LMFDB - Embedded newform 336.2.s.a.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (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:	$2.68297350792$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	336.323
Dual form			336.2.s.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} -2.00000i q^{4} +(-2.41421 - 2.41421i) q^{5} +(2.41421 + 0.414214i) q^{6} -1.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} -2.00000i q^{4} +(-2.41421 - 2.41421i) q^{5} +(2.41421 + 0.414214i) q^{6} -1.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +4.82843 q^{10} +(1.82843 - 1.82843i) q^{11} +(-2.82843 + 2.00000i) q^{12} +(-1.58579 - 1.58579i) q^{13} +(1.00000 - 1.00000i) q^{14} +(-1.00000 + 5.82843i) q^{15} -4.00000 q^{16} +6.82843i q^{17} +(-1.82843 - 3.82843i) q^{18} +(-2.41421 + 2.41421i) q^{19} +(-4.82843 + 4.82843i) q^{20} +(1.00000 + 1.41421i) q^{21} +3.65685i q^{22} +3.65685i q^{23} +(0.828427 - 4.82843i) q^{24} +6.65685i q^{25} +3.17157 q^{26} +(5.00000 - 1.41421i) q^{27} +2.00000i q^{28} +(-3.00000 + 3.00000i) q^{29} +(-4.82843 - 6.82843i) q^{30} -10.4853i q^{31} +(4.00000 - 4.00000i) q^{32} +(-4.41421 - 0.757359i) q^{33} +(-6.82843 - 6.82843i) q^{34} +(2.41421 + 2.41421i) q^{35} +(5.65685 + 2.00000i) q^{36} +(-3.82843 + 3.82843i) q^{37} -4.82843i q^{38} +(-0.656854 + 3.82843i) q^{39} -9.65685i q^{40} -11.6569 q^{41} +(-2.41421 - 0.414214i) q^{42} +(1.82843 + 1.82843i) q^{43} +(-3.65685 - 3.65685i) q^{44} +(9.24264 - 4.41421i) q^{45} +(-3.65685 - 3.65685i) q^{46} +5.65685 q^{47} +(4.00000 + 5.65685i) q^{48} +1.00000 q^{49} +(-6.65685 - 6.65685i) q^{50} +(9.65685 - 6.82843i) q^{51} +(-3.17157 + 3.17157i) q^{52} +(-0.171573 - 0.171573i) q^{53} +(-3.58579 + 6.41421i) q^{54} -8.82843 q^{55} +(-2.00000 - 2.00000i) q^{56} +(5.82843 + 1.00000i) q^{57} -6.00000i q^{58} +(4.07107 - 4.07107i) q^{59} +(11.6569 + 2.00000i) q^{60} +(-0.414214 - 0.414214i) q^{61} +(10.4853 + 10.4853i) q^{62} +(1.00000 - 2.82843i) q^{63} +8.00000i q^{64} +7.65685i q^{65} +(5.17157 - 3.65685i) q^{66} +(-7.00000 + 7.00000i) q^{67} +13.6569 q^{68} +(5.17157 - 3.65685i) q^{69} -4.82843 q^{70} -6.00000i q^{71} +(-7.65685 + 3.65685i) q^{72} +10.8284i q^{73} -7.65685i q^{74} +(9.41421 - 6.65685i) q^{75} +(4.82843 + 4.82843i) q^{76} +(-1.82843 + 1.82843i) q^{77} +(-3.17157 - 4.48528i) q^{78} +2.00000i q^{79} +(9.65685 + 9.65685i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(11.6569 - 11.6569i) q^{82} +(-10.8995 - 10.8995i) q^{83} +(2.82843 - 2.00000i) q^{84} +(16.4853 - 16.4853i) q^{85} -3.65685 q^{86} +(7.24264 + 1.24264i) q^{87} +7.31371 q^{88} -4.34315 q^{89} +(-4.82843 + 13.6569i) q^{90} +(1.58579 + 1.58579i) q^{91} +7.31371 q^{92} +(-14.8284 + 10.4853i) q^{93} +(-5.65685 + 5.65685i) q^{94} +11.6569 q^{95} +(-9.65685 - 1.65685i) q^{96} -2.00000 q^{97} +(-1.00000 + 1.00000i) q^{98} +(3.34315 + 7.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 8 q^{10} - 4 q^{11} - 12 q^{13} + 4 q^{14} - 4 q^{15} - 16 q^{16} + 4 q^{18} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 8 q^{24} + 24 q^{26} + 20 q^{27} - 12 q^{29} - 8 q^{30} + 16 q^{32} - 12 q^{33} - 16 q^{34} + 4 q^{35} - 4 q^{37} + 20 q^{39} - 24 q^{41} - 4 q^{42} - 4 q^{43} + 8 q^{44} + 20 q^{45} + 8 q^{46} + 16 q^{48} + 4 q^{49} - 4 q^{50} + 16 q^{51} - 24 q^{52} - 12 q^{53} - 20 q^{54} - 24 q^{55} - 8 q^{56} + 12 q^{57} - 12 q^{59} + 24 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{63} + 32 q^{66} - 28 q^{67} + 32 q^{68} + 32 q^{69} - 8 q^{70} - 8 q^{72} + 32 q^{75} + 8 q^{76} + 4 q^{77} - 24 q^{78} + 16 q^{80} - 28 q^{81} + 24 q^{82} - 4 q^{83} + 32 q^{85} + 8 q^{86} + 12 q^{87} - 16 q^{88} - 40 q^{89} - 8 q^{90} + 12 q^{91} - 16 q^{92} - 48 q^{93} + 24 q^{95} - 16 q^{96} - 8 q^{97} - 4 q^{98} + 36 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 8 * q^10 - 4 * q^11 - 12 * q^13 + 4 * q^14 - 4 * q^15 - 16 * q^16 + 4 * q^18 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 8 * q^24 + 24 * q^26 + 20 * q^27 - 12 * q^29 - 8 * q^30 + 16 * q^32 - 12 * q^33 - 16 * q^34 + 4 * q^35 - 4 * q^37 + 20 * q^39 - 24 * q^41 - 4 * q^42 - 4 * q^43 + 8 * q^44 + 20 * q^45 + 8 * q^46 + 16 * q^48 + 4 * q^49 - 4 * q^50 + 16 * q^51 - 24 * q^52 - 12 * q^53 - 20 * q^54 - 24 * q^55 - 8 * q^56 + 12 * q^57 - 12 * q^59 + 24 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^63 + 32 * q^66 - 28 * q^67 + 32 * q^68 + 32 * q^69 - 8 * q^70 - 8 * q^72 + 32 * q^75 + 8 * q^76 + 4 * q^77 - 24 * q^78 + 16 * q^80 - 28 * q^81 + 24 * q^82 - 4 * q^83 + 32 * q^85 + 8 * q^86 + 12 * q^87 - 16 * q^88 - 40 * q^89 - 8 * q^90 + 12 * q^91 - 16 * q^92 - 48 * q^93 + 24 * q^95 - 16 * q^96 - 8 * q^97 - 4 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$		−	2.00000i		−	1.00000i
$5$	−2.41421	−	2.41421i	−1.07967	−	1.07967i	−0.996539	−	0.0831305i	$-0.973508\pi$
$5$	−2.41421	−	2.41421i	−1.07967	−	1.07967i	−0.0831305	−	0.996539i	$-0.526492\pi$
$6$	2.41421	+	0.414214i	0.985599	+	0.169102i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	4.82843			1.52688
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	−0.375522	−	0.926813i	$-0.622537\pi$
$11$	1.82843	−	1.82843i	0.551292	−	0.551292i	0.926813	+	0.375522i	$0.122537\pi$
$12$	−2.82843	+	2.00000i	−0.816497	+	0.577350i
$13$	−1.58579	−	1.58579i	−0.439818	−	0.439818i	0.452133	−	0.891951i	$-0.350663\pi$
$13$	−1.58579	−	1.58579i	−0.439818	−	0.439818i	−0.891951	+	0.452133i	$0.850663\pi$
$14$	1.00000	−	1.00000i	0.267261	−	0.267261i
$15$	−1.00000	+	5.82843i	−0.258199	+	1.50489i
$16$	−4.00000			−1.00000
$17$			6.82843i			1.65614i	0.560627	+	0.828068i	$0.310560\pi$
$17$			6.82843i			1.65614i	−0.560627	+	0.828068i	$0.689440\pi$
$18$	−1.82843	−	3.82843i	−0.430964	−	0.902369i
$19$	−2.41421	+	2.41421i	−0.553859	+	0.553859i	−0.927552	−	0.373694i	$-0.878091\pi$
$19$	−2.41421	+	2.41421i	−0.553859	+	0.553859i	0.373694	+	0.927552i	$0.378091\pi$
$20$	−4.82843	+	4.82843i	−1.07967	+	1.07967i
$21$	1.00000	+	1.41421i	0.218218	+	0.308607i
$22$			3.65685i			0.779644i
$23$			3.65685i			0.762507i	0.924471	+	0.381253i	$0.124507\pi$
$23$			3.65685i			0.762507i	−0.924471	+	0.381253i	$0.875493\pi$
$24$	0.828427	−	4.82843i	0.169102	−	0.985599i
$25$			6.65685i			1.33137i
$26$	3.17157			0.621997
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$			2.00000i			0.377964i
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−3.00000	+	3.00000i	−0.557086	+	0.557086i	0.371391	+	0.928477i	$0.378881\pi$
$30$	−4.82843	−	6.82843i	−0.881546	−	1.24669i
$31$		−	10.4853i		−	1.88321i	−0.336717	−	0.941606i	$-0.609316\pi$
$31$		−	10.4853i		−	1.88321i	0.336717	−	0.941606i	$-0.390684\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−4.41421	−	0.757359i	−0.768416	−	0.131839i
$34$	−6.82843	−	6.82843i	−1.17107	−	1.17107i
$35$	2.41421	+	2.41421i	0.408077	+	0.408077i
$36$	5.65685	+	2.00000i	0.942809	+	0.333333i
$37$	−3.82843	+	3.82843i	−0.629390	+	0.629390i	−0.947914	−	0.318525i	$-0.896813\pi$
$37$	−3.82843	+	3.82843i	−0.629390	+	0.629390i	0.318525	+	0.947914i	$0.396813\pi$
$38$		−	4.82843i		−	0.783274i
$39$	−0.656854	+	3.82843i	−0.105181	+	0.613039i
$40$		−	9.65685i		−	1.52688i
$41$	−11.6569			−1.82049			−0.910247	−	0.414065i	$-0.864109\pi$
$41$	−11.6569			−1.82049			−0.910247	+	0.414065i	$0.864109\pi$
$42$	−2.41421	−	0.414214i	−0.372521	−	0.0639145i
$43$	1.82843	+	1.82843i	0.278833	+	0.278833i	0.832643	−	0.553810i	$-0.186827\pi$
$43$	1.82843	+	1.82843i	0.278833	+	0.278833i	−0.553810	+	0.832643i	$0.686827\pi$
$44$	−3.65685	−	3.65685i	−0.551292	−	0.551292i
$45$	9.24264	−	4.41421i	1.37781	−	0.658032i
$46$	−3.65685	−	3.65685i	−0.539174	−	0.539174i
$47$	5.65685			0.825137			0.412568	−	0.910927i	$-0.364632\pi$
$47$	5.65685			0.825137			0.412568	+	0.910927i	$0.364632\pi$
$48$	4.00000	+	5.65685i	0.577350	+	0.816497i
$49$	1.00000			0.142857
$50$	−6.65685	−	6.65685i	−0.941421	−	0.941421i
$51$	9.65685	−	6.82843i	1.35223	−	0.956171i
$52$	−3.17157	+	3.17157i	−0.439818	+	0.439818i
$53$	−0.171573	−	0.171573i	−0.0235673	−	0.0235673i	0.695225	−	0.718792i	$-0.255305\pi$
$53$	−0.171573	−	0.171573i	−0.0235673	−	0.0235673i	−0.718792	+	0.695225i	$0.755305\pi$
$54$	−3.58579	+	6.41421i	−0.487964	+	0.872864i
$55$	−8.82843			−1.19042
$56$	−2.00000	−	2.00000i	−0.267261	−	0.267261i
$57$	5.82843	+	1.00000i	0.771994	+	0.132453i
$58$		−	6.00000i		−	0.787839i
$59$	4.07107	−	4.07107i	0.530008	−	0.530008i	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	4.07107	−	4.07107i	0.530008	−	0.530008i	0.920575	+	0.390567i	$0.127721\pi$
$60$	11.6569	+	2.00000i	1.50489	+	0.258199i
$61$	−0.414214	−	0.414214i	−0.0530346	−	0.0530346i	0.680092	−	0.733127i	$-0.261940\pi$
