LMFDB - Embedded newform 52.2.f.b.47.4

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			47.4
Root			$0.500000 - 0.691860i$ of defining polynomial
Character	$\chi$	$=$	52.47
Dual form			52.2.f.b.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.842772 - 1.13567i) q^{2} +2.79793i q^{3} +(-0.579471 - 1.91421i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(3.17751 + 2.35802i) q^{6} +(-1.97844 - 1.97844i) q^{7} +(-2.66227 - 0.955161i) 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} +(-4.06926 + 5.48348i) q^{18} +(1.63899 - 1.63899i) q^{19} +(-0.943806 + 1.76330i) q^{20} +(5.53553 - 5.53553i) q^{21} +(2.29289 - 0.339446i) q^{22} -3.95687 q^{23} +(2.67248 - 7.44885i) q^{24} -4.00000i q^{25} +(3.78269 - 3.41925i) q^{26} -5.11582i q^{27} +(-2.64070 + 4.93360i) q^{28} -0.585786 q^{29} +(-0.579471 - 3.91421i) q^{30} +(3.95687 - 3.95687i) q^{31} +(-0.285675 + 5.64964i) q^{32} +(-3.24264 + 3.24264i) q^{33} +(6.61914 + 4.91203i) 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} +(1.54689 - 2.89003i) q^{44} +(3.41421 + 3.41421i) q^{45} +(-3.33474 + 4.49368i) q^{46} +(1.97844 + 1.97844i) q^{47} +(-6.20711 - 9.31271i) q^{48} +0.828427i q^{49} +(-4.54266 - 3.37109i) q^{50} -16.3075 q^{51} +(-0.695185 - 7.17751i) q^{52} -0.242641 q^{53} +(-5.80985 - 4.31147i) q^{54} -1.63899i q^{55} +(3.37740 + 7.15685i) q^{56} +(4.58579 + 4.58579i) q^{57} +(-0.493684 + 0.665257i) q^{58} +(-2.31788 - 2.31788i) q^{59} +(-4.93360 - 2.64070i) 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} +(3.17751 + 2.35802i) q^{70} +(-5.25642 + 5.25642i) q^{71} +(12.8546 + 4.61192i) q^{72} +(-9.65685 + 9.65685i) q^{73} +(0.550253 + 3.71685i) q^{74} +11.1917 q^{75} +(-4.08713 - 2.18763i) q^{76} -4.58579i q^{77} +(9.56684 + 10.5837i) q^{78} -9.55274i q^{79} +(3.92224 + 0.784864i) q^{80} -0.171573 q^{81} +(-8.39380 + 1.24264i) q^{82} +(6.75481 - 6.75481i) q^{83} +(-13.8039 - 7.38851i) q^{84} +(4.12132 - 4.12132i) q^{85} +(4.31147 - 5.80985i) 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} +(-15.8073 - 0.799300i) q^{96} +(0.414214 + 0.414214i) q^{97} +(0.940816 + 0.698175i) 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} - 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}+ \cdots - 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

Character values

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

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

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 $

$2$	0.842772	−	1.13567i	0.595930	−	0.803037i
$2$	0.842772	−	1.13567i	0.595930	−	0.803037i
$3$			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	0.531089	−	0.847316i	$-0.321783\pi$
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i	−0.847316	+	0.531089i	$0.821783\pi$
$6$	3.17751	+	2.35802i	1.29721	+	0.962657i
$7$	−1.97844	−	1.97844i	−0.747779	−	0.747779i	0.226283	−	0.974062i	$-0.427343\pi$
$7$	−1.97844	−	1.97844i	−0.747779	−	0.747779i	−0.974062	+	0.226283i	$0.927343\pi$
$8$	−2.66227	−	0.955161i	−0.941254	−	0.337700i
$9$	−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	$-0.170527\pi$
$11$	1.15894	+	1.15894i	0.349434	+	0.349434i	−0.510465	+	0.859899i	$0.670527\pi$
$12$	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	$0.249862\pi$
$17$			5.82843i			1.41360i	−0.707413	+	0.706801i	$0.750138\pi$
$18$	−4.06926	+	5.48348i	−0.959134	+	1.29247i
$19$	1.63899	−	1.63899i	0.376010	−	0.376010i	−0.493650	−	0.869661i	$-0.664338\pi$
$19$	1.63899	−	1.63899i	0.376010	−	0.376010i	0.869661	+	0.493650i	$0.164338\pi$
$20$	−0.943806	+	1.76330i	−0.211041	+	0.394286i
$21$	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	$-0.635356\pi$
$23$	−3.95687			−0.825065			−0.412533	+	0.910943i	$0.635356\pi$
$24$	2.67248	−	7.44885i	0.545517	−	1.52049i
$25$		−	4.00000i		−	0.800000i
$26$	3.78269	−	3.41925i	0.741846	−	0.670571i
$27$		−	5.11582i		−	0.984539i
$28$	−2.64070	+	4.93360i	−0.499046	+	0.932362i
$29$	−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	$-0.582405\pi$
$31$	3.95687	−	3.95687i	0.710676	−	0.710676i	0.966677	+	0.256001i	$0.0824050\pi$
$32$	−0.285675	+	5.64964i	−0.0505007	+	0.998724i
$33$	−3.24264	+	3.24264i	−0.564471	+	0.564471i
$34$	6.61914	+	4.91203i	1.13517	+	0.842407i
$35$			2.79793i			0.472937i
$36$	2.79793	+	9.24264i	0.466322	+	1.54044i
$37$	−1.87868	+	1.87868i	−0.308853	+	0.308853i	−0.844465	−	0.535611i	$-0.820081\pi$
$37$	−1.87868	+	1.87868i	−0.308853	+	0.308853i	0.535611	+	0.844465i	$0.320081\pi$
$38$	−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	0.293400	−	0.955990i	$-0.405213\pi$
$41$	−4.24264	−	4.24264i	−0.662589	−	0.662589i	−0.955990	+	0.293400i	$0.905213\pi$
$42$	−1.62132	−	10.9517i	−0.250175	−	1.68988i
$43$	5.11582			0.780155			0.390077	−	0.920782i	$-0.372448\pi$
$43$	5.11582			0.780155			0.390077	+	0.920782i	$0.372448\pi$
$44$	1.54689	−	2.89003i	0.233202	−	0.435689i
$45$	3.41421	+	3.41421i	0.508961	+	0.508961i
$46$	−3.33474	+	4.49368i	−0.491681	+	0.662558i
$47$	1.97844	+	1.97844i	0.288585	+	0.288585i	0.836520	−	0.547936i	$-0.184586\pi$
$47$	1.97844	+	1.97844i	0.288585	+	0.288585i	−0.547936	+	0.836520i	$0.684586\pi$
$48$	−6.20711	−	9.31271i	−0.895919	−	1.34417i
$49$			0.828427i			0.118347i
$50$	−4.54266	−	3.37109i	−0.642429	−	0.476744i
$51$	−16.3075			−2.28351
$52$	−0.695185	−	7.17751i	−0.0964049	−	0.995342i
$53$	−0.242641			−0.0333293			−0.0166646	−	0.999861i	$-0.505305\pi$
$53$	−0.242641			−0.0333293			−0.0166646	+	0.999861i	$0.505305\pi$
$54$	−5.80985	−	4.31147i	−0.790621	−	0.586716i
$55$		−	1.63899i		−	0.221002i
$56$	3.37740	+	7.15685i	0.451325	+	0.956375i
$57$	4.58579	+	4.58579i	0.607402	+	0.607402i
$58$	−0.493684	+	0.665257i	−0.0648239	+	0.0873526i
$59$	−2.31788	−	2.31788i	−0.301763	−	0.301763i	0.539940	−	0.841703i	$-0.318447\pi$
$59$	−2.31788	−	2.31788i	−0.301763	−	0.301763i	−0.841703	+	0.539940i	$0.818447\pi$
$60$	−4.93360	−	2.64070i	−0.636925	−	0.340914i
$61$	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	$-0.827706\pi$
$67$	−2.79793	+	2.79793i	−0.341822	+	0.341822i	0.515230	+	0.857052i	$0.327706\pi$
$68$	11.1569	−	3.37740i	1.35297	−	0.409570i
$69$		−	11.0711i		−	1.33280i
$70$	3.17751	+	2.35802i	0.379786	+	0.281837i
$71$	−5.25642	+	5.25642i	−0.623822	+	0.623822i	−0.946507	−	0.322684i	$-0.895415\pi$
$71$	−5.25642	+	5.25642i	−0.623822	+	0.623822i	0.322684	+	0.946507i	$0.395415\pi$
$72$	12.8546	+	4.61192i	1.51492	+	0.543520i
$73$	−9.65685	+	9.65685i	−1.13025	+	1.13025i	−0.140114	+	0.990135i	$0.544747\pi$
$73$	−9.65685	+	9.65685i	−1.13025	+	1.13025i	−0.990135	+	0.140114i	$0.955253\pi$
$74$	0.550253	+	3.71685i	0.0639656	+	0.432075i
