LMFDB - Embedded newform 930.2.n.c.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 205x^{8} + 675x^{6} + 795x^{4} + 230x^{2} + 5 $ x^12 + 25x^10 + 205x^8 + 675x^6 + 795x^4 + 230*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.1
Root			$-0.153723i$ of defining polynomial
Character	$\chi$	$=$	930.481
Dual form			930.2.n.c.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-1.26952 + 3.90719i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-1.26952 + 3.90719i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.769524 - 2.36835i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.662817 - 0.481565i) q^{13} +(-1.26952 - 3.90719i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.162817 + 0.501100i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-2.35182 + 1.70870i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(3.32366 - 2.41478i) q^{21} +(0.769524 + 2.36835i) q^{22} +(-0.293932 - 0.904630i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +0.819287 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.32366 + 2.41478i) q^{28} +(0.589079 - 0.427991i) q^{29} -1.00000 q^{30} +(-1.17309 - 5.44278i) q^{31} +1.00000 q^{32} +(-2.01464 + 1.46372i) q^{33} +(-0.426262 - 0.309697i) q^{34} +(1.26952 - 3.90719i) q^{35} +1.00000 q^{36} -3.68397 q^{37} +(0.898316 - 2.76473i) q^{38} +(0.253174 + 0.779189i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(9.06701 - 6.58757i) q^{41} +(-1.26952 + 3.90719i) q^{42} +(-3.80256 + 2.76272i) q^{43} +(-2.01464 - 1.46372i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(0.769524 + 0.559092i) q^{46} +(0.555410 + 0.403529i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-7.99135 - 5.80605i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(0.162817 - 0.501100i) q^{51} +(-0.662817 + 0.481565i) q^{52} +(-2.65305 - 8.16525i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.769524 + 2.36835i) q^{55} -4.10827 q^{56} +2.90701 q^{57} +(-0.225008 + 0.692504i) q^{58} +(-10.7116 - 7.78244i) q^{59} +(0.809017 - 0.587785i) q^{60} -14.4527 q^{61} +(4.14823 + 3.71378i) q^{62} -4.10827 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.662817 + 0.481565i) q^{65} +(0.769524 - 2.36835i) q^{66} -8.88436 q^{67} +0.526888 q^{68} +(-0.293932 + 0.904630i) q^{69} +(1.26952 + 3.90719i) q^{70} +(-3.98026 - 12.2500i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(0.0958121 - 0.294879i) q^{73} +(2.98039 - 2.16538i) q^{74} +(-0.809017 - 0.587785i) q^{75} +(0.898316 + 2.76473i) q^{76} +(8.27667 + 6.01336i) q^{77} +(-0.662817 - 0.481565i) q^{78} +(0.715905 + 2.20333i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.46329 + 10.6589i) q^{82} +(-3.81517 + 2.77188i) q^{83} +(-1.26952 - 3.90719i) q^{84} +(-0.162817 - 0.501100i) q^{85} +(1.45245 - 4.47018i) q^{86} -0.728142 q^{87} +2.49023 q^{88} +(2.01464 - 6.20042i) q^{89} +(0.809017 + 0.587785i) q^{90} +(2.72303 - 1.97840i) q^{91} -0.951184 q^{92} +(-2.25014 + 5.09283i) q^{93} -0.686525 q^{94} +(2.35182 - 1.70870i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(5.06656 - 15.5933i) q^{97} +9.87785 q^{98} +2.49023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.00000			0.408248
$7$	−1.26952	+	3.90719i	−0.479835	+	1.47678i	0.359489	+	0.933149i	$0.382951\pi$
$7$	−1.26952	+	3.90719i	−0.479835	+	1.47678i	−0.839324	+	0.543631i	$0.817049\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	0.809017	−	0.587785i	0.255834	−	0.185874i
$11$	0.769524	−	2.36835i	0.232020	−	0.714085i	−0.765483	−	0.643457i	$-0.777500\pi$
$11$	0.769524	−	2.36835i	0.232020	−	0.714085i	0.997503	−	0.0706280i	$-0.0225003\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−0.662817	−	0.481565i	−0.183832	−	0.133562i	0.492063	−	0.870560i	$-0.336243\pi$
$13$	−0.662817	−	0.481565i	−0.183832	−	0.133562i	−0.675896	+	0.736997i	$0.736243\pi$
$14$	−1.26952	−	3.90719i	−0.339295	−	1.04424i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.162817	+	0.501100i	0.0394890	+	0.121535i	0.968858	−	0.247618i	$-0.0796479\pi$
$17$	0.162817	+	0.501100i	0.0394890	+	0.121535i	−0.929369	+	0.369153i	$0.879648\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−2.35182	+	1.70870i	−0.539545	+	0.392002i	−0.823916	−	0.566712i	$-0.808215\pi$
$19$	−2.35182	+	1.70870i	−0.539545	+	0.392002i	0.284371	+	0.958714i	$0.408215\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	3.32366	−	2.41478i	0.725281	−	0.526948i
$22$	0.769524	+	2.36835i	0.164063	+	0.504934i
$23$	−0.293932	−	0.904630i	−0.0612891	−	0.188628i	0.915724	−	0.401808i	$-0.131618\pi$
$23$	−0.293932	−	0.904630i	−0.0612891	−	0.188628i	−0.977013	+	0.213180i	$0.931618\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	0.819287			0.160675
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	3.32366	+	2.41478i	0.628112	+	0.456350i
$29$	0.589079	−	0.427991i	0.109389	−	0.0794759i	−0.531746	−	0.846904i	$-0.678464\pi$
$29$	0.589079	−	0.427991i	0.109389	−	0.0794759i	0.641135	+	0.767428i	$0.278464\pi$
$30$	−1.00000			−0.182574
$31$	−1.17309	−	5.44278i	−0.210693	−	0.977552i
$31$	−1.17309	−	5.44278i	−0.210693	−	0.977552i
$32$	1.00000			0.176777
$33$	−2.01464	+	1.46372i	−0.350704	+	0.254801i
$34$	−0.426262	−	0.309697i	−0.0731032	−	0.0531126i
$35$	1.26952	−	3.90719i	0.214589	−	0.660436i
$36$	1.00000			0.166667
$37$	−3.68397			−0.605641			−0.302820	−	0.953048i	$-0.597928\pi$
$37$	−3.68397			−0.605641			−0.302820	+	0.953048i	$0.597928\pi$
$38$	0.898316	−	2.76473i	0.145726	−	0.448499i
$39$	0.253174	+	0.779189i	0.0405402	+	0.124770i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	9.06701	−	6.58757i	1.41603	−	1.02881i	0.423617	−	0.905841i	$-0.360760\pi$
$41$	9.06701	−	6.58757i	1.41603	−	1.02881i	0.992411	−	0.122964i	$-0.0392399\pi$
$42$	−1.26952	+	3.90719i	−0.195892	+	0.602893i
$43$	−3.80256	+	2.76272i	−0.579885	+	0.421311i	−0.838683	−	0.544620i	$-0.816674\pi$
$43$	−3.80256	+	2.76272i	−0.579885	+	0.421311i	0.258798	+	0.965932i	$0.416674\pi$
$44$	−2.01464	−	1.46372i	−0.303718	−	0.220664i
$45$	−0.309017	−	0.951057i	−0.0460655	−	0.141775i
$46$	0.769524	+	0.559092i	0.113460	+	0.0824336i
$47$	0.555410	+	0.403529i	0.0810149	+	0.0588608i	0.627555	−	0.778572i	$-0.284056\pi$
$47$	0.555410	+	0.403529i	0.0810149	+	0.0588608i	−0.546541	+	0.837433i	$0.684056\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−7.99135	−	5.80605i	−1.14162	−	0.829436i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	0.162817	−	0.501100i	0.0227990	−	0.0701681i
$52$	−0.662817	+	0.481565i	−0.0919162	+	0.0667811i
$53$	−2.65305	−	8.16525i	−0.364424	−	1.12158i	−0.950341	−	0.311211i	$-0.899265\pi$
$53$	−2.65305	−	8.16525i	−0.364424	−	1.12158i	0.585916	−	0.810371i	$-0.300735\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−0.769524	+	2.36835i	−0.103763	+	0.319348i
$56$	−4.10827			−0.548990
$57$	2.90701			0.385043
$58$	−0.225008	+	0.692504i	−0.0295450	+	0.0909302i
$59$	−10.7116	−	7.78244i	−1.39453	−	1.01319i	−0.995351	−	0.0963154i	$-0.969294\pi$
$59$	−10.7116	−	7.78244i	−1.39453	−	1.01319i	−0.399182	−	0.916872i	$-0.630706\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	−14.4527			−1.85048			−0.925238	−	0.379386i	$-0.876135\pi$
$61$	−14.4527			−1.85048			−0.925238	+	0.379386i	$0.876135\pi$
$62$	4.14823	+	3.71378i	0.526826	+	0.471650i
$63$	−4.10827			−0.517593
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.662817	+	0.481565i	0.0822124	+	0.0597308i
$66$	0.769524	−	2.36835i	0.0947218	−	0.291524i
$67$	−8.88436			−1.08540			−0.542698	−	0.839928i	$-0.682597\pi$
$67$	−8.88436			−1.08540			−0.542698	+	0.839928i	$0.682597\pi$
$68$	0.526888			0.0638946
$69$	−0.293932	+	0.904630i	−0.0353853	+	0.108905i
$70$	1.26952	+	3.90719i	0.151737	+	0.466999i
$71$	−3.98026	−	12.2500i	−0.472370	−	1.45381i	−0.849472	−	0.527634i	$-0.823079\pi$
$71$	−3.98026	−	12.2500i	−0.472370	−	1.45381i	0.377101	−	0.926172i	$-0.376921\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	0.0958121	−	0.294879i	0.0112140	−	0.0345130i	−0.945293	−	0.326223i	$-0.894224\pi$
$73$	0.0958121	−	0.294879i	0.0112140	−	0.0345130i	0.956507	+	0.291710i	$0.0942241\pi$
$74$	2.98039	−	2.16538i	0.346464	−	0.251721i
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$	0.898316	+	2.76473i	0.103044	+	0.317137i
$77$	8.27667	+	6.01336i	0.943215	+	0.685286i
$78$	−0.662817	−	0.481565i	−0.0750493	−	0.0545265i
$79$	0.715905	+	2.20333i	0.0805456	+	0.247894i	0.983218	−	0.182434i	$-0.0583977\pi$
$79$	0.715905	+	2.20333i	0.0805456	+	0.247894i	−0.902672	+	0.430328i	$0.858398\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.46329	+	10.6589i	−0.382456	+	1.17708i
$83$	−3.81517	+	2.77188i	−0.418769	+	0.304253i	−0.777142	−	0.629325i	$-0.783331\pi$
$83$	−3.81517	+	2.77188i	−0.418769	+	0.304253i	0.358373	+	0.933578i	$0.383331\pi$
