LMFDB - Embedded newform 544.2.v.a.461.52

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(253,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.253"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.v (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			461.52
Character	$\chi$	$=$	544.461
Dual form			544.2.v.a.485.52

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.906372 - 1.08558i) q^{2} -0.100368i q^{3} +(-0.356979 - 1.96788i) q^{4} +(-2.92504 - 2.92504i) q^{5} +(-0.108957 - 0.0909704i) q^{6} +(0.436118 + 1.05288i) q^{7} +(-2.45986 - 1.39610i) q^{8} +2.98993 q^{9} +(-5.82655 + 0.524198i) q^{10} -2.07878i q^{11} +(-0.197512 + 0.0358292i) q^{12} +(-0.796050 + 1.92184i) q^{13} +(1.53828 + 0.480861i) q^{14} +(-0.293579 + 0.293579i) q^{15} +(-3.74513 + 1.40499i) q^{16} +(-3.59022 + 2.02739i) q^{17} +(2.70999 - 3.24581i) q^{18} +(-1.92257 - 4.64149i) q^{19} +(-4.71196 + 6.80032i) q^{20} +(0.105675 - 0.0437721i) q^{21} +(-2.25668 - 1.88414i) q^{22} +(-1.71870 - 4.14931i) q^{23} +(-0.140124 + 0.246890i) q^{24} +12.1117i q^{25} +(1.36479 + 2.60608i) q^{26} -0.601195i q^{27} +(1.91626 - 1.23409i) q^{28} +0.0802030 q^{29} +(0.0526125 + 0.584797i) q^{30} +(-8.68138 + 3.59595i) q^{31} +(-1.86925 + 5.33909i) q^{32} -0.208642 q^{33} +(-1.05317 + 5.73505i) q^{34} +(1.80406 - 4.35538i) q^{35} +(-1.06734 - 5.88383i) q^{36} +(6.95738 - 6.95738i) q^{37} +(-6.78128 - 2.11981i) q^{38} +(0.192890 + 0.0798977i) q^{39} +(3.11152 + 11.2788i) q^{40} +(8.18046 - 3.38846i) q^{41} +(0.0482628 - 0.154393i) q^{42} +(7.75710 + 3.21310i) q^{43} +(-4.09079 + 0.742080i) q^{44} +(-8.74566 - 8.74566i) q^{45} +(-6.06221 - 1.89503i) q^{46} +0.385124 q^{47} +(0.141015 + 0.375890i) q^{48} +(4.03139 - 4.03139i) q^{49} +(13.1483 + 10.9777i) q^{50} +(0.203485 + 0.360342i) q^{51} +(4.06612 + 0.880479i) q^{52} +(1.59078 - 3.84049i) q^{53} +(-0.652647 - 0.544906i) q^{54} +(-6.08050 + 6.08050i) q^{55} +(0.397145 - 3.19880i) q^{56} +(-0.465855 + 0.192964i) q^{57} +(0.0726938 - 0.0870670i) q^{58} +(4.91222 - 11.8591i) q^{59} +(0.682532 + 0.472928i) q^{60} +(-4.25797 - 4.25797i) q^{61} +(-3.96487 + 12.6836i) q^{62} +(1.30396 + 3.14804i) q^{63} +(4.10179 + 6.86843i) q^{64} +(7.94993 - 3.29297i) q^{65} +(-0.189107 + 0.226498i) q^{66} +(-2.58048 + 6.22983i) q^{67} +(5.27131 + 6.34140i) q^{68} +(-0.416457 + 0.172502i) q^{69} +(-3.09298 - 5.90605i) q^{70} +(6.02773 - 14.5522i) q^{71} +(-7.35479 - 4.17425i) q^{72} +(3.14759 - 7.59896i) q^{73} +(-1.24684 - 13.8588i) q^{74} +1.21563 q^{75} +(-8.44759 + 5.44030i) q^{76} +(2.18870 - 0.906591i) q^{77} +(0.261566 - 0.136981i) q^{78} +(-2.10664 + 5.08589i) q^{79} +(15.0643 + 6.84502i) q^{80} +8.90944 q^{81} +(3.73609 - 11.9518i) q^{82} +(0.0451999 + 0.109122i) q^{83} +(-0.123862 - 0.192331i) q^{84} +(16.4317 + 4.57133i) q^{85} +(10.5189 - 5.50871i) q^{86} -0.00804979i q^{87} +(-2.90219 + 5.11349i) q^{88} +(3.36692 + 3.36692i) q^{89} +(-17.4210 + 1.56731i) q^{90} -2.37064 q^{91} +(-7.55183 + 4.86342i) q^{92} +(0.360917 + 0.871330i) q^{93} +(0.349066 - 0.418084i) q^{94} +(-7.95295 + 19.2001i) q^{95} +(0.535872 + 0.187613i) q^{96} +(-2.64025 - 6.37414i) q^{97} +(-0.722467 - 8.03034i) q^{98} -6.21539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 272 q^{9} - 4 q^{10} + 28 q^{12} - 28 q^{14} - 24 q^{16} + 4 q^{18} - 20 q^{19} - 4 q^{20} + 12 q^{21} + 4 q^{22} - 4 q^{23} + 36 q^{24}+ \cdots - 8 q^{97}+O(q^{100}) $ 280 * q - 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 272 * q^9 - 4 * q^10 + 28 * q^12 - 28 * q^14 - 24 * q^16 + 4 * q^18 - 20 * q^19 - 4 * q^20 + 12 * q^21 + 4 * q^22 - 4 * q^23 + 36 * q^24 - 4 * q^26 - 4 * q^28 - 8 * q^29 - 8 * q^30 - 24 * q^31 - 24 * q^32 + 8 * q^33 - 4 * q^34 + 12 * q^35 - 52 * q^36 - 4 * q^37 - 4 * q^39 + 32 * q^40 - 4 * q^41 + 40 * q^42 - 4 * q^43 + 20 * q^44 - 12 * q^45 - 8 * q^46 + 80 * q^47 - 76 * q^48 + 12 * q^50 + 24 * q^51 - 28 * q^52 - 4 * q^53 + 24 * q^54 + 20 * q^56 - 4 * q^57 + 20 * q^58 - 4 * q^59 + 4 * q^60 - 36 * q^61 + 104 * q^62 - 36 * q^63 + 8 * q^64 + 12 * q^65 - 24 * q^66 - 8 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^70 + 28 * q^71 - 52 * q^72 - 4 * q^73 - 8 * q^74 + 16 * q^75 - 20 * q^76 - 4 * q^77 + 24 * q^78 - 92 * q^80 + 240 * q^81 + 4 * q^82 - 44 * q^83 + 36 * q^84 - 4 * q^85 + 32 * q^86 + 4 * q^88 + 160 * q^90 + 56 * q^91 + 20 * q^92 + 20 * q^93 + 8 * q^94 + 12 * q^95 - 168 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.906372	−	1.08558i	0.640902	−	0.767623i
$2$	0.906372	−	1.08558i	0.640902	−	0.767623i
$3$		−	0.100368i		−	0.0579473i	−0.999580	−	0.0289736i	$-0.990776\pi$
$3$		−	0.100368i		−	0.0579473i	0.999580	−	0.0289736i	$-0.00922389\pi$
$4$	−0.356979	−	1.96788i	−0.178490	−	0.983942i
$5$	−2.92504	−	2.92504i	−1.30812	−	1.30812i	−0.922772	−	0.385346i	$-0.874082\pi$
$5$	−2.92504	−	2.92504i	−1.30812	−	1.30812i	−0.385346	−	0.922772i	$-0.625918\pi$
$6$	−0.108957	−	0.0909704i	−0.0444817	−	0.0371385i
$7$	0.436118	+	1.05288i	0.164837	+	0.397952i	0.984617	−	0.174727i	$-0.0559043\pi$
$7$	0.436118	+	1.05288i	0.164837	+	0.397952i	−0.819780	+	0.572679i	$0.805904\pi$
$8$	−2.45986	−	1.39610i	−0.869691	−	0.493597i
$9$	2.98993			0.996642
$10$	−5.82655	+	0.524198i	−1.84252	+	0.165766i
$11$		−	2.07878i		−	0.626774i	−0.949625	−	0.313387i	$-0.898536\pi$
$11$		−	2.07878i		−	0.626774i	0.949625	−	0.313387i	$-0.101464\pi$
$12$	−0.197512	+	0.0358292i	−0.0570168	+	0.0103430i
$13$	−0.796050	+	1.92184i	−0.220785	+	0.533021i	−0.994997	−	0.0999046i	$-0.968146\pi$
$13$	−0.796050	+	1.92184i	−0.220785	+	0.533021i	0.774212	+	0.632926i	$0.218146\pi$
$14$	1.53828	+	0.480861i	0.411121	+	0.128515i
$15$	−0.293579	+	0.293579i	−0.0758019	+	0.0758019i
$16$	−3.74513	+	1.40499i	−0.936283	+	0.351247i
$17$	−3.59022	+	2.02739i	−0.870756	+	0.491715i
$17$	−3.59022	+	2.02739i	−0.870756	+	0.491715i
$18$	2.70999	−	3.24581i	0.638750	−	0.765045i
$19$	−1.92257	−	4.64149i	−0.441067	−	1.06483i	−0.975575	−	0.219667i	$-0.929503\pi$
$19$	−1.92257	−	4.64149i	−0.441067	−	1.06483i	0.534508	−	0.845164i	$-0.320497\pi$
$20$	−4.71196	+	6.80032i	−1.05363	+	1.52060i
$21$	0.105675	−	0.0437721i	0.0230602	−	0.00955186i
$22$	−2.25668	−	1.88414i	−0.481126	−	0.401701i
$23$	−1.71870	−	4.14931i	−0.358374	−	0.865192i	−0.995529	−	0.0944560i	$-0.969889\pi$
$23$	−1.71870	−	4.14931i	−0.358374	−	0.865192i	0.637155	−	0.770736i	$-0.280111\pi$
$24$	−0.140124	+	0.246890i	−0.0286026	+	0.0503962i
$25$			12.1117i			2.42235i
$26$	1.36479	+	2.60608i	0.267658	+	0.511094i
$27$		−	0.601195i		−	0.115700i
$28$	1.91626	−	1.23409i	0.362140	−	0.233220i
$29$	0.0802030			0.0148933			0.00744666	−	0.999972i	$-0.497630\pi$
$29$	0.0802030			0.0148933			0.00744666	+	0.999972i	$0.497630\pi$
$30$	0.0526125	+	0.584797i	0.00960569	+	0.106769i
$31$	−8.68138	+	3.59595i	−1.55922	+	0.645851i	−0.984954	−	0.172816i	$-0.944713\pi$
$31$	−8.68138	+	3.59595i	−1.55922	+	0.645851i	−0.574268	+	0.818667i	$0.694713\pi$
$32$	−1.86925	+	5.33909i	−0.330440	+	0.943827i
$33$	−0.208642			−0.0363199
$34$	−1.05317	+	5.73505i	−0.180618	+	0.983553i
$35$	1.80406	−	4.35538i	0.304942	−	0.736194i
$36$	−1.06734	−	5.88383i	−0.177890	−	0.980638i
$37$	6.95738	−	6.95738i	1.14379	−	1.14379i	0.156035	−	0.987752i	$-0.450129\pi$
$37$	6.95738	−	6.95738i	1.14379	−	1.14379i	0.987752	−	0.156035i	$-0.0498712\pi$
$38$	−6.78128	−	2.11981i	−1.10007	−	0.343879i
$39$	0.192890	+	0.0798977i	0.0308871	+	0.0127939i
$40$	3.11152	+	11.2788i	0.491974	+	1.78334i
$41$	8.18046	−	3.38846i	1.27757	−	0.529188i	0.362315	−	0.932056i	$-0.381987\pi$
$41$	8.18046	−	3.38846i	1.27757	−	0.529188i	0.915258	+	0.402868i	$0.131987\pi$
$42$	0.0482628	−	0.154393i	0.00744712	−	0.0238234i
$43$	7.75710	+	3.21310i	1.18295	+	0.489992i	0.885452	−	0.464731i	$-0.153849\pi$
$43$	7.75710	+	3.21310i	1.18295	+	0.489992i	0.297495	+	0.954724i	$0.403849\pi$
$44$	−4.09079	+	0.742080i	−0.616710	+	0.111873i
$45$	−8.74566	−	8.74566i	−1.30373	−	1.30373i
$46$	−6.06221	−	1.89503i	−0.893824	−	0.279407i
$47$	0.385124			0.0561761			0.0280881	−	0.999605i	$-0.491058\pi$
$47$	0.385124			0.0561761			0.0280881	+	0.999605i	$0.491058\pi$
$48$	0.141015	+	0.375890i	0.0203538	+	0.0542551i
$49$	4.03139	−	4.03139i	0.575912	−	0.575912i
$50$	13.1483	+	10.9777i	1.85945	+	1.55249i
$51$	0.203485	+	0.360342i	0.0284935	+	0.0504580i
$52$	4.06612	+	0.880479i	0.563870	+	0.122100i
$53$	1.59078	−	3.84049i	0.218511	−	0.527532i	−0.776171	−	0.630522i	$-0.782841\pi$
$53$	1.59078	−	3.84049i	0.218511	−	0.527532i	0.994682	+	0.102990i	$0.0328409\pi$
$54$	−0.652647	−	0.544906i	−0.0888140	−	0.0741523i
$55$	−6.08050	+	6.08050i	−0.819895	+	0.819895i
$56$	0.397145	−	3.19880i	0.0530708	−	0.427458i
$57$	−0.465855	+	0.192964i	−0.0617040	+	0.0255586i
$58$	0.0726938	−	0.0870670i	0.00954516	−	0.0114325i
$59$	4.91222	−	11.8591i	0.639516	−	1.54393i	−0.187808	−	0.982206i	$-0.560138\pi$
$59$	4.91222	−	11.8591i	0.639516	−	1.54393i	0.827325	−	0.561724i	$-0.189862\pi$
$60$	0.682532	+	0.472928i	0.0881145	+	0.0610548i
$61$	−4.25797	−	4.25797i	−0.545178	−	0.545178i	0.379865	−	0.925042i	$-0.375971\pi$
$61$	−4.25797	−	4.25797i	−0.545178	−	0.545178i	−0.925042	+	0.379865i	$0.875971\pi$
$62$	−3.96487	+	12.6836i	−0.503539	+	1.61082i
$63$	1.30396	+	3.14804i	0.164284	+	0.396616i
$64$	4.10179	+	6.86843i	0.512723	+	0.858554i
$65$	7.94993	−	3.29297i	0.986067	−	0.408442i
$66$	−0.189107	+	0.226498i	−0.0232775	+	0.0278800i