$61$	−0.414214	−	0.414214i	−0.0530346	−	0.0530346i	−0.733127	+	0.680092i	$0.761940\pi$
$62$	10.4853	+	10.4853i	1.33163	+	1.33163i
$63$	1.00000	−	2.82843i	0.125988	−	0.356348i
$64$			8.00000i			1.00000i
$65$			7.65685i			0.949716i
$66$	5.17157	−	3.65685i	0.636577	−	0.450128i
$67$	−7.00000	+	7.00000i	−0.855186	+	0.855186i	−0.990766	−	0.135580i	$-0.956710\pi$
$67$	−7.00000	+	7.00000i	−0.855186	+	0.855186i	0.135580	+	0.990766i	$0.456710\pi$
$68$	13.6569			1.65614
$69$	5.17157	−	3.65685i	0.622584	−	0.440234i
$70$	−4.82843			−0.577107
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	−7.65685	+	3.65685i	−0.902369	+	0.430964i
$73$			10.8284i			1.26737i	0.773591	+	0.633686i	$0.218459\pi$
$73$			10.8284i			1.26737i	−0.773591	+	0.633686i	$0.781541\pi$
$74$		−	7.65685i		−	0.890091i
$75$	9.41421	−	6.65685i	1.08706	−	0.768667i
$76$	4.82843	+	4.82843i	0.553859	+	0.553859i
$77$	−1.82843	+	1.82843i	−0.208369	+	0.208369i
$78$	−3.17157	−	4.48528i	−0.359110	−	0.507858i
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$	9.65685	+	9.65685i	1.07967	+	1.07967i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	11.6569	−	11.6569i	1.28728	−	1.28728i
$83$	−10.8995	−	10.8995i	−1.19637	−	1.19637i	−0.975244	−	0.221131i	$-0.929025\pi$
$83$	−10.8995	−	10.8995i	−1.19637	−	1.19637i	−0.221131	−	0.975244i	$-0.570975\pi$
$84$	2.82843	−	2.00000i	0.308607	−	0.218218i
$85$	16.4853	−	16.4853i	1.78808	−	1.78808i
$86$	−3.65685			−0.394329
$87$	7.24264	+	1.24264i	0.776493	+	0.133225i
$88$	7.31371			0.779644
$89$	−4.34315			−0.460373			−0.230186	−	0.973147i	$-0.573934\pi$
$89$	−4.34315			−0.460373			−0.230186	+	0.973147i	$0.573934\pi$
$90$	−4.82843	+	13.6569i	−0.508961	+	1.43956i
$91$	1.58579	+	1.58579i	0.166236	+	0.166236i
$92$	7.31371			0.762507
$93$	−14.8284	+	10.4853i	−1.53764	+	1.08727i
$94$	−5.65685	+	5.65685i	−0.583460	+	0.583460i
$95$	11.6569			1.19597
$96$	−9.65685	−	1.65685i	−0.985599	−	0.169102i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	+	1.00000i	−0.101015	+	0.101015i
$99$	3.34315	+	7.00000i	0.335999	+	0.703526i
$100$	13.3137			1.33137
$101$	−4.07107	−	4.07107i	−0.405086	−	0.405086i	0.474935	−	0.880021i	$-0.342472\pi$
$101$	−4.07107	−	4.07107i	−0.405086	−	0.405086i	−0.880021	+	0.474935i	$0.842472\pi$
$102$	−2.82843	+	16.4853i	−0.280056	+	1.63229i
$103$	−11.3137			−1.11477			−0.557386	−	0.830253i	$-0.688196\pi$
$103$	−11.3137			−1.11477			−0.557386	+	0.830253i	$0.688196\pi$
$104$		−	6.34315i		−	0.621997i
$105$	1.00000	−	5.82843i	0.0975900	−	0.568796i
$106$	0.343146			0.0333293
$107$	−5.00000	+	5.00000i	−0.483368	+	0.483368i	−0.906206	−	0.422837i	$-0.861034\pi$
$107$	−5.00000	+	5.00000i	−0.483368	+	0.483368i	0.422837	+	0.906206i	$0.361034\pi$
$108$	−2.82843	−	10.0000i	−0.272166	−	0.962250i
$109$	0.171573	+	0.171573i	0.0164337	+	0.0164337i	0.715276	−	0.698842i	$-0.246301\pi$
$109$	0.171573	+	0.171573i	0.0164337	+	0.0164337i	−0.698842	+	0.715276i	$0.746301\pi$
$110$	8.82843	−	8.82843i	0.841757	−	0.841757i
$111$	9.24264	+	1.58579i	0.877273	+	0.150516i
$112$	4.00000			0.377964
$113$		−	9.65685i		−	0.908440i	−0.890889	−	0.454220i	$-0.849918\pi$
$113$		−	9.65685i		−	0.908440i	0.890889	−	0.454220i	$-0.150082\pi$
$114$	−6.82843	+	4.82843i	−0.639541	+	0.452224i
$115$	8.82843	−	8.82843i	0.823255	−	0.823255i
$116$	6.00000	+	6.00000i	0.557086	+	0.557086i
$117$	6.07107	−	2.89949i	0.561270	−	0.268058i
$118$			8.14214i			0.749544i
$119$		−	6.82843i		−	0.625961i
$120$	−13.6569	+	9.65685i	−1.24669	+	0.881546i
$121$			4.31371i			0.392155i
$122$	0.828427			0.0750023
$123$	11.6569	+	16.4853i	1.05106	+	1.48643i
$124$	−20.9706			−1.88321
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	1.82843	+	3.82843i	0.162889	+	0.341063i
$127$		−	4.34315i		−	0.385392i	−0.981259	−	0.192696i	$-0.938277\pi$
$127$		−	4.34315i		−	0.385392i	0.981259	−	0.192696i	$-0.0617231\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	0.757359	−	4.41421i	0.0666818	−	0.388650i
$130$	−7.65685	−	7.65685i	−0.671551	−	0.671551i
$131$	10.0711	+	10.0711i	0.879913	+	0.879913i	0.993525	−	0.113612i	$-0.0362421\pi$
$131$	10.0711	+	10.0711i	0.879913	+	0.879913i	−0.113612	+	0.993525i	$0.536242\pi$
$132$	−1.51472	+	8.82843i	−0.131839	+	0.768416i
$133$	2.41421	−	2.41421i	0.209339	−	0.209339i
$134$		−	14.0000i		−	1.20942i
$135$	−15.4853	−	8.65685i	−1.33276	−	0.745063i
$136$	−13.6569	+	13.6569i	−1.17107	+	1.17107i
$137$	3.65685			0.312426			0.156213	−	0.987723i	$-0.450071\pi$
$137$	3.65685			0.312426			0.156213	+	0.987723i	$0.450071\pi$
$138$	−1.51472	+	8.82843i	−0.128941	+	0.751526i
$139$	−1.58579	−	1.58579i	−0.134505	−	0.134505i	0.636649	−	0.771154i	$-0.280320\pi$
$139$	−1.58579	−	1.58579i	−0.134505	−	0.134505i	−0.771154	+	0.636649i	$0.780320\pi$
$140$	4.82843	−	4.82843i	0.408077	−	0.408077i
$141$	−5.65685	−	8.00000i	−0.476393	−	0.673722i
$142$	6.00000	+	6.00000i	0.503509	+	0.503509i
$143$	−5.79899			−0.484936
$144$	4.00000	−	11.3137i	0.333333	−	0.942809i
$145$	14.4853			1.20294
$146$	−10.8284	−	10.8284i	−0.896167	−	0.896167i
$147$	−1.00000	−	1.41421i	−0.0824786	−	0.116642i
$148$	7.65685	+	7.65685i	0.629390	+	0.629390i
$149$	−7.48528	−	7.48528i	−0.613218	−	0.613218i	0.330565	−	0.943783i	$-0.392761\pi$
$149$	−7.48528	−	7.48528i	−0.613218	−	0.613218i	−0.943783	+	0.330565i	$0.892761\pi$
$150$	−2.75736	+	16.0711i	−0.225137	+	1.31220i
$151$	−6.34315			−0.516198			−0.258099	−	0.966118i	$-0.583096\pi$
$151$	−6.34315			−0.516198			−0.258099	+	0.966118i	$0.583096\pi$
$152$	−9.65685			−0.783274
$153$	−19.3137	−	6.82843i	−1.56142	−	0.552046i
$154$		−	3.65685i		−	0.294678i
$155$	−25.3137	+	25.3137i	−2.03325	+	2.03325i
$156$	7.65685	+	1.31371i	0.613039	+	0.105181i
$157$	−16.8995	−	16.8995i	−1.34873	−	1.34873i	−0.887047	−	0.461680i	$-0.847247\pi$
$157$	−16.8995	−	16.8995i	−1.34873	−	1.34873i	−0.461680	−	0.887047i	$-0.652753\pi$
$158$	−2.00000	−	2.00000i	−0.159111	−	0.159111i
$159$	−0.0710678	+	0.414214i	−0.00563604	+	0.0328493i
$160$	−19.3137			−1.52688
$161$		−	3.65685i		−	0.288200i
$162$	12.6569	−	1.34315i	0.994416	−	0.105527i
$163$	3.82843	−	3.82843i	0.299866	−	0.299866i	−0.541096	−	0.840961i	$-0.681990\pi$
$163$	3.82843	−	3.82843i	0.299866	−	0.299866i	0.840961	+	0.541096i	$0.181990\pi$
$164$			23.3137i			1.82049i
$165$	8.82843	+	12.4853i	0.687292	+	0.971978i
$166$	21.7990			1.69193
$167$			12.8284i			0.992693i	0.868124	+	0.496347i	$0.165326\pi$
$167$			12.8284i			0.992693i	−0.868124	+	0.496347i	$0.834674\pi$
$168$	−0.828427	+	4.82843i	−0.0639145	+	0.372521i
$169$		−	7.97056i		−	0.613120i
$170$			32.9706i			2.52873i
$171$	−4.41421	−	9.24264i	−0.337563	−	0.706802i
$172$	3.65685	−	3.65685i	0.278833	−	0.278833i
$173$	−14.8995	+	14.8995i	−1.13279	+	1.13279i	−0.143076	+	0.989712i	$0.545699\pi$
$173$	−14.8995	+	14.8995i	−1.13279	+	1.13279i	−0.989712	+	0.143076i	$0.954301\pi$
$174$	−8.48528	+	6.00000i	−0.643268	+	0.454859i
$175$		−	6.65685i		−	0.503211i
$176$	−7.31371	+	7.31371i	−0.551292	+	0.551292i
$177$	−9.82843	−	1.68629i	−0.738750	−	0.126749i
$178$	4.34315	−	4.34315i	0.325533	−	0.325533i
$179$	−15.0000	−	15.0000i	−1.12115	−	1.12115i	−0.991568	−	0.129584i	$-0.958636\pi$
$179$	−15.0000	−	15.0000i	−1.12115	−	1.12115i	−0.129584	−	0.991568i	$-0.541364\pi$
$180$	−8.82843	−	18.4853i	−0.658032	−	1.37781i
$181$	12.0711	−	12.0711i	0.897235	−	0.897235i	−0.0979554	−	0.995191i	$-0.531230\pi$
$181$	12.0711	−	12.0711i	0.897235	−	0.897235i	0.995191	+	0.0979554i	$0.0312303\pi$
$182$	−3.17157			−0.235093
$183$	−0.171573	+	1.00000i	−0.0126830	+	0.0739221i
$184$	−7.31371	+	7.31371i	−0.539174	+	0.539174i
$185$	18.4853			1.35906
$186$	4.34315	−	25.3137i	0.318455	−	1.85609i
$187$	12.4853	+	12.4853i	0.913014	+	0.913014i
$188$		−	11.3137i		−	0.825137i
$189$	−5.00000	+	1.41421i	−0.363696	+	0.102869i
$190$	−11.6569	+	11.6569i	−0.845677	+	0.845677i
$191$	−17.6569			−1.27761			−0.638803	−	0.769371i	$-0.720570\pi$
$191$	−17.6569			−1.27761			−0.638803	+	0.769371i	$0.720570\pi$
$192$	11.3137	−	8.00000i	0.816497	−	0.577350i
$193$	4.34315			0.312626			0.156313	−	0.987708i	$-0.450039\pi$
$193$	4.34315			0.312626			0.156313	+	0.987708i	$0.450039\pi$
$194$	2.00000	−	2.00000i	0.143592	−	0.143592i
$195$	10.8284	−	7.65685i	0.775440	−	0.548319i
$196$		−	2.00000i		−	0.142857i
$197$	−0.171573	−	0.171573i	−0.0122241	−	0.0122241i	0.700968	−	0.713192i	$-0.252751\pi$
$197$	−0.171573	−	0.171573i	−0.0122241	−	0.0122241i	−0.713192	+	0.700968i	$0.752751\pi$
$198$	−10.3431	−	3.65685i	−0.735055	−	0.259881i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−13.3137	+	13.3137i	−0.941421	+	0.941421i
$201$	16.8995	+	2.89949i	1.19200	+	0.204515i