$84$	−1.26952	−	3.90719i	−0.138516	−	0.426310i
$85$	−0.162817	−	0.501100i	−0.0176600	−	0.0543520i
$86$	1.45245	−	4.47018i	0.156622	−	0.482032i
$87$	−0.728142			−0.0780650
$88$	2.49023			0.265460
$89$	2.01464	−	6.20042i	0.213551	−	0.657244i	−0.785702	−	0.618605i	$-0.787698\pi$
$89$	2.01464	−	6.20042i	0.213551	−	0.657244i	0.999253	−	0.0386382i	$-0.0123020\pi$
$90$	0.809017	+	0.587785i	0.0852779	+	0.0619580i
$91$	2.72303	−	1.97840i	0.285451	−	0.207392i
$92$	−0.951184			−0.0991678
$93$	−2.25014	+	5.09283i	−0.233328	+	0.528101i
$94$	−0.686525			−0.0708096
$95$	2.35182	−	1.70870i	0.241292	−	0.175309i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	5.06656	−	15.5933i	0.514431	−	1.58326i	−0.269883	−	0.962893i	$-0.586985\pi$
$97$	5.06656	−	15.5933i	0.514431	−	1.58326i	0.784314	−	0.620363i	$-0.213015\pi$
$98$	9.87785			0.997813
$99$	2.49023			0.250278
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	0.923170	+	2.84122i	0.0918588	+	0.282712i	0.986422	−	0.164229i	$-0.0525134\pi$
$101$	0.923170	+	2.84122i	0.0918588	+	0.282712i	−0.894564	+	0.446941i	$0.852513\pi$
$102$	0.162817	+	0.501100i	0.0161213	+	0.0496163i
$103$	5.63623	−	4.09496i	0.555354	−	0.403489i	−0.274401	−	0.961615i	$-0.588480\pi$
$103$	5.63623	−	4.09496i	0.555354	−	0.403489i	0.829756	+	0.558127i	$0.188480\pi$
$104$	0.253174	−	0.779189i	0.0248257	−	0.0764057i
$105$	−3.32366	+	2.41478i	−0.324356	+	0.235658i
$106$	6.94577	+	5.04640i	0.674633	+	0.490150i
$107$	0.392279	+	1.20731i	0.0379230	+	0.116715i	0.968226	−	0.250077i	$-0.0804560\pi$
$107$	0.392279	+	1.20731i	0.0379230	+	0.116715i	−0.930303	+	0.366792i	$0.880456\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−2.13118	−	1.54840i	−0.204130	−	0.148309i	0.481024	−	0.876708i	$-0.340265\pi$
$109$	−2.13118	−	1.54840i	−0.204130	−	0.148309i	−0.685154	+	0.728398i	$0.740265\pi$
$110$	−0.769524	−	2.36835i	−0.0733712	−	0.225813i
$111$	2.98039	+	2.16538i	0.282887	+	0.205529i
$112$	3.32366	−	2.41478i	0.314056	−	0.228175i
$113$	3.22132	−	9.91420i	0.303036	−	0.932650i	−0.677366	−	0.735646i	$-0.736879\pi$
$113$	3.22132	−	9.91420i	0.303036	−	0.932650i	0.980403	−	0.197004i	$-0.0631212\pi$
$114$	−2.35182	+	1.70870i	−0.220268	+	0.160034i
$115$	0.293932	+	0.904630i	0.0274093	+	0.0843571i
$116$	−0.225008	−	0.692504i	−0.0208915	−	0.0642974i
$117$	0.253174	−	0.779189i	0.0234059	−	0.0720360i
$118$	13.2403			1.21887
$119$	−2.16460			−0.198428
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	3.88227	+	2.82063i	0.352933	+	0.256421i
$122$	11.6925	−	8.49507i	1.05859	−	0.769108i
$123$	−11.2074			−1.01054
$124$	−5.53890	−	0.566239i	−0.497408	−	0.0508498i
$125$	−1.00000			−0.0894427
$126$	3.32366	−	2.41478i	0.296095	−	0.215126i
$127$	8.97018	+	6.51722i	0.795975	+	0.578310i	0.909731	−	0.415199i	$-0.136288\pi$
$127$	8.97018	+	6.51722i	0.795975	+	0.578310i	−0.113756	+	0.993509i	$0.536288\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.70022			0.413832
$130$	−0.819287			−0.0718563
$131$	−0.0493304	+	0.151823i	−0.00431002	+	0.0132649i	−0.953188	−	0.302377i	$-0.902220\pi$
$131$	−0.0493304	+	0.151823i	−0.00431002	+	0.0132649i	0.948878	+	0.315642i	$0.102220\pi$
$132$	0.769524	+	2.36835i	0.0669785	+	0.206138i
$133$	−3.69052	−	11.3583i	−0.320009	−	0.984886i
$134$	7.18760	−	5.22209i	0.620914	−	0.451120i
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$	−0.426262	+	0.309697i	−0.0365516	+	0.0265563i
$137$	10.6110	+	7.70933i	0.906557	+	0.658652i	0.940142	−	0.340783i	$-0.110692\pi$
$137$	10.6110	+	7.70933i	0.906557	+	0.658652i	−0.0335845	+	0.999436i	$0.510692\pi$
$138$	−0.293932	−	0.904630i	−0.0250212	−	0.0770072i
$139$	−0.574508	−	0.417405i	−0.0487291	−	0.0354038i	0.563154	−	0.826352i	$-0.309588\pi$
$139$	−0.574508	−	0.417405i	−0.0487291	−	0.0354038i	−0.611883	+	0.790948i	$0.709588\pi$
$140$	−3.32366	−	2.41478i	−0.280900	−	0.204086i
$141$	−0.212148	−	0.652924i	−0.0178661	−	0.0549861i
$142$	10.4205	+	7.57091i	0.874466	+	0.635337i
$143$	−1.65057	+	1.19921i	−0.138028	+	0.100283i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−0.589079	+	0.427991i	−0.0489203	+	0.0355427i
$146$	0.0958121	+	0.294879i	0.00792946	+	0.0244044i
$147$	3.05242	+	9.39439i	0.251760	+	0.774836i
$148$	−1.13841	+	3.50366i	−0.0935767	+	0.287999i
$149$	3.48060			0.285142			0.142571	−	0.989785i	$-0.454463\pi$
$149$	3.48060			0.285142			0.142571	+	0.989785i	$0.454463\pi$
$150$	1.00000			0.0816497
$151$	−4.88277	+	15.0276i	−0.397354	+	1.22293i	0.529759	+	0.848148i	$0.322282\pi$
$151$	−4.88277	+	15.0276i	−0.397354	+	1.22293i	−0.927113	+	0.374782i	$0.877718\pi$
$152$	−2.35182	−	1.70870i	−0.190758	−	0.138594i
$153$	−0.426262	+	0.309697i	−0.0344612	+	0.0250375i
$154$	−10.2305			−0.824400
$155$	1.17309	+	5.44278i	0.0942247	+	0.437175i
$156$	0.819287			0.0655955
$157$	−3.99181	+	2.90022i	−0.318581	+	0.231463i	−0.735570	−	0.677449i	$-0.763085\pi$
$157$	−3.99181	+	2.90022i	−0.318581	+	0.231463i	0.416989	+	0.908912i	$0.363085\pi$
$158$	−1.87426	−	1.36173i	−0.149108	−	0.108334i
$159$	−2.65305	+	8.16525i	−0.210400	+	0.647546i
$160$	−1.00000			−0.0790569
$161$	3.90772			0.307971
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	5.64976	+	17.3882i	0.442524	+	1.36195i	0.885177	+	0.465255i	$0.154037\pi$
$163$	5.64976	+	17.3882i	0.442524	+	1.36195i	−0.442653	+	0.896693i	$0.645963\pi$
$164$	−3.46329	−	10.6589i	−0.270437	−	0.832321i
$165$	2.01464	−	1.46372i	0.156839	−	0.113951i
$166$	1.45726	−	4.48500i	0.113106	−	0.348103i
$167$	−14.8829	+	10.8130i	−1.15167	+	0.836738i	−0.988702	−	0.149893i	$-0.952107\pi$
$167$	−14.8829	+	10.8130i	−1.15167	+	0.836738i	−0.162969	+	0.986631i	$0.552107\pi$
$168$	3.32366	+	2.41478i	0.256426	+	0.186304i
$169$	−3.80980	−	11.7254i	−0.293061	−	0.901950i
$170$	0.426262	+	0.309697i	0.0326928	+	0.0237527i
$171$	−2.35182	−	1.70870i	−0.179848	−	0.130667i
$172$	1.45245	+	4.47018i	0.110748	+	0.340848i
$173$	−14.4388	−	10.4904i	−1.09777	−	0.797573i	−0.117072	−	0.993123i	$-0.537351\pi$
$173$	−14.4388	−	10.4904i	−1.09777	−	0.797573i	−0.980694	+	0.195550i	$0.937351\pi$
$174$	0.589079	−	0.427991i	0.0446580	−	0.0324459i
$175$	−1.26952	+	3.90719i	−0.0959670	+	0.295356i
$176$	−2.01464	+	1.46372i	−0.151859	+	0.110332i
$177$	4.09147	+	12.5923i	0.307534	+	0.946491i
$178$	2.01464	+	6.20042i	0.151004	+	0.464741i
$179$	1.35476	−	4.16951i	0.101259	−	0.311644i	−0.887575	−	0.460663i	$-0.847612\pi$
$179$	1.35476	−	4.16951i	0.101259	−	0.311644i	0.988834	+	0.149019i	$0.0476117\pi$
$180$	−1.00000			−0.0745356
$181$	10.6364			0.790600			0.395300	−	0.918552i	$-0.370641\pi$
$181$	10.6364			0.790600			0.395300	+	0.918552i	$0.370641\pi$
$182$	−1.04010	+	3.20111i	−0.0770977	+	0.237282i
$183$	11.6925	+	8.49507i	0.864332	+	0.627974i
$184$	0.769524	−	0.559092i	0.0567301	−	0.0412168i
$185$	3.68397			0.270851
$186$	−1.17309	−	5.44278i	−0.0860150	−	0.399084i
$187$	1.31207			0.0959483
$188$	0.555410	−	0.403529i	0.0405074	−	0.0294304i
$189$	3.32366	+	2.41478i	0.241760	+	0.175649i
$190$	−0.898316	+	2.76473i	−0.0651707	+	0.200575i
$191$	−16.4183			−1.18799			−0.593994	−	0.804469i	$-0.702450\pi$
$191$	−16.4183			−1.18799			−0.593994	+	0.804469i	$0.702450\pi$
$192$	1.00000			0.0721688
$193$	3.28260	−	10.1028i	0.236286	−	0.727215i	−0.760662	−	0.649149i	$-0.775125\pi$
$193$	3.28260	−	10.1028i	0.236286	−	0.727215i	0.996948	−	0.0780665i	$-0.0248746\pi$
$194$	5.06656	+	15.5933i	0.363758	+	1.11953i
$195$	−0.253174	−	0.779189i	−0.0181301	−	0.0557989i
$196$	−7.99135	+	5.80605i	−0.570810	+	0.414718i
$197$	−7.48415	+	23.0338i	−0.533223	+	1.64109i	0.214233	+	0.976782i	$0.431275\pi$
$197$	−7.48415	+	23.0338i	−0.533223	+	1.64109i	−0.747457	+	0.664310i	$0.768725\pi$
$198$	−2.01464	+	1.46372i	−0.143174	+	0.104022i
$199$	7.76634	+	5.64257i	0.550541	+	0.399991i	0.827985	−	0.560750i	$-0.189487\pi$
$199$	7.76634	+	5.64257i	0.550541	+	0.399991i	−0.277444	+	0.960742i	$0.589487\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	7.18760	+	5.22209i	0.506974	+	0.368338i
$202$	−2.41689	−	1.75597i	−0.170052	−	0.123550i
$203$	0.924393	+	2.84499i	0.0648797	+	0.199679i
$204$	−0.426262	−	0.309697i	−0.0298443	−	0.0216831i
$205$	−9.06701	+	6.58757i	−0.633267	+	0.460096i
$206$	−2.15285	+	6.62579i	−0.149996	+	0.461640i
$207$	0.769524	−	0.559092i	0.0534856	−	0.0388596i
$208$	0.253174	+	0.779189i	0.0175544	+	0.0540270i
$209$	2.23702	+	6.88483i	0.154738	+	0.476233i
$210$	1.26952	−	3.90719i	0.0876055	−	0.269622i
$211$	−12.4410			−0.856473			−0.428237	−	0.903667i	$-0.640865\pi$
$211$	−12.4410			−0.856473			−0.428237	+	0.903667i	$0.640865\pi$
$212$	−8.58545			−0.589651
$213$	−3.98026	+	12.2500i	−0.272723	+	0.839355i
$214$	−1.02700	−	0.746159i	−0.0702043	−	0.0510064i
$215$	3.80256	−	2.76272i	0.259332	−	0.188416i
