LMFDB - Embedded newform 230.2.e.a.183.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.e (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			183.3
Root			$-0.814115i$ of defining polynomial
Character	$\chi$	$=$	230.183
Dual form			230.2.e.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.868559 - 0.868559i) q^{3} -1.00000i q^{4} +(-2.22833 + 0.185885i) q^{5} -1.22833 q^{6} +(-1.38978 - 1.38978i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.49121i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.868559 - 0.868559i) q^{3} -1.00000i q^{4} +(-2.22833 + 0.185885i) q^{5} -1.22833 q^{6} +(-1.38978 - 1.38978i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.49121i q^{9} +(-1.44423 + 1.70711i) q^{10} +0.642542i q^{11} +(-0.868559 + 0.868559i) q^{12} +(-2.12690 - 2.12690i) q^{13} -1.96545 q^{14} +(2.09689 + 1.77398i) q^{15} -1.00000 q^{16} +(-0.903113 - 0.903113i) q^{17} +(-1.05444 - 1.05444i) q^{18} +2.55123 q^{19} +(0.185885 + 2.22833i) q^{20} +2.41421i q^{21} +(0.454346 + 0.454346i) q^{22} +(4.74955 - 0.664664i) q^{23} +1.22833i q^{24} +(4.93089 - 0.828427i) q^{25} -3.00789 q^{26} +(-3.90088 + 3.90088i) q^{27} +(-1.38978 + 1.38978i) q^{28} -0.214016i q^{29} +(2.73712 - 0.228328i) q^{30} +6.15922 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.558086 - 0.558086i) q^{33} -1.27719 q^{34} +(3.35523 + 2.83855i) q^{35} -1.49121 q^{36} +(-7.20809 - 7.20809i) q^{37} +(1.80399 - 1.80399i) q^{38} +3.69468i q^{39} +(1.70711 + 1.44423i) q^{40} +3.33722 q^{41} +(1.70711 + 1.70711i) q^{42} +(7.85390 - 7.85390i) q^{43} +0.642542 q^{44} +(0.277194 + 3.32290i) q^{45} +(2.88845 - 3.82843i) q^{46} +(-4.15133 + 4.15133i) q^{47} +(0.868559 + 0.868559i) q^{48} -3.13702i q^{49} +(2.90088 - 4.07245i) q^{50} +1.56881i q^{51} +(-2.12690 + 2.12690i) q^{52} +(2.93732 - 2.93732i) q^{53} +5.51668i q^{54} +(-0.119439 - 1.43179i) q^{55} +1.96545i q^{56} +(-2.21590 - 2.21590i) q^{57} +(-0.151332 - 0.151332i) q^{58} +7.08223i q^{59} +(1.77398 - 2.09689i) q^{60} +5.29743i q^{61} +(4.35523 - 4.35523i) q^{62} +(-2.07245 + 2.07245i) q^{63} +1.00000i q^{64} +(5.13479 + 4.34407i) q^{65} -0.789252i q^{66} +(3.65370 + 3.65370i) q^{67} +(-0.903113 + 0.903113i) q^{68} +(-4.70257 - 3.54797i) q^{69} +(4.37966 - 0.365348i) q^{70} -1.83812 q^{71} +(-1.05444 + 1.05444i) q^{72} +(-5.20166 - 5.20166i) q^{73} -10.1938 q^{74} +(-5.00231 - 3.56323i) q^{75} -2.55123i q^{76} +(0.892992 - 0.892992i) q^{77} +(2.61253 + 2.61253i) q^{78} -6.19754 q^{79} +(2.22833 - 0.185885i) q^{80} +2.30266 q^{81} +(2.35977 - 2.35977i) q^{82} +(-6.04767 + 6.04767i) q^{83} +2.41421 q^{84} +(2.18031 + 1.84456i) q^{85} -11.1071i q^{86} +(-0.185885 + 0.185885i) q^{87} +(0.454346 - 0.454346i) q^{88} +15.7567 q^{89} +(2.54565 + 2.15364i) q^{90} +5.91185i q^{91} +(-0.664664 - 4.74955i) q^{92} +(-5.34965 - 5.34965i) q^{93} +5.87087i q^{94} +(-5.68498 + 0.474237i) q^{95} +1.22833 q^{96} +(-10.7898 - 10.7898i) q^{97} +(-2.21821 - 2.21821i) q^{98} +0.958165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6	$ 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{12} + 4 q^{14} - 8 q^{16} - 24 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 12 q^{22} + 16 q^{23} + 12 q^{26} + 8 q^{27} + 16 q^{30} - 4 q^{31} - 20 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 8 q^{40} + 12 q^{41} + 8 q^{42} + 20 q^{43} - 20 q^{44} - 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} - 20 q^{57} + 16 q^{58} - 8 q^{60} + 4 q^{62} - 12 q^{65} + 4 q^{67} - 24 q^{68} - 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} - 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} - 8 q^{79} + 4 q^{80} - 16 q^{81} + 8 q^{82} + 28 q^{83} + 8 q^{84} + 20 q^{85} - 4 q^{87} + 12 q^{88} + 40 q^{89} + 12 q^{90} - 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} + 8 q^{97} + 16 q^{98} + 36 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^12 + 4 * q^14 - 8 * q^16 - 24 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 12 * q^22 + 16 * q^23 + 12 * q^26 + 8 * q^27 + 16 * q^30 - 4 * q^31 - 20 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 8 * q^40 + 12 * q^41 + 8 * q^42 + 20 * q^43 - 20 * q^44 - 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 - 20 * q^57 + 16 * q^58 - 8 * q^60 + 4 * q^62 - 12 * q^65 + 4 * q^67 - 24 * q^68 - 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 - 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 - 8 * q^79 + 4 * q^80 - 16 * q^81 + 8 * q^82 + 28 * q^83 + 8 * q^84 + 20 * q^85 - 4 * q^87 + 12 * q^88 + 40 * q^89 + 12 * q^90 - 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 + 8 * q^97 + 16 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.868559	−	0.868559i	−0.501463	−	0.501463i	0.410429	−	0.911892i	$-0.365379\pi$
$3$	−0.868559	−	0.868559i	−0.501463	−	0.501463i	−0.911892	+	0.410429i	$0.865379\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−2.22833	+	0.185885i	−0.996539	+	0.0831305i
$5$	−2.22833	+	0.185885i	−0.996539	+	0.0831305i
$6$	−1.22833			−0.501463
$7$	−1.38978	−	1.38978i	−0.525288	−	0.525288i	0.393876	−	0.919164i	$-0.371134\pi$
$7$	−1.38978	−	1.38978i	−0.525288	−	0.525288i	−0.919164	+	0.393876i	$0.871134\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.49121i		−	0.497070i
$10$	−1.44423	+	1.70711i	−0.456704	+	0.539835i
$11$			0.642542i			0.193734i	0.995297	+	0.0968668i	$0.0308821\pi$
$11$			0.642542i			0.193734i	−0.995297	+	0.0968668i	$0.969118\pi$
$12$	−0.868559	+	0.868559i	−0.250731	+	0.250731i
$13$	−2.12690	−	2.12690i	−0.589896	−	0.589896i	0.347707	−	0.937603i	$-0.386960\pi$
$13$	−2.12690	−	2.12690i	−0.589896	−	0.589896i	−0.937603	+	0.347707i	$0.886960\pi$
$14$	−1.96545			−0.525288
$15$	2.09689	+	1.77398i	0.541414	+	0.458040i
$16$	−1.00000			−0.250000
$17$	−0.903113	−	0.903113i	−0.219037	−	0.219037i	0.589056	−	0.808093i	$-0.299500\pi$
$17$	−0.903113	−	0.903113i	−0.219037	−	0.219037i	−0.808093	+	0.589056i	$0.799500\pi$
$18$	−1.05444	−	1.05444i	−0.248535	−	0.248535i
$19$	2.55123			0.585293			0.292647	−	0.956221i	$-0.405464\pi$
$19$	2.55123			0.585293			0.292647	+	0.956221i	$0.405464\pi$
$20$	0.185885	+	2.22833i	0.0415652	+	0.498269i
$21$			2.41421i			0.526825i
$22$	0.454346	+	0.454346i	0.0968668	+	0.0968668i
$23$	4.74955	−	0.664664i	0.990350	−	0.138592i
$23$	4.74955	−	0.664664i	0.990350	−	0.138592i
$24$			1.22833i			0.250731i
$25$	4.93089	−	0.828427i	0.986179	−	0.165685i
$26$	−3.00789			−0.589896
$27$	−3.90088	+	3.90088i	−0.750725	+	0.750725i
$28$	−1.38978	+	1.38978i	−0.262644	+	0.262644i
$29$		−	0.214016i		−	0.0397417i	−0.999803	−	0.0198709i	$-0.993674\pi$
$29$		−	0.214016i		−	0.0397417i	0.999803	−	0.0198709i	$-0.00632551\pi$
$30$	2.73712	−	0.228328i	0.499727	−	0.0416868i
$31$	6.15922			1.10623			0.553114	−	0.833105i	$-0.313439\pi$
$31$	6.15922			1.10623			0.553114	+	0.833105i	$0.313439\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.558086	−	0.558086i	0.0971502	−	0.0971502i
$34$	−1.27719			−0.219037
$35$	3.35523	+	2.83855i	0.567137	+	0.479802i
$36$	−1.49121			−0.248535
$37$	−7.20809	−	7.20809i	−1.18500	−	1.18500i	−0.978432	−	0.206571i	$-0.933770\pi$
$37$	−7.20809	−	7.20809i	−1.18500	−	1.18500i	−0.206571	−	0.978432i	$-0.566230\pi$
$38$	1.80399	−	1.80399i	0.292647	−	0.292647i
$39$			3.69468i			0.591622i
$40$	1.70711	+	1.44423i	0.269917	+	0.228352i
$41$	3.33722			0.521186			0.260593	−	0.965449i	$-0.416082\pi$
$41$	3.33722			0.521186			0.260593	+	0.965449i	$0.416082\pi$
$42$	1.70711	+	1.70711i	0.263412	+	0.263412i
$43$	7.85390	−	7.85390i	1.19771	−	1.19771i	0.222857	−	0.974851i	$-0.428462\pi$
$43$	7.85390	−	7.85390i	1.19771	−	1.19771i	0.974851	−	0.222857i	$-0.0715383\pi$
$44$	0.642542			0.0968668
$45$	0.277194	+	3.32290i	0.0413216	+	0.495349i
$46$	2.88845	−	3.82843i	0.425879	−	0.564471i
$47$	−4.15133	+	4.15133i	−0.605534	+	0.605534i	−0.941776	−	0.336242i	$-0.890844\pi$
$47$	−4.15133	+	4.15133i	−0.605534	+	0.605534i	0.336242	+	0.941776i	$0.390844\pi$
$48$	0.868559	+	0.868559i	0.125366	+	0.125366i
$49$		−	3.13702i		−	0.448146i
$50$	2.90088	−	4.07245i	0.410247	−	0.575932i
$51$			1.56881i			0.219678i
$52$	−2.12690	+	2.12690i	−0.294948	+	0.294948i
$53$	2.93732	−	2.93732i	0.403471	−	0.403471i	−0.475983	−	0.879454i	$-0.657908\pi$
$53$	2.93732	−	2.93732i	0.403471	−	0.403471i	0.879454	+	0.475983i	$0.157908\pi$
$54$			5.51668i			0.750725i
$55$	−0.119439	−	1.43179i	−0.0161052	−	0.193063i
$56$			1.96545i			0.262644i
$57$	−2.21590	−	2.21590i	−0.293503	−	0.293503i
$58$	−0.151332	−	0.151332i	−0.0198709	−	0.0198709i
$59$			7.08223i			0.922027i	0.887393	+	0.461014i	$0.152514\pi$
$59$			7.08223i			0.922027i	−0.887393	+	0.461014i	$0.847486\pi$
