LMFDB - Embedded newform 585.2.i.h.196.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.7
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264400 + 0.457954i) q^{2} +(1.72073 - 0.197726i) q^{3} +(0.860185 + 1.48988i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.364411 + 0.840293i) q^{6} +(-1.64961 + 2.85721i) q^{7} -1.96733 q^{8} +(2.92181 - 0.680465i) q^{9} +O(q^{10})$	\(q+(-0.264400 + 0.457954i) q^{2} +(1.72073 - 0.197726i) q^{3} +(0.860185 + 1.48988i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.364411 + 0.840293i) q^{6} +(-1.64961 + 2.85721i) q^{7} -1.96733 q^{8} +(2.92181 - 0.680465i) q^{9} -0.528800 q^{10} +(0.276109 - 0.478235i) q^{11} +(1.77473 + 2.39361i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.872313 - 1.51089i) q^{14} +(1.03160 + 1.39133i) q^{15} +(-1.20021 + 2.07882i) q^{16} +6.44948 q^{17} +(-0.460904 + 1.51797i) q^{18} -7.62544 q^{19} +(-0.860185 + 1.48988i) q^{20} +(-2.27358 + 5.24265i) q^{21} +(0.146006 + 0.252891i) q^{22} +(1.05742 + 1.83151i) q^{23} +(-3.38524 + 0.388992i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.528800 q^{26} +(4.89309 - 1.74861i) q^{27} -5.67588 q^{28} +(-0.658520 + 1.14059i) q^{29} +(-0.909921 + 0.104557i) q^{30} +(-4.07808 - 7.06344i) q^{31} +(-2.60200 - 4.50680i) q^{32} +(0.380549 - 0.877506i) q^{33} +(-1.70524 + 2.95357i) q^{34} -3.29922 q^{35} +(3.52711 + 3.76783i) q^{36} +8.74375 q^{37} +(2.01617 - 3.49210i) q^{38} +(-1.03160 - 1.39133i) q^{39} +(-0.983666 - 1.70376i) q^{40} +(4.67562 + 8.09842i) q^{41} +(-1.79976 - 2.42735i) q^{42} +(3.37267 - 5.84163i) q^{43} +0.950020 q^{44} +(2.05020 + 2.19013i) q^{45} -1.11833 q^{46} +(2.84773 - 4.93241i) q^{47} +(-1.65420 + 3.81440i) q^{48} +(-1.94242 - 3.36437i) q^{49} +(-0.264400 - 0.457954i) q^{50} +(11.0978 - 1.27523i) q^{51} +(0.860185 - 1.48988i) q^{52} -4.88532 q^{53} +(-0.492949 + 2.70314i) q^{54} +0.552218 q^{55} +(3.24533 - 5.62107i) q^{56} +(-13.1213 + 1.50775i) q^{57} +(-0.348225 - 0.603144i) q^{58} +(-0.860957 - 1.49122i) q^{59} +(-1.18556 + 2.73377i) q^{60} +(-0.714433 + 1.23743i) q^{61} +4.31298 q^{62} +(-2.87561 + 9.47071i) q^{63} -2.04896 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.301240 + 0.406287i) q^{66} +(-0.567134 - 0.982304i) q^{67} +(5.54775 + 9.60898i) q^{68} +(2.18167 + 2.94245i) q^{69} +(0.872313 - 1.51089i) q^{70} +8.65531 q^{71} +(-5.74817 + 1.33870i) q^{72} +3.42341 q^{73} +(-2.31185 + 4.00424i) q^{74} +(-0.689128 + 1.58906i) q^{75} +(-6.55929 - 11.3610i) q^{76} +(0.910944 + 1.57780i) q^{77} +(0.909921 - 0.104557i) q^{78} +(-5.38562 + 9.32817i) q^{79} -2.40042 q^{80} +(8.07393 - 3.97638i) q^{81} -4.94494 q^{82} +(5.45979 - 9.45663i) q^{83} +(-9.76664 + 1.12227i) q^{84} +(3.22474 + 5.58541i) q^{85} +(1.78347 + 3.08905i) q^{86} +(-0.907610 + 2.09285i) q^{87} +(-0.543198 + 0.940847i) q^{88} +8.64261 q^{89} +(-1.54505 + 0.359830i) q^{90} +3.29922 q^{91} +(-1.81916 + 3.15087i) q^{92} +(-8.41389 - 11.3479i) q^{93} +(1.50588 + 2.60826i) q^{94} +(-3.81272 - 6.60383i) q^{95} +(-5.36845 - 7.24049i) q^{96} +(-3.18971 + 5.52473i) q^{97} +2.05430 q^{98} +(0.481316 - 1.58519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.264400	+	0.457954i	−0.186959	+	0.323822i	−0.944235	−	0.329273i	$-0.893196\pi$
$2$	−0.264400	+	0.457954i	−0.186959	+	0.323822i	0.757276	+	0.653095i	$0.226530\pi$
$3$	1.72073	−	0.197726i	0.993463	−	0.114157i
$3$	1.72073	−	0.197726i	0.993463	−	0.114157i
$4$	0.860185	+	1.48988i	0.430093	+	0.744942i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.364411	+	0.840293i	−0.148770	+	0.343048i
$7$	−1.64961	+	2.85721i	−0.623494	+	1.07992i	0.365337	+	0.930876i	$0.380954\pi$
$7$	−1.64961	+	2.85721i	−0.623494	+	1.07992i	−0.988830	+	0.149047i	$0.952379\pi$
$8$	−1.96733			−0.695557
$9$	2.92181	−	0.680465i	0.973936	−	0.226822i
$10$	−0.528800			−0.167221
$11$	0.276109	−	0.478235i	0.0832500	−	0.144193i	−0.821394	−	0.570361i	$-0.806803\pi$
$11$	0.276109	−	0.478235i	0.0832500	−	0.144193i	0.904644	+	0.426168i	$0.140137\pi$
$12$	1.77473	+	2.39361i	0.512322	+	0.690974i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−0.872313	−	1.51089i	−0.233135	−	0.403802i
$15$	1.03160	+	1.39133i	0.266358	+	0.359240i
$16$	−1.20021	+	2.07882i	−0.300052	+	0.519706i
$17$	6.44948			1.56423			0.782114	−	0.623135i	$-0.214141\pi$
$17$	6.44948			1.56423			0.782114	+	0.623135i	$0.214141\pi$
$18$	−0.460904	+	1.51797i	−0.108636	+	0.357789i
$19$	−7.62544			−1.74940			−0.874698	−	0.484668i	$-0.838941\pi$
$19$	−7.62544			−1.74940			−0.874698	+	0.484668i	$0.838941\pi$
$20$	−0.860185	+	1.48988i	−0.192343	+	0.333148i
$21$	−2.27358	+	5.24265i	−0.496137	+	1.14404i
$22$	0.146006	+	0.252891i	0.0311287	+	0.0539165i
$23$	1.05742	+	1.83151i	0.220488	+	0.381896i	0.954956	−	0.296747i	$-0.0959018\pi$
$23$	1.05742	+	1.83151i	0.220488	+	0.381896i	−0.734468	+	0.678643i	$0.762568\pi$
$24$	−3.38524	+	0.388992i	−0.691010	+	0.0794027i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.528800			0.103706
$27$	4.89309	−	1.74861i	0.941676	−	0.336521i
$28$	−5.67588			−1.07264
$29$	−0.658520	+	1.14059i	−0.122284	+	0.211802i	−0.920668	−	0.390346i	$-0.872355\pi$
$29$	−0.658520	+	1.14059i	−0.122284	+	0.211802i	0.798384	+	0.602149i	$0.205689\pi$
$30$	−0.909921	+	0.104557i	−0.166128	+	0.0190895i
$31$	−4.07808	−	7.06344i	−0.732445	−	1.26863i	−0.955835	−	0.293903i	$-0.905046\pi$
$31$	−4.07808	−	7.06344i	−0.732445	−	1.26863i	0.223390	−	0.974729i	$-0.428288\pi$
$32$	−2.60200	−	4.50680i	−0.459973	−	0.796697i
$33$	0.380549	−	0.877506i	0.0662451	−	0.152754i
$34$	−1.70524	+	2.95357i	−0.292447	+	0.506532i
$35$	−3.29922			−0.557670
$36$	3.52711	+	3.76783i	0.587852	+	0.627972i
$37$	8.74375			1.43746			0.718732	−	0.695287i	$-0.244723\pi$
$37$	8.74375			1.43746			0.718732	+	0.695287i	$0.244723\pi$
$38$	2.01617	−	3.49210i	0.327065	−	0.566494i
$39$	−1.03160	−	1.39133i	−0.165188	−	0.222791i
$40$	−0.983666	−	1.70376i	−0.155531	−	0.269388i
$41$	4.67562	+	8.09842i	0.730210	+	1.26476i	0.956793	+	0.290768i	$0.0939109\pi$
$41$	4.67562	+	8.09842i	0.730210	+	1.26476i	−0.226584	+	0.973992i	$0.572756\pi$
$42$	−1.79976	−	2.42735i	−0.277708	−	0.374549i
$43$	3.37267	−	5.84163i	0.514327	−	0.890840i	−0.485535	−	0.874217i	$-0.661375\pi$
$43$	3.37267	−	5.84163i	0.514327	−	0.890840i	0.999862	−	0.0166231i	$-0.00529153\pi$
$44$	0.950020			0.143221
$45$	2.05020	+	2.19013i	0.305626	+	0.326485i
$46$	−1.11833			−0.164889
$47$	2.84773	−	4.93241i	0.415384	−	0.719466i	−0.580085	−	0.814556i	$-0.696981\pi$
$47$	2.84773	−	4.93241i	0.415384	−	0.719466i	0.995469	+	0.0950904i	$0.0303140\pi$
$48$	−1.65420	+	3.81440i	−0.238763	+	0.550561i
$49$	−1.94242	−	3.36437i	−0.277488	−	0.480624i
$50$	−0.264400	−	0.457954i	−0.0373918	−	0.0647645i
$51$	11.0978	−	1.27523i	1.55400	−	0.178568i
$52$	0.860185	−	1.48988i	0.119286	−	0.206610i
$53$	−4.88532			−0.671050			−0.335525	−	0.942031i	$-0.608914\pi$
$53$	−4.88532			−0.671050			−0.335525	+	0.942031i	$0.608914\pi$
$54$	−0.492949	+	2.70314i	−0.0670818	+	0.367851i
$55$	0.552218			0.0744611
$56$	3.24533	−	5.62107i	0.433675	−	0.751147i
$57$	−13.1213	+	1.50775i	−1.73796	+	0.199706i
$58$	−0.348225	−	0.603144i	−0.0457242	−	0.0791967i
$59$	−0.860957	−	1.49122i	−0.112087	−	0.194140i	0.804525	−	0.593919i	$-0.202420\pi$
$59$	−0.860957	−	1.49122i	−0.112087	−	0.194140i	−0.916612	+	0.399779i	$0.869087\pi$
$60$	−1.18556	+	2.73377i	−0.153055	+	0.352928i
$61$	−0.714433	+	1.23743i	−0.0914738	+	0.158437i	−0.908131	−	0.418685i	$-0.862491\pi$
$61$	−0.714433	+	1.23743i	−0.0914738	+	0.158437i	0.816658	+	0.577122i	$0.195824\pi$
$62$	4.31298			0.547749
$63$	−2.87561	+	9.47071i	−0.362293	+	1.19320i
$64$	−2.04896			−0.256120
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	0.301240	+	0.406287i	0.0370801	+	0.0500104i
$67$	−0.567134	−	0.982304i	−0.0692864	−	0.120008i	0.829301	−	0.558802i	$-0.188739\pi$
$67$	−0.567134	−	0.982304i	−0.0692864	−	0.120008i	−0.898587	+	0.438795i	$0.855406\pi$
$68$	5.54775	+	9.60898i	0.672763	+	1.16526i
$69$	2.18167	+	2.94245i	0.262642	+	0.354229i
$70$	0.872313	−	1.51089i	0.104261	−	0.180586i
$71$	8.65531			1.02720			0.513598	−	0.858031i	$-0.328312\pi$
$71$	8.65531			1.02720			0.513598	+	0.858031i	$0.328312\pi$
$72$	−5.74817	+	1.33870i	−0.677428	+	0.157767i
$73$	3.42341			0.400679			0.200340	−	0.979726i	$-0.435795\pi$
$73$	3.42341			0.400679			0.200340	+	0.979726i	$0.435795\pi$
$74$	−2.31185	+	4.00424i	−0.268747	+	0.465483i
$75$	−0.689128	+	1.58906i	−0.0795737	+	0.183489i
$76$	−6.55929	−	11.3610i	−0.752403	−	1.30320i
$77$	0.910944	+	1.57780i	0.103812	+	0.179807i
$78$	0.909921	−	0.104557i	0.103028	−	0.0118388i
$79$	−5.38562	+	9.32817i	−0.605930	+	1.04950i	0.385974	+	0.922510i	$0.373865\pi$