$216$	1.00000			0.0680414
$217$	22.7553	+	2.32626i	1.54473	+	0.157917i
$218$	2.63429			0.178416
$219$	−0.250839	+	0.182245i	−0.0169501	+	0.0123150i
$220$	2.01464	+	1.46372i	0.135827	+	0.0986841i
$221$	0.133394	−	0.410545i	0.00897307	−	0.0276163i
$222$	−3.68397			−0.247252
$223$	−9.06100			−0.606770			−0.303385	−	0.952868i	$-0.598117\pi$
$223$	−9.06100			−0.606770			−0.303385	+	0.952868i	$0.598117\pi$
$224$	−1.26952	+	3.90719i	−0.0848236	+	0.261060i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	3.22132	+	9.91420i	0.214279	+	0.659483i
$227$	0.0216299	−	0.0157151i	0.00143563	−	0.00104305i	−0.587067	−	0.809538i	$-0.699718\pi$
$227$	0.0216299	−	0.0157151i	0.00143563	−	0.00104305i	0.588503	+	0.808495i	$0.299718\pi$
$228$	0.898316	−	2.76473i	0.0594924	−	0.183099i
$229$	10.6139	−	7.71142i	0.701383	−	0.509585i	−0.178999	−	0.983849i	$-0.557286\pi$
$229$	10.6139	−	7.71142i	0.701383	−	0.509585i	0.880382	+	0.474264i	$0.157286\pi$
$230$	−0.769524	−	0.559092i	−0.0507409	−	0.0368654i
$231$	−3.16141	−	9.72981i	−0.208005	−	0.640175i
$232$	0.589079	+	0.427991i	0.0386749	+	0.0280990i
$233$	−4.37426	−	3.17809i	−0.286568	−	0.208204i	0.435209	−	0.900329i	$-0.356674\pi$
$233$	−4.37426	−	3.17809i	−0.286568	−	0.208204i	−0.721777	+	0.692126i	$0.756674\pi$
$234$	0.253174	+	0.779189i	0.0165505	+	0.0509372i
$235$	−0.555410	−	0.403529i	−0.0362310	−	0.0263233i
$236$	−10.7116	+	7.78244i	−0.697266	+	0.506594i
$237$	0.715905	−	2.20333i	0.0465030	−	0.143122i
$238$	1.75120	−	1.27232i	0.113513	−	0.0824721i
$239$	5.26275	+	16.1971i	0.340419	+	1.04770i	0.963991	+	0.265936i	$0.0856809\pi$
$239$	5.26275	+	16.1971i	0.340419	+	1.04770i	−0.623572	+	0.781766i	$0.714319\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−2.30519	+	7.09465i	−0.148490	+	0.457007i	−0.997443	−	0.0714619i	$-0.977234\pi$
$241$	−2.30519	+	7.09465i	−0.148490	+	0.457007i	0.848953	+	0.528469i	$0.177234\pi$
$242$	−4.79875			−0.308475
$243$	1.00000			0.0641500
$244$	−4.46613	+	13.7453i	−0.285914	+	0.879954i
$245$	7.99135	+	5.80605i	0.510548	+	0.370935i
$246$	9.06701	−	6.58757i	0.578091	−	0.420008i
$247$	2.38168			0.151543
$248$	4.81389	−	2.79758i	0.305682	−	0.177647i
$249$	4.71580			0.298852
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−9.57258	−	6.95489i	−0.604216	−	0.438989i	0.243157	−	0.969987i	$-0.421817\pi$
$251$	−9.57258	−	6.95489i	−0.604216	−	0.438989i	−0.847373	+	0.530998i	$0.821817\pi$
$252$	−1.26952	+	3.90719i	−0.0799725	+	0.246130i
$253$	−2.36867			−0.148917
$254$	−11.0878			−0.695707
$255$	−0.162817	+	0.501100i	−0.0101960	+	0.0313801i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.09253	−	12.5955i	−0.255285	−	0.785686i	−0.993773	−	0.111420i	$-0.964460\pi$
$257$	−4.09253	−	12.5955i	−0.255285	−	0.785686i	0.738489	−	0.674266i	$-0.235540\pi$
$258$	−3.80256	+	2.76272i	−0.236737	+	0.172000i
$259$	4.67689	−	14.3940i	0.290608	−	0.894398i
$260$	0.662817	−	0.481565i	0.0411062	−	0.0298654i
$261$	0.589079	+	0.427991i	0.0364631	+	0.0264920i
$262$	−0.0493304	−	0.151823i	−0.00304764	−	0.00937968i
$263$	2.52472	+	1.83432i	0.155681	+	0.113109i	0.662899	−	0.748709i	$-0.269326\pi$
$263$	2.52472	+	1.83432i	0.155681	+	0.113109i	−0.507218	+	0.861818i	$0.669326\pi$
$264$	−2.01464	−	1.46372i	−0.123993	−	0.0900858i
$265$	2.65305	+	8.16525i	0.162976	+	0.501587i
$266$	9.66191	+	7.01979i	0.592410	+	0.430411i
$267$	−5.27440	+	3.83207i	−0.322788	+	0.234519i
$268$	−2.74542	+	8.44953i	−0.167703	+	0.516137i
$269$	12.7927	−	9.29444i	0.779985	−	0.566692i	−0.124990	−	0.992158i	$-0.539890\pi$
$269$	12.7927	−	9.29444i	0.779985	−	0.566692i	0.904974	+	0.425466i	$0.139890\pi$
$270$	−0.309017	−	0.951057i	−0.0188062	−	0.0578795i
$271$	4.02189	+	12.3781i	0.244313	+	0.751917i	0.995749	+	0.0921110i	$0.0293615\pi$
$271$	4.02189	+	12.3781i	0.244313	+	0.751917i	−0.751436	+	0.659806i	$0.770639\pi$
$272$	0.162817	−	0.501100i	0.00987226	−	0.0303837i
$273$	−3.36585			−0.203711
$274$	−13.1159			−0.792360
$275$	0.769524	−	2.36835i	0.0464040	−	0.142817i
$276$	0.769524	+	0.559092i	0.0463199	+	0.0336534i
$277$	−10.9251	+	7.93758i	−0.656428	+	0.476923i	−0.865455	−	0.500987i	$-0.832970\pi$
$277$	−10.9251	+	7.93758i	−0.656428	+	0.476923i	0.209027	+	0.977910i	$0.432970\pi$
$278$	0.710131			0.0425908
$279$	4.81389	−	2.79758i	0.288200	−	0.167487i
$280$	4.10827			0.245516
$281$	21.6515	−	15.7307i	1.29162	−	0.938417i	0.291783	−	0.956484i	$-0.405751\pi$
$281$	21.6515	−	15.7307i	1.29162	−	0.938417i	0.999837	+	0.0180676i	$0.00575142\pi$
$282$	0.555410	+	0.403529i	0.0330742	+	0.0240298i
$283$	6.98994	−	21.5128i	0.415509	−	1.27880i	−0.496287	−	0.868159i	$-0.665304\pi$
$283$	6.98994	−	21.5128i	0.415509	−	1.27880i	0.911795	−	0.410645i	$-0.134696\pi$
$284$	−12.8804			−0.764311
$285$	−2.90701			−0.172197
$286$	0.630461	−	1.94036i	0.0372800	−	0.114736i
$287$	14.2281	+	43.7896i	0.839859	+	2.58482i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	13.5287	−	9.82917i	0.795806	−	0.578187i
$290$	0.225008	−	0.692504i	0.0132129	−	0.0406652i
$291$	−13.2644	+	9.63717i	−0.777574	+	0.564941i
$292$	−0.250839	−	0.182245i	−0.0146793	−	0.0106651i
$293$	−4.59076	−	14.1289i	−0.268195	−	0.825419i	−0.990940	−	0.134304i	$-0.957120\pi$
$293$	−4.59076	−	14.1289i	−0.268195	−	0.825419i	0.722745	−	0.691114i	$-0.242880\pi$
$294$	−7.99135	−	5.80605i	−0.466065	−	0.338616i
$295$	10.7116	+	7.78244i	0.623654	+	0.453111i
$296$	−1.13841	−	3.50366i	−0.0661687	−	0.203646i
$297$	−2.01464	−	1.46372i	−0.116901	−	0.0849337i
$298$	−2.81587	+	2.04585i	−0.163119	+	0.118513i
$299$	−0.240815	+	0.741152i	−0.0139267	+	0.0428619i
$300$	−0.809017	+	0.587785i	−0.0467086	+	0.0339358i
$301$	−5.96705	−	18.3647i	−0.343935	−	1.05852i
$302$	−4.88277	−	15.0276i	−0.280972	−	0.864742i
$303$	0.923170	−	2.84122i	0.0530347	−	0.163224i
$304$	2.90701			0.166729
$305$	14.4527			0.827558
$306$	0.162817	−	0.501100i	0.00930765	−	0.0286460i
$307$	12.7374	+	9.25424i	0.726960	+	0.528168i	0.888600	−	0.458682i	$-0.151678\pi$
$307$	12.7374	+	9.25424i	0.726960	+	0.528168i	−0.161640	+	0.986850i	$0.551678\pi$
$308$	8.27667	−	6.01336i	0.471607	−	0.342643i
$309$	−6.96676			−0.396325
$310$	−4.14823	−	3.71378i	−0.235604	−	0.210928i
$311$	2.07787			0.117825			0.0589127	−	0.998263i	$-0.481237\pi$
$311$	2.07787			0.117825			0.0589127	+	0.998263i	$0.481237\pi$
$312$	−0.662817	+	0.481565i	−0.0375246	+	0.0272633i
$313$	−14.2951	−	10.3860i	−0.808008	−	0.587052i	0.105244	−	0.994446i	$-0.466438\pi$
$313$	−14.2951	−	10.3860i	−0.808008	−	0.587052i	−0.913253	+	0.407394i	$0.866438\pi$
$314$	1.52474	−	4.69265i	0.0860458	−	0.264822i
$315$	4.10827			0.231475
$316$	2.31672			0.130326
$317$	−5.23442	+	16.1099i	−0.293994	+	0.904822i	0.689563	+	0.724226i	$0.257803\pi$
$317$	−5.23442	+	16.1099i	−0.293994	+	0.904822i	−0.983557	+	0.180596i	$0.942197\pi$
$318$	−2.65305	−	8.16525i	−0.148776	−	0.457884i
$319$	−0.560322	−	1.72449i	−0.0313720	−	0.0965532i
$320$	0.809017	−	0.587785i	0.0452254	−	0.0328582i
$321$	0.392279	−	1.20731i	0.0218949	−	0.0673855i
$322$	−3.16141	+	2.29690i	−0.176178	+	0.128001i
$323$	−1.23915	−	0.900293i	−0.0689480	−	0.0500937i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−0.662817	−	0.481565i	−0.0367665	−	0.0267124i
$326$	−14.7913	−	10.7465i	−0.819213	−	0.595193i
$327$	0.814040	+	2.50536i	0.0450165	+	0.138547i
$328$	9.06701	+	6.58757i	0.500642	+	0.363738i
$329$	−2.28177	+	1.65780i	−0.125798	+	0.0913977i
$330$	−0.769524	+	2.36835i	−0.0423609	+	0.130373i
$331$	−1.56699	+	1.13849i	−0.0861298	+	0.0625770i	−0.630017	−	0.776581i	$-0.716952\pi$
$331$	−1.56699	+	1.13849i	−0.0861298	+	0.0625770i	0.543887	+	0.839158i	$0.316952\pi$
$332$	1.45726	+	4.48500i	0.0799777	+	0.246146i
$333$	−1.13841	−	3.50366i	−0.0623844	−	0.192000i
$334$	5.68475	−	17.4959i	0.311056	−	0.957331i
$335$	8.88436			0.485404
$336$	−4.10827			−0.224124
$337$	0.736316	−	2.26615i	0.0401097	−	0.123445i	−0.928997	−	0.370088i	$-0.879328\pi$
$337$	0.736316	−	2.26615i	0.0401097	−	0.123445i	0.969106	+	0.246643i	$0.0793275\pi$
$338$	9.97418	+	7.24667i	0.542524	+	0.394167i
$339$	−8.43352	+	6.12731i	−0.458046	+	0.332790i
$340$	−0.526888			−0.0285745
$341$	−13.7931	−	1.41007i	−0.746940	−	0.0763594i
$342$	2.90701			0.157193
$343$	9.56497	−	6.94936i	0.516460	−	0.375230i
$344$	−3.80256	−	2.76272i	−0.205020	−	0.148956i
$345$	0.293932	−	0.904630i	0.0158248	−	0.0487036i
$346$	17.8474			0.959482
$347$	−28.0389			−1.50520			−0.752602	−	0.658475i	$-0.771202\pi$
$347$	−28.0389			−1.50520			−0.752602	+	0.658475i	$0.771202\pi$
$348$	−0.225008	+	0.692504i	−0.0120617	+	0.0371221i
$349$	2.63393	+	8.10641i	0.140991	+	0.433926i	0.996474	−	0.0839054i	$-0.0267394\pi$
$349$	2.63393	+	8.10641i	0.140991	+	0.433926i	−0.855483	+	0.517832i	$0.826739\pi$
