LMFDB - Embedded newform 52.2.f.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(31,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("52.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.f (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:	$0.415222090511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.2
Root			$0.500000 - 2.10607i$ of defining polynomial
Character	$\chi$	$=$	52.31
Dual form			52.2.f.b.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13567 - 0.842772i) q^{2} +2.79793i q^{3} +(0.579471 + 1.91421i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.35802 - 3.17751i) q^{6} +(1.97844 - 1.97844i) q^{7} +(0.955161 - 2.66227i) q^{8} -4.82843 q^{9} +O(q^{10})$	\(q+(-1.13567 - 0.842772i) q^{2} +2.79793i q^{3} +(0.579471 + 1.91421i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.35802 - 3.17751i) q^{6} +(1.97844 - 1.97844i) q^{7} +(0.955161 - 2.66227i) q^{8} -4.82843 q^{9} +(1.39897 - 0.207107i) q^{10} +(-1.15894 + 1.15894i) q^{11} +(-5.35584 + 1.62132i) q^{12} +(3.53553 - 0.707107i) q^{13} +(-3.91421 + 0.579471i) q^{14} +(-1.97844 - 1.97844i) q^{15} +(-3.32843 + 2.21846i) q^{16} -5.82843i q^{17} +(5.48348 + 4.06926i) q^{18} +(-1.63899 - 1.63899i) q^{19} +(-1.76330 - 0.943806i) q^{20} +(5.53553 + 5.53553i) q^{21} +(2.29289 - 0.339446i) q^{22} +3.95687 q^{23} +(7.44885 + 2.67248i) q^{24} +4.00000i q^{25} +(-4.61111 - 2.17661i) q^{26} -5.11582i q^{27} +(4.93360 + 2.64070i) q^{28} -0.585786 q^{29} +(0.579471 + 3.91421i) q^{30} +(-3.95687 - 3.95687i) q^{31} +(5.64964 + 0.285675i) q^{32} +(-3.24264 - 3.24264i) q^{33} +(-4.91203 + 6.61914i) q^{34} +2.79793i q^{35} +(-2.79793 - 9.24264i) q^{36} +(-1.87868 - 1.87868i) q^{37} +(0.480049 + 3.24264i) q^{38} +(1.97844 + 9.89219i) q^{39} +(1.20711 + 2.55791i) q^{40} +(-4.24264 + 4.24264i) q^{41} +(-1.62132 - 10.9517i) q^{42} -5.11582 q^{43} +(-2.89003 - 1.54689i) q^{44} +(3.41421 - 3.41421i) q^{45} +(-4.49368 - 3.33474i) q^{46} +(-1.97844 + 1.97844i) q^{47} +(-6.20711 - 9.31271i) q^{48} -0.828427i q^{49} +(3.37109 - 4.54266i) q^{50} +16.3075 q^{51} +(3.40229 + 6.35802i) q^{52} -0.242641 q^{53} +(-4.31147 + 5.80985i) q^{54} -1.63899i q^{55} +(-3.37740 - 7.15685i) q^{56} +(4.58579 - 4.58579i) q^{57} +(0.665257 + 0.493684i) q^{58} +(2.31788 - 2.31788i) q^{59} +(2.64070 - 4.93360i) q^{60} +0.828427 q^{61} +(1.15894 + 7.82843i) q^{62} +(-9.55274 + 9.55274i) q^{63} +(-6.17534 - 5.08579i) q^{64} +(-2.00000 + 3.00000i) q^{65} +(0.949747 + 6.41536i) q^{66} +(2.79793 + 2.79793i) q^{67} +(11.1569 - 3.37740i) q^{68} +11.0711i q^{69} +(2.35802 - 3.17751i) q^{70} +(5.25642 + 5.25642i) q^{71} +(-4.61192 + 12.8546i) q^{72} +(-9.65685 - 9.65685i) q^{73} +(0.550253 + 3.71685i) q^{74} -11.1917 q^{75} +(2.18763 - 4.08713i) q^{76} +4.58579i q^{77} +(6.09001 - 12.9016i) q^{78} -9.55274i q^{79} +(0.784864 - 3.92224i) q^{80} -0.171573 q^{81} +(8.39380 - 1.24264i) q^{82} +(-6.75481 - 6.75481i) q^{83} +(-7.38851 + 13.8039i) q^{84} +(4.12132 + 4.12132i) q^{85} +(5.80985 + 4.31147i) q^{86} -1.63899i q^{87} +(1.97844 + 4.19239i) q^{88} +(6.24264 + 6.24264i) q^{89} +(-6.75481 + 1.00000i) q^{90} +(5.59587 - 8.39380i) q^{91} +(2.29289 + 7.57430i) q^{92} +(11.0711 - 11.0711i) q^{93} +(3.91421 - 0.579471i) q^{94} +2.31788 q^{95} +(-0.799300 + 15.8073i) q^{96} +(0.414214 - 0.414214i) q^{97} +(-0.698175 + 0.940816i) q^{98} +(5.59587 - 5.59587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9	$ 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9 - 20 * q^14 - 4 * q^16 - 8 * q^20 + 16 * q^21 + 24 * q^22 + 32 * q^24 + 8 * q^26 + 12 * q^28 - 16 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^34 - 32 * q^37 + 4 * q^40 + 4 * q^42 - 28 * q^44 + 16 * q^45 - 20 * q^46 - 44 * q^48 - 16 * q^50 + 8 * q^52 + 32 * q^53 - 32 * q^54 + 48 * q^57 + 12 * q^58 - 12 * q^60 - 16 * q^61 - 16 * q^65 - 32 * q^66 + 44 * q^68 + 8 * q^70 + 16 * q^72 - 32 * q^73 + 44 * q^74 + 32 * q^76 + 40 * q^78 + 16 * q^80 - 24 * q^81 - 48 * q^84 + 16 * q^85 + 32 * q^86 + 16 * q^89 + 24 * q^92 + 32 * q^93 + 20 * q^94 - 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.13567	−	0.842772i	−0.803037	−	0.595930i
$2$	−1.13567	−	0.842772i	−0.803037	−	0.595930i
$3$			2.79793i			1.61539i	0.589602	+	0.807694i	$0.299284\pi$
$3$			2.79793i			1.61539i	−0.589602	+	0.807694i	$0.700716\pi$
$4$	0.579471	+	1.91421i	0.289735	+	0.957107i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	−0.847316	−	0.531089i	$-0.821783\pi$
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	0.531089	+	0.847316i	$0.321783\pi$
$6$	2.35802	−	3.17751i	0.962657	−	1.29721i
$7$	1.97844	−	1.97844i	0.747779	−	0.747779i	−0.226283	−	0.974062i	$-0.572657\pi$
$7$	1.97844	−	1.97844i	0.747779	−	0.747779i	0.974062	+	0.226283i	$0.0726573\pi$
$8$	0.955161	−	2.66227i	0.337700	−	0.941254i
$9$	−4.82843			−1.60948
$10$	1.39897	−	0.207107i	0.442392	−	0.0654929i
$11$	−1.15894	+	1.15894i	−0.349434	+	0.349434i	−0.859899	−	0.510465i	$-0.829473\pi$
$11$	−1.15894	+	1.15894i	−0.349434	+	0.349434i	0.510465	+	0.859899i	$0.329473\pi$
$12$	−5.35584	+	1.62132i	−1.54610	+	0.468035i
$13$	3.53553	−	0.707107i	0.980581	−	0.196116i
$13$	3.53553	−	0.707107i	0.980581	−	0.196116i
$14$	−3.91421	+	0.579471i	−1.04612	+	0.154870i
$15$	−1.97844	−	1.97844i	−0.510830	−	0.510830i
$16$	−3.32843	+	2.21846i	−0.832107	+	0.554615i
$17$		−	5.82843i		−	1.41360i	−0.707413	−	0.706801i	$-0.750138\pi$
$17$		−	5.82843i		−	1.41360i	0.707413	−	0.706801i	$-0.249862\pi$
$18$	5.48348	+	4.06926i	1.29247	+	0.959134i
$19$	−1.63899	−	1.63899i	−0.376010	−	0.376010i	0.493650	−	0.869661i	$-0.335662\pi$
$19$	−1.63899	−	1.63899i	−0.376010	−	0.376010i	−0.869661	+	0.493650i	$0.835662\pi$
$20$	−1.76330	−	0.943806i	−0.394286	−	0.211041i
$21$	5.53553	+	5.53553i	1.20795	+	1.20795i
$22$	2.29289	−	0.339446i	0.488846	−	0.0723702i
$23$	3.95687			0.825065			0.412533	−	0.910943i	$-0.364644\pi$
$23$	3.95687			0.825065			0.412533	+	0.910943i	$0.364644\pi$
$24$	7.44885	+	2.67248i	1.52049	+	0.545517i
$25$			4.00000i			0.800000i
$26$	−4.61111	−	2.17661i	−0.904314	−	0.426869i
$27$		−	5.11582i		−	0.984539i
$28$	4.93360	+	2.64070i	0.932362	+	0.499046i
$29$	−0.585786			−0.108778			−0.0543889	−	0.998520i	$-0.517321\pi$
$29$	−0.585786			−0.108778			−0.0543889	+	0.998520i	$0.517321\pi$
$30$	0.579471	+	3.91421i	0.105796	+	0.714634i
$31$	−3.95687	−	3.95687i	−0.710676	−	0.710676i	0.256001	−	0.966677i	$-0.417595\pi$
$31$	−3.95687	−	3.95687i	−0.710676	−	0.710676i	−0.966677	+	0.256001i	$0.917595\pi$
$32$	5.64964	+	0.285675i	0.998724	+	0.0505007i
$33$	−3.24264	−	3.24264i	−0.564471	−	0.564471i
$34$	−4.91203	+	6.61914i	−0.842407	+	1.13517i
$35$			2.79793i			0.472937i
$36$	−2.79793	−	9.24264i	−0.466322	−	1.54044i
$37$	−1.87868	−	1.87868i	−0.308853	−	0.308853i	0.535611	−	0.844465i	$-0.320081\pi$
$37$	−1.87868	−	1.87868i	−0.308853	−	0.308853i	−0.844465	+	0.535611i	$0.820081\pi$
$38$	0.480049	+	3.24264i	0.0778743	+	0.526026i
$39$	1.97844	+	9.89219i	0.316803	+	1.58402i
$40$	1.20711	+	2.55791i	0.190860	+	0.404441i
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	−0.955990	−	0.293400i	$-0.905213\pi$
$41$	−4.24264	+	4.24264i	−0.662589	+	0.662589i	0.293400	+	0.955990i	$0.405213\pi$
$42$	−1.62132	−	10.9517i	−0.250175	−	1.68988i
$43$	−5.11582			−0.780155			−0.390077	−	0.920782i	$-0.627552\pi$
$43$	−5.11582			−0.780155			−0.390077	+	0.920782i	$0.627552\pi$
$44$	−2.89003	−	1.54689i	−0.435689	−	0.233202i
$45$	3.41421	−	3.41421i	0.508961	−	0.508961i
$46$	−4.49368	−	3.33474i	−0.662558	−	0.491681i
$47$	−1.97844	+	1.97844i	−0.288585	+	0.288585i	−0.836520	−	0.547936i	$-0.815414\pi$
$47$	−1.97844	+	1.97844i	−0.288585	+	0.288585i	0.547936	+	0.836520i	$0.315414\pi$
$48$	−6.20711	−	9.31271i	−0.895919	−	1.34417i
$49$		−	0.828427i		−	0.118347i
$50$	3.37109	−	4.54266i	0.476744	−	0.642429i
$51$	16.3075			2.28351
$52$	3.40229	+	6.35802i	0.471813	+	0.881699i
$53$	−0.242641			−0.0333293			−0.0166646	−	0.999861i	$-0.505305\pi$
$53$	−0.242641			−0.0333293			−0.0166646	+	0.999861i	$0.505305\pi$
$54$	−4.31147	+	5.80985i	−0.586716	+	0.790621i
$55$		−	1.63899i		−	0.221002i
$56$	−3.37740	−	7.15685i	−0.451325	−	0.956375i
$57$	4.58579	−	4.58579i	0.607402	−	0.607402i
$58$	0.665257	+	0.493684i	0.0873526	+	0.0648239i
$59$	2.31788	−	2.31788i	0.301763	−	0.301763i	−0.539940	−	0.841703i	$-0.681553\pi$
$59$	2.31788	−	2.31788i	0.301763	−	0.301763i	0.841703	+	0.539940i	$0.181553\pi$
$60$	2.64070	−	4.93360i	0.340914	−	0.636925i
$61$	0.828427			0.106069			0.0530346	−	0.998593i	$-0.483111\pi$
$61$	0.828427			0.106069			0.0530346	+	0.998593i	$0.483111\pi$
$62$	1.15894	+	7.82843i	0.147186	+	0.994211i
$63$	−9.55274	+	9.55274i	−1.20353	+	1.20353i
$64$	−6.17534	−	5.08579i	−0.771917	−	0.635723i
$65$	−2.00000	+	3.00000i	−0.248069	+	0.372104i
$66$	0.949747	+	6.41536i	0.116906	+	0.789676i
$67$	2.79793	+	2.79793i	0.341822	+	0.341822i	0.857052	−	0.515230i	$-0.172294\pi$
$67$	2.79793	+	2.79793i	0.341822	+	0.341822i	−0.515230	+	0.857052i	$0.672294\pi$