$79$	−5.38562	+	9.32817i	−0.605930	+	1.04950i	−0.991904	+	0.126991i	$0.959468\pi$
$80$	−2.40042			−0.268375
$81$	8.07393	−	3.97638i	0.897104	−	0.441820i
$82$	−4.94494			−0.546077
$83$	5.45979	−	9.45663i	0.599290	−	1.03800i	−0.393636	−	0.919266i	$-0.628783\pi$
$83$	5.45979	−	9.45663i	0.599290	−	1.03800i	0.992926	−	0.118734i	$-0.0378836\pi$
$84$	−9.76664	+	1.12227i	−1.06563	+	0.122450i
$85$	3.22474	+	5.58541i	0.349772	+	0.605823i
$86$	1.78347	+	3.08905i	0.192316	+	0.333101i
$87$	−0.907610	+	2.09285i	−0.0973060	+	0.224377i
$88$	−0.543198	+	0.940847i	−0.0579051	+	0.100295i
$89$	8.64261			0.916114			0.458057	−	0.888923i	$-0.348545\pi$
$89$	8.64261			0.916114			0.458057	+	0.888923i	$0.348545\pi$
$90$	−1.54505	+	0.359830i	−0.162863	+	0.0379294i
$91$	3.29922			0.345852
$92$	−1.81916	+	3.15087i	−0.189660	+	0.328501i
$93$	−8.41389	−	11.3479i	−0.872480	−	1.17672i
$94$	1.50588	+	2.60826i	0.155319	+	0.269021i
$95$	−3.81272	−	6.60383i	−0.391177	−	0.677538i
$96$	−5.36845	−	7.24049i	−0.547915	−	0.738979i
$97$	−3.18971	+	5.52473i	−0.323865	+	0.560951i	−0.981282	−	0.192576i	$-0.938316\pi$
$97$	−3.18971	+	5.52473i	−0.323865	+	0.560951i	0.657417	+	0.753527i	$0.271649\pi$
$98$	2.05430			0.207516
$99$	0.481316	−	1.58519i	0.0483741	−	0.159318i
$100$	−1.72037			−0.172037
$101$	−0.440569	+	0.763089i	−0.0438383	+	0.0759302i	−0.887112	−	0.461554i	$-0.847292\pi$
$101$	−0.440569	+	0.763089i	−0.0438383	+	0.0759302i	0.843274	+	0.537484i	$0.180625\pi$
$102$	−2.35026	+	5.41945i	−0.232711	+	0.536606i
$103$	−4.12581	−	7.14611i	−0.406528	−	0.704127i	0.587970	−	0.808883i	$-0.299927\pi$
$103$	−4.12581	−	7.14611i	−0.406528	−	0.704127i	−0.994498	+	0.104755i	$0.966594\pi$
$104$	0.983666	+	1.70376i	0.0964563	+	0.167067i
$105$	−5.67706	+	0.652341i	−0.554024	+	0.0636620i
$106$	1.29168	−	2.23725i	0.125459	−	0.217301i
$107$	7.95638			0.769173			0.384586	−	0.923089i	$-0.374344\pi$
$107$	7.95638			0.769173			0.384586	+	0.923089i	$0.374344\pi$
$108$	6.81420	+	5.78601i	0.655697	+	0.556759i
$109$	−9.28002			−0.888865			−0.444433	−	0.895812i	$-0.646595\pi$
$109$	−9.28002			−0.888865			−0.444433	+	0.895812i	$0.646595\pi$
$110$	−0.146006	+	0.252891i	−0.0139212	+	0.0241122i
$111$	15.0456	−	1.72887i	1.42807	−	0.164097i
$112$	−3.95975	−	6.85849i	−0.374161	−	0.648066i
$113$	−3.15265	−	5.46056i	−0.296577	−	0.513686i	0.678774	−	0.734347i	$-0.262512\pi$
$113$	−3.15265	−	5.46056i	−0.296577	−	0.513686i	−0.975350	+	0.220662i	$0.929178\pi$
$114$	2.77879	−	6.40761i	0.260258	−	0.600127i
$115$	−1.05742	+	1.83151i	−0.0986051	+	0.170789i
$116$	−2.26580			−0.210374
$117$	−2.05020	−	2.19013i	−0.189541	−	0.202477i
$118$	0.910548			0.0838227
$119$	−10.6391	+	18.4275i	−0.975287	+	1.68925i
$120$	−2.02950	−	2.73721i	−0.185267	−	0.249872i
$121$	5.34753	+	9.26219i	0.486139	+	0.842017i
$122$	−0.377792	−	0.654355i	−0.0342037	−	0.0592425i
$123$	9.64674	+	13.0107i	0.869817	+	1.17313i
$124$	7.01581	−	12.1517i	0.630038	−	1.09126i
$125$	−1.00000			−0.0894427
$126$	−3.57684	−	3.82095i	−0.318650	−	0.340398i
$127$	6.63912			0.589126			0.294563	−	0.955632i	$-0.404826\pi$
$127$	6.63912			0.589126			0.294563	+	0.955632i	$0.404826\pi$
$128$	5.74575	−	9.95193i	0.507857	−	0.879634i
$129$	4.64840	−	10.7187i	0.409269	−	0.943731i
$130$	0.264400	+	0.457954i	0.0231894	+	0.0401652i
$131$	−9.95215	−	17.2376i	−0.869524	−	1.50606i	−0.862484	−	0.506084i	$-0.831093\pi$
$131$	−9.95215	−	17.2376i	−0.869524	−	1.50606i	−0.00703934	−	0.999975i	$-0.502241\pi$
$132$	1.63473	−	0.187844i	0.142285	−	0.0163497i
$133$	12.5790	−	21.7875i	1.09074	−	1.88921i
$134$	0.599800			0.0518149
$135$	3.96089	+	3.36324i	0.340899	+	0.289461i
$136$	−12.6883			−1.08801
$137$	7.76926	−	13.4568i	0.663773	−	1.14969i	−0.315843	−	0.948811i	$-0.602287\pi$
$137$	7.76926	−	13.4568i	0.663773	−	1.14969i	0.979616	−	0.200877i	$-0.0643793\pi$
$138$	−1.92434	+	0.221123i	−0.163811	+	0.0188232i
$139$	−11.1218	−	19.2635i	−0.943340	−	1.63391i	−0.759042	−	0.651042i	$-0.774332\pi$
$139$	−11.1218	−	19.2635i	−0.943340	−	1.63391i	−0.184297	−	0.982871i	$-0.559001\pi$
$140$	−2.83794	−	4.91545i	−0.239850	−	0.415432i
$141$	3.92490	−	9.05040i	0.330536	−	0.762181i
$142$	−2.28846	+	3.96373i	−0.192044	+	0.332629i
$143$	−0.552218			−0.0461788
$144$	−2.09221	+	6.89062i	−0.174351	+	0.574218i
$145$	−1.31704			−0.109374
$146$	−0.905148	+	1.56776i	−0.0749106	+	0.129749i
$147$	−4.00760	−	5.40510i	−0.330541	−	0.445805i
$148$	7.52125	+	13.0272i	0.618243	+	1.07083i
$149$	−7.02763	−	12.1722i	−0.575726	−	0.997186i	−0.995962	−	0.0897718i	$-0.971386\pi$
$149$	−7.02763	−	12.1722i	−0.575726	−	0.997186i	0.420237	−	0.907415i	$-0.361947\pi$
$150$	−0.545510	−	0.735736i	−0.0445407	−	0.0600726i
$151$	−8.22137	+	14.2398i	−0.669045	+	1.15882i	0.309126	+	0.951021i	$0.399963\pi$
$151$	−8.22137	+	14.2398i	−0.669045	+	1.15882i	−0.978171	+	0.207799i	$0.933370\pi$
$152$	15.0018			1.21680
$153$	18.8442	−	4.38865i	1.52346	−	0.354801i
$154$	−0.963414			−0.0776341
$155$	4.07808	−	7.06344i	0.327559	−	0.567349i
$156$	1.18556	−	2.73377i	0.0949205	−	0.218877i
$157$	5.07918	+	8.79740i	0.405363	+	0.702109i	0.994364	−	0.106024i	$-0.0338119\pi$
$157$	5.07918	+	8.79740i	0.405363	+	0.702109i	−0.589001	+	0.808132i	$0.700479\pi$
$158$	−2.84791	−	4.93273i	−0.226568	−	0.392427i
$159$	−8.40631	+	0.965955i	−0.666664	+	0.0766052i
$160$	2.60200	−	4.50680i	0.205706	−	0.356294i
$161$	−6.97733			−0.549891
$162$	−0.313749	+	4.74884i	−0.0246505	+	0.373104i
$163$	13.2149			1.03507			0.517535	−	0.855662i	$-0.326850\pi$
$163$	13.2149			1.03507			0.517535	+	0.855662i	$0.326850\pi$
$164$	−8.04380	+	13.9323i	−0.628116	+	1.08793i
$165$	0.950218	−	0.109188i	0.0739743	−	0.00850027i
$166$	2.88714	+	5.00067i	0.224085	+	0.388127i
$167$	−0.0441173	−	0.0764134i	−0.00341390	−	0.00591305i	0.864313	−	0.502954i	$-0.167753\pi$
$167$	−0.0441173	−	0.0764134i	−0.00341390	−	0.00591305i	−0.867727	+	0.497041i	$0.834420\pi$
$168$	4.47289	−	10.3140i	0.345091	−	0.795744i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−3.41048			−0.261572
$171$	−22.2801	+	5.18885i	−1.70380	+	0.396801i
$172$	11.6045			0.884833
$173$	−2.36616	+	4.09831i	−0.179896	+	0.311589i	−0.941845	−	0.336048i	$-0.890909\pi$
$173$	−2.36616	+	4.09831i	−0.179896	+	0.311589i	0.761949	+	0.647637i	$0.224243\pi$
$174$	−0.718458	−	0.968994i	−0.0544662	−	0.0734592i
$175$	−1.64961	−	2.85721i	−0.124699	−	0.215985i
$176$	0.662777	+	1.14796i	0.0499587	+	0.0865310i
$177$	−1.77633	−	2.39575i	−0.133517	−	0.180076i
$178$	−2.28510	+	3.95792i	−0.171276	+	0.296658i
$179$	1.08785			0.0813097			0.0406548	−	0.999173i	$-0.487056\pi$
$179$	1.08785			0.0813097			0.0406548	+	0.999173i	$0.487056\pi$
$180$	−1.49948	+	4.93848i	−0.111765	+	0.368093i
$181$	2.66381			0.197999			0.0989997	−	0.995087i	$-0.468436\pi$
$181$	2.66381			0.197999			0.0989997	+	0.995087i	$0.468436\pi$
$182$	−0.872313	+	1.51089i	−0.0646601	+	0.111995i
$183$	−0.984672	+	2.27055i	−0.0727891	+	0.167844i
$184$	−2.08030	−	3.60318i	−0.153362	−	0.265630i
$185$	4.37187	+	7.57231i	0.321427	+	0.556727i
$186$	7.42146	−	0.852787i	0.544168	−	0.0625294i
$187$	1.78076	−	3.08437i	0.130222	−	0.225551i
$188$	9.79829			0.714614
$189$	−3.07554	+	16.8651i	−0.223713	+	1.22676i
$190$	4.03233			0.292536
$191$	7.77194	−	13.4614i	0.562358	−	0.974033i	−0.434932	−	0.900463i	$-0.643228\pi$
$191$	7.77194	−	13.4614i	0.562358	−	0.974033i	0.997290	−	0.0735693i	$-0.0234390\pi$
$192$	−3.52570	+	0.405132i	−0.254446	+	0.0292379i
$193$	−9.05801	−	15.6889i	−0.652010	−	1.12931i	−0.982634	−	0.185552i	$-0.940593\pi$
$193$	−9.05801	−	15.6889i	−0.652010	−	1.12931i	0.330624	−	0.943762i	$-0.392741\pi$
$194$	−1.68672	−	2.92148i	−0.121099	−	0.209750i
$195$	0.689128	−	1.58906i	0.0493495	−	0.113795i
$196$	3.34168	−	5.78796i	0.238691	−	0.413426i
$197$	−22.6581			−1.61432			−0.807162	−	0.590330i	$-0.798998\pi$
$197$	−22.6581			−1.61432			−0.807162	+	0.590330i	$0.798998\pi$
$198$	0.598686	+	0.639546i	0.0425468	+	0.0454505i
$199$	−15.9484			−1.13056			−0.565278	−	0.824901i	$-0.691231\pi$
$199$	−15.9484			−1.13056			−0.565278	+	0.824901i	$0.691231\pi$
$200$	0.983666	−	1.70376i	0.0695557	−	0.120474i
$201$	−1.17011	−	1.57814i	−0.0825332	−	0.111314i
$202$	−0.232973	−	0.403521i	−0.0163919	−	0.0283916i
$203$	−2.17260	−	3.76306i	−0.152487	−	0.264115i
$204$	11.4461	+	15.4375i	0.801388	+	1.08084i
$205$	−4.67562	+	8.09842i	−0.326560	+	0.565618i
$206$	4.36345			0.304016
$207$	4.33586	+	4.63178i	0.301363	+	0.321931i
$208$	2.40042			0.166439
$209$	−2.10545	+	3.64675i	−0.145637	+	0.252251i
$210$	1.20227	−	2.77231i	0.0829646	−	0.191308i
$211$	−9.29744	−	16.1036i	−0.640062	−	1.10862i	−0.985418	−	0.170149i	$-0.945575\pi$
