LMFDB - Embedded newform 225.2.w.a.212.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			212.21
Character	$\chi$	$=$	225.212
Dual form			225.2.w.a.173.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908228 + 1.12157i) q^{2} +(-1.73026 - 0.0786898i) q^{3} +(-0.0172140 + 0.0809854i) q^{4} +(1.65203 - 1.50691i) q^{5} +(-1.48322 - 2.01208i) q^{6} +(0.615345 - 2.29650i) q^{7} +(2.46532 - 1.25614i) q^{8} +(2.98762 + 0.272308i) q^{9} +O(q^{10})$	\(q+(0.908228 + 1.12157i) q^{2} +(-1.73026 - 0.0786898i) q^{3} +(-0.0172140 + 0.0809854i) q^{4} +(1.65203 - 1.50691i) q^{5} +(-1.48322 - 2.01208i) q^{6} +(0.615345 - 2.29650i) q^{7} +(2.46532 - 1.25614i) q^{8} +(2.98762 + 0.272308i) q^{9} +(3.19053 + 0.484249i) q^{10} +(-5.69377 - 0.598439i) q^{11} +(0.0361574 - 0.138771i) q^{12} +(3.51284 + 2.84464i) q^{13} +(3.13456 - 1.39559i) q^{14} +(-2.97703 + 2.47736i) q^{15} +(3.79919 + 1.69151i) q^{16} +(0.475579 + 0.933377i) q^{17} +(2.40803 + 3.59813i) q^{18} +(0.637208 + 0.207042i) q^{19} +(0.0935999 + 0.159731i) q^{20} +(-1.24542 + 3.92512i) q^{21} +(-4.50005 - 6.92947i) q^{22} +(4.59135 + 1.76246i) q^{23} +(-4.36449 + 1.97946i) q^{24} +(0.458430 - 4.97894i) q^{25} +6.52348i q^{26} +(-5.14793 - 0.706260i) q^{27} +(0.175390 + 0.0893659i) q^{28} +(-4.25021 + 4.72034i) q^{29} +(-5.48235 - 1.08894i) q^{30} +(-4.93512 - 5.48101i) q^{31} +(0.121143 + 0.452112i) q^{32} +(9.80462 + 1.48350i) q^{33} +(-0.614912 + 1.38111i) q^{34} +(-2.44405 - 4.72117i) q^{35} +(-0.0734818 + 0.237266i) q^{36} +(1.11926 + 0.177274i) q^{37} +(0.346519 + 0.902714i) q^{38} +(-5.85430 - 5.19841i) q^{39} +(2.17989 - 5.79020i) q^{40} +(-8.23737 + 0.865782i) q^{41} +(-5.53342 + 2.16809i) q^{42} +(3.13180 + 0.839162i) q^{43} +(0.146477 - 0.450811i) q^{44} +(5.34599 - 4.05221i) q^{45} +(2.19328 + 6.75023i) q^{46} +(0.384093 + 7.32894i) q^{47} +(-6.44050 - 3.22571i) q^{48} +(1.16692 + 0.673721i) q^{49} +(6.00058 - 4.00785i) q^{50} +(-0.749430 - 1.65241i) q^{51} +(-0.290845 + 0.235521i) q^{52} +(-3.29405 + 6.46493i) q^{53} +(-3.88338 - 6.41520i) q^{54} +(-10.3081 + 7.59137i) q^{55} +(-1.36771 - 6.43456i) q^{56} +(-1.08625 - 0.408378i) q^{57} +(-9.15435 - 0.479759i) q^{58} +(0.836580 + 7.95952i) q^{59} +(-0.149383 - 0.283741i) q^{60} +(-0.308741 + 2.93747i) q^{61} +(1.66511 - 10.5131i) q^{62} +(2.46377 - 6.69349i) q^{63} +(4.49184 - 6.18248i) q^{64} +(10.0900 - 0.594098i) q^{65} +(7.24099 + 12.3439i) q^{66} +(0.0164080 - 0.313083i) q^{67} +(-0.0837766 + 0.0224479i) q^{68} +(-7.80556 - 3.41080i) q^{69} +(3.07535 - 7.02907i) q^{70} +(8.29452 - 2.69505i) q^{71} +(7.70748 - 3.08154i) q^{72} +(2.35393 - 0.372825i) q^{73} +(0.817723 + 1.41634i) q^{74} +(-1.18500 + 8.57880i) q^{75} +(-0.0277362 + 0.0480406i) q^{76} +(-4.87795 + 12.7075i) q^{77} +(0.513332 - 11.2873i) q^{78} +(5.95146 + 5.35872i) q^{79} +(8.82535 - 2.93062i) q^{80} +(8.85170 + 1.62710i) q^{81} +(-8.45245 - 8.45245i) q^{82} +(0.894540 + 0.580921i) q^{83} +(-0.296439 - 0.168428i) q^{84} +(2.19219 + 0.825314i) q^{85} +(1.90321 + 4.27467i) q^{86} +(7.72543 - 7.83298i) q^{87} +(-14.7887 + 5.67684i) q^{88} +(-11.2732 - 8.19045i) q^{89} +(9.40021 + 2.31556i) q^{90} +(8.69433 - 6.31680i) q^{91} +(-0.221769 + 0.341494i) q^{92} +(8.10776 + 9.87193i) q^{93} +(-7.87106 + 7.08713i) q^{94} +(1.36468 - 0.618177i) q^{95} +(-0.174033 - 0.791805i) q^{96} +(-3.01383 + 0.157948i) q^{97} +(0.304204 + 1.92067i) q^{98} +(-16.8478 - 3.33837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	0.908228	+	1.12157i	0.642214	+	0.793069i	0.989476	−	0.144700i	$-0.0462216\pi$
$2$	0.908228	+	1.12157i	0.642214	+	0.793069i	−0.347261	+	0.937768i	$0.612888\pi$
$3$	−1.73026	−	0.0786898i	−0.998967	−	0.0454316i
$3$	−1.73026	−	0.0786898i	−0.998967	−	0.0454316i
$4$	−0.0172140	+	0.0809854i	−0.00860699	+	0.0404927i
$5$	1.65203	−	1.50691i	0.738812	−	0.673912i
$5$	1.65203	−	1.50691i	0.738812	−	0.673912i
$6$	−1.48322	−	2.01208i	−0.605521	−	0.821427i
$7$	0.615345	−	2.29650i	0.232579	−	0.867995i	−0.746647	−	0.665221i	$-0.768337\pi$
$7$	0.615345	−	2.29650i	0.232579	−	0.867995i	0.979225	−	0.202775i	$-0.0649959\pi$
$8$	2.46532	−	1.25614i	0.871621	−	0.444113i
$9$	2.98762	+	0.272308i	0.995872	+	0.0907694i
$10$	3.19053	+	0.484249i	1.00893	+	0.153133i
$11$	−5.69377	−	0.598439i	−1.71674	−	0.180436i	−0.805577	−	0.592491i	$-0.798144\pi$
$11$	−5.69377	−	0.598439i	−1.71674	−	0.180436i	−0.911159	+	0.412055i	$0.864811\pi$
$12$	0.0361574	−	0.138771i	0.0104378	−	0.0400599i
$13$	3.51284	+	2.84464i	0.974287	+	0.788962i	0.977479	−	0.211033i	$-0.0676826\pi$
$13$	3.51284	+	2.84464i	0.974287	+	0.788962i	−0.00319168	+	0.999995i	$0.501016\pi$
$14$	3.13456	−	1.39559i	0.837745	−	0.372988i
$15$	−2.97703	+	2.47736i	−0.768666	+	0.639650i
$16$	3.79919	+	1.69151i	0.949798	+	0.422877i
$17$	0.475579	+	0.933377i	0.115345	+	0.226377i	0.941460	−	0.337124i	$-0.109454\pi$
$17$	0.475579	+	0.933377i	0.115345	+	0.226377i	−0.826115	+	0.563501i	$0.809454\pi$
$18$	2.40803	+	3.59813i	0.567577	+	0.848088i
$19$	0.637208	+	0.207042i	0.146186	+	0.0474986i	0.381196	−	0.924494i	$-0.375512\pi$
$19$	0.637208	+	0.207042i	0.146186	+	0.0474986i	−0.235010	+	0.971993i	$0.575512\pi$
$20$	0.0935999	+	0.159731i	0.0209296	+	0.0357169i
$21$	−1.24542	+	3.92512i	−0.271773	+	0.856532i
$22$	−4.50005	−	6.92947i	−0.959414	−	1.47737i
$23$	4.59135	+	1.76246i	0.957363	+	0.367497i	0.786357	−	0.617773i	$-0.211965\pi$
$23$	4.59135	+	1.76246i	0.957363	+	0.367497i	0.171006	+	0.985270i	$0.445298\pi$
$24$	−4.36449	+	1.97946i	−0.890898	+	0.404055i
$25$	0.458430	−	4.97894i	0.0916861	−	0.995788i
$26$			6.52348i			1.27936i
$27$	−5.14793	−	0.706260i	−0.990720	−	0.135920i
$28$	0.175390	+	0.0893659i	0.0331457	+	0.0168886i
$29$	−4.25021	+	4.72034i	−0.789245	+	0.876545i	−0.994774	−	0.102106i	$-0.967442\pi$
$29$	−4.25021	+	4.72034i	−0.789245	+	0.876545i	0.205529	+	0.978651i	$0.434109\pi$
$30$	−5.48235	−	1.08894i	−1.00094	−	0.198812i
$31$	−4.93512	−	5.48101i	−0.886374	−	0.984418i	0.113584	−	0.993528i	$-0.463767\pi$
$31$	−4.93512	−	5.48101i	−0.886374	−	0.984418i	−0.999959	+	0.00911009i	$0.997100\pi$
$32$	0.121143	+	0.452112i	0.0214153	+	0.0799228i
$33$	9.80462	+	1.48350i	1.70677	+	0.258244i
$34$	−0.614912	+	1.38111i	−0.105457	+	0.236859i
$35$	−2.44405	−	4.72117i	−0.413120	−	0.798023i
$36$	−0.0734818	+	0.237266i	−0.0122470	+	0.0395443i
$37$	1.11926	+	0.177274i	0.184006	+	0.0291437i	0.247757	−	0.968822i	$-0.420306\pi$
$37$	1.11926	+	0.177274i	0.184006	+	0.0291437i	−0.0637513	+	0.997966i	$0.520306\pi$
$38$	0.346519	+	0.902714i	0.0562129	+	0.146439i
$39$	−5.85430	−	5.19841i	−0.937438	−	0.832411i
$40$	2.17989	−	5.79020i	0.344671	−	0.915512i
$41$	−8.23737	+	0.865782i	−1.28646	+	0.135212i	−0.722952	−	0.690898i	$-0.757215\pi$
$41$	−8.23737	+	0.865782i	−1.28646	+	0.135212i	−0.563508	+	0.826110i	$0.690549\pi$
$42$	−5.53342	+	2.16809i	−0.853826	+	0.334543i
$43$	3.13180	+	0.839162i	0.477594	+	0.127971i	0.489582	−	0.871957i	$-0.337149\pi$
$43$	3.13180	+	0.839162i	0.477594	+	0.127971i	−0.0119879	+	0.999928i	$0.503816\pi$
$44$	0.146477	−	0.450811i	0.0220823	−	0.0679623i
$45$	5.34599	−	4.05221i	0.796933	−	0.604068i
$46$	2.19328	+	6.75023i	0.323382	+	0.995267i
$47$	0.384093	+	7.32894i	0.0560258	+	1.06904i	0.871548	+	0.490310i	$0.163116\pi$
$47$	0.384093	+	7.32894i	0.0560258	+	1.06904i	−0.815522	+	0.578725i	$0.803550\pi$
$48$	−6.44050	−	3.22571i	−0.929606	−	0.465592i
$49$	1.16692	+	0.673721i	0.166703	+	0.0962458i
$50$	6.00058	−	4.00785i	0.848610	−	0.566796i
$51$	−0.749430	−	1.65241i	−0.104941	−	0.231384i
$52$	−0.290845	+	0.235521i	−0.0403329	+	0.0326610i
$53$	−3.29405	+	6.46493i	−0.452472	+	0.888027i	0.546256	+	0.837618i	$0.316052\pi$
$53$	−3.29405	+	6.46493i	−0.452472	+	0.888027i	−0.998729	+	0.0504089i	$0.983948\pi$
$54$	−3.88338	−	6.41520i	−0.528461	−	0.872999i
$55$	−10.3081	+	7.59137i	−1.38994	+	1.02362i
$56$	−1.36771	−	6.43456i	−0.182768	−	0.859854i
$57$	−1.08625	−	0.408378i	−0.143877	−	0.0540910i
$58$	−9.15435	−	0.479759i	−1.20202	−	0.0629955i
$59$	0.836580	+	7.95952i	0.108913	+	1.03624i	0.903353	+	0.428898i	$0.141098\pi$
$59$	0.836580	+	7.95952i	0.108913	+	1.03624i	−0.794439	+	0.607343i	$0.792235\pi$
$60$	−0.149383	−	0.283741i	−0.0192853	−	0.0366308i
$61$	−0.308741	+	2.93747i	−0.0395302	+	0.376105i	0.956816	+	0.290695i	$0.0938866\pi$
$61$	−0.308741	+	2.93747i	−0.0395302	+	0.376105i	−0.996346	+	0.0854098i	$0.972780\pi$
$62$	1.66511	−	10.5131i	0.211469	−	1.33516i
$63$	2.46377	−	6.69349i	0.310406	−	0.843301i
$64$	4.49184	−	6.18248i	0.561480	−	0.772810i
$65$	10.0900	−	0.594098i	1.25151	−	0.0736888i
$66$	7.24099	+	12.3439i	0.891304	+	1.51943i
$67$	0.0164080	−	0.313083i	0.00200455	−	0.0382492i	−0.997444	−	0.0714509i	$-0.977237\pi$
$67$	0.0164080	−	0.313083i	0.00200455	−	0.0382492i	0.999449	+	0.0332018i	$0.0105704\pi$
$68$	−0.0837766	+	0.0224479i	−0.0101594	+	0.00272220i
$69$	−7.80556	−	3.41080i	−0.939679	−	0.410612i
$70$	3.07535	−	7.02907i	0.367575	−	0.840134i
$71$	8.29452	−	2.69505i	0.984378	−	0.319844i	0.227772	−	0.973714i	$-0.426856\pi$
$71$	8.29452	−	2.69505i	0.984378	−	0.319844i	0.756606	+	0.653871i	$0.226856\pi$
$72$	7.70748	−	3.08154i	0.908335	−	0.363163i
$73$	2.35393	−	0.372825i	0.275506	−	0.0436359i	−0.0171524	−	0.999853i	$-0.505460\pi$
$73$	2.35393	−	0.372825i	0.275506	−	0.0436359i	0.292659	+	0.956217i	$0.405460\pi$
$74$	0.817723	+	1.41634i	0.0950583	+	0.164646i
$75$	−1.18500	+	8.57880i	−0.136832	+	0.990594i
$76$	−0.0277362	+	0.0480406i	−0.00318157	+	0.00551063i
$77$	−4.87795	+	12.7075i	−0.555894	+	1.44815i