$60$	1.77398	−	2.09689i	0.229020	−	0.270707i
$61$			5.29743i			0.678267i	0.940738	+	0.339134i	$0.110134\pi$
$61$			5.29743i			0.678267i	−0.940738	+	0.339134i	$0.889866\pi$
$62$	4.35523	−	4.35523i	0.553114	−	0.553114i
$63$	−2.07245	+	2.07245i	−0.261105	+	0.261105i
$64$			1.00000i			0.125000i
$65$	5.13479	+	4.34407i	0.636892	+	0.538816i
$66$		−	0.789252i		−	0.0971502i
$67$	3.65370	+	3.65370i	0.446370	+	0.446370i	0.894146	−	0.447776i	$-0.147784\pi$
$67$	3.65370	+	3.65370i	0.446370	+	0.446370i	−0.447776	+	0.894146i	$0.647784\pi$
$68$	−0.903113	+	0.903113i	−0.109518	+	0.109518i
$69$	−4.70257	−	3.54797i	−0.566122	−	0.427125i
$70$	4.37966	−	0.365348i	0.523470	−	0.0436674i
$71$	−1.83812			−0.218144			−0.109072	−	0.994034i	$-0.534788\pi$
$71$	−1.83812			−0.218144			−0.109072	+	0.994034i	$0.534788\pi$
$72$	−1.05444	+	1.05444i	−0.124267	+	0.124267i
$73$	−5.20166	−	5.20166i	−0.608809	−	0.608809i	0.333826	−	0.942635i	$-0.391660\pi$
$73$	−5.20166	−	5.20166i	−0.608809	−	0.608809i	−0.942635	+	0.333826i	$0.891660\pi$
$74$	−10.1938			−1.18500
$75$	−5.00231	−	3.56323i	−0.577617	−	0.411447i
$76$		−	2.55123i		−	0.292647i
$77$	0.892992	−	0.892992i	0.101766	−	0.101766i
$78$	2.61253	+	2.61253i	0.295811	+	0.295811i
$79$	−6.19754			−0.697277			−0.348639	−	0.937257i	$-0.613356\pi$
$79$	−6.19754			−0.697277			−0.348639	+	0.937257i	$0.613356\pi$
$80$	2.22833	−	0.185885i	0.249135	−	0.0207826i
$81$	2.30266			0.255852
$82$	2.35977	−	2.35977i	0.260593	−	0.260593i
$83$	−6.04767	+	6.04767i	−0.663818	+	0.663818i	−0.956278	−	0.292460i	$-0.905526\pi$
$83$	−6.04767	+	6.04767i	−0.663818	+	0.663818i	0.292460	+	0.956278i	$0.405526\pi$
$84$	2.41421			0.263412
$85$	2.18031	+	1.84456i	0.236487	+	0.200070i
$86$		−	11.1071i		−	1.19771i
$87$	−0.185885	+	0.185885i	−0.0199290	+	0.0199290i
$88$	0.454346	−	0.454346i	0.0484334	−	0.0484334i
$89$	15.7567			1.67020			0.835101	−	0.550096i	$-0.185409\pi$
$89$	15.7567			1.67020			0.835101	+	0.550096i	$0.185409\pi$
$90$	2.54565	+	2.15364i	0.268336	+	0.227014i
$91$			5.91185i			0.619730i
$92$	−0.664664	−	4.74955i	−0.0692960	−	0.495175i
$93$	−5.34965	−	5.34965i	−0.554733	−	0.554733i
$94$			5.87087i			0.605534i
$95$	−5.68498	+	0.474237i	−0.583267	+	0.0486557i
$96$	1.22833			0.125366
$97$	−10.7898	−	10.7898i	−1.09553	−	1.09553i	−0.994926	−	0.100608i	$-0.967921\pi$
$97$	−10.7898	−	10.7898i	−1.09553	−	1.09553i	−0.100608	−	0.994926i	$-0.532079\pi$
$98$	−2.21821	−	2.21821i	−0.224073	−	0.224073i
$99$	0.958165			0.0962992
$100$	−0.828427	−	4.93089i	−0.0828427	−	0.493089i
$101$	−10.2824			−1.02314			−0.511570	−	0.859242i	$-0.670936\pi$
$101$	−10.2824			−1.02314			−0.511570	+	0.859242i	$0.670936\pi$
$102$	1.10932	+	1.10932i	0.109839	+	0.109839i
$103$	0.0571050	−	0.0571050i	0.00562673	−	0.00562673i	−0.704288	−	0.709915i	$-0.748734\pi$
$103$	0.0571050	−	0.0571050i	0.00562673	−	0.00562673i	0.709915	+	0.704288i	$0.248734\pi$
$104$			3.00789i			0.294948i
$105$	−0.448767	−	5.37966i	−0.0437952	−	0.525001i
$106$		−	4.15399i		−	0.403471i
$107$	11.8709	+	11.8709i	1.14760	+	1.14760i	0.987023	+	0.160577i	$0.0513355\pi$
$107$	11.8709	+	11.8709i	1.14760	+	1.14760i	0.160577	+	0.987023i	$0.448665\pi$
$108$	3.90088	+	3.90088i	0.375363	+	0.375363i
$109$	−13.9610			−1.33722			−0.668610	−	0.743613i	$-0.733110\pi$
$109$	−13.9610			−1.33722			−0.668610	+	0.743613i	$0.733110\pi$
$110$	−1.09689	−	0.927975i	−0.104584	−	0.0884789i
$111$			12.5213i			1.18847i
$112$	1.38978	+	1.38978i	0.131322	+	0.131322i
$113$	4.83958	−	4.83958i	0.455270	−	0.455270i	−0.441829	−	0.897099i	$-0.645670\pi$
$113$	4.83958	−	4.83958i	0.455270	−	0.455270i	0.897099	+	0.441829i	$0.145670\pi$
$114$	−3.13375			−0.293503
$115$	−10.4600	+	2.36396i	−0.975400	+	0.220441i
$116$	−0.214016			−0.0198709
$117$	−3.17165	+	3.17165i	−0.293219	+	0.293219i
$118$	5.00789	+	5.00789i	0.461014	+	0.461014i
$119$			2.51026i			0.230115i
$120$	−0.228328	−	2.73712i	−0.0208434	−	0.249864i
$121$	10.5871			0.962467
$122$	3.74585	+	3.74585i	0.339134	+	0.339134i
$123$	−2.89857	−	2.89857i	−0.261355	−	0.261355i
$124$		−	6.15922i		−	0.553114i
$125$	−10.8337	+	2.76259i	−0.968992	+	0.247093i
$126$			2.93089i			0.261105i
$127$	8.13375	−	8.13375i	0.721754	−	0.721754i	−0.247209	−	0.968962i	$-0.579513\pi$
$127$	8.13375	−	8.13375i	0.721754	−	0.721754i	0.968962	+	0.247209i	$0.0795133\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−13.6431			−1.20121
$130$	6.70257	−	0.559123i	0.587854	−	0.0490383i
$131$	−10.5942			−0.925617			−0.462808	−	0.886458i	$-0.653158\pi$
$131$	−10.5942			−0.925617			−0.462808	+	0.886458i	$0.653158\pi$
$132$	−0.558086	−	0.558086i	−0.0485751	−	0.0485751i
$133$	−3.54565	−	3.54565i	−0.307447	−	0.307447i
$134$	5.16711			0.446370
$135$	7.96733	−	9.41756i	0.685718	−	0.810535i
$136$			1.27719i			0.109518i
$137$	5.23252	+	5.23252i	0.447044	+	0.447044i	0.894371	−	0.447326i	$-0.147624\pi$
$137$	5.23252	+	5.23252i	0.447044	+	0.447044i	−0.447326	+	0.894371i	$0.647624\pi$
$138$	−5.83401	+	0.816425i	−0.496624	+	0.0694987i
$139$		−	13.2197i		−	1.12128i	−0.828058	−	0.560642i	$-0.810554\pi$
$139$		−	13.2197i		−	1.12128i	0.828058	−	0.560642i	$-0.189446\pi$
$140$	2.83855	−	3.35523i	0.239901	−	0.283568i
$141$	7.21136			0.607306
$142$	−1.29975	+	1.29975i	−0.109072	+	0.109072i
$143$	1.36662	−	1.36662i	0.114283	−	0.114283i
$144$			1.49121i			0.124267i
$145$	0.0397824	+	0.476897i	0.00330375	+	0.0396042i
$146$	−7.35626			−0.608809
$147$	−2.72469	+	2.72469i	−0.224728	+	0.224728i
$148$	−7.20809	+	7.20809i	−0.592501	+	0.592501i
$149$	2.59634			0.212700			0.106350	−	0.994329i	$-0.466084\pi$
$149$	2.59634			0.212700			0.106350	+	0.994329i	$0.466084\pi$
$150$	−6.05676	+	1.01758i	−0.494532	+	0.0830851i
$151$	6.72281			0.547094			0.273547	−	0.961859i	$-0.411803\pi$
$151$	6.72281			0.547094			0.273547	+	0.961859i	$0.411803\pi$
$152$	−1.80399	−	1.80399i	−0.146323	−	0.146323i
$153$	−1.34673	+	1.34673i	−0.108877	+	0.108877i
$154$		−	1.26288i		−	0.101766i
$155$	−13.7248	+	1.14491i	−1.10240	+	0.0919613i
$156$	3.69468			0.295811
$157$	7.59041	+	7.59041i	0.605781	+	0.605781i	0.941841	−	0.336060i	$-0.109095\pi$
$157$	7.59041	+	7.59041i	0.605781	+	0.605781i	−0.336060	+	0.941841i	$0.609095\pi$
$158$	−4.38232	+	4.38232i	−0.348639	+	0.348639i
$159$	−5.10247			−0.404652
$160$	1.44423	−	1.70711i	0.114176	−	0.134959i
$161$	−7.52457	−	5.67710i	−0.593019	−	0.447418i
$162$	1.62823	−	1.62823i	0.127926	−	0.127926i
$163$	−3.33122	−	3.33122i	−0.260922	−	0.260922i	0.564507	−	0.825428i	$-0.309066\pi$
$163$	−3.33122	−	3.33122i	−0.260922	−	0.260922i	−0.825428	+	0.564507i	$0.809066\pi$
$164$		−	3.33722i		−	0.260593i
$165$	−1.13986	+	1.34734i	−0.0887378	+	0.104890i
$166$			8.55270i			0.663818i
$167$	4.74235	−	4.74235i	0.366974	−	0.366974i	−0.499399	−	0.866372i	$-0.666446\pi$
$167$	4.74235	−	4.74235i	0.366974	−	0.366974i	0.866372	+	0.499399i	$0.166446\pi$
$168$	1.70711	−	1.70711i	0.131706	−	0.131706i
$169$		−	3.95260i		−	0.304046i
$170$	2.84601	−	0.237412i	0.218279	−	0.0182086i
$171$		−	3.80442i		−	0.290932i
$172$	−7.85390	−	7.85390i	−0.598854	−	0.598854i
$173$	−10.0023	−	10.0023i	−0.760462	−	0.760462i	0.215944	−	0.976406i	$-0.430717\pi$
$173$	−10.0023	−	10.0023i	−0.760462	−	0.760462i	−0.976406	+	0.215944i	$0.930717\pi$
$174$			0.262882i			0.0199290i
$175$	−8.00419	−	5.70153i	−0.605060	−	0.430995i
$176$		−	0.642542i		−	0.0484334i
$177$	6.15133	−	6.15133i	0.462362	−	0.462362i
$178$	11.1416	−	11.1416i	0.835101	−	0.835101i
$179$			10.8330i			0.809700i	0.914383	+	0.404850i	$0.132676\pi$
$179$			10.8330i			0.809700i	−0.914383	+	0.404850i	$0.867324\pi$
$180$	3.32290	−	0.277194i	0.247675	−	0.0206608i
$181$			1.32410i			0.0984195i	0.998788	+	0.0492097i	$0.0156703\pi$
$181$			1.32410i			0.0984195i	−0.998788	+	0.0492097i	$0.984330\pi$
$182$	4.18031	+	4.18031i	0.309865	+	0.309865i
$183$	4.60114	−	4.60114i	0.340126	−	0.340126i
$184$	−3.82843	−	2.88845i	−0.282235	−	0.212939i
$185$	17.4019	+	14.7221i	1.27941	+	1.08239i
$186$	−7.56555			−0.554733
$187$	0.580288	−	0.580288i	0.0424348	−	0.0424348i
$188$	4.15133	+	4.15133i	0.302767	+	0.302767i
$189$	10.8427			0.788693
$190$	−3.68456	+	4.35523i	−0.267306	+	0.315961i
$191$		−	2.47158i		−	0.178837i	−0.995994	−	0.0894185i	$-0.971499\pi$
$191$		−	2.47158i		−	0.178837i	0.995994	−	0.0894185i	$-0.0285009\pi$
$192$	0.868559	−	0.868559i	0.0626829	−	0.0626829i
$193$	17.4273	+	17.4273i	1.25445	+	1.25445i	0.953706	+	0.300741i	$0.0972340\pi$
$193$	17.4273	+	17.4273i	1.25445	+	1.25445i	0.300741	+	0.953706i	$0.402766\pi$
$194$	−15.2590			−1.09553
$195$	−0.686786	−	8.23295i	−0.0491818	−	0.589574i
$196$	−3.13702			−0.224073
$197$	−3.19412	+	3.19412i	−0.227572	+	0.227572i	−0.811678	−	0.584106i	$-0.801445\pi$