$211$	−9.29744	−	16.1036i	−0.640062	−	1.10862i	0.345356	−	0.938472i	$-0.387758\pi$
$212$	−4.20228	−	7.27857i	−0.288614	−	0.499894i
$213$	14.8934	−	1.71138i	1.02048	−	0.117262i
$214$	−2.10367	+	3.64366i	−0.143804	+	0.249075i
$215$	6.74533			0.460028
$216$	−9.62633	+	3.44010i	−0.654989	+	0.234069i
$217$	26.9090			1.82670
$218$	2.45364	−	4.24982i	0.166181	−	0.287834i
$219$	5.89075	−	0.676896i	0.398060	−	0.0457404i
$220$	0.475010	+	0.822742i	0.0320252	+	0.0554692i
$221$	−3.22474	−	5.58541i	−0.216920	−	0.375716i
$222$	−3.18632	+	7.34731i	−0.213852	+	0.493119i
$223$	−8.22510	+	14.2463i	−0.550793	+	0.954002i	0.447424	+	0.894322i	$0.352341\pi$
$223$	−8.22510	+	14.2463i	−0.550793	+	0.954002i	−0.998218	+	0.0596803i	$0.980992\pi$
$224$	17.1691			1.14716
$225$	−0.871604	+	2.87059i	−0.0581070	+	0.191373i
$226$	3.33424			0.221791
$227$	−2.51598	+	4.35781i	−0.166991	+	0.289238i	−0.937361	−	0.348360i	$-0.886739\pi$
$227$	−2.51598	+	4.35781i	−0.166991	+	0.289238i	0.770369	+	0.637598i	$0.220072\pi$
$228$	−13.5331	−	18.2523i	−0.896254	−	1.20879i
$229$	−3.98701	−	6.90571i	−0.263469	−	0.456342i	0.703692	−	0.710505i	$-0.251533\pi$
$229$	−3.98701	−	6.90571i	−0.263469	−	0.456342i	−0.967161	+	0.254163i	$0.918200\pi$
$230$	−0.559164	−	0.968501i	−0.0368702	−	0.0638611i
$231$	1.87946	+	2.53485i	0.123659	+	0.166781i
$232$	1.29553	−	2.24392i	0.0850556	−	0.147321i
$233$	−1.37152			−0.0898515			−0.0449257	−	0.998990i	$-0.514305\pi$
$233$	−1.37152			−0.0898515			−0.0449257	+	0.998990i	$0.514305\pi$
$234$	1.54505	−	0.359830i	0.101003	−	0.0235228i
$235$	5.69545			0.371530
$236$	1.48117	−	2.56545i	0.0964156	−	0.166997i
$237$	−7.42277	+	17.1161i	−0.482160	+	1.11181i
$238$	−5.62597	−	9.74446i	−0.364677	−	0.631639i
$239$	10.6791	+	18.4967i	0.690772	+	1.19645i	0.971585	+	0.236690i	$0.0760625\pi$
$239$	10.6791	+	18.4967i	0.690772	+	1.19645i	−0.280813	+	0.959762i	$0.590604\pi$
$240$	−4.13047	+	0.474625i	−0.266620	+	0.0306369i
$241$	−8.36953	+	14.4965i	−0.539129	+	0.933799i	0.459822	+	0.888011i	$0.347913\pi$
$241$	−8.36953	+	14.4965i	−0.539129	+	0.933799i	−0.998951	+	0.0457876i	$0.985420\pi$
$242$	−5.65554			−0.363552
$243$	13.1068	−	8.43869i	0.840802	−	0.541342i
$244$	−2.45818			−0.157369
$245$	1.94242	−	3.36437i	0.124097	−	0.214942i
$246$	−8.50889	+	0.977742i	−0.542507	+	0.0623386i
$247$	3.81272	+	6.60383i	0.242598	+	0.420191i
$248$	8.02294	+	13.8961i	0.509457	+	0.882405i
$249$	7.52499	−	17.3518i	0.476877	−	1.09963i
$250$	0.264400	−	0.457954i	0.0167221	−	0.0289636i
$251$	23.9800			1.51360			0.756802	−	0.653644i	$-0.226761\pi$
$251$	23.9800			1.51360			0.756802	+	0.653644i	$0.226761\pi$
$252$	−16.5838	+	3.86224i	−1.04468	+	0.243298i
$253$	1.16786			0.0734224
$254$	−1.75538	+	3.04041i	−0.110142	+	0.190772i
$255$	6.65328	+	8.97336i	0.416645	+	0.561934i
$256$	0.989390	+	1.71367i	0.0618369	+	0.107105i
$257$	−14.7624	−	25.5692i	−0.920851	−	1.59496i	−0.798102	−	0.602523i	$-0.794162\pi$
$257$	−14.7624	−	25.5692i	−0.920851	−	1.59496i	−0.122749	−	0.992438i	$-0.539171\pi$
$258$	3.67964	+	4.96278i	0.229085	+	0.308969i
$259$	−14.4238	+	24.9827i	−0.896249	+	1.55235i
$260$	1.72037			0.106693
$261$	−1.14794	+	3.78069i	−0.0710556	+	0.234019i
$262$	10.5254			0.650261
$263$	−10.9241	+	18.9211i	−0.673609	+	1.16673i	0.303264	+	0.952907i	$0.401924\pi$
$263$	−10.9241	+	18.9211i	−0.673609	+	1.16673i	−0.976873	+	0.213819i	$0.931410\pi$
$264$	−0.748666	+	1.72635i	−0.0460772	+	0.106249i
$265$	−2.44266	−	4.23081i	−0.150051	−	0.259897i
$266$	6.65177	+	11.5212i	0.407846	+	0.706410i
$267$	14.8716	−	1.70887i	0.910125	−	0.104581i
$268$	0.975680	−	1.68993i	0.0595992	−	0.103229i
$269$	−30.1026			−1.83539			−0.917695	−	0.397286i	$-0.869952\pi$
$269$	−30.1026			−1.83539			−0.917695	+	0.397286i	$0.869952\pi$
$270$	−2.58747	+	0.924666i	−0.157468	+	0.0562734i
$271$	11.5977			0.704512			0.352256	−	0.935904i	$-0.385415\pi$
$271$	11.5977			0.704512			0.352256	+	0.935904i	$0.385415\pi$
$272$	−7.74072	+	13.4073i	−0.469350	+	0.812939i
$273$	5.67706	−	0.652341i	0.343591	−	0.0394815i
$274$	4.10839	+	7.11593i	0.248197	+	0.429889i
$275$	0.276109	+	0.478235i	0.0166500	+	0.0288387i
$276$	−2.50727	+	5.78149i	−0.150920	+	0.348005i
$277$	−5.26326	+	9.11624i	−0.316239	+	0.547742i	−0.979700	−	0.200469i	$-0.935753\pi$
$277$	−5.26326	+	9.11624i	−0.316239	+	0.547742i	0.663461	+	0.748211i	$0.269087\pi$
$278$	11.7624			0.705463
$279$	−16.7218	−	17.8630i	−1.00111	−	1.06943i
$280$	6.49065			0.387891
$281$	−4.50843	+	7.80883i	−0.268950	+	0.465836i	−0.968591	−	0.248659i	$-0.920010\pi$
$281$	−4.50843	+	7.80883i	−0.268950	+	0.465836i	0.699641	+	0.714495i	$0.253343\pi$
$282$	3.10692	+	4.19035i	0.185015	+	0.249532i
$283$	7.15938	+	12.4004i	0.425581	+	0.737128i	0.996475	−	0.0838959i	$-0.0267363\pi$
$283$	7.15938	+	12.4004i	0.425581	+	0.737128i	−0.570893	+	0.821024i	$0.693403\pi$
$284$	7.44517	+	12.8954i	0.441790	+	0.765202i
$285$	−7.86640	−	10.6095i	−0.465966	−	0.628453i
$286$	0.146006	−	0.252891i	0.00863354	−	0.0149537i
$287$	−30.8518			−1.82112
$288$	−10.6693	−	11.3974i	−0.628693	−	0.671600i
$289$	24.5958			1.44681
$290$	0.348225	−	0.603144i	0.0204485	−	0.0354178i
$291$	−4.39623	+	10.1372i	−0.257712	+	0.594256i
$292$	2.94476	+	5.10048i	0.172329	+	0.298483i
$293$	15.2575	+	26.4268i	0.891354	+	1.54387i	0.838253	+	0.545281i	$0.183577\pi$
$293$	15.2575	+	26.4268i	0.891354	+	1.54387i	0.0531004	+	0.998589i	$0.483090\pi$
$294$	3.53489	−	0.406189i	0.206159	−	0.0236894i
$295$	0.860957	−	1.49122i	0.0501268	−	0.0868222i
$296$	−17.2019			−0.999837
$297$	0.514780	−	2.82286i	0.0298706	−	0.163799i
$298$	7.43242			0.430548
$299$	1.05742	−	1.83151i	0.0611523	−	0.105919i
$300$	−2.96029	+	0.340162i	−0.170912	+	0.0196393i
$301$	11.1272	+	19.2728i	0.641359	+	1.11087i
$302$	−4.34746	−	7.53002i	−0.250168	−	0.433304i
$303$	−0.607218	+	1.40018i	−0.0348837	+	0.0804382i
$304$	9.15212	−	15.8519i	0.524910	−	0.909171i
$305$	−1.42887			−0.0818167
$306$	−2.97259	+	9.79011i	−0.169932	+	0.559664i
$307$	−8.50257			−0.485267			−0.242634	−	0.970118i	$-0.578011\pi$
$307$	−8.50257			−0.485267			−0.242634	+	0.970118i	$0.578011\pi$
$308$	−1.56716	+	2.71440i	−0.0892973	+	0.154668i
$309$	−8.51237	−	11.4807i	−0.484252	−	0.653116i
$310$	2.15649	+	3.73515i	0.122480	+	0.212142i
$311$	−8.09674	−	14.0240i	−0.459124	−	0.795226i	0.539791	−	0.841799i	$-0.318503\pi$
$311$	−8.09674	−	14.0240i	−0.459124	−	0.795226i	−0.998915	+	0.0465733i	$0.985170\pi$
$312$	2.02950	+	2.73721i	0.114898	+	0.154964i
$313$	−13.7726	+	23.8548i	−0.778471	+	1.34835i	0.154353	+	0.988016i	$0.450671\pi$
$313$	−13.7726	+	23.8548i	−0.778471	+	1.34835i	−0.932823	+	0.360335i	$0.882662\pi$
$314$	−5.37174			−0.303145
$315$	−9.63968	+	2.24500i	−0.543135	+	0.126492i
$316$	−18.5305			−1.04242
$317$	−0.987970	+	1.71121i	−0.0554899	+	0.0961114i	−0.892436	−	0.451174i	$-0.851005\pi$
$317$	−0.987970	+	1.71121i	−0.0554899	+	0.0961114i	0.836946	+	0.547285i	$0.184339\pi$
$318$	1.78026	−	4.10510i	0.0998323	−	0.230203i
$319$	0.363647	+	0.629855i	0.0203603	+	0.0352651i
$320$	−1.02448	−	1.77445i	−0.0572702	−	0.0991948i
$321$	13.6908	−	1.57318i	0.764144	−	0.0878065i
$322$	1.84481	−	3.19530i	0.102807	−	0.178067i
$323$	−49.1802			−2.73646
$324$	12.8694	+	8.60881i	0.714968	+	0.478267i
$325$	1.00000			0.0554700
$326$	−3.49402	+	6.05182i	−0.193516	+	0.335179i
$327$	−15.9684	+	1.83490i	−0.883054	+	0.101470i
$328$	−9.19850	−	15.9323i	−0.507902	−	0.879712i
$329$	9.39527	+	16.2731i	0.517978	+	0.897164i
$330$	−0.201234	+	0.464025i	−0.0110776	+	0.0255437i
$331$	−8.95389	+	15.5086i	−0.492150	+	0.852429i	−0.999959	−	0.00904063i	$-0.997122\pi$
$331$	−8.95389	+	15.5086i	−0.492150	+	0.852429i	0.507809	+	0.861470i	$0.330456\pi$
$332$	18.7857			1.03100
$333$	25.5476	−	5.94982i	1.40000	−	0.326048i
$334$	0.0466584			0.00255304
$335$	0.567134	−	0.982304i	0.0309858	−	0.0536690i
$336$	−8.16975	−	11.0186i	−0.445697	−	0.601116i
$337$	−2.57381	−	4.45797i	−0.140204	−	0.242841i	0.787369	−	0.616482i	$-0.211443\pi$
$337$	−2.57381	−	4.45797i	−0.140204	−	0.242841i	−0.927573	+	0.373641i	$0.878109\pi$
$338$	−0.264400	−	0.457954i	−0.0143815	−	0.0249094i
$339$	−6.50455	−	8.77277i	−0.353279	−	0.476471i
$340$	−5.54775	+	9.60898i	−0.300869	+	0.521120i
$341$	−4.50398			−0.243904
$342$	3.51460	−	11.5752i	0.190048	−	0.625914i
$343$	−10.2776			−0.554938
$344$	−6.63515	+	11.4924i	−0.357743	+	0.619630i
$345$	−1.45740	+	3.36061i	−0.0784637	+	0.180929i
$346$	−1.25123	−	2.16719i	−0.0672663	−	0.116509i
$347$	−3.06489	−	5.30855i	−0.164532	−	0.284978i	0.771957	−	0.635675i	$-0.219278\pi$
$347$	−3.06489	−	5.30855i	−0.164532	−	0.284978i	−0.936489	+	0.350697i	$0.885945\pi$
$348$	−3.89882	+	0.448007i	−0.208999	+	0.0240157i
