201	−	6.65114i	0.375545	−	0.216821i	0.675878	+	0.737013i	$0.263765\pi$
$942$	0.860340	+	16.6064i	0.0280314	+	0.541066i
$943$	9.76234	+	16.9089i	0.317906	+	0.550629i
$944$			10.0175i			0.326043i
$945$	−9.71626	+	51.1408i	−0.316070	+	1.66361i
$946$	2.59041	+	4.48673i	0.0842216	+	0.145876i
$947$	−28.1586			−0.915033			−0.457516	−	0.889201i	$-0.651261\pi$
$947$	−28.1586			−0.915033			−0.457516	+	0.889201i	$0.651261\pi$
$948$	15.8369	+	24.4187i	0.514358	+	0.793081i
$949$	−15.1962	+	4.32354i	−0.493289	+	0.140348i
$950$	−13.3375	+	23.1012i	−0.432725	+	0.749502i
$951$	−13.2315	−	20.4015i	−0.429062	−	0.661564i
$952$	−2.15682	−	11.8150i	−0.0699031	−	0.382926i
$953$	−6.01165	−	3.47083i	−0.194736	−	0.112431i	0.399462	−	0.916750i	$-0.369197\pi$
$953$	−6.01165	−	3.47083i	−0.194736	−	0.112431i	−0.594198	+	0.804319i	$0.702530\pi$
$954$	−17.1259	−	7.64952i	−0.554471	−	0.247662i
$955$	73.9183			2.39194
$956$	22.2321			0.719037
$957$	22.7922	+	11.6304i	0.736766	+	0.375957i
$958$	−12.4718	−	7.20059i	−0.402945	−	0.232641i
$959$	7.38935	+	40.4785i	0.238614	+	1.30712i
$960$	−5.50246	+	3.56866i	−0.177591	+	0.115178i
$961$	14.1389	−	24.4893i	0.456094	−	0.789977i
$962$	3.49458	+	0.878957i	0.112670	+	0.0283387i
$963$	−21.4932	+	15.5765i	−0.692609	+	0.501945i
$964$	12.1874			0.392528
$965$	−12.0124	−	20.8060i	−0.386692	−	0.669770i
$966$	6.38124	−	21.2848i	0.205313	−	0.684827i
$967$		−	54.9103i		−	1.76580i	−0.469563	−	0.882899i	$-0.655589\pi$
$967$		−	54.9103i		−	1.76580i	0.469563	−	0.882899i	$-0.344411\pi$
$968$	11.3686	+	19.6910i	0.365401	+	0.632892i
$969$	−22.4314	+	1.16212i	−0.720599	+	0.0373326i
$970$	41.3815	−	23.8916i	1.32868	−	0.767113i
$971$	−15.1332	−	26.2115i	−0.485649	−	0.841169i	0.514215	−	0.857661i	$-0.328083\pi$
$971$	−15.1332	−	26.2115i	−0.485649	−	0.841169i	−0.999864	+	0.0164927i	$0.994750\pi$
$972$	10.9897	+	11.0556i	0.352494	+	0.354610i
$973$	7.80994	−	21.8669i	0.250375	−	0.701022i
$974$			30.5356i			0.978423i
$975$	−11.2788	+	57.2114i	−0.361212	+	1.83223i
$976$	−3.15624	+	1.82226i	−0.101029	+	0.0583290i
$977$	−25.8818	+	44.8286i	−0.828031	+	1.43419i	0.0715488	+	0.997437i	$0.477206\pi$
$977$	−25.8818	+	44.8286i	−0.828031	+	1.43419i	−0.899580	+	0.436755i	$0.856128\pi$
$978$	0.571466	+	11.0305i	0.0182735	+	0.352717i
$979$	11.0074	+	6.35515i	0.351799	+	0.203111i
$980$	26.1563	+	4.28756i	0.835533	+	0.136961i
$981$	−8.10002	−	3.61798i	−0.258614	−	0.115513i
