LMFDB - Embedded newform 572.2.j.a.463.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.3
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39906 + 0.206499i) q^{2} +2.87009i q^{3} +(1.91472 - 0.577808i) q^{4} +(0.956348 + 0.956348i) q^{5} +(-0.592670 - 4.01541i) q^{6} +(3.01968 + 3.01968i) q^{7} +(-2.55948 + 1.20377i) q^{8} -5.23740 q^{9} +O(q^{10})$	\(q+(-1.39906 + 0.206499i) q^{2} +2.87009i q^{3} +(1.91472 - 0.577808i) q^{4} +(0.956348 + 0.956348i) q^{5} +(-0.592670 - 4.01541i) q^{6} +(3.01968 + 3.01968i) q^{7} +(-2.55948 + 1.20377i) q^{8} -5.23740 q^{9} +(-1.53547 - 1.14050i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.65836 + 5.49540i) q^{12} +(3.54996 - 0.630715i) q^{13} +(-4.84826 - 3.60114i) q^{14} +(-2.74480 + 2.74480i) q^{15} +(3.33228 - 2.21268i) q^{16} +3.09441i q^{17} +(7.32741 - 1.08152i) q^{18} +(-0.799483 + 0.799483i) q^{19} +(2.38372 + 1.27855i) q^{20} +(-8.66674 + 8.66674i) q^{21} +(-1.13530 - 0.843265i) q^{22} +4.89130 q^{23} +(-3.45493 - 7.34593i) q^{24} -3.17080i q^{25} +(-4.83635 + 1.61547i) q^{26} -6.42153i q^{27} +(7.52662 + 4.03703i) q^{28} +1.75141 q^{29} +(3.27333 - 4.40693i) q^{30} +(4.62689 - 4.62689i) q^{31} +(-4.20513 + 3.78377i) q^{32} +(-2.02946 + 2.02946i) q^{33} +(-0.638993 - 4.32926i) q^{34} +5.77573i q^{35} +(-10.0281 + 3.02621i) q^{36} +(6.64423 - 6.64423i) q^{37} +(0.953429 - 1.28361i) q^{38} +(1.81021 + 10.1887i) q^{39} +(-3.59898 - 1.29653i) q^{40} +(-7.43710 - 7.43710i) q^{41} +(10.3356 - 13.9149i) q^{42} -8.36259 q^{43} +(1.76248 + 0.945337i) q^{44} +(-5.00878 - 5.00878i) q^{45} +(-6.84320 + 1.01005i) q^{46} +(-1.37496 - 1.37496i) q^{47} +(6.35057 + 9.56392i) q^{48} +11.2369i q^{49} +(0.654766 + 4.43612i) q^{50} -8.88123 q^{51} +(6.43273 - 3.25883i) q^{52} -7.60379 q^{53} +(1.32604 + 8.98408i) q^{54} +1.35248i q^{55} +(-11.3638 - 4.09380i) q^{56} +(-2.29458 - 2.29458i) q^{57} +(-2.45032 + 0.361665i) q^{58} +(-4.10707 - 4.10707i) q^{59} +(-3.66955 + 6.84149i) q^{60} -12.6247 q^{61} +(-5.51784 + 7.42873i) q^{62} +(-15.8153 - 15.8153i) q^{63} +(5.10186 - 6.16206i) q^{64} +(3.99818 + 2.79181i) q^{65} +(2.42024 - 3.25841i) q^{66} +(0.199114 - 0.199114i) q^{67} +(1.78798 + 5.92492i) q^{68} +14.0384i q^{69} +(-1.19268 - 8.08057i) q^{70} +(0.835261 - 0.835261i) q^{71} +(13.4050 - 6.30464i) q^{72} +(11.4791 - 11.4791i) q^{73} +(-7.92363 + 10.6677i) q^{74} +9.10046 q^{75} +(-1.06884 + 1.99273i) q^{76} +4.27047i q^{77} +(-4.63654 - 13.8807i) q^{78} +3.28563i q^{79} +(5.30291 + 1.07073i) q^{80} +2.71815 q^{81} +(11.9407 + 8.86917i) q^{82} +(-2.54139 + 2.54139i) q^{83} +(-11.5866 + 21.6020i) q^{84} +(-2.95934 + 2.95934i) q^{85} +(11.6997 - 1.72687i) q^{86} +5.02670i q^{87} +(-2.66102 - 0.958629i) q^{88} +(1.90868 - 1.90868i) q^{89} +(8.04187 + 5.97325i) q^{90} +(12.6243 + 8.81517i) q^{91} +(9.36545 - 2.82623i) q^{92} +(13.2796 + 13.2796i) q^{93} +(2.20758 + 1.63972i) q^{94} -1.52917 q^{95} +(-10.8597 - 12.0691i) q^{96} +(-3.14829 - 3.14829i) q^{97} +(-2.32041 - 15.7211i) q^{98} +(-3.70340 - 3.70340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.39906	+	0.206499i	−0.989282	+	0.146017i
$2$	−1.39906	+	0.206499i	−0.989282	+	0.146017i
$3$			2.87009i			1.65705i	0.559955	+	0.828523i	$0.310818\pi$
$3$			2.87009i			1.65705i	−0.559955	+	0.828523i	$0.689182\pi$
$4$	1.91472	−	0.577808i	0.957358	−	0.288904i
$5$	0.956348	+	0.956348i	0.427692	+	0.427692i	0.887841	−	0.460149i	$-0.152204\pi$
$5$	0.956348	+	0.956348i	0.427692	+	0.427692i	−0.460149	+	0.887841i	$0.652204\pi$
$6$	−0.592670	−	4.01541i	−0.241957	−	1.63929i
$7$	3.01968	+	3.01968i	1.14133	+	1.14133i	0.988207	+	0.153124i	$0.0489333\pi$
$7$	3.01968	+	3.01968i	1.14133	+	1.14133i	0.153124	+	0.988207i	$0.451067\pi$
$8$	−2.55948	+	1.20377i	−0.904912	+	0.425598i
$9$	−5.23740			−1.74580
$10$	−1.53547	−	1.14050i	−0.485558	−	0.360658i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	1.65836	+	5.49540i	0.478727	+	1.58639i
$13$	3.54996	−	0.630715i	0.984581	−	0.174929i
$13$	3.54996	−	0.630715i	0.984581	−	0.174929i
$14$	−4.84826	−	3.60114i	−1.29575	−	0.962445i
$15$	−2.74480	+	2.74480i	−0.708705	+	0.708705i
$16$	3.33228	−	2.21268i	0.833069	−	0.553169i
$17$			3.09441i			0.750505i	0.926923	+	0.375253i	$0.122444\pi$
$17$			3.09441i			0.750505i	−0.926923	+	0.375253i	$0.877556\pi$
$18$	7.32741	−	1.08152i	1.72709	−	0.254916i
$19$	−0.799483	+	0.799483i	−0.183414	+	0.183414i	−0.792842	−	0.609428i	$-0.791399\pi$
$19$	−0.799483	+	0.799483i	−0.183414	+	0.183414i	0.609428	+	0.792842i	$0.291399\pi$
$20$	2.38372	+	1.27855i	0.533016	+	0.285893i
$21$	−8.66674	+	8.66674i	−1.89124	+	1.89124i
$22$	−1.13530	−	0.843265i	−0.242047	−	0.179785i
$23$	4.89130			1.01991			0.509953	−	0.860202i	$-0.329663\pi$
$23$	4.89130			1.01991			0.509953	+	0.860202i	$0.329663\pi$
$24$	−3.45493	−	7.34593i	−0.705235	−	1.49948i
$25$		−	3.17080i		−	0.634159i
$26$	−4.83635	+	1.61547i	−0.948486	+	0.316819i
$27$		−	6.42153i		−	1.23582i
$28$	7.52662	+	4.03703i	1.42240	+	0.762927i
$29$	1.75141			0.325229			0.162615	−	0.986690i	$-0.448007\pi$
$29$	1.75141			0.325229			0.162615	+	0.986690i	$0.448007\pi$
$30$	3.27333	−	4.40693i	0.597626	−	0.804592i
$31$	4.62689	−	4.62689i	0.831015	−	0.831015i	−0.156641	−	0.987656i	$-0.550067\pi$
$31$	4.62689	−	4.62689i	0.831015	−	0.831015i	0.987656	+	0.156641i	$0.0500665\pi$
$32$	−4.20513	+	3.78377i	−0.743368	+	0.668882i
$33$	−2.02946	+	2.02946i	−0.353283	+	0.353283i
$34$	−0.638993	−	4.32926i	−0.109586	−	0.742462i
$35$			5.77573i			0.976276i
$36$	−10.0281	+	3.02621i	−1.67136	+	0.504368i
$37$	6.64423	−	6.64423i	1.09231	−	1.09231i	0.0970230	−	0.995282i	$-0.469068\pi$
$37$	6.64423	−	6.64423i	1.09231	−	1.09231i	0.995282	−	0.0970230i	$-0.0309320\pi$
$38$	0.953429	−	1.28361i	0.154667	−	0.208230i
$39$	1.81021	+	10.1887i	0.289865	+	1.63150i
$40$	−3.59898	−	1.29653i	−0.569049	−	0.204999i
$41$	−7.43710	−	7.43710i	−1.16148	−	1.16148i	−0.984152	−	0.177328i	$-0.943255\pi$
$41$	−7.43710	−	7.43710i	−1.16148	−	1.16148i	−0.177328	−	0.984152i	$-0.556745\pi$
$42$	10.3356	−	13.9149i	1.59481	−	2.14712i
$43$	−8.36259			−1.27528			−0.637642	−	0.770333i	$-0.720090\pi$
$43$	−8.36259			−1.27528			−0.637642	+	0.770333i	$0.720090\pi$
$44$	1.76248	+	0.945337i	0.265704	+	0.142515i
$45$	−5.00878	−	5.00878i	−0.746665	−	0.746665i
$46$	−6.84320	+	1.01005i	−1.00897	+	0.148924i
$47$	−1.37496	−	1.37496i	−0.200559	−	0.200559i	0.599680	−	0.800240i	$-0.295294\pi$
$47$	−1.37496	−	1.37496i	−0.200559	−	0.200559i	−0.800240	+	0.599680i	$0.795294\pi$
$48$	6.35057	+	9.56392i	0.916626	+	1.38043i
$49$			11.2369i			1.60527i
$50$	0.654766	+	4.43612i	0.0925979	+	0.627362i
$51$	−8.88123			−1.24362
$52$	6.43273	−	3.25883i	0.892059	−	0.451919i
$53$	−7.60379			−1.04446			−0.522230	−	0.852804i	$-0.674900\pi$
$53$	−7.60379			−1.04446			−0.522230	+	0.852804i	$0.674900\pi$
$54$	1.32604	+	8.98408i	0.180451	+	1.22258i
$55$			1.35248i			0.182368i
$56$	−11.3638	−	4.09380i	−1.51855	−	0.547056i
$57$	−2.29458	−	2.29458i	−0.303925	−	0.303925i
$58$	−2.45032	+	0.361665i	−0.321743	+	0.0474889i
$59$	−4.10707	−	4.10707i	−0.534695	−	0.534695i	0.387271	−	0.921966i	$-0.373418\pi$
$59$	−4.10707	−	4.10707i	−0.534695	−	0.534695i	−0.921966	+	0.387271i	$0.873418\pi$
$60$	−3.66955	+	6.84149i	−0.473737	+	0.883232i
$61$	−12.6247			−1.61643			−0.808216	−	0.588886i	$-0.799567\pi$
$61$	−12.6247			−1.61643			−0.808216	+	0.588886i	$0.799567\pi$
$62$	−5.51784	+	7.42873i	−0.700766	+	0.943450i
$63$	−15.8153	−	15.8153i	−1.99253	−	1.99253i
$64$	5.10186	−	6.16206i	0.637733	−	0.770258i
$65$	3.99818	+	2.79181i	0.495913	+	0.346282i
$66$	2.42024	−	3.25841i	0.297911	−	0.401082i
$67$	0.199114	−	0.199114i	0.0243257	−	0.0243257i	−0.694839	−	0.719165i	$-0.744525\pi$
$67$	0.199114	−	0.199114i	0.0243257	−	0.0243257i	0.719165	+	0.694839i	$0.244525\pi$
$68$	1.78798	+	5.92492i	0.216824	+	0.718502i
$69$			14.0384i			1.69003i
$70$	−1.19268	−	8.08057i	−0.142553	−	0.965813i
$71$	0.835261	−	0.835261i	0.0991272	−	0.0991272i	−0.655804	−	0.754931i	$-0.727670\pi$
$71$	0.835261	−	0.835261i	0.0991272	−	0.0991272i	0.754931	+	0.655804i	$0.227670\pi$
$72$	13.4050	−	6.30464i	1.57980	−	0.743009i
$73$	11.4791	−	11.4791i	1.34353	−	1.34353i	0.451014	−	0.892517i	$-0.351062\pi$
$73$	11.4791	−	11.4791i	1.34353	−	1.34353i	0.892517	−	0.451014i	$-0.148938\pi$
$74$	−7.92363	+	10.6677i	−0.921103	+	1.24009i
$75$	9.10046			1.05083
$76$	−1.06884	+	1.99273i	−0.122604	+	0.228582i
$77$			4.27047i			0.486665i
$78$	−4.63654	−	13.8807i	−0.524984	−	1.57168i
$79$			3.28563i			0.369662i	0.982770	+	0.184831i	$0.0591737\pi$