$349$	−8.96650	+	15.5304i	−0.479966	+	0.831325i	−0.999736	−	0.0229809i	$-0.992684\pi$
$349$	−8.96650	+	15.5304i	−0.479966	+	0.831325i	0.519770	+	0.854306i	$0.326018\pi$
$350$	1.74463			0.0932542
$351$	−3.96089	−	3.36324i	−0.211417	−	0.179516i
$352$	−2.87375			−0.153171
$353$	4.42477	−	7.66392i	0.235506	−	0.407909i	−0.723913	−	0.689891i	$-0.757658\pi$
$353$	4.42477	−	7.66392i	0.235506	−	0.407909i	0.959420	+	0.281982i	$0.0909918\pi$
$354$	1.56680	−	0.180039i	0.0832747	−	0.00956896i
$355$	4.32765	+	7.49572i	0.229688	+	0.397831i
$356$	7.43424	+	12.8765i	0.394014	+	0.682452i
$357$	−14.6634	+	33.8123i	−0.776071	+	1.78954i
$358$	−0.287627	+	0.498185i	−0.0152016	+	0.0263299i
$359$	13.0409			0.688273			0.344137	−	0.938920i	$-0.388172\pi$
$359$	13.0409			0.688273			0.344137	+	0.938920i	$0.388172\pi$
$360$	−4.03343	−	4.30871i	−0.212580	−	0.227089i
$361$	39.1474			2.06039
$362$	−0.704311	+	1.21990i	−0.0370178	+	0.0641166i
$363$	11.0330	+	14.8804i	0.579083	+	0.781016i
$364$	2.83794	+	4.91545i	0.148748	+	0.257640i
$365$	1.71170	+	2.96476i	0.0895946	+	0.155182i
$366$	−0.779460	−	1.05127i	−0.0407430	−	0.0549507i
$367$	3.07177	−	5.32046i	0.160345	−	0.277726i	−0.774647	−	0.632393i	$-0.782073\pi$
$367$	3.07177	−	5.32046i	0.160345	−	0.277726i	0.934992	+	0.354668i	$0.115406\pi$
$368$	−5.07651			−0.264631
$369$	19.1720	+	20.4804i	0.998053	+	1.06617i
$370$	−4.62369			−0.240374
$371$	8.05887	−	13.9584i	0.418396	−	0.724683i
$372$	9.66959	−	22.2971i	0.501345	−	1.15605i
$373$	10.6741	+	18.4880i	0.552683	+	0.957275i	0.998080	+	0.0619414i	$0.0197292\pi$
$373$	10.6741	+	18.4880i	0.552683	+	0.957275i	−0.445397	+	0.895333i	$0.646937\pi$
$374$	0.941666	+	1.63101i	0.0486924	+	0.0843377i
$375$	−1.72073	+	0.197726i	−0.0888580	+	0.0102105i
$376$	−5.60242	+	9.70368i	−0.288923	+	0.500429i
$377$	1.31704			0.0678310
$378$	−6.91027	−	5.86759i	−0.355426	−	0.301796i
$379$	0.639090			0.0328279			0.0164139	−	0.999865i	$-0.494775\pi$
$379$	0.639090			0.0328279			0.0164139	+	0.999865i	$0.494775\pi$
$380$	6.55929	−	11.3610i	0.336485	−	0.582809i
$381$	11.4241	−	1.31273i	0.585275	−	0.0672530i
$382$	4.10980	+	7.11838i	0.210276	+	0.364208i
$383$	0.422583	+	0.731935i	0.0215930	+	0.0374001i	0.876620	−	0.481183i	$-0.159793\pi$
$383$	0.422583	+	0.731935i	0.0215930	+	0.0374001i	−0.855027	+	0.518583i	$0.826460\pi$
$384$	7.91911	−	18.2606i	0.404121	−	0.931859i
$385$	−0.910944	+	1.57780i	−0.0464260	+	0.0804122i
$386$	9.57975			0.487597
$387$	5.87926	−	19.3631i	0.298860	−	0.984282i
$388$	−10.9750			−0.557169
$389$	−5.48753	+	9.50469i	−0.278229	+	0.481907i	−0.970945	−	0.239304i	$-0.923081\pi$
$389$	−5.48753	+	9.50469i	−0.278229	+	0.481907i	0.692716	+	0.721211i	$0.256414\pi$
$390$	0.545510	+	0.735736i	0.0276230	+	0.0372554i
$391$	6.81982	+	11.8123i	0.344893	+	0.597373i
$392$	3.82138	+	6.61883i	0.193009	+	0.334301i
$393$	−20.5333	−	27.6935i	−1.03577	−	1.39695i
$394$	5.99080	−	10.3764i	0.301812	−	0.522754i
$395$	−10.7712			−0.541960
$396$	2.77578	−	0.646456i	0.139488	−	0.0324856i
$397$	21.3930			1.07368			0.536842	−	0.843683i	$-0.319617\pi$
$397$	21.3930			1.07368			0.536842	+	0.843683i	$0.319617\pi$
$398$	4.21677	−	7.30366i	0.211367	−	0.366099i
$399$	17.3371	−	39.9775i	0.867940	−	2.00138i
$400$	−1.20021	−	2.07882i	−0.0600104	−	0.103941i
$401$	11.3858	+	19.7208i	0.568581	+	0.984811i	0.996707	+	0.0810919i	$0.0258407\pi$
$401$	11.3858	+	19.7208i	0.568581	+	0.984811i	−0.428126	+	0.903719i	$0.640826\pi$
$402$	1.03209	−	0.118596i	0.0514761	−	0.00591503i
$403$	−4.07808	+	7.06344i	−0.203144	+	0.351855i
$404$	−1.51589			−0.0754181
$405$	7.48061	+	5.00404i	0.371715	+	0.248653i
$406$	2.29774			0.114035
$407$	2.41423	−	4.18157i	0.119669	−	0.207273i
$408$	−21.8331	+	2.50880i	−1.08090	+	0.124204i
$409$	−18.3213	−	31.7334i	−0.905928	−	1.56911i	−0.819666	−	0.572841i	$-0.805841\pi$
$409$	−18.3213	−	31.7334i	−0.905928	−	1.56911i	−0.0862619	−	0.996272i	$-0.527492\pi$
$410$	−2.47247	−	4.28244i	−0.122106	−	0.211495i
$411$	10.7080	−	24.6916i	0.528189	−	1.21795i
$412$	7.09792	−	12.2940i	0.349690	−	0.605680i
$413$	5.68097			0.279542
$414$	−3.26754	+	0.760984i	−0.160591	+	0.0374003i
$415$	10.9196			0.536021
$416$	−2.60200	+	4.50680i	−0.127574	+	0.220964i
$417$	−22.9465	−	30.9482i	−1.12370	−	1.51554i
$418$	−1.11336	−	1.92840i	−0.0544564	−	0.0943213i
$419$	−1.85742	−	3.21715i	−0.0907411	−	0.157168i	0.817082	−	0.576521i	$-0.195590\pi$
$419$	−1.85742	−	3.21715i	−0.0907411	−	0.157168i	−0.907823	+	0.419353i	$0.862257\pi$
$420$	−5.85523	−	7.89703i	−0.285706	−	0.385335i
$421$	9.52785	−	16.5027i	0.464359	−	0.804293i	−0.534814	−	0.844970i	$-0.679618\pi$
$421$	9.52785	−	16.5027i	0.464359	−	0.804293i	0.999172	+	0.0406771i	$0.0129515\pi$
$422$	9.83297			0.478662
$423$	4.96418	−	16.3493i	0.241367	−	0.794932i
$424$	9.61105			0.466754
$425$	−3.22474	+	5.58541i	−0.156423	+	0.270932i
$426$	−3.15409	+	7.27300i	−0.152816	+	0.352378i
$427$	−2.35707	−	4.08257i	−0.114067	−	0.197569i
$428$	6.84397	+	11.8541i	0.330816	+	0.572989i
$429$	−0.950218	+	0.109188i	−0.0458769	+	0.00527164i
$430$	−1.78347	+	3.08905i	−0.0860063	+	0.148967i
$431$	−25.3961			−1.22329			−0.611644	−	0.791133i	$-0.709492\pi$
$431$	−25.3961			−1.22329			−0.611644	+	0.791133i	$0.709492\pi$
$432$	−2.23768	+	12.2706i	−0.107660	+	0.590368i
$433$	35.0659			1.68516			0.842580	−	0.538571i	$-0.181036\pi$
$433$	35.0659			1.68516			0.842580	+	0.538571i	$0.181036\pi$
$434$	−7.11472	+	12.3231i	−0.341518	+	0.591526i
$435$	−2.26627	+	0.260413i	−0.108659	+	0.0124859i
$436$	−7.98254	−	13.8262i	−0.382294	−	0.662153i
$437$	−8.06331	−	13.9661i	−0.385720	−	0.668087i
$438$	−1.24753	+	2.87666i	−0.0596091	+	0.137452i
$439$	10.3602	−	17.9444i	0.494467	−	0.856442i	−0.505513	−	0.862819i	$-0.668697\pi$
$439$	10.3602	−	17.9444i	0.494467	−	0.856442i	0.999980	+	0.00637739i	$0.00203000\pi$
$440$	−1.08640			−0.0517919
$441$	−7.96471	−	8.50829i	−0.379272	−	0.405157i
$442$	3.41048			0.162220
$443$	−20.6878	+	35.8323i	−0.982905	+	1.70244i	−0.332007	+	0.943277i	$0.607726\pi$
$443$	−20.6878	+	35.8323i	−0.982905	+	1.70244i	−0.650899	+	0.759165i	$0.725608\pi$
$444$	15.5178	+	20.9291i	0.736444	+	0.993250i
$445$	4.32130	+	7.48472i	0.204849	+	0.354810i
$446$	−4.34943	−	7.53344i	−0.205952	−	0.356719i
$447$	−14.4994	−	19.5555i	−0.685798	−	0.924944i
$448$	3.37998	−	5.85430i	0.159689	−	0.276590i
$449$	16.8485			0.795131			0.397566	−	0.917574i	$-0.369855\pi$
$449$	16.8485			0.795131			0.397566	+	0.917574i	$0.369855\pi$
$450$	−1.08415	−	1.15814i	−0.0511072	−	0.0545952i
$451$	5.16393			0.243160
$452$	5.42373	−	9.39418i	0.255111	−	0.441865i
$453$	−11.3312	+	26.1284i	−0.532384	+	1.22762i
$454$	−1.33045	−	2.30441i	−0.0624411	−	0.108151i
$455$	1.64961	+	2.85721i	0.0773349	+	0.133948i
$456$	25.8140	−	2.96624i	1.20885	−	0.138907i
$457$	9.82743	−	17.0216i	0.459708	−	0.796237i	−0.539238	−	0.842154i	$-0.681288\pi$
$457$	9.82743	−	17.0216i	0.459708	−	0.796237i	0.998945	+	0.0459166i	$0.0146208\pi$
$458$	4.21666			0.197032
$459$	31.5579	−	11.2776i	1.47300	−	0.526395i
$460$	−3.63831			−0.169637
$461$	−7.07284	+	12.2505i	−0.329415	+	0.570564i	−0.982396	−	0.186811i	$-0.940185\pi$
$461$	−7.07284	+	12.2505i	−0.329415	+	0.570564i	0.652981	+	0.757374i	$0.273518\pi$
$462$	−1.65777	+	0.190492i	−0.0771266	+	0.00886249i
$463$	−0.458168	−	0.793570i	−0.0212929	−	0.0368803i	0.855183	−	0.518327i	$-0.173445\pi$
$463$	−0.458168	−	0.793570i	−0.0212929	−	0.0368803i	−0.876475	+	0.481446i	$0.840112\pi$
$464$	−1.58072	−	2.73789i	−0.0733833	−	0.127104i
$465$	5.62064	−	12.9606i	0.260651	−	0.601034i
$466$	0.362630	−	0.628094i	0.0167985	−	0.0290959i
$467$	−6.14949			−0.284565			−0.142282	−	0.989826i	$-0.545444\pi$
$467$	−6.14949			−0.284565			−0.142282	+	0.989826i	$0.545444\pi$
$468$	1.49948	−	4.93848i	0.0693136	−	0.228282i
$469$	3.74219			0.172798
$470$	−1.50588	+	2.60826i	−0.0694609	+	0.120310i
$471$	10.4794	+	14.1336i	0.482863	+	0.651244i
$472$	1.69379	+	2.93373i	0.0779629	+	0.135036i
$473$	−1.86245	−	3.22586i	−0.0856355	−	0.148325i
$474$	−5.87582	−	7.92478i	−0.269885	−	0.363997i
$475$	3.81272	−	6.60383i	0.174940	−	0.303004i
$476$	−36.6065			−1.67785
$477$	−14.2740	+	3.32429i	−0.653560	+	0.152209i
$478$	−11.2942			−0.516584
$479$	−0.250429	+	0.433755i	−0.0114424	+	0.0198188i	−0.871690	−	0.490058i	$-0.836976\pi$
$479$	−0.250429	+	0.433755i	−0.0114424	+	0.0198188i	0.860248	+	0.509877i	$0.170309\pi$
$480$	3.58623	−	8.26946i	0.163688	−	0.377447i
$481$	−4.37187	−	7.57231i	−0.199340	−	0.345268i
$482$	−4.42581	−	7.66572i	−0.201590	−	0.349164i
$483$	−12.0061	+	1.37960i	−0.546296	+	0.0627739i
$484$	−9.19973	+	15.9344i	−0.418170	+	0.724291i
$485$	−6.37941			−0.289674
$486$	0.399093	+	8.23351i	0.0181032	+	0.373479i