$78$	0.513332	−	11.2873i	0.0581234	−	1.27804i
$79$	5.95146	+	5.35872i	0.669592	+	0.602903i	0.932176	−	0.362006i	$-0.117908\pi$
$79$	5.95146	+	5.35872i	0.669592	+	0.602903i	−0.262584	+	0.964909i	$0.584575\pi$
$80$	8.82535	−	2.93062i	0.986704	−	0.327653i
$81$	8.85170	+	1.62710i	0.983522	+	0.180789i
$82$	−8.45245	−	8.45245i	−0.933416	−	0.933416i
$83$	0.894540	+	0.580921i	0.0981886	+	0.0637644i	0.592799	−	0.805350i	$-0.298023\pi$
$83$	0.894540	+	0.580921i	0.0981886	+	0.0637644i	−0.494611	+	0.869115i	$0.664689\pi$
$84$	−0.296439	−	0.168428i	−0.0323442	−	0.0183770i
$85$	2.19219	+	0.825314i	0.237776	+	0.0895179i
$86$	1.90321	+	4.27467i	0.205228	+	0.460950i
$87$	7.72543	−	7.83298i	0.828253	−	0.839783i
$88$	−14.7887	+	5.67684i	−1.57648	+	0.605153i
$89$	−11.2732	−	8.19045i	−1.19496	−	0.868186i	−0.201176	−	0.979555i	$-0.564476\pi$
$89$	−11.2732	−	8.19045i	−1.19496	−	0.868186i	−0.993779	+	0.111369i	$0.964476\pi$
$90$	9.40021	+	2.31556i	0.990869	+	0.244081i
$91$	8.69433	−	6.31680i	0.911414	−	0.662181i
$92$	−0.221769	+	0.341494i	−0.0231210	+	0.0356032i
$93$	8.10776	+	9.87193i	0.840735	+	1.02367i
$94$	−7.87106	+	7.08713i	−0.811838	+	0.730982i
$95$	1.36468	−	0.618177i	0.140014	−	0.0634237i
$96$	−0.174033	−	0.791805i	−0.0177621	−	0.0808132i
$97$	−3.01383	+	0.157948i	−0.306008	+	0.0160372i	−0.204722	−	0.978820i	$-0.565629\pi$
$97$	−3.01383	+	0.157948i	−0.306008	+	0.0160372i	−0.101286	+	0.994857i	$0.532296\pi$
$98$	0.304204	+	1.92067i	0.0307293	+	0.194017i
$99$	−16.8478	−	3.33837i	−1.69327	−	0.335518i
$100$	0.395330	+	0.122834i	0.0395330	+	0.0122834i
$101$	−16.8143	+	9.70775i	−1.67309	+	0.965957i	−0.707192	+	0.707022i	$0.750038\pi$
$101$	−16.8143	+	9.70775i	−1.67309	+	0.965957i	−0.965895	+	0.258935i	$0.916628\pi$
$102$	1.17264	−	2.34130i	0.116109	−	0.231824i
$103$	−13.7666	+	8.94016i	−1.35647	+	0.880900i	−0.998601	−	0.0528727i	$-0.983162\pi$
$103$	−13.7666	+	8.94016i	−1.35647	+	0.880900i	−0.357866	+	0.933773i	$0.616496\pi$
$104$	12.2335	+	2.60032i	1.19960	+	0.254982i
$105$	3.85734	+	8.36118i	0.376438	+	0.815967i
$106$	−10.2426	+	2.17713i	−0.994851	+	0.211462i
$107$	−3.46125	+	3.46125i	−0.334611	+	0.334611i	−0.854335	−	0.519723i	$-0.826035\pi$
$107$	−3.46125	+	3.46125i	−0.334611	+	0.334611i	0.519723	+	0.854335i	$0.326035\pi$
$108$	0.145813	−	0.404750i	0.0140309	−	0.0389471i
$109$	−1.23567	−	1.70075i	−0.118355	−	0.162902i	0.745729	−	0.666250i	$-0.232102\pi$
$109$	−1.23567	−	1.70075i	−0.118355	−	0.162902i	−0.864084	+	0.503348i	$0.832102\pi$
$110$	−17.8763	−	4.66654i	−1.70444	−	0.444937i
$111$	−1.92267	−	0.394805i	−0.182492	−	0.0374733i
$112$	6.22237	−	7.68398i	0.587958	−	0.726068i
$113$	8.72877	−	10.7791i	0.821133	−	1.01402i	−0.178415	−	0.983955i	$-0.557097\pi$
$113$	8.72877	−	10.7791i	0.821133	−	1.01402i	0.999548	−	0.0300599i	$-0.00956981\pi$
$114$	−0.528535	−	1.58920i	−0.0495018	−	0.148842i
$115$	10.2409	−	4.00713i	0.954972	−	0.373667i
$116$	−0.309116	−	0.425461i	−0.0287007	−	0.0395031i
$117$	9.72041	+	9.45528i	0.898652	+	0.874141i
$118$	−8.16735	+	8.16735i	−0.751865	+	0.751865i
$119$	2.43615	−	0.517819i	0.223321	−	0.0474684i
$120$	−4.22741	+	9.84704i	−0.385908	+	0.898907i
$121$	21.3012	+	4.52772i	1.93648	+	0.411611i
$122$	−3.57499	+	2.32162i	−0.323664	+	0.210190i
$123$	14.3209	−	0.849833i	1.29128	−	0.0766269i
$124$	0.528835	−	0.305323i	0.0474908	−	0.0274188i
$125$	−6.74548	−	8.91619i	−0.603334	−	0.797488i
$126$	9.74488	−	3.31593i	0.868143	−	0.295407i
$127$	−1.55632	−	9.82620i	−0.138101	−	0.871934i	−0.955313	−	0.295597i	$-0.904482\pi$
$127$	−1.55632	−	9.82620i	−0.138101	−	0.871934i	0.817212	−	0.576337i	$-0.195518\pi$
$128$	11.9485	−	0.626196i	1.05611	−	0.0553484i
$129$	−5.35279	−	1.69841i	−0.471287	−	0.149537i
$130$	9.83031	+	10.7770i	0.862176	+	0.945206i
$131$	5.05820	−	4.55442i	0.441937	−	0.397922i	−0.417898	−	0.908494i	$-0.637233\pi$
$131$	5.05820	−	4.55442i	0.441937	−	0.397922i	0.859835	+	0.510572i	$0.170566\pi$
$132$	−0.288918	+	0.768495i	−0.0251471	+	0.0668889i
$133$	0.867574	−	1.33595i	0.0752282	−	0.115841i
$134$	0.366046	−	0.265948i	0.0316216	−	0.0229744i
$135$	−9.56883	+	6.59072i	−0.823554	+	0.567239i
$136$	2.34491	+	1.70368i	0.201074	+	0.146089i
$137$	8.03246	−	3.08337i	0.686260	−	0.263430i	0.00984506	−	0.999952i	$-0.496866\pi$
$137$	8.03246	−	3.08337i	0.686260	−	0.263430i	0.676414	+	0.736521i	$0.263533\pi$
$138$	−3.26378	−	11.8523i	−0.277831	−	1.00893i
$139$	8.10299	+	18.1996i	0.687287	+	1.54367i	0.832351	+	0.554249i	$0.186995\pi$
$139$	8.10299	+	18.1996i	0.687287	+	1.54367i	−0.145064	+	0.989422i	$0.546339\pi$
$140$	0.424418	−	0.116663i	0.0358698	−	0.00985979i
$141$	−0.0878693	−	12.7112i	−0.00739993	−	1.07048i
$142$	10.5560	+	6.85515i	0.885840	+	0.575271i
$143$	−18.2990	−	18.2990i	−1.53024	−	1.53024i
$144$	10.8899	+	6.08813i	0.907493	+	0.507344i
$145$	0.0916432	+	14.2029i	0.00761056	+	1.17948i
$146$	2.55605	+	2.30148i	0.211540	+	0.190472i
$147$	−1.96606	−	1.25754i	−0.162158	−	0.103720i
$148$	−0.0336236	+	0.0875925i	−0.00276385	+	0.00720006i
$149$	10.6281	−	18.4084i	0.870685	−	1.50807i	0.00939624	−	0.999956i	$-0.497009\pi$
$149$	10.6281	−	18.4084i	0.870685	−	1.50807i	0.861289	−	0.508115i	$-0.169658\pi$
$150$	−10.6980	+	6.46245i	−0.873485	+	0.527657i
$151$	−4.90434	−	8.49457i	−0.399110	−	0.691279i	0.594506	−	0.804091i	$-0.297347\pi$
$151$	−4.90434	−	8.49457i	−0.399110	−	0.691279i	−0.993616	+	0.112812i	$0.964014\pi$
$152$	1.83099	−	0.290001i	0.148513	−	0.0235222i
$153$	1.16668	+	2.91808i	0.0943207	+	0.235913i
$154$	−18.6826	+	6.07035i	−1.50549	+	0.489163i
$155$	−16.4124	−	1.61801i	−1.31827	−	0.129962i
$156$	0.521771	−	0.384627i	0.0417751	−	0.0307948i
$157$	12.8574	−	3.44512i	1.02613	−	0.274951i	0.293776	−	0.955874i	$-0.405088\pi$
$157$	12.8574	−	3.44512i	1.02613	−	0.274951i	0.732354	+	0.680924i	$0.238422\pi$
$158$	−0.604886	+	11.5419i	−0.0481222	+	0.918226i
$159$	6.20829	−	10.9268i	0.492350	−	0.866553i
$160$	0.881425	+	0.564352i	0.0696828	+	0.0446160i
$161$	6.87274	−	9.45952i	0.541648	−	0.745515i
$162$	6.21445	+	11.4056i	0.488253	+	0.896106i
$163$	1.52328	−	9.61761i	0.119312	−	0.753309i	−0.853393	−	0.521267i	$-0.825459\pi$
$163$	1.52328	−	9.61761i	0.119312	−	0.753309i	0.972706	−	0.232042i	$-0.0745406\pi$
$164$	0.0716822	−	0.682010i	0.00559744	−	0.0532561i
$165$	18.4331	−	12.3239i	1.43501	−	0.959416i
$166$	0.160904	+	1.53090i	0.0124886	+	0.118821i
$167$	−18.8795	−	0.989435i	−1.46094	−	0.0765648i	−0.694785	−	0.719217i	$-0.744501\pi$
$167$	−18.8795	−	0.989435i	−1.46094	−	0.0765648i	−0.766158	+	0.642652i	$0.777834\pi$
$168$	1.86016	+	11.2411i	0.143514	+	0.867270i
$169$	1.54521	+	7.26966i	0.118863	+	0.559204i
$170$	1.06536	+	3.20827i	0.0817096	+	0.246063i
$171$	1.84735	+	0.792077i	0.141271	+	0.0605717i
$172$	−0.121871	+	0.239185i	−0.00929255	+	0.0182376i
$173$	3.68688	−	2.98558i	0.280308	−	0.226989i	−0.478848	−	0.877898i	$-0.658945\pi$
$173$	3.68688	−	2.98558i	0.280308	−	0.226989i	0.759156	+	0.650909i	$0.225612\pi$
$174$	15.8017	+	1.55046i	1.19792	+	0.117540i
$175$	−11.1520	−	4.11655i	−0.843015	−	0.311182i
$176$	−20.6195	−	11.9047i	−1.55425	−	0.897347i
$177$	−0.821169	−	13.8379i	−0.0617228	−	1.04012i
$178$	−1.05248	−	20.0824i	−0.0788865	−	1.50524i
$179$	1.77854	+	5.47378i	0.132934	+	0.409130i	0.995263	−	0.0972192i	$-0.0309948\pi$
$179$	1.77854	+	5.47378i	0.132934	+	0.409130i	−0.862329	+	0.506349i	$0.830995\pi$
$180$	0.236144	+	0.502702i	0.0176012	+	0.0374692i
$181$	1.02607	−	3.15791i	0.0762670	−	0.234726i	−0.905654	−	0.424018i	$-0.860619\pi$
$181$	1.02607	−	3.15791i	0.0762670	−	0.234726i	0.981921	+	0.189292i	$0.0606194\pi$
$182$	14.9812	+	4.01419i	1.11048	+	0.297552i
$183$	0.765352	−	5.05831i	0.0565765	−	0.373921i
$184$	13.5330	−	1.42238i	0.997668	−	0.104859i
$185$	2.11620	−	1.39377i	0.155586	−	0.102472i
$186$	−3.70835	+	18.0594i	−0.271909	+	1.32418i
$187$	−2.14927	−	5.59904i	−0.157170	−	0.409442i
$188$	−0.600149	−	0.0950542i	−0.0437704	−	0.00693254i
$189$	−4.78968	+	11.3876i	−0.348398	+	0.828328i
$190$	1.93277	+	0.969139i	0.140218	+	0.0703087i
$191$	−1.72923	+	3.88391i	−0.125123	+	0.281030i	−0.965236	−	0.261381i	$-0.915822\pi$
$191$	−1.72923	+	3.88391i	−0.125123	+	0.281030i	0.840113	+	0.542411i	$0.182489\pi$
$192$	−8.25855	+	10.3439i	−0.596010	+	0.746503i
$193$	−1.35874	−	5.07090i	−0.0978044	−	0.365011i	0.899625	−	0.436663i	$-0.143840\pi$
$193$	−1.35874	−	5.07090i	−0.0978044	−	0.365011i	−0.997430	+	0.0716517i	$0.977173\pi$
$194$	−2.91439	−	3.23676i	−0.209241	−	0.232386i
$195$	−17.5050	+	0.233969i	−1.25356	+	0.0167548i
$196$	−0.0746489	+	0.0829060i	−0.00533206	+	0.00592186i
$197$	3.67679	+	1.87342i	0.261960	+	0.133475i	0.580038	−	0.814589i	$-0.303038\pi$
$197$	3.67679	+	1.87342i	0.261960	+	0.133475i	−0.318078	+	0.948064i	$0.603038\pi$
$198$	−11.5575	−	21.9280i	−0.821354	−	1.55836i
$199$			2.17095i			0.153895i	0.997035	+	0.0769474i	$0.0245174\pi$
$199$			2.17095i			0.153895i	−0.997035	+	0.0769474i	$0.975483\pi$
$200$	−5.12408	−	12.8505i	−0.362327	−	0.908669i
$201$	−0.0530265	+	0.540424i	−0.00374020	+	0.0381186i
$202$	−26.1591	−	10.0416i	−1.84055	−	0.706521i
$203$	8.22491	+	12.6652i	0.577275	+	0.888926i
$204$	0.146722	−	0.0322483i	0.0102726	−	0.00225783i
$205$	−12.3038	+	13.8433i	−0.859331	+	0.966858i
$206$	−22.5303	−	7.32052i	−1.56976	−	0.510045i
$207$	13.2373	+	6.51580i	0.920054	+	0.452879i
$208$	8.53423	+	16.7494i	0.591742	+	1.16136i
$209$	−3.50421	−	1.56018i	−0.242392	−	0.107920i
$210$	−5.87428	+	11.9201i	−0.405364	+	0.822567i
