LMFDB - Embedded newform 225.2.q.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22593 + 1.36154i) q^{2} +(-1.29127 + 1.15439i) q^{3} +(-0.141814 - 1.34927i) q^{4} +(1.94663 - 1.10028i) q^{5} +(0.0112662 - 3.17332i) q^{6} +(-2.15924 - 3.73991i) q^{7} +(-0.953512 - 0.692767i) q^{8} +(0.334762 - 2.98126i) q^{9} +O(q^{10})$	\(q+(-1.22593 + 1.36154i) q^{2} +(-1.29127 + 1.15439i) q^{3} +(-0.141814 - 1.34927i) q^{4} +(1.94663 - 1.10028i) q^{5} +(0.0112662 - 3.17332i) q^{6} +(-2.15924 - 3.73991i) q^{7} +(-0.953512 - 0.692767i) q^{8} +(0.334762 - 2.98126i) q^{9} +(-0.888371 + 3.99929i) q^{10} +(-0.605752 + 0.672756i) q^{11} +(1.74071 + 1.57856i) q^{12} +(-4.13776 - 4.59545i) q^{13} +(7.73912 + 1.64500i) q^{14} +(-1.24348 + 3.66794i) q^{15} +(4.76628 - 1.01310i) q^{16} +(4.65336 + 3.38087i) q^{17} +(3.64871 + 4.11063i) q^{18} +(-2.14825 - 1.56079i) q^{19} +(-1.76064 - 2.47050i) q^{20} +(7.10548 + 2.33663i) q^{21} +(-0.173370 - 1.64951i) q^{22} +(-3.44271 - 0.731772i) q^{23} +(2.03097 - 0.206176i) q^{24} +(2.57876 - 4.28369i) q^{25} +11.3295 q^{26} +(3.00928 + 4.23607i) q^{27} +(-4.73994 + 3.44377i) q^{28} +(-2.08431 - 0.927996i) q^{29} +(-3.46962 - 6.18969i) q^{30} +(-2.13557 + 0.950816i) q^{31} +(-3.28516 + 5.69007i) q^{32} +(0.00556681 - 1.56798i) q^{33} +(-10.3079 + 2.19101i) q^{34} +(-8.31820 - 4.90447i) q^{35} +(-4.07000 - 0.0288998i) q^{36} +(-0.704813 + 2.16919i) q^{37} +(4.75869 - 1.01149i) q^{38} +(10.6479 + 1.15738i) q^{39} +(-2.61838 - 0.299432i) q^{40} +(-4.04708 - 4.49473i) q^{41} +(-11.8923 + 6.80983i) q^{42} +(-1.16011 - 2.00937i) q^{43} +(0.993634 + 0.721917i) q^{44} +(-2.62857 - 6.17176i) q^{45} +(5.21688 - 3.79028i) q^{46} +(5.09769 + 2.26964i) q^{47} +(-4.98504 + 6.81035i) q^{48} +(-5.82462 + 10.0885i) q^{49} +(2.67101 + 8.76261i) q^{50} +(-9.91160 + 1.00619i) q^{51} +(-5.61371 + 6.23466i) q^{52} +(3.50455 - 2.54621i) q^{53} +(-9.45674 - 1.09590i) q^{54} +(-0.438957 + 1.97611i) q^{55} +(-0.532027 + 5.06190i) q^{56} +(4.57574 - 0.464511i) q^{57} +(3.81874 - 1.70021i) q^{58} +(-8.79570 - 9.76861i) q^{59} +(5.12538 + 1.15762i) q^{60} +(9.45934 - 10.5057i) q^{61} +(1.32349 - 4.07330i) q^{62} +(-11.8725 + 5.18528i) q^{63} +(-0.708321 - 2.17999i) q^{64} +(-13.1110 - 4.39296i) q^{65} +(2.12805 + 1.92983i) q^{66} +(6.96006 - 3.09882i) q^{67} +(3.90179 - 6.75810i) q^{68} +(5.29023 - 3.02932i) q^{69} +(16.8752 - 5.31299i) q^{70} +(-4.21064 + 3.05921i) q^{71} +(-2.38452 + 2.61076i) q^{72} +(0.0260643 + 0.0802177i) q^{73} +(-2.08938 - 3.61892i) q^{74} +(1.61517 + 8.50830i) q^{75} +(-1.80128 + 3.11991i) q^{76} +(3.82401 + 0.812818i) q^{77} +(-14.6295 + 13.0787i) q^{78} +(-0.815175 - 0.362939i) q^{79} +(8.16350 - 7.21639i) q^{80} +(-8.77587 - 1.99603i) q^{81} +11.0812 q^{82} +(-0.108872 + 1.03584i) q^{83} +(2.14509 - 9.91858i) q^{84} +(12.7783 + 1.46130i) q^{85} +(4.15806 + 0.883823i) q^{86} +(3.76269 - 1.20782i) q^{87} +(1.04365 - 0.221836i) q^{88} +(1.84560 + 5.68017i) q^{89} +(11.6255 + 3.98728i) q^{90} +(-8.25216 + 25.3975i) q^{91} +(-0.499132 + 4.74893i) q^{92} +(1.65998 - 3.69304i) q^{93} +(-9.33964 + 4.15827i) q^{94} +(-5.89916 - 0.674617i) q^{95} +(-2.32653 - 11.1398i) q^{96} +(-1.49796 - 0.666933i) q^{97} +(-6.59533 - 20.2983i) q^{98} +(1.80288 + 2.03112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.22593	+	1.36154i	−0.866867	+	0.962753i	−0.999597	−	0.0283992i	$-0.990959\pi$
$2$	−1.22593	+	1.36154i	−0.866867	+	0.962753i	0.132730	+	0.991152i	$0.457626\pi$
$3$	−1.29127	+	1.15439i	−0.745516	+	0.666488i
$3$	−1.29127	+	1.15439i	−0.745516	+	0.666488i
$4$	−0.141814	−	1.34927i	−0.0709070	−	0.674635i
$5$	1.94663	−	1.10028i	0.870561	−	0.492061i
$5$	1.94663	−	1.10028i	0.870561	−	0.492061i
$6$	0.0112662	−	3.17332i	0.00459942	−	1.29550i
$7$	−2.15924	−	3.73991i	−0.816115	−	1.41355i	−0.908524	−	0.417832i	$-0.862790\pi$
$7$	−2.15924	−	3.73991i	−0.816115	−	1.41355i	0.0924090	−	0.995721i	$-0.470543\pi$
$8$	−0.953512	−	0.692767i	−0.337117	−	0.244930i
$9$	0.334762	−	2.98126i	0.111587	−	0.993755i
$10$	−0.888371	+	3.99929i	−0.280928	+	1.26469i
$11$	−0.605752	+	0.672756i	−0.182641	+	0.202844i	−0.827512	−	0.561448i	$-0.810244\pi$
$11$	−0.605752	+	0.672756i	−0.182641	+	0.202844i	0.644871	+	0.764292i	$0.276911\pi$
$12$	1.74071	+	1.57856i	0.502499	+	0.455692i
$13$	−4.13776	−	4.59545i	−1.14761	−	1.27455i	−0.956094	−	0.293059i	$-0.905327\pi$
$13$	−4.13776	−	4.59545i	−1.14761	−	1.27455i	−0.191515	−	0.981490i	$-0.561340\pi$
$14$	7.73912	+	1.64500i	2.06837	+	0.439645i
$15$	−1.24348	+	3.66794i	−0.321064	+	0.947057i
$16$	4.76628	−	1.01310i	1.19157	−	0.253276i
$17$	4.65336	+	3.38087i	1.12861	+	0.819981i	0.985491	−	0.169726i	$-0.0542881\pi$
$17$	4.65336	+	3.38087i	1.12861	+	0.819981i	0.143115	+	0.989706i	$0.454288\pi$
$18$	3.64871	+	4.11063i	0.860009	+	0.968884i
$19$	−2.14825	−	1.56079i	−0.492842	−	0.358070i	0.313434	−	0.949610i	$-0.398520\pi$
$19$	−2.14825	−	1.56079i	−0.492842	−	0.358070i	−0.806276	+	0.591539i	$0.798520\pi$
$20$	−1.76064	−	2.47050i	−0.393690	−	0.552421i
$21$	7.10548	+	2.33663i	1.55054	+	0.509895i
$22$	−0.173370	−	1.64951i	−0.0369627	−	0.351677i
$23$	−3.44271	−	0.731772i	−0.717856	−	0.152585i	−0.165520	−	0.986206i	$-0.552930\pi$
$23$	−3.44271	−	0.731772i	−0.717856	−	0.152585i	−0.552336	+	0.833622i	$0.686263\pi$
$24$	2.03097	−	0.206176i	0.414569	−	0.0420854i
$25$	2.57876	−	4.28369i	0.515753	−	0.856737i
$26$	11.3295			2.22190
$27$	3.00928	+	4.23607i	0.579135	+	0.815231i
$28$	−4.73994	+	3.44377i	−0.895764	+	0.650811i
$29$	−2.08431	−	0.927996i	−0.387047	−	0.172325i	0.203982	−	0.978975i	$-0.434612\pi$
$29$	−2.08431	−	0.927996i	−0.387047	−	0.172325i	−0.591029	+	0.806650i	$0.701278\pi$
$30$	−3.46962	−	6.18969i	−0.633462	−	1.13008i
$31$	−2.13557	+	0.950816i	−0.383559	+	0.170772i	−0.589453	−	0.807803i	$-0.700657\pi$
$31$	−2.13557	+	0.950816i	−0.383559	+	0.170772i	0.205893	+	0.978574i	$0.433990\pi$
$32$	−3.28516	+	5.69007i	−0.580740	+	1.00587i
$33$	0.00556681	−	1.56798i	0.000969057	−	0.272951i
$34$	−10.3079	+	2.19101i	−1.76779	+	0.375755i
$35$	−8.31820	−	4.90447i	−1.40603	−	0.829006i
$36$	−4.07000	−	0.0288998i	−0.678334	−	0.00481663i
$37$	−0.704813	+	2.16919i	−0.115871	+	0.356613i	−0.992128	−	0.125231i	$-0.960033\pi$
$37$	−0.704813	+	2.16919i	−0.115871	+	0.356613i	0.876257	+	0.481844i	$0.160033\pi$
$38$	4.75869	−	1.01149i	0.771961	−	0.164085i
$39$	10.6479	+	1.15738i	1.70503	+	0.185329i
$40$	−2.61838	−	0.299432i	−0.414001	−	0.0473444i
$41$	−4.04708	−	4.49473i	−0.632047	−	0.701960i	0.339016	−	0.940780i	$-0.389906\pi$
$41$	−4.04708	−	4.49473i	−0.632047	−	0.701960i	−0.971064	+	0.238821i	$0.923239\pi$
$42$	−11.8923	+	6.80983i	−1.83502	+	1.05078i
$43$	−1.16011	−	2.00937i	−0.176915	−	0.306427i	0.763907	−	0.645326i	$-0.223279\pi$
$43$	−1.16011	−	2.00937i	−0.176915	−	0.306427i	−0.940822	+	0.338900i	$0.889945\pi$
$44$	0.993634	+	0.721917i	0.149796	+	0.108833i
$45$	−2.62857	−	6.17176i	−0.391844	−	0.920032i
$46$	5.21688	−	3.79028i	0.769187	−	0.558847i
$47$	5.09769	+	2.26964i	0.743575	+	0.331061i	0.743317	−	0.668939i	$-0.233251\pi$
$47$	5.09769	+	2.26964i	0.743575	+	0.331061i	0.000257570		1.00000i	$0.499918\pi$
$48$	−4.98504	+	6.81035i	−0.719529	+	0.982989i
$49$	−5.82462	+	10.0885i	−0.832088	+	1.44122i
$50$	2.67101	+	8.76261i	0.377738	+	1.23922i
$51$	−9.91160	+	1.00619i	−1.38790	+	0.140894i
$52$	−5.61371	+	6.23466i	−0.778482	+	0.864592i
$53$	3.50455	−	2.54621i	0.481387	−	0.349748i	−0.320475	−	0.947257i	$-0.603843\pi$
$53$	3.50455	−	2.54621i	0.481387	−	0.349748i	0.801862	+	0.597509i	$0.203843\pi$
$54$	−9.45674	−	1.09590i	−1.28690	−	0.149133i
$55$	−0.438957	+	1.97611i	−0.0591889	+	0.266458i
$56$	−0.532027	+	5.06190i	−0.0710951	+	0.676424i
$57$	4.57574	−	0.464511i	0.606071	−	0.0615259i
$58$	3.81874	−	1.70021i	0.501425	−	0.223249i
$59$	−8.79570	−	9.76861i	−1.14510	−	1.27177i	−0.957152	−	0.289587i	$-0.906482\pi$
$59$	−8.79570	−	9.76861i	−1.14510	−	1.27177i	−0.187951	−	0.982178i	$-0.560185\pi$
$60$	5.12538	+	1.15762i	0.661684	+	0.149448i
$61$	9.45934	−	10.5057i	1.21114	−	1.34511i	0.289450	−	0.957193i	$-0.406528\pi$
$61$	9.45934	−	10.5057i	1.21114	−	1.34511i	0.921694	−	0.387918i	$-0.126806\pi$
$62$	1.32349	−	4.07330i	0.168084	−	0.517309i
$63$	−11.8725	+	5.18528i	−1.49579	+	0.653284i
$64$	−0.708321	−	2.17999i	−0.0885401	−	0.272498i
$65$	−13.1110	−	4.39296i	−1.62622	−	0.544880i
$66$	2.12805	+	1.92983i	0.261944	+	0.237545i
$67$	6.96006	−	3.09882i	0.850306	−	0.378581i	0.0651477	−	0.997876i	$-0.479248\pi$
$67$	6.96006	−	3.09882i	0.850306	−	0.378581i	0.785158	+	0.619295i	$0.212581\pi$
$68$	3.90179	−	6.75810i	0.473162	−	0.819540i
$69$	5.29023	−	3.02932i	0.636869	−	0.364688i
$70$	16.8752	−	5.31299i	2.01697	−	0.635024i
$71$	−4.21064	+	3.05921i	−0.499711	+	0.363061i	−0.808907	−	0.587937i	$-0.799940\pi$
$71$	−4.21064	+	3.05921i	−0.499711	+	0.363061i	0.309195	+	0.950999i	$0.399940\pi$
$72$	−2.38452	+	2.61076i	−0.281018	+	0.307681i
$73$	0.0260643	+	0.0802177i	0.00305060	+	0.00938878i	0.952570	−	0.304319i	$-0.0984288\pi$
$73$	0.0260643	+	0.0802177i	0.00305060	+	0.00938878i	−0.949520	+	0.313708i	$0.898429\pi$
$74$	−2.08938	−	3.61892i	−0.242886	−	0.420691i
$75$	1.61517	+	8.50830i	0.186503	+	0.982454i
$76$	−1.80128	+	3.11991i	−0.206621	+	0.357878i
$77$	3.82401	+	0.812818i	0.435786	+	0.0926292i
$78$	−14.6295	+	13.0787i	−1.65646	+	1.48087i