$79$			3.28563i			0.369662i	−0.982770	+	0.184831i	$0.940826\pi$
$80$	5.30291	+	1.07073i	0.592883	+	0.119711i
$81$	2.71815			0.302016
$82$	11.9407	+	8.86917i	1.31863	+	0.979436i
$83$	−2.54139	+	2.54139i	−0.278954	+	0.278954i	−0.832691	−	0.553737i	$-0.813201\pi$
$83$	−2.54139	+	2.54139i	−0.278954	+	0.278954i	0.553737	+	0.832691i	$0.313201\pi$
$84$	−11.5866	+	21.6020i	−1.26421	+	2.35698i
$85$	−2.95934	+	2.95934i	−0.320985	+	0.320985i
$86$	11.6997	−	1.72687i	1.26161	−	0.186213i
$87$			5.02670i			0.538919i
$88$	−2.66102	−	0.958629i	−0.283666	−	0.102190i
$89$	1.90868	−	1.90868i	0.202319	−	0.202319i	−0.598674	−	0.800993i	$-0.704305\pi$
$89$	1.90868	−	1.90868i	0.202319	−	0.202319i	0.800993	+	0.598674i	$0.204305\pi$
$90$	8.04187	+	5.97325i	0.847688	+	0.629636i
$91$	12.6243	+	8.81517i	1.32338	+	0.924081i
$92$	9.36545	−	2.82623i	0.976415	−	0.294655i
$93$	13.2796	+	13.2796i	1.37703	+	1.37703i
$94$	2.20758	+	1.63972i	0.227694	+	0.169124i
$95$	−1.52917			−0.156889
$96$	−10.8597	−	12.0691i	−1.10837	−	1.23180i
$97$	−3.14829	−	3.14829i	−0.319660	−	0.319660i	0.528976	−	0.848637i	$-0.322576\pi$
$97$	−3.14829	−	3.14829i	−0.319660	−	0.319660i	−0.848637	+	0.528976i	$0.822576\pi$
$98$	−2.32041	−	15.7211i	−0.234397	−	1.58807i
$99$	−3.70340	−	3.70340i	−0.372206	−	0.372206i
$100$	−1.83211	−	6.07117i	−0.183211	−	0.607117i
$101$		−	15.4324i		−	1.53558i	−0.640699	−	0.767792i	$-0.721355\pi$
$101$		−	15.4324i		−	1.53558i	0.640699	−	0.767792i	$-0.278645\pi$
$102$	12.4253	−	1.83397i	1.23029	−	0.181590i
$103$	9.94044			0.979461			0.489730	−	0.871874i	$-0.337095\pi$
$103$	9.94044			0.979461			0.489730	+	0.871874i	$0.337095\pi$
$104$	−8.32680	+	5.88764i	−0.816510	+	0.577331i
$105$	−16.5768			−1.61773
$106$	10.6381	−	1.57018i	1.03327	−	0.152509i
$107$		−	9.02118i		−	0.872110i	−0.899920	−	0.436055i	$-0.856375\pi$
$107$		−	9.02118i		−	0.872110i	0.899920	−	0.436055i	$-0.143625\pi$
$108$	−3.71041	−	12.2954i	−0.357034	−	1.18313i
$109$	3.02629	+	3.02629i	0.289866	+	0.289866i	0.837027	−	0.547161i	$-0.184291\pi$
$109$	3.02629	+	3.02629i	0.289866	+	0.289866i	−0.547161	+	0.837027i	$0.684291\pi$
$110$	−0.279286	−	1.89220i	−0.0266289	−	0.180414i
$111$	19.0695	+	19.0695i	1.81000	+	1.81000i
$112$	16.7440	+	3.38083i	1.58216	+	0.319459i
$113$	−7.99996			−0.752573			−0.376287	−	0.926503i	$-0.622799\pi$
$113$	−7.99996			−0.752573			−0.376287	+	0.926503i	$0.622799\pi$
$114$	3.68408	+	2.73642i	0.345046	+	0.256289i
$115$	4.67778	+	4.67778i	0.436206	+	0.436206i
$116$	3.35346	−	1.01198i	0.311361	−	0.0939599i
$117$	−18.5925	+	3.30331i	−1.71888	+	0.305391i
$118$	6.59413	+	4.89792i	0.607039	+	0.450890i
$119$	−9.34413	+	9.34413i	−0.856575	+	0.856575i
$120$	3.72115	−	10.3294i	0.339693	−	0.942939i
$121$			1.00000i			0.0909091i
$122$	17.6627	−	2.60700i	1.59911	−	0.236026i
$123$	21.3451	−	21.3451i	1.92463	−	1.92463i
$124$	6.18574	−	11.5326i	0.555495	−	1.03566i
$125$	7.81413	−	7.81413i	0.698917	−	0.698917i
$126$	25.3923	+	18.8606i	2.26212	+	1.68024i
$127$	−8.72641			−0.774344			−0.387172	−	0.922008i	$-0.626548\pi$
$127$	−8.72641			−0.774344			−0.387172	+	0.922008i	$0.626548\pi$
$128$	−5.86533	+	9.67460i	−0.518427	+	0.855122i
$129$		−	24.0014i		−	2.11320i
$130$	−6.17018	−	3.08028i	−0.541161	−	0.270159i
$131$			7.83008i			0.684117i	0.939679	+	0.342059i	$0.111124\pi$
$131$			7.83008i			0.684117i	−0.939679	+	0.342059i	$0.888876\pi$
$132$	−2.71320	+	5.05847i	−0.236154	+	0.440283i
$133$	−4.82836			−0.418672
$134$	−0.237455	+	0.319689i	−0.0205130	+	0.0276169i
$135$	6.14122	−	6.14122i	0.528552	−	0.528552i
$136$	−3.72497	−	7.92009i	−0.319413	−	0.679142i
$137$	3.52799	−	3.52799i	0.301416	−	0.301416i	−0.540151	−	0.841568i	$-0.681633\pi$
$137$	3.52799	−	3.52799i	0.301416	−	0.301416i	0.841568	+	0.540151i	$0.181633\pi$
$138$	−2.89893	−	19.6406i	−0.246773	−	1.67192i
$139$			15.4133i			1.30734i	0.756779	+	0.653670i	$0.226772\pi$
$139$			15.4133i			1.30734i	−0.756779	+	0.653670i	$0.773228\pi$
$140$	3.33726	+	11.0589i	0.282050	+	0.934646i
$141$	3.94626	−	3.94626i	0.332335	−	0.332335i
$142$	−0.996096	+	1.34106i	−0.0835905	+	0.112539i
$143$	2.95618	+	2.06422i	0.247208	+	0.172618i
$144$	−17.4525	+	11.5887i	−1.45437	+	0.965722i
$145$	1.67496	+	1.67496i	0.139098	+	0.139098i
$146$	−13.6895	+	18.4304i	−1.13295	+	1.52531i
$147$	−32.2509			−2.66001
$148$	8.88273	−	16.5609i	0.730156	−	1.36130i
$149$	12.3704	+	12.3704i	1.01343	+	1.01343i	0.999909	+	0.0135174i	$0.00430286\pi$
$149$	12.3704	+	12.3704i	1.01343	+	1.01343i	0.0135174	+	0.999909i	$0.495697\pi$
$150$	−12.7321	+	1.87924i	−1.03957	+	0.153439i
$151$	−0.335448	−	0.335448i	−0.0272984	−	0.0272984i	0.693326	−	0.720624i	$-0.256145\pi$
$151$	−0.335448	−	0.335448i	−0.0272984	−	0.0272984i	−0.720624	+	0.693326i	$0.756145\pi$
$152$	1.08386	−	3.00865i	0.0879129	−	0.244034i
$153$		−	16.2067i		−	1.31023i
$154$	−0.881848	−	5.97463i	−0.0710613	−	0.481449i
$155$	8.84985			0.710837
$156$	9.35313	+	18.4625i	0.748850	+	1.47818i
$157$	−3.40997			−0.272146			−0.136073	−	0.990699i	$-0.543448\pi$
$157$	−3.40997			−0.272146			−0.136073	+	0.990699i	$0.543448\pi$
$158$	−0.678479	−	4.59677i	−0.0539769	−	0.365700i
$159$		−	21.8235i		−	1.73072i
$160$	−7.64017	−	0.402965i	−0.604008	−	0.0318572i
$161$	14.7701	+	14.7701i	1.16405	+	1.16405i
$162$	−3.80284	+	0.561295i	−0.298780	+	0.0440995i
$163$	7.41942	+	7.41942i	0.581134	+	0.581134i	0.935215	−	0.354081i	$-0.115206\pi$
$163$	7.41942	+	7.41942i	0.581134	+	0.581134i	−0.354081	+	0.935215i	$0.615206\pi$
$164$	−18.5372	−	9.94272i	−1.44751	−	0.776396i
$165$	−3.88174			−0.302193
$166$	3.03076	−	4.08035i	0.235232	−	0.316697i
$167$	−10.7550	−	10.7550i	−0.832245	−	0.832245i	0.155579	−	0.987823i	$-0.450276\pi$
$167$	−10.7550	−	10.7550i	−0.832245	−	0.832245i	−0.987823	+	0.155579i	$0.950276\pi$
$168$	11.7495	−	32.6151i	0.906497	−	2.51631i
$169$	12.2044	−	4.47802i	0.938800	−	0.344463i
$170$	3.52918	−	4.75138i	0.270676	−	0.364414i
$171$	4.18721	−	4.18721i	0.320204	−	0.320204i
$172$	−16.0120	+	4.83197i	−1.22090	+	0.368434i
$173$			24.5007i			1.86275i	0.364060	+	0.931375i	$0.381390\pi$
$173$			24.5007i			1.86275i	−0.364060	+	0.931375i	$0.618610\pi$
$174$	−1.03801	−	7.03264i	−0.0786913	−	0.533143i
$175$	9.57478	−	9.57478i	0.723785	−	0.723785i
$176$	3.92087	+	0.791678i	0.295547	+	0.0596750i
$177$	11.7877	−	11.7877i	0.886014	−	0.886014i
$178$	−2.27621	+	3.06449i	−0.170609	+	0.229693i
$179$	21.4050			1.59988			0.799941	−	0.600079i	$-0.204864\pi$
$179$	21.4050			1.59988			0.799941	+	0.600079i	$0.204864\pi$
$180$	−12.4845	−	6.69628i	−0.930540	−	0.499111i
$181$		−	1.28642i		−	0.0956186i	−0.998856	−	0.0478093i	$-0.984776\pi$
$181$		−	1.28642i		−	0.0956186i	0.998856	−	0.0478093i	$-0.0152240\pi$
$182$	−19.4824	−	9.72602i	−1.44413	−	0.720940i
$183$		−	36.2341i		−	2.67850i
$184$	−12.5192	+	5.88801i	−0.922926	+	0.434070i
$185$	12.7084			0.934340
$186$	−21.3211	−	15.8367i	−1.56334	−	1.16120i
$187$	−2.18808	+	2.18808i	−0.160008	+	0.160008i
$188$	−3.42713	−	1.83820i	−0.249949	−	0.134065i
$189$	19.3909	−	19.3909i	1.41048	−	1.41048i
$190$	2.13939	−	0.315772i	0.155208	−	0.0229085i
$191$		−	16.5842i		−	1.19999i	−0.800005	−	0.599994i	$-0.795170\pi$
$191$		−	16.5842i		−	1.19999i	0.800005	−	0.599994i	$-0.204830\pi$
$192$	17.6856	+	14.6428i	1.27635	+	1.05675i
$193$	18.6333	−	18.6333i	1.34125	−	1.34125i	0.446441	−	0.894813i	$-0.352691\pi$
$193$	18.6333	−	18.6333i	1.34125	−	1.34125i	0.894813	−	0.446441i	$-0.147309\pi$
$194$	5.05475	+	3.75451i	0.362910	+	0.269558i
$195$	−8.01275	+	11.4751i	−0.573805	+	0.821751i
$196$	6.49277	+	21.5155i	0.463769	+	1.53682i
$197$	−0.958368	−	0.958368i	−0.0682809	−	0.0682809i	0.672142	−	0.740423i	$-0.265375\pi$
$197$	−0.958368	−	0.958368i	−0.0682809	−	0.0682809i	−0.740423	+	0.672142i	$0.765375\pi$
$198$	5.94601	+	4.41652i	0.422565	+	0.313868i
$199$	−19.6428			−1.39244			−0.696220	−	0.717828i	$-0.745136\pi$
$199$	−19.6428			−1.39244			−0.696220	+	0.717828i	$0.745136\pi$
$200$	3.81692	+	8.11558i	0.269897	+	0.573858i
$201$	0.571475	+	0.571475i	0.0403087	+	0.0403087i
$202$	3.18678	+	21.5908i	0.224221	+	1.51913i
$203$	5.28870	+	5.28870i	0.371194	+	0.371194i
$204$	−17.0050	+	5.13165i	−1.19059	+	0.359287i
$205$		−	14.2249i		−	0.993511i
$206$	−13.9072	+	2.05269i	−0.968963	+	0.143018i
$207$	−25.6177			−1.78055
$208$	10.4339	−	9.95662i	0.723459	−	0.690367i
$209$	−1.13064			−0.0782079
$210$	23.1919	−	3.42310i	1.60040	−	0.236217i
$211$			22.8011i			1.56969i	0.619691	+	0.784846i	$0.287258\pi$
$211$			22.8011i			1.56969i	−0.619691	+	0.784846i	$0.712742\pi$
