LMFDB - Embedded newform 930.2.n.e.721.2

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} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} + \cdots + 25 $ x^12 - x^11 + 16x^10 - 6x^9 + 161x^8 - 180x^7 + 1725x^6 - 2255x^5 + 17635x^4 - 18375x^3 + 60975x^2 + 2000x + 25
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			721.2
Root			$0.716623 + 2.20554i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.e.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.06713 - 0.775312i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.06713 - 0.775312i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-0.567126 - 0.412041i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.501242 + 1.54266i) q^{13} +(1.06713 - 0.775312i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.24133 + 3.08151i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.71786 + 5.28704i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(0.407606 - 1.25448i) q^{21} +(0.567126 - 0.412041i) q^{22} +(-0.350503 + 0.254655i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -1.62205 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.407606 + 1.25448i) q^{28} +(-2.62129 + 8.06749i) q^{29} -1.00000 q^{30} +(4.55035 + 3.20848i) q^{31} -1.00000 q^{32} +(0.216623 - 0.666696i) q^{33} +(-1.62004 - 4.98598i) q^{34} +(-1.06713 - 0.775312i) q^{35} +1.00000 q^{36} -3.49029 q^{37} +(-4.49743 - 3.26757i) q^{38} +(-1.31227 + 0.953419i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-3.60803 + 11.1044i) q^{41} +(1.06713 + 0.775312i) q^{42} +(0.841722 - 2.59055i) q^{43} +(0.216623 + 0.666696i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-0.133880 - 0.412041i) q^{46} +(0.650739 + 2.00277i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.62547 - 5.00268i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-4.24133 - 3.08151i) q^{51} +(0.501242 - 1.54266i) q^{52} +(5.37558 - 3.90559i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.567126 - 0.412041i) q^{55} -1.31904 q^{56} -5.55913 q^{57} +(-6.86262 - 4.98598i) q^{58} +(0.567996 + 1.74811i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.50971 q^{61} +(-4.45758 + 3.33616i) q^{62} +1.31904 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.501242 + 1.54266i) q^{65} +(0.567126 + 0.412041i) q^{66} +1.84114 q^{67} +5.24257 q^{68} +(-0.350503 - 0.254655i) q^{69} +(1.06713 - 0.775312i) q^{70} +(0.612773 - 0.445205i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-0.635289 - 0.461564i) q^{73} +(1.07856 - 3.31946i) q^{74} +(0.309017 + 0.951057i) q^{75} +(4.49743 - 3.26757i) q^{76} +(0.285734 + 0.879399i) q^{77} +(-0.501242 - 1.54266i) q^{78} +(8.87264 - 6.44635i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.44593 - 6.86287i) q^{82} +(2.02222 - 6.22376i) q^{83} +(-1.06713 + 0.775312i) q^{84} +(-4.24133 + 3.08151i) q^{85} +(2.20366 + 1.60105i) q^{86} -8.48266 q^{87} -0.701006 q^{88} +(4.32494 + 3.14225i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(0.661158 - 2.03484i) q^{91} +0.433246 q^{92} +(-1.64531 + 5.31911i) q^{93} -2.10584 q^{94} +(-1.71786 + 5.28704i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.7430 - 7.80528i) q^{97} +5.26013 q^{98} +0.701006 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	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 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 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	−1.06713	−	0.775312i	−0.403336	−	0.293040i	0.367563	−	0.929999i	$-0.380192\pi$
$7$	−1.06713	−	0.775312i	−0.403336	−	0.293040i	−0.770898	+	0.636958i	$0.780192\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.309017	+	0.951057i	−0.0977198	+	0.300750i
$11$	−0.567126	−	0.412041i	−0.170995	−	0.124235i	0.498996	−	0.866604i	$-0.333702\pi$
$11$	−0.567126	−	0.412041i	−0.170995	−	0.124235i	−0.669991	+	0.742369i	$0.733702\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	0.501242	+	1.54266i	0.139020	+	0.427858i	0.996194	−	0.0871688i	$-0.0277819\pi$
$13$	0.501242	+	1.54266i	0.139020	+	0.427858i	−0.857174	+	0.515027i	$0.827782\pi$
$14$	1.06713	−	0.775312i	0.285201	−	0.207211i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.24133	+	3.08151i	−1.02867	+	0.747375i	−0.968043	−	0.250785i	$-0.919311\pi$
$17$	−4.24133	+	3.08151i	−1.02867	+	0.747375i	−0.0606307	+	0.998160i	$0.519311\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−1.71786	+	5.28704i	−0.394105	+	1.21293i	0.535551	+	0.844503i	$0.320104\pi$
$19$	−1.71786	+	5.28704i	−0.394105	+	1.21293i	−0.929656	+	0.368428i	$0.879896\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	0.407606	−	1.25448i	0.0889469	−	0.273750i
$22$	0.567126	−	0.412041i	0.120912	−	0.0878474i
$23$	−0.350503	+	0.254655i	−0.0730849	+	0.0530993i	−0.623728	−	0.781642i	$-0.714383\pi$
$23$	−0.350503	+	0.254655i	−0.0730849	+	0.0530993i	0.550643	+	0.834741i	$0.314383\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	−1.62205			−0.318111
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.407606	+	1.25448i	0.0770303	+	0.237075i
$29$	−2.62129	+	8.06749i	−0.486761	+	1.49809i	0.342654	+	0.939462i	$0.388674\pi$
$29$	−2.62129	+	8.06749i	−0.486761	+	1.49809i	−0.829415	+	0.558633i	$0.811326\pi$
$30$	−1.00000			−0.182574
$31$	4.55035	+	3.20848i	0.817266	+	0.576260i
$31$	4.55035	+	3.20848i	0.817266	+	0.576260i
$32$	−1.00000			−0.176777
$33$	0.216623	−	0.666696i	0.0377092	−	0.116057i
$34$	−1.62004	−	4.98598i	−0.277835	−	0.855089i
$35$	−1.06713	−	0.775312i	−0.180377	−	0.131052i
$36$	1.00000			0.166667
$37$	−3.49029			−0.573799			−0.286900	−	0.957961i	$-0.592625\pi$
$37$	−3.49029			−0.573799			−0.286900	+	0.957961i	$0.592625\pi$
$38$	−4.49743	−	3.26757i	−0.729579	−	0.530070i
$39$	−1.31227	+	0.953419i	−0.210131	+	0.152669i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−3.60803	+	11.1044i	−0.563479	+	1.73421i	0.108949	+	0.994047i	$0.465251\pi$
$41$	−3.60803	+	11.1044i	−0.563479	+	1.73421i	−0.672428	+	0.740163i	$0.734749\pi$
$42$	1.06713	+	0.775312i	0.164661	+	0.119633i
$43$	0.841722	−	2.59055i	0.128361	−	0.395056i	−0.866137	−	0.499806i	$-0.833404\pi$
$43$	0.841722	−	2.59055i	0.128361	−	0.395056i	0.994499	+	0.104751i	$0.0334045\pi$
$44$	0.216623	+	0.666696i	0.0326571	+	0.100508i
$45$	−0.809017	+	0.587785i	−0.120601	+	0.0876219i
$46$	−0.133880	−	0.412041i	−0.0197396	−	0.0607521i
$47$	0.650739	+	2.00277i	0.0949200	+	0.292134i	0.987233	−	0.159284i	$-0.0509185\pi$
$47$	0.650739	+	2.00277i	0.0949200	+	0.292134i	−0.892313	+	0.451418i	$0.850918\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−1.62547	−	5.00268i	−0.232210	−	0.714669i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−4.24133	−	3.08151i	−0.593905	−	0.431497i
$52$	0.501242	−	1.54266i	0.0695098	−	0.213929i
$53$	5.37558	−	3.90559i	0.738393	−	0.536474i	−0.153815	−	0.988100i	$-0.549156\pi$
$53$	5.37558	−	3.90559i	0.738393	−	0.536474i	0.892207	+	0.451626i	$0.149156\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−0.567126	−	0.412041i	−0.0764712	−	0.0555596i
$56$	−1.31904			−0.176264
$57$	−5.55913			−0.736324
$58$	−6.86262	−	4.98598i	−0.901106	−	0.654691i
$59$	0.567996	+	1.74811i	0.0739468	+	0.227585i	0.981198	−	0.193005i	$-0.0618232\pi$
$59$	0.567996	+	1.74811i	0.0739468	+	0.227585i	−0.907251	+	0.420590i	$0.861823\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	−3.50971			−0.449373			−0.224686	−	0.974431i	$-0.572136\pi$
$61$	−3.50971			−0.449373			−0.224686	+	0.974431i	$0.572136\pi$
$62$	−4.45758	+	3.33616i	−0.566113	+	0.423693i
$63$	1.31904			0.166183
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.501242	+	1.54266i	0.0621714	+	0.191344i
$66$	0.567126	+	0.412041i	0.0698084	+	0.0507187i
$67$	1.84114			0.224931			0.112466	−	0.993656i	$-0.464125\pi$
$67$	1.84114			0.224931			0.112466	+	0.993656i	$0.464125\pi$
$68$	5.24257			0.635755
$69$	−0.350503	−	0.254655i	−0.0421956	−	0.0306569i
$70$	1.06713	−	0.775312i	0.127546	−	0.0926675i
$71$	0.612773	−	0.445205i	0.0727227	−	0.0528362i	−0.550830	−	0.834618i	$-0.685689\pi$
$71$	0.612773	−	0.445205i	0.0727227	−	0.0528362i	0.623553	+	0.781781i	$0.285689\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−0.635289	−	0.461564i	−0.0743550	−	0.0540220i	0.549987	−	0.835173i	$-0.314633\pi$
$73$	−0.635289	−	0.461564i	−0.0743550	−	0.0540220i	−0.624342	+	0.781151i	$0.714633\pi$
$74$	1.07856	−	3.31946i	0.125380	−	0.385879i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	4.49743	−	3.26757i	0.515890	−	0.374816i
$77$	0.285734	+	0.879399i	0.0325624	+	0.100217i
$78$	−0.501242	−	1.54266i	−0.0567545	−	0.174672i
$79$	8.87264	−	6.44635i	0.998250	−	0.725271i	0.0365376	−	0.999332i	$-0.488367\pi$
$79$	8.87264	−	6.44635i	0.998250	−	0.725271i	0.961712	+	0.274061i	$0.0883671\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−9.44593	−	6.86287i	−1.04313	−	0.757878i