$79$	−0.815175	−	0.362939i	−0.0917144	−	0.0408339i	0.360367	−	0.932811i	$-0.382652\pi$
$79$	−0.815175	−	0.362939i	−0.0917144	−	0.0408339i	−0.452081	+	0.891977i	$0.649318\pi$
$80$	8.16350	−	7.21639i	0.912708	−	0.806817i
$81$	−8.77587	−	1.99603i	−0.975096	−	0.221781i
$82$	11.0812			1.22371
$83$	−0.108872	+	1.03584i	−0.0119502	+	0.113699i	−0.998871	−	0.0475082i	$-0.984872\pi$
$83$	−0.108872	+	1.03584i	−0.0119502	+	0.113699i	0.986921	+	0.161207i	$0.0515387\pi$
$84$	2.14509	−	9.91858i	0.234049	−	1.08221i
$85$	12.7783	+	1.46130i	1.38600	+	0.158500i
$86$	4.15806	+	0.883823i	0.448375	+	0.0953051i
$87$	3.76269	−	1.20782i	0.403402	−	0.129492i
$88$	1.04365	−	0.221836i	0.111254	−	0.0236478i
$89$	1.84560	+	5.68017i	0.195633	+	0.602096i	0.999969	+	0.00792122i	$0.00252143\pi$
$89$	1.84560	+	5.68017i	0.195633	+	0.602096i	−0.804336	+	0.594175i	$0.797479\pi$
$90$	11.6255	+	3.98728i	1.22544	+	0.420296i
$91$	−8.25216	+	25.3975i	−0.865062	+	2.66239i
$92$	−0.499132	+	4.74893i	−0.0520382	+	0.495110i
$93$	1.65998	−	3.69304i	0.172132	−	0.382951i
$94$	−9.33964	+	4.15827i	−0.963310	+	0.428893i
$95$	−5.89916	−	0.674617i	−0.605241	−	0.0692142i
$96$	−2.32653	−	11.1398i	−0.237450	−	1.13695i
$97$	−1.49796	−	0.666933i	−0.152094	−	0.0677168i	0.329278	−	0.944233i	$-0.393195\pi$
$97$	−1.49796	−	0.666933i	−0.152094	−	0.0677168i	−0.481372	+	0.876516i	$0.659861\pi$
$98$	−6.59533	−	20.2983i	−0.666229	−	2.05044i
$99$	1.80288	+	2.03112i	0.181196	+	0.204135i
$100$	−6.14556	−	2.87196i	−0.614556	−	0.287196i
$101$	3.92357	+	6.79582i	0.390410	+	0.676209i	0.992504	−	0.122216i	$-0.0390000\pi$
$101$	3.92357	+	6.79582i	0.390410	+	0.676209i	−0.602094	+	0.798425i	$0.705667\pi$
$102$	10.7810	−	14.7285i	1.06748	−	1.45834i
$103$	1.30490	+	12.4153i	0.128576	+	1.22331i	0.848475	+	0.529236i	$0.177521\pi$
$103$	1.30490	+	12.4153i	0.128576	+	1.22331i	−0.719899	+	0.694079i	$0.755812\pi$
$104$	0.761829	+	7.24832i	0.0747035	+	0.710756i
$105$	16.4027	−	3.26946i	1.60074	−	0.319066i
$106$	−0.829594	+	7.89306i	−0.0805773	+	0.766642i
$107$	6.18859			0.598273			0.299137	−	0.954210i	$-0.403301\pi$
$107$	6.18859			0.598273			0.299137	+	0.954210i	$0.403301\pi$
$108$	5.28884	−	4.66106i	0.508919	−	0.448511i
$109$	5.35768	−	16.4892i	0.513173	−	1.57938i	−0.273410	−	0.961898i	$-0.588152\pi$
$109$	5.35768	−	16.4892i	0.513173	−	1.57938i	0.786582	−	0.617485i	$-0.211848\pi$
$110$	−2.15241	−	3.02023i	−0.205224	−	0.287968i
$111$	−1.59399	−	3.61464i	−0.151295	−	0.343087i
$112$	−14.0805	−	15.6379i	−1.33048	−	1.47765i
$113$	4.01244	+	4.45627i	0.377459	+	0.419210i	0.901702	−	0.432358i	$-0.142318\pi$
$113$	4.01244	+	4.45627i	0.377459	+	0.419210i	−0.524243	+	0.851569i	$0.675652\pi$
$114$	−4.97710	+	6.79950i	−0.466148	+	0.636831i
$115$	−7.50686	+	2.36346i	−0.700018	+	0.220394i
$116$	−0.956533	+	2.94391i	−0.0888119	+	0.273335i
$117$	−15.0854	+	10.7974i	−1.39465	+	0.998218i
$118$	24.0833			2.21705
$119$	2.59642	−	24.7033i	0.238013	−	2.26454i
$120$	3.72669	−	2.63598i	0.340199	−	0.240631i
$121$	1.06415	+	10.1247i	0.0967408	+	0.920427i
$122$	2.70733	+	25.7585i	0.245110	+	2.33206i
$123$	10.4146	+	1.13201i	0.939049	+	0.102070i
$124$	1.58576	+	2.74662i	0.142406	+	0.246654i
$125$	0.306650	−	11.1761i	0.0274276	−	0.999624i
$126$	7.49494	−	22.5217i	0.667703	−	2.00639i
$127$	−3.86196	−	11.8859i	−0.342694	−	1.05470i	−0.962807	−	0.270190i	$-0.912913\pi$
$127$	−3.86196	−	11.8859i	−0.342694	−	1.05470i	0.620113	−	0.784512i	$-0.287087\pi$
$128$	−8.16810	−	3.63667i	−0.721965	−	0.321439i
$129$	3.81762	+	1.25542i	0.336123	+	0.110534i
$130$	22.0544	−	12.4656i	1.93430	−	1.09331i
$131$	4.74442	−	2.11235i	0.414522	−	0.184557i	−0.188870	−	0.982002i	$-0.560482\pi$
$131$	4.74442	−	2.11235i	0.414522	−	0.184557i	0.603391	+	0.797445i	$0.293816\pi$
$132$	−2.11642	+	0.214851i	−0.184211	+	0.0187004i
$133$	−1.19865	+	11.4044i	−0.103936	+	0.988885i
$134$	−4.31342	+	13.2753i	−0.372622	+	1.14681i
$135$	10.5188	+	4.93502i	0.905316	+	0.424739i
$136$	−2.09488	−	6.44739i	−0.179635	−	0.552859i
$137$	−9.92347	+	2.10930i	−0.847819	+	0.180210i	−0.611282	−	0.791413i	$-0.709346\pi$
$137$	−9.92347	+	2.10930i	−0.847819	+	0.180210i	−0.236537	+	0.971622i	$0.576013\pi$
$138$	−2.36093	+	10.9166i	−0.200976	+	0.929283i
$139$	3.34344	+	0.710671i	0.283587	+	0.0602783i	0.347509	−	0.937677i	$-0.387028\pi$
$139$	3.34344	+	0.710671i	0.283587	+	0.0602783i	−0.0639220	+	0.997955i	$0.520361\pi$
$140$	−5.43781	+	11.9190i	−0.459579	+	1.00734i
$141$	−9.20255	+	2.95401i	−0.774995	+	0.248773i
$142$	0.996739	−	9.48334i	0.0836445	−	0.795824i
$143$	5.59808			0.468135
$144$	−1.42476	−	14.5487i	−0.118730	−	1.21239i
$145$	−5.07845	+	0.486862i	−0.421742	+	0.0404317i
$146$	−0.141173	−	0.0628541i	−0.0116835	−	0.00520184i
$147$	−4.12495	−	19.7509i	−0.340220	−	1.62903i
$148$	3.02678	+	0.643362i	0.248800	+	0.0528840i
$149$	−7.01283	+	12.1466i	−0.574514	+	0.995087i	0.421581	+	0.906791i	$0.361475\pi$
$149$	−7.01283	+	12.1466i	−0.574514	+	0.995087i	−0.996094	+	0.0882960i	$0.971858\pi$
$150$	−13.5645	−	8.23151i	−1.10753	−	0.672100i
$151$	−0.171017	−	0.296210i	−0.0139171	−	0.0241052i	0.858983	−	0.512004i	$-0.171097\pi$
$151$	−0.171017	−	0.296210i	−0.0139171	−	0.0241052i	−0.872900	+	0.487899i	$0.837763\pi$
$152$	0.967113	+	2.97647i	0.0784432	+	0.241423i
$153$	11.6370	−	12.7411i	0.940798	−	1.03006i
$154$	−5.79467	+	4.21007i	−0.466948	+	0.339257i
$155$	−3.11100	+	4.20062i	−0.249882	+	0.337402i
$156$	0.0515895	−	14.5311i	0.00413047	−	1.16342i
$157$	6.47430	−	11.2138i	0.516705	−	0.894959i	−0.483107	−	0.875561i	$-0.660492\pi$
$157$	6.47430	−	11.2138i	0.516705	−	0.894959i	0.999812	−	0.0193980i	$-0.00617496\pi$
$158$	1.49351	−	0.664953i	0.118817	−	0.0529008i
$159$	−1.58601	+	7.33346i	−0.125779	+	0.581581i
$160$	−0.134334	+	14.6911i	−0.0106201	+	1.16143i
$161$	4.69688	+	14.4555i	0.370166	+	1.13925i
$162$	13.4763	−	9.50168i	1.05880	−	0.746522i
$163$	0.350556	−	1.07890i	0.0274577	−	0.0845060i	−0.936389	−	0.350965i	$-0.885854\pi$
$163$	0.350556	−	1.07890i	0.0274577	−	0.0845060i	0.963846	+	0.266459i	$0.0858536\pi$
$164$	−5.49068	+	6.09802i	−0.428750	+	0.476175i
$165$	−1.71439	−	3.05842i	−0.133465	−	0.238097i
$166$	−1.27687	−	1.41811i	−0.0991046	−	0.110067i
$167$	−1.01332	+	0.451160i	−0.0784132	+	0.0349118i	−0.445569	−	0.895248i	$-0.646998\pi$
$167$	−1.01332	+	0.451160i	−0.0784132	+	0.0349118i	0.367155	+	0.930160i	$0.380332\pi$
$168$	−5.15642	−	7.15045i	−0.397826	−	0.551669i
$169$	−2.63822	+	25.1010i	−0.202940	+	1.93085i
$170$	−17.6550	+	15.6067i	−1.35407	+	1.19698i
$171$	−5.37229	+	5.88200i	−0.410829	+	0.449808i
$172$	−2.54667	+	1.85026i	−0.194182	+	0.141081i
$173$	−3.29083	+	3.65484i	−0.250197	+	0.277872i	−0.855140	−	0.518396i	$-0.826529\pi$
$173$	−3.29083	+	3.65484i	−0.250197	+	0.277872i	0.604943	+	0.796269i	$0.293196\pi$
$174$	−2.96831	+	6.60375i	−0.225027	+	0.500629i
$175$	−21.5888	−	0.394845i	−1.63196	−	0.0298475i
$176$	−2.20561	+	3.82023i	−0.166254	+	0.287961i
$177$	22.6344	+	2.46025i	1.70131	+	0.184924i
$178$	−9.99635	−	4.45066i	−0.749258	−	0.333591i
$179$	−1.61240	+	1.17148i	−0.120516	+	0.0875602i	−0.646411	−	0.762990i	$-0.723731\pi$
$179$	−1.61240	+	1.17148i	−0.120516	+	0.0875602i	0.525894	+	0.850550i	$0.323731\pi$
$180$	−7.95461	+	4.42189i	−0.592901	+	0.329588i
$181$	7.03514	+	5.11133i	0.522918	+	0.379922i	0.817702	−	0.575642i	$-0.195248\pi$
$181$	7.03514	+	5.11133i	0.522918	+	0.379922i	−0.294784	+	0.955564i	$0.595248\pi$
$182$	−24.4631	−	42.3714i	−1.81333	−	3.14077i
$183$	−0.0869304	+	24.4854i	−0.00642608	+	1.81001i
$184$	2.77572	+	3.08275i	0.204629	+	0.227263i
$185$	1.01471	+	4.99811i	0.0746028	+	0.367469i
$186$	2.99319	+	6.78756i	0.219471	+	0.497688i
$187$	−5.09328	+	1.08261i	−0.372458	+	0.0791683i
$188$	2.33943	−	7.20003i	0.170621	−	0.525116i
$189$	9.34477	−	20.4011i	0.679732	−	1.48396i
$190$	8.15050	−	7.20490i	0.591300	−	0.522698i
$191$	22.0101	−	4.67839i	1.59259	−	0.338516i	0.675554	−	0.737311i	$-0.263905\pi$
$191$	22.0101	−	4.67839i	1.59259	−	0.338516i	0.917040	+	0.398794i	$0.130571\pi$
$192$	3.43119	+	1.99727i	0.247625	+	0.144141i
$193$	−5.49895	+	9.52446i	−0.395823	+	0.685586i	−0.993206	−	0.116371i	$-0.962874\pi$
$193$	−5.49895	+	9.52446i	−0.395823	+	0.685586i	0.597383	+	0.801956i	$0.296207\pi$
$194$	2.74445	−	1.22191i	0.197040	−	0.0877279i
$195$	22.0010	−	9.46272i	1.57553	−	0.677639i
$196$	14.4382	+	6.42829i	1.03130	+	0.459164i
$197$	−4.79140	+	3.48116i	−0.341373	+	0.248022i	−0.745241	−	0.666795i	$-0.767666\pi$
$197$	−4.79140	+	3.48116i	−0.341373	+	0.248022i	0.403868	+	0.914817i	$0.367666\pi$
$198$	−4.97566	−	0.0353306i	−0.353605	−	0.00251083i
$199$	8.53871			0.605293			0.302646	−	0.953103i	$-0.402130\pi$
$199$	8.53871			0.605293			0.302646	+	0.953103i	$0.402130\pi$
$200$	−5.42648	+	2.29806i	−0.383710	+	0.162498i
$201$	−5.41007	+	12.0360i	−0.381597	+	0.848957i
$202$	−14.0628	−	2.98914i	−0.989456	−	0.210315i
$203$	1.02991	+	9.79891i	0.0722853	+	0.687749i
$204$	2.76322	+	13.2307i	0.193464	+	0.926336i
$205$	−12.8236	−	4.29668i	−0.895642	−	0.300093i
$206$	−18.5036	−	13.4437i	−1.28921	−	0.936664i
$207$	−3.33410	+	10.0187i	−0.231736	+	0.696346i
$208$	−24.3774	−	17.7112i	−1.69027	−	1.22805i
$209$	2.35134	−	0.499792i	0.162645	−	0.0345714i
$210$	−15.6572	+	26.3411i	−1.08045	+	1.81771i
$211$	−26.2461	−	5.57878i	−1.80686	−	0.384059i	−0.823730	−	0.566983i	$-0.808111\pi$
