LMFDB - Embedded newform 430.2.e.g.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.e (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 12x^{8} + x^{7} + 106x^{6} - 27x^{5} + 233x^{4} - 164x^{3} + 460x^{2} - 240x + 144 $ x^10 - x^9 + 12x^8 + x^7 + 106x^6 - 27x^5 + 233x^4 - 164x^3 + 460x^2 - 240*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.5
Root			$1.69398 - 2.93406i$ of defining polynomial
Character	$\chi$	$=$	430.221
Dual form			430.2.e.g.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.69398 - 2.93406i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.69398 + 2.93406i) q^{6} +(0.736679 + 1.27596i) q^{7} -1.00000 q^{8} +(-4.23916 - 7.34244i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.69398 - 2.93406i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.69398 + 2.93406i) q^{6} +(0.736679 + 1.27596i) q^{7} -1.00000 q^{8} +(-4.23916 - 7.34244i) q^{9} +(-0.500000 + 0.866025i) q^{10} -2.07708 q^{11} +(1.69398 - 2.93406i) q^{12} +(-2.30850 - 3.99843i) q^{13} +(-0.736679 - 1.27596i) q^{14} +(-1.69398 - 2.93406i) q^{15} +1.00000 q^{16} +(3.97584 + 6.88635i) q^{17} +(4.23916 + 7.34244i) q^{18} +(2.34943 - 4.06933i) q^{19} +(0.500000 - 0.866025i) q^{20} +4.99169 q^{21} +2.07708 q^{22} +(0.581234 - 1.00673i) q^{23} +(-1.69398 + 2.93406i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.30850 + 3.99843i) q^{26} -18.5604 q^{27} +(0.736679 + 1.27596i) q^{28} +(1.27522 + 2.20874i) q^{29} +(1.69398 + 2.93406i) q^{30} +(0.416373 - 0.721178i) q^{31} -1.00000 q^{32} +(-3.51853 + 6.09428i) q^{33} +(-3.97584 - 6.88635i) q^{34} +1.47336 q^{35} +(-4.23916 - 7.34244i) q^{36} +(-0.937299 + 1.62345i) q^{37} +(-2.34943 + 4.06933i) q^{38} -15.6422 q^{39} +(-0.500000 + 0.866025i) q^{40} +5.77593 q^{41} -4.99169 q^{42} +(5.98643 + 2.67632i) q^{43} -2.07708 q^{44} -8.47832 q^{45} +(-0.581234 + 1.00673i) q^{46} -2.59320 q^{47} +(1.69398 - 2.93406i) q^{48} +(2.41461 - 4.18223i) q^{49} +(0.500000 + 0.866025i) q^{50} +26.9400 q^{51} +(-2.30850 - 3.99843i) q^{52} +(-6.46504 + 11.1978i) q^{53} +18.5604 q^{54} +(-1.03854 + 1.79880i) q^{55} +(-0.736679 - 1.27596i) q^{56} +(-7.95978 - 13.7868i) q^{57} +(-1.27522 - 2.20874i) q^{58} +7.95167 q^{59} +(-1.69398 - 2.93406i) q^{60} +(-7.43075 - 12.8704i) q^{61} +(-0.416373 + 0.721178i) q^{62} +(6.24579 - 10.8180i) q^{63} +1.00000 q^{64} -4.61699 q^{65} +(3.51853 - 6.09428i) q^{66} +(0.820306 - 1.42081i) q^{67} +(3.97584 + 6.88635i) q^{68} +(-1.96920 - 3.41075i) q^{69} -1.47336 q^{70} +(2.33930 + 4.05178i) q^{71} +(4.23916 + 7.34244i) q^{72} +(1.06934 + 1.85215i) q^{73} +(0.937299 - 1.62345i) q^{74} -3.38797 q^{75} +(2.34943 - 4.06933i) q^{76} +(-1.53014 - 2.65028i) q^{77} +15.6422 q^{78} +(5.45802 + 9.45357i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-18.7234 + 32.4300i) q^{81} -5.77593 q^{82} +(5.75353 - 9.96541i) q^{83} +4.99169 q^{84} +7.95167 q^{85} +(-5.98643 - 2.67632i) q^{86} +8.64078 q^{87} +2.07708 q^{88} +(-1.72550 + 2.98865i) q^{89} +8.47832 q^{90} +(3.40124 - 5.89112i) q^{91} +(0.581234 - 1.00673i) q^{92} +(-1.41066 - 2.44333i) q^{93} +2.59320 q^{94} +(-2.34943 - 4.06933i) q^{95} +(-1.69398 + 2.93406i) q^{96} +14.1058 q^{97} +(-2.41461 + 4.18223i) q^{98} +(8.80505 + 15.2508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9} - 5 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 10 q^{16} + 4 q^{17} + 8 q^{18} + 4 q^{19} + 5 q^{20} - 4 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} - 5 q^{25} + 6 q^{26} - 26 q^{27} + 6 q^{28} - q^{29} + q^{30} - 8 q^{31} - 10 q^{32} - 14 q^{33} - 4 q^{34} + 12 q^{35} - 8 q^{36} + 14 q^{37} - 4 q^{38} + 8 q^{39} - 5 q^{40} - 6 q^{41} + 4 q^{42} + 15 q^{43} + 4 q^{44} - 16 q^{45} - 8 q^{46} - 22 q^{47} + q^{48} - 5 q^{49} + 5 q^{50} + 24 q^{51} - 6 q^{52} - 8 q^{53} + 26 q^{54} + 2 q^{55} - 6 q^{56} - 32 q^{57} + q^{58} + 8 q^{59} - q^{60} - 14 q^{61} + 8 q^{62} + 22 q^{63} + 10 q^{64} - 12 q^{65} + 14 q^{66} + 19 q^{67} + 4 q^{68} + 10 q^{69} - 12 q^{70} + 36 q^{71} + 8 q^{72} + 28 q^{73} - 14 q^{74} - 2 q^{75} + 4 q^{76} + 8 q^{77} - 8 q^{78} - 10 q^{79} + 5 q^{80} - 25 q^{81} + 6 q^{82} - 25 q^{83} - 4 q^{84} + 8 q^{85} - 15 q^{86} + 22 q^{87} - 4 q^{88} + 19 q^{89} + 16 q^{90} - 10 q^{91} + 8 q^{92} + 12 q^{93} + 22 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 5 q^{98} - 6 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9 - 5 * q^10 + 4 * q^11 + q^12 - 6 * q^13 - 6 * q^14 - q^15 + 10 * q^16 + 4 * q^17 + 8 * q^18 + 4 * q^19 + 5 * q^20 - 4 * q^21 - 4 * q^22 + 8 * q^23 - q^24 - 5 * q^25 + 6 * q^26 - 26 * q^27 + 6 * q^28 - q^29 + q^30 - 8 * q^31 - 10 * q^32 - 14 * q^33 - 4 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 - 4 * q^38 + 8 * q^39 - 5 * q^40 - 6 * q^41 + 4 * q^42 + 15 * q^43 + 4 * q^44 - 16 * q^45 - 8 * q^46 - 22 * q^47 + q^48 - 5 * q^49 + 5 * q^50 + 24 * q^51 - 6 * q^52 - 8 * q^53 + 26 * q^54 + 2 * q^55 - 6 * q^56 - 32 * q^57 + q^58 + 8 * q^59 - q^60 - 14 * q^61 + 8 * q^62 + 22 * q^63 + 10 * q^64 - 12 * q^65 + 14 * q^66 + 19 * q^67 + 4 * q^68 + 10 * q^69 - 12 * q^70 + 36 * q^71 + 8 * q^72 + 28 * q^73 - 14 * q^74 - 2 * q^75 + 4 * q^76 + 8 * q^77 - 8 * q^78 - 10 * q^79 + 5 * q^80 - 25 * q^81 + 6 * q^82 - 25 * q^83 - 4 * q^84 + 8 * q^85 - 15 * q^86 + 22 * q^87 - 4 * q^88 + 19 * q^89 + 16 * q^90 - 10 * q^91 + 8 * q^92 + 12 * q^93 + 22 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 5 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.69398	−	2.93406i	0.978022	−	1.69398i	0.308442	−	0.951243i	$-0.400193\pi$
$3$	1.69398	−	2.93406i	0.978022	−	1.69398i	0.669580	−	0.742740i	$-0.266474\pi$
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.69398	+	2.93406i	−0.691566	+	1.19783i
$7$	0.736679	+	1.27596i	0.278438	+	0.482269i	0.970997	−	0.239092i	$-0.0768499\pi$
$7$	0.736679	+	1.27596i	0.278438	+	0.482269i	−0.692558	+	0.721362i	$0.743517\pi$
$8$	−1.00000			−0.353553
$9$	−4.23916	−	7.34244i	−1.41305	−	2.44748i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.07708			−0.626262			−0.313131	−	0.949710i	$-0.601378\pi$
$11$	−2.07708			−0.626262			−0.313131	+	0.949710i	$0.601378\pi$
$12$	1.69398	−	2.93406i	0.489011	−	0.846992i
$13$	−2.30850	−	3.99843i	−0.640262	−	1.10897i	−0.985374	−	0.170404i	$-0.945493\pi$
$13$	−2.30850	−	3.99843i	−0.640262	−	1.10897i	0.345113	−	0.938561i	$-0.387841\pi$
$14$	−0.736679	−	1.27596i	−0.196886	−	0.341016i
$15$	−1.69398	−	2.93406i	−0.437385	−	0.757572i
$16$	1.00000			0.250000
$17$	3.97584	+	6.88635i	0.964282	+	1.67019i	0.711532	+	0.702654i	$0.248002\pi$
$17$	3.97584	+	6.88635i	0.964282	+	1.67019i	0.252750	+	0.967532i	$0.418665\pi$
$18$	4.23916	+	7.34244i	0.999179	+	1.73063i
$19$	2.34943	−	4.06933i	0.538996	−	0.933568i	−0.459963	−	0.887938i	$-0.652137\pi$
$19$	2.34943	−	4.06933i	0.538996	−	0.933568i	0.998958	−	0.0456298i	$-0.0145295\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	4.99169			1.08928
$22$	2.07708			0.442834
$23$	0.581234	−	1.00673i	0.121196	−	0.209917i	−0.799044	−	0.601273i	$-0.794661\pi$
$23$	0.581234	−	1.00673i	0.121196	−	0.209917i	0.920239	+	0.391356i	$0.127994\pi$
$24$	−1.69398	+	2.93406i	−0.345783	+	0.598914i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.30850	+	3.99843i	0.452733	+	0.784157i
$27$	−18.5604			−3.57194
$28$	0.736679	+	1.27596i	0.139219	+	0.241135i
$29$	1.27522	+	2.20874i	0.236802	+	0.410153i	0.959795	−	0.280703i	$-0.0905675\pi$
$29$	1.27522	+	2.20874i	0.236802	+	0.410153i	−0.722993	+	0.690855i	$0.757234\pi$
$30$	1.69398	+	2.93406i	0.309278	+	0.535685i
$31$	0.416373	−	0.721178i	0.0747827	−	0.129527i	−0.826209	−	0.563364i	$-0.809507\pi$
$31$	0.416373	−	0.721178i	0.0747827	−	0.129527i	0.900992	+	0.433836i	$0.142840\pi$
$32$	−1.00000			−0.176777
$33$	−3.51853	+	6.09428i	−0.612498	+	1.06088i
$34$	−3.97584	−	6.88635i	−0.681850	−	1.18100i
$35$	1.47336			0.249043
$36$	−4.23916	−	7.34244i	−0.706526	−	1.22374i
$37$	−0.937299	+	1.62345i	−0.154091	+	0.266893i	−0.932728	−	0.360582i	$-0.882578\pi$
$37$	−0.937299	+	1.62345i	−0.154091	+	0.266893i	0.778637	+	0.627475i	$0.215912\pi$
$38$	−2.34943	+	4.06933i	−0.381128	+	0.660132i
$39$	−15.6422			−2.50476
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	5.77593			0.902049			0.451025	−	0.892512i	$-0.351059\pi$
$41$	5.77593			0.902049			0.451025	+	0.892512i	$0.351059\pi$
$42$	−4.99169			−0.770234
$43$	5.98643	+	2.67632i	0.912921	+	0.408135i
$43$	5.98643	+	2.67632i	0.912921	+	0.408135i
$44$	−2.07708			−0.313131
$45$	−8.47832			−1.26387
$46$	−0.581234	+	1.00673i	−0.0856982	+	0.148434i
$47$	−2.59320			−0.378257			−0.189129	−	0.981952i	$-0.560566\pi$
$47$	−2.59320			−0.378257			−0.189129	+	0.981952i	$0.560566\pi$
$48$	1.69398	−	2.93406i	0.244505	−	0.423496i
$49$	2.41461	−	4.18223i	0.344944	−	0.597461i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	26.9400			3.77235