$487$	25.1464			1.13949			0.569746	−	0.821821i	$-0.307042\pi$
$487$	25.1464			1.13949			0.569746	+	0.821821i	$0.307042\pi$
$488$	1.40553	−	2.43444i	0.0636252	−	0.110202i
$489$	22.7392	−	2.61293i	1.02830	−	0.118161i
$490$	1.02715	+	1.77908i	0.0464019	+	0.0803705i
$491$	9.69116	+	16.7856i	0.437356	+	0.757523i	0.997485	−	0.0708829i	$-0.0225817\pi$
$491$	9.69116	+	16.7856i	0.437356	+	0.757523i	−0.560129	+	0.828406i	$0.689248\pi$
$492$	−11.0864	+	25.5641i	−0.499815	+	1.15252i
$493$	−4.24711	+	7.35622i	−0.191280	+	0.331307i
$494$	−4.03233			−0.181423
$495$	1.61348	−	0.375765i	0.0725204	−	0.0168894i
$496$	19.5782			0.879087
$497$	−14.2779	+	24.7300i	−0.640450	+	1.10929i
$498$	5.95674	+	8.03392i	0.266928	+	0.360009i
$499$	−6.33303	−	10.9691i	−0.283506	−	0.491046i	0.688740	−	0.725008i	$-0.258164\pi$
$499$	−6.33303	−	10.9691i	−0.283506	−	0.491046i	−0.972246	+	0.233962i	$0.924831\pi$
$500$	−0.860185	−	1.48988i	−0.0384687	−	0.0666297i
$501$	−0.0910228	−	0.122764i	−0.00406660	−	0.00548467i
$502$	−6.34031	+	10.9817i	−0.282982	+	0.490139i
$503$	15.8072			0.704807			0.352403	−	0.935848i	$-0.385364\pi$
$503$	15.8072			0.704807			0.352403	+	0.935848i	$0.385364\pi$
$504$	5.65728	−	18.6320i	0.251995	−	0.829936i
$505$	−0.881139			−0.0392102
$506$	−0.308781	+	0.534824i	−0.0137270	+	0.0237758i
$507$	−0.689128	+	1.58906i	−0.0306053	+	0.0705725i
$508$	5.71087	+	9.89152i	0.253379	+	0.438865i
$509$	4.91259	+	8.50886i	0.217747	+	0.377149i	0.954119	−	0.299428i	$-0.0967960\pi$
$509$	4.91259	+	8.50886i	0.217747	+	0.377149i	−0.736372	+	0.676577i	$0.763463\pi$
$510$	−5.86852	+	0.674341i	−0.259862	+	0.0298603i
$511$	−5.64728	+	9.78138i	−0.249821	+	0.432703i
$512$	21.9366			0.969470
$513$	−37.3120	+	13.3339i	−1.64736	+	0.588708i
$514$	15.6127			0.688645
$515$	4.12581	−	7.14611i	0.181805	−	0.314895i
$516$	19.9681	−	2.29451i	0.879049	−	0.101010i
$517$	−1.57257	−	2.72377i	−0.0691614	−	0.119791i
$518$	−7.62728	−	13.2108i	−0.335124	−	0.580451i
$519$	−3.26118	+	7.51994i	−0.143150	+	0.330089i
$520$	−0.983666	+	1.70376i	−0.0431366	+	0.0747148i
$521$	−41.6128			−1.82309			−0.911545	−	0.411200i	$-0.865110\pi$
$521$	−41.6128			−1.82309			−0.911545	+	0.411200i	$0.865110\pi$
$522$	−1.42787	−	1.52532i	−0.0624960	−	0.0667613i
$523$	−44.9958			−1.96753			−0.983763	−	0.179470i	$-0.942562\pi$
$523$	−44.9958			−1.96753			−0.983763	+	0.179470i	$0.942562\pi$
$524$	17.1214	−	29.6551i	0.747952	−	1.29549i
$525$	−3.40347	−	4.59030i	−0.148540	−	0.200337i
$526$	−5.77666	−	10.0055i	−0.251875	−	0.436260i
$527$	−26.3015	−	45.5555i	−1.14571	−	1.98443i
$528$	1.36744	+	1.84429i	0.0595103	+	0.0802622i
$529$	9.26372	−	16.0452i	0.402770	−	0.697619i
$530$	2.58336			0.112214
$531$	−3.53028	−	3.77121i	−0.153201	−	0.163657i
$532$	43.2811			1.87647
$533$	4.67562	−	8.09842i	0.202524	−	0.350781i
$534$	−3.14946	+	7.26232i	−0.136290	+	0.314271i
$535$	3.97819	+	6.89043i	0.171992	+	0.297899i
$536$	1.11574	+	1.93252i	0.0481926	+	0.0834721i
$537$	1.87189	−	0.215096i	0.0807781	−	0.00928208i
$538$	7.95913	−	13.7856i	0.343142	−	0.594340i
$539$	−2.14528			−0.0924037
$540$	−1.60374	+	8.79428i	−0.0690138	+	0.378445i
$541$	−31.7028			−1.36301			−0.681504	−	0.731814i	$-0.738674\pi$
$541$	−31.7028			−1.36301			−0.681504	+	0.731814i	$0.738674\pi$
$542$	−3.06644	+	5.31123i	−0.131715	+	0.228137i
$543$	4.58369	−	0.526704i	0.196705	−	0.0226030i
$544$	−16.7816	−	29.0665i	−0.719503	−	1.24622i
$545$	−4.64001	−	8.03674i	−0.198756	−	0.344256i
$546$	−1.20227	+	2.77231i	−0.0514524	+	0.118644i
$547$	−4.13402	+	7.16033i	−0.176758	+	0.306154i	−0.940768	−	0.339050i	$-0.889894\pi$
$547$	−4.13402	+	7.16033i	−0.176758	+	0.306154i	0.764010	+	0.645204i	$0.223228\pi$
$548$	26.7320			1.14194
$549$	−1.24541	+	4.10169i	−0.0531526	+	0.175056i
$550$	−0.292013			−0.0124515
$551$	5.02151	−	8.69751i	0.213924	−	0.370526i
$552$	−4.29207	−	5.78877i	−0.182683	−	0.246386i
$553$	−17.7683	−	30.7757i	−0.755586	−	1.30871i
$554$	−2.78321	−	4.82067i	−0.118247	−	0.204810i
$555$	9.02005	+	12.1654i	0.382880	+	0.516395i
$556$	19.1336	−	33.1404i	0.811447	−	1.40547i
$557$	41.8970			1.77523			0.887615	−	0.460585i	$-0.152360\pi$
$557$	41.8970			1.77523			0.887615	+	0.460585i	$0.152360\pi$
$558$	12.6017	−	2.93483i	0.533472	−	0.124241i
$559$	−6.74533			−0.285297
$560$	3.95975	−	6.85849i	0.167330	−	0.289824i
$561$	2.45435	−	5.65946i	0.103623	−	0.238943i
$562$	−2.38406	−	4.12931i	−0.100565	−	0.174184i
$563$	−5.18447	−	8.97977i	−0.218500	−	0.378452i	0.735850	−	0.677145i	$-0.236783\pi$
$563$	−5.18447	−	8.97977i	−0.218500	−	0.378452i	−0.954349	+	0.298692i	$0.903450\pi$
$564$	16.8602	−	1.93738i	0.709942	−	0.0815783i
$565$	3.15265	−	5.46056i	0.132633	−	0.229727i
$566$	−7.57176			−0.318265
$567$	−1.95750	+	29.6284i	−0.0822074	+	1.24427i
$568$	−17.0279			−0.714473
$569$	−17.6907	+	30.6411i	−0.741631	+	1.28454i	0.210121	+	0.977675i	$0.432614\pi$
$569$	−17.6907	+	30.6411i	−0.741631	+	1.28454i	−0.951752	+	0.306868i	$0.900719\pi$
$570$	6.93855	−	0.797297i	0.290624	−	0.0333951i
$571$	−1.86066	−	3.22275i	−0.0778661	−	0.134868i	0.824463	−	0.565916i	$-0.191477\pi$
$571$	−1.86066	−	3.22275i	−0.0778661	−	0.134868i	−0.902329	+	0.431048i	$0.858144\pi$
$572$	−0.475010	−	0.822742i	−0.0198612	−	0.0344006i
$573$	10.7117	−	24.7001i	0.447489	−	1.03186i
$574$	8.15721	−	14.1287i	0.340475	−	0.589721i
$575$	−2.11484			−0.0881951
$576$	−5.98667	+	1.39425i	−0.249444	+	0.0580936i
$577$	−22.7206			−0.945870			−0.472935	−	0.881097i	$-0.656806\pi$
$577$	−22.7206			−0.945870			−0.472935	+	0.881097i	$0.656806\pi$
$578$	−6.50313	+	11.2638i	−0.270495	+	0.468510i
$579$	−18.6885	−	25.2054i	−0.776667	−	1.04750i
$580$	−1.13290	−	1.96224i	−0.0470411	−	0.0814775i
$581$	18.0130	+	31.1995i	0.747307	+	1.29437i
$582$	−3.48003	−	4.69356i	−0.144252	−	0.194554i
$583$	−1.34888	+	2.33633i	−0.0558650	+	0.0967610i
$584$	−6.73497			−0.278695
$585$	0.871604	−	2.87059i	0.0360364	−	0.118684i
$586$	−16.1363			−0.666586
$587$	18.0815	−	31.3182i	0.746305	−	1.29264i	−0.203277	−	0.979121i	$-0.565159\pi$
$587$	18.0815	−	31.3182i	0.746305	−	1.29264i	0.949582	−	0.313518i	$-0.101507\pi$
$588$	4.60569	−	10.6202i	0.189936	−	0.437971i
$589$	31.0972	+	53.8619i	1.28134	+	2.21934i
$590$	0.455274	+	0.788557i	0.0187433	+	0.0324644i
$591$	−38.9885	+	4.48010i	−1.60377	+	0.184287i
$592$	−10.4943	+	18.1767i	−0.431314	+	0.747058i
$593$	−31.7318			−1.30307			−0.651534	−	0.758619i	$-0.725874\pi$
$593$	−31.7318			−1.30307			−0.651534	+	0.758619i	$0.725874\pi$
$594$	1.15663	+	0.982108i	0.0474571	+	0.0402964i
$595$	−21.2782			−0.872323
$596$	12.0901	−	20.9407i	0.495231	−	0.857765i
$597$	−27.4429	+	3.15342i	−1.12316	+	0.129061i
$598$	0.559164	+	0.968501i	0.0228659	+	0.0396050i
$599$	−11.0956	−	19.2181i	−0.453353	−	0.785230i	0.545239	−	0.838281i	$-0.316439\pi$
$599$	−11.0956	−	19.2181i	−0.453353	−	0.785230i	−0.998592	+	0.0530506i	$0.983106\pi$
$600$	1.35574	−	3.12620i	0.0553480	−	0.127627i
$601$	13.4369	−	23.2734i	0.548102	−	0.949340i	−0.450303	−	0.892876i	$-0.648684\pi$
$601$	13.4369	−	23.2734i	0.548102	−	0.949340i	0.998405	−	0.0564642i	$-0.0179827\pi$
$602$	−11.7681			−0.479631
$603$	−2.32548	−	2.48419i	−0.0947009	−	0.101164i
$604$	−28.2876			−1.15101
$605$	−5.34753	+	9.26219i	−0.217408	+	0.376562i
$606$	−0.480670	−	0.648285i	−0.0195259	−	0.0263348i
$607$	7.36656	+	12.7593i	0.299000	+	0.517883i	0.975907	−	0.218185i	$-0.0700137\pi$
$607$	7.36656	+	12.7593i	0.299000	+	0.517883i	−0.676908	+	0.736068i	$0.736680\pi$
$608$	19.8414	+	34.3663i	0.804676	+	1.39374i
$609$	−4.48251	−	6.04562i	−0.181641	−	0.244981i
$610$	0.377792	−	0.654355i	0.0152964	−	0.0264941i
$611$	−5.69545			−0.230413
$612$	22.7480	+	24.3006i	0.919535	+	0.982292i
$613$	−31.6705			−1.27916			−0.639579	−	0.768725i	$-0.720891\pi$
$613$	−31.6705			−1.27916			−0.639579	+	0.768725i	$0.720891\pi$
$614$	2.24808	−	3.89379i	0.0907250	−	0.157140i
$615$	−6.44421	+	14.8597i	−0.259855	+	0.599199i
$616$	−1.79213	−	3.10406i	−0.0722069	−	0.125066i
$617$	20.5685	+	35.6256i	0.828055	+	1.43423i	0.899562	+	0.436793i	$0.143886\pi$
$617$	20.5685	+	35.6256i	0.828055	+	1.43423i	−0.0715070	+	0.997440i	$0.522781\pi$
$618$	7.50832	−	0.862768i	0.302029	−	0.0347056i
$619$	−7.99428	+	13.8465i	−0.321317	+	0.556538i	−0.980760	−	0.195217i	$-0.937459\pi$
$619$	−7.99428	+	13.8465i	−0.321317	+	0.556538i	0.659443	+	0.751755i	$0.270792\pi$
$620$	14.0316			0.563524
$621$	8.37666	+	7.11272i	0.336144	+	0.285424i
$622$	8.56310			0.343349
$623$	−14.2569	+	24.6937i	−0.571191	+	0.989333i
$624$	4.13047	−	0.474625i	0.165351	−	0.0190002i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.28292	−	12.6144i	−0.291084	−	0.504172i
$627$	−2.90186	+	6.69138i	−0.115889	+	0.267228i
$628$	−8.73807	+	15.1348i	−0.348687	+	0.603944i
