LMFDB - Embedded newform 336.2.s.b.323.2

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:	$0$
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			323.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	336.323
Dual form			336.2.s.b.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.41421 + 1.00000i) q^{3} -2.00000i q^{4} +(2.41421 + 2.41421i) q^{5} +(2.41421 - 0.414214i) q^{6} -1.00000 q^{7} +(-2.00000 - 2.00000i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.41421 + 1.00000i) 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} +(2.00000 - 2.82843i) 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} +(3.82843 + 1.82843i) q^{18} +(-2.41421 + 2.41421i) q^{19} +(4.82843 - 4.82843i) q^{20} +(-1.41421 - 1.00000i) q^{21} +3.65685i q^{22} -3.65685i q^{23} +(-0.828427 - 4.82843i) q^{24} +6.65685i q^{25} -3.17157 q^{26} +(-1.41421 + 5.00000i) q^{27} +2.00000i q^{28} +(3.00000 - 3.00000i) q^{29} +(6.82843 + 4.82843i) 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} +(-4.41421 + 9.24264i) q^{45} +(-3.65685 - 3.65685i) q^{46} -5.65685 q^{47} +(-5.65685 - 4.00000i) q^{48} +1.00000 q^{49} +(6.65685 + 6.65685i) q^{50} +(6.82843 - 9.65685i) 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} +(-3.65685 + 5.17157i) q^{66} +(-7.00000 + 7.00000i) q^{67} -13.6569 q^{68} +(3.65685 - 5.17157i) q^{69} -4.82843 q^{70} +6.00000i q^{71} +(3.65685 - 7.65685i) q^{72} +10.8284i q^{73} +7.65685i q^{74} +(-6.65685 + 9.41421i) q^{75} +(4.82843 + 4.82843i) q^{76} +(1.82843 - 1.82843i) q^{77} +(-4.48528 - 3.17157i) 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} +(-2.00000 + 2.82843i) 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} +(10.4853 - 14.8284i) 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} +(-7.00000 - 3.34315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 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^5 + 4 * q^6 - 4 * q^7 - 8 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{5} + 4 q^{6} - 4 q^{7} - 8 q^{8} + 4 q^{9} + 8 q^{10} + 4 q^{11} + 8 q^{12} - 12 q^{13} - 4 q^{14} + 4 q^{15} - 16 q^{16} + 4 q^{18} - 4 q^{19} + 8 q^{20} + 8 q^{24} - 24 q^{26} + 12 q^{29} + 16 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} - 12 q^{45} + 8 q^{46} + 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} + 8 q^{66} - 28 q^{67} - 32 q^{68} - 8 q^{69} - 8 q^{70} - 8 q^{72} - 4 q^{75} + 8 q^{76} - 4 q^{77} + 16 q^{78} - 16 q^{80} - 28 q^{81} + 24 q^{82} + 4 q^{83} - 8 q^{84} + 32 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} + 40 q^{89} + 8 q^{90} + 12 q^{91} + 16 q^{92} + 8 q^{93} - 24 q^{95} - 16 q^{96} - 8 q^{97} + 4 q^{98} - 28 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^5 + 4 * q^6 - 4 * q^7 - 8 * q^8 + 4 * q^9 + 8 * q^10 + 4 * q^11 + 8 * q^12 - 12 * q^13 - 4 * q^14 + 4 * q^15 - 16 * q^16 + 4 * q^18 - 4 * q^19 + 8 * q^20 + 8 * q^24 - 24 * q^26 + 12 * q^29 + 16 * 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 - 12 * q^45 + 8 * q^46 + 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 + 8 * q^66 - 28 * q^67 - 32 * q^68 - 8 * q^69 - 8 * q^70 - 8 * q^72 - 4 * q^75 + 8 * q^76 - 4 * q^77 + 16 * q^78 - 16 * q^80 - 28 * q^81 + 24 * q^82 + 4 * q^83 - 8 * q^84 + 32 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 + 40 * q^89 + 8 * q^90 + 12 * q^91 + 16 * q^92 + 8 * q^93 - 24 * q^95 - 16 * q^96 - 8 * q^97 + 4 * q^98 - 28 * 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
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$4$		−	2.00000i		−	1.00000i
$5$	2.41421	+	2.41421i	1.07967	+	1.07967i	0.996539	+	0.0831305i	$0.0264918\pi$
$5$	2.41421	+	2.41421i	1.07967	+	1.07967i	0.0831305	+	0.996539i	$0.473508\pi$
$6$	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	−0.926813	−	0.375522i	$-0.877463\pi$
$11$	−1.82843	+	1.82843i	−0.551292	+	0.551292i	0.375522	+	0.926813i	$0.377463\pi$
$12$	2.00000	−	2.82843i	0.577350	−	0.816497i
$13$	−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	$-0.689440\pi$
$17$		−	6.82843i		−	1.65614i	0.560627	−	0.828068i	$-0.310560\pi$
$18$	3.82843	+	1.82843i	0.902369	+	0.430964i
$19$	−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
$21$	−1.41421	−	1.00000i	−0.308607	−	0.218218i
$22$			3.65685i			0.779644i
$23$		−	3.65685i		−	0.762507i	−0.924471	−	0.381253i	$-0.875493\pi$