$197$	−3.19412	+	3.19412i	−0.227572	+	0.227572i	0.584106	+	0.811678i	$0.301445\pi$
$198$	0.677525	−	0.677525i	0.0481496	−	0.0481496i
$199$	23.6231			1.67459			0.837297	−	0.546748i	$-0.184134\pi$
$199$	23.6231			1.67459			0.837297	+	0.546748i	$0.184134\pi$
$200$	−4.07245	−	2.90088i	−0.287966	−	0.205123i
$201$		−	6.34691i		−	0.447676i
$202$	−7.27077	+	7.27077i	−0.511570	+	0.511570i
$203$	−0.297435	+	0.297435i	−0.0208758	+	0.0208758i
$204$	1.56881			0.109839
$205$	−7.43642	+	0.620340i	−0.519382	+	0.0433264i
$206$		−	0.0807587i		−	0.00562673i
$207$	−0.991153	−	7.08257i	−0.0688899	−	0.492273i
$208$	2.12690	+	2.12690i	0.147474	+	0.147474i
$209$			1.63927i			0.113391i
$210$	−4.12132	−	3.48667i	−0.284398	−	0.240603i
$211$	19.5012			1.34252			0.671258	−	0.741224i	$-0.265754\pi$
$211$	19.5012			1.34252			0.671258	+	0.741224i	$0.265754\pi$
$212$	−2.93732	−	2.93732i	−0.201736	−	0.201736i
$213$	1.59651	+	1.59651i	0.109391	+	0.109391i
$214$	16.7879			1.14760
$215$	−16.0411	+	18.9610i	−1.09400	+	1.29313i
$216$	5.51668			0.375363
$217$	−8.55997	−	8.55997i	−0.581088	−	0.581088i
$218$	−9.87191	+	9.87191i	−0.668610	+	0.668610i
$219$			9.03591i			0.610590i
$220$	−1.43179	+	0.119439i	−0.0965315	+	0.00805258i
$221$			3.84166i			0.258418i
$222$	8.85390	+	8.85390i	0.594235	+	0.594235i
$223$	0.502862	+	0.502862i	0.0336741	+	0.0336741i	0.723743	−	0.690069i	$-0.242420\pi$
$223$	0.502862	+	0.502862i	0.0336741	+	0.0336741i	−0.690069	+	0.723743i	$0.742420\pi$
$224$	1.96545			0.131322
$225$	−1.23536	−	7.35300i	−0.0823572	−	0.490200i
$226$		−	6.84421i		−	0.455270i
$227$	17.7631	+	17.7631i	1.17898	+	1.17898i	0.980005	+	0.198972i	$0.0637603\pi$
$227$	17.7631	+	17.7631i	1.17898	+	1.17898i	0.198972	+	0.980005i	$0.436240\pi$
$228$	−2.21590	+	2.21590i	−0.146751	+	0.146751i
$229$	29.8213			1.97065			0.985324	−	0.170697i	$-0.0546018\pi$
$229$	29.8213			1.97065			0.985324	+	0.170697i	$0.0546018\pi$
$230$	−5.72477	+	9.06791i	−0.377480	+	0.597920i
$231$	−1.55123			−0.102064
$232$	−0.151332	+	0.151332i	−0.00993543	+	0.00993543i
$233$	20.1495	+	20.1495i	1.32004	+	1.32004i	0.913740	+	0.406300i	$0.133181\pi$
$233$	20.1495	+	20.1495i	1.32004	+	1.32004i	0.406300	+	0.913740i	$0.366819\pi$
$234$			4.48539i			0.293219i
$235$	8.47886	−	10.0222i	0.553100	−	0.653776i
$236$	7.08223			0.461014
$237$	5.38293	+	5.38293i	0.349659	+	0.349659i
$238$	1.77502	+	1.77502i	0.115057	+	0.115057i
$239$		−	20.2780i		−	1.31167i	−0.754903	−	0.655836i	$-0.772316\pi$
$239$		−	20.2780i		−	1.31167i	0.754903	−	0.655836i	$-0.227684\pi$
$240$	−2.09689	−	1.77398i	−0.135354	−	0.114510i
$241$			5.76782i			0.371538i	0.982593	+	0.185769i	$0.0594776\pi$
$241$			5.76782i			0.371538i	−0.982593	+	0.185769i	$0.940522\pi$
$242$	7.48624	−	7.48624i	0.481234	−	0.481234i
$243$	9.70264	+	9.70264i	0.622425	+	0.622425i
$244$	5.29743			0.339134
$245$	0.583126	+	6.99031i	0.0372546	+	0.446594i
$246$	−4.09920			−0.261355
$247$	−5.42622	−	5.42622i	−0.345262	−	0.345262i
$248$	−4.35523	−	4.35523i	−0.276557	−	0.276557i
$249$	10.5055			0.665760
$250$	−5.70711	+	9.61400i	−0.360949	+	0.608043i
$251$		−	16.9960i		−	1.07278i	−0.843970	−	0.536390i	$-0.819788\pi$
$251$		−	16.9960i		−	1.07278i	0.843970	−	0.536390i	$-0.180212\pi$
$252$	2.07245	+	2.07245i	0.130552	+	0.130552i
$253$	0.427074	+	3.05178i	0.0268499	+	0.191864i
$254$		−	11.5029i		−	0.721754i
$255$	−0.291619	−	3.49583i	−0.0182619	−	0.218917i
$256$	1.00000			0.0625000
$257$	−7.80296	+	7.80296i	−0.486735	+	0.486735i	−0.907274	−	0.420539i	$-0.861841\pi$
$257$	−7.80296	+	7.80296i	−0.486735	+	0.486735i	0.420539	+	0.907274i	$0.361841\pi$
$258$	−9.64716	+	9.64716i	−0.600606	+	0.600606i
$259$			20.0353i			1.24493i
$260$	4.34407	−	5.13479i	0.269408	−	0.318446i
$261$	−0.319142			−0.0197544
$262$	−7.49121	+	7.49121i	−0.462808	+	0.462808i
$263$	−2.55731	+	2.55731i	−0.157690	+	0.157690i	−0.781542	−	0.623852i	$-0.785567\pi$
$263$	−2.55731	+	2.55731i	−0.157690	+	0.157690i	0.623852	+	0.781542i	$0.285567\pi$
$264$	−0.789252			−0.0485751
$265$	−5.99930	+	7.09131i	−0.368534	+	0.435616i
$266$	−5.01431			−0.307447
$267$	−13.6856	−	13.6856i	−0.837545	−	0.837545i
$268$	3.65370	−	3.65370i	0.223185	−	0.223185i
$269$		−	5.04706i		−	0.307725i	−0.988092	−	0.153862i	$-0.950829\pi$
$269$		−	5.04706i		−	0.307725i	0.988092	−	0.153862i	$-0.0491713\pi$
$270$	−1.02547	−	12.2930i	−0.0624081	−	0.748127i
$271$	2.03917			0.123871			0.0619355	−	0.998080i	$-0.480273\pi$
$271$	2.03917			0.123871			0.0619355	+	0.998080i	$0.480273\pi$
$272$	0.903113	+	0.903113i	0.0547592	+	0.0547592i
$273$	5.13479	−	5.13479i	0.310772	−	0.310772i
$274$	7.39990			0.447044
$275$	0.532299	+	3.16830i	0.0320988	+	0.191056i
$276$	−3.54797	+	4.70257i	−0.213562	+	0.283061i
$277$	−16.5499	+	16.5499i	−0.994389	+	0.994389i	−0.999984	−	0.00559565i	$-0.998219\pi$
$277$	−16.5499	+	16.5499i	−0.994389	+	0.994389i	0.00559565	+	0.999984i	$0.498219\pi$
$278$	−9.34777	−	9.34777i	−0.560642	−	0.560642i
$279$		−	9.18469i		−	0.549873i
$280$	−0.365348	−	4.37966i	−0.0218337	−	0.261735i
$281$		−	27.3323i		−	1.63051i	−0.579105	−	0.815253i	$-0.696598\pi$
$281$		−	27.3323i		−	1.63051i	0.579105	−	0.815253i	$-0.303402\pi$
$282$	5.09920	−	5.09920i	0.303653	−	0.303653i
$283$	−8.18528	+	8.18528i	−0.486564	+	0.486564i	−0.907220	−	0.420656i	$-0.861800\pi$
$283$	−8.18528	+	8.18528i	−0.486564	+	0.486564i	0.420656	+	0.907220i	$0.361800\pi$
$284$			1.83812i			0.109072i
$285$	5.34965	+	4.52584i	0.316886	+	0.268088i
$286$		−	1.93269i		−	0.114283i
$287$	−4.63800	−	4.63800i	−0.273772	−	0.273772i
$288$	1.05444	+	1.05444i	0.0621337	+	0.0621337i
$289$		−	15.3688i		−	0.904046i
$290$	0.365348	+	0.309087i	0.0214540	+	0.0181502i
$291$			18.7431i			1.09874i
$292$	−5.20166	+	5.20166i	−0.304404	+	0.304404i
$293$	−17.9498	+	17.9498i	−1.04864	+	1.04864i	−0.0498851	+	0.998755i	$0.515886\pi$
$293$	−17.9498	+	17.9498i	−1.04864	+	1.04864i	−0.998755	+	0.0498851i	$0.984114\pi$
$294$			3.85329i			0.224728i
$295$	−1.31648	−	15.7815i	−0.0766485	−	0.918836i
$296$			10.1938i			0.592501i
$297$	−2.50648	−	2.50648i	−0.145441	−	0.145441i
$298$	1.83589	−	1.83589i	0.106350	−	0.106350i
$299$	−11.5155	−	8.68814i	−0.665958	−	0.502448i
$300$	−3.56323	+	5.00231i	−0.205723	+	0.288809i
$301$	−21.8304			−1.25828
$302$	4.75374	−	4.75374i	0.273547	−	0.273547i
$303$	8.93089	+	8.93089i	0.513066	+	0.513066i
$304$	−2.55123			−0.146323
$305$	−0.984716	−	11.8044i	−0.0563846	−	0.675919i
$306$			1.90456i			0.108877i
$307$	22.4211	−	22.4211i	1.27964	−	1.27964i	0.338775	−	0.940867i	$-0.389987\pi$
$307$	22.4211	−	22.4211i	1.27964	−	1.27964i	0.940867	−	0.338775i	$-0.110013\pi$
$308$	−0.892992	−	0.892992i	−0.0508829	−	0.0508829i
$309$	−0.0991982			−0.00564319
$310$	−8.89530	+	10.5144i	−0.505219	+	0.597181i
$311$	−10.9356			−0.620103			−0.310051	−	0.950720i	$-0.600346\pi$
$311$	−10.9356			−0.620103			−0.310051	+	0.950720i	$0.600346\pi$
$312$	2.61253	−	2.61253i	0.147905	−	0.147905i
$313$	−15.6312	+	15.6312i	−0.883529	+	0.883529i	−0.993891	−	0.110362i	$-0.964799\pi$
$313$	−15.6312	+	15.6312i	−0.883529	+	0.883529i	0.110362	+	0.993891i	$0.464799\pi$
$314$	10.7345			0.605781
$315$	4.23287	−	5.00335i	0.238495	−	0.281907i
$316$			6.19754i			0.348639i
$317$	11.8078	−	11.8078i	0.663190	−	0.663190i	−0.292941	−	0.956131i	$-0.594634\pi$
$317$	11.8078	−	11.8078i	0.663190	−	0.663190i	0.956131	+	0.292941i	$0.0946339\pi$
$318$	−3.60799	+	3.60799i	−0.202326	+	0.202326i
$319$	0.137514			0.00769931
$320$	−0.185885	−	2.22833i	−0.0103913	−	0.124567i
$321$		−	20.6211i		−	1.15096i
$322$	−9.33499	+	1.30636i	−0.520218	+	0.0728007i
$323$	−2.30405	−	2.30405i	−0.128201	−	0.128201i
$324$		−	2.30266i		−	0.127926i
$325$	−12.2495	−	8.72553i	−0.679480	−	0.484005i
$326$	−4.71106			−0.260922
$327$	12.1259	+	12.1259i	0.670566	+	0.670566i
$328$	−2.35977	−	2.35977i	−0.130296	−	0.130296i
$329$	11.5389			0.636159
$330$	0.146710	+	1.75871i	0.00807614	+	0.0968140i
$331$	−9.49002			−0.521618			−0.260809	−	0.965390i	$-0.583989\pi$
$331$	−9.49002			−0.521618			−0.260809	+	0.965390i	$0.583989\pi$
$332$	6.04767	+	6.04767i	0.331909	+	0.331909i
$333$	−10.7488	+	10.7488i	−0.589029	+	0.589029i
$334$		−	6.70669i		−	0.366974i
$335$	−8.82081	−	7.46247i	−0.481932	−	0.407718i
$336$		−	2.41421i		−	0.131706i
$337$	−1.94367	−	1.94367i	−0.105879	−	0.105879i	0.652183	−	0.758062i	$-0.273853\pi$
$337$	−1.94367	−	1.94367i	−0.105879	−	0.105879i	−0.758062	+	0.652183i	$0.773853\pi$
$338$	−2.79491	−	2.79491i	−0.152023	−	0.152023i
$339$	−8.40693			−0.456602
$340$	1.84456	−	2.18031i	0.100035	−	0.118244i
$341$			3.95756i			0.214314i
$342$	−2.69013	−	2.69013i	−0.145466	−	0.145466i
$343$	−14.0882	+	14.0882i	−0.760693	+	0.760693i
