LMFDB - Embedded newform 690.2.i.c.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, degree $2$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.c.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(-2.22474 + 0.224745i) q^{10} +5.65685i q^{11} +(0.292893 + 1.70711i) q^{12} +(1.44949 - 1.44949i) q^{13} -3.46410 q^{14} +(3.37101 + 1.90691i) q^{15} -1.00000 q^{16} +(-5.19615 + 5.19615i) q^{17} +(1.29289 - 2.70711i) q^{18} -2.44949i q^{19} +(-1.41421 + 1.73205i) q^{20} +(4.89898 + 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.41421 + 1.00000i) q^{24} +(1.00000 + 4.89898i) q^{25} -2.04989i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-2.44949 + 2.44949i) q^{28} +9.12096 q^{29} +(3.73205 - 1.03528i) q^{30} -4.89898 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.65685 - 9.65685i) q^{33} +7.34847i q^{34} +(0.778539 + 7.70674i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(2.44949 + 2.44949i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-2.04989 + 2.89898i) q^{39} +(0.224745 + 2.22474i) q^{40} +8.48528i q^{41} +(5.91359 - 1.01461i) q^{42} +(-6.89898 + 6.89898i) q^{43} +5.65685 q^{44} +(-6.31319 - 2.26795i) q^{45} +1.00000 q^{46} +(-2.04989 + 2.04989i) q^{47} +(1.70711 - 0.292893i) q^{48} +5.00000i q^{49} +(4.17121 + 2.75699i) q^{50} +(7.34847 - 10.3923i) q^{51} +(-1.44949 - 1.44949i) q^{52} +(-9.43879 - 9.43879i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(8.00000 - 9.79796i) q^{55} +3.46410i q^{56} +(0.717439 + 4.18154i) q^{57} +(6.44949 - 6.44949i) q^{58} -8.34242 q^{59} +(1.90691 - 3.37101i) q^{60} -8.89898 q^{61} +(-3.46410 + 3.46410i) q^{62} +(-9.37769 - 4.47871i) q^{63} +1.00000i q^{64} +(-4.56048 + 0.460702i) q^{65} +(-8.00000 - 5.65685i) q^{66} +(-1.10102 - 1.10102i) q^{67} +(5.19615 + 5.19615i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(6.00000 + 4.89898i) q^{70} +6.14966i q^{71} +(-2.70711 - 1.29289i) q^{72} +(7.89898 - 7.89898i) q^{73} +3.46410 q^{74} +(-3.14198 - 8.07019i) q^{75} -2.44949 q^{76} +(13.8564 - 13.8564i) q^{77} +(0.600398 + 3.49938i) q^{78} -0.449490i q^{79} +(1.73205 + 1.41421i) q^{80} +(7.00000 - 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(3.46410 - 4.89898i) q^{84} +(16.3485 - 1.65153i) q^{85} +9.75663i q^{86} +(-15.5704 + 2.67147i) q^{87} +(4.00000 - 4.00000i) q^{88} -2.19275 q^{89} +(-6.06778 + 2.86042i) q^{90} -7.10102 q^{91} +(0.707107 - 0.707107i) q^{92} +(8.36308 - 1.43488i) q^{93} +2.89898i q^{94} +(-3.46410 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +(4.44949 + 4.44949i) q^{97} +(3.53553 + 3.53553i) q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 8 * q - 8 * q^3 - 8 * q^6	$ 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		−	1.00000i		−	0.500000i
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	−0.997433	+	0.0716124i	$0.977186\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$	−2.22474	+	0.224745i	−0.703526	+	0.0710706i
$11$			5.65685i			1.70561i	0.522233	+	0.852803i	$0.325099\pi$
$11$			5.65685i			1.70561i	−0.522233	+	0.852803i	$0.674901\pi$
$12$	0.292893	+	1.70711i	0.0845510	+	0.492799i
$13$	1.44949	−	1.44949i	0.402016	−	0.402016i	−0.476927	−	0.878943i	$-0.658249\pi$
$13$	1.44949	−	1.44949i	0.402016	−	0.402016i	0.878943	+	0.476927i	$0.158249\pi$
$14$	−3.46410			−0.925820
$15$	3.37101	+	1.90691i	0.870391	+	0.492361i
$16$	−1.00000			−0.250000
$17$	−5.19615	+	5.19615i	−1.26025	+	1.26025i	−0.309282	+	0.950971i	$0.600089\pi$
$17$	−5.19615	+	5.19615i	−1.26025	+	1.26025i	−0.950971	+	0.309282i	$0.899911\pi$
$18$	1.29289	−	2.70711i	0.304738	−	0.638071i
$19$		−	2.44949i		−	0.561951i	−0.959715	−	0.280976i	$-0.909342\pi$
$19$		−	2.44949i		−	0.561951i	0.959715	−	0.280976i	$-0.0906580\pi$
$20$	−1.41421	+	1.73205i	−0.316228	+	0.387298i
$21$	4.89898	+	3.46410i	1.06904	+	0.755929i
$22$	4.00000	+	4.00000i	0.852803	+	0.852803i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	1.41421	+	1.00000i	0.288675	+	0.204124i
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$		−	2.04989i		−	0.402016i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	−2.44949	+	2.44949i	−0.462910	+	0.462910i
$29$	9.12096			1.69372			0.846859	−	0.531817i	$-0.178490\pi$
$29$	9.12096			1.69372			0.846859	+	0.531817i	$0.178490\pi$
$30$	3.73205	−	1.03528i	0.681376	−	0.189015i
$31$	−4.89898			−0.879883			−0.439941	−	0.898027i	$-0.645001\pi$
$31$	−4.89898			−0.879883			−0.439941	+	0.898027i	$0.645001\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.65685	−	9.65685i	−0.288421	−	1.68104i
$34$			7.34847i			1.26025i
$35$	0.778539	+	7.70674i	0.131597	+	1.30268i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	2.44949	+	2.44949i	0.402694	+	0.402694i	0.879181	−	0.476488i	$-0.158090\pi$
$37$	2.44949	+	2.44949i	0.402694	+	0.402694i	−0.476488	+	0.879181i	$0.658090\pi$
$38$	−1.73205	−	1.73205i	−0.280976	−	0.280976i
$39$	−2.04989	+	2.89898i	−0.328245	+	0.464208i
$40$	0.224745	+	2.22474i	0.0355353	+	0.351763i
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$	5.91359	−	1.01461i	0.912487	−	0.156558i
$43$	−6.89898	+	6.89898i	−1.05208	+	1.05208i	−0.0535176	+	0.998567i	$0.517043\pi$
$43$	−6.89898	+	6.89898i	−1.05208	+	1.05208i	−0.998567	+	0.0535176i	$0.982957\pi$
$44$	5.65685			0.852803
$45$	−6.31319	−	2.26795i	−0.941115	−	0.338086i
$46$	1.00000			0.147442
$47$	−2.04989	+	2.04989i	−0.299007	+	0.299007i	−0.840625	−	0.541618i	$-0.817812\pi$
$47$	−2.04989	+	2.04989i	−0.299007	+	0.299007i	0.541618	+	0.840625i	$0.317812\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$			5.00000i			0.714286i
$50$	4.17121	+	2.75699i	0.589898	+	0.389898i
$51$	7.34847	−	10.3923i	1.02899	−	1.45521i
$52$	−1.44949	−	1.44949i	−0.201008	−	0.201008i
$53$	−9.43879	−	9.43879i	−1.29652	−	1.29652i	−0.930678	−	0.365840i	$-0.880782\pi$
$53$	−9.43879	−	9.43879i	−1.29652	−	1.29652i	−0.365840	−	0.930678i	$-0.619218\pi$
$54$	−1.41421	+	5.00000i	−0.192450	+	0.680414i
$55$	8.00000	−	9.79796i	1.07872	−	1.32116i
$56$			3.46410i			0.462910i
$57$	0.717439	+	4.18154i	0.0950271	+	0.553859i
$58$	6.44949	−	6.44949i	0.846859	−	0.846859i
$59$	−8.34242			−1.08609			−0.543045	−	0.839704i	$-0.682729\pi$
$59$	−8.34242			−1.08609			−0.543045	+	0.839704i	$0.682729\pi$
$60$	1.90691	−	3.37101i	0.246181	−	0.435195i
$61$	−8.89898			−1.13940			−0.569699	−	0.821854i	$-0.692940\pi$
$61$	−8.89898			−1.13940			−0.569699	+	0.821854i	$0.692940\pi$
$62$	−3.46410	+	3.46410i	−0.439941	+	0.439941i
$63$	−9.37769	−	4.47871i	−1.18148	−	0.564265i
$64$			1.00000i			0.125000i
$65$	−4.56048	+	0.460702i	−0.565658	+	0.0571430i
$66$	−8.00000	−	5.65685i	−0.984732	−	0.696311i
$67$	−1.10102	−	1.10102i	−0.134511	−	0.134511i	0.636646	−	0.771157i	$-0.280321\pi$
$67$	−1.10102	−	1.10102i	−0.134511	−	0.134511i	−0.771157	+	0.636646i	$0.780321\pi$
$68$	5.19615	+	5.19615i	0.630126	+	0.630126i
$69$	−1.41421	−	1.00000i	−0.170251	−	0.120386i
$70$	6.00000	+	4.89898i	0.717137	+	0.585540i
$71$			6.14966i			0.729831i	0.931041	+	0.364915i	$0.118902\pi$
$71$			6.14966i			0.729831i	−0.931041	+	0.364915i	$0.881098\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$	7.89898	−	7.89898i	0.924506	−	0.924506i	−0.0728382	−	0.997344i	$-0.523206\pi$
$73$	7.89898	−	7.89898i	0.924506	−	0.924506i	0.997344	+	0.0728382i	$0.0232057\pi$
$74$	3.46410			0.402694
$75$	−3.14198	−	8.07019i	−0.362805	−	0.931865i
$76$	−2.44949			−0.280976
$77$	13.8564	−	13.8564i	1.57908	−	1.57908i
$78$	0.600398	+	3.49938i	0.0679817	+	0.396227i
$79$		−	0.449490i		−	0.0505715i	−0.999680	−	0.0252858i	$-0.991950\pi$
$79$		−	0.449490i		−	0.0505715i	0.999680	−	0.0252858i	$-0.00804957\pi$
$80$	1.73205	+	1.41421i	0.193649	+	0.158114i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	0.625219	−	0.780449i	$-0.285010\pi$
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	−0.780449	+	0.625219i	$0.785010\pi$
$84$	3.46410	−	4.89898i	0.377964	−	0.534522i
$85$	16.3485	−	1.65153i	1.77324	−	0.179134i
$86$			9.75663i			1.05208i
$87$	−15.5704	+	2.67147i	−1.66933	+	0.286411i
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$	−2.19275			−0.232431			−0.116216	−	0.993224i	$-0.537076\pi$
$89$	−2.19275			−0.232431			−0.116216	+	0.993224i	$0.537076\pi$
$90$	−6.06778	+	2.86042i	−0.639601	+	0.301515i
$91$	−7.10102			−0.744389
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	8.36308	−	1.43488i	0.867211	−	0.148790i