$83$	2.02222	−	6.22376i	0.221968	−	0.683147i	−0.776618	−	0.629972i	$-0.783066\pi$
$83$	2.02222	−	6.22376i	0.221968	−	0.683147i	0.998585	−	0.0531741i	$-0.0169338\pi$
$84$	−1.06713	+	0.775312i	−0.116433	+	0.0845935i
$85$	−4.24133	+	3.08151i	−0.460037	+	0.334236i
$86$	2.20366	+	1.60105i	0.237626	+	0.172646i
$87$	−8.48266			−0.909436
$88$	−0.701006			−0.0747275
$89$	4.32494	+	3.14225i	0.458443	+	0.333078i	0.792920	−	0.609326i	$-0.208560\pi$
$89$	4.32494	+	3.14225i	0.458443	+	0.333078i	−0.334477	+	0.942404i	$0.608560\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	0.661158	−	2.03484i	0.0693082	−	0.213309i
$92$	0.433246			0.0451690
$93$	−1.64531	+	5.31911i	−0.170611	+	0.551566i
$94$	−2.10584			−0.217200
$95$	−1.71786	+	5.28704i	−0.176249	+	0.542439i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−10.7430	−	7.80528i	−1.09079	−	0.792506i	−0.111259	−	0.993791i	$-0.535488\pi$
$97$	−10.7430	−	7.80528i	−1.09079	−	0.792506i	−0.979533	+	0.201285i	$0.935488\pi$
$98$	5.26013			0.531354
$99$	0.701006			0.0704538
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−7.88732	+	5.73047i	−0.784818	+	0.570204i	−0.906421	−	0.422375i	$-0.861196\pi$
$101$	−7.88732	+	5.73047i	−0.784818	+	0.570204i	0.121603	+	0.992579i	$0.461196\pi$
$102$	4.24133	−	3.08151i	0.419954	−	0.305115i
$103$	1.30921	−	4.02933i	0.129000	−	0.397021i	−0.865609	−	0.500721i	$-0.833068\pi$
$103$	1.30921	−	4.02933i	0.129000	−	0.397021i	0.994609	+	0.103700i	$0.0330681\pi$
$104$	1.31227	+	0.953419i	0.128679	+	0.0934904i
$105$	0.407606	−	1.25448i	0.0397783	−	0.122425i
$106$	2.05329	+	6.31937i	0.199433	+	0.613792i
$107$	−7.60927	+	5.52846i	−0.735616	+	0.534456i	−0.891335	−	0.453345i	$-0.850230\pi$
$107$	−7.60927	+	5.52846i	−0.735616	+	0.534456i	0.155719	+	0.987801i	$0.450230\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	1.34531	+	4.14042i	0.128857	+	0.396581i	0.994584	−	0.103935i	$-0.0331435\pi$
$109$	1.34531	+	4.14042i	0.128857	+	0.396581i	−0.865727	+	0.500516i	$0.833144\pi$
$110$	0.567126	−	0.412041i	0.0540733	−	0.0392866i
$111$	−1.07856	−	3.31946i	−0.102372	−	0.315069i
$112$	0.407606	−	1.25448i	0.0385151	−	0.118537i
$113$	3.67420	+	2.66947i	0.345640	+	0.251122i	0.747038	−	0.664782i	$-0.231475\pi$
$113$	3.67420	+	2.66947i	0.345640	+	0.251122i	−0.401398	+	0.915904i	$0.631475\pi$
$114$	1.71786	−	5.28704i	0.160893	−	0.495177i
$115$	−0.350503	+	0.254655i	−0.0326846	+	0.0237467i
$116$	6.86262	−	4.98598i	0.637178	−	0.462937i
$117$	−1.31227	−	0.953419i	−0.121319	−	0.0881436i
$118$	−1.83808			−0.169209
$119$	6.91516			0.633912
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−3.24733	−	9.99426i	−0.295212	−	0.908569i
$122$	1.08456	−	3.33794i	0.0981916	−	0.302203i
$123$	−11.6758			−1.05277
$124$	−1.79541	−	5.27034i	−0.161233	−	0.473291i
$125$	1.00000			0.0894427
$126$	−0.407606	+	1.25448i	−0.0363124	+	0.111758i
$127$	−5.76991	−	17.7580i	−0.511997	−	1.57576i	−0.788680	−	0.614803i	$-0.789235\pi$
$127$	−5.76991	−	17.7580i	−0.511997	−	1.57576i	0.276684	−	0.960961i	$-0.410765\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	2.72387			0.239823
$130$	−1.62205			−0.142263
$131$	11.0203	+	8.00674i	0.962851	+	0.699552i	0.953811	−	0.300407i	$-0.0971225\pi$
$131$	11.0203	+	8.00674i	0.962851	+	0.699552i	0.00903972	+	0.999959i	$0.497123\pi$
$132$	−0.567126	+	0.412041i	−0.0493620	+	0.0358636i
$133$	5.93229	−	4.31006i	0.514395	−	0.373730i
$134$	−0.568945	+	1.75103i	−0.0491493	+	0.151266i
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$	−1.62004	+	4.98598i	−0.138918	+	0.427544i
$137$	−1.31981	−	4.06195i	−0.112759	−	0.347036i	0.878714	−	0.477348i	$-0.158402\pi$
$137$	−1.31981	−	4.06195i	−0.112759	−	0.347036i	−0.991473	+	0.130312i	$0.958402\pi$
$138$	0.350503	−	0.254655i	0.0298368	−	0.0216777i
$139$	−0.408618	−	1.25760i	−0.0346586	−	0.106668i	0.932231	−	0.361865i	$-0.117860\pi$
$139$	−0.408618	−	1.25760i	−0.0346586	−	0.106668i	−0.966889	+	0.255197i	$0.917860\pi$
$140$	0.407606	+	1.25448i	0.0344490	+	0.106023i
$141$	−1.70366	+	1.23778i	−0.143474	+	0.104240i
$142$	0.234058	+	0.720357i	0.0196417	+	0.0604511i
$143$	0.351374	−	1.08142i	0.0293833	−	0.0904326i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	−2.62129	+	8.06749i	−0.217686	+	0.669968i
$146$	0.635289	−	0.461564i	0.0525769	−	0.0381993i
$147$	4.25554	−	3.09183i	0.350991	−	0.255010i
$148$	2.82370	+	2.05154i	0.232107	+	0.168635i
$149$	4.21167			0.345034			0.172517	−	0.985007i	$-0.444810\pi$
$149$	4.21167			0.345034			0.172517	+	0.985007i	$0.444810\pi$
$150$	−1.00000			−0.0816497
$151$	18.9133	+	13.7414i	1.53915	+	1.11826i	0.950868	+	0.309597i	$0.100194\pi$
$151$	18.9133	+	13.7414i	1.53915	+	1.11826i	0.588279	+	0.808658i	$0.299806\pi$
$152$	1.71786	+	5.28704i	0.139337	+	0.428836i
$153$	1.62004	−	4.98598i	0.130973	−	0.403093i
$154$	−0.924655			−0.0745108
$155$	4.55035	+	3.20848i	0.365493	+	0.257711i
$156$	1.62205			0.129868
$157$	−5.35410	+	16.4782i	−0.427304	+	1.31511i	0.473467	+	0.880812i	$0.343002\pi$
$157$	−5.35410	+	16.4782i	−0.427304	+	1.31511i	−0.900771	+	0.434295i	$0.856998\pi$
$158$	3.38905	+	10.4304i	0.269618	+	0.829799i
$159$	5.37558	+	3.90559i	0.426311	+	0.309733i
$160$	−1.00000			−0.0790569
$161$	0.571468			0.0450380
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	11.7293	−	8.52184i	0.918711	−	0.667482i	−0.0244921	−	0.999700i	$-0.507797\pi$
$163$	11.7293	−	8.52184i	0.918711	−	0.667482i	0.943203	+	0.332218i	$0.107797\pi$
$164$	9.44593	−	6.86287i	0.737604	−	0.535900i
$165$	0.216623	−	0.666696i	0.0168641	−	0.0519022i
$166$	5.29425	+	3.84650i	0.410913	+	0.298546i
$167$	−4.28136	+	13.1767i	−0.331301	+	1.01964i	0.637214	+	0.770687i	$0.280087\pi$
$167$	−4.28136	+	13.1767i	−0.331301	+	1.01964i	−0.968515	+	0.248954i	$0.919913\pi$
$168$	−0.407606	−	1.25448i	−0.0314475	−	0.0967854i
$169$	8.38865	−	6.09471i	0.645281	−	0.468824i
$170$	−1.62004	−	4.98598i	−0.124252	−	0.382407i
$171$	−1.71786	−	5.28704i	−0.131368	−	0.404310i
$172$	−2.20366	+	1.60105i	−0.168027	+	0.122079i
$173$	1.36625	+	4.20488i	0.103874	+	0.319691i	0.989464	−	0.144776i	$-0.0462461\pi$
$173$	1.36625	+	4.20488i	0.103874	+	0.319691i	−0.885591	+	0.464467i	$0.846246\pi$
$174$	2.62129	−	8.06749i	0.198719	−	0.611595i
$175$	−1.06713	−	0.775312i	−0.0806671	−	0.0586081i
$176$	0.216623	−	0.666696i	0.0163286	−	0.0502541i
$177$	−1.48703	+	1.08039i	−0.111772	+	0.0812073i
$178$	−4.32494	+	3.14225i	−0.324168	+	0.235522i
$179$	12.6343	+	9.17939i	0.944335	+	0.686100i	0.949460	−	0.313887i	$-0.101631\pi$
$179$	12.6343	+	9.17939i	0.944335	+	0.686100i	−0.00512498	+	0.999987i	$0.501631\pi$
$180$	1.00000			0.0745356
$181$	4.48494			0.333363			0.166681	−	0.986011i	$-0.446695\pi$
$181$	4.48494			0.333363			0.166681	+	0.986011i	$0.446695\pi$
$182$	1.73093	+	1.25760i	0.128305	+	0.0932194i
$183$	−1.08456	−	3.33794i	−0.0801731	−	0.246747i
$184$	−0.133880	+	0.412041i	−0.00986978	+	0.0303761i
$185$	−3.49029			−0.256611
$186$	−4.55035	−	3.20848i	−0.333648	−	0.235257i
$187$	3.67507			0.268748
$188$	0.650739	−	2.00277i	0.0474600	−	0.146067i
$189$	0.407606	+	1.25448i	0.0296490	+	0.0912501i
$190$	−4.49743	−	3.26757i	−0.326278	−	0.237055i
$191$	4.53875			0.328412			0.164206	−	0.986426i	$-0.447494\pi$
$191$	4.53875			0.328412			0.164206	+	0.986426i	$0.447494\pi$
$192$	1.00000			0.0721688
$193$	−11.9695	−	8.69637i	−0.861585	−	0.625978i	0.0667306	−	0.997771i	$-0.478743\pi$
$193$	−11.9695	−	8.69637i	−0.861585	−	0.625978i	−0.928316	+	0.371793i	$0.878743\pi$
$194$	10.7430	−	7.80528i	0.771306	−	0.560386i
$195$	−1.31227	+	0.953419i	−0.0939735	+	0.0682758i
$196$	−1.62547	+	5.00268i	−0.116105	+	0.357335i
$197$	−11.2530	−	8.17577i	−0.801742	−	0.582499i	0.109683	−	0.993967i	$-0.465016\pi$
$197$	−11.2530	−	8.17577i	−0.801742	−	0.582499i	−0.911425	+	0.411467i	$0.865016\pi$
$198$	−0.216623	+	0.666696i	−0.0153947	+	0.0473800i
$199$	−0.924939	−	2.84667i	−0.0655672	−	0.201795i	0.912906	−	0.408171i	$-0.133833\pi$
$199$	−0.924939	−	2.84667i	−0.0655672	−	0.201795i	−0.978473	+	0.206376i	$0.933833\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	0.568945	+	1.75103i	0.0401303	+	0.123508i
$202$	−3.01269	−	9.27210i	−0.211972	−	0.652383i
$203$	9.05206	−	6.57671i	0.635330	−	0.461595i
$204$	1.62004	+	4.98598i	0.113426	+	0.349089i
$205$	−3.60803	+	11.1044i	−0.251995	+	0.775562i
$206$	3.42755	+	2.49026i	0.238809	+	0.173505i
$207$	0.133880	−	0.412041i	0.00930532	−	0.0286388i
$208$	−1.31227	+	0.953419i	−0.0909895	+	0.0661077i
$209$	3.15272	−	2.29059i	0.218079	−	0.158443i
$210$	1.06713	+	0.775312i	0.0736387	+	0.0535016i
$211$	9.66804			0.665575			0.332787	−	0.943002i	$-0.392011\pi$
$211$	9.66804			0.665575			0.332787	+	0.943002i	$0.392011\pi$
$212$	−6.64458			−0.456352
