LMFDB - Embedded newform 225.2.q.a.106.13

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			106.13
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.511634 - 0.108751i) q^{2} +(1.18489 + 1.26334i) q^{3} +(-1.57715 - 0.702192i) q^{4} +(1.99861 + 1.00277i) q^{5} +(-0.468843 - 0.775225i) q^{6} +(-1.68864 + 2.92481i) q^{7} +(1.57689 + 1.14568i) q^{8} +(-0.192048 + 2.99385i) q^{9} +O(q^{10})$	\(q+(-0.511634 - 0.108751i) q^{2} +(1.18489 + 1.26334i) q^{3} +(-1.57715 - 0.702192i) q^{4} +(1.99861 + 1.00277i) q^{5} +(-0.468843 - 0.775225i) q^{6} +(-1.68864 + 2.92481i) q^{7} +(1.57689 + 1.14568i) q^{8} +(-0.192048 + 2.99385i) q^{9} +(-0.913505 - 0.730402i) q^{10} +(-4.04299 - 0.859364i) q^{11} +(-0.981649 - 2.82450i) q^{12} +(4.96974 - 1.05635i) q^{13} +(1.18204 - 1.31279i) q^{14} +(1.10131 + 3.71310i) q^{15} +(1.62818 + 1.80828i) q^{16} +(0.0810977 + 0.0589209i) q^{17} +(0.423842 - 1.51087i) q^{18} +(2.55513 + 1.85641i) q^{19} +(-2.44797 - 2.98493i) q^{20} +(-5.69589 + 1.33227i) q^{21} +(1.97507 + 0.879359i) q^{22} +(-1.31885 + 1.46473i) q^{23} +(0.421071 + 3.34966i) q^{24} +(2.98891 + 4.00830i) q^{25} -2.65757 q^{26} +(-4.00980 + 3.30477i) q^{27} +(4.71702 - 3.42711i) q^{28} +(-0.709179 - 6.74738i) q^{29} +(-0.159663 - 2.01952i) q^{30} +(-0.254537 + 2.42176i) q^{31} +(-2.58553 - 4.47827i) q^{32} +(-3.70485 - 6.12592i) q^{33} +(-0.0350846 - 0.0389654i) q^{34} +(-6.30785 + 4.15225i) q^{35} +(2.40514 - 4.58689i) q^{36} +(0.930291 - 2.86314i) q^{37} +(-1.10541 - 1.22768i) q^{38} +(7.22315 + 5.02680i) q^{39} +(2.00275 + 3.87103i) q^{40} +(5.68382 - 1.20813i) q^{41} +(3.05909 - 0.0621998i) q^{42} +(5.61908 - 9.73253i) q^{43} +(5.77296 + 4.19430i) q^{44} +(-3.38597 + 5.79096i) q^{45} +(0.834057 - 0.605978i) q^{46} +(-0.973397 - 9.26125i) q^{47} +(-0.355244 + 4.19957i) q^{48} +(-2.20301 - 3.81573i) q^{49} +(-1.09332 - 2.37583i) q^{50} +(0.0216552 + 0.172269i) q^{51} +(-8.57978 - 1.82369i) q^{52} +(1.84804 - 1.34268i) q^{53} +(2.41095 - 1.25476i) q^{54} +(-7.21862 - 5.77172i) q^{55} +(-6.01370 + 2.67747i) q^{56} +(0.682287 + 5.42765i) q^{57} +(-0.370946 + 3.52931i) q^{58} +(-8.28217 + 1.76043i) q^{59} +(0.870382 - 6.62944i) q^{60} +(-3.39787 - 0.722239i) q^{61} +(0.393599 - 1.21137i) q^{62} +(-8.43214 - 5.61724i) q^{63} +(-0.668023 - 2.05596i) q^{64} +(10.9919 + 2.87227i) q^{65} +(1.22933 + 3.53713i) q^{66} +(1.41822 - 13.4935i) q^{67} +(-0.0865293 - 0.149873i) q^{68} +(-3.41314 + 0.0693985i) q^{69} +(3.67887 - 1.43844i) q^{70} +(6.75154 - 4.90528i) q^{71} +(-3.73283 + 4.50095i) q^{72} +(3.28345 + 10.1054i) q^{73} +(-0.787338 + 1.36371i) q^{74} +(-1.52230 + 8.52541i) q^{75} +(-2.72627 - 4.72203i) q^{76} +(9.34063 - 10.3738i) q^{77} +(-3.14894 - 3.35741i) q^{78} +(1.50231 + 14.2935i) q^{79} +(1.44082 + 5.24674i) q^{80} +(-8.92623 - 1.14993i) q^{81} -3.03942 q^{82} +(-5.66643 + 2.52286i) q^{83} +(9.91877 + 1.89842i) q^{84} +(0.102999 + 0.199082i) q^{85} +(-3.93333 + 4.36841i) q^{86} +(7.68393 - 8.89087i) q^{87} +(-5.39081 - 5.98710i) q^{88} +(-2.14728 - 6.60864i) q^{89} +(2.36215 - 2.59462i) q^{90} +(-5.30248 + 16.3193i) q^{91} +(3.10854 - 1.38401i) q^{92} +(-3.36110 + 2.54796i) q^{93} +(-0.509149 + 4.84423i) q^{94} +(3.24517 + 6.27246i) q^{95} +(2.59399 - 8.57267i) q^{96} +(0.182492 + 1.73630i) q^{97} +(0.712171 + 2.19184i) q^{98} +(3.34925 - 11.9390i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.511634	−	0.108751i	−0.361780	−	0.0768986i	0.0234357	−	0.999725i	$-0.492539\pi$
$2$	−0.511634	−	0.108751i	−0.361780	−	0.0768986i	−0.385215	+	0.922827i	$0.625873\pi$
$3$	1.18489	+	1.26334i	0.684099	+	0.729389i
$3$	1.18489	+	1.26334i	0.684099	+	0.729389i
$4$	−1.57715	−	0.702192i	−0.788574	−	0.351096i
$5$	1.99861	+	1.00277i	0.893807	+	0.448452i
$5$	1.99861	+	1.00277i	0.893807	+	0.448452i
$6$	−0.468843	−	0.775225i	−0.191404	−	0.316484i
$7$	−1.68864	+	2.92481i	−0.638246	+	1.10547i	0.347571	+	0.937654i	$0.387006\pi$
$7$	−1.68864	+	2.92481i	−0.638246	+	1.10547i	−0.985817	+	0.167821i	$0.946327\pi$
$8$	1.57689	+	1.14568i	0.557516	+	0.405059i
$9$	−0.192048	+	2.99385i	−0.0640161	+	0.997949i
$10$	−0.913505	−	0.730402i	−0.288876	−	0.230973i
$11$	−4.04299	−	0.859364i	−1.21901	−	0.259108i	−0.446890	−	0.894589i	$-0.647469\pi$
$11$	−4.04299	−	0.859364i	−1.21901	−	0.259108i	−0.772117	+	0.635481i	$0.780802\pi$
$12$	−0.981649	−	2.82450i	−0.283378	−	0.815362i
$13$	4.96974	−	1.05635i	1.37836	−	0.292979i	0.541639	−	0.840611i	$-0.317804\pi$
$13$	4.96974	−	1.05635i	1.37836	−	0.292979i	0.836719	+	0.547632i	$0.184471\pi$
$14$	1.18204	−	1.31279i	0.315914	−	0.350858i
$15$	1.10131	+	3.71310i	0.284357	+	0.958719i
$16$	1.62818	+	1.80828i	0.407045	+	0.452070i
$17$	0.0810977	+	0.0589209i	0.0196691	+	0.0142904i	0.597576	−	0.801812i	$-0.296130\pi$
$17$	0.0810977	+	0.0589209i	0.0196691	+	0.0142904i	−0.577907	+	0.816102i	$0.696130\pi$
$18$	0.423842	−	1.51087i	0.0999006	−	0.356115i
$19$	2.55513	+	1.85641i	0.586188	+	0.425890i	0.840950	−	0.541113i	$-0.181997\pi$
$19$	2.55513	+	1.85641i	0.586188	+	0.425890i	−0.254762	+	0.967004i	$0.581997\pi$
$20$	−2.44797	−	2.98493i	−0.547383	−	0.667450i
$21$	−5.69589	+	1.33227i	−1.24294	+	0.290725i
$22$	1.97507	+	0.879359i	0.421087	+	0.187480i
$23$	−1.31885	+	1.46473i	−0.274998	+	0.305417i	−0.864785	−	0.502143i	$-0.832545\pi$
$23$	−1.31885	+	1.46473i	−0.274998	+	0.305417i	0.589786	+	0.807559i	$0.299212\pi$
$24$	0.421071	+	3.34966i	0.0859508	+	0.683747i
$25$	2.98891	+	4.00830i	0.597781	+	0.801659i
$26$	−2.65757			−0.521192
$27$	−4.00980	+	3.30477i	−0.771686	+	0.636004i
$28$	4.71702	−	3.42711i	0.891432	−	0.647663i
$29$	−0.709179	−	6.74738i	−0.131691	−	1.25296i	−0.838243	−	0.545297i	$-0.816417\pi$
$29$	−0.709179	−	6.74738i	−0.131691	−	1.25296i	0.706552	−	0.707661i	$-0.250250\pi$
$30$	−0.159663	−	2.01952i	−0.0291503	−	0.368712i
$31$	−0.254537	+	2.42176i	−0.0457162	+	0.434961i	0.947593	+	0.319479i	$0.103508\pi$
$31$	−0.254537	+	2.42176i	−0.0457162	+	0.434961i	−0.993310	+	0.115482i	$0.963159\pi$
$32$	−2.58553	−	4.47827i	−0.457061	−	0.791653i
$33$	−3.70485	−	6.12592i	−0.644931	−	1.06639i
$34$	−0.0350846	−	0.0389654i	−0.00601696	−	0.00668251i
$35$	−6.30785	+	4.15225i	−1.06622	+	0.701858i
$36$	2.40514	−	4.58689i	0.400857	−	0.764481i
$37$	0.930291	−	2.86314i	0.152939	−	0.470698i	−0.845007	−	0.534755i	$-0.820404\pi$
$37$	0.930291	−	2.86314i	0.152939	−	0.470698i	0.997946	+	0.0640571i	$0.0204040\pi$
$38$	−1.10541	−	1.22768i	−0.179320	−	0.199156i
$39$	7.22315	+	5.02680i	1.15663	+	0.804932i
$40$	2.00275	+	3.87103i	0.316662	+	0.612064i
$41$	5.68382	−	1.20813i	0.887663	−	0.188679i	0.258555	−	0.965996i	$-0.416754\pi$
$41$	5.68382	−	1.20813i	0.887663	−	0.188679i	0.629108	+	0.777318i	$0.283420\pi$
$42$	3.05909	−	0.0621998i	0.472028	−	0.00959763i
$43$	5.61908	−	9.73253i	0.856902	−	1.48420i	−0.0179676	−	0.999839i	$-0.505720\pi$
$43$	5.61908	−	9.73253i	0.856902	−	1.48420i	0.874869	−	0.484359i	$-0.160947\pi$
$44$	5.77296	+	4.19430i	0.870306	+	0.632314i
$45$	−3.38597	+	5.79096i	−0.504750	+	0.863265i
$46$	0.834057	−	0.605978i	0.122975	−	0.0893465i
$47$	−0.973397	−	9.26125i	−0.141985	−	1.35089i	−0.800955	−	0.598724i	$-0.795675\pi$
$47$	−0.973397	−	9.26125i	−0.141985	−	1.35089i	0.658971	−	0.752168i	$-0.270992\pi$
$48$	−0.355244	+	4.19957i	−0.0512751	+	0.606155i
$49$	−2.20301	−	3.81573i	−0.314716	−	0.545105i
$50$	−1.09332	−	2.37583i	−0.154619	−	0.335993i
$51$	0.0216552	+	0.172269i	0.00303233	+	0.0241225i
$52$	−8.57978	−	1.82369i	−1.18980	−	0.252900i
$53$	1.84804	−	1.34268i	0.253848	−	0.184432i	−0.453582	−	0.891214i	$-0.649854\pi$
$53$	1.84804	−	1.34268i	0.253848	−	0.184432i	0.707431	+	0.706783i	$0.249854\pi$
$54$	2.41095	−	1.25476i	0.328088	−	0.170752i
$55$	−7.21862	−	5.77172i	−0.973359	−	0.778259i
$56$	−6.01370	+	2.67747i	−0.803615	+	0.357792i
$57$	0.682287	+	5.42765i	0.0903711	+	0.718910i
$58$	−0.370946	+	3.52931i	−0.0487076	+	0.463421i
$59$	−8.28217	+	1.76043i	−1.07825	+	0.229188i	−0.712604	−	0.701567i	$-0.752484\pi$
$59$	−8.28217	+	1.76043i	−1.07825	+	0.229188i	−0.365643	+	0.930755i	$0.619151\pi$
$60$	0.870382	−	6.62944i	0.112366	−	0.855857i
$61$	−3.39787	−	0.722239i	−0.435052	−	0.0924732i	−0.0148208	−	0.999890i	$-0.504718\pi$
$61$	−3.39787	−	0.722239i	−0.435052	−	0.0924732i	−0.420231	+	0.907417i	$0.638051\pi$
$62$	0.393599	−	1.21137i	0.0499871	−	0.153844i
$63$	−8.43214	−	5.61724i	−1.06235	−	0.707705i
$64$	−0.668023	−	2.05596i	−0.0835028	−	0.256995i
$65$	10.9919	+	2.87227i	1.36337	+	0.356261i
$66$	1.22933	+	3.53713i	0.151319	+	0.435391i
$67$	1.41822	−	13.4935i	0.173264	−	1.64849i	−0.469868	−	0.882737i	$-0.655699\pi$
$67$	1.41822	−	13.4935i	0.173264	−	1.64849i	0.643132	−	0.765756i	$-0.277635\pi$
$68$	−0.0865293	−	0.149873i	−0.0104932	−	0.0181748i
$69$	−3.41314	+	0.0693985i	−0.410894	+	0.00835460i
$70$	3.67887	−	1.43844i	0.439709	−	0.171927i
$71$	6.75154	−	4.90528i	0.801260	−	0.582149i	−0.110024	−	0.993929i	$-0.535093\pi$
$71$	6.75154	−	4.90528i	0.801260	−	0.582149i	0.911283	+	0.411780i	$0.135093\pi$
$72$	−3.73283	+	4.50095i	−0.439918	+	0.530442i
$73$	3.28345	+	10.1054i	0.384299	+	1.18275i	0.936988	+	0.349362i	$0.113602\pi$
$73$	3.28345	+	10.1054i	0.384299	+	1.18275i	−0.552689	+	0.833387i	$0.686398\pi$
$74$	−0.787338	+	1.36371i	−0.0915262	+	0.158528i
$75$	−1.52230	+	8.52541i	−0.175780	+	0.984430i
$76$	−2.72627	−	4.72203i	−0.312724	−	0.541654i
$77$	9.34063	−	10.3738i	1.06446	−	1.18221i