$94$			2.89898i			0.299007i
$95$	−3.46410	+	4.24264i	−0.355409	+	0.435286i
$96$	1.00000	−	1.41421i	0.102062	−	0.144338i
$97$	4.44949	+	4.44949i	0.451777	+	0.451777i	0.895944	−	0.444167i	$-0.146500\pi$
$97$	4.44949	+	4.44949i	0.451777	+	0.451777i	−0.444167	+	0.895944i	$0.646500\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	5.65685	+	16.0000i	0.568535	+	1.60806i
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$		−	6.29253i		−	0.626130i	−0.949732	−	0.313065i	$-0.898644\pi$
$101$		−	6.29253i		−	0.626130i	0.949732	−	0.313065i	$-0.101356\pi$
$102$	−2.15232	−	12.5446i	−0.213111	−	1.24210i
$103$	−1.10102	+	1.10102i	−0.108487	+	0.108487i	−0.759267	−	0.650780i	$-0.774442\pi$
$103$	−1.10102	+	1.10102i	−0.108487	+	0.108487i	0.650780	+	0.759267i	$0.274442\pi$
$104$	−2.04989			−0.201008
$105$	−3.58630	−	12.9282i	−0.349987	−	1.26166i
$106$	−13.3485			−1.29652
$107$	−0.778539	+	0.778539i	−0.0752642	+	0.0752642i	−0.743737	−	0.668473i	$-0.766948\pi$
$107$	−0.778539	+	0.778539i	−0.0752642	+	0.0752642i	0.668473	+	0.743737i	$0.266948\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$		−	5.79796i		−	0.555344i	−0.960676	−	0.277672i	$-0.910437\pi$
$109$		−	5.79796i		−	0.555344i	0.960676	−	0.277672i	$-0.0895628\pi$
$110$	−1.27135	−	12.5851i	−0.121218	−	1.19994i
$111$	−4.89898	−	3.46410i	−0.464991	−	0.328798i
$112$	2.44949	+	2.44949i	0.231455	+	0.231455i
$113$	2.36773	+	2.36773i	0.222737	+	0.222737i	0.809650	−	0.586913i	$-0.199657\pi$
$113$	2.36773	+	2.36773i	0.222737	+	0.222737i	−0.586913	+	0.809650i	$0.699657\pi$
$114$	3.46410	+	2.44949i	0.324443	+	0.229416i
$115$	−0.224745	−	2.22474i	−0.0209576	−	0.207459i
$116$		−	9.12096i		−	0.846859i
$117$	2.65029	−	5.54927i	0.245019	−	0.513030i
$118$	−5.89898	+	5.89898i	−0.543045	+	0.543045i
$119$	25.4558			2.33353
$120$	−1.03528	−	3.73205i	−0.0945074	−	0.340688i
$121$	−21.0000			−1.90909
$122$	−6.29253	+	6.29253i	−0.569699	+	0.569699i
$123$	−2.48528	−	14.4853i	−0.224090	−	1.30609i
$124$			4.89898i			0.439941i
$125$	5.19615	−	9.89949i	0.464758	−	0.885438i
$126$	−9.79796	+	3.46410i	−0.872872	+	0.308607i
$127$	−8.44949	−	8.44949i	−0.749771	−	0.749771i	0.224665	−	0.974436i	$-0.427871\pi$
$127$	−8.44949	−	8.44949i	−0.749771	−	0.749771i	−0.974436	+	0.224665i	$0.927871\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	9.75663	−	13.7980i	0.859023	−	1.21484i
$130$	−2.89898	+	3.55051i	−0.254257	+	0.311400i
$131$			13.9993i			1.22312i	0.791197	+	0.611561i	$0.209458\pi$
$131$			13.9993i			1.22312i	−0.791197	+	0.611561i	$0.790542\pi$
$132$	−9.65685	+	1.65685i	−0.840521	+	0.144211i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−1.55708			−0.134511
$135$	11.4416	+	2.02254i	0.984733	+	0.174073i
$136$	7.34847			0.630126
$137$	3.28913	−	3.28913i	0.281009	−	0.281009i	−0.552502	−	0.833511i	$-0.686327\pi$
$137$	3.28913	−	3.28913i	0.281009	−	0.281009i	0.833511	+	0.552502i	$0.186327\pi$
$138$	−1.70711	+	0.292893i	−0.145319	+	0.0249327i
$139$		−	10.6969i		−	0.907302i	−0.891179	−	0.453651i	$-0.850121\pi$
$139$		−	10.6969i		−	0.907302i	0.891179	−	0.453651i	$-0.149879\pi$
$140$	7.70674	−	0.778539i	0.651339	−	0.0657986i
$141$	2.89898	−	4.09978i	0.244138	−	0.345263i
$142$	4.34847	+	4.34847i	0.364915	+	0.364915i
$143$	8.19955	+	8.19955i	0.685681	+	0.685681i
$144$	−2.82843	+	1.00000i	−0.235702	+	0.0833333i
$145$	−15.7980	−	12.8990i	−1.31195	−	1.07120i
$146$		−	11.1708i		−	0.924506i
$147$	−1.46447	−	8.53553i	−0.120787	−	0.703999i
$148$	2.44949	−	2.44949i	0.201347	−	0.201347i
$149$	−16.6848			−1.36687			−0.683437	−	0.730009i	$-0.739516\pi$
$149$	−16.6848			−1.36687			−0.683437	+	0.730009i	$0.739516\pi$
$150$	−7.92820	−	3.48477i	−0.647335	−	0.284530i
$151$	8.89898			0.724189			0.362094	−	0.932141i	$-0.382062\pi$
$151$	8.89898			0.724189			0.362094	+	0.932141i	$0.382062\pi$
$152$	−1.73205	+	1.73205i	−0.140488	+	0.140488i
$153$	−9.50079	+	19.8931i	−0.768093	+	1.60826i
$154$		−	19.5959i		−	1.57908i
$155$	8.48528	+	6.92820i	0.681554	+	0.556487i
$156$	2.89898	+	2.04989i	0.232104	+	0.164122i
$157$	−3.55051	−	3.55051i	−0.283362	−	0.283362i	0.551087	−	0.834448i	$-0.314213\pi$
$157$	−3.55051	−	3.55051i	−0.283362	−	0.283362i	−0.834448	+	0.551087i	$0.814213\pi$
$158$	−0.317837	−	0.317837i	−0.0252858	−	0.0252858i
$159$	18.8776	+	13.3485i	1.49709	+	1.05860i
$160$	2.22474	−	0.224745i	0.175882	−	0.0177676i
$161$		−	3.46410i		−	0.273009i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	8.48528			0.662589
$165$	−10.7871	+	19.0693i	−0.839774	+	1.48454i
$166$	−2.00000			−0.155230
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	−0.891251	−	0.453510i	$-0.850171\pi$
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	0.453510	+	0.891251i	$0.350171\pi$
$168$	−1.01461	−	5.91359i	−0.0782790	−	0.456243i
$169$			8.79796i			0.676766i
$170$	10.3923	−	12.7279i	0.797053	−	0.976187i
$171$	−2.44949	−	6.92820i	−0.187317	−	0.529813i
$172$	6.89898	+	6.89898i	0.526042	+	0.526042i
$173$	−10.5352	−	10.5352i	−0.800974	−	0.800974i	0.182274	−	0.983248i	$-0.441654\pi$
$173$	−10.5352	−	10.5352i	−0.800974	−	0.800974i	−0.983248	+	0.182274i	$0.941654\pi$
$174$	−9.12096	+	12.8990i	−0.691458	+	0.977869i
$175$	9.55051	−	14.4495i	0.721951	−	1.09228i
$176$		−	5.65685i		−	0.426401i
$177$	14.2414	−	2.44344i	1.07045	−	0.183660i
$178$	−1.55051	+	1.55051i	−0.116216	+	0.116216i
$179$	−12.4422			−0.929973			−0.464987	−	0.885318i	$-0.653941\pi$
$179$	−12.4422			−0.929973			−0.464987	+	0.885318i	$0.653941\pi$
$180$	−2.26795	+	6.31319i	−0.169043	+	0.470558i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−5.02118	+	5.02118i	−0.372195	+	0.372195i
$183$	15.1915	−	2.60645i	1.12299	−	0.192674i
$184$		−	1.00000i		−	0.0737210i
$185$	−0.778539	−	7.70674i	−0.0572393	−	0.566611i
$186$	4.89898	−	6.92820i	0.359211	−	0.508001i
$187$	−29.3939	−	29.3939i	−2.14949	−	2.14949i
$188$	2.04989	+	2.04989i	0.149503	+	0.149503i
$189$	17.3205	+	4.89898i	1.25988	+	0.356348i
$190$	0.550510	+	5.44949i	0.0399382	+	0.395348i
$191$			23.6130i			1.70858i	0.519797	+	0.854290i	$0.326008\pi$
$191$			23.6130i			1.70858i	−0.519797	+	0.854290i	$0.673992\pi$
$192$	−0.292893	−	1.70711i	−0.0211377	−	0.123200i
$193$	−7.89898	+	7.89898i	−0.568581	+	0.568581i	−0.931731	−	0.363150i	$-0.881701\pi$
$193$	−7.89898	+	7.89898i	−0.568581	+	0.568581i	0.363150	+	0.931731i	$0.381701\pi$
$194$	6.29253			0.451777
$195$	7.65029	−	2.12220i	0.547848	−	0.151974i
$196$	5.00000			0.357143
$197$	0.778539	−	0.778539i	0.0554686	−	0.0554686i	−0.678828	−	0.734297i	$-0.737512\pi$
$197$	0.778539	−	0.778539i	0.0554686	−	0.0554686i	0.734297	+	0.678828i	$0.237512\pi$
$198$	15.3137	+	7.31371i	1.08830	+	0.519763i
$199$			12.4495i			0.882521i	0.897379	+	0.441260i	$0.145469\pi$
$199$			12.4495i			0.882521i	−0.897379	+	0.441260i	$0.854531\pi$
$200$	2.75699	−	4.17121i	0.194949	−	0.294949i
$201$	2.20204	+	1.55708i	0.155320	+	0.109828i
$202$	−4.44949	−	4.44949i	−0.313065	−	0.313065i
$203$	−22.3417	−	22.3417i	−1.56808	−	1.56808i
$204$	−10.3923	−	7.34847i	−0.727607	−	0.514496i
$205$	12.0000	−	14.6969i	0.838116	−	1.02648i
$206$			1.55708i			0.108487i
$207$	2.70711	+	1.29289i	0.188157	+	0.0898623i
$208$	−1.44949	+	1.44949i	−0.100504	+	0.100504i
$209$	13.8564			0.958468
$210$	−11.6775	−	6.60572i	−0.805825	−	0.455838i
$211$	−10.6969			−0.736408			−0.368204	−	0.929745i	$-0.620027\pi$
$211$	−10.6969			−0.736408			−0.368204	+	0.929745i	$0.620027\pi$
$212$	−9.43879	+	9.43879i	−0.648259	+	0.648259i
$213$	−1.80119	−	10.4981i	−0.123416	−	0.719320i
$214$			1.10102i			0.0752642i
$215$	21.7060	−	2.19275i	1.48034	−	0.149544i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	−4.09978	−	4.09978i	−0.277672	−	0.277672i
$219$	−11.1708	+	15.7980i	−0.754856	+	1.06753i
$220$	−9.79796	−	8.00000i	−0.660578	−	0.539360i
$221$			15.0635i			1.01328i
$222$	−5.91359	+	1.01461i	−0.396894	+	0.0680963i
$223$	−7.55051	+	7.55051i	−0.505620	+	0.505620i	−0.913179	−	0.407559i	$-0.866380\pi$
$223$	−7.55051	+	7.55051i	−0.505620	+	0.505620i	0.407559	+	0.913179i	$0.366380\pi$
$224$	3.46410			0.231455
$225$	7.72741	+	12.8564i	0.515160	+	0.857094i
$226$	3.34847			0.222737
$227$	−7.70674	+	7.70674i	−0.511514	+	0.511514i	−0.914990	−	0.403476i	$-0.867802\pi$
$227$	−7.70674	+	7.70674i	−0.511514	+	0.511514i	0.403476	+	0.914990i	$0.367802\pi$
$228$	4.18154	−	0.717439i	0.276929	−	0.0475136i
$229$			22.6969i			1.49986i	0.661520	+	0.749928i	$0.269912\pi$