$68$	11.1569	−	3.37740i	1.35297	−	0.409570i
$69$			11.0711i			1.33280i
$70$	2.35802	−	3.17751i	0.281837	−	0.379786i
$71$	5.25642	+	5.25642i	0.623822	+	0.623822i	0.946507	−	0.322684i	$-0.104585\pi$
$71$	5.25642	+	5.25642i	0.623822	+	0.623822i	−0.322684	+	0.946507i	$0.604585\pi$
$72$	−4.61192	+	12.8546i	−0.543520	+	1.51492i
$73$	−9.65685	−	9.65685i	−1.13025	−	1.13025i	−0.990135	−	0.140114i	$-0.955253\pi$
$73$	−9.65685	−	9.65685i	−1.13025	−	1.13025i	−0.140114	−	0.990135i	$-0.544747\pi$
$74$	0.550253	+	3.71685i	0.0639656	+	0.432075i
$75$	−11.1917			−1.29231
$76$	2.18763	−	4.08713i	0.250939	−	0.468826i
$77$			4.58579i			0.522599i
$78$	6.09001	−	12.9016i	0.689558	−	1.46082i
$79$		−	9.55274i		−	1.07477i	−0.843338	−	0.537384i	$-0.819413\pi$
$79$		−	9.55274i		−	1.07477i	0.843338	−	0.537384i	$-0.180587\pi$
$80$	0.784864	−	3.92224i	0.0877505	−	0.438520i
$81$	−0.171573			−0.0190637
$82$	8.39380	−	1.24264i	0.926940	−	0.137227i
$83$	−6.75481	−	6.75481i	−0.741436	−	0.741436i	0.231418	−	0.972854i	$-0.425663\pi$
$83$	−6.75481	−	6.75481i	−0.741436	−	0.741436i	−0.972854	+	0.231418i	$0.925663\pi$
$84$	−7.38851	+	13.8039i	−0.806153	+	1.50613i
$85$	4.12132	+	4.12132i	0.447020	+	0.447020i
$86$	5.80985	+	4.31147i	0.626493	+	0.464917i
$87$		−	1.63899i		−	0.175718i
$88$	1.97844	+	4.19239i	0.210902	+	0.446910i
$89$	6.24264	+	6.24264i	0.661719	+	0.661719i	0.955785	−	0.294066i	$-0.0950087\pi$
$89$	6.24264	+	6.24264i	0.661719	+	0.661719i	−0.294066	+	0.955785i	$0.595009\pi$
$90$	−6.75481	+	1.00000i	−0.712019	+	0.105409i
$91$	5.59587	−	8.39380i	0.586606	−	0.879909i
$92$	2.29289	+	7.57430i	0.239051	+	0.789676i
$93$	11.0711	−	11.0711i	1.14802	−	1.14802i
$94$	3.91421	−	0.579471i	0.403720	−	0.0597679i
$95$	2.31788			0.237810
$96$	−0.799300	+	15.8073i	−0.0815782	+	1.61333i
$97$	0.414214	−	0.414214i	0.0420570	−	0.0420570i	−0.685766	−	0.727823i	$-0.740532\pi$
$97$	0.414214	−	0.414214i	0.0420570	−	0.0420570i	0.727823	+	0.685766i	$0.240532\pi$
$98$	−0.698175	+	0.940816i	−0.0705263	+	0.0950368i
$99$	5.59587	−	5.59587i	0.562406	−	0.562406i
$100$	−7.65685	+	2.31788i	−0.765685	+	0.231788i
$101$		−	10.8284i		−	1.07747i	−0.842476	−	0.538734i	$-0.818903\pi$
$101$		−	10.8284i		−	1.07747i	0.842476	−	0.538734i	$-0.181097\pi$
$102$	−18.5199	−	13.7435i	−1.83374	−	1.36081i
$103$	−4.91697			−0.484484			−0.242242	−	0.970216i	$-0.577883\pi$
$103$	−4.91697			−0.484484			−0.242242	+	0.970216i	$0.577883\pi$
$104$	1.49450	−	10.0879i	0.146547	−	0.989204i
$105$	−7.82843			−0.763976
$106$	0.275559	+	0.204491i	0.0267646	+	0.0198619i
$107$			10.2316i			0.989129i	0.869141	+	0.494565i	$0.164672\pi$
$107$			10.2316i			0.989129i	−0.869141	+	0.494565i	$0.835328\pi$
$108$	9.79276	−	2.96447i	0.942309	−	0.285256i
$109$	−4.70711	+	4.70711i	−0.450859	+	0.450859i	−0.895640	−	0.444781i	$-0.853282\pi$
$109$	−4.70711	+	4.70711i	−0.450859	+	0.450859i	0.444781	+	0.895640i	$0.353282\pi$
$110$	−1.38130	+	1.86135i	−0.131701	+	0.177472i
$111$	5.25642	−	5.25642i	0.498917	−	0.498917i
$112$	−2.19600	+	10.9742i	−0.207502	+	1.03696i
$113$	15.3137			1.44059			0.720296	−	0.693667i	$-0.244006\pi$
$113$	15.3137			1.44059			0.720296	+	0.693667i	$0.244006\pi$
$114$	−9.07269	+	1.34315i	−0.849735	+	0.125797i
$115$	−2.79793	+	2.79793i	−0.260909	+	0.260909i
$116$	−0.339446	−	1.12132i	−0.0315168	−	0.104112i
$117$	−17.0711	+	3.41421i	−1.57822	+	0.315644i
$118$	−4.58579	+	0.678892i	−0.422156	+	0.0624971i
$119$	−11.5312	−	11.5312i	−1.05706	−	1.05706i
$120$	−7.15685	+	3.37740i	−0.653328	+	0.308313i
$121$			8.31371i			0.755792i
$122$	−0.940816	−	0.698175i	−0.0851775	−	0.0632098i
$123$	−11.8706	−	11.8706i	−1.07034	−	1.07034i
$124$	5.28141	−	9.86720i	0.474285	−	0.886100i
$125$	−6.36396	−	6.36396i	−0.569210	−	0.569210i
$126$	18.8995	−	2.79793i	1.68370	−	0.249260i
$127$	18.4266			1.63510			0.817548	−	0.575861i	$-0.195333\pi$
$127$	18.4266			1.63510			0.817548	+	0.575861i	$0.195333\pi$
$128$	2.72696	+	10.9802i	0.241031	+	0.970517i
$129$		−	14.3137i		−	1.26025i
$130$	4.79965	−	1.72145i	0.420957	−	0.150981i
$131$			10.7117i			0.935884i	0.883759	+	0.467942i	$0.155004\pi$
$131$			10.7117i			0.935884i	−0.883759	+	0.467942i	$0.844996\pi$
$132$	4.32809	−	8.08612i	0.376712	−	0.703807i
$133$	−6.48528			−0.562345
$134$	−0.819496	−	5.53553i	−0.0707936	−	0.478197i
$135$	3.61743	+	3.61743i	0.311339	+	0.311339i
$136$	−15.5168	−	5.56708i	−1.33056	−	0.477374i
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	0.972502	−	0.232897i	$-0.0748204\pi$
$137$	8.65685	+	8.65685i	0.739605	+	0.739605i	−0.232897	+	0.972502i	$0.574820\pi$
$138$	9.33039	−	12.5730i	0.794255	−	1.07029i
$139$			21.9034i			1.85782i	0.370302	+	0.928912i	$0.379254\pi$
$139$			21.9034i			1.85782i	−0.370302	+	0.928912i	$0.620746\pi$
$140$	−5.35584	+	1.62132i	−0.452651	+	0.137027i
$141$	−5.53553	−	5.53553i	−0.466176	−	0.466176i
$142$	−1.53957	−	10.3995i	−0.129198	−	0.872706i
$143$	−3.27798	+	4.91697i	−0.274119	+	0.411178i
$144$	16.0711	−	10.7117i	1.33926	−	0.892640i
$145$	0.414214	−	0.414214i	0.0343986	−	0.0343986i
$146$	2.82843	+	19.1055i	0.234082	+	1.58118i
$147$	2.31788			0.191176
$148$	2.50755	−	4.68483i	0.206120	−	0.385091i
$149$	−6.48528	+	6.48528i	−0.531295	+	0.531295i	−0.920958	−	0.389663i	$-0.872592\pi$
$149$	−6.48528	+	6.48528i	−0.531295	+	0.531295i	0.389663	+	0.920958i	$0.372592\pi$
$150$	12.7101	+	9.43208i	1.03777	+	0.770126i
$151$	−1.29954	+	1.29954i	−0.105755	+	0.105755i	−0.758005	−	0.652249i	$-0.773826\pi$
$151$	−1.29954	+	1.29954i	−0.105755	+	0.105755i	0.652249	+	0.758005i	$0.273826\pi$
$152$	−5.92893	+	2.79793i	−0.480900	+	0.226942i
$153$			28.1421i			2.27516i
$154$	3.86477	−	5.20792i	0.311432	−	0.419666i
$155$	5.59587			0.449471
$156$	−17.7893	+	9.51938i	−1.42428	+	0.762161i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	−8.05078	+	10.8487i	−0.640486	+	0.863077i
$159$		−	0.678892i		−	0.0538397i
$160$	−4.19690	+	3.79289i	−0.331794	+	0.299855i
$161$	7.82843	−	7.82843i	0.616966	−	0.616966i
$162$	0.194849	+	0.144597i	0.0153088	+	0.0113606i
$163$	−10.7117	+	10.7117i	−0.839004	+	0.839004i	−0.988728	−	0.149724i	$-0.952161\pi$
$163$	−10.7117	+	10.7117i	−0.839004	+	0.839004i	0.149724	+	0.988728i	$0.452161\pi$
$164$	−10.5798	−	5.66283i	−0.826144	−	0.442193i
$165$	4.58579			0.357003
$166$	1.97844	+	13.3640i	0.153557	+	1.03724i
$167$	9.55274	−	9.55274i	0.739213	−	0.739213i	−0.233213	−	0.972426i	$-0.574924\pi$
$167$	9.55274	−	9.55274i	0.739213	−	0.739213i	0.972426	+	0.233213i	$0.0749238\pi$
$168$	20.0244	−	9.44975i	1.54492	−	0.729064i
$169$	12.0000	−	5.00000i	0.923077	−	0.384615i
$170$	−1.20711	−	8.15377i	−0.0925809	−	0.625366i
$171$	7.91375	+	7.91375i	0.605179	+	0.605179i
$172$	−2.96447	−	9.79276i	−0.226038	−	0.746691i
$173$		−	12.3848i		−	0.941597i	−0.882241	−	0.470799i	$-0.843966\pi$
$173$		−	12.3848i		−	0.941597i	0.882241	−	0.470799i	$-0.156034\pi$
$174$	−1.38130	+	1.86135i	−0.104716	+	0.141108i
$175$	7.91375	+	7.91375i	0.598223	+	0.598223i
$176$	1.28639	−	6.42852i	0.0969649	−	0.484568i
$177$	6.48528	+	6.48528i	0.487464	+	0.487464i
$178$	−1.82843	−	12.3507i	−0.137046	−	0.925722i
$179$	−7.43370			−0.555621			−0.277810	−	0.960636i	$-0.589609\pi$
$179$	−7.43370			−0.555621			−0.277810	+	0.960636i	$0.589609\pi$
$180$	8.51397	+	4.55710i	0.634594	+	0.339666i
$181$		−	11.4142i		−	0.848412i	−0.905566	−	0.424206i	$-0.860553\pi$
$181$		−	11.4142i		−	0.848412i	0.905566	−	0.424206i	$-0.139447\pi$
$182$	−13.4291	+	4.81651i	−0.995430	+	0.357023i
$183$			2.31788i			0.171343i
$184$	3.77945	−	10.5343i	0.278625	−	0.776596i
$185$	2.65685			0.195336
$186$	−21.9034	+	3.24264i	−1.60604	+	0.237762i
$187$	6.75481	+	6.75481i	0.493960	+	0.493960i
$188$	−4.93360	−	2.64070i	−0.359820	−	0.192593i
$189$	−10.1213	−	10.1213i	−0.736218	−	0.736218i
$190$	−2.63234	−	1.95345i	−0.190970	−	0.141718i
$191$		−	24.0225i		−	1.73820i	−0.494633	−	0.869102i	$-0.664698\pi$
$191$		−	24.0225i		−	1.73820i	0.494633	−	0.869102i	$-0.335302\pi$
$192$	14.2297	−	17.2782i	1.02694	−	1.24694i
$193$	−6.07107	−	6.07107i	−0.437005	−	0.437005i	0.453998	−	0.891003i	$-0.349997\pi$
$193$	−6.07107	−	6.07107i	−0.437005	−	0.437005i	−0.891003	+	0.453998i	$0.849997\pi$
$194$	−0.819496	+	0.121320i	−0.0588363	+	0.00871029i
$195$	−8.39380	−	5.59587i	−0.601092	−	0.400728i
$196$	1.58579	−	0.480049i	0.113270	−	0.0342892i
$197$	−18.6066	+	18.6066i	−1.32567	+	1.32567i	−0.416555	+	0.909111i	$0.636763\pi$
$197$	−18.6066	+	18.6066i	−1.32567	+	1.32567i	−0.909111	+	0.416555i	$0.863237\pi$
$198$	−11.0711	+	1.63899i	−0.786787	+	0.116478i
$199$	−16.5064			−1.17011			−0.585053	−	0.810995i	$-0.698926\pi$
$199$	−16.5064			−1.17011			−0.585053	+	0.810995i	$0.698926\pi$
$200$	10.6491	+	3.82064i	0.753003	+	0.270160i
$201$	−7.82843	+	7.82843i	−0.552175	+	0.552175i
$202$	−9.12589	+	12.2975i	−0.642096	+	0.865247i
$203$	−1.15894	+	1.15894i	−0.0813418	+	0.0813418i
$204$	9.44975	+	31.2161i	0.661615	+	2.18557i
$205$		−	6.00000i		−	0.419058i
$206$	5.58404	+	4.14389i	0.389058	+	0.288718i
$207$	−19.1055			−1.32792
$208$	−10.1991	+	10.1970i	−0.707179	+	0.707035i
