LMFDB - Embedded newform 165.2.k.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(23,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("165.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.31753163335$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	165.23
Dual form			165.2.k.a.122.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 - 0.292893i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.82843i q^{4} +(-2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.292893 - 0.292893i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.82843i q^{4} +(-2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(0.292893 + 0.878680i) q^{10} +1.00000i q^{11} +(2.58579 + 1.82843i) q^{12} +(-2.00000 - 2.00000i) q^{13} +2.00000 q^{14} +(3.41421 - 1.82843i) q^{15} -3.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-0.535534 + 1.12132i) q^{18} +2.82843i q^{19} +(-1.82843 + 3.65685i) q^{20} +(-1.41421 - 8.24264i) q^{21} +(0.292893 - 0.292893i) q^{22} +(3.24264 - 3.24264i) q^{23} +(-0.464466 - 2.70711i) q^{24} +(3.00000 + 4.00000i) q^{25} +1.17157i q^{26} +(5.00000 + 1.41421i) q^{27} +(6.24264 + 6.24264i) q^{28} +0.828427 q^{29} +(-1.53553 - 0.464466i) q^{30} -3.17157 q^{31} +(3.12132 + 3.12132i) q^{32} +(-1.41421 - 1.00000i) q^{33} +1.65685i q^{34} +(10.2426 - 3.41421i) q^{35} +(-5.17157 + 1.82843i) q^{36} +(-0.171573 + 0.171573i) q^{37} +(0.828427 - 0.828427i) q^{38} +(4.82843 - 0.828427i) q^{39} +(3.36396 - 1.12132i) q^{40} +7.65685i q^{41} +(-2.00000 + 2.82843i) q^{42} +(0.242641 + 0.242641i) q^{43} +1.82843 q^{44} +(-0.828427 + 6.65685i) q^{45} -1.89949 q^{46} +(-7.24264 - 7.24264i) q^{47} +(3.00000 - 4.24264i) q^{48} -16.3137i q^{49} +(0.292893 - 2.05025i) q^{50} +(6.82843 - 1.17157i) q^{51} +(-3.65685 + 3.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(-1.05025 - 1.87868i) q^{54} +(1.00000 - 2.00000i) q^{55} -7.65685i q^{56} +(-4.00000 - 2.82843i) q^{57} +(-0.242641 - 0.242641i) q^{58} -4.00000 q^{59} +(-3.34315 - 6.24264i) q^{60} -6.48528 q^{61} +(0.928932 + 0.928932i) q^{62} +(13.0711 + 6.24264i) q^{63} +4.17157i q^{64} +(2.00000 + 6.00000i) q^{65} +(0.121320 + 0.707107i) q^{66} +(-6.41421 + 6.41421i) q^{67} +(-5.17157 + 5.17157i) q^{68} +(1.34315 + 7.82843i) q^{69} +(-4.00000 - 2.00000i) q^{70} +2.48528i q^{71} +(4.29289 + 2.05025i) q^{72} +0.100505 q^{74} +(-8.65685 + 0.242641i) q^{75} +5.17157 q^{76} +(-3.41421 - 3.41421i) q^{77} +(-1.65685 - 1.17157i) q^{78} -10.8284i q^{79} +(6.00000 + 3.00000i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(2.24264 - 2.24264i) q^{82} +(-9.07107 + 9.07107i) q^{83} +(-15.0711 + 2.58579i) q^{84} +(2.82843 + 8.48528i) q^{85} -0.142136i q^{86} +(-0.828427 + 1.17157i) q^{87} +(-1.12132 - 1.12132i) q^{88} -9.65685 q^{89} +(2.19239 - 1.70711i) q^{90} +13.6569 q^{91} +(-5.92893 - 5.92893i) q^{92} +(3.17157 - 4.48528i) q^{93} +4.24264i q^{94} +(2.82843 - 5.65685i) q^{95} +(-7.53553 + 1.29289i) q^{96} +(10.6569 - 10.6569i) q^{97} +(-4.77817 + 4.77817i) q^{98} +(2.82843 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 8 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{14} + 8 q^{15} - 12 q^{16} + 12 q^{18} + 4 q^{20} + 4 q^{22} - 4 q^{23} - 16 q^{24} + 12 q^{25} + 20 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{30} - 24 q^{31} + 4 q^{32} + 24 q^{35} - 32 q^{36} - 12 q^{37} - 8 q^{38} + 8 q^{39} - 12 q^{40} - 8 q^{42} - 16 q^{43} - 4 q^{44} + 8 q^{45} + 32 q^{46} - 12 q^{47} + 12 q^{48} + 4 q^{50} + 16 q^{51} + 8 q^{52} + 4 q^{53} - 24 q^{54} + 4 q^{55} - 16 q^{57} + 16 q^{58} - 16 q^{59} - 36 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{63} + 8 q^{65} - 8 q^{66} - 20 q^{67} - 32 q^{68} + 28 q^{69} - 16 q^{70} + 20 q^{72} + 40 q^{74} - 12 q^{75} + 32 q^{76} - 8 q^{77} + 16 q^{78} + 24 q^{80} - 28 q^{81} - 8 q^{82} - 8 q^{83} - 32 q^{84} + 8 q^{87} + 4 q^{88} - 16 q^{89} - 28 q^{90} + 32 q^{91} - 52 q^{92} + 24 q^{93} - 16 q^{96} + 20 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^14 + 8 * q^15 - 12 * q^16 + 12 * q^18 + 4 * q^20 + 4 * q^22 - 4 * q^23 - 16 * q^24 + 12 * q^25 + 20 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^30 - 24 * q^31 + 4 * q^32 + 24 * q^35 - 32 * q^36 - 12 * q^37 - 8 * q^38 + 8 * q^39 - 12 * q^40 - 8 * q^42 - 16 * q^43 - 4 * q^44 + 8 * q^45 + 32 * q^46 - 12 * q^47 + 12 * q^48 + 4 * q^50 + 16 * q^51 + 8 * q^52 + 4 * q^53 - 24 * q^54 + 4 * q^55 - 16 * q^57 + 16 * q^58 - 16 * q^59 - 36 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^63 + 8 * q^65 - 8 * q^66 - 20 * q^67 - 32 * q^68 + 28 * q^69 - 16 * q^70 + 20 * q^72 + 40 * q^74 - 12 * q^75 + 32 * q^76 - 8 * q^77 + 16 * q^78 + 24 * q^80 - 28 * q^81 - 8 * q^82 - 8 * q^83 - 32 * q^84 + 8 * q^87 + 4 * q^88 - 16 * q^89 - 28 * q^90 + 32 * q^91 - 52 * q^92 + 24 * q^93 - 16 * q^96 + 20 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.292893	−	0.292893i	−0.207107	−	0.207107i	0.595930	−	0.803037i	$-0.296784\pi$
$2$	−0.292893	−	0.292893i	−0.207107	−	0.207107i	−0.803037	+	0.595930i	$0.796784\pi$
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$		−	1.82843i		−	0.914214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	0.707107	−	0.121320i	0.288675	−	0.0495288i
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.355944	+	0.934507i	$0.615841\pi$
$7$	−3.41421	+	3.41421i	−1.29045	+	1.29045i	−0.934507	+	0.355944i	$0.884159\pi$
$8$	−1.12132	+	1.12132i	−0.396447	+	0.396447i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	0.292893	+	0.878680i	0.0926210	+	0.277863i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	2.58579	+	1.82843i	0.746452	+	0.527821i
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$	2.00000			0.534522
$15$	3.41421	−	1.82843i	0.881546	−	0.472098i
$16$	−3.00000			−0.750000
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	0.275350	−	0.961344i	$-0.411206\pi$
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	−0.961344	+	0.275350i	$0.911206\pi$
$18$	−0.535534	+	1.12132i	−0.126227	+	0.264298i
$19$			2.82843i			0.648886i	0.945905	+	0.324443i	$0.105177\pi$
$19$			2.82843i			0.648886i	−0.945905	+	0.324443i	$0.894823\pi$
$20$	−1.82843	+	3.65685i	−0.408849	+	0.817697i
$21$	−1.41421	−	8.24264i	−0.308607	−	1.79869i
$22$	0.292893	−	0.292893i	0.0624450	−	0.0624450i
$23$	3.24264	−	3.24264i	0.676137	−	0.676137i	−0.282987	−	0.959124i	$-0.591325\pi$
$23$	3.24264	−	3.24264i	0.676137	−	0.676137i	0.959124	+	0.282987i	$0.0913252\pi$
$24$	−0.464466	−	2.70711i	−0.0948087	−	0.552586i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$			1.17157i			0.229764i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$	6.24264	+	6.24264i	1.17975	+	1.17975i
$29$	0.828427			0.153835			0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427			0.153835			0.0769175	+	0.997037i	$0.475492\pi$
$30$	−1.53553	−	0.464466i	−0.280349	−	0.0847995i
$31$	−3.17157			−0.569631			−0.284816	−	0.958582i	$-0.591932\pi$
$31$	−3.17157			−0.569631			−0.284816	+	0.958582i	$0.591932\pi$
$32$	3.12132	+	3.12132i	0.551777	+	0.551777i
$33$	−1.41421	−	1.00000i	−0.246183	−	0.174078i
$34$			1.65685i			0.284148i
$35$	10.2426	−	3.41421i	1.73132	−	0.577107i
$36$	−5.17157	+	1.82843i	−0.861929	+	0.304738i
$37$	−0.171573	+	0.171573i	−0.0282064	+	0.0282064i	−0.721069	−	0.692863i	$-0.756349\pi$
$37$	−0.171573	+	0.171573i	−0.0282064	+	0.0282064i	0.692863	+	0.721069i	$0.256349\pi$
$38$	0.828427	−	0.828427i	0.134389	−	0.134389i
$39$	4.82843	−	0.828427i	0.773167	−	0.132655i
$40$	3.36396	−	1.12132i	0.531889	−	0.177296i
$41$			7.65685i			1.19580i	0.801571	+	0.597900i	$0.203998\pi$
$41$			7.65685i			1.19580i	−0.801571	+	0.597900i	$0.796002\pi$
$42$	−2.00000	+	2.82843i	−0.308607	+	0.436436i
$43$	0.242641	+	0.242641i	0.0370024	+	0.0370024i	0.725366	−	0.688364i	$-0.241671\pi$
$43$	0.242641	+	0.242641i	0.0370024	+	0.0370024i	−0.688364	+	0.725366i	$0.741671\pi$
$44$	1.82843			0.275646
$45$	−0.828427	+	6.65685i	−0.123495	+	0.992345i
$46$	−1.89949			−0.280065
$47$	−7.24264	−	7.24264i	−1.05645	−	1.05645i	−0.998308	−	0.0581392i	$-0.981483\pi$
$47$	−7.24264	−	7.24264i	−1.05645	−	1.05645i	−0.0581392	−	0.998308i	$-0.518517\pi$
$48$	3.00000	−	4.24264i	0.433013	−	0.612372i
$49$		−	16.3137i		−	2.33053i
$50$	0.292893	−	2.05025i	0.0414214	−	0.289949i
$51$	6.82843	−	1.17157i	0.956171	−	0.164053i
$52$	−3.65685	+	3.65685i	−0.507114	+	0.507114i
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$	−1.05025	−	1.87868i	−0.142921	−	0.255656i
$55$	1.00000	−	2.00000i	0.134840	−	0.269680i
$56$		−	7.65685i		−	1.02319i
$57$	−4.00000	−	2.82843i	−0.529813	−	0.374634i
$58$	−0.242641	−	0.242641i	−0.0318603	−	0.0318603i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	−3.34315	−	6.24264i	−0.431598	−	0.805921i
$61$	−6.48528			−0.830355			−0.415178	−	0.909740i	$-0.636281\pi$
$61$	−6.48528			−0.830355			−0.415178	+	0.909740i	$0.636281\pi$
