LMFDB - Embedded newform 585.2.i.g.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.1
Character	$\chi$	$=$	585.196
Dual form			585.2.i.g.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23671 + 2.14204i) q^{2} +(-1.15563 - 1.29016i) q^{3} +(-2.05890 - 3.56612i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.19276 - 0.879859i) q^{6} +(-2.17152 + 3.76119i) q^{7} +5.23822 q^{8} +(-0.329032 + 2.98190i) q^{9} +O(q^{10})$	\(q+(-1.23671 + 2.14204i) q^{2} +(-1.15563 - 1.29016i) q^{3} +(-2.05890 - 3.56612i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.19276 - 0.879859i) q^{6} +(-2.17152 + 3.76119i) q^{7} +5.23822 q^{8} +(-0.329032 + 2.98190i) q^{9} +2.47342 q^{10} +(-0.444329 + 0.769600i) q^{11} +(-2.22154 + 6.77744i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-5.37109 - 9.30300i) q^{14} +(-0.539497 + 1.64589i) q^{15} +(-2.36035 + 4.08825i) q^{16} -4.74588 q^{17} +(-5.98045 - 4.39255i) q^{18} +3.52948 q^{19} +(-2.05890 + 3.56612i) q^{20} +(7.36202 - 1.54493i) q^{21} +(-1.09901 - 1.90354i) q^{22} +(-2.58653 - 4.48000i) q^{23} +(-6.05345 - 6.75815i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.47342 q^{26} +(4.22737 - 3.02148i) q^{27} +17.8838 q^{28} +(4.43847 - 7.68765i) q^{29} +(-2.85836 - 3.19111i) q^{30} +(-0.291814 - 0.505437i) q^{31} +(-0.599920 - 1.03909i) q^{32} +(1.50639 - 0.316118i) q^{33} +(5.86928 - 10.1659i) q^{34} +4.34305 q^{35} +(11.3113 - 4.96608i) q^{36} +6.33198 q^{37} +(-4.36494 + 7.56031i) q^{38} +(0.539497 - 1.64589i) q^{39} +(-2.61911 - 4.53643i) q^{40} +(-6.04202 - 10.4651i) q^{41} +(-5.79537 + 17.6804i) q^{42} +(2.91628 - 5.05115i) q^{43} +3.65932 q^{44} +(2.74692 - 1.20600i) q^{45} +12.7951 q^{46} +(-2.01923 + 3.49741i) q^{47} +(8.00219 - 1.67928i) q^{48} +(-5.93104 - 10.2729i) q^{49} +(-1.23671 - 2.14204i) q^{50} +(5.48449 + 6.12295i) q^{51} +(2.05890 - 3.56612i) q^{52} -2.86796 q^{53} +(1.24410 + 12.7919i) q^{54} +0.888658 q^{55} +(-11.3749 + 19.7019i) q^{56} +(-4.07878 - 4.55360i) q^{57} +(10.9782 + 19.0148i) q^{58} +(4.54864 + 7.87848i) q^{59} +(6.98021 - 1.46481i) q^{60} +(4.21747 - 7.30487i) q^{61} +1.44356 q^{62} +(-10.5010 - 7.71282i) q^{63} -6.47369 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.18583 + 3.61770i) q^{66} +(-2.71820 - 4.70805i) q^{67} +(9.77131 + 16.9244i) q^{68} +(-2.79085 + 8.51426i) q^{69} +(-5.37109 + 9.30300i) q^{70} -7.75292 q^{71} +(-1.72354 + 15.6199i) q^{72} +4.60343 q^{73} +(-7.83082 + 13.5634i) q^{74} +(1.69513 - 0.355726i) q^{75} +(-7.26686 - 12.5866i) q^{76} +(-1.92974 - 3.34241i) q^{77} +(2.85836 + 3.19111i) q^{78} +(-4.24149 + 7.34648i) q^{79} +4.72070 q^{80} +(-8.78348 - 1.96228i) q^{81} +29.8889 q^{82} +(6.02416 - 10.4342i) q^{83} +(-20.6671 - 23.0730i) q^{84} +(2.37294 + 4.11006i) q^{85} +(7.21319 + 12.4936i) q^{86} +(-15.0475 + 3.15775i) q^{87} +(-2.32749 + 4.03133i) q^{88} +10.5268 q^{89} +(-0.813833 + 7.37549i) q^{90} -4.34305 q^{91} +(-10.6508 + 18.4478i) q^{92} +(-0.314865 + 0.960585i) q^{93} +(-4.99441 - 8.65057i) q^{94} +(-1.76474 - 3.05662i) q^{95} +(-0.647310 + 1.97480i) q^{96} +(-1.09816 + 1.90207i) q^{97} +29.3399 q^{98} +(-2.14867 - 1.57817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−1.23671	+	2.14204i	−0.874486	+	1.51465i	−0.0171764	+	0.999852i	$0.505468\pi$
$2$	−1.23671	+	2.14204i	−0.874486	+	1.51465i	−0.857309	+	0.514801i	$0.827866\pi$
$3$	−1.15563	−	1.29016i	−0.667204	−	0.744875i
$3$	−1.15563	−	1.29016i	−0.667204	−	0.744875i
$4$	−2.05890	−	3.56612i	−1.02945	−	1.78306i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	4.19276	−	0.879859i	1.71169	−	0.359201i
$7$	−2.17152	+	3.76119i	−0.820759	+	1.42160i	0.0843587	+	0.996435i	$0.473116\pi$
$7$	−2.17152	+	3.76119i	−0.820759	+	1.42160i	−0.905118	+	0.425161i	$0.860217\pi$
$8$	5.23822			1.85199
$9$	−0.329032	+	2.98190i	−0.109677	+	0.993967i
$10$	2.47342			0.782164
$11$	−0.444329	+	0.769600i	−0.133970	+	0.232043i	−0.925204	−	0.379471i	$-0.876106\pi$
$11$	−0.444329	+	0.769600i	−0.133970	+	0.232043i	0.791233	+	0.611514i	$0.209439\pi$
$12$	−2.22154	+	6.77744i	−0.641304	+	1.95648i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−5.37109	−	9.30300i	−1.43548	−	2.48633i
$15$	−0.539497	+	1.64589i	−0.139297	+	0.424966i
$16$	−2.36035	+	4.08825i	−0.590088	+	1.02206i
$17$	−4.74588			−1.15105			−0.575523	−	0.817786i	$-0.695201\pi$
$17$	−4.74588			−1.15105			−0.575523	+	0.817786i	$0.695201\pi$
$18$	−5.98045	−	4.39255i	−1.40961	−	1.03533i
$19$	3.52948			0.809719			0.404859	−	0.914379i	$-0.367320\pi$
$19$	3.52948			0.809719			0.404859	+	0.914379i	$0.367320\pi$
$20$	−2.05890	+	3.56612i	−0.460384	+	0.797409i
$21$	7.36202	−	1.54493i	1.60653	−	0.337132i
$22$	−1.09901	−	1.90354i	−0.234310	−	0.405837i
$23$	−2.58653	−	4.48000i	−0.539328	−	0.934144i	−0.998940	−	0.0460242i	$-0.985345\pi$
$23$	−2.58653	−	4.48000i	−0.539328	−	0.934144i	0.459612	−	0.888120i	$-0.347988\pi$
$24$	−6.05345	−	6.75815i	−1.23566	−	1.37950i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.47342			−0.485077
$27$	4.22737	−	3.02148i	0.813558	−	0.581483i
$28$	17.8838			3.37972
$29$	4.43847	−	7.68765i	0.824203	−	1.42756i	−0.0783247	−	0.996928i	$-0.524957\pi$
$29$	4.43847	−	7.68765i	0.824203	−	1.42756i	0.902527	−	0.430633i	$-0.141710\pi$
$30$	−2.85836	−	3.19111i	−0.521863	−	0.582614i
$31$	−0.291814	−	0.505437i	−0.0524113	−	0.0907791i	0.838629	−	0.544702i	$-0.183357\pi$
$31$	−0.291814	−	0.505437i	−0.0524113	−	0.0907791i	−0.891041	+	0.453923i	$0.850024\pi$
$32$	−0.599920	−	1.03909i	−0.106052	−	0.183687i
$33$	1.50639	−	0.316118i	0.262229	−	0.0550291i
$34$	5.86928	−	10.1659i	1.00657	−	1.74344i
$35$	4.34305			0.734109
$36$	11.3113	−	4.96608i	1.88521	−	0.827679i
$37$	6.33198			1.04097			0.520486	−	0.853870i	$-0.325751\pi$
$37$	6.33198			1.04097			0.520486	+	0.853870i	$0.325751\pi$
$38$	−4.36494	+	7.56031i	−0.708088	+	1.22644i
$39$	0.539497	−	1.64589i	0.0863886	−	0.263553i
$40$	−2.61911	−	4.53643i	−0.414117	−	0.717273i
$41$	−6.04202	−	10.4651i	−0.943605	−	1.63437i	−0.758521	−	0.651649i	$-0.774077\pi$
$41$	−6.04202	−	10.4651i	−0.943605	−	1.63437i	−0.185084	−	0.982723i	$-0.559256\pi$
$42$	−5.79537	+	17.6804i	−0.894245	+	2.72815i
$43$	2.91628	−	5.05115i	0.444729	−	0.770293i	−0.553304	−	0.832979i	$-0.686633\pi$
$43$	2.91628	−	5.05115i	0.444729	−	0.770293i	0.998033	+	0.0626861i	$0.0199667\pi$
$44$	3.65932			0.551663
$45$	2.74692	−	1.20600i	0.409486	−	0.179780i
$46$	12.7951			1.88654
$47$	−2.01923	+	3.49741i	−0.294535	+	0.510150i	−0.974877	−	0.222745i	$-0.928498\pi$
$47$	−2.01923	+	3.49741i	−0.294535	+	0.510150i	0.680341	+	0.732895i	$0.261832\pi$
$48$	8.00219	−	1.67928i	1.15502	−	0.242382i
$49$	−5.93104	−	10.2729i	−0.847291	−	1.46755i
$50$	−1.23671	−	2.14204i	−0.174897	−	0.302931i
$51$	5.48449	+	6.12295i	0.767983	+	0.857385i
$52$	2.05890	−	3.56612i	0.285518	−	0.494532i
$53$	−2.86796			−0.393945			−0.196972	−	0.980409i	$-0.563111\pi$
$53$	−2.86796			−0.393945			−0.196972	+	0.980409i	$0.563111\pi$
$54$	1.24410	+	12.7919i	0.169301	+	1.74076i
$55$	0.888658			0.119827
$56$	−11.3749	+	19.7019i	−1.52004	+	2.63278i
$57$	−4.07878	−	4.55360i	−0.540248	−	0.603139i
$58$	10.9782	+	19.0148i	1.44151	+	2.49676i
$59$	4.54864	+	7.87848i	0.592183	+	1.02569i	0.993938	+	0.109944i	$0.0350671\pi$
$59$	4.54864	+	7.87848i	0.592183	+	1.02569i	−0.401755	+	0.915747i	$0.631600\pi$
$60$	6.98021	−	1.46481i	0.901141	−	0.189106i
$61$	4.21747	−	7.30487i	0.539991	−	0.935292i	−0.458912	−	0.888482i	$-0.651761\pi$
$61$	4.21747	−	7.30487i	0.539991	−	0.935292i	0.998904	−	0.0468109i	$-0.0149058\pi$
$62$	1.44356			0.183332
$63$	−10.5010	−	7.71282i	−1.32300	−	0.971724i
$64$	−6.47369			−0.809212
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	−1.18583	+	3.61770i	−0.145965	+	0.445308i
$67$	−2.71820	−	4.70805i	−0.332080	−	0.575180i	0.650839	−	0.759216i	$-0.274417\pi$
$67$	−2.71820	−	4.70805i	−0.332080	−	0.575180i	−0.982920	+	0.184035i	$0.941084\pi$
$68$	9.77131	+	16.9244i	1.18495	+	2.05239i
$69$	−2.79085	+	8.51426i	−0.335978	+	1.02500i
$70$	−5.37109	+	9.30300i	−0.641968	+	1.11192i
$71$	−7.75292			−0.920102			−0.460051	−	0.887892i	$-0.652169\pi$
$71$	−7.75292			−0.920102			−0.460051	+	0.887892i	$0.652169\pi$
$72$	−1.72354	+	15.6199i	−0.203121	+	1.84082i
$73$	4.60343			0.538791			0.269395	−	0.963030i	$-0.413176\pi$
$73$	4.60343			0.538791			0.269395	+	0.963030i	$0.413176\pi$
$74$	−7.83082	+	13.5634i	−0.910315	+	1.57671i
$75$	1.69513	−	0.355726i	0.195737	−	0.0410757i
$76$	−7.26686	−	12.5866i	−0.833566	−	1.44378i
$77$	−1.92974	−	3.34241i	−0.219914	−	0.380903i
$78$	2.85836	+	3.19111i	0.323646	+	0.361322i