$209$	3.79899			0.262782
$210$	8.89047	+	6.59758i	0.613501	+	0.455276i
$211$		−	9.75158i		−	0.671327i	−0.941982	−	0.335663i	$-0.891040\pi$
$211$		−	9.75158i		−	0.671327i	0.941982	−	0.335663i	$-0.108960\pi$
$212$	−0.140603	−	0.464466i	−0.00965667	−	0.0318997i
$213$	−14.7071	+	14.7071i	−1.00771	+	1.00771i
$214$	8.62293	−	11.6197i	0.589452	−	0.794307i
$215$	3.61743	−	3.61743i	0.246707	−	0.246707i
$216$	−13.6197	−	4.88643i	−0.926701	−	0.332479i
$217$	−15.6569			−1.06286
$218$	9.31271	−	1.37868i	0.630737	−	0.0933760i
$219$	27.0192	−	27.0192i	1.82579	−	1.82579i
$220$	3.13738	−	0.949747i	0.211522	−	0.0640320i
$221$	−4.12132	−	20.6066i	−0.277230	−	1.38615i
$222$	−10.3995	+	1.53957i	−0.697968	+	0.103329i
$223$	17.8059	+	17.8059i	1.19237	+	1.19237i	0.976399	+	0.215975i	$0.0692928\pi$
$223$	17.8059	+	17.8059i	1.19237	+	1.19237i	0.215975	+	0.976399i	$0.430707\pi$
$224$	11.7426	−	10.6123i	0.784588	−	0.709061i
$225$		−	19.3137i		−	1.28758i
$226$	−17.3912	−	12.9060i	−1.15685	−	0.858492i
$227$	−12.8307	−	12.8307i	−0.851605	−	0.851605i	0.138726	−	0.990331i	$-0.455699\pi$
$227$	−12.8307	−	12.8307i	−0.851605	−	0.851605i	−0.990331	+	0.138726i	$0.955699\pi$
$228$	11.4355	+	6.12085i	0.757335	+	0.405363i
$229$	14.7071	+	14.7071i	0.971873	+	0.971873i	0.999615	−	0.0277421i	$-0.00883173\pi$
$229$	14.7071	+	14.7071i	0.971873	+	0.971873i	−0.0277421	+	0.999615i	$0.508832\pi$
$230$	5.53553	−	0.819496i	0.365002	−	0.0540359i
$231$	−12.8307			−0.844200
$232$	−0.559520	+	1.55952i	−0.0367343	+	0.102388i
$233$			11.9706i			0.784218i	0.919919	+	0.392109i	$0.128254\pi$
$233$			11.9706i			0.784218i	−0.919919	+	0.392109i	$0.871746\pi$
$234$	22.2644	+	10.5096i	1.45547	+	0.687035i
$235$		−	2.79793i		−	0.182517i
$236$	5.78007	+	3.09378i	0.376250	+	0.201388i
$237$	26.7279			1.73617
$238$	3.37740	+	22.8137i	0.218925	+	1.47879i
$239$	8.25319	+	8.25319i	0.533855	+	0.533855i	0.921717	−	0.387862i	$-0.126786\pi$
$239$	8.25319	+	8.25319i	0.533855	+	0.533855i	−0.387862	+	0.921717i	$0.626786\pi$
$240$	10.9742	+	2.19600i	0.708380	+	0.141751i
$241$	13.0711	+	13.0711i	0.841981	+	0.841981i	0.989116	−	0.147135i	$-0.0470052\pi$
$241$	13.0711	+	13.0711i	0.841981	+	0.841981i	−0.147135	+	0.989116i	$0.547005\pi$
$242$	7.00656	−	9.44159i	0.450399	−	0.606928i
$243$		−	15.8275i		−	1.01533i
$244$	0.480049	+	1.58579i	0.0307320	+	0.101520i
$245$	0.585786	+	0.585786i	0.0374245	+	0.0374245i
$246$	3.47682	+	23.4853i	0.221674	+	1.49737i
$247$	−6.95365	−	4.63577i	−0.442450	−	0.294967i
$248$	−14.3137	+	6.75481i	−0.908921	+	0.428931i
$249$	18.8995	−	18.8995i	1.19771	−	1.19771i
$250$	1.86396	+	12.5907i	0.117887	+	0.796306i
$251$	18.1454			1.14533			0.572663	−	0.819791i	$-0.305910\pi$
$251$	18.1454			1.14533			0.572663	+	0.819791i	$0.305910\pi$
$252$	−23.8215	−	12.7504i	−1.50061	−	0.803203i
$253$	−4.58579	+	4.58579i	−0.288306	+	0.288306i
$254$	−20.9264	−	15.5294i	−1.31304	−	0.974402i
$255$	−11.5312	+	11.5312i	−0.722110	+	0.722110i
$256$	6.15685	−	14.7680i	0.384803	−	0.922999i
$257$		−	0.656854i		−	0.0409734i	−0.999790	−	0.0204867i	$-0.993478\pi$
$257$		−	0.656854i		−	0.0409734i	0.999790	−	0.0204867i	$-0.00652158\pi$
$258$	−12.0632	+	16.2556i	−0.751022	+	1.01203i
$259$	−7.43370			−0.461908
$260$	−6.90158	−	2.09001i	−0.428018	−	0.129617i
$261$	2.82843			0.175075
$262$	9.02750	−	12.1649i	0.557721	−	0.751549i
$263$		−	8.87385i		−	0.547185i	−0.961846	−	0.273592i	$-0.911788\pi$
$263$		−	8.87385i		−	0.547185i	0.961846	−	0.273592i	$-0.0882119\pi$
$264$	−11.7300	+	5.53553i	−0.721933	+	0.340689i
$265$	0.171573	−	0.171573i	0.0105396	−	0.0105396i
$266$	7.36511	+	5.46561i	0.451584	+	0.335118i
$267$	−17.4665	+	17.4665i	−1.06893	+	1.06893i
$268$	−3.73452	+	6.97716i	−0.228122	+	0.426198i
$269$	−8.14214			−0.496435			−0.248217	−	0.968704i	$-0.579845\pi$
$269$	−8.14214			−0.496435			−0.248217	+	0.968704i	$0.579845\pi$
$270$	−1.05952	−	7.15685i	−0.0644803	−	0.435552i
$271$	−13.1702	+	13.1702i	−0.800031	+	0.800031i	−0.983100	−	0.183069i	$-0.941397\pi$
$271$	−13.1702	+	13.1702i	−0.800031	+	0.800031i	0.183069	+	0.983100i	$0.441397\pi$
$272$	12.9301	+	19.3995i	0.784005	+	1.17627i
$273$	23.4853	+	15.6569i	1.42139	+	0.947596i
$274$	−2.53553	−	17.1270i	−0.153177	−	1.03468i
$275$	−4.63577	−	4.63577i	−0.279547	−	0.279547i
$276$	−21.1924	+	6.41536i	−1.27563	+	0.386159i
$277$		−	6.00000i		−	0.360505i	−0.983620	−	0.180253i	$-0.942309\pi$
$277$		−	6.00000i		−	0.360505i	0.983620	−	0.180253i	$-0.0576915\pi$
$278$	18.4596	−	24.8749i	1.10713	−	1.49190i
$279$	19.1055	+	19.1055i	1.14382	+	1.14382i
$280$	7.44885	+	2.67248i	0.445154	+	0.159711i
$281$	−7.75736	−	7.75736i	−0.462765	−	0.462765i	0.436796	−	0.899561i	$-0.356113\pi$
$281$	−7.75736	−	7.75736i	−0.462765	−	0.462765i	−0.899561	+	0.436796i	$0.856113\pi$
$282$	1.62132	+	10.9517i	0.0965482	+	0.652165i
$283$	1.35778			0.0807119			0.0403560	−	0.999185i	$-0.487151\pi$
$283$	1.35778			0.0807119			0.0403560	+	0.999185i	$0.487151\pi$
$284$	−7.01597	+	13.1079i	−0.416321	+	0.777808i
$285$			6.48528i			0.384155i
$286$	7.86658	−	2.82144i	0.465160	−	0.166835i
$287$			16.7876i			0.990940i
$288$	−27.2789	−	1.37936i	−1.60742	−	0.0812797i
$289$	−16.9706			−0.998268
$290$	−0.819496	+	0.121320i	−0.0481224	+	0.00712418i
$291$	1.15894	+	1.15894i	0.0679384	+	0.0679384i
$292$	12.8894	−	24.0811i	0.754296	−	1.40924i
$293$	−19.1924	−	19.1924i	−1.12123	−	1.12123i	−0.991557	−	0.129675i	$-0.958607\pi$
$293$	−19.1924	−	19.1924i	−1.12123	−	1.12123i	−0.129675	−	0.991557i	$-0.541393\pi$
$294$	−2.63234	−	1.95345i	−0.153521	−	0.113927i
$295$			3.27798i			0.190851i
$296$	−6.79599	+	3.20711i	−0.395009	+	0.186409i
$297$	5.92893	+	5.92893i	0.344032	+	0.344032i
$298$	12.8307	−	1.89949i	0.743264	−	0.110035i
$299$	13.9897	−	2.79793i	0.809043	−	0.161809i
$300$	−6.48528	−	21.4234i	−0.374428	−	1.23688i
$301$	−10.1213	+	10.1213i	−0.583383	+	0.583383i
$302$	2.57107	−	0.380628i	0.147948	−	0.0219027i
$303$	30.2972			1.74053
$304$	9.09130	+	1.81922i	0.521422	+	0.104340i
$305$	−0.585786	+	0.585786i	−0.0335420	+	0.0335420i
$306$	23.7174	−	31.9600i	1.35583	−	1.82703i
$307$	19.1055	−	19.1055i	1.09041	−	1.09041i	0.0949226	−	0.995485i	$-0.469740\pi$
$307$	19.1055	−	19.1055i	1.09041	−	1.09041i	0.995485	−	0.0949226i	$-0.0302604\pi$
$308$	−8.77817	+	2.65733i	−0.500183	+	0.151415i
$309$		−	13.7574i		−	0.782629i
$310$	−6.35503	−	4.71604i	−0.360941	−	0.267853i
$311$	−22.7811			−1.29180			−0.645900	−	0.763422i	$-0.723518\pi$
$311$	−22.7811			−1.29180			−0.645900	+	0.763422i	$0.723518\pi$
$312$	28.2254	+	4.18150i	1.59795	+	0.236731i
$313$	−13.4853			−0.762233			−0.381117	−	0.924527i	$-0.624460\pi$
$313$	−13.4853			−0.762233			−0.381117	+	0.924527i	$0.624460\pi$
$314$	−13.6280	−	10.1133i	−0.769072	−	0.570724i
$315$		−	13.5096i		−	0.761181i
$316$	18.2860	−	5.53553i	1.02867	−	0.311398i
$317$	−4.34315	+	4.34315i	−0.243935	+	0.243935i	−0.818476	−	0.574541i	$-0.805181\pi$
$317$	−4.34315	+	4.34315i	−0.243935	+	0.243935i	0.574541	+	0.818476i	$0.305181\pi$
$318$	−0.572151	+	0.770994i	−0.0320847	+	0.0432352i
$319$	0.678892	−	0.678892i	0.0380107	−	0.0380107i
$320$	7.96282	−	0.770428i	0.445135	−	0.0430682i
$321$	−28.6274			−1.59783
$322$	−15.4881	+	2.29289i	−0.863115	+	0.127778i
$323$	−9.55274	+	9.55274i	−0.531529	+	0.531529i
$324$	−0.0994215	−	0.328427i	−0.00552342	−	0.0182460i
$325$	2.82843	+	14.1421i	0.156893	+	0.784465i
$326$	21.1924	−	3.13738i	1.17374	−	0.173763i
$327$	−13.1702	−	13.1702i	−0.728312	−	0.728312i
$328$	7.24264	+	15.3474i	0.399908	+	0.847421i
$329$			7.82843i			0.431595i
$330$	−5.20792	−	3.86477i	−0.286686	−	0.212749i
$331$	14.6686	+	14.6686i	0.806257	+	0.806257i	0.984065	−	0.177808i	$-0.0569007\pi$
$331$	14.6686	+	14.6686i	0.806257	+	0.806257i	−0.177808	+	0.984065i	$0.556901\pi$
$332$	9.01593	−	16.8444i	0.494813	−	0.924454i
$333$	9.07107	+	9.07107i	0.497091	+	0.497091i
$334$	−18.8995	+	2.79793i	−1.03413	+	0.153096i
$335$	−3.95687			−0.216187
$336$	−30.7050	−	6.14425i	−1.67509	−	0.335196i
$337$		−	8.17157i		−	0.445134i	−0.974917	−	0.222567i	$-0.928556\pi$
$337$		−	8.17157i		−	0.445134i	0.974917	−	0.222567i	$-0.0714436\pi$
$338$	−17.8418	−	4.43494i	−0.970468	−	0.241229i
$339$			42.8467i			2.32711i
$340$	−5.50090	+	10.2773i	−0.298328	+	0.557363i
$341$	9.17157			0.496669
$342$	−2.31788	−	15.6569i	−0.125337	−	0.846626i
$343$	12.2101	+	12.2101i	0.659282	+	0.659282i
$344$	−4.88643	+	13.6197i	−0.263458	+	0.734323i
$345$	−7.82843	−	7.82843i	−0.421468	−	0.421468i
$346$	−10.4375	+	14.0650i	−0.561126	+	0.756137i
$347$			9.35390i			0.502143i	0.967968	+	0.251072i	$0.0807830\pi$
$347$			9.35390i			0.502143i	−0.967968	+	0.251072i	$0.919217\pi$
$348$	3.13738	−	0.949747i	0.168181	−	0.0509118i
$349$	−0.464466	−	0.464466i	−0.0248623	−	0.0248623i	0.694566	−	0.719429i	$-0.255596\pi$
$349$	−0.464466	−	0.464466i	−0.0248623	−	0.0248623i	−0.719429	+	0.694566i	$0.755596\pi$
$350$	−2.31788	−	15.6569i	−0.123896	−	0.836894i
$351$	−3.61743	−	18.0871i	−0.193084	−	0.965420i
$352$	−6.87868	+	6.21652i	−0.366635	+	0.331342i