$52$	−2.30850	−	3.99843i	−0.320131	−	0.554483i
$53$	−6.46504	+	11.1978i	−0.888042	+	1.53813i	−0.0458549	+	0.998948i	$0.514601\pi$
$53$	−6.46504	+	11.1978i	−0.888042	+	1.53813i	−0.842187	+	0.539186i	$0.818732\pi$
$54$	18.5604			2.52574
$55$	−1.03854	+	1.79880i	−0.140036	+	0.242550i
$56$	−0.736679	−	1.27596i	−0.0984428	−	0.170508i
$57$	−7.95978	−	13.7868i	−1.05430	−	1.82610i
$58$	−1.27522	−	2.20874i	−0.167444	−	0.290022i
$59$	7.95167			1.03522			0.517610	−	0.855617i	$-0.326822\pi$
$59$	7.95167			1.03522			0.517610	+	0.855617i	$0.326822\pi$
$60$	−1.69398	−	2.93406i	−0.218692	−	0.378786i
$61$	−7.43075	−	12.8704i	−0.951410	−	1.64789i	−0.742378	−	0.669981i	$-0.766302\pi$
$61$	−7.43075	−	12.8704i	−0.951410	−	1.64789i	−0.209032	−	0.977909i	$-0.567031\pi$
$62$	−0.416373	+	0.721178i	−0.0528794	+	0.0915897i
$63$	6.24579	−	10.8180i	0.786896	−	1.36294i
$64$	1.00000			0.125000
$65$	−4.61699			−0.572667
$66$	3.51853	−	6.09428i	0.433101	−	0.750154i
$67$	0.820306	−	1.42081i	0.100216	−	0.173580i	−0.811557	−	0.584273i	$-0.801380\pi$
$67$	0.820306	−	1.42081i	0.100216	−	0.173580i	0.911774	+	0.410693i	$0.134713\pi$
$68$	3.97584	+	6.88635i	0.482141	+	0.835093i
$69$	−1.96920	−	3.41075i	−0.237064	−	0.410607i
$70$	−1.47336			−0.176100
$71$	2.33930	+	4.05178i	0.277623	+	0.480858i	0.970794	−	0.239916i	$-0.0771199\pi$
$71$	2.33930	+	4.05178i	0.277623	+	0.480858i	−0.693170	+	0.720774i	$0.743787\pi$
$72$	4.23916	+	7.34244i	0.499590	+	0.865315i
$73$	1.06934	+	1.85215i	0.125157	+	0.216778i	0.921794	−	0.387680i	$-0.126723\pi$
$73$	1.06934	+	1.85215i	0.125157	+	0.216778i	−0.796638	+	0.604457i	$0.793390\pi$
$74$	0.937299	−	1.62345i	0.108959	−	0.188722i
$75$	−3.38797			−0.391209
$76$	2.34943	−	4.06933i	0.269498	−	0.466784i
$77$	−1.53014	−	2.65028i	−0.174375	−	0.302027i
$78$	15.6422			1.77113
$79$	5.45802	+	9.45357i	0.614075	+	1.06361i	0.990546	+	0.137181i	$0.0438042\pi$
$79$	5.45802	+	9.45357i	0.614075	+	1.06361i	−0.376471	+	0.926429i	$0.622862\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−18.7234	+	32.4300i	−2.08038	+	3.60333i
$82$	−5.77593			−0.637845
$83$	5.75353	−	9.96541i	0.631532	−	1.09385i	−0.355706	−	0.934598i	$-0.615760\pi$
$83$	5.75353	−	9.96541i	0.631532	−	1.09385i	0.987239	−	0.159248i	$-0.0509070\pi$
$84$	4.99169			0.544638
$85$	7.95167			0.862480
$86$	−5.98643	−	2.67632i	−0.645533	−	0.288595i
$87$	8.64078			0.926389
$88$	2.07708			0.221417
$89$	−1.72550	+	2.98865i	−0.182903	+	0.316796i	−0.942868	−	0.333167i	$-0.891883\pi$
$89$	−1.72550	+	2.98865i	−0.182903	+	0.316796i	0.759965	+	0.649964i	$0.225216\pi$
$90$	8.47832			0.893693
$91$	3.40124	−	5.89112i	0.356547	−	0.617557i
$92$	0.581234	−	1.00673i	0.0605978	−	0.104958i
$93$	−1.41066	−	2.44333i	−0.146278	−	0.253361i
$94$	2.59320			0.267468
$95$	−2.34943	−	4.06933i	−0.241046	−	0.417504i
$96$	−1.69398	+	2.93406i	−0.172891	+	0.299457i
$97$	14.1058			1.43223			0.716115	−	0.697982i	$-0.245919\pi$
$97$	14.1058			1.43223			0.716115	+	0.697982i	$0.245919\pi$
$98$	−2.41461	+	4.18223i	−0.243912	+	0.422469i
$99$	8.80505	+	15.2508i	0.884941	+	1.53276i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	0.767564	+	1.32946i	0.0763755	+	0.132286i	0.901684	−	0.432396i	$-0.142332\pi$
$101$	0.767564	+	1.32946i	0.0763755	+	0.132286i	−0.825308	+	0.564683i	$0.808999\pi$
$102$	−26.9400			−2.66746
$103$	7.80921	+	13.5260i	0.769465	+	1.33275i	0.937854	+	0.347031i	$0.112810\pi$
$103$	7.80921	+	13.5260i	0.769465	+	1.33275i	−0.168389	+	0.985721i	$0.553857\pi$
$104$	2.30850	+	3.99843i	0.226367	+	0.392079i
$105$	2.49584	−	4.32293i	0.243569	−	0.421874i
$106$	6.46504	−	11.1978i	0.627940	−	1.08762i
$107$	−9.83974			−0.951243			−0.475622	−	0.879650i	$-0.657777\pi$
$107$	−9.83974			−0.951243			−0.475622	+	0.879650i	$0.657777\pi$
$108$	−18.5604			−1.78597
$109$	0.957305	−	1.65810i	0.0916931	−	0.158817i	−0.816531	−	0.577302i	$-0.804105\pi$
$109$	0.957305	−	1.65810i	0.0916931	−	0.158817i	0.908224	+	0.418485i	$0.137439\pi$
$110$	1.03854	−	1.79880i	0.0990207	−	0.171509i
$111$	3.17554	+	5.50019i	0.301409	+	0.522055i
$112$	0.736679	+	1.27596i	0.0696096	+	0.120567i
$113$	−8.80804			−0.828591			−0.414295	−	0.910143i	$-0.635972\pi$
$113$	−8.80804			−0.828591			−0.414295	+	0.910143i	$0.635972\pi$
$114$	7.95978	+	13.7868i	0.745502	+	1.29125i
$115$	−0.581234	−	1.00673i	−0.0542003	−	0.0938777i
$116$	1.27522	+	2.20874i	0.118401	+	0.205076i
$117$	−19.5722	+	33.9000i	−1.80945	+	3.13405i
$118$	−7.95167			−0.732011
$119$	−5.85783	+	10.1461i	−0.536986	+	0.930087i
$120$	1.69398	+	2.93406i	0.154639	+	0.267842i
$121$	−6.68575			−0.607796
$122$	7.43075	+	12.8704i	0.672748	+	1.16523i
$123$	9.78433	−	16.9470i	0.882224	−	1.52806i
$124$	0.416373	−	0.721178i	0.0373914	−	0.0647637i
$125$	−1.00000			−0.0894427
$126$	−6.24579	+	10.8180i	−0.556420	+	0.963747i
$127$	11.0918			0.984236			0.492118	−	0.870528i	$-0.336223\pi$
$127$	11.0918			0.984236			0.492118	+	0.870528i	$0.336223\pi$
$128$	−1.00000			−0.0883883
$129$	17.9934	−	13.0309i	1.58423	−	1.14731i
$130$	4.61699			0.404937
$131$	16.9083			1.47729			0.738643	−	0.674097i	$-0.235467\pi$
$131$	16.9083			1.47729			0.738643	+	0.674097i	$0.235467\pi$
$132$	−3.51853	+	6.09428i	−0.306249	+	0.530439i
$133$	6.92309			0.600308
$134$	−0.820306	+	1.42081i	−0.0708637	+	0.122739i
$135$	−9.28018	+	16.0737i	−0.798710	+	1.38341i
$136$	−3.97584	−	6.88635i	−0.340925	−	0.590500i
$137$	−10.3776			−0.886620			−0.443310	−	0.896368i	$-0.646196\pi$
$137$	−10.3776			−0.886620			−0.443310	+	0.896368i	$0.646196\pi$
$138$	1.96920	+	3.41075i	0.167629	+	0.290343i
$139$	1.42062	−	2.46058i	0.120495	−	0.208704i	−0.799468	−	0.600709i	$-0.794885\pi$
$139$	1.42062	−	2.46058i	0.120495	−	0.208704i	0.919963	+	0.392005i	$0.128218\pi$
$140$	1.47336			0.124521
$141$	−4.39284	+	7.60862i	−0.369944	+	0.640762i
$142$	−2.33930	−	4.05178i	−0.196309	−	0.340018i
$143$	4.79492	+	8.30505i	0.400972	+	0.694503i
$144$	−4.23916	−	7.34244i	−0.353263	−	0.611870i
$145$	2.55043			0.211802
$146$	−1.06934	−	1.85215i	−0.0884991	−	0.153285i
$147$	−8.18061	−	14.1692i	−0.674726	−	1.16866i
$148$	−0.937299	+	1.62345i	−0.0770455	+	0.133447i
$149$	2.43066	−	4.21003i	0.199128	−	0.344899i	−0.749118	−	0.662436i	$-0.769523\pi$
$149$	2.43066	−	4.21003i	0.199128	−	0.344899i	0.948246	+	0.317537i	$0.102856\pi$
$150$	3.38797			0.276626
$151$	4.68558			0.381307			0.190654	−	0.981657i	$-0.438939\pi$
$151$	4.68558			0.381307			0.190654	+	0.981657i	$0.438939\pi$
$152$	−2.34943	+	4.06933i	−0.190564	+	0.330066i
$153$	33.7084	−	58.3847i	2.72516	−	4.72012i
$154$	1.53014	+	2.65028i	0.123302	+	0.213565i
$155$	−0.416373	−	0.721178i	−0.0334438	−	0.0579264i
$156$	−15.6422			−1.25238
$157$	4.60611	+	7.97802i	0.367608	+	0.636715i	0.989191	−	0.146633i	$-0.0468436\pi$
$157$	4.60611	+	7.97802i	0.367608	+	0.636715i	−0.621583	+	0.783348i	$0.713510\pi$
$158$	−5.45802	−	9.45357i	−0.434217	−	0.752086i
$159$	21.9033	+	37.9377i	1.73705	+	3.00866i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	1.71273			0.134982
$162$	18.7234	−	32.4300i	1.47105	−	2.54794i
$163$	−0.734915	−	1.27291i	−0.0575630	−	0.0997020i	0.835808	−	0.549022i	$-0.185000\pi$
$163$	−0.734915	−	1.27291i	−0.0575630	−	0.0997020i	−0.893371	+	0.449320i	$0.851666\pi$
$164$	5.77593			0.451025
$165$	3.51853	+	6.09428i	0.273917	+	0.474439i
$166$	−5.75353	+	9.96541i	−0.446561	+	0.773466i
$167$	−1.76996	+	3.06566i	−0.136963	+	0.237228i	−0.926346	−	0.376674i	$-0.877068\pi$
$167$	−1.76996	+	3.06566i	−0.136963	+	0.237228i	0.789382	+	0.613902i	$0.210401\pi$
$168$	−4.99169			−0.385117
$169$	−4.15831	+	7.20240i	−0.319870	+	0.554031i
$170$	−7.95167			−0.609866
$171$	−39.8384			−3.04652
$172$	5.98643	+	2.67632i	0.456461	+	0.204068i
$173$	2.16373			0.164505			0.0822526	−	0.996612i	$-0.473789\pi$
$173$	2.16373			0.164505			0.0822526	+	0.996612i	$0.473789\pi$
$174$	−8.64078			−0.655056
$175$	0.736679	−	1.27596i	0.0556877	−	0.0964539i
$176$	−2.07708			−0.156566
$177$	13.4700	−	23.3307i	1.01247	−	1.75364i
$178$	1.72550	−	2.98865i	0.129332	−	0.224009i
$179$	−4.35053	−	7.53534i	−0.325174	−	0.563218i	0.656374	−	0.754436i	$-0.272089\pi$
$179$	−4.35053	−	7.53534i	−0.325174	−	0.563218i	−0.981548	+	0.191218i	$0.938756\pi$
$180$	−8.47832			−0.631936
$181$	−6.30258	−	10.9164i	−0.468467	−	0.811408i	0.530884	−	0.847445i	$-0.321860\pi$
$181$	−6.30258	−	10.9164i	−0.468467	−	0.811408i	−0.999350	+	0.0360365i	$0.988527\pi$
$182$	−3.40124	+	5.89112i	−0.252117	+	0.436679i
$183$	−50.3502			−3.72200
$184$	−0.581234	+	1.00673i	−0.0428491	+	0.0742168i
$185$	0.937299	+	1.62345i	0.0689116	+	0.119358i
$186$	1.41066	+	2.44333i	0.103434	+	0.179154i
$187$	−8.25812	−	14.3035i	−0.603893	−	1.04597i
$188$	−2.59320			−0.189129
$189$	−13.6730	−	23.6824i	−0.994566	−	1.72264i
$190$	2.34943	+	4.06933i	0.170445	+	0.295220i
$191$	0.546938	−	0.947325i	0.0395751	−	0.0685460i	−0.845559	−	0.533881i	$-0.820733\pi$
