LMFDB - Embedded newform 930.2.z.c.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	930.109
Dual form			930.2.z.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.54336i) q^{5} -1.00000 q^{6} +(-1.81154 - 0.588604i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.54336i) q^{5} -1.00000 q^{6} +(-1.81154 - 0.588604i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.19966 + 0.401852i) q^{10} +(-0.756512 + 2.32830i) q^{11} +(0.587785 + 0.809017i) q^{12} +(0.212426 - 0.292379i) q^{13} +(0.588604 + 1.81154i) q^{14} +(0.297550 + 2.21618i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(7.45492 - 2.42225i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.271681 - 0.197388i) q^{19} +(-0.967824 - 2.01577i) q^{20} +(-1.54099 + 1.11959i) q^{21} +(2.32830 - 0.756512i) q^{22} +(5.35263 - 1.73917i) q^{23} +(0.309017 - 0.951057i) q^{24} +(0.236068 - 4.99442i) q^{25} -0.361401 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.11959 - 1.54099i) q^{28} +(-0.744761 + 0.541100i) q^{29} +(1.61803 - 1.54336i) q^{30} +(-1.17113 - 5.44320i) q^{31} +1.00000i q^{32} +(1.43897 + 1.98057i) q^{33} +(-6.34153 - 4.60739i) q^{34} +(3.83956 - 1.84348i) q^{35} +1.00000 q^{36} -7.23494i q^{37} +(-0.319380 - 0.103773i) q^{38} +(-0.111679 - 0.343713i) q^{39} +(-1.06192 + 1.96782i) q^{40} +(2.34817 - 1.70604i) q^{41} +(1.81154 + 0.588604i) q^{42} +(7.69684 + 10.5938i) q^{43} +(-1.98057 - 1.43897i) q^{44} +(1.96782 + 1.06192i) q^{45} +(-4.55322 - 3.30810i) q^{46} +(2.11577 - 2.91211i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-2.72791 - 1.98194i) q^{49} +(-4.17933 + 2.74467i) q^{50} +(2.42225 - 7.45492i) q^{51} +(0.212426 + 0.292379i) q^{52} +(8.90648 - 2.89389i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-2.36935 - 4.93485i) q^{55} -1.90476 q^{56} -0.335816i q^{57} +(0.875519 + 0.284473i) q^{58} +(12.1366 + 8.81777i) q^{59} +(-2.19966 - 0.401852i) q^{60} -1.28497 q^{61} +(-3.71527 + 4.14690i) q^{62} +1.90476i q^{63} +(0.809017 - 0.587785i) q^{64} +(0.107535 + 0.800930i) q^{65} +(0.756512 - 2.32830i) q^{66} -2.36310i q^{67} +7.83857i q^{68} +(1.73917 - 5.35263i) q^{69} +(-3.74824 - 2.02270i) q^{70} +(-3.19565 - 9.83521i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-0.291725 - 0.0947870i) q^{73} +(-5.85319 + 4.25259i) q^{74} +(-3.90182 - 3.12663i) q^{75} +(0.103773 + 0.319380i) q^{76} +(2.74090 - 3.77252i) q^{77} +(-0.212426 + 0.292379i) q^{78} +(2.04685 + 6.29957i) q^{79} +(2.21618 - 0.297550i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.76044 - 0.896920i) q^{82} +(2.22984 + 3.06911i) q^{83} +(-0.588604 - 1.81154i) q^{84} +(-8.32391 + 15.4249i) q^{85} +(4.04647 - 12.4537i) q^{86} +0.920575i q^{87} +2.44812i q^{88} +(-0.715769 + 2.20291i) q^{89} +(-0.297550 - 2.21618i) q^{90} +(-0.556913 + 0.404621i) q^{91} +5.62808i q^{92} +(-5.09202 - 2.25197i) q^{93} -3.59956 q^{94} +(-0.134948 + 0.738682i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-15.3548 - 4.98909i) q^{97} +3.37188i q^{98} +2.44812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.61803	+	1.54336i	−0.723607	+	0.690212i
$5$	−1.61803	+	1.54336i	−0.723607	+	0.690212i
$6$	−1.00000			−0.408248
$7$	−1.81154	−	0.588604i	−0.684697	−	0.222471i	−0.0540462	−	0.998538i	$-0.517212\pi$
$7$	−1.81154	−	0.588604i	−0.684697	−	0.222471i	−0.630650	+	0.776067i	$0.717212\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	2.19966	+	0.401852i	0.695594	+	0.127077i
$11$	−0.756512	+	2.32830i	−0.228097	+	0.702010i	0.769865	+	0.638206i	$0.220323\pi$
$11$	−0.756512	+	2.32830i	−0.228097	+	0.702010i	−0.997962	+	0.0638041i	$0.979677\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	0.212426	−	0.292379i	0.0589164	−	0.0810914i	−0.778542	−	0.627592i	$-0.784040\pi$
$13$	0.212426	−	0.292379i	0.0589164	−	0.0810914i	0.837459	+	0.546501i	$0.184040\pi$
$14$	0.588604	+	1.81154i	0.157311	+	0.484154i
$15$	0.297550	+	2.21618i	0.0768270	+	0.572216i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	7.45492	−	2.42225i	1.80808	−	0.587482i	0.808085	−	0.589066i	$-0.200504\pi$
$17$	7.45492	−	2.42225i	1.80808	−	0.587482i	0.999999	+	0.00158394i	$0.000504185\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	0.271681	−	0.197388i	0.0623279	−	0.0452839i	−0.556185	−	0.831058i	$-0.687735\pi$
$19$	0.271681	−	0.197388i	0.0623279	−	0.0452839i	0.618513	+	0.785775i	$0.287735\pi$
$20$	−0.967824	−	2.01577i	−0.216412	−	0.450739i
$21$	−1.54099	+	1.11959i	−0.336271	+	0.244315i
$22$	2.32830	−	0.756512i	0.496396	−	0.161289i
$23$	5.35263	−	1.73917i	1.11610	−	0.362643i	0.307822	−	0.951444i	$-0.400400\pi$
$23$	5.35263	−	1.73917i	1.11610	−	0.362643i	0.808278	+	0.588801i	$0.200400\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	0.236068	−	4.99442i	0.0472136	−	0.998885i
$26$	−0.361401			−0.0708765
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	1.11959	−	1.54099i	0.211583	−	0.291219i
$29$	−0.744761	+	0.541100i	−0.138299	+	0.100480i	−0.654784	−	0.755816i	$-0.727240\pi$
$29$	−0.744761	+	0.541100i	−0.138299	+	0.100480i	0.516485	+	0.856296i	$0.327240\pi$
$30$	1.61803	−	1.54336i	0.295411	−	0.281778i
$31$	−1.17113	−	5.44320i	−0.210342	−	0.977628i
$31$	−1.17113	−	5.44320i	−0.210342	−	0.977628i
$32$			1.00000i			0.176777i
$33$	1.43897	+	1.98057i	0.250493	+	0.344774i
$34$	−6.34153	−	4.60739i	−1.08756	−	0.790162i
$35$	3.83956	−	1.84348i	0.649004	−	0.311604i
$36$	1.00000			0.166667
$37$		−	7.23494i		−	1.18942i	−0.803941	−	0.594709i	$-0.797267\pi$
$37$		−	7.23494i		−	1.18942i	0.803941	−	0.594709i	$-0.202733\pi$
$38$	−0.319380	−	0.103773i	−0.0518103	−	0.0168342i
$39$	−0.111679	−	0.343713i	−0.0178829	−	0.0550380i
$40$	−1.06192	+	1.96782i	−0.167904	+	0.311140i
$41$	2.34817	−	1.70604i	0.366722	−	0.266439i	−0.389128	−	0.921184i	$-0.627224\pi$
$41$	2.34817	−	1.70604i	0.366722	−	0.266439i	0.755850	+	0.654744i	$0.227224\pi$
$42$	1.81154	+	0.588604i	0.279526	+	0.0908236i
$43$	7.69684	+	10.5938i	1.17376	+	1.61554i	0.631800	+	0.775131i	$0.282316\pi$
$43$	7.69684	+	10.5938i	1.17376	+	1.61554i	0.541956	+	0.840407i	$0.317684\pi$
$44$	−1.98057	−	1.43897i	−0.298583	−	0.216933i
$45$	1.96782	+	1.06192i	0.293346	+	0.158301i
$46$	−4.55322	−	3.30810i	−0.671335	−	0.487753i
$47$	2.11577	−	2.91211i	0.308617	−	0.424774i	−0.626333	−	0.779556i	$-0.715445\pi$
$47$	2.11577	−	2.91211i	0.308617	−	0.424774i	0.934949	+	0.354782i	$0.115445\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−2.72791	−	1.98194i	−0.389701	−	0.283134i
$50$	−4.17933	+	2.74467i	−0.591047	+	0.388154i
$51$	2.42225	−	7.45492i	0.339183	−	1.04390i
$52$	0.212426	+	0.292379i	0.0294582	+	0.0405457i
$53$	8.90648	−	2.89389i	1.22340	−	0.397506i	0.375080	−	0.926992i	$-0.377615\pi$
$53$	8.90648	−	2.89389i	1.22340	−	0.397506i	0.848319	+	0.529486i	$0.177615\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−2.36935	−	4.93485i	−0.319484	−	0.665415i
$56$	−1.90476			−0.254535
$57$		−	0.335816i		−	0.0444799i
$58$	0.875519	+	0.284473i	0.114961	+	0.0373532i
$59$	12.1366	+	8.81777i	1.58005	+	1.14798i	0.916634	+	0.399728i	$0.130895\pi$
$59$	12.1366	+	8.81777i	1.58005	+	1.14798i	0.663419	+	0.748248i	$0.269105\pi$
$60$	−2.19966	−	0.401852i	−0.283975	−	0.0518788i
$61$	−1.28497			−0.164523			−0.0822617	−	0.996611i	$-0.526214\pi$
$61$	−1.28497			−0.164523			−0.0822617	+	0.996611i	$0.526214\pi$
$62$	−3.71527	+	4.14690i	−0.471839	+	0.526657i
$63$			1.90476i			0.239978i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	0.107535	+	0.800930i	0.0133380	+	0.0993431i
$66$	0.756512	−	2.32830i	0.0931202	−	0.286595i
$67$		−	2.36310i		−	0.288699i	−0.989527	−	0.144349i	$-0.953891\pi$
$67$		−	2.36310i		−	0.288699i	0.989527	−	0.144349i	$-0.0461089\pi$
$68$			7.83857i			0.950566i
$69$	1.73917	−	5.35263i	0.209372	−	0.644380i
$70$	−3.74824	−	2.02270i	−0.448000	−	0.241759i
$71$	−3.19565	−	9.83521i	−0.379254	−	1.16723i	−0.940563	−	0.339619i	$-0.889702\pi$
$71$	−3.19565	−	9.83521i	−0.379254	−	1.16723i	0.561309	−	0.827606i	$-0.310298\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−0.291725	−	0.0947870i	−0.0341438	−	0.0110940i	0.291895	−	0.956450i	$-0.405714\pi$
$73$	−0.291725	−	0.0947870i	−0.0341438	−	0.0110940i	−0.326039	+	0.945356i	$0.605714\pi$
$74$	−5.85319	+	4.25259i	−0.680420	+	0.494354i
$75$	−3.90182	−	3.12663i	−0.450543	−	0.361032i
$76$	0.103773	+	0.319380i	0.0119036	+	0.0366354i
$77$	2.74090	−	3.77252i	0.312354	−	0.429919i
$78$	−0.212426	+	0.292379i	−0.0240525	+	0.0331054i
$79$	2.04685	+	6.29957i	0.230289	+	0.708757i	0.997711	+	0.0676151i	$0.0215390\pi$
$79$	2.04685	+	6.29957i	0.230289	+	0.708757i	−0.767422	+	0.641142i	$0.778461\pi$
$80$	2.21618	−	0.297550i	0.247777	−	0.0332670i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.76044	−	0.896920i	−0.304839	−	0.0990482i
$83$	2.22984	+	3.06911i	0.244757	+	0.336879i	0.913666	−	0.406465i	$-0.133239\pi$
$83$	2.22984	+	3.06911i	0.244757	+	0.336879i	−0.668910	+	0.743344i	$0.733239\pi$
