LMFDB - Embedded newform 336.2.s.a.155.1

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			155.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	336.155
Dual form			336.2.s.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} +2.00000i q^{4} +(0.414214 - 0.414214i) q^{5} +(-0.414214 + 2.41421i) q^{6} -1.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} +2.00000i q^{4} +(0.414214 - 0.414214i) q^{5} +(-0.414214 + 2.41421i) q^{6} -1.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} -0.828427 q^{10} +(-3.82843 - 3.82843i) q^{11} +(2.82843 - 2.00000i) q^{12} +(-4.41421 + 4.41421i) q^{13} +(1.00000 + 1.00000i) q^{14} +(-1.00000 - 0.171573i) q^{15} -4.00000 q^{16} -1.17157i q^{17} +(3.82843 - 1.82843i) q^{18} +(0.414214 + 0.414214i) q^{19} +(0.828427 + 0.828427i) q^{20} +(1.00000 + 1.41421i) q^{21} +7.65685i q^{22} +7.65685i q^{23} +(-4.82843 - 0.828427i) q^{24} +4.65685i q^{25} +8.82843 q^{26} +(5.00000 - 1.41421i) q^{27} -2.00000i q^{28} +(-3.00000 - 3.00000i) q^{29} +(0.828427 + 1.17157i) q^{30} -6.48528i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.58579 + 9.24264i) q^{33} +(-1.17157 + 1.17157i) q^{34} +(-0.414214 + 0.414214i) q^{35} +(-5.65685 - 2.00000i) q^{36} +(1.82843 + 1.82843i) q^{37} -0.828427i q^{38} +(10.6569 + 1.82843i) q^{39} -1.65685i q^{40} -0.343146 q^{41} +(0.414214 - 2.41421i) q^{42} +(-3.82843 + 3.82843i) q^{43} +(7.65685 - 7.65685i) q^{44} +(0.757359 + 1.58579i) q^{45} +(7.65685 - 7.65685i) q^{46} -5.65685 q^{47} +(4.00000 + 5.65685i) q^{48} +1.00000 q^{49} +(4.65685 - 4.65685i) q^{50} +(-1.65685 + 1.17157i) q^{51} +(-8.82843 - 8.82843i) q^{52} +(-5.82843 + 5.82843i) q^{53} +(-6.41421 - 3.58579i) q^{54} -3.17157 q^{55} +(-2.00000 + 2.00000i) q^{56} +(0.171573 - 1.00000i) q^{57} +6.00000i q^{58} +(-10.0711 - 10.0711i) q^{59} +(0.343146 - 2.00000i) q^{60} +(2.41421 - 2.41421i) q^{61} +(-6.48528 + 6.48528i) q^{62} +(1.00000 - 2.82843i) q^{63} -8.00000i q^{64} +3.65685i q^{65} +(10.8284 - 7.65685i) q^{66} +(-7.00000 - 7.00000i) q^{67} +2.34315 q^{68} +(10.8284 - 7.65685i) q^{69} +0.828427 q^{70} +6.00000i q^{71} +(3.65685 + 7.65685i) q^{72} -5.17157i q^{73} -3.65685i q^{74} +(6.58579 - 4.65685i) q^{75} +(-0.828427 + 0.828427i) q^{76} +(3.82843 + 3.82843i) q^{77} +(-8.82843 - 12.4853i) q^{78} -2.00000i q^{79} +(-1.65685 + 1.65685i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(0.343146 + 0.343146i) q^{82} +(8.89949 - 8.89949i) q^{83} +(-2.82843 + 2.00000i) q^{84} +(-0.485281 - 0.485281i) q^{85} +7.65685 q^{86} +(-1.24264 + 7.24264i) q^{87} -15.3137 q^{88} -15.6569 q^{89} +(0.828427 - 2.34315i) q^{90} +(4.41421 - 4.41421i) q^{91} -15.3137 q^{92} +(-9.17157 + 6.48528i) q^{93} +(5.65685 + 5.65685i) q^{94} +0.343146 q^{95} +(1.65685 - 9.65685i) q^{96} -2.00000 q^{97} +(-1.00000 - 1.00000i) q^{98} +(14.6569 - 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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
$5$	0.414214	−	0.414214i	0.185242	−	0.185242i	−0.608394	−	0.793635i	$-0.708186\pi$
$5$	0.414214	−	0.414214i	0.185242	−	0.185242i	0.793635	+	0.608394i	$0.208186\pi$
$6$	−0.414214	+	2.41421i	−0.169102	+	0.985599i
$7$	−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
$10$	−0.828427			−0.261972
$11$	−3.82843	−	3.82843i	−1.15431	−	1.15431i	−0.985678	−	0.168636i	$-0.946064\pi$
$11$	−3.82843	−	3.82843i	−1.15431	−	1.15431i	−0.168636	−	0.985678i	$-0.553936\pi$
$12$	2.82843	−	2.00000i	0.816497	−	0.577350i
$13$	−4.41421	+	4.41421i	−1.22428	+	1.22428i	−0.258188	+	0.966095i	$0.583125\pi$
$13$	−4.41421	+	4.41421i	−1.22428	+	1.22428i	−0.966095	+	0.258188i	$0.916875\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$	−1.00000	−	0.171573i	−0.258199	−	0.0442999i
$16$	−4.00000			−1.00000
$17$		−	1.17157i		−	0.284148i	−0.989856	−	0.142074i	$-0.954623\pi$
$17$		−	1.17157i		−	0.284148i	0.989856	−	0.142074i	$-0.0453771\pi$
$18$	3.82843	−	1.82843i	0.902369	−	0.430964i
$19$	0.414214	+	0.414214i	0.0950271	+	0.0950271i	0.753022	−	0.657995i	$-0.228595\pi$
$19$	0.414214	+	0.414214i	0.0950271	+	0.0950271i	−0.657995	+	0.753022i	$0.728595\pi$
$20$	0.828427	+	0.828427i	0.185242	+	0.185242i
$21$	1.00000	+	1.41421i	0.218218	+	0.308607i
$22$			7.65685i			1.63245i
$23$			7.65685i			1.59656i	0.602284	+	0.798282i	$0.294258\pi$
$23$			7.65685i			1.59656i	−0.602284	+	0.798282i	$0.705742\pi$
$24$	−4.82843	−	0.828427i	−0.985599	−	0.169102i
$25$			4.65685i			0.931371i
$26$	8.82843			1.73140
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		−	2.00000i		−	0.377964i
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0.828427	+	1.17157i	0.151249	+	0.213899i
$31$		−	6.48528i		−	1.16479i	−0.812906	−	0.582395i	$-0.802116\pi$
$31$		−	6.48528i		−	1.16479i	0.812906	−	0.582395i	$-0.197884\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	−1.58579	+	9.24264i	−0.276050	+	1.60894i
$34$	−1.17157	+	1.17157i	−0.200923	+	0.200923i
$35$	−0.414214	+	0.414214i	−0.0700149	+	0.0700149i
$36$	−5.65685	−	2.00000i	−0.942809	−	0.333333i
$37$	1.82843	+	1.82843i	0.300592	+	0.300592i	0.841245	−	0.540654i	$-0.181823\pi$
$37$	1.82843	+	1.82843i	0.300592	+	0.300592i	−0.540654	+	0.841245i	$0.681823\pi$
$38$		−	0.828427i		−	0.134389i
$39$	10.6569	+	1.82843i	1.70646	+	0.292783i
$40$		−	1.65685i		−	0.261972i
$41$	−0.343146			−0.0535904			−0.0267952	−	0.999641i	$-0.508530\pi$
$41$	−0.343146			−0.0535904			−0.0267952	+	0.999641i	$0.508530\pi$
$42$	0.414214	−	2.41421i	0.0639145	−	0.372521i
$43$	−3.82843	+	3.82843i	−0.583830	+	0.583830i	−0.935953	−	0.352124i	$-0.885460\pi$
$43$	−3.82843	+	3.82843i	−0.583830	+	0.583830i	0.352124	+	0.935953i	$0.385460\pi$
$44$	7.65685	−	7.65685i	1.15431	−	1.15431i
$45$	0.757359	+	1.58579i	0.112900	+	0.236395i
$46$	7.65685	−	7.65685i	1.12894	−	1.12894i
$47$	−5.65685			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$47$	−5.65685			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$48$	4.00000	+	5.65685i	0.577350	+	0.816497i
$49$	1.00000			0.142857
$50$	4.65685	−	4.65685i	0.658579	−	0.658579i
$51$	−1.65685	+	1.17157i	−0.232006	+	0.164053i
$52$	−8.82843	−	8.82843i	−1.22428	−	1.22428i
$53$	−5.82843	+	5.82843i	−0.800596	+	0.800596i	−0.983189	−	0.182593i	$-0.941551\pi$
$53$	−5.82843	+	5.82843i	−0.800596	+	0.800596i	0.182593	+	0.983189i	$0.441551\pi$
$54$	−6.41421	−	3.58579i	−0.872864	−	0.487964i
$55$	−3.17157			−0.427655
$56$	−2.00000	+	2.00000i	−0.267261	+	0.267261i
$57$	0.171573	−	1.00000i	0.0227254	−	0.132453i
$58$			6.00000i			0.787839i
$59$	−10.0711	−	10.0711i	−1.31114	−	1.31114i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$	−10.0711	−	10.0711i	−1.31114	−	1.31114i	−0.390567	−	0.920575i	$-0.627721\pi$
$60$	0.343146	−	2.00000i	0.0442999	−	0.258199i
$61$	2.41421	−	2.41421i	0.309108	−	0.309108i	−0.535455	−	0.844564i	$-0.679860\pi$
$61$	2.41421	−	2.41421i	0.309108	−	0.309108i	0.844564	+	0.535455i	$0.179860\pi$
$62$	−6.48528	+	6.48528i	−0.823632	+	0.823632i
$63$	1.00000	−	2.82843i	0.125988	−	0.356348i
$64$		−	8.00000i		−	1.00000i
$65$			3.65685i			0.453577i
$66$	10.8284	−	7.65685i	1.33289	−	0.942494i
$67$	−7.00000	−	7.00000i	−0.855186	−	0.855186i	0.135580	−	0.990766i	$-0.456710\pi$
$67$	−7.00000	−	7.00000i	−0.855186	−	0.855186i	−0.990766	+	0.135580i	$0.956710\pi$
$68$	2.34315			0.284148
$69$	10.8284	−	7.65685i	1.30359	−	0.921777i
$70$	0.828427			0.0990160
$71$			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
$73$		−	5.17157i		−	0.605287i	−0.953104	−	0.302643i	$-0.902131\pi$
$73$		−	5.17157i		−	0.605287i	0.953104	−	0.302643i	$-0.0978691\pi$
$74$		−	3.65685i		−	0.425101i
$75$	6.58579	−	4.65685i	0.760461	−	0.537727i
$76$	−0.828427	+	0.828427i	−0.0950271	+	0.0950271i
$77$	3.82843	+	3.82843i	0.436290	+	0.436290i
$78$	−8.82843	−	12.4853i	−0.999623	−	1.41368i
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−1.65685	+	1.65685i	−0.185242	+	0.185242i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	0.343146	+	0.343146i	0.0378941	+	0.0378941i
$83$	8.89949	−	8.89949i	0.976846	−	0.976846i	−0.0228915	−	0.999738i	$-0.507287\pi$
$83$	8.89949	−	8.89949i	0.976846	−	0.976846i	0.999738	+	0.0228915i	$0.00728722\pi$
$84$	−2.82843	+	2.00000i	−0.308607	+	0.218218i