$191$	0.546938	−	0.947325i	0.0395751	−	0.0685460i	0.885134	+	0.465335i	$0.154066\pi$
$192$	1.69398	−	2.93406i	0.122253	−	0.211748i
$193$	−19.4076			−1.39699			−0.698496	−	0.715614i	$-0.746147\pi$
$193$	−19.4076			−1.39699			−0.698496	+	0.715614i	$0.746147\pi$
$194$	−14.1058			−1.01274
$195$	−7.82111	+	13.5466i	−0.560081	+	0.970089i
$196$	2.41461	−	4.18223i	0.172472	−	0.298730i
$197$	6.38444	+	11.0582i	0.454872	+	0.787862i	0.998681	−	0.0513472i	$-0.0163515\pi$
$197$	6.38444	+	11.0582i	0.454872	+	0.787862i	−0.543808	+	0.839209i	$0.683018\pi$
$198$	−8.80505	−	15.2508i	−0.625748	−	1.08383i
$199$	7.82005			0.554349			0.277174	−	0.960820i	$-0.410602\pi$
$199$	7.82005			0.554349			0.277174	+	0.960820i	$0.410602\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−2.77917	−	4.81366i	−0.196028	−	0.339530i
$202$	−0.767564	−	1.32946i	−0.0540056	−	0.0935405i
$203$	−1.87885	+	3.25426i	−0.131869	+	0.228405i
$204$	26.9400			1.88618
$205$	2.88797	−	5.00210i	0.201704	−	0.349362i
$206$	−7.80921	−	13.5260i	−0.544094	−	0.942398i
$207$	−9.85577			−0.685023
$208$	−2.30850	−	3.99843i	−0.160065	−	0.277241i
$209$	−4.87994	+	8.45231i	−0.337553	+	0.584658i
$210$	−2.49584	+	4.32293i	−0.172230	+	0.298310i
$211$	17.8481			1.22871			0.614355	−	0.789030i	$-0.289416\pi$
$211$	17.8481			1.22871			0.614355	+	0.789030i	$0.289416\pi$
$212$	−6.46504	+	11.1978i	−0.444021	+	0.769067i
$213$	15.8509			1.08609
$214$	9.83974			0.672630
$215$	5.31098	−	3.84624i	0.362206	−	0.262311i
$216$	18.5604			1.26287
$217$	1.22693			0.0832895
$218$	−0.957305	+	1.65810i	−0.0648368	+	0.112301i
$219$	7.24576			0.489623
$220$	−1.03854	+	1.79880i	−0.0700182	+	0.121275i
$221$	18.3564	−	31.7942i	1.23479	−	2.13871i
$222$	−3.17554	−	5.50019i	−0.213128	−	0.369149i
$223$	−12.8901			−0.863183			−0.431592	−	0.902069i	$-0.642048\pi$
$223$	−12.8901			−0.863183			−0.431592	+	0.902069i	$0.642048\pi$
$224$	−0.736679	−	1.27596i	−0.0492214	−	0.0852540i
$225$	−4.23916	+	7.34244i	−0.282611	+	0.489496i
$226$	8.80804			0.585902
$227$	6.74819	−	11.6882i	0.447893	−	0.775773i	−0.550356	−	0.834930i	$-0.685508\pi$
$227$	6.74819	−	11.6882i	0.447893	−	0.775773i	0.998249	+	0.0591568i	$0.0188412\pi$
$228$	−7.95978	−	13.7868i	−0.527150	−	0.913050i
$229$	−8.27522	−	14.3331i	−0.546842	−	0.947158i	−0.998489	−	0.0549608i	$-0.982497\pi$
$229$	−8.27522	−	14.3331i	−0.546842	−	0.947158i	0.451647	−	0.892197i	$-0.350837\pi$
$230$	0.581234	+	1.00673i	0.0383254	+	0.0663816i
$231$	−10.3681			−0.682172
$232$	−1.27522	−	2.20874i	−0.0837221	−	0.145011i
$233$	12.3022	+	21.3080i	0.805944	+	1.39594i	0.915652	+	0.401972i	$0.131675\pi$
$233$	12.3022	+	21.3080i	0.805944	+	1.39594i	−0.109708	+	0.993964i	$0.534991\pi$
$234$	19.5722	−	33.9000i	1.27947	−	2.21611i
$235$	−1.29660	+	2.24578i	−0.0845809	+	0.146498i
$236$	7.95167			0.517610
$237$	36.9832			2.40232
$238$	5.85783	−	10.1461i	0.379707	−	0.657671i
$239$	−9.76782	+	16.9184i	−0.631828	+	1.09436i	0.355350	+	0.934733i	$0.384362\pi$
$239$	−9.76782	+	16.9184i	−0.631828	+	1.09436i	−0.987178	+	0.159625i	$0.948972\pi$
$240$	−1.69398	−	2.93406i	−0.109346	−	0.189393i
$241$	−12.2447	−	21.2085i	−0.788754	−	1.36616i	−0.926731	−	0.375726i	$-0.877393\pi$
$241$	−12.2447	−	21.2085i	−0.788754	−	1.36616i	0.137977	−	0.990435i	$-0.455940\pi$
$242$	6.68575			0.429777
$243$	35.5939	+	61.6504i	2.28335	+	3.95488i
$244$	−7.43075	−	12.8704i	−0.475705	−	0.823945i
$245$	−2.41461	−	4.18223i	−0.154264	−	0.267193i
$246$	−9.78433	+	16.9470i	−0.623826	+	1.08050i
$247$	−21.6946			−1.38039
$248$	−0.416373	+	0.721178i	−0.0264397	+	0.0457949i
$249$	−19.4928	−	33.7625i	−1.23530	−	2.13961i
$250$	1.00000			0.0632456
$251$	−0.381534	−	0.660836i	−0.0240822	−	0.0417116i	0.853733	−	0.520711i	$-0.174333\pi$
$251$	−0.381534	−	0.660836i	−0.0240822	−	0.0417116i	−0.877815	+	0.478999i	$0.841000\pi$
$252$	6.24579	−	10.8180i	0.393448	−	0.681472i
$253$	−1.20727	+	2.09105i	−0.0759002	+	0.131463i
$254$	−11.0918			−0.695960
$255$	13.4700	−	23.3307i	0.843524	−	1.46103i
$256$	1.00000			0.0625000
$257$	10.7343			0.669584			0.334792	−	0.942292i	$-0.391334\pi$
$257$	10.7343			0.669584			0.334792	+	0.942292i	$0.391334\pi$
$258$	−17.9934	+	13.0309i	−1.12022	+	0.811270i
$259$	−2.76195			−0.171619
$260$	−4.61699			−0.286334
$261$	10.8117	−	18.7264i	0.669227	−	1.15914i
$262$	−16.9083			−1.04460
$263$	−9.37292	+	16.2344i	−0.577959	+	1.00105i	0.417754	+	0.908560i	$0.362817\pi$
$263$	−9.37292	+	16.2344i	−0.577959	+	1.00105i	−0.995713	+	0.0924942i	$0.970516\pi$
$264$	3.51853	−	6.09428i	0.216551	−	0.375077i
$265$	6.46504	+	11.1978i	0.397144	+	0.687874i
$266$	−6.92309			−0.424482
$267$	5.84593	+	10.1255i	0.357765	+	0.619668i
$268$	0.820306	−	1.42081i	0.0501082	−	0.0867899i
$269$	−15.2507			−0.929853			−0.464926	−	0.885349i	$-0.653919\pi$
$269$	−15.2507			−0.929853			−0.464926	+	0.885349i	$0.653919\pi$
$270$	9.28018	−	16.0737i	0.564774	−	0.978216i
$271$	−8.60372	−	14.9021i	−0.522639	−	0.905237i	−0.999653	−	0.0263413i	$-0.991614\pi$
$271$	−8.60372	−	14.9021i	−0.522639	−	0.905237i	0.477014	−	0.878896i	$-0.341719\pi$
$272$	3.97584	+	6.88635i	0.241071	+	0.417546i
$273$	−11.5233	−	19.9589i	−0.697421	−	1.20797i
$274$	10.3776			0.626935
$275$	1.03854	+	1.79880i	0.0626262	+	0.108472i
$276$	−1.96920	−	3.41075i	−0.118532	−	0.205303i
$277$	−8.85301	+	15.3339i	−0.531926	+	0.921322i	0.467380	+	0.884057i	$0.345198\pi$
$277$	−8.85301	+	15.3339i	−0.531926	+	0.921322i	−0.999305	+	0.0372657i	$0.988135\pi$
$278$	−1.42062	+	2.46058i	−0.0852029	+	0.147576i
$279$	−7.06028			−0.422688
$280$	−1.47336			−0.0880499
$281$	−11.3625	+	19.6804i	−0.677831	+	1.17404i	0.297802	+	0.954628i	$0.403746\pi$
$281$	−11.3625	+	19.6804i	−0.677831	+	1.17404i	−0.975633	+	0.219409i	$0.929587\pi$
$282$	4.39284	−	7.60862i	0.261590	−	0.453087i
$283$	6.44217	+	11.1582i	0.382947	+	0.663284i	0.991482	−	0.130243i	$-0.0415757\pi$
$283$	6.44217	+	11.1582i	0.382947	+	0.663284i	−0.608535	+	0.793527i	$0.708242\pi$
$284$	2.33930	+	4.05178i	0.138812	+	0.240429i
$285$	−15.9196			−0.942994
$286$	−4.79492	−	8.30505i	−0.283530	−	0.491088i
$287$	4.25501	+	7.36989i	0.251165	+	0.435031i
$288$	4.23916	+	7.34244i	0.249795	+	0.432657i
$289$	−23.1146	+	40.0356i	−1.35968	+	2.35503i
$290$	−2.55043			−0.149767
$291$	23.8950	−	41.3874i	1.40075	−	2.42617i
$292$	1.06934	+	1.85215i	0.0625783	+	0.108389i
$293$	−4.97033			−0.290370			−0.145185	−	0.989405i	$-0.546378\pi$
$293$	−4.97033			−0.290370			−0.145185	+	0.989405i	$0.546378\pi$
$294$	8.18061	+	14.1692i	0.477103	+	0.826367i
$295$	3.97584	−	6.88635i	0.231482	−	0.400939i
$296$	0.937299	−	1.62345i	0.0544794	−	0.0943611i
$297$	38.5513			2.23697
$298$	−2.43066	+	4.21003i	−0.140804	+	0.243880i
$299$	−5.36710			−0.310388
$300$	−3.38797			−0.195604
$301$	0.995181	+	9.61006i	0.0573613	+	0.553915i
$302$	−4.68558			−0.269625
$303$	5.20096			0.298788
$304$	2.34943	−	4.06933i	0.134749	−	0.233392i
$305$	−14.8615			−0.850967
$306$	−33.7084	+	58.3847i	−1.92698	+	3.33763i
$307$	−10.2490	+	17.7518i	−0.584941	+	1.01315i	0.409942	+	0.912112i	$0.365549\pi$
$307$	−10.2490	+	17.7518i	−0.584941	+	1.01315i	−0.994883	+	0.101036i	$0.967784\pi$
$308$	−1.53014	−	2.65028i	−0.0871877	−	0.151014i
$309$	52.9147			3.01021
$310$	0.416373	+	0.721178i	0.0236484	+	0.0409602i
$311$	−12.4748	+	21.6070i	−0.707380	+	1.22522i	0.258445	+	0.966026i	$0.416790\pi$
$311$	−12.4748	+	21.6070i	−0.707380	+	1.22522i	−0.965826	+	0.259193i	$0.916543\pi$
$312$	15.6422			0.885566
$313$	−12.5368	+	21.7143i	−0.708620	+	1.22737i	0.256749	+	0.966478i	$0.417349\pi$
$313$	−12.5368	+	21.7143i	−0.708620	+	1.22737i	−0.965369	+	0.260888i	$0.915985\pi$
$314$	−4.60611	−	7.97802i	−0.259938	−	0.450226i
$315$	−6.24579	−	10.8180i	−0.351911	−	0.609527i
$316$	5.45802	+	9.45357i	0.307038	+	0.531805i
$317$	−29.7443			−1.67061			−0.835304	−	0.549788i	$-0.814709\pi$
$317$	−29.7443			−1.67061			−0.835304	+	0.549788i	$0.814709\pi$
$318$	−21.9033	−	37.9377i	−1.22828	−	2.12744i
$319$	−2.64872	−	4.58772i	−0.148300	−	0.256863i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−16.6683	+	28.8704i	−0.930336	+	1.61139i
$322$	−1.71273			−0.0954467
$323$	37.3638			2.07898
$324$	−18.7234	+	32.4300i	−1.04019	+	1.80166i
$325$	−2.30850	+	3.99843i	−0.128052	+	0.221793i
$326$	0.734915	+	1.27291i	0.0407032	+	0.0705000i
$327$	−3.24332	−	5.61759i	−0.179356	−	0.310653i
$328$	−5.77593			−0.318923
$329$	−1.91036	−	3.30883i	−0.105321	−	0.182422i
$330$	−3.51853	−	6.09428i	−0.193689	−	0.335479i
$331$	−6.45415	−	11.1789i	−0.354752	−	0.614449i	0.632323	−	0.774705i	$-0.282101\pi$
$331$	−6.45415	−	11.1789i	−0.354752	−	0.614449i	−0.987076	+	0.160256i	$0.948768\pi$
$332$	5.75353	−	9.96541i	0.315766	−	0.546923i
$333$	15.8934			0.870955
$334$	1.76996	−	3.06566i	0.0968478	−	0.167745i
$335$	−0.820306	−	1.42081i	−0.0448181	−	0.0776273i
$336$	4.99169			0.272319