$62$	0.928932	+	0.928932i	0.117975	+	0.117975i
$63$	13.0711	+	6.24264i	1.64680	+	0.786499i
$64$			4.17157i			0.521447i
$65$	2.00000	+	6.00000i	0.248069	+	0.744208i
$66$	0.121320	+	0.707107i	0.0149335	+	0.0870388i
$67$	−6.41421	+	6.41421i	−0.783621	+	0.783621i	−0.980440	−	0.196819i	$-0.936939\pi$
$67$	−6.41421	+	6.41421i	−0.783621	+	0.783621i	0.196819	+	0.980440i	$0.436939\pi$
$68$	−5.17157	+	5.17157i	−0.627145	+	0.627145i
$69$	1.34315	+	7.82843i	0.161696	+	0.942432i
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$			2.48528i			0.294949i	0.989066	+	0.147474i	$0.0471144\pi$
$71$			2.48528i			0.294949i	−0.989066	+	0.147474i	$0.952886\pi$
$72$	4.29289	+	2.05025i	0.505922	+	0.241625i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$	0.100505			0.0116835
$75$	−8.65685	+	0.242641i	−0.999607	+	0.0280177i
$76$	5.17157			0.593220
$77$	−3.41421	−	3.41421i	−0.389086	−	0.389086i
$78$	−1.65685	−	1.17157i	−0.187602	−	0.132655i
$79$		−	10.8284i		−	1.21829i	−0.793058	−	0.609147i	$-0.791512\pi$
$79$		−	10.8284i		−	1.21829i	0.793058	−	0.609147i	$-0.208488\pi$
$80$	6.00000	+	3.00000i	0.670820	+	0.335410i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	2.24264	−	2.24264i	0.247658	−	0.247658i
$83$	−9.07107	+	9.07107i	−0.995679	+	0.995679i	−0.999991	−	0.00431166i	$-0.998628\pi$
$83$	−9.07107	+	9.07107i	−0.995679	+	0.995679i	0.00431166	+	0.999991i	$0.498628\pi$
$84$	−15.0711	+	2.58579i	−1.64439	+	0.282132i
$85$	2.82843	+	8.48528i	0.306786	+	0.920358i
$86$		−	0.142136i		−	0.0153269i
$87$	−0.828427	+	1.17157i	−0.0888167	+	0.125606i
$88$	−1.12132	−	1.12132i	−0.119533	−	0.119533i
$89$	−9.65685			−1.02362			−0.511812	−	0.859097i	$-0.671026\pi$
$89$	−9.65685			−1.02362			−0.511812	+	0.859097i	$0.671026\pi$
$90$	2.19239	−	1.70711i	0.231098	−	0.179945i
$91$	13.6569			1.43163
$92$	−5.92893	−	5.92893i	−0.618134	−	0.618134i
$93$	3.17157	−	4.48528i	0.328877	−	0.465102i
$94$			4.24264i			0.437595i
$95$	2.82843	−	5.65685i	0.290191	−	0.580381i
$96$	−7.53553	+	1.29289i	−0.769092	+	0.131955i
$97$	10.6569	−	10.6569i	1.08204	−	1.08204i	0.0857204	−	0.996319i	$-0.472681\pi$
$97$	10.6569	−	10.6569i	1.08204	−	1.08204i	0.996319	−	0.0857204i	$-0.0273192\pi$
$98$	−4.77817	+	4.77817i	−0.482669	+	0.482669i
$99$	2.82843	−	1.00000i	0.284268	−	0.100504i
$100$	7.31371	−	5.48528i	0.731371	−	0.548528i
$101$			7.17157i			0.713598i	0.934181	+	0.356799i	$0.116132\pi$
$101$			7.17157i			0.713598i	−0.934181	+	0.356799i	$0.883868\pi$
$102$	−2.34315	−	1.65685i	−0.232006	−	0.164053i
$103$	−6.41421	−	6.41421i	−0.632011	−	0.632011i	0.316561	−	0.948572i	$-0.397472\pi$
$103$	−6.41421	−	6.41421i	−0.632011	−	0.632011i	−0.948572	+	0.316561i	$0.897472\pi$
$104$	4.48528			0.439818
$105$	−5.41421	+	17.8995i	−0.528373	+	1.74681i
$106$	−0.585786			−0.0568966
$107$	0.242641	+	0.242641i	0.0234570	+	0.0234570i	0.718738	−	0.695281i	$-0.244720\pi$
$107$	0.242641	+	0.242641i	0.0234570	+	0.0234570i	−0.695281	+	0.718738i	$0.744720\pi$
$108$	2.58579	−	9.14214i	0.248817	−	0.879702i
$109$		−	3.17157i		−	0.303782i	−0.988397	−	0.151891i	$-0.951464\pi$
$109$		−	3.17157i		−	0.303782i	0.988397	−	0.151891i	$-0.0485362\pi$
$110$	−0.878680	+	0.292893i	−0.0837788	+	0.0279263i
$111$	−0.0710678	−	0.414214i	−0.00674546	−	0.0393154i
$112$	10.2426	−	10.2426i	0.967839	−	0.967839i
$113$	−5.82843	+	5.82843i	−0.548292	+	0.548292i	−0.925947	−	0.377654i	$-0.876731\pi$
$113$	−5.82843	+	5.82843i	−0.548292	+	0.548292i	0.377654	+	0.925947i	$0.376731\pi$
$114$	0.343146	+	2.00000i	0.0321385	+	0.187317i
$115$	−9.72792	+	3.24264i	−0.907133	+	0.302378i
$116$		−	1.51472i		−	0.140638i
$117$	−3.65685	+	7.65685i	−0.338076	+	0.707876i
$118$	1.17157	+	1.17157i	0.107852	+	0.107852i
$119$	19.3137			1.77048
$120$	−1.77817	+	5.87868i	−0.162324	+	0.536648i
$121$	−1.00000			−0.0909091
$122$	1.89949	+	1.89949i	0.171972	+	0.171972i
$123$	−10.8284	−	7.65685i	−0.976366	−	0.690395i
$124$			5.79899i			0.520765i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−2.00000	−	5.65685i	−0.178174	−	0.503953i
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	−0.641572	−	0.767063i	$-0.721717\pi$
$127$	1.41421	−	1.41421i	0.125491	−	0.125491i	0.767063	+	0.641572i	$0.221717\pi$
$128$	7.46447	−	7.46447i	0.659772	−	0.659772i
$129$	−0.585786	+	0.100505i	−0.0515756	+	0.00884898i
$130$	1.17157	−	2.34315i	0.102754	−	0.205507i
$131$		−	6.82843i		−	0.596602i	−0.954472	−	0.298301i	$-0.903580\pi$
$131$		−	6.82843i		−	0.596602i	0.954472	−	0.298301i	$-0.0964200\pi$
$132$	−1.82843	+	2.58579i	−0.159144	+	0.225064i
$133$	−9.65685	−	9.65685i	−0.837355	−	0.837355i
$134$	3.75736			0.324586
$135$	−8.58579	−	7.82843i	−0.738947	−	0.673764i
$136$	6.34315			0.543920
$137$	0.171573	+	0.171573i	0.0146585	+	0.0146585i	0.714398	−	0.699740i	$-0.246701\pi$
$137$	0.171573	+	0.171573i	0.0146585	+	0.0146585i	−0.699740	+	0.714398i	$0.746701\pi$
$138$	1.89949	−	2.68629i	0.161696	−	0.228672i
$139$			17.6569i			1.49763i	0.662776	+	0.748817i	$0.269378\pi$
$139$			17.6569i			1.49763i	−0.662776	+	0.748817i	$0.730622\pi$
$140$	−6.24264	−	18.7279i	−0.527599	−	1.58280i
$141$	17.4853	−	3.00000i	1.47253	−	0.252646i
$142$	0.727922	−	0.727922i	0.0610859	−	0.0610859i
$143$	2.00000	−	2.00000i	0.167248	−	0.167248i
$144$	3.00000	+	8.48528i	0.250000	+	0.707107i
$145$	−1.65685	−	0.828427i	−0.137594	−	0.0687971i
$146$		0			0
$147$	23.0711	+	16.3137i	1.90287	+	1.34553i
$148$	0.313708	+	0.313708i	0.0257867	+	0.0257867i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	2.60660	+	2.46447i	0.212828	+	0.201223i
$151$	10.1421			0.825355			0.412678	−	0.910877i	$-0.364594\pi$
$151$	10.1421			0.825355			0.412678	+	0.910877i	$0.364594\pi$
$152$	−3.17157	−	3.17157i	−0.257249	−	0.257249i
$153$	−5.17157	+	10.8284i	−0.418097	+	0.875426i
$154$			2.00000i			0.161165i
$155$	6.34315	+	3.17157i	0.509494	+	0.254747i
$156$	−1.51472	−	8.82843i	−0.121275	−	0.706840i
$157$	−9.48528	+	9.48528i	−0.757008	+	0.757008i	−0.975777	−	0.218769i	$-0.929796\pi$
$157$	−9.48528	+	9.48528i	−0.757008	+	0.757008i	0.218769	+	0.975777i	$0.429796\pi$
$158$	−3.17157	+	3.17157i	−0.252317	+	0.252317i
$159$	0.414214	+	2.41421i	0.0328493	+	0.191460i
$160$	−3.12132	−	9.36396i	−0.246762	−	0.740286i
$161$			22.1421i			1.74504i
$162$	3.70711	+	0.393398i	0.291258	+	0.0309083i
$163$	3.58579	+	3.58579i	0.280860	+	0.280860i	0.833452	−	0.552592i	$-0.186361\pi$
$163$	3.58579	+	3.58579i	0.280860	+	0.280860i	−0.552592	+	0.833452i	$0.686361\pi$
$164$	14.0000			1.09322
$165$	1.82843	+	3.41421i	0.142343	+	0.265796i
$166$	5.31371			0.412424
$167$	14.7279	+	14.7279i	1.13968	+	1.13968i	0.988507	+	0.151174i	$0.0483052\pi$
$167$	14.7279	+	14.7279i	1.13968	+	1.13968i	0.151174	+	0.988507i	$0.451695\pi$
$168$	10.8284	+	7.65685i	0.835431	+	0.590739i
$169$		−	5.00000i		−	0.384615i
$170$	1.65685	−	3.31371i	0.127075	−	0.254150i
$171$	8.00000	−	2.82843i	0.611775	−	0.216295i
$172$	0.443651	−	0.443651i	0.0338281	−	0.0338281i
$173$	8.48528	−	8.48528i	0.645124	−	0.645124i	−0.306687	−	0.951811i	$-0.599220\pi$
$173$	8.48528	−	8.48528i	0.645124	−	0.645124i	0.951811	+	0.306687i	$0.0992203\pi$
$174$	0.585786	−	0.100505i	0.0444084	−	0.00761927i
$175$	−23.8995	−	3.41421i	−1.80663	−	0.258090i
$176$		−	3.00000i		−	0.226134i
$177$	4.00000	−	5.65685i	0.300658	−	0.425195i
$178$	2.82843	+	2.82843i	0.212000	+	0.212000i
$179$	24.1421			1.80447			0.902234	−	0.431247i	$-0.141926\pi$
$179$	24.1421			1.80447			0.902234	+	0.431247i	$0.141926\pi$
$180$	12.1716	+	1.51472i	0.907215	+	0.112900i
$181$	5.65685			0.420471			0.210235	−	0.977651i	$-0.432577\pi$
$181$	5.65685			0.420471			0.210235	+	0.977651i	$0.432577\pi$
$182$	−4.00000	−	4.00000i	−0.296500	−	0.296500i
$183$	6.48528	−	9.17157i	0.479406	−	0.677982i
$184$			7.27208i			0.536105i
$185$	0.514719	−	0.171573i	0.0378429	−	0.0126143i
$186$	−2.24264	+	0.384776i	−0.164438	+	0.0282132i
$187$	2.82843	−	2.82843i	0.206835	−	0.206835i
$188$	−13.2426	+	13.2426i	−0.965819	+	0.965819i
$189$	−21.8995	+	12.2426i	−1.59295	+	0.890521i
$190$	−2.48528	+	0.828427i	−0.180301	+	0.0601004i
$191$		−	11.3137i		−	0.818631i	−0.912393	−	0.409316i	$-0.865768\pi$
$191$		−	11.3137i		−	0.818631i	0.912393	−	0.409316i	$-0.134232\pi$
$192$	−5.89949	−	4.17157i	−0.425759	−	0.301057i
$193$	8.00000	+	8.00000i	0.575853	+	0.575853i	0.933758	−	0.357905i	$-0.116509\pi$
$193$	8.00000	+	8.00000i	0.575853	+	0.575853i	−0.357905	+	0.933758i	$0.616509\pi$
$194$	−6.24264			−0.448195
$195$	−10.4853	−	3.17157i	−0.750867	−	0.227121i
$196$	−29.8284			−2.13060
$197$	−14.1421	−	14.1421i	−1.00759	−	1.00759i	−0.999971	−	0.00761443i	$-0.997576\pi$
$197$	−14.1421	−	14.1421i	−1.00759	−	1.00759i	−0.00761443	−	0.999971i	$-0.502424\pi$
$198$	−1.12132	−	0.535534i	−0.0796888	−	0.0380587i
$199$			14.4853i			1.02683i	0.858139	+	0.513417i	$0.171621\pi$