$85$	−0.485281	−	0.485281i	−0.0526362	−	0.0526362i
$86$	7.65685			0.825660
$87$	−1.24264	+	7.24264i	−0.133225	+	0.776493i
$88$	−15.3137			−1.63245
$89$	−15.6569			−1.65962			−0.829812	−	0.558044i	$-0.811552\pi$
$89$	−15.6569			−1.65962			−0.829812	+	0.558044i	$0.811552\pi$
$90$	0.828427	−	2.34315i	0.0873239	−	0.246989i
$91$	4.41421	−	4.41421i	0.462735	−	0.462735i
$92$	−15.3137			−1.59656
$93$	−9.17157	+	6.48528i	−0.951048	+	0.672492i
$94$	5.65685	+	5.65685i	0.583460	+	0.583460i
$95$	0.343146			0.0352060
$96$	1.65685	−	9.65685i	0.169102	−	0.985599i
$97$	−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
$99$	14.6569	−	7.00000i	1.47307	−	0.703526i
$100$	−9.31371			−0.931371
$101$	10.0711	−	10.0711i	1.00211	−	1.00211i	0.00211093	−	0.999998i	$-0.499328\pi$
$101$	10.0711	−	10.0711i	1.00211	−	1.00211i	0.999998	−	0.00211093i	$-0.000671930\pi$
$102$	2.82843	+	0.485281i	0.280056	+	0.0480500i
$103$	11.3137			1.11477			0.557386	−	0.830253i	$-0.311804\pi$
$103$	11.3137			1.11477			0.557386	+	0.830253i	$0.311804\pi$
$104$			17.6569i			1.73140i
$105$	1.00000	+	0.171573i	0.0975900	+	0.0167438i
$106$	11.6569			1.13221
$107$	−5.00000	−	5.00000i	−0.483368	−	0.483368i	0.422837	−	0.906206i	$-0.361034\pi$
$107$	−5.00000	−	5.00000i	−0.483368	−	0.483368i	−0.906206	+	0.422837i	$0.861034\pi$
$108$	2.82843	+	10.0000i	0.272166	+	0.962250i
$109$	5.82843	−	5.82843i	0.558262	−	0.558262i	−0.370550	−	0.928812i	$-0.620831\pi$
$109$	5.82843	−	5.82843i	0.558262	−	0.558262i	0.928812	+	0.370550i	$0.120831\pi$
$110$	3.17157	+	3.17157i	0.302398	+	0.302398i
$111$	0.757359	−	4.41421i	0.0718854	−	0.418979i
$112$	4.00000			0.377964
$113$		−	1.65685i		−	0.155864i	−0.996959	−	0.0779319i	$-0.975168\pi$
$113$		−	1.65685i		−	0.155864i	0.996959	−	0.0779319i	$-0.0248317\pi$
$114$	−1.17157	+	0.828427i	−0.109728	+	0.0775893i
$115$	3.17157	+	3.17157i	0.295751	+	0.295751i
$116$	6.00000	−	6.00000i	0.557086	−	0.557086i
$117$	−8.07107	−	16.8995i	−0.746170	−	1.56236i
$118$			20.1421i			1.85423i
$119$			1.17157i			0.107398i
$120$	−2.34315	+	1.65685i	−0.213899	+	0.151249i
$121$			18.3137i			1.66488i
$122$	−4.82843			−0.437145
$123$	0.343146	+	0.485281i	0.0309404	+	0.0437563i
$124$	12.9706			1.16479
$125$	4.00000	+	4.00000i	0.357771	+	0.357771i
$126$	−3.82843	+	1.82843i	−0.341063	+	0.162889i
$127$			15.6569i			1.38932i	0.719338	+	0.694661i	$0.244445\pi$
$127$			15.6569i			1.38932i	−0.719338	+	0.694661i	$0.755555\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	9.24264	+	1.58579i	0.813769	+	0.139621i
$130$	3.65685	−	3.65685i	0.320727	−	0.320727i
$131$	−4.07107	+	4.07107i	−0.355691	+	0.355691i	−0.862222	−	0.506531i	$-0.830928\pi$
$131$	−4.07107	+	4.07107i	−0.355691	+	0.355691i	0.506531	+	0.862222i	$0.330928\pi$
$132$	−18.4853	−	3.17157i	−1.60894	−	0.276050i
$133$	−0.414214	−	0.414214i	−0.0359169	−	0.0359169i
$134$			14.0000i			1.20942i
$135$	1.48528	−	2.65685i	0.127833	−	0.228666i
$136$	−2.34315	−	2.34315i	−0.200923	−	0.200923i
$137$	−7.65685			−0.654169			−0.327085	−	0.944995i	$-0.606066\pi$
$137$	−7.65685			−0.654169			−0.327085	+	0.944995i	$0.606066\pi$
$138$	−18.4853	−	3.17157i	−1.57357	−	0.269982i
$139$	−4.41421	+	4.41421i	−0.374409	+	0.374409i	−0.869080	−	0.494671i	$-0.835288\pi$
$139$	−4.41421	+	4.41421i	−0.374409	+	0.374409i	0.494671	+	0.869080i	$0.335288\pi$
$140$	−0.828427	−	0.828427i	−0.0700149	−	0.0700149i
$141$	5.65685	+	8.00000i	0.476393	+	0.673722i
$142$	6.00000	−	6.00000i	0.503509	−	0.503509i
$143$	33.7990			2.82641
$144$	4.00000	−	11.3137i	0.333333	−	0.942809i
$145$	−2.48528			−0.206391
$146$	−5.17157	+	5.17157i	−0.428002	+	0.428002i
$147$	−1.00000	−	1.41421i	−0.0824786	−	0.116642i
$148$	−3.65685	+	3.65685i	−0.300592	+	0.300592i
$149$	9.48528	−	9.48528i	0.777065	−	0.777065i	−0.202266	−	0.979331i	$-0.564831\pi$
$149$	9.48528	−	9.48528i	0.777065	−	0.777065i	0.979331	+	0.202266i	$0.0648306\pi$
$150$	−11.2426	−	1.92893i	−0.917958	−	0.157497i
$151$	−17.6569			−1.43689			−0.718447	−	0.695581i	$-0.755147\pi$
$151$	−17.6569			−1.43689			−0.718447	+	0.695581i	$0.755147\pi$
$152$	1.65685			0.134389
$153$	3.31371	+	1.17157i	0.267897	+	0.0947161i
$154$		−	7.65685i		−	0.617007i
$155$	−2.68629	−	2.68629i	−0.215768	−	0.215768i
$156$	−3.65685	+	21.3137i	−0.292783	+	1.70646i
$157$	2.89949	−	2.89949i	0.231405	−	0.231405i	−0.581874	−	0.813279i	$-0.697680\pi$
$157$	2.89949	−	2.89949i	0.231405	−	0.231405i	0.813279	+	0.581874i	$0.197680\pi$
$158$	−2.00000	+	2.00000i	−0.159111	+	0.159111i
$159$	14.0711	+	2.41421i	1.11591	+	0.191460i
$160$	3.31371			0.261972
$161$		−	7.65685i		−	0.603445i
$162$	1.34315	+	12.6569i	0.105527	+	0.994416i
$163$	−1.82843	−	1.82843i	−0.143213	−	0.143213i	0.631865	−	0.775078i	$-0.282290\pi$
$163$	−1.82843	−	1.82843i	−0.143213	−	0.143213i	−0.775078	+	0.631865i	$0.782290\pi$
$164$		−	0.686292i		−	0.0535904i
$165$	3.17157	+	4.48528i	0.246907	+	0.349179i
$166$	−17.7990			−1.38147
$167$		−	7.17157i		−	0.554953i	−0.960732	−	0.277476i	$-0.910502\pi$
$167$		−	7.17157i		−	0.554953i	0.960732	−	0.277476i	$-0.0894981\pi$
$168$	4.82843	+	0.828427i	0.372521	+	0.0639145i
$169$		−	25.9706i		−	1.99774i
$170$			0.970563i			0.0744388i
$171$	−1.58579	+	0.757359i	−0.121268	+	0.0579167i
$172$	−7.65685	−	7.65685i	−0.583830	−	0.583830i
$173$	4.89949	+	4.89949i	0.372502	+	0.372502i	0.868388	−	0.495886i	$-0.165157\pi$
$173$	4.89949	+	4.89949i	0.372502	+	0.372502i	−0.495886	+	0.868388i	$0.665157\pi$
$174$	8.48528	−	6.00000i	0.643268	−	0.454859i
$175$		−	4.65685i		−	0.352025i
$176$	15.3137	+	15.3137i	1.15431	+	1.15431i
$177$	−4.17157	+	24.3137i	−0.313555	+	1.82753i
$178$	15.6569	+	15.6569i	1.17353	+	1.17353i
$179$	−15.0000	+	15.0000i	−1.12115	+	1.12115i	−0.129584	+	0.991568i	$0.541364\pi$
$179$	−15.0000	+	15.0000i	−1.12115	+	1.12115i	−0.991568	+	0.129584i	$0.958636\pi$
$180$	−3.17157	+	1.51472i	−0.236395	+	0.112900i
$181$	−2.07107	−	2.07107i	−0.153941	−	0.153941i	0.625934	−	0.779876i	$-0.284718\pi$
$181$	−2.07107	−	2.07107i	−0.153941	−	0.153941i	−0.779876	+	0.625934i	$0.784718\pi$
$182$	−8.82843			−0.654407
$183$	−5.82843	−	1.00000i	−0.430850	−	0.0739221i
$184$	15.3137	+	15.3137i	1.12894	+	1.12894i
$185$	1.51472			0.111364
$186$	15.6569	+	2.68629i	1.14802	+	0.196968i
$187$	−4.48528	+	4.48528i	−0.327996	+	0.327996i
$188$		−	11.3137i		−	0.825137i
$189$	−5.00000	+	1.41421i	−0.363696	+	0.102869i
$190$	−0.343146	−	0.343146i	−0.0248944	−	0.0248944i
$191$	−6.34315			−0.458974			−0.229487	−	0.973312i	$-0.573705\pi$
$191$	−6.34315			−0.458974			−0.229487	+	0.973312i	$0.573705\pi$
$192$	−11.3137	+	8.00000i	−0.816497	+	0.577350i
$193$	15.6569			1.12701			0.563503	−	0.826114i	$-0.309454\pi$
$193$	15.6569			1.12701			0.563503	+	0.826114i	$0.309454\pi$
$194$	2.00000	+	2.00000i	0.143592	+	0.143592i
$195$	5.17157	−	3.65685i	0.370344	−	0.261873i
$196$			2.00000i			0.142857i
$197$	−5.82843	+	5.82843i	−0.415258	+	0.415258i	−0.883566	−	0.468307i	$-0.844864\pi$
$197$	−5.82843	+	5.82843i	−0.415258	+	0.415258i	0.468307	+	0.883566i	$0.344864\pi$
$198$	−21.6569	−	7.65685i	−1.53909	−	0.544149i
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	9.31371	+	9.31371i	0.658579	+	0.658579i
$201$	−2.89949	+	16.8995i	−0.204515	+	1.19200i
$202$	−20.1421			−1.41720
$203$	3.00000	+	3.00000i	0.210559	+	0.210559i
$204$	−2.34315	−	3.31371i	−0.164053	−	0.232006i
$205$	−0.142136	+	0.142136i	−0.00992718	+	0.00992718i
$206$	−11.3137	−	11.3137i	−0.788263	−	0.788263i
$207$	−21.6569	−	7.65685i	−1.50526	−	0.532188i
$208$	17.6569	−	17.6569i	1.22428	−	1.22428i
$209$		−	3.17157i		−	0.219382i
$210$	−0.828427	−	1.17157i	−0.0571669	−	0.0808462i
$211$	5.00000	+	5.00000i	0.344214	+	0.344214i	0.857949	−	0.513735i	$-0.171738\pi$
$211$	5.00000	+	5.00000i	0.344214	+	0.344214i	−0.513735	+	0.857949i	$0.671738\pi$
$212$	−11.6569	−	11.6569i	−0.800596	−	0.800596i
$213$	8.48528	−	6.00000i	0.581402	−	0.411113i
$214$			10.0000i			0.683586i
$215$			3.17157i			0.216299i
$216$	7.17157	−	12.8284i	0.487964	−	0.872864i
$217$			6.48528i			0.440250i
$218$	−11.6569			−0.789502
$219$	−7.31371	+	5.17157i	−0.494215	+	0.349463i
$220$		−	6.34315i		−	0.427655i
$221$	5.17157	+	5.17157i	0.347878	+	0.347878i
