LMFDB - Embedded newform 731.2.m.c.87.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.10
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.692528 - 0.692528i) q^{2} +(0.747939 - 0.309806i) q^{3} -1.04081i q^{4} +(-1.63001 - 3.93520i) q^{5} +(-0.732518 - 0.303419i) q^{6} +(-0.263818 + 0.636914i) q^{7} +(-2.10585 + 2.10585i) q^{8} +(-1.65789 + 1.65789i) q^{9} +O(q^{10})$	\(q+(-0.692528 - 0.692528i) q^{2} +(0.747939 - 0.309806i) q^{3} -1.04081i q^{4} +(-1.63001 - 3.93520i) q^{5} +(-0.732518 - 0.303419i) q^{6} +(-0.263818 + 0.636914i) q^{7} +(-2.10585 + 2.10585i) q^{8} +(-1.65789 + 1.65789i) q^{9} +(-1.59641 + 3.85406i) q^{10} +(-1.48957 - 0.617000i) q^{11} +(-0.322449 - 0.778462i) q^{12} -2.88774i q^{13} +(0.623783 - 0.258379i) q^{14} +(-2.43830 - 2.43830i) q^{15} +0.835097 q^{16} +(2.13370 + 3.52808i) q^{17} +2.29627 q^{18} +(0.262874 + 0.262874i) q^{19} +(-4.09579 + 1.69653i) q^{20} +0.558105i q^{21} +(0.604280 + 1.45886i) q^{22} +(-1.85786 - 0.769551i) q^{23} +(-0.922640 + 2.22745i) q^{24} +(-9.29331 + 9.29331i) q^{25} +(-1.99984 + 1.99984i) q^{26} +(-1.65579 + 3.99744i) q^{27} +(0.662906 + 0.274585i) q^{28} +(-2.34739 - 5.66709i) q^{29} +3.37718i q^{30} +(8.67787 - 3.59449i) q^{31} +(3.63336 + 3.63336i) q^{32} -1.30526 q^{33} +(0.965643 - 3.92094i) q^{34} +2.93641 q^{35} +(1.72555 + 1.72555i) q^{36} +(-0.0896326 + 0.0371270i) q^{37} -0.364095i q^{38} +(-0.894641 - 2.15985i) q^{39} +(11.7195 + 4.85437i) q^{40} +(-0.640398 + 1.54606i) q^{41} +(0.386504 - 0.386504i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-0.642180 + 1.55036i) q^{44} +(9.22649 + 3.82174i) q^{45} +(0.753685 + 1.81956i) q^{46} -9.07791i q^{47} +(0.624602 - 0.258718i) q^{48} +(4.61369 + 4.61369i) q^{49} +12.8718 q^{50} +(2.68890 + 1.97775i) q^{51} -3.00559 q^{52} +(-4.98110 - 4.98110i) q^{53} +(3.91502 - 1.62166i) q^{54} +6.86747i q^{55} +(-0.785682 - 1.89680i) q^{56} +(0.278053 + 0.115174i) q^{57} +(-2.29899 + 5.55025i) q^{58} +(-7.71463 + 7.71463i) q^{59} +(-2.53780 + 2.53780i) q^{60} +(3.09201 - 7.46478i) q^{61} +(-8.49896 - 3.52038i) q^{62} +(-0.618551 - 1.49331i) q^{63} -6.70261i q^{64} +(-11.3638 + 4.70705i) q^{65} +(0.903928 + 0.903928i) q^{66} -13.4250 q^{67} +(3.67205 - 2.22078i) q^{68} -1.62798 q^{69} +(-2.03355 - 2.03355i) q^{70} +(-8.62058 + 3.57076i) q^{71} -6.98251i q^{72} +(4.79092 + 11.5663i) q^{73} +(0.0877846 + 0.0363616i) q^{74} +(-4.07170 + 9.82995i) q^{75} +(0.273601 - 0.273601i) q^{76} +(0.785953 - 0.785953i) q^{77} +(-0.876196 + 2.11532i) q^{78} +(-8.64265 - 3.57990i) q^{79} +(-1.36122 - 3.28627i) q^{80} -3.53101i q^{81} +(1.51418 - 0.627195i) q^{82} +(-10.0813 - 10.0813i) q^{83} +0.580881 q^{84} +(10.4057 - 14.1473i) q^{85} +0.979383 q^{86} +(-3.51140 - 3.51140i) q^{87} +(4.43612 - 1.83750i) q^{88} -1.65962i q^{89} +(-3.74295 - 9.03627i) q^{90} +(1.83924 + 0.761839i) q^{91} +(-0.800956 + 1.93368i) q^{92} +(5.37692 - 5.37692i) q^{93} +(-6.28671 + 6.28671i) q^{94} +(0.605973 - 1.46295i) q^{95} +(3.84317 + 1.59189i) q^{96} +(4.39668 + 10.6145i) q^{97} -6.39022i q^{98} +(3.49246 - 1.44662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.692528	−	0.692528i	−0.489691	−	0.489691i	0.418517	−	0.908209i	$-0.362550\pi$
$2$	−0.692528	−	0.692528i	−0.489691	−	0.489691i	−0.908209	+	0.418517i	$0.862550\pi$
$3$	0.747939	−	0.309806i	0.431823	−	0.178867i	−0.156175	−	0.987729i	$-0.549916\pi$
$3$	0.747939	−	0.309806i	0.431823	−	0.178867i	0.587998	+	0.808863i	$0.299916\pi$
$4$		−	1.04081i		−	0.520405i
$5$	−1.63001	−	3.93520i	−0.728964	−	1.75987i	−0.646021	−	0.763320i	$-0.723568\pi$
$5$	−1.63001	−	3.93520i	−0.728964	−	1.75987i	−0.0829425	−	0.996554i	$-0.526432\pi$
$6$	−0.732518	−	0.303419i	−0.299049	−	0.123870i
$7$	−0.263818	+	0.636914i	−0.0997140	+	0.240731i	−0.965862	−	0.259056i	$-0.916588\pi$
$7$	−0.263818	+	0.636914i	−0.0997140	+	0.240731i	0.866148	+	0.499787i	$0.166588\pi$
$8$	−2.10585	+	2.10585i	−0.744529	+	0.744529i
$9$	−1.65789	+	1.65789i	−0.552629	+	0.552629i
$10$	−1.59641	+	3.85406i	−0.504828	+	1.21876i
$11$	−1.48957	−	0.617000i	−0.449123	−	0.186033i	0.146646	−	0.989189i	$-0.453152\pi$
$11$	−1.48957	−	0.617000i	−0.449123	−	0.186033i	−0.595768	+	0.803156i	$0.703152\pi$
$12$	−0.322449	−	0.778462i	−0.0930831	−	0.224723i
$13$		−	2.88774i		−	0.800915i	−0.916315	−	0.400458i	$-0.868851\pi$
$13$		−	2.88774i		−	0.800915i	0.916315	−	0.400458i	$-0.131149\pi$
$14$	0.623783	−	0.258379i	0.166713	−	0.0690548i
$15$	−2.43830	−	2.43830i	−0.629566	−	0.629566i
$16$	0.835097			0.208774
$17$	2.13370	+	3.52808i	0.517499	+	0.855684i
$17$	2.13370	+	3.52808i	0.517499	+	0.855684i
$18$	2.29627			0.541236
$19$	0.262874	+	0.262874i	0.0603074	+	0.0603074i	0.736617	−	0.676310i	$-0.236422\pi$
$19$	0.262874	+	0.262874i	0.0603074	+	0.0603074i	−0.676310	+	0.736617i	$0.736422\pi$
$20$	−4.09579	+	1.69653i	−0.915847	+	0.379356i
$21$			0.558105i			0.121789i
$22$	0.604280	+	1.45886i	0.128833	+	0.311030i
$23$	−1.85786	−	0.769551i	−0.387391	−	0.160462i	0.180483	−	0.983578i	$-0.442234\pi$
$23$	−1.85786	−	0.769551i	−0.387391	−	0.160462i	−0.567874	+	0.823116i	$0.692234\pi$
$24$	−0.922640	+	2.22745i	−0.188333	+	0.454676i
$25$	−9.29331	+	9.29331i	−1.85866	+	1.85866i
$26$	−1.99984	+	1.99984i	−0.392201	+	0.392201i
$27$	−1.65579	+	3.99744i	−0.318658	+	0.769308i
$28$	0.662906	+	0.274585i	0.125277	+	0.0518916i
$29$	−2.34739	−	5.66709i	−0.435899	−	1.05235i	−0.977352	−	0.211622i	$-0.932125\pi$
$29$	−2.34739	−	5.66709i	−0.435899	−	1.05235i	0.541453	−	0.840731i	$-0.317875\pi$
$30$			3.37718i			0.616586i
$31$	8.67787	−	3.59449i	1.55859	−	0.645590i	0.573747	−	0.819032i	$-0.305489\pi$
$31$	8.67787	−	3.59449i	1.55859	−	0.645590i	0.984844	+	0.173443i	$0.0554891\pi$
$32$	3.63336	+	3.63336i	0.642294	+	0.642294i
$33$	−1.30526			−0.227216
$34$	0.965643	−	3.92094i	0.165606	−	0.672436i
$35$	2.93641			0.496344
$36$	1.72555	+	1.72555i	0.287591	+	0.287591i
$37$	−0.0896326	+	0.0371270i	−0.0147355	+	0.00610365i	−0.390039	−	0.920798i	$-0.627538\pi$
$37$	−0.0896326	+	0.0371270i	−0.0147355	+	0.00610365i	0.375304	+	0.926902i	$0.377538\pi$
$38$		−	0.364095i		−	0.0590640i
$39$	−0.894641	−	2.15985i	−0.143257	−	0.345853i
$40$	11.7195	+	4.85437i	1.85301	+	0.767543i
$41$	−0.640398	+	1.54606i	−0.100013	+	0.241454i	−0.965964	−	0.258675i	$-0.916714\pi$
$41$	−0.640398	+	1.54606i	−0.100013	+	0.241454i	0.865951	+	0.500129i	$0.166714\pi$
$42$	0.386504	−	0.386504i	0.0596388	−	0.0596388i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	−0.642180	+	1.55036i	−0.0968123	+	0.233725i
$45$	9.22649	+	3.82174i	1.37540	+	0.569711i
$46$	0.753685	+	1.81956i	0.111125	+	0.268279i
$47$		−	9.07791i		−	1.32415i	−0.749438	−	0.662074i	$-0.769676\pi$
$47$		−	9.07791i		−	1.32415i	0.749438	−	0.662074i	$-0.230324\pi$
$48$	0.624602	−	0.258718i	0.0901535	−	0.0373428i
$49$	4.61369	+	4.61369i	0.659098	+	0.659098i
$50$	12.8718			1.82034
$51$	2.68890	+	1.97775i	0.376521	+	0.276940i
$52$	−3.00559			−0.416800
$53$	−4.98110	−	4.98110i	−0.684207	−	0.684207i	0.276738	−	0.960945i	$-0.410747\pi$
$53$	−4.98110	−	4.98110i	−0.684207	−	0.684207i	−0.960945	+	0.276738i	$0.910747\pi$
$54$	3.91502	−	1.62166i	0.532767	−	0.220679i
$55$			6.86747i			0.926010i
$56$	−0.785682	−	1.89680i	−0.104991	−	0.253471i
$57$	0.278053	+	0.115174i	0.0368291	+	0.0152551i
$58$	−2.29899	+	5.55025i	−0.301872	+	0.728784i
$59$	−7.71463	+	7.71463i	−1.00436	+	1.00436i	−0.00436818	+	0.999990i	$0.501390\pi$
$59$	−7.71463	+	7.71463i	−1.00436	+	1.00436i	−0.999990	+	0.00436818i	$0.998610\pi$
$60$	−2.53780	+	2.53780i	−0.327629	+	0.327629i
$61$	3.09201	−	7.46478i	0.395892	−	0.955768i	−0.592738	−	0.805396i	$-0.701953\pi$
$61$	3.09201	−	7.46478i	0.395892	−	0.955768i	0.988629	−	0.150372i	$-0.0480471\pi$
$62$	−8.49896	−	3.52038i	−1.07937	−	0.447089i
$63$	−0.618551	−	1.49331i	−0.0779301	−	0.188140i
$64$		−	6.70261i		−	0.837826i
$65$	−11.3638	+	4.70705i	−1.40951	+	0.583838i
$66$	0.903928	+	0.903928i	0.111266	+	0.111266i
$67$	−13.4250			−1.64012			−0.820061	−	0.572276i	$-0.806061\pi$
$67$	−13.4250			−1.64012			−0.820061	+	0.572276i	$0.806061\pi$
$68$	3.67205	−	2.22078i	0.445302	−	0.269309i
$69$	−1.62798			−0.195986
$70$	−2.03355	−	2.03355i	−0.243055	−	0.243055i
$71$	−8.62058	+	3.57076i	−1.02308	+	0.423772i	−0.830208	−	0.557453i	$-0.811779\pi$
$71$	−8.62058	+	3.57076i	−1.02308	+	0.423772i	−0.192867	+	0.981225i	$0.561779\pi$
$72$		−	6.98251i		−	0.822897i
$73$	4.79092	+	11.5663i	0.560734	+	1.35373i	0.909180	+	0.416403i	$0.136710\pi$
$73$	4.79092	+	11.5663i	0.560734	+	1.35373i	−0.348446	+	0.937329i	$0.613290\pi$
$74$	0.0877846	+	0.0363616i	0.0102048	+	0.00422695i
$75$	−4.07170	+	9.82995i	−0.470159	+	1.13506i
$76$	0.273601	−	0.273601i	0.0313842	−	0.0313842i
$77$	0.785953	−	0.785953i	0.0895676	−	0.0895676i