$211$	−3.20946	+	1.42894i	−0.220948	+	0.0983726i	−0.514226	−	0.857655i	$-0.671921\pi$
$211$	−3.20946	+	1.42894i	−0.220948	+	0.0983726i	0.293277	+	0.956027i	$0.405254\pi$
$212$	−0.466862	−	0.378057i	−0.0320642	−	0.0259651i
$213$	−14.5638	+	4.01045i	−0.997893	+	0.274792i
$214$	−7.02563	−	0.738423i	−0.480262	−	0.0504776i
$215$	6.43838	−	3.33302i	0.439094	−	0.227310i
$216$	−13.5784	+	4.72538i	−0.923896	+	0.321521i
$217$	−15.6239	+	7.96079i	−1.06062	+	0.540414i
$218$	0.785239	−	2.93055i	0.0531831	−	0.198482i
$219$	−4.10225	+	0.459856i	−0.277204	+	0.0310742i
$220$	−0.437347	−	0.965483i	−0.0294859	−	0.0650929i
$221$	−0.984490	+	4.63166i	−0.0662240	+	0.311559i
$222$	−1.30342	−	2.51498i	−0.0874801	−	0.168795i
$223$	11.6361	+	14.3694i	0.779213	+	0.962248i	0.999914	−	0.0130934i	$-0.00416786\pi$
$223$	11.6361	+	14.3694i	0.779213	+	0.962248i	−0.220701	+	0.975341i	$0.570835\pi$
$224$	1.11282			0.0743534
$225$	2.72542	−	14.7503i	0.181695	−	0.983355i
$226$	20.0172			1.33153
$227$	−11.7160	−	14.4681i	−0.777619	−	0.960280i	0.222272	−	0.974985i	$-0.428653\pi$
$227$	−11.7160	−	14.4681i	−0.777619	−	0.960280i	−0.999892	+	0.0147046i	$0.995319\pi$
$228$	0.0517713	−	0.0809402i	0.00342864	−	0.00536040i
$229$	−0.619137	+	2.91281i	−0.0409137	+	0.192484i	−0.993858	−	0.110661i	$-0.964703\pi$
$229$	−0.619137	+	2.91281i	−0.0409137	+	0.192484i	0.952945	+	0.303145i	$0.0980366\pi$
$230$	13.7954	+	7.84652i	0.909640	+	0.517384i
$231$	9.44008	−	21.6034i	0.621112	−	1.42140i
$232$	−4.54871	+	16.9760i	−0.298637	+	1.11453i
$233$	5.24435	−	2.67213i	0.343569	−	0.175057i	−0.273688	−	0.961818i	$-0.588244\pi$
$233$	5.24435	−	2.67213i	0.343569	−	0.175057i	0.617257	+	0.786761i	$0.288244\pi$
$234$	−1.77640	+	19.4897i	−0.116127	+	1.27408i
$235$	11.6786	+	11.5289i	0.761828	+	0.752060i
$236$	−0.659006	−	0.0692644i	−0.0428977	−	0.00450873i
$237$	−9.87592	−	9.74031i	−0.641510	−	0.632701i
$238$	2.79335	+	2.26201i	0.181066	+	0.146624i
$239$	−0.190717	+	0.0849127i	−0.0123365	+	0.00549254i	−0.412896	−	0.910778i	$-0.635483\pi$
$239$	−0.190717	+	0.0849127i	−0.0123365	+	0.00549254i	0.400559	+	0.916271i	$0.368816\pi$
$240$	−15.5008	+	4.37628i	−1.00057	+	0.282487i
$241$	−14.4194	−	6.41992i	−0.928834	−	0.413544i	−0.114160	−	0.993462i	$-0.536418\pi$
$241$	−14.4194	−	6.41992i	−0.928834	−	0.413544i	−0.814674	+	0.579919i	$0.803084\pi$
$242$	14.2682	+	28.0030i	0.917198	+	1.80010i
$243$	−15.1877	−	3.51186i	−0.974293	−	0.225286i
$244$	−0.232578	−	0.0755692i	−0.0148893	−	0.00483782i
$245$	2.94303	−	0.645435i	0.188023	−	0.0412353i
$246$	13.9598	+	15.2901i	0.890046	+	0.974859i
$247$	1.64945	+	2.53994i	0.104952	+	0.161612i
$248$	−19.0516	−	7.31321i	−1.20978	−	0.464389i
$249$	−1.50208	−	1.07554i	−0.0951903	−	0.0681594i
$250$	3.87368	−	15.6635i	0.244993	−	0.990644i
$251$		−	12.9995i		−	0.820518i	−0.911969	−	0.410259i	$-0.865438\pi$
$251$		−	12.9995i		−	0.820518i	0.911969	−	0.410259i	$-0.134562\pi$
$252$	0.499664	+	0.314751i	0.0314759	+	0.0198275i
$253$	−25.0874	−	12.7827i	−1.57723	−	0.803639i
$254$	9.60726	−	10.6699i	0.602813	−	0.669492i
$255$	−3.72812	−	1.60051i	−0.233464	−	0.100228i
$256$	1.32736	+	1.47419i	0.0829603	+	0.0921367i
$257$	−1.67762	−	6.26096i	−0.104647	−	0.390548i	0.893658	−	0.448749i	$-0.148130\pi$
$257$	−1.67762	−	6.26096i	−0.104647	−	0.390548i	−0.998305	+	0.0582010i	$0.981464\pi$
$258$	−2.95667	−	7.54607i	−0.184075	−	0.469798i
$259$	1.09584	−	2.46131i	0.0680924	−	0.152938i
$260$	−0.125575	+	0.827367i	−0.00778784	+	0.0513111i
$261$	−13.9834	+	12.9452i	−0.865550	+	0.801287i
$262$	9.70209	+	1.53666i	0.599397	+	0.0949352i
$263$	9.46627	+	24.6605i	0.583715	+	1.52063i	0.833608	+	0.552356i	$0.186271\pi$
$263$	9.46627	+	24.6605i	0.583715	+	1.52063i	−0.249893	+	0.968273i	$0.580395\pi$
$264$	26.0350	−	8.65870i	1.60234	−	0.532906i
$265$	4.30021	+	15.6441i	0.264160	+	0.961011i
$266$	2.28631	−	0.240301i	0.140183	−	0.0147338i
$267$	18.8611	+	15.0587i	1.15428	+	0.921578i
$268$	0.0250727	+	0.00671821i	0.00153156	+	0.000410380i
$269$	4.92089	−	15.1449i	0.300032	−	0.923404i	−0.681452	−	0.731862i	$-0.738651\pi$
$269$	4.92089	−	15.1449i	0.300032	−	0.923404i	0.981485	−	0.191541i	$-0.0613486\pi$
$270$	−16.0826	−	4.74622i	−0.978757	−	0.288846i
$271$	−9.63134	−	29.6422i	−0.585062	−	1.80064i	−0.599020	−	0.800734i	$-0.704443\pi$
$271$	−9.63134	−	29.6422i	−0.585062	−	1.80064i	0.0139572	−	0.999903i	$-0.495557\pi$
$272$	0.228001	+	4.35053i	0.0138246	+	0.263789i
$273$	−15.5405	+	10.2456i	−0.940557	+	0.620090i
$274$	10.7535	+	6.20855i	0.649644	+	0.375072i
$275$	−5.58979	+	28.0746i	−0.337077	+	1.69296i
$276$	0.410590	−	0.573423i	0.0247146	−	0.0345160i
$277$	−18.3074	+	14.8251i	−1.09999	+	0.890752i	−0.994611	−	0.103681i	$-0.966938\pi$
$277$	−18.3074	+	14.8251i	−1.09999	+	0.890752i	−0.105376	+	0.994432i	$0.533605\pi$
$278$	−13.0528	+	25.6175i	−0.782852	+	1.53643i
$279$	−13.2517	−	17.7190i	−0.793360	−	1.06081i
$280$	−11.9558	−	8.56909i	−0.714497	−	0.512101i
$281$	−3.79520	−	17.8550i	−0.226403	−	1.06514i	−0.933653	−	0.358178i	$-0.883398\pi$
$281$	−3.79520	−	17.8550i	−0.226403	−	1.06514i	0.707251	−	0.706963i	$-0.249935\pi$
$282$	14.1767	−	11.6432i	0.844209	−	0.693344i
$283$	−13.1523	−	0.689281i	−0.781821	−	0.0409735i	−0.342751	−	0.939426i	$-0.611359\pi$
$283$	−13.1523	−	0.689281i	−0.781821	−	0.0409735i	−0.439070	+	0.898453i	$0.644692\pi$
$284$	0.0754783	+	0.718128i	0.00447881	+	0.0426131i
$285$	−2.40990	+	0.962222i	−0.142750	+	0.0569971i
$286$	3.90391	−	37.1432i	0.230843	−	2.19632i
$287$	−3.08056	+	19.4499i	−0.181839	+	1.14809i
$288$	0.238815	+	1.38372i	0.0140723	+	0.0815368i
$289$	9.34733	−	12.8655i	0.549843	−	0.756794i
$290$	−15.8462	+	13.0022i	−0.930524	+	0.763517i
$291$	5.22714	−	0.0361339i	0.306420	−	0.00211821i
$292$	−0.0103270	+	0.197052i	−0.000604344	+	0.0115316i
$293$	−2.65039	+	0.710170i	−0.154837	+	0.0414886i	−0.335405	−	0.942074i	$-0.608873\pi$
$293$	−2.65039	+	0.710170i	−0.154837	+	0.0414886i	0.180568	+	0.983563i	$0.442207\pi$
$294$	−0.375216	−	3.34720i	−0.0218831	−	0.195213i
$295$	13.3764	+	11.8887i	0.778802	+	0.692190i
$296$	2.98202	−	0.968918i	0.173327	−	0.0563172i
$297$	28.8885	+	7.10200i	1.67628	+	0.412100i
$298$	30.2989	−	4.79888i	1.75517	−	0.277992i
$299$	11.1151	+	19.2520i	0.642805	+	1.11337i
$300$	−0.674359	−	0.243643i	−0.0389341	−	0.0140667i
$301$	3.85427	−	6.67579i	0.222156	−	0.384786i
$302$	5.07298	−	13.2156i	0.291917	−	0.760471i
$303$	29.8571	−	15.4738i	1.71524	−	0.888949i
$304$	2.07066	+	1.86443i	0.118761	+	0.106933i
$305$	3.91647	+	5.31805i	0.224256	+	0.304511i
$306$	−2.21321	+	3.95879i	−0.126521	+	0.226309i
$307$	10.7081	+	10.7081i	0.611146	+	0.611146i	0.943245	−	0.332099i	$-0.107757\pi$
$307$	10.7081	+	10.7081i	0.611146	+	0.611146i	−0.332099	+	0.943245i	$0.607757\pi$
$308$	−0.945153	−	0.613789i	−0.0538551	−	0.0349739i
$309$	24.5234	−	14.3855i	1.39509	−	0.818364i
$310$	−13.0915	−	19.8771i	−0.743546	−	1.12895i
$311$	5.21896	+	11.7220i	0.295940	+	0.664693i	0.998917	−	0.0465197i	$-0.0148130\pi$
$311$	5.21896	+	11.7220i	0.295940	+	0.664693i	−0.702977	+	0.711213i	$0.748146\pi$
$312$	−20.9626	−	5.46189i	−1.18678	−	0.309219i
$313$	10.9473	−	4.20228i	0.618778	−	0.237527i	−0.0287274	−	0.999587i	$-0.509145\pi$
$313$	10.9473	−	4.20228i	0.618778	−	0.237527i	0.647506	+	0.762061i	$0.275812\pi$
$314$	15.5414	+	11.2915i	0.877050	+	0.637214i
$315$	−6.01628	−	14.7706i	−0.338979	−	0.832227i
$316$	−0.536427	+	0.389737i	−0.0301764	+	0.0219244i
$317$	−9.77941	+	15.0590i	−0.549266	+	0.845796i	−0.998875	−	0.0474299i	$-0.984897\pi$
$317$	−9.77941	+	15.0590i	−0.549266	+	0.845796i	0.449608	+	0.893226i	$0.351564\pi$
$318$	17.8937	−	2.96102i	1.00343	−	0.166046i
$319$	27.0246	−	24.3330i	1.51309	−	1.36239i
$320$	−1.89579	−	16.9825i	−0.105978	−	0.949349i
$321$	6.26123	−	5.71650i	0.349468	−	0.319064i
$322$	16.8515	−	0.883151i	0.939098	−	0.0492161i
$323$	0.109795	+	0.693220i	0.00610917	+	0.0385718i
$324$	−0.284145	+	0.688850i	−0.0157858	+	0.0382694i
$325$	15.7737	−	16.1862i	0.874968	−	0.897847i
$326$	12.1703	−	7.02652i	0.674050	−	0.389163i
$327$	2.00420	+	3.03998i	0.110832	+	0.168111i
$328$	−19.2202	+	12.4817i	−1.06126	+	0.689188i
$329$	17.0672	+	3.62776i	0.940948	+	0.200005i
$330$	30.5636	+	9.48102i	1.68247	+	0.521913i
$331$	−27.2620	+	5.79471i	−1.49845	+	0.318506i	−0.882889	−	0.469581i	$-0.844405\pi$
$331$	−27.2620	+	5.79471i	−1.49845	+	0.318506i	−0.615564	+	0.788087i	$0.711072\pi$
$332$	−0.0624448	+	0.0624448i	−0.00342710	+	0.00342710i
$333$	3.29566	+	0.834412i	0.180601	+	0.0457255i
$334$	−16.0372	−	22.0733i	−0.877518	−	1.20780i
$335$	−0.444682	−	0.541949i	−0.0242956	−	0.0296098i
$336$	−11.3710	+	12.8057i	−0.620338	+	0.698606i
$337$	−2.05006	+	2.53161i	−0.111674	+	0.137905i	−0.829918	−	0.557886i	$-0.811613\pi$
$337$	−2.05006	+	2.53161i	−0.111674	+	0.137905i	0.718244	+	0.695791i	$0.244946\pi$
$338$	−6.75001	+	8.33557i	−0.367152	+	0.453395i
$339$	−15.9513	+	17.9639i	−0.866354	+	0.975663i
$340$	−0.104575	+	0.163329i	−0.00567136	+	0.00885774i
$341$	24.8194	+	34.1610i	1.34405	+	1.84992i
$342$	0.789450	+	2.79132i	0.0426886	+	0.150937i
$343$	14.0333	−	14.0333i	0.757729	−	0.757729i
$344$	8.77497	−	1.86518i	0.473115	−	0.100564i
$345$	−18.0348	+	6.12753i	−0.970962	+	0.329895i
$346$	6.69706	+	1.42350i	0.360036	+	0.0765280i
$347$	−2.35444	+	1.52899i	−0.126393	+	0.0820804i	−0.606287	−	0.795246i	$-0.707342\pi$
$347$	−2.35444	+	1.52899i	−0.126393	+	0.0820804i	0.479894	+	0.877326i	$0.340675\pi$
$348$	0.501372	+	0.760484i	0.0268763	+	0.0407662i
$349$	−14.1628	+	8.17690i	−0.758118	+	0.437699i	−0.828619	−	0.559812i	$-0.810873\pi$
