LMFDB - Embedded newform 462.2.ba.b.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.b.409.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.192170 - 0.173031i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.35536 + 2.27222i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.192170 - 0.173031i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.35536 + 2.27222i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.129295 - 0.223946i) q^{10} +(-0.415022 + 3.29056i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.973262 + 2.99539i) q^{13} +(1.94077 + 1.79816i) q^{14} +(-0.209204 + 0.151996i) q^{15} +(0.669131 + 0.743145i) q^{16} +(2.54905 - 0.541818i) q^{17} +(0.406737 - 0.913545i) q^{18} +(-0.290713 + 0.129434i) q^{19} +(-0.245934 + 0.0799088i) q^{20} +(1.58545 - 2.11810i) q^{21} +(3.13236 + 1.09010i) q^{22} +(1.34602 - 2.33137i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.515653 + 4.90611i) q^{25} +(3.13229 - 0.329217i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(2.16238 - 1.52450i) q^{28} +(4.37934 + 6.02764i) q^{29} +(0.105178 + 0.236234i) q^{30} +(-4.41406 - 3.97443i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.756705 - 3.22915i) q^{33} -2.60600i q^{34} +(0.132705 + 0.671173i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.496275 + 4.72175i) q^{37} +(0.0661627 + 0.311271i) q^{38} +(-0.654827 - 3.08072i) q^{39} +(0.0270301 + 0.257174i) q^{40} +(3.59720 + 2.61352i) q^{41} +(-1.74218 - 1.99118i) q^{42} +5.99231i q^{43} +(1.71753 - 2.83727i) q^{44} +(0.223946 - 0.129295i) q^{45} +(-2.00058 - 1.80133i) q^{46} +(0.396578 + 0.890728i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-3.32600 - 6.15936i) q^{49} +(4.69169 + 1.52442i) q^{50} +(-2.59172 + 0.272401i) q^{51} +(0.329217 - 3.13229i) q^{52} +(7.12566 - 7.91385i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.489613 + 0.704158i) q^{55} +(-1.04161 - 2.43209i) q^{56} +(0.302650 - 0.0983369i) q^{57} +(6.80644 - 3.03042i) q^{58} +(-4.58871 + 10.3064i) q^{59} +(0.252940 - 0.0537640i) q^{60} +(-3.72405 - 4.13598i) q^{61} +(-4.80532 + 3.49127i) q^{62} +(-1.79816 + 1.94077i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.705327 + 0.407221i) q^{65} +(-3.00126 - 1.41155i) q^{66} +(-4.11073 - 7.11999i) q^{67} +(-2.54905 - 0.541818i) q^{68} +(-1.58234 + 2.17791i) q^{69} +(0.684097 + 0.00973980i) q^{70} +(-4.39747 + 13.5340i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-12.9197 - 5.75224i) q^{73} +(4.72175 + 0.496275i) q^{74} +(1.02566 - 4.82533i) q^{75} +0.318225 q^{76} +(-6.91437 - 5.40291i) q^{77} -3.14954 q^{78} +(-2.53635 + 11.9326i) q^{79} +(0.257174 + 0.0270301i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.30431 - 2.97521i) q^{82} +(5.00447 - 15.4022i) q^{83} +(-2.30989 + 1.29012i) q^{84} +(0.396101 - 0.545186i) q^{85} +(5.86136 + 1.24587i) q^{86} +(-3.72529 - 6.45239i) q^{87} +(-2.41817 - 2.26990i) q^{88} +(1.08367 + 0.625657i) q^{89} +(-0.0799088 - 0.245934i) q^{90} +(-8.12532 - 1.84837i) q^{91} +(-2.17791 + 1.58234i) q^{92} +(3.97443 + 4.41406i) q^{93} +(0.953716 - 0.202719i) q^{94} +(-0.0334703 + 0.0751756i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-1.62713 + 0.528688i) q^{97} +(-6.71628 + 1.97271i) q^{98} +(-1.09010 + 3.13236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$3$	−0.994522	−	0.104528i	−0.574187	−	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	0.192170	−	0.173031i	0.0859411	−	0.0773817i	−0.625041	−	0.780592i	$-0.714918\pi$
$5$	0.192170	−	0.173031i	0.0859411	−	0.0773817i	0.710982	+	0.703211i	$0.248251\pi$
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−1.35536	+	2.27222i	−0.512278	+	0.858820i
$7$	−1.35536	+	2.27222i	−0.512278	+	0.858820i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	−0.129295	−	0.223946i	−0.0408867	−	0.0708179i
$11$	−0.415022	+	3.29056i	−0.125134	+	0.992140i
$11$	−0.415022	+	3.29056i	−0.125134	+	0.992140i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	0.973262	+	2.99539i	0.269934	+	0.830772i	0.990515	+	0.137402i	$0.0438751\pi$
$13$	0.973262	+	2.99539i	0.269934	+	0.830772i	−0.720581	+	0.693371i	$0.756125\pi$
$14$	1.94077	+	1.79816i	0.518694	+	0.480580i
$15$	−0.209204	+	0.151996i	−0.0540163	+	0.0392451i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	2.54905	−	0.541818i	0.618236	−	0.131410i	0.111862	−	0.993724i	$-0.464319\pi$
$17$	2.54905	−	0.541818i	0.618236	−	0.131410i	0.506375	+	0.862314i	$0.330985\pi$
$18$	0.406737	−	0.913545i	0.0958687	−	0.215325i
$19$	−0.290713	+	0.129434i	−0.0666941	+	0.0296941i	−0.439813	−	0.898090i	$-0.644955\pi$
$19$	−0.290713	+	0.129434i	−0.0666941	+	0.0296941i	0.373119	+	0.927784i	$0.378288\pi$
$20$	−0.245934	+	0.0799088i	−0.0549925	+	0.0178682i
$21$	1.58545	−	2.11810i	0.345973	−	0.462208i
$22$	3.13236	+	1.09010i	0.667822	+	0.232410i
$23$	1.34602	−	2.33137i	0.280665	−	0.486125i	−0.690884	−	0.722966i	$-0.742779\pi$
$23$	1.34602	−	2.33137i	0.280665	−	0.486125i	0.971549	+	0.236840i	$0.0761118\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−0.515653	+	4.90611i	−0.103131	+	0.981221i
$26$	3.13229	−	0.329217i	0.614292	−	0.0645647i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	2.16238	−	1.52450i	0.408651	−	0.288104i
$29$	4.37934	+	6.02764i	0.813222	+	1.11930i	0.990818	+	0.135201i	$0.0431681\pi$
$29$	4.37934	+	6.02764i	0.813222	+	1.11930i	−0.177596	+	0.984104i	$0.556832\pi$
$30$	0.105178	+	0.236234i	0.0192028	+	0.0431303i
$31$	−4.41406	−	3.97443i	−0.792788	−	0.713829i	0.169599	−	0.985513i	$-0.445753\pi$