$202$	8.14214			0.572879
$203$	3.00000	−	3.00000i	0.210559	−	0.210559i
$204$	−13.6569	−	19.3137i	−0.956171	−	1.35223i
$205$	28.1421	+	28.1421i	1.96553	+	1.96553i
$206$	11.3137	−	11.3137i	0.788263	−	0.788263i
$207$	−10.3431	−	3.65685i	−0.718898	−	0.254169i
$208$	6.34315	+	6.34315i	0.439818	+	0.439818i
$209$			8.82843i			0.610675i
$210$	4.82843	+	6.82843i	0.333193	+	0.471206i
$211$	5.00000	−	5.00000i	0.344214	−	0.344214i	−0.513735	−	0.857949i	$-0.671738\pi$
$211$	5.00000	−	5.00000i	0.344214	−	0.344214i	0.857949	+	0.513735i	$0.171738\pi$
$212$	−0.343146	+	0.343146i	−0.0235673	+	0.0235673i
$213$	−8.48528	+	6.00000i	−0.581402	+	0.411113i
$214$		−	10.0000i		−	0.683586i
$215$		−	8.82843i		−	0.602094i
$216$	12.8284	+	7.17157i	0.872864	+	0.487964i
$217$			10.4853i			0.711787i
$218$	−0.343146			−0.0232408
$219$	15.3137	−	10.8284i	1.03480	−	0.731717i
$220$			17.6569i			1.19042i
$221$	10.8284	−	10.8284i	0.728399	−	0.728399i
$222$	−10.8284	+	7.65685i	−0.726756	+	0.513894i
$223$		−	12.8284i		−	0.859055i	−0.903054	−	0.429528i	$-0.858680\pi$
$223$		−	12.8284i		−	0.859055i	0.903054	−	0.429528i	$-0.141320\pi$
$224$	−4.00000	+	4.00000i	−0.267261	+	0.267261i
$225$	−18.8284	−	6.65685i	−1.25523	−	0.443790i
$226$	9.65685	+	9.65685i	0.642364	+	0.642364i
$227$	6.07107	+	6.07107i	0.402951	+	0.402951i	0.879272	−	0.476321i	$-0.158030\pi$
$227$	6.07107	+	6.07107i	0.402951	+	0.402951i	−0.476321	+	0.879272i	$0.658030\pi$
$228$	2.00000	−	11.6569i	0.132453	−	0.771994i
$229$	−8.89949	+	8.89949i	−0.588095	+	0.588095i	−0.937115	−	0.349020i	$-0.886515\pi$
$229$	−8.89949	+	8.89949i	−0.588095	+	0.588095i	0.349020	+	0.937115i	$0.386515\pi$
$230$			17.6569i			1.16426i
$231$	4.41421	+	0.757359i	0.290434	+	0.0498306i
$232$	−12.0000			−0.787839
$233$	21.3137			1.39631			0.698154	−	0.715948i	$-0.254005\pi$
$233$	21.3137			1.39631			0.698154	+	0.715948i	$0.254005\pi$
$234$	−3.17157	+	8.97056i	−0.207332	+	0.586424i
$235$	−13.6569	−	13.6569i	−0.890875	−	0.890875i
$236$	−8.14214	−	8.14214i	−0.530008	−	0.530008i
$237$	2.82843	−	2.00000i	0.183726	−	0.129914i
$238$	6.82843	+	6.82843i	0.442621	+	0.442621i
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$	4.00000	−	23.3137i	0.258199	−	1.50489i
$241$	11.6569			0.750884			0.375442	−	0.926846i	$-0.377491\pi$
$241$	11.6569			0.750884			0.375442	+	0.926846i	$0.377491\pi$
$242$	−4.31371	−	4.31371i	−0.277296	−	0.277296i
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$	−0.828427	+	0.828427i	−0.0530346	+	0.0530346i
$245$	−2.41421	−	2.41421i	−0.154238	−	0.154238i
$246$	−28.1421	−	4.82843i	−1.79428	−	0.307849i
$247$	7.65685			0.487194
$248$	20.9706	−	20.9706i	1.33163	−	1.33163i
$249$	−4.51472	+	26.3137i	−0.286109	+	1.66756i
$250$			8.00000i			0.505964i
$251$	−0.414214	+	0.414214i	−0.0261449	+	0.0261449i	−0.720058	−	0.693913i	$-0.755885\pi$
$251$	−0.414214	+	0.414214i	−0.0261449	+	0.0261449i	0.693913	+	0.720058i	$0.255885\pi$
$252$	−5.65685	−	2.00000i	−0.356348	−	0.125988i
$253$	6.68629	+	6.68629i	0.420364	+	0.420364i
$254$	4.34315	+	4.34315i	0.272513	+	0.272513i
$255$	−39.7990	−	6.82843i	−2.49231	−	0.427613i
$256$	16.0000			1.00000
$257$			21.1716i			1.32065i	0.750982	+	0.660323i	$0.229581\pi$
$257$			21.1716i			1.32065i	−0.750982	+	0.660323i	$0.770419\pi$
$258$	3.65685	+	5.17157i	0.227666	+	0.321968i
$259$	3.82843	−	3.82843i	0.237887	−	0.237887i
$260$	15.3137			0.949716
$261$	−5.48528	−	11.4853i	−0.339530	−	0.710921i
$262$	−20.1421			−1.24439
$263$		−	0.343146i		−	0.0211593i	−0.999944	−	0.0105796i	$-0.996632\pi$
$263$		−	0.343146i		−	0.0211593i	0.999944	−	0.0105796i	$-0.00336767\pi$
$264$	−7.31371	−	10.3431i	−0.450128	−	0.636577i
$265$			0.828427i			0.0508899i
$266$			4.82843i			0.296050i
$267$	4.34315	+	6.14214i	0.265796	+	0.375893i
$268$	14.0000	+	14.0000i	0.855186	+	0.855186i
$269$	8.41421	−	8.41421i	0.513024	−	0.513024i	−0.402428	−	0.915452i	$-0.631834\pi$
$269$	8.41421	−	8.41421i	0.513024	−	0.513024i	0.915452	+	0.402428i	$0.131834\pi$
$270$	24.1421	−	6.82843i	1.46924	−	0.415565i
$271$			11.1716i			0.678625i	0.940674	+	0.339312i	$0.110194\pi$
$271$			11.1716i			0.678625i	−0.940674	+	0.339312i	$0.889806\pi$
$272$		−	27.3137i		−	1.65614i
$273$	0.656854	−	3.82843i	0.0397546	−	0.231707i
$274$	−3.65685	+	3.65685i	−0.220919	+	0.220919i
$275$	12.1716	+	12.1716i	0.733973	+	0.733973i
$276$	−7.31371	−	10.3431i	−0.440234	−	0.622584i
$277$	−16.3137	+	16.3137i	−0.980196	+	0.980196i	−0.999808	−	0.0196119i	$-0.993757\pi$
$277$	−16.3137	+	16.3137i	−0.980196	+	0.980196i	0.0196119	+	0.999808i	$0.493757\pi$
$278$	3.17157			0.190218
$279$	29.6569	+	10.4853i	1.77551	+	0.627737i
$280$			9.65685i			0.577107i
$281$	29.3137			1.74871			0.874355	−	0.485288i	$-0.161285\pi$
$281$	29.3137			1.74871			0.874355	+	0.485288i	$0.161285\pi$
$282$	13.6569	+	2.34315i	0.813254	+	0.139532i
$283$	6.89949	+	6.89949i	0.410132	+	0.410132i	0.881785	−	0.471652i	$-0.156342\pi$
$283$	6.89949	+	6.89949i	0.410132	+	0.410132i	−0.471652	+	0.881785i	$0.656342\pi$
$284$	−12.0000			−0.712069
$285$	−11.6569	−	16.4853i	−0.690492	−	0.976504i
$286$	5.79899	−	5.79899i	0.342901	−	0.342901i
$287$	11.6569			0.688082
$288$	7.31371	+	15.3137i	0.430964	+	0.902369i
$289$	−29.6274			−1.74279
$290$	−14.4853	+	14.4853i	−0.850605	+	0.850605i
$291$	2.00000	+	2.82843i	0.117242	+	0.165805i
$292$	21.6569			1.26737
$293$	−0.757359	−	0.757359i	−0.0442454	−	0.0442454i	0.684638	−	0.728883i	$-0.259960\pi$
$293$	−0.757359	−	0.757359i	−0.0442454	−	0.0442454i	−0.728883	+	0.684638i	$0.759960\pi$
$294$	2.41421	+	0.414214i	0.140800	+	0.0241574i
$295$	−19.6569			−1.14447
$296$	−15.3137			−0.890091
$297$	6.55635	−	11.7279i	0.380438	−	0.680523i
$298$	14.9706			0.867221
$299$	5.79899	−	5.79899i	0.335364	−	0.335364i
$300$	−13.3137	−	18.8284i	−0.768667	−	1.08706i
$301$	−1.82843	−	1.82843i	−0.105389	−	0.105389i
$302$	6.34315	−	6.34315i	0.365007	−	0.365007i
$303$	−1.68629	+	9.82843i	−0.0968749	+	0.564628i
$304$	9.65685	−	9.65685i	0.553859	−	0.553859i
$305$			2.00000i			0.114520i
$306$	26.1421	−	12.4853i	1.49445	−	0.713736i
$307$	4.89949	−	4.89949i	0.279629	−	0.279629i	−0.553332	−	0.832961i	$-0.686644\pi$
$307$	4.89949	−	4.89949i	0.279629	−	0.279629i	0.832961	+	0.553332i	$0.186644\pi$
$308$	3.65685	+	3.65685i	0.208369	+	0.208369i
$309$	11.3137	+	16.0000i	0.643614	+	0.910208i
$310$		−	50.6274i		−	2.87544i
$311$			18.4853i			1.04820i	0.851655	+	0.524102i	$0.175599\pi$
$311$			18.4853i			1.04820i	−0.851655	+	0.524102i	$0.824401\pi$
$312$	−8.97056	+	6.34315i	−0.507858	+	0.359110i
$313$			3.51472i			0.198664i	0.995054	+	0.0993318i	$0.0316705\pi$
$313$			3.51472i			0.198664i	−0.995054	+	0.0993318i	$0.968329\pi$
$314$	33.7990			1.90739
$315$	−9.24264	+	4.41421i	−0.520764	+	0.248713i
$316$	4.00000			0.225018
$317$	15.1421	−	15.1421i	0.850467	−	0.850467i	−0.139723	−	0.990191i	$-0.544621\pi$
$317$	15.1421	−	15.1421i	0.850467	−	0.850467i	0.990191	+	0.139723i	$0.0446214\pi$
$318$	−0.343146	−	0.485281i	−0.0192427	−	0.0272132i
$319$			10.9706i			0.614234i
$320$	19.3137	−	19.3137i	1.07967	−	1.07967i
$321$	12.0711	+	2.07107i	0.673741	+	0.115596i
$322$	3.65685	+	3.65685i	0.203789	+	0.203789i
$323$	−16.4853	−	16.4853i	−0.917266	−	0.917266i
$324$	−11.3137	+	14.0000i	−0.628539	+	0.777778i
$325$	10.5563	−	10.5563i	0.585561	−	0.585561i
$326$			7.65685i			0.424074i
$327$	0.0710678	−	0.414214i	0.00393006	−	0.0229061i
$328$	−23.3137	−	23.3137i	−1.28728	−	1.28728i
$329$	−5.65685			−0.311872
$330$	−21.3137	−	3.65685i	−1.17328	−	0.201303i
$331$	−11.1421	−	11.1421i	−0.612427	−	0.612427i	0.331151	−	0.943578i	$-0.392563\pi$
$331$	−11.1421	−	11.1421i	−0.612427	−	0.612427i	−0.943578	+	0.331151i	$0.892563\pi$
$332$	−21.7990	+	21.7990i	−1.19637	+	1.19637i
$333$	−7.00000	−	14.6569i	−0.383598	−	0.803191i
$334$	−12.8284	−	12.8284i	−0.701940	−	0.701940i
$335$	33.7990			1.84664
$336$	−4.00000	−	5.65685i	−0.218218	−	0.308607i
$337$	2.68629			0.146332			0.0731658	−	0.997320i	$-0.476690\pi$
$337$	2.68629			0.146332			0.0731658	+	0.997320i	$0.476690\pi$
$338$	7.97056	+	7.97056i	0.433541	+	0.433541i
$339$	−13.6569	+	9.65685i	−0.741739	+	0.524488i
$340$	−32.9706	−	32.9706i	−1.78808	−	1.78808i
$341$	−19.1716	−	19.1716i	−1.03820	−	1.03820i
$342$	13.6569	+	4.82843i	0.738478	+	0.261091i
$343$	−1.00000			−0.0539949
$344$			7.31371i			0.394329i
$345$	−21.3137	−	3.65685i	−1.14749	−	0.196878i
$346$		−	29.7990i		−	1.60200i
$347$	−15.1421	+	15.1421i	−0.812872	+	0.812872i	−0.985064	−	0.172191i	$-0.944915\pi$
$347$	−15.1421	+	15.1421i	−0.812872	+	0.812872i	0.172191	+	0.985064i	$0.444915\pi$
$348$	2.48528	−	14.4853i	0.133225	−	0.776493i