$337$	−10.5631	−	18.2959i	−0.575410	−	0.996640i	−0.995997	−	0.0893876i	$-0.971509\pi$
$337$	−10.5631	−	18.2959i	−0.575410	−	0.996640i	0.420587	−	0.907252i	$-0.361824\pi$
$338$	4.15831	−	7.20240i	0.226182	−	0.391759i
$339$	−14.9207	+	25.8434i	−0.810380	+	1.40362i
$340$	7.95167			0.431240
$341$	−0.864837	+	1.49794i	−0.0468336	+	0.0811181i
$342$	39.8384			2.15421
$343$	17.4287			0.941059
$344$	−5.98643	−	2.67632i	−0.322766	−	0.144298i
$345$	−3.93840			−0.212036
$346$	−2.16373			−0.116323
$347$	1.66137	−	2.87757i	0.0891868	−	0.154476i	−0.817981	−	0.575245i	$-0.804907\pi$
$347$	1.66137	−	2.87757i	0.0891868	−	0.154476i	0.907168	+	0.420769i	$0.138240\pi$
$348$	8.64078			0.463195
$349$	−11.0583	+	19.1536i	−0.591939	+	1.02527i	0.402032	+	0.915626i	$0.368304\pi$
$349$	−11.0583	+	19.1536i	−0.591939	+	1.02527i	−0.993971	+	0.109643i	$0.965029\pi$
$350$	−0.736679	+	1.27596i	−0.0393771	+	0.0682032i
$351$	42.8465	+	74.2123i	2.28698	+	3.96116i
$352$	2.07708			0.110709
$353$	−11.5582	−	20.0193i	−0.615179	−	1.06552i	−0.990353	−	0.138567i	$-0.955750\pi$
$353$	−11.5582	−	20.0193i	−0.615179	−	1.06552i	0.375174	−	0.926955i	$-0.377583\pi$
$354$	−13.4700	+	23.3307i	−0.715923	+	1.24001i
$355$	4.67859			0.248314
$356$	−1.72550	+	2.98865i	−0.0914513	+	0.158398i
$357$	19.8461	+	34.3745i	1.05037	+	1.81929i
$358$	4.35053	+	7.53534i	0.229933	+	0.398255i
$359$	−14.3478	−	24.8510i	−0.757245	−	1.31159i	−0.944250	−	0.329228i	$-0.893211\pi$
$359$	−14.3478	−	24.8510i	−0.757245	−	1.31159i	0.187005	−	0.982359i	$-0.440122\pi$
$360$	8.47832			0.446847
$361$	−1.53963	−	2.66671i	−0.0810330	−	0.140353i
$362$	6.30258	+	10.9164i	0.331256	+	0.573752i
$363$	−11.3256	+	19.6164i	−0.594437	+	1.02960i
$364$	3.40124	−	5.89112i	0.178273	−	0.308779i
$365$	2.13868			0.111943
$366$	50.3502			2.63185
$367$	−7.15192	+	12.3875i	−0.373327	+	0.646621i	−0.990075	−	0.140539i	$-0.955116\pi$
$367$	−7.15192	+	12.3875i	−0.373327	+	0.646621i	0.616748	+	0.787161i	$0.288450\pi$
$368$	0.581234	−	1.00673i	0.0302989	−	0.0524792i
$369$	−24.4851	−	42.4094i	−1.27464	−	2.20775i
$370$	−0.937299	−	1.62345i	−0.0487278	−	0.0843991i
$371$	−19.0506			−0.989060
$372$	−1.41066	−	2.44333i	−0.0731391	−	0.126681i
$373$	5.13183	+	8.88858i	0.265716	+	0.460233i	0.967751	−	0.251909i	$-0.0810584\pi$
$373$	5.13183	+	8.88858i	0.265716	+	0.460233i	−0.702035	+	0.712142i	$0.747725\pi$
$374$	8.25812	+	14.3035i	0.427017	+	0.739615i
$375$	−1.69398	+	2.93406i	−0.0874769	+	0.151514i
$376$	2.59320			0.133734
$377$	5.88767	−	10.1977i	0.303230	−	0.525210i
$378$	13.6730	+	23.6824i	0.703264	+	1.21809i
$379$	−6.07708			−0.312158			−0.156079	−	0.987745i	$-0.549886\pi$
$379$	−6.07708			−0.312158			−0.156079	+	0.987745i	$0.549886\pi$
$380$	−2.34943	−	4.06933i	−0.120523	−	0.208752i
$381$	18.7893	−	32.5440i	0.962605	−	1.66728i
$382$	−0.546938	+	0.947325i	−0.0279838	+	0.0484694i
$383$	22.2542			1.13714			0.568570	−	0.822635i	$-0.307497\pi$
$383$	22.2542			1.13714			0.568570	+	0.822635i	$0.307497\pi$
$384$	−1.69398	+	2.93406i	−0.0864457	+	0.149728i
$385$	−3.06028			−0.155966
$386$	19.4076			0.987822
$387$	−5.72669	−	55.3003i	−0.291104	−	2.81107i
$388$	14.1058			0.716115
$389$	−31.5449			−1.59939			−0.799694	−	0.600407i	$-0.795005\pi$
$389$	−31.5449			−1.59939			−0.799694	+	0.600407i	$0.795005\pi$
$390$	7.82111	−	13.5466i	0.396037	−	0.685957i
$391$	9.24356			0.467467
$392$	−2.41461	+	4.18223i	−0.121956	+	0.211234i
$393$	28.6424	−	49.6101i	1.44482	−	2.50250i
$394$	−6.38444	−	11.0582i	−0.321643	−	0.557103i
$395$	10.9160			0.549246
$396$	8.80505	+	15.2508i	0.442471	+	0.766382i
$397$	−2.20394	+	3.81734i	−0.110613	+	0.191587i	−0.916017	−	0.401138i	$-0.868615\pi$
$397$	−2.20394	+	3.81734i	−0.110613	+	0.191587i	0.805405	+	0.592725i	$0.201948\pi$
$398$	−7.82005			−0.391984
$399$	11.7276	−	20.3128i	0.587115	−	1.01691i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−1.96920	−	3.41075i	−0.0983372	−	0.170325i	0.812659	−	0.582739i	$-0.198019\pi$
$401$	−1.96920	−	3.41075i	−0.0983372	−	0.170325i	−0.910996	+	0.412414i	$0.864686\pi$
$402$	2.77917	+	4.81366i	0.138612	+	0.240084i
$403$	−3.84478			−0.191522
$404$	0.767564	+	1.32946i	0.0381877	+	0.0661431i
$405$	18.7234	+	32.4300i	0.930376	+	1.61146i
$406$	1.87885	−	3.25426i	0.0932458	−	0.161506i
$407$	1.94684	−	3.37203i	0.0965013	−	0.167145i
$408$	−26.9400			−1.33373
$409$	−20.9749			−1.03714			−0.518570	−	0.855035i	$-0.673535\pi$
$409$	−20.9749			−1.03714			−0.518570	+	0.855035i	$0.673535\pi$
$410$	−2.88797	+	5.00210i	−0.142626	+	0.247036i
$411$	−17.5795	+	30.4486i	−0.867133	+	1.50192i
$412$	7.80921	+	13.5260i	0.384732	+	0.666376i
$413$	5.85783	+	10.1461i	0.288245	+	0.499255i
$414$	9.85577			0.484384
$415$	−5.75353	−	9.96541i	−0.282430	−	0.489183i
$416$	2.30850	+	3.99843i	0.113183	+	0.196039i
$417$	−4.81300	−	8.33636i	−0.235693	−	0.408233i
$418$	4.87994	−	8.45231i	0.238686	−	0.413416i
$419$	14.3444			0.700771			0.350386	−	0.936606i	$-0.386051\pi$
$419$	14.3444			0.700771			0.350386	+	0.936606i	$0.386051\pi$
$420$	2.49584	−	4.32293i	0.121785	−	0.210937i
$421$	−7.47121	−	12.9405i	−0.364124	−	0.630682i	0.624511	−	0.781016i	$-0.285298\pi$
$421$	−7.47121	−	12.9405i	−0.364124	−	0.630682i	−0.988635	+	0.150334i	$0.951965\pi$
$422$	−17.8481			−0.868829
$423$	10.9930	+	19.0404i	0.534498	+	0.925777i
$424$	6.46504	−	11.1978i	0.313970	−	0.543812i
$425$	3.97584	−	6.88635i	0.192856	−	0.334037i
$426$	−15.8509			−0.767979
$427$	10.9481	−	18.9627i	0.529818	−	0.917672i
$428$	−9.83974			−0.475622
$429$	32.4901			1.56864
$430$	−5.31098	+	3.84624i	−0.256118	+	0.185482i
$431$	−0.104394			−0.00502850			−0.00251425	−	0.999997i	$-0.500800\pi$
$431$	−0.104394			−0.00502850			−0.00251425	+	0.999997i	$0.500800\pi$
$432$	−18.5604			−0.892985
$433$	−7.73572	+	13.3987i	−0.371755	+	0.643898i	−0.989836	−	0.142216i	$-0.954577\pi$
$433$	−7.73572	+	13.3987i	−0.371755	+	0.643898i	0.618081	+	0.786115i	$0.287910\pi$
$434$	−1.22693			−0.0588946
$435$	4.32039	−	7.48314i	0.207147	−	0.358789i
$436$	0.957305	−	1.65810i	0.0458466	−	0.0794086i
$437$	−2.73113	−	4.73046i	−0.130648	−	0.226289i
$438$	−7.24576			−0.346216
$439$	20.4468	+	35.4148i	0.975871	+	1.69026i	0.677032	+	0.735954i	$0.263266\pi$
$439$	20.4468	+	35.4148i	0.975871	+	1.69026i	0.298839	+	0.954304i	$0.403401\pi$
$440$	1.03854	−	1.79880i	0.0495104	−	0.0857545i
$441$	−40.9436			−1.94970
$442$	−18.3564	+	31.7942i	−0.873125	+	1.51230i
$443$	2.57910	+	4.46713i	0.122537	+	0.212240i	0.920767	−	0.390112i	$-0.127564\pi$
$443$	2.57910	+	4.46713i	0.122537	+	0.212240i	−0.798231	+	0.602352i	$0.794230\pi$
$444$	3.17554	+	5.50019i	0.150704	+	0.261027i
$445$	1.72550	+	2.98865i	0.0817965	+	0.141676i
$446$	12.8901			0.610363
$447$	−8.23500	−	14.2634i	−0.389502	−	0.674638i
$448$	0.736679	+	1.27596i	0.0348048	+	0.0602837i
$449$	15.7340	−	27.2521i	0.742533	−	1.28610i	−0.208806	−	0.977957i	$-0.566958\pi$
$449$	15.7340	−	27.2521i	0.742533	−	1.28610i	0.951339	−	0.308147i	$-0.0997089\pi$
$450$	4.23916	−	7.34244i	0.199836	−	0.346126i
$451$	−11.9971			−0.564919
$452$	−8.80804			−0.414295
$453$	7.93730	−	13.7478i	0.372927	−	0.645928i
$454$	−6.74819	+	11.6882i	−0.316708	+	0.548555i
$455$	−3.40124	−	5.89112i	−0.159453	−	0.276180i
$456$	7.95978	+	13.7868i	0.372751	+	0.645624i
$457$	15.0525			0.704128			0.352064	−	0.935976i	$-0.385480\pi$
$457$	15.0525			0.704128			0.352064	+	0.935976i	$0.385480\pi$
$458$	8.27522	+	14.3331i	0.386675	+	0.669742i
$459$	−73.7929	−	127.813i	−3.44436	−	5.96580i
$460$	−0.581234	−	1.00673i	−0.0271002	−	0.0469389i
$461$	7.06649	−	12.2395i	0.329119	−	0.570051i	−0.653218	−	0.757170i	$-0.726582\pi$
$461$	7.06649	−	12.2395i	0.329119	−	0.570051i	0.982337	+	0.187119i	$0.0599149\pi$
$462$	10.3681			0.482368
$463$	−2.68882	+	4.65717i	−0.124960	+	0.216437i	−0.921717	−	0.387862i	$-0.873214\pi$
$463$	−2.68882	+	4.65717i	−0.124960	+	0.216437i	0.796757	+	0.604299i	$0.206547\pi$
$464$	1.27522	+	2.20874i	0.0592005	+	0.102538i
$465$	−2.82131			−0.130835
$466$	−12.3022	−	21.3080i	−0.569889	−	0.987076i
$467$	11.1215	−	19.2631i	0.514643	−	0.891388i	−0.485212	−	0.874396i	$-0.661258\pi$
$467$	11.1215	−	19.2631i	0.514643	−	0.891388i	0.999856	−	0.0169920i	$-0.00540897\pi$
$468$	−19.5722	+	33.9000i	−0.904723	+	1.56703i
$469$	2.41721			0.111616
$470$	1.29660	−	2.24578i	0.0598077	−	0.103590i
$471$	31.2107			1.43811
$472$	−7.95167			−0.366005
$473$	−12.4343	−	5.55892i	−0.571728	−	0.255600i
$474$	−36.9832			−1.69869
$475$	−4.69886			−0.215598
$476$	−5.85783	+	10.1461i	−0.268493	+	0.465044i
$477$	109.625			5.01940
$478$	9.76782	−	16.9184i	0.446770	−	0.773828i
$479$	2.82775	−	4.89781i	0.129203	−	0.223787i	−0.794165	−	0.607702i	$-0.792091\pi$
$479$	2.82775	−	4.89781i	0.129203	−	0.223787i	0.923368	+	0.383916i	$0.125425\pi$
$480$	1.69398	+	2.93406i	0.0773194	+	0.133921i
$481$	8.65500			0.394634
$482$	12.2447	+	21.2085i	0.557733	+	0.966022i