$84$	−0.588604	−	1.81154i	−0.0642220	−	0.197655i
$85$	−8.32391	+	15.4249i	−0.902854	+	1.67307i
$86$	4.04647	−	12.4537i	0.436342	−	1.34292i
$87$			0.920575i			0.0986960i
$88$			2.44812i			0.260971i
$89$	−0.715769	+	2.20291i	−0.0758714	+	0.233508i	−0.981799	−	0.189926i	$-0.939175\pi$
$89$	−0.715769	+	2.20291i	−0.0758714	+	0.233508i	0.905927	+	0.423434i	$0.139175\pi$
$90$	−0.297550	−	2.21618i	−0.0313645	−	0.233606i
$91$	−0.556913	+	0.404621i	−0.0583804	+	0.0424158i
$92$			5.62808i			0.586768i
$93$	−5.09202	−	2.25197i	−0.528018	−	0.233518i
$94$	−3.59956			−0.371266
$95$	−0.134948	+	0.738682i	−0.0138454	+	0.0757872i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−15.3548	−	4.98909i	−1.55905	−	0.506565i	−0.602495	−	0.798123i	$-0.705827\pi$
$97$	−15.3548	−	4.98909i	−1.55905	−	0.506565i	−0.956553	+	0.291557i	$0.905827\pi$
$98$			3.37188i			0.340611i
$99$	2.44812			0.246046
$100$	4.67703	+	1.76788i	0.467703	+	0.176788i
$101$	1.91953	+	5.90772i	0.191001	+	0.587840i	1.00000		3.02152e-5i	$9.61780e-6\pi$
$101$	1.91953	+	5.90772i	0.191001	+	0.587840i	−0.808999	+	0.587810i	$0.799990\pi$
$102$	−7.45492	+	2.42225i	−0.738147	+	0.239839i
$103$	−3.68154	−	5.06721i	−0.362753	−	0.499287i	0.588160	−	0.808744i	$-0.299852\pi$
$103$	−3.68154	−	5.06721i	−0.362753	−	0.499287i	−0.950913	+	0.309458i	$0.899852\pi$
$104$	0.111679	−	0.343713i	0.0109510	−	0.0337038i
$105$	0.765432	−	4.18984i	0.0746985	−	0.408886i
$106$	−7.57630	−	5.50451i	−0.735875	−	0.534645i
$107$	12.0827	−	3.92590i	1.16808	−	0.379531i	0.340152	−	0.940371i	$-0.389522\pi$
$107$	12.0827	−	3.92590i	1.16808	−	0.379531i	0.827925	+	0.560839i	$0.189522\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	−10.5554	−	7.66895i	−1.01102	−	0.734552i	−0.0466008	−	0.998914i	$-0.514839\pi$
$109$	−10.5554	−	7.66895i	−1.01102	−	0.734552i	−0.964424	+	0.264361i	$0.914839\pi$
$110$	−2.59970	+	4.81748i	−0.247872	+	0.459329i
$111$	−5.85319	−	4.25259i	−0.555560	−	0.403638i
$112$	1.11959	+	1.54099i	0.105791	+	0.145609i
$113$	−11.8933	−	3.86437i	−1.11883	−	0.363530i	−0.309509	−	0.950897i	$-0.600165\pi$
$113$	−11.8933	−	3.86437i	−1.11883	−	0.363530i	−0.809321	+	0.587367i	$0.800165\pi$
$114$	−0.271681	+	0.197388i	−0.0254453	+	0.0184871i
$115$	−5.97656	+	11.0751i	−0.557317	+	1.03276i
$116$	−0.284473	−	0.875519i	−0.0264127	−	0.0812899i
$117$	−0.343713	−	0.111679i	−0.0317762	−	0.0103247i
$118$		−	15.0017i		−	1.38102i
$119$	−14.9306			−1.36869
$120$	0.967824	+	2.01577i	0.0883499	+	0.184013i
$121$	4.05049	+	2.94286i	0.368227	+	0.267532i
$122$	0.755286	+	1.03956i	0.0683804	+	0.0941175i
$123$		−	2.90249i		−	0.261709i
$124$	5.53869	+	0.568226i	0.497389	+	0.0510282i
$125$	7.32624	+	8.44549i	0.655279	+	0.755387i
$126$	1.54099	−	1.11959i	0.137282	−	0.0997411i
$127$	11.1380	−	15.3302i	0.988341	−	1.36033i	0.0561276	−	0.998424i	$-0.482125\pi$
$127$	11.1380	−	15.3302i	0.988341	−	1.36033i	0.932213	−	0.361910i	$-0.117875\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	13.0946			1.15292
$130$	0.584759	−	0.557772i	0.0512867	−	0.0489198i
$131$	−1.46528	+	4.50968i	−0.128022	+	0.394013i	−0.994440	−	0.105308i	$-0.966417\pi$
$131$	−1.46528	+	4.50968i	−0.128022	+	0.394013i	0.866417	+	0.499321i	$0.166417\pi$
$132$	−2.32830	+	0.756512i	−0.202653	+	0.0658459i
$133$	−0.608343	+	0.197663i	−0.0527501	+	0.0171395i
$134$	−1.91179	+	1.38900i	−0.165153	+	0.119991i
$135$	2.01577	−	0.967824i	0.173490	−	0.0832971i
$136$	6.34153	−	4.60739i	0.543782	−	0.395081i
$137$	−8.68529	+	11.9543i	−0.742035	+	1.02132i	0.256464	+	0.966554i	$0.417442\pi$
$137$	−8.68529	+	11.9543i	−0.742035	+	1.02132i	−0.998499	+	0.0547695i	$0.982558\pi$
$138$	−5.35263	+	1.73917i	−0.455646	+	0.148048i
$139$	14.3152	+	10.4006i	1.21420	+	0.882167i	0.995605	−	0.0936496i	$-0.0298534\pi$
$139$	14.3152	+	10.4006i	1.21420	+	0.882167i	0.218593	+	0.975816i	$0.429853\pi$
$140$	0.566761	+	4.22130i	0.0479001	+	0.356765i
$141$	−1.11233	−	3.42339i	−0.0936747	−	0.288301i
$142$	−6.07850	+	8.36633i	−0.510096	+	0.702087i
$143$	0.520045	+	0.715781i	0.0434884	+	0.0598566i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	0.369934	−	2.02495i	0.0307214	−	0.168163i
$146$	0.0947870	+	0.291725i	0.00784463	+	0.0241433i
$147$	−3.20685	+	1.04197i	−0.264496	+	0.0859401i
$148$	6.88084	+	2.23572i	0.565602	+	0.183775i
$149$	−0.251150			−0.0205750			−0.0102875	−	0.999947i	$-0.503275\pi$
$149$	−0.251150			−0.0205750			−0.0102875	+	0.999947i	$0.503275\pi$
$150$	−0.236068	+	4.99442i	−0.0192749	+	0.407793i
$151$	4.28157	−	13.1773i	0.348430	−	1.07236i	−0.611292	−	0.791405i	$-0.709350\pi$
$151$	4.28157	−	13.1773i	0.348430	−	1.07236i	0.959722	−	0.280951i	$-0.0906499\pi$
$152$	0.197388	−	0.271681i	0.0160103	−	0.0220362i
$153$	−4.60739	−	6.34153i	−0.372486	−	0.512683i
$154$	−4.66310			−0.375763
$155$	10.2958	+	6.99980i	0.826976	+	0.562238i
$156$	0.361401			0.0289352
$157$	−8.17998	−	11.2588i	−0.652834	−	0.898548i	0.346384	−	0.938093i	$-0.387409\pi$
$157$	−8.17998	−	11.2588i	−0.652834	−	0.898548i	−0.999218	+	0.0395445i	$0.987409\pi$
$158$	3.89335	−	5.35873i	0.309738	−	0.426318i
$159$	2.89389	−	8.90648i	0.229500	−	0.706330i
$160$	−1.54336	−	1.61803i	−0.122013	−	0.127917i
$161$	−10.7202			−0.844867
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	4.43906	−	1.44234i	0.347694	−	0.112973i	−0.129964	−	0.991519i	$-0.541486\pi$
$163$	4.43906	−	1.44234i	0.347694	−	0.112973i	0.477657	+	0.878546i	$0.341486\pi$
$164$	0.896920	+	2.76044i	0.0700377	+	0.215554i
$165$	−5.38505	−	0.983783i	−0.419225	−	0.0765874i
$166$	1.17230	−	3.60796i	0.0909879	−	0.280032i
$167$	8.98794	+	12.3708i	0.695508	+	0.957284i	0.999989	+	0.00476600i	$0.00151707\pi$
$167$	8.98794	+	12.3708i	0.695508	+	0.957284i	−0.304481	+	0.952518i	$0.598483\pi$
$168$	−1.11959	+	1.54099i	−0.0863784	+	0.118890i
$169$	3.97686	+	12.2395i	0.305912	+	0.941501i
$170$	17.3717	−	2.33236i	1.33235	−	0.178884i
$171$	−0.271681	−	0.197388i	−0.0207760	−	0.0150946i
$172$	−12.4537	+	4.04647i	−0.949589	+	0.308540i
$173$	13.5517	−	18.6524i	1.03032	−	1.41811i	0.125611	−	0.992080i	$-0.459911\pi$
$173$	13.5517	−	18.6524i	1.03032	−	1.41811i	0.904708	−	0.426033i	$-0.140089\pi$
$174$	0.744761	−	0.541100i	0.0564602	−	0.0410207i
$175$	−3.36738	+	8.90863i	−0.254550	+	0.673429i
$176$	1.98057	−	1.43897i	0.149291	−	0.108467i
$177$	14.2675	−	4.63578i	1.07241	−	0.348446i
$178$	2.20291	−	0.715769i	0.165115	−	0.0536492i
$179$	−4.36962	+	13.4483i	−0.326601	+	1.00517i	0.644112	+	0.764931i	$0.277227\pi$
$179$	−4.36962	+	13.4483i	−0.326601	+	1.00517i	−0.970713	+	0.240242i	$0.922773\pi$
$180$	−1.61803	+	1.54336i	−0.120601	+	0.115035i
$181$	−3.97440			−0.295415			−0.147707	−	0.989031i	$-0.547189\pi$
$181$	−3.97440			−0.295415			−0.147707	+	0.989031i	$0.547189\pi$
$182$	0.654691	+	0.212722i	0.0485289	+	0.0157680i
$183$	−0.755286	+	1.03956i	−0.0558323	+	0.0768466i
$184$	4.55322	−	3.30810i	0.335667	−	0.243877i
$185$	11.1661	+	11.7064i	0.820951	+	0.860670i
$186$	1.17113	+	5.44320i	0.0858718	+	0.399115i
$187$			19.1898i			1.40330i
$188$	2.11577	+	2.91211i	0.154308	+	0.212387i
$189$	1.54099	+	1.11959i	0.112090	+	0.0814383i
$190$	0.676927	−	0.325011i	0.0491094	−	0.0235788i
$191$	−2.33382			−0.168869			−0.0844345	−	0.996429i	$-0.526908\pi$
$191$	−2.33382			−0.168869			−0.0844345	+	0.996429i	$0.526908\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	0.455826	+	0.148107i	0.0328111	+	0.0106610i	0.325377	−	0.945585i	$-0.394509\pi$
$193$	0.455826	+	0.148107i	0.0328111	+	0.0106610i	−0.292565	+	0.956245i	$0.594509\pi$
$194$	4.98909	+	15.3548i	0.358196	+	1.10241i
$195$	0.711173	+	0.383777i	0.0509282	+	0.0274829i
$196$	2.72791	−	1.98194i	0.194851	−	0.141567i
$197$	3.55263	+	1.15432i	0.253114	+	0.0822418i	0.432826	−	0.901478i	$-0.357517\pi$
$197$	3.55263	+	1.15432i	0.253114	+	0.0822418i	−0.179712	+	0.983719i	$0.557517\pi$
$198$	−1.43897	−	1.98057i	−0.102263	−	0.140753i
$199$	15.0346	+	10.9233i	1.06578	+	0.774333i	0.975149	−	0.221552i	$-0.0711123\pi$
$199$	15.0346	+	10.9233i	1.06578	+	0.774333i	0.0906289	+	0.995885i	$0.471112\pi$
$200$	−1.31885	−	4.82293i	−0.0932566	−	0.341033i
$201$	−1.91179	−	1.38900i	−0.134847	−	0.0979722i
$202$	3.65117	−	5.02541i	0.256895	−	0.353586i
$203$	1.66766	−	0.541854i	0.117046	−	0.0380307i
$204$	6.34153	+	4.60739i	0.443996	+	0.322582i
$205$	−1.16637	+	6.38451i	−0.0814630	+	0.445913i
$206$	−1.93550	+	5.95686i	−0.134853	+	0.415034i
$207$	−3.30810	−	4.55322i	−0.229929	−	0.316470i
$208$	−0.343713	+	0.111679i	−0.0238322	+	0.00774354i
$209$	0.254049	+	0.781882i	0.0175729	+	0.0540839i
$210$	−3.83956	+	1.84348i	−0.264955	+	0.127212i
$211$	−14.4341			−0.993686			−0.496843	−	0.867840i	$-0.665508\pi$
$211$	−14.4341			−0.993686			−0.496843	+	0.867840i	$0.665508\pi$
$212$			9.36482i			0.643179i
$213$	−9.83521	−	3.19565i	−0.673898	−	0.218963i
$214$	−10.2781	−	7.46750i	−0.702599	−	0.510468i
$215$	−28.8038	−	5.26210i	−1.96440	−	0.358872i
$216$	−1.00000			−0.0680414