$353$	−4.41421	+	4.41421i	−0.234945	+	0.234945i	−0.814753	−	0.579808i	$-0.803127\pi$
$353$	−4.41421	+	4.41421i	−0.234945	+	0.234945i	0.579808	+	0.814753i	$0.303127\pi$
$354$	−1.89949	−	12.8307i	−0.100957	−	0.681945i
$355$	−7.43370			−0.394540
$356$	−8.33232	+	15.5672i	−0.441612	+	0.825059i
$357$	32.2635	−	32.2635i	1.70756	−	1.70756i
$358$	8.44219	+	6.26491i	0.446184	+	0.331111i
$359$	−3.95687	+	3.95687i	−0.208836	+	0.208836i	−0.803773	−	0.594937i	$-0.797177\pi$
$359$	−3.95687	+	3.95687i	−0.208836	+	0.208836i	0.594937	+	0.803773i	$0.297177\pi$
$360$	−5.82843	−	12.3507i	−0.307185	−	0.650938i
$361$		−	13.6274i		−	0.717232i
$362$	−9.61958	+	12.9627i	−0.505594	+	0.681306i
$363$	−23.2612			−1.22090
$364$	19.3102	+	5.84772i	1.01213	+	0.306504i
$365$	13.6569			0.714832
$366$	1.95345	−	2.63234i	0.102108	−	0.137595i
$367$		−	15.1486i		−	0.790751i	−0.918520	−	0.395375i	$-0.870615\pi$
$367$		−	15.1486i		−	0.790751i	0.918520	−	0.395375i	$-0.129385\pi$
$368$	−13.1702	+	8.77817i	−0.686542	+	0.457594i
$369$	20.4853	−	20.4853i	1.06642	−	1.06642i
$370$	−3.01730	−	2.23912i	−0.156862	−	0.116406i
$371$	−0.480049	+	0.480049i	−0.0249229	+	0.0249229i
$372$	27.6077	+	14.7770i	1.43140	+	0.766153i
$373$	30.6274			1.58583			0.792914	−	0.609334i	$-0.208563\pi$
$373$	30.6274			1.58583			0.792914	+	0.609334i	$0.208563\pi$
$374$	−1.97844	−	13.3640i	−0.102303	−	0.691034i
$375$	17.8059	−	17.8059i	0.919494	−	0.919494i
$376$	3.37740	+	7.15685i	0.174176	+	0.369087i
$377$	−2.07107	+	0.414214i	−0.106665	+	0.0213331i
$378$	2.96447	+	20.0244i	0.152476	+	1.02994i
$379$	−13.9897	−	13.9897i	−0.718601	−	0.718601i	0.249718	−	0.968319i	$-0.419662\pi$
$379$	−13.9897	−	13.9897i	−0.718601	−	0.718601i	−0.968319	+	0.249718i	$0.919662\pi$
$380$	1.34315	+	4.43692i	0.0689019	+	0.227609i
$381$			51.5563i			2.64131i
$382$	−20.2454	+	27.2815i	−1.03585	+	1.39584i
$383$	−11.5312	−	11.5312i	−0.589216	−	0.589216i	0.348203	−	0.937419i	$-0.386792\pi$
$383$	−11.5312	−	11.5312i	−0.589216	−	0.589216i	−0.937419	+	0.348203i	$0.886792\pi$
$384$	−30.7217	+	7.62984i	−1.56776	+	0.389359i
$385$	−3.24264	−	3.24264i	−0.165260	−	0.165260i
$386$	1.77817	+	12.0112i	0.0905067	+	0.611355i
$387$	24.7013			1.25564
$388$	1.03292	+	0.552869i	0.0524385	+	0.0280676i
$389$			22.1421i			1.12265i	0.827595	+	0.561325i	$0.189708\pi$
$389$			22.1421i			1.12265i	−0.827595	+	0.561325i	$0.810292\pi$
$390$	4.81651	+	13.4291i	0.243893	+	0.680008i
$391$		−	23.0624i		−	1.16631i
$392$	−2.20549	−	0.791281i	−0.111394	−	0.0399657i
$393$	−29.9706			−1.51181
$394$	36.8120	−	5.44975i	1.85456	−	0.274554i
$395$	6.75481	+	6.75481i	0.339871	+	0.339871i
$396$	13.9543	+	7.46904i	0.701231	+	0.375333i
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	0.668074	−	0.744095i	$-0.267119\pi$
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	−0.744095	+	0.668074i	$0.767119\pi$
$398$	18.7457	+	13.9111i	0.939639	+	0.697302i
$399$		−	18.1454i		−	0.908405i
$400$	−8.87385	−	13.3137i	−0.443692	−	0.665685i
$401$	19.4853	+	19.4853i	0.973049	+	0.973049i	0.999646	−	0.0265977i	$-0.00846731\pi$
$401$	19.4853	+	19.4853i	0.973049	+	0.973049i	−0.0265977	+	0.999646i	$0.508467\pi$
$402$	15.4881	−	2.29289i	0.772474	−	0.114359i
$403$	−16.7876	−	11.1917i	−0.836250	−	0.557500i
$404$	20.7279	−	6.27476i	1.03125	−	0.312181i
$405$	0.121320	−	0.121320i	0.00602846	−	0.00602846i
$406$	2.29289	−	0.339446i	0.113794	−	0.0168464i
$407$	4.35456			0.215848
$408$	15.5763	−	43.4151i	0.771143	−	2.14937i
$409$	5.14214	−	5.14214i	0.254262	−	0.254262i	−0.568453	−	0.822716i	$-0.692458\pi$
$409$	5.14214	−	5.14214i	0.254262	−	0.254262i	0.822716	+	0.568453i	$0.192458\pi$
$410$	−5.05663	+	6.81399i	−0.249729	+	0.336519i
$411$	−24.2213	+	24.2213i	−1.19475	+	1.19475i
$412$	−2.84924	−	9.41214i	−0.140372	−	0.463703i
$413$		−	9.17157i		−	0.451304i
$414$	21.6974	+	16.1016i	1.06637	+	0.791349i
$415$	9.55274			0.468926
$416$	20.1765	−	2.98488i	0.989233	−	0.146346i
$417$	−61.2843			−3.00110
$418$	−4.31438	−	3.20168i	−0.211023	−	0.156599i
$419$			5.11582i			0.249924i	0.992162	+	0.124962i	$0.0398809\pi$
$419$			5.11582i			0.249924i	−0.992162	+	0.124962i	$0.960119\pi$
$420$	−4.53635	−	14.9853i	−0.221351	−	0.731207i
$421$	0.0208153	−	0.0208153i	0.00101447	−	0.00101447i	−0.706599	−	0.707614i	$-0.749772\pi$
$421$	0.0208153	−	0.0208153i	0.00101447	−	0.00101447i	0.707614	+	0.706599i	$0.249772\pi$
$422$	−8.21836	+	11.0745i	−0.400064	+	0.539100i
$423$	9.55274	−	9.55274i	0.464470	−	0.464470i
$424$	−0.231761	+	0.645974i	−0.0112553	+	0.0313713i
$425$	23.3137			1.13088
$426$	29.0971	−	4.30761i	1.40976	−	0.208704i
$427$	1.63899	−	1.63899i	0.0793163	−	0.0793163i
$428$	−19.5855	+	5.92893i	−0.946702	+	0.286586i
$429$	−13.7574	−	9.17157i	−0.664212	−	0.442808i
$430$	−7.15685	+	1.05952i	−0.345134	+	0.0510946i
$431$	26.0009	+	26.0009i	1.25242	+	1.25242i	0.954633	+	0.297786i	$0.0962482\pi$
$431$	26.0009	+	26.0009i	1.25242	+	1.25242i	0.297786	+	0.954633i	$0.403752\pi$
$432$	11.3492	+	17.0276i	0.546041	+	0.819242i
$433$		−	9.68629i		−	0.465493i	−0.972537	−	0.232747i	$-0.925229\pi$
$433$		−	9.68629i		−	0.465493i	0.972537	−	0.232747i	$-0.0747713\pi$
$434$	17.7809	+	13.1952i	0.853513	+	0.633388i
$435$	1.15894	+	1.15894i	0.0555670	+	0.0555670i
$436$	−11.7380	−	6.28278i	−0.562150	−	0.300890i
$437$	−6.48528	−	6.48528i	−0.310233	−	0.310233i
$438$	−53.4558	+	7.91375i	−2.55422	+	0.378134i
$439$	−23.7412			−1.13311			−0.566554	−	0.824025i	$-0.691724\pi$
$439$	−23.7412			−1.13311			−0.566554	+	0.824025i	$0.691724\pi$
$440$	−4.36343	−	1.56550i	−0.208018	−	0.0746323i
$441$			4.00000i			0.190476i
$442$	−12.6862	+	26.8755i	−0.603422	+	1.27834i
$443$		−	27.4993i		−	1.30653i	−0.757129	−	0.653265i	$-0.773399\pi$
$443$		−	27.4993i		−	1.30653i	0.757129	−	0.653265i	$-0.226601\pi$
$444$	13.1079	+	7.01597i	0.622071	+	0.332963i
$445$	−8.82843			−0.418508
$446$	−5.21524	−	35.2279i	−0.246949	−	1.66809i
$447$	−18.1454	−	18.1454i	−0.858247	−	0.858247i
$448$	−22.2794	+	2.15561i	−1.05260	+	0.101843i
$449$	0.272078	+	0.272078i	0.0128402	+	0.0128402i	0.713498	−	0.700658i	$-0.247110\pi$
$449$	0.272078	+	0.272078i	0.0128402	+	0.0128402i	−0.700658	+	0.713498i	$0.747110\pi$
$450$	−16.2771	+	21.9339i	−0.767308	+	1.03397i
$451$		−	9.83395i		−	0.463062i
$452$	8.87385	+	29.3137i	0.417391	+	1.37880i
$453$	−3.63604	−	3.63604i	−0.170836	−	0.170836i
$454$	3.75803	+	25.3848i	0.176373	+	1.19137i
$455$	1.97844	+	9.89219i	0.0927506	+	0.463753i
$456$	−7.82843	−	16.5888i	−0.366600	−	0.776840i
$457$	3.41421	−	3.41421i	0.159710	−	0.159710i	−0.622728	−	0.782438i	$-0.713976\pi$
$457$	3.41421	−	3.41421i	0.159710	−	0.159710i	0.782438	+	0.622728i	$0.213976\pi$
$458$	−4.30761	−	29.0971i	−0.201281	−	1.35962i
$459$	−29.8172			−1.39175
$460$	−6.97716	−	3.73452i	−0.325312	−	0.174123i
$461$	13.5355	−	13.5355i	0.630413	−	0.630413i	−0.317759	−	0.948172i	$-0.602930\pi$
$461$	13.5355	−	13.5355i	0.630413	−	0.630413i	0.948172	+	0.317759i	$0.102930\pi$
$462$	14.5714	+	10.8134i	0.677923	+	0.503084i
$463$	16.1087	−	16.1087i	0.748635	−	0.748635i	−0.225588	−	0.974223i	$-0.572430\pi$
$463$	16.1087	−	16.1087i	0.748635	−	0.748635i	0.974223	+	0.225588i	$0.0724303\pi$
$464$	1.94975	−	1.29954i	0.0905148	−	0.0603299i
$465$			15.6569i			0.726069i
$466$	10.0885	−	13.5946i	0.467339	−	0.629755i
$467$	6.95365			0.321777			0.160888	−	0.986973i	$-0.448564\pi$
$467$	6.95365			0.321777			0.160888	+	0.986973i	$0.448564\pi$
$468$	−16.4277	−	30.6992i	−0.759372	−	1.41907i
$469$	11.0711			0.511214
$470$	−2.35802	+	3.17751i	−0.108767	+	0.146568i
$471$			33.5752i			1.54706i
$472$	−3.95687	−	8.38478i	−0.182130	−	0.385941i
$473$	5.92893	−	5.92893i	0.272613	−	0.272613i
$474$	−30.3540	−	22.5255i	−1.39420	−	1.03463i
$475$	6.55596	−	6.55596i	0.300808	−	0.300808i
$476$	15.3912	−	28.7551i	0.705452	−	1.31799i
$477$	1.17157			0.0536426
$478$	−2.41730	−	16.3284i	−0.110565	−	0.746845i
$479$	7.57430	−	7.57430i	0.346079	−	0.346079i	−0.512568	−	0.858647i	$-0.671306\pi$
$479$	7.57430	−	7.57430i	0.346079	−	0.346079i	0.858647	+	0.512568i	$0.171306\pi$
$480$	−10.6123	−	11.7426i	−0.484381	−	0.535976i
$481$	−7.97056	−	5.31371i	−0.363426	−	0.242284i
$482$	−3.82843	−	25.8603i	−0.174380	−	1.17790i
$483$	21.9034	+	21.9034i	0.996640	+	0.996640i
$484$	−15.9142	+	4.81755i	−0.723373	+	0.218980i
$485$			0.585786i			0.0265992i
$486$	−13.3390	+	17.9747i	−0.605068	+	0.815351i
$487$	6.27476	+	6.27476i	0.284336	+	0.284336i	0.834836	−	0.550499i	$-0.185563\pi$
$487$	6.27476	+	6.27476i	0.284336	+	0.284336i	−0.550499	+	0.834836i	$0.685563\pi$
$488$	0.791281	−	2.20549i	0.0358196	−	0.0998380i
$489$	−29.9706	−	29.9706i	−1.35532	−	1.35532i
$490$	−0.171573	−	1.15894i	−0.00775087	−	0.0523556i
$491$	−2.79793			−0.126269			−0.0631345	−	0.998005i	$-0.520110\pi$
$491$	−2.79793			−0.126269			−0.0631345	+	0.998005i	$0.520110\pi$
$492$	15.8442	−	29.6016i	0.714313	−	1.33454i
$493$			3.41421i			0.153768i
$494$	3.99012	+	11.1250i	0.179524	+	0.500538i
$495$			7.91375i			0.355697i
$496$	21.9483	+	4.39199i	0.985510	+	0.197206i
