LMFDB - Embedded newform 240.2.bk.b.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.371549 + 1.36453i) q^{2} +(-1.65322 - 0.516584i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.31915 - 2.06394i) q^{6} -1.29120 q^{7} +(2.02413 - 1.97558i) q^{8} +(2.46628 + 1.70806i) q^{9} +O(q^{10})$	\(q+(-0.371549 + 1.36453i) q^{2} +(-1.65322 - 0.516584i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.31915 - 2.06394i) q^{6} -1.29120 q^{7} +(2.02413 - 1.97558i) q^{8} +(2.46628 + 1.70806i) q^{9} +(0.702146 + 1.22760i) q^{10} +(4.09936 + 4.09936i) q^{11} +(2.32619 + 2.56688i) q^{12} +(4.40407 - 4.40407i) q^{13} +(0.479744 - 1.76189i) q^{14} +(-1.53428 + 0.803724i) q^{15} +(1.94368 + 3.49601i) q^{16} -2.75677i q^{17} +(-3.24704 + 2.73070i) q^{18} +(1.31048 + 1.31048i) q^{19} +(-1.93598 + 0.501989i) q^{20} +(2.13464 + 0.667013i) q^{21} +(-7.11683 + 4.07060i) q^{22} +2.76043i q^{23} +(-4.36688 + 2.22044i) q^{24} -1.00000i q^{25} +(4.37317 + 7.64582i) q^{26} +(-3.19496 - 4.09784i) q^{27} +(2.22590 + 1.30925i) q^{28} +(4.08036 + 4.08036i) q^{29} +(-0.526646 - 2.39220i) q^{30} -10.0767i q^{31} +(-5.49260 + 1.35327i) q^{32} +(-4.65948 - 8.89481i) q^{33} +(3.76170 + 1.02428i) q^{34} +(-0.913016 + 0.913016i) q^{35} +(-2.51969 - 5.44529i) q^{36} +(3.31466 + 3.31466i) q^{37} +(-2.27511 + 1.30129i) q^{38} +(-9.55596 + 5.00582i) q^{39} +(0.0343297 - 2.82822i) q^{40} +0.387829 q^{41} +(-1.70329 + 2.66496i) q^{42} +(3.66350 - 3.66350i) q^{43} +(-2.91022 - 11.2236i) q^{44} +(2.95170 - 0.536147i) q^{45} +(-3.76670 - 1.02564i) q^{46} +0.00218401 q^{47} +(-1.40735 - 6.78376i) q^{48} -5.33280 q^{49} +(1.36453 + 0.371549i) q^{50} +(-1.42410 + 4.55755i) q^{51} +(-12.0578 + 3.12653i) q^{52} +(-1.76845 + 1.76845i) q^{53} +(6.77872 - 2.83708i) q^{54} +5.79737 q^{55} +(-2.61355 + 2.55087i) q^{56} +(-1.48954 - 2.84349i) q^{57} +(-7.08384 + 4.05173i) q^{58} +(0.279145 + 0.279145i) q^{59} +(3.45992 + 0.170196i) q^{60} +(5.12461 - 5.12461i) q^{61} +(13.7500 + 3.74399i) q^{62} +(-3.18446 - 2.20544i) q^{63} +(0.194184 - 7.99764i) q^{64} -6.22829i q^{65} +(13.8685 - 3.05316i) q^{66} +(0.763263 + 0.763263i) q^{67} +(-2.79532 + 4.75240i) q^{68} +(1.42600 - 4.56361i) q^{69} +(-0.906611 - 1.58507i) q^{70} -9.45616i q^{71} +(8.36647 - 1.41501i) q^{72} +14.2158i q^{73} +(-5.75453 + 3.29141i) q^{74} +(-0.516584 + 1.65322i) q^{75} +(-0.930338 - 3.58795i) q^{76} +(-5.29309 - 5.29309i) q^{77} +(-3.28010 - 14.8993i) q^{78} +8.54188i q^{79} +(3.84644 + 1.09767i) q^{80} +(3.16509 + 8.42509i) q^{81} +(-0.144098 + 0.529206i) q^{82} +(-8.60385 + 8.60385i) q^{83} +(-3.00357 - 3.31435i) q^{84} +(-1.94933 - 1.94933i) q^{85} +(3.63780 + 6.36015i) q^{86} +(-4.63789 - 8.85358i) q^{87} +(16.3962 + 0.199022i) q^{88} -4.67026 q^{89} +(-0.365112 + 4.22690i) q^{90} +(-5.68653 + 5.68653i) q^{91} +(2.79903 - 4.75872i) q^{92} +(-5.20547 + 16.6590i) q^{93} +(-0.000811466 + 0.00298015i) q^{94} +1.85330 q^{95} +(9.77956 + 0.600128i) q^{96} -6.69158 q^{97} +(1.98140 - 7.27679i) q^{98} +(3.10824 + 17.1121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.371549	+	1.36453i	−0.262725	+	0.964871i
$2$	−0.371549	+	1.36453i	−0.262725	+	0.964871i
$3$	−1.65322	−	0.516584i	−0.954488	−	0.298250i
$3$	−1.65322	−	0.516584i	−0.954488	−	0.298250i
$4$	−1.72390	−	1.01398i	−0.861951	−	0.506991i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	1.31915	−	2.06394i	0.538540	−	0.842600i
$7$	−1.29120			−0.488028			−0.244014	−	0.969772i	$-0.578464\pi$
$7$	−1.29120			−0.488028			−0.244014	+	0.969772i	$0.578464\pi$
$8$	2.02413	−	1.97558i	0.715637	−	0.698472i
$9$	2.46628	+	1.70806i	0.822094	+	0.569352i
$10$	0.702146	+	1.22760i	0.222038	+	0.388200i
$11$	4.09936	+	4.09936i	1.23600	+	1.23600i	0.961621	+	0.274383i	$0.0884735\pi$
$11$	4.09936	+	4.09936i	1.23600	+	1.23600i	0.274383	+	0.961621i	$0.411526\pi$
$12$	2.32619	+	2.56688i	0.671512	+	0.740994i
$13$	4.40407	−	4.40407i	1.22147	−	1.22147i	0.254358	−	0.967110i	$-0.418136\pi$
$13$	4.40407	−	4.40407i	1.22147	−	1.22147i	0.967110	−	0.254358i	$-0.0818641\pi$
$14$	0.479744	−	1.76189i	0.128217	−	0.470884i
$15$	−1.53428	+	0.803724i	−0.396150	+	0.207521i
$16$	1.94368	+	3.49601i	0.485920	+	0.874003i
$17$		−	2.75677i		−	0.668615i	−0.942464	−	0.334307i	$-0.891498\pi$
$17$		−	2.75677i		−	0.668615i	0.942464	−	0.334307i	$-0.108502\pi$
$18$	−3.24704	+	2.73070i	−0.765336	+	0.643631i
$19$	1.31048	+	1.31048i	0.300646	+	0.300646i	0.841266	−	0.540621i	$-0.181811\pi$
$19$	1.31048	+	1.31048i	0.300646	+	0.300646i	−0.540621	+	0.841266i	$0.681811\pi$
$20$	−1.93598	+	0.501989i	−0.432898	+	0.112248i
$21$	2.13464	+	0.667013i	0.465816	+	0.145554i
$22$	−7.11683	+	4.07060i	−1.51731	+	0.867855i
$23$			2.76043i			0.575590i	0.957692	+	0.287795i	$0.0929222\pi$
$23$			2.76043i			0.575590i	−0.957692	+	0.287795i	$0.907078\pi$
$24$	−4.36688	+	2.22044i	−0.891386	+	0.453245i
$25$		−	1.00000i		−	0.200000i
$26$	4.37317	+	7.64582i	0.857649	+	1.49947i
$27$	−3.19496	−	4.09784i	−0.614869	−	0.788629i
$28$	2.22590	+	1.30925i	0.420656	+	0.247426i
$29$	4.08036	+	4.08036i	0.757703	+	0.757703i	0.975904	−	0.218201i	$-0.0700187\pi$
$29$	4.08036	+	4.08036i	0.757703	+	0.757703i	−0.218201	+	0.975904i	$0.570019\pi$
$30$	−0.526646	−	2.39220i	−0.0961520	−	0.436755i
$31$		−	10.0767i		−	1.80983i	−0.425592	−	0.904915i	$-0.639934\pi$
$31$		−	10.0767i		−	1.80983i	0.425592	−	0.904915i	$-0.360066\pi$
$32$	−5.49260	+	1.35327i	−0.970964	+	0.239227i
$33$	−4.65948	−	8.89481i	−0.811112	−	1.54839i
$34$	3.76170	+	1.02428i	0.645127	+	0.175662i
$35$	−0.913016	+	0.913016i	−0.154328	+	0.154328i
$36$	−2.51969	−	5.44529i	−0.419948	−	0.907548i
$37$	3.31466	+	3.31466i	0.544927	+	0.544927i	0.924969	−	0.380042i	$-0.124090\pi$
$37$	3.31466	+	3.31466i	0.544927	+	0.544927i	−0.380042	+	0.924969i	$0.624090\pi$
$38$	−2.27511	+	1.30129i	−0.369071	+	0.211097i
$39$	−9.55596	+	5.00582i	−1.53018	+	0.801573i
$40$	0.0343297	−	2.82822i	0.00542800	−	0.447181i
$41$	0.387829			0.0605687			0.0302844	−	0.999541i	$-0.490359\pi$
$41$	0.387829			0.0605687			0.0302844	+	0.999541i	$0.490359\pi$
$42$	−1.70329	+	2.66496i	−0.262823	+	0.411212i
$43$	3.66350	−	3.66350i	0.558679	−	0.558679i	−0.370252	−	0.928931i	$-0.620729\pi$
$43$	3.66350	−	3.66350i	0.558679	−	0.558679i	0.928931	+	0.370252i	$0.120729\pi$
$44$	−2.91022	−	11.2236i	−0.438732	−	1.69202i
$45$	2.95170	−	0.536147i	0.440014	−	0.0799240i
$46$	−3.76670	−	1.02564i	−0.555370	−	0.151222i
$47$	0.00218401			0.000318570			0.000159285	−	1.00000i	$-0.499949\pi$
$47$	0.00218401			0.000318570			0.000159285		1.00000i	$0.499949\pi$
$48$	−1.40735	−	6.78376i	−0.203133	−	0.979151i
$49$	−5.33280			−0.761829
$50$	1.36453	+	0.371549i	0.192974	+	0.0525450i
$51$	−1.42410	+	4.55755i	−0.199414	+	0.638185i
$52$	−12.0578	+	3.12653i	−1.67212	+	0.433572i
$53$	−1.76845	+	1.76845i	−0.242916	+	0.242916i	−0.818055	−	0.575140i	$-0.804948\pi$
$53$	−1.76845	+	1.76845i	−0.242916	+	0.242916i	0.575140	+	0.818055i	$0.304948\pi$
$54$	6.77872	−	2.83708i	0.922467	−	0.386077i
$55$	5.79737			0.781717
$56$	−2.61355	+	2.55087i	−0.349251	+	0.340874i
$57$	−1.48954	−	2.84349i	−0.197295	−	0.376630i
$58$	−7.08384	+	4.05173i	−0.930153	+	0.532018i
$59$	0.279145	+	0.279145i	0.0363416	+	0.0363416i	0.725044	−	0.688702i	$-0.241819\pi$
$59$	0.279145	+	0.279145i	0.0363416	+	0.0363416i	−0.688702	+	0.725044i	$0.741819\pi$
$60$	3.45992	+	0.170196i	0.446674	+	0.0219722i
$61$	5.12461	−	5.12461i	0.656140	−	0.656140i	−0.298325	−	0.954464i	$-0.596428\pi$
$61$	5.12461	−	5.12461i	0.656140	−	0.656140i	0.954464	+	0.298325i	$0.0964279\pi$
$62$	13.7500	+	3.74399i	1.74625	+	0.475488i
$63$	−3.18446	−	2.20544i	−0.401205	−	0.277859i
$64$	0.194184	−	7.99764i	0.0242730	−	0.999705i
$65$		−	6.22829i		−	0.772524i
$66$	13.8685	−	3.05316i	1.70709	−	0.375818i
$67$	0.763263	+	0.763263i	0.0932475	+	0.0932475i	0.752192	−	0.658944i	$-0.228997\pi$
$67$	0.763263	+	0.763263i	0.0932475	+	0.0932475i	−0.658944	+	0.752192i	$0.728997\pi$
$68$	−2.79532	+	4.75240i	−0.338982	+	0.576313i
$69$	1.42600	−	4.56361i	0.171670	−	0.549394i
$70$	−0.906611	−	1.58507i	−0.108361	−	0.189452i
$71$		−	9.45616i		−	1.12224i	−0.827735	−	0.561120i	$-0.810371\pi$
$71$		−	9.45616i		−	1.12224i	0.827735	−	0.561120i	$-0.189629\pi$
$72$	8.36647	−	1.41501i	0.985997	−	0.166760i
$73$			14.2158i			1.66383i	0.554904	+	0.831914i	$0.312755\pi$
$73$			14.2158i			1.66383i	−0.554904	+	0.831914i	$0.687245\pi$
$74$	−5.75453	+	3.29141i	−0.668951	+	0.382619i
$75$	−0.516584	+	1.65322i	−0.0596500	+	0.190898i
$76$	−0.930338	−	3.58795i	−0.106717	−	0.411566i
$77$	−5.29309	−	5.29309i	−0.603204	−	0.603204i
$78$	−3.28010	−	14.8993i	−0.371399	−	1.68702i
$79$			8.54188i			0.961037i	0.876985	+	0.480519i	$0.159552\pi$
$79$			8.54188i			0.961037i	−0.876985	+	0.480519i	$0.840448\pi$
$80$	3.84644	+	1.09767i	0.430045	+	0.122723i