$213$	0.612773	+	0.445205i	0.0419865	+	0.0305050i
$214$	−2.90648	−	8.94523i	−0.198683	−	0.611483i
$215$	0.841722	−	2.59055i	0.0574050	−	0.176674i
$216$	−1.00000			−0.0680414
$217$	−2.36822	−	6.95179i	−0.160765	−	0.471918i
$218$	−4.35350			−0.294856
$219$	0.242659	−	0.746827i	0.0163974	−	0.0504659i
$220$	0.216623	+	0.666696i	0.0146047	+	0.0449487i
$221$	−6.87966	−	4.99837i	−0.462776	−	0.336227i
$222$	3.49029			0.234253
$223$	26.6230			1.78281			0.891403	−	0.453211i	$-0.149721\pi$
$223$	26.6230			1.78281			0.891403	+	0.453211i	$0.149721\pi$
$224$	1.06713	+	0.775312i	0.0713003	+	0.0518027i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−3.67420	+	2.66947i	−0.244404	+	0.177570i
$227$	−7.39897	+	22.7717i	−0.491087	+	1.51141i	0.331880	+	0.943322i	$0.392317\pi$
$227$	−7.39897	+	22.7717i	−0.491087	+	1.51141i	−0.822967	+	0.568089i	$0.807683\pi$
$228$	4.49743	+	3.26757i	0.297849	+	0.216400i
$229$	−3.94775	+	12.1499i	−0.260874	+	0.802889i	0.731741	+	0.681583i	$0.238708\pi$
$229$	−3.94775	+	12.1499i	−0.260874	+	0.802889i	−0.992615	+	0.121306i	$0.961292\pi$
$230$	−0.133880	−	0.412041i	−0.00882780	−	0.0271692i
$231$	−0.748062	+	0.543499i	−0.0492188	+	0.0357596i
$232$	2.62129	+	8.06749i	0.172096	+	0.529657i
$233$	3.94870	+	12.1528i	0.258688	+	0.796159i	0.993081	+	0.117434i	$0.0374669\pi$
$233$	3.94870	+	12.1528i	0.258688	+	0.796159i	−0.734393	+	0.678724i	$0.762533\pi$
$234$	1.31227	−	0.953419i	0.0857857	−	0.0623270i
$235$	0.650739	+	2.00277i	0.0424495	+	0.130646i
$236$	0.567996	−	1.74811i	0.0369734	−	0.113792i
$237$	8.87264	+	6.44635i	0.576340	+	0.418735i
$238$	−2.13690	+	6.57671i	−0.138515	+	0.426305i
$239$	3.05540	−	2.21988i	0.197638	−	0.143592i	−0.484565	−	0.874755i	$-0.661022\pi$
$239$	3.05540	−	2.21988i	0.197638	−	0.143592i	0.682203	+	0.731163i	$0.261022\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	16.2697	+	11.8206i	1.04802	+	0.761432i	0.971835	−	0.235662i	$-0.0757258\pi$
$241$	16.2697	+	11.8206i	1.04802	+	0.761432i	0.0761858	+	0.997094i	$0.475726\pi$
$242$	10.5086			0.675518
$243$	1.00000			0.0641500
$244$	2.83942	+	2.06296i	0.181775	+	0.132067i
$245$	−1.62547	−	5.00268i	−0.103848	−	0.319610i
$246$	3.60803	−	11.1044i	0.230039	−	0.707988i
$247$	−9.01720			−0.573751
$248$	5.56721	−	0.0789111i	0.353518	−	0.00501086i
$249$	6.54405			0.414712
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−9.61175	−	29.5819i	−0.606688	−	1.86719i	−0.484740	−	0.874659i	$-0.661086\pi$
$251$	−9.61175	−	29.5819i	−0.606688	−	1.86719i	−0.121949	−	0.992536i	$-0.538914\pi$
$252$	−1.06713	−	0.775312i	−0.0672226	−	0.0488401i
$253$	0.303708			0.0190939
$254$	18.6718			1.17157
$255$	−4.24133	−	3.08151i	−0.265602	−	0.192971i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	17.2931	−	12.5642i	1.07872	−	0.783733i	0.101258	−	0.994860i	$-0.467713\pi$
$257$	17.2931	−	12.5642i	1.07872	−	0.783733i	0.977459	+	0.211127i	$0.0677134\pi$
$258$	−0.841722	+	2.59055i	−0.0524033	+	0.161281i
$259$	3.72457	+	2.70606i	0.231434	+	0.168146i
$260$	0.501242	−	1.54266i	0.0310857	−	0.0956720i
$261$	−2.62129	−	8.06749i	−0.162254	−	0.499365i
$262$	−11.0203	+	8.00674i	−0.680838	+	0.494658i
$263$	6.14624	+	18.9162i	0.378993	+	1.16642i	0.940745	+	0.339115i	$0.110128\pi$
$263$	6.14624	+	18.9162i	0.378993	+	1.16642i	−0.561752	+	0.827306i	$0.689872\pi$
$264$	−0.216623	−	0.666696i	−0.0133322	−	0.0410323i
$265$	5.37558	−	3.90559i	0.330219	−	0.239918i
$266$	2.26593	+	6.97382i	0.138933	+	0.427593i
$267$	−1.65198	+	5.08427i	−0.101100	+	0.311153i
$268$	−1.48952	−	1.08220i	−0.0909867	−	0.0661057i
$269$	−2.32478	+	7.15492i	−0.141744	+	0.436243i	−0.996578	−	0.0826584i	$-0.973659\pi$
$269$	−2.32478	+	7.15492i	−0.141744	+	0.436243i	0.854834	+	0.518902i	$0.173659\pi$
$270$	0.809017	−	0.587785i	0.0492352	−	0.0357715i
$271$	8.63481	−	6.27355i	0.524527	−	0.381091i	−0.293779	−	0.955873i	$-0.594913\pi$
$271$	8.63481	−	6.27355i	0.524527	−	0.381091i	0.818307	+	0.574782i	$0.194913\pi$
$272$	−4.24133	−	3.08151i	−0.257168	−	0.186844i
$273$	2.13955			0.129492
$274$	4.27099			0.258020
$275$	−0.567126	−	0.412041i	−0.0341990	−	0.0248470i
$276$	0.133880	+	0.412041i	0.00805864	+	0.0248020i
$277$	4.09312	−	12.5973i	0.245932	−	0.756900i	−0.749550	−	0.661948i	$-0.769730\pi$
$277$	4.09312	−	12.5973i	0.245932	−	0.756900i	0.995482	−	0.0949526i	$-0.0302700\pi$
$278$	1.32232			0.0793073
$279$	−5.56721	+	0.0789111i	−0.333300	+	0.00472428i
$280$	−1.31904			−0.0788277
$281$	−5.40094	+	16.6224i	−0.322193	+	0.991608i	0.650499	+	0.759507i	$0.274560\pi$
$281$	−5.40094	+	16.6224i	−0.322193	+	0.991608i	−0.972692	+	0.232101i	$0.925440\pi$
$282$	−0.650739	−	2.00277i	−0.0387509	−	0.119263i
$283$	−3.87871	−	2.81805i	−0.230566	−	0.167516i	0.466504	−	0.884519i	$-0.345513\pi$
$283$	−3.87871	−	2.81805i	−0.230566	−	0.167516i	−0.697070	+	0.717003i	$0.745513\pi$
$284$	−0.757429			−0.0449451
$285$	−5.55913			−0.329294
$286$	0.919908	+	0.668352i	0.0543953	+	0.0395205i
$287$	12.4596	−	9.05240i	0.735465	−	0.534347i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	3.23991	−	9.97140i	0.190583	−	0.586553i
$290$	−6.86262	−	4.98598i	−0.402987	−	0.292787i
$291$	4.10348	−	12.6292i	0.240550	−	0.740337i
$292$	0.242659	+	0.746827i	0.0142005	+	0.0437047i
$293$	1.87322	−	1.36098i	0.109435	−	0.0795091i	−0.531722	−	0.846919i	$-0.678455\pi$
$293$	1.87322	−	1.36098i	0.109435	−	0.0795091i	0.641157	+	0.767410i	$0.278455\pi$
$294$	1.62547	+	5.00268i	0.0947994	+	0.291762i
$295$	0.567996	+	1.74811i	0.0330700	+	0.101779i
$296$	−2.82370	+	2.05154i	−0.164124	+	0.119243i
$297$	0.216623	+	0.666696i	0.0125697	+	0.0386856i
$298$	−1.30148	+	4.00554i	−0.0753926	+	0.232035i
$299$	−0.568535	−	0.413065i	−0.0328792	−	0.0238881i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	−2.90671	+	2.11185i	−0.167540	+	0.121725i
$302$	−18.9133	+	13.7414i	−1.08834	+	0.790726i
$303$	−7.88732	−	5.73047i	−0.453115	−	0.329207i
$304$	−5.55913			−0.318838
$305$	−3.50971			−0.200966
$306$	4.24133	+	3.08151i	0.242461	+	0.176158i
$307$	−0.702992	−	2.16359i	−0.0401218	−	0.123482i	0.928989	−	0.370106i	$-0.120679\pi$
$307$	−0.702992	−	2.16359i	−0.0401218	−	0.123482i	−0.969111	+	0.246624i	$0.920679\pi$
$308$	0.285734	−	0.879399i	0.0162812	−	0.0501084i
$309$	4.23669			0.241017
$310$	−4.45758	+	3.33616i	−0.253174	+	0.189481i
$311$	−11.6448			−0.660314			−0.330157	−	0.943926i	$-0.607102\pi$
$311$	−11.6448			−0.660314			−0.330157	+	0.943926i	$0.607102\pi$
$312$	−0.501242	+	1.54266i	−0.0283772	+	0.0873362i
$313$	8.85515	+	27.2534i	0.500523	+	1.54045i	0.808169	+	0.588950i	$0.200459\pi$
$313$	8.85515	+	27.2534i	0.500523	+	1.54045i	−0.307646	+	0.951501i	$0.599541\pi$
$314$	−14.0172	−	10.1841i	−0.791038	−	0.574722i
$315$	1.31904			0.0743195
$316$	−10.9672			−0.616952
$317$	3.33745	+	2.42480i	0.187450	+	0.136190i	0.677552	−	0.735475i	$-0.263041\pi$
$317$	3.33745	+	2.42480i	0.187450	+	0.136190i	−0.490103	+	0.871665i	$0.663041\pi$
$318$	−5.37558	+	3.90559i	−0.301448	+	0.219015i
$319$	4.81073	−	3.49520i	0.269349	−	0.195694i
$320$	0.309017	−	0.951057i	0.0172746	−	0.0531657i
$321$	−7.60927	−	5.52846i	−0.424708	−	0.308568i
$322$	−0.176593	+	0.543499i	−0.00984117	+	0.0302880i
$323$	−9.00603	−	27.7177i	−0.501109	−	1.54225i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	0.501242	+	1.54266i	0.0278039	+	0.0855716i
$326$	4.48020	+	13.7886i	0.248135	+	0.763682i
$327$	−3.52206	+	2.55892i	−0.194770	+	0.141509i
$328$	3.60803	+	11.1044i	0.199220	+	0.613136i
$329$	0.858351	−	2.64173i	0.0473224	−	0.145643i
$330$	0.567126	+	0.412041i	0.0312192	+	0.0226821i
$331$	3.44839	−	10.6130i	0.189541	−	0.583346i	−0.810456	−	0.585799i	$-0.800781\pi$
$331$	3.44839	−	10.6130i	0.189541	−	0.583346i	0.999997	+	0.00245302i	$0.000780823\pi$
$332$	−5.29425	+	3.84650i	−0.290560	+	0.211104i
$333$	2.82370	−	2.05154i	0.154738	−	0.112424i
$334$	−11.2087	−	8.14363i	−0.613315	−	0.445600i
$335$	1.84114			0.100592
$336$	1.31904			0.0719595
$337$	−6.12441	−	4.44965i	−0.333618	−	0.242388i	0.408346	−	0.912827i	$-0.366106\pi$
$337$	−6.12441	−	4.44965i	−0.333618	−	0.242388i	−0.741964	+	0.670439i	$0.766106\pi$
$338$	3.20418	+	9.86145i	0.174284	+	0.536392i
$339$	−1.40342	+	4.31929i	−0.0762234	+	0.234591i
$340$	5.24257			0.284318
$341$	−1.25859	−	3.69454i	−0.0681566	−	0.200071i
$342$	5.55913			0.300603
$343$	−4.99730	+	15.3801i	−0.269829	+	0.830448i
$344$	−0.841722	−	2.59055i	−0.0453826	−	0.139673i
$345$	−0.350503	−	0.254655i	−0.0188704	−	0.0137102i
$346$	−4.42127			−0.237689
$347$	18.0585			0.969431			0.484716	−	0.874672i	$-0.338923\pi$
$347$	18.0585			0.969431			0.484716	+	0.874672i	$0.338923\pi$
$348$	6.86262	+	4.98598i	0.367875	+	0.267277i
$349$	17.5770	−	12.7704i	0.940874	−	0.683585i	−0.00775696	−	0.999970i	$-0.502469\pi$
$349$	17.5770	−	12.7704i	0.940874	−	0.683585i	0.948631	+	0.316385i	$0.102469\pi$