$78$	−0.876196	+	2.11532i	−0.0992096	+	0.239513i
$79$	−8.64265	−	3.57990i	−0.972374	−	0.402770i	−0.160778	−	0.986991i	$-0.551400\pi$
$79$	−8.64265	−	3.57990i	−0.972374	−	0.402770i	−0.811595	+	0.584220i	$0.801400\pi$
$80$	−1.36122	−	3.28627i	−0.152189	−	0.367416i
$81$		−	3.53101i		−	0.392334i
$82$	1.51418	−	0.627195i	0.167214	−	0.0692621i
$83$	−10.0813	−	10.0813i	−1.10657	−	1.10657i	−0.993598	−	0.112972i	$-0.963963\pi$
$83$	−10.0813	−	10.0813i	−1.10657	−	1.10657i	−0.112972	−	0.993598i	$-0.536037\pi$
$84$	0.580881			0.0633794
$85$	10.4057	−	14.1473i	1.12866	−	1.53449i
$86$	0.979383			0.105610
$87$	−3.51140	−	3.51140i	−0.376462	−	0.376462i
$88$	4.43612	−	1.83750i	0.472891	−	0.195878i
$89$		−	1.65962i		−	0.175920i	−0.996124	−	0.0879598i	$-0.971965\pi$
$89$		−	1.65962i		−	0.175920i	0.996124	−	0.0879598i	$-0.0280347\pi$
$90$	−3.74295	−	9.03627i	−0.394541	−	0.952506i
$91$	1.83924	+	0.761839i	0.192805	+	0.0798625i
$92$	−0.800956	+	1.93368i	−0.0835054	+	0.201600i
$93$	5.37692	−	5.37692i	0.557561	−	0.557561i
$94$	−6.28671	+	6.28671i	−0.648424	+	0.648424i
$95$	0.605973	−	1.46295i	0.0621715	−	0.150095i
$96$	3.84317	+	1.59189i	0.392242	+	0.162472i
$97$	4.39668	+	10.6145i	0.446415	+	1.07774i	0.973655	+	0.228025i	$0.0732267\pi$
$97$	4.39668	+	10.6145i	0.446415	+	1.07774i	−0.527241	+	0.849716i	$0.676773\pi$
$98$		−	6.39022i		−	0.645510i
$99$	3.49246	−	1.44662i	0.351005	−	0.145391i
$100$	9.67256	+	9.67256i	0.967256	+	0.967256i
$101$	−10.7021			−1.06490			−0.532449	−	0.846462i	$-0.678728\pi$
$101$	−10.7021			−1.06490			−0.532449	+	0.846462i	$0.678728\pi$
$102$	−0.492490	−	3.23179i	−0.0487638	−	0.319995i
$103$	−2.94014			−0.289700			−0.144850	−	0.989454i	$-0.546270\pi$
$103$	−2.94014			−0.289700			−0.144850	+	0.989454i	$0.546270\pi$
$104$	6.08114	+	6.08114i	0.596305	+	0.596305i
$105$	2.19626	−	0.909719i	0.214333	−	0.0887795i
$106$			6.89911i			0.670101i
$107$	−0.350667	−	0.846585i	−0.0339003	−	0.0818425i	0.906023	−	0.423229i	$-0.139103\pi$
$107$	−0.350667	−	0.846585i	−0.0339003	−	0.0818425i	−0.939923	+	0.341387i	$0.889103\pi$
$108$	4.16057	+	1.72337i	0.400351	+	0.165831i
$109$	−1.42953	+	3.45119i	−0.136924	+	0.330564i	−0.977437	−	0.211228i	$-0.932254\pi$
$109$	−1.42953	+	3.45119i	−0.136924	+	0.330564i	0.840513	+	0.541792i	$0.182254\pi$
$110$	4.75592	−	4.75592i	0.453459	−	0.453459i
$111$	−0.0555375	+	0.0555375i	−0.00527139	+	0.00527139i
$112$	−0.220314	+	0.531885i	−0.0208177	+	0.0502584i
$113$	−17.8481	−	7.39291i	−1.67901	−	0.695467i	−0.679728	−	0.733465i	$-0.737902\pi$
$113$	−17.8481	−	7.39291i	−1.67901	−	0.695467i	−0.999278	+	0.0379979i	$0.987902\pi$
$114$	−0.112799	−	0.272321i	−0.0105646	−	0.0255052i
$115$			8.56543i			0.798730i
$116$	−5.89836	+	2.44318i	−0.547649	+	0.226844i
$117$	4.78755	+	4.78755i	0.442609	+	0.442609i
$118$	10.6852			0.983652
$119$	−2.80999	+	0.428213i	−0.257591	+	0.0392542i
$120$	10.2694			0.937461
$121$	−5.94004	−	5.94004i	−0.540004	−	0.540004i
$122$	−7.31088	+	3.02827i	−0.661896	+	0.274166i
$123$			1.35476i			0.122154i
$124$	−3.74118	−	9.03201i	−0.335968	−	0.811098i
$125$	32.0432	+	13.2727i	2.86603	+	1.18715i
$126$	−0.605798	+	1.46253i	−0.0539688	+	0.130292i
$127$	−2.23177	+	2.23177i	−0.198037	+	0.198037i	−0.799158	−	0.601121i	$-0.794721\pi$
$127$	−2.23177	+	2.23177i	−0.198037	+	0.198037i	0.601121	+	0.799158i	$0.294721\pi$
$128$	2.62498	−	2.62498i	0.232018	−	0.232018i
$129$	−0.309806	+	0.747939i	−0.0272769	+	0.0658523i
$130$	11.1295	+	4.61001i	0.976125	+	0.404324i
$131$	−4.77920	−	11.5380i	−0.417561	−	1.00808i	−0.983052	−	0.183327i	$-0.941313\pi$
$131$	−4.77920	−	11.5380i	−0.417561	−	1.00808i	0.565491	−	0.824754i	$-0.308687\pi$
$132$			1.35853i			0.118244i
$133$	−0.236779	+	0.0980771i	−0.0205313	+	0.00850436i
$134$	9.29718	+	9.29718i	0.803154	+	0.803154i
$135$	18.4297			1.58617
$136$	−11.9228	−	2.93634i	−1.02237	−	0.251789i
$137$	20.5978			1.75979			0.879894	−	0.475171i	$-0.157614\pi$
$137$	20.5978			1.75979			0.879894	+	0.475171i	$0.157614\pi$
$138$	1.12742	+	1.12742i	0.0959724	+	0.0959724i
$139$	17.6200	−	7.29846i	1.49451	−	0.619047i	0.522219	−	0.852812i	$-0.325105\pi$
$139$	17.6200	−	7.29846i	1.49451	−	0.619047i	0.972293	+	0.233765i	$0.0751045\pi$
$140$		−	3.05624i		−	0.258300i
$141$	−2.81239	−	6.78972i	−0.236846	−	0.571797i
$142$	8.44285	+	3.49714i	0.708508	+	0.293474i
$143$	−1.78174	+	4.30149i	−0.148996	+	0.359709i
$144$	−1.38450	+	1.38450i	−0.115375	+	0.115375i
$145$	−18.4749	+	18.4749i	−1.53425	+	1.53425i
$146$	4.69214	−	11.3278i	0.388324	−	0.937498i
$147$	4.88011	+	2.02141i	0.402504	+	0.166723i
$148$	0.0386422	+	0.0932905i	0.00317637	+	0.00766843i
$149$		−	2.72743i		−	0.223440i	−0.993740	−	0.111720i	$-0.964364\pi$
$149$		−	2.72743i		−	0.223440i	0.993740	−	0.111720i	$-0.0356359\pi$
$150$	9.62728	−	3.98775i	0.786065	−	0.325599i
$151$	−4.19636	−	4.19636i	−0.341495	−	0.341495i	0.515434	−	0.856929i	$-0.327631\pi$
$151$	−4.19636	−	4.19636i	−0.341495	−	0.341495i	−0.856929	+	0.515434i	$0.827631\pi$
$152$	−1.10714			−0.0898012
$153$	−9.38659	−	2.31172i	−0.758861	−	0.186891i
$154$	−1.08859			−0.0877210
$155$	−28.2901	−	28.2901i	−2.27231	−	2.27231i
$156$	−2.24800	+	0.931150i	−0.179984	+	0.0745517i
$157$		−	9.13974i		−	0.729431i	−0.931119	−	0.364715i	$-0.881166\pi$
$157$		−	9.13974i		−	0.729431i	0.931119	−	0.364715i	$-0.118834\pi$
$158$	3.50609	+	8.46446i	0.278930	+	0.673396i
$159$	−5.26874	−	2.18238i	−0.417838	−	0.173074i
$160$	8.37558	−	20.2204i	0.662148	−	1.59857i
$161$	0.980276	−	0.980276i	0.0772566	−	0.0772566i
$162$	−2.44532	+	2.44532i	−0.192123	+	0.192123i
$163$	−0.323361	+	0.780663i	−0.0253276	+	0.0611462i	−0.936037	−	0.351901i	$-0.885535\pi$
$163$	−0.323361	+	0.780663i	−0.0253276	+	0.0611462i	0.910710	+	0.413047i	$0.135535\pi$
$164$	1.60915	+	0.666533i	0.125654	+	0.0520475i
$165$	2.12759	+	5.13645i	0.165632	+	0.399872i
$166$			13.9632i			1.08376i
$167$	4.78432	−	1.98173i	0.370222	−	0.153351i	−0.189812	−	0.981820i	$-0.560788\pi$
$167$	4.78432	−	1.98173i	0.370222	−	0.153351i	0.560034	+	0.828469i	$0.310788\pi$
$168$	−1.17528	−	1.17528i	−0.0906752	−	0.0906752i
$169$	4.66095			0.358535
$170$	−17.0037	+	2.59118i	−1.30412	+	0.198735i
$171$	−0.871630			−0.0666552
$172$	0.735963	+	0.735963i	0.0561167	+	0.0561167i
$173$	3.04250	−	1.26024i	0.231317	−	0.0958146i	−0.264014	−	0.964519i	$-0.585047\pi$
$173$	3.04250	−	1.26024i	0.231317	−	0.0958146i	0.495331	+	0.868704i	$0.335047\pi$
$174$			4.86349i			0.368700i
$175$	−3.46729	−	8.37078i	−0.262103	−	0.632772i
$176$	−1.24394	−	0.515255i	−0.0937652	−	0.0388388i
$177$	−3.38003	+	8.16011i	−0.254058	+	0.613351i
$178$	−1.14934	+	1.14934i	−0.0861463	+	0.0861463i
$179$	13.3637	−	13.3637i	0.998852	−	0.998852i	−0.00114703	−	0.999999i	$-0.500365\pi$
$179$	13.3637	−	13.3637i	0.998852	−	0.998852i	0.999999	+	0.00114703i	$0.000365110\pi$
$180$	3.97770	−	9.60302i	0.296480	−	0.715767i
$181$	−24.3399	−	10.0819i	−1.80917	−	0.749381i	−0.982387	−	0.186855i	$-0.940170\pi$
$181$	−24.3399	−	10.0819i	−1.80917	−	0.749381i	−0.826780	−	0.562526i	$-0.809830\pi$
$182$	−0.746132	−	1.80132i	−0.0553070	−	0.133523i
$183$		−	6.54113i		−	0.483534i
$184$	5.53293	−	2.29181i	0.407893	−	0.168955i
$185$	0.292205	+	0.292205i	0.0214833	+	0.0214833i
$186$	−7.44734			−0.546065
$187$	−1.00148	−	6.57181i	−0.0732351	−	0.480579i
$188$	−9.44837			−0.689093
$189$	−2.10920	−	2.10920i	−0.153421	−	0.153421i
$190$	−1.43279	+	0.593479i	−0.103945	+	0.0430555i
$191$			21.1353i			1.52929i	0.644450	+	0.764647i	$0.277087\pi$
$191$			21.1353i			1.52929i	−0.644450	+	0.764647i	$0.722913\pi$
$192$	−2.07651	−	5.01314i	−0.149859	−	0.361792i
$193$	12.3987	+	5.13571i	0.892478	+	0.369676i	0.781323	−	0.624127i	$-0.214545\pi$
$193$	12.3987	+	5.13571i	0.892478	+	0.369676i	0.111154	+	0.993803i	$0.464545\pi$
$194$	4.30603	−	10.3957i	0.309155	−	0.746366i
$195$	−7.04117	+	7.04117i	−0.504229	+	0.504229i
$196$	4.80197	−	4.80197i	0.342998	−	0.342998i
$197$	0.0296641	−	0.0716155i	0.00211348	−	0.00510240i	−0.922819	−	0.385233i	$-0.874121\pi$
$197$	0.0296641	−	0.0716155i	0.00211348	−	0.00510240i	0.924933	+	0.380131i	$0.124121\pi$
$198$	−3.42045	−	1.41680i	−0.243081	−	0.100687i
$199$	−0.260640	−	0.629240i	−0.0184763	−	0.0446056i	0.914372	−	0.404875i	$-0.132685\pi$
$199$	−0.260640	−	0.629240i	−0.0184763	−	0.0446056i	−0.932848	+	0.360269i	$0.882685\pi$
$200$		−	39.1405i		−	2.76765i
$201$	−10.0411	+	4.15914i	−0.708242	+	0.293363i
$202$	7.41150	+	7.41150i	0.521472	+	0.521472i
$203$	4.22874			0.296799
$204$	2.05846	−	2.79863i	0.144121	−	0.195943i
$205$	7.12790			0.497834
$206$	2.03613	+	2.03613i	0.141864	+	0.141864i
$207$	4.35595	−	1.80430i	0.302760	−	0.125407i
$208$		−	2.41154i		−	0.167210i
$209$	−0.229376	−	0.553762i	−0.0158663	−	0.0383045i