$497$	20.7990			0.932962
$498$	−37.3915	+	5.53553i	−1.67555	+	0.248053i
$499$	3.95687	+	3.95687i	0.177134	+	0.177134i	0.790105	−	0.612971i	$-0.210026\pi$
$499$	3.95687	+	3.95687i	0.177134	+	0.177134i	−0.612971	+	0.790105i	$0.710026\pi$
$500$	8.49425	−	15.8697i	0.379874	−	0.709715i
$501$	26.7279	+	26.7279i	1.19412	+	1.19412i
$502$	−20.6071	−	15.2924i	−0.919739	−	0.682534i
$503$			23.3436i			1.04084i	0.853911	+	0.520419i	$0.174224\pi$
$503$			23.3436i			1.04084i	−0.853911	+	0.520419i	$0.825776\pi$
$504$	16.3075	+	34.5563i	0.726396	+	1.53926i
$505$	7.65685	+	7.65685i	0.340726	+	0.340726i
$506$	9.07269	−	1.34315i	0.403330	−	0.0597101i
$507$	13.9897	+	33.5752i	0.621303	+	1.49113i
$508$	10.6777	+	35.2724i	0.473745	+	1.56496i
$509$	8.34315	−	8.34315i	0.369803	−	0.369803i	−0.497602	−	0.867405i	$-0.665786\pi$
$509$	8.34315	−	8.34315i	0.369803	−	0.369803i	0.867405	+	0.497602i	$0.165786\pi$
$510$	22.8137	−	3.37740i	1.01021	−	0.149554i
$511$	−38.2110			−1.69035
$512$	−19.4382	+	11.5827i	−0.859054	+	0.511886i
$513$	−8.38478	+	8.38478i	−0.370197	+	0.370197i
$514$	−0.553578	+	0.745967i	−0.0244173	+	0.0329032i
$515$	3.47682	−	3.47682i	0.153207	−	0.153207i
$516$	27.3995	−	8.29438i	1.20620	−	0.365140i
$517$		−	4.58579i		−	0.201683i
$518$	8.44219	+	6.26491i	0.370929	+	0.275264i
$519$	34.6518			1.52104
$520$	6.07648	+	8.19002i	0.266471	+	0.359156i
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	−3.21215	−	2.38372i	−0.140592	−	0.104333i
$523$		−	14.8674i		−	0.650106i	−0.945696	−	0.325053i	$-0.894618\pi$
$523$		−	14.8674i		−	0.650106i	0.945696	−	0.325053i	$-0.105382\pi$
$524$	−20.5044	+	6.20711i	−0.895741	+	0.271159i
$525$	−22.1421	+	22.1421i	−0.966362	+	0.966362i
$526$	−7.47863	+	10.0777i	−0.326084	+	0.439409i
$527$	−23.0624	+	23.0624i	−1.00461	+	1.00461i
$528$	17.9866	+	3.59922i	0.782765	+	0.156636i
$529$	−7.34315			−0.319267
$530$	−0.339446	+	0.0502525i	−0.0147446	+	0.00218283i
$531$	−11.1917	+	11.1917i	−0.485680	+	0.485680i
$532$	−3.75803	−	12.4142i	−0.162931	−	0.538224i
$533$	−12.0000	+	18.0000i	−0.519778	+	0.779667i
$534$	34.5563	−	5.11582i	1.49540	−	0.221383i
$535$	−7.23486	−	7.23486i	−0.312790	−	0.312790i
$536$	10.1213	−	4.77637i	0.437174	−	0.206308i
$537$		−	20.7990i		−	0.897543i
$538$	9.24674	+	6.86196i	0.398655	+	0.295840i
$539$	0.960099	+	0.960099i	0.0413544	+	0.0413544i
$540$	−4.82834	+	9.02072i	−0.207778	+	0.388190i
$541$	16.1213	+	16.1213i	0.693110	+	0.693110i	0.962915	−	0.269805i	$-0.0869593\pi$
$541$	16.1213	+	16.1213i	0.693110	+	0.693110i	−0.269805	+	0.962915i	$0.586959\pi$
$542$	26.0563	−	3.85745i	1.11922	−	0.165692i
$543$	31.9362			1.37051
$544$	1.66504	−	32.9285i	0.0713879	−	1.41180i
$545$		−	6.65685i		−	0.285148i
$546$	−13.4763	−	37.5737i	−0.576731	−	1.60801i
$547$		−	14.3873i		−	0.615159i	−0.951522	−	0.307579i	$-0.900481\pi$
$547$		−	14.3873i		−	0.615159i	0.951522	−	0.307579i	$-0.0995189\pi$
$548$	−11.5547	+	21.5875i	−0.493591	+	0.922171i
$549$	−4.00000			−0.170716
$550$	1.35778	+	9.17157i	0.0578961	+	0.391077i
$551$	0.960099	+	0.960099i	0.0409016	+	0.0409016i
$552$	29.4741	+	10.5746i	1.25450	+	0.450087i
$553$	−18.8995	−	18.8995i	−0.803688	−	0.803688i
$554$	−5.05663	+	6.81399i	−0.214836	+	0.289499i
$555$			7.43370i			0.315543i
$556$	−41.9278	+	12.6924i	−1.77814	+	0.538277i
$557$	−8.36396	−	8.36396i	−0.354392	−	0.354392i	0.507349	−	0.861741i	$-0.330626\pi$
$557$	−8.36396	−	8.36396i	−0.354392	−	0.354392i	−0.861741	+	0.507349i	$0.830626\pi$
$558$	−5.59587	−	37.7990i	−0.236892	−	1.60016i
$559$	−18.0871	+	3.61743i	−0.765005	+	0.153001i
$560$	−6.20711	−	9.31271i	−0.262298	−	0.393534i
$561$	−18.8995	+	18.8995i	−0.797937	+	0.797937i
$562$	2.27208	+	15.3474i	0.0958418	+	0.647393i
$563$	28.4594			1.19942			0.599710	−	0.800218i	$-0.295283\pi$
$563$	28.4594			1.19942			0.599710	+	0.800218i	$0.295283\pi$
$564$	7.38851	−	13.8039i	0.311113	−	0.581248i
$565$	−10.8284	+	10.8284i	−0.455555	+	0.455555i
$566$	−1.54199	−	1.14430i	−0.0648146	−	0.0480986i
$567$	−0.339446	+	0.339446i	−0.0142554	+	0.0142554i
$568$	19.0147	−	8.97327i	0.797840	−	0.376510i
$569$			29.4853i			1.23609i	0.786144	+	0.618044i	$0.212075\pi$
$569$			29.4853i			1.23609i	−0.786144	+	0.618044i	$0.787925\pi$
$570$	5.46561	−	7.36511i	0.228929	−	0.308490i
$571$	−11.6718			−0.488449			−0.244224	−	0.969719i	$-0.578533\pi$
$571$	−11.6718			−0.488449			−0.244224	+	0.969719i	$0.578533\pi$
$572$	−11.3116	−	3.42552i	−0.472963	−	0.143228i
$573$	67.2132			2.80787
$574$	14.1481	−	19.0651i	0.590531	−	0.795761i
$575$			15.8275i			0.660052i
$576$	29.8172	+	24.5563i	1.24238	+	1.02318i
$577$	−0.485281	+	0.485281i	−0.0202025	+	0.0202025i	−0.717136	−	0.696933i	$-0.754547\pi$
$577$	−0.485281	+	0.485281i	−0.0202025	+	0.0202025i	0.696933	+	0.717136i	$0.254547\pi$
$578$	19.2729	+	14.3023i	0.801646	+	0.594898i
$579$	16.9864	−	16.9864i	0.705932	−	0.705932i
$580$	1.03292	+	0.552869i	0.0428896	+	0.0229566i
$581$	−26.7279			−1.10886
$582$	−0.339446	−	2.29289i	−0.0140705	−	0.0950435i
$583$	0.281206	−	0.281206i	0.0116464	−	0.0116464i
$584$	−34.9330	+	16.4853i	−1.44554	+	0.682166i
$585$	9.65685	−	14.4853i	0.399262	−	0.598893i
$586$	5.62132	+	37.9709i	0.232215	+	1.56856i
$587$	−25.1814	−	25.1814i	−1.03935	−	1.03935i	−0.999194	−	0.0401538i	$-0.987215\pi$
$587$	−25.1814	−	25.1814i	−1.03935	−	1.03935i	−0.0401538	−	0.999194i	$-0.512785\pi$
$588$	1.34315	+	4.43692i	0.0553904	+	0.182976i
$589$			12.9706i			0.534443i
$590$	2.76259	−	3.72269i	0.113734	−	0.153261i
$591$	−52.0600	−	52.0600i	−2.14146	−	2.14146i
$592$	10.4208	+	2.08527i	0.428293	+	0.0857040i
$593$	−1.44365	−	1.44365i	−0.0592836	−	0.0592836i	0.676843	−	0.736127i	$-0.263347\pi$
$593$	−1.44365	−	1.44365i	−0.0592836	−	0.0592836i	−0.736127	+	0.676843i	$0.763347\pi$
$594$	−1.73654	−	11.7300i	−0.0712513	−	0.481289i
$595$	16.3075			0.668544
$596$	−16.1722	−	8.65618i	−0.662441	−	0.354571i
$597$		−	46.1838i		−	1.89018i
$598$	−18.2456	−	8.61258i	−0.746118	−	0.352195i
$599$			13.9073i			0.568237i	0.958789	+	0.284118i	$0.0917009\pi$
$599$			13.9073i			0.568237i	−0.958789	+	0.284118i	$0.908299\pi$
$600$	−10.6899	+	29.7954i	−0.436413	+	1.21639i
$601$	15.9706			0.651453			0.325726	−	0.945464i	$-0.394391\pi$
$601$	15.9706			0.651453			0.325726	+	0.945464i	$0.394391\pi$
$602$	20.0244	−	2.96447i	0.816133	−	0.120823i
$603$	−13.5096	−	13.5096i	−0.550154	−	0.550154i
$604$	−3.24065	−	1.73456i	−0.131860	−	0.0705782i
$605$	−5.87868	−	5.87868i	−0.239002	−	0.239002i
$606$	−34.4075	−	25.5336i	−1.39771	−	1.03723i
$607$			25.0990i			1.01874i	0.860548	+	0.509369i	$0.170121\pi$
$607$			25.0990i			1.01874i	−0.860548	+	0.509369i	$0.829879\pi$
$608$	−8.79148	−	9.72792i	−0.356542	−	0.394519i
$609$	−3.24264	−	3.24264i	−0.131398	−	0.131398i
$610$	1.15894	−	0.171573i	0.0469242	−	0.00694678i
$611$	−5.59587	+	8.39380i	−0.226384	+	0.339577i
$612$	−53.8701	+	16.3075i	−2.17757	+	0.659193i
$613$	30.8701	−	30.8701i	1.24683	−	1.24683i	0.289718	−	0.957112i	$-0.406439\pi$
$613$	30.8701	−	30.8701i	1.24683	−	1.24683i	0.957112	−	0.289718i	$-0.0935614\pi$
$614$	−37.7990	+	5.59587i	−1.52544	+	0.225831i
$615$	16.7876			0.676941
$616$	12.2086	+	4.38016i	0.491898	+	0.176482i
$617$	−24.4853	+	24.4853i	−0.985740	+	0.985740i	−0.999900	−	0.0141594i	$-0.995493\pi$
$617$	−24.4853	+	24.4853i	−0.985740	+	0.985740i	0.0141594	+	0.999900i	$0.495493\pi$
$618$	−11.5943	+	15.6238i	−0.466392	+	0.628480i
$619$	21.1422	−	21.1422i	0.849775	−	0.849775i	−0.140330	−	0.990105i	$-0.544816\pi$
$619$	21.1422	−	21.1422i	0.849775	−	0.849775i	0.990105	+	0.140330i	$0.0448163\pi$
$620$	3.24264	+	10.7117i	0.130228	+	0.430191i
$621$		−	20.2426i		−	0.812309i
$622$	25.8718	+	19.1993i	1.03736	+	0.769822i
$623$	24.7013			0.989638
$624$	−28.5305	−	28.5363i	−1.14213	−	1.14237i
$625$	−11.0000			−0.440000
$626$	15.3148	+	11.3650i	0.612101	+	0.454237i
$627$			10.6293i			0.424494i
$628$	6.95365	+	22.9706i	0.277481	+	0.916625i
$629$	−10.9497	+	10.9497i	−0.436595	+	0.436595i
$630$	−11.3855	+	15.3424i	−0.453610	+	0.611256i
$631$	−1.97844	+	1.97844i	−0.0787603	+	0.0787603i	−0.745390	−	0.666629i	$-0.767736\pi$
$631$	−1.97844	+	1.97844i	−0.0787603	+	0.0787603i	0.666629	+	0.745390i	$0.267736\pi$
$632$	−25.4319	−	9.12440i	−1.01163	−	0.362949i
$633$	27.2843			1.08445
$634$	8.59264	−	1.27208i	0.341257	−	0.0505207i
$635$	−13.0296	+	13.0296i	−0.517062	+	0.517062i
$636$	1.29954	−	0.393398i	0.0515303	−	0.0155993i
$637$	−0.585786	−	2.92893i	−0.0232097	−	0.116049i
$638$	−1.34315	+	0.198843i	−0.0531756	+	0.00787227i
$639$	−25.3802	−	25.3802i	−1.00403	−	1.00403i
$640$	−9.69239	−	5.83589i	−0.383125	−	0.230684i
$641$		−	38.1421i		−	1.50652i	−0.657721	−	0.753262i	$-0.728479\pi$
$641$		−	38.1421i		−	1.50652i	0.657721	−	0.753262i	$-0.271521\pi$
$642$	32.5112	+	24.1264i	1.28311	+	0.952192i
$643$	17.2676	+	17.2676i	0.680969	+	0.680969i	0.960219	−	0.279249i	$-0.0900856\pi$
$643$	17.2676	+	17.2676i	0.680969	+	0.680969i	−0.279249	+	0.960219i	$0.590086\pi$
$644$	19.5216	+	10.4489i	0.769260	+	0.411746i
$645$	10.1213	+	10.1213i	0.398527	+	0.398527i