$75$	11.1917			1.29231
$76$	−4.08713	−	2.18763i	−0.468826	−	0.250939i
$77$		−	4.58579i		−	0.522599i
$78$	9.56684	+	10.5837i	1.08323	+	1.19837i
$79$		−	9.55274i		−	1.07477i	−0.843338	−	0.537384i	$-0.819413\pi$
$79$		−	9.55274i		−	1.07477i	0.843338	−	0.537384i	$-0.180587\pi$
$80$	3.92224	+	0.784864i	0.438520	+	0.0877505i
$81$	−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	$-0.574337\pi$
$83$	6.75481	−	6.75481i	0.741436	−	0.741436i	0.972854	+	0.231418i	$0.0743365\pi$
$84$	−13.8039	−	7.38851i	−1.50613	−	0.806153i
$85$	4.12132	−	4.12132i	0.447020	−	0.447020i
$86$	4.31147	−	5.80985i	0.464917	−	0.626493i
$87$		−	1.63899i		−	0.175718i
$88$	−1.97844	−	4.19239i	−0.210902	−	0.446910i
$89$	6.24264	−	6.24264i	0.661719	−	0.661719i	−0.294066	−	0.955785i	$-0.595009\pi$
$89$	6.24264	−	6.24264i	0.661719	−	0.661719i	0.955785	+	0.294066i	$0.0950087\pi$
$90$	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
$96$	−15.8073	−	0.799300i	−1.61333	−	0.0815782i
$97$	0.414214	+	0.414214i	0.0420570	+	0.0420570i	0.727823	−	0.685766i	$-0.240532\pi$
$97$	0.414214	+	0.414214i	0.0420570	+	0.0420570i	−0.685766	+	0.727823i	$0.740532\pi$
$98$	0.940816	+	0.698175i	0.0950368	+	0.0705263i
$99$	−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	$0.181097\pi$
$101$			10.8284i			1.07747i	−0.842476	+	0.538734i	$0.818903\pi$
$102$	−13.7435	+	18.5199i	−1.36081	+	1.83374i
$103$	4.91697			0.484484			0.242242	−	0.970216i	$-0.422117\pi$
$103$	4.91697			0.484484			0.242242	+	0.970216i	$0.422117\pi$
$104$	−8.73714	−	5.25951i	−0.856747	−	0.515737i
$105$	−7.82843			−0.763976
$106$	−0.204491	+	0.275559i	−0.0198619	+	0.0267646i
$107$			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	0.444781	−	0.895640i	$-0.353282\pi$
$109$	−4.70711	−	4.70711i	−0.450859	−	0.450859i	−0.895640	+	0.444781i	$0.853282\pi$
$110$	−1.86135	−	1.38130i	−0.177472	−	0.131701i
$111$	−5.25642	−	5.25642i	−0.498917	−	0.498917i
$112$	10.9742	+	2.19600i	1.03696	+	0.207502i
$113$	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
$122$	0.698175	−	0.940816i	0.0632098	−	0.0851775i
$123$	11.8706	−	11.8706i	1.07034	−	1.07034i
$124$	−9.86720	−	5.28141i	−0.886100	−	0.474285i
$125$	−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	$-0.804667\pi$
$127$	−18.4266			−1.63510			−0.817548	+	0.575861i	$0.804667\pi$
$128$	10.9802	−	2.72696i	0.970517	−	0.241031i
$129$			14.3137i			1.26025i
$130$	−5.09254	−	0.256986i	−0.446645	−	0.0225391i
$131$			10.7117i			0.935884i	0.883759	+	0.467942i	$0.155004\pi$
$131$			10.7117i			0.935884i	−0.883759	+	0.467942i	$0.844996\pi$
$132$	8.08612	+	4.32809i	0.703807	+	0.376712i
$133$	−6.48528			−0.562345
$134$	0.819496	+	5.53553i	0.0707936	+	0.478197i
$135$	−3.61743	+	3.61743i	−0.311339	+	0.311339i
$136$	5.56708	−	15.5168i	0.477374	−	1.33056i
$137$	8.65685	−	8.65685i	0.739605	−	0.739605i	−0.232897	−	0.972502i	$-0.574820\pi$
$137$	8.65685	−	8.65685i	0.739605	−	0.739605i	0.972502	+	0.232897i	$0.0748204\pi$
$138$	−12.5730	−	9.33039i	−1.07029	−	0.794255i
$139$			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
$148$	4.68483	+	2.50755i	0.385091	+	0.206120i
$149$	−6.48528	−	6.48528i	−0.531295	−	0.531295i	0.389663	−	0.920958i	$-0.372592\pi$
$149$	−6.48528	−	6.48528i	−0.531295	−	0.531295i	−0.920958	+	0.389663i	$0.872592\pi$
$150$	9.43208	−	12.7101i	0.770126	−	1.03777i
$151$	1.29954	+	1.29954i	0.105755	+	0.105755i	0.758005	−	0.652249i	$-0.226174\pi$
$151$	1.29954	+	1.29954i	0.105755	+	0.105755i	−0.652249	+	0.758005i	$0.726174\pi$
$152$	−5.92893	+	2.79793i	−0.480900	+	0.226942i
$153$		−	28.1421i		−	2.27516i
$154$	−5.20792	−	3.86477i	−0.419666	−	0.311432i
$155$	−5.59587			−0.449471
$156$	20.0822	−	1.94508i	1.60786	−	0.155731i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$	−10.8487	−	8.05078i	−0.863077	−	0.640486i
$159$		−	0.678892i		−	0.0538397i
$160$	4.19690	−	3.79289i	0.331794	−	0.299855i
$161$	7.82843	+	7.82843i	0.616966	+	0.616966i
$162$	−0.144597	+	0.194849i	−0.0113606	+	0.0153088i
$163$	10.7117	+	10.7117i	0.839004	+	0.839004i	0.988728	−	0.149724i	$-0.0478386\pi$
$163$	10.7117	+	10.7117i	0.839004	+	0.839004i	−0.149724	+	0.988728i	$0.547839\pi$
$164$	−5.66283	+	10.5798i	−0.442193	+	0.826144i
$165$	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	$-0.425076\pi$
$167$	−9.55274	−	9.55274i	−0.739213	−	0.739213i	−0.972426	+	0.233213i	$0.925076\pi$
$168$	−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	$0.156034\pi$
$173$			12.3848i			0.941597i	−0.882241	+	0.470799i	$0.843966\pi$
$174$	−1.86135	−	1.38130i	−0.141108	−	0.104716i
$175$	−7.91375	+	7.91375i	−0.598223	+	0.598223i
$176$	−6.42852	−	1.28639i	−0.484568	−	0.0969649i
$177$	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	$-0.410391\pi$
$179$	7.43370			0.555621			0.277810	+	0.960636i	$0.410391\pi$
$180$	4.55710	−	8.51397i	0.339666	−	0.634594i
$181$			11.4142i			0.848412i	0.905566	+	0.424206i	$0.139447\pi$
$181$			11.4142i			0.848412i	−0.905566	+	0.424206i	$0.860553\pi$
$182$	−14.2486	−	0.719028i	−1.05618	−	0.0532979i
$183$			2.31788i			0.171343i
$184$	10.5343	+	3.77945i	0.776596	+	0.278625i
$185$	2.65685			0.195336
$186$	21.9034	−	3.24264i	1.60604	−	0.237762i
$187$	−6.75481	+	6.75481i	−0.493960	+	0.493960i
$188$	2.64070	−	4.93360i	0.192593	−	0.359820i
$189$	−10.1213	+	10.1213i	−0.736218	+	0.736218i
$190$	−1.95345	+	2.63234i	−0.141718	+	0.190970i
$191$		−	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	−0.891003	−	0.453998i	$-0.849997\pi$
$193$	−6.07107	+	6.07107i	−0.437005	+	0.437005i	0.453998	+	0.891003i	$0.349997\pi$
$194$	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	−0.909111	−	0.416555i	$-0.863237\pi$
$197$	−18.6066	−	18.6066i	−1.32567	−	1.32567i	−0.416555	−	0.909111i	$-0.636763\pi$
$198$	−11.0711	+	1.63899i	−0.786787	+	0.116478i
$199$	16.5064			1.17011			0.585053	−	0.810995i	$-0.301074\pi$
$199$	16.5064			1.17011			0.585053	+	0.810995i	$0.301074\pi$
$200$	−3.82064	+	10.6491i	−0.270160	+	0.753003i
$201$	−7.82843	−	7.82843i	−0.552175	−	0.552175i
$202$	12.2975	+	9.12589i	0.865247	+	0.642096i
$203$	1.15894	+	1.15894i	0.0813418	+	0.0813418i
$204$	9.44975	+	31.2161i	0.661615	+	2.18557i
$205$			6.00000i			0.419058i
$206$	4.14389	−	5.58404i	0.288718	−	0.389058i
$207$	19.1055			1.32792
$208$	−13.3365	+	5.48989i	−0.924717	+	0.380656i
$209$	3.79899			0.262782
$210$	−6.59758	+	8.89047i	−0.455276	+	0.613501i
$211$		−	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
$214$	11.6197	+	8.62293i	0.794307	+	0.589452i
$215$	−3.61743	−	3.61743i	−0.246707	−	0.246707i
$216$	−4.88643	+	13.6197i	−0.332479	+	0.926701i