$229$			22.6969i			1.49986i	−0.661520	+	0.749928i	$0.730088\pi$
$230$	−1.73205	−	1.41421i	−0.114208	−	0.0932505i
$231$	−19.5959	+	27.7128i	−1.28932	+	1.82337i
$232$	−6.44949	−	6.44949i	−0.423430	−	0.423430i
$233$	10.5352	+	10.5352i	0.690182	+	0.690182i	0.962272	−	0.272090i	$-0.0877148\pi$
$233$	10.5352	+	10.5352i	0.690182	+	0.690182i	−0.272090	+	0.962272i	$0.587715\pi$
$234$	−2.04989	−	5.79796i	−0.134005	−	0.379024i
$235$	6.44949	−	0.651531i	0.420718	−	0.0425012i
$236$			8.34242i			0.543045i
$237$	0.131652	+	0.767327i	0.00855175	+	0.0498432i
$238$	18.0000	−	18.0000i	1.16677	−	1.16677i
$239$	−6.43539			−0.416271			−0.208135	−	0.978100i	$-0.566739\pi$
$239$	−6.43539			−0.416271			−0.208135	+	0.978100i	$0.566739\pi$
$240$	−3.37101	−	1.90691i	−0.217598	−	0.123090i
$241$	−18.8990			−1.21739			−0.608695	−	0.793404i	$-0.708307\pi$
$241$	−18.8990			−1.21739			−0.608695	+	0.793404i	$0.708307\pi$
$242$	−14.8492	+	14.8492i	−0.954545	+	0.954545i
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$			8.89898i			0.569699i
$245$	7.07107	−	8.66025i	0.451754	−	0.553283i
$246$	−12.0000	−	8.48528i	−0.765092	−	0.541002i
$247$	−3.55051	−	3.55051i	−0.225914	−	0.225914i
$248$	3.46410	+	3.46410i	0.219971	+	0.219971i
$249$	2.82843	+	2.00000i	0.179244	+	0.126745i
$250$	−3.32577	−	10.6742i	−0.210340	−	0.675098i
$251$		−	26.7272i		−	1.68701i	−0.537125	−	0.843503i	$-0.680490\pi$
$251$		−	26.7272i		−	1.68701i	0.537125	−	0.843503i	$-0.319510\pi$
$252$	−4.47871	+	9.37769i	−0.282132	+	0.590739i
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$	−11.9494			−0.749771
$255$	−27.4249	+	7.60770i	−1.71741	+	0.476412i
$256$	1.00000			0.0625000
$257$	−18.0990	+	18.0990i	−1.12899	+	1.12899i	−0.138645	+	0.990342i	$0.544275\pi$
$257$	−18.0990	+	18.0990i	−1.12899	+	1.12899i	−0.990342	+	0.138645i	$0.955725\pi$
$258$	−2.85765	−	16.6556i	−0.177910	−	1.03693i
$259$		−	12.0000i		−	0.745644i
$260$	0.460702	+	4.56048i	0.0285715	+	0.282829i
$261$	25.7980	−	9.12096i	1.59685	−	0.564573i
$262$	9.89898	+	9.89898i	0.611561	+	0.611561i
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	0.859669	−	0.510852i	$-0.170670\pi$
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	−0.510852	+	0.859669i	$0.670670\pi$
$264$	−5.65685	+	8.00000i	−0.348155	+	0.492366i
$265$	3.00000	+	29.6969i	0.184289	+	1.82427i
$266$			8.48528i			0.520266i
$267$	3.74326	−	0.642242i	0.229084	−	0.0393046i
$268$	−1.10102	+	1.10102i	−0.0672555	+	0.0672555i
$269$	0.635674			0.0387578			0.0193789	−	0.999812i	$-0.493831\pi$
$269$	0.635674			0.0387578			0.0193789	+	0.999812i	$0.493831\pi$
$270$	9.52056	−	6.66025i	0.579403	−	0.405330i
$271$	24.4949			1.48796			0.743980	−	0.668202i	$-0.232936\pi$
$271$	24.4949			1.48796			0.743980	+	0.668202i	$0.232936\pi$
$272$	5.19615	−	5.19615i	0.315063	−	0.315063i
$273$	12.1222	−	2.07984i	0.733669	−	0.125878i
$274$		−	4.65153i		−	0.281009i
$275$	−27.7128	+	5.65685i	−1.67115	+	0.341121i
$276$	−1.00000	+	1.41421i	−0.0601929	+	0.0851257i
$277$	−4.55051	−	4.55051i	−0.273414	−	0.273414i	0.557059	−	0.830473i	$-0.311930\pi$
$277$	−4.55051	−	4.55051i	−0.273414	−	0.273414i	−0.830473	+	0.557059i	$0.811930\pi$
$278$	−7.56388	−	7.56388i	−0.453651	−	0.453651i
$279$	−13.8564	+	4.89898i	−0.829561	+	0.293294i
$280$	4.89898	−	6.00000i	0.292770	−	0.358569i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$	−0.849091	−	4.94887i	−0.0505627	−	0.294701i
$283$	−9.34847	+	9.34847i	−0.555709	+	0.555709i	−0.928083	−	0.372374i	$-0.878544\pi$
$283$	−9.34847	+	9.34847i	−0.555709	+	0.555709i	0.372374	+	0.928083i	$0.378544\pi$
$284$	6.14966			0.364915
$285$	4.67095	−	8.25725i	0.276683	−	0.489117i
$286$	11.5959			0.685681
$287$	20.7846	−	20.7846i	1.22688	−	1.22688i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$		−	37.0000i		−	2.17647i
$290$	−20.2918	+	2.04989i	−1.19158	+	0.120374i
$291$	−8.89898	−	6.29253i	−0.521667	−	0.368875i
$292$	−7.89898	−	7.89898i	−0.462253	−	0.462253i
$293$	10.7101	+	10.7101i	0.625693	+	0.625693i	0.946981	−	0.321288i	$-0.104116\pi$
$293$	10.7101	+	10.7101i	0.625693	+	0.625693i	−0.321288	+	0.946981i	$0.604116\pi$
$294$	−7.07107	−	5.00000i	−0.412393	−	0.291606i
$295$	14.4495	+	11.7980i	0.841282	+	0.686904i
$296$		−	3.46410i		−	0.201347i
$297$	−14.3431	−	25.6569i	−0.832274	−	1.48876i
$298$	−11.7980	+	11.7980i	−0.683437	+	0.683437i
$299$	2.04989			0.118548
$300$	−8.07019	+	3.14198i	−0.465933	+	0.181403i
$301$	33.7980			1.94808
$302$	6.29253	−	6.29253i	0.362094	−	0.362094i
$303$	1.84304	+	10.7420i	0.105880	+	0.617113i
$304$			2.44949i			0.140488i
$305$	15.4135	+	12.5851i	0.882574	+	0.720618i
$306$	7.34847	+	20.7846i	0.420084	+	1.18818i
$307$	6.69694	+	6.69694i	0.382214	+	0.382214i	0.871899	−	0.489685i	$-0.162888\pi$
$307$	6.69694	+	6.69694i	0.382214	+	0.382214i	−0.489685	+	0.871899i	$0.662888\pi$
$308$	−13.8564	−	13.8564i	−0.789542	−	0.789542i
$309$	1.55708	−	2.20204i	0.0885791	−	0.125270i
$310$	10.8990	−	1.10102i	0.619020	−	0.0625338i
$311$		−	34.1482i		−	1.93637i	−0.250241	−	0.968184i	$-0.580510\pi$
$311$		−	34.1482i		−	1.93637i	0.250241	−	0.968184i	$-0.419490\pi$
$312$	3.49938	−	0.600398i	0.198113	−	0.0339909i
$313$	19.1464	−	19.1464i	1.08222	−	1.08222i	0.0859179	−	0.996302i	$-0.472618\pi$
$313$	19.1464	−	19.1464i	1.08222	−	1.08222i	0.996302	−	0.0859179i	$-0.0273823\pi$
$314$	−5.02118			−0.283362
$315$	9.90878	+	21.0194i	0.558297	+	1.18431i
$316$	−0.449490			−0.0252858
$317$	6.43539	−	6.43539i	0.361448	−	0.361448i	−0.502898	−	0.864346i	$-0.667733\pi$
$317$	6.43539	−	6.43539i	0.361448	−	0.361448i	0.864346	+	0.502898i	$0.167733\pi$
$318$	22.7873	−	3.90968i	1.27785	−	0.219244i
$319$			51.5959i			2.88882i
$320$	1.41421	−	1.73205i	0.0790569	−	0.0968246i
$321$	1.10102	−	1.55708i	0.0614530	−	0.0869076i
$322$	−2.44949	−	2.44949i	−0.136505	−	0.136505i
$323$	12.7279	+	12.7279i	0.708201	+	0.708201i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	8.55051	+	5.65153i	0.474297	+	0.313491i
$326$			5.65685i			0.313304i
$327$	1.69818	+	9.89774i	0.0939097	+	0.547346i
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	10.0424			0.553653
$330$	5.85641	+	21.1117i	0.322385	+	1.16216i
$331$	10.6969			0.587957			0.293978	−	0.955812i	$-0.405021\pi$
$331$	10.6969			0.587957			0.293978	+	0.955812i	$0.405021\pi$
$332$	−1.41421	+	1.41421i	−0.0776151	+	0.0776151i
$333$	9.37769	+	4.47871i	0.513894	+	0.245432i
$334$			8.00000i			0.437741i
$335$	0.349945	+	3.46410i	0.0191196	+	0.189264i
$336$	−4.89898	−	3.46410i	−0.267261	−	0.188982i
$337$	9.55051	+	9.55051i	0.520249	+	0.520249i	0.917647	−	0.397397i	$-0.130086\pi$
$337$	9.55051	+	9.55051i	0.520249	+	0.520249i	−0.397397	+	0.917647i	$0.630086\pi$
$338$	6.22110	+	6.22110i	0.338383	+	0.338383i
$339$	−4.73545	−	3.34847i	−0.257194	−	0.181864i
$340$	−1.65153	−	16.3485i	−0.0895668	−	0.886620i
$341$		−	27.7128i		−	1.50073i
$342$	−6.63103	−	3.16693i	−0.358565	−	0.171248i
$343$	−4.89898	+	4.89898i	−0.264520	+	0.264520i
$344$	9.75663			0.526042
$345$	1.03528	+	3.73205i	0.0557374	+	0.200927i
$346$	−14.8990			−0.800974
$347$	13.9993	−	13.9993i	0.751520	−	0.751520i	−0.223243	−	0.974763i	$-0.571664\pi$
$347$	13.9993	−	13.9993i	0.751520	−	0.751520i	0.974763	+	0.223243i	$0.0716642\pi$
$348$	2.67147	+	15.5704i	0.143206	+	0.834663i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$	−3.46410	−	16.9706i	−0.185164	−	0.907115i
$351$	−2.89898	+	10.2494i	−0.154736	+	0.547075i
$352$	−4.00000	−	4.00000i	−0.213201	−	0.213201i
$353$	−2.33562	−	2.33562i	−0.124312	−	0.124312i	0.642213	−	0.766526i	$-0.278016\pi$
$353$	−2.33562	−	2.33562i	−0.124312	−	0.124312i	−0.766526	+	0.642213i	$0.778016\pi$
$354$	8.34242	−	11.7980i	0.443394	−	0.627054i
$355$	8.69694	−	10.6515i	0.461586	−	0.565325i
$356$			2.19275i			0.116216i
$357$	−43.4558	+	7.45584i	−2.29993	+	0.394605i
$358$	−8.79796	+	8.79796i	−0.464987	+	0.464987i
$359$	−12.8708			−0.679294			−0.339647	−	0.940553i	$-0.610308\pi$
$359$	−12.8708			−0.679294			−0.339647	+	0.940553i	$0.610308\pi$
$360$	2.86042	+	6.06778i	0.150757	+	0.319800i
$361$	13.0000			0.684211
$362$	5.65685	−	5.65685i	0.297318	−	0.297318i
$363$	35.8492	−	6.15076i	1.88160	−	0.322831i
$364$			7.10102i			0.372195i
$365$	−24.8523	+	2.51059i	−1.30083	+	0.131410i
$366$	8.89898	−	12.5851i	0.465157	−	0.657831i
$367$	0.202041	+	0.202041i	0.0105465	+	0.0105465i	0.712360	−	0.701814i	$-0.247626\pi$