$31$	−4.41406	−	3.97443i	−0.792788	−	0.713829i	−0.962387	+	0.271684i	$0.912420\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.756705	−	3.22915i	0.131725	−	0.562123i
$34$		−	2.60600i		−	0.446925i
$35$	0.132705	+	0.671173i	0.0224312	+	0.113449i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	0.496275	+	4.72175i	0.0815872	+	0.776250i	0.956453	+	0.291885i	$0.0942826\pi$
$37$	0.496275	+	4.72175i	0.0815872	+	0.776250i	−0.874866	+	0.484365i	$0.839051\pi$
$38$	0.0661627	+	0.311271i	0.0107330	+	0.0504948i
$39$	−0.654827	−	3.08072i	−0.104856	−	0.493309i
$40$	0.0270301	+	0.257174i	0.00427383	+	0.0406628i
$41$	3.59720	+	2.61352i	0.561789	+	0.408163i	0.832113	−	0.554606i	$-0.187131\pi$
$41$	3.59720	+	2.61352i	0.561789	+	0.408163i	−0.270324	+	0.962769i	$0.587131\pi$
$42$	−1.74218	−	1.99118i	−0.268825	−	0.307246i
$43$			5.99231i			0.913818i	0.889513	+	0.456909i	$0.151044\pi$
$43$			5.99231i			0.913818i	−0.889513	+	0.456909i	$0.848956\pi$
$44$	1.71753	−	2.83727i	0.258928	−	0.427734i
$45$	0.223946	−	0.129295i	0.0333839	−	0.0192742i
$46$	−2.00058	−	1.80133i	−0.294969	−	0.265591i
$47$	0.396578	+	0.890728i	0.0578468	+	0.129926i	0.940156	−	0.340744i	$-0.110679\pi$
$47$	0.396578	+	0.890728i	0.0578468	+	0.129926i	−0.882309	+	0.470670i	$0.844012\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−3.32600	−	6.15936i	−0.475142	−	0.879909i
$50$	4.69169	+	1.52442i	0.663505	+	0.215586i
$51$	−2.59172	+	0.272401i	−0.362914	+	0.0381438i
$52$	0.329217	−	3.13229i	0.0456541	−	0.434370i
$53$	7.12566	−	7.91385i	0.978785	−	1.08705i	−0.0174056	−	0.999849i	$-0.505541\pi$
$53$	7.12566	−	7.91385i	0.978785	−	1.08705i	0.996191	−	0.0872023i	$-0.0277927\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.489613	+	0.704158i	0.0660194	+	0.0949487i
$56$	−1.04161	−	2.43209i	−0.139190	−	0.325002i
$57$	0.302650	−	0.0983369i	0.0400869	−	0.0130250i
$58$	6.80644	−	3.03042i	0.893729	−	0.397914i
$59$	−4.58871	+	10.3064i	−0.597399	+	1.34178i	0.321359	+	0.946957i	$0.395860\pi$
$59$	−4.58871	+	10.3064i	−0.597399	+	1.34178i	−0.918758	+	0.394822i	$0.870806\pi$
$60$	0.252940	−	0.0537640i	0.0326544	−	0.00694090i
$61$	−3.72405	−	4.13598i	−0.476816	−	0.529558i	0.455967	−	0.889997i	$-0.349294\pi$
$61$	−3.72405	−	4.13598i	−0.476816	−	0.529558i	−0.932783	+	0.360439i	$0.882627\pi$
$62$	−4.80532	+	3.49127i	−0.610276	+	0.443391i
$63$	−1.79816	+	1.94077i	−0.226547	+	0.244515i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.705327	+	0.407221i	0.0874850	+	0.0505095i
$66$	−3.00126	−	1.41155i	−0.369429	−	0.173749i
$67$	−4.11073	−	7.11999i	−0.502206	−	0.869846i	−0.999997	−	0.00254874i	$-0.999189\pi$
$67$	−4.11073	−	7.11999i	−0.502206	−	0.869846i	0.497791	−	0.867297i	$-0.334145\pi$
$68$	−2.54905	−	0.541818i	−0.309118	−	0.0657051i
$69$	−1.58234	+	2.17791i	−0.190491	+	0.262189i