$79$	−4.24149	+	7.34648i	−0.477205	+	0.826543i	−0.999659	−	0.0261243i	$-0.991683\pi$
$79$	−4.24149	+	7.34648i	−0.477205	+	0.826543i	0.522454	+	0.852668i	$0.325017\pi$
$80$	4.72070			0.527791
$81$	−8.78348	−	1.96228i	−0.975942	−	0.218031i
$82$	29.8889			3.30068
$83$	6.02416	−	10.4342i	0.661238	−	1.14530i	−0.319053	−	0.947737i	$-0.603365\pi$
$83$	6.02416	−	10.4342i	0.661238	−	1.14530i	0.980291	−	0.197561i	$-0.0633019\pi$
$84$	−20.6671	−	23.0730i	−2.25497	−	2.51747i
$85$	2.37294	+	4.11006i	0.257382	+	0.445798i
$86$	7.21319	+	12.4936i	0.777818	+	1.34722i
$87$	−15.0475	+	3.15775i	−1.61327	+	0.338547i
$88$	−2.32749	+	4.03133i	−0.248111	+	0.429742i
$89$	10.5268			1.11584			0.557922	−	0.829894i	$-0.311599\pi$
$89$	10.5268			1.11584			0.557922	+	0.829894i	$0.311599\pi$
$90$	−0.813833	+	7.37549i	−0.0857855	+	0.777445i
$91$	−4.34305			−0.455275
$92$	−10.6508	+	18.4478i	−1.11042	+	1.92331i
$93$	−0.314865	+	0.960585i	−0.0326500	+	0.0996081i
$94$	−4.99441	−	8.65057i	−0.515134	−	0.892238i
$95$	−1.76474	−	3.05662i	−0.181059	−	0.313603i
$96$	−0.647310	+	1.97480i	−0.0660658	+	0.201552i
$97$	−1.09816	+	1.90207i	−0.111501	+	0.193126i	−0.916376	−	0.400319i	$-0.868899\pi$
$97$	−1.09816	+	1.90207i	−0.111501	+	0.193126i	0.804875	+	0.593445i	$0.202233\pi$
$98$	29.3399			2.96378
$99$	−2.14867	−	1.57817i	−0.215950	−	0.158612i
$100$	4.11780			0.411780
$101$	5.60268	−	9.70413i	0.557488	−	0.965597i	−0.440217	−	0.897891i	$-0.645099\pi$
$101$	5.60268	−	9.70413i	0.557488	−	0.965597i	0.997705	−	0.0677062i	$-0.0215681\pi$
$102$	−19.8984	+	4.17571i	−1.97023	+	0.413457i
$103$	3.08243	+	5.33893i	0.303721	+	0.526060i	0.976976	−	0.213350i	$-0.0684376\pi$
$103$	3.08243	+	5.33893i	0.303721	+	0.526060i	−0.673255	+	0.739411i	$0.735104\pi$
$104$	2.61911	+	4.53643i	0.256825	+	0.444834i
$105$	−5.01896	−	5.60323i	−0.489801	−	0.546820i
$106$	3.54683	−	6.14330i	0.344499	−	0.596690i
$107$	−7.73644			−0.747909			−0.373955	−	0.927447i	$-0.621998\pi$
$107$	−7.73644			−0.747909			−0.373955	+	0.927447i	$0.621998\pi$
$108$	−19.4787	−	8.85441i	−1.87434	−	0.852016i
$109$	−1.76788			−0.169332			−0.0846661	−	0.996409i	$-0.526982\pi$
$109$	−1.76788			−0.169332			−0.0846661	+	0.996409i	$0.526982\pi$
$110$	−1.09901	+	1.90354i	−0.104787	+	0.181496i
$111$	−7.31744	−	8.16928i	−0.694541	−	0.775394i
$112$	−10.2511	−	17.7555i	−0.968640	−	1.67773i
$113$	−1.11582	−	1.93266i	−0.104968	−	0.181810i	0.808757	−	0.588143i	$-0.200141\pi$
$113$	−1.11582	−	1.93266i	−0.104968	−	0.181810i	−0.913725	+	0.406333i	$0.866807\pi$
$114$	14.7983	−	3.10545i	1.38599	−	0.290852i
$115$	−2.58653	+	4.48000i	−0.241195	+	0.417762i
$116$	−36.5535			−3.39390
$117$	−2.74692	+	1.20600i	−0.253953	+	0.111495i
$118$	−22.5014			−2.07142
$119$	10.3058	−	17.8502i	0.944731	−	1.63632i
$120$	−2.82600	+	8.62151i	−0.257977	+	0.787033i
$121$	5.10514	+	8.84237i	0.464104	+	0.803852i
$122$	10.4316	+	18.0680i	0.944430	+	1.63580i
$123$	−6.51930	+	19.8890i	−0.587825	+	1.79333i
$124$	−1.20163	+	2.08129i	−0.107910	+	0.186905i
$125$	1.00000			0.0894427
$126$	29.5079	−	12.9551i	2.62877	−	1.15413i
$127$	15.4037			1.36685			0.683427	−	0.730019i	$-0.260489\pi$
$127$	15.4037			1.36685			0.683427	+	0.730019i	$0.260489\pi$
$128$	9.20592	−	15.9451i	0.813696	−	1.40936i
$129$	−9.88694	+	2.07479i	−0.870497	+	0.182675i
$130$	1.23671	+	2.14204i	0.108467	+	0.187870i
$131$	1.09244	+	1.89216i	0.0954469	+	0.165319i	0.909795	−	0.415058i	$-0.136239\pi$
$131$	1.09244	+	1.89216i	0.0954469	+	0.165319i	−0.814348	+	0.580377i	$0.802905\pi$
$132$	−4.22882	−	4.72111i	−0.368072	−	0.410920i
$133$	−7.66436	+	13.2751i	−0.664584	+	1.15109i
$134$	13.4465			1.16160
$135$	−4.73036	−	2.15027i	−0.407125	−	0.185066i
$136$	−24.8600			−2.13173
$137$	10.8107	−	18.7247i	0.923621	−	1.59976i	0.129857	−	0.991533i	$-0.458548\pi$
$137$	10.8107	−	18.7247i	0.923621	−	1.59976i	0.793764	−	0.608226i	$-0.208119\pi$
$138$	−14.7865	−	16.5078i	−1.25871	−	1.40524i
$139$	0.530148	+	0.918244i	0.0449666	+	0.0778844i	0.887633	−	0.460552i	$-0.152349\pi$
$139$	0.530148	+	0.918244i	0.0449666	+	0.0778844i	−0.842666	+	0.538436i	$0.819015\pi$
$140$	−8.94191	−	15.4878i	−0.755729	−	1.30896i
$141$	6.84571	−	1.43659i	0.576513	−	0.120982i
$142$	9.58811	−	16.6071i	0.804617	−	1.39364i
$143$	−0.888658			−0.0743133
$144$	−11.4141	−	8.38350i	−0.951177	−	0.698625i
$145$	−8.87693			−0.737189
$146$	−5.69311	+	9.86075i	−0.471165	+	0.816082i
$147$	−6.39955	+	19.5236i	−0.527826	+	1.61028i
$148$	−13.0369	−	22.5806i	−1.07163	−	1.85612i
$149$	−9.63869	−	16.6947i	−0.789632	−	1.36768i	−0.926192	−	0.377051i	$-0.876938\pi$
$149$	−9.63869	−	16.6947i	−0.789632	−	1.36768i	0.136560	−	0.990632i	$-0.456395\pi$
$150$	−1.33440	+	4.07097i	−0.108953	+	0.332393i
$151$	7.73634	−	13.3997i	0.629574	−	1.09045i	−0.358063	−	0.933697i	$-0.616563\pi$
$151$	7.73634	−	13.3997i	0.629574	−	1.09045i	0.987637	−	0.156757i	$-0.0501040\pi$
$152$	18.4882			1.49959
$153$	1.56155	−	14.1518i	0.126243	−	1.14410i
$154$	9.54612			0.769248
$155$	−0.291814	+	0.505437i	−0.0234391	+	0.0405976i
$156$	−6.98021	+	1.46481i	−0.558864	+	0.117279i
$157$	−7.98254	−	13.8262i	−0.637076	−	1.10345i	−0.986071	−	0.166324i	$-0.946810\pi$
$157$	−7.98254	−	13.8262i	−0.637076	−	1.10345i	0.348995	−	0.937125i	$-0.386523\pi$
$158$	−10.4910	−	18.1709i	−0.834618	−	1.44560i
$159$	3.31431	+	3.70013i	0.262842	+	0.293439i
$160$	−0.599920	+	1.03909i	−0.0474279	+	0.0821475i
$161$	22.4668			1.77063
$162$	15.0659	−	16.3878i	1.18369	−	1.28755i
$163$	−17.3991			−1.36280			−0.681401	−	0.731911i	$-0.738629\pi$
$163$	−17.3991			−1.36280			−0.681401	+	0.731911i	$0.738629\pi$
$164$	−24.8799	+	43.0932i	−1.94279	+	3.36501i
$165$	−1.02696	−	1.14651i	−0.0799488	−	0.0892558i
$166$	14.9003	+	25.8080i	1.15649	+	2.00309i
$167$	10.6050	+	18.3684i	0.820638	+	1.42139i	0.905207	+	0.424970i	$0.139715\pi$
$167$	10.6050	+	18.3684i	0.820638	+	1.42139i	−0.0845691	+	0.996418i	$0.526951\pi$
$168$	38.5639	−	8.09270i	2.97527	−	0.624365i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−11.7386			−0.900307
$171$	−1.16131	+	10.5246i	−0.0888077	+	0.804834i
$172$	−24.0174			−1.83131
$173$	−6.84438	+	11.8548i	−0.520368	+	0.901304i	0.479351	+	0.877623i	$0.340872\pi$
$173$	−6.84438	+	11.8548i	−0.520368	+	0.901304i	−0.999720	+	0.0236811i	$0.992461\pi$
$174$	11.8454	−	36.1377i	0.897997	−	2.73959i
$175$	−2.17152	−	3.76119i	−0.164152	−	0.284319i
$176$	−2.09754	−	3.63305i	−0.158108	−	0.273852i
$177$	4.90795	−	14.9731i	0.368904	−	1.12545i
$178$	−13.0186	+	22.5490i	−0.975789	+	1.69012i
$179$	11.1452			0.833034			0.416517	−	0.909128i	$-0.363251\pi$
$179$	11.1452			0.833034			0.416517	+	0.909128i	$0.363251\pi$
$180$	−9.95638	−	7.31281i	−0.742105	−	0.545065i
$181$	−14.9974			−1.11475			−0.557374	−	0.830262i	$-0.688191\pi$
$181$	−14.9974			−1.11475			−0.557374	+	0.830262i	$0.688191\pi$
$182$	5.37109	−	9.30300i	0.398132	−	0.689584i
$183$	−14.2983	+	3.00052i	−1.05696	+	0.221805i
$184$	−13.5488	−	23.4672i	−0.998830	−	1.73002i
$185$	−3.16599	−	5.48366i	−0.232768	−	0.403167i
$186$	−1.66822	−	1.86242i	−0.122320	−	0.136559i
$187$	2.10873	−	3.65243i	0.154206	−	0.267092i
$188$	16.6296			1.21284
$189$	2.18450	+	22.4612i	0.158899	+	1.63381i
$190$	8.72989			0.633333
$191$	−12.9305	+	22.3962i	−0.935616	+	1.62054i	−0.162086	+	0.986777i	$0.551822\pi$
$191$	−12.9305	+	22.3962i	−0.935616	+	1.62054i	−0.773531	+	0.633759i	$0.781511\pi$
$192$	7.48121	+	8.35211i	0.539909	+	0.602762i
$193$	−8.48216	−	14.6915i	−0.610559	−	1.05752i	−0.991146	−	0.132774i	$-0.957611\pi$
$193$	−8.48216	−	14.6915i	−0.610559	−	1.05752i	0.380587	−	0.924745i	$-0.375722\pi$
$194$	−2.71621	−	4.70461i	−0.195012	−	0.337771i
$195$	−1.69513	+	0.355726i	−0.121391	+	0.0254740i
$196$	−24.4228	+	42.3016i	−1.74449	+	3.02154i
$197$	−11.9043			−0.848146			−0.424073	−	0.905628i	$-0.639400\pi$
$197$	−11.9043			−0.848146			−0.424073	+	0.905628i	$0.639400\pi$
$198$	6.03779	−	2.65082i	0.429087	−	0.188385i
$199$	1.87186			0.132693			0.0663463	−	0.997797i	$-0.478866\pi$
$199$	1.87186			0.132693			0.0663463	+	0.997797i	$0.478866\pi$
$200$	−2.61911	+	4.53643i	−0.185199	+	0.320774i
$201$	−2.93291	+	8.94768i	−0.206872	+	0.631121i
$202$	13.8578	+	24.0024i	0.975031	+	1.68880i
$203$	19.2765	+	33.3878i	1.35294	+	2.34337i
$204$	10.5432	−	32.1649i	0.738170	−	2.25200i
$205$	−6.04202	+	10.4651i	−0.421993	+	0.730913i
$206$	−15.2483			−1.06240
$207$	14.2100	−	6.23871i	0.987661	−	0.433620i
$208$	−4.72070			−0.327322
$209$	−1.56825	+	2.71629i	−0.108478	+	0.187890i
$210$	18.2094	−	3.82127i	1.25657	−	0.263693i
$211$	4.62728	+	8.01468i	0.318555	+	0.551753i	0.980187	−	0.198076i	$-0.0634692\pi$