$81$	3.16509	+	8.42509i	0.351677	+	0.936121i
$82$	−0.144098	+	0.529206i	−0.0159129	+	0.0584410i
$83$	−8.60385	+	8.60385i	−0.944395	+	0.944395i	−0.998533	−	0.0541387i	$-0.982759\pi$
$83$	−8.60385	+	8.60385i	−0.944395	+	0.944395i	0.0541387	+	0.998533i	$0.482759\pi$
$84$	−3.00357	−	3.31435i	−0.327716	−	0.361626i
$85$	−1.94933	−	1.94933i	−0.211435	−	0.211435i
$86$	3.63780	+	6.36015i	0.392274	+	0.685832i
$87$	−4.63789	−	8.85358i	−0.497234	−	0.949203i
$88$	16.3962	+	0.199022i	1.74784	+	0.0212158i
$89$	−4.67026			−0.495047			−0.247523	−	0.968882i	$-0.579617\pi$
$89$	−4.67026			−0.495047			−0.247523	+	0.968882i	$0.579617\pi$
$90$	−0.365112	+	4.22690i	−0.0384862	+	0.445554i
$91$	−5.68653	+	5.68653i	−0.596110	+	0.596110i
$92$	2.79903	−	4.75872i	0.291819	−	0.496131i
$93$	−5.20547	+	16.6590i	−0.539782	+	1.72746i
$94$	−0.000811466		0.00298015i	−8.36963e−5		0.000307379i
$95$	1.85330			0.190145
$96$	9.77956	+	0.600128i	0.998122	+	0.0612504i
$97$	−6.69158			−0.679427			−0.339714	−	0.940529i	$-0.610330\pi$
$97$	−6.69158			−0.679427			−0.339714	+	0.940529i	$0.610330\pi$
$98$	1.98140	−	7.27679i	0.200151	−	0.735067i
$99$	3.10824	+	17.1121i	0.312390	+	1.71983i
$100$	−1.01398	+	1.72390i	−0.101398	+	0.172390i
$101$	−6.31315	+	6.31315i	−0.628182	+	0.628182i	−0.947610	−	0.319429i	$-0.896509\pi$
$101$	−6.31315	+	6.31315i	−0.628182	+	0.628182i	0.319429	+	0.947610i	$0.396509\pi$
$102$	−5.68980	−	3.63659i	−0.563375	−	0.360076i
$103$	−2.23091			−0.219818			−0.109909	−	0.993942i	$-0.535056\pi$
$103$	−2.23091			−0.219818			−0.109909	+	0.993942i	$0.535056\pi$
$104$	0.213815	−	17.6150i	0.0209663	−	1.72729i
$105$	1.98107	−	1.03777i	0.193332	−	0.101276i
$106$	−1.75605	−	3.07018i	−0.170562	−	0.298202i
$107$	−1.88115	−	1.88115i	−0.181857	−	0.181857i	0.610307	−	0.792165i	$-0.291046\pi$
$107$	−1.88115	−	1.88115i	−0.181857	−	0.181857i	−0.792165	+	0.610307i	$0.791046\pi$
$108$	1.35266	+	10.3039i	0.130159	+	0.991493i
$109$	7.31517	−	7.31517i	0.700666	−	0.700666i	−0.263887	−	0.964554i	$-0.585005\pi$
$109$	7.31517	−	7.31517i	0.700666	−	0.700666i	0.964554	+	0.263887i	$0.0850047\pi$
$110$	−2.15401	+	7.91070i	−0.205377	+	0.754256i
$111$	−3.76757	−	7.19218i	−0.357602	−	0.682651i
$112$	−2.50968	−	4.51405i	−0.237142	−	0.426538i
$113$			3.64060i			0.342478i	0.985229	+	0.171239i	$0.0547771\pi$
$113$			3.64060i			0.342478i	−0.985229	+	0.171239i	$0.945223\pi$
$114$	4.43348	−	0.976035i	0.415234	−	0.0914140i
$115$	1.95192	+	1.95192i	0.182018	+	0.182018i
$116$	−2.89673	−	11.1715i	−0.268954	−	1.03725i
$117$	18.3841	−	3.33928i	1.69961	−	0.308716i
$118$	−0.484618	+	0.277186i	−0.0446127	+	0.0255171i
$119$			3.55954i			0.326303i
$120$	−1.51777	+	4.65794i	−0.138553	+	0.425210i
$121$			22.6095i			2.05541i
$122$	5.08866	+	8.89675i	0.460706	+	0.805474i
$123$	−0.641167	−	0.200346i	−0.0578121	−	0.0180646i
$124$	−10.2176	+	17.3713i	−0.917568	+	1.55999i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	4.19258	−	3.52588i	0.373505	−	0.314110i
$127$		−	10.0049i		−	0.887794i	−0.896078	−	0.443897i	$-0.853596\pi$
$127$		−	10.0049i		−	0.887794i	0.896078	−	0.443897i	$-0.146404\pi$
$128$	10.8409	+	3.23649i	0.958209	+	0.286068i
$129$	−7.94909	+	4.16408i	−0.699878	+	0.366626i
$130$	8.49871	+	2.31412i	0.745386	+	0.202961i
$131$	12.2224	−	12.2224i	1.06787	−	1.06787i	0.0703493	−	0.997522i	$-0.477589\pi$
$131$	12.2224	−	12.2224i	1.06787	−	1.06787i	0.997522	−	0.0703493i	$-0.0224114\pi$
$132$	−0.986687	+	20.0584i	−0.0858801	+	1.74586i
$133$	−1.69210	−	1.69210i	−0.146723	−	0.146723i
$134$	−1.32509	+	0.757908i	−0.114470	+	0.0654733i
$135$	−5.15678	−	0.638433i	−0.443825	−	0.0549476i
$136$	−5.44621	−	5.58005i	−0.467009	−	0.478486i
$137$	−17.6432			−1.50736			−0.753682	−	0.657239i	$-0.771724\pi$
$137$	−17.6432			−1.50736			−0.753682	+	0.657239i	$0.771724\pi$
$138$	5.69737	+	3.64142i	0.484992	+	0.309979i
$139$	−15.1869	+	15.1869i	−1.28814	+	1.28814i	−0.352222	+	0.935916i	$0.614574\pi$
$139$	−15.1869	+	15.1869i	−1.28814	+	1.28814i	−0.935916	+	0.352222i	$0.885426\pi$
$140$	2.49973	−	0.648168i	0.211266	−	0.0547802i
$141$	−0.00361065	−	0.00112822i	−0.000304071	−	9.50135e-5i
$142$	12.9032	+	3.51343i	1.08282	+	0.294840i
$143$	36.1077			3.01948
$144$	−1.17773	+	11.9421i	−0.0981438	+	0.995172i
$145$	5.77050			0.479214
$146$	−19.3979	−	5.28185i	−1.60538	−	0.437129i
$147$	8.81630	+	2.75484i	0.727156	+	0.227215i
$148$	−2.35315	−	9.07517i	−0.193427	−	0.745974i
$149$	2.32635	−	2.32635i	0.190582	−	0.190582i	−0.605365	−	0.795948i	$-0.706973\pi$
$149$	2.32635	−	2.32635i	0.190582	−	0.190582i	0.795948	+	0.605365i	$0.206973\pi$
$150$	−2.06394	−	1.31915i	−0.168520	−	0.107708i
$151$	3.65301			0.297277			0.148639	−	0.988892i	$-0.452511\pi$
$151$	3.65301			0.297277			0.148639	+	0.988892i	$0.452511\pi$
$152$	5.24155	+	0.0636233i	0.425146	+	0.00516053i
$153$	4.70872	−	6.79897i	0.380677	−	0.549664i
$154$	9.18924	−	5.25596i	0.740490	−	0.423537i
$155$	−7.12531	−	7.12531i	−0.572319	−	0.572319i
$156$	21.5494	+	1.06003i	1.72533	+	0.0848701i
$157$	5.57374	−	5.57374i	0.444833	−	0.444833i	−0.448800	−	0.893632i	$-0.648148\pi$
$157$	5.57374	−	5.57374i	0.444833	−	0.444833i	0.893632	+	0.448800i	$0.148148\pi$
$158$	−11.6557	−	3.17373i	−0.927277	−	0.252488i
$159$	3.83720	−	2.01009i	0.304310	−	0.159411i
$160$	−2.92695	+	4.84076i	−0.231395	+	0.382696i
$161$		−	3.56427i		−	0.280904i
$162$	−12.6723	+	1.18854i	−0.995631	+	0.0933802i
$163$	1.78354	+	1.78354i	0.139698	+	0.139698i	0.773497	−	0.633800i	$-0.218506\pi$
$163$	1.78354	+	1.78354i	0.139698	+	0.139698i	−0.633800	+	0.773497i	$0.718506\pi$
$164$	−0.668579	−	0.393252i	−0.0522073	−	0.0307078i
$165$	−9.58434	−	2.99483i	−0.746140	−	0.233147i
$166$	−8.54348	−	14.9370i	−0.663103	−	1.15933i
$167$			1.33852i			0.103578i	0.998658	+	0.0517890i	$0.0164923\pi$
$167$			1.33852i			0.103578i	−0.998658	+	0.0517890i	$0.983508\pi$
$168$	5.63852	−	2.86703i	0.435021	−	0.221196i
$169$		−	25.7916i		−	1.98397i
$170$	3.38420	−	1.93565i	0.259556	−	0.148458i
$171$	0.993643	+	5.47040i	0.0759858	+	0.418332i
$172$	−10.0303	+	2.60079i	−0.764800	+	0.198309i
$173$	0.228324	+	0.228324i	0.0173592	+	0.0173592i	0.715733	−	0.698374i	$-0.246093\pi$
$173$	0.228324	+	0.228324i	0.0173592	+	0.0173592i	−0.698374	+	0.715733i	$0.746093\pi$
$174$	13.8042	−	3.03901i	1.04649	−	0.230387i
$175$			1.29120i			0.0976055i
$176$	−6.36358	+	22.2993i	−0.479673	+	1.68087i
$177$	−0.317286	−	0.605690i	−0.0238487	−	0.0455264i
$178$	1.73523	−	6.37273i	0.130061	−	0.477656i
$179$	1.48748	−	1.48748i	0.111180	−	0.111180i	−0.649328	−	0.760508i	$-0.724950\pi$
$179$	1.48748	−	1.48748i	0.111180	−	0.111180i	0.760508	+	0.649328i	$0.224950\pi$
$180$	−5.63209	−	2.06871i	−0.419791	−	0.154193i
$181$	−8.95808	−	8.95808i	−0.665849	−	0.665849i	0.290903	−	0.956752i	$-0.406044\pi$
$181$	−8.95808	−	8.95808i	−0.665849	−	0.665849i	−0.956752	+	0.290903i	$0.906044\pi$
$182$	−5.64663	−	9.87228i	−0.418556	−	0.731782i
$183$	−11.1194	+	5.82483i	−0.821971	+	0.430584i
$184$	5.45345	+	5.58747i	0.402034	+	0.411914i
$185$	4.68764			0.344642
$186$	−20.7977	−	13.2927i	−1.52496	−	0.974667i
$187$	11.3010	−	11.3010i	0.826410	−	0.826410i
$188$	−0.00376501	−	0.00221454i	−0.000274592	−	0.000161512i
$189$	4.12533	+	5.29113i	0.300073	+	0.384873i
$190$	−0.688593	+	2.52889i	−0.0499558	+	0.183465i
$191$	−5.20483			−0.376608			−0.188304	−	0.982111i	$-0.560299\pi$
$191$	−5.20483			−0.376608			−0.188304	+	0.982111i	$0.560299\pi$
$192$	−4.45248	+	13.1216i	−0.321330	+	0.946967i
$193$	14.0219			1.00932			0.504660	−	0.863318i	$-0.331618\pi$
$193$	14.0219			1.00932			0.504660	+	0.863318i	$0.331618\pi$
$194$	2.48625	−	9.13089i	0.178503	−	0.655560i
$195$	−3.21743	+	10.2967i	−0.230405	+	0.737365i
$196$	9.19323	+	5.40737i	0.656659	+	0.386241i
$197$	−3.22869	+	3.22869i	−0.230034	+	0.230034i	−0.812707	−	0.582673i	$-0.802007\pi$
$197$	−3.22869	+	3.22869i	−0.230034	+	0.230034i	0.582673	+	0.812707i	$0.302007\pi$
$198$	−24.5049	−	2.11669i	−1.74149	−	0.150427i
$199$	8.52513			0.604330			0.302165	−	0.953256i	$-0.402291\pi$
$199$	8.52513			0.604330			0.302165	+	0.953256i	$0.402291\pi$
$200$	−1.97558	−	2.02413i	−0.139694	−	0.143127i
$201$	−0.867554	−	1.65613i	−0.0611925	−	0.116815i
$202$	−6.26886	−	10.9601i	−0.441075	−	0.771153i
$203$	−5.26856	−	5.26856i	−0.369780	−	0.369780i
$204$	7.07629	−	6.41276i	0.495439	−	0.448983i
$205$	0.274237	−	0.274237i	0.0191535	−	0.0191535i
$206$	0.828894	−	3.04416i	0.0577518	−	0.212096i
$207$	−4.71497	+	6.80801i	−0.327713	+	0.473189i
$208$	23.9568	+	6.83658i	1.66110	+	0.474032i
$209$			10.7443i			0.743198i
$210$	0.680005	+	3.08881i	0.0469248	+	0.213148i
$211$	−7.83228	−	7.83228i	−0.539197	−	0.539197i	0.384096	−	0.923293i	$-0.374513\pi$
$211$	−7.83228	−	7.83228i	−0.539197	−	0.539197i	−0.923293	+	0.384096i	$0.874513\pi$
$212$	4.84182	−	1.25546i	0.332538	−	0.0862254i
$213$	−4.88490	+	15.6331i	−0.334708	+	1.07116i