$210$	−2.15097	−	0.890963i	−0.148431	−	0.0614823i
$211$	10.1781	−	24.5720i	0.700686	−	1.69161i	−0.0213700	−	0.999772i	$-0.506803\pi$
$211$	10.1781	−	24.5720i	0.700686	−	1.69161i	0.722056	−	0.691834i	$-0.243197\pi$
$212$	−5.18438	+	5.18438i	−0.356065	+	0.356065i
$213$	−5.34142	+	5.34142i	−0.365988	+	0.365988i
$214$	−0.343437	+	0.829131i	−0.0234769	+	0.0566782i
$215$	3.93520	+	1.63001i	0.268378	+	0.111166i
$216$	−4.93115	−	11.9048i	−0.335522	−	0.810022i
$217$			6.47535i			0.439575i
$218$	3.38003	−	1.40006i	0.228925	−	0.0948238i
$219$	7.16662	+	7.16662i	0.484276	+	0.484276i
$220$	7.14773			0.481900
$221$	10.1882	−	6.16158i	0.685330	−	0.414472i
$222$	0.0769226			0.00516271
$223$	5.16211	+	5.16211i	0.345681	+	0.345681i	0.858498	−	0.512817i	$-0.171398\pi$
$223$	5.16211	+	5.16211i	0.345681	+	0.345681i	−0.512817	+	0.858498i	$0.671398\pi$
$224$	−3.27269	+	1.35559i	−0.218666	+	0.0905743i
$225$		−	30.8145i		−	2.05430i
$226$	7.24049	+	17.4801i	0.481630	+	1.16276i
$227$	8.50390	+	3.52243i	0.564424	+	0.233792i	0.646604	−	0.762826i	$-0.276188\pi$
$227$	8.50390	+	3.52243i	0.564424	+	0.233792i	−0.0821807	+	0.996617i	$0.526188\pi$
$228$	0.119874	−	0.289401i	0.00793883	−	0.0191660i
$229$	−3.11637	+	3.11637i	−0.205935	+	0.205935i	−0.802537	−	0.596602i	$-0.796517\pi$
$229$	−3.11637	+	3.11637i	−0.205935	+	0.205935i	0.596602	+	0.802537i	$0.296517\pi$
$230$	5.93180	−	5.93180i	0.391131	−	0.391131i
$231$	0.344351	−	0.831338i	0.0226567	−	0.0546980i
$232$	16.8773	+	6.99079i	1.10805	+	0.458968i
$233$	−4.18074	−	10.0932i	−0.273889	−	0.661227i	0.725754	−	0.687955i	$-0.241491\pi$
$233$	−4.18074	−	10.0932i	−0.273889	−	0.661227i	−0.999643	+	0.0267277i	$0.991491\pi$
$234$		−	6.63103i		−	0.433484i
$235$	−35.7234	+	14.7971i	−2.33033	+	0.965256i
$236$	8.02945	+	8.02945i	0.522673	+	0.522673i
$237$	−7.57325			−0.491935
$238$	2.24255	+	1.64945i	0.145363	+	0.106918i
$239$	−10.8426			−0.701349			−0.350675	−	0.936497i	$-0.614048\pi$
$239$	−10.8426			−0.701349			−0.350675	+	0.936497i	$0.614048\pi$
$240$	−2.03622	−	2.03622i	−0.131437	−	0.131437i
$241$	8.57272	−	3.55094i	0.552217	−	0.228736i	−0.0890852	−	0.996024i	$-0.528394\pi$
$241$	8.57272	−	3.55094i	0.552217	−	0.228736i	0.641303	+	0.767288i	$0.278394\pi$
$242$			8.22729i			0.528871i
$243$	−6.06131	−	14.6333i	−0.388833	−	0.938726i
$244$	−7.76942	−	3.21820i	−0.497386	−	0.206024i
$245$	10.6354	−	25.6761i	0.679471	−	1.64039i
$246$	0.938207	−	0.938207i	0.0598179	−	0.0598179i
$247$	0.759111	−	0.759111i	0.0483011	−	0.0483011i
$248$	−10.7048	+	25.8437i	−0.679756	+	1.64108i
$249$	−10.6635	−	4.41696i	−0.675771	−	0.279913i
$250$	−12.9991	−	31.3826i	−0.822134	−	1.98481i
$251$			9.21553i			0.581679i	0.956772	+	0.290840i	$0.0939346\pi$
$251$			9.21553i			0.581679i	−0.956772	+	0.290840i	$0.906065\pi$
$252$	−1.55425	+	0.643793i	−0.0979088	+	0.0405552i
$253$	2.29260	+	2.29260i	0.144135	+	0.144135i
$254$	3.09112			0.193954
$255$	3.39990	−	13.8051i	0.212910	−	0.864509i
$256$	−17.0410			−1.06506
$257$	6.14012	+	6.14012i	0.383010	+	0.383010i	0.872186	−	0.489175i	$-0.162702\pi$
$257$	6.14012	+	6.14012i	0.383010	+	0.383010i	−0.489175	+	0.872186i	$0.662702\pi$
$258$	0.732518	−	0.303419i	0.0456046	−	0.0188900i
$259$		−	0.0668831i		−	0.00415591i
$260$	4.89914	+	11.8276i	0.303832	+	0.733515i
$261$	13.2871	+	5.50370i	0.822452	+	0.340671i
$262$	−4.68067	+	11.3001i	−0.289173	+	0.698125i
$263$	4.63811	−	4.63811i	0.285998	−	0.285998i	−0.549497	−	0.835496i	$-0.685181\pi$
$263$	4.63811	−	4.63811i	0.285998	−	0.285998i	0.835496	+	0.549497i	$0.185181\pi$
$264$	2.74867	−	2.74867i	0.169169	−	0.169169i
$265$	−11.4824	+	27.7209i	−0.705356	+	1.70288i
$266$	0.231897	+	0.0960550i	0.0142185	+	0.00588951i
$267$	−0.514162	−	1.24130i	−0.0314662	−	0.0759661i
$268$			13.9728i			0.853527i
$269$	11.5596	−	4.78815i	0.704802	−	0.291939i	−0.00134975	−	0.999999i	$-0.500430\pi$
$269$	11.5596	−	4.78815i	0.704802	−	0.291939i	0.706152	+	0.708061i	$0.250430\pi$
$270$	−12.7631	−	12.7631i	−0.776736	−	0.776736i
$271$	−17.4578			−1.06049			−0.530243	−	0.847846i	$-0.677899\pi$
$271$	−17.4578			−1.06049			−0.530243	+	0.847846i	$0.677899\pi$
$272$	1.78185	+	2.94629i	0.108040	+	0.178645i
$273$	1.61166			0.0975423
$274$	−14.2645	−	14.2645i	−0.861753	−	0.861753i
$275$	19.5770	−	8.10906i	1.18054	−	0.488995i
$276$			1.69441i			0.101992i
$277$	1.97174	+	4.76020i	0.118470	+	0.286012i	0.971980	−	0.235065i	$-0.0755303\pi$
$277$	1.97174	+	4.76020i	0.118470	+	0.286012i	−0.853509	+	0.521077i	$0.825530\pi$
$278$	−17.2568	−	7.14798i	−1.03499	−	0.428708i
$279$	−8.42767	+	20.3462i	−0.504551	+	1.21809i
$280$	−6.18363	+	6.18363i	−0.369542	+	0.369542i
$281$	12.8591	−	12.8591i	0.767107	−	0.767107i	−0.210489	−	0.977596i	$-0.567506\pi$
$281$	12.8591	−	12.8591i	0.767107	−	0.767107i	0.977596	+	0.210489i	$0.0675056\pi$
$282$	−2.75441	+	6.64973i	−0.164023	+	0.395986i
$283$	−2.44584	−	1.01310i	−0.145390	−	0.0602226i	0.308802	−	0.951126i	$-0.400072\pi$
$283$	−2.44584	−	1.01310i	−0.145390	−	0.0602226i	−0.454192	+	0.890904i	$0.650072\pi$
$284$	3.71648	+	8.97238i	0.220533	+	0.532413i
$285$		−	1.28193i		−	0.0759350i
$286$	4.21281	−	1.74500i	0.249109	−	0.103184i
$287$	−0.815757	−	0.815757i	−0.0481526	−	0.0481526i
$288$	−12.0474			−0.709901
$289$	−7.89463	+	15.0557i	−0.464390	+	0.885631i
$290$	25.5887			1.50262
$291$	6.57689	+	6.57689i	0.385544	+	0.385544i
$292$	12.0383	−	4.98643i	0.704489	−	0.291809i
$293$		−	14.0423i		−	0.820361i	−0.912004	−	0.410180i	$-0.865466\pi$
$293$		−	14.0423i		−	0.820361i	0.912004	−	0.410180i	$-0.134534\pi$
$294$	−1.97973	−	4.77949i	−0.115460	−	0.278746i
$295$	42.9335	+	17.7836i	2.49969	+	1.03540i
$296$	0.110569	−	0.266936i	0.00642667	−	0.0155154i
$297$	4.93284	−	4.93284i	0.286233	−	0.286233i
$298$	−1.88882	+	1.88882i	−0.109417	+	0.109417i
$299$	−2.22226	+	5.36502i	−0.128517	+	0.310267i
$300$	10.2311	+	4.23786i	0.590693	+	0.244673i
$301$	−0.263818	−	0.636914i	−0.0152062	−	0.0367111i
$302$			5.81219i			0.334454i
$303$	−8.00452	+	3.31558i	−0.459847	+	0.190475i
$304$	0.219525	+	0.219525i	0.0125906	+	0.0125906i
$305$	−34.4154			−1.97062
$306$	4.89955	+	8.10141i	0.280089	+	0.463127i
$307$	3.77538			0.215472			0.107736	−	0.994180i	$-0.465640\pi$
$307$	3.77538			0.215472			0.107736	+	0.994180i	$0.465640\pi$
$308$	−0.818027	−	0.818027i	−0.0466114	−	0.0466114i
$309$	−2.19904	+	0.910873i	−0.125099	+	0.0518178i
$310$			39.1833i			2.22546i
$311$	−5.16493	−	12.4692i	−0.292876	−	0.707066i	0.707124	−	0.707090i	$-0.249992\pi$
$311$	−5.16493	−	12.4692i	−0.292876	−	0.707066i	−1.00000		2.41730e-5i	$0.999992\pi$
$312$	6.43229	+	2.66434i	0.364157	+	0.150839i
$313$	−0.875256	+	2.11306i	−0.0494724	+	0.119437i	−0.946684	−	0.322165i	$-0.895590\pi$
$313$	−0.875256	+	2.11306i	−0.0494724	+	0.119437i	0.897211	+	0.441602i	$0.145590\pi$
$314$	−6.32953	+	6.32953i	−0.357196	+	0.357196i
$315$	−4.86824	+	4.86824i	−0.274294	+	0.274294i
$316$	−3.72599	+	8.99535i	−0.209604	+	0.506028i
$317$	19.8022	+	8.20234i	1.11220	+	0.460689i	0.861696	−	0.507426i	$-0.169403\pi$
$317$	19.8022	+	8.20234i	1.11220	+	0.460689i	0.250507	+	0.968115i	$0.419403\pi$
$318$	2.13739	+	5.16011i	0.119859	+	0.289365i
$319$			9.88988i			0.553727i
$320$	−26.3761	+	10.9253i	−1.47447	+	0.610745i
$321$	−0.524555	−	0.524555i	−0.0292778	−	0.0292778i
$322$	−1.35774			−0.0756637
$323$	−0.366544	+	1.48833i	−0.0203951	+	0.0828130i
$324$	−3.67510			−0.204172
$325$	26.8367	+	26.8367i	1.48863	+	1.48863i
$326$	0.764568	−	0.316694i	0.0423455	−	0.0175401i
$327$			3.02416i			0.167236i
$328$	−1.90718	−	4.60434i	−0.105306	−	0.254232i
$329$	5.78185	+	2.39492i	0.318763	+	0.132036i
$330$	2.08372	−	5.03055i	0.114705	−	0.276923i
$331$	1.42182	−	1.42182i	0.0781501	−	0.0781501i	−0.666951	−	0.745101i	$-0.732401\pi$
$331$	1.42182	−	1.42182i	0.0781501	−	0.0781501i	0.745101	+	0.666951i	$0.232401\pi$
$332$	−10.4927	+	10.4927i	−0.575864	+	0.575864i
$333$	0.0870484	−	0.210153i	0.00477022	−	0.0115163i
$334$	−4.68568	−	1.94087i	−0.256389	−	0.106200i
$335$	21.8829	+	52.8299i	1.19559	+	2.88641i
$336$			0.466072i			0.0254263i
$337$	−12.2039	+	5.05503i	−0.664791	+	0.275365i	−0.689453	−	0.724331i	$-0.742149\pi$
$337$	−12.2039	+	5.05503i	−0.664791	+	0.275365i	0.0246623	+	0.999696i	$0.492149\pi$
$338$	−3.22784	−	3.22784i	−0.175571	−	0.175571i
$339$	−15.6396			−0.849429
$340$	−14.7247	−	10.8304i	−0.798558	−	0.587359i
$341$	−15.1441			−0.820099
$342$	0.603629	+	0.603629i	0.0326405	+	0.0326405i
$343$	−8.61410	+	3.56808i	−0.465118	+	0.192658i
$344$		−	2.97812i		−	0.160569i
$345$	2.65362	+	6.40642i	0.142866	+	0.344910i
$346$	−2.97977	−	1.23426i	−0.160194	−	0.0663543i
$347$	−7.37729	+	17.8104i	−0.396034	+	0.956110i	0.592563	+	0.805524i	$0.298116\pi$