$217$	−1.08234	+	10.5499i	−0.0734738	+	0.716174i
$218$			13.0472i			0.883668i
$219$	−0.248156	+	0.180296i	−0.0167688	+	0.0121833i
$220$	5.42549	−	0.728438i	0.365786	−	0.0491113i
$221$	0.875403	−	2.69421i	0.0588860	−	0.181232i
$222$			7.23494i			0.485578i
$223$			27.5036i			1.84178i	0.389822	+	0.920890i	$0.372537\pi$
$223$			27.5036i			1.84178i	−0.389822	+	0.920890i	$0.627463\pi$
$224$	0.588604	−	1.81154i	0.0393278	−	0.121038i
$225$	−4.82293	+	1.31885i	−0.321529	+	0.0879232i
$226$	3.86437	+	11.8933i	0.257054	+	0.791132i
$227$	−12.2565	−	16.8696i	−0.813491	−	1.11967i	−0.990775	−	0.135514i	$-0.956731\pi$
$227$	−12.2565	−	16.8696i	−0.813491	−	1.11967i	0.177285	−	0.984160i	$-0.443269\pi$
$228$	0.319380	+	0.103773i	0.0211515	+	0.00687253i
$229$	6.28532	−	4.56655i	0.415345	−	0.301766i	−0.360417	−	0.932791i	$-0.617366\pi$
$229$	6.28532	−	4.56655i	0.415345	−	0.301766i	0.775762	+	0.631025i	$0.217366\pi$
$230$	12.4729	−	1.67463i	0.822436	−	0.110422i
$231$	−1.44098	−	4.43487i	−0.0948093	−	0.291793i
$232$	−0.541100	+	0.744761i	−0.0355250	+	0.0488959i
$233$	−10.4914	+	14.4401i	−0.687312	+	0.946003i	−0.999993	−	0.00385486i	$-0.998773\pi$
$233$	−10.4914	+	14.4401i	−0.687312	+	0.946003i	0.312681	+	0.949858i	$0.398773\pi$
$234$	0.111679	+	0.343713i	0.00730068	+	0.0224692i
$235$	1.07105	+	7.97728i	0.0698674	+	0.520381i
$236$	−12.1366	+	8.81777i	−0.790027	+	0.573988i
$237$	6.29957	+	2.04685i	0.409201	+	0.132957i
$238$	8.77599	+	12.0791i	0.568863	+	0.782973i
$239$	0.00180378	+	0.00555146i	0.000116677	+	0.000359094i	0.951115	−	0.308837i	$-0.0999399\pi$
$239$	0.00180378	+	0.00555146i	0.000116677	+	0.000359094i	−0.950998	+	0.309197i	$0.899940\pi$
$240$	1.06192	−	1.96782i	0.0685464	−	0.127023i
$241$	4.67462	−	14.3870i	0.301119	−	0.926749i	−0.679978	−	0.733232i	$-0.738011\pi$
$241$	4.67462	−	14.3870i	0.301119	−	0.926749i	0.981097	−	0.193516i	$-0.0619893\pi$
$242$		−	5.00669i		−	0.321842i
$243$			1.00000i			0.0641500i
$244$	0.397077	−	1.22208i	0.0254203	−	0.0782355i
$245$	7.47270	−	1.00330i	0.477413	−	0.0640986i
$246$	−2.34817	+	1.70604i	−0.149714	+	0.108773i
$247$		−	0.121364i		−	0.00772222i
$248$	−2.79586	−	4.81489i	−0.177537	−	0.305746i
$249$	3.79363			0.240412
$250$	2.52629	−	10.8912i	0.159776	−	0.688819i
$251$	−6.17078	−	4.48333i	−0.389496	−	0.282986i	0.375753	−	0.926720i	$-0.377384\pi$
$251$	−6.17078	−	4.48333i	−0.389496	−	0.282986i	−0.765249	+	0.643734i	$0.777384\pi$
$252$	−1.81154	−	0.588604i	−0.114116	−	0.0370786i
$253$			13.7782i			0.866231i
$254$	−18.9492			−1.18898
$255$	7.58636	+	15.8007i	0.475076	+	0.989480i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.38927	−	2.07600i	0.398552	−	0.129497i	−0.102881	−	0.994694i	$-0.532806\pi$
$257$	6.38927	−	2.07600i	0.398552	−	0.129497i	0.501433	+	0.865196i	$0.332806\pi$
$258$	−7.69684	−	10.5938i	−0.479184	−	0.659541i
$259$	−4.25852	+	13.1064i	−0.264611	+	0.814390i
$260$	−0.794960	−	0.145229i	−0.0493013	−	0.00900675i
$261$	0.744761	+	0.541100i	0.0460995	+	0.0334933i
$262$	4.50968	−	1.46528i	0.278609	−	0.0905256i
$263$	−14.3973	+	19.8162i	−0.887774	+	1.22192i	0.0864320	+	0.996258i	$0.472453\pi$
$263$	−14.3973	+	19.8162i	−0.887774	+	1.22192i	−0.974206	+	0.225659i	$0.927547\pi$
$264$	1.98057	+	1.43897i	0.121896	+	0.0885626i
$265$	−9.94466	+	18.4283i	−0.610896	+	1.13204i
$266$	0.517488	+	0.375977i	0.0317292	+	0.0230526i
$267$	1.36147	+	1.87391i	0.0833209	+	0.114681i
$268$	2.24744	+	0.730238i	0.137284	+	0.0446064i
$269$	−5.89328	+	4.28172i	−0.359320	+	0.261061i	−0.752768	−	0.658286i	$-0.771282\pi$
$269$	−5.89328	+	4.28172i	−0.359320	+	0.261061i	0.393449	+	0.919347i	$0.371282\pi$
$270$	−1.96782	−	1.06192i	−0.119758	−	0.0646262i
$271$	0.332384	+	1.02297i	0.0201909	+	0.0621412i	0.960644	−	0.277781i	$-0.0895991\pi$
$271$	0.332384	+	1.02297i	0.0201909	+	0.0621412i	−0.940453	+	0.339923i	$0.889599\pi$
$272$	−7.45492	−	2.42225i	−0.452021	−	0.146871i
$273$			0.688383i			0.0416628i
$274$	14.7763			0.892669
$275$	11.4500	+	4.32798i	0.690458	+	0.260987i
$276$	4.55322	+	3.30810i	0.274071	+	0.199124i
$277$	−15.1507	−	20.8531i	−0.910314	−	1.25294i	−0.967059	−	0.254552i	$-0.918072\pi$
$277$	−15.1507	−	20.8531i	−0.910314	−	1.25294i	0.0567449	−	0.998389i	$-0.481928\pi$
$278$		−	17.6945i		−	1.06125i
$279$	−4.81489	+	2.79586i	−0.288260	+	0.167384i
$280$	3.08197	−	2.93974i	0.184183	−	0.175683i
$281$	13.2700	−	9.64123i	0.791622	−	0.575147i	−0.116822	−	0.993153i	$-0.537271\pi$
$281$	13.2700	−	9.64123i	0.791622	−	0.575147i	0.908444	+	0.418006i	$0.137271\pi$
$282$	−2.11577	+	2.91211i	−0.125992	+	0.173413i
$283$	7.81726	+	2.53998i	0.464688	+	0.150986i	0.531998	−	0.846746i	$-0.321442\pi$
$283$	7.81726	+	2.53998i	0.464688	+	0.150986i	−0.0673096	+	0.997732i	$0.521442\pi$
$284$	10.3414			0.613647
$285$	0.518286	+	0.543362i	0.0307006	+	0.0321860i
$286$	0.273404	−	0.841451i	0.0161667	−	0.0497560i
$287$	−5.25798	+	1.70842i	−0.310368	+	0.100845i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	35.9552	−	26.1230i	2.11501	−	1.53665i
$290$	−1.85566	+	0.890955i	−0.108968	+	0.0523187i
$291$	−13.0616	+	9.48982i	−0.765685	+	0.556303i
$292$	0.180296	−	0.248156i	0.0105510	−	0.0145222i
$293$	−22.9277	+	7.44967i	−1.33945	+	0.435215i	−0.889131	−	0.457652i	$-0.848691\pi$
$293$	−22.9277	+	7.44967i	−1.33945	+	0.435215i	−0.450321	+	0.892867i	$0.648691\pi$
$294$	2.72791	+	1.98194i	0.159095	+	0.115589i
$295$	−33.2465	+	4.46374i	−1.93568	+	0.259889i
$296$	−2.23572	−	6.88084i	−0.129949	−	0.399941i
$297$	1.43897	−	1.98057i	0.0834976	−	0.114925i
$298$	0.147622	+	0.203185i	0.00855154	+	0.0117702i
$299$	0.628539	−	1.93444i	0.0363493	−	0.111872i
$300$	4.17933	−	2.74467i	0.241294	−	0.158463i
$301$	−7.70756	−	23.7214i	−0.444256	−	1.36728i
$302$	−13.1773	+	4.28157i	−0.758270	+	0.246377i
$303$	5.90772	+	1.91953i	0.339390	+	0.110274i
$304$	−0.335816			−0.0192604
$305$	2.07912	−	1.98317i	0.119050	−	0.113556i
$306$	−2.42225	+	7.45492i	−0.138471	+	0.426169i
$307$	−3.67555	+	5.05895i	−0.209774	+	0.288730i	−0.900919	−	0.433986i	$-0.857107\pi$
$307$	−3.67555	+	5.05895i	−0.209774	+	0.288730i	0.691145	+	0.722716i	$0.257107\pi$
$308$	2.74090	+	3.77252i	0.156177	+	0.214960i
$309$	−6.26341			−0.356313
$310$	−0.388742	−	12.4438i	−0.0220790	−	0.706762i
$311$	11.0536			0.626795			0.313397	−	0.949622i	$-0.398533\pi$
$311$	11.0536			0.626795			0.313397	+	0.949622i	$0.398533\pi$
$312$	−0.212426	−	0.292379i	−0.0120263	−	0.0165527i
$313$	17.5346	−	24.1343i	0.991113	−	1.36415i	0.0604912	−	0.998169i	$-0.480733\pi$
$313$	17.5346	−	24.1343i	0.991113	−	1.36415i	0.930622	−	0.365982i	$-0.119267\pi$
$314$	−4.30047	+	13.2355i	−0.242690	+	0.746922i
$315$	−2.93974	−	3.08197i	−0.165635	−	0.173649i
$316$	−6.62376			−0.372616
$317$	9.86664	+	3.20587i	0.554166	+	0.180059i	0.572694	−	0.819769i	$-0.305898\pi$
$317$	9.86664	+	3.20587i	0.554166	+	0.180059i	−0.0185286	+	0.999828i	$0.505898\pi$
$318$	−8.90648	+	2.89389i	−0.499450	+	0.162281i
$319$	−0.696426	−	2.14338i	−0.0389924	−	0.120006i
$320$	−0.401852	+	2.19966i	−0.0224642	+	0.122965i
$321$	3.92590	−	12.0827i	0.219122	−	0.674389i
$322$	6.30115	+	8.67279i	0.351150	+	0.483316i
$323$	1.54724	−	2.12959i	0.0860906	−	0.118494i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−1.41012	−	1.12997i	−0.0782193	−	0.0626793i
$326$	−3.77609	−	2.74349i	−0.209138	−	0.151948i
$327$	−12.4086	+	4.03181i	−0.686198	+	0.222959i
$328$	1.70604	−	2.34817i	0.0942005	−	0.129656i
$329$	−5.54687	+	4.03004i	−0.305809	+	0.222183i
$330$	2.36935	+	4.93485i	0.130429	+	0.271654i
$331$	−17.6686	+	12.8370i	−0.971156	+	0.705586i	−0.955715	−	0.294294i	$-0.904915\pi$
$331$	−17.6686	+	12.8370i	−0.971156	+	0.705586i	−0.0154416	+	0.999881i	$0.504915\pi$
$332$	−3.60796	+	1.17230i	−0.198012	+	0.0643381i
$333$	−6.88084	+	2.23572i	−0.377068	+	0.122517i
$334$	4.72524	−	14.5428i	0.258554	−	0.795746i
$335$	3.64712	+	3.82358i	0.199263	+	0.208904i
$336$	1.90476			0.103913
$337$	1.98517	+	0.645019i	0.108139	+	0.0351364i	0.362587	−	0.931950i	$-0.381894\pi$
$337$	1.98517	+	0.645019i	0.108139	+	0.0351364i	−0.254448	+	0.967087i	$0.581894\pi$
$338$	7.56444	−	10.4116i	0.411451	−	0.566314i
$339$	−10.1171	+	7.35048i	−0.549483	+	0.399223i
$340$	−12.0977	−	12.6831i	−0.656092	−	0.687836i
$341$	13.5594	+	1.39109i	0.734283	+	0.0753317i
$342$			0.335816i			0.0181589i
$343$	11.6123	+	15.9829i	0.627003	+	0.862996i
$344$	10.5938	+	7.69684i	0.571179	+	0.414986i
$345$	5.44700	+	11.3449i	0.293256	+	0.610789i
$346$	−23.0556			−1.23948
$347$		−	12.1358i		−	0.651484i	−0.945459	−	0.325742i	$-0.894386\pi$
$347$		−	12.1358i		−	0.651484i	0.945459	−	0.325742i	$-0.105614\pi$
$348$	−0.875519	−	0.284473i	−0.0469327	−	0.0152494i
$349$	−1.16752	−	3.59326i	−0.0624960	−	0.192343i	0.914934	−	0.403604i	$-0.132243\pi$
$349$	−1.16752	−	3.59326i	−0.0624960	−	0.192343i	−0.977430	+	0.211262i	$0.932243\pi$
$350$	9.18653	−	2.51209i	0.491041	−	0.134277i
$351$	−0.292379	+	0.212426i	−0.0156061	+	0.0113385i