$212$	−14.5591	+	4.39353i	−0.999923	+	0.301749i
$213$	2.39727	+	2.39727i	0.164258	+	0.164258i
$214$	1.86287	+	12.6211i	0.127343	+	0.862763i
$215$	−7.99755	−	7.99755i	−0.545428	−	0.545428i
$216$	7.73006	+	16.4358i	0.525964	+	1.11831i
$217$	27.9435			1.89693
$218$	−4.85888	−	3.60903i	−0.329085	−	0.244434i
$219$	32.9461	+	32.9461i	2.22629	+	2.22629i
$220$	0.781474	+	2.58962i	0.0526870	+	0.174592i
$221$	1.95169	+	10.9850i	0.131285	+	0.738933i
$222$	−30.6172	−	22.7415i	−2.05489	−	1.52631i
$223$	−2.94843	+	2.94843i	−0.197442	+	0.197442i	−0.798902	−	0.601461i	$-0.794586\pi$
$223$	−2.94843	+	2.94843i	−0.197442	+	0.197442i	0.601461	+	0.798902i	$0.294586\pi$
$224$	−24.1239	−	1.27236i	−1.61185	−	0.0850134i
$225$			16.6067i			1.10711i
$226$	11.1924	−	1.65198i	0.744507	−	0.109888i
$227$	−17.7471	+	17.7471i	−1.17791	+	1.17791i	−0.197639	+	0.980275i	$0.563327\pi$
$227$	−17.7471	+	17.7471i	−1.17791	+	1.17791i	−0.980275	+	0.197639i	$0.936673\pi$
$228$	−5.71931	−	3.06765i	−0.378770	−	0.203160i
$229$	−7.47691	+	7.47691i	−0.494088	+	0.494088i	−0.909592	−	0.415503i	$-0.863605\pi$
$229$	−7.47691	+	7.47691i	−0.494088	+	0.494088i	0.415503	+	0.909592i	$0.363605\pi$
$230$	−7.51044	−	5.57853i	−0.495224	−	0.367837i
$231$	−12.2566			−0.806426
$232$	−4.48270	+	2.10830i	−0.294304	+	0.138417i
$233$			14.9531i			0.979609i	0.871832	+	0.489805i	$0.162932\pi$
$233$			14.9531i			0.979609i	−0.871832	+	0.489805i	$0.837068\pi$
$234$	25.3299	−	8.46085i	1.65587	−	0.553103i
$235$		−	2.62989i		−	0.171555i
$236$	−10.2370	−	5.49078i	−0.666370	−	0.357419i
$237$	−9.43003			−0.612546
$238$	11.1434	−	15.0025i	0.722320	−	0.972469i
$239$	−14.5582	+	14.5582i	−0.941690	+	0.941690i	−0.998391	−	0.0567009i	$-0.981942\pi$
$239$	−14.5582	+	14.5582i	−0.941690	+	0.941690i	0.0567009	+	0.998391i	$0.481942\pi$
$240$	−3.07309	+	15.2198i	−0.198367	+	0.982434i
$241$	3.48722	−	3.48722i	0.224632	−	0.224632i	−0.585814	−	0.810446i	$-0.699225\pi$
$241$	3.48722	−	3.48722i	0.224632	−	0.224632i	0.810446	+	0.585814i	$0.199225\pi$
$242$	−0.206499	−	1.39906i	−0.0132743	−	0.0899347i
$243$		−	11.4633i		−	0.735369i
$244$	−24.1728	+	7.29467i	−1.54750	+	0.466993i
$245$	−10.7464	+	10.7464i	−0.686562	+	0.686562i
$246$	−25.4553	+	34.2708i	−1.62297	+	2.18502i
$247$	−2.33388	+	3.34237i	−0.148501	+	0.212670i
$248$	−6.27271	+	17.4122i	−0.398318	+	1.10567i
$249$	−7.29402	−	7.29402i	−0.462240	−	0.462240i
$250$	−9.31879	+	12.5460i	−0.589372	+	0.793480i
$251$	−14.7030			−0.928048			−0.464024	−	0.885823i	$-0.653595\pi$
$251$	−14.7030			−0.928048			−0.464024	+	0.885823i	$0.653595\pi$
$252$	−39.4199	−	21.1436i	−2.48322	−	1.33192i
$253$	3.45867	+	3.45867i	0.217445	+	0.217445i
$254$	12.2087	−	1.80200i	0.766045	−	0.113067i
$255$	−8.49355	−	8.49355i	−0.531887	−	0.531887i
$256$	6.20814	−	14.7465i	0.388008	−	0.921656i
$257$			5.00605i			0.312269i	0.987736	+	0.156134i	$0.0499033\pi$
$257$			5.00605i			0.312269i	−0.987736	+	0.156134i	$0.950097\pi$
$258$	4.95626	+	33.5793i	0.308563	+	2.09055i
$259$	40.1269			2.49336
$260$	9.26851	+	3.03535i	0.574809	+	0.188244i
$261$	−9.17284			−0.567785
$262$	−1.61690	−	10.9547i	−0.0998927	−	0.676785i
$263$			16.0531i			0.989874i	0.868929	+	0.494937i	$0.164809\pi$
$263$			16.0531i			0.989874i	−0.868929	+	0.494937i	$0.835191\pi$
$264$	2.75135	−	7.63736i	0.169334	−	0.470047i
$265$	−7.27187	−	7.27187i	−0.446707	−	0.446707i
$266$	6.75514	−	0.997052i	0.414185	−	0.0611332i
$267$	5.47807	+	5.47807i	0.335252	+	0.335252i
$268$	0.266197	−	0.496297i	0.0162606	−	0.0303161i
$269$	16.6526			1.01533			0.507663	−	0.861556i	$-0.330510\pi$
$269$	16.6526			1.01533			0.507663	+	0.861556i	$0.330510\pi$
$270$	−7.32375	+	9.86007i	−0.445709	+	0.600064i
$271$	−6.26412	−	6.26412i	−0.380518	−	0.380518i	0.490770	−	0.871289i	$-0.336715\pi$
$271$	−6.26412	−	6.26412i	−0.380518	−	0.380518i	−0.871289	+	0.490770i	$0.836715\pi$
$272$	6.84693	+	10.3114i	0.415156	+	0.625223i
$273$	−25.3003	+	36.2328i	−1.53124	+	2.19291i
$274$	−4.20733	+	5.66438i	−0.254174	+	0.342198i
$275$	2.24209	−	2.24209i	0.135203	−	0.135203i
$276$	8.11152	+	26.8796i	0.488256	+	1.61796i
$277$			14.1493i			0.850150i	0.905158	+	0.425075i	$0.139752\pi$
$277$			14.1493i			0.850150i	−0.905158	+	0.425075i	$0.860248\pi$
$278$	−3.18284	−	21.5641i	−0.190894	−	1.29333i
$279$	−24.2329	+	24.2329i	−1.45079	+	1.45079i
$280$	−6.95266	−	14.7829i	−0.415501	−	0.883444i
$281$	11.6908	−	11.6908i	0.697415	−	0.697415i	−0.266437	−	0.963852i	$-0.585847\pi$
$281$	11.6908	−	11.6908i	0.697415	−	0.697415i	0.963852	+	0.266437i	$0.0858465\pi$
$282$	−4.70615	+	6.33595i	−0.280247	+	0.377300i
$283$	−9.60095			−0.570717			−0.285359	−	0.958421i	$-0.592113\pi$
$283$	−9.60095			−0.570717			−0.285359	+	0.958421i	$0.592113\pi$
$284$	1.11667	−	2.08191i	0.0662620	−	0.123538i
$285$		−	4.38884i		−	0.259973i
$286$	−4.56212	−	2.27751i	−0.269764	−	0.134672i
$287$		−	44.9153i		−	2.65127i
$288$	22.0239	−	19.8171i	1.29777	−	1.16773i
$289$	7.42461			0.436742
$290$	−2.68924	−	1.99749i	−0.157918	−	0.117296i
$291$	9.03586	−	9.03586i	0.529691	−	0.529691i
$292$	15.3466	−	28.6120i	0.898089	−	1.67439i
$293$	5.05519	−	5.05519i	0.295327	−	0.295327i	−0.543853	−	0.839180i	$-0.683035\pi$
$293$	5.05519	−	5.05519i	0.295327	−	0.295327i	0.839180	+	0.543853i	$0.183035\pi$
$294$	45.1208	−	6.65978i	2.63150	−	0.388406i
$295$		−	7.85558i		−	0.457370i
$296$	−9.00763	+	25.0039i	−0.523558	+	1.45332i
$297$	4.54071	−	4.54071i	0.263479	−	0.263479i
$298$	−19.8614	−	14.7525i	−1.15054	−	0.854587i
$299$	17.3639	−	3.08501i	1.00418	−	0.178411i
$300$	17.4248	−	5.25831i	1.00602	−	0.303589i
$301$	−25.2523	−	25.2523i	−1.45552	−	1.45552i
$302$	0.538581	+	0.400041i	0.0309919	+	0.0230198i
$303$	44.2924			2.54453
$304$	−0.895102	+	4.43309i	−0.0513376	+	0.254255i
$305$	−12.0736	−	12.0736i	−0.691335	−	0.691335i
$306$	3.34666	+	22.6740i	0.191316	+	1.29619i
$307$	−5.53884	−	5.53884i	−0.316118	−	0.316118i	0.531156	−	0.847274i	$-0.321758\pi$
$307$	−5.53884	−	5.53884i	−0.316118	−	0.316118i	−0.847274	+	0.531156i	$0.821758\pi$
$308$	2.46751	+	8.17674i	0.140599	+	0.465913i
$309$			28.5299i			1.62301i
$310$	−12.3814	+	1.82749i	−0.703218	+	0.103794i
$311$	−12.1254			−0.687568			−0.343784	−	0.939049i	$-0.611709\pi$
$311$	−12.1254			−0.687568			−0.343784	+	0.939049i	$0.611709\pi$
$312$	−16.8980	−	23.8987i	−0.956663	−	1.35299i
$313$	−20.0427			−1.13288			−0.566442	−	0.824102i	$-0.691680\pi$
$313$	−20.0427			−1.13288			−0.566442	+	0.824102i	$0.691680\pi$
$314$	4.77075	−	0.704157i	0.269229	−	0.0397379i
$315$		−	30.2498i		−	1.70438i
$316$	1.89846	+	6.29104i	0.106797	+	0.353899i
$317$	0.965364	+	0.965364i	0.0542202	+	0.0542202i	0.733697	−	0.679477i	$-0.237793\pi$
$317$	0.965364	+	0.965364i	0.0542202	+	0.0542202i	−0.679477	+	0.733697i	$0.737793\pi$
$318$	4.50654	+	30.5323i	0.252714	+	1.71217i
$319$	1.23844	+	1.23844i	0.0693391	+	0.0693391i
$320$	10.7722	−	1.01392i	0.602186	−	0.0566797i
$321$	25.8916			1.44513
$322$	−23.7143	−	17.6142i	−1.32155	−	0.981603i
$323$	−2.47393	−	2.47393i	−0.137653	−	0.137653i
$324$	5.20448	−	1.57057i	0.289138	−	0.0872537i
$325$	−1.99987	−	11.2562i	−0.110933	−	0.624381i
$326$	−11.9123	−	8.84808i	−0.659761	−	0.490050i
$327$	−8.68573	+	8.68573i	−0.480322	+	0.480322i
$328$	27.9877	+	10.0825i	1.54536	+	0.556714i
$329$		−	8.30389i		−	0.457808i
$330$	5.43077	−	0.801575i	0.298954	−	0.0441253i
$331$	1.46498	−	1.46498i	0.0805226	−	0.0805226i	−0.665698	−	0.746221i	$-0.731866\pi$
$331$	1.46498	−	1.46498i	0.0805226	−	0.0805226i	0.746221	+	0.665698i	$0.231866\pi$
$332$	−3.39761	+	6.33449i	−0.186468	+	0.347650i
$333$	−34.7985	+	34.7985i	−1.90695	+	1.90695i
$334$	17.2677	+	12.8259i	0.944846	+	0.701803i
$335$	0.380845			0.0208078
$336$	−9.70329	+	48.0566i	−0.529358	+	2.62170i
$337$		−	0.0311687i		−	0.00169787i	−1.00000		0.000848933i	$-0.999730\pi$
$337$		−	0.0311687i		−	0.00169787i	1.00000		0.000848933i	$-0.000270224\pi$
$338$	−16.1499	+	8.78520i	−0.878440	+	0.477852i
$339$		−	22.9606i		−	1.24705i
$340$	−3.95636	+	7.37622i	−0.214564	+	0.400032i
$341$	6.54342			0.354346
$342$	−4.99349	+	6.72279i	−0.270017	+	0.363527i
$343$	−12.7941	+	12.7941i	−0.690816	+	0.690816i
$344$	21.4039	−	10.0667i	1.15402	−	0.542758i
$345$	−13.4256	+	13.4256i	−0.722813	+	0.722813i
$346$	−5.05936	−	34.2778i	−0.271993	−	1.84279i
$347$		−	9.59599i		−	0.515140i	−0.966260	−	0.257570i	$-0.917078\pi$
$347$		−	9.59599i		−	0.515140i	0.966260	−	0.257570i	$-0.0829218\pi$
$348$	2.90447	+	9.62471i	0.155696	+	0.515939i
$349$	−2.56773	+	2.56773i	−0.137448	+	0.137448i	−0.772483	−	0.635035i	$-0.780985\pi$