$347$	−7.37729	+	17.8104i	−0.396034	+	0.956110i	−0.988597	+	0.150586i	$0.951884\pi$
$348$	−3.65470	+	3.65470i	−0.195913	+	0.195913i
$349$	25.2608	−	25.2608i	1.35218	−	1.35218i	0.468962	−	0.883218i	$-0.344628\pi$
$349$	25.2608	−	25.2608i	1.35218	−	1.35218i	0.883218	−	0.468962i	$-0.155372\pi$
$350$	−3.39581	+	8.19820i	−0.181513	+	0.438212i
$351$	11.5436	+	4.78150i	0.616150	+	0.255218i
$352$	−3.17037	−	7.65394i	−0.168981	−	0.407956i
$353$		−	20.0852i		−	1.06903i	−0.845159	−	0.534515i	$-0.820494\pi$
$353$		−	20.0852i		−	1.06903i	0.845159	−	0.534515i	$-0.179506\pi$
$354$	7.99187	−	3.31034i	0.424763	−	0.175943i
$355$	28.1033	+	28.1033i	1.49157	+	1.49157i
$356$	−1.72735			−0.0915494
$357$	−1.96904	+	1.19083i	−0.104213	+	0.0630254i
$358$	−18.5095			−0.978259
$359$	−12.6955	−	12.6955i	−0.670040	−	0.670040i	0.287685	−	0.957725i	$-0.407114\pi$
$359$	−12.6955	−	12.6955i	−0.670040	−	0.670040i	−0.957725	+	0.287685i	$0.907114\pi$
$360$	−27.4776	+	11.3816i	−1.44820	+	0.599862i
$361$		−	18.8618i		−	0.992726i
$362$	9.87404	+	23.8380i	0.518968	+	1.25290i
$363$	−6.28305	−	2.60253i	−0.329775	−	0.136597i
$364$	0.792929	−	1.91430i	0.0415608	−	0.100337i
$365$	37.7064	−	37.7064i	1.97364	−	1.97364i
$366$	−4.52992	+	4.52992i	−0.236782	+	0.236782i
$367$	−3.54924	+	8.56863i	−0.185269	+	0.447279i	−0.989038	−	0.147663i	$-0.952825\pi$
$367$	−3.54924	+	8.56863i	−0.185269	+	0.447279i	0.803769	+	0.594942i	$0.202825\pi$
$368$	−1.55149	−	0.642650i	−0.0808772	−	0.0335004i
$369$	−1.50148	−	3.62490i	−0.0781641	−	0.188705i
$370$		−	0.404720i		−	0.0210404i
$371$	4.48664	−	1.85843i	0.232935	−	0.0964848i
$372$	−5.59635	−	5.59635i	−0.290157	−	0.290157i
$373$	−14.5383			−0.752767			−0.376384	−	0.926464i	$-0.622833\pi$
$373$	−14.5383			−0.752767			−0.376384	+	0.926464i	$0.622833\pi$
$374$	−3.85762	+	5.24472i	−0.199473	+	0.271198i
$375$	28.0783			1.44996
$376$	19.1167	+	19.1167i	0.985867	+	0.985867i
$377$	−16.3651	+	6.77865i	−0.842845	+	0.349118i
$378$			2.92136i			0.150258i
$379$	0.741763	+	1.79078i	0.0381018	+	0.0919859i	0.941785	−	0.336216i	$-0.109147\pi$
$379$	0.741763	+	1.79078i	0.0381018	+	0.0919859i	−0.903683	+	0.428202i	$0.859147\pi$
$380$	−1.52265	−	0.630702i	−0.0781103	−	0.0323543i
$381$	−0.977809	+	2.36064i	−0.0500947	+	0.120939i
$382$	14.6368	−	14.6368i	0.748882	−	0.748882i
$383$	−12.3813	+	12.3813i	−0.632653	+	0.632653i	−0.948733	−	0.316079i	$-0.897633\pi$
$383$	−12.3813	+	12.3813i	−0.632653	+	0.632653i	0.316079	+	0.948733i	$0.397633\pi$
$384$	1.15009	−	2.77656i	0.0586903	−	0.141691i
$385$	−4.37399	−	1.81177i	−0.222919	−	0.0923362i
$386$	−5.02982	−	12.1431i	−0.256011	−	0.618066i
$387$		−	2.34461i		−	0.119183i
$388$	11.0477	−	4.57610i	0.560861	−	0.232316i
$389$	3.18259	+	3.18259i	0.161364	+	0.161364i	0.783171	−	0.621807i	$-0.213601\pi$
$389$	3.18259	+	3.18259i	0.161364	+	0.161364i	−0.621807	+	0.783171i	$0.713601\pi$
$390$	9.75242			0.493833
$391$	−1.24909	−	8.19667i	−0.0631690	−	0.414523i
$392$	−19.4314			−0.981436
$393$	−7.14910	−	7.14910i	−0.360625	−	0.360625i
$394$	−0.0701390	+	0.0290525i	−0.00353355	+	0.00146365i
$395$			39.8458i			2.00486i
$396$	−1.50566	−	3.63498i	−0.0756622	−	0.182665i
$397$	18.7361	+	7.76074i	0.940337	+	0.389500i	0.799591	−	0.600545i	$-0.205050\pi$
$397$	18.7361	+	7.76074i	0.940337	+	0.389500i	0.140746	+	0.990046i	$0.455050\pi$
$398$	−0.255266	+	0.616266i	−0.0127953	+	0.0308906i
$399$	−0.146711	+	0.146711i	−0.00734475	+	0.00734475i
$400$	−7.76081	+	7.76081i	−0.388041	+	0.388041i
$401$	−1.12644	+	2.71947i	−0.0562519	+	0.135804i	−0.949507	−	0.313746i	$-0.898416\pi$
$401$	−1.12644	+	2.71947i	−0.0562519	+	0.135804i	0.893255	+	0.449550i	$0.148416\pi$
$402$	9.83404	+	4.07339i	0.490478	+	0.203162i
$403$	−10.3800	−	25.0594i	−0.517063	−	1.24830i
$404$			11.1388i			0.554178i
$405$	−13.8952	+	5.75558i	−0.690458	+	0.285997i
$406$	−2.92852	−	2.92852i	−0.145340	−	0.145340i
$407$	0.156422			0.00775353
$408$	−9.82725	+	1.49757i	−0.486521	+	0.0741407i
$409$	7.90911			0.391080			0.195540	−	0.980696i	$-0.437354\pi$
$409$	7.90911			0.391080			0.195540	+	0.980696i	$0.437354\pi$
$410$	−4.93627	−	4.93627i	−0.243785	−	0.243785i
$411$	15.4059	−	6.38133i	0.759916	−	0.314768i
$412$			3.06012i			0.150761i
$413$	−2.87829	−	6.94881i	−0.141632	−	0.341929i
$414$	−4.26615	−	1.76710i	−0.209670	−	0.0868480i
$415$	−23.2393	+	56.1047i	−1.14077	+	2.75407i
$416$	10.4922	−	10.4922i	0.514423	−	0.514423i
$417$	10.9176	−	10.9176i	0.534637	−	0.534637i
$418$	−0.224647	+	0.542345i	−0.0109878	+	0.0265270i
$419$	24.3386	+	10.0814i	1.18902	+	0.492508i	0.887435	−	0.460932i	$-0.152485\pi$
$419$	24.3386	+	10.0814i	1.18902	+	0.492508i	0.301583	+	0.953440i	$0.402485\pi$
$420$	−0.946844	−	2.28588i	−0.0462012	−	0.111540i
$421$		−	18.0060i		−	0.877561i	−0.898594	−	0.438780i	$-0.855411\pi$
$421$		−	18.0060i		−	0.877561i	0.898594	−	0.438780i	$-0.144589\pi$
$422$	−24.0654	+	9.96821i	−1.17148	+	0.485245i
$423$	15.0501	+	15.0501i	0.731763	+	0.731763i
$424$	20.9789			1.01882
$425$	−52.6166	−	12.9583i	−2.55228	−	0.628572i
$426$	7.39817			0.358443
$427$	3.93870	+	3.93870i	0.190607	+	0.190607i
$428$	−0.881134	+	0.364978i	−0.0425912	+	0.0176419i
$429$			3.76925i			0.181981i
$430$	−1.59641	−	3.85406i	−0.0769855	−	0.185860i
$431$	−25.1792	−	10.4296i	−1.21284	−	0.502375i	−0.317714	−	0.948187i	$-0.602915\pi$
$431$	−25.1792	−	10.4296i	−1.21284	−	0.502375i	−0.895127	+	0.445812i	$0.852915\pi$
$432$	−1.38275	+	3.33825i	−0.0665275	+	0.160612i
$433$	28.5460	−	28.5460i	1.37183	−	1.37183i	0.514109	−	0.857725i	$-0.328123\pi$
$433$	28.5460	−	28.5460i	1.37183	−	1.37183i	0.857725	−	0.514109i	$-0.171877\pi$
$434$	4.48436	−	4.48436i	0.215256	−	0.215256i
$435$	−8.09444	+	19.5417i	−0.388099	+	0.936953i
$436$	3.59203	+	1.48787i	0.172027	+	0.0712559i
$437$	−0.286088	−	0.690678i	−0.0136854	−	0.0330396i
$438$		−	9.92618i		−	0.474291i
$439$	−28.6460	+	11.8656i	−1.36720	+	0.566312i	−0.941027	−	0.338331i	$-0.890138\pi$
$439$	−28.6460	+	11.8656i	−1.36720	+	0.566312i	−0.426171	+	0.904643i	$0.640138\pi$
$440$	−14.4618	−	14.4618i	−0.689441	−	0.689441i
$441$	−15.2980			−0.728474
$442$	−11.3227	−	2.78853i	−0.538564	−	0.132637i
$443$	13.9616			0.663334			0.331667	−	0.943396i	$-0.392389\pi$
$443$	13.9616			0.663334			0.331667	+	0.943396i	$0.392389\pi$
$444$	0.0578040	+	0.0578040i	0.00274326	+	0.00274326i
$445$	−6.53094	+	2.70521i	−0.309596	+	0.128239i
$446$		−	7.14982i		−	0.338554i
$447$	−0.844976	−	2.03995i	−0.0399660	−	0.0964864i
$448$	4.26899	+	1.76827i	0.201691	+	0.0835430i
$449$	4.34999	−	10.5018i	0.205289	−	0.495611i	−0.787381	−	0.616466i	$-0.788564\pi$
$449$	4.34999	−	10.5018i	0.205289	−	0.495611i	0.992670	+	0.120855i	$0.0385638\pi$
$450$	−21.3399	+	21.3399i	−1.00597	+	1.00597i
$451$	1.90784	−	1.90784i	0.0898366	−	0.0898366i
$452$	−7.69461	+	18.5764i	−0.361924	+	0.873762i
$453$	−4.43868	−	1.83856i	−0.208547	−	0.0863831i
$454$	−3.44981	−	8.32857i	−0.161908	−	0.390879i
$455$		−	8.47959i		−	0.397529i
$456$	−0.828076	+	0.343000i	−0.0387782	+	0.0160625i
$457$	5.11611	+	5.11611i	0.239321	+	0.239321i	0.816569	−	0.577248i	$-0.195873\pi$
$457$	5.11611	+	5.11611i	0.239321	+	0.239321i	−0.577248	+	0.816569i	$0.695873\pi$
$458$	4.31635			0.201690
$459$	−17.6362	+	2.68758i	−0.823189	+	0.125445i
$460$	8.91498			0.415663
$461$	−20.1018	−	20.1018i	−0.936235	−	0.936235i	0.0618503	−	0.998085i	$-0.480300\pi$
$461$	−20.1018	−	20.1018i	−0.936235	−	0.936235i	−0.998085	+	0.0618503i	$0.980300\pi$
$462$	−0.814198	+	0.337252i	−0.0378799	+	0.0156904i
$463$			2.34672i			0.109061i	0.998512	+	0.0545307i	$0.0173663\pi$
$463$			2.34672i			0.109061i	−0.998512	+	0.0545307i	$0.982634\pi$
$464$	−1.96030	−	4.73257i	−0.0910045	−	0.219704i
$465$	−29.9237	−	12.3948i	−1.38768	−	0.574795i
$466$	−4.09454	+	9.88510i	−0.189676	+	0.457918i
$467$	−5.38642	+	5.38642i	−0.249254	+	0.249254i	−0.820664	−	0.571410i	$-0.806396\pi$
$467$	−5.38642	+	5.38642i	−0.249254	+	0.249254i	0.571410	+	0.820664i	$0.306396\pi$
$468$	4.98293	−	4.98293i	0.230336	−	0.230336i
$469$	3.54176	−	8.55056i	0.163543	−	0.394828i
$470$	34.9868	+	14.4920i	1.61382	+	0.668467i
$471$	−2.83155	−	6.83597i	−0.130471	−	0.314985i
$472$		−	32.4916i		−	1.49555i
$473$	1.48957	−	0.617000i	0.0684905	−	0.0283697i
$474$	5.24469	+	5.24469i	0.240896	+	0.240896i
$475$	−4.88593			−0.224182
$476$	0.445688	+	2.92466i	0.0204281	+	0.134052i
$477$	16.5162			0.756226
$478$	7.50880	+	7.50880i	0.343445	+	0.343445i
$479$	−5.21518	+	2.16020i	−0.238288	+	0.0987020i	−0.498632	−	0.866814i	$-0.666164\pi$
$479$	−5.21518	+	2.16020i	−0.238288	+	0.0987020i	0.260344	+	0.965516i	$0.416164\pi$
$480$		−	17.7185i		−	0.808733i
$481$	0.107213	+	0.258836i	0.00488850	+	0.0118019i
$482$	−8.39597	−	3.47773i	−0.382426	−	0.158406i
$483$	0.429491	−	1.03688i	0.0195425	−	0.0471798i