$352$	−2.32830	−	0.756512i	−0.124099	−	0.0403222i
$353$	5.65396	+	7.78200i	0.300930	+	0.414194i	0.932526	−	0.361103i	$-0.117600\pi$
$353$	5.65396	+	7.78200i	0.300930	+	0.414194i	−0.631596	+	0.775298i	$0.717600\pi$
$354$	−12.1366	−	8.81777i	−0.645054	−	0.468659i
$355$	20.3500	+	10.9817i	1.08006	+	0.582846i
$356$	−1.87391	−	1.36147i	−0.0993170	−	0.0721580i
$357$	−8.77599	+	12.0791i	−0.464475	+	0.639295i
$358$	13.4483	−	4.36962i	0.710765	−	0.230941i
$359$	−14.4270	−	10.4819i	−0.761430	−	0.553211i	0.137919	−	0.990444i	$-0.455959\pi$
$359$	−14.4270	−	10.4819i	−0.761430	−	0.553211i	−0.899348	+	0.437233i	$0.855959\pi$
$360$	2.19966	+	0.401852i	0.115932	+	0.0211794i
$361$	−5.83647	+	17.9628i	−0.307183	+	0.945412i
$362$	2.33609	+	3.21536i	0.122782	+	0.168995i
$363$	4.76164	−	1.54715i	0.249921	−	0.0812044i
$364$	−0.212722	−	0.654691i	−0.0111497	−	0.0343151i
$365$	0.618311	−	0.296868i	0.0323639	−	0.0155388i
$366$	1.28497			0.0671664
$367$			19.0738i			0.995646i	0.867279	+	0.497823i	$0.165867\pi$
$367$			19.0738i			0.995646i	−0.867279	+	0.497823i	$0.834133\pi$
$368$	−5.35263	−	1.73917i	−0.279025	−	0.0906607i
$369$	−2.34817	−	1.70604i	−0.122241	−	0.0888131i
$370$	2.90737	−	15.9144i	0.151147	−	0.827352i
$371$	−17.8378			−0.926091
$372$	3.71527	−	4.14690i	0.192628	−	0.215007i
$373$		−	10.6155i		−	0.549648i	−0.961495	−	0.274824i	$-0.911380\pi$
$373$		−	10.6155i		−	0.549648i	0.961495	−	0.274824i	$-0.0886196\pi$
$374$	15.5249	−	11.2795i	0.802772	−	0.583248i
$375$	11.1388	−	0.962919i	0.575205	−	0.0497249i
$376$	1.11233	−	3.42339i	0.0573638	−	0.176548i
$377$			0.332696i			0.0171347i
$378$		−	1.90476i		−	0.0979704i
$379$	3.49860	−	10.7676i	0.179711	−	0.553094i	−0.820106	−	0.572211i	$-0.806086\pi$
$379$	3.49860	−	10.7676i	0.179711	−	0.553094i	0.999817	+	0.0191176i	$0.00608571\pi$
$380$	−0.660827	−	0.356609i	−0.0338997	−	0.0182936i
$381$	−5.85561	−	18.0217i	−0.299992	−	0.923280i
$382$	1.37178	+	1.88810i	0.0701865	+	0.0966035i
$383$	−15.1065	−	4.90841i	−0.771908	−	0.250808i	−0.103527	−	0.994627i	$-0.533013\pi$
$383$	−15.1065	−	4.90841i	−0.771908	−	0.250808i	−0.668382	+	0.743818i	$0.733013\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	1.38750	+	10.3343i	0.0707136	+	0.526683i
$386$	−0.148107	−	0.455826i	−0.00753844	−	0.0232009i
$387$	7.69684	−	10.5938i	0.391252	−	0.538513i
$388$	9.48982	−	13.0616i	0.481772	−	0.663103i
$389$	7.94792	+	24.4612i	0.402976	+	1.24023i	0.922574	+	0.385821i	$0.126082\pi$
$389$	7.94792	+	24.4612i	0.402976	+	1.24023i	−0.519598	+	0.854411i	$0.673918\pi$
$390$	−0.107535	−	0.800930i	−0.00544523	−	0.0405567i
$391$	35.6907	−	25.9308i	1.80496	−	1.31138i
$392$	−3.20685	−	1.04197i	−0.161970	−	0.0526273i
$393$	2.78714	+	3.83616i	0.140592	+	0.193509i
$394$	−1.15432	−	3.55263i	−0.0581537	−	0.178979i
$395$	−13.0344	−	7.03388i	−0.655832	−	0.353913i
$396$	−0.756512	+	2.32830i	−0.0380162	+	0.117002i
$397$		−	16.5037i		−	0.828295i	−0.910210	−	0.414147i	$-0.864080\pi$
$397$		−	16.5037i		−	0.828295i	0.910210	−	0.414147i	$-0.135920\pi$
$398$		−	18.5838i		−	0.931524i
$399$	−0.197663	+	0.608343i	−0.00989551	+	0.0304553i
$400$	−3.12663	+	3.90182i	−0.156332	+	0.195091i
$401$	18.7663	−	13.6345i	0.937142	−	0.680874i	−0.0105889	−	0.999944i	$-0.503371\pi$
$401$	18.7663	−	13.6345i	0.937142	−	0.680874i	0.947731	+	0.319070i	$0.103371\pi$
$402$			2.36310i			0.117861i
$403$	−1.84026	−	0.813862i	−0.0916698	−	0.0405414i
$404$	−6.21174			−0.309046
$405$	0.401852	−	2.19966i	0.0199682	−	0.109302i
$406$	−1.41859	−	1.03067i	−0.0704036	−	0.0511512i
$407$	16.8452	+	5.47332i	0.834983	+	0.271302i
$408$		−	7.83857i		−	0.388067i
$409$	−18.3634			−0.908011			−0.454006	−	0.890999i	$-0.650005\pi$
$409$	−18.3634			−0.908011			−0.454006	+	0.890999i	$0.650005\pi$
$410$	5.85075	−	2.80910i	0.288948	−	0.138732i
$411$	4.56613	+	14.0531i	0.225231	+	0.693188i
$412$	5.95686	−	1.93550i	0.293473	−	0.0953553i
$413$	−16.7958	−	23.1174i	−0.826465	−	1.13753i
$414$	−1.73917	+	5.35263i	−0.0854757	+	0.263067i
$415$	−8.34471	−	1.52448i	−0.409626	−	0.0748336i
$416$	0.292379	+	0.212426i	0.0143351	+	0.0104150i
$417$	16.8285	−	5.46791i	0.824096	−	0.267765i
$418$	0.483230	−	0.665109i	0.0236355	−	0.0325315i
$419$	−2.22996	−	1.62016i	−0.108940	−	0.0791499i	0.531981	−	0.846756i	$-0.321448\pi$
$419$	−2.22996	−	1.62016i	−0.108940	−	0.0791499i	−0.640922	+	0.767606i	$0.721448\pi$
$420$	3.74824	+	2.02270i	0.182895	+	0.0986976i
$421$	−5.99535	−	4.35588i	−0.292196	−	0.212292i	0.432024	−	0.901862i	$-0.357800\pi$
$421$	−5.99535	−	4.35588i	−0.292196	−	0.212292i	−0.724219	+	0.689570i	$0.757800\pi$
$422$	8.48417	+	11.6775i	0.413003	+	0.568450i
$423$	−3.42339	−	1.11233i	−0.166451	−	0.0540831i
$424$	7.57630	−	5.50451i	0.367938	−	0.267322i
$425$	−10.3379	−	37.8048i	−0.501461	−	1.83380i
$426$	3.19565	+	9.83521i	0.154830	+	0.476518i
$427$	2.32777	+	0.756338i	0.112649	+	0.0366017i
$428$			12.7045i			0.614094i
$429$	0.884754			0.0427163
$430$	12.6733	+	26.3957i	0.611162	+	1.27292i
$431$	−12.8900	−	9.36512i	−0.620888	−	0.451102i	0.232343	−	0.972634i	$-0.425361\pi$
$431$	−12.8900	−	9.36512i	−0.620888	−	0.451102i	−0.853232	+	0.521532i	$0.825361\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$		−	15.6680i		−	0.752956i	−0.926426	−	0.376478i	$-0.877135\pi$
$433$		−	15.6680i		−	0.752956i	0.926426	−	0.376478i	$-0.122865\pi$
$434$	9.17123	−	5.32544i	0.440233	−	0.255629i
$435$	−1.42078	−	1.48952i	−0.0681212	−	0.0714171i
$436$	10.5554	−	7.66895i	0.505512	−	0.367276i
$437$	1.11091	−	1.52904i	0.0531423	−	0.0731441i
$438$	0.291725	+	0.0947870i	0.0139391	+	0.00452910i
$439$	−25.6217			−1.22286			−0.611429	−	0.791299i	$-0.709405\pi$
$439$	−25.6217			−1.22286			−0.611429	+	0.791299i	$0.709405\pi$
$440$	−3.77834	−	3.96115i	−0.180125	−	0.188840i
$441$	−1.04197	+	3.20685i	−0.0496175	+	0.152707i
$442$	−2.69421	+	0.875403i	−0.128151	+	0.0416387i
$443$	27.0382	−	8.78523i	1.28462	−	0.417399i	0.414416	−	0.910088i	$-0.363986\pi$
$443$	27.0382	−	8.78523i	1.28462	−	0.417399i	0.870206	+	0.492689i	$0.163986\pi$
$444$	5.85319	−	4.25259i	0.277780	−	0.201819i
$445$	−2.24175	−	4.66908i	−0.106269	−	0.221336i
$446$	22.2509	−	16.1662i	1.05361	−	0.765494i
$447$	−0.147622	+	0.203185i	−0.00698230	+	0.00961031i
$448$	−1.81154	+	0.588604i	−0.0855871	+	0.0278089i
$449$	2.97074	+	2.15837i	0.140198	+	0.101860i	0.655673	−	0.755045i	$-0.272385\pi$
$449$	2.97074	+	2.15837i	0.140198	+	0.101860i	−0.515476	+	0.856904i	$0.672385\pi$
$450$	3.90182	+	3.12663i	0.183933	+	0.147391i
$451$	2.19577	+	6.75789i	0.103395	+	0.318217i
$452$	7.35048	−	10.1171i	0.345737	−	0.475867i
$453$	−8.14404	−	11.2093i	−0.382640	−	0.526659i
$454$	−6.44361	+	19.8314i	−0.302414	+	0.930733i
$455$	0.276628	−	1.51421i	0.0129685	−	0.0709872i
$456$	−0.103773	−	0.319380i	−0.00485961	−	0.0149563i
$457$	−5.42768	+	1.76356i	−0.253896	+	0.0824959i	−0.433200	−	0.901298i	$-0.642616\pi$
$457$	−5.42768	+	1.76356i	−0.253896	+	0.0824959i	0.179304	+	0.983794i	$0.442616\pi$
$458$	−7.38883	−	2.40078i	−0.345257	−	0.112181i
$459$	−7.83857			−0.365873
$460$	−8.68617	−	9.10643i	−0.404995	−	0.424590i
$461$	4.42947	−	13.6325i	0.206301	−	0.634929i	−0.793356	−	0.608757i	$-0.791668\pi$
$461$	4.42947	−	13.6325i	0.206301	−	0.634929i	0.999657	−	0.0261719i	$-0.00833173\pi$
$462$	−2.74090	+	3.77252i	−0.127518	+	0.175514i
$463$	7.61285	+	10.4782i	0.353799	+	0.486963i	0.948408	−	0.317052i	$-0.102693\pi$
$463$	7.61285	+	10.4782i	0.353799	+	0.486963i	−0.594609	+	0.804015i	$0.702693\pi$
$464$	0.920575			0.0427366
$465$	11.7147	−	4.21507i	0.543254	−	0.195469i
$466$	17.8490			0.826837
$467$	4.40993	+	6.06975i	0.204067	+	0.280874i	0.898768	−	0.438424i	$-0.144463\pi$
$467$	4.40993	+	6.06975i	0.204067	+	0.280874i	−0.694701	+	0.719299i	$0.744463\pi$
$468$	0.212426	−	0.292379i	0.00981940	−	0.0135152i
$469$	−1.39093	+	4.28084i	−0.0642272	+	0.197671i
$470$	5.82421	−	5.55543i	0.268651	−	0.256253i
$471$	−13.9166			−0.641244
$472$	14.2675	+	4.63578i	0.656713	+	0.213379i
$473$	−30.4883	+	9.90626i	−1.40185	+	0.455490i
$474$	−2.04685	−	6.29957i	−0.0940151	−	0.289349i
$475$	−0.921703	−	1.40349i	−0.0422906	−	0.0643964i
$476$	4.61381	−	14.1999i	0.211474	−	0.650849i
$477$	−5.50451	−	7.57630i	−0.252034	−	0.346895i
$478$	0.00343099	−	0.00472236i	0.000156930	−	0.000215995i
$479$	−10.0314	−	30.8734i	−0.458346	−	1.41064i	−0.867162	−	0.498027i	$-0.834058\pi$
$479$	−10.0314	−	30.8734i	−0.458346	−	1.41064i	0.408816	−	0.912617i	$-0.365942\pi$
$480$	−2.21618	+	0.297550i	−0.101154	+	0.0135812i
$481$	−2.11535	−	1.53689i	−0.0964516	−	0.0700762i
$482$	−14.3870	+	4.67462i	−0.655310	+	0.212923i
$483$	−6.30115	+	8.67279i	−0.286712	+	0.394626i
$484$	−4.05049	+	2.94286i	−0.184113	+	0.133766i
$485$	32.5446	−	15.6256i	1.47778	−	0.709520i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−1.05343	+	0.342279i	−0.0477353	+	0.0155101i	−0.332787	−	0.943002i	$-0.607989\pi$
$487$	−1.05343	+	0.342279i	−0.0477353	+	0.0155101i	0.285052	+	0.958512i	$0.407989\pi$