$67$	−2.58048	+	6.22983i	−0.315256	+	0.761094i	0.684238	+	0.729259i	$0.260135\pi$
$67$	−2.58048	+	6.22983i	−0.315256	+	0.761094i	−0.999493	+	0.0318352i	$0.989865\pi$
$68$	5.27131	+	6.34140i	0.639240	+	0.769007i
$69$	−0.416457	+	0.172502i	−0.0501355	+	0.0207668i
$70$	−3.09298	−	5.90605i	−0.369682	−	0.705909i
$71$	6.02773	−	14.5522i	0.715359	−	1.72703i	0.0292063	−	0.999573i	$-0.490702\pi$
$71$	6.02773	−	14.5522i	0.715359	−	1.72703i	0.686153	−	0.727457i	$-0.259298\pi$
$72$	−7.35479	−	4.17425i	−0.866770	−	0.491940i
$73$	3.14759	−	7.59896i	0.368398	−	0.889391i	−0.625615	−	0.780132i	$-0.715152\pi$
$73$	3.14759	−	7.59896i	0.368398	−	0.889391i	0.994013	−	0.109259i	$-0.0348479\pi$
$74$	−1.24684	−	13.8588i	−0.144942	−	1.61105i
$75$	1.21563			0.140368
$76$	−8.44759	+	5.44030i	−0.969005	+	0.624046i
$77$	2.18870	−	0.906591i	0.249426	−	0.103316i
$78$	0.261566	−	0.136981i	0.0296165	−	0.0155101i
$79$	−2.10664	+	5.08589i	−0.237016	+	0.572207i	−0.996971	−	0.0777678i	$-0.975221\pi$
$79$	−2.10664	+	5.08589i	−0.237016	+	0.572207i	0.759955	+	0.649975i	$0.225221\pi$
$80$	15.0643	+	6.84502i	1.68424	+	0.765296i
$81$	8.90944			0.989938
$82$	3.73609	−	11.9518i	0.412582	−	1.31985i
$83$	0.0451999	+	0.109122i	0.00496133	+	0.0119777i	0.926341	−	0.376687i	$-0.122937\pi$
$83$	0.0451999	+	0.109122i	0.00496133	+	0.0119777i	−0.921379	+	0.388664i	$0.872937\pi$
$84$	−0.123862	−	0.192331i	−0.0135145	−	0.0209850i
$85$	16.4317	+	4.57133i	1.78227	+	0.495831i
$86$	10.5189	−	5.50871i	1.13428	−	0.594020i
$87$		−	0.00804979i		−	0.000863028i
$88$	−2.90219	+	5.11349i	−0.309374	+	0.545100i
$89$	3.36692	+	3.36692i	0.356893	+	0.356893i	0.862666	−	0.505774i	$-0.168793\pi$
$89$	3.36692	+	3.36692i	0.356893	+	0.356893i	−0.505774	+	0.862666i	$0.668793\pi$
$90$	−17.4210	+	1.56731i	−1.83633	+	0.165209i
$91$	−2.37064			−0.248510
$92$	−7.55183	+	4.86342i	−0.787332	+	0.507047i
$93$	0.360917	+	0.871330i	0.0374253	+	0.0903527i
$94$	0.349066	−	0.418084i	0.0360034	−	0.0431221i
$95$	−7.95295	+	19.2001i	−0.815956	+	1.96989i
$96$	0.535872	+	0.187613i	0.0546922	+	0.0191481i
$97$	−2.64025	−	6.37414i	−0.268077	−	0.647196i	0.731316	−	0.682039i	$-0.238907\pi$
$97$	−2.64025	−	6.37414i	−0.268077	−	0.647196i	−0.999393	+	0.0348437i	$0.988907\pi$
$98$	−0.722467	−	8.03034i	−0.0729802	−	0.811187i
$99$		−	6.21539i		−	0.624670i
$100$	23.8345	−	4.32364i	2.38345	−	0.432364i
$101$	−1.05173	+	0.435642i	−0.104651	+	0.0433480i	−0.434395	−	0.900723i	$-0.643038\pi$
$101$	−1.05173	+	0.435642i	−0.104651	+	0.0433480i	0.329744	+	0.944071i	$0.393038\pi$
$102$	0.575614	+	0.105704i	0.0569943	+	0.0104663i
$103$	−10.6940	+	10.6940i	−1.05371	+	1.05371i	−0.0552415	+	0.998473i	$0.517593\pi$
$103$	−10.6940	+	10.6940i	−1.05371	+	1.05371i	−0.998473	+	0.0552415i	$0.982407\pi$
$104$	4.64125	−	3.61607i	0.455112	−	0.354585i
$105$	−0.437140	−	0.181069i	−0.0426605	−	0.0176705i
$106$	−2.72733	−	5.20784i	−0.264902	−	0.505830i
$107$	−6.96544	+	6.96544i	−0.673375	+	0.673375i	−0.958493	−	0.285118i	$-0.907967\pi$
$107$	−6.96544	+	6.96544i	−0.673375	+	0.673375i	0.285118	+	0.958493i	$0.407967\pi$
$108$	−1.18308	+	0.214614i	−0.113842	+	0.0206512i
$109$	−5.81362	+	5.81362i	−0.556844	+	0.556844i	−0.928407	−	0.371564i	$-0.878822\pi$
$109$	−5.81362	+	5.81362i	−0.556844	+	0.556844i	0.371564	+	0.928407i	$0.378822\pi$
$110$	1.08969	+	12.1121i	0.103898	+	1.15484i
$111$	−0.698296	−	0.698296i	−0.0662793	−	0.0662793i
$112$	−3.11260	−	3.33044i	−0.294113	−	0.314697i
$113$	−2.70762	+	6.53677i	−0.254712	+	0.614928i	−0.998573	−	0.0534060i	$-0.982992\pi$
$113$	−2.70762	+	6.53677i	−0.254712	+	0.614928i	0.743861	+	0.668334i	$0.232992\pi$
$114$	−0.212760	+	0.680621i	−0.0199268	+	0.0637460i
$115$	−7.10964	+	17.1642i	−0.662977	+	1.60057i
$116$	−0.0286308	−	0.157830i	−0.00265830	−	0.0146542i
$117$	−2.38013	+	5.74615i	−0.220043	+	0.531231i
$118$	−8.42178	−	16.0814i	−0.775288	−	1.48041i
$119$	−3.70036	−	2.89589i	−0.339212	−	0.265466i
$120$	1.13203	−	0.312296i	0.103340	−	0.0285086i
$121$	6.67869			0.607154
$122$	−8.48169	+	0.763074i	−0.767896	+	0.0690854i
$123$	−0.340091	−	0.821053i	−0.0306650	−	0.0740319i
$124$	10.1755	+	15.8003i	0.913785	+	1.41891i
$125$	20.8021	−	20.8021i	1.86060	−	1.86060i
$126$	4.59933	+	1.43774i	0.409741	+	0.128084i
$127$	1.80969	−	1.80969i	0.160584	−	0.160584i	−0.622242	−	0.782825i	$-0.713778\pi$
$127$	1.80969	−	1.80969i	0.160584	−	0.160584i	0.782825	+	0.622242i	$0.213778\pi$
$128$	11.1740	+	1.77253i	0.987651	+	0.156671i
$129$	0.322491	−	0.778562i	0.0283937	−	0.0685485i
$130$	3.63080	−	11.6150i	0.318443	−	1.01870i
$131$	−10.0446			−0.877598			−0.438799	−	0.898585i	$-0.644596\pi$
$131$	−10.0446			−0.877598			−0.438799	+	0.898585i	$0.644596\pi$
$132$	0.0744808	+	0.410583i	0.00648272	+	0.0357366i
$133$	4.04847	−	4.04847i	0.351047	−	0.351047i
$134$	4.42412	+	8.44786i	0.382186	+	0.729784i
$135$	−1.75852	+	1.75852i	−0.151349	+	0.151349i
$136$	11.6619	+	0.0252266i	0.999998	+	0.00216316i
$137$	2.37223	+	2.37223i	0.202673	+	0.202673i	0.801144	−	0.598471i	$-0.204225\pi$
$137$	2.37223	+	2.37223i	0.202673	+	0.202673i	−0.598471	+	0.801144i	$0.704225\pi$
$138$	−0.190200	+	0.608449i	−0.0161909	+	0.0517947i
$139$	4.01478	+	4.01478i	0.340529	+	0.340529i	0.856566	−	0.516037i	$-0.172593\pi$
$139$	4.01478	+	4.01478i	0.340529	+	0.340529i	−0.516037	+	0.856566i	$0.672593\pi$
$140$	−9.21490	−	1.99540i	−0.778801	−	0.168642i
$141$		−	0.0386540i		−	0.00325525i
$142$	−10.3343	−	19.7333i	−0.867233	−	1.65598i
$143$	3.99507	+	1.65481i	0.334084	+	0.138382i
$144$	−11.1977	+	4.20081i	−0.933139	+	0.350067i
$145$	−0.234597	−	0.234597i	−0.0194822	−	0.0194822i
$146$	−5.39641	−	10.3045i	−0.446610	−	0.852803i
$147$	−0.404621	−	0.404621i	−0.0333726	−	0.0333726i
$148$	−16.1750	−	11.2077i	−1.32957	−	0.921265i
$149$	−11.1370	+	4.61311i	−0.912381	+	0.377921i	−0.788968	−	0.614435i	$-0.789384\pi$
$149$	−11.1370	+	4.61311i	−0.912381	+	0.377921i	−0.123413	+	0.992355i	$0.539384\pi$
$150$	1.10181	−	1.31966i	0.0899624	−	0.107750i
$151$		−	18.7792i		−	1.52823i	−0.645080	−	0.764115i	$-0.723176\pi$
$151$		−	18.7792i		−	1.52823i	0.645080	−	0.764115i	$-0.276824\pi$
$152$	−1.75076	+	14.1015i	−0.142006	+	1.14378i
$153$	−10.7345	+	6.06176i	−0.867832	+	0.490064i
$154$	0.999601	−	3.19773i	0.0805502	−	0.257680i
$155$	35.9117	+	14.8751i	2.88450	+	1.19480i
$156$	0.0883716	−	0.408107i	0.00707539	−	0.0326747i
$157$	12.8608	+	5.32712i	1.02640	+	0.425150i	0.831413	−	0.555655i	$-0.187532\pi$
$157$	12.8608	+	5.32712i	1.02640	+	0.425150i	0.194990	+	0.980805i	$0.437532\pi$
$158$	3.61175	+	6.89665i	0.287335	+	0.548668i
$159$	−0.385461	−	0.159663i	−0.0305691	−	0.0126621i
$160$	21.0847	−	10.1494i	1.66689	−	0.802382i
$161$	3.61918	−	3.61918i	0.285231	−	0.285231i
$162$	8.07527	−	9.67193i	0.634453	−	0.759899i
$163$	−10.7208	−	10.7208i	−0.839717	−	0.839717i	0.149104	−	0.988822i	$-0.452361\pi$
$163$	−10.7208	−	10.7208i	−0.839717	−	0.839717i	−0.988822	+	0.149104i	$0.952361\pi$
$164$	−9.58834	−	14.8886i	−0.748724	−	1.16260i
$165$	0.610286	+	0.610286i	0.0475107	+	0.0475107i
$166$	0.159429	+	0.0498371i	0.0123741	+	0.00386811i
$167$	1.99880	−	4.82552i	0.154672	−	0.373410i	−0.827482	−	0.561493i	$-0.810227\pi$
$167$	1.99880	−	4.82552i	0.154672	−	0.373410i	0.982153	+	0.188082i	$0.0602272\pi$
$168$	−0.321056	−	0.0398605i	−0.0247700	−	0.00307531i
$169$	6.13263	+	6.13263i	0.471741	+	0.471741i
$170$	19.8558	−	13.6947i	1.52287	−	1.05033i
$171$	−5.74833	−	13.8777i	−0.439586	−	1.06125i
$172$	3.55387	−	16.4121i	0.270980	−	1.25141i
$173$	21.9090			1.66571			0.832854	−	0.553493i	$-0.186706\pi$
$173$	21.9090			1.66571			0.832854	+	0.553493i	$0.186706\pi$
$174$	−0.00873871	−	0.00729610i	−0.000662480	−	0.000553116i
$175$	−12.7522	+	5.28214i	−0.963977	+	0.399292i
$176$	2.92065	+	7.78529i	0.220152	+	0.586838i
$177$	−1.19027	−	0.493028i	−0.0894665	−	0.0370582i
$178$	6.70675	−	0.603387i	0.502692	−	0.0452258i
$179$	−4.06465	+	1.68363i	−0.303806	+	0.125841i	−0.529378	−	0.848386i	$-0.677575\pi$
$179$	−4.06465	+	1.68363i	−0.303806	+	0.125841i	0.225572	+	0.974226i	$0.427575\pi$
$180$	−14.0884	+	20.3325i	−1.05009	+	1.51549i
$181$			1.21540i			0.0903400i	0.998979	+	0.0451700i	$0.0143830\pi$
$181$			1.21540i			0.0903400i	−0.998979	+	0.0451700i	$0.985617\pi$
$182$	−2.14868	+	2.57352i	−0.159271	+	0.190762i
$183$	−0.427363	+	0.427363i	−0.0315916	+	0.0315916i
$184$	−1.56512	+	12.6062i	−0.115382	+	0.929342i
$185$	−40.7013			−2.99242
$186$	1.27303	+	0.397944i	0.0933428	+	0.0291787i
$187$	4.21449	+	7.46326i	0.308194	+	0.545768i
$188$	−0.137481	−	0.757879i	−0.0100269	−	0.0552740i
$189$	0.632987	−	0.262192i	0.0460430	−	0.0190716i
$190$	13.6350	+	26.0361i	0.989186	+	1.88885i
$191$		−	20.6078i		−	1.49113i	−0.666435	−	0.745563i	$-0.732180\pi$
$191$		−	20.6078i		−	1.49113i	0.666435	−	0.745563i	$-0.267820\pi$
$192$	0.689368	−	0.411687i	0.0497509	−	0.0297109i
$193$	22.4951	+	9.31777i	1.61923	+	0.670708i	0.993964	−	0.109703i	$-0.0349901\pi$
$193$	22.4951	+	9.31777i	1.61923	+	0.670708i	0.625267	+	0.780411i	$0.284990\pi$
$194$	−9.31270	−	2.91113i	−0.668613	−	0.209007i
$195$	−0.330507	−	0.797916i	−0.0236681	−	0.0571399i
$196$	−9.37242	−	6.49418i	−0.669459	−	0.463870i
$197$		−	0.794356i		−	0.0565955i	−0.999600	−	0.0282978i	$-0.990991\pi$
$197$		−	0.794356i		−	0.0565955i	0.999600	−	0.0282978i	$-0.00900866\pi$
$198$	−6.74731	−	5.63345i	−0.479511	−	0.400352i
$199$	−2.57931	−	1.06839i	−0.182843	−	0.0757359i	0.289384	−	0.957213i	$-0.406550\pi$