$78$	−3.14894	−	3.35741i	−0.356547	−	0.380151i
$79$	1.50231	+	14.2935i	0.169023	+	1.60815i	0.669780	+	0.742559i	$0.266388\pi$
$79$	1.50231	+	14.2935i	0.169023	+	1.60815i	−0.500757	+	0.865588i	$0.666945\pi$
$80$	1.44082	+	5.24674i	0.161088	+	0.586604i
$81$	−8.92623	−	1.14993i	−0.991804	−	0.127770i
$82$	−3.03942			−0.335648
$83$	−5.66643	+	2.52286i	−0.621971	+	0.276919i	−0.693430	−	0.720524i	$-0.743901\pi$
$83$	−5.66643	+	2.52286i	−0.621971	+	0.276919i	0.0714586	+	0.997444i	$0.477235\pi$
$84$	9.91877	+	1.89842i	1.08223	+	0.207135i
$85$	0.102999	+	0.199082i	0.0111718	+	0.0215935i
$86$	−3.93333	+	4.36841i	−0.424142	+	0.471058i
$87$	7.68393	−	8.89087i	0.823803	−	0.953202i
$88$	−5.39081	−	5.98710i	−0.574662	−	0.638227i
$89$	−2.14728	−	6.60864i	−0.227611	−	0.700514i	−0.998016	−	0.0629597i	$-0.979946\pi$
$89$	−2.14728	−	6.60864i	−0.227611	−	0.700514i	0.770405	−	0.637555i	$-0.220054\pi$
$90$	2.36215	−	2.59462i	0.248992	−	0.273497i
$91$	−5.30248	+	16.3193i	−0.555851	+	1.71073i
$92$	3.10854	−	1.38401i	0.324087	−	0.144293i
$93$	−3.36110	+	2.54796i	−0.348530	+	0.264211i
$94$	−0.509149	+	4.84423i	−0.0525147	+	0.499644i
$95$	3.24517	+	6.27246i	0.332947	+	0.643541i
$96$	2.59399	−	8.57267i	0.264748	−	0.874945i
$97$	0.182492	+	1.73630i	0.0185293	+	0.176294i	0.999872	−	0.0159700i	$-0.00508364\pi$
$97$	0.182492	+	1.73630i	0.0185293	+	0.176294i	−0.981343	+	0.192264i	$0.938417\pi$
$98$	0.712171	+	2.19184i	0.0719402	+	0.221409i
$99$	3.34925	−	11.9390i	0.336612	−	1.19992i
$100$	−1.89935	−	8.42047i	−0.189935	−	0.842047i
$101$	−6.20087	+	10.7402i	−0.617010	+	1.06869i	0.373019	+	0.927824i	$0.378323\pi$
$101$	−6.20087	+	10.7402i	−0.617010	+	1.06869i	−0.990028	+	0.140868i	$0.955011\pi$
$102$	0.00765492	−	0.0904936i	0.000757950	−	0.00896020i
$103$	8.00291	+	3.56312i	0.788550	+	0.351085i	0.761180	−	0.648540i	$-0.224620\pi$
$103$	8.00291	+	3.56312i	0.788550	+	0.351085i	0.0273697	+	0.999625i	$0.491287\pi$
$104$	9.04699	+	4.02798i	0.887130	+	0.394976i
$105$	−12.7198	−	3.04897i	−1.24133	−	0.297549i
$106$	−1.09154	+	0.485985i	−0.106020	+	0.0472030i
$107$	3.09879			0.299571			0.149786	−	0.988718i	$-0.452142\pi$
$107$	3.09879			0.299571			0.149786	+	0.988718i	$0.452142\pi$
$108$	8.64463	−	2.39647i	0.831830	−	0.230600i
$109$	−0.863050	+	2.65620i	−0.0826652	+	0.254417i	−0.983843	−	0.179032i	$-0.942704\pi$
$109$	−0.863050	+	2.65620i	−0.0826652	+	0.254417i	0.901178	+	0.433449i	$0.142704\pi$
$110$	3.06561	+	3.73804i	0.292294	+	0.356408i
$111$	4.71942	−	2.21725i	0.447947	−	0.210452i
$112$	−8.03829	+	1.70859i	−0.759547	+	0.161447i
$113$	8.15534	−	1.73347i	0.767190	−	0.163071i	0.192338	−	0.981329i	$-0.438393\pi$
$113$	8.15534	−	1.73347i	0.767190	−	0.163071i	0.574852	+	0.818257i	$0.305060\pi$
$114$	0.241183	−	2.85117i	0.0225888	−	0.267037i
$115$	−4.10465	+	1.60492i	−0.382760	+	0.149660i
$116$	−3.61948	+	11.1396i	−0.336060	+	1.03429i
$117$	2.20812	+	15.0815i	0.204141	+	1.39429i
$118$	4.42888			0.407712
$119$	−0.309277	+	0.137699i	−0.0283514	+	0.0126229i
$120$	−2.51738	+	7.11691i	−0.229804	+	0.649682i
$121$	5.55825	+	2.47469i	0.505295	+	0.224972i
$122$	1.65992	+	0.739043i	0.150282	+	0.0669098i
$123$	8.26101	+	5.74908i	0.744870	+	0.518377i
$124$	2.10198	−	3.64074i	0.188764	−	0.326948i
$125$	1.95426	+	11.0082i	0.174795	+	0.984605i
$126$	3.70328	+	3.79097i	0.329915	+	0.337727i
$127$	2.69804	+	8.30372i	0.239412	+	0.736836i	0.996505	+	0.0835285i	$0.0266189\pi$
$127$	2.69804	+	8.30372i	0.239412	+	0.736836i	−0.757093	+	0.653307i	$0.773381\pi$
$128$	1.19924	+	11.4100i	0.105999	+	1.00851i
$129$	18.9535	−	4.43323i	1.66876	−	0.390324i
$130$	−5.31144	−	2.66493i	−0.465845	−	0.233730i
$131$	−0.0976235	+	0.928826i	−0.00852941	+	0.0811519i	−0.997959	−	0.0638655i	$-0.979657\pi$
$131$	−0.0976235	+	0.928826i	−0.00852941	+	0.0811519i	0.989429	+	0.145017i	$0.0463238\pi$
$132$	1.54153	+	12.2630i	0.134173	+	1.06736i
$133$	−9.74436	+	4.33847i	−0.844943	+	0.376193i
$134$	−2.19304	+	6.74949i	−0.189450	+	0.583067i
$135$	−11.3280	+	2.58405i	−0.974956	+	0.222400i
$136$	0.0603779	+	0.185824i	0.00517736	+	0.0159343i
$137$	4.15156	+	4.61078i	0.354692	+	0.393925i	0.893914	−	0.448238i	$-0.147948\pi$
$137$	4.15156	+	4.61078i	0.354692	+	0.393925i	−0.539222	+	0.842163i	$0.681282\pi$
$138$	1.75382	+	0.335676i	0.149295	+	0.0285746i
$139$	−3.82314	+	4.24603i	−0.324275	+	0.360143i	−0.883136	−	0.469118i	$-0.844572\pi$
$139$	−3.82314	+	4.24603i	−0.324275	+	0.360143i	0.558861	+	0.829261i	$0.311239\pi$
$140$	12.8641	−	2.11939i	1.08721	−	0.179121i
$141$	10.5467	−	12.2033i	0.888194	−	1.02771i
$142$	−3.98777	+	1.77547i	−0.334646	+	0.148994i
$143$	−21.0004			−1.75614
$144$	−5.72640	+	4.52725i	−0.477200	+	0.377271i
$145$	5.34870	−	14.1965i	0.444185	−	1.17896i
$146$	−0.580948	−	5.52735i	−0.0480796	−	0.457447i
$147$	2.21022	−	7.30439i	0.182296	−	0.602456i
$148$	−3.47768	+	3.86236i	−0.285864	+	0.317484i
$149$	−10.5541	−	18.2802i	−0.864623	−	1.49757i	−0.867421	−	0.497575i	$-0.834224\pi$
$149$	−10.5541	−	18.2802i	−0.864623	−	1.49757i	0.00279771	−	0.999996i	$-0.499109\pi$
$150$	1.70601	−	4.19634i	0.139295	−	0.342629i
$151$	8.84475	−	15.3196i	0.719776	−	1.24669i	−0.241313	−	0.970447i	$-0.577578\pi$
$151$	8.84475	−	15.3196i	0.719776	−	1.24669i	0.961088	−	0.276241i	$-0.0890888\pi$
$152$	1.90232	+	5.85473i	0.154298	+	0.474882i
$153$	−0.191975	+	0.231478i	−0.0155202	+	0.0187139i
$154$	−5.90715	+	4.29179i	−0.476011	+	0.345843i
$155$	−2.93719	+	4.58491i	−0.235921	+	0.368269i
$156$	−7.86220	−	13.0000i	−0.629480	−	1.04084i
$157$	0.489023	+	0.847013i	0.0390283	+	0.0675990i	0.884880	−	0.465820i	$-0.154240\pi$
$157$	0.489023	+	0.847013i	0.0390283	+	0.0675990i	−0.845851	+	0.533419i	$0.820907\pi$
$158$	0.785804	−	7.47643i	0.0625152	−	0.594793i
$159$	3.88600	+	0.743767i	0.308180	+	0.0589846i
$160$	−0.676799	−	11.5430i	−0.0535057	−	0.912555i
$161$	−2.05699	−	6.33077i	−0.162114	−	0.498935i
$162$	4.44191	+	1.55908i	0.348989	+	0.122493i
$163$	3.86004	−	11.8800i	0.302341	−	0.930511i	−0.678314	−	0.734772i	$-0.737289\pi$
$163$	3.86004	−	11.8800i	0.302341	−	0.930511i	0.980656	−	0.195740i	$-0.0627107\pi$
$164$	−9.81257	−	2.08573i	−0.766233	−	0.162868i
$165$	−1.26167	−	15.9584i	−0.0982210	−	1.24236i
$166$	3.17350	−	0.674548i	0.246311	−	0.0523551i
$167$	−2.05606	+	19.5621i	−0.159103	+	1.51376i	0.565588	+	0.824688i	$0.308649\pi$
$167$	−2.05606	+	19.5621i	−0.159103	+	1.51376i	−0.724691	+	0.689074i	$0.758018\pi$
$168$	−10.5082	−	4.42482i	−0.810722	−	0.341382i
$169$	11.7063	−	5.21200i	0.900488	−	0.400923i
$170$	−0.0310472	−	0.113058i	−0.00238121	−	0.00867119i
$171$	−6.04853	+	7.29316i	−0.462542	+	0.557722i
$172$	−15.6962	+	11.4040i	−1.19683	+	0.869545i
$173$	−3.71248	−	0.789111i	−0.282254	−	0.0599950i	0.0646091	−	0.997911i	$-0.479420\pi$
$173$	−3.71248	−	0.789111i	−0.282254	−	0.0599950i	−0.346864	+	0.937916i	$0.612753\pi$
$174$	−4.89825	+	3.71323i	−0.371335	+	0.281500i
$175$	−16.7707	+	1.97341i	−1.26775	+	0.149176i
$176$	−5.02875	−	8.71005i	−0.379056	−	0.656545i
$177$	−12.0375	−	8.37726i	−0.904795	−	0.629673i
$178$	0.379922	+	3.61472i	0.0284764	+	0.270935i
$179$	3.68369	−	2.67636i	0.275332	−	0.200040i	−0.441547	−	0.897238i	$-0.645570\pi$
$179$	3.68369	−	2.67636i	0.275332	−	0.200040i	0.716879	+	0.697198i	$0.245570\pi$
$180$	9.40654	−	6.75560i	0.701122	−	0.503533i
$181$	15.5083	+	11.2674i	1.15272	+	0.837501i	0.988840	−	0.148979i	$-0.0475988\pi$
$181$	15.5083	+	11.2674i	1.15272	+	0.837501i	0.163881	+	0.986480i	$0.447599\pi$
$182$	4.48767	−	7.77288i	0.332648	−	0.576164i
$183$	−3.11368	−	5.14843i	−0.230170	−	0.380583i
$184$	−3.75779	+	0.798743i	−0.277028	+	0.0588841i
$185$	4.73036	−	4.78944i	0.347783	−	0.352127i
$186$	1.99675	−	0.938100i	0.146409	−	0.0687848i
$187$	−0.277242	−	0.307909i	−0.0202740	−	0.0225165i
$188$	−4.96798	+	15.2899i	−0.362328	+	1.11513i
$189$	−2.89473	−	17.3085i	−0.210560	−	1.25901i
$190$	−0.978200	−	3.56212i	−0.0709661	−	0.258423i
$191$	−11.7657	−	13.0671i	−0.851336	−	0.945504i	0.147717	−	0.989030i	$-0.452808\pi$
$191$	−11.7657	−	13.0671i	−0.851336	−	0.945504i	−0.999052	+	0.0435258i	$0.986141\pi$
$192$	1.80584	−	3.28004i	0.130325	−	0.236716i
$193$	−9.88753	−	17.1257i	−0.711720	−	1.23273i	−0.964211	−	0.265136i	$-0.914583\pi$
$193$	−9.88753	−	17.1257i	−0.711720	−	1.23273i	0.252491	−	0.967599i	$-0.418750\pi$
$194$	0.0954550	−	0.908193i	0.00685327	−	0.0652045i
$195$	9.39555	+	17.2898i	0.672830	+	1.23815i
$196$	0.795105	+	7.56492i	0.0567932	+	0.540351i
$197$	0.487820	−	0.354422i	0.0347558	−	0.0252515i	−0.570272	−	0.821456i	$-0.693162\pi$
$197$	0.487820	−	0.354422i	0.0347558	−	0.0252515i	0.605028	+	0.796205i	$0.293162\pi$
$198$	−3.01197	+	5.74418i	−0.214052	+	0.408221i
$199$	−18.7806			−1.33132			−0.665659	−	0.746256i	$-0.731850\pi$
$199$	−18.7806			−1.33132			−0.665659	+	0.746256i	$0.731850\pi$
$200$	0.120959	+	9.74499i	0.00855308	+	0.689075i
$201$	18.7273	−	14.1967i	1.32092	−	1.00136i
$202$	4.34059	−	4.82071i	0.305403	−	0.339184i
$203$	20.9324	+	9.31969i	1.46916	+	0.654114i
$204$	0.0868124	−	0.286900i	0.00607808	−	0.0200870i
$205$	12.5712	+	3.28497i	0.878013	+	0.229432i
$206$	−3.70706	−	2.69334i	−0.258283	−	0.187654i
$207$	−4.13189	−	4.22972i	−0.287186	−	0.293986i
$208$	10.0018	+	7.26675i	0.693501	+	0.503858i
$209$	−8.73504	−	9.70125i	−0.604216	−	0.671049i
$210$	6.17632	+	2.94325i	0.426206	+	0.203104i
$211$	−11.1072	+	12.3358i	−0.764650	+	0.849229i	−0.992215	−	0.124533i	$-0.960257\pi$
