LMFDB - Embedded newform 289.2.d.c.134.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,2,Mod(110,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.110"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			134.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	289.134
Dual form			289.2.d.c.110.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.292893 + 0.292893i) q^{2} +(1.00000 + 2.41421i) q^{3} -1.82843i q^{4} +(1.70711 - 0.707107i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 + 0.414214i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.70711 + 2.70711i) q^{9} +(0.707107 + 0.292893i) q^{10} +(0.414214 - 1.00000i) q^{11} +(4.41421 - 1.82843i) q^{12} +1.41421i q^{13} +(0.171573 + 0.414214i) q^{14} +(3.41421 + 3.41421i) q^{15} -3.00000 q^{16} -1.58579 q^{18} +(-3.41421 - 3.41421i) q^{19} +(-1.29289 - 3.12132i) q^{20} +2.82843i q^{21} +(0.414214 - 0.171573i) q^{22} +(-1.58579 + 3.82843i) q^{23} +(3.82843 + 1.58579i) q^{24} +(-1.12132 + 1.12132i) q^{25} +(-0.414214 + 0.414214i) q^{26} +(-2.00000 - 0.828427i) q^{27} +(0.757359 - 1.82843i) q^{28} +(-4.12132 + 1.70711i) q^{29} +2.00000i q^{30} +(1.24264 + 3.00000i) q^{31} +(-3.12132 - 3.12132i) q^{32} +2.82843 q^{33} +2.00000 q^{35} +(4.94975 + 4.94975i) q^{36} +(1.46447 + 3.53553i) q^{37} -2.00000i q^{38} +(-3.41421 + 1.41421i) q^{39} +(1.12132 - 2.70711i) q^{40} +(-7.53553 - 3.12132i) q^{41} +(-0.828427 + 0.828427i) q^{42} +(3.41421 - 3.41421i) q^{43} +(-1.82843 - 0.757359i) q^{44} +(-2.70711 + 6.53553i) q^{45} +(-1.58579 + 0.656854i) q^{46} -10.8284i q^{47} +(-3.00000 - 7.24264i) q^{48} +(-4.12132 - 4.12132i) q^{49} -0.656854 q^{50} +2.58579 q^{52} +(1.00000 + 1.00000i) q^{53} +(-0.343146 - 0.828427i) q^{54} -2.00000i q^{55} +(1.58579 - 0.656854i) q^{56} +(4.82843 - 11.6569i) q^{57} +(-1.70711 - 0.707107i) q^{58} +(4.24264 - 4.24264i) q^{59} +(6.24264 - 6.24264i) q^{60} +(8.53553 + 3.53553i) q^{61} +(-0.514719 + 1.24264i) q^{62} +(-3.82843 + 1.58579i) q^{63} +4.17157i q^{64} +(1.00000 + 2.41421i) q^{65} +(0.828427 + 0.828427i) q^{66} +6.82843 q^{67} -10.8284 q^{69} +(0.585786 + 0.585786i) q^{70} +(-5.00000 - 12.0711i) q^{71} +6.07107i q^{72} +(-4.94975 + 2.05025i) q^{73} +(-0.606602 + 1.46447i) q^{74} +(-3.82843 - 1.58579i) q^{75} +(-6.24264 + 6.24264i) q^{76} +(0.828427 - 0.828427i) q^{77} +(-1.41421 - 0.585786i) q^{78} +(1.58579 - 3.82843i) q^{79} +(-5.12132 + 2.12132i) q^{80} +5.82843i q^{81} +(-1.29289 - 3.12132i) q^{82} +(0.242641 + 0.242641i) q^{83} +5.17157 q^{84} +2.00000 q^{86} +(-8.24264 - 8.24264i) q^{87} +(-0.656854 - 1.58579i) q^{88} +9.41421i q^{89} +(-2.70711 + 1.12132i) q^{90} +(-0.585786 + 1.41421i) q^{91} +(7.00000 + 2.89949i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(3.17157 - 3.17157i) q^{94} +(-8.24264 - 3.41421i) q^{95} +(4.41421 - 10.6569i) q^{96} +(5.94975 - 2.46447i) q^{97} -2.41421i q^{98} +(1.58579 + 3.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 12 q^{12} + 12 q^{14} + 8 q^{15} - 12 q^{16} - 12 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{25}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 12 * q^12 + 12 * q^14 + 8 * q^15 - 12 * q^16 - 12 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 - 8 * q^27 + 20 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^32 + 8 * q^35 + 20 * q^37 - 8 * q^39 - 4 * q^40 - 16 * q^41 + 8 * q^42 + 8 * q^43 + 4 * q^44 - 8 * q^45 - 12 * q^46 - 12 * q^48 - 8 * q^49 + 20 * q^50 + 16 * q^52 + 4 * q^53 - 24 * q^54 + 12 * q^56 + 8 * q^57 - 4 * q^58 + 8 * q^60 + 20 * q^61 - 36 * q^62 - 4 * q^63 + 4 * q^65 - 8 * q^66 + 16 * q^67 - 32 * q^69 + 8 * q^70 - 20 * q^71 + 40 * q^74 - 4 * q^75 - 8 * q^76 - 8 * q^77 + 12 * q^79 - 12 * q^80 - 8 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 - 8 * q^91 + 28 * q^92 - 24 * q^93 + 24 * q^94 - 16 * q^95 + 12 * q^96 + 4 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	0.803037	−	0.595930i	$-0.203216\pi$
$2$	0.292893	+	0.292893i	0.207107	+	0.207107i	−0.595930	+	0.803037i	$0.703216\pi$
$3$	1.00000	+	2.41421i	0.577350	+	1.39385i	0.895182	+	0.445700i	$0.147045\pi$
$3$	1.00000	+	2.41421i	0.577350	+	1.39385i	−0.317832	+	0.948147i	$0.602955\pi$
$4$		−	1.82843i		−	0.914214i
$5$	1.70711	−	0.707107i	0.763441	−	0.316228i	0.0332288	−	0.999448i	$-0.489421\pi$
$5$	1.70711	−	0.707107i	0.763441	−	0.316228i	0.730213	+	0.683220i	$0.239421\pi$
$6$	−0.414214	+	1.00000i	−0.169102	+	0.408248i
$7$	1.00000	+	0.414214i	0.377964	+	0.156558i	0.563574	−	0.826066i	$-0.309426\pi$
$7$	1.00000	+	0.414214i	0.377964	+	0.156558i	−0.185610	+	0.982624i	$0.559426\pi$
$8$	1.12132	−	1.12132i	0.396447	−	0.396447i
$9$	−2.70711	+	2.70711i	−0.902369	+	0.902369i
$10$	0.707107	+	0.292893i	0.223607	+	0.0926210i
$11$	0.414214	−	1.00000i	0.124890	−	0.301511i	−0.849052	−	0.528310i	$-0.822826\pi$
$11$	0.414214	−	1.00000i	0.124890	−	0.301511i	0.973942	+	0.226799i	$0.0728259\pi$
$12$	4.41421	−	1.82843i	1.27427	−	0.527821i
$13$			1.41421i			0.392232i	0.980581	+	0.196116i	$0.0628330\pi$
$13$			1.41421i			0.392232i	−0.980581	+	0.196116i	$0.937167\pi$
$14$	0.171573	+	0.414214i	0.0458548	+	0.110703i
$15$	3.41421	+	3.41421i	0.881546	+	0.881546i
$16$	−3.00000			−0.750000
$17$		0			0
$17$		0			0
$18$	−1.58579			−0.373773
$19$	−3.41421	−	3.41421i	−0.783274	−	0.783274i	0.197108	−	0.980382i	$-0.436845\pi$
$19$	−3.41421	−	3.41421i	−0.783274	−	0.783274i	−0.980382	+	0.197108i	$0.936845\pi$
$20$	−1.29289	−	3.12132i	−0.289100	−	0.697948i
$21$			2.82843i			0.617213i
$22$	0.414214	−	0.171573i	0.0883106	−	0.0365795i
$23$	−1.58579	+	3.82843i	−0.330659	+	0.798282i	0.667881	+	0.744268i	$0.267202\pi$
$23$	−1.58579	+	3.82843i	−0.330659	+	0.798282i	−0.998540	+	0.0540140i	$0.982798\pi$
$24$	3.82843	+	1.58579i	0.781474	+	0.323697i
$25$	−1.12132	+	1.12132i	−0.224264	+	0.224264i
$26$	−0.414214	+	0.414214i	−0.0812340	+	0.0812340i
$27$	−2.00000	−	0.828427i	−0.384900	−	0.159431i
$28$	0.757359	−	1.82843i	0.143127	−	0.345540i
$29$	−4.12132	+	1.70711i	−0.765310	+	0.317002i	−0.730971	−	0.682408i	$-0.760933\pi$
$29$	−4.12132	+	1.70711i	−0.765310	+	0.317002i	−0.0343389	+	0.999410i	$0.510933\pi$
$30$			2.00000i			0.365148i
$31$	1.24264	+	3.00000i	0.223185	+	0.538816i	0.995319	−	0.0966436i	$-0.0308107\pi$
$31$	1.24264	+	3.00000i	0.223185	+	0.538816i	−0.772134	+	0.635460i	$0.780811\pi$
$32$	−3.12132	−	3.12132i	−0.551777	−	0.551777i
$33$	2.82843			0.492366
$34$		0			0
$35$	2.00000			0.338062
$36$	4.94975	+	4.94975i	0.824958	+	0.824958i
$37$	1.46447	+	3.53553i	0.240757	+	0.581238i	0.997358	−	0.0726379i	$-0.0231417\pi$
$37$	1.46447	+	3.53553i	0.240757	+	0.581238i	−0.756602	+	0.653876i	$0.773142\pi$
$38$		−	2.00000i		−	0.324443i
$39$	−3.41421	+	1.41421i	−0.546712	+	0.226455i
$40$	1.12132	−	2.70711i	0.177296	−	0.428031i
$41$	−7.53553	−	3.12132i	−1.17685	−	0.487468i	−0.293400	−	0.955990i	$-0.594787\pi$
$41$	−7.53553	−	3.12132i	−1.17685	−	0.487468i	−0.883452	+	0.468521i	$0.844787\pi$
$42$	−0.828427	+	0.828427i	−0.127829	+	0.127829i
$43$	3.41421	−	3.41421i	0.520663	−	0.520663i	−0.397109	−	0.917772i	$-0.629986\pi$
$43$	3.41421	−	3.41421i	0.520663	−	0.520663i	0.917772	+	0.397109i	$0.129986\pi$
$44$	−1.82843	−	0.757359i	−0.275646	−	0.114176i
$45$	−2.70711	+	6.53553i	−0.403552	+	0.974260i
$46$	−1.58579	+	0.656854i	−0.233811	+	0.0968479i
$47$		−	10.8284i		−	1.57949i	−0.613436	−	0.789744i	$-0.710213\pi$
$47$		−	10.8284i		−	1.57949i	0.613436	−	0.789744i	$-0.289787\pi$
$48$	−3.00000	−	7.24264i	−0.433013	−	1.04539i
$49$	−4.12132	−	4.12132i	−0.588760	−	0.588760i
$50$	−0.656854			−0.0928932
$51$		0			0
$52$	2.58579			0.358584
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	−0.343146	−	0.828427i	−0.0466962	−	0.112735i
$55$		−	2.00000i		−	0.269680i
$56$	1.58579	−	0.656854i	0.211910	−	0.0877758i
$57$	4.82843	−	11.6569i	0.639541	−	1.54399i
$58$	−1.70711	−	0.707107i	−0.224154	−	0.0928477i
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	−0.374772	−	0.927117i	$-0.622279\pi$
$59$	4.24264	−	4.24264i	0.552345	−	0.552345i	0.927117	+	0.374772i	$0.122279\pi$
$60$	6.24264	−	6.24264i	0.805921	−	0.805921i
$61$	8.53553	+	3.53553i	1.09286	+	0.452679i	0.855004	−	0.518621i	$-0.173554\pi$
$61$	8.53553	+	3.53553i	1.09286	+	0.452679i	0.237859	+	0.971300i	$0.423554\pi$
$62$	−0.514719	+	1.24264i	−0.0653693	+	0.157816i
$63$	−3.82843	+	1.58579i	−0.482336	+	0.199790i
$64$			4.17157i			0.521447i
$65$	1.00000	+	2.41421i	0.124035	+	0.299446i
$66$	0.828427	+	0.828427i	0.101972	+	0.101972i
$67$	6.82843			0.834225			0.417113	−	0.908855i	$-0.363042\pi$
$67$	6.82843			0.834225			0.417113	+	0.908855i	$0.363042\pi$
$68$		0			0
$69$	−10.8284			−1.30359
$70$	0.585786	+	0.585786i	0.0700149	+	0.0700149i
$71$	−5.00000	−	12.0711i	−0.593391	−	1.43257i	−0.880209	−	0.474587i	$-0.842597\pi$
$71$	−5.00000	−	12.0711i	−0.593391	−	1.43257i	0.286818	−	0.957985i	$-0.407403\pi$
$72$			6.07107i			0.715482i