$199$			14.4853i			1.02683i	−0.858139	+	0.513417i	$0.828379\pi$
$200$	−7.84924	−	1.12132i	−0.555025	−	0.0792893i
$201$	−2.65685	−	15.4853i	−0.187400	−	1.09225i
$202$	2.10051	−	2.10051i	0.147791	−	0.147791i
$203$	−2.82843	+	2.82843i	−0.198517	+	0.198517i
$204$	−2.14214	−	12.4853i	−0.149979	−	0.874145i
$205$	7.65685	−	15.3137i	0.534778	−	1.06956i
$206$			3.75736i			0.261788i
$207$	−12.4142	−	5.92893i	−0.862847	−	0.412089i
$208$	6.00000	+	6.00000i	0.416025	+	0.416025i
$209$	−2.82843			−0.195646
$210$	6.82843	−	3.65685i	0.471206	−	0.252347i
$211$	−4.48528			−0.308780			−0.154390	−	0.988010i	$-0.549341\pi$
$211$	−4.48528			−0.308780			−0.154390	+	0.988010i	$0.549341\pi$
$212$	−1.82843	−	1.82843i	−0.125577	−	0.125577i
$213$	−3.51472	−	2.48528i	−0.240825	−	0.170289i
$214$		−	0.142136i		−	0.00971619i
$215$	−0.242641	−	0.727922i	−0.0165480	−	0.0496439i
$216$	−7.19239	+	4.02082i	−0.489380	+	0.273582i
$217$	10.8284	−	10.8284i	0.735082	−	0.735082i
$218$	−0.928932	+	0.928932i	−0.0629152	+	0.0629152i
$219$		0			0
$220$	−3.65685	−	1.82843i	−0.246545	−	0.123273i
$221$			11.3137i			0.761042i
$222$	−0.100505	+	0.142136i	−0.00674546	+	0.00953952i
$223$	−16.5563	−	16.5563i	−1.10870	−	1.10870i	−0.993322	−	0.115373i	$-0.963194\pi$
$223$	−16.5563	−	16.5563i	−1.10870	−	1.10870i	−0.115373	−	0.993322i	$-0.536806\pi$
$224$	−21.3137			−1.42408
$225$	8.31371	−	12.4853i	0.554247	−	0.832352i
$226$	3.41421			0.227110
$227$	10.2426	+	10.2426i	0.679828	+	0.679828i	0.959961	−	0.280133i	$-0.0903786\pi$
$227$	10.2426	+	10.2426i	0.679828	+	0.679828i	−0.280133	+	0.959961i	$0.590379\pi$
$228$	−5.17157	+	7.31371i	−0.342496	+	0.484362i
$229$			9.65685i			0.638143i	0.947731	+	0.319071i	$0.103371\pi$
$229$			9.65685i			0.638143i	−0.947731	+	0.319071i	$0.896629\pi$
$230$	3.79899	+	1.89949i	0.250498	+	0.125249i
$231$	8.24264	−	1.41421i	0.542326	−	0.0930484i
$232$	−0.928932	+	0.928932i	−0.0609874	+	0.0609874i
$233$	19.6569	−	19.6569i	1.28776	−	1.28776i	0.351621	−	0.936143i	$-0.385631\pi$
$233$	19.6569	−	19.6569i	1.28776	−	1.28776i	0.936143	−	0.351621i	$-0.114369\pi$
$234$	3.31371	−	1.17157i	0.216624	−	0.0765881i
$235$	7.24264	+	21.7279i	0.472458	+	1.41737i
$236$			7.31371i			0.476082i
$237$	15.3137	+	10.8284i	0.994732	+	0.703382i
$238$	−5.65685	−	5.65685i	−0.366679	−	0.366679i
$239$	−23.7990			−1.53943			−0.769714	−	0.638388i	$-0.779601\pi$
$239$	−23.7990			−1.53943			−0.769714	+	0.638388i	$0.779601\pi$
$240$	−10.2426	+	5.48528i	−0.661160	+	0.354073i
$241$	0.142136			0.00915576			0.00457788	−	0.999990i	$-0.498543\pi$
$241$	0.142136			0.00915576			0.00457788	+	0.999990i	$0.498543\pi$
$242$	0.292893	+	0.292893i	0.0188279	+	0.0188279i
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$			11.8579i			0.759122i
$245$	−16.3137	+	32.6274i	−1.04224	+	2.08449i
$246$	0.928932	+	5.41421i	0.0592266	+	0.345198i
$247$	5.65685	−	5.65685i	0.359937	−	0.359937i
$248$	3.55635	−	3.55635i	0.225828	−	0.225828i
$249$	−3.75736	−	21.8995i	−0.238113	−	1.38782i
$250$	−2.63604	+	3.80761i	−0.166718	+	0.240815i
$251$			16.1421i			1.01888i	0.860505	+	0.509441i	$0.170148\pi$
$251$			16.1421i			1.01888i	−0.860505	+	0.509441i	$0.829852\pi$
$252$	11.4142	−	23.8995i	0.719028	−	1.50553i
$253$	3.24264	+	3.24264i	0.203863	+	0.203863i
$254$	−0.828427			−0.0519801
$255$	−14.8284	−	4.48528i	−0.928592	−	0.280879i
$256$	3.97056			0.248160
$257$	−1.82843	−	1.82843i	−0.114054	−	0.114054i	0.647776	−	0.761831i	$-0.275699\pi$
$257$	−1.82843	−	1.82843i	−0.114054	−	0.114054i	−0.761831	+	0.647776i	$0.775699\pi$
$258$	0.201010	+	0.142136i	0.0125143	+	0.00884898i
$259$		−	1.17157i		−	0.0727980i
$260$	10.9706	−	3.65685i	0.680365	−	0.226788i
$261$	−0.828427	−	2.34315i	−0.0512784	−	0.145037i
$262$	−2.00000	+	2.00000i	−0.123560	+	0.123560i
$263$	−1.75736	+	1.75736i	−0.108363	+	0.108363i	−0.759210	−	0.650846i	$-0.774414\pi$
$263$	−1.75736	+	1.75736i	−0.108363	+	0.108363i	0.650846	+	0.759210i	$0.274414\pi$
$264$	2.70711	−	0.464466i	0.166611	−	0.0285859i
$265$	−3.00000	+	1.00000i	−0.184289	+	0.0614295i
$266$			5.65685i			0.346844i
$267$	9.65685	−	13.6569i	0.590990	−	0.835786i
$268$	11.7279	+	11.7279i	0.716397	+	0.716397i
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$	0.221825	+	4.80761i	0.0134999	+	0.292582i
$271$	8.48528			0.515444			0.257722	−	0.966219i	$-0.417028\pi$
$271$	8.48528			0.515444			0.257722	+	0.966219i	$0.417028\pi$
$272$	8.48528	+	8.48528i	0.514496	+	0.514496i
$273$	−13.6569	+	19.3137i	−0.826550	+	1.16892i
$274$		−	0.100505i		−	0.00607173i
$275$	−4.00000	+	3.00000i	−0.241209	+	0.180907i
$276$	14.3137	−	2.45584i	0.861584	−	0.147824i
$277$	−18.4853	+	18.4853i	−1.11067	+	1.11067i	−0.117613	+	0.993059i	$0.537524\pi$
$277$	−18.4853	+	18.4853i	−1.11067	+	1.11067i	−0.993059	+	0.117613i	$0.962476\pi$
$278$	5.17157	−	5.17157i	0.310170	−	0.310170i
$279$	3.17157	+	8.97056i	0.189877	+	0.537054i
$280$	−7.65685	+	15.3137i	−0.457585	+	0.915169i
$281$		−	28.6274i		−	1.70777i	−0.520463	−	0.853884i	$-0.674241\pi$
$281$		−	28.6274i		−	1.70777i	0.520463	−	0.853884i	$-0.325759\pi$
$282$	−6.00000	−	4.24264i	−0.357295	−	0.252646i
$283$	−15.0711	−	15.0711i	−0.895882	−	0.895882i	0.0991868	−	0.995069i	$-0.468376\pi$
$283$	−15.0711	−	15.0711i	−0.895882	−	0.895882i	−0.995069	+	0.0991868i	$0.968376\pi$
$284$	4.54416			0.269646
$285$	5.17157	+	9.65685i	0.306338	+	0.572023i
$286$	−1.17157			−0.0692766
$287$	−26.1421	−	26.1421i	−1.54312	−	1.54312i
$288$	5.70711	−	11.9497i	0.336294	−	0.704146i
$289$		−	1.00000i		−	0.0588235i
$290$	0.242641	+	0.727922i	0.0142484	+	0.0427451i
$291$	4.41421	+	25.7279i	0.258766	+	1.50820i
$292$		0			0
$293$	−3.65685	+	3.65685i	−0.213636	+	0.213636i	−0.805810	−	0.592174i	$-0.798270\pi$
$293$	−3.65685	+	3.65685i	−0.213636	+	0.213636i	0.592174	+	0.805810i	$0.298270\pi$
$294$	−1.97918	−	11.5355i	−0.115428	−	0.672766i
$295$	8.00000	+	4.00000i	0.465778	+	0.232889i
$296$		−	0.384776i		−	0.0223647i
$297$	−1.41421	+	5.00000i	−0.0820610	+	0.290129i
$298$	2.92893	+	2.92893i	0.169668	+	0.169668i
$299$	−12.9706			−0.750107
$300$	0.443651	+	15.8284i	0.0256142	+	0.913855i
$301$	−1.65685			−0.0954995
$302$	−2.97056	−	2.97056i	−0.170937	−	0.170937i
$303$	−10.1421	−	7.17157i	−0.582650	−	0.411996i
$304$		−	8.48528i		−	0.486664i
$305$	12.9706	+	6.48528i	0.742692	+	0.371346i
$306$	4.68629	−	1.65685i	0.267897	−	0.0947161i
$307$	−11.8995	+	11.8995i	−0.679140	+	0.679140i	−0.959806	−	0.280666i	$-0.909445\pi$
$307$	−11.8995	+	11.8995i	−0.679140	+	0.679140i	0.280666	+	0.959806i	$0.409445\pi$
$308$	−6.24264	+	6.24264i	−0.355707	+	0.355707i
$309$	15.4853	−	2.65685i	0.880927	−	0.151143i
$310$	−0.928932	−	2.78680i	−0.0527598	−	0.158279i
$311$		−	28.1421i		−	1.59579i	−0.602794	−	0.797897i	$-0.705946\pi$
$311$		−	28.1421i		−	1.59579i	0.602794	−	0.797897i	$-0.294054\pi$
$312$	−4.48528	+	6.34315i	−0.253929	+	0.359110i
$313$	12.6569	+	12.6569i	0.715408	+	0.715408i	0.967661	−	0.252253i	$-0.0811717\pi$
$313$	12.6569	+	12.6569i	0.715408	+	0.715408i	−0.252253	+	0.967661i	$0.581172\pi$
$314$	5.55635			0.313563
$315$	−19.8995	−	25.5563i	−1.12121	−	1.43994i
$316$	−19.7990			−1.11378
$317$	2.31371	+	2.31371i	0.129951	+	0.129951i	0.769091	−	0.639140i	$-0.220709\pi$
$317$	2.31371	+	2.31371i	0.129951	+	0.129951i	−0.639140	+	0.769091i	$0.720709\pi$
$318$	0.585786	−	0.828427i	0.0328493	−	0.0464559i
$319$			0.828427i			0.0463830i
$320$	4.17157	−	8.34315i	0.233198	−	0.466396i
$321$	−0.585786	+	0.100505i	−0.0326954	+	0.00560965i
$322$	6.48528	−	6.48528i	0.361411	−	0.361411i
$323$	8.00000	−	8.00000i	0.445132	−	0.445132i
$324$	10.3431	+	12.7990i	0.574619	+	0.711055i
$325$	2.00000	−	14.0000i	0.110940	−	0.776580i
$326$		−	2.10051i		−	0.116336i
$327$	4.48528	+	3.17157i	0.248037	+	0.175388i
$328$	−8.58579	−	8.58579i	−0.474071	−	0.474071i
$329$	49.4558			2.72659
$330$	0.464466	−	1.53553i	0.0255680	−	0.0845284i
$331$	−6.48528			−0.356463			−0.178232	−	0.983989i	$-0.557038\pi$
$331$	−6.48528			−0.356463			−0.178232	+	0.983989i	$0.557038\pi$
$332$	16.5858	+	16.5858i	0.910263	+	0.910263i
$333$	0.656854	+	0.313708i	0.0359954	+	0.0171911i
$334$		−	8.62742i		−	0.472071i
$335$	19.2426	−	6.41421i	1.05134	−	0.350446i
$336$	4.24264	+	24.7279i	0.231455	+	1.34902i
$337$	−10.8284	+	10.8284i	−0.589862	+	0.589862i	−0.937594	−	0.347732i	$-0.886952\pi$
$337$	−10.8284	+	10.8284i	−0.589862	+	0.589862i	0.347732	+	0.937594i	$0.386952\pi$
$338$	−1.46447	+	1.46447i	−0.0796565	+	0.0796565i
$339$	−2.41421	−	14.0711i	−0.131122	−	0.764235i
$340$	15.5147	−	5.17157i	0.841404	−	0.280468i
$341$		−	3.17157i		−	0.171750i
$342$	−3.17157	−	1.51472i	−0.171499	−	0.0819066i
$343$	31.7990	+	31.7990i	1.71698	+	1.71698i
$344$	−0.544156			−0.0293389
$345$	5.14214	−	17.0000i	0.276843	−	0.915249i
$346$	−4.97056			−0.267219
$347$	1.89949	+	1.89949i	0.101970	+	0.101970i	0.756251	−	0.654281i	$-0.227029\pi$