$214$	3.26583	−	1.86795i	0.223247	−	0.127690i
$215$		−	5.18098i		−	0.353340i
$216$	−14.5626	−	1.98266i	−0.990859	−	0.134903i
$217$			13.0110i			0.883247i
$218$	7.26385	+	12.6997i	0.491970	+	0.860135i
$219$	7.34363	−	23.5018i	0.496237	−	1.58810i
$220$	−9.99410	−	5.87843i	−0.673802	−	0.396324i
$221$	−12.1410	−	12.1410i	−0.816692	−	0.816692i
$222$	11.2138	−	2.46873i	0.752621	−	0.165690i
$223$		−	2.86107i		−	0.191592i	−0.995401	−	0.0957958i	$-0.969460\pi$
$223$		−	2.86107i		−	0.191592i	0.995401	−	0.0957958i	$-0.0305396\pi$
$224$	7.09204	−	1.74735i	0.473857	−	0.116750i
$225$	1.70806	−	2.46628i	0.113870	−	0.164419i
$226$	−4.96771	−	1.35266i	−0.330447	−	0.0899776i
$227$	8.16483	−	8.16483i	0.541919	−	0.541919i	−0.382172	−	0.924091i	$-0.624824\pi$
$227$	8.16483	−	8.16483i	0.541919	−	0.541919i	0.924091	+	0.382172i	$0.124824\pi$
$228$	−0.315424	+	6.41228i	−0.0208895	+	0.424664i
$229$	−10.6262	−	10.6262i	−0.702197	−	0.702197i	0.262685	−	0.964882i	$-0.415392\pi$
$229$	−10.6262	−	10.6262i	−0.702197	−	0.702197i	−0.964882	+	0.262685i	$0.915392\pi$
$230$	−3.38870	+	1.93823i	−0.223444	+	0.127803i
$231$	6.01633	+	11.4850i	0.395845	+	0.755656i
$232$	16.3202	+	0.198099i	1.07148	+	0.0130059i
$233$	−13.2569			−0.868486			−0.434243	−	0.900796i	$-0.642984\pi$
$233$	−13.2569			−0.868486			−0.434243	+	0.900796i	$0.642984\pi$
$234$	−2.27403	+	26.3264i	−0.148658	+	1.72101i
$235$	0.00154433	−	0.00154433i	0.000100741	−	0.000100741i
$236$	−0.198170	−	0.764266i	−0.0128998	−	0.0497495i
$237$	4.41260	−	14.1216i	0.286629	−	0.917298i
$238$	−4.85711	−	1.32254i	−0.314840	−	0.0857278i
$239$	−18.5733			−1.20141			−0.600704	−	0.799471i	$-0.705113\pi$
$239$	−18.5733			−1.20141			−0.600704	+	0.799471i	$0.705113\pi$
$240$	−5.79199	−	3.80170i	−0.373871	−	0.245398i
$241$	−25.2869			−1.62887			−0.814437	−	0.580253i	$-0.802954\pi$
$241$	−25.2869			−1.62887			−0.814437	+	0.580253i	$0.802954\pi$
$242$	−30.8514	−	8.40054i	−1.98320	−	0.540007i
$243$	−0.880327	−	15.5636i	−0.0564730	−	0.998404i
$244$	−14.0306	+	3.63807i	−0.898217	+	0.232903i
$245$	−3.77086	+	3.77086i	−0.240911	+	0.240911i
$246$	0.511604	−	0.800455i	0.0326187	−	0.0510352i
$247$	11.5429			0.734458
$248$	−19.9073	−	20.3965i	−1.26412	−	1.29518i
$249$	18.6687	−	9.77945i	1.18308	−	0.619748i
$250$	1.22760	−	0.702146i	0.0776400	−	0.0444076i
$251$	13.1481	+	13.1481i	0.829899	+	0.829899i	0.987502	−	0.157604i	$-0.0503768\pi$
$251$	13.1481	+	13.1481i	0.829899	+	0.829899i	−0.157604	+	0.987502i	$0.550377\pi$
$252$	3.25342	+	7.03095i	0.204946	+	0.442909i
$253$	−11.3160	+	11.3160i	−0.711431	+	0.711431i
$254$	13.6521	+	3.71732i	0.856606	+	0.233246i
$255$	2.21568	+	4.22967i	0.138751	+	0.264872i
$256$	−8.44422	+	13.5903i	−0.527764	+	0.849391i
$257$			27.4878i			1.71464i	0.514784	+	0.857320i	$0.327872\pi$
$257$			27.4878i			1.71464i	−0.514784	+	0.857320i	$0.672128\pi$
$258$	−2.72854	−	12.3940i	−0.169872	−	0.771614i
$259$	−4.27989	−	4.27989i	−0.265940	−	0.265940i
$260$	−6.31538	+	10.7370i	−0.391663	+	0.665878i
$261$	3.09383	+	17.0328i	0.191503	+	1.05430i
$262$	12.1366	+	21.2190i	0.749802	+	1.31091i
$263$		−	12.3115i		−	0.759157i	−0.925160	−	0.379579i	$-0.876069\pi$
$263$		−	12.3115i		−	0.759157i	0.925160	−	0.379579i	$-0.123931\pi$
$264$	−27.0038	−	8.79906i	−1.66197	−	0.541545i
$265$			2.50097i			0.153633i
$266$	2.93762	−	1.68022i	0.180117	−	0.103021i
$267$	7.72098	+	2.41258i	0.472516	+	0.147648i
$268$	−0.541856	−	2.08973i	−0.0330991	−	0.127650i
$269$	5.00088	+	5.00088i	0.304909	+	0.304909i	0.842931	−	0.538022i	$-0.180828\pi$
$269$	5.00088	+	5.00088i	0.304909	+	0.304909i	−0.538022	+	0.842931i	$0.680828\pi$
$270$	2.78716	−	6.79939i	0.169621	−	0.413798i
$271$			2.62351i			0.159367i	0.996820	+	0.0796835i	$0.0253910\pi$
$271$			2.62351i			0.159367i	−0.996820	+	0.0796835i	$0.974609\pi$
$272$	9.63770	−	5.35827i	0.584372	−	0.324893i
$273$	12.3387	−	6.46352i	0.746770	−	0.391190i
$274$	6.55533	−	24.0748i	0.396022	−	1.45441i
$275$	4.09936	−	4.09936i	0.247201	−	0.247201i
$276$	−7.08570	+	6.42128i	−0.426509	+	0.386516i
$277$	−3.14259	−	3.14259i	−0.188820	−	0.188820i	0.606366	−	0.795186i	$-0.292627\pi$
$277$	−3.14259	−	3.14259i	−0.188820	−	0.188820i	−0.795186	+	0.606366i	$0.792627\pi$
$278$	−15.0804	−	26.3658i	−0.904461	−	1.58131i
$279$	17.2116	−	24.8520i	1.03043	−	1.48785i
$280$	−0.0443265	+	3.65180i	−0.00264901	+	0.218237i
$281$	−2.04783			−0.122163			−0.0610816	−	0.998133i	$-0.519455\pi$
$281$	−2.04783			−0.122163			−0.0610816	+	0.998133i	$0.519455\pi$
$282$	0.00288103	−	0.00450766i	0.000171563	−	0.000268427i
$283$	7.60983	−	7.60983i	0.452357	−	0.452357i	−0.443779	−	0.896136i	$-0.646362\pi$
$283$	7.60983	−	7.60983i	0.452357	−	0.452357i	0.896136	+	0.443779i	$0.146362\pi$
$284$	−9.58838	+	16.3015i	−0.568966	+	0.967316i
$285$	−3.06392	−	0.957387i	−0.181491	−	0.0567107i
$286$	−13.4158	+	49.2702i	−0.793292	+	2.91341i
$287$	−0.500765			−0.0295592
$288$	−15.8578	−	6.04411i	−0.934428	−	0.356153i
$289$	9.40022			0.552954
$290$	−2.14402	+	7.87403i	−0.125901	+	0.462379i
$291$	11.0627	+	3.45677i	0.648505	+	0.202639i
$292$	14.4145	−	24.5066i	0.843546	−	1.43414i
$293$	−22.8324	+	22.8324i	−1.33388	+	1.33388i	−0.432018	+	0.901865i	$0.642198\pi$
$293$	−22.8324	+	22.8324i	−1.33388	+	1.33388i	−0.901865	+	0.432018i	$0.857802\pi$
$294$	−7.03476	+	11.0066i	−0.410276	+	0.641917i
$295$	0.394770			0.0229844
$296$	13.2577	+	0.160925i	0.770587	+	0.00935360i
$297$	3.70123	−	29.8958i	0.214767	−	1.73473i
$298$	2.31003	+	4.03874i	0.133817	+	0.233958i
$299$	12.1571	+	12.1571i	0.703065	+	0.703065i
$300$	2.56688	−	2.32619i	0.148199	−	0.134302i
$301$	−4.73032	+	4.73032i	−0.272651	+	0.272651i
$302$	−1.35727	+	4.98465i	−0.0781022	+	0.286834i
$303$	13.6983	−	7.17576i	0.786947	−	0.412237i
$304$	−2.03431	+	7.12863i	−0.116676	+	0.408855i
$305$		−	7.24730i		−	0.414979i
$306$	7.52790	+	8.95135i	0.430341	+	0.511715i
$307$	−5.25264	−	5.25264i	−0.299784	−	0.299784i	0.541145	−	0.840929i	$-0.317991\pi$
$307$	−5.25264	−	5.25264i	−0.299784	−	0.299784i	−0.840929	+	0.541145i	$0.817991\pi$
$308$	3.75767	+	14.4919i	0.214113	+	0.825751i
$309$	3.68819	+	1.15245i	0.209814	+	0.0655608i
$310$	12.3701	−	7.07532i	0.702576	−	0.401851i
$311$		−	14.6871i		−	0.832831i	−0.909175	−	0.416415i	$-0.863286\pi$
$311$		−	14.6871i		−	0.832831i	0.909175	−	0.416415i	$-0.136714\pi$
$312$	−9.45309	+	29.0110i	−0.535176	+	1.64242i
$313$			4.35735i			0.246292i	0.992389	+	0.123146i	$0.0392983\pi$
$313$			4.35735i			0.246292i	−0.992389	+	0.123146i	$0.960702\pi$
$314$	5.53463	+	9.67647i	0.312337	+	0.546075i
$315$	−3.81124	+	0.692273i	−0.214739	+	0.0390051i
$316$	8.66132	−	14.7254i	0.487237	−	0.828367i
$317$	11.8740	+	11.8740i	0.666911	+	0.666911i	0.957000	−	0.290089i	$-0.0936848\pi$
$317$	11.8740	+	11.8740i	0.666911	+	0.666911i	−0.290089	+	0.957000i	$0.593685\pi$
$318$	1.31713	+	5.98283i	0.0738608	+	0.335501i
$319$			33.4537i			1.87305i
$320$	−5.51788	−	5.79250i	−0.308459	−	0.323810i
$321$	2.13818	+	4.08172i	0.119342	+	0.227820i
$322$	4.86357	+	1.32430i	0.271036	+	0.0738005i
$323$	3.61270	−	3.61270i	0.201016	−	0.201016i
$324$	3.08659	−	17.7334i	0.171477	−	0.985188i
$325$	−4.40407	−	4.40407i	−0.244294	−	0.244294i
$326$	−3.09637	+	1.77103i	−0.171492	+	0.0980882i
$327$	−15.8725	+	8.31469i	−0.877751	+	0.459804i
$328$	0.785015	−	0.766186i	0.0433452	−	0.0423056i
$329$	−0.00281999			−0.000155471
$330$	7.64760	−	11.9654i	0.420986	−	0.658675i
$331$	−17.4316	+	17.4316i	−0.958128	+	0.958128i	−0.999158	−	0.0410301i	$-0.986936\pi$
$331$	−17.4316	+	17.4316i	−0.958128	+	0.958128i	0.0410301	+	0.999158i	$0.486936\pi$
$332$	23.5563	−	6.10804i	1.29282	−	0.335222i
$333$	2.51326	+	13.8365i	0.137726	+	0.758237i
$334$	−1.82646	−	0.497327i	−0.0999394	−	0.0272125i
$335$	1.07942			0.0589749
$336$	1.81717	+	8.75919i	0.0991345	+	0.477853i
$337$	−18.4419			−1.00460			−0.502298	−	0.864694i	$-0.667512\pi$
$337$	−18.4419			−1.00460			−0.502298	+	0.864694i	$0.667512\pi$
$338$	35.1935	+	9.58284i	1.91427	+	0.521238i
$339$	1.88067	−	6.01871i	0.102144	−	0.326892i
$340$	1.38387	+	5.33704i	0.0750508	+	0.289442i
$341$	41.3080	−	41.3080i	2.23696	−	2.23696i
$342$	−7.83373	−	0.676664i	−0.423600	−	0.0365898i
$343$	15.9241			0.859821
$344$	0.177861	−	14.6529i	0.00958964	−	0.790033i
$345$	−2.21863	−	4.23529i	−0.119447	−	0.228020i
$346$	−0.396390	+	0.226722i	−0.0213100	+	0.0121887i
$347$	4.81148	+	4.81148i	0.258294	+	0.258294i	0.824360	−	0.566066i	$-0.191535\pi$
$347$	4.81148	+	4.81148i	0.258294	+	0.258294i	−0.566066	+	0.824360i	$0.691535\pi$
$348$	−0.982113	+	19.9654i	−0.0526468	+	1.07026i
$349$	11.3752	−	11.3752i	0.608899	−	0.608899i	−0.333759	−	0.942658i	$-0.608317\pi$
$349$	11.3752	−	11.3752i	0.608899	−	0.608899i	0.942658	+	0.333759i	$0.108317\pi$
$350$	−1.76189	−	0.479744i	−0.0941767	−	0.0256434i