$349$	−2.56773	+	2.56773i	−0.137448	+	0.137448i	0.635035	+	0.772483i	$0.280985\pi$
$350$	−11.4185	+	15.3728i	−0.610343	+	0.821713i
$351$	−4.05015	−	22.7962i	−0.216181	−	1.21677i
$352$	−5.64900	−	0.297945i	−0.301093	−	0.0158805i
$353$	19.7562	+	19.7562i	1.05152	+	1.05152i	0.998599	+	0.0529173i	$0.0168520\pi$
$353$	19.7562	+	19.7562i	1.05152	+	1.05152i	0.0529173	+	0.998599i	$0.483148\pi$
$354$	−14.0574	+	18.9257i	−0.747145	+	1.00589i
$355$	1.59760			0.0847918
$356$	2.55173	−	4.75742i	0.135241	−	0.252143i
$357$	−26.8185	−	26.8185i	−1.41938	−	1.41938i
$358$	−29.9467	+	4.42010i	−1.58273	+	0.233610i
$359$	−11.5911	−	11.5911i	−0.611753	−	0.611753i	0.331650	−	0.943403i	$-0.392395\pi$
$359$	−11.5911	−	11.5911i	−0.611753	−	0.611753i	−0.943403	+	0.331650i	$0.892395\pi$
$360$	18.8493	+	6.79043i	0.993445	+	0.357887i
$361$			17.7217i			0.932719i
$362$	0.265644	+	1.79977i	0.0139619	+	0.0945938i
$363$	−2.87009			−0.150640
$364$	29.2654	+	9.58414i	1.53392	+	0.502346i
$365$	21.9561			1.14924
$366$	7.48231	+	50.6935i	0.391107	+	2.64979i
$367$		−	21.0484i		−	1.09872i	−0.835587	−	0.549359i	$-0.814872\pi$
$367$		−	21.0484i		−	1.09872i	0.835587	−	0.549359i	$-0.185128\pi$
$368$	16.2992	−	10.8229i	0.849652	−	0.564180i
$369$	38.9511	+	38.9511i	2.02771	+	2.02771i
$370$	−17.7798	+	2.62427i	−0.924326	+	0.136429i
$371$	−22.9610	−	22.9610i	−1.19208	−	1.19208i
$372$	33.0997	+	17.7536i	1.71614	+	0.920481i
$373$	20.0266			1.03694			0.518468	−	0.855097i	$-0.326503\pi$
$373$	20.0266			1.03694			0.518468	+	0.855097i	$0.326503\pi$
$374$	2.60941	−	3.51308i	0.134929	−	0.181657i
$375$	22.4272	+	22.4272i	1.15814	+	1.15814i
$376$	5.17433	+	1.86405i	0.266846	+	0.0961309i
$377$	6.21744	−	1.10464i	0.320214	−	0.0568919i
$378$	−23.1248	+	31.1332i	−1.18941	+	1.60132i
$379$	−9.73287	+	9.73287i	−0.499944	+	0.499944i	−0.911420	−	0.411477i	$-0.865013\pi$
$379$	−9.73287	+	9.73287i	−0.499944	+	0.499944i	0.411477	+	0.911420i	$0.365013\pi$
$380$	−2.92792	+	0.883565i	−0.150199	+	0.0453259i
$381$		−	25.0456i		−	1.28312i
$382$	3.42461	+	23.2022i	0.175218	+	1.18713i
$383$	18.8107	−	18.8107i	0.961181	−	0.961181i	−0.0380930	−	0.999274i	$-0.512128\pi$
$383$	18.8107	−	18.8107i	0.961181	−	0.961181i	0.999274	+	0.0380930i	$0.0121283\pi$
$384$	−27.7669	−	16.8340i	−1.41698	−	0.859057i
$385$	−4.08406	+	4.08406i	−0.208143	+	0.208143i
$386$	−22.2213	+	29.9168i	−1.13103	+	1.52272i
$387$	43.7982			2.22639
$388$	−7.84718	−	4.20897i	−0.398380	−	0.213678i
$389$		−	5.97775i		−	0.303084i	−0.988451	−	0.151542i	$-0.951576\pi$
$389$		−	5.97775i		−	0.303084i	0.988451	−	0.151542i	$-0.0484239\pi$
$390$	8.84068	−	17.7090i	0.447665	−	0.896728i
$391$			15.1357i			0.765445i
$392$	−13.5267	−	28.7606i	−0.683200	−	1.45263i
$393$	−22.4730			−1.13361
$394$	1.53871	+	1.14291i	0.0775193	+	0.0575789i
$395$	−3.14220	+	3.14220i	−0.158101	+	0.158101i
$396$	−9.23081	−	4.95111i	−0.463866	−	0.248803i
$397$	−19.1957	+	19.1957i	−0.963405	+	0.963405i	−0.999354	−	0.0359483i	$-0.988555\pi$
$397$	−19.1957	+	19.1957i	−0.963405	+	0.963405i	0.0359483	+	0.999354i	$0.488555\pi$
$398$	27.4814	−	4.05622i	1.37752	−	0.203320i
$399$		−	13.8578i		−	0.693758i
$400$	−7.01594	−	10.5660i	−0.350797	−	0.528298i
$401$	12.7410	−	12.7410i	0.636258	−	0.636258i	−0.313373	−	0.949630i	$-0.601459\pi$
$401$	12.7410	−	12.7410i	0.636258	−	0.636258i	0.949630	+	0.313373i	$0.101459\pi$
$402$	−0.917534	−	0.681516i	−0.0457625	−	0.0339909i
$403$	13.5070	−	19.3435i	0.672833	−	0.963570i
$404$	−8.91697	−	29.5487i	−0.443636	−	1.47010i
$405$	2.59950	+	2.59950i	0.129170	+	0.129170i
$406$	−8.49130	−	6.30708i	−0.421416	−	0.313015i
$407$	9.39636			0.465760
$408$	22.7313	−	10.6910i	1.12537	−	0.529283i
$409$	−19.1454	−	19.1454i	−0.946681	−	0.946681i	0.0519674	−	0.998649i	$-0.483451\pi$
$409$	−19.1454	−	19.1454i	−0.946681	−	0.946681i	−0.998649	+	0.0519674i	$0.983451\pi$
$410$	2.93743	+	19.9015i	0.145069	+	0.982863i
$411$	10.1256	+	10.1256i	0.499461	+	0.499461i
$412$	19.0331	−	5.74366i	0.937695	−	0.282970i
$413$		−	24.8041i		−	1.22053i
$414$	35.8406	−	5.29003i	1.76147	−	0.259991i
$415$	−4.86092			−0.238613
$416$	−12.5415	+	16.0845i	−0.614900	+	0.788605i
$417$	−44.2376			−2.16632
$418$	1.58183	−	0.233476i	0.0773697	−	0.0114197i
$419$			17.6887i			0.864148i	0.901838	+	0.432074i	$0.142218\pi$
$419$			17.6887i			0.864148i	−0.901838	+	0.432074i	$0.857782\pi$
$420$	−31.7399	+	9.57822i	−1.54875	+	0.467370i
$421$	−23.1303	−	23.1303i	−1.12730	−	1.12730i	−0.990614	−	0.136687i	$-0.956354\pi$
$421$	−23.1303	−	23.1303i	−1.12730	−	1.12730i	−0.136687	−	0.990614i	$-0.543646\pi$
$422$	−4.70840	−	31.9000i	−0.229201	−	1.55287i
$423$	7.20123	+	7.20123i	0.350136	+	0.350136i
$424$	19.4617	−	9.15323i	0.945145	−	0.444520i
$425$	9.81175			0.475940
$426$	−3.84895	−	2.85888i	−0.186482	−	0.138513i
$427$	−38.1226	−	38.1226i	−1.84488	−	1.84488i
$428$	−5.21251	−	17.2730i	−0.251956	−	0.834922i
$429$	−5.92448	+	8.48450i	−0.286037	+	0.409635i
$430$	12.8405	+	9.53754i	0.619224	+	0.459941i
$431$	0.263939	−	0.263939i	0.0127135	−	0.0127135i	−0.700721	−	0.713435i	$-0.747138\pi$
$431$	0.263939	−	0.263939i	0.0127135	−	0.0127135i	0.713435	+	0.700721i	$0.247138\pi$
$432$	−14.2088	−	21.3983i	−0.683619	−	1.02953i
$433$			17.5599i			0.843873i	0.906625	+	0.421936i	$0.138649\pi$
$433$			17.5599i			0.843873i	−0.906625	+	0.421936i	$0.861351\pi$
$434$	−39.0945	+	5.77030i	−1.87659	+	0.276983i
$435$	−4.80728	+	4.80728i	−0.230491	+	0.230491i
$436$	7.54311	+	4.04588i	0.361249	+	0.193762i
$437$	−3.91051	+	3.91051i	−0.187065	+	0.187065i
$438$	−52.8968	−	39.2901i	−2.52751	−	1.87735i
$439$	−29.3200			−1.39937			−0.699684	−	0.714453i	$-0.746676\pi$
$439$	−29.3200			−1.39937			−0.699684	+	0.714453i	$0.746676\pi$
$440$	−1.62808	−	3.46165i	−0.0776156	−	0.165028i
$441$		−	58.8521i		−	2.80248i
$442$	−4.99893	−	14.9657i	−0.237775	−	0.711844i
$443$		−	1.79828i		−	0.0854387i	−0.999087	−	0.0427193i	$-0.986398\pi$
$443$		−	1.79828i		−	0.0854387i	0.999087	−	0.0427193i	$-0.0136021\pi$
$444$	47.5312	+	25.4942i	2.25573	+	1.20990i
$445$	3.65072			0.173061
$446$	3.51617	−	4.73387i	0.166496	−	0.224155i
$447$	−35.5042	+	35.5042i	−1.67929	+	1.67929i
$448$	34.0134	−	3.20145i	1.60698	−	0.151254i
$449$	11.7027	−	11.7027i	0.552285	−	0.552285i	−0.374815	−	0.927100i	$-0.622294\pi$
$449$	11.7027	−	11.7027i	0.552285	−	0.552285i	0.927100	+	0.374815i	$0.122294\pi$
$450$	−3.42927	−	23.2337i	−0.161657	−	1.09525i
$451$		−	10.5176i		−	0.495257i
$452$	−15.3177	+	4.62244i	−0.720482	+	0.217421i
$453$	0.962766	−	0.962766i	0.0452347	−	0.0452347i
$454$	21.1644	−	28.4939i	0.993294	−	1.33728i
$455$	3.64284	+	20.5036i	0.170779	+	0.961223i
$456$	8.63510	+	3.11078i	0.404375	+	0.145676i
$457$	−8.87483	−	8.87483i	−0.415147	−	0.415147i	0.468380	−	0.883527i	$-0.344838\pi$
$457$	−8.87483	−	8.87483i	−0.415147	−	0.415147i	−0.883527	+	0.468380i	$0.844838\pi$
$458$	8.91665	−	12.0046i	0.416648	−	0.560938i
$459$	19.8709			0.927492
$460$	11.6595	+	6.25377i	0.543627	+	0.291584i
$461$	−15.3673	−	15.3673i	−0.715725	−	0.715725i	0.252002	−	0.967727i	$-0.418911\pi$
$461$	−15.3673	−	15.3673i	−0.715725	−	0.715725i	−0.967727	+	0.252002i	$0.918911\pi$
$462$	17.1477	−	2.53098i	0.797783	−	0.117752i
$463$	29.1472	+	29.1472i	1.35458	+	1.35458i	0.880456	+	0.474128i	$0.157237\pi$
$463$	29.1472	+	29.1472i	1.35458	+	1.35458i	0.474128	+	0.880456i	$0.342763\pi$
$464$	5.83619	−	3.87531i	0.270938	−	0.179907i
$465$			25.3998i			1.17789i
$466$	−3.08780	−	20.9202i	−0.143040	−	0.969110i
$467$	−9.18823			−0.425181			−0.212590	−	0.977141i	$-0.568190\pi$
$467$	−9.18823			−0.425181			−0.212590	+	0.977141i	$0.568190\pi$
$468$	−33.6908	+	17.0678i	−1.55736	+	0.788960i
$469$	1.20252			0.0555273
$470$	0.543070	+	3.67936i	0.0250499	+	0.169716i
$471$		−	9.78692i		−	0.450958i
$472$	15.4559	+	5.56798i	0.711417	+	0.256287i
$473$	−5.91324	−	5.91324i	−0.271891	−	0.271891i
$474$	13.1931	−	1.94729i	0.605981	−	0.0894421i
$475$	2.53500	+	2.53500i	0.116314	+	0.116314i
$476$	−12.4922	+	23.2905i	−0.572581	+	1.06752i
$477$	39.8241			1.82342
$478$	17.3615	−	23.3740i	0.794095	−	1.06910i
$479$	10.5131	+	10.5131i	0.480357	+	0.480357i	0.905246	−	0.424889i	$-0.139687\pi$
$479$	10.5131	+	10.5131i	0.480357	+	0.480357i	−0.424889	+	0.905246i	$0.639687\pi$
$480$	1.15654	−	21.9279i	0.0527888	−	1.00087i
$481$	19.3961	−	27.7774i	0.884387	−	1.26654i
$482$	−4.15871	+	5.59893i	−0.189424	+	0.255024i
$483$	−42.3916	+	42.3916i	−1.92888	+	1.92888i
$484$	0.577808	+	1.91472i	0.0262640	+	0.0870326i
$485$		−	6.02172i		−	0.273432i
$486$	2.36715	+	16.0377i	0.107376	+	0.727487i