$350$	−1.26952	−	3.90719i	−0.0678589	−	0.208848i
$351$	−0.662817	+	0.481565i	−0.0353786	+	0.0257040i
$352$	0.769524	−	2.36835i	0.0410158	−	0.126234i
$353$	16.2318	−	11.7931i	0.863933	−	0.627684i	−0.0650194	−	0.997884i	$-0.520711\pi$
$353$	16.2318	−	11.7931i	0.863933	−	0.627684i	0.928952	+	0.370200i	$0.120711\pi$
$354$	−10.7116	−	7.78244i	−0.569316	−	0.413632i
$355$	3.98026	+	12.2500i	0.211250	+	0.650162i
$356$	−5.27440	−	3.83207i	−0.279542	−	0.203099i
$357$	1.75120	+	1.27232i	0.0926831	+	0.0673382i
$358$	1.35476	+	4.16951i	0.0716010	+	0.220365i
$359$	0.961120	+	0.698295i	0.0507260	+	0.0368546i	0.612859	−	0.790192i	$-0.290019\pi$
$359$	0.961120	+	0.698295i	0.0507260	+	0.0368546i	−0.562133	+	0.827047i	$0.690019\pi$
$360$	0.809017	−	0.587785i	0.0426389	−	0.0309790i
$361$	−3.25991	+	10.0330i	−0.171574	+	0.528051i
$362$	−8.60505	+	6.25194i	−0.452272	+	0.328594i
$363$	−1.48289	−	4.56388i	−0.0778318	−	0.239542i
$364$	−1.04010	−	3.20111i	−0.0545163	−	0.167784i
$365$	−0.0958121	+	0.294879i	−0.00501503	+	0.0154347i
$366$	−14.4527			−0.755454
$367$	−0.760783			−0.0397126			−0.0198563	−	0.999803i	$-0.506321\pi$
$367$	−0.760783			−0.0397126			−0.0198563	+	0.999803i	$0.506321\pi$
$368$	−0.293932	+	0.904630i	−0.0153223	+	0.0471571i
$369$	9.06701	+	6.58757i	0.472010	+	0.342935i
$370$	−2.98039	+	2.16538i	−0.154943	+	0.112573i
$371$	35.2713			1.83119
$372$	4.14823	+	3.71378i	0.215076	+	0.192550i
$373$	−36.5486			−1.89242			−0.946208	−	0.323558i	$-0.895121\pi$
$373$	−36.5486			−1.89242			−0.946208	+	0.323558i	$0.895121\pi$
$374$	−1.06149	+	0.771218i	−0.0548883	+	0.0398787i
$375$	0.809017	+	0.587785i	0.0417775	+	0.0303531i
$376$	−0.212148	+	0.652924i	−0.0109407	+	0.0336720i
$377$	−0.596557			−0.0307243
$378$	−4.10827			−0.211306
$379$	1.17275	−	3.60936i	0.0602403	−	0.185400i	−0.916408	−	0.400246i	$-0.868925\pi$
$379$	1.17275	−	3.60936i	0.0602403	−	0.185400i	0.976648	+	0.214845i	$0.0689247\pi$
$380$	−0.898316	−	2.76473i	−0.0460826	−	0.141828i
$381$	−3.42630	−	10.5451i	−0.175535	−	0.540241i
$382$	13.2827	−	9.65045i	0.679602	−	0.493760i
$383$	−6.19190	+	19.0567i	−0.316391	+	0.973752i	0.658787	+	0.752330i	$0.271070\pi$
$383$	−6.19190	+	19.0567i	−0.316391	+	0.973752i	−0.975178	+	0.221422i	$0.928930\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	−8.27667	−	6.01336i	−0.421818	−	0.306469i
$386$	3.28260	+	10.1028i	0.167080	+	0.514219i
$387$	−3.80256	−	2.76272i	−0.193295	−	0.140437i
$388$	−13.2644	−	9.63717i	−0.673399	−	0.489253i
$389$	−2.32460	−	7.15437i	−0.117862	−	0.362741i	0.874671	−	0.484716i	$-0.161077\pi$
$389$	−2.32460	−	7.15437i	−0.117862	−	0.362741i	−0.992533	+	0.121975i	$0.961077\pi$
$390$	0.662817	+	0.481565i	0.0335631	+	0.0243850i
$391$	0.405453	−	0.294579i	0.0205046	−	0.0148975i
$392$	3.05242	−	9.39439i	0.154171	−	0.474488i
$393$	0.129149	−	0.0938320i	0.00651469	−	0.00473320i
$394$	−7.48415	−	23.0338i	−0.377046	−	1.16043i
$395$	−0.715905	−	2.20333i	−0.0360211	−	0.110862i
$396$	0.769524	−	2.36835i	0.0386700	−	0.119014i
$397$	2.71251			0.136137			0.0680684	−	0.997681i	$-0.478316\pi$
$397$	2.71251			0.136137			0.0680684	+	0.997681i	$0.478316\pi$
$398$	−9.59972			−0.481191
$399$	−3.69052	+	11.3583i	−0.184757	+	0.568624i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−21.1317	+	15.3531i	−1.05527	+	0.766697i	−0.973207	−	0.229930i	$-0.926150\pi$
$401$	−21.1317	+	15.3531i	−1.05527	+	0.766697i	−0.0820613	+	0.996627i	$0.526150\pi$
$402$	−8.88436			−0.443111
$403$	−1.84351	+	4.17249i	−0.0918318	+	0.207846i
$404$	2.98744			0.148631
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−2.42009	−	1.75830i	−0.120107	−	0.0872630i
$407$	−2.83490	+	8.72493i	−0.140521	+	0.432479i
$408$	0.526888			0.0260849
$409$	6.77725			0.335113			0.167557	−	0.985862i	$-0.446412\pi$
$409$	6.77725			0.335113			0.167557	+	0.985862i	$0.446412\pi$
$410$	3.46329	−	10.6589i	0.171040	−	0.526406i
$411$	−4.05303	−	12.4740i	−0.199921	−	0.615295i
$412$	−2.15285	−	6.62579i	−0.106063	−	0.326429i
$413$	44.0061	−	31.9723i	2.16540	−	1.57326i
$414$	−0.293932	+	0.904630i	−0.0144460	+	0.0444601i
$415$	3.81517	−	2.77188i	0.187279	−	0.136066i
$416$	−0.662817	−	0.481565i	−0.0324973	−	0.0236107i
$417$	0.219443	+	0.675375i	0.0107461	+	0.0330732i
$418$	−5.85658	−	4.25506i	−0.286455	−	0.208122i
$419$	4.62960	+	3.36360i	0.226171	+	0.164323i	0.695100	−	0.718913i	$-0.255360\pi$
$419$	4.62960	+	3.36360i	0.226171	+	0.164323i	−0.468929	+	0.883236i	$0.655360\pi$
$420$	1.26952	+	3.90719i	0.0619464	+	0.190651i
$421$	28.4439	+	20.6657i	1.38627	+	1.00718i	0.996263	+	0.0863718i	$0.0275273\pi$
$421$	28.4439	+	20.6657i	1.38627	+	1.00718i	0.390007	+	0.920812i	$0.372473\pi$
$422$	10.0650	−	7.31263i	0.489955	−	0.355973i
$423$	−0.212148	+	0.652924i	−0.0103150	+	0.0317462i
$424$	6.94577	−	5.04640i	0.337317	−	0.245075i
$425$	0.162817	+	0.501100i	0.00789780	+	0.0243069i
$426$	−3.98026	−	12.2500i	−0.192844	−	0.593514i
$427$	18.3480	−	56.4694i	0.887923	−	2.73275i
$428$	1.26944			0.0613608
$429$	2.04022			0.0985025
$430$	−1.45245	+	4.47018i	−0.0700433	+	0.215571i
$431$	9.42085	+	6.84465i	0.453786	+	0.329695i	0.791089	−	0.611701i	$-0.209515\pi$
$431$	9.42085	+	6.84465i	0.453786	+	0.329695i	−0.337303	+	0.941396i	$0.609515\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−22.2862			−1.07101			−0.535504	−	0.844532i	$-0.679878\pi$
$433$	−22.2862			−1.07101			−0.535504	+	0.844532i	$0.679878\pi$
$434$	−19.7767	+	11.4932i	−0.949313	+	0.551692i
$435$	0.728142			0.0349117
$436$	−2.13118	+	1.54840i	−0.102065	+	0.0741547i
$437$	2.23702	+	1.62529i	0.107011	+	0.0777480i
$438$	0.0958121	−	0.294879i	0.00457808	−	0.0140899i
$439$	−37.1444			−1.77280			−0.886402	−	0.462917i	$-0.846803\pi$
$439$	−37.1444			−1.77280			−0.886402	+	0.462917i	$0.846803\pi$
$440$	−2.49023			−0.118717
$441$	3.05242	−	9.39439i	0.145353	−	0.447352i
$442$	0.133394	+	0.410545i	0.00634492	+	0.0195276i
$443$	−6.13167	−	18.8713i	−0.291325	−	0.896605i	−0.984431	−	0.175770i	$-0.943759\pi$
$443$	−6.13167	−	18.8713i	−0.291325	−	0.896605i	0.693107	−	0.720835i	$-0.256241\pi$
$444$	2.98039	−	2.16538i	0.141443	−	0.102765i
$445$	−2.01464	+	6.20042i	−0.0955031	+	0.293928i
$446$	7.33051	−	5.32592i	0.347110	−	0.252190i
$447$	−2.81587	−	2.04585i	−0.133186	−	0.0967652i
$448$	−1.26952	−	3.90719i	−0.0599794	−	0.184598i
$449$	21.5950	+	15.6897i	1.01913	+	0.740443i	0.966105	−	0.258150i	$-0.0831129\pi$
$449$	21.5950	+	15.6897i	1.01913	+	0.740443i	0.0530274	+	0.998593i	$0.483113\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	−8.62439	−	26.5431i	−0.406107	−	1.24987i
$452$	−8.43352	−	6.12731i	−0.396680	−	0.288205i
$453$	12.7833	−	9.28758i	0.600610	−	0.436369i
$454$	−0.00826190	+	0.0254275i	−0.000387750	+	0.00119337i
$455$	−2.72303	+	1.97840i	−0.127658	+	0.0927487i
$456$	0.898316	+	2.76473i	0.0420675	+	0.129470i
$457$	−7.27654	−	22.3949i	−0.340382	−	1.04759i	−0.964010	−	0.265867i	$-0.914342\pi$
$457$	−7.27654	−	22.3949i	−0.340382	−	1.04759i	0.623627	−	0.781722i	$-0.285658\pi$
$458$	−4.05413	+	12.4773i	−0.189437	+	0.583028i
$459$	0.526888			0.0245930
$460$	0.951184			0.0443492
$461$	−0.862202	+	2.65359i	−0.0401568	+	0.123590i	−0.969125	−	0.246569i	$-0.920697\pi$
$461$	−0.862202	+	2.65359i	−0.0401568	+	0.123590i	0.928968	+	0.370159i	$0.120697\pi$
$462$	8.27667	+	6.01336i	0.385066	+	0.279767i
$463$	−21.7973	+	15.8367i	−1.01301	+	0.735994i	−0.964838	−	0.262846i	$-0.915339\pi$
$463$	−21.7973	+	15.8367i	−1.01301	+	0.735994i	−0.0481704	+	0.998839i	$0.515339\pi$
$464$	−0.728142			−0.0338031
$465$	2.25014	−	5.09283i	0.104348	−	0.236174i
$466$	5.40689			0.250469
$467$	−6.08392	+	4.42023i	−0.281530	+	0.204544i	−0.719585	−	0.694405i	$-0.755668\pi$
$467$	−6.08392	+	4.42023i	−0.281530	+	0.204544i	0.438054	+	0.898949i	$0.355668\pi$
$468$	−0.662817	−	0.481565i	−0.0306387	−	0.0222604i
$469$	11.2789	−	34.7129i	0.520811	−	1.60289i
$470$	0.686525			0.0316670
$471$	4.93415			0.227354
$472$	4.09147	−	12.5923i	0.188325	−	0.579605i
$473$	3.61693	+	11.1318i	0.166307	+	0.511840i
$474$	0.715905	+	2.20333i	0.0328826	+	0.101202i
$475$	−2.35182	+	1.70870i	−0.107909	+	0.0784005i
$476$	−0.668897	+	2.05865i	−0.0306589	+	0.0943582i
$477$	6.94577	−	5.04640i	0.318025	−	0.231059i
$478$	−13.7781	−	10.0103i	−0.630194	−	0.457863i
$479$	−12.7143	−	39.1307i	−0.580933	−	1.78793i	−0.615022	−	0.788510i	$-0.710853\pi$
$479$	−12.7143	−	39.1307i	−0.580933	−	1.78793i	0.0340888	−	0.999419i	$-0.489147\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	2.44180	+	1.77407i	0.111336	+	0.0808907i
$482$	−2.30519	−	7.09465i	−0.104999	−	0.323153i
$483$	−3.16141	−	2.29690i	−0.143849	−	0.104512i
$484$	3.88227	−	2.82063i	0.176467	−	0.128211i
$485$	−5.06656	+	15.5933i	−0.230061	+	0.708054i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−9.68007	−	29.7922i	−0.438646	−	1.35001i	−0.889304	−	0.457316i	$-0.848811\pi$
