LMFDB - Embedded newform 525.2.bo.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	525.4
Dual form			525.2.bo.a.394.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0648139 - 0.304925i) q^{2} +(0.406737 + 0.913545i) q^{3} +(1.73831 - 0.773947i) q^{4} +(-1.65210 - 1.50684i) q^{5} +(0.252201 - 0.183235i) q^{6} +(-0.00949525 + 2.64573i) q^{7} +(-0.715132 - 0.984294i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.0648139 - 0.304925i) q^{2} +(0.406737 + 0.913545i) q^{3} +(1.73831 - 0.773947i) q^{4} +(-1.65210 - 1.50684i) q^{5} +(0.252201 - 0.183235i) q^{6} +(-0.00949525 + 2.64573i) q^{7} +(-0.715132 - 0.984294i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(-0.352395 + 0.601431i) q^{10} +(0.471760 + 0.523943i) q^{11} +(1.41407 + 1.27323i) q^{12} +(3.22932 - 1.04927i) q^{13} +(0.807366 - 0.168585i) q^{14} +(0.704599 - 2.12215i) q^{15} +(2.29268 - 2.54628i) q^{16} +(7.65922 - 0.805017i) q^{17} +(0.269973 + 0.155869i) q^{18} +(5.62679 + 2.50521i) q^{19} +(-4.03808 - 1.34072i) q^{20} +(-2.42086 + 1.06744i) q^{21} +(0.129187 - 0.177810i) q^{22} +(0.345852 + 1.62710i) q^{23} +(0.608327 - 1.05365i) q^{24} +(0.458860 + 4.97890i) q^{25} +(-0.529253 - 0.916693i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(2.03115 + 4.60646i) q^{28} +(-8.28528 - 6.01961i) q^{29} +(-0.692766 - 0.0773049i) q^{30} +(-0.880903 - 8.38123i) q^{31} +(-3.03233 - 1.75072i) q^{32} +(-0.286763 + 0.644081i) q^{33} +(-0.741893 - 2.28331i) q^{34} +(4.00239 - 4.35671i) q^{35} +(-0.588004 + 1.80969i) q^{36} +(-2.33194 - 2.09969i) q^{37} +(0.399207 - 1.87812i) q^{38} +(2.27204 + 2.52335i) q^{39} +(-0.301707 + 2.70374i) q^{40} +(-0.156832 - 0.482679i) q^{41} +(0.482395 + 0.668996i) q^{42} +11.4020i q^{43} +(1.22557 + 0.545659i) q^{44} +(2.22527 - 0.219475i) q^{45} +(0.473729 - 0.210918i) q^{46} +(1.04262 + 0.109583i) q^{47} +(3.25866 + 1.05880i) q^{48} +(-6.99982 - 0.0502438i) q^{49} +(1.48845 - 0.462620i) q^{50} +(3.85070 + 6.66962i) q^{51} +(4.80148 - 4.32328i) q^{52} +(2.85452 + 6.41135i) q^{53} +(-0.0325854 + 0.310030i) q^{54} +(0.0101041 - 1.57647i) q^{55} +(2.61097 - 1.88270i) q^{56} +6.15929i q^{57} +(-1.29853 + 2.91654i) q^{58} +(1.94679 + 0.413803i) q^{59} +(-0.417622 - 4.23429i) q^{60} +(-4.83997 + 1.02877i) q^{61} +(-2.49855 + 0.811830i) q^{62} +(-1.95981 - 1.77740i) q^{63} +(1.78031 - 5.47922i) q^{64} +(-6.91623 - 3.13257i) q^{65} +(0.214983 + 0.0456960i) q^{66} +(-3.72648 + 0.391669i) q^{67} +(12.6911 - 7.32720i) q^{68} +(-1.34576 + 0.977754i) q^{69} +(-1.58788 - 0.938054i) q^{70} +(-4.40873 - 3.20313i) q^{71} +(1.20999 + 0.127175i) q^{72} +(-0.518575 + 0.466927i) q^{73} +(-0.489105 + 0.847155i) q^{74} +(-4.36182 + 2.44429i) q^{75} +11.7200 q^{76} +(-1.39069 + 1.24318i) q^{77} +(0.622174 - 0.856349i) q^{78} +(-1.02928 + 9.79296i) q^{79} +(-7.62459 + 0.752001i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-0.137016 + 0.0791063i) q^{82} +(5.04868 + 6.94891i) q^{83} +(-3.38207 + 3.72917i) q^{84} +(-13.8668 - 10.2113i) q^{85} +(3.47676 - 0.739007i) q^{86} +(2.12926 - 10.0174i) q^{87} +(0.178343 - 0.839039i) q^{88} +(-14.2656 + 3.03224i) q^{89} +(-0.211152 - 0.664316i) q^{90} +(2.74542 + 8.55388i) q^{91} +(1.86049 + 2.56074i) q^{92} +(7.29834 - 4.21370i) q^{93} +(-0.0341613 - 0.325023i) q^{94} +(-5.52106 - 12.6175i) q^{95} +(0.366000 - 3.48225i) q^{96} +(7.96180 - 10.9585i) q^{97} +(0.438365 + 2.13768i) q^{98} -0.705034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0648139	−	0.304925i	−0.0458303	−	0.215615i	0.949273	−	0.314452i	$-0.101821\pi$
$2$	−0.0648139	−	0.304925i	−0.0458303	−	0.215615i	−0.995104	+	0.0988377i	$0.968488\pi$
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$4$	1.73831	−	0.773947i	0.869156	−	0.386973i
$5$	−1.65210	−	1.50684i	−0.738841	−	0.673880i
$5$	−1.65210	−	1.50684i	−0.738841	−	0.673880i
$6$	0.252201	−	0.183235i	0.102961	−	0.0748052i
$7$	−0.00949525	+	2.64573i	−0.00358887	+	0.999994i
$7$	−0.00949525	+	2.64573i	−0.00358887	+	0.999994i
$8$	−0.715132	−	0.984294i	−0.252837	−	0.348001i
$9$	−0.669131	+	0.743145i	−0.223044	+	0.247715i
$10$	−0.352395	+	0.601431i	−0.111437	+	0.190189i
$11$	0.471760	+	0.523943i	0.142241	+	0.157975i	0.810056	−	0.586353i	$-0.199437\pi$
$11$	0.471760	+	0.523943i	0.142241	+	0.157975i	−0.667815	+	0.744328i	$0.732770\pi$
$12$	1.41407	+	1.27323i	0.408207	+	0.367551i
$13$	3.22932	−	1.04927i	0.895651	−	0.291015i	0.175210	−	0.984531i	$-0.443939\pi$
$13$	3.22932	−	1.04927i	0.895651	−	0.291015i	0.720441	+	0.693516i	$0.243939\pi$
$14$	0.807366	−	0.168585i	0.215778	−	0.0450562i
$15$	0.704599	−	2.12215i	0.181927	−	0.547938i
$16$	2.29268	−	2.54628i	0.573171	−	0.636571i
$17$	7.65922	−	0.805017i	1.85763	−	0.195245i	0.891453	−	0.453112i	$-0.149686\pi$
$17$	7.65922	−	0.805017i	1.85763	−	0.195245i	0.966180	+	0.257867i	$0.0830197\pi$
$18$	0.269973	+	0.155869i	0.0636331	+	0.0367386i
$19$	5.62679	+	2.50521i	1.29087	+	0.574734i	0.933282	−	0.359144i	$-0.116931\pi$
$19$	5.62679	+	2.50521i	1.29087	+	0.574734i	0.357592	+	0.933878i	$0.383598\pi$
$20$	−4.03808	−	1.34072i	−0.902942	−	0.299795i
$21$	−2.42086	+	1.06744i	−0.528275	+	0.232935i
$22$	0.129187	−	0.177810i	0.0275427	−	0.0379093i
$23$	0.345852	+	1.62710i	0.0721151	+	0.339275i	0.999383	−	0.0351238i	$-0.0111826\pi$
$23$	0.345852	+	1.62710i	0.0721151	+	0.339275i	−0.927268	+	0.374398i	$0.877849\pi$
$24$	0.608327	−	1.05365i	0.124174	−	0.215076i
$25$	0.458860	+	4.97890i	0.0917720	+	0.995780i
$26$	−0.529253	−	0.916693i	−0.103795	−	0.179778i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	2.03115	+	4.60646i	0.383851	+	0.870539i
$29$	−8.28528	−	6.01961i	−1.53854	−	1.11781i	−0.951244	−	0.308439i	$-0.900193\pi$
$29$	−8.28528	−	6.01961i	−1.53854	−	1.11781i	−0.587294	−	0.809374i	$-0.699807\pi$
$30$	−0.692766	−	0.0773049i	−0.126481	−	0.0141139i
$31$	−0.880903	−	8.38123i	−0.158215	−	1.50531i	−0.729170	−	0.684333i	$-0.760094\pi$
$31$	−0.880903	−	8.38123i	−0.158215	−	1.50531i	0.570955	−	0.820981i	$-0.306573\pi$
$32$	−3.03233	−	1.75072i	−0.536046	−	0.309486i
$33$	−0.286763	+	0.644081i	−0.0499191	+	0.112120i
$34$	−0.741893	−	2.28331i	−0.127234	−	0.391585i
$35$	4.00239	−	4.35671i	0.676527	−	0.736418i
$36$	−0.588004	+	1.80969i	−0.0980006	+	0.301615i
$37$	−2.33194	−	2.09969i	−0.383368	−	0.345186i	0.454804	−	0.890591i	$-0.349709\pi$
$37$	−2.33194	−	2.09969i	−0.383368	−	0.345186i	−0.838173	+	0.545405i	$0.816376\pi$
$38$	0.399207	−	1.87812i	0.0647599	−	0.304672i
$39$	2.27204	+	2.52335i	0.363817	+	0.404060i
$40$	−0.301707	+	2.70374i	−0.0477041	+	0.427499i
$41$	−0.156832	−	0.482679i	−0.0244930	−	0.0753818i	0.938063	−	0.346465i	$-0.112618\pi$
$41$	−0.156832	−	0.482679i	−0.0244930	−	0.0753818i	−0.962556	+	0.271083i	$0.912618\pi$
$42$	0.482395	+	0.668996i	0.0744352	+	0.103228i
$43$			11.4020i			1.73879i	0.494119	+	0.869394i	$0.335491\pi$
$43$			11.4020i			1.73879i	−0.494119	+	0.869394i	$0.664509\pi$
$44$	1.22557	+	0.545659i	0.184762	+	0.0822612i
$45$	2.22527	−	0.219475i	0.331724	−	0.0327174i
$46$	0.473729	−	0.210918i	0.0698475	−	0.0310981i
$47$	1.04262	+	0.109583i	0.152081	+	0.0159844i	0.180263	−	0.983618i	$-0.442305\pi$
$47$	1.04262	+	0.109583i	0.152081	+	0.0159844i	−0.0281818	+	0.999603i	$0.508972\pi$
$48$	3.25866	+	1.05880i	0.470348	+	0.152825i
$49$	−6.99982	−	0.0502438i	−0.999974	−	0.00717769i
$50$	1.48845	−	0.462620i	0.210499	−	0.0654243i
$51$	3.85070	+	6.66962i	0.539207	+	0.933933i
$52$	4.80148	−	4.32328i	0.665846	−	0.599530i
$53$	2.85452	+	6.41135i	0.392098	+	0.880667i	0.996469	+	0.0839635i	$0.0267579\pi$
$53$	2.85452	+	6.41135i	0.392098	+	0.880667i	−0.604371	+	0.796703i	$0.706575\pi$
$54$	−0.0325854	+	0.310030i	−0.00443432	+	0.0421897i
$55$	0.0101041	−	1.57647i	0.00136243	−	0.212572i
$56$	2.61097	−	1.88270i	0.348906	−	0.251587i
$57$			6.15929i			0.815817i
$58$	−1.29853	+	2.91654i	−0.170505	+	0.382961i
$59$	1.94679	+	0.413803i	0.253450	+	0.0538725i	0.332885	−	0.942968i	$-0.391978\pi$
$59$	1.94679	+	0.413803i	0.253450	+	0.0538725i	−0.0794343	+	0.996840i	$0.525311\pi$
$60$	−0.417622	−	4.23429i	−0.0539147	−	0.546644i
$61$	−4.83997	+	1.02877i	−0.619694	+	0.131720i	−0.507052	−	0.861915i	$-0.669265\pi$
$61$	−4.83997	+	1.02877i	−0.619694	+	0.131720i	−0.112642	+	0.993636i	$0.535931\pi$
$62$	−2.49855	+	0.811830i	−0.317317	+	0.103102i
$63$	−1.95981	−	1.77740i	−0.246913	−	0.223931i
$64$	1.78031	−	5.47922i	0.222538	−	0.684903i
$65$	−6.91623	−	3.13257i	−0.857853	−	0.388548i
$66$	0.214983	+	0.0456960i	0.0264625	+	0.00562479i
$67$	−3.72648	+	0.391669i	−0.455262	+	0.0478500i	−0.329385	−	0.944196i	$-0.606841\pi$
$67$	−3.72648	+	0.391669i	−0.455262	+	0.0478500i	−0.125877	+	0.992046i	$0.540175\pi$
$68$	12.6911	−	7.32720i	1.53902	−	0.888553i
$69$	−1.34576	+	0.977754i	−0.162011	+	0.117708i
$70$	−1.58788	−	0.938054i	−0.189788	−	0.112119i
$71$	−4.40873	−	3.20313i	−0.523220	−	0.380141i	0.294596	−	0.955622i	$-0.404815\pi$
$71$	−4.40873	−	3.20313i	−0.523220	−	0.380141i	−0.817815	+	0.575481i	$0.804815\pi$
$72$	1.20999	+	0.127175i	0.142599	+	0.0149877i
$73$	−0.518575	+	0.466927i	−0.0606946	+	0.0546497i	−0.698920	−	0.715200i	$-0.746336\pi$
$73$	−0.518575	+	0.466927i	−0.0606946	+	0.0546497i	0.638225	+	0.769850i	$0.279669\pi$
$74$	−0.489105	+	0.847155i	−0.0568573	+	0.0984798i
$75$	−4.36182	+	2.44429i	−0.503659	+	0.282242i
$76$	11.7200			1.34438
$77$	−1.39069	+	1.24318i	−0.158484	+	0.141673i
$78$	0.622174	−	0.856349i	0.0704473	−	0.0969625i