$347$	1.89949	+	1.89949i	0.101970	+	0.101970i	−0.654281	+	0.756251i	$0.727029\pi$
$348$	2.14214	+	1.51472i	0.114831	+	0.0811974i
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$	6.00000	+	8.00000i	0.320713	+	0.427618i
$351$	−7.17157	−	12.8284i	−0.382790	−	0.684731i
$352$	−3.12132	+	3.12132i	−0.166367	+	0.166367i
$353$	7.82843	−	7.82843i	0.416665	−	0.416665i	−0.467387	−	0.884053i	$-0.654805\pi$
$353$	7.82843	−	7.82843i	0.416665	−	0.416665i	0.884053	+	0.467387i	$0.154805\pi$
$354$	−2.82843	+	0.485281i	−0.150329	+	0.0257924i
$355$	2.48528	−	4.97056i	0.131905	−	0.263810i
$356$			17.6569i			0.935811i
$357$	−19.3137	+	27.3137i	−1.02219	+	1.44559i
$358$	−7.07107	−	7.07107i	−0.373718	−	0.373718i
$359$	−22.1421			−1.16862			−0.584309	−	0.811532i	$-0.698634\pi$
$359$	−22.1421			−1.16862			−0.584309	+	0.811532i	$0.698634\pi$
$360$	−6.53553	−	8.39340i	−0.344453	−	0.442371i
$361$	11.0000			0.578947
$362$	−1.65685	−	1.65685i	−0.0870823	−	0.0870823i
$363$	1.00000	−	1.41421i	0.0524864	−	0.0742270i
$364$		−	24.9706i		−	1.30881i
$365$		0			0
$366$	−4.58579	+	0.786797i	−0.239703	+	0.0411265i
$367$	−1.10051	+	1.10051i	−0.0574459	+	0.0574459i	−0.735246	−	0.677800i	$-0.762933\pi$
$367$	−1.10051	+	1.10051i	−0.0574459	+	0.0574459i	0.677800	+	0.735246i	$0.262933\pi$
$368$	−9.72792	+	9.72792i	−0.507103	+	0.507103i
$369$	21.6569	−	7.65685i	1.12741	−	0.398600i
$370$	−0.201010	−	0.100505i	−0.0104500	−	0.00522501i
$371$			6.82843i			0.354514i
$372$	−8.20101	−	5.79899i	−0.425203	−	0.300664i
$373$	3.51472	+	3.51472i	0.181985	+	0.181985i	0.792220	−	0.610235i	$-0.208925\pi$
$373$	3.51472	+	3.51472i	0.181985	+	0.181985i	−0.610235	+	0.792220i	$0.708925\pi$
$374$	−1.65685			−0.0856739
$375$	17.5563	+	8.17157i	0.906606	+	0.421978i
$376$	16.2426			0.837650
$377$	−1.65685	−	1.65685i	−0.0853323	−	0.0853323i
$378$	10.0000	+	2.82843i	0.514344	+	0.145479i
$379$			28.1421i			1.44556i	0.691076	+	0.722782i	$0.257137\pi$
$379$			28.1421i			1.44556i	−0.691076	+	0.722782i	$0.742863\pi$
$380$	−10.3431	−	5.17157i	−0.530592	−	0.265296i
$381$	0.585786	+	3.41421i	0.0300107	+	0.174915i
$382$	−3.31371	+	3.31371i	−0.169544	+	0.169544i
$383$	−6.07107	+	6.07107i	−0.310217	+	0.310217i	−0.844994	−	0.534776i	$-0.820396\pi$
$383$	−6.07107	+	6.07107i	−0.310217	+	0.310217i	0.534776	+	0.844994i	$0.320396\pi$
$384$	3.09188	+	18.0208i	0.157782	+	0.919621i
$385$	3.41421	+	10.2426i	0.174004	+	0.522013i
$386$		−	4.68629i		−	0.238526i
$387$	0.443651	−	0.928932i	0.0225520	−	0.0472203i
$388$	−19.4853	−	19.4853i	−0.989215	−	0.989215i
$389$	−17.3137			−0.877840			−0.438920	−	0.898526i	$-0.644639\pi$
$389$	−17.3137			−0.877840			−0.438920	+	0.898526i	$0.644639\pi$
$390$	2.14214	+	4.00000i	0.108471	+	0.202548i
$391$	−18.3431			−0.927653
$392$	18.2929	+	18.2929i	0.923931	+	0.923931i
$393$	9.65685	+	6.82843i	0.487124	+	0.344449i
$394$			8.28427i			0.417356i
$395$	−10.8284	+	21.6569i	−0.544837	+	1.08967i
$396$	−1.82843	−	5.17157i	−0.0918819	−	0.259881i
$397$	6.17157	−	6.17157i	0.309742	−	0.309742i	−0.535067	−	0.844810i	$-0.679714\pi$
$397$	6.17157	−	6.17157i	0.309742	−	0.309742i	0.844810	+	0.535067i	$0.179714\pi$
$398$	4.24264	−	4.24264i	0.212664	−	0.212664i
$399$	23.3137	−	4.00000i	1.16715	−	0.200250i
$400$	−9.00000	−	12.0000i	−0.450000	−	0.600000i
$401$		−	35.6569i		−	1.78062i	−0.455357	−	0.890309i	$-0.650488\pi$
$401$		−	35.6569i		−	1.78062i	0.455357	−	0.890309i	$-0.349512\pi$
$402$	−3.75736	+	5.31371i	−0.187400	+	0.265024i
$403$	6.34315	+	6.34315i	0.315975	+	0.315975i
$404$	13.1127			0.652381
$405$	19.6569	−	4.31371i	0.976757	−	0.214350i
$406$	1.65685			0.0822283
$407$	−0.171573	−	0.171573i	−0.00850455	−	0.00850455i
$408$	−6.34315	+	8.97056i	−0.314033	+	0.444109i
$409$		−	18.4853i		−	0.914038i	−0.889457	−	0.457019i	$-0.848917\pi$
$409$		−	18.4853i		−	0.914038i	0.889457	−	0.457019i	$-0.151083\pi$
$410$	−6.72792	+	2.24264i	−0.332268	+	0.110756i
$411$	−0.414214	+	0.0710678i	−0.0204316	+	0.00350552i
$412$	−11.7279	+	11.7279i	−0.577793	+	0.577793i
$413$	13.6569	−	13.6569i	0.672010	−	0.672010i
$414$	1.89949	+	5.37258i	0.0933551	+	0.264048i
$415$	27.2132	−	9.07107i	1.33584	−	0.445281i
$416$		−	12.4853i		−	0.612141i
$417$	−24.9706	−	17.6569i	−1.22281	−	0.864660i
$418$	0.828427	+	0.828427i	0.0405197	+	0.0405197i
$419$	15.4558			0.755067			0.377534	−	0.925996i	$-0.376772\pi$
$419$	15.4558			0.755067			0.377534	+	0.925996i	$0.376772\pi$
$420$	32.7279	+	9.89949i	1.59696	+	0.483046i
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	1.31371	+	1.31371i	0.0639503	+	0.0639503i
$423$	−13.2426	+	27.7279i	−0.643879	+	1.34818i
$424$			2.24264i			0.108912i
$425$	2.82843	−	19.7990i	0.137199	−	0.960392i
$426$	0.301515	+	1.75736i	0.0146085	+	0.0851443i
$427$	22.1421	−	22.1421i	1.07153	−	1.07153i
$428$	0.443651	−	0.443651i	0.0214447	−	0.0214447i
$429$	0.828427	+	4.82843i	0.0399968	+	0.233119i
$430$	−0.142136	+	0.284271i	−0.00685439	+	0.0137088i
$431$			6.34315i			0.305539i	0.988262	+	0.152769i	$0.0488191\pi$
$431$			6.34315i			0.305539i	−0.988262	+	0.152769i	$0.951181\pi$
$432$	−15.0000	−	4.24264i	−0.721688	−	0.204124i
$433$	−0.313708	−	0.313708i	−0.0150759	−	0.0150759i	0.699529	−	0.714605i	$-0.253393\pi$
$433$	−0.313708	−	0.313708i	−0.0150759	−	0.0150759i	−0.714605	+	0.699529i	$0.753393\pi$
$434$	−6.34315			−0.304481
$435$	2.82843	−	1.51472i	0.135613	−	0.0726252i
$436$	−5.79899			−0.277721
$437$	9.17157	+	9.17157i	0.438736	+	0.438736i
$438$		0			0
$439$		−	7.31371i		−	0.349064i	−0.984651	−	0.174532i	$-0.944159\pi$
$439$		−	7.31371i		−	0.349064i	0.984651	−	0.174532i	$-0.0558413\pi$
$440$	1.12132	+	3.36396i	0.0534568	+	0.160371i
$441$	−46.1421	+	16.3137i	−2.19724	+	0.776843i
$442$	3.31371	−	3.31371i	0.157617	−	0.157617i
$443$	−20.7574	+	20.7574i	−0.986212	+	0.986212i	−0.999906	−	0.0136943i	$-0.995641\pi$
$443$	−20.7574	+	20.7574i	−0.986212	+	0.986212i	0.0136943	+	0.999906i	$0.495641\pi$
$444$	−0.757359	+	0.129942i	−0.0359427	+	0.00616679i
$445$	19.3137	+	9.65685i	0.915558	+	0.457779i
$446$			9.69848i			0.459237i
$447$	10.0000	−	14.1421i	0.472984	−	0.668900i
$448$	−14.2426	−	14.2426i	−0.672902	−	0.672902i
$449$	−3.02944			−0.142968			−0.0714840	−	0.997442i	$-0.522773\pi$
$449$	−3.02944			−0.142968			−0.0714840	+	0.997442i	$0.522773\pi$
$450$	−6.09188	+	1.22183i	−0.287174	+	0.0575974i
$451$	−7.65685			−0.360547
$452$	10.6569	+	10.6569i	0.501256	+	0.501256i
$453$	−10.1421	+	14.3431i	−0.476519	+	0.673900i
$454$		−	6.00000i		−	0.281594i
$455$	−27.3137	−	13.6569i	−1.28049	−	0.640243i
$456$	7.65685	−	1.31371i	0.358565	−	0.0615200i
$457$	−6.48528	+	6.48528i	−0.303369	+	0.303369i	−0.842330	−	0.538962i	$-0.818817\pi$
$457$	−6.48528	+	6.48528i	−0.303369	+	0.303369i	0.538962	+	0.842330i	$0.318817\pi$
$458$	2.82843	−	2.82843i	0.132164	−	0.132164i
$459$	−10.1421	−	18.1421i	−0.473394	−	0.846802i
$460$	5.92893	+	17.7868i	0.276438	+	0.829314i
$461$			13.5147i			0.629443i	0.949184	+	0.314722i	$0.101911\pi$
$461$			13.5147i			0.629443i	−0.949184	+	0.314722i	$0.898089\pi$
$462$	−2.82843	−	2.00000i	−0.131590	−	0.0930484i
$463$	11.7279	+	11.7279i	0.545043	+	0.545043i	0.925003	−	0.379960i	$-0.124062\pi$
$463$	11.7279	+	11.7279i	0.545043	+	0.545043i	−0.379960	+	0.925003i	$0.624062\pi$
$464$	−2.48528			−0.115376
$465$	−10.8284	+	5.79899i	−0.502156	+	0.268922i
$466$	−11.5147			−0.533409
$467$	−0.414214	−	0.414214i	−0.0191675	−	0.0191675i	0.697458	−	0.716626i	$-0.254314\pi$
$467$	−0.414214	−	0.414214i	−0.0191675	−	0.0191675i	−0.716626	+	0.697458i	$0.754314\pi$
$468$	14.0000	+	6.68629i	0.647150	+	0.309074i
$469$		−	43.7990i		−	2.02245i
$470$	4.24264	−	8.48528i	0.195698	−	0.391397i
$471$	−3.92893	−	22.8995i	−0.181036	−	1.05515i
$472$	4.48528	−	4.48528i	0.206452	−	0.206452i
$473$	−0.242641	+	0.242641i	−0.0111566	+	0.0111566i
$474$	−1.31371	−	7.65685i	−0.0603406	−	0.351691i
$475$	−11.3137	+	8.48528i	−0.519109	+	0.389331i
$476$		−	35.3137i		−	1.61860i
$477$	−3.82843	−	1.82843i	−0.175292	−	0.0837179i
$478$	6.97056	+	6.97056i	0.318826	+	0.318826i
$479$	−30.1421			−1.37723			−0.688615	−	0.725127i	$-0.741781\pi$
$479$	−30.1421			−1.37723			−0.688615	+	0.725127i	$0.741781\pi$
$480$	16.3640	+	4.94975i	0.746909	+	0.225924i
$481$	0.686292			0.0312922
$482$	−0.0416306	−	0.0416306i	−0.00189622	−	0.00189622i
$483$	−31.3137	−	22.1421i	−1.42482	−	1.00750i
$484$			1.82843i			0.0831103i
$485$	−31.9706	+	10.6569i	−1.45171	+	0.483903i
$486$	−4.26346	+	4.84924i	−0.193394	+	0.219966i
$487$	11.7279	−	11.7279i	0.531443	−	0.531443i	−0.389559	−	0.921002i	$-0.627372\pi$
$487$	11.7279	−	11.7279i	0.531443	−	0.531443i	0.921002	+	0.389559i	$0.127372\pi$
$488$	7.27208	−	7.27208i	0.329192	−	0.329192i
$489$	−8.65685	+	1.48528i	−0.391476	+	0.0671667i
$490$	14.3345	−	4.77817i	0.647568	−	0.215856i
$491$			20.0000i			0.902587i	0.892375	+	0.451294i	$0.149037\pi$