$222$	−5.17157	+	3.65685i	−0.347093	+	0.245432i
$223$			7.17157i			0.480244i	0.970743	+	0.240122i	$0.0771875\pi$
$223$			7.17157i			0.480244i	−0.970743	+	0.240122i	$0.922813\pi$
$224$	−4.00000	−	4.00000i	−0.267261	−	0.267261i
$225$	−13.1716	−	4.65685i	−0.878105	−	0.310457i
$226$	−1.65685	+	1.65685i	−0.110212	+	0.110212i
$227$	−8.07107	+	8.07107i	−0.535696	+	0.535696i	−0.922262	−	0.386566i	$-0.873661\pi$
$227$	−8.07107	+	8.07107i	−0.535696	+	0.535696i	0.386566	+	0.922262i	$0.373661\pi$
$228$	2.00000	+	0.343146i	0.132453	+	0.0227254i
$229$	10.8995	+	10.8995i	0.720259	+	0.720259i	0.968658	−	0.248399i	$-0.0799044\pi$
$229$	10.8995	+	10.8995i	0.720259	+	0.720259i	−0.248399	+	0.968658i	$0.579904\pi$
$230$		−	6.34315i		−	0.418255i
$231$	1.58579	−	9.24264i	0.104337	−	0.608121i
$232$	−12.0000			−0.787839
$233$	−1.31371			−0.0860639			−0.0430320	−	0.999074i	$-0.513702\pi$
$233$	−1.31371			−0.0860639			−0.0430320	+	0.999074i	$0.513702\pi$
$234$	−8.82843	+	24.9706i	−0.577132	+	1.63238i
$235$	−2.34315	+	2.34315i	−0.152850	+	0.152850i
$236$	20.1421	−	20.1421i	1.31114	−	1.31114i
$237$	−2.82843	+	2.00000i	−0.183726	+	0.129914i
$238$	1.17157	−	1.17157i	0.0759418	−	0.0759418i
$239$	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	+	0.686292i	0.258199	+	0.0442999i
$241$	0.343146			0.0221040			0.0110520	−	0.999939i	$-0.496482\pi$
$241$	0.343146			0.0221040			0.0110520	+	0.999939i	$0.496482\pi$
$242$	18.3137	−	18.3137i	1.17725	−	1.17725i
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$	4.82843	+	4.82843i	0.309108	+	0.309108i
$245$	0.414214	−	0.414214i	0.0264631	−	0.0264631i
$246$	0.142136	−	0.828427i	0.00906224	−	0.0528186i
$247$	−3.65685			−0.232680
$248$	−12.9706	−	12.9706i	−0.823632	−	0.823632i
$249$	−21.4853	−	3.68629i	−1.36157	−	0.233609i
$250$		−	8.00000i		−	0.505964i
$251$	2.41421	+	2.41421i	0.152384	+	0.152384i	0.779182	−	0.626798i	$-0.215635\pi$
$251$	2.41421	+	2.41421i	0.152384	+	0.152384i	−0.626798	+	0.779182i	$0.715635\pi$
$252$	5.65685	+	2.00000i	0.356348	+	0.125988i
$253$	29.3137	−	29.3137i	1.84294	−	1.84294i
$254$	15.6569	−	15.6569i	0.982398	−	0.982398i
$255$	−0.201010	+	1.17157i	−0.0125877	+	0.0733667i
$256$	16.0000			1.00000
$257$		−	26.8284i		−	1.67351i	−0.547576	−	0.836756i	$-0.684449\pi$
$257$		−	26.8284i		−	1.67351i	0.547576	−	0.836756i	$-0.315551\pi$
$258$	−7.65685	−	10.8284i	−0.476695	−	0.674148i
$259$	−1.82843	−	1.82843i	−0.113613	−	0.113613i
$260$	−7.31371			−0.453577
$261$	11.4853	−	5.48528i	0.710921	−	0.339530i
$262$	8.14214			0.503023
$263$			11.6569i			0.718792i	0.933185	+	0.359396i	$0.117017\pi$
$263$			11.6569i			0.718792i	−0.933185	+	0.359396i	$0.882983\pi$
$264$	15.3137	+	21.6569i	0.942494	+	1.33289i
$265$			4.82843i			0.296608i
$266$			0.828427i			0.0507941i
$267$	15.6569	+	22.1421i	0.958184	+	1.35508i
$268$	14.0000	−	14.0000i	0.855186	−	0.855186i
$269$	5.58579	+	5.58579i	0.340571	+	0.340571i	0.856582	−	0.516011i	$-0.172584\pi$
$269$	5.58579	+	5.58579i	0.340571	+	0.340571i	−0.516011	+	0.856582i	$0.672584\pi$
$270$	−4.14214	+	1.17157i	−0.252082	+	0.0712997i
$271$		−	16.8284i		−	1.02225i	−0.859505	−	0.511127i	$-0.829228\pi$
$271$		−	16.8284i		−	1.02225i	0.859505	−	0.511127i	$-0.170772\pi$
$272$			4.68629i			0.284148i
$273$	−10.6569	−	1.82843i	−0.644982	−	0.110661i
$274$	7.65685	+	7.65685i	0.462567	+	0.462567i
$275$	17.8284	−	17.8284i	1.07509	−	1.07509i
$276$	15.3137	+	21.6569i	0.921777	+	1.30359i
$277$	6.31371	+	6.31371i	0.379354	+	0.379354i	0.870869	−	0.491515i	$-0.163557\pi$
$277$	6.31371	+	6.31371i	0.379354	+	0.379354i	−0.491515	+	0.870869i	$0.663557\pi$
$278$	8.82843			0.529494
$279$	18.3431	+	6.48528i	1.09818	+	0.388264i
$280$			1.65685i			0.0990160i
$281$	6.68629			0.398871			0.199435	−	0.979911i	$-0.436089\pi$
$281$	6.68629			0.398871			0.199435	+	0.979911i	$0.436089\pi$
$282$	2.34315	−	13.6569i	0.139532	−	0.813254i
$283$	−12.8995	+	12.8995i	−0.766795	+	0.766795i	−0.977541	−	0.210746i	$-0.932411\pi$
$283$	−12.8995	+	12.8995i	−0.766795	+	0.766795i	0.210746	+	0.977541i	$0.432411\pi$
$284$	−12.0000			−0.712069
$285$	−0.343146	−	0.485281i	−0.0203262	−	0.0287456i
$286$	−33.7990	−	33.7990i	−1.99858	−	1.99858i
$287$	0.343146			0.0202553
$288$	−15.3137	+	7.31371i	−0.902369	+	0.430964i
$289$	15.6274			0.919260
$290$	2.48528	+	2.48528i	0.145941	+	0.145941i
$291$	2.00000	+	2.82843i	0.117242	+	0.165805i
$292$	10.3431			0.605287
$293$	−9.24264	+	9.24264i	−0.539961	+	0.539961i	−0.923517	−	0.383557i	$-0.874699\pi$
$293$	−9.24264	+	9.24264i	−0.539961	+	0.539961i	0.383557	+	0.923517i	$0.374699\pi$
$294$	−0.414214	+	2.41421i	−0.0241574	+	0.140800i
$295$	−8.34315			−0.485757
$296$	7.31371			0.425101
$297$	−24.5563	−	13.7279i	−1.42490	−	0.796575i
$298$	−18.9706			−1.09894
$299$	−33.7990	−	33.7990i	−1.95465	−	1.95465i
$300$	9.31371	+	13.1716i	0.537727	+	0.760461i
$301$	3.82843	−	3.82843i	0.220667	−	0.220667i
$302$	17.6569	+	17.6569i	1.01604	+	1.01604i
$303$	−24.3137	−	4.17157i	−1.39679	−	0.239651i
$304$	−1.65685	−	1.65685i	−0.0950271	−	0.0950271i
$305$		−	2.00000i		−	0.114520i
$306$	−2.14214	−	4.48528i	−0.122458	−	0.256406i
$307$	−14.8995	−	14.8995i	−0.850359	−	0.850359i	0.139818	−	0.990177i	$-0.455348\pi$
$307$	−14.8995	−	14.8995i	−0.850359	−	0.850359i	−0.990177	+	0.139818i	$0.955348\pi$
$308$	−7.65685	+	7.65685i	−0.436290	+	0.436290i
$309$	−11.3137	−	16.0000i	−0.643614	−	0.910208i
$310$			5.37258i			0.305142i
$311$		−	1.51472i		−	0.0858918i	−0.999077	−	0.0429459i	$-0.986326\pi$
$311$		−	1.51472i		−	0.0858918i	0.999077	−	0.0429459i	$-0.0136743\pi$
$312$	24.9706	−	17.6569i	1.41368	−	0.999623i
$313$		−	20.4853i		−	1.15790i	−0.815364	−	0.578948i	$-0.803463\pi$
$313$		−	20.4853i		−	1.15790i	0.815364	−	0.578948i	$-0.196537\pi$
$314$	−5.79899			−0.327256
$315$	−0.757359	−	1.58579i	−0.0426724	−	0.0893489i
$316$	4.00000			0.225018
$317$	−13.1421	−	13.1421i	−0.738136	−	0.738136i	0.234081	−	0.972217i	$-0.424792\pi$
$317$	−13.1421	−	13.1421i	−0.738136	−	0.738136i	−0.972217	+	0.234081i	$0.924792\pi$
$318$	−11.6569	−	16.4853i	−0.653684	−	0.924449i
$319$			22.9706i			1.28610i
$320$	−3.31371	−	3.31371i	−0.185242	−	0.185242i
$321$	−2.07107	+	12.0711i	−0.115596	+	0.673741i
$322$	−7.65685	+	7.65685i	−0.426700	+	0.426700i
$323$	0.485281	−	0.485281i	0.0270018	−	0.0270018i
$324$	11.3137	−	14.0000i	0.628539	−	0.777778i
$325$	−20.5563	−	20.5563i	−1.14026	−	1.14026i
$326$			3.65685i			0.202534i
$327$	−14.0711	−	2.41421i	−0.778132	−	0.133506i
$328$	−0.686292	+	0.686292i	−0.0378941	+	0.0378941i
$329$	5.65685			0.311872
$330$	1.31371	−	7.65685i	0.0723173	−	0.421496i
$331$	17.1421	−	17.1421i	0.942217	−	0.942217i	−0.0562024	−	0.998419i	$-0.517899\pi$
$331$	17.1421	−	17.1421i	0.942217	−	0.942217i	0.998419	+	0.0562024i	$0.0178992\pi$
$332$	17.7990	+	17.7990i	0.976846	+	0.976846i
$333$	−7.00000	+	3.34315i	−0.383598	+	0.183203i
$334$	−7.17157	+	7.17157i	−0.392411	+	0.392411i
$335$	−5.79899			−0.316833
$336$	−4.00000	−	5.65685i	−0.218218	−	0.308607i
$337$	25.3137			1.37893			0.689463	−	0.724321i	$-0.257847\pi$
$337$	25.3137			1.37893			0.689463	+	0.724321i	$0.257847\pi$
$338$	−25.9706	+	25.9706i	−1.41261	+	1.41261i
$339$	−2.34315	+	1.65685i	−0.127262	+	0.0899880i
$340$	0.970563	−	0.970563i	0.0526362	−	0.0526362i
$341$	−24.8284	+	24.8284i	−1.34453	+	1.34453i
$342$	2.34315	+	0.828427i	0.126703	+	0.0447962i
$343$	−1.00000			−0.0539949
$344$			15.3137i			0.825660i
$345$	1.31371	−	7.65685i	0.0707277	−	0.412231i
$346$		−	9.79899i		−	0.526797i
$347$	13.1421	+	13.1421i	0.705507	+	0.705507i	0.965587	−	0.260080i	$-0.0837490\pi$
$347$	13.1421	+	13.1421i	0.705507	+	0.705507i	−0.260080	+	0.965587i	$0.583749\pi$
$348$	−14.4853	−	2.48528i	−0.776493	−	0.133225i
$349$	−2.07107	+	2.07107i	−0.110862	+	0.110862i	−0.760362	−	0.649500i	$-0.774978\pi$
$349$	−2.07107	+	2.07107i	−0.110862	+	0.110862i	0.649500	+	0.760362i	$0.274978\pi$
$350$	−4.65685	+	4.65685i	−0.248919	+	0.248919i
$351$	−15.8284	+	28.3137i	−0.844859	+	1.51127i
$352$		−	30.6274i		−	1.63245i
$353$			8.48528i			0.451626i	0.974171	+	0.225813i	$0.0725038\pi$
$353$			8.48528i			0.451626i	−0.974171	+	0.225813i	$0.927496\pi$