$79$	−1.02928	+	9.79296i	−0.115803	+	1.10179i	0.770100	+	0.637923i	$0.220206\pi$
$79$	−1.02928	+	9.79296i	−0.115803	+	1.10179i	−0.885903	+	0.463871i	$0.846460\pi$
$80$	−7.62459	+	0.752001i	−0.852455	+	0.0840763i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−0.137016	+	0.0791063i	−0.0151309	+	0.00873583i
$83$	5.04868	+	6.94891i	0.554165	+	0.762742i	0.990570	−	0.137008i	$-0.0437486\pi$
$83$	5.04868	+	6.94891i	0.554165	+	0.762742i	−0.436405	+	0.899750i	$0.643749\pi$
$84$	−3.38207	+	3.72917i	−0.369014	+	0.406885i
$85$	−13.8668	−	10.2113i	−1.50407	−	1.10757i
$86$	3.47676	−	0.739007i	0.374908	−	0.0796892i
$87$	2.12926	−	10.0174i	0.228280	−	1.07398i
$88$	0.178343	−	0.839039i	0.0190115	−	0.0894419i
$89$	−14.2656	+	3.03224i	−1.51215	+	0.321417i	−0.887983	−	0.459876i	$-0.847894\pi$
$89$	−14.2656	+	3.03224i	−1.51215	+	0.321417i	−0.624165	+	0.781293i	$0.714561\pi$
$90$	−0.211152	−	0.664316i	−0.0222574	−	0.0700251i
$91$	2.74542	+	8.55388i	0.287799	+	0.896690i
$92$	1.86049	+	2.56074i	0.193969	+	0.266976i
$93$	7.29834	−	4.21370i	0.756803	−	0.436940i
$94$	−0.0341613	−	0.325023i	−0.00352346	−	0.0335235i
$95$	−5.52106	−	12.6175i	−0.566449	−	1.29453i
$96$	0.366000	−	3.48225i	0.0373547	−	0.355406i
$97$	7.96180	−	10.9585i	0.808399	−	1.11267i	−0.183170	−	0.983081i	$-0.558636\pi$
$97$	7.96180	−	10.9585i	0.808399	−	1.11267i	0.991568	−	0.129584i	$-0.0413642\pi$
$98$	0.438365	+	2.13768i	0.0442815	+	0.215938i
$99$	−0.705034			−0.0708586
$100$	4.65104	+	8.29975i	0.465104	+	0.829975i
$101$	0.306193	−	0.530342i	0.0304674	−	0.0527710i	−0.850390	−	0.526153i	$-0.823634\pi$
$101$	0.306193	−	0.530342i	0.0304674	−	0.0527710i	0.880857	+	0.473382i	$0.156967\pi$
$102$	1.78416	−	1.60646i	0.176658	−	0.159063i
$103$	−11.8085	−	1.24112i	−1.16352	−	0.122291i	−0.496982	−	0.867761i	$-0.665559\pi$
$103$	−11.8085	−	1.24112i	−1.16352	−	0.122291i	−0.666540	+	0.745470i	$0.732225\pi$
$104$	−3.34218	−	2.42823i	−0.327727	−	0.238108i
$105$	5.60797	+	1.88433i	0.547282	+	0.183892i
$106$	1.76997	−	1.28596i	0.171915	−	0.124903i
$107$	−2.46879	+	1.42536i	−0.238667	+	0.137794i	−0.614564	−	0.788867i	$-0.710668\pi$
$107$	−2.46879	+	1.42536i	−0.238667	+	0.137794i	0.375897	+	0.926661i	$0.377335\pi$
$108$	−1.89240	+	0.198899i	−0.182096	+	0.0191390i
$109$	−1.38974	−	0.295398i	−0.133113	−	0.0282940i	0.140873	−	0.990028i	$-0.455009\pi$
$109$	−1.38974	−	0.295398i	−0.133113	−	0.0282940i	−0.273986	+	0.961734i	$0.588342\pi$
$110$	−0.481361	+	0.0990963i	−0.0458960	+	0.00944846i
$111$	0.969674	−	2.98435i	0.0920374	−	0.283262i
$112$	6.71502	+	6.09001i	0.634510	+	0.575452i
$113$	−17.5750	+	5.71046i	−1.65331	+	0.537194i	−0.979455	−	0.201665i	$-0.935365\pi$
$113$	−17.5750	+	5.71046i	−1.65331	+	0.537194i	−0.673860	+	0.738859i	$0.735365\pi$
$114$	1.87812	−	0.399207i	0.175902	−	0.0373892i
$115$	1.88041	−	3.20928i	0.175349	−	0.299267i
$116$	−19.0613	−	4.05160i	−1.76979	−	0.376181i
$117$	−1.38108	+	3.10195i	−0.127681	+	0.286775i
$118$		−	0.620445i		−	0.0571166i
$119$	2.05713	+	20.2719i	0.188577	+	1.85832i
$120$	−2.59271	+	0.824088i	−0.236681	+	0.0752286i
$121$	1.09785	−	10.4454i	0.0998050	−	0.949581i
$122$	0.627394	+	1.40915i	0.0568016	+	0.127578i
$123$	0.377160	−	0.339597i	0.0340074	−	0.0306204i
$124$	−8.01791	−	13.8874i	−0.720030	−	1.24713i
$125$	6.74433	−	8.91706i	0.603231	−	0.797566i
$126$	−0.414951	+	0.712796i	−0.0369667	+	0.0635009i
$127$	−6.21942	−	2.02081i	−0.551885	−	0.179318i	0.0197818	−	0.999804i	$-0.493703\pi$
$127$	−6.21942	−	2.02081i	−0.551885	−	0.179318i	−0.571666	+	0.820486i	$0.693703\pi$
$128$	−8.75065	−	0.919730i	−0.773456	−	0.0812934i
$129$	−10.4162	+	4.63761i	−0.917099	+	0.408319i
$130$	−0.506932	+	2.31197i	−0.0444609	+	0.202773i
$131$	5.08372	+	2.26342i	0.444167	+	0.197756i	0.616618	−	0.787262i	$-0.288502\pi$
$131$	5.08372	+	2.26342i	0.444167	+	0.197756i	−0.172452	+	0.985018i	$0.555169\pi$
$132$			1.34155i			0.116767i
$133$	−6.68154	+	14.8632i	−0.579363	+	1.28880i
$134$	0.360957	+	1.11091i	0.0311819	+	0.0959682i
$135$	1.10560	+	1.94362i	0.0951549	+	0.167280i
$136$	−6.26973	−	6.96324i	−0.537625	−	0.597093i
$137$	3.96305	−	18.6447i	0.338586	−	1.59292i	−0.398530	−	0.917155i	$-0.630480\pi$
$137$	3.96305	−	18.6447i	0.338586	−	1.59292i	0.737116	−	0.675766i	$-0.236187\pi$
$138$	0.385366	+	0.346985i	0.0328045	+	0.0295373i
$139$	−4.20749	+	12.9493i	−0.356875	+	1.09835i	0.598040	+	0.801467i	$0.295947\pi$
$139$	−4.20749	+	12.9493i	−0.356875	+	1.09835i	−0.954914	+	0.296881i	$0.904053\pi$
$140$	3.58554	−	10.6710i	0.303034	−	0.901860i
$141$	0.323961	+	0.997050i	0.0272824	+	0.0839667i
$142$	−0.690968	+	1.55194i	−0.0579847	+	0.130236i
$143$	2.07322	+	1.19697i	0.173371	+	0.100096i
$144$	0.358152	+	3.40759i	0.0298460	+	0.283966i
$145$	4.61751	+	22.4296i	0.383463	+	1.86268i
$146$	0.175989	+	0.127863i	0.0145649	+	0.0105820i
$147$	−2.80118	−	6.41509i	−0.231038	−	0.529108i
$148$	−5.67868	−	1.84511i	−0.466785	−	0.151668i
$149$	2.77739	+	4.81059i	0.227533	+	0.394099i	0.957076	−	0.289836i	$-0.0936007\pi$
$149$	2.77739	+	4.81059i	0.227533	+	0.394099i	−0.729543	+	0.683935i	$0.760267\pi$
$150$	1.02803	+	1.17160i	0.0839385	+	0.0956611i
$151$	11.0087	−	19.0676i	0.895874	−	1.55170i	0.0631548	−	0.998004i	$-0.479884\pi$
$151$	11.0087	−	19.0676i	0.895874	−	1.55170i	0.832719	−	0.553696i	$-0.186783\pi$
$152$	−1.55803	−	7.32997i	−0.126373	−	0.594539i
$153$	−4.52678	+	6.23057i	−0.365968	+	0.503712i
$154$	0.469212	+	0.343482i	0.0378102	+	0.0276786i
$155$	−11.1738	+	15.1740i	−0.897505	+	1.21881i
$156$	5.90245	+	2.62794i	0.472574	+	0.210404i
$157$	5.50818	+	3.18015i	0.439601	+	0.253803i	0.703428	−	0.710766i	$-0.251652\pi$
$157$	5.50818	+	3.18015i	0.439601	+	0.253803i	−0.263828	+	0.964570i	$0.584985\pi$
$158$	3.05283	−	0.320866i	0.242870	−	0.0255267i
$159$	−4.69602	+	5.21546i	−0.372419	+	0.413613i
$160$	2.37166	+	7.46160i	0.187496	+	0.589891i
$161$	−4.30817	+	0.899582i	−0.339531	+	0.0708970i
$162$	−0.296480	+	0.0963322i	−0.0232937	+	0.00756857i
$163$	−0.815910	−	0.734649i	−0.0639070	−	0.0575421i	0.636558	−	0.771229i	$-0.280357\pi$
$163$	−0.815910	−	0.734649i	−0.0639070	−	0.0575421i	−0.700465	+	0.713686i	$0.747024\pi$
$164$	−0.646191	−	0.717668i	−0.0504590	−	0.0560404i
$165$	1.44429	−	0.631979i	0.112438	−	0.0491995i
$166$	1.79167	−	1.98986i	0.139061	−	0.154443i
$167$	6.38349	+	8.78612i	0.493969	+	0.679890i	0.981114	−	0.193431i	$-0.0619616\pi$
$167$	6.38349	+	8.78612i	0.493969	+	0.679890i	−0.487145	+	0.873321i	$0.661962\pi$
$168$	2.78191	+	1.61948i	0.214629	+	0.124945i
$169$	−1.18970	+	0.864366i	−0.0915153	+	0.0664897i
$170$	−2.21491	+	4.89017i	−0.169876	+	0.375059i
$171$	−5.62679	+	2.50521i	−0.430291	+	0.191578i
$172$	8.82454	+	19.8202i	0.672865	+	1.51128i
$173$	−2.20466	−	10.3721i	−0.167617	−	0.788576i	−0.978968	−	0.204016i	$-0.934601\pi$
$173$	−2.20466	−	10.3721i	−0.167617	−	0.788576i	0.811351	−	0.584560i	$-0.198733\pi$
$174$	−3.19256			−0.242027
$175$	−13.1772	+	1.16675i	−0.996103	+	0.0881977i
$176$	2.41570			0.182091
$177$	0.413803	+	1.94679i	0.0311033	+	0.146330i
$178$	1.84921	+	4.15340i	0.138604	+	0.311311i
$179$	−8.37489	+	3.72874i	−0.625969	+	0.278699i	−0.695105	−	0.718908i	$-0.744642\pi$
$179$	−8.37489	+	3.72874i	−0.625969	+	0.278699i	0.0691364	+	0.997607i	$0.477976\pi$
$180$	3.69835	−	2.10376i	0.275659	−	0.156805i
$181$	−8.52859	+	6.19638i	−0.633925	+	0.460573i	−0.857758	−	0.514054i	$-0.828143\pi$
$181$	−8.52859	+	6.19638i	−0.633925	+	0.460573i	0.223833	+	0.974628i	$0.428143\pi$
$182$	2.43035	−	1.39156i	0.180150	−	0.103149i
$183$	−2.90842	−	4.00309i	−0.214996	−	0.295917i
$184$	1.35422	−	1.50401i	0.0998344	−	0.110877i
$185$	0.688698	+	6.98275i	0.0506341	+	0.513382i
$186$	−1.75790	−	1.95234i	−0.128895	−	0.143153i
$187$	4.03510	+	3.63322i	0.295076	+	0.265687i
$188$	1.89721	−	0.616439i	0.138368	−	0.0449585i
$189$	0.826607	−	2.51331i	0.0601268	−	0.182816i
$190$	−3.48956	+	2.50130i	−0.253159	+	0.181463i
$191$	−3.81799	+	4.24031i	−0.276260	+	0.306818i	−0.865268	−	0.501309i	$-0.832852\pi$
$191$	−3.81799	+	4.24031i	−0.276260	+	0.306818i	0.589008	+	0.808127i	$0.299519\pi$
$192$	5.72964	−	0.602209i	0.413501	−	0.0434607i
$193$	8.12322	+	4.68994i	0.584722	+	0.337590i	0.763008	−	0.646389i	$-0.223722\pi$
$193$	8.12322	+	4.68994i	0.584722	+	0.337590i	−0.178286	+	0.983979i	$0.557055\pi$
$194$	−3.85755	−	1.71749i	−0.276956	−	0.123309i
$195$	0.0486621	−	7.59242i	0.00348476	−	0.543705i
$196$	−12.2068	+	5.33015i	−0.871911	+	0.380725i
$197$	−3.46272	+	4.76603i	−0.246709	+	0.339566i	−0.914355	−	0.404913i	$-0.867302\pi$
$197$	−3.46272	+	4.76603i	−0.246709	+	0.339566i	0.667646	+	0.744479i	$0.267302\pi$
$198$	0.0456960	+	0.214983i	0.00324747	+	0.0152782i
$199$	5.99133	−	10.3773i	0.424714	−	0.735626i	−0.571680	−	0.820477i	$-0.693708\pi$
$199$	5.99133	−	10.3773i	0.424714	−	0.735626i	0.996394	+	0.0848507i	$0.0270413\pi$
$200$	4.57256	−	4.01222i	0.323329	−	0.283707i
$201$	−1.87350	−	3.24500i	−0.132147	−	0.228885i
$202$	−0.181560	−	0.0589925i	−0.0127745	−	0.00415070i
$203$	16.0050	−	21.8635i	1.12333	−	1.53452i
$204$	11.8557	+	8.61364i	0.830062	+	0.603075i
$205$	−0.468219	+	1.03375i	−0.0327018	+	0.0722006i
$206$	0.386903	+	3.68114i	0.0269568	+	0.256477i
$207$	−1.44059	−	0.831727i	−0.100128	−	0.0578090i
$208$	4.73207	−	10.6284i	0.328110	−	0.736947i
$209$	1.34191	+	4.12997i	0.0928218	+	0.285676i
$210$	0.211106	−	1.83214i	0.0145677	−	0.126430i