$350$	1.06713	−	0.775312i	0.0570403	−	0.0414422i
$351$	0.501242	−	1.54266i	0.0267543	−	0.0823413i
$352$	0.567126	+	0.412041i	0.0302279	+	0.0219619i
$353$	7.31600	−	22.5163i	0.389392	−	1.19842i	−0.543852	−	0.839181i	$-0.683035\pi$
$353$	7.31600	−	22.5163i	0.389392	−	1.19842i	0.933244	−	0.359243i	$-0.116965\pi$
$354$	−0.567996	−	1.74811i	−0.0301887	−	0.0929112i
$355$	0.612773	−	0.445205i	0.0325226	−	0.0236290i
$356$	−1.65198	−	5.08427i	−0.0875548	−	0.269466i
$357$	2.13690	+	6.57671i	0.113097	+	0.348076i
$358$	−12.6343	+	9.17939i	−0.667746	+	0.485146i
$359$	−8.00797	−	24.6460i	−0.422645	−	1.30077i	−0.905232	−	0.424919i	$-0.860303\pi$
$359$	−8.00797	−	24.6460i	−0.422645	−	1.30077i	0.482587	−	0.875848i	$-0.339697\pi$
$360$	−0.309017	+	0.951057i	−0.0162866	+	0.0501251i
$361$	−9.63045	−	6.99694i	−0.506866	−	0.368260i
$362$	−1.38592	+	4.26543i	−0.0728424	+	0.224186i
$363$	8.50163	−	6.17679i	0.446220	−	0.324198i
$364$	−1.73093	+	1.25760i	−0.0907256	+	0.0659160i
$365$	−0.635289	−	0.461564i	−0.0332525	−	0.0241594i
$366$	3.50971			0.183456
$367$	−20.6526			−1.07806			−0.539029	−	0.842288i	$-0.681208\pi$
$367$	−20.6526			−1.07806			−0.539029	+	0.842288i	$0.681208\pi$
$368$	−0.350503	−	0.254655i	−0.0182712	−	0.0132748i
$369$	−3.60803	−	11.1044i	−0.187826	−	0.578070i
$370$	1.07856	−	3.31946i	0.0560715	−	0.172570i
$371$	−8.76447			−0.455029
$372$	4.45758	−	3.33616i	0.231115	−	0.172972i
$373$	1.10245			0.0570826			0.0285413	−	0.999593i	$-0.490914\pi$
$373$	1.10245			0.0570826			0.0285413	+	0.999593i	$0.490914\pi$
$374$	−1.13566	+	3.49520i	−0.0587236	+	0.180733i
$375$	0.309017	+	0.951057i	0.0159576	+	0.0491123i
$376$	1.70366	+	1.23778i	0.0878594	+	0.0638336i
$377$	−13.7593			−0.708641
$378$	−1.31904			−0.0678441
$379$	−3.74040	−	2.71756i	−0.192131	−	0.139592i	0.487561	−	0.873089i	$-0.337887\pi$
$379$	−3.74040	−	2.71756i	−0.192131	−	0.139592i	−0.679692	+	0.733497i	$0.737887\pi$
$380$	4.49743	−	3.26757i	0.230713	−	0.167623i
$381$	15.1058	−	10.9750i	0.773895	−	0.562268i
$382$	−1.40255	+	4.31661i	−0.0717607	+	0.220857i
$383$	−21.3116	−	15.4838i	−1.08897	−	0.791183i	−0.109745	−	0.993960i	$-0.535004\pi$
$383$	−21.3116	−	15.4838i	−1.08897	−	0.791183i	−0.979225	+	0.202776i	$0.935004\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	0.285734	+	0.879399i	0.0145624	+	0.0448183i
$386$	11.9695	−	8.69637i	0.609233	−	0.442633i
$387$	0.841722	+	2.59055i	0.0427871	+	0.131685i
$388$	4.10348	+	12.6292i	0.208323	+	0.641151i
$389$	−23.2091	+	16.8624i	−1.17675	+	0.854959i	−0.991801	−	0.127790i	$-0.959212\pi$
$389$	−23.2091	+	16.8624i	−1.17675	+	0.854959i	−0.184948	+	0.982748i	$0.559212\pi$
$390$	−0.501242	−	1.54266i	−0.0253814	−	0.0781158i
$391$	0.701877	−	2.16015i	0.0354954	−	0.109244i
$392$	−4.25554	−	3.09183i	−0.214937	−	0.156161i
$393$	−4.20939	+	12.9552i	−0.212336	+	0.653502i
$394$	11.2530	−	8.17577i	0.566917	−	0.411889i
$395$	8.87264	−	6.44635i	0.446431	−	0.324351i
$396$	−0.567126	−	0.412041i	−0.0284991	−	0.0207058i
$397$	−37.4265			−1.87838			−0.939192	−	0.343392i	$-0.888424\pi$
$397$	−37.4265			−1.87838			−0.939192	+	0.343392i	$0.888424\pi$
$398$	2.99317			0.150034
$399$	5.93229	+	4.31006i	0.296986	+	0.215773i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	0.830726	−	2.55671i	0.0414845	−	0.127676i	−0.928169	−	0.372158i	$-0.878618\pi$
$401$	0.830726	−	2.55671i	0.0414845	−	0.127676i	0.969654	+	0.244482i	$0.0786179\pi$
$402$	−1.84114			−0.0918279
$403$	−2.66878	+	8.62788i	−0.132942	+	0.429785i
$404$	9.74927			0.485044
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	3.45758	+	10.6413i	0.171597	+	0.528121i
$407$	1.97943	+	1.43814i	0.0981168	+	0.0712860i
$408$	−5.24257			−0.259546
$409$	5.31932			0.263024			0.131512	−	0.991315i	$-0.458017\pi$
$409$	5.31932			0.263024			0.131512	+	0.991315i	$0.458017\pi$
$410$	−9.44593	−	6.86287i	−0.466501	−	0.338933i
$411$	3.45530	−	2.51042i	0.170437	−	0.123830i
$412$	−3.42755	+	2.49026i	−0.168863	+	0.122686i
$413$	0.749210	−	2.30583i	0.0368662	−	0.113463i
$414$	0.350503	+	0.254655i	0.0172263	+	0.0125156i
$415$	2.02222	−	6.22376i	0.0992670	−	0.305512i
$416$	−0.501242	−	1.54266i	−0.0245754	−	0.0756353i
$417$	1.06978	−	0.777238i	0.0523872	−	0.0380615i
$418$	1.20423	+	3.70625i	0.0589010	+	0.181279i
$419$	−1.96031	−	6.03321i	−0.0957674	−	0.294742i	0.891686	−	0.452655i	$-0.149523\pi$
$419$	−1.96031	−	6.03321i	−0.0957674	−	0.294742i	−0.987453	+	0.157914i	$0.949523\pi$
$420$	−1.06713	+	0.775312i	−0.0520704	+	0.0378314i
$421$	11.6196	+	35.7616i	0.566307	+	1.74291i	0.664036	+	0.747701i	$0.268842\pi$
$421$	11.6196	+	35.7616i	0.566307	+	1.74291i	−0.0977289	+	0.995213i	$0.531158\pi$
$422$	−2.98759	+	9.19485i	−0.145433	+	0.447598i
$423$	−1.70366	−	1.23778i	−0.0828346	−	0.0601829i
$424$	2.05329	−	6.31937i	0.0997165	−	0.306896i
$425$	−4.24133	+	3.08151i	−0.205735	+	0.149475i
$426$	−0.612773	+	0.445205i	−0.0296889	+	0.0215703i
$427$	3.74531	+	2.72112i	0.181248	+	0.131684i
$428$	9.40557			0.454636
$429$	1.13707			0.0548982
$430$	2.20366	+	1.60105i	0.106270	+	0.0772095i
$431$	−10.0440	−	30.9124i	−0.483804	−	1.48900i	−0.833705	−	0.552209i	$-0.813785\pi$
$431$	−10.0440	−	30.9124i	−0.483804	−	1.48900i	0.349901	−	0.936787i	$-0.386215\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−24.5734			−1.18092			−0.590462	−	0.807066i	$-0.701054\pi$
$433$	−24.5734			−1.18092			−0.590462	+	0.807066i	$0.701054\pi$
$434$	7.34337	−	0.104087i	0.352493	−	0.00499633i
$435$	−8.48266			−0.406712
$436$	1.34531	−	4.14042i	0.0644285	−	0.198290i
$437$	−0.744257	−	2.29059i	−0.0356027	−	0.109574i
$438$	0.635289	+	0.461564i	0.0303553	+	0.0220544i
$439$	−2.46581			−0.117687			−0.0588433	−	0.998267i	$-0.518741\pi$
$439$	−2.46581			−0.117687			−0.0588433	+	0.998267i	$0.518741\pi$
$440$	−0.701006			−0.0334192
$441$	4.25554	+	3.09183i	0.202645	+	0.147230i
$442$	6.87966	−	4.99837i	0.327232	−	0.237748i
$443$	29.6738	−	21.5593i	1.40984	−	1.02431i	0.416498	−	0.909137i	$-0.363257\pi$
$443$	29.6738	−	21.5593i	1.40984	−	1.02431i	0.993345	−	0.115174i	$-0.0367426\pi$
$444$	−1.07856	+	3.31946i	−0.0511861	+	0.157535i
$445$	4.32494	+	3.14225i	0.205022	+	0.148957i
$446$	−8.22695	+	25.3200i	−0.389558	+	1.19893i
$447$	1.30148	+	4.00554i	0.0615578	+	0.189455i
$448$	−1.06713	+	0.775312i	−0.0504170	+	0.0366301i
$449$	7.06425	+	21.7415i	0.333382	+	1.02605i	0.967513	+	0.252820i	$0.0813580\pi$
$449$	7.06425	+	21.7415i	0.333382	+	1.02605i	−0.634131	+	0.773226i	$0.718642\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	6.62166	−	4.81092i	0.311802	−	0.226537i
$452$	−1.40342	−	4.31929i	−0.0660114	−	0.203162i
$453$	−7.22426	+	22.2340i	−0.339425	+	1.04464i
$454$	−19.3708	−	14.0737i	−0.909115	−	0.660511i
$455$	0.661158	−	2.03484i	0.0309956	−	0.0953946i
$456$	−4.49743	+	3.26757i	−0.210611	+	0.153018i
$457$	−0.922036	+	0.669899i	−0.0431310	+	0.0313365i	−0.609142	−	0.793061i	$-0.708486\pi$
$457$	−0.922036	+	0.669899i	−0.0431310	+	0.0313365i	0.566011	+	0.824398i	$0.308486\pi$
$458$	−10.3353	−	7.50906i	−0.482939	−	0.350875i
$459$	5.24257			0.244702
$460$	0.433246			0.0202002
$461$	−14.7434	−	10.7117i	−0.686668	−	0.498894i	0.188895	−	0.981997i	$-0.439509\pi$
$461$	−14.7434	−	10.7117i	−0.686668	−	0.498894i	−0.875563	+	0.483104i	$0.839509\pi$
$462$	−0.285734	−	0.879399i	−0.0132936	−	0.0409134i
$463$	4.62702	−	14.2405i	0.215036	−	0.661812i	−0.784115	−	0.620615i	$-0.786883\pi$
$463$	4.62702	−	14.2405i	0.215036	−	0.661812i	0.999151	−	0.0411971i	$-0.0131171\pi$
$464$	−8.48266			−0.393798
$465$	−1.64531	+	5.31911i	−0.0762995	+	0.246668i
$466$	−12.7782			−0.591941
$467$	−4.19346	+	12.9061i	−0.194050	+	0.597225i	0.805936	+	0.592002i	$0.201662\pi$
$467$	−4.19346	+	12.9061i	−0.194050	+	0.597225i	−0.999986	+	0.00522246i	$0.998338\pi$
$468$	0.501242	+	1.54266i	0.0231699	+	0.0713097i
$469$	−1.96473	−	1.42746i	−0.0907229	−	0.0659140i
$470$	−2.10584			−0.0971350
$471$	−17.3262			−0.798351
$472$	1.48703	+	1.08039i	0.0684463	+	0.0497291i
$473$	−1.54478	+	1.12235i	−0.0710289	+	0.0516055i
$474$	−8.87264	+	6.44635i	−0.407534	+	0.296091i
$475$	−1.71786	+	5.28704i	−0.0788210	+	0.242586i
$476$	−5.59448	−	4.06463i	−0.256423	−	0.186302i
$477$	−2.05329	+	6.31937i	−0.0940137	+	0.289344i
$478$	1.16706	+	3.59184i	0.0533801	+	0.164287i
$479$	−34.5830	+	25.1260i	−1.58014	+	1.14804i	−0.663603	+	0.748085i	$0.730974\pi$
$479$	−34.5830	+	25.1260i	−1.58014	+	1.14804i	−0.916536	+	0.399953i	$0.869026\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	−1.74948	−	5.38434i	−0.0797693	−	0.245505i
$482$	−16.2697	+	11.8206i	−0.741063	+	0.538414i
$483$	0.176593	+	0.543499i	0.00803528	+	0.0247300i
$484$	−3.24733	+	9.99426i	−0.147606	+	0.454285i