$73$	−4.94975	+	2.05025i	−0.579324	+	0.239964i	−0.653050	−	0.757315i	$-0.726511\pi$
$73$	−4.94975	+	2.05025i	−0.579324	+	0.239964i	0.0737261	+	0.997279i	$0.476511\pi$
$74$	−0.606602	+	1.46447i	−0.0705160	+	0.170241i
$75$	−3.82843	−	1.58579i	−0.442069	−	0.183111i
$76$	−6.24264	+	6.24264i	−0.716080	+	0.716080i
$77$	0.828427	−	0.828427i	0.0944080	−	0.0944080i
$78$	−1.41421	−	0.585786i	−0.160128	−	0.0663273i
$79$	1.58579	−	3.82843i	0.178415	−	0.430732i	−0.809219	−	0.587506i	$-0.800110\pi$
$79$	1.58579	−	3.82843i	0.178415	−	0.430732i	0.987634	+	0.156775i	$0.0501097\pi$
$80$	−5.12132	+	2.12132i	−0.572581	+	0.237171i
$81$			5.82843i			0.647603i
$82$	−1.29289	−	3.12132i	−0.142776	−	0.344692i
$83$	0.242641	+	0.242641i	0.0266333	+	0.0266333i	0.720298	−	0.693665i	$-0.244005\pi$
$83$	0.242641	+	0.242641i	0.0266333	+	0.0266333i	−0.693665	+	0.720298i	$0.744005\pi$
$84$	5.17157			0.564265
$85$		0			0
$86$	2.00000			0.215666
$87$	−8.24264	−	8.24264i	−0.883704	−	0.883704i
$88$	−0.656854	−	1.58579i	−0.0700209	−	0.169045i
$89$			9.41421i			0.997905i	0.866629	+	0.498952i	$0.166282\pi$
$89$			9.41421i			0.997905i	−0.866629	+	0.498952i	$0.833718\pi$
$90$	−2.70711	+	1.12132i	−0.285354	+	0.118198i
$91$	−0.585786	+	1.41421i	−0.0614071	+	0.148250i
$92$	7.00000	+	2.89949i	0.729800	+	0.302293i
$93$	−6.00000	+	6.00000i	−0.622171	+	0.622171i
$94$	3.17157	−	3.17157i	0.327123	−	0.327123i
$95$	−8.24264	−	3.41421i	−0.845677	−	0.350291i
$96$	4.41421	−	10.6569i	0.450524	−	1.08766i
$97$	5.94975	−	2.46447i	0.604105	−	0.250229i	−0.0596005	−	0.998222i	$-0.518983\pi$
$97$	5.94975	−	2.46447i	0.604105	−	0.250229i	0.663706	+	0.747994i	$0.268983\pi$
$98$		−	2.41421i		−	0.243872i
$99$	1.58579	+	3.82843i	0.159378	+	0.384771i
$100$	2.05025	+	2.05025i	0.205025	+	0.205025i
$101$	−13.4142			−1.33476			−0.667382	−	0.744715i	$-0.732585\pi$
$101$	−13.4142			−1.33476			−0.667382	+	0.744715i	$0.732585\pi$
$102$		0			0
$103$	−4.48528			−0.441948			−0.220974	−	0.975280i	$-0.570924\pi$
$103$	−4.48528			−0.441948			−0.220974	+	0.975280i	$0.570924\pi$
$104$	1.58579	+	1.58579i	0.155499	+	0.155499i
$105$	2.00000	+	4.82843i	0.195180	+	0.471206i
$106$			0.585786i			0.0568966i
$107$	−5.82843	+	2.41421i	−0.563455	+	0.233391i	−0.646184	−	0.763181i	$-0.723636\pi$
$107$	−5.82843	+	2.41421i	−0.563455	+	0.233391i	0.0827292	+	0.996572i	$0.473636\pi$
$108$	−1.51472	+	3.65685i	−0.145754	+	0.351881i
$109$	3.94975	+	1.63604i	0.378317	+	0.156704i	0.563735	−	0.825956i	$-0.309364\pi$
$109$	3.94975	+	1.63604i	0.378317	+	0.156704i	−0.185418	+	0.982660i	$0.559364\pi$
$110$	0.585786	−	0.585786i	0.0558525	−	0.0558525i
$111$	−7.07107	+	7.07107i	−0.671156	+	0.671156i
$112$	−3.00000	−	1.24264i	−0.283473	−	0.117419i
$113$	−6.19239	+	14.9497i	−0.582531	+	1.40635i	0.307980	+	0.951393i	$0.400347\pi$
$113$	−6.19239	+	14.9497i	−0.582531	+	1.40635i	−0.890511	+	0.454961i	$0.849653\pi$
$114$	4.82843	−	2.00000i	0.452224	−	0.187317i
$115$			7.65685i			0.714005i
$116$	3.12132	+	7.53553i	0.289807	+	0.699657i
$117$	−3.82843	−	3.82843i	−0.353938	−	0.353938i
$118$	2.48528			0.228789
$119$		0			0
$120$	7.65685			0.698972
$121$	6.94975	+	6.94975i	0.631795	+	0.631795i
$122$	1.46447	+	3.53553i	0.132587	+	0.320092i
$123$		−	21.3137i		−	1.92179i
$124$	5.48528	−	2.27208i	0.492593	−	0.204039i
$125$	−4.65685	+	11.2426i	−0.416522	+	1.00557i
$126$	−1.58579	−	0.656854i	−0.141273	−	0.0585172i
$127$	12.2426	−	12.2426i	1.08636	−	1.08636i	0.0904585	−	0.995900i	$-0.471167\pi$
$127$	12.2426	−	12.2426i	1.08636	−	1.08636i	0.995900	−	0.0904585i	$-0.0288332\pi$
$128$	−7.46447	+	7.46447i	−0.659772	+	0.659772i
$129$	11.6569	+	4.82843i	1.02633	+	0.425119i
$130$	−0.414214	+	1.00000i	−0.0363289	+	0.0877058i
$131$	0.171573	−	0.0710678i	0.0149904	−	0.00620922i	−0.375176	−	0.926954i	$-0.622418\pi$
$131$	0.171573	−	0.0710678i	0.0149904	−	0.00620922i	0.390166	+	0.920745i	$0.372418\pi$
$132$		−	5.17157i		−	0.450128i
$133$	−2.00000	−	4.82843i	−0.173422	−	0.418678i
$134$	2.00000	+	2.00000i	0.172774	+	0.172774i
$135$	−4.00000			−0.344265
$136$		0			0
$137$	8.72792			0.745677			0.372838	−	0.927896i	$-0.378385\pi$
$137$	8.72792			0.745677			0.372838	+	0.927896i	$0.378385\pi$
$138$	−3.17157	−	3.17157i	−0.269982	−	0.269982i
$139$	5.72792	+	13.8284i	0.485836	+	1.17291i	0.956797	+	0.290758i	$0.0939074\pi$
$139$	5.72792	+	13.8284i	0.485836	+	1.17291i	−0.470961	+	0.882154i	$0.656093\pi$
$140$		−	3.65685i		−	0.309061i
$141$	26.1421	−	10.8284i	2.20156	−	0.911918i
$142$	2.07107	−	5.00000i	0.173800	−	0.419591i
$143$	1.41421	+	0.585786i	0.118262	+	0.0489859i
$144$	8.12132	−	8.12132i	0.676777	−	0.676777i
$145$	−5.82843	+	5.82843i	−0.484025	+	0.484025i
$146$	−2.05025	−	0.849242i	−0.169680	−	0.0702838i
$147$	5.82843	−	14.0711i	0.480721	−	1.16056i
$148$	6.46447	−	2.67767i	0.531376	−	0.220103i
$149$		−	16.9706i		−	1.39028i	−0.718873	−	0.695141i	$-0.755342\pi$
$149$		−	16.9706i		−	1.39028i	0.718873	−	0.695141i	$-0.244658\pi$
$150$	−0.656854	−	1.58579i	−0.0536319	−	0.129479i
$151$	9.07107	+	9.07107i	0.738193	+	0.738193i	0.972228	−	0.234035i	$-0.0751931\pi$
$151$	9.07107	+	9.07107i	0.738193	+	0.738193i	−0.234035	+	0.972228i	$0.575193\pi$
$152$	−7.65685			−0.621053
$153$		0			0
$154$	0.485281			0.0391051
$155$	4.24264	+	4.24264i	0.340777	+	0.340777i
$156$	2.58579	+	6.24264i	0.207029	+	0.499811i
$157$			1.65685i			0.132231i	0.997812	+	0.0661157i	$0.0210606\pi$
$157$			1.65685i			0.132231i	−0.997812	+	0.0661157i	$0.978939\pi$
$158$	1.58579	−	0.656854i	0.126158	−	0.0522565i
$159$	−1.41421	+	3.41421i	−0.112154	+	0.270765i
$160$	−7.53553	−	3.12132i	−0.595736	−	0.246762i
$161$	−3.17157	+	3.17157i	−0.249955	+	0.249955i
$162$	−1.70711	+	1.70711i	−0.134123	+	0.134123i
$163$	−5.24264	−	2.17157i	−0.410635	−	0.170091i	0.167796	−	0.985822i	$-0.446335\pi$
$163$	−5.24264	−	2.17157i	−0.410635	−	0.170091i	−0.578431	+	0.815731i	$0.696335\pi$
$164$	−5.70711	+	13.7782i	−0.445650	+	1.07589i
$165$	4.82843	−	2.00000i	0.375893	−	0.155700i
$166$			0.142136i			0.0110319i
$167$	−3.82843	−	9.24264i	−0.296253	−	0.715217i	−0.999989	−	0.00475555i	$-0.998486\pi$
$167$	−3.82843	−	9.24264i	−0.296253	−	0.715217i	0.703736	−	0.710461i	$-0.251514\pi$
$168$	3.17157	+	3.17157i	0.244692	+	0.244692i
$169$	11.0000			0.846154
$170$		0			0
$171$	18.4853			1.41360
$172$	−6.24264	−	6.24264i	−0.475997	−	0.475997i
$173$	1.29289	+	3.12132i	0.0982969	+	0.237310i	0.965377	−	0.260859i	$-0.0840059\pi$
$173$	1.29289	+	3.12132i	0.0982969	+	0.237310i	−0.867080	+	0.498169i	$0.834006\pi$
$174$		−	4.82843i		−	0.366042i
$175$	−1.58579	+	0.656854i	−0.119874	+	0.0496535i
$176$	−1.24264	+	3.00000i	−0.0936676	+	0.226134i
$177$	14.4853	+	6.00000i	1.08878	+	0.450988i
$178$	−2.75736	+	2.75736i	−0.206673	+	0.206673i
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	−0.847656	−	0.530546i	$-0.821987\pi$
$179$	−4.24264	+	4.24264i	−0.317110	+	0.317110i	0.530546	+	0.847656i	$0.321987\pi$
$180$	11.9497	+	4.94975i	0.890682	+	0.368932i
$181$	4.77817	−	11.5355i	0.355159	−	0.857429i	−0.640807	−	0.767702i	$-0.721400\pi$
$181$	4.77817	−	11.5355i	0.355159	−	0.857429i	0.995966	−	0.0897278i	$-0.0285997\pi$
$182$	−0.585786	+	0.242641i	−0.0434214	+	0.0179857i
$183$			24.1421i			1.78464i
$184$	2.51472	+	6.07107i	0.185388	+	0.447565i
$185$	5.00000	+	5.00000i	0.367607	+	0.367607i
$186$	−3.51472			−0.257712
$187$		0			0
$188$	−19.7990			−1.44399
$189$	−1.65685	−	1.65685i	−0.120518	−	0.120518i
$190$	−1.41421	−	3.41421i	−0.102598	−	0.247693i
$191$			20.0000i			1.44715i	0.690246	+	0.723575i	$0.257502\pi$
$191$			20.0000i			1.44715i	−0.690246	+	0.723575i	$0.742498\pi$
$192$	−10.0711	+	4.17157i	−0.726817	+	0.301057i
$193$	−2.12132	+	5.12132i	−0.152696	+	0.368641i	−0.981654	−	0.190670i	$-0.938934\pi$
$193$	−2.12132	+	5.12132i	−0.152696	+	0.368641i	0.828958	+	0.559310i	$0.188934\pi$
$194$	2.46447	+	1.02082i	0.176938	+	0.0732903i
$195$	−4.82843	+	4.82843i	−0.345771	+	0.345771i
$196$	−7.53553	+	7.53553i	−0.538252	+	0.538252i
$197$	−13.7782	−	5.70711i	−0.981654	−	0.406615i	−0.166616	−	0.986022i	$-0.553284\pi$
$197$	−13.7782	−	5.70711i	−0.981654	−	0.406615i	−0.815038	+	0.579407i	$0.803284\pi$
$198$	−0.656854	+	1.58579i	−0.0466806	+	0.112697i
$199$	−1.58579	+	0.656854i	−0.112413	+	0.0465632i	−0.438181	−	0.898887i	$-0.644377\pi$
$199$	−1.58579	+	0.656854i	−0.112413	+	0.0465632i	0.325768	+	0.945450i	$0.394377\pi$
$200$			2.51472i			0.177817i
$201$	6.82843	+	16.4853i	0.481640	+	1.16278i
$202$	−3.92893	−	3.92893i	−0.276439	−	0.276439i
$203$	−4.82843			−0.338889
$204$		0			0
$205$	−15.0711			−1.05261
$206$	−1.31371	−	1.31371i	−0.0915304	−	0.0915304i
$207$	−6.07107	−	14.6569i	−0.421968	−	1.01872i
$208$		−	4.24264i		−	0.294174i
$209$	−4.82843	+	2.00000i	−0.333989	+	0.138343i
$210$	−0.828427	+	2.00000i	−0.0571669	+	0.138013i
$211$	13.8284	+	5.72792i	0.951988	+	0.394326i	0.803978	−	0.594659i	$-0.202713\pi$