$646$	18.8995	−	2.79793i	0.743591	−	0.110083i
$647$	−33.5752			−1.31998			−0.659988	−	0.751276i	$-0.729439\pi$
$647$	−33.5752			−1.31998			−0.659988	+	0.751276i	$0.729439\pi$
$648$	−0.163880	+	0.456773i	−0.00643780	+	0.0179437i
$649$			5.37258i			0.210892i
$650$	8.70645	−	18.4445i	0.341495	−	0.723451i
$651$		−	43.8068i		−	1.71692i
$652$	−26.7116	−	14.2973i	−1.04611	−	0.559927i
$653$	−14.8284			−0.580281			−0.290141	−	0.956984i	$-0.593702\pi$
$653$	−14.8284			−0.580281			−0.290141	+	0.956984i	$0.593702\pi$
$654$	3.85745	+	26.0563i	0.150838	+	1.01888i
$655$	−7.57430	−	7.57430i	−0.295952	−	0.295952i
$656$	4.70918	−	23.5335i	0.183863	−	0.918827i
$657$	46.6274	+	46.6274i	1.81911	+	1.81911i
$658$	6.59758	−	8.89047i	0.257200	−	0.346587i
$659$		−	34.5353i		−	1.34530i	−0.739959	−	0.672652i	$-0.765155\pi$
$659$		−	34.5353i		−	1.34530i	0.739959	−	0.672652i	$-0.234845\pi$
$660$	2.65733	+	8.77817i	0.103436	+	0.341690i
$661$	−31.0711	−	31.0711i	−1.20852	−	1.20852i	−0.971505	−	0.237020i	$-0.923829\pi$
$661$	−31.0711	−	31.0711i	−1.20852	−	1.20852i	−0.237020	−	0.971505i	$-0.576171\pi$
$662$	−4.29632	−	29.0208i	−0.166981	−	1.12793i
$663$	57.6559	−	11.5312i	2.23917	−	0.447834i
$664$	−24.4350	+	11.5312i	−0.948263	+	0.447496i
$665$	4.58579	−	4.58579i	0.177829	−	0.177829i
$666$	−2.65685	−	17.9465i	−0.102951	−	0.695414i
$667$	−2.31788			−0.0897488
$668$	23.8215	+	12.7504i	0.921682	+	0.493330i
$669$	−49.8198	+	49.8198i	−1.92614	+	1.92614i
$670$	4.49368	+	3.33474i	0.173606	+	0.128832i
$671$	−0.960099	+	0.960099i	−0.0370642	+	0.0370642i
$672$	29.6924	+	32.8551i	1.14541	+	1.26741i
$673$			42.7990i			1.64978i	0.565293	+	0.824890i	$0.308763\pi$
$673$			42.7990i			1.64978i	−0.565293	+	0.824890i	$0.691237\pi$
$674$	−6.88677	+	9.28017i	−0.265269	+	0.357459i
$675$	20.4633			0.787631
$676$	16.5247	+	20.0732i	0.635566	+	0.772046i
$677$	−31.2132			−1.19962			−0.599810	−	0.800142i	$-0.704757\pi$
$677$	−31.2132			−1.19962			−0.599810	+	0.800142i	$0.704757\pi$
$678$	36.1100	−	48.6595i	1.38680	−	1.86876i
$679$		−	1.63899i		−	0.0628987i
$680$	14.9086	−	7.03553i	0.571718	−	0.269800i
$681$	35.8995	−	35.8995i	1.37567	−	1.37567i
$682$	−10.4158	−	7.72954i	−0.398843	−	0.295980i
$683$	31.4562	−	31.4562i	1.20364	−	1.20364i	0.230584	−	0.973052i	$-0.425936\pi$
$683$	31.4562	−	31.4562i	1.20364	−	1.20364i	0.973052	−	0.230584i	$-0.0740635\pi$
$684$	−10.5628	+	19.7344i	−0.403879	+	0.754563i
$685$	−12.2426			−0.467767
$686$	−3.57625	−	24.1569i	−0.136542	−	0.922313i
$687$	−41.1495	+	41.1495i	−1.56995	+	1.56995i
$688$	17.0276	−	11.3492i	0.649172	−	0.432686i
$689$	−0.857864	+	0.171573i	−0.0326820	+	0.00653641i
$690$	2.29289	+	15.4881i	0.0872890	+	0.589620i
$691$	2.31788	+	2.31788i	0.0881764	+	0.0881764i	0.749819	−	0.661643i	$-0.230140\pi$
$691$	2.31788	+	2.31788i	0.0881764	+	0.0881764i	−0.661643	+	0.749819i	$0.730140\pi$
$692$	23.7071	−	7.17662i	0.901209	−	0.272814i
$693$		−	22.1421i		−	0.841110i
$694$	7.88320	−	10.6229i	0.299242	−	0.403240i
$695$	−15.4881	−	15.4881i	−0.587495	−	0.587495i
$696$	−4.36343	−	1.56550i	−0.165395	−	0.0593401i
$697$	24.7279	+	24.7279i	0.936637	+	0.936637i
$698$	0.136039	+	0.918917i	0.00514915	+	0.0347815i
$699$	−33.4928			−1.26682
$700$	−10.5628	+	19.7344i	−0.399237	+	0.745890i
$701$		−	31.3553i		−	1.18427i	−0.805837	−	0.592137i	$-0.798284\pi$
$701$		−	31.3553i		−	1.18427i	0.805837	−	0.592137i	$-0.201716\pi$
$702$	−11.1351	+	23.5896i	−0.420269	+	0.890332i
$703$			6.15828i			0.232264i
$704$	13.0510	−	1.26272i	0.491877	−	0.0475907i
$705$	7.82843			0.294836
$706$	8.73324	−	1.29289i	0.328680	−	0.0486587i
$707$	−21.4234	−	21.4234i	−0.805708	−	0.805708i
$708$	−8.65618	+	16.1722i	−0.325319	+	0.607790i
$709$	−2.97056	−	2.97056i	−0.111562	−	0.111562i	0.649122	−	0.760684i	$-0.275136\pi$
$709$	−2.97056	−	2.97056i	−0.111562	−	0.111562i	−0.760684	+	0.649122i	$0.775136\pi$
$710$	8.44219	+	6.26491i	0.316830	+	0.235118i
$711$			46.1247i			1.72981i
$712$	22.5823	−	10.6569i	0.846308	−	0.399382i
$713$	−15.6569	−	15.6569i	−0.586354	−	0.586354i
$714$	−63.8312	+	9.44975i	−2.38882	+	0.353648i
$715$	−1.15894	−	5.79471i	−0.0433420	−	0.216710i
$716$	−4.30761	−	14.2297i	−0.160983	−	0.531788i
$717$	−23.0919	+	23.0919i	−0.862382	+	0.862382i
$718$	7.82843	−	1.15894i	0.292154	−	0.0432513i
$719$	17.0688			0.636559			0.318279	−	0.947997i	$-0.396895\pi$
$719$	17.0688			0.636559			0.318279	+	0.947997i	$0.396895\pi$
$720$	−3.78966	+	18.9383i	−0.141232	+	0.705787i
$721$	−9.72792	+	9.72792i	−0.362287	+	0.362287i
$722$	−11.4848	+	15.4762i	−0.427420	+	0.575964i
$723$	−36.5720	+	36.5720i	−1.36013	+	1.36013i
$724$	21.8492	−	6.61420i	0.812021	−	0.245815i
$725$		−	2.34315i		−	0.0870222i
$726$	26.4169	+	19.6039i	0.980424	+	0.727568i
$727$	43.1279			1.59953			0.799763	−	0.600316i	$-0.204958\pi$
$727$	43.1279			1.59953			0.799763	+	0.600316i	$0.204958\pi$
$728$	−17.0016	−	22.9151i	−0.630121	−	0.849291i
$729$	43.7696			1.62109
$730$	−15.5096	−	11.5096i	−0.574037	−	0.425990i
$731$			29.8172i			1.10283i
$732$	−4.43692	+	1.34315i	−0.163993	+	0.0496441i
$733$	−14.8492	+	14.8492i	−0.548469	+	0.548469i	−0.925998	−	0.377529i	$-0.876774\pi$
$733$	−14.8492	+	14.8492i	−0.548469	+	0.548469i	0.377529	+	0.925998i	$0.376774\pi$
$734$	−12.7668	+	17.2037i	−0.471232	+	0.635002i
$735$	−1.63899	+	1.63899i	−0.0604551	+	0.0604551i
$736$	22.3549	+	1.13038i	0.824013	+	0.0416664i
$737$	−6.48528			−0.238888
$738$	−40.5288	+	6.00000i	−1.49189	+	0.220863i
$739$	−37.5321	+	37.5321i	−1.38064	+	1.38064i	−0.537157	+	0.843482i	$0.680502\pi$
$739$	−37.5321	+	37.5321i	−1.38064	+	1.38064i	−0.843482	+	0.537157i	$0.819498\pi$
$740$	1.53957	+	5.08579i	0.0565957	+	0.186957i
$741$	12.9706	−	19.4558i	0.476486	−	0.714728i
$742$	0.949747	−	0.140603i	0.0348663	−	0.00516171i
$743$	9.21329	+	9.21329i	0.338003	+	0.338003i	0.855615	−	0.517612i	$-0.173179\pi$
$743$	9.21329	+	9.21329i	0.338003	+	0.338003i	−0.517612	+	0.855615i	$0.673179\pi$
$744$	−18.8995	−	40.0488i	−0.692889	−	1.46826i
$745$		−	9.17157i		−	0.336020i
$746$	−34.7825	−	25.8119i	−1.27348	−	0.945042i
$747$	32.6151	+	32.6151i	1.19332	+	1.19332i
$748$	−9.01593	+	16.8444i	−0.329655	+	0.615891i
$749$	20.2426	+	20.2426i	0.739650	+	0.739650i
$750$	−35.2279	+	5.21524i	−1.28634	+	0.190434i
$751$	8.31143			0.303289			0.151644	−	0.988435i	$-0.451543\pi$
$751$	8.31143			0.303289			0.151644	+	0.988435i	$0.451543\pi$
$752$	2.19600	−	10.9742i	0.0800798	−	0.400187i
$753$			50.7696i			1.85015i
$754$	2.70113	+	1.27503i	0.0983693	+	0.0464339i
$755$		−	1.83783i		−	0.0668856i
$756$	13.5094	−	25.2394i	0.491331	−	0.917947i
$757$	44.7279			1.62566			0.812832	−	0.582498i	$-0.197925\pi$
$757$	44.7279			1.62566			0.812832	+	0.582498i	$0.197925\pi$
$758$	4.09748	+	27.6777i	0.148827	+	1.00530i
$759$	−12.8307	−	12.8307i	−0.465726	−	0.465726i
$760$	2.21395	−	6.17083i	0.0803084	−	0.223839i
$761$	−0.343146	−	0.343146i	−0.0124390	−	0.0124390i	0.700860	−	0.713299i	$-0.252800\pi$
$761$	−0.343146	−	0.343146i	−0.0124390	−	0.0124390i	−0.713299	+	0.700860i	$0.752800\pi$
$762$	43.4502	−	58.5508i	1.57404	−	2.12107i
$763$			18.6254i			0.674286i
$764$	45.9841	−	13.9203i	1.66365	−	0.503619i
$765$	−19.8995	−	19.8995i	−0.719468	−	0.719468i
$766$	3.37740	+	22.8137i	0.122031	+	0.824293i
$767$	6.55596	−	9.83395i	0.236722	−	0.355083i
$768$	41.3198	+	17.2265i	1.49100	+	0.621606i
$769$	−1.65685	+	1.65685i	−0.0597477	+	0.0597477i	−0.736349	−	0.676602i	$-0.763452\pi$
$769$	−1.65685	+	1.65685i	−0.0597477	+	0.0597477i	0.676602	+	0.736349i	$0.263452\pi$
$770$	0.949747	+	6.41536i	0.0342265	+	0.231194i
$771$	1.83783			0.0661880
$772$	8.10331	−	15.1393i	0.291645	−	0.544876i
$773$	32.1213	−	32.1213i	1.15532	−	1.15532i	0.169854	−	0.985469i	$-0.445670\pi$
$773$	32.1213	−	32.1213i	1.15532	−	1.15532i	0.985469	−	0.169854i	$-0.0543298\pi$
$774$	−28.0525	−	20.8176i	−1.00832	−	0.748273i
$775$	15.8275	−	15.8275i	0.568540	−	0.568540i
$776$	−0.707107	−	1.49839i	−0.0253837	−	0.0537890i
$777$		−	20.7990i		−	0.746160i
$778$	18.6608	−	25.1461i	0.669021	−	0.901530i
$779$	13.9073			0.498281
$780$	5.84772	−	19.3102i	0.209382	−	0.691415i
$781$	−12.1838			−0.435969
$782$	−19.4363	+	26.1911i	−0.695041	+	0.936592i
$783$			2.99678i			0.107096i
$784$	1.83783	+	2.75736i	0.0656369	+	0.0984771i
$785$	−8.48528	+	8.48528i	−0.302853	+	0.302853i
$786$	34.0365	+	25.2584i	1.21404	+	0.900936i
$787$	18.4266	−	18.4266i	0.656837	−	0.656837i	−0.297793	−	0.954630i	$-0.596251\pi$
$787$	18.4266	−	18.4266i	0.656837	−	0.656837i	0.954630	+	0.297793i	$0.0962507\pi$
$788$	−46.3990	−	24.8350i	−1.65290	−	0.884711i
$789$	24.8284			0.883915
$790$	−1.97844	−	13.3640i	−0.0703896	−	0.475468i
$791$	30.2972	−	30.2972i	1.07724	−	1.07724i
$792$	−9.55274	−	20.2426i	−0.339442	−	0.719291i
$793$	2.92893	−	0.585786i	0.104009	−	0.0208019i
$794$	0.443651	+	2.99678i	0.0157446	+	0.106352i
$795$	0.480049	+	0.480049i	0.0170256	+	0.0170256i
$796$	−9.56497	−	31.5968i	−0.339021	−	1.11992i
$797$			31.1716i			1.10415i	0.833793	+	0.552077i	$0.186165\pi$