$485$	−10.7430	−	7.80528i	−0.487817	−	0.354420i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	9.33753	−	6.78411i	0.423124	−	0.307417i	−0.355770	−	0.934574i	$-0.615781\pi$
$487$	9.33753	−	6.78411i	0.423124	−	0.307417i	0.778893	+	0.627156i	$0.215781\pi$
$488$	−2.83942	+	2.06296i	−0.128534	+	0.0933857i
$489$	11.7293	+	8.52184i	0.530418	+	0.385371i
$490$	5.26013			0.237629
$491$	9.41786			0.425022			0.212511	−	0.977159i	$-0.431836\pi$
$491$	9.41786			0.425022			0.212511	+	0.977159i	$0.431836\pi$
$492$	9.44593	+	6.86287i	0.425856	+	0.309402i
$493$	−13.7423	−	42.2944i	−0.618921	−	1.90484i
$494$	2.78647	−	8.57587i	0.125369	−	0.385847i
$495$	0.701006			0.0315079
$496$	−1.64531	+	5.31911i	−0.0738767	+	0.238835i
$497$	−0.999079			−0.0448148
$498$	−2.02222	+	6.22376i	−0.0906180	+	0.278893i
$499$	−5.77872	−	17.7851i	−0.258691	−	0.796169i	−0.993080	−	0.117440i	$-0.962531\pi$
$499$	−5.77872	−	17.7851i	−0.258691	−	0.796169i	0.734389	−	0.678729i	$-0.237469\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−13.8548			−0.618985
$502$	31.1043			1.38825
$503$	−9.88977	−	7.18534i	−0.440963	−	0.320378i	0.345054	−	0.938583i	$-0.387860\pi$
$503$	−9.88977	−	7.18534i	−0.440963	−	0.320378i	−0.786017	+	0.618204i	$0.787860\pi$
$504$	1.06713	−	0.775312i	0.0475336	−	0.0345352i
$505$	−7.88732	+	5.73047i	−0.350981	+	0.255003i
$506$	−0.0938509	+	0.288843i	−0.00417218	+	0.0128406i
$507$	8.38865	+	6.09471i	0.372553	+	0.270676i
$508$	−5.76991	+	17.7580i	−0.255998	+	0.787882i
$509$	8.09179	+	24.9040i	0.358662	+	1.10385i	0.953855	+	0.300267i	$0.0970757\pi$
$509$	8.09179	+	24.9040i	0.358662	+	1.10385i	−0.595193	+	0.803583i	$0.702924\pi$
$510$	4.24133	−	3.08151i	0.187809	−	0.136451i
$511$	0.320077	+	0.985095i	0.0141594	+	0.0435780i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	4.49743	−	3.26757i	0.198566	−	0.144267i
$514$	6.60539	+	20.3293i	0.291351	+	0.896687i
$515$	1.30921	−	4.02933i	0.0576906	−	0.177553i
$516$	−2.20366	−	1.60105i	−0.0970106	−	0.0704823i
$517$	0.456172	−	1.40395i	0.0200624	−	0.0617458i
$518$	−3.72457	+	2.70606i	−0.163648	+	0.118898i
$519$	−3.57688	+	2.59876i	−0.157008	+	0.114073i
$520$	1.31227	+	0.953419i	0.0575468	+	0.0418102i
$521$	−0.175315			−0.00768069			−0.00384034	−	0.999993i	$-0.501222\pi$
$521$	−0.175315			−0.00768069			−0.00384034	+	0.999993i	$0.501222\pi$
$522$	8.48266			0.371276
$523$	6.23356	+	4.52895i	0.272575	+	0.198037i	0.715672	−	0.698436i	$-0.246120\pi$
$523$	6.23356	+	4.52895i	0.272575	+	0.198037i	−0.443098	+	0.896473i	$0.646120\pi$
$524$	−4.20939	−	12.9552i	−0.183888	−	0.565950i
$525$	0.407606	−	1.25448i	0.0177894	−	0.0547501i
$526$	−19.8896			−0.867229
$527$	−29.1865	+	0.413697i	−1.27138	+	0.0180209i
$528$	0.701006			0.0305074
$529$	−7.04939	+	21.6958i	−0.306495	+	0.943295i
$530$	2.05329	+	6.31937i	0.0891892	+	0.274496i
$531$	−1.48703	−	1.08039i	−0.0645318	−	0.0468851i
$532$	−7.33271			−0.317913
$533$	−18.9388			−0.820330
$534$	−4.32494	−	3.14225i	−0.187159	−	0.135979i
$535$	−7.60927	+	5.52846i	−0.328977	+	0.239016i
$536$	1.48952	−	1.08220i	0.0643373	−	0.0467438i
$537$	−4.82589	+	14.8526i	−0.208253	+	0.640935i
$538$	−6.08634	−	4.42199i	−0.262401	−	0.190645i
$539$	−1.13946	+	3.50691i	−0.0490802	+	0.151053i
$540$	0.309017	+	0.951057i	0.0132980	+	0.0409270i
$541$	−12.3228	+	8.95307i	−0.529800	+	0.384923i	−0.820283	−	0.571958i	$-0.806184\pi$
$541$	−12.3228	+	8.95307i	−0.529800	+	0.384923i	0.290483	+	0.956880i	$0.406184\pi$
$542$	3.29820	+	10.1508i	0.141670	+	0.436015i
$543$	1.38592	+	4.26543i	0.0594756	+	0.183047i
$544$	4.24133	−	3.08151i	0.181845	−	0.132118i
$545$	1.34531	+	4.14042i	0.0576266	+	0.177356i
$546$	−0.661158	+	2.03484i	−0.0282950	+	0.0870829i
$547$	16.9387	+	12.3067i	0.724248	+	0.526197i	0.887739	−	0.460348i	$-0.152275\pi$
$547$	16.9387	+	12.3067i	0.724248	+	0.526197i	−0.163490	+	0.986545i	$0.552275\pi$
$548$	−1.31981	+	4.06195i	−0.0563794	+	0.173518i
$549$	2.83942	−	2.06296i	0.121183	−	0.0880449i
$550$	0.567126	−	0.412041i	0.0241823	−	0.0175695i
$551$	−38.1502	−	27.7177i	−1.62525	−	1.18081i
$552$	−0.433246			−0.0184402
$553$	−14.4662			−0.615163
$554$	10.7159	+	7.78558i	0.455276	+	0.330778i
$555$	−1.07856	−	3.31946i	−0.0457822	−	0.140903i
$556$	−0.408618	+	1.25760i	−0.0173293	+	0.0533340i
$557$	33.0958			1.40231			0.701157	−	0.713007i	$-0.252667\pi$
$557$	33.0958			1.40231			0.701157	+	0.713007i	$0.252667\pi$
$558$	1.64531	−	5.31911i	0.0696516	−	0.225176i
$559$	4.41826			0.186873
$560$	0.407606	−	1.25448i	0.0172245	−	0.0530115i
$561$	1.13566	+	3.49520i	0.0479476	+	0.147568i
$562$	−14.1398	−	10.2732i	−0.596453	−	0.433348i
$563$	−5.66250			−0.238646			−0.119323	−	0.992856i	$-0.538072\pi$
$563$	−5.66250			−0.238646			−0.119323	+	0.992856i	$0.538072\pi$
$564$	2.10584			0.0886717
$565$	3.67420	+	2.66947i	0.154575	+	0.112305i
$566$	3.87871	−	2.81805i	0.163035	−	0.118452i
$567$	−1.06713	+	0.775312i	−0.0448151	+	0.0325601i
$568$	0.234058	−	0.720357i	0.00982087	−	0.0302255i
$569$	−19.5503	−	14.2041i	−0.819591	−	0.595468i	0.0970045	−	0.995284i	$-0.469074\pi$
$569$	−19.5503	−	14.2041i	−0.819591	−	0.595468i	−0.916595	+	0.399816i	$0.869074\pi$
$570$	1.71786	−	5.28704i	0.0719534	−	0.221450i
$571$	9.80876	+	30.1883i	0.410484	+	1.26334i	0.916228	+	0.400656i	$0.131218\pi$
$571$	9.80876	+	30.1883i	0.410484	+	1.26334i	−0.505744	+	0.862683i	$0.668782\pi$
$572$	−0.919908	+	0.668352i	−0.0384633	+	0.0279452i
$573$	1.40255	+	4.31661i	0.0585924	+	0.180329i
$574$	4.75913	+	14.6471i	0.198642	+	0.611358i
$575$	−0.350503	+	0.254655i	−0.0146170	+	0.0106199i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	5.96614	−	18.3619i	0.248374	−	0.764416i	−0.746689	−	0.665173i	$-0.768358\pi$
$577$	5.96614	−	18.3619i	0.248374	−	0.764416i	0.995063	−	0.0992430i	$-0.0316421\pi$
$578$	8.48218	+	6.16267i	0.352812	+	0.256333i
$579$	4.57195	−	14.0710i	0.190004	−	0.584772i
$580$	6.86262	−	4.98598i	0.284955	−	0.207032i
$581$	−6.98332	+	5.07368i	−0.289717	+	0.210492i
$582$	10.7430	+	7.80528i	0.445314	+	0.323539i
$583$	−4.65789			−0.192910
$584$	−0.785260			−0.0324943
$585$	−1.31227	−	0.953419i	−0.0542556	−	0.0394190i
$586$	0.715508	+	2.20211i	0.0295574	+	0.0909682i
$587$	6.03645	−	18.5783i	0.249151	−	0.766808i	−0.745775	−	0.666198i	$-0.767921\pi$
$587$	6.03645	−	18.5783i	0.249151	−	0.766808i	0.994926	−	0.100610i	$-0.0320794\pi$
$588$	−5.26013			−0.216924
$589$	−24.7803	+	18.5461i	−1.02105	+	0.764181i
$590$	−1.83808			−0.0756724
$591$	4.29826	−	13.2287i	0.176807	−	0.544155i
$592$	−1.07856	−	3.31946i	−0.0443284	−	0.136429i
$593$	−27.2280	−	19.7823i	−1.11812	−	0.812360i	−0.134195	−	0.990955i	$-0.542845\pi$
$593$	−27.2280	−	19.7823i	−1.11812	−	0.812360i	−0.983923	+	0.178594i	$0.942845\pi$
$594$	−0.701006			−0.0287626
$595$	6.91516			0.283494
$596$	−3.40731	−	2.47556i	−0.139569	−	0.101403i
$597$	2.42152	−	1.75934i	0.0991063	−	0.0720049i
$598$	0.568535	−	0.413065i	0.0232491	−	0.0168915i
$599$	−3.12791	+	9.62671i	−0.127803	+	0.393337i	−0.994401	−	0.105669i	$-0.966301\pi$
$599$	−3.12791	+	9.62671i	−0.127803	+	0.393337i	0.866599	+	0.499006i	$0.166301\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	5.94474	−	18.2960i	0.242491	−	0.746311i	−0.753548	−	0.657393i	$-0.771659\pi$
$601$	5.94474	−	18.2960i	0.242491	−	0.746311i	0.996039	−	0.0889177i	$-0.0283408\pi$
$602$	−1.11027	−	3.41704i	−0.0452510	−	0.139268i
$603$	−1.48952	+	1.08220i	−0.0606578	+	0.0440705i
$604$	−7.22426	−	22.2340i	−0.293951	−	0.904688i
$605$	−3.24733	−	9.99426i	−0.132023	−	0.406325i
$606$	7.88732	−	5.73047i	0.320401	−	0.232785i
$607$	10.7341	+	33.0363i	0.435686	+	1.34090i	0.892382	+	0.451280i	$0.149032\pi$
$607$	10.7341	+	33.0363i	0.435686	+	1.34090i	−0.456697	+	0.889622i	$0.650968\pi$
$608$	1.71786	−	5.28704i	0.0696686	−	0.214418i
$609$	9.05206	+	6.57671i	0.366808	+	0.266502i
$610$	1.08456	−	3.33794i	0.0439126	−	0.135149i
$611$	−2.76342	+	2.00774i	−0.111796	+	0.0812246i
$612$	−4.24133	+	3.08151i	−0.171446	+	0.124563i
$613$	−9.45743	−	6.87122i	−0.381982	−	0.277526i	0.380180	−	0.924912i	$-0.375862\pi$
$613$	−9.45743	−	6.87122i	−0.381982	−	0.277526i	−0.762162	+	0.647386i	$0.775862\pi$
$614$	2.27493			0.0918086
$615$	−11.6758			−0.470814
$616$	0.748062	+	0.543499i	0.0301403	+	0.0218982i
$617$	6.45760	+	19.8745i	0.259973	+	0.800116i	0.992809	+	0.119710i	$0.0381965\pi$
$617$	6.45760	+	19.8745i	0.259973	+	0.800116i	−0.732836	+	0.680406i	$0.761804\pi$
$618$	−1.30921	+	4.02933i	−0.0526641	+	0.162083i
$619$	8.53462			0.343035			0.171518	−	0.985181i	$-0.445133\pi$
$619$	8.53462			0.343035			0.171518	+	0.985181i	$0.445133\pi$
$620$	−1.79541	−	5.27034i	−0.0721054	−	0.211662i
$621$	0.433246			0.0173855
$622$	3.59843	−	11.0748i	0.144284	−	0.444060i
$623$	−2.17903	−	6.70636i	−0.0873010	−	0.268685i
$624$	−1.31227	−	0.953419i	−0.0525328	−	0.0381673i
$625$	1.00000			0.0400000