$344$	−11.1071			−0.598854
$345$	11.1384	+	7.03189i	0.599670	+	0.378584i
$346$	−14.1454			−0.760462
$347$	8.71457	−	8.71457i	0.467822	−	0.467822i	−0.433386	−	0.901208i	$-0.642681\pi$
$347$	8.71457	−	8.71457i	0.467822	−	0.467822i	0.901208	+	0.433386i	$0.142681\pi$
$348$	0.185885	+	0.185885i	0.00996450	+	0.00996450i
$349$		−	33.2153i		−	1.77797i	−0.457933	−	0.888987i	$-0.651410\pi$
$349$		−	33.2153i		−	1.77797i	0.457933	−	0.888987i	$-0.348590\pi$
$350$	−9.69141	+	1.62823i	−0.518028	+	0.0870325i
$351$	16.5936			0.885699
$352$	−0.454346	−	0.454346i	−0.0242167	−	0.0242167i
$353$	1.23246	+	1.23246i	0.0655970	+	0.0655970i	0.739144	−	0.673547i	$-0.235230\pi$
$353$	1.23246	+	1.23246i	0.0655970	+	0.0655970i	−0.673547	+	0.739144i	$0.735230\pi$
$354$		−	8.69930i		−	0.462362i
$355$	4.09593	−	0.341679i	0.217389	−	0.0181344i
$356$		−	15.7567i		−	0.835101i
$357$	2.18031	−	2.18031i	0.115394	−	0.115394i
$358$	7.66012	+	7.66012i	0.404850	+	0.404850i
$359$	−23.9816			−1.26570			−0.632850	−	0.774274i	$-0.718115\pi$
$359$	−23.9816			−1.26570			−0.632850	+	0.774274i	$0.718115\pi$
$360$	2.15364	−	2.54565i	0.113507	−	0.134168i
$361$	−12.4912			−0.657432
$362$	0.936279	+	0.936279i	0.0492097	+	0.0492097i
$363$	−9.19556	−	9.19556i	−0.482642	−	0.482642i
$364$	5.91185			0.309865
$365$	12.5579	+	10.6241i	0.657312	+	0.556091i
$366$		−	6.50699i		−	0.340126i
$367$	15.1199	+	15.1199i	0.789254	+	0.789254i	0.981372	−	0.192118i	$-0.0615356\pi$
$367$	15.1199	+	15.1199i	0.789254	+	0.789254i	−0.192118	+	0.981372i	$0.561536\pi$
$368$	−4.74955	+	0.664664i	−0.247587	+	0.0346480i
$369$		−	4.97649i		−	0.259066i
$370$	22.7151	−	1.89487i	1.18090	−	0.0985098i
$371$	−8.16445			−0.423877
$372$	−5.34965	+	5.34965i	−0.277366	+	0.277366i
$373$	9.41748	−	9.41748i	0.487619	−	0.487619i	−0.419935	−	0.907554i	$-0.637947\pi$
$373$	9.41748	−	9.41748i	0.487619	−	0.487619i	0.907554	+	0.419935i	$0.137947\pi$
$374$		−	0.820651i		−	0.0424348i
$375$	11.8091	+	7.01020i	0.609822	+	0.362005i
$376$	5.87087			0.302767
$377$	−0.455190	+	0.455190i	−0.0234435	+	0.0234435i
$378$	7.66697	−	7.66697i	0.394347	−	0.394347i
$379$	−31.0682			−1.59587			−0.797933	−	0.602746i	$-0.794073\pi$
$379$	−31.0682			−1.59587			−0.797933	+	0.602746i	$0.794073\pi$
$380$	0.474237	+	5.68498i	0.0243278	+	0.291634i
$381$	−14.1293			−0.723865
$382$	−1.74767	−	1.74767i	−0.0894185	−	0.0894185i
$383$	4.28242	−	4.28242i	0.218822	−	0.218822i	−0.589180	−	0.808002i	$-0.700549\pi$
$383$	4.28242	−	4.28242i	0.218822	−	0.218822i	0.808002	+	0.589180i	$0.200549\pi$
$384$		−	1.22833i		−	0.0626829i
$385$	−1.82389	+	2.15587i	−0.0929538	+	0.109873i
$386$	24.6460			1.25445
$387$	−11.7118	−	11.7118i	−0.595345	−	0.595345i
$388$	−10.7898	+	10.7898i	−0.547767	+	0.547767i
$389$	3.94324			0.199930			0.0999652	−	0.994991i	$-0.468127\pi$
$389$	3.94324			0.199930			0.0999652	+	0.994991i	$0.468127\pi$
$390$	−6.30721	−	5.33594i	−0.319378	−	0.270196i
$391$	−4.88964	−	3.68911i	−0.247280	−	0.186566i
$392$	−2.21821	+	2.21821i	−0.112036	+	0.112036i
$393$	9.20166	+	9.20166i	0.464163	+	0.464163i
$394$			4.51717i			0.227572i
$395$	13.8101	−	1.15203i	0.694864	−	0.0579650i
$396$		−	0.958165i		−	0.0481496i
$397$	−26.3079	+	26.3079i	−1.32036	+	1.32036i	−0.406870	+	0.913486i	$0.633380\pi$
$397$	−26.3079	+	26.3079i	−1.32036	+	1.32036i	−0.913486	+	0.406870i	$0.866620\pi$
$398$	16.7040	−	16.7040i	0.837297	−	0.837297i
$399$			6.15922i			0.308347i
$400$	−4.93089	+	0.828427i	−0.246545	+	0.0414214i
$401$		−	32.4613i		−	1.62104i	−0.585712	−	0.810519i	$-0.699185\pi$
$401$		−	32.4613i		−	1.62104i	0.585712	−	0.810519i	$-0.300815\pi$
$402$	−4.48794	−	4.48794i	−0.223838	−	0.223838i
$403$	−13.1000	−	13.1000i	−0.652560	−	0.652560i
$404$			10.2824i			0.511570i
$405$	−5.13109	+	0.428031i	−0.254966	+	0.0212691i
$406$			0.420637i			0.0208758i
$407$	4.63150	−	4.63150i	0.229575	−	0.229575i
$408$	1.10932	−	1.10932i	0.0549195	−	0.0549195i
$409$			34.1052i			1.68639i	0.537605	+	0.843197i	$0.319329\pi$
$409$			34.1052i			1.68639i	−0.537605	+	0.843197i	$0.680671\pi$
$410$	−4.81969	+	5.69699i	−0.238028	+	0.281354i
$411$		−	9.08951i		−	0.448352i
$412$	−0.0571050	−	0.0571050i	−0.00281336	−	0.00281336i
$413$	9.84274	−	9.84274i	0.484330	−	0.484330i
$414$	−5.70899	−	4.30729i	−0.280581	−	0.211692i
$415$	12.3520	−	14.6004i	0.606337	−	0.716704i
$416$	3.00789			0.147474
$417$	−11.4821	+	11.4821i	−0.562282	+	0.562282i
$418$	1.15914	+	1.15914i	0.0566955	+	0.0566955i
$419$	16.1569			0.789317			0.394659	−	0.918828i	$-0.370863\pi$
$419$	16.1569			0.789317			0.394659	+	0.918828i	$0.370863\pi$
$420$	−5.37966	+	0.448767i	−0.262501	+	0.0218976i
$421$			29.1132i			1.41889i	0.704761	+	0.709445i	$0.251054\pi$
$421$			29.1132i			1.41889i	−0.704761	+	0.709445i	$0.748946\pi$
$422$	13.7894	−	13.7894i	0.671258	−	0.671258i
$423$	6.19051	+	6.19051i	0.300993	+	0.300993i
$424$	−4.15399			−0.201736
$425$	−5.20131	−	3.70499i	−0.252301	−	0.179718i
$426$	2.25781			0.109391
$427$	7.36227	−	7.36227i	0.356285	−	0.356285i
$428$	11.8709	−	11.8709i	0.573800	−	0.573800i
$429$	−2.37398			−0.114617
$430$	2.06464	+	24.7502i	0.0995660	+	1.19356i
$431$			26.5548i			1.27910i	0.768750	+	0.639549i	$0.220879\pi$
$431$			26.5548i			1.27910i	−0.768750	+	0.639549i	$0.779121\pi$
$432$	3.90088	−	3.90088i	0.187681	−	0.187681i
$433$	2.16607	−	2.16607i	0.104095	−	0.104095i	−0.653141	−	0.757236i	$-0.726549\pi$
$433$	2.16607	−	2.16607i	0.104095	−	0.104095i	0.757236	+	0.653141i	$0.226549\pi$
$434$	−12.1056			−0.581088
$435$	0.379660	−	0.448767i	0.0182033	−	0.0215167i
$436$			13.9610i			0.668610i
$437$	12.1172	−	1.69571i	0.579645	−	0.0811169i
$438$	6.38935	+	6.38935i	0.305295	+	0.305295i
$439$			6.18032i			0.294971i	0.989064	+	0.147485i	$0.0471179\pi$
$439$			6.18032i			0.294971i	−0.989064	+	0.147485i	$0.952882\pi$
$440$	−0.927975	+	1.09689i	−0.0442395	+	0.0522921i
$441$	−4.67795			−0.222760
$442$	2.71646	+	2.71646i	0.129209	+	0.129209i
$443$	−21.1563	−	21.1563i	−1.00517	−	1.00517i	−0.999987	−	0.00517914i	$-0.998351\pi$
$443$	−21.1563	−	21.1563i	−1.00517	−	1.00517i	−0.00517914	−	0.999987i	$-0.501649\pi$
$444$	12.5213			0.594235
$445$	−35.1110	+	2.92893i	−1.66442	+	0.138845i
$446$	0.711154			0.0336741
$447$	−2.25507	−	2.25507i	−0.106661	−	0.106661i
$448$	1.38978	−	1.38978i	0.0656610	−	0.0656610i
$449$			37.4969i			1.76959i	0.465981	+	0.884795i	$0.345702\pi$
$449$			37.4969i			1.76959i	−0.465981	+	0.884795i	$0.654298\pi$
$450$	−6.07288	−	4.32582i	−0.286278	−	0.203921i
$451$			2.14430i			0.100971i
$452$	−4.83958	−	4.83958i	−0.227635	−	0.227635i
$453$	−5.83916	−	5.83916i	−0.274347	−	0.274347i
$454$	25.1208			1.17898
$455$	−1.09893	−	13.1735i	−0.0515184	−	0.617585i
$456$			3.13375i			0.146751i
$457$	12.5415	+	12.5415i	0.586669	+	0.586669i	0.936728	−	0.350059i	$-0.113838\pi$
$457$	12.5415	+	12.5415i	0.586669	+	0.586669i	−0.350059	+	0.936728i	$0.613838\pi$
$458$	21.0868	−	21.0868i	0.985324	−	0.985324i
$459$	7.04587			0.328873
$460$	2.36396	+	10.4600i	0.110220	+	0.487700i
$461$	2.25004			0.104795			0.0523973	−	0.998626i	$-0.483314\pi$
$461$	2.25004			0.104795			0.0523973	+	0.998626i	$0.483314\pi$
$462$	−1.09689	+	1.09689i	−0.0510318	+	0.0510318i
$463$	0.606522	+	0.606522i	0.0281875	+	0.0281875i	0.721060	−	0.692873i	$-0.243655\pi$
$463$	0.606522	+	0.606522i	0.0281875	+	0.0281875i	−0.692873	+	0.721060i	$0.743655\pi$
$464$			0.214016i			0.00993543i
$465$	12.9152	+	10.9264i	0.598928	+	0.506697i
$466$	28.4957			1.32004
$467$	4.28132	+	4.28132i	0.198116	+	0.198116i	0.799192	−	0.601076i	$-0.205261\pi$
$467$	4.28132	+	4.28132i	0.198116	+	0.198116i	−0.601076	+	0.799192i	$0.705261\pi$
$468$	3.17165	+	3.17165i	0.146610	+	0.146610i
$469$		−	10.1557i		−	0.468946i
$470$	−1.09131	−	13.0822i	−0.0503383	−	0.603438i
$471$		−	13.1854i		−	0.607553i
$472$	5.00789	−	5.00789i	0.230507	−	0.230507i
$473$	5.04646	+	5.04646i	0.232036	+	0.232036i
$474$	7.61261			0.349659
$475$	12.5799	−	2.11351i	0.577203	−	0.0969745i
$476$	2.51026			0.115057
$477$	−4.38015	−	4.38015i	−0.200554	−	0.200554i
$478$	−14.3387	−	14.3387i	−0.655836	−	0.655836i
$479$	−34.9788			−1.59822			−0.799111	−	0.601183i	$-0.794696\pi$
$479$	−34.9788			−1.59822			−0.799111	+	0.601183i	$0.794696\pi$
$480$	−2.73712	+	0.228328i	−0.124932	+	0.0104217i
$481$			30.6617i			1.39806i
$482$	4.07846	+	4.07846i	0.185769	+	0.185769i
$483$	1.60464	+	11.4664i	0.0730137	+	0.521741i
$484$		−	10.5871i		−	0.481234i
$485$	26.0488	+	22.0375i	1.18281	+	1.00067i
$486$	13.7216			0.622425
$487$	−24.9791	+	24.9791i	−1.13191	+	1.13191i	−0.142050	+	0.989860i	$0.545369\pi$
$487$	−24.9791	+	24.9791i	−1.13191	+	1.13191i	−0.989860	+	0.142050i	$0.954631\pi$