$349$	12.0711	+	12.0711i	0.646149	+	0.646149i	0.952060	−	0.305911i	$-0.0989609\pi$
$349$	12.0711	+	12.0711i	0.646149	+	0.646149i	−0.305911	+	0.952060i	$0.598961\pi$
$350$	6.65685	+	6.65685i	0.355824	+	0.355824i
$351$	−10.1716	−	5.68629i	−0.542918	−	0.303512i
$352$		−	14.6274i		−	0.779644i
$353$			8.48528i			0.451626i	0.974171	+	0.225813i	$0.0725038\pi$
$353$			8.48528i			0.451626i	−0.974171	+	0.225813i	$0.927496\pi$
$354$	11.5147	−	8.14214i	0.612000	−	0.432750i
$355$	−14.4853	+	14.4853i	−0.768799	+	0.768799i
$356$			8.68629i			0.460373i
$357$	−9.65685	+	6.82843i	−0.511095	+	0.361399i
$358$	30.0000			1.58555
$359$		−	31.6569i		−	1.67078i	−0.549654	−	0.835392i	$-0.685240\pi$
$359$		−	31.6569i		−	1.67078i	0.549654	−	0.835392i	$-0.314760\pi$
$360$	27.3137	+	9.65685i	1.43956	+	0.508961i
$361$			7.34315i			0.386481i
$362$			24.1421i			1.26888i
$363$	6.10051	−	4.31371i	0.320193	−	0.226411i
$364$	3.17157	−	3.17157i	0.166236	−	0.166236i
$365$	26.1421	−	26.1421i	1.36834	−	1.36834i
$366$	−0.828427	−	1.17157i	−0.0433026	−	0.0612391i
$367$			12.1421i			0.633814i	0.948457	+	0.316907i	$0.102644\pi$
$367$			12.1421i			0.633814i	−0.948457	+	0.316907i	$0.897356\pi$
$368$		−	14.6274i		−	0.762507i
$369$	11.6569	−	32.9706i	0.606832	−	1.71638i
$370$	−18.4853	+	18.4853i	−0.961004	+	0.961004i
$371$	0.171573	+	0.171573i	0.00890762	+	0.00890762i
$372$	20.9706	+	29.6569i	1.08727	+	1.53764i
$373$	14.3137	−	14.3137i	0.741136	−	0.741136i	−0.231661	−	0.972797i	$-0.574416\pi$
$373$	14.3137	−	14.3137i	0.741136	−	0.741136i	0.972797	+	0.231661i	$0.0744160\pi$
$374$	−24.9706			−1.29120
$375$	−9.65685	−	1.65685i	−0.498678	−	0.0855596i
$376$	11.3137	+	11.3137i	0.583460	+	0.583460i
$377$	9.51472			0.490033
$378$	3.58579	−	6.41421i	0.184433	−	0.329912i
$379$	1.14214	+	1.14214i	0.0586676	+	0.0586676i	0.735832	−	0.677164i	$-0.236791\pi$
$379$	1.14214	+	1.14214i	0.0586676	+	0.0586676i	−0.677164	+	0.735832i	$0.736791\pi$
$380$		−	23.3137i		−	1.19597i
$381$	−6.14214	+	4.34315i	−0.314671	+	0.222506i
$382$	17.6569	−	17.6569i	0.903403	−	0.903403i
$383$	−3.31371			−0.169323			−0.0846613	−	0.996410i	$-0.526981\pi$
$383$	−3.31371			−0.169323			−0.0846613	+	0.996410i	$0.526981\pi$
$384$	−3.31371	+	19.3137i	−0.169102	+	0.985599i
$385$	8.82843			0.449938
$386$	−4.34315	+	4.34315i	−0.221060	+	0.221060i
$387$	−7.00000	+	3.34315i	−0.355830	+	0.169942i
$388$			4.00000i			0.203069i
$389$	13.9706	+	13.9706i	0.708336	+	0.708336i	0.966185	−	0.257849i	$-0.0830139\pi$
$389$	13.9706	+	13.9706i	0.708336	+	0.708336i	−0.257849	+	0.966185i	$0.583014\pi$
$390$	−3.17157	+	18.4853i	−0.160599	+	0.936039i
$391$	−24.9706			−1.26282
$392$	2.00000	+	2.00000i	0.101015	+	0.101015i
$393$	4.17157	−	24.3137i	0.210428	−	1.22646i
$394$	0.343146			0.0172874
$395$	4.82843	−	4.82843i	0.242945	−	0.242945i
$396$	14.0000	−	6.68629i	0.703526	−	0.335999i
$397$	1.72792	+	1.72792i	0.0867219	+	0.0867219i	0.749137	−	0.662415i	$-0.230468\pi$
$397$	1.72792	+	1.72792i	0.0867219	+	0.0867219i	−0.662415	+	0.749137i	$0.730468\pi$
$398$		0			0
$399$	−5.82843	−	1.00000i	−0.291786	−	0.0500626i
$400$		−	26.6274i		−	1.33137i
$401$			3.31371i			0.165479i	0.996571	+	0.0827394i	$0.0263669\pi$
$401$			3.31371i			0.165479i	−0.996571	+	0.0827394i	$0.973633\pi$
$402$	−19.7990	+	14.0000i	−0.987484	+	0.698257i
$403$	−16.6274	+	16.6274i	−0.828271	+	0.828271i
$404$	−8.14214	+	8.14214i	−0.405086	+	0.405086i
$405$	3.24264	+	30.5563i	0.161128	+	1.51836i
$406$			6.00000i			0.297775i
$407$			14.0000i			0.693954i
$408$	32.9706	+	5.65685i	1.63229	+	0.280056i
$409$		−	30.8284i		−	1.52437i	−0.647361	−	0.762184i	$-0.724127\pi$
$409$		−	30.8284i		−	1.52437i	0.647361	−	0.762184i	$-0.275873\pi$
$410$	−56.2843			−2.77968
$411$	−3.65685	−	5.17157i	−0.180379	−	0.255095i
$412$			22.6274i			1.11477i
$413$	−4.07107	+	4.07107i	−0.200324	+	0.200324i
$414$	14.0000	−	6.68629i	0.688062	−	0.328613i
$415$			52.6274i			2.58338i
$416$	−12.6863			−0.621997
$417$	−0.656854	+	3.82843i	−0.0321663	+	0.187479i
$418$	−8.82843	−	8.82843i	−0.431812	−	0.431812i
$419$	−4.75736	−	4.75736i	−0.232412	−	0.232412i	0.581287	−	0.813699i	$-0.302550\pi$
$419$	−4.75736	−	4.75736i	−0.232412	−	0.232412i	−0.813699	+	0.581287i	$0.802550\pi$
$420$	−11.6569	−	2.00000i	−0.568796	−	0.0975900i
$421$	−24.3137	+	24.3137i	−1.18498	+	1.18498i	−0.206539	+	0.978438i	$0.566220\pi$
$421$	−24.3137	+	24.3137i	−1.18498	+	1.18498i	−0.978438	+	0.206539i	$0.933780\pi$
$422$			10.0000i			0.486792i
$423$	−5.65685	+	16.0000i	−0.275046	+	0.777947i
$424$		−	0.686292i		−	0.0333293i
$425$	−45.4558			−2.20493
$426$	2.48528	−	14.4853i	0.120412	−	0.701814i
$427$	0.414214	+	0.414214i	0.0200452	+	0.0200452i
$428$	10.0000	+	10.0000i	0.483368	+	0.483368i
$429$	5.79899	+	8.20101i	0.279978	+	0.395949i
$430$	8.82843	+	8.82843i	0.425745	+	0.425745i
$431$	19.3137			0.930309			0.465154	−	0.885230i	$-0.345999\pi$
$431$	19.3137			0.930309			0.465154	+	0.885230i	$0.345999\pi$
$432$	−20.0000	+	5.65685i	−0.962250	+	0.272166i
$433$	−37.3137			−1.79318			−0.896591	−	0.442859i	$-0.853964\pi$
$433$	−37.3137			−1.79318			−0.896591	+	0.442859i	$0.853964\pi$
$434$	−10.4853	−	10.4853i	−0.503310	−	0.503310i
$435$	−14.4853	−	20.4853i	−0.694516	−	0.982194i
$436$	0.343146	−	0.343146i	0.0164337	−	0.0164337i
$437$	−8.82843	−	8.82843i	−0.422321	−	0.422321i
$438$	−4.48528	+	26.1421i	−0.214315	+	1.24912i
$439$	32.9706			1.57360			0.786800	−	0.617209i	$-0.211737\pi$
$439$	32.9706			1.57360			0.786800	+	0.617209i	$0.211737\pi$
$440$	−17.6569	−	17.6569i	−0.841757	−	0.841757i
$441$	−1.00000	+	2.82843i	−0.0476190	+	0.134687i
$442$			21.6569i			1.03011i
$443$	5.34315	−	5.34315i	0.253861	−	0.253861i	−0.568691	−	0.822551i	$-0.692550\pi$
$443$	5.34315	−	5.34315i	0.253861	−	0.253861i	0.822551	+	0.568691i	$0.192550\pi$
$444$	3.17157	−	18.4853i	0.150516	−	0.877273i
$445$	10.4853	+	10.4853i	0.497050	+	0.497050i
$446$	12.8284	+	12.8284i	0.607444	+	0.607444i
$447$	−3.10051	+	18.0711i	−0.146649	+	0.854732i
$448$		−	8.00000i		−	0.377964i
$449$		−	20.9706i		−	0.989662i	−0.868989	−	0.494831i	$-0.835230\pi$
$449$		−	20.9706i		−	0.989662i	0.868989	−	0.494831i	$-0.164770\pi$
$450$	25.4853	−	12.1716i	1.20139	−	0.573773i
$451$	−21.3137	+	21.3137i	−1.00362	+	1.00362i
$452$	−19.3137			−0.908440
$453$	6.34315	+	8.97056i	0.298027	+	0.421474i
$454$	−12.1421			−0.569859
$455$		−	7.65685i		−	0.358959i
$456$	9.65685	+	13.6569i	0.452224	+	0.639541i
$457$		−	37.9411i		−	1.77481i	−0.460990	−	0.887405i	$-0.652505\pi$
$457$		−	37.9411i		−	1.77481i	0.460990	−	0.887405i	$-0.347495\pi$
$458$		−	17.7990i		−	0.831692i
$459$	9.65685	+	34.1421i	0.450743	+	1.59362i
$460$	−17.6569	−	17.6569i	−0.823255	−	0.823255i
$461$	−19.5858	+	19.5858i	−0.912201	+	0.912201i	−0.996445	−	0.0842441i	$-0.973152\pi$
$461$	−19.5858	+	19.5858i	−0.912201	+	0.912201i	0.0842441	+	0.996445i	$0.473152\pi$
$462$	−5.17157	+	3.65685i	−0.240603	+	0.170132i
$463$		−	0.343146i		−	0.0159473i	−0.999968	−	0.00797367i	$-0.997462\pi$
$463$		−	0.343146i		−	0.0159473i	0.999968	−	0.00797367i	$-0.00253812\pi$
$464$	12.0000	−	12.0000i	0.557086	−	0.557086i
$465$	61.1127	+	10.4853i	2.83403	+	0.486243i
$466$	−21.3137	+	21.3137i	−0.987338	+	0.987338i
$467$	−11.5858	−	11.5858i	−0.536126	−	0.536126i	0.386263	−	0.922389i	$-0.373766\pi$
$467$	−11.5858	−	11.5858i	−0.536126	−	0.536126i	−0.922389	+	0.386263i	$0.873766\pi$
$468$	−5.79899	−	12.1421i	−0.268058	−	0.561270i
$469$	7.00000	−	7.00000i	0.323230	−	0.323230i
$470$	27.3137			1.25989
$471$	−7.00000	+	40.7990i	−0.322543	+	1.87992i
$472$	16.2843			0.749544
$473$	6.68629			0.307436
$474$	−0.828427	+	4.82843i	−0.0380509	+	0.221777i
$475$	−16.0711	−	16.0711i	−0.737391	−	0.737391i
$476$	−13.6569			−0.625961
$477$	0.656854	−	0.313708i	0.0300753	−	0.0143637i
$478$	11.3137	−	11.3137i	0.517477	−	0.517477i
$479$	4.68629			0.214122			0.107061	−	0.994252i	$-0.465856\pi$
$479$	4.68629			0.214122			0.107061	+	0.994252i	$0.465856\pi$
$480$	19.3137	+	27.3137i	0.881546	+	1.24669i
$481$	12.1421			0.553634
$482$	−11.6569	+	11.6569i	−0.530955	+	0.530955i
$483$	−5.17157	+	3.65685i	−0.235315	+	0.166393i
$484$	8.62742			0.392155
$485$	4.82843	+	4.82843i	0.219248	+	0.219248i
$486$	−14.5563	−	16.5563i	−0.660289	−	0.751011i
$487$	40.2843			1.82545			0.912727	−	0.408569i	$-0.133972\pi$
$487$	40.2843			1.82545			0.912727	+	0.408569i	$0.133972\pi$
$488$		−	1.65685i		−	0.0750023i
$489$	−9.24264	−	1.58579i	−0.417967	−	0.0717117i
$490$	4.82843			0.218126
$491$	−12.3137	+	12.3137i	−0.555710	+	0.555710i	−0.928083	−	0.372373i	$-0.878544\pi$
$491$	−12.3137	+	12.3137i	−0.555710	+	0.555710i	0.372373	+	0.928083i	$0.378544\pi$
$492$	32.9706	−	23.3137i	1.48643	−	1.05106i
