LMFDB - Embedded newform 825.2.bv.a.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(229,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1, 6]))

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

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

chi := DirichletCharacter("825.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bv (of order $10$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	825.229
Dual form			825.2.bv.a.544.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44907 + 1.99448i) q^{2} -1.00000i q^{3} +(-1.26009 - 3.87817i) q^{4} +(0.402508 - 2.19954i) q^{5} +(1.99448 + 1.44907i) q^{6} +(-1.80478 + 2.48406i) q^{7} +(4.87158 + 1.58287i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.44907 + 1.99448i) q^{2} -1.00000i q^{3} +(-1.26009 - 3.87817i) q^{4} +(0.402508 - 2.19954i) q^{5} +(1.99448 + 1.44907i) q^{6} +(-1.80478 + 2.48406i) q^{7} +(4.87158 + 1.58287i) q^{8} -1.00000 q^{9} +(3.80367 + 3.99009i) q^{10} +(-0.359185 + 3.29712i) q^{11} +(-3.87817 + 1.26009i) q^{12} +1.06982i q^{13} +(-2.33915 - 7.19917i) q^{14} +(-2.19954 - 0.402508i) q^{15} +(-3.61835 + 2.62888i) q^{16} +(-0.0124310 + 0.0171097i) q^{17} +(1.44907 - 1.99448i) q^{18} +(1.77672 - 5.46818i) q^{19} +(-9.03739 + 1.21063i) q^{20} +(2.48406 + 1.80478i) q^{21} +(-6.05554 - 5.49415i) q^{22} +(3.29402 + 1.07029i) q^{23} +(1.58287 - 4.87158i) q^{24} +(-4.67597 - 1.77067i) q^{25} +(-2.13373 - 1.55025i) q^{26} +1.00000i q^{27} +(11.9078 + 3.86908i) q^{28} +(1.97568 + 6.08052i) q^{29} +(3.99009 - 3.80367i) q^{30} +(-3.14839 - 9.68974i) q^{31} -0.781580i q^{32} +(3.29712 + 0.359185i) q^{33} +(-0.0161116 - 0.0495865i) q^{34} +(4.73736 + 4.96954i) q^{35} +(1.26009 + 3.87817i) q^{36} +(5.47058 + 1.77750i) q^{37} +(8.33157 + 11.4674i) q^{38} +1.06982 q^{39} +(5.44245 - 10.0781i) q^{40} +(8.18339 + 5.94558i) q^{41} +(-7.19917 + 2.33915i) q^{42} +3.89921i q^{43} +(13.2394 - 2.76170i) q^{44} +(-0.402508 + 2.19954i) q^{45} +(-6.90795 + 5.01892i) q^{46} +1.83076i q^{47} +(2.62888 + 3.61835i) q^{48} +(-0.750229 - 2.30897i) q^{49} +(10.3074 - 6.76030i) q^{50} +(0.0171097 + 0.0124310i) q^{51} +(4.14895 - 1.34807i) q^{52} +(7.04969 + 9.70306i) q^{53} +(-1.99448 - 1.44907i) q^{54} +(7.10758 + 2.11716i) q^{55} +(-12.7241 + 9.24459i) q^{56} +(-5.46818 - 1.77672i) q^{57} +(-14.9904 - 4.87067i) q^{58} +(0.234171 - 0.720705i) q^{59} +(1.21063 + 9.03739i) q^{60} +8.09517 q^{61} +(23.8882 + 7.76175i) q^{62} +(1.80478 - 2.48406i) q^{63} +(-5.67785 - 4.12520i) q^{64} +(2.35312 + 0.430612i) q^{65} +(-5.49415 + 6.05554i) q^{66} +(9.27602 + 12.7674i) q^{67} +(0.0820186 + 0.0266495i) q^{68} +(1.07029 - 3.29402i) q^{69} +(-16.7764 + 2.24734i) q^{70} +(2.68645 - 8.26803i) q^{71} +(-4.87158 - 1.58287i) q^{72} +(-0.164500 - 0.226415i) q^{73} +(-11.4725 + 8.33523i) q^{74} +(-1.77067 + 4.67597i) q^{75} -23.4454 q^{76} +(-7.54200 - 6.84280i) q^{77} +(-1.55025 + 2.13373i) q^{78} +(10.9805 - 7.97783i) q^{79} +(4.32593 + 9.01686i) q^{80} +1.00000 q^{81} +(-23.7166 + 7.70600i) q^{82} +(3.84346 - 5.29008i) q^{83} +(3.86908 - 11.9078i) q^{84} +(0.0326300 + 0.0342292i) q^{85} +(-7.77689 - 5.65024i) q^{86} +(6.08052 - 1.97568i) q^{87} +(-6.96872 + 15.4936i) q^{88} +(-3.52667 + 10.8540i) q^{89} +(-3.80367 - 3.99009i) q^{90} +(-2.65750 - 1.93079i) q^{91} -14.1234i q^{92} +(-9.68974 + 3.14839i) q^{93} +(-3.65141 - 2.65291i) q^{94} +(-11.3124 - 6.10896i) q^{95} -0.781580 q^{96} +(-1.51490 - 2.08508i) q^{97} +(5.69232 + 1.84955i) q^{98} +(0.359185 - 3.29712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 60 q^{4} + 6 q^{5} + 4 q^{6} + 20 q^{7} - 240 q^{9}+O(q^{10}) $ 240 * q + 60 * q^4 + 6 * q^5 + 4 * q^6 + 20 * q^7 - 240 * q^9	$ 240 q + 60 q^{4} + 6 q^{5} + 4 q^{6} + 20 q^{7} - 240 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{12} - 10 q^{15} - 64 q^{16} + 10 q^{17} - 14 q^{19} - 44 q^{20} + 8 q^{21} + 70 q^{22} - 12 q^{24} + 24 q^{25} - 10 q^{26} - 10 q^{28} - 16 q^{30} - 2 q^{31} - 30 q^{33} - 40 q^{35} - 60 q^{36} + 10 q^{37} + 64 q^{39} + 28 q^{40} - 6 q^{41} - 10 q^{42} - 44 q^{44} - 6 q^{45} + 32 q^{46} + 68 q^{49} - 78 q^{50} + 16 q^{51} - 20 q^{52} + 30 q^{53} - 4 q^{54} - 20 q^{55} - 20 q^{57} - 70 q^{58} + 6 q^{59} - 52 q^{60} - 72 q^{61} + 40 q^{62} - 20 q^{63} + 104 q^{64} - 70 q^{65} - 12 q^{66} + 20 q^{67} + 150 q^{68} + 2 q^{69} + 16 q^{70} + 24 q^{71} + 30 q^{73} + 22 q^{74} - 40 q^{75} - 188 q^{76} + 90 q^{77} - 38 q^{79} - 48 q^{80} + 240 q^{81} + 140 q^{82} - 24 q^{84} - 100 q^{85} + 28 q^{86} + 270 q^{88} + 2 q^{90} - 34 q^{94} - 2 q^{95} - 112 q^{96} + 80 q^{98} + 6 q^{99}+O(q^{100}) $ 240 * q + 60 * q^4 + 6 * q^5 + 4 * q^6 + 20 * q^7 - 240 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^12 - 10 * q^15 - 64 * q^16 + 10 * q^17 - 14 * q^19 - 44 * q^20 + 8 * q^21 + 70 * q^22 - 12 * q^24 + 24 * q^25 - 10 * q^26 - 10 * q^28 - 16 * q^30 - 2 * q^31 - 30 * q^33 - 40 * q^35 - 60 * q^36 + 10 * q^37 + 64 * q^39 + 28 * q^40 - 6 * q^41 - 10 * q^42 - 44 * q^44 - 6 * q^45 + 32 * q^46 + 68 * q^49 - 78 * q^50 + 16 * q^51 - 20 * q^52 + 30 * q^53 - 4 * q^54 - 20 * q^55 - 20 * q^57 - 70 * q^58 + 6 * q^59 - 52 * q^60 - 72 * q^61 + 40 * q^62 - 20 * q^63 + 104 * q^64 - 70 * q^65 - 12 * q^66 + 20 * q^67 + 150 * q^68 + 2 * q^69 + 16 * q^70 + 24 * q^71 + 30 * q^73 + 22 * q^74 - 40 * q^75 - 188 * q^76 + 90 * q^77 - 38 * q^79 - 48 * q^80 + 240 * q^81 + 140 * q^82 - 24 * q^84 - 100 * q^85 + 28 * q^86 + 270 * q^88 + 2 * q^90 - 34 * q^94 - 2 * q^95 - 112 * q^96 + 80 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.44907	+	1.99448i	−1.02465	+	1.41031i	−0.115756	+	0.993278i	$0.536929\pi$
$2$	−1.44907	+	1.99448i	−1.02465	+	1.41031i	−0.908893	+	0.417030i	$0.863071\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.26009	−	3.87817i	−0.630047	−	1.93908i
$5$	0.402508	−	2.19954i	0.180007	−	0.983665i
$5$	0.402508	−	2.19954i	0.180007	−	0.983665i
$6$	1.99448	+	1.44907i	0.814242	+	0.591581i
$7$	−1.80478	+	2.48406i	−0.682142	+	0.938888i	−0.999957	−	0.00926500i	$-0.997051\pi$
$7$	−1.80478	+	2.48406i	−0.682142	+	0.938888i	0.317815	+	0.948153i	$0.397051\pi$
$8$	4.87158	+	1.58287i	1.72237	+	0.559630i
$9$	−1.00000			−0.333333
$10$	3.80367	+	3.99009i	1.20283	+	1.26178i
$11$	−0.359185	+	3.29712i	−0.108298	+	0.994118i
$11$	−0.359185	+	3.29712i	−0.108298	+	0.994118i
$12$	−3.87817	+	1.26009i	−1.11953	+	0.363758i
$13$			1.06982i			0.296715i	0.988934	+	0.148358i	$0.0473986\pi$
$13$			1.06982i			0.296715i	−0.988934	+	0.148358i	$0.952601\pi$
$14$	−2.33915	−	7.19917i	−0.625165	−	1.92406i
$15$	−2.19954	−	0.402508i	−0.567919	−	0.103927i
$16$	−3.61835	+	2.62888i	−0.904587	+	0.657221i
$17$	−0.0124310	+	0.0171097i	−0.00301495	+	0.00414972i	−0.810522	−	0.585708i	$-0.800816\pi$
$17$	−0.0124310	+	0.0171097i	−0.00301495	+	0.00414972i	0.807507	+	0.589858i	$0.200816\pi$
$18$	1.44907	−	1.99448i	0.341550	−	0.470103i
$19$	1.77672	−	5.46818i	0.407608	−	1.25449i	−0.511090	−	0.859527i	$-0.670758\pi$
$19$	1.77672	−	5.46818i	0.407608	−	1.25449i	0.918698	−	0.394961i	$-0.129242\pi$
$20$	−9.03739	+	1.21063i	−2.02082	+	0.270706i
$21$	2.48406	+	1.80478i	0.542067	+	0.393835i
$22$	−6.05554	−	5.49415i	−1.29105	−	1.17136i
$23$	3.29402	+	1.07029i	0.686851	+	0.223172i	0.631593	−	0.775301i	$-0.282402\pi$
$23$	3.29402	+	1.07029i	0.686851	+	0.223172i	0.0552589	+	0.998472i	$0.482402\pi$
$24$	1.58287	−	4.87158i	0.323103	−	0.994408i
$25$	−4.67597	−	1.77067i	−0.935195	−	0.354134i
$26$	−2.13373	−	1.55025i	−0.418460	−	0.304029i
$27$			1.00000i			0.192450i
$28$	11.9078	+	3.86908i	2.25036	+	0.731187i
$29$	1.97568	+	6.08052i	0.366875	+	1.12913i	0.948799	+	0.315882i	$0.102300\pi$
$29$	1.97568	+	6.08052i	0.366875	+	1.12913i	−0.581924	+	0.813243i	$0.697700\pi$
$30$	3.99009	−	3.80367i	0.728487	−	0.694452i
$31$	−3.14839	−	9.68974i	−0.565467	−	1.74033i	−0.666560	−	0.745451i	$-0.732234\pi$
$31$	−3.14839	−	9.68974i	−0.565467	−	1.74033i	0.101093	−	0.994877i	$-0.467766\pi$
$32$		−	0.781580i		−	0.138165i
$33$	3.29712	+	0.359185i	0.573955	+	0.0625261i
$34$	−0.0161116	−	0.0495865i	−0.00276312	−	0.00850401i
$35$	4.73736	+	4.96954i	0.800761	+	0.840006i
$36$	1.26009	+	3.87817i	0.210016	+	0.646361i
$37$	5.47058	+	1.77750i	0.899358	+	0.292219i	0.721972	−	0.691922i	$-0.243236\pi$
$37$	5.47058	+	1.77750i	0.899358	+	0.292219i	0.177386	+	0.984141i	$0.443236\pi$
$38$	8.33157	+	11.4674i	1.35156	+	1.86026i
$39$	1.06982			0.171309
$40$	5.44245	−	10.0781i	0.860527	−	1.59349i
$41$	8.18339	+	5.94558i	1.27803	+	0.928543i	0.999492	−	0.0318815i	$-0.0101499\pi$
$41$	8.18339	+	5.94558i	1.27803	+	0.928543i	0.278539	+	0.960425i	$0.410150\pi$
$42$	−7.19917	+	2.33915i	−1.11086	+	0.360939i
$43$			3.89921i			0.594625i	0.954780	+	0.297312i	$0.0960903\pi$
$43$			3.89921i			0.594625i	−0.954780	+	0.297312i	$0.903910\pi$
$44$	13.2394	−	2.76170i	1.99591	−	0.416341i
$45$	−0.402508	+	2.19954i	−0.0600024	+	0.327888i
$46$	−6.90795	+	5.01892i	−1.01852	+	0.740000i
$47$			1.83076i			0.267044i	0.991046	+	0.133522i	$0.0426287\pi$
$47$			1.83076i			0.267044i	−0.991046	+	0.133522i	$0.957371\pi$
$48$	2.62888	+	3.61835i	0.379447	+	0.522264i
$49$	−0.750229	−	2.30897i	−0.107176	−	0.329853i
$50$	10.3074	−	6.76030i	1.45768	−	0.956050i
$51$	0.0171097	+	0.0124310i	0.00239584	+	0.00174068i
$52$	4.14895	−	1.34807i	0.575355	−	0.186944i
$53$	7.04969	+	9.70306i	0.968349	+	1.33282i	0.942877	+	0.333142i	$0.108109\pi$
$53$	7.04969	+	9.70306i	0.968349	+	1.33282i	0.0254724	+	0.999676i	$0.491891\pi$
$54$	−1.99448	−	1.44907i	−0.271414	−	0.197194i