$626$	−28.6559			−1.14532
$627$	3.15272	+	2.29059i	0.125908	+	0.0914773i
$628$	14.0172	−	10.1841i	0.559348	−	0.406390i
$629$	14.8035	−	10.7553i	0.590252	−	0.428843i
$630$	−0.407606	+	1.25448i	−0.0162394	+	0.0499797i
$631$	−7.69191	−	5.58850i	−0.306210	−	0.222475i	0.424059	−	0.905635i	$-0.360605\pi$
$631$	−7.69191	−	5.58850i	−0.306210	−	0.222475i	−0.730269	+	0.683160i	$0.760605\pi$
$632$	3.38905	−	10.4304i	0.134809	−	0.414899i
$633$	2.98759	+	9.19485i	0.118746	+	0.365462i
$634$	−3.33745	+	2.42480i	−0.132547	+	0.0963010i
$635$	−5.76991	−	17.7580i	−0.228972	−	0.704703i
$636$	−2.05329	−	6.31937i	−0.0814182	−	0.250579i
$637$	6.90271	−	5.01511i	0.273495	−	0.198706i
$638$	1.83754	+	5.65536i	0.0727488	+	0.223898i
$639$	−0.234058	+	0.720357i	−0.00925920	+	0.0284969i
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	−2.06489	+	6.35507i	−0.0815581	+	0.251010i	−0.983518	−	0.180809i	$-0.942128\pi$
$641$	−2.06489	+	6.35507i	−0.0815581	+	0.251010i	0.901960	+	0.431820i	$0.142128\pi$
$642$	7.60927	−	5.52846i	0.300314	−	0.218191i
$643$	13.7868	−	10.0167i	0.543697	−	0.395019i	−0.281759	−	0.959485i	$-0.590918\pi$
$643$	13.7868	−	10.0167i	0.543697	−	0.395019i	0.825456	+	0.564466i	$0.190918\pi$
$644$	−0.462328	−	0.335901i	−0.0182183	−	0.0132363i
$645$	2.72387			0.107252
$646$	29.1441			1.14666
$647$	0.0217941	+	0.0158343i	0.000856814	+	0.000622512i	0.588214	−	0.808706i	$-0.299831\pi$
$647$	0.0217941	+	0.0158343i	0.000856814	+	0.000622512i	−0.587357	+	0.809328i	$0.699831\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	0.398169	−	1.22544i	0.0156295	−	0.0481027i
$650$	−1.62205			−0.0636222
$651$	5.87973	−	4.40053i	0.230445	−	0.172470i
$652$	−14.4982			−0.567794
$653$	−0.514990	+	1.58498i	−0.0201531	+	0.0620249i	−0.960627	−	0.277840i	$-0.910381\pi$
$653$	−0.514990	+	1.58498i	−0.0201531	+	0.0620249i	0.940474	+	0.339865i	$0.110381\pi$
$654$	−1.34531	−	4.14042i	−0.0526056	−	0.161903i
$655$	11.0203	+	8.00674i	0.430600	+	0.312849i
$656$	−11.6758			−0.455864
$657$	0.785260			0.0306359
$658$	2.24719	+	1.63268i	0.0876047	+	0.0636485i
$659$	−7.26075	+	5.27524i	−0.282839	+	0.205494i	−0.720155	−	0.693814i	$-0.755929\pi$
$659$	−7.26075	+	5.27524i	−0.282839	+	0.205494i	0.437316	+	0.899308i	$0.355929\pi$
$660$	−0.567126	+	0.412041i	−0.0220753	+	0.0160387i
$661$	−10.9343	+	33.6522i	−0.425294	+	1.30892i	0.477419	+	0.878676i	$0.341573\pi$
$661$	−10.9343	+	33.6522i	−0.425294	+	1.30892i	−0.902713	+	0.430244i	$0.858427\pi$
$662$	9.02800	+	6.55922i	0.350883	+	0.254932i
$663$	2.62780	−	8.08753i	0.102055	−	0.314094i
$664$	−2.02222	−	6.22376i	−0.0784775	−	0.241529i
$665$	5.93229	−	4.31006i	0.230044	−	0.167137i
$666$	1.07856	+	3.31946i	0.0417933	+	0.128626i
$667$	−1.13566	−	3.49520i	−0.0439729	−	0.135335i
$668$	11.2087	−	8.14363i	0.433679	−	0.315086i
$669$	8.22695	+	25.3200i	0.318072	+	0.978926i
$670$	−0.568945	+	1.75103i	−0.0219802	+	0.0676482i
$671$	1.99045	+	1.44615i	0.0768404	+	0.0558279i
$672$	−0.407606	+	1.25448i	−0.0157237	+	0.0483927i
$673$	16.1299	−	11.7191i	0.621762	−	0.451737i	−0.231774	−	0.972770i	$-0.574453\pi$
$673$	16.1299	−	11.7191i	0.621762	−	0.451737i	0.853537	+	0.521033i	$0.174453\pi$
$674$	6.12441	−	4.44965i	0.235904	−	0.171394i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	−10.3689			−0.398806
$677$	34.8027			1.33758			0.668789	−	0.743453i	$-0.266813\pi$
$677$	34.8027			1.33758			0.668789	+	0.743453i	$0.266813\pi$
$678$	−3.67420	−	2.66947i	−0.141107	−	0.102520i
$679$	5.41265	+	16.6584i	0.207719	+	0.639292i
$680$	−1.62004	+	4.98598i	−0.0621258	+	0.191204i
$681$	−23.9436			−0.917520
$682$	3.90264	−	0.0553172i	0.149440	−	0.00211820i
$683$	14.0179			0.536381			0.268190	−	0.963366i	$-0.413574\pi$
$683$	14.0179			0.536381			0.268190	+	0.963366i	$0.413574\pi$
$684$	−1.71786	+	5.28704i	−0.0656842	+	0.202155i
$685$	−1.31981	−	4.06195i	−0.0504273	−	0.155199i
$686$	−13.0831	−	9.50543i	−0.499515	−	0.362919i
$687$	−12.7752			−0.487403
$688$	2.72387			0.103847
$689$	8.71948	+	6.33507i	0.332186	+	0.241347i
$690$	0.350503	−	0.254655i	0.0133434	−	0.00969456i
$691$	27.2335	−	19.7863i	1.03601	−	0.752707i	0.0665096	−	0.997786i	$-0.478814\pi$
$691$	27.2335	−	19.7863i	1.03601	−	0.752707i	0.969503	+	0.245078i	$0.0788137\pi$
$692$	1.36625	−	4.20488i	0.0519369	−	0.159845i
$693$	−0.748062	−	0.543499i	−0.0284165	−	0.0206458i
$694$	−5.58039	+	17.1747i	−0.211829	+	0.651941i
$695$	−0.408618	−	1.25760i	−0.0154998	−	0.0477034i
$696$	−6.86262	+	4.98598i	−0.260127	+	0.188993i
$697$	−18.9153	−	58.2154i	−0.716469	−	2.20507i
$698$	6.71381	+	20.6630i	0.254121	+	0.782105i
$699$	−10.3378	+	7.51087i	−0.391012	+	0.284087i
$700$	0.407606	+	1.25448i	0.0154061	+	0.0474149i
$701$	4.65979	−	14.3414i	0.175998	−	0.541666i	−0.823680	−	0.567055i	$-0.808083\pi$
$701$	4.65979	−	14.3414i	0.175998	−	0.541666i	0.999678	+	0.0253896i	$0.00808264\pi$
$702$	1.31227	+	0.953419i	0.0495284	+	0.0359845i
$703$	5.99584	−	18.4533i	0.226137	−	0.695979i
$704$	−0.567126	+	0.412041i	−0.0213744	+	0.0155294i
$705$	−1.70366	+	1.23778i	−0.0641634	+	0.0466175i
$706$	19.1535	+	13.9159i	0.720853	+	0.523730i
$707$	12.8597			0.483638
$708$	1.83808			0.0690791
$709$	39.2410	+	28.5103i	1.47373	+	1.07073i	0.979512	+	0.201386i	$0.0645444\pi$
$709$	39.2410	+	28.5103i	1.47373	+	1.07073i	0.494215	+	0.869340i	$0.335456\pi$
$710$	0.234058	+	0.720357i	0.00878405	+	0.0270345i
$711$	−3.38905	+	10.4304i	−0.127099	+	0.391171i
$712$	5.34592			0.200347
$713$	−2.41197	+	0.0341879i	−0.0903289	+	0.00128035i
$714$	−6.91516			−0.258793
$715$	0.351374	−	1.08142i	0.0131406	−	0.0404427i
$716$	−4.82589	−	14.8526i	−0.180352	−	0.555066i
$717$	3.05540	+	2.21988i	0.114106	+	0.0829029i
$718$	25.9144			0.967115
$719$	29.9835			1.11820			0.559098	−	0.829102i	$-0.311148\pi$
$719$	29.9835			1.11820			0.559098	+	0.829102i	$0.311148\pi$
$720$	−0.809017	−	0.587785i	−0.0301503	−	0.0219055i
$721$	−4.52108	+	3.28475i	−0.168374	+	0.122331i
$722$	9.63045	−	6.99694i	0.358408	−	0.260399i
$723$	−6.21446	+	19.1261i	−0.231118	+	0.711308i
$724$	−3.62839	−	2.63618i	−0.134848	−	0.0979728i
$725$	−2.62129	+	8.06749i	−0.0973521	+	0.299619i
$726$	3.24733	+	9.99426i	0.120520	+	0.370922i
$727$	0.725548	−	0.527142i	0.0269091	−	0.0195506i	−0.574249	−	0.818680i	$-0.694706\pi$
$727$	0.725548	−	0.527142i	0.0269091	−	0.0195506i	0.601159	+	0.799130i	$0.294706\pi$
$728$	−0.661158	−	2.03484i	−0.0245042	−	0.0754160i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.635289	−	0.461564i	0.0235131	−	0.0170833i
$731$	4.41279	+	13.5812i	0.163213	+	0.502318i
$732$	−1.08456	+	3.33794i	−0.0400865	+	0.123374i
$733$	28.9346	+	21.0222i	1.06872	+	0.776474i	0.975683	−	0.219189i	$-0.0703410\pi$
$733$	28.9346	+	21.0222i	1.06872	+	0.776474i	0.0930418	+	0.995662i	$0.470341\pi$
$734$	6.38200	−	19.6418i	0.235564	−	0.724992i
$735$	4.25554	−	3.09183i	0.156968	−	0.114044i
$736$	0.350503	−	0.254655i	0.0129197	−	0.00938672i
$737$	−1.04416	−	0.758627i	−0.0384621	−	0.0279444i
$738$	11.6758			0.429793
$739$	−25.6475			−0.943460			−0.471730	−	0.881743i	$-0.656370\pi$
$739$	−25.6475			−0.943460			−0.471730	+	0.881743i	$0.656370\pi$
$740$	2.82370	+	2.05154i	0.103801	+	0.0754161i
$741$	−2.78647	−	8.57587i	−0.102363	−	0.315042i
$742$	2.70837	−	8.33551i	0.0994274	−	0.306006i
$743$	18.9992			0.697013			0.348506	−	0.937306i	$-0.386689\pi$
$743$	18.9992			0.697013			0.348506	+	0.937306i	$0.386689\pi$
$744$	1.79541	+	5.27034i	0.0658229	+	0.193220i
$745$	4.21167			0.154304
$746$	−0.340675	+	1.04849i	−0.0124730	+	0.0383880i
$747$	2.02222	+	6.22376i	0.0739893	+	0.227716i
$748$	−2.97320	−	2.16015i	−0.108711	−	0.0789831i
$749$	12.4063			0.453317
$750$	−1.00000			−0.0365148
$751$	10.2677	+	7.45990i	0.374673	+	0.272216i	0.759146	−	0.650920i	$-0.225617\pi$
$751$	10.2677	+	7.45990i	0.374673	+	0.272216i	−0.384473	+	0.923136i	$0.625617\pi$
$752$	−1.70366	+	1.23778i	−0.0621260	+	0.0451372i
$753$	25.1639	−	18.2826i	0.917023	−	0.666256i
$754$	4.25187	−	13.0859i	0.154844	−	0.476560i
$755$	18.9133	+	13.7414i	0.688327	+	0.500099i
$756$	0.407606	−	1.25448i	0.0148245	−	0.0456251i
$757$	−2.12746	−	6.54765i	−0.0773239	−	0.237979i	0.904922	−	0.425578i	$-0.139929\pi$
$757$	−2.12746	−	6.54765i	−0.0773239	−	0.237979i	−0.982246	+	0.187600i	$0.939929\pi$
$758$	3.74040	−	2.71756i	0.135857	−	0.0987061i
$759$	0.0938509	+	0.288843i	0.00340657	+	0.0104843i
$760$	1.71786	+	5.28704i	0.0623135	+	0.191781i
$761$	30.1282	−	21.8894i	1.09215	−	0.793490i	0.112385	−	0.993665i	$-0.464151\pi$
$761$	30.1282	−	21.8894i	1.09215	−	0.793490i	0.979760	+	0.200175i	$0.0641510\pi$
$762$	5.76991	+	17.7580i	0.209022	+	0.643303i
$763$	1.77451	−	5.46139i	0.0642416	−	0.197715i
$764$	−3.67192	−	2.66781i	−0.132846	−	0.0965179i
$765$	1.62004	−	4.98598i	0.0585728	−	0.180269i