$211$	13.8284	+	5.72792i	0.951988	+	0.394326i	0.148010	+	0.988986i	$0.452713\pi$
$212$	1.82843	−	1.82843i	0.125577	−	0.125577i
$213$	24.1421	−	24.1421i	1.65419	−	1.65419i
$214$	−2.41421	−	1.00000i	−0.165032	−	0.0683586i
$215$	3.41421	−	8.24264i	0.232847	−	0.562143i
$216$	−3.17157	+	1.31371i	−0.215798	+	0.0893865i
$217$			3.51472i			0.238595i
$218$	0.677670	+	1.63604i	0.0458976	+	0.110807i
$219$	−9.89949	−	9.89949i	−0.668946	−	0.668946i
$220$	−3.65685			−0.246545
$221$		0			0
$222$	−4.14214			−0.278002
$223$	−0.585786	−	0.585786i	−0.0392272	−	0.0392272i	0.687221	−	0.726448i	$-0.258830\pi$
$223$	−0.585786	−	0.585786i	−0.0392272	−	0.0392272i	−0.726448	+	0.687221i	$0.758830\pi$
$224$	−1.82843	−	4.41421i	−0.122167	−	0.294937i
$225$		−	6.07107i		−	0.404738i
$226$	−6.19239	+	2.56497i	−0.411912	+	0.170619i
$227$	1.92893	−	4.65685i	0.128028	−	0.309086i	−0.846848	−	0.531835i	$-0.821503\pi$
$227$	1.92893	−	4.65685i	0.128028	−	0.309086i	0.974876	+	0.222748i	$0.0715028\pi$
$228$	−21.3137	−	8.82843i	−1.41153	−	0.584677i
$229$	−16.1421	+	16.1421i	−1.06670	+	1.06670i	−0.0690921	+	0.997610i	$0.522010\pi$
$229$	−16.1421	+	16.1421i	−1.06670	+	1.06670i	−0.997610	+	0.0690921i	$0.977990\pi$
$230$	−2.24264	+	2.24264i	−0.147875	+	0.147875i
$231$	2.82843	+	1.17157i	0.186097	+	0.0770838i
$232$	−2.70711	+	6.53553i	−0.177730	+	0.429079i
$233$	9.36396	−	3.87868i	0.613453	−	0.254101i	−0.0542508	−	0.998527i	$-0.517277\pi$
$233$	9.36396	−	3.87868i	0.613453	−	0.254101i	0.667704	+	0.744427i	$0.267277\pi$
$234$		−	2.24264i		−	0.146606i
$235$	−7.65685	−	18.4853i	−0.499478	−	1.20585i
$236$	−7.75736	−	7.75736i	−0.504961	−	0.504961i
$237$	10.8284			0.703382
$238$		0			0
$239$	9.17157			0.593260			0.296630	−	0.954993i	$-0.404137\pi$
$239$	9.17157			0.593260			0.296630	+	0.954993i	$0.404137\pi$
$240$	−10.2426	−	10.2426i	−0.661160	−	0.661160i
$241$	−4.70711	−	11.3640i	−0.303211	−	0.732017i	−0.999893	−	0.0146365i	$-0.995341\pi$
$241$	−4.70711	−	11.3640i	−0.303211	−	0.732017i	0.696681	−	0.717381i	$-0.254659\pi$
$242$			4.07107i			0.261698i
$243$	−20.0711	+	8.31371i	−1.28756	+	0.533325i
$244$	6.46447	−	15.6066i	0.413845	−	0.999110i
$245$	−9.94975	−	4.12132i	−0.635666	−	0.263301i
$246$	6.24264	−	6.24264i	0.398016	−	0.398016i
$247$	4.82843	−	4.82843i	0.307225	−	0.307225i
$248$	4.75736	+	1.97056i	0.302093	+	0.125131i
$249$	−0.343146	+	0.828427i	−0.0217460	+	0.0524994i
$250$	−4.65685	+	1.92893i	−0.294525	+	0.121996i
$251$		−	3.51472i		−	0.221847i	−0.993829	−	0.110924i	$-0.964619\pi$
$251$		−	3.51472i		−	0.221847i	0.993829	−	0.110924i	$-0.0353809\pi$
$252$	2.89949	+	7.00000i	0.182651	+	0.440959i
$253$	3.17157	+	3.17157i	0.199395	+	0.199395i
$254$	7.17157			0.449985
$255$		0			0
$256$	3.97056			0.248160
$257$	15.6569	+	15.6569i	0.976648	+	0.976648i	0.999733	−	0.0230858i	$-0.00734908\pi$
$257$	15.6569	+	15.6569i	0.976648	+	0.976648i	−0.0230858	+	0.999733i	$0.507349\pi$
$258$	2.00000	+	4.82843i	0.124515	+	0.300605i
$259$			4.14214i			0.257380i
$260$	4.41421	−	1.82843i	0.273758	−	0.113394i
$261$	6.53553	−	15.7782i	0.404539	−	0.976644i
$262$	0.0710678	+	0.0294373i	0.00439058	+	0.00181864i
$263$	4.58579	−	4.58579i	0.282772	−	0.282772i	−0.551442	−	0.834213i	$-0.685922\pi$
$263$	4.58579	−	4.58579i	0.282772	−	0.282772i	0.834213	+	0.551442i	$0.185922\pi$
$264$	3.17157	−	3.17157i	0.195197	−	0.195197i
$265$	2.41421	+	1.00000i	0.148304	+	0.0614295i
$266$	0.828427	−	2.00000i	0.0507941	−	0.122628i
$267$	−22.7279	+	9.41421i	−1.39093	+	0.576141i
$268$		−	12.4853i		−	0.762660i
$269$	−2.43503	−	5.87868i	−0.148466	−	0.358429i	0.832098	−	0.554629i	$-0.187140\pi$
$269$	−2.43503	−	5.87868i	−0.148466	−	0.358429i	−0.980564	+	0.196200i	$0.937140\pi$
$270$	−1.17157	−	1.17157i	−0.0712997	−	0.0712997i
$271$	−6.14214			−0.373108			−0.186554	−	0.982445i	$-0.559732\pi$
$271$	−6.14214			−0.373108			−0.186554	+	0.982445i	$0.559732\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$	2.55635	+	2.55635i	0.154435	+	0.154435i
$275$	0.656854	+	1.58579i	0.0396098	+	0.0956265i
$276$			19.7990i			1.19176i
$277$	20.3640	−	8.43503i	1.22355	−	0.506812i	0.325015	−	0.945709i	$-0.394631\pi$
$277$	20.3640	−	8.43503i	1.22355	−	0.506812i	0.898537	+	0.438897i	$0.144631\pi$
$278$	−2.37258	+	5.72792i	−0.142298	+	0.343538i
$279$	−11.4853	−	4.75736i	−0.687606	−	0.284816i
$280$	2.24264	−	2.24264i	0.134023	−	0.134023i
$281$	12.6569	−	12.6569i	0.755045	−	0.755045i	−0.220371	−	0.975416i	$-0.570727\pi$
$281$	12.6569	−	12.6569i	0.755045	−	0.755045i	0.975416	+	0.220371i	$0.0707269\pi$
$282$	10.8284	+	4.48528i	0.644823	+	0.267095i
$283$	−8.75736	+	21.1421i	−0.520571	+	1.25677i	0.416978	+	0.908917i	$0.363089\pi$
$283$	−8.75736	+	21.1421i	−0.520571	+	1.25677i	−0.937549	+	0.347853i	$0.886911\pi$
$284$	−22.0711	+	9.14214i	−1.30968	+	0.542486i
$285$		−	23.3137i		−	1.38098i
$286$	0.242641	+	0.585786i	0.0143476	+	0.0346383i
$287$	−6.24264	−	6.24264i	−0.368491	−	0.368491i
$288$	16.8995			0.995812
$289$		0			0
$290$	−3.41421			−0.200490
$291$	11.8995	+	11.8995i	0.697561	+	0.697561i
$292$	3.74874	+	9.05025i	0.219378	+	0.529626i
$293$		−	23.6569i		−	1.38205i	−0.722832	−	0.691024i	$-0.757160\pi$
$293$		−	23.6569i		−	1.38205i	0.722832	−	0.691024i	$-0.242840\pi$
$294$	5.82843	−	2.41421i	0.339921	−	0.140800i
$295$	4.24264	−	10.2426i	0.247016	−	0.596350i
$296$	5.60660	+	2.32233i	0.325877	+	0.134983i
$297$	−1.65685	+	1.65685i	−0.0961404	+	0.0961404i
$298$	4.97056	−	4.97056i	0.287937	−	0.287937i
$299$	−5.41421	−	2.24264i	−0.313112	−	0.129695i
$300$	−2.89949	+	7.00000i	−0.167402	+	0.404145i
$301$	4.82843	−	2.00000i	0.278306	−	0.115278i
$302$			5.31371i			0.305770i
$303$	−13.4142	−	32.3848i	−0.770626	−	1.86046i
$304$	10.2426	+	10.2426i	0.587456	+	0.587456i
$305$	17.0711			0.977486
$306$		0			0
$307$	2.14214			0.122258			0.0611291	−	0.998130i	$-0.480530\pi$
$307$	2.14214			0.122258			0.0611291	+	0.998130i	$0.480530\pi$
$308$	−1.51472	−	1.51472i	−0.0863091	−	0.0863091i
$309$	−4.48528	−	10.8284i	−0.255159	−	0.616008i
$310$			2.48528i			0.141154i
$311$	−4.17157	+	1.72792i	−0.236548	+	0.0979815i	−0.497809	−	0.867287i	$-0.665862\pi$
$311$	−4.17157	+	1.72792i	−0.236548	+	0.0979815i	0.261261	+	0.965268i	$0.415862\pi$
$312$	−2.24264	+	5.41421i	−0.126965	+	0.306519i
$313$	−11.7782	−	4.87868i	−0.665742	−	0.275759i	0.0241106	−	0.999709i	$-0.492325\pi$
$313$	−11.7782	−	4.87868i	−0.665742	−	0.275759i	−0.689852	+	0.723950i	$0.742325\pi$
$314$	−0.485281	+	0.485281i	−0.0273860	+	0.0273860i
$315$	−5.41421	+	5.41421i	−0.305056	+	0.305056i
$316$	−7.00000	−	2.89949i	−0.393781	−	0.163109i
$317$	2.22183	−	5.36396i	0.124790	−	0.301270i	−0.849122	−	0.528198i	$-0.822868\pi$
$317$	2.22183	−	5.36396i	0.124790	−	0.301270i	0.973912	+	0.226927i	$0.0728680\pi$
$318$	−1.41421	+	0.585786i	−0.0793052	+	0.0328493i
$319$			4.82843i			0.270340i
$320$	2.94975	+	7.12132i	0.164896	+	0.398094i
$321$	−11.6569	−	11.6569i	−0.650622	−	0.650622i
$322$	−1.85786			−0.103535
$323$		0			0
$324$	10.6569			0.592047
$325$	−1.58579	−	1.58579i	−0.0879636	−	0.0879636i
$326$	−0.899495	−	2.17157i	−0.0498184	−	0.120272i
$327$			11.1716i			0.617789i
$328$	−11.9497	+	4.94975i	−0.659814	+	0.273304i
$329$	4.48528	−	10.8284i	0.247282	−	0.596991i
$330$	2.00000	+	0.828427i	0.110096	+	0.0456034i
$331$	12.5858	−	12.5858i	0.691777	−	0.691777i	−0.270845	−	0.962623i	$-0.587303\pi$
$331$	12.5858	−	12.5858i	0.691777	−	0.691777i	0.962623	+	0.270845i	$0.0873032\pi$
$332$	0.443651	−	0.443651i	0.0243485	−	0.0243485i
$333$	−13.5355	−	5.60660i	−0.741743	−	0.307240i
$334$	1.58579	−	3.82843i	0.0867704	−	0.209482i
$335$	11.6569	−	4.82843i	0.636882	−	0.263805i
$336$		−	8.48528i		−	0.462910i
$337$	13.1924	+	31.8492i	0.718635	+	1.73494i	0.677202	+	0.735798i	$0.263192\pi$
$337$	13.1924	+	31.8492i	0.718635	+	1.73494i	0.0414336	+	0.999141i	$0.486808\pi$
$338$	3.22183	+	3.22183i	0.175244	+	0.175244i
$339$	−42.2843			−2.29657
$340$		0			0
$341$	3.51472			0.190333
$342$	5.41421	+	5.41421i	0.292767	+	0.292767i
$343$	−5.31371	−	12.8284i	−0.286913	−	0.692670i
$344$		−	7.65685i		−	0.412830i
$345$	−18.4853	+	7.65685i	−0.995214	+	0.412231i
$346$	−0.535534	+	1.29289i	−0.0287905	+	0.0695064i
$347$	−3.58579	−	1.48528i	−0.192495	−	0.0797341i	0.284354	−	0.958719i	$-0.408221\pi$
$347$	−3.58579	−	1.48528i	−0.192495	−	0.0797341i	−0.476849	+	0.878985i	$0.658221\pi$
$348$	−15.0711	+	15.0711i	−0.807894	+	0.807894i
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$	−0.656854	−	0.272078i	−0.0351103	−	0.0145432i
$351$	1.17157	−	2.82843i	0.0625339	−	0.150970i
$352$	−4.41421	+	1.82843i	−0.235278	+	0.0974555i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$	2.48528	+	6.00000i	0.132091	+	0.318896i
$355$	−17.0711	−	17.0711i	−0.906038	−	0.906038i
$356$	17.2132			0.912298
$357$		0			0
$358$	−2.48528			−0.131351
$359$	−16.3848	−	16.3848i	−0.864755	−	0.864755i	0.127131	−	0.991886i	$-0.459423\pi$