$487$	−23.9025	+	23.9025i	−1.08313	+	1.08313i	−0.0869099	+	0.996216i	$0.527699\pi$
$487$	−23.9025	+	23.9025i	−1.08313	+	1.08313i	−0.996216	+	0.0869099i	$0.972301\pi$
$488$	32.3128	−	15.1973i	1.46273	−	0.687950i
$489$	−21.2944	+	21.2944i	−0.962965	+	0.962965i
$490$	12.8157	−	17.2539i	0.578954	−	0.779453i
$491$	3.84988			0.173743			0.0868714	−	0.996220i	$-0.472313\pi$
$491$	3.84988			0.173743			0.0868714	+	0.996220i	$0.472313\pi$
$492$	28.5365	−	53.2032i	1.28652	−	2.39859i
$493$			5.41959i			0.244086i
$494$	2.57504	−	5.15811i	0.115856	−	0.232075i
$495$		−	7.08348i		−	0.318379i
$496$	5.18028	−	25.6559i	0.232601	−	1.15198i
$497$	5.04443			0.226274
$498$	11.7110	+	8.69854i	0.524781	+	0.389791i
$499$	7.78377	−	7.78377i	0.348450	−	0.348450i	−0.511082	−	0.859532i	$-0.670755\pi$
$499$	7.78377	−	7.78377i	0.348450	−	0.348450i	0.859532	+	0.511082i	$0.170755\pi$
$500$	10.4468	−	19.4769i	0.467194	−	0.871033i
$501$	30.8677	−	30.8677i	1.37907	−	1.37907i
$502$	20.5704	−	3.03616i	0.918101	−	0.135511i
$503$		−	24.4217i		−	1.08891i	−0.838790	−	0.544454i	$-0.816737\pi$
$503$		−	24.4217i		−	1.08891i	0.838790	−	0.544454i	$-0.183263\pi$
$504$	59.5168	+	21.4408i	2.65109	+	0.955051i
$505$	14.7588	−	14.7588i	0.656757	−	0.656757i
$506$	−5.55309	−	4.12466i	−0.246865	−	0.183364i
$507$	12.8523	+	35.0277i	0.570791	+	1.55563i
$508$	−16.7086	+	5.04219i	−0.741325	+	0.223711i
$509$	13.3156	+	13.3156i	0.590202	+	0.590202i	0.937686	−	0.347484i	$-0.112964\pi$
$509$	13.3156	+	13.3156i	0.590202	+	0.590202i	−0.347484	+	0.937686i	$0.612964\pi$
$510$	13.6369	+	10.1290i	0.603851	+	0.448522i
$511$	69.3266			3.06683
$512$	−5.64039	+	21.9131i	−0.249273	+	0.968433i
$513$	5.13390	+	5.13390i	0.226667	+	0.226667i
$514$	−1.03374	−	7.00374i	−0.0455965	−	0.308922i
$515$	9.50653	+	9.50653i	0.418908	+	0.418908i
$516$	−13.8682	−	45.9558i	−0.610512	−	2.02309i
$517$		−	1.94449i		−	0.0855187i
$518$	−56.1398	+	8.28616i	−2.46664	+	0.364073i
$519$	−70.3190			−3.08666
$520$	−13.5940	−	2.33269i	−0.596135	−	0.102295i
$521$	−39.9175			−1.74882			−0.874408	−	0.485192i	$-0.838750\pi$
$521$	−39.9175			−1.74882			−0.874408	+	0.485192i	$0.838750\pi$
$522$	12.8333	−	1.89418i	0.561699	−	0.0829062i
$523$		−	2.11378i		−	0.0924292i	−0.998932	−	0.0462146i	$-0.985284\pi$
$523$		−	2.11378i		−	0.0924292i	0.998932	−	0.0462146i	$-0.0147158\pi$
$524$	4.52428	+	14.9924i	0.197644	+	0.654945i
$525$	27.4804	+	27.4804i	1.19935	+	1.19935i
$526$	−3.31494	−	22.4591i	−0.144538	−	0.979264i
$527$	14.3175	+	14.3175i	0.623681	+	0.623681i
$528$	−2.27218	+	11.2532i	−0.0988841	+	0.489735i
$529$	0.924793			0.0402084
$530$	11.6754	+	8.67212i	0.507147	+	0.376693i
$531$	21.5104	+	21.5104i	0.933471	+	0.933471i
$532$	−9.24494	+	2.78986i	−0.400819	+	0.120956i
$533$	−31.0921	−	21.7107i	−1.34675	−	0.940395i
$534$	−8.79534	−	6.53291i	−0.380612	−	0.282707i
$535$	8.62739	−	8.62739i	0.372995	−	0.372995i
$536$	−0.269940	+	0.749317i	−0.0116596	+	0.0323655i
$537$			61.4341i			2.65108i
$538$	−23.2979	+	3.43874i	−1.00444	+	0.148255i
$539$	−7.94569	+	7.94569i	−0.342245	+	0.342245i
$540$	8.21025	−	15.3071i	0.353313	−	0.658714i
$541$	−29.1148	+	29.1148i	−1.25175	+	1.25175i	−0.296808	+	0.954937i	$0.595922\pi$
$541$	−29.1148	+	29.1148i	−1.25175	+	1.25175i	−0.954937	+	0.296808i	$0.904078\pi$
$542$	10.0574	+	7.47033i	0.432002	+	0.320878i
$543$	3.69213			0.158444
$544$	−11.7085	−	13.0124i	−0.502000	−	0.557902i
$545$			5.78838i			0.247947i
$546$	27.9145	−	55.9162i	1.19463	−	2.39299i
$547$			3.28485i			0.140450i	0.997531	+	0.0702250i	$0.0223717\pi$
$547$			3.28485i			0.140450i	−0.997531	+	0.0702250i	$0.977628\pi$
$548$	4.71660	−	8.79360i	0.201483	−	0.375644i
$549$	66.1208			2.82197
$550$	−2.67382	+	3.59980i	−0.114012	+	0.153496i
$551$	−1.40022	+	1.40022i	−0.0596515	+	0.0596515i
$552$	−16.8991	−	35.9311i	−0.719273	−	1.52933i
$553$	−9.92153	+	9.92153i	−0.421906	+	0.421906i
$554$	−2.92182	−	19.7957i	−0.124136	−	0.841038i
$555$			36.4742i			1.54824i
$556$	8.90593	+	29.5121i	0.377696	+	1.25159i
$557$	19.7446	−	19.7446i	0.836605	−	0.836605i	−0.151806	−	0.988410i	$-0.548509\pi$
$557$	19.7446	−	19.7446i	0.836605	−	0.836605i	0.988410	+	0.151806i	$0.0485088\pi$
$558$	28.8991	−	38.9072i	1.22340	−	1.64708i
$559$	−29.6868	+	5.27441i	−1.25562	+	0.223084i
$560$	12.7798	+	19.2463i	0.540046	+	0.813306i
$561$	−6.27998	−	6.27998i	−0.265141	−	0.265141i
$562$	−13.9420	+	18.7702i	−0.588106	+	0.791774i
$563$	25.2991			1.06623			0.533115	−	0.846043i	$-0.321021\pi$
$563$	25.2991			1.06623			0.533115	+	0.846043i	$0.321021\pi$
$564$	5.27580	−	9.83616i	0.222151	−	0.414177i
$565$	−7.65075	−	7.65075i	−0.321870	−	0.321870i
$566$	13.4323	−	1.98259i	0.564600	−	0.0833344i
$567$	8.20793	+	8.20793i	0.344701	+	0.344701i
$568$	−1.13237	+	3.14330i	−0.0475131	+	0.131890i
$569$			5.47428i			0.229494i	0.993395	+	0.114747i	$0.0366057\pi$
$569$			5.47428i			0.229494i	−0.993395	+	0.114747i	$0.963394\pi$
$570$	0.906292	+	6.14024i	0.0379604	+	0.257186i
$571$	10.6251			0.444647			0.222324	−	0.974973i	$-0.428636\pi$
$571$	10.6251			0.444647			0.222324	+	0.974973i	$0.428636\pi$
$572$	6.85297	+	2.24428i	0.286537	+	0.0938382i
$573$	47.5980			1.98843
$574$	9.27497	+	62.8390i	0.387130	+	2.62285i
$575$		−	15.5093i		−	0.646783i
$576$	−26.7205	+	32.2732i	−1.11335	+	1.34472i
$577$	16.9407	+	16.9407i	0.705251	+	0.705251i	0.965533	−	0.260282i	$-0.0838156\pi$
$577$	16.9407	+	16.9407i	0.705251	+	0.705251i	−0.260282	+	0.965533i	$0.583816\pi$
$578$	−10.3874	+	1.53317i	−0.432061	+	0.0637717i
$579$	53.4792	+	53.4792i	2.22252	+	2.22252i
$580$	4.17488	+	2.23927i	0.173352	+	0.0929806i
$581$	−15.3484			−0.636758
$582$	−10.7758	+	14.5076i	−0.446670	+	0.601358i
$583$	−5.37669	−	5.37669i	−0.222680	−	0.222680i
$584$	−15.5623	+	43.1989i	−0.643974	+	1.78758i
$585$	−20.9401	−	14.6218i	−0.865765	−	0.604539i
$586$	−6.02860	+	8.11638i	−0.249039	+	0.335285i
$587$	7.35222	−	7.35222i	0.303459	−	0.303459i	−0.538907	−	0.842365i	$-0.681162\pi$
$587$	7.35222	−	7.35222i	0.303459	−	0.303459i	0.842365	+	0.538907i	$0.181162\pi$
$588$	−61.7513	+	18.6348i	−2.54658	+	0.768487i
$589$			7.39824i			0.304839i
$590$	1.62217	+	10.9904i	0.0667837	+	0.452468i
$591$	2.75060	−	2.75060i	0.113145	−	0.113145i
$592$	7.43889	−	36.8420i	0.305737	−	1.51419i
$593$	7.38998	−	7.38998i	0.303470	−	0.303470i	−0.538900	−	0.842370i	$-0.681160\pi$
$593$	7.38998	−	7.38998i	0.303470	−	0.303470i	0.842370	+	0.538900i	$0.181160\pi$
$594$	−5.41505	+	7.29035i	−0.222182	+	0.299127i
$595$	−17.8725			−0.732701
$596$	30.8336	+	16.5381i	1.26299	+	0.677429i
$597$		−	56.3765i		−	2.30734i
$598$	−23.6560	+	7.90174i	−0.967366	+	0.323126i
$599$		−	23.3621i		−	0.954548i	−0.878755	−	0.477274i	$-0.841625\pi$
$599$		−	23.3621i		−	0.954548i	0.878755	−	0.477274i	$-0.158375\pi$
$600$	−23.2924	+	10.9549i	−0.950909	+	0.447231i
$601$	−29.0519			−1.18505			−0.592527	−	0.805551i	$-0.701869\pi$
$601$	−29.0519			−1.18505			−0.592527	+	0.805551i	$0.701869\pi$
$602$	40.5440	+	30.1148i	1.65245	+	1.22739i
$603$	−1.04284	+	1.04284i	−0.0424677	+	0.0424677i
$604$	−0.836113	−	0.448464i	−0.0340210	−	0.0182477i
$605$	−0.956348	+	0.956348i	−0.0388811	+	0.0388811i
$606$	−61.9676	+	9.14634i	−2.51726	+	0.371545i
$607$		−	6.99470i		−	0.283906i	−0.989873	−	0.141953i	$-0.954662\pi$
$607$		−	6.99470i		−	0.283906i	0.989873	−	0.141953i	$-0.0453382\pi$
$608$	0.336868	−	6.38698i	0.0136618	−	0.259026i
$609$	−15.1790	+	15.1790i	−0.615085	+	0.615085i
$610$	19.3849	+	14.3985i	0.784872	+	0.582979i
$611$	−5.74827	−	4.01385i	−0.232550	−	0.162383i
$612$	−9.36434	−	31.0312i	−0.378531	−	1.25436i
$613$	6.49906	+	6.49906i	0.262495	+	0.262495i	0.826067	−	0.563572i	$-0.190573\pi$
$613$	6.49906	+	6.49906i	0.262495	+	0.262495i	−0.563572	+	0.826067i	$0.690573\pi$
$614$	8.89291	+	6.60538i	0.358889	+	0.266572i
$615$	40.8268			1.64629
$616$	−5.14067	−	10.9302i	−0.207124	−	0.440389i
$617$	11.3119	+	11.3119i	0.455401	+	0.455401i	0.897142	−	0.441741i	$-0.145639\pi$
$617$	11.3119	+	11.3119i	0.455401	+	0.455401i	−0.441741	+	0.897142i	$0.645639\pi$
$618$	−5.89141	−	39.9150i	−0.236987	−	1.60562i
$619$	−9.81340	−	9.81340i	−0.394434	−	0.394434i	0.481831	−	0.876264i	$-0.339972\pi$
$619$	−9.81340	−	9.81340i	−0.394434	−	0.394434i	−0.876264	+	0.481831i	$0.839972\pi$
$620$	16.9449	−	5.11351i	0.680525	−	0.205363i
$621$		−	31.4096i		−	1.26042i
$622$	16.9641	−	2.50388i	0.680199	−	0.100397i
$623$	11.5272			0.461827
$624$	28.5764	+	29.9461i	1.14397	+	1.19880i
$625$	−0.907920			−0.0363168
$626$	28.0409	−	4.13881i	1.12074	−	0.165420i
$627$		−	3.24503i		−	0.129594i