$55$	7.10758	+	2.11716i	0.958385	+	0.285478i
$56$	−12.7241	+	9.24459i	−1.70033	+	1.23536i
$57$	−5.46818	−	1.77672i	−0.724279	−	0.235332i
$58$	−14.9904	−	4.87067i	−1.96833	−	0.639550i
$59$	0.234171	−	0.720705i	0.0304865	−	0.0938277i	−0.934655	−	0.355555i	$-0.884292\pi$
$59$	0.234171	−	0.720705i	0.0304865	−	0.0938277i	0.965142	+	0.261727i	$0.0842920\pi$
$60$	1.21063	+	9.03739i	0.156292	+	1.16672i
$61$	8.09517			1.03648			0.518240	−	0.855235i	$-0.326587\pi$
$61$	8.09517			1.03648			0.518240	+	0.855235i	$0.326587\pi$
$62$	23.8882	+	7.76175i	3.03380	+	0.985743i
$63$	1.80478	−	2.48406i	0.227381	−	0.312963i
$64$	−5.67785	−	4.12520i	−0.709732	−	0.515650i
$65$	2.35312	+	0.430612i	0.291868	+	0.0534108i
$66$	−5.49415	+	6.05554i	−0.676283	+	0.745385i
$67$	9.27602	+	12.7674i	1.13325	+	1.55978i	0.781751	+	0.623591i	$0.214327\pi$
$67$	9.27602	+	12.7674i	1.13325	+	1.55978i	0.351495	+	0.936190i	$0.385673\pi$
$68$	0.0820186	+	0.0266495i	0.00994621	+	0.00323172i
$69$	1.07029	−	3.29402i	0.128848	−	0.396554i
$70$	−16.7764	+	2.24734i	−2.00517	+	0.268608i
$71$	2.68645	−	8.26803i	0.318822	−	0.981234i	−0.655330	−	0.755343i	$-0.727470\pi$
$71$	2.68645	−	8.26803i	0.318822	−	0.981234i	0.974152	−	0.225892i	$-0.0725296\pi$
$72$	−4.87158	−	1.58287i	−0.574122	−	0.186543i
$73$	−0.164500	−	0.226415i	−0.0192533	−	0.0264999i	0.799282	−	0.600956i	$-0.205213\pi$
$73$	−0.164500	−	0.226415i	−0.0192533	−	0.0264999i	−0.818535	+	0.574456i	$0.805213\pi$
$74$	−11.4725	+	8.33523i	−1.33365	+	0.968950i
$75$	−1.77067	+	4.67597i	−0.204459	+	0.539935i
$76$	−23.4454			−2.68937
$77$	−7.54200	−	6.84280i	−0.859491	−	0.779810i
$78$	−1.55025	+	2.13373i	−0.175531	+	0.241598i
$79$	10.9805	−	7.97783i	1.23541	−	0.897576i	0.238124	−	0.971235i	$-0.423468\pi$
$79$	10.9805	−	7.97783i	1.23541	−	0.897576i	0.997284	+	0.0736587i	$0.0234675\pi$
$80$	4.32593	+	9.01686i	0.483653	+	1.00812i
$81$	1.00000			0.111111
$82$	−23.7166	+	7.70600i	−2.61906	+	0.850986i
$83$	3.84346	−	5.29008i	0.421875	−	0.580661i	−0.544189	−	0.838962i	$-0.683163\pi$
$83$	3.84346	−	5.29008i	0.421875	−	0.580661i	0.966064	+	0.258301i	$0.0831627\pi$
$84$	3.86908	−	11.9078i	0.422151	−	1.29925i
$85$	0.0326300	+	0.0342292i	0.00353922	+	0.00371268i
$86$	−7.77689	−	5.65024i	−0.838604	−	0.609281i
$87$	6.08052	−	1.97568i	0.651901	−	0.211815i
$88$	−6.96872	+	15.4936i	−0.742868	+	1.65163i
$89$	−3.52667	+	10.8540i	−0.373826	+	1.15052i	0.570441	+	0.821339i	$0.306772\pi$
$89$	−3.52667	+	10.8540i	−0.373826	+	1.15052i	−0.944267	+	0.329181i	$0.893228\pi$
$90$	−3.80367	−	3.99009i	−0.400942	−	0.420592i
$91$	−2.65750	−	1.93079i	−0.278582	−	0.202402i
$92$		−	14.1234i		−	1.47247i
$93$	−9.68974	+	3.14839i	−1.00478	+	0.326473i
$94$	−3.65141	−	2.65291i	−0.376615	−	0.273627i
$95$	−11.3124	−	6.10896i	−1.16062	−	0.626766i
$96$	−0.781580			−0.0797696
$97$	−1.51490	−	2.08508i	−0.153815	−	0.211708i	0.725155	−	0.688586i	$-0.241768\pi$
$97$	−1.51490	−	2.08508i	−0.153815	−	0.211708i	−0.878969	+	0.476878i	$0.841768\pi$
$98$	5.69232	+	1.84955i	0.575011	+	0.186832i
$99$	0.359185	−	3.29712i	0.0360994	−	0.331373i
$100$	−0.974785	+	20.3654i	−0.0974785	+	2.03654i
$101$	−3.24744	+	9.99459i	−0.323132	+	0.994499i	0.649144	+	0.760665i	$0.275127\pi$
$101$	−3.24744	+	9.99459i	−0.323132	+	0.994499i	−0.972277	+	0.233833i	$0.924873\pi$
$102$	−0.0495865	+	0.0161116i	−0.00490979	+	0.00159529i
$103$	1.91665	−	0.622757i	0.188853	−	0.0613621i	−0.213064	−	0.977038i	$-0.568344\pi$
$103$	1.91665	−	0.622757i	0.188853	−	0.0613621i	0.401917	+	0.915676i	$0.368344\pi$
$104$	−1.69339	+	5.21172i	−0.166051	+	0.511052i
$105$	4.96954	−	4.73736i	0.484978	−	0.462319i
$106$	−29.5680			−2.87190
$107$	−5.14989	−	7.08821i	−0.497858	−	0.685243i	0.483955	−	0.875093i	$-0.339200\pi$
$107$	−5.14989	−	7.08821i	−0.497858	−	0.685243i	−0.981813	+	0.189850i	$0.939200\pi$
$108$	3.87817	−	1.26009i	0.373177	−	0.121253i
$109$	−0.349262	−	1.07492i	−0.0334532	−	0.102958i	0.932936	−	0.360043i	$-0.117238\pi$
$109$	−0.349262	−	1.07492i	−0.0334532	−	0.102958i	−0.966389	+	0.257085i	$0.917238\pi$
$110$	−14.5220	+	11.1080i	−1.38462	+	1.05910i
$111$	1.77750	−	5.47058i	0.168713	−	0.519245i
$112$		−	13.7328i		−	1.29762i
$113$	6.30586	−	8.67928i	0.593206	−	0.816478i	−0.401859	−	0.915701i	$-0.631636\pi$
$113$	6.30586	−	8.67928i	0.593206	−	0.816478i	0.995065	+	0.0992238i	$0.0316360\pi$
$114$	11.4674	−	8.33157i	1.07402	−	0.780323i
$115$	3.68003	−	6.81454i	0.343164	−	0.635459i
$116$	21.0917	−	15.3241i	1.95832	−	1.42280i
$117$		−	1.06982i		−	0.0989050i
$118$	1.09810	+	1.51140i	0.101088	+	0.139136i
$119$	−0.0200666	−	0.0617585i	−0.00183950	−	0.00566140i
$120$	−10.0781	−	5.44245i	−0.920004	−	0.496826i
$121$	−10.7420	−	2.36855i	−0.976543	−	0.215323i
$122$	−11.7305	+	16.1456i	−1.06203	+	1.46176i
$123$	5.94558	−	8.18339i	0.536095	−	0.737871i
$124$	−33.6112	+	24.4199i	−3.01837	+	2.19298i
$125$	−5.77678	+	9.57230i	−0.516691	+	0.856172i
$126$	2.33915	+	7.19917i	0.208388	+	0.641353i
$127$			4.52030i			0.401112i	0.979682	+	0.200556i	$0.0642748\pi$
$127$			4.52030i			0.401112i	−0.979682	+	0.200556i	$0.935725\pi$
$128$	17.9419	−	5.82967i	1.58585	−	0.515275i
$129$	3.89921			0.343307
$130$	−4.26868	+	4.06925i	−0.374388	+	0.356897i
$131$	12.0655	−	8.76608i	1.05417	−	0.765896i	0.0811655	−	0.996701i	$-0.474136\pi$
$131$	12.0655	−	8.76608i	1.05417	−	0.765896i	0.973000	+	0.230804i	$0.0741358\pi$
$132$	−2.76170	−	13.2394i	−0.240375	−	1.15234i
$133$	10.3767	+	14.2823i	0.899777	+	1.23844i
$134$	−38.9058			−3.36095
$135$	2.19954	+	0.402508i	0.189306	+	0.0346424i
$136$	−0.0876410	+	0.0636749i	−0.00751515	+	0.00546008i
$137$	11.1174	+	15.3018i	0.949826	+	1.30732i	0.951605	+	0.307325i	$0.0994338\pi$
$137$	11.1174	+	15.3018i	0.949826	+	1.30732i	−0.00177866	+	0.999998i	$0.500566\pi$
$138$	5.01892	+	6.90795i	0.427239	+	0.588044i
$139$	3.35464	−	2.43729i	0.284537	−	0.206728i	−0.436357	−	0.899774i	$-0.643731\pi$
$139$	3.35464	−	2.43729i	0.284537	−	0.206728i	0.720894	+	0.693045i	$0.243731\pi$
$140$	13.3032	−	24.6344i	1.12432	−	2.08198i
$141$	1.83076			0.154178
$142$	12.5975	+	17.3390i	1.05716	+	1.45506i
$143$	−3.52733	−	0.384264i	−0.294970	−	0.0321337i
$144$	3.61835	−	2.62888i	0.301529	−	0.219074i
$145$	14.1696	−	1.89814i	1.17672	−	0.157632i
$146$	0.689952			0.0571009
$147$	−2.30897	+	0.750229i	−0.190440	+	0.0618779i
$148$		−	23.4557i		−	1.92804i
$149$	1.22970	+	3.78461i	0.100741	+	0.310048i	0.988707	−	0.149860i	$-0.0478824\pi$
$149$	1.22970	+	3.78461i	0.100741	+	0.310048i	−0.887967	+	0.459908i	$0.847882\pi$
$150$	−6.76030	−	10.3074i	−0.551976	−	0.841594i
$151$	−17.4277	+	12.6619i	−1.41824	+	1.03041i	−0.426185	+	0.904636i	$0.640143\pi$
$151$	−17.4277	+	12.6619i	−1.41824	+	1.03041i	−0.992058	+	0.125778i	$0.959857\pi$
$152$	17.3109	−	23.8264i	1.40410	−	1.93258i
$153$	0.0124310	−	0.0171097i	0.00100498	−	0.00138324i
$154$	24.5767	−	5.12663i	1.98045	−	0.413116i
$155$	−22.5802	+	3.02481i	−1.81369	+	0.242959i
$156$	−1.34807	−	4.14895i	−0.107932	−	0.332182i
$157$	−4.72779	−	6.50724i	−0.377319	−	0.519335i	0.577553	−	0.816353i	$-0.304008\pi$
$157$	−4.72779	−	6.50724i	−0.377319	−	0.519335i	−0.954872	+	0.297019i	$0.904008\pi$
$158$			33.4609i			2.66201i
$159$	9.70306	−	7.04969i	0.769503	−	0.559077i
$160$	−1.71912	−	0.314592i	−0.135908	−	0.0248707i
$161$	−8.60366	+	6.25092i	−0.678063	+	0.492642i
$162$	−1.44907	+	1.99448i	−0.113850	+	0.156701i
$163$		−	8.31206i		−	0.651051i	−0.945533	−	0.325525i	$-0.894459\pi$
$163$		−	8.31206i		−	0.651051i	0.945533	−	0.325525i	$-0.105541\pi$
$164$	12.7461	−	39.2285i	0.995305	−	3.06323i
$165$	2.11716	−	7.10758i	0.164821	−	0.553324i
$166$	4.98147	+	15.3314i	0.386637	+	1.18995i
$167$	−2.30100	+	0.747639i	−0.178056	+	0.0578541i	−0.396688	−	0.917953i	$-0.629841\pi$
$167$	−2.30100	+	0.747639i	−0.178056	+	0.0578541i	0.218632	+	0.975807i	$0.429841\pi$
$168$	9.24459	+	12.7241i	0.713235	+	0.981684i
$169$	11.8555			0.911960
$170$	−0.115553	+	0.0154792i	−0.00886248	+	0.00118720i
$171$	−1.77672	+	5.46818i	−0.135869	+	0.418163i
$172$	15.1218	−	4.91337i	1.15303	−	0.374641i
$173$	−6.74875	+	2.19280i	−0.513098	+	0.166716i	−0.554111	−	0.832443i	$-0.686942\pi$
$173$	−6.74875	+	2.19280i	−0.513098	+	0.166716i	0.0410127	+	0.999159i	$0.486942\pi$
$174$	−4.87067	+	14.9904i	−0.369244	+	1.13642i
$175$	12.8375	−	8.41975i	0.970427	−	0.636474i
$176$	−7.36808	−	12.8744i	−0.555390	−	0.970443i
$177$	−0.720705	−	0.234171i	−0.0541715	−	0.0176014i
$178$	−16.5376	−	22.7621i	−1.23955	−	1.70609i
$179$	−13.5629			−1.01374			−0.506871	−	0.862022i	$-0.669198\pi$
$179$	−13.5629			−1.01374			−0.506871	+	0.862022i	$0.669198\pi$
$180$	9.03739	−	1.21063i	0.673607	−	0.0902353i
$181$	−4.83525	−	3.51301i	−0.359401	−	0.261120i	0.393401	−	0.919367i	$-0.371298\pi$
$181$	−4.83525	−	3.51301i	−0.359401	−	0.261120i	−0.752802	+	0.658247i	$0.771298\pi$
$182$	7.70183	−	2.50248i	0.570898	−	0.185496i
$183$		−	8.09517i		−	0.598412i
$184$	14.3530	+	10.4280i	1.05812	+	0.768766i
$185$	6.11164	−	11.3173i	0.449337	−	0.832066i
$186$	7.76175	−	23.8882i	0.569119	−	1.75157i
$187$	−0.0519478	−	0.0471319i	−0.00379880	−	0.00344662i
$188$	7.10001	−	2.30693i	0.517821	−	0.168250i
$189$	−2.48406	−	1.80478i	−0.180689	−	0.131278i
$190$	28.5766	−	13.7099i	2.07317	−	0.994621i
$191$	1.44450	−	4.44572i	0.104521	−	0.321681i	−0.885097	−	0.465407i	$-0.845908\pi$
$191$	1.44450	−	4.44572i	0.104521	−	0.321681i	0.989618	+	0.143725i	$0.0459081\pi$
$192$	−4.12520	+	5.67785i	−0.297711	+	0.409764i