$488$	−1.22208	+	0.397077i	−0.0553209	+	0.0179748i
$489$	1.44234	−	4.43906i	0.0652247	−	0.200741i
$490$	−5.20403	−	5.45582i	−0.235094	−	0.246469i
$491$	−19.5355			−0.881625			−0.440812	−	0.897599i	$-0.645310\pi$
$491$	−19.5355			−0.881625			−0.440812	+	0.897599i	$0.645310\pi$
$492$	2.76044	+	0.896920i	0.124450	+	0.0404363i
$493$	−4.24145	+	5.83786i	−0.191025	+	0.262924i
$494$	−0.0981857	+	0.0713361i	−0.00441758	+	0.00320956i
$495$	−3.96115	+	3.77834i	−0.178040	+	0.169824i
$496$	−2.25197	+	5.09202i	−0.101116	+	0.228638i
$497$			19.6978i			0.883568i
$498$	−2.22984	−	3.06911i	−0.0999216	−	0.137530i
$499$	9.29364	+	6.75223i	0.416041	+	0.302271i	0.776043	−	0.630680i	$-0.217224\pi$
$499$	9.29364	+	6.75223i	0.416041	+	0.302271i	−0.360002	+	0.932951i	$0.617224\pi$
$500$	−10.2961	+	4.35787i	−0.460454	+	0.194890i
$501$	15.2912			0.683161
$502$			7.62750i			0.340432i
$503$	−5.74006	−	1.86506i	−0.255937	−	0.0831588i	0.178239	−	0.983987i	$-0.442960\pi$
$503$	−5.74006	−	1.86506i	−0.255937	−	0.0831588i	−0.434175	+	0.900828i	$0.642960\pi$
$504$	0.588604	+	1.81154i	0.0262185	+	0.0806923i
$505$	−12.2236	−	6.59635i	−0.543944	−	0.293534i
$506$	11.1468	−	8.09865i	0.495537	−	0.360029i
$507$	12.2395	+	3.97686i	0.543576	+	0.176619i
$508$	11.1380	+	15.3302i	0.494170	+	0.680167i
$509$	−6.88152	−	4.99971i	−0.305018	−	0.221608i	0.424738	−	0.905316i	$-0.360366\pi$
$509$	−6.88152	−	4.99971i	−0.305018	−	0.221608i	−0.729756	+	0.683708i	$0.760366\pi$
$510$	8.32391	−	15.4249i	0.368589	−	0.683027i
$511$	0.472678	+	0.343420i	0.0209100	+	0.0151920i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−0.319380	+	0.103773i	−0.0141010	+	0.00458169i
$514$	−5.43504	−	3.94879i	−0.239729	−	0.174174i
$515$	13.7774	+	2.51696i	0.607105	+	0.110911i
$516$	−4.04647	+	12.4537i	−0.178136	+	0.548246i
$517$	5.17967	+	7.12920i	0.227801	+	0.313542i
$518$	13.1064	−	4.25852i	0.575861	−	0.187108i
$519$	−7.12457	−	21.9272i	−0.312734	−	0.962496i
$520$	0.349772	+	0.728500i	0.0153385	+	0.0319468i
$521$	−19.3416			−0.847369			−0.423685	−	0.905810i	$-0.639263\pi$
$521$	−19.3416			−0.847369			−0.423685	+	0.905810i	$0.639263\pi$
$522$		−	0.920575i		−	0.0402925i
$523$	−3.63352	−	1.18060i	−0.158883	−	0.0516241i	0.228496	−	0.973545i	$-0.426619\pi$
$523$	−3.63352	−	1.18060i	−0.158883	−	0.0516241i	−0.387378	+	0.921921i	$0.626619\pi$
$524$	−3.83616	−	2.78714i	−0.167584	−	0.121757i
$525$	5.22794	+	7.96063i	0.228166	+	0.347431i
$526$	24.4941			1.06799
$527$	−21.9155	−	37.7419i	−0.954655	−	1.64406i
$528$		−	2.44812i		−	0.106541i
$529$	7.01848	−	5.09923i	0.305151	−	0.221706i
$530$	20.7542	−	2.78650i	0.901503	−	0.121038i
$531$	4.63578	−	14.2675i	0.201176	−	0.619155i
$532$		−	0.639650i		−	0.0277323i
$533$		−	1.04896i		−	0.0454357i
$534$	0.715769	−	2.20291i	0.0309744	−	0.0953293i
$535$	−13.4911	+	25.0002i	−0.583271	+	1.08085i
$536$	−0.730238	−	2.24744i	−0.0315415	−	0.0970747i
$537$	8.31151	+	11.4398i	0.358668	+	0.493664i
$538$	6.92797	+	2.25103i	0.298686	+	0.0970489i
$539$	6.67826	−	4.85204i	0.287653	−	0.208992i
$540$	0.297550	+	2.21618i	0.0128045	+	0.0953693i
$541$	1.39800	+	4.30261i	0.0601049	+	0.184984i	0.976601	−	0.215060i	$-0.0689948\pi$
$541$	1.39800	+	4.30261i	0.0601049	+	0.184984i	−0.916496	+	0.400044i	$0.868995\pi$
$542$	0.632233	−	0.870194i	0.0271567	−	0.0373780i
$543$	−2.33609	+	3.21536i	−0.100251	+	0.137984i
$544$	2.42225	+	7.45492i	0.103853	+	0.319627i
$545$	28.9150	−	3.88219i	1.23858	−	0.166295i
$546$	0.556913	−	0.404621i	0.0238337	−	0.0173162i
$547$	25.1004	+	8.15563i	1.07322	+	0.348710i	0.791740	−	0.610858i	$-0.209175\pi$
$547$	25.1004	+	8.15563i	1.07322	+	0.348710i	0.281478	+	0.959568i	$0.409175\pi$
$548$	−8.68529	−	11.9543i	−0.371017	−	0.510662i
$549$	0.397077	+	1.22208i	0.0169468	+	0.0521570i
$550$	−3.22870	−	11.8071i	−0.137672	−	0.503458i
$551$	−0.0955307	+	0.294013i	−0.00406974	+	0.0125254i
$552$		−	5.62808i		−	0.239547i
$553$		−	12.6167i		−	0.536516i
$554$	−7.96517	+	24.5143i	−0.338408	+	1.04151i
$555$	16.0340	−	2.15275i	0.680603	−	0.0913793i
$556$	−14.3152	+	10.4006i	−0.607099	+	0.441083i
$557$		−	30.3219i		−	1.28478i	−0.766378	−	0.642389i	$-0.777943\pi$
$557$		−	30.3219i		−	1.28478i	0.766378	−	0.642389i	$-0.222057\pi$
$558$	5.09202	+	2.25197i	0.215562	+	0.0953333i
$559$	4.73241			0.200160
$560$	−4.18984	−	0.765432i	−0.177053	−	0.0323454i
$561$	15.5249	+	11.2795i	0.655460	+	0.476220i
$562$	−15.5998	−	5.06869i	−0.658039	−	0.213810i
$563$			21.4026i			0.902010i	0.892521	+	0.451005i	$0.148934\pi$
$563$			21.4026i			0.902010i	−0.892521	+	0.451005i	$0.851066\pi$
$564$	3.59956			0.151569
$565$	25.2079	−	12.1030i	1.06051	−	0.509177i
$566$	−2.53998	−	7.81726i	−0.106763	−	0.328584i
$567$	1.81154	−	0.588604i	0.0760774	−	0.0247190i
$568$	−6.07850	−	8.36633i	−0.255048	−	0.351043i
$569$	9.19539	−	28.3005i	0.385491	−	1.18642i	−0.550633	−	0.834748i	$-0.685613\pi$
$569$	9.19539	−	28.3005i	0.385491	−	1.18642i	0.936123	−	0.351671i	$-0.114387\pi$
$570$	0.134948	−	0.738682i	0.00565236	−	0.0309400i
$571$	0.434379	+	0.315595i	0.0181782	+	0.0132072i	0.596837	−	0.802362i	$-0.296424\pi$
$571$	0.434379	+	0.315595i	0.0181782	+	0.0132072i	−0.578659	+	0.815570i	$0.696424\pi$
$572$	−0.841451	+	0.273404i	−0.0351828	+	0.0114316i
$573$	−1.37178	+	1.88810i	−0.0573071	+	0.0788764i
$574$	4.47270	+	3.24961i	0.186687	+	0.135636i
$575$	−7.42259	−	27.1438i	−0.309543	−	1.13198i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−2.64920	−	3.64631i	−0.110288	−	0.151798i	0.750305	−	0.661092i	$-0.229907\pi$
$577$	−2.64920	−	3.64631i	−0.110288	−	0.151798i	−0.860593	+	0.509294i	$0.829907\pi$
$578$	−42.2679	−	13.7337i	−1.75811	−	0.571246i
$579$	0.387749	−	0.281716i	0.0161143	−	0.0117077i
$580$	1.81153	+	0.977574i	0.0752197	+	0.0405915i
$581$	−2.23295	−	6.87230i	−0.0926383	−	0.285111i
$582$	15.3548	+	4.98909i	0.636479	+	0.206804i
$583$			22.9263i			0.949508i
$584$	−0.306737			−0.0126929
$585$	0.728500	−	0.349772i	0.0301198	−	0.0144613i
$586$	19.5035	+	14.1701i	0.805682	+	0.585362i
$587$	−13.8428	−	19.0530i	−0.571355	−	0.786403i	0.421359	−	0.906894i	$-0.361553\pi$
$587$	−13.8428	−	19.0530i	−0.571355	−	0.786403i	−0.992714	+	0.120491i	$0.961553\pi$
$588$		−	3.37188i		−	0.139054i
$589$	−1.39260	−	1.24765i	−0.0573809	−	0.0514084i
$590$	23.1530	+	24.2732i	0.953195	+	0.999313i
$591$	3.02204	−	2.19564i	0.124310	−	0.0903167i
$592$	−4.25259	+	5.85319i	−0.174780	+	0.240565i
$593$	−46.0642	−	14.9672i	−1.89163	−	0.614628i	−0.978212	−	0.207608i	$-0.933432\pi$
$593$	−46.0642	−	14.9672i	−1.89163	−	0.614628i	−0.913419	−	0.407020i	$-0.866568\pi$
$594$	−2.44812			−0.100448
$595$	24.1582	−	23.0433i	0.990391	−	0.944685i
$596$	0.0776097	−	0.238858i	0.00317902	−	0.00978401i
$597$	17.6743	−	5.74272i	0.723360	−	0.235034i
$598$	−1.93444	+	0.628539i	−0.0791052	+	0.0257029i
$599$	−26.3588	+	19.1508i	−1.07699	+	0.782480i	−0.977156	−	0.212524i	$-0.931832\pi$
$599$	−26.3588	+	19.1508i	−1.07699	+	0.782480i	−0.0998355	+	0.995004i	$0.531832\pi$
$600$	−4.67703	−	1.76788i	−0.190939	−	0.0721732i
$601$	−32.7330	+	23.7819i	−1.33521	+	0.970083i	−0.335599	+	0.942005i	$0.608939\pi$
$601$	−32.7330	+	23.7819i	−1.33521	+	0.970083i	−0.999606	+	0.0280784i	$0.991061\pi$
$602$	−14.6607	+	20.1787i	−0.597523	+	0.822421i
$603$	−2.24744	+	0.730238i	−0.0915229	+	0.0297376i
$604$	11.2093	+	8.14404i	0.456100	+	0.331376i
$605$	−11.0957	+	1.48974i	−0.451106	+	0.0605664i
$606$	−1.91953	−	5.90772i	−0.0779757	−	0.239985i
$607$	4.34809	−	5.98464i	0.176484	−	0.242909i	−0.711606	−	0.702578i	$-0.752032\pi$
$607$	4.34809	−	5.98464i	0.176484	−	0.242909i	0.888090	+	0.459669i	$0.152032\pi$
$608$	0.197388	+	0.271681i	0.00800513	+	0.0110181i
$609$	0.541854	−	1.66766i	0.0219570	−	0.0675768i
$610$	−2.82650	−	0.516367i	−0.114442	−	0.0209071i
$611$	−0.401995	−	1.23721i	−0.0162630	−	0.0500523i
$612$	7.45492	−	2.42225i	0.301347	−	0.0979137i
$613$	34.7348	+	11.2860i	1.40293	+	0.455838i	0.910136	−	0.414310i	$-0.135977\pi$
$613$	34.7348	+	11.2860i	1.40293	+	0.455838i	0.492791	+	0.870148i	$0.335977\pi$
$614$	6.25321			0.252359
$615$	4.47960	+	4.69633i	0.180635	+	0.189374i
$616$	1.44098	−	4.43487i	0.0580586	−	0.178686i
$617$	12.4887	−	17.1892i	0.502775	−	0.692010i	−0.479905	−	0.877320i	$-0.659329\pi$
$617$	12.4887	−	17.1892i	0.502775	−	0.692010i	0.982680	+	0.185310i	$0.0593290\pi$
$618$	3.68154	+	5.06721i	0.148093	+	0.203833i
$619$	−41.7129			−1.67658			−0.838292	−	0.545222i	$-0.816445\pi$
$619$	−41.7129			−1.67658			−0.838292	+	0.545222i	$0.816445\pi$
$620$	−9.83877	+	7.62880i	−0.395135	+	0.306380i
$621$	−5.62808			−0.225847
$622$	−6.49717	−	8.94258i	−0.260513	−	0.358565i
$623$	2.59329	−	3.56935i	0.103898	−	0.143003i
$624$	−0.111679	+	0.343713i	−0.00447074	+	0.0137595i
$625$	−24.8885	−	2.35805i	−0.995542	−	0.0943219i
$626$	−29.8316			−1.19231
$627$	0.781882	+	0.254049i	0.0312254	+	0.0101457i
$628$	13.2355	−	4.30047i	0.528153	−	0.171607i