$354$	28.4853	−	20.1421i	1.51398	−	1.07054i
$355$	2.48528	+	2.48528i	0.131905	+	0.131905i
$356$		−	31.3137i		−	1.65962i
$357$	1.65685	−	1.17157i	0.0876900	−	0.0620062i
$358$	30.0000			1.58555
$359$			20.3431i			1.07367i	0.843687	+	0.536835i	$0.180380\pi$
$359$			20.3431i			1.07367i	−0.843687	+	0.536835i	$0.819620\pi$
$360$	4.68629	+	1.65685i	0.246989	+	0.0873239i
$361$		−	18.6569i		−	0.981940i
$362$			4.14214i			0.217706i
$363$	25.8995	−	18.3137i	1.35937	−	0.961220i
$364$	8.82843	+	8.82843i	0.462735	+	0.462735i
$365$	−2.14214	−	2.14214i	−0.112125	−	0.112125i
$366$	4.82843	+	6.82843i	0.252386	+	0.356928i
$367$			16.1421i			0.842613i	0.906918	+	0.421306i	$0.138428\pi$
$367$			16.1421i			0.842613i	−0.906918	+	0.421306i	$0.861572\pi$
$368$		−	30.6274i		−	1.59656i
$369$	0.343146	−	0.970563i	0.0178635	−	0.0505255i
$370$	−1.51472	−	1.51472i	−0.0787465	−	0.0787465i
$371$	5.82843	−	5.82843i	0.302597	−	0.302597i
$372$	−12.9706	−	18.3431i	−0.672492	−	0.951048i
$373$	−8.31371	−	8.31371i	−0.430468	−	0.430468i	0.458320	−	0.888787i	$-0.348451\pi$
$373$	−8.31371	−	8.31371i	−0.430468	−	0.430468i	−0.888787	+	0.458320i	$0.848451\pi$
$374$	8.97056			0.463857
$375$	1.65685	−	9.65685i	0.0855596	−	0.498678i
$376$	−11.3137	+	11.3137i	−0.583460	+	0.583460i
$377$	26.4853			1.36406
$378$	6.41421	+	3.58579i	0.329912	+	0.184433i
$379$	−27.1421	+	27.1421i	−1.39420	+	1.39420i	−0.578553	+	0.815645i	$0.696382\pi$
$379$	−27.1421	+	27.1421i	−1.39420	+	1.39420i	−0.815645	+	0.578553i	$0.803618\pi$
$380$			0.686292i			0.0352060i
$381$	22.1421	−	15.6569i	1.13438	−	0.802125i
$382$	6.34315	+	6.34315i	0.324544	+	0.324544i
$383$	19.3137			0.986884			0.493442	−	0.869779i	$-0.335738\pi$
$383$	19.3137			0.986884			0.493442	+	0.869779i	$0.335738\pi$
$384$	19.3137	+	3.31371i	0.985599	+	0.169102i
$385$	3.17157			0.161638
$386$	−15.6569	−	15.6569i	−0.796913	−	0.796913i
$387$	−7.00000	−	14.6569i	−0.355830	−	0.745050i
$388$		−	4.00000i		−	0.203069i
$389$	−19.9706	+	19.9706i	−1.01255	+	1.01255i	−0.0126275	+	0.999920i	$0.504020\pi$
$389$	−19.9706	+	19.9706i	−1.01255	+	1.01255i	−0.999920	+	0.0126275i	$0.995980\pi$
$390$	−8.82843	−	1.51472i	−0.447045	−	0.0767008i
$391$	8.97056			0.453661
$392$	2.00000	−	2.00000i	0.101015	−	0.101015i
$393$	9.82843	+	1.68629i	0.495779	+	0.0850622i
$394$	11.6569			0.587264
$395$	−0.828427	−	0.828427i	−0.0416827	−	0.0416827i
$396$	14.0000	+	29.3137i	0.703526	+	1.47307i
$397$	−23.7279	+	23.7279i	−1.19087	+	1.19087i	−0.214047	+	0.976823i	$0.568665\pi$
$397$	−23.7279	+	23.7279i	−1.19087	+	1.19087i	−0.976823	+	0.214047i	$0.931335\pi$
$398$		0			0
$399$	−0.171573	+	1.00000i	−0.00858939	+	0.0500626i
$400$		−	18.6274i		−	0.931371i
$401$			19.3137i			0.964481i	0.876039	+	0.482240i	$0.160177\pi$
$401$			19.3137i			0.964481i	−0.876039	+	0.482240i	$0.839823\pi$
$402$	19.7990	−	14.0000i	0.987484	−	0.698257i
$403$	28.6274	+	28.6274i	1.42603	+	1.42603i
$404$	20.1421	+	20.1421i	1.00211	+	1.00211i
$405$	−5.24264	+	0.556349i	−0.260509	+	0.0276452i
$406$		−	6.00000i		−	0.297775i
$407$		−	14.0000i		−	0.693954i
$408$	−0.970563	+	5.65685i	−0.0480500	+	0.280056i
$409$			25.1716i			1.24465i	0.782757	+	0.622327i	$0.213813\pi$
$409$			25.1716i			1.24465i	−0.782757	+	0.622327i	$0.786187\pi$
$410$	0.284271			0.0140392
$411$	7.65685	+	10.8284i	0.377685	+	0.534127i
$412$			22.6274i			1.11477i
$413$	10.0711	+	10.0711i	0.495565	+	0.495565i
$414$	14.0000	+	29.3137i	0.688062	+	1.44069i
$415$		−	7.37258i		−	0.361906i
$416$	−35.3137			−1.73140
$417$	10.6569	+	1.82843i	0.521868	+	0.0895385i
$418$	−3.17157	+	3.17157i	−0.155127	+	0.155127i
$419$	−13.2426	+	13.2426i	−0.646945	+	0.646945i	−0.952254	−	0.305308i	$-0.901241\pi$
$419$	−13.2426	+	13.2426i	−0.646945	+	0.646945i	0.305308	+	0.952254i	$0.401241\pi$
$420$	−0.343146	+	2.00000i	−0.0167438	+	0.0975900i
$421$	−1.68629	−	1.68629i	−0.0821848	−	0.0821848i	0.664819	−	0.747004i	$-0.268509\pi$
$421$	−1.68629	−	1.68629i	−0.0821848	−	0.0821848i	−0.747004	+	0.664819i	$0.768509\pi$
$422$		−	10.0000i		−	0.486792i
$423$	5.65685	−	16.0000i	0.275046	−	0.777947i
$424$			23.3137i			1.13221i
$425$	5.45584			0.264647
$426$	−14.4853	−	2.48528i	−0.701814	−	0.120412i
$427$	−2.41421	+	2.41421i	−0.116832	+	0.116832i
$428$	10.0000	−	10.0000i	0.483368	−	0.483368i
$429$	−33.7990	−	47.7990i	−1.63183	−	2.30776i
$430$	3.17157	−	3.17157i	0.152947	−	0.152947i
$431$	−3.31371			−0.159616			−0.0798079	−	0.996810i	$-0.525431\pi$
$431$	−3.31371			−0.159616			−0.0798079	+	0.996810i	$0.525431\pi$
$432$	−20.0000	+	5.65685i	−0.962250	+	0.272166i
$433$	−14.6863			−0.705778			−0.352889	−	0.935665i	$-0.614801\pi$
$433$	−14.6863			−0.705778			−0.352889	+	0.935665i	$0.614801\pi$
$434$	6.48528	−	6.48528i	0.311303	−	0.311303i
$435$	2.48528	+	3.51472i	0.119160	+	0.168518i
$436$	11.6569	+	11.6569i	0.558262	+	0.558262i
$437$	−3.17157	+	3.17157i	−0.151717	+	0.151717i
$438$	12.4853	+	2.14214i	0.596570	+	0.102355i
$439$	−0.970563			−0.0463224			−0.0231612	−	0.999732i	$-0.507373\pi$
$439$	−0.970563			−0.0463224			−0.0231612	+	0.999732i	$0.507373\pi$
$440$	−6.34315	+	6.34315i	−0.302398	+	0.302398i
$441$	−1.00000	+	2.82843i	−0.0476190	+	0.134687i
$442$		−	10.3431i		−	0.491973i
$443$	16.6569	+	16.6569i	0.791391	+	0.791391i	0.981720	−	0.190329i	$-0.0609556\pi$
$443$	16.6569	+	16.6569i	0.791391	+	0.791391i	−0.190329	+	0.981720i	$0.560956\pi$
$444$	8.82843	+	1.51472i	0.418979	+	0.0718854i
$445$	−6.48528	+	6.48528i	−0.307432	+	0.307432i
$446$	7.17157	−	7.17157i	0.339584	−	0.339584i
$447$	−22.8995	−	3.92893i	−1.08311	−	0.185832i
$448$			8.00000i			0.377964i
$449$		−	12.9706i		−	0.612119i	−0.952012	−	0.306059i	$-0.900989\pi$
$449$		−	12.9706i		−	0.612119i	0.952012	−	0.306059i	$-0.0990106\pi$
$450$	8.51472	+	17.8284i	0.401388	+	0.840440i
$451$	1.31371	+	1.31371i	0.0618601	+	0.0618601i
$452$	3.31371			0.155864
$453$	17.6569	+	24.9706i	0.829591	+	1.17322i
$454$	16.1421			0.757588
$455$		−	3.65685i		−	0.171436i
$456$	−1.65685	−	2.34315i	−0.0775893	−	0.109728i
$457$		−	29.9411i		−	1.40059i	−0.713855	−	0.700293i	$-0.753053\pi$
$457$		−	29.9411i		−	1.40059i	0.713855	−	0.700293i	$-0.246947\pi$
$458$		−	21.7990i		−	1.01860i
$459$	−1.65685	−	5.85786i	−0.0773353	−	0.273422i
$460$	−6.34315	+	6.34315i	−0.295751	+	0.295751i
$461$	−22.4142	−	22.4142i	−1.04393	−	1.04393i	−0.998989	−	0.0449445i	$-0.985689\pi$
$461$	−22.4142	−	22.4142i	−1.04393	−	1.04393i	−0.0449445	−	0.998989i	$-0.514311\pi$
$462$	−10.8284	+	7.65685i	−0.503784	+	0.356229i
$463$			11.6569i			0.541740i	0.962616	+	0.270870i	$0.0873113\pi$
$463$			11.6569i			0.541740i	−0.962616	+	0.270870i	$0.912689\pi$
$464$	12.0000	+	12.0000i	0.557086	+	0.557086i
$465$	−1.11270	+	6.48528i	−0.0516002	+	0.300748i
$466$	1.31371	+	1.31371i	0.0608564	+	0.0608564i
$467$	−14.4142	+	14.4142i	−0.667010	+	0.667010i	−0.957023	−	0.290013i	$-0.906341\pi$
$467$	−14.4142	+	14.4142i	−0.667010	+	0.667010i	0.290013	+	0.957023i	$0.406341\pi$
$468$	33.7990	−	16.1421i	1.56236	−	0.746170i
$469$	7.00000	+	7.00000i	0.323230	+	0.323230i
$470$	4.68629			0.216163
$471$	−7.00000	−	1.20101i	−0.322543	−	0.0553396i
$472$	−40.2843			−1.85423
$473$	29.3137			1.34785
$474$	4.82843	+	0.828427i	0.221777	+	0.0380509i
$475$	−1.92893	+	1.92893i	−0.0885055	+	0.0885055i
$476$	−2.34315			−0.107398
$477$	−10.6569	−	22.3137i	−0.487944	−	1.02167i
$478$	−11.3137	−	11.3137i	−0.517477	−	0.517477i
$479$	27.3137			1.24800			0.623998	−	0.781426i	$-0.285507\pi$
$479$	27.3137			1.24800			0.623998	+	0.781426i	$0.285507\pi$
$480$	−3.31371	−	4.68629i	−0.151249	−	0.213899i
$481$	−16.1421			−0.736018
$482$	−0.343146	−	0.343146i	−0.0156299	−	0.0156299i
$483$	−10.8284	+	7.65685i	−0.492710	+	0.348399i
$484$	−36.6274			−1.66488
$485$	−0.828427	+	0.828427i	−0.0376169	+	0.0376169i
$486$	16.5563	−	14.5563i	0.751011	−	0.660289i
$487$	−16.2843			−0.737911			−0.368955	−	0.929447i	$-0.620284\pi$
$487$	−16.2843			−0.737911			−0.368955	+	0.929447i	$0.620284\pi$
$488$		−	9.65685i		−	0.437145i
$489$	−0.757359	+	4.41421i	−0.0342490	+	0.199618i
$490$	−0.828427			−0.0374245
$491$	10.3137	+	10.3137i	0.465451	+	0.465451i	0.900437	−	0.434986i	$-0.143247\pi$
$491$	10.3137	+	10.3137i	0.465451	+	0.465451i	−0.434986	+	0.900437i	$0.643247\pi$