$797$			31.1716i			1.10415i	−0.833793	+	0.552077i	$0.813835\pi$
$798$	−15.2924	+	20.6071i	−0.541346	+	0.729483i
$799$	11.5312	+	11.5312i	0.407944	+	0.407944i
$800$	−1.14270	+	22.5985i	−0.0404006	+	0.798979i
$801$	−30.1421	−	30.1421i	−1.06502	−	1.06502i
$802$	−5.70711	−	38.5504i	−0.201525	−	1.36126i
$803$	22.3835			0.789895
$804$	−19.5216	−	10.4489i	−0.688475	−	0.368506i
$805$			11.0711i			0.390204i
$806$	9.63301	+	26.8582i	0.339308	+	0.946039i
$807$		−	22.7811i		−	0.801934i
$808$	−28.8282	−	10.3429i	−1.01417	−	0.363862i
$809$	−6.85786			−0.241110			−0.120555	−	0.992707i	$-0.538467\pi$
$809$	−6.85786			−0.241110			−0.120555	+	0.992707i	$0.538467\pi$
$810$	−0.240025	+	0.0355339i	−0.00843361	+	0.00124853i
$811$	6.55596	+	6.55596i	0.230211	+	0.230211i	0.812781	−	0.582570i	$-0.197953\pi$
$811$	6.55596	+	6.55596i	0.230211	+	0.230211i	−0.582570	+	0.812781i	$0.697953\pi$
$812$	−2.89003	−	1.54689i	−0.101420	−	0.0542852i
$813$	−36.8492	−	36.8492i	−1.29236	−	1.29236i
$814$	−4.94532	−	3.66990i	−0.173333	−	0.128630i
$815$		−	15.1486i		−	0.530632i
$816$	−54.2785	+	36.1777i	−1.90013	+	1.26647i
$817$	8.38478	+	8.38478i	0.293346	+	0.293346i
$818$	−10.1734	+	1.50610i	−0.355704	+	0.0526594i
$819$	−27.0192	+	40.5288i	−0.944128	+	1.41619i
$820$	11.4853	−	3.47682i	0.401083	−	0.121416i
$821$	−2.22183	+	2.22183i	−0.0775422	+	0.0775422i	−0.744814	−	0.667272i	$-0.767462\pi$
$821$	−2.22183	+	2.22183i	−0.0775422	+	0.0775422i	0.667272	+	0.744814i	$0.267462\pi$
$822$	47.9203	−	7.09425i	1.67141	−	0.247440i
$823$	−54.0385			−1.88366			−0.941831	−	0.336087i	$-0.890897\pi$
$823$	−54.0385			−1.88366			−0.941831	+	0.336087i	$0.890897\pi$
$824$	−4.69650	+	13.0903i	−0.163610	+	0.456022i
$825$	12.9706	−	12.9706i	0.451577	−	0.451577i
$826$	−7.72954	+	10.4158i	−0.268945	+	0.362413i
$827$	−32.3339	+	32.3339i	−1.12436	+	1.12436i	−0.133281	+	0.991078i	$0.542551\pi$
$827$	−32.3339	+	32.3339i	−1.12436	+	1.12436i	−0.991078	+	0.133281i	$0.957449\pi$
$828$	−11.0711	−	36.5720i	−0.384746	−	1.27096i
$829$			22.3848i			0.777455i	0.921353	+	0.388728i	$0.127085\pi$
$829$			22.3848i			0.777455i	−0.921353	+	0.388728i	$0.872915\pi$
$830$	−10.8487	−	8.05078i	−0.376564	−	0.279447i
$831$	16.7876			0.582355
$832$	−25.4293	−	13.6143i	−0.881603	−	0.471993i
$833$	−4.82843			−0.167295
$834$	69.5984	+	51.6487i	2.41000	+	1.78845i
$835$			13.5096i			0.467519i
$836$	2.20140	+	7.27208i	0.0761371	+	0.251510i
$837$	−20.2426	+	20.2426i	−0.699688	+	0.699688i
$838$	4.31147	−	5.80985i	0.148937	−	0.200698i
$839$	−24.0225	+	24.0225i	−0.829347	+	0.829347i	−0.987426	−	0.158079i	$-0.949470\pi$
$839$	−24.0225	+	24.0225i	−0.829347	+	0.829347i	0.158079	+	0.987426i	$0.449470\pi$
$840$	−7.47741	+	20.8414i	−0.257995	+	0.719095i
$841$	−28.6569			−0.988167
$842$	−0.0411817	+	0.00609665i	−0.00141922	+	0.000210105i
$843$	21.7046	−	21.7046i	0.747545	−	0.747545i
$844$	18.6666	−	5.65076i	0.642531	−	0.194507i
$845$	−4.94975	+	12.0208i	−0.170276	+	0.413529i
$846$	−18.8995	+	2.79793i	−0.649778	+	0.0961949i
$847$	16.4481	+	16.4481i	0.565165	+	0.565165i
$848$	0.807612	−	0.538289i	0.0277335	−	0.0184849i
$849$			3.79899i			0.130381i
$850$	−26.4766	−	19.6481i	−0.908139	−	0.673926i
$851$	−7.43370	−	7.43370i	−0.254824	−	0.254824i
$852$	−36.6749	−	19.6302i	−1.25646	−	0.672520i
$853$	−39.5772	−	39.5772i	−1.35510	−	1.35510i	−0.879856	−	0.475240i	$-0.842361\pi$
$853$	−39.5772	−	39.5772i	−1.35510	−	1.35510i	−0.475240	−	0.879856i	$-0.657639\pi$
$854$	−3.24264	+	0.480049i	−0.110961	+	0.0164270i
$855$	−11.1917			−0.382749
$856$	27.2393	+	9.77285i	0.931022	+	0.334029i
$857$		−	30.1421i		−	1.02964i	−0.857300	−	0.514818i	$-0.827860\pi$
$857$		−	30.1421i		−	1.02964i	0.857300	−	0.514818i	$-0.172140\pi$
$858$	7.89421	+	22.0102i	0.269504	+	0.751414i
$859$			35.3307i			1.20547i	0.797943	+	0.602733i	$0.205922\pi$
$859$			35.3307i			1.20547i	−0.797943	+	0.602733i	$0.794078\pi$
$860$	9.02072	+	4.82834i	0.307604	+	0.164645i
$861$	−46.9706			−1.60075
$862$	−7.61548	−	51.4411i	−0.259384	−	1.75209i
$863$	−25.3220	−	25.3220i	−0.861971	−	0.861971i	0.129596	−	0.991567i	$-0.458632\pi$
$863$	−25.3220	−	25.3220i	−0.861971	−	0.861971i	−0.991567	+	0.129596i	$0.958632\pi$
$864$	1.46146	−	28.9025i	0.0497199	−	0.983283i
$865$	8.75736	+	8.75736i	0.297759	+	0.297759i
$866$	−8.16333	+	11.0004i	−0.277401	+	0.373808i
$867$		−	47.4825i		−	1.61259i
$868$	−9.07269	−	29.9706i	−0.307947	−	1.01727i
$869$	11.0711	+	11.0711i	0.375560	+	0.375560i
$870$	−0.339446	−	2.29289i	−0.0115083	−	0.0777364i
$871$	11.8706	+	7.91375i	0.402221	+	0.268147i
$872$	8.03553	+	17.0276i	0.272118	+	0.576628i
$873$	−2.00000	+	2.00000i	−0.0676897	+	0.0676897i
$874$	1.89949	+	12.8307i	0.0642514	+	0.434006i
$875$	−25.1814			−0.851286
$876$	67.3774	+	36.0637i	2.27647	+	1.21848i
$877$	14.2635	−	14.2635i	0.481643	−	0.481643i	−0.424013	−	0.905656i	$-0.639379\pi$
$877$	14.2635	−	14.2635i	0.481643	−	0.481643i	0.905656	+	0.424013i	$0.139379\pi$
$878$	26.9621	+	20.0085i	0.909927	+	0.675253i
$879$	53.6990	−	53.6990i	1.81122	−	1.81122i
$880$	3.63604	+	5.45526i	0.122571	+	0.183897i
$881$			12.3137i			0.414859i	0.978250	+	0.207430i	$0.0665098\pi$
$881$			12.3137i			0.414859i	−0.978250	+	0.207430i	$0.933490\pi$
$882$	3.37109	−	4.54266i	0.113510	−	0.152959i
$883$	−34.4529			−1.15943			−0.579717	−	0.814818i	$-0.696837\pi$
$883$	−34.4529			−1.15943			−0.579717	+	0.814818i	$0.696837\pi$
$884$	37.0573	−	19.8300i	1.24637	−	0.666955i
$885$	−9.17157			−0.308299
$886$	−23.1756	+	31.2300i	−0.778600	+	1.04919i
$887$		−	46.5224i		−	1.56207i	−0.624488	−	0.781035i	$-0.714692\pi$
$887$		−	46.5224i		−	1.56207i	0.624488	−	0.781035i	$-0.285308\pi$
$888$	−8.97327	−	19.0147i	−0.301123	−	0.638092i
$889$	36.4558	−	36.4558i	1.22269	−	1.22269i
$890$	10.0261	+	7.44035i	0.336077	+	0.249401i
$891$	0.198843	−	0.198843i	0.00666149	−	0.00666149i
$892$	−23.7663	+	44.4024i	−0.795756	+	1.48670i
$893$	6.48528			0.217022
$894$	5.31466	+	35.8995i	0.177749	+	1.20066i
$895$	5.25642	−	5.25642i	0.175703	−	0.175703i
$896$	27.1186	+	16.3284i	0.905970	+	0.545494i
$897$	7.82843	+	39.1421i	0.261384	+	1.30692i
$898$	−0.0796898	−	0.538289i	−0.00265928	−	0.0179629i
$899$	2.31788	+	2.31788i	0.0773057	+	0.0773057i
$900$	36.9706	−	11.1917i	1.23235	−	0.373058i
$901$			1.41421i			0.0471143i
$902$	−8.28777	+	11.1681i	−0.275953	+	0.371856i
$903$	−28.3188	−	28.3188i	−0.942390	−	0.942390i
$904$	14.6271	−	40.7692i	0.486489	−	1.35596i
$905$	8.07107	+	8.07107i	0.268291	+	0.268291i
$906$	1.06497	+	7.19367i	0.0353813	+	0.238994i
$907$	16.3075			0.541483			0.270742	−	0.962652i	$-0.412731\pi$
$907$	16.3075			0.541483			0.270742	+	0.962652i	$0.412731\pi$
$908$	17.1257	−	31.9958i	0.568337	−	1.06182i
$909$			52.2843i			1.73416i
$910$	6.09001	−	12.9016i	0.201882	−	0.427683i
$911$		−	4.91697i		−	0.162907i	−0.996677	−	0.0814533i	$-0.974044\pi$
$911$		−	4.91697i		−	0.162907i	0.996677	−	0.0814533i	$-0.0259561\pi$
$912$	−5.09006	+	25.4368i	−0.168549	+	0.842298i
$913$	15.6569			0.518166
$914$	−6.75481	+	1.00000i	−0.223429	+	0.0330771i
$915$	−1.63899	−	1.63899i	−0.0541834	−	0.0541834i
$916$	−19.6302	+	36.6749i	−0.648600	+	1.21177i
$917$	21.1924	+	21.1924i	0.699834	+	0.699834i
$918$	33.8623	+	25.1291i	1.11762	+	0.829383i
$919$			25.6614i			0.846493i	0.906015	+	0.423246i	$0.139110\pi$
$919$			25.6614i			0.846493i	−0.906015	+	0.423246i	$0.860890\pi$
$920$	4.77637	+	10.1213i	0.157472	+	0.333690i
$921$	53.4558	+	53.4558i	1.76143	+	1.76143i
$922$	−26.7792	+	3.96447i	−0.881926	+	0.130563i
$923$	22.3011	+	14.8674i	0.734050	+	0.489366i
$924$	−7.43503	−	24.5607i	−0.244594	−	0.807989i
$925$	7.51472	−	7.51472i	0.247082	−	0.247082i
$926$	−31.8701	+	4.71813i	−1.04732	+	0.155047i
$927$	23.7412			0.779765
$928$	−3.30948	−	0.167345i	−0.108639	−	0.00549336i
$929$	20.6274	−	20.6274i	0.676764	−	0.676764i	−0.282503	−	0.959266i	$-0.591165\pi$
$929$	20.6274	−	20.6274i	0.676764	−	0.676764i	0.959266	+	0.282503i	$0.0911647\pi$
$930$	13.1952	−	17.7809i	0.432686	−	0.583060i
$931$	−1.35778	+	1.35778i	−0.0444996	+	0.0444996i
$932$	−22.9142	+	6.93659i	−0.750580	+	0.227216i
$933$		−	63.7401i		−	2.08676i
$934$	−7.89702	−	5.86034i	−0.258398	−	0.191756i
$935$	−9.55274			−0.312408
$936$	−7.21606	+	48.7089i	−0.235864	+	1.59210i
$937$	−8.97056			−0.293056			−0.146528	−	0.989207i	$-0.546810\pi$
$937$	−8.97056			−0.293056			−0.146528	+	0.989207i	$0.546810\pi$
$938$	−12.5730	−	9.33039i	−0.410524	−	0.304648i
$939$		−	37.7309i		−	1.23130i
$940$	5.35584	−	1.62132i	0.174688	−	0.0528816i
$941$	34.2635	−	34.2635i	1.11696	−	1.11696i	0.124771	−	0.992186i	$-0.460180\pi$
$941$	34.2635	−	34.2635i	1.11696	−	1.11696i	0.992186	−	0.124771i	$-0.0398197\pi$
$942$	28.2962	−	38.1302i	0.921941	−	1.24235i
$943$	−16.7876	+	16.7876i	−0.546679	+	0.546679i
$944$	−2.57277	+	12.8570i	−0.0837365	+	0.418461i
$945$	14.3137			0.465625
$946$	−11.7300	+	1.73654i	−0.381376	+	0.0564599i
$947$	−3.07914	+	3.07914i	−0.100059	+	0.100059i	−0.755364	−	0.655305i	$-0.772540\pi$
$947$	−3.07914	+	3.07914i	−0.100059	+	0.100059i	0.655305	+	0.755364i	$0.272540\pi$