$211$	6.61404	−	20.3559i	0.455329	−	1.40136i	−0.415419	−	0.909630i	$-0.636365\pi$
$211$	6.61404	−	20.3559i	0.455329	−	1.40136i	0.870748	−	0.491729i	$-0.163635\pi$
$212$	9.92408	+	8.93569i	0.681589	+	0.613705i
$213$	1.13301	−	5.33040i	0.0776327	−	0.365233i
$214$	0.594638	+	0.660413i	0.0406486	+	0.0451449i
$215$	17.1810	−	18.8372i	1.17173	−	1.28469i
$216$	0.375967	+	1.15711i	0.0255813	+	0.0787312i
$217$	22.1829	−	2.25105i	1.50587	−	0.152812i
$218$			0.442913i			0.0299978i
$219$	−0.637482	−	0.283825i	−0.0430771	−	0.0191791i
$220$	−1.20254	−	2.74822i	−0.0810753	−	0.185285i
$221$	23.8894	−	10.6362i	1.60697	−	0.715470i
$222$	−0.972852	−	0.102251i	−0.0652935	−	0.00686263i
$223$	−10.1134	−	3.28604i	−0.677243	−	0.220050i	−0.0498553	−	0.998756i	$-0.515876\pi$
$223$	−10.1134	−	3.28604i	−0.677243	−	0.220050i	−0.627388	+	0.778707i	$0.715876\pi$
$224$	4.66073	−	8.00612i	0.311408	−	0.534931i
$225$	−4.00708	−	2.99053i	−0.267139	−	0.199369i
$226$	2.88036	+	4.98894i	0.191599	+	0.331859i
$227$	10.1623	−	9.15015i	0.674493	−	0.607317i	−0.259014	−	0.965873i	$-0.583398\pi$
$227$	10.1623	−	9.15015i	0.674493	−	0.607317i	0.933508	+	0.358557i	$0.116731\pi$
$228$	4.76696	+	10.7068i	0.315700	+	0.709073i
$229$	0.960890	−	9.14225i	0.0634974	−	0.604137i	−0.915789	−	0.401659i	$-0.868434\pi$
$229$	0.960890	−	9.14225i	0.0634974	−	0.604137i	0.979287	−	0.202478i	$-0.0648996\pi$
$230$	−1.10047	−	0.365377i	−0.0725626	−	0.0240923i
$231$	−1.70134	−	0.764815i	−0.111940	−	0.0503212i
$232$			12.4600i			0.818037i
$233$	4.11254	−	9.23691i	0.269421	−	0.605130i	−0.727275	−	0.686346i	$-0.759214\pi$
$233$	4.11254	−	9.23691i	0.269421	−	0.605130i	0.996697	+	0.0812157i	$0.0258803\pi$
$234$	1.03537	+	0.220076i	0.0676846	+	0.0143868i
$235$	−1.55738	−	1.75210i	−0.101592	−	0.114294i
$236$	3.70439	−	0.787392i	0.241135	−	0.0512548i
$237$	−9.36496	+	3.04286i	−0.608320	+	0.197655i
$238$	6.04808	−	1.94117i	0.392039	−	0.125828i
$239$	1.61001	−	4.95509i	0.104143	−	0.320518i	−0.885386	−	0.464857i	$-0.846106\pi$
$239$	1.61001	−	4.95509i	0.104143	−	0.320518i	0.989528	+	0.144339i	$0.0461056\pi$
$240$	−3.78819	−	6.65954i	−0.244526	−	0.429871i
$241$	−13.4622	−	2.86147i	−0.867174	−	0.184324i	−0.247218	−	0.968960i	$-0.579516\pi$
$241$	−13.4622	−	2.86147i	−0.867174	−	0.184324i	−0.619956	+	0.784636i	$0.712850\pi$
$242$	−3.25622	+	0.342242i	−0.209318	+	0.0220002i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−7.61717	+	5.53419i	−0.487639	+	0.354290i
$245$	11.4887	+	10.6306i	0.733985	+	0.679166i
$246$	−0.127997	−	0.0929951i	−0.00816077	−	0.00592915i
$247$	20.7993	+	2.18610i	1.32343	+	0.139098i
$248$	−7.61964	+	6.86076i	−0.483848	+	0.435658i
$249$	−4.29466	+	7.43858i	−0.272163	+	0.471401i
$250$	−3.15616	−	1.47857i	−0.199613	−	0.0935128i
$251$	22.3926			1.41341			0.706703	−	0.707511i	$-0.250182\pi$
$251$	22.3926			1.41341			0.706703	+	0.707511i	$0.250182\pi$
$252$	−4.78237	−	1.57288i	−0.301261	−	0.0990824i
$253$	−0.689350	+	0.948809i	−0.0433391	+	0.0596511i
$254$	−0.213092	+	2.02744i	−0.0133706	+	0.127213i
$255$	3.68831	−	16.8213i	0.230971	−	1.05339i
$256$	−0.917704	−	8.73137i	−0.0573565	−	0.545711i
$257$	−25.7664	+	14.8762i	−1.60726	+	0.927953i	−0.617282	+	0.786742i	$0.711766\pi$
$257$	−25.7664	+	14.8762i	−1.60726	+	0.927953i	−0.989979	+	0.141212i	$0.954900\pi$
$258$	2.08924	+	2.87559i	0.130070	+	0.179027i
$259$	5.57735	−	6.14975i	0.346560	−	0.382127i
$260$	−14.4470	−	0.0925952i	−0.895966	−	0.00574251i
$261$	10.0174	−	2.12926i	0.620060	−	0.131798i
$262$	0.360678	−	1.69685i	0.0222827	−	0.104832i
$263$	−1.77061	+	8.33007i	−0.109181	+	0.513654i	0.889238	+	0.457444i	$0.151235\pi$
$263$	−1.77061	+	8.33007i	−0.109181	+	0.513654i	−0.998419	+	0.0562099i	$0.982098\pi$
$264$	0.839039	−	0.178343i	0.0516393	−	0.0109763i
$265$	4.94494	−	14.8935i	0.303765	−	0.914900i
$266$	4.96522	+	1.07403i	0.304437	+	0.0658530i
$267$	−8.57242	−	11.7989i	−0.524624	−	0.722083i
$268$	−6.17465	+	3.56494i	−0.377177	+	0.217763i
$269$	1.06035	+	10.0885i	0.0646505	+	0.615109i	0.978097	+	0.208150i	$0.0667441\pi$
$269$	1.06035	+	10.0885i	0.0646505	+	0.615109i	−0.913446	+	0.406959i	$0.866589\pi$
$270$	0.521000	−	0.463099i	0.0317070	−	0.0281833i
$271$	1.86391	−	17.7339i	0.113224	−	1.07726i	−0.779422	−	0.626499i	$-0.784487\pi$
$271$	1.86391	−	17.7339i	0.113224	−	1.07726i	0.892646	−	0.450758i	$-0.148846\pi$
$272$	15.5104	−	21.3482i	0.940455	−	1.29442i
$273$	−6.69769	+	5.98724i	−0.405363	+	0.362364i
$274$	−5.94209			−0.358975
$275$	−2.39219	+	2.58926i	−0.144254	+	0.156138i
$276$	−1.58263	+	2.74119i	−0.0952630	+	0.165000i
$277$	−11.0529	+	9.95211i	−0.664106	+	0.597964i	−0.930673	−	0.365852i	$-0.880777\pi$
$277$	−11.0529	+	9.95211i	−0.664106	+	0.597964i	0.266566	+	0.963817i	$0.414111\pi$
$278$	4.22128	+	0.443675i	0.253176	+	0.0266098i
$279$	6.81791	+	4.95350i	0.408178	+	0.296558i
$280$	−7.15052	−	0.823909i	−0.427325	−	0.0492380i
$281$	−14.9752	+	10.8801i	−0.893346	+	0.649054i	−0.936748	−	0.350004i	$-0.886180\pi$
$281$	−14.9752	+	10.8801i	−0.893346	+	0.649054i	0.0434021	+	0.999058i	$0.486180\pi$
$282$	0.283028	−	0.163406i	0.0168541	−	0.00973072i
$283$	−15.2643	+	1.60434i	−0.907369	+	0.0953683i	−0.546703	−	0.837327i	$-0.684117\pi$
$283$	−15.2643	+	1.60434i	−0.907369	+	0.0953683i	−0.360666	+	0.932695i	$0.617451\pi$
$284$	−10.1428	−	2.15592i	−0.601864	−	0.127930i
$285$	9.28107	−	10.1757i	0.549763	−	0.602759i
$286$	0.230614	−	0.709757i	0.0136365	−	0.0419688i
$287$	1.27853	−	0.410353i	0.0754693	−	0.0242224i
$288$	3.33006	−	1.08200i	0.196226	−	0.0637576i
$289$	41.3871	−	8.79710i	2.43454	−	0.517476i
$290$	6.54007	−	2.86174i	0.384046	−	0.168047i
$291$	13.2494	+	2.81625i	0.776695	+	0.165092i
$292$	−0.540069	+	1.21301i	−0.0316051	+	0.0709863i
$293$			16.8921i			0.986845i	0.869790	+	0.493422i	$0.164254\pi$
$293$			16.8921i			0.986845i	−0.869790	+	0.493422i	$0.835746\pi$
$294$	−1.77457	+	1.26994i	−0.103495	+	0.0740643i
$295$	−2.59275	−	3.61714i	−0.150956	−	0.210598i
$296$	−0.399067	+	3.79686i	−0.0231953	+	0.220688i
$297$	−0.286763	−	0.644081i	−0.0166397	−	0.0373734i
$298$	1.28686	−	1.15869i	0.0745456	−	0.0671211i
$299$	2.82413	+	4.89154i	0.163324	+	0.282885i
$300$	−5.69045	+	7.62475i	−0.328538	+	0.440215i
$301$	−30.1667	−	0.108265i	−1.73878	−	0.00624028i
$302$	−6.52771	−	2.12098i	−0.375627	−	0.122049i
$303$	0.609032	+	0.0640118i	0.0349880	+	0.00367738i
$304$	19.2794	−	8.58375i	1.10575	−	0.492312i
$305$	9.54629	+	5.59344i	0.546619	+	0.320279i
$306$	2.19326	+	0.976500i	0.125380	+	0.0558228i
$307$		−	13.0065i		−	0.742319i	−0.928569	−	0.371159i	$-0.878960\pi$
$307$		−	13.0065i		−	0.742319i	0.928569	−	0.371159i	$-0.121040\pi$
$308$	−1.45531	+	3.23735i	−0.0829237	+	0.184465i
$309$	−3.66911	−	11.2924i	−0.208729	−	0.642400i
$310$	5.35116	+	2.42370i	0.303925	+	0.137657i
$311$	12.7082	+	14.1138i	0.720614	+	0.800323i	0.986514	−	0.163678i	$-0.0523357\pi$
$311$	12.7082	+	14.1138i	0.720614	+	0.800323i	−0.265900	+	0.964001i	$0.585669\pi$
$312$	0.858916	−	4.04088i	0.0486265	−	0.228770i
$313$	−10.5351	−	9.48583i	−0.595478	−	0.536171i	0.315340	−	0.948979i	$-0.397881\pi$
$313$	−10.5351	−	9.48583i	−0.595478	−	0.536171i	−0.910818	+	0.412808i	$0.864548\pi$
$314$	0.612701	−	1.88570i	0.0345767	−	0.106416i
$315$	0.559543	+	5.88956i	0.0315267	+	0.331839i
$316$	5.79001	+	17.8198i	0.325714	+	1.00244i
$317$	−9.72631	+	21.8457i	−0.546284	+	1.22697i	0.403762	+	0.914864i	$0.367702\pi$
$317$	−9.72631	+	21.8457i	−0.546284	+	1.22697i	−0.950046	+	0.312110i	$0.898964\pi$
$318$	1.89469	+	1.09390i	0.106249	+	0.0613430i
$319$	−0.754735	−	7.18082i	−0.0422570	−	0.402049i
$320$	−11.1976	+	6.36958i	−0.625963	+	0.356070i
$321$	−2.30627	−	1.67561i	−0.128724	−	0.0935232i
$322$	0.553534	+	1.25536i	0.0308473	+	0.0699587i
$323$	45.1135	+	14.6583i	2.51019	+	0.815609i
$324$	−0.951410	−	1.64789i	−0.0528561	−	0.0915495i
$325$	6.70601	+	15.5970i	0.371982	+	0.865165i
$326$	−0.171131	+	0.296407i	−0.00947805	+	0.0164165i
$327$	−0.295398	−	1.38974i	−0.0163356	−	0.0768528i
$328$	−0.362943	+	0.499548i	−0.0200402	+	0.0275829i
$329$	−0.299829	+	2.75745i	−0.0165301	+	0.152023i
$330$	−0.286316	−	0.399439i	−0.0157612	−	0.0219884i
$331$	−28.0340	−	12.4815i	−1.54089	−	0.686047i	−0.551880	−	0.833924i	$-0.686089\pi$
$331$	−28.0340	−	12.4815i	−1.54089	−	0.686047i	−0.989006	+	0.147877i	$0.952756\pi$
$332$	14.1543	+	8.17197i	0.776816	+	0.448495i
$333$	3.12074	−	0.328003i	0.171016	−	0.0179745i
$334$	2.26537	−	2.51595i	0.123956	−	0.137667i
$335$	6.74669	+	4.96814i	0.368611	+	0.271438i
$336$	−2.83226	+	8.61151i	−0.154512	+	0.469796i
$337$	4.18205	−	1.35883i	0.227811	−	0.0740202i	−0.192887	−	0.981221i	$-0.561785\pi$
$337$	4.18205	−	1.35883i	0.227811	−	0.0740202i	0.420698	+	0.907201i	$0.361785\pi$
$338$	0.340676	+	0.306746i	0.0185303	+	0.0166848i
$339$	−12.3651	−	13.7329i	−0.671583	−	0.745868i
$340$	−32.0078	−	7.01818i	−1.73587	−	0.380614i
$341$	3.97571	−	4.41548i	0.215297	−	0.239111i
$342$	1.12859	+	1.55338i	0.0610274	+	0.0839970i
$343$	0.199397	−	18.5192i	0.0107664	−	0.999942i
$344$	11.2229	−	8.15393i	0.605099	−	0.439630i
$345$	3.69665	+	0.412505i	0.199021	+	0.0222085i
$346$	−3.01982	+	1.34451i	−0.162347	+	0.0722814i
$347$	−3.09479	−	6.95102i	−0.166137	−	0.373150i	0.811222	−	0.584739i	$-0.198803\pi$
$347$	−3.09479	−	6.95102i	−0.166137	−	0.373150i	−0.977359	+	0.211588i	$0.932136\pi$
$348$	−4.05160	−	19.0613i	−0.217188	−	1.02179i