$23$		−	3.65685i		−	0.762507i	0.924471	−	0.381253i	$-0.124507\pi$
$24$	−0.828427	−	4.82843i	−0.169102	−	0.985599i
$25$			6.65685i			1.33137i
$26$	−3.17157			−0.621997
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$			2.00000i			0.377964i
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	0.928477	+	0.371391i	$0.121119\pi$
$30$	6.82843	+	4.82843i	1.24669	+	0.881546i
$31$		−	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	$-0.135891\pi$
$41$	11.6569			1.82049			0.910247	+	0.414065i	$0.135891\pi$
$42$	−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
$45$	−4.41421	+	9.24264i	−0.658032	+	1.37781i
$46$	−3.65685	−	3.65685i	−0.539174	−	0.539174i
$47$	−5.65685			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$47$	−5.65685			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$48$	−5.65685	−	4.00000i	−0.816497	−	0.577350i
$49$	1.00000			0.142857
$50$	6.65685	+	6.65685i	0.941421	+	0.941421i
$51$	6.82843	−	9.65685i	0.956171	−	1.35223i
$52$	−3.17157	+	3.17157i	−0.439818	+	0.439818i
$53$	0.171573	+	0.171573i	0.0235673	+	0.0235673i	0.718792	−	0.695225i	$-0.244695\pi$
$53$	0.171573	+	0.171573i	0.0235673	+	0.0235673i	−0.695225	+	0.718792i	$0.744695\pi$
$54$	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	−0.920575	−	0.390567i	$-0.872279\pi$
$59$	−4.07107	+	4.07107i	−0.530008	+	0.530008i	0.390567	+	0.920575i	$0.372279\pi$
$60$	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
$66$	−3.65685	+	5.17157i	−0.450128	+	0.636577i
$67$	−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
$69$	3.65685	−	5.17157i	0.440234	−	0.622584i
$70$	−4.82843			−0.577107
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$	3.65685	−	7.65685i	0.430964	−	0.902369i
$73$			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
$75$	−6.65685	+	9.41421i	−0.768667	+	1.08706i
$76$	4.82843	+	4.82843i	0.553859	+	0.553859i
$77$	1.82843	−	1.82843i	0.208369	−	0.208369i
$78$	−4.48528	−	3.17157i	−0.507858	−	0.359110i
$79$			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	$0.0709748\pi$
$83$	10.8995	+	10.8995i	1.19637	+	1.19637i	0.221131	+	0.975244i	$0.429025\pi$
$84$	−2.00000	+	2.82843i	−0.218218	+	0.308607i
$85$	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	$-0.426066\pi$
$89$	4.34315			0.460373			0.230186	+	0.973147i	$0.426066\pi$
$90$	4.82843	+	13.6569i	0.508961	+	1.43956i
$91$	1.58579	+	1.58579i	0.166236	+	0.166236i
$92$	−7.31371			−0.762507
$93$	10.4853	−	14.8284i	1.08727	−	1.53764i
$94$	−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
$99$	−7.00000	−	3.34315i	−0.703526	−	0.335999i
$100$	13.3137			1.33137
$101$	4.07107	+	4.07107i	0.405086	+	0.405086i	0.880021	−	0.474935i	$-0.157528\pi$
$101$	4.07107	+	4.07107i	0.405086	+	0.405086i	−0.474935	+	0.880021i	$0.657528\pi$
$102$	−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	−0.422837	−	0.906206i	$-0.638966\pi$
$107$	5.00000	−	5.00000i	0.483368	−	0.483368i	0.906206	+	0.422837i	$0.138966\pi$
$108$	10.0000	+	2.82843i	0.962250	+	0.272166i
$109$	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	$0.150082\pi$
$113$			9.65685i			0.908440i	−0.890889	+	0.454220i	$0.849918\pi$
$114$	−4.82843	+	6.82843i	−0.452224	+	0.639541i
$115$	8.82843	−	8.82843i	0.823255	−	0.823255i
$116$	−6.00000	−	6.00000i	−0.557086	−	0.557086i
$117$	2.89949	−	6.07107i	0.268058	−	0.561270i
$118$			8.14214i			0.749544i
$119$			6.82843i			0.625961i
$120$	9.65685	−	13.6569i	0.881546	−	1.24669i
$121$			4.31371i			0.392155i
$122$	−0.828427			−0.0750023
$123$	16.4853	+	11.6569i	1.48643	+	1.05106i
$124$	−20.9706			−1.88321
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$	−3.82843	−	1.82843i	−0.341063	−	0.162889i
$127$		−	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	0.113612	−	0.993525i	$-0.463758\pi$
$131$	−10.0711	−	10.0711i	−0.879913	−	0.879913i	−0.993525	+	0.113612i	$0.963758\pi$
$132$	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	$-0.549929\pi$
$137$	−3.65685			−0.312426			−0.156213	+	0.987723i	$0.549929\pi$
$138$	−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
$141$	−8.00000	−	5.65685i	−0.673722	−	0.476393i
$142$	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
$147$	1.41421	+	1.00000i	0.116642	+	0.0824786i
$148$	7.65685	+	7.65685i	0.629390	+	0.629390i
$149$	7.48528	+	7.48528i	0.613218	+	0.613218i	0.943783	−	0.330565i	$-0.107239\pi$