$211$	−26.2461	−	5.57878i	−1.80686	−	0.384059i	−0.983127	+	0.182923i	$0.941444\pi$
$212$	−3.93251	−	4.36750i	−0.270086	−	0.299961i
$213$	1.90555	−	8.81100i	0.130566	−	0.603720i
$214$	−7.58680	+	8.42600i	−0.518623	+	0.575989i
$215$	−4.46919	−	2.63506i	−0.304796	−	0.179710i
$216$	0.0652267	−	6.12386i	0.00443812	−	0.416676i
$217$	8.16717	+	5.93380i	0.554424	+	0.402812i
$218$	15.8826	+	27.5094i	1.07570	+	1.86317i
$219$	−0.126259	−	0.0734944i	−0.00853177	−	0.00496629i
$220$	2.72855	+	0.312032i	0.183959	+	0.0210372i
$221$	−3.71791	−	35.3735i	−0.250094	−	2.37948i
$222$	6.87561	+	2.26104i	0.461460	+	0.151751i
$223$	9.91315	−	11.0097i	0.663834	−	0.737262i	−0.313355	−	0.949636i	$-0.601453\pi$
$223$	9.91315	−	11.0097i	0.663834	−	0.737262i	0.977188	+	0.212374i	$0.0681195\pi$
$224$	28.3738			1.89580
$225$	−11.9075	−	9.12199i	−0.793835	−	0.608133i
$226$	−10.9864			−0.730802
$227$	−8.29081	+	9.20787i	−0.550280	+	0.611148i	−0.952553	−	0.304372i	$-0.901554\pi$
$227$	−8.29081	+	9.20787i	−0.550280	+	0.611148i	0.402273	+	0.915520i	$0.368220\pi$
$228$	−1.27565	−	6.10803i	−0.0844822	−	0.404514i
$229$	−1.65335	−	15.7306i	−0.109256	−	1.03950i	−0.902526	−	0.430635i	$-0.858290\pi$
$229$	−1.65335	−	15.7306i	−0.109256	−	1.03950i	0.793270	−	0.608870i	$-0.208377\pi$
$230$	5.98497	−	13.1183i	0.394637	−	0.864997i
$231$	−5.87614	+	3.36483i	−0.386622	+	0.221390i
$232$	1.34453	+	2.32880i	0.0882729	+	0.152893i
$233$	−10.4851	−	7.61788i	−0.686903	−	0.499064i	0.188738	−	0.982028i	$-0.439560\pi$
$233$	−10.4851	−	7.61788i	−0.686903	−	0.499064i	−0.875640	+	0.482964i	$0.839560\pi$
$234$	3.79269	−	33.7763i	0.247936	−	2.20802i
$235$	12.4206	−	1.19074i	0.810229	−	0.0776752i
$236$	−11.9331	+	13.2531i	−0.776782	+	0.862704i
$237$	1.47159	−	0.472378i	0.0955898	−	0.0306842i
$238$	30.4514	+	33.8197i	1.97387	+	2.19221i
$239$	4.77002	+	1.01390i	0.308547	+	0.0655837i	0.359583	−	0.933113i	$-0.382919\pi$
$239$	4.77002	+	1.01390i	0.308547	+	0.0655837i	−0.0510358	+	0.998697i	$0.516252\pi$
$240$	−2.21076	+	18.7422i	−0.142704	+	1.20980i
$241$	2.51591	−	0.534773i	0.162064	−	0.0344477i	−0.126165	−	0.992009i	$-0.540267\pi$
$241$	2.51591	−	0.534773i	0.162064	−	0.0344477i	0.288229	+	0.957562i	$0.406934\pi$
$242$	−15.0897	−	10.9633i	−0.970005	−	0.704750i
$243$	13.6362	−	7.55337i	0.874764	−	0.484549i
$244$	−15.5164	−	11.2734i	−0.993338	−	0.721702i
$245$	−0.238176	+	26.0474i	−0.0152165	+	1.66411i
$246$	−14.3088	+	12.7920i	−0.912298	+	0.815591i
$247$	1.71639	+	16.3304i	0.109211	+	1.03908i
$248$	2.69498	+	0.572836i	0.171132	+	0.0363751i
$249$	−1.05519	−	1.46324i	−0.0668698	−	0.0927289i
$250$	14.8408	+	14.1187i	0.938615	+	0.892947i
$251$	12.4805			0.787764			0.393882	−	0.919161i	$-0.371132\pi$
$251$	12.4805			0.787764			0.393882	+	0.919161i	$0.371132\pi$
$252$	8.68003	+	15.2839i	0.546790	+	0.962792i
$253$	2.57774	−	1.87283i	0.162061	−	0.117744i
$254$	20.9176	+	9.31312i	1.31249	+	0.584357i
$255$	−18.1872	+	12.8642i	−1.13892	+	0.805588i
$256$	19.1530	−	8.52748i	1.19706	−	0.532967i
$257$	−6.11612	+	10.5934i	−0.381513	+	0.660800i	−0.991279	−	0.131782i	$-0.957930\pi$
$257$	−6.11612	+	10.5934i	−0.381513	+	0.660800i	0.609766	+	0.792582i	$0.291263\pi$
$258$	−6.38946	+	3.65877i	−0.397790	+	0.227785i
$259$	9.63444	−	2.04786i	0.598655	−	0.127248i
$260$	−4.06797	+	18.3133i	−0.252285	+	1.13574i
$261$	−3.46435	+	5.90323i	−0.214438	+	0.365401i
$262$	−2.94030	+	9.04931i	−0.181652	+	0.559068i
$263$	10.7842	−	2.29225i	0.664981	−	0.141346i	0.136959	−	0.990577i	$-0.456267\pi$
$263$	10.7842	−	2.29225i	0.664981	−	0.141346i	0.528022	+	0.849231i	$0.322934\pi$
$264$	−1.09156	+	1.49124i	−0.0671806	+	0.0917792i
$265$	4.02054	−	8.81252i	0.246980	−	0.541349i
$266$	−14.0580	−	15.6130i	−0.861953	−	0.957296i
$267$	−8.94030	−	5.20409i	−0.547138	−	0.318485i
$268$	−5.16817	−	8.95154i	−0.315696	−	0.546802i
$269$	5.11244	+	3.71441i	0.311711	+	0.226471i	0.732630	−	0.680627i	$-0.238292\pi$
$269$	5.11244	+	3.71441i	0.311711	+	0.226471i	−0.420919	+	0.907098i	$0.638292\pi$
$270$	−19.6146	+	8.27176i	−1.19371	+	0.503404i
$271$	−4.89989	+	3.55998i	−0.297647	+	0.216253i	−0.726578	−	0.687084i	$-0.758890\pi$
$271$	−4.89989	+	3.55998i	−0.297647	+	0.216253i	0.428931	+	0.903337i	$0.358890\pi$
$272$	25.6044	+	11.3998i	1.55250	+	0.691216i
$273$	−18.6629	−	42.3213i	−1.12953	−	2.56140i
$274$	9.29363	−	16.0970i	0.561449	−	0.972458i
$275$	1.31978	+	4.32973i	0.0795860	+	0.261093i
$276$	−4.83761	−	6.70835i	−0.291190	−	0.403795i
$277$	19.9612	−	22.1692i	1.19935	−	1.33202i	0.269985	−	0.962865i	$-0.412981\pi$
$277$	19.9612	−	22.1692i	1.19935	−	1.33202i	0.929369	−	0.369153i	$-0.120352\pi$
$278$	−5.06645	+	3.68099i	−0.303865	+	0.220771i
$279$	2.11973	+	6.68499i	0.126905	+	0.400220i
$280$	4.53385	+	10.4390i	0.270949	+	0.623852i
$281$	2.33067	−	22.1749i	0.139036	−	1.32284i	−0.673178	−	0.739481i	$-0.735071\pi$
$281$	2.33067	−	22.1749i	0.139036	−	1.32284i	0.812214	−	0.583360i	$-0.198262\pi$
$282$	7.25973	−	16.1511i	0.432311	−	0.961781i
$283$	23.1782	−	10.3196i	1.37780	−	0.613437i	0.421770	−	0.906703i	$-0.361409\pi$
$283$	23.1782	−	10.3196i	1.37780	−	0.613437i	0.956031	+	0.293266i	$0.0947422\pi$
$284$	4.72483	+	5.24745i	0.280367	+	0.311379i
$285$	8.39619	−	5.93883i	0.497347	−	0.351786i
$286$	−6.86288	+	7.62199i	−0.405810	+	0.450698i
$287$	−8.07130	+	24.8409i	−0.476434	+	1.46631i
$288$	15.8639	+	11.6988i	0.934787	+	0.689356i
$289$	4.97024	+	15.2968i	0.292367	+	0.899814i
$290$	5.56297	−	7.51137i	0.326669	−	0.441083i
$291$	2.70417	−	0.868036i	0.158521	−	0.0508852i
$292$	0.104539	−	0.0465438i	0.00611769	−	0.00272377i
$293$	8.32257	−	14.4151i	0.486210	−	0.842140i	−0.513664	−	0.857991i	$-0.671712\pi$
$293$	8.32257	−	14.4151i	0.486210	−	0.842140i	0.999874	+	0.0158509i	$0.00504570\pi$
$294$	31.9486	+	18.5971i	1.86328	+	1.08460i
$295$	−27.8702	−	9.33817i	−1.62267	−	0.543689i
$296$	2.17479	−	1.58008i	0.126407	−	0.0918402i
$297$	−4.67271	−	0.541498i	−0.271138	−	0.0314209i
$298$	−7.94076	−	24.4392i	−0.459996	−	1.41572i
$299$	10.8823	+	18.8487i	0.629341	+	1.09005i
$300$	11.2509	−	3.38589i	0.649574	−	0.195485i
$301$	−5.00992	+	8.67743i	−0.288767	+	0.500159i
$302$	0.612956	+	0.130288i	0.0352717	+	0.00749723i
$303$	−12.9114	−	4.24591i	−0.741742	−	0.243921i
$304$	−11.8204	−	5.26278i	−0.677946	−	0.301841i
$305$	6.85469	−	30.8586i	0.392498	−	1.76696i
$306$	3.08129	+	31.4640i	0.176145	+	1.79868i
$307$	−0.293679			−0.0167612			−0.00838058	−	0.999965i	$-0.502668\pi$
$307$	−0.293679			−0.0167612			−0.00838058	+	0.999965i	$0.502668\pi$
$308$	0.554413	−	5.27489i	0.0315906	−	0.300565i
$309$	−16.0171	−	14.5251i	−0.911180	−	0.826306i
$310$	−1.90541	−	9.38543i	−0.108220	−	0.533057i
$311$	19.6920	+	4.18566i	1.11663	+	0.237347i	0.729030	−	0.684481i	$-0.239971\pi$
$311$	19.6920	+	4.18566i	1.11663	+	0.237347i	0.387599	+	0.921828i	$0.373305\pi$
$312$	−9.35113	−	8.48010i	−0.529403	−	0.480091i
$313$	−6.40947	+	1.36237i	−0.362285	+	0.0770060i	−0.385458	−	0.922725i	$-0.625956\pi$
$313$	−6.40947	+	1.36237i	−0.362285	+	0.0770060i	0.0231731	+	0.999731i	$0.492623\pi$
$314$	7.33097	+	22.5624i	0.413710	+	1.27327i
$315$	−17.4061	+	23.1569i	−0.980724	+	1.30474i
$316$	−0.374100	+	1.15136i	−0.0210448	+	0.0647692i
$317$	2.51998	−	23.9760i	0.141536	−	1.34663i	−0.661162	−	0.750243i	$-0.729936\pi$
$317$	2.51998	−	23.9760i	0.141536	−	1.34663i	0.802698	−	0.596385i	$-0.203397\pi$
$318$	−8.04045	−	11.1498i	−0.450886	−	0.625247i
$319$	1.88689	−	0.840099i	0.105646	−	0.0470365i
$320$	−3.77744	−	3.46428i	−0.211165	−	0.193659i
$321$	−7.99114	+	7.14405i	−0.446022	+	0.398742i
$322$	−25.4398	−	11.3265i	−1.41770	−	0.631203i
$323$	−4.71974	−	14.5259i	−0.262613	−	0.808241i
$324$	−1.44864	+	12.1241i	−0.0804801	+	0.673560i
$325$	−30.3558	+	5.87430i	−1.68384	+	0.325847i
$326$	1.03921	+	1.79996i	0.0575563	+	0.0996904i
$327$	12.1168	+	27.4769i	0.670062	+	1.51948i
$328$	0.745132	+	7.08946i	0.0411431	+	0.391450i
$329$	−2.51889	−	23.9656i	−0.138871	−	1.32127i
$330$	6.26588	+	1.41522i	0.344925	+	0.0779050i
$331$	−1.78479	+	16.9811i	−0.0981008	+	0.933367i	0.829175	+	0.558989i	$0.188810\pi$
$331$	−1.78479	+	16.9811i	−0.0981008	+	0.933367i	−0.927276	+	0.374378i	$0.877856\pi$
$332$	1.41307			0.0775525
$333$	6.23099	+	2.82740i	0.341456	+	0.154940i
$334$	0.627995	−	1.93277i	0.0343624	−	0.105756i
$335$	10.1391	−	13.6903i	0.553959	−	0.747980i
$336$	36.2340	+	3.93846i	1.97673	+	0.214860i
$337$	17.1186	+	19.0122i	0.932512	+	1.03566i	0.999282	+	0.0378910i	$0.0120640\pi$
$337$	17.1186	+	19.0122i	0.932512	+	1.03566i	−0.0667700	+	0.997768i	$0.521269\pi$
$338$	−30.9417	−	34.3642i	−1.68301	−	1.86917i
$339$	−10.3254	−	1.12232i	−0.560800	−	0.0609562i
$340$	0.159549	−	17.4486i	0.00865275	−	0.946284i
$341$	0.653958	−	2.01268i	0.0354138	−	0.108992i
$342$	−1.42249	−	14.5255i	−0.0769195	−	0.785450i
$343$	20.0776			1.08409
$344$	−0.285846	+	2.71965i	−0.0154118	+	0.146634i
$345$	6.96503	−	11.7177i	0.374985	−	0.630861i
$346$	−0.941859	−	8.96119i	−0.0506347	−	0.481757i
$347$	−2.76150	−	26.2739i	−0.148245	−	1.41046i	−0.775354	−	0.631527i	$-0.782429\pi$
$347$	−2.76150	−	26.2739i	−0.148245	−	1.41046i	0.627109	−	0.778932i	$-0.284238\pi$
$348$	−2.16328	−	4.90559i	−0.115964	−	0.262967i
$349$	6.45615	+	11.1824i	0.345590	+	0.598579i	0.985461	−	0.169903i	$-0.0543455\pi$
$349$	6.45615	+	11.1824i	0.345590	+	0.598579i	−0.639871	+	0.768482i	$0.721012\pi$