$193$	−12.5892	+	4.09047i	−0.906189	+	0.294439i	−0.724789	−	0.688971i	$-0.758063\pi$
$193$	−12.5892	+	4.09047i	−0.906189	+	0.294439i	−0.181400	+	0.983409i	$0.558063\pi$
$194$	6.35384			0.456179
$195$	0.430612	−	2.35312i	0.0308368	−	0.168510i
$196$	−8.00921	+	5.81903i	−0.572086	+	0.415645i
$197$	−0.572150	+	0.787497i	−0.0407640	+	0.0561069i	−0.828912	−	0.559378i	$-0.811040\pi$
$197$	−0.572150	+	0.787497i	−0.0407640	+	0.0561069i	0.788148	+	0.615485i	$0.211040\pi$
$198$	6.05554	+	5.49415i	0.430348	+	0.390452i
$199$	−9.56077			−0.677745			−0.338872	−	0.940832i	$-0.610045\pi$
$199$	−9.56077			−0.677745			−0.338872	+	0.940832i	$0.610045\pi$
$200$	−19.9767	−	16.0274i	−1.41256	−	1.13331i
$201$	12.7674	−	9.27602i	0.900539	−	0.654280i
$202$	−15.2282	−	20.9598i	−1.07145	−	1.47473i
$203$	−18.6701	−	6.06627i	−1.31038	−	0.425769i
$204$	0.0266495	−	0.0820186i	0.00186583	−	0.00574245i
$205$	16.3714	−	15.6066i	1.14343	−	1.09001i
$206$	−1.53529	+	4.72513i	−0.106969	+	0.329216i
$207$	−3.29402	−	1.07029i	−0.228950	−	0.0743905i
$208$	−2.81244	−	3.87099i	−0.195007	−	0.268405i
$209$	17.3911	+	7.82215i	1.20297	+	0.541069i
$210$	2.24734	+	16.7764i	0.155081	+	1.15768i
$211$	11.6878	+	8.49171i	0.804624	+	0.584593i	0.912267	−	0.409596i	$-0.134330\pi$
$211$	11.6878	+	8.49171i	0.804624	+	0.584593i	−0.107643	+	0.994190i	$0.534330\pi$
$212$	28.7468	−	39.5666i	1.97434	−	2.71745i
$213$	−8.26803	−	2.68645i	−0.566516	−	0.184072i
$214$	21.5998			1.47653
$215$	8.57649	+	1.56947i	0.584912	+	0.107037i
$216$	−1.58287	+	4.87158i	−0.107701	+	0.331469i
$217$	29.7521	+	9.66703i	2.01970	+	0.656241i
$218$	2.65000	+	0.861038i	0.179481	+	0.0583168i
$219$	−0.226415	+	0.164500i	−0.0152997	+	0.0111159i
$220$	−0.745507	−	30.2322i	−0.0502621	−	2.03825i
$221$	−0.0183044	−	0.0132989i	−0.00123128	−	0.000894581i
$222$	8.33523	+	11.4725i	0.559424	+	0.769981i
$223$	3.15088	−	1.02378i	0.210998	−	0.0685575i	−0.201611	−	0.979466i	$-0.564618\pi$
$223$	3.15088	−	1.02378i	0.210998	−	0.0685575i	0.412609	+	0.910908i	$0.364618\pi$
$224$	1.94149	+	1.41058i	0.129721	+	0.0942482i
$225$	4.67597	+	1.77067i	0.311732	+	0.118045i
$226$	8.17296	+	25.1538i	0.543657	+	1.67321i
$227$	11.3710	+	15.6508i	0.754718	+	1.03878i	0.997635	+	0.0687336i	$0.0218958\pi$
$227$	11.3710	+	15.6508i	0.754718	+	1.03878i	−0.242917	+	0.970047i	$0.578104\pi$
$228$			23.4454i			1.55271i
$229$	7.41549	−	5.38767i	0.490029	−	0.356027i	−0.315166	−	0.949036i	$-0.602060\pi$
$229$	7.41549	−	5.38767i	0.490029	−	0.356027i	0.805195	+	0.593009i	$0.202060\pi$
$230$	8.25882	+	17.2145i	0.544571	+	1.13509i
$231$	−6.84280	+	7.54200i	−0.450223	+	0.496227i
$232$			32.7490i			2.15008i
$233$	−18.2616	+	5.93356i	−1.19636	+	0.388721i	−0.838420	−	0.545024i	$-0.816520\pi$
$233$	−18.2616	+	5.93356i	−1.19636	+	0.388721i	−0.357939	+	0.933745i	$0.616520\pi$
$234$	2.13373	+	1.55025i	0.139487	+	0.101343i
$235$	4.02684	+	0.736897i	0.262682	+	0.0480699i
$236$	−3.09009			−0.201148
$237$	−7.97783	−	10.9805i	−0.518216	−	0.713263i
$238$	0.152254	+	0.0494703i	0.00986915	+	0.00320668i
$239$	−3.22587	−	9.92820i	−0.208664	−	0.642202i	−0.999543	−	0.0302294i	$-0.990376\pi$
$239$	−3.22587	−	9.92820i	−0.208664	−	0.642202i	0.790879	−	0.611973i	$-0.209624\pi$
$240$	9.01686	−	4.32593i	0.582036	−	0.279237i
$241$	−0.383762	−	1.18110i	−0.0247203	−	0.0760812i	0.937935	−	0.346810i	$-0.112735\pi$
$241$	−0.383762	−	1.18110i	−0.0247203	−	0.0760812i	−0.962656	+	0.270729i	$0.912735\pi$
$242$	20.2899	−	17.9924i	1.30428	−	1.15660i
$243$		−	1.00000i		−	0.0641500i
$244$	−10.2007	−	31.3944i	−0.653031	−	2.00982i
$245$	−5.38065	+	0.720782i	−0.343757	+	0.0460491i
$246$	7.70600	+	23.7166i	0.491317	+	1.51212i
$247$	5.84998	+	1.90077i	0.372225	+	0.120943i
$248$		−	52.1879i		−	3.31393i
$249$	−5.29008	−	3.84346i	−0.335245	−	0.243570i
$250$	−10.7208	−	25.3926i	−0.678040	−	1.60597i
$251$	7.00805	−	21.5685i	0.442344	−	1.36139i	−0.443026	−	0.896509i	$-0.646095\pi$
$251$	7.00805	−	21.5685i	0.442344	−	1.36139i	0.885370	−	0.464886i	$-0.153905\pi$
$252$	−11.9078	−	3.86908i	−0.750121	−	0.243729i
$253$	−4.71205	+	10.4764i	−0.296244	+	0.658643i
$254$	−9.01563	−	6.55024i	−0.565691	−	0.410998i
$255$	0.0342292	−	0.0326300i	0.00214352	−	0.00204337i
$256$	−10.0345	+	30.8829i	−0.627153	+	1.93018i
$257$	15.1064	−	20.7922i	0.942313	−	1.29698i	−0.0125455	−	0.999921i	$-0.503993\pi$
$257$	15.1064	−	20.7922i	0.942313	−	1.29698i	0.954858	−	0.297061i	$-0.0960065\pi$
$258$	−5.65024	+	7.77689i	−0.351769	+	0.484168i
$259$	−14.2886	+	10.3813i	−0.887851	+	0.645062i
$260$	−1.29516	−	9.66840i	−0.0803225	−	0.599608i
$261$	−1.97568	−	6.08052i	−0.122292	−	0.376375i
$262$			36.7670i			2.27147i
$263$	−22.1136	+	7.18513i	−1.36358	+	0.443054i	−0.897237	−	0.441549i	$-0.854429\pi$
$263$	−22.1136	+	7.18513i	−1.36358	+	0.443054i	−0.466344	+	0.884604i	$0.654429\pi$
$264$	15.4936	+	6.96872i	0.953568	+	0.428895i
$265$	24.1799	−	11.6005i	1.48536	−	0.712614i
$266$	−43.5224			−2.66853
$267$	10.8540	+	3.52667i	0.664253	+	0.215829i
$268$	37.8253	−	52.0620i	2.31055	−	3.18019i
$269$	−20.0960	−	14.6006i	−1.22527	−	0.890213i	−0.228747	−	0.973486i	$-0.573463\pi$
$269$	−20.0960	−	14.6006i	−1.22527	−	0.890213i	−0.996527	+	0.0832724i	$0.973463\pi$
$270$	−3.99009	+	3.80367i	−0.242829	+	0.231484i
$271$	4.86217	+	14.9642i	0.295356	+	0.909011i	0.983102	+	0.183060i	$0.0586003\pi$
$271$	4.86217	+	14.9642i	0.295356	+	0.909011i	−0.687746	+	0.725951i	$0.741400\pi$
$272$		−	0.0945885i		−	0.00573527i
$273$	−1.93079	+	2.65750i	−0.116857	+	0.160839i
$274$	−46.6291			−2.81697
$275$	7.51764	−	14.7812i	0.453331	−	0.891342i
$276$	−14.1234			−0.850131
$277$	−11.2049	+	15.4222i	−0.673237	+	0.926631i	−0.999828	−	0.0185344i	$-0.994100\pi$
$277$	−11.2049	+	15.4222i	−0.673237	+	0.926631i	0.326591	+	0.945166i	$0.394100\pi$
$278$			10.2226i			0.613109i
$279$	3.14839	+	9.68974i	0.188489	+	0.580109i
$280$	15.2123	+	31.7082i	0.909110	+	1.89493i
$281$	3.93826	+	2.86131i	0.234937	+	0.170692i	0.699025	−	0.715098i	$-0.253618\pi$
$281$	3.93826	+	2.86131i	0.234937	+	0.170692i	−0.464088	+	0.885789i	$0.653618\pi$
$282$	−2.65291	+	3.65141i	−0.157978	+	0.217439i
$283$	−23.6907	−	7.69757i	−1.40827	−	0.457573i	−0.496411	−	0.868087i	$-0.665349\pi$
$283$	−23.6907	−	7.69757i	−1.40827	−	0.457573i	−0.911854	+	0.410514i	$0.865349\pi$
$284$	−35.4500			−2.10357
$285$	−6.10896	+	11.3124i	−0.361864	+	0.670086i
$286$	5.87776	−	6.47835i	0.347559	−	0.383073i
$287$	−29.5384	+	9.59760i	−1.74360	+	0.566529i
$288$			0.781580i			0.0460550i
$289$	5.25315	+	16.1675i	0.309009	+	0.951031i
$290$	−16.7470	+	31.0115i	−0.983417	+	1.82106i
$291$	−2.08508	+	1.51490i	−0.122230	+	0.0888050i
$292$	−0.670790	+	0.923263i	−0.0392550	+	0.0540299i
$293$	−3.09402	+	4.25856i	−0.180755	+	0.248788i	−0.889774	−	0.456402i	$-0.849138\pi$
$293$	−3.09402	+	4.25856i	−0.180755	+	0.248788i	0.709019	+	0.705189i	$0.249138\pi$
$294$	1.84955	−	5.69232i	0.107868	−	0.331983i
$295$	−1.49096	−	0.805159i	−0.0868073	−	0.0468782i
$296$	23.8369	+	17.3185i	1.38549	+	1.00662i
$297$	−3.29712	−	0.359185i	−0.191318	−	0.0208420i
$298$	−9.33024	−	3.03158i	−0.540486	−	0.175615i
$299$	−1.14502	+	3.52402i	−0.0662184	+	0.203799i
$300$	20.3654	+	0.974785i	1.17580	+	0.0562793i
$301$	−9.68590	−	7.03721i	−0.558286	−	0.405618i
$302$		−	53.1071i		−	3.05597i
$303$	9.99459	+	3.24744i	0.574174	+	0.186560i
$304$	7.94643	+	24.4566i	0.455759	+	1.40268i
$305$	3.25837	−	17.8057i	0.186574	−	1.01955i
$306$	0.0161116	+	0.0495865i	0.000921040	+	0.00283467i
$307$		−	12.9440i		−	0.738754i	−0.929280	−	0.369377i	$-0.879571\pi$
$307$		−	12.9440i		−	0.738754i	0.929280	−	0.369377i	$-0.120429\pi$
$308$	−17.0339	+	37.8717i	−0.970597	+	2.15794i
$309$	−0.622757	−	1.91665i	−0.0354274	−	0.109034i
$310$	26.6875	−	49.4189i	1.51575	−	2.80681i
$311$	7.22164	+	22.2259i	0.409502	+	1.26032i	0.917077	+	0.398710i	$0.130542\pi$
$311$	7.22164	+	22.2259i	0.409502	+	1.26032i	−0.507575	+	0.861607i	$0.669458\pi$
$312$	5.21172	+	1.69339i	0.295056	+	0.0958694i
$313$	−5.98092	−	8.23203i	−0.338062	−	0.465302i	0.605812	−	0.795608i	$-0.292848\pi$
$313$	−5.98092	−	8.23203i	−0.338062	−	0.465302i	−0.943874	+	0.330306i	$0.892848\pi$
$314$	19.8295			1.11904
$315$	−4.73736	−	4.96954i	−0.266920	−	0.280002i
$316$	−44.7759	−	32.5316i	−2.51884	−	1.83004i
$317$	−3.21315	+	1.04402i	−0.180469	+	0.0586378i	−0.397857	−	0.917447i	$-0.630246\pi$
$317$	−3.21315	+	1.04402i	−0.180469	+	0.0586378i	0.217389	+	0.976085i	$0.430246\pi$
$318$			29.5680i			1.65809i
$319$	−20.7578	+	4.33002i	−1.16222	+	0.242435i
$320$	−11.3589	+	10.8283i	−0.634984	+	0.605318i
$321$	−7.08821	+	5.14989i	−0.395625	+	0.287439i
$322$		−	26.2178i		−	1.46106i
$323$	0.0714729	+	0.0983740i	0.00397686	+	0.00547367i
$324$	−1.26009	−	3.87817i	−0.0700052	−	0.215454i
$325$	1.89430	−	5.00246i	0.105077	−	0.277486i
$326$	16.5782	+	12.0448i	0.918182	+	0.667098i
$327$	−1.07492	+	0.349262i	−0.0594430	+	0.0193142i
$328$	30.4550	+	41.9177i	1.68159	+	2.31452i
$329$	−4.54773	−	3.30412i	−0.250725	−	0.182162i
$330$	11.1080	+	14.5220i	0.611474	+	0.799411i
$331$	−6.32918	+	4.59842i	−0.347883	+	0.252752i	−0.747980	−	0.663721i	$-0.768976\pi$
$331$	−6.32918	+	4.59842i	−0.347883	+	0.252752i	0.400097	+	0.916473i	$0.368976\pi$
$332$	−25.3589	−	8.23961i	−1.39175	−	0.452208i
$333$	−5.47058	−	1.77750i	−0.299786	−	0.0974064i
$334$	1.84316	−	5.67267i	0.100853	−	0.310395i
$335$	31.8160	−	15.2640i	1.73829	−	0.833964i
$336$	−13.7328			−0.749183
$337$	3.08414	+	1.00210i	0.168004	+	0.0545878i	0.391811	−	0.920046i	$-0.371849\pi$