$629$	56.3926			2.24852
$630$	1.52062	−	5.00811i	0.0605831	−	0.199528i
$631$	0.549340			0.0218689			0.0109344	−	0.999940i	$-0.496519\pi$
$631$	0.549340			0.0218689			0.0109344	+	0.999940i	$0.496519\pi$
$632$	10.5953	−	18.3516i	0.421458	−	0.729987i
$633$	−19.1825	−	25.8716i	−0.762435	−	1.02831i
$634$	−0.522438	−	0.904890i	−0.0207487	−	0.0359378i
$635$	3.31956	+	5.74964i	0.131733	+	0.228168i
$636$	−8.67015	−	11.6935i	−0.343794	−	0.463679i
$637$	−1.94242	+	3.36437i	−0.0769614	+	0.133301i
$638$	−0.384593			−0.0152262
$639$	25.2892	−	5.88964i	1.00042	−	0.232990i
$640$	11.4915			0.454241
$641$	4.82212	−	8.35216i	0.190462	−	0.329891i	−0.754941	−	0.655793i	$-0.772335\pi$
$641$	4.82212	−	8.35216i	0.190462	−	0.329891i	0.945404	+	0.325902i	$0.105668\pi$
$642$	−2.89939	+	6.68569i	−0.114430	+	0.263863i
$643$	−0.840288	−	1.45542i	−0.0331377	−	0.0573962i	0.848981	−	0.528424i	$-0.177217\pi$
$643$	−0.840288	−	1.45542i	−0.0331377	−	0.0573962i	−0.882119	+	0.471027i	$0.843883\pi$
$644$	−6.00180	−	10.3954i	−0.236504	−	0.409637i
$645$	11.6069	−	1.33373i	0.457021	−	0.0525155i
$646$	13.0032	−	22.5222i	0.511605	−	0.886126i
$647$	−14.8836			−0.585136			−0.292568	−	0.956245i	$-0.594510\pi$
$647$	−14.8836			−0.585136			−0.292568	+	0.956245i	$0.594510\pi$
$648$	−15.8841	+	7.82285i	−0.623987	+	0.307311i
$649$	−0.950872			−0.0373250
$650$	−0.264400	+	0.457954i	−0.0103706	+	0.0179624i
$651$	46.3030	−	5.32060i	1.81476	−	0.208531i
$652$	11.3673	+	19.6887i	0.445176	+	0.771068i
$653$	13.7167	+	23.7581i	0.536777	+	0.929725i	0.999075	+	0.0430005i	$0.0136917\pi$
$653$	13.7167	+	23.7581i	0.536777	+	0.929725i	−0.462298	+	0.886725i	$0.652975\pi$
$654$	3.38174	−	7.79794i	0.132237	−	0.304924i
$655$	9.95215	−	17.2376i	0.388863	−	0.673530i
$656$	−22.4469			−0.876404
$657$	10.0025	−	2.32951i	0.390236	−	0.0908828i
$658$	−9.93643			−0.387362
$659$	13.5560	−	23.4796i	0.528066	−	0.914637i	−0.471399	−	0.881920i	$-0.656251\pi$
$659$	13.5560	−	23.4796i	0.528066	−	0.914637i	0.999465	−	0.0327170i	$-0.0104160\pi$
$660$	0.980041	+	1.32179i	0.0381480	+	0.0514507i
$661$	1.81117	+	3.13703i	0.0704463	+	0.122017i	0.899097	−	0.437750i	$-0.144224\pi$
$661$	1.81117	+	3.13703i	0.0704463	+	0.122017i	−0.828651	+	0.559766i	$0.810891\pi$
$662$	−4.73481	−	8.20094i	−0.184024	−	0.318738i
$663$	−6.65328	−	8.97336i	−0.258392	−	0.348497i
$664$	−10.7412	+	18.6043i	−0.416840	+	0.721988i
$665$	25.1580			0.975585
$666$	−4.03003	+	13.2727i	−0.156161	+	0.514308i
$667$	−2.78534			−0.107849
$668$	0.0758981	−	0.131459i	0.00293659	−	0.00508632i
$669$	−11.3363	+	26.1403i	−0.438287	+	1.01064i
$670$	0.299900	+	0.519442i	0.0115862	+	0.0200678i
$671$	0.394523	+	0.683334i	0.0152304	+	0.0263798i
$672$	29.5434	−	3.39478i	1.13966	−	0.130957i
$673$	−4.59326	+	7.95577i	−0.177057	+	0.306672i	−0.940871	−	0.338764i	$-0.889991\pi$
$673$	−4.59326	+	7.95577i	−0.177057	+	0.306672i	0.763814	+	0.645436i	$0.223324\pi$
$674$	2.72206			0.104850
$675$	−0.932203	+	5.11185i	−0.0358805	+	0.196755i
$676$	−1.72037			−0.0661681
$677$	20.5137	−	35.5307i	0.788404	−	1.36556i	−0.138540	−	0.990357i	$-0.544241\pi$
$677$	20.5137	−	35.5307i	0.788404	−	1.36556i	0.926944	−	0.375200i	$-0.122426\pi$
$678$	5.73733	−	0.659267i	0.220341	−	0.0253190i
$679$	−10.5235	−	18.2273i	−0.403856	−	0.699499i
$680$	−6.34413	−	10.9884i	−0.243286	−	0.421384i
$681$	−3.46767	+	7.99607i	−0.132881	+	0.306410i
$682$	1.19085	−	2.06262i	0.0456001	−	0.0789817i
$683$	−26.9519			−1.03128			−0.515642	−	0.856804i	$-0.672447\pi$
$683$	−26.9519			−1.03128			−0.515642	+	0.856804i	$0.672447\pi$
$684$	−26.8958	−	28.7314i	−1.02839	−	1.09857i
$685$	15.5385			0.593697
$686$	2.71740	−	4.70667i	0.103751	−	0.179701i
$687$	−8.22600	−	11.0945i	−0.313842	−	0.423282i
$688$	8.09581	+	14.0224i	0.308650	+	0.534597i
$689$	2.44266	+	4.23081i	0.0930580	+	0.161181i
$690$	−1.15367	−	1.55597i	−0.0439194	−	0.0592346i
$691$	−18.1572	+	31.4492i	−0.690733	+	1.19638i	0.280865	+	0.959747i	$0.409379\pi$
$691$	−18.1572	+	31.4492i	−0.690733	+	1.19638i	−0.971598	+	0.236637i	$0.923955\pi$
$692$	−8.14136			−0.309488
$693$	3.73524	+	3.99017i	0.141890	+	0.151574i
$694$	3.24143			0.123043
$695$	11.1218	−	19.2635i	0.421874	−	0.730708i
$696$	1.78557	−	4.11733i	0.0676818	−	0.156067i
$697$	30.1553	+	52.2306i	1.14221	+	1.97837i
$698$	−4.74148	−	8.21249i	−0.179468	−	0.310847i
$699$	−2.36002	+	0.271186i	−0.0892641	+	0.0102572i
$700$	2.83794	−	4.91545i	0.107264	−	0.185787i
$701$	−3.85347			−0.145543			−0.0727717	−	0.997349i	$-0.523184\pi$
$701$	−3.85347			−0.145543			−0.0727717	+	0.997349i	$0.523184\pi$
$702$	2.58747	−	0.924666i	0.0976576	−	0.0348993i
$703$	−66.6750			−2.51469
$704$	−0.565736	+	0.979884i	−0.0213220	+	0.0369308i
$705$	9.80032	−	1.12614i	0.369102	−	0.0424128i
$706$	2.33981	+	4.05268i	0.0880601	+	0.152525i
$707$	−1.45353	−	2.51760i	−0.0546658	−	0.0946839i
$708$	2.04143	−	4.70731i	0.0767215	−	0.176912i
$709$	−4.46815	+	7.73907i	−0.167805	+	0.290647i	−0.937648	−	0.347587i	$-0.887001\pi$
$709$	−4.46815	+	7.73907i	−0.167805	+	0.290647i	0.769843	+	0.638233i	$0.220335\pi$
$710$	−4.57693			−0.171769
$711$	−9.38826	+	30.9199i	−0.352087	+	1.15959i
$712$	−17.0029			−0.637209
$713$	8.62450	−	14.9381i	0.322990	−	0.559435i
$714$	−11.6075	−	15.6552i	−0.434399	−	0.585880i
$715$	−0.276109	−	0.478235i	−0.0103259	−	0.0178850i
$716$	0.935752	+	1.62077i	0.0349707	+	0.0605710i
$717$	22.0331	+	29.7163i	0.822840	+	1.10977i
$718$	−3.44802	+	5.97214i	−0.128679	+	0.222878i
$719$	−22.8346			−0.851587			−0.425793	−	0.904820i	$-0.640005\pi$
$719$	−22.8346			−0.851587			−0.425793	+	0.904820i	$0.640005\pi$
$720$	−7.01356	+	1.63340i	−0.261380	+	0.0608732i
$721$	27.2239			1.01387
$722$	−10.3506	+	17.9277i	−0.385208	+	0.667200i
$723$	−11.5354	+	26.5993i	−0.429005	+	0.989239i
$724$	2.29137	+	3.96877i	0.0851581	+	0.147498i
$725$	−0.658520	−	1.14059i	−0.0244568	−	0.0423605i
$726$	−9.73165	+	1.11825i	−0.361175	+	0.0415021i
$727$	−4.50796	+	7.80801i	−0.167191	+	0.289583i	−0.937431	−	0.348171i	$-0.886803\pi$
$727$	−4.50796	+	7.80801i	−0.167191	+	0.289583i	0.770240	+	0.637754i	$0.220136\pi$
$728$	−6.49065			−0.240560
$729$	20.8847	−	17.1122i	0.773508	−	0.633787i
$730$	−1.81030			−0.0670021
$731$	21.7520	−	37.6755i	0.804525	−	1.39348i
$732$	−4.22986	+	0.486046i	−0.156340	+	0.0179648i
$733$	−6.30216	−	10.9157i	−0.232775	−	0.403179i	0.725848	−	0.687855i	$-0.241447\pi$
$733$	−6.30216	−	10.9157i	−0.232775	−	0.403179i	−0.958624	+	0.284676i	$0.908114\pi$
$734$	1.62435	+	2.81346i	0.0599559	+	0.103847i
$735$	2.67715	−	6.17323i	0.0987482	−	0.227703i
$736$	5.50283	−	9.53117i	0.202837	−	0.351324i
$737$	−0.626363			−0.0230724
$738$	−14.4482	+	3.36486i	−0.531844	+	0.123862i
$739$	1.70896			0.0628651			0.0314325	−	0.999506i	$-0.489993\pi$
$739$	1.70896			0.0628651			0.0314325	+	0.999506i	$0.489993\pi$
$740$	−7.52125	+	13.0272i	−0.276486	+	0.478889i
$741$	7.86640	+	10.6095i	0.288980	+	0.389750i
$742$	4.26153	+	7.38118i	0.156446	+	0.270972i
$743$	−3.49698	−	6.05695i	−0.128292	−	0.222208i	0.794723	−	0.606972i	$-0.207616\pi$
$743$	−3.49698	−	6.05695i	−0.128292	−	0.222208i	−0.923015	+	0.384764i	$0.874283\pi$
$744$	16.5529	+	22.3251i	0.606859	+	0.818479i
$745$	7.02763	−	12.1722i	0.257472	−	0.445955i
$746$	−11.2889			−0.413316
$747$	9.51755	−	31.3457i	0.348229	−	1.14688i
$748$	6.12714			0.224030
$749$	−13.1249	+	22.7330i	−0.479574	+	0.830647i
$750$	0.364411	−	0.840293i	0.0133064	−	0.0306832i
$751$	−11.8054	−	20.4475i	−0.430783	−	0.746139i	0.566158	−	0.824297i	$-0.308429\pi$
$751$	−11.8054	−	20.4475i	−0.430783	−	0.746139i	−0.996941	+	0.0781583i	$0.975096\pi$
$752$	6.83573	+	11.8398i	0.249273	+	0.431754i
$753$	41.2630	−	4.74147i	1.50371	−	0.172789i
$754$	−0.348225	+	0.603144i	−0.0126816	+	0.0219652i
$755$	−16.4427			−0.598412
$756$	−27.7726	+	9.92491i	−1.01008	+	0.360966i
$757$	−36.0882			−1.31165			−0.655824	−	0.754914i	$-0.727679\pi$
$757$	−36.0882			−1.31165			−0.655824	+	0.754914i	$0.727679\pi$
$758$	−0.168975	+	0.292674i	−0.00613746	+	0.0106304i
$759$	2.00956	−	0.230915i	0.0729425	−	0.00838169i
$760$	7.50089	+	12.9919i	0.272086	+	0.471266i
$761$	14.1498	+	24.5082i	0.512930	+	0.888421i	0.999888	+	0.0149956i	$0.00477341\pi$
$761$	14.1498	+	24.5082i	0.512930	+	0.888421i	−0.486957	+	0.873426i	$0.661893\pi$
$762$	−2.41937	+	5.57880i	−0.0876444	+	0.202099i
$763$	15.3084	−	26.5149i	0.554202	−	0.959905i
$764$	26.7412			0.967464
$765$	13.2228	+	14.1252i	0.478070	+	0.510697i
$766$	−0.446923			−0.0161480
$767$	−0.860957	+	1.49122i	−0.0310873	+	0.0538449i
$768$	2.04131	+	2.75314i	0.0736594	+	0.0993454i
$769$	5.96044	+	10.3238i	0.214939	+	0.372285i	0.953254	−	0.302171i	$-0.0977114\pi$