$350$	27.0040	−	28.9099i	1.44343	−	1.54530i
$351$	7.01497	−	31.3568i	0.374431	−	1.67370i
$352$	−1.83803	−	5.65689i	−0.0979675	−	0.301513i
$353$	0.971952	+	0.432741i	0.0517318	+	0.0230325i	0.432439	−	0.901663i	$-0.357653\pi$
$353$	0.971952	+	0.432741i	0.0517318	+	0.0230325i	−0.380708	+	0.924695i	$0.624320\pi$
$354$	−31.0981	+	27.8015i	−1.65284	+	1.47764i
$355$	−4.83059	+	10.5880i	−0.256381	+	0.561955i
$356$	7.40235	−	3.29574i	0.392324	−	0.174674i
$357$	25.1645	+	34.8959i	1.33185	+	1.84689i
$358$	0.381685	−	3.63149i	0.0201727	−	0.191930i
$359$	−1.89849	+	5.84296i	−0.100199	+	0.308380i	−0.988574	−	0.150739i	$-0.951835\pi$
$359$	−1.89849	+	5.84296i	−0.100199	+	0.308380i	0.888375	+	0.459119i	$0.151835\pi$
$360$	−1.76922	+	7.70583i	−0.0932461	+	0.406133i
$361$	−3.69243	−	11.3641i	−0.194339	−	0.598112i
$362$	−15.5839	+	3.31246i	−0.819071	+	0.174099i
$363$	−13.0620	−	11.8453i	−0.685575	−	0.621716i
$364$	35.4384	+	7.53267i	1.85748	+	0.394819i
$365$	0.139000	+	0.127476i	0.00727558	+	0.00667242i
$366$	−33.2313	−	30.1359i	−1.73703	−	1.57523i
$367$	1.46186	−	13.9087i	0.0763086	−	0.726028i	−0.887748	−	0.460330i	$-0.847731\pi$
$367$	1.46186	−	13.9087i	0.0763086	−	0.726028i	0.964056	−	0.265698i	$-0.0856024\pi$
$368$	−17.1503			−0.894022
$369$	−14.7548	+	10.5607i	−0.768104	+	0.549770i
$370$	−8.04909	−	4.74580i	−0.418452	−	0.246722i
$371$	−17.0897	−	7.60884i	−0.887255	−	0.395031i
$372$	−5.21832	−	1.71604i	−0.270557	−	0.0889726i
$373$	−1.46137	−	0.310623i	−0.0756667	−	0.0160835i	0.169923	−	0.985457i	$-0.445648\pi$
$373$	−1.46137	−	0.310623i	−0.0756667	−	0.0160835i	−0.245589	+	0.969374i	$0.578982\pi$
$374$	4.77001	−	8.26191i	0.246652	−	0.427213i
$375$	12.5057	+	14.7854i	0.645790	+	0.763515i
$376$	−3.28838	−	5.69564i	−0.169585	−	0.293730i
$377$	4.35984	+	13.4182i	0.224543	+	0.691072i
$378$	16.3208	+	37.7337i	0.839452	+	1.94081i
$379$	−0.536836	+	0.390034i	−0.0275754	+	0.0200347i	−0.601488	−	0.798882i	$-0.705425\pi$
$379$	−0.536836	+	0.390034i	−0.0275754	+	0.0200347i	0.573912	+	0.818917i	$0.305425\pi$
$380$	−0.0736565	+	8.05523i	−0.00377850	+	0.413225i
$381$	18.7078	+	10.8897i	0.958430	+	0.557896i
$382$	−20.6131	+	35.7030i	−1.05466	+	1.82672i
$383$	19.2398	−	8.56610i	0.983106	−	0.437707i	0.148715	−	0.988880i	$-0.452486\pi$
$383$	19.2398	−	8.56610i	0.983106	−	0.437707i	0.834391	+	0.551173i	$0.185820\pi$
$384$	14.7454	−	4.73325i	0.752472	−	0.241543i
$385$	8.33827	−	2.62522i	0.424958	−	0.133794i
$386$	−6.22657	−	19.1634i	−0.316924	−	0.975391i
$387$	−6.37883	+	2.78594i	−0.324254	+	0.141617i
$388$	−0.687442	+	2.11573i	−0.0348996	+	0.107410i
$389$	−10.8617	+	12.0631i	−0.550710	+	0.611625i	−0.952660	−	0.304036i	$-0.901666\pi$
$389$	−10.8617	+	12.0631i	−0.550710	+	0.611625i	0.401951	+	0.915661i	$0.368332\pi$
$390$	−14.0880	+	41.5559i	−0.713373	+	2.10427i
$391$	−13.5462	−	15.0446i	−0.685060	−	0.760836i
$392$	12.5428	−	5.58443i	0.633509	−	0.282056i
$393$	−3.68785	+	8.20453i	−0.186027	+	0.413864i
$394$	1.13422	−	10.7914i	0.0571410	−	0.543660i
$395$	−1.98618	+	0.190412i	−0.0999357	+	0.00958065i
$396$	2.48486	−	2.72061i	0.124869	−	0.136716i
$397$	−13.0288	+	9.46597i	−0.653896	+	0.475083i	−0.864596	−	0.502467i	$-0.832426\pi$
$397$	−13.0288	+	9.46597i	−0.653896	+	0.475083i	0.210700	+	0.977551i	$0.432426\pi$
$398$	−10.4679	+	11.6258i	−0.524708	+	0.582748i
$399$	−11.6173	−	16.1098i	−0.581594	−	0.806501i
$400$	7.95129	−	23.0298i	0.397565	−	1.15149i
$401$	−9.75500	+	16.8962i	−0.487142	+	0.843754i	−0.999891	−	0.0147845i	$-0.995294\pi$
$401$	−9.75500	+	16.8962i	−0.487142	+	0.843754i	0.512749	+	0.858539i	$0.328627\pi$
$402$	−9.75513	−	22.1214i	−0.486542	−	1.10332i
$403$	13.2059	+	5.87965i	0.657833	+	0.292886i
$404$	8.61298	−	6.25770i	0.428512	−	0.311332i
$405$	−19.2796	+	5.77038i	−0.958011	+	0.286733i
$406$	−14.6042	−	10.6106i	−0.724794	−	0.526594i
$407$	−1.03239	−	1.78816i	−0.0511739	−	0.0886358i
$408$	10.1479	+	5.90701i	0.502395	+	0.292441i
$409$	11.4065	+	12.6682i	0.564014	+	0.626401i	0.955928	−	0.293601i	$-0.0948536\pi$
$409$	11.4065	+	12.6682i	0.564014	+	0.626401i	−0.391914	+	0.920002i	$0.628187\pi$
$410$	21.5710	−	12.1924i	1.06532	−	0.602142i
$411$	10.3789	−	14.1792i	0.511955	−	0.699410i
$412$	16.5665	−	3.52132i	0.816174	−	0.173483i
$413$	−17.5417	+	53.9879i	−0.863172	+	2.65657i
$414$	−9.55342	−	16.8217i	−0.469525	−	0.826743i
$415$	0.927787	+	2.13620i	0.0455433	+	0.104862i
$416$	39.7417	−	8.44736i	1.94850	−	0.414166i
$417$	−5.13768	+	2.94197i	−0.251593	+	0.144069i
$418$	−2.20210	+	3.81415i	−0.107708	+	0.186556i
$419$	−28.4147	+	12.6511i	−1.38815	+	0.618044i	−0.958537	−	0.284969i	$-0.908017\pi$
$419$	−28.4147	+	12.6511i	−1.38815	+	0.618044i	−0.429613	+	0.903013i	$0.641350\pi$
$420$	−6.73752	−	21.6680i	−0.328757	−	1.05729i
$421$	−23.9324	−	10.6554i	−1.16639	−	0.519311i	−0.270125	−	0.962825i	$-0.587065\pi$
$421$	−23.9324	−	10.6554i	−1.16639	−	0.519311i	−0.896267	+	0.443514i	$0.853732\pi$
$422$	39.7717	−	28.8959i	1.93606	−	1.40663i
$423$	8.47291	−	14.4378i	0.411967	−	0.701989i
$424$	−5.10556			−0.247948
$425$	26.4825	−	11.2151i	1.28459	−	0.544012i
$426$	9.66042	+	13.3962i	0.468049	+	0.649048i
$427$	−59.7152	−	12.6929i	−2.88982	−	0.614250i
$428$	−0.877628	−	8.35007i	−0.0424218	−	0.403616i
$429$	−7.22863	+	6.46237i	−0.349002	+	0.312006i
$430$	9.06667	−	2.85455i	0.437234	−	0.137659i
$431$	25.1191	+	18.2501i	1.20995	+	0.879078i	0.995226	−	0.0975980i	$-0.0311159\pi$
$431$	25.1191	+	18.2501i	1.20995	+	0.879078i	0.214721	+	0.976676i	$0.431116\pi$
$432$	18.6346	+	17.1416i	0.896559	+	0.824724i
$433$	21.1261	+	15.3490i	1.01526	+	0.737628i	0.965305	−	0.261124i	$-0.0840931\pi$
$433$	21.1261	+	15.3490i	1.01526	+	0.737628i	0.0499521	+	0.998752i	$0.484093\pi$
$434$	−18.0915	+	3.84547i	−0.868420	+	0.184588i
$435$	5.99563	−	6.49119i	0.287468	−	0.311229i
$436$	−23.0082	−	4.89055i	−1.10189	−	0.234215i
$437$	6.25366	+	6.94539i	0.299153	+	0.332243i
$438$	0.254850	−	0.0818068i	0.0121772	−	0.00390888i
$439$	5.83202	−	6.47712i	0.278347	−	0.309136i	−0.587719	−	0.809065i	$-0.699974\pi$
$439$	5.83202	−	6.47712i	0.278347	−	0.309136i	0.866066	+	0.499929i	$0.166641\pi$
$440$	1.78753	−	1.58015i	0.0852172	−	0.0753305i
$441$	28.1267	+	20.7420i	1.33937	+	0.987714i
$442$	52.7203	+	38.3036i	2.50765	+	1.82191i
$443$	−9.84019	−	17.0437i	−0.467521	−	0.809771i	0.531790	−	0.846876i	$-0.321520\pi$
$443$	−9.84019	−	17.0437i	−0.467521	−	0.809771i	−0.999311	+	0.0371056i	$0.988186\pi$
$444$	−4.65108	+	2.66333i	−0.220731	+	0.126396i
$445$	9.84248	+	9.02653i	0.466578	+	0.427898i
$446$	2.83721	+	26.9943i	0.134346	+	1.27822i
$447$	−4.96644	−	23.7801i	−0.234905	−	1.12476i
$448$	−6.62352	+	7.35617i	−0.312932	+	0.347546i
$449$	−4.17634			−0.197094			−0.0985469	−	0.995132i	$-0.531419\pi$
$449$	−4.17634			−0.197094			−0.0985469	+	0.995132i	$0.531419\pi$
$450$	27.0178	−	5.02959i	1.27363	−	0.237097i
$451$	5.47538			0.257826
$452$	5.44369	−	6.04583i	0.256050	−	0.284372i
$453$	0.562771	+	0.185067i	0.0264413	+	0.00869520i
$454$	−2.37289	−	22.5765i	−0.111365	−	1.05957i
$455$	11.8805	+	58.5194i	0.556966	+	2.74343i
$456$	−4.68481	−	2.72700i	−0.219386	−	0.127703i
$457$	7.74545	+	13.4155i	0.362317	+	0.627551i	0.988342	−	0.152252i	$-0.0486525\pi$
$457$	7.74545	+	13.4155i	0.362317	+	0.627551i	−0.626025	+	0.779803i	$0.715319\pi$
$458$	23.4447	+	17.0335i	1.09550	+	0.795925i
$459$	−0.318322	+	29.8859i	−0.0148580	+	1.39496i
$460$	4.25353	+	9.79361i	0.198322	+	0.456629i
$461$	1.52663	−	1.69550i	0.0711023	−	0.0789671i	−0.706544	−	0.707669i	$-0.749747\pi$
$461$	1.52663	−	1.69550i	0.0711023	−	0.0789671i	0.777646	+	0.628702i	$0.216413\pi$
$462$	2.62242	−	12.1257i	0.122006	−	0.564137i
$463$	−10.0422	−	11.1530i	−0.466701	−	0.518324i	0.463140	−	0.886285i	$-0.346723\pi$
$463$	−10.0422	−	11.1530i	−0.466701	−	0.518324i	−0.929841	+	0.367961i	$0.880056\pi$
$464$	−10.8746	−	2.31146i	−0.504840	−	0.107307i
$465$	−0.832004	−	9.01545i	−0.0385833	−	0.418082i
$466$	23.2261	−	4.93686i	1.07593	−	0.228696i
$467$	−4.68683	−	3.40518i	−0.216881	−	0.157573i	0.474041	−	0.880503i	$-0.342795\pi$
$467$	−4.68683	−	3.40518i	−0.216881	−	0.157573i	−0.690921	+	0.722930i	$0.742795\pi$
$468$	16.7079	+	18.8231i	0.772323	+	0.870098i
$469$	−26.6177	−	19.3389i	−1.22909	−	0.892987i
$470$	−13.6056	+	18.3709i	−0.627579	+	0.847385i
$471$	4.58505	+	21.9539i	0.211268	+	1.01158i
$472$	1.61943	+	15.4079i	0.0745403	+	0.709204i
$473$	2.05456	+	0.436710i	0.0944687	+	0.0200799i
$474$	−1.16091	+	2.58273i	−0.0533223	+	0.118629i
$475$	−12.2258	+	5.17750i	−0.560957	+	0.237560i
$476$	−33.6996			−1.54462
$477$	−6.41772	−	11.3004i	−0.293847	−	0.517408i
$478$	−7.22820	+	5.25160i	−0.330610	+	0.240202i
$479$	18.2495	+	8.12520i	0.833841	+	0.371250i	0.778830	−	0.627236i	$-0.215814\pi$
$479$	18.2495	+	8.12520i	0.833841	+	0.371250i	0.0550118	+	0.998486i	$0.482480\pi$
$480$	−16.7858	−	19.1253i	−0.766163	−	0.872944i
$481$	12.8848	−	5.73667i	0.587495	−	0.261570i
$482$	−2.35623	+	4.08110i	−0.107323	+	0.185889i
$483$	−22.7523	−	13.2439i	−1.03526	−	0.602621i
$484$	13.5100	−	2.87165i	0.614093	−	0.130529i
$485$	−3.64979	+	0.349898i	−0.165728	+	0.0158881i
$486$	−6.43292	+	27.8262i	−0.291803	+	1.26222i
$487$	9.06469	−	27.8982i	0.410760	−	1.26419i	−0.505228	−	0.862986i	$-0.668592\pi$
$487$	9.06469	−	27.8982i	0.410760	−	1.26419i	0.915988	−	0.401205i	$-0.131408\pi$