$488$	3.74585	−	3.74585i	0.169567	−	0.169567i
$489$			5.78673i			0.261685i
$490$	5.35523	+	4.53056i	0.241925	+	0.204670i
$491$	10.7180			0.483696			0.241848	−	0.970314i	$-0.422247\pi$
$491$	10.7180			0.483696			0.241848	+	0.970314i	$0.422247\pi$
$492$	−2.89857	+	2.89857i	−0.130678	+	0.130678i
$493$	−0.193280	+	0.193280i	−0.00870491	+	0.00870491i
$494$	−7.67383			−0.345262
$495$	−2.13511	+	0.178109i	−0.0959658	+	0.00800539i
$496$	−6.15922			−0.276557
$497$	2.55458	+	2.55458i	0.114589	+	0.114589i
$498$	7.42853	−	7.42853i	0.332880	−	0.332880i
$499$			32.0187i			1.43335i	0.697405	+	0.716677i	$0.254338\pi$
$499$			32.0187i			1.43335i	−0.697405	+	0.716677i	$0.745662\pi$
$500$	2.76259	+	10.8337i	0.123547	+	0.484496i
$501$	−8.23802			−0.368048
$502$	−12.0180	−	12.0180i	−0.536390	−	0.536390i
$503$	7.00239	−	7.00239i	0.312221	−	0.312221i	−0.533548	−	0.845770i	$-0.679142\pi$
$503$	7.00239	−	7.00239i	0.312221	−	0.312221i	0.845770	+	0.533548i	$0.179142\pi$
$504$	2.93089			0.130552
$505$	22.9126	−	1.91135i	1.01960	−	0.0850540i
$506$	2.45992	+	1.85595i	0.109357	+	0.0825070i
$507$	−3.43307	+	3.43307i	−0.152468	+	0.152468i
$508$	−8.13375	−	8.13375i	−0.360877	−	0.360877i
$509$			6.57514i			0.291438i	0.989326	+	0.145719i	$0.0465496\pi$
$509$			6.57514i			0.291438i	−0.989326	+	0.145719i	$0.953450\pi$
$510$	−2.67813	−	2.26572i	−0.118590	−	0.100328i
$511$			14.4583i			0.639600i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−9.95206	+	9.95206i	−0.439394	+	0.439394i
$514$			11.0350i			0.486735i
$515$	−0.116634	+	0.137864i	−0.00513950	+	0.00607500i
$516$			13.6431i			0.600606i
$517$	−2.66740	−	2.66740i	−0.117312	−	0.117312i
$518$	14.1671	+	14.1671i	0.622467	+	0.622467i
$519$			17.3752i			0.762687i
$520$	−0.559123	−	6.70257i	−0.0245191	−	0.293927i
$521$		−	33.5270i		−	1.46885i	−0.678692	−	0.734423i	$-0.737453\pi$
$521$		−	33.5270i		−	1.46885i	0.678692	−	0.734423i	$-0.262547\pi$
$522$	−0.225668	+	0.225668i	−0.00987721	+	0.00987721i
$523$	15.4410	−	15.4410i	0.675189	−	0.675189i	−0.283718	−	0.958908i	$-0.591568\pi$
$523$	15.4410	−	15.4410i	0.675189	−	0.675189i	0.958908	+	0.283718i	$0.0915680\pi$
$524$			10.5942i			0.462808i
$525$	2.00000	+	11.9042i	0.0872872	+	0.519543i
$526$			3.61658i			0.157690i
$527$	−5.56247	−	5.56247i	−0.242305	−	0.242305i
$528$	−0.558086	+	0.558086i	−0.0242876	+	0.0242876i
$529$	22.1164	−	6.31371i	0.961585	−	0.274509i
$530$	0.772166	+	9.25646i	0.0335408	+	0.402075i
$531$	10.5611			0.458312
$532$	−3.54565	+	3.54565i	−0.153724	+	0.153724i
$533$	−7.09792	−	7.09792i	−0.307445	−	0.307445i
$534$	−19.3543			−0.837545
$535$	−28.6588	−	24.2456i	−1.23903	−	1.04823i
$536$		−	5.16711i		−	0.223185i
$537$	9.40914	−	9.40914i	0.406035	−	0.406035i
$538$	−3.56881	−	3.56881i	−0.153862	−	0.153862i
$539$	2.01567			0.0868209
$540$	−9.41756	−	7.96733i	−0.405267	−	0.342859i
$541$	31.1573			1.33956			0.669779	−	0.742560i	$-0.266389\pi$
$541$	31.1573			1.33956			0.669779	+	0.742560i	$0.266389\pi$
$542$	1.44191	−	1.44191i	0.0619355	−	0.0619355i
$543$	1.15006	−	1.15006i	0.0493537	−	0.0493537i
$544$	1.27719			0.0547592
$545$	31.1097	−	2.59514i	1.33259	−	0.111164i
$546$		−	7.26169i		−	0.310772i
$547$	−5.56016	+	5.56016i	−0.237735	+	0.237735i	−0.815912	−	0.578176i	$-0.803765\pi$
$547$	−5.56016	+	5.56016i	−0.237735	+	0.237735i	0.578176	+	0.815912i	$0.303765\pi$
$548$	5.23252	−	5.23252i	0.223522	−	0.223522i
$549$	7.89959			0.337146
$550$	2.61672	+	1.86394i	0.111577	+	0.0794786i
$551$		−	0.546004i		−	0.0232606i
$552$	0.816425	+	5.83401i	0.0347494	+	0.248312i
$553$	8.61322	+	8.61322i	0.366271	+	0.366271i
$554$			23.4051i			0.994389i
$555$	−2.32753	−	27.9016i	−0.0987980	−	1.18436i
$556$	−13.2197			−0.560642
$557$	−4.12733	−	4.12733i	−0.174881	−	0.174881i	0.614239	−	0.789120i	$-0.289463\pi$
$557$	−4.12733	−	4.12733i	−0.174881	−	0.174881i	−0.789120	+	0.614239i	$0.789463\pi$
$558$	−6.49456	−	6.49456i	−0.274937	−	0.274937i
$559$	−33.4089			−1.41305
$560$	−3.35523	−	2.83855i	−0.141784	−	0.119951i
$561$	−1.00803			−0.0425590
$562$	−19.3268	−	19.3268i	−0.815253	−	0.815253i
$563$	22.0716	−	22.0716i	0.930205	−	0.930205i	−0.0675129	−	0.997718i	$-0.521506\pi$
$563$	22.0716	−	22.0716i	0.930205	−	0.930205i	0.997718	+	0.0675129i	$0.0215064\pi$
$564$		−	7.21136i		−	0.303653i
$565$	−9.88458	+	11.6838i	−0.415847	+	0.491541i
$566$			11.5757i			0.486564i
$567$	−3.20020	−	3.20020i	−0.134396	−	0.134396i
$568$	1.29975	+	1.29975i	0.0545361	+	0.0545361i
$569$	−15.5745			−0.652918			−0.326459	−	0.945211i	$-0.605855\pi$
$569$	−15.5745			−0.652918			−0.326459	+	0.945211i	$0.605855\pi$
$570$	6.98303	−	0.582518i	0.292487	−	0.0243990i
$571$		−	28.0477i		−	1.17376i	−0.809674	−	0.586879i	$-0.800356\pi$
$571$		−	28.0477i		−	1.17376i	0.809674	−	0.586879i	$-0.199644\pi$
$572$	−1.36662	−	1.36662i	−0.0571413	−	0.0571413i
$573$	−2.14671	+	2.14671i	−0.0896801	+	0.0896801i
$574$	−6.55912			−0.273772
$575$	22.8689	−	7.21204i	0.953699	−	0.300763i
$576$	1.49121			0.0621337
$577$	13.3583	−	13.3583i	0.556114	−	0.556114i	−0.372085	−	0.928199i	$-0.621357\pi$
$577$	13.3583	−	13.3583i	0.556114	−	0.556114i	0.928199	+	0.372085i	$0.121357\pi$
$578$	−10.8674	−	10.8674i	−0.452023	−	0.452023i
$579$		−	30.2733i		−	1.25812i
$580$	0.476897	−	0.0397824i	0.0198021	−	0.00165187i
$581$	16.8099			0.697391
$582$	13.2534	+	13.2534i	0.549370	+	0.549370i
$583$	1.88735	+	1.88735i	0.0781660	+	0.0781660i
$584$			7.35626i			0.304404i
$585$	6.47792	−	7.65705i	0.267829	−	0.316580i
$586$			25.3849i			1.04864i
$587$	17.6702	−	17.6702i	0.729328	−	0.729328i	−0.241158	−	0.970486i	$-0.577527\pi$
$587$	17.6702	−	17.6702i	0.729328	−	0.729328i	0.970486	+	0.241158i	$0.0775273\pi$
$588$	2.72469	+	2.72469i	0.112364	+	0.112364i
$589$	15.7136			0.647468
$590$	−12.0901	−	10.2283i	−0.497742	−	0.421094i
$591$	5.54857			0.228238
$592$	7.20809	+	7.20809i	0.296251	+	0.296251i
$593$	3.45323	+	3.45323i	0.141807	+	0.141807i	0.774447	−	0.632639i	$-0.218028\pi$
$593$	3.45323	+	3.45323i	0.141807	+	0.141807i	−0.632639	+	0.774447i	$0.718028\pi$
$594$	−3.54470			−0.145441
$595$	−0.466620	−	5.59368i	−0.0191296	−	0.229318i
$596$		−	2.59634i		−	0.106350i
$597$	−20.5180	−	20.5180i	−0.839747	−	0.839747i
$598$	−14.2861	+	1.99924i	−0.584203	+	0.0817548i
$599$		−	13.6711i		−	0.558584i	−0.960206	−	0.279292i	$-0.909900\pi$
$599$		−	13.6711i		−	0.558584i	0.960206	−	0.279292i	$-0.0900998\pi$
$600$	1.01758	+	6.05676i	0.0415425	+	0.247266i
$601$	−12.6714			−0.516879			−0.258439	−	0.966027i	$-0.583208\pi$
$601$	−12.6714			−0.516879			−0.258439	+	0.966027i	$0.583208\pi$
$602$	−15.4364	+	15.4364i	−0.629141	+	0.629141i
$603$	5.44843	−	5.44843i	0.221877	−	0.221877i
$604$		−	6.72281i		−	0.273547i
$605$	−23.5916	+	1.96799i	−0.959136	+	0.0800103i
$606$	12.6302			0.513066
$607$	−3.83219	+	3.83219i	−0.155544	+	0.155544i	−0.780589	−	0.625045i	$-0.785081\pi$
$607$	−3.83219	+	3.83219i	−0.155544	+	0.155544i	0.625045	+	0.780589i	$0.285081\pi$
$608$	−1.80399	+	1.80399i	−0.0731616	+	0.0731616i
$609$	0.516680			0.0209369
$610$	−9.04329	−	7.65069i	−0.366152	−	0.309767i
$611$	17.6589			0.714404
$612$	1.34673	+	1.34673i	0.0544383	+	0.0544383i
$613$	6.13229	−	6.13229i	0.247681	−	0.247681i	−0.572338	−	0.820018i	$-0.693963\pi$
$613$	6.13229	−	6.13229i	0.247681	−	0.247681i	0.820018	+	0.572338i	$0.193963\pi$
$614$		−	31.7083i		−	1.27964i
$615$	6.99777	+	5.92017i	0.282177	+	0.238724i
$616$	−1.26288			−0.0508829
$617$	13.1922	+	13.1922i	0.531099	+	0.531099i	0.920899	−	0.389800i	$-0.127456\pi$
$617$	13.1922	+	13.1922i	0.531099	+	0.531099i	−0.389800	+	0.920899i	$0.627456\pi$
$618$	−0.0701437	+	0.0701437i	−0.00282159	+	0.00282159i
$619$	−38.9948			−1.56733			−0.783667	−	0.621181i	$-0.786653\pi$
$619$	−38.9948			−1.56733			−0.783667	+	0.621181i	$0.786653\pi$
$620$	1.14491	+	13.7248i	0.0459807	+	0.551200i
$621$	−15.9347	+	21.1202i	−0.639436	+	0.847525i
$622$	−7.73266	+	7.73266i	−0.310051	+	0.310051i
$623$	−21.8983	−	21.8983i	−0.877337	−	0.877337i
$624$		−	3.69468i		−	0.147905i
$625$	23.6274	−	8.16977i	0.945097	−	0.326791i
$626$			22.1059i			0.883529i
$627$	1.42381	−	1.42381i	0.0568614	−	0.0568614i
$628$	7.59041	−	7.59041i	0.302890	−	0.302890i
$629$			13.0194i			0.519119i
$630$	−0.544810	−	6.53099i	−0.0217058	−	0.260201i
$631$			24.6310i			0.980547i	0.871569	+	0.490273i	$0.163103\pi$
$631$			24.6310i			0.980547i	−0.871569	+	0.490273i	$0.836897\pi$
$632$	4.38232	+	4.38232i	0.174319	+	0.174319i
$633$	−16.9379	−	16.9379i	−0.673222	−	0.673222i
$634$		−	16.6987i		−	0.663190i
$635$	−16.6127	+	19.6366i	−0.659256	+	0.779255i
$636$			5.10247i			0.202326i
$637$	−6.67212	+	6.67212i	−0.264359	+	0.264359i
$638$	0.0972371	−	0.0972371i	0.00384965	−	0.00384965i