$629$	−17.5248	−	53.9359i	−0.698761	−	2.15057i
$630$	−0.765432	+	4.18984i	−0.0304955	+	0.166927i
$631$	−8.38025	+	25.7918i	−0.333613	+	1.02675i	0.633789	+	0.773506i	$0.281499\pi$
$631$	−8.38025	+	25.7918i	−0.333613	+	1.02675i	−0.967401	+	0.253248i	$0.918501\pi$
$632$	3.89335	+	5.35873i	0.154869	+	0.213159i
$633$	−8.48417	+	11.6775i	−0.337215	+	0.464137i
$634$	−3.20587	−	9.86664i	−0.127321	−	0.391854i
$635$	5.63831	+	41.9948i	0.223750	+	1.66651i
$636$	7.57630	+	5.50451i	0.300420	+	0.218268i
$637$	−1.15896	+	0.376568i	−0.0459196	+	0.0149202i
$638$	−1.32468	+	1.82327i	−0.0524446	+	0.0721838i
$639$	−8.36633	+	6.07850i	−0.330967	+	0.240462i
$640$	2.01577	−	0.967824i	0.0796802	−	0.0382566i
$641$	−21.4473	+	15.5824i	−0.847119	+	0.615468i	−0.924350	−	0.381546i	$-0.875392\pi$
$641$	−21.4473	+	15.5824i	−0.847119	+	0.615468i	0.0772315	+	0.997013i	$0.475392\pi$
$642$	−12.0827	+	3.92590i	−0.476865	+	0.154943i
$643$	−3.46866	+	1.12704i	−0.136791	+	0.0444460i	−0.376612	−	0.926371i	$-0.622911\pi$
$643$	−3.46866	+	1.12704i	−0.136791	+	0.0444460i	0.239822	+	0.970817i	$0.422911\pi$
$644$	3.31271	−	10.1955i	0.130539	−	0.401758i
$645$	−21.1876	+	20.2098i	−0.834260	+	0.795759i
$646$	−2.63232			−0.103567
$647$	37.5997	+	12.2169i	1.47820	+	0.480295i	0.933573	−	0.358387i	$-0.116673\pi$
$647$	37.5997	+	12.2169i	1.47820	+	0.480295i	0.544622	+	0.838681i	$0.316673\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	−29.7120	+	21.5870i	−1.16630	+	0.847364i
$650$	−0.0853151	+	1.80499i	−0.00334633	+	0.0707975i
$651$	7.89886	+	7.07670i	0.309581	+	0.277358i
$652$			4.66750i			0.182793i
$653$	17.9004	+	24.6377i	0.700495	+	0.964149i	0.999950	+	0.0100383i	$0.00319535\pi$
$653$	17.9004	+	24.6377i	0.700495	+	0.964149i	−0.299454	+	0.954111i	$0.596805\pi$
$654$	10.5554	+	7.66895i	0.412749	+	0.299880i
$655$	−4.58919	−	9.55828i	−0.179315	−	0.373473i
$656$	−2.90249			−0.113323
$657$			0.306737i			0.0119670i
$658$	6.52074	+	2.11872i	0.254205	+	0.0825962i
$659$	10.1606	+	31.2712i	0.395801	+	1.21815i	0.928336	+	0.371743i	$0.121240\pi$
$659$	10.1606	+	31.2712i	0.395801	+	1.21815i	−0.532534	+	0.846408i	$0.678760\pi$
$660$	2.59970	−	4.81748i	0.101193	−	0.187520i
$661$	−35.8664	+	26.0585i	−1.39504	+	1.01356i	−0.399750	+	0.916624i	$0.630903\pi$
$661$	−35.8664	+	26.0585i	−1.39504	+	1.01356i	−0.995291	+	0.0969326i	$0.969097\pi$
$662$	20.7707	+	6.74882i	0.807278	+	0.262300i
$663$	−1.66512	−	2.29183i	−0.0646677	−	0.0890075i
$664$	3.06911	+	2.22984i	0.119105	+	0.0865346i
$665$	0.679255	−	1.25872i	0.0263404	−	0.0488110i
$666$	5.85319	+	4.25259i	0.226807	+	0.164785i
$667$	−3.04536	+	4.19158i	−0.117917	+	0.162298i
$668$	−14.5428	+	4.72524i	−0.562678	+	0.182825i
$669$	22.2509	+	16.1662i	0.860270	+	0.625023i
$670$	0.949616	−	5.19802i	0.0366869	−	0.200817i
$671$	0.972094	−	2.99180i	0.0375273	−	0.115497i
$672$	−1.11959	−	1.54099i	−0.0431892	−	0.0594448i
$673$	28.1966	−	9.16162i	1.08690	−	0.353155i	0.289851	−	0.957072i	$-0.406394\pi$
$673$	28.1966	−	9.16162i	1.08690	−	0.353155i	0.797047	+	0.603917i	$0.206394\pi$
$674$	−0.645019	−	1.98517i	−0.0248452	−	0.0764657i
$675$	−1.76788	+	4.67703i	−0.0680456	+	0.180019i
$676$	−12.8694			−0.494977
$677$			19.5894i			0.752882i	0.926441	+	0.376441i	$0.122852\pi$
$677$			19.5894i			0.752882i	−0.926441	+	0.376441i	$0.877148\pi$
$678$	11.8933	+	3.86437i	0.456760	+	0.148410i
$679$	24.8793	+	18.0758i	0.954779	+	0.693687i
$680$	−3.14994	+	17.2422i	−0.120795	+	0.661208i
$681$	−20.8520			−0.799049
$682$	−6.84461	−	11.7875i	−0.262094	−	0.451365i
$683$		−	12.3924i		−	0.474181i	−0.971488	−	0.237091i	$-0.923806\pi$
$683$		−	12.3924i		−	0.474181i	0.971488	−	0.237091i	$-0.0761939\pi$
$684$	0.271681	−	0.197388i	0.0103880	−	0.00754731i
$685$	−4.39668	−	32.7470i	−0.167989	−	1.25120i
$686$	6.10493	−	18.7890i	0.233087	−	0.717369i
$687$		−	7.76908i		−	0.296409i
$688$		−	13.0946i		−	0.499229i
$689$	1.04585	−	3.21881i	0.0398439	−	0.122627i
$690$	5.97656	−	11.0751i	0.227524	−	0.421621i
$691$	−2.02584	−	6.23488i	−0.0770664	−	0.237186i	0.905100	−	0.425198i	$-0.139796\pi$
$691$	−2.02584	−	6.23488i	−0.0770664	−	0.237186i	−0.982167	+	0.188012i	$0.939796\pi$
$692$	13.5517	+	18.6524i	0.515160	+	0.709056i
$693$	−4.43487	−	1.44098i	−0.168467	−	0.0547382i
$694$	−9.81808	+	7.13325i	−0.372689	+	0.270774i
$695$	−39.2143	+	5.26500i	−1.48748	+	0.199713i
$696$	0.284473	+	0.875519i	0.0107829	+	0.0331864i
$697$	13.3729	−	18.4063i	0.506536	−	0.697187i
$698$	−2.22076	+	3.05661i	−0.0840569	+	0.115694i
$699$	5.51563	+	16.9754i	0.208620	+	0.642068i
$700$	−7.43203	−	5.95549i	−0.280905	−	0.225096i
$701$	24.8206	−	18.0332i	0.937460	−	0.681104i	−0.0103482	−	0.999946i	$-0.503294\pi$
$701$	24.8206	−	18.0332i	0.937460	−	0.681104i	0.947808	+	0.318842i	$0.103294\pi$
$702$	0.343713	+	0.111679i	0.0129726	+	0.00421505i
$703$	−1.42809	−	1.96560i	−0.0538614	−	0.0741339i
$704$	0.756512	+	2.32830i	0.0285121	+	0.0877513i
$705$	7.08330	+	3.82243i	0.266773	+	0.143961i
$706$	2.97246	−	9.14830i	0.111870	−	0.344301i
$707$		−	11.8319i		−	0.444984i
$708$			15.0017i			0.563798i
$709$	2.56482	−	7.89371i	0.0963239	−	0.296455i	−0.891273	−	0.453468i	$-0.850187\pi$
$709$	2.56482	−	7.89371i	0.0963239	−	0.296455i	0.987596	+	0.157013i	$0.0501866\pi$
$710$	−3.07707	−	22.9183i	−0.115480	−	0.860110i
$711$	5.35873	−	3.89335i	0.200968	−	0.146012i
$712$			2.31628i			0.0868062i
$713$	−15.7353	−	27.0986i	−0.589292	−	1.01485i
$714$	14.9306			0.558764
$715$	−1.94616	−	0.355540i	−0.0727823	−	0.0132964i
$716$	−11.4398	−	8.31151i	−0.427526	−	0.310616i
$717$	0.00555146	+	0.00180378i	0.000207323	+	6.73634e-5i
$718$			17.8328i			0.665514i
$719$	−3.95627			−0.147544			−0.0737719	−	0.997275i	$-0.523504\pi$
$719$	−3.95627			−0.147544			−0.0737719	+	0.997275i	$0.523504\pi$
$720$	−0.967824	−	2.01577i	−0.0360687	−	0.0751232i
$721$	3.68667	+	11.3464i	0.137299	+	0.422562i
$722$	17.9628	−	5.83647i	0.668507	−	0.217211i
$723$	−8.89166	−	12.2383i	−0.330684	−	0.455148i
$724$	1.22816	−	3.77988i	0.0456441	−	0.140478i
$725$	2.52667	+	3.84739i	0.0938382	+	0.142888i
$726$	−4.05049	−	2.94286i	−0.150328	−	0.109220i
$727$	−34.5530	+	11.2269i	−1.28150	+	0.416384i	−0.869108	−	0.494622i	$-0.835306\pi$
$727$	−34.5530	+	11.2269i	−1.28150	+	0.416384i	−0.412391	+	0.911007i	$0.635306\pi$
$728$	−0.404621	+	0.556913i	−0.0149963	+	0.0206406i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.603605	−	0.325729i	−0.0223404	−	0.0120558i
$731$	83.0401	+	60.3322i	3.07135	+	2.23147i
$732$	−0.755286	−	1.03956i	−0.0279162	−	0.0384233i
$733$	−30.0169	−	9.75308i	−1.10870	−	0.360238i	−0.303255	−	0.952909i	$-0.598073\pi$
$733$	−30.0169	−	9.75308i	−1.10870	−	0.360238i	−0.805445	+	0.592671i	$0.798073\pi$
$734$	15.4310	−	11.2113i	0.569570	−	0.413817i
$735$	3.58065	−	6.63527i	0.132074	−	0.244745i
$736$	1.73917	+	5.35263i	0.0641068	+	0.197300i
$737$	5.50202	+	1.78771i	0.202669	+	0.0658513i
$738$			2.90249i			0.106842i
$739$	26.6088			0.978821			0.489410	−	0.872054i	$-0.337212\pi$
$739$	26.6088			0.978821			0.489410	+	0.872054i	$0.337212\pi$
$740$	−14.5840	+	7.00215i	−0.536117	+	0.257404i
$741$	−0.0981857	−	0.0713361i	−0.00360694	−	0.00262060i
$742$	10.4848	+	14.4311i	0.384908	+	0.529781i
$743$		−	17.0948i		−	0.627146i	−0.949564	−	0.313573i	$-0.898474\pi$
$743$		−	17.0948i		−	0.627146i	0.949564	−	0.313573i	$-0.101526\pi$
$744$	−5.53869	−	0.568226i	−0.203058	−	0.0208322i
$745$	0.406370	−	0.387616i	0.0148882	−	0.0142011i
$746$	−8.58809	+	6.23961i	−0.314432	+	0.228448i
$747$	2.22984	−	3.06911i	0.0815856	−	0.112293i
$748$	−18.2506	−	5.92997i	−0.667307	−	0.216821i
$749$	−24.1990			−0.884213
$750$	−7.32624	−	8.44549i	−0.267516	−	0.308386i
$751$	6.51603	−	20.0543i	0.237773	−	0.731791i	−0.758968	−	0.651128i	$-0.774296\pi$
$751$	6.51603	−	20.0543i	0.237773	−	0.731791i	0.996741	−	0.0806631i	$-0.0257038\pi$
$752$	−3.42339	+	1.11233i	−0.124838	+	0.0405623i
$753$	−7.25419	+	2.35703i	−0.264357	+	0.0858949i
$754$	0.269157	−	0.195554i	0.00980212	−	0.00712166i
$755$	13.4097	+	27.9294i	0.488027	+	1.01645i
$756$	−1.54099	+	1.11959i	−0.0560451	+	0.0407191i
$757$	5.12200	−	7.04983i	0.186162	−	0.256230i	−0.705727	−	0.708484i	$-0.749380\pi$
$757$	5.12200	−	7.04983i	0.186162	−	0.256230i	0.891890	+	0.452253i	$0.149380\pi$
$758$	−10.7676	+	3.49860i	−0.391096	+	0.127075i
$759$	11.1468	+	8.09865i	0.404605	+	0.293962i
$760$	0.0999219	+	0.744230i	0.00362455	+	0.0269961i
$761$	14.6993	+	45.2397i	0.532848	+	1.63994i	0.748253	+	0.663413i	$0.230893\pi$
$761$	14.6993	+	45.2397i	0.532848	+	1.63994i	−0.215405	+	0.976525i	$0.569107\pi$
$762$	−11.1380	+	15.3302i	−0.403488	+	0.555354i
$763$	14.6075	+	20.1055i	0.528828	+	0.727870i
$764$	0.721189	−	2.21959i	0.0260917	−	0.0803020i
$765$	17.2422	+	3.14994i	0.623393	+	0.113886i
$766$	4.90841	+	15.1065i	0.177348	+	0.545822i
$767$	5.15627	−	1.67537i	0.186182	−	0.0604942i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	4.68139			0.168815			0.0844077	−	0.996431i	$-0.473100\pi$