$488$	−16.2976	+	3.46415i	−0.737756	+	0.156815i
$489$	0.792810	+	1.79783i	0.0358521	+	0.0813008i
$490$	−35.1725	−	32.2567i	−1.58893	−	1.45721i
$491$	−5.37446	−	5.96895i	−0.242546	−	0.269375i	0.609564	−	0.792736i	$-0.291344\pi$
$491$	−5.37446	−	5.96895i	−0.242546	−	0.269375i	−0.852111	+	0.523362i	$0.824678\pi$
$492$	0.0504588	−	14.2126i	0.00227486	−	0.640753i
$493$	−6.56164	−	11.3651i	−0.295521	−	0.511858i
$494$	−24.3386	−	17.6830i	−1.09505	−	0.795597i
$495$	5.74435	+	1.97017i	0.258189	+	0.0885527i
$496$	−9.21545	+	6.69541i	−0.413786	+	0.300633i
$497$	20.5329	+	9.14186i	0.921029	+	0.410068i
$498$	3.28584	+	0.357155i	0.147242	+	0.0160045i
$499$	14.0871	−	24.3995i	0.630623	−	1.09227i	−0.356801	−	0.934180i	$-0.616133\pi$
$499$	14.0871	−	24.3995i	0.630623	−	1.09227i	0.987425	−	0.158091i	$-0.0505339\pi$
$500$	−15.1231	+	1.17118i	−0.676326	+	0.0523767i
$501$	0.787659	−	1.75234i	0.0351900	−	0.0782888i
$502$	−15.3003	+	16.9927i	−0.682886	+	0.758422i
$503$	−4.88620	+	3.55003i	−0.217865	+	0.158288i	−0.691365	−	0.722506i	$-0.742990\pi$
$503$	−4.88620	+	3.55003i	−0.217865	+	0.158288i	0.473500	+	0.880794i	$0.342990\pi$
$504$	14.9127	+	3.28064i	0.664266	+	0.146131i
$505$	15.1151	+	8.91194i	0.672611	+	0.396576i
$506$	−0.610199	+	5.80566i	−0.0271267	+	0.258093i
$507$	−25.5697	−	35.4577i	−1.13559	−	1.57473i
$508$	−15.4896	+	6.89641i	−0.687240	+	0.305979i
$509$	−26.8278	−	29.7953i	−1.18912	−	1.32065i	−0.935490	−	0.353353i	$-0.885042\pi$
$509$	−26.8278	−	29.7953i	−1.18912	−	1.32065i	−0.253632	−	0.967301i	$-0.581625\pi$
$510$	4.78114	−	40.5332i	0.211713	−	1.79484i
$511$	0.243728	−	0.270687i	0.0107819	−	0.0119745i
$512$	−6.34397	+	19.5247i	−0.280367	+	0.862880i
$513$	0.146955	−	13.7970i	0.00648822	−	0.609151i
$514$	−6.92539	−	21.3142i	−0.305466	−	0.940128i
$515$	16.2005	+	22.7323i	0.713878	+	1.00170i
$516$	1.15251	−	5.32904i	0.0507365	−	0.234598i
$517$	−4.61485	+	2.05466i	−0.202961	+	0.0903640i
$518$	−9.02295	+	15.6282i	−0.396446	+	0.686664i
$519$	0.0302425	−	8.51830i	0.00132750	−	0.373912i
$520$	9.45819	+	13.2716i	0.414769	+	0.581998i
$521$	−23.0314	+	16.7333i	−1.00902	+	0.733098i	−0.964004	−	0.265888i	$-0.914335\pi$
$521$	−23.0314	+	16.7333i	−1.00902	+	0.733098i	−0.0450190	+	0.998986i	$0.514335\pi$
$522$	−3.79041	−	11.9538i	−0.165902	−	0.523205i
$523$	9.53164	+	29.3354i	0.416790	+	1.28275i	0.910640	+	0.413200i	$0.135589\pi$
$523$	9.53164	+	29.3354i	0.416790	+	1.28275i	−0.493851	+	0.869547i	$0.664411\pi$
$524$	−3.52296	−	6.10194i	−0.153901	−	0.266564i
$525$	28.3328	−	24.4120i	1.23654	−	1.06543i
$526$	−10.0997	+	17.4932i	−0.440368	+	0.762740i
$527$	−13.1522	−	2.79558i	−0.572917	−	0.121777i
$528$	−1.56200	−	7.47910i	−0.0679773	−	0.325486i
$529$	−9.69475	−	4.31638i	−0.421511	−	0.187669i
$530$	7.06967	+	16.2777i	0.307087	+	0.707057i
$531$	−32.0673	+	22.9521i	−1.39160	+	0.996038i
$532$	15.5576			0.674506
$533$	−3.90949	+	37.1963i	−0.169339	+	1.61115i
$534$	18.0458	−	5.79268i	0.780918	−	0.250674i
$535$	12.0469	−	6.80918i	0.520833	−	0.294387i
$536$	−8.78325	−	1.86694i	−0.379379	−	0.0806394i
$537$	0.729702	−	3.37403i	0.0314890	−	0.145600i
$538$	−11.3248	+	2.40717i	−0.488248	+	0.103780i
$539$	−3.25885	−	10.0297i	−0.140368	−	0.432010i
$540$	5.16696	−	14.8926i	0.222351	−	0.640875i
$541$	−3.48166	+	10.7154i	−0.149688	+	0.460693i	−0.997584	−	0.0694700i	$-0.977869\pi$
$541$	−3.48166	+	10.7154i	−0.149688	+	0.460693i	0.847896	+	0.530163i	$0.177869\pi$
$542$	1.15990	−	11.0357i	0.0498219	−	0.474024i
$543$	−14.9847	+	1.52119i	−0.643057	+	0.0652806i
$544$	−34.5244	+	15.3713i	−1.48022	+	0.659038i
$545$	−7.71336	−	37.9935i	−0.330404	−	1.62746i
$546$	80.5016	+	26.4729i	3.44515	+	1.13294i
$547$	−24.5114	−	10.9132i	−1.04803	−	0.466615i	−0.190846	−	0.981620i	$-0.561123\pi$
$547$	−24.5114	−	10.9132i	−1.04803	−	0.466615i	−0.857187	+	0.515005i	$0.827790\pi$
$548$	4.25330	+	13.0903i	0.181692	+	0.559190i
$549$	−28.1535	−	31.7177i	−1.20156	−	1.35368i
$550$	−7.51306	−	3.51103i	−0.320358	−	0.149711i
$551$	3.02921	+	5.24675i	0.129049	+	0.223519i
$552$	−7.14291	−	0.776399i	−0.304022	−	0.0330457i
$553$	0.402797	+	3.83236i	0.0171287	+	0.162968i
$554$	5.71304	+	54.3559i	0.242724	+	2.30936i
$555$	−7.08004	−	5.28255i	−0.300531	−	0.224232i
$556$	0.484740	−	4.61199i	0.0205575	−	0.195592i
$557$	−35.4517			−1.50214			−0.751069	−	0.660224i	$-0.770461\pi$
$557$	−35.4517			−1.50214			−0.751069	+	0.660224i	$0.770461\pi$
$558$	−11.7005	−	5.30927i	−0.495322	−	0.224759i
$559$	−4.43371	+	13.6456i	−0.187526	+	0.577145i
$560$	−44.6156	−	14.9489i	−1.88535	−	0.631705i
$561$	5.32705	−	7.27758i	0.224908	−	0.307260i
$562$	27.3347	+	30.3582i	1.15304	+	1.28058i
$563$	26.2620	+	29.1669i	1.10681	+	1.22924i	0.971147	+	0.238483i	$0.0766502\pi$
$563$	26.2620	+	29.1669i	1.10681	+	1.22924i	0.135664	+	0.990755i	$0.456683\pi$
$564$	5.29081	+	11.9978i	0.222783	+	0.505199i
$565$	12.7139	+	4.25991i	0.534878	+	0.179216i
$566$	−14.3644	+	44.2092i	−0.603782	+	1.85825i
$567$	11.4842	+	37.1309i	0.482292	+	1.55935i
$568$	6.13421			0.257386
$569$	4.29417	−	40.8563i	0.180021	−	1.71278i	−0.415624	−	0.909537i	$-0.636437\pi$
$569$	4.29417	−	40.8563i	0.180021	−	1.71278i	0.595645	−	0.803248i	$-0.296897\pi$
$570$	−2.20724	+	18.7123i	−0.0924510	+	0.783774i
$571$	−4.85569	−	46.1988i	−0.203204	−	1.93336i	−0.335274	−	0.942121i	$-0.608829\pi$
$571$	−4.85569	−	46.1988i	−0.203204	−	1.93336i	0.132070	−	0.991240i	$-0.457838\pi$
$572$	−0.793886	−	7.55332i	−0.0331940	−	0.315820i
$573$	−23.0203	+	31.4493i	−0.961687	+	1.31381i
$574$	−23.9270	−	41.4427i	−0.998692	−	1.72979i
$575$	−12.0126	+	12.8604i	−0.500961	+	0.536318i
$576$	−6.73623	+	1.38191i	−0.280676	+	0.0575797i
$577$	0.870205	+	2.67822i	0.0362271	+	0.111496i	0.967535	−	0.252738i	$-0.0813310\pi$
$577$	0.870205	+	2.67822i	0.0362271	+	0.111496i	−0.931308	+	0.364233i	$0.881331\pi$
$578$	−26.9204	−	11.9857i	−1.11974	−	0.498541i
$579$	−3.89432	−	18.6466i	−0.161842	−	0.774926i
$580$	1.37710	+	6.78316i	0.0571811	+	0.281655i
$581$	4.10905	−	1.82947i	0.170472	−	0.0758990i
$582$	−2.13327	+	4.74599i	−0.0884269	+	0.196727i
$583$	−0.409914	+	3.90008i	−0.0169769	+	0.161525i
$584$	0.0307195	−	0.0945450i	0.00127118	−	0.00391230i
$585$	−17.4856	+	37.6167i	−0.722942	+	1.55526i
$586$	9.42381	+	29.0035i	0.389294	+	1.19812i
$587$	7.32326	−	1.55661i	0.302263	−	0.0642480i	−0.0542834	−	0.998526i	$-0.517287\pi$
$587$	7.32326	−	1.55661i	0.302263	−	0.0642480i	0.356547	+	0.934278i	$0.383954\pi$
$588$	−26.0644	+	8.36664i	−1.07488	+	0.345034i
$589$	6.07176	+	1.29059i	0.250182	+	0.0531779i
$590$	46.8814	−	26.4984i	1.93007	−	1.09092i
$591$	2.16838	−	10.0263i	0.0891953	−	0.412426i
$592$	−1.16172	+	11.0530i	−0.0477464	+	0.454277i
$593$	14.1652			0.581694			0.290847	−	0.956770i	$-0.406063\pi$
$593$	14.1652			0.581694			0.290847	+	0.956770i	$0.406063\pi$
$594$	6.46571	−	5.69824i	0.265291	−	0.233801i
$595$	−22.1262	−	50.9450i	−0.907088	−	2.08854i
$596$	17.3835	+	7.73965i	0.712058	+	0.317029i
$597$	−11.0258	+	9.85701i	−0.451255	+	0.403421i
$598$	−39.0043	−	8.29062i	−1.59500	−	0.339028i
$599$	17.7180	−	30.6885i	0.723939	−	1.25390i	−0.235470	−	0.971882i	$-0.575663\pi$
$599$	17.7180	−	30.6885i	0.723939	−	1.25390i	0.959409	−	0.282018i	$-0.0910037\pi$
$600$	4.35419	−	9.23170i	0.177759	−	0.376883i
$601$	0.756431	+	1.31018i	0.0308555	+	0.0534433i	0.881041	−	0.473040i	$-0.156844\pi$
$601$	0.756431	+	1.31018i	0.0308555	+	0.0534433i	−0.850185	+	0.526484i	$0.823510\pi$
$602$	−5.67282	−	17.4592i	−0.231207	−	0.711582i
$603$	−6.90842	−	21.7871i	−0.281333	−	0.887240i
$604$	−0.375414	+	0.272755i	−0.0152754	+	0.0110982i
$605$	13.2115	+	18.5382i	0.537124	+	0.753685i
$606$	21.6095	−	12.3742i	0.877828	−	0.502667i
$607$	−6.39122	+	11.0699i	−0.259412	+	0.449314i	−0.966084	−	0.258226i	$-0.916862\pi$
$607$	−6.39122	+	11.0699i	−0.259412	+	0.449314i	0.706673	+	0.707540i	$0.250195\pi$
$608$	15.9384	−	7.09622i	0.646386	−	0.287790i
$609$	−12.6417	−	11.4641i	−0.512266	−	0.464550i
$610$	33.6118	+	47.1635i	1.36090	+	1.90960i
$611$	−10.6630	−	32.8174i	−0.431380	−	1.32765i
$612$	−18.8415	−	13.8946i	−0.761623	−	0.561657i
$613$	9.49601	−	29.2257i	0.383540	−	1.18042i	−0.553994	−	0.832521i	$-0.686897\pi$
$613$	9.49601	−	29.2257i	0.383540	−	1.18042i	0.937534	−	0.347894i	$-0.113103\pi$
$614$	0.360031	−	0.399855i	0.0145297	−	0.0161369i
$615$	21.5189	−	9.25532i	0.867724	−	0.373211i
$616$	−3.08314	−	3.42418i	−0.124223	−	0.137964i
$617$	−27.7851	+	12.3707i	−1.11859	+	0.498027i	−0.880894	−	0.473314i	$-0.843058\pi$
$617$	−27.7851	+	12.3707i	−1.11859	+	0.498027i	−0.237692	+	0.971341i	$0.576391\pi$
$618$	39.4124	−	4.00099i	1.58540	−	0.160944i
$619$	−3.00135	+	28.5560i	−0.120635	+	1.14776i	0.751924	+	0.659250i	$0.229126\pi$
$619$	−3.00135	+	28.5560i	−0.120635	+	1.14776i	−0.872558	+	0.488510i	$0.837540\pi$
$620$	6.10895	+	3.60188i	0.245341	+	0.144655i
$621$	−7.26024	−	16.7857i	−0.291344	−	0.673586i
$622$	−29.8400	+	21.6800i	−1.19648	+	0.869290i
$623$	17.2582	−	19.1672i	0.691436	−	0.767918i
$624$	51.9235	−	5.27107i	2.07861	−	0.211012i
$625$	−11.7000	−	22.0932i	−0.467998	−	0.883729i
$626$	6.00266	−	10.3969i	0.239915	−	0.415545i
$627$	−2.45926	+	3.35973i	−0.0982133	+	0.134175i
$628$	−16.0486	−	7.14530i	−0.640409	−	0.285129i
$629$	−10.6135	+	7.71116i	−0.423188	+	0.307464i
$630$	−10.1902	−	52.0880i	−0.405989	−	2.07523i