$639$			2.74102i			0.108433i
$640$	−1.70711	−	1.44423i	−0.0674793	−	0.0570880i
$641$			22.1791i			0.876024i	0.898969	+	0.438012i	$0.144317\pi$
$641$			22.1791i			0.876024i	−0.898969	+	0.438012i	$0.855683\pi$
$642$	−14.5813	−	14.5813i	−0.575479	−	0.575479i
$643$	4.00739	−	4.00739i	0.158036	−	0.158036i	−0.623660	−	0.781696i	$-0.714355\pi$
$643$	4.00739	−	4.00739i	0.158036	−	0.158036i	0.781696	+	0.623660i	$0.214355\pi$
$644$	−5.67710	+	7.52457i	−0.223709	+	0.296510i
$645$	30.4014	−	2.53606i	1.19705	−	0.0998573i
$646$	−3.25842			−0.128201
$647$	4.43702	−	4.43702i	0.174437	−	0.174437i	−0.614488	−	0.788926i	$-0.710638\pi$
$647$	4.43702	−	4.43702i	0.174437	−	0.174437i	0.788926	+	0.614488i	$0.210638\pi$
$648$	−1.62823	−	1.62823i	−0.0639629	−	0.0639629i
$649$	−4.55063			−0.178628
$650$	−14.8316	+	2.49182i	−0.581743	+	0.0977371i
$651$			14.8697i			0.582789i
$652$	−3.33122	+	3.33122i	−0.130461	+	0.130461i
$653$	12.0206	+	12.0206i	0.470401	+	0.470401i	0.902044	−	0.431644i	$-0.142066\pi$
$653$	12.0206	+	12.0206i	0.470401	+	0.470401i	−0.431644	+	0.902044i	$0.642066\pi$
$654$	17.1487			0.670566
$655$	23.6073	−	1.96930i	0.922413	−	0.0769470i
$656$	−3.33722			−0.130296
$657$	−7.75677	+	7.75677i	−0.302621	+	0.302621i
$658$	8.15922	−	8.15922i	0.318080	−	0.318080i
$659$	−23.9828			−0.934238			−0.467119	−	0.884194i	$-0.654708\pi$
$659$	−23.9828			−0.934238			−0.467119	+	0.884194i	$0.654708\pi$
$660$	1.34734	+	1.13986i	0.0524451	+	0.0443689i
$661$		−	7.25064i		−	0.282017i	−0.990008	−	0.141009i	$-0.954965\pi$
$661$		−	7.25064i		−	0.282017i	0.990008	−	0.141009i	$-0.0450345\pi$
$662$	−6.71045	+	6.71045i	−0.260809	+	0.260809i
$663$	3.33671	−	3.33671i	0.129587	−	0.129587i
$664$	8.55270			0.331909
$665$	8.55997	+	7.24180i	0.331941	+	0.280825i
$666$			15.2011i			0.589029i
$667$	−0.142249	−	1.01648i	−0.00550789	−	0.0393582i
$668$	−4.74235	−	4.74235i	−0.183487	−	0.183487i
$669$		−	0.873530i		−	0.0337726i
$670$	−11.5140	+	0.960490i	−0.444825	+	0.0371070i
$671$	−3.40382			−0.131403
$672$	−1.70711	−	1.70711i	−0.0658531	−	0.0658531i
$673$	−12.2034	−	12.2034i	−0.470405	−	0.470405i	0.431641	−	0.902046i	$-0.357935\pi$
$673$	−12.2034	−	12.2034i	−0.470405	−	0.470405i	−0.902046	+	0.431641i	$0.857935\pi$
$674$	−2.74877			−0.105879
$675$	−16.0032	+	22.4664i	−0.615965	+	0.864733i
$676$	−3.95260			−0.152023
$677$	−11.3637	−	11.3637i	−0.436741	−	0.436741i	0.454173	−	0.890914i	$-0.349935\pi$
$677$	−11.3637	−	11.3637i	−0.436741	−	0.436741i	−0.890914	+	0.454173i	$0.849935\pi$
$678$	−5.94460	+	5.94460i	−0.228301	+	0.228301i
$679$			29.9908i			1.15094i
$680$	−0.237412	−	2.84601i	−0.00910432	−	0.109139i
$681$		−	30.8566i		−	1.18243i
$682$	2.79842	+	2.79842i	0.107157	+	0.107157i
$683$	3.03440	+	3.03440i	0.116108	+	0.116108i	0.762774	−	0.646666i	$-0.223837\pi$
$683$	3.03440	+	3.03440i	0.116108	+	0.116108i	−0.646666	+	0.762774i	$0.723837\pi$
$684$	−3.80442			−0.145466
$685$	−12.6324	−	10.6871i	−0.482660	−	0.408334i
$686$			19.9238i			0.760693i
$687$	−25.9016	−	25.9016i	−0.988206	−	0.988206i
$688$	−7.85390	+	7.85390i	−0.299427	+	0.299427i
$689$	−12.4948			−0.476012
$690$	12.8483	−	2.90372i	0.489127	−	0.110543i
$691$	−11.4557			−0.435795			−0.217897	−	0.975972i	$-0.569920\pi$
$691$	−11.4557			−0.435795			−0.217897	+	0.975972i	$0.569920\pi$
$692$	−10.0023	+	10.0023i	−0.380231	+	0.380231i
$693$	−1.33164	−	1.33164i	−0.0505848	−	0.0505848i
$694$		−	12.3243i		−	0.467822i
$695$	2.45736	+	29.4579i	0.0932128	+	1.11740i
$696$	0.262882			0.00996450
$697$	−3.01388	−	3.01388i	−0.114159	−	0.114159i
$698$	−23.4867	−	23.4867i	−0.888987	−	0.888987i
$699$		−	35.0021i		−	1.32390i
$700$	−5.70153	+	8.00419i	−0.215498	+	0.302530i
$701$		−	15.8931i		−	0.600274i	−0.953896	−	0.300137i	$-0.902968\pi$
$701$		−	15.8931i		−	0.600274i	0.953896	−	0.300137i	$-0.0970324\pi$
$702$	11.7334	−	11.7334i	0.442849	−	0.442849i
$703$	−18.3895	−	18.3895i	−0.693574	−	0.693574i
$704$	−0.642542			−0.0242167
$705$	−16.0693	+	1.34049i	−0.605204	+	0.0504856i
$706$	1.74295			0.0655970
$707$	14.2903	+	14.2903i	0.537443	+	0.537443i
$708$	−6.15133	−	6.15133i	−0.231181	−	0.231181i
$709$	1.80382			0.0677437			0.0338719	−	0.999426i	$-0.489216\pi$
$709$	1.80382			0.0677437			0.0338719	+	0.999426i	$0.489216\pi$
$710$	2.65466	−	3.13786i	0.0996275	−	0.117762i
$711$			9.24183i			0.346596i
$712$	−11.1416	−	11.1416i	−0.417551	−	0.417551i
$713$	29.2535	−	4.09381i	1.09555	−	0.153314i
$714$		−	3.08342i		−	0.115394i
$715$	−2.79125	+	3.29932i	−0.104387	+	0.123387i
$716$	10.8330			0.404850
$717$	−17.6126	+	17.6126i	−0.657755	+	0.657755i
$718$	−16.9576	+	16.9576i	−0.632850	+	0.632850i
$719$			42.3914i			1.58093i	0.612506	+	0.790466i	$0.290161\pi$
$719$			42.3914i			1.58093i	−0.612506	+	0.790466i	$0.709839\pi$
$720$	−0.277194	−	3.32290i	−0.0103304	−	0.123837i
$721$	−0.158727			−0.00591130
$722$	−8.83262	+	8.83262i	−0.328716	+	0.328716i
$723$	5.00969	−	5.00969i	0.186312	−	0.186312i
$724$	1.32410			0.0492097
$725$	−0.177296	−	1.05529i	−0.00658462	−	0.0391924i
$726$	−13.0045			−0.482642
$727$	21.8812	+	21.8812i	0.811528	+	0.811528i	0.984863	−	0.173335i	$-0.0554543\pi$
$727$	21.8812	+	21.8812i	0.811528	+	0.811528i	−0.173335	+	0.984863i	$0.555454\pi$
$728$	4.18031	−	4.18031i	0.154932	−	0.154932i
$729$		−	23.7626i		−	0.880098i
$730$	16.3922	−	1.36742i	0.606701	−	0.0506105i
$731$	−14.1859			−0.524685
$732$	−4.60114	−	4.60114i	−0.170063	−	0.170063i
$733$	−4.98172	+	4.98172i	−0.184004	+	0.184004i	−0.793098	−	0.609094i	$-0.791533\pi$
$733$	−4.98172	+	4.98172i	−0.184004	+	0.184004i	0.609094	+	0.793098i	$0.291533\pi$
$734$	21.3828			0.789254
$735$	5.56502	−	6.57798i	0.205269	−	0.242632i
$736$	−2.88845	+	3.82843i	−0.106470	+	0.141118i
$737$	−2.34765	+	2.34765i	−0.0864770	+	0.0864770i
$738$	−3.51891	−	3.51891i	−0.129533	−	0.129533i
$739$			35.5481i			1.30766i	0.756642	+	0.653829i	$0.226839\pi$
$739$			35.5481i			1.30766i	−0.756642	+	0.653829i	$0.773161\pi$
$740$	14.7221	−	17.4019i	0.541195	−	0.639705i
$741$			9.42598i			0.346272i
$742$	−5.77314	+	5.77314i	−0.211939	+	0.211939i
$743$	1.12483	−	1.12483i	0.0412658	−	0.0412658i	−0.686173	−	0.727439i	$-0.740711\pi$
$743$	1.12483	−	1.12483i	0.0412658	−	0.0412658i	0.727439	+	0.686173i	$0.240711\pi$
$744$			7.56555i			0.277366i
$745$	−5.78549	+	0.482621i	−0.211964	+	0.0176819i
$746$		−	13.3183i		−	0.487619i
$747$	9.01835	+	9.01835i	0.329964	+	0.329964i
$748$	−0.580288	−	0.580288i	−0.0212174	−	0.0212174i
$749$		−	32.9958i		−	1.20564i
$750$	13.3073	−	3.39337i	0.485913	−	0.123908i
$751$		−	24.1881i		−	0.882636i	−0.897351	−	0.441318i	$-0.854511\pi$
$751$		−	24.1881i		−	0.882636i	0.897351	−	0.441318i	$-0.145489\pi$
$752$	4.15133	−	4.15133i	0.151384	−	0.151384i
$753$	−14.7621	+	14.7621i	−0.537959	+	0.537959i
$754$			0.643736i			0.0234435i
$755$	−14.9806	+	1.24967i	−0.545201	+	0.0454802i
$756$		−	10.8427i		−	0.394347i
$757$	3.23306	+	3.23306i	0.117508	+	0.117508i	0.763415	−	0.645908i	$-0.223521\pi$
$757$	3.23306	+	3.23306i	0.117508	+	0.117508i	−0.645908	+	0.763415i	$0.723521\pi$
$758$	−21.9685	+	21.9685i	−0.797933	+	0.797933i
$759$	2.27972	−	3.02159i	0.0827484	−	0.109677i
$760$	4.35523	+	3.68456i	0.157981	+	0.133653i
$761$	−18.8841			−0.684547			−0.342274	−	0.939600i	$-0.611197\pi$
$761$	−18.8841			−0.684547			−0.342274	+	0.939600i	$0.611197\pi$
$762$	−9.99092	+	9.99092i	−0.361933	+	0.361933i
$763$	19.4027	+	19.4027i	0.702425	+	0.702425i
$764$	−2.47158			−0.0894185
$765$	2.75062	−	3.25129i	0.0994489	−	0.117551i
$766$		−	6.05626i		−	0.218822i
$767$	15.0632	−	15.0632i	0.543900	−	0.543900i
$768$	−0.868559	−	0.868559i	−0.0313414	−	0.0313414i
$769$	−19.4309			−0.700694			−0.350347	−	0.936620i	$-0.613936\pi$
$769$	−19.4309			−0.700694			−0.350347	+	0.936620i	$0.613936\pi$
$770$	0.234751	+	2.81411i	0.00845985	+	0.101414i
$771$	13.5547			0.488159
$772$	17.4273	−	17.4273i	0.627223	−	0.627223i
$773$	8.42929	−	8.42929i	0.303181	−	0.303181i	−0.539076	−	0.842257i	$-0.681227\pi$
$773$	8.42929	−	8.42929i	0.303181	−	0.303181i	0.842257	+	0.539076i	$0.181227\pi$
$774$	−16.5630			−0.595345
$775$	30.3705	−	5.10247i	1.09094	−	0.183286i
$776$			15.2590i			0.547767i
$777$	17.4019	−	17.4019i	0.624288	−	0.624288i
$778$	2.78830	−	2.78830i	0.0999652	−	0.0999652i
$779$	8.51402			0.305046
$780$	−8.23295	+	0.686786i	−0.294787	+	0.0245909i
$781$		−	1.18107i		−	0.0422619i
$782$	−6.06610	+	0.848905i	−0.216923	+	0.0303568i
$783$	0.834850	+	0.834850i	0.0298351	+	0.0298351i
$784$			3.13702i			0.112036i
$785$	−18.3249	−	15.5030i	−0.654043	−	0.553325i
$786$	13.0131			0.464163
$787$	28.9454	+	28.9454i	1.03179	+	1.03179i	0.999478	+	0.0323130i	$0.0102874\pi$