$484$	−6.18245	+	6.18245i	−0.281021	+	0.281021i
$485$	34.6036	−	34.6036i	1.57127	−	1.57127i
$486$	−5.93634	+	14.3316i	−0.269278	+	0.650094i
$487$	32.8164	+	13.5930i	1.48705	+	0.615957i	0.970673	−	0.240403i	$-0.0772797\pi$
$487$	32.8164	+	13.5930i	1.48705	+	0.615957i	0.516379	+	0.856360i	$0.327280\pi$
$488$	9.20838	+	22.2310i	0.416844	+	1.00635i
$489$			0.684067i			0.0309346i
$490$	−25.1468	+	10.4161i	−1.13602	+	0.470553i
$491$	−15.0786	−	15.0786i	−0.680485	−	0.680485i	0.279624	−	0.960110i	$-0.409790\pi$
$491$	−15.0786	−	15.0786i	−0.680485	−	0.680485i	−0.960110	+	0.279624i	$0.909790\pi$
$492$	1.41004			0.0635697
$493$	14.9853	−	20.3736i	0.674905	−	0.917583i
$494$	−1.05141			−0.0473053
$495$	−11.3855	−	11.3855i	−0.511740	−	0.511740i
$496$	7.24686	−	3.00175i	0.325394	−	0.134783i
$497$		−	6.43260i		−	0.288542i
$498$	4.32589	+	10.4436i	0.193848	+	0.467990i
$499$	−6.70625	−	2.77782i	−0.300213	−	0.124352i	0.227492	−	0.973780i	$-0.426947\pi$
$499$	−6.70625	−	2.77782i	−0.300213	−	0.124352i	−0.527705	+	0.849428i	$0.676947\pi$
$500$	13.8144	−	33.3509i	0.617798	−	1.49150i
$501$	2.96443	−	2.96443i	0.132441	−	0.132441i
$502$	6.38202	−	6.38202i	0.284843	−	0.284843i
$503$	0.717727	−	1.73275i	0.0320019	−	0.0772593i	−0.907071	−	0.420978i	$-0.861687\pi$
$503$	0.717727	−	1.73275i	0.0320019	−	0.0772593i	0.939073	+	0.343719i	$0.111687\pi$
$504$	4.44726	+	1.84212i	0.198097	+	0.0820544i
$505$	17.4445	+	42.1149i	0.776272	+	1.87409i
$506$		−	3.17538i		−	0.141163i
$507$	3.48611	−	1.44399i	0.154824	−	0.0641300i
$508$	2.32284	+	2.32284i	0.103059	+	0.103059i
$509$	−18.3652			−0.814023			−0.407011	−	0.913423i	$-0.633429\pi$
$509$	−18.3652			−0.814023			−0.407011	+	0.913423i	$0.633429\pi$
$510$	−11.9150	+	7.20590i	−0.527603	+	0.319083i
$511$	−8.63067			−0.381798
$512$	6.55138	+	6.55138i	0.289533	+	0.289533i
$513$	−1.48609	+	0.615557i	−0.0656123	+	0.0271775i
$514$		−	8.50442i		−	0.375114i
$515$	4.79246	+	11.5700i	0.211181	+	0.509836i
$516$	0.778462	+	0.322449i	0.0342699	+	0.0141950i
$517$	−5.60107	+	13.5222i	−0.246335	+	0.594705i
$518$	−0.0463184	+	0.0463184i	−0.00203511	+	0.00203511i
$519$	1.88517	−	1.88517i	0.0827499	−	0.0827499i
$520$	14.0181	−	33.8428i	0.614737	−	1.48411i
$521$	21.4410	+	8.88115i	0.939347	+	0.389090i	0.799217	−	0.601043i	$-0.205248\pi$
$521$	21.4410	+	8.88115i	0.939347	+	0.389090i	0.140130	+	0.990133i	$0.455248\pi$
$522$	−5.39023	−	13.0132i	−0.235924	−	0.569571i
$523$			18.7527i			0.819996i	0.912086	+	0.409998i	$0.134471\pi$
$523$			18.7527i			0.819996i	−0.912086	+	0.409998i	$0.865529\pi$
$524$	−12.0089	+	4.97424i	−0.524610	+	0.217301i
$525$	−5.18665	−	5.18665i	−0.226364	−	0.226364i
$526$	−6.42405			−0.280102
$527$	31.1976	+	22.9466i	1.35899	+	0.999570i
$528$	−1.09002			−0.0474369
$529$	−13.4040	−	13.4040i	−0.582783	−	0.582783i
$530$	27.1494	−	11.2456i	1.17929	−	0.488479i
$531$		−	25.5800i		−	1.11008i
$532$	0.102080	+	0.246442i	0.00442571	+	0.0106846i
$533$	4.46462	+	1.84930i	0.193384	+	0.0801023i
$534$	−0.503561	+	1.21570i	−0.0217912	+	0.0526087i
$535$	−2.75989	+	2.75989i	−0.119320	+	0.119320i
$536$	28.2709	−	28.2709i	1.22112	−	1.22112i
$537$	5.85509	−	14.1354i	0.252666	−	0.609989i
$538$	−11.3213	−	4.68943i	−0.488095	−	0.202176i
$539$	−4.02577	−	9.71906i	−0.173402	−	0.418630i
$540$		−	19.1818i		−	0.825453i
$541$	−40.4473	+	16.7538i	−1.73897	+	0.720303i	−0.740109	+	0.672487i	$0.765226\pi$
$541$	−40.4473	+	16.7538i	−1.73897	+	0.720303i	−0.998856	+	0.0478165i	$0.984774\pi$
$542$	12.0900	+	12.0900i	0.519310	+	0.519310i
$543$	−21.3282			−0.915279
$544$	−5.06627	+	20.5713i	−0.217214	+	0.881987i
$545$	15.9113			0.681564
$546$	−1.11612	−	1.11612i	−0.0477656	−	0.0477656i
$547$	27.5357	−	11.4057i	1.17734	−	0.487671i	0.293729	−	0.955889i	$-0.405104\pi$
$547$	27.5357	−	11.4057i	1.17734	−	0.487671i	0.883613	+	0.468218i	$0.155104\pi$
$548$		−	21.4384i		−	0.915802i
$549$	7.24956	+	17.5020i	0.309404	+	0.746967i
$550$	−19.1734	−	7.94188i	−0.817556	−	0.338643i
$551$	0.872664	−	2.10680i	0.0371767	−	0.0897526i
$552$	3.42827	−	3.42827i	0.145917	−	0.145917i
$553$	4.56018	−	4.56018i	0.193919	−	0.193919i
$554$	1.93109	−	4.66205i	0.0820440	−	0.198072i
$555$	0.309078	+	0.128024i	0.0131196	+	0.00543433i
$556$	−7.59630	−	18.3391i	−0.322155	−	0.777751i
$557$			10.6896i			0.452935i	0.974019	+	0.226467i	$0.0727177\pi$
$557$			10.6896i			0.452935i	−0.974019	+	0.226467i	$0.927282\pi$
$558$	19.9267	−	8.25392i	0.843565	−	0.349416i
$559$	2.04194	+	2.04194i	0.0863649	+	0.0863649i
$560$	2.45219			0.103624
$561$	−2.78503	−	4.60505i	−0.117584	−	0.194425i
$562$	−17.8105			−0.751292
$563$	−15.0971	−	15.0971i	−0.636265	−	0.636265i	0.313367	−	0.949632i	$-0.398543\pi$
$563$	−15.0971	−	15.0971i	−0.636265	−	0.636265i	−0.949632	+	0.313367i	$0.898543\pi$
$564$	−7.06680	+	2.92717i	−0.297566	+	0.123256i
$565$			82.2862i			3.46181i
$566$	0.992214	+	2.39542i	0.0417059	+	0.100687i
$567$	2.24895	+	0.931545i	0.0944469	+	0.0391212i
$568$	10.6341	−	25.6731i	0.446199	−	1.07722i
$569$	−12.9046	+	12.9046i	−0.540988	+	0.540988i	−0.923818	−	0.382831i	$-0.874949\pi$
$569$	−12.9046	+	12.9046i	−0.540988	+	0.540988i	0.382831	+	0.923818i	$0.374949\pi$
$570$	−0.887772	+	0.887772i	−0.0371847	+	0.0371847i
$571$	−16.4316	+	39.6693i	−0.687639	+	1.66011i	0.0618456	+	0.998086i	$0.480301\pi$
$571$	−16.4316	+	39.6693i	−0.687639	+	1.66011i	−0.749485	+	0.662022i	$0.769699\pi$
$572$	4.47704	+	1.85445i	0.187194	+	0.0775384i
$573$	6.54784	+	15.8079i	0.273540	+	0.660384i
$574$			1.12987i			0.0471599i
$575$	24.4173	−	10.1140i	1.01827	−	0.421783i
$576$	11.1122	+	11.1122i	0.463007	+	0.463007i
$577$	−11.3658			−0.473162			−0.236581	−	0.971612i	$-0.576027\pi$
$577$	−11.3658			−0.473162			−0.236581	+	0.971612i	$0.576027\pi$
$578$	15.8938	−	4.95925i	0.661094	−	0.206278i
$579$	10.8645			0.451515
$580$	19.2288	+	19.2288i	0.798433	+	0.798433i
$581$	9.08059	−	3.76130i	0.376726	−	0.156045i
$582$		−	9.10936i		−	0.377595i
$583$	4.34636	+	10.4930i	0.180008	+	0.434578i
$584$	−34.4458	−	14.2679i	−1.42538	−	0.590410i
$585$	11.0362	−	26.6437i	0.456290	−	1.10158i
$586$	−9.72470	+	9.72470i	−0.401724	+	0.401724i
$587$	−24.5818	+	24.5818i	−1.01460	+	1.01460i	−0.0147064	+	0.999892i	$0.504681\pi$
$587$	−24.5818	+	24.5818i	−1.01460	+	1.01460i	−0.999892	+	0.0147064i	$0.995319\pi$
$588$	2.10390	−	5.07926i	0.0867633	−	0.209465i
$589$	3.22608	+	1.33629i	0.132928	+	0.0550607i
$590$	−17.4170	−	42.0483i	−0.717046	−	1.73110i
$591$		−	0.0627542i		−	0.00258136i
$592$	−0.0748519	+	0.0310047i	−0.00307640	+	0.00127428i
$593$	29.4201	+	29.4201i	1.20814	+	1.20814i	0.971629	+	0.236510i	$0.0760038\pi$
$593$	29.4201	+	29.4201i	1.20814	+	1.20814i	0.236510	+	0.971629i	$0.423996\pi$
$594$	−6.83227			−0.280331
$595$	6.26542	+	10.3599i	0.256857	+	0.424714i
$596$	−2.83874			−0.116279
$597$	−0.389885	−	0.389885i	−0.0159569	−	0.0159569i
$598$	5.25441	−	2.17645i	0.214869	−	0.0890015i
$599$		−	39.0810i		−	1.59681i	−0.602123	−	0.798403i	$-0.705678\pi$
$599$		−	39.0810i		−	1.59681i	0.602123	−	0.798403i	$-0.294322\pi$
$600$	−12.1260	−	29.2747i	−0.495042	−	1.19514i
$601$	−16.1751	−	6.69993i	−0.659795	−	0.273296i	0.0275575	−	0.999620i	$-0.491227\pi$
$601$	−16.1751	−	6.69993i	−0.659795	−	0.273296i	−0.687352	+	0.726324i	$0.741227\pi$
$602$	−0.258379	+	0.623783i	−0.0105308	+	0.0254235i
$603$	22.2571	−	22.2571i	0.906379	−	0.906379i
$604$	−4.36761	+	4.36761i	−0.177715	+	0.177715i
$605$	−13.6929	+	33.0576i	−0.556696	+	1.34398i
$606$	7.83948	+	3.24722i	0.318457	+	0.131909i
$607$	−7.70189	−	18.5940i	−0.312610	−	0.754707i	−0.999607	−	0.0280467i	$-0.991071\pi$
$607$	−7.70189	−	18.5940i	−0.312610	−	0.754707i	0.686997	−	0.726661i	$-0.258929\pi$
$608$			1.91023i			0.0774701i
$609$	3.16284	−	1.31009i	0.128165	−	0.0530875i
$610$	23.8336	+	23.8336i	0.964996	+	0.964996i
$611$	−26.2146			−1.06053
$612$	−2.40606	+	9.76965i	−0.0972590	+	0.394915i
$613$	−5.98927			−0.241904			−0.120952	−	0.992658i	$-0.538595\pi$
$613$	−5.98927			−0.241904			−0.120952	+	0.992658i	$0.538595\pi$
$614$	−2.61456	−	2.61456i	−0.105515	−	0.105515i
$615$	5.33124	−	2.20827i	0.214976	−	0.0890460i
$616$			3.31019i			0.133371i
$617$	7.88282	+	19.0308i	0.317350	+	0.766152i	0.999393	+	0.0348391i	$0.0110919\pi$
$617$	7.88282	+	19.0308i	0.317350	+	0.766152i	−0.682043	+	0.731312i	$0.738908\pi$
$618$	2.15370	+	0.892093i	0.0866347	+	0.0358853i
$619$	5.29195	−	12.7759i	0.212701	−	0.513507i	−0.781135	−	0.624362i	$-0.785359\pi$
$619$	5.29195	−	12.7759i	0.212701	−	0.513507i	0.993837	+	0.110855i	$0.0353590\pi$
$620$	−29.4446	+	29.4446i	−1.18252	+	1.18252i
$621$	6.15247	−	6.15247i	0.246890	−	0.246890i
$622$	−5.05844	+	12.2122i	−0.202825	+	0.489663i
$623$	1.05704	+	0.437839i	0.0423493	+	0.0175417i