$491$			20.0000i			0.902587i	−0.892375	+	0.451294i	$0.850963\pi$
$492$	−14.0000	+	19.7990i	−0.631169	+	0.892607i
$493$	−2.34315	−	2.34315i	−0.105530	−	0.105530i
$494$	−3.31371			−0.149091
$495$	−6.65685	−	0.828427i	−0.299203	−	0.0372350i
$496$	9.51472			0.427223
$497$	−8.48528	−	8.48528i	−0.380617	−	0.380617i
$498$	−5.31371	+	7.51472i	−0.238113	+	0.336743i
$499$			24.8284i			1.11147i	0.831358	+	0.555737i	$0.187564\pi$
$499$			24.8284i			1.11147i	−0.831358	+	0.555737i	$0.812436\pi$
$500$	−20.1127	+	3.65685i	−0.899467	+	0.163539i
$501$	−35.5563	+	6.10051i	−1.58854	+	0.272550i
$502$	4.72792	−	4.72792i	0.211017	−	0.211017i
$503$	0.928932	−	0.928932i	0.0414190	−	0.0414190i	−0.686094	−	0.727513i	$-0.740676\pi$
$503$	0.928932	−	0.928932i	0.0414190	−	0.0414190i	0.727513	+	0.686094i	$0.240676\pi$
$504$	−21.6569	+	7.65685i	−0.964673	+	0.341063i
$505$	7.17157	−	14.3431i	0.319131	−	0.638262i
$506$		−	1.89949i		−	0.0844428i
$507$	7.07107	+	5.00000i	0.314037	+	0.222058i
$508$	−2.58579	−	2.58579i	−0.114726	−	0.114726i
$509$	35.6569			1.58046			0.790231	−	0.612809i	$-0.209960\pi$
$509$	35.6569			1.58046			0.790231	+	0.612809i	$0.209960\pi$
$510$	3.02944	+	5.65685i	0.134146	+	0.250490i
$511$		0			0
$512$	−16.0919	−	16.0919i	−0.711167	−	0.711167i
$513$	−4.00000	+	14.1421i	−0.176604	+	0.624391i
$514$			1.07107i			0.0472428i
$515$	6.41421	+	19.2426i	0.282644	+	0.847932i
$516$	0.183766	+	1.07107i	0.00808986	+	0.0471511i
$517$	7.24264	−	7.24264i	0.318531	−	0.318531i
$518$	−0.343146	+	0.343146i	−0.0150770	+	0.0150770i
$519$	3.51472	+	20.4853i	0.154279	+	0.899204i
$520$	−8.97056	−	4.48528i	−0.393385	−	0.196693i
$521$			27.6569i			1.21167i	0.795591	+	0.605834i	$0.207161\pi$
$521$			27.6569i			1.21167i	−0.795591	+	0.605834i	$0.792839\pi$
$522$	−0.443651	+	0.928932i	−0.0194181	+	0.0406583i
$523$	−27.2132	−	27.2132i	−1.18995	−	1.18995i	−0.977081	−	0.212870i	$-0.931719\pi$
$523$	−27.2132	−	27.2132i	−1.18995	−	1.18995i	−0.212870	−	0.977081i	$-0.568281\pi$
$524$	−12.4853			−0.545422
$525$	28.7279	−	30.3848i	1.25379	−	1.32610i
$526$	1.02944			0.0448856
$527$	8.97056	+	8.97056i	0.390764	+	0.390764i
$528$	4.24264	+	3.00000i	0.184637	+	0.130558i
$529$			1.97056i			0.0856766i
$530$	1.17157	+	0.585786i	0.0508899	+	0.0254449i
$531$	4.00000	+	11.3137i	0.173585	+	0.490973i
$532$	−17.6569	+	17.6569i	−0.765522	+	0.765522i
$533$	15.3137	−	15.3137i	0.663310	−	0.663310i
$534$	−6.82843	+	1.17157i	−0.295495	+	0.0506989i
$535$	−0.242641	−	0.727922i	−0.0104903	−	0.0314708i
$536$		−	14.3848i		−	0.621328i
$537$	−24.1421	+	34.1421i	−1.04181	+	1.47334i
$538$	4.10051	+	4.10051i	0.176785	+	0.176785i
$539$	16.3137			0.702681
$540$	−14.3137	+	15.6985i	−0.615964	+	0.675555i
$541$	−10.6863			−0.459440			−0.229720	−	0.973257i	$-0.573781\pi$
$541$	−10.6863			−0.459440			−0.229720	+	0.973257i	$0.573781\pi$
$542$	−2.48528	−	2.48528i	−0.106752	−	0.106752i
$543$	−5.65685	+	8.00000i	−0.242759	+	0.343313i
$544$		−	17.6569i		−	0.757031i
$545$	−3.17157	+	6.34315i	−0.135855	+	0.271711i
$546$	9.65685	−	1.65685i	0.413275	−	0.0709068i
$547$	2.10051	−	2.10051i	0.0898111	−	0.0898111i	−0.660774	−	0.750585i	$-0.729772\pi$
$547$	2.10051	−	2.10051i	0.0898111	−	0.0898111i	0.750585	+	0.660774i	$0.229772\pi$
$548$	0.313708	−	0.313708i	0.0134010	−	0.0134010i
$549$	6.48528	+	18.3431i	0.276785	+	0.782866i
$550$	2.05025	+	0.292893i	0.0874231	+	0.0124890i
$551$			2.34315i			0.0998214i
$552$	−10.2843	−	7.27208i	−0.437728	−	0.309520i
$553$	36.9706	+	36.9706i	1.57215	+	1.57215i
$554$	10.8284			0.460056
$555$	−0.272078	+	0.899495i	−0.0115491	+	0.0381814i
$556$	32.2843			1.36916
$557$	8.97056	+	8.97056i	0.380095	+	0.380095i	0.871136	−	0.491041i	$-0.163384\pi$
$557$	8.97056	+	8.97056i	0.380095	+	0.380095i	−0.491041	+	0.871136i	$0.663384\pi$
$558$	1.69848	−	3.55635i	0.0719026	−	0.150552i
$559$		−	0.970563i		−	0.0410504i
$560$	−30.7279	+	10.2426i	−1.29849	+	0.432831i
$561$	1.17157	+	6.82843i	0.0494638	+	0.288296i
$562$	−8.38478	+	8.38478i	−0.353690	+	0.353690i
$563$	−9.89949	+	9.89949i	−0.417214	+	0.417214i	−0.884242	−	0.467028i	$-0.845325\pi$
$563$	−9.89949	+	9.89949i	−0.417214	+	0.417214i	0.467028	+	0.884242i	$0.345325\pi$
$564$	−5.48528	−	31.9706i	−0.230972	−	1.34620i
$565$	17.4853	−	5.82843i	0.735611	−	0.245204i
$566$			8.82843i			0.371086i
$567$	4.58579	−	43.2132i	0.192585	−	1.81478i
$568$	−2.78680	−	2.78680i	−0.116931	−	0.116931i
$569$	−28.3431			−1.18821			−0.594103	−	0.804389i	$-0.702493\pi$
$569$	−28.3431			−1.18821			−0.594103	+	0.804389i	$0.702493\pi$
$570$	1.31371	−	4.34315i	0.0550252	−	0.181914i
$571$	29.6569			1.24110			0.620550	−	0.784167i	$-0.286909\pi$
$571$	29.6569			1.24110			0.620550	+	0.784167i	$0.286909\pi$
$572$	−3.65685	−	3.65685i	−0.152901	−	0.152901i
$573$	16.0000	+	11.3137i	0.668410	+	0.472637i
$574$			15.3137i			0.639182i
$575$	22.6985	+	3.24264i	0.946592	+	0.135227i
$576$	11.7990	−	4.17157i	0.491625	−	0.173816i
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	−0.258336	−	0.966055i	$-0.583174\pi$
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	0.966055	+	0.258336i	$0.0831741\pi$
$578$	−0.292893	+	0.292893i	−0.0121828	+	0.0121828i
$579$	−19.3137	+	3.31371i	−0.802650	+	0.137713i
$580$	−1.51472	+	3.02944i	−0.0628953	+	0.125791i
$581$		−	61.9411i		−	2.56975i
$582$	6.24264	−	8.82843i	0.258766	−	0.365950i
$583$	1.00000	+	1.00000i	0.0414158	+	0.0414158i
$584$		0			0
$585$	14.9706	−	11.6569i	0.618957	−	0.481952i
$586$	2.14214			0.0884908
$587$	−0.414214	−	0.414214i	−0.0170964	−	0.0170964i	0.698507	−	0.715603i	$-0.253848\pi$
$587$	−0.414214	−	0.414214i	−0.0170964	−	0.0170964i	−0.715603	+	0.698507i	$0.753848\pi$
$588$	29.8284	−	42.1838i	1.23010	−	1.73963i
$589$		−	8.97056i		−	0.369626i
$590$	−1.17157	−	3.51472i	−0.0482329	−	0.144699i
$591$	34.1421	−	5.85786i	1.40442	−	0.240960i
$592$	0.514719	−	0.514719i	0.0211548	−	0.0211548i
$593$	5.85786	−	5.85786i	0.240554	−	0.240554i	−0.576525	−	0.817079i	$-0.695592\pi$
$593$	5.85786	−	5.85786i	0.240554	−	0.240554i	0.817079	+	0.576525i	$0.195592\pi$
$594$	1.87868	−	1.05025i	0.0770832	−	0.0430924i
$595$	−38.6274	−	19.3137i	−1.58357	−	0.791785i
$596$			18.2843i			0.748953i
$597$	−20.4853	−	14.4853i	−0.838407	−	0.592843i
$598$	3.79899	+	3.79899i	0.155352	+	0.155352i
$599$	−3.45584			−0.141202			−0.0706010	−	0.997505i	$-0.522492\pi$
$599$	−3.45584			−0.141202			−0.0706010	+	0.997505i	$0.522492\pi$
$600$	9.43503	−	9.97918i	0.385183	−	0.407399i
$601$	−27.4558			−1.11995			−0.559974	−	0.828510i	$-0.689189\pi$
$601$	−27.4558			−1.11995			−0.559974	+	0.828510i	$0.689189\pi$
$602$	0.485281	+	0.485281i	0.0197786	+	0.0197786i
$603$	24.5563	+	11.7279i	1.00001	+	0.477598i
$604$		−	18.5442i		−	0.754551i
$605$	2.00000	+	1.00000i	0.0813116	+	0.0406558i
$606$	0.870058	+	5.07107i	0.0353437	+	0.205998i
$607$	−21.8995	+	21.8995i	−0.888873	+	0.888873i	−0.994415	−	0.105542i	$-0.966342\pi$
$607$	−21.8995	+	21.8995i	−0.888873	+	0.888873i	0.105542	+	0.994415i	$0.466342\pi$
$608$	−8.82843	+	8.82843i	−0.358040	+	0.358040i
$609$	−1.17157	−	6.82843i	−0.0474745	−	0.276702i
$610$	−1.89949	−	5.69848i	−0.0769083	−	0.230725i
$611$			28.9706i			1.17202i
$612$	19.7990	+	9.45584i	0.800327	+	0.382230i
$613$	−16.0000	−	16.0000i	−0.646234	−	0.646234i	0.305847	−	0.952081i	$-0.401060\pi$
$613$	−16.0000	−	16.0000i	−0.646234	−	0.646234i	−0.952081	+	0.305847i	$0.901060\pi$
$614$	6.97056			0.281309
$615$	14.0000	+	26.1421i	0.564534	+	1.05415i
$616$	7.65685			0.308503
$617$	29.8284	+	29.8284i	1.20085	+	1.20085i	0.973909	+	0.226938i	$0.0728715\pi$
$617$	29.8284	+	29.8284i	1.20085	+	1.20085i	0.226938	+	0.973909i	$0.427129\pi$
$618$	−5.31371	−	3.75736i	−0.213749	−	0.151143i
$619$		−	0.686292i		−	0.0275844i	−0.999905	−	0.0137922i	$-0.995610\pi$
$619$		−	0.686292i		−	0.0275844i	0.999905	−	0.0137922i	$-0.00439033\pi$
$620$	5.79899	−	11.5980i	0.232893	−	0.465786i
$621$	20.7990	−	11.6274i	0.834635	−	0.466592i
$622$	−8.24264	+	8.24264i	−0.330500	+	0.330500i
$623$	32.9706	−	32.9706i	1.32094	−	1.32094i
$624$	−14.4853	+	2.48528i	−0.579875	+	0.0994909i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		−	7.41421i		−	0.296332i
$627$	2.82843	−	4.00000i	0.112956	−	0.159745i
$628$	17.3431	+	17.3431i	0.692067	+	0.692067i
$629$	0.970563			0.0386989
$630$	−1.65685	+	13.3137i	−0.0660107	+	0.530431i
$631$	−16.9706			−0.675587			−0.337794	−	0.941220i	$-0.609681\pi$
$631$	−16.9706			−0.675587			−0.337794	+	0.941220i	$0.609681\pi$
$632$	12.1421	+	12.1421i	0.482988	+	0.482988i
$633$	4.48528	−	6.34315i	0.178274	−	0.252117i
$634$		−	1.35534i		−	0.0538274i
$635$	−4.24264	+	1.41421i	−0.168364	+	0.0561214i
$636$	4.41421	−	0.757359i	0.175035	−	0.0300313i
$637$	−32.6274	+	32.6274i	−1.29275	+	1.29275i
$638$	0.242641	−	0.242641i	0.00960624	−	0.00960624i
$639$	7.02944	−	2.48528i	0.278080	−	0.0983162i