$217$	−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	−0.215975	+	0.976399i	$0.569293\pi$
$223$	−17.8059	+	17.8059i	−1.19237	+	1.19237i	−0.976399	+	0.215975i	$0.930707\pi$
$224$	11.7426	−	10.6123i	0.784588	−	0.709061i
$225$			19.3137i			1.28758i
$226$	12.9060	−	17.3912i	0.858492	−	1.15685i
$227$	12.8307	−	12.8307i	0.851605	−	0.851605i	−0.138726	−	0.990331i	$-0.544301\pi$
$227$	12.8307	−	12.8307i	0.851605	−	0.851605i	0.990331	+	0.138726i	$0.0443007\pi$
$228$	6.12085	−	11.4355i	0.405363	−	0.757335i
$229$	14.7071	−	14.7071i	0.971873	−	0.971873i	−0.0277421	−	0.999615i	$-0.508832\pi$
$229$	14.7071	−	14.7071i	0.971873	−	0.971873i	0.999615	+	0.0277421i	$0.00883173\pi$
$230$	5.53553	−	0.819496i	0.365002	−	0.0540359i
$231$	12.8307			0.844200
$232$	1.55952	+	0.559520i	0.102388	+	0.0367343i
$233$		−	11.9706i		−	0.784218i	−0.919919	−	0.392109i	$-0.871746\pi$
$233$		−	11.9706i		−	0.784218i	0.919919	−	0.392109i	$-0.128254\pi$
$234$	−18.2644	+	16.5096i	−1.19398	+	1.07927i
$235$		−	2.79793i		−	0.182517i
$236$	−3.09378	+	5.78007i	−0.201388	+	0.376250i
$237$	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	$-0.873214\pi$
$239$	−8.25319	+	8.25319i	−0.533855	+	0.533855i	0.387862	+	0.921717i	$0.373214\pi$
$240$	−2.19600	+	10.9742i	−0.141751	+	0.708380i
$241$	13.0711	−	13.0711i	0.841981	−	0.841981i	−0.147135	−	0.989116i	$-0.547005\pi$
$241$	13.0711	−	13.0711i	0.841981	−	0.841981i	0.989116	+	0.147135i	$0.0470052\pi$
$242$	−9.44159	−	7.00656i	−0.606928	−	0.450399i
$243$		−	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	$-0.694090\pi$
$251$	−18.1454			−1.14533			−0.572663	+	0.819791i	$0.694090\pi$
$252$	12.7504	−	23.8215i	0.803203	−	1.50061i
$253$	−4.58579	−	4.58579i	−0.288306	−	0.288306i
$254$	−15.5294	+	20.9264i	−0.974402	+	1.31304i
$255$	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	$0.00652158\pi$
$257$			0.656854i			0.0409734i	−0.999790	+	0.0204867i	$0.993478\pi$
$258$	16.2556	+	12.0632i	1.01203	+	0.751022i
$259$	7.43370			0.461908
$260$	−4.58370	+	5.56684i	−0.284269	+	0.345241i
$261$	2.82843			0.175075
$262$	12.1649	+	9.02750i	0.751549	+	0.557721i
$263$		−	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
$266$	−5.46561	+	7.36511i	−0.335118	+	0.451584i
$267$	17.4665	+	17.4665i	1.06893	+	1.06893i
$268$	6.97716	+	3.73452i	0.426198	+	0.228122i
$269$	−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	$-0.0586033\pi$
$271$	13.1702	+	13.1702i	0.800031	+	0.800031i	−0.183069	+	0.983100i	$0.558603\pi$
$272$	−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	$0.0576915\pi$
$277$			6.00000i			0.360505i	−0.983620	+	0.180253i	$0.942309\pi$
$278$	24.8749	+	18.4596i	1.49190	+	1.10713i
$279$	−19.1055	+	19.1055i	−1.14382	+	1.14382i
$280$	2.67248	−	7.44885i	0.159711	−	0.445154i
$281$	−7.75736	+	7.75736i	−0.462765	+	0.462765i	−0.899561	−	0.436796i	$-0.856113\pi$
$281$	−7.75736	+	7.75736i	−0.462765	+	0.462765i	0.436796	+	0.899561i	$0.356113\pi$
$282$	1.62132	+	10.9517i	0.0965482	+	0.652165i
$283$	−1.35778			−0.0807119			−0.0403560	−	0.999185i	$-0.512849\pi$
$283$	−1.35778			−0.0807119			−0.0403560	+	0.999185i	$0.512849\pi$
$284$	13.1079	+	7.01597i	0.777808	+	0.416321i
$285$		−	6.48528i		−	0.384155i
$286$	8.34663	+	0.421197i	0.493546	+	0.0249059i
$287$			16.7876i			0.990940i
$288$	1.37936	−	27.2789i	0.0812797	−	1.60742i
$289$	−16.9706			−0.998268
$290$	0.819496	−	0.121320i	0.0481224	−	0.00712418i
$291$	−1.15894	+	1.15894i	−0.0679384	+	0.0679384i
$292$	24.0811	+	12.8894i	1.40924	+	0.754296i
$293$	−19.1924	+	19.1924i	−1.12123	+	1.12123i	−0.129675	+	0.991557i	$0.541393\pi$
$293$	−19.1924	+	19.1924i	−1.12123	+	1.12123i	−0.991557	+	0.129675i	$0.958607\pi$
$294$	−1.95345	+	2.63234i	−0.113927	+	0.153521i
$295$			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
$304$	−1.81922	+	9.09130i	−0.104340	+	0.521422i
$305$	−0.585786	−	0.585786i	−0.0335420	−	0.0335420i
$306$	−31.9600	−	23.7174i	−1.82703	−	1.35583i
$307$	−19.1055	−	19.1055i	−1.09041	−	1.09041i	−0.995485	−	0.0949226i	$-0.969740\pi$
$307$	−19.1055	−	19.1055i	−1.09041	−	1.09041i	−0.0949226	−	0.995485i	$-0.530260\pi$
$308$	−8.77817	+	2.65733i	−0.500183	+	0.151415i
$309$			13.7574i			0.782629i
$310$	−4.71604	+	6.35503i	−0.267853	+	0.360941i
$311$	22.7811			1.29180			0.645900	−	0.763422i	$-0.276482\pi$
$311$	22.7811			1.29180			0.645900	+	0.763422i	$0.276482\pi$
$312$	14.7158	−	24.4459i	0.833116	−	1.38398i
$313$	−13.4853			−0.762233			−0.381117	−	0.924527i	$-0.624460\pi$
$313$	−13.4853			−0.762233			−0.381117	+	0.924527i	$0.624460\pi$
$314$	10.1133	−	13.6280i	0.570724	−	0.769072i
$315$		−	13.5096i		−	0.761181i
$316$	−18.2860	+	5.53553i	−1.02867	+	0.311398i
$317$	−4.34315	−	4.34315i	−0.243935	−	0.243935i	0.574541	−	0.818476i	$-0.305181\pi$
$317$	−4.34315	−	4.34315i	−0.243935	−	0.243935i	−0.818476	+	0.574541i	$0.805181\pi$
$318$	−0.770994	−	0.572151i	−0.0432352	−	0.0320847i
$319$	−0.678892	−	0.678892i	−0.0380107	−	0.0380107i
$320$	−0.770428	−	7.96282i	−0.0430682	−	0.445135i
$321$	−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
$330$	3.86477	−	5.20792i	0.212749	−	0.286686i
$331$	−14.6686	+	14.6686i	−0.806257	+	0.806257i	−0.984065	−	0.177808i	$-0.943099\pi$
$331$	−14.6686	+	14.6686i	−0.806257	+	0.806257i	0.177808	+	0.984065i	$0.443099\pi$
$332$	−16.8444	−	9.01593i	−0.924454	−	0.494813i
$333$	9.07107	−	9.07107i	0.497091	−	0.497091i
$334$	−18.8995	+	2.79793i	−1.03413	+	0.153096i
$335$	3.95687			0.216187
$336$	−6.14425	+	30.7050i	−0.335196	+	1.67509i
$337$			8.17157i			0.445134i	0.974917	+	0.222567i	$0.0714436\pi$
$337$			8.17157i			0.445134i	−0.974917	+	0.222567i	$0.928556\pi$
$338$	15.7916	−	9.41412i	0.858949	−	0.512061i
$339$			42.8467i			2.32711i
$340$	−10.2773	−	5.50090i	−0.557363	−	0.298328i
$341$	9.17157			0.496669
$342$	2.31788	+	15.6569i	0.125337	+	0.846626i
$343$	−12.2101	+	12.2101i	−0.659282	+	0.659282i
$344$	−13.6197	−	4.88643i	−0.734323	−	0.263458i
$345$	−7.82843	+	7.82843i	−0.421468	+	0.421468i
$346$	14.0650	+	10.4375i	0.756137	+	0.561126i
$347$			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	−0.719429	−	0.694566i	$-0.755596\pi$
$349$	−0.464466	+	0.464466i	−0.0248623	+	0.0248623i	0.694566	+	0.719429i	$0.255596\pi$
$350$	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	0.579808	−	0.814753i	$-0.303127\pi$
$353$	−4.41421	−	4.41421i	−0.234945	−	0.234945i	−0.814753	+	0.579808i	$0.803127\pi$
$354$	−1.89949	−	12.8307i	−0.100957	−	0.681945i
$355$	7.43370			0.394540
$356$	−15.5672	−	8.33232i	−0.825059	−	0.441612i
$357$	32.2635	+	32.2635i	1.70756	+	1.70756i
$358$	6.26491	−	8.44219i	0.331111	−	0.446184i