$149$	7.48528	+	7.48528i	0.613218	+	0.613218i	−0.330565	+	0.943783i	$0.607239\pi$
$150$	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
$162$	−1.34315	+	12.6569i	−0.105527	+	0.994416i
$163$	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
$165$	−12.4853	−	8.82843i	−0.971978	−	0.687292i
$166$	21.7990			1.69193
$167$		−	12.8284i		−	0.992693i	−0.868124	−	0.496347i	$-0.834674\pi$
$167$		−	12.8284i		−	0.992693i	0.868124	−	0.496347i	$-0.165326\pi$
$168$	0.828427	+	4.82843i	0.0639145	+	0.372521i
$169$		−	7.97056i		−	0.613120i
$170$		−	32.9706i		−	2.52873i
$171$	−9.24264	−	4.41421i	−0.706802	−	0.337563i
$172$	3.65685	−	3.65685i	0.278833	−	0.278833i
$173$	14.8995	−	14.8995i	1.13279	−	1.13279i	0.143076	−	0.989712i	$-0.454301\pi$
$173$	14.8995	−	14.8995i	1.13279	−	1.13279i	0.989712	−	0.143076i	$-0.0456993\pi$
$174$	6.00000	−	8.48528i	0.454859	−	0.643268i
$175$		−	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	$0.0413643\pi$
$179$	15.0000	+	15.0000i	1.12115	+	1.12115i	0.129584	+	0.991568i	$0.458636\pi$
$180$	18.4853	+	8.82843i	1.37781	+	0.658032i
$181$	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
$189$	1.41421	−	5.00000i	0.102869	−	0.363696i
$190$	−11.6569	+	11.6569i	−0.845677	+	0.845677i
$191$	17.6569			1.27761			0.638803	−	0.769371i	$-0.279430\pi$
$191$	17.6569			1.27761			0.638803	+	0.769371i	$0.279430\pi$
$192$	−8.00000	+	11.3137i	−0.577350	+	0.816497i
$193$	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
$195$	7.65685	−	10.8284i	0.548319	−	0.775440i
$196$		−	2.00000i		−	0.142857i
$197$	0.171573	+	0.171573i	0.0122241	+	0.0122241i	0.713192	−	0.700968i	$-0.247249\pi$
$197$	0.171573	+	0.171573i	0.0122241	+	0.0122241i	−0.700968	+	0.713192i	$0.747249\pi$
$198$	−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
$204$	−19.3137	−	13.6569i	−1.35223	−	0.956171i
$205$	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
$210$	−6.82843	−	4.82843i	−0.471206	−	0.333193i
$211$	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
$213$	−6.00000	+	8.48528i	−0.411113	+	0.581402i
$214$		−	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
$219$	−10.8284	+	15.3137i	−0.731717	+	1.03480i
$220$			17.6569i			1.19042i
$221$	−10.8284	+	10.8284i	−0.728399	+	0.728399i
$222$	−7.65685	+	10.8284i	−0.513894	+	0.726756i
$223$		−	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	0.476321	−	0.879272i	$-0.341970\pi$
$227$	−6.07107	−	6.07107i	−0.402951	−	0.402951i	−0.879272	+	0.476321i	$0.841970\pi$
$228$	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	$-0.745995\pi$
$233$	−21.3137			−1.39631			−0.698154	+	0.715948i	$0.745995\pi$
$234$	−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
$237$	−2.00000	+	2.82843i	−0.129914	+	0.183726i
$238$	6.82843	+	6.82843i	0.442621	+	0.442621i
$239$	11.3137			0.731823			0.365911	−	0.930650i	$-0.380757\pi$
$239$	11.3137			0.731823			0.365911	+	0.930650i	$0.380757\pi$
$240$	−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
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$	−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	−0.693913	−	0.720058i	$-0.744115\pi$
$251$	0.414214	−	0.414214i	0.0261449	−	0.0261449i	0.720058	+	0.693913i	$0.244115\pi$
$252$	−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	$-0.770419\pi$
$257$		−	21.1716i		−	1.32065i	0.750982	−	0.660323i	$-0.229581\pi$
$258$	5.17157	+	3.65685i	0.321968	+	0.227666i
$259$	3.82843	−	3.82843i	0.237887	−	0.237887i
$260$	−15.3137			−0.949716
$261$	11.4853	+	5.48528i	0.710921	+	0.339530i
$262$	−20.1421			−1.24439
$263$			0.343146i			0.0211593i	0.999944	+	0.0105796i	$0.00336767\pi$
$263$			0.343146i			0.0211593i	−0.999944	+	0.0105796i	$0.996632\pi$
$264$	10.3431	+	7.31371i	0.636577	+	0.450128i
$265$			0.828427i			0.0508899i
$266$		−	4.82843i		−	0.296050i
$267$	6.14214	+	4.34315i	0.375893	+	0.265796i
$268$	14.0000	+	14.0000i	0.855186	+	0.855186i
$269$	−8.41421	+	8.41421i	−0.513024	+	0.513024i	−0.915452	−	0.402428i	$-0.868166\pi$
$269$	−8.41421	+	8.41421i	−0.513024	+	0.513024i	0.402428	+	0.915452i	$0.368166\pi$
$270$	−6.82843	+	24.1421i	−0.415565	+	1.46924i
$271$			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
$276$	−10.3431	−	7.31371i	−0.622584	−	0.440234i
$277$	−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	$-0.838715\pi$
$281$	−29.3137			−1.74871			−0.874355	+	0.485288i	$0.838715\pi$