$199$	−2.57931	−	1.06839i	−0.182843	−	0.0757359i	−0.472227	+	0.881477i	$0.656550\pi$
$200$	16.9092	−	29.7931i	1.19566	−	2.10669i
$201$	0.625273	+	0.258997i	0.0441034	+	0.0182682i
$202$	−0.480336	+	1.53660i	−0.0337963	+	0.108115i
$203$	0.0349780	+	0.0844443i	0.00245497	+	0.00592683i
$204$	0.636471	−	0.529069i	0.0445619	−	0.0370422i
$205$	−33.8396	−	14.0168i	−2.36346	−	0.978976i
$206$	1.91648	+	21.3020i	0.133528	+	1.48418i
$207$	−5.13879	−	12.4061i	−0.357171	−	0.862287i
$208$	0.281159	−	8.31597i	0.0194949	−	0.576609i
$209$	−9.64861	+	3.99659i	−0.667408	+	0.276450i
$210$	−0.592777	+	0.310435i	−0.0409055	+	0.0214221i
$211$	6.56528	−	6.56528i	0.451972	−	0.451972i	−0.444036	−	0.896009i	$-0.646454\pi$
$211$	6.56528	−	6.56528i	0.451972	−	0.451972i	0.896009	+	0.444036i	$0.146454\pi$
$212$	−8.12552	−	1.75950i	−0.558063	−	0.120843i
$213$	−1.46057	−	0.604989i	−0.100077	−	0.0414531i
$214$	1.24828	+	13.8749i	0.0853307	+	0.948465i
$215$	−13.2914	−	32.0883i	−0.906466	−	2.18840i
$216$	−0.839331	+	1.47885i	−0.0571092	+	0.100623i
$217$	−7.57221	−	7.57221i	−0.514035	−	0.514035i
$218$	1.04186	+	11.5805i	0.0705638	+	0.784328i
$219$	−0.762690	−	0.315916i	−0.0515378	−	0.0213477i
$220$	14.1363	+	9.79511i	0.953072	+	0.660386i
$221$	−1.03832	−	8.51372i	−0.0698450	−	0.572695i
$222$	−1.39097	+	0.125142i	−0.0933561	+	0.00839898i
$223$	15.0993	+	15.0993i	1.01112	+	1.01112i	0.999937	+	0.0111836i	$0.00355992\pi$
$223$	15.0993	+	15.0993i	1.01112	+	1.01112i	0.0111836	+	0.999937i	$0.496440\pi$
$224$	−6.43665	+	0.360370i	−0.430066	+	0.0240783i
$225$			36.2132i			2.41421i
$226$	4.64210	+	8.86410i	0.308788	+	0.589631i
$227$	−7.42247	+	7.42247i	−0.492647	+	0.492647i	−0.909139	−	0.416493i	$-0.863259\pi$
$227$	−7.42247	+	7.42247i	−0.492647	+	0.492647i	0.416493	+	0.909139i	$0.363259\pi$
$228$	0.546030	+	0.847865i	0.0361617	+	0.0561512i
$229$	−7.49674	+	18.0987i	−0.495398	+	1.19600i	0.456539	+	0.889703i	$0.349089\pi$
$229$	−7.49674	+	18.0987i	−0.495398	+	1.19600i	−0.951937	+	0.306294i	$0.900911\pi$
$230$	12.1892	+	23.2752i	0.803730	+	1.53472i
$231$	−0.0909924	−	0.219675i	−0.00598686	−	0.0144536i
$232$	−0.197288	−	0.111972i	−0.0129526	−	0.00735131i
$233$	−1.02165	+	2.46648i	−0.0669305	+	0.161585i	−0.953805	−	0.300425i	$-0.902871\pi$
$233$	−1.02165	+	2.46648i	−0.0669305	+	0.161585i	0.886875	+	0.462010i	$0.152871\pi$
$234$	4.08063	+	7.79198i	0.266759	+	0.509378i
$235$	−1.12650	−	1.12650i	−0.0734850	−	0.0734850i
$236$	−25.0910	−	5.43321i	−1.63328	−	0.353672i
$237$	0.510459	+	0.211439i	0.0331579	+	0.0137344i
$238$	−6.49764	+	1.39229i	−0.421179	+	0.0902489i
$239$			13.3331i			0.862447i	0.902245	+	0.431224i	$0.141918\pi$
$239$			13.3331i			0.862447i	−0.902245	+	0.431224i	$0.858082\pi$
$240$	0.687018	−	1.51197i	0.0443468	−	0.0975972i
$241$	2.68479	+	6.48164i	0.172942	+	0.417519i	0.986456	−	0.164026i	$-0.0524482\pi$
$241$	2.68479	+	6.48164i	0.172942	+	0.417519i	−0.813514	+	0.581546i	$0.802448\pi$
$242$	6.05338	−	7.25027i	0.389126	−	0.466065i
$243$		−	2.69780i		−	0.173064i
$244$	−6.85919	+	9.89920i	−0.439114	+	0.633732i
$245$	−23.5839			−1.50672
$246$	−1.19957	−	0.374982i	−0.0764818	−	0.0239080i
$247$	10.4506			0.664958
$248$	26.3753	+	3.27461i	1.67483	+	0.207938i
$249$	0.0109523	−	0.00453661i	0.000694076	−	0.000287496i
$250$	−3.72796	−	41.4368i	−0.235777	−	2.62070i
$251$	1.40353	+	3.38842i	0.0885900	+	0.213875i	0.961965	−	0.273174i	$-0.0880734\pi$
$251$	1.40353	+	3.38842i	0.0885900	+	0.213875i	−0.873375	+	0.487049i	$0.838073\pi$
$252$	5.72949	−	3.68983i	0.360924	−	0.232437i
$253$	−8.62549	+	3.57280i	−0.542280	+	0.224620i
$254$	−0.324315	−	3.60481i	−0.0203493	−	0.226186i
$255$	0.458814	−	1.64922i	0.0287320	−	0.103278i
$256$	12.0520	−	10.5237i	0.753251	−	0.657733i
$257$	−2.92885	−	2.92885i	−0.182697	−	0.182697i	0.609833	−	0.792530i	$-0.291236\pi$
$257$	−2.92885	−	2.92885i	−0.182697	−	0.182697i	−0.792530	+	0.609833i	$0.791236\pi$
$258$	−0.552896	−	1.05576i	−0.0344218	−	0.0657286i
$259$	10.3595	+	4.29106i	0.643710	+	0.266634i
$260$	−9.31814	−	14.4690i	−0.577886	−	0.897330i
$261$	0.239801			0.0148433
$262$	−9.10412	+	10.9042i	−0.562454	+	0.673665i
$263$			19.9376i			1.22940i	0.788759	+	0.614702i	$0.210724\pi$
$263$			19.9376i			1.22940i	−0.788759	+	0.614702i	$0.789276\pi$
$264$	0.513229	+	0.291286i	0.0315871	+	0.0179274i
$265$	−15.8867	+	6.58049i	−0.975913	+	0.404236i
$266$	−0.725529	−	8.06437i	−0.0444850	−	0.494458i
$267$	0.337930	−	0.337930i	0.0206810	−	0.0206810i
$268$	13.1808	+	2.85416i	0.805142	+	0.174346i
$269$	10.9186			0.665719			0.332859	−	0.942976i	$-0.391987\pi$
$269$	10.9186			0.665719			0.332859	+	0.942976i	$0.391987\pi$
$270$	0.315145	+	3.50289i	0.0191791	+	0.213179i
$271$			19.1064i			1.16063i	0.814392	+	0.580315i	$0.197071\pi$
$271$			19.1064i			1.16063i	−0.814392	+	0.580315i	$0.802929\pi$
$272$	10.5974	−	12.6371i	0.642561	−	0.766235i
$273$			0.237935i			0.0144005i
$274$	4.72537	−	0.425128i	0.285470	−	0.0256829i
$275$	25.1776			1.51826
$276$	0.488130	+	0.757959i	0.0293820	+	0.0456238i
$277$	−4.10267	+	4.10267i	−0.246506	+	0.246506i	−0.819535	−	0.573029i	$-0.805768\pi$
$277$	−4.10267	+	4.10267i	−0.246506	+	0.246506i	0.573029	+	0.819535i	$0.305768\pi$
$278$	7.99725	−	0.719490i	0.479643	−	0.0431521i
$279$	−25.9567	+	10.7516i	−1.55399	+	0.643682i
$280$	−10.5183	+	8.19496i	−0.628589	+	0.489743i
$281$			4.44888i			0.265398i	0.991156	+	0.132699i	$0.0423644\pi$
$281$			4.44888i			0.265398i	−0.991156	+	0.132699i	$0.957636\pi$
$282$	−0.0419621	−	0.0350349i	−0.00249881	−	0.00208630i
$283$	−2.52514			−0.150104			−0.0750519	−	0.997180i	$-0.523912\pi$
$283$	−2.52514			−0.150104			−0.0750519	+	0.997180i	$0.523912\pi$
$284$	−30.7888	−	6.66702i	−1.82698	−	0.395615i
$285$	1.92707	+	0.798219i	0.114150	+	0.0472824i
$286$	5.41745	−	2.83710i	0.320340	−	0.167761i
$287$	7.13529	+	7.13529i	0.421183	+	0.421183i
$288$	−5.58893	+	15.9635i	−0.329331	+	0.940658i
$289$	8.77936	−	14.5576i	0.516433	−	0.856328i
$290$	−0.467307	+	0.0420423i	−0.0274412	+	0.00246881i
$291$	−0.639757	+	0.264996i	−0.0375032	+	0.0155343i
$292$	−16.0775	−	3.48142i	−0.940864	−	0.203735i
$293$	−0.0186718	−	0.0450777i	−0.00109082	−	0.00263347i	0.923333	−	0.384000i	$-0.125454\pi$
$293$	−0.0186718	−	0.0450777i	−0.00109082	−	0.00263347i	−0.924424	+	0.381366i	$0.875454\pi$
$294$	−0.805986	+	0.0725123i	−0.0470061	+	0.00422900i
$295$	−49.0569	+	20.3200i	−2.85621	+	1.18308i
$296$	−26.8274	+	7.40093i	−1.55931	+	0.430170i
$297$	−1.24975			−0.0725178
$298$	−5.08638	+	16.2714i	−0.294646	+	0.942574i
$299$	9.34247			0.540289
$300$	−0.433953	−	2.39221i	−0.0250543	−	0.138114i
$301$			9.56859i			0.551525i
$302$	−20.3864	−	17.0209i	−1.17310	−	0.979446i
$303$	0.0437244	+	0.105560i	0.00251190	+	0.00606426i
$304$	13.7215	+	14.6818i	0.786982	+	0.842059i
$305$			24.9095i			1.42631i
$306$	−3.14891	+	17.1474i	−0.180011	+	0.980251i
$307$	11.4054	+	4.72427i	0.650940	+	0.269628i	0.683621	−	0.729838i	$-0.260404\pi$
$307$	11.4054	+	4.72427i	0.650940	+	0.269628i	−0.0326804	+	0.999466i	$0.510404\pi$
$308$	−2.56539	−	3.98348i	−0.146177	−	0.226980i
$309$	1.07334	+	1.07334i	0.0610599	+	0.0610599i
$310$	48.6975	−	25.5027i	2.76583	−	1.44846i
$311$	−1.80633	+	4.36087i	−0.102428	+	0.247283i	−0.966783	−	0.255600i	$-0.917727\pi$
$311$	−1.80633	+	4.36087i	−0.102428	+	0.247283i	0.864355	+	0.502882i	$0.167727\pi$
$312$	−0.362936	−	0.465832i	−0.0205472	−	0.0263725i
$313$	−0.474685	−	1.14599i	−0.0268308	−	0.0647753i	0.909896	−	0.414836i	$-0.136161\pi$
$313$	−0.474685	−	1.14599i	−0.0268308	−	0.0647753i	−0.936727	+	0.350061i	$0.886161\pi$
$314$	17.4397	−	9.13311i	0.984179	−	0.515411i
$315$	5.39400	−	13.0223i	0.303918	−	0.733722i
$316$	10.7605	+	2.33007i	0.605324	+	0.131077i
$317$	7.28967	−	7.28967i	0.409429	−	0.409429i	−0.472111	−	0.881539i	$-0.656508\pi$
$317$	7.28967	−	7.28967i	0.409429	−	0.409429i	0.881539	+	0.472111i	$0.156508\pi$
$318$	−0.522699	+	0.273736i	−0.0293115	+	0.0153503i
$319$		−	0.166724i		−	0.00933476i
$320$	8.09255	−	32.0883i	0.452388	−	1.79379i
$321$	0.699105	+	0.699105i	0.0390203	+	0.0390203i
$322$	−0.648595	−	7.20924i	−0.0361448	−	0.401755i
$323$	16.3126	+	12.7662i	0.907655	+	0.710328i
$324$	−3.18048	−	17.5327i	−0.176694	−	0.974041i
$325$	−23.2768	−	9.64155i	−1.29116	−	0.534817i
$326$	−21.3553	+	1.92128i	−1.18276	+	0.106410i
$327$	0.583499	+	0.583499i	0.0322676	+	0.0322676i
$328$	−24.8534	−	3.08566i	−1.37230	−	0.170377i
$329$	0.167959	+	0.405490i	0.00925991	+	0.0223554i
$330$	1.21566	−	0.109370i	0.0669200	−	0.00602060i
$331$	−33.0723	−	13.6990i	−1.81782	−	0.752966i	−0.977520	−	0.210844i	$-0.932379\pi$
$331$	−33.0723	−	13.6990i	−1.81782	−	0.752966i	−0.840300	−	0.542122i	$-0.817621\pi$
$332$	0.198604	−	0.127903i	0.0108998	−	0.00701956i
$333$	20.8021	−	20.8021i	1.13995	−	1.13995i
$334$	−3.42685	−	6.54358i	−0.187509	−	0.358049i
$335$	25.7705	−	10.6745i	1.40799	−	0.583210i
$336$	−0.334268	+	0.312405i	−0.0182358	+	0.0170431i
$337$	0.950480	+	2.29466i	0.0517760	+	0.124998i	0.947651	−	0.319308i	$-0.103450\pi$
$337$	0.950480	+	2.29466i	0.0517760	+	0.124998i	−0.895875	+	0.444306i	$0.853450\pi$
$338$	12.2159	−	1.09903i	0.664459	−	0.0597795i
$339$	0.656081	+	0.271757i	0.0356334	+	0.0147598i
$340$	3.13006	−	33.9676i	0.169751	−	1.84215i
$341$	7.47517	+	18.0466i	0.404803	+	0.977281i
$342$	−20.2755	−	6.33807i	−1.09637	−	0.342724i
$343$	13.3729	+	5.53924i	0.722069	+	0.299091i