$211$	4.62728	+	8.01468i	0.318555	+	0.551753i	−0.661632	+	0.749829i	$0.730136\pi$
$212$	5.90485	+	10.2275i	0.405547	+	0.702428i
$213$	8.95952	+	10.0025i	0.613896	+	0.685361i
$214$	9.56773	−	16.5718i	0.654036	−	1.13282i
$215$	−5.83256			−0.397778
$216$	22.1439	−	15.8271i	1.50670	−	1.07690i
$217$	2.53472			0.172068
$218$	2.18635	−	3.78688i	0.148079	−	0.256480i
$219$	−5.31987	−	5.93917i	−0.359484	−	0.401332i
$220$	−1.82966	−	3.16906i	−0.123356	−	0.213658i
$221$	−2.37294	−	4.11006i	−0.159621	−	0.276472i
$222$	26.5485	−	5.57125i	1.78182	−	0.373918i
$223$	−0.511021	+	0.885115i	−0.0342205	+	0.0592717i	−0.882628	−	0.470071i	$-0.844228\pi$
$223$	−0.511021	+	0.885115i	−0.0342205	+	0.0592717i	0.848408	+	0.529343i	$0.177562\pi$
$224$	5.21097			0.348172
$225$	−2.41789	−	1.77590i	−0.161192	−	0.118393i
$226$	5.51980			0.367172
$227$	−1.91029	+	3.30872i	−0.126791	+	0.219608i	−0.922431	−	0.386161i	$-0.873801\pi$
$227$	−1.91029	+	3.30872i	−0.126791	+	0.219608i	0.795641	+	0.605769i	$0.207134\pi$
$228$	−7.84089	+	23.9209i	−0.519276	+	1.58420i
$229$	1.75403	+	3.03807i	0.115909	+	0.200761i	0.918143	−	0.396249i	$-0.129688\pi$
$229$	1.75403	+	3.03807i	0.115909	+	0.200761i	−0.802233	+	0.597010i	$0.796355\pi$
$230$	−6.39757	−	11.0809i	−0.421843	−	0.730654i
$231$	−2.08218	+	6.35227i	−0.136997	+	0.417949i
$232$	23.2497	−	40.2696i	1.52641	−	2.64383i
$233$	−8.13259			−0.532784			−0.266392	−	0.963865i	$-0.585832\pi$
$233$	−8.13259			−0.532784			−0.266392	+	0.963865i	$0.585832\pi$
$234$	0.813833	−	7.37549i	0.0532019	−	0.482151i
$235$	4.03846			0.263440
$236$	18.7304	−	32.4420i	1.21925	−	2.11180i
$237$	14.3797	−	3.01761i	0.934065	−	0.196015i
$238$	25.4906	+	44.1510i	1.65231	+	2.86188i
$239$	−3.32356	−	5.75657i	−0.214983	−	0.372361i	0.738284	−	0.674490i	$-0.235636\pi$
$239$	−3.32356	−	5.75657i	−0.214983	−	0.372361i	−0.953267	+	0.302128i	$0.902303\pi$
$240$	−5.45539	−	6.09047i	−0.352144	−	0.393138i
$241$	−11.4539	+	19.8388i	−0.737814	+	1.27793i	0.215664	+	0.976468i	$0.430808\pi$
$241$	−11.4539	+	19.8388i	−0.737814	+	1.27793i	−0.953478	+	0.301463i	$0.902525\pi$
$242$	−25.2543			−1.62341
$243$	7.61881	+	13.5998i	0.488747	+	0.872426i
$244$	−34.7334			−2.22358
$245$	−5.93104	+	10.2729i	−0.378920	+	0.656309i
$246$	−34.5406	−	38.5615i	−2.20223	−	2.45859i
$247$	1.76474	+	3.05662i	0.112288	+	0.194488i
$248$	−1.52859	−	2.64759i	−0.0970652	−	0.168122i
$249$	−20.4235	+	4.28590i	−1.29428	+	0.271608i
$250$	−1.23671	+	2.14204i	−0.0782164	+	0.135475i
$251$	−11.7731			−0.743113			−0.371556	−	0.928410i	$-0.621176\pi$
$251$	−11.7731			−0.743113			−0.371556	+	0.928410i	$0.621176\pi$
$252$	−5.88434	+	53.3278i	−0.370679	+	3.35934i
$253$	4.59707			0.289016
$254$	−19.0499	+	32.9953i	−1.19530	+	2.07031i
$255$	2.56039	−	7.81119i	0.160338	−	0.489156i
$256$	16.2964	+	28.2262i	1.01853	+	1.76414i
$257$	−14.2446	−	24.6723i	−0.888551	−	1.53902i	−0.841589	−	0.540119i	$-0.818379\pi$
$257$	−14.2446	−	24.6723i	−0.888551	−	1.53902i	−0.0469621	−	0.998897i	$-0.514954\pi$
$258$	7.78298	−	23.7442i	0.484547	−	1.47825i
$259$	−13.7501	+	23.8158i	−0.854387	+	1.47984i
$260$	−4.11780			−0.255375
$261$	21.4634	+	15.7646i	1.32855	+	0.975801i
$262$	−5.40412			−0.333868
$263$	3.23976	−	5.61143i	0.199772	−	0.346016i	−0.748682	−	0.662929i	$-0.769313\pi$
$263$	3.23976	−	5.61143i	0.199772	−	0.346016i	0.948455	+	0.316913i	$0.102646\pi$
$264$	7.89079	−	1.65590i	0.485645	−	0.101913i
$265$	1.43398	+	2.48373i	0.0880887	+	0.152574i
$266$	−18.9572	−	32.8348i	−1.16234	−	2.01323i
$267$	−12.1652	−	13.5813i	−0.744495	−	0.831163i
$268$	−11.1930	+	19.3868i	−0.683721	+	1.18424i
$269$	8.69007			0.529843			0.264922	−	0.964270i	$-0.414654\pi$
$269$	8.69007			0.529843			0.264922	+	0.964270i	$0.414654\pi$
$270$	10.4561	−	7.47338i	0.636336	−	0.454815i
$271$	21.3118			1.29460			0.647301	−	0.762234i	$-0.275898\pi$
$271$	21.3118			1.29460			0.647301	+	0.762234i	$0.275898\pi$
$272$	11.2020	−	19.4023i	0.679218	−	1.17644i
$273$	5.01896	+	5.60323i	0.303762	+	0.339123i
$274$	26.7394	+	46.3140i	1.61539	+	2.79793i
$275$	−0.444329	−	0.769600i	−0.0267940	−	0.0464086i
$276$	36.1090	−	7.57754i	2.17351	−	0.456114i
$277$	16.2730	−	28.1856i	0.977748	−	1.69351i	0.307196	−	0.951646i	$-0.400609\pi$
$277$	16.2730	−	28.1856i	0.977748	−	1.69351i	0.670552	−	0.741863i	$-0.266058\pi$
$278$	−2.62256			−0.157291
$279$	1.60318	−	0.703856i	0.0959798	−	0.0421388i
$280$	22.7498			1.35956
$281$	11.3089	−	19.5875i	0.674630	−	1.16849i	−0.301947	−	0.953325i	$-0.597637\pi$
$281$	11.3089	−	19.5875i	0.674630	−	1.16849i	0.976577	−	0.215168i	$-0.0690300\pi$
$282$	−5.38893	+	16.4405i	−0.320906	+	0.979015i
$283$	−13.2952	−	23.0279i	−0.790317	−	1.36887i	−0.925771	−	0.378086i	$-0.876582\pi$
$283$	−13.2952	−	23.0279i	−0.790317	−	1.36887i	0.135453	−	0.990784i	$-0.456751\pi$
$284$	15.9625	+	27.6479i	0.947200	+	1.64060i
$285$	−1.90414	+	5.80913i	−0.112792	+	0.344103i
$286$	1.09901	−	1.90354i	0.0649859	−	0.112559i
$287$	52.4816			3.09789
$288$	3.29586	−	1.44701i	0.194211	−	0.0852658i
$289$	5.52341			0.324907
$290$	10.9782	−	19.0148i	0.644662	−	1.11659i
$291$	3.72304	−	0.781287i	0.218248	−	0.0457998i
$292$	−9.47802	−	16.4164i	−0.554659	−	0.960697i
$293$	4.92075	+	8.52299i	0.287473	+	0.497919i	0.973206	−	0.229935i	$-0.0738514\pi$
$293$	4.92075	+	8.52299i	0.287473	+	0.497919i	−0.685733	+	0.727854i	$0.740518\pi$
$294$	−33.9061	−	37.8532i	−1.97744	−	2.20764i
$295$	4.54864	−	7.87848i	0.264832	−	0.458703i
$296$	33.1683			1.92787
$297$	0.446985	+	4.59592i	0.0259367	+	0.266682i
$298$	47.6810			2.76209
$299$	2.58653	−	4.48000i	0.149583	−	0.259085i
$300$	−4.75866	−	5.31263i	−0.274742	−	0.306725i
$301$	12.6656	+	21.9374i	0.730031	+	1.26445i
$302$	19.1352	+	33.1432i	1.10111	+	1.90717i
$303$	−18.9945	+	3.98604i	−1.09121	+	0.228992i
$304$	−8.33082	+	14.4294i	−0.477805	+	0.827583i
$305$	−8.43493			−0.482983
$306$	28.3825	+	20.8465i	1.62252	+	1.19172i
$307$	−27.1744			−1.55093			−0.775463	−	0.631392i	$-0.782484\pi$
$307$	−27.1744			−1.55093			−0.775463	+	0.631392i	$0.782484\pi$
$308$	−7.94630	+	13.7634i	−0.452782	+	0.784242i
$309$	3.32592	−	10.1467i	0.189205	−	0.577224i
$310$	−0.721778	−	1.25016i	−0.0409943	−	0.0710041i
$311$	5.91725	+	10.2490i	0.335537	+	0.581167i	0.983588	−	0.180430i	$-0.0577490\pi$
$311$	5.91725	+	10.2490i	0.335537	+	0.581167i	−0.648051	+	0.761597i	$0.724416\pi$
$312$	2.82600	−	8.62151i	0.159991	−	0.488097i
$313$	7.93086	−	13.7366i	0.448279	−	0.776441i	−0.549996	−	0.835168i	$-0.685371\pi$
$313$	7.93086	−	13.7366i	0.448279	−	0.776441i	0.998274	+	0.0587263i	$0.0187039\pi$
$314$	39.4884			2.22846
$315$	−1.42900	+	12.9505i	−0.0805150	+	0.729681i
$316$	34.9313			1.96504
$317$	0.734690	−	1.27252i	0.0412643	−	0.0714719i	−0.844656	−	0.535310i	$-0.820195\pi$
$317$	0.734690	−	1.27252i	0.0412643	−	0.0714719i	0.885920	+	0.463838i	$0.153528\pi$
$318$	−12.0247	+	2.52340i	−0.674310	+	0.141505i
$319$	3.94428	+	6.83169i	0.220837	+	0.382501i
$320$	3.23685	+	5.60638i	0.180945	+	0.313406i
$321$	8.94047	+	9.98125i	0.499008	+	0.557099i
$322$	−27.7849	+	48.1249i	−1.54839	+	2.68190i
$323$	−16.7505			−0.932023
$324$	11.0866	+	35.3631i	0.615922	+	1.96462i
$325$	−1.00000			−0.0554700
$326$	21.5176	−	37.2696i	1.19175	−	2.06417i
$327$	2.04302	+	2.28085i	0.112979	+	0.126131i
$328$	−31.6494	−	54.8184i	−1.74755	−	3.02684i
$329$	−8.76962	−	15.1894i	−0.483485	−	0.837421i
$330$	3.72593	−	0.781893i	0.205106	−	0.0430418i
$331$	9.91001	−	17.1646i	0.544703	−	0.943454i	−0.453922	−	0.891041i	$-0.649976\pi$
$331$	9.91001	−	17.1646i	0.544703	−	0.943454i	0.998626	−	0.0524124i	$-0.0166910\pi$
$332$	−49.6127			−2.72285
$333$	−2.08342	+	18.8814i	−0.114171	+	1.03469i
$334$	−52.4612			−2.87055
$335$	−2.71820	+	4.70805i	−0.148511	+	0.257228i
$336$	−11.0609	+	33.7444i	−0.603421	+	1.84091i
$337$	−14.2757	−	24.7262i	−0.777647	−	1.34692i	−0.933295	−	0.359111i	$-0.883080\pi$
$337$	−14.2757	−	24.7262i	−0.777647	−	1.34692i	0.155648	−	0.987813i	$-0.450253\pi$
$338$	−1.23671	−	2.14204i	−0.0672681	−	0.116512i
$339$	−1.20397	+	3.67304i	−0.0653905	+	0.199492i
$340$	9.77131	−	16.9244i	0.529924	−	0.917855i
$341$	0.518645			0.0280862
$342$	−21.1079	−	15.5034i	−1.14138	−	0.838329i
$343$	21.1162			1.14017
$344$	15.2761	−	26.4590i	0.823633	−	1.42657i
$345$	8.76899	−	1.84019i	0.472107	−	0.0990724i
$346$	−16.9290	−	29.3219i	−0.910109	−	1.57636i
$347$	−2.51702	−	4.35960i	−0.135121	−	0.234036i	0.790523	−	0.612432i	$-0.209809\pi$
$347$	−2.51702	−	4.35960i	−0.135121	−	0.234036i	−0.925644	+	0.378397i	$0.876476\pi$
$348$	42.2423	+	47.1599i	2.26443	+	2.52803i