$211$	−11.1072	+	12.3358i	−0.764650	+	0.849229i	0.227566	+	0.973763i	$0.426923\pi$
$212$	−3.85746	+	0.819929i	−0.264931	+	0.0563129i
$213$	14.1969	+	2.71724i	0.972755	+	0.186182i
$214$	−1.58545	−	0.336997i	−0.108379	−	0.0230366i
$215$	20.9899	−	13.8169i	1.43150	−	0.942306i
$216$	−10.1092	+	0.617326i	−0.687846	+	0.0420037i
$217$	−6.65336	−	4.83395i	−0.451660	−	0.328150i
$218$	0.730430	−	1.26514i	0.0494709	−	0.0856862i
$219$	−8.87602	+	16.1220i	−0.599786	+	1.08942i
$220$	7.33199	+	14.1717i	0.494322	+	0.955457i
$221$	0.465275	+	0.207154i	0.0312978	+	0.0139347i
$222$	−2.65574	+	0.621178i	−0.178242	+	0.0416907i
$223$	−2.86581	−	0.609147i	−0.191909	−	0.0407915i	0.110954	−	0.993825i	$-0.464609\pi$
$223$	−2.86581	−	0.609147i	−0.191909	−	0.0407915i	−0.302863	+	0.953034i	$0.597943\pi$
$224$	17.4641			1.16687
$225$	−12.5742	+	8.17854i	−0.838283	+	0.545236i
$226$	−4.36106			−0.290094
$227$	21.6311	+	4.59782i	1.43570	+	0.305168i	0.859080	−	0.511842i	$-0.171037\pi$
$227$	21.6311	+	4.59782i	1.43570	+	0.305168i	0.576624	+	0.817010i	$0.304370\pi$
$228$	2.73519	−	9.03931i	0.181142	−	0.598643i
$229$	−16.5508	−	7.36890i	−1.09371	−	0.486950i	−0.221041	−	0.975265i	$-0.570945\pi$
$229$	−16.5508	−	7.36890i	−1.09371	−	0.486950i	−0.872668	+	0.488314i	$0.837612\pi$
$230$	2.27461	−	0.374748i	0.149984	−	0.0247101i
$231$	24.1733	−	0.491510i	1.59049	−	0.0323390i
$232$	6.61204	−	11.4524i	0.434102	−	0.751887i
$233$	6.92161	+	5.02884i	0.453450	+	0.329450i	0.790956	−	0.611873i	$-0.209584\pi$
$233$	6.92161	+	5.02884i	0.453450	+	0.329450i	−0.337507	+	0.941323i	$0.609584\pi$
$234$	0.510381	−	7.95634i	0.0333646	−	0.520122i
$235$	7.34146	−	19.4858i	0.478904	−	1.27111i
$236$	14.2984	+	3.03921i	0.930745	+	0.197836i
$237$	−16.2775	+	18.8343i	−1.05734	+	1.22342i
$238$	0.173212	−	0.0368173i	0.0112276	−	0.00238651i
$239$	−14.2452	+	15.8209i	−0.921443	+	1.02337i	0.0782072	+	0.996937i	$0.475080\pi$
$239$	−14.2452	+	15.8209i	−0.921443	+	1.02337i	−0.999651	+	0.0264295i	$0.991586\pi$
$240$	−4.92119	+	8.03708i	−0.317662	+	0.518791i
$241$	1.90768	+	2.11869i	0.122884	+	0.136477i	0.801447	−	0.598065i	$-0.204064\pi$
$241$	1.90768	+	2.11869i	0.122884	+	0.136477i	−0.678563	+	0.734542i	$0.737397\pi$
$242$	−2.57466	−	1.87060i	−0.165506	−	0.120247i
$243$	−9.12390	−	12.6394i	−0.585299	−	0.810818i
$244$	4.85179	+	3.52503i	0.310604	+	0.225667i
$245$	−0.576671	−	9.83529i	−0.0368421	−	0.628353i
$246$	−3.60139	−	3.83982i	−0.229616	−	0.244818i
$247$	14.6594	+	6.52677i	0.932754	+	0.415289i
$248$	−3.17594	+	3.52724i	−0.201672	+	0.223980i
$249$	−9.90134	−	4.16930i	−0.627472	−	0.264218i
$250$	0.197288	−	5.84470i	0.0124776	−	0.369651i
$251$	1.54809			0.0977144			0.0488572	−	0.998806i	$-0.484442\pi$
$251$	1.54809			0.0977144			0.0488572	+	0.998806i	$0.484442\pi$
$252$	9.35436	+	14.7802i	0.589269	+	0.931065i
$253$	6.59081	−	4.78851i	0.414361	−	0.301051i
$254$	−0.477370	−	4.54188i	−0.0299529	−	0.284983i
$255$	−0.129466	+	0.366014i	−0.00810746	+	0.0229207i
$256$	0.175347	−	1.66831i	0.0109592	−	0.104269i
$257$	−5.00583	−	8.67035i	−0.312255	−	0.540842i	0.666595	−	0.745420i	$-0.267751\pi$
$257$	−5.00583	−	8.67035i	−0.312255	−	0.540842i	−0.978850	+	0.204578i	$0.934418\pi$
$258$	−10.1794	+	0.206975i	−0.633740	+	0.0128857i
$259$	6.80322	+	7.55575i	0.422732	+	0.469491i
$260$	−15.3189	−	12.2484i	−0.950039	−	0.759613i
$261$	20.3368	−	0.827349i	1.25882	−	0.0512116i
$262$	0.150958	−	0.464602i	0.00932623	−	0.0287032i
$263$	9.67179	+	10.7416i	0.596388	+	0.662356i	0.963465	−	0.267834i	$-0.0863080\pi$
$263$	9.67179	+	10.7416i	0.596388	+	0.662356i	−0.367077	+	0.930191i	$0.619641\pi$
$264$	1.17619	−	13.9045i	0.0723895	−	0.855762i
$265$	5.03993	−	0.830340i	0.309600	−	0.0510074i
$266$	5.45736	−	1.16000i	0.334612	−	0.0711240i
$267$	5.80465	−	10.5433i	0.355239	−	0.645238i
$268$	−11.7118	+	20.2854i	−0.715410	+	1.23913i
$269$	−24.3691	−	17.7052i	−1.48581	−	1.07951i	−0.975626	−	0.219442i	$-0.929576\pi$
$269$	−24.3691	−	17.7052i	−1.48581	−	1.07951i	−0.510187	−	0.860064i	$-0.670424\pi$
$270$	6.07678	−	0.0901608i	0.369821	−	0.00548701i
$271$	−7.60294	+	5.52386i	−0.461846	+	0.335551i	−0.794255	−	0.607585i	$-0.792139\pi$
$271$	−7.60294	+	5.52386i	−0.461846	+	0.335551i	0.332409	+	0.943135i	$0.392139\pi$
$272$	0.0254963	+	0.242581i	0.00154594	+	0.0147086i
$273$	−26.8997	+	12.6379i	−1.62805	+	0.764880i
$274$	−1.62265	−	2.81051i	−0.0980280	−	0.169789i
$275$	−8.63952	−	18.7741i	−0.520983	−	1.13212i
$276$	5.43176	+	2.28723i	0.326954	+	0.137675i
$277$	−10.0183	−	2.12946i	−0.601943	−	0.127947i	−0.103147	−	0.994666i	$-0.532891\pi$
$277$	−10.0183	−	2.12946i	−0.601943	−	0.127947i	−0.498796	+	0.866719i	$0.666224\pi$
$278$	2.41781	−	1.75664i	0.145011	−	0.105356i
$279$	−7.20149	−	1.22714i	−0.431142	−	0.0734669i
$280$	−14.7040	−	0.679129i	−0.878729	−	0.0405857i
$281$	1.38210	−	0.615351i	0.0824492	−	0.0367087i	−0.365098	−	0.930969i	$-0.618964\pi$
$281$	1.38210	−	0.615351i	0.0824492	−	0.0367087i	0.447547	+	0.894260i	$0.352298\pi$
$282$	−6.72319	+	5.09667i	−0.400360	+	0.303502i
$283$	2.49158	−	23.7058i	0.148109	−	1.40916i	−0.627829	−	0.778351i	$-0.716056\pi$
$283$	2.49158	−	23.7058i	0.148109	−	1.40916i	0.775938	−	0.630810i	$-0.217277\pi$
$284$	−14.0926	+	2.99548i	−0.836243	+	0.177749i
$285$	−4.07906	+	11.5320i	−0.241623	+	0.683094i
$286$	10.7445	+	2.28382i	0.635336	+	0.135045i
$287$	−6.06437	+	18.6642i	−0.357968	+	1.10171i
$288$	13.9038	−	6.88063i	0.819288	−	0.405445i
$289$	−5.25018	−	16.1584i	−0.308834	−	0.950494i
$290$	−4.28046	+	6.68176i	−0.251358	+	0.392366i
$291$	−1.97729	+	2.28788i	−0.115911	+	0.134118i
$292$	1.91745	−	18.2434i	0.112210	−	1.06761i
$293$	−0.224026	−	0.388025i	−0.0130878	−	0.0226687i	0.859407	−	0.511292i	$-0.170833\pi$
$293$	−0.224026	−	0.388025i	−0.0130878	−	0.0226687i	−0.872495	+	0.488623i	$0.837499\pi$
$294$	−1.92518	+	3.49681i	−0.112279	+	0.203938i
$295$	−18.3182	−	4.78669i	−1.06652	−	0.278692i
$296$	4.74722	−	3.44905i	0.275926	−	0.200472i
$297$	19.0516	−	9.91528i	1.10548	−	0.575343i
$298$	3.41183	+	10.5005i	0.197642	+	0.608279i
$299$	−5.00706	+	8.67248i	−0.289566	+	0.501542i
$300$	8.38736	−	12.3769i	0.484245	−	0.714580i
$301$	18.9772	+	32.8695i	1.09383	+	1.89457i
$302$	−6.19129	+	6.87613i	−0.356269	+	0.395677i
$303$	−20.9159	+	4.89224i	−1.20159	+	0.281052i
$304$	0.803309	+	7.64297i	0.0460729	+	0.438355i
$305$	−6.06678	−	4.85075i	−0.347383	−	0.277753i
$306$	0.123394	−	0.0975546i	0.00705398	−	0.00557683i
$307$	5.99405			0.342099			0.171049	−	0.985262i	$-0.445284\pi$
$307$	5.99405			0.342099			0.171049	+	0.985262i	$0.445284\pi$
$308$	−22.0160	+	9.80214i	−1.25448	+	0.558529i
$309$	4.98117	+	14.3323i	0.283369	+	0.815337i
$310$	2.00138	−	2.02637i	0.113671	−	0.115090i
$311$	−14.8967	+	16.5445i	−0.844716	+	0.938152i	−0.998754	−	0.0499127i	$-0.984106\pi$
$311$	−14.8967	+	16.5445i	−0.844716	+	0.938152i	0.154037	+	0.988065i	$0.450772\pi$
$312$	5.63103	+	16.2021i	0.318794	+	0.917266i
$313$	2.35212	+	2.61229i	0.132949	+	0.147655i	0.805943	−	0.591993i	$-0.201659\pi$
$313$	2.35212	+	2.61229i	0.132949	+	0.147655i	−0.672994	+	0.739648i	$0.734992\pi$
$314$	−0.158087	−	0.486542i	−0.00892137	−	0.0274572i
$315$	−11.2198	−	19.6822i	−0.632163	−	1.10896i
$316$	7.66743	−	23.5979i	0.431327	−	1.32749i
$317$	3.76678	−	1.67708i	0.211564	−	0.0941942i	−0.298219	−	0.954498i	$-0.596393\pi$
$317$	3.76678	−	1.67708i	0.211564	−	0.0941942i	0.509783	+	0.860303i	$0.329726\pi$
$318$	−1.90732	−	0.803143i	−0.106957	−	0.0450380i
$319$	−2.93126	+	27.8890i	−0.164119	+	1.56149i
$320$	0.726539	−	4.77895i	0.0406147	−	0.267151i
$321$	3.67174	+	3.91482i	0.204937	+	0.218504i
$322$	0.363948	+	3.46274i	0.0202820	+	0.192971i
$323$	0.0978338	+	0.301102i	0.00544362	+	0.0167537i
$324$	13.2705	+	8.08153i	0.737252	+	0.448974i
$325$	19.0883	+	16.7629i	1.05883	+	0.929836i
$326$	−3.26689	+	5.65841i	−0.180936	+	0.313390i
$327$	−4.37830	+	2.05699i	−0.242120	+	0.113752i
$328$	10.3469	+	4.60674i	0.571313	+	0.254365i
$329$	28.7311	+	12.7919i	1.58400	+	0.705242i
$330$	−1.08998	+	8.30209i	−0.0600017	+	0.457015i
$331$	14.3453	−	6.38692i	0.788487	−	0.351057i	0.0273314	−	0.999626i	$-0.491299\pi$
$331$	14.3453	−	6.38692i	0.788487	−	0.351057i	0.761155	+	0.648569i	$0.224632\pi$
$332$	10.7083			0.587696
$333$	8.39315	+	3.33501i	0.459942	+	0.182757i
$334$	3.17935	−	9.78504i	0.173966	−	0.535413i
$335$	16.3653	−	25.5461i	0.894134	−	1.39573i
$336$	−11.6831	−	8.13058i	−0.637363	−	0.443559i
$337$	25.4247	−	5.40419i	1.38497	−	0.294385i	0.545648	−	0.838014i	$-0.316284\pi$
$337$	25.4247	−	5.40419i	1.38497	−	0.294385i	0.839325	+	0.543629i	$0.182950\pi$
$338$	−6.55617	+	1.39356i	−0.356609	+	0.0757995i
$339$	11.8532	+	8.24898i	0.643777	+	0.448023i
$340$	−0.0226503	−	0.386307i	−0.00122838	−	0.0209505i
$341$	3.11026	−	9.57240i	0.168430	−	0.518375i
$342$	3.88777	−	3.07364i	0.210226	−	0.166204i
$343$	−8.76057			−0.473026
$344$	20.0111	−	8.90950i	1.07892	−	0.480368i
$345$	−6.89114	−	3.28389i	−0.371006	−	0.176799i
$346$	1.81361	+	0.807472i	0.0975004	+	0.0434100i
$347$	−11.2161	−	4.99372i	−0.602111	−	0.268077i	0.0829607	−	0.996553i	$-0.473562\pi$
$347$	−11.2161	−	4.99372i	−0.602111	−	0.268077i	−0.685071	+	0.728476i	$0.740229\pi$
$348$	−18.3618	+	8.62664i	−0.984295	+	0.462436i
$349$	−12.3258	+	21.3489i	−0.659784	+	1.14278i	0.320888	+	0.947117i	$0.396019\pi$
$349$	−12.3258	+	21.3489i	−0.659784	+	1.14278i	−0.980671	+	0.195662i	$0.937314\pi$