$349$	−0.182298			−0.00975821			−0.00487910	−	0.999988i	$-0.501553\pi$
$349$	−0.182298			−0.00975821			−0.00487910	+	0.999988i	$0.501553\pi$
$350$	1.20984	+	3.94244i	0.0646684	+	0.210732i
$351$	−3.39550			−0.181239
$352$	−0.513258	−	2.41469i	−0.0273567	−	0.128703i
$353$	2.69996	+	6.06420i	0.143704	+	0.322765i	0.971030	−	0.238957i	$-0.0768056\pi$
$353$	2.69996	+	6.06420i	0.143704	+	0.322765i	−0.827326	+	0.561722i	$0.810139\pi$
$354$	0.566804	−	0.252358i	0.0301253	−	0.0134127i
$355$	2.45705	+	11.9351i	0.130407	+	0.633451i
$356$	−22.4512	+	16.3118i	−1.18991	+	0.864522i
$357$	−17.6826	+	10.1246i	−0.935862	+	0.535851i
$358$	1.67980	+	2.31204i	0.0887800	+	0.122195i
$359$	−1.04804	+	1.16396i	−0.0553132	+	0.0614316i	−0.770166	−	0.637843i	$-0.779827\pi$
$359$	−1.04804	+	1.16396i	−0.0553132	+	0.0614316i	0.714853	+	0.699275i	$0.246494\pi$
$360$	−1.80739	−	2.03337i	−0.0952578	−	0.107168i
$361$	12.6712	+	14.0728i	0.666905	+	0.740673i
$362$	2.44220	+	2.19897i	0.128359	+	0.115575i
$363$	9.98888	−	3.24558i	0.524280	−	0.170349i
$364$	11.3926	+	12.7445i	0.597137	+	0.667993i
$365$	1.56032	+	0.0100006i	0.0816710	+	0.000523453i
$366$	−1.03214	+	1.14631i	−0.0539507	+	0.0599184i
$367$	7.99910	−	0.840739i	0.417550	−	0.0438862i	0.106576	−	0.994305i	$-0.466011\pi$
$367$	7.99910	−	0.840739i	0.417550	−	0.0438862i	0.310974	+	0.950418i	$0.399345\pi$
$368$	4.93600	+	2.84980i	0.257307	+	0.148556i
$369$	0.463642	+	0.206427i	0.0241362	+	0.0107461i
$370$	2.08458	−	0.662580i	0.108372	−	0.0344459i
$371$	−16.9898	+	7.49142i	−0.882068	+	0.388935i
$372$	9.42562	−	12.9733i	0.488696	−	0.672632i
$373$	5.28317	+	24.8554i	0.273552	+	1.28696i	0.873461	+	0.486894i	$0.161870\pi$
$373$	5.28317	+	24.8554i	0.273552	+	1.28696i	−0.599909	+	0.800068i	$0.704797\pi$
$374$	0.846330	−	1.46589i	0.0437627	−	0.0757991i
$375$	10.8893	+	2.53435i	0.562321	+	0.130874i
$376$	−0.637746	−	1.10461i	−0.0328892	−	0.0569658i
$377$	−33.0720	−	10.7457i	−1.70329	−	0.553434i
$378$	−0.819947	−	0.0891562i	−0.0421735	−	0.00458570i
$379$	−5.02005	−	3.64728i	−0.257863	−	0.187348i	0.451342	−	0.892351i	$-0.350946\pi$
$379$	−5.02005	−	3.64728i	−0.257863	−	0.187348i	−0.709204	+	0.705003i	$0.750946\pi$
$380$	−19.3626	−	17.6602i	−0.993281	−	0.905949i
$381$	−0.683563	−	6.50366i	−0.0350200	−	0.333193i
$382$	1.54044	+	0.889371i	0.0788155	+	0.0455042i
$383$	−0.291323	+	0.654322i	−0.0148859	+	0.0334343i	−0.920835	−	0.389951i	$-0.872492\pi$
$383$	−0.291323	+	0.654322i	−0.0148859	+	0.0334343i	0.905950	+	0.423386i	$0.139158\pi$
$384$	−2.71899	−	8.36820i	−0.138753	−	0.427038i
$385$	4.17083	+	0.0417017i	0.212565	+	0.00212532i
$386$	0.903585	−	2.78095i	0.0459913	−	0.141547i
$387$	−8.47333	−	7.62942i	−0.430724	−	0.387825i
$388$	5.35882	−	25.2113i	0.272053	−	1.27991i
$389$	8.64276	+	9.59876i	0.438206	+	0.486677i	0.921278	−	0.388904i	$-0.127146\pi$
$389$	8.64276	+	9.59876i	0.438206	+	0.486677i	−0.483073	+	0.875580i	$0.660479\pi$
$390$	−2.31828	+	0.477256i	−0.117390	+	0.0241668i
$391$	3.95880	+	12.1839i	0.200205	+	0.616168i
$392$	4.95634	+	6.92581i	0.250333	+	0.349806i
$393$			5.56482i			0.280708i
$394$	1.67771	+	0.746967i	0.0845220	+	0.0376316i
$395$	16.4569	−	14.6280i	0.828037	−	0.736013i
$396$	−1.22557	+	0.545659i	−0.0615872	+	0.0274204i
$397$	22.7521	+	2.39134i	1.14189	+	0.120018i	0.656534	−	0.754297i	$-0.272022\pi$
$397$	22.7521	+	2.39134i	1.14189	+	0.120018i	0.485360	+	0.874315i	$0.338689\pi$
$398$	−3.55262	−	1.15432i	−0.178077	−	0.0578606i
$399$	−16.2958	−	0.0584840i	−0.815812	−	0.00292786i
$400$	13.7297	+	10.2467i	0.686486	+	0.512333i
$401$	14.9023	+	25.8116i	0.744186	+	1.28897i	0.950574	+	0.310498i	$0.100496\pi$
$401$	14.9023	+	25.8116i	0.744186	+	1.28897i	−0.206388	+	0.978470i	$0.566171\pi$
$402$	−0.868054	+	0.781599i	−0.0432946	+	0.0389826i
$403$	−11.6389	−	26.1414i	−0.579774	−	1.30219i
$404$	0.121803	−	1.15888i	0.00605992	−	0.0576563i
$405$	−1.32590	+	1.80056i	−0.0658843	+	0.0894704i
$406$	−7.70407	−	3.46326i	−0.382347	−	0.171879i
$407$		−	2.21235i		−	0.109662i
$408$	3.81111	−	8.55988i	0.188678	−	0.423777i
$409$	12.7156	+	2.70279i	0.628748	+	0.133644i	0.511255	−	0.859429i	$-0.329181\pi$
$409$	12.7156	+	2.70279i	0.628748	+	0.133644i	0.117493	+	0.993074i	$0.462514\pi$
$410$	0.345565	+	0.0757702i	0.0170662	+	0.00374202i
$411$	18.6447	−	3.96305i	0.919674	−	0.195483i
$412$	−21.4873	+	6.98166i	−1.05861	+	0.343962i
$413$	−1.11330	+	5.14675i	−0.0547817	+	0.253255i
$414$	−0.160244	+	0.493181i	−0.00787557	+	0.0242385i
$415$	2.12999	−	19.0878i	0.104557	−	0.936986i
$416$	−11.6293	−	2.47189i	−0.570175	−	0.121194i
$417$	−13.5411	+	1.42323i	−0.663113	+	0.0696959i
$418$	1.17236	−	0.676861i	0.0573419	−	0.0331064i
$419$	27.7610	−	20.1695i	1.35621	−	0.985346i	0.357537	−	0.933899i	$-0.383617\pi$
$419$	27.7610	−	20.1695i	1.35621	−	0.985346i	0.998676	−	0.0514474i	$-0.0163835\pi$
$420$	11.2068	−	1.06471i	0.546834	−	0.0519525i
$421$	16.3222	+	11.8588i	0.795497	+	0.577963i	0.909590	−	0.415507i	$-0.136396\pi$
$421$	16.3222	+	11.8588i	0.795497	+	0.577963i	−0.114092	+	0.993470i	$0.536396\pi$
$422$	−6.63571	−	0.697441i	−0.323021	−	0.0339509i
$423$	−0.779083	+	0.701490i	−0.0378803	+	0.0341076i
$424$	4.26930	−	7.39465i	0.207336	−	0.359116i
$425$	7.52261	+	37.7651i	0.364900	+	1.83188i
$426$	−1.69881			−0.0823076
$427$	−2.67589	−	12.8150i	−0.129495	−	0.620163i
$428$	−3.18838	+	4.38842i	−0.154116	+	0.212122i
$429$	−0.250236	+	2.38083i	−0.0120815	+	0.114948i
$430$	−6.85751	−	4.01801i	−0.330699	−	0.193765i
$431$	−0.0189036	−	0.179856i	−0.000910555	−	0.00866335i	0.994057	−	0.108859i	$-0.0347197\pi$
$431$	−0.0189036	−	0.179856i	−0.000910555	−	0.00866335i	−0.994968	+	0.100196i	$0.968053\pi$
$432$	−2.96732	+	1.71318i	−0.142765	+	0.0824255i
$433$	−4.10699	−	5.65279i	−0.197369	−	0.271656i	0.698849	−	0.715270i	$-0.253696\pi$
$433$	−4.10699	−	5.65279i	−0.197369	−	0.271656i	−0.896218	+	0.443614i	$0.853696\pi$
$434$	−2.12416	−	6.61822i	−0.101963	−	0.317685i
$435$	−18.6123	+	13.3412i	−0.892393	+	0.639663i
$436$	−2.64442	+	0.562090i	−0.126645	+	0.0269192i
$437$	−2.13020	+	10.0218i	−0.101901	+	0.479408i
$438$	−0.0452278	+	0.212780i	−0.00216107	+	0.0101670i
$439$	−33.0460	+	7.02414i	−1.57720	+	0.335244i	−0.911604	−	0.411069i	$-0.865155\pi$
$439$	−33.0460	+	7.02414i	−1.57720	+	0.335244i	−0.665595	+	0.746313i	$0.731822\pi$
$440$	−1.55894	+	1.11744i	−0.0743195	+	0.0532719i
$441$	4.72113	−	5.16826i	0.224816	−	0.246108i
$442$	−4.79162	−	6.59510i	−0.227914	−	0.313697i
$443$	−11.8539	+	6.84382i	−0.563193	+	0.325160i	−0.754426	−	0.656385i	$-0.772085\pi$
$443$	−11.8539	+	6.84382i	−0.563193	+	0.325160i	0.191233	+	0.981545i	$0.438751\pi$
$444$	−0.624131	−	5.93821i	−0.0296199	−	0.281815i
$445$	28.1372	+	16.4864i	1.33383	+	0.781530i
$446$	−0.346509	+	3.29681i	−0.0164077	+	0.156109i
$447$	−3.26502	+	4.49392i	−0.154430	+	0.212555i
$448$	14.4797	+	4.76225i	0.684100	+	0.224995i
$449$	19.8012			0.934476			0.467238	−	0.884132i	$-0.345249\pi$
$449$	19.8012			0.934476			0.467238	+	0.884132i	$0.345249\pi$
$450$	−0.652175	+	1.41569i	−0.0307438	+	0.0667362i
$451$	0.178909	−	0.309880i	0.00842451	−	0.0145917i
$452$	−26.1312	+	23.5286i	−1.22911	+	1.10669i
$453$	21.8968	+	2.30144i	1.02880	+	0.108131i
$454$	−3.44877	−	2.50568i	−0.161859	−	0.117597i
$455$	8.35362	−	18.2688i	0.391624	−	0.856453i
$456$	6.06255	−	4.40470i	0.283905	−	0.206269i
$457$	−7.36884	+	4.25440i	−0.344700	+	0.199013i	−0.662348	−	0.749196i	$-0.730440\pi$
$457$	−7.36884	+	4.25440i	−0.344700	+	0.199013i	0.317648	+	0.948209i	$0.397107\pi$
$458$	−2.84998	+	0.299545i	−0.133171	+	0.0139968i
$459$	−7.53312	−	1.60121i	−0.351616	−	0.0747382i
$460$	0.784922	−	7.03407i	0.0365972	−	0.327965i
$461$	12.9824	−	39.9557i	0.604651	−	1.86092i	0.105477	−	0.994422i	$-0.466363\pi$
$461$	12.9824	−	39.9557i	0.604651	−	1.86092i	0.499174	−	0.866502i	$-0.333637\pi$
$462$	−0.122941	+	0.568353i	−0.00571972	+	0.0264422i
$463$	−18.3017	+	5.94659i	−0.850553	+	0.276361i	−0.701678	−	0.712495i	$-0.747565\pi$
$463$	−18.3017	+	5.94659i	−0.850553	+	0.276361i	−0.148875	+	0.988856i	$0.547565\pi$
$464$	−34.3232	+	7.29561i	−1.59341	+	0.338690i
$465$	−18.4070	−	4.03599i	−0.853602	−	0.187165i
$466$	−3.08312	−	0.655337i	−0.142823	−	0.0303579i
$467$	−9.43054	+	21.1813i	−0.436393	+	0.980155i	0.552770	+	0.833334i	$0.313571\pi$
$467$	−9.43054	+	21.1813i	−0.436393	+	0.980155i	−0.989163	+	0.146821i	$0.953096\pi$
$468$			6.46103i			0.298661i
$469$	−1.00087	−	9.86299i	−0.0462158	−	0.455431i
$470$	−0.433320	+	0.588445i	−0.0199875	+	0.0271429i
$471$	−0.664832	+	6.32545i	−0.0306338	+	0.291462i
$472$	−0.984906	−	2.21214i	−0.0453340	−	0.101822i
$473$	−5.97399	+	5.37901i	−0.274684	+	0.247327i
$474$	1.53482	+	2.65839i	0.0704968	+	0.122104i
$475$	−9.89127	+	29.1648i	−0.453843	+	1.33817i
$476$	19.2653	+	33.6468i	0.883024	+	1.54220i
$477$	−6.67461	−	2.16871i	−0.305609	−	0.0992985i
$478$	−1.61528	−	0.169773i	−0.0738813	−	0.00776524i
$479$	−2.32369	+	1.03457i	−0.106172	+	0.0472709i	−0.459135	−	0.888366i	$-0.651841\pi$
$479$	−2.32369	+	1.03457i	−0.106172	+	0.0472709i	0.352963	+	0.935637i	$0.385174\pi$
$480$	−5.85187	+	5.20152i	−0.267100	+	0.237416i
$481$	−9.73370	−	4.33372i	−0.443818	−	0.197601i
$482$			4.29042i			0.195423i
$483$	−2.57410	−	3.56982i	−0.117126	−	0.162432i
$484$	−6.17576	−	19.0070i	−0.280716	−	0.863956i
$485$	−29.6664	+	6.10732i	−1.34708	+	0.277319i
$486$	−0.208593	−	0.231666i	−0.00946197	−	0.0105086i