$769$	5.96044	+	10.3238i	0.214939	+	0.372285i	−0.738315	+	0.674456i	$0.764378\pi$
$770$	−0.481707	−	0.834341i	−0.0173595	−	0.0300676i
$771$	−30.4577	−	41.0787i	−1.09691	−	1.47941i
$772$	15.5831	−	26.9908i	0.560850	−	0.971420i
$773$	40.0242			1.43957			0.719785	−	0.694197i	$-0.244240\pi$
$773$	40.0242			1.43957			0.719785	+	0.694197i	$0.244240\pi$
$774$	7.31294	+	7.81204i	0.262858	+	0.280798i
$775$	8.15616			0.292978
$776$	6.27521	−	10.8690i	0.225267	−	0.390174i
$777$	−19.8796	+	45.8404i	−0.713178	+	1.64451i
$778$	−2.90181	−	5.02608i	−0.104035	−	0.180194i
$779$	−35.6537	−	61.7540i	−1.27743	−	2.21257i
$780$	2.96029	−	0.340162i	0.105995	−	0.0121798i
$781$	2.38981	−	4.13927i	0.0855141	−	0.148115i
$782$	−7.21264			−0.257923
$783$	−1.22775	+	6.73251i	−0.0438762	+	0.240600i
$784$	9.32523			0.333044
$785$	−5.07918	+	8.79740i	−0.181284	+	0.313992i
$786$	18.1113	−	2.08114i	0.646010	−	0.0742319i
$787$	8.75713	+	15.1678i	0.312158	+	0.540673i	0.978829	−	0.204678i	$-0.0656149\pi$
$787$	8.75713	+	15.1678i	0.312158	+	0.540673i	−0.666671	+	0.745352i	$0.732282\pi$
$788$	−19.4902	−	33.7580i	−0.694309	−	1.20258i
$789$	−15.0562	+	34.7181i	−0.536016	+	1.23600i
$790$	2.84791	−	4.93273i	0.101324	−	0.175499i
$791$	20.8026			0.739655
$792$	−0.946908	+	3.11860i	−0.0336469	+	0.110815i
$793$	1.42887			0.0507405
$794$	−5.65630	+	9.79701i	−0.200735	+	0.347683i
$795$	−5.03970	−	6.79710i	−0.178740	−	0.241068i
$796$	−13.7186	−	23.7614i	−0.486244	−	0.842199i
$797$	−24.5654	−	42.5484i	−0.870149	−	1.50714i	−0.861842	−	0.507178i	$-0.830689\pi$
$797$	−24.5654	−	42.5484i	−0.870149	−	1.50714i	−0.00830790	−	0.999965i	$-0.502645\pi$
$798$	13.7239	+	18.5096i	0.485822	+	0.655234i
$799$	18.3664	−	31.8115i	0.649755	−	1.12541i
$800$	5.20400			0.183989
$801$	25.2520	−	5.88099i	0.892237	−	0.207795i
$802$	−12.0416			−0.425205
$803$	0.945234	−	1.63719i	0.0333566	−	0.0577753i
$804$	1.34474	−	3.10082i	0.0474252	−	0.109358i
$805$	−3.48866	−	6.04254i	−0.122959	−	0.212972i
$806$	−2.15649	−	3.73515i	−0.0759591	−	0.131565i
$807$	−51.7984	+	5.95207i	−1.82339	+	0.209523i
$808$	0.866746	−	1.50125i	0.0304920	−	0.0528137i
$809$	19.9875			0.702724			0.351362	−	0.936240i	$-0.385719\pi$
$809$	19.9875			0.702724			0.351362	+	0.936240i	$0.385719\pi$
$810$	−4.26949	+	2.10271i	−0.150015	+	0.0738816i
$811$	4.67105			0.164023			0.0820114	−	0.996631i	$-0.473866\pi$
$811$	4.67105			0.164023			0.0820114	+	0.996631i	$0.473866\pi$
$812$	3.73768	−	6.47385i	0.131167	−	0.227188i
$813$	19.9565	−	2.29317i	0.699906	−	0.0804251i
$814$	1.27664	+	2.21121i	0.0447463	+	0.0775029i
$815$	6.60745	+	11.4444i	0.231449	+	0.400881i
$816$	−10.6687	+	24.6009i	−0.373479	+	0.861204i
$817$	−25.7181	+	44.5450i	−0.899762	+	1.55843i
$818$	19.3766			0.677486
$819$	9.63968	−	2.24500i	0.336838	−	0.0784467i
$820$	−16.0876			−0.561804
$821$	14.4422	−	25.0147i	0.504038	−	0.873019i	−0.495951	−	0.868350i	$-0.665181\pi$
$821$	14.4422	−	25.0147i	0.504038	−	0.873019i	0.999989	−	0.00466881i	$-0.00148613\pi$
$822$	8.47642	+	11.4322i	0.295649	+	0.398745i
$823$	16.2775	+	28.1935i	0.567398	+	0.982763i	0.996822	+	0.0796595i	$0.0253833\pi$
$823$	16.2775	+	28.1935i	0.567398	+	0.982763i	−0.429424	+	0.903103i	$0.641283\pi$
$824$	8.11684	+	14.0588i	0.282763	+	0.489760i
$825$	0.569668	+	0.768319i	0.0198333	+	0.0267494i
$826$	−1.50205	+	2.60162i	−0.0522629	+	0.0905220i
$827$	−27.0068			−0.939117			−0.469559	−	0.882901i	$-0.655587\pi$
$827$	−27.0068			−0.939117			−0.469559	+	0.882901i	$0.655587\pi$
$828$	−3.17117	+	10.4441i	−0.110206	+	0.362958i
$829$	−8.07689			−0.280522			−0.140261	−	0.990115i	$-0.544794\pi$
$829$	−8.07689			−0.280522			−0.140261	+	0.990115i	$0.544794\pi$
$830$	−2.88714	+	5.00067i	−0.100214	+	0.173576i
$831$	−7.25413	+	16.7273i	−0.251643	+	0.580262i
$832$	1.02448	+	1.77445i	0.0355174	+	0.0615180i
$833$	−12.5276	−	21.6984i	−0.434055	−	0.751806i
$834$	20.2399	−	2.32574i	0.700851	−	0.0805336i
$835$	0.0441173	−	0.0764134i	0.00152674	−	0.00264439i
$836$	−7.24433			−0.250550
$837$	−32.3057	−	27.4311i	−1.11665	−	0.948157i
$838$	1.96441			0.0678594
$839$	20.1703	−	34.9361i	0.696358	−	1.20613i	−0.273363	−	0.961911i	$-0.588136\pi$
$839$	20.1703	−	34.9361i	0.696358	−	1.20613i	0.969721	−	0.244216i	$-0.0785305\pi$
$840$	11.1686	−	1.28337i	0.385355	−	0.0442805i
$841$	13.6327	+	23.6125i	0.470093	+	0.814225i
$842$	5.03832	+	8.72663i	0.173632	+	0.300740i
$843$	−6.21378	+	14.3283i	−0.214014	+	0.493493i
$844$	15.9951	−	27.7042i	0.550572	−	0.953619i
$845$	−1.00000			−0.0344010
$846$	6.17471	+	6.59613i	0.212291	+	0.226780i
$847$	−35.2853			−1.21242
$848$	5.86340	−	10.1557i	0.201350	−	0.348749i
$849$	14.7712	+	19.9221i	0.506948	+	0.683726i
$850$	−1.70524	−	2.95357i	−0.0584893	−	0.101306i
$851$	9.24583	+	16.0142i	0.316943	+	0.548961i
$852$	15.3609	+	20.7174i	0.526255	+	0.709766i
$853$	22.9769	−	39.7972i	0.786715	−	1.36263i	−0.141254	−	0.989973i	$-0.545113\pi$
$853$	22.9769	−	39.7972i	0.786715	−	1.36263i	0.927969	−	0.372657i	$-0.121553\pi$
$854$	2.49284			0.0853031
$855$	−15.6337	−	16.7007i	−0.534662	−	0.571152i
$856$	−15.6528			−0.535003
$857$	−1.91683	+	3.32005i	−0.0654777	+	0.113411i	−0.896906	−	0.442222i	$-0.854190\pi$
$857$	−1.91683	+	3.32005i	−0.0654777	+	0.113411i	0.831428	+	0.555632i	$0.187524\pi$
$858$	0.201234	−	0.464025i	0.00687003	−	0.0158416i
$859$	8.81093	+	15.2610i	0.300625	+	0.520698i	0.976278	−	0.216522i	$-0.0694714\pi$
$859$	8.81093	+	15.2610i	0.300625	+	0.520698i	−0.675653	+	0.737220i	$0.736138\pi$
$860$	5.80224	+	10.0498i	0.197855	+	0.342694i
$861$	−53.0875	+	6.10020i	−1.80922	+	0.207894i
$862$	6.71474	−	11.6303i	0.228705	−	0.396128i
$863$	26.8643			0.914472			0.457236	−	0.889345i	$-0.348840\pi$
$863$	26.8643			0.914472			0.457236	+	0.889345i	$0.348840\pi$
$864$	−20.6125	−	17.5023i	−0.701251	−	0.595440i
$865$	−4.73233			−0.160904
$866$	−9.27142	+	16.0586i	−0.315056	+	0.545693i
$867$	42.3227	−	4.86323i	1.43735	−	0.165164i
$868$	23.1467	+	40.0912i	0.785650	+	1.36079i
$869$	2.97404	+	5.15119i	0.100887	+	0.174742i
$870$	0.479944	−	1.10670i	0.0162716	−	0.0375206i
$871$	−0.567134	+	0.982304i	−0.0192166	+	0.0332841i
$872$	18.2569			0.618256
$873$	−5.56032	+	18.3127i	−0.188188	+	0.619791i
$874$	8.52775			0.288456
$875$	1.64961	−	2.85721i	0.0557670	−	0.0965912i
$876$	6.07563	+	8.19428i	0.205277	+	0.276859i
$877$	0.582111	+	1.00825i	0.0196565	+	0.0340461i	0.875686	−	0.482880i	$-0.160409\pi$
$877$	0.582111	+	1.00825i	0.0196565	+	0.0340461i	−0.856030	+	0.516926i	$0.827076\pi$
$878$	5.47849	+	9.48902i	0.184890	+	0.320239i
$879$	31.4793	+	42.4565i	1.06177	+	1.43202i
$880$	−0.662777	+	1.14796i	−0.0223422	+	0.0386979i
$881$	10.6651			0.359318			0.179659	−	0.983729i	$-0.442501\pi$
$881$	10.6651			0.359318			0.179659	+	0.983729i	$0.442501\pi$
$882$	6.00228	−	1.39788i	0.202107	−	0.0470691i
$883$	6.65292			0.223889			0.111944	−	0.993714i	$-0.464292\pi$
$883$	6.65292			0.223889			0.111944	+	0.993714i	$0.464292\pi$
$884$	5.54775	−	9.60898i	0.186591	−	0.323185i
$885$	1.18662	−	2.73622i	0.0398878	−	0.0919770i
$886$	−10.9397	−	18.9481i	−0.367526	−	0.636573i
$887$	6.57291	+	11.3846i	0.220697	+	0.382258i	0.955020	−	0.296542i	$-0.0958336\pi$
$887$	6.57291	+	11.3846i	0.220697	+	0.382258i	−0.734323	+	0.678800i	$0.762500\pi$
$888$	−29.5997	+	3.40125i	−0.993301	+	0.114139i
$889$	−10.9519	+	18.9693i	−0.367317	+	0.636211i
$890$	−4.57021			−0.153194
$891$	0.327644	−	4.95915i	0.0109765	−	0.166138i
$892$	−28.3004			−0.947569
$893$	−21.7152	+	37.6118i	−0.726671	+	1.25863i
$894$	12.7892	−	1.46958i	0.427734	−	0.0491502i
$895$	0.543925	+	0.942105i	0.0181814	+	0.0314911i
$896$	18.9565	+	32.8336i	0.633291	+	1.09689i
$897$	1.45740	−	3.36061i	0.0486611	−	0.112207i
$898$	−4.45475	+	7.71585i	−0.148657	+	0.257481i
$899$	10.7420			0.358266
$900$	−5.02659	+	1.17065i	−0.167553	+	0.0390217i
$901$	−31.5078			−1.04968
$902$	−1.36534	+	2.36484i	−0.0454609	+	0.0787406i
$903$	22.9576	+	30.9631i	0.763980	+	1.03039i
$904$	6.20231	+	10.7427i	0.206286	+	0.357298i
$905$	1.33190	+	2.30693i	0.0442740	+	0.0766848i
$906$	−8.96967	−	12.0975i	−0.297997	−	0.401913i
$907$	−3.73226	+	6.46447i	−0.123928	+	0.214649i	−0.921313	−	0.388821i	$-0.872882\pi$
$907$	−3.73226	+	6.46447i	−0.123928	+	0.214649i	0.797386	+	0.603470i	$0.206216\pi$
$908$	−8.65684			−0.287287
$909$	−0.768005	+	2.52939i	−0.0254731	+	0.0838946i
$910$	−1.74463			−0.0578338
$911$	−21.9491	+	38.0170i	−0.727207	+	1.25956i	0.230852	+	0.972989i	$0.425849\pi$
$911$	−21.9491	+	38.0170i	−0.727207	+	1.25956i	−0.958059	+	0.286571i	$0.907485\pi$
$912$	12.6140	−	29.0865i	0.417690	−	0.963150i
$913$	−3.01500	−	5.22213i	−0.0997818	−	0.172827i
$914$	5.19674	+	9.00102i	0.171893	+	0.297727i
$915$	−2.45869	+	0.282524i	−0.0812818	+	0.00933995i