$282$	−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
$285$	−16.4853	−	11.6569i	−0.976504	−	0.690492i
$286$	5.79899	−	5.79899i	0.342901	−	0.342901i
$287$	−11.6569			−0.688082
$288$	−15.3137	−	7.31371i	−0.902369	−	0.430964i
$289$	−29.6274			−1.74279
$290$	14.4853	−	14.4853i	0.850605	−	0.850605i
$291$	−2.82843	−	2.00000i	−0.165805	−	0.117242i
$292$	21.6569			1.26737
$293$	0.757359	+	0.757359i	0.0442454	+	0.0442454i	0.728883	−	0.684638i	$-0.240040\pi$
$293$	0.757359	+	0.757359i	0.0442454	+	0.0442454i	−0.684638	+	0.728883i	$0.740040\pi$
$294$	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
$300$	18.8284	+	13.3137i	1.08706	+	0.768667i
$301$	−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
$306$	12.4853	−	26.1421i	0.713736	−	1.49445i
$307$	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
$309$	−16.0000	−	11.3137i	−0.910208	−	0.643614i
$310$		−	50.6274i		−	2.87544i
$311$		−	18.4853i		−	1.04820i	−0.851655	−	0.524102i	$-0.824401\pi$
$311$		−	18.4853i		−	1.04820i	0.851655	−	0.524102i	$-0.175599\pi$
$312$	−6.34315	+	8.97056i	−0.359110	+	0.507858i
$313$			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
$315$	4.41421	−	9.24264i	0.248713	−	0.520764i
$316$	4.00000			0.225018
$317$	−15.1421	+	15.1421i	−0.850467	+	0.850467i	−0.990191	−	0.139723i	$-0.955379\pi$
$317$	−15.1421	+	15.1421i	−0.850467	+	0.850467i	0.139723	+	0.990191i	$0.455379\pi$
$318$	0.485281	+	0.343146i	0.0272132	+	0.0192427i
$319$			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
$333$	−14.6569	−	7.00000i	−0.803191	−	0.383598i
$334$	−12.8284	−	12.8284i	−0.701940	−	0.701940i
$335$	−33.7990			−1.84664
$336$	5.65685	+	4.00000i	0.308607	+	0.218218i
$337$	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
$339$	−9.65685	+	13.6569i	−0.524488	+	0.741739i
$340$	−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	−0.172191	−	0.985064i	$-0.555085\pi$
$347$	15.1421	−	15.1421i	0.812872	−	0.812872i	0.985064	+	0.172191i	$0.0550847\pi$
$348$	−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	$-0.927496\pi$
$353$		−	8.48528i		−	0.451626i	0.974171	−	0.225813i	$-0.0725038\pi$
$354$	−8.14214	+	11.5147i	−0.432750	+	0.612000i
$355$	−14.4853	+	14.4853i	−0.768799	+	0.768799i
$356$		−	8.68629i		−	0.460373i
$357$	−6.82843	+	9.65685i	−0.361399	+	0.511095i
$358$	30.0000			1.58555
$359$			31.6569i			1.67078i	0.549654	+	0.835392i	$0.314760\pi$
$359$			31.6569i			1.67078i	−0.549654	+	0.835392i	$0.685240\pi$
$360$	27.3137	−	9.65685i	1.43956	−	0.508961i
$361$			7.34315i			0.386481i
$362$		−	24.1421i		−	1.26888i
$363$	−4.31371	+	6.10051i	−0.226411	+	0.320193i
$364$	3.17157	−	3.17157i	0.166236	−	0.166236i
$365$	−26.1421	+	26.1421i	−1.36834	+	1.36834i
$366$	−1.17157	−	0.828427i	−0.0612391	−	0.0433026i
$367$			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
$372$	−29.6569	−	20.9706i	−1.53764	−	1.08727i
$373$	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
$381$	4.34315	−	6.14214i	0.222506	−	0.314671i
$382$	17.6569	−	17.6569i	0.903403	−	0.903403i
$383$	3.31371			0.169323			0.0846613	−	0.996410i	$-0.473019\pi$
$383$	3.31371			0.169323			0.0846613	+	0.996410i	$0.473019\pi$
$384$	3.31371	+	19.3137i	0.169102	+	0.985599i
$385$	8.82843			0.449938
$386$	4.34315	−	4.34315i	0.221060	−	0.221060i
$387$	−3.34315	+	7.00000i	−0.169942	+	0.355830i
$388$			4.00000i			0.203069i
$389$	−13.9706	−	13.9706i	−0.708336	−	0.708336i	0.257849	−	0.966185i	$-0.416986\pi$
$389$	−13.9706	−	13.9706i	−0.708336	−	0.708336i	−0.966185	+	0.257849i	$0.916986\pi$
$390$	−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
$396$	−6.68629	+	14.0000i	−0.335999	+	0.703526i
$397$	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	$-0.973633\pi$
$401$		−	3.31371i		−	0.165479i	0.996571	−	0.0827394i	$-0.0263669\pi$
$402$	−14.0000	+	19.7990i	−0.698257	+	0.987484i
$403$	−16.6274	+	16.6274i	−0.828271	+	0.828271i
$404$	8.14214	−	8.14214i	0.405086	−	0.405086i
$405$	−30.5563	−	3.24264i	−1.51836	−	0.161128i
$406$			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
$411$	−5.17157	−	3.65685i	−0.255095	−	0.180379i
$412$			22.6274i			1.11477i
$413$	4.07107	−	4.07107i	0.200324	−	0.200324i
$414$	6.68629	−	14.0000i	0.328613	−	0.688062i
$415$			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	0.813699	−	0.581287i	$-0.197450\pi$