$492$	−0.970563	+	0.686292i	−0.0437563	+	0.0309404i
$493$	−3.51472	+	3.51472i	−0.158295	+	0.158295i
$494$	3.65685	+	3.65685i	0.164530	+	0.164530i
$495$	3.17157	−	8.97056i	0.142552	−	0.403197i
$496$			25.9411i			1.16479i
$497$		−	6.00000i		−	0.269137i
$498$	17.7990	+	25.1716i	0.797592	+	1.12797i
$499$	5.68629	+	5.68629i	0.254553	+	0.254553i	0.822834	−	0.568281i	$-0.192391\pi$
$499$	5.68629	+	5.68629i	0.254553	+	0.254553i	−0.568281	+	0.822834i	$0.692391\pi$
$500$	−8.00000	+	8.00000i	−0.357771	+	0.357771i
$501$	−10.1421	+	7.17157i	−0.453117	+	0.320402i
$502$		−	4.82843i		−	0.215503i
$503$			16.8284i			0.750342i	0.926956	+	0.375171i	$0.122416\pi$
$503$			16.8284i			0.750342i	−0.926956	+	0.375171i	$0.877584\pi$
$504$	−3.65685	−	7.65685i	−0.162889	−	0.341063i
$505$		−	8.34315i		−	0.371265i
$506$	−58.6274			−2.60631
$507$	−36.7279	+	25.9706i	−1.63114	+	1.15339i
$508$	−31.3137			−1.38932
$509$	7.24264	+	7.24264i	0.321024	+	0.321024i	0.849160	−	0.528136i	$-0.177109\pi$
$509$	7.24264	+	7.24264i	0.321024	+	0.321024i	−0.528136	+	0.849160i	$0.677109\pi$
$510$	1.37258	−	0.970563i	0.0607790	−	0.0429772i
$511$			5.17157i			0.228777i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	2.65685	+	1.48528i	0.117303	+	0.0655768i
$514$	−26.8284	+	26.8284i	−1.18335	+	1.18335i
$515$	4.68629	−	4.68629i	0.206503	−	0.206503i
$516$	−3.17157	+	18.4853i	−0.139621	+	0.813769i
$517$	21.6569	+	21.6569i	0.952467	+	0.952467i
$518$			3.65685i			0.160673i
$519$	2.02944	−	11.8284i	0.0890824	−	0.519210i
$520$	7.31371	+	7.31371i	0.320727	+	0.320727i
$521$	13.3137			0.583284			0.291642	−	0.956528i	$-0.405798\pi$
$521$	13.3137			0.583284			0.291642	+	0.956528i	$0.405798\pi$
$522$	−16.9706	−	6.00000i	−0.742781	−	0.262613i
$523$	21.0416	−	21.0416i	0.920086	−	0.920086i	−0.0769488	−	0.997035i	$-0.524518\pi$
$523$	21.0416	−	21.0416i	0.920086	−	0.920086i	0.997035	+	0.0769488i	$0.0245178\pi$
$524$	−8.14214	−	8.14214i	−0.355691	−	0.355691i
$525$	−6.58579	+	4.65685i	−0.287427	+	0.203242i
$526$	11.6569	−	11.6569i	0.508263	−	0.508263i
$527$	−7.59798			−0.330973
$528$	6.34315	−	36.9706i	0.276050	−	1.60894i
$529$	−35.6274			−1.54902
$530$	4.82843	−	4.82843i	0.209733	−	0.209733i
$531$	38.5563	−	18.4142i	1.67320	−	0.799109i
$532$	0.828427	−	0.828427i	0.0359169	−	0.0359169i
$533$	1.51472	−	1.51472i	0.0656097	−	0.0656097i
$534$	6.48528	−	37.7990i	0.280646	−	1.63572i
$535$	−4.14214			−0.179080
$536$	−28.0000			−1.20942
$537$	36.2132	+	6.21320i	1.56272	+	0.268120i
$538$		−	11.1716i		−	0.481641i
$539$	−3.82843	−	3.82843i	−0.164902	−	0.164902i
$540$	5.31371	+	2.97056i	0.228666	+	0.127833i
$541$	−21.0000	+	21.0000i	−0.902861	+	0.902861i	−0.995683	−	0.0928222i	$-0.970411\pi$
$541$	−21.0000	+	21.0000i	−0.902861	+	0.902861i	0.0928222	+	0.995683i	$0.470411\pi$
$542$	−16.8284	+	16.8284i	−0.722843	+	0.722843i
$543$	−0.857864	+	5.00000i	−0.0368145	+	0.214571i
$544$	4.68629	−	4.68629i	0.200923	−	0.200923i
$545$		−	4.82843i		−	0.206827i
$546$	8.82843	+	12.4853i	0.377822	+	0.534321i
$547$	−17.1421	−	17.1421i	−0.732945	−	0.732945i	0.238257	−	0.971202i	$-0.423424\pi$
$547$	−17.1421	−	17.1421i	−0.732945	−	0.732945i	−0.971202	+	0.238257i	$0.923424\pi$
$548$		−	15.3137i		−	0.654169i
$549$	4.41421	+	9.24264i	0.188394	+	0.394466i
$550$	−35.6569			−1.52041
$551$		−	2.48528i		−	0.105877i
$552$	6.34315	−	36.9706i	0.269982	−	1.57357i
$553$			2.00000i			0.0850487i
$554$		−	12.6274i		−	0.536488i
$555$	−1.51472	−	2.14214i	−0.0642962	−	0.0909286i
$556$	−8.82843	−	8.82843i	−0.374409	−	0.374409i
$557$	15.1421	+	15.1421i	0.641593	+	0.641593i	0.950947	−	0.309354i	$-0.100113\pi$
$557$	15.1421	+	15.1421i	0.641593	+	0.641593i	−0.309354	+	0.950947i	$0.600113\pi$
$558$	−11.8579	−	24.8284i	−0.501983	−	1.05107i
$559$		−	33.7990i		−	1.42954i
$560$	1.65685	−	1.65685i	0.0700149	−	0.0700149i
$561$	10.8284	+	1.85786i	0.457177	+	0.0784391i
$562$	−6.68629	−	6.68629i	−0.282044	−	0.282044i
$563$	−19.5858	+	19.5858i	−0.825442	+	0.825442i	−0.986883	−	0.161440i	$-0.948386\pi$
$563$	−19.5858	+	19.5858i	−0.825442	+	0.825442i	0.161440	+	0.986883i	$0.448386\pi$
$564$	−16.0000	+	11.3137i	−0.673722	+	0.476393i
$565$	−0.686292	−	0.686292i	−0.0288725	−	0.0288725i
$566$	25.7990			1.08441
$567$	7.00000	+	5.65685i	0.293972	+	0.237566i
$568$	12.0000	+	12.0000i	0.503509	+	0.503509i
$569$	32.6274			1.36781			0.683906	−	0.729570i	$-0.260280\pi$
$569$	32.6274			1.36781			0.683906	+	0.729570i	$0.260280\pi$
$570$	−0.142136	+	0.828427i	−0.00595341	+	0.0346990i
$571$	−6.17157	+	6.17157i	−0.258272	+	0.258272i	−0.824351	−	0.566079i	$-0.808460\pi$
$571$	−6.17157	+	6.17157i	−0.258272	+	0.258272i	0.566079	+	0.824351i	$0.308460\pi$
$572$			67.5980i			2.82641i
$573$	6.34315	+	8.97056i	0.264989	+	0.374751i
$574$	−0.343146	−	0.343146i	−0.0143226	−	0.0143226i
$575$	−35.6569			−1.48699
$576$	22.6274	+	8.00000i	0.942809	+	0.333333i
$577$	−0.343146			−0.0142853			−0.00714267	−	0.999974i	$-0.502274\pi$
$577$	−0.343146			−0.0142853			−0.00714267	+	0.999974i	$0.502274\pi$
$578$	−15.6274	−	15.6274i	−0.650015	−	0.650015i
$579$	−15.6569	−	22.1421i	−0.650677	−	0.920196i
$580$		−	4.97056i		−	0.206391i
$581$	−8.89949	+	8.89949i	−0.369213	+	0.369213i
$582$	0.828427	−	4.82843i	0.0343394	−	0.200145i
$583$	44.6274			1.84828
$584$	−10.3431	−	10.3431i	−0.428002	−	0.428002i
$585$	−10.3431	−	3.65685i	−0.427636	−	0.151192i
$586$	18.4853			0.763620
$587$	16.0711	+	16.0711i	0.663324	+	0.663324i	0.956162	−	0.292838i	$-0.0945997\pi$
$587$	16.0711	+	16.0711i	0.663324	+	0.663324i	−0.292838	+	0.956162i	$0.594600\pi$
$588$	2.82843	−	2.00000i	0.116642	−	0.0824786i
$589$	2.68629	−	2.68629i	0.110687	−	0.110687i
$590$	8.34315	+	8.34315i	0.343482	+	0.343482i
$591$	14.0711	+	2.41421i	0.578806	+	0.0993075i
$592$	−7.31371	−	7.31371i	−0.300592	−	0.300592i
$593$		−	1.85786i		−	0.0762933i	−0.999272	−	0.0381467i	$-0.987855\pi$
$593$		−	1.85786i		−	0.0762933i	0.999272	−	0.0381467i	$-0.0121454\pi$
$594$	10.8284	+	38.2843i	0.444296	+	1.57082i
$595$	0.485281	+	0.485281i	0.0198946	+	0.0198946i
$596$	18.9706	+	18.9706i	0.777065	+	0.777065i
$597$		0			0
$598$			67.5980i			2.76429i
$599$		−	42.9706i		−	1.75573i	−0.478909	−	0.877865i	$-0.658967\pi$
$599$		−	42.9706i		−	1.75573i	0.478909	−	0.877865i	$-0.341033\pi$
$600$	3.85786	−	22.4853i	0.157497	−	0.917958i
$601$			16.4853i			0.672449i	0.941782	+	0.336224i	$0.109150\pi$
$601$			16.4853i			0.672449i	−0.941782	+	0.336224i	$0.890850\pi$
$602$	−7.65685			−0.312070
$603$	26.7990	−	12.7990i	1.09134	−	0.521215i
$604$		−	35.3137i		−	1.43689i
$605$	7.58579	+	7.58579i	0.308406	+	0.308406i
$606$	20.1421	+	28.4853i	0.818218	+	1.15714i
$607$		−	21.1127i		−	0.856938i	−0.903556	−	0.428469i	$-0.859053\pi$
$607$		−	21.1127i		−	0.856938i	0.903556	−	0.428469i	$-0.140947\pi$
$608$			3.31371i			0.134389i
$609$	1.24264	−	7.24264i	0.0503543	−	0.293487i
$610$	−2.00000	+	2.00000i	−0.0809776	+	0.0809776i
$611$	24.9706	−	24.9706i	1.01020	−	1.01020i
$612$	−2.34315	+	6.62742i	−0.0947161	+	0.267897i
$613$	−14.1716	−	14.1716i	−0.572384	−	0.572384i	0.360410	−	0.932794i	$-0.382637\pi$
$613$	−14.1716	−	14.1716i	−0.572384	−	0.572384i	−0.932794	+	0.360410i	$0.882637\pi$
$614$			29.7990i			1.20259i
$615$	0.343146	+	0.0588745i	0.0138370	+	0.00237405i
$616$	15.3137			0.617007
$617$	−26.0000			−1.04672			−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000			−1.04672			−0.523360	+	0.852111i	$0.675322\pi$
$618$	−4.68629	+	27.3137i	−0.188510	+	1.09872i
$619$	26.4142	−	26.4142i	1.06168	−	1.06168i	0.0637083	−	0.997969i	$-0.479707\pi$
$619$	26.4142	−	26.4142i	1.06168	−	1.06168i	0.997969	−	0.0637083i	$-0.0202927\pi$
$620$	5.37258	−	5.37258i	0.215768	−	0.215768i
$621$	10.8284	+	38.2843i	0.434530	+	1.53629i
$622$	−1.51472	+	1.51472i	−0.0607347	+	0.0607347i
$623$	15.6569			0.627279
$624$	−42.6274	−	7.31371i	−1.70646	−	0.292783i
$625$	−19.9706			−0.798823
$626$	−20.4853	+	20.4853i	−0.818757	+	0.818757i
$627$	−4.48528	+	3.17157i	−0.179125	+	0.126660i
$628$	5.79899	+	5.79899i	0.231405	+	0.231405i
$629$	2.14214	−	2.14214i	0.0854125	−	0.0854125i
$630$	−0.828427	+	2.34315i	−0.0330053	+	0.0933532i