$337$	3.08414	+	1.00210i	0.168004	+	0.0545878i	−0.223807	+	0.974633i	$0.571849\pi$
$338$	−17.1794	+	23.6455i	−0.934439	+	1.28614i
$339$	−8.67928	−	6.30586i	−0.471394	−	0.342487i
$340$	0.0916298	−	0.169677i	0.00496932	−	0.00920201i
$341$	33.0791	−	6.90020i	1.79133	−	0.373667i
$342$	−8.33157	−	11.4674i	−0.450520	−	0.620087i
$343$	−13.3517	−	4.33824i	−0.720925	−	0.234243i
$344$	−6.17196	+	18.9954i	−0.332770	+	1.02416i
$345$	−6.81454	−	3.68003i	−0.366883	−	0.198126i
$346$	5.40593	−	16.6378i	0.290625	−	0.894451i
$347$	−12.8913	−	4.18864i	−0.692042	−	0.224858i	−0.0581822	−	0.998306i	$-0.518530\pi$
$347$	−12.8913	−	4.18864i	−0.692042	−	0.224858i	−0.633860	+	0.773448i	$0.718530\pi$
$348$	−15.3241	−	21.0917i	−0.821455	−	1.13064i
$349$	−4.30642	+	3.12880i	−0.230517	+	0.167481i	−0.697048	−	0.717024i	$-0.745504\pi$
$349$	−4.30642	+	3.12880i	−0.230517	+	0.167481i	0.466531	+	0.884505i	$0.345504\pi$
$350$	−1.80953	+	37.8050i	−0.0967233	+	2.02076i
$351$	−1.06982			−0.0571028
$352$	2.57696	+	0.280732i	0.137352	+	0.0149630i
$353$	−2.80487	+	3.86058i	−0.149288	+	0.205478i	−0.877111	−	0.480287i	$-0.840532\pi$
$353$	−2.80487	+	3.86058i	−0.149288	+	0.205478i	0.727823	+	0.685765i	$0.240532\pi$
$354$	1.51140	−	1.09810i	0.0803301	−	0.0583632i
$355$	−17.1046	−	9.23690i	−0.907816	−	0.490244i
$356$	46.5375			2.46648
$357$	−0.0617585	+	0.0200666i	−0.00326861	+	0.00106204i
$358$	19.6537	−	27.0510i	1.03873	−	1.42969i
$359$	−7.69994	+	23.6980i	−0.406387	+	1.25073i	0.513344	+	0.858183i	$0.328406\pi$
$359$	−7.69994	+	23.6980i	−0.406387	+	1.25073i	−0.919731	+	0.392548i	$0.871594\pi$
$360$	−5.44245	+	10.0781i	−0.286842	+	0.531164i
$361$	−11.3730	−	8.26296i	−0.598578	−	0.434892i
$362$	14.0132	−	4.55318i	0.736519	−	0.239310i
$363$	−2.36855	+	10.7420i	−0.124317	+	0.563807i
$364$	−4.13922	+	12.7392i	−0.216954	+	0.667717i
$365$	−0.564222	+	0.270691i	−0.0295327	+	0.0141686i
$366$	16.1456	+	11.7305i	0.843945	+	0.613162i
$367$		−	4.01338i		−	0.209497i	−0.994499	−	0.104748i	$-0.966596\pi$
$367$		−	4.01338i		−	0.209497i	0.994499	−	0.104748i	$-0.0334037\pi$
$368$	−14.7326	+	4.78691i	−0.767990	+	0.249535i
$369$	−8.18339	−	5.94558i	−0.426010	−	0.309514i
$370$	13.7159	+	28.5891i	0.713057	+	1.48628i
$371$	−36.8261			−1.91192
$372$	24.4199	+	33.6112i	1.26612	+	1.74266i
$373$	6.03644	+	1.96136i	0.312555	+	0.101555i	0.461094	−	0.887351i	$-0.347457\pi$
$373$	6.03644	+	1.96136i	0.312555	+	0.101555i	−0.148539	+	0.988907i	$0.547457\pi$
$374$	0.169280	−	0.0353112i	0.00875324	−	0.00182590i
$375$	9.57230	+	5.77678i	0.494311	+	0.298312i
$376$	−2.89787	+	8.91872i	−0.149446	+	0.459948i
$377$	−6.50508	+	2.11363i	−0.335028	+	0.108857i
$378$	7.19917	−	2.33915i	0.370286	−	0.120313i
$379$	−7.50958	+	23.1121i	−0.385741	+	1.18719i	0.550200	+	0.835033i	$0.314552\pi$
$379$	−7.50958	+	23.1121i	−0.385741	+	1.18719i	−0.935941	+	0.352157i	$0.885448\pi$
$380$	−9.43696	+	51.5691i	−0.484106	+	2.64544i
$381$	4.52030			0.231582
$382$	6.77370	+	9.32320i	0.346573	+	0.477017i
$383$	13.2181	−	4.29482i	0.675413	−	0.219455i	0.0488270	−	0.998807i	$-0.484452\pi$
$383$	13.2181	−	4.29482i	0.675413	−	0.219455i	0.626586	+	0.779352i	$0.284452\pi$
$384$	−5.82967	−	17.9419i	−0.297494	−	0.915593i
$385$	−18.0868	+	13.8347i	−0.921786	+	0.705080i
$386$	10.0843	−	31.0362i	0.513276	−	1.57970i
$387$		−	3.89921i		−	0.198208i
$388$	−6.17738	+	8.50243i	−0.313609	+	0.431646i
$389$	−0.0275426	+	0.0200108i	−0.00139646	+	0.00101459i	−0.588483	−	0.808509i	$-0.700275\pi$
$389$	−0.0275426	+	0.0200108i	−0.00139646	+	0.00101459i	0.587087	+	0.809524i	$0.300275\pi$
$390$	4.06925	+	4.26868i	0.206054	+	0.216153i
$391$	−0.0592603	+	0.0430551i	−0.00299692	+	0.00217739i
$392$		−	12.4358i		−	0.628105i
$393$	−8.76608	−	12.0655i	−0.442190	−	0.608623i
$394$	−0.741558	−	2.28228i	−0.0373591	−	0.114980i
$395$	−13.1278	−	27.3633i	−0.660532	−	1.37680i
$396$	−13.2394	+	2.76170i	−0.665304	+	0.138780i
$397$	19.0352	−	26.1996i	0.955347	−	1.31492i	0.00623588	−	0.999981i	$-0.498015\pi$
$397$	19.0352	−	26.1996i	0.955347	−	1.31492i	0.949111	−	0.314942i	$-0.101985\pi$
$398$	13.8542	−	19.0687i	0.694450	−	0.955829i
$399$	14.2823	−	10.3767i	0.715012	−	0.519486i
$400$	21.5742	−	5.88570i	1.07871	−	0.294285i
$401$	6.13271	+	18.8746i	0.306253	+	0.942550i	0.979207	+	0.202865i	$0.0650254\pi$
$401$	6.13271	+	18.8746i	0.306253	+	0.942550i	−0.672954	+	0.739685i	$0.734975\pi$
$402$			38.9058i			1.94045i
$403$	10.3663	−	3.36821i	0.516382	−	0.167783i
$404$	42.8528			2.13200
$405$	0.402508	−	2.19954i	0.0200008	−	0.109296i
$406$	39.1533	−	28.4466i	1.94315	−	1.41178i
$407$	−7.82558	+	17.3987i	−0.387900	+	0.862422i
$408$	0.0636749	+	0.0876410i	0.00315238	+	0.00433887i
$409$	28.8748			1.42777			0.713885	−	0.700263i	$-0.246934\pi$
$409$	28.8748			1.42777			0.713885	+	0.700263i	$0.246934\pi$
$410$	7.40354	+	55.2675i	0.365635	+	2.72947i
$411$	15.3018	−	11.1174i	0.754783	−	0.548382i
$412$	−4.83031	−	6.64836i	−0.237972	−	0.327541i
$413$	1.36765	+	1.88241i	0.0672976	+	0.0926272i
$414$	6.90795	−	5.01892i	0.339507	−	0.246667i
$415$	−10.0887	−	10.5832i	−0.495236	−	0.519507i
$416$	0.836150			0.0409957
$417$	−2.43729	−	3.35464i	−0.119355	−	0.164278i
$418$	−40.8020	+	23.3512i	−1.99569	+	1.14215i
$419$	19.9766	−	14.5139i	0.975922	−	0.709049i	0.0191284	−	0.999817i	$-0.493911\pi$
$419$	19.9766	−	14.5139i	0.975922	−	0.709049i	0.956794	+	0.290768i	$0.0939109\pi$
$420$	−24.6344	−	13.3032i	−1.20203	−	0.649129i
$421$	28.1841			1.37361			0.686805	−	0.726842i	$-0.259013\pi$
$421$	28.1841			1.37361			0.686805	+	0.726842i	$0.259013\pi$
$422$	−33.8730	+	11.0060i	−1.64891	+	0.535764i
$423$		−	1.83076i		−	0.0890148i
$424$	18.9844	+	58.4280i	0.921965	+	2.83752i
$425$	0.0884225	−	0.0579936i	0.00428912	−	0.00281310i
$426$	17.3390	−	12.5975i	0.840078	−	0.610353i
$427$	−14.6100	+	20.1089i	−0.707026	+	0.973138i
$428$	−20.9999	+	28.9039i	−1.01507	+	1.39712i
$429$	−0.384264	+	3.52733i	−0.0185524	+	0.170301i
$430$	−15.5582	+	14.8313i	−0.750284	+	0.715230i
$431$	10.4089	+	32.0352i	0.501377	+	1.54308i	0.806777	+	0.590856i	$0.201210\pi$
$431$	10.4089	+	32.0352i	0.501377	+	1.54308i	−0.305399	+	0.952224i	$0.598790\pi$
$432$	−2.62888	−	3.61835i	−0.126482	−	0.174088i
$433$			14.1422i			0.679632i	0.940492	+	0.339816i	$0.110365\pi$
$433$			14.1422i			0.679632i	−0.940492	+	0.339816i	$0.889635\pi$
$434$	−62.3935	+	45.3316i	−2.99499	+	2.17598i
$435$	−1.89814	−	14.1696i	−0.0910086	−	0.679380i
$436$	−3.72861	+	2.70899i	−0.178568	+	0.129737i
$437$	11.7051	−	16.1107i	0.559932	−	0.770680i
$438$		−	0.689952i		−	0.0329672i
$439$	6.90481	−	21.2508i	0.329549	−	1.01425i	−0.639797	−	0.768544i	$-0.720981\pi$
$439$	6.90481	−	21.2508i	0.329549	−	1.01425i	0.969345	−	0.245702i	$-0.0790186\pi$
$440$	31.2740	+	21.5643i	1.49093	+	1.02804i
$441$	0.750229	+	2.30897i	0.0357252	+	0.109951i
$442$	0.0530487	−	0.0172366i	0.00252327	−	0.000819860i
$443$	−14.5893	−	20.0805i	−0.693160	−	0.954053i	−0.999997	−	0.00229099i	$-0.999271\pi$
$443$	−14.5893	−	20.0805i	−0.693160	−	0.954053i	0.306837	−	0.951762i	$-0.400729\pi$
$444$	−23.4557			−1.11316
$445$	22.4543	+	12.1259i	1.06443	+	0.574822i
$446$	−2.52394	+	7.76789i	−0.119512	+	0.367820i
$447$	3.78461	−	1.22970i	0.179006	−	0.0581626i
$448$	20.4945	−	6.65908i	0.968275	−	0.314612i
$449$	2.68108	−	8.25152i	0.126528	−	0.389414i	−0.867648	−	0.497179i	$-0.834369\pi$
$449$	2.68108	−	8.25152i	0.126528	−	0.389414i	0.994176	+	0.107765i	$0.0343694\pi$
$450$	−10.3074	+	6.76030i	−0.485895	+	0.318683i
$451$	−22.5426	+	24.8460i	−1.06149	+	1.16995i
$452$	−41.6057	−	13.5185i	−1.95697	−	0.635857i
$453$	12.6619	+	17.4277i	0.594910	+	0.818823i
$454$	−47.6925			−2.23832
$455$	−5.31652	+	5.06813i	−0.249242	+	0.237598i
$456$	−23.8264	−	17.3109i	−1.11577	−	0.810657i
$457$	33.1543	−	10.7725i	1.55089	−	0.503916i	0.596537	−	0.802586i	$-0.296543\pi$
$457$	33.1543	−	10.7725i	1.55089	−	0.503916i	0.954356	+	0.298670i	$0.0965431\pi$
$458$			22.5971i			1.05589i
$459$	−0.0171097	−	0.0124310i	−0.000798614	−	0.000580227i
$460$	−31.0651	−	5.68480i	−1.44842	−	0.265055i
$461$	1.71097	−	5.26582i	0.0796877	−	0.245254i	−0.903274	−	0.429064i	$-0.858843\pi$
$461$	1.71097	−	5.26582i	0.0796877	−	0.245254i	0.982962	+	0.183811i	$0.0588434\pi$
$462$	−5.12663	−	24.5767i	−0.238512	−	1.14341i
$463$	−18.0697	+	5.87119i	−0.839768	+	0.272857i	−0.697154	−	0.716921i	$-0.745551\pi$
$463$	−18.0697	+	5.87119i	−0.839768	+	0.272857i	−0.142614	+	0.989778i	$0.545551\pi$
$464$	−23.1337	−	16.8076i	−1.07396	−	0.780274i
$465$	3.02481	+	22.5802i	0.140272	+	1.04713i
$466$	14.6281	−	45.0206i	0.677632	−	2.08554i
$467$	−23.3326	+	32.1145i	−1.07970	+	1.48608i	−0.219856	+	0.975532i	$0.570559\pi$
$467$	−23.3326	+	32.1145i	−1.07970	+	1.48608i	−0.859847	+	0.510551i	$0.829441\pi$
$468$	−4.14895	+	1.34807i	−0.191785	+	0.0623148i
$469$	−48.4561			−2.23749
$470$	−7.30491	+	6.96362i	−0.336950	+	0.321208i
$471$	−6.50724	+	4.72779i	−0.299838	+	0.217845i
$472$	2.28157	−	3.14031i	0.105018	−	0.144544i
$473$	−12.8562	−	1.40054i	−0.591127	−	0.0643968i
$474$	33.4609			1.53691
$475$	−17.9902	+	22.4231i	−0.825449	+	1.02884i
$476$	−0.214224	+	0.155643i	−0.00981895	+	0.00713389i
$477$	−7.04969	−	9.70306i	−0.322783	−	0.444273i
$478$	24.4761	+	7.95276i	1.11951	+	0.363751i
$479$	9.75795	−	30.0319i	0.445852	−	1.37219i	−0.435695	−	0.900094i	$-0.643497\pi$
$479$	9.75795	−	30.0319i	0.445852	−	1.37219i	0.881547	−	0.472097i	$-0.156503\pi$
$480$	−0.314592	+	1.71912i	−0.0143591	+	0.0784666i
$481$	−1.90161	+	5.85255i	−0.0867059	+	0.266853i
$482$	2.91177	+	0.946092i	0.132628	+	0.0430933i