$359$	3.95687	+	3.95687i	0.208836	+	0.208836i	0.803773	−	0.594937i	$-0.202823\pi$
$359$	3.95687	+	3.95687i	0.208836	+	0.208836i	−0.594937	+	0.803773i	$0.702823\pi$
$360$	−5.82843	−	12.3507i	−0.307185	−	0.650938i
$361$			13.6274i			0.717232i
$362$	12.9627	+	9.61958i	0.681306	+	0.505594i
$363$	23.2612			1.22090
$364$	−12.8249	+	15.5756i	−0.672206	+	0.816385i
$365$	13.6569			0.714832
$366$	2.63234	+	1.95345i	0.137595	+	0.102108i
$367$		−	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
$370$	2.23912	−	3.01730i	0.116406	−	0.156862i
$371$	0.480049	+	0.480049i	0.0249229	+	0.0249229i
$372$	14.7770	−	27.6077i	0.766153	−	1.43140i
$373$	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	$-0.580338\pi$
$379$	13.9897	−	13.9897i	0.718601	−	0.718601i	0.968319	+	0.249718i	$0.0803379\pi$
$380$	1.34315	+	4.43692i	0.0689019	+	0.227609i
$381$		−	51.5563i		−	2.64131i
$382$	−27.2815	−	20.2454i	−1.39584	−	1.03585i
$383$	11.5312	−	11.5312i	0.589216	−	0.589216i	−0.348203	−	0.937419i	$-0.613208\pi$
$383$	11.5312	−	11.5312i	0.589216	−	0.589216i	0.937419	+	0.348203i	$0.113208\pi$
$384$	7.62984	+	30.7217i	0.389359	+	1.56776i
$385$	−3.24264	+	3.24264i	−0.165260	+	0.165260i
$386$	1.77817	+	12.0112i	0.0905067	+	0.611355i
$387$	−24.7013			−1.25564
$388$	0.552869	−	1.03292i	0.0280676	−	0.0524385i
$389$		−	22.1421i		−	1.12265i	−0.827595	−	0.561325i	$-0.810292\pi$
$389$		−	22.1421i		−	1.12265i	0.827595	−	0.561325i	$-0.189708\pi$
$390$	0.719028	−	14.2486i	0.0364094	−	0.721505i
$391$		−	23.0624i		−	1.16631i
$392$	0.791281	−	2.20549i	0.0399657	−	0.111394i
$393$	−29.9706			−1.51181
$394$	−36.8120	+	5.44975i	−1.85456	+	0.274554i
$395$	−6.75481	+	6.75481i	−0.339871	+	0.339871i
$396$	−7.46904	+	13.9543i	−0.375333	+	0.701231i
$397$	−1.51472	+	1.51472i	−0.0760215	+	0.0760215i	−0.744095	−	0.668074i	$-0.767119\pi$
$397$	−1.51472	+	1.51472i	−0.0760215	+	0.0760215i	0.668074	+	0.744095i	$0.267119\pi$
$398$	13.9111	−	18.7457i	0.697302	−	0.939639i
$399$		−	18.1454i		−	0.908405i
$400$	8.87385	+	13.3137i	0.443692	+	0.665685i
$401$	19.4853	−	19.4853i	0.973049	−	0.973049i	−0.0265977	−	0.999646i	$-0.508467\pi$
$401$	19.4853	−	19.4853i	0.973049	−	0.973049i	0.999646	+	0.0265977i	$0.00846731\pi$
$402$	−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
$408$	43.4151	+	15.5763i	2.14937	+	0.771143i
$409$	5.14214	+	5.14214i	0.254262	+	0.254262i	0.822716	−	0.568453i	$-0.192458\pi$
$409$	5.14214	+	5.14214i	0.254262	+	0.254262i	−0.568453	+	0.822716i	$0.692458\pi$
$410$	6.81399	+	5.05663i	0.336519	+	0.249729i
$411$	24.2213	+	24.2213i	1.19475	+	1.19475i
$412$	−2.84924	−	9.41214i	−0.140372	−	0.463703i
$413$			9.17157i			0.451304i
$414$	16.1016	−	21.6974i	0.791349	−	1.06637i
$415$	−9.55274			−0.468926
$416$	−5.00491	+	19.7725i	−0.245386	+	0.969425i
$417$	−61.2843			−3.00110
$418$	3.20168	−	4.31438i	0.156599	−	0.211023i
$419$			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	0.707614	−	0.706599i	$-0.249772\pi$
$421$	0.0208153	+	0.0208153i	0.00101447	+	0.00101447i	−0.706599	+	0.707614i	$0.749772\pi$
$422$	−11.0745	−	8.21836i	−0.539100	−	0.400064i
$423$	−9.55274	−	9.55274i	−0.464470	−	0.464470i
$424$	0.645974	+	0.231761i	0.0313713	+	0.0112553i
$425$	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	−0.297786	+	0.954633i	$0.596248\pi$
$431$	−26.0009	+	26.0009i	−1.25242	+	1.25242i	−0.954633	+	0.297786i	$0.903752\pi$
$432$	11.3492	+	17.0276i	0.546041	+	0.819242i
$433$			9.68629i			0.465493i	0.972537	+	0.232747i	$0.0747713\pi$
$433$			9.68629i			0.465493i	−0.972537	+	0.232747i	$0.925229\pi$
$434$	−13.1952	+	17.7809i	−0.633388	+	0.853513i
$435$	−1.15894	+	1.15894i	−0.0555670	+	0.0555670i
$436$	−6.28278	+	11.7380i	−0.300890	+	0.562150i
$437$	−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	$-0.308276\pi$
$439$	23.7412			1.13311			0.566554	+	0.824025i	$0.308276\pi$
$440$	−1.56550	+	4.36343i	−0.0746323	+	0.208018i
$441$		−	4.00000i		−	0.190476i
$442$	19.9289	+	22.0471i	0.947920	+	1.04867i
$443$		−	27.4993i		−	1.30653i	−0.757129	−	0.653265i	$-0.773399\pi$
$443$		−	27.4993i		−	1.30653i	0.757129	−	0.653265i	$-0.226601\pi$
$444$	−7.01597	+	13.1079i	−0.332963	+	0.622071i
$445$	−8.82843			−0.418508
$446$	5.21524	+	35.2279i	0.246949	+	1.66809i
$447$	18.1454	−	18.1454i	0.858247	−	0.858247i
$448$	−2.15561	−	22.2794i	−0.101843	−	1.05260i
$449$	0.272078	−	0.272078i	0.0128402	−	0.0128402i	−0.700658	−	0.713498i	$-0.747110\pi$
$449$	0.272078	−	0.272078i	0.0128402	−	0.0128402i	0.713498	+	0.700658i	$0.247110\pi$
$450$	21.9339	+	16.2771i	1.03397	+	0.767308i
$451$		−	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	0.782438	−	0.622728i	$-0.213976\pi$
$457$	3.41421	+	3.41421i	0.159710	+	0.159710i	−0.622728	+	0.782438i	$0.713976\pi$
$458$	−4.30761	−	29.0971i	−0.201281	−	1.35962i
$459$	29.8172			1.39175
$460$	3.73452	−	6.97716i	0.174123	−	0.325312i
$461$	13.5355	+	13.5355i	0.630413	+	0.630413i	0.948172	−	0.317759i	$-0.102930\pi$
$461$	13.5355	+	13.5355i	0.630413	+	0.630413i	−0.317759	+	0.948172i	$0.602930\pi$
$462$	10.8134	−	14.5714i	0.503084	−	0.677923i
$463$	−16.1087	−	16.1087i	−0.748635	−	0.748635i	0.225588	−	0.974223i	$-0.427570\pi$
$463$	−16.1087	−	16.1087i	−0.748635	−	0.748635i	−0.974223	+	0.225588i	$0.927570\pi$
$464$	1.94975	−	1.29954i	0.0905148	−	0.0603299i
$465$		−	15.6569i		−	0.726069i
$466$	−13.5946	−	10.0885i	−0.629755	−	0.467339i
$467$	−6.95365			−0.321777			−0.160888	−	0.986973i	$-0.551436\pi$
$467$	−6.95365			−0.321777			−0.160888	+	0.986973i	$0.551436\pi$
$468$	3.35665	+	34.6561i	0.155161	+	1.60198i
$469$	11.0711			0.511214
$470$	−3.17751	−	2.35802i	−0.146568	−	0.108767i
$471$			33.5752i			1.54706i
$472$	3.95687	+	8.38478i	0.182130	+	0.385941i
$473$	5.92893	+	5.92893i	0.272613	+	0.272613i
$474$	22.5255	−	30.3540i	1.03463	−	1.39420i
$475$	−6.55596	−	6.55596i	−0.300808	−	0.300808i
$476$	−28.7551	−	15.3912i	−1.31799	−	0.705452i
$477$	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	$-0.328694\pi$
$479$	−7.57430	−	7.57430i	−0.346079	−	0.346079i	−0.858647	+	0.512568i	$0.828694\pi$
$480$	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
$486$	−17.9747	−	13.3390i	−0.815351	−	0.605068i
$487$	−6.27476	+	6.27476i	−0.284336	+	0.284336i	−0.834836	−	0.550499i	$-0.814437\pi$
$487$	−6.27476	+	6.27476i	−0.284336	+	0.284336i	0.550499	+	0.834836i	$0.314437\pi$
$488$	−2.20549	−	0.791281i	−0.0998380	−	0.0358196i
$489$	−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	$-0.479890\pi$
$491$	2.79793			0.126269			0.0631345	+	0.998005i	$0.479890\pi$
$492$	−29.6016	−	15.8442i	−1.33454	−	0.714313i
$493$		−	3.41421i		−	0.153768i