$350$	8.79507	+	0.814168i	0.470116	+	0.0435191i
$351$	−16.4367	+	20.6596i	−0.877324	+	1.10273i
$352$	6.60480	+	20.3275i	0.352037	+	1.08346i
$353$	−2.66609	−	25.3662i	−0.141902	−	1.35011i	−0.801278	−	0.598292i	$-0.795846\pi$
$353$	−2.66609	−	25.3662i	−0.141902	−	1.35011i	0.659376	−	0.751813i	$-0.270821\pi$
$354$	5.24776	+	5.59518i	0.278915	+	0.297380i
$355$	18.4126	−	3.03351i	0.977238	−	0.161002i
$356$	−1.25396	+	11.9306i	−0.0664596	+	0.632321i
$357$	−0.540422	−	0.227563i	−0.0286021	−	0.0120439i
$358$	−2.17576	+	0.968709i	−0.114992	+	0.0511978i
$359$	2.79781	−	8.61076i	0.147663	−	0.454459i	−0.849681	−	0.527297i	$-0.823206\pi$
$359$	2.79781	−	8.61076i	0.147663	−	0.454459i	0.997344	+	0.0728380i	$0.0232056\pi$
$360$	−11.9739	+	5.25249i	−0.631080	+	0.276830i
$361$	−2.78888	−	8.58330i	−0.146783	−	0.451753i
$362$	−6.70921	−	7.45133i	−0.352628	−	0.391633i
$363$	3.45957	+	9.95420i	0.181580	+	0.522460i
$364$	19.8221	−	22.0147i	1.03896	−	1.15388i
$365$	−3.57106	+	23.4894i	−0.186918	+	1.22949i
$366$	1.03317	+	2.97273i	0.0540045	+	0.155387i
$367$	−21.5890	+	9.61205i	−1.12694	+	0.501745i	−0.883621	−	0.468202i	$-0.844902\pi$
$367$	−21.5890	+	9.61205i	−1.12694	+	0.501745i	−0.243316	+	0.969947i	$0.578235\pi$
$368$	−4.79596			−0.250007
$369$	2.52540	+	17.2485i	0.131467	+	0.897921i
$370$	−2.94107	+	1.93601i	−0.152899	+	0.100648i
$371$	0.806411	+	7.67249i	0.0418668	+	0.398336i
$372$	7.09011	−	1.65838i	0.367605	−	0.0859829i
$373$	−1.10252	+	1.22447i	−0.0570864	+	0.0634009i	−0.771012	−	0.636821i	$-0.780249\pi$
$373$	−1.10252	+	1.22447i	−0.0570864	+	0.0634009i	0.713925	+	0.700222i	$0.246916\pi$
$374$	0.108361	+	0.187687i	0.00560322	+	0.00970506i
$375$	−11.5915	+	15.5125i	−0.598583	+	0.801061i
$376$	9.07549	−	15.7192i	0.468033	−	0.810656i
$377$	−10.6520	−	32.7836i	−0.548608	−	1.68844i
$378$	−0.401277	+	9.17040i	−0.0206395	+	0.471675i
$379$	17.3280	−	12.5895i	0.890077	−	0.646679i	−0.0458208	−	0.998950i	$-0.514590\pi$
$379$	17.3280	−	12.5895i	0.890077	−	0.646679i	0.935898	+	0.352271i	$0.114590\pi$
$380$	−0.713640	−	12.1713i	−0.0366089	−	0.624376i
$381$	−7.29351	+	13.2476i	−0.373658	+	0.678693i
$382$	4.59866	+	7.96511i	0.235288	+	0.407531i
$383$	1.18840	−	11.3069i	0.0607244	−	0.577755i	−0.921280	−	0.388899i	$-0.872856\pi$
$383$	1.18840	−	11.3069i	0.0607244	−	0.577755i	0.982005	−	0.188856i	$-0.0604778\pi$
$384$	−12.9937	+	15.0347i	−0.663083	+	0.767236i
$385$	29.0709	−	11.3667i	1.48159	−	0.579303i
$386$	3.19635	+	9.83736i	0.162690	+	0.500709i
$387$	28.0586	+	18.6918i	1.42630	+	0.950157i
$388$	0.931395	−	2.86654i	0.0472844	−	0.145527i
$389$	14.2155	+	3.02160i	0.720755	+	0.153201i	0.553664	−	0.832740i	$-0.313229\pi$
$389$	14.2155	+	3.02160i	0.720755	+	0.153201i	0.167091	+	0.985941i	$0.446563\pi$
$390$	−2.92680	−	9.86781i	−0.148204	−	0.499676i
$391$	−0.193258	+	0.0410783i	−0.00977349	+	0.00207742i
$392$	0.897690	−	8.54095i	0.0453402	−	0.431383i
$393$	−1.28909	+	0.977229i	−0.0650262	+	0.0492947i
$394$	−0.288129	+	0.128283i	−0.0145157	+	0.00646282i
$395$	−11.3306	+	30.0737i	−0.570103	+	1.51317i
$396$	−13.6658	+	16.4778i	−0.686731	+	0.828042i
$397$	−22.7814	+	16.5516i	−1.14336	+	0.830703i	−0.987584	−	0.157089i	$-0.949789\pi$
$397$	−22.7814	+	16.5516i	−1.14336	+	0.830703i	−0.155780	+	0.987792i	$0.549789\pi$
$398$	9.60876	+	2.04241i	0.481644	+	0.102377i
$399$	−17.0270	−	7.16980i	−0.852416	−	0.358939i
$400$	−2.38164	+	11.9310i	−0.119082	+	0.596551i
$401$	−4.58244	−	7.93701i	−0.228836	−	0.396356i	0.728627	−	0.684910i	$-0.240159\pi$
$401$	−4.58244	−	7.93701i	−0.228836	−	0.396356i	−0.957463	+	0.288555i	$0.906825\pi$
$402$	−11.1254	+	5.22688i	−0.554885	+	0.260693i
$403$	1.29324	+	12.3044i	0.0644210	+	0.612925i
$404$	17.3214	−	12.5847i	0.861772	−	0.626114i
$405$	−16.6870	−	11.2492i	−0.829182	−	0.558978i
$406$	−9.69618	−	7.04469i	−0.481213	−	0.349622i
$407$	−6.22164	+	10.7762i	−0.308395	+	0.534156i
$408$	−0.163217	+	0.296460i	−0.00808045	+	0.0146769i
$409$	−15.6809	+	3.33308i	−0.775371	+	0.164810i	−0.578570	−	0.815633i	$-0.696389\pi$
$409$	−15.6809	+	3.33308i	−0.775371	+	0.164810i	−0.196802	+	0.980443i	$0.563056\pi$
$410$	−6.07462	−	3.04784i	−0.300004	−	0.150522i
$411$	−0.905807	+	10.7081i	−0.0446802	+	0.528192i
$412$	−10.1198	−	11.2392i	−0.498566	−	0.553713i
$413$	8.83668	−	27.1965i	0.434825	−	1.33825i
$414$	1.65403	+	2.61341i	0.0812909	+	0.128442i
$415$	−13.8548	−	0.639911i	−0.680107	−	0.0314120i
$416$	−17.5800	−	19.5246i	−0.861931	−	0.957272i
$417$	−9.89419	+	0.201176i	−0.484521	+	0.00985164i
$418$	3.41412	+	5.91343i	0.166990	+	0.289235i
$419$	3.08754	−	29.3760i	0.150836	−	1.43511i	−0.613196	−	0.789931i	$-0.710116\pi$
$419$	3.08754	−	29.3760i	0.150836	−	1.43511i	0.764032	−	0.645179i	$-0.223217\pi$
$420$	17.9201	+	13.7405i	0.874412	+	0.670465i
$421$	−2.80431	−	26.6813i	−0.136674	−	1.30037i	−0.820890	−	0.571086i	$-0.806522\pi$
$421$	−2.80431	−	26.6813i	−0.136674	−	1.30037i	0.684216	−	0.729279i	$-0.260145\pi$
$422$	7.02433	−	5.10348i	0.341939	−	0.248433i
$423$	27.9137	−	1.13559i	1.35721	−	0.0552145i
$424$	4.45245			0.216230
$425$	0.00622076	+	0.501172i	0.000301751	+	0.0243104i
$426$	−6.96810	−	2.93416i	−0.337606	−	0.142160i
$427$	7.85019	−	8.71852i	0.379897	−	0.421919i
$428$	−4.88726	−	2.17595i	−0.236234	−	0.105178i
$429$	−24.8833	−	26.5306i	−1.20137	−	1.28091i
$430$	−12.2417	+	4.78653i	−0.590348	+	0.230827i
$431$	7.77127	+	5.64616i	0.374329	+	0.271966i	0.759004	−	0.651086i	$-0.225686\pi$
$431$	7.77127	+	5.64616i	0.374329	+	0.271966i	−0.384675	+	0.923052i	$0.625686\pi$
$432$	−12.5046	−	1.87007i	−0.601629	−	0.0899736i
$433$	10.7896	+	7.83912i	0.518516	+	0.376724i	0.816045	−	0.577989i	$-0.196162\pi$
$433$	10.7896	+	7.83912i	0.518516	+	0.376724i	−0.297529	+	0.954713i	$0.596162\pi$
$434$	2.87839	+	3.19677i	0.138167	+	0.153450i
$435$	24.2727	−	10.0642i	1.16379	−	0.482541i
$436$	3.22632	−	3.58319i	0.154513	−	0.171604i
$437$	−6.08897	+	1.29425i	−0.291275	+	0.0619124i
$438$	6.29455	−	7.28326i	0.300765	−	0.348008i
$439$	7.13546	+	1.51669i	0.340557	+	0.0723876i	0.375015	−	0.927019i	$-0.377637\pi$
$439$	7.13546	+	1.51669i	0.340557	+	0.0723876i	−0.0344588	+	0.999406i	$0.510971\pi$
$440$	−4.77045	−	17.3716i	−0.227422	−	0.828160i
$441$	11.8468	−	5.86268i	0.564133	−	0.279175i
$442$	−0.215522	−	0.156586i	−0.0102514	−	0.00744804i
$443$	−5.86605	+	10.1603i	−0.278704	+	0.482730i	−0.971063	−	0.238823i	$-0.923238\pi$
$443$	−5.86605	+	10.1603i	−0.278704	+	0.482730i	0.692359	+	0.721554i	$0.256572\pi$
$444$	−9.00015	+	0.182998i	−0.427128	+	0.00868469i
$445$	2.33537	−	15.3613i	0.110707	−	0.728197i
$446$	1.40000	+	0.623320i	0.0662919	+	0.0295151i
$447$	10.5886	−	34.9935i	0.500824	−	1.65513i
$448$	7.14135	+	1.51794i	0.337397	+	0.0717160i
$449$	−11.6170			−0.548239			−0.274120	−	0.961696i	$-0.588386\pi$
$449$	−11.6170			−0.548239			−0.274120	+	0.961696i	$0.588386\pi$
$450$	7.32283	−	2.81695i	0.345202	−	0.132792i
$451$	−24.0178			−1.13096
$452$	−14.0794	−	2.99267i	−0.662240	−	0.140763i
$453$	29.8339	−	6.97815i	1.40172	−	0.327862i
$454$	−10.5672	−	4.70480i	−0.495941	−	0.220807i
$455$	−26.9622	+	27.2989i	−1.26401	+	1.27979i
$456$	−5.14246	+	9.34051i	−0.240818	+	0.437410i
$457$	5.87515	−	10.1761i	0.274828	−	0.476016i	−0.695264	−	0.718755i	$-0.744712\pi$
$457$	5.87515	−	10.1761i	0.274828	−	0.476016i	0.970092	+	0.242739i	$0.0780457\pi$
$458$	7.66658	+	5.57009i	0.358236	+	0.260273i
$459$	−0.519905	+	0.0317483i	−0.0242671	+	0.00148188i
$460$	7.60060	+	0.351047i	0.354380	+	0.0163677i
$461$	24.6800	+	5.24590i	1.14946	+	0.244326i	0.742968	−	0.669327i	$-0.233418\pi$
$461$	24.6800	+	5.24590i	1.14946	+	0.244326i	0.406495	+	0.913653i	$0.366751\pi$
$462$	−12.4213	−	2.37740i	−0.577893	−	0.110607i
$463$	−20.1283	+	4.27840i	−0.935442	+	0.198834i	−0.650323	−	0.759658i	$-0.725366\pi$
$463$	−20.1283	+	4.27840i	−0.935442	+	0.198834i	−0.285119	+	0.958492i	$0.592033\pi$
$464$	11.0465	−	12.2684i	0.512820	−	0.569544i
$465$	−9.27256	+	1.72198i	−0.430005	+	0.0798549i
$466$	−2.99444	−	3.32566i	−0.138715	−	0.154058i
$467$	9.19766	+	6.68249i	0.425617	+	0.309229i	0.779894	−	0.625912i	$-0.215273\pi$
$467$	9.19766	+	6.68249i	0.425617	+	0.309229i	−0.354277	+	0.935141i	$0.615273\pi$
$468$	7.10758	−	25.3363i	0.328548	−	1.17117i
$469$	37.0710	+	26.9337i	1.71178	+	1.24368i
$470$	−5.87524	+	9.17117i	−0.271004	+	0.423035i
$471$	−0.490623	+	1.62142i	−0.0226067	+	0.0747112i
$472$	−15.0770	−	6.71271i	−0.693974	−	0.308977i
$473$	−31.0817	+	34.5197i	−1.42914	+	1.58722i
$474$	10.3764	−	7.86604i	0.476602	−	0.361299i
$475$	0.195997	+	15.7904i	0.00899295	+	0.724512i
$476$	0.584467			0.0267890
$477$	3.66487	+	5.79062i	0.167803	+	0.265134i
$478$	9.00885	−	6.54531i	0.412055	−	0.299375i
$479$	4.40749	+	41.9345i	0.201383	+	1.91604i	0.367668	+	0.929957i	$0.380156\pi$
$479$	4.40749	+	41.9345i	0.201383	+	1.91604i	−0.166284	+	0.986078i	$0.553177\pi$
$480$	13.7808	−	14.5323i	0.629004	−	0.663305i
$481$	1.59882	−	15.2118i	0.0729001	−	0.693598i
$482$	−0.745621	−	1.29145i	−0.0339621	−	0.0588241i
$483$	5.56059	−	10.1000i	0.253016	−	0.459565i
$484$	−7.02848	−	7.80591i	−0.319476	−	0.354814i
$485$	−1.37637	+	3.65318i	−0.0624979	+	0.165882i
$486$	3.29355	+	7.45898i	0.149398	+	0.338346i
$487$	5.00668	−	15.4090i	0.226874	−	0.698248i	−0.771221	−	0.636567i	$-0.780354\pi$
$487$	5.00668	−	15.4090i	0.226874	−	0.698248i	0.998096	−	0.0616809i	$-0.0196461\pi$