$628$	−6.52913	+	1.97031i	−0.260541	+	0.0786239i
$629$	20.5600	+	20.5600i	0.819781	+	0.819781i
$630$	6.24655	+	42.3212i	0.248869	+	1.68612i
$631$	22.5263	+	22.5263i	0.896759	+	0.896759i	0.995148	−	0.0983892i	$-0.0313690\pi$
$631$	22.5263	+	22.5263i	0.896759	+	0.896759i	−0.0983892	+	0.995148i	$0.531369\pi$
$632$	−3.95515	−	8.40949i	−0.157327	−	0.334511i
$633$	−65.4411			−2.60105
$634$	−1.54995	−	1.15125i	−0.0615562	−	0.0457220i
$635$	−8.34549	−	8.34549i	−0.331181	−	0.331181i
$636$	−12.6098	−	41.7859i	−0.500011	−	1.65692i
$637$	7.08728	+	39.8905i	0.280808	+	1.58052i
$638$	−1.98838	−	1.47690i	−0.0787206	−	0.0584712i
$639$	−4.37459	+	4.37459i	−0.173056	+	0.173056i
$640$	−14.8616	+	3.64298i	−0.587456	+	0.144002i
$641$		−	24.7155i		−	0.976204i	−0.872787	−	0.488102i	$-0.837689\pi$
$641$		−	24.7155i		−	0.976204i	0.872787	−	0.488102i	$-0.162311\pi$
$642$	−36.2238	+	5.34659i	−1.42964	+	0.211013i
$643$	−10.6852	+	10.6852i	−0.421382	+	0.421382i	−0.885679	−	0.464298i	$-0.846307\pi$
$643$	−10.6852	+	10.6852i	−0.421382	+	0.421382i	0.464298	+	0.885679i	$0.346307\pi$
$644$	36.8149	+	19.7463i	1.45071	+	0.778114i
$645$	22.9537	−	22.9537i	0.903800	−	0.903800i
$646$	3.97203	+	2.95030i	0.156277	+	0.116078i
$647$	−6.18098			−0.243000			−0.121500	−	0.992591i	$-0.538770\pi$
$647$	−6.18098			−0.243000			−0.121500	+	0.992591i	$0.538770\pi$
$648$	−6.95704	+	3.27203i	−0.273298	+	0.128538i
$649$		−	5.80828i		−	0.227995i
$650$	5.12232	+	15.3351i	0.200914	+	0.601491i
$651$			80.2002i			3.14329i
$652$	18.4931	+	9.91909i	0.724245	+	0.388462i
$653$	2.80307			0.109693			0.0548463	−	0.998495i	$-0.482533\pi$
$653$	2.80307			0.109693			0.0548463	+	0.998495i	$0.482533\pi$
$654$	10.3582	−	13.9454i	0.405039	−	0.545309i
$655$	−7.48828	+	7.48828i	−0.292591	+	0.292591i
$656$	−41.2384	−	8.32659i	−1.61009	−	0.325099i
$657$	−60.1208	+	60.1208i	−2.34554	+	2.34554i
$658$	1.71475	+	11.6176i	0.0668478	+	0.452902i
$659$		−	8.14994i		−	0.317477i	−0.987321	−	0.158738i	$-0.949257\pi$
$659$		−	8.14994i		−	0.317477i	0.987321	−	0.158738i	$-0.0507426\pi$
$660$	−7.43243	+	2.24290i	−0.289307	+	0.0873047i
$661$	−4.20084	+	4.20084i	−0.163394	+	0.163394i	−0.784068	−	0.620675i	$-0.786859\pi$
$661$	−4.20084	+	4.20084i	−0.163394	+	0.163394i	0.620675	+	0.784068i	$0.286859\pi$
$662$	−1.74707	+	2.35211i	−0.0679019	+	0.0914172i
$663$	−31.5280	+	5.60153i	−1.22445	+	0.217545i
$664$	3.44538	−	9.56391i	0.133707	−	0.371152i
$665$	−4.61759	−	4.61759i	−0.179063	−	0.179063i
$666$	41.4992	−	55.8709i	1.60806	−	2.16495i
$667$	8.56668			0.331703
$668$	−26.8070	−	14.3784i	−1.03719	−	0.556318i
$669$	−8.46225	−	8.46225i	−0.327170	−	0.327170i
$670$	−0.532824	+	0.0786441i	−0.0205848	+	0.00303829i
$671$	−8.92704	−	8.92704i	−0.344625	−	0.344625i
$672$	3.65180	−	69.2377i	0.140871	−	2.67090i
$673$		−	11.9478i		−	0.460553i	−0.973125	−	0.230277i	$-0.926037\pi$
$673$		−	11.9478i		−	0.460553i	0.973125	−	0.230277i	$-0.0739631\pi$
$674$	0.00643630	+	0.0436067i	0.000247917	+	0.00167967i
$675$	−20.3614			−0.783709
$676$	20.7805	−	15.6259i	0.799251	−	0.600998i
$677$	20.7536			0.797624			0.398812	−	0.917033i	$-0.369423\pi$
$677$	20.7536			0.797624			0.398812	+	0.917033i	$0.369423\pi$
$678$	4.74134	+	32.1231i	0.182090	+	1.23368i
$679$		−	19.0136i		−	0.729676i
$680$	4.01199	−	11.1367i	0.153853	−	0.427074i
$681$	−50.9356	−	50.9356i	−1.95186	−	1.95186i
$682$	−9.15461	+	1.35121i	−0.350548	+	0.0517405i
$683$	−13.0194	−	13.0194i	−0.498172	−	0.498172i	0.412697	−	0.910868i	$-0.364587\pi$
$683$	−13.0194	−	13.0194i	−0.498172	−	0.498172i	−0.910868	+	0.412697i	$0.864587\pi$
$684$	5.59792	−	10.4367i	0.214042	−	0.399058i
$685$	6.74797			0.257827
$686$	15.2577	−	20.5416i	0.582541	−	0.784282i
$687$	−21.4594	−	21.4594i	−0.818727	−	0.818727i
$688$	−27.8665	+	18.5037i	−1.06240	+	0.705447i
$689$	−26.9931	+	4.79582i	−1.02836	+	0.182706i
$690$	16.0109	−	21.5556i	0.609523	−	0.820608i
$691$	−31.3106	+	31.3106i	−1.19111	+	1.19111i	−0.214357	+	0.976755i	$0.568765\pi$
$691$	−31.3106	+	31.3106i	−1.19111	+	1.19111i	−0.976755	+	0.214357i	$0.931235\pi$
$692$	14.1567	+	46.9118i	0.538156	+	1.78332i
$693$		−	22.3661i		−	0.849620i
$694$	1.98156	+	13.4253i	0.0752191	+	0.509619i
$695$	−14.7405	+	14.7405i	−0.559139	+	0.559139i
$696$	−6.05101	−	12.8657i	−0.229363	−	0.487675i
$697$	23.0135	−	23.0135i	0.871697	−	0.871697i
$698$	3.06217	−	4.12264i	0.115905	−	0.156044i
$699$	−42.9167			−1.62326
$700$	12.8006	−	23.8654i	0.483817	−	0.902026i
$701$			39.7773i			1.50237i	0.660093	+	0.751184i	$0.270517\pi$
$701$			39.7773i			1.50237i	−0.660093	+	0.751184i	$0.729483\pi$
$702$	10.3738	+	31.0567i	0.391533	+	1.17216i
$703$			10.6239i			0.400688i
$704$	7.96480	−	0.749672i	0.300185	−	0.0282543i
$705$	7.54801			0.284274
$706$	−31.7197	−	23.5604i	−1.19379	−	0.886707i
$707$	46.6010	−	46.6010i	1.75261	−	1.75261i
$708$	15.7590	−	29.3810i	0.592260	−	1.10421i
$709$	−25.4547	+	25.4547i	−0.955970	+	0.955970i	−0.999071	−	0.0431006i	$-0.986276\pi$
$709$	−25.4547	+	25.4547i	−0.955970	+	0.955970i	0.0431006	+	0.999071i	$0.486276\pi$
$710$	−2.23513	+	0.329903i	−0.0838830	+	0.0123810i
$711$		−	17.2081i		−	0.645355i
$712$	−2.58761	+	7.18283i	−0.0969746	+	0.269188i
$713$	22.6315	−	22.6315i	0.847557	−	0.847557i
$714$	43.0585	+	31.9825i	1.61142	+	1.19692i
$715$	0.853030	+	4.80125i	0.0319015	+	0.179557i
$716$	40.9844	−	12.3679i	1.53166	−	0.462212i
$717$	−41.7832	−	41.7832i	−1.56042	−	1.56042i
$718$	18.6101	+	13.8230i	0.694522	+	0.515870i
$719$	−17.8649			−0.666247			−0.333123	−	0.942883i	$-0.608103\pi$
$719$	−17.8649			−0.666247			−0.333123	+	0.942883i	$0.608103\pi$
$720$	−27.7734	−	5.60783i	−1.03505	−	0.208992i
$721$	30.0169	+	30.0169i	1.11789	+	1.11789i
$722$	−3.65951	−	24.7936i	−0.136193	−	0.922722i
$723$	10.0086	+	10.0086i	0.372225	+	0.372225i
$724$	−0.743301	−	2.46312i	−0.0276246	−	0.0915412i
$725$		−	5.55337i		−	0.206247i
$726$	4.01541	−	0.592670i	0.149026	−	0.0219961i
$727$	48.6883			1.80575			0.902874	−	0.429905i	$-0.141453\pi$
$727$	48.6883			1.80575			0.902874	+	0.429905i	$0.141453\pi$
$728$	−42.9230	−	7.36548i	−1.59083	−	0.272983i
$729$	41.0550			1.52056
$730$	−30.7178	+	4.53392i	−1.13692	+	0.167808i
$731$		−	25.8773i		−	0.957107i
$732$	−20.9363	−	69.3780i	−0.773829	−	2.56429i
$733$	−10.8674	−	10.8674i	−0.401396	−	0.401396i	0.477329	−	0.878725i	$-0.341605\pi$
$733$	−10.8674	−	10.8674i	−0.401396	−	0.401396i	−0.878725	+	0.477329i	$0.841605\pi$
$734$	4.34647	+	29.4479i	0.160431	+	1.08694i
$735$	−30.8431	−	30.8431i	−1.13766	−	1.13766i
$736$	−20.5685	+	18.5075i	−0.758166	+	0.682197i
$737$	0.281590			0.0103725
$738$	−62.5381	−	46.4514i	−2.30206	−	1.70990i
$739$	3.73826	+	3.73826i	0.137514	+	0.137514i	0.772513	−	0.634999i	$-0.218999\pi$
$739$	3.73826	+	3.73826i	0.137514	+	0.137514i	−0.634999	+	0.772513i	$0.718999\pi$
$740$	24.3330	−	7.34301i	0.894498	−	0.269935i
$741$	−9.59291	−	6.69845i	−0.352404	−	0.246074i
$742$	36.8651	+	27.3823i	1.35336	+	1.00524i
$743$	23.2583	−	23.2583i	0.853263	−	0.853263i	−0.137271	−	0.990534i	$-0.543833\pi$
$743$	23.2583	−	23.2583i	0.853263	−	0.853263i	0.990534	+	0.137271i	$0.0438331\pi$
$744$	−49.9744	−	18.0032i	−1.83215	−	0.660030i
$745$			23.6609i			0.866868i
$746$	−28.0183	+	4.13547i	−1.02582	+	0.151410i
$747$	13.3103	−	13.3103i	0.486998	−	0.486998i
$748$	−2.92526	+	5.45384i	−0.106958	+	0.199412i
$749$	27.2411	−	27.2411i	0.995366	−	0.995366i
$750$	−36.0081	−	26.7457i	−1.31483	−	0.976617i
$751$	9.70026			0.353967			0.176984	−	0.984214i	$-0.443366\pi$
$751$	9.70026			0.353967			0.176984	+	0.984214i	$0.443366\pi$
$752$	−7.62411	−	1.53941i	−0.278023	−	0.0561365i
$753$		−	42.1990i		−	1.53782i
$754$	−8.47044	+	2.82935i	−0.308475	+	0.103039i
$755$		−	0.641611i		−	0.0233506i
$756$	25.9239	−	48.3324i	0.942844	−	1.75783i
$757$	−36.0182			−1.30910			−0.654552	−	0.756017i	$-0.727143\pi$
$757$	−36.0182			−1.30910			−0.654552	+	0.756017i	$0.727143\pi$
$758$	11.6070	−	15.6267i	0.421585	−	0.567586i
$759$	−9.92668	+	9.92668i	−0.360316	+	0.360316i
$760$	3.91387	−	1.84077i	0.141971	−	0.0667717i
$761$	−23.8457	+	23.8457i	−0.864407	+	0.864407i	−0.991846	−	0.127439i	$-0.959324\pi$
$761$	−23.8457	+	23.8457i	−0.864407	+	0.864407i	0.127439	+	0.991846i	$0.459324\pi$
$762$	5.17189	+	35.0402i	0.187358	+	1.26937i
$763$			18.2769i			0.661667i
$764$	−9.58245	−	31.7539i	−0.346681	−	1.14882i
$765$	15.4992	−	15.4992i	0.560376	−	0.560376i
$766$	−22.4328	+	30.2016i	−0.810531	+	1.09123i
$767$	−17.1703	−	11.9895i	−0.619984	−	0.432917i
$768$	42.3237	+	17.8179i	1.52723	+	0.642948i
$769$	32.1913	+	32.1913i	1.16085	+	1.16085i	0.984290	+	0.176558i	$0.0564964\pi$