$351$	−32.1179	−	3.97635i	−1.71433	−	0.212242i
$352$	−28.0637	−	16.9686i	−1.49580	−	0.904429i
$353$		−	28.4101i		−	1.51212i	−0.654504	−	0.756059i	$-0.727122\pi$
$353$		−	28.4101i		−	1.51212i	0.654504	−	0.756059i	$-0.272878\pi$
$354$	0.944372	−	0.207904i	0.0501928	−	0.0110500i
$355$	−6.68652	−	6.68652i	−0.354883	−	0.354883i
$356$	8.05108	+	4.73557i	0.426706	+	0.250984i
$357$	1.83880	−	5.88471i	0.0973197	−	0.311452i
$358$	1.47705	+	2.58239i	0.0780643	+	0.136484i
$359$			26.5436i			1.40092i	0.713692	+	0.700460i	$0.247022\pi$
$359$			26.5436i			1.40092i	−0.713692	+	0.700460i	$0.752978\pi$
$360$	4.91542	−	6.91655i	0.259065	−	0.364534i
$361$		−	15.5653i		−	0.819225i
$362$	15.5520	−	8.89523i	0.817393	−	0.467523i
$363$	11.6797	−	37.3785i	0.613026	−	1.96186i
$364$	15.5691	−	4.03698i	0.816040	−	0.211595i
$365$	10.0521	+	10.0521i	0.526149	+	0.526149i
$366$	−3.81676	−	17.3370i	−0.199505	−	0.906221i
$367$			4.45350i			0.232471i	0.993222	+	0.116235i	$0.0370827\pi$
$367$			4.45350i			0.232471i	−0.993222	+	0.116235i	$0.962917\pi$
$368$	−9.65051	+	5.36540i	−0.503068	+	0.279691i
$369$	0.956496	+	0.662434i	0.0497932	+	0.0344849i
$370$	−1.74169	+	6.39645i	−0.0905462	+	0.332535i
$371$	2.28343	−	2.28343i	0.118550	−	0.118550i
$372$	25.8657	−	23.4403i	1.34107	−	1.21532i
$373$	5.51867	+	5.51867i	0.285746	+	0.285746i	0.835395	−	0.549650i	$-0.185239\pi$
$373$	5.51867	+	5.51867i	0.285746	+	0.285746i	−0.549650	+	0.835395i	$0.685239\pi$
$374$	11.2217	+	19.6194i	0.580260	+	1.01450i
$375$	0.803724	+	1.53428i	0.0415041	+	0.0792301i
$376$	0.00442071	−	0.00431467i	0.000227981	−	0.000222512i
$377$	35.9403			1.85102
$378$	−8.75268	+	3.66323i	−0.450189	+	0.188416i
$379$	−11.0044	+	11.0044i	−0.565256	+	0.565256i	−0.930796	−	0.365540i	$-0.880884\pi$
$379$	−11.0044	+	11.0044i	−0.565256	+	0.565256i	0.365540	+	0.930796i	$0.380884\pi$
$380$	−3.19491	−	1.87922i	−0.163896	−	0.0964018i
$381$	−5.16839	+	16.5404i	−0.264784	+	0.847388i
$382$	1.93385	−	7.10216i	0.0989444	−	0.363378i
$383$	−1.74498			−0.0891642			−0.0445821	−	0.999006i	$-0.514196\pi$
$383$	−1.74498			−0.0891642			−0.0445821	+	0.999006i	$0.514196\pi$
$384$	−16.2505	−	10.9509i	−0.829279	−	0.558834i
$385$	−7.48556			−0.381500
$386$	−5.20983	+	19.1334i	−0.265173	+	0.973863i
$387$	15.2927	−	2.77776i	0.777372	−	0.141202i
$388$	11.5356	+	6.78515i	0.585633	+	0.344464i
$389$	0.0192068	−	0.0192068i	0.000973822	−	0.000973822i	−0.706620	−	0.707594i	$-0.749781\pi$
$389$	0.0192068	−	0.0192068i	0.000973822	−	0.000973822i	0.707594	+	0.706620i	$0.249781\pi$
$390$	−12.8548	−	8.21604i	−0.650929	−	0.416035i
$391$	7.60988			0.384848
$392$	−10.7943	+	10.5354i	−0.545193	+	0.532116i
$393$	−26.5201	+	13.8924i	−1.33776	+	0.700778i
$394$	−3.20603	−	5.60527i	−0.161518	−	0.282389i
$395$	6.04002	+	6.04002i	0.303907	+	0.303907i
$396$	11.9931	−	32.6513i	0.602675	−	1.64079i
$397$	−22.2917	+	22.2917i	−1.11879	+	1.11879i	−0.126872	+	0.991919i	$0.540494\pi$
$397$	−22.2917	+	22.2917i	−1.11879	+	1.11879i	−0.991919	+	0.126872i	$0.959506\pi$
$398$	−3.16750	+	11.6328i	−0.158773	+	0.583101i
$399$	1.92330	+	3.67152i	0.0962854	+	0.183806i
$400$	3.49601	−	1.94368i	0.174801	−	0.0971840i
$401$			31.9602i			1.59602i	0.602647	+	0.798008i	$0.294113\pi$
$401$			31.9602i			1.59602i	−0.602647	+	0.798008i	$0.705887\pi$
$402$	2.58219	−	0.568471i	0.128788	−	0.0283528i
$403$	−44.3785	−	44.3785i	−2.21065	−	2.21065i
$404$	17.2847	−	4.48183i	0.859945	−	0.222979i
$405$	8.19550	+	3.71938i	0.407238	+	0.184818i
$406$	9.14665	−	5.23159i	0.453940	−	0.259640i
$407$			27.1760i			1.34706i
$408$	6.12123	+	12.0385i	0.303046	+	0.595994i
$409$			15.9890i			0.790605i	0.918551	+	0.395303i	$0.129360\pi$
$409$			15.9890i			0.790605i	−0.918551	+	0.395303i	$0.870640\pi$
$410$	0.272313	+	0.476097i	0.0134486	+	0.0235128i
$411$	29.1682	+	9.11422i	1.43876	+	0.449571i
$412$	3.84588	+	2.26211i	0.189473	+	0.111446i
$413$	−0.360432	−	0.360432i	−0.0177357	−	0.0177357i
$414$	−7.53791	−	8.96325i	−0.370468	−	0.440520i
$415$			12.1677i			0.597288i
$416$	−18.2299	+	30.1497i	−0.893792	+	1.47821i
$417$	32.9527	−	17.2620i	1.61370	−	0.845325i
$418$	−14.6609	−	3.99203i	−0.717090	−	0.195257i
$419$	−0.759220	+	0.759220i	−0.0370903	+	0.0370903i	−0.725409	−	0.688318i	$-0.758349\pi$
$419$	−0.759220	+	0.759220i	−0.0370903	+	0.0370903i	0.688318	+	0.725409i	$0.258349\pi$
$420$	−4.46745	−	0.219757i	−0.217989	−	0.0107230i
$421$	12.4294	+	12.4294i	0.605771	+	0.605771i	0.941838	−	0.336067i	$-0.109097\pi$
$421$	12.4294	+	12.4294i	0.605771	+	0.605771i	−0.336067	+	0.941838i	$0.609097\pi$
$422$	13.5975	−	7.77733i	0.661915	−	0.378595i
$423$	0.00538638	+	0.00373040i	0.000261895	+	0.000181378i
$424$	−0.0858576	+	7.07329i	−0.00416961	+	0.343509i
$425$	−2.75677			−0.133723
$426$	−19.5169	−	12.4741i	−0.945599	−	0.604372i
$427$	−6.61690	+	6.61690i	−0.320214	+	0.320214i
$428$	1.33546	+	5.15036i	0.0645521	+	0.248952i
$429$	−59.6940	−	18.6527i	−2.88205	−	0.900559i
$430$	7.06962	+	1.92499i	0.340927	+	0.0928312i
$431$	−24.6661			−1.18812			−0.594062	−	0.804419i	$-0.702477\pi$
$431$	−24.6661			−1.18812			−0.594062	+	0.804419i	$0.702477\pi$
$432$	8.11612	−	19.1345i	0.390487	−	0.920608i
$433$	17.7512			0.853070			0.426535	−	0.904471i	$-0.359734\pi$
$433$	17.7512			0.853070			0.426535	+	0.904471i	$0.359734\pi$
$434$	−17.7540	−	4.83424i	−0.852219	−	0.232051i
$435$	−9.53991	−	2.98095i	−0.457404	−	0.142925i
$436$	−20.0281	+	5.19318i	−0.959172	+	0.248708i
$437$	−3.61750	+	3.61750i	−0.173049	+	0.173049i
$438$	29.3405	+	18.7527i	1.40194	+	0.896039i
$439$	−15.5759			−0.743397			−0.371698	−	0.928354i	$-0.621224\pi$
$439$	−15.5759			−0.743397			−0.371698	+	0.928354i	$0.621224\pi$
$440$	11.7346	−	11.4532i	0.559426	−	0.546008i
$441$	−13.1522	−	9.10872i	−0.626295	−	0.433749i
$442$	21.0778	−	12.0558i	1.00257	−	0.573437i
$443$	−19.5993	−	19.5993i	−0.931192	−	0.931192i	0.0665888	−	0.997781i	$-0.478788\pi$
$443$	−19.5993	−	19.5993i	−0.931192	−	0.931192i	−0.997781	+	0.0665888i	$0.978788\pi$
$444$	−0.797817	+	16.2189i	−0.0378627	+	0.769713i
$445$	−3.30237	+	3.30237i	−0.156548	+	0.156548i
$446$	3.90403	+	1.06303i	0.184861	+	0.0503359i
$447$	−5.04774	+	2.64422i	−0.238750	+	0.125067i
$448$	−0.250730	+	10.3266i	−0.0118459	+	0.487884i
$449$		−	35.6088i		−	1.68048i	−0.542211	−	0.840242i	$-0.682413\pi$
$449$		−	35.6088i		−	1.68048i	0.542211	−	0.840242i	$-0.317587\pi$
$450$	2.73070	+	3.24704i	0.128726	+	0.153067i
$451$	1.58985	+	1.58985i	0.0748631	+	0.0748631i
$452$	3.69150	−	6.27603i	0.173634	−	0.295200i
$453$	−6.03923	−	1.88709i	−0.283748	−	0.0886630i
$454$	8.10755	+	14.1748i	0.380506	+	0.665257i
$455$			8.04197i			0.377013i
$456$	−8.63257	−	2.81288i	−0.404257	−	0.131725i
$457$			19.8497i			0.928530i	0.885696	+	0.464265i	$0.153681\pi$
$457$			19.8497i			0.928530i	−0.885696	+	0.464265i	$0.846319\pi$
$458$	18.4479	−	10.5516i	0.862014	−	0.493044i
$459$	−11.2968	+	8.80775i	−0.527289	+	0.411111i
$460$	−1.38571	−	5.34414i	−0.0646090	−	0.249172i
$461$	−29.9766	−	29.9766i	−1.39615	−	1.39615i	−0.810733	−	0.585417i	$-0.800931\pi$
$461$	−29.9766	−	29.9766i	−1.39615	−	1.39615i	−0.585417	−	0.810733i	$-0.699069\pi$
$462$	−17.9070	+	3.94224i	−0.833109	+	0.183410i
$463$			32.1223i			1.49285i	0.665469	+	0.746426i	$0.268232\pi$
$463$			32.1223i			1.49285i	−0.665469	+	0.746426i	$0.731768\pi$
$464$	−6.33408	+	22.1959i	−0.294052	+	1.03042i
$465$	8.09889	+	15.4605i	0.375577	+	0.716965i
$466$	4.92558	−	18.0894i	0.228173	−	0.837977i
$467$	−28.7271	+	28.7271i	−1.32933	+	1.32933i	−0.423376	+	0.905954i	$0.639155\pi$
$467$	−28.7271	+	28.7271i	−1.32933	+	1.32933i	−0.905954	+	0.423376i	$0.860845\pi$
$468$	−35.0783	−	12.8845i	−1.62149	−	0.595587i
$469$	−0.985526	−	0.985526i	−0.0455073	−	0.0455073i
$470$	0.00153349	+	0.00268108i	7.07347e−5	+	0.000123669i
$471$	−12.0939	+	6.33532i	−0.557259	+	0.291916i
$472$	1.11650	+	0.0135523i	0.0513909	+	0.000623797i
$473$	30.0360			1.38106
$474$	17.6299	+	11.2680i	0.809769	+	0.517557i
$475$	1.31048	−	1.31048i	0.0601291	−	0.0601291i
$476$	3.60931	−	6.13630i	0.165433	−	0.281257i
$477$	−7.38212	+	1.34089i	−0.338004	+	0.0613950i
$478$	6.90090	−	25.3439i	0.315640	−	1.15920i
$479$	−12.8567			−0.587436			−0.293718	−	0.955892i	$-0.594893\pi$
$479$	−12.8567			−0.587436			−0.293718	+	0.955892i	$0.594893\pi$
$480$	7.33955	−	6.49084i	0.335003	−	0.296265i
$481$	29.1960			1.33122
$482$	9.39533	−	34.5048i	0.427946	−	1.57165i
$483$	−1.84125	+	5.89253i	−0.0837796	+	0.268119i
$484$	22.9256	−	38.9766i	1.04207	−	1.77166i
$485$	−4.73166	+	4.73166i	−0.214854	+	0.214854i
$486$	21.5641	+	4.58140i	0.978168	+	0.207816i
$487$	19.9584			0.904402			0.452201	−	0.891916i	$-0.350639\pi$
$487$	19.9584			0.904402			0.452201	+	0.891916i	$0.350639\pi$
$488$	0.248798	−	20.4969i	0.0112625	−	0.927853i
$489$	−2.02724	−	3.86994i	−0.0916749	−	0.175005i
$490$	−3.74441	−	6.54653i	−0.169155	−	0.295742i