$488$	−4.53062	−	5.03176i	−0.205091	−	0.227777i
$489$	19.5822	−	9.19999i	0.885536	−	0.416038i
$490$	−0.774554	+	5.09478i	−0.0349908	+	0.230159i
$491$	−3.78682	+	0.804914i	−0.170897	+	0.0363253i	−0.292565	−	0.956246i	$-0.594509\pi$
$491$	−3.78682	+	0.804914i	−0.170897	+	0.0363253i	0.121668	+	0.992571i	$0.461176\pi$
$492$	−8.99189	−	14.8680i	−0.405385	−	0.670300i
$493$	0.340049	−	0.588982i	0.0153150	−	0.0265264i
$494$	−6.79044	−	4.93354i	−0.305516	−	0.221971i
$495$	18.6660	−	20.5030i	0.838973	−	0.921541i
$496$	−4.79365	+	3.48279i	−0.215241	+	0.156382i
$497$	2.94609	+	28.0302i	0.132150	+	1.25733i
$498$	4.61245	+	3.20993i	0.206689	+	0.143841i
$499$	−5.14142	−	8.90521i	−0.230162	−	0.398652i	0.727694	−	0.685902i	$-0.240592\pi$
$499$	−5.14142	−	8.90521i	−0.230162	−	0.398652i	−0.957856	+	0.287250i	$0.907259\pi$
$500$	4.64771	−	18.7339i	0.207852	−	0.837804i
$501$	−27.1498	+	20.5815i	−1.21296	+	0.919516i
$502$	−0.792054	−	0.168356i	−0.0353511	−	0.00751411i
$503$	16.4188	−	11.9290i	0.732078	−	0.531886i	−0.158142	−	0.987416i	$-0.550550\pi$
$503$	16.4188	−	11.9290i	0.732078	−	0.531886i	0.890220	+	0.455531i	$0.150550\pi$
$504$	−6.86102	−	18.5183i	−0.305614	−	0.824871i
$505$	−23.1631	+	15.2475i	−1.03075	+	0.678505i
$506$	−3.89284	+	1.73320i	−0.173058	+	0.0770503i
$507$	20.4553	+	8.61341i	0.908452	+	0.382535i
$508$	1.57559	−	14.9907i	0.0699055	−	0.665106i
$509$	−36.2239	+	7.69962i	−1.60559	+	0.341280i	−0.921580	−	0.388189i	$-0.873101\pi$
$509$	−36.2239	+	7.69962i	−1.60559	+	0.341280i	−0.684014	+	0.729468i	$0.739767\pi$
$510$	0.106043	−	0.173185i	0.00469568	−	0.00766878i
$511$	−35.1010	−	7.46095i	−1.55278	−	0.330053i
$512$	6.81947	−	20.9882i	0.301381	−	0.927555i
$513$	−16.3806	+	1.00029i	−0.723221	+	0.0441639i
$514$	1.61824	+	4.98044i	0.0713776	+	0.219678i
$515$	12.4217	+	15.1464i	0.547366	+	0.667429i
$516$	−33.0055	−	6.31714i	−1.45298	−	0.278096i
$517$	−4.02335	+	38.2796i	−0.176947	+	1.68354i
$518$	−2.65906	−	4.60563i	−0.116833	−	0.202360i
$519$	−3.40198	−	5.62513i	−0.149330	−	0.246916i
$520$	14.0423	+	17.1224i	0.615795	+	0.750868i
$521$	−11.4682	+	8.33217i	−0.502433	+	0.365039i	−0.809946	−	0.586505i	$-0.800503\pi$
$521$	−11.4682	+	8.33217i	−0.502433	+	0.365039i	0.307513	+	0.951544i	$0.400503\pi$
$522$	−10.4950	−	1.78835i	−0.459353	−	0.0782741i
$523$	−3.47821	−	10.7048i	−0.152092	−	0.468090i	0.845763	−	0.533559i	$-0.179146\pi$
$523$	−3.47821	−	10.7048i	−0.152092	−	0.468090i	−0.997855	+	0.0654688i	$0.979146\pi$
$524$	0.806181	−	1.39635i	0.0352182	−	0.0609996i
$525$	−22.3646	−	18.8488i	−0.976071	−	0.822628i
$526$	−3.78025	−	6.54759i	−0.164827	−	0.285488i
$527$	−0.163335	+	0.181401i	−0.00711496	+	0.00790197i
$528$	5.04520	−	16.6735i	0.219564	−	0.725621i
$529$	1.99808	+	19.0105i	0.0868732	+	0.826544i
$530$	−2.66890	−	0.123268i	−0.115929	−	0.00535441i
$531$	−3.67988	−	25.1336i	−0.159693	−	1.09071i
$532$	18.4147			0.798381
$533$	26.9709	−	12.0082i	1.16824	−	0.520134i
$534$	−4.11645	+	4.76303i	−0.178136	+	0.206117i
$535$	6.19328	+	3.10737i	0.267759	+	0.134344i
$536$	17.6956	−	19.6530i	0.764334	−	0.848879i
$537$	7.74593	+	1.48254i	0.334261	+	0.0639765i
$538$	10.5426	+	11.7088i	0.454524	+	0.504800i
$539$	5.62766	+	17.3202i	0.242400	+	0.746032i
$540$	19.6804	+	3.87896i	0.846909	+	0.166924i
$541$	−4.62861	+	14.2454i	−0.199000	+	0.612458i	0.800907	+	0.598789i	$0.204351\pi$
$541$	−4.62861	+	14.2454i	−0.199000	+	0.612458i	−0.999907	+	0.0136691i	$0.995649\pi$
$542$	4.49065	−	1.99937i	0.192890	−	0.0858801i
$543$	4.14111	+	32.9429i	0.177712	+	1.41372i
$544$	0.0541832	−	0.515518i	0.00232308	−	0.0221027i
$545$	−4.38846	+	4.44327i	−0.187981	+	0.190329i
$546$	15.1372	−	3.54059i	0.647812	−	0.151523i
$547$	−1.39143	−	13.2386i	−0.0594932	−	0.566040i	−0.983148	−	0.182813i	$-0.941480\pi$
$547$	−1.39143	−	13.2386i	−0.0594932	−	0.566040i	0.923654	−	0.383226i	$-0.125187\pi$
$548$	−3.30998	−	10.1871i	−0.141395	−	0.435170i
$549$	2.81483	−	10.0340i	0.120134	−	0.428240i
$550$	2.37857	+	10.5450i	0.101423	+	0.449640i
$551$	10.7139	−	18.5570i	0.456427	−	0.790555i
$552$	−5.46167	−	3.80093i	−0.232464	−	0.161778i
$553$	−44.3427	−	19.7427i	−1.88564	−	0.839543i
$554$	4.89413	+	2.17901i	0.207932	+	0.0925772i
$555$	11.6557	+	0.301064i	0.494756	+	0.0127794i
$556$	9.01119	−	4.01204i	0.382160	−	0.170148i
$557$	−11.7342			−0.497192			−0.248596	−	0.968607i	$-0.579969\pi$
$557$	−11.7342			−0.497192			−0.248596	+	0.968607i	$0.579969\pi$
$558$	3.55107	+	1.41102i	0.150329	+	0.0597331i
$559$	17.6444	−	54.3039i	0.746279	−	2.29681i
$560$	−17.7788	−	4.64574i	−0.751289	−	0.196318i
$561$	0.0604900	−	0.715091i	0.00255389	−	0.0301912i
$562$	−0.774049	+	0.164529i	−0.0326513	+	0.00694025i
$563$	1.67720	−	0.356499i	0.0706854	−	0.0150247i	−0.172433	−	0.985021i	$-0.555163\pi$
$563$	1.67720	−	0.356499i	0.0706854	−	0.0150247i	0.243119	+	0.969997i	$0.421830\pi$
$564$	−25.2028	+	11.8407i	−1.06123	+	0.498582i
$565$	18.0376	+	4.71339i	0.758849	+	0.198294i
$566$	−3.85280	+	11.8577i	−0.161945	+	0.498416i
$567$	18.4365	−	24.1657i	0.774261	−	1.01487i
$568$	16.2663			0.682520
$569$	15.7340	−	7.00522i	0.659603	−	0.293674i	−0.0495050	−	0.998774i	$-0.515764\pi$
$569$	15.7340	−	7.00522i	0.659603	−	0.293674i	0.709108	+	0.705100i	$0.249098\pi$
$570$	3.34110	−	5.45653i	0.139943	−	0.228549i
$571$	−0.892675	−	0.397445i	−0.0373573	−	0.0166325i	0.387973	−	0.921671i	$-0.373175\pi$
$571$	−0.892675	−	0.397445i	−0.0373573	−	0.0166325i	−0.425330	+	0.905038i	$0.639842\pi$
$572$	33.1207	+	14.7463i	1.38485	+	0.616574i
$573$	2.56709	−	30.3472i	0.107242	−	1.26777i
$574$	5.13249	−	8.88973i	0.214226	−	0.371050i
$575$	−9.81297	−	0.908397i	−0.409229	−	0.0378828i
$576$	6.28353	−	1.60511i	0.261814	−	0.0668797i
$577$	−1.42881	−	4.39743i	−0.0594822	−	0.183067i	0.916900	−	0.399116i	$-0.130683\pi$
$577$	−1.42881	−	4.39743i	−0.0594822	−	0.183067i	−0.976383	+	0.216049i	$0.930683\pi$
$578$	0.928927	+	8.83815i	0.0386383	+	0.367618i
$579$	9.91987	−	32.7834i	0.412256	−	1.36243i
$580$	−18.4044	+	18.6343i	−0.764201	+	0.773745i
$581$	2.18968	−	20.8334i	0.0908433	−	0.864316i
$582$	1.26046	−	0.955522i	0.0522477	−	0.0396076i
$583$	−8.62547	+	3.84031i	−0.357231	+	0.159049i
$584$	−6.39992	+	19.6969i	−0.264831	+	0.815065i
$585$	−10.7101	+	32.3563i	−0.442808	+	1.33777i
$586$	0.0724213	+	0.222890i	0.00299170	+	0.00920749i
$587$	−26.1074	−	28.9952i	−1.07757	−	1.19676i	−0.979471	−	0.201584i	$-0.935391\pi$
$587$	−26.1074	−	28.9952i	−1.07757	−	1.19676i	−0.0980972	−	0.995177i	$-0.531276\pi$
$588$	−8.61493	+	9.96812i	−0.355274	+	0.411078i
$589$	−5.14616	+	5.71539i	−0.212044	+	0.235499i
$590$	8.85163	+	4.44115i	0.364416	+	0.182839i
$591$	1.02577	+	0.196329i	0.0421946	+	0.00807590i
$592$	6.69204	−	2.97949i	0.275041	−	0.122456i
$593$	−0.233927			−0.00960624			−0.00480312	−	0.999988i	$-0.501529\pi$
$593$	−0.233927			−0.00960624			−0.00480312	+	0.999988i	$0.501529\pi$
$594$	−10.8257	+	3.00111i	−0.444185	+	0.123137i
$595$	−0.756206	−	0.0349267i	−0.0310014	−	0.00143186i
$596$	3.80914	+	36.2416i	0.156028	+	1.48451i
$597$	−22.2530	−	23.7262i	−0.910754	−	0.971049i
$598$	3.50492	−	3.89261i	0.143327	−	0.159181i
$599$	17.3587	+	30.0662i	0.709258	+	1.22847i	0.965133	+	0.261761i	$0.0843032\pi$
$599$	17.3587	+	30.0662i	0.709258	+	1.22847i	−0.255875	+	0.966710i	$0.582363\pi$
$600$	−12.1679	+	11.6996i	−0.496752	+	0.477634i
$601$	−15.4400	+	26.7429i	−0.629811	+	1.09086i	0.357779	+	0.933806i	$0.383534\pi$
$601$	−15.4400	+	26.7429i	−0.629811	+	1.09086i	−0.987589	+	0.157058i	$0.949799\pi$
$602$	−6.13479	−	18.8809i	−0.250035	−	0.769530i
$603$	40.1251	+	6.83734i	1.63402	+	0.278438i
$604$	−24.7068	+	17.9505i	−1.00530	+	0.730396i
$605$	8.62724	+	10.5196i	0.350747	+	0.427682i
$606$	11.2333	−	0.228404i	0.456323	−	0.00927829i
$607$	−3.80766	−	6.59506i	−0.154548	−	0.267685i	0.778346	−	0.627835i	$-0.216059\pi$
$607$	−3.80766	−	6.59506i	−0.154548	−	0.267685i	−0.932894	+	0.360150i	$0.882725\pi$
$608$	1.70714	−	16.2424i	0.0692338	−	0.658715i
$609$	13.0287	+	37.4875i	0.527951	+	1.51907i
$610$	2.57644	+	3.14158i	0.104317	+	0.127199i
$611$	−14.6207	−	44.9978i	−0.591489	−	1.82041i
$612$	0.465315	−	0.230273i	0.0188092	−	0.00930822i
$613$	−9.39803	+	28.9242i	−0.379583	+	1.16824i	0.560752	+	0.827984i	$0.310512\pi$
$613$	−9.39803	+	28.9242i	−0.379583	+	1.16824i	−0.940334	+	0.340252i	$0.889488\pi$
$614$	−3.06676	−	0.651860i	−0.123764	−	0.0263069i
$615$	10.7456	+	19.7741i	0.433303	+	0.797367i
$616$	26.6143	−	5.65704i	1.07232	−	0.227928i
$617$	−4.85610	+	46.2027i	−0.195499	+	1.86005i	0.254565	+	0.967056i	$0.418068\pi$
$617$	−4.85610	+	46.2027i	−0.195499	+	1.86005i	−0.450064	+	0.892996i	$0.648599\pi$
$618$	−0.989882	−	7.87460i	−0.0398189	−	0.316763i
$619$	11.6372	−	5.18120i	0.467737	−	0.208250i	−0.159314	−	0.987228i	$-0.550928\pi$
$619$	11.6372	−	5.18120i	0.467737	−	0.208250i	0.627051	+	0.778978i	$0.284262\pi$
$620$	7.85187	−	5.16862i	0.315339	−	0.207577i
$621$	0.447719	−	10.2317i	0.0179663	−	0.410586i
$622$	9.42090	−	6.84469i	0.377744	−	0.274447i
$623$	22.9550	+	4.87924i	0.919673	+	0.195482i
$624$	2.67074	+	21.2460i	0.106915	+	0.850521i
$625$	−7.13289	+	23.9608i	−0.285316	+	0.958434i
$626$	−0.919333	−	1.59233i	−0.0367439	−	0.0636423i
$627$	1.90585	−	22.5303i	0.0761124	−	0.899772i
$628$	−0.176497	−	1.67925i	−0.00704298	−	0.0670095i
$629$	0.244143	−	0.177381i	0.00973463	−	0.00707263i
$630$	3.59996	+	11.2902i	0.143426	+	0.449813i