$349$	−11.9409	+	20.6823i	−0.639183	+	1.10710i	0.346429	+	0.938076i	$0.387394\pi$
$349$	−11.9409	+	20.6823i	−0.639183	+	1.10710i	−0.985612	+	0.169022i	$0.945939\pi$
$350$	10.7422			0.574194
$351$	4.73036	+	2.15027i	0.252488	+	0.114773i
$352$	1.06625			0.0568312
$353$	−6.90193	+	11.9545i	−0.367353	+	0.636273i	−0.989151	−	0.146904i	$-0.953069\pi$
$353$	−6.90193	+	11.9545i	−0.367353	+	0.636273i	0.621798	+	0.783178i	$0.286402\pi$
$354$	26.0033	+	29.0304i	1.38206	+	1.54295i
$355$	3.87646	+	6.71423i	0.205741	+	0.356354i
$356$	−21.6737	−	37.5400i	−1.14871	−	1.98962i
$357$	−34.9393	+	7.33208i	−1.84918	+	0.388055i
$358$	−13.7834	+	23.8736i	−0.728476	+	1.26176i
$359$	3.63544			0.191871			0.0959356	−	0.995388i	$-0.469416\pi$
$359$	3.63544			0.191871			0.0959356	+	0.995388i	$0.469416\pi$
$360$	14.3890	−	6.31730i	0.758365	−	0.332951i
$361$	−6.54276			−0.344356
$362$	18.5474	−	32.1251i	0.974831	−	1.68846i
$363$	5.50841	−	16.8050i	0.289117	−	0.882033i
$364$	8.94191	+	15.4878i	0.468684	+	0.811784i
$365$	−2.30172	−	3.98669i	−0.120477	−	0.208673i
$366$	11.2556	−	34.3384i	0.588339	−	1.79489i
$367$	9.14200	−	15.8344i	0.477208	−	0.826549i	−0.522450	−	0.852670i	$-0.674982\pi$
$367$	9.14200	−	15.8344i	0.477208	−	0.826549i	0.999659	+	0.0261204i	$0.00831533\pi$
$368$	24.4205			1.27300
$369$	33.1939	−	14.5734i	1.72800	−	0.758659i
$370$	15.6616			0.814210
$371$	6.22785	−	10.7869i	0.323334	−	0.560030i
$372$	4.07384	−	0.854903i	0.211219	−	0.0443247i
$373$	−7.92769	−	13.7312i	−0.410480	−	0.710973i	0.584462	−	0.811421i	$-0.301306\pi$
$373$	−7.92769	−	13.7312i	−0.410480	−	0.710973i	−0.994942	+	0.100448i	$0.967972\pi$
$374$	5.21578	+	9.03400i	0.269702	+	0.467137i
$375$	−1.15563	−	1.29016i	−0.0596766	−	0.0666236i
$376$	−10.5772	+	18.3202i	−0.545476	+	0.944793i
$377$	8.87693			0.457185
$378$	−50.8144	−	23.0986i	−2.61361	−	1.18807i
$379$	−26.3095			−1.35143			−0.675715	−	0.737163i	$-0.736165\pi$
$379$	−26.3095			−1.35143			−0.675715	+	0.737163i	$0.736165\pi$
$380$	−7.26686	+	12.5866i	−0.372782	+	0.645677i
$381$	−17.8010	−	19.8732i	−0.911971	−	1.01814i
$382$	−31.9825	−	55.3953i	−1.63637	−	2.83427i
$383$	8.29470	+	14.3668i	0.423839	+	0.734112i	0.996311	−	0.0858129i	$-0.0273487\pi$
$383$	8.29470	+	14.3668i	0.423839	+	0.734112i	−0.572472	+	0.819924i	$0.694015\pi$
$384$	−31.2104	+	6.54957i	−1.59270	+	0.334231i
$385$	−1.92974	+	3.34241i	−0.0983487	+	0.170345i
$386$	41.9599			2.13570
$387$	14.1025	+	10.3581i	0.716869	+	0.526530i
$388$	9.04401			0.459140
$389$	3.74398	−	6.48476i	0.189827	−	0.328790i	−0.755365	−	0.655304i	$-0.772541\pi$
$389$	3.74398	−	6.48476i	0.189827	−	0.328790i	0.945192	+	0.326514i	$0.105874\pi$
$390$	1.33440	−	4.07097i	0.0675700	−	0.206142i
$391$	12.2754	+	21.2615i	0.620792	+	1.07524i
$392$	−31.0681	−	53.8115i	−1.56917	−	2.71789i
$393$	1.17873	−	3.59606i	0.0594593	−	0.181397i
$394$	14.7222	−	25.4995i	0.741692	−	1.28465i
$395$	8.48298			0.426825
$396$	−1.20403	+	10.9117i	−0.0605048	+	0.548335i
$397$	25.6054			1.28510			0.642549	−	0.766245i	$-0.277877\pi$
$397$	25.6054			1.28510			0.642549	+	0.766245i	$0.277877\pi$
$398$	−2.31495	+	4.00960i	−0.116038	+	0.200983i
$399$	25.9841	−	5.45282i	1.30083	−	0.272982i
$400$	−2.36035	−	4.08825i	−0.118018	−	0.204412i
$401$	7.81466	+	13.5354i	0.390246	+	0.675925i	0.992482	−	0.122393i	$-0.0390567\pi$
$401$	7.81466	+	13.5354i	0.390246	+	0.675925i	−0.602236	+	0.798318i	$0.705723\pi$
$402$	−15.5392	−	17.3481i	−0.775023	−	0.865246i
$403$	0.291814	−	0.505437i	0.0145363	−	0.0251776i
$404$	−46.1415			−2.29563
$405$	2.69235	+	8.58785i	0.133784	+	0.426734i
$406$	−95.3576			−4.73252
$407$	−2.81348	+	4.87309i	−0.139459	+	0.241550i
$408$	28.7290	+	32.0734i	1.42230	+	1.58787i
$409$	−2.92021	−	5.05795i	−0.144395	−	0.250100i	0.784752	−	0.619810i	$-0.212790\pi$
$409$	−2.92021	−	5.05795i	−0.144395	−	0.250100i	−0.929147	+	0.369710i	$0.879457\pi$
$410$	−14.9444	−	25.8845i	−0.738054	−	1.27835i
$411$	−36.6511	+	7.69129i	−1.80786	+	0.379383i
$412$	12.6929	−	21.9847i	0.625332	−	1.08311i
$413$	−39.5100			−1.94416
$414$	−4.21000	+	38.1538i	−0.206910	+	1.87516i
$415$	−12.0483			−0.591429
$416$	0.599920	−	1.03909i	0.0294135	−	0.0509457i
$417$	0.572026	−	1.74513i	0.0280123	−	0.0854593i
$418$	−3.87894	−	6.71852i	−0.189725	−	0.328614i
$419$	3.91300	+	6.77751i	0.191162	+	0.331103i	0.945636	−	0.325228i	$-0.105441\pi$
$419$	3.91300	+	6.77751i	0.191162	+	0.331103i	−0.754473	+	0.656331i	$0.772108\pi$
$420$	−9.64826	+	29.4347i	−0.470787	+	1.43627i
$421$	9.43253	−	16.3376i	0.459713	−	0.796247i	−0.539232	−	0.842157i	$-0.681285\pi$
$421$	9.43253	−	16.3376i	0.459713	−	0.796247i	0.998946	+	0.0459102i	$0.0146188\pi$
$422$	−22.8904			−1.11429
$423$	−9.76455	−	7.17191i	−0.474769	−	0.348710i
$424$	−15.0230			−0.729581
$425$	2.37294	−	4.11006i	0.115105	−	0.199367i
$426$	−32.5062	+	6.82148i	−1.57493	+	0.330502i
$427$	18.3167	+	31.7254i	0.886406	+	1.53530i
$428$	15.9286	+	27.5891i	0.769936	+	1.33357i
$429$	1.02696	+	1.14651i	0.0495821	+	0.0553541i
$430$	7.21319	−	12.4936i	0.347851	−	0.602495i
$431$	−12.6251			−0.608129			−0.304065	−	0.952651i	$-0.598344\pi$
$431$	−12.6251			−0.608129			−0.304065	+	0.952651i	$0.598344\pi$
$432$	2.37446	+	24.4143i	0.114241	+	1.17463i
$433$	17.1403			0.823710			0.411855	−	0.911249i	$-0.364881\pi$
$433$	17.1403			0.823710			0.411855	+	0.911249i	$0.364881\pi$
$434$	−3.13472	+	5.42949i	−0.150471	+	0.260624i
$435$	10.2585	+	11.4527i	0.491856	+	0.549114i
$436$	3.63989	+	6.30448i	0.174319	+	0.301930i
$437$	−9.12910	−	15.8121i	−0.436704	−	0.756394i
$438$	19.3011	−	4.05037i	0.922242	−	0.193534i
$439$	8.36186	−	14.4832i	0.399090	−	0.691244i	−0.594524	−	0.804078i	$-0.702660\pi$
$439$	8.36186	−	14.4832i	0.399090	−	0.691244i	0.993614	+	0.112834i	$0.0359928\pi$
$440$	4.65498			0.221918
$441$	32.5841	−	14.3057i	1.55163	−	0.681223i
$442$	11.7386			0.558346
$443$	−1.75338	+	3.03694i	−0.0833054	+	0.144289i	−0.904668	−	0.426117i	$-0.859881\pi$
$443$	−1.75338	+	3.03694i	−0.0833054	+	0.144289i	0.821362	+	0.570407i	$0.193214\pi$
$444$	−14.0668	+	42.9146i	−0.667579	+	2.03664i
$445$	−5.26342	−	9.11651i	−0.249510	−	0.432164i
$446$	−1.26397	−	2.18926i	−0.0598507	−	0.103664i
$447$	−10.4001	+	31.7284i	−0.491907	+	1.50070i
$448$	14.0578	−	24.3488i	0.664168	−	1.15037i
$449$	−4.93092			−0.232705			−0.116352	−	0.993208i	$-0.537120\pi$
$449$	−4.93092			−0.232705			−0.116352	+	0.993208i	$0.537120\pi$
$450$	6.79428	−	2.98295i	0.320286	−	0.140617i
$451$	10.7386			0.505660
$452$	−4.59475	+	7.95833i	−0.216119	+	0.374329i
$453$	−26.2282	+	5.50403i	−1.23231	+	0.258602i
$454$	−4.72496	−	8.18386i	−0.221753	−	0.384088i
$455$	2.17152	+	3.76119i	0.101803	+	0.176327i
$456$	−21.3655	−	23.8528i	−1.00053	−	1.11701i
$457$	−13.7798	+	23.8674i	−0.644593	+	1.11647i	0.339802	+	0.940497i	$0.389640\pi$
$457$	−13.7798	+	23.8674i	−0.644593	+	1.11647i	−0.984395	+	0.175971i	$0.943693\pi$
$458$	−8.67690			−0.405445
$459$	−20.0626	+	14.3396i	−0.936443	+	0.669314i
$460$	21.3016			0.993193
$461$	−3.93798	+	6.82078i	−0.183410	+	0.317676i	−0.943040	−	0.332680i	$-0.892047\pi$
$461$	−3.93798	+	6.82078i	−0.183410	+	0.317676i	0.759630	+	0.650356i	$0.225380\pi$
$462$	−11.0318	−	12.3160i	−0.513246	−	0.572994i
$463$	−17.8622	−	30.9383i	−0.830128	−	1.43782i	−0.897936	−	0.440126i	$-0.854934\pi$
$463$	−17.8622	−	30.9383i	−0.830128	−	1.43782i	0.0678081	−	0.997698i	$-0.478399\pi$
$464$	20.9527	+	36.2911i	0.972704	+	1.68477i
$465$	0.989324	−	0.207611i	0.0458788	−	0.00962775i
$466$	10.0577	−	17.4204i	0.465912	−	0.806983i
$467$	27.3014			1.26336			0.631679	−	0.775230i	$-0.282366\pi$
$467$	27.3014			1.26336			0.631679	+	0.775230i	$0.282366\pi$
$468$	9.95638	+	7.31281i	0.460234	+	0.338035i
$469$	23.6105			1.09023
$470$	−4.99441	+	8.65057i	−0.230375	+	0.399021i
$471$	−8.61311	+	26.2767i	−0.396871	+	1.21077i
$472$	23.8268	+	41.2692i	1.09672	+	1.89957i
$473$	2.59158	+	4.48874i	0.119161	+	0.206393i
$474$	−11.3197	+	34.5340i	−0.519931	+	1.58620i
$475$	−1.76474	+	3.05662i	−0.0809719	+	0.140247i
$476$	−84.8745			−3.89022
$477$	0.943649	−	8.55198i	0.0432067	−	0.391568i
$478$	16.4411			0.751998
$479$	−1.08155	+	1.87329i	−0.0494171	+	0.0855930i	−0.889676	−	0.456593i	$-0.849070\pi$
$479$	−1.08155	+	1.87329i	−0.0494171	+	0.0855930i	0.840259	+	0.542186i	$0.182403\pi$
$480$	2.03388	−	0.426814i	0.0928337	−	0.0194813i
$481$	3.16599	+	5.48366i	0.144357	+	0.250033i
$482$	−28.3304	−	49.0697i	−1.29042	−	2.23507i
$483$	−25.9634	−	28.9858i	−1.18137	−	1.31890i
$484$	21.0220	−	36.4111i	0.955545	−	1.65505i
$485$	2.19632			0.0997296
$486$	−38.5536	−	0.499152i	−1.74883	−	0.0226420i