$367$	0.202041	+	0.202041i	0.0105465	+	0.0105465i	−0.701814	+	0.712360i	$0.747626\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	8.48528	+	24.0000i	0.441726	+	1.24939i
$370$	−6.00000	−	4.89898i	−0.311925	−	0.254686i
$371$			46.2405i			2.40068i
$372$	−1.43488	−	8.36308i	−0.0743950	−	0.433606i
$373$	7.55051	−	7.55051i	0.390951	−	0.390951i	−0.484076	−	0.875026i	$-0.660844\pi$
$373$	7.55051	−	7.55051i	0.390951	−	0.390951i	0.875026	+	0.484076i	$0.160844\pi$
$374$	−41.5692			−2.14949
$375$	−5.97089	+	18.4214i	−0.308336	+	0.951278i
$376$	2.89898			0.149503
$377$	13.2207	−	13.2207i	0.680902	−	0.680902i
$378$	15.7116	−	8.78335i	0.808115	−	0.451767i
$379$		−	29.1464i		−	1.49715i	−0.663049	−	0.748576i	$-0.730738\pi$
$379$		−	29.1464i		−	1.49715i	0.663049	−	0.748576i	$-0.269262\pi$
$380$	4.24264	+	3.46410i	0.217643	+	0.177705i
$381$	16.8990	+	11.9494i	0.865761	+	0.612185i
$382$	16.6969	+	16.6969i	0.854290	+	0.854290i
$383$	−16.0492	−	16.0492i	−0.820074	−	0.820074i	0.166045	−	0.986118i	$-0.446900\pi$
$383$	−16.0492	−	16.0492i	−0.820074	−	0.820074i	−0.986118	+	0.166045i	$0.946900\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	−43.5959	+	4.40408i	−2.22185	+	0.224453i
$386$			11.1708i			0.568581i
$387$	−12.6143	+	26.4122i	−0.641220	+	1.34261i
$388$	4.44949	−	4.44949i	0.225889	−	0.225889i
$389$	−31.1127			−1.57748			−0.788738	−	0.614729i	$-0.789265\pi$
$389$	−31.1127			−1.57748			−0.788738	+	0.614729i	$0.789265\pi$
$390$	3.90895	−	6.91019i	0.197937	−	0.349911i
$391$	−7.34847			−0.371628
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	−4.10029	−	23.8983i	−0.206832	−	1.20551i
$394$		−	1.10102i		−	0.0554686i
$395$	−0.635674	+	0.778539i	−0.0319843	+	0.0391726i
$396$	16.0000	−	5.65685i	0.804030	−	0.284268i
$397$	13.4495	+	13.4495i	0.675011	+	0.675011i	0.958867	−	0.283856i	$-0.0916139\pi$
$397$	13.4495	+	13.4495i	0.675011	+	0.675011i	−0.283856	+	0.958867i	$0.591614\pi$
$398$	8.80312	+	8.80312i	0.441260	+	0.441260i
$399$	8.48528	−	12.0000i	0.424795	−	0.600751i
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$			14.7778i			0.737969i	0.929436	+	0.368984i	$0.120294\pi$
$401$			14.7778i			0.737969i	−0.929436	+	0.368984i	$0.879706\pi$
$402$	2.65810	−	0.456058i	0.132574	−	0.0227461i
$403$	−7.10102	+	7.10102i	−0.353727	+	0.353727i
$404$	−6.29253			−0.313065
$405$	−20.1244	−	0.101536i	−0.999987	−	0.00504536i
$406$	−31.5959			−1.56808
$407$	−13.8564	+	13.8564i	−0.686837	+	0.686837i
$408$	−12.5446	+	2.15232i	−0.621051	+	0.106556i
$409$		−	5.79796i		−	0.286691i	−0.989673	−	0.143345i	$-0.954214\pi$
$409$		−	5.79796i		−	0.286691i	0.989673	−	0.143345i	$-0.0457860\pi$
$410$	−1.90702	−	18.8776i	−0.0941812	−	0.932298i
$411$	−4.65153	+	6.57826i	−0.229443	+	0.324482i
$412$	1.10102	+	1.10102i	0.0542434	+	0.0542434i
$413$	20.4347	+	20.4347i	1.00552	+	1.00552i
$414$	2.82843	−	1.00000i	0.139010	−	0.0491473i
$415$	0.449490	+	4.44949i	0.0220646	+	0.218417i
$416$			2.04989i			0.100504i
$417$	3.13306	+	18.2608i	0.153427	+	0.894236i
$418$	9.79796	−	9.79796i	0.479234	−	0.479234i
$419$	18.2419			0.891176			0.445588	−	0.895238i	$-0.352995\pi$
$419$	18.2419			0.891176			0.445588	+	0.895238i	$0.352995\pi$
$420$	−12.9282	+	3.58630i	−0.630832	+	0.174994i
$421$	−8.89898			−0.433710			−0.216855	−	0.976204i	$-0.569580\pi$
$421$	−8.89898			−0.433710			−0.216855	+	0.976204i	$0.569580\pi$
$422$	−7.56388	+	7.56388i	−0.368204	+	0.368204i
$423$	−3.74807	+	7.84785i	−0.182237	+	0.381575i
$424$			13.3485i			0.648259i
$425$	−30.6520	−	20.2597i	−1.48684	−	0.982739i
$426$	−8.69694	−	6.14966i	−0.421368	−	0.297952i
$427$	21.7980	+	21.7980i	1.05488	+	1.05488i
$428$	0.778539	+	0.778539i	0.0376321	+	0.0376321i
$429$	−16.3991	−	11.5959i	−0.791756	−	0.559856i
$430$	13.7980	−	16.8990i	0.665397	−	0.814941i
$431$			5.37113i			0.258718i	0.991598	+	0.129359i	$0.0412920\pi$
$431$			5.37113i			0.258718i	−0.991598	+	0.129359i	$0.958708\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	14.6515	−	14.6515i	0.704108	−	0.704108i	−0.261182	−	0.965290i	$-0.584112\pi$
$433$	14.6515	−	14.6515i	0.704108	−	0.704108i	0.965290	+	0.261182i	$0.0841123\pi$
$434$	16.9706			0.814613
$435$	30.7468	+	17.3928i	1.47420	+	0.833922i
$436$	−5.79796			−0.277672
$437$	1.73205	−	1.73205i	0.0828552	−	0.0828552i
$438$	3.27186	+	19.0698i	0.156336	+	0.911191i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	−12.5851	+	1.27135i	−0.599969	+	0.0606092i
$441$	5.00000	+	14.1421i	0.238095	+	0.673435i
$442$	10.6515	+	10.6515i	0.506642	+	0.506642i
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	0.385272	−	0.922803i	$-0.374107\pi$
$443$	−11.3137	−	11.3137i	−0.537531	−	0.537531i	−0.922803	+	0.385272i	$0.874107\pi$
$444$	−3.46410	+	4.89898i	−0.164399	+	0.232495i
$445$	3.79796	+	3.10102i	0.180041	+	0.147002i
$446$			10.6780i			0.505620i
$447$	28.4828	−	4.88687i	1.34719	−	0.231141i
$448$	2.44949	−	2.44949i	0.115728	−	0.115728i
$449$	26.4415			1.24785			0.623925	−	0.781484i	$-0.285537\pi$
$449$	26.4415			1.24785			0.623925	+	0.781484i	$0.285537\pi$
$450$	14.5550	+	3.62675i	0.686127	+	0.170967i
$451$	−48.0000			−2.26023
$452$	2.36773	−	2.36773i	0.111368	−	0.111368i
$453$	−15.1915	+	2.60645i	−0.713759	+	0.122462i
$454$			10.8990i			0.511514i
$455$	12.2993	+	10.0424i	0.576601	+	0.470793i
$456$	2.44949	−	3.46410i	0.114708	−	0.162221i
$457$	6.44949	+	6.44949i	0.301694	+	0.301694i	0.841677	−	0.539982i	$-0.181569\pi$
$457$	6.44949	+	6.44949i	0.301694	+	0.301694i	−0.539982	+	0.841677i	$0.681569\pi$
$458$	16.0492	+	16.0492i	0.749928	+	0.749928i
$459$	10.3923	−	36.7423i	0.485071	−	1.71499i
$460$	−2.22474	+	0.224745i	−0.103729	+	0.0104788i
$461$		−	3.17837i		−	0.148032i	−0.997257	−	0.0740158i	$-0.976418\pi$
$461$		−	3.17837i		−	0.148032i	0.997257	−	0.0740158i	$-0.0235815\pi$
$462$	5.73951	+	33.4523i	0.267026	+	1.55634i
$463$	−18.0454	+	18.0454i	−0.838641	+	0.838641i	−0.988680	−	0.150039i	$-0.952060\pi$
$463$	−18.0454	+	18.0454i	−0.838641	+	0.838641i	0.150039	+	0.988680i	$0.452060\pi$
$464$	−9.12096			−0.423430
$465$	−16.5145	−	9.34190i	−0.765842	−	0.433220i
$466$	14.8990			0.690182
$467$	10.5352	−	10.5352i	0.487510	−	0.487510i	−0.420010	−	0.907519i	$-0.637973\pi$
$467$	10.5352	−	10.5352i	0.487510	−	0.487510i	0.907519	+	0.420010i	$0.137973\pi$
$468$	−5.54927	−	2.65029i	−0.256515	−	0.122510i
$469$			5.39388i			0.249066i
$470$	4.09978	−	5.02118i	0.189109	−	0.231610i
$471$	7.10102	+	5.02118i	0.327198	+	0.231364i
$472$	5.89898	+	5.89898i	0.271523	+	0.271523i
$473$	−39.0265	−	39.0265i	−1.79444	−	1.79444i
$474$	0.635674	+	0.449490i	0.0291975	+	0.0206457i
$475$	12.0000	−	2.44949i	0.550598	−	0.112390i
$476$		−	25.4558i		−	1.16677i
$477$	−36.1357	−	17.2581i	−1.65454	−	0.790196i
$478$	−4.55051	+	4.55051i	−0.208135	+	0.208135i
$479$	15.1278			0.691205			0.345602	−	0.938381i	$-0.387675\pi$
$479$	15.1278			0.691205			0.345602	+	0.938381i	$0.387675\pi$
$480$	−3.73205	+	1.03528i	−0.170344	+	0.0472537i
$481$	7.10102			0.323779
$482$	−13.3636	+	13.3636i	−0.608695	+	0.608695i
$483$	1.01461	+	5.91359i	0.0461664	+	0.269078i
$484$			21.0000i			0.954545i
$485$	−1.41421	−	13.9993i	−0.0642161	−	0.635674i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	4.65153	+	4.65153i	0.210781	+	0.210781i	0.804599	−	0.593818i	$-0.202380\pi$
$487$	4.65153	+	4.65153i	0.210781	+	0.210781i	−0.593818	+	0.804599i	$0.702380\pi$
$488$	6.29253	+	6.29253i	0.284849	+	0.284849i
$489$	5.65685	−	8.00000i	0.255812	−	0.361773i
$490$	−1.12372	−	11.1237i	−0.0507647	−	0.502519i
$491$		−	11.4566i		−	0.517028i	−0.966008	−	0.258514i	$-0.916767\pi$
$491$		−	11.4566i		−	0.517028i	0.966008	−	0.258514i	$-0.0832328\pi$
$492$	−14.4853	+	2.48528i	−0.653047	+	0.112045i
$493$	−47.3939	+	47.3939i	−2.13451	+	2.13451i
$494$	−5.02118			−0.225914
$495$	12.8295	−	35.7128i	0.576641	−	1.60517i
$496$	4.89898			0.219971
$497$	15.0635	−	15.0635i	0.675692	−	0.675692i
$498$	3.41421	−	0.585786i	0.152995	−	0.0262497i
$499$		−	14.2020i		−	0.635771i	−0.948129	−	0.317885i	$-0.897027\pi$
$499$		−	14.2020i		−	0.635771i	0.948129	−	0.317885i	$-0.102973\pi$
$500$	−9.89949	−	5.19615i	−0.442719	−	0.232379i
$501$	8.00000	−	11.3137i	0.357414	−	0.505459i
$502$	−18.8990	−	18.8990i	−0.843503	−	0.843503i
$503$	−18.8776	−	18.8776i	−0.841710	−	0.841710i	0.147371	−	0.989081i	$-0.452919\pi$
$503$	−18.8776	−	18.8776i	−0.841710	−	0.841710i	−0.989081	+	0.147371i	$0.952919\pi$