$487$	−9.68007	−	29.7922i	−0.438646	−	1.35001i	0.450659	−	0.892696i	$-0.351189\pi$
$488$	−4.46613	−	13.7453i	−0.202172	−	0.622221i
$489$	5.64976	−	17.3882i	0.255491	−	0.786321i
$490$	−9.87785			−0.446236
$491$	−16.3144			−0.736259			−0.368130	−	0.929775i	$-0.620002\pi$
$491$	−16.3144			−0.736259			−0.368130	+	0.929775i	$0.620002\pi$
$492$	−3.46329	+	10.6589i	−0.156137	+	0.480541i
$493$	0.310379	+	0.225503i	0.0139788	+	0.0101562i
$494$	−1.92682	+	1.39992i	−0.0866917	+	0.0629852i
$495$	−2.49023			−0.111928
$496$	−2.25014	+	5.09283i	−0.101034	+	0.228675i
$497$	52.9161			2.37361
$498$	−3.81517	+	2.77188i	−0.170962	+	0.124211i
$499$	33.6809	+	24.4706i	1.50777	+	1.09546i	0.967157	+	0.254181i	$0.0818059\pi$
$499$	33.6809	+	24.4706i	1.50777	+	1.09546i	0.540608	+	0.841274i	$0.318194\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	18.3962			0.821884
$502$	11.8324			0.528104
$503$	−4.19723	+	12.9177i	−0.187145	+	0.575973i	−0.999979	−	0.00652252i	$-0.997924\pi$
$503$	−4.19723	+	12.9177i	−0.187145	+	0.575973i	0.812834	+	0.582496i	$0.197924\pi$
$504$	−1.26952	−	3.90719i	−0.0565491	−	0.174040i
$505$	−0.923170	−	2.84122i	−0.0410805	−	0.126433i
$506$	1.91629	−	1.39227i	0.0851896	−	0.0618939i
$507$	−3.80980	+	11.7254i	−0.169199	+	0.520741i
$508$	8.97018	−	6.51722i	0.397987	−	0.289155i
$509$	9.38997	+	6.82221i	0.416203	+	0.302389i	0.776108	−	0.630600i	$-0.217191\pi$
$509$	9.38997	+	6.82221i	0.416203	+	0.302389i	−0.359905	+	0.932989i	$0.617191\pi$
$510$	−0.162817	−	0.501100i	−0.00720968	−	0.0221891i
$511$	1.03051	+	0.748712i	0.0455873	+	0.0331211i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	0.898316	+	2.76473i	0.0396616	+	0.122066i
$514$	10.7144	+	7.78445i	0.472591	+	0.343357i
$515$	−5.63623	+	4.09496i	−0.248362	+	0.180446i
$516$	1.45245	−	4.47018i	0.0639405	−	0.196789i
$517$	1.38310	−	1.00488i	0.0608287	−	0.0441946i
$518$	4.67689	+	14.3940i	0.205491	+	0.632435i
$519$	5.51515	+	16.9739i	0.242088	+	0.745071i
$520$	−0.253174	+	0.779189i	−0.0111024	+	0.0341697i
$521$	−40.3599			−1.76820			−0.884100	−	0.467297i	$-0.845228\pi$
$521$	−40.3599			−1.76820			−0.884100	+	0.467297i	$0.845228\pi$
$522$	−0.728142			−0.0318699
$523$	3.89921	−	12.0005i	0.170501	−	0.524747i	−0.828899	−	0.559399i	$-0.811032\pi$
$523$	3.89921	−	12.0005i	0.170501	−	0.524747i	0.999399	+	0.0346515i	$0.0110321\pi$
$524$	0.129149	+	0.0938320i	0.00564188	+	0.00409907i
$525$	3.32366	−	2.41478i	0.145056	−	0.105390i
$526$	−3.12073			−0.136070
$527$	2.53638	−	1.47401i	0.110486	−	0.0642091i
$528$	2.49023			0.108373
$529$	17.8754	−	12.9873i	0.777193	−	0.564664i
$530$	−6.94577	−	5.04640i	−0.301705	−	0.219202i
$531$	4.09147	−	12.5923i	0.177555	−	0.546457i
$532$	−11.9428			−0.517785
$533$	−9.18211			−0.397721
$534$	2.01464	−	6.20042i	0.0871820	−	0.268319i
$535$	−0.392279	−	1.20731i	−0.0169597	−	0.0521966i
$536$	−2.74542	−	8.44953i	−0.118584	−	0.364964i
$537$	−3.54680	+	2.57690i	−0.153056	+	0.111201i
$538$	−4.88638	+	15.0387i	−0.210667	+	0.648365i
$539$	−19.9003	+	14.4584i	−0.857167	+	0.622768i
$540$	0.809017	+	0.587785i	0.0348145	+	0.0252942i
$541$	11.3946	+	35.0691i	0.489894	+	1.50774i	0.824765	+	0.565475i	$0.191307\pi$
$541$	11.3946	+	35.0691i	0.489894	+	1.50774i	−0.334871	+	0.942264i	$0.608693\pi$
$542$	−10.5295	−	7.65009i	−0.452279	−	0.328600i
$543$	−8.60505	−	6.25194i	−0.369278	−	0.268296i
$544$	0.162817	+	0.501100i	0.00698074	+	0.0214845i
$545$	2.13118	+	1.54840i	0.0912899	+	0.0663260i
$546$	2.72303	−	1.97840i	0.116535	−	0.0846676i
$547$	7.09785	−	21.8449i	0.303482	−	0.934022i	−0.676757	−	0.736206i	$-0.736615\pi$
$547$	7.09785	−	21.8449i	0.303482	−	0.934022i	0.980239	−	0.197815i	$-0.0633847\pi$
$548$	10.6110	−	7.70933i	0.453279	−	0.329326i
$549$	−4.46613	−	13.7453i	−0.190610	−	0.586636i
$550$	0.769524	+	2.36835i	0.0328126	+	0.100987i
$551$	−0.654101	+	2.01312i	−0.0278657	+	0.0857617i
$552$	−0.951184			−0.0404851
$553$	−9.51769			−0.404734
$554$	4.17303	−	12.8433i	0.177295	−	0.545658i
$555$	−2.98039	−	2.16538i	−0.126511	−	0.0919154i
$556$	−0.574508	+	0.417405i	−0.0243646	+	0.0177019i
$557$	14.6643			0.621345			0.310673	−	0.950517i	$-0.399446\pi$
$557$	14.6643			0.621345			0.310673	+	0.950517i	$0.399446\pi$
$558$	−2.25014	+	5.09283i	−0.0952560	+	0.215597i
$559$	3.85083			0.162873
$560$	−3.32366	+	2.41478i	−0.140450	+	0.102043i
$561$	−1.06149	−	0.771218i	−0.0448161	−	0.0325608i
$562$	−8.27014	+	25.4529i	−0.348855	+	1.07366i
$563$	−14.2154			−0.599109			−0.299555	−	0.954079i	$-0.596838\pi$
$563$	−14.2154			−0.599109			−0.299555	+	0.954079i	$0.596838\pi$
$564$	−0.686525			−0.0289079
$565$	−3.22132	+	9.91420i	−0.135522	+	0.417094i
$566$	6.98994	+	21.5128i	0.293809	+	0.904251i
$567$	−1.26952	−	3.90719i	−0.0533150	−	0.164087i
$568$	10.4205	−	7.57091i	0.437233	−	0.317668i
$569$	−1.87163	+	5.76030i	−0.0784630	+	0.241484i	−0.982592	−	0.185774i	$-0.940521\pi$
$569$	−1.87163	+	5.76030i	−0.0784630	+	0.241484i	0.904129	+	0.427259i	$0.140521\pi$
$570$	2.35182	−	1.70870i	0.0985070	−	0.0715695i
$571$	7.92580	+	5.75843i	0.331685	+	0.240983i	0.741145	−	0.671345i	$-0.234283\pi$
$571$	7.92580	+	5.75843i	0.331685	+	0.240983i	−0.409461	+	0.912328i	$0.634283\pi$
$572$	0.630461	+	1.94036i	0.0263609	+	0.0811305i
$573$	13.2827	+	9.65045i	0.554893	+	0.403153i
$574$	−37.2497	−	27.0635i	−1.55477	−	1.12961i
$575$	−0.293932	−	0.904630i	−0.0122578	−	0.0377257i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	36.1168	−	26.2404i	1.50356	−	1.09240i	0.534625	−	0.845089i	$-0.320453\pi$
$577$	36.1168	−	26.2404i	1.50356	−	1.09240i	0.968936	−	0.247312i	$-0.0795471\pi$
$578$	−5.16750	+	15.9039i	−0.214940	+	0.661517i
$579$	−8.59395	+	6.24387i	−0.357152	+	0.259486i
$580$	0.225008	+	0.692504i	0.00934295	+	0.0287547i
$581$	−5.98683	−	18.4256i	−0.248375	−	0.764421i
$582$	5.06656	−	15.5933i	0.210016	−	0.646362i
$583$	−21.3798			−0.885459
$584$	0.310054			0.0128301
$585$	−0.253174	+	0.779189i	−0.0104674	+	0.0322155i
$586$	12.0188	+	8.73214i	0.496490	+	0.360721i
$587$	−36.9365	+	26.8359i	−1.52453	+	1.10764i	−0.565349	+	0.824852i	$0.691258\pi$
$587$	−36.9365	+	26.8359i	−1.52453	+	1.10764i	−0.959183	+	0.282785i	$0.908742\pi$
$588$	9.87785			0.407356
$589$	12.0590	+	10.7960i	0.496881	+	0.444841i
$590$	−13.2403			−0.545094
$591$	19.5938	−	14.2357i	0.805979	−	0.585578i
$592$	2.98039	+	2.16538i	0.122493	+	0.0889967i
$593$	−10.5579	+	32.4940i	−0.433562	+	1.33437i	0.460991	+	0.887405i	$0.347494\pi$
$593$	−10.5579	+	32.4940i	−0.433562	+	1.33437i	−0.894553	+	0.446962i	$0.852506\pi$
$594$	2.49023			0.102175
$595$	2.16460			0.0887398
$596$	1.07557	−	3.31025i	0.0440569	−	0.135593i
$597$	−2.96648	−	9.12988i	−0.121410	−	0.373661i
$598$	−0.240815	−	0.741152i	−0.00984765	−	0.0303079i
$599$	−21.3728	+	15.5283i	−0.873270	+	0.634468i	−0.931462	−	0.363838i	$-0.881466\pi$
$599$	−21.3728	+	15.5283i	−0.873270	+	0.634468i	0.0581926	+	0.998305i	$0.481466\pi$
$600$	0.309017	−	0.951057i	0.0126156	−	0.0388267i
$601$	−29.0783	+	21.1266i	−1.18613	+	0.861773i	−0.992850	−	0.119371i	$-0.961912\pi$
$601$	−29.0783	+	21.1266i	−1.18613	+	0.861773i	−0.193279	+	0.981144i	$0.561912\pi$
$602$	15.6219	+	11.3500i	0.636702	+	0.462591i
$603$	−2.74542	−	8.44953i	−0.111802	−	0.344091i
$604$	12.7833	+	9.28758i	0.520143	+	0.377906i
$605$	−3.88227	−	2.82063i	−0.157837	−	0.114675i
$606$	0.923170	+	2.84122i	0.0375012	+	0.115417i
$607$	−30.3333	−	22.0384i	−1.23119	−	0.894512i	−0.234212	−	0.972186i	$-0.575251\pi$
$607$	−30.3333	−	22.0384i	−1.23119	−	0.894512i	−0.996979	+	0.0776733i	$0.975251\pi$
$608$	−2.35182	+	1.70870i	−0.0953790	+	0.0692969i
$609$	0.924393	−	2.84499i	0.0374583	−	0.115285i
$610$	−11.6925	+	8.49507i	−0.473414	+	0.343956i
$611$	−0.173810	−	0.534932i	−0.00703160	−	0.0216410i
$612$	0.162817	+	0.501100i	0.00658150	+	0.0202558i
$613$	11.7171	−	36.0615i	0.473248	−	1.45651i	−0.375057	−	0.927002i	$-0.622377\pi$
$613$	11.7171	−	36.0615i	0.473248	−	1.45651i	0.848306	−	0.529507i	$-0.177623\pi$
$614$	−15.7443			−0.635387
$615$	11.2074			0.451927
$616$	−3.16141	+	9.72981i	−0.127377	+	0.392025i
$617$	−19.9525	−	14.4963i	−0.803257	−	0.583601i	0.108611	−	0.994084i	$-0.465360\pi$
$617$	−19.9525	−	14.4963i	−0.803257	−	0.583601i	−0.911868	+	0.410484i	$0.865360\pi$
$618$	5.63623	−	4.09496i	0.226722	−	0.164724i
$619$	−16.5775			−0.666305			−0.333152	−	0.942873i	$-0.608112\pi$
$619$	−16.5775			−0.666305			−0.333152	+	0.942873i	$0.608112\pi$
$620$	5.53890	+	0.566239i	0.222447	+	0.0227407i
$621$	−0.951184			−0.0381697
$622$	−1.68103	+	1.22134i	−0.0674033	+	0.0489714i
$623$	21.6686	+	15.7432i	0.868135	+	0.630737i
$624$	0.253174	−	0.779189i	0.0101351	−	0.0311925i
$625$	1.00000			0.0400000