$344$	−14.5955	−	18.7335i	−0.786938	−	1.01004i
$345$	1.72273	+	0.713578i	0.0927486	+	0.0384177i
$346$	19.8577	−	23.7840i	1.06755	−	1.27863i
$347$		−	24.6590i		−	1.32376i	−0.749608	−	0.661882i	$-0.769758\pi$
$347$		−	24.6590i		−	1.32376i	0.749608	−	0.661882i	$-0.230242\pi$
$348$	−0.0158410	+	0.00287361i	−0.000849169	+	0.000154042i
$349$	−9.78088	−	23.6131i	−0.523558	−	1.26398i	−0.935679	−	0.352852i	$-0.885212\pi$
$349$	−9.78088	−	23.6131i	−0.523558	−	1.26398i	0.412121	−	0.911129i	$-0.364788\pi$
$350$	−5.82405	+	18.6312i	−0.311309	+	0.995878i
$351$	1.15540	+	0.478581i	0.0616706	+	0.0255448i
$352$	11.0988	+	3.88576i	0.591567	+	0.207112i
$353$			0.441749i			0.0235119i	0.999931	+	0.0117560i	$0.00374213\pi$
$353$			0.441749i			0.0235119i	−0.999931	+	0.0117560i	$0.996258\pi$
$354$	−1.61405	+	0.845275i	−0.0857860	+	0.0449258i
$355$	−60.1972	+	24.9345i	−3.19493	+	1.32339i
$356$	5.42378	−	7.82762i	0.287460	−	0.414863i
$357$	−0.290654	+	0.371397i	−0.0153830	+	0.0196564i
$358$	−1.85636	+	5.93850i	−0.0981117	+	0.313860i
$359$	25.1841			1.32916			0.664582	−	0.747215i	$-0.268609\pi$
$359$	25.1841			1.32916			0.664582	+	0.747215i	$0.268609\pi$
$360$	9.30321	+	33.7229i	0.490322	+	1.77735i
$361$	−4.41211	+	4.41211i	−0.232217	+	0.232217i
$362$	1.31942	+	1.10161i	0.0693471	+	0.0578991i
$363$		−	0.670325i		−	0.0351829i
$364$	0.846268	+	4.66514i	0.0443565	+	0.244520i
$365$	−31.4341	+	13.0204i	−1.64534	+	0.681521i
$366$	0.0765879	+	0.851287i	0.00400331	+	0.0444975i
$367$	−14.6894	−	6.08457i	−0.766783	−	0.317612i	−0.0352142	−	0.999380i	$-0.511211\pi$
$367$	−14.6894	−	6.08457i	−0.766783	−	0.317612i	−0.731568	+	0.681768i	$0.761211\pi$
$368$	12.2665	+	13.1250i	0.639435	+	0.684186i
$369$	24.4590	−	10.1312i	1.27328	−	0.527411i
$370$	−36.8905	+	44.1846i	−1.91784	+	2.29705i
$371$	4.73735			0.245951
$372$	1.58584	−	1.02129i	0.0822218	−	0.0529514i
$373$	−0.331150	−	0.799468i	−0.0171463	−	0.0413949i	0.915075	−	0.403285i	$-0.132132\pi$
$373$	−0.331150	−	0.799468i	−0.0171463	−	0.0413949i	−0.932221	+	0.361890i	$0.882132\pi$
$374$	11.9219	+	2.18931i	0.616466	+	0.113207i
$375$	−2.08786	−	2.08786i	−0.107817	−	0.107817i
$376$	−0.947350	−	0.537673i	−0.0488558	−	0.0277284i
$377$	−0.0638456	+	0.154137i	−0.00328822	+	0.00793846i
$378$	0.289091	−	0.924803i	0.0148692	−	0.0475667i
$379$	5.02524	+	5.02524i	0.258129	+	0.258129i	0.824293	−	0.566164i	$-0.191573\pi$
$379$	5.02524	+	5.02524i	0.258129	+	0.258129i	−0.566164	+	0.824293i	$0.691573\pi$
$380$	40.6227	+	8.79644i	2.08390	+	0.451248i
$381$	−0.181634	−	0.181634i	−0.00930539	−	0.00930539i
$382$	−22.3715	−	18.6783i	−1.14462	−	0.955666i
$383$	13.8901	−	13.8901i	0.709753	−	0.709753i	−0.256730	−	0.966483i	$-0.582645\pi$
$383$	13.8901	−	13.8901i	0.709753	−	0.709753i	0.966483	+	0.256730i	$0.0826452\pi$
$384$	0.177904	−	1.12151i	0.00907865	−	0.0572317i
$385$	−9.05387	−	3.75023i	−0.461428	−	0.191130i
$386$	30.5041	−	15.9749i	1.55262	−	0.813101i
$387$	23.1932	+	9.60692i	1.17897	+	0.488347i
$388$	−11.6010	+	7.47115i	−0.588954	+	0.379290i
$389$	25.0172	+	10.3625i	1.26842	+	0.525399i	0.912485	−	0.409111i	$-0.134161\pi$
$389$	25.0172	+	10.3625i	1.26842	+	0.525399i	0.355939	+	0.934509i	$0.384161\pi$
$390$	−1.16577	−	0.364415i	−0.0590309	−	0.0184529i
$391$	14.5828	+	11.4125i	0.737484	+	0.577153i
$392$	−15.5449	+	4.28840i	−0.785134	+	0.216597i
$393$			1.00815i			0.0508544i
$394$	−0.862339	−	0.719982i	−0.0434440	−	0.0362722i
$395$	21.0385	−	8.71442i	1.05856	−	0.438470i
$396$	−12.2312	+	2.21876i	−0.614639	+	0.111497i
$397$	1.43490	+	1.43490i	0.0720154	+	0.0720154i	0.742197	−	0.670182i	$-0.233784\pi$
$397$	1.43490	+	1.43490i	0.0720154	+	0.0720154i	−0.670182	+	0.742197i	$0.733784\pi$
$398$	−3.49764	+	1.83170i	−0.175321	+	0.0918150i
$399$	−0.406336	−	0.406336i	−0.0203422	−	0.0203422i
$400$	−17.0168	−	45.3600i	−0.850841	−	2.26800i
$401$	7.32961	+	3.03602i	0.366023	+	0.151612i	0.558112	−	0.829766i	$-0.311526\pi$
$401$	7.32961	+	3.03602i	0.366023	+	0.151612i	−0.192089	+	0.981378i	$0.561526\pi$
$402$	0.847892	−	0.444038i	0.0422890	−	0.0221466i
$403$		−	19.5467i		−	0.973693i
$404$	1.23274	+	1.91417i	0.0613311	+	0.0952336i
$405$	−26.0605	−	26.0605i	−1.29496	−	1.29496i
$406$	0.123374	+	0.0385665i	0.00612296	+	0.00191402i
$407$	−14.4628	−	14.4628i	−0.716896	−	0.716896i
$408$	0.00253193	−	1.17048i	0.000125349	−	0.0579472i
$409$	4.01102	−	4.01102i	0.198332	−	0.198332i	−0.600952	−	0.799285i	$-0.705212\pi$
$409$	4.01102	−	4.01102i	0.198332	−	0.198332i	0.799285	+	0.600952i	$0.205212\pi$
$410$	−45.8876	+	24.0312i	−2.26623	+	1.18682i
$411$	0.238095	−	0.238095i	0.0117444	−	0.0117444i
$412$	24.8622	+	17.2271i	1.22487	+	0.848717i
$413$	14.6286			0.719826
$414$	−18.1256	−	5.66600i	−0.890822	−	0.278469i
$415$	0.186975	−	0.451399i	0.00917826	−	0.0221583i
$416$	−8.77284	−	7.84258i	−0.430124	−	0.384514i
$417$	0.402954	−	0.402954i	0.0197327	−	0.0197327i
$418$	−4.40661	+	14.0968i	−0.215534	+	0.689495i
$419$	−24.4759	+	24.4759i	−1.19573	+	1.19573i	−0.220292	+	0.975434i	$0.570701\pi$
$419$	−24.4759	+	24.4759i	−1.19573	+	1.19573i	−0.975434	+	0.220292i	$0.929299\pi$
$420$	−0.200273	+	0.924878i	−0.00977234	+	0.0451294i
$421$	−6.41756	−	15.4934i	−0.312773	−	0.755100i	−0.999600	−	0.0282795i	$-0.990997\pi$
$421$	−6.41756	−	15.4934i	−0.312773	−	0.755100i	0.686827	−	0.726821i	$-0.259003\pi$
$422$	−1.17657	−	13.0777i	−0.0572744	−	0.636614i
$423$	1.15149			0.0559875
$424$	−9.27483	+	7.22616i	−0.450426	+	0.350933i
$425$	−24.5552	−	43.4838i	−1.19110	−	2.10927i
$426$	−1.98059	+	1.03723i	−0.0959597	+	0.0502538i
$427$	2.62616	−	6.34012i	0.127089	−	0.306820i
$428$	16.1937	+	11.2207i	0.782752	+	0.542371i
$429$	0.166089	−	0.400975i	0.00801887	−	0.0193593i
$430$	−46.8814	−	14.6550i	−2.26082	−	0.706727i
$431$	−4.64457	+	11.2130i	−0.223721	+	0.540110i	−0.995390	−	0.0959145i	$-0.969422\pi$
$431$	−4.64457	+	11.2130i	−0.223721	+	0.540110i	0.771669	+	0.636025i	$0.219422\pi$
$432$	0.844671	+	2.25155i	0.0406393	+	0.108328i
$433$	1.21852	+	1.21852i	0.0585583	+	0.0585583i	0.735779	−	0.677221i	$-0.236816\pi$
$433$	1.21852	+	1.21852i	0.0585583	+	0.0585583i	−0.677221	+	0.735779i	$0.736816\pi$
$434$	−15.0835	+	1.35702i	−0.724031	+	0.0651391i
$435$	−0.0235460	+	0.0235460i	−0.00112894	+	0.00112894i
$436$	13.5159	+	9.36519i	0.647293	+	0.448511i
$437$	−15.9547	+	15.9547i	−0.763215	+	0.763215i
$438$	−1.03423	+	0.541625i	−0.0494176	+	0.0258798i
$439$	−8.41988	−	3.48763i	−0.401859	−	0.166456i	0.172594	−	0.984993i	$-0.444785\pi$
$439$	−8.41988	−	3.48763i	−0.401859	−	0.166456i	−0.574453	+	0.818538i	$0.694785\pi$
$440$	23.4462	−	6.46815i	1.11775	−	0.308357i
$441$	12.0535	−	12.0535i	0.573979	−	0.573979i
$442$	−10.1835	−	6.58942i	−0.484377	−	0.313427i
$443$	−9.39370	+	3.89100i	−0.446308	+	0.184867i	−0.594506	−	0.804091i	$-0.702653\pi$
$443$	−9.39370	+	3.89100i	−0.446308	+	0.184867i	0.148198	+	0.988958i	$0.452653\pi$
$444$	−1.12489	+	1.62344i	−0.0533848	+	0.0770452i
$445$		−	19.6967i		−	0.933715i
$446$	30.0770	−	2.70595i	1.42419	−	0.128130i
$447$	0.463007	+	1.11780i	0.0218995	+	0.0528700i
$448$	−5.44278	+	7.31414i	−0.257147	+	0.345561i
$449$	−13.0839	+	31.5873i	−0.617467	+	1.49070i	0.237168	+	0.971469i	$0.423781\pi$
$449$	−13.0839	+	31.5873i	−0.617467	+	1.49070i	−0.854635	+	0.519229i	$0.826219\pi$
$450$	39.3124	+	32.8226i	1.85320	+	1.54727i
$451$	−7.04384	−	17.0053i	−0.331682	−	0.800750i
$452$	13.8302	+	2.99479i	0.650517	+	0.140863i
$453$	−1.88482			−0.0885568
$454$	1.33018	+	14.7852i	0.0624287	+	0.693905i
$455$	6.93421	+	6.93421i	0.325081	+	0.325081i
$456$	1.41533	+	0.175720i	0.0662791	+	0.00822884i
$457$		−	7.61516i		−	0.356222i	−0.984010	−	0.178111i	$-0.943001\pi$
$457$		−	7.61516i		−	0.356222i	0.984010	−	0.178111i	$-0.0569986\pi$
$458$	12.8528	+	24.5425i	0.600573	+	1.14680i
$459$	1.21886	+	2.15842i	0.0568914	+	0.100746i
$460$	36.3151	+	7.86368i	1.69320	+	0.366646i
$461$	−4.77312	−	11.5233i	−0.222307	−	0.536696i	0.772896	−	0.634533i	$-0.218808\pi$
$461$	−4.77312	−	11.5233i	−0.222307	−	0.536696i	−0.995202	+	0.0978373i	$0.968808\pi$
$462$	−0.320948	−	0.100328i	−0.0149319	−	0.00466766i
$463$	−16.6351			−0.773100			−0.386550	−	0.922268i	$-0.626333\pi$
$463$	−16.6351			−0.773100			−0.386550	+	0.922268i	$0.626333\pi$
$464$	−0.300371	+	0.112684i	−0.0139444	+	0.00523123i
$465$	1.49298	−	3.60437i	0.0692353	−	0.167149i
$466$	1.75157	+	3.34464i	0.0811401	+	0.154937i
$467$	21.7076	−	8.99160i	1.00451	−	0.416082i	0.181061	−	0.983472i	$-0.442047\pi$
$467$	21.7076	−	8.99160i	1.00451	−	0.416082i	0.823449	+	0.567390i	$0.192047\pi$
$468$	12.1574	+	2.63257i	0.561976	+	0.121690i
$469$	−7.68466			−0.354845
$470$	−2.24394	+	0.201881i	−0.103505	+	0.00931209i
$471$	0.534670	−	1.29081i	0.0246363	−	0.0594773i
$472$	−28.6400	+	22.3138i	−1.31826	+	1.02708i
$473$	6.67930	−	16.1253i	0.307115	−	0.741441i
$474$	0.692200	−	0.362503i	0.0317938	−	0.0166503i
$475$	56.2164	−	23.2856i	2.57939	−	1.06842i
$476$	−4.37783	+	8.31566i	−0.200658	+	0.381148i
$477$	4.75633	−	11.4828i	0.217777	−	0.525761i
$478$	14.4742	+	12.0848i	0.662034	+	0.552744i
$479$	−13.0509	+	5.40585i	−0.596310	+	0.247000i	−0.660363	−	0.750947i	$-0.729597\pi$
$479$	−13.0509	+	5.40585i	−0.596310	+	0.247000i	0.0640528	+	0.997947i	$0.479597\pi$
$480$	−1.01867	−	2.11622i	−0.0464959	−	0.0965919i
$481$	7.83252	+	18.9094i	0.357132	+	0.862193i
$482$	9.46978	+	2.96023i	0.431336	+	0.134835i