$624$	−0.747112	−	1.80369i	−0.0299084	−	0.0722053i
$625$		−	82.0175i		−	3.28070i
$626$	2.06949	−	0.857211i	0.0827135	−	0.0342610i
$627$	−0.343118	−	0.343118i	−0.0137028	−	0.0137028i
$628$	−9.51273			−0.379599
$629$	−0.322236	−	0.237013i	−0.0128484	−	0.00945031i
$630$	6.74278			0.268639
$631$	19.1582	+	19.1582i	0.762675	+	0.762675i	0.976805	−	0.214130i	$-0.0686917\pi$
$631$	19.1582	+	19.1582i	0.762675	+	0.762675i	−0.214130	+	0.976805i	$0.568692\pi$
$632$	25.7388	−	10.6614i	1.02383	−	0.424086i
$633$		−	21.5316i		−	0.855803i
$634$	−8.03323	−	19.3939i	−0.319040	−	0.770231i
$635$	12.4202	+	5.14463i	0.492882	+	0.204159i
$636$	−2.27144	+	5.48375i	−0.0900686	+	0.217445i
$637$	13.3231	−	13.3231i	0.527882	−	0.527882i
$638$	6.84902	−	6.84902i	0.271155	−	0.271155i
$639$	8.37204	−	20.2119i	0.331193	−	0.799570i
$640$	−14.6086	−	6.05107i	−0.577455	−	0.239190i
$641$	7.75280	+	18.7169i	0.306217	+	0.739273i	0.999821	+	0.0189169i	$0.00602178\pi$
$641$	7.75280	+	18.7169i	0.306217	+	0.739273i	−0.693604	+	0.720356i	$0.743978\pi$
$642$			0.726538i			0.0286742i
$643$	34.8785	−	14.4471i	1.37547	−	0.569740i	0.432207	−	0.901775i	$-0.357735\pi$
$643$	34.8785	−	14.4471i	1.37547	−	0.569740i	0.943267	+	0.332035i	$0.107735\pi$
$644$	−1.02028	−	1.02028i	−0.0402047	−	0.0402047i
$645$	3.44828			0.135776
$646$	1.28455	−	0.776870i	0.0505401	−	0.0305655i
$647$	29.5069			1.16003			0.580017	−	0.814604i	$-0.303046\pi$
$647$	29.5069			1.16003			0.580017	+	0.814604i	$0.303046\pi$
$648$	7.43576	+	7.43576i	0.292104	+	0.292104i
$649$	16.2514	−	6.73155i	0.637924	−	0.264237i
$650$		−	37.1703i		−	1.45794i
$651$	2.00611	+	4.84317i	0.0786255	+	0.189819i
$652$	0.812521	+	0.336557i	0.0318208	+	0.0131806i
$653$	−12.0580	+	29.1106i	−0.471866	+	1.13919i	0.491472	+	0.870894i	$0.336459\pi$
$653$	−12.0580	+	29.1106i	−0.471866	+	1.13919i	−0.963338	+	0.268292i	$0.913541\pi$
$654$	2.09431	−	2.09431i	0.0818941	−	0.0818941i
$655$	−37.6142	+	37.6142i	−1.46971	+	1.46971i
$656$	−0.534795	+	1.29111i	−0.0208802	+	0.0504093i
$657$	−27.1184	−	11.2328i	−1.05799	−	0.438234i
$658$	−2.34554	−	5.66264i	−0.0914388	−	0.220753i
$659$			19.0489i			0.742039i	0.928625	+	0.371019i	$0.120992\pi$
$659$			19.0489i			0.742039i	−0.928625	+	0.371019i	$0.879008\pi$
$660$	5.34607	−	2.21441i	0.208095	−	0.0861959i
$661$	−9.01257	−	9.01257i	−0.350548	−	0.350548i	0.509765	−	0.860314i	$-0.329732\pi$
$661$	−9.01257	−	9.01257i	−0.350548	−	0.350548i	−0.860314	+	0.509765i	$0.829732\pi$
$662$	−1.96930			−0.0765389
$663$	5.71123	−	7.76484i	0.221806	−	0.301561i
$664$	42.4595			1.64775
$665$	0.771905	+	0.771905i	0.0299332	+	0.0299332i
$666$	−0.205821	+	0.0852537i	−0.00797538	+	0.00330351i
$667$			12.3351i			0.477617i
$668$	−2.06261	−	4.97957i	−0.0798046	−	0.192665i
$669$	5.46020	+	2.26169i	0.211103	+	0.0874419i
$670$	21.4317	−	51.7407i	0.827979	−	1.99892i
$671$	−9.21155	+	9.21155i	−0.355608	+	0.355608i
$672$	−2.02780	+	2.02780i	−0.0782241	+	0.0782241i
$673$	10.5194	−	25.3960i	0.405493	−	0.978946i	−0.580816	−	0.814035i	$-0.697266\pi$
$673$	10.5194	−	25.3960i	0.405493	−	0.978946i	0.986308	−	0.164911i	$-0.0527336\pi$
$674$	11.9523	+	4.95081i	0.460386	+	0.190698i
$675$	−21.7616	−	52.5372i	−0.837606	−	2.02216i
$676$		−	4.85117i		−	0.186583i
$677$	27.1879	−	11.2616i	1.04492	−	0.432819i	0.206843	−	0.978374i	$-0.433681\pi$
$677$	27.1879	−	11.2616i	1.04492	−	0.432819i	0.838075	+	0.545555i	$0.183681\pi$
$678$	10.8309	+	10.8309i	0.415958	+	0.415958i
$679$	−7.92046			−0.303959
$680$	7.87930	+	51.7050i	0.302157	+	1.98279i
$681$	7.45167			0.285549
$682$	10.4877	+	10.4877i	0.401596	+	0.401596i
$683$	−37.7397	+	15.6323i	−1.44407	+	0.598153i	−0.960781	−	0.277308i	$-0.910558\pi$
$683$	−37.7397	+	15.6323i	−1.44407	+	0.598153i	−0.483289	+	0.875461i	$0.660558\pi$
$684$			0.907201i			0.0346877i
$685$	−33.5746	−	81.0563i	−1.28282	−	3.09700i
$686$	8.43650	+	3.49451i	0.322107	+	0.133421i
$687$	−1.36538	+	3.29632i	−0.0520926	+	0.125763i
$688$	−0.590503	+	0.590503i	−0.0225127	+	0.0225127i
$689$	−14.3841	+	14.3841i	−0.547992	+	0.547992i
$690$	2.59891	−	6.27433i	0.0989390	−	0.238860i
$691$	−4.18271	−	1.73254i	−0.159118	−	0.0659088i	0.301703	−	0.953402i	$-0.402445\pi$
$691$	−4.18271	−	1.73254i	−0.159118	−	0.0659088i	−0.460821	+	0.887493i	$0.652445\pi$
$692$	−1.31167	−	3.16666i	−0.0498624	−	0.120378i
$693$			2.60604i			0.0989954i
$694$	17.4432	−	7.22519i	0.662133	−	0.274265i
$695$	−57.4417	−	57.4417i	−2.17889	−	2.17889i
$696$	14.7890			0.560574
$697$	−6.82103	+	1.03945i	−0.258365	+	0.0393721i
$698$	−34.9876			−1.32430
$699$	−6.25387	−	6.25387i	−0.236543	−	0.236543i
$700$	−8.71239	+	3.60879i	−0.329297	+	0.136399i
$701$		−	25.3423i		−	0.957167i	−0.878042	−	0.478584i	$-0.841150\pi$
$701$		−	25.3423i		−	0.957167i	0.878042	−	0.478584i	$-0.158850\pi$
$702$	−4.68292	−	11.3056i	−0.176745	−	0.426701i
$703$	−0.0333218	−	0.0138023i	−0.00125676	−	0.000520565i
$704$	−4.13551	+	9.98401i	−0.155863	+	0.376287i
$705$	−22.1346	+	22.1346i	−0.833639	+	0.833639i
$706$	−13.9096	+	13.9096i	−0.523495	+	0.523495i
$707$	2.82341	−	6.81632i	0.106185	−	0.256354i
$708$	8.49312	+	3.51796i	0.319191	+	0.132213i
$709$	−9.98505	−	24.1060i	−0.374996	−	0.905321i	−0.992887	−	0.119058i	$-0.962013\pi$
$709$	−9.98505	−	24.1060i	−0.374996	−	0.905321i	0.617891	−	0.786264i	$-0.287987\pi$
$710$		−	38.9247i		−	1.46082i
$711$	20.2636	−	8.39346i	0.759945	−	0.314779i
$712$	3.49491	+	3.49491i	0.130977	+	0.130977i
$713$	−18.8884			−0.707377
$714$	2.18830	+	0.538931i	0.0818950	+	0.0201690i
$715$	19.8315			0.741655
$716$	−13.9091	−	13.9091i	−0.519807	−	0.519807i
$717$	−8.10960	+	3.35910i	−0.302858	+	0.125448i
$718$			17.5839i			0.656226i
$719$	10.1076	+	24.4018i	0.376948	+	0.910033i	0.992535	+	0.121964i	$0.0389192\pi$
$719$	10.1076	+	24.4018i	0.376948	+	0.910033i	−0.615586	+	0.788069i	$0.711081\pi$
$720$	7.70502	+	3.19152i	0.287149	+	0.118941i
$721$	0.775662	−	1.87261i	0.0288872	−	0.0697398i
$722$	−13.0623	+	13.0623i	−0.486129	+	0.486129i
$723$	5.31177	−	5.31177i	0.197547	−	0.197547i
$724$	−10.4933	+	25.3331i	−0.389982	+	0.941499i
$725$	74.4810	+	30.8511i	2.76616	+	1.14578i
$726$	2.54887	+	6.15351i	0.0945974	+	0.228378i
$727$			41.5495i			1.54099i	0.637449	+	0.770493i	$0.279990\pi$
$727$			41.5495i			1.54099i	−0.637449	+	0.770493i	$0.720010\pi$
$728$	−5.47748	+	2.26885i	−0.203009	+	0.0840890i
$729$	−1.57658	−	1.57658i	−0.0583920	−	0.0583920i
$730$	−52.2255			−1.93295
$731$	−4.00348	−	0.985971i	−0.148074	−	0.0364675i
$732$	−6.80807			−0.251633
$733$	5.33581	+	5.33581i	0.197083	+	0.197083i	0.798748	−	0.601666i	$-0.205496\pi$
$733$	5.33581	+	5.33581i	0.197083	+	0.197083i	−0.601666	+	0.798748i	$0.705496\pi$
$734$	8.39197	−	3.47607i	0.309753	−	0.128304i
$735$		−	22.4991i		−	0.829892i
$736$	−3.95423	−	9.54634i	−0.145755	−	0.351883i
$737$	19.9975	+	8.28322i	0.736616	+	0.305116i
$738$	−1.47053	+	3.55016i	−0.0541308	+	0.130683i
$739$	−18.0816	+	18.0816i	−0.665144	+	0.665144i	−0.956588	−	0.291444i	$-0.905864\pi$
$739$	−18.0816	+	18.0816i	−0.665144	+	0.665144i	0.291444	+	0.956588i	$0.405864\pi$
$740$	0.304129	−	0.304129i	0.0111800	−	0.0111800i
$741$	0.332591	−	0.802946i	0.0122180	−	0.0294970i
$742$	−4.39414	−	1.82011i	−0.161314	−	0.0668184i
$743$	−2.51708	−	6.07677i	−0.0923427	−	0.222935i	0.870959	−	0.491355i	$-0.163498\pi$
$743$	−2.51708	−	6.07677i	−0.0923427	−	0.222935i	−0.963302	+	0.268420i	$0.913498\pi$
$744$			22.6459i			0.830240i
$745$	−10.7330	+	4.44575i	−0.393226	+	0.162880i
$746$	10.0682	+	10.0682i	0.368624	+	0.368624i
$747$	33.4274			1.22305
$748$	−6.84000	+	1.04235i	−0.250095	+	0.0381119i
$749$	0.631715			0.0230823
$750$	−19.4450	−	19.4450i	−0.710033	−	0.710033i
$751$	32.2536	−	13.3599i	1.17695	−	0.487509i	0.293467	−	0.955969i	$-0.405191\pi$
$751$	32.2536	−	13.3599i	1.17695	−	0.487509i	0.883485	+	0.468460i	$0.155191\pi$
$752$		−	7.58093i		−	0.276448i
$753$	2.85503	+	6.89266i	0.104043	+	0.251182i
$754$	16.0277	+	6.63889i	0.583694	+	0.241774i
$755$	−9.67338	+	23.3536i	−0.352050	+	0.849925i
$756$	−2.19527	+	2.19527i	−0.0798413	+	0.0798413i
$757$	33.4876	−	33.4876i	1.21713	−	1.21713i	0.248492	−	0.968634i	$-0.420065\pi$
$757$	33.4876	−	33.4876i	1.21713	−	1.21713i	0.968634	−	0.248492i	$-0.0799351\pi$
$758$	0.726470	−	1.75385i	0.0263866	−	0.0637029i
$759$	2.42499	+	1.00446i	0.0880215	+	0.0364597i
$760$	1.80466	+	4.35683i	0.0654618	+	0.158039i
$761$		−	23.3859i		−	0.847739i	−0.905723	−	0.423870i	$-0.860671\pi$
$761$		−	23.3859i		−	0.847739i	0.905723	−	0.423870i	$-0.139329\pi$
$762$	2.31197	−	0.957649i	0.0837538	−	0.0346920i
$763$	−1.82097	−	1.82097i	−0.0659237	−	0.0659237i
$764$	21.9978			0.795852
$765$	6.20320	+	40.7062i	0.224277	+	1.47174i
$766$	17.1488			0.619610
$767$	22.2778	+	22.2778i	0.804406	+	0.804406i