$640$	−22.3934	+	7.46447i	−0.885177	+	0.295059i
$641$			32.6274i			1.28871i	0.764728	+	0.644353i	$0.222873\pi$
$641$			32.6274i			1.28871i	−0.764728	+	0.644353i	$0.777127\pi$
$642$	0.201010	+	0.142136i	0.00793324	+	0.00560965i
$643$	−9.24264	−	9.24264i	−0.364494	−	0.364494i	0.500970	−	0.865464i	$-0.332977\pi$
$643$	−9.24264	−	9.24264i	−0.364494	−	0.364494i	−0.865464	+	0.500970i	$0.832977\pi$
$644$	40.4853			1.59534
$645$	1.27208	+	0.384776i	0.0500880	+	0.0151506i
$646$	−4.68629			−0.184380
$647$	11.7279	+	11.7279i	0.461072	+	0.461072i	0.899007	−	0.437935i	$-0.144290\pi$
$647$	11.7279	+	11.7279i	0.461072	+	0.461072i	−0.437935	+	0.899007i	$0.644290\pi$
$648$	1.50610	−	14.1924i	0.0591651	−	0.557530i
$649$		−	4.00000i		−	0.157014i
$650$	−4.68629	+	3.51472i	−0.183811	+	0.137859i
$651$	4.48528	+	26.1421i	0.175792	+	1.02459i
$652$	6.55635	−	6.55635i	0.256766	−	0.256766i
$653$	8.65685	−	8.65685i	0.338769	−	0.338769i	−0.517135	−	0.855904i	$-0.673001\pi$
$653$	8.65685	−	8.65685i	0.338769	−	0.338769i	0.855904	+	0.517135i	$0.173001\pi$
$654$	−0.384776	−	2.24264i	−0.0150459	−	0.0876942i
$655$	−6.82843	+	13.6569i	−0.266809	+	0.533617i
$656$		−	22.9706i		−	0.896850i
$657$		0			0
$658$	−14.4853	−	14.4853i	−0.564695	−	0.564695i
$659$	−24.9706			−0.972715			−0.486358	−	0.873760i	$-0.661675\pi$
$659$	−24.9706			−0.972715			−0.486358	+	0.873760i	$0.661675\pi$
$660$	6.24264	−	3.34315i	0.242994	−	0.130132i
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	1.89949	+	1.89949i	0.0738260	+	0.0738260i
$663$	−16.0000	−	11.3137i	−0.621389	−	0.439388i
$664$		−	20.3431i		−	0.789467i
$665$	9.65685	+	28.9706i	0.374477	+	1.12343i
$666$	−0.100505	−	0.284271i	−0.00389449	−	0.0110153i
$667$	2.68629	−	2.68629i	0.104014	−	0.104014i
$668$	26.9289	−	26.9289i	1.04191	−	1.04191i
$669$	39.9706	−	6.85786i	1.54535	−	0.265140i
$670$	−7.51472	−	3.75736i	−0.290319	−	0.145159i
$671$		−	6.48528i		−	0.250362i
$672$	21.3137	−	30.1421i	0.822194	−	1.16276i
$673$	−22.3431	−	22.3431i	−0.861265	−	0.861265i	0.130220	−	0.991485i	$-0.458432\pi$
$673$	−22.3431	−	22.3431i	−0.861265	−	0.861265i	−0.991485	+	0.130220i	$0.958432\pi$
$674$	6.34315			0.244329
$675$	9.34315	+	24.2426i	0.359618	+	0.933100i
$676$	−9.14214			−0.351621
$677$	19.6569	+	19.6569i	0.755474	+	0.755474i	0.975495	−	0.220021i	$-0.0706126\pi$
$677$	19.6569	+	19.6569i	0.755474	+	0.755474i	−0.220021	+	0.975495i	$0.570613\pi$
$678$	−3.41421	+	4.82843i	−0.131122	+	0.185435i
$679$			72.7696i			2.79264i
$680$	−12.6863	−	6.34315i	−0.486497	−	0.243249i
$681$	−24.7279	+	4.24264i	−0.947576	+	0.162578i
$682$	−0.928932	+	0.928932i	−0.0355707	+	0.0355707i
$683$	7.72792	−	7.72792i	0.295701	−	0.295701i	−0.543627	−	0.839327i	$-0.682949\pi$
$683$	7.72792	−	7.72792i	0.295701	−	0.295701i	0.839327	+	0.543627i	$0.182949\pi$
$684$	−5.17157	−	14.6274i	−0.197740	−	0.559293i
$685$	−0.171573	−	0.514719i	−0.00655546	−	0.0196664i
$686$		−	18.6274i		−	0.711198i
$687$	−13.6569	−	9.65685i	−0.521041	−	0.368432i
$688$	−0.727922	−	0.727922i	−0.0277518	−	0.0277518i
$689$	−4.00000			−0.152388
$690$	−6.48528	+	3.47309i	−0.246890	+	0.132218i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−15.5147	−	15.5147i	−0.589781	−	0.589781i
$693$	−6.24264	+	13.0711i	−0.237138	+	0.496529i
$694$		−	1.11270i		−	0.0422375i
$695$	17.6569	−	35.3137i	0.669763	−	1.33953i
$696$	−0.384776	−	2.24264i	−0.0145849	−	0.0850071i
$697$	21.6569	−	21.6569i	0.820312	−	0.820312i
$698$	−8.78680	+	8.78680i	−0.332585	+	0.332585i
$699$	8.14214	+	47.4558i	0.307964	+	1.79494i
$700$	−6.24264	+	43.6985i	−0.235950	+	1.65165i
$701$		−	1.31371i		−	0.0496181i	−0.999692	−	0.0248090i	$-0.992102\pi$
$701$		−	1.31371i		−	0.0496181i	0.999692	−	0.0248090i	$-0.00789777\pi$
$702$	−1.65685	+	5.85786i	−0.0625339	+	0.221091i
$703$	−0.485281	−	0.485281i	−0.0183027	−	0.0183027i
$704$	−4.17157			−0.157222
$705$	−37.9706	−	11.4853i	−1.43005	−	0.432561i
$706$	−4.58579			−0.172588
$707$	−24.4853	−	24.4853i	−0.920864	−	0.920864i
$708$	−10.3431	−	7.31371i	−0.388719	−	0.274866i
$709$			29.3137i			1.10090i	0.834868	+	0.550450i	$0.185544\pi$
$709$			29.3137i			1.10090i	−0.834868	+	0.550450i	$0.814456\pi$
$710$	−2.18377	+	0.727922i	−0.0819553	+	0.0273184i
$711$	−30.6274	+	10.8284i	−1.14862	+	0.406098i
$712$	10.8284	−	10.8284i	0.405812	−	0.405812i
$713$	−10.2843	+	10.2843i	−0.385149	+	0.385149i
$714$	13.6569	−	2.34315i	0.511095	−	0.0876900i
$715$	−6.00000	+	2.00000i	−0.224387	+	0.0747958i
$716$		−	44.1421i		−	1.64967i
$717$	23.7990	−	33.6569i	0.888790	−	1.25694i
$718$	6.48528	+	6.48528i	0.242029	+	0.242029i
$719$	−22.7696			−0.849161			−0.424581	−	0.905390i	$-0.639578\pi$
$719$	−22.7696			−0.849161			−0.424581	+	0.905390i	$0.639578\pi$
$720$	2.48528	−	19.9706i	0.0926210	−	0.744259i
$721$	43.7990			1.63116
$722$	−3.22183	−	3.22183i	−0.119904	−	0.119904i
$723$	−0.142136	+	0.201010i	−0.00528608	+	0.00747565i
$724$		−	10.3431i		−	0.384400i
$725$	2.48528	+	3.31371i	0.0923010	+	0.123068i
$726$	−0.707107	+	0.121320i	−0.0262432	+	0.00450262i
$727$	20.2132	−	20.2132i	0.749666	−	0.749666i	−0.224750	−	0.974416i	$-0.572157\pi$
$727$	20.2132	−	20.2132i	0.749666	−	0.749666i	0.974416	+	0.224750i	$0.0721566\pi$
$728$	−15.3137	+	15.3137i	−0.567564	+	0.567564i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$		−	1.37258i		−	0.0507668i
$732$	−16.7696	−	11.8579i	−0.619821	−	0.438279i
$733$	3.79899	+	3.79899i	0.140319	+	0.140319i	0.773777	−	0.633458i	$-0.218365\pi$
$733$	3.79899	+	3.79899i	0.140319	+	0.140319i	−0.633458	+	0.773777i	$0.718365\pi$
$734$	0.644661			0.0237949
$735$	−29.8284	−	55.6985i	−1.10024	−	2.05447i
$736$	20.2426			0.746154
$737$	−6.41421	−	6.41421i	−0.236271	−	0.236271i
$738$	−8.58579	−	4.10051i	−0.316047	−	0.150942i
$739$		−	14.6274i		−	0.538078i	−0.963129	−	0.269039i	$-0.913294\pi$
$739$		−	14.6274i		−	0.538078i	0.963129	−	0.269039i	$-0.0867061\pi$
$740$	−0.313708	−	0.941125i	−0.0115322	−	0.0345965i
$741$	2.34315	+	13.6569i	0.0860776	+	0.501697i
$742$	2.00000	−	2.00000i	0.0734223	−	0.0734223i
$743$	−26.0416	+	26.0416i	−0.955375	+	0.955375i	−0.999046	−	0.0436712i	$-0.986095\pi$
$743$	−26.0416	+	26.0416i	−0.955375	+	0.955375i	0.0436712	+	0.999046i	$0.486095\pi$
$744$	1.47309	+	8.58579i	0.0540060	+	0.314770i
$745$	20.0000	+	10.0000i	0.732743	+	0.366372i
$746$		−	2.05887i		−	0.0753808i
$747$	34.7279	+	16.5858i	1.27063	+	0.606842i
$748$	−5.17157	−	5.17157i	−0.189091	−	0.189091i
$749$	−1.65685			−0.0605401
$750$	−2.74874	−	7.53553i	−0.100370	−	0.275159i
$751$	−46.6274			−1.70146			−0.850729	−	0.525604i	$-0.823839\pi$
$751$	−46.6274			−1.70146			−0.850729	+	0.525604i	$0.823839\pi$
$752$	21.7279	+	21.7279i	0.792336	+	0.792336i
$753$	−22.8284	−	16.1421i	−0.831914	−	0.588252i
$754$			0.970563i			0.0353458i
$755$	−20.2843	−	10.1421i	−0.738220	−	0.369110i
$756$	22.3848	+	40.0416i	0.814126	+	1.45630i
$757$	0.171573	−	0.171573i	0.00623592	−	0.00623592i	−0.703982	−	0.710218i	$-0.748596\pi$
$757$	0.171573	−	0.171573i	0.00623592	−	0.00623592i	0.710218	+	0.703982i	$0.248596\pi$
$758$	8.24264	−	8.24264i	0.299386	−	0.299386i
$759$	−7.82843	+	1.34315i	−0.284154	+	0.0487531i
$760$	3.17157	+	9.51472i	0.115045	+	0.345135i
$761$		−	1.51472i		−	0.0549085i	−0.999623	−	0.0274543i	$-0.991260\pi$
$761$		−	1.51472i		−	0.0549085i	0.999623	−	0.0274543i	$-0.00874006\pi$
$762$	0.828427	−	1.17157i	0.0300107	−	0.0424416i
$763$	10.8284	+	10.8284i	0.392015	+	0.392015i
$764$	−20.6863			−0.748404
$765$	21.1716	−	16.4853i	0.765460	−	0.596027i
$766$	3.55635			0.128496
$767$	8.00000	+	8.00000i	0.288863	+	0.288863i
$768$	−3.97056	+	5.61522i	−0.143275	+	0.202622i
$769$			52.6274i			1.89779i	0.315587	+	0.948897i	$0.397799\pi$
$769$			52.6274i			1.89779i	−0.315587	+	0.948897i	$0.602201\pi$
$770$	2.00000	−	4.00000i	0.0720750	−	0.144150i
$771$	4.41421	−	0.757359i	0.158974	−	0.0272756i
$772$	14.6274	−	14.6274i	0.526452	−	0.526452i
$773$	10.6569	−	10.6569i	0.383300	−	0.383300i	−0.488989	−	0.872290i	$-0.662634\pi$
$773$	10.6569	−	10.6569i	0.383300	−	0.383300i	0.872290	+	0.488989i	$0.162634\pi$
$774$	−0.402020	+	0.142136i	−0.0144503	+	0.00510896i
$775$	−9.51472	−	12.6863i	−0.341779	−	0.455705i
$776$			23.8995i			0.857942i
$777$	1.65685	+	1.17157i	0.0594393	+	0.0420299i
$778$	5.07107	+	5.07107i	0.181807	+	0.181807i
$779$	−21.6569			−0.775937
$780$	−5.79899	+	19.1716i	−0.207637	+	0.686452i
$781$	−2.48528			−0.0889304
$782$	5.37258	+	5.37258i	0.192123	+	0.192123i
$783$	4.14214	+	1.17157i	0.148028	+	0.0418686i
$784$			48.9411i			1.74790i
$785$	28.4558	−	9.48528i	1.01563	−	0.338544i
$786$	−0.828427	−	4.82843i	−0.0295490	−	0.172224i
$787$	−28.5858	+	28.5858i	−1.01897	+	1.01897i	−0.0191567	+	0.999816i	$0.506098\pi$
$787$	−28.5858	+	28.5858i	−1.01897	+	1.01897i	−0.999816	+	0.0191567i	$0.993902\pi$
$788$	−25.8579	+	25.8579i	−0.921148	+	0.921148i