$487$	−4.50019			−0.203923			−0.101962	−	0.994788i	$-0.532512\pi$
$487$	−4.50019			−0.203923			−0.101962	+	0.994788i	$0.532512\pi$
$488$	22.0920	−	38.2645i	1.00006	−	1.73215i
$489$	20.1069	+	22.4476i	0.909267	+	1.01512i
$490$	−14.6699	−	25.4091i	−0.662720	−	1.14787i
$491$	8.81571	+	15.2693i	0.397848	+	0.689092i	0.993460	−	0.114180i	$-0.0364239\pi$
$491$	8.81571	+	15.2693i	0.397848	+	0.689092i	−0.595612	+	0.803272i	$0.703091\pi$
$492$	84.3491	−	17.7008i	3.80275	−	0.798014i
$493$	−21.0644	+	36.4847i	−0.948695	+	1.64319i
$494$	−8.72989			−0.392776
$495$	−0.292396	+	2.64989i	−0.0131422	+	0.119104i
$496$	2.75513			0.123709
$497$	16.8357	−	29.1602i	0.755182	−	1.30801i
$498$	16.0773	−	49.0484i	0.720441	−	2.19791i
$499$	−5.71603	−	9.90045i	−0.255885	−	0.443205i	0.709251	−	0.704956i	$-0.249033\pi$
$499$	−5.71603	−	9.90045i	−0.255885	−	0.443205i	−0.965135	+	0.261751i	$0.915700\pi$
$500$	−2.05890	−	3.56612i	−0.0920769	−	0.159482i
$501$	11.4427	−	34.9092i	0.511222	−	1.55963i
$502$	14.5599	−	25.2185i	0.649841	−	1.12556i
$503$	−12.5249			−0.558457			−0.279229	−	0.960225i	$-0.590079\pi$
$503$	−12.5249			−0.558457			−0.279229	+	0.960225i	$0.590079\pi$
$504$	−55.0065	−	40.4014i	−2.45019	−	1.79962i
$505$	−11.2054			−0.498632
$506$	−5.68525	+	9.84714i	−0.252740	+	0.437759i
$507$	1.69513	−	0.355726i	0.0752833	−	0.0157983i
$508$	−31.7146	−	54.9314i	−1.40711	−	2.43719i
$509$	11.4030	+	19.7506i	0.505429	+	0.875428i	0.999980	+	0.00628001i	$0.00199900\pi$
$509$	11.4030	+	19.7506i	0.505429	+	0.875428i	−0.494551	+	0.869148i	$0.664668\pi$
$510$	13.5655	+	15.1446i	0.600688	+	0.670616i
$511$	−9.99647	+	17.3144i	−0.442218	+	0.765943i
$512$	−43.7920			−1.93535
$513$	14.9204	−	10.6642i	0.658753	−	0.470838i
$514$	70.4655			3.10810
$515$	3.08243	−	5.33893i	0.135828	−	0.235261i
$516$	27.7552	+	30.9863i	1.22186	+	1.36409i
$517$	−1.79441	−	3.10800i	−0.0789179	−	0.136690i
$518$	−34.0097	−	58.9064i	−1.49430	−	2.58820i
$519$	23.2042	−	4.86944i	1.01855	−	0.213745i
$520$	2.61911	−	4.53643i	0.114856	−	0.198936i
$521$	−3.17336			−0.139028			−0.0695138	−	0.997581i	$-0.522145\pi$
$521$	−3.17336			−0.139028			−0.0695138	+	0.997581i	$0.522145\pi$
$522$	−60.3124	+	26.4794i	−2.63980	+	1.15897i
$523$	−13.4847			−0.589645			−0.294823	−	0.955552i	$-0.595261\pi$
$523$	−13.4847			−0.589645			−0.294823	+	0.955552i	$0.595261\pi$
$524$	4.49845	−	7.79154i	0.196516	−	0.340375i
$525$	−2.34306	+	7.14817i	−0.102260	+	0.311972i
$526$	8.01329	+	13.8794i	0.349396	+	0.605172i
$527$	1.38492	+	2.39874i	0.0603278	+	0.104491i
$528$	−2.26324	+	6.90464i	−0.0984947	+	0.300486i
$529$	−1.88025	+	3.25669i	−0.0817500	+	0.141595i
$530$	−7.09367			−0.308129
$531$	−24.9895	+	10.9713i	−1.08445	+	0.476116i
$532$	63.1206			2.73663
$533$	6.04202	−	10.4651i	0.261709	−	0.453293i
$534$	44.1366	−	9.26214i	1.90998	−	0.400812i
$535$	3.86822	+	6.69995i	0.167238	+	0.289664i
$536$	−14.2385	−	24.6618i	−0.615010	−	1.06523i
$537$	−12.8798	−	14.3791i	−0.555804	−	0.620506i
$538$	−10.7471	+	18.6145i	−0.463340	+	0.802529i
$539$	10.5413			0.454047
$540$	2.07121	+	21.2963i	0.0891306	+	0.916445i
$541$	−6.45227			−0.277405			−0.138702	−	0.990334i	$-0.544293\pi$
$541$	−6.45227			−0.277405			−0.138702	+	0.990334i	$0.544293\pi$
$542$	−26.3566	+	45.6509i	−1.13211	+	1.96088i
$543$	17.3315	+	19.3491i	0.743764	+	0.830347i
$544$	2.84715	+	4.93141i	0.122071	+	0.211433i
$545$	0.883940	+	1.53103i	0.0378638	+	0.0655821i
$546$	−18.2094	+	3.82127i	−0.779289	+	0.163535i
$547$	8.93119	−	15.4693i	0.381870	−	0.661419i	−0.609459	−	0.792817i	$-0.708613\pi$
$547$	8.93119	−	15.4693i	0.381870	−	0.661419i	0.991330	+	0.131399i	$0.0419468\pi$
$548$	−89.0327			−3.80329
$549$	20.3947	+	14.9796i	0.870425	+	0.639314i
$550$	2.19802			0.0937240
$551$	15.6655	−	27.1334i	0.667372	−	1.15592i
$552$	−14.6191	+	44.5996i	−0.622228	+	1.89828i
$553$	−18.4210	−	31.9061i	−0.783341	−	1.35679i
$554$	40.2499	+	69.7148i	1.71005	+	2.96190i
$555$	−3.41608	+	10.4217i	−0.145005	+	0.442378i
$556$	2.18305	−	3.78115i	0.0925818	−	0.160356i
$557$	4.43451			0.187896			0.0939480	−	0.995577i	$-0.470051\pi$
$557$	4.43451			0.187896			0.0939480	+	0.995577i	$0.470051\pi$
$558$	−0.474976	+	4.30454i	−0.0201073	+	0.182226i
$559$	5.83256			0.246691
$560$	−10.2511	+	17.7555i	−0.433189	+	0.750305i
$561$	−7.14914	+	1.50026i	−0.301837	+	0.0633411i
$562$	27.9715	+	48.4481i	1.17991	+	2.04366i
$563$	5.00422	+	8.66757i	0.210903	+	0.365294i	0.951997	−	0.306106i	$-0.0990263\pi$
$563$	5.00422	+	8.66757i	0.210903	+	0.365294i	−0.741094	+	0.671401i	$0.765693\pi$
$564$	−19.2177	−	21.4549i	−0.809211	−	0.903413i
$565$	−1.11582	+	1.93266i	−0.0469431	+	0.0813078i
$566$	65.7692			2.76448
$567$	26.4540	−	28.7752i	1.11097	−	1.20844i
$568$	−40.6115			−1.70402
$569$	10.4958	−	18.1793i	0.440007	−	0.762115i	−0.557682	−	0.830054i	$-0.688309\pi$
$569$	10.4958	−	18.1793i	0.440007	−	0.762115i	0.997689	+	0.0679398i	$0.0216426\pi$
$570$	−10.0885	−	11.2630i	−0.422562	−	0.471754i
$571$	−6.22463	−	10.7814i	−0.260493	−	0.451186i	0.705880	−	0.708331i	$-0.250552\pi$
$571$	−6.22463	−	10.7814i	−0.260493	−	0.451186i	−0.966373	+	0.257145i	$0.917218\pi$
$572$	1.82966	+	3.16906i	0.0765019	+	0.132505i
$573$	43.8376	−	9.19941i	1.83134	−	0.384311i
$574$	−64.9045	+	112.418i	−2.70906	+	4.69223i
$575$	5.17306			0.215731
$576$	2.13005	−	19.3039i	0.0887521	−	0.804330i
$577$	9.02648			0.375777			0.187889	−	0.982190i	$-0.439836\pi$
$577$	9.02648			0.375777			0.187889	+	0.982190i	$0.439836\pi$
$578$	−6.83086	+	11.8314i	−0.284126	+	0.492121i
$579$	−9.15219	+	27.9213i	−0.380352	+	1.16037i
$580$	18.2767	+	31.6562i	0.758900	+	1.31445i
$581$	26.1632	+	45.3161i	1.08543	+	1.88003i
$582$	−2.93077	+	8.94114i	−0.121484	+	0.370622i
$583$	1.27432	−	2.20718i	0.0527768	−	0.0914122i
$584$	24.1138			0.997835
$585$	2.41789	+	1.77590i	0.0999673	+	0.0734245i
$586$	−24.3422			−1.00557
$587$	20.6462	−	35.7603i	0.852160	−	1.47598i	−0.0270943	−	0.999633i	$-0.508625\pi$
$587$	20.6462	−	35.7603i	0.852160	−	1.47598i	0.879255	−	0.476352i	$-0.158041\pi$
$588$	82.7997	−	17.3757i	3.41460	−	0.716560i
$589$	−1.02995	−	1.78393i	−0.0424384	−	0.0735055i
$590$	11.2507	+	19.4868i	0.463184	+	0.802258i
$591$	13.7570	+	15.3585i	0.565887	+	0.631763i
$592$	−14.9457	+	25.8867i	−0.614265	+	1.06394i
$593$	−26.0675			−1.07047			−0.535233	−	0.844704i	$-0.679776\pi$
$593$	−26.0675			−1.07047			−0.535233	+	0.844704i	$0.679776\pi$
$594$	−10.3974	−	4.72635i	−0.426612	−	0.193925i
$595$	−20.6116			−0.844993
$596$	−39.6902	+	68.7455i	−1.62578	+	2.81593i
$597$	−2.16318	−	2.41500i	−0.0885330	−	0.0988394i
$598$	6.39757	+	11.0809i	0.261616	+	0.453132i
$599$	−21.6431	−	37.4870i	−0.884313	−	1.53168i	−0.846499	−	0.532391i	$-0.821294\pi$
$599$	−21.6431	−	37.4870i	−0.884313	−	1.53168i	−0.0378143	−	0.999285i	$-0.512040\pi$
$600$	8.87945	−	1.86337i	0.362502	−	0.0760717i
$601$	−9.48027	+	16.4203i	−0.386708	+	0.669798i	−0.992005	−	0.126202i	$-0.959721\pi$
$601$	−9.48027	+	16.4203i	−0.386708	+	0.669798i	0.605296	+	0.796000i	$0.293055\pi$
$602$	−62.6545			−2.55361
$603$	14.9333	−	6.55629i	0.608132	−	0.266993i
$604$	−63.7134			−2.59246
$605$	5.10514	−	8.84237i	0.207554	−	0.359493i
$606$	14.9525	−	45.6167i	0.607402	−	1.85305i
$607$	−5.18348	−	8.97806i	−0.210391	−	0.364408i	0.741446	−	0.671013i	$-0.234140\pi$
$607$	−5.18348	−	8.97806i	−0.210391	−	0.364408i	−0.951837	+	0.306605i	$0.900807\pi$
$608$	−2.11741	−	3.66746i	−0.0858722	−	0.148735i
$609$	20.7992	−	63.4538i	0.842826	−	2.57128i
$610$	10.4316	−	18.0680i	0.422362	−	0.731552i
$611$	−4.03846			−0.163379
$612$	−53.6820	+	23.5684i	−2.16997	+	0.952697i
$613$	29.7259			1.20062			0.600309	−	0.799768i	$-0.295044\pi$
$613$	29.7259			1.20062			0.600309	+	0.799768i	$0.295044\pi$
$614$	33.6069	−	58.2088i	1.35626	−	2.34912i
$615$	20.4840	−	4.29860i	0.825994	−	0.173336i
$616$	−10.1084	−	17.5083i	−0.407279	−	0.705429i
$617$	−0.659220	−	1.14180i	−0.0265392	−	0.0459673i	0.852451	−	0.522808i	$-0.175115\pi$
$617$	−0.659220	−	1.14180i	−0.0265392	−	0.0459673i	−0.878990	+	0.476840i	$0.841782\pi$
$618$	17.6214	+	19.6728i	0.708837	+	0.791355i
$619$	−17.5689	+	30.4303i	−0.706155	+	1.22310i	0.260119	+	0.965577i	$0.416238\pi$
$619$	−17.5689	+	30.4303i	−0.706155	+	1.22310i	−0.966273	+	0.257519i	$0.917095\pi$
$620$	2.40327			0.0965175
$621$	−24.4704	−	11.1235i	−0.981964	−	0.446370i
$622$	−29.2717			−1.17369
$623$	−22.8593	+	39.5935i	−0.915838	+	1.58628i
$624$	5.45539	+	6.09047i	0.218390	+	0.243814i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	19.6163	+	33.9765i	0.784027	+	1.35797i
$627$	5.31677	−	1.11573i	0.212331	−	0.0445581i