$487$	−0.804674	+	3.78570i	−0.0364633	+	0.171546i	−0.992611	−	0.121338i	$-0.961282\pi$
$487$	−0.804674	+	3.78570i	−0.0364633	+	0.171546i	0.956148	+	0.292884i	$0.0946149\pi$
$488$	4.47382	+	4.02825i	0.202521	+	0.182350i
$489$	0.339274	−	1.04418i	0.0153425	−	0.0472194i
$490$	2.49692	−	4.19220i	0.112799	−	0.189384i
$491$	5.49148	+	16.9010i	0.247827	+	0.762734i	0.995159	+	0.0982822i	$0.0313348\pi$
$491$	5.49148	+	16.9010i	0.247827	+	0.762734i	−0.747331	+	0.664451i	$0.768665\pi$
$492$	0.392793	−	0.882227i	0.0177085	−	0.0397739i
$493$	−68.3047	−	39.4357i	−3.07629	−	1.77610i
$494$	−0.681488	−	6.48393i	−0.0306616	−	0.291726i
$495$	1.16479	+	1.06237i	0.0523533	+	0.0477502i
$496$	−23.3606	−	16.9725i	−1.04892	−	0.762087i
$497$	8.51649	−	11.6339i	0.382017	−	0.521852i
$498$	2.54656	+	0.827428i	0.114114	+	0.0370780i
$499$	12.5759	+	21.7822i	0.562976	+	0.975104i	0.997235	+	0.0743154i	$0.0236771\pi$
$499$	12.5759	+	21.7822i	0.562976	+	0.975104i	−0.434258	+	0.900788i	$0.642990\pi$
$500$	4.82242	−	20.7204i	0.215665	−	0.926644i
$501$	−5.43012	+	9.40524i	−0.242600	+	0.420195i
$502$	−1.45135	−	6.82805i	−0.0647768	−	0.304751i
$503$	23.4851	−	32.3244i	1.04715	−	1.44128i	0.155893	−	0.987774i	$-0.450175\pi$
$503$	23.4851	−	32.3244i	1.04715	−	1.44128i	0.891255	−	0.453502i	$-0.149825\pi$
$504$	−0.347961	+	3.20010i	−0.0154994	+	0.142544i
$505$	−1.30500	+	0.414793i	−0.0580719	+	0.0184581i
$506$	0.333995	+	0.148704i	0.0148479	+	0.00661071i
$507$	−1.27353	−	0.735274i	−0.0565595	−	0.0326547i
$508$	−12.3753	+	1.30070i	−0.549065	+	0.0577091i
$509$	−10.5186	+	11.6821i	−0.466230	+	0.517801i	−0.929703	−	0.368310i	$-0.879937\pi$
$509$	−10.5186	+	11.6821i	−0.466230	+	0.517801i	0.463473	+	0.886111i	$0.346603\pi$
$510$	−5.36828	−	0.0344069i	−0.237711	−	0.00152356i
$511$	−1.23044	−	1.37644i	−0.0544315	−	0.0608903i
$512$	−19.3393	+	6.28373i	−0.854686	+	0.277704i
$513$	−4.57724	−	4.12137i	−0.202090	−	0.181963i
$514$	6.20615	+	6.89263i	0.273742	+	0.304021i
$515$	17.6386	+	19.8439i	0.777248	+	0.874427i
$516$	−14.5174	+	16.1232i	−0.639094	+	0.709786i
$517$	0.434450	+	0.597969i	0.0191071	+	0.0262986i
$518$	−2.23670	−	1.30209i	−0.0982751	−	0.0572104i
$519$	8.57867	−	6.23277i	0.376562	−	0.273588i
$520$	1.86264	+	9.04781i	0.0816823	+	0.396773i
$521$	−0.134641	+	0.0599461i	−0.00589874	+	0.00262629i	−0.409684	−	0.912228i	$-0.634361\pi$
$521$	−0.134641	+	0.0599461i	−0.00589874	+	0.00262629i	0.403785	+	0.914854i	$0.367694\pi$
$522$	−1.29853	−	2.91654i	−0.0568351	−	0.127654i
$523$	6.33267	+	29.7929i	0.276908	+	1.30275i	0.868168	+	0.496270i	$0.165297\pi$
$523$	6.33267	+	29.7929i	0.276908	+	1.30275i	−0.591260	+	0.806481i	$0.701369\pi$
$524$	10.5889			0.462576
$525$	−6.42553	−	11.5634i	−0.280433	−	0.504669i
$526$	2.65481			0.115755
$527$	−13.4941	−	63.4846i	−0.587811	−	2.76543i
$528$	0.982555	+	2.20686i	0.0427602	+	0.0960410i
$529$	18.4837	−	8.22947i	0.803639	−	0.357803i
$530$	−4.86190	−	0.542533i	−0.211187	−	0.0235661i
$531$	−1.61017	+	1.16986i	−0.0698754	+	0.0507675i
$532$	−0.111284	+	31.0080i	−0.00482479	+	1.34437i
$533$	−1.01292	−	1.39417i	−0.0438745	−	0.0603880i
$534$	−3.04218	+	3.37868i	−0.131648	+	0.146210i
$535$	6.22647	+	1.36524i	0.269194	+	0.0590246i
$536$	3.05044	+	3.38786i	0.131759	+	0.146333i
$537$	−6.81275	−	6.13423i	−0.293992	−	0.264712i
$538$	3.00752	−	0.977203i	0.129663	−	0.0421302i
$539$	−3.27591	−	3.69121i	−0.141103	−	0.158992i
$540$	3.42613	+	2.52294i	0.147437	+	0.108570i
$541$	9.74633	−	10.8244i	0.419028	−	0.465377i	−0.496262	−	0.868173i	$-0.665295\pi$
$541$	9.74633	−	10.8244i	0.419028	−	0.465377i	0.915290	+	0.402795i	$0.131961\pi$
$542$	−5.52832	+	0.581049i	−0.237461	+	0.0249582i
$543$	−9.12957	−	5.27096i	−0.391787	−	0.226198i
$544$	−24.6347	−	10.9681i	−1.05620	−	0.470251i
$545$	1.85087	+	2.58214i	0.0792825	+	0.110607i
$546$	2.25976	+	1.65424i	0.0967090	+	0.0707949i
$547$	19.6748	−	27.0800i	0.841234	−	1.15786i	−0.144493	−	0.989506i	$-0.546155\pi$
$547$	19.6748	−	27.0800i	0.841234	−	1.15786i	0.985727	−	0.168353i	$-0.0538449\pi$
$548$	−7.54096	−	35.4774i	−0.322134	−	1.51552i
$549$	2.47405	−	4.28518i	0.105590	−	0.182887i
$550$	0.944578	+	0.561618i	0.0402770	+	0.0239475i
$551$	−31.5391	−	54.6274i	−1.34361	−	2.32721i
$552$	1.92480	+	0.625404i	0.0819248	+	0.0266190i
$553$	−25.8998	−	2.81619i	−1.10137	−	0.119757i
$554$	3.75103	+	2.72528i	0.159366	+	0.115786i
$555$	−6.09894	+	3.46930i	−0.258885	+	0.147263i
$556$	2.70815	+	25.7664i	0.114851	+	1.09274i
$557$	−15.3155	−	8.84240i	−0.648938	−	0.374664i	0.139111	−	0.990277i	$-0.455575\pi$
$557$	−15.3155	−	8.84240i	−0.648938	−	0.374664i	−0.788049	+	0.615612i	$0.788909\pi$
$558$	1.06855	−	2.40001i	0.0452354	−	0.101600i
$559$	11.9638	+	36.8207i	0.506013	+	1.55735i
$560$	−1.91720	−	20.1798i	−0.0810164	−	0.852751i
$561$	−1.67789	+	5.16401i	−0.0708405	+	0.218025i
$562$	4.28823	+	3.86114i	0.180888	+	0.162872i
$563$	−6.31352	+	29.7028i	−0.266083	+	1.25182i	0.618628	+	0.785684i	$0.287689\pi$
$563$	−6.31352	+	29.7028i	−0.266083	+	1.25182i	−0.884711	+	0.466140i	$0.845644\pi$
$564$	1.33481	+	1.48245i	0.0562056	+	0.0624226i
$565$	37.6403	+	17.0485i	1.58354	+	0.717234i
$566$	1.47854	+	4.55049i	0.0621478	+	0.191271i
$567$	2.63223	−	0.267111i	0.110543	−	0.0112176i
$568$			6.63015i			0.278195i
$569$	−8.18093	−	3.64238i	−0.342962	−	0.152697i	0.228026	−	0.973655i	$-0.426773\pi$
$569$	−8.18093	−	3.64238i	−0.342962	−	0.152697i	−0.570988	+	0.820959i	$0.693440\pi$
$570$	−3.70438	−	2.17050i	−0.155160	−	0.0909123i
$571$	−25.1421	+	11.1940i	−1.05216	+	0.468453i	−0.858606	−	0.512636i	$-0.828669\pi$
$571$	−25.1421	+	11.1940i	−1.05216	+	0.468453i	−0.193556	+	0.981089i	$0.562002\pi$
$572$	4.53030	+	0.476153i	0.189421	+	0.0199090i
$573$	−5.42663	−	1.76322i	−0.226701	−	0.0736595i
$574$	−0.207993	−	0.363260i	−0.00868148	−	0.0151622i
$575$	−7.94249	+	2.46857i	−0.331225	+	0.102947i
$576$	2.88060	+	4.98934i	0.120025	+	0.207889i
$577$	−11.2704	+	10.1479i	−0.469191	+	0.422462i	−0.869511	−	0.493914i	$-0.835566\pi$
$577$	−11.2704	+	10.1479i	−0.469191	+	0.422462i	0.400319	+	0.916376i	$0.368899\pi$
$578$	−5.36491	−	12.0498i	−0.223151	−	0.501205i
$579$	−0.980465	+	9.32850i	−0.0407467	+	0.387679i
$580$	25.3860	+	35.4159i	1.05409	+	1.47057i
$581$	−18.4329	+	13.2915i	−0.764726	+	0.551424i
$582$		−	4.22262i		−	0.175033i
$583$	−2.01253	+	4.52022i	−0.0833506	+	0.187209i
$584$	0.830443	+	0.176516i	0.0343640	+	0.00730429i
$585$	6.95582	−	3.04366i	0.287588	−	0.125840i
$586$	5.15082	−	1.09484i	0.212778	−	0.0452274i
$587$	31.5511	−	10.2516i	1.30225	−	0.423128i	0.425889	−	0.904776i	$-0.359962\pi$
$587$	31.5511	−	10.2516i	1.30225	−	0.423128i	0.876365	+	0.481648i	$0.159962\pi$
$588$	−9.83427	−	8.98346i	−0.405558	−	0.370472i
$589$	16.0401	−	49.3663i	0.660920	−	2.03410i
$590$	−0.934912	+	1.02504i	−0.0384897	+	0.0422001i
$591$	−5.76240	−	1.22484i	−0.237033	−	0.0503830i
$592$	−10.6928	+	1.12386i	−0.439471	+	0.0461903i
$593$	3.87536	−	2.23744i	0.159142	−	0.0918807i	−0.418314	−	0.908302i	$-0.637379\pi$
$593$	3.87536	−	2.23744i	0.159142	−	0.0918807i	0.577456	+	0.816422i	$0.304045\pi$
$594$	−0.177810	+	0.129187i	−0.00729564	+	0.00530060i
$595$	27.1480	−	36.5910i	1.11296	−	1.50008i
$596$	8.55112	+	6.21275i	0.350267	+	0.254484i
$597$	11.9170	+	1.25253i	0.487731	+	0.0512626i
$598$	1.30851	−	1.17819i	0.0535090	−	0.0481797i
$599$	14.7521	−	25.5514i	0.602755	−	1.04400i	−0.389648	−	0.920964i	$-0.627403\pi$
$599$	14.7521	−	25.5514i	0.602755	−	1.04400i	0.992402	−	0.123037i	$-0.0392635\pi$
$600$	5.52518	+	2.54532i	0.225564	+	0.103912i
$601$	11.3325			0.462261			0.231130	−	0.972923i	$-0.425758\pi$
$601$	11.3325			0.462261			0.231130	+	0.972923i	$0.425758\pi$
$602$	1.92220	+	9.20559i	0.0783432	+	0.375192i
$603$	2.20243	−	3.03139i	0.0896901	−	0.123448i
$604$	4.37923	−	41.6656i	0.178188	−	1.69535i
$605$	−17.5533	+	15.6025i	−0.713643	+	0.634333i
$606$	−0.0199549	−	0.189858i	−0.000810612	−	0.00771245i
$607$	−10.8587	+	6.26930i	−0.440743	+	0.254463i	−0.703913	−	0.710287i	$-0.748565\pi$
$607$	−10.8587	+	6.26930i	−0.440743	+	0.254463i	0.263170	+	0.964750i	$0.415232\pi$
$608$	−12.6764	−	17.4475i	−0.514095	−	0.707591i
$609$	26.4831	+	5.72857i	1.07315	+	0.232133i
$610$	1.08685	−	3.27344i	0.0440052	−	0.132538i
$611$	3.48192	−	0.740106i	0.140864	−	0.0299415i
$612$	−3.04682	+	14.3342i	−0.123160	+	0.579424i
$613$	−4.31409	+	20.2962i	−0.174245	+	0.819756i	0.801006	+	0.598656i	$0.204298\pi$
$613$	−4.31409	+	20.2962i	−0.174245	+	0.819756i	−0.975251	+	0.221101i	$0.929035\pi$
$614$	−3.96600	+	0.843000i	−0.160055	+	0.0340207i
$615$	−1.13482	−	0.00727342i	−0.0457605	−	0.000293293i
$616$	2.21818	+	0.479816i	0.0893731	+	0.0193323i
$617$	−11.9736	−	16.4803i	−0.482040	−	0.663471i	0.496856	−	0.867833i	$-0.334488\pi$
$617$	−11.9736	−	16.4803i	−0.482040	−	0.663471i	−0.978895	+	0.204363i	$0.934488\pi$
$618$	−3.20552	+	1.85071i	−0.128945	+	0.0744464i
$619$	2.21856	+	21.1081i	0.0891713	+	0.848408i	0.944099	+	0.329661i	$0.106935\pi$
$619$	2.21856	+	21.1081i	0.0891713	+	0.848408i	−0.854928	+	0.518747i	$0.826399\pi$
$620$	−7.67977	+	35.0251i	−0.308427	+	1.40664i
$621$	0.173878	−	1.65434i	0.00697750	−	0.0663865i
$622$	3.48000	−	4.78981i	0.139535	−	0.192054i
$623$	−7.88705	−	37.7717i	−0.315988	−	1.51329i
$624$	11.6342			0.465742
$625$	−24.5789	+	4.56924i	−0.983156	+	0.182770i
$626$	−2.20965	+	3.82722i	−0.0883153	+	0.152967i
$627$	−3.22711	+	2.90571i	−0.128878	+	0.116043i