$768$	−12.7456	+	5.27940i	−0.459917	+	0.190504i
$769$		−	44.7659i		−	1.61430i	−0.590348	−	0.807149i	$-0.701009\pi$
$769$		−	44.7659i		−	1.61430i	0.590348	−	0.807149i	$-0.298991\pi$
$770$	1.77441	+	4.28381i	0.0639454	+	0.154378i
$771$	6.49469	+	2.69019i	0.233900	+	0.0968847i
$772$	5.34529	−	12.9047i	0.192381	−	0.464449i
$773$	6.06051	−	6.06051i	0.217981	−	0.217981i	−0.589666	−	0.807647i	$-0.700741\pi$
$773$	6.06051	−	6.06051i	0.217981	−	0.217981i	0.807647	+	0.589666i	$0.200741\pi$
$774$	−1.62371	+	1.62371i	−0.0583629	+	0.0583629i
$775$	−47.2414	+	114.051i	−1.69696	+	4.09683i
$776$	−31.6113	−	13.0938i	−1.13478	−	0.470040i
$777$	−0.0207208	−	0.0500245i	−0.000743355	−	0.00179462i
$778$		−	4.40807i		−	0.158037i
$779$	−0.574762	+	0.238074i	−0.0205930	+	0.00852990i
$780$	7.32852	+	7.32852i	0.262403	+	0.262403i
$781$	15.0441			0.538321
$782$	−4.81139	+	6.54145i	−0.172055	+	0.233922i
$783$	26.5407			0.948486
$784$	3.85288	+	3.85288i	0.137603	+	0.137603i
$785$	−35.9667	+	14.8979i	−1.28371	+	0.531728i
$786$			9.90191i			0.353190i
$787$	11.8363	+	28.5755i	0.421920	+	1.01861i	0.981780	+	0.190019i	$0.0608548\pi$
$787$	11.8363	+	28.5755i	0.421920	+	1.01861i	−0.559860	+	0.828587i	$0.689145\pi$
$788$	−0.0745381	−	0.0308747i	−0.00265531	−	0.00109987i
$789$	2.03211	−	4.90594i	0.0723450	−	0.174656i
$790$	27.5943	−	27.5943i	0.981763	−	0.981763i
$791$	9.41730	−	9.41730i	0.334841	−	0.334841i
$792$	−4.30821	+	10.4009i	−0.153086	+	0.369582i
$793$	−21.5564	−	8.92894i	−0.765489	−	0.317076i
$794$	−7.60074	−	18.3498i	−0.269740	−	0.651210i
$795$			24.2908i			0.861507i
$796$	−0.654919	+	0.271276i	−0.0232130	+	0.00961513i
$797$	−8.03043	−	8.03043i	−0.284452	−	0.284452i	0.550429	−	0.834882i	$-0.314464\pi$
$797$	−8.03043	−	8.03043i	−0.284452	−	0.284452i	−0.834882	+	0.550429i	$0.814464\pi$
$798$	0.203203			0.00719332
$799$	32.0275	−	19.3695i	1.13305	−	0.685245i
$800$	−67.5319			−2.38761
$801$	2.75147	+	2.75147i	0.0972183	+	0.0972183i
$802$	2.66341	−	1.10322i	0.0940481	−	0.0389560i
$803$		−	20.1848i		−	0.712307i
$804$	4.32888	+	10.4508i	0.152668	+	0.368572i
$805$	−5.45544	−	2.25972i	−0.192279	−	0.0796446i
$806$	−10.1660	+	24.5428i	−0.358080	+	0.864483i
$807$	7.16248	−	7.16248i	0.252131	−	0.252131i
$808$	22.5370	−	22.5370i	0.792848	−	0.792848i
$809$	8.92675	−	21.5511i	0.313848	−	0.757696i	−0.685708	−	0.727877i	$-0.740507\pi$
$809$	8.92675	−	21.5511i	0.313848	−	0.757696i	0.999555	−	0.0298184i	$-0.00949290\pi$
$810$	13.6087	+	5.63692i	0.478162	+	0.198061i
$811$	−0.542853	−	1.31056i	−0.0190622	−	0.0460201i	0.914062	−	0.405575i	$-0.132929\pi$
$811$	−0.542853	−	1.31056i	−0.0190622	−	0.0460201i	−0.933124	+	0.359555i	$0.882929\pi$
$812$		−	4.40131i		−	0.154456i
$813$	−13.0574	+	5.40854i	−0.457942	+	0.189686i
$814$	−0.108326	−	0.108326i	−0.00379684	−	0.00379684i
$815$	3.59914			0.126073
$816$	2.24549	+	1.65161i	0.0786079	+	0.0578180i
$817$	−0.371760			−0.0130062
$818$	−5.47728	−	5.47728i	−0.191509	−	0.191509i
$819$	−4.31230	+	1.78621i	−0.150684	+	0.0624154i
$820$		−	7.41879i		−	0.259075i
$821$	0.0749599	+	0.180969i	0.00261612	+	0.00631587i	0.925182	−	0.379523i	$-0.123912\pi$
$821$	0.0749599	+	0.180969i	0.00261612	+	0.00631587i	−0.922566	+	0.385839i	$0.873912\pi$
$822$	−15.0883	−	6.24976i	−0.526263	−	0.217985i
$823$	8.71964	−	21.0511i	0.303947	−	0.733794i	−0.695930	−	0.718110i	$-0.745007\pi$
$823$	8.71964	−	21.0511i	0.303947	−	0.733794i	0.999877	−	0.0156840i	$-0.00499256\pi$
$824$	6.19147	−	6.19147i	0.215690	−	0.215690i
$825$	12.1302	−	12.1302i	0.422318	−	0.422318i
$826$	−2.81895	+	6.80555i	−0.0980838	+	0.236795i
$827$	40.4122	+	16.7393i	1.40527	+	0.582082i	0.951114	−	0.308839i	$-0.0999406\pi$
$827$	40.4122	+	16.7393i	1.40527	+	0.582082i	0.454157	+	0.890922i	$0.349941\pi$
$828$	−1.87793	−	4.53372i	−0.0652625	−	0.157558i
$829$		−	34.4161i		−	1.19532i	−0.801749	−	0.597661i	$-0.796097\pi$
$829$		−	34.4161i		−	1.19532i	0.801749	−	0.597661i	$-0.203903\pi$
$830$	54.9480	−	22.7602i	1.90727	−	0.790019i
$831$	2.94948	+	2.94948i	0.102316	+	0.102316i
$832$	−19.3554			−0.671028
$833$	−6.43321	+	26.1217i	−0.222897	+	0.905062i
$834$	−15.1215			−0.523614
$835$	−15.5970	−	15.5970i	−0.539757	−	0.539757i
$836$	−0.576361	+	0.238737i	−0.0199339	+	0.00825688i
$837$			40.6410i			1.40476i
$838$	−9.87353	−	23.8368i	−0.341075	−	0.823429i
$839$	7.18524	+	2.97623i	0.248062	+	0.102751i	0.503250	−	0.864141i	$-0.332137\pi$
$839$	7.18524	+	2.97623i	0.248062	+	0.102751i	−0.255188	+	0.966891i	$0.582137\pi$
$840$	−2.70925	+	6.54070i	−0.0934779	+	0.225676i
$841$	−6.09963	+	6.09963i	−0.210332	+	0.210332i
$842$	−12.4697	+	12.4697i	−0.429734	+	0.429734i
$843$	5.63397	−	13.6016i	0.194044	−	0.468464i
$844$	−25.5748	−	10.5934i	−0.880320	−	0.364640i
$845$	−7.59741	−	18.3418i	−0.261359	−	0.630976i
$846$		−	20.8453i		−	0.716676i
$847$	5.35039	−	2.21620i	0.183842	−	0.0761497i
$848$	−4.15970	−	4.15970i	−0.142845	−	0.142845i
$849$	−2.14321			−0.0735546
$850$	27.4645	+	45.4125i	0.942024	+	1.55764i
$851$	0.195096			0.00668781
$852$	5.55941	+	5.55941i	0.190462	+	0.190462i
$853$	4.56714	−	1.89177i	0.156376	−	0.0647730i	−0.303123	−	0.952952i	$-0.598029\pi$
$853$	4.56714	−	1.89177i	0.156376	−	0.0647730i	0.459498	+	0.888179i	$0.348029\pi$
$854$		−	5.45531i		−	0.186677i
$855$	1.42077	+	3.43004i	0.0485892	+	0.117305i
$856$	2.52123	+	1.04433i	0.0861739	+	0.0356944i
$857$	−9.46813	+	22.8581i	−0.323425	+	0.780818i	0.675625	+	0.737245i	$0.263874\pi$
$857$	−9.46813	+	22.8581i	−0.323425	+	0.780818i	−0.999050	+	0.0435721i	$0.986126\pi$
$858$	2.61031	−	2.61031i	0.0891145	−	0.0891145i
$859$	0.262924	−	0.262924i	0.00897086	−	0.00897086i	−0.702607	−	0.711578i	$-0.747981\pi$
$859$	0.262924	−	0.262924i	0.00897086	−	0.00897086i	0.711578	+	0.702607i	$0.247981\pi$
$860$	1.69653	−	4.09579i	0.0578513	−	0.139665i
$861$	−0.862864	−	0.357410i	−0.0294063	−	0.0121805i
$862$	10.2145	+	24.6601i	0.347909	+	0.839926i
$863$			8.66033i			0.294801i	0.989077	+	0.147400i	$0.0470906\pi$
$863$			8.66033i			0.294801i	−0.989077	+	0.147400i	$0.952909\pi$
$864$	−20.5403	+	8.50805i	−0.698794	+	0.289450i
$865$	−9.91863	−	9.91863i	−0.337243	−	0.337243i
$866$	−39.5378			−1.34355
$867$	−1.24035	+	13.7066i	−0.0421243	+	0.465499i
$868$	6.73961			0.228757
$869$	10.6650	+	10.6650i	0.361786	+	0.361786i
$870$	19.1388	−	7.92755i	0.648866	−	0.268769i
$871$			38.7679i			1.31360i
$872$	−4.25730	−	10.2780i	−0.144171	−	0.348058i
$873$	−24.8869	−	10.3085i	−0.842293	−	0.348889i
$874$	−0.280190	+	0.676438i	−0.00947756	+	0.0228808i
$875$	−16.9072	+	16.9072i	−0.571567	+	0.571567i
$876$	7.45909	−	7.45909i	0.252019	−	0.252019i
$877$	−10.2772	+	24.8114i	−0.347037	+	0.837821i	0.649930	+	0.759994i	$0.274798\pi$
$877$	−10.2772	+	24.8114i	−0.347037	+	0.837821i	−0.996967	+	0.0778267i	$0.975202\pi$
$878$	28.0554	+	11.6209i	0.946823	+	0.392187i
$879$	−4.35040	−	10.5028i	−0.146735	−	0.354250i
$880$			5.73501i			0.193327i
$881$	14.0784	−	5.83148i	0.474315	−	0.196468i	−0.132703	−	0.991156i	$-0.542366\pi$
$881$	14.0784	−	5.83148i	0.474315	−	0.196468i	0.607018	+	0.794688i	$0.292366\pi$
$882$	10.5943	+	10.5943i	0.356727	+	0.356727i
$883$	29.8878			1.00580			0.502902	−	0.864343i	$-0.332266\pi$
$883$	29.8878			1.00580			0.502902	+	0.864343i	$0.332266\pi$
$884$	−6.41303	−	10.6039i	−0.215693	−	0.356649i
$885$	37.6211			1.26462
$886$	−9.66878	−	9.66878i	−0.324829	−	0.324829i
$887$	5.26292	−	2.17997i	0.176711	−	0.0731963i	−0.292574	−	0.956243i	$-0.594512\pi$
$887$	5.26292	−	2.17997i	0.176711	−	0.0731963i	0.469285	+	0.883047i	$0.344512\pi$
$888$		−	0.233907i		−	0.00784940i
$889$	−0.832662	−	2.01022i	−0.0279266	−	0.0674208i
$890$	6.39629	+	2.64943i	0.214404	+	0.0888091i
$891$	−2.17863	+	5.25968i	−0.0729869	+	0.176206i
$892$	5.37277	−	5.37277i	0.179894	−	0.179894i
$893$	2.38634	−	2.38634i	0.0798559	−	0.0798559i
$894$	−0.827554	+	1.99789i	−0.0276776	+	0.0668195i
$895$	−74.3720	−	30.8059i	−2.48598	−	1.02973i
$896$	0.979370	+	2.36441i	0.0327184	+	0.0789893i
$897$			4.70118i			0.156968i
$898$	−10.2853	+	4.26030i	−0.343224	+	0.142168i
$899$	−40.7406	−	40.7406i	−1.35878	−	1.35878i
$900$	−32.0720			−1.06907
$901$	6.94552	−	28.2019i	0.231389	−	0.939541i
$902$	−2.64246			−0.0879844
$903$	−0.394640	−	0.394640i	−0.0131328	−	0.0131328i
$904$	53.1536	−	22.0170i	1.76786	−	0.732273i
$905$			112.216i			3.73018i
$906$	1.80065	+	4.34716i	0.0598227	+	0.144425i
$907$	−27.1514	−	11.2465i	−0.901546	−	0.373433i	−0.116732	−	0.993164i	$-0.537242\pi$
$907$	−27.1514	−	11.2465i	−0.901546	−	0.373433i	−0.784814	+	0.619731i	$0.787242\pi$
$908$	3.66618	−	8.85094i	0.121666	−	0.293729i
$909$	17.7429	−	17.7429i	0.588494	−	0.588494i
$910$	−5.87236	+	5.87236i	−0.194667	+	0.194667i
$911$	1.84898	−	4.46384i	0.0612596	−	0.147894i	−0.890286	−	0.455403i	$-0.849495\pi$