$70$	0.684097	+	0.00973980i	0.0817652	+	0.00116413i
$71$	−4.39747	+	13.5340i	−0.521883	+	1.60619i	0.248514	+	0.968628i	$0.420058\pi$
$71$	−4.39747	+	13.5340i	−0.521883	+	1.60619i	−0.770398	+	0.637564i	$0.779942\pi$
$72$	−0.743145	+	0.669131i	−0.0875805	+	0.0788578i
$73$	−12.9197	−	5.75224i	−1.51214	−	0.673249i	−0.527775	−	0.849384i	$-0.676974\pi$
$73$	−12.9197	−	5.75224i	−1.51214	−	0.673249i	−0.984366	+	0.176135i	$0.943640\pi$
$74$	4.72175	+	0.496275i	0.548892	+	0.0576909i
$75$	1.02566	−	4.82533i	0.118433	−	0.557181i
$76$	0.318225			0.0365029
$77$	−6.91437	−	5.40291i	−0.787966	−	0.615719i
$78$	−3.14954			−0.356615
$79$	−2.53635	+	11.9326i	−0.285362	+	1.34252i	0.568784	+	0.822487i	$0.307414\pi$
$79$	−2.53635	+	11.9326i	−0.285362	+	1.34252i	−0.854145	+	0.520034i	$0.825919\pi$
$80$	0.257174	+	0.0270301i	0.0287529	+	0.00302205i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	3.30431	−	2.97521i	0.364900	−	0.328557i
$83$	5.00447	−	15.4022i	0.549312	−	1.69061i	−0.161197	−	0.986922i	$-0.551535\pi$
$83$	5.00447	−	15.4022i	0.549312	−	1.69061i	0.710510	−	0.703688i	$-0.248465\pi$
$84$	−2.30989	+	1.29012i	−0.252029	+	0.140764i
$85$	0.396101	−	0.545186i	0.0429632	−	0.0591337i
$86$	5.86136	+	1.24587i	0.632047	+	0.134346i
$87$	−3.72529	−	6.45239i	−0.399393	−	0.691768i
$88$	−2.41817	−	2.26990i	−0.257778	−	0.241972i
$89$	1.08367	+	0.625657i	0.114869	+	0.0663196i	0.556334	−	0.830959i	$-0.312208\pi$
$89$	1.08367	+	0.625657i	0.114869	+	0.0663196i	−0.441465	+	0.897279i	$0.645541\pi$
$90$	−0.0799088	−	0.245934i	−0.00842313	−	0.0259237i
$91$	−8.12532	−	1.84837i	−0.851765	−	0.193762i
$92$	−2.17791	+	1.58234i	−0.227062	+	0.164970i
$93$	3.97443	+	4.41406i	0.412130	+	0.457716i
$94$	0.953716	−	0.202719i	0.0983683	−	0.0209088i
$95$	−0.0334703	+	0.0751756i	−0.00343398	+	0.00771285i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−1.62713	+	0.528688i	−0.165210	+	0.0536801i	−0.390454	−	0.920622i	$-0.627682\pi$
$97$	−1.62713	+	0.528688i	−0.165210	+	0.0536801i	0.225244	+	0.974302i	$0.427682\pi$
$98$	−6.71628	+	1.97271i	−0.678447	+	0.199274i
$99$	−1.09010	+	3.13236i	−0.109559	+	0.314814i
$100$	2.46657	−	4.27222i	0.246657	−	0.427222i
$101$	7.24860	−	8.05039i	0.721263	−	0.801044i	−0.265345	−	0.964154i	$-0.585486\pi$
$101$	7.24860	−	8.05039i	0.721263	−	0.801044i	0.986608	+	0.163110i	$0.0521525\pi$
$102$	−0.272401	+	2.59172i	−0.0269717	+	0.256619i
$103$	−10.1592	+	1.06777i	−1.00101	+	0.105211i	−0.590833	−	0.806794i	$-0.701201\pi$
$103$	−10.1592	+	1.06777i	−1.00101	+	0.105211i	−0.410180	+	0.912004i	$0.634534\pi$
$104$	−2.99539	−	0.973262i	−0.293722	−	0.0954362i
$105$	−0.0618211	−	0.681367i	−0.00603313	−	0.0664946i
$106$	−6.25940	−	8.61533i	−0.607967	−	0.836795i
$107$	1.04506	+	2.34725i	0.101030	+	0.226917i	0.956988	−	0.290129i	$-0.0936982\pi$