$631$	−31.3529	−	22.7792i	−1.24814	−	0.906827i	−0.250028	−	0.968239i	$-0.580440\pi$
$631$	−31.3529	−	22.7792i	−1.24814	−	0.906827i	−0.998113	+	0.0614115i	$0.980440\pi$
$632$	−14.0068	+	24.2605i	−0.557162	+	0.965032i
$633$	−28.7451	+	0.584466i	−1.14251	+	0.0232305i
$634$	−2.10960	+	0.448409i	−0.0837828	+	0.0178086i
$635$	−2.93438	+	19.3014i	−0.116447	+	0.765954i
$636$	−5.60653	−	3.90175i	−0.222313	−	0.154714i
$637$	−14.9792	−	16.6360i	−0.593496	−	0.659144i
$638$	4.53269	−	13.9502i	0.179451	−	0.552293i
$639$	13.3890	+	21.1551i	0.529662	+	0.836883i
$640$	−9.04479	+	24.0067i	−0.357527	+	0.948950i
$641$	22.4290	+	24.9100i	0.885894	+	0.983885i	0.999954	−	0.00958888i	$-0.00305228\pi$
$641$	22.4290	+	24.9100i	0.885894	+	0.983885i	−0.114060	+	0.993474i	$0.536386\pi$
$642$	−1.45285	−	2.40226i	−0.0573393	−	0.0948097i
$643$	−12.4860	−	21.6263i	−0.492399	−	0.852860i	0.507563	−	0.861615i	$-0.330546\pi$
$643$	−12.4860	−	21.6263i	−0.492399	−	0.852860i	−0.999962	+	0.00875512i	$0.997213\pi$
$644$	−1.20123	+	11.4290i	−0.0473352	+	0.450365i
$645$	42.3262	+	10.1457i	1.66659	+	0.399486i
$646$	−0.0173100	−	0.164693i	−0.000681051	−	0.00647977i
$647$	−17.8362	+	12.9588i	−0.701214	+	0.509462i	−0.880327	−	0.474367i	$-0.842677\pi$
$647$	−17.8362	+	12.9588i	−0.701214	+	0.509462i	0.179114	+	0.983828i	$0.442677\pi$
$648$	−12.7583	−	12.0399i	−0.501192	−	0.472973i
$649$	34.9976			1.37377
$650$	−7.94321	−	10.6523i	−0.311558	−	0.417818i
$651$	−1.77662	−	14.1332i	−0.0696312	−	0.553923i
$652$	−14.4299	+	16.0260i	−0.565117	+	0.627627i
$653$	−5.01165	−	2.23133i	−0.196121	−	0.0873186i	0.306326	−	0.951927i	$-0.400900\pi$
$653$	−5.01165	−	2.23133i	−0.196121	−	0.0873186i	−0.502447	+	0.864608i	$0.667567\pi$
$654$	2.46378	−	0.576280i	0.0963416	−	0.0225343i
$655$	−1.12651	+	1.75847i	−0.0440164	+	0.0687091i
$656$	11.4389	+	8.31087i	0.446615	+	0.324485i
$657$	−30.8846	+	7.88941i	−1.20492	+	0.307795i
$658$	−13.3087	−	9.66932i	−0.518826	−	0.376949i
$659$	13.5361	+	15.0334i	0.527292	+	0.585617i	0.946674	−	0.322193i	$-0.104420\pi$
$659$	13.5361	+	15.0334i	0.527292	+	0.585617i	−0.419382	+	0.907810i	$0.637753\pi$
$660$	−9.21605	+	26.0548i	−0.358734	+	1.01418i
$661$	9.09626	−	10.1024i	0.353803	−	0.392939i	−0.539802	−	0.841792i	$-0.681501\pi$
$661$	9.09626	−	10.1024i	0.353803	−	0.392939i	0.893605	+	0.448854i	$0.148168\pi$
$662$	−8.03410	+	1.70770i	−0.312254	+	0.0663717i
$663$	0.289597	+	0.833256i	0.0112470	+	0.0323610i
$664$	−11.8257	−	2.51364i	−0.458928	−	0.0975481i
$665$	−23.8257	−	1.10043i	−0.923921	−	0.0426729i
$666$	−3.93153	−	2.61907i	−0.152344	−	0.101487i
$667$	10.8184	+	7.86001i	0.418889	+	0.304341i
$668$	16.9791	−	29.4086i	0.656940	−	1.13785i
$669$	−2.62613	−	4.34227i	−0.101532	−	0.167882i
$670$	−11.1512	+	11.2905i	−0.430810	+	0.436190i
$671$	13.1169	+	5.84001i	0.506371	+	0.225451i
$672$	20.6931	+	22.0631i	0.798255	+	0.851102i
$673$	−23.2455	−	4.94099i	−0.896049	−	0.190461i	−0.263205	−	0.964740i	$-0.584779\pi$
$673$	−23.2455	−	4.94099i	−0.896049	−	0.190461i	−0.632845	+	0.774279i	$0.718113\pi$
$674$	−13.5959			−0.523693
$675$	−25.2314	−	6.19481i	−0.971158	−	0.238439i
$676$	−22.1225			−0.850865
$677$	34.3311	+	7.29729i	1.31945	+	0.280458i	0.813228	−	0.581946i	$-0.197708\pi$
$677$	34.3311	+	7.29729i	1.31945	+	0.280458i	0.506222	+	0.862403i	$0.331042\pi$
$678$	−5.16740	−	5.50950i	−0.198453	−	0.211591i
$679$	−5.38650	−	2.39822i	−0.206715	−	0.0920354i
$680$	−0.0656667	+	0.431935i	−0.00251820	+	0.0165640i
$681$	19.8219	+	32.7753i	0.759578	+	1.25595i
$682$	−2.63232	+	4.55932i	−0.100797	+	0.174585i
$683$	35.4803	+	25.7779i	1.35762	+	0.986365i	0.998593	+	0.0530363i	$0.0168899\pi$
$683$	35.4803	+	25.7779i	1.35762	+	0.986365i	0.359023	+	0.933329i	$0.383110\pi$
$684$	14.6606	−	7.25517i	0.560563	−	0.277408i
$685$	3.67382	+	13.3782i	0.140369	+	0.511155i
$686$	4.48220	+	0.952722i	0.171131	+	0.0363751i
$687$	−10.3016	−	29.6406i	−0.393029	−	1.13086i
$688$	26.7480	−	5.68547i	1.01976	−	0.216756i
$689$	7.76595	−	8.62497i	0.295859	−	0.328585i
$690$	3.16861	+	2.42957i	0.120627	+	0.0924921i
$691$	−16.7862	−	18.6430i	−0.638579	−	0.709214i	0.333794	−	0.942646i	$-0.391671\pi$
$691$	−16.7862	−	18.6430i	−0.638579	−	0.709214i	−0.972373	+	0.233432i	$0.925004\pi$
$692$	5.30102	+	3.85142i	0.201515	+	0.146409i
$693$	29.2638	+	29.9567i	1.11164	+	1.13796i
$694$	5.19545	+	3.77472i	0.197217	+	0.143286i
$695$	−11.8988	+	4.65244i	−0.451346	+	0.176477i
$696$	22.3028	−	5.21664i	0.845387	−	0.197736i
$697$	0.532129	+	0.236919i	0.0201558	+	0.00897395i
$698$	8.62800	−	9.58236i	0.326575	−	0.362698i
$699$	1.84825	+	14.7030i	0.0699071	+	0.556118i
$700$	27.8356	+	8.66389i	1.05209	+	0.327464i
$701$	4.91096			0.185485			0.0927423	−	0.995690i	$-0.470437\pi$
$701$	4.91096			0.185485			0.0927423	+	0.995690i	$0.470437\pi$
$702$	10.6563	−	8.78265i	0.402196	−	0.331480i
$703$	7.69220	−	5.58871i	0.290117	−	0.210782i
$704$	0.933989	+	8.88631i	0.0352010	+	0.334915i
$705$	33.3160	−	13.8138i	1.25475	−	0.520258i
$706$	−1.39454	+	13.2681i	−0.0524841	+	0.499353i
$707$	−20.9421	−	36.2728i	−0.787608	−	1.36418i
$708$	13.1025	+	21.6648i	0.492423	+	0.814214i
$709$	−12.4749	−	13.8548i	−0.468505	−	0.520328i	0.461865	−	0.886950i	$-0.347181\pi$
$709$	−12.4749	−	13.8548i	−0.468505	−	0.520328i	−0.930370	+	0.366623i	$0.880514\pi$
$710$	−9.75039	−	0.450339i	−0.365926	−	0.0169009i
$711$	−43.0811	+	1.75264i	−1.61567	+	0.0657291i
$712$	4.18536	−	12.8812i	0.156853	−	0.482744i
$713$	−3.21152	−	3.56675i	−0.120272	−	0.133576i
$714$	0.251750	+	0.175200i	0.00942152	+	0.00655671i
$715$	−41.9716	−	21.0586i	−1.56965	−	0.787545i
$716$	−7.68904	+	1.63436i	−0.287353	+	0.0610787i
$717$	−36.8661	+	0.749590i	−1.37679	+	0.0279939i
$718$	−2.36788	+	4.10129i	−0.0883686	+	0.153059i
$719$	12.2939	+	8.93208i	0.458487	+	0.333110i	0.792937	−	0.609303i	$-0.208551\pi$
$719$	12.2939	+	8.93208i	0.458487	+	0.333110i	−0.334451	+	0.942413i	$0.608551\pi$
$720$	−15.9846	+	3.30596i	−0.595713	+	0.123206i
$721$	−23.9355	+	17.3902i	−0.891405	+	0.647643i
$722$	0.493443	+	4.69480i	0.0183641	+	0.174722i
$723$	−0.416225	+	4.92046i	−0.0154796	+	0.182994i
$724$	−16.5470	−	28.6602i	−0.614963	−	1.06515i
$725$	24.9258	−	23.0099i	0.925723	−	0.854566i
$726$	−0.687501	−	5.46913i	−0.0255156	−	0.202979i
$727$	31.3004	+	6.65310i	1.16087	+	0.246750i	0.747783	−	0.663943i	$-0.231118\pi$
$727$	31.3004	+	6.65310i	1.16087	+	0.246750i	0.413084	+	0.910693i	$0.364452\pi$
$728$	−27.0582	+	19.6589i	−1.00284	+	0.728608i
$729$	5.15697	−	26.5029i	0.190999	−	0.981590i
$730$	4.38157	−	11.6296i	0.162169	−	0.430430i
$731$	1.02914	−	0.458204i	0.0380643	−	0.0169473i
$732$	1.29555	+	10.3062i	0.0478850	+	0.380930i
$733$	−2.13492	+	20.3124i	−0.0788549	+	0.750254i	0.881634	+	0.471935i	$0.156444\pi$
$733$	−2.13492	+	20.3124i	−0.0788549	+	0.750254i	−0.960488	+	0.278320i	$0.910223\pi$
$734$	12.0910	−	2.57002i	0.446286	−	0.0948611i
$735$	11.7420	−	12.3823i	0.433110	−	0.456728i
$736$	9.96935	+	2.11905i	0.367475	+	0.0781092i
$737$	−17.3297	+	53.3353i	−0.638347	+	1.96463i
$738$	0.583715	−	9.09955i	0.0214868	−	0.334959i
$739$	−9.35272	−	28.7847i	−0.344045	−	1.05886i	−0.962093	−	0.272722i	$-0.912076\pi$
$739$	−9.35272	−	28.7847i	−0.344045	−	1.05886i	0.618048	−	0.786141i	$-0.287924\pi$
$740$	−10.8236	+	4.23204i	−0.397883	+	0.155573i
$741$	9.12429	+	26.2533i	0.335189	+	0.964439i
$742$	0.421804	−	4.01320i	0.0154849	−	0.147329i
$743$	−2.81735	−	4.87980i	−0.103359	−	0.179022i	0.809708	−	0.586833i	$-0.199626\pi$
$743$	−2.81735	−	4.87980i	−0.103359	−	0.179022i	−0.913066	+	0.407811i	$0.866292\pi$
$744$	−8.21925	+	0.167120i	−0.301332	+	0.00612691i
$745$	−2.76268	−	47.1183i	−0.101217	−	1.72628i
$746$	0.697250	−	0.506582i	0.0255281	−	0.0185473i
$747$	−6.46482	−	17.4489i	−0.236535	−	0.638423i
$748$	0.221041	+	0.680295i	0.00808207	+	0.0248741i
$749$	−5.23275	+	9.06338i	−0.191200	+	0.331169i
$750$	7.61760	−	6.67612i	0.278156	−	0.243777i
$751$	11.3957	+	19.7379i	0.415835	+	0.720247i	0.995516	−	0.0945967i	$-0.0301561\pi$
$751$	11.3957	+	19.7379i	0.415835	+	0.720247i	−0.579681	+	0.814844i	$0.696823\pi$
$752$	15.1621	−	16.8392i	0.552904	−	0.614062i
$753$	1.83432	+	1.95576i	0.0668464	+	0.0712718i
$754$	1.88469	+	17.9316i	0.0686363	+	0.653031i
$755$	33.0392	−	21.7486i	1.20242	−	0.791513i
$756$	−7.58846	+	29.3307i	−0.275990	+	1.06675i
$757$	41.0082			1.49047			0.745234	−	0.666803i	$-0.232338\pi$
$757$	41.0082			1.49047			0.745234	+	0.666803i	$0.232338\pi$
$758$	−10.2347	+	4.55678i	−0.371741	+	0.165510i
$759$	13.8589	+	2.65255i	0.503047	+	0.0962815i
$760$	−2.06895	+	13.6089i	−0.0750488	+	0.493648i
$761$	−2.79394	+	3.10299i	−0.101280	+	0.112483i	−0.791654	−	0.610970i	$-0.790780\pi$
$761$	−2.79394	+	3.10299i	−0.101280	+	0.112483i	0.690373	+	0.723453i	$0.257446\pi$
$762$	5.17229	−	5.98472i	0.187372	−	0.216804i
$763$	−6.31149	−	7.00962i	−0.228491	−	0.253765i
$764$	9.38062	+	28.8706i	0.339379	+	1.04450i
$765$	−0.615803	+	0.270129i	−0.0222644	+	0.00976653i
$766$	−1.83766	+	5.65574i	−0.0663974	+	0.204350i
$767$	−39.3006	+	17.4978i	−1.41906	+	0.631807i
$768$	2.31541	−	1.75525i	0.0835501	−	0.0633372i
$769$	0.728689	−	6.93301i	0.0262772	−	0.250011i	−0.973496	−	0.228705i	$-0.926551\pi$
$769$	0.728689	−	6.93301i	0.0262772	−	0.250011i	0.999773	−	0.0213059i	$-0.00678240\pi$
$770$	−16.1098	+	2.65412i	−0.580556	+	0.0956480i
$771$	5.02221	−	16.5975i	0.180870	−	0.597745i
$772$	3.56857	+	33.9527i	0.128436	+	1.22198i