$483$	−0.363249	−	0.363249i	−0.0165284	−	0.0165284i
$484$	−2.38415	−	13.1429i	−0.108371	−	0.597404i
$485$	−10.9218	+	26.3675i	−0.495932	+	1.19728i
$486$	−2.92869	−	2.44521i	−0.132848	−	0.110917i
$487$	28.0567	−	11.6215i	1.27137	−	0.526619i	0.357990	−	0.933726i	$-0.383462\pi$
$487$	28.0567	−	11.6215i	1.27137	−	0.526619i	0.913381	+	0.407107i	$0.133462\pi$
$488$	4.52943	+	16.4186i	0.205038	+	0.743234i
$489$	−1.07602	+	1.07602i	−0.0486593	+	0.0486593i
$490$	−21.3758	+	25.6023i	−0.965661	+	1.15659i
$491$	2.37770	−	5.74027i	0.107304	−	0.259055i	−0.861103	−	0.508431i	$-0.830226\pi$
$491$	2.37770	−	5.74027i	0.107304	−	0.259055i	0.968407	+	0.249376i	$0.0802257\pi$
$492$	−1.49433	+	0.962359i	−0.0673697	+	0.0433865i
$493$	−0.287946	+	0.162603i	−0.0129685	+	0.00732327i
$494$	9.47217	−	11.3450i	0.426173	−	0.510437i
$495$	−18.1803	+	18.1803i	−0.817142	+	0.817142i
$496$	27.4607	−	25.6645i	1.23302	−	1.15237i
$497$	17.9506			0.805193
$498$	0.00500203	−	0.0160015i	0.000224146	−	0.000717045i
$499$	−21.1528	−	21.1528i	−0.946928	−	0.946928i	0.0517330	−	0.998661i	$-0.483526\pi$
$499$	−21.1528	−	21.1528i	−0.946928	−	0.946928i	−0.998661	+	0.0517330i	$0.983526\pi$
$500$	−48.3620	−	33.5102i	−2.16282	−	1.49862i
$501$	−0.484327	−	0.200615i	−0.0216381	−	0.00896280i
$502$	4.95053	+	1.54752i	0.220953	+	0.0690693i
$503$	−7.73253	+	3.20292i	−0.344776	+	0.142811i	−0.548351	−	0.836248i	$-0.684744\pi$
$503$	−7.73253	+	3.20292i	−0.344776	+	0.142811i	0.203574	+	0.979059i	$0.434744\pi$
$504$	1.18744	−	9.56419i	0.0528926	−	0.426023i
$505$	4.35063	+	1.80209i	0.193601	+	0.0801920i
$506$	−3.93934	+	12.6020i	−0.175125	+	0.560226i
$507$	0.615518	−	0.615518i	0.0273361	−	0.0273361i
$508$	−4.20727	−	2.91523i	−0.186668	−	0.129343i
$509$	−1.16375	+	2.80954i	−0.0515823	+	0.124531i	−0.947570	−	0.319548i	$-0.896469\pi$
$509$	−1.16375	+	2.80954i	−0.0515823	+	0.124531i	0.895988	+	0.444079i	$0.146469\pi$
$510$	−1.37450	−	1.99288i	−0.0608641	−	0.0882464i
$511$	9.37353			0.414660
$512$	−0.500755	−	22.6219i	−0.0221304	−	0.999755i
$513$	−2.79044	+	1.15584i	−0.123201	+	0.0510315i
$514$	−5.83414	+	0.524881i	−0.257333	+	0.0231515i
$515$	62.5610			2.75677
$516$	−1.64724	−	0.356694i	−0.0725158	−	0.0157026i
$517$		−	0.800586i		−	0.0352098i
$518$	14.0479	−	7.35684i	0.617229	−	0.323241i
$519$		−	2.19895i		−	0.0965232i
$520$	−24.1530	−	2.99870i	−1.05918	−	0.131502i
$521$	−15.6018	−	37.6661i	−0.683528	−	1.65018i	−0.757430	−	0.652916i	$-0.773545\pi$
$521$	−15.6018	−	37.6661i	−0.683528	−	1.65018i	0.0739028	−	0.997265i	$-0.476455\pi$
$522$	0.217349	−	0.260324i	0.00951311	−	0.0113941i
$523$	16.3055	−	6.75397i	0.712991	−	0.295331i	0.00344958	−	0.999994i	$-0.498902\pi$
$523$	16.3055	−	6.75397i	0.712991	−	0.295331i	0.709542	+	0.704663i	$0.248902\pi$
$524$	3.58570	+	19.7666i	0.156642	+	0.863506i
$525$	0.530156	+	1.27991i	0.0231379	+	0.0558599i
$526$	21.6439	+	18.0709i	0.943719	+	0.787928i
$527$	23.8777	−	30.5108i	1.04013	−	1.32907i
$528$	0.781391	−	0.293139i	0.0340057	−	0.0127572i
$529$	2.00059	−	2.00059i	0.0869821	−	0.0869821i
$530$	−7.25560	+	23.2107i	−0.315163	+	1.00821i
$531$	14.6872	−	35.4580i	0.637369	−	1.53875i
$532$	−9.41214	−	6.52170i	−0.408068	−	0.282752i
$533$			18.4189i			0.797810i
$534$	−0.0605605	−	0.673140i	−0.00262071	−	0.0291296i
$535$	40.7484			1.76171
$536$	15.0451	−	11.7219i	0.649849	−	0.506307i
$537$	0.168982	+	0.407959i	0.00729212	+	0.0176047i
$538$	9.89632	−	11.8530i	0.426660	−	0.511021i
$539$	−8.38035	−	8.38035i	−0.360967	−	0.360967i
$540$	4.08832	+	2.83281i	0.175933	+	0.121905i
$541$			23.4584i			1.00855i	0.863542	+	0.504277i	$0.168241\pi$
$541$			23.4584i			1.00855i	−0.863542	+	0.504277i	$0.831759\pi$
$542$	20.7416	+	17.3175i	0.890926	+	0.743850i
$543$	0.121987			0.00523496
$544$	−4.11340	−	22.9582i	−0.176361	−	0.984326i
$545$	34.0102			1.45683
$546$	0.258298	+	0.215658i	0.0110542	+	0.00922931i
$547$			17.1805i			0.734587i	0.930105	+	0.367293i	$0.119716\pi$
$547$			17.1805i			0.734587i	−0.930105	+	0.367293i	$0.880284\pi$
$548$	3.82143	−	5.51511i	0.163244	−	0.235594i
$549$	−12.7310	−	12.7310i	−0.543347	−	0.543347i
$550$	22.8202	−	27.3323i	0.973059	−	1.16545i
$551$	−0.154196	−	0.372261i	−0.00656896	−	0.0158589i
$552$	1.26525	+	0.157087i	0.0538528	+	0.00668606i
$553$	−6.27359			−0.266780
$554$	0.735242	+	8.17233i	0.0312374	+	0.347209i
$555$			4.08509i			0.173402i
$556$	6.46742	−	9.33380i	0.274280	−	0.395841i
$557$	9.58768	−	23.1467i	0.406243	−	0.980758i	−0.579874	−	0.814706i	$-0.696898\pi$
$557$	9.58768	−	23.1467i	0.406243	−	0.980758i	0.986117	−	0.166051i	$-0.0531018\pi$
$558$	−11.8547	+	37.9231i	−0.501848	+	1.60541i
$559$	−12.3501	+	12.3501i	−0.522353	+	0.522353i
$560$	−0.637181	+	18.8462i	−0.0269258	+	0.796396i
$561$	0.749070	−	0.422999i	0.0316258	−	0.0178590i
$562$	4.82963	+	4.03234i	0.203726	+	0.170094i
$563$	−9.15342	−	22.0983i	−0.385771	−	0.931333i	−0.990825	−	0.135149i	$-0.956849\pi$
$563$	−9.15342	−	22.0983i	−0.385771	−	0.931333i	0.605055	−	0.796184i	$-0.293151\pi$
$564$	−0.0760666	+	0.0137987i	−0.00320298	+	0.000581029i
$565$	27.0402	−	11.2004i	1.13759	−	0.471206i
$566$	−2.28871	+	2.74125i	−0.0962019	+	0.115223i
$567$	3.88557	+	9.38058i	0.163178	+	0.393948i
$568$	−35.1438	+	27.3810i	−1.47460	+	1.14888i
$569$			32.3759i			1.35727i	0.734477	+	0.678633i	$0.237427\pi$
$569$			32.3759i			1.35727i	−0.734477	+	0.678633i	$0.762573\pi$
$570$	2.61318	−	1.36851i	0.109454	−	0.0573207i
$571$			28.3247i			1.18535i	0.805441	+	0.592676i	$0.201928\pi$
$571$			28.3247i			1.18535i	−0.805441	+	0.592676i	$0.798072\pi$
$572$	1.83032	−	8.45256i	0.0765295	−	0.353419i
$573$	−2.06835			−0.0864068
$574$	14.2132	−	1.27872i	0.593246	−	0.0533727i
$575$	50.2554	−	20.8165i	2.09579	−	0.868106i
$576$	12.2640	+	20.5361i	0.511002	+	0.855671i
$577$	25.3973			1.05730			0.528652	−	0.848839i	$-0.322698\pi$
$577$	25.3973			1.05730			0.528652	+	0.848839i	$0.322698\pi$
$578$	−7.84608	−	22.7253i	−0.326354	−	0.945248i
$579$	0.935202	−	2.25778i	0.0388657	−	0.0938301i
$580$	−0.377914	+	0.545406i	−0.0156920	+	0.0226468i
$581$	−0.0951803	+	0.0951803i	−0.00394874	+	0.00394874i
$582$	−0.292183	+	0.934694i	−0.0121114	+	0.0387443i
$583$	−7.98352	−	3.30688i	−0.330644	−	0.136957i
$584$	−18.3516	+	14.2980i	−0.759393	+	0.591655i
$585$	23.7697	−	9.84573i	0.982756	−	0.407071i
$586$	−0.0658592	−	0.0205874i	−0.00272062	−	0.000850457i
$587$	−15.2976	−	6.33647i	−0.631399	−	0.261534i	0.0439483	−	0.999034i	$-0.486006\pi$
$587$	−15.2976	−	6.33647i	−0.631399	−	0.261534i	−0.675347	+	0.737500i	$0.736006\pi$
$588$	−0.651805	+	0.940688i	−0.0268800	+	0.0387933i
$589$	33.3811	+	33.3811i	1.37544	+	1.37544i
$590$	−22.4047	+	71.6729i	−0.922389	+	2.95073i
$591$	−0.0797277			−0.00327956
$592$	−16.2813	+	35.8313i	−0.669156	+	1.47266i
$593$	−8.47926	+	8.47926i	−0.348202	+	0.348202i	−0.859439	−	0.511238i	$-0.829187\pi$
$593$	−8.47926	+	8.47926i	−0.348202	+	0.348202i	0.511238	+	0.859439i	$0.329187\pi$
$594$	−1.13274	+	1.35671i	−0.0464768	+	0.0556663i
$595$	2.35311	+	19.2943i	0.0964679	+	0.790990i
$596$	13.0537	+	20.2696i	0.534702	+	0.830275i
$597$	−0.107231	+	0.258880i	−0.00438869	+	0.0105952i
$598$	8.46776	−	10.1420i	0.346272	−	0.414738i
$599$	16.7026	−	16.7026i	0.682451	−	0.682451i	−0.278101	−	0.960552i	$-0.589705\pi$
$599$	16.7026	−	16.7026i	0.682451	−	0.682451i	0.960552	+	0.278101i	$0.0897050\pi$
$600$	−2.99026	−	1.69714i	−0.122077	−	0.0692855i
$601$	−7.01586	+	2.90606i	−0.286183	+	0.118541i	−0.521157	−	0.853461i	$-0.674499\pi$
$601$	−7.01586	+	2.90606i	−0.286183	+	0.118541i	0.234974	+	0.972002i	$0.424499\pi$
$602$	10.3875	+	8.67271i	0.423363	+	0.353473i
$603$	−7.71544	+	18.6267i	−0.314197	+	0.758539i
$604$	−36.9553	+	6.70379i	−1.50369	+	0.272773i
$605$	−19.5354	−	19.5354i	−0.794229	−	0.794229i
$606$	0.154225	+	0.0482102i	0.00626494	+	0.00195840i
$607$	14.2670	+	34.4435i	0.579078	+	1.39802i	0.893641	+	0.448782i	$0.148142\pi$
$607$	14.2670	+	34.4435i	0.579078	+	1.39802i	−0.314563	+	0.949237i	$0.601858\pi$
$608$	28.3751	−	1.58864i	1.15076	−	0.0644281i
$609$	0.00847547	−	0.00351066i	0.000343444	−	0.000142259i
$610$	27.0413	+	22.5773i	1.09487	+	0.914127i
$611$	−0.306578	+	0.740145i	−0.0124028	+	0.0299431i
$612$	15.7608	+	18.9603i	0.637093	+	0.766425i
$613$	−20.6678	+	8.56089i	−0.834765	+	0.345771i	−0.758787	−	0.651338i	$-0.774208\pi$
$613$	−20.6678	+	8.56089i	−0.834765	+	0.345771i	−0.0759778	+	0.997110i	$0.524208\pi$
$614$	15.4661	−	8.09955i	0.624162	−	0.326871i
$615$	−1.40683	+	3.39640i	−0.0567290	+	0.136956i
$616$	−6.64959	−	0.825576i	−0.267920	−	0.0332634i
$617$	−11.3303	+	27.3537i	−0.456140	+	1.10122i	0.513808	+	0.857905i	$0.328234\pi$
$617$	−11.3303	+	27.3537i	−0.456140	+	1.10122i	−0.969948	+	0.243313i	$0.921766\pi$
$618$	2.13803	−	0.192353i	0.0860044	−	0.00773757i
$619$	9.23915			0.371353			0.185676	−	0.982611i	$-0.440552\pi$
$619$	9.23915			0.371353			0.185676	+	0.982611i	$0.440552\pi$
$620$	16.4528	−	75.9801i	0.660759	−	3.05144i
$621$	−2.49455	+	1.03327i	−0.100103	+	0.0414639i
$622$	3.09688	+	5.91350i	0.124174	+	0.237110i
$623$	−2.07659	+	5.01334i	−0.0831969	+	0.200855i
$624$	−0.834654	−	0.0282193i	−0.0334129	−	0.00112968i
$625$	−61.1354			−2.44541
$626$	−1.67431	−	0.523385i	−0.0669189	−	0.0209187i
$627$	0.401128	+	0.968408i	0.0160195	+	0.0386745i
$628$	5.89211	−	27.2102i	0.235121	−	1.08581i
$629$	−10.8732	+	39.0839i	−0.433542	+	1.55838i
$630$	−9.24778	−	17.6587i	−0.368441	−	0.703538i