$491$	−14.8307	−	14.8307i	−0.669300	−	0.669300i	0.288254	−	0.957554i	$-0.406925\pi$
$491$	−14.8307	−	14.8307i	−0.669300	−	0.669300i	−0.957554	+	0.288254i	$0.906925\pi$
$492$	0.902162	+	0.995510i	0.0406726	+	0.0448810i
$493$	11.2486	−	11.2486i	0.506612	−	0.506612i
$494$	−4.28876	+	15.7507i	−0.192960	+	0.708657i
$495$	14.2979	+	9.90223i	0.642645	+	0.445072i
$496$	35.2283	−	19.5859i	1.58180	−	0.879432i
$497$			12.2098i			0.547684i
$498$	6.40806	+	29.1076i	0.287152	+	1.30434i
$499$	18.6393	+	18.6393i	0.834410	+	0.834410i	0.988117	−	0.153706i	$-0.0491209\pi$
$499$	18.6393	+	18.6393i	0.834410	+	0.834410i	−0.153706	+	0.988117i	$0.549121\pi$
$500$	0.501989	+	1.93598i	0.0224496	+	0.0865795i
$501$	0.691460	−	2.21287i	0.0308921	−	0.0988639i
$502$	−22.8261	+	13.0558i	−1.01878	+	0.582710i
$503$			13.4262i			0.598646i	0.954152	+	0.299323i	$0.0967608\pi$
$503$			13.4262i			0.598646i	−0.954152	+	0.299323i	$0.903239\pi$
$504$	−10.8028	+	1.82706i	−0.481194	+	0.0813837i
$505$			8.92814i			0.397297i
$506$	−11.2366	−	19.6455i	−0.499529	−	0.873350i
$507$	−13.3235	+	42.6392i	−0.591718	+	1.89367i
$508$	−10.1448	+	17.2475i	−0.450104	+	0.765235i
$509$	11.9058	+	11.9058i	0.527714	+	0.527714i	0.919890	−	0.392176i	$-0.128278\pi$
$509$	11.9058	+	11.9058i	0.527714	+	0.527714i	−0.392176	+	0.919890i	$0.628278\pi$
$510$	−6.59476	+	1.45184i	−0.292021	+	0.0642886i
$511$		−	18.3554i		−	0.811994i
$512$	−15.4069	−	16.5719i	−0.680896	−	0.732380i
$513$	1.18321	−	9.55708i	0.0522400	−	0.421955i
$514$	−37.5080	−	10.2131i	−1.65441	−	0.450479i
$515$	−1.57749	+	1.57749i	−0.0695127	+	0.0695127i
$516$	17.9258	+	0.881780i	0.789137	+	0.0388182i
$517$	0.00895303	+	0.00895303i	0.000393754	+	0.000393754i
$518$	7.43025	−	4.24987i	0.326466	−	0.186728i
$519$	−0.259522	−	0.495419i	−0.0113917	−	0.0217465i
$520$	−12.3045	−	12.6069i	−0.539587	−	0.552847i
$521$	19.2979			0.845457			0.422729	−	0.906256i	$-0.361072\pi$
$521$	19.2979			0.845457			0.422729	+	0.906256i	$0.361072\pi$
$522$	−24.3913	−	2.10688i	−1.06758	−	0.0922156i
$523$	−12.5948	+	12.5948i	−0.550734	+	0.550734i	−0.926653	−	0.375919i	$-0.877327\pi$
$523$	−12.5948	+	12.5948i	−0.550734	+	0.550734i	0.375919	+	0.926653i	$0.377327\pi$
$524$	−33.4634	+	8.67689i	−1.46185	+	0.379052i
$525$	0.667013	−	2.13464i	0.0291108	−	0.0931633i
$526$	16.7994	+	4.57431i	0.732488	+	0.199449i
$527$	−27.7792			−1.21008
$528$	22.0398	−	33.5783i	0.959161	−	1.46131i
$529$	15.3800			0.668696
$530$	−3.41266	−	0.929234i	−0.148236	−	0.0403633i
$531$	0.211655	+	1.16524i	0.00918504	+	0.0505673i
$532$	1.20125	+	4.63276i	0.0520809	+	0.200856i
$533$	1.70802	−	1.70802i	0.0739827	−	0.0739827i
$534$	−6.16077	+	9.63914i	−0.266603	+	0.417126i
$535$	−2.66034			−0.115017
$536$	3.05283	+	0.0370561i	0.131862	+	0.00160058i
$537$	−3.22755	+	1.69073i	−0.139279	+	0.0729603i
$538$	−8.68195	+	4.96580i	−0.374305	+	0.214091i
$539$	−21.8611	−	21.8611i	−0.941623	−	0.941623i
$540$	8.24243	+	6.32948i	0.354698	+	0.272378i
$541$	2.34334	−	2.34334i	0.100748	−	0.100748i	−0.654936	−	0.755684i	$-0.727305\pi$
$541$	2.34334	−	2.34334i	0.100748	−	0.100748i	0.755684	+	0.654936i	$0.227305\pi$
$542$	−3.57987	−	0.974764i	−0.153769	−	0.0418697i
$543$	10.1821	+	19.4373i	0.436955	+	0.834134i
$544$	3.73066	+	15.1418i	0.159951	+	0.649201i
$545$		−	10.3452i		−	0.443140i
$546$	4.23527	+	19.2380i	0.181253	+	0.823312i
$547$	−24.2081	−	24.2081i	−1.03506	−	1.03506i	−0.999362	−	0.0357024i	$-0.988633\pi$
$547$	−24.2081	−	24.2081i	−1.03506	−	1.03506i	−0.0357024	−	0.999362i	$-0.511367\pi$
$548$	30.4152	+	17.8899i	1.29927	+	0.764220i
$549$	21.3919	−	3.88562i	0.912983	−	0.165834i
$550$	4.07060	+	7.11683i	0.173571	+	0.303462i
$551$			10.6945i			0.455600i
$552$	−6.12936	−	12.0545i	−0.260883	−	0.513073i
$553$		−	11.0293i		−	0.469013i
$554$	5.45579	−	3.12054i	0.231794	−	0.132579i
$555$	−7.74971	−	2.42156i	−0.328957	−	0.102790i
$556$	41.5801	−	10.7815i	1.76339	−	0.457238i
$557$	−27.4760	−	27.4760i	−1.16420	−	1.16420i	−0.983548	−	0.180649i	$-0.942180\pi$
$557$	−27.4760	−	27.4760i	−1.16420	−	1.16420i	−0.180649	−	0.983548i	$-0.557820\pi$
$558$	27.5164	+	32.7195i	1.16486	+	1.38513i
$559$		−	32.2686i		−	1.36482i
$560$	−4.96653	−	1.41731i	−0.209874	−	0.0598921i
$561$	−24.5209	+	12.8451i	−1.03528	+	0.542322i
$562$	0.760869	−	2.79433i	0.0320953	−	0.117872i
$563$	−15.9779	+	15.9779i	−0.673389	+	0.673389i	−0.958496	−	0.285107i	$-0.907971\pi$
$563$	−15.9779	+	15.9779i	−0.673389	+	0.673389i	0.285107	+	0.958496i	$0.407971\pi$
$564$	0.00508040	+	0.00560608i	0.000213924	+	0.000236058i
$565$	2.57429	+	2.57429i	0.108301	+	0.108301i
$566$	7.55644	+	13.2113i	0.317621	+	0.555312i
$567$	−4.08677	−	10.8785i	−0.171628	−	0.456853i
$568$	−18.6814	−	19.1405i	−0.783853	−	0.803116i
$569$	4.90717			0.205719			0.102860	−	0.994696i	$-0.467201\pi$
$569$	4.90717			0.205719			0.102860	+	0.994696i	$0.467201\pi$
$570$	2.44478	−	3.82511i	0.102401	−	0.160216i
$571$	18.1855	−	18.1855i	0.761040	−	0.761040i	−0.215470	−	0.976510i	$-0.569128\pi$
$571$	18.1855	−	18.1855i	0.761040	−	0.761040i	0.976510	+	0.215470i	$0.0691285\pi$
$572$	−62.2461	−	36.6126i	−2.60264	−	1.53085i
$573$	8.60473	+	2.68873i	0.359468	+	0.112323i
$574$	0.186059	−	0.683310i	0.00776594	−	0.0285208i
$575$	2.76043			0.115118
$576$	14.1393	−	19.3928i	0.589139	−	0.808032i
$577$	−3.08085			−0.128257			−0.0641287	−	0.997942i	$-0.520427\pi$
$577$	−3.08085			−0.128257			−0.0641287	+	0.997942i	$0.520427\pi$
$578$	−3.49265	+	12.8269i	−0.145275	+	0.533529i
$579$	−23.1813	−	7.24350i	−0.963383	−	0.301029i
$580$	−9.94777	−	5.85118i	−0.413059	−	0.242957i
$581$	11.1093	−	11.1093i	0.460891	−	0.460891i
$582$	−8.82720	+	13.8110i	−0.365899	+	0.572485i
$583$	−14.4991			−0.600489
$584$	28.0843	+	28.7745i	1.16214	+	1.19070i
$585$	10.6383	−	15.3607i	0.439838	−	0.635087i
$586$	−22.6722	−	39.6389i	−0.936581	−	1.63747i
$587$	19.9102	+	19.9102i	0.821782	+	0.821782i	0.986363	−	0.164582i	$-0.0526274\pi$
$587$	19.9102	+	19.9102i	0.821782	+	0.821782i	−0.164582	+	0.986363i	$0.552627\pi$
$588$	−12.4051	−	13.6887i	−0.511577	−	0.564511i
$589$	13.2054	−	13.2054i	0.544117	−	0.544117i
$590$	−0.146677	+	0.538677i	−0.00603858	+	0.0221770i
$591$	7.00562	−	3.66985i	0.288173	−	0.150957i
$592$	−5.14547	+	18.0308i	−0.211477	+	0.741059i
$593$		−	13.0729i		−	0.536838i	−0.963302	−	0.268419i	$-0.913499\pi$
$593$		−	13.0729i		−	0.536838i	0.963302	−	0.268419i	$-0.0865012\pi$
$594$	39.4186	+	16.1582i	1.61736	+	0.662979i
$595$	2.51697	+	2.51697i	0.103186	+	0.103186i
$596$	−6.36929	+	1.65153i	−0.260896	+	0.0676491i
$597$	−14.0939	−	4.40395i	−0.576826	−	0.180242i
$598$	−21.1058	+	12.0718i	−0.863079	+	0.493654i
$599$		−	20.7034i		−	0.845917i	−0.906149	−	0.422959i	$-0.860992\pi$
$599$		−	20.7034i		−	0.845917i	0.906149	−	0.422959i	$-0.139008\pi$
$600$	2.22044	+	4.36688i	0.0906489	+	0.178277i
$601$		−	31.6818i		−	1.29233i	−0.763199	−	0.646163i	$-0.776373\pi$
$601$		−	31.6818i		−	1.29233i	0.763199	−	0.646163i	$-0.223627\pi$
$602$	−4.69713	−	8.21222i	−0.191441	−	0.334705i
$603$	0.578726	+	3.18612i	0.0235676	+	0.129749i
$604$	−6.29743	−	3.70408i	−0.256239	−	0.150717i
$605$	15.9873	+	15.9873i	0.649977	+	0.649977i
$606$	4.70197	+	21.3579i	0.191004	+	0.867607i
$607$		−	31.9791i		−	1.29799i	−0.760791	−	0.648997i	$-0.775189\pi$
$607$		−	31.9791i		−	1.29799i	0.760791	−	0.648997i	$-0.224811\pi$
$608$	−8.97140	−	5.42452i	−0.363838	−	0.219993i
$609$	5.98844	+	11.4317i	0.242664	+	0.463238i
$610$	9.88918	+	2.69273i	0.400401	+	0.109025i
$611$	0.00961851	−	0.00961851i	0.000389123	−	0.000389123i
$612$	−15.0114	+	6.94621i	−0.606800	+	0.280784i
$613$	−19.4142	−	19.4142i	−0.784133	−	0.784133i	0.196392	−	0.980525i	$-0.437077\pi$
$613$	−19.4142	−	19.4142i	−0.784133	−	0.784133i	−0.980525	+	0.196392i	$0.937077\pi$
$614$	9.11902	−	5.21579i	0.368014	−	0.210492i
$615$	−0.595040	+	0.311707i	−0.0239943	+	0.0125693i
$616$	−21.1708	−	0.256977i	−0.852996	−	0.0103539i
$617$	−21.0941			−0.849216			−0.424608	−	0.905377i	$-0.639588\pi$
$617$	−21.0941			−0.849216			−0.424608	+	0.905377i	$0.639588\pi$
$618$	−2.94291	+	4.60447i	−0.118381	+	0.185219i
$619$	23.5547	−	23.5547i	0.946744	−	0.946744i	−0.0519076	−	0.998652i	$-0.516530\pi$
$619$	23.5547	−	23.5547i	0.946744	−	0.946744i	0.998652	+	0.0519076i	$0.0165301\pi$
$620$	5.05840	+	19.5083i	0.203150	+	0.783471i
$621$	11.3118	−	8.81946i	0.453927	−	0.353913i
$622$	20.0411	+	5.45699i	0.803574	+	0.218805i
$623$	6.03024			0.241597
$624$	−36.0742	−	23.6781i	−1.44412	−	0.947881i
$625$	−1.00000			−0.0400000
$626$	−5.94574	−	1.61897i	−0.237640	−	0.0647070i
$627$	5.55033	−	17.7627i	0.221659	−	0.709373i
$628$	−15.2603	+	3.95691i	−0.608950	+	0.157898i
$629$	9.13776	−	9.13776i	0.364347	−	0.364347i
$630$	0.471433	−	5.45777i	0.0187823	−	0.217443i
$631$	−0.795228			−0.0316575			−0.0158288	−	0.999875i	$-0.505039\pi$