$483$	2.90134	−	5.02526i	0.132015	−	0.228657i
$484$	−6.68575			−0.303898
$485$	7.05291	−	12.2160i	0.320256	−	0.554700i
$486$	−35.5939	−	61.6504i	−1.61457	−	2.79652i
$487$	−2.53041	−	4.38281i	−0.114664	−	0.198604i	0.802981	−	0.596004i	$-0.203246\pi$
$487$	−2.53041	−	4.38281i	−0.114664	−	0.198604i	−0.917645	+	0.397400i	$0.869912\pi$
$488$	7.43075	+	12.8704i	0.336374	+	0.582617i
$489$	−4.97974			−0.225191
$490$	2.41461	+	4.18223i	0.109081	+	0.188934i
$491$	9.31732	+	16.1381i	0.420485	+	0.728301i	0.995987	−	0.0894992i	$-0.0285266\pi$
$491$	9.31732	+	16.1381i	0.420485	+	0.728301i	−0.575502	+	0.817800i	$0.695193\pi$
$492$	9.78433	−	16.9470i	0.441112	−	0.764028i
$493$	−10.1401	+	17.5632i	−0.456688	+	0.791006i
$494$	21.6946			0.976086
$495$	17.6101			0.791516
$496$	0.416373	−	0.721178i	0.0186957	−	0.0323819i
$497$	−3.44662	+	5.96972i	−0.154602	+	0.267779i
$498$	19.4928	+	33.7625i	0.873492	+	1.51293i
$499$	2.81304	+	4.87233i	0.125929	+	0.218115i	0.922096	−	0.386962i	$-0.126476\pi$
$499$	2.81304	+	4.87233i	0.125929	+	0.218115i	−0.796167	+	0.605077i	$0.793142\pi$
$500$	−1.00000			−0.0447214
$501$	5.99656	+	10.3863i	0.267906	+	0.464028i
$502$	0.381534	+	0.660836i	0.0170287	+	0.0294946i
$503$	−15.3471	−	26.5819i	−0.684292	−	1.18523i	−0.973659	−	0.228011i	$-0.926778\pi$
$503$	−15.3471	−	26.5819i	−0.684292	−	1.18523i	0.289366	−	0.957218i	$-0.406555\pi$
$504$	−6.24579	+	10.8180i	−0.278210	+	0.481874i
$505$	1.53513			0.0683123
$506$	1.20727	−	2.09105i	0.0536695	−	0.0929584i
$507$	14.0882	+	24.4015i	0.625680	+	1.08371i
$508$	11.0918			0.492118
$509$	9.07844	+	15.7243i	0.402395	+	0.696968i	0.994014	−	0.109249i	$-0.0348447\pi$
$509$	9.07844	+	15.7243i	0.402395	+	0.696968i	−0.591620	+	0.806217i	$0.701511\pi$
$510$	−13.4700	+	23.3307i	−0.596462	+	1.03310i
$511$	−1.57552	+	2.72888i	−0.0696968	+	0.120718i
$512$	−1.00000			−0.0441942
$513$	−43.6062	+	75.5282i	−1.92526	+	3.33465i
$514$	−10.7343			−0.473468
$515$	15.6184			0.688230
$516$	17.9934	−	13.0309i	0.792116	−	0.573654i
$517$	5.38628			0.236888
$518$	2.76195			0.121353
$519$	3.66532	−	6.34852i	0.160890	−	0.278669i
$520$	4.61699			0.202469
$521$	0.774287	−	1.34110i	0.0339221	−	0.0587548i	−0.848566	−	0.529090i	$-0.822534\pi$
$521$	0.774287	−	1.34110i	0.0339221	−	0.0587548i	0.882488	+	0.470335i	$0.155867\pi$
$522$	−10.8117	+	18.7264i	−0.473215	+	0.819632i
$523$	−17.1455	−	29.6969i	−0.749722	−	1.29856i	−0.947956	−	0.318402i	$-0.896854\pi$
$523$	−17.1455	−	29.6969i	−0.749722	−	1.29856i	0.198234	−	0.980155i	$-0.436479\pi$
$524$	16.9083			0.738643
$525$	−2.49584	−	4.32293i	−0.108928	−	0.188668i
$526$	9.37292	−	16.2344i	0.408679	−	0.707852i
$527$	6.62172			0.288447
$528$	−3.51853	+	6.09428i	−0.153124	+	0.265219i
$529$	10.8243	+	18.7483i	0.470623	+	0.815143i
$530$	−6.46504	−	11.1978i	−0.280824	−	0.486401i
$531$	−33.7084	−	58.3847i	−1.46282	−	2.53368i
$532$	6.92309			0.300154
$533$	−13.3337	−	23.0947i	−0.577547	−	1.00034i
$534$	−5.84593	−	10.1255i	−0.252978	−	0.438171i
$535$	−4.91987	+	8.52146i	−0.212704	+	0.368415i
$536$	−0.820306	+	1.42081i	−0.0354318	+	0.0613697i
$537$	−29.4789			−1.27211
$538$	15.2507			0.657505
$539$	−5.01533	+	8.68680i	−0.216025	+	0.374167i
$540$	−9.28018	+	16.0737i	−0.399355	+	0.691703i
$541$	20.2997	+	35.1601i	0.872753	+	1.51165i	0.859137	+	0.511745i	$0.171001\pi$
$541$	20.2997	+	35.1601i	0.872753	+	1.51165i	0.0136155	+	0.999907i	$0.495666\pi$
$542$	8.60372	+	14.9021i	0.369561	+	0.640099i
$543$	−42.7058			−1.83268
$544$	−3.97584	−	6.88635i	−0.170463	−	0.295250i
$545$	−0.957305	−	1.65810i	−0.0410064	−	0.0710252i
$546$	11.5233	+	19.9589i	0.493151	+	0.854163i
$547$	−10.1730	+	17.6202i	−0.434967	+	0.753385i	−0.997293	−	0.0735306i	$-0.976573\pi$
$547$	−10.1730	+	17.6202i	−0.434967	+	0.753385i	0.562326	+	0.826916i	$0.309907\pi$
$548$	−10.3776			−0.443310
$549$	−63.0002	+	109.120i	−2.68878	+	4.65711i
$550$	−1.03854	−	1.79880i	−0.0442834	−	0.0767011i
$551$	11.9841			0.510541
$552$	1.96920	+	3.41075i	0.0838147	+	0.145171i
$553$	−8.04161	+	13.9285i	−0.341964	+	0.592299i
$554$	8.85301	−	15.3339i	0.376128	−	0.651473i
$555$	6.35107			0.269588
$556$	1.42062	−	2.46058i	0.0602475	−	0.104352i
$557$	−25.1638			−1.06623			−0.533113	−	0.846044i	$-0.678978\pi$
$557$	−25.1638			−1.06623			−0.533113	+	0.846044i	$0.678978\pi$
$558$	7.06028			0.298885
$559$	−3.11855	−	30.1146i	−0.131901	−	1.27371i
$560$	1.47336			0.0622607
$561$	−55.9564			−2.36248
$562$	11.3625	−	19.6804i	0.479299	−	0.830170i
$563$	−40.3571			−1.70085			−0.850425	−	0.526096i	$-0.823655\pi$
$563$	−40.3571			−1.70085			−0.850425	+	0.526096i	$0.823655\pi$
$564$	−4.39284	+	7.60862i	−0.184972	+	0.320381i
$565$	−4.40402	+	7.62799i	−0.185278	+	0.320912i
$566$	−6.44217	−	11.1582i	−0.270785	−	0.469013i
$567$	−55.1727			−2.31703
$568$	−2.33930	−	4.05178i	−0.0981547	−	0.170009i
$569$	7.87266	−	13.6358i	0.330039	−	0.571645i	−0.652480	−	0.757806i	$-0.726271\pi$
$569$	7.87266	−	13.6358i	0.330039	−	0.571645i	0.982519	+	0.186161i	$0.0596047\pi$
$570$	15.9196			0.666797
$571$	10.1174	−	17.5239i	0.423401	−	0.733352i	−0.572869	−	0.819647i	$-0.694170\pi$
$571$	10.1174	−	17.5239i	0.423401	−	0.733352i	0.996270	+	0.0862954i	$0.0275029\pi$
$572$	4.79492	+	8.30505i	0.200486	+	0.347252i
$573$	−1.85301	−	3.20951i	−0.0774106	−	0.134079i
$574$	−4.25501	−	7.36989i	−0.177601	−	0.307613i
$575$	−1.16247			−0.0484782
$576$	−4.23916	−	7.34244i	−0.176632	−	0.305935i
$577$	4.53880	+	7.86143i	0.188953	+	0.327275i	0.944901	−	0.327355i	$-0.106157\pi$
$577$	4.53880	+	7.86143i	0.188953	+	0.327275i	−0.755949	+	0.654631i	$0.772824\pi$
$578$	23.1146	−	40.0356i	0.961439	−	1.66526i
$579$	−32.8762	+	56.9432i	−1.36629	+	2.36648i
$580$	2.55043			0.105901
$581$	16.9540			0.703371
$582$	−23.8950	+	41.3874i	−0.990481	+	1.71556i
$583$	13.4284	−	23.2586i	0.556147	−	0.963275i
$584$	−1.06934	−	1.85215i	−0.0442495	−	0.0766424i
$585$	19.5722	+	33.9000i	0.809209	+	1.40159i
$586$	4.97033			0.205323
$587$	11.9652	+	20.7244i	0.493859	+	0.855388i	0.999975	−	0.00707702i	$-0.00225270\pi$
$587$	11.9652	+	20.7244i	0.493859	+	0.855388i	−0.506116	+	0.862465i	$0.668919\pi$
$588$	−8.18061	−	14.1692i	−0.337363	−	0.584330i
$589$	−1.95647	−	3.38871i	−0.0806151	−	0.139630i
$590$	−3.97584	+	6.88635i	−0.163683	+	0.283507i
$591$	43.2605			1.77950
$592$	−0.937299	+	1.62345i	−0.0385227	+	0.0667233i
$593$	2.92751	+	5.07060i	0.120218	+	0.208224i	0.919854	−	0.392262i	$-0.128307\pi$
$593$	2.92751	+	5.07060i	0.120218	+	0.208224i	−0.799635	+	0.600486i	$0.794974\pi$
$594$	−38.5513			−1.58178
$595$	5.85783	+	10.1461i	0.240148	+	0.415948i
$596$	2.43066	−	4.21003i	0.0995638	−	0.172450i
$597$	13.2470	−	22.9445i	0.542165	−	0.939057i
$598$	5.36710			0.219477
$599$	−3.06194	+	5.30344i	−0.125108	+	0.216693i	−0.921775	−	0.387725i	$-0.873261\pi$
$599$	−3.06194	+	5.30344i	−0.125108	+	0.216693i	0.796667	+	0.604418i	$0.206594\pi$
$600$	3.38797			0.138313
$601$	−0.634537			−0.0258833			−0.0129417	−	0.999916i	$-0.504120\pi$
$601$	−0.634537			−0.0258833			−0.0129417	+	0.999916i	$0.504120\pi$
$602$	−0.995181	−	9.61006i	−0.0405605	−	0.391677i
$603$	−13.9096			−0.566444
$604$	4.68558			0.190654
$605$	−3.34288	+	5.79003i	−0.135907	+	0.235398i
$606$	−5.20096			−0.211275
$607$	−3.49042	+	6.04558i	−0.141672	+	0.245382i	−0.928126	−	0.372266i	$-0.878581\pi$
$607$	−3.49042	+	6.04558i	−0.141672	+	0.245382i	0.786455	+	0.617648i	$0.211914\pi$
$608$	−2.34943	+	4.06933i	−0.0952819	+	0.165033i
$609$	6.36548	+	11.0253i	0.257942	+	0.446769i
$610$	14.8615			0.601724
$611$	5.98640	+	10.3687i	0.242184	+	0.419474i
$612$	33.7084	−	58.3847i	1.36258	−	2.36006i
$613$	35.7636			1.44448			0.722239	−	0.691644i	$-0.243113\pi$
$613$	35.7636			1.44448			0.722239	+	0.691644i	$0.243113\pi$
$614$	10.2490	−	17.7518i	0.413616	−	0.716403i
$615$	−9.78433	−	16.9470i	−0.394542	−	0.683367i
$616$	1.53014	+	2.65028i	0.0616510	+	0.106783i
$617$	−16.7300	−	28.9772i	−0.673525	−	1.16658i	−0.976898	−	0.213708i	$-0.931446\pi$
$617$	−16.7300	−	28.9772i	−0.673525	−	1.16658i	0.303373	−	0.952872i	$-0.401887\pi$
$618$	−52.9147			−2.12854
$619$	12.3588	+	21.4061i	0.496742	+	0.860383i	0.999993	−	0.00375768i	$-0.00119611\pi$
$619$	12.3588	+	21.4061i	0.496742	+	0.860383i	−0.503251	+	0.864140i	$0.667863\pi$
$620$	−0.416373	−	0.721178i	−0.0167219	−	0.0289632i
$621$	−10.7879	+	18.6852i	−0.432904	+	0.749811i
$622$	12.4748	−	21.6070i	0.500193	−	0.866361i
$623$	−5.08455			−0.203708
$624$	−15.6422			−0.626190
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.5368	−	21.7143i	0.501070	−	0.867879i
$627$	16.5331	+	28.6361i	0.660268	+	1.14362i
$628$	4.60611	+	7.97802i	0.183804	+	0.318358i
$629$	−14.9062			−0.594349
$630$	6.24579	+	10.8180i	0.248838	+	0.431001i
$631$	−20.9266	−	36.2459i	−0.833074	−	1.44293i	−0.895589	−	0.444883i	$-0.853245\pi$
$631$	−20.9266	−	36.2459i	−0.833074	−	1.44293i	0.0625142	−	0.998044i	$-0.480088\pi$