$628$	−32.8705	+	56.9335i	−1.31168	+	2.27189i
$629$	−30.0509			−1.19821
$630$	−25.9734	−	19.0770i	−1.03480	−	0.760048i
$631$	40.6118			1.61673			0.808364	−	0.588683i	$-0.200353\pi$
$631$	40.6118			1.61673			0.808364	+	0.588683i	$0.200353\pi$
$632$	−22.2179	+	38.4825i	−0.883779	+	1.53075i
$633$	4.99280	−	15.2319i	0.198446	−	0.605415i
$634$	1.81720	+	3.14748i	0.0721701	+	0.125002i
$635$	−7.70184	−	13.3400i	−0.305638	−	0.529381i
$636$	6.37129	−	19.4374i	0.252638	−	0.770744i
$637$	5.93104	−	10.2729i	0.234996	−	0.407025i
$638$	−19.5117			−0.772476
$639$	2.55096	−	23.1184i	0.100914	−	0.914552i
$640$	−18.4118			−0.727792
$641$	5.83127	−	10.1001i	0.230321	−	0.398928i	−0.727581	−	0.686021i	$-0.759356\pi$
$641$	5.83127	−	10.1001i	0.230321	−	0.398928i	0.957903	+	0.287093i	$0.0926889\pi$
$642$	−32.4370	+	6.80697i	−1.28019	+	0.268650i
$643$	2.97184	+	5.14738i	0.117198	+	0.202993i	0.918656	−	0.395058i	$-0.129275\pi$
$643$	2.97184	+	5.14738i	0.117198	+	0.202993i	−0.801458	+	0.598051i	$0.795942\pi$
$644$	−46.2570	−	80.1195i	−1.82278	−	3.15715i
$645$	6.74030	+	7.52495i	0.265399	+	0.296295i
$646$	20.7155	−	35.8803i	0.815041	−	1.41169i
$647$	−23.6276			−0.928897			−0.464449	−	0.885600i	$-0.653747\pi$
$647$	−23.6276			−0.928897			−0.464449	+	0.885600i	$0.653747\pi$
$648$	−46.0098	−	10.2788i	−1.80743	−	0.403791i
$649$	−8.08437			−0.317339
$650$	1.23671	−	2.14204i	0.0485077	−	0.0840179i
$651$	−2.92921	−	3.27020i	−0.114805	−	0.128169i
$652$	35.8230	+	62.0473i	1.40294	+	2.42996i
$653$	19.1836	+	33.2269i	0.750711	+	1.30027i	0.947479	+	0.319819i	$0.103622\pi$
$653$	19.1836	+	33.2269i	0.750711	+	1.30027i	−0.196768	+	0.980450i	$0.563044\pi$
$654$	−7.41230	+	1.55548i	−0.289844	+	0.0608243i
$655$	1.09244	−	1.89216i	0.0426851	−	0.0739328i
$656$	57.0451			2.22724
$657$	−1.51467	+	13.7270i	−0.0590931	+	0.535541i
$658$	43.3819			1.69120
$659$	−9.13788	+	15.8273i	−0.355961	+	0.616543i	−0.987282	−	0.158979i	$-0.949180\pi$
$659$	−9.13788	+	15.8273i	−0.355961	+	0.616543i	0.631321	+	0.775522i	$0.282513\pi$
$660$	−1.97419	+	6.02282i	−0.0768452	+	0.234438i
$661$	11.7663	+	20.3798i	0.457655	+	0.792682i	0.998837	−	0.0482241i	$-0.0153562\pi$
$661$	11.7663	+	20.3798i	0.457655	+	0.792682i	−0.541182	+	0.840906i	$0.682023\pi$
$662$	24.5116	+	42.4553i	0.952670	+	1.65007i
$663$	−2.56039	+	7.81119i	−0.0994372	+	0.303361i
$664$	31.5559	−	54.6564i	1.22461	−	2.12108i
$665$	15.3287			0.594422
$666$	−37.8681	−	27.8135i	−1.46736	−	1.07775i
$667$	−45.9209			−1.77806
$668$	43.6693	−	75.6374i	1.68961	−	2.92650i
$669$	1.73249	−	0.363567i	0.0669821	−	0.0140563i
$670$	−6.72324	−	11.6450i	−0.259741	−	0.449885i
$671$	3.74788	+	6.49153i	0.144685	+	0.250603i
$672$	−6.02196	−	6.72299i	−0.232302	−	0.259345i
$673$	19.1513	−	33.1709i	0.738227	−	1.27865i	−0.215067	−	0.976599i	$-0.568997\pi$
$673$	19.1513	−	33.1709i	0.738227	−	1.27865i	0.953293	−	0.302047i	$-0.0976698\pi$
$674$	70.6196			2.72016
$675$	0.502989	+	5.17175i	0.0193600	+	0.199061i
$676$	4.11780			0.158377
$677$	3.92845	−	6.80427i	0.150982	−	0.261509i	−0.780606	−	0.625023i	$-0.785090\pi$
$677$	3.92845	−	6.80427i	0.150982	−	0.261509i	0.931589	+	0.363514i	$0.118423\pi$
$678$	−6.37886	−	7.12144i	−0.244979	−	0.273497i
$679$	−4.76936	−	8.26077i	−0.183031	−	0.317019i
$680$	12.4300	+	21.5294i	0.476668	+	0.825614i
$681$	6.47638	−	1.35908i	0.248176	−	0.0520801i
$682$	−0.641414	+	1.11096i	−0.0245610	+	0.0425409i
$683$	−1.16565			−0.0446023			−0.0223011	−	0.999751i	$-0.507099\pi$
$683$	−1.16565			−0.0446023			−0.0223011	+	0.999751i	$0.507099\pi$
$684$	39.9229	−	17.5277i	1.52649	−	0.670188i
$685$	−21.6214			−0.826112
$686$	−26.1146	+	45.2319i	−0.997061	+	1.72696i
$687$	1.89258	−	5.77386i	0.0722066	−	0.220287i
$688$	13.7669	+	23.8450i	0.524858	+	0.909081i
$689$	−1.43398	−	2.48373i	−0.0546303	−	0.0946225i
$690$	−6.90293	+	21.0593i	−0.262790	+	0.801716i
$691$	−2.81629	+	4.87796i	−0.107137	+	0.185566i	−0.914609	−	0.404339i	$-0.867502\pi$
$691$	−2.81629	+	4.87796i	−0.107137	+	0.185566i	0.807472	+	0.589905i	$0.200835\pi$
$692$	56.3676			2.14277
$693$	10.6017	−	4.65454i	0.402725	−	0.176811i
$694$	12.4513			0.472644
$695$	0.530148	−	0.918244i	0.0201097	−	0.0348310i
$696$	−78.8223	+	16.5410i	−2.98775	+	0.626985i
$697$	28.6747	+	49.6661i	1.08613	+	1.88124i
$698$	−29.5349	−	51.1560i	−1.11791	−	1.93628i
$699$	9.39828	+	10.4924i	0.355476	+	0.396857i
$700$	−8.94191	+	15.4878i	−0.337972	+	0.585386i
$701$	−29.3775			−1.10957			−0.554786	−	0.831993i	$-0.687200\pi$
$701$	−29.3775			−1.10957			−0.554786	+	0.831993i	$0.687200\pi$
$702$	−10.4561	+	7.47338i	−0.394639	+	0.282064i
$703$	22.3486			0.842894
$704$	2.87645	−	4.98216i	0.108410	−	0.187772i
$705$	−4.66698	−	5.21027i	−0.175769	−	0.196230i
$706$	−17.0714	−	29.5685i	−0.642489	−	1.11282i
$707$	24.3327	+	42.1455i	0.915127	+	1.58505i
$708$	−63.5009	+	13.3258i	−2.38651	+	0.500814i
$709$	11.4199	−	19.7798i	0.428883	−	0.742848i	−0.567891	−	0.823104i	$-0.692240\pi$
$709$	11.4199	−	19.7798i	0.428883	−	0.742848i	0.996774	+	0.0802560i	$0.0255738\pi$
$710$	−19.1762			−0.719671
$711$	−20.5109	−	15.0649i	−0.769219	−	0.564979i
$712$	55.1419			2.06653
$713$	−1.50957	+	2.61465i	−0.0565338	+	0.0979195i
$714$	27.5042	−	83.9092i	1.02932	−	3.14022i
$715$	0.444329	+	0.769600i	0.0166170	+	0.0287814i
$716$	−22.9469	−	39.7453i	−0.857567	−	1.48535i
$717$	−3.58609	+	10.9404i	−0.133925	+	0.408576i
$718$	−4.49599	+	7.78728i	−0.167789	+	0.290619i
$719$	5.93567			0.221363			0.110682	−	0.993856i	$-0.464697\pi$
$719$	5.93567			0.221363			0.110682	+	0.993856i	$0.464697\pi$
$720$	−1.55326	+	14.0767i	−0.0578866	+	0.524607i
$721$	−26.7743			−0.997127
$722$	8.09149	−	14.0149i	0.301134	−	0.521580i
$723$	38.8318	−	8.14893i	1.44417	−	0.303062i
$724$	30.8782	+	53.4825i	1.14758	+	1.98766i
$725$	4.43847	+	7.68765i	0.164841	+	0.285512i
$726$	29.1847	+	32.5821i	1.08315	+	1.20924i
$727$	−12.0885	+	20.9380i	−0.448339	+	0.776546i	−0.998278	−	0.0586585i	$-0.981318\pi$
$727$	−12.0885	+	20.9380i	−0.448339	+	0.776546i	0.549939	+	0.835205i	$0.314651\pi$
$728$	−22.7498			−0.843165
$729$	8.74136	−	25.5458i	0.323754	−	0.946141i
$730$	11.3862			0.421423
$731$	−13.8403	+	23.9722i	−0.511903	+	0.886643i
$732$	40.1390	+	44.8117i	1.48358	+	1.65629i
$733$	14.3488	+	24.8528i	0.529984	+	0.917960i	0.999388	+	0.0349760i	$0.0111355\pi$
$733$	14.3488	+	24.8528i	0.529984	+	0.917960i	−0.469404	+	0.882984i	$0.655531\pi$
$734$	22.6120	+	39.1651i	0.834624	+	1.44561i
$735$	20.1077	−	4.21964i	0.741685	−	0.155644i
$736$	−3.10342	+	5.37528i	−0.114394	+	0.198136i
$737$	4.83109			0.177956
$738$	−9.83439	+	89.1258i	−0.362009	+	3.28076i
$739$	−16.4924			−0.606683			−0.303342	−	0.952882i	$-0.598102\pi$
$739$	−16.4924			−0.606683			−0.303342	+	0.952882i	$0.598102\pi$
$740$	−13.0369	+	22.5806i	−0.479247	+	0.830080i
$741$	1.90414	−	5.80913i	0.0699505	−	0.213404i
$742$	15.4041	+	26.6806i	0.565501	+	0.979477i
$743$	7.51592	+	13.0180i	0.275733	+	0.477583i	0.970320	−	0.241826i	$-0.0777463\pi$
$743$	7.51592	+	13.0180i	0.275733	+	0.477583i	−0.694587	+	0.719409i	$0.744413\pi$
$744$	−1.64933	+	5.03176i	−0.0604675	+	0.184473i
$745$	−9.63869	+	16.6947i	−0.353134	+	0.611646i
$746$	39.2170			1.43584
$747$	29.1315	+	21.3966i	1.06587	+	0.782862i
$748$	−17.3667			−0.634989
$749$	16.7999	−	29.0982i	0.613853	−	1.06323i
$750$	4.19276	−	0.879859i	0.153098	−	0.0321279i
$751$	−8.28226	−	14.3453i	−0.302224	−	0.523467i	0.674415	−	0.738352i	$-0.264396\pi$
$751$	−8.28226	−	14.3453i	−0.302224	−	0.523467i	−0.976639	+	0.214885i	$0.931062\pi$
$752$	−9.53219	−	16.5102i	−0.347603	−	0.602067i
$753$	13.6054	+	15.1892i	0.495808	+	0.553526i
$754$	−10.9782	+	19.0148i	−0.399802	+	0.692478i
$755$	−15.4727			−0.563108
$756$	75.6016	−	54.0355i	2.74960	−	1.96525i
$757$	−23.7085			−0.861699			−0.430849	−	0.902424i	$-0.641786\pi$
$757$	−23.7085			−0.861699			−0.430849	+	0.902424i	$0.641786\pi$
$758$	32.5372	−	56.3562i	1.18181	−	2.04695i
$759$	−5.31252	−	5.93097i	−0.192832	−	0.215280i
$760$	−9.24410	−	16.0112i	−0.335319	−	0.580789i
$761$	3.35971	+	5.81919i	0.121789	+	0.210945i	0.920473	−	0.390805i	$-0.127803\pi$
$761$	3.35971	+	5.81919i	0.121789	+	0.210945i	−0.798684	+	0.601751i	$0.794470\pi$
$762$	64.5839	−	13.5531i	2.33963	−	0.490975i
$763$	3.83899	−	6.64933i	0.138981	−	0.240722i
$764$	106.490			3.85269
$765$	−13.0366	+	5.72354i	−0.471338	+	0.206935i
$766$	−41.0326			−1.48257
$767$	−4.54864	+	7.87848i	−0.164242	+	0.284475i
$768$	17.5837	−	53.6441i	0.634498	−	1.93571i
$769$	−19.6675	−	34.0652i	−0.709230	−	1.22842i	−0.965143	−	0.261723i	$-0.915709\pi$