$359$	−16.3848	−	16.3848i	−0.864755	−	0.864755i	−0.991886	+	0.127131i	$0.959423\pi$
$360$	4.29289	+	10.3640i	0.226255	+	0.546229i
$361$			4.31371i			0.227037i
$362$	4.77817	−	1.97918i	0.251135	−	0.104024i
$363$	−9.82843	+	23.7279i	−0.515859	+	1.24539i
$364$	2.58579	+	1.07107i	0.135532	+	0.0561392i
$365$	−7.00000	+	7.00000i	−0.366397	+	0.366397i
$366$	−7.07107	+	7.07107i	−0.369611	+	0.369611i
$367$	24.3137	+	10.0711i	1.26917	+	0.525705i	0.912710	−	0.408607i	$-0.133985\pi$
$367$	24.3137	+	10.0711i	1.26917	+	0.525705i	0.356455	+	0.934313i	$0.383985\pi$
$368$	4.75736	−	11.4853i	0.247994	−	0.598712i
$369$	28.8492	−	11.9497i	1.50183	−	0.622079i
$370$			2.92893i			0.152268i
$371$	0.585786	+	1.41421i	0.0304125	+	0.0734223i
$372$	10.9706	+	10.9706i	0.568797	+	0.568797i
$373$	−19.5563			−1.01259			−0.506295	−	0.862361i	$-0.668985\pi$
$373$	−19.5563			−1.01259			−0.506295	+	0.862361i	$0.668985\pi$
$374$		0			0
$375$	−31.7990			−1.64209
$376$	−12.1421	−	12.1421i	−0.626183	−	0.626183i
$377$	−2.41421	−	5.82843i	−0.124338	−	0.300179i
$378$		−	0.970563i		−	0.0499204i
$379$	1.00000	−	0.414214i	0.0513665	−	0.0212767i	−0.356852	−	0.934161i	$-0.616150\pi$
$379$	1.00000	−	0.414214i	0.0513665	−	0.0212767i	0.408219	+	0.912884i	$0.366150\pi$
$380$	−6.24264	+	15.0711i	−0.320241	+	0.773129i
$381$	41.7990	+	17.3137i	2.14143	+	0.887008i
$382$	−5.85786	+	5.85786i	−0.299714	+	0.299714i
$383$	−3.89949	+	3.89949i	−0.199255	+	0.199255i	−0.799681	−	0.600426i	$-0.794998\pi$
$383$	−3.89949	+	3.89949i	−0.199255	+	0.199255i	0.600426	+	0.799681i	$0.294998\pi$
$384$	−25.4853	−	10.5563i	−1.30054	−	0.538701i
$385$	0.828427	−	2.00000i	0.0422206	−	0.101929i
$386$	−2.12132	+	0.878680i	−0.107972	+	0.0447236i
$387$			18.4853i			0.939660i
$388$	−4.50610	−	10.8787i	−0.228762	−	0.552281i
$389$	11.4142	+	11.4142i	0.578724	+	0.578724i	0.934551	−	0.355828i	$-0.115801\pi$
$389$	11.4142	+	11.4142i	0.578724	+	0.578724i	−0.355828	+	0.934551i	$0.615801\pi$
$390$	−2.82843			−0.143223
$391$		0			0
$392$	−9.24264			−0.466824
$393$	0.343146	+	0.343146i	0.0173094	+	0.0173094i
$394$	−2.36396	−	5.70711i	−0.119095	−	0.287520i
$395$		−	7.65685i		−	0.385258i
$396$	7.00000	−	2.89949i	0.351763	−	0.145705i
$397$	−10.4350	+	25.1924i	−0.523719	+	1.26437i	0.411858	+	0.911248i	$0.364880\pi$
$397$	−10.4350	+	25.1924i	−0.523719	+	1.26437i	−0.935577	+	0.353122i	$0.885120\pi$
$398$	−0.656854	−	0.272078i	−0.0329251	−	0.0136380i
$399$	9.65685	−	9.65685i	0.483447	−	0.483447i
$400$	3.36396	−	3.36396i	0.168198	−	0.168198i
$401$	15.7782	+	6.53553i	0.787924	+	0.326369i	0.740109	−	0.672487i	$-0.234774\pi$
$401$	15.7782	+	6.53553i	0.787924	+	0.326369i	0.0478157	+	0.998856i	$0.484774\pi$
$402$	−2.82843	+	6.82843i	−0.141069	+	0.340571i
$403$	−4.24264	+	1.75736i	−0.211341	+	0.0875403i
$404$			24.5269i			1.22026i
$405$	4.12132	+	9.94975i	0.204790	+	0.494407i
$406$	−1.41421	−	1.41421i	−0.0701862	−	0.0701862i
$407$	4.14214			0.205318
$408$		0			0
$409$	19.3137			0.955001			0.477501	−	0.878631i	$-0.341543\pi$
$409$	19.3137			0.955001			0.477501	+	0.878631i	$0.341543\pi$
$410$	−4.41421	−	4.41421i	−0.218002	−	0.218002i
$411$	8.72792	+	21.0711i	0.430517	+	1.03936i
$412$			8.20101i			0.404035i
$413$	6.00000	−	2.48528i	0.295241	−	0.122293i
$414$	2.51472	−	6.07107i	0.123592	−	0.298377i
$415$	0.585786	+	0.242641i	0.0287551	+	0.0119108i
$416$	4.41421	−	4.41421i	0.216425	−	0.216425i
$417$	−27.6569	+	27.6569i	−1.35436	+	1.35436i
$418$	−2.00000	−	0.828427i	−0.0978232	−	0.0405197i
$419$	10.3137	−	24.8995i	0.503858	−	1.21642i	−0.443509	−	0.896270i	$-0.646267\pi$
$419$	10.3137	−	24.8995i	0.503858	−	1.21642i	0.947367	−	0.320150i	$-0.103733\pi$
$420$	8.82843	−	3.65685i	0.430783	−	0.178436i
$421$		−	17.4142i		−	0.848717i	−0.905494	−	0.424358i	$-0.860500\pi$
$421$		−	17.4142i		−	0.848717i	0.905494	−	0.424358i	$-0.139500\pi$
$422$	2.37258	+	5.72792i	0.115496	+	0.278831i
$423$	29.3137	+	29.3137i	1.42528	+	1.42528i
$424$	2.24264			0.108912
$425$		0			0
$426$	14.1421			0.685189
$427$	7.07107	+	7.07107i	0.342193	+	0.342193i
$428$	4.41421	+	10.6569i	0.213369	+	0.515118i
$429$			4.00000i			0.193122i
$430$	3.41421	−	1.41421i	0.164648	−	0.0681994i
$431$	15.2426	−	36.7990i	0.734212	−	1.77254i	0.106195	−	0.994345i	$-0.466133\pi$
$431$	15.2426	−	36.7990i	0.734212	−	1.77254i	0.628017	−	0.778200i	$-0.283867\pi$
$432$	6.00000	+	2.48528i	0.288675	+	0.119573i
$433$	10.7279	−	10.7279i	0.515551	−	0.515551i	−0.400671	−	0.916222i	$-0.631223\pi$
$433$	10.7279	−	10.7279i	0.515551	−	0.515551i	0.916222	+	0.400671i	$0.131223\pi$
$434$	−1.02944	+	1.02944i	−0.0494146	+	0.0494146i
$435$	−19.8995	−	8.24264i	−0.954108	−	0.395204i
$436$	2.99138	−	7.22183i	0.143261	−	0.345863i
$437$	18.4853	−	7.65685i	0.884271	−	0.366277i
$438$		−	5.79899i		−	0.277086i
$439$	−4.17157	−	10.0711i	−0.199098	−	0.480666i	0.792523	−	0.609841i	$-0.208767\pi$
$439$	−4.17157	−	10.0711i	−0.199098	−	0.480666i	−0.991622	+	0.129176i	$0.958767\pi$
$440$	−2.24264	−	2.24264i	−0.106914	−	0.106914i
$441$	22.3137			1.06256
$442$		0			0
$443$	15.7990			0.750633			0.375316	−	0.926897i	$-0.377534\pi$
$443$	15.7990			0.750633			0.375316	+	0.926897i	$0.377534\pi$
$444$	12.9289	+	12.9289i	0.613580	+	0.613580i
$445$	6.65685	+	16.0711i	0.315565	+	0.761842i
$446$		−	0.343146i		−	0.0162484i
$447$	40.9706	−	16.9706i	1.93784	−	0.802680i
$448$	−1.72792	+	4.17157i	−0.0816366	+	0.197088i
$449$	−17.3640	−	7.19239i	−0.819456	−	0.339430i	−0.0667361	−	0.997771i	$-0.521259\pi$
$449$	−17.3640	−	7.19239i	−0.819456	−	0.339430i	−0.752720	+	0.658341i	$0.771259\pi$
$450$	1.77817	−	1.77817i	0.0838240	−	0.0838240i
$451$	−6.24264	+	6.24264i	−0.293954	+	0.293954i
$452$	27.3345	+	11.3223i	1.28571	+	0.532558i
$453$	−12.8284	+	30.9706i	−0.602732	+	1.45512i
$454$	1.92893	−	0.798990i	0.0905293	−	0.0374985i
$455$			2.82843i			0.132599i
$456$	−7.65685	−	18.4853i	−0.358565	−	0.865653i
$457$	13.3137	+	13.3137i	0.622789	+	0.622789i	0.946244	−	0.323455i	$-0.104844\pi$
$457$	13.3137	+	13.3137i	0.622789	+	0.622789i	−0.323455	+	0.946244i	$0.604844\pi$
$458$	−9.45584			−0.441843
$459$		0			0
$460$	14.0000			0.652753
$461$	−17.0000	−	17.0000i	−0.791769	−	0.791769i	0.190013	−	0.981782i	$-0.439147\pi$
$461$	−17.0000	−	17.0000i	−0.791769	−	0.791769i	−0.981782	+	0.190013i	$0.939147\pi$
$462$	0.485281	+	1.17157i	0.0225773	+	0.0545065i
$463$		−	30.6274i		−	1.42338i	−0.702495	−	0.711688i	$-0.747931\pi$
$463$		−	30.6274i		−	1.42338i	0.702495	−	0.711688i	$-0.252069\pi$
$464$	12.3640	−	5.12132i	0.573982	−	0.237751i
$465$	−6.00000	+	14.4853i	−0.278243	+	0.671739i
$466$	3.87868	+	1.60660i	0.179676	+	0.0744244i
$467$	−8.92893	+	8.92893i	−0.413182	+	0.413182i	−0.882845	−	0.469664i	$-0.844375\pi$
$467$	−8.92893	+	8.92893i	−0.413182	+	0.413182i	0.469664	+	0.882845i	$0.344375\pi$
$468$	−7.00000	+	7.00000i	−0.323575	+	0.323575i
$469$	6.82843	+	2.82843i	0.315307	+	0.130605i
$470$	3.17157	−	7.65685i	0.146294	−	0.353184i
$471$	−4.00000	+	1.65685i	−0.184310	+	0.0763438i
$472$		−	9.51472i		−	0.437950i
$473$	−2.00000	−	4.82843i	−0.0919601	−	0.222011i
$474$	3.17157	+	3.17157i	0.145675	+	0.145675i
$475$	7.65685			0.351321
$476$		0			0
$477$	−5.41421			−0.247900
$478$	2.68629	+	2.68629i	0.122868	+	0.122868i
$479$	13.2426	+	31.9706i	0.605072	+	1.46077i	0.868300	+	0.496039i	$0.165213\pi$
$479$	13.2426	+	31.9706i	0.605072	+	1.46077i	−0.263229	+	0.964733i	$0.584787\pi$
$480$		−	21.3137i		−	0.972833i
$481$	−5.00000	+	2.07107i	−0.227980	+	0.0944326i
$482$	1.94975	−	4.70711i	0.0888086	−	0.214403i
$483$	−10.8284	−	4.48528i	−0.492710	−	0.204087i
$484$	12.7071	−	12.7071i	0.577596	−	0.577596i
$485$	8.41421	−	8.41421i	0.382070	−	0.382070i
$486$	−8.31371	−	3.44365i	−0.377117	−	0.156207i
$487$	1.68629	−	4.07107i	0.0764132	−	0.184478i	−0.881057	−	0.473010i	$-0.843167\pi$
$487$	1.68629	−	4.07107i	0.0764132	−	0.184478i	0.957470	+	0.288533i	$0.0931674\pi$
$488$	13.5355	−	5.60660i	0.612725	−	0.253799i
$489$		−	14.8284i		−	0.670565i
$490$	−1.70711	−	4.12132i	−0.0771192	−	0.186182i
$491$	−17.7574	−	17.7574i	−0.801378	−	0.801378i	0.181933	−	0.983311i	$-0.441765\pi$
$491$	−17.7574	−	17.7574i	−0.801378	−	0.801378i	−0.983311	+	0.181933i	$0.941765\pi$
$492$	−38.9706			−1.75693
$493$		0			0
$494$	2.82843			0.127257
$495$	5.41421	+	5.41421i	0.243351	+	0.243351i
$496$	−3.72792	−	9.00000i	−0.167389	−	0.404112i
$497$		−	14.1421i		−	0.634361i
$498$	−0.343146	+	0.142136i	−0.0153767	+	0.00636925i
$499$	−14.1716	+	34.2132i	−0.634407	+	1.53159i	0.199622	+	0.979873i	$0.436028\pi$
$499$	−14.1716	+	34.2132i	−0.634407	+	1.53159i	−0.834029	+	0.551720i	$0.813972\pi$
$500$	20.5563	+	8.51472i	0.919308	+	0.380790i
$501$	18.4853	−	18.4853i	0.825861	−	0.825861i
$502$	1.02944	−	1.02944i	0.0459460	−	0.0459460i
$503$	13.8284	+	5.72792i	0.616579	+	0.255395i	0.669039	−	0.743228i	$-0.266706\pi$
$503$	13.8284	+	5.72792i	0.616579	+	0.255395i	−0.0524595	+	0.998623i	$0.516706\pi$