$631$	13.4714	+	9.78757i	0.536289	+	0.389637i	0.822705	−	0.568468i	$-0.192464\pi$
$631$	13.4714	+	9.78757i	0.536289	+	0.389637i	−0.286416	+	0.958105i	$0.592464\pi$
$632$	0.525847	+	0.910793i	0.0209171	+	0.0362294i
$633$	40.3309	−	23.0946i	1.60301	−	0.917926i
$634$	29.5550	+	32.8241i	1.17378	+	1.30361i
$635$	−20.5956	−	18.8882i	−0.817313	−	0.749557i
$636$	10.1197	+	1.09997i	0.401274	+	0.0436165i
$637$	70.4623	−	14.9772i	2.79182	−	0.593419i
$638$	−1.16938	+	3.59898i	−0.0462962	+	0.142485i
$639$	7.71075	+	13.5771i	0.305032	+	0.537103i
$640$	−19.9017	+	1.90794i	−0.786682	+	0.0754178i
$641$	7.45307	−	1.58420i	0.294379	−	0.0625721i	−0.0583550	−	0.998296i	$-0.518586\pi$
$641$	7.45307	−	1.58420i	0.294379	−	0.0625721i	0.352734	+	0.935724i	$0.385252\pi$
$642$	0.0697220	−	19.6384i	0.00275171	−	0.775065i
$643$	−2.09689	+	3.63192i	−0.0826933	+	0.143229i	−0.904406	−	0.426673i	$-0.859686\pi$
$643$	−2.09689	+	3.63192i	−0.0826933	+	0.143229i	0.821713	+	0.569902i	$0.193019\pi$
$644$	18.8383	−	8.38736i	0.742333	−	0.330508i
$645$	8.81283	−	1.75661i	0.347005	−	0.0691664i
$646$	25.5636	+	11.3817i	1.00579	+	0.447805i
$647$	40.9094	−	29.7224i	1.60831	−	1.16851i	0.739821	−	0.672804i	$-0.234910\pi$
$647$	40.9094	−	29.7224i	1.60831	−	1.16851i	0.868492	−	0.495703i	$-0.165090\pi$
$648$	6.98511	+	7.98287i	0.274401	+	0.313597i
$649$	11.8999			0.467112
$650$	29.2161	−	48.5321i	1.14595	−	1.90359i
$651$	−17.3960	+	1.76597i	−0.681801	+	0.0692138i
$652$	−1.50544	−	0.319992i	−0.0589577	−	0.0125318i
$653$	3.96661	+	37.7398i	0.155226	+	1.47687i	0.743785	+	0.668419i	$0.233028\pi$
$653$	3.96661	+	37.7398i	0.155226	+	1.47687i	−0.588560	+	0.808454i	$0.700305\pi$
$654$	−52.2653	−	17.1874i	−2.04374	−	0.672081i
$655$	6.91146	−	9.33216i	0.270053	−	0.364638i
$656$	−23.8431	−	17.3231i	−0.930918	−	0.676352i
$657$	0.247876	−	0.0508507i	0.00967055	−	0.00198388i
$658$	35.7181	+	25.9507i	1.39244	+	1.01166i
$659$	13.1783	−	2.80114i	0.513355	−	0.109117i	0.0560518	−	0.998428i	$-0.482149\pi$
$659$	13.1783	−	2.80114i	0.513355	−	0.109117i	0.457303	+	0.889311i	$0.348815\pi$
$660$	−3.88351	+	2.74690i	−0.151165	+	0.106923i
$661$	45.5425	+	9.68036i	1.77140	+	0.376522i	0.973932	−	0.226840i	$-0.0728396\pi$
$661$	45.5425	+	9.68036i	1.77140	+	0.376522i	0.797467	+	0.603363i	$0.206173\pi$
$662$	−20.9324	−	23.2478i	−0.813561	−	0.903551i
$663$	45.6357	+	41.3849i	1.77234	+	1.60726i
$664$	0.821409	−	0.912267i	0.0318769	−	0.0354028i
$665$	10.2147	+	23.5190i	0.396109	+	0.912027i
$666$	−11.4884	+	5.01752i	−0.445166	+	0.194425i
$667$	6.49662	+	4.72007i	0.251550	+	0.182762i
$668$	0.752440	+	1.30327i	0.0291128	+	0.0504248i
$669$	−0.0911010	+	25.6601i	−0.00352217	+	0.992078i
$670$	6.20995	+	30.5882i	0.239911	+	1.18172i
$671$	1.33773	+	12.7276i	0.0516425	+	0.491345i
$672$	−36.6383	+	32.7545i	−1.41335	+	1.26353i
$673$	4.60871	−	5.11849i	0.177653	−	0.197303i	−0.647741	−	0.761860i	$-0.724286\pi$
$673$	4.60871	−	5.11849i	0.177653	−	0.197303i	0.825394	+	0.564557i	$0.190953\pi$
$674$	−46.8721			−1.80545
$675$	25.9062	−	1.96698i	0.997130	−	0.0757091i
$676$	34.2422			1.31701
$677$	−24.1380	+	26.8080i	−0.927699	+	1.03031i	0.0717600	+	0.997422i	$0.477138\pi$
$677$	−24.1380	+	26.8080i	−0.927699	+	1.03031i	−0.999459	+	0.0328921i	$0.989528\pi$
$678$	14.1864	−	12.6826i	0.544825	−	0.487071i
$679$	0.740175	+	7.04229i	0.0284053	+	0.270258i
$680$	−11.1719	−	10.2457i	−0.428423	−	0.392906i
$681$	0.0761918	−	21.4607i	0.00291967	−	0.822376i
$682$	1.93862	+	3.35780i	0.0742338	+	0.128577i
$683$	−27.9970	−	20.3410i	−1.07127	−	0.778326i	−0.0951333	−	0.995465i	$-0.530328\pi$
$683$	−27.9970	−	20.3410i	−1.07127	−	0.778326i	−0.976141	+	0.217138i	$0.930328\pi$
$684$	8.69827	+	6.41452i	0.332587	+	0.245265i
$685$	−16.9965	+	15.0246i	−0.649404	+	0.574062i
$686$	−24.6139	+	27.3365i	−0.939761	+	1.04371i
$687$	20.2941	+	18.4038i	0.774270	+	0.702149i
$688$	−7.56513	−	8.40192i	−0.288418	−	0.320320i
$689$	−26.2020	−	5.56940i	−0.998215	−	0.212177i
$690$	7.41545	+	23.8483i	0.282302	+	0.907890i
$691$	47.8971	−	10.1808i	1.82209	−	0.387297i	0.835365	−	0.549695i	$-0.185256\pi$
$691$	47.8971	−	10.1808i	1.82209	−	0.387297i	0.986725	+	0.162398i	$0.0519228\pi$
$692$	5.39806	+	3.92192i	0.205203	+	0.149089i
$693$	3.70336	−	11.1283i	0.140679	−	0.422728i
$694$	39.1584	+	28.4502i	1.48643	+	1.07996i
$695$	7.29040	−	2.29531i	0.276540	−	0.0870661i
$696$	−4.42450	−	1.45499i	−0.167710	−	0.0551514i
$697$	−3.63642	−	34.5983i	−0.137739	−	1.31050i
$698$	−23.1401	−	4.91857i	−0.875864	−	0.186171i
$699$	22.3331	−	2.26717i	0.844717	−	0.0857523i
$700$	2.52884	+	29.1851i	0.0955811	+	1.10309i
$701$	6.00618			0.226850			0.113425	−	0.993547i	$-0.463818\pi$
$701$	6.00618			0.226850			0.113425	+	0.993547i	$0.463818\pi$
$702$	34.0936	+	47.9926i	1.28678	+	1.81136i
$703$	4.89977	−	3.55989i	0.184798	−	0.134264i
$704$	1.89567	+	0.844005i	0.0714456	+	0.0318096i
$705$	−14.6638	+	15.8758i	−0.552269	+	0.597916i
$706$	−1.78074	+	0.792838i	−0.0670191	+	0.0298388i
$707$	16.9438	−	29.3476i	0.637239	−	1.10373i
$708$	0.109665	−	30.8889i	0.00412145	−	1.16087i
$709$	37.3871	−	7.94688i	1.40410	−	0.298451i	0.557279	−	0.830325i	$-0.311845\pi$
$709$	37.3871	−	7.94688i	1.40410	−	0.298451i	0.846824	+	0.531874i	$0.178512\pi$
$710$	−8.49405	−	19.5573i	−0.318776	−	0.733972i
$711$	−1.35491	+	2.30875i	−0.0508130	+	0.0865851i
$712$	2.17523	−	6.69467i	0.0815202	−	0.250893i
$713$	8.04793	−	1.71064i	0.301397	−	0.0640640i
$714$	−78.3622	−	8.51758i	−2.93263	−	0.318763i
$715$	10.8974	−	6.15946i	0.407540	−	0.230351i
$716$	1.80930	+	2.00943i	0.0676166	+	0.0750959i
$717$	−7.32983	+	4.19725i	−0.273738	+	0.156749i
$718$	−5.62798	−	9.74795i	−0.210035	−	0.363790i
$719$	−18.5111	−	13.4491i	−0.690348	−	0.501567i	0.186426	−	0.982469i	$-0.440309\pi$
$719$	−18.5111	−	13.4491i	−0.690348	−	0.501567i	−0.876775	+	0.480901i	$0.840309\pi$
$720$	−18.7811	−	26.7533i	−0.699932	−	0.997038i
$721$	43.6145	−	31.6878i	1.62429	−	1.18011i
$722$	19.9994	+	8.90430i	0.744300	+	0.331384i
$723$	−2.63138	+	3.59488i	−0.0978622	+	0.133695i
$724$	5.89888	−	10.2172i	0.219230	−	0.379718i
$725$	−9.35020	+	6.53547i	−0.347258	+	0.242721i
$726$	32.1409	−	3.26282i	1.19286	−	0.121095i
$727$	12.1687	−	13.5147i	0.451311	−	0.501231i	−0.473956	−	0.880549i	$-0.657174\pi$
$727$	12.1687	−	13.5147i	0.451311	−	0.501231i	0.925267	+	0.379317i	$0.123841\pi$
$728$	25.4631	−	18.5000i	0.943725	−	0.685657i
$729$	−8.88852	+	25.4950i	−0.329204	+	0.944259i
$730$	−0.343969	+	0.0329756i	−0.0127309	+	0.00122048i
$731$	1.39500	−	13.2725i	0.0515959	−	0.490902i
$732$	33.0498	−	3.35508i	1.22156	−	0.124007i
$733$	−29.3911	+	13.0857i	−1.08558	+	0.483333i	−0.869949	−	0.493141i	$-0.835849\pi$
$733$	−29.3911	+	13.0857i	−1.08558	+	0.483333i	−0.215634	+	0.976474i	$0.569182\pi$
$734$	17.1451	+	19.0415i	0.632836	+	0.702836i
$735$	−29.7613	−	33.9092i	−1.09776	−	1.25076i
$736$	15.4737	−	17.1853i	0.570369	−	0.633459i
$737$	−2.13132	+	6.55953i	−0.0785082	+	0.241623i
$738$	3.70957	−	33.0360i	0.136551	−	1.21607i
$739$	−9.10517	−	28.0228i	−0.334939	−	1.03084i	−0.966752	−	0.255716i	$-0.917689\pi$
$739$	−9.10517	−	28.0228i	−0.334939	−	1.03084i	0.631813	−	0.775121i	$-0.282311\pi$
$740$	6.59991	−	2.07792i	0.242617	−	0.0763857i
$741$	−21.0679	−	19.1055i	−0.773950	−	0.701859i
$742$	31.3106	−	13.9404i	1.14945	−	0.511768i
$743$	3.85790	−	6.68207i	0.141533	−	0.245142i	−0.786541	−	0.617538i	$-0.788130\pi$
$743$	3.85790	−	6.68207i	0.141533	−	0.245142i	0.928074	+	0.372396i	$0.121464\pi$
$744$	−4.14123	+	2.37138i	−0.151825	+	0.0869389i
$745$	−0.286763	+	31.3610i	−0.0105062	+	1.14898i
$746$	2.21447	−	1.60890i	0.0810773	−	0.0589061i
$747$	3.05168	+	0.671337i	0.111655	+	0.0245629i
$748$	2.18303	+	6.71868i	0.0798196	+	0.245659i
$749$	−13.3626	−	23.1448i	−0.488260	−	0.845691i
$750$	−35.4620	−	1.09901i	−1.29489	−	0.0401302i
$751$	−26.7485	+	46.3297i	−0.976066	+	1.69060i	−0.299694	+	0.954035i	$0.596885\pi$
$751$	−26.7485	+	46.3297i	−0.976066	+	1.69060i	−0.676372	+	0.736560i	$0.736449\pi$
$752$	26.5964	+	5.65324i	0.969871	+	0.206153i
$753$	−16.1157	+	14.4074i	−0.587290	+	0.525035i
$754$	−23.6143	−	10.5137i	−0.859981	−	0.382888i
$755$	−0.658821	−	0.388445i	−0.0239770	−	0.0141370i
$756$	−28.8518	−	9.71545i	−1.04933	−	0.353348i
$757$	−10.3719			−0.376971			−0.188486	−	0.982076i	$-0.560358\pi$
$757$	−10.3719			−0.376971			−0.188486	+	0.982076i	$0.560358\pi$
$758$	0.127079	−	1.20908i	0.00461573	−	0.0439157i
$759$	−1.16657	+	5.39405i	−0.0423439	+	0.195792i
$760$	5.15757	+	4.73000i	0.187085	+	0.171575i
$761$	−22.3424	−	4.74901i	−0.809910	−	0.172152i	−0.215698	−	0.976460i	$-0.569203\pi$
$761$	−22.3424	−	4.74901i	−0.809910	−	0.172152i	−0.594212	+	0.804309i	$0.702536\pi$
$762$	−37.7613	+	12.1213i	−1.36795	+	0.439110i
$763$	−73.2368	+	15.5670i	−2.65135	+	0.563562i
$764$	−9.43375	−	29.0341i	−0.341301	−	1.05042i
$765$	8.63422	−	37.6063i	0.312171	−	1.35966i
$766$	−11.9236	+	36.6972i	−0.430818	+	1.32592i
$767$	−8.49667	+	80.8404i	−0.306797	+	2.91898i
$768$	−14.8877	+	33.1214i	−0.537214	+	1.19516i
$769$	17.1427	−	7.63243i	0.618182	−	0.275232i	−0.0736574	−	0.997284i	$-0.523467\pi$
$769$	17.1427	−	7.63243i	0.618182	−	0.275232i	0.691840	+	0.722051i	$0.256800\pi$
$770$	−6.64783	+	14.5712i	−0.239571	+	0.525111i
$771$	−4.33139	−	20.7394i	−0.155991	−	0.746910i
$772$	13.6309	+	6.06887i	0.490587	+	0.218423i