$419$	4.75736	+	4.75736i	0.232412	+	0.232412i	−0.581287	+	0.813699i	$0.697450\pi$
$420$	−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
$429$	8.20101	+	5.79899i	0.395949	+	0.279978i
$430$	8.82843	+	8.82843i	0.425745	+	0.425745i
$431$	−19.3137			−0.930309			−0.465154	−	0.885230i	$-0.654001\pi$
$431$	−19.3137			−0.930309			−0.465154	+	0.885230i	$0.654001\pi$
$432$	5.65685	−	20.0000i	0.272166	−	0.962250i
$433$	−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
$435$	20.4853	+	14.4853i	0.982194	+	0.694516i
$436$	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	−0.822551	−	0.568691i	$-0.807450\pi$
$443$	−5.34315	+	5.34315i	−0.253861	+	0.253861i	0.568691	+	0.822551i	$0.307450\pi$
$444$	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	$0.164770\pi$
$449$			20.9706i			0.989662i	−0.868989	+	0.494831i	$0.835230\pi$
$450$	−12.1716	+	25.4853i	−0.573773	+	1.20139i
$451$	−21.3137	+	21.3137i	−1.00362	+	1.00362i
$452$	19.3137			0.908440
$453$	−8.97056	−	6.34315i	−0.421474	−	0.298027i
$454$	−12.1421			−0.569859
$455$			7.65685i			0.358959i
$456$	13.6569	+	9.65685i	0.639541	+	0.452224i
$457$		−	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
$459$	34.1421	+	9.65685i	1.59362	+	0.450743i
$460$	−17.6569	−	17.6569i	−0.823255	−	0.823255i
$461$	19.5858	−	19.5858i	0.912201	−	0.912201i	−0.0842441	−	0.996445i	$-0.526848\pi$
$461$	19.5858	−	19.5858i	0.912201	−	0.912201i	0.996445	+	0.0842441i	$0.0268476\pi$
$462$	3.65685	−	5.17157i	0.170132	−	0.240603i
$463$		−	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	0.922389	−	0.386263i	$-0.126234\pi$
$467$	11.5858	+	11.5858i	0.536126	+	0.536126i	−0.386263	+	0.922389i	$0.626234\pi$
$468$	−12.1421	−	5.79899i	−0.561270	−	0.268058i
$469$	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
$477$	−0.313708	+	0.656854i	−0.0143637	+	0.0300753i
$478$	11.3137	−	11.3137i	0.517477	−	0.517477i
$479$	−4.68629			−0.214122			−0.107061	−	0.994252i	$-0.534144\pi$
$479$	−4.68629			−0.214122			−0.107061	+	0.994252i	$0.534144\pi$
$480$	−27.3137	−	19.3137i	−1.24669	−	0.881546i
$481$	12.1421			0.553634
$482$	11.6569	−	11.6569i	0.530955	−	0.530955i
$483$	−3.65685	+	5.17157i	−0.166393	+	0.235315i
$484$	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	−0.372373	−	0.928083i	$-0.621456\pi$
$491$	12.3137	−	12.3137i	0.555710	−	0.555710i	0.928083	+	0.372373i	$0.121456\pi$
$492$	23.3137	−	32.9706i	1.05106	−	1.48643i
$493$	−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
$498$	30.8284	+	21.7990i	1.38145	+	0.976836i
$499$	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
$501$	12.8284	−	18.1421i	0.573132	−	0.810531i
$502$		−	0.828427i		−	0.0369745i
$503$			11.1716i			0.498116i	0.968489	+	0.249058i	$0.0801210\pi$
$503$			11.1716i			0.498116i	−0.968489	+	0.249058i	$0.919879\pi$
$504$	−3.65685	+	7.65685i	−0.162889	+	0.341063i
$505$			19.6569i			0.874719i
$506$	13.3726			0.594484
$507$	7.97056	−	11.2721i	0.353985	−	0.500611i
$508$	−8.68629			−0.385392
$509$	1.24264	−	1.24264i	0.0550791	−	0.0550791i	−0.679031	−	0.734110i	$-0.737600\pi$
$509$	1.24264	−	1.24264i	0.0550791	−	0.0550791i	0.734110	+	0.679031i	$0.237600\pi$
$510$	32.9706	−	46.6274i	1.45996	−	2.06470i
$511$		−	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	$-0.434599\pi$
$521$	9.31371			0.408041			0.204020	+	0.978967i	$0.434599\pi$
$522$	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
$525$	6.65685	−	9.41421i	0.290529	−	0.410870i
$526$	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
$531$	−15.5858	−	7.44365i	−0.676366	−	0.323027i
$532$	−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
$546$	4.48528	+	3.17157i	0.191952	+	0.135731i
$547$	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
$549$	0.757359	−	1.58579i	0.0323233	−	0.0676797i
$550$	−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
$555$	−26.1421	−	18.4853i	−1.10967	−	0.784656i
$556$	−3.17157	+	3.17157i	−0.134505	+	0.134505i
$557$	13.1421	−	13.1421i	0.556850	−	0.556850i	−0.371559	−	0.928409i	$-0.621177\pi$
$557$	13.1421	−	13.1421i	0.556850	−	0.556850i	0.928409	+	0.371559i	$0.121177\pi$
$558$	19.1716	−	40.1421i	0.811597	−	1.69935i
$559$		−	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	0.998546	−	0.0538999i	$-0.0171652\pi$
$563$	22.4142	+	22.4142i	0.944646	+	0.944646i	−0.0538999	+	0.998546i	$0.517165\pi$