$493$	−20.4853	−	20.4853i	−0.922611	−	0.922611i
$494$	−7.65685	+	7.65685i	−0.344498	+	0.344498i
$495$	8.82843	−	24.9706i	0.396808	−	1.12234i
$496$			41.9411i			1.88321i
$497$			6.00000i			0.269137i
$498$	−21.7990	−	30.8284i	−0.976836	−	1.38145i
$499$	28.3137	−	28.3137i	1.26750	−	1.26750i	0.320118	−	0.947378i	$-0.396277\pi$
$499$	28.3137	−	28.3137i	1.26750	−	1.26750i	0.947378	−	0.320118i	$-0.103723\pi$
$500$	−8.00000	−	8.00000i	−0.357771	−	0.357771i
$501$	18.1421	−	12.8284i	0.810531	−	0.573132i
$502$		−	0.828427i		−	0.0369745i
$503$		−	11.1716i		−	0.498116i	−0.968489	−	0.249058i	$-0.919879\pi$
$503$		−	11.1716i		−	0.498116i	0.968489	−	0.249058i	$-0.0801210\pi$
$504$	7.65685	−	3.65685i	0.341063	−	0.162889i
$505$			19.6569i			0.874719i
$506$	−13.3726			−0.594484
$507$	−11.2721	+	7.97056i	−0.500611	+	0.353985i
$508$	−8.68629			−0.385392
$509$	−1.24264	+	1.24264i	−0.0550791	+	0.0550791i	−0.734110	−	0.679031i	$-0.762400\pi$
$509$	−1.24264	+	1.24264i	−0.0550791	+	0.0550791i	0.679031	+	0.734110i	$0.262400\pi$
$510$	46.6274	−	32.9706i	2.06470	−	1.45996i
$511$		−	10.8284i		−	0.479021i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−8.65685	+	15.4853i	−0.382209	+	0.683692i
$514$	−21.1716	−	21.1716i	−0.933838	−	0.933838i
$515$	27.3137	+	27.3137i	1.20359	+	1.20359i
$516$	−8.82843	−	1.51472i	−0.388650	−	0.0666818i
$517$	10.3431	−	10.3431i	0.454891	−	0.454891i
$518$			7.65685i			0.336423i
$519$	35.9706	+	6.17157i	1.57893	+	0.270902i
$520$	−15.3137	+	15.3137i	−0.671551	+	0.671551i
$521$	−9.31371			−0.408041			−0.204020	−	0.978967i	$-0.565401\pi$
$521$	−9.31371			−0.408041			−0.204020	+	0.978967i	$0.565401\pi$
$522$	16.9706	+	6.00000i	0.742781	+	0.262613i
$523$	−27.0416	−	27.0416i	−1.18245	−	1.18245i	−0.979108	−	0.203340i	$-0.934820\pi$
$523$	−27.0416	−	27.0416i	−1.18245	−	1.18245i	−0.203340	−	0.979108i	$-0.565180\pi$
$524$	20.1421	−	20.1421i	0.879913	−	0.879913i
$525$	−9.41421	+	6.65685i	−0.410870	+	0.290529i
$526$	0.343146	+	0.343146i	0.0149619	+	0.0149619i
$527$	71.5980			3.11886
$528$	17.6569	+	3.02944i	0.768416	+	0.131839i
$529$	9.62742			0.418583
$530$	−0.828427	−	0.828427i	−0.0359846	−	0.0359846i
$531$	7.44365	+	15.5858i	0.323027	+	0.676366i
$532$	−4.82843	−	4.82843i	−0.209339	−	0.209339i
$533$	18.4853	+	18.4853i	0.800686	+	0.800686i
$534$	−10.4853	−	1.79899i	−0.453743	−	0.0778499i
$535$	24.1421			1.04376
$536$	−28.0000			−1.20942
$537$	−6.21320	+	36.2132i	−0.268120	+	1.56272i
$538$			16.8284i			0.725525i
$539$	1.82843	−	1.82843i	0.0787559	−	0.0787559i
$540$	−17.3137	+	30.9706i	−0.745063	+	1.33276i
$541$	−21.0000	−	21.0000i	−0.902861	−	0.902861i	0.0928222	−	0.995683i	$-0.470411\pi$
$541$	−21.0000	−	21.0000i	−0.902861	−	0.902861i	−0.995683	+	0.0928222i	$0.970411\pi$
$542$	−11.1716	−	11.1716i	−0.479860	−	0.479860i
$543$	−29.1421	−	5.00000i	−1.25061	−	0.214571i
$544$	27.3137	+	27.3137i	1.17107	+	1.17107i
$545$		−	0.828427i		−	0.0354859i
$546$	3.17157	+	4.48528i	0.135731	+	0.191952i
$547$	11.1421	−	11.1421i	0.476403	−	0.476403i	−0.427576	−	0.903979i	$-0.640632\pi$
$547$	11.1421	−	11.1421i	0.476403	−	0.476403i	0.903979	+	0.427576i	$0.140632\pi$
$548$		−	7.31371i		−	0.312426i
$549$	1.58579	−	0.757359i	0.0676797	−	0.0323233i
$550$	−24.3431			−1.03800
$551$		−	14.4853i		−	0.617094i
$552$	17.6569	+	3.02944i	0.751526	+	0.128941i
$553$		−	2.00000i		−	0.0850487i
$554$		−	32.6274i		−	1.38621i
$555$	−18.4853	−	26.1421i	−0.784656	−	1.10967i
$556$	−3.17157	+	3.17157i	−0.134505	+	0.134505i
$557$	−13.1421	+	13.1421i	−0.556850	+	0.556850i	−0.928409	−	0.371559i	$-0.878823\pi$
$557$	−13.1421	+	13.1421i	−0.556850	+	0.556850i	0.371559	+	0.928409i	$0.378823\pi$
$558$	−40.1421	+	19.1716i	−1.69935	+	0.811597i
$559$		−	5.79899i		−	0.245271i
$560$	−9.65685	−	9.65685i	−0.408077	−	0.408077i
$561$	5.17157	−	30.1421i	0.218344	−	1.27260i
$562$	−29.3137	+	29.3137i	−1.23652	+	1.23652i
$563$	−22.4142	−	22.4142i	−0.944646	−	0.944646i	0.0538999	−	0.998546i	$-0.482835\pi$
$563$	−22.4142	−	22.4142i	−0.944646	−	0.944646i	−0.998546	+	0.0538999i	$0.982835\pi$
$564$	−16.0000	+	11.3137i	−0.673722	+	0.476393i
$565$	−23.3137	+	23.3137i	−0.980815	+	0.980815i
$566$	−13.7990			−0.580015
$567$	7.00000	+	5.65685i	0.293972	+	0.237566i
$568$	12.0000	−	12.0000i	0.503509	−	0.503509i
$569$	−12.6274			−0.529369			−0.264684	−	0.964335i	$-0.585268\pi$
$569$	−12.6274			−0.529369			−0.264684	+	0.964335i	$0.585268\pi$
$570$	28.1421	+	4.82843i	1.17874	+	0.202241i
$571$	−11.8284	−	11.8284i	−0.495004	−	0.495004i	0.414874	−	0.909879i	$-0.363826\pi$
$571$	−11.8284	−	11.8284i	−0.495004	−	0.495004i	−0.909879	+	0.414874i	$0.863826\pi$
$572$			11.5980i			0.484936i
$573$	17.6569	+	24.9706i	0.737626	+	1.04316i
$574$	−11.6569	+	11.6569i	−0.486548	+	0.486548i
$575$	−24.3431			−1.01518
$576$	−22.6274	−	8.00000i	−0.942809	−	0.333333i
$577$	−11.6569			−0.485281			−0.242641	−	0.970116i	$-0.578014\pi$
$577$	−11.6569			−0.485281			−0.242641	+	0.970116i	$0.578014\pi$
$578$	29.6274	−	29.6274i	1.23234	−	1.23234i
$579$	−4.34315	−	6.14214i	−0.180495	−	0.255258i
$580$		−	28.9706i		−	1.20294i
$581$	10.8995	+	10.8995i	0.452187	+	0.452187i
$582$	−4.82843	−	0.828427i	−0.200145	−	0.0343394i
$583$	−0.627417			−0.0259850
$584$	−21.6569	+	21.6569i	−0.896167	+	0.896167i
$585$	−21.6569	−	7.65685i	−0.895401	−	0.316572i
$586$	1.51472			0.0625724
$587$	1.92893	−	1.92893i	0.0796156	−	0.0796156i	−0.666178	−	0.745793i	$-0.732071\pi$
$587$	1.92893	−	1.92893i	0.0796156	−	0.0796156i	0.745793	+	0.666178i	$0.232071\pi$
$588$	−2.82843	+	2.00000i	−0.116642	+	0.0824786i
$589$	25.3137	+	25.3137i	1.04303	+	1.04303i
$590$	19.6569	−	19.6569i	0.809260	−	0.809260i
$591$	−0.0710678	+	0.414214i	−0.00292334	+	0.0170385i
$592$	15.3137	−	15.3137i	0.629390	−	0.629390i
$593$			30.1421i			1.23779i	0.785474	+	0.618895i	$0.212419\pi$
$593$			30.1421i			1.23779i	−0.785474	+	0.618895i	$0.787581\pi$
$594$	5.17157	+	18.2843i	0.212192	+	0.750213i
$595$	−16.4853	+	16.4853i	−0.675831	+	0.675831i
$596$	−14.9706	+	14.9706i	−0.613218	+	0.613218i
$597$		0			0
$598$			11.5980i			0.474277i
$599$			9.02944i			0.368933i	0.982839	+	0.184466i	$0.0590557\pi$
$599$			9.02944i			0.368933i	−0.982839	+	0.184466i	$0.940944\pi$
$600$	32.1421	+	5.51472i	1.31220	+	0.225137i
$601$			0.485281i			0.0197950i	0.999951	+	0.00989752i	$0.00315053\pi$
$601$			0.485281i			0.0197950i	−0.999951	+	0.00989752i	$0.996849\pi$
$602$	3.65685			0.149042
$603$	−12.7990	−	26.7990i	−0.521215	−	1.09134i
$604$			12.6863i			0.516198i
$605$	10.4142	−	10.4142i	0.423398	−	0.423398i
$606$	−8.14214	−	11.5147i	−0.330752	−	0.467753i
$607$		−	41.1127i		−	1.66871i	−0.551225	−	0.834356i	$-0.685840\pi$
$607$		−	41.1127i		−	1.66871i	0.551225	−	0.834356i	$-0.314160\pi$
$608$			19.3137i			0.783274i
$609$	−7.24264	−	1.24264i	−0.293487	−	0.0503543i
$610$	−2.00000	−	2.00000i	−0.0809776	−	0.0809776i
$611$	−8.97056	−	8.97056i	−0.362910	−	0.362910i
$612$	−13.6569	+	38.6274i	−0.552046	+	1.56142i
$613$	−19.8284	+	19.8284i	−0.800863	+	0.800863i	−0.983230	−	0.182368i	$-0.941624\pi$
$613$	−19.8284	+	19.8284i	−0.800863	+	0.800863i	0.182368	+	0.983230i	$0.441624\pi$
$614$			9.79899i			0.395455i
$615$	11.6569	−	67.9411i	0.470050	−	2.73965i
$616$	−7.31371			−0.294678
$617$	−26.0000			−1.04672			−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000			−1.04672			−0.523360	+	0.852111i	$0.675322\pi$
$618$	−27.3137	−	4.68629i	−1.09872	−	0.188510i
$619$	23.5858	+	23.5858i	0.947993	+	0.947993i	0.998713	−	0.0507201i	$-0.0161516\pi$
$619$	23.5858	+	23.5858i	0.947993	+	0.947993i	−0.0507201	+	0.998713i	$0.516152\pi$
$620$	50.6274	+	50.6274i	2.03325	+	2.03325i
$621$	5.17157	+	18.2843i	0.207528	+	0.733723i
$622$	−18.4853	−	18.4853i	−0.741192	−	0.741192i
$623$	4.34315			0.174004
$624$	2.62742	−	15.3137i	0.105181	−	0.613039i
$625$	13.9706			0.558823
$626$	−3.51472	−	3.51472i	−0.140476	−	0.140476i
$627$	12.4853	−	8.82843i	0.498614	−	0.352573i
$628$	−33.7990	+	33.7990i	−1.34873	+	1.34873i
$629$	−26.1421	−	26.1421i	−1.04236	−	1.04236i
$630$	4.82843	−	13.6569i	0.192369	−	0.544102i
$631$	−2.34315			−0.0932792			−0.0466396	−	0.998912i	$-0.514851\pi$
$631$	−2.34315			−0.0932792			−0.0466396	+	0.998912i	$0.514851\pi$
$632$	−4.00000	+	4.00000i	−0.159111	+	0.159111i
$633$	−12.0711	−	2.07107i	−0.479782	−	0.0823176i
$634$			30.2843i			1.20274i
$635$	−10.4853	+	10.4853i	−0.416096	+	0.416096i
$636$	0.828427	+	0.142136i	0.0328493	+	0.00563604i
$637$	−1.58579	−	1.58579i	−0.0628311	−	0.0628311i
$638$	−10.9706	−	10.9706i	−0.434329	−	0.434329i
$639$	16.9706	+	6.00000i	0.671345	+	0.237356i
$640$			38.6274i			1.52688i