$769$	4.68139			0.168815			0.0844077	+	0.996431i	$0.473100\pi$
$770$	7.54505	−	7.19685i	0.271905	−	0.259356i
$771$	2.07600	−	6.38927i	0.0747654	−	0.230104i
$772$	−0.281716	+	0.387749i	−0.0101392	+	0.0139554i
$773$	−5.03024	−	6.92353i	−0.180925	−	0.249022i	0.708916	−	0.705293i	$-0.249185\pi$
$773$	−5.03024	−	6.92353i	−0.180925	−	0.249022i	−0.889841	+	0.456271i	$0.849185\pi$
$774$	−13.0946			−0.470677
$775$	−27.4621	+	4.56418i	−0.986469	+	0.163950i
$776$	−16.1450			−0.579573
$777$	8.10018	+	11.1489i	0.290592	+	0.399966i
$778$	15.1178	−	20.8079i	0.542001	−	0.746000i
$779$	0.301200	−	0.926999i	0.0107916	−	0.0332132i
$780$	−0.584759	+	0.557772i	−0.0209377	+	0.0199714i
$781$	25.3169			0.905911
$782$	−41.9569	−	13.6326i	−1.50038	−	0.487502i
$783$	0.875519	−	0.284473i	0.0312885	−	0.0101662i
$784$	1.04197	+	3.20685i	0.0372131	+	0.114530i
$785$	30.6119	+	5.59241i	1.09258	+	0.199602i
$786$	1.46528	−	4.50968i	0.0522650	−	0.160855i
$787$	−1.09997	−	1.51398i	−0.0392097	−	0.0539676i	0.788962	−	0.614442i	$-0.210619\pi$
$787$	−1.09997	−	1.51398i	−0.0392097	−	0.0539676i	−0.828172	+	0.560474i	$0.810619\pi$
$788$	−2.19564	+	3.02204i	−0.0782166	+	0.107656i
$789$	7.56910	+	23.2953i	0.269467	+	0.829334i
$790$	1.97090	+	14.6795i	0.0701213	+	0.522272i
$791$	19.2706	+	14.0009i	0.685184	+	0.497815i
$792$	2.32830	−	0.756512i	0.0827327	−	0.0268815i
$793$	−0.272961	+	0.375698i	−0.00969312	+	0.0133414i
$794$	−13.3517	+	9.70060i	−0.473835	+	0.344262i
$795$	9.06350	+	18.8773i	0.321449	+	0.669509i
$796$	−15.0346	+	10.9233i	−0.532889	+	0.387166i
$797$	−32.4528	+	10.5446i	−1.14954	+	0.373507i	−0.820969	−	0.570973i	$-0.806566\pi$
$797$	−32.4528	+	10.5446i	−1.14954	+	0.373507i	−0.328568	+	0.944480i	$0.606566\pi$
$798$	0.608343	−	0.197663i	0.0215351	−	0.00699718i
$799$	8.71904	−	26.8344i	0.308457	−	0.949334i
$800$	4.99442	+	0.236068i	0.176580	+	0.00834626i
$801$	2.31628			0.0818417
$802$	−22.0611	−	7.16807i	−0.779003	−	0.253113i
$803$	0.441386	−	0.607516i	0.0155762	−	0.0214388i
$804$	1.91179	−	1.38900i	0.0674236	−	0.0489861i
$805$	17.3456	−	16.5451i	0.611352	−	0.583138i
$806$	0.423249	+	1.96718i	0.0149083	+	0.0692909i
$807$			7.28450i			0.256426i
$808$	3.65117	+	5.02541i	0.128448	+	0.176793i
$809$	−18.3589	−	13.3386i	−0.645466	−	0.468959i	0.216258	−	0.976336i	$-0.430615\pi$
$809$	−18.3589	−	13.3386i	−0.645466	−	0.468959i	−0.861724	+	0.507378i	$0.830615\pi$
$810$	−2.01577	+	0.967824i	−0.0708268	+	0.0340059i
$811$	17.7777			0.624261			0.312131	−	0.950039i	$-0.398957\pi$
$811$	17.7777			0.624261			0.312131	+	0.950039i	$0.398957\pi$
$812$			1.75348i			0.0615350i
$813$	1.02297	+	0.332384i	0.0358773	+	0.0116572i
$814$	−5.47332	−	16.8452i	−0.191840	−	0.590422i
$815$	−4.95650	+	9.18482i	−0.173618	+	0.321730i
$816$	−6.34153	+	4.60739i	−0.221998	+	0.161291i
$817$	4.18217	+	1.35887i	0.146316	+	0.0475408i
$818$	10.7937	+	14.8563i	0.377394	+	0.519438i
$819$	0.556913	+	0.404621i	0.0194601	+	0.0141386i
$820$	−5.71160	−	3.08221i	−0.199458	−	0.107635i
$821$	34.0938	+	24.7706i	1.18988	+	0.864499i	0.993252	−	0.115979i	$-0.0370006\pi$
$821$	34.0938	+	24.7706i	1.18988	+	0.864499i	0.196629	+	0.980478i	$0.437001\pi$
$822$	8.68529	−	11.9543i	0.302934	−	0.416953i
$823$	35.8219	−	11.6392i	1.24867	−	0.405718i	0.391228	−	0.920294i	$-0.372050\pi$
$823$	35.8219	−	11.6392i	1.24867	−	0.405718i	0.857445	+	0.514575i	$0.172050\pi$
$824$	−5.06721	−	3.68154i	−0.176525	−	0.128253i
$825$	10.2315	−	6.71928i	0.356216	−	0.233935i
$826$	−8.83005	+	27.1761i	−0.307237	+	0.945578i
$827$	16.3253	+	22.4699i	0.567686	+	0.781353i	0.992278	−	0.124032i	$-0.0395824\pi$
$827$	16.3253	+	22.4699i	0.567686	+	0.781353i	−0.424592	+	0.905385i	$0.639582\pi$
$828$	5.35263	−	1.73917i	0.186017	−	0.0604405i
$829$	12.9922	+	39.9858i	0.451237	+	1.38876i	0.875497	+	0.483224i	$0.160534\pi$
$829$	12.9922	+	39.9858i	0.451237	+	1.38876i	−0.424260	+	0.905540i	$0.639466\pi$
$830$	3.67157	+	7.64708i	0.127442	+	0.265434i
$831$	−25.7758			−0.894153
$832$		−	0.361401i		−	0.0125293i
$833$	−25.1371	−	8.16754i	−0.870949	−	0.282988i
$834$	−14.3152	−	10.4006i	−0.495694	−	0.360143i
$835$	−33.6355	−	6.14479i	−1.16400	−	0.212649i
$836$	−0.822120			−0.0284336
$837$	−0.568226	+	5.53869i	−0.0196408	+	0.191445i
$838$			2.75638i			0.0952174i
$839$	10.3755	−	7.53822i	0.358201	−	0.260248i	−0.394100	−	0.919067i	$-0.628944\pi$
$839$	10.3755	−	7.53822i	0.358201	−	0.260248i	0.752301	+	0.658819i	$0.228944\pi$
$840$	−0.566761	−	4.22130i	−0.0195551	−	0.145649i
$841$	−8.69961	+	26.7747i	−0.299987	+	0.923264i
$842$			7.41066i			0.255388i
$843$		−	16.4026i		−	0.564937i
$844$	4.46039	−	13.7277i	0.153533	−	0.472526i
$845$	−25.3247	−	13.6662i	−0.871196	−	0.470132i
$846$	1.11233	+	3.42339i	0.0382425	+	0.117698i
$847$	−5.60544	−	7.71523i	−0.192605	−	0.265098i
$848$	−8.90648	−	2.89389i	−0.305850	−	0.0993766i
$849$	6.64976	−	4.83133i	0.228219	−	0.165811i
$850$	−24.5083	+	30.5847i	−0.840628	+	1.04904i
$851$	−12.5828	−	38.7259i	−0.431334	−	1.32751i
$852$	6.07850	−	8.36633i	0.208246	−	0.286626i
$853$	−13.4759	+	18.5479i	−0.461405	+	0.635069i	−0.974799	−	0.223083i	$-0.928388\pi$
$853$	−13.4759	+	18.5479i	−0.461405	+	0.635069i	0.513395	+	0.858153i	$0.328388\pi$
$854$	−0.756338	−	2.32777i	−0.0258813	−	0.0796546i
$855$	0.744230	−	0.0999219i	0.0254521	−	0.00341726i
$856$	10.2781	−	7.46750i	0.351300	−	0.255234i
$857$	−20.7870	−	6.75411i	−0.710071	−	0.230716i	−0.0683577	−	0.997661i	$-0.521776\pi$
$857$	−20.7870	−	6.75411i	−0.710071	−	0.230716i	−0.641713	+	0.766945i	$0.721776\pi$
$858$	−0.520045	−	0.715781i	−0.0177541	−	0.0244364i
$859$	2.41961	+	7.44679i	0.0825560	+	0.254081i	0.983811	−	0.179207i	$-0.0573532\pi$
$859$	2.41961	+	7.44679i	0.0825560	+	0.254081i	−0.901255	+	0.433288i	$0.857353\pi$
$860$	13.9054	−	25.7680i	0.474171	−	0.878680i
$861$	−1.70842	+	5.25798i	−0.0582228	+	0.179191i
$862$			15.9329i			0.542676i
$863$			40.6749i			1.38459i	0.721615	+	0.692295i	$0.243400\pi$
$863$			40.6749i			1.38459i	−0.721615	+	0.692295i	$0.756600\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	6.86018	+	51.0954i	0.233253	+	1.73729i
$866$	−12.6757	+	9.20942i	−0.430737	+	0.312949i
$867$		−	44.4431i		−	1.50937i
$868$	−9.69909	−	4.28946i	−0.329208	−	0.145594i
$869$	−16.2158			−0.550083
$870$	−0.369934	+	2.02495i	−0.0125420	+	0.0686524i
$871$	−0.690922	−	0.501984i	−0.0234110	−	0.0170091i
$872$	−12.4086	−	4.03181i	−0.420209	−	0.136534i
$873$			16.1450i			0.546427i
$874$	−1.89000			−0.0639302
$875$	−8.30070	−	19.6116i	−0.280615	−	0.662992i
$876$	−0.0947870	−	0.291725i	−0.00320256	−	0.00985646i
$877$	47.9147	−	15.5684i	1.61796	−	0.525709i	0.646504	−	0.762911i	$-0.276230\pi$
$877$	47.9147	−	15.5684i	1.61796	−	0.525709i	0.971460	+	0.237202i	$0.0762303\pi$
$878$	15.0601	+	20.7284i	0.508253	+	0.699550i
$879$	−7.44967	+	22.9277i	−0.251271	+	0.773333i
$880$	−0.983783	+	5.38505i	−0.0331633	+	0.181530i
$881$	45.2388	+	32.8679i	1.52413	+	1.10735i	0.959391	+	0.282079i	$0.0910239\pi$
$881$	45.2388	+	32.8679i	1.52413	+	1.10735i	0.564741	+	0.825268i	$0.308976\pi$
$882$	3.20685	−	1.04197i	0.107980	−	0.0350849i
$883$	−2.54814	+	3.50721i	−0.0857516	+	0.118027i	−0.849738	−	0.527206i	$-0.823240\pi$
$883$	−2.54814	+	3.50721i	−0.0857516	+	0.118027i	0.763986	+	0.645233i	$0.223240\pi$
$884$	2.29183	+	1.66512i	0.0770827	+	0.0560039i
$885$	−15.9305	+	29.5207i	−0.535499	+	0.992327i
$886$	−23.0000	−	16.7105i	−0.772701	−	0.561400i
$887$	−6.13151	−	8.43929i	−0.205876	−	0.283364i	0.693576	−	0.720383i	$-0.256034\pi$
$887$	−6.13151	−	8.43929i	−0.205876	−	0.283364i	−0.899452	+	0.437020i	$0.856034\pi$
$888$	−6.88084	−	2.23572i	−0.230906	−	0.0750259i
$889$	−29.2004	+	21.2153i	−0.979349	+	0.711539i
$890$	−2.45970	+	4.55803i	−0.0824492	+	0.152786i
$891$	−0.756512	−	2.32830i	−0.0253441	−	0.0780011i
$892$	−26.1575	−	8.49909i	−0.875819	−	0.284571i
$893$		−	1.20879i		−	0.0404506i
$894$	0.251150			0.00839972
$895$	−13.6854	−	28.5037i	−0.457453	−	0.952774i
$896$	1.54099	+	1.11959i	0.0514807	+	0.0374029i
$897$	−1.19555	−	1.64554i	−0.0399183	−	0.0549428i
$898$		−	3.67203i		−	0.122537i
$899$	3.81753	+	3.42018i	0.127322	+	0.114069i
$900$	0.236068	−	4.99442i	0.00786893	−	0.166481i
$901$	59.3873	−	43.1474i	1.97848	−	1.43745i
$902$	4.17661	−	5.74861i	0.139066	−	0.191408i
$903$	−23.7214	−	7.70756i	−0.789400	−	0.256492i
$904$	−12.5054			−0.415923
$905$	6.43072	−	6.13394i	0.213764	−	0.203899i
$906$	−4.28157	+	13.1773i	−0.142246	+	0.437788i
$907$	−21.8931	+	7.11348i	−0.726947	+	0.236199i	−0.649032	−	0.760761i	$-0.724826\pi$
$907$	−21.8931	+	7.11348i	−0.726947	+	0.236199i	−0.0779144	+	0.996960i	$0.524826\pi$
$908$	19.8314	−	6.44361i	0.658128	−	0.213839i
$909$	5.02541	−	3.65117i	0.166682	−	0.121102i
$910$	−1.38762	+	0.666233i	−0.0459991	+	0.0220854i
$911$	−1.97255	+	1.43314i	−0.0653536	+	0.0474821i	−0.619982	−	0.784616i	$-0.712860\pi$