$631$		−	44.2420i		−	1.76124i	−0.473819	−	0.880622i	$-0.657125\pi$
$631$		−	44.2420i		−	1.76124i	0.473819	−	0.880622i	$-0.342875\pi$
$632$	12.2825	−	9.56946i	0.488571	−	0.380653i
$633$	−0.658942	−	0.658942i	−0.0261906	−	0.0261906i
$634$	−1.30639	−	14.5207i	−0.0518832	−	0.576690i
$635$	−10.5868			−0.420125
$636$	−0.176597	+	0.815539i	−0.00700253	+	0.0323382i
$637$	4.53848	+	10.9568i	0.179821	+	0.434126i
$638$	−0.180993	−	0.151114i	−0.00716557	−	0.00598266i
$639$	18.0225	−	43.5101i	0.712957	−	1.72123i
$640$	−27.4997	−	37.8691i	−1.08702	−	1.49691i
$641$	−16.5781	−	40.0230i	−0.654795	−	1.58081i	−0.805738	−	0.592272i	$-0.798231\pi$
$641$	−16.5781	−	40.0230i	−0.654795	−	1.58081i	0.150944	−	0.988542i	$-0.451769\pi$
$642$	1.39259	−	0.125287i	0.0549610	−	0.00494468i
$643$			13.6645i			0.538874i	0.963018	+	0.269437i	$0.0868377\pi$
$643$			13.6645i			0.538874i	−0.963018	+	0.269437i	$0.913162\pi$
$644$	−8.41410	−	5.83015i	−0.331562	−	0.229740i
$645$	−3.22062	+	1.33403i	−0.126812	+	0.0525272i
$646$	28.6440	−	6.13774i	1.12698	−	0.241486i
$647$	−18.0850	+	18.0850i	−0.710995	+	0.710995i	−0.966743	−	0.255749i	$-0.917678\pi$
$647$	−18.0850	+	18.0850i	−0.710995	+	0.710995i	0.255749	+	0.966743i	$0.417678\pi$
$648$	−21.9159	−	12.4385i	−0.860939	−	0.488631i
$649$	−24.6525	−	10.2114i	−0.967695	−	0.400833i
$650$	−31.5641	+	16.5300i	−1.23805	+	0.648360i
$651$	−0.760005	+	0.760005i	−0.0297870	+	0.0297870i
$652$	−17.2702	+	24.9244i	−0.676352	+	0.976114i
$653$	−17.7126	+	17.7126i	−0.693147	+	0.693147i	−0.962923	−	0.269776i	$-0.913050\pi$
$653$	−17.7126	+	17.7126i	−0.693147	+	0.693147i	0.269776	+	0.962923i	$0.413050\pi$
$654$	1.16230	−	0.104569i	0.0454497	−	0.00408898i
$655$	29.3808	+	29.3808i	1.14800	+	1.14800i
$656$	−25.8762	+	24.1837i	−1.01029	+	0.944213i
$657$	9.41107	−	22.7203i	0.367161	−	0.886405i
$658$	0.592427	+	0.185191i	0.0230952	+	0.00721950i
$659$	−1.81333	+	4.37776i	−0.0706372	+	0.170533i	−0.955255	−	0.295784i	$-0.904419\pi$
$659$	−1.81333	+	4.37776i	−0.0706372	+	0.170533i	0.884618	+	0.466317i	$0.154419\pi$
$660$	0.983112	−	1.41883i	0.0382676	−	0.0552279i
$661$	5.32536	−	12.8565i	0.207132	−	0.500062i	−0.785837	−	0.618434i	$-0.787768\pi$
$661$	5.32536	−	12.8565i	0.207132	−	0.500062i	0.992969	+	0.118372i	$0.0377675\pi$
$662$	−44.8472	+	23.4863i	−1.74304	+	0.912823i
$663$	−0.854502	+	0.104214i	−0.0331861	+	0.00404733i
$664$	0.0411607	−	0.331529i	0.00159735	−	0.0128658i
$665$	−23.6839			−0.918422
$666$	−3.72795	−	41.4368i	−0.144455	−	1.60564i
$667$	−0.137845	−	0.332787i	−0.00533738	−	0.0128856i
$668$	−10.2096	−	2.21079i	−0.395021	−	0.0855380i
$669$	1.51548	−	1.51548i	0.0585917	−	0.0585917i
$670$	11.7696	−	37.6511i	0.454700	−	1.45459i
$671$	−8.85137	+	8.85137i	−0.341703	+	0.341703i
$672$	0.0361695	+	0.646031i	0.00139527	+	0.0249212i
$673$	−6.49650	+	15.6839i	−0.250422	+	0.604572i	−0.998238	−	0.0593340i	$-0.981102\pi$
$673$	−6.49650	+	15.6839i	−0.250422	+	0.604572i	0.747816	+	0.663906i	$0.231102\pi$
$674$	3.35253	+	1.04799i	0.129135	+	0.0403672i
$675$	7.28151			0.280265
$676$	9.87908	−	14.2575i	0.379965	−	0.548366i
$677$	26.7059	−	26.7059i	1.02639	−	1.02639i	0.0267504	−	0.999642i	$-0.491484\pi$
$677$	26.7059	−	26.7059i	1.02639	−	1.02639i	0.999642	−	0.0267504i	$-0.00851594\pi$
$678$	0.889668	−	0.465916i	0.0341675	−	0.0178934i
$679$	5.55975	−	5.55975i	0.213364	−	0.213364i
$680$	−34.0377	−	34.1853i	−1.30529	−	1.31094i
$681$	0.744976	+	0.744976i	0.0285475	+	0.0285475i
$682$	26.3664	+	8.24207i	1.00962	+	0.315605i
$683$	22.9381	+	22.9381i	0.877703	+	0.877703i	0.993297	−	0.115594i	$-0.0368771\pi$
$683$	22.9381	+	22.9381i	0.877703	+	0.877703i	−0.115594	+	0.993297i	$0.536877\pi$
$684$	−25.2577	+	16.2661i	−0.965751	+	0.621950i
$685$		−	13.8777i		−	0.530241i
$686$	18.1341	−	9.49678i	0.692364	−	0.362589i
$687$	1.81653	+	0.752430i	0.0693048	+	0.0287070i
$688$	−33.5657	−	1.13484i	−1.27968	−	0.0432654i
$689$	6.11445	+	6.11445i	0.232942	+	0.232942i
$690$	2.33608	−	1.22340i	0.0889331	−	0.0465740i
$691$	−1.11223	−	1.11223i	−0.0423111	−	0.0423111i	0.685635	−	0.727946i	$-0.259525\pi$
$691$	−1.11223	−	1.11223i	−0.0423111	−	0.0423111i	−0.727946	+	0.685635i	$0.759525\pi$
$692$	−7.82104	−	43.1143i	−0.297311	−	1.63896i
$693$	6.54407	−	2.71064i	0.248588	−	0.102969i
$694$	−26.7694	−	22.3502i	−1.01615	−	0.848402i
$695$		−	23.4868i		−	0.890904i
$696$	−0.0112383	+	0.0198013i	−0.000425988	+	0.000750567i
$697$	−22.4999	+	28.7503i	−0.852245	+	1.08900i
$698$	−34.4991	−	10.7843i	−1.30581	−	0.408193i
$699$	0.247555	+	0.102541i	0.00936339	+	0.00387844i
$700$	14.9469	+	23.2093i	0.564940	+	0.877228i
$701$	5.03769	+	2.08668i	0.190271	+	0.0788128i	0.475785	−	0.879562i	$-0.342164\pi$
$701$	5.03769	+	2.08668i	0.190271	+	0.0788128i	−0.285514	+	0.958375i	$0.592164\pi$
$702$	1.56676	−	0.820507i	0.0591335	−	0.0309680i
$703$	−45.6686	−	18.9166i	−1.72243	−	0.713452i
$704$	14.2779	−	8.52669i	0.538120	−	0.321362i
$705$	−0.113065	+	0.113065i	−0.00425826	+	0.00425826i
$706$	0.479555	+	0.400389i	0.0180483	+	0.0150689i
$707$	−0.917359	−	0.917359i	−0.0345008	−	0.0345008i
$708$	−0.545318	+	2.51832i	−0.0204943	+	0.0946444i
$709$	23.3673	+	23.3673i	0.877578	+	0.877578i	0.993284	−	0.115706i	$-0.0369130\pi$
$709$	23.3673	+	23.3673i	0.877578	+	0.877578i	−0.115706	+	0.993284i	$0.536913\pi$
$710$	−27.4926	+	87.9489i	−1.03178	+	3.30066i
$711$	−6.29871	+	15.2064i	−0.236220	+	0.570286i
$712$	−3.58157	−	12.9827i	−0.134225	−	0.486547i
$713$	29.8414	+	29.8414i	1.11757	+	1.11757i
$714$	0.139741	+	0.652153i	0.00522968	+	0.0244062i
$715$	−6.84534	−	16.5261i	−0.256001	−	0.618042i
$716$	4.76418	+	7.39773i	0.178046	+	0.276466i
$717$	1.33821			0.0499765
$718$	22.8261	−	27.3394i	0.851864	−	1.02030i
$719$	34.5789	−	14.3231i	1.28958	−	0.534160i	0.370717	−	0.928746i	$-0.379112\pi$
$719$	34.5789	−	14.3231i	1.28958	−	0.534160i	0.918859	+	0.394586i	$0.129112\pi$
$720$	45.0412	+	20.4661i	1.67859	+	0.762727i
$721$	−15.9234	−	6.59569i	−0.593019	−	0.245636i
$722$	0.790697	+	8.78873i	0.0294267	+	0.327083i
$723$	0.650547	−	0.269466i	0.0241941	−	0.0100215i
$724$	2.39177	−	0.433873i	0.0888893	−	0.0161248i
$725$			0.971397i			0.0360768i
$726$	−0.727693	−	0.607564i	−0.0270072	−	0.0225488i
$727$	3.51978	−	3.51978i	0.130541	−	0.130541i	−0.638817	−	0.769359i	$-0.720576\pi$
$727$	3.51978	−	3.51978i	0.130541	−	0.130541i	0.769359	+	0.638817i	$0.220576\pi$
$728$	5.83143	+	3.30966i	0.216127	+	0.122664i
$729$	26.4575			0.979909
$730$	−14.3562	+	45.9257i	−0.531348	+	1.69979i
$731$	−34.3639	+	4.19097i	−1.27099	+	0.155009i
$732$	0.993560	+	0.688440i	0.0367230	+	0.0254455i
$733$	−12.6612	+	5.24445i	−0.467653	+	0.193708i	−0.604051	−	0.796946i	$-0.706448\pi$
$733$	−12.6612	+	5.24445i	−0.467653	+	0.193708i	0.136398	+	0.990654i	$0.456448\pi$
$734$	−19.9194	+	10.4317i	−0.735238	+	0.385042i
$735$			2.36706i			0.0873105i
$736$	25.3663	−	1.42019i	0.935012	−	0.0523488i
$737$	12.9504	+	5.36424i	0.477035	+	0.197594i
$738$	11.1706	−	35.7349i	0.411197	−	1.31542i
$739$	−17.5827	−	42.4483i	−0.646789	−	1.56149i	−0.817351	−	0.576141i	$-0.804558\pi$
$739$	−17.5827	−	42.4483i	−0.646789	−	1.56149i	0.170561	−	0.985347i	$-0.445442\pi$
$740$	14.5295	+	80.0953i	0.534115	+	2.94436i
$741$		−	1.04891i		−	0.0385325i
$742$	4.29381	−	5.14279i	0.157631	−	0.188798i
$743$	18.0606	+	7.48096i	0.662581	+	0.274450i	0.688524	−	0.725213i	$-0.258259\pi$
$743$	18.0606	+	7.48096i	0.662581	+	0.274450i	−0.0259433	+	0.999663i	$0.508259\pi$
$744$	0.328664	−	2.64722i	0.0120494	−	0.0970519i
$745$	46.0698	+	19.0827i	1.68787	+	0.699137i
$746$	−1.16803	−	0.365124i	−0.0427647	−	0.0133681i
$747$	0.135144	+	0.326267i	0.00494467	+	0.0119375i
$748$	13.1823	−	10.9579i	0.481994	−	0.400659i
$749$	−10.3715	−	4.29603i	−0.378968	−	0.156974i
$750$	−4.15892	+	0.374166i	−0.151862	+	0.0136626i
$751$	−12.8591	−	31.0447i	−0.469236	−	1.13284i	−0.964497	−	0.264092i	$-0.914928\pi$
$751$	−12.8591	−	31.0447i	−0.469236	−	1.13284i	0.495261	−	0.868744i	$-0.335072\pi$
$752$	−1.44234	+	0.541094i	−0.0525967	+	0.0197317i
$753$	0.340088	−	0.140869i	0.0123935	−	0.00513355i
$754$	0.109461	+	0.209015i	0.00398632	+	0.00761189i
$755$	−54.9300	+	54.9300i	−1.99911	+	1.99911i
$756$	−0.741926	−	1.15205i	−0.0269836	−	0.0418996i
$757$	32.7966	+	13.5848i	1.19201	+	0.493748i	0.888410	−	0.459051i	$-0.151811\pi$
$757$	32.7966	+	13.5848i	1.19201	+	0.493748i	0.303602	+	0.952799i	$0.401811\pi$
$758$	10.0101	−	0.900576i	0.363582	−	0.0327104i
$759$	0.358593	+	0.865720i	0.0130161	+	0.0314237i
$760$	46.3685	−	36.1264i	1.68196	−	1.31044i
$761$	−22.3346	−	22.3346i	−0.809628	−	0.809628i	0.174949	−	0.984577i	$-0.444024\pi$
$761$	−22.3346	−	22.3346i	−0.809628	−	0.809628i	−0.984577	+	0.174949i	$0.944024\pi$
$762$	−0.361807	+	0.0325507i	−0.0131069	+	0.00117919i
$763$	−8.65648	−	3.58563i	−0.313385	−	0.129809i
$764$	−40.5537	+	7.35655i	−1.46718	+	0.266151i
$765$	49.1297	+	13.6679i	1.77629	+	0.494166i
$766$	−2.48926	−	27.6685i	−0.0899406	−	0.999705i
$767$	18.8810	+	18.8810i	0.681752	+	0.681752i
$768$	−1.05624	−	1.20963i	−0.0381138	−	0.0436489i
$769$		−	12.5956i		−	0.454210i	−0.973870	−	0.227105i	$-0.927074\pi$
$769$		−	12.5956i		−	0.454210i	0.973870	−	0.227105i	$-0.0729260\pi$
$770$	−12.2774	+	6.42961i	−0.442445	+	0.231707i
$771$	−0.293962	+	0.293962i	−0.0105868	+	0.0105868i
$772$	10.3060	−	47.5939i	0.370921	−	1.71294i
$773$	−10.4316	+	25.1840i	−0.375197	+	0.905807i	0.617654	+	0.786450i	$0.288083\pi$