$349$	−14.1628	+	8.17690i	−0.758118	+	0.437699i	0.0705019	+	0.997512i	$0.477540\pi$
$350$	−5.51160	−	16.2465i	−0.294608	−	0.868414i
$351$	−16.0748	−	17.1250i	−0.858010	−	0.914066i
$352$	−0.419199	−	2.64672i	−0.0223434	−	0.141070i
$353$	22.1563	−	1.16116i	1.17926	−	0.0618024i	0.547391	−	0.836877i	$-0.315621\pi$
$353$	22.1563	−	1.16116i	1.17926	−	0.0618024i	0.631870	+	0.775075i	$0.282288\pi$
$354$	14.7743	−	13.4890i	0.785247	−	0.716930i
$355$	9.64162	−	16.9514i	0.511724	−	0.899689i
$356$	0.857364	−	0.771974i	0.0454402	−	0.0409145i
$357$	−4.25592	+	0.704262i	−0.225247	+	0.0372735i
$358$	−4.52390	+	6.96620i	−0.239096	+	0.368175i
$359$	−5.30402	+	3.85360i	−0.279936	+	0.203385i	−0.718889	−	0.695125i	$-0.755349\pi$
$359$	−5.30402	+	3.85360i	−0.279936	+	0.203385i	0.438954	+	0.898510i	$0.355349\pi$
$360$	8.08940	−	16.7053i	0.426349	−	0.880447i
$361$	−15.0082	−	10.9041i	−0.789903	−	0.573898i
$362$	4.47372	−	1.71730i	0.235133	−	0.0902592i
$363$	−36.5005	−	9.51034i	−1.91578	−	0.499163i
$364$	0.361905	+	0.812852i	0.0189690	+	0.0426050i
$365$	3.32695	−	4.16308i	0.174141	−	0.217906i
$366$	6.36835	−	3.73570i	0.332879	−	0.195268i
$367$	12.8378	+	8.33698i	0.670129	+	0.435187i	0.834349	−	0.551237i	$-0.185844\pi$
$367$	12.8378	+	8.33698i	0.670129	+	0.435187i	−0.164220	+	0.986424i	$0.552511\pi$
$368$	14.4622	+	14.4622i	0.753896	+	0.753896i
$369$	−24.8459	+	0.343522i	−1.29342	+	0.0178831i
$370$	3.48520	+	1.10760i	0.181187	+	0.0575814i
$371$	12.8197	+	11.5429i	0.665568	+	0.599280i
$372$	−0.939049	+	0.486675i	−0.0486874	+	0.0252329i
$373$	1.17238	−	3.05414i	0.0607033	−	0.158138i	−0.899874	−	0.436149i	$-0.856342\pi$
$373$	1.17238	−	3.05414i	0.0607033	−	0.158138i	0.960578	+	0.278012i	$0.0896754\pi$
$374$	4.32768	−	7.49576i	0.223779	−	0.387596i
$375$	10.9698	+	15.9582i	0.566480	+	0.824075i
$376$	10.1531	+	17.5857i	0.523606	+	0.906912i
$377$	−28.3580	+	4.49147i	−1.46051	+	0.231322i
$378$	−17.1221	+	4.97061i	−0.880667	+	0.255661i
$379$	−17.1413	+	5.56955i	−0.880490	+	0.286088i	−0.714161	−	0.699982i	$-0.753191\pi$
$379$	−17.1413	+	5.56955i	−0.880490	+	0.286088i	−0.166329	+	0.986070i	$0.553191\pi$
$380$	0.0265717	+	0.121161i	0.00136310	+	0.00621541i
$381$	1.91961	+	17.1244i	0.0983448	+	0.877308i
$382$	−5.92661	+	1.58803i	−0.303232	+	0.0812507i
$383$	1.55870	−	29.7418i	0.0796460	−	1.51974i	−0.608144	−	0.793827i	$-0.708086\pi$
$383$	1.55870	−	29.7418i	0.0796460	−	1.51974i	0.687790	−	0.725910i	$-0.258581\pi$
$384$	−20.7234	+	0.143255i	−1.05753	+	0.00731047i
$385$	11.0905	+	28.3438i	0.565226	+	1.44454i
$386$	4.45331	−	6.12945i	0.226667	−	0.311981i
$387$	9.12809	+	3.35991i	0.464007	+	0.170794i
$388$	0.0390885	−	0.246795i	0.00198442	−	0.0125291i
$389$	2.11969	−	20.1675i	0.107472	−	1.02253i	−0.799306	−	0.600924i	$-0.794799\pi$
$389$	2.11969	−	20.1675i	0.107472	−	1.02253i	0.906778	−	0.421608i	$-0.138534\pi$
$390$	−16.1610	−	19.4206i	−0.818343	−	0.983400i
$391$	0.538517	+	5.12365i	0.0272340	+	0.259114i
$392$	3.72311	+	0.195120i	0.188046	+	0.00985505i
$393$	−9.11039	+	7.48231i	−0.459559	+	0.377433i
$394$	1.23820	+	5.82526i	0.0623794	+	0.293472i
$395$	17.9071	−	0.115545i	0.901006	−	0.00581370i
$396$	0.560377	−	1.30696i	0.0281600	−	0.0656773i
$397$	−0.761380	+	1.49429i	−0.0382125	+	0.0749963i	−0.909323	−	0.416090i	$-0.863400\pi$
$397$	−0.761380	+	1.49429i	−0.0382125	+	0.0749963i	0.871111	+	0.491086i	$0.163400\pi$
$398$	−2.43487	+	1.97172i	−0.122049	+	0.0988335i
$399$	−1.60626	+	2.24327i	−0.0804134	+	0.112304i
$400$	10.1636	−	18.1405i	0.508180	−	0.907026i
$401$	1.78678	+	1.03160i	0.0892275	+	0.0515155i	0.543950	−	0.839118i	$-0.316928\pi$
$401$	1.78678	+	1.03160i	0.0892275	+	0.0515155i	−0.454722	+	0.890633i	$0.650262\pi$
$402$	−0.654283	+	0.431356i	−0.0326327	+	0.0215141i
$403$	−1.74479	−	33.2926i	−0.0869142	−	1.65842i
$404$	−0.496745	−	1.52882i	−0.0247140	−	0.0760618i
$405$	17.0752	−	10.6507i	0.848474	−	0.529238i
$406$	−6.73485	+	20.7277i	−0.334245	+	1.02870i
$407$	−6.26675	−	1.67917i	−0.310631	−	0.0832334i
$408$	−3.92324	−	3.13233i	−0.194230	−	0.155073i
$409$	−28.7521	+	3.02197i	−1.42170	+	0.149427i	−0.783954	−	0.620819i	$-0.786800\pi$
$409$	−28.7521	+	3.02197i	−1.42170	+	0.149427i	−0.637747	+	0.770246i	$0.720134\pi$
$410$	−26.7008	−	1.22663i	−1.31866	−	0.0605789i
$411$	−14.1409	+	4.70297i	−0.697519	+	0.231980i
$412$	−0.487044	−	1.26879i	−0.0239949	−	0.0625090i
$413$	18.7938	+	2.97665i	0.924784	+	0.146471i
$414$	4.71454	+	20.7643i	0.231707	+	1.02051i
$415$	2.35321	−	0.388292i	0.115514	−	0.0190605i
$416$	−0.860541	+	1.93281i	−0.0421915	+	0.0947636i
$417$	−12.5882	−	32.1277i	−0.616446	−	1.57330i
$418$	−1.43278	−	5.34721i	−0.0700796	−	0.261541i
$419$	3.79690	+	4.21689i	0.185491	+	0.206008i	0.828717	−	0.559668i	$-0.189071\pi$
$419$	3.79690	+	4.21689i	0.185491	+	0.206008i	−0.643226	+	0.765676i	$0.722405\pi$
$420$	−0.743534	+	0.168460i	−0.0362807	+	0.00821998i
$421$	−0.617603	+	0.685918i	−0.0301001	+	0.0334296i	−0.758007	−	0.652247i	$-0.773827\pi$
$421$	−0.617603	+	0.685918i	−0.0301001	+	0.0334296i	0.727907	+	0.685676i	$0.240493\pi$
$422$	−4.51758	−	2.30182i	−0.219913	−	0.112051i
$423$	−0.848206	+	22.0006i	−0.0412412	+	1.06971i
$424$			20.0759i			0.974972i
$425$	4.86525	−	1.93999i	0.235999	−	0.0941035i
$426$	−17.7252	−	12.6919i	−0.858790	−	0.614923i
$427$	6.55593	+	2.51658i	0.317264	+	0.121786i
$428$	−0.220729	−	0.339892i	−0.0106693	−	0.0164293i
$429$	30.2221	+	33.1020i	1.45914	+	1.59818i
$430$	9.58572	+	4.19394i	0.462265	+	0.202250i
$431$	23.8570	+	7.75160i	1.14915	+	0.373381i	0.820823	−	0.571183i	$-0.193515\pi$
$431$	23.8570	+	7.75160i	1.14915	+	0.373381i	0.328326	+	0.944564i	$0.393515\pi$
$432$	−18.3633	−	11.3910i	−0.883507	−	0.548049i
$433$	13.0530	+	25.6180i	0.627287	+	1.23112i	0.957832	+	0.287330i	$0.0927677\pi$
$433$	13.0530	+	25.6180i	0.627287	+	1.23112i	−0.330544	+	0.943790i	$0.607232\pi$
$434$	−23.1187	−	10.2931i	−1.10973	−	0.494085i
$435$	0.959054	−	24.5819i	0.0459831	−	1.17861i
$436$	0.159007	−	0.0707943i	0.00761504	−	0.00339043i
$437$	2.56075	+	2.07365i	0.122497	+	0.0991962i
$438$	−4.24154	−	4.18330i	−0.202669	−	0.199886i
$439$	−16.6885	−	1.75403i	−0.796497	−	0.0837152i	−0.302467	−	0.953160i	$-0.597810\pi$
$439$	−16.6885	−	1.75403i	−0.796497	−	0.0837152i	−0.494030	+	0.869445i	$0.664477\pi$
$440$	−15.8769	+	31.6636i	−0.756901	+	1.50950i
$441$	3.30284	+	2.33058i	0.157278	+	0.110980i
$442$	−6.08887	+	3.10243i	−0.289618	+	0.147568i
$443$	0.716229	−	2.67300i	0.0340291	−	0.126998i	−0.946822	−	0.321758i	$-0.895726\pi$
$443$	0.716229	−	2.67300i	0.0340291	−	0.126998i	0.980851	+	0.194760i	$0.0623928\pi$
$444$	0.0650703	−	0.148912i	0.00308810	−	0.00706706i
$445$	−30.9660	+	3.45681i	−1.46793	+	0.163868i
$446$	−5.54803	+	26.1014i	−0.262707	+	1.23594i
$447$	−19.8379	+	31.0150i	−0.938300	+	1.46696i
$448$	−11.4340	−	14.1199i	−0.540207	−	0.667101i
$449$	−30.6897			−1.44833			−0.724167	−	0.689625i	$-0.757776\pi$
$449$	−30.6897			−1.44833			−0.724167	+	0.689625i	$0.757776\pi$
$450$	19.0188	−	10.3399i	0.896555	−	0.487428i
$451$	47.4198			2.23291
$452$	0.722696	+	0.892455i	0.0339927	+	0.0419775i
$453$	7.81737	+	15.0838i	0.367292	+	0.708697i
$454$	5.58612	−	26.2806i	0.262170	−	1.23341i
$455$	4.84446	−	23.5372i	0.227112	−	1.10344i
$456$	−3.19092	+	0.357697i	−0.149429	+	0.0167507i
$457$	3.41788	−	12.7557i	0.159881	−	0.596686i	−0.838756	−	0.544507i	$-0.816717\pi$
$457$	3.41788	−	12.7557i	0.159881	−	0.596686i	0.998638	−	0.0521788i	$-0.0166166\pi$
$458$	−3.82923	+	1.95109i	−0.178928	+	0.0911685i
$459$	−1.78904	−	5.14084i	−0.0835054	−	0.239954i
$460$	0.148232	+	0.898345i	0.00691135	+	0.0418856i
$461$	22.3583	+	2.34995i	1.04133	+	0.109448i	0.609723	−	0.792614i	$-0.291281\pi$
$461$	22.3583	+	2.34995i	1.04133	+	0.109448i	0.431605	+	0.902063i	$0.357947\pi$
$462$	32.8035	−	9.03316i	1.52616	−	0.420261i
$463$	6.48754	+	5.25351i	0.301502	+	0.244151i	0.768118	−	0.640309i	$-0.221194\pi$
$463$	6.48754	+	5.25351i	0.301502	+	0.244151i	−0.466616	+	0.884460i	$0.654527\pi$
$464$	−24.1319	+	10.7442i	−1.12029	+	0.498787i
$465$	28.2704	+	4.09108i	1.31101	+	0.189719i
$466$	7.76005	+	3.45500i	0.359477	+	0.160050i
$467$	−7.64286	−	15.0000i	−0.353669	−	0.694115i	0.643801	−	0.765193i	$-0.277356\pi$
$467$	−7.64286	−	15.0000i	−0.353669	−	0.694115i	−0.997471	+	0.0710772i	$0.977356\pi$
$468$	−0.933067	+	0.624448i	−0.0431310	+	0.0288651i
$469$	−0.708898	−	0.230335i	−0.0327339	−	0.0106359i
$470$	−2.32357	+	23.5692i	−0.107178	+	1.08717i
$471$	−22.5177	+	4.94922i	−1.03756	+	0.228048i
$472$	12.0607	+	18.5719i	0.555140	+	0.854840i
$473$	−17.3295	−	6.65218i	−0.796813	−	0.305868i
$474$	1.95484	−	19.9229i	0.0897889	−	0.915091i
$475$	1.32296	−	3.07771i	0.0607017	−	0.141215i
$476$			0.206206i			0.00945144i
$477$	−11.6018	+	18.4177i	−0.531210	+	0.843290i
$478$	−0.268450	−	0.136782i	−0.0122786	−	0.00625627i
$479$	7.01025	−	7.78568i	0.320307	−	0.355737i	−0.561392	−	0.827550i	$-0.689734\pi$
$479$	7.01025	−	7.78568i	0.320307	−	0.355737i	0.881698	+	0.471814i	$0.156401\pi$
$480$	−1.48069	−	1.04584i	−0.0675839	−	0.0477357i
$481$	3.42752	+	3.80665i	0.156281	+	0.173568i
$482$	−5.89571	−	22.0031i	−0.268542	−	1.00221i
$483$	−12.6360	+	15.8266i	−0.574959	+	0.720137i
$484$	−0.733359	+	1.64715i	−0.0333345	+	0.0748705i
$485$	−4.74093	+	4.80251i	−0.215275	+	0.218071i
$486$	−9.85513	−	20.2236i	−0.447038	−	0.917363i
$487$	−7.16742	−	1.13521i	−0.324787	−	0.0514412i	−0.00808797	−	0.999967i	$-0.502575\pi$