$632$	−5.45802	−	9.45357i	−0.217108	−	0.376043i
$633$	30.2343	−	52.3673i	1.20171	−	2.08141i
$634$	29.7443			1.18130
$635$	5.54589	−	9.60576i	0.220082	−	0.381193i
$636$	21.9033	+	37.9377i	0.868524	+	1.50433i
$637$	−22.2965			−0.883418
$638$	2.64872	+	4.58772i	0.104864	+	0.181630i
$639$	19.8333	−	34.3523i	0.784593	−	1.35895i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	19.4245			0.767220			0.383610	−	0.923495i	$-0.374681\pi$
$641$	19.4245			0.767220			0.383610	+	0.923495i	$0.374681\pi$
$642$	16.6683	−	28.8704i	0.657847	−	1.13942i
$643$	26.5950			1.04880			0.524402	−	0.851471i	$-0.324289\pi$
$643$	26.5950			1.04880			0.524402	+	0.851471i	$0.324289\pi$
$644$	1.71273			0.0674910
$645$	−2.28840	−	22.0982i	−0.0901059	−	0.870116i
$646$	−37.3638			−1.47006
$647$	29.2680			1.15065			0.575323	−	0.817927i	$-0.304876\pi$
$647$	29.2680			1.15065			0.575323	+	0.817927i	$0.304876\pi$
$648$	18.7234	−	32.4300i	0.735527	−	1.27397i
$649$	−16.5162			−0.648319
$650$	2.30850	−	3.99843i	0.0905467	−	0.156831i
$651$	2.07840	−	3.59990i	0.0814589	−	0.141091i
$652$	−0.734915	−	1.27291i	−0.0287815	−	0.0498510i
$653$	−11.1510			−0.436374			−0.218187	−	0.975907i	$-0.570014\pi$
$653$	−11.1510			−0.436374			−0.218187	+	0.975907i	$0.570014\pi$
$654$	3.24332	+	5.61759i	0.126824	+	0.219665i
$655$	8.45415	−	14.6430i	0.330331	−	0.572150i
$656$	5.77593			0.225512
$657$	9.06619	−	15.7031i	0.353706	−	0.612636i
$658$	1.91036	+	3.30883i	0.0744734	+	0.128992i
$659$	4.27291	+	7.40090i	0.166449	+	0.288298i	0.937169	−	0.348876i	$-0.113437\pi$
$659$	4.27291	+	7.40090i	0.166449	+	0.288298i	−0.770720	+	0.637174i	$0.780103\pi$
$660$	3.51853	+	6.09428i	0.136959	+	0.237219i
$661$	−16.3275			−0.635068			−0.317534	−	0.948247i	$-0.602855\pi$
$661$	−16.3275			−0.635068			−0.317534	+	0.948247i	$0.602855\pi$
$662$	6.45415	+	11.1789i	0.250848	+	0.434481i
$663$	−62.1909	−	107.718i	−2.41529	−	4.18341i
$664$	−5.75353	+	9.96541i	−0.223280	+	0.386733i
$665$	3.46155	−	5.99558i	0.134233	−	0.232498i
$666$	−15.8934			−0.615858
$667$	2.96480			0.114797
$668$	−1.76996	+	3.06566i	−0.0684817	+	0.118614i
$669$	−21.8356	+	37.8203i	−0.844212	+	1.46222i
$670$	0.820306	+	1.42081i	0.0316912	+	0.0548908i
$671$	15.4342	+	26.7329i	0.595832	+	1.03201i
$672$	−4.99169			−0.192558
$673$	1.46541	+	2.53817i	0.0564876	+	0.0978394i	0.892886	−	0.450282i	$-0.148677\pi$
$673$	1.46541	+	2.53817i	0.0564876	+	0.0978394i	−0.836399	+	0.548121i	$0.815343\pi$
$674$	10.5631	+	18.2959i	0.406877	+	0.704731i
$675$	9.28018	+	16.0737i	0.357194	+	0.618678i
$676$	−4.15831	+	7.20240i	−0.159935	+	0.277016i
$677$	11.4376			0.439584			0.219792	−	0.975547i	$-0.429462\pi$
$677$	11.4376			0.439584			0.219792	+	0.975547i	$0.429462\pi$
$678$	14.9207	−	25.8434i	0.573025	−	0.992508i
$679$	10.3915	+	17.9985i	0.398788	+	0.690721i
$680$	−7.95167			−0.304933
$681$	−22.8626	−	39.5992i	−0.876098	−	1.51745i
$682$	0.864837	−	1.49794i	0.0331163	−	0.0573592i
$683$	−0.881071	+	1.52606i	−0.0337133	+	0.0583931i	−0.882390	−	0.470519i	$-0.844067\pi$
$683$	−0.881071	+	1.52606i	−0.0337133	+	0.0583931i	0.848676	+	0.528912i	$0.177400\pi$
$684$	−39.8384			−1.52326
$685$	−5.18881	+	8.98728i	−0.198254	+	0.343386i
$686$	−17.4287			−0.665430
$687$	−56.0723			−2.13929
$688$	5.98643	+	2.67632i	0.228230	+	0.102034i
$689$	59.6981			2.27432
$690$	3.93840			0.149932
$691$	−4.74445	+	8.21763i	−0.180487	+	0.312613i	−0.942047	−	0.335482i	$-0.891101\pi$
$691$	−4.74445	+	8.21763i	−0.180487	+	0.312613i	0.761559	+	0.648095i	$0.224434\pi$
$692$	2.16373			0.0822526
$693$	−12.9730	+	22.4699i	−0.492803	+	0.853560i
$694$	−1.66137	+	2.87757i	−0.0630646	+	0.109231i
$695$	−1.42062	−	2.46058i	−0.0538870	−	0.0933350i
$696$	−8.64078			−0.327528
$697$	22.9642	+	39.7751i	0.869830	+	1.50659i
$698$	11.0583	−	19.1536i	0.418564	−	0.724974i
$699$	83.3589			3.15292
$700$	0.736679	−	1.27596i	0.0278438	−	0.0482269i
$701$	0.460327	+	0.797310i	0.0173863	+	0.0301140i	0.874588	−	0.484867i	$-0.161132\pi$
$701$	0.460327	+	0.797310i	0.0173863	+	0.0301140i	−0.857201	+	0.514981i	$0.827799\pi$
$702$	−42.8465	−	74.2123i	−1.61714	−	2.80096i
$703$	4.40423	+	7.62835i	0.166109	+	0.287709i
$704$	−2.07708			−0.0782828
$705$	4.39284	+	7.60862i	0.165444	+	0.286557i
$706$	11.5582	+	20.0193i	0.434998	+	0.753438i
$707$	−1.13090	+	1.95877i	−0.0425317	+	0.0736671i
$708$	13.4700	−	23.3307i	0.506234	−	0.876822i
$709$	−22.2731			−0.836483			−0.418242	−	0.908336i	$-0.637353\pi$
$709$	−22.2731			−0.836483			−0.418242	+	0.908336i	$0.637353\pi$
$710$	−4.67859			−0.175584
$711$	46.2748	−	80.1503i	1.73544	−	3.00587i
$712$	1.72550	−	2.98865i	0.0646658	−	0.112004i
$713$	−0.484019	−	0.838346i	−0.0181267	−	0.0313963i
$714$	−19.8461	−	34.3745i	−0.742723	−	1.28643i
$715$	9.58985			0.358640
$716$	−4.35053	−	7.53534i	−0.162587	−	0.281609i
$717$	33.0931	+	57.3189i	1.23588	+	2.14061i
$718$	14.3478	+	24.8510i	0.535453	+	0.927432i
$719$	−8.32637	+	14.4217i	−0.310521	+	0.537838i	−0.978475	−	0.206364i	$-0.933837\pi$
$719$	−8.32637	+	14.4217i	−0.310521	+	0.537838i	0.667954	+	0.744202i	$0.267170\pi$
$720$	−8.47832			−0.315968
$721$	−11.5058	+	19.9286i	−0.428497	+	0.742178i
$722$	1.53963	+	2.66671i	0.0572990	+	0.0992447i
$723$	−82.9696			−3.08567
$724$	−6.30258	−	10.9164i	−0.234233	−	0.405704i
$725$	1.27522	−	2.20874i	0.0473604	−	0.0820306i
$726$	11.3256	−	19.6164i	0.420331	−	0.728034i
$727$	38.1692			1.41562			0.707809	−	0.706404i	$-0.249684\pi$
$727$	38.1692			1.41562			0.707809	+	0.706404i	$0.249684\pi$
$728$	−3.40124	+	5.89112i	−0.126058	+	0.218339i
$729$	128.841			4.77189
$730$	−2.13868			−0.0791560
$731$	5.37096	+	51.8653i	0.198652	+	1.91831i
$732$	−50.3502			−1.86100
$733$	45.9519			1.69727			0.848636	−	0.528978i	$-0.177425\pi$
$733$	45.9519			1.69727			0.848636	+	0.528978i	$0.177425\pi$
$734$	7.15192	−	12.3875i	0.263982	−	0.457230i
$735$	−16.3612			−0.603493
$736$	−0.581234	+	1.00673i	−0.0214246	+	0.0371084i
$737$	−1.70384	+	2.95113i	−0.0627617	+	0.108706i
$738$	24.4851	+	42.4094i	0.901309	+	1.56111i
$739$	−5.99074			−0.220373			−0.110187	−	0.993911i	$-0.535145\pi$
$739$	−5.99074			−0.220373			−0.110187	+	0.993911i	$0.535145\pi$
$740$	0.937299	+	1.62345i	0.0344558	+	0.0596792i
$741$	−36.7503	+	63.6533i	−1.35005	+	2.33836i
$742$	19.0506			0.699371
$743$	26.4027	−	45.7308i	0.968620	−	1.67770i	0.269063	−	0.963123i	$-0.413286\pi$
$743$	26.4027	−	45.7308i	0.968620	−	1.67770i	0.699557	−	0.714577i	$-0.253381\pi$
$744$	1.41066	+	2.44333i	0.0517172	+	0.0895768i
$745$	−2.43066	−	4.21003i	−0.0890526	−	0.154244i
$746$	−5.13183	−	8.88858i	−0.187889	−	0.325434i
$747$	−97.5605			−3.56955
$748$	−8.25812	−	14.3035i	−0.301947	−	0.522987i
$749$	−7.24872	−	12.5552i	−0.264863	−	0.458755i
$750$	1.69398	−	2.93406i	0.0618555	−	0.107137i
$751$	−2.57864	+	4.46633i	−0.0940958	+	0.162979i	−0.909231	−	0.416292i	$-0.863329\pi$
$751$	−2.57864	+	4.46633i	−0.0940958	+	0.162979i	0.815135	+	0.579271i	$0.196663\pi$
$752$	−2.59320			−0.0945643
$753$	−2.58525			−0.0942117
$754$	−5.88767	+	10.1977i	−0.214416	+	0.371380i
$755$	2.34279	−	4.05783i	0.0852629	−	0.147680i
$756$	−13.6730	−	23.6824i	−0.497283	−	0.861319i
$757$	−10.0319	−	17.3758i	−0.364617	−	0.631536i	0.624097	−	0.781347i	$-0.285467\pi$
$757$	−10.0319	−	17.3758i	−0.364617	−	0.631536i	−0.988715	+	0.149811i	$0.952134\pi$
$758$	6.07708			0.220729
$759$	4.09018	+	7.08440i	0.148464	+	0.257147i
$760$	2.34943	+	4.06933i	0.0852227	+	0.147610i
$761$	−6.40095	−	11.0868i	−0.232034	−	0.401895i	0.726372	−	0.687301i	$-0.241205\pi$
$761$	−6.40095	−	11.0868i	−0.232034	−	0.401895i	−0.958407	+	0.285406i	$0.907871\pi$
$762$	−18.7893	+	32.5440i	−0.680664	+	1.17895i
$763$	2.82090			0.102124
$764$	0.546938	−	0.947325i	0.0197875	−	0.0342730i
$765$	−33.7084	−	58.3847i	−1.21873	−	2.11090i
$766$	−22.2542			−0.804079
$767$	−18.3564	−	31.7942i	−0.662812	−	1.14802i
$768$	1.69398	−	2.93406i	0.0611264	−	0.105874i
$769$	9.48862	−	16.4348i	0.342168	−	0.592653i	−0.642667	−	0.766146i	$-0.722172\pi$
$769$	9.48862	−	16.4348i	0.342168	−	0.592653i	0.984835	+	0.173493i	$0.0555053\pi$
$770$	3.06028			0.110285
$771$	18.1836	−	31.4950i	0.654868	−	1.13426i
$772$	−19.4076			−0.698496
$773$	−34.6412			−1.24596			−0.622979	−	0.782238i	$-0.714078\pi$
$773$	−34.6412			−1.24596			−0.622979	+	0.782238i	$0.714078\pi$
$774$	5.72669	+	55.3003i	0.205841	+	1.98773i
$775$	−0.832745			−0.0299131
$776$	−14.1058			−0.506370
$777$	−4.67870	+	8.10375i	−0.167847	+	0.290720i
$778$	31.5449			1.13094
$779$	13.5701	−	23.5042i	0.486201	−	0.842124i
$780$	−7.82111	+	13.5466i	−0.280041	+	0.485045i
$781$	−4.85890	−	8.41586i	−0.173865	−	0.301143i
$782$	−9.24356			−0.330549
$783$	−23.6685	−	40.9950i	−0.845842	−	1.46504i
$784$	2.41461	−	4.18223i	0.0862360	−	0.149365i
$785$	9.21223			0.328798
$786$	−28.6424	+	49.6101i	−1.02164	+	1.76953i