$982$	−2.79101	+	1.61139i	−0.0890648	+	0.0514216i
$983$	20.1979	−	11.6613i	0.644213	−	0.371936i	−0.142023	−	0.989863i	$-0.545361\pi$
$983$	20.1979	−	11.6613i	0.644213	−	0.371936i	0.786235	+	0.617927i	$0.212027\pi$
$984$	0.360834	+	6.96487i	0.0115030	+	0.222032i
$985$			32.2419i			1.02731i
$986$	−9.99898	+	5.77291i	−0.318432	+	0.183847i
$987$	−22.6310	−	24.0061i	−0.720354	−	0.764123i
$988$	9.90703	−	2.81870i	0.315185	−	0.0896747i
$989$	−3.74563	−	2.16254i	−0.119104	−	0.0687647i
$990$	60.2435	+	26.9086i	1.91467	+	0.855211i
$991$	−12.1157	+	20.9851i	−0.384869	+	0.666612i	−0.991751	−	0.128179i	$-0.959087\pi$
$991$	−12.1157	+	20.9851i	−0.384869	+	0.666612i	0.606882	+	0.794792i	$0.292420\pi$
$992$	0.824954	+	1.42886i	0.0261923	+	0.0453664i
$993$	0.741022	+	14.3033i	0.0235156	+	0.453902i
$994$	33.7846	+	12.0664i	1.07158	+	0.382724i
$995$	3.20254	−	5.54697i	0.101527	−	0.175851i
$996$	18.4698	+	9.42475i	0.585237	+	0.298635i
$997$			13.5078i			0.427797i	0.976856	+	0.213898i	$0.0686161\pi$
$997$			13.5078i			0.427797i	−0.976856	+	0.213898i	$0.931384\pi$
$998$	−15.8562	−	9.15459i	−0.501920	−	0.289783i
$999$	−0.803168	−	5.13060i	−0.0254111	−	0.162325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.257.10	yes	34
3.2	odd	2		546.2.bi.f.257.5	yes	34
7.3	odd	6		546.2.bn.f.101.16	yes	34
13.4	even	6		546.2.bn.e.173.2	yes	34
21.17	even	6		546.2.bn.e.101.2	yes	34
39.17	odd	6		546.2.bn.f.173.16	yes	34
91.17	odd	6		546.2.bi.f.17.5	yes	34
273.17	even	6	inner	546.2.bi.e.17.10	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.10	✓	34	273.17	even	6	inner
546.2.bi.e.257.10	yes	34	1.1	even	1	trivial
546.2.bi.f.17.5	yes	34	91.17	odd	6
546.2.bi.f.257.5	yes	34	3.2	odd	2
546.2.bn.e.101.2	yes	34	21.17	even	6
546.2.bn.e.173.2	yes	34	13.4	even	6
546.2.bn.f.101.16	yes	34	7.3	odd	6
546.2.bn.f.173.16	yes	34	39.17	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.787258 - 1.54280i) q^{3} +1.00000 q^{4} +(-3.27919 - 1.89324i) q^{5} +(-0.787258 + 1.54280i) q^{6} +(0.475130 + 2.60274i) q^{7} -1.00000 q^{8} +(-1.76045 - 2.42916i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.787258 - 1.54280i) q^{3} +1.00000 q^{4} +(-3.27919 - 1.89324i) q^{5} +(-0.787258 + 1.54280i) q^{6} +(0.475130 + 2.60274i) q^{7} -1.00000 q^{8} +(-1.76045 - 2.42916i) q^{9} +(3.27919 + 1.89324i) q^{10} +(-2.90419 + 5.03020i) q^{11} +(0.787258 - 1.54280i) q^{12} +(-0.879475 + 3.49664i) q^{13} +(-0.475130 - 2.60274i) q^{14} +(-5.50246 + 