$487$	−7.16742	−	1.13521i	−0.324787	−	0.0514412i	−0.316699	+	0.948526i	$0.602575\pi$
$488$	2.92874	+	7.62963i	0.132578	+	0.345377i
$489$	−3.39248	+	16.5211i	−0.153413	+	0.747111i
$490$	3.39684	+	2.71460i	0.153454	+	0.122633i
$491$	−8.52764	+	0.896292i	−0.384847	+	0.0404491i	−0.294977	−	0.955504i	$-0.595312\pi$
$491$	−8.52764	+	0.896292i	−0.384847	+	0.0404491i	−0.0898704	+	0.995953i	$0.528645\pi$
$492$	−0.177696	+	1.17442i	−0.00801117	+	0.0529468i
$493$	−6.42717	−	1.72216i	−0.289465	−	0.0775620i
$494$	−1.35063	+	4.15682i	−0.0607678	+	0.187024i
$495$	−32.8638	+	19.8731i	−1.47712	+	0.893230i
$496$	−9.47830	−	29.1712i	−0.425588	−	1.30983i
$497$	−1.08519	−	20.7067i	−0.0486776	−	0.928825i
$498$	−0.157940	−	2.66152i	−0.00707745	−	0.119265i
$499$	13.7063	+	7.91332i	0.613577	+	0.354249i	0.774364	−	0.632740i	$-0.218070\pi$
$499$	13.7063	+	7.91332i	0.613577	+	0.354249i	−0.160787	+	0.986989i	$0.551403\pi$
$500$	0.838198	−	0.392803i	0.0374854	−	0.0175667i
$501$	32.5887	+	3.19761i	1.45596	+	0.142859i
$502$	14.5798	−	11.8065i	0.650727	−	0.526949i
$503$	−4.46877	+	8.77045i	−0.199253	+	0.391055i	−0.968914	−	0.247397i	$-0.920425\pi$
$503$	−4.46877	+	8.77045i	−0.199253	+	0.391055i	0.769662	+	0.638452i	$0.220425\pi$
$504$	−2.33400	−	19.5964i	−0.103965	−	0.872894i
$505$	−13.1491	+	41.3752i	−0.585127	+	1.84117i
$506$	−8.44844	−	39.7468i	−0.375579	−	1.76696i
$507$	−2.10158	−	12.7000i	−0.0933343	−	0.564027i
$508$	0.822569	+	0.0431090i	0.0364956	+	0.00191265i
$509$	1.03536	+	9.85078i	0.0458915	+	0.436628i	0.993210	+	0.116335i	$0.0371147\pi$
$509$	1.03536	+	9.85078i	0.0458915	+	0.436628i	−0.947319	+	0.320293i	$0.896219\pi$
$510$	−1.59090	−	5.63497i	−0.0704463	−	0.249521i
$511$	0.592284	−	5.63521i	0.0262011	−	0.249287i
$512$	3.29560	−	20.8076i	0.145646	−	0.919575i
$513$	−3.13408	−	1.51587i	−0.138373	−	0.0669273i
$514$	5.49843	−	7.56794i	0.242526	−	0.333808i
$515$	−9.27091	+	35.5146i	−0.408525	+	1.56496i
$516$	0.229689	−	0.404262i	0.0101115	−	0.0177966i
$517$	2.19898	−	41.9591i	0.0967112	−	1.84536i
$518$	3.75580	−	1.00636i	0.165020	−	0.0442171i
$519$	−6.61420	+	4.87571i	−0.290331	+	0.214020i
$520$	24.1287	−	14.1391i	1.05811	−	0.620039i
$521$	9.56204	−	3.10689i	0.418920	−	0.136115i	−0.0919691	−	0.995762i	$-0.529316\pi$
$521$	9.56204	−	3.10689i	0.418920	−	0.136115i	0.510890	+	0.859646i	$0.329316\pi$
$522$	−27.2190	−	3.92614i	−1.19134	−	0.171842i
$523$	−2.39569	+	0.379441i	−0.104756	+	0.0165918i	−0.208593	−	0.978003i	$-0.566888\pi$
$523$	−2.39569	+	0.379441i	−0.104756	+	0.0165918i	0.103836	+	0.994594i	$0.466888\pi$
$524$	0.281770	+	0.488040i	0.0123092	+	0.0213201i
$525$	18.9720	+	8.00027i	0.828007	+	0.349160i
$526$	−19.0609	+	33.0144i	−0.831094	+	1.43950i
$527$	2.76881	−	7.21299i	0.120611	−	0.314203i
$528$	34.7403	+	22.2207i	1.51188	+	0.967032i
$529$	0.881938	+	0.794100i	0.0383451	+	0.0345261i
$530$	−13.6404	+	19.0314i	−0.592501	+	0.826672i
$531$	0.331935	+	24.0078i	0.0144048	+	1.04185i
$532$	0.0932578	+	0.0932578i	0.00404324	+	0.00404324i
$533$	−31.3994	−	20.3910i	−1.36006	−	0.883233i
$534$	0.240776	+	34.8307i	0.0104194	+	1.50727i
$535$	−0.502301	+	10.9339i	−0.0217164	+	0.472713i
$536$	−0.352826	−	0.792459i	−0.0152397	−	0.0342290i
$537$	−2.64661	−	9.61103i	−0.114210	−	0.414747i
$538$	21.4554	−	8.23595i	0.925008	−	0.355077i
$539$	−6.24098	−	4.53434i	−0.268818	−	0.195308i
$540$	−0.369034	−	0.888388i	−0.0158807	−	0.0382301i
$541$	−29.1528	+	21.1807i	−1.25338	+	0.910631i	−0.998413	−	0.0563192i	$-0.982064\pi$
$541$	−29.1528	+	21.1807i	−1.25338	+	0.910631i	−0.254964	+	0.966951i	$0.582064\pi$
$542$	24.4983	−	37.7241i	1.05229	−	1.62039i
$543$	−2.02386	+	5.38327i	−0.0868522	+	0.231018i
$544$	−0.364378	+	0.328087i	−0.0156226	+	0.0140666i
$545$	−4.60424	−	0.947653i	−0.197224	−	0.0405930i
$546$	−25.6055	−	8.12447i	−1.09581	−	0.347695i
$547$	−19.2924	+	1.01107i	−0.824882	+	0.0432302i	−0.460105	−	0.887865i	$-0.652188\pi$
$547$	−19.2924	+	1.01107i	−0.824882	+	0.0432302i	−0.364777	+	0.931095i	$0.618855\pi$
$548$	0.111438	+	0.703590i	0.00476038	+	0.0300559i
$549$	−1.72230	+	8.69197i	−0.0735059	+	0.370964i
$550$	−36.5644	+	19.2288i	−1.55911	+	0.819919i
$551$	−3.68558	+	2.12787i	−0.157011	+	0.0906503i
$552$	−23.5276	+	1.39618i	−1.00140	+	0.0594252i
$553$	15.9685	−	10.3701i	0.679050	−	0.440980i
$554$	−33.2546	−	7.06849i	−1.41285	−	0.300311i
$555$	−3.77126	+	2.24507i	−0.160081	+	0.0952977i
$556$	−1.61339	+	0.342936i	−0.0684229	+	0.0145437i
$557$	12.5312	−	12.5312i	0.530965	−	0.530965i	−0.389894	−	0.920860i	$-0.627488\pi$
$557$	12.5312	−	12.5312i	0.530965	−	0.530965i	0.920860	+	0.389894i	$0.127488\pi$
$558$	7.83751	−	30.9556i	0.331788	−	1.31046i
$559$	8.61439	+	11.8567i	0.364350	+	0.501484i
$560$	−1.29953	−	22.0708i	−0.0549151	−	0.932660i
$561$	3.27821	+	9.85693i	0.138406	+	0.416160i
$562$	16.5787	−	20.4730i	0.699330	−	0.863601i
$563$	0.864259	−	1.06727i	0.0364242	−	0.0449801i	−0.758608	−	0.651547i	$-0.774120\pi$
$563$	0.864259	−	1.06727i	0.0364242	−	0.0449801i	0.795033	+	0.606567i	$0.207454\pi$
$564$	1.03094	+	0.211694i	0.0434102	+	0.00891394i
$565$	−1.82299	−	30.9610i	−0.0766936	−	1.30254i
$566$	−11.1722	−	15.3772i	−0.469602	−	0.646352i
$567$	9.18349	−	19.3267i	0.385670	−	0.811644i
$568$	17.0633	−	17.0633i	0.715958	−	0.715958i
$569$	−28.5848	+	6.07589i	−1.19834	+	0.254715i	−0.763508	−	0.645798i	$-0.776525\pi$
$569$	−28.5848	+	6.07589i	−1.19834	+	0.254715i	−0.434830	+	0.900513i	$0.643192\pi$
$570$	−3.26794	−	1.82895i	−0.136879	−	0.0766065i
$571$	−19.2731	−	4.09663i	−0.806555	−	0.171438i	−0.213859	−	0.976865i	$-0.568603\pi$
$571$	−19.2731	−	4.09663i	−0.806555	−	0.171438i	−0.592696	+	0.805426i	$0.701936\pi$
$572$	1.79695	−	1.16695i	0.0751342	−	0.0487927i
$573$	3.29764	−	6.58411i	0.137761	−	0.275055i
$574$	−24.6122	+	14.2099i	−1.02729	+	0.593108i
$575$	10.8800	−	22.0521i	0.453726	−	0.919636i
$576$	15.1034	−	17.2477i	0.629309	−	0.718655i
$577$	4.87968	+	30.8091i	0.203144	+	1.28260i	0.852747	+	0.522325i	$0.174935\pi$
$577$	4.87968	+	30.8091i	0.203144	+	1.28260i	−0.649603	+	0.760273i	$0.725065\pi$
$578$	22.9191	−	1.20114i	0.953307	−	0.0499607i
$579$	1.95195	+	8.88090i	0.0811204	+	0.369078i
$580$	−1.15180	−	0.237066i	−0.0478260	−	0.00984363i
$581$	1.88454	−	1.69684i	0.0781838	−	0.0703970i
$582$	4.78796	+	5.82978i	0.198467	+	0.241652i
$583$	22.6244	−	34.8385i	0.937008	−	1.44287i
$584$	5.33485	−	3.87600i	0.220758	−	0.160390i
$585$	30.3067	+	0.972641i	1.25303	+	0.0402138i
$586$	−3.20366	−	2.32760i	−0.132342	−	0.0961522i
$587$	−11.0427	+	4.23890i	−0.455781	+	0.174958i	−0.575418	−	0.817860i	$-0.695160\pi$
$587$	−11.0427	+	4.23890i	−0.455781	+	0.174958i	0.119636	+	0.992818i	$0.461827\pi$
$588$	0.135686	−	0.137575i	0.00559560	−	0.00567350i
$589$	−2.00990	−	4.51432i	−0.0828167	−	0.186009i
$590$	−1.18526	+	25.8002i	−0.0487962	+	1.06218i
$591$	−6.21439	−	3.53083i	−0.255626	−	0.145239i
$592$	3.95244	+	2.56675i	0.162444	+	0.105493i
$593$	−25.7487	−	25.7487i	−1.05737	−	1.05737i	−0.998251	−	0.0591233i	$-0.981169\pi$
$593$	−25.7487	−	25.7487i	−1.05737	−	1.05737i	−0.0591233	−	0.998251i	$-0.518831\pi$
$594$	18.2719	+	38.8506i	0.749707	+	1.59406i
$595$	3.24429	−	4.52651i	0.133003	−	0.185569i
$596$	1.30786	+	1.17760i	0.0535719	+	0.0482364i
$597$	0.170832	−	3.75632i	0.00699169	−	0.153736i
$598$	−11.4973	+	29.9516i	−0.470161	+	1.22481i
$599$	16.8385	−	29.1651i	0.688001	−	1.19165i	−0.284482	−	0.958681i	$-0.591822\pi$
$599$	16.8385	−	29.1651i	0.688001	−	1.19165i	0.972483	−	0.232972i	$-0.0748451\pi$
$600$	7.85479	+	22.6380i	0.320671	+	0.924192i
$601$	−1.22578	−	2.12312i	−0.0500008	−	0.0866039i	0.839942	−	0.542677i	$-0.182589\pi$
$601$	−1.22578	−	2.12312i	−0.0500008	−	0.0866039i	−0.889943	+	0.456073i	$0.849256\pi$
$602$	10.9879	−	1.74031i	0.447834	−	0.0709299i
$603$	0.134276	−	0.930903i	0.00546813	−	0.0379093i
$604$	0.772360	−	0.250955i	0.0314269	−	0.0102112i
$605$	42.0133	−	24.6192i	1.70808	−	1.00091i
$606$	44.4720	+	19.4330i	1.80655	+	0.789411i
$607$	21.4338	−	5.74317i	0.869972	−	0.233108i	0.203896	−	0.978993i	$-0.434640\pi$
$607$	21.4338	−	5.74317i	0.869972	−	0.233108i	0.666075	+	0.745884i	$0.267973\pi$
$608$	−0.0164126	+	0.313171i	−0.000665619	+	0.0127008i
$609$	−13.2346	−	22.5614i	−0.536294	−	0.914235i
$610$	−2.40752	+	9.22259i	−0.0974774	+	0.373412i
$611$	−19.4990	+	26.8380i	−0.788843	+	1.08575i
$612$	−0.256405	+	0.0442526i	−0.0103646	+	0.00178880i
$613$	−5.51473	+	34.8186i	−0.222738	+	1.40631i	0.582246	+	0.813013i	$0.302174\pi$
$613$	−5.51473	+	34.8186i	−0.222738	+	1.40631i	−0.804983	+	0.593298i	$0.797826\pi$
$614$	−2.28448	+	21.7353i	−0.0921940	+	0.877167i
$615$	22.3780	−	22.9843i	0.902370	−	0.926818i
$616$	3.93672	+	37.4554i	0.158615	+	1.50912i
$617$	25.6870	+	1.34620i	1.03412	+	0.0541960i	0.561835	−	0.827249i	$-0.310096\pi$
$617$	25.6870	+	1.34620i	1.03412	+	0.0541960i	0.472286	+	0.881445i	$0.343429\pi$
$618$	38.4072	+	14.4393i	1.54496	+	0.580835i
$619$	5.80270	+	27.2995i	0.233230	+	1.09726i	0.926416	+	0.376502i	$0.122873\pi$
$619$	5.80270	+	27.2995i	0.233230	+	1.09726i	−0.693186	+	0.720759i	$0.743793\pi$
$620$	0.413558	−	1.30131i	0.0166089	−	0.0522619i
$621$	−22.3912	−	12.3157i	−0.898529	−	0.494211i
$622$	−8.40700	+	16.4997i	−0.337090	+	0.661576i
$623$	−25.7463	+	20.8489i	−1.03150	+	0.835294i
$624$	−13.4484	−	29.6523i	−0.538369	−	1.18704i
$625$	−24.5797	−	4.56500i	−0.983187	−	0.182600i
$626$	14.6558	+	8.46153i	0.585763	+	0.338191i
$627$	5.94044	+	2.97526i	0.237238	+	0.118820i
$628$	0.0576781	+	1.10056i	0.00230161	+	0.0439173i
$629$	0.366836	+	1.12900i	0.0146267	+	0.0450163i