$564$	−11.3137	+	16.0000i	−0.476393	+	0.673722i
$565$	−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	$-0.414732\pi$
$569$	12.6274			0.529369			0.264684	+	0.964335i	$0.414732\pi$
$570$	−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
$573$	24.9706	+	17.6569i	1.04316	+	0.737626i
$574$	−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
$579$	6.14214	+	4.34315i	0.255258	+	0.180495i
$580$		−	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	−0.745793	−	0.666178i	$-0.767929\pi$
$587$	−1.92893	+	1.92893i	−0.0796156	+	0.0796156i	0.666178	+	0.745793i	$0.267929\pi$
$588$	2.00000	−	2.82843i	0.0824786	−	0.116642i
$589$	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	$-0.787581\pi$
$593$		−	30.1421i		−	1.23779i	0.785474	−	0.618895i	$-0.212419\pi$
$594$	−18.2843	−	5.17157i	−0.750213	−	0.212192i
$595$	−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	$-0.940944\pi$
$599$		−	9.02944i		−	0.368933i	0.982839	−	0.184466i	$-0.0590557\pi$
$600$	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
$603$	−26.7990	−	12.7990i	−1.09134	−	0.521215i
$604$			12.6863i			0.516198i
$605$	−10.4142	+	10.4142i	−0.423398	+	0.423398i
$606$	11.5147	+	8.14214i	0.467753	+	0.330752i
$607$		−	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	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$	−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
$621$	18.2843	+	5.17157i	0.733723	+	0.207528i
$622$	−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
$627$	8.82843	−	12.4853i	0.352573	−	0.498614i
$628$	−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	$0.351920\pi$
$641$			45.2548i			1.78746i	−0.448607	+	0.893729i	$0.648080\pi$
$642$	10.0000	−	14.1421i	0.394669	−	0.558146i
$643$	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
$645$	−8.82843	+	12.4853i	−0.347619	+	0.491607i
$646$	32.9706			1.29721
$647$			12.1421i			0.477357i	0.971099	+	0.238678i	$0.0767141\pi$
$647$			12.1421i			0.477357i	−0.971099	+	0.238678i	$0.923286\pi$
$648$	25.3137	+	2.68629i	0.994416	+	0.105527i
$649$		−	14.8873i		−	0.584378i
$650$		−	21.1127i		−	0.828108i
$651$	−10.4853	+	14.8284i	−0.410951	+	0.581172i
$652$	−7.65685	−	7.65685i	−0.299866	−	0.299866i
$653$	−22.6569	+	22.6569i	−0.886631	+	0.886631i	−0.994198	−	0.107567i	$-0.965694\pi$
$653$	−22.6569	+	22.6569i	−0.886631	+	0.886631i	0.107567	+	0.994198i	$0.465694\pi$
$654$	0.485281	+	0.343146i	0.0189760	+	0.0134181i
$655$		−	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	0.521540	−	0.853227i	$-0.325358\pi$
$659$	−8.51472	−	8.51472i	−0.331686	−	0.331686i	−0.853227	+	0.521540i	$0.825358\pi$
$660$	−17.6569	+	24.9706i	−0.687292	+	0.971978i
$661$	−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
$669$	12.8284	−	18.1421i	0.495976	−	0.701415i
$670$	−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
$675$	−33.2843	−	9.41421i	−1.28111	−	0.362353i
$676$	−15.9411			−0.613120
$677$	−1.10051	−	1.10051i	−0.0422958	−	0.0422958i	0.685643	−	0.727938i	$-0.259521\pi$
$677$	−1.10051	−	1.10051i	−0.0422958	−	0.0422958i	−0.727938	+	0.685643i	$0.759521\pi$
$678$	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	−0.990600	−	0.136790i	$-0.956322\pi$
$683$	−22.3137	+	22.3137i	−0.853810	+	0.853810i	0.136790	+	0.990600i	$0.456322\pi$
$684$	−8.82843	+	18.4853i	−0.337563	+	0.706802i
$685$	−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
$690$	17.6569	−	24.9706i	0.672185	−	0.950613i
$691$	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
$693$	7.00000	+	3.34315i	0.265908	+	0.126996i
$694$		−	30.2843i		−	1.14958i
$695$		−	7.65685i		−	0.290441i
$696$	−16.9706	−	12.0000i	−0.643268	−	0.454859i
$697$		−	79.5980i		−	3.01499i
$698$	24.1421			0.913793
$699$	−30.1421	−	21.3137i	−1.14008	−	0.806158i
$700$	−13.3137			−0.503211
$701$	−10.6569	+	10.6569i	−0.402504	+	0.402504i	−0.879114	−	0.476611i	$-0.841865\pi$
$701$	−10.6569	+	10.6569i	−0.402504	+	0.402504i	0.476611	+	0.879114i	$0.341865\pi$
$702$	4.48528	−	15.8579i	0.169286	−	0.598517i
$703$		−	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
$717$	16.0000	+	11.3137i	0.597531	+	0.422518i
$718$	31.6569	+	31.6569i	1.18142	+	1.18142i
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$	17.6569	−	36.9706i	0.658032	−	1.37781i
$721$	11.3137			0.421345
$722$	7.34315	+	7.34315i	0.273284	+	0.273284i
$723$	16.4853	+	11.6569i	0.613094	+	0.433523i