$631$	−13.6569			−0.543671			−0.271835	−	0.962344i	$-0.587631\pi$
$631$	−13.6569			−0.543671			−0.271835	+	0.962344i	$0.587631\pi$
$632$	−4.00000	−	4.00000i	−0.159111	−	0.159111i
$633$	2.07107	−	12.0711i	0.0823176	−	0.479782i
$634$			26.2843i			1.04388i
$635$	6.48528	+	6.48528i	0.257361	+	0.257361i
$636$	−4.82843	+	28.1421i	−0.191460	+	1.11591i
$637$	−4.41421	+	4.41421i	−0.174898	+	0.174898i
$638$	22.9706	−	22.9706i	0.909413	−	0.909413i
$639$	−16.9706	−	6.00000i	−0.671345	−	0.237356i
$640$			6.62742i			0.261972i
$641$		−	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
$643$	−21.0416	−	21.0416i	−0.829801	−	0.829801i	0.157688	−	0.987489i	$-0.449596\pi$
$643$	−21.0416	−	21.0416i	−0.829801	−	0.829801i	−0.987489	+	0.157688i	$0.949596\pi$
$644$	15.3137			0.603445
$645$	4.48528	−	3.17157i	0.176608	−	0.124881i
$646$	−0.970563			−0.0381863
$647$		−	16.1421i		−	0.634613i	−0.948323	−	0.317306i	$-0.897222\pi$
$647$		−	16.1421i		−	0.634613i	0.948323	−	0.317306i	$-0.102778\pi$
$648$	−25.3137	+	2.68629i	−0.994416	+	0.105527i
$649$			77.1127i			3.02694i
$650$			41.1127i			1.61257i
$651$	9.17157	−	6.48528i	0.359462	−	0.254178i
$652$	3.65685	−	3.65685i	0.143213	−	0.143213i
$653$	11.3431	+	11.3431i	0.443892	+	0.443892i	0.893318	−	0.449426i	$-0.148371\pi$
$653$	11.3431	+	11.3431i	0.443892	+	0.443892i	−0.449426	+	0.893318i	$0.648371\pi$
$654$	11.6569	+	16.4853i	0.455819	+	0.644626i
$655$			3.37258i			0.131778i
$656$	1.37258			0.0535904
$657$	14.6274	+	5.17157i	0.570670	+	0.201762i
$658$	−5.65685	−	5.65685i	−0.220527	−	0.220527i
$659$	25.4853	−	25.4853i	0.992766	−	0.992766i	−0.00720841	−	0.999974i	$-0.502295\pi$
$659$	25.4853	−	25.4853i	0.992766	−	0.992766i	0.999974	+	0.00720841i	$0.00229453\pi$
$660$	−8.97056	+	6.34315i	−0.349179	+	0.246907i
$661$	11.3848	+	11.3848i	0.442816	+	0.442816i	0.892957	−	0.450141i	$-0.148626\pi$
$661$	11.3848	+	11.3848i	0.442816	+	0.442816i	−0.450141	+	0.892957i	$0.648626\pi$
$662$	−34.2843			−1.33250
$663$	2.14214	−	12.4853i	0.0831937	−	0.484888i
$664$		−	35.5980i		−	1.38147i
$665$	−0.343146			−0.0133066
$666$	10.3431	+	3.65685i	0.400789	+	0.141700i
$667$	22.9706	−	22.9706i	0.889424	−	0.889424i
$668$	14.3431			0.554953
$669$	10.1421	−	7.17157i	0.392118	−	0.277269i
$670$	5.79899	+	5.79899i	0.224035	+	0.224035i
$671$	−18.4853			−0.713616
$672$	−1.65685	+	9.65685i	−0.0639145	+	0.372521i
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−25.3137	−	25.3137i	−0.975048	−	0.975048i
$675$	6.58579	+	23.2843i	0.253487	+	0.896212i
$676$	51.9411			1.99774
$677$	20.8995	−	20.8995i	0.803233	−	0.803233i	−0.180367	−	0.983599i	$-0.557728\pi$
$677$	20.8995	−	20.8995i	0.803233	−	0.803233i	0.983599	+	0.180367i	$0.0577284\pi$
$678$	4.00000	+	0.686292i	0.153619	+	0.0263569i
$679$	2.00000			0.0767530
$680$	−1.94113			−0.0744388
$681$	19.4853	+	3.34315i	0.746678	+	0.128110i
$682$	49.6569			1.90146
$683$	−0.313708	−	0.313708i	−0.0120037	−	0.0120037i	0.701079	−	0.713083i	$-0.252702\pi$
$683$	−0.313708	−	0.313708i	−0.0120037	−	0.0120037i	−0.713083	+	0.701079i	$0.752702\pi$
$684$	−1.51472	−	3.17157i	−0.0579167	−	0.121268i
$685$	−3.17157	+	3.17157i	−0.121180	+	0.121180i
$686$	1.00000	+	1.00000i	0.0381802	+	0.0381802i
$687$	4.51472	−	26.3137i	0.172247	−	1.00393i
$688$	15.3137	−	15.3137i	0.583830	−	0.583830i
$689$		−	51.4558i		−	1.96031i
$690$	−8.97056	+	6.34315i	−0.341503	+	0.241479i
$691$	−14.8995	−	14.8995i	−0.566803	−	0.566803i	0.364428	−	0.931232i	$-0.381265\pi$
$691$	−14.8995	−	14.8995i	−0.566803	−	0.566803i	−0.931232	+	0.364428i	$0.881265\pi$
$692$	−9.79899	+	9.79899i	−0.372502	+	0.372502i
$693$	−14.6569	+	7.00000i	−0.556768	+	0.265908i
$694$		−	26.2843i		−	0.997737i
$695$			3.65685i			0.138712i
$696$	12.0000	+	16.9706i	0.454859	+	0.643268i
$697$			0.402020i			0.0152276i
$698$	4.14214			0.156782
$699$	1.31371	+	1.85786i	0.0496890	+	0.0702709i
$700$	9.31371			0.352025
$701$	−0.656854	−	0.656854i	−0.0248090	−	0.0248090i	0.694593	−	0.719402i	$-0.255584\pi$
$701$	−0.656854	−	0.656854i	−0.0248090	−	0.0248090i	−0.719402	+	0.694593i	$0.755584\pi$
$702$	44.1421	−	12.4853i	1.66604	−	0.471227i
$703$			1.51472i			0.0571287i
$704$	−30.6274	+	30.6274i	−1.15431	+	1.15431i
$705$	5.65685	+	0.970563i	0.213049	+	0.0365535i
$706$	8.48528	−	8.48528i	0.319348	−	0.319348i
$707$	−10.0711	+	10.0711i	−0.378761	+	0.378761i
$708$	−48.6274	−	8.34315i	−1.82753	−	0.313555i
$709$	−2.17157	−	2.17157i	−0.0815551	−	0.0815551i	0.665152	−	0.746708i	$-0.268367\pi$
$709$	−2.17157	−	2.17157i	−0.0815551	−	0.0815551i	−0.746708	+	0.665152i	$0.768367\pi$
$710$		−	4.97056i		−	0.186542i
$711$	5.65685	+	2.00000i	0.212149	+	0.0750059i
$712$	−31.3137	+	31.3137i	−1.17353	+	1.17353i
$713$	49.6569			1.85966
$714$	−2.82843	−	0.485281i	−0.105851	−	0.0181612i
$715$	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
$718$	20.3431	−	20.3431i	0.759199	−	0.759199i
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$	−3.02944	−	6.34315i	−0.112900	−	0.236395i
$721$	−11.3137			−0.421345
$722$	−18.6569	+	18.6569i	−0.694336	+	0.694336i
$723$	−0.343146	−	0.485281i	−0.0127617	−	0.0180478i
$724$	4.14214	−	4.14214i	0.153941	−	0.153941i
$725$	13.9706	−	13.9706i	0.518854	−	0.518854i
$726$	−44.2132	−	7.58579i	−1.64091	−	0.281535i
$727$	−35.3137			−1.30971			−0.654856	−	0.755753i	$-0.727271\pi$
$727$	−35.3137			−1.30971			−0.654856	+	0.755753i	$0.727271\pi$
$728$		−	17.6569i		−	0.654407i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$			4.28427i			0.158568i
$731$	4.48528	+	4.48528i	0.165894	+	0.165894i
$732$	2.00000	−	11.6569i	0.0739221	−	0.430850i
$733$	−2.27208	+	2.27208i	−0.0839211	+	0.0839211i	−0.747821	−	0.663900i	$-0.768900\pi$
$733$	−2.27208	+	2.27208i	−0.0839211	+	0.0839211i	0.663900	+	0.747821i	$0.268900\pi$
$734$	16.1421	−	16.1421i	0.595817	−	0.595817i
$735$	−1.00000	−	0.171573i	−0.0368856	−	0.00632856i
$736$	−30.6274	+	30.6274i	−1.12894	+	1.12894i
$737$			53.5980i			1.97431i
$738$	−1.31371	+	0.627417i	−0.0483583	+	0.0230955i
$739$	−21.8284	−	21.8284i	−0.802972	−	0.802972i	0.180587	−	0.983559i	$-0.442200\pi$
$739$	−21.8284	−	21.8284i	−0.802972	−	0.802972i	−0.983559	+	0.180587i	$0.942200\pi$
$740$			3.02944i			0.111364i
$741$	3.65685	+	5.17157i	0.134338	+	0.189982i
$742$	−11.6569			−0.427937
$743$			4.34315i			0.159335i	0.996822	+	0.0796673i	$0.0253858\pi$
$743$			4.34315i			0.159335i	−0.996822	+	0.0796673i	$0.974614\pi$
$744$	−5.37258	+	31.3137i	−0.196968	+	1.14802i
$745$		−	7.85786i		−	0.287890i
$746$			16.6274i			0.608773i
$747$	16.2721	+	34.0711i	0.595364	+	1.24660i
$748$	−8.97056	−	8.97056i	−0.327996	−	0.327996i
$749$	5.00000	+	5.00000i	0.182696	+	0.182696i
$750$	−11.3137	+	8.00000i	−0.413118	+	0.292119i
$751$		−	18.6863i		−	0.681872i	−0.940086	−	0.340936i	$-0.889256\pi$
$751$		−	18.6863i		−	0.681872i	0.940086	−	0.340936i	$-0.110744\pi$
$752$	22.6274			0.825137
$753$	1.00000	−	5.82843i	0.0364420	−	0.212400i
$754$	−26.4853	−	26.4853i	−0.964537	−	0.964537i
$755$	−7.31371	+	7.31371i	−0.266173	+	0.266173i
$756$	−2.82843	−	10.0000i	−0.102869	−	0.363696i
$757$	14.5147	+	14.5147i	0.527546	+	0.527546i	0.919840	−	0.392294i	$-0.128318\pi$
$757$	14.5147	+	14.5147i	0.527546	+	0.527546i	−0.392294	+	0.919840i	$0.628318\pi$
$758$	54.2843			1.97169
$759$	−70.7696	−	12.1421i	−2.56877	−	0.440732i
$760$	0.686292	−	0.686292i	0.0248944	−	0.0248944i
$761$	−36.6274			−1.32774			−0.663871	−	0.747847i	$-0.731088\pi$
$761$	−36.6274			−1.32774			−0.663871	+	0.747847i	$0.731088\pi$
$762$	−37.7990	−	6.48528i	−1.36931	−	0.234937i
$763$	−5.82843	+	5.82843i	−0.211003	+	0.211003i
$764$		−	12.6863i		−	0.458974i
$765$	1.85786	−	0.887302i	0.0671712	−	0.0320805i
$766$	−19.3137	−	19.3137i	−0.697833	−	0.697833i
$767$	88.9117			3.21041
$768$	−16.0000	−	22.6274i	−0.577350	−	0.816497i
$769$	24.3431			0.877836			0.438918	−	0.898527i	$-0.355362\pi$
$769$	24.3431			0.877836			0.438918	+	0.898527i	$0.355362\pi$
$770$	−3.17157	−	3.17157i	−0.114296	−	0.114296i
$771$	−37.9411	+	26.8284i	−1.36642	+	0.966202i
$772$			31.3137i			1.12701i
$773$	−36.5563	+	36.5563i	−1.31484	+	1.31484i	−0.397039	+	0.917802i	$0.629962\pi$
$773$	−36.5563	+	36.5563i	−1.31484	+	1.31484i	−0.917802	+	0.397039i	$0.870038\pi$