$628$	12.0362	+	1.26506i	0.480297	+	0.0504812i
$629$	−19.5511	−	14.2047i	−0.779554	−	0.566379i
$630$	1.75961	−	0.552344i	0.0701045	−	0.0220059i
$631$	20.9804	−	15.2431i	0.835216	−	0.606820i	−0.0858140	−	0.996311i	$-0.527349\pi$
$631$	20.9804	−	15.2431i	0.835216	−	0.606820i	0.921030	+	0.389491i	$0.127349\pi$
$632$	10.3752	−	5.99014i	0.412704	−	0.238275i
$633$	21.2862	−	2.23727i	0.846051	−	0.0889236i
$634$	7.29169	+	1.54990i	0.289590	+	0.0615543i
$635$	7.23006	+	12.7103i	0.286916	+	0.504391i
$636$	−4.12667	+	12.7006i	−0.163633	+	0.503611i
$637$	−22.6574	+	7.18244i	−0.897717	+	0.284579i
$638$	−2.14070	+	0.695554i	−0.0847510	+	0.0275373i
$639$	5.33040	−	1.13301i	0.210867	−	0.0448213i
$640$	13.0711	+	14.7053i	0.516679	+	0.581279i
$641$	14.3384	+	3.04773i	0.566334	+	0.120378i	0.482176	−	0.876074i	$-0.339847\pi$
$641$	14.3384	+	3.04773i	0.566334	+	0.120378i	0.0841579	+	0.996452i	$0.473180\pi$
$642$	−0.361456	+	0.811843i	−0.0142655	+	0.0320409i
$643$			3.60045i			0.141988i	0.997477	+	0.0709940i	$0.0226171\pi$
$643$			3.60045i			0.141988i	−0.997477	+	0.0709940i	$0.977383\pi$
$644$	−6.79272	+	4.89805i	−0.267670	+	0.193010i
$645$	24.1968	+	8.03383i	0.952748	+	0.316332i
$646$	1.54570	−	14.7063i	0.0608146	−	0.578612i
$647$	2.94385	+	6.61200i	0.115735	+	0.259944i	0.962120	−	0.272627i	$-0.0878925\pi$
$647$	2.94385	+	6.61200i	0.115735	+	0.259944i	−0.846385	+	0.532571i	$0.821226\pi$
$648$	−0.904151	+	0.814101i	−0.0355184	+	0.0319809i
$649$	0.701608	+	1.21522i	0.0275405	+	0.0477016i
$650$	4.32127	−	3.05573i	0.169494	−	0.119856i
$651$	11.0790	+	19.3495i	0.434221	+	0.758366i
$652$	−1.98689	−	0.645578i	−0.0778124	−	0.0252828i
$653$	−28.9431	−	3.04204i	−1.13263	−	0.119044i	−0.480389	−	0.877055i	$-0.659505\pi$
$653$	−28.9431	−	3.04204i	−1.13263	−	0.119044i	−0.652242	+	0.758011i	$0.726171\pi$
$654$	−0.404621	+	0.180149i	−0.0158219	+	0.00704438i
$655$	−4.98819	−	11.3997i	−0.194905	−	0.445425i
$656$	−1.58860	−	0.707292i	−0.0620246	−	0.0276151i
$657$		−	0.697811i		−	0.0272242i
$658$	0.860248	−	0.0872954i	0.0335360	−	0.00340313i
$659$	3.62472	+	11.1557i	0.141199	+	0.434566i	0.996503	−	0.0835610i	$-0.0266293\pi$
$659$	3.62472	+	11.1557i	0.141199	+	0.434566i	−0.855304	+	0.518127i	$0.826629\pi$
$660$	2.02151	−	2.21638i	0.0786871	−	0.0862724i
$661$	11.7455	+	13.0447i	0.456848	+	0.507381i	0.926926	−	0.375244i	$-0.122441\pi$
$661$	11.7455	+	13.0447i	0.456848	+	0.507381i	−0.470078	+	0.882625i	$0.655774\pi$
$662$	−1.98894	+	9.35724i	−0.0773024	+	0.363679i
$663$	19.4334	+	17.4979i	0.754729	+	0.679561i
$664$	3.22930	−	9.93878i	0.125321	−	0.385699i
$665$	33.4350	−	14.4875i	1.29656	−	0.561799i
$666$	−0.302284	−	0.930333i	−0.0117133	−	0.0360497i
$667$	6.92905	−	15.5629i	0.268294	−	0.602598i
$668$	17.8965	+	10.3325i	0.692436	+	0.399778i
$669$	−1.11154	−	10.5756i	−0.0429747	−	0.408876i
$670$	1.07763	−	2.37924i	0.0416325	−	0.0919181i
$671$	−2.82232	−	2.05053i	−0.108954	−	0.0791600i
$672$	9.20964	+	1.00140i	0.355270	+	0.0386299i
$673$	−31.1919	−	10.1349i	−1.20236	−	0.390670i	−0.361730	−	0.932283i	$-0.617814\pi$
$673$	−31.1919	−	10.1349i	−1.20236	−	0.390670i	−0.840628	+	0.541613i	$0.817814\pi$
$674$	−0.685397	−	1.18714i	−0.0264005	−	0.0457270i
$675$	1.10216	−	4.87701i	0.0424223	−	0.187716i
$676$	−1.39909	+	2.42330i	−0.0538113	+	0.0932039i
$677$	0.122196	+	0.574889i	0.00469639	+	0.0220948i	0.980433	−	0.196851i	$-0.0630715\pi$
$677$	0.122196	+	0.574889i	0.00469639	+	0.0220948i	−0.975737	+	0.218946i	$0.929738\pi$
$678$	−3.38607	+	4.66053i	−0.130041	+	0.178986i
$679$	28.9176	+	21.1689i	1.10976	+	0.812387i
$680$	−0.134284	+	20.9514i	−0.00514955	+	0.803451i
$681$	12.4924	+	5.56199i	0.478711	+	0.213136i
$682$	−1.60407	−	0.926111i	−0.0614230	−	0.0354626i
$683$	1.73644	−	0.182507i	0.0664430	−	0.00698344i	−0.0712486	−	0.997459i	$-0.522698\pi$
$683$	1.73644	−	0.182507i	0.0664430	−	0.00698344i	0.137692	+	0.990475i	$0.456032\pi$
$684$	−7.84222	+	8.70967i	−0.299855	+	0.333022i
$685$	−34.6419	+	24.8311i	−1.32360	+	0.948749i
$686$	−5.65989	+	1.13950i	−0.216096	+	0.0435063i
$687$	8.74269	−	2.84067i	0.333555	−	0.108378i
$688$	29.0327	+	26.1412i	1.10686	+	0.996623i
$689$	15.9454	+	17.7091i	0.607470	+	0.674664i
$690$	−0.113811	−	1.15394i	−0.00433272	−	0.0439297i
$691$	−14.2490	+	15.8252i	−0.542059	+	0.602017i	−0.950484	−	0.310775i	$-0.899412\pi$
$691$	−14.2490	+	15.8252i	−0.542059	+	0.602017i	0.408425	+	0.912792i	$0.366078\pi$
$692$	−11.8598	−	16.3237i	−0.450843	−	0.620532i
$693$	0.00669448	−	1.86533i	0.000254302	−	0.0708582i
$694$	−1.91896	+	1.39420i	−0.0728426	+	0.0529232i
$695$	26.4638	−	15.0535i	1.00383	−	0.571014i
$696$	−11.3827	+	5.06793i	−0.431462	+	0.192099i
$697$	−1.58978	−	3.57070i	−0.0602171	−	0.135250i
$698$	0.0118155	+	0.0555874i	0.000447222	+	0.00210401i
$699$	10.1111			0.382435
$700$	−22.0031	+	12.2266i	−0.831639	+	0.462123i
$701$	38.9399			1.47074			0.735370	−	0.677665i	$-0.237008\pi$
$701$	38.9399			1.47074			0.735370	+	0.677665i	$0.237008\pi$
$702$	0.220076	+	1.03537i	0.00830622	+	0.0390777i
$703$	−7.86117	−	17.6565i	−0.296490	−	0.665927i
$704$	3.71068	−	1.65210i	0.139851	−	0.0622659i
$705$	0.967180	−	2.13538i	0.0364261	−	0.0804231i
$706$	1.67413	−	1.21633i	0.0630069	−	0.0457772i
$707$	1.40024	+	0.815142i	0.0526613	+	0.0306566i
$708$	2.22603	+	3.06386i	0.0836592	+	0.115147i
$709$	−17.7070	+	19.6657i	−0.665002	+	0.738560i	−0.977402	−	0.211391i	$-0.932201\pi$
$709$	−17.7070	+	19.6657i	−0.665002	+	0.738560i	0.312399	+	0.949951i	$0.398867\pi$
$710$	3.48007	−	1.52278i	0.130605	−	0.0571488i
$711$	−6.58886	−	7.31767i	−0.247102	−	0.274434i
$712$	13.1864	+	11.8731i	0.494181	+	0.444962i
$713$	13.3325	−	4.33199i	0.499305	−	0.162234i
$714$	4.23333	+	4.73565i	0.158428	+	0.177227i
$715$	−1.62151	−	5.10153i	−0.0606412	−	0.190786i
$716$	−11.6723	+	12.9634i	−0.436216	+	0.484466i
$717$	5.18155	−	0.544603i	0.193509	−	0.0203386i
$718$	0.422849	+	0.244132i	0.0157806	+	0.00911092i
$719$	−6.04565	−	2.69170i	−0.225465	−	0.100383i	0.290896	−	0.956755i	$-0.406047\pi$
$719$	−6.04565	−	2.69170i	−0.225465	−	0.100383i	−0.516360	+	0.856371i	$0.672713\pi$
$720$	4.54300	−	6.16936i	0.169308	−	0.229918i
$721$	3.39579	−	31.2302i	0.126466	−	1.16308i
$722$	3.46988	−	4.77588i	0.129136	−	0.177740i
$723$	−2.86147	−	13.4622i	−0.106419	−	0.500663i
$724$	−10.0297	+	17.3719i	−0.372750	+	0.645622i
$725$	26.1692	−	44.0137i	0.971901	−	1.63463i
$726$	−1.63708	−	2.83550i	−0.0607576	−	0.105235i
$727$	−30.2004	−	9.81270i	−1.12007	−	0.363933i	−0.310276	−	0.950647i	$-0.600421\pi$
$727$	−30.2004	−	9.81270i	−1.12007	−	0.363933i	−0.809794	+	0.586714i	$0.800421\pi$
$728$	6.45620	−	8.81945i	0.239283	−	0.326871i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.0980810	−	0.476430i	−0.00363014	−	0.0176334i
$731$	9.17880	+	87.3304i	0.339490	+	3.23003i
$732$	−8.15392	−	4.70767i	−0.301377	−	0.174000i
$733$	21.4927	−	48.2734i	0.793851	−	1.78302i	0.197484	−	0.980306i	$-0.436723\pi$
$733$	21.4927	−	48.2734i	0.793851	−	1.78302i	0.596367	−	0.802712i	$-0.296610\pi$
$734$	−0.774815	−	2.38464i	−0.0285989	−	0.0880185i
$735$	−5.03869	+	14.8193i	−0.185855	+	0.546618i
$736$	1.79986	−	5.53941i	0.0663438	−	0.204185i
$737$	−1.96322	−	1.76769i	−0.0723160	−	0.0651136i
$738$	0.0328943	−	0.154755i	0.00121085	−	0.00569662i
$739$	3.29370	+	3.65803i	0.121161	+	0.134563i	0.800673	−	0.599101i	$-0.204475\pi$
$739$	3.29370	+	3.65803i	0.121161	+	0.134563i	−0.679512	+	0.733664i	$0.737809\pi$
$740$	6.60144	+	11.6052i	0.242674	+	0.426615i
$741$	6.46275	+	19.8903i	0.237415	+	0.730688i
$742$	3.38550	+	4.69508i	0.124286	+	0.172362i
$743$		−	15.5814i		−	0.571628i	−0.958285	−	0.285814i	$-0.907736\pi$
$743$		−	15.5814i		−	0.571628i	0.958285	−	0.285814i	$-0.0922639\pi$
$744$	−9.36680	−	4.17037i	−0.343404	−	0.152893i
$745$	2.66026	−	12.1327i	0.0974645	−	0.444506i
$746$	7.23660	−	3.22194i	0.264951	−	0.117964i
$747$	−8.54227	−	0.897829i	−0.312545	−	0.0328499i
$748$	9.82618	+	3.19272i	0.359281	+	0.116737i
$749$	−3.74767	−	6.54529i	−0.136937	−	0.239160i
$750$	0.0670105	−	3.48469i	0.00244688	−	0.127243i
$751$	−5.38641	−	9.32954i	−0.196553	−	0.340440i	0.750856	−	0.660466i	$-0.229641\pi$
$751$	−5.38641	−	9.32954i	−0.196553	−	0.340440i	−0.947408	+	0.320027i	$0.896308\pi$
$752$	2.66942	−	2.40356i	0.0973438	−	0.0876487i
$753$	9.10787	+	20.4566i	0.331909	+	0.745480i
$754$	−1.13312	+	10.7810i	−0.0412659	+	0.392619i
$755$	−46.9193	+	14.9132i	−1.70757	+	0.542748i
$756$	−0.508265	−	5.00867i	−0.0184854	−	0.182163i
$757$			12.7805i			0.464516i	0.972654	+	0.232258i	$0.0746113\pi$
$757$			12.7805i			0.464516i	−0.972654	+	0.232258i	$0.925389\pi$
$758$	−0.786779	+	1.76713i	−0.0285771	+	0.0641852i
$759$	−1.14716	−	0.243837i	−0.0416394	−	0.00885073i
$760$	−8.47108	+	14.4575i	−0.307278	+	0.524430i
$761$	8.29761	−	1.76371i	0.300788	−	0.0639345i	−0.0550454	−	0.998484i	$-0.517530\pi$
$761$	8.29761	−	1.76371i	0.300788	−	0.0639345i	0.355833	+	0.934549i	$0.384197\pi$
$762$	−1.93883	+	0.629963i	−0.0702363	+	0.0228212i
$763$	0.794742	−	3.67408i	0.0287716	−	0.133011i
$764$	−3.35509	+	10.3259i	−0.121383	+	0.373578i
$765$	16.8672	−	3.47239i	0.609833	−	0.125544i
$766$	0.218401	+	0.0464226i	0.00789115	+	0.00167731i
$767$	6.72098	−	0.706404i	0.242681	−	0.0255068i
$768$	7.60324	−	4.38973i	0.274358	−	0.158401i
$769$	4.03113	−	2.92878i	0.145366	−	0.105615i	−0.512725	−	0.858553i	$-0.671364\pi$