$504$	3.46410	+	9.79796i	0.154303	+	0.436436i
$505$	−8.89898	+	10.8990i	−0.395999	+	0.484998i
$506$			5.65685i			0.251478i
$507$	−2.57686	−	15.0191i	−0.114442	−	0.667020i
$508$	−8.44949	+	8.44949i	−0.374885	+	0.374885i
$509$	−42.4906			−1.88336			−0.941682	−	0.336504i	$-0.890755\pi$
$509$	−42.4906			−1.88336			−0.941682	+	0.336504i	$0.890755\pi$
$510$	−14.0129	+	24.7718i	−0.620500	+	1.09691i
$511$	−38.6969			−1.71185
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	6.21076	+	11.1097i	0.274212	+	0.490507i
$514$			25.5959i			1.12899i
$515$	3.46410	−	0.349945i	0.152647	−	0.0154204i
$516$	−13.7980	−	9.75663i	−0.607421	−	0.429512i
$517$	−11.5959	−	11.5959i	−0.509988	−	0.509988i
$518$	−8.48528	−	8.48528i	−0.372822	−	0.372822i
$519$	21.0703	+	14.8990i	0.924885	+	0.653993i
$520$	3.55051	+	2.89898i	0.155700	+	0.127129i
$521$			42.4906i			1.86155i	0.365595	+	0.930774i	$0.380866\pi$
$521$			42.4906i			1.86155i	−0.365595	+	0.930774i	$0.619134\pi$
$522$	11.7924	−	24.6914i	0.516140	−	1.08071i
$523$	2.24745	−	2.24745i	0.0982741	−	0.0982741i	−0.656260	−	0.754534i	$-0.727863\pi$
$523$	2.24745	−	2.24745i	0.0982741	−	0.0982741i	0.754534	+	0.656260i	$0.227863\pi$
$524$	13.9993			0.611561
$525$	−12.0716	+	27.4641i	−0.526847	+	1.19863i
$526$	8.00000			0.348817
$527$	25.4558	−	25.4558i	1.10887	−	1.10887i
$528$	1.65685	+	9.65685i	0.0721053	+	0.420261i
$529$			1.00000i			0.0434783i
$530$	23.1202	+	18.8776i	1.00428	+	0.819990i
$531$	−23.5959	+	8.34242i	−1.02398	+	0.362030i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	12.2993	+	12.2993i	0.532743	+	0.532743i
$534$	2.19275	−	3.10102i	0.0948897	−	0.134194i
$535$	2.44949	−	0.247449i	0.105901	−	0.0106981i
$536$			1.55708i			0.0672555i
$537$	21.2402	−	3.64423i	0.916580	−	0.157260i
$538$	0.449490	−	0.449490i	0.0193789	−	0.0193789i
$539$	−28.2843			−1.21829
$540$	2.02254	−	11.4416i	0.0870363	−	0.492366i
$541$	−10.6969			−0.459897			−0.229949	−	0.973203i	$-0.573856\pi$
$541$	−10.6969			−0.459897			−0.229949	+	0.973203i	$0.573856\pi$
$542$	17.3205	−	17.3205i	0.743980	−	0.743980i
$543$	−13.6569	+	2.34315i	−0.586072	+	0.100554i
$544$		−	7.34847i		−	0.315063i
$545$	−8.19955	+	10.0424i	−0.351230	+	0.430167i
$546$	7.10102	−	10.0424i	0.303896	−	0.429773i
$547$	27.5959	+	27.5959i	1.17992	+	1.17992i	0.979765	+	0.200151i	$0.0641433\pi$
$547$	27.5959	+	27.5959i	1.17992	+	1.17992i	0.200151	+	0.979765i	$0.435857\pi$
$548$	−3.28913	−	3.28913i	−0.140505	−	0.140505i
$549$	−25.1701	+	8.89898i	−1.07423	+	0.379799i
$550$	−15.5959	+	23.5959i	−0.665012	+	1.00613i
$551$		−	22.3417i		−	0.951788i
$552$	0.292893	+	1.70711i	0.0124664	+	0.0726593i
$553$	−1.10102	+	1.10102i	−0.0468202	+	0.0468202i
$554$	−6.43539			−0.273414
$555$	3.58630	+	12.9282i	0.152230	+	0.548772i
$556$	−10.6969			−0.453651
$557$	23.9309	−	23.9309i	1.01398	−	1.01398i	0.0140828	−	0.999901i	$-0.495517\pi$
$557$	23.9309	−	23.9309i	1.01398	−	1.01398i	0.999901	−	0.0140828i	$-0.00448286\pi$
$558$	−6.33386	+	13.2621i	−0.268134	+	0.561428i
$559$			20.0000i			0.845910i
$560$	−0.778539	−	7.70674i	−0.0328993	−	0.325669i
$561$	58.7878	+	41.5692i	2.48202	+	1.75505i
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	−1.12848	−	1.12848i	−0.0475599	−	0.0475599i	0.682927	−	0.730487i	$-0.260707\pi$
$563$	−1.12848	−	1.12848i	−0.0475599	−	0.0475599i	−0.730487	+	0.682927i	$0.760707\pi$
$564$	−4.09978	−	2.89898i	−0.172632	−	0.122069i
$565$	−0.752551	−	7.44949i	−0.0316601	−	0.313402i
$566$			13.2207i			0.555709i
$567$	−31.0028	−	3.29002i	−1.30200	−	0.138168i
$568$	4.34847	−	4.34847i	0.182458	−	0.182458i
$569$	10.0424			0.420998			0.210499	−	0.977594i	$-0.432491\pi$
$569$	10.0424			0.420998			0.210499	+	0.977594i	$0.432491\pi$
$570$	−2.53590	−	9.14162i	−0.106217	−	0.382900i
$571$	26.4495			1.10688			0.553438	−	0.832890i	$-0.313315\pi$
$571$	26.4495			1.10688			0.553438	+	0.832890i	$0.313315\pi$
$572$	8.19955	−	8.19955i	0.342841	−	0.342841i
$573$	−6.91610	−	40.3100i	−0.288924	−	1.68397i
$574$		−	29.3939i		−	1.22688i
$575$	−2.75699	+	4.17121i	−0.114975	+	0.173951i
$576$	1.00000	+	2.82843i	0.0416667	+	0.117851i
$577$	18.7980	+	18.7980i	0.782569	+	0.782569i	0.980264	−	0.197694i	$-0.0633454\pi$
$577$	18.7980	+	18.7980i	0.782569	+	0.782569i	−0.197694	+	0.980264i	$0.563345\pi$
$578$	−26.1630	−	26.1630i	−1.08824	−	1.08824i
$579$	11.1708	−	15.7980i	0.464244	−	0.656541i
$580$	−12.8990	+	15.7980i	−0.535601	+	0.655975i
$581$			6.92820i			0.287430i
$582$	−10.7420	+	1.84304i	−0.445271	+	0.0763964i
$583$	53.3939	−	53.3939i	2.21135	−	2.21135i
$584$	−11.1708			−0.462253
$585$	−12.4383	+	5.86354i	−0.514259	+	0.242428i
$586$	15.1464			0.625693
$587$	−0.142865	+	0.142865i	−0.00589665	+	0.00589665i	−0.710049	−	0.704152i	$-0.751327\pi$
$587$	−0.142865	+	0.142865i	−0.00589665	+	0.00589665i	0.704152	+	0.710049i	$0.251327\pi$
$588$	−8.53553	+	1.46447i	−0.351999	+	0.0603936i
$589$			12.0000i			0.494451i
$590$	18.5597	−	1.87492i	0.764093	−	0.0771890i
$591$	−1.10102	+	1.55708i	−0.0452899	+	0.0640496i
$592$	−2.44949	−	2.44949i	−0.100673	−	0.100673i
$593$	−2.68556	−	2.68556i	−0.110283	−	0.110283i	0.649812	−	0.760095i	$-0.274848\pi$
$593$	−2.68556	−	2.68556i	−0.110283	−	0.110283i	−0.760095	+	0.649812i	$0.774848\pi$
$594$	−28.2843	−	8.00000i	−1.16052	−	0.328244i
$595$	−44.0908	−	36.0000i	−1.80755	−	1.47586i
$596$			16.6848i			0.683437i
$597$	−3.64637	−	21.2526i	−0.149236	−	0.869811i
$598$	1.44949	−	1.44949i	0.0592740	−	0.0592740i
$599$	17.4634			0.713534			0.356767	−	0.934193i	$-0.383879\pi$
$599$	17.4634			0.713534			0.356767	+	0.934193i	$0.383879\pi$
$600$	−3.48477	+	7.92820i	−0.142265	+	0.323668i
$601$	−35.7980			−1.46023			−0.730115	−	0.683325i	$-0.760533\pi$
$601$	−35.7980			−1.46023			−0.730115	+	0.683325i	$0.760533\pi$
$602$	23.8988	−	23.8988i	0.974041	−	0.974041i
$603$	−4.21518	−	2.01314i	−0.171655	−	0.0819812i
$604$		−	8.89898i		−	0.362094i
$605$	36.3731	+	29.6985i	1.47878	+	1.20742i
$606$	8.89898	+	6.29253i	0.361496	+	0.255617i
$607$	7.34847	+	7.34847i	0.298265	+	0.298265i	0.840334	−	0.542069i	$-0.182359\pi$
$607$	7.34847	+	7.34847i	0.298265	+	0.298265i	−0.542069	+	0.840334i	$0.682359\pi$
$608$	1.73205	+	1.73205i	0.0702439	+	0.0702439i
$609$	44.6834	+	31.5959i	1.81066	+	1.28033i
$610$	19.7980	−	2.00000i	0.801596	−	0.0809776i
$611$			5.94258i			0.240411i
$612$	19.8931	+	9.50079i	0.804131	+	0.384047i
$613$	−11.3485	+	11.3485i	−0.458360	+	0.458360i	−0.898117	−	0.439757i	$-0.855065\pi$
$613$	−11.3485	+	11.3485i	−0.458360	+	0.458360i	0.439757	+	0.898117i	$0.355065\pi$
$614$	9.47090			0.382214
$615$	−16.1806	+	28.6040i	−0.652467	+	1.15342i
$616$	−19.5959			−0.789542
$617$	12.7600	−	12.7600i	0.513699	−	0.513699i	−0.401958	−	0.915658i	$-0.631670\pi$
$617$	12.7600	−	12.7600i	0.513699	−	0.513699i	0.915658	+	0.401958i	$0.131670\pi$
$618$	−0.456058	−	2.65810i	−0.0183453	−	0.106924i
$619$		−	14.0454i		−	0.564533i	−0.959336	−	0.282266i	$-0.908914\pi$
$619$		−	14.0454i		−	0.564533i	0.959336	−	0.282266i	$-0.0910862\pi$
$620$	6.92820	−	8.48528i	0.278243	−	0.340777i
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$	−24.1464	−	24.1464i	−0.968184	−	0.968184i
$623$	5.37113	+	5.37113i	0.215190	+	0.215190i
$624$	2.04989	−	2.89898i	0.0820612	−	0.116052i
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$		−	27.0771i		−	1.08222i
$627$	−23.6544	+	4.05845i	−0.944664	+	0.162079i
$628$	−3.55051	+	3.55051i	−0.141681	+	0.141681i
$629$	−25.4558			−1.01499
$630$	21.8695	+	7.85641i	0.871303	+	0.313007i
$631$	19.5505			0.778294			0.389147	−	0.921176i	$-0.372770\pi$
$631$	19.5505			0.778294			0.389147	+	0.921176i	$0.372770\pi$
$632$	−0.317837	+	0.317837i	−0.0126429	+	0.0126429i
$633$	18.2608	−	3.13306i	0.725802	−	0.124528i
$634$		−	9.10102i		−	0.361448i
$635$	2.68556	+	26.5843i	0.106573	+	1.05497i
$636$	13.3485	−	18.8776i	0.529301	−	0.748545i
$637$	7.24745	+	7.24745i	0.287154	+	0.287154i
$638$	36.4838	+	36.4838i	1.44441	+	1.44441i
$639$	6.14966	+	17.3939i	0.243277	+	0.688091i
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$		−	13.5065i		−	0.533473i	−0.963769	−	0.266737i	$-0.914055\pi$
$641$		−	13.5065i		−	0.533473i	0.963769	−	0.266737i	$-0.0859454\pi$
$642$	−0.322481	−	1.87956i	−0.0127273	−	0.0741803i
$643$	−13.1010	+	13.1010i	−0.516654	+	0.516654i	−0.916557	−	0.399903i	$-0.869044\pi$
$643$	−13.1010	+	13.1010i	−0.516654	+	0.516654i	0.399903	+	0.916557i	$0.369044\pi$