$483$	6.25092	+	8.60366i	0.284427	+	0.391480i
$484$	4.35025	+	44.6438i	0.197739	+	2.02926i
$485$	−5.19598	+	2.49282i	−0.235937	+	0.113193i
$486$	1.99448	+	1.44907i	0.0904713	+	0.0657312i
$487$	6.82755	−	9.39731i	0.309386	−	0.425833i	−0.625804	−	0.779980i	$-0.715229\pi$
$487$	6.82755	−	9.39731i	0.309386	−	0.425833i	0.935190	+	0.354148i	$0.115229\pi$
$488$	39.4363	+	12.8136i	1.78520	+	0.580046i
$489$	−8.31206			−0.375884
$490$	6.35936	−	11.7760i	0.287287	−	0.531987i
$491$	8.58046	−	26.4079i	0.387231	−	1.19177i	−0.547619	−	0.836728i	$-0.684466\pi$
$491$	8.58046	−	26.4079i	0.387231	−	1.19177i	0.934849	−	0.355045i	$-0.115534\pi$
$492$	−39.2285	−	12.7461i	−1.76856	−	0.574640i
$493$	−0.128596	−	0.0417833i	−0.00579166	−	0.00188183i
$494$	−12.2681	+	8.91329i	−0.551968	+	0.401028i
$495$	−7.10758	−	2.11716i	−0.319462	−	0.0951592i
$496$	36.8652	+	26.7841i	1.65529	+	1.20264i
$497$	15.6899	+	21.5953i	0.703787	+	0.968679i
$498$	15.3314	−	4.98147i	0.687016	−	0.223225i
$499$	7.64331	+	5.55319i	0.342161	+	0.248595i	0.745573	−	0.666424i	$-0.232176\pi$
$499$	7.64331	+	5.55319i	0.342161	+	0.248595i	−0.403412	+	0.915019i	$0.632176\pi$
$500$	44.4022	+	10.3413i	1.98573	+	0.462478i
$501$	0.747639	+	2.30100i	0.0334021	+	0.102801i
$502$	32.8628	+	45.2318i	1.46674	+	2.01879i
$503$			30.3595i			1.35366i	0.736138	+	0.676832i	$0.236648\pi$
$503$			30.3595i			1.35366i	−0.736138	+	0.676832i	$0.763352\pi$
$504$	12.7241	−	9.24459i	0.566776	−	0.411787i
$505$	20.6764	+	11.1658i	0.920088	+	0.496871i
$506$	−14.0667	−	24.5791i	−0.625343	−	1.09267i
$507$		−	11.8555i		−	0.526520i
$508$	17.5305	−	5.69600i	0.777789	−	0.252719i
$509$	12.7829	+	9.28732i	0.566592	+	0.411653i	0.833866	−	0.551967i	$-0.186123\pi$
$509$	12.7829	+	9.28732i	0.566592	+	0.411653i	−0.267273	+	0.963621i	$0.586123\pi$
$510$	0.0154792	+	0.115553i	0.000685432	+	0.00511676i
$511$	0.859316			0.0380139
$512$	−24.8771	−	34.2404i	−1.09942	−	1.51323i
$513$	5.46818	+	1.77672i	0.241426	+	0.0784441i
$514$	19.5793	+	60.2588i	0.863605	+	2.65790i
$515$	−0.598313	−	4.46642i	−0.0263648	−	0.196814i
$516$	−4.91337	−	15.1218i	−0.216299	−	0.665700i
$517$	−6.03624	−	0.657582i	−0.265474	−	0.0289204i
$518$		−	43.5415i		−	1.91310i
$519$	2.19280	+	6.74875i	0.0962533	+	0.296237i
$520$	10.7818	+	5.82245i	0.472813	+	0.255331i
$521$	−2.86166	−	8.80727i	−0.125371	−	0.385853i	0.868597	−	0.495519i	$-0.165022\pi$
$521$	−2.86166	−	8.80727i	−0.125371	−	0.385853i	−0.993969	+	0.109665i	$0.965022\pi$
$522$	14.9904	+	4.87067i	0.656111	+	0.213183i
$523$		−	4.75761i		−	0.208036i	−0.994575	−	0.104018i	$-0.966830\pi$
$523$		−	4.75761i		−	0.208036i	0.994575	−	0.104018i	$-0.0331699\pi$
$524$	−49.2000	−	35.7459i	−2.14931	−	1.56157i
$525$	−8.41975	−	12.8375i	−0.367468	−	0.560276i
$526$	17.7136	−	54.5168i	0.772348	−	2.37704i
$527$	0.204926	+	0.0665846i	0.00892673	+	0.00290047i
$528$	−12.8744	+	7.36808i	−0.560285	+	0.320655i
$529$	−8.90233	−	6.46792i	−0.387058	−	0.281214i
$530$	−11.9014	+	65.0361i	−0.516963	+	2.82499i
$531$	−0.234171	+	0.720705i	−0.0101622	+	0.0312759i
$532$	42.3137	−	58.2398i	1.83453	−	2.52501i
$533$	−6.36071	+	8.75476i	−0.275513	+	0.379211i
$534$	−22.7621	+	16.5376i	−0.985011	+	0.715652i
$535$	−17.6637	+	8.47433i	−0.763668	+	0.366377i
$536$	24.9798	+	76.8800i	1.07896	+	3.32071i
$537$			13.5629i			0.585284i
$538$	58.2411	−	18.9237i	2.51095	−	0.815857i
$539$	7.88241	−	1.64425i	0.339519	−	0.0708228i
$540$	−1.21063	−	9.03739i	−0.0520974	−	0.388907i
$541$	43.0985			1.85295			0.926475	−	0.376357i	$-0.122823\pi$
$541$	43.0985			1.85295			0.926475	+	0.376357i	$0.122823\pi$
$542$	−36.8914	−	11.9867i	−1.58462	−	0.514875i
$543$	−3.51301	+	4.83525i	−0.150758	+	0.207500i
$544$	0.0133726	+	0.00971578i	0.000573346	+	0.000416560i
$545$	−2.50491	+	0.335553i	−0.107298	+	0.0143735i
$546$	−2.50248	−	7.70183i	−0.107096	−	0.329608i
$547$		−	22.2979i		−	0.953389i	−0.879069	−	0.476695i	$-0.841835\pi$
$547$		−	22.2979i		−	0.953389i	0.879069	−	0.476695i	$-0.158165\pi$
$548$	45.3341	−	62.3970i	1.93657	−	2.66547i
$549$	−8.09517			−0.345493
$550$	18.5872	+	36.4128i	0.792562	+	1.55265i
$551$	36.7597			1.56601
$552$	10.4280	−	14.3530i	0.443847	−	0.610903i
$553$			41.6746i			1.77218i
$554$	−14.5225	−	44.6958i	−0.617004	−	1.89894i
$555$	−11.3173	−	6.11164i	−0.480394	−	0.259425i
$556$	−13.6794	−	9.93865i	−0.580135	−	0.421493i
$557$	0.803412	−	1.10580i	0.0340417	−	0.0468543i	−0.791657	−	0.610966i	$-0.790781\pi$
$557$	0.803412	−	1.10580i	0.0340417	−	0.0468543i	0.825699	+	0.564112i	$0.190781\pi$
$558$	−23.8882	−	7.76175i	−1.01127	−	0.328581i
$559$	−4.17146			−0.176434
$560$	−30.2058	−	5.52755i	−1.27643	−	0.233582i
$561$	−0.0471319	+	0.0519478i	−0.00198991	+	0.00219324i
$562$	−11.4136	+	3.70852i	−0.481456	+	0.156434i
$563$		−	23.2847i		−	0.981335i	−0.871347	−	0.490667i	$-0.836753\pi$
$563$		−	23.2847i		−	0.981335i	0.871347	−	0.490667i	$-0.163247\pi$
$564$	−2.30693	−	7.10001i	−0.0971394	−	0.298964i
$565$	−16.5523	−	17.3635i	−0.696359	−	0.730488i
$566$	49.6822	−	36.0962i	2.08830	−	1.51724i
$567$	−1.80478	+	2.48406i	−0.0757935	+	0.104321i
$568$	26.1745	−	36.0261i	1.09826	−	1.51162i
$569$	7.84143	−	24.1334i	0.328730	−	1.01173i	−0.640999	−	0.767542i	$-0.721480\pi$
$569$	7.84143	−	24.1334i	0.328730	−	1.01173i	0.969729	−	0.244184i	$-0.0785202\pi$
$570$	−13.7099	−	28.5766i	−0.574245	−	1.19694i
$571$	22.0351	+	16.0095i	0.922142	+	0.669975i	0.944056	−	0.329785i	$-0.106976\pi$
$571$	22.0351	+	16.0095i	0.922142	+	0.669975i	−0.0219145	+	0.999760i	$0.506976\pi$
$572$	2.95452	+	14.1638i	0.123535	+	0.592217i
$573$	−4.44572	−	1.44450i	−0.185723	−	0.0603450i
$574$	23.6611	−	72.8212i	0.987593	−	3.03950i
$575$	−13.5076	−	10.8373i	−0.563307	−	0.451946i
$576$	5.67785	+	4.12520i	0.236577	+	0.171883i
$577$		−	28.9320i		−	1.20446i	−0.798324	−	0.602228i	$-0.794280\pi$
$577$		−	28.9320i		−	1.20446i	0.798324	−	0.602228i	$-0.205720\pi$
$578$	−39.8580	−	12.9506i	−1.65787	−	0.538676i
$579$	4.09047	+	12.5892i	0.169994	+	0.523188i
$580$	−25.2163	−	52.5603i	−1.04705	−	2.18245i
$581$	6.20428	+	19.0948i	0.257397	+	0.792187i
$582$		−	6.35384i		−	0.263375i
$583$	−34.5243	+	19.7585i	−1.42985	+	0.818312i
$584$	−0.442990	−	1.36338i	−0.0183311	−	0.0564172i
$585$	−2.35312	−	0.430612i	−0.0972894	−	0.0178036i
$586$	−4.01013	−	12.3419i	−0.165657	−	0.509840i
$587$	4.62924	+	1.50413i	0.191069	+	0.0620821i	0.402989	−	0.915205i	$-0.367971\pi$
$587$	4.62924	+	1.50413i	0.191069	+	0.0620821i	−0.211919	+	0.977287i	$0.567971\pi$
$588$	5.81903	+	8.00921i	0.239973	+	0.330294i
$589$	−58.5791			−2.41371
$590$	3.76639	−	1.80696i	0.155060	−	0.0743914i
$591$	0.787497	+	0.572150i	0.0323933	+	0.0235351i
$592$	−24.4673	+	7.94991i	−1.00560	+	0.326739i
$593$		−	28.9197i		−	1.18759i	−0.804617	−	0.593794i	$-0.797629\pi$
$593$		−	28.9197i		−	1.18759i	0.804617	−	0.593794i	$-0.202371\pi$
$594$	5.49415	−	6.05554i	0.225428	−	0.248462i
$595$	−0.143917	+	0.0192789i	−0.00590004	+	0.000790359i
$596$	13.1278	−	9.53793i	0.537737	−	0.390689i
$597$			9.56077i			0.391296i
$598$	−5.36935	−	7.39028i	−0.219569	−	0.302211i
$599$	10.7867	+	33.1981i	0.440734	+	1.35644i	0.887095	+	0.461587i	$0.152720\pi$
$599$	10.7867	+	33.1981i	0.440734	+	1.35644i	−0.446361	+	0.894853i	$0.647280\pi$
$600$	−16.0274	+	19.9767i	−0.654317	+	0.815544i
$601$	−15.5949	−	11.3304i	−0.636130	−	0.462175i	0.222389	−	0.974958i	$-0.428615\pi$
$601$	−15.5949	−	11.3304i	−0.636130	−	0.462175i	−0.858518	+	0.512783i	$0.828615\pi$
$602$	28.0711	−	9.12086i	1.14409	−	0.371739i
$603$	−9.27602	−	12.7674i	−0.377749	−	0.519927i
$604$	71.0656	+	51.6322i	2.89162	+	2.10088i
$605$	−9.53346	+	22.6741i	−0.387590	+	0.921832i
$606$	−20.9598	+	15.2282i	−0.851434	+	0.618603i
$607$	−10.6302	−	3.45397i	−0.431467	−	0.140192i	0.0852283	−	0.996361i	$-0.472838\pi$
$607$	−10.6302	−	3.45397i	−0.431467	−	0.140192i	−0.516695	+	0.856169i	$0.672838\pi$
$608$	−4.27382	−	1.38865i	−0.173326	−	0.0563171i
$609$	−6.06627	+	18.6701i	−0.245818	+	0.756550i
$610$	30.7914	+	32.3004i	1.24671	+	1.30781i
$611$	−1.95859			−0.0792361
$612$	−0.0820186	−	0.0266495i	−0.00331540	−	0.00107724i
$613$	−28.6406	+	39.4203i	−1.15678	+	1.59217i	−0.434325	+	0.900756i	$0.643013\pi$
$613$	−28.6406	+	39.4203i	−1.15678	+	1.59217i	−0.722456	+	0.691416i	$0.756987\pi$
$614$	25.8165	+	18.7568i	1.04187	+	0.756963i
$615$	−15.6066	−	16.3714i	−0.629317	−	0.660160i
$616$	−25.9102	−	45.2733i	−1.04395	−	1.82411i
$617$	12.4209	+	17.0959i	0.500046	+	0.688254i	0.982201	−	0.187831i	$-0.0601459\pi$
$617$	12.4209	+	17.0959i	0.500046	+	0.688254i	−0.482155	+	0.876086i	$0.660146\pi$
$618$	4.72513	+	1.53529i	0.190073	+	0.0617584i
$619$	3.00246	−	9.24061i	0.120679	−	0.371411i	−0.872410	−	0.488774i	$-0.837444\pi$
$619$	3.00246	−	9.24061i	0.120679	−	0.371411i	0.993089	+	0.117363i	$0.0374441\pi$
$620$	40.1839	+	83.7584i	1.61383	+	3.36382i
$621$	−1.07029	+	3.29402i	−0.0429494	+	0.132185i
$622$	−54.7938	−	17.8036i	−2.19703	−	0.713858i
$623$	−20.5971	−	28.3495i	−0.825206	−	1.13580i
$624$	−3.87099	+	2.81244i	−0.154963	+	0.112588i
$625$	18.7295	+	16.5592i	0.749179	+	0.662368i
$626$	25.0854			1.00261
$627$	7.82215	−	17.3911i	0.312386	−	0.694533i
$628$	−19.2787	+	26.5349i	−0.769305	+	1.05886i
$629$	−0.0984171	+	0.0715042i	−0.00392415	+	0.00285106i
$630$	16.7764	−	2.24734i	0.668388	−	0.0895362i
$631$	−7.36134			−0.293050			−0.146525	−	0.989207i	$-0.546809\pi$
$631$	−7.36134			−0.293050			−0.146525	+	0.989207i	$0.546809\pi$
$632$	66.1205	−	21.4839i	2.63013	−	0.854582i
$633$	8.49171	−	11.6878i	0.337515	−	0.464550i