$626$	17.6698			0.706225
$627$	2.23702	−	6.88483i	0.0893378	−	0.274953i
$628$	1.52474	+	4.69265i	0.0608436	+	0.187257i
$629$	−0.599814	−	1.84604i	−0.0239162	−	0.0736064i
$630$	−3.32366	+	2.41478i	−0.132418	+	0.0962071i
$631$	7.46164	−	22.9646i	0.297043	−	0.914205i	−0.685484	−	0.728087i	$-0.740409\pi$
$631$	7.46164	−	22.9646i	0.297043	−	0.914205i	0.982527	−	0.186117i	$-0.0595905\pi$
$632$	−1.87426	+	1.36173i	−0.0745542	+	0.0541668i
$633$	10.0650	+	7.31263i	0.400047	+	0.290651i
$634$	−5.23442	−	16.1099i	−0.207885	−	0.639806i
$635$	−8.97018	−	6.51722i	−0.355971	−	0.258628i
$636$	6.94577	+	5.04640i	0.275418	+	0.200103i
$637$	2.50081	+	7.69671i	0.0990857	+	0.304955i
$638$	1.46694	+	1.06580i	0.0580768	+	0.0421953i
$639$	10.4205	−	7.57091i	0.412227	−	0.299501i
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−34.6837	+	25.1992i	−1.36992	+	0.995307i	−0.372180	+	0.928161i	$0.621389\pi$
$641$	−34.6837	+	25.1992i	−1.36992	+	0.995307i	−0.997743	+	0.0671465i	$0.978611\pi$
$642$	0.392279	+	1.20731i	0.0154820	+	0.0476487i
$643$	0.910434	+	2.80203i	0.0359040	+	0.110501i	0.967402	−	0.253244i	$-0.0814977\pi$
$643$	0.910434	+	2.80203i	0.0359040	+	0.110501i	−0.931498	+	0.363746i	$0.881498\pi$
$644$	1.20755	−	3.71646i	0.0475842	−	0.146449i
$645$	−4.70022			−0.185071
$646$	1.53167			0.0602628
$647$	6.85992	−	21.1127i	0.269691	−	0.830025i	−0.720884	−	0.693056i	$-0.756264\pi$
$647$	6.85992	−	21.1127i	0.269691	−	0.830025i	0.990575	−	0.136969i	$-0.0437361\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−26.6744	+	19.3801i	−1.04706	+	0.760734i
$650$	0.819287			0.0321351
$651$	−17.0420	−	15.2572i	−0.667931	−	0.597976i
$652$	18.2830			0.716018
$653$	28.7170	−	20.8641i	1.12378	−	0.816477i	0.139006	−	0.990292i	$-0.455609\pi$
$653$	28.7170	−	20.8641i	1.12378	−	0.816477i	0.984778	+	0.173814i	$0.0556092\pi$
$654$	−2.13118	−	1.54840i	−0.0833359	−	0.0605471i
$655$	0.0493304	−	0.151823i	0.00192750	−	0.00593223i
$656$	−11.2074			−0.437577
$657$	0.310054			0.0120964
$658$	0.871560	−	2.68238i	0.0339769	−	0.104570i
$659$	−3.93898	−	12.1229i	−0.153441	−	0.472242i	0.844559	−	0.535463i	$-0.179863\pi$
$659$	−3.93898	−	12.1229i	−0.153441	−	0.472242i	−0.998000	+	0.0632206i	$0.979863\pi$
$660$	−0.769524	−	2.36835i	−0.0299537	−	0.0921879i
$661$	−11.2273	+	8.15711i	−0.436691	+	0.317275i	−0.784319	−	0.620358i	$-0.786987\pi$
$661$	−11.2273	+	8.15711i	−0.436691	+	0.317275i	0.347628	+	0.937633i	$0.386987\pi$
$662$	0.598539	−	1.84211i	0.0232629	−	0.0715957i
$663$	−0.349231	+	0.253731i	−0.0135630	+	0.00985409i
$664$	−3.81517	−	2.77188i	−0.148057	−	0.107570i
$665$	3.69052	+	11.3583i	0.143112	+	0.440454i
$666$	2.98039	+	2.16538i	0.115488	+	0.0839069i
$667$	−0.560322	−	0.407098i	−0.0216958	−	0.0157629i
$668$	5.68475	+	17.4959i	0.219950	+	0.676935i
$669$	7.33051	+	5.32592i	0.283414	+	0.205912i
$670$	−7.18760	+	5.22209i	−0.277681	+	0.201747i
$671$	−11.1217	+	34.2290i	−0.429348	+	1.32140i
$672$	3.32366	−	2.41478i	0.128213	−	0.0931521i
$673$	8.77150	+	26.9959i	0.338116	+	1.04062i	0.965167	+	0.261636i	$0.0842621\pi$
$673$	8.77150	+	26.9959i	0.338116	+	1.04062i	−0.627050	+	0.778979i	$0.715738\pi$
$674$	0.736316	+	2.26615i	0.0283618	+	0.0872887i
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$	−12.3288			−0.474183
$677$	2.29177			0.0880798			0.0440399	−	0.999030i	$-0.485977\pi$
$677$	2.29177			0.0880798			0.0440399	+	0.999030i	$0.485977\pi$
$678$	3.22132	−	9.91420i	0.123714	−	0.380753i
$679$	54.4938	+	39.5921i	2.09128	+	1.51940i
$680$	0.426262	−	0.309697i	0.0163464	−	0.0118763i
$681$	−0.0267361			−0.00102453
$682$	11.9877	−	6.96663i	0.459033	−	0.266766i
$683$	3.96863			0.151855			0.0759277	−	0.997113i	$-0.475808\pi$
$683$	3.96863			0.151855			0.0759277	+	0.997113i	$0.475808\pi$
$684$	−2.35182	+	1.70870i	−0.0899242	+	0.0653337i
$685$	−10.6110	−	7.70933i	−0.405425	−	0.294558i
$686$	−3.65349	+	11.2443i	−0.139491	+	0.429309i
$687$	−13.1194			−0.500538
$688$	4.70022			0.179194
$689$	−2.17361	+	6.68968i	−0.0828079	+	0.254857i
$690$	0.293932	+	0.904630i	0.0111898	+	0.0344387i
$691$	0.761673	+	2.34419i	0.0289754	+	0.0891772i	0.964498	−	0.264089i	$-0.0850711\pi$
$691$	0.761673	+	2.34419i	0.0289754	+	0.0891772i	−0.935523	+	0.353266i	$0.885071\pi$
$692$	−14.4388	+	10.4904i	−0.548883	+	0.398787i
$693$	−3.16141	+	9.72981i	−0.120092	+	0.369605i
$694$	22.6839	−	16.4808i	0.861069	−	0.625603i
$695$	0.574508	+	0.417405i	0.0217923	+	0.0158331i
$696$	−0.225008	−	0.692504i	−0.00852891	−	0.0262493i
$697$	4.77730	+	3.47091i	0.180953	+	0.131470i
$698$	−6.89572	−	5.01004i	−0.261007	−	0.189633i
$699$	1.67082	+	5.14226i	0.0631962	+	0.194498i
$700$	3.32366	+	2.41478i	0.125622	+	0.0912700i
$701$	−5.68106	+	4.12753i	−0.214571	+	0.155895i	−0.689879	−	0.723924i	$-0.742336\pi$
$701$	−5.68106	+	4.12753i	−0.214571	+	0.155895i	0.475309	+	0.879819i	$0.342336\pi$
$702$	0.253174	−	0.779189i	0.00955543	−	0.0294086i
$703$	8.66404	−	6.29480i	0.326771	−	0.237413i
$704$	0.769524	+	2.36835i	0.0290025	+	0.0892606i
$705$	0.212148	+	0.652924i	0.00798995	+	0.0245905i
$706$	−6.20000	+	19.0816i	−0.233340	+	0.718147i
$707$	−12.2732			−0.461581
$708$	13.2403			0.497600
$709$	0.0674431	−	0.207569i	0.00253288	−	0.00779540i	−0.949782	−	0.312912i	$-0.898695\pi$
$709$	0.0674431	−	0.207569i	0.00253288	−	0.00779540i	0.952315	+	0.305117i	$0.0986955\pi$
$710$	−10.4205	−	7.57091i	−0.391073	−	0.284131i
$711$	−1.87426	+	1.36173i	−0.0702904	+	0.0510690i
$712$	6.51951			0.244329
$713$	−4.57889	+	2.66102i	−0.171481	+	0.0996559i
$714$	−2.16460			−0.0810080
$715$	1.65057	−	1.19921i	0.0617278	−	0.0448479i
$716$	−3.54680	−	2.57690i	−0.132550	−	0.0963032i
$717$	5.26275	−	16.1971i	0.196541	−	0.604891i
$718$	−1.18801			−0.0443361
$719$	15.3092			0.570939			0.285469	−	0.958388i	$-0.407851\pi$
$719$	15.3092			0.570939			0.285469	+	0.958388i	$0.407851\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	8.84447	+	27.2205i	0.329385	+	1.01374i
$722$	−3.25991	−	10.0330i	−0.121321	−	0.373388i
$723$	6.03507	−	4.38474i	0.224447	−	0.163070i
$724$	3.28684	−	10.1158i	0.122154	−	0.375952i
$725$	0.589079	−	0.427991i	0.0218778	−	0.0158952i
$726$	3.88227	+	2.82063i	0.144084	+	0.104683i
$727$	−5.11073	−	15.7292i	−0.189547	−	0.583364i	0.810450	−	0.585807i	$-0.199222\pi$
$727$	−5.11073	−	15.7292i	−0.189547	−	0.583364i	−0.999997	+	0.00244282i	$0.999222\pi$
$728$	2.72303	+	1.97840i	0.100922	+	0.0733243i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.0958121	−	0.294879i	−0.00354616	−	0.0109140i
$731$	−2.00352	−	1.45565i	−0.0741030	−	0.0538390i
$732$	11.6925	−	8.49507i	0.432166	−	0.313987i
$733$	−4.77172	+	14.6858i	−0.176248	+	0.542434i	−0.999688	−	0.0249682i	$-0.992052\pi$
$733$	−4.77172	+	14.6858i	−0.176248	+	0.542434i	0.823441	+	0.567402i	$0.192052\pi$
$734$	0.615487	−	0.447177i	0.0227180	−	0.0165056i
$735$	−3.05242	−	9.39439i	−0.112590	−	0.346517i
$736$	−0.293932	−	0.904630i	−0.0108345	−	0.0333451i
$737$	−6.83673	+	21.0413i	−0.251834	+	0.775065i
$738$	−11.2074			−0.412551
$739$	1.44586			0.0531868			0.0265934	−	0.999646i	$-0.491534\pi$
$739$	1.44586			0.0531868			0.0265934	+	0.999646i	$0.491534\pi$
$740$	1.13841	−	3.50366i	0.0418488	−	0.128797i
$741$	−1.92682	−	1.39992i	−0.0707834	−	0.0514272i
$742$	−28.5351	+	20.7319i	−1.04756	+	0.761094i
$743$	0.977222			0.0358508			0.0179254	−	0.999839i	$-0.494294\pi$
$743$	0.977222			0.0358508			0.0179254	+	0.999839i	$0.494294\pi$
$744$	−5.53890	−	0.566239i	−0.203066	−	0.0207593i
$745$	−3.48060			−0.127519
$746$	29.5685	−	21.4828i	1.08258	−	0.786539i
$747$	−3.81517	−	2.77188i	−0.139590	−	0.101418i
$748$	0.405453	−	1.24786i	0.0148248	−	0.0456261i
$749$	−5.21520			−0.190559
$750$	−1.00000			−0.0365148
$751$	−4.44847	+	13.6910i	−0.162327	+	0.499591i	−0.998829	−	0.0483720i	$-0.984597\pi$
$751$	−4.44847	+	13.6910i	−0.162327	+	0.499591i	0.836502	+	0.547963i	$0.184597\pi$
$752$	−0.212148	−	0.652924i	−0.00773623	−	0.0238097i
$753$	3.65640	+	11.2532i	0.133247	+	0.410091i
$754$	0.482625	−	0.350648i	0.0175762	−	0.0127698i
$755$	4.88277	−	15.0276i	0.177702	−	0.546911i
$756$	3.32366	−	2.41478i	0.120880	−	0.0878246i
$757$	−40.2231	−	29.2238i	−1.46193	−	1.06216i	−0.982854	−	0.184385i	$-0.940971\pi$
$757$	−40.2231	−	29.2238i	−1.46193	−	1.06216i	−0.479079	−	0.877772i	$-0.659029\pi$
$758$	1.17275	+	3.60936i	0.0425963	+	0.131098i
$759$	1.91629	+	1.39227i	0.0695570	+	0.0505361i
$760$	2.35182	+	1.70870i	0.0853096	+	0.0619810i
$761$	−7.82084	−	24.0701i	−0.283505	−	0.872539i	−0.986843	−	0.161683i	$-0.948308\pi$
$761$	−7.82084	−	24.0701i	−0.283505	−	0.872539i	0.703338	−	0.710856i	$-0.251692\pi$
$762$	8.97018	+	6.51722i	0.324955	+	0.236094i
$763$	8.75547	−	6.36122i	0.316969	−	0.230292i
$764$	−5.07354	+	15.6148i	−0.183554	+	0.564922i