$641$		−	45.2548i		−	1.78746i	−0.448607	−	0.893729i	$-0.648080\pi$
$641$		−	45.2548i		−	1.78746i	0.448607	−	0.893729i	$-0.351920\pi$
$642$	−14.1421	+	10.0000i	−0.558146	+	0.394669i
$643$	27.0416	−	27.0416i	1.06642	−	1.06642i	0.0687864	−	0.997631i	$-0.478087\pi$
$643$	27.0416	−	27.0416i	1.06642	−	1.06642i	0.997631	−	0.0687864i	$-0.0219127\pi$
$644$	−7.31371			−0.288200
$645$	−12.4853	+	8.82843i	−0.491607	+	0.347619i
$646$	32.9706			1.29721
$647$		−	12.1421i		−	0.477357i	−0.971099	−	0.238678i	$-0.923286\pi$
$647$		−	12.1421i		−	0.477357i	0.971099	−	0.238678i	$-0.0767141\pi$
$648$	−2.68629	−	25.3137i	−0.105527	−	0.994416i
$649$		−	14.8873i		−	0.584378i
$650$			21.1127i			0.828108i
$651$	14.8284	−	10.4853i	0.581172	−	0.410951i
$652$	−7.65685	−	7.65685i	−0.299866	−	0.299866i
$653$	22.6569	−	22.6569i	0.886631	−	0.886631i	−0.107567	−	0.994198i	$-0.534306\pi$
$653$	22.6569	−	22.6569i	0.886631	−	0.886631i	0.994198	+	0.107567i	$0.0343059\pi$
$654$	0.343146	+	0.485281i	0.0134181	+	0.0189760i
$655$		−	48.6274i		−	1.90003i
$656$	46.6274			1.82049
$657$	−30.6274	−	10.8284i	−1.19489	−	0.422457i
$658$	5.65685	−	5.65685i	0.220527	−	0.220527i
$659$	8.51472	+	8.51472i	0.331686	+	0.331686i	0.853227	−	0.521540i	$-0.174642\pi$
$659$	8.51472	+	8.51472i	0.331686	+	0.331686i	−0.521540	+	0.853227i	$0.674642\pi$
$660$	24.9706	−	17.6569i	0.971978	−	0.687292i
$661$	−25.3848	+	25.3848i	−0.987353	+	0.987353i	−0.999921	−	0.0125677i	$-0.995999\pi$
$661$	−25.3848	+	25.3848i	−0.987353	+	0.987353i	0.0125677	+	0.999921i	$0.495999\pi$
$662$	22.2843			0.866103
$663$	−26.1421	−	4.48528i	−1.01528	−	0.174194i
$664$		−	43.5980i		−	1.69193i
$665$	−11.6569			−0.452033
$666$	21.6569	+	7.65685i	0.839186	+	0.296697i
$667$	−10.9706	−	10.9706i	−0.424782	−	0.424782i
$668$	25.6569			0.992693
$669$	−18.1421	+	12.8284i	−0.701415	+	0.495976i
$670$	−33.7990	+	33.7990i	−1.30577	+	1.30577i
$671$	−1.51472			−0.0584751
$672$	9.65685	+	1.65685i	0.372521	+	0.0639145i
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−2.68629	+	2.68629i	−0.103472	+	0.103472i
$675$	9.41421	+	33.2843i	0.362353	+	1.28111i
$676$	−15.9411			−0.613120
$677$	1.10051	+	1.10051i	0.0422958	+	0.0422958i	0.727938	−	0.685643i	$-0.240479\pi$
$677$	1.10051	+	1.10051i	0.0422958	+	0.0422958i	−0.685643	+	0.727938i	$0.740479\pi$
$678$	4.00000	−	23.3137i	0.153619	−	0.895358i
$679$	2.00000			0.0767530
$680$	65.9411			2.52873
$681$	2.51472	−	14.6569i	0.0963642	−	0.561652i
$682$	38.3431			1.46823
$683$	22.3137	−	22.3137i	0.853810	−	0.853810i	−0.136790	−	0.990600i	$-0.543678\pi$
$683$	22.3137	−	22.3137i	0.853810	−	0.853810i	0.990600	+	0.136790i	$0.0436785\pi$
$684$	−18.4853	+	8.82843i	−0.706802	+	0.337563i
$685$	−8.82843	−	8.82843i	−0.337317	−	0.337317i
$686$	1.00000	−	1.00000i	0.0381802	−	0.0381802i
$687$	21.4853	+	3.68629i	0.819715	+	0.140641i
$688$	−7.31371	−	7.31371i	−0.278833	−	0.278833i
$689$			0.544156i			0.0207307i
$690$	24.9706	−	17.6569i	0.950613	−	0.672185i
$691$	4.89949	−	4.89949i	0.186386	−	0.186386i	−0.607746	−	0.794132i	$-0.707926\pi$
$691$	4.89949	−	4.89949i	0.186386	−	0.186386i	0.794132	+	0.607746i	$0.207926\pi$
$692$	29.7990	+	29.7990i	1.13279	+	1.13279i
$693$	−3.34315	−	7.00000i	−0.126996	−	0.265908i
$694$		−	30.2843i		−	1.14958i
$695$			7.65685i			0.290441i
$696$	12.0000	+	16.9706i	0.454859	+	0.643268i
$697$		−	79.5980i		−	3.01499i
$698$	−24.1421			−0.913793
$699$	−21.3137	−	30.1421i	−0.806158	−	1.14008i
$700$	−13.3137			−0.503211
$701$	10.6569	−	10.6569i	0.402504	−	0.402504i	−0.476611	−	0.879114i	$-0.658135\pi$
$701$	10.6569	−	10.6569i	0.402504	−	0.402504i	0.879114	+	0.476611i	$0.158135\pi$
$702$	15.8579	−	4.48528i	0.598517	−	0.169286i
$703$		−	18.4853i		−	0.697186i
$704$	14.6274	+	14.6274i	0.551292	+	0.551292i
$705$	−5.65685	+	32.9706i	−0.213049	+	1.24174i
$706$	−8.48528	−	8.48528i	−0.319348	−	0.319348i
$707$	4.07107	+	4.07107i	0.153108	+	0.153108i
$708$	−3.37258	+	19.6569i	−0.126749	+	0.738750i
$709$	−7.82843	+	7.82843i	−0.294003	+	0.294003i	−0.838659	−	0.544656i	$-0.816660\pi$
$709$	−7.82843	+	7.82843i	−0.294003	+	0.294003i	0.544656	+	0.838659i	$0.316660\pi$
$710$		−	28.9706i		−	1.08725i
$711$	−5.65685	−	2.00000i	−0.212149	−	0.0750059i
$712$	−8.68629	−	8.68629i	−0.325533	−	0.325533i
$713$	38.3431			1.43596
$714$	2.82843	−	16.4853i	0.105851	−	0.616946i
$715$	14.0000	+	14.0000i	0.523570	+	0.523570i
$716$	−30.0000	+	30.0000i	−1.12115	+	1.12115i
$717$	11.3137	+	16.0000i	0.422518	+	0.597531i
$718$	31.6569	+	31.6569i	1.18142	+	1.18142i
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$	−36.9706	+	17.6569i	−1.37781	+	0.658032i
$721$	11.3137			0.421345
$722$	−7.34315	−	7.34315i	−0.273284	−	0.273284i
$723$	−11.6569	−	16.4853i	−0.433523	−	0.613094i
$724$	−24.1421	−	24.1421i	−0.897235	−	0.897235i
$725$	−19.9706	−	19.9706i	−0.741688	−	0.741688i
$726$	−1.78680	+	10.4142i	−0.0663142	+	0.386508i
$727$	−12.6863			−0.470509			−0.235254	−	0.971934i	$-0.575592\pi$
$727$	−12.6863			−0.470509			−0.235254	+	0.971934i	$0.575592\pi$
$728$			6.34315i			0.235093i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$			52.2843i			1.93513i
$731$	−12.4853	+	12.4853i	−0.461785	+	0.461785i
$732$	2.00000	+	0.343146i	0.0739221	+	0.0126830i
$733$	−27.7279	−	27.7279i	−1.02415	−	1.02415i	−0.999701	−	0.0244532i	$-0.992216\pi$
$733$	−27.7279	−	27.7279i	−1.02415	−	1.02415i	−0.0244532	−	0.999701i	$-0.507784\pi$
$734$	−12.1421	−	12.1421i	−0.448174	−	0.448174i
$735$	−1.00000	+	5.82843i	−0.0368856	+	0.214985i
$736$	14.6274	+	14.6274i	0.539174	+	0.539174i
$737$			25.5980i			0.942914i
$738$	21.3137	+	44.6274i	0.784568	+	1.64276i
$739$	−16.1716	+	16.1716i	−0.594881	+	0.594881i	−0.938946	−	0.344065i	$-0.888196\pi$
$739$	−16.1716	+	16.1716i	−0.594881	+	0.594881i	0.344065	+	0.938946i	$0.388196\pi$
$740$		−	36.9706i		−	1.35906i
$741$	−7.65685	−	10.8284i	−0.281282	−	0.397792i
$742$	−0.343146			−0.0125973
$743$		−	15.6569i		−	0.574394i	−0.957871	−	0.287197i	$-0.907277\pi$
$743$		−	15.6569i		−	0.574394i	0.957871	−	0.287197i	$-0.0927235\pi$
$744$	−50.6274	−	8.68629i	−1.85609	−	0.318455i
$745$			36.1421i			1.32415i
$746$			28.6274i			1.04812i
$747$	41.7279	−	19.9289i	1.52674	−	0.729161i
$748$	24.9706	−	24.9706i	0.913014	−	0.913014i
$749$	5.00000	−	5.00000i	0.182696	−	0.182696i
$750$	11.3137	−	8.00000i	0.413118	−	0.292119i
$751$			41.3137i			1.50756i	0.657128	+	0.753779i	$0.271771\pi$
$751$			41.3137i			1.50756i	−0.657128	+	0.753779i	$0.728229\pi$
$752$	−22.6274			−0.825137
$753$	1.00000	+	0.171573i	0.0364420	+	0.00625246i
$754$	−9.51472	+	9.51472i	−0.346506	+	0.346506i
$755$	15.3137	+	15.3137i	0.557323	+	0.557323i
$756$	2.82843	+	10.0000i	0.102869	+	0.363696i
$757$	31.4853	−	31.4853i	1.14435	−	1.14435i	0.156707	−	0.987645i	$-0.449912\pi$
$757$	31.4853	−	31.4853i	1.14435	−	1.14435i	0.987645	−	0.156707i	$-0.0500878\pi$
$758$	−2.28427			−0.0829685
$759$	2.76955	−	16.1421i	0.100528	−	0.585922i
$760$	23.3137	+	23.3137i	0.845677	+	0.845677i
$761$	8.62742			0.312744			0.156372	−	0.987698i	$-0.450020\pi$
$761$	8.62742			0.312744			0.156372	+	0.987698i	$0.450020\pi$
$762$	1.79899	−	10.4853i	0.0651705	−	0.379842i
$763$	−0.171573	−	0.171573i	−0.00621136	−	0.00621136i
$764$			35.3137i			1.27761i
$765$	30.1421	+	63.1127i	1.08979	+	2.28184i
$766$	3.31371	−	3.31371i	0.119729	−	0.119729i
$767$	−12.9117			−0.466214
$768$	−16.0000	−	22.6274i	−0.577350	−	0.816497i
$769$	35.6569			1.28582			0.642910	−	0.765942i	$-0.277727\pi$
$769$	35.6569			1.28582			0.642910	+	0.765942i	$0.277727\pi$
$770$	−8.82843	+	8.82843i	−0.318154	+	0.318154i
$771$	29.9411	−	21.1716i	1.07830	−	0.762476i
$772$		−	8.68629i		−	0.312626i
$773$	−5.44365	−	5.44365i	−0.195795	−	0.195795i	0.602400	−	0.798194i	$-0.294211\pi$
$773$	−5.44365	−	5.44365i	−0.195795	−	0.195795i	−0.798194	+	0.602400i	$0.794211\pi$
$774$	3.65685	−	10.3431i	0.131443	−	0.371777i
$775$	69.7990			2.50725
$776$	−4.00000	−	4.00000i	−0.143592	−	0.143592i
$777$	−9.24264	−	1.58579i	−0.331578	−	0.0568898i
$778$	−27.9411			−1.00174
$779$	28.1421	−	28.1421i	1.00830	−	1.00830i
$780$	−15.3137	−	21.6569i	−0.548319	−	0.775440i
$781$	−10.9706	−	10.9706i	−0.392558	−	0.392558i
$782$	24.9706	−	24.9706i	0.892946	−	0.892946i
$783$	−10.7574	+	19.2426i	−0.384437	+	0.687676i
$784$	−4.00000			−0.142857
$785$			81.5980i			2.91236i
$786$	20.1421	+	28.4853i	0.718446	+	1.01604i
$787$	−25.0416	+	25.0416i	−0.892638	+	0.892638i	−0.994771	−	0.102133i	$-0.967433\pi$
$787$	−25.0416	+	25.0416i	−0.892638	+	0.892638i	0.102133	+	0.994771i	$0.467433\pi$
$788$	−0.343146	+	0.343146i	−0.0122241	+	0.0122241i
$789$	−0.485281	+	0.343146i	−0.0172765	+	0.0122163i
$790$			9.65685i			0.343575i