$494$	0.595662	−	11.8039i	0.0268001	−	0.531083i
$495$			7.91375i			0.355697i
$496$	−4.39199	+	21.9483i	−0.197206	+	0.985510i
$497$	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	$-0.789974\pi$
$499$	−3.95687	+	3.95687i	−0.177134	+	0.177134i	0.612971	+	0.790105i	$0.289974\pi$
$500$	15.8697	+	8.49425i	0.709715	+	0.379874i
$501$	26.7279	−	26.7279i	1.19412	−	1.19412i
$502$	−15.2924	+	20.6071i	−0.682534	+	0.919739i
$503$			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	0.867405	−	0.497602i	$-0.165786\pi$
$509$	8.34315	+	8.34315i	0.369803	+	0.369803i	−0.497602	+	0.867405i	$0.665786\pi$
$510$	22.8137	−	3.37740i	1.01021	−	0.149554i
$511$	38.2110			1.69035
$512$	−11.5827	−	19.4382i	−0.511886	−	0.859054i
$513$	−8.38478	−	8.38478i	−0.370197	−	0.370197i
$514$	0.745967	+	0.553578i	0.0329032	+	0.0244173i
$515$	−3.47682	−	3.47682i	−0.153207	−	0.153207i
$516$	27.3995	−	8.29438i	1.20620	−	0.365140i
$517$			4.58579i			0.201683i
$518$	6.26491	−	8.44219i	0.275264	−	0.370929i
$519$	−34.6518			−1.52104
$520$	2.45905	+	9.89712i	0.107837	+	0.434018i
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	2.38372	−	3.21215i	0.104333	−	0.140592i
$523$		−	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
$526$	−10.0777	−	7.47863i	−0.439409	−	0.326084i
$527$	23.0624	+	23.0624i	1.00461	+	1.00461i
$528$	3.59922	−	17.9866i	0.156636	−	0.782765i
$529$	−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
$538$	−6.86196	+	9.24674i	−0.295840	+	0.398655i
$539$	−0.960099	+	0.960099i	−0.0413544	+	0.0413544i
$540$	9.02072	+	4.82834i	0.388190	+	0.207778i
$541$	16.1213	−	16.1213i	0.693110	−	0.693110i	−0.269805	−	0.962915i	$-0.586959\pi$
$541$	16.1213	−	16.1213i	0.693110	−	0.693110i	0.962915	+	0.269805i	$0.0869593\pi$
$542$	26.0563	−	3.85745i	1.11922	−	0.165692i
$543$	−31.9362			−1.37051
$544$	−32.9285	−	1.66504i	−1.41180	−	0.0713879i
$545$			6.65685i			0.285148i
$546$	2.01179	−	39.8666i	0.0860968	−	1.70613i
$547$		−	14.3873i		−	0.615159i	−0.951522	−	0.307579i	$-0.900481\pi$
$547$		−	14.3873i		−	0.615159i	0.951522	−	0.307579i	$-0.0995189\pi$
$548$	−21.5875	−	11.5547i	−0.922171	−	0.493591i
$549$	−4.00000			−0.170716
$550$	−1.35778	−	9.17157i	−0.0578961	−	0.391077i
$551$	−0.960099	+	0.960099i	−0.0409016	+	0.0409016i
$552$	−10.5746	+	29.4741i	−0.450087	+	1.25450i
$553$	−18.8995	+	18.8995i	−0.803688	+	0.803688i
$554$	6.81399	+	5.05663i	0.289499	+	0.214836i
$555$			7.43370i			0.315543i
$556$	41.9278	−	12.6924i	1.77814	−	0.538277i
$557$	−8.36396	+	8.36396i	−0.354392	+	0.354392i	−0.861741	−	0.507349i	$-0.830626\pi$
$557$	−8.36396	+	8.36396i	−0.354392	+	0.354392i	0.507349	+	0.861741i	$0.330626\pi$
$558$	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	$-0.704717\pi$
$563$	−28.4594			−1.19942			−0.599710	+	0.800218i	$0.704717\pi$
$564$	13.8039	+	7.38851i	0.581248	+	0.311113i
$565$	−10.8284	−	10.8284i	−0.455555	−	0.455555i
$566$	−1.14430	+	1.54199i	−0.0480986	+	0.0648146i
$567$	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	$-0.787925\pi$
$569$		−	29.4853i		−	1.23609i	0.786144	−	0.618044i	$-0.212075\pi$
$570$	−7.36511	−	5.46561i	−0.308490	−	0.228929i
$571$	11.6718			0.488449			0.244224	−	0.969719i	$-0.421467\pi$
$571$	11.6718			0.488449			0.244224	+	0.969719i	$0.421467\pi$
$572$	7.51264	−	9.12400i	0.314119	−	0.381494i
$573$	67.2132			2.80787
$574$	19.0651	+	14.1481i	0.795761	+	0.590531i
$575$			15.8275i			0.660052i
$576$	−29.8172	−	24.5563i	−1.24238	−	1.02318i
$577$	−0.485281	−	0.485281i	−0.0202025	−	0.0202025i	0.696933	−	0.717136i	$-0.254547\pi$
$577$	−0.485281	−	0.485281i	−0.0202025	−	0.0202025i	−0.717136	+	0.696933i	$0.754547\pi$
$578$	−14.3023	+	19.2729i	−0.594898	+	0.801646i
$579$	−16.9864	−	16.9864i	−0.705932	−	0.705932i
$580$	0.552869	−	1.03292i	0.0229566	−	0.0428896i
$581$	−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	0.0401538	−	0.999194i	$-0.487215\pi$
$587$	25.1814	−	25.1814i	1.03935	−	1.03935i	0.999194	−	0.0401538i	$-0.0127848\pi$
$588$	1.34315	+	4.43692i	0.0553904	+	0.182976i
$589$		−	12.9706i		−	0.534443i
$590$	3.72269	+	2.76259i	0.153261	+	0.113734i
$591$	52.0600	−	52.0600i	2.14146	−	2.14146i
$592$	2.08527	−	10.4208i	0.0857040	−	0.428293i
$593$	−1.44365	+	1.44365i	−0.0592836	+	0.0592836i	−0.736127	−	0.676843i	$-0.763347\pi$
$593$	−1.44365	+	1.44365i	−0.0592836	+	0.0592836i	0.676843	+	0.736127i	$0.263347\pi$
$594$	−1.73654	−	11.7300i	−0.0712513	−	0.481289i
$595$	−16.3075			−0.668544
$596$	−8.65618	+	16.1722i	−0.354571	+	0.662441i
$597$			46.1838i			1.89018i
$598$	−14.9676	+	13.5296i	−0.612071	+	0.553265i
$599$			13.9073i			0.568237i	0.958789	+	0.284118i	$0.0917009\pi$
$599$			13.9073i			0.568237i	−0.958789	+	0.284118i	$0.908299\pi$
$600$	−29.7954	−	10.6899i	−1.21639	−	0.436413i
$601$	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
$604$	1.73456	−	3.24065i	0.0705782	−	0.131860i
$605$	−5.87868	+	5.87868i	−0.239002	+	0.239002i
$606$	−25.5336	+	34.4075i	−1.03723	+	1.39771i
$607$			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	0.957112	+	0.289718i	$0.0935614\pi$
$613$	30.8701	+	30.8701i	1.24683	+	1.24683i	0.289718	+	0.957112i	$0.406439\pi$
$614$	−37.7990	+	5.59587i	−1.52544	+	0.225831i
$615$	−16.7876			−0.676941
$616$	−4.38016	+	12.2086i	−0.176482	+	0.491898i
$617$	−24.4853	−	24.4853i	−0.985740	−	0.985740i	0.0141594	−	0.999900i	$-0.495493\pi$
$617$	−24.4853	−	24.4853i	−0.985740	−	0.985740i	−0.999900	+	0.0141594i	$0.995493\pi$
$618$	15.6238	+	11.5943i	0.628480	+	0.466392i
$619$	−21.1422	−	21.1422i	−0.849775	−	0.849775i	0.140330	−	0.990105i	$-0.455184\pi$
$619$	−21.1422	−	21.1422i	−0.849775	−	0.849775i	−0.990105	+	0.140330i	$0.955184\pi$
$620$	3.24264	+	10.7117i	0.130228	+	0.430191i
$621$			20.2426i			0.812309i
$622$	19.1993	−	25.8718i	0.769822	−	1.03736i
$623$	−24.7013			−0.989638
$624$	−15.3604	−	37.3145i	−0.614906	−	1.49378i
$625$	−11.0000			−0.440000
$626$	−11.3650	+	15.3148i	−0.454237	+	0.612101i
$627$			10.6293i			0.424494i
$628$	−6.95365	−	22.9706i	−0.277481	−	0.916625i
$629$	−10.9497	−	10.9497i	−0.436595	−	0.436595i
$630$	−15.3424	−	11.3855i	−0.611256	−	0.453610i
$631$	1.97844	+	1.97844i	0.0787603	+	0.0787603i	0.745390	−	0.666629i	$-0.232264\pi$
$631$	1.97844	+	1.97844i	0.0787603	+	0.0787603i	−0.666629	+	0.745390i	$0.732264\pi$
$632$	−9.12440	+	25.4319i	−0.362949	+	1.01163i
$633$	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	$0.271521\pi$
$641$			38.1421i			1.50652i	−0.657721	+	0.753262i	$0.728479\pi$
$642$	−24.1264	+	32.5112i	−0.952192	+	1.28311i
$643$	−17.2676	+	17.2676i	−0.680969	+	0.680969i	−0.960219	−	0.279249i	$-0.909914\pi$