$765$	0.426262	−	0.309697i	0.0154115	−	0.0111971i
$766$	−6.19190	−	19.0567i	−0.223722	−	0.688546i
$767$	3.35209	+	10.3167i	0.121037	+	0.372513i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	−8.32004			−0.300028			−0.150014	−	0.988684i	$-0.547932\pi$
$769$	−8.32004			−0.300028			−0.150014	+	0.988684i	$0.547932\pi$
$770$	10.2305			0.368683
$771$	−4.09253	+	12.5955i	−0.147389	+	0.453616i
$772$	−8.59395	−	6.24387i	−0.309303	−	0.224722i
$773$	−25.3678	+	18.4308i	−0.912415	+	0.662908i	−0.941624	−	0.336665i	$-0.890701\pi$
$773$	−25.3678	+	18.4308i	−0.912415	+	0.662908i	0.0292096	+	0.999573i	$0.490701\pi$
$774$	4.70022			0.168946
$775$	−1.17309	−	5.44278i	−0.0421386	−	0.195510i
$776$	16.3957			0.588572
$777$	−12.2443	+	8.89597i	−0.439260	+	0.319141i
$778$	6.08587	+	4.42164i	0.218189	+	0.158524i
$779$	−10.0678	+	30.9856i	−0.360717	+	1.11017i
$780$	−0.819287			−0.0293352
$781$	−32.0752			−1.14774
$782$	−0.154869	+	0.476639i	−0.00553811	+	0.0170446i
$783$	−0.225008	−	0.692504i	−0.00804113	−	0.0247481i
$784$	3.05242	+	9.39439i	0.109015	+	0.335514i
$785$	3.99181	−	2.90022i	0.142474	−	0.103513i
$786$	−0.0493304	+	0.151823i	−0.00175956	+	0.00541536i
$787$	18.5682	−	13.4906i	0.661883	−	0.480886i	−0.205415	−	0.978675i	$-0.565854\pi$
$787$	18.5682	−	13.4906i	0.661883	−	0.480886i	0.867298	+	0.497789i	$0.165854\pi$
$788$	19.5938	+	14.2357i	0.697999	+	0.507126i
$789$	−0.964358	−	2.96799i	−0.0343321	−	0.105663i
$790$	1.87426	+	1.36173i	0.0666833	+	0.0484483i
$791$	34.6472	+	25.1726i	1.23191	+	0.895036i
$792$	0.769524	+	2.36835i	0.0273438	+	0.0841557i
$793$	9.57949	+	6.95991i	0.340178	+	0.247154i
$794$	−2.19447	+	1.59437i	−0.0778787	+	0.0565822i
$795$	2.65305	−	8.16525i	0.0940940	−	0.289591i
$796$	7.76634	−	5.64257i	0.275271	−	0.199996i
$797$	−3.21243	−	9.88683i	−0.113790	−	0.350210i	0.877903	−	0.478839i	$-0.158942\pi$
$797$	−3.21243	−	9.88683i	−0.113790	−	0.350210i	−0.991693	+	0.128629i	$0.958942\pi$
$798$	−3.69052	−	11.3583i	−0.130643	−	0.402078i
$799$	−0.111778	+	0.344018i	−0.00395443	+	0.0121705i
$800$	1.00000			0.0353553
$801$	6.51951			0.230356
$802$	8.07160	−	24.8418i	0.285018	−	0.877196i
$803$	−0.624648	−	0.453833i	−0.0220433	−	0.0160154i
$804$	7.18760	−	5.22209i	0.253487	−	0.184169i
$805$	−3.90772			−0.137729
$806$	−0.961096	−	4.45920i	−0.0338532	−	0.157069i
$807$	−15.8126			−0.556631
$808$	−2.41689	+	1.75597i	−0.0850259	+	0.0617749i
$809$	35.1444	+	25.5339i	1.23561	+	0.897724i	0.997298	−	0.0734649i	$-0.0234057\pi$
$809$	35.1444	+	25.5339i	1.23561	+	0.897724i	0.238313	+	0.971188i	$0.423406\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−30.1235			−1.05778			−0.528889	−	0.848691i	$-0.677391\pi$
$811$	−30.1235			−1.05778			−0.528889	+	0.848691i	$0.677391\pi$
$812$	2.99140			0.104978
$813$	4.02189	−	12.3781i	0.141054	−	0.434119i
$814$	−2.83490	−	8.72493i	−0.0993633	−	0.305809i
$815$	−5.64976	−	17.3882i	−0.197903	−	0.609081i
$816$	−0.426262	+	0.309697i	−0.0149221	+	0.0108416i
$817$	4.22229	−	12.9949i	0.147719	−	0.454633i
$818$	−5.48291	+	3.98357i	−0.191705	+	0.139282i
$819$	2.72303	+	1.97840i	0.0951504	+	0.0691308i
$820$	3.46329	+	10.6589i	0.120943	+	0.372225i
$821$	28.7807	+	20.9104i	1.00445	+	0.729777i	0.963038	−	0.269365i	$-0.0868137\pi$
$821$	28.7807	+	20.9104i	1.00445	+	0.729777i	0.0414142	+	0.999142i	$0.486814\pi$
$822$	10.6110	+	7.70933i	0.370100	+	0.268894i
$823$	11.1045	+	34.1761i	0.387078	+	1.19130i	0.934962	+	0.354749i	$0.115434\pi$
$823$	11.1045	+	34.1761i	0.387078	+	1.19130i	−0.547884	+	0.836555i	$0.684566\pi$
$824$	5.63623	+	4.09496i	0.196347	+	0.142655i
$825$	−2.01464	+	1.46372i	−0.0701408	+	0.0509602i
$826$	−16.8088	+	51.7323i	−0.584855	+	1.80000i
$827$	42.0472	−	30.5490i	1.46212	−	1.06229i	0.479319	−	0.877641i	$-0.340884\pi$
$827$	42.0472	−	30.5490i	1.46212	−	1.06229i	0.982804	−	0.184654i	$-0.0591164\pi$
$828$	−0.293932	−	0.904630i	−0.0102148	−	0.0314381i
$829$	−2.70536	−	8.32624i	−0.0939610	−	0.289182i	0.893020	−	0.450016i	$-0.148582\pi$
$829$	−2.70536	−	8.32624i	−0.0939610	−	0.289182i	−0.986982	+	0.160834i	$0.948582\pi$
$830$	−1.45726	+	4.48500i	−0.0505824	+	0.155676i
$831$	13.5042			0.468456
$832$	0.819287			0.0284037
$833$	1.60829	−	4.94979i	0.0557238	−	0.171500i
$834$	−0.574508	−	0.417405i	−0.0198936	−	0.0144535i
$835$	14.8829	−	10.8130i	0.515043	−	0.374201i
$836$	7.23913			0.250371
$837$	−5.53890	−	0.566239i	−0.191452	−	0.0195721i
$838$	−5.72250			−0.197681
$839$	15.7586	−	11.4493i	0.544047	−	0.395273i	−0.281539	−	0.959550i	$-0.590845\pi$
$839$	15.7586	−	11.4493i	0.544047	−	0.395273i	0.825586	+	0.564276i	$0.190845\pi$
$840$	−3.32366	−	2.41478i	−0.114677	−	0.0833178i
$841$	−8.79766	+	27.0764i	−0.303367	+	0.933669i
$842$	−35.1586			−1.21164
$843$	−26.7627			−0.921757
$844$	−3.84448	+	11.8321i	−0.132332	+	0.407277i
$845$	3.80980	+	11.7254i	0.131061	+	0.403364i
$846$	−0.212148	−	0.652924i	−0.00729379	−	0.0224480i
$847$	−15.9494	+	11.5879i	−0.548027	+	0.398165i
$848$	−2.65305	+	8.16525i	−0.0911061	+	0.280396i
$849$	−18.2999	+	13.2956i	−0.628051	+	0.456305i
$850$	−0.426262	−	0.309697i	−0.0146206	−	0.0106225i
$851$	1.08284	+	3.33263i	0.0371192	+	0.114241i
$852$	10.4205	+	7.57091i	0.356999	+	0.259375i
$853$	43.3207	+	31.4743i	1.48327	+	1.07766i	0.976484	+	0.215591i	$0.0691679\pi$
$853$	43.3207	+	31.4743i	1.48327	+	1.07766i	0.506790	+	0.862070i	$0.330832\pi$
$854$	18.3480	+	56.4694i	0.627857	+	1.93234i
$855$	2.35182	+	1.70870i	0.0804306	+	0.0584363i
$856$	−1.02700	+	0.746159i	−0.0351021	+	0.0255032i
$857$	6.64280	−	20.4444i	0.226914	−	0.698369i	−0.771178	−	0.636620i	$-0.780332\pi$
$857$	6.64280	−	20.4444i	0.226914	−	0.698369i	0.998092	−	0.0617492i	$-0.0196679\pi$
$858$	−1.65057	+	1.19921i	−0.0563495	+	0.0409403i
$859$	−0.351227	−	1.08097i	−0.0119837	−	0.0368821i	0.944886	−	0.327400i	$-0.106172\pi$
$859$	−0.351227	−	1.08097i	−0.0119837	−	0.0368821i	−0.956870	+	0.290518i	$0.906172\pi$
$860$	−1.45245	−	4.47018i	−0.0495281	−	0.152432i
$861$	14.2281	−	43.7896i	0.484893	−	1.49235i
$862$	−11.6448			−0.396624
$863$	−26.7275			−0.909814			−0.454907	−	0.890539i	$-0.650327\pi$
$863$	−26.7275			−0.909814			−0.454907	+	0.890539i	$0.650327\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	14.4388	+	10.4904i	0.490936	+	0.356686i
$866$	18.0300	−	13.0995i	0.612683	−	0.445140i
$867$	−16.7224			−0.567922
$868$	9.24417	−	20.9227i	0.313767	−	0.710162i
$869$	5.76916			0.195706
$870$	−0.589079	+	0.427991i	−0.0199716	+	0.0145103i
$871$	5.88871	+	4.27840i	0.199531	+	0.144968i
$872$	0.814040	−	2.50536i	0.0275669	−	0.0848421i
$873$	16.3957			0.554911
$874$	−2.76510			−0.0935310
$875$	1.26952	−	3.90719i	0.0429177	−	0.132087i
$876$	0.0958121	+	0.294879i	0.00323719	+	0.00996304i
$877$	2.72961	+	8.40088i	0.0921724	+	0.283678i	0.986506	−	0.163722i	$-0.0523501\pi$
$877$	2.72961	+	8.40088i	0.0921724	+	0.283678i	−0.894334	+	0.447400i	$0.852350\pi$
$878$	30.0504	−	21.8329i	1.01415	−	0.736825i
$879$	−4.59076	+	14.1289i	−0.154842	+	0.476556i
$880$	2.01464	−	1.46372i	0.0679135	−	0.0493420i
$881$	−41.0700	−	29.8391i	−1.38368	−	1.00531i	−0.996525	−	0.0832933i	$-0.973456\pi$
$881$	−41.0700	−	29.8391i	−1.38368	−	1.00531i	−0.387160	−	0.922013i	$-0.626544\pi$
$882$	3.05242	+	9.39439i	0.102780	+	0.316326i
$883$	30.6545	+	22.2718i	1.03161	+	0.749505i	0.968629	−	0.248510i	$-0.0799409\pi$
$883$	30.6545	+	22.2718i	1.03161	+	0.749505i	0.0629758	+	0.998015i	$0.479941\pi$
$884$	−0.349231	−	0.253731i	−0.0117459	−	0.00853390i
$885$	−4.09147	−	12.5923i	−0.137533	−	0.423284i
$886$	16.0529	+	11.6631i	0.539309	+	0.391831i
$887$	25.9769	−	18.8734i	0.872220	−	0.633705i	−0.0589616	−	0.998260i	$-0.518779\pi$
$887$	25.9769	−	18.8734i	0.872220	−	0.633705i	0.931182	+	0.364555i	$0.118779\pi$
$888$	−1.13841	+	3.50366i	−0.0382025	+	0.117575i
$889$	−36.8519	+	26.7745i	−1.23597	+	0.897987i
$890$	−2.01464	−	6.20042i	−0.0675309	−	0.207839i
$891$	0.769524	+	2.36835i	0.0257800	+	0.0793427i
$892$	−2.80000	+	8.61753i	−0.0937511	+	0.288536i
$893$	−1.99574			−0.0667847
$894$	3.48060			0.116409
$895$	−1.35476	+	4.16951i	−0.0452845	+	0.139371i
$896$	3.32366	+	2.41478i	0.111036	+	0.0806721i
$897$	0.630461	−	0.458057i	0.0210505	−	0.0152941i
$898$	−26.6929			−0.890754
$899$	−3.02050	−	2.70416i	−0.100739	−	0.0901887i
$900$	1.00000			0.0333333
$901$	3.65965	−	2.65889i	0.121920	−	0.0885804i
$902$	22.5789	+	16.4046i	0.751797	+	0.546212i
$903$	−5.96705	+	18.3647i	−0.198571	+	0.611138i
$904$	10.4244			0.346711
$905$	−10.6364			−0.353567
$906$	−4.88277	+	15.0276i	−0.162219	+	0.499259i
$907$	−0.965422	−	2.97126i	−0.0320563	−	0.0986591i	0.933748	−	0.357931i	$-0.116518\pi$
$907$	−0.965422	−	2.97126i	−0.0320563	−	0.0986591i	−0.965804	+	0.259271i	$0.916518\pi$