$630$	11.1020	−	20.1627i	0.442316	−	0.803302i
$631$	−2.14590	+	6.60439i	−0.0854268	+	0.262917i	−0.984641	−	0.174592i	$-0.944139\pi$
$631$	−2.14590	+	6.60439i	−0.0854268	+	0.262917i	0.899214	+	0.437509i	$0.144139\pi$
$632$	21.4036	+	5.73507i	0.851388	+	0.228129i
$633$	5.66566	−	2.21990i	0.225190	−	0.0882330i
$634$	−25.7716	+	2.70870i	−1.02352	+	0.107576i
$635$	−17.3783	−	13.8880i	−0.689637	−	0.551127i
$636$	0.778044	+	0.690875i	0.0308515	+	0.0273950i
$637$	2.18271	+	5.68614i	0.0864819	+	0.225293i
$638$	51.8356	+	8.20996i	2.05219	+	0.325035i
$639$	25.5147	−	5.79312i	1.00935	−	0.229172i
$640$	18.7958	−	19.0399i	0.742967	−	0.752617i
$641$	1.22377	−	2.74863i	0.0483359	−	0.108564i	−0.887763	−	0.460300i	$-0.847742\pi$
$641$	1.22377	−	2.74863i	0.0483359	−	0.108564i	0.936099	+	0.351736i	$0.114408\pi$
$642$	12.0981	+	1.83051i	0.477473	+	0.0722445i
$643$	−2.11525	−	7.89424i	−0.0834175	−	0.311318i	0.911592	−	0.411095i	$-0.134854\pi$
$643$	−2.11525	−	7.89424i	−0.0834175	−	0.311318i	−0.995010	+	0.0997771i	$0.968187\pi$
$644$	0.647776	+	0.719428i	0.0255260	+	0.0283494i
$645$	−11.4024	+	5.26036i	−0.448967	+	0.207126i
$646$	−0.677775	+	0.752745i	−0.0266667	+	0.0296164i
$647$	4.06703	+	2.07226i	0.159891	+	0.0814688i	0.532105	−	0.846678i	$-0.321401\pi$
$647$	4.06703	+	2.07226i	0.159891	+	0.0814688i	−0.372214	+	0.928147i	$0.621401\pi$
$648$	23.8661	−	7.10766i	0.937549	−	0.279215i
$649$		−	45.8203i		−	1.79860i
$650$	32.4800	+	2.99056i	1.27397	+	0.117299i
$651$	27.6599	−	12.5448i	1.08408	−	0.491670i
$652$	0.752664	+	0.288921i	0.0294766	+	0.0113150i
$653$	0.637808	+	0.982138i	0.0249594	+	0.0384340i	0.850930	−	0.525279i	$-0.176039\pi$
$653$	0.637808	+	0.982138i	0.0249594	+	0.0384340i	−0.825971	+	0.563713i	$0.809372\pi$
$654$	−1.58927	+	5.00883i	−0.0621456	+	0.195861i
$655$	1.49320	−	15.1463i	0.0583441	−	0.591816i
$656$	−32.7598	−	10.6443i	−1.27906	−	0.415591i
$657$	7.13415	−	0.472866i	0.278330	−	0.0184482i
$658$	11.4322	+	22.4369i	0.445673	+	0.874682i
$659$	25.7499	+	11.4646i	1.00307	+	0.446598i	0.841497	−	0.540262i	$-0.181675\pi$
$659$	25.7499	+	11.4646i	1.00307	+	0.446598i	0.161578	+	0.986860i	$0.448342\pi$
$660$	0.680751	+	1.70495i	0.0264982	+	0.0663652i
$661$	−38.4510	+	17.1195i	−1.49557	+	0.665871i	−0.981427	−	0.191834i	$-0.938556\pi$
$661$	−38.4510	+	17.1195i	−1.49557	+	0.665871i	−0.514142	+	0.857705i	$0.671890\pi$
$662$	−31.2592	−	25.3132i	−1.21493	−	0.983827i
$663$	2.06789	−	7.93652i	0.0803102	−	0.308229i
$664$	2.93505	+	0.308486i	0.113902	+	0.0119716i
$665$	−0.579893	−	3.51439i	−0.0224873	−	0.136282i
$666$	2.05736	+	4.45414i	0.0797211	+	0.172595i
$667$	−27.8336	+	14.1819i	−1.07772	+	0.549127i
$668$	0.405122	−	1.51194i	0.0156746	−	0.0584986i
$669$	−19.0028	−	25.7785i	−0.734692	−	0.996655i
$670$	0.203960	−	0.990954i	0.00787966	−	0.0382839i
$671$	3.51580	−	16.5405i	0.135726	−	0.638540i
$672$	−1.92547	−	0.0875676i	−0.0742766	−	0.00337799i
$673$	25.5478	+	31.5490i	0.984797	+	1.21612i	0.976358	+	0.216159i	$0.0693529\pi$
$673$	25.5478	+	31.5490i	0.984797	+	1.21612i	0.00843902	+	0.999964i	$0.497314\pi$
$674$	−4.70129			−0.181087
$675$	−5.87639	+	25.3075i	−0.226182	+	0.974085i
$676$	−0.615336			−0.0236668
$677$	−22.1137	−	27.3081i	−0.849898	−	1.04954i	−0.998163	−	0.0605890i	$-0.980702\pi$
$677$	−22.1137	−	27.3081i	−0.849898	−	1.04954i	0.148265	−	0.988948i	$-0.452631\pi$
$678$	−34.6351	−	1.57515i	−1.33015	−	0.0604934i
$679$	−1.49182	+	7.01844i	−0.0572507	+	0.269343i
$680$	6.44116	−	0.719042i	0.247007	−	0.0275740i
$681$	19.1333	+	25.9555i	0.733189	+	0.994617i
$682$	−15.7722	+	58.8626i	−0.603948	+	2.25397i
$683$	−24.2361	+	12.3489i	−0.927369	+	0.472518i	−0.851356	−	0.524589i	$-0.824219\pi$
$683$	−24.2361	+	12.3489i	−0.927369	+	0.472518i	−0.0760130	+	0.997107i	$0.524219\pi$
$684$	−0.0959471	+	0.135974i	−0.00366863	+	0.00519910i
$685$	8.62352	−	17.1981i	0.329488	−	0.657104i
$686$	28.4848	+	2.99388i	1.08756	+	0.114307i
$687$	1.30048	−	4.99120i	0.0496163	−	0.190426i
$688$	10.4788	+	8.48560i	0.399502	+	0.323511i
$689$	−29.9619	+	13.3399i	−1.14146	+	0.508210i
$690$	−23.2522	−	14.6621i	−0.885195	−	0.558176i
$691$	26.3444	+	11.7293i	1.00219	+	0.446202i	0.841183	−	0.540751i	$-0.181860\pi$
$691$	26.3444	+	11.7293i	1.00219	+	0.446202i	0.161004	+	0.986954i	$0.448527\pi$
$692$	0.178322	+	0.349977i	0.00677880	+	0.0133041i
$693$	−18.0338	+	36.6368i	−0.685047	+	1.39172i
$694$	−3.85323	−	1.25199i	−0.146267	−	0.0475249i
$695$	40.8116	+	17.8559i	1.54807	+	0.677312i
$696$	9.20629	−	29.0150i	0.348964	−	1.09981i
$697$	−4.72562	−	7.27682i	−0.178996	−	0.275629i
$698$	−22.0340	−	8.45807i	−0.834000	−	0.320143i
$699$	−9.28438	+	4.21081i	−0.351167	+	0.159268i
$700$	0.525352	−	0.832290i	0.0198564	−	0.0314576i
$701$			39.1975i			1.48047i	0.672349	+	0.740234i	$0.265285\pi$
$701$			39.1975i			1.48047i	−0.672349	+	0.740234i	$0.734715\pi$
$702$	4.60727	−	33.5824i	0.173890	−	1.26749i
$703$	0.676502	+	0.344695i	0.0255147	+	0.0130004i
$704$	−29.2753	+	32.5135i	−1.10336	+	1.22540i
$705$	−19.2998	−	20.8669i	−0.726874	−	0.785894i
$706$	21.4253	+	23.7952i	0.806352	+	0.895544i
$707$	11.9472	+	44.5877i	0.449322	+	1.67689i
$708$	1.13480	+	0.171703i	0.0426485	+	0.00645298i
$709$	10.6322	−	23.8803i	0.399300	−	0.896842i	−0.596267	−	0.802786i	$-0.703350\pi$
$709$	10.6322	−	23.8803i	0.399300	−	0.896842i	0.995567	−	0.0940560i	$-0.0299833\pi$
$710$	27.7690	−	4.58204i	1.04215	−	0.171961i
$711$	16.3215	+	17.6304i	0.612103	+	0.661193i
$712$	−38.0803	−	6.03133i	−1.42712	−	0.226034i
$713$	−12.9989	−	33.8632i	−0.486811	−	1.26819i
$714$	−4.65522	−	4.13367i	−0.174217	−	0.154699i
$715$	−57.8055	−	2.65557i	−2.16180	−	0.0993127i
$716$	−0.473912	+	0.0498102i	−0.0177109	+	0.00186149i
$717$	0.336672	−	0.131914i	0.0125733	−	0.00492641i
$718$	−9.13934	−	2.44888i	−0.341077	−	0.0913913i
$719$	5.11850	−	15.7531i	0.190888	−	0.587492i	−0.809112	−	0.587654i	$-0.800052\pi$
$719$	5.11850	−	15.7531i	0.190888	−	0.587492i	1.00000		0.000162162i	$5.16178e-5\pi$
$720$	27.1648	−	6.35235i	1.01237	−	0.236738i
$721$	12.0598	+	37.1164i	0.449132	+	1.38229i
$722$	−1.40118	−	26.7361i	−0.0521464	−	0.995013i
$723$	24.4441	+	12.2428i	0.909087	+	0.455315i
$724$	0.238082	+	0.137457i	0.00884825	+	0.00510854i
$725$	21.5539	+	23.3255i	0.800490	+	0.866287i
$726$	−22.4843	−	49.5753i	−0.834469	−	1.83991i
$727$	39.1351	−	31.6910i	1.45144	−	1.17535i	0.500600	−	0.865679i	$-0.333113\pi$
$727$	39.1351	−	31.6910i	1.45144	−	1.17535i	0.950842	−	0.309676i	$-0.100220\pi$
$728$	13.4995	−	26.4942i	0.500324	−	0.981942i
$729$	26.0024	+	7.27155i	0.963052	+	0.269317i
$730$	7.69081	−	0.0496246i	0.284650	−	0.00183669i
$731$	0.706163	+	3.32223i	0.0261184	+	0.122877i
$732$	0.396474	+	0.149056i	0.0146541	+	0.00550927i
$733$	17.8172	+	0.933760i	0.658093	+	0.0344892i	0.378460	−	0.925618i	$-0.376454\pi$
$733$	17.8172	+	0.933760i	0.658093	+	0.0344892i	0.279633	+	0.960107i	$0.409787\pi$
$734$	2.30918	+	21.9704i	0.0852334	+	0.810941i
$735$	−5.14300	+	0.885185i	−0.189702	+	0.0326505i
$736$	−0.240617	+	2.28931i	−0.00886924	+	0.0843852i
$737$	−0.280784	+	1.77280i	−0.0103428	+	0.0653020i
$738$	−22.9510	−	27.5543i	−0.844838	−	1.01429i
$739$	22.0167	−	30.3034i	0.809898	−	1.11473i	−0.181441	−	0.983402i	$-0.558076\pi$
$739$	22.0167	−	30.3034i	0.809898	−	1.11473i	0.991339	−	0.131327i	$-0.0419237\pi$
$740$	0.0764469	+	0.195374i	0.00281024	+	0.00718208i
$741$	−2.65412	−	4.52455i	−0.0975015	−	0.166213i
$742$	−1.30295	+	24.8618i	−0.0478329	+	0.912707i
$743$	30.3170	−	8.12342i	1.11222	−	0.298019i	0.344491	−	0.938790i	$-0.388052\pi$
$743$	30.3170	−	8.12342i	1.11222	−	0.298019i	0.767732	+	0.640771i	$0.221385\pi$
$744$	32.3887	+	14.1529i	1.18743	+	0.518872i
$745$	−10.1818	−	46.4268i	−0.373034	−	1.70095i
$746$	4.49022	−	1.45896i	0.164399	−	0.0534163i
$747$	2.51435	+	1.97916i	0.0919954	+	0.0724137i
$748$	0.490438	−	0.0776778i	0.0179322	−	0.00284018i
$749$	5.81889	+	10.0786i	0.212618	+	0.368264i
$750$	−7.93504	+	26.7971i	−0.289747	+	0.978491i
$751$	5.24021	−	9.07630i	0.191218	−	0.331199i	−0.754436	−	0.656373i	$-0.772090\pi$
$751$	5.24021	−	9.07630i	0.191218	−	0.331199i	0.945654	+	0.325174i	$0.105423\pi$
$752$	−10.9377	+	28.4937i	−0.398858	+	1.03906i
$753$	−1.02293	+	22.4925i	−0.0372775	+	0.819671i
$754$	−30.7930	−	27.7262i	−1.12142	−	1.00973i
$755$	−20.9027	−	6.64290i	−0.760728	−	0.241760i
$756$	−0.839783	−	0.583921i	−0.0305426	−	0.0212370i
$757$	−37.0266	−	37.0266i	−1.34575	−	1.34575i	−0.890216	−	0.455539i	$-0.849447\pi$
$757$	−37.0266	−	37.0266i	−1.34575	−	1.34575i	−0.455539	−	0.890216i	$-0.650553\pi$
$758$	−21.8148	−	14.1667i	−0.792351	−	0.514559i
$759$	42.4019	+	24.0915i	1.53909	+	0.874465i
$760$	2.58786	−	3.23824i	0.0938714	−	0.117463i
$761$	7.83328	+	17.5938i	0.283956	+	0.637776i	0.998060	−	0.0622640i	$-0.0198321\pi$
$761$	7.83328	+	17.5938i	0.283956	+	0.637776i	−0.714103	+	0.700040i	$0.753165\pi$
$762$	−17.4627	+	17.7058i	−0.632607	+	0.641414i
$763$	−4.66613	+	1.79116i	−0.168925	+	0.0648443i
$764$	−0.284773	−	0.206900i	−0.0103027	−	0.00748538i
$765$	6.32468	+	3.06267i	0.228669	+	0.110731i
$766$	34.7732	−	25.2642i	1.25641	−	0.912832i
$767$	−19.7032	+	30.3403i	−0.711443	+	1.09553i
$768$	−2.18068	−	2.65518i	−0.0786887	−	0.0958106i
$769$	14.6305	−	13.1734i	0.527591	−	0.475045i	−0.361760	−	0.932271i	$-0.617824\pi$
$769$	14.6305	−	13.1734i	0.527591	−	0.475045i	0.889350	+	0.457227i	$0.151157\pi$
$770$	−21.7168	+	38.1815i	−0.782620	+	1.37596i
$771$	2.41005	+	10.9651i	0.0867957	+	0.394899i