$769$	−19.6675	−	34.0652i	−0.709230	−	1.22842i	0.255913	−	0.966700i	$-0.417624\pi$
$770$	−4.77306	−	8.26718i	−0.172009	−	0.297929i
$771$	−15.3698	+	46.8899i	−0.553529	+	1.68870i
$772$	−34.9279	+	60.4968i	−1.25708	+	2.17733i
$773$	35.3909			1.27292			0.636461	−	0.771309i	$-0.280398\pi$
$773$	35.3909			1.27292			0.636461	+	0.771309i	$0.280398\pi$
$774$	−39.6281	+	17.3982i	−1.42440	+	0.625366i
$775$	0.583628			0.0209645
$776$	−5.75240	+	9.96344i	−0.206499	+	0.357667i
$777$	46.6162	−	9.78250i	1.67235	−	0.350945i
$778$	9.26042	+	16.0395i	0.332002	+	0.575045i
$779$	−21.3252	−	36.9363i	−0.764055	−	1.32338i
$780$	4.75866	+	5.31263i	0.170388	+	0.190223i
$781$	3.44485	−	5.96665i	0.123266	−	0.213503i
$782$	−60.7242			−2.17149
$783$	−4.46500	−	45.9093i	−0.159566	−	1.64066i
$784$	55.9973			1.99990
$785$	−7.98254	+	13.8262i	−0.284909	+	0.493477i
$786$	6.24517	+	6.97219i	0.222758	+	0.248690i
$787$	−20.9806	−	36.3395i	−0.747878	−	1.29536i	−0.948838	−	0.315763i	$-0.897740\pi$
$787$	−20.9806	−	36.3395i	−0.747878	−	1.29536i	0.200960	−	0.979599i	$-0.435594\pi$
$788$	24.5098	+	42.4522i	0.873125	+	1.51230i
$789$	−10.9836	+	2.30493i	−0.391027	+	0.0820578i
$790$	−10.4910	+	18.1709i	−0.373253	+	0.646492i
$791$	9.69216			0.344613
$792$	−11.2552	−	8.26679i	−0.399937	−	0.293747i
$793$	8.43493			0.299533
$794$	−31.6664	+	54.8479i	−1.12380	+	1.94648i
$795$	1.54725	−	4.72034i	0.0548755	−	0.167413i
$796$	−3.85397	−	6.67528i	−0.136601	−	0.236599i
$797$	15.8121	+	27.3874i	0.560094	+	0.970111i	0.997488	+	0.0708411i	$0.0225683\pi$
$797$	15.8121	+	27.3874i	0.560094	+	0.970111i	−0.437394	+	0.899270i	$0.644098\pi$
$798$	−20.4547	+	62.4027i	−0.724087	+	2.20903i
$799$	9.58304	−	16.5983i	0.339024	−	0.587206i
$800$	1.19984			0.0424208
$801$	−3.46366	+	31.3900i	−0.122383	+	1.10911i
$802$	−38.6579			−1.36506
$803$	−2.04544	+	3.54280i	−0.0721819	+	0.125023i
$804$	37.9471	−	7.96327i	1.33829	−	0.280843i
$805$	−11.2334	−	19.4568i	−0.395926	−	0.685764i
$806$	0.721778	+	1.25016i	0.0254236	+	0.0440349i
$807$	−10.0425	−	11.2116i	−0.353514	−	0.394667i
$808$	29.3481	−	50.8324i	1.03246	−	1.78828i
$809$	−29.0869			−1.02264			−0.511320	−	0.859390i	$-0.670843\pi$
$809$	−29.0869			−1.02264			−0.511320	+	0.859390i	$0.670843\pi$
$810$	−21.7252	−	4.85354i	−0.763346	−	0.170536i
$811$	−9.39642			−0.329953			−0.164976	−	0.986298i	$-0.552755\pi$
$811$	−9.39642			−0.329953			−0.164976	+	0.986298i	$0.552755\pi$
$812$	79.3768	−	137.485i	2.78558	−	4.82476i
$813$	−24.6286	−	27.4957i	−0.863764	−	0.964317i
$814$	−6.95892	−	12.0532i	−0.243910	−	0.422465i
$815$	8.69954	+	15.0680i	0.304732	+	0.527811i
$816$	−37.9775	+	7.96964i	−1.32948	+	0.278993i
$817$	10.2930	−	17.8279i	0.360105	−	0.623721i
$818$	14.4458			0.505086
$819$	1.42900	−	12.9505i	0.0499333	−	0.452529i
$820$	49.7597			1.73768
$821$	16.1877	−	28.0379i	0.564955	−	0.978530i	−0.432099	−	0.901826i	$-0.642227\pi$
$821$	16.1877	−	28.0379i	0.564955	−	0.978530i	0.997054	−	0.0767041i	$-0.0244397\pi$
$822$	28.8516	−	88.0201i	1.00632	−	3.07005i
$823$	−8.08433	−	14.0025i	−0.281802	−	0.488095i	0.690027	−	0.723784i	$-0.257599\pi$
$823$	−8.08433	−	14.0025i	−0.281802	−	0.488095i	−0.971829	+	0.235689i	$0.924265\pi$
$824$	16.1465	+	27.9665i	0.562488	+	0.974258i
$825$	−0.479428	+	1.46263i	−0.0166915	+	0.0509222i
$826$	48.8624	−	84.6321i	1.70014	−	2.94473i
$827$	−36.1272			−1.25627			−0.628133	−	0.778106i	$-0.716180\pi$
$827$	−36.1272			−1.25627			−0.628133	+	0.778106i	$0.716180\pi$
$828$	−51.5049	−	37.8296i	−1.78992	−	1.31467i
$829$	21.4440			0.744781			0.372391	−	0.928076i	$-0.378538\pi$
$829$	21.4440			0.744781			0.372391	+	0.928076i	$0.378538\pi$
$830$	14.9003	−	25.8080i	0.517196	−	0.895810i
$831$	−55.1695	+	11.5774i	−1.91381	+	0.401616i
$832$	−3.23685	−	5.60638i	−0.112217	−	0.194366i
$833$	28.1480	+	48.7538i	0.975271	+	1.68922i
$834$	3.03071	+	3.38352i	0.104945	+	0.117162i
$835$	10.6050	−	18.3684i	0.367001	−	0.635664i
$836$	12.9155			0.446692
$837$	−2.76077	−	1.25496i	−0.0954262	−	0.0433778i
$838$	−19.3570			−0.668676
$839$	14.9853	−	25.9554i	0.517352	−	0.896079i	−0.482445	−	0.875926i	$-0.660251\pi$
$839$	14.9853	−	25.9554i	0.517352	−	0.896079i	0.999797	−	0.0201531i	$-0.00641536\pi$
$840$	−26.2904	−	29.3510i	−0.907106	−	1.01270i
$841$	−24.9000	−	43.1280i	−0.858620	−	1.48717i
$842$	23.3306	+	40.4098i	0.804026	+	1.39261i
$843$	−38.3399	+	8.04570i	−1.32050	+	0.277109i
$844$	19.0542	−	33.0029i	0.655873	−	1.13601i
$845$	1.00000			0.0344010
$846$	27.4385	−	12.0465i	0.943354	−	0.414168i
$847$	−44.3438			−1.52367
$848$	6.76939	−	11.7249i	0.232462	−	0.402636i
$849$	−14.3454	+	43.7648i	−0.492334	+	1.50200i
$850$	5.86928	+	10.1659i	0.201315	+	0.348687i
$851$	−16.3778	−	28.3673i	−0.561425	−	0.972417i
$852$	17.2234	−	52.5450i	0.590065	−	1.80016i
$853$	3.31610	−	5.74365i	0.113541	−	0.196659i	−0.803655	−	0.595096i	$-0.797114\pi$
$853$	3.31610	−	5.74365i	0.113541	−	0.196659i	0.917196	+	0.398437i	$0.130447\pi$
$854$	−90.6096			−3.10060
$855$	9.69520	−	4.25656i	0.331569	−	0.145571i
$856$	−40.5251			−1.38512
$857$	−12.3397	+	21.3731i	−0.421517	+	0.730090i	−0.996088	−	0.0883654i	$-0.971836\pi$
$857$	−12.3397	+	21.3731i	−0.421517	+	0.730090i	0.574571	+	0.818455i	$0.305169\pi$
$858$	−3.72593	+	0.781893i	−0.127201	+	0.0266934i
$859$	−26.8787	−	46.5553i	−0.917089	−	1.58845i	−0.803813	−	0.594882i	$-0.797199\pi$
$859$	−26.8787	−	46.5553i	−0.917089	−	1.58845i	−0.113276	−	0.993564i	$-0.536134\pi$
$860$	12.0087	+	20.7996i	0.409493	+	0.709262i
$861$	−60.6494	−	67.7097i	−2.06692	−	2.30754i
$862$	15.6136	−	27.0435i	0.531800	−	0.921105i
$863$	−18.8107			−0.640323			−0.320161	−	0.947363i	$-0.603737\pi$
$863$	−18.8107			−0.640323			−0.320161	+	0.947363i	$0.603737\pi$
$864$	−5.67568	−	2.57999i	−0.193091	−	0.0877729i
$865$	13.6888			0.465431
$866$	−21.1976	+	36.7152i	−0.720322	+	1.24763i
$867$	−6.38303	−	7.12609i	−0.216779	−	0.242015i
$868$	−5.21875	−	9.03914i	−0.177136	−	0.306808i
$869$	−3.76923	−	6.52850i	−0.127862	−	0.221464i
$870$	−37.2189	+	7.81045i	−1.26184	+	0.264799i
$871$	2.71820	−	4.70805i	0.0921025	−	0.159526i
$872$	−9.26054			−0.313601
$873$	−5.31045	−	3.90044i	−0.179731	−	0.132010i
$874$	45.1602			1.52757
$875$	−2.17152	+	3.76119i	−0.0734109	+	0.127151i
$876$	−10.2267	+	31.1995i	−0.345529	+	1.05413i
$877$	4.09641	+	7.09520i	0.138326	+	0.239588i	0.926863	−	0.375399i	$-0.122494\pi$
$877$	4.09641	+	7.09520i	0.138326	+	0.239588i	−0.788537	+	0.614987i	$0.789161\pi$
$878$	20.6824	+	35.8229i	0.697997	+	1.20897i
$879$	5.30946	−	16.1980i	0.179084	−	0.546345i
$880$	−2.09754	+	3.63305i	−0.0707082	+	0.122470i
$881$	−26.5398			−0.894150			−0.447075	−	0.894497i	$-0.647534\pi$
$881$	−26.5398			−0.894150			−0.447075	+	0.894497i	$0.647534\pi$
$882$	−9.65375	+	87.4886i	−0.325059	+	2.94590i
$883$	−5.30885			−0.178657			−0.0893285	−	0.996002i	$-0.528472\pi$
$883$	−5.30885			−0.178657			−0.0893285	+	0.996002i	$0.528472\pi$
$884$	−9.77131	+	16.9244i	−0.328645	+	0.569229i
$885$	−15.4211	+	3.23614i	−0.518373	+	0.108782i
$886$	−4.33683	−	7.51162i	−0.145699	−	0.252358i
$887$	−27.0317	−	46.8203i	−0.907636	−	1.57207i	−0.817339	−	0.576157i	$-0.804552\pi$
$887$	−27.0317	−	46.8203i	−0.907636	−	1.57207i	−0.0902968	−	0.995915i	$-0.528782\pi$
$888$	−38.3303	−	42.7925i	−1.28628	−	1.43602i
$889$	−33.4494	+	57.9361i	−1.12186	+	1.94312i
$890$	26.0373			0.872772
$891$	5.41292	−	5.88787i	0.181340	−	0.197251i
$892$	4.20857			0.140913
$893$	−7.12684	+	12.3441i	−0.238491	+	0.413078i
$894$	−55.1017	−	61.5162i	−1.84288	−	2.05741i
$895$	−5.57262	−	9.65205i	−0.186272	−	0.322633i
$896$	39.9818	+	69.2505i	1.33570	+	2.31350i
$897$	−8.76899	+	1.84019i	−0.292788	+	0.0614421i
$898$	6.09812	−	10.5623i	0.203497	−	0.352467i
$899$	−5.18083			−0.172790
$900$	−1.35489	+	12.2789i	−0.0451629	+	0.409296i
$901$	13.6110			0.453448
$902$	−13.2805	+	23.0025i	−0.442192	+	0.765899i
$903$	13.6660	−	41.6921i	0.454778	−	1.38743i
$904$	−5.84493	−	10.1237i	−0.194400	−	0.336710i
$905$	7.49870	+	12.9881i	0.249265	+	0.431740i
$906$	20.6468	−	62.9888i	0.685943	−	2.09266i
$907$	7.20264	−	12.4753i	0.239160	−	0.414237i	−0.721314	−	0.692609i	$-0.756461\pi$
$907$	7.20264	−	12.4753i	0.239160	−	0.414237i	0.960473	+	0.278372i	$0.0897947\pi$
$908$	15.7324			0.522099
$909$	27.0933	+	19.8996i	0.898629	+	0.660029i
$910$	−10.7422			−0.356100
$911$	−21.4708	+	37.1885i	−0.711359	+	1.23211i	0.252988	+	0.967469i	$0.418587\pi$
$911$	−21.4708	+	37.1885i	−0.711359	+	1.23211i	−0.964347	+	0.264641i	$0.914747\pi$
$912$	28.2436	−	5.92697i	0.935239	−	0.196262i
$913$	5.35342	+	9.27239i	0.177172	+	0.306871i
$914$	−34.0833	−	59.0340i	−1.12738	−	1.95267i