$773$	11.9727	+	36.8481i	0.430627	+	1.32533i	0.897502	+	0.441010i	$0.145380\pi$
$773$	11.9727	+	36.8481i	0.430627	+	1.32533i	−0.466875	+	0.884323i	$0.654620\pi$
$774$	4.02687	−	12.1004i	0.144743	−	0.434940i
$775$	−1.43413	+	11.6000i	−0.0515154	+	0.416686i
$776$	0.966290	+	1.67366i	0.0346878	+	0.0600810i
$777$	−10.0766	+	13.7663i	−0.361497	+	0.493862i
$778$	−3.10869	−	29.5772i	−0.111452	−	1.06039i
$779$	1.67877	+	15.9724i	0.0601482	+	0.572272i
$780$	−15.8878	−	28.3434i	−0.568875	−	1.01486i
$781$	0.492503	−	4.68586i	0.0176232	−	0.167673i
$782$	37.0905			1.32635
$783$	−2.34122	−	11.6219i	−0.0836684	−	0.415332i
$784$	−17.5410	+	53.9858i	−0.626466	+	1.92806i
$785$	0.264742	−	28.9527i	0.00944904	−	1.03337i
$786$	−6.64972	−	15.0794i	−0.237188	−	0.537863i
$787$	5.79895	+	6.44039i	0.206710	+	0.229575i	0.837581	−	0.546313i	$-0.183969\pi$
$787$	5.79895	+	6.44039i	0.206710	+	0.229575i	−0.630871	+	0.775888i	$0.717302\pi$
$788$	5.37651	+	5.97122i	0.191530	+	0.212716i
$789$	−11.2791	+	15.4091i	−0.401548	+	0.548577i
$790$	2.17568	−	2.93770i	0.0774071	−	0.104519i
$791$	8.00222	−	24.6283i	0.284526	−	0.875682i
$792$	−0.311974	−	3.18567i	−0.0110855	−	0.113198i
$793$	−87.4187			−3.10433
$794$	3.08416	−	29.3439i	0.109453	−	1.04137i
$795$	4.98149	+	16.0206i	0.176675	+	0.568193i
$796$	−1.21091	−	11.5210i	−0.0429195	−	0.408352i
$797$	1.80598	+	17.1828i	0.0639712	+	0.608645i	0.978802	+	0.204808i	$0.0656570\pi$
$797$	1.80598	+	17.1828i	0.0639712	+	0.608645i	−0.914831	+	0.403837i	$0.867676\pi$
$798$	36.1763	+	3.93218i	1.28063	+	0.139198i
$799$	16.0481	+	27.7961i	0.567740	+	0.983354i
$800$	15.9028	+	28.7460i	0.562250	+	1.01632i
$801$	17.5519	−	3.60071i	0.620166	−	0.127225i
$802$	−11.0458	−	33.9954i	−0.390040	−	1.20042i
$803$	−0.0697555	−	0.0310571i	−0.00246162	−	0.00109598i
$804$	17.0071	+	5.59277i	0.599794	+	0.197242i
$805$	25.0482	+	22.9717i	0.882834	+	0.809646i
$806$	−24.1950	+	10.7723i	−0.852231	+	0.379438i
$807$	−10.8894	+	1.10545i	−0.383326	+	0.0389137i
$808$	0.966750	−	9.19801i	0.0340101	−	0.323585i
$809$	−7.51279	+	23.1220i	−0.264136	+	0.812925i	0.727756	+	0.685836i	$0.240563\pi$
$809$	−7.51279	+	23.1220i	−0.264136	+	0.812925i	−0.991891	+	0.127089i	$0.959437\pi$
$810$	15.7789	−	33.3240i	0.554415	−	1.17089i
$811$	−6.22416	−	19.1560i	−0.218560	−	0.672658i	−0.998882	−	0.0472798i	$-0.984945\pi$
$811$	−6.22416	−	19.1560i	−0.218560	−	0.672658i	0.780322	−	0.625378i	$-0.215055\pi$
$812$	13.0753	−	2.77925i	0.458854	−	0.0975324i
$813$	2.21748	−	10.2533i	0.0777704	−	0.359599i
$814$	3.70030	+	0.786522i	0.129695	+	0.0275676i
$815$	−0.504689	−	2.48593i	−0.0176785	−	0.0870785i
$816$	−46.2221	+	14.8372i	−1.61810	+	0.519408i
$817$	−0.644008	+	6.12733i	−0.0225310	+	0.214368i
$818$	−31.2318			−1.09199
$819$	72.9543	+	33.1040i	2.54923	+	1.15675i
$820$	−3.97881	+	17.9119i	−0.138946	+	0.625510i
$821$	−28.4737	−	12.6773i	−0.993739	−	0.442441i	−0.155554	−	0.987827i	$-0.549716\pi$
$821$	−28.4737	−	12.6773i	−0.993739	−	0.442441i	−0.838185	+	0.545386i	$0.816383\pi$
$822$	6.58169	+	31.5141i	0.229563	+	1.09918i
$823$	7.36472	+	1.56542i	0.256718	+	0.0545671i	0.334473	−	0.942405i	$-0.391442\pi$
$823$	7.36472	+	1.56542i	0.256718	+	0.0545671i	−0.0777548	+	0.996973i	$0.524775\pi$
$824$	7.35666	−	12.7421i	0.256281	−	0.443892i
$825$	−6.70240	−	4.06731i	−0.233348	−	0.141606i
$826$	−52.0016	−	90.0694i	−1.80937	−	3.13391i
$827$	−11.4110	−	35.1194i	−0.396798	−	1.22122i	−0.927552	−	0.373694i	$-0.878091\pi$
$827$	−11.4110	−	35.1194i	−0.396798	−	1.22122i	0.530754	−	0.847526i	$-0.321909\pi$
$828$	13.9907	+	3.07781i	0.486211	+	0.106961i
$829$	37.5208	−	27.2605i	1.30315	−	0.946796i	0.303171	−	0.952936i	$-0.401955\pi$
$829$	37.5208	−	27.2605i	1.30315	−	0.946796i	0.999981	+	0.00614051i	$0.00195460\pi$
$830$	−4.04592	−	1.35562i	−0.140436	−	0.0470544i
$831$	−0.183442	+	51.6695i	−0.00636353	+	1.79239i
$832$	−7.08716	+	12.2753i	−0.245703	+	0.425570i
$833$	−61.2121	+	27.2534i	−2.12087	+	0.944273i
$834$	2.29286	−	10.6018i	0.0793951	−	0.367111i
$835$	−1.47616	+	1.99318i	−0.0510848	+	0.0689769i
$836$	−1.00781	−	3.10171i	−0.0348558	−	0.107275i
$837$	−10.4542	−	6.18514i	−0.361351	−	0.213790i
$838$	17.6097	−	54.1971i	0.608317	−	1.87221i
$839$	−1.71729	+	1.90725i	−0.0592875	+	0.0658454i	−0.772059	−	0.635551i	$-0.780773\pi$
$839$	−1.71729	+	1.90725i	−0.0592875	+	0.0658454i	0.712771	+	0.701396i	$0.247440\pi$
$840$	−17.9052	−	8.24579i	−0.617786	−	0.284507i
$841$	−15.9216	−	17.6827i	−0.549021	−	0.609749i
$842$	43.8472	−	19.5220i	1.51107	−	0.672774i
$843$	22.5889	+	31.3243i	0.778004	+	1.07886i
$844$	−3.80522	+	36.2043i	−0.130981	+	1.24620i
$845$	22.4825	+	51.7652i	0.773422	+	1.78078i
$846$	9.27035	+	29.2360i	0.318721	+	1.00515i
$847$	35.5677	−	25.8414i	1.22212	−	0.887923i
$848$	14.1241	−	15.6864i	0.485024	−	0.538673i
$849$	−18.0165	+	40.0821i	−0.618324	+	1.37561i
$850$	−17.1960	+	49.8059i	−0.589819	+	1.70833i
$851$	4.01382	−	6.95215i	0.137592	−	0.238316i
$852$	−12.1587	−	1.32159i	−0.416549	−	0.0452768i
$853$	0.319722	+	0.142349i	0.0109471	+	0.00487395i	0.412203	−	0.911092i	$-0.364759\pi$
$853$	0.319722	+	0.142349i	0.0109471	+	0.00487395i	−0.401256	+	0.915966i	$0.631426\pi$
$854$	90.4887	−	65.7439i	3.09646	−	2.24971i
$855$	−3.98603	+	17.3611i	−0.136319	+	0.593738i
$856$	−5.90089	−	4.28725i	−0.201688	−	0.146535i
$857$	0.706787	+	1.22419i	0.0241434	+	0.0418175i	0.877845	−	0.478945i	$-0.158981\pi$
$857$	0.706787	+	1.22419i	0.0241434	+	0.0418175i	−0.853701	+	0.520763i	$0.825648\pi$
$858$	0.0630692	−	17.7645i	0.00215315	−	0.606470i
$859$	16.3422	+	18.1499i	0.557589	+	0.619265i	0.954362	−	0.298651i	$-0.0965368\pi$
$859$	16.3422	+	18.1499i	0.557589	+	0.619265i	−0.396773	+	0.917917i	$0.629870\pi$
$860$	−2.92162	+	6.40383i	−0.0996264	+	0.218369i
$861$	−18.2539	−	41.3938i	−0.622091	−	1.41070i
$862$	−55.6427	+	11.8272i	−1.89520	+	0.402837i
$863$	11.4015	−	35.0901i	0.388111	−	1.19448i	−0.546087	−	0.837728i	$-0.683883\pi$
$863$	11.4015	−	35.0901i	0.388111	−	1.19448i	0.934198	−	0.356754i	$-0.116117\pi$
$864$	−33.9895	+	3.20682i	−1.15635	+	0.109098i
$865$	−2.38470	+	10.7355i	−0.0810821	+	0.365017i
$866$	−46.7976	+	9.94713i	−1.59025	+	0.338017i
$867$	−24.0765	−	14.0148i	−0.817680	−	0.475966i
$868$	6.84808	−	11.8612i	0.232439	−	0.402596i
$869$	0.737964	−	0.328563i	0.0250337	−	0.0111457i
$870$	1.48776	+	16.1211i	0.0504396	+	0.546555i
$871$	−43.0395	−	19.1624i	−1.45834	−	0.649294i
$872$	−16.5318	+	12.0111i	−0.559838	+	0.406746i
$873$	−2.48976	+	4.24254i	−0.0842657	+	0.143588i
$874$	−17.1230			−0.579194
$875$	−42.4599	+	22.9851i	−1.43541	+	0.777038i
$876$	−0.0812586	+	0.180780i	−0.00274547	+	0.00610798i
$877$	37.1903	+	7.90505i	1.25583	+	0.266934i	0.787331	−	0.616531i	$-0.211462\pi$
$877$	37.1903	+	7.90505i	1.25583	+	0.266934i	0.468497	+	0.883465i	$0.344796\pi$
$878$	1.66916	+	15.8810i	0.0563316	+	0.535959i
$879$	5.89399	+	28.2213i	0.198799	+	0.951882i
$880$	−0.0901901	+	9.86339i	−0.00304031	+	0.332495i
$881$	34.5989	+	25.1376i	1.16567	+	0.846907i	0.990484	−	0.137629i	$-0.0439483\pi$
$881$	34.5989	+	25.1376i	1.16567	+	0.846907i	0.175183	+	0.984536i	$0.443948\pi$
$882$	−62.7225	+	12.8673i	−2.11198	+	0.433264i
$883$	−33.9890	−	24.6945i	−1.14382	−	0.831036i	−0.156175	−	0.987729i	$-0.549916\pi$
$883$	−33.9890	−	24.6945i	−1.14382	−	0.831036i	−0.987647	+	0.156694i	$0.949916\pi$
$884$	−47.2012	+	10.0329i	−1.58755	+	0.337444i
$885$	46.7679	−	20.1150i	1.57209	−	0.676159i
$886$	35.2691	+	7.49667i	1.18489	+	0.251856i
$887$	−18.3209	−	20.3474i	−0.615155	−	0.683199i	0.352402	−	0.935849i	$-0.385365\pi$
$887$	−18.3209	−	20.3474i	−0.615155	−	0.683199i	−0.967558	+	0.252649i	$0.918698\pi$
$888$	−0.984217	+	4.55087i	−0.0330281	+	0.152717i
$889$	−36.1133	+	40.1079i	−1.21120	+	1.34517i
$890$	−24.3562	+	2.33498i	−0.816422	+	0.0782689i
$891$	6.65884	−	4.69492i	0.223080	−	0.157286i
$892$	−16.2608	−	11.8142i	−0.544453	−	0.395569i
$893$	−7.40867	−	12.8322i	−0.247922	−	0.429413i
$894$	38.4660	+	22.3908i	1.28650	+	0.748862i
$895$	−1.84980	+	4.05452i	−0.0618319	+	0.135528i
$896$	4.03604	+	38.4004i	0.134835	+	1.28287i
$897$	−35.8108	−	11.7764i	−1.19569	−	0.393201i
$898$	5.11992	−	5.68625i	0.170854	−	0.189753i
$899$	5.33355			0.177884
$900$	−10.6194	+	17.3601i	−0.353979	+	0.578670i
$901$	24.9163			0.830083
$902$	−6.71246	+	7.45494i	−0.223501	+	0.248223i
$903$	−3.54799	−	16.9883i	−0.118070	−	0.565336i
$904$	−0.738755	−	7.02879i	−0.0245706	−	0.233774i
$905$	19.3187	+	2.20925i	0.642176	+	0.0734381i
$906$	−0.941896	+	0.539354i	−0.0312924	+	0.0179189i
$907$	−1.09709	−	1.90022i	−0.0364283	−	0.0630956i	0.847236	−	0.531216i	$-0.178265\pi$
$907$	−1.09709	−	1.90022i	−0.0364283	−	0.0630956i	−0.883665	+	0.468120i	$0.844931\pi$
$908$	13.5997	+	9.88073i	0.451321	+	0.327904i
$909$	21.5736	−	9.42221i	0.715551	−	0.312515i
$910$	−94.2411	−	55.5652i	−3.12406	−	1.84197i
$911$	−7.31104	+	8.11974i	−0.242226	+	0.269019i	−0.851983	−	0.523569i	$-0.824600\pi$
$911$	−7.31104	+	8.11974i	−0.242226	+	0.269019i	0.609757	+	0.792588i	$0.291267\pi$
$912$	21.3386	−	6.84969i	0.706593	−	0.226816i
$913$	−0.630921	−	0.700709i	−0.0208805	−	0.0231901i
$914$	−27.7612	−	5.90082i	−0.918257	−	0.195182i
$915$	26.7716	+	47.7598i	0.885042	+	1.57889i
$916$	−20.9903	+	4.46163i	−0.693539	+	0.147416i
$917$	−18.1443	−	13.1826i	−0.599178	−	0.435329i
$918$	−40.3006	−	37.0716i	−1.33012	−	1.22354i