$772$	0.434058	−	0.0227480i	0.0156221	−	0.000818719i
$773$	−2.20101	−	13.8967i	−0.0791649	−	0.499828i	−0.995130	−	0.0985700i	$-0.968573\pi$
$773$	−2.20101	−	13.8967i	−0.0791649	−	0.499828i	0.915965	−	0.401258i	$-0.131427\pi$
$774$	4.52202	+	13.2893i	0.162541	+	0.477676i
$775$	−29.5520	+	22.0590i	−1.06154	+	0.792383i
$776$	−7.23163	+	4.17519i	−0.259600	+	0.149880i
$777$	−2.08978	+	4.17247i	−0.0749703	+	0.149687i
$778$	24.5444	−	15.9393i	0.879959	−	0.571452i
$779$	−5.42817	−	1.15379i	−0.194484	−	0.0413389i
$780$	0.282383	−	1.42168i	0.0101109	−	0.0509043i
$781$	−48.8399	+	10.3812i	−1.74763	+	0.371470i
$782$	−5.25743	+	5.25743i	−0.188005	+	0.188005i
$783$	25.2136	−	21.2982i	0.901060	−	0.761137i
$784$	3.29374	+	4.53345i	0.117634	+	0.161909i
$785$	16.0493	−	25.0664i	0.572824	−	0.894658i
$786$	−16.6662	−	3.42228i	−0.594465	−	0.122069i
$787$	−19.9773	+	24.6699i	−0.712113	+	0.879387i	−0.996857	−	0.0792168i	$-0.974758\pi$
$787$	−19.9773	+	24.6699i	−0.712113	+	0.879387i	0.284744	+	0.958604i	$0.408091\pi$
$788$	−0.215012	+	0.265517i	−0.00765947	+	0.00945866i
$789$	−14.4386	−	43.4140i	−0.514028	−	1.54558i
$790$	16.3934	+	19.9791i	0.583250	+	0.710826i
$791$	−19.3831	−	26.6785i	−0.689182	−	0.948578i
$792$	−45.7287	+	12.9331i	−1.62490	+	0.459559i
$793$	−9.44063	+	9.44063i	−0.335247	+	0.335247i
$794$	−2.36746	+	0.503219i	−0.0840179	+	0.0178586i
$795$	−6.20946	−	27.4068i	−0.220227	−	0.972020i
$796$	−0.175816	−	0.0373708i	−0.00623162	−	0.00132457i
$797$	25.0280	−	16.2533i	0.886536	−	0.575723i	−0.0190819	−	0.999818i	$-0.506074\pi$
$797$	25.0280	−	16.2533i	0.886536	−	0.575723i	0.905618	+	0.424095i	$0.139408\pi$
$798$	−3.97483	+	0.235874i	−0.140707	+	0.00834986i
$799$	−6.65799	+	3.84400i	−0.235543	+	0.135991i
$800$	2.30657	−	0.395902i	0.0815497	−	0.0139972i
$801$	−31.4496	−	27.5397i	−1.11122	−	0.973067i
$802$	0.465796	+	2.94092i	0.0164478	+	0.103848i
$803$	−13.6258	+	0.714099i	−0.480845	+	0.0252000i
$804$	−0.0428537	−	0.0135972i	−0.00151133	−	0.000479538i
$805$	−2.90066	−	25.9841i	−0.102235	−	0.915818i
$806$	35.7553	−	32.1942i	1.25943	−	1.13399i
$807$	−9.70619	+	25.8175i	−0.341674	+	0.908819i
$808$	−29.2583	+	45.0538i	−1.02930	+	1.58499i
$809$	−18.6590	+	13.5565i	−0.656015	+	0.476623i	−0.865315	−	0.501229i	$-0.832881\pi$
$809$	−18.6590	+	13.5565i	−0.656015	+	0.476623i	0.209300	+	0.977851i	$0.432881\pi$
$810$	27.4537	+	9.47775i	0.964624	+	0.333014i
$811$	−33.8941	−	24.6255i	−1.19018	−	0.864719i	−0.196900	−	0.980424i	$-0.563087\pi$
$811$	−33.8941	−	24.6255i	−1.19018	−	0.864719i	−0.993284	+	0.115705i	$0.963087\pi$
$812$	−1.16728	+	0.448078i	−0.0409636	+	0.0157245i
$813$	14.3322	+	52.0467i	0.502652	+	1.82536i
$814$	−3.80833	−	8.55366i	−0.133482	−	0.299805i
$815$	−11.9764	−	18.1841i	−0.419514	−	0.636960i
$816$	−0.0521601	−	7.54549i	−0.00182597	−	0.264145i
$817$	1.82186	+	1.18313i	0.0637390	+	0.0413926i
$818$	−29.5029	−	29.5029i	−1.03154	−	1.03154i
$819$	27.6954	−	16.5046i	0.967757	−	0.576719i
$820$	−0.909309	−	1.23472i	−0.0317544	−	0.0431184i
$821$	−10.7390	−	9.66942i	−0.374793	−	0.337465i	0.460110	−	0.887862i	$-0.347810\pi$
$821$	−10.7390	−	9.66942i	−0.374793	−	0.337465i	−0.834903	+	0.550397i	$0.814476\pi$
$822$	−18.1179	−	11.5886i	−0.631933	−	0.404199i
$823$	−0.204976	+	0.533981i	−0.00714501	+	0.0186134i	−0.937107	−	0.349043i	$-0.886507\pi$
$823$	−0.204976	+	0.533981i	−0.00714501	+	0.0186134i	0.929962	+	0.367657i	$0.119840\pi$
$824$	−22.7090	+	39.3332i	−0.791106	+	1.37024i
$825$	11.8810	−	48.1365i	0.413643	−	1.67590i
$826$	13.7306	+	23.7820i	0.477748	+	0.827483i
$827$	36.7706	−	5.82389i	1.27864	−	0.202516i	0.520078	−	0.854119i	$-0.325903\pi$
$827$	36.7706	−	5.82389i	1.27864	−	0.202516i	0.758561	+	0.651602i	$0.225903\pi$
$828$	−0.755551	+	0.959863i	−0.0262572	+	0.0333575i
$829$	15.0321	−	4.88421i	0.522085	−	0.169636i	−0.0361065	−	0.999348i	$-0.511496\pi$
$829$	15.0321	−	4.88421i	0.522085	−	0.169636i	0.558191	+	0.829712i	$0.311496\pi$
$830$	2.57275	+	2.28663i	0.0893014	+	0.0793700i
$831$	32.8432	−	24.2106i	1.13932	−	0.839858i
$832$	33.3661	−	8.94041i	1.15676	−	0.309953i
$833$	−0.0738731	+	1.40958i	−0.00255955	+	0.0488391i
$834$	24.6005	−	43.2978i	0.851847	−	1.49928i
$835$	−32.6806	+	26.8152i	−1.13096	+	0.927980i
$836$	0.186673	−	0.256933i	0.00645622	−	0.00888623i
$837$	21.5347	+	31.7013i	0.744347	+	1.09576i
$838$	−1.28107	+	8.08838i	−0.0442540	+	0.279409i
$839$	−0.103782	+	0.987421i	−0.00358296	+	0.0340895i	−0.996167	−	0.0874683i	$-0.972122\pi$
$839$	−0.103782	+	0.987421i	−0.00358296	+	0.0340895i	0.992584	+	0.121558i	$0.0387890\pi$
$840$	20.0124	+	15.7676i	0.690493	+	0.544033i
$841$	−1.18597	−	11.2838i	−0.0408956	−	0.389095i
$842$	−1.33023	−	0.0697143i	−0.0458427	−	0.00240251i
$843$	5.16168	+	31.1925i	0.177778	+	1.07433i
$844$	−0.0604761	−	0.284518i	−0.00208167	−	0.00979350i
$845$	13.5075	+	9.68122i	0.464671	+	0.333044i
$846$	−25.4456	+	19.0303i	−0.874837	+	0.654275i
$847$	23.5055	−	46.1322i	0.807659	−	1.58512i
$848$	−23.4502	+	18.9896i	−0.805284	+	0.652106i
$849$	22.7026	+	2.22759i	0.779152	+	0.0764506i
$850$	6.59459	+	3.69475i	0.226193	+	0.126729i
$851$	4.82650	+	2.78658i	0.165450	+	0.0955228i
$852$	−0.0740879	−	1.24849i	−0.00253821	−	0.0427725i
$853$	−1.12296	−	21.4273i	−0.0384494	−	0.733658i	−0.948040	−	0.318152i	$-0.896938\pi$
$853$	−1.12296	−	21.4273i	−0.0384494	−	0.733658i	0.909590	−	0.415506i	$-0.136396\pi$
$854$	3.13176	+	9.63855i	0.107166	+	0.329825i
$855$	4.24548	−	1.47526i	0.145192	−	0.0504529i
$856$	−4.18525	+	12.8809i	−0.143049	+	0.440260i
$857$	−27.6113	−	7.39842i	−0.943184	−	0.252725i	−0.245716	−	0.969342i	$-0.579023\pi$
$857$	−27.6113	−	7.39842i	−0.943184	−	0.252725i	−0.697467	+	0.716616i	$0.745690\pi$
$858$	−9.67757	+	63.9603i	−0.330387	+	2.18357i
$859$	22.9284	−	2.40987i	0.782307	−	0.0822238i	0.295049	−	0.955482i	$-0.404664\pi$
$859$	22.9284	−	2.40987i	0.782307	−	0.0822238i	0.487258	+	0.873258i	$0.337997\pi$
$860$	0.159096	+	0.578789i	0.00542512	+	0.0197365i
$861$	6.86068	−	33.4110i	0.233811	−	1.13864i
$862$	12.9736	+	33.7974i	0.441883	+	1.15115i
$863$	18.5671	+	2.94074i	0.632032	+	0.100104i	0.464227	−	0.885716i	$-0.346332\pi$
$863$	18.5671	+	2.94074i	0.632032	+	0.100104i	0.167805	+	0.985820i	$0.446332\pi$
$864$	−0.304328	−	2.41300i	−0.0103534	−	0.0820919i
$865$	1.59185	−	10.4881i	0.0541244	−	0.356605i
$866$	−16.8772	+	37.9068i	−0.573510	+	1.28813i
$867$	−17.1857	+	21.5251i	−0.583658	+	0.731032i
$868$	−0.375758	−	1.40235i	−0.0127541	−	0.0475988i
$869$	−30.6794	−	34.0729i	−1.04073	−	1.15584i
$870$	28.4413	−	21.2503i	0.964251	−	0.720453i
$871$	0.948248	−	1.05314i	0.0321302	−	0.0356842i
$872$	−5.18269	−	2.64071i	−0.175508	−	0.0894258i
$873$	−9.04717	−	0.348802i	−0.306200	−	0.0118052i
$874$			4.75540i			0.160854i
$875$	−24.6268	+	10.0045i	−0.832539	+	0.338213i
$876$	0.0333744	−	0.340138i	0.00112762	−	0.0114922i
$877$	24.0861	+	9.24578i	0.813329	+	0.312208i	0.729247	−	0.684251i	$-0.239871\pi$
$877$	24.0861	+	9.24578i	0.813329	+	0.312208i	0.0840827	+	0.996459i	$0.473204\pi$
$878$	−13.1897	−	20.3103i	−0.445130	−	0.685440i
$879$	4.64175	−	1.02022i	0.156562	−	0.0344112i
$880$	−52.0033	+	11.4048i	−1.75303	+	0.384457i
$881$	6.44445	+	2.09393i	0.217119	+	0.0705462i	0.415557	−	0.909567i	$-0.363587\pi$
$881$	6.44445	+	2.09393i	0.217119	+	0.0705462i	−0.198438	+	0.980113i	$0.563587\pi$
$882$	0.385832	+	5.82106i	0.0129916	+	0.196005i
$883$	−13.4027	−	26.3043i	−0.451037	−	0.885210i	−0.998819	−	0.0485886i	$-0.984528\pi$
$883$	−13.4027	−	26.3043i	−0.451037	−	0.885210i	0.547782	−	0.836621i	$-0.315472\pi$
$884$	−0.358150	−	0.159459i	−0.0120459	−	0.00536318i
$885$	−22.2091	−	21.6232i	−0.746550	−	0.726857i
$886$	3.64846	−	1.62440i	0.122572	−	0.0545727i
$887$	36.3581	+	29.4422i	1.22079	+	0.988574i	0.999912	+	0.0132715i	$0.00422456\pi$
$887$	36.3581	+	29.4422i	1.22079	+	0.988574i	0.220875	+	0.975302i	$0.429109\pi$
$888$	−5.23593	+	1.44183i	−0.175706	+	0.0483846i
$889$	−23.5235	−	2.47242i	−0.788954	−	0.0829224i
$890$	−32.0012	−	31.5909i	−1.07268	−	1.05893i
$891$	−49.4258	−	14.5616i	−1.65583	−	0.487831i
$892$	−1.36402	+	0.695002i	−0.0456707	+	0.0232704i
$893$	−1.27265	+	4.74958i	−0.0425875	+	0.158939i
$894$	−52.8027	+	5.91910i	−1.76599	+	0.197964i
$895$	11.1867	+	6.36277i	0.373931	+	0.212684i
$896$	5.91441	−	27.8251i	0.197587	−	0.929572i
$897$	−17.7172	−	34.1856i	−0.591559	−	1.14143i
$898$	−27.8732	−	34.4205i	−0.930141	−	1.14863i
$899$	46.8475			1.56245
$900$	1.14765	+	0.474631i	0.0382549	+	0.0158210i
$901$	−7.60080			−0.253219
$902$	43.0680	+	53.1845i	1.43401	+	1.77085i
$903$	−7.19422	+	11.2476i	−0.239409	+	0.374296i
$904$	7.97906	−	37.5385i	0.265380	−	1.24851i
$905$	−3.06360	−	6.76317i	−0.101837	−	0.224815i
$906$	−9.81752	+	22.4672i	−0.326165	+	0.746423i
$907$	12.6598	−	47.2469i	0.420360	−	1.56881i	−0.353490	−	0.935438i	$-0.615005\pi$
$907$	12.6598	−	47.2469i	0.420360	−	1.56881i	0.773850	−	0.633368i	$-0.218328\pi$
$908$	1.37338	−	0.699774i	0.0455773	−	0.0232228i
$909$	−52.8782	+	24.4243i	−1.75386	+	0.810104i
$910$	30.7984	−	15.9437i	1.02096	−	0.528529i
$911$	34.2617	+	3.60105i	1.13514	+	0.119308i	0.653405	−	0.757009i	$-0.273340\pi$
$911$	34.2617	+	3.60105i	1.13514	+	0.119308i	0.481735	+	0.876317i	$0.340007\pi$
$912$	−3.43608	−	3.38890i	−0.113780	−	0.112218i
$913$	−4.74566	−	3.84296i	−0.157058	−	0.127183i
$914$	17.4106	−	7.75169i	0.575891	−	0.256403i
$915$	−6.35804	−	9.50981i	−0.210190	−	0.314385i
$916$	−0.225237	−	0.100282i	−0.00744205	−	0.00331341i
$917$	−7.34669	−	14.4187i	−0.242609	−	0.476147i