$774$	−7.65685	+	21.6569i	−0.275220	+	0.778440i
$775$	30.2010			1.08485
$776$	−4.00000	+	4.00000i	−0.143592	+	0.143592i
$777$	−0.757359	+	4.41421i	−0.0271701	+	0.158359i
$778$	39.9411			1.43196
$779$	−0.142136	−	0.142136i	−0.00509254	−	0.00509254i
$780$	7.31371	+	10.3431i	0.261873	+	0.370344i
$781$	22.9706	−	22.9706i	0.821951	−	0.821951i
$782$	−8.97056	−	8.97056i	−0.320787	−	0.320787i
$783$	−19.2426	−	10.7574i	−0.687676	−	0.384437i
$784$	−4.00000			−0.142857
$785$		−	2.40202i		−	0.0857318i
$786$	−8.14214	−	11.5147i	−0.290420	−	0.410716i
$787$	23.0416	+	23.0416i	0.821345	+	0.821345i	0.986301	−	0.164956i	$-0.0527481\pi$
$787$	23.0416	+	23.0416i	0.821345	+	0.821345i	−0.164956	+	0.986301i	$0.552748\pi$
$788$	−11.6569	−	11.6569i	−0.415258	−	0.415258i
$789$	16.4853	−	11.6569i	0.586892	−	0.414995i
$790$			1.65685i			0.0589482i
$791$			1.65685i			0.0589110i
$792$	15.3137	−	43.3137i	0.544149	−	1.53909i
$793$			21.3137i			0.756872i
$794$	47.4558			1.68414
$795$	6.82843	−	4.82843i	0.242179	−	0.171247i
$796$		0			0
$797$	−34.4142	−	34.4142i	−1.21901	−	1.21901i	−0.967978	−	0.251036i	$-0.919229\pi$
$797$	−34.4142	−	34.4142i	−1.21901	−	1.21901i	−0.251036	−	0.967978i	$-0.580771\pi$
$798$	1.17157	−	0.828427i	0.0414732	−	0.0293260i
$799$			6.62742i			0.234461i
$800$	−18.6274	+	18.6274i	−0.658579	+	0.658579i
$801$	15.6569	−	44.2843i	0.553208	−	1.56471i
$802$	19.3137	−	19.3137i	0.681991	−	0.681991i
$803$	−19.7990	+	19.7990i	−0.698691	+	0.698691i
$804$	−33.7990	−	5.79899i	−1.19200	−	0.204515i
$805$	−3.17157	−	3.17157i	−0.111783	−	0.111783i
$806$		−	57.2548i		−	2.01672i
$807$	2.31371	−	13.4853i	0.0814464	−	0.474704i
$808$		−	40.2843i		−	1.41720i
$809$	22.6863			0.797608			0.398804	−	0.917036i	$-0.369425\pi$
$809$	22.6863			0.797608			0.398804	+	0.917036i	$0.369425\pi$
$810$	5.79899	+	4.68629i	0.203756	+	0.164659i
$811$	16.0711	−	16.0711i	0.564332	−	0.564332i	−0.366203	−	0.930535i	$-0.619343\pi$
$811$	16.0711	−	16.0711i	0.564332	−	0.564332i	0.930535	+	0.366203i	$0.119343\pi$
$812$	−6.00000	+	6.00000i	−0.210559	+	0.210559i
$813$	−23.7990	+	16.8284i	−0.834667	+	0.590199i
$814$	−14.0000	+	14.0000i	−0.490700	+	0.490700i
$815$	−1.51472			−0.0530583
$816$	6.62742	−	4.68629i	0.232006	−	0.164053i
$817$	−3.17157			−0.110959
$818$	25.1716	−	25.1716i	0.880103	−	0.880103i
$819$	8.07107	+	16.8995i	0.282026	+	0.590516i
$820$	−0.284271	−	0.284271i	−0.00992718	−	0.00992718i
$821$	−15.4853	+	15.4853i	−0.540440	+	0.540440i	−0.923658	−	0.383218i	$-0.874816\pi$
$821$	−15.4853	+	15.4853i	−0.540440	+	0.540440i	0.383218	+	0.923658i	$0.374816\pi$
$822$	3.17157	−	18.4853i	0.110621	−	0.644748i
$823$	24.9706			0.870419			0.435210	−	0.900329i	$-0.356674\pi$
$823$	24.9706			0.870419			0.435210	+	0.900329i	$0.356674\pi$
$824$	22.6274	−	22.6274i	0.788263	−	0.788263i
$825$	−43.0416	−	7.38478i	−1.49852	−	0.257105i
$826$		−	20.1421i		−	0.700835i
$827$	−9.00000	−	9.00000i	−0.312961	−	0.312961i	0.533095	−	0.846055i	$-0.321029\pi$
$827$	−9.00000	−	9.00000i	−0.312961	−	0.312961i	−0.846055	+	0.533095i	$0.821029\pi$
$828$	15.3137	−	43.3137i	0.532188	−	1.50526i
$829$	−24.8995	+	24.8995i	−0.864795	+	0.864795i	−0.991891	−	0.127095i	$-0.959435\pi$
$829$	−24.8995	+	24.8995i	−0.864795	+	0.864795i	0.127095	+	0.991891i	$0.459435\pi$
$830$	−7.37258	+	7.37258i	−0.255906	+	0.255906i
$831$	2.61522	−	15.2426i	0.0907211	−	0.528761i
$832$	35.3137	+	35.3137i	1.22428	+	1.22428i
$833$		−	1.17157i		−	0.0405926i
$834$	−8.82843	−	12.4853i	−0.305703	−	0.432330i
$835$	−2.97056	−	2.97056i	−0.102801	−	0.102801i
$836$	6.34315			0.219382
$837$	−9.17157	−	32.4264i	−0.317016	−	1.12082i
$838$	26.4853			0.914919
$839$		−	51.4558i		−	1.77645i	−0.459406	−	0.888227i	$-0.651938\pi$
$839$		−	51.4558i		−	1.77645i	0.459406	−	0.888227i	$-0.348062\pi$
$840$	2.34315	−	1.65685i	0.0808462	−	0.0571669i
$841$		−	11.0000i		−	0.379310i
$842$			3.37258i			0.116227i
$843$	−6.68629	−	9.45584i	−0.230288	−	0.325677i
$844$	−10.0000	+	10.0000i	−0.344214	+	0.344214i
$845$	−10.7574	−	10.7574i	−0.370064	−	0.370064i
$846$	−21.6569	+	10.3431i	−0.744578	+	0.355605i
$847$		−	18.3137i		−	0.629266i
$848$	23.3137	−	23.3137i	0.800596	−	0.800596i
$849$	31.1421	+	5.34315i	1.06880	+	0.183376i
$850$	−5.45584	−	5.45584i	−0.187134	−	0.187134i
$851$	−14.0000	+	14.0000i	−0.479914	+	0.479914i
$852$	12.0000	+	16.9706i	0.411113	+	0.581402i
$853$	−28.4142	−	28.4142i	−0.972884	−	0.972884i	0.0267578	−	0.999642i	$-0.491482\pi$
$853$	−28.4142	−	28.4142i	−0.972884	−	0.972884i	−0.999642	+	0.0267578i	$0.991482\pi$
$854$	4.82843			0.165225
$855$	−0.343146	+	0.970563i	−0.0117353	+	0.0331925i
$856$	−20.0000			−0.683586
$857$	−31.9411			−1.09109			−0.545544	−	0.838082i	$-0.683677\pi$
$857$	−31.9411			−1.09109			−0.545544	+	0.838082i	$0.683677\pi$
$858$	−14.0000	+	81.5980i	−0.477952	+	2.78571i
$859$	22.8995	−	22.8995i	0.781321	−	0.781321i	−0.198733	−	0.980054i	$-0.563683\pi$
$859$	22.8995	−	22.8995i	0.781321	−	0.781321i	0.980054	+	0.198733i	$0.0636827\pi$
$860$	−6.34315			−0.216299
$861$	−0.343146	−	0.485281i	−0.0116944	−	0.0165383i
$862$	3.31371	+	3.31371i	0.112865	+	0.112865i
$863$	−39.3137			−1.33825			−0.669127	−	0.743148i	$-0.733332\pi$
$863$	−39.3137			−1.33825			−0.669127	+	0.743148i	$0.733332\pi$
$864$	25.6569	+	14.3431i	0.872864	+	0.487964i
$865$	4.05887			0.138006
$866$	14.6863	+	14.6863i	0.499061	+	0.499061i
$867$	−15.6274	−	22.1005i	−0.530735	−	0.750573i
$868$	−12.9706			−0.440250
$869$	−7.65685	+	7.65685i	−0.259741	+	0.259741i
$870$	1.02944	−	6.00000i	0.0349012	−	0.203419i
$871$	61.7990			2.09398
$872$		−	23.3137i		−	0.789502i
$873$	2.00000	−	5.65685i	0.0676897	−	0.191456i
$874$	6.34315			0.214560
$875$	−4.00000	−	4.00000i	−0.135225	−	0.135225i
$876$	−10.3431	−	14.6274i	−0.349463	−	0.494215i
$877$	6.51472	−	6.51472i	0.219986	−	0.219986i	−0.588506	−	0.808493i	$-0.700284\pi$
$877$	6.51472	−	6.51472i	0.219986	−	0.219986i	0.808493	+	0.588506i	$0.200284\pi$
$878$	0.970563	+	0.970563i	0.0327549	+	0.0327549i
$879$	22.3137	+	3.82843i	0.752623	+	0.129130i
$880$	12.6863			0.427655
$881$			48.4853i			1.63351i	0.576984	+	0.816755i	$0.304229\pi$
$881$			48.4853i			1.63351i	−0.576984	+	0.816755i	$0.695771\pi$
$882$	3.82843	−	1.82843i	0.128910	−	0.0615663i
$883$	38.9411	+	38.9411i	1.31047	+	1.31047i	0.921065	+	0.389408i	$0.127320\pi$
$883$	38.9411	+	38.9411i	1.31047	+	1.31047i	0.389408	+	0.921065i	$0.372680\pi$
$884$	−10.3431	+	10.3431i	−0.347878	+	0.347878i
$885$	8.34315	+	11.7990i	0.280452	+	0.396619i
$886$		−	33.3137i		−	1.11920i
$887$		−	39.1716i		−	1.31525i	−0.753344	−	0.657626i	$-0.771561\pi$
$887$		−	39.1716i		−	1.31525i	0.753344	−	0.657626i	$-0.228439\pi$
$888$	−7.31371	−	10.3431i	−0.245432	−	0.347093i
$889$		−	15.6569i		−	0.525114i
$890$	12.9706			0.434774
$891$	5.14214	+	48.4558i	0.172268	+	1.62333i
$892$	−14.3431			−0.480244
$893$	−2.34315	−	2.34315i	−0.0784104	−	0.0784104i
$894$	18.9706	+	26.8284i	0.634471	+	0.897277i
$895$			12.4264i			0.415369i
$896$	8.00000	−	8.00000i	0.267261	−	0.267261i
$897$	−14.0000	+	81.5980i	−0.467446	+	2.72448i
$898$	−12.9706	+	12.9706i	−0.432833	+	0.432833i
$899$	−19.4558	+	19.4558i	−0.648889	+	0.648889i
$900$	9.31371	−	26.3431i	0.310457	−	0.878105i
$901$	6.82843	+	6.82843i	0.227488	+	0.227488i
$902$		−	2.62742i		−	0.0874834i
$903$	−9.24264	−	1.58579i	−0.307576	−	0.0527717i
$904$	−3.31371	−	3.31371i	−0.110212	−	0.110212i
$905$	−1.71573			−0.0570328
$906$	7.31371	−	42.6274i	0.242982	−	1.41620i
$907$	−20.3137	+	20.3137i	−0.674506	+	0.674506i	−0.958751	−	0.284246i	$-0.908257\pi$
$907$	−20.3137	+	20.3137i	−0.674506	+	0.674506i	0.284246	+	0.958751i	$0.408257\pi$
$908$	−16.1421	−	16.1421i	−0.535696	−	0.535696i
$909$	18.4142	+	38.5563i	0.610761	+	1.27883i
$910$	−3.65685	+	3.65685i	−0.121224	+	0.121224i
$911$	−44.2843			−1.46720			−0.733602	−	0.679580i	$-0.762162\pi$
$911$	−44.2843			−1.46720			−0.733602	+	0.679580i	$0.762162\pi$
$912$	−0.686292	+	4.00000i	−0.0227254	+	0.132453i
$913$	−68.1421			−2.25518
$914$	−29.9411	+	29.9411i	−0.990364	+	0.990364i
$915$	−2.82843	+	2.00000i	−0.0935049	+	0.0661180i
$916$	−21.7990	+	21.7990i	−0.720259	+	0.720259i
$917$	4.07107	−	4.07107i	0.134439	−	0.134439i