$769$	32.1913	+	32.1913i	1.16085	+	1.16085i	0.176558	+	0.984290i	$0.443504\pi$
$770$	4.87047	−	6.55718i	0.175520	−	0.236304i
$771$	−14.3678			−0.517443
$772$	24.9110	−	46.4439i	0.896567	−	1.67155i
$773$	14.1810	+	14.1810i	0.510055	+	0.510055i	0.914543	−	0.404488i	$-0.132550\pi$
$773$	14.1810	+	14.1810i	0.510055	+	0.510055i	−0.404488	+	0.914543i	$0.632550\pi$
$774$	−61.2762	+	9.04429i	−2.20253	+	0.325090i
$775$	−14.6709	−	14.6709i	−0.526996	−	0.526996i
$776$	11.8478	+	4.26815i	0.425311	+	0.153218i
$777$			115.168i			4.13162i
$778$	1.23440	+	8.36321i	0.0442554	+	0.299835i
$779$	11.8917			0.426063
$780$	−8.71172	+	26.6014i	−0.311930	+	0.952484i
$781$	1.18124			0.0422680
$782$	−3.12551	−	21.1757i	−0.111768	−	0.757241i
$783$		−	11.2467i		−	0.401926i
$784$	24.8636	+	37.4445i	0.887986	+	1.33730i
$785$	−3.26112	−	3.26112i	−0.116394	−	0.116394i
$786$	31.4410	−	4.64066i	1.12146	−	0.165527i
$787$	−10.9385	−	10.9385i	−0.389916	−	0.389916i	0.484742	−	0.874657i	$-0.338914\pi$
$787$	−10.9385	−	10.9385i	−0.389916	−	0.389916i	−0.874657	+	0.484742i	$0.838914\pi$
$788$	−2.38876	−	1.28125i	−0.0850959	−	0.0456427i
$789$	−46.0737			−1.64027
$790$	3.74726	−	5.04498i	0.133321	−	0.179492i
$791$	−24.1573	−	24.1573i	−0.858935	−	0.858935i
$792$	13.9368	+	5.02072i	0.495224	+	0.178404i
$793$	−44.8173	+	7.96261i	−1.59151	+	0.282761i
$794$	22.8920	−	30.8198i	0.812406	−	1.09375i
$795$	20.8709	−	20.8709i	0.740215	−	0.740215i
$796$	−37.6104	+	11.3498i	−1.33306	+	0.402281i
$797$			31.6553i			1.12129i	0.828057	+	0.560644i	$0.189446\pi$
$797$			31.6553i			1.12129i	−0.828057	+	0.560644i	$0.810554\pi$
$798$	2.86162	+	19.3879i	0.101300	+	0.686323i
$799$	4.25471	−	4.25471i	0.150521	−	0.150521i
$800$	11.9976	+	13.3336i	0.424178	+	0.471414i
$801$	−9.99650	+	9.99650i	−0.353209	+	0.353209i
$802$	−15.1944	+	20.4565i	−0.536534	+	0.722343i
$803$	16.2339			0.572884
$804$	1.42441	+	0.764010i	0.0502352	+	0.0269445i
$805$			28.2508i			0.995710i
$806$	−14.9027	+	29.8519i	−0.524924	+	1.05149i
$807$			47.7944i			1.68244i
$808$	18.5771	+	39.4990i	0.653541	+	1.38957i
$809$	−26.7423			−0.940210			−0.470105	−	0.882610i	$-0.655784\pi$
$809$	−26.7423			−0.940210			−0.470105	+	0.882610i	$0.655784\pi$
$810$	−4.17364	−	3.10005i	−0.146647	−	0.108925i
$811$	8.51512	−	8.51512i	0.299006	−	0.299006i	−0.541618	−	0.840625i	$-0.682188\pi$
$811$	8.51512	−	8.51512i	0.299006	−	0.299006i	0.840625	+	0.541618i	$0.182188\pi$
$812$	13.1822	+	7.07051i	0.462605	+	0.248126i
$813$	17.9786	−	17.9786i	0.630536	−	0.630536i
$814$	−13.1460	+	1.94034i	−0.460769	+	0.0680089i
$815$			14.1911i			0.497093i
$816$	−29.5947	+	19.6513i	−1.03602	+	0.687933i
$817$	6.68575	−	6.68575i	0.233905	−	0.233905i
$818$	30.7391	+	22.8320i	1.07477	+	0.798303i
$819$	−66.1184	−	46.1686i	−2.31036	−	1.61326i
$820$	−8.21927	−	27.2367i	−0.287029	−	0.951146i
$821$	−22.5698	−	22.5698i	−0.787690	−	0.787690i	0.193425	−	0.981115i	$-0.438040\pi$
$821$	−22.5698	−	22.5698i	−0.787690	−	0.787690i	−0.981115	+	0.193425i	$0.938040\pi$
$822$	−16.2573	−	12.0754i	−0.567037	−	0.421178i
$823$	0.583983			0.0203564			0.0101782	−	0.999948i	$-0.496760\pi$
$823$	0.583983			0.0203564			0.0101782	+	0.999948i	$0.496760\pi$
$824$	−25.4424	+	11.9660i	−0.886326	+	0.416856i
$825$	6.43500	+	6.43500i	0.224038	+	0.224038i
$826$	5.12202	+	34.7023i	0.178218	+	1.20745i
$827$	27.4237	+	27.4237i	0.953617	+	0.953617i	0.998971	−	0.0453540i	$-0.0144416\pi$
$827$	27.4237	+	27.4237i	0.953617	+	0.953617i	−0.0453540	+	0.998971i	$0.514442\pi$
$828$	−49.0506	+	14.8021i	−1.70463	+	0.514408i
$829$			11.9270i			0.414242i	0.978315	+	0.207121i	$0.0664095\pi$
$829$			11.9270i			0.414242i	−0.978315	+	0.207121i	$0.933591\pi$
$830$	6.80070	−	1.00378i	0.236056	−	0.0348415i
$831$	−40.6097			−1.40874
$832$	14.2249	−	25.0929i	0.493160	−	0.869939i
$833$	−34.7716			−1.20477
$834$	61.8908	−	9.13502i	2.14310	−	0.316320i
$835$		−	20.5710i		−	0.711889i
$836$	−2.16485	+	0.653292i	−0.0748730	+	0.0225946i
$837$	−29.7117	−	29.7117i	−1.02699	−	1.02699i
$838$	−3.65269	−	24.7474i	−0.126180	−	0.854886i
$839$	7.85723	+	7.85723i	0.271262	+	0.271262i	0.829608	−	0.558346i	$-0.188564\pi$
$839$	7.85723	+	7.85723i	0.271262	+	0.271262i	−0.558346	+	0.829608i	$0.688564\pi$
$840$	42.4281	−	19.9547i	1.46391	−	0.688504i
$841$	−25.9326			−0.894226
$842$	37.1370	+	27.5842i	1.27982	+	0.950614i
$843$	33.5536	+	33.5536i	1.15565	+	1.15565i
$844$	13.1746	+	43.6576i	0.453490	+	1.50276i
$845$	15.9542	+	7.38911i	0.548841	+	0.254193i
$846$	−11.5620	−	8.58788i	−0.397509	−	0.295257i
$847$	−3.01968	+	3.01968i	−0.103757	+	0.103757i
$848$	−25.3379	+	16.8247i	−0.870108	+	0.577763i
$849$		−	27.5556i		−	0.945705i
$850$	−13.7272	+	2.02612i	−0.470839	+	0.0694953i
$851$	32.4989	−	32.4989i	1.11405	−	1.11405i
$852$	5.97525	+	3.20493i	0.204709	+	0.109799i
$853$	−23.1740	+	23.1740i	−0.793463	+	0.793463i	−0.982055	−	0.188593i	$-0.939607\pi$
$853$	−23.1740	+	23.1740i	−0.793463	+	0.793463i	0.188593	+	0.982055i	$0.439607\pi$
$854$	61.2080	+	45.4634i	2.09449	+	1.55573i
$855$	8.00886			0.273897
$856$	10.8594	+	23.0895i	0.371168	+	0.789184i
$857$		−	50.8306i		−	1.73634i	−0.496268	−	0.868169i	$-0.665297\pi$
$857$		−	50.8306i		−	1.73634i	0.496268	−	0.868169i	$-0.334703\pi$
$858$	6.53664	−	13.0937i	0.223157	−	0.447011i
$859$		−	6.53538i		−	0.222984i	−0.993765	−	0.111492i	$-0.964437\pi$
$859$		−	6.53538i		−	0.222984i	0.993765	−	0.111492i	$-0.0355630\pi$
$860$	−19.9341	−	10.6920i	−0.679747	−	0.364594i
$861$	128.911			4.39327
$862$	−0.314763	+	0.423769i	−0.0107209	+	0.0144336i
$863$	−27.7909	+	27.7909i	−0.946013	+	0.946013i	−0.998616	−	0.0526027i	$-0.983248\pi$
$863$	−27.7909	+	27.7909i	−0.946013	+	0.946013i	0.0526027	+	0.998616i	$0.483248\pi$
$864$	24.2976	+	27.0033i	0.826620	+	0.918672i
$865$	−23.4312	+	23.4312i	−0.796684	+	0.796684i
$866$	−3.62609	−	24.5672i	−0.123220	−	0.834828i
$867$			21.3093i			0.723701i
$868$	53.5038	−	16.1459i	1.81604	−	0.548029i
$869$	−2.32329	+	2.32329i	−0.0788121	+	0.0788121i
$870$	5.73296	−	7.71836i	0.194365	−	0.261677i
$871$	0.581262	−	0.832431i	0.0196953	−	0.0282058i
$872$	−11.3887	−	4.10277i	−0.385670	−	0.138937i
$873$	16.4888	+	16.4888i	0.558062	+	0.558062i
$874$	4.66350	−	6.27853i	0.157745	−	0.212375i
$875$	47.1923			1.59539
$876$	82.1190	+	44.0459i	2.77454	+	1.48817i
$877$	12.3351	+	12.3351i	0.416528	+	0.416528i	0.884005	−	0.467477i	$-0.154837\pi$
$877$	12.3351	+	12.3351i	0.416528	+	0.416528i	−0.467477	+	0.884005i	$0.654837\pi$
$878$	41.0203	−	6.05456i	1.38437	−	0.204331i
$879$	14.5088	+	14.5088i	0.489370	+	0.489370i
$880$	2.99260	+	4.50684i	0.100881	+	0.151926i
$881$			4.46180i			0.150322i	0.997171	+	0.0751609i	$0.0239470\pi$
$881$			4.46180i			0.150322i	−0.997171	+	0.0751609i	$0.976053\pi$
$882$	12.1529	+	82.3375i	0.409210	+	2.77245i
$883$	−53.0506			−1.78529			−0.892647	−	0.450757i	$-0.851154\pi$
$883$	−53.0506			−1.78529			−0.892647	+	0.450757i	$0.851154\pi$
$884$	10.0842	+	19.9055i	0.339168	+	0.669495i
$885$	22.5462			0.757882
$886$	0.371342	+	2.51589i	0.0124755	+	0.0845230i
$887$			51.4052i			1.72602i	0.505188	+	0.863010i	$0.331423\pi$
$887$			51.4052i			1.72602i	−0.505188	+	0.863010i	$0.668577\pi$
$888$	−71.7634	−	25.8527i	−2.40822	−	0.867559i
$889$	−26.3510	−	26.3510i	−0.883783	−	0.883783i
$890$	−5.10756	+	0.753871i	−0.171206	+	0.0252698i
$891$	1.92202	+	1.92202i	0.0643901	+	0.0643901i
$892$	−3.94178	+	7.34904i	−0.131981	+	0.246064i
$893$	2.19852			0.0735706
$894$	42.3408	−	57.0040i	1.41609	−	1.90650i
$895$	20.4706	+	20.4706i	0.684256	+	0.684256i
$896$	−46.9256	+	11.5028i	−1.56767	+	0.384280i
$897$	8.85426	+	49.8359i	0.295635	+	1.66397i
$898$	−13.9562	+	18.7893i	−0.465723	+	0.627009i
$899$	8.10360	−	8.10360i	0.270270	−	0.270270i
$900$	9.59549	+	31.7972i	0.319850	+	1.05991i
$901$		−	23.5293i		−	0.783873i
$902$	2.17188	+	14.7148i	0.0723159	+	0.489949i
$903$	72.4764	−	72.4764i	2.41186	−	2.41186i
$904$	20.4757	−	9.63013i	0.681013	−	0.320293i
$905$	1.23026	−	1.23026i	0.0408953	−	0.0408953i
$906$	−1.14815	+	1.54577i	−0.0381448	+	0.0513549i
$907$	−16.6521			−0.552925			−0.276463	−	0.961025i	$-0.589162\pi$
$907$	−16.6521			−0.552925			−0.276463	+	0.961025i	$0.589162\pi$
$908$	−23.7262	+	44.2350i	−0.787381	+	1.46799i
$909$			80.8258i			2.68082i
$910$	−9.33051	−	27.9334i	−0.309303	−	0.925984i
$911$		−	32.7185i		−	1.08401i	−0.840374	−	0.542007i	$-0.817665\pi$
$911$		−	32.7185i		−	1.08401i	0.840374	−	0.542007i	$-0.182335\pi$
$912$	−12.7234	−	2.56902i	−0.421313	−	0.0850687i
$913$	−3.59407			−0.118947