$634$	2.57382	−	7.92141i	0.102220	−	0.314599i
$635$	9.94259	+	1.81946i	0.394560	+	0.0722030i
$636$	−39.5666	−	28.7468i	−1.56892	−	1.13989i
$637$	2.47018	−	0.802611i	0.0978722	−	0.0318006i
$638$	21.4435	−	47.6755i	0.848955	−	1.88749i
$639$	−2.68645	+	8.26803i	−0.106274	+	0.327078i
$640$	−5.60086	−	41.8104i	−0.221393	−	1.65270i
$641$	35.0356	+	25.4549i	1.38382	+	1.00541i	0.996511	+	0.0834595i	$0.0265969\pi$
$641$	35.0356	+	25.4549i	1.38382	+	1.00541i	0.387314	+	0.921948i	$0.373403\pi$
$642$		−	21.5998i		−	0.852477i
$643$	−17.1583	+	5.57507i	−0.676658	+	0.219859i	−0.627132	−	0.778913i	$-0.715771\pi$
$643$	−17.1583	+	5.57507i	−0.676658	+	0.219859i	−0.0495262	+	0.998773i	$0.515771\pi$
$644$	35.0835	+	25.4897i	1.38248	+	1.00443i
$645$	1.56947	−	8.57649i	0.0617977	−	0.337699i
$646$	−0.299774			−0.0117944
$647$	−12.2624	−	16.8777i	−0.482083	−	0.663531i	0.496820	−	0.867853i	$-0.334501\pi$
$647$	−12.2624	−	16.8777i	−0.482083	−	0.663531i	−0.978904	+	0.204323i	$0.934501\pi$
$648$	4.87158	+	1.58287i	0.191374	+	0.0621811i
$649$	2.29214	+	1.03096i	0.0899742	+	0.0404686i
$650$	7.23231	+	11.0271i	0.283674	+	0.432517i
$651$	9.66703	−	29.7521i	0.378881	−	1.16608i
$652$	−32.2356	+	10.4740i	−1.26244	+	0.410192i
$653$	−31.5704	+	10.2578i	−1.23545	+	0.401421i	−0.852684	−	0.522427i	$-0.825027\pi$
$653$	−31.5704	+	10.2578i	−1.23545	+	0.401421i	−0.382761	+	0.923847i	$0.625027\pi$
$654$	0.861038	−	2.65000i	0.0336692	−	0.103623i
$655$	−14.4249	−	30.0670i	−0.563628	−	1.17481i
$656$	−45.2406			−1.76635
$657$	0.164500	+	0.226415i	0.00641776	+	0.00883329i
$658$	13.1800	−	4.28244i	0.513809	−	0.166947i
$659$	−11.9363	−	36.7362i	−0.464973	−	1.43104i	−0.859017	−	0.511947i	$-0.828924\pi$
$659$	−11.9363	−	36.7362i	−0.464973	−	1.43104i	0.394044	−	0.919091i	$-0.371076\pi$
$660$	−30.2322	+	0.745507i	−1.17679	+	0.0290188i
$661$	7.17238	−	22.0743i	0.278973	−	0.858592i	−0.709167	−	0.705040i	$-0.750929\pi$
$661$	7.17238	−	22.0743i	0.278973	−	0.858592i	0.988141	−	0.153551i	$-0.0490711\pi$
$662$		−	19.2868i		−	0.749604i
$663$	−0.0132989	+	0.0183044i	−0.000516486	+	0.000710882i
$664$	27.0973	−	19.6873i	1.05158	−	0.764016i
$665$	35.5913	−	17.0753i	1.38017	−	0.662152i
$666$	11.4725	−	8.33523i	0.444549	−	0.322983i
$667$			22.1440i			0.857417i
$668$	5.79894	+	7.98156i	0.224368	+	0.308816i
$669$	−1.02378	−	3.15088i	−0.0395817	−	0.121820i
$670$	−15.6599	+	85.5750i	−0.604995	+	3.30605i
$671$	−2.90766	+	26.6907i	−0.112249	+	1.03038i
$672$	1.41058	−	1.94149i	0.0544142	−	0.0748947i
$673$	−0.248314	+	0.341775i	−0.00957181	+	0.0131745i	−0.813776	−	0.581179i	$-0.802592\pi$
$673$	−0.248314	+	0.341775i	−0.00957181	+	0.0131745i	0.804204	+	0.594353i	$0.202592\pi$
$674$	−6.46781	+	4.69914i	−0.249131	+	0.181004i
$675$	1.77067	−	4.67597i	0.0681530	−	0.179978i
$676$	−14.9390	−	45.9775i	−0.574577	−	1.76837i
$677$			30.8174i			1.18441i	0.805788	+	0.592204i	$0.201742\pi$
$677$			30.8174i			1.18441i	−0.805788	+	0.592204i	$0.798258\pi$
$678$	25.1538	−	8.17296i	0.966026	−	0.313881i
$679$	7.91353			0.303693
$680$	0.104779	+	0.218400i	0.00401811	+	0.00837525i
$681$	15.6508	−	11.3710i	0.599740	−	0.435737i
$682$	−34.1717	+	75.9743i	−1.30850	+	2.90921i
$683$	−9.33946	−	12.8547i	−0.357364	−	0.491870i	0.592048	−	0.805903i	$-0.298320\pi$
$683$	−9.33946	−	12.8547i	−0.357364	−	0.491870i	−0.949412	+	0.314033i	$0.898320\pi$
$684$	23.4454			0.896456
$685$	38.1319	−	18.2941i	1.45694	−	0.698983i
$686$	28.0001	−	20.3433i	1.06905	−	0.776710i
$687$	−5.38767	−	7.41549i	−0.205552	−	0.282918i
$688$	−10.2506	−	14.1087i	−0.390800	−	0.537890i
$689$	−10.3805	+	7.54191i	−0.395467	+	0.287324i
$690$	17.2145	−	8.25882i	0.655345	−	0.314408i
$691$	−22.8656			−0.869850			−0.434925	−	0.900467i	$-0.643225\pi$
$691$	−22.8656			−0.869850			−0.434925	+	0.900467i	$0.643225\pi$
$692$	17.0081	+	23.4097i	0.646551	+	0.889901i
$693$	7.54200	+	6.84280i	0.286497	+	0.259937i
$694$	27.0346	−	19.6418i	1.02622	−	0.745592i
$695$	−4.01065	−	8.35971i	−0.152133	−	0.317102i
$696$	32.7490			1.24135
$697$	−0.203455	+	0.0661064i	−0.00770639	+	0.00250396i
$698$		−	13.1229i		−	0.496709i
$699$	5.93356	+	18.2616i	0.224428	+	0.690718i
$700$	−48.8297	−	39.1765i	−1.84559	−	1.48073i
$701$	−9.70511	+	7.05118i	−0.366557	+	0.266319i	−0.755782	−	0.654824i	$-0.772743\pi$
$701$	−9.70511	+	7.05118i	−0.366557	+	0.266319i	0.389225	+	0.921143i	$0.372743\pi$
$702$	1.55025	−	2.13373i	0.0585104	−	0.0805326i
$703$	19.4394	−	26.7560i	0.733171	−	1.00912i
$704$	15.6407	−	17.2388i	0.589480	−	0.649713i
$705$	0.736897	−	4.02684i	0.0277532	−	0.151660i
$706$	−3.63537	−	11.1885i	−0.136819	−	0.421085i
$707$	−18.9663	−	26.1048i	−0.713301	−	0.981774i
$708$			3.09009i			0.116133i
$709$	29.1523	−	21.1804i	1.09484	−	0.795445i	0.114627	−	0.993409i	$-0.463433\pi$
$709$	29.1523	−	21.1804i	1.09484	−	0.795445i	0.980209	+	0.197964i	$0.0634328\pi$
$710$	43.2085	−	20.7297i	1.62159	−	0.777972i
$711$	−10.9805	+	7.97783i	−0.411803	+	0.299192i
$712$	−34.3610	+	47.2938i	−1.28773	+	1.77241i
$713$		−	35.2879i		−	1.32154i
$714$	0.0494703	−	0.152254i	0.00185138	−	0.00569796i
$715$	−2.26498	+	7.60384i	−0.0847055	+	0.284367i
$716$	17.0906	+	52.5994i	0.638705	+	1.96573i
$717$	−9.92820	+	3.22587i	−0.370776	+	0.120472i
$718$	−36.1073	−	49.6974i	−1.34751	−	1.85469i
$719$	8.78890			0.327771			0.163885	−	0.986479i	$-0.447597\pi$
$719$	8.78890			0.327771			0.163885	+	0.986479i	$0.447597\pi$
$720$	−4.32593	−	9.01686i	−0.161218	−	0.336038i
$721$	−1.91216	+	5.88502i	−0.0712125	+	0.219169i
$722$	32.9605	−	10.7095i	1.22666	−	0.398567i
$723$	−1.18110	+	0.383762i	−0.0439255	+	0.0142723i
$724$	−7.53119	+	23.1786i	−0.279894	+	0.861426i
$725$	1.52835	−	31.9307i	0.0567616	−	1.18587i
$726$	−17.9924	−	20.2899i	−0.667761	−	0.753029i
$727$	50.4920	+	16.4058i	1.87264	+	0.608459i	0.990506	+	0.137468i	$0.0438963\pi$
$727$	50.4920	+	16.4058i	1.87264	+	0.608459i	0.882138	+	0.470991i	$0.156104\pi$
$728$	−9.89006	−	13.6125i	−0.366550	−	0.504513i
$729$	−1.00000			−0.0370370
$730$	0.277712	−	1.51758i	0.0102786	−	0.0561681i
$731$	−0.0667145	−	0.0484709i	−0.00246753	−	0.00179276i
$732$	−31.3944	+	10.2007i	−1.16037	+	0.377027i
$733$			4.02790i			0.148774i	0.997229	+	0.0743869i	$0.0237000\pi$
$733$			4.02790i			0.148774i	−0.997229	+	0.0743869i	$0.976300\pi$
$734$	8.00459	+	5.81567i	0.295455	+	0.214660i
$735$	0.720782	+	5.38065i	0.0265864	+	0.198468i
$736$	0.836519	−	2.57454i	0.0308345	−	0.0948989i
$737$	−45.4273	+	25.9983i	−1.67333	+	0.957660i
$738$	23.7166	−	7.70600i	0.873021	−	0.283662i
$739$	33.7391	+	24.5129i	1.24111	+	0.901721i	0.997672	−	0.0681950i	$-0.0217240\pi$
$739$	33.7391	+	24.5129i	1.24111	+	0.901721i	0.243440	+	0.969916i	$0.421724\pi$
$740$	−51.5917	−	9.44110i	−1.89655	−	0.347062i
$741$	1.90077	−	5.84998i	0.0698267	−	0.214904i
$742$	53.3637	−	73.4489i	1.95904	−	2.69639i
$743$	−11.2169	+	3.64458i	−0.411506	+	0.133707i	−0.507452	−	0.861680i	$-0.669413\pi$
$743$	−11.2169	+	3.64458i	−0.411506	+	0.133707i	0.0959456	+	0.995387i	$0.469413\pi$
$744$	−52.1879			−1.91330
$745$	8.81938	−	1.18143i	0.323117	−	0.0432842i
$746$	−12.6591	+	9.19739i	−0.463484	+	0.336741i
$747$	−3.84346	+	5.29008i	−0.140625	+	0.193554i
$748$	−0.117326	+	0.260853i	−0.00428987	+	0.00953772i
$749$	26.9020			0.982976
$750$	−25.3926	+	10.7208i	−0.927206	+	0.391466i
$751$	2.90685	−	2.11195i	0.106073	−	0.0770662i	−0.533485	−	0.845810i	$-0.679118\pi$
$751$	2.90685	−	2.11195i	0.106073	−	0.0770662i	0.639557	+	0.768744i	$0.279118\pi$
$752$	−4.81286	−	6.62434i	−0.175507	−	0.241565i
$753$	−21.5685	−	7.00805i	−0.786002	−	0.255387i
$754$	5.21074	−	16.0370i	0.189764	−	0.584034i
$755$	20.8357	+	43.4294i	0.758289	+	1.58056i
$756$	−3.86908	+	11.9078i	−0.140717	+	0.433083i
$757$	−33.0757	−	10.7470i	−1.20216	−	0.390605i	−0.361604	−	0.932332i	$-0.617771\pi$
$757$	−33.0757	−	10.7470i	−1.20216	−	0.390605i	−0.840554	+	0.541727i	$0.817771\pi$
$758$	−35.2147	−	48.4688i	−1.27905	−	1.76047i
$759$	10.4764	+	4.71205i	0.380267	+	0.171036i
$760$	−45.4394	−	47.6664i	−1.64826	−	1.72904i
$761$	−19.6457	−	14.2734i	−0.712155	−	0.517411i	0.171713	−	0.985147i	$-0.445070\pi$
$761$	−19.6457	−	14.2734i	−0.712155	−	0.517411i	−0.883868	+	0.467736i	$0.845070\pi$
$762$	−6.55024	+	9.01563i	−0.237290	+	0.326602i
$763$	3.30050	+	1.07240i	0.119486	+	0.0388234i
$764$	−19.0615			−0.689620
$765$	−0.0326300	−	0.0342292i	−0.00117974	−	0.00123756i
$766$	−10.5881	+	32.5867i	−0.382562	+	1.17740i
$767$	0.771025	+	0.250521i	0.0278401	+	0.00904580i
$768$	30.8829	+	10.0345i	1.11439	+	0.362087i
$769$	20.2027	−	14.6781i	0.728529	−	0.529307i	−0.160569	−	0.987025i	$-0.551333\pi$
$769$	20.2027	−	14.6781i	0.728529	−	0.529307i	0.889098	+	0.457717i	$0.151333\pi$
$770$	−1.38391	−	56.1210i	−0.0498726	−	2.02246i
$771$	−20.7922	−	15.1064i	−0.748813	−	0.544045i
$772$	31.7271	+	43.6686i	1.14188	+	1.57167i
$773$	−20.7611	+	6.74570i	−0.746726	+	0.242626i	−0.657572	−	0.753392i	$-0.728416\pi$
$773$	−20.7611	+	6.74570i	−0.746726	+	0.242626i	−0.0891544	+	0.996018i	$0.528416\pi$
$774$	7.77689	+	5.65024i	0.279535	+	0.203094i
$775$	−2.43554	+	50.8837i	−0.0874870	+	1.82780i
$776$	−4.07954	−	12.5555i	−0.146447	−	0.450718i
$777$	10.3813	+	14.2886i	0.372426	+	0.512601i
$778$		−	0.0839302i		−	0.00300904i
$779$	47.0511	−	34.1846i	1.68578	−	1.22479i
$780$	−9.66840	+	1.29516i	−0.346184	+	0.0463742i
$781$	26.2957	+	11.8273i	0.940935	+	0.423213i
$782$		−	0.180583i		−	0.00645764i
$783$	−6.08052	+	1.97568i	−0.217300	+	0.0706051i
$784$	8.78460	+	6.38238i	0.313736	+	0.227942i