$787$	28.9454	+	28.9454i	1.03179	+	1.03179i	0.0323130	+	0.999478i	$0.489713\pi$
$788$	3.19412	+	3.19412i	0.113786	+	0.113786i
$789$	4.44234			0.158152
$790$	8.95064	−	10.5799i	0.318449	−	0.376414i
$791$	−13.4519			−0.478295
$792$	−0.677525	−	0.677525i	−0.0240748	−	0.0240748i
$793$	11.2671	−	11.2671i	0.400107	−	0.400107i
$794$			37.2050i			1.32036i
$795$	11.3700	−	0.948474i	0.403251	−	0.0336389i
$796$		−	23.6231i		−	0.837297i
$797$	−37.8670	−	37.8670i	−1.34132	−	1.34132i	−0.894749	−	0.446570i	$-0.852646\pi$
$797$	−37.8670	−	37.8670i	−1.34132	−	1.34132i	−0.446570	−	0.894749i	$-0.647354\pi$
$798$	4.35523	+	4.35523i	0.154173	+	0.154173i
$799$	7.49824			0.265269
$800$	−2.90088	+	4.07245i	−0.102562	+	0.143983i
$801$		−	23.4965i		−	0.830207i
$802$	−22.9536	−	22.9536i	−0.810519	−	0.810519i
$803$	3.34229	−	3.34229i	0.117947	−	0.117947i
$804$	−6.34691			−0.223838
$805$	17.8225	+	11.2517i	0.628161	+	0.396571i
$806$	−18.5263			−0.652560
$807$	−4.38367	+	4.38367i	−0.154313	+	0.154313i
$808$	7.27077	+	7.27077i	0.255785	+	0.255785i
$809$			4.75714i			0.167252i	0.996497	+	0.0836260i	$0.0266501\pi$
$809$			4.75714i			0.167252i	−0.996497	+	0.0836260i	$0.973350\pi$
$810$	−3.32557	+	3.93089i	−0.116848	+	0.138118i
$811$	40.1787			1.41086			0.705432	−	0.708778i	$-0.250753\pi$
$811$	40.1787			1.41086			0.705432	+	0.708778i	$0.250753\pi$
$812$	0.297435	+	0.297435i	0.0104379	+	0.0104379i
$813$	−1.77114	−	1.77114i	−0.0621167	−	0.0621167i
$814$		−	6.54993i		−	0.229575i
$815$	8.04229	+	6.80383i	0.281709	+	0.238328i
$816$		−	1.56881i		−	0.0549195i
$817$	20.0371	−	20.0371i	0.701010	−	0.701010i
$818$	24.1160	+	24.1160i	0.843197	+	0.843197i
$819$	8.81580			0.308049
$820$	0.620340	+	7.43642i	0.0216632	+	0.259691i
$821$	−29.5514			−1.03135			−0.515676	−	0.856784i	$-0.672459\pi$
$821$	−29.5514			−1.03135			−0.515676	+	0.856784i	$0.672459\pi$
$822$	−6.42725	−	6.42725i	−0.224176	−	0.224176i
$823$	26.6811	+	26.6811i	0.930046	+	0.930046i	0.997708	−	0.0676625i	$-0.0215541\pi$
$823$	26.6811	+	26.6811i	0.930046	+	0.930046i	−0.0676625	+	0.997708i	$0.521554\pi$
$824$	−0.0807587			−0.00281336
$825$	2.28953	−	3.21419i	0.0797111	−	0.111904i
$826$		−	13.9197i		−	0.484330i
$827$	−7.39267	−	7.39267i	−0.257068	−	0.257068i	0.566792	−	0.823861i	$-0.308184\pi$
$827$	−7.39267	−	7.39267i	−0.257068	−	0.257068i	−0.823861	+	0.566792i	$0.808184\pi$
$828$	−7.08257	+	0.991153i	−0.246136	+	0.0344450i
$829$		−	14.8212i		−	0.514761i	−0.966310	−	0.257381i	$-0.917141\pi$
$829$		−	14.8212i		−	0.514761i	0.966310	−	0.257381i	$-0.0828594\pi$
$830$	−1.58982	−	19.0582i	−0.0551835	−	0.661521i
$831$	28.7492			0.997298
$832$	2.12690	−	2.12690i	0.0737370	−	0.0737370i
$833$	−2.83308	+	2.83308i	−0.0981605	+	0.0981605i
$834$			16.2382i			0.562282i
$835$	−9.68597	+	11.4490i	−0.335197	+	0.396210i
$836$	1.63927			0.0566955
$837$	−24.0264	+	24.0264i	−0.830474	+	0.830474i
$838$	11.4247	−	11.4247i	0.394659	−	0.394659i
$839$	46.9210			1.61989			0.809946	−	0.586504i	$-0.199496\pi$
$839$	46.9210			1.61989			0.809946	+	0.586504i	$0.199496\pi$
$840$	−3.48667	+	4.12132i	−0.120301	+	0.142199i
$841$	28.9542			0.998421
$842$	20.5861	+	20.5861i	0.709445	+	0.709445i
$843$	−23.7397	+	23.7397i	−0.817638	+	0.817638i
$844$		−	19.5012i		−	0.671258i
$845$	0.734731	+	8.80769i	0.0252755	+	0.302994i
$846$	8.75470			0.300993
$847$	−14.7138	−	14.7138i	−0.505572	−	0.505572i
$848$	−2.93732	+	2.93732i	−0.100868	+	0.100868i
$849$	14.2188			0.487988
$850$	−6.29771	+	1.05806i	−0.216010	+	0.0362912i
$851$	−39.0261	−	29.4442i	−1.33780	−	1.00933i
$852$	1.59651	−	1.59651i	0.0546957	−	0.0546957i
$853$	−2.22294	−	2.22294i	−0.0761121	−	0.0761121i	0.668026	−	0.744138i	$-0.267140\pi$
$853$	−2.22294	−	2.22294i	−0.0761121	−	0.0761121i	−0.744138	+	0.668026i	$0.767140\pi$
$854$		−	10.4118i		−	0.356285i
$855$	0.707187	+	8.47750i	0.0241853	+	0.289925i
$856$		−	16.7879i		−	0.573800i
$857$	37.5650	−	37.5650i	1.28320	−	1.28320i	0.344358	−	0.938839i	$-0.388097\pi$
$857$	37.5650	−	37.5650i	1.28320	−	1.28320i	0.938839	−	0.344358i	$-0.111903\pi$
$858$	−1.67866	+	1.67866i	−0.0573085	+	0.0573085i
$859$			22.8026i			0.778016i	0.921234	+	0.389008i	$0.127182\pi$
$859$			22.8026i			0.778016i	−0.921234	+	0.389008i	$0.872818\pi$
$860$	18.9610	+	16.0411i	0.646564	+	0.546998i
$861$			8.05676i			0.274573i
$862$	18.7771	+	18.7771i	0.639549	+	0.639549i
$863$	−29.6759	−	29.6759i	−1.01018	−	1.01018i	−0.999948	−	0.0102318i	$-0.996743\pi$
$863$	−29.6759	−	29.6759i	−1.01018	−	1.01018i	−0.0102318	−	0.999948i	$-0.503257\pi$
$864$		−	5.51668i		−	0.187681i
$865$	24.1477	+	20.4291i	0.821047	+	0.694612i
$866$		−	3.06329i		−	0.104095i
$867$	−13.3487	+	13.3487i	−0.453345	+	0.453345i
$868$	−8.55997	+	8.55997i	−0.290544	+	0.290544i
$869$		−	3.98218i		−	0.135086i
$870$	−0.0488658	−	0.585786i	−0.00165671	−	0.0198600i
$871$		−	15.5421i		−	0.526624i
$872$	9.87191	+	9.87191i	0.334305	+	0.334305i
$873$	−16.0898	+	16.0898i	−0.544557	+	0.544557i
$874$	7.36911	−	9.76721i	0.249264	−	0.330381i
$875$	18.8958	+	11.2170i	0.638795	+	0.379204i
$876$	9.03591			0.305295
$877$	17.8883	−	17.8883i	0.604044	−	0.604044i	−0.337339	−	0.941383i	$-0.609527\pi$
$877$	17.8883	−	17.8883i	0.604044	−	0.604044i	0.941383	+	0.337339i	$0.109527\pi$
$878$	4.37015	+	4.37015i	0.147485	+	0.147485i
$879$	31.1810			1.05171
$880$	0.119439	+	1.43179i	0.00402629	+	0.0482658i
$881$		−	36.3203i		−	1.22366i	−0.790989	−	0.611831i	$-0.790433\pi$
$881$		−	36.3203i		−	1.22366i	0.790989	−	0.611831i	$-0.209567\pi$
$882$	−3.30781	+	3.30781i	−0.111380	+	0.111380i
$883$	11.7232	+	11.7232i	0.394518	+	0.394518i	0.876294	−	0.481776i	$-0.160008\pi$
$883$	11.7232	+	11.7232i	0.394518	+	0.394518i	−0.481776	+	0.876294i	$0.660008\pi$
$884$	3.84166			0.129209
$885$	−12.5637	+	14.8506i	−0.422326	+	0.499198i
$886$	−29.9195			−1.00517
$887$	−29.4426	+	29.4426i	−0.988586	+	0.988586i	−0.999936	−	0.0113493i	$-0.996387\pi$
$887$	−29.4426	+	29.4426i	−0.988586	+	0.988586i	0.0113493	+	0.999936i	$0.496387\pi$
$888$	8.85390	−	8.85390i	0.297117	−	0.297117i
$889$	−22.6083			−0.758257
$890$	−22.7562	+	26.8983i	−0.762788	+	0.901633i
$891$			1.47956i			0.0495671i
$892$	0.502862	−	0.502862i	0.0168371	−	0.0168371i
$893$	−10.5910	+	10.5910i	−0.354415	+	0.354415i
$894$	−3.18915			−0.106661
$895$	−2.01371	−	24.1396i	−0.0673107	−	0.806897i
$896$		−	1.96545i		−	0.0656610i
$897$	2.45572	+	17.5480i	0.0819940	+	0.585912i
$898$	26.5143	+	26.5143i	0.884795	+	0.884795i
$899$		−	1.31817i		−	0.0439634i
$900$	−7.35300	+	1.23536i	−0.245100	+	0.0411786i
$901$	−5.30545			−0.176750
$902$	1.51625	+	1.51625i	0.0504856	+	0.0504856i
$903$	18.9610	+	18.9610i	0.630982	+	0.630982i
$904$	−6.84421			−0.227635
$905$	−0.246131	−	2.95053i	−0.00818166	−	0.0980788i
$906$	−8.25781			−0.274347
$907$	12.5819	+	12.5819i	0.417775	+	0.417775i	0.884436	−	0.466661i	$-0.154543\pi$
$907$	12.5819	+	12.5819i	0.417775	+	0.417775i	−0.466661	+	0.884436i	$0.654543\pi$
$908$	17.7631	−	17.7631i	0.589489	−	0.589489i
$909$			15.3332i			0.508572i
$910$	−10.0922	−	8.53804i	−0.334552	−	0.283033i
$911$			42.6504i			1.41307i	0.707677	+	0.706536i	$0.249743\pi$
$911$			42.6504i			1.41307i	−0.707677	+	0.706536i	$0.750257\pi$
$912$	2.21590	+	2.21590i	0.0733757	+	0.0733757i
$913$	−3.88588	−	3.88588i	−0.128604	−	0.128604i
$914$	17.7364			0.586669
$915$	−9.39756	+	11.1081i	−0.310674	+	0.367223i
$916$		−	29.8213i		−	0.985324i
$917$	14.7236	+	14.7236i	0.486215	+	0.486215i
$918$	4.98218	−	4.98218i	0.164437	−	0.164437i
$919$	−18.4930			−0.610027			−0.305013	−	0.952348i	$-0.598661\pi$
$919$	−18.4930			−0.610027			−0.305013	+	0.952348i	$0.598661\pi$
$920$	9.06791	+	5.72477i	0.298960	+	0.188740i
$921$	−38.9482			−1.28339
$922$	1.59102	−	1.59102i	0.0523973	−	0.0523973i
$923$	3.90949	+	3.90949i	0.128682	+	0.128682i
$924$			1.55123i			0.0510318i
$925$	−41.5137	−	29.5709i	−1.36496	−	0.972286i
$926$	0.857751			0.0281875
$927$	−0.0851556	−	0.0851556i	−0.00279688	−	0.00279688i
$928$	0.151332	+	0.151332i	0.00496772	+	0.00496772i
$929$		−	42.1800i		−	1.38388i	−0.721955	−	0.691941i	$-0.756756\pi$
$929$		−	42.1800i		−	1.38388i	0.721955	−	0.691941i	$-0.243244\pi$
$930$	16.8585	−	1.40632i	0.552813	−	0.0461152i
$931$		−	8.00327i		−	0.262297i
$932$	20.1495	−	20.1495i	0.660020	−	0.660020i
$933$	9.49824	+	9.49824i	0.310958	+	0.310958i
$934$	6.05470			0.198116
$935$	−1.18520	+	1.40094i	−0.0387603	+	0.0458156i
$936$	4.48539			0.146610
$937$	−9.84986	−	9.84986i	−0.321781	−	0.321781i	0.527669	−	0.849450i	$-0.323066\pi$
$937$	−9.84986	−	9.84986i	−0.321781	−	0.321781i	−0.849450	+	0.527669i	$0.823066\pi$
$938$	−7.18115	−	7.18115i	−0.234473	−	0.234473i
$939$	27.1533			0.886114
$940$	−10.0222	−	8.47886i	−0.326888	−	0.276550i