$911$	1.84898	−	4.46384i	0.0612596	−	0.147894i	0.951545	+	0.307509i	$0.0994954\pi$
$912$	0.232202	+	0.0961811i	0.00768896	+	0.00318487i
$913$	8.79668	+	21.2371i	0.291127	+	0.702844i
$914$		−	7.08610i		−	0.234387i
$915$	−25.7406	+	10.6621i	−0.850959	+	0.352479i
$916$	3.24354	+	3.24354i	0.107170	+	0.107170i
$917$	8.60957			0.284313
$918$	14.0748	+	10.3524i	0.464538	+	0.341679i
$919$	6.40234			0.211194			0.105597	−	0.994409i	$-0.466325\pi$
$919$	6.40234			0.211194			0.105597	+	0.994409i	$0.466325\pi$
$920$	−18.0375	−	18.0375i	−0.594678	−	0.594678i
$921$	2.82375	−	1.16964i	0.0930459	−	0.0385409i
$922$			27.8422i			0.916933i
$923$	10.3114	+	24.8940i	0.339405	+	0.819396i
$924$	−0.865264	−	0.358404i	−0.0284651	−	0.0117906i
$925$	0.487950	−	1.17802i	0.0160437	−	0.0387329i
$926$	1.62517	−	1.62517i	0.0534064	−	0.0534064i
$927$	4.87442	−	4.87442i	0.160097	−	0.160097i
$928$	12.0617	−	29.1195i	0.395945	−	0.955895i
$929$	18.0321	+	7.46916i	0.591616	+	0.245055i	0.658345	−	0.752716i	$-0.271257\pi$
$929$	18.0321	+	7.46916i	0.591616	+	0.245055i	−0.0667300	+	0.997771i	$0.521257\pi$
$930$	12.1392	+	29.3067i	0.398062	+	0.961006i
$931$			2.42564i			0.0794970i
$932$	−10.5051	+	4.35135i	−0.344106	+	0.142533i
$933$	−7.72610	−	7.72610i	−0.252941	−	0.252941i
$934$	7.46050			0.244115
$935$	−24.2290	+	14.6531i	−0.792372	+	0.479209i
$936$	−20.1637			−0.659071
$937$	−31.2466	−	31.2466i	−1.02078	−	1.02078i	−0.999779	−	0.0210021i	$-0.993314\pi$
$937$	−31.2466	−	31.2466i	−1.02078	−	1.02078i	−0.0210021	−	0.999779i	$-0.506686\pi$
$938$	−8.37427	+	3.46874i	−0.273430	+	0.113258i
$939$			1.85160i			0.0604246i
$940$	15.4010	+	37.1812i	0.502324	+	1.21272i
$941$	52.3529	+	21.6853i	1.70666	+	0.706920i	1.00000		0.000637273i	$-0.000202850\pi$
$941$	52.3529	+	21.6853i	1.70666	+	0.706920i	0.706656	+	0.707557i	$0.250203\pi$
$942$	−2.77317	+	6.69503i	−0.0903548	+	0.218136i
$943$	2.37954	−	2.37954i	0.0774885	−	0.0774885i
$944$	−6.44246	+	6.44246i	−0.209684	+	0.209684i
$945$	−4.86209	+	11.7381i	−0.158164	+	0.381841i
$946$	−1.45886	−	0.604280i	−0.0474316	−	0.0196468i
$947$	15.6752	+	37.8432i	0.509375	+	1.22974i	0.944244	+	0.329246i	$0.106795\pi$
$947$	15.6752	+	37.8432i	0.509375	+	1.22974i	−0.434869	+	0.900494i	$0.643205\pi$
$948$			7.88231i			0.256005i
$949$	33.4005	−	13.8349i	1.08422	−	0.449101i
$950$	3.38365	+	3.38365i	0.109780	+	0.109780i
$951$	17.3520			0.562676
$952$	5.01566	−	6.81916i	0.162558	−	0.221010i
$953$	14.4348			0.467588			0.233794	−	0.972286i	$-0.424886\pi$
$953$	14.4348			0.467588			0.233794	+	0.972286i	$0.424886\pi$
$954$	−11.4379	−	11.4379i	−0.370317	−	0.370317i
$955$	83.1714	−	34.4507i	2.69136	−	1.11480i
$956$			11.2851i			0.364985i
$957$	3.06395	+	7.39702i	0.0990434	+	0.239112i
$958$	5.10766	+	2.11566i	0.165021	+	0.0683539i
$959$	−5.43408	+	13.1190i	−0.175475	+	0.423635i
$960$	−16.3430	+	16.3430i	−0.527467	+	0.527467i
$961$	40.4647	−	40.4647i	1.30531	−	1.30531i
$962$	0.105003	−	0.253499i	0.00338543	−	0.00817314i
$963$	1.98491	+	0.822177i	0.0639628	+	0.0264943i
$964$	−3.69585	−	8.92257i	−0.119035	−	0.287377i
$965$		−	57.1626i		−	1.84013i
$966$	−1.01550	+	0.420636i	−0.0326733	+	0.0135337i
$967$	−26.3003	−	26.3003i	−0.845761	−	0.845761i	0.143840	−	0.989601i	$-0.454055\pi$
$967$	−26.3003	−	26.3003i	−0.845761	−	0.845761i	−0.989601	+	0.143840i	$0.954055\pi$
$968$	25.0176			0.804097
$969$	0.186942	+	1.22674i	0.00600545	+	0.0394086i
$970$	−47.9279			−1.53887
$971$	5.87001	+	5.87001i	0.188378	+	0.188378i	0.794994	−	0.606617i	$-0.207474\pi$
$971$	5.87001	+	5.87001i	0.188378	+	0.188378i	−0.606617	+	0.794994i	$0.707474\pi$
$972$	−15.2305	+	6.30867i	−0.488518	+	0.202351i
$973$			13.1479i			0.421503i
$974$	−13.3127	−	32.1398i	−0.426568	−	1.02983i
$975$	28.3863	+	11.7580i	0.909091	+	0.376558i
$976$	2.58213	−	6.23382i	0.0826520	−	0.199540i
$977$	−11.2135	+	11.2135i	−0.358752	+	0.358752i	−0.863353	−	0.504601i	$-0.831640\pi$
$977$	−11.2135	+	11.2135i	−0.358752	+	0.358752i	0.504601	+	0.863353i	$0.331640\pi$
$978$	0.473736	−	0.473736i	0.0151484	−	0.0151484i
$979$	−1.02399	+	2.47213i	−0.0327268	+	0.0790095i
$980$	−26.7240	−	11.0694i	−0.853666	−	0.353600i
$981$	−3.35168	−	8.09168i	−0.107011	−	0.258348i
$982$			20.8846i			0.666456i
$983$	13.8896	−	5.75324i	0.443008	−	0.183500i	−0.150018	−	0.988683i	$-0.547933\pi$
$983$	13.8896	−	5.75324i	0.443008	−	0.183500i	0.593026	+	0.805183i	$0.297933\pi$
$984$	−2.85291	−	2.85291i	−0.0909474	−	0.0909474i
$985$	−0.330174			−0.0105202
$986$	−24.4871	+	3.73157i	−0.779827	+	0.118838i
$987$	5.06643			0.161266
$988$	−0.790090	−	0.790090i	−0.0251361	−	0.0251361i
$989$	1.85786	−	0.769551i	0.0590765	−	0.0244703i
$990$			15.7696i			0.501190i
$991$	−0.0270670	−	0.0653455i	−0.000859811	−	0.00207577i	0.923449	−	0.383721i	$-0.125358\pi$
$991$	−0.0270670	−	0.0653455i	−0.000859811	−	0.00207577i	−0.924309	+	0.381645i	$0.875358\pi$
$992$	44.5900	+	18.4698i	1.41573	+	0.586416i
$993$	0.622944	−	1.50392i	0.0197685	−	0.0477255i
$994$	−4.45476	+	4.45476i	−0.141296	+	0.141296i
$995$	−2.05134	+	2.05134i	−0.0650317	+	0.0650317i
$996$	−4.59721	+	11.0987i	−0.145668	+	0.351674i
$997$	−52.4780	−	21.7371i	−1.66200	−	0.688421i	−0.663768	−	0.747938i	$-0.731044\pi$
$997$	−52.4780	−	21.7371i	−1.66200	−	0.688421i	−0.998227	+	0.0595174i	$0.981044\pi$
$998$	2.72055	+	6.56799i	0.0861175	+	0.207906i
$999$		−	0.419776i		−	0.0132811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.10	✓	128
17.9	even	8	inner	731.2.m.c.689.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.10	✓	128	1.1	even	1	trivial
731.2.m.c.689.10	yes	128	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.692528 - 0.692528i) q^{2} +(0.747939 - 0.309806i) q^{3} -1.04081i q^{4} +(-1.63001 - 3.93520i) q^{5} +(-0.732518 - 0.303419i) q^{6} +(-0.263818 + 0.636914i) q^{7} +(-2.10585 + 2.10585i) q^{8} +(-1.65789 + 1.65789i) q^{9} +O(q^{10})\)	\(q+(-0.692528 - 0.692528i) q^{2} +(0.747939 - 0.309806i) q^{3} -1.04081i q^{4} +(-1.63001 - 3.93520i) q^{5} +(-0.732518 - 0.303419i) q^{6} +(-0.263818 + 0.636914i) q^{7} +(-2.10585 + 2.10585i) q^{8} +(-1.65789 + 1.65789i) q^{9} +(-1.59641 + 3.85406i) q^{10} +(-1.48957 - 0.617000i) q^{11} +(-0.322449 - 0.778462i) q^{12} -2.88774i q^{13} +(0.623783 - 0.258379i) q^{14} +(-2.43830 - 2.43830i) q^{15} +0.835097 q^{16} +(2.13370 + 3.52808i) q^{17} +2.29627 q^{18} +(0.262874 + 0.262874i) q^{19} +(-4.09579 + 1.69653i) q^{20} +0.558105i q^{21} +(0.604280 + 1.45886i) q^{22} +(-1.85786 - 0.769551i) q^{23} +(-0.922640 + 2.22745i) q^{24} +(-9.29331 + 9.29331i) q^{25} +(-1.99984 + 1.99984i) q^{26} +(-1.65579 + 3.99744i) q^{27} +(0.662906 + 0.274585i) q^{28} +(-2.34739 - 5.66709i) q^{29} +3.37718i q^{30} +(8.67787 - 3.59449i) q^{31} +(3.63336 + 3.63336i) q^{32} -1.30526 q^{33} +(0.965643 - 3.92094i) q^{34} +2.93641 q^{35} +(1.72555 + 1.72555i) q^{36} +(-0.0896326 + 0.0371270i) q^{37} -0.364095i q^{38} +(-0.894641 - 2.15985i) q^{39} +(11.7195 + 4.85437i) q^{40} +(-0.640398 + 1.54606i) q^{41} +(0.386504 - 0.386504i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-0.642180 + 1.55036i) q^{44} +(9.22649 + 3.82174i) q^{45} +(0.753685 + 1.81956i) q^{46} -9.07791i q^{47} +(0.624602 - 0.258718i) q^{48} +(4.61369 + 4.61369i) q^{49} +12.8718 q^{50} +(2.68890 + 1.97775i) q^{51} -3.00559 q^{52} +(-4.98110 - 4.98110i) q^{53} +(3.91502 - 1.62166i) q^{54} +6.86747i q^{55} +(-0.785682 - 1.89680i) q^{56} +(0.278053 + 0.115174i) q^{57} +(-2.29899 + 5.55025i) q^{58} +(-7.71463 + 7.71463i) q^{59} +(-2.53780 + 2.53780i) q^{60} +(3.09201 - 7.46478i) q^{61} +(-8.49896 - 3.52038i) q^{62} +(-0.618551 - 1.49331i) q^{63} -6.70261i q^{64} +(-11.3638 + 4.70705i) q^{65} +(0.903928 + 0.903928i) q^{66} -13.4250 q^{67} +(3.67205 - 2.22078i) q^{68} -1.62798 q^{69} +(-2.03355 - 2.03355i) q^{70} +(-8.62058 + 3.57076i) q^{71} -6.98251i q^{72} +(4.79092 + 11.5663i) q^{73} +(0.0877846 + 0.0363616i) q^{74} +(-4.07170 + 9.82995i) q^{75} +(0.273601 - 0.273601i) q^{76} +(0.785953 - 0.785953i) q^{77} +(-0.876196 + 2.11532i) q^{78} +(-8.64265 - 3.57990i) q^{79} +(-1.36122 - 3.28627i) q^{80} -3.53101i q^{81} +(1.51418 - 0.627195i) q^{82} +(-10.0813 - 10.0813i) q^{83} +0.580881 q^{84} +(10.4057 - 14.1473i) q^{85} +0.979383 q^{86} +(-3.51140 - 3.51140i) q^{87} +(4.43612 - 1.83750i) q^{88} -1.65962i q^{89} +(-3.74295 - 9.03627i) q^{90} +(1.83924 + 0.761839i) q^{91} +(-0.800956 + 1.93368i) q^{92} +(5.37692 - 5.37692i) q^{93} +(-6.28671 + 6.28671i) q^{94} +(0.605973 - 1.46295i) q^{95} +(3.84317 + 1.59189i) q^{96} +(4.39668 + 10.6145i) q^{97} -6.39022i q^{98} +(3.49246 - 1.44662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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