$107$	1.04506	+	2.34725i	0.101030	+	0.226917i	−0.855958	+	0.517046i	$0.827032\pi$
$108$	0.743145	+	0.669131i	0.0715091	+	0.0643871i
$109$	5.98422	−	3.45499i	0.573184	−	0.330928i	−0.185236	−	0.982694i	$-0.559305\pi$
$109$	5.98422	−	3.45499i	0.573184	−	0.330928i	0.758420	+	0.651766i	$0.225972\pi$
$110$	0.790567	−	0.332511i	0.0753776	−	0.0317036i
$111$		−	4.74775i		−	0.450637i
$112$	−2.59550	+	0.513185i	−0.245252	+	0.0484914i
$113$	6.18267	+	4.49197i	0.581616	+	0.422569i	0.839306	−	0.543659i	$-0.182961\pi$
$113$	6.18267	+	4.49197i	0.581616	+	0.422569i	−0.257690	+	0.966228i	$0.582961\pi$
$114$	−0.0332636	−	0.316482i	−0.00311542	−	0.0296412i
$115$	−0.144735	−	0.680924i	−0.0134966	−	0.0634964i
$116$	−1.54906	−	7.28776i	−0.143827	−	0.676652i
$117$	0.329217	+	3.13229i	0.0304361	+	0.289580i
$118$	9.12714	+	6.63125i	0.840221	+	0.610456i
$119$	−2.22375	+	6.52637i	−0.203851	+	0.598272i
$120$		−	0.258590i		−	0.0236060i
$121$	−10.6555	−	2.73131i	−0.968683	−	0.248301i
$122$	−4.81987	+	2.78275i	−0.436370	+	0.251939i
$123$	−3.30431	−	2.97521i	−0.297940	−	0.268266i
$124$	2.41589	+	5.42619i	0.216954	+	0.487286i
$125$	1.50979	+	2.07805i	0.135040	+	0.185867i
$126$	1.52450	+	2.16238i	0.135814	+	0.192640i
$127$	7.70245	+	2.50268i	0.683482	+	0.222077i	0.630119	−	0.776498i	$-0.283006\pi$
$127$	7.70245	+	2.50268i	0.683482	+	0.222077i	0.0533629	+	0.998575i	$0.483006\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	0.626367	−	5.95948i	0.0551485	−	0.524703i
$130$	0.544968	−	0.605248i	0.0477968	−	0.0530838i
$131$	3.01306	−	5.21877i	0.263252	−	0.455966i	−0.703852	−	0.710347i	$-0.748538\pi$
$131$	3.01306	−	5.21877i	0.263252	−	0.455966i	0.967104	+	0.254381i	$0.0818716\pi$
$132$	−2.00470	+	2.64219i	−0.174487	+	0.229973i
$133$	0.0999184	−	0.835994i	0.00866403	−	0.0724899i
$134$	−7.81907	+	2.54057i	−0.675465	+	0.219472i
$135$	−0.236234	+	0.105178i	−0.0203318	+	0.00905230i
$136$	−1.05996	+	2.38070i	−0.0908904	+	0.204143i
$137$	−4.46899	+	0.949914i	−0.381812	+	0.0811566i	−0.394819	−	0.918759i	$-0.629193\pi$
$137$	−4.46899	+	0.949914i	−0.381812	+	0.0811566i	0.0130074	+	0.999915i	$0.495859\pi$
$138$	1.80133	+	2.00058i	0.153339	+	0.170300i
$139$	−3.26304	+	2.37074i	−0.276768	+	0.201084i	−0.717506	−	0.696552i	$-0.754717\pi$
$139$	−3.26304	+	2.37074i	−0.276768	+	0.201084i	0.440739	+	0.897636i	$0.354717\pi$
$140$	0.151759	−	0.667123i	0.0128259	−	0.0563821i
$141$	−0.301299	−	0.927302i	−0.0253739	−	0.0780929i
$142$	12.3240	+	7.11525i	1.03421	+	0.597099i
$143$	−10.2604	+	1.95942i	−0.858020	+	0.163855i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.88455	+	0.400572i	0.156503	+	0.0332657i
$146$	−8.31270	+	11.4415i	−0.687964	+	0.946902i
$147$	2.66395	+	6.47328i	0.219719	+	0.533907i