$787$	−17.5472	−	30.3926i	−0.625489	−	1.08338i	−0.988446	−	0.151573i	$-0.951566\pi$
$787$	−17.5472	−	30.3926i	−0.625489	−	1.08338i	0.362957	−	0.931806i	$-0.381767\pi$
$788$	6.38444	+	11.0582i	0.227436	+	0.393931i
$789$	31.7551	+	55.0015i	1.13051	+	1.95811i
$790$	−10.9160			−0.388375
$791$	−6.48869	−	11.2387i	−0.230711	−	0.399604i
$792$	−8.80505	−	15.2508i	−0.312874	−	0.541914i
$793$	−34.3077	+	59.4227i	−1.21830	+	2.11016i
$794$	2.20394	−	3.81734i	0.0782150	−	0.135472i
$795$	43.8067			1.55366
$796$	7.82005			0.277174
$797$	−0.444416	+	0.769752i	−0.0157420	+	0.0272660i	−0.873789	−	0.486305i	$-0.838344\pi$
$797$	−0.444416	+	0.769752i	−0.0157420	+	0.0272660i	0.858047	+	0.513571i	$0.171678\pi$
$798$	−11.7276	+	20.3128i	−0.415153	+	0.719066i
$799$	−10.3101	−	17.8577i	−0.364747	−	0.631760i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	29.2587			1.03380
$802$	1.96920	+	3.41075i	0.0695349	+	0.120438i
$803$	−2.22110	−	3.84705i	−0.0783808	−	0.135760i
$804$	−2.77917	−	4.81366i	−0.0980138	−	0.169765i
$805$	0.856365	−	1.48327i	0.0301829	−	0.0522783i
$806$	3.84478			0.135427
$807$	−25.8345	+	44.7466i	−0.909416	+	1.57516i
$808$	−0.767564	−	1.32946i	−0.0270028	−	0.0467703i
$809$	3.99091			0.140313			0.0701565	−	0.997536i	$-0.477650\pi$
$809$	3.99091			0.140313			0.0701565	+	0.997536i	$0.477650\pi$
$810$	−18.7234	−	32.4300i	−0.657875	−	1.13947i
$811$	−0.0450072	+	0.0779548i	−0.00158042	+	0.00273736i	−0.866815	−	0.498631i	$-0.833836\pi$
$811$	−0.0450072	+	0.0779548i	−0.00158042	+	0.00273736i	0.865234	+	0.501368i	$0.167170\pi$
$812$	−1.87885	+	3.25426i	−0.0659347	+	0.114202i
$813$	−58.2982			−2.04461
$814$	−1.94684	+	3.37203i	−0.0682367	+	0.118189i
$815$	−1.46983			−0.0514859
$816$	26.9400			0.943089
$817$	24.9555	−	18.0729i	0.873083	−	0.632291i
$818$	20.9749			0.733369
$819$	−57.6736			−2.01528
$820$	2.88797	−	5.00210i	0.100852	−	0.174681i
$821$	37.3726			1.30431			0.652156	−	0.758084i	$-0.273865\pi$
$821$	37.3726			1.30431			0.652156	+	0.758084i	$0.273865\pi$
$822$	17.5795	−	30.4486i	0.613156	−	1.06202i
$823$	10.8190	−	18.7390i	0.377125	−	0.653200i	−0.613517	−	0.789681i	$-0.710246\pi$
$823$	10.8190	−	18.7390i	0.377125	−	0.653200i	0.990643	+	0.136481i	$0.0435793\pi$
$824$	−7.80921	−	13.5260i	−0.272047	−	0.471199i
$825$	7.03706			0.244999
$826$	−5.85783	−	10.1461i	−0.203820	−	0.353026i
$827$	17.8072	−	30.8431i	0.619219	−	1.07252i	−0.370410	−	0.928868i	$-0.620783\pi$
$827$	17.8072	−	30.8431i	0.619219	−	1.07252i	0.989629	−	0.143650i	$-0.0458838\pi$
$828$	−9.85577			−0.342512
$829$	2.06795	−	3.58179i	0.0718229	−	0.124401i	−0.827877	−	0.560909i	$-0.810452\pi$
$829$	2.06795	−	3.58179i	0.0718229	−	0.124401i	0.899700	+	0.436508i	$0.143785\pi$
$830$	5.75353	+	9.96541i	0.199708	+	0.345904i
$831$	29.9937	+	51.9506i	1.04047	+	1.80215i
$832$	−2.30850	−	3.99843i	−0.0800327	−	0.138621i
$833$	38.4004			1.33049
$834$	4.81300	+	8.33636i	0.166660	+	0.288664i
$835$	1.76996	+	3.06566i	0.0612519	+	0.106091i
$836$	−4.87994	+	8.45231i	−0.168776	+	0.292329i
$837$	−7.72802	+	13.3853i	−0.267119	+	0.462664i
$838$	−14.3444			−0.495520
$839$	−55.8497			−1.92815			−0.964074	−	0.265635i	$-0.914418\pi$
$839$	−55.8497			−1.92815			−0.964074	+	0.265635i	$0.914418\pi$
$840$	−2.49584	+	4.32293i	−0.0861148	+	0.149155i
$841$	11.2476	−	19.4815i	0.387850	−	0.671776i
$842$	7.47121	+	12.9405i	0.257475	+	0.445960i
$843$	38.4958	+	66.6767i	1.32587	+	2.29647i
$844$	17.8481			0.614355
$845$	4.15831	+	7.20240i	0.143050	+	0.247770i
$846$	−10.9930	−	19.0404i	−0.377947	−	0.654623i
$847$	−4.92525	−	8.53079i	−0.169234	−	0.293121i
$848$	−6.46504	+	11.1978i	−0.222010	+	0.384533i
$849$	43.6517			1.49812
$850$	−3.97584	+	6.88635i	−0.136370	+	0.236200i
$851$	1.08958	+	1.88721i	0.0373503	+	0.0646926i
$852$	15.8509			0.543043
$853$	13.5222	+	23.4211i	0.462991	+	0.801924i	0.999108	−	0.0422197i	$-0.0134430\pi$
$853$	13.5222	+	23.4211i	0.462991	+	0.801924i	−0.536118	+	0.844143i	$0.680110\pi$
$854$	−10.9481	+	18.9627i	−0.374638	+	0.648892i
$855$	−19.9192	+	34.5011i	−0.681222	+	1.17991i
$856$	9.83974			0.336315
$857$	−0.334886	+	0.580039i	−0.0114395	+	0.0198137i	−0.871688	−	0.490060i	$-0.836975\pi$
$857$	−0.334886	+	0.580039i	−0.0114395	+	0.0198137i	0.860249	+	0.509874i	$0.170308\pi$
$858$	−32.4901			−1.10919
$859$	18.1482			0.619208			0.309604	−	0.950866i	$-0.399804\pi$
$859$	18.1482			0.619208			0.309604	+	0.950866i	$0.399804\pi$
$860$	5.31098	−	3.84624i	0.181103	−	0.131156i
$861$	28.8316			0.982580
$862$	0.104394			0.00355569
$863$	−3.73814	+	6.47465i	−0.127248	+	0.220400i	−0.922609	−	0.385736i	$-0.873948\pi$
$863$	−3.73814	+	6.47465i	−0.127248	+	0.220400i	0.795362	+	0.606135i	$0.207281\pi$
$864$	18.5604			0.631436
$865$	1.08186	−	1.87384i	0.0367845	−	0.0637126i
$866$	7.73572	−	13.3987i	0.262870	−	0.455305i
$867$	78.3113	+	135.639i	2.65959	+	4.60655i
$868$	1.22693			0.0416448
$869$	−11.3367	−	19.6358i	−0.384572	−	0.666098i
$870$	−4.32039	+	7.48314i	−0.146475	+	0.253702i
$871$	−7.57469			−0.256659
$872$	−0.957305	+	1.65810i	−0.0324184	+	0.0561504i
$873$	−59.7968	−	103.571i	−2.02382	−	3.50535i
$874$	2.73113	+	4.73046i	0.0923820	+	0.160010i
$875$	−0.736679	−	1.27596i	−0.0249043	−	0.0431355i
$876$	7.24576			0.244812
$877$	−25.6960	−	44.5069i	−0.867694	−	1.50289i	−0.864347	−	0.502896i	$-0.832268\pi$
$877$	−25.6960	−	44.5069i	−0.867694	−	1.50289i	−0.00334673	−	0.999994i	$-0.501065\pi$
$878$	−20.4468	−	35.4148i	−0.690045	−	1.19519i
$879$	−8.41966	+	14.5833i	−0.283988	+	0.491882i
$880$	−1.03854	+	1.79880i	−0.0350091	+	0.0606376i
$881$	16.6135			0.559722			0.279861	−	0.960041i	$-0.409712\pi$
$881$	16.6135			0.559722			0.279861	+	0.960041i	$0.409712\pi$
$882$	40.9436			1.37864
$883$	2.28000	−	3.94908i	0.0767283	−	0.132897i	−0.825108	−	0.564975i	$-0.808886\pi$
$883$	2.28000	−	3.94908i	0.0767283	−	0.132897i	0.901837	+	0.432077i	$0.142219\pi$
$884$	18.3564	−	31.7942i	0.617393	−	1.06936i
$885$	−13.4700	−	23.3307i	−0.452789	−	0.784254i
$886$	−2.57910	−	4.46713i	−0.0866465	−	0.150076i
$887$	18.3164			0.615003			0.307502	−	0.951548i	$-0.400507\pi$
$887$	18.3164			0.615003			0.307502	+	0.951548i	$0.400507\pi$
$888$	−3.17554	−	5.50019i	−0.106564	−	0.184574i
$889$	8.17108	+	14.1527i	0.274049	+	0.474667i
$890$	−1.72550	−	2.98865i	−0.0578389	−	0.100180i
$891$	38.8900	−	67.3595i	1.30287	−	2.25663i
$892$	−12.8901			−0.431592
$893$	−6.09254	+	10.5526i	−0.203879	+	0.353129i
$894$	8.23500	+	14.2634i	0.275420	+	0.477041i
$895$	−8.70106			−0.290844
$896$	−0.736679	−	1.27596i	−0.0246107	−	0.0426270i
$897$	−9.09178	+	15.7474i	−0.303566	+	0.525791i
$898$	−15.7340	+	27.2521i	−0.525050	+	0.909413i
$899$	2.12386			0.0708347
$900$	−4.23916	+	7.34244i	−0.141305	+	0.244748i
$901$	−102.816			−3.42529
$902$	11.9971			0.399458
$903$	29.8824	+	13.3594i	0.994423	+	0.444571i
$904$	8.80804			0.292951
$905$	−12.6052			−0.419009
$906$	−7.93730	+	13.7478i	−0.263699	+	0.456740i
$907$	−38.1477			−1.26667			−0.633337	−	0.773876i	$-0.718315\pi$
$907$	−38.1477			−1.26667			−0.633337	+	0.773876i	$0.718315\pi$
$908$	6.74819	−	11.6882i	0.223947	−	0.387887i
$909$	6.50765	−	11.2716i	0.215845	−	0.373855i
$910$	3.40124	+	5.89112i	0.112750	+	0.195289i
$911$	−13.2049			−0.437498			−0.218749	−	0.975781i	$-0.570198\pi$
$911$	−13.2049			−0.437498			−0.218749	+	0.975781i	$0.570198\pi$
$912$	−7.95978	−	13.7868i	−0.263575	−	0.456525i
$913$	−11.9505	+	20.6989i	−0.395505	+	0.685034i
$914$	−15.0525			−0.497894
$915$	−25.1751	+	43.6046i	−0.832264	+	1.44152i
$916$	−8.27522	−	14.3331i	−0.273421	−	0.473579i
$917$	12.4560	+	21.5744i	0.411333	+	0.712450i
$918$	73.7929	+	127.813i	2.43553	+	4.21846i
$919$	46.8097			1.54411			0.772056	−	0.635555i	$-0.219229\pi$
$919$	46.8097			1.54411			0.772056	+	0.635555i	$0.219229\pi$
$920$	0.581234	+	1.00673i	0.0191627	+	0.0331908i
$921$	34.7232	+	60.1424i	1.14417	+	1.98176i
$922$	−7.06649	+	12.2395i	−0.232722	+	0.403087i
$923$	10.8005	−	18.7070i	0.355503	−	0.615750i
$924$	−10.3681			−0.341086
$925$	1.87460			0.0616364
$926$	2.68882	−	4.65717i	0.0883601	−	0.153044i
$927$	66.2090	−	114.677i	2.17459	−	3.76650i
$928$	−1.27522	−	2.20874i	−0.0418610	−	0.0725055i
$929$	−0.533828	−	0.924617i	−0.0175143	−	0.0303357i	0.857135	−	0.515091i	$-0.172242\pi$
$929$	−0.533828	−	0.924617i	−0.0175143	−	0.0303357i	−0.874650	+	0.484755i	$0.838909\pi$
$930$	2.82131			0.0925145
$931$	−11.3459	−	19.6517i	−0.371847	−	0.644058i
$932$	12.3022	+	21.3080i	0.402972	+	0.697968i
$933$	42.2642	+	73.2037i	1.38367	+	2.39658i
$934$	−11.1215	+	19.2631i	−0.363908	+	0.630307i
$935$	−16.5162			−0.540139
$936$	19.5722	−	33.9000i	0.639736	−	1.10806i
$937$	−22.8338	−	39.5493i	−0.745948	−	1.29202i	−0.949751	−	0.313008i	$-0.898663\pi$
$937$	−22.8338	−	39.5493i	−0.745948	−	1.29202i	0.203803	−	0.979012i	$-0.434670\pi$
$938$	−2.41721			−0.0789246
$939$	42.4741	+	73.5674i	1.38609	+	2.40078i