$631$	−0.795228			−0.0316575			−0.0158288	+	0.999875i	$0.505039\pi$
$632$	16.8752	+	17.2899i	0.671258	+	0.687754i
$633$	8.90246	+	16.9945i	0.353841	+	0.675472i
$634$	−20.6143	+	11.7907i	−0.818697	+	0.468269i
$635$	−7.07455	−	7.07455i	−0.280745	−	0.280745i
$636$	−8.65315	−	0.425654i	−0.343120	−	0.0168783i
$637$	−23.4860	+	23.4860i	−0.930550	+	0.930550i
$638$	−45.6487	−	12.4297i	−1.80725	−	0.492096i
$639$	16.1516	−	23.3216i	0.638949	−	0.922587i
$640$	9.95422	−	5.37713i	0.393475	−	0.212550i
$641$			11.6040i			0.458331i	0.973387	+	0.229165i	$0.0735997\pi$
$641$			11.6040i			0.458331i	−0.973387	+	0.229165i	$0.926400\pi$
$642$	−6.36409	+	1.40106i	−0.251170	+	0.0552954i
$643$	18.3792	+	18.3792i	0.724805	+	0.724805i	0.969580	−	0.244775i	$-0.0787141\pi$
$643$	18.3792	+	18.3792i	0.724805	+	0.724805i	−0.244775	+	0.969580i	$0.578714\pi$
$644$	−3.61411	+	6.14446i	−0.142416	+	0.242125i
$645$	−2.67641	+	8.56530i	−0.105384	+	0.337258i
$646$	3.58735	+	6.27195i	0.141143	+	0.246766i
$647$		−	12.5667i		−	0.494049i	−0.969009	−	0.247024i	$-0.920547\pi$
$647$		−	12.5667i		−	0.494049i	0.969009	−	0.247024i	$-0.0794528\pi$
$648$	23.0510	+	10.8006i	0.905528	+	0.424287i
$649$			2.28863i			0.0898366i
$650$	7.64582	−	4.37317i	0.299894	−	0.171530i
$651$	6.72130	−	21.5101i	0.263428	−	0.843049i
$652$	−1.26617	−	4.88313i	−0.0495871	−	0.191238i
$653$	−0.988002	−	0.988002i	−0.0386635	−	0.0386635i	0.687511	−	0.726174i	$-0.258703\pi$
$653$	−0.988002	−	0.988002i	−0.0386635	−	0.0386635i	−0.726174	+	0.687511i	$0.758703\pi$
$654$	−5.44827	−	24.7479i	−0.213044	−	0.967718i
$655$		−	17.2850i		−	0.675381i
$656$	0.753815	+	1.35586i	0.0294315	+	0.0529373i
$657$	−24.2813	+	35.0601i	−0.947304	+	1.36782i
$658$	0.00104776	−	0.00384797i	4.08461e−5	−	0.000150009i
$659$	21.1873	−	21.1873i	0.825341	−	0.825341i	−0.161527	−	0.986868i	$-0.551642\pi$
$659$	21.1873	−	21.1873i	0.825341	−	0.825341i	0.986868	+	0.161527i	$0.0516418\pi$
$660$	13.4858	+	14.8811i	0.524932	+	0.579248i
$661$	26.2853	+	26.2853i	1.02238	+	1.02238i	0.999744	+	0.0226362i	$0.00720595\pi$
$661$	26.2853	+	26.2853i	1.02238	+	1.02238i	0.0226362	+	0.999744i	$0.492794\pi$
$662$	−17.3093	−	30.2627i	−0.672745	−	1.17619i
$663$	13.7999	+	26.3436i	0.535944	+	1.02310i
$664$	−0.417713	+	34.4128i	−0.0162104	+	1.33548i
$665$	−2.39299			−0.0927960
$666$	−19.8142	−	1.71152i	−0.767785	−	0.0663199i
$667$	−11.2636	+	11.2636i	−0.436126	+	0.436126i
$668$	1.35724	−	2.30748i	0.0525131	−	0.0892792i
$669$	−1.47798	+	4.72999i	−0.0571422	+	0.182872i
$670$	−0.401057	+	1.47290i	−0.0154942	+	0.0569031i
$671$	42.0153			1.62198
$672$	−12.6274	−	0.774886i	−0.487111	−	0.0298919i
$673$	27.0401			1.04232			0.521159	−	0.853459i	$-0.325500\pi$
$673$	27.0401			1.04232			0.521159	+	0.853459i	$0.325500\pi$
$674$	6.85209	−	25.1647i	0.263933	−	0.969306i
$675$	−4.09784	+	3.19496i	−0.157726	+	0.122974i
$676$	−26.1522	+	44.4622i	−1.00585	+	1.71008i
$677$	24.4176	−	24.4176i	0.938445	−	0.938445i	−0.0597673	−	0.998212i	$-0.519036\pi$
$677$	24.4176	−	24.4176i	0.938445	−	0.938445i	0.998212	+	0.0597673i	$0.0190359\pi$
$678$	7.51397	+	4.80249i	0.288572	+	0.184438i
$679$	8.64017			0.331579
$680$	−7.79675	−	0.0946390i	−0.298992	−	0.00362924i
$681$	−17.7161	+	9.28045i	−0.678882	+	0.355628i
$682$	41.0182	+	71.7142i	1.57067	+	2.74608i
$683$	11.1883	+	11.1883i	0.428110	+	0.428110i	0.887984	−	0.459874i	$-0.152105\pi$
$683$	11.1883	+	11.1883i	0.428110	+	0.428110i	−0.459874	+	0.887984i	$0.652105\pi$
$684$	3.83395	−	10.4380i	0.146595	−	0.399106i
$685$	−12.4757	+	12.4757i	−0.476670	+	0.476670i
$686$	−5.91659	+	21.7290i	−0.225897	+	0.829616i
$687$	12.0781	+	23.0567i	0.460808	+	0.879668i
$688$	19.9283	+	5.68698i	0.759761	+	0.216814i
$689$			15.5768i			0.593428i
$690$	6.60352	−	1.45377i	0.251392	−	0.0553441i
$691$	18.8638	+	18.8638i	0.717613	+	0.717613i	0.968116	−	0.250503i	$-0.0805960\pi$
$691$	18.8638	+	18.8638i	0.717613	+	0.717613i	−0.250503	+	0.968116i	$0.580596\pi$
$692$	−0.162092	−	0.625126i	−0.00616181	−	0.0237637i
$693$	−4.01336	−	22.0952i	−0.152455	−	0.839325i
$694$	−8.35313	+	4.77772i	−0.317080	+	0.181360i
$695$			21.4776i			0.814690i
$696$	−26.8786	−	8.75827i	−1.01883	−	0.331981i
$697$		−	1.06916i		−	0.0404971i
$698$	11.2954	+	19.7482i	0.427536	+	0.747482i
$699$	21.9165	+	6.84828i	0.828959	+	0.259026i
$700$	1.30925	−	2.22590i	0.0494852	−	0.0841312i
$701$	9.26133	+	9.26133i	0.349796	+	0.349796i	0.860033	−	0.510238i	$-0.170443\pi$
$701$	9.26133	+	9.26133i	0.349796	+	0.349796i	−0.510238	+	0.860033i	$0.670443\pi$
$702$	17.3592	−	42.3486i	0.655183	−	1.59834i
$703$			8.68763i			0.327660i
$704$	33.5812	−	31.9892i	1.26564	−	1.20564i
$705$	−0.00335089	+	0.00175534i	−0.000126202	+	6.61099e-5i
$706$	38.7665	+	10.5558i	1.45900	+	0.397271i
$707$	8.15154	−	8.15154i	0.306570	−	0.306570i
$708$	−0.0671882	+	1.36587i	−0.00252509	+	0.0513327i
$709$	−21.8388	−	21.8388i	−0.820174	−	0.820174i	0.165959	−	0.986133i	$-0.446928\pi$
$709$	−21.8388	−	21.8388i	−0.820174	−	0.820174i	−0.986133	+	0.165959i	$0.946928\pi$
$710$	11.6083	−	6.63960i	0.435653	−	0.249180i
$711$	−14.5900	+	21.0667i	−0.547168	+	0.790063i
$712$	−9.45321	+	9.22647i	−0.354274	+	0.345777i
$713$	27.8161			1.04172
$714$	7.34667	+	4.69556i	0.274942	+	0.175727i
$715$	25.5320	−	25.5320i	0.954842	−	0.954842i
$716$	−4.07255	+	1.05599i	−0.152198	+	0.0394643i
$717$	30.7058	+	9.59468i	1.14673	+	0.358320i
$718$	−36.2197	−	9.86227i	−1.35171	−	0.368057i
$719$	−45.7622			−1.70664			−0.853322	−	0.521385i	$-0.825416\pi$
$719$	−45.7622			−1.70664			−0.853322	+	0.521385i	$0.825416\pi$
$720$	7.61154	+	9.27709i	0.283665	+	0.345737i
$721$	2.88055			0.107277
$722$	21.2393	+	5.78326i	0.790446	+	0.215231i
$723$	41.8049	+	13.0628i	1.55474	+	0.485811i
$724$	6.35952	+	24.5262i	0.236350	+	0.911509i
$725$	4.08036	−	4.08036i	0.151541	−	0.151541i
$726$	46.6646	+	29.8253i	1.73189	+	1.10692i
$727$	18.7642			0.695926			0.347963	−	0.937508i	$-0.386873\pi$
$727$	18.7642			0.695926			0.347963	+	0.937508i	$0.386873\pi$
$728$	−0.276078	+	22.7444i	−0.0102321	+	0.842965i
$729$	−6.58452	+	26.1848i	−0.243871	+	0.969808i
$730$	−17.4512	+	9.98153i	−0.645898	+	0.369433i
$731$	−10.0994	−	10.0994i	−0.373541	−	0.373541i
$732$	25.0751	+	1.23346i	0.926801	+	0.0455899i
$733$	−21.7504	+	21.7504i	−0.803370	+	0.803370i	−0.983621	−	0.180251i	$-0.942309\pi$
$733$	−21.7504	+	21.7504i	−0.803370	+	0.803370i	0.180251	+	0.983621i	$0.442309\pi$
$734$	−6.07695	−	1.65469i	−0.224304	−	0.0610759i
$735$	8.18204	−	4.28610i	0.301799	−	0.158095i
$736$	−3.73562	−	15.1620i	−0.137697	−	0.558877i
$737$			6.25778i			0.230508i
$738$	−1.25930	+	1.05904i	−0.0463554	+	0.0389839i
$739$	−3.50532	−	3.50532i	−0.128945	−	0.128945i	0.639689	−	0.768634i	$-0.279063\pi$
$739$	−3.50532	−	3.50532i	−0.128945	−	0.128945i	−0.768634	+	0.639689i	$0.779063\pi$
$740$	−8.08104	−	4.75319i	−0.297065	−	0.174731i
$741$	−19.0830	−	5.96288i	−0.701031	−	0.219052i
$742$	2.26741	+	3.96422i	0.0832391	+	0.145531i
$743$		−	47.3640i		−	1.73762i	−0.495148	−	0.868809i	$-0.664886\pi$
$743$		−	47.3640i		−	1.73762i	0.495148	−	0.868809i	$-0.335114\pi$
$744$	22.3747	+	44.0038i	0.820296	+	1.61326i
$745$		−	3.28996i		−	0.120535i
$746$	−9.58087	+	5.47995i	−0.350780	+	0.200635i
$747$	−35.9154	+	6.52366i	−1.31407	+	0.238688i
$748$	−30.9408	+	8.02280i	−1.13131	+	0.293343i
$749$	2.42894	+	2.42894i	0.0887514	+	0.0887514i
$750$	−2.39220	+	0.526646i	−0.0873510	+	0.0192304i
$751$			39.3076i			1.43436i	0.696890	+	0.717178i	$0.254567\pi$
$751$			39.3076i			1.43436i	−0.696890	+	0.717178i	$0.745433\pi$
$752$	0.00424501	+	0.00763532i	0.000154799	+	0.000278431i
$753$	−14.9446	−	28.5288i	−0.544611	−	1.03965i
$754$	−13.3536	+	49.0418i	−0.486309	+	1.78600i
$755$	2.58307	−	2.58307i	0.0940074	−	0.0940074i
$756$	−1.74655	−	13.3044i	−0.0635214	−	0.483876i
$757$	10.8046	+	10.8046i	0.392702	+	0.392702i	0.875649	−	0.482948i	$-0.160434\pi$
$757$	10.8046	+	10.8046i	0.392702	+	0.392702i	−0.482948	+	0.875649i	$0.660434\pi$
$758$	−10.9272	−	19.1045i	−0.396892	−	0.693906i
$759$	24.5535	−	12.8622i	0.891237	−	0.466868i
$760$	3.75132	−	3.66135i	0.136075	−	0.132811i
$761$	5.48314			0.198764			0.0993818	−	0.995049i	$-0.468313\pi$
$761$	5.48314			0.198764			0.0993818	+	0.995049i	$0.468313\pi$
$762$	−20.6496	−	13.1980i	−0.748055	−	0.478113i
$763$	−9.44535	+	9.44535i	−0.341944	+	0.341944i
$764$	8.97262	+	5.27761i	0.324618	+	0.190937i
$765$	−1.47803	−	8.13716i	−0.0534384	−	0.294200i
$766$	0.648345	−	2.38108i	0.0234256	−	0.0860319i
$767$	2.45874			0.0887801
$768$	20.9807	−	18.1056i	0.757075	−	0.653328i
$769$	−8.83223			−0.318498			−0.159249	−	0.987238i	$-0.550907\pi$
$769$	−8.83223			−0.318498			−0.159249	+	0.987238i	$0.550907\pi$
$770$	2.78125	−	10.2143i	0.100229	−	0.368098i
$771$	14.1997	−	45.4434i	0.511391	−	1.63660i
$772$	−24.1724	−	14.2180i	−0.869984	−	0.511716i