$766$	21.3116	−	15.4838i	0.770018	−	0.559451i
$767$	−2.41205	+	1.75246i	−0.0870940	+	0.0632775i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	−18.3667			−0.662321			−0.331160	−	0.943575i	$-0.607440\pi$
$769$	−18.3667			−0.662321			−0.331160	+	0.943575i	$0.607440\pi$
$770$	−0.924655			−0.0333223
$771$	17.2931	+	12.5642i	0.622797	+	0.452489i
$772$	4.57195	+	14.0710i	0.164548	+	0.506427i
$773$	−12.5674	+	38.6784i	−0.452017	+	1.39117i	0.422584	+	0.906324i	$0.361123\pi$
$773$	−12.5674	+	38.6784i	−0.452017	+	1.39117i	−0.874602	+	0.484842i	$0.838877\pi$
$774$	−2.72387			−0.0979075
$775$	4.55035	+	3.20848i	0.163453	+	0.115252i
$776$	−13.2791			−0.476693
$777$	−1.42266	+	4.37850i	−0.0510377	+	0.157078i
$778$	−8.86510	−	27.2840i	−0.317829	−	0.978178i
$779$	−52.5112	−	38.1516i	−1.88141	−	1.36692i
$780$	1.62205			0.0580788
$781$	−0.530962			−0.0189993
$782$	1.83754	+	1.33505i	0.0657102	+	0.0477412i
$783$	6.86262	−	4.98598i	0.245250	−	0.178184i
$784$	4.25554	−	3.09183i	0.151983	−	0.110422i
$785$	−5.35410	+	16.4782i	−0.191096	+	0.588133i
$786$	−11.0203	−	8.00674i	−0.393082	−	0.285591i
$787$	10.8370	−	33.3528i	0.386296	−	1.18890i	−0.549239	−	0.835665i	$-0.685082\pi$
$787$	10.8370	−	33.3528i	0.386296	−	1.18890i	0.935535	−	0.353233i	$-0.114918\pi$
$788$	4.29826	+	13.2287i	0.153119	+	0.471252i
$789$	−16.0911	+	11.6908i	−0.572857	+	0.416205i
$790$	3.38905	+	10.4304i	0.120577	+	0.371097i
$791$	−1.85117	−	5.69731i	−0.0658200	−	0.202573i
$792$	0.567126	−	0.412041i	0.0201519	−	0.0146412i
$793$	−1.75922	−	5.41431i	−0.0624716	−	0.192268i
$794$	11.5654	−	35.5948i	0.410442	−	1.26321i
$795$	5.37558	+	3.90559i	0.190652	+	0.138517i
$796$	−0.924939	+	2.84667i	−0.0327836	+	0.100898i
$797$	10.9924	−	7.98646i	0.389371	−	0.282895i	−0.375827	−	0.926690i	$-0.622641\pi$
$797$	10.9924	−	7.98646i	0.389371	−	0.282895i	0.765198	+	0.643795i	$0.222641\pi$
$798$	−5.93229	+	4.31006i	−0.210001	+	0.152574i
$799$	−8.93154	−	6.48915i	−0.315975	−	0.229569i
$800$	−1.00000			−0.0353553
$801$	−5.34592			−0.188889
$802$	2.17487	+	1.58013i	0.0767973	+	0.0557965i
$803$	0.170105	+	0.523530i	0.00600289	+	0.0184750i
$804$	0.568945	−	1.75103i	0.0200651	−	0.0617541i
$805$	0.571468			0.0201416
$806$	−7.38090	−	5.20433i	−0.259981	−	0.183315i
$807$	−7.52313			−0.264827
$808$	−3.01269	+	9.27210i	−0.105986	+	0.326191i
$809$	1.97999	+	6.09378i	0.0696127	+	0.214246i	0.979811	−	0.199928i	$-0.0640707\pi$
$809$	1.97999	+	6.09378i	0.0696127	+	0.214246i	−0.910198	+	0.414174i	$0.864071\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	42.1860			1.48135			0.740676	−	0.671863i	$-0.234506\pi$
$811$	42.1860			1.48135			0.740676	+	0.671863i	$0.234506\pi$
$812$	−11.1890			−0.392656
$813$	8.63481	+	6.27355i	0.302836	+	0.220023i
$814$	−1.97943	+	1.43814i	−0.0693790	+	0.0504068i
$815$	11.7293	−	8.52184i	0.410860	−	0.298507i
$816$	1.62004	−	4.98598i	0.0567129	−	0.174544i
$817$	12.2504	+	8.90044i	0.428588	+	0.311387i
$818$	−1.64376	+	5.05898i	−0.0574728	+	0.176883i
$819$	0.661158	+	2.03484i	0.0231027	+	0.0711029i
$820$	9.44593	−	6.86287i	0.329866	−	0.239662i
$821$	0.184912	+	0.569100i	0.00645347	+	0.0198617i	0.954231	−	0.299069i	$-0.0966762\pi$
$821$	0.184912	+	0.569100i	0.00645347	+	0.0198617i	−0.947778	+	0.318931i	$0.896676\pi$
$822$	1.31981	+	4.06195i	0.0460336	+	0.141677i
$823$	−26.4966	+	19.2509i	−0.923615	+	0.671046i	−0.944421	−	0.328738i	$-0.893377\pi$
$823$	−26.4966	+	19.2509i	−0.923615	+	0.671046i	0.0208062	+	0.999784i	$0.493377\pi$
$824$	−1.30921	−	4.02933i	−0.0456084	−	0.140368i
$825$	0.216623	−	0.666696i	0.00754184	−	0.0232114i
$826$	1.96146	+	1.42508i	0.0682478	+	0.0495850i
$827$	3.27550	−	10.0809i	0.113900	−	0.350549i	−0.877816	−	0.478998i	$-0.841000\pi$
$827$	3.27550	−	10.0809i	0.113900	−	0.350549i	0.991716	+	0.128450i	$0.0410000\pi$
$828$	−0.350503	+	0.254655i	−0.0121808	+	0.00884989i
$829$	0.578517	−	0.420317i	0.0200927	−	0.0145982i	−0.577694	−	0.816254i	$-0.696047\pi$
$829$	0.578517	−	0.420317i	0.0200927	−	0.0145982i	0.597786	+	0.801655i	$0.296047\pi$
$830$	5.29425	+	3.84650i	0.183766	+	0.133514i
$831$	13.2456			0.459486
$832$	1.62205			0.0562346
$833$	22.3100	+	16.2091i	0.772994	+	0.561613i
$834$	0.408618	+	1.25760i	0.0141493	+	0.0435471i
$835$	−4.28136	+	13.1767i	−0.148163	+	0.455997i
$836$	−3.89698			−0.134780
$837$	−1.79541	−	5.27034i	−0.0620584	−	0.182170i
$838$	6.34369			0.219139
$839$	−6.55570	+	20.1764i	−0.226328	+	0.696565i	0.771826	+	0.635833i	$0.219343\pi$
$839$	−6.55570	+	20.1764i	−0.226328	+	0.696565i	−0.998154	+	0.0607318i	$0.980657\pi$
$840$	−0.407606	−	1.25448i	−0.0140637	−	0.0432837i
$841$	−34.7517	−	25.2486i	−1.19834	−	0.870642i
$842$	−37.6020			−1.29585
$843$	−17.4778			−0.601967
$844$	−7.82160	−	5.68273i	−0.269231	−	0.195608i
$845$	8.38865	−	6.09471i	0.288578	−	0.209664i
$846$	1.70366	−	1.23778i	0.0585729	−	0.0425557i
$847$	−4.28336	+	13.1828i	−0.147178	+	0.452968i
$848$	5.37558	+	3.90559i	0.184598	+	0.134118i
$849$	1.48154	−	4.55970i	0.0508462	−	0.156489i
$850$	−1.62004	−	4.98598i	−0.0555670	−	0.171018i
$851$	1.22336	−	0.888820i	0.0419361	−	0.0304684i
$852$	−0.234058	−	0.720357i	−0.00801871	−	0.0246790i
$853$	−5.63181	−	17.3329i	−0.192829	−	0.593468i	−0.999995	−	0.00314296i	$-0.999000\pi$
$853$	−5.63181	−	17.3329i	−0.192829	−	0.593468i	0.807166	−	0.590325i	$-0.201000\pi$
$854$	−3.74531	+	2.72112i	−0.128162	+	0.0931150i
$855$	−1.71786	−	5.28704i	−0.0587497	−	0.180813i
$856$	−2.90648	+	8.94523i	−0.0993415	+	0.305742i
$857$	43.0472	+	31.2756i	1.47046	+	1.06835i	0.980479	+	0.196624i	$0.0629977\pi$
$857$	43.0472	+	31.2756i	1.47046	+	1.06835i	0.489985	+	0.871731i	$0.337002\pi$
$858$	−0.351374	+	1.08142i	−0.0119957	+	0.0369190i
$859$	10.6521	−	7.73923i	0.363446	−	0.264059i	−0.391042	−	0.920373i	$-0.627885\pi$
$859$	10.6521	−	7.73923i	0.363446	−	0.264059i	0.754488	+	0.656314i	$0.227885\pi$
$860$	−2.20366	+	1.60105i	−0.0751441	+	0.0545954i
$861$	12.4596	+	9.05240i	0.424621	+	0.308505i
$862$	32.5032			1.10706
$863$	−51.7778			−1.76254			−0.881268	−	0.472616i	$-0.843310\pi$
$863$	−51.7778			−1.76254			−0.881268	+	0.472616i	$0.843310\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	1.36625	+	4.20488i	0.0464538	+	0.142970i
$866$	7.59360	−	23.3707i	0.258041	−	0.794169i
$867$	10.4846			0.356074
$868$	−2.17023	+	7.01612i	−0.0736625	+	0.238143i
$869$	−7.68806			−0.260800
$870$	2.62129	−	8.06749i	0.0888699	−	0.273513i
$871$	0.922858	+	2.84027i	0.0312699	+	0.0962388i
$872$	3.52206	+	2.55892i	0.119272	+	0.0866561i
$873$	13.2791			0.449431
$874$	2.40847			0.0814676
$875$	−1.06713	−	0.775312i	−0.0360754	−	0.0262103i
$876$	−0.635289	+	0.461564i	−0.0214644	+	0.0155948i
$877$	23.9410	−	17.3942i	0.808431	−	0.587359i	−0.104945	−	0.994478i	$-0.533467\pi$
$877$	23.9410	−	17.3942i	0.808431	−	0.587359i	0.913375	+	0.407119i	$0.133467\pi$
$878$	0.761977	−	2.34512i	0.0257155	−	0.0791441i
$879$	1.87322	+	1.36098i	0.0631823	+	0.0459046i
$880$	0.216623	−	0.666696i	0.00730235	−	0.0224743i
$881$	9.34062	+	28.7475i	0.314694	+	0.968527i	0.975880	+	0.218306i	$0.0700530\pi$
$881$	9.34062	+	28.7475i	0.314694	+	0.968527i	−0.661187	+	0.750221i	$0.729947\pi$
$882$	−4.25554	+	3.09183i	−0.143291	+	0.104107i
$883$	−2.17911	−	6.70660i	−0.0733328	−	0.225695i	0.907671	−	0.419682i	$-0.137858\pi$
$883$	−2.17911	−	6.70660i	−0.0733328	−	0.225695i	−0.981004	+	0.193986i	$0.937858\pi$
$884$	2.62780	+	8.08753i	0.0883824	+	0.272013i
$885$	−1.48703	+	1.08039i	−0.0499861	+	0.0363170i
$886$	11.3344	+	34.8836i	0.380786	+	1.17194i
$887$	1.22995	−	3.78538i	0.0412975	−	0.127101i	−0.928282	−	0.371877i	$-0.878714\pi$
$887$	1.22995	−	3.78538i	0.0412975	−	0.127101i	0.969580	+	0.244776i	$0.0787144\pi$
$888$	−2.82370	−	2.05154i	−0.0947572	−	0.0688451i
$889$	−7.61074	+	23.4235i	−0.255256	+	0.785598i
$890$	−4.32494	+	3.14225i	−0.144972	+	0.105329i
$891$	−0.567126	+	0.412041i	−0.0189994	+	0.0138039i
$892$	−21.5384	−	15.6486i	−0.721161	−	0.523954i
$893$	−11.7066			−0.391747
$894$	−4.21167			−0.140859
$895$	12.6343	+	9.17939i	0.422320	+	0.306833i
$896$	−0.407606	−	1.25448i	−0.0136172	−	0.0419093i
$897$	0.217161	−	0.668352i	0.00725079	−	0.0223156i
$898$	−22.8604			−0.762861
$899$	−37.8121	+	28.2995i	−1.26111	+	0.943842i
$900$	1.00000			0.0333333
$901$	−10.7645	+	33.1298i	−0.358618	+	1.10371i
$902$	2.52925	+	7.78422i	0.0842147	+	0.259186i
$903$	−2.90671	−	2.11185i	−0.0967293	−	0.0702780i
$904$	4.54157			0.151050
$905$	4.48494			0.149084
$906$	−18.9133	−	13.7414i	−0.628354	−	0.456526i
$907$	−17.0567	+	12.3924i	−0.566360	+	0.411484i	−0.833781	−	0.552095i	$-0.813828\pi$
$907$	−17.0567	+	12.3924i	−0.566360	+	0.411484i	0.267421	+	0.963580i	$0.413828\pi$
$908$	19.3708	−	14.0737i	0.642841	−	0.467052i
$909$	3.01269	−	9.27210i	0.0999246	−	0.307536i
$910$	1.73093	+	1.25760i	0.0573799	+	0.0416890i