$914$	14.2490	+	10.5837i	0.471316	+	0.350079i
$915$	34.6524	−	34.6524i	1.14557	−	1.14557i
$916$	−9.99595	+	18.6364i	−0.330275	+	0.615764i
$917$	−23.6443	+	23.6443i	−0.780804	+	0.780804i
$918$	−27.8005	+	4.10331i	−0.917552	+	0.135430i
$919$		−	9.07606i		−	0.299392i	−0.988732	−	0.149696i	$-0.952171\pi$
$919$		−	9.07606i		−	0.299392i	0.988732	−	0.149696i	$-0.0478294\pi$
$920$	−17.6037	−	6.34170i	−0.580376	−	0.209080i
$921$	15.8970	−	15.8970i	0.523822	−	0.523822i
$922$	24.6730	+	18.3263i	0.812562	+	0.603546i
$923$	2.43833	−	3.49195i	0.0802585	−	0.114939i
$924$	−23.4679	+	7.08197i	−0.772039	+	0.232980i
$925$	−21.0675	−	21.0675i	−0.692695	−	0.692695i
$926$	−46.7974	−	34.7597i	−1.53786	−	1.14227i
$927$	−52.0621			−1.70994
$928$	−7.36491	+	6.62694i	−0.241765	+	0.217540i
$929$	−5.77386	−	5.77386i	−0.189434	−	0.189434i	0.606017	−	0.795452i	$-0.292766\pi$
$929$	−5.77386	−	5.77386i	−0.189434	−	0.189434i	−0.795452	+	0.606017i	$0.792766\pi$
$930$	−5.24504	−	35.5358i	−0.171992	−	1.16526i
$931$	−8.98371	−	8.98371i	−0.294429	−	0.294429i
$932$	8.64001	+	28.6309i	0.283013	+	0.937837i
$933$		−	34.8010i		−	1.13933i
$934$	12.8548	−	1.89736i	0.420623	−	0.0620835i
$935$	−4.18513			−0.136869
$936$	43.6108	−	30.8359i	1.42546	−	1.00790i
$937$	40.8209			1.33356			0.666780	−	0.745254i	$-0.267672\pi$
$937$	40.8209			1.33356			0.666780	+	0.745254i	$0.267672\pi$
$938$	−1.68239	+	0.248319i	−0.0549321	+	0.00810792i
$939$		−	57.5244i		−	1.87724i
$940$	−1.51957	−	5.03549i	−0.0495629	−	0.164240i
$941$	−16.4104	−	16.4104i	−0.534964	−	0.534964i	0.387081	−	0.922046i	$-0.373483\pi$
$941$	−16.4104	−	16.4104i	−0.534964	−	0.534964i	−0.922046	+	0.387081i	$0.873483\pi$
$942$	2.02099	+	13.6925i	0.0658474	+	0.446124i
$943$	−36.3771	−	36.3771i	−1.18460	−	1.18460i
$944$	−22.7735	−	4.59828i	−0.741215	−	0.149661i
$945$	37.0890			1.20651
$946$	9.49404	+	7.05188i	0.308678	+	0.229276i
$947$	−28.2576	−	28.2576i	−0.918248	−	0.918248i	0.0786538	−	0.996902i	$-0.474938\pi$
$947$	−28.2576	−	28.2576i	−0.918248	−	0.918248i	−0.996902	+	0.0786538i	$0.974938\pi$
$948$	−18.0558	+	5.44874i	−0.586426	+	0.176967i
$949$	33.5104	−	47.9905i	1.08779	−	1.55784i
$950$	−4.07008	−	3.02313i	−0.132051	−	0.0980832i
$951$	−2.77068	+	2.77068i	−0.0898454	+	0.0898454i
$952$	12.6679	−	35.1643i	0.410569	−	1.13968i
$953$			24.7435i			0.801522i	0.916183	+	0.400761i	$0.131254\pi$
$953$			24.7435i			0.801522i	−0.916183	+	0.400761i	$0.868746\pi$
$954$	−55.7161	+	8.22363i	−1.80388	+	0.266250i
$955$	15.8602	−	15.8602i	0.513225	−	0.513225i
$956$	−19.4630	+	36.2866i	−0.629477	+	1.17359i
$957$	−3.55442	+	3.55442i	−0.114898	+	0.114898i
$958$	−16.8794	−	12.5375i	−0.545349	−	0.405068i
$959$	21.3068			0.688032
$960$	2.91003	+	30.9173i	0.0939208	+	0.997850i
$961$		−	11.8163i		−	0.381171i
$962$	−21.4003	+	42.8674i	−0.689972	+	1.38210i
$963$			47.2475i			1.52253i
$964$	4.66210	−	8.69199i	0.150156	−	0.279950i
$965$	35.6399			1.14729
$966$	50.5544	−	68.0620i	1.62656	−	2.18986i
$967$	39.1894	−	39.1894i	1.26025	−	1.26025i	0.309273	−	0.950973i	$-0.399914\pi$
$967$	39.1894	−	39.1894i	1.26025	−	1.26025i	0.950973	−	0.309273i	$-0.100086\pi$
$968$	−1.20377	−	2.55948i	−0.0386907	−	0.0822648i
$969$	7.10039	−	7.10039i	0.228097	−	0.228097i
$970$	1.24348	+	8.42472i	0.0399257	+	0.270502i
$971$		−	13.1932i		−	0.423391i	−0.977336	−	0.211695i	$-0.932102\pi$
$971$		−	13.1932i		−	0.423391i	0.977336	−	0.211695i	$-0.0678985\pi$
$972$	−6.62356	−	21.9489i	−0.212451	−	0.704011i
$973$	−46.5432	+	46.5432i	−1.49211	+	1.49211i
$974$	28.5051	−	38.3768i	0.913363	−	1.22967i
$975$	32.3062	−	5.73980i	1.03463	−	0.183821i
$976$	−42.0691	+	27.9344i	−1.34660	+	0.894160i
$977$	−11.3537	−	11.3537i	−0.363236	−	0.363236i	0.501767	−	0.865003i	$-0.332684\pi$
$977$	−11.3537	−	11.3537i	−0.363236	−	0.363236i	−0.865003	+	0.501767i	$0.832684\pi$
$978$	25.3948	−	34.1893i	0.812035	−	1.09325i
$979$	2.69928			0.0862693
$980$	−14.3669	+	26.7856i	−0.458935	+	0.855636i
$981$	−15.8499	−	15.8499i	−0.506049	−	0.506049i
$982$	−5.38620	+	0.794997i	−0.171881	+	0.0253694i
$983$	22.9851	+	22.9851i	0.733112	+	0.733112i	0.971235	−	0.238123i	$-0.0765320\pi$
$983$	22.9851	+	22.9851i	0.733112	+	0.733112i	−0.238123	+	0.971235i	$0.576532\pi$
$984$	−28.9377	+	80.3271i	−0.922501	+	2.56073i
$985$		−	1.83307i		−	0.0584064i
$986$	−1.11914	−	7.58231i	−0.0356407	−	0.241470i
$987$	23.8329			0.758609
$988$	−2.53747	+	7.74823i	−0.0807278	+	0.246504i
$989$	−40.9039			−1.30067
$990$	1.46273	+	9.91019i	0.0464887	+	0.314966i
$991$			15.5409i			0.493672i	0.969057	+	0.246836i	$0.0793909\pi$
$991$			15.5409i			0.493672i	−0.969057	+	0.246836i	$0.920609\pi$
$992$	−1.94958	+	36.9638i	−0.0618991	+	1.17360i
$993$	4.20462	+	4.20462i	0.133430	+	0.133430i
$994$	−7.05745	+	1.04167i	−0.223849	+	0.0330398i
$995$	−18.7854	−	18.7854i	−0.595536	−	0.595536i
$996$	−18.1805	−	9.75144i	−0.576072	−	0.308986i
$997$	12.9191			0.409151			0.204576	−	0.978851i	$-0.434419\pi$
$997$	12.9191			0.409151			0.204576	+	0.978851i	$0.434419\pi$
$998$	−9.28259	+	12.4973i	−0.293835	+	0.395594i
$999$	−42.6661	−	42.6661i	−1.34990	−	1.34990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.3	✓	140
4.3	odd	2	inner	572.2.j.a.463.38	yes	140
13.5	odd	4	inner	572.2.j.a.551.38	yes	140
52.31	even	4	inner	572.2.j.a.551.3	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.3	✓	140	1.1	even	1	trivial
572.2.j.a.463.38	yes	140	4.3	odd	2	inner
572.2.j.a.551.3	yes	140	52.31	even	4	inner
572.2.j.a.551.38	yes	140	13.5	odd	4	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39906 + 0.206499i) q^{2} +2.87009i q^{3} +(1.91472 - 0.577808i) q^{4} +(0.956348 + 0.956348i) q^{5} +(-0.592670 - 4.01541i) q^{6} +(3.01968 + 3.01968i) q^{7} +(-2.55948 + 1.20377i) q^{8} -5.23740 q^{9} +O(q^{10})\)	\(q+(-1.39906 + 0.206499i) q^{2} +2.87009i q^{3} +(1.91472 - 0.577808i) q^{4} +(0.956348 + 0.956348i) q^{5} +(-0.592670 - 4.01541i) q^{6} +(3.01968 + 3.01968i) q^{7} +(-2.55948 + 1.20377i) q^{8} -5.23740 q^{9} +(-1.53547 - 1.14050i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.65836 + 5.49540i) q^{12} +(3.54996 - 0.630715i) q^{13} +(-4.84826 - 3.60114i) q^{14} +(-2.74480 + 2.74480i) q^{15} +(3.33228 - 2.21268i) q^{16} +3.09441i q^{17} +(7.32741 - 1.08152i) q^{18} +(-0.799483 + 0.799483i) q^{19} +(2.38372 + 1.27855i) q^{20} +(-8.66674 + 8.66674i) q^{21} +(-1.13530 - 0.843265i) q^{22} +4.89130 q^{23} +(-3.45493 - 7.34593i) q^{24} -3.17080i q^{25} +(-4.83635 + 1.61547i) q^{26} -6.42153i q^{27} +(7.52662 + 4.03703i) q^{28} +1.75141 q^{29} +(3.27333 - 4.40693i) q^{30} +(4.62689 - 4.62689i) q^{31} +(-4.20513 + 3.78377i) q^{32} +(-2.02946 + 2.02946i) q^{33} +(-0.638993 - 4.32926i) q^{34} +5.77573i q^{35} +(-10.0281 + 3.02621i) q^{36} +(6.64423 - 6.64423i) q^{37} +(0.953429 - 1.28361i) q^{38} +(1.81021 + 10.1887i) q^{39} +(-3.59898 - 1.29653i) q^{40} +(-7.43710 - 7.43710i) q^{41} +(10.3356 - 13.9149i) q^{42} -8.36259 q^{43} +(1.76248 + 0.945337i) q^{44} +(-5.00878 - 5.00878i) q^{45} +(-6.84320 + 1.01005i) q^{46} +(-1.37496 - 1.37496i) q^{47} +(6.35057 + 9.56392i) q^{48} +11.2369i q^{49} +(0.654766 + 4.43612i) q^{50} -8.88123 q^{51} +(6.43273 - 3.25883i) q^{52} -7.60379 q^{53} +(1.32604 + 8.98408i) q^{54} +1.35248i q^{55} +(-11.3638 - 4.09380i) q^{56} +(-2.29458 - 2.29458i) q^{57} +(-2.45032 + 0.361665i) q^{58} +(-4.10707 - 4.10707i) q^{59} +(-3.66955 + 6.84149i) q^{60} -12.6247 q^{61} +(-5.51784 + 7.42873i) q^{62} +(-15.8153 - 15.8153i) q^{63} +(5.10186 - 6.16206i) q^{64} +(3.99818 + 2.79181i) q^{65} +(2.42024 - 3.25841i) q^{66} +(0.199114 - 0.199114i) q^{67} +(1.78798 + 5.92492i) q^{68} +14.0384i q^{69} +(-1.19268 - 8.08057i) q^{70} +(0.835261 - 0.835261i) q^{71} +(13.4050 - 6.30464i) q^{72} +(11.4791 - 11.4791i) q^{73} +(-7.92363 + 10.6677i) q^{74} +9.10046 q^{75} +(-1.06884 + 1.99273i) q^{76} +4.27047i q^{77} +(-4.63654 - 13.8807i) q^{78} +3.28563i q^{79} +(5.30291 + 1.07073i) q^{80} +2.71815 q^{81} +(11.9407 + 8.86917i) q^{82} +(-2.54139 + 2.54139i) q^{83} +(-11.5866 + 21.6020i) q^{84} +(-2.95934 + 2.95934i) q^{85} +(11.6997 - 1.72687i) q^{86} +5.02670i q^{87} +(-2.66102 - 0.958629i) q^{88} +(1.90868 - 1.90868i) q^{89} +(8.04187 + 5.97325i) q^{90} +(12.6243 + 8.81517i) q^{91} +(9.36545 - 2.82623i) q^{92} +(13.2796 + 13.2796i) q^{93} +(2.20758 + 1.63972i) q^{94} -1.52917 q^{95} +(-10.8597 - 12.0691i) q^{96} +(-3.14829 - 3.14829i) q^{97} +(-2.32041 - 15.7211i) q^{98} +(-3.70340 - 3.70340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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