$504$	−2.51472	+	6.07107i	−0.112014	+	0.270427i
$505$	−22.8995	+	9.48528i	−1.01901	+	0.422089i
$506$			1.85786i			0.0825921i
$507$	11.0000	+	26.5563i	0.488527	+	1.17941i
$508$	−22.3848	−	22.3848i	−0.993164	−	0.993164i
$509$	−3.02944			−0.134277			−0.0671387	−	0.997744i	$-0.521387\pi$
$509$	−3.02944			−0.134277			−0.0671387	+	0.997744i	$0.521387\pi$
$510$		0			0
$511$	−5.79899			−0.256532
$512$	16.0919	+	16.0919i	0.711167	+	0.711167i
$513$	4.00000	+	9.65685i	0.176604	+	0.426361i
$514$			9.17157i			0.404541i
$515$	−7.65685	+	3.17157i	−0.337401	+	0.139756i
$516$	8.82843	−	21.3137i	0.388650	−	0.938284i
$517$	−10.8284	−	4.48528i	−0.476234	−	0.197262i
$518$	−1.21320	+	1.21320i	−0.0533051	+	0.0533051i
$519$	−6.24264	+	6.24264i	−0.274022	+	0.274022i
$520$	3.82843	+	1.58579i	0.167888	+	0.0695413i
$521$	−1.19239	+	2.87868i	−0.0522395	+	0.126117i	−0.947845	−	0.318732i	$-0.896743\pi$
$521$	−1.19239	+	2.87868i	−0.0522395	+	0.126117i	0.895605	+	0.444850i	$0.146743\pi$
$522$	6.53553	−	2.70711i	0.286053	−	0.118487i
$523$		−	6.82843i		−	0.298586i	−0.988793	−	0.149293i	$-0.952300\pi$
$523$		−	6.82843i		−	0.298586i	0.988793	−	0.149293i	$-0.0476998\pi$
$524$	−0.129942	−	0.313708i	−0.00567656	−	0.0137044i
$525$	−3.17157	−	3.17157i	−0.138419	−	0.138419i
$526$	2.68629			0.117128
$527$		0			0
$528$	−8.48528			−0.369274
$529$	4.12132	+	4.12132i	0.179188	+	0.179188i
$530$	0.414214	+	1.00000i	0.0179923	+	0.0434372i
$531$			22.9706i			0.996838i
$532$	−8.82843	+	3.65685i	−0.382761	+	0.158545i
$533$	4.41421	−	10.6569i	0.191201	−	0.461600i
$534$	−9.41421	−	3.89949i	−0.407393	−	0.168748i
$535$	−8.24264	+	8.24264i	−0.356360	+	0.356360i
$536$	7.65685	−	7.65685i	0.330726	−	0.330726i
$537$	−14.4853	−	6.00000i	−0.625086	−	0.258919i
$538$	1.00862	−	2.43503i	0.0434848	−	0.104982i
$539$	−5.82843	+	2.41421i	−0.251048	+	0.103988i
$540$			7.31371i			0.314732i
$541$	7.02082	+	16.9497i	0.301848	+	0.728727i	0.999919	+	0.0126980i	$0.00404200\pi$
$541$	7.02082	+	16.9497i	0.301848	+	0.728727i	−0.698071	+	0.716029i	$0.745958\pi$
$542$	−1.79899	−	1.79899i	−0.0772732	−	0.0772732i
$543$	32.6274			1.40018
$544$		0			0
$545$	7.89949			0.338377
$546$	−1.17157	−	1.17157i	−0.0501387	−	0.0501387i
$547$	−9.48528	−	22.8995i	−0.405561	−	0.979112i	−0.986291	−	0.165015i	$-0.947233\pi$
$547$	−9.48528	−	22.8995i	−0.405561	−	0.979112i	0.580730	−	0.814096i	$-0.302767\pi$
$548$		−	15.9584i		−	0.681708i
$549$	−32.6777	+	13.5355i	−1.39465	+	0.577683i
$550$	−0.272078	+	0.656854i	−0.0116014	+	0.0280084i
$551$	19.8995	+	8.24264i	0.847747	+	0.351148i
$552$	−12.1421	+	12.1421i	−0.516804	+	0.516804i
$553$	3.17157	−	3.17157i	0.134869	−	0.134869i
$554$	8.43503	+	3.49390i	0.358370	+	0.148442i
$555$	−7.07107	+	17.0711i	−0.300150	+	0.724626i
$556$	25.2843	−	10.4731i	1.07229	−	0.444158i
$557$			28.2426i			1.19668i	0.801243	+	0.598340i	$0.204173\pi$
$557$			28.2426i			1.19668i	−0.801243	+	0.598340i	$0.795827\pi$
$558$	−1.97056	−	4.75736i	−0.0834206	−	0.201395i
$559$	4.82843	+	4.82843i	0.204221	+	0.204221i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	7.41421			0.312750
$563$	−27.4142	−	27.4142i	−1.15537	−	1.15537i	−0.985459	−	0.169912i	$-0.945652\pi$
$563$	−27.4142	−	27.4142i	−1.15537	−	1.15537i	−0.169912	−	0.985459i	$-0.554348\pi$
$564$	−19.7990	−	47.7990i	−0.833688	−	2.01270i
$565$			29.8995i			1.25788i
$566$	−8.75736	+	3.62742i	−0.368099	+	0.152472i
$567$	−2.41421	+	5.82843i	−0.101387	+	0.244771i
$568$	−19.1421	−	7.92893i	−0.803186	−	0.332691i
$569$	−25.4853	+	25.4853i	−1.06840	+	1.06840i	−0.0709163	+	0.997482i	$0.522592\pi$
$569$	−25.4853	+	25.4853i	−1.06840	+	1.06840i	−0.997482	+	0.0709163i	$0.977408\pi$
$570$	6.82843	−	6.82843i	0.286011	−	0.286011i
$571$	−43.6274	−	18.0711i	−1.82575	−	0.756251i	−0.971764	−	0.235956i	$-0.924178\pi$
$571$	−43.6274	−	18.0711i	−1.82575	−	0.756251i	−0.853987	−	0.520295i	$-0.825822\pi$
$572$	1.07107	−	2.58579i	0.0447836	−	0.108117i
$573$	−48.2843	+	20.0000i	−2.01710	+	0.835512i
$574$		−	3.65685i		−	0.152634i
$575$	−2.51472	−	6.07107i	−0.104871	−	0.253181i
$576$	−11.2929	−	11.2929i	−0.470537	−	0.470537i
$577$	−12.9289			−0.538238			−0.269119	−	0.963107i	$-0.586733\pi$
$577$	−12.9289			−0.538238			−0.269119	+	0.963107i	$0.586733\pi$
$578$		0			0
$579$	−14.4853			−0.601988
$580$	10.6569	+	10.6569i	0.442502	+	0.442502i
$581$	0.142136	+	0.343146i	0.00589678	+	0.0142361i
$582$			6.97056i			0.288939i
$583$	1.41421	−	0.585786i	0.0585707	−	0.0242608i
$584$	−3.25126	+	7.84924i	−0.134538	+	0.324804i
$585$	−9.24264	−	3.82843i	−0.382136	−	0.158286i
$586$	6.92893	−	6.92893i	0.286232	−	0.286232i
$587$	16.0416	−	16.0416i	0.662109	−	0.662109i	−0.293768	−	0.955877i	$-0.594909\pi$
$587$	16.0416	−	16.0416i	0.662109	−	0.662109i	0.955877	+	0.293768i	$0.0949093\pi$
$588$	−25.7279	−	10.6569i	−1.06100	−	0.439481i
$589$	6.00000	−	14.4853i	0.247226	−	0.596856i
$590$	4.24264	−	1.75736i	0.174667	−	0.0723493i
$591$		−	38.9706i		−	1.60303i
$592$	−4.39340	−	10.6066i	−0.180568	−	0.435929i
$593$	19.1421	+	19.1421i	0.786073	+	0.786073i	0.980848	−	0.194775i	$-0.0623976\pi$
$593$	19.1421	+	19.1421i	0.786073	+	0.786073i	−0.194775	+	0.980848i	$0.562398\pi$
$594$	−0.970563			−0.0398227
$595$		0			0
$596$	−31.0294			−1.27102
$597$	−3.17157	−	3.17157i	−0.129804	−	0.129804i
$598$	−0.928932	−	2.24264i	−0.0379869	−	0.0917084i
$599$			34.6274i			1.41484i	0.706794	+	0.707419i	$0.250141\pi$
$599$			34.6274i			1.41484i	−0.706794	+	0.707419i	$0.749859\pi$
$600$	−6.07107	+	2.51472i	−0.247850	+	0.102663i
$601$	7.77817	−	18.7782i	0.317278	−	0.765978i	−0.682118	−	0.731242i	$-0.738941\pi$
$601$	7.77817	−	18.7782i	0.317278	−	0.765978i	0.999397	−	0.0347358i	$-0.0110590\pi$
$602$	2.00000	+	0.828427i	0.0815139	+	0.0337642i
$603$	−18.4853	+	18.4853i	−0.752779	+	0.752779i
$604$	16.5858	−	16.5858i	0.674866	−	0.674866i
$605$	16.7782	+	6.94975i	0.682130	+	0.282547i
$606$	5.55635	−	13.4142i	0.225711	−	0.544915i
$607$	−31.7279	+	13.1421i	−1.28780	+	0.533423i	−0.918328	−	0.395820i	$-0.870460\pi$
$607$	−31.7279	+	13.1421i	−1.28780	+	0.533423i	−0.369469	+	0.929243i	$0.620460\pi$
$608$			21.3137i			0.864385i
$609$	−4.82843	−	11.6569i	−0.195658	−	0.472360i
$610$	5.00000	+	5.00000i	0.202444	+	0.202444i
$611$	15.3137			0.619526
$612$		0			0
$613$	−17.3137			−0.699294			−0.349647	−	0.936881i	$-0.613698\pi$
$613$	−17.3137			−0.699294			−0.349647	+	0.936881i	$0.613698\pi$
$614$	0.627417	+	0.627417i	0.0253205	+	0.0253205i
$615$	−15.0711	−	36.3848i	−0.607724	−	1.46718i
$616$		−	1.85786i		−	0.0748555i
$617$	−3.12132	+	1.29289i	−0.125660	+	0.0520499i	−0.444627	−	0.895716i	$-0.646664\pi$
$617$	−3.12132	+	1.29289i	−0.125660	+	0.0520499i	0.318968	+	0.947766i	$0.396664\pi$
$618$	1.85786	−	4.48528i	0.0747343	−	0.180424i
$619$	8.89949	+	3.68629i	0.357701	+	0.148165i	0.554295	−	0.832320i	$-0.312988\pi$
$619$	8.89949	+	3.68629i	0.357701	+	0.148165i	−0.196594	+	0.980485i	$0.562988\pi$
$620$	7.75736	−	7.75736i	0.311543	−	0.311543i
$621$	6.34315	−	6.34315i	0.254542	−	0.254542i
$622$	−1.72792	−	0.715729i	−0.0692834	−	0.0286981i
$623$	−3.89949	+	9.41421i	−0.156230	+	0.377173i
$624$	10.2426	−	4.24264i	0.410034	−	0.169842i
$625$			14.5563i			0.582254i
$626$	−2.02082	−	4.87868i	−0.0807680	−	0.194991i
$627$	−9.65685	−	9.65685i	−0.385658	−	0.385658i
$628$	3.02944			0.120888
$629$		0			0
$630$	−3.17157			−0.126358
$631$	−4.72792	−	4.72792i	−0.188216	−	0.188216i	0.606709	−	0.794924i	$-0.292489\pi$
$631$	−4.72792	−	4.72792i	−0.188216	−	0.188216i	−0.794924	+	0.606709i	$0.792489\pi$
$632$	−2.51472	−	6.07107i	−0.100030	−	0.241494i
$633$			39.1127i			1.55459i
$634$	2.22183	−	0.920310i	0.0882400	−	0.0365502i
$635$	12.2426	−	29.5563i	0.485834	−	1.17291i
$636$	6.24264	+	2.58579i	0.247537	+	0.102533i
$637$	5.82843	−	5.82843i	0.230931	−	0.230931i
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	46.2132	+	19.1421i	1.82817	+	0.757251i
$640$	−7.46447	+	18.0208i	−0.295059	+	0.712335i
$641$	−13.8492	+	5.73654i	−0.547012	+	0.226580i	−0.639036	−	0.769177i	$-0.720666\pi$
$641$	−13.8492	+	5.73654i	−0.547012	+	0.226580i	0.0920237	+	0.995757i	$0.470666\pi$
$642$		−	6.82843i		−	0.269497i
$643$	15.3431	+	37.0416i	0.605075	+	1.46078i	0.868297	+	0.496044i	$0.165215\pi$
$643$	15.3431	+	37.0416i	0.605075	+	1.46078i	−0.263223	+	0.964735i	$0.584785\pi$
$644$	5.79899	+	5.79899i	0.228512	+	0.228512i
$645$	23.3137			0.917976
$646$		0			0
$647$	2.82843			0.111197			0.0555985	−	0.998453i	$-0.482293\pi$
$647$	2.82843			0.111197			0.0555985	+	0.998453i	$0.482293\pi$
$648$	6.53553	+	6.53553i	0.256740	+	0.256740i
$649$	−2.48528	−	6.00000i	−0.0975558	−	0.235521i
$650$		−	0.928932i		−	0.0364357i
$651$	−8.48528	+	3.51472i	−0.332564	+	0.137753i
$652$	−3.97056	+	9.58579i	−0.155499	+	0.375408i
$653$	−16.3640	−	6.77817i	−0.640371	−	0.265250i	0.0387812	−	0.999248i	$-0.487652\pi$