$773$	−10.4316	+	25.1840i	−0.375197	+	0.905807i	−0.992851	+	0.119357i	$0.961917\pi$
$774$	31.4507	−	16.4706i	1.13047	−	0.592025i
$775$	−43.5531	−	105.147i	−1.56447	−	3.77698i
$776$	−2.40431	+	19.3655i	−0.0863099	+	0.695182i
$777$	0.430684	−	1.03976i	0.0154507	−	0.0373013i
$778$	33.9243	−	17.7660i	1.21624	−	0.636943i
$779$	−31.4550	−	31.4550i	−1.12699	−	1.12699i
$780$	−1.45222	+	0.935240i	−0.0519978	+	0.0334869i
$781$	−30.2508	−	12.5303i	−1.08246	−	0.448369i
$782$	25.6066	−	5.48690i	0.915691	−	0.196211i
$783$		−	0.0482176i		−	0.00172316i
$784$	−9.43403	+	20.7621i	−0.336930	+	0.741504i
$785$	−22.0363	−	53.2004i	−0.786510	−	1.89880i
$786$	1.09443	+	0.913759i	0.0390370	+	0.0325927i
$787$			37.5751i			1.33941i	0.742629	+	0.669703i	$0.233579\pi$
$787$			37.5751i			1.33941i	−0.742629	+	0.669703i	$0.766421\pi$
$788$	−1.56320	+	0.283569i	−0.0556867	+	0.0101017i
$789$	2.00109			0.0712407
$790$	9.60846	−	30.7375i	0.341853	−	1.09359i
$791$	−8.06329			−0.286698
$792$	−8.67733	+	15.2890i	−0.308335	+	0.543269i
$793$	11.5727	−	4.79356i	0.410958	−	0.170224i
$794$	2.85825	−	0.257149i	0.101436	−	0.00912587i
$795$	0.660468	+	1.59451i	0.0234244	+	0.0565515i
$796$	−1.18170	+	5.45718i	−0.0418842	+	0.193425i
$797$	−22.6701	+	9.39026i	−0.803016	+	0.332620i	−0.746164	−	0.665763i	$-0.768106\pi$
$797$	−22.6701	+	9.39026i	−0.803016	+	0.332620i	−0.0568520	+	0.998383i	$0.518106\pi$
$798$	−0.809402	+	0.0728196i	−0.0286525	+	0.00257779i
$799$	−1.38268	+	0.780798i	−0.0489157	+	0.0276226i
$800$	−64.6656	−	22.6399i	−2.28628	−	0.800441i
$801$	10.0668	+	10.0668i	0.355694	+	0.355694i
$802$	9.93921	−	5.20513i	0.350966	−	0.183799i
$803$	−15.7965	−	6.54314i	−0.557448	−	0.230902i
$804$	0.286466	−	1.32292i	0.0101029	−	0.0466558i
$805$	−21.1725			−0.746232
$806$	−21.2196	−	17.7166i	−0.747429	−	0.624042i
$807$		−	1.09587i		−	0.0385766i
$808$	3.19531	+	0.396712i	0.112411	+	0.0139563i
$809$	−23.7919	+	9.85492i	−0.836478	+	0.346480i	−0.759464	−	0.650550i	$-0.774539\pi$
$809$	−23.7919	+	9.85492i	−0.836478	+	0.346480i	−0.0770139	+	0.997030i	$0.524539\pi$
$810$	−51.9113	+	4.67031i	−1.82398	+	0.164098i
$811$	−1.74401	+	1.74401i	−0.0612404	+	0.0612404i	−0.737064	−	0.675823i	$-0.763788\pi$
$811$	−1.74401	+	1.74401i	−0.0612404	+	0.0612404i	0.675823	+	0.737064i	$0.263788\pi$
$812$	0.153690	−	0.0989774i	0.00539347	−	0.00347343i
$813$	1.91766			0.0672553
$814$	−28.8093	+	2.59189i	−1.00977	+	0.0908458i
$815$			62.7175i			2.19690i
$816$	−1.26835	−	1.06363i	−0.0444012	−	0.0372347i
$817$		−	42.1819i		−	1.47576i
$818$	−0.718818	−	7.98978i	−0.0251329	−	0.279356i
$819$	−7.08803			−0.247676
$820$	−15.5034	+	71.5960i	−0.541403	+	2.50024i
$821$	8.06857	−	8.06857i	0.281595	−	0.281595i	−0.552150	−	0.833745i	$-0.686192\pi$
$821$	8.06857	−	8.06857i	0.281595	−	0.281595i	0.833745	+	0.552150i	$0.186192\pi$
$822$	−0.0426691	−	0.474275i	−0.00148826	−	0.0165422i
$823$	32.2228	−	13.3471i	1.12322	−	0.465252i	0.257747	−	0.966213i	$-0.417020\pi$
$823$	32.2228	−	13.3471i	1.12322	−	0.465252i	0.865470	+	0.500961i	$0.167020\pi$
$824$	41.2358	−	11.3758i	1.43652	−	0.396295i
$825$		−	2.52701i		−	0.0879793i
$826$	13.2589	−	15.8805i	0.461338	−	0.552555i
$827$	20.2433			0.703929			0.351964	−	0.936013i	$-0.385514\pi$
$827$	20.2433			0.703929			0.351964	+	0.936013i	$0.385514\pi$
$828$	−22.5794	+	14.5413i	−0.784688	+	0.505344i
$829$	−8.74352	−	3.62168i	−0.303675	−	0.125786i	0.225642	−	0.974210i	$-0.427552\pi$
$829$	−8.74352	−	3.62168i	−0.303675	−	0.125786i	−0.529317	+	0.848424i	$0.677552\pi$
$830$	−0.320561	−	0.612112i	−0.0111268	−	0.0212467i
$831$	0.411775	+	0.411775i	0.0142843	+	0.0142843i
$832$	−16.4652	+	2.41534i	−0.570829	+	0.0837368i
$833$	−6.30036	+	22.6468i	−0.218295	+	0.784664i
$834$	−0.0722135	−	0.802665i	−0.00250055	−	0.0277940i
$835$	−19.9614	+	8.26829i	−0.690794	+	0.286136i
$836$	11.3092	+	17.5606i	0.391136	+	0.607348i
$837$	2.16186	+	5.21920i	0.0747250	+	0.180402i
$838$	4.38634	+	48.7549i	0.151524	+	1.68421i
$839$	12.8147	−	5.30804i	0.442414	−	0.183254i	−0.150345	−	0.988634i	$-0.548039\pi$
$839$	12.8147	−	5.30804i	0.442414	−	0.183254i	0.592759	+	0.805380i	$0.298039\pi$
$840$	0.822509	+	1.05570i	0.0283793	+	0.0364250i
$841$	−28.9936			−0.999778
$842$	−22.6360	−	7.07596i	−0.780089	−	0.243854i
$843$	0.446524			0.0153791
$844$	−15.2634	−	10.5760i	−0.525387	−	0.364042i
$845$		−	35.8764i		−	1.23419i
$846$	1.04368	−	1.25004i	0.0358825	−	0.0429773i
$847$	2.91270	+	7.03187i	0.100081	+	0.241618i
$848$	−0.561853	+	16.6182i	−0.0192941	+	0.570671i
$849$			0.253442i			0.00869811i
$850$	−69.4614	−	12.7557i	−2.38251	−	0.437518i
$851$	−40.8260	−	16.9107i	−1.39950	−	0.579691i
$852$	−0.669153	+	3.09020i	−0.0229248	+	0.105869i
$853$	36.3413	+	36.3413i	1.24430	+	1.24430i	0.958199	+	0.286103i	$0.0923598\pi$
$853$	36.3413	+	36.3413i	1.24430	+	1.24430i	0.286103	+	0.958199i	$0.407640\pi$
$854$	−4.50244	−	8.59743i	−0.154070	−	0.294198i
$855$	−23.7787	+	57.4070i	−0.813216	+	1.96328i
$856$	26.8585	−	7.40951i	0.918004	−	0.253252i
$857$	−13.6905	−	33.0518i	−0.467659	−	1.12903i	−0.965182	−	0.261577i	$-0.915757\pi$
$857$	−13.6905	−	33.0518i	−0.467659	−	1.12903i	0.497524	−	0.867450i	$-0.334243\pi$
$858$	−0.284753	−	0.543737i	−0.00972131	−	0.0185629i
$859$	−8.78952	+	21.2198i	−0.299895	+	0.724010i	0.700056	+	0.714088i	$0.253158\pi$
$859$	−8.78952	+	21.2198i	−0.299895	+	0.724010i	−0.999951	+	0.00992191i	$0.996842\pi$
$860$	−58.4012	+	37.6108i	−1.99147	+	1.28252i
$861$	0.716152	−	0.716152i	0.0244064	−	0.0244064i
$862$	7.96291	+	15.2052i	0.271218	+	0.517891i
$863$		−	12.3720i		−	0.421148i	−0.977578	−	0.210574i	$-0.932467\pi$
$863$		−	12.3720i		−	0.421148i	0.977578	−	0.210574i	$-0.0675332\pi$
$864$	3.20983	+	1.12379i	0.109201	+	0.0382320i
$865$	−64.0846	−	64.0846i	−2.17894	−	2.17894i
$866$	2.42723	−	0.218371i	0.0824807	−	0.00742056i
$867$	−1.46111	−	0.881163i	−0.0496219	−	0.0299259i
$868$	−12.1981	+	17.6044i	−0.414031	+	0.597531i
$869$	10.5724	+	4.37924i	0.358645	+	0.148556i
$870$	0.00421968	+	0.0469025i	0.000143061	+	0.00159014i
$871$	−9.91851	−	9.91851i	−0.336076	−	0.336076i
$872$	22.4171	−	6.18425i	0.759138	−	0.209425i
$873$	−7.89416	−	19.0582i	−0.267177	−	0.645022i
$874$	2.85924	+	31.7810i	0.0967154	+	1.07501i
$875$	30.9743	+	12.8300i	1.04712	+	0.433733i
$876$	−0.349422	+	1.61366i	−0.0118059	+	0.0545205i
$877$	−17.1420	+	17.1420i	−0.578846	+	0.578846i	−0.934585	−	0.355739i	$-0.884229\pi$
$877$	−17.1420	+	17.1420i	−0.578846	+	0.578846i	0.355739	+	0.934585i	$0.384229\pi$
$878$	−11.4177	+	5.97939i	−0.385327	+	0.201795i
$879$	−0.00452434	+	0.00187404i	−0.000152602	+	6.32099e-5i
$880$	14.2293	−	31.3153i	0.479668	−	1.05564i
$881$	−19.6982	−	47.5556i	−0.663648	−	1.60219i	−0.792043	−	0.610466i	$-0.790982\pi$
$881$	−19.6982	−	47.5556i	−0.663648	−	1.60219i	0.128394	−	0.991723i	$-0.459018\pi$
$882$	−2.16012	−	24.0101i	−0.0727351	−	0.808463i
$883$	−32.0166	−	13.2617i	−1.07745	−	0.446293i	−0.227833	−	0.973700i	$-0.573164\pi$
$883$	−32.0166	−	13.2617i	−1.07745	−	0.446293i	−0.849612	+	0.527408i	$0.823164\pi$
$884$	−16.3834	+	5.08251i	−0.551032	+	0.170943i
$885$	2.03948	+	4.92373i	0.0685562	+	0.165509i
$886$	−4.29019	+	13.7243i	−0.144132	+	0.461078i
$887$	−2.79162	−	1.15633i	−0.0937334	−	0.0388257i	0.335324	−	0.942103i	$-0.391154\pi$
$887$	−2.79162	−	1.15633i	−0.0937334	−	0.0388257i	−0.429057	+	0.903277i	$0.641154\pi$
$888$	0.742814	+	2.69260i	0.0249272	+	0.0903578i
$889$	2.69462	+	1.11615i	0.0903747	+	0.0374344i
$890$	−21.3824	−	17.8526i	−0.716741	−	0.598420i
$891$		−	18.5207i		−	0.620468i
$892$	24.3235	−	35.1037i	0.814410	−	1.17536i
$893$	−0.740427	−	1.78755i	−0.0247774	−	0.0598180i
$894$	1.63312	+	0.510508i	0.0546196	+	0.0170739i
$895$	16.8139	+	6.96456i	0.562028	+	0.232800i
$896$	3.00692	+	12.5379i	0.100454	+	0.418863i
$897$		−	0.937682i		−	0.0313083i
$898$	22.4318	+	42.8335i	0.748558	+	1.42937i
$899$	−0.696273	+	0.288406i	−0.0232220	+	0.00961887i
$900$	71.2633	−	12.9274i	2.37544	−	0.430912i
$901$	2.07492	+	17.0134i	0.0691257	+	0.566797i
$902$	−24.8450	−	7.76649i	−0.827249	−	0.258596i
$903$	0.960377			0.0319594
$904$	15.7864	−	12.2994i	0.525047	−	0.409072i
$905$	3.55510	−	3.55510i	0.118175	−	0.118175i
$906$	−1.70835	+	2.04613i	−0.0567562	+	0.0679782i
$907$		−	4.65621i		−	0.154607i	−0.997008	−	0.0773035i	$-0.975369\pi$
$907$		−	4.65621i		−	0.154607i	0.997008	−	0.0773035i	$-0.0246310\pi$
$908$	17.2562	+	11.9569i	0.572668	+	0.396803i
$909$	−3.14460	+	1.30254i	−0.104300	+	0.0432024i
$910$	13.8126	−	1.24268i	0.457884	−	0.0411946i
$911$	−21.9362	−	9.08627i	−0.726779	−	0.301042i	−0.0115513	−	0.999933i	$-0.503677\pi$
$911$	−21.9362	−	9.08627i	−0.726779	−	0.301042i	−0.715228	+	0.698892i	$0.753677\pi$
$912$	1.47358	−	1.37719i	0.0487950	−	0.0456035i
$913$	0.226841	−	0.0939605i	0.00750733	−	0.00310964i
$914$	−8.26689	−	6.90217i	−0.273444	−	0.228303i
$915$	2.50011			0.0826510
$916$	38.2924	+	8.29184i	1.26521	+	0.273970i
$917$	−4.38062	−	10.5757i	−0.144661	−	0.349242i
$918$	3.44788	+	0.633162i	0.113797	+	0.0208975i
$919$	37.7588	+	37.7588i	1.24555	+	1.24555i	0.957666	+	0.287881i	$0.0929506\pi$
$919$	37.7588	+	37.7588i	1.24555	+	1.24555i	0.287881	+	0.957666i	$0.407049\pi$
$920$	41.4517	−	32.2956i	1.36662	−	1.06476i
$921$	0.474164	−	1.14473i	0.0156242	−	0.0377202i
$922$	−16.8358	−	5.26282i	−0.554456	−	0.173322i
$923$	23.1686	+	23.1686i	0.762604	+	0.762604i