$789$	−0.727922	−	4.24264i	−0.0259147	−	0.151042i
$790$	9.51472	−	3.17157i	0.338518	−	0.112839i
$791$		−	39.7990i		−	1.41509i
$792$	−2.05025	+	4.29289i	−0.0728526	+	0.152541i
$793$	12.9706	+	12.9706i	0.460598	+	0.460598i
$794$	−3.61522			−0.128299
$795$	1.58579	−	5.24264i	0.0562420	−	0.185937i
$796$	26.4853			0.938746
$797$	25.9706	+	25.9706i	0.919925	+	0.919925i	0.997023	−	0.0770989i	$-0.0245657\pi$
$797$	25.9706	+	25.9706i	0.919925	+	0.919925i	−0.0770989	+	0.997023i	$0.524566\pi$
$798$	−8.00000	−	5.65685i	−0.283197	−	0.200250i
$799$			40.9706i			1.44943i
$800$	−3.12132	+	21.8492i	−0.110355	+	0.772487i
$801$	9.65685	+	27.3137i	0.341208	+	0.965082i
$802$	−10.4437	+	10.4437i	−0.368778	+	0.368778i
$803$		0			0
$804$	−28.3137	+	4.85786i	−0.998548	+	0.171324i
$805$	22.1421	−	44.2843i	0.780408	−	1.56082i
$806$		−	3.71573i		−	0.130881i
$807$	14.0000	−	19.7990i	0.492823	−	0.696957i
$808$	−8.04163	−	8.04163i	−0.282904	−	0.282904i
$809$	−15.8579			−0.557533			−0.278766	−	0.960359i	$-0.589926\pi$
$809$	−15.8579			−0.557533			−0.278766	+	0.960359i	$0.589926\pi$
$810$	−7.02082	−	4.49390i	−0.246686	−	0.157900i
$811$	−41.6569			−1.46277			−0.731385	−	0.681965i	$-0.761126\pi$
$811$	−41.6569			−1.46277			−0.731385	+	0.681965i	$0.761126\pi$
$812$	5.17157	+	5.17157i	0.181487	+	0.181487i
$813$	−8.48528	+	12.0000i	−0.297592	+	0.420858i
$814$			0.100505i			0.00352270i
$815$	−3.58579	−	10.7574i	−0.125605	−	0.376814i
$816$	−20.4853	+	3.51472i	−0.717128	+	0.123040i
$817$	−0.686292	+	0.686292i	−0.0240103	+	0.0240103i
$818$	−5.41421	+	5.41421i	−0.189304	+	0.189304i
$819$	−13.6569	−	38.6274i	−0.477209	−	1.34975i
$820$	−28.0000	−	14.0000i	−0.977802	−	0.488901i
$821$			0.343146i			0.0119759i	0.999982	+	0.00598793i	$0.00190603\pi$
$821$			0.343146i			0.0119759i	−0.999982	+	0.00598793i	$0.998094\pi$
$822$	0.142136	+	0.100505i	0.00495755	+	0.00350552i
$823$	−18.4142	−	18.4142i	−0.641879	−	0.641879i	0.309138	−	0.951017i	$-0.399959\pi$
$823$	−18.4142	−	18.4142i	−0.641879	−	0.641879i	−0.951017	+	0.309138i	$0.899959\pi$
$824$	14.3848			0.501117
$825$	−0.242641	−	8.65685i	−0.00844766	−	0.301393i
$826$	−8.00000			−0.278356
$827$	−28.0416	−	28.0416i	−0.975103	−	0.975103i	0.0245945	−	0.999698i	$-0.492171\pi$
$827$	−28.0416	−	28.0416i	−0.975103	−	0.975103i	−0.999698	+	0.0245945i	$0.992171\pi$
$828$	−10.8406	+	22.6985i	−0.376738	+	0.788827i
$829$		−	10.9706i		−	0.381023i	−0.981685	−	0.190512i	$-0.938985\pi$
$829$		−	10.9706i		−	0.381023i	0.981685	−	0.190512i	$-0.0610147\pi$
$830$	−10.6274	−	5.31371i	−0.368883	−	0.184442i
$831$	−7.65685	−	44.6274i	−0.265613	−	1.54811i
$832$	8.34315	−	8.34315i	0.289247	−	0.289247i
$833$	−46.1421	+	46.1421i	−1.59873	+	1.59873i
$834$	2.14214	+	12.4853i	0.0741761	+	0.432330i
$835$	−14.7279	−	44.1838i	−0.509681	−	1.52904i
$836$			5.17157i			0.178863i
$837$	−15.8579	−	4.48528i	−0.548128	−	0.155034i
$838$	−4.52691	−	4.52691i	−0.156380	−	0.156380i
$839$	−21.6569			−0.747678			−0.373839	−	0.927494i	$-0.621959\pi$
$839$	−21.6569			−0.747678			−0.373839	+	0.927494i	$0.621959\pi$
$840$	−14.0000	−	26.1421i	−0.483046	−	0.901989i
$841$	−28.3137			−0.976335
$842$	1.17157	+	1.17157i	0.0403751	+	0.0403751i
$843$	40.4853	+	28.6274i	1.39439	+	0.985981i
$844$			8.20101i			0.282290i
$845$	−5.00000	+	10.0000i	−0.172005	+	0.344010i
$846$	12.0000	−	4.24264i	0.412568	−	0.145865i
$847$	3.41421	−	3.41421i	0.117314	−	0.117314i
$848$	−3.00000	+	3.00000i	−0.103020	+	0.103020i
$849$	36.3848	−	6.24264i	1.24872	−	0.214247i
$850$	−6.62742	+	4.97056i	−0.227319	+	0.170489i
$851$			1.11270i			0.0381428i
$852$	−4.54416	+	6.42641i	−0.155680	+	0.220165i
$853$	18.1421	+	18.1421i	0.621175	+	0.621175i	0.945832	−	0.324657i	$-0.105249\pi$
$853$	18.1421	+	18.1421i	0.621175	+	0.621175i	−0.324657	+	0.945832i	$0.605249\pi$
$854$	−12.9706			−0.443844
$855$	−18.8284	−	2.34315i	−0.643919	−	0.0801339i
$856$	−0.544156			−0.0185989
$857$	−16.4853	−	16.4853i	−0.563126	−	0.563126i	0.367068	−	0.930194i	$-0.380362\pi$
$857$	−16.4853	−	16.4853i	−0.563126	−	0.563126i	−0.930194	+	0.367068i	$0.880362\pi$
$858$	1.17157	−	1.65685i	0.0399968	−	0.0565641i
$859$		−	36.0000i		−	1.22830i	−0.789188	−	0.614152i	$-0.789498\pi$
$859$		−	36.0000i		−	1.22830i	0.789188	−	0.614152i	$-0.210502\pi$
$860$	−1.33095	+	0.443651i	−0.0453851	+	0.0151284i
$861$	63.1127	−	10.8284i	2.15088	−	0.369032i
$862$	1.85786	−	1.85786i	0.0632791	−	0.0632791i
$863$	12.5563	−	12.5563i	0.427423	−	0.427423i	−0.460327	−	0.887750i	$-0.652268\pi$
$863$	12.5563	−	12.5563i	0.427423	−	0.427423i	0.887750	+	0.460327i	$0.152268\pi$
$864$	11.1924	+	20.0208i	0.380773	+	0.681122i
$865$	−25.4558	+	8.48528i	−0.865525	+	0.288508i
$866$			0.183766i			0.00624463i
$867$	1.41421	+	1.00000i	0.0480292	+	0.0339618i
$868$	−19.7990	−	19.7990i	−0.672022	−	0.672022i
$869$	10.8284			0.367329
$870$	−1.27208	−	0.384776i	−0.0431275	−	0.0130451i
$871$	25.6569			0.869349
$872$	3.55635	+	3.55635i	0.120433	+	0.120433i
$873$	−40.7990	−	19.4853i	−1.38084	−	0.659477i
$874$		−	5.37258i		−	0.181730i
$875$	44.3848	+	30.7279i	1.50048	+	1.03879i
$876$		0			0
$877$	6.62742	−	6.62742i	0.223792	−	0.223792i	−0.586301	−	0.810093i	$-0.699416\pi$
$877$	6.62742	−	6.62742i	0.223792	−	0.223792i	0.810093	+	0.586301i	$0.199416\pi$
$878$	−2.14214	+	2.14214i	−0.0722936	+	0.0722936i
$879$	−1.51472	−	8.82843i	−0.0510902	−	0.297775i
$880$	−3.00000	+	6.00000i	−0.101130	+	0.202260i
$881$		−	12.9706i		−	0.436989i	−0.975838	−	0.218495i	$-0.929885\pi$
$881$		−	12.9706i		−	0.436989i	0.975838	−	0.218495i	$-0.0701146\pi$
$882$	18.2929	+	8.73654i	0.615954	+	0.294175i
$883$	−3.58579	−	3.58579i	−0.120671	−	0.120671i	0.644192	−	0.764864i	$-0.277194\pi$
$883$	−3.58579	−	3.58579i	−0.120671	−	0.120671i	−0.764864	+	0.644192i	$0.777194\pi$
$884$	20.6863			0.695755
$885$	−13.6569	+	7.31371i	−0.459070	+	0.245848i
$886$	12.1594			0.408502
$887$	−9.75736	−	9.75736i	−0.327620	−	0.327620i	0.524061	−	0.851681i	$-0.324416\pi$
$887$	−9.75736	−	9.75736i	−0.327620	−	0.327620i	−0.851681	+	0.524061i	$0.824416\pi$
$888$	0.544156	+	0.384776i	0.0182607	+	0.0129122i
$889$			9.65685i			0.323880i
$890$	−2.82843	−	8.48528i	−0.0948091	−	0.284427i
$891$	−5.65685	−	7.00000i	−0.189512	−	0.234509i
$892$	−30.2721	+	30.2721i	−1.01358	+	1.01358i
$893$	20.4853	−	20.4853i	0.685514	−	0.685514i
$894$	−7.07107	+	1.21320i	−0.236492	+	0.0405756i
$895$	−48.2843	−	24.1421i	−1.61397	−	0.806983i
$896$			50.9706i			1.70281i
$897$	12.9706	−	18.3431i	0.433074	−	0.612460i
$898$	0.887302	+	0.887302i	0.0296096	+	0.0296096i
$899$	−2.62742			−0.0876293
$900$	−22.8284	−	15.2010i	−0.760948	−	0.506700i
$901$	−5.65685			−0.188457
$902$	2.24264	+	2.24264i	0.0746718	+	0.0746718i
$903$	1.65685	−	2.34315i	0.0551367	−	0.0779750i
$904$		−	13.0711i		−	0.434737i
$905$	−11.3137	−	5.65685i	−0.376080	−	0.188040i
$906$	7.17157	−	1.23045i	0.238260	−	0.0408789i
$907$	29.0416	−	29.0416i	0.964312	−	0.964312i	−0.0350732	−	0.999385i	$-0.511166\pi$
$907$	29.0416	−	29.0416i	0.964312	−	0.964312i	0.999385	+	0.0350732i	$0.0111664\pi$
$908$	18.7279	−	18.7279i	0.621508	−	0.621508i
$909$	20.2843	−	7.17157i	0.672787	−	0.237866i
$910$	4.00000	+	12.0000i	0.132599	+	0.397796i
$911$			56.0000i			1.85536i	0.373373	+	0.927681i	$0.378201\pi$
$911$			56.0000i			1.85536i	−0.373373	+	0.927681i	$0.621799\pi$
$912$	12.0000	+	8.48528i	0.397360	+	0.280976i
$913$	−9.07107	−	9.07107i	−0.300209	−	0.300209i
$914$	3.79899			0.125659
$915$	−22.1421	+	11.8579i	−0.731996	+	0.392009i
$916$	17.6569			0.583399
$917$	23.3137	+	23.3137i	0.769886	+	0.769886i
$918$	−2.34315	+	8.28427i	−0.0773353	+	0.273422i
$919$			14.6274i			0.482514i	0.970461	+	0.241257i	$0.0775597\pi$
$919$			14.6274i			0.482514i	−0.970461	+	0.241257i	$0.922440\pi$
$920$	7.27208	−	14.5442i	0.239753	−	0.479507i
$921$	−4.92893	−	28.7279i	−0.162414	−	0.946617i
$922$	3.95837	−	3.95837i	0.130362	−	0.130362i
$923$	4.97056	−	4.97056i	0.163608	−	0.163608i
$924$	−2.58579	−	15.0711i	−0.0850661	−	0.495802i
$925$	−1.20101	−	0.171573i	−0.0394890	−	0.00564128i
$926$		−	6.87006i		−	0.225764i
$927$	−11.7279	+	24.5563i	−0.385195	+	0.806536i
$928$	2.58579	+	2.58579i	0.0848826	+	0.0848826i
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$	4.87006	+	1.47309i	0.159695	+	0.0483045i
$931$	46.1421			1.51225
$932$	−35.9411	−	35.9411i	−1.17729	−	1.17729i
$933$	39.7990	+	28.1421i	1.30296	+	0.921332i
$934$			0.242641i			0.00793945i
$935$	−8.48528	+	2.82843i	−0.277498	+	0.0924995i
$936$	−4.48528	−	12.6863i	−0.146606	−	0.414664i
$937$	−10.9706	+	10.9706i	−0.358393	+	0.358393i	−0.863220	−	0.504828i	$-0.831556\pi$
$937$	−10.9706	+	10.9706i	−0.358393	+	0.358393i	0.504828	+	0.863220i	$0.331556\pi$
$938$	−12.8284	+	12.8284i	−0.418863	+	0.418863i
$939$	−30.5563	+	5.24264i	−0.997169	+	0.171087i
$940$	39.7279	−	13.2426i	1.29578	−	0.431927i
$941$		−	37.1127i		−	1.20984i	−0.796286	−	0.604920i	$-0.793205\pi$