$644$	−3.46410			−0.136505
$645$	−36.4122	+	10.1008i	−1.43373	+	0.397719i
$646$	18.0000			0.708201
$647$	13.6493	−	13.6493i	0.536610	−	0.536610i	−0.385921	−	0.922532i	$-0.626116\pi$
$647$	13.6493	−	13.6493i	0.536610	−	0.536610i	0.922532	+	0.385921i	$0.126116\pi$
$648$	−8.94975	−	0.949747i	−0.351579	−	0.0373096i
$649$		−	47.1918i		−	1.85244i
$650$	10.0424	−	2.04989i	0.393894	−	0.0804032i
$651$	−24.0000	−	16.9706i	−0.940634	−	0.665129i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	9.26382	+	9.26382i	0.362521	+	0.362521i	0.864740	−	0.502219i	$-0.167483\pi$
$653$	9.26382	+	9.26382i	0.362521	+	0.362521i	−0.502219	+	0.864740i	$0.667483\pi$
$654$	8.19955	+	5.79796i	0.320628	+	0.226718i
$655$	19.7980	−	24.2474i	0.773570	−	0.947426i
$656$		−	8.48528i		−	0.331295i
$657$	14.4427	−	30.2407i	0.563464	−	1.17980i
$658$	7.10102	−	7.10102i	0.276827	−	0.276827i
$659$	−4.09978			−0.159705			−0.0798523	−	0.996807i	$-0.525445\pi$
$659$	−4.09978			−0.159705			−0.0798523	+	0.996807i	$0.525445\pi$
$660$	19.0693	+	10.7871i	0.742272	+	0.419887i
$661$	7.10102			0.276198			0.138099	−	0.990418i	$-0.455901\pi$
$661$	7.10102			0.276198			0.138099	+	0.990418i	$0.455901\pi$
$662$	7.56388	−	7.56388i	0.293978	−	0.293978i
$663$	−4.41201	−	25.7151i	−0.171348	−	0.998691i
$664$			2.00000i			0.0776151i
$665$	18.8776	−	1.90702i	0.732041	−	0.0739512i
$666$	9.79796	−	3.46410i	0.379663	−	0.134231i
$667$	6.44949	+	6.44949i	0.249725	+	0.249725i
$668$	5.65685	+	5.65685i	0.218870	+	0.218870i
$669$	10.6780	−	15.1010i	0.412837	−	0.583839i
$670$	2.69694	+	2.20204i	0.104192	+	0.0850723i
$671$		−	50.3402i		−	1.94336i
$672$	−5.91359	+	1.01461i	−0.228122	+	0.0391395i
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	−0.646918	−	0.762560i	$-0.723942\pi$
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	0.762560	+	0.646918i	$0.223942\pi$
$674$	13.5065			0.520249
$675$	−16.9571	−	19.6840i	−0.652678	−	0.757636i
$676$	8.79796			0.338383
$677$	−22.6595	+	22.6595i	−0.870876	+	0.870876i	−0.992568	−	0.121692i	$-0.961168\pi$
$677$	−22.6595	+	22.6595i	−0.870876	+	0.870876i	0.121692	+	0.992568i	$0.461168\pi$
$678$	−5.71619	+	0.980744i	−0.219529	+	0.0376652i
$679$		−	21.7980i		−	0.836529i
$680$	−12.7279	−	10.3923i	−0.488094	−	0.398527i
$681$	10.8990	−	15.4135i	0.417650	−	0.590646i
$682$	−19.5959	−	19.5959i	−0.750366	−	0.750366i
$683$	−4.24264	−	4.24264i	−0.162340	−	0.162340i	0.621262	−	0.783603i	$-0.286620\pi$
$683$	−4.24264	−	4.24264i	−0.162340	−	0.162340i	−0.783603	+	0.621262i	$0.786620\pi$
$684$	−6.92820	+	2.44949i	−0.264906	+	0.0936586i
$685$	−10.3485	+	1.04541i	−0.395395	+	0.0399430i
$686$			6.92820i			0.264520i
$687$	−6.64778	−	38.7461i	−0.253629	−	1.47826i
$688$	6.89898	−	6.89898i	0.263021	−	0.263021i
$689$	−27.3629			−1.04244
$690$	3.37101	+	1.90691i	0.128332	+	0.0725947i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	−10.5352	+	10.5352i	−0.400487	+	0.400487i
$693$	25.3354	−	53.0482i	0.962413	−	2.01514i
$694$		−	19.7980i		−	0.751520i
$695$	−15.1278	+	18.5276i	−0.573828	+	0.702793i
$696$	12.8990	+	9.12096i	0.488935	+	0.345729i
$697$	−44.0908	−	44.0908i	−1.67006	−	1.67006i
$698$	−15.5563	−	15.5563i	−0.588817	−	0.588817i
$699$	−21.0703	−	14.8990i	−0.796953	−	0.563531i
$700$	−14.4495	−	9.55051i	−0.546139	−	0.360975i
$701$		−	43.0621i		−	1.62643i	−0.581962	−	0.813216i	$-0.697715\pi$
$701$		−	43.0621i		−	1.62643i	0.581962	−	0.813216i	$-0.302285\pi$
$702$	5.19756	+	9.29734i	0.196169	+	0.350905i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	−5.65685			−0.213201
$705$	−10.8191	+	3.00124i	−0.407472	+	0.113033i
$706$	−3.30306			−0.124312
$707$	−15.4135	+	15.4135i	−0.579684	+	0.579684i
$708$	−2.44344	−	14.2414i	−0.0918300	−	0.535224i
$709$		−	7.10102i		−	0.266684i	−0.991070	−	0.133342i	$-0.957429\pi$
$709$		−	7.10102i		−	0.266684i	0.991070	−	0.133342i	$-0.0425709\pi$
$710$	−1.38211	−	13.6814i	−0.0518695	−	0.513455i
$711$	−0.449490	−	1.27135i	−0.0168572	−	0.0476793i
$712$	1.55051	+	1.55051i	0.0581078	+	0.0581078i
$713$	−3.46410	−	3.46410i	−0.129732	−	0.129732i
$714$	−25.4558	+	36.0000i	−0.952661	+	1.34727i
$715$	−2.60612	−	25.7980i	−0.0974635	−	0.964789i
$716$			12.4422i			0.464987i
$717$	10.9859	−	1.88488i	0.410276	−	0.0703922i
$718$	−9.10102	+	9.10102i	−0.339647	+	0.339647i
$719$	32.8769			1.22610			0.613050	−	0.790044i	$-0.289942\pi$
$719$	32.8769			1.22610			0.613050	+	0.790044i	$0.289942\pi$
$720$	6.31319	+	2.26795i	0.235279	+	0.0845215i
$721$	5.39388			0.200878
$722$	9.19239	−	9.19239i	0.342105	−	0.342105i
$723$	32.2626	−	5.53538i	1.19986	−	0.205863i
$724$		−	8.00000i		−	0.297318i
$725$	9.12096	+	44.6834i	0.338744	+	1.65950i
$726$	21.0000	−	29.6985i	0.779383	−	1.10221i
$727$	−0.247449	−	0.247449i	−0.00917736	−	0.00917736i	0.702503	−	0.711681i	$-0.252066\pi$
$727$	−0.247449	−	0.247449i	−0.00917736	−	0.00917736i	−0.711681	+	0.702503i	$0.752066\pi$
$728$	5.02118	+	5.02118i	0.186097	+	0.186097i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−15.7980	+	19.3485i	−0.584709	+	0.716119i
$731$		−	71.6963i		−	2.65178i
$732$	−2.60645	−	15.1915i	−0.0963372	−	0.561494i
$733$	9.14643	−	9.14643i	0.337831	−	0.337831i	−0.517719	−	0.855550i	$-0.673219\pi$
$733$	9.14643	−	9.14643i	0.337831	−	0.337831i	0.855550	+	0.517719i	$0.173219\pi$
$734$	0.285729			0.0105465
$735$	−9.53454	+	16.8550i	−0.351687	+	0.621708i
$736$	−1.00000			−0.0368605
$737$	6.22831	−	6.22831i	0.229423	−	0.229423i
$738$	22.9706	+	10.9706i	0.845558	+	0.403832i
$739$			1.30306i			0.0479339i	0.999713	+	0.0239669i	$0.00762965\pi$
$739$			1.30306i			0.0479339i	−0.999713	+	0.0239669i	$0.992370\pi$
$740$	−7.70674	+	0.778539i	−0.283305	+	0.0286197i
$741$	7.10102	+	5.02118i	0.260863	+	0.184458i
$742$	32.6969	+	32.6969i	1.20034	+	1.20034i
$743$	−17.6062	−	17.6062i	−0.645910	−	0.645910i	0.306092	−	0.952002i	$-0.400979\pi$
$743$	−17.6062	−	17.6062i	−0.645910	−	0.645910i	−0.952002	+	0.306092i	$0.900979\pi$
$744$	−6.92820	−	4.89898i	−0.254000	−	0.179605i
$745$	28.8990	+	23.5959i	1.05878	+	0.864488i
$746$		−	10.6780i		−	0.390951i
$747$	−5.41421	−	2.58579i	−0.198096	−	0.0946090i
$748$	−29.3939	+	29.3939i	−1.07475	+	1.07475i
$749$	3.81405			0.139362
$750$	8.80385	+	17.2480i	0.321471	+	0.629807i
$751$	−17.7526			−0.647800			−0.323900	−	0.946091i	$-0.604994\pi$
$751$	−17.7526			−0.647800			−0.323900	+	0.946091i	$0.604994\pi$
$752$	2.04989	−	2.04989i	0.0747517	−	0.0747517i
$753$	7.82821	+	45.6262i	0.285276	+	1.66271i
$754$		−	18.6969i		−	0.680902i
$755$	−15.4135	−	12.5851i	−0.560954	−	0.458017i
$756$	4.89898	−	17.3205i	0.178174	−	0.629941i
$757$	−10.6515	−	10.6515i	−0.387136	−	0.387136i	0.486528	−	0.873665i	$-0.338263\pi$
$757$	−10.6515	−	10.6515i	−0.387136	−	0.387136i	−0.873665	+	0.486528i	$0.838263\pi$
$758$	−20.6096	−	20.6096i	−0.748576	−	0.748576i
$759$	5.65685	−	8.00000i	0.205331	−	0.290382i
$760$	5.44949	−	0.550510i	0.197674	−	0.0199691i
$761$			14.4279i			0.523010i	0.965202	+	0.261505i	$0.0842187\pi$
$761$			14.4279i			0.523010i	−0.965202	+	0.261505i	$0.915781\pi$
$762$	20.3989	−	3.49989i	0.738973	−	0.126788i
$763$	−14.2020	+	14.2020i	−0.514148	+	0.514148i
$764$	23.6130			0.854290
$765$	44.5889	−	21.0197i	1.61212	−	0.759969i
$766$	−22.6969			−0.820074
$767$	−12.0922	+	12.0922i	−0.436626	+	0.436626i
$768$	−1.70711	+	0.292893i	−0.0615999	+	0.0105689i
$769$		−	0.696938i		−	0.0251322i	−0.999921	−	0.0125661i	$-0.996000\pi$
$769$		−	0.696938i		−	0.0251322i	0.999921	−	0.0125661i	$-0.00400003\pi$
$770$	−27.7128	+	33.9411i	−0.998700	+	1.22315i
$771$	25.5959	−	36.1981i	0.921814	−	1.30364i
$772$	7.89898	+	7.89898i	0.284290	+	0.284290i
$773$	18.2740	+	18.2740i	0.657271	+	0.657271i	0.954733	−	0.297463i	$-0.0961404\pi$
$773$	18.2740	+	18.2740i	0.657271	+	0.657271i	−0.297463	+	0.954733i	$0.596140\pi$
$774$	9.75663	+	27.5959i	0.350695	+	0.991915i
$775$	−4.89898	−	24.0000i	−0.175977	−	0.862105i
$776$		−	6.29253i		−	0.225889i
$777$	3.51472	+	20.4853i	0.126090	+	0.734905i
$778$	−22.0000	+	22.0000i	−0.788738	+	0.788738i
$779$	20.7846			0.744686
$780$	−2.12220	−	7.65029i	−0.0759870	−	0.273924i
$781$	−34.7878			−1.24480
$782$	−5.19615	+	5.19615i	−0.185814	+	0.185814i
$783$	−41.3684	+	23.1265i	−1.47839	+	0.826473i
$784$		−	5.00000i		−	0.178571i
$785$	1.12848	+	11.1708i	0.0402773	+	0.398705i
$786$	−19.7980	−	13.9993i	−0.706170	−	0.499337i