$924$	−0.399813	+	0.257482i	−0.0131529	+	0.00847053i
$925$	84.2659	+	84.2659i	2.77065	+	2.77065i
$926$	−15.0776	+	18.0588i	−0.495481	+	0.593449i
$927$	−31.9744	+	31.9744i	−1.05018	+	1.05018i
$928$	−0.149920	+	0.428211i	−0.00492136	+	0.0140567i
$929$	18.1021	+	7.49812i	0.593910	+	0.246005i	0.659332	−	0.751852i	$-0.270839\pi$
$929$	18.1021	+	7.49812i	0.593910	+	0.246005i	−0.0654220	+	0.997858i	$0.520839\pi$
$930$	−2.55965	−	4.88766i	−0.0839342	−	0.160273i
$931$	−26.4622	−	10.9610i	−0.867265	−	0.359233i
$932$	5.21846	+	1.13001i	0.170936	+	0.0370146i
$933$	0.437691	+	0.181297i	0.0143294	+	0.00593541i
$934$	9.91408	−	31.7152i	0.324398	−	1.03775i
$935$	9.50278	−	34.1579i	0.310774	−	1.11708i
$936$	13.8770	−	10.8118i	0.453584	−	0.353394i
$937$		−	16.2634i		−	0.531304i	−0.964069	−	0.265652i	$-0.914413\pi$
$937$		−	16.2634i		−	0.531304i	0.964069	−	0.265652i	$-0.0855872\pi$
$938$	−6.96516	+	8.34234i	−0.227421	+	0.272387i
$939$	−0.115020	+	0.0476430i	−0.00375355	+	0.00155477i
$940$	−1.81469	+	2.61897i	−0.0591887	+	0.0854213i
$941$	−17.5752	−	17.5752i	−0.572935	−	0.572935i	0.360013	−	0.932947i	$-0.382772\pi$
$941$	−17.5752	−	17.5752i	−0.572935	−	0.572935i	−0.932947	+	0.360013i	$0.882772\pi$
$942$	−0.916669	−	1.75038i	−0.0298667	−	0.0570305i
$943$	−28.1195	−	28.1195i	−0.915698	−	0.915698i
$944$	−1.73496	+	51.3157i	−0.0564681	+	1.67018i
$945$	−2.61843	−	1.08459i	−0.0851777	−	0.0352818i
$946$	−11.4514	−	21.8664i	−0.372316	−	0.710939i
$947$			43.3357i			1.40822i	0.710090	+	0.704111i	$0.248654\pi$
$947$			43.3357i			1.40822i	−0.710090	+	0.704111i	$0.751346\pi$
$948$	0.233864	−	1.08000i	0.00759555	−	0.0350769i
$949$	12.0983	+	12.0983i	0.392728	+	0.392728i
$950$	25.6746	−	82.1330i	0.832993	−	2.66475i
$951$	−0.731647	−	0.731647i	−0.0237253	−	0.0237253i
$952$	5.05939	+	12.2896i	0.163976	+	0.398307i
$953$	−8.21263	+	8.21263i	−0.266033	+	0.266033i	−0.827500	−	0.561466i	$-0.810237\pi$
$953$	−8.21263	+	8.21263i	−0.266033	+	0.266033i	0.561466	+	0.827500i	$0.310237\pi$
$954$	−8.15452	−	15.5711i	−0.264012	−	0.504132i
$955$	−60.2786	+	60.2786i	−1.95057	+	1.95057i
$956$	26.2380	−	4.75964i	0.848598	−	0.153938i
$957$	−0.0167337			−0.000540924
$958$	−5.96045	+	19.0675i	−0.192574	+	0.616044i
$959$	−1.46311	+	3.53225i	−0.0472461	+	0.114062i
$960$	−3.22063	−	0.812231i	−0.103945	−	0.0262146i
$961$	40.5153	−	40.5153i	1.30694	−	1.30694i
$962$	27.6269	+	8.63608i	0.890726	+	0.278438i
$963$	−20.8262	+	20.8262i	−0.671114	+	0.671114i
$964$	11.7967	−	7.59716i	0.379946	−	0.244688i
$965$	−38.5442	−	93.0539i	−1.24078	−	2.99551i
$966$	−0.723575	+	0.0650980i	−0.0232806	+	0.00209449i
$967$	45.1805			1.45291			0.726454	−	0.687215i	$-0.241167\pi$
$967$	45.1805			1.45291			0.726454	+	0.687215i	$0.241167\pi$
$968$	−16.4286	−	9.32415i	−0.528036	−	0.299690i
$969$	1.28131	−	1.63725i	0.0411616	−	0.0525961i
$970$	18.7249	+	35.7552i	0.601220	+	1.14803i
$971$	4.23815	−	10.2318i	0.136009	−	0.328354i	−0.841171	−	0.540770i	$-0.818133\pi$
$971$	4.23815	−	10.2318i	0.136009	−	0.328354i	0.977179	+	0.212416i	$0.0681331\pi$
$972$	−5.30896	+	0.963060i	−0.170285	+	0.0308902i
$973$	−2.47617	+	5.97800i	−0.0793823	+	0.191646i
$974$	12.8137	−	40.9912i	0.410579	−	1.31344i
$975$	−0.967699	+	2.33623i	−0.0309912	+	0.0748193i
$976$	21.9291	+	9.96427i	0.701932	+	0.318949i
$977$	21.4552	+	21.4552i	0.686411	+	0.686411i	0.961437	−	0.275026i	$-0.0886863\pi$
$977$	21.4552	+	21.4552i	0.686411	+	0.686411i	−0.275026	+	0.961437i	$0.588686\pi$
$978$	0.192834	+	2.14339i	0.00616616	+	0.0685379i
$979$	6.99907	−	6.99907i	0.223691	−	0.223691i
$980$	8.41898	+	46.4105i	0.268934	+	1.48253i
$981$	−17.3823	+	17.3823i	−0.554974	+	0.554974i
$982$	−4.07646	−	7.78400i	−0.130085	−	0.248398i
$983$	−4.63652	−	1.92051i	−0.147882	−	0.0612548i	0.307515	−	0.951543i	$-0.400503\pi$
$983$	−4.63652	−	1.92051i	−0.147882	−	0.0612548i	−0.455397	+	0.890289i	$0.650503\pi$
$984$	−0.309700	+	2.49448i	−0.00987288	+	0.0795210i
$985$	−2.32353	+	2.32353i	−0.0740337	+	0.0740337i
$986$	−0.0844676	+	0.459968i	−0.00269000	+	0.0146484i
$987$	0.0406981	−	0.0168577i	0.00129543	−	0.000536586i
$988$	−3.73066	−	20.5656i	−0.118688	−	0.654280i
$989$		−	37.7090i		−	1.19908i
$990$	3.25809	+	36.2143i	0.103549	+	1.15096i
$991$	11.7747	+	28.4265i	0.374034	+	0.902999i	0.993058	+	0.117627i	$0.0375286\pi$
$991$	11.7747	+	28.4265i	0.374034	+	0.902999i	−0.619023	+	0.785372i	$0.712471\pi$
$992$	−2.97138	−	53.0724i	−0.0943415	−	1.68505i
$993$	−1.37494	+	3.31939i	−0.0436323	+	0.105338i
$994$	16.2699	−	19.4868i	0.516050	−	0.618084i
$995$	4.41952	+	10.6697i	0.140108	+	0.338251i
$996$	−0.0128373	−	0.0199335i	−0.000406765	−	0.000631616i
$997$	26.9908			0.854808			0.427404	−	0.904061i	$-0.359428\pi$
$997$	26.9908			0.854808			0.427404	+	0.904061i	$0.359428\pi$
$998$	−42.1354	+	3.79080i	−1.33377	+	0.119996i
$999$	−4.18274	−	4.18274i	−0.132336	−	0.132336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.v.a.461.52	✓	280
17.9	even	8		544.2.x.a.77.15	yes	280
32.5	even	8		544.2.x.a.325.15	yes	280
544.485	even	8	inner	544.2.v.a.485.52	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.v.a.461.52	✓	280	1.1	even	1	trivial
544.2.v.a.485.52	yes	280	544.485	even	8	inner
544.2.x.a.77.15	yes	280	17.9	even	8
544.2.x.a.325.15	yes	280	32.5	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.906372 - 1.08558i) q^{2} -0.100368i q^{3} +(-0.356979 - 1.96788i) q^{4} +(-2.92504 - 2.92504i) q^{5} +(-0.108957 - 0.0909704i) q^{6} +(0.436118 + 1.05288i) q^{7} +(-2.45986 - 1.39610i) q^{8} +2.98993 q^{9} +(-5.82655 + 0.524198i) q^{10} -2.07878i q^{11} +(-0.197512 + 0.0358292i) q^{12} +(-0.796050 + 1.92184i) q^{13} +(1.53828 + 0.480861i) q^{14} +(-0.293579 + 0.293579i) q^{15} +(-3.74513 + 1.40499i) q^{16} +(-3.59022 + 2.02739i) q^{17} +(2.70999 - 3.24581i) q^{18} +(-1.92257 - 4.64149i) q^{19} +(-4.71196 + 6.80032i) q^{20} +(0.105675 - 0.0437721i) q^{21} +(-2.25668 - 1.88414i) q^{22} +(-1.71870 - 4.14931i) q^{23} +(-0.140124 + 0.246890i) q^{24} +12.1117i q^{25} +(1.36479 + 2.60608i) q^{26} -0.601195i q^{27} +(1.91626 - 1.23409i) q^{28} +0.0802030 q^{29} +(0.0526125 + 0.584797i) q^{30} +(-8.68138 + 3.59595i) q^{31} +(-1.86925 + 5.33909i) q^{32} -0.208642 q^{33} +(-1.05317 + 5.73505i) q^{34} +(1.80406 - 4.35538i) q^{35} +(-1.06734 - 5.88383i) q^{36} +(6.95738 - 6.95738i) q^{37} +(-6.78128 - 2.11981i) q^{38} +(0.192890 + 0.0798977i) q^{39} +(3.11152 + 11.2788i) q^{40} +(8.18046 - 3.38846i) q^{41} +(0.0482628 - 0.154393i) q^{42} +(7.75710 + 3.21310i) q^{43} +(-4.09079 + 0.742080i) q^{44} +(-8.74566 - 8.74566i) q^{45} +(-6.06221 - 1.89503i) q^{46} +0.385124 q^{47} +(0.141015 + 0.375890i) q^{48} +(4.03139 - 4.03139i) q^{49} +(13.1483 + 10.9777i) q^{50} +(0.203485 + 0.360342i) q^{51} +(4.06612 + 0.880479i) q^{52} +(1.59078 - 3.84049i) q^{53} +(-0.652647 - 0.544906i) q^{54} +(-6.08050 + 6.08050i) q^{55} +(0.397145 - 3.19880i) q^{56} +(-0.465855 + 0.192964i) q^{57} +(0.0726938 - 0.0870670i) q^{58} +(4.91222 - 11.8591i) q^{59} +(0.682532 + 0.472928i) q^{60} +(-4.25797 - 4.25797i) q^{61} +(-3.96487 + 12.6836i) q^{62} +(1.30396 + 3.14804i) q^{63} +(4.10179 + 6.86843i) q^{64} +(7.94993 - 3.29297i) q^{65} +(-0.189107 + 0.226498i) q^{66} +(-2.58048 + 6.22983i) q^{67} +(5.27131 + 6.34140i) q^{68} +(-0.416457 + 0.172502i) q^{69} +(-3.09298 - 5.90605i) q^{70} +(6.02773 - 14.5522i) q^{71} +(-7.35479 - 4.17425i) q^{72} +(3.14759 - 7.59896i) q^{73} +(-1.24684 - 13.8588i) q^{74} +1.21563 q^{75} +(-8.44759 + 5.44030i) q^{76} +(2.18870 - 0.906591i) q^{77} +(0.261566 - 0.136981i) q^{78} +(-2.10664 + 5.08589i) q^{79} +(15.0643 + 6.84502i) q^{80} +8.90944 q^{81} +(3.73609 - 11.9518i) q^{82} +(0.0451999 + 0.109122i) q^{83} +(-0.123862 - 0.192331i) q^{84} +(16.4317 + 4.57133i) q^{85} +(10.5189 - 5.50871i) q^{86} -0.00804979i q^{87} +(-2.90219 + 5.11349i) q^{88} +(3.36692 + 3.36692i) q^{89} +(-17.4210 + 1.56731i) q^{90} -2.37064 q^{91} +(-7.55183 + 4.86342i) q^{92} +(0.360917 + 0.871330i) q^{93} +(0.349066 - 0.418084i) q^{94} +(-7.95295 + 19.2001i) q^{95} +(0.535872 + 0.187613i) q^{96} +(-2.64025 - 6.37414i) q^{97} +(-0.722467 - 8.03034i) q^{98} -6.21539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 272 q^{9} - 4 q^{10} + 28 q^{12} - 28 q^{14} - 24 q^{16} + 4 q^{18} - 20 q^{19} - 4 q^{20} + 12 q^{21} + 4 q^{22} - 4 q^{23} + 36 q^{24}+ \cdots - 8 q^{97}+O(q^{100}) \) 280 * q - 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 272 * q^9 - 4 * q^10 + 28 * q^12 - 28 * q^14 - 24 * q^16 + 4 * q^18 - 20 * q^19 - 4 * q^20 + 12 * q^21 + 4 * q^22 - 4 * q^23 + 36 * q^24 - 4 * q^26 - 4 * q^28 - 8 * q^29 - 8 * q^30 - 24 * q^31 - 24 * q^32 + 8 * q^33 - 4 * q^34 + 12 * q^35 - 52 * q^36 - 4 * q^37 - 4 * q^39 + 32 * q^40 - 4 * q^41 + 40 * q^42 - 4 * q^43 + 20 * q^44 - 12 * q^45 - 8 * q^46 + 80 * q^47 - 76 * q^48 + 12 * q^50 + 24 * q^51 - 28 * q^52 - 4 * q^53 + 24 * q^54 + 20 * q^56 - 4 * q^57 + 20 * q^58 - 4 * q^59 + 4 * q^60 - 36 * q^61 + 104 * q^62 - 36 * q^63 + 8 * q^64 + 12 * q^65 - 24 * q^66 - 8 * q^67 + 8 * q^68 + 4 * q^69 - 4 * q^70 + 28 * q^71 - 52 * q^72 - 4 * q^73 - 8 * q^74 + 16 * q^75 - 20 * q^76 - 4 * q^77 + 24 * q^78 - 92 * q^80 + 240 * q^81 + 4 * q^82 - 44 * q^83 + 36 * q^84 - 4 * q^85 + 32 * q^86 + 4 * q^88 + 160 * q^90 + 56 * q^91 + 20 * q^92 + 20 * q^93 + 8 * q^94 + 12 * q^95 - 168 * q^96 - 8 * q^97

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