$785$	−16.2159	+	7.77975i	−0.578771	+	0.277671i
$786$	36.7670			1.31144
$787$	19.9181	+	27.4149i	0.710003	+	0.977235i	0.999797	+	0.0201458i	$0.00641305\pi$
$787$	19.9181	+	27.4149i	0.710003	+	0.977235i	−0.289794	+	0.957089i	$0.593587\pi$
$788$	3.77501	+	1.22657i	0.134479	+	0.0436949i
$789$	7.18513	+	22.1136i	0.255797	+	0.787264i
$790$	73.5986	+	13.4683i	2.61852	+	0.479180i
$791$	10.1792	+	31.3283i	0.361930	+	1.11391i
$792$	6.96872	−	15.4936i	0.247623	−	0.550543i
$793$			8.66038i			0.307539i
$794$	24.6713	+	75.9303i	0.875550	+	2.69467i
$795$	−11.6005	−	24.1799i	−0.411428	−	0.857571i
$796$	12.0475	+	37.0783i	0.427011	+	1.31420i
$797$	−28.5541	−	9.27780i	−1.01144	−	0.328637i	−0.244012	−	0.969772i	$-0.578464\pi$
$797$	−28.5541	−	9.27780i	−1.01144	−	0.328637i	−0.767428	+	0.641136i	$0.778464\pi$
$798$			43.5224i			1.54068i
$799$	−0.0313239	−	0.0227581i	−0.00110816	−	0.000805125i
$800$	−1.38392	+	3.65465i	−0.0489289	+	0.129211i
$801$	3.52667	−	10.8540i	0.124609	−	0.383507i
$802$	−46.5316	−	15.1190i	−1.64309	−	0.533872i
$803$	0.805603	−	0.461052i	0.0284291	−	0.0162702i
$804$	−52.0620	−	37.8253i	−1.83609	−	1.33399i
$805$	10.2861	+	21.4402i	0.362538	+	0.755666i
$806$	−8.30368	+	25.5561i	−0.292485	+	0.900175i
$807$	−14.6006	+	20.0960i	−0.513965	+	0.707412i
$808$	−31.6403	+	43.5492i	−1.11310	+	1.53206i
$809$	−23.1188	+	16.7968i	−0.812813	+	0.590543i	−0.914645	−	0.404259i	$-0.867530\pi$
$809$	−23.1188	+	16.7968i	−0.812813	+	0.590543i	0.101832	+	0.994802i	$0.467530\pi$
$810$	3.80367	+	3.99009i	0.133647	+	0.140197i
$811$	3.79670	+	11.6850i	0.133320	+	0.410317i	0.995325	−	0.0965828i	$-0.0307913\pi$
$811$	3.79670	+	11.6850i	0.133320	+	0.410317i	−0.862005	+	0.506900i	$0.830791\pi$
$812$			80.0497i			2.80920i
$813$	14.9642	−	4.86217i	0.524818	−	0.170524i
$814$	−23.3615	−	40.8199i	−0.818820	−	1.43074i
$815$	−18.2827	−	3.34567i	−0.640416	−	0.117194i
$816$	−0.0945885			−0.00331126
$817$	21.3216	+	6.92782i	0.745949	+	0.242374i
$818$	−41.8417	+	57.5902i	−1.46296	+	2.01359i
$819$	2.65750	+	1.93079i	0.0928607	+	0.0674673i
$820$	−81.1544	−	43.8254i	−2.83403	−	1.53045i
$821$	−1.17751	−	3.62401i	−0.0410955	−	0.126479i	0.928404	−	0.371573i	$-0.121181\pi$
$821$	−1.17751	−	3.62401i	−0.0410955	−	0.126479i	−0.969499	+	0.245094i	$0.921181\pi$
$822$			46.6291i			1.62638i
$823$	18.8881	−	25.9972i	0.658398	−	0.906207i	−0.341029	−	0.940053i	$-0.610776\pi$
$823$	18.8881	−	25.9972i	0.658398	−	0.906207i	0.999427	+	0.0338459i	$0.0107755\pi$
$824$	10.3229			0.359614
$825$	−14.7812	−	7.51764i	−0.514617	−	0.261731i
$826$	−5.73624			−0.199589
$827$	11.0104	−	15.1546i	0.382871	−	0.526976i	−0.573471	−	0.819226i	$-0.694404\pi$
$827$	11.0104	−	15.1546i	0.382871	−	0.526976i	0.956342	+	0.292249i	$0.0944036\pi$
$828$			14.1234i			0.490824i
$829$	−5.59514	−	17.2201i	−0.194327	−	0.598078i	−0.999984	−	0.00569507i	$-0.998187\pi$
$829$	−5.59514	−	17.2201i	−0.194327	−	0.598078i	0.805656	−	0.592383i	$-0.201813\pi$
$830$	35.7272	−	4.78595i	1.24011	−	0.166123i
$831$	15.4222	+	11.2049i	0.534991	+	0.388694i
$832$	4.41323	−	6.07429i	0.153001	−	0.210588i
$833$	0.0488319	+	0.0158664i	0.00169192	+	0.000549740i
$834$	10.2226			0.353979
$835$	0.718294	+	5.36207i	0.0248576	+	0.185562i
$836$	8.42122	−	77.3021i	0.291254	−	2.67355i
$837$	9.68974	−	3.14839i	0.334926	−	0.108824i
$838$			60.8745i			2.10288i
$839$	3.33193	+	10.2546i	0.115031	+	0.354029i	0.991954	−	0.126603i	$-0.0404073\pi$
$839$	3.33193	+	10.2546i	0.115031	+	0.354029i	−0.876922	+	0.480632i	$0.840407\pi$
$840$	31.7082	−	15.2123i	1.09404	−	0.524875i
$841$	−9.60797	+	6.98060i	−0.331309	+	0.240710i
$842$	−40.8408	+	56.2126i	−1.40747	+	1.93721i
$843$	2.86131	−	3.93826i	0.0985489	−	0.135641i
$844$	18.2045	−	56.0277i	0.626625	−	1.92855i
$845$	4.77193	−	26.0766i	0.164159	−	0.897064i
$846$	3.65141	+	2.65291i	0.125538	+	0.0912089i
$847$	25.2705	−	22.4090i	0.868305	−	0.769984i
$848$	−51.0164	−	16.5762i	−1.75191	−	0.569231i
$849$	−7.69757	+	23.6907i	−0.264180	+	0.813063i
$850$	−0.0124637	+	0.260393i	−0.000427500	+	0.00893142i
$851$	16.1178	+	11.7103i	0.552511	+	0.401422i
$852$			35.4500i			1.21450i
$853$	10.7480	+	3.49222i	0.368003	+	0.119571i	0.487180	−	0.873302i	$-0.338026\pi$
$853$	10.7480	+	3.49222i	0.368003	+	0.119571i	−0.119177	+	0.992873i	$0.538026\pi$
$854$	−18.9358	−	58.2785i	−0.647971	−	1.99425i
$855$	11.3124	+	6.10896i	0.386875	+	0.208922i
$856$	−13.8684	−	42.6824i	−0.474011	−	1.45886i
$857$			11.9975i			0.409828i	0.978780	+	0.204914i	$0.0656914\pi$
$857$			11.9975i			0.409828i	−0.978780	+	0.204914i	$0.934309\pi$
$858$	−6.47835	−	5.87776i	−0.221167	−	0.200663i
$859$	−14.5510	−	44.7832i	−0.496472	−	1.52798i	−0.814650	−	0.579953i	$-0.803071\pi$
$859$	−14.5510	−	44.7832i	−0.496472	−	1.52798i	0.318178	−	0.948031i	$-0.396929\pi$
$860$	−4.72052	−	35.2387i	−0.160968	−	1.20163i
$861$	9.59760	+	29.5384i	0.327085	+	1.00667i
$862$	−78.9766	−	25.6611i	−2.68995	−	0.874019i
$863$	7.42339	+	10.2174i	0.252695	+	0.347805i	0.916453	−	0.400143i	$-0.131039\pi$
$863$	7.42339	+	10.2174i	0.252695	+	0.347805i	−0.663758	+	0.747948i	$0.731039\pi$
$864$	0.781580			0.0265899
$865$	2.10673	+	15.7268i	0.0716311	+	0.534727i
$866$	−28.2063	−	20.4931i	−0.958490	−	0.696384i
$867$	16.1675	−	5.25315i	0.549078	−	0.178406i
$868$		−	127.565i		−	4.32983i
$869$	22.3598	+	39.0697i	0.758504	+	1.32535i
$870$	31.0115	+	16.7470i	1.05139	+	0.567776i
$871$	−13.6588	+	9.92369i	−0.462810	+	0.336251i
$872$		−	5.78939i		−	0.196053i
$873$	1.51490	+	2.08508i	0.0512716	+	0.0705693i
$874$	15.1709	+	46.6912i	0.513163	+	1.57935i
$875$	−13.3524	−	31.6257i	−0.451393	−	1.06915i
$876$	0.923263	+	0.670790i	0.0311942	+	0.0226639i
$877$	−32.1859	+	10.4578i	−1.08684	+	0.353136i	−0.797025	−	0.603946i	$-0.793594\pi$
$877$	−32.1859	+	10.4578i	−1.08684	+	0.353136i	−0.289816	+	0.957082i	$0.593594\pi$
$878$	32.3787	+	44.5655i	1.09273	+	1.50401i
$879$	4.25856	+	3.09402i	0.143638	+	0.104359i
$880$	−31.2835	+	11.0244i	−1.05456	+	0.371631i
$881$	−27.5081	+	19.9858i	−0.926771	+	0.673339i	−0.945200	−	0.326492i	$-0.894134\pi$
$881$	−27.5081	+	19.9858i	−0.926771	+	0.673339i	0.0184291	+	0.999830i	$0.494134\pi$
$882$	−5.69232	−	1.84955i	−0.191670	−	0.0622775i
$883$	−53.1540	−	17.2708i	−1.78878	−	0.581208i	−0.789313	−	0.613992i	$-0.789563\pi$
$883$	−53.1540	−	17.2708i	−1.78878	−	0.581208i	−0.999462	+	0.0327833i	$0.989563\pi$
$884$	−0.0285102	+	0.0877452i	−0.000958900	+	0.00295119i
$885$	−0.805159	+	1.49096i	−0.0270651	+	0.0501182i
$886$	61.1911			2.05575
$887$	−0.351460	−	0.114196i	−0.0118009	−	0.00383434i	0.303111	−	0.952955i	$-0.401975\pi$
$887$	−0.351460	−	0.114196i	−0.0118009	−	0.00383434i	−0.314911	+	0.949121i	$0.601975\pi$
$888$	17.3185	−	23.8369i	0.581170	−	0.799912i
$889$	−11.2287	−	8.15813i	−0.376599	−	0.273615i
$890$	−56.7226	+	27.2132i	−1.90135	+	0.912190i
$891$	−0.359185	+	3.29712i	−0.0120331	+	0.110458i
$892$	−7.94080	−	10.9296i	−0.265878	−	0.365949i
$893$	10.0110	+	3.25276i	0.335004	+	0.108849i
$894$	−3.03158	+	9.33024i	−0.101391	+	0.312050i
$895$	−5.45920	+	29.8323i	−0.182481	+	0.997183i
$896$	−17.8998	+	55.0901i	−0.597992	+	1.84043i
$897$	3.52402	+	1.14502i	0.117664	+	0.0382312i
$898$	12.5724	+	17.3044i	0.419546	+	0.577456i
$899$	52.6985	−	38.2877i	1.75759	−	1.27697i
$900$	0.974785	−	20.3654i	0.0324928	−	0.678847i
$901$	−0.253651			−0.00845034
$902$	−16.8889	−	80.9644i	−0.562340	−	2.69582i
$903$	−7.03721	+	9.68590i	−0.234184	+	0.322326i
$904$	44.4577	−	32.3004i	1.47864	−	1.07430i
$905$	−9.67324	+	9.22131i	−0.321549	+	0.306527i
$906$	−53.1071			−1.76437
$907$	43.6761	−	14.1912i	1.45024	−	0.471212i	0.525167	−	0.850999i	$-0.324003\pi$
$907$	43.6761	−	14.1912i	1.45024	−	0.471212i	0.925074	+	0.379787i	$0.124003\pi$
$908$	46.3680	−	63.8200i	1.53878	−	2.11794i
$909$	3.24744	−	9.99459i	0.107711	−	0.331500i
$910$	−2.40425	−	17.9478i	−0.0797002	−	0.594963i
$911$	−38.5982	−	28.0432i	−1.27882	−	0.929114i	−0.279300	−	0.960204i	$-0.590102\pi$
$911$	−38.5982	−	28.0432i	−1.27882	−	0.929114i	−0.999517	+	0.0310897i	$0.990102\pi$
$912$	24.4566	−	7.94643i	0.809839	−	0.263133i
$913$	16.0615	+	14.5725i	0.531558	+	0.482278i
$914$	−26.5575	+	81.7356i	−0.878444	+	2.70357i
$915$	−17.8057	−	3.25837i	−0.588637	−	0.107718i
$916$	−30.2385	−	21.9695i	−0.999107	−	0.725894i
$917$			45.7922i			1.51219i
$918$	0.0495865	−	0.0161116i	0.00163660	−	0.000531763i
$919$	9.68791	+	7.03868i	0.319575	+	0.232185i	0.735994	−	0.676988i	$-0.236715\pi$
$919$	9.68791	+	7.03868i	0.319575	+	0.232185i	−0.416419	+	0.909173i	$0.636715\pi$
$920$	28.7141	−	27.3726i	0.946677	−	0.902448i
$921$	−12.9440			−0.426520
$922$	8.02323	+	11.0430i	0.264231	+	0.363683i
$923$	8.84531	+	2.87402i	0.291147	+	0.0945994i
$924$	37.8717	+	17.0339i	1.24589	+	0.560375i
$925$	−22.4329	−	17.9981i	−0.737591	−	0.591775i
$926$	14.4743	−	44.5473i	0.475655	−	1.46391i
$927$	−1.91665	+	0.622757i	−0.0629510	+	0.0204540i
$928$	4.75241	−	1.54415i	0.156006	−	0.0506893i
$929$	−8.49898	+	26.1572i	−0.278843	+	0.858189i	0.709334	+	0.704872i	$0.248996\pi$
$929$	−8.49898	+	26.1572i	−0.278843	+	0.858189i	−0.988177	+	0.153317i	$0.951004\pi$
$930$	−49.4189	−	26.6875i	−1.62051	−	0.875117i
$931$	−13.9588			−0.457482
$932$	46.0227	+	63.3448i	1.50752	+	2.07493i
$933$	22.2259	−	7.22164i	0.727644	−	0.236426i
$934$	−30.2411	−	93.0726i	−0.989519	−	3.04543i
$935$	−0.124578	+	0.0952904i	−0.00407414	+	0.00311633i
$936$	1.69339	−	5.21172i	0.0553503	−	0.170351i
$937$			37.0975i			1.21192i	0.795494	+	0.605962i	$0.207212\pi$