$773$	−3.04988	−	9.38657i	−0.109697	−	0.337611i	0.881107	−	0.472916i	$-0.156799\pi$
$773$	−3.04988	−	9.38657i	−0.109697	−	0.337611i	−0.990804	+	0.135305i	$0.956799\pi$
$774$	−12.3230	−	12.6147i	−0.442940	−	0.453428i
$775$	−10.4679	+	6.21815i	−0.376019	+	0.223362i
$776$	−1.70147	+	2.94703i	−0.0610792	+	0.105792i
$777$	−1.48436	+	17.5475i	−0.0532511	+	0.629514i
$778$	−6.94454	−	3.09191i	−0.248974	−	0.110850i
$779$	16.7657	+	7.46458i	0.600694	+	0.267446i
$780$	−2.67744	−	33.8660i	−0.0958678	−	1.21260i
$781$	−31.5118	+	14.0300i	−1.12758	+	0.502031i
$782$	0.103345			0.00369560
$783$	25.1422	+	24.7120i	0.898510	+	0.883134i
$784$	3.31300	−	10.1964i	0.118322	−	0.364156i
$785$	0.128009	+	2.18323i	0.00456883	+	0.0779228i
$786$	0.765819	−	0.359793i	0.0273159	−	0.0128334i
$787$	34.6614	−	7.36750i	1.23554	−	0.262623i	0.456575	−	0.889685i	$-0.349076\pi$
$787$	34.6614	−	7.36750i	1.23554	−	0.262623i	0.778969	+	0.627062i	$0.215743\pi$
$788$	−1.01824	+	0.216433i	−0.0362732	+	0.00771011i
$789$	−2.11024	+	24.9464i	−0.0751264	+	0.888116i
$790$	9.06765	−	14.1545i	0.322613	−	0.503595i
$791$	−8.70136	+	26.7800i	−0.309385	+	0.952189i
$792$	18.9597	−	14.9894i	0.673705	−	0.532626i
$793$	−17.6494			−0.626750
$794$	13.4557	−	5.99088i	0.477526	−	0.212608i
$795$	7.02078	+	5.38327i	0.249001	+	0.190925i
$796$	29.6197	+	13.1876i	1.04984	+	0.467420i
$797$	32.3072	+	14.3841i	1.14438	+	0.509510i	0.889261	−	0.457400i	$-0.151219\pi$
$797$	32.3072	+	14.3841i	1.14438	+	0.509510i	0.255117	+	0.966910i	$0.417886\pi$
$798$	7.93186	+	5.52001i	0.280785	+	0.195406i
$799$	0.466741	−	0.808419i	0.0165121	−	0.0285998i
$800$	10.2223	−	23.7487i	0.361414	−	0.839642i
$801$	20.1976	−	5.15944i	0.713648	−	0.182300i
$802$	1.48137	+	4.55919i	0.0523090	+	0.160991i
$803$	−4.59072	−	43.6777i	−0.162003	−	1.54135i
$804$	−39.5045	+	9.24011i	−1.39322	+	0.325874i
$805$	2.23718	−	14.7155i	0.0788501	−	0.518652i
$806$	0.676449	−	6.43598i	0.0238269	−	0.226698i
$807$	−6.50719	−	51.7653i	−0.229064	−	1.82222i
$808$	−22.0830	+	9.83197i	−0.776876	+	0.345888i
$809$	−4.45186	+	13.7014i	−0.156519	+	0.481716i	−0.998312	−	0.0580852i	$-0.981500\pi$
$809$	−4.45186	+	13.7014i	−0.156519	+	0.481716i	0.841793	+	0.539801i	$0.181500\pi$
$810$	7.31425	+	7.57020i	0.256997	+	0.265990i
$811$	5.51450	+	16.9719i	0.193640	+	0.595964i	0.999990	+	0.00452443i	$0.00144017\pi$
$811$	5.51450	+	16.9719i	0.193640	+	0.595964i	−0.806349	+	0.591440i	$0.798560\pi$
$812$	−26.4692	−	29.3971i	−0.928889	−	1.03164i
$813$	−15.9872	−	3.05990i	−0.560695	−	0.107315i
$814$	4.35512	−	4.83685i	0.152647	−	0.169532i
$815$	19.6276	−	19.8727i	0.687525	−	0.696112i
$816$	−0.276252	+	0.319644i	−0.00967074	+	0.0111898i
$817$	32.4251	−	14.4366i	1.13441	−	0.505072i
$818$	8.38536			0.293187
$819$	−47.8393	−	19.0089i	−1.67164	−	0.664225i
$820$	−17.5200	−	14.0083i	−0.611826	−	0.489191i
$821$	−2.78340	−	26.4823i	−0.0971414	−	0.924239i	−0.929207	−	0.369561i	$-0.879508\pi$
$821$	−2.78340	−	26.4823i	−0.0971414	−	0.924239i	0.832065	−	0.554678i	$-0.187159\pi$
$822$	1.62796	−	5.38012i	0.0567816	−	0.187653i
$823$	−1.84785	+	2.05225i	−0.0644122	+	0.0715369i	−0.774490	−	0.632587i	$-0.781993\pi$
$823$	−1.84785	+	2.05225i	−0.0644122	+	0.0715369i	0.710077	+	0.704124i	$0.248660\pi$
$824$	8.53753	+	14.7874i	0.297419	+	0.515145i
$825$	13.4811	−	33.1599i	0.469350	−	1.15448i
$826$	−7.47879	+	12.9537i	−0.260221	+	0.450715i
$827$	−5.30684	−	16.3328i	−0.184537	−	0.567946i	0.815403	−	0.578893i	$-0.196515\pi$
$827$	−5.30684	−	16.3328i	−0.184537	−	0.567946i	−0.999940	+	0.0109475i	$0.996515\pi$
$828$	3.54652	+	9.57228i	0.123250	+	0.332660i
$829$	−7.77371	+	5.64793i	−0.269992	+	0.196161i	−0.714541	−	0.699594i	$-0.753364\pi$
$829$	−7.77371	+	5.64793i	−0.269992	+	0.196161i	0.444548	+	0.895755i	$0.353364\pi$
$830$	7.01901	+	1.83413i	0.243633	+	0.0636635i
$831$	−9.18044	−	15.1797i	−0.318466	−	0.526579i
$832$	−5.49172	−	9.51193i	−0.190391	−	0.329767i
$833$	0.0461671	−	0.439251i	0.00159959	−	0.0152191i
$834$	5.08408	+	0.973076i	0.176047	+	0.0336949i
$835$	−23.7256	+	37.0353i	−0.821057	+	1.28166i
$836$	6.96432	+	21.4340i	0.240866	+	0.741310i
$837$	−6.98272	−	10.5519i	−0.241358	−	0.364729i
$838$	−4.77436	+	14.6940i	−0.164927	+	0.507594i
$839$	−41.7253	−	8.86899i	−1.44052	−	0.306192i	−0.579586	−	0.814911i	$-0.696786\pi$
$839$	−41.7253	−	8.86899i	−1.44052	−	0.306192i	−0.860932	+	0.508720i	$0.830119\pi$
$840$	−16.5647	−	19.3808i	−0.571536	−	0.668700i
$841$	−16.6580	+	3.54076i	−0.574413	+	0.122095i
$842$	−1.46684	+	13.9560i	−0.0505505	+	0.480956i
$843$	2.41504	+	1.01693i	0.0831784	+	0.0350251i
$844$	26.1797	−	11.6560i	0.901144	−	0.401215i
$845$	28.6229	+	1.32200i	0.984658	+	0.0454782i
$846$	−14.4051	−	2.45464i	−0.495257	−	0.0843922i
$847$	−16.6239	+	12.0780i	−0.571204	+	0.415004i
$848$	5.43690	+	1.15565i	0.186704	+	0.0396851i
$849$	32.9007	−	24.9411i	1.12915	−	0.855977i
$850$	0.0513203	−	0.257093i	0.00176027	−	0.00881823i
$851$	2.96681	+	5.13867i	0.101701	+	0.176151i
$852$	−20.4826	−	14.2544i	−0.701722	−	0.488348i
$853$	2.19324	+	20.8673i	0.0750951	+	0.714483i	0.965692	+	0.259689i	$0.0836202\pi$
$853$	2.19324	+	20.8673i	0.0750951	+	0.714483i	−0.890597	+	0.454793i	$0.849713\pi$
$854$	−4.96457	+	3.60697i	−0.169884	+	0.123428i
$855$	−19.4020	+	8.51092i	−0.663535	+	0.291067i
$856$	4.88646	+	3.55022i	0.167016	+	0.121344i
$857$	−7.64159	+	13.2356i	−0.261032	+	0.452120i	−0.966516	−	0.256605i	$-0.917396\pi$
$857$	−7.64159	+	13.2356i	−0.261032	+	0.452120i	0.705485	+	0.708725i	$0.250729\pi$
$858$	9.84588	+	16.2800i	0.336133	+	0.555791i
$859$	42.5046	−	9.03462i	1.45024	−	0.308257i	0.585578	−	0.810616i	$-0.300868\pi$
$859$	42.5046	−	9.03462i	1.45024	−	0.308257i	0.864659	+	0.502359i	$0.167534\pi$
$860$	−42.8063	+	7.05243i	−1.45968	+	0.240486i
$861$	−30.7648	+	14.4538i	−1.04846	+	0.492583i
$862$	−3.36202	−	3.73390i	−0.114511	−	0.127177i
$863$	2.99160	−	9.20721i	0.101835	−	0.313417i	−0.887139	−	0.461502i	$-0.847311\pi$
$863$	2.99160	−	9.20721i	0.101835	−	0.313417i	0.988975	+	0.148085i	$0.0473108\pi$
$864$	25.1671	+	9.41236i	0.856202	+	0.320215i
$865$	−6.62851	−	5.29989i	−0.225376	−	0.180202i
$866$	−4.66782	−	5.18414i	−0.158619	−	0.176164i
$867$	14.1926	−	25.7788i	0.482007	−	0.875493i
$868$	7.09898	+	12.2958i	0.240955	+	0.417347i
$869$	6.20952	−	59.0796i	0.210643	−	2.00414i
$870$	−13.5132	+	2.50950i	−0.458141	+	0.0850801i
$871$	−7.20566	−	68.5573i	−0.244154	−	2.32297i
$872$	−4.40409	+	3.19976i	−0.149141	+	0.108357i
$873$	−5.23325	+	0.212901i	−0.177119	+	0.00720559i
$874$	3.25607			0.110138
$875$	−35.4970	−	12.8731i	−1.20002	−	0.435189i
$876$	25.3195	−	19.1941i	0.855467	−	0.648507i
$877$	−9.39196	+	10.4308i	−0.317144	+	0.352224i	−0.880548	−	0.473958i	$-0.842825\pi$
$877$	−9.39196	+	10.4308i	−0.317144	+	0.352224i	0.563404	+	0.826182i	$0.309492\pi$
$878$	−3.48580	−	1.55198i	−0.117640	−	0.0523767i
$879$	0.224759	−	0.742790i	0.00758094	−	0.0250537i
$880$	−1.31635	−	22.4507i	−0.0443741	−	0.756813i
$881$	−6.11208	−	4.44068i	−0.205921	−	0.149610i	0.480045	−	0.877244i	$-0.340620\pi$
$881$	−6.11208	−	4.44068i	−0.205921	−	0.149610i	−0.685966	+	0.727633i	$0.740620\pi$
$882$	−6.69880	+	1.71119i	−0.225560	+	0.0576189i
$883$	−7.80285	−	5.66910i	−0.262587	−	0.190781i	0.448700	−	0.893683i	$-0.351887\pi$
$883$	−7.80285	−	5.66910i	−0.262587	−	0.190781i	−0.711287	+	0.702902i	$0.751887\pi$
$884$	−0.588347	−	0.653425i	−0.0197882	−	0.0219771i
$885$	−15.6579	−	28.8138i	−0.526334	−	0.968564i
$886$	4.10621	−	4.56041i	0.137951	−	0.153210i
$887$	32.2257	−	6.84979i	1.08203	−	0.229994i	0.367804	−	0.929904i	$-0.380110\pi$
$887$	32.2257	−	6.84979i	1.08203	−	0.229994i	0.714231	+	0.699910i	$0.246777\pi$
$888$	9.98227	+	1.91057i	0.334983	+	0.0641147i
$889$	−28.8428	−	6.13073i	−0.967357	−	0.205618i
$890$	−2.86542	+	7.60540i	−0.0960489	+	0.254934i
$891$	35.1005	+	12.3200i	1.17591	+	0.412736i
$892$	4.09207	+	2.97307i	0.137013	+	0.0995456i
$893$	14.7056	−	25.4708i	0.492103	−	0.852347i
$894$	−9.22306	+	16.7523i	−0.308465	+	0.560281i
$895$	10.0460	−	1.65511i	0.335802	−	0.0553241i
$896$	−35.3972	−	15.7598i	−1.18254	−	0.526500i
$897$	−16.8891	+	3.95037i	−0.563911	+	0.131899i
$898$	5.94364	+	1.26336i	0.198342	+	0.0421589i
$899$	16.5210			0.551008
$900$	25.5743	−	4.06924i	0.852478	−	0.135641i
$901$	0.228984			0.00762857
$902$	12.2883	+	2.61197i	0.409157	+	0.0869690i
$903$	−19.0393	+	62.9216i	−0.633588	+	2.09390i
$904$	14.8461	+	6.60991i	0.493774	+	0.219842i
$905$	19.6964	+	38.0704i	0.654731	+	1.26550i
$906$	−16.0229	+	0.325790i	−0.532325	+	0.0108236i
$907$	13.7736	−	23.8565i	0.457344	−	0.792144i	−0.541475	−	0.840717i	$-0.682134\pi$
$907$	13.7736	−	23.8565i	0.457344	−	0.792144i	0.998820	+	0.0485730i	$0.0154673\pi$
$908$	−30.8868	−	22.4406i	−1.02502	−	0.744717i
$909$	−30.9637	−	20.6271i	−1.02700	−	0.684158i
$910$	16.7635	−	11.0349i	0.555706	−	0.365802i
$911$	−11.0714	−	2.35329i	−0.366810	−	0.0779679i	0.0208191	−	0.999783i	$-0.493373\pi$
$911$	−11.0714	−	2.35329i	−0.366810	−	0.0779679i	−0.387629	+	0.921815i	$0.626706\pi$
$912$	−8.70383	+	10.0710i	−0.288213	+	0.333483i
$913$	25.0774	−	5.33036i	0.829939	−	0.176409i
$914$	−4.11258	+	4.56749i	−0.136032	+	0.151079i
$915$	−1.06035	−	13.4120i	−0.0350542	−	0.443388i
$916$	20.9287	+	23.2437i	0.691504	+	0.767993i
$917$	−2.55179	−	1.85398i	−0.0842675	−	0.0612239i
$918$	0.269454	+	0.0402968i	0.00889330	+	0.00132999i