$918$	−4.20101	+	7.51472i	−0.138654	+	0.248023i
$919$	−2.34315			−0.0772932			−0.0386466	−	0.999253i	$-0.512305\pi$
$919$	−2.34315			−0.0772932			−0.0386466	+	0.999253i	$0.512305\pi$
$920$	12.6863			0.418255
$921$	−6.17157	+	35.9706i	−0.203360	+	1.18527i
$922$			44.8284i			1.47635i
$923$	−26.4853	−	26.4853i	−0.871774	−	0.871774i
$924$	18.4853	+	3.17157i	0.608121	+	0.104337i
$925$	−8.51472	+	8.51472i	−0.279962	+	0.279962i
$926$	11.6569	−	11.6569i	0.383068	−	0.383068i
$927$	−11.3137	+	32.0000i	−0.371591	+	1.05102i
$928$		−	24.0000i		−	0.787839i
$929$		−	19.1127i		−	0.627067i	−0.949577	−	0.313534i	$-0.898487\pi$
$929$		−	19.1127i		−	0.627067i	0.949577	−	0.313534i	$-0.101513\pi$
$930$	7.59798	−	5.37258i	0.249148	−	0.176174i
$931$	0.414214	+	0.414214i	0.0135753	+	0.0135753i
$932$		−	2.62742i		−	0.0860639i
$933$	−2.14214	+	1.51472i	−0.0701304	+	0.0495897i
$934$	28.8284			0.943295
$935$			3.71573i			0.121517i
$936$	−49.9411	−	17.6569i	−1.63238	−	0.577132i
$937$		−	1.85786i		−	0.0606938i	−0.999539	−	0.0303469i	$-0.990339\pi$
$937$		−	1.85786i		−	0.0606938i	0.999539	−	0.0303469i	$-0.00966120\pi$
$938$		−	14.0000i		−	0.457116i
$939$	−28.9706	+	20.4853i	−0.945419	+	0.668512i
$940$	−4.68629	−	4.68629i	−0.152850	−	0.152850i
$941$	42.3553	+	42.3553i	1.38074	+	1.38074i	0.843297	+	0.537447i	$0.180611\pi$
$941$	42.3553	+	42.3553i	1.38074	+	1.38074i	0.537447	+	0.843297i	$0.319389\pi$
$942$	5.79899	+	8.20101i	0.188941	+	0.267203i
$943$		−	2.62742i		−	0.0855605i
$944$	40.2843	+	40.2843i	1.31114	+	1.31114i
$945$	−1.48528	+	2.65685i	−0.0483162	+	0.0864275i
$946$	−29.3137	−	29.3137i	−0.953071	−	0.953071i
$947$	19.1421	−	19.1421i	0.622036	−	0.622036i	−0.324016	−	0.946052i	$-0.605033\pi$
$947$	19.1421	−	19.1421i	0.622036	−	0.622036i	0.946052	+	0.324016i	$0.105033\pi$
$948$	−4.00000	−	5.65685i	−0.129914	−	0.183726i
$949$	22.8284	+	22.8284i	0.741042	+	0.741042i
$950$	3.85786			0.125166
$951$	−5.44365	+	31.7279i	−0.176522	+	1.02885i
$952$	2.34315	+	2.34315i	0.0759418	+	0.0759418i
$953$	−20.3431			−0.658979			−0.329490	−	0.944159i	$-0.606877\pi$
$953$	−20.3431			−0.658979			−0.329490	+	0.944159i	$0.606877\pi$
$954$	−11.6569	+	32.9706i	−0.377405	+	1.06746i
$955$	−2.62742	+	2.62742i	−0.0850212	+	0.0850212i
$956$			22.6274i			0.731823i
$957$	32.4853	−	22.9706i	1.05010	−	0.742533i
$958$	−27.3137	−	27.3137i	−0.882466	−	0.882466i
$959$	7.65685			0.247253
$960$	−1.37258	+	8.00000i	−0.0442999	+	0.258199i
$961$	−11.0589			−0.356738
$962$	16.1421	+	16.1421i	0.520443	+	0.520443i
$963$	19.1421	−	9.14214i	0.616847	−	0.294601i
$964$			0.686292i			0.0221040i
$965$	6.48528	−	6.48528i	0.208769	−	0.208769i
$966$	18.4853	+	3.17157i	0.594754	+	0.102044i
$967$	−23.3137			−0.749718			−0.374859	−	0.927082i	$-0.622309\pi$
$967$	−23.3137			−0.749718			−0.374859	+	0.927082i	$0.622309\pi$
$968$	36.6274	+	36.6274i	1.17725	+	1.17725i
$969$	−1.17157	−	0.201010i	−0.0376363	−	0.00645738i
$970$	1.65685			0.0531984
$971$	2.89949	+	2.89949i	0.0930492	+	0.0930492i	0.752099	−	0.659050i	$-0.229041\pi$
$971$	2.89949	+	2.89949i	0.0930492	+	0.0930492i	−0.659050	+	0.752099i	$0.729041\pi$
$972$	−31.1127	−	2.00000i	−0.997940	−	0.0641500i
$973$	4.41421	−	4.41421i	0.141513	−	0.141513i
$974$	16.2843	+	16.2843i	0.521782	+	0.521782i
$975$	−8.51472	+	49.6274i	−0.272689	+	1.58935i
$976$	−9.65685	+	9.65685i	−0.309108	+	0.309108i
$977$		−	8.68629i		−	0.277899i	−0.990299	−	0.138950i	$-0.955627\pi$
$977$		−	8.68629i		−	0.277899i	0.990299	−	0.138950i	$-0.0443726\pi$
$978$	5.17157	−	3.65685i	0.165369	−	0.116933i
$979$	59.9411	+	59.9411i	1.91573	+	1.91573i
$980$	0.828427	+	0.828427i	0.0264631	+	0.0264631i
$981$	10.6569	+	22.3137i	0.340247	+	0.712422i
$982$		−	20.6274i		−	0.658247i
$983$			37.5147i			1.19653i	0.801297	+	0.598267i	$0.204144\pi$
$983$			37.5147i			1.19653i	−0.801297	+	0.598267i	$0.795856\pi$
$984$	1.65685	+	0.284271i	0.0528186	+	0.00906224i
$985$			4.82843i			0.153846i
$986$	7.02944			0.223863
$987$	−5.65685	−	8.00000i	−0.180060	−	0.254643i
$988$		−	7.31371i		−	0.232680i
$989$	−29.3137	−	29.3137i	−0.932122	−	0.932122i
$990$	−12.1421	+	5.79899i	−0.385902	+	0.184304i
$991$		−	22.6863i		−	0.720654i	−0.932826	−	0.360327i	$-0.882665\pi$
$991$		−	22.6863i		−	0.720654i	0.932826	−	0.360327i	$-0.117335\pi$
$992$	25.9411	−	25.9411i	0.823632	−	0.823632i
$993$	−41.3848	−	7.10051i	−1.31331	−	0.225328i
$994$	−6.00000	+	6.00000i	−0.190308	+	0.190308i
$995$		0			0
$996$	7.37258	−	42.9706i	0.233609	−	1.36157i
$997$	−19.9289	−	19.9289i	−0.631156	−	0.631156i	0.317202	−	0.948358i	$-0.397257\pi$
$997$	−19.9289	−	19.9289i	−0.631156	−	0.631156i	−0.948358	+	0.317202i	$0.897257\pi$
$998$		−	11.3726i		−	0.359993i
$999$	11.7279	+	6.55635i	0.371055	+	0.207434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.a.155.1	✓	4
3.2	odd	2		336.2.s.b.155.1	yes	4
4.3	odd	2		1344.2.s.b.911.2		4
12.11	even	2		1344.2.s.a.911.2		4
16.3	odd	4		336.2.s.b.323.1	yes	4
16.13	even	4		1344.2.s.a.239.2		4
48.29	odd	4		1344.2.s.b.239.1		4
48.35	even	4	inner	336.2.s.a.323.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.a.155.1	✓	4	1.1	even	1	trivial
336.2.s.a.323.2	yes	4	48.35	even	4	inner
336.2.s.b.155.1	yes	4	3.2	odd	2
336.2.s.b.323.1	yes	4	16.3	odd	4
1344.2.s.a.239.2		4	16.13	even	4
1344.2.s.a.911.2		4	12.11	even	2
1344.2.s.b.239.1		4	48.29	odd	4
1344.2.s.b.911.2		4	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} +2.00000i q^{4} +(0.414214 - 0.414214i) q^{5} +(-0.414214 + 2.41421i) q^{6} -1.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 - 1.41421i) q^{3} +2.00000i q^{4} +(0.414214 - 0.414214i) q^{5} +(-0.414214 + 2.41421i) q^{6} -1.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 2.82843i) q^{9} -0.828427 q^{10} +(-3.82843 - 3.82843i) q^{11} +(2.82843 - 2.00000i) q^{12} +(-4.41421 + 4.41421i) q^{13} +(1.00000 + 1.00000i) q^{14} +(-1.00000 - 0.171573i) q^{15} -4.00000 q^{16} -1.17157i q^{17} +(3.82843 - 1.82843i) q^{18} +(0.414214 + 0.414214i) q^{19} +(0.828427 + 0.828427i) q^{20} +(1.00000 + 1.41421i) q^{21} +7.65685i q^{22} +7.65685i q^{23} +(-4.82843 - 0.828427i) q^{24} +4.65685i q^{25} +8.82843 q^{26} +(5.00000 - 1.41421i) q^{27} -2.00000i q^{28} +(-3.00000 - 3.00000i) q^{29} +(0.828427 + 1.17157i) q^{30} -6.48528i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.58579 + 9.24264i) q^{33} +(-1.17157 + 1.17157i) q^{34} +(-0.414214 + 0.414214i) q^{35} +(-5.65685 - 2.00000i) q^{36} +(1.82843 + 1.82843i) q^{37} -0.828427i q^{38} +(10.6569 + 1.82843i) q^{39} -1.65685i q^{40} -0.343146 q^{41} +(0.414214 - 2.41421i) q^{42} +(-3.82843 + 3.82843i) q^{43} +(7.65685 - 7.65685i) q^{44} +(0.757359 + 1.58579i) q^{45} +(7.65685 - 7.65685i) q^{46} -5.65685 q^{47} +(4.00000 + 5.65685i) q^{48} +1.00000 q^{49} +(4.65685 - 4.65685i) q^{50} +(-1.65685 + 1.17157i) q^{51} +(-8.82843 - 8.82843i) q^{52} +(-5.82843 + 5.82843i) q^{53} +(-6.41421 - 3.58579i) q^{54} -3.17157 q^{55} +(-2.00000 + 2.00000i) q^{56} +(0.171573 - 1.00000i) q^{57} +6.00000i q^{58} +(-10.0711 - 10.0711i) q^{59} +(0.343146 - 2.00000i) q^{60} +(2.41421 - 2.41421i) q^{61} +(-6.48528 + 6.48528i) q^{62} +(1.00000 - 2.82843i) q^{63} -8.00000i q^{64} +3.65685i q^{65} +(10.8284 - 7.65685i) q^{66} +(-7.00000 - 7.00000i) q^{67} +2.34315 q^{68} +(10.8284 - 7.65685i) q^{69} +0.828427 q^{70} +6.00000i q^{71} +(3.65685 + 7.65685i) q^{72} -5.17157i q^{73} -3.65685i q^{74} +(6.58579 - 4.65685i) q^{75} +(-0.828427 + 0.828427i) q^{76} +(3.82843 + 3.82843i) q^{77} +(-8.82843 - 12.4853i) q^{78} -2.00000i q^{79} +(-1.65685 + 1.65685i) q^{80} +(-7.00000 - 5.65685i) q^{81} +(0.343146 + 0.343146i) q^{82} +(8.89949 - 8.89949i) q^{83} +(-2.82843 + 2.00000i) q^{84} +(-0.485281 - 0.485281i) q^{85} +7.65685 q^{86} +(-1.24264 + 7.24264i) q^{87} -15.3137 q^{88} -15.6569 q^{89} +(0.828427 - 2.34315i) q^{90} +(4.41421 - 4.41421i) q^{91} -15.3137 q^{92} +(-9.17157 + 6.48528i) q^{93} +(5.65685 + 5.65685i) q^{94} +0.343146 q^{95} +(1.65685 - 9.65685i) q^{96} -2.00000 q^{97} +(-1.00000 - 1.00000i) q^{98} +(14.6569 - 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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