$653$	−16.3640	−	6.77817i	−0.640371	−	0.265250i	−0.679152	+	0.733997i	$0.737652\pi$
$654$	−3.27208	+	3.27208i	−0.127948	+	0.127948i
$655$	0.242641	−	0.242641i	0.00948076	−	0.00948076i
$656$	22.6066	+	9.36396i	0.882640	+	0.365601i
$657$	7.84924	−	18.9497i	0.306228	−	0.739300i
$658$	4.48528	−	1.85786i	0.174854	−	0.0724271i
$659$		−	8.48528i		−	0.330540i	−0.986248	−	0.165270i	$-0.947151\pi$
$659$		−	8.48528i		−	0.330540i	0.986248	−	0.165270i	$-0.0528495\pi$
$660$	−3.65685	−	8.82843i	−0.142343	−	0.343646i
$661$	−29.1421	−	29.1421i	−1.13350	−	1.13350i	−0.989591	−	0.143906i	$-0.954034\pi$
$661$	−29.1421	−	29.1421i	−1.13350	−	1.13350i	−0.143906	−	0.989591i	$-0.545966\pi$
$662$	7.37258			0.286544
$663$		0			0
$664$	0.544156			0.0211173
$665$	−6.82843	−	6.82843i	−0.264795	−	0.264795i
$666$	−2.32233	−	5.60660i	−0.0899885	−	0.217251i
$667$		−	18.4853i		−	0.715753i
$668$	−16.8995	+	7.00000i	−0.653861	+	0.270838i
$669$	0.828427	−	2.00000i	0.0320288	−	0.0773245i
$670$	4.82843	+	2.00000i	0.186538	+	0.0772667i
$671$	7.07107	−	7.07107i	0.272976	−	0.272976i
$672$	8.82843	−	8.82843i	0.340564	−	0.340564i
$673$	−0.292893	−	0.121320i	−0.0112902	−	0.00467656i	0.377031	−	0.926201i	$-0.376945\pi$
$673$	−0.292893	−	0.121320i	−0.0112902	−	0.00467656i	−0.388321	+	0.921524i	$0.626945\pi$
$674$	−5.46447	+	13.1924i	−0.210483	+	0.508152i
$675$	3.17157	−	1.31371i	0.122074	−	0.0505647i
$676$		−	20.1127i		−	0.773565i
$677$	−16.8076	−	40.5772i	−0.645969	−	1.55951i	−0.818502	−	0.574503i	$-0.805195\pi$
$677$	−16.8076	−	40.5772i	−0.645969	−	1.55951i	0.172533	−	0.985004i	$-0.444805\pi$
$678$	−12.3848	−	12.3848i	−0.475634	−	0.475634i
$679$	6.97056			0.267506
$680$		0			0
$681$	13.1716			0.504736
$682$	1.02944	+	1.02944i	0.0394192	+	0.0394192i
$683$	11.9706	+	28.8995i	0.458041	+	1.10581i	0.969190	+	0.246316i	$0.0792201\pi$
$683$	11.9706	+	28.8995i	0.458041	+	1.10581i	−0.511149	+	0.859492i	$0.670780\pi$
$684$		−	33.7990i		−	1.29234i
$685$	14.8995	−	6.17157i	0.569280	−	0.235804i
$686$	2.20101	−	5.31371i	0.0840350	−	0.202878i
$687$	−55.1127	−	22.8284i	−2.10268	−	0.870959i
$688$	−10.2426	+	10.2426i	−0.390497	+	0.390497i
$689$	−1.41421	+	1.41421i	−0.0538772	+	0.0538772i
$690$	−7.65685	−	3.17157i	−0.291491	−	0.120740i
$691$	−15.5858	+	37.6274i	−0.592911	+	1.43141i	0.287767	+	0.957700i	$0.407087\pi$
$691$	−15.5858	+	37.6274i	−0.592911	+	1.43141i	−0.880679	+	0.473714i	$0.842913\pi$
$692$	5.70711	−	2.36396i	0.216952	−	0.0898643i
$693$			4.48528i			0.170382i
$694$	−0.615224	−	1.48528i	−0.0233536	−	0.0563805i
$695$	19.5563	+	19.5563i	0.741815	+	0.741815i
$696$	−18.4853			−0.700683
$697$		0			0
$698$	−1.75736			−0.0665170
$699$	18.7279	+	18.7279i	0.708355	+	0.708355i
$700$	1.20101	+	2.89949i	0.0453939	+	0.109591i
$701$		−	21.6985i		−	0.819540i	−0.912189	−	0.409770i	$-0.865609\pi$
$701$		−	21.6985i		−	0.819540i	0.912189	−	0.409770i	$-0.134391\pi$
$702$	1.17157	−	0.485281i	0.0442182	−	0.0183158i
$703$	7.07107	−	17.0711i	0.266690	−	0.643848i
$704$	4.17157	+	1.72792i	0.157222	+	0.0651235i
$705$	36.9706	−	36.9706i	1.39239	−	1.39239i
$706$	−4.10051	+	4.10051i	−0.154325	+	0.154325i
$707$	−13.4142	−	5.55635i	−0.504493	−	0.208968i
$708$	10.9706	−	26.4853i	0.412299	−	0.995378i
$709$	−10.7071	+	4.43503i	−0.402114	+	0.166561i	−0.574569	−	0.818456i	$-0.694830\pi$
$709$	−10.7071	+	4.43503i	−0.402114	+	0.166561i	0.172455	+	0.985017i	$0.444830\pi$
$710$		−	10.0000i		−	0.375293i
$711$	6.07107	+	14.6569i	0.227683	+	0.549675i
$712$	10.5563	+	10.5563i	0.395616	+	0.395616i
$713$	−13.4558			−0.503925
$714$		0			0
$715$	2.82843			0.105777
$716$	7.75736	+	7.75736i	0.289906	+	0.289906i
$717$	9.17157	+	22.1421i	0.342519	+	0.826913i
$718$		−	9.59798i		−	0.358193i
$719$	13.0000	−	5.38478i	0.484818	−	0.200818i	−0.126867	−	0.991920i	$-0.540492\pi$
$719$	13.0000	−	5.38478i	0.484818	−	0.200818i	0.611685	+	0.791102i	$0.290492\pi$
$720$	8.12132	−	19.6066i	0.302664	−	0.730695i
$721$	−4.48528	−	1.85786i	−0.167041	−	0.0691905i
$722$	−1.26346	+	1.26346i	−0.0470210	+	0.0470210i
$723$	22.7279	−	22.7279i	0.845261	−	0.845261i
$724$	−21.0919	−	8.73654i	−0.783874	−	0.324691i
$725$	2.70711	−	6.53553i	0.100539	−	0.242724i
$726$	−9.82843	+	4.07107i	−0.364767	+	0.151091i
$727$		−	19.1127i		−	0.708851i	−0.935084	−	0.354425i	$-0.884676\pi$
$727$		−	19.1127i		−	0.708851i	0.935084	−	0.354425i	$-0.115324\pi$
$728$	0.928932	+	2.24264i	0.0344285	+	0.0831178i
$729$	−27.7782	−	27.7782i	−1.02882	−	1.02882i
$730$	−4.10051			−0.151767
$731$		0			0
$732$	44.1421			1.63154
$733$	8.51472	+	8.51472i	0.314498	+	0.314498i	0.846649	−	0.532151i	$-0.178616\pi$
$733$	8.51472	+	8.51472i	0.314498	+	0.314498i	−0.532151	+	0.846649i	$0.678616\pi$
$734$	4.17157	+	10.0711i	0.153976	+	0.371730i
$735$		−	28.1421i		−	1.03804i
$736$	16.8995	−	7.00000i	0.622924	−	0.258023i
$737$	2.82843	−	6.82843i	0.104186	−	0.251528i
$738$	11.9497	+	4.94975i	0.439876	+	0.182203i
$739$	−24.2426	+	24.2426i	−0.891780	+	0.891780i	−0.994691	−	0.102911i	$-0.967184\pi$
$739$	−24.2426	+	24.2426i	−0.891780	+	0.891780i	0.102911	+	0.994691i	$0.467184\pi$
$740$	9.14214	−	9.14214i	0.336072	−	0.336072i
$741$	16.4853	+	6.82843i	0.605602	+	0.250849i
$742$	−0.242641	+	0.585786i	−0.00890762	+	0.0215049i
$743$	45.5269	−	18.8579i	1.67022	−	0.691828i	0.671433	−	0.741065i	$-0.265679\pi$
$743$	45.5269	−	18.8579i	1.67022	−	0.691828i	0.998787	+	0.0492371i	$0.0156790\pi$
$744$			13.4558i			0.493315i
$745$	−12.0000	−	28.9706i	−0.439646	−	1.06140i
$746$	−5.72792	−	5.72792i	−0.209714	−	0.209714i
$747$	−1.31371			−0.0480661
$748$		0			0
$749$	−6.82843			−0.249505
$750$	−9.31371	−	9.31371i	−0.340089	−	0.340089i
$751$	10.0294	+	24.2132i	0.365979	+	0.883552i	0.994400	+	0.105679i	$0.0337016\pi$
$751$	10.0294	+	24.2132i	0.365979	+	0.883552i	−0.628421	+	0.777873i	$0.716298\pi$
$752$			32.4853i			1.18462i
$753$	8.48528	−	3.51472i	0.309221	−	0.128083i
$754$	1.00000	−	2.41421i	0.0364179	−	0.0879205i
$755$	21.8995	+	9.07107i	0.797004	+	0.330130i
$756$	−3.02944	+	3.02944i	−0.110180	+	0.110180i
$757$	−37.7990	+	37.7990i	−1.37383	+	1.37383i	−0.519136	+	0.854692i	$0.673746\pi$
$757$	−37.7990	+	37.7990i	−1.37383	+	1.37383i	−0.854692	+	0.519136i	$0.826254\pi$
$758$	0.414214	+	0.171573i	0.0150449	+	0.00623181i
$759$	−4.48528	+	10.8284i	−0.162805	+	0.393047i
$760$	−13.0711	+	5.41421i	−0.474137	+	0.196394i
$761$			21.6985i			0.786569i	0.919417	+	0.393285i	$0.128661\pi$
$761$			21.6985i			0.786569i	−0.919417	+	0.393285i	$0.871339\pi$
$762$	7.17157	+	17.3137i	0.259799	+	0.627209i
$763$	3.27208	+	3.27208i	0.118457	+	0.118457i
$764$	36.5685			1.32300
$765$		0			0
$766$	−2.28427			−0.0825341
$767$	6.00000	+	6.00000i	0.216647	+	0.216647i
$768$	3.97056	+	9.58579i	0.143275	+	0.345897i
$769$		−	12.7279i		−	0.458981i	−0.973311	−	0.229490i	$-0.926294\pi$
$769$		−	12.7279i		−	0.458981i	0.973311	−	0.229490i	$-0.0737059\pi$
$770$	0.828427	−	0.343146i	0.0298544	−	0.0123661i
$771$	−22.1421	+	53.4558i	−0.797430	+	1.92517i
$772$	9.36396	+	3.87868i	0.337016	+	0.139597i
$773$	3.41421	−	3.41421i	0.122801	−	0.122801i	−0.643036	−	0.765836i	$-0.722325\pi$
$773$	3.41421	−	3.41421i	0.122801	−	0.122801i	0.765836	+	0.643036i	$0.222325\pi$
$774$	−5.41421	+	5.41421i	−0.194610	+	0.194610i
$775$	−4.75736	−	1.97056i	−0.170889	−	0.0707847i
$776$	3.90812	−	9.43503i	0.140293	−	0.338698i
$777$	−10.0000	+	4.14214i	−0.358748	+	0.148598i
$778$			6.68629i			0.239715i
$779$	15.0711	+	36.3848i	0.539977	+	1.30362i
$780$	8.82843	+	8.82843i	0.316108	+	0.316108i
$781$	−14.1421			−0.506045
$782$		0			0
$783$	9.65685			0.345108
$784$	12.3640	+	12.3640i	0.441570	+	0.441570i
$785$	1.17157	+	2.82843i	0.0418152	+	0.100951i
$786$			0.201010i			0.00716979i
$787$	−45.8701	+	19.0000i	−1.63509	+	0.677277i	−0.995789	−	0.0916786i	$-0.970777\pi$
$787$	−45.8701	+	19.0000i	−1.63509	+	0.677277i	−0.639302	+	0.768955i	$0.720777\pi$
$788$	−10.4350	+	25.1924i	−0.371733	+	0.897442i
$789$	15.6569	+	6.48528i	0.557399	+	0.230882i
$790$	2.24264	−	2.24264i	0.0797896	−	0.0797896i
$791$	−12.3848	+	12.3848i	−0.440352	+	0.440352i
$792$	6.07107	+	2.51472i	0.215726	+	0.0893566i
$793$	−5.00000	+	12.0711i	−0.177555	+	0.428656i
$794$	−10.4350	+	4.32233i	−0.370325	+	0.153394i
$795$			6.82843i			0.242179i
$796$	1.20101	+	2.89949i	0.0425687	+	0.102770i
$797$	12.1716	+	12.1716i	0.431139	+	0.431139i	0.889016	−	0.457877i	$-0.151390\pi$
$797$	12.1716	+	12.1716i	0.431139	+	0.431139i	−0.457877	+	0.889016i	$0.651390\pi$
$798$	5.65685			0.200250
$799$		0			0
$800$	7.00000			0.247487
$801$	−25.4853	−	25.4853i	−0.900478	−	0.900478i
$802$	2.70711	+	6.53553i	0.0955913	+	0.230778i
$803$			5.79899i			0.204642i
$804$	30.1421	−	12.4853i	1.06303	−	0.440322i
$805$	−3.17157	+	7.65685i	−0.111783	+	0.269869i
$806$	−1.75736	−	0.727922i	−0.0619003	−	0.0256400i
$807$	11.7574	−	11.7574i	0.413879	−	0.413879i
$808$	−15.0416	+	15.0416i	−0.529163	+	0.529163i