$724$	−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
$738$	44.6274	+	21.3137i	1.64276	+	0.784568i
$739$	−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
$741$	10.8284	+	7.65685i	0.397792	+	0.281282i
$742$	−0.343146			−0.0125973
$743$			15.6569i			0.574394i	0.957871	+	0.287197i	$0.0927235\pi$
$743$			15.6569i			0.574394i	−0.957871	+	0.287197i	$0.907277\pi$
$744$	−50.6274	+	8.68629i	−1.85609	+	0.318455i
$745$			36.1421i			1.32415i
$746$		−	28.6274i		−	1.04812i
$747$	−19.9289	+	41.7279i	−0.729161	+	1.52674i
$748$	24.9706	−	24.9706i	0.913014	−	0.913014i
$749$	−5.00000	+	5.00000i	−0.182696	+	0.182696i
$750$	−8.00000	+	11.3137i	−0.292119	+	0.413118i
$751$			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
$756$	−10.0000	−	2.82843i	−0.363696	−	0.102869i
$757$	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	$-0.549980\pi$
$761$	−8.62742			−0.312744			−0.156372	+	0.987698i	$0.549980\pi$
$762$	−1.79899	−	10.4853i	−0.0651705	−	0.379842i
$763$	−0.171573	−	0.171573i	−0.00621136	−	0.00621136i
$764$		−	35.3137i		−	1.27761i
$765$	63.1127	+	30.1421i	2.28184	+	1.08979i
$766$	3.31371	−	3.31371i	0.119729	−	0.119729i
$767$	12.9117			0.466214
$768$	22.6274	+	16.0000i	0.816497	+	0.577350i
$769$	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
$771$	21.1716	−	29.9411i	0.762476	−	1.07830i
$772$		−	8.68629i		−	0.312626i
$773$	5.44365	+	5.44365i	0.195795	+	0.195795i	0.798194	−	0.602400i	$-0.205789\pi$
$773$	5.44365	+	5.44365i	0.195795	+	0.195795i	−0.602400	+	0.798194i	$0.705789\pi$
$774$	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
$780$	−21.6569	−	15.3137i	−0.775440	−	0.548319i
$781$	−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
$786$	−28.4853	−	20.1421i	−1.01604	−	0.718446i
$787$	−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
$789$	−0.343146	+	0.485281i	−0.0122163	+	0.0172765i
$790$			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
$795$	−0.828427	+	1.17157i	−0.0293813	+	0.0415514i
$796$		0			0
$797$	31.5858	−	31.5858i	1.11883	−	1.11883i	0.126912	−	0.991914i	$-0.459493\pi$
$797$	31.5858	−	31.5858i	1.11883	−	1.11883i	0.991914	−	0.126912i	$-0.0405066\pi$
$798$	4.82843	−	6.82843i	0.170924	−	0.241724i
$799$			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	$-0.793356\pi$
$809$	−45.3137			−1.59315			−0.796573	+	0.604543i	$0.793356\pi$
$810$	−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
$813$	−11.1716	+	15.7990i	−0.391804	+	0.554095i
$814$	−14.0000	−	14.0000i	−0.490700	−	0.490700i
$815$	18.4853			0.647511
$816$	−27.3137	+	38.6274i	−0.956171	+	1.35223i
$817$	−8.82843			−0.308868
$818$	−30.8284	−	30.8284i	−1.07789	−	1.07789i
$819$	−2.89949	+	6.07107i	−0.101317	+	0.212140i
$820$	56.2843	−	56.2843i	1.96553	−	1.96553i
$821$	−1.48528	−	1.48528i	−0.0518367	−	0.0518367i	0.680713	−	0.732550i	$-0.261670\pi$
$821$	−1.48528	−	1.48528i	−0.0518367	−	0.0518367i	−0.732550	+	0.680713i	$0.761670\pi$
$822$	−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	−0.533095	−	0.846055i	$-0.678971\pi$
$827$	9.00000	−	9.00000i	0.312961	−	0.312961i	0.846055	+	0.533095i	$0.178971\pi$
$828$	−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
$834$	−4.48528	−	3.17157i	−0.155313	−	0.109823i
$835$	30.9706	−	30.9706i	1.07178	−	1.07178i
$836$	−17.6569			−0.610675
$837$	52.4264	+	14.8284i	1.81212	+	0.512545i
$838$	9.51472			0.328681
$839$		−	0.544156i		−	0.0187863i	−0.999956	−	0.00939317i	$-0.997010\pi$
$839$		−	0.544156i		−	0.0187863i	0.999956	−	0.00939317i	$-0.00298998\pi$
$840$	−9.65685	+	13.6569i	−0.333193	+	0.471206i
$841$			11.0000i			0.379310i
$842$			48.6274i			1.67581i
$843$	−41.4558	−	29.3137i	−1.42782	−	1.00962i
$844$	−10.0000	−	10.0000i	−0.344214	−	0.344214i
$845$	19.2426	−	19.2426i	0.661967	−	0.661967i
$846$	−21.6569	−	10.3431i	−0.744578	−	0.355605i
$847$		−	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
$852$	16.9706	+	12.0000i	0.581402	+	0.411113i
$853$	−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	$-0.710385\pi$
$857$	−35.9411			−1.22773			−0.613863	+	0.789413i	$0.710385\pi$
$858$	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
$861$	−16.4853	−	11.6569i	−0.561817	−	0.397265i
$862$	−19.3137	+	19.3137i	−0.657828	+	0.657828i
$863$	16.6863			0.568008			0.284004	−	0.958823i	$-0.408337\pi$
$863$	16.6863			0.568008			0.284004	+	0.958823i	$0.408337\pi$