$916$	6.85914	−	11.8804i	0.226632	−	0.392539i
$917$	65.6686			2.16857
$918$	−3.17926	+	17.4339i	−0.104931	+	0.575404i
$919$	−45.7211			−1.50820			−0.754100	−	0.656760i	$-0.771927\pi$
$919$	−45.7211			−1.50820			−0.754100	+	0.656760i	$0.771927\pi$
$920$	2.08030	−	3.60318i	0.0685854	−	0.118793i
$921$	−14.6306	+	1.68118i	−0.482095	+	0.0553967i
$922$	−3.74012	−	6.47807i	−0.123174	−	0.213344i
$923$	−4.32765	−	7.49572i	−0.142446	−	0.246725i
$924$	−2.15995	+	4.98062i	−0.0710572	+	0.163850i
$925$	−4.37187	+	7.57231i	−0.143746	+	0.248976i
$926$	0.484558			0.0159236
$927$	−16.9175	−	18.0721i	−0.555644	−	0.593566i
$928$	6.85388			0.224990
$929$	2.38287	−	4.12725i	0.0781793	−	0.135411i	−0.824285	−	0.566175i	$-0.808423\pi$
$929$	2.38287	−	4.12725i	0.0781793	−	0.135411i	0.902464	+	0.430764i	$0.141756\pi$
$930$	4.44927	+	6.00078i	0.145897	+	0.196773i
$931$	14.8118	+	25.6548i	0.485437	+	0.840802i
$932$	−1.17976	−	2.04341i	−0.0386445	−	0.0669342i
$933$	−16.7052	−	22.5305i	−0.546903	−	0.737615i
$934$	1.62592	−	2.81618i	0.0532019	−	0.0921484i
$935$	3.56152			0.116474
$936$	4.03343	+	4.30871i	0.131837	+	0.140835i
$937$	24.1279			0.788224			0.394112	−	0.919062i	$-0.371052\pi$
$937$	24.1279			0.788224			0.394112	+	0.919062i	$0.371052\pi$
$938$	−0.989436	+	1.71375i	−0.0323062	+	0.0559560i
$939$	−18.9821	+	43.7707i	−0.619458	+	1.42840i
$940$	4.89915	+	8.48557i	0.159793	+	0.276769i
$941$	15.7882	+	27.3460i	0.514681	+	0.891454i	0.999855	+	0.0170363i	$0.00542309\pi$
$941$	15.7882	+	27.3460i	0.514681	+	0.891454i	−0.485174	+	0.874418i	$0.661244\pi$
$942$	−9.24330	+	1.06213i	−0.301163	+	0.0346061i
$943$	−9.88821	+	17.1269i	−0.322004	+	0.557728i
$944$	4.13331			0.134528
$945$	−16.1434	+	5.76905i	−0.525144	+	0.187667i
$946$	1.96972			0.0640413
$947$	−1.27871	+	2.21479i	−0.0415525	+	0.0719711i	−0.886054	−	0.463583i	$-0.846564\pi$
$947$	−1.27871	+	2.21479i	−0.0415525	+	0.0719711i	0.844501	+	0.535554i	$0.179897\pi$
$948$	−31.8860	+	3.66397i	−1.03561	+	0.119000i
$949$	−1.71170	−	2.96476i	−0.0555642	−	0.0962401i
$950$	2.01617	+	3.49210i	0.0654131	+	0.113299i
$951$	−1.36168	+	3.13988i	−0.0441554	+	0.101818i
$952$	20.9307	−	36.2530i	0.678367	−	1.17497i
$953$	−21.8166			−0.706710			−0.353355	−	0.935489i	$-0.614959\pi$
$953$	−21.8166			−0.706710			−0.353355	+	0.935489i	$0.614959\pi$
$954$	2.25167	−	7.41577i	0.0729004	−	0.240094i
$955$	15.5439			0.502988
$956$	−18.3720	+	31.8212i	−0.594192	+	1.02917i
$957$	0.750276	+	1.01191i	0.0242530	+	0.0327103i
$958$	−0.132427	−	0.229370i	−0.00427851	−	0.00741060i
$959$	25.6325	+	44.3968i	0.827716	+	1.43365i
$960$	−2.11371	−	2.85078i	−0.0682196	−	0.0920086i
$961$	−17.7615	+	30.7638i	−0.572951	+	0.992381i
$962$	4.62369			0.149074
$963$	23.2470	−	5.41404i	0.749125	−	0.174465i
$964$	−28.7974			−0.927502
$965$	9.05801	−	15.6889i	0.291588	−	0.505045i
$966$	2.54261	−	5.86300i	0.0818073	−	0.188639i
$967$	−25.6356	−	44.4022i	−0.824386	−	1.42788i	−0.902388	−	0.430925i	$-0.858187\pi$
$967$	−25.6356	−	44.4022i	−0.824386	−	1.42788i	0.0780022	−	0.996953i	$-0.475146\pi$
$968$	−10.5204	−	18.2218i	−0.338137	−	0.585671i
$969$	−84.6257	+	9.72419i	−2.71857	+	0.312386i
$970$	1.68672	−	2.92148i	0.0541572	−	0.0938030i
$971$	−47.7853			−1.53350			−0.766752	−	0.641943i	$-0.778129\pi$
$971$	−47.7853			−1.53350			−0.766752	+	0.641943i	$0.778129\pi$
$972$	23.8470	+	12.2688i	0.764892	+	0.393522i
$973$	73.3865			2.35266
$974$	−6.64870	+	11.5159i	−0.213038	+	0.368993i
$975$	1.72073	−	0.197726i	0.0551074	−	0.00633230i
$976$	−1.71494	−	2.97036i	−0.0548938	−	0.0950789i
$977$	−20.2313	−	35.0417i	−0.647257	−	1.12108i	−0.983775	−	0.179405i	$-0.942583\pi$
$977$	−20.2313	−	35.0417i	−0.647257	−	1.12108i	0.336518	−	0.941677i	$-0.390751\pi$
$978$	−4.81565	+	11.1044i	−0.153988	+	0.355079i
$979$	2.38630	−	4.13320i	0.0762666	−	0.132098i
$980$	6.68336			0.213492
$981$	−27.1145	+	6.31473i	−0.865698	+	0.201614i
$982$	−10.2494			−0.327070
$983$	−2.87501	+	4.97967i	−0.0916987	+	0.158827i	−0.908226	−	0.418480i	$-0.862563\pi$
$983$	−2.87501	+	4.97967i	−0.0916987	+	0.158827i	0.816527	+	0.577307i	$0.195896\pi$
$984$	−18.9783	−	25.5963i	−0.605007	−	0.815981i
$985$	−11.3291	−	19.6225i	−0.360974	−	0.625225i
$986$	−2.24587	−	3.88997i	−0.0715232	−	0.123882i
$987$	19.3843	+	26.1439i	0.617010	+	0.832168i
$988$	−6.55929	+	11.3610i	−0.208679	+	0.361443i
$989$	14.2653			0.453611
$990$	−0.254520	+	0.838250i	−0.00808917	+	0.0266413i
$991$	−16.0295			−0.509194			−0.254597	−	0.967047i	$-0.581943\pi$
$991$	−16.0295			−0.509194			−0.254597	+	0.967047i	$0.581943\pi$
$992$	−21.2223	+	36.7582i	−0.673810	+	1.16707i
$993$	−12.3408	+	28.4565i	−0.391622	+	0.903039i
$994$	−7.55014	−	13.0772i	−0.239476	−	0.414784i
$995$	−7.97422	−	13.8118i	−0.252800	−	0.437862i
$996$	32.3251	−	3.71443i	1.02426	−	0.117696i
$997$	16.1572	−	27.9851i	0.511704	−	0.886296i	−0.488204	−	0.872729i	$-0.662348\pi$
$997$	16.1572	−	27.9851i	0.511704	−	0.886296i	0.999908	−	0.0135672i	$-0.00431870\pi$
$998$	6.69781			0.212016
$999$	42.7840	−	15.2894i	1.35362	−	0.483736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.7	✓	30
3.2	odd	2		1755.2.i.h.586.9		30
9.2	odd	6		5265.2.a.bl.1.7		15
9.4	even	3	inner	585.2.i.h.391.7	yes	30
9.5	odd	6		1755.2.i.h.1171.9		30
9.7	even	3		5265.2.a.bk.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.7	✓	30	1.1	even	1	trivial
585.2.i.h.391.7	yes	30	9.4	even	3	inner
1755.2.i.h.586.9		30	3.2	odd	2
1755.2.i.h.1171.9		30	9.5	odd	6
5265.2.a.bk.1.9		15	9.7	even	3
5265.2.a.bl.1.7		15	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.264400 + 0.457954i) q^{2} +(1.72073 - 0.197726i) q^{3} +(0.860185 + 1.48988i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.364411 + 0.840293i) q^{6} +(-1.64961 + 2.85721i) q^{7} -1.96733 q^{8} +(2.92181 - 0.680465i) q^{9} +O(q^{10})\)	\(q+(-0.264400 + 0.457954i) q^{2} +(1.72073 - 0.197726i) q^{3} +(0.860185 + 1.48988i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.364411 + 0.840293i) q^{6} +(-1.64961 + 2.85721i) q^{7} -1.96733 q^{8} +(2.92181 - 0.680465i) q^{9} -0.528800 q^{10} +(0.276109 - 0.478235i) q^{11} +(1.77473 + 2.39361i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.872313 - 1.51089i) q^{14} +(1.03160 + 1.39133i) q^{15} +(-1.20021 + 2.07882i) q^{16} +6.44948 q^{17} +(-0.460904 + 1.51797i) q^{18} -7.62544 q^{19} +(-0.860185 + 1.48988i) q^{20} +(-2.27358 + 5.24265i) q^{21} +(0.146006 + 0.252891i) q^{22} +(1.05742 + 1.83151i) q^{23} +(-3.38524 + 0.388992i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.528800 q^{26} +(4.89309 - 1.74861i) q^{27} -5.67588 q^{28} +(-0.658520 + 1.14059i) q^{29} +(-0.909921 + 0.104557i) q^{30} +(-4.07808 - 7.06344i) q^{31} +(-2.60200 - 4.50680i) q^{32} +(0.380549 - 0.877506i) q^{33} +(-1.70524 + 2.95357i) q^{34} -3.29922 q^{35} +(3.52711 + 3.76783i) q^{36} +8.74375 q^{37} +(2.01617 - 3.49210i) q^{38} +(-1.03160 - 1.39133i) q^{39} +(-0.983666 - 1.70376i) q^{40} +(4.67562 + 8.09842i) q^{41} +(-1.79976 - 2.42735i) q^{42} +(3.37267 - 5.84163i) q^{43} +0.950020 q^{44} +(2.05020 + 2.19013i) q^{45} -1.11833 q^{46} +(2.84773 - 4.93241i) q^{47} +(-1.65420 + 3.81440i) q^{48} +(-1.94242 - 3.36437i) q^{49} +(-0.264400 - 0.457954i) q^{50} +(11.0978 - 1.27523i) q^{51} +(0.860185 - 1.48988i) q^{52} -4.88532 q^{53} +(-0.492949 + 2.70314i) q^{54} +0.552218 q^{55} +(3.24533 - 5.62107i) q^{56} +(-13.1213 + 1.50775i) q^{57} +(-0.348225 - 0.603144i) q^{58} +(-0.860957 - 1.49122i) q^{59} +(-1.18556 + 2.73377i) q^{60} +(-0.714433 + 1.23743i) q^{61} +4.31298 q^{62} +(-2.87561 + 9.47071i) q^{63} -2.04896 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.301240 + 0.406287i) q^{66} +(-0.567134 - 0.982304i) q^{67} +(5.54775 + 9.60898i) q^{68} +(2.18167 + 2.94245i) q^{69} +(0.872313 - 1.51089i) q^{70} +8.65531 q^{71} +(-5.74817 + 1.33870i) q^{72} +3.42341 q^{73} +(-2.31185 + 4.00424i) q^{74} +(-0.689128 + 1.58906i) q^{75} +(-6.55929 - 11.3610i) q^{76} +(0.910944 + 1.57780i) q^{77} +(0.909921 - 0.104557i) q^{78} +(-5.38562 + 9.32817i) q^{79} -2.40042 q^{80} +(8.07393 - 3.97638i) q^{81} -4.94494 q^{82} +(5.45979 - 9.45663i) q^{83} +(-9.76664 + 1.12227i) q^{84} +(3.22474 + 5.58541i) q^{85} +(1.78347 + 3.08905i) q^{86} +(-0.907610 + 2.09285i) q^{87} +(-0.543198 + 0.940847i) q^{88} +8.64261 q^{89} +(-1.54505 + 0.359830i) q^{90} +3.29922 q^{91} +(-1.81916 + 3.15087i) q^{92} +(-8.41389 - 11.3479i) q^{93} +(1.50588 + 2.60826i) q^{94} +(-3.81272 - 6.60383i) q^{95} +(-5.36845 - 7.24049i) q^{96} +(-3.18971 + 5.52473i) q^{97} +2.05430 q^{98} +(0.481316 - 1.58519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

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