$941$		−	3.04670i		−	0.0993196i	−0.998766	−	0.0496598i	$-0.984186\pi$
$941$		−	3.04670i		−	0.0993196i	0.998766	−	0.0496598i	$-0.0158137\pi$
$942$	−9.32351	−	9.32351i	−0.303776	−	0.303776i
$943$	15.8503	−	2.21813i	0.516156	−	0.0722322i
$944$		−	7.08223i		−	0.230507i
$945$	−24.1612	+	2.01551i	−0.785963	+	0.0655644i
$946$	7.13677			0.232036
$947$	−28.0876	+	28.0876i	−0.912725	+	0.912725i	−0.996486	−	0.0837611i	$-0.973307\pi$
$947$	−28.0876	+	28.0876i	−0.912725	+	0.912725i	0.0837611	+	0.996486i	$0.473307\pi$
$948$	5.38293	−	5.38293i	0.174829	−	0.174829i
$949$			22.1268i			0.718267i
$950$	7.40083	−	10.3898i	0.240114	−	0.337089i
$951$	−20.5115			−0.665130
$952$	1.77502	−	1.77502i	0.0575287	−	0.0575287i
$953$	−7.75178	+	7.75178i	−0.251105	+	0.251105i	−0.821424	−	0.570319i	$-0.806820\pi$
$953$	−7.75178	+	7.75178i	−0.251105	+	0.251105i	0.570319	+	0.821424i	$0.306820\pi$
$954$	−6.19447			−0.200554
$955$	0.459430	+	5.50748i	0.0148668	+	0.178218i
$956$	−20.2780			−0.655836
$957$	−0.119439	−	0.119439i	−0.00386092	−	0.00386092i
$958$	−24.7338	+	24.7338i	−0.799111	+	0.799111i
$959$		−	14.5441i		−	0.469654i
$960$	−1.77398	+	2.09689i	−0.0572550	+	0.0676768i
$961$	6.93601			0.223742
$962$	21.6811	+	21.6811i	0.699028	+	0.699028i
$963$	17.7020	−	17.7020i	0.570438	−	0.570438i
$964$	5.76782			0.185769
$965$	−42.0733	−	35.5943i	−1.35439	−	1.14582i
$966$	9.24264	+	6.97334i	0.297377	+	0.224363i
$967$	−12.0260	+	12.0260i	−0.386729	+	0.386729i	−0.873519	−	0.486790i	$-0.838168\pi$
$967$	−12.0260	+	12.0260i	−0.386729	+	0.386729i	0.486790	+	0.873519i	$0.338168\pi$
$968$	−7.48624	−	7.48624i	−0.240617	−	0.240617i
$969$			4.00241i			0.128576i
$970$	34.0021	−	2.83643i	1.09174	−	0.0910723i
$971$			4.87849i			0.156558i	0.996931	+	0.0782790i	$0.0249425\pi$
$971$			4.87849i			0.156558i	−0.996931	+	0.0782790i	$0.975057\pi$
$972$	9.70264	−	9.70264i	0.311212	−	0.311212i
$973$	−18.3725	+	18.3725i	−0.588997	+	0.588997i
$974$			35.3257i			1.13191i
$975$	3.06077	+	18.2181i	0.0980231	+	0.583445i
$976$		−	5.29743i		−	0.169567i
$977$	27.6900	+	27.6900i	0.885883	+	0.885883i	0.994125	−	0.108242i	$-0.0345221\pi$
$977$	27.6900	+	27.6900i	0.885883	+	0.885883i	−0.108242	+	0.994125i	$0.534522\pi$
$978$	4.09184	+	4.09184i	0.130842	+	0.130842i
$979$			10.1243i			0.323574i
$980$	6.99031	−	0.583126i	0.223297	−	0.0186273i
$981$			20.8188i			0.664692i
$982$	7.57876	−	7.57876i	0.241848	−	0.241848i
$983$	−16.5470	+	16.5470i	−0.527768	+	0.527768i	−0.919906	−	0.392139i	$-0.871735\pi$
$983$	−16.5470	+	16.5470i	−0.527768	+	0.527768i	0.392139	+	0.919906i	$0.371735\pi$
$984$			4.09920i			0.130678i
$985$	6.52382	−	7.71130i	0.207866	−	0.245702i
$986$			0.273340i			0.00870491i
$987$	−10.0222	−	10.0222i	−0.319010	−	0.319010i
$988$	−5.42622	+	5.42622i	−0.172631	+	0.172631i
$989$	32.0823	−	42.5227i	1.02016	−	1.35214i
$990$	−1.38381	+	1.63569i	−0.0439802	+	0.0519856i
$991$	12.2831			0.390187			0.195093	−	0.980785i	$-0.437499\pi$
$991$	12.2831			0.390187			0.195093	+	0.980785i	$0.437499\pi$
$992$	−4.35523	+	4.35523i	−0.138279	+	0.138279i
$993$	8.24264	+	8.24264i	0.261572	+	0.261572i
$994$	3.61272			0.114589
$995$	−52.6399	+	4.39118i	−1.66880	+	0.139210i
$996$		−	10.5055i		−	0.332880i
$997$	24.6017	−	24.6017i	0.779144	−	0.779144i	−0.200542	−	0.979685i	$-0.564270\pi$
$997$	24.6017	−	24.6017i	0.779144	−	0.779144i	0.979685	+	0.200542i	$0.0642702\pi$
$998$	22.6406	+	22.6406i	0.716677	+	0.716677i
$999$	56.2358			1.77922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.e.a.183.3	yes	8
5.2	odd	4		230.2.e.b.137.3	yes	8
5.3	odd	4		1150.2.e.b.1057.2		8
5.4	even	2		1150.2.e.c.643.2		8
23.22	odd	2		230.2.e.b.183.3	yes	8
115.22	even	4	inner	230.2.e.a.137.3	✓	8
115.68	even	4		1150.2.e.c.1057.2		8
115.114	odd	2		1150.2.e.b.643.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.a.137.3	✓	8	115.22	even	4	inner
230.2.e.a.183.3	yes	8	1.1	even	1	trivial
230.2.e.b.137.3	yes	8	5.2	odd	4
230.2.e.b.183.3	yes	8	23.22	odd	2
1150.2.e.b.643.2		8	115.114	odd	2
1150.2.e.b.1057.2		8	5.3	odd	4
1150.2.e.c.643.2		8	5.4	even	2
1150.2.e.c.1057.2		8	115.68	even	4

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.868559 - 0.868559i) q^{3} -1.00000i q^{4} +(-2.22833 + 0.185885i) q^{5} -1.22833 q^{6} +(-1.38978 - 1.38978i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.49121i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.868559 - 0.868559i) q^{3} -1.00000i q^{4} +(-2.22833 + 0.185885i) q^{5} -1.22833 q^{6} +(-1.38978 - 1.38978i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.49121i q^{9} +(-1.44423 + 1.70711i) q^{10} +0.642542i q^{11} +(-0.868559 + 0.868559i) q^{12} +(-2.12690 - 2.12690i) q^{13} -1.96545 q^{14} +(2.09689 + 1.77398i) q^{15} -1.00000 q^{16} +(-0.903113 - 0.903113i) q^{17} +(-1.05444 - 1.05444i) q^{18} +2.55123 q^{19} +(0.185885 + 2.22833i) q^{20} +2.41421i q^{21} +(0.454346 + 0.454346i) q^{22} +(4.74955 - 0.664664i) q^{23} +1.22833i q^{24} +(4.93089 - 0.828427i) q^{25} -3.00789 q^{26} +(-3.90088 + 3.90088i) q^{27} +(-1.38978 + 1.38978i) q^{28} -0.214016i q^{29} +(2.73712 - 0.228328i) q^{30} +6.15922 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.558086 - 0.558086i) q^{33} -1.27719 q^{34} +(3.35523 + 2.83855i) q^{35} -1.49121 q^{36} +(-7.20809 - 7.20809i) q^{37} +(1.80399 - 1.80399i) q^{38} +3.69468i q^{39} +(1.70711 + 1.44423i) q^{40} +3.33722 q^{41} +(1.70711 + 1.70711i) q^{42} +(7.85390 - 7.85390i) q^{43} +0.642542 q^{44} +(0.277194 + 3.32290i) q^{45} +(2.88845 - 3.82843i) q^{46} +(-4.15133 + 4.15133i) q^{47} +(0.868559 + 0.868559i) q^{48} -3.13702i q^{49} +(2.90088 - 4.07245i) q^{50} +1.56881i q^{51} +(-2.12690 + 2.12690i) q^{52} +(2.93732 - 2.93732i) q^{53} +5.51668i q^{54} +(-0.119439 - 1.43179i) q^{55} +1.96545i q^{56} +(-2.21590 - 2.21590i) q^{57} +(-0.151332 - 0.151332i) q^{58} +7.08223i q^{59} +(1.77398 - 2.09689i) q^{60} +5.29743i q^{61} +(4.35523 - 4.35523i) q^{62} +(-2.07245 + 2.07245i) q^{63} +1.00000i q^{64} +(5.13479 + 4.34407i) q^{65} -0.789252i q^{66} +(3.65370 + 3.65370i) q^{67} +(-0.903113 + 0.903113i) q^{68} +(-4.70257 - 3.54797i) q^{69} +(4.37966 - 0.365348i) q^{70} -1.83812 q^{71} +(-1.05444 + 1.05444i) q^{72} +(-5.20166 - 5.20166i) q^{73} -10.1938 q^{74} +(-5.00231 - 3.56323i) q^{75} -2.55123i q^{76} +(0.892992 - 0.892992i) q^{77} +(2.61253 + 2.61253i) q^{78} -6.19754 q^{79} +(2.22833 - 0.185885i) q^{80} +2.30266 q^{81} +(2.35977 - 2.35977i) q^{82} +(-6.04767 + 6.04767i) q^{83} +2.41421 q^{84} +(2.18031 + 1.84456i) q^{85} -11.1071i q^{86} +(-0.185885 + 0.185885i) q^{87} +(0.454346 - 0.454346i) q^{88} +15.7567 q^{89} +(2.54565 + 2.15364i) q^{90} +5.91185i q^{91} +(-0.664664 - 4.74955i) q^{92} +(-5.34965 - 5.34965i) q^{93} +5.87087i q^{94} +(-5.68498 + 0.474237i) q^{95} +1.22833 q^{96} +(-10.7898 - 10.7898i) q^{97} +(-2.21821 - 2.21821i) q^{98} +0.958165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6	\( 8 q - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{12} + 4 q^{14} - 8 q^{16} - 24 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 12 q^{22} + 16 q^{23} + 12 q^{26} + 8 q^{27} + 16 q^{30} - 4 q^{31} - 20 q^{33} + 4 q^{34} - 4 q^{35} - 4 q^{36} - 4 q^{37} - 8 q^{38} + 8 q^{40} + 12 q^{41} + 8 q^{42} + 20 q^{43} - 20 q^{44} - 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} - 20 q^{57} + 16 q^{58} - 8 q^{60} + 4 q^{62} - 12 q^{65} + 4 q^{67} - 24 q^{68} - 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} - 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} - 8 q^{79} + 4 q^{80} - 16 q^{81} + 8 q^{82} + 28 q^{83} + 8 q^{84} + 20 q^{85} - 4 q^{87} + 12 q^{88} + 40 q^{89} + 12 q^{90} - 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} + 8 q^{97} + 16 q^{98} + 36 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^12 + 4 * q^14 - 8 * q^16 - 24 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 12 * q^22 + 16 * q^23 + 12 * q^26 + 8 * q^27 + 16 * q^30 - 4 * q^31 - 20 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 - 4 * q^37 - 8 * q^38 + 8 * q^40 + 12 * q^41 + 8 * q^42 + 20 * q^43 - 20 * q^44 - 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 - 20 * q^57 + 16 * q^58 - 8 * q^60 + 4 * q^62 - 12 * q^65 + 4 * q^67 - 24 * q^68 - 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 - 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 - 8 * q^79 + 4 * q^80 - 16 * q^81 + 8 * q^82 + 28 * q^83 + 8 * q^84 + 20 * q^85 - 4 * q^87 + 12 * q^88 + 40 * q^89 + 12 * q^90 - 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 + 8 * q^97 + 16 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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