$643$	−17.2676	+	17.2676i	−0.680969	+	0.680969i	0.279249	+	0.960219i	$0.409914\pi$
$644$	10.4489	−	19.5216i	0.411746	−	0.769260i
$645$	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	$-0.270561\pi$
$647$	33.5752			1.31998			0.659988	+	0.751276i	$0.270561\pi$
$648$	0.456773	+	0.163880i	0.0179437	+	0.00643780i
$649$		−	5.37258i		−	0.210892i
$650$	−13.6770	−	15.1307i	−0.536457	−	0.593477i
$651$		−	43.8068i		−	1.71692i
$652$	14.2973	−	26.7116i	0.559927	−	1.04611i
$653$	−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
$656$	23.5335	+	4.70918i	0.918827	+	0.183863i
$657$	46.6274	−	46.6274i	1.81911	−	1.81911i
$658$	−8.89047	−	6.59758i	−0.346587	−	0.257200i
$659$		−	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	−0.237020	+	0.971505i	$0.576171\pi$
$661$	−31.0711	+	31.0711i	−1.20852	+	1.20852i	−0.971505	+	0.237020i	$0.923829\pi$
$662$	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
$668$	−12.7504	+	23.8215i	−0.493330	+	0.921682i
$669$	−49.8198	−	49.8198i	−1.92614	−	1.92614i
$670$	3.33474	−	4.49368i	0.128832	−	0.173606i
$671$	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	$-0.691237\pi$
$673$		−	42.7990i		−	1.64978i	0.565293	−	0.824890i	$-0.308763\pi$
$674$	9.28017	+	6.88677i	0.357459	+	0.265269i
$675$	−20.4633			−0.787631
$676$	2.61742	−	25.8679i	0.100670	−	0.994920i
$677$	−31.2132			−1.19962			−0.599810	−	0.800142i	$-0.704757\pi$
$677$	−31.2132			−1.19962			−0.599810	+	0.800142i	$0.704757\pi$
$678$	48.6595	+	36.1100i	1.86876	+	1.38680i
$679$		−	1.63899i		−	0.0628987i
$680$	−14.9086	+	7.03553i	−0.571718	+	0.269800i
$681$	35.8995	+	35.8995i	1.37567	+	1.37567i
$682$	7.72954	−	10.4158i	0.295980	−	0.398843i
$683$	−31.4562	−	31.4562i	−1.20364	−	1.20364i	−0.973052	−	0.230584i	$-0.925936\pi$
$683$	−31.4562	−	31.4562i	−1.20364	−	1.20364i	−0.230584	−	0.973052i	$-0.574064\pi$
$684$	19.7344	+	10.5628i	0.754563	+	0.403879i
$685$	−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	$-0.769860\pi$
$691$	−2.31788	+	2.31788i	−0.0881764	+	0.0881764i	0.661643	+	0.749819i	$0.269860\pi$
$692$	23.7071	−	7.17662i	0.901209	−	0.272814i
$693$			22.1421i			0.841110i
$694$	10.6229	+	7.88320i	0.403240	+	0.299242i
$695$	15.4881	−	15.4881i	0.587495	−	0.587495i
$696$	−1.56550	+	4.36343i	−0.0593401	+	0.165395i
$697$	24.7279	−	24.7279i	0.936637	−	0.936637i
$698$	0.136039	+	0.918917i	0.00514915	+	0.0347815i
$699$	33.4928			1.26682
$700$	19.7344	+	10.5628i	0.745890	+	0.399237i
$701$			31.3553i			1.18427i	0.805837	+	0.592137i	$0.201716\pi$
$701$			31.3553i			1.18427i	−0.805837	+	0.592137i	$0.798284\pi$
$702$	−17.4923	−	19.3515i	−0.660203	−	0.730376i
$703$			6.15828i			0.232264i
$704$	1.26272	+	13.0510i	0.0475907	+	0.491877i
$705$	7.82843			0.294836
$706$	−8.73324	+	1.29289i	−0.328680	+	0.0486587i
$707$	21.4234	−	21.4234i	0.805708	−	0.805708i
$708$	−16.1722	−	8.65618i	−0.607790	−	0.325319i
$709$	−2.97056	+	2.97056i	−0.111562	+	0.111562i	−0.760684	−	0.649122i	$-0.775136\pi$
$709$	−2.97056	+	2.97056i	−0.111562	+	0.111562i	0.649122	+	0.760684i	$0.275136\pi$
$710$	6.26491	−	8.44219i	0.235118	−	0.316830i
$711$			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	$-0.603105\pi$
$719$	−17.0688			−0.636559			−0.318279	+	0.947997i	$0.603105\pi$
$720$	−18.9383	−	3.78966i	−0.705787	−	0.141232i
$721$	−9.72792	−	9.72792i	−0.362287	−	0.362287i
$722$	15.4762	+	11.4848i	0.575964	+	0.427420i
$723$	36.5720	+	36.5720i	1.36013	+	1.36013i
$724$	21.8492	−	6.61420i	0.812021	−	0.245815i
$725$			2.34315i			0.0870222i
$726$	19.6039	−	26.4169i	0.727568	−	0.980424i
$727$	−43.1279			−1.59953			−0.799763	−	0.600316i	$-0.795042\pi$
$727$	−43.1279			−1.59953			−0.799763	+	0.600316i	$0.795042\pi$
$728$	6.88026	+	27.6915i	0.255000	+	1.02631i
$729$	43.7696			1.62109
$730$	11.5096	−	15.5096i	0.425990	−	0.574037i
$731$			29.8172i			1.10283i
$732$	4.43692	−	1.34315i	0.163993	−	0.0496441i
$733$	−14.8492	−	14.8492i	−0.548469	−	0.548469i	0.377529	−	0.925998i	$-0.376774\pi$
$733$	−14.8492	−	14.8492i	−0.548469	−	0.548469i	−0.925998	+	0.377529i	$0.876774\pi$
$734$	−17.2037	−	12.7668i	−0.635002	−	0.471232i
$735$	1.63899	+	1.63899i	0.0604551	+	0.0604551i
$736$	1.13038	−	22.3549i	0.0416664	−	0.824013i
$737$	−6.48528			−0.238888
$738$	40.5288	−	6.00000i	1.49189	−	0.220863i
$739$	37.5321	+	37.5321i	1.38064	+	1.38064i	0.843482	+	0.537157i	$0.180502\pi$
$739$	37.5321	+	37.5321i	1.38064	+	1.38064i	0.537157	+	0.843482i	$0.319498\pi$
$740$	−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	$-0.826821\pi$
$743$	−9.21329	+	9.21329i	−0.338003	+	0.338003i	0.517612	+	0.855615i	$0.326821\pi$
$744$	−18.8995	−	40.0488i	−0.692889	−	1.46826i
$745$			9.17157i			0.336020i
$746$	25.8119	−	34.7825i	0.945042	−	1.27348i
$747$	−32.6151	+	32.6151i	−1.19332	+	1.19332i
$748$	16.8444	+	9.01593i	0.615891	+	0.329655i
$749$	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	$-0.548457\pi$
$751$	−8.31143			−0.303289			−0.151644	+	0.988435i	$0.548457\pi$
$752$	−10.9742	−	2.19600i	−0.400187	−	0.0800798i
$753$		−	50.7696i		−	1.85015i
$754$	−2.21585	+	2.00295i	−0.0806963	+	0.0729432i
$755$		−	1.83783i		−	0.0668856i
$756$	25.2394	+	13.5094i	0.917947	+	0.491331i
$757$	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
$760$	6.17083	+	2.21395i	0.223839	+	0.0803084i
$761$	−0.343146	+	0.343146i	−0.0124390	+	0.0124390i	−0.713299	−	0.700860i	$-0.752800\pi$
$761$	−0.343146	+	0.343146i	−0.0124390	+	0.0124390i	0.700860	+	0.713299i	$0.252800\pi$
$762$	−58.5508	−	43.4502i	−2.12107	−	1.57404i
$763$			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	0.676602	−	0.736349i	$-0.263452\pi$
$769$	−1.65685	−	1.65685i	−0.0597477	−	0.0597477i	−0.736349	+	0.676602i	$0.763452\pi$
$770$	0.949747	+	6.41536i	0.0342265	+	0.231194i
$771$	−1.83783			−0.0661880
$772$	15.1393	+	8.10331i	0.544876	+	0.291645i
$773$	32.1213	+	32.1213i	1.15532	+	1.15532i	0.985469	+	0.169854i	$0.0543298\pi$
$773$	32.1213	+	32.1213i	1.15532	+	1.15532i	0.169854	+	0.985469i	$0.445670\pi$
$774$	−20.8176	+	28.0525i	−0.748273	+	1.00832i
$775$	−15.8275	−	15.8275i	−0.568540	−	0.568540i
$776$	−0.707107	−	1.49839i	−0.0253837	−	0.0537890i
$777$			20.7990i			0.746160i
$778$	−25.1461	−	18.6608i	−0.901530	−	0.669021i
$779$	−13.9073			−0.498281
$780$	−15.5756	−	12.8249i	−0.557697	−	0.459204i
$781$	−12.1838			−0.435969
$782$	−26.1911	−	19.4363i	−0.936592	−	0.695041i
$783$			2.99678i			0.107096i
$784$	−1.83783	−	2.75736i	−0.0656369	−	0.0984771i
$785$	−8.48528	−	8.48528i	−0.302853	−	0.302853i
$786$	−25.2584	+	34.0365i	−0.900936	+	1.21404i
$787$	−18.4266	−	18.4266i	−0.656837	−	0.656837i	0.297793	−	0.954630i	$-0.403749\pi$