3.56866i) q^{15} +1.00000 q^{16} +4.53944 q^{17} +(1.76045 + 2.42916i) q^{18} +(-1.42838 - 2.47403i) q^{19} +(-3.27919 - 1.89324i) q^{20} +(4.38955 + 1.31600i) q^{21} +(2.90419 - 5.03020i) q^{22} +4.84897i q^{23} +(-0.787258 + 1.54280i) q^{24} +(4.66874 + 8.08650i) q^{25} +(0.879475 - 3.49664i) q^{26} +(-5.13363 + 0.803642i) q^{27} +(0.475130 + 2.60274i) q^{28} +(2.20269 - 1.27172i) q^{29} +(5.50246 - 3.56866i) q^{30} +(-0.824954 - 1.42886i) q^{31} -1.00000 q^{32} +(5.47423 + 8.44064i) q^{33} -4.53944 q^{34} +(3.36958 - 9.43442i) q^{35} +(-1.76045 - 2.42916i) q^{36} +0.999410i q^{37} +(1.42838 + 2.47403i) q^{38} +(4.70224 + 4.10961i) q^{39} +(3.27919 + 1.89324i) q^{40} +(3.48711 - 2.01328i) q^{41} +(-4.38955 - 1.31600i) q^{42} +(-0.445979 + 0.772459i) q^{43} +(-2.90419 + 5.03020i) q^{44} +(1.17386 + 11.2986i) q^{45} -4.84897i q^{46} +(-6.23486 - 3.59970i) q^{47} +(0.787258 - 1.54280i) q^{48} +(-6.54850 + 2.47328i) q^{49} +(-4.66874 - 8.08650i) q^{50} +(3.57371 - 7.00344i) q^{51} +(-0.879475 + 3.49664i) q^{52} +(-5.41458 + 3.12611i) q^{53} +(5.13363 - 0.803642i) q^{54} +(19.0468 - 10.9967i) q^{55} +(-0.475130 - 2.60274i) q^{56} +(-4.94143 + 0.256004i) q^{57} +(-2.20269 + 1.27172i) q^{58} +10.0175i q^{59} +(-5.50246 + 3.56866i) q^{60} +(-3.15624 + 1.82226i) q^{61} +(0.824954 + 1.42886i) q^{62} +(5.48603 - 5.73616i) q^{63} +1.00000 q^{64} +(9.50397 - 9.80111i) q^{65} +(-5.47423 - 8.44064i) q^{66} +(-9.24567 - 5.33799i) q^{67} +4.53944 q^{68} +(7.48098 + 3.81739i) q^{69} +(-3.36958 + 9.43442i) q^{70} +(-6.77969 + 11.7428i) q^{71} +(1.76045 + 2.42916i) q^{72} +(2.19097 + 3.79486i) q^{73} -0.999410i q^{74} +(16.1513 - 0.836763i) q^{75} +(-1.42838 - 2.47403i) q^{76} +(-14.4722 - 5.16884i) q^{77} +(-4.70224 - 4.10961i) q^{78} +(-8.40177 + 14.5523i) q^{79} +(-3.27919 - 1.89324i) q^{80} +(-2.80163 + 8.55283i) q^{81} +(-3.48711 + 2.01328i) q^{82} +11.9716i q^{83} +(4.38955 + 1.31600i) q^{84} +(-14.8857 - 8.59427i) q^{85} +(0.445979 - 0.772459i) q^{86} +(-0.227927 - 4.39948i) q^{87} +(2.90419 - 5.03020i) q^{88} -2.18827i q^{89} +(-1.17386 - 11.2986i) q^{90} +(-9.51872 - 0.627686i) q^{91} +4.84897i q^{92} +(-2.85390 + 0.147854i) q^{93} +(6.23486 + 3.59970i) q^{94} +10.8171i q^{95} +(-0.787258 + 1.54280i) q^{96} +(6.30970 - 10.9287i) q^{97} +(6.54850 - 2.47328i) q^{98} +(17.3318 - 1.80068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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