$911$	10.4099	−	32.0382i	0.344894	−	1.06147i	−0.616747	−	0.787162i	$-0.711550\pi$
$911$	10.4099	−	32.0382i	0.344894	−	1.06147i	0.961641	−	0.274313i	$-0.0884503\pi$
$912$	−1.71786	−	5.28704i	−0.0568842	−	0.175072i
$913$	−3.71130	+	2.69642i	−0.122826	+	0.0892384i
$914$	−0.352187	−	1.08392i	−0.0116493	−	0.0358528i
$915$	−1.08456	−	3.33794i	−0.0358545	−	0.110349i
$916$	10.3353	−	7.50906i	0.341489	−	0.248106i
$917$	−5.55236	−	17.0884i	−0.183355	−	0.564309i
$918$	−1.62004	+	4.98598i	−0.0534694	+	0.164562i
$919$	15.6586	+	11.3766i	0.516529	+	0.375280i	0.815295	−	0.579046i	$-0.196575\pi$
$919$	15.6586	+	11.3766i	0.516529	+	0.375280i	−0.298766	+	0.954326i	$0.596575\pi$
$920$	−0.133880	+	0.412041i	−0.00441390	+	0.0135846i
$921$	1.84046	−	1.33717i	0.0606451	−	0.0440612i
$922$	14.7434	−	10.7117i	0.485548	−	0.352771i
$923$	0.993950	+	0.722147i	0.0327163	+	0.0237698i
$924$	0.924655			0.0304189
$925$	−3.49029			−0.114760
$926$	12.1137	+	8.80112i	0.398081	+	0.289223i
$927$	1.30921	+	4.02933i	0.0430000	+	0.132340i
$928$	2.62129	−	8.06749i	0.0860479	−	0.264828i
$929$	−50.3811			−1.65295			−0.826476	−	0.562972i	$-0.809658\pi$
$929$	−50.3811			−1.65295			−0.826476	+	0.562972i	$0.809658\pi$
$930$	−4.55035	−	3.20848i	−0.149212	−	0.105210i
$931$	29.2418			0.958360
$932$	3.94870	−	12.1528i	0.129344	−	0.398079i
$933$	−3.59843	−	11.0748i	−0.117807	−	0.362574i
$934$	−10.9786	−	7.97643i	−0.359231	−	0.260997i
$935$	3.67507			0.120188
$936$	−1.62205			−0.0530185
$937$	−7.45553	−	5.41676i	−0.243562	−	0.176958i	0.459307	−	0.888278i	$-0.348098\pi$
$937$	−7.45553	−	5.41676i	−0.243562	−	0.176958i	−0.702869	+	0.711320i	$0.748098\pi$
$938$	1.96473	−	1.42746i	0.0641508	−	0.0466083i
$939$	−23.1831	+	16.8435i	−0.756552	+	0.549667i
$940$	0.650739	−	2.00277i	0.0212248	−	0.0653231i
$941$	7.12638	+	5.17762i	0.232313	+	0.168786i	0.697852	−	0.716242i	$-0.254139\pi$
$941$	7.12638	+	5.17762i	0.232313	+	0.168786i	−0.465539	+	0.885028i	$0.654139\pi$
$942$	5.35410	−	16.4782i	0.174446	−	0.536890i
$943$	−1.56316	−	4.81092i	−0.0509035	−	0.156665i
$944$	−1.48703	+	1.08039i	−0.0483988	+	0.0351638i
$945$	0.407606	+	1.25448i	0.0132594	+	0.0408083i
$946$	−0.590052	−	1.81599i	−0.0191843	−	0.0590431i
$947$	32.1622	−	23.3672i	1.04513	−	0.759331i	0.0738493	−	0.997269i	$-0.476472\pi$
$947$	32.1622	−	23.3672i	1.04513	−	0.759331i	0.971280	+	0.237938i	$0.0764716\pi$
$948$	−3.38905	−	10.4304i	−0.110071	−	0.338764i
$949$	0.393606	−	1.21139i	0.0127770	−	0.0393235i
$950$	−4.49743	−	3.26757i	−0.145916	−	0.106014i
$951$	−1.27479	+	3.92341i	−0.0413380	+	0.127225i
$952$	5.59448	−	4.06463i	0.181318	−	0.131735i
$953$	6.53436	−	4.74749i	0.211669	−	0.153786i	−0.476900	−	0.878958i	$-0.658240\pi$
$953$	6.53436	−	4.74749i	0.211669	−	0.153786i	0.688568	+	0.725171i	$0.258240\pi$
$954$	−5.37558	−	3.90559i	−0.174041	−	0.126448i
$955$	4.53875			0.146870
$956$	−3.77668			−0.122147
$957$	4.81073	+	3.49520i	0.155509	+	0.112984i
$958$	−13.2095	−	40.6548i	−0.426781	−	1.31350i
$959$	−1.74088	+	5.35788i	−0.0562159	+	0.173015i
$960$	1.00000			0.0322749
$961$	10.4113	+	29.1994i	0.335849	+	0.941916i
$962$	5.66143			0.182532
$963$	2.90648	−	8.94523i	0.0936601	−	0.288256i
$964$	−6.21446	−	19.1261i	−0.200154	−	0.616011i
$965$	−11.9695	−	8.69637i	−0.385313	−	0.279946i
$966$	−0.571468			−0.0183867
$967$	21.2696			0.683983			0.341992	−	0.939703i	$-0.388899\pi$
$967$	21.2696			0.683983			0.341992	+	0.939703i	$0.388899\pi$
$968$	−8.50163	−	6.17679i	−0.273253	−	0.198530i
$969$	23.5781	−	17.1305i	0.757437	−	0.550310i
$970$	10.7430	−	7.80528i	0.344938	−	0.250612i
$971$	2.35269	−	7.24083i	0.0755014	−	0.232369i	−0.906182	−	0.422887i	$-0.861017\pi$
$971$	2.35269	−	7.24083i	0.0755014	−	0.232369i	0.981684	+	0.190518i	$0.0610167\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−0.538984	+	1.65882i	−0.0172790	+	0.0531794i
$974$	3.56662	+	10.9769i	0.114282	+	0.351723i
$975$	−1.31227	+	0.953419i	−0.0420262	+	0.0305338i
$976$	−1.08456	−	3.33794i	−0.0347160	−	0.106845i
$977$	6.45673	+	19.8718i	0.206569	+	0.635755i	0.999645	+	0.0266321i	$0.00847826\pi$
$977$	6.45673	+	19.8718i	0.206569	+	0.635755i	−0.793076	+	0.609123i	$0.791522\pi$
$978$	−11.7293	+	8.52184i	−0.375062	+	0.272499i
$979$	−1.15805	−	3.56411i	−0.0370114	−	0.113909i
$980$	−1.62547	+	5.00268i	−0.0519238	+	0.159805i
$981$	−3.52206	−	2.55892i	−0.112451	−	0.0817001i
$982$	−2.91028	+	8.95692i	−0.0928708	+	0.285827i
$983$	−34.5145	+	25.0763i	−1.10084	+	0.799809i	−0.981197	−	0.193007i	$-0.938176\pi$
$983$	−34.5145	+	25.0763i	−1.10084	+	0.799809i	−0.119646	+	0.992817i	$0.538176\pi$
$984$	−9.44593	+	6.86287i	−0.301125	+	0.218780i
$985$	−11.2530	−	8.17577i	−0.358550	−	0.260502i
$986$	44.4709			1.41624
$987$	2.77768			0.0884146
$988$	7.29507	+	5.30018i	0.232087	+	0.168621i
$989$	0.364672	+	1.12235i	0.0115959	+	0.0356885i
$990$	−0.216623	+	0.666696i	−0.00688472	+	0.0211890i
$991$	−20.7202			−0.658200			−0.329100	−	0.944295i	$-0.606745\pi$
$991$	−20.7202			−0.658200			−0.329100	+	0.944295i	$0.606745\pi$
$992$	−4.55035	−	3.20848i	−0.144474	−	0.101869i
$993$	11.1592			0.354127
$994$	0.308732	−	0.950180i	0.00979239	−	0.0301379i
$995$	−0.924939	−	2.84667i	−0.0293225	−	0.0902455i
$996$	−5.29425	−	3.84650i	−0.167755	−	0.121881i
$997$	−7.11158			−0.225226			−0.112613	−	0.993639i	$-0.535922\pi$
$997$	−7.11158			−0.225226			−0.112613	+	0.993639i	$0.535922\pi$
$998$	18.7003			0.591948
$999$	2.82370	+	2.05154i	0.0893379	+	0.0649078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.e.721.2	✓	12
31.4	even	5	inner	930.2.n.e.841.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.e.721.2	✓	12	1.1	even	1	trivial
930.2.n.e.841.2	yes	12	31.4	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.06713 - 0.775312i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.06713 - 0.775312i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-0.567126 - 0.412041i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.501242 + 1.54266i) q^{13} +(1.06713 - 0.775312i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.24133 + 3.08151i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.71786 + 5.28704i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(0.407606 - 1.25448i) q^{21} +(0.567126 - 0.412041i) q^{22} +(-0.350503 + 0.254655i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -1.62205 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.407606 + 1.25448i) q^{28} +(-2.62129 + 8.06749i) q^{29} -1.00000 q^{30} +(4.55035 + 3.20848i) q^{31} -1.00000 q^{32} +(0.216623 - 0.666696i) q^{33} +(-1.62004 - 4.98598i) q^{34} +(-1.06713 - 0.775312i) q^{35} +1.00000 q^{36} -3.49029 q^{37} +(-4.49743 - 3.26757i) q^{38} +(-1.31227 + 0.953419i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-3.60803 + 11.1044i) q^{41} +(1.06713 + 0.775312i) q^{42} +(0.841722 - 2.59055i) q^{43} +(0.216623 + 0.666696i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-0.133880 - 0.412041i) q^{46} +(0.650739 + 2.00277i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.62547 - 5.00268i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-4.24133 - 3.08151i) q^{51} +(0.501242 - 1.54266i) q^{52} +(5.37558 - 3.90559i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.567126 - 0.412041i) q^{55} -1.31904 q^{56} -5.55913 q^{57} +(-6.86262 - 4.98598i) q^{58} +(0.567996 + 1.74811i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.50971 q^{61} +(-4.45758 + 3.33616i) q^{62} +1.31904 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.501242 + 1.54266i) q^{65} +(0.567126 + 0.412041i) q^{66} +1.84114 q^{67} +5.24257 q^{68} +(-0.350503 - 0.254655i) q^{69} +(1.06713 - 0.775312i) q^{70} +(0.612773 - 0.445205i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-0.635289 - 0.461564i) q^{73} +(1.07856 - 3.31946i) q^{74} +(0.309017 + 0.951057i) q^{75} +(4.49743 - 3.26757i) q^{76} +(0.285734 + 0.879399i) q^{77} +(-0.501242 - 1.54266i) q^{78} +(8.87264 - 6.44635i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.44593 - 6.86287i) q^{82} +(2.02222 - 6.22376i) q^{83} +(-1.06713 + 0.775312i) q^{84} +(-4.24133 + 3.08151i) q^{85} +(2.20366 + 1.60105i) q^{86} -8.48266 q^{87} -0.701006 q^{88} +(4.32494 + 3.14225i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(0.661158 - 2.03484i) q^{91} +0.433246 q^{92} +(-1.64531 + 5.31911i) q^{93} -2.10584 q^{94} +(-1.71786 + 5.28704i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.7430 - 7.80528i) q^{97} +5.26013 q^{98} +0.701006 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	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 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 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

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