$919$	25.7130	+	18.6816i	0.848195	+	0.616250i	0.924648	−	0.380823i	$-0.124359\pi$
$919$	25.7130	+	18.6816i	0.848195	+	0.616250i	−0.0764527	+	0.997073i	$0.524359\pi$
$920$	−8.31132	−	2.17182i	−0.274016	−	0.0716028i
$921$	7.10232	+	7.57252i	0.234030	+	0.249523i
$922$	−12.0566	−	5.36796i	−0.397064	−	0.176784i
$923$	28.3717	−	31.5099i	0.933865	−	1.03716i
$924$	−38.4700	−	16.1991i	−1.26557	−	0.532912i
$925$	14.2569	−	4.82878i	0.468763	−	0.158769i
$926$	10.7636			0.353714
$927$	−12.2044	+	23.2752i	−0.400845	+	0.764457i
$928$	−28.3830	+	20.6214i	−0.931717	+	0.676932i
$929$	−2.03561	−	19.3676i	−0.0667863	−	0.635429i	−0.975800	−	0.218664i	$-0.929830\pi$
$929$	−2.03561	−	19.3676i	−0.0667863	−	0.635429i	0.909014	−	0.416766i	$-0.136836\pi$
$930$	4.93142	+	0.127378i	0.161708	+	0.00417687i
$931$	1.45458	−	13.8394i	0.0476720	−	0.453568i
$932$	−7.38519	−	12.7915i	−0.241910	−	0.419000i
$933$	−38.5524	+	0.783875i	−1.26215	+	0.0256629i
$934$	−3.97910	−	4.41924i	−0.130200	−	0.144602i
$935$	−0.245338	−	0.893401i	−0.00802342	−	0.0292173i
$936$	−13.7966	+	26.3117i	−0.450956	+	0.860026i
$937$	−6.71741	+	20.6741i	−0.219448	+	0.675393i	0.779359	+	0.626577i	$0.215545\pi$
$937$	−6.71741	+	20.6741i	−0.219448	+	0.675393i	−0.998808	+	0.0488155i	$0.984455\pi$
$938$	−16.0377	−	17.8117i	−0.523650	−	0.581573i
$939$	−0.513196	+	6.06681i	−0.0167475	+	0.197983i
$940$	−25.2613	+	25.5768i	−0.823933	+	0.834224i
$941$	41.2306	−	8.76383i	1.34408	−	0.285693i	0.520969	−	0.853576i	$-0.325571\pi$
$941$	41.2306	−	8.76383i	1.34408	−	0.285693i	0.823109	+	0.567883i	$0.192238\pi$
$942$	0.427351	−	0.776219i	0.0139238	−	0.0252906i
$943$	−5.72650	+	9.91858i	−0.186480	+	0.322994i
$944$	−16.6682	−	12.1102i	−0.542504	−	0.394153i
$945$	11.5710	−	37.4957i	0.376404	−	1.21973i
$946$	19.6565	−	14.2813i	0.639087	−	0.464324i
$947$	−0.396586	−	3.77326i	−0.0128873	−	0.122615i	0.986187	−	0.165637i	$-0.0529680\pi$
$947$	−0.396586	−	3.77326i	−0.0128873	−	0.122615i	−0.999074	+	0.0430224i	$0.986301\pi$
$948$	38.8973	−	18.2745i	1.26332	−	0.593528i
$949$	26.9927	+	46.7528i	0.876222	+	1.51766i
$950$	1.61694	−	8.10021i	0.0524605	−	0.262805i
$951$	6.58196	+	2.77156i	0.213435	+	0.0898740i
$952$	−0.645456	−	0.137196i	−0.0209194	−	0.00444655i
$953$	−43.1844	+	31.3753i	−1.39888	+	1.01635i	−0.404056	+	0.914734i	$0.632400\pi$
$953$	−43.1844	+	31.3753i	−1.39888	+	1.01635i	−0.994824	+	0.101612i	$0.967600\pi$
$954$	−1.24534	−	3.36123i	−0.0403192	−	0.108824i
$955$	−10.4117	−	37.9144i	−0.336916	−	1.22688i
$956$	33.5760	−	14.9490i	1.08593	−	0.483486i
$957$	−38.7065	+	29.3424i	−1.25120	+	0.948505i
$958$	2.30540	−	21.9344i	0.0744841	−	0.708669i
$959$	−20.4961	+	4.35659i	−0.661855	+	0.140682i
$960$	6.89830	−	4.74468i	0.222642	−	0.153134i
$961$	24.5225	+	5.21241i	0.791047	+	0.168142i
$962$	−2.47231	+	7.60899i	−0.0797105	+	0.245324i
$963$	−0.595117	+	9.27731i	−0.0191774	+	0.298957i
$964$	−1.52096	−	4.68104i	−0.0489869	−	0.150766i
$965$	−2.58820	−	44.1426i	−0.0833172	−	1.42100i
$966$	−3.94337	+	4.56277i	−0.126876	+	0.146805i
$967$	1.59455	−	15.1711i	0.0512772	−	0.487870i	−0.938503	−	0.345270i	$-0.887787\pi$
$967$	1.59455	−	15.1711i	0.0512772	−	0.487870i	0.989780	−	0.142599i	$-0.0455461\pi$
$968$	5.92956	+	10.2703i	0.190583	+	0.330100i
$969$	−0.264470	+	0.480371i	−0.00849601	+	0.0154317i
$970$	1.10149	−	1.71941i	0.0353666	−	0.0552068i
$971$	15.5289	−	11.2824i	0.498345	−	0.362069i	−0.310040	−	0.950724i	$-0.600342\pi$
$971$	15.5289	−	11.2824i	0.498345	−	0.362069i	0.808384	+	0.588655i	$0.200342\pi$
$972$	5.51447	+	26.3409i	0.176877	+	0.844886i
$973$	−5.96292	−	18.3520i	−0.191162	−	0.588338i
$974$	−4.23733	+	7.33927i	−0.135773	+	0.235166i
$975$	1.44040	+	43.9772i	0.0461298	+	1.40840i
$976$	−4.22633	−	7.32023i	−0.135282	−	0.234315i
$977$	−25.5421	+	28.3674i	−0.817165	+	0.907554i	−0.997098	−	0.0761249i	$-0.975745\pi$
$977$	−25.5421	+	28.3674i	−0.817165	+	0.907554i	0.179933	+	0.983679i	$0.442412\pi$
$978$	−11.0194	+	2.57744i	−0.352362	+	0.0824175i
$979$	3.00219	+	28.5639i	0.0959504	+	0.912907i
$980$	−5.99676	+	15.9166i	−0.191560	+	0.508439i
$981$	−7.78649	−	3.09396i	−0.248604	−	0.0987825i
$982$	2.02500			0.0646204
$983$	−42.0157	+	18.7066i	−1.34009	+	0.596648i	−0.946520	−	0.322645i	$-0.895428\pi$
$983$	−42.0157	+	18.7066i	−1.34009	+	0.596648i	−0.393574	+	0.919293i	$0.628761\pi$
$984$	6.44013	+	18.5302i	0.205304	+	0.590720i
$985$	1.33037	−	0.219181i	0.0423890	−	0.00698370i
$986$	−0.238033	+	0.264363i	−0.00758052	+	0.00841902i
$987$	17.8828	+	51.4542i	0.569217	+	1.63781i
$988$	−18.5370	−	20.5874i	−0.589740	−	0.654972i
$989$	6.84480	+	21.0661i	0.217652	+	0.669864i
$990$	−11.7799	+	8.46008i	−0.374389	+	0.268879i
$991$	12.7035	−	39.0974i	0.403541	−	1.24197i	−0.518567	−	0.855037i	$-0.673534\pi$
$991$	12.7035	−	39.0974i	0.403541	−	1.24197i	0.922107	−	0.386934i	$-0.126466\pi$
$992$	11.5034	−	5.12164i	0.365233	−	0.162612i
$993$	25.0665	+	10.5551i	0.795460	+	0.334956i
$994$	1.54100	−	14.6616i	0.0488774	−	0.465038i
$995$	−37.5351	−	18.8326i	−1.18994	−	0.597033i
$996$	12.6882	+	13.5282i	0.402042	+	0.428659i
$997$	−2.31258	−	22.0028i	−0.0732403	−	0.696835i	−0.968113	−	0.250514i	$-0.919401\pi$
$997$	−2.31258	−	22.0028i	−0.0732403	−	0.696835i	0.894873	−	0.446321i	$-0.147266\pi$
$998$	1.66207	+	5.11534i	0.0526120	+	0.161923i
$999$	5.73175	+	14.5550i	0.181345	+	0.460501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.13	yes	224
3.2	odd	2		675.2.r.a.181.16		224
9.4	even	3	inner	225.2.q.a.31.16	✓	224
9.5	odd	6		675.2.r.a.631.13		224
25.21	even	5	inner	225.2.q.a.196.16	yes	224
75.71	odd	10		675.2.r.a.46.13		224
225.121	even	15	inner	225.2.q.a.121.13	yes	224
225.221	odd	30		675.2.r.a.496.16		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.16	✓	224	9.4	even	3	inner
225.2.q.a.106.13	yes	224	1.1	even	1	trivial
225.2.q.a.121.13	yes	224	225.121	even	15	inner
225.2.q.a.196.16	yes	224	25.21	even	5	inner
675.2.r.a.46.13		224	75.71	odd	10
675.2.r.a.181.16		224	3.2	odd	2
675.2.r.a.496.16		224	225.221	odd	30
675.2.r.a.631.13		224	9.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.511634 - 0.108751i) q^{2} +(1.18489 + 1.26334i) q^{3} +(-1.57715 - 0.702192i) q^{4} +(1.99861 + 1.00277i) q^{5} +(-0.468843 - 0.775225i) q^{6} +(-1.68864 + 2.92481i) q^{7} +(1.57689 + 1.14568i) q^{8} +(-0.192048 + 2.99385i) q^{9} +O(q^{10})\)	\(q+(-0.511634 - 0.108751i) q^{2} +(1.18489 + 1.26334i) q^{3} +(-1.57715 - 0.702192i) q^{4} +(1.99861 + 1.00277i) q^{5} +(-0.468843 - 0.775225i) q^{6} +(-1.68864 + 2.92481i) q^{7} +(1.57689 + 1.14568i) q^{8} +(-0.192048 + 2.99385i) q^{9} +(-0.913505 - 0.730402i) q^{10} +(-4.04299 - 0.859364i) q^{11} +(-0.981649 - 2.82450i) q^{12} +(4.96974 - 1.05635i) q^{13} +(1.18204 - 1.31279i) q^{14} +(1.10131 + 3.71310i) q^{15} +(1.62818 + 1.80828i) q^{16} +(0.0810977 + 0.0589209i) q^{17} +(0.423842 - 1.51087i) q^{18} +(2.55513 + 1.85641i) q^{19} +(-2.44797 - 2.98493i) q^{20} +(-5.69589 + 1.33227i) q^{21} +(1.97507 + 0.879359i) q^{22} +(-1.31885 + 1.46473i) q^{23} +(0.421071 + 3.34966i) q^{24} +(2.98891 + 4.00830i) q^{25} -2.65757 q^{26} +(-4.00980 + 3.30477i) q^{27} +(4.71702 - 3.42711i) q^{28} +(-0.709179 - 6.74738i) q^{29} +(-0.159663 - 2.01952i) q^{30} +(-0.254537 + 2.42176i) q^{31} +(-2.58553 - 4.47827i) q^{32} +(-3.70485 - 6.12592i) q^{33} +(-0.0350846 - 0.0389654i) q^{34} +(-6.30785 + 4.15225i) q^{35} +(2.40514 - 4.58689i) q^{36} +(0.930291 - 2.86314i) q^{37} +(-1.10541 - 1.22768i) q^{38} +(7.22315 + 5.02680i) q^{39} +(2.00275 + 3.87103i) q^{40} +(5.68382 - 1.20813i) q^{41} +(3.05909 - 0.0621998i) q^{42} +(5.61908 - 9.73253i) q^{43} +(5.77296 + 4.19430i) q^{44} +(-3.38597 + 5.79096i) q^{45} +(0.834057 - 0.605978i) q^{46} +(-0.973397 - 9.26125i) q^{47} +(-0.355244 + 4.19957i) q^{48} +(-2.20301 - 3.81573i) q^{49} +(-1.09332 - 2.37583i) q^{50} +(0.0216552 + 0.172269i) q^{51} +(-8.57978 - 1.82369i) q^{52} +(1.84804 - 1.34268i) q^{53} +(2.41095 - 1.25476i) q^{54} +(-7.21862 - 5.77172i) q^{55} +(-6.01370 + 2.67747i) q^{56} +(0.682287 + 5.42765i) q^{57} +(-0.370946 + 3.52931i) q^{58} +(-8.28217 + 1.76043i) q^{59} +(0.870382 - 6.62944i) q^{60} +(-3.39787 - 0.722239i) q^{61} +(0.393599 - 1.21137i) q^{62} +(-8.43214 - 5.61724i) q^{63} +(-0.668023 - 2.05596i) q^{64} +(10.9919 + 2.87227i) q^{65} +(1.22933 + 3.53713i) q^{66} +(1.41822 - 13.4935i) q^{67} +(-0.0865293 - 0.149873i) q^{68} +(-3.41314 + 0.0693985i) q^{69} +(3.67887 - 1.43844i) q^{70} +(6.75154 - 4.90528i) q^{71} +(-3.73283 + 4.50095i) q^{72} +(3.28345 + 10.1054i) q^{73} +(-0.787338 + 1.36371i) q^{74} +(-1.52230 + 8.52541i) q^{75} +(-2.72627 - 4.72203i) q^{76} +(9.34063 - 10.3738i) q^{77} +(-3.14894 - 3.35741i) q^{78} +(1.50231 + 14.2935i) q^{79} +(1.44082 + 5.24674i) q^{80} +(-8.92623 - 1.14993i) q^{81} -3.03942 q^{82} +(-5.66643 + 2.52286i) q^{83} +(9.91877 + 1.89842i) q^{84} +(0.102999 + 0.199082i) q^{85} +(-3.93333 + 4.36841i) q^{86} +(7.68393 - 8.89087i) q^{87} +(-5.39081 - 5.98710i) q^{88} +(-2.14728 - 6.60864i) q^{89} +(2.36215 - 2.59462i) q^{90} +(-5.30248 + 16.3193i) q^{91} +(3.10854 - 1.38401i) q^{92} +(-3.36110 + 2.54796i) q^{93} +(-0.509149 + 4.84423i) q^{94} +(3.24517 + 6.27246i) q^{95} +(2.59399 - 8.57267i) q^{96} +(0.182492 + 1.73630i) q^{97} +(0.712171 + 2.19184i) q^{98} +(3.34925 - 11.9390i) 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

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