$809$	−27.5061	−	11.3934i	−0.967063	−	0.400571i	−0.157445	−	0.987528i	$-0.550326\pi$
$809$	−27.5061	−	11.3934i	−0.967063	−	0.400571i	−0.809618	+	0.586957i	$0.800326\pi$
$810$	−1.70711	+	4.12132i	−0.0599816	+	0.144808i
$811$	40.8995	−	16.9411i	1.43618	−	0.594883i	0.477308	−	0.878736i	$-0.341613\pi$
$811$	40.8995	−	16.9411i	1.43618	−	0.594883i	0.958868	+	0.283853i	$0.0916127\pi$
$812$			8.82843i			0.309817i
$813$	−6.14214	−	14.8284i	−0.215414	−	0.520056i
$814$	1.21320	+	1.21320i	0.0425228	+	0.0425228i
$815$	−10.4853			−0.367283
$816$		0			0
$817$	−23.3137			−0.815643
$818$	5.65685	+	5.65685i	0.197787	+	0.197787i
$819$	−2.24264	−	5.41421i	−0.0783642	−	0.189188i
$820$			27.5563i			0.962309i
$821$	−13.2929	+	5.50610i	−0.463925	+	0.192164i	−0.602388	−	0.798204i	$-0.705784\pi$
$821$	−13.2929	+	5.50610i	−0.463925	+	0.192164i	0.138463	+	0.990368i	$0.455784\pi$
$822$	−3.61522	+	8.72792i	−0.126095	+	0.304421i
$823$	21.7279	+	9.00000i	0.757388	+	0.313720i	0.727752	−	0.685840i	$-0.240565\pi$
$823$	21.7279	+	9.00000i	0.757388	+	0.313720i	0.0296358	+	0.999561i	$0.490565\pi$
$824$	−5.02944	+	5.02944i	−0.175209	+	0.175209i
$825$	−3.17157	+	3.17157i	−0.110420	+	0.110420i
$826$	2.48528	+	1.02944i	0.0864740	+	0.0358187i
$827$	13.2843	−	32.0711i	0.461939	−	1.11522i	−0.505661	−	0.862732i	$-0.668751\pi$
$827$	13.2843	−	32.0711i	0.461939	−	1.11522i	0.967600	−	0.252488i	$-0.0812488\pi$
$828$	−26.7990	+	11.1005i	−0.931329	+	0.385769i
$829$			13.9411i			0.484195i	0.970252	+	0.242098i	$0.0778354\pi$
$829$			13.9411i			0.484195i	−0.970252	+	0.242098i	$0.922165\pi$
$830$	0.100505	+	0.242641i	0.00348858	+	0.00842218i
$831$	40.7279	+	40.7279i	1.41284	+	1.41284i
$832$	−5.89949			−0.204528
$833$		0			0
$834$	−16.2010			−0.560995
$835$	−13.0711	−	13.0711i	−0.452343	−	0.452343i
$836$	3.65685	+	8.82843i	0.126475	+	0.305338i
$837$		−	7.02944i		−	0.242973i
$838$	10.3137	−	4.27208i	0.356281	−	0.147576i
$839$	1.48528	−	3.58579i	0.0512776	−	0.123795i	−0.896165	−	0.443721i	$-0.853658\pi$
$839$	1.48528	−	3.58579i	0.0512776	−	0.123795i	0.947443	+	0.319926i	$0.103658\pi$
$840$	7.65685	+	3.17157i	0.264187	+	0.109430i
$841$	−6.43503	+	6.43503i	−0.221898	+	0.221898i
$842$	5.10051	−	5.10051i	0.175775	−	0.175775i
$843$	43.2132	+	17.8995i	1.48834	+	0.616491i
$844$	10.4731	−	25.2843i	0.360499	−	0.870321i
$845$	18.7782	−	7.77817i	0.645989	−	0.267577i
$846$			17.1716i			0.590371i
$847$	4.07107	+	9.82843i	0.139884	+	0.337709i
$848$	−3.00000	−	3.00000i	−0.103020	−	0.103020i
$849$	−59.7990			−2.05230
$850$		0			0
$851$	−15.8579			−0.543601
$852$	−44.1421	−	44.1421i	−1.51228	−	1.51228i
$853$	−16.2929	−	39.3345i	−0.557858	−	1.34679i	−0.911459	−	0.411392i	$-0.865043\pi$
$853$	−16.2929	−	39.3345i	−0.557858	−	1.34679i	0.353601	−	0.935397i	$-0.384957\pi$
$854$			4.14214i			0.141741i
$855$	31.5563	−	13.0711i	1.07920	−	0.447021i
$856$	−3.82843	+	9.24264i	−0.130853	+	0.315907i
$857$	−3.53553	−	1.46447i	−0.120772	−	0.0500252i	0.321479	−	0.946917i	$-0.395820\pi$
$857$	−3.53553	−	1.46447i	−0.120772	−	0.0500252i	−0.442251	+	0.896891i	$0.645820\pi$
$858$	−1.17157	+	1.17157i	−0.0399968	+	0.0399968i
$859$	0.727922	−	0.727922i	0.0248364	−	0.0248364i	−0.694580	−	0.719416i	$-0.744410\pi$
$859$	0.727922	−	0.727922i	0.0248364	−	0.0248364i	0.719416	+	0.694580i	$0.244410\pi$
$860$	−15.0711	−	6.24264i	−0.513919	−	0.212872i
$861$	8.82843	−	21.3137i	0.300872	−	0.726369i
$862$	15.2426	−	6.31371i	0.519166	−	0.215046i
$863$		−	34.6274i		−	1.17873i	−0.807867	−	0.589365i	$-0.799378\pi$
$863$		−	34.6274i		−	1.17873i	0.807867	−	0.589365i	$-0.200622\pi$
$864$	3.65685	+	8.82843i	0.124409	+	0.300349i
$865$	4.41421	+	4.41421i	0.150088	+	0.150088i
$866$	6.28427			0.213548
$867$		0			0
$868$	6.42641			0.218126
$869$	−3.17157	−	3.17157i	−0.107588	−	0.107588i
$870$	−3.41421	−	8.24264i	−0.115753	−	0.279452i
$871$			9.65685i			0.327210i
$872$	6.26346	−	2.59441i	0.212107	−	0.0878578i
$873$	−9.43503	+	22.7782i	−0.319327	+	0.770924i
$874$	7.65685	+	3.17157i	0.258997	+	0.107280i
$875$	−9.31371	+	9.31371i	−0.314861	+	0.314861i
$876$	−18.1005	+	18.1005i	−0.611559	+	0.611559i
$877$	−34.7782	−	14.4056i	−1.17438	−	0.486442i	−0.291739	−	0.956498i	$-0.594234\pi$
$877$	−34.7782	−	14.4056i	−1.17438	−	0.486442i	−0.882637	+	0.470056i	$0.844234\pi$
$878$	1.72792	−	4.17157i	0.0583145	−	0.140784i
$879$	57.1127	−	23.6569i	1.92636	−	0.797926i
$880$			6.00000i			0.202260i
$881$	−7.09188	−	17.1213i	−0.238932	−	0.576832i	0.758241	−	0.651974i	$-0.226059\pi$
$881$	−7.09188	−	17.1213i	−0.238932	−	0.576832i	−0.997173	+	0.0751422i	$0.976059\pi$
$882$	6.53553	+	6.53553i	0.220063	+	0.220063i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		0			0
$885$	28.9706			0.973835
$886$	4.62742	+	4.62742i	0.155461	+	0.155461i
$887$	−18.6985	−	45.1421i	−0.627834	−	1.51572i	−0.842309	−	0.538995i	$-0.818804\pi$
$887$	−18.6985	−	45.1421i	−0.627834	−	1.51572i	0.214475	−	0.976729i	$-0.431196\pi$
$888$			15.8579i			0.532155i
$889$	17.3137	−	7.17157i	0.580683	−	0.240527i
$890$	−2.75736	+	6.65685i	−0.0924269	+	0.223138i
$891$	5.82843	+	2.41421i	0.195260	+	0.0808792i
$892$	−1.07107	+	1.07107i	−0.0358620	+	0.0358620i
$893$	−36.9706	+	36.9706i	−1.23717	+	1.23717i
$894$	16.9706	+	7.02944i	0.567581	+	0.235100i
$895$	−4.24264	+	10.2426i	−0.141816	+	0.342374i
$896$	−10.5563	+	4.37258i	−0.352663	+	0.146078i
$897$		−	15.3137i		−	0.511310i
$898$	−2.97918	−	7.19239i	−0.0994167	−	0.240013i
$899$	−10.2426	−	10.2426i	−0.341611	−	0.341611i
$900$	−11.1005			−0.370017
$901$		0			0
$902$	−3.65685			−0.121760
$903$	9.65685	+	9.65685i	0.321360	+	0.321360i
$904$	9.81981	+	23.7071i	0.326602	+	0.788487i
$905$		−	23.0711i		−	0.766908i
$906$	−12.8284	+	5.31371i	−0.426196	+	0.176536i
$907$	9.58579	−	23.1421i	0.318291	−	0.768422i	−0.681054	−	0.732233i	$-0.738478\pi$
$907$	9.58579	−	23.1421i	0.318291	−	0.768422i	0.999345	−	0.0361889i	$-0.0115218\pi$
$908$	−8.51472	−	3.52691i	−0.282571	−	0.117045i
$909$	36.3137	−	36.3137i	1.20445	−	1.20445i
$910$	−0.828427	+	0.828427i	−0.0274621	+	0.0274621i
$911$	−7.82843	−	3.24264i	−0.259367	−	0.107433i	0.249211	−	0.968449i	$-0.419829\pi$
$911$	−7.82843	−	3.24264i	−0.259367	−	0.107433i	−0.508578	+	0.861016i	$0.669829\pi$
$912$	−14.4853	+	34.9706i	−0.479656	+	1.15799i
$913$	0.343146	−	0.142136i	0.0113565	−	0.00470400i
$914$			7.79899i			0.257968i
$915$	17.0711	+	41.2132i	0.564352	+	1.36247i
$916$	29.5147	+	29.5147i	0.975194	+	0.975194i
$917$	0.201010			0.00663794
$918$		0			0
$919$	−3.31371			−0.109309			−0.0546546	−	0.998505i	$-0.517406\pi$
$919$	−3.31371			−0.109309			−0.0546546	+	0.998505i	$0.517406\pi$
$920$	8.58579	+	8.58579i	0.283065	+	0.283065i
$921$	2.14214	+	5.17157i	0.0705858	+	0.170409i
$922$		−	9.95837i		−	0.327961i
$923$	17.0711	−	7.07107i	0.561901	−	0.232747i
$924$	2.14214	−	5.17157i	0.0704711	−	0.170132i
$925$	−5.60660	−	2.32233i	−0.184344	−	0.0763578i
$926$	8.97056	−	8.97056i	0.294791	−	0.294791i
$927$	12.1421	−	12.1421i	0.398800	−	0.398800i
$928$	18.1924	+	7.53553i	0.597194	+	0.247366i
$929$	−8.02082	+	19.3640i	−0.263154	+	0.635311i	−0.999130	−	0.0416968i	$-0.986724\pi$
$929$	−8.02082	+	19.3640i	−0.263154	+	0.635311i	0.735976	+	0.677008i	$0.236724\pi$
$930$	−6.00000	+	2.48528i	−0.196748	+	0.0814956i
$931$			28.1421i			0.922321i
$932$	−7.09188	−	17.1213i	−0.232302	−	0.560827i
$933$	−8.34315	−	8.34315i	−0.273142	−	0.273142i
$934$	−5.23045			−0.171145
$935$		0			0
$936$	−8.58579			−0.280635
$937$	−2.51472	−	2.51472i	−0.0821523	−	0.0821523i	0.664837	−	0.746989i	$-0.268501\pi$
$937$	−2.51472	−	2.51472i	−0.0821523	−	0.0821523i	−0.746989	+	0.664837i	$0.768501\pi$
$938$	1.17157	+	2.82843i	0.0382532	+	0.0923514i
$939$		−	33.3137i		−	1.08715i
$940$	−33.7990	+	14.0000i	−1.10240	+	0.456630i
$941$	−7.15076	+	17.2635i	−0.233108	+	0.562773i	−0.996540	−	0.0831158i	$-0.973513\pi$
$941$	−7.15076	+	17.2635i	−0.233108	+	0.562773i	0.763432	+	0.645888i	$0.223513\pi$
$942$	−1.65685	−	0.686292i	−0.0539832	−	0.0223606i
$943$	23.8995	−	23.8995i	0.778275	−	0.778275i
$944$	−12.7279	+	12.7279i	−0.414259	+	0.414259i
$945$	−4.00000	−	1.65685i	−0.130120	−	0.0538975i
$946$	0.828427	−	2.00000i	0.0269345	−	0.0650256i
$947$	13.7279	−	5.68629i	0.446098	−	0.184780i	−0.148315	−	0.988940i	$-0.547385\pi$
$947$	13.7279	−	5.68629i	0.446098	−	0.184780i	0.594412	+	0.804161i	$0.297385\pi$
$948$		−	19.7990i		−	0.643041i
$949$	−2.89949	−	7.00000i	−0.0941216	−	0.227230i
$950$	2.24264	+	2.24264i	0.0727609	+	0.0727609i
$951$	15.1716			0.491972
$952$		0			0
$953$	−9.69848			−0.314165			−0.157082	−	0.987586i	$-0.550209\pi$
$953$	−9.69848			−0.314165			−0.157082	+	0.987586i	$0.550209\pi$
$954$	−1.58579	−	1.58579i	−0.0513417	−	0.0513417i
$955$	14.1421	+	34.1421i	0.457629	+	1.10481i
$956$		−	16.7696i		−	0.542366i
$957$	−11.6569	+	4.82843i	−0.376813	+	0.156081i
$958$	−5.48528	+	13.2426i	−0.177221	+	0.427850i
$959$	8.72792	+	3.61522i	0.281839	+	0.116742i