$773$	−6.38774	+	6.38774i	−0.229751	+	0.229751i	−0.812589	−	0.582838i	$-0.801942\pi$
$773$	−6.38774	+	6.38774i	−0.229751	+	0.229751i	0.582838	+	0.812589i	$0.301942\pi$
$774$	−1.89164	+	21.8995i	−0.0679936	+	0.787160i
$775$	−10.0767			−0.361966
$776$	−13.5446	+	13.2197i	−0.486223	+	0.474561i
$777$	4.86469	+	9.28654i	0.174520	+	0.333153i
$778$	0.0190720	+	0.0333446i	0.000683765	+	0.00119546i
$779$	0.508243	+	0.508243i	0.0182097	+	0.0182097i
$780$	15.9873	−	14.4882i	0.572436	−	0.518759i
$781$	38.7642	−	38.7642i	1.38709	−	1.38709i
$782$	−2.82744	+	10.3839i	−0.101109	+	0.371329i
$783$	3.68408	−	29.7572i	0.131658	−	1.06344i
$784$	−10.3653	−	18.6436i	−0.370188	−	0.665841i
$785$		−	7.88246i		−	0.281337i
$786$	−9.10308	−	41.3493i	−0.324696	−	1.47488i
$787$	28.0915	+	28.0915i	1.00135	+	1.00135i	0.999999	+	0.00135518i	$0.000431367\pi$
$787$	28.0915	+	28.0915i	1.00135	+	1.00135i	0.00135518	+	0.999999i	$0.499569\pi$
$788$	8.83977	−	2.29211i	0.314904	−	0.0816530i
$789$	−6.35990	+	20.3536i	−0.226419	+	0.724606i
$790$	−10.4860	+	5.99765i	−0.373074	+	0.213387i
$791$		−	4.70074i		−	0.167139i
$792$	40.0978	+	28.4965i	1.42481	+	1.01258i
$793$		−	45.1383i		−	1.60291i
$794$	−22.1354	−	38.7003i	−0.785554	−	1.37342i
$795$	1.29196	−	4.13466i	0.0458212	−	0.146641i
$796$	−14.6965	−	8.64433i	−0.520903	−	0.306390i
$797$	33.0086	+	33.0086i	1.16922	+	1.16922i	0.982392	+	0.186832i	$0.0598220\pi$
$797$	33.0086	+	33.0086i	1.16922	+	1.16922i	0.186832	+	0.982392i	$0.440178\pi$
$798$	−5.72451	+	1.26026i	−0.202645	+	0.0446126i
$799$		−	0.00602080i		−	0.000213001i
$800$	1.35327	+	5.49260i	0.0478455	+	0.194193i
$801$	−11.5182	−	7.97707i	−0.406975	−	0.281856i
$802$	−43.6108	−	11.8748i	−1.53995	−	0.419313i
$803$	−58.2755	+	58.2755i	−2.05650	+	2.05650i
$804$	−0.183712	+	3.73470i	−0.00647903	+	0.131713i
$805$	−2.52032	−	2.52032i	−0.0888296	−	0.0888296i
$806$	77.0447	−	44.0671i	2.71378	−	1.55220i
$807$	−5.68419	−	10.8509i	−0.200093	−	0.381971i
$808$	−0.306500	+	25.2507i	−0.0107826	+	0.888318i
$809$	−47.8351			−1.68179			−0.840897	−	0.541195i	$-0.817972\pi$
$809$	−47.8351			−1.68179			−0.840897	+	0.541195i	$0.817972\pi$
$810$	−8.12025	+	9.80110i	−0.285317	+	0.344375i
$811$	7.63096	−	7.63096i	0.267959	−	0.267959i	−0.560318	−	0.828277i	$-0.689321\pi$
$811$	7.63096	−	7.63096i	0.267959	−	0.267959i	0.828277	+	0.560318i	$0.189321\pi$
$812$	3.74025	+	14.4247i	0.131257	+	0.506208i
$813$	1.35527	−	4.33725i	0.0475312	−	0.152114i
$814$	−37.0826	−	10.0972i	−1.29974	−	0.353907i
$815$	2.52231			0.0883526
$816$	−18.7013	+	3.87973i	−0.654675	+	0.135818i
$817$	9.60192			0.335929
$818$	−21.8175	−	5.94070i	−0.762832	−	0.207712i
$819$	−23.7375	+	4.31167i	−0.829455	+	0.150662i
$820$	−0.750828	+	0.194686i	−0.0262201	+	0.00679873i
$821$	−7.10751	+	7.10751i	−0.248054	+	0.248054i	−0.820171	−	0.572118i	$-0.806122\pi$
$821$	−7.10751	+	7.10751i	−0.248054	+	0.248054i	0.572118	+	0.820171i	$0.306122\pi$
$822$	−23.2741	+	36.4146i	−0.811777	+	1.27010i
$823$	−0.240830			−0.00839482			−0.00419741	−	0.999991i	$-0.501336\pi$
$823$	−0.240830			−0.00839482			−0.00419741	+	0.999991i	$0.501336\pi$
$824$	−4.51565	+	4.40734i	−0.157310	+	0.153537i
$825$	−8.89481	+	4.65948i	−0.309678	+	0.162222i
$826$	0.625739	−	0.357903i	0.0217723	−	0.0124530i
$827$	18.9041	+	18.9041i	0.657359	+	0.657359i	0.954754	−	0.297395i	$-0.0961180\pi$
$827$	18.9041	+	18.9041i	0.657359	+	0.657359i	−0.297395	+	0.954754i	$0.596118\pi$
$828$	15.0314	−	6.95544i	0.522376	−	0.241718i
$829$	12.3933	−	12.3933i	0.430437	−	0.430437i	−0.458340	−	0.888777i	$-0.651556\pi$
$829$	12.3933	−	12.3933i	0.430437	−	0.430437i	0.888777	+	0.458340i	$0.151556\pi$
$830$	−16.6032	−	4.52089i	−0.576305	−	0.156922i
$831$	3.57198	+	6.81880i	0.123911	+	0.236542i
$832$	−34.3669	−	36.0773i	−1.19146	−	1.25076i
$833$			14.7013i			0.509370i
$834$	11.3111	+	51.3787i	0.391670	+	1.77910i
$835$	0.946479	+	0.946479i	0.0327542	+	0.0327542i
$836$	10.8945	−	18.5221i	0.376795	−	0.640600i
$837$	−41.2927	+	32.1946i	−1.42728	+	1.11281i
$838$	−0.753894	−	1.31807i	−0.0260428	−	0.0455319i
$839$		−	8.32262i		−	0.287329i	−0.989626	−	0.143664i	$-0.954111\pi$
$839$		−	8.32262i		−	0.287329i	0.989626	−	0.143664i	$-0.0458886\pi$
$840$	1.95974	−	6.01433i	0.0676175	−	0.207514i
$841$			4.29862i			0.148228i
$842$	−21.5784	+	12.3422i	−0.743641	+	0.425339i
$843$	3.38551	+	1.05788i	0.116603	+	0.0364352i
$844$	5.56029	+	21.4439i	0.191393	+	0.738129i
$845$	−18.2374	−	18.2374i	−0.627386	−	0.627386i
$846$	−0.00709156	+	0.00596386i	−0.000243813	+	0.000205042i
$847$		−	29.1934i		−	1.00310i
$848$	−9.61984	−	2.74523i	−0.330347	−	0.0942716i
$849$	−16.5118	+	8.64961i	−0.566685	+	0.296854i
$850$	1.02428	−	3.76170i	0.0351324	−	0.129025i
$851$	−9.14991	+	9.14991i	−0.313655	+	0.313655i
$852$	24.2728	−	21.9968i	0.831573	−	0.753597i
$853$	−22.3562	−	22.3562i	−0.765462	−	0.765462i	0.211842	−	0.977304i	$-0.432054\pi$
$853$	−22.3562	−	22.3562i	−0.765462	−	0.765462i	−0.977304	+	0.211842i	$0.932054\pi$
$854$	−6.57048	−	11.4875i	−0.224837	−	0.393094i
$855$	4.57077	+	3.16555i	0.156317	+	0.108259i
$856$	−7.52403	−	0.0913288i	−0.257166	−	0.00312155i
$857$	11.4518			0.391185			0.195593	−	0.980685i	$-0.437337\pi$
$857$	11.4518			0.391185			0.195593	+	0.980685i	$0.437337\pi$
$858$	47.6314	−	74.5241i	1.62611	−	2.54421i
$859$	−16.6861	+	16.6861i	−0.569323	+	0.569323i	−0.931939	−	0.362615i	$-0.881884\pi$
$859$	−16.6861	+	16.6861i	−0.569323	+	0.569323i	0.362615	+	0.931939i	$0.381884\pi$
$860$	−5.25342	+	8.93150i	−0.179140	+	0.304562i
$861$	0.827875	+	0.258687i	0.0282139	+	0.00881603i
$862$	9.16467	−	33.6577i	0.312150	−	1.14639i
$863$	30.8952			1.05168			0.525842	−	0.850582i	$-0.323750\pi$
$863$	30.8952			1.05168			0.525842	+	0.850582i	$0.323750\pi$
$864$	23.0941	+	18.1841i	0.785677	+	0.618636i
$865$	0.322899			0.0109789
$866$	−6.59546	+	24.2222i	−0.224123	+	0.823103i
$867$	−15.5406	−	4.85601i	−0.527788	−	0.164919i
$868$	13.1930	−	22.4298i	0.447799	−	0.761316i
$869$	−35.0163	+	35.0163i	−1.18785	+	1.18785i
$870$	7.61214	−	11.9100i	0.258076	−	0.403785i
$871$	6.72292			0.227798
$872$	0.355148	−	29.2585i	0.0120268	−	0.990819i
$873$	−16.5033	−	11.4296i	−0.558553	−	0.386833i
$874$	−3.59212	−	6.28028i	−0.121505	−	0.212434i
$875$	0.913016	+	0.913016i	0.0308656	+	0.0308656i
$876$	−36.4901	+	33.0685i	−1.23289	+	1.11728i
$877$	38.6385	−	38.6385i	1.30473	−	1.30473i	0.379563	−	0.925166i	$-0.376074\pi$
$877$	38.6385	−	38.6385i	1.30473	−	1.30473i	0.925166	−	0.379563i	$-0.123926\pi$
$878$	5.78721	−	21.2538i	0.195309	−	0.717282i
$879$	49.5419	−	25.9522i	1.67101	−	0.875345i
$880$	11.2682	+	20.2677i	0.379852	+	0.683223i
$881$			18.6527i			0.628425i	0.949353	+	0.314212i	$0.101740\pi$
$881$			18.6527i			0.628425i	−0.949353	+	0.314212i	$0.898260\pi$
$882$	17.3158	−	14.5623i	0.583055	−	0.490337i
$883$	31.4827	+	31.4827i	1.05948	+	1.05948i	0.998116	+	0.0613603i	$0.0195439\pi$
$883$	31.4827	+	31.4827i	1.05948	+	1.05948i	0.0613603	+	0.998116i	$0.480456\pi$
$884$	8.61913	+	33.2406i	0.289893	+	1.11800i
$885$	−0.652643	−	0.203932i	−0.0219383	−	0.00685510i
$886$	34.0260	−	19.4618i	1.14313	−	0.653832i
$887$		−	31.5055i		−	1.05785i	−0.848669	−	0.528925i	$-0.822595\pi$
$887$		−	31.5055i		−	1.05785i	0.848669	−	0.528925i	$-0.177405\pi$
$888$	−21.8347	−	7.11475i	−0.732726	−	0.238755i
$889$			12.9184i			0.433268i
$890$	−3.27921	−	5.73319i	−0.109919	−	0.192177i
$891$	−21.5626	+	47.5123i	−0.722376	+	1.59172i
$892$	−2.90108	+	4.93221i	−0.0971353	+	0.165143i
$893$	0.00286210	+	0.00286210i	9.57767e−5	+	9.57767e-5i
$894$	−1.73265	−	7.87026i	−0.0579483	−	0.263221i
$895$		−	2.10362i		−	0.0703162i
$896$	−13.9978	−	4.17895i	−0.467633	−	0.139609i
$897$	−13.8182	−	26.3786i	−0.461378	−	0.880756i
$898$	48.5894	+	13.2304i	1.62145	+	0.441505i
$899$	41.1166	−	41.1166i	1.37131	−	1.37131i
$900$	−5.44529	+	2.51969i	−0.181510	+	0.0839897i
$901$	4.87522	+	4.87522i	0.162417	+	0.162417i
$902$	−2.76011	+	1.57870i	−0.0919017	+	0.0525648i
$903$	10.2639	−	5.37665i	0.341560	−	0.178924i
$904$	7.19228	+	7.36903i	0.239212	+	0.245090i
$905$	−12.6686			−0.421120
$906$	4.81886	−	7.53958i	0.160096	−	0.250486i
$907$	26.6887	−	26.6887i	0.886183	−	0.886183i	−0.107971	−	0.994154i	$-0.534436\pi$
$907$	26.6887	−	26.6887i	0.886183	−	0.886183i	0.994154	+	0.107971i	$0.0344355\pi$
$908$	−22.3544	+	5.79638i	−0.741856	+	0.192360i
$909$	−26.3532	+	4.78679i	−0.874081	+	0.158768i
$910$	−10.9735	−	2.98799i	−0.363769	−	0.0990508i
$911$	−39.3861			−1.30492			−0.652460	−	0.757823i	$-0.726263\pi$
$911$	−39.3861			−1.30492			−0.652460	+	0.757823i	$0.726263\pi$
$912$	7.04570	−	10.7343i	0.233306	−	0.355448i
$913$	−70.5405			−2.33455
$914$	−27.0856	−	7.37514i	−0.895911	−	0.243948i
$915$	−3.74384	+	11.9814i	−0.123767	+	0.396092i
$916$	7.54373	+	29.0932i	0.249252	+	0.961267i
$917$	−15.7815	+	15.7815i	−0.521151	+	0.521151i