$787$	30.8990	+	30.8990i	1.10143	+	1.10143i	0.994238	+	0.107191i	$0.0341857\pi$
$787$	30.8990	+	30.8990i	1.10143	+	1.10143i	0.107191	+	0.994238i	$0.465814\pi$
$788$	−0.778539	−	0.778539i	−0.0277343	−	0.0277343i
$789$	−11.3137	−	8.00000i	−0.402779	−	0.284808i
$790$	0.101021	+	1.00000i	0.00359415	+	0.0355784i
$791$		−	11.5994i		−	0.412429i
$792$	7.31371	−	15.3137i	0.259881	−	0.544149i
$793$	−12.8990	+	12.8990i	−0.458056	+	0.458056i
$794$	19.0205			0.675011
$795$	−13.8194	−	49.8172i	−0.490122	−	1.76683i
$796$	12.4495			0.441260
$797$	−37.4373	+	37.4373i	−1.32610	+	1.32610i	−0.417355	+	0.908744i	$0.637043\pi$
$797$	−37.4373	+	37.4373i	−1.32610	+	1.32610i	−0.908744	+	0.417355i	$0.862957\pi$
$798$	−2.48528	−	14.4853i	−0.0879780	−	0.512773i
$799$		−	21.3031i		−	0.753648i
$800$	−4.17121	−	2.75699i	−0.147474	−	0.0974745i
$801$	−6.20204	+	2.19275i	−0.219138	+	0.0774771i
$802$	10.4495	+	10.4495i	0.368984	+	0.368984i
$803$	44.6834	+	44.6834i	1.57684	+	1.57684i
$804$	1.55708	−	2.20204i	0.0549139	−	0.0776600i
$805$	−4.89898	+	6.00000i	−0.172666	+	0.211472i
$806$			10.0424i			0.353727i
$807$	−1.08516	+	0.186185i	−0.0381996	+	0.00655401i
$808$	−4.44949	+	4.44949i	−0.156533	+	0.156533i
$809$	−8.48528			−0.298327			−0.149163	−	0.988813i	$-0.547658\pi$
$809$	−8.48528			−0.298327			−0.149163	+	0.988813i	$0.547658\pi$
$810$	−14.3019	+	14.1583i	−0.502516	+	0.497471i
$811$	7.59592			0.266729			0.133364	−	0.991067i	$-0.457422\pi$
$811$	7.59592			0.266729			0.133364	+	0.991067i	$0.457422\pi$
$812$	−22.3417	+	22.3417i	−0.784040	+	0.784040i
$813$	−41.8154	+	7.17439i	−1.46653	+	0.251617i
$814$			19.5959i			0.686837i
$815$	12.5851	−	1.27135i	0.440835	−	0.0445334i
$816$	−7.34847	+	10.3923i	−0.257248	+	0.363803i
$817$	16.8990	+	16.8990i	0.591220	+	0.591220i
$818$	−4.09978	−	4.09978i	−0.143345	−	0.143345i
$819$	−20.0847	+	7.10102i	−0.701817	+	0.248130i
$820$	−14.6969	−	12.0000i	−0.513239	−	0.419058i
$821$			24.8202i			0.866230i	0.901339	+	0.433115i	$0.142586\pi$
$821$			24.8202i			0.866230i	−0.901339	+	0.433115i	$0.857414\pi$
$822$	1.36240	+	7.94066i	0.0475192	+	0.276962i
$823$	−5.14643	+	5.14643i	−0.179393	+	0.179393i	−0.791091	−	0.611698i	$-0.790487\pi$
$823$	−5.14643	+	5.14643i	−0.179393	+	0.179393i	0.611698	+	0.791091i	$0.290487\pi$
$824$	1.55708			0.0542434
$825$	45.6519	−	17.7737i	1.58939	−	0.618803i
$826$	28.8990			1.00552
$827$	−21.8489	+	21.8489i	−0.759760	+	0.759760i	−0.976278	−	0.216519i	$-0.930530\pi$
$827$	−21.8489	+	21.8489i	−0.759760	+	0.759760i	0.216519	+	0.976278i	$0.430530\pi$
$828$	1.29289	−	2.70711i	0.0449311	−	0.0940785i
$829$		−	23.1010i		−	0.802332i	−0.916005	−	0.401166i	$-0.868605\pi$
$829$		−	23.1010i		−	0.802332i	0.916005	−	0.401166i	$-0.131395\pi$
$830$	3.46410	+	2.82843i	0.120241	+	0.0981761i
$831$	9.10102	+	6.43539i	0.315711	+	0.223241i
$832$	1.44949	+	1.44949i	0.0502520	+	0.0502520i
$833$	−25.9808	−	25.9808i	−0.900180	−	0.900180i
$834$	15.1278	+	10.6969i	0.523831	+	0.370405i
$835$	17.7980	−	1.79796i	0.615924	−	0.0622209i
$836$		−	13.8564i		−	0.479234i
$837$	22.2195	−	12.4215i	0.768018	−	0.429351i
$838$	12.8990	−	12.8990i	0.445588	−	0.445588i
$839$	0.285729			0.00986447			0.00493223	−	0.999988i	$-0.498430\pi$
$839$	0.285729			0.00986447			0.00493223	+	0.999988i	$0.498430\pi$
$840$	−6.60572	+	11.6775i	−0.227919	+	0.402913i
$841$	54.1918			1.86868
$842$	−6.29253	+	6.29253i	−0.216855	+	0.216855i
$843$	1.65685	+	9.65685i	0.0570651	+	0.332600i
$844$			10.6969i			0.368204i
$845$	12.4422	−	15.2385i	0.428024	−	0.524221i
$846$	2.89898	+	8.19955i	0.0996690	+	0.281906i
$847$	51.4393	+	51.4393i	1.76747	+	1.76747i
$848$	9.43879	+	9.43879i	0.324129	+	0.324129i
$849$	13.2207	−	18.6969i	0.453734	−	0.641677i
$850$	−36.0000	+	7.34847i	−1.23479	+	0.252050i
$851$			3.46410i			0.118748i
$852$	−10.4981	+	1.80119i	−0.359660	+	0.0617079i
$853$	−19.2474	+	19.2474i	−0.659020	+	0.659020i	−0.955148	−	0.296128i	$-0.904304\pi$
$853$	−19.2474	+	19.2474i	−0.659020	+	0.659020i	0.296128	+	0.955148i	$0.404304\pi$
$854$	30.8270			1.05488
$855$	−5.55532	+	15.4641i	−0.189988	+	0.528861i
$856$	1.10102			0.0376321
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	−0.855675	−	0.517514i	$-0.826857\pi$
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	0.517514	+	0.855675i	$0.326857\pi$
$858$	−19.7955	+	3.39637i	−0.675806	+	0.115950i
$859$		−	35.1010i		−	1.19763i	−0.800887	−	0.598816i	$-0.795638\pi$
$859$		−	35.1010i		−	1.19763i	0.800887	−	0.598816i	$-0.204362\pi$
$860$	−2.19275	−	21.7060i	−0.0747722	−	0.740169i
$861$	−29.3939	+	41.5692i	−1.00174	+	1.41668i
$862$	3.79796	+	3.79796i	0.129359	+	0.129359i
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	0.604240	−	0.796802i	$-0.293477\pi$
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	−0.796802	+	0.604240i	$0.793477\pi$
$864$	1.41421	−	5.00000i	0.0481125	−	0.170103i
$865$	3.34847	+	33.1464i	0.113851	+	1.12701i
$866$		−	20.7204i		−	0.704108i
$867$	10.8370	+	63.1630i	0.368045	+	2.14513i
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	2.54270			0.0862551
$870$	34.0399	−	9.44271i	1.15406	−	0.320138i
$871$	−3.19184			−0.108151
$872$	−4.09978	+	4.09978i	−0.138836	+	0.138836i
$873$	17.0345	+	8.13557i	0.576532	+	0.275347i
$874$		−	2.44949i		−	0.0828552i
$875$	−36.9766	+	11.5208i	−1.25004	+	0.389474i
$876$	15.7980	+	11.1708i	0.533764	+	0.377428i
$877$	11.2474	+	11.2474i	0.379799	+	0.379799i	0.871030	−	0.491230i	$-0.163453\pi$
$877$	11.2474	+	11.2474i	0.379799	+	0.379799i	−0.491230	+	0.871030i	$0.663453\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$	−21.4203	−	15.1464i	−0.722488	−	0.510876i
$880$	−8.00000	+	9.79796i	−0.269680	+	0.330289i
$881$		−	22.6274i		−	0.762337i	−0.924506	−	0.381169i	$-0.875522\pi$
$881$		−	22.6274i		−	0.762337i	0.924506	−	0.381169i	$-0.124478\pi$
$882$	13.5355	+	6.46447i	0.455765	+	0.217670i
$883$	41.3939	−	41.3939i	1.39301	−	1.39301i	0.574535	−	0.818480i	$-0.305183\pi$
$883$	41.3939	−	41.3939i	1.39301	−	1.39301i	0.818480	−	0.574535i	$-0.194817\pi$
$884$	15.0635			0.506642
$885$	−28.1224	−	15.9082i	−0.945323	−	0.534749i
$886$	−16.0000			−0.537531
$887$	2.54270	−	2.54270i	0.0853754	−	0.0853754i	−0.663129	−	0.748505i	$-0.730772\pi$
$887$	2.54270	−	2.54270i	0.0853754	−	0.0853754i	0.748505	+	0.663129i	$0.230772\pi$
$888$	1.01461	+	5.91359i	0.0340481	+	0.198447i
$889$			41.3939i			1.38831i
$890$	4.87832	−	0.492810i	0.163521	−	0.0165190i
$891$	32.0000	+	39.5980i	1.07204	+	1.32658i
$892$	7.55051	+	7.55051i	0.252810	+	0.252810i
$893$	5.02118	+	5.02118i	0.168027	+	0.168027i
$894$	16.6848	−	23.5959i	0.558024	−	0.789166i
$895$	21.5505	+	17.5959i	0.720354	+	0.588167i
$896$		−	3.46410i		−	0.115728i
$897$	−3.49938	+	0.600398i	−0.116841	+	0.0200467i
$898$	18.6969	−	18.6969i	0.623925	−	0.623925i
$899$	−44.6834			−1.49027
$900$	12.8564	−	7.72741i	0.428547	−	0.257580i
$901$	98.0908			3.26788
$902$	−33.9411	+	33.9411i	−1.13012	+	1.13012i
$903$	−57.6967	+	9.89919i	−1.92003	+	0.329425i
$904$		−	3.34847i		−	0.111368i
$905$	−13.8564	−	11.3137i	−0.460603	−	0.376080i
$906$	−8.89898	+	12.5851i	−0.295649	+	0.418111i
$907$	8.44949	+	8.44949i	0.280561	+	0.280561i	0.833333	−	0.552772i	$-0.186430\pi$
$907$	8.44949	+	8.44949i	0.280561	+	0.280561i	−0.552772	+	0.833333i	$0.686430\pi$
$908$	7.70674	+	7.70674i	0.255757	+	0.255757i
$909$	−6.29253	−	17.7980i	−0.208710	−	0.590321i
$910$	15.7980	−	1.59592i	0.523697	−	0.0529042i
$911$		−	33.3697i		−	1.10559i	−0.833318	−	0.552793i	$-0.813562\pi$
$911$		−	33.3697i		−	1.10559i	0.833318	−	0.552793i	$-0.186438\pi$
$912$	−0.717439	−	4.18154i	−0.0237568	−	0.138465i
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	9.12096			0.301694
$915$	−29.9985	−	16.9695i	−0.991721	−	0.560995i
$916$	22.6969			0.749928
$917$	34.2911	−	34.2911i	1.13239	−	1.13239i
$918$	−18.6323	−	33.3292i	−0.614957	−	1.10003i
$919$			32.4495i			1.07041i	0.844722	+	0.535205i	$0.179766\pi$
$919$			32.4495i			1.07041i	−0.844722	+	0.535205i	$0.820234\pi$
$920$	−1.41421	+	1.73205i	−0.0466252	+	0.0571040i
$921$	−13.3939	−	9.47090i	−0.441343	−	0.312077i
$922$	−2.24745	−	2.24745i	−0.0740158	−	0.0740158i
$923$	8.91388	+	8.91388i	0.293404	+	0.293404i
$924$	27.7128	+	19.5959i	0.911685	+	0.644658i
$925$	−9.55051	+	14.4495i	−0.314019	+	0.475096i
$926$			25.5201i			0.838641i
$927$	−2.01314	+	4.21518i	−0.0661201	+	0.138445i
$928$	−6.44949	+	6.44949i	−0.211715	+	0.211715i