$960$	−14.2426	+	14.2426i	−0.459679	+	0.459679i
$961$	14.4645	−	14.4645i	0.466596	−	0.466596i
$962$	−2.07107	−	0.857864i	−0.0667739	−	0.0276587i
$963$	9.24264	−	22.3137i	0.297840	−	0.719049i
$964$	−20.7782	+	8.60660i	−0.669220	+	0.277200i
$965$			10.2426i			0.329722i
$966$	−1.85786	−	4.48528i	−0.0597758	−	0.144312i
$967$	−22.8701	−	22.8701i	−0.735451	−	0.735451i	0.236243	−	0.971694i	$-0.424084\pi$
$967$	−22.8701	−	22.8701i	−0.735451	−	0.735451i	−0.971694	+	0.236243i	$0.924084\pi$
$968$	15.5858			0.500946
$969$		0			0
$970$	4.92893			0.158258
$971$	39.4142	+	39.4142i	1.26486	+	1.26486i	0.948708	+	0.316155i	$0.102392\pi$
$971$	39.4142	+	39.4142i	1.26486	+	1.26486i	0.316155	+	0.948708i	$0.397608\pi$
$972$	15.2010	+	36.6985i	0.487573	+	1.17710i
$973$			16.2010i			0.519381i
$974$	1.68629	−	0.698485i	0.0540323	−	0.0223809i
$975$	2.24264	−	5.41421i	0.0718220	−	0.173394i
$976$	−25.6066	−	10.6066i	−0.819647	−	0.339509i
$977$	−1.14214	+	1.14214i	−0.0365402	+	0.0365402i	−0.725141	−	0.688601i	$-0.758225\pi$
$977$	−1.14214	+	1.14214i	−0.0365402	+	0.0365402i	0.688601	+	0.725141i	$0.258225\pi$
$978$	4.34315	−	4.34315i	0.138878	−	0.138878i
$979$	9.41421	+	3.89949i	0.300880	+	0.124628i
$980$	−7.53553	+	18.1924i	−0.240714	+	0.581135i
$981$	−15.1213	+	6.26346i	−0.482787	+	0.199977i
$982$		−	10.4020i		−	0.331942i
$983$	9.00000	+	21.7279i	0.287055	+	0.693013i	0.999966	−	0.00824183i	$-0.00262348\pi$
$983$	9.00000	+	21.7279i	0.287055	+	0.693013i	−0.712911	+	0.701255i	$0.752623\pi$
$984$	−23.8995	−	23.8995i	−0.761888	−	0.761888i
$985$	−27.5563			−0.878018
$986$		0			0
$987$	30.6274			0.974881
$988$	−8.82843	−	8.82843i	−0.280870	−	0.280870i
$989$	7.65685	+	18.4853i	0.243474	+	0.587798i
$990$			3.17157i			0.100799i
$991$	29.6274	−	12.2721i	0.941146	−	0.389835i	0.141250	−	0.989974i	$-0.454888\pi$
$991$	29.6274	−	12.2721i	0.941146	−	0.389835i	0.799896	+	0.600139i	$0.204888\pi$
$992$	5.48528	−	13.2426i	0.174158	−	0.420454i
$993$	42.9706	+	17.7990i	1.36363	+	0.564834i
$994$	4.14214	−	4.14214i	0.131381	−	0.131381i
$995$	−2.24264	+	2.24264i	−0.0710965	+	0.0710965i
$996$	1.51472	+	0.627417i	0.0479957	+	0.0198805i
$997$	2.94975	−	7.12132i	0.0934194	−	0.225534i	−0.870262	−	0.492589i	$-0.836050\pi$
$997$	2.94975	−	7.12132i	0.0934194	−	0.225534i	0.963681	+	0.267055i	$0.0860505\pi$
$998$	−14.1716	+	5.87006i	−0.448593	+	0.185813i
$999$		−	8.28427i		−	0.262103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.c.134.1		4
17.2	even	8		289.2.d.a.179.1		4
17.3	odd	16		289.2.b.b.288.4		4
17.4	even	4		289.2.d.a.155.1		4
17.5	odd	16		289.2.a.f.1.1		4
17.6	odd	16		289.2.c.c.251.4		8
17.7	odd	16		289.2.c.c.38.2		8
17.8	even	8	inner	289.2.d.c.110.1		4
17.9	even	8		289.2.d.b.110.1		4
17.10	odd	16		289.2.c.c.38.1		8
17.11	odd	16		289.2.c.c.251.3		8
17.12	odd	16		289.2.a.f.1.2		4
17.13	even	4		17.2.d.a.2.1	✓	4
17.14	odd	16		289.2.b.b.288.3		4
17.15	even	8		17.2.d.a.9.1	yes	4
17.16	even	2		289.2.d.b.134.1		4
51.5	even	16		2601.2.a.bb.1.4		4
51.29	even	16		2601.2.a.bb.1.3		4
51.32	odd	8		153.2.l.c.145.1		4
51.47	odd	4		153.2.l.c.19.1		4
68.15	odd	8		272.2.v.d.145.1		4
68.39	even	16		4624.2.a.bp.1.4		4
68.47	odd	4		272.2.v.d.257.1		4
68.63	even	16		4624.2.a.bp.1.1		4
85.13	odd	4		425.2.n.a.274.1		4
85.29	odd	16		7225.2.a.u.1.3		4
85.32	odd	8		425.2.n.a.349.1		4
85.39	odd	16		7225.2.a.u.1.4		4
85.47	odd	4		425.2.n.b.274.1		4
85.49	even	8		425.2.m.a.26.1		4
85.64	even	4		425.2.m.a.376.1		4
85.83	odd	8		425.2.n.b.349.1		4
119.13	odd	4		833.2.l.a.393.1		4
119.30	even	12		833.2.v.b.410.1		8
119.32	even	24		833.2.v.b.128.1		8
119.47	odd	12		833.2.v.a.410.1		8
119.66	odd	24		833.2.v.a.128.1		8
119.81	even	12		833.2.v.b.716.1		8
119.83	odd	8		833.2.l.a.638.1		4
119.100	even	24		833.2.v.b.655.1		8
119.115	odd	12		833.2.v.a.716.1		8
119.117	odd	24		833.2.v.a.655.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.2.1	✓	4	17.13	even	4
17.2.d.a.9.1	yes	4	17.15	even	8
153.2.l.c.19.1		4	51.47	odd	4
153.2.l.c.145.1		4	51.32	odd	8
272.2.v.d.145.1		4	68.15	odd	8
272.2.v.d.257.1		4	68.47	odd	4
289.2.a.f.1.1		4	17.5	odd	16
289.2.a.f.1.2		4	17.12	odd	16
289.2.b.b.288.3		4	17.14	odd	16
289.2.b.b.288.4		4	17.3	odd	16
289.2.c.c.38.1		8	17.10	odd	16
289.2.c.c.38.2		8	17.7	odd	16
289.2.c.c.251.3		8	17.11	odd	16
289.2.c.c.251.4		8	17.6	odd	16
289.2.d.a.155.1		4	17.4	even	4
289.2.d.a.179.1		4	17.2	even	8
289.2.d.b.110.1		4	17.9	even	8
289.2.d.b.134.1		4	17.16	even	2
289.2.d.c.110.1		4	17.8	even	8	inner
289.2.d.c.134.1		4	1.1	even	1	trivial
425.2.m.a.26.1		4	85.49	even	8
425.2.m.a.376.1		4	85.64	even	4
425.2.n.a.274.1		4	85.13	odd	4
425.2.n.a.349.1		4	85.32	odd	8
425.2.n.b.274.1		4	85.47	odd	4
425.2.n.b.349.1		4	85.83	odd	8
833.2.l.a.393.1		4	119.13	odd	4
833.2.l.a.638.1		4	119.83	odd	8
833.2.v.a.128.1		8	119.66	odd	24
833.2.v.a.410.1		8	119.47	odd	12
833.2.v.a.655.1		8	119.117	odd	24
833.2.v.a.716.1		8	119.115	odd	12
833.2.v.b.128.1		8	119.32	even	24
833.2.v.b.410.1		8	119.30	even	12
833.2.v.b.655.1		8	119.100	even	24
833.2.v.b.716.1		8	119.81	even	12
2601.2.a.bb.1.3		4	51.29	even	16
2601.2.a.bb.1.4		4	51.5	even	16
4624.2.a.bp.1.1		4	68.63	even	16
4624.2.a.bp.1.4		4	68.39	even	16
7225.2.a.u.1.3		4	85.29	odd	16
7225.2.a.u.1.4		4	85.39	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.292893 + 0.292893i) q^{2} +(1.00000 + 2.41421i) q^{3} -1.82843i q^{4} +(1.70711 - 0.707107i) q^{5} +(-0.414214 + 1.00000i) q^{6} +(1.00000 + 0.414214i) q^{7} +(1.12132 - 1.12132i) q^{8} +(-2.70711 + 2.70711i) q^{9} +(0.707107 + 0.292893i) q^{10} +(0.414214 - 1.00000i) q^{11} +(4.41421 - 1.82843i) q^{12} +1.41421i q^{13} +(0.171573 + 0.414214i) q^{14} +(3.41421 + 3.41421i) q^{15} -3.00000 q^{16} -1.58579 q^{18} +(-3.41421 - 3.41421i) q^{19} +(-1.29289 - 3.12132i) q^{20} +2.82843i q^{21} +(0.414214 - 0.171573i) q^{22} +(-1.58579 + 3.82843i) q^{23} +(3.82843 + 1.58579i) q^{24} +(-1.12132 + 1.12132i) q^{25} +(-0.414214 + 0.414214i) q^{26} +(-2.00000 - 0.828427i) q^{27} +(0.757359 - 1.82843i) q^{28} +(-4.12132 + 1.70711i) q^{29} +2.00000i q^{30} +(1.24264 + 3.00000i) q^{31} +(-3.12132 - 3.12132i) q^{32} +2.82843 q^{33} +2.00000 q^{35} +(4.94975 + 4.94975i) q^{36} +(1.46447 + 3.53553i) q^{37} -2.00000i q^{38} +(-3.41421 + 1.41421i) q^{39} +(1.12132 - 2.70711i) q^{40} +(-7.53553 - 3.12132i) q^{41} +(-0.828427 + 0.828427i) q^{42} +(3.41421 - 3.41421i) q^{43} +(-1.82843 - 0.757359i) q^{44} +(-2.70711 + 6.53553i) q^{45} +(-1.58579 + 0.656854i) q^{46} -10.8284i q^{47} +(-3.00000 - 7.24264i) q^{48} +(-4.12132 - 4.12132i) q^{49} -0.656854 q^{50} +2.58579 q^{52} +(1.00000 + 1.00000i) q^{53} +(-0.343146 - 0.828427i) q^{54} -2.00000i q^{55} +(1.58579 - 0.656854i) q^{56} +(4.82843 - 11.6569i) q^{57} +(-1.70711 - 0.707107i) q^{58} +(4.24264 - 4.24264i) q^{59} +(6.24264 - 6.24264i) q^{60} +(8.53553 + 3.53553i) q^{61} +(-0.514719 + 1.24264i) q^{62} +(-3.82843 + 1.58579i) q^{63} +4.17157i q^{64} +(1.00000 + 2.41421i) q^{65} +(0.828427 + 0.828427i) q^{66} +6.82843 q^{67} -10.8284 q^{69} +(0.585786 + 0.585786i) q^{70} +(-5.00000 - 12.0711i) q^{71} +6.07107i q^{72} +(-4.94975 + 2.05025i) q^{73} +(-0.606602 + 1.46447i) q^{74} +(-3.82843 - 1.58579i) q^{75} +(-6.24264 + 6.24264i) q^{76} +(0.828427 - 0.828427i) q^{77} +(-1.41421 - 0.585786i) q^{78} +(1.58579 - 3.82843i) q^{79} +(-5.12132 + 2.12132i) q^{80} +5.82843i q^{81} +(-1.29289 - 3.12132i) q^{82} +(0.242641 + 0.242641i) q^{83} +5.17157 q^{84} +2.00000 q^{86} +(-8.24264 - 8.24264i) q^{87} +(-0.656854 - 1.58579i) q^{88} +9.41421i q^{89} +(-2.70711 + 1.12132i) q^{90} +(-0.585786 + 1.41421i) q^{91} +(7.00000 + 2.89949i) q^{92} +(-6.00000 + 6.00000i) q^{93} +(3.17157 - 3.17157i) q^{94} +(-8.24264 - 3.41421i) q^{95} +(4.41421 - 10.6569i) q^{96} +(5.94975 - 2.46447i) q^{97} -2.41421i q^{98} +(1.58579 + 3.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 12 q^{12} + 12 q^{14} + 8 q^{15} - 12 q^{16} - 12 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{25}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 12 * q^12 + 12 * q^14 + 8 * q^15 - 12 * q^16 - 12 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 - 8 * q^27 + 20 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^32 + 8 * q^35 + 20 * q^37 - 8 * q^39 - 4 * q^40 - 16 * q^41 + 8 * q^42 + 8 * q^43 + 4 * q^44 - 8 * q^45 - 12 * q^46 - 12 * q^48 - 8 * q^49 + 20 * q^50 + 16 * q^52 + 4 * q^53 - 24 * q^54 + 12 * q^56 + 8 * q^57 - 4 * q^58 + 8 * q^60 + 20 * q^61 - 36 * q^62 - 4 * q^63 + 4 * q^65 - 8 * q^66 + 16 * q^67 - 32 * q^69 + 8 * q^70 - 20 * q^71 + 40 * q^74 - 4 * q^75 - 8 * q^76 - 8 * q^77 + 12 * q^79 - 12 * q^80 - 8 * q^82 - 16 * q^83 + 32 * q^84 + 8 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 - 8 * q^91 + 28 * q^92 - 24 * q^93 + 24 * q^94 - 16 * q^95 + 12 * q^96 + 4 * q^97 + 12 * q^99

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