$791$			9.65685i			0.343358i
$792$	−7.31371	+	20.6863i	−0.259881	+	0.735055i
$793$			1.31371i			0.0466512i
$794$	−3.45584			−0.122643
$795$	1.17157	−	0.828427i	0.0415514	−	0.0293813i
$796$		0			0
$797$	−31.5858	+	31.5858i	−1.11883	+	1.11883i	−0.126912	+	0.991914i	$0.540507\pi$
$797$	−31.5858	+	31.5858i	−1.11883	+	1.11883i	−0.991914	+	0.126912i	$0.959493\pi$
$798$	6.82843	−	4.82843i	0.241724	−	0.170924i
$799$			38.6274i			1.36654i
$800$	26.6274	+	26.6274i	0.941421	+	0.941421i
$801$	4.34315	−	12.2843i	0.153458	−	0.434043i
$802$	−3.31371	−	3.31371i	−0.117011	−	0.117011i
$803$	19.7990	+	19.7990i	0.698691	+	0.698691i
$804$	5.79899	−	33.7990i	0.204515	−	1.19200i
$805$	−8.82843	+	8.82843i	−0.311161	+	0.311161i
$806$		−	33.2548i		−	1.17135i
$807$	−20.3137	−	3.48528i	−0.715076	−	0.122688i
$808$		−	16.2843i		−	0.572879i
$809$	45.3137			1.59315			0.796573	−	0.604543i	$-0.206644\pi$
$809$	45.3137			1.59315			0.796573	+	0.604543i	$0.206644\pi$
$810$	−33.7990	−	27.3137i	−1.18758	−	0.959706i
$811$	1.92893	+	1.92893i	0.0677340	+	0.0677340i	0.740162	−	0.672428i	$-0.234749\pi$
$811$	1.92893	+	1.92893i	0.0677340	+	0.0677340i	−0.672428	+	0.740162i	$0.734749\pi$
$812$	−6.00000	−	6.00000i	−0.210559	−	0.210559i
$813$	15.7990	−	11.1716i	0.554095	−	0.391804i
$814$	−14.0000	−	14.0000i	−0.490700	−	0.490700i
$815$	−18.4853			−0.647511
$816$	−38.6274	+	27.3137i	−1.35223	+	0.956171i
$817$	−8.82843			−0.308868
$818$	30.8284	+	30.8284i	1.07789	+	1.07789i
$819$	−6.07107	+	2.89949i	−0.212140	+	0.101317i
$820$	56.2843	−	56.2843i	1.96553	−	1.96553i
$821$	1.48528	+	1.48528i	0.0518367	+	0.0518367i	0.732550	−	0.680713i	$-0.238330\pi$
$821$	1.48528	+	1.48528i	0.0518367	+	0.0518367i	−0.680713	+	0.732550i	$0.738330\pi$
$822$	8.82843	+	1.51472i	0.307927	+	0.0528319i
$823$	−8.97056			−0.312694			−0.156347	−	0.987702i	$-0.549972\pi$
$823$	−8.97056			−0.312694			−0.156347	+	0.987702i	$0.549972\pi$
$824$	−22.6274	−	22.6274i	−0.788263	−	0.788263i
$825$	5.04163	−	29.3848i	0.175527	−	1.02305i
$826$		−	8.14214i		−	0.283301i
$827$	−9.00000	+	9.00000i	−0.312961	+	0.312961i	−0.846055	−	0.533095i	$-0.821029\pi$
$827$	−9.00000	+	9.00000i	−0.312961	+	0.312961i	0.533095	+	0.846055i	$0.321029\pi$
$828$	−7.31371	+	20.6863i	−0.254169	+	0.718898i
$829$	−5.10051	−	5.10051i	−0.177148	−	0.177148i	0.612963	−	0.790111i	$-0.289977\pi$
$829$	−5.10051	−	5.10051i	−0.177148	−	0.177148i	−0.790111	+	0.612963i	$0.789977\pi$
$830$	−52.6274	−	52.6274i	−1.82672	−	1.82672i
$831$	39.3848	+	6.75736i	1.36624	+	0.234410i
$832$	12.6863	−	12.6863i	0.439818	−	0.439818i
$833$			6.82843i			0.236591i
$834$	−3.17157	−	4.48528i	−0.109823	−	0.155313i
$835$	30.9706	−	30.9706i	1.07178	−	1.07178i
$836$	17.6569			0.610675
$837$	−14.8284	−	52.4264i	−0.512545	−	1.81212i
$838$	9.51472			0.328681
$839$			0.544156i			0.0187863i	0.999956	+	0.00939317i	$0.00298998\pi$
$839$			0.544156i			0.0187863i	−0.999956	+	0.00939317i	$0.997010\pi$
$840$	13.6569	−	9.65685i	0.471206	−	0.333193i
$841$			11.0000i			0.379310i
$842$		−	48.6274i		−	1.67581i
$843$	−29.3137	−	41.4558i	−1.00962	−	1.42782i
$844$	−10.0000	−	10.0000i	−0.344214	−	0.344214i
$845$	−19.2426	+	19.2426i	−0.661967	+	0.661967i
$846$	−10.3431	−	21.6569i	−0.355605	−	0.744578i
$847$		−	4.31371i		−	0.148221i
$848$	0.686292	+	0.686292i	0.0235673	+	0.0235673i
$849$	2.85786	−	16.6569i	0.0980817	−	0.571662i
$850$	45.4558	−	45.4558i	1.55912	−	1.55912i
$851$	−14.0000	−	14.0000i	−0.479914	−	0.479914i
$852$	12.0000	+	16.9706i	0.411113	+	0.581402i
$853$	−25.5858	+	25.5858i	−0.876041	+	0.876041i	−0.993122	−	0.117082i	$-0.962646\pi$
$853$	−25.5858	+	25.5858i	−0.876041	+	0.876041i	0.117082	+	0.993122i	$0.462646\pi$
$854$	−0.828427			−0.0283482
$855$	−11.6569	+	32.9706i	−0.398656	+	1.12757i
$856$	−20.0000			−0.683586
$857$	35.9411			1.22773			0.613863	−	0.789413i	$-0.289615\pi$
$857$	35.9411			1.22773			0.613863	+	0.789413i	$0.289615\pi$
$858$	−14.0000	−	2.40202i	−0.477952	−	0.0820036i
$859$	3.10051	+	3.10051i	0.105788	+	0.105788i	0.758020	−	0.652232i	$-0.226167\pi$
$859$	3.10051	+	3.10051i	0.105788	+	0.105788i	−0.652232	+	0.758020i	$0.726167\pi$
$860$	−17.6569			−0.602094
$861$	−11.6569	−	16.4853i	−0.397265	−	0.561817i
$862$	−19.3137	+	19.3137i	−0.657828	+	0.657828i
$863$	−16.6863			−0.568008			−0.284004	−	0.958823i	$-0.591663\pi$
$863$	−16.6863			−0.568008			−0.284004	+	0.958823i	$0.591663\pi$
$864$	14.3431	−	25.6569i	0.487964	−	0.872864i
$865$	71.9411			2.44607
$866$	37.3137	−	37.3137i	1.26797	−	1.26797i
$867$	29.6274	+	41.8995i	1.00620	+	1.42298i
$868$	20.9706			0.711787
$869$	3.65685	+	3.65685i	0.124050	+	0.124050i
$870$	34.9706	+	6.00000i	1.18561	+	0.203419i
$871$	22.2010			0.752253
$872$			0.686292i			0.0232408i
$873$	2.00000	−	5.65685i	0.0676897	−	0.191456i
$874$	17.6569			0.597252
$875$	−4.00000	+	4.00000i	−0.135225	+	0.135225i
$876$	−21.6569	−	30.6274i	−0.731717	−	1.03480i
$877$	23.4853	+	23.4853i	0.793042	+	0.793042i	0.981987	−	0.188946i	$-0.0605071\pi$
$877$	23.4853	+	23.4853i	0.793042	+	0.793042i	−0.188946	+	0.981987i	$0.560507\pi$
$878$	−32.9706	+	32.9706i	−1.11270	+	1.11270i
$879$	−0.313708	+	1.82843i	−0.0105811	+	0.0616713i
$880$	35.3137			1.19042
$881$		−	31.5147i		−	1.06176i	−0.847448	−	0.530879i	$-0.821862\pi$
$881$		−	31.5147i		−	1.06176i	0.847448	−	0.530879i	$-0.178138\pi$
$882$	−1.82843	−	3.82843i	−0.0615663	−	0.128910i
$883$	−28.9411	+	28.9411i	−0.973946	+	0.973946i	−0.999669	−	0.0257227i	$-0.991811\pi$
$883$	−28.9411	+	28.9411i	−0.973946	+	0.973946i	0.0257227	+	0.999669i	$0.491811\pi$
$884$	−21.6569	−	21.6569i	−0.728399	−	0.728399i
$885$	19.6569	+	27.7990i	0.660758	+	0.934453i
$886$			10.6863i			0.359013i
$887$			44.8284i			1.50519i	0.658483	+	0.752596i	$0.271198\pi$
$887$			44.8284i			1.50519i	−0.658483	+	0.752596i	$0.728802\pi$
$888$	15.3137	+	21.6569i	0.513894	+	0.726756i
$889$			4.34315i			0.145664i
$890$	−20.9706			−0.702935
$891$	−23.1421	+	2.45584i	−0.775291	+	0.0822739i
$892$	−25.6569			−0.859055
$893$	−13.6569	+	13.6569i	−0.457009	+	0.457009i
$894$	−14.9706	−	21.1716i	−0.500691	−	0.708083i
$895$			72.4264i			2.42095i
$896$	8.00000	+	8.00000i	0.267261	+	0.267261i
$897$	−14.0000	−	2.40202i	−0.467446	−	0.0802011i
$898$	20.9706	+	20.9706i	0.699797	+	0.699797i
$899$	31.4558	+	31.4558i	1.04911	+	1.04911i
$900$	−13.3137	+	37.6569i	−0.443790	+	1.25523i
$901$	1.17157	−	1.17157i	0.0390308	−	0.0390308i
$902$		−	42.6274i		−	1.41934i
$903$	−0.757359	+	4.41421i	−0.0252033	+	0.146896i
$904$	19.3137	−	19.3137i	0.642364	−	0.642364i
$905$	−58.2843			−1.93743
$906$	−15.3137	−	2.62742i	−0.508764	−	0.0872901i
$907$	2.31371	+	2.31371i	0.0768254	+	0.0768254i	0.744475	−	0.667650i	$-0.232700\pi$
$907$	2.31371	+	2.31371i	0.0768254	+	0.0768254i	−0.667650	+	0.744475i	$0.732700\pi$
$908$	12.1421	−	12.1421i	0.402951	−	0.402951i
$909$	15.5858	−	7.44365i	0.516948	−	0.246890i
$910$	7.65685	+	7.65685i	0.253822	+	0.253822i
$911$	12.2843			0.406996			0.203498	−	0.979075i	$-0.434769\pi$
$911$	12.2843			0.406996			0.203498	+	0.979075i	$0.434769\pi$
$912$	−23.3137	−	4.00000i	−0.771994	−	0.132453i
$913$	−39.8579			−1.31910
$914$	37.9411	+	37.9411i	1.25498	+	1.25498i
$915$	2.82843	−	2.00000i	0.0935049	−	0.0661180i
$916$	17.7990	+	17.7990i	0.588095	+	0.588095i
$917$	−10.0711	−	10.0711i	−0.332576	−	0.332576i
$918$	−43.7990	−	24.4853i	−1.44558	−	0.808135i
$919$	−13.6569			−0.450498			−0.225249	−	0.974301i	$-0.572320\pi$
$919$	−13.6569			−0.450498			−0.225249	+	0.974301i	$0.572320\pi$
$920$	35.3137			1.16426
$921$	−11.8284	−	2.02944i	−0.389760	−	0.0668722i
$922$		−	39.1716i		−	1.29005i
$923$	−9.51472	+	9.51472i	−0.313181	+	0.313181i
$924$	1.51472	−	8.82843i	0.0498306	−	0.290434i
$925$	−25.4853	−	25.4853i	−0.837951	−	0.837951i
$926$	0.343146	+	0.343146i	0.0112765	+	0.0112765i
$927$	11.3137	−	32.0000i	0.371591	−	1.05102i
$928$			24.0000i			0.787839i
$929$		−	43.1127i		−	1.41448i	−0.706973	−	0.707241i	$-0.749940\pi$
$929$		−	43.1127i		−	1.41448i	0.706973	−	0.707241i	$-0.250060\pi$
$930$	−71.5980	+	50.6274i	−2.34779	+	1.66014i
$931$	−2.41421	+	2.41421i	−0.0791227	+	0.0791227i
$932$		−	42.6274i		−	1.39631i
$933$	26.1421	−	18.4853i	0.855855	−	0.605181i
$934$	23.1716			0.758197
$935$		−	60.2843i		−	1.97151i
$936$	17.9411	+	6.34315i	0.586424	+	0.207332i
$937$			30.1421i			0.984701i	0.870397	+	0.492350i	$0.163862\pi$
$937$			30.1421i			0.984701i	−0.870397	+	0.492350i	$0.836138\pi$
$938$			14.0000i			0.457116i
$939$	4.97056	−	3.51472i	0.162208	−	0.114699i
$940$	−27.3137	+	27.3137i	−0.890875	+	0.890875i
$941$	−28.3553	+	28.3553i	−0.924358	+	0.924358i	−0.997334	−	0.0729761i	$-0.976750\pi$