$787$	−18.4266	−	18.4266i	−0.656837	−	0.656837i	−0.954630	+	0.297793i	$0.903749\pi$
$788$	−24.8350	+	46.3990i	−0.884711	+	1.65290i
$789$	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	$-0.813835\pi$
$797$		−	31.1716i		−	1.10415i	0.833793	−	0.552077i	$-0.186165\pi$
$798$	−20.6071	−	15.2924i	−0.729483	−	0.541346i
$799$	−11.5312	+	11.5312i	−0.407944	+	0.407944i
$800$	22.5985	+	1.14270i	0.798979	+	0.0404006i
$801$	−30.1421	+	30.1421i	−1.06502	+	1.06502i
$802$	−5.70711	−	38.5504i	−0.201525	−	1.36126i
$803$	−22.3835			−0.789895
$804$	−10.4489	+	19.5216i	−0.368506	+	0.688475i
$805$		−	11.0711i		−	0.390204i
$806$	1.43806	−	28.4972i	0.0506534	−	1.00377i
$807$		−	22.7811i		−	0.801934i
$808$	10.3429	−	28.8282i	0.363862	−	1.01417i
$809$	−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	$-0.802047\pi$
$811$	−6.55596	+	6.55596i	−0.230211	+	0.230211i	0.582570	+	0.812781i	$0.302047\pi$
$812$	1.54689	−	2.89003i	0.0542852	−	0.101420i
$813$	−36.8492	+	36.8492i	−1.29236	+	1.29236i
$814$	−3.66990	+	4.94532i	−0.128630	+	0.173333i
$815$		−	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	0.667272	−	0.744814i	$-0.267462\pi$
$821$	−2.22183	−	2.22183i	−0.0775422	−	0.0775422i	−0.744814	+	0.667272i	$0.767462\pi$
$822$	47.9203	−	7.09425i	1.67141	−	0.247440i
$823$	54.0385			1.88366			0.941831	−	0.336087i	$-0.109103\pi$
$823$	54.0385			1.88366			0.941831	+	0.336087i	$0.109103\pi$
$824$	−13.0903	−	4.69650i	−0.456022	−	0.163610i
$825$	12.9706	+	12.9706i	0.451577	+	0.451577i
$826$	10.4158	+	7.72954i	0.362413	+	0.268945i
$827$	32.3339	+	32.3339i	1.12436	+	1.12436i	0.991078	+	0.133281i	$0.0425513\pi$
$827$	32.3339	+	32.3339i	1.12436	+	1.12436i	0.133281	+	0.991078i	$0.457449\pi$
$828$	−11.0711	−	36.5720i	−0.384746	−	1.27096i
$829$		−	22.3848i		−	0.777455i	−0.921353	−	0.388728i	$-0.872915\pi$
$829$		−	22.3848i		−	0.777455i	0.921353	−	0.388728i	$-0.127085\pi$
$830$	−8.05078	+	10.8487i	−0.279447	+	0.376564i
$831$	−16.7876			−0.582355
$832$	18.2369	+	22.3476i	0.632251	+	0.774763i
$833$	−4.82843			−0.167295
$834$	−51.6487	+	69.5984i	−1.78845	+	2.41000i
$835$			13.5096i			0.467519i
$836$	−2.20140	−	7.27208i	−0.0761371	−	0.251510i
$837$	−20.2426	−	20.2426i	−0.699688	−	0.699688i
$838$	5.80985	+	4.31147i	0.200698	+	0.148937i
$839$	24.0225	+	24.0225i	0.829347	+	0.829347i	0.987426	−	0.158079i	$-0.0505302\pi$
$839$	24.0225	+	24.0225i	0.829347	+	0.829347i	−0.158079	+	0.987426i	$0.550530\pi$
$840$	20.8414	+	7.47741i	0.719095	+	0.257995i
$841$	−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
$850$	19.6481	−	26.4766i	0.673926	−	0.908139i
$851$	7.43370	−	7.43370i	0.254824	−	0.254824i
$852$	−19.6302	+	36.6749i	−0.672520	+	1.25646i
$853$	−39.5772	+	39.5772i	−1.35510	+	1.35510i	−0.475240	+	0.879856i	$0.657639\pi$
$853$	−39.5772	+	39.5772i	−1.35510	+	1.35510i	−0.879856	+	0.475240i	$0.842361\pi$
$854$	−3.24264	+	0.480049i	−0.110961	+	0.0164270i
$855$	11.1917			0.382749
$856$	9.77285	−	27.2393i	0.334029	−	0.931022i
$857$			30.1421i			1.02964i	0.857300	+	0.514818i	$0.172140\pi$
$857$			30.1421i			1.02964i	−0.857300	+	0.514818i	$0.827860\pi$
$858$	−1.17848	+	23.3533i	−0.0402327	+	0.797268i
$859$			35.3307i			1.20547i	0.797943	+	0.602733i	$0.205922\pi$
$859$			35.3307i			1.20547i	−0.797943	+	0.602733i	$0.794078\pi$
$860$	−4.82834	+	9.02072i	−0.164645	+	0.307604i
$861$	−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	$-0.541368\pi$
$863$	25.3220	−	25.3220i	0.861971	−	0.861971i	0.991567	+	0.129596i	$0.0413681\pi$
$864$	28.9025	+	1.46146i	0.983283	+	0.0497199i
$865$	8.75736	−	8.75736i	0.297759	−	0.297759i
$866$	11.0004	+	8.16333i	0.373808	+	0.277401i
$867$		−	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
$876$	−36.0637	+	67.3774i	−1.21848	+	2.27647i
$877$	14.2635	+	14.2635i	0.481643	+	0.481643i	0.905656	−	0.424013i	$-0.139379\pi$
$877$	14.2635	+	14.2635i	0.481643	+	0.481643i	−0.424013	+	0.905656i	$0.639379\pi$
$878$	20.0085	−	26.9621i	0.675253	−	0.909927i
$879$	−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	$-0.933490\pi$
$881$		−	12.3137i		−	0.414859i	0.978250	−	0.207430i	$-0.0665098\pi$
$882$	−4.54266	−	3.37109i	−0.152959	−	0.113510i
$883$	34.4529			1.15943			0.579717	−	0.814818i	$-0.303163\pi$
$883$	34.4529			1.15943			0.579717	+	0.814818i	$0.303163\pi$
$884$	41.8336	−	4.05184i	1.40702	−	0.136278i
$885$	−9.17157			−0.308299
$886$	−31.2300	−	23.1756i	−1.04919	−	0.778600i
$887$		−	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
$890$	−7.44035	+	10.0261i	−0.249401	+	0.336077i
$891$	−0.198843	−	0.198843i	−0.00666149	−	0.00666149i
$892$	44.4024	+	23.7663i	1.48670	+	0.795756i
$893$	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
$902$	−11.1681	−	8.28777i	−0.371856	−	0.275953i
$903$	28.3188	−	28.3188i	0.942390	−	0.942390i
$904$	−40.7692	−	14.6271i	−1.35596	−	0.486489i
$905$	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	$-0.587269\pi$
$907$	−16.3075			−0.541483			−0.270742	+	0.962652i	$0.587269\pi$
$908$	−31.9958	−	17.1257i	−1.06182	−	0.568337i
$909$		−	52.2843i		−	1.73416i
$910$	9.56684	+	10.5837i	0.317138	+	0.350846i
$911$		−	4.91697i		−	0.162907i	−0.996677	−	0.0814533i	$-0.974044\pi$
$911$		−	4.91697i		−	0.162907i	0.996677	−	0.0814533i	$-0.0259561\pi$
$912$	−25.4368	−	5.09006i	−0.842298	−	0.168549i
$913$	15.6569			0.518166
$914$	6.75481	−	1.00000i	0.223429	−	0.0330771i
$915$	1.63899	−	1.63899i	0.0541834	−	0.0541834i
$916$	−36.6749	−	19.6302i	−1.21177	−	0.648600i
$917$	21.1924	−	21.1924i	0.699834	−	0.699834i
$918$	25.1291	−	33.8623i	0.829383	−	1.11762i
$919$			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
$928$	0.167345	−	3.30948i	0.00549336	−	0.108639i
$929$	20.6274	+	20.6274i	0.676764	+	0.676764i	0.959266	−	0.282503i	$-0.0911647\pi$
$929$	20.6274	+	20.6274i	0.676764	+	0.676764i	−0.282503	+	0.959266i	$0.591165\pi$
$930$	−17.7809	−	13.1952i	−0.583060	−	0.432686i
$931$	1.35778	+	1.35778i	0.0444996	+	0.0444996i
$932$	−22.9142	+	6.93659i	−0.750580	+	0.227216i
$933$			63.7401i			2.08676i
$934$	−5.86034	+	7.89702i	−0.191756	+	0.258398i
$935$	9.55274			0.312408
$936$	42.1866	+	25.3952i	1.37891	+	0.830067i
$937$	−8.97056			−0.293056			−0.146528	−	0.989207i	$-0.546810\pi$
$937$	−8.97056			−0.293056			−0.146528	+	0.989207i	$0.546810\pi$
$938$	9.33039	−	12.5730i	0.304648	−	0.410524i
$939$		−	37.7309i		−	1.23130i
$940$	−5.35584	+	1.62132i	−0.174688	+	0.0528816i
$941$	34.2635	+	34.2635i	1.11696	+	1.11696i	0.992186	+	0.124771i	$0.0398197\pi$
$941$	34.2635	+	34.2635i	1.11696	+	1.11696i	0.124771	+	0.992186i	$0.460180\pi$
$942$	38.1302	+	28.2962i	1.24235	+	0.921941i