$911$	−1.97255	+	1.43314i	−0.0653536	+	0.0474821i	0.554629	+	0.832098i	$0.312860\pi$
$912$	−0.197388	+	0.271681i	−0.00653616	+	0.00899626i
$913$	−8.83273	+	2.86993i	−0.292321	+	0.0949808i
$914$	4.61706	+	3.35449i	0.152719	+	0.110957i
$915$	−0.382342	−	2.84773i	−0.0126398	−	0.0941429i
$916$	2.40078	+	7.38883i	0.0793239	+	0.244134i
$917$	5.30883	−	7.30698i	0.175313	−	0.241298i
$918$	4.60739	+	6.34153i	0.152067	+	0.209302i
$919$	4.28039	−	13.1737i	0.141197	−	0.434560i	−0.855305	−	0.518124i	$-0.826630\pi$
$919$	4.28039	−	13.1737i	0.141197	−	0.434560i	0.996502	+	0.0835644i	$0.0266304\pi$
$920$	−2.26165	+	12.3799i	−0.0745645	+	0.408153i
$921$	1.93235	+	5.94716i	0.0636730	+	0.195965i
$922$	−13.6325	+	4.42947i	−0.448963	+	0.145877i
$923$	−3.55445	−	1.15491i	−0.116996	−	0.0380144i
$924$	4.66310			0.153405
$925$	−36.1344	−	1.70794i	−1.18809	−	0.0561567i
$926$	4.00231	−	12.3179i	0.131524	−	0.404790i
$927$	−3.68154	+	5.06721i	−0.120918	+	0.166429i
$928$	−0.541100	−	0.744761i	−0.0177625	−	0.0244480i
$929$	43.8786			1.43961			0.719805	−	0.694176i	$-0.244231\pi$
$929$	43.8786			1.43961			0.719805	+	0.694176i	$0.244231\pi$
$930$	−10.2958	−	6.99980i	−0.337611	−	0.229532i
$931$	−1.13233			−0.0371107
$932$	−10.4914	−	14.4401i	−0.343656	−	0.473002i
$933$	6.49717	−	8.94258i	0.212708	−	0.292767i
$934$	2.31844	−	7.13542i	0.0758616	−	0.233478i
$935$	−29.6168	−	31.0497i	−0.968573	−	1.01543i
$936$	−0.361401			−0.0118128
$937$	13.5922	+	4.41637i	0.444038	+	0.144277i	0.522498	−	0.852641i	$-0.325000\pi$
$937$	13.5922	+	4.41637i	0.444038	+	0.144277i	−0.0784601	+	0.996917i	$0.525000\pi$
$938$	4.28084	−	1.39093i	0.139775	−	0.0454155i
$939$	−9.21848	−	28.3716i	−0.300834	−	0.925871i
$940$	−7.91782	−	1.44649i	−0.258251	−	0.0471793i
$941$	−12.1017	+	37.2453i	−0.394505	+	1.21416i	0.534842	+	0.844952i	$0.320371\pi$
$941$	−12.1017	+	37.2453i	−0.394505	+	1.21416i	−0.929347	+	0.369209i	$0.879629\pi$
$942$	8.17998	+	11.2588i	0.266518	+	0.366831i
$943$	9.60175	−	13.2157i	0.312676	−	0.430362i
$944$	−4.63578	−	14.2675i	−0.150882	−	0.464366i
$945$	−4.22130	+	0.566761i	−0.137319	+	0.0184367i
$946$	25.9349	+	18.8428i	0.843217	+	0.612633i
$947$	−19.2886	+	6.26725i	−0.626796	+	0.203658i	−0.605155	−	0.796108i	$-0.706889\pi$
$947$	−19.2886	+	6.26725i	−0.626796	+	0.203658i	−0.0216405	+	0.999766i	$0.506889\pi$
$948$	−3.89335	+	5.35873i	−0.126450	+	0.174044i
$949$	−0.0896836	+	0.0651590i	−0.00291125	+	0.00211515i
$950$	−0.593681	+	1.57062i	−0.0192616	+	0.0509577i
$951$	8.39307	−	6.09792i	0.272164	−	0.197739i
$952$	−14.1999	+	4.61381i	−0.460220	+	0.149535i
$953$	11.8470	−	3.84932i	0.383762	−	0.124692i	−0.110781	−	0.993845i	$-0.535335\pi$
$953$	11.8470	−	3.84932i	0.383762	−	0.124692i	0.494543	+	0.869153i	$0.335335\pi$
$954$	−2.89389	+	8.90648i	−0.0936931	+	0.288358i
$955$	3.77619	−	3.60192i	0.122195	−	0.116556i
$956$	−0.00583715			−0.000188787
$957$	−2.14338	−	0.696426i	−0.0692856	−	0.0225123i
$958$	−19.0808	+	26.2625i	−0.616474	+	0.848504i
$959$	22.7701	−	16.5434i	0.735284	−	0.534215i
$960$	1.54336	+	1.61803i	0.0498118	+	0.0522218i
$961$	−28.2569	+	12.7494i	−0.911512	+	0.411272i
$962$			2.61471i			0.0843018i
$963$	−7.46750	−	10.2781i	−0.240637	−	0.331208i
$964$	12.2383	+	8.89166i	0.394170	+	0.286381i
$965$	−0.966125	+	0.463863i	−0.0311007	+	0.0149323i
$966$	10.7202			0.344916
$967$		−	56.2670i		−	1.80942i	−0.426024	−	0.904712i	$-0.640086\pi$
$967$		−	56.2670i		−	1.80942i	0.426024	−	0.904712i	$-0.359914\pi$
$968$	4.76164	+	1.54715i	0.153045	+	0.0497273i
$969$	−0.813431	−	2.50348i	−0.0261312	−	0.0804234i
$970$	−31.7706	−	17.1447i	−1.02009	−	0.550483i
$971$	16.8467	−	12.2398i	0.540635	−	0.392794i	−0.283686	−	0.958917i	$-0.591557\pi$
$971$	16.8467	−	12.2398i	0.540635	−	0.392794i	0.824321	+	0.566123i	$0.191557\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	−19.8107	−	27.2670i	−0.635100	−	0.874141i
$974$	0.896097	+	0.651053i	0.0287128	+	0.0208611i
$975$	−1.74301	+	0.476633i	−0.0558210	+	0.0152645i
$976$	1.03956	+	0.755286i	0.0332756	+	0.0241761i
$977$	−9.03904	+	12.4412i	−0.289184	+	0.398028i	−0.928749	−	0.370709i	$-0.879115\pi$
$977$	−9.03904	+	12.4412i	−0.289184	+	0.398028i	0.639565	+	0.768737i	$0.279115\pi$
$978$	−4.43906	+	1.44234i	−0.141945	+	0.0461208i
$979$	−4.58756	−	3.33306i	−0.146619	−	0.106525i
$980$	−1.35500	+	7.41700i	−0.0432837	+	0.236927i
$981$	−4.03181	+	12.4086i	−0.128726	+	0.396177i
$982$	11.4827	+	15.8046i	0.366427	+	0.504343i
$983$	−21.7459	+	7.06567i	−0.693586	+	0.225360i	−0.634534	−	0.772895i	$-0.718808\pi$
$983$	−21.7459	+	7.06567i	−0.693586	+	0.225360i	−0.0590524	+	0.998255i	$0.518808\pi$
$984$	−0.896920	−	2.76044i	−0.0285928	−	0.0879995i
$985$	−7.52980	+	3.61526i	−0.239919	+	0.115192i
$986$	7.21599			0.229804
$987$			6.85631i			0.218239i
$988$	0.115424	+	0.0375036i	0.00367213	+	0.00119315i
$989$	59.6227	+	43.3184i	1.89589	+	1.37745i
$990$	5.38505	+	0.983783i	0.171148	+	0.0312667i
$991$	27.4451			0.871821			0.435911	−	0.899990i	$-0.356426\pi$
$991$	27.4451			0.871821			0.435911	+	0.899990i	$0.356426\pi$
$992$	5.44320	−	1.17113i	0.172822	−	0.0371836i
$993$			21.8396i			0.693060i
$994$	15.9359	−	11.5781i	0.505455	−	0.367235i
$995$	−41.1852	+	5.52961i	−1.30566	+	0.175300i
$996$	−1.17230	+	3.60796i	−0.0371456	+	0.114323i
$997$		−	24.3120i		−	0.769970i	−0.922923	−	0.384985i	$-0.874207\pi$
$997$		−	24.3120i		−	0.769970i	0.922923	−	0.384985i	$-0.125793\pi$
$998$		−	11.4876i		−	0.363633i
$999$	−2.23572	+	6.88084i	−0.0707351	+	0.217700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.c.109.3	✓	32
5.4	even	2	inner	930.2.z.c.109.6	yes	32
31.2	even	5	inner	930.2.z.c.529.8	yes	32
155.64	even	10	inner	930.2.z.c.529.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.c.109.3	✓	32	1.1	even	1	trivial
930.2.z.c.109.6	yes	32	5.4	even	2	inner
930.2.z.c.529.1	yes	32	155.64	even	10	inner
930.2.z.c.529.8	yes	32	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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.54336i) q^{5} -1.00000 q^{6} +(-1.81154 - 0.588604i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.61803 + 1.54336i) q^{5} -1.00000 q^{6} +(-1.81154 - 0.588604i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.19966 + 0.401852i) q^{10} +(-0.756512 + 2.32830i) q^{11} +(0.587785 + 0.809017i) q^{12} +(0.212426 - 0.292379i) q^{13} +(0.588604 + 1.81154i) q^{14} +(0.297550 + 2.21618i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(7.45492 - 2.42225i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.271681 - 0.197388i) q^{19} +(-0.967824 - 2.01577i) q^{20} +(-1.54099 + 1.11959i) q^{21} +(2.32830 - 0.756512i) q^{22} +(5.35263 - 1.73917i) q^{23} +(0.309017 - 0.951057i) q^{24} +(0.236068 - 4.99442i) q^{25} -0.361401 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.11959 - 1.54099i) q^{28} +(-0.744761 + 0.541100i) q^{29} +(1.61803 - 1.54336i) q^{30} +(-1.17113 - 5.44320i) q^{31} +1.00000i q^{32} +(1.43897 + 1.98057i) q^{33} +(-6.34153 - 4.60739i) q^{34} +(3.83956 - 1.84348i) q^{35} +1.00000 q^{36} -7.23494i q^{37} +(-0.319380 - 0.103773i) q^{38} +(-0.111679 - 0.343713i) q^{39} +(-1.06192 + 1.96782i) q^{40} +(2.34817 - 1.70604i) q^{41} +(1.81154 + 0.588604i) q^{42} +(7.69684 + 10.5938i) q^{43} +(-1.98057 - 1.43897i) q^{44} +(1.96782 + 1.06192i) q^{45} +(-4.55322 - 3.30810i) q^{46} +(2.11577 - 2.91211i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-2.72791 - 1.98194i) q^{49} +(-4.17933 + 2.74467i) q^{50} +(2.42225 - 7.45492i) q^{51} +(0.212426 + 0.292379i) q^{52} +(8.90648 - 2.89389i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-2.36935 - 4.93485i) q^{55} -1.90476 q^{56} -0.335816i q^{57} +(0.875519 + 0.284473i) q^{58} +(12.1366 + 8.81777i) q^{59} +(-2.19966 - 0.401852i) q^{60} -1.28497 q^{61} +(-3.71527 + 4.14690i) q^{62} +1.90476i q^{63} +(0.809017 - 0.587785i) q^{64} +(0.107535 + 0.800930i) q^{65} +(0.756512 - 2.32830i) q^{66} -2.36310i q^{67} +7.83857i q^{68} +(1.73917 - 5.35263i) q^{69} +(-3.74824 - 2.02270i) q^{70} +(-3.19565 - 9.83521i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-0.291725 - 0.0947870i) q^{73} +(-5.85319 + 4.25259i) q^{74} +(-3.90182 - 3.12663i) q^{75} +(0.103773 + 0.319380i) q^{76} +(2.74090 - 3.77252i) q^{77} +(-0.212426 + 0.292379i) q^{78} +(2.04685 + 6.29957i) q^{79} +(2.21618 - 0.297550i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.76044 - 0.896920i) q^{82} +(2.22984 + 3.06911i) q^{83} +(-0.588604 - 1.81154i) q^{84} +(-8.32391 + 15.4249i) q^{85} +(4.04647 - 12.4537i) q^{86} +0.920575i q^{87} +2.44812i q^{88} +(-0.715769 + 2.20291i) q^{89} +(-0.297550 - 2.21618i) q^{90} +(-0.556913 + 0.404621i) q^{91} +5.62808i q^{92} +(-5.09202 - 2.25197i) q^{93} -3.59956 q^{94} +(-0.134948 + 0.738682i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-15.3548 - 4.98909i) q^{97} +3.37188i q^{98} +2.44812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

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