$864$	−14.3431	−	25.6569i	−0.487964	−	0.872864i
$865$	71.9411			2.44607
$866$	−37.3137	+	37.3137i	−1.26797	+	1.26797i
$867$	−41.8995	−	29.6274i	−1.42298	−	1.00620i
$868$	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
$876$	30.6274	+	21.6569i	1.03480	+	0.731717i
$877$	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	$0.178138\pi$
$881$			31.5147i			1.06176i	−0.847448	+	0.530879i	$0.821862\pi$
$882$	3.82843	+	1.82843i	0.128910	+	0.0615663i
$883$	−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
$885$	−27.7990	−	19.6569i	−0.934453	−	0.660758i
$886$			10.6863i			0.359013i
$887$		−	44.8284i		−	1.50519i	−0.658483	−	0.752596i	$-0.728802\pi$
$887$		−	44.8284i		−	1.50519i	0.658483	−	0.752596i	$-0.271198\pi$
$888$	21.6569	+	15.3137i	0.726756	+	0.513894i
$889$			4.34315i			0.145664i
$890$	20.9706			0.702935
$891$	2.45584	−	23.1421i	0.0822739	−	0.775291i
$892$	−25.6569			−0.859055
$893$	13.6569	−	13.6569i	0.457009	−	0.457009i
$894$	21.1716	+	14.9706i	0.708083	+	0.500691i
$895$			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
$909$	−7.44365	+	15.5858i	−0.246890	+	0.516948i
$910$	7.65685	+	7.65685i	0.253822	+	0.253822i
$911$	−12.2843			−0.406996			−0.203498	−	0.979075i	$-0.565231\pi$
$911$	−12.2843			−0.406996			−0.203498	+	0.979075i	$0.565231\pi$
$912$	23.3137	−	4.00000i	0.771994	−	0.132453i
$913$	−39.8579			−1.31910
$914$	−37.9411	−	37.9411i	−1.25498	−	1.25498i
$915$	2.00000	−	2.82843i	0.0661180	−	0.0935049i
$916$	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	$0.250060\pi$
$929$			43.1127i			1.41448i	−0.706973	+	0.707241i	$0.749940\pi$
$930$	50.6274	−	71.5980i	1.66014	−	2.34779i
$931$	−2.41421	+	2.41421i	−0.0791227	+	0.0791227i
$932$			42.6274i			1.39631i
$933$	18.4853	−	26.1421i	0.605181	−	0.855855i
$934$	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
$939$	−3.51472	+	4.97056i	−0.114699	+	0.162208i
$940$	−27.3137	+	27.3137i	−0.890875	+	0.890875i
$941$	28.3553	−	28.3553i	0.924358	−	0.924358i	−0.0729761	−	0.997334i	$-0.523250\pi$
$941$	28.3553	−	28.3553i	0.924358	−	0.924358i	0.997334	+	0.0729761i	$0.0232497\pi$
$942$	−47.7990	−	33.7990i	−1.55738	−	1.10123i
$943$		−	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	0.839869	−	0.542789i	$-0.182632\pi$
$947$	9.14214	+	9.14214i	0.297079	+	0.297079i	−0.542789	+	0.839869i	$0.682632\pi$
$948$	5.65685	+	4.00000i	0.183726	+	0.129914i
$949$	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	$-0.328633\pi$
$953$	31.6569			1.02547			0.512733	+	0.858548i	$0.328633\pi$
$954$	0.343146	+	0.970563i	0.0111098	+	0.0314231i
$955$	42.6274	+	42.6274i	1.37939	+	1.37939i
$956$		−	22.6274i		−	0.731823i
$957$	−10.9706	+	15.5147i	−0.354628	+	0.501520i
$958$	−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
$963$	19.1421	+	9.14214i	0.616847	+	0.294601i
$964$		−	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	−0.381881	−	0.924212i	$-0.624724\pi$
$971$	16.8995	−	16.8995i	0.542331	−	0.542331i	0.924212	+	0.381881i	$0.124724\pi$
$972$	2.00000	+	31.1127i	0.0641500	+	0.997940i
$973$	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	$-0.833000\pi$
$977$		−	31.3137i		−	1.00181i	0.865501	−	0.500907i	$-0.167000\pi$
$978$	7.65685	−	10.8284i	0.244839	−	0.346255i
$979$	−7.94113	+	7.94113i	−0.253799	+	0.253799i
$980$	4.82843	−	4.82843i	0.154238	−	0.154238i
$981$	−0.313708	+	0.656854i	−0.0100159	+	0.0209717i
$982$		−	24.6274i		−	0.785892i
$983$			54.4853i			1.73781i	0.494978	+	0.868905i	$0.335176\pi$
$983$			54.4853i			1.73781i	−0.494978	+	0.868905i	$0.664824\pi$
$984$	−9.65685	−	56.2843i	−0.307849	−	1.79428i
$985$			0.828427i			0.0263959i
$986$	−40.9706			−1.30477
$987$	8.00000	+	5.65685i	0.254643	+	0.180060i
$988$		−	15.3137i		−	0.487194i
$989$	6.68629	−	6.68629i	0.212612	−	0.212612i
$990$	−33.7990	−	16.1421i	−1.07420	−	0.513031i
$991$			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.b.323.2	yes	4
3.2	odd	2		336.2.s.a.323.1	yes	4
4.3	odd	2		1344.2.s.a.239.1		4
12.11	even	2		1344.2.s.b.239.2		4
16.5	even	4		1344.2.s.b.911.1		4
16.11	odd	4		336.2.s.a.155.2	✓	4
48.5	odd	4		1344.2.s.a.911.1		4
48.11	even	4	inner	336.2.s.b.155.2	yes	4

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

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

Introduction

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