$943$	16.7876	+	16.7876i	0.546679	+	0.546679i
$944$	12.8570	+	2.57277i	0.418461	+	0.0837365i
$945$	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	$-0.227460\pi$
$947$	3.07914	+	3.07914i	0.100059	+	0.100059i	−0.655305	+	0.755364i	$0.727460\pi$
$948$	−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	$-0.689292\pi$
$953$		−	51.1421i		−	1.65666i	0.560243	−	0.828328i	$-0.310708\pi$
$954$	0.987369	−	1.33051i	0.0319672	−	0.0430770i
$955$	−16.9864	+	16.9864i	−0.549668	+	0.549668i
$956$	20.5809	+	11.0159i	0.665633	+	0.356279i
$957$	1.89949	−	1.89949i	0.0614020	−	0.0614020i
$958$	−14.9853	+	2.21846i	−0.484152	+	0.0716752i
$959$	−34.2541			−1.10612
$960$	22.2794	−	2.15561i	0.719065	−	0.0695719i
$961$		−	0.313708i		−	0.0101196i
$962$	−0.682773	+	13.5301i	−0.0220135	+	0.436229i
$963$		−	49.4027i		−	1.59198i
$964$	−32.5951	−	17.4465i	−1.04982	−	0.561914i
$965$	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	$-0.807165\pi$
$967$	−7.85551	+	7.85551i	−0.252616	+	0.252616i	0.569426	+	0.822042i	$0.307165\pi$
$968$	−7.94093	+	22.1333i	−0.255231	+	0.711392i
$969$	−26.7279	+	26.7279i	−0.858625	+	0.858625i
$970$	−0.665257	−	0.493684i	−0.0213601	−	0.0158513i
$971$		−	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	0.988482	+	0.151340i	$0.0483589\pi$
$977$	35.6274	+	35.6274i	1.13982	+	1.13982i	0.151340	+	0.988482i	$0.451641\pi$
$978$	8.77817	+	59.2949i	0.280695	+	1.89604i
$979$	14.4697			0.462454
$980$	−1.46077	−	0.781874i	−0.0466625	−	0.0249761i
$981$	22.7279	+	22.7279i	0.725647	+	0.725647i
$982$	2.35802	−	3.17751i	0.0752474	−	0.101399i
$983$	31.3155	+	31.3155i	0.998811	+	0.998811i	0.999999	−	0.00118842i	$-0.000378287\pi$
$983$	31.3155	+	31.3155i	0.998811	+	0.998811i	−0.00118842	+	0.999999i	$0.500378\pi$
$984$	−42.9411	+	20.2644i	−1.36891	+	0.646006i
$985$			26.3137i			0.838424i
$986$	−3.87740	−	2.87740i	−0.123482	−	0.0916352i
$987$	21.9034			0.697193
$988$	−12.9033	−	10.6245i	−0.410508	−	0.338010i
$989$	−20.2426			−0.643679
$990$	8.98737	+	6.66949i	0.285637	+	0.211970i
$991$			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
$994$	17.5288	−	23.6207i	0.555980	−	0.749203i
$995$	−11.6718	−	11.6718i	−0.370020	−	0.370020i
$996$	25.2260	−	47.1294i	0.799315	−	1.49335i
$997$	−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.47.4	yes	8
3.2	odd	2		468.2.n.i.307.1		8
4.3	odd	2	inner	52.2.f.b.47.2	yes	8
8.3	odd	2		832.2.k.h.255.4		8
8.5	even	2		832.2.k.h.255.1		8
12.11	even	2		468.2.n.i.307.3		8
13.2	odd	12		676.2.l.l.19.4		16
13.3	even	3		676.2.l.l.319.2		16
13.4	even	6		676.2.l.h.427.4		16
13.5	odd	4	inner	52.2.f.b.31.2	✓	8
13.6	odd	12		676.2.l.l.587.1		16
13.7	odd	12		676.2.l.h.587.4		16
13.8	odd	4		676.2.f.g.239.3		8
13.9	even	3		676.2.l.l.427.1		16
13.10	even	6		676.2.l.h.319.3		16
13.11	odd	12		676.2.l.h.19.1		16
13.12	even	2		676.2.f.g.99.1		8
39.5	even	4		468.2.n.i.343.3		8
52.3	odd	6		676.2.l.l.319.1		16
52.7	even	12		676.2.l.h.587.3		16
52.11	even	12		676.2.l.h.19.4		16
52.15	even	12		676.2.l.l.19.1		16
52.19	even	12		676.2.l.l.587.2		16
52.23	odd	6		676.2.l.h.319.4		16
52.31	even	4	inner	52.2.f.b.31.4	yes	8
52.35	odd	6		676.2.l.l.427.4		16
52.43	odd	6		676.2.l.h.427.1		16
52.47	even	4		676.2.f.g.239.1		8
52.51	odd	2		676.2.f.g.99.3		8
104.5	odd	4		832.2.k.h.447.1		8
104.83	even	4		832.2.k.h.447.4		8
156.83	odd	4		468.2.n.i.343.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.f.b.31.2	✓	8	13.5	odd	4	inner
52.2.f.b.31.4	yes	8	52.31	even	4	inner
52.2.f.b.47.2	yes	8	4.3	odd	2	inner
52.2.f.b.47.4	yes	8	1.1	even	1	trivial
468.2.n.i.307.1		8	3.2	odd	2
468.2.n.i.307.3		8	12.11	even	2
468.2.n.i.343.1		8	156.83	odd	4
468.2.n.i.343.3		8	39.5	even	4
676.2.f.g.99.1		8	13.12	even	2
676.2.f.g.99.3		8	52.51	odd	2
676.2.f.g.239.1		8	52.47	even	4
676.2.f.g.239.3		8	13.8	odd	4
676.2.l.h.19.1		16	13.11	odd	12
676.2.l.h.19.4		16	52.11	even	12
676.2.l.h.319.3		16	13.10	even	6
676.2.l.h.319.4		16	52.23	odd	6
676.2.l.h.427.1		16	52.43	odd	6
676.2.l.h.427.4		16	13.4	even	6
676.2.l.h.587.3		16	52.7	even	12
676.2.l.h.587.4		16	13.7	odd	12
676.2.l.l.19.1		16	52.15	even	12
676.2.l.l.19.4		16	13.2	odd	12
676.2.l.l.319.1		16	52.3	odd	6
676.2.l.l.319.2		16	13.3	even	3
676.2.l.l.427.1		16	13.9	even	3
676.2.l.l.427.4		16	52.35	odd	6
676.2.l.l.587.1		16	13.6	odd	12
676.2.l.l.587.2		16	52.19	even	12
832.2.k.h.255.1		8	8.5	even	2
832.2.k.h.255.4		8	8.3	odd	2
832.2.k.h.447.1		8	104.5	odd	4
832.2.k.h.447.4		8	104.83	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.842772 - 1.13567i) q^{2} +2.79793i q^{3} +(-0.579471 - 1.91421i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(3.17751 + 2.35802i) q^{6} +(-1.97844 - 1.97844i) q^{7} +(-2.66227 - 0.955161i) 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} +(-4.06926 + 5.48348i) q^{18} +(1.63899 - 1.63899i) q^{19} +(-0.943806 + 1.76330i) q^{20} +(5.53553 - 5.53553i) q^{21} +(2.29289 - 0.339446i) q^{22} -3.95687 q^{23} +(2.67248 - 7.44885i) q^{24} -4.00000i q^{25} +(3.78269 - 3.41925i) q^{26} -5.11582i q^{27} +(-2.64070 + 4.93360i) q^{28} -0.585786 q^{29} +(-0.579471 - 3.91421i) q^{30} +(3.95687 - 3.95687i) q^{31} +(-0.285675 + 5.64964i) q^{32} +(-3.24264 + 3.24264i) q^{33} +(6.61914 + 4.91203i) 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} +(1.54689 - 2.89003i) q^{44} +(3.41421 + 3.41421i) q^{45} +(-3.33474 + 4.49368i) q^{46} +(1.97844 + 1.97844i) q^{47} +(-6.20711 - 9.31271i) q^{48} +0.828427i q^{49} +(-4.54266 - 3.37109i) q^{50} -16.3075 q^{51} +(-0.695185 - 7.17751i) q^{52} -0.242641 q^{53} +(-5.80985 - 4.31147i) q^{54} -1.63899i q^{55} +(3.37740 + 7.15685i) q^{56} +(4.58579 + 4.58579i) q^{57} +(-0.493684 + 0.665257i) q^{58} +(-2.31788 - 2.31788i) q^{59} +(-4.93360 - 2.64070i) 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} +(3.17751 + 2.35802i) q^{70} +(-5.25642 + 5.25642i) q^{71} +(12.8546 + 4.61192i) q^{72} +(-9.65685 + 9.65685i) q^{73} +(0.550253 + 3.71685i) q^{74} +11.1917 q^{75} +(-4.08713 - 2.18763i) q^{76} -4.58579i q^{77} +(9.56684 + 10.5837i) q^{78} -9.55274i q^{79} +(3.92224 + 0.784864i) q^{80} -0.171573 q^{81} +(-8.39380 + 1.24264i) q^{82} +(6.75481 - 6.75481i) q^{83} +(-13.8039 - 7.38851i) q^{84} +(4.12132 - 4.12132i) q^{85} +(4.31147 - 5.80985i) 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} +(-15.8073 - 0.799300i) q^{96} +(0.414214 + 0.414214i) q^{97} +(0.940816 + 0.698175i) q^{98} +(-5.59587 - 5.59587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40}+ \cdots - 16 q^{98}+O(q^{100}) \) 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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