$948$	15.4881	+	51.1630i	0.503029	+	1.66170i
$949$	−40.9706	−	27.3137i	−1.32996	−	0.886640i
$950$	−12.9706	+	1.92020i	−0.420821	+	0.0622994i
$951$	−12.1518	−	12.1518i	−0.394050	−	0.394050i
$952$	−41.7132	+	19.6850i	−1.35193	+	0.637993i
$953$			51.1421i			1.65666i	0.560243	+	0.828328i	$0.310708\pi$
$953$			51.1421i			1.65666i	−0.560243	+	0.828328i	$0.689292\pi$
$954$	−1.33051	−	0.987369i	−0.0430770	−	0.0319672i
$955$	16.9864	+	16.9864i	0.549668	+	0.549668i
$956$	−11.0159	+	20.5809i	−0.356279	+	0.665633i
$957$	1.89949	+	1.89949i	0.0614020	+	0.0614020i
$958$	−14.9853	+	2.21846i	−0.484152	+	0.0716752i
$959$	34.2541			1.10612
$960$	2.15561	+	22.2794i	0.0695719	+	0.719065i
$961$			0.313708i			0.0101196i
$962$	4.57365	+	12.7520i	0.147460	+	0.411140i
$963$		−	49.4027i		−	1.59198i
$964$	−17.4465	+	32.5951i	−0.561914	+	1.04982i
$965$	8.58579			0.276386
$966$	−6.41536	−	43.3345i	−0.206411	−	1.39427i
$967$	7.85551	+	7.85551i	0.252616	+	0.252616i	0.822042	−	0.569426i	$-0.192835\pi$
$967$	7.85551	+	7.85551i	0.252616	+	0.252616i	−0.569426	+	0.822042i	$0.692835\pi$
$968$	22.1333	+	7.94093i	0.711392	+	0.255231i
$969$	−26.7279	−	26.7279i	−0.858625	−	0.858625i
$970$	0.493684	−	0.665257i	0.0158513	−	0.0213601i
$971$		−	0.877735i		−	0.0281679i	−0.999901	−	0.0140839i	$-0.995517\pi$
$971$		−	0.877735i		−	0.0281679i	0.999901	−	0.0140839i	$-0.00448320\pi$
$972$	30.2972	−	9.17157i	0.971783	−	0.294178i
$973$	43.3345	+	43.3345i	1.38924	+	1.38924i
$974$	−1.83783	−	12.4142i	−0.0588880	−	0.397777i
$975$	−39.5687	+	7.91375i	−1.26721	+	0.253443i
$976$	−2.75736	+	1.83783i	−0.0882609	+	0.0588276i
$977$	35.6274	−	35.6274i	1.13982	−	1.13982i	0.151340	−	0.988482i	$-0.451641\pi$
$977$	35.6274	−	35.6274i	1.13982	−	1.13982i	0.988482	−	0.151340i	$-0.0483589\pi$
$978$	8.77817	+	59.2949i	0.280695	+	1.89604i
$979$	−14.4697			−0.462454
$980$	−0.781874	+	1.46077i	−0.0249761	+	0.0466625i
$981$	22.7279	−	22.7279i	0.725647	−	0.725647i
$982$	3.17751	+	2.35802i	0.101399	+	0.0752474i
$983$	−31.3155	+	31.3155i	−0.998811	+	0.998811i	−0.999999	−	0.00118842i	$-0.999622\pi$
$983$	−31.3155	+	31.3155i	−0.998811	+	0.998811i	0.00118842	+	0.999999i	$0.499622\pi$
$984$	−42.9411	+	20.2644i	−1.36891	+	0.646006i
$985$		−	26.3137i		−	0.838424i
$986$	2.87740	−	3.87740i	0.0916352	−	0.123482i
$987$	−21.9034			−0.697193
$988$	4.84441	−	15.9971i	0.154121	−	0.508934i
$989$	−20.2426			−0.643679
$990$	6.66949	−	8.98737i	0.211970	−	0.285637i
$991$			21.4234i			0.680536i	0.940329	+	0.340268i	$0.110518\pi$
$991$			21.4234i			0.680536i	−0.940329	+	0.340268i	$0.889482\pi$
$992$	−21.2245	−	23.4853i	−0.673879	−	0.745658i
$993$	−41.0416	+	41.0416i	−1.30242	+	1.30242i
$994$	−23.6207	−	17.5288i	−0.749203	−	0.555980i
$995$	11.6718	−	11.6718i	0.370020	−	0.370020i
$996$	47.1294	+	25.2260i	1.49335	+	0.799315i
$997$	−17.0711			−0.540646			−0.270323	−	0.962770i	$-0.587131\pi$
$997$	−17.0711			−0.540646			−0.270323	+	0.962770i	$0.587131\pi$
$998$	−1.15894	−	7.82843i	−0.0366857	−	0.247805i
$999$	−9.61098	+	9.61098i	−0.304078	+	0.304078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.2.f.b.31.2	✓	8
3.2	odd	2		468.2.n.i.343.3		8
4.3	odd	2	inner	52.2.f.b.31.4	yes	8
8.3	odd	2		832.2.k.h.447.4		8
8.5	even	2		832.2.k.h.447.1		8
12.11	even	2		468.2.n.i.343.1		8
13.2	odd	12		676.2.l.h.319.3		16
13.3	even	3		676.2.l.l.19.4		16
13.4	even	6		676.2.l.h.587.4		16
13.5	odd	4		676.2.f.g.99.1		8
13.6	odd	12		676.2.l.h.427.4		16
13.7	odd	12		676.2.l.l.427.1		16
13.8	odd	4	inner	52.2.f.b.47.4	yes	8
13.9	even	3		676.2.l.l.587.1		16
13.10	even	6		676.2.l.h.19.1		16
13.11	odd	12		676.2.l.l.319.2		16
13.12	even	2		676.2.f.g.239.3		8
39.8	even	4		468.2.n.i.307.1		8
52.3	odd	6		676.2.l.l.19.1		16
52.7	even	12		676.2.l.l.427.4		16
52.11	even	12		676.2.l.l.319.1		16
52.15	even	12		676.2.l.h.319.4		16
52.19	even	12		676.2.l.h.427.1		16
52.23	odd	6		676.2.l.h.19.4		16
52.31	even	4		676.2.f.g.99.3		8
52.35	odd	6		676.2.l.l.587.2		16
52.43	odd	6		676.2.l.h.587.3		16
52.47	even	4	inner	52.2.f.b.47.2	yes	8
52.51	odd	2		676.2.f.g.239.1		8
104.21	odd	4		832.2.k.h.255.1		8
104.99	even	4		832.2.k.h.255.4		8
156.47	odd	4		468.2.n.i.307.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.f.b.31.2	✓	8	1.1	even	1	trivial
52.2.f.b.31.4	yes	8	4.3	odd	2	inner
52.2.f.b.47.2	yes	8	52.47	even	4	inner
52.2.f.b.47.4	yes	8	13.8	odd	4	inner
468.2.n.i.307.1		8	39.8	even	4
468.2.n.i.307.3		8	156.47	odd	4
468.2.n.i.343.1		8	12.11	even	2
468.2.n.i.343.3		8	3.2	odd	2
676.2.f.g.99.1		8	13.5	odd	4
676.2.f.g.99.3		8	52.31	even	4
676.2.f.g.239.1		8	52.51	odd	2
676.2.f.g.239.3		8	13.12	even	2
676.2.l.h.19.1		16	13.10	even	6
676.2.l.h.19.4		16	52.23	odd	6
676.2.l.h.319.3		16	13.2	odd	12
676.2.l.h.319.4		16	52.15	even	12
676.2.l.h.427.1		16	52.19	even	12
676.2.l.h.427.4		16	13.6	odd	12
676.2.l.h.587.3		16	52.43	odd	6
676.2.l.h.587.4		16	13.4	even	6
676.2.l.l.19.1		16	52.3	odd	6
676.2.l.l.19.4		16	13.3	even	3
676.2.l.l.319.1		16	52.11	even	12
676.2.l.l.319.2		16	13.11	odd	12
676.2.l.l.427.1		16	13.7	odd	12
676.2.l.l.427.4		16	52.7	even	12
676.2.l.l.587.1		16	13.9	even	3
676.2.l.l.587.2		16	52.35	odd	6
832.2.k.h.255.1		8	104.21	odd	4
832.2.k.h.255.4		8	104.99	even	4
832.2.k.h.447.1		8	8.5	even	2
832.2.k.h.447.4		8	8.3	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13567 - 0.842772i) q^{2} +2.79793i q^{3} +(0.579471 + 1.91421i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.35802 - 3.17751i) q^{6} +(1.97844 - 1.97844i) q^{7} +(0.955161 - 2.66227i) q^{8} -4.82843 q^{9} +O(q^{10})\)	\(q+(-1.13567 - 0.842772i) q^{2} +2.79793i q^{3} +(0.579471 + 1.91421i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.35802 - 3.17751i) q^{6} +(1.97844 - 1.97844i) q^{7} +(0.955161 - 2.66227i) q^{8} -4.82843 q^{9} +(1.39897 - 0.207107i) q^{10} +(-1.15894 + 1.15894i) q^{11} +(-5.35584 + 1.62132i) q^{12} +(3.53553 - 0.707107i) q^{13} +(-3.91421 + 0.579471i) q^{14} +(-1.97844 - 1.97844i) q^{15} +(-3.32843 + 2.21846i) q^{16} -5.82843i q^{17} +(5.48348 + 4.06926i) q^{18} +(-1.63899 - 1.63899i) q^{19} +(-1.76330 - 0.943806i) q^{20} +(5.53553 + 5.53553i) q^{21} +(2.29289 - 0.339446i) q^{22} +3.95687 q^{23} +(7.44885 + 2.67248i) q^{24} +4.00000i q^{25} +(-4.61111 - 2.17661i) q^{26} -5.11582i q^{27} +(4.93360 + 2.64070i) q^{28} -0.585786 q^{29} +(0.579471 + 3.91421i) q^{30} +(-3.95687 - 3.95687i) q^{31} +(5.64964 + 0.285675i) q^{32} +(-3.24264 - 3.24264i) q^{33} +(-4.91203 + 6.61914i) q^{34} +2.79793i q^{35} +(-2.79793 - 9.24264i) q^{36} +(-1.87868 - 1.87868i) q^{37} +(0.480049 + 3.24264i) q^{38} +(1.97844 + 9.89219i) q^{39} +(1.20711 + 2.55791i) q^{40} +(-4.24264 + 4.24264i) q^{41} +(-1.62132 - 10.9517i) q^{42} -5.11582 q^{43} +(-2.89003 - 1.54689i) q^{44} +(3.41421 - 3.41421i) q^{45} +(-4.49368 - 3.33474i) q^{46} +(-1.97844 + 1.97844i) q^{47} +(-6.20711 - 9.31271i) q^{48} -0.828427i q^{49} +(3.37109 - 4.54266i) q^{50} +16.3075 q^{51} +(3.40229 + 6.35802i) q^{52} -0.242641 q^{53} +(-4.31147 + 5.80985i) q^{54} -1.63899i q^{55} +(-3.37740 - 7.15685i) q^{56} +(4.58579 - 4.58579i) q^{57} +(0.665257 + 0.493684i) q^{58} +(2.31788 - 2.31788i) q^{59} +(2.64070 - 4.93360i) q^{60} +0.828427 q^{61} +(1.15894 + 7.82843i) q^{62} +(-9.55274 + 9.55274i) q^{63} +(-6.17534 - 5.08579i) q^{64} +(-2.00000 + 3.00000i) q^{65} +(0.949747 + 6.41536i) q^{66} +(2.79793 + 2.79793i) q^{67} +(11.1569 - 3.37740i) q^{68} +11.0711i q^{69} +(2.35802 - 3.17751i) q^{70} +(5.25642 + 5.25642i) q^{71} +(-4.61192 + 12.8546i) q^{72} +(-9.65685 - 9.65685i) q^{73} +(0.550253 + 3.71685i) q^{74} -11.1917 q^{75} +(2.18763 - 4.08713i) q^{76} +4.58579i q^{77} +(6.09001 - 12.9016i) q^{78} -9.55274i q^{79} +(0.784864 - 3.92224i) q^{80} -0.171573 q^{81} +(8.39380 - 1.24264i) q^{82} +(-6.75481 - 6.75481i) q^{83} +(-7.38851 + 13.8039i) q^{84} +(4.12132 + 4.12132i) q^{85} +(5.80985 + 4.31147i) q^{86} -1.63899i q^{87} +(1.97844 + 4.19239i) q^{88} +(6.24264 + 6.24264i) q^{89} +(-6.75481 + 1.00000i) q^{90} +(5.59587 - 8.39380i) q^{91} +(2.29289 + 7.57430i) q^{92} +(11.0711 - 11.0711i) q^{93} +(3.91421 - 0.579471i) q^{94} +2.31788 q^{95} +(-0.799300 + 15.8073i) q^{96} +(0.414214 - 0.414214i) q^{97} +(-0.698175 + 0.940816i) q^{98} +(5.59587 - 5.59587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9	\( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^6 - 4 * q^8 - 16 * q^9 - 20 * q^14 - 4 * q^16 - 8 * q^20 + 16 * q^21 + 24 * q^22 + 32 * q^24 + 8 * q^26 + 12 * q^28 - 16 * q^29 - 4 * q^32 + 8 * q^33 + 4 * q^34 - 32 * q^37 + 4 * q^40 + 4 * q^42 - 28 * q^44 + 16 * q^45 - 20 * q^46 - 44 * q^48 - 16 * q^50 + 8 * q^52 + 32 * q^53 - 32 * q^54 + 48 * q^57 + 12 * q^58 - 12 * q^60 - 16 * q^61 - 16 * q^65 - 32 * q^66 + 44 * q^68 + 8 * q^70 + 16 * q^72 - 32 * q^73 + 44 * q^74 + 32 * q^76 + 40 * q^78 + 16 * q^80 - 24 * q^81 - 48 * q^84 + 16 * q^85 + 32 * q^86 + 16 * q^89 + 24 * q^92 + 32 * q^93 + 20 * q^94 - 24 * q^96 - 8 * q^97 - 16 * q^98

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