$937$			37.0975i			1.21192i	−0.795494	+	0.605962i	$0.792788\pi$
$938$	70.2163	−	96.6445i	2.29264	−	3.15555i
$939$	−8.23203	+	5.98092i	−0.268642	+	0.195180i
$940$	−2.21638	−	16.5453i	−0.0722905	−	0.539649i
$941$	−49.3267	+	35.8380i	−1.60801	+	1.16828i	−0.738662	+	0.674076i	$0.764542\pi$
$941$	−49.3267	+	35.8380i	−1.60801	+	1.16828i	−0.869343	+	0.494209i	$0.835458\pi$
$942$		−	19.8295i		−	0.646078i
$943$	20.5928	+	28.3435i	0.670593	+	0.922991i
$944$	1.04734	+	3.22337i	0.0340879	+	0.104912i
$945$	−4.96954	+	4.73736i	−0.161659	+	0.154106i
$946$	21.4229	−	23.6118i	0.696517	−	0.767687i
$947$	−11.1964	+	15.4105i	−0.363833	+	0.500773i	−0.951212	−	0.308539i	$-0.900160\pi$
$947$	−11.1964	+	15.4105i	−0.363833	+	0.500773i	0.587379	+	0.809312i	$0.300160\pi$
$948$	−32.5316	+	44.7759i	−1.05658	+	1.45425i
$949$	0.242224	−	0.175986i	0.00786292	−	0.00571274i
$950$	−18.6532	−	68.3738i	−0.605190	−	2.21834i
$951$	1.04402	+	3.21315i	0.0338545	+	0.104194i
$952$		−	0.332625i		−	0.0107804i
$953$	41.1892	−	13.3832i	1.33425	−	0.433523i	0.446884	−	0.894592i	$-0.352534\pi$
$953$	41.1892	−	13.3832i	1.33425	−	0.433523i	0.887364	+	0.461069i	$0.152534\pi$
$954$	29.5680			0.957300
$955$	−9.19713	−	4.96669i	−0.297612	−	0.160718i
$956$	−34.4383	+	25.0209i	−1.11382	+	0.809234i
$957$	4.33002	+	20.7578i	0.139970	+	0.671006i
$958$	45.7579	+	62.9803i	1.47837	+	2.03480i
$959$	−58.0752			−1.87535
$960$	10.8283	+	11.3589i	0.349480	+	0.366608i
$961$	−58.8992	+	42.7927i	−1.89997	+	1.38041i
$962$	−8.91720	−	12.2735i	−0.287502	−	0.395713i
$963$	5.14989	+	7.08821i	0.165953	+	0.228414i
$964$	−4.09692	+	2.97659i	−0.131953	+	0.0958694i
$965$	3.92992	+	29.3369i	0.126509	+	0.944387i
$966$	−26.2178			−0.843545
$967$	−5.21712	−	7.18075i	−0.167771	−	0.230917i	0.716850	−	0.697227i	$-0.245583\pi$
$967$	−5.21712	−	7.18075i	−0.167771	−	0.230917i	−0.884621	+	0.466310i	$0.845583\pi$
$968$	−48.5813	−	28.5418i	−1.56146	−	0.917367i
$969$	0.0983740	−	0.0714729i	0.00316023	−	0.00229604i
$970$	2.55747	−	13.9755i	0.0821156	−	0.448728i
$971$	53.4061			1.71388			0.856942	−	0.515413i	$-0.172361\pi$
$971$	53.4061			1.71388			0.856942	+	0.515413i	$0.172361\pi$
$972$	−3.87817	+	1.26009i	−0.124392	+	0.0404175i
$973$			12.7319i			0.408166i
$974$	8.84911	+	27.2348i	0.283544	+	0.872658i
$975$	−5.00246	−	1.89430i	−0.160207	−	0.0606661i
$976$	−29.2911	+	21.2813i	−0.937586	+	0.681196i
$977$	29.0805	−	40.0258i	0.930367	−	1.28054i	−0.0293497	−	0.999569i	$-0.509344\pi$
$977$	29.0805	−	40.0258i	0.930367	−	1.28054i	0.959716	−	0.280971i	$-0.0906564\pi$
$978$	12.0448	−	16.5782i	0.385149	−	0.530113i
$979$	−34.5201	−	15.5264i	−1.10327	−	0.496227i
$980$	9.57543	+	19.9588i	0.305876	+	0.637560i
$981$	0.349262	+	1.07492i	0.0111511	+	0.0343195i
$982$	40.2363	+	55.3805i	1.28399	+	1.76726i
$983$			22.7406i			0.725313i	0.931923	+	0.362656i	$0.118130\pi$
$983$			22.7406i			0.725313i	−0.931923	+	0.362656i	$0.881870\pi$
$984$	41.9177	−	30.4550i	1.33629	−	0.970869i
$985$	1.50184	+	1.57544i	0.0478526	+	0.0501978i
$986$	0.269680	−	0.195934i	0.00858837	−	0.00623982i
$987$	−3.30412	+	4.54773i	−0.105171	+	0.144756i
$988$		−	25.0824i		−	0.797976i
$989$	−4.17330	+	12.8441i	−0.132703	+	0.408419i
$990$	14.5220	−	11.1080i	0.461540	−	0.353035i
$991$	−14.0020	−	43.0936i	−0.444787	−	1.36891i	−0.882718	−	0.469904i	$-0.844289\pi$
$991$	−14.0020	−	43.0936i	−0.444787	−	1.36891i	0.437931	−	0.899009i	$-0.355711\pi$
$992$	−7.57330	+	2.46071i	−0.240453	+	0.0781278i
$993$	4.59842	+	6.32918i	0.145926	+	0.200850i
$994$	−65.8070			−2.08727
$995$	−3.84829	+	21.0293i	−0.121999	+	0.666674i
$996$	−8.23961	+	25.3589i	−0.261082	+	0.803528i
$997$	17.1326	−	5.56672i	0.542595	−	0.176300i	−0.0248799	−	0.999690i	$-0.507920\pi$
$997$	17.1326	−	5.56672i	0.542595	−	0.176300i	0.567475	+	0.823391i	$0.307920\pi$
$998$	−22.1514	+	7.19743i	−0.701191	+	0.227831i
$999$	−1.77750	+	5.47058i	−0.0562376	+	0.173082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bv.a.229.6	yes	240
11.5	even	5		825.2.v.a.379.6	✓	240
25.19	even	10		825.2.v.a.394.55	yes	240
275.269	even	10	inner	825.2.bv.a.544.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.v.a.379.6	✓	240	11.5	even	5
825.2.v.a.394.55	yes	240	25.19	even	10
825.2.bv.a.229.6	yes	240	1.1	even	1	trivial
825.2.bv.a.544.6	yes	240	275.269	even	10	inner

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bv (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44907 + 1.99448i) q^{2} -1.00000i q^{3} +(-1.26009 - 3.87817i) q^{4} +(0.402508 - 2.19954i) q^{5} +(1.99448 + 1.44907i) q^{6} +(-1.80478 + 2.48406i) q^{7} +(4.87158 + 1.58287i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.44907 + 1.99448i) q^{2} -1.00000i q^{3} +(-1.26009 - 3.87817i) q^{4} +(0.402508 - 2.19954i) q^{5} +(1.99448 + 1.44907i) q^{6} +(-1.80478 + 2.48406i) q^{7} +(4.87158 + 1.58287i) q^{8} -1.00000 q^{9} +(3.80367 + 3.99009i) q^{10} +(-0.359185 + 3.29712i) q^{11} +(-3.87817 + 1.26009i) q^{12} +1.06982i q^{13} +(-2.33915 - 7.19917i) q^{14} +(-2.19954 - 0.402508i) q^{15} +(-3.61835 + 2.62888i) q^{16} +(-0.0124310 + 0.0171097i) q^{17} +(1.44907 - 1.99448i) q^{18} +(1.77672 - 5.46818i) q^{19} +(-9.03739 + 1.21063i) q^{20} +(2.48406 + 1.80478i) q^{21} +(-6.05554 - 5.49415i) q^{22} +(3.29402 + 1.07029i) q^{23} +(1.58287 - 4.87158i) q^{24} +(-4.67597 - 1.77067i) q^{25} +(-2.13373 - 1.55025i) q^{26} +1.00000i q^{27} +(11.9078 + 3.86908i) q^{28} +(1.97568 + 6.08052i) q^{29} +(3.99009 - 3.80367i) q^{30} +(-3.14839 - 9.68974i) q^{31} -0.781580i q^{32} +(3.29712 + 0.359185i) q^{33} +(-0.0161116 - 0.0495865i) q^{34} +(4.73736 + 4.96954i) q^{35} +(1.26009 + 3.87817i) q^{36} +(5.47058 + 1.77750i) q^{37} +(8.33157 + 11.4674i) q^{38} +1.06982 q^{39} +(5.44245 - 10.0781i) q^{40} +(8.18339 + 5.94558i) q^{41} +(-7.19917 + 2.33915i) q^{42} +3.89921i q^{43} +(13.2394 - 2.76170i) q^{44} +(-0.402508 + 2.19954i) q^{45} +(-6.90795 + 5.01892i) q^{46} +1.83076i q^{47} +(2.62888 + 3.61835i) q^{48} +(-0.750229 - 2.30897i) q^{49} +(10.3074 - 6.76030i) q^{50} +(0.0171097 + 0.0124310i) q^{51} +(4.14895 - 1.34807i) q^{52} +(7.04969 + 9.70306i) q^{53} +(-1.99448 - 1.44907i) q^{54} +(7.10758 + 2.11716i) q^{55} +(-12.7241 + 9.24459i) q^{56} +(-5.46818 - 1.77672i) q^{57} +(-14.9904 - 4.87067i) q^{58} +(0.234171 - 0.720705i) q^{59} +(1.21063 + 9.03739i) q^{60} +8.09517 q^{61} +(23.8882 + 7.76175i) q^{62} +(1.80478 - 2.48406i) q^{63} +(-5.67785 - 4.12520i) q^{64} +(2.35312 + 0.430612i) q^{65} +(-5.49415 + 6.05554i) q^{66} +(9.27602 + 12.7674i) q^{67} +(0.0820186 + 0.0266495i) q^{68} +(1.07029 - 3.29402i) q^{69} +(-16.7764 + 2.24734i) q^{70} +(2.68645 - 8.26803i) q^{71} +(-4.87158 - 1.58287i) q^{72} +(-0.164500 - 0.226415i) q^{73} +(-11.4725 + 8.33523i) q^{74} +(-1.77067 + 4.67597i) q^{75} -23.4454 q^{76} +(-7.54200 - 6.84280i) q^{77} +(-1.55025 + 2.13373i) q^{78} +(10.9805 - 7.97783i) q^{79} +(4.32593 + 9.01686i) q^{80} +1.00000 q^{81} +(-23.7166 + 7.70600i) q^{82} +(3.84346 - 5.29008i) q^{83} +(3.86908 - 11.9078i) q^{84} +(0.0326300 + 0.0342292i) q^{85} +(-7.77689 - 5.65024i) q^{86} +(6.08052 - 1.97568i) q^{87} +(-6.96872 + 15.4936i) q^{88} +(-3.52667 + 10.8540i) q^{89} +(-3.80367 - 3.99009i) q^{90} +(-2.65750 - 1.93079i) q^{91} -14.1234i q^{92} +(-9.68974 + 3.14839i) q^{93} +(-3.65141 - 2.65291i) q^{94} +(-11.3124 - 6.10896i) q^{95} -0.781580 q^{96} +(-1.51490 - 2.08508i) q^{97} +(5.69232 + 1.84955i) q^{98} +(0.359185 - 3.29712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 60 q^{4} + 6 q^{5} + 4 q^{6} + 20 q^{7} - 240 q^{9}+O(q^{10}) \) 240 * q + 60 * q^4 + 6 * q^5 + 4 * q^6 + 20 * q^7 - 240 * q^9	\( 240 q + 60 q^{4} + 6 q^{5} + 4 q^{6} + 20 q^{7} - 240 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{12} - 10 q^{15} - 64 q^{16} + 10 q^{17} - 14 q^{19} - 44 q^{20} + 8 q^{21} + 70 q^{22} - 12 q^{24} + 24 q^{25} - 10 q^{26} - 10 q^{28} - 16 q^{30} - 2 q^{31} - 30 q^{33} - 40 q^{35} - 60 q^{36} + 10 q^{37} + 64 q^{39} + 28 q^{40} - 6 q^{41} - 10 q^{42} - 44 q^{44} - 6 q^{45} + 32 q^{46} + 68 q^{49} - 78 q^{50} + 16 q^{51} - 20 q^{52} + 30 q^{53} - 4 q^{54} - 20 q^{55} - 20 q^{57} - 70 q^{58} + 6 q^{59} - 52 q^{60} - 72 q^{61} + 40 q^{62} - 20 q^{63} + 104 q^{64} - 70 q^{65} - 12 q^{66} + 20 q^{67} + 150 q^{68} + 2 q^{69} + 16 q^{70} + 24 q^{71} + 30 q^{73} + 22 q^{74} - 40 q^{75} - 188 q^{76} + 90 q^{77} - 38 q^{79} - 48 q^{80} + 240 q^{81} + 140 q^{82} - 24 q^{84} - 100 q^{85} + 28 q^{86} + 270 q^{88} + 2 q^{90} - 34 q^{94} - 2 q^{95} - 112 q^{96} + 80 q^{98} + 6 q^{99}+O(q^{100}) \) 240 * q + 60 * q^4 + 6 * q^5 + 4 * q^6 + 20 * q^7 - 240 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^12 - 10 * q^15 - 64 * q^16 + 10 * q^17 - 14 * q^19 - 44 * q^20 + 8 * q^21 + 70 * q^22 - 12 * q^24 + 24 * q^25 - 10 * q^26 - 10 * q^28 - 16 * q^30 - 2 * q^31 - 30 * q^33 - 40 * q^35 - 60 * q^36 + 10 * q^37 + 64 * q^39 + 28 * q^40 - 6 * q^41 - 10 * q^42 - 44 * q^44 - 6 * q^45 + 32 * q^46 + 68 * q^49 - 78 * q^50 + 16 * q^51 - 20 * q^52 + 30 * q^53 - 4 * q^54 - 20 * q^55 - 20 * q^57 - 70 * q^58 + 6 * q^59 - 52 * q^60 - 72 * q^61 + 40 * q^62 - 20 * q^63 + 104 * q^64 - 70 * q^65 - 12 * q^66 + 20 * q^67 + 150 * q^68 + 2 * q^69 + 16 * q^70 + 24 * q^71 + 30 * q^73 + 22 * q^74 - 40 * q^75 - 188 * q^76 + 90 * q^77 - 38 * q^79 - 48 * q^80 + 240 * q^81 + 140 * q^82 - 24 * q^84 - 100 * q^85 + 28 * q^86 + 270 * q^88 + 2 * q^90 - 34 * q^94 - 2 * q^95 - 112 * q^96 + 80 * q^98 + 6 * q^99

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