$769$	4.03113	−	2.92878i	0.145366	−	0.105615i	0.658091	+	0.752938i	$0.271364\pi$
$770$	−0.257612	−	1.27449i	−0.00928368	−	0.0459296i
$771$	−24.0702	−	17.4880i	−0.866868	−	0.629817i
$772$	17.7505	+	1.86565i	0.638853	+	0.0671462i
$773$	15.8164	−	14.2411i	0.568876	−	0.512218i	−0.333740	−	0.942665i	$-0.608311\pi$
$773$	15.8164	−	14.2411i	0.568876	−	0.512218i	0.902616	+	0.430447i	$0.141644\pi$
$774$	−1.77721	+	3.07823i	−0.0638807	+	0.110645i
$775$	41.3251	−	8.23174i	1.48444	−	0.295693i
$776$	−16.4801			−0.591601
$777$	7.88659	+	2.59384i	0.282930	+	0.0930534i
$778$	2.36673	−	3.25753i	0.0848515	−	0.116788i
$779$	0.326751	−	3.10883i	0.0117071	−	0.111385i
$780$	−5.79154	−	13.2357i	−0.207370	−	0.473913i
$781$	−0.401606	−	3.82103i	−0.0143706	−	0.136727i
$782$	3.45860	−	1.99683i	0.123679	−	0.0714063i
$783$	6.01961	+	8.28528i	0.215123	+	0.296092i
$784$	−16.1763	+	17.7083i	−0.577725	+	0.632440i
$785$	−4.30808	−	13.5539i	−0.153762	−	0.483758i
$786$	1.69685	−	0.360678i	0.0605248	−	0.0128649i
$787$	−1.31726	+	6.19723i	−0.0469553	+	0.220907i	−0.995369	−	0.0961282i	$-0.969354\pi$
$787$	−1.31726	+	6.19723i	−0.0469553	+	0.220907i	0.948414	+	0.317036i	$0.102687\pi$
$788$	−2.33064	+	10.9648i	−0.0830257	+	0.390605i
$789$	−8.33007	+	1.77061i	−0.296558	+	0.0630354i
$790$	−5.52707	−	4.07003i	−0.196644	−	0.144805i
$791$	−14.9415	−	46.5529i	−0.531257	−	1.65523i
$792$	0.504193	+	0.693962i	0.0179157	+	0.0246588i
$793$	−14.5503	+	8.40064i	−0.516698	+	0.298315i
$794$	−0.745470	−	7.09267i	−0.0264557	−	0.251709i
$795$	15.6172	−	1.54030i	0.553884	−	0.0546287i
$796$	2.38334	−	22.6759i	0.0844751	−	0.803727i
$797$	−17.5157	+	24.1083i	−0.620437	+	0.853959i	−0.997385	−	0.0722759i	$-0.976974\pi$
$797$	−17.5157	+	24.1083i	−0.620437	+	0.853959i	0.376947	+	0.926235i	$0.376974\pi$
$798$	1.03836	+	4.97280i	0.0367576	+	0.176035i
$799$	8.07385			0.285632
$800$	7.32523	−	15.9010i	0.258986	−	0.562186i
$801$	7.29214	−	12.6304i	0.257655	−	0.446272i
$802$	6.90472	−	6.21704i	0.243814	−	0.219531i
$803$	−0.489286	−	0.0514260i	−0.0172665	−	0.00181478i
$804$	−5.76819	−	4.19084i	−0.203428	−	0.147799i
$805$	8.47305	+	5.00553i	0.298636	+	0.176422i
$806$	−7.21680	+	5.24331i	−0.254201	+	0.184688i
$807$	−8.78505	+	5.07205i	−0.309248	+	0.178545i
$808$	−0.740981	+	0.0778803i	−0.0260676	+	0.00273982i
$809$	−34.0586	−	7.23938i	−1.19744	−	0.254523i	−0.434305	−	0.900766i	$-0.643006\pi$
$809$	−34.0586	−	7.23938i	−1.19744	−	0.254523i	−0.763132	+	0.646243i	$0.776339\pi$
$810$	0.634971	+	0.287598i	0.0223106	+	0.0101052i
$811$	−3.62658	+	11.1615i	−0.127346	+	0.391932i	−0.994321	−	0.106420i	$-0.966061\pi$
$811$	−3.62658	+	11.1615i	−0.127346	+	0.391932i	0.866975	+	0.498352i	$0.166061\pi$
$812$	10.9004	−	50.3926i	0.382530	−	1.76843i
$813$	16.9588	−	5.51026i	0.594772	−	0.193253i
$814$	−0.674601	+	0.143391i	−0.0236448	+	0.00502585i
$815$	0.240965	+	2.44316i	0.00844064	+	0.0855801i
$816$	25.8112	+	5.48634i	0.903572	+	0.192060i
$817$	−28.5644	+	64.1566i	−0.999341	+	2.24456i
$818$		−	4.05250i		−	0.141692i
$819$	−8.19382	−	3.68341i	−0.286315	−	0.128709i
$820$	−0.0138400	+	2.15937i	−0.000483314	+	0.0754083i
$821$	1.60977	−	15.3160i	0.0561815	−	0.534531i	−0.929846	−	0.367949i	$-0.880060\pi$
$821$	1.60977	−	15.3160i	0.0561815	−	0.534531i	0.986028	−	0.166583i	$-0.0532732\pi$
$822$	−2.41687	−	5.42837i	−0.0842979	−	0.189336i
$823$	23.3865	−	21.0573i	0.815201	−	0.734010i	−0.151902	−	0.988396i	$-0.548540\pi$
$823$	23.3865	−	21.0573i	0.815201	−	0.734010i	0.967103	+	0.254385i	$0.0818731\pi$
$824$	7.22298	+	12.5106i	0.251624	+	0.435826i
$825$	−3.33840	−	1.13222i	−0.116228	−	0.0394189i
$826$	1.64153	+	0.00589128i	0.0571162	+	0.000204984i
$827$	−37.0513	−	12.0387i	−1.28840	−	0.418627i	−0.416869	−	0.908966i	$-0.636873\pi$
$827$	−37.0513	−	12.0387i	−1.28840	−	0.418627i	−0.871531	+	0.490340i	$0.836873\pi$
$828$	−3.14791	−	0.330859i	−0.109398	−	0.0114982i
$829$	−11.4453	+	5.09577i	−0.397511	+	0.176983i	−0.595749	−	0.803170i	$-0.703145\pi$
$829$	−11.4453	+	5.09577i	−0.397511	+	0.176983i	0.198238	+	0.980154i	$0.436478\pi$
$830$	−5.95842	+	0.587670i	−0.206820	+	0.0203983i
$831$	−13.5873	−	6.04947i	−0.471339	−	0.209854i
$832$		−	19.5622i		−	0.678196i
$833$	−53.6536	+	5.25014i	−1.85899	+	0.181907i
$834$	1.31163	+	4.03679i	0.0454181	+	0.139783i
$835$	2.69313	−	24.1344i	0.0931996	−	0.835207i
$836$	5.52903	+	6.14062i	0.191226	+	0.212378i
$837$	−1.75216	+	8.24324i	−0.0605633	+	0.284928i
$838$	−7.94950	−	7.15776i	−0.274611	−	0.247261i
$839$	0.398535	−	1.22656i	0.0137589	−	0.0423457i	−0.943941	−	0.330113i	$-0.892913\pi$
$839$	0.398535	−	1.22656i	0.0137589	−	0.0423457i	0.957700	+	0.287768i	$0.0929131\pi$
$840$	−2.15570	−	6.86744i	−0.0743787	−	0.236949i
$841$	23.4487	+	72.1676i	0.808575	+	2.48854i
$842$	2.55814	−	5.74568i	0.0881593	−	0.198009i
$843$	−16.0305	−	9.25519i	−0.552118	−	0.318766i
$844$	−4.25713	−	40.5038i	−0.146536	−	1.39420i
$845$	3.26796	+	0.364668i	0.112421	+	0.0125449i
$846$	0.264397	+	0.192096i	0.00909017	+	0.00660439i
$847$	27.6253	+	3.00381i	0.949217	+	0.103212i
$848$	22.8696	+	7.43079i	0.785346	+	0.255174i
$849$	−7.67419	−	13.2921i	−0.263378	−	0.456183i
$850$	11.0280	−	4.74153i	0.378256	−	0.162633i
$851$	2.60990	−	4.52048i	0.0894663	−	0.154960i
$852$	−2.15592	−	10.1428i	−0.0738605	−	0.347486i
$853$	−15.6754	+	21.5754i	−0.536717	+	0.738727i	−0.988135	−	0.153585i	$-0.950918\pi$
$853$	−15.6754	+	21.5754i	−0.536717	+	0.738727i	0.451419	+	0.892312i	$0.350918\pi$
$854$	−3.73419	+	1.64654i	−0.127781	+	0.0563433i
$855$	13.0710	+	4.33983i	0.447017	+	0.148419i
$856$	3.16848	+	1.41070i	0.108296	+	0.0482166i
$857$	15.1126	+	8.72525i	0.516236	+	0.298049i	0.735393	−	0.677641i	$-0.236997\pi$
$857$	15.1126	+	8.72525i	0.516236	+	0.298049i	−0.219157	+	0.975690i	$0.570331\pi$
$858$	0.742195	−	0.0780078i	0.0253381	−	0.00266314i
$859$	24.9503	−	27.7102i	0.851295	−	0.945458i	−0.147756	−	0.989024i	$-0.547205\pi$
$859$	24.9503	−	27.7102i	0.851295	−	0.945458i	0.999051	+	0.0435654i	$0.0138717\pi$
$860$	15.2869	−	46.0421i	0.521280	−	1.57002i
$861$	0.894901	+	1.00109i	0.0304981	+	0.0341171i
$862$	−0.0536174	+	0.0174213i	−0.00182621	+	0.000593373i
$863$	13.0183	+	11.7217i	0.443147	+	0.399011i	0.860270	−	0.509839i	$-0.170295\pi$
$863$	13.0183	+	11.7217i	0.443147	+	0.399011i	−0.417123	+	0.908850i	$0.636962\pi$
$864$	2.34292	+	2.60207i	0.0797077	+	0.0885243i
$865$	−11.9868	+	20.4578i	−0.407563	+	0.695586i
$866$	−1.45749	+	1.61870i	−0.0495274	+	0.0550058i
$867$	24.8702	+	34.2309i	0.844636	+	1.16254i
$868$	36.8186	−	21.0814i	1.24970	−	0.715549i
$869$	−5.61652	+	4.08064i	−0.190528	+	0.138426i
$870$	5.27442	+	4.81067i	0.178819	+	0.163097i
$871$	−11.6230	+	5.17490i	−0.393831	+	0.175345i
$872$	0.703088	+	1.57916i	0.0238096	+	0.0534772i
$873$	2.81625	+	13.2494i	0.0953157	+	0.448425i
$874$	3.19397			0.108038
$875$	23.5281	+	17.9284i	0.795396	+	0.606090i
$876$	−1.32781			−0.0448625
$877$	−10.1854	−	47.9186i	−0.343937	−	1.61810i	−0.721709	−	0.692197i	$-0.756643\pi$
$877$	−10.1854	−	47.9186i	−0.343937	−	1.61810i	0.377772	−	0.925899i	$-0.376690\pi$
$878$	4.28368	+	9.62129i	0.144567	+	0.324703i
$879$	−15.4317	+	6.87062i	−0.520497	+	0.231740i
$880$	−3.99098	−	3.64008i	−0.134536	−	0.122707i
$881$	−9.21077	+	6.69202i	−0.310319	+	0.225460i	−0.732033	−	0.681269i	$-0.761428\pi$
$881$	−9.21077	+	6.69202i	−0.310319	+	0.225460i	0.421714	+	0.906729i	$0.361428\pi$
$882$	−1.88193	−	1.10462i	−0.0633678	−	0.0371944i
$883$	30.9772	+	42.6365i	1.04247	+	1.43483i	0.895162	+	0.445741i	$0.147060\pi$
$883$	30.9772	+	42.6365i	1.04247	+	1.43483i	0.147304	+	0.989091i	$0.452940\pi$
$884$	33.2953	−	36.9782i	1.11984	−	1.24371i
$885$	2.24986	−	3.83982i	0.0756281	−	0.129074i
$886$	2.85515	+	3.17096i	0.0959206	+	0.106531i
$887$	23.7863	+	21.4172i	0.798665	+	0.719121i	0.963648	−	0.267176i	$-0.0860904\pi$
$887$	23.7863	+	21.4172i	0.798665	+	0.719121i	−0.164983	+	0.986296i	$0.552757\pi$
$888$	−3.63092	+	1.17976i	−0.121846	+	0.0395901i
$889$	5.40559	−	16.4358i	0.181298	−	0.551237i
$890$	3.20343	−	9.64830i	0.107379	−	0.323412i
$891$	0.471760	−	0.523943i	0.0158046	−	0.0175527i
$892$	−20.1235	+	2.11506i	−0.673784	+	0.0708175i
$893$	5.59206	+	3.22857i	0.187131	+	0.108040i
$894$	1.58193	+	0.704320i	0.0529076	+	0.0235560i
$895$	19.4548	+	6.45938i	0.650301	+	0.215913i
$896$	2.51645	−	23.1432i	0.0840688	−	0.773159i
$897$	−3.31997	+	4.56954i	−0.110851	+	0.152573i
$898$	−1.28339	−	6.03788i	−0.0428273	−	0.201487i
$899$	−43.1532	+	74.7436i	−1.43924	+	2.49284i
$900$	−9.28007	−	2.09722i	−0.309336	−	0.0699072i
$901$	27.0246	+	46.8080i	0.900321	+	1.55940i
$902$	−0.106086	−	0.0344694i	−0.00353228	−	0.00114771i
$903$	−12.1710	−	27.6026i	−0.405025	−	0.918558i
$904$	18.1892	+	13.2152i	0.604964	+	0.439532i
$905$	23.4270	+	2.61419i	0.778741	+	0.0868987i
$906$	−0.717445	−	6.82604i	−0.0238355	−	0.226780i
$907$	−3.14646	−	1.81661i	−0.104477	−	0.0603196i	0.446851	−	0.894608i	$-0.352545\pi$
$907$	−3.14646	−	1.81661i	−0.104477	−	0.0603196i	−0.551328	+	0.834289i	$0.685879\pi$
$908$	10.5835	−	23.7709i	0.351225	−	0.788864i
$909$	0.189238	+	0.582414i	0.00627662	+	0.0193175i
$910$	−6.11204	−	1.36316i	−0.202612	−	0.0451884i
$911$	5.10748	−	15.7192i	0.169219	−	0.520801i	−0.830104	−	0.557609i	$-0.811719\pi$
$911$	5.10748	−	15.7192i	0.169219	−	0.520801i	0.999322	+	0.0368078i	$0.0117189\pi$
$912$	15.6833	+	14.1213i	0.519326	+	0.467603i
$913$	−1.25907	+	5.92344i	−0.0416690	+	0.196037i