$941$	−28.3553	+	28.3553i	−0.924358	+	0.924358i	0.0729761	+	0.997334i	$0.476750\pi$
$942$	−33.7990	−	47.7990i	−1.10123	−	1.55738i
$943$		−	42.6274i		−	1.38814i
$944$	−16.2843	+	16.2843i	−0.530008	+	0.530008i
$945$	15.4853	+	8.65685i	0.503736	+	0.281607i
$946$	−6.68629	+	6.68629i	−0.217390	+	0.217390i
$947$	−9.14214	−	9.14214i	−0.297079	−	0.297079i	0.542789	−	0.839869i	$-0.317368\pi$
$947$	−9.14214	−	9.14214i	−0.297079	−	0.297079i	−0.839869	+	0.542789i	$0.817368\pi$
$948$	−4.00000	−	5.65685i	−0.129914	−	0.183726i
$949$	17.1716	−	17.1716i	0.557413	−	0.557413i
$950$	32.1421			1.04283
$951$	−36.5563	−	6.27208i	−1.18542	−	0.203386i
$952$	13.6569	−	13.6569i	0.442621	−	0.442621i
$953$	−31.6569			−1.02547			−0.512733	−	0.858548i	$-0.671367\pi$
$953$	−31.6569			−1.02547			−0.512733	+	0.858548i	$0.671367\pi$
$954$	−0.343146	+	0.970563i	−0.0111098	+	0.0314231i
$955$	42.6274	+	42.6274i	1.37939	+	1.37939i
$956$			22.6274i			0.731823i
$957$	15.5147	−	10.9706i	0.501520	−	0.354628i
$958$	−4.68629	+	4.68629i	−0.151407	+	0.151407i
$959$	−3.65685			−0.118086
$960$	−46.6274	−	8.00000i	−1.50489	−	0.258199i
$961$	−78.9411			−2.54649
$962$	−12.1421	+	12.1421i	−0.391478	+	0.391478i
$963$	−9.14214	−	19.1421i	−0.294601	−	0.616847i
$964$		−	23.3137i		−	0.750884i
$965$	−10.4853	−	10.4853i	−0.337533	−	0.337533i
$966$	1.51472	−	8.82843i	0.0487353	−	0.284050i
$967$	−0.686292			−0.0220696			−0.0110348	−	0.999939i	$-0.503513\pi$
$967$	−0.686292			−0.0220696			−0.0110348	+	0.999939i	$0.503513\pi$
$968$	−8.62742	+	8.62742i	−0.277296	+	0.277296i
$969$	−6.82843	+	39.7990i	−0.219361	+	1.27853i
$970$	−9.65685			−0.310063
$971$	−16.8995	+	16.8995i	−0.542331	+	0.542331i	−0.924212	−	0.381881i	$-0.875276\pi$
$971$	−16.8995	+	16.8995i	−0.542331	+	0.542331i	0.381881	+	0.924212i	$0.375276\pi$
$972$	31.1127	+	2.00000i	0.997940	+	0.0641500i
$973$	1.58579	+	1.58579i	0.0508380	+	0.0508380i
$974$	−40.2843	+	40.2843i	−1.29079	+	1.29079i
$975$	−25.4853	−	4.37258i	−0.816182	−	0.140035i
$976$	1.65685	+	1.65685i	0.0530346	+	0.0530346i
$977$			31.3137i			1.00181i	0.865501	+	0.500907i	$0.167000\pi$
$977$			31.3137i			1.00181i	−0.865501	+	0.500907i	$0.833000\pi$
$978$	10.8284	−	7.65685i	0.346255	−	0.244839i
$979$	−7.94113	+	7.94113i	−0.253799	+	0.253799i
$980$	−4.82843	+	4.82843i	−0.154238	+	0.154238i
$981$	−0.656854	+	0.313708i	−0.0209717	+	0.0100159i
$982$		−	24.6274i		−	0.785892i
$983$		−	54.4853i		−	1.73781i	−0.494978	−	0.868905i	$-0.664824\pi$
$983$		−	54.4853i		−	1.73781i	0.494978	−	0.868905i	$-0.335176\pi$
$984$	−9.65685	+	56.2843i	−0.307849	+	1.79428i
$985$			0.828427i			0.0263959i
$986$	40.9706			1.30477
$987$	5.65685	+	8.00000i	0.180060	+	0.254643i
$988$		−	15.3137i		−	0.487194i
$989$	−6.68629	+	6.68629i	−0.212612	+	0.212612i
$990$	16.1421	+	33.7990i	0.513031	+	1.07420i
$991$			45.3137i			1.43944i	0.694266	+	0.719719i	$0.255729\pi$
$991$			45.3137i			1.43944i	−0.694266	+	0.719719i	$0.744271\pi$
$992$	−41.9411	−	41.9411i	−1.33163	−	1.33163i
$993$	−4.61522	+	26.8995i	−0.146460	+	0.853630i
$994$	−6.00000	−	6.00000i	−0.190308	−	0.190308i
$995$		0			0
$996$	52.6274	+	9.02944i	1.66756	+	0.286109i
$997$	−34.0711	+	34.0711i	−1.07904	+	1.07904i	−0.0824460	+	0.996596i	$0.526273\pi$
$997$	−34.0711	+	34.0711i	−1.07904	+	1.07904i	−0.996596	+	0.0824460i	$0.973727\pi$
$998$			56.6274i			1.79251i
$999$	−13.7279	+	24.5563i	−0.434332	+	0.776929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.a.323.1	yes	4
3.2	odd	2		336.2.s.b.323.2	yes	4
4.3	odd	2		1344.2.s.b.239.2		4
12.11	even	2		1344.2.s.a.239.1		4
16.5	even	4		1344.2.s.a.911.1		4
16.11	odd	4		336.2.s.b.155.2	yes	4
48.5	odd	4		1344.2.s.b.911.1		4
48.11	even	4	inner	336.2.s.a.155.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.a.155.2	✓	4	48.11	even	4	inner
336.2.s.a.323.1	yes	4	1.1	even	1	trivial
336.2.s.b.155.2	yes	4	16.11	odd	4
336.2.s.b.323.2	yes	4	3.2	odd	2
1344.2.s.a.239.1		4	12.11	even	2
1344.2.s.a.911.1		4	16.5	even	4
1344.2.s.b.239.2		4	4.3	odd	2
1344.2.s.b.911.1		4	48.5	odd	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} -2.00000i q^{4} +(-2.41421 - 2.41421i) q^{5} +(2.41421 + 0.414214i) q^{6} -1.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} -2.00000i q^{4} +(-2.41421 - 2.41421i) q^{5} +(2.41421 + 0.414214i) q^{6} -1.00000 q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +4.82843 q^{10} +(1.82843 - 1.82843i) q^{11} +(-2.82843 + 2.00000i) q^{12} +(-1.58579 - 1.58579i) q^{13} +(1.00000 - 1.00000i) q^{14} +(-1.00000 + 5.82843i) q^{15} -4.00000 q^{16} +6.82843i q^{17} +(-1.82843 - 3.82843i) q^{18} +(-2.41421 + 2.41421i) q^{19} +(-4.82843 + 4.82843i) q^{20} +(1.00000 + 1.41421i) q^{21} +3.65685i q^{22} +3.65685i q^{23} +(0.828427 - 4.82843i) q^{24} +6.65685i q^{25} +3.17157 q^{26} +(5.00000 - 1.41421i) q^{27} +2.00000i q^{28} +(-3.00000 + 3.00000i) q^{29} +(-4.82843 - 6.82843i) q^{30} -10.4853i q^{31} +(4.00000 - 4.00000i) q^{32} +(-4.41421 - 0.757359i) q^{33} +(-6.82843 - 6.82843i) q^{34} +(2.41421 + 2.41421i) q^{35} +(5.65685 + 2.00000i) q^{36} +(-3.82843 + 3.82843i) q^{37} -4.82843i q^{38} +(-0.656854 + 3.82843i) q^{39} -9.65685i q^{40} -11.6569 q^{41} +(-2.41421 - 0.414214i) q^{42} +(1.82843 + 1.82843i) q^{43} +(-3.65685 - 3.65685i) q^{44} +(9.24264 - 4.41421i) q^{45} +(-3.65685 - 3.65685i) q^{46} +5.65685 q^{47} +(4.00000 + 5.65685i) q^{48} +1.00000 q^{49} +(-6.65685 - 6.65685i) q^{50} +(9.65685 - 6.82843i) q^{51} +(-3.17157 + 3.17157i) q^{52} +(-0.171573 - 0.171573i) q^{53} +(-3.58579 + 6.41421i) q^{54} -8.82843 q^{55} +(-2.00000 - 2.00000i) q^{56} +(5.82843 + 1.00000i) q^{57} -6.00000i q^{58} +(4.07107 - 4.07107i) q^{59} +(11.6569 + 2.00000i) q^{60} +(-0.414214 - 0.414214i) q^{61} +(10.4853 + 10.4853i) q^{62} +(1.00000 - 2.82843i) q^{63} +8.00000i q^{64} +7.65685i q^{65} +(5.17157 - 3.65685i) q^{66} +(-7.00000 + 7.00000i) q^{67} +13.6569 q^{68} +(5.17157 - 3.65685i) q^{69} -4.82843 q^{70} -6.00000i q^{71} +(-7.65685 + 3.65685i) q^{72} +10.8284i q^{73} -7.65685i q^{74} +(9.41421 - 6.65685i) q^{75} +(4.82843 + 4.82843i) q^{76} +(-1.82843 + 1.82843i) q^{77} +(-3.17157 - 4.48528i) q^{78} +2.00000i q^{79} +(9.65685 + 9.65685i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(11.6569 - 11.6569i) q^{82} +(-10.8995 - 10.8995i) q^{83} +(2.82843 - 2.00000i) q^{84} +(16.4853 - 16.4853i) q^{85} -3.65685 q^{86} +(7.24264 + 1.24264i) q^{87} +7.31371 q^{88} -4.34315 q^{89} +(-4.82843 + 13.6569i) q^{90} +(1.58579 + 1.58579i) q^{91} +7.31371 q^{92} +(-14.8284 + 10.4853i) q^{93} +(-5.65685 + 5.65685i) q^{94} +11.6569 q^{95} +(-9.65685 - 1.65685i) q^{96} -2.00000 q^{97} +(-1.00000 + 1.00000i) q^{98} +(3.34315 + 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 4 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 8 q^{10} - 4 q^{11} - 12 q^{13} + 4 q^{14} - 4 q^{15} - 16 q^{16} + 4 q^{18} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 8 q^{24} + 24 q^{26} + 20 q^{27} - 12 q^{29} - 8 q^{30} + 16 q^{32} - 12 q^{33} - 16 q^{34} + 4 q^{35} - 4 q^{37} + 20 q^{39} - 24 q^{41} - 4 q^{42} - 4 q^{43} + 8 q^{44} + 20 q^{45} + 8 q^{46} + 16 q^{48} + 4 q^{49} - 4 q^{50} + 16 q^{51} - 24 q^{52} - 12 q^{53} - 20 q^{54} - 24 q^{55} - 8 q^{56} + 12 q^{57} - 12 q^{59} + 24 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{63} + 32 q^{66} - 28 q^{67} + 32 q^{68} + 32 q^{69} - 8 q^{70} - 8 q^{72} + 32 q^{75} + 8 q^{76} + 4 q^{77} - 24 q^{78} + 16 q^{80} - 28 q^{81} + 24 q^{82} - 4 q^{83} + 32 q^{85} + 8 q^{86} + 12 q^{87} - 16 q^{88} - 40 q^{89} - 8 q^{90} + 12 q^{91} - 16 q^{92} - 48 q^{93} + 24 q^{95} - 16 q^{96} - 8 q^{97} - 4 q^{98} + 36 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 4 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 8 * q^10 - 4 * q^11 - 12 * q^13 + 4 * q^14 - 4 * q^15 - 16 * q^16 + 4 * q^18 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 8 * q^24 + 24 * q^26 + 20 * q^27 - 12 * q^29 - 8 * q^30 + 16 * q^32 - 12 * q^33 - 16 * q^34 + 4 * q^35 - 4 * q^37 + 20 * q^39 - 24 * q^41 - 4 * q^42 - 4 * q^43 + 8 * q^44 + 20 * q^45 + 8 * q^46 + 16 * q^48 + 4 * q^49 - 4 * q^50 + 16 * q^51 - 24 * q^52 - 12 * q^53 - 20 * q^54 - 24 * q^55 - 8 * q^56 + 12 * q^57 - 12 * q^59 + 24 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^63 + 32 * q^66 - 28 * q^67 + 32 * q^68 + 32 * q^69 - 8 * q^70 - 8 * q^72 + 32 * q^75 + 8 * q^76 + 4 * q^77 - 24 * q^78 + 16 * q^80 - 28 * q^81 + 24 * q^82 - 4 * q^83 + 32 * q^85 + 8 * q^86 + 12 * q^87 - 16 * q^88 - 40 * q^89 - 8 * q^90 + 12 * q^91 - 16 * q^92 - 48 * q^93 + 24 * q^95 - 16 * q^96 - 8 * q^97 - 4 * q^98 + 36 * q^99

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