$941$		−	37.1127i		−	1.20984i	0.796286	−	0.604920i	$-0.206795\pi$
$942$	−5.55635	+	7.85786i	−0.181036	+	0.256023i
$943$	24.8284	+	24.8284i	0.808525	+	0.808525i
$944$	12.0000			0.390567
$945$	56.0416	−	2.58579i	1.82303	−	0.0841156i
$946$	0.142136			0.00462123
$947$	−17.2426	−	17.2426i	−0.560311	−	0.560311i	0.369085	−	0.929396i	$-0.379671\pi$
$947$	−17.2426	−	17.2426i	−0.560311	−	0.560311i	−0.929396	+	0.369085i	$0.879671\pi$
$948$	19.7990	−	28.0000i	0.643041	−	0.909398i
$949$		0			0
$950$	5.79899	+	0.828427i	0.188144	+	0.0268777i
$951$	−5.58579	+	0.958369i	−0.181132	+	0.0310773i
$952$	−21.6569	+	21.6569i	−0.701903	+	0.701903i
$953$	5.79899	−	5.79899i	0.187848	−	0.187848i	−0.606917	−	0.794765i	$-0.707594\pi$
$953$	5.79899	−	5.79899i	0.187848	−	0.187848i	0.794765	+	0.606917i	$0.207594\pi$
$954$	0.585786	+	1.65685i	0.0189655	+	0.0536426i
$955$	−11.3137	+	22.6274i	−0.366103	+	0.732206i
$956$			43.5147i			1.40737i
$957$	−1.17157	−	0.828427i	−0.0378716	−	0.0267792i
$958$	8.82843	+	8.82843i	0.285234	+	0.285234i
$959$	−1.17157			−0.0378321
$960$	7.62742	+	14.2426i	0.246174	+	0.459679i
$961$	−20.9411			−0.675520
$962$	−0.201010	−	0.201010i	−0.00648083	−	0.00648083i
$963$	0.443651	−	0.928932i	0.0142964	−	0.0299344i
$964$		−	0.259885i		−	0.00837032i
$965$	−8.00000	−	24.0000i	−0.257529	−	0.772587i
$966$	2.68629	+	15.6569i	0.0864300	+	0.503751i
$967$	38.3848	−	38.3848i	1.23437	−	1.23437i	0.272103	−	0.962268i	$-0.412281\pi$
$967$	38.3848	−	38.3848i	1.23437	−	1.23437i	0.962268	−	0.272103i	$-0.0877192\pi$
$968$	1.12132	−	1.12132i	0.0360406	−	0.0360406i
$969$	3.31371	+	19.3137i	0.106452	+	0.620446i
$970$	12.4853	+	6.24264i	0.400878	+	0.200439i
$971$			20.0000i			0.641831i	0.947108	+	0.320915i	$0.103990\pi$
$971$			20.0000i			0.641831i	−0.947108	+	0.320915i	$0.896010\pi$
$972$	−28.4437	+	1.82843i	−0.912331	+	0.0586468i
$973$	−60.2843	−	60.2843i	−1.93263	−	1.93263i
$974$	−6.87006			−0.220131
$975$	17.7990	+	16.8284i	0.570024	+	0.538941i
$976$	19.4558			0.622766
$977$	−38.1127	−	38.1127i	−1.21933	−	1.21933i	−0.967866	−	0.251468i	$-0.919087\pi$
$977$	−38.1127	−	38.1127i	−1.21933	−	1.21933i	−0.251468	−	0.967866i	$-0.580913\pi$
$978$	2.97056	+	2.10051i	0.0949881	+	0.0671667i
$979$		−	9.65685i		−	0.308634i
$980$	59.6569	+	29.8284i	1.90567	+	0.952834i
$981$	−8.97056	+	3.17157i	−0.286408	+	0.101261i
$982$	5.85786	−	5.85786i	0.186932	−	0.186932i
$983$	23.7279	−	23.7279i	0.756803	−	0.756803i	−0.218936	−	0.975739i	$-0.570259\pi$
$983$	23.7279	−	23.7279i	0.756803	−	0.756803i	0.975739	+	0.218936i	$0.0702586\pi$
$984$	20.7279	−	3.55635i	0.660782	−	0.113372i
$985$	14.1421	+	42.4264i	0.450606	+	1.35182i
$986$			1.37258i			0.0437119i
$987$	−49.4558	+	69.9411i	−1.57420	+	2.22625i
$988$	−10.3431	−	10.3431i	−0.329059	−	0.329059i
$989$	1.57359			0.0500374
$990$	1.70711	+	2.19239i	0.0542554	+	0.0696787i
$991$	24.8284			0.788701			0.394350	−	0.918960i	$-0.370970\pi$
$991$	24.8284			0.788701			0.394350	+	0.918960i	$0.370970\pi$
$992$	−9.89949	−	9.89949i	−0.314309	−	0.314309i
$993$	6.48528	−	9.17157i	0.205804	−	0.291051i
$994$			4.97056i			0.157657i
$995$	14.4853	−	28.9706i	0.459214	−	0.918429i
$996$	−40.0416	+	6.87006i	−1.26877	+	0.217686i
$997$	36.7696	−	36.7696i	1.16450	−	1.16450i	0.181025	−	0.983479i	$-0.442059\pi$
$997$	36.7696	−	36.7696i	1.16450	−	1.16450i	0.983479	−	0.181025i	$-0.0579415\pi$
$998$	7.27208	−	7.27208i	0.230194	−	0.230194i
$999$	−1.10051	+	0.615224i	−0.0348184	+	0.0194648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.k.a.23.2	✓	4
3.2	odd	2		165.2.k.b.23.1	yes	4
5.2	odd	4		165.2.k.b.122.1	yes	4
5.3	odd	4		825.2.k.c.782.2		4
5.4	even	2		825.2.k.f.518.1		4
15.2	even	4	inner	165.2.k.a.122.2	yes	4
15.8	even	4		825.2.k.f.782.1		4
15.14	odd	2		825.2.k.c.518.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.a.23.2	✓	4	1.1	even	1	trivial
165.2.k.a.122.2	yes	4	15.2	even	4	inner
165.2.k.b.23.1	yes	4	3.2	odd	2
165.2.k.b.122.1	yes	4	5.2	odd	4
825.2.k.c.518.2		4	15.14	odd	2
825.2.k.c.782.2		4	5.3	odd	4
825.2.k.f.518.1		4	5.4	even	2
825.2.k.f.782.1		4	15.8	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 - 0.292893i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.82843i q^{4} +(-2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.292893 - 0.292893i) q^{2} +(-1.00000 + 1.41421i) q^{3} -1.82843i q^{4} +(-2.00000 - 1.00000i) q^{5} +(0.707107 - 0.121320i) q^{6} +(-3.41421 + 3.41421i) q^{7} +(-1.12132 + 1.12132i) q^{8} +(-1.00000 - 2.82843i) q^{9} +(0.292893 + 0.878680i) q^{10} +1.00000i q^{11} +(2.58579 + 1.82843i) q^{12} +(-2.00000 - 2.00000i) q^{13} +2.00000 q^{14} +(3.41421 - 1.82843i) q^{15} -3.00000 q^{16} +(-2.82843 - 2.82843i) q^{17} +(-0.535534 + 1.12132i) q^{18} +2.82843i q^{19} +(-1.82843 + 3.65685i) q^{20} +(-1.41421 - 8.24264i) q^{21} +(0.292893 - 0.292893i) q^{22} +(3.24264 - 3.24264i) q^{23} +(-0.464466 - 2.70711i) q^{24} +(3.00000 + 4.00000i) q^{25} +1.17157i q^{26} +(5.00000 + 1.41421i) q^{27} +(6.24264 + 6.24264i) q^{28} +0.828427 q^{29} +(-1.53553 - 0.464466i) q^{30} -3.17157 q^{31} +(3.12132 + 3.12132i) q^{32} +(-1.41421 - 1.00000i) q^{33} +1.65685i q^{34} +(10.2426 - 3.41421i) q^{35} +(-5.17157 + 1.82843i) q^{36} +(-0.171573 + 0.171573i) q^{37} +(0.828427 - 0.828427i) q^{38} +(4.82843 - 0.828427i) q^{39} +(3.36396 - 1.12132i) q^{40} +7.65685i q^{41} +(-2.00000 + 2.82843i) q^{42} +(0.242641 + 0.242641i) q^{43} +1.82843 q^{44} +(-0.828427 + 6.65685i) q^{45} -1.89949 q^{46} +(-7.24264 - 7.24264i) q^{47} +(3.00000 - 4.24264i) q^{48} -16.3137i q^{49} +(0.292893 - 2.05025i) q^{50} +(6.82843 - 1.17157i) q^{51} +(-3.65685 + 3.65685i) q^{52} +(1.00000 - 1.00000i) q^{53} +(-1.05025 - 1.87868i) q^{54} +(1.00000 - 2.00000i) q^{55} -7.65685i q^{56} +(-4.00000 - 2.82843i) q^{57} +(-0.242641 - 0.242641i) q^{58} -4.00000 q^{59} +(-3.34315 - 6.24264i) q^{60} -6.48528 q^{61} +(0.928932 + 0.928932i) q^{62} +(13.0711 + 6.24264i) q^{63} +4.17157i q^{64} +(2.00000 + 6.00000i) q^{65} +(0.121320 + 0.707107i) q^{66} +(-6.41421 + 6.41421i) q^{67} +(-5.17157 + 5.17157i) q^{68} +(1.34315 + 7.82843i) q^{69} +(-4.00000 - 2.00000i) q^{70} +2.48528i q^{71} +(4.29289 + 2.05025i) q^{72} +0.100505 q^{74} +(-8.65685 + 0.242641i) q^{75} +5.17157 q^{76} +(-3.41421 - 3.41421i) q^{77} +(-1.65685 - 1.17157i) q^{78} -10.8284i q^{79} +(6.00000 + 3.00000i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(2.24264 - 2.24264i) q^{82} +(-9.07107 + 9.07107i) q^{83} +(-15.0711 + 2.58579i) q^{84} +(2.82843 + 8.48528i) q^{85} -0.142136i q^{86} +(-0.828427 + 1.17157i) q^{87} +(-1.12132 - 1.12132i) q^{88} -9.65685 q^{89} +(2.19239 - 1.70711i) q^{90} +13.6569 q^{91} +(-5.92893 - 5.92893i) q^{92} +(3.17157 - 4.48528i) q^{93} +4.24264i q^{94} +(2.82843 - 5.65685i) q^{95} +(-7.53553 + 1.29289i) q^{96} +(10.6569 - 10.6569i) q^{97} +(-4.77817 + 4.77817i) q^{98} +(2.82843 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 8 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{14} + 8 q^{15} - 12 q^{16} + 12 q^{18} + 4 q^{20} + 4 q^{22} - 4 q^{23} - 16 q^{24} + 12 q^{25} + 20 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{30} - 24 q^{31} + 4 q^{32} + 24 q^{35} - 32 q^{36} - 12 q^{37} - 8 q^{38} + 8 q^{39} - 12 q^{40} - 8 q^{42} - 16 q^{43} - 4 q^{44} + 8 q^{45} + 32 q^{46} - 12 q^{47} + 12 q^{48} + 4 q^{50} + 16 q^{51} + 8 q^{52} + 4 q^{53} - 24 q^{54} + 4 q^{55} - 16 q^{57} + 16 q^{58} - 16 q^{59} - 36 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{63} + 8 q^{65} - 8 q^{66} - 20 q^{67} - 32 q^{68} + 28 q^{69} - 16 q^{70} + 20 q^{72} + 40 q^{74} - 12 q^{75} + 32 q^{76} - 8 q^{77} + 16 q^{78} + 24 q^{80} - 28 q^{81} - 8 q^{82} - 8 q^{83} - 32 q^{84} + 8 q^{87} + 4 q^{88} - 16 q^{89} - 28 q^{90} + 32 q^{91} - 52 q^{92} + 24 q^{93} - 16 q^{96} + 20 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 - 8 * q^5 - 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^14 + 8 * q^15 - 12 * q^16 + 12 * q^18 + 4 * q^20 + 4 * q^22 - 4 * q^23 - 16 * q^24 + 12 * q^25 + 20 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^30 - 24 * q^31 + 4 * q^32 + 24 * q^35 - 32 * q^36 - 12 * q^37 - 8 * q^38 + 8 * q^39 - 12 * q^40 - 8 * q^42 - 16 * q^43 - 4 * q^44 + 8 * q^45 + 32 * q^46 - 12 * q^47 + 12 * q^48 + 4 * q^50 + 16 * q^51 + 8 * q^52 + 4 * q^53 - 24 * q^54 + 4 * q^55 - 16 * q^57 + 16 * q^58 - 16 * q^59 - 36 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^63 + 8 * q^65 - 8 * q^66 - 20 * q^67 - 32 * q^68 + 28 * q^69 - 16 * q^70 + 20 * q^72 + 40 * q^74 - 12 * q^75 + 32 * q^76 - 8 * q^77 + 16 * q^78 + 24 * q^80 - 28 * q^81 - 8 * q^82 - 8 * q^83 - 32 * q^84 + 8 * q^87 + 4 * q^88 - 16 * q^89 - 28 * q^90 + 32 * q^91 - 52 * q^92 + 24 * q^93 - 16 * q^96 + 20 * q^97 + 12 * q^98

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