$929$	−41.5692			−1.36384			−0.681921	−	0.731426i	$-0.738855\pi$
$929$	−41.5692			−1.36384			−0.681921	+	0.731426i	$0.738855\pi$
$930$	−18.2832	+	5.07180i	−0.599531	+	0.166311i
$931$	12.2474			0.401394
$932$	10.5352	−	10.5352i	0.345091	−	0.345091i
$933$	10.0018	+	58.2946i	0.327444	+	1.90848i
$934$		−	14.8990i		−	0.487510i
$935$	9.34247	+	92.4809i	0.305531	+	3.02445i
$936$	−5.79796	+	2.04989i	−0.189512	+	0.0670027i
$937$	4.85357	+	4.85357i	0.158559	+	0.158559i	0.781928	−	0.623369i	$-0.214236\pi$
$937$	4.85357	+	4.85357i	0.158559	+	0.158559i	−0.623369	+	0.781928i	$0.714236\pi$
$938$	3.81405	+	3.81405i	0.124533	+	0.124533i
$939$	−27.0771	+	38.2929i	−0.883629	+	1.24964i
$940$	−0.651531	−	6.44949i	−0.0212506	−	0.210359i
$941$			6.64247i			0.216538i	0.994122	+	0.108269i	$0.0345309\pi$
$941$			6.64247i			0.216538i	−0.994122	+	0.108269i	$0.965469\pi$
$942$	8.57169	−	1.47067i	0.279281	−	0.0479170i
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$	8.34242			0.271523
$945$	−23.0718	−	32.9802i	−0.750526	−	1.07285i
$946$	−55.1918			−1.79444
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	−0.987129	−	0.159925i	$-0.948875\pi$
$947$	−25.4558	+	25.4558i	−0.827204	+	0.827204i	0.159925	+	0.987129i	$0.448875\pi$
$948$	0.767327	−	0.131652i	0.0249216	−	0.00427587i
$949$		−	22.8990i		−	0.743332i
$950$	6.75323	−	10.2173i	0.219104	−	0.331494i
$951$	−9.10102	+	12.8708i	−0.295121	+	0.417364i
$952$	−18.0000	−	18.0000i	−0.583383	−	0.583383i
$953$	4.21053	+	4.21053i	0.136393	+	0.136393i	0.772007	−	0.635614i	$-0.219253\pi$
$953$	4.21053	+	4.21053i	0.136393	+	0.136393i	−0.635614	+	0.772007i	$0.719253\pi$
$954$	−37.7552	+	13.3485i	−1.22237	+	0.432173i
$955$	33.3939	−	40.8990i	1.08060	−	1.32346i
$956$			6.43539i			0.208135i
$957$	−15.1121	−	88.0797i	−0.488505	−	2.84721i
$958$	10.6969	−	10.6969i	0.345602	−	0.345602i
$959$	−16.1134			−0.520328
$960$	−1.90691	+	3.37101i	−0.0615452	+	0.108799i
$961$	−7.00000			−0.225806
$962$	5.02118	−	5.02118i	0.161889	−	0.161889i
$963$	−1.42350	+	2.98058i	−0.0458717	+	0.0960479i
$964$			18.8990i			0.608695i
$965$	24.8523	−	2.51059i	0.800023	−	0.0808187i
$966$	4.89898	+	3.46410i	0.157622	+	0.111456i
$967$	−2.44949	−	2.44949i	−0.0787703	−	0.0787703i	0.666624	−	0.745394i	$-0.267739\pi$
$967$	−2.44949	−	2.44949i	−0.0787703	−	0.0787703i	−0.745394	+	0.666624i	$0.767739\pi$
$968$	14.8492	+	14.8492i	0.477273	+	0.477273i
$969$	−25.4558	−	18.0000i	−0.817760	−	0.578243i
$970$	−10.8990	−	8.89898i	−0.349945	−	0.285729i
$971$		−	15.6992i		−	0.503812i	−0.967752	−	0.251906i	$-0.918943\pi$
$971$		−	15.6992i		−	0.503812i	0.967752	−	0.251906i	$-0.0810573\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$	−26.2020	+	26.2020i	−0.839999	+	0.839999i
$974$	6.57826			0.210781
$975$	−16.2519	−	7.14338i	−0.520478	−	0.228771i
$976$	8.89898			0.284849
$977$	−39.7730	+	39.7730i	−1.27245	+	1.27245i	−0.327650	+	0.944799i	$0.606257\pi$
$977$	−39.7730	+	39.7730i	−1.27245	+	1.27245i	−0.944799	+	0.327650i	$0.893743\pi$
$978$	−1.65685	−	9.65685i	−0.0529804	−	0.308792i
$979$		−	12.4041i		−	0.396436i
$980$	−8.66025	−	7.07107i	−0.276642	−	0.225877i
$981$	−5.79796	−	16.3991i	−0.185115	−	0.523583i
$982$	−8.10102	−	8.10102i	−0.258514	−	0.258514i
$983$	−16.3991	−	16.3991i	−0.523050	−	0.523050i	0.395441	−	0.918491i	$-0.370592\pi$
$983$	−16.3991	−	16.3991i	−0.523050	−	0.523050i	−0.918491	+	0.395441i	$0.870592\pi$
$984$	−8.48528	+	12.0000i	−0.270501	+	0.382546i
$985$	−2.44949	+	0.247449i	−0.0780472	+	0.00788437i
$986$			67.0251i			2.13451i
$987$	−17.1434	+	2.94134i	−0.545680	+	0.0936239i
$988$	−3.55051	+	3.55051i	−0.112957	+	0.112957i
$989$	−9.75663			−0.310243
$990$	−16.1810	−	34.3246i	−0.514265	−	1.09091i
$991$	5.79796			0.184178			0.0920891	−	0.995751i	$-0.470646\pi$
$991$	5.79796			0.184178			0.0920891	+	0.995751i	$0.470646\pi$
$992$	3.46410	−	3.46410i	0.109985	−	0.109985i
$993$	−18.2608	+	3.13306i	−0.579489	+	0.0994247i
$994$		−	21.3031i		−	0.675692i
$995$	17.6062	−	21.5631i	0.558155	−	0.683598i
$996$	2.00000	−	2.82843i	0.0633724	−	0.0896221i
$997$	0.550510	+	0.550510i	0.0174348	+	0.0174348i	0.715770	−	0.698336i	$-0.246076\pi$
$997$	0.550510	+	0.550510i	0.0174348	+	0.0174348i	−0.698336	+	0.715770i	$0.746076\pi$
$998$	−10.0424	−	10.0424i	−0.317885	−	0.317885i
$999$	−17.3205	−	4.89898i	−0.547997	−	0.154997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.c.47.3	yes	8
3.2	odd	2	inner	690.2.i.c.47.2	✓	8
5.3	odd	4	inner	690.2.i.c.323.2	yes	8
15.8	even	4	inner	690.2.i.c.323.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.c.47.2	✓	8	3.2	odd	2	inner
690.2.i.c.47.3	yes	8	1.1	even	1	trivial
690.2.i.c.323.2	yes	8	5.3	odd	4	inner
690.2.i.c.323.3	yes	8	15.8	even	4	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.70711 + 0.292893i) q^{3} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.82843 - 1.00000i) q^{9} +(-2.22474 + 0.224745i) q^{10} +5.65685i q^{11} +(0.292893 + 1.70711i) q^{12} +(1.44949 - 1.44949i) q^{13} -3.46410 q^{14} +(3.37101 + 1.90691i) q^{15} -1.00000 q^{16} +(-5.19615 + 5.19615i) q^{17} +(1.29289 - 2.70711i) q^{18} -2.44949i q^{19} +(-1.41421 + 1.73205i) q^{20} +(4.89898 + 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(1.41421 + 1.00000i) q^{24} +(1.00000 + 4.89898i) q^{25} -2.04989i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-2.44949 + 2.44949i) q^{28} +9.12096 q^{29} +(3.73205 - 1.03528i) q^{30} -4.89898 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.65685 - 9.65685i) q^{33} +7.34847i q^{34} +(0.778539 + 7.70674i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(2.44949 + 2.44949i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-2.04989 + 2.89898i) q^{39} +(0.224745 + 2.22474i) q^{40} +8.48528i q^{41} +(5.91359 - 1.01461i) q^{42} +(-6.89898 + 6.89898i) q^{43} +5.65685 q^{44} +(-6.31319 - 2.26795i) q^{45} +1.00000 q^{46} +(-2.04989 + 2.04989i) q^{47} +(1.70711 - 0.292893i) q^{48} +5.00000i q^{49} +(4.17121 + 2.75699i) q^{50} +(7.34847 - 10.3923i) q^{51} +(-1.44949 - 1.44949i) q^{52} +(-9.43879 - 9.43879i) q^{53} +(-1.41421 + 5.00000i) q^{54} +(8.00000 - 9.79796i) q^{55} +3.46410i q^{56} +(0.717439 + 4.18154i) q^{57} +(6.44949 - 6.44949i) q^{58} -8.34242 q^{59} +(1.90691 - 3.37101i) q^{60} -8.89898 q^{61} +(-3.46410 + 3.46410i) q^{62} +(-9.37769 - 4.47871i) q^{63} +1.00000i q^{64} +(-4.56048 + 0.460702i) q^{65} +(-8.00000 - 5.65685i) q^{66} +(-1.10102 - 1.10102i) q^{67} +(5.19615 + 5.19615i) q^{68} +(-1.41421 - 1.00000i) q^{69} +(6.00000 + 4.89898i) q^{70} +6.14966i q^{71} +(-2.70711 - 1.29289i) q^{72} +(7.89898 - 7.89898i) q^{73} +3.46410 q^{74} +(-3.14198 - 8.07019i) q^{75} -2.44949 q^{76} +(13.8564 - 13.8564i) q^{77} +(0.600398 + 3.49938i) q^{78} -0.449490i q^{79} +(1.73205 + 1.41421i) q^{80} +(7.00000 - 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(3.46410 - 4.89898i) q^{84} +(16.3485 - 1.65153i) q^{85} +9.75663i q^{86} +(-15.5704 + 2.67147i) q^{87} +(4.00000 - 4.00000i) q^{88} -2.19275 q^{89} +(-6.06778 + 2.86042i) q^{90} -7.10102 q^{91} +(0.707107 - 0.707107i) q^{92} +(8.36308 - 1.43488i) q^{93} +2.89898i q^{94} +(-3.46410 + 4.24264i) q^{95} +(1.00000 - 1.41421i) q^{96} +(4.44949 + 4.44949i) q^{97} +(3.53553 + 3.53553i) q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 8 * q - 8 * q^3 - 8 * q^6	\( 8 q - 8 q^{3} - 8 q^{6} - 8 q^{10} + 8 q^{12} - 8 q^{13} - 8 q^{15} - 8 q^{16} + 16 q^{18} + 32 q^{22} + 8 q^{25} - 8 q^{27} + 16 q^{30} + 32 q^{33} - 8 q^{36} - 8 q^{40} - 16 q^{43} + 8 q^{46} + 8 q^{48} + 8 q^{52} + 64 q^{55} + 32 q^{58} + 8 q^{60} - 32 q^{61} - 64 q^{66} - 48 q^{67} + 48 q^{70} - 16 q^{72} + 24 q^{73} - 8 q^{75} + 8 q^{78} + 56 q^{81} + 48 q^{82} + 72 q^{85} - 32 q^{87} + 32 q^{88} - 8 q^{90} - 96 q^{91} + 8 q^{96} + 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^3 - 8 * q^6 - 8 * q^10 + 8 * q^12 - 8 * q^13 - 8 * q^15 - 8 * q^16 + 16 * q^18 + 32 * q^22 + 8 * q^25 - 8 * q^27 + 16 * q^30 + 32 * q^33 - 8 * q^36 - 8 * q^40 - 16 * q^43 + 8 * q^46 + 8 * q^48 + 8 * q^52 + 64 * q^55 + 32 * q^58 + 8 * q^60 - 32 * q^61 - 64 * q^66 - 48 * q^67 + 48 * q^70 - 16 * q^72 + 24 * q^73 - 8 * q^75 + 8 * q^78 + 56 * q^81 + 48 * q^82 + 72 * q^85 - 32 * q^87 + 32 * q^88 - 8 * q^90 - 96 * q^91 + 8 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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