$908$	−0.00826190	−	0.0254275i	−0.000274181	−	0.000843842i
$909$	−2.41689	+	1.75597i	−0.0801632	+	0.0582419i
$910$	1.04010	−	3.20111i	0.0344791	−	0.106116i
$911$	20.1558	−	14.6441i	0.667792	−	0.485180i	−0.201493	−	0.979490i	$-0.564579\pi$
$911$	20.1558	−	14.6441i	0.667792	−	0.485180i	0.869285	+	0.494310i	$0.164579\pi$
$912$	−2.35182	−	1.70870i	−0.0778766	−	0.0565807i
$913$	3.62892	+	11.1687i	0.120100	+	0.369629i
$914$	19.0502	+	13.8408i	0.630126	+	0.457813i
$915$	−11.6925	−	8.49507i	−0.386541	−	0.280839i
$916$	−4.05413	−	12.4773i	−0.133952	−	0.412263i
$917$	−0.530577	−	0.385487i	−0.0175212	−	0.0127299i
$918$	−0.426262	+	0.309697i	−0.0140687	+	0.0102215i
$919$	−4.27041	+	13.1430i	−0.140868	+	0.433546i	−0.996456	−	0.0841099i	$-0.973195\pi$
$919$	−4.27041	+	13.1430i	−0.140868	+	0.433546i	0.855589	+	0.517656i	$0.173195\pi$
$920$	−0.769524	+	0.559092i	−0.0253705	+	0.0184327i
$921$	−4.86524	−	14.9737i	−0.160315	−	0.493399i
$922$	−0.862202	−	2.65359i	−0.0283951	−	0.0873912i
$923$	−3.26098	+	10.0363i	−0.107336	+	0.330348i
$924$	−10.2305			−0.336560
$925$	−3.68397			−0.121128
$926$	8.32584	−	25.6243i	0.273604	−	0.842067i
$927$	5.63623	+	4.09496i	0.185118	+	0.134496i
$928$	0.589079	−	0.427991i	0.0193375	−	0.0140495i
$929$	17.5131			0.574585			0.287292	−	0.957843i	$-0.407245\pi$
$929$	17.5131			0.574585			0.287292	+	0.957843i	$0.407245\pi$
$930$	1.17309	+	5.44278i	0.0384671	+	0.178476i
$931$	28.7150			0.941097
$932$	−4.37426	+	3.17809i	−0.143284	+	0.104102i
$933$	−1.68103	−	1.22134i	−0.0550346	−	0.0399850i
$934$	2.32385	−	7.15208i	0.0760388	−	0.234023i
$935$	−1.31207			−0.0429094
$936$	0.819287			0.0267792
$937$	0.458668	−	1.41163i	0.0149840	−	0.0461161i	−0.943285	−	0.331984i	$-0.892282\pi$
$937$	0.458668	−	1.41163i	0.0149840	−	0.0461161i	0.958269	+	0.285868i	$0.0922819\pi$
$938$	11.2789	+	34.7129i	0.368269	+	1.13342i
$939$	5.46025	+	16.8049i	0.178189	+	0.548408i
$940$	−0.555410	+	0.403529i	−0.0181155	+	0.0131617i
$941$	0.860859	−	2.64945i	0.0280632	−	0.0863697i	−0.936044	−	0.351883i	$-0.885541\pi$
$941$	0.860859	−	2.64945i	0.0280632	−	0.0863697i	0.964107	+	0.265513i	$0.0855415\pi$
$942$	−3.99181	+	2.90022i	−0.130060	+	0.0944943i
$943$	−8.62439	−	6.26599i	−0.280849	−	0.204049i
$944$	4.09147	+	12.5923i	0.133166	+	0.409843i
$945$	−3.32366	−	2.41478i	−0.108119	−	0.0785527i
$946$	−9.46926	−	6.87982i	−0.307872	−	0.223682i
$947$	17.4367	+	53.6646i	0.566616	+	1.74386i	0.663101	+	0.748530i	$0.269240\pi$
$947$	17.4367	+	53.6646i	0.566616	+	1.74386i	−0.0964855	+	0.995334i	$0.530760\pi$
$948$	−1.87426	−	1.36173i	−0.0608733	−	0.0442270i
$949$	−0.205509	+	0.149311i	−0.00667112	+	0.00484685i
$950$	0.898316	−	2.76473i	0.0291452	−	0.0896998i
$951$	13.7039	−	9.95646i	0.444379	−	0.322860i
$952$	−0.668897	−	2.05865i	−0.0216791	−	0.0667214i
$953$	1.18327	+	3.64173i	0.0383299	+	0.117967i	0.968391	−	0.249439i	$-0.0802461\pi$
$953$	1.18327	+	3.64173i	0.0383299	+	0.117967i	−0.930061	+	0.367406i	$0.880246\pi$
$954$	−2.65305	+	8.16525i	−0.0858956	+	0.264360i
$955$	16.4183			0.531284
$956$	17.0306			0.550809
$957$	−0.560322	+	1.72449i	−0.0181126	+	0.0557450i
$958$	33.2866	+	24.1841i	1.07544	+	0.781353i
$959$	−43.5927	+	31.6720i	−1.40768	+	1.02274i
$960$	−1.00000			−0.0322749
$961$	−28.2477	+	12.7697i	−0.911217	+	0.411926i
$962$	−3.01823			−0.0973116
$963$	−1.02700	+	0.746159i	−0.0330946	+	0.0240446i
$964$	6.03507	+	4.38474i	0.194377	+	0.141223i
$965$	−3.28260	+	10.1028i	−0.105671	+	0.325220i
$966$	3.90772			0.125729
$967$	−40.2802			−1.29532			−0.647661	−	0.761928i	$-0.724253\pi$
$967$	−40.2802			−1.29532			−0.647661	+	0.761928i	$0.724253\pi$
$968$	−1.48289	+	4.56388i	−0.0476620	+	0.146689i
$969$	0.473312	+	1.45671i	0.0152050	+	0.0467961i
$970$	−5.06656	−	15.5933i	−0.162677	−	0.500670i
$971$	31.8541	−	23.1433i	1.02225	−	0.742705i	0.0555036	−	0.998458i	$-0.482324\pi$
$971$	31.8541	−	23.1433i	1.02225	−	0.742705i	0.966742	+	0.255754i	$0.0823236\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	2.36023	−	1.71481i	0.0756656	−	0.0549743i
$974$	25.3427	+	18.4126i	0.812034	+	0.589977i
$975$	0.253174	+	0.779189i	0.00810805	+	0.0249540i
$976$	11.6925	+	8.49507i	0.374267	+	0.271921i
$977$	8.09854	+	5.88393i	0.259095	+	0.188244i	0.709748	−	0.704456i	$-0.248809\pi$
$977$	8.09854	+	5.88393i	0.259095	+	0.188244i	−0.450653	+	0.892699i	$0.648809\pi$
$978$	5.64976	+	17.3882i	0.180660	+	0.556013i
$979$	−13.1345	−	9.54275i	−0.419779	−	0.304988i
$980$	7.99135	−	5.80605i	0.255274	−	0.185468i
$981$	0.814040	−	2.50536i	0.0259903	−	0.0799899i
$982$	13.1986	−	9.58937i	0.421185	−	0.306009i
$983$	−9.78512	−	30.1155i	−0.312097	−	0.960536i	−0.976933	−	0.213546i	$-0.931499\pi$
$983$	−9.78512	−	30.1155i	−0.312097	−	0.960536i	0.664836	−	0.746989i	$-0.268501\pi$
$984$	−3.46329	−	10.6589i	−0.110406	−	0.339794i
$985$	7.48415	−	23.0338i	0.238465	−	0.733919i
$986$	−0.383649			−0.0122179
$987$	2.82043			0.0897751
$988$	0.735979	−	2.26511i	0.0234146	−	0.0720628i
$989$	3.61693	+	2.62786i	0.115012	+	0.0835610i
$990$	2.01464	−	1.46372i	0.0640295	−	0.0465201i
$991$	45.3107			1.43934			0.719672	−	0.694315i	$-0.244292\pi$
$991$	45.3107			1.43934			0.719672	+	0.694315i	$0.244292\pi$
$992$	−1.17309	−	5.44278i	−0.0372456	−	0.172808i
$993$	1.93691			0.0614660
$994$	−42.8100	+	31.1033i	−1.35785	+	0.986537i
$995$	−7.76634	−	5.64257i	−0.246209	−	0.178882i
$996$	1.45726	−	4.48500i	0.0461752	−	0.142113i
$997$	−25.3062			−0.801455			−0.400727	−	0.916197i	$-0.631243\pi$
$997$	−25.3062			−0.801455			−0.400727	+	0.916197i	$0.631243\pi$
$998$	−41.6319			−1.31784
$999$	−1.13841	+	3.50366i	−0.0360177	+	0.110851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.c.481.1	✓	12
31.2	even	5	inner	930.2.n.c.901.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.c.481.1	✓	12	1.1	even	1	trivial
930.2.n.c.901.1	yes	12	31.2	even	5	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-1.26952 + 3.90719i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-1.26952 + 3.90719i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.769524 - 2.36835i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-0.662817 - 0.481565i) q^{13} +(-1.26952 - 3.90719i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.162817 + 0.501100i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-2.35182 + 1.70870i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(3.32366 - 2.41478i) q^{21} +(0.769524 + 2.36835i) q^{22} +(-0.293932 - 0.904630i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +0.819287 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.32366 + 2.41478i) q^{28} +(0.589079 - 0.427991i) q^{29} -1.00000 q^{30} +(-1.17309 - 5.44278i) q^{31} +1.00000 q^{32} +(-2.01464 + 1.46372i) q^{33} +(-0.426262 - 0.309697i) q^{34} +(1.26952 - 3.90719i) q^{35} +1.00000 q^{36} -3.68397 q^{37} +(0.898316 - 2.76473i) q^{38} +(0.253174 + 0.779189i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(9.06701 - 6.58757i) q^{41} +(-1.26952 + 3.90719i) q^{42} +(-3.80256 + 2.76272i) q^{43} +(-2.01464 - 1.46372i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(0.769524 + 0.559092i) q^{46} +(0.555410 + 0.403529i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-7.99135 - 5.80605i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(0.162817 - 0.501100i) q^{51} +(-0.662817 + 0.481565i) q^{52} +(-2.65305 - 8.16525i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.769524 + 2.36835i) q^{55} -4.10827 q^{56} +2.90701 q^{57} +(-0.225008 + 0.692504i) q^{58} +(-10.7116 - 7.78244i) q^{59} +(0.809017 - 0.587785i) q^{60} -14.4527 q^{61} +(4.14823 + 3.71378i) q^{62} -4.10827 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.662817 + 0.481565i) q^{65} +(0.769524 - 2.36835i) q^{66} -8.88436 q^{67} +0.526888 q^{68} +(-0.293932 + 0.904630i) q^{69} +(1.26952 + 3.90719i) q^{70} +(-3.98026 - 12.2500i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(0.0958121 - 0.294879i) q^{73} +(2.98039 - 2.16538i) q^{74} +(-0.809017 - 0.587785i) q^{75} +(0.898316 + 2.76473i) q^{76} +(8.27667 + 6.01336i) q^{77} +(-0.662817 - 0.481565i) q^{78} +(0.715905 + 2.20333i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.46329 + 10.6589i) q^{82} +(-3.81517 + 2.77188i) q^{83} +(-1.26952 - 3.90719i) q^{84} +(-0.162817 - 0.501100i) q^{85} +(1.45245 - 4.47018i) q^{86} -0.728142 q^{87} +2.49023 q^{88} +(2.01464 - 6.20042i) q^{89} +(0.809017 + 0.587785i) q^{90} +(2.72303 - 1.97840i) q^{91} -0.951184 q^{92} +(-2.25014 + 5.09283i) q^{93} -0.686525 q^{94} +(2.35182 - 1.70870i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(5.06656 - 15.5933i) q^{97} +9.87785 q^{98} +2.49023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

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