$918$	−7.82116	−	18.6874i	−0.258137	−	0.616775i
$919$	−46.3916			−1.53032			−0.765158	−	0.643842i	$-0.777339\pi$
$919$	−46.3916			−1.53032			−0.765158	+	0.643842i	$0.777339\pi$
$920$	7.80711	+	0.0947648i	0.257393	+	0.00312430i
$921$	5.97035	+	11.3972i	0.196730	+	0.375551i
$922$	52.0418	−	29.7663i	1.71391	−	0.980300i
$923$	−41.6455	−	41.6455i	−1.37078	−	1.37078i
$924$	1.27401	−	25.8994i	0.0419119	−	0.852029i
$925$	3.31466	−	3.31466i	0.108985	−	0.108985i
$926$	−43.8320	−	11.9350i	−1.44041	−	0.392209i
$927$	−5.50206	−	3.81052i	−0.180711	−	0.125154i
$928$	−27.9336	−	16.8899i	−0.916965	−	0.554439i
$929$		−	52.7805i		−	1.73167i	−0.500329	−	0.865836i	$-0.666787\pi$
$929$		−	52.7805i		−	1.73167i	0.500329	−	0.865836i	$-0.333213\pi$
$930$	−24.1055	+	5.30686i	−0.790452	+	0.174019i
$931$	−6.98855	−	6.98855i	−0.229040	−	0.229040i
$932$	22.8535	+	13.4422i	0.748593	+	0.440315i
$933$	−7.58714	+	24.2811i	−0.248392	+	0.794927i
$934$	−28.5255	−	49.8726i	−0.933383	−	1.63188i
$935$		−	15.9820i		−	0.522668i
$936$	30.6147	−	43.0783i	1.00067	−	1.40806i
$937$			29.1746i			0.953093i	0.879149	+	0.476547i	$0.158112\pi$
$937$			29.1746i			0.953093i	−0.879149	+	0.476547i	$0.841888\pi$
$938$	1.71095	−	0.978611i	0.0558646	−	0.0319528i
$939$	2.25094	−	7.20366i	0.0734565	−	0.235082i
$940$	−0.00422819	+	0.00109635i	−0.000137908	+	3.57589e-5i
$941$	35.4103	+	35.4103i	1.15434	+	1.15434i	0.985673	+	0.168668i	$0.0539467\pi$
$941$	35.4103	+	35.4103i	1.15434	+	1.15434i	0.168668	+	0.985673i	$0.446053\pi$
$942$	−4.15126	−	18.8565i	−0.135256	−	0.614376i
$943$			1.07058i			0.0348628i
$944$	−0.433326	+	1.51846i	−0.0141036	+	0.0494217i
$945$	6.65844	+	0.824345i	0.216599	+	0.0268159i
$946$	−11.1599	+	40.9852i	−0.362839	+	1.33254i
$947$	16.4926	−	16.4926i	0.535937	−	0.535937i	−0.386396	−	0.922333i	$-0.626280\pi$
$947$	16.4926	−	16.4926i	0.535937	−	0.535937i	0.922333	+	0.386396i	$0.126280\pi$
$948$	−21.9260	+	19.8700i	−0.712123	+	0.645348i
$949$	62.6071	+	62.6071i	2.03231	+	2.03231i
$950$	1.30129	+	2.27511i	0.0422194	+	0.0738142i
$951$	−13.4964	−	25.7643i	−0.437652	−	0.835465i
$952$	7.03215	+	7.20496i	0.227913	+	0.233514i
$953$	19.2911			0.624902			0.312451	−	0.949934i	$-0.398850\pi$
$953$	19.2911			0.624902			0.312451	+	0.949934i	$0.398850\pi$
$954$	0.913136	−	10.5714i	0.0295639	−	0.342260i
$955$	−3.68037	+	3.68037i	−0.119094	+	0.119094i
$956$	32.0186	+	18.8330i	1.03556	+	0.609104i
$957$	17.2816	−	55.3064i	0.558636	−	1.78780i
$958$	4.77688	−	17.5433i	0.154334	−	0.566799i
$959$	22.7810			0.735635
$960$	6.12996	+	12.4267i	0.197844	+	0.401071i
$961$	−70.5400			−2.27548
$962$	−10.8477	+	39.8389i	−0.349745	+	1.28446i
$963$	−1.42633	−	7.85254i	−0.0459630	−	0.253045i
$964$	43.5922	+	25.6405i	1.40401	+	0.825824i
$965$	9.91499	−	9.91499i	0.319175	−	0.319175i
$966$	−7.35644	−	4.70181i	−0.236690	−	0.151278i
$967$	−10.5225			−0.338381			−0.169190	−	0.985583i	$-0.554115\pi$
$967$	−10.5225			−0.338381			−0.169190	+	0.985583i	$0.554115\pi$
$968$	44.6668	+	45.7645i	1.43565	+	1.47093i
$969$	−7.83886	+	4.10633i	−0.251820	+	0.131914i
$970$	−4.69847	−	8.21456i	−0.150859	−	0.263754i
$971$	18.2860	+	18.2860i	0.586825	+	0.586825i	0.936770	−	0.349945i	$-0.113800\pi$
$971$	18.2860	+	18.2860i	0.586825	+	0.586825i	−0.349945	+	0.936770i	$0.613800\pi$
$972$	−14.2636	+	27.7227i	−0.457505	+	0.889207i
$973$	19.6094	−	19.6094i	0.628647	−	0.628647i
$974$	−7.41553	+	27.2339i	−0.237609	+	0.872631i
$975$	5.00582	+	9.55596i	0.160315	+	0.306036i
$976$	27.8763	+	7.95512i	0.892299	+	0.254637i
$977$		−	22.4622i		−	0.718629i	−0.933216	−	0.359315i	$-0.883010\pi$
$977$		−	22.4622i		−	0.718629i	0.933216	−	0.359315i	$-0.116990\pi$
$978$	6.03388	−	1.32836i	0.192942	−	0.0424764i
$979$	−19.1451	−	19.1451i	−0.611880	−	0.611880i
$980$	10.3242	−	2.67701i	0.329794	−	0.0855139i
$981$	30.5360	−	5.54655i	0.974939	−	0.177088i
$982$	25.7473	−	14.7266i	0.821629	−	0.469946i
$983$			23.7731i			0.758245i	0.925346	+	0.379123i	$0.123774\pi$
$983$			23.7731i			0.758245i	−0.925346	+	0.379123i	$0.876226\pi$
$984$	−1.69360	+	0.861149i	−0.0539901	+	0.0274524i
$985$			4.56605i			0.145487i
$986$	11.1697	+	19.5285i	0.355715	+	0.621914i
$987$	0.00466207	+	0.00145676i	0.000148395	+	4.63692e-5i
$988$	−19.8988	−	11.7043i	−0.633067	−	0.372364i
$989$	10.1129	+	10.1129i	0.321570	+	0.321570i
$990$	−18.8243	+	15.8309i	−0.598276	+	0.503138i
$991$		−	6.71379i		−	0.213271i	−0.994298	−	0.106635i	$-0.965992\pi$
$991$		−	6.71379i		−	0.213271i	0.994298	−	0.106635i	$-0.0340077\pi$
$992$	13.6365	+	55.3473i	0.432961	+	1.75728i
$993$	37.8232	−	19.8134i	1.20028	−	0.628760i
$994$	−16.6607	−	4.53654i	−0.528444	−	0.143890i
$995$	6.02818	−	6.02818i	0.191106	−	0.191106i
$996$	−42.0992	−	2.07089i	−1.33396	−	0.0656185i
$997$	−23.6160	−	23.6160i	−0.747925	−	0.747925i	0.226164	−	0.974089i	$-0.427381\pi$
$997$	−23.6160	−	23.6160i	−0.747925	−	0.747925i	−0.974089	+	0.226164i	$0.927381\pi$
$998$	−32.3594	+	18.5085i	−1.02432	+	0.585878i
$999$	2.99275	−	24.1732i	0.0946863	−	0.764805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.14	✓	60
3.2	odd	2	inner	240.2.bk.b.11.17	yes	60
4.3	odd	2		960.2.bk.b.911.28		60
12.11	even	2		960.2.bk.b.911.20		60
16.3	odd	4	inner	240.2.bk.b.131.17	yes	60
16.13	even	4		960.2.bk.b.431.20		60
48.29	odd	4		960.2.bk.b.431.28		60
48.35	even	4	inner	240.2.bk.b.131.14	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.14	✓	60	1.1	even	1	trivial
240.2.bk.b.11.17	yes	60	3.2	odd	2	inner
240.2.bk.b.131.14	yes	60	48.35	even	4	inner
240.2.bk.b.131.17	yes	60	16.3	odd	4	inner
960.2.bk.b.431.20		60	16.13	even	4
960.2.bk.b.431.28		60	48.29	odd	4
960.2.bk.b.911.20		60	12.11	even	2
960.2.bk.b.911.28		60	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.371549 + 1.36453i) q^{2} +(-1.65322 - 0.516584i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.31915 - 2.06394i) q^{6} -1.29120 q^{7} +(2.02413 - 1.97558i) q^{8} +(2.46628 + 1.70806i) q^{9} +O(q^{10})\)	\(q+(-0.371549 + 1.36453i) q^{2} +(-1.65322 - 0.516584i) q^{3} +(-1.72390 - 1.01398i) q^{4} +(0.707107 - 0.707107i) q^{5} +(1.31915 - 2.06394i) q^{6} -1.29120 q^{7} +(2.02413 - 1.97558i) q^{8} +(2.46628 + 1.70806i) q^{9} +(0.702146 + 1.22760i) q^{10} +(4.09936 + 4.09936i) q^{11} +(2.32619 + 2.56688i) q^{12} +(4.40407 - 4.40407i) q^{13} +(0.479744 - 1.76189i) q^{14} +(-1.53428 + 0.803724i) q^{15} +(1.94368 + 3.49601i) q^{16} -2.75677i q^{17} +(-3.24704 + 2.73070i) q^{18} +(1.31048 + 1.31048i) q^{19} +(-1.93598 + 0.501989i) q^{20} +(2.13464 + 0.667013i) q^{21} +(-7.11683 + 4.07060i) q^{22} +2.76043i q^{23} +(-4.36688 + 2.22044i) q^{24} -1.00000i q^{25} +(4.37317 + 7.64582i) q^{26} +(-3.19496 - 4.09784i) q^{27} +(2.22590 + 1.30925i) q^{28} +(4.08036 + 4.08036i) q^{29} +(-0.526646 - 2.39220i) q^{30} -10.0767i q^{31} +(-5.49260 + 1.35327i) q^{32} +(-4.65948 - 8.89481i) q^{33} +(3.76170 + 1.02428i) q^{34} +(-0.913016 + 0.913016i) q^{35} +(-2.51969 - 5.44529i) q^{36} +(3.31466 + 3.31466i) q^{37} +(-2.27511 + 1.30129i) q^{38} +(-9.55596 + 5.00582i) q^{39} +(0.0343297 - 2.82822i) q^{40} +0.387829 q^{41} +(-1.70329 + 2.66496i) q^{42} +(3.66350 - 3.66350i) q^{43} +(-2.91022 - 11.2236i) q^{44} +(2.95170 - 0.536147i) q^{45} +(-3.76670 - 1.02564i) q^{46} +0.00218401 q^{47} +(-1.40735 - 6.78376i) q^{48} -5.33280 q^{49} +(1.36453 + 0.371549i) q^{50} +(-1.42410 + 4.55755i) q^{51} +(-12.0578 + 3.12653i) q^{52} +(-1.76845 + 1.76845i) q^{53} +(6.77872 - 2.83708i) q^{54} +5.79737 q^{55} +(-2.61355 + 2.55087i) q^{56} +(-1.48954 - 2.84349i) q^{57} +(-7.08384 + 4.05173i) q^{58} +(0.279145 + 0.279145i) q^{59} +(3.45992 + 0.170196i) q^{60} +(5.12461 - 5.12461i) q^{61} +(13.7500 + 3.74399i) q^{62} +(-3.18446 - 2.20544i) q^{63} +(0.194184 - 7.99764i) q^{64} -6.22829i q^{65} +(13.8685 - 3.05316i) q^{66} +(0.763263 + 0.763263i) q^{67} +(-2.79532 + 4.75240i) q^{68} +(1.42600 - 4.56361i) q^{69} +(-0.906611 - 1.58507i) q^{70} -9.45616i q^{71} +(8.36647 - 1.41501i) q^{72} +14.2158i q^{73} +(-5.75453 + 3.29141i) q^{74} +(-0.516584 + 1.65322i) q^{75} +(-0.930338 - 3.58795i) q^{76} +(-5.29309 - 5.29309i) q^{77} +(-3.28010 - 14.8993i) q^{78} +8.54188i q^{79} +(3.84644 + 1.09767i) q^{80} +(3.16509 + 8.42509i) q^{81} +(-0.144098 + 0.529206i) q^{82} +(-8.60385 + 8.60385i) q^{83} +(-3.00357 - 3.31435i) q^{84} +(-1.94933 - 1.94933i) q^{85} +(3.63780 + 6.36015i) q^{86} +(-4.63789 - 8.85358i) q^{87} +(16.3962 + 0.199022i) q^{88} -4.67026 q^{89} +(-0.365112 + 4.22690i) q^{90} +(-5.68653 + 5.68653i) q^{91} +(2.79903 - 4.75872i) q^{92} +(-5.20547 + 16.6590i) q^{93} +(-0.000811466 + 0.00298015i) q^{94} +1.85330 q^{95} +(9.77956 + 0.600128i) q^{96} -6.69158 q^{97} +(1.98140 - 7.27679i) q^{98} +(3.10824 + 17.1121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

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