$914$	1.77488	+	1.97120i	0.0587077	+	0.0652016i
$915$	−1.22703	+	10.9960i	−0.0405644	+	0.363517i
$916$	−5.40529	−	16.6358i	−0.178596	−	0.549661i
$917$	−6.03667	+	13.4287i	−0.199348	+	0.443454i
$918$			2.40082i			0.0792388i
$919$	16.7502	+	7.45766i	0.552537	+	0.246005i	0.663961	−	0.747768i	$-0.268874\pi$
$919$	16.7502	+	7.45766i	0.552537	+	0.246005i	−0.111423	+	0.993773i	$0.535541\pi$
$920$	−4.50362	+	0.444185i	−0.148480	+	0.0146443i
$921$	11.8820	−	5.29021i	0.391525	−	0.174318i
$922$	−13.0249	−	1.36898i	−0.428954	−	0.0450849i
$923$	−17.5981	−	5.71798i	−0.579249	−	0.188209i
$924$	−3.54939	−	0.0127384i	−0.116766	−	0.000419062i
$925$	9.38409	−	12.5739i	0.308547	−	0.413429i
$926$	2.99947	+	5.19523i	0.0985687	+	0.170726i
$927$	8.82373	−	7.94492i	0.289809	−	0.260945i
$928$	14.5851	+	32.7586i	0.478779	+	1.07535i
$929$	3.07661	−	29.2720i	0.100940	−	0.960383i	−0.820443	−	0.571728i	$-0.806273\pi$
$929$	3.07661	−	29.2720i	0.100940	−	0.960383i	0.921383	−	0.388655i	$-0.127060\pi$
$930$	−0.0376503	+	5.87433i	−0.00123460	+	0.192627i
$931$	−39.2606	−	17.8187i	−1.28672	−	0.583985i
$932$		−	19.2395i		−	0.630212i
$933$	−7.72477	+	17.3501i	−0.252897	+	0.568017i
$934$	7.06995	+	1.50276i	0.231336	+	0.0491720i
$935$	−1.19170	−	12.0827i	−0.0389727	−	0.395146i
$936$	4.04088	−	0.858916i	0.132080	−	0.0280745i
$937$	43.8477	−	14.2470i	1.43244	−	0.465428i	0.512909	−	0.858443i	$-0.328568\pi$
$937$	43.8477	−	14.2470i	1.43244	−	0.465428i	0.919532	+	0.393015i	$0.128568\pi$
$938$	−2.94260	+	0.944448i	−0.0960795	+	0.0308373i
$939$	4.38073	−	13.4825i	0.142960	−	0.439985i
$940$	−4.06325	−	1.84037i	−0.132529	−	0.0600262i
$941$	−58.6890	−	12.4747i	−1.91321	−	0.406665i	−0.913208	−	0.407495i	$-0.866403\pi$
$941$	−58.6890	−	12.4747i	−1.91321	−	0.406665i	−1.00000		0.000829863i	$0.999736\pi$
$942$	1.97188	−	0.207253i	0.0642474	−	0.00675267i
$943$	0.731129	−	0.422118i	0.0238088	−	0.0137460i
$944$	5.51703	−	4.00836i	0.179564	−	0.130461i
$945$	−5.15279	+	2.90667i	−0.167620	+	0.0945539i
$946$	2.02739	+	1.47299i	0.0659162	+	0.0478909i
$947$	9.30975	+	0.978494i	0.302526	+	0.0317968i	0.254575	−	0.967053i	$-0.418064\pi$
$947$	9.30975	+	0.978494i	0.302526	+	0.0317968i	0.0479508	+	0.998850i	$0.484731\pi$
$948$	−13.9242	+	12.5374i	−0.452237	+	0.407196i
$949$	−1.18471	+	2.05198i	−0.0384573	+	0.0666101i
$950$	9.53416	+	1.12582i	0.309329	+	0.0365263i
$951$	−23.9130			−0.775434
$952$	18.4824	−	16.5219i	0.599018	−	0.535478i
$953$	9.96619	−	13.7173i	0.322836	−	0.444346i	−0.616494	−	0.787360i	$-0.711448\pi$
$953$	9.96619	−	13.7173i	0.322836	−	0.444346i	0.939331	+	0.343013i	$0.111448\pi$
$954$	−0.228688	+	2.17582i	−0.00740404	+	0.0704447i
$955$	12.6972	−	1.25230i	0.410871	−	0.0405235i
$956$	−1.03628	−	9.85956i	−0.0335157	−	0.318881i
$957$	6.25303	−	3.61019i	0.202132	−	0.116701i
$958$	0.466075	+	0.641497i	0.0150582	+	0.0207258i
$959$	49.2912	+	10.6622i	1.59170	+	0.344300i
$960$	−10.3734	−	7.63874i	−0.334799	−	0.246539i
$961$	−39.1465	+	8.32085i	−1.26279	+	0.268415i
$962$	−0.690582	+	3.24894i	−0.0222653	+	0.104750i
$963$	0.592696	−	2.78842i	0.0190994	−	0.0898554i
$964$	−25.6161	+	5.44486i	−0.825038	+	0.175367i
$965$	−6.35336	−	19.9887i	−0.204522	−	0.643458i
$966$	−0.921689	+	1.01628i	−0.0296549	+	0.0326983i
$967$	4.32930	+	5.95877i	0.139221	+	0.191621i	0.872934	−	0.487838i	$-0.162214\pi$
$967$	4.32930	+	5.95877i	0.139221	+	0.191621i	−0.733713	+	0.679459i	$0.762214\pi$
$968$	−11.0665	+	6.38922i	−0.355689	+	0.205357i
$969$	4.95833	+	47.1753i	0.159284	+	1.51549i
$970$	3.78507	+	8.65019i	0.121531	+	0.277741i
$971$	3.64939	−	34.7216i	0.117115	−	1.11427i	−0.765259	−	0.643722i	$-0.777389\pi$
$971$	3.64939	−	34.7216i	0.117115	−	1.11427i	0.882374	−	0.470549i	$-0.155944\pi$
$972$	1.11845	−	1.53941i	0.0358743	−	0.0493767i
$973$	−34.2205	−	11.2549i	−1.09706	−	0.360814i
$974$	1.20651			0.0386590
$975$	−11.5210	+	12.4701i	−0.368966	+	0.399363i
$976$	−8.47698	+	14.6826i	−0.271342	+	0.469978i
$977$	16.2744	−	14.6535i	0.520663	−	0.468807i	−0.366398	−	0.930458i	$-0.619409\pi$
$977$	16.2744	−	14.6535i	0.520663	−	0.468807i	0.887062	+	0.461651i	$0.152743\pi$
$978$	−0.340386	−	0.0357760i	−0.0108844	−	0.00114399i
$979$	−8.31865	−	6.04385i	−0.265865	−	0.193162i
$980$	28.1985	+	9.58772i	0.900767	+	0.306268i
$981$	1.14944	−	0.835118i	0.0366988	−	0.0266633i
$982$	4.79763	−	2.76991i	0.153099	−	0.0883915i
$983$	−6.74366	+	0.708788i	−0.215089	+	0.0226068i	−0.211460	−	0.977387i	$-0.567822\pi$
$983$	−6.74366	+	0.708788i	−0.215089	+	0.0226068i	−0.00362924	+	0.999993i	$0.501155\pi$
$984$	−0.603982	−	0.128380i	−0.0192543	−	0.00409262i
$985$	12.9024	−	2.65618i	0.411105	−	0.0846329i
$986$	−7.59786	+	23.3838i	−0.241965	+	0.744692i
$987$	−2.64100	+	0.847648i	−0.0840641	+	0.0269809i
$988$	37.8476	−	12.2974i	1.20409	−	0.391234i
$989$	−18.5522	+	3.94340i	−0.589927	+	0.125393i
$990$	0.248451	−	0.424029i	0.00789628	−	0.0134765i
$991$	10.0643	+	2.13922i	0.319702	+	0.0679547i	0.364967	−	0.931020i	$-0.381080\pi$
$991$	10.0643	+	2.13922i	0.319702	+	0.0679547i	−0.0452657	+	0.998975i	$0.514413\pi$
$992$	−12.0020	+	26.9569i	−0.381063	+	0.855882i
$993$		−	30.6870i		−	0.973822i
$994$	−4.09946	−	1.84285i	−0.130027	−	0.0584518i
$995$	−25.5352	+	8.11632i	−0.809520	+	0.257305i
$996$	−1.70841	+	16.2544i	−0.0541330	+	0.515041i
$997$	−19.5340	−	43.8740i	−0.618647	−	1.38950i	−0.902522	−	0.430643i	$-0.858287\pi$
$997$	−19.5340	−	43.8740i	−0.618647	−	1.38950i	0.283875	−	0.958861i	$-0.408380\pi$
$998$	5.82684	−	5.24651i	0.184445	−	0.166075i
$999$	1.56897	+	2.71753i	0.0496399	+	0.0859788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.4.19	✓	320
7.2	even	3	inner	525.2.bo.a.79.19	yes	320
25.19	even	10	inner	525.2.bo.a.319.19	yes	320
175.44	even	30	inner	525.2.bo.a.394.19	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.19	✓	320	1.1	even	1	trivial
525.2.bo.a.79.19	yes	320	7.2	even	3	inner
525.2.bo.a.319.19	yes	320	25.19	even	10	inner
525.2.bo.a.394.19	yes	320	175.44	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0648139 - 0.304925i) q^{2} +(0.406737 + 0.913545i) q^{3} +(1.73831 - 0.773947i) q^{4} +(-1.65210 - 1.50684i) q^{5} +(0.252201 - 0.183235i) q^{6} +(-0.00949525 + 2.64573i) q^{7} +(-0.715132 - 0.984294i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.0648139 - 0.304925i) q^{2} +(0.406737 + 0.913545i) q^{3} +(1.73831 - 0.773947i) q^{4} +(-1.65210 - 1.50684i) q^{5} +(0.252201 - 0.183235i) q^{6} +(-0.00949525 + 2.64573i) q^{7} +(-0.715132 - 0.984294i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(-0.352395 + 0.601431i) q^{10} +(0.471760 + 0.523943i) q^{11} +(1.41407 + 1.27323i) q^{12} +(3.22932 - 1.04927i) q^{13} +(0.807366 - 0.168585i) q^{14} +(0.704599 - 2.12215i) q^{15} +(2.29268 - 2.54628i) q^{16} +(7.65922 - 0.805017i) q^{17} +(0.269973 + 0.155869i) q^{18} +(5.62679 + 2.50521i) q^{19} +(-4.03808 - 1.34072i) q^{20} +(-2.42086 + 1.06744i) q^{21} +(0.129187 - 0.177810i) q^{22} +(0.345852 + 1.62710i) q^{23} +(0.608327 - 1.05365i) q^{24} +(0.458860 + 4.97890i) q^{25} +(-0.529253 - 0.916693i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(2.03115 + 4.60646i) q^{28} +(-8.28528 - 6.01961i) q^{29} +(-0.692766 - 0.0773049i) q^{30} +(-0.880903 - 8.38123i) q^{31} +(-3.03233 - 1.75072i) q^{32} +(-0.286763 + 0.644081i) q^{33} +(-0.741893 - 2.28331i) q^{34} +(4.00239 - 4.35671i) q^{35} +(-0.588004 + 1.80969i) q^{36} +(-2.33194 - 2.09969i) q^{37} +(0.399207 - 1.87812i) q^{38} +(2.27204 + 2.52335i) q^{39} +(-0.301707 + 2.70374i) q^{40} +(-0.156832 - 0.482679i) q^{41} +(0.482395 + 0.668996i) q^{42} +11.4020i q^{43} +(1.22557 + 0.545659i) q^{44} +(2.22527 - 0.219475i) q^{45} +(0.473729 - 0.210918i) q^{46} +(1.04262 + 0.109583i) q^{47} +(3.25866 + 1.05880i) q^{48} +(-6.99982 - 0.0502438i) q^{49} +(1.48845 - 0.462620i) q^{50} +(3.85070 + 6.66962i) q^{51} +(4.80148 - 4.32328i) q^{52} +(2.85452 + 6.41135i) q^{53} +(-0.0325854 + 0.310030i) q^{54} +(0.0101041 - 1.57647i) q^{55} +(2.61097 - 1.88270i) q^{56} +6.15929i q^{57} +(-1.29853 + 2.91654i) q^{58} +(1.94679 + 0.413803i) q^{59} +(-0.417622 - 4.23429i) q^{60} +(-4.83997 + 1.02877i) q^{61} +(-2.49855 + 0.811830i) q^{62} +(-1.95981 - 1.77740i) q^{63} +(1.78031 - 5.47922i) q^{64} +(-6.91623 - 3.13257i) q^{65} +(0.214983 + 0.0456960i) q^{66} +(-3.72648 + 0.391669i) q^{67} +(12.6911 - 7.32720i) q^{68} +(-1.34576 + 0.977754i) q^{69} +(-1.58788 - 0.938054i) q^{70} +(-4.40873 - 3.20313i) q^{71} +(1.20999 + 0.127175i) q^{72} +(-0.518575 + 0.466927i) q^{73} +(-0.489105 + 0.847155i) q^{74} +(-4.36182 + 2.44429i) q^{75} +11.7200 q^{76} +(-1.39069 + 1.24318i) q^{77} +(0.622174 - 0.856349i) q^{78} +(-1.02928 + 9.79296i) q^{79} +(-7.62459 + 0.752001i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-0.137016 + 0.0791063i) q^{82} +(5.04868 + 6.94891i) q^{83} +(-3.38207 + 3.72917i) q^{84} +(-13.8668 - 10.2113i) q^{85} +(3.47676 - 0.739007i) q^{86} +(2.12926 - 10.0174i) q^{87} +(0.178343 - 0.839039i) q^{88} +(-14.2656 + 3.03224i) q^{89} +(-0.211152 - 0.664316i) q^{90} +(2.74542 + 8.55388i) q^{91} +(1.86049 + 2.56074i) q^{92} +(7.29834 - 4.21370i) q^{93} +(-0.0341613 - 0.325023i) q^{94} +(-5.52106 - 12.6175i) q^{95} +(0.366000 - 3.48225i) q^{96} +(7.96180 - 10.9585i) q^{97} +(0.438365 + 2.13768i) q^{98} -0.705034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

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