$915$	9.74768	+	10.8824i	0.322248	+	0.359762i
$916$	7.22274	−	12.5102i	0.238646	−	0.413347i
$917$	−9.48903			−0.313355
$918$	−5.90436	−	60.7089i	−0.194873	−	2.00369i
$919$	−13.5773			−0.447874			−0.223937	−	0.974604i	$-0.571891\pi$
$919$	−13.5773			−0.447874			−0.223937	+	0.974604i	$0.571891\pi$
$920$	−13.5488	+	23.4672i	−0.446691	+	0.773691i
$921$	31.4036	+	35.0594i	1.03478	+	1.15525i
$922$	−9.74028	−	16.8707i	−0.320779	−	0.555606i
$923$	−3.87646	−	6.71423i	−0.127595	−	0.221001i
$924$	26.9400	−	5.65340i	0.886260	−	0.185983i
$925$	−3.16599	+	5.48366i	−0.104097	+	0.180302i
$926$	88.3616			2.90374
$927$	−16.9344	+	7.43484i	−0.556198	+	0.244192i
$928$	−10.6509			−0.349633
$929$	−7.52143	+	13.0275i	−0.246770	+	0.427418i	−0.962628	−	0.270828i	$-0.912703\pi$
$929$	−7.52143	+	13.0275i	−0.246770	+	0.427418i	0.715858	+	0.698246i	$0.246036\pi$
$930$	−0.778794	+	2.37593i	−0.0255377	+	0.0779098i
$931$	−20.9335	−	36.2579i	−0.686067	−	1.18830i
$932$	16.7442	+	29.0018i	0.548475	+	0.949987i
$933$	6.38468	−	19.4783i	0.209025	−	0.637690i
$934$	−33.7639	+	58.4808i	−1.10479	+	1.91355i
$935$	−4.21747			−0.137926
$936$	−14.3890	+	6.31730i	−0.470318	+	0.206487i
$937$	21.1049			0.689466			0.344733	−	0.938701i	$-0.387970\pi$
$937$	21.1049			0.689466			0.344733	+	0.938701i	$0.387970\pi$
$938$	−29.1994	+	50.5748i	−0.953393	+	1.65132i
$939$	−26.8876	+	5.64242i	−0.877445	+	0.184133i
$940$	−8.31480	−	14.4017i	−0.271199	−	0.469730i
$941$	−1.61830	−	2.80297i	−0.0527549	−	0.0913742i	0.838442	−	0.544991i	$-0.183467\pi$
$941$	−1.61830	−	2.80297i	−0.0527549	−	0.0913742i	−0.891197	+	0.453617i	$0.850134\pi$
$942$	−45.6340	−	50.9463i	−1.48684	−	1.65992i
$943$	−31.2557	+	54.1365i	−1.01783	+	1.76293i
$944$	−42.9456			−1.39776
$945$	18.3597	−	13.1224i	0.597241	−	0.426872i
$946$	−12.8201			−0.416818
$947$	−15.9240	+	27.5812i	−0.517461	+	0.896269i	0.482333	+	0.875988i	$0.339789\pi$
$947$	−15.9240	+	27.5812i	−0.517461	+	0.896269i	−0.999794	+	0.0202810i	$0.993544\pi$
$948$	−40.3677	−	45.0670i	−1.31108	−	1.46371i
$949$	2.30172	+	3.98669i	0.0747169	+	0.129413i
$950$	−4.36494	−	7.56031i	−0.141618	−	0.245289i
$951$	−2.49079	+	0.522696i	−0.0807693	+	0.0169496i
$952$	53.9840	−	93.5031i	1.74963	−	3.03045i
$953$	38.4086			1.24418			0.622089	−	0.782947i	$-0.286284\pi$
$953$	38.4086			1.24418			0.622089	+	0.782947i	$0.286284\pi$
$954$	17.1517	+	12.5977i	0.555306	+	0.407864i
$955$	25.8610			0.836841
$956$	−13.6857	+	23.7044i	−0.442629	+	0.766656i
$957$	4.25585	−	12.9837i	0.137572	−	0.419702i
$958$	−2.67512	−	4.63344i	−0.0864292	−	0.149700i
$959$	46.9514	+	81.3223i	1.51614	+	2.62603i
$960$	3.49254	−	10.6550i	0.112721	−	0.343888i
$961$	15.3297	−	26.5518i	0.494506	−	0.856510i
$962$	−15.6616			−0.504952
$963$	2.54553	−	23.0693i	0.0820286	−	0.743398i
$964$	94.3302			3.03817
$965$	−8.48216	+	14.6915i	−0.273050	+	0.472937i
$966$	94.1981	−	19.7676i	3.03077	−	0.636013i
$967$	9.04803	+	15.6716i	0.290965	+	0.503966i	0.974038	−	0.226384i	$-0.0726903\pi$
$967$	9.04803	+	15.6716i	0.290965	+	0.503966i	−0.683073	+	0.730350i	$0.739357\pi$
$968$	26.7419	+	46.3183i	0.859516	+	1.48872i
$969$	19.3574	+	21.6109i	0.621850	+	0.694241i
$970$	−2.71621	+	4.70461i	−0.0872122	+	0.151056i
$971$	41.3033			1.32549			0.662743	−	0.748847i	$-0.269392\pi$
$971$	41.3033			1.32549			0.662743	+	0.748847i	$0.269392\pi$
$972$	32.8121	−	55.1702i	1.05245	−	1.76958i
$973$	−4.60492			−0.147627
$974$	5.56543	−	9.63960i	0.178328	−	0.308873i
$975$	1.15563	+	1.29016i	0.0370098	+	0.0413182i
$976$	19.9094	+	34.4841i	0.637285	+	1.10381i
$977$	16.7022	+	28.9291i	0.534352	+	0.925525i	0.999194	+	0.0401315i	$0.0127777\pi$
$977$	16.7022	+	28.9291i	0.534352	+	0.925525i	−0.464842	+	0.885393i	$0.653889\pi$
$978$	−72.9502	+	15.3087i	−2.33269	+	0.489520i
$979$	−4.67738	+	8.10146i	−0.149490	+	0.258924i
$980$	48.8457			1.56032
$981$	0.581688	−	5.27164i	0.0185719	−	0.168311i
$982$	−43.6099			−1.39165
$983$	23.9091	−	41.4117i	0.762581	−	1.32083i	−0.178935	−	0.983861i	$-0.557265\pi$
$983$	23.9091	−	41.4117i	0.762581	−	1.32083i	0.941516	−	0.336968i	$-0.109401\pi$
$984$	−34.1495	+	104.183i	−1.08865	+	3.32122i
$985$	5.95215	+	10.3094i	0.189651	+	0.328486i
$986$	−52.1012	−	90.2419i	−1.65924	−	2.87389i
$987$	−9.46236	+	28.8676i	−0.301190	+	0.918866i
$988$	7.26686	−	12.5866i	0.231190	−	0.400432i
$989$	−30.1722			−0.959419
$990$	−5.31457	−	3.90347i	−0.168908	−	0.124060i
$991$	−21.1584			−0.672119			−0.336059	−	0.941841i	$-0.609094\pi$
$991$	−21.1584			−0.672119			−0.336059	+	0.941841i	$0.609094\pi$
$992$	−0.350130	+	0.606443i	−0.0111166	+	0.0192546i
$993$	−33.5975	+	7.05049i	−1.06618	+	0.223740i
$994$	41.6416	+	72.1254i	1.32079	+	2.28768i
$995$	−0.935930	−	1.62108i	−0.0296710	−	0.0513916i
$996$	57.3339	+	64.0083i	1.81670	+	2.02818i
$997$	−3.45823	+	5.98982i	−0.109523	+	0.189700i	−0.915577	−	0.402142i	$-0.868266\pi$
$997$	−3.45823	+	5.98982i	−0.109523	+	0.189700i	0.806054	+	0.591842i	$0.201599\pi$
$998$	28.2763			0.895070
$999$	26.7677	−	19.1319i	0.846891	−	0.605308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.196.1	✓	26
3.2	odd	2		1755.2.i.g.586.13		26
9.2	odd	6		5265.2.a.bh.1.1		13
9.4	even	3	inner	585.2.i.g.391.1	yes	26
9.5	odd	6		1755.2.i.g.1171.13		26
9.7	even	3		5265.2.a.bg.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.1	✓	26	1.1	even	1	trivial
585.2.i.g.391.1	yes	26	9.4	even	3	inner
1755.2.i.g.586.13		26	3.2	odd	2
1755.2.i.g.1171.13		26	9.5	odd	6
5265.2.a.bg.1.13		13	9.7	even	3
5265.2.a.bh.1.1		13	9.2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23671 + 2.14204i) q^{2} +(-1.15563 - 1.29016i) q^{3} +(-2.05890 - 3.56612i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.19276 - 0.879859i) q^{6} +(-2.17152 + 3.76119i) q^{7} +5.23822 q^{8} +(-0.329032 + 2.98190i) q^{9} +O(q^{10})\)	\(q+(-1.23671 + 2.14204i) q^{2} +(-1.15563 - 1.29016i) q^{3} +(-2.05890 - 3.56612i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.19276 - 0.879859i) q^{6} +(-2.17152 + 3.76119i) q^{7} +5.23822 q^{8} +(-0.329032 + 2.98190i) q^{9} +2.47342 q^{10} +(-0.444329 + 0.769600i) q^{11} +(-2.22154 + 6.77744i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-5.37109 - 9.30300i) q^{14} +(-0.539497 + 1.64589i) q^{15} +(-2.36035 + 4.08825i) q^{16} -4.74588 q^{17} +(-5.98045 - 4.39255i) q^{18} +3.52948 q^{19} +(-2.05890 + 3.56612i) q^{20} +(7.36202 - 1.54493i) q^{21} +(-1.09901 - 1.90354i) q^{22} +(-2.58653 - 4.48000i) q^{23} +(-6.05345 - 6.75815i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.47342 q^{26} +(4.22737 - 3.02148i) q^{27} +17.8838 q^{28} +(4.43847 - 7.68765i) q^{29} +(-2.85836 - 3.19111i) q^{30} +(-0.291814 - 0.505437i) q^{31} +(-0.599920 - 1.03909i) q^{32} +(1.50639 - 0.316118i) q^{33} +(5.86928 - 10.1659i) q^{34} +4.34305 q^{35} +(11.3113 - 4.96608i) q^{36} +6.33198 q^{37} +(-4.36494 + 7.56031i) q^{38} +(0.539497 - 1.64589i) q^{39} +(-2.61911 - 4.53643i) q^{40} +(-6.04202 - 10.4651i) q^{41} +(-5.79537 + 17.6804i) q^{42} +(2.91628 - 5.05115i) q^{43} +3.65932 q^{44} +(2.74692 - 1.20600i) q^{45} +12.7951 q^{46} +(-2.01923 + 3.49741i) q^{47} +(8.00219 - 1.67928i) q^{48} +(-5.93104 - 10.2729i) q^{49} +(-1.23671 - 2.14204i) q^{50} +(5.48449 + 6.12295i) q^{51} +(2.05890 - 3.56612i) q^{52} -2.86796 q^{53} +(1.24410 + 12.7919i) q^{54} +0.888658 q^{55} +(-11.3749 + 19.7019i) q^{56} +(-4.07878 - 4.55360i) q^{57} +(10.9782 + 19.0148i) q^{58} +(4.54864 + 7.87848i) q^{59} +(6.98021 - 1.46481i) q^{60} +(4.21747 - 7.30487i) q^{61} +1.44356 q^{62} +(-10.5010 - 7.71282i) q^{63} -6.47369 q^{64} +(0.500000 - 0.866025i) q^{65} +(-1.18583 + 3.61770i) q^{66} +(-2.71820 - 4.70805i) q^{67} +(9.77131 + 16.9244i) q^{68} +(-2.79085 + 8.51426i) q^{69} +(-5.37109 + 9.30300i) q^{70} -7.75292 q^{71} +(-1.72354 + 15.6199i) q^{72} +4.60343 q^{73} +(-7.83082 + 13.5634i) q^{74} +(1.69513 - 0.355726i) q^{75} +(-7.26686 - 12.5866i) q^{76} +(-1.92974 - 3.34241i) q^{77} +(2.85836 + 3.19111i) q^{78} +(-4.24149 + 7.34648i) q^{79} +4.72070 q^{80} +(-8.78348 - 1.96228i) q^{81} +29.8889 q^{82} +(6.02416 - 10.4342i) q^{83} +(-20.6671 - 23.0730i) q^{84} +(2.37294 + 4.11006i) q^{85} +(7.21319 + 12.4936i) q^{86} +(-15.0475 + 3.15775i) q^{87} +(-2.32749 + 4.03133i) q^{88} +10.5268 q^{89} +(-0.813833 + 7.37549i) q^{90} -4.34305 q^{91} +(-10.6508 + 18.4478i) q^{92} +(-0.314865 + 0.960585i) q^{93} +(-4.99441 - 8.65057i) q^{94} +(-1.76474 - 3.05662i) q^{95} +(-0.647310 + 1.97480i) q^{96} +(-1.09816 + 1.90207i) q^{97} +29.3399 q^{98} +(-2.14867 - 1.57817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more