$919$	−13.1150	−	9.52858i	−0.432623	−	0.314319i	0.350074	−	0.936722i	$-0.386156\pi$
$919$	−13.1150	−	9.52858i	−0.432623	−	0.314319i	−0.782697	+	0.622403i	$0.786156\pi$
$920$	8.79520	+	2.94691i	0.289969	+	0.0971568i
$921$	0.379219	−	0.339021i	0.0124957	−	0.0111711i
$922$	0.436932	+	4.15713i	0.0143896	+	0.136908i
$923$	31.4811	+	6.69151i	1.03621	+	0.220254i
$924$	5.37339	+	7.45132i	0.176772	+	0.245131i
$925$	7.47459	+	8.61303i	0.245763	+	0.283195i
$926$	27.4963			0.903586
$927$	37.4501	+	0.265921i	1.23002	+	0.00873399i
$928$	12.1277	−	8.81128i	0.398111	−	0.289244i
$929$	−10.7595	−	4.79042i	−0.353007	−	0.157169i	0.222570	−	0.974917i	$-0.428556\pi$
$929$	−10.7595	−	4.79042i	−0.353007	−	0.157169i	−0.575576	+	0.817748i	$0.695222\pi$
$930$	13.2949	+	9.91955i	0.435956	+	0.325275i
$931$	28.2588	−	12.5816i	0.926146	−	0.412347i
$932$	−8.79165	+	15.2276i	−0.287980	+	0.498796i
$933$	−30.2596	+	17.3274i	−0.990654	+	0.567274i
$934$	10.3820	−	2.20677i	0.339710	−	0.0722077i
$935$	−8.72358	+	7.71149i	−0.285291	+	0.252193i
$936$	21.8642	+	0.155251i	0.714653	+	0.00507452i
$937$	−18.1426	+	55.8372i	−0.592693	+	1.82412i	−0.0268057	+	0.999641i	$0.508534\pi$
$937$	−18.1426	+	55.8372i	−0.592693	+	1.82412i	−0.565888	+	0.824482i	$0.691466\pi$
$938$	58.9622	−	12.5328i	1.92518	−	0.409211i
$939$	6.70365	−	9.15823i	0.218765	−	0.298868i
$940$	−3.36804	−	16.5899i	−0.109853	−	0.541101i
$941$	36.2928	+	40.3072i	1.18311	+	1.31398i	0.938873	+	0.344262i	$0.111871\pi$
$941$	36.2928	+	40.3072i	1.18311	+	1.31398i	0.244238	+	0.969715i	$0.421462\pi$
$942$	−35.5121	−	20.6714i	−1.15705	−	0.673510i
$943$	10.6438	+	18.4356i	0.346610	+	0.600346i
$944$	−51.8194	−	37.6490i	−1.68658	−	1.22537i
$945$	−4.25610	−	49.9953i	−0.138451	−	1.62635i
$946$	−3.11335	+	2.26198i	−0.101224	+	0.0735434i
$947$	−6.86583	−	3.05687i	−0.223110	−	0.0993348i	0.292138	−	0.956376i	$-0.405633\pi$
$947$	−6.86583	−	3.05687i	−0.223110	−	0.0993348i	−0.515248	+	0.857041i	$0.672300\pi$
$948$	−0.846057	−	1.91858i	−0.0274787	−	0.0623125i
$949$	0.260789	−	0.451699i	0.00846556	−	0.0146628i
$950$	7.93863	−	22.9931i	0.257563	−	0.745996i
$951$	24.4237	+	33.8686i	0.791994	+	1.09826i
$952$	−19.5893	+	21.7561i	−0.634893	+	0.705120i
$953$	23.0950	−	16.7795i	0.748119	−	0.543540i	−0.147124	−	0.989118i	$-0.547002\pi$
$953$	23.0950	−	16.7795i	0.748119	−	0.543540i	0.895243	+	0.445578i	$0.147002\pi$
$954$	23.2536	+	5.11554i	0.752863	+	0.165622i
$955$	37.6980	−	33.3244i	1.21988	−	1.07835i
$956$	0.691569	−	6.57984i	0.0223669	−	0.212807i
$957$	−1.46669	+	3.26301i	−0.0474113	+	0.105478i
$958$	−33.4355	+	14.8864i	−1.08025	+	0.480959i
$959$	29.3157	+	32.5584i	0.946654	+	1.05137i
$960$	8.87683	+	0.112688i	0.286499	+	0.00363700i
$961$	−17.0864	+	18.9764i	−0.551176	+	0.612143i
$962$	−7.98519	+	24.5759i	−0.257453	+	0.792358i
$963$	2.07170	−	18.4498i	0.0667598	−	0.594537i
$964$	−1.07834	−	3.31880i	−0.0347311	−	0.106891i
$965$	−0.224859	+	24.5910i	−0.00723846	+	0.791613i
$966$	45.9249	−	14.7419i	1.47761	−	0.474312i
$967$	23.8286	−	10.6092i	0.766277	−	0.341168i	0.0139016	−	0.999903i	$-0.495575\pi$
$967$	23.8286	−	10.6092i	0.766277	−	0.341168i	0.752375	+	0.658735i	$0.228908\pi$
$968$	5.99937	−	10.3912i	0.192827	−	0.333986i
$969$	22.8630	+	13.3084i	0.734466	+	0.427528i
$970$	3.99800	−	5.39828i	0.128368	−	0.173328i
$971$	45.5475	−	33.0922i	1.46169	−	1.06198i	0.478769	−	0.877941i	$-0.341083\pi$
$971$	45.5475	−	33.0922i	1.46169	−	1.06198i	0.982919	−	0.184037i	$-0.0589167\pi$
$972$	−12.1253	−	17.3278i	−0.388921	−	0.555789i
$973$	−4.56144	−	14.0387i	−0.146233	−	0.450060i
$974$	26.8718	+	46.5434i	0.861029	+	1.49135i
$975$	32.4163	−	42.6278i	1.03815	−	1.36518i
$976$	34.4425	−	59.6562i	1.10248	−	1.90955i
$977$	11.7376	+	2.49491i	0.375520	+	0.0798193i	0.391805	−	0.920048i	$-0.371851\pi$
$977$	11.7376	+	2.49491i	0.375520	+	0.0798193i	−0.0162853	+	0.999867i	$0.505184\pi$
$978$	−3.41975	−	1.12458i	−0.109352	−	0.0359602i
$979$	−4.93934	−	2.19914i	−0.157862	−	0.0702847i
$980$	35.1788	−	3.37252i	1.12374	−	0.107731i
$981$	−47.3652	−	21.4926i	−1.51226	−	0.686207i
$982$	14.7157			0.469597
$983$	4.33583	−	41.2526i	0.138291	−	1.31575i	−0.676690	−	0.736268i	$-0.736586\pi$
$983$	4.33583	−	41.2526i	0.138291	−	1.31575i	0.814982	−	0.579487i	$-0.196747\pi$
$984$	−9.14618	−	8.29424i	−0.291570	−	0.264411i
$985$	−5.49685	+	12.0484i	−0.175144	+	0.383895i
$986$	23.5181	+	4.99894i	0.748970	+	0.159199i
$987$	30.9182	+	28.0383i	0.984138	+	0.892469i
$988$	21.7907	−	4.63175i	0.693253	−	0.147356i
$989$	2.52353	+	7.76664i	0.0802437	+	0.246965i
$990$	−9.72466	+	5.40585i	−0.309070	+	0.171809i
$991$	−13.7209	+	42.2286i	−0.435858	+	1.34143i	0.456346	+	0.889802i	$0.349158\pi$
$991$	−13.7209	+	42.2286i	−0.435858	+	1.34143i	−0.892204	+	0.451632i	$0.850842\pi$
$992$	1.60548	−	15.2751i	0.0509741	−	0.484986i
$993$	−17.2982	−	23.9876i	−0.548942	−	0.761223i
$994$	−37.6190	+	16.7491i	−1.19320	+	0.531248i
$995$	16.6217	−	9.39498i	0.526944	−	0.297841i
$996$	−1.82466	+	1.63124i	−0.0578166	+	0.0516878i
$997$	−27.3540	−	12.1788i	−0.866310	−	0.385706i	−0.0750454	−	0.997180i	$-0.523910\pi$
$997$	−27.3540	−	12.1788i	−0.866310	−	0.385706i	−0.791264	+	0.611474i	$0.790577\pi$
$998$	15.9510	+	49.0922i	0.504921	+	1.55399i
$999$	−11.3098	+	3.54206i	−0.357827	+	0.112066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.6	✓	224
3.2	odd	2		675.2.r.a.631.23		224
9.2	odd	6		675.2.r.a.181.6		224
9.7	even	3	inner	225.2.q.a.106.23	yes	224
25.21	even	5	inner	225.2.q.a.121.23	yes	224
75.71	odd	10		675.2.r.a.496.6		224
225.146	odd	30		675.2.r.a.46.23		224
225.196	even	15	inner	225.2.q.a.196.6	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.6	✓	224	1.1	even	1	trivial
225.2.q.a.106.23	yes	224	9.7	even	3	inner
225.2.q.a.121.23	yes	224	25.21	even	5	inner
225.2.q.a.196.6	yes	224	225.196	even	15	inner
675.2.r.a.46.23		224	225.146	odd	30
675.2.r.a.181.6		224	9.2	odd	6
675.2.r.a.496.6		224	75.71	odd	10
675.2.r.a.631.23		224	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22593 + 1.36154i) q^{2} +(-1.29127 + 1.15439i) q^{3} +(-0.141814 - 1.34927i) q^{4} +(1.94663 - 1.10028i) q^{5} +(0.0112662 - 3.17332i) q^{6} +(-2.15924 - 3.73991i) q^{7} +(-0.953512 - 0.692767i) q^{8} +(0.334762 - 2.98126i) q^{9} +O(q^{10})\)	\(q+(-1.22593 + 1.36154i) q^{2} +(-1.29127 + 1.15439i) q^{3} +(-0.141814 - 1.34927i) q^{4} +(1.94663 - 1.10028i) q^{5} +(0.0112662 - 3.17332i) q^{6} +(-2.15924 - 3.73991i) q^{7} +(-0.953512 - 0.692767i) q^{8} +(0.334762 - 2.98126i) q^{9} +(-0.888371 + 3.99929i) q^{10} +(-0.605752 + 0.672756i) q^{11} +(1.74071 + 1.57856i) q^{12} +(-4.13776 - 4.59545i) q^{13} +(7.73912 + 1.64500i) q^{14} +(-1.24348 + 3.66794i) q^{15} +(4.76628 - 1.01310i) q^{16} +(4.65336 + 3.38087i) q^{17} +(3.64871 + 4.11063i) q^{18} +(-2.14825 - 1.56079i) q^{19} +(-1.76064 - 2.47050i) q^{20} +(7.10548 + 2.33663i) q^{21} +(-0.173370 - 1.64951i) q^{22} +(-3.44271 - 0.731772i) q^{23} +(2.03097 - 0.206176i) q^{24} +(2.57876 - 4.28369i) q^{25} +11.3295 q^{26} +(3.00928 + 4.23607i) q^{27} +(-4.73994 + 3.44377i) q^{28} +(-2.08431 - 0.927996i) q^{29} +(-3.46962 - 6.18969i) q^{30} +(-2.13557 + 0.950816i) q^{31} +(-3.28516 + 5.69007i) q^{32} +(0.00556681 - 1.56798i) q^{33} +(-10.3079 + 2.19101i) q^{34} +(-8.31820 - 4.90447i) q^{35} +(-4.07000 - 0.0288998i) q^{36} +(-0.704813 + 2.16919i) q^{37} +(4.75869 - 1.01149i) q^{38} +(10.6479 + 1.15738i) q^{39} +(-2.61838 - 0.299432i) q^{40} +(-4.04708 - 4.49473i) q^{41} +(-11.8923 + 6.80983i) q^{42} +(-1.16011 - 2.00937i) q^{43} +(0.993634 + 0.721917i) q^{44} +(-2.62857 - 6.17176i) q^{45} +(5.21688 - 3.79028i) q^{46} +(5.09769 + 2.26964i) q^{47} +(-4.98504 + 6.81035i) q^{48} +(-5.82462 + 10.0885i) q^{49} +(2.67101 + 8.76261i) q^{50} +(-9.91160 + 1.00619i) q^{51} +(-5.61371 + 6.23466i) q^{52} +(3.50455 - 2.54621i) q^{53} +(-9.45674 - 1.09590i) q^{54} +(-0.438957 + 1.97611i) q^{55} +(-0.532027 + 5.06190i) q^{56} +(4.57574 - 0.464511i) q^{57} +(3.81874 - 1.70021i) q^{58} +(-8.79570 - 9.76861i) q^{59} +(5.12538 + 1.15762i) q^{60} +(9.45934 - 10.5057i) q^{61} +(1.32349 - 4.07330i) q^{62} +(-11.8725 + 5.18528i) q^{63} +(-0.708321 - 2.17999i) q^{64} +(-13.1110 - 4.39296i) q^{65} +(2.12805 + 1.92983i) q^{66} +(6.96006 - 3.09882i) q^{67} +(3.90179 - 6.75810i) q^{68} +(5.29023 - 3.02932i) q^{69} +(16.8752 - 5.31299i) q^{70} +(-4.21064 + 3.05921i) q^{71} +(-2.38452 + 2.61076i) q^{72} +(0.0260643 + 0.0802177i) q^{73} +(-2.08938 - 3.61892i) q^{74} +(1.61517 + 8.50830i) q^{75} +(-1.80128 + 3.11991i) q^{76} +(3.82401 + 0.812818i) q^{77} +(-14.6295 + 13.0787i) q^{78} +(-0.815175 - 0.362939i) q^{79} +(8.16350 - 7.21639i) q^{80} +(-8.77587 - 1.99603i) q^{81} +11.0812 q^{82} +(-0.108872 + 1.03584i) q^{83} +(2.14509 - 9.91858i) q^{84} +(12.7783 + 1.46130i) q^{85} +(4.15806 + 0.883823i) q^{86} +(3.76269 - 1.20782i) q^{87} +(1.04365 - 0.221836i) q^{88} +(1.84560 + 5.68017i) q^{89} +(11.6255 + 3.98728i) q^{90} +(-8.25216 + 25.3975i) q^{91} +(-0.499132 + 4.74893i) q^{92} +(1.65998 - 3.69304i) q^{93} +(-9.33964 + 4.15827i) q^{94} +(-5.89916 - 0.674617i) q^{95} +(-2.32653 - 11.1398i) q^{96} +(-1.49796 - 0.666933i) q^{97} +(-6.59533 - 20.2983i) q^{98} +(1.80288 + 2.03112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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