$918$	4.14095	−	6.67560i	0.136672	−	0.220327i
$919$	18.1977	+	5.91278i	0.600285	+	0.195045i	0.593368	−	0.804932i	$-0.297798\pi$
$919$	18.1977	+	5.91278i	0.600285	+	0.195045i	0.00691771	+	0.999976i	$0.497798\pi$
$920$	20.2136	−	22.7429i	0.666423	−	0.749812i
$921$	−17.6853	−	19.3705i	−0.582749	−	0.638280i
$922$	17.6708	+	27.2106i	0.581956	+	0.896134i
$923$	36.8038	+	14.1277i	1.21141	+	0.465018i
$924$	1.58706	+	1.13639i	0.0522105	+	0.0373845i
$925$	1.39574	−	5.49148i	0.0458917	−	0.180559i
$926$			12.0476i			0.395909i
$927$	−43.5639	+	22.9610i	−1.43083	+	0.754138i
$928$	−2.64901	−	1.34974i	−0.0869579	−	0.0443072i
$929$	3.61319	−	4.01285i	0.118545	−	0.131657i	−0.680951	−	0.732329i	$-0.738433\pi$
$929$	3.61319	−	4.01285i	0.118545	−	0.131657i	0.799496	+	0.600672i	$0.205100\pi$
$930$	21.0876	+	35.4228i	0.691489	+	1.16156i
$931$	0.604082	+	0.670901i	0.0197980	+	0.0219879i
$932$	0.126128	+	0.470714i	0.00413144	+	0.0154188i
$933$	−8.10778	−	20.6928i	−0.265437	−	0.677451i
$934$	9.88202	−	22.1954i	0.323350	−	0.726255i
$935$	−11.9879	−	6.01104i	−0.392047	−	0.196582i
$936$	35.8410	+	11.1001i	1.17150	+	0.362817i
$937$	33.7576	+	5.34668i	1.10281	+	0.174668i	0.681193	−	0.732104i	$-0.261462\pi$
$937$	33.7576	+	5.34668i	1.10281	+	0.174668i	0.421620	+	0.906773i	$0.361462\pi$
$938$	−0.385505	−	1.00427i	−0.0125872	−	0.0327907i
$939$	−19.2724	+	6.40960i	−0.628931	+	0.209169i
$940$	−1.13470	+	0.747339i	−0.0370100	+	0.0243755i
$941$	15.8317	−	1.66398i	0.516098	−	0.0542441i	0.157100	−	0.987583i	$-0.449785\pi$
$941$	15.8317	−	1.66398i	0.516098	−	0.0542441i	0.358997	+	0.933339i	$0.383119\pi$
$942$	−26.0021	−	20.7601i	−0.847195	−	0.676402i
$943$	−39.3466	−	10.5429i	−1.28130	−	0.343323i
$944$	−10.2853	+	31.6548i	−0.334757	+	1.03028i
$945$	9.24745	+	26.0304i	0.300819	+	0.846768i
$946$	−8.27829	−	25.4780i	−0.269150	−	0.828360i
$947$	2.20649	+	42.1023i	0.0717012	+	1.36814i	0.763387	+	0.645942i	$0.223535\pi$
$947$	2.20649	+	42.1023i	0.0717012	+	1.36814i	−0.691686	+	0.722199i	$0.743132\pi$
$948$	0.958827	−	0.632136i	0.0311413	−	0.0205308i
$949$	9.32953	+	5.38641i	0.302849	+	0.174850i
$950$	4.65341	−	1.31147i	0.150977	−	0.0425496i
$951$	18.1059	−	25.2864i	0.587125	−	0.819969i
$952$	5.35542	−	4.33673i	0.173570	−	0.140554i
$953$	−5.35094	+	10.5018i	−0.173334	+	0.340187i	−0.961287	−	0.275548i	$-0.911141\pi$
$953$	−5.35094	+	10.5018i	−0.173334	+	0.340187i	0.787953	+	0.615735i	$0.211141\pi$
$954$	−31.1938	+	3.71530i	−1.00994	+	0.120287i
$955$	2.99597	+	9.02215i	0.0969473	+	0.291950i
$956$	−0.00359369	−	0.0169070i	−0.000116228	−	0.000546811i
$957$	−48.6744	+	39.9760i	−1.57342	+	1.29224i
$958$	15.0991	+	0.791309i	0.487829	+	0.0255660i
$959$	−2.13823	−	20.3439i	−0.0690470	−	0.656938i
$960$	1.94387	+	29.5333i	0.0627382	+	0.953184i
$961$	−2.44564	+	23.2687i	−0.0788917	+	0.750604i
$962$	−1.15644	+	7.30150i	−0.0372853	+	0.235410i
$963$	−11.2834	+	9.39835i	−0.363602	+	0.302858i
$964$	0.768135	−	1.05725i	0.0247400	−	0.0340517i
$965$	−9.88608	−	6.32978i	−0.318244	−	0.203763i
$966$	−29.2270	+	0.202039i	−0.940365	+	0.00650050i
$967$	−1.07980	+	20.6039i	−0.0347242	+	0.662577i	0.924715	+	0.380661i	$0.124303\pi$
$967$	−1.07980	+	20.6039i	−0.0347242	+	0.662577i	−0.959439	+	0.281916i	$0.909030\pi$
$968$	58.2018	−	15.5951i	1.87068	−	0.501246i
$969$	−0.135425	−	1.20809i	−0.00435049	−	0.0388095i
$970$	−9.69219	−	0.955504i	−0.311197	−	0.0306794i
$971$	−35.3946	+	11.5004i	−1.13587	+	0.369065i	−0.815802	−	0.578331i	$-0.803704\pi$
$971$	−35.3946	+	11.5004i	−1.13587	+	0.369065i	−0.320064	+	0.947396i	$0.603704\pi$
$972$	0.545850	−	1.16953i	0.0175082	−	0.0375127i
$973$	46.7816	−	7.40947i	1.49975	−	0.237537i
$974$	−5.23644	−	9.06979i	−0.167786	−	0.290615i
$975$	−28.5663	+	26.7651i	−0.914855	+	0.857168i
$976$	−6.14173	+	10.6378i	−0.196592	+	0.340508i
$977$	15.1933	−	39.5800i	0.486078	−	1.26628i	−0.443042	−	0.896501i	$-0.646101\pi$
$977$	15.1933	−	39.5800i	0.486078	−	1.26628i	0.929121	−	0.369777i	$-0.120566\pi$
$978$	−21.6107	+	11.2000i	−0.691034	+	0.358138i
$979$	59.2854	+	53.3808i	1.89477	+	1.70606i
$980$	0.00160958	+	0.249453i	5.14162e−5	+	0.00796848i
$981$	−3.22857	−	5.41767i	−0.103080	−	0.172973i
$982$	−8.75030	−	8.75030i	−0.279233	−	0.279233i
$983$	−39.4923	−	25.6466i	−1.25961	−	0.818000i	−0.270151	−	0.962818i	$-0.587074\pi$
$983$	−39.4923	−	25.6466i	−1.25961	−	0.818000i	−0.989458	+	0.144818i	$0.953740\pi$
$984$	34.2381	−	20.0842i	1.09147	−	0.640262i
$985$	8.89725	−	2.44565i	0.283490	−	0.0779248i
$986$	−3.90582	−	8.77262i	−0.124387	−	0.279377i
$987$	−29.2453	−	7.61999i	−0.930890	−	0.242547i
$988$	−0.234091	+	0.0898593i	−0.00744744	+	0.00285880i
$989$	12.9002	+	9.37254i	0.410202	+	0.298029i
$990$	−52.1369	−	18.8097i	−1.65702	−	0.597811i
$991$	37.3490	−	27.1357i	1.18643	−	0.861993i	0.193548	−	0.981091i	$-0.438000\pi$
$991$	37.3490	−	27.1357i	1.18643	−	0.861993i	0.992882	+	0.119098i	$0.0380003\pi$
$992$	1.88017	−	2.89521i	0.0596956	−	0.0919231i
$993$	47.6263	−	7.88113i	1.51138	−	0.250100i
$994$	22.2384	−	20.0236i	0.705360	−	0.635109i
$995$	3.27144	+	3.58649i	0.103712	+	0.113699i
$996$	0.112960	−	0.103132i	0.00357926	−	0.00326787i
$997$	8.34316	−	0.437247i	0.264231	−	0.0138477i	0.0802394	−	0.996776i	$-0.474432\pi$
$997$	8.34316	−	0.437247i	0.264231	−	0.0138477i	0.183991	+	0.982928i	$0.441098\pi$
$998$	3.57309	+	22.5596i	0.113104	+	0.714112i
$999$	−5.63670	−	1.70309i	−0.178337	−	0.0538833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.212.21	yes	448
3.2	odd	2		675.2.bd.a.287.8		448
9.2	odd	6	inner	225.2.w.a.137.8	yes	448
9.7	even	3		675.2.bd.a.62.21		448
25.23	odd	20	inner	225.2.w.a.23.8	✓	448
75.23	even	20		675.2.bd.a.98.21		448
225.173	even	60	inner	225.2.w.a.173.21	yes	448
225.223	odd	60		675.2.bd.a.548.8		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.23.8	✓	448	25.23	odd	20	inner
225.2.w.a.137.8	yes	448	9.2	odd	6	inner
225.2.w.a.173.21	yes	448	225.173	even	60	inner
225.2.w.a.212.21	yes	448	1.1	even	1	trivial
675.2.bd.a.62.21		448	9.7	even	3
675.2.bd.a.98.21		448	75.23	even	20
675.2.bd.a.287.8		448	3.2	odd	2
675.2.bd.a.548.8		448	225.223	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.908228 + 1.12157i) q^{2} +(-1.73026 - 0.0786898i) q^{3} +(-0.0172140 + 0.0809854i) q^{4} +(1.65203 - 1.50691i) q^{5} +(-1.48322 - 2.01208i) q^{6} +(0.615345 - 2.29650i) q^{7} +(2.46532 - 1.25614i) q^{8} +(2.98762 + 0.272308i) q^{9} +O(q^{10})\)	\(q+(0.908228 + 1.12157i) q^{2} +(-1.73026 - 0.0786898i) q^{3} +(-0.0172140 + 0.0809854i) q^{4} +(1.65203 - 1.50691i) q^{5} +(-1.48322 - 2.01208i) q^{6} +(0.615345 - 2.29650i) q^{7} +(2.46532 - 1.25614i) q^{8} +(2.98762 + 0.272308i) q^{9} +(3.19053 + 0.484249i) q^{10} +(-5.69377 - 0.598439i) q^{11} +(0.0361574 - 0.138771i) q^{12} +(3.51284 + 2.84464i) q^{13} +(3.13456 - 1.39559i) q^{14} +(-2.97703 + 2.47736i) q^{15} +(3.79919 + 1.69151i) q^{16} +(0.475579 + 0.933377i) q^{17} +(2.40803 + 3.59813i) q^{18} +(0.637208 + 0.207042i) q^{19} +(0.0935999 + 0.159731i) q^{20} +(-1.24542 + 3.92512i) q^{21} +(-4.50005 - 6.92947i) q^{22} +(4.59135 + 1.76246i) q^{23} +(-4.36449 + 1.97946i) q^{24} +(0.458430 - 4.97894i) q^{25} +6.52348i q^{26} +(-5.14793 - 0.706260i) q^{27} +(0.175390 + 0.0893659i) q^{28} +(-4.25021 + 4.72034i) q^{29} +(-5.48235 - 1.08894i) q^{30} +(-4.93512 - 5.48101i) q^{31} +(0.121143 + 0.452112i) q^{32} +(9.80462 + 1.48350i) q^{33} +(-0.614912 + 1.38111i) q^{34} +(-2.44405 - 4.72117i) q^{35} +(-0.0734818 + 0.237266i) q^{36} +(1.11926 + 0.177274i) q^{37} +(0.346519 + 0.902714i) q^{38} +(-5.85430 - 5.19841i) q^{39} +(2.17989 - 5.79020i) q^{40} +(-8.23737 + 0.865782i) q^{41} +(-5.53342 + 2.16809i) q^{42} +(3.13180 + 0.839162i) q^{43} +(0.146477 - 0.450811i) q^{44} +(5.34599 - 4.05221i) q^{45} +(2.19328 + 6.75023i) q^{46} +(0.384093 + 7.32894i) q^{47} +(-6.44050 - 3.22571i) q^{48} +(1.16692 + 0.673721i) q^{49} +(6.00058 - 4.00785i) q^{50} +(-0.749430 - 1.65241i) q^{51} +(-0.290845 + 0.235521i) q^{52} +(-3.29405 + 6.46493i) q^{53} +(-3.88338 - 6.41520i) q^{54} +(-10.3081 + 7.59137i) q^{55} +(-1.36771 - 6.43456i) q^{56} +(-1.08625 - 0.408378i) q^{57} +(-9.15435 - 0.479759i) q^{58} +(0.836580 + 7.95952i) q^{59} +(-0.149383 - 0.283741i) q^{60} +(-0.308741 + 2.93747i) q^{61} +(1.66511 - 10.5131i) q^{62} +(2.46377 - 6.69349i) q^{63} +(4.49184 - 6.18248i) q^{64} +(10.0900 - 0.594098i) q^{65} +(7.24099 + 12.3439i) q^{66} +(0.0164080 - 0.313083i) q^{67} +(-0.0837766 + 0.0224479i) q^{68} +(-7.80556 - 3.41080i) q^{69} +(3.07535 - 7.02907i) q^{70} +(8.29452 - 2.69505i) q^{71} +(7.70748 - 3.08154i) q^{72} +(2.35393 - 0.372825i) q^{73} +(0.817723 + 1.41634i) q^{74} +(-1.18500 + 8.57880i) q^{75} +(-0.0277362 + 0.0480406i) q^{76} +(-4.87795 + 12.7075i) q^{77} +(0.513332 - 11.2873i) q^{78} +(5.95146 + 5.35872i) q^{79} +(8.82535 - 2.93062i) q^{80} +(8.85170 + 1.62710i) q^{81} +(-8.45245 - 8.45245i) q^{82} +(0.894540 + 0.580921i) q^{83} +(-0.296439 - 0.168428i) q^{84} +(2.19219 + 0.825314i) q^{85} +(1.90321 + 4.27467i) q^{86} +(7.72543 - 7.83298i) q^{87} +(-14.7887 + 5.67684i) q^{88} +(-11.2732 - 8.19045i) q^{89} +(9.40021 + 2.31556i) q^{90} +(8.69433 - 6.31680i) q^{91} +(-0.221769 + 0.341494i) q^{92} +(8.10776 + 9.87193i) q^{93} +(-7.87106 + 7.08713i) q^{94} +(1.36468 - 0.618177i) q^{95} +(-0.174033 - 0.791805i) q^{96} +(-3.01383 + 0.157948i) q^{97} +(0.304204 + 1.92067i) q^{98} +(-16.8478 - 3.33837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

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