$940$	−1.29660	+	2.24578i	−0.0422905	+	0.0732492i
$941$	−24.5646	+	42.5471i	−0.800783	+	1.38700i	0.118318	+	0.992976i	$0.462250\pi$
$941$	−24.5646	+	42.5471i	−0.800783	+	1.38700i	−0.919101	+	0.394021i	$0.871084\pi$
$942$	−31.2107			−1.01690
$943$	3.35717	−	5.81478i	0.109324	−	0.189355i
$944$	7.95167			0.258805
$945$	−27.3460			−0.889566
$946$	12.4343	+	5.55892i	0.404273	+	0.180736i
$947$	−43.4866			−1.41313			−0.706563	−	0.707650i	$-0.749755\pi$
$947$	−43.4866			−1.41313			−0.706563	+	0.707650i	$0.749755\pi$
$948$	36.9832			1.20116
$949$	4.93713	−	8.55135i	0.160266	−	0.277589i
$950$	4.69886			0.152451
$951$	−50.3864	+	87.2718i	−1.63389	+	2.82998i
$952$	5.85783	−	10.1461i	0.189853	−	0.328836i
$953$	−10.6922	−	18.5194i	−0.346354	−	0.599902i	0.639245	−	0.769003i	$-0.279247\pi$
$953$	−10.6922	−	18.5194i	−0.346354	−	0.599902i	−0.985599	+	0.169101i	$0.945914\pi$
$954$	−109.625			−3.54925
$955$	−0.546938	−	0.947325i	−0.0176985	−	0.0306547i
$956$	−9.76782	+	16.9184i	−0.315914	+	0.547179i
$957$	−17.9476			−0.580162
$958$	−2.82775	+	4.89781i	−0.0913606	+	0.158241i
$959$	−7.64497	−	13.2415i	−0.246869	−	0.427590i
$960$	−1.69398	−	2.93406i	−0.0546731	−	0.0946965i
$961$	15.1533	+	26.2462i	0.488815	+	0.846653i
$962$	−8.65500			−0.279048
$963$	41.7122	+	72.2476i	1.34416	+	2.32815i
$964$	−12.2447	−	21.2085i	−0.394377	−	0.683081i
$965$	−9.70382	+	16.8075i	−0.312377	+	0.541053i
$966$	−2.90134	+	5.02526i	−0.0933489	+	0.161685i
$967$	33.2705			1.06991			0.534953	−	0.844882i	$-0.320329\pi$
$967$	33.2705			1.06991			0.534953	+	0.844882i	$0.320329\pi$
$968$	6.68575			0.214888
$969$	63.2936	−	109.628i	2.03328	−	3.52175i
$970$	−7.05291	+	12.2160i	−0.226455	+	0.392232i
$971$	−12.7741	−	22.1254i	−0.409940	−	0.710037i	0.584943	−	0.811075i	$-0.301117\pi$
$971$	−12.7741	−	22.1254i	−0.409940	−	0.710037i	−0.994883	+	0.101038i	$0.967784\pi$
$972$	35.5939	+	61.6504i	1.14167	+	1.97744i
$973$	4.18615			0.134202
$974$	2.53041	+	4.38281i	0.0810797	+	0.140434i
$975$	7.82111	+	13.5466i	0.250476	+	0.433837i
$976$	−7.43075	−	12.8704i	−0.237852	−	0.411972i
$977$	1.56093	−	2.70361i	0.0499385	−	0.0864960i	−0.839976	−	0.542624i	$-0.817431\pi$
$977$	1.56093	−	2.70361i	0.0499385	−	0.0864960i	0.889914	+	0.456128i	$0.150764\pi$
$978$	4.97974			0.159234
$979$	3.58399	−	6.20766i	0.114545	−	0.198398i
$980$	−2.41461	−	4.18223i	−0.0771319	−	0.133596i
$981$	−16.2327			−0.518269
$982$	−9.31732	−	16.1381i	−0.297328	−	0.514987i
$983$	−2.98848	+	5.17620i	−0.0953177	+	0.165095i	−0.909741	−	0.415176i	$-0.863720\pi$
$983$	−2.98848	+	5.17620i	−0.0953177	+	0.165095i	0.814423	+	0.580271i	$0.197053\pi$
$984$	−9.78433	+	16.9470i	−0.311913	+	0.540249i
$985$	12.7689			0.406850
$986$	10.1401	−	17.5632i	0.322927	−	0.559326i
$987$	−12.9444			−0.412026
$988$	−21.6946			−0.690197
$989$	6.17384	−	4.47112i	0.196317	−	0.142173i
$990$	−17.6101			−0.559686
$991$	−29.4118			−0.934295			−0.467148	−	0.884179i	$-0.654718\pi$
$991$	−29.4118			−0.934295			−0.467148	+	0.884179i	$0.654718\pi$
$992$	−0.416373	+	0.721178i	−0.0132198	+	0.0228974i
$993$	−43.7329			−1.38782
$994$	3.44662	−	5.96972i	0.109320	−	0.189348i
$995$	3.91003	−	6.77236i	0.123956	−	0.214698i
$996$	−19.4928	−	33.7625i	−0.617652	−	1.06981i
$997$	21.8421			0.691745			0.345873	−	0.938282i	$-0.387583\pi$
$997$	21.8421			0.691745			0.345873	+	0.938282i	$0.387583\pi$
$998$	−2.81304	−	4.87233i	−0.0890452	−	0.154231i
$999$	17.3966	−	30.1318i	0.550404	−	0.953327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.g.221.5	✓	10
43.36	even	3	inner	430.2.e.g.251.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.g.221.5	✓	10	1.1	even	1	trivial
430.2.e.g.251.5	yes	10	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.69398 - 2.93406i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.69398 + 2.93406i) q^{6} +(0.736679 + 1.27596i) q^{7} -1.00000 q^{8} +(-4.23916 - 7.34244i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.69398 - 2.93406i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.69398 + 2.93406i) q^{6} +(0.736679 + 1.27596i) q^{7} -1.00000 q^{8} +(-4.23916 - 7.34244i) q^{9} +(-0.500000 + 0.866025i) q^{10} -2.07708 q^{11} +(1.69398 - 2.93406i) q^{12} +(-2.30850 - 3.99843i) q^{13} +(-0.736679 - 1.27596i) q^{14} +(-1.69398 - 2.93406i) q^{15} +1.00000 q^{16} +(3.97584 + 6.88635i) q^{17} +(4.23916 + 7.34244i) q^{18} +(2.34943 - 4.06933i) q^{19} +(0.500000 - 0.866025i) q^{20} +4.99169 q^{21} +2.07708 q^{22} +(0.581234 - 1.00673i) q^{23} +(-1.69398 + 2.93406i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.30850 + 3.99843i) q^{26} -18.5604 q^{27} +(0.736679 + 1.27596i) q^{28} +(1.27522 + 2.20874i) q^{29} +(1.69398 + 2.93406i) q^{30} +(0.416373 - 0.721178i) q^{31} -1.00000 q^{32} +(-3.51853 + 6.09428i) q^{33} +(-3.97584 - 6.88635i) q^{34} +1.47336 q^{35} +(-4.23916 - 7.34244i) q^{36} +(-0.937299 + 1.62345i) q^{37} +(-2.34943 + 4.06933i) q^{38} -15.6422 q^{39} +(-0.500000 + 0.866025i) q^{40} +5.77593 q^{41} -4.99169 q^{42} +(5.98643 + 2.67632i) q^{43} -2.07708 q^{44} -8.47832 q^{45} +(-0.581234 + 1.00673i) q^{46} -2.59320 q^{47} +(1.69398 - 2.93406i) q^{48} +(2.41461 - 4.18223i) q^{49} +(0.500000 + 0.866025i) q^{50} +26.9400 q^{51} +(-2.30850 - 3.99843i) q^{52} +(-6.46504 + 11.1978i) q^{53} +18.5604 q^{54} +(-1.03854 + 1.79880i) q^{55} +(-0.736679 - 1.27596i) q^{56} +(-7.95978 - 13.7868i) q^{57} +(-1.27522 - 2.20874i) q^{58} +7.95167 q^{59} +(-1.69398 - 2.93406i) q^{60} +(-7.43075 - 12.8704i) q^{61} +(-0.416373 + 0.721178i) q^{62} +(6.24579 - 10.8180i) q^{63} +1.00000 q^{64} -4.61699 q^{65} +(3.51853 - 6.09428i) q^{66} +(0.820306 - 1.42081i) q^{67} +(3.97584 + 6.88635i) q^{68} +(-1.96920 - 3.41075i) q^{69} -1.47336 q^{70} +(2.33930 + 4.05178i) q^{71} +(4.23916 + 7.34244i) q^{72} +(1.06934 + 1.85215i) q^{73} +(0.937299 - 1.62345i) q^{74} -3.38797 q^{75} +(2.34943 - 4.06933i) q^{76} +(-1.53014 - 2.65028i) q^{77} +15.6422 q^{78} +(5.45802 + 9.45357i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-18.7234 + 32.4300i) q^{81} -5.77593 q^{82} +(5.75353 - 9.96541i) q^{83} +4.99169 q^{84} +7.95167 q^{85} +(-5.98643 - 2.67632i) q^{86} +8.64078 q^{87} +2.07708 q^{88} +(-1.72550 + 2.98865i) q^{89} +8.47832 q^{90} +(3.40124 - 5.89112i) q^{91} +(0.581234 - 1.00673i) q^{92} +(-1.41066 - 2.44333i) q^{93} +2.59320 q^{94} +(-2.34943 - 4.06933i) q^{95} +(-1.69398 + 2.93406i) q^{96} +14.1058 q^{97} +(-2.41461 + 4.18223i) q^{98} +(8.80505 + 15.2508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + q^{3} + 10 q^{4} + 5 q^{5} - q^{6} + 6 q^{7} - 10 q^{8} - 8 q^{9} - 5 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 10 q^{16} + 4 q^{17} + 8 q^{18} + 4 q^{19} + 5 q^{20} - 4 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} - 5 q^{25} + 6 q^{26} - 26 q^{27} + 6 q^{28} - q^{29} + q^{30} - 8 q^{31} - 10 q^{32} - 14 q^{33} - 4 q^{34} + 12 q^{35} - 8 q^{36} + 14 q^{37} - 4 q^{38} + 8 q^{39} - 5 q^{40} - 6 q^{41} + 4 q^{42} + 15 q^{43} + 4 q^{44} - 16 q^{45} - 8 q^{46} - 22 q^{47} + q^{48} - 5 q^{49} + 5 q^{50} + 24 q^{51} - 6 q^{52} - 8 q^{53} + 26 q^{54} + 2 q^{55} - 6 q^{56} - 32 q^{57} + q^{58} + 8 q^{59} - q^{60} - 14 q^{61} + 8 q^{62} + 22 q^{63} + 10 q^{64} - 12 q^{65} + 14 q^{66} + 19 q^{67} + 4 q^{68} + 10 q^{69} - 12 q^{70} + 36 q^{71} + 8 q^{72} + 28 q^{73} - 14 q^{74} - 2 q^{75} + 4 q^{76} + 8 q^{77} - 8 q^{78} - 10 q^{79} + 5 q^{80} - 25 q^{81} + 6 q^{82} - 25 q^{83} - 4 q^{84} + 8 q^{85} - 15 q^{86} + 22 q^{87} - 4 q^{88} + 19 q^{89} + 16 q^{90} - 10 q^{91} + 8 q^{92} + 12 q^{93} + 22 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 5 q^{98} - 6 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + q^3 + 10 * q^4 + 5 * q^5 - q^6 + 6 * q^7 - 10 * q^8 - 8 * q^9 - 5 * q^10 + 4 * q^11 + q^12 - 6 * q^13 - 6 * q^14 - q^15 + 10 * q^16 + 4 * q^17 + 8 * q^18 + 4 * q^19 + 5 * q^20 - 4 * q^21 - 4 * q^22 + 8 * q^23 - q^24 - 5 * q^25 + 6 * q^26 - 26 * q^27 + 6 * q^28 - q^29 + q^30 - 8 * q^31 - 10 * q^32 - 14 * q^33 - 4 * q^34 + 12 * q^35 - 8 * q^36 + 14 * q^37 - 4 * q^38 + 8 * q^39 - 5 * q^40 - 6 * q^41 + 4 * q^42 + 15 * q^43 + 4 * q^44 - 16 * q^45 - 8 * q^46 - 22 * q^47 + q^48 - 5 * q^49 + 5 * q^50 + 24 * q^51 - 6 * q^52 - 8 * q^53 + 26 * q^54 + 2 * q^55 - 6 * q^56 - 32 * q^57 + q^58 + 8 * q^59 - q^60 - 14 * q^61 + 8 * q^62 + 22 * q^63 + 10 * q^64 - 12 * q^65 + 14 * q^66 + 19 * q^67 + 4 * q^68 + 10 * q^69 - 12 * q^70 + 36 * q^71 + 8 * q^72 + 28 * q^73 - 14 * q^74 - 2 * q^75 + 4 * q^76 + 8 * q^77 - 8 * q^78 - 10 * q^79 + 5 * q^80 - 25 * q^81 + 6 * q^82 - 25 * q^83 - 4 * q^84 + 8 * q^85 - 15 * q^86 + 22 * q^87 - 4 * q^88 + 19 * q^89 + 16 * q^90 - 10 * q^91 + 8 * q^92 + 12 * q^93 + 22 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 5 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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