$148$	1.46714	−	4.51538i	0.120598	−	0.371162i
$149$	−1.16736	+	1.05110i	−0.0956341	+	0.0861093i	−0.715561	−	0.698550i	$-0.753829\pi$
$149$	−1.16736	+	1.05110i	−0.0956341	+	0.0861093i	0.619927	+	0.784660i	$0.287162\pi$
$150$	−4.50664	−	2.00649i	−0.367966	−	0.163829i
$151$	12.8354	+	1.34906i	1.04453	+	0.109785i	0.611222	−	0.791459i	$-0.290678\pi$
$151$	12.8354	+	1.34906i	1.04453	+	0.109785i	0.433312	+	0.901244i	$0.357345\pi$
$152$	0.0661627	−	0.311271i	0.00536650	−	0.0252474i
$153$	2.60600			0.210683
$154$	−6.72242	+	5.63995i	−0.541708	+	0.454480i
$155$	−1.53595			−0.123370
$156$	−0.654827	+	3.08072i	−0.0524281	+	0.246655i
$157$	0.731312	+	0.0768640i	0.0583650	+	0.00613441i	0.133666	−	0.991026i	$-0.457325\pi$
$157$	0.731312	+	0.0768640i	0.0583650	+	0.00613441i	−0.0753009	+	0.997161i	$0.523992\pi$
$158$	11.1445	+	4.96185i	0.886609	+	0.394744i
$159$	−7.91385	+	7.12566i	−0.627609	+	0.565102i
$160$	0.0799088	−	0.245934i	0.00631735	−	0.0194428i
$161$	3.47306	+	6.21831i	0.273716	+	0.490071i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	12.0390	+	2.55896i	0.942965	+	0.200433i	0.653647	−	0.756800i	$-0.273238\pi$
$163$	12.0390	+	2.55896i	0.942965	+	0.200433i	0.289318	+	0.957233i	$0.406571\pi$
$164$	−2.22319	−	3.85068i	−0.173602	−	0.300688i
$165$	−0.413326	−	0.751479i	−0.0321774	−	0.0585026i
$166$	−14.0251	−	8.09741i	−1.08856	−	0.628481i
$167$	−2.24029	−	6.89490i	−0.173359	−	0.533543i	0.826196	−	0.563383i	$-0.190500\pi$
$167$	−2.24029	−	6.89490i	−0.173359	−	0.533543i	−0.999555	+	0.0298395i	$0.990500\pi$
$168$	0.781678	+	2.52764i	0.0603077	+	0.195012i
$169$	2.49209	−	1.81061i	0.191699	−	0.139277i
$170$	−0.450918	−	0.500795i	−0.0345839	−	0.0384093i
$171$	−0.311271	+	0.0661627i	−0.0238035	+	0.00505959i
$172$	2.43729	−	5.47424i	0.185842	−	0.417407i
$173$	23.6377	−	10.5242i	1.79714	−	0.800139i	0.825230	−	0.564796i	$-0.191045\pi$
$173$	23.6377	−	10.5242i	1.79714	−	0.800139i	0.971912	−	0.235343i	$-0.0756213\pi$
$174$	−7.08592	+	2.30235i	−0.537182	+	0.174541i
$175$	−10.4489	−	7.82122i	−0.789861	−	0.591229i
$176$	−2.72306	+	1.89339i	−0.205259	+	0.142720i
$177$	5.64088	−	9.77029i	0.423995	−	0.734380i
$178$	0.837293	−	0.929908i	0.0627578	−	0.0696996i
$179$	0.0960677	−	0.914023i	0.00718044	−	0.0683173i	−0.990345	−	0.138625i	$-0.955732\pi$
$179$	0.0960677	−	0.914023i	0.00718044	−	0.0683173i	0.997525	+	0.0703081i	$0.0223983\pi$
$180$	−0.257174	+	0.0270301i	−0.0191686	+	0.00201470i
$181$	6.33717	+	2.05907i	0.471038	+	0.153049i	0.534911	−	0.844909i	$-0.320345\pi$
$181$	6.33717	+	2.05907i	0.471038	+	0.153049i	−0.0638729	+	0.997958i	$0.520345\pi$
$182$	−3.49733	+	7.56346i	−0.259239	+	0.560641i
$183$	3.27132	+	4.50259i	0.241823	+	0.332841i
$184$	1.09495	+	2.45930i	0.0807209	+	0.181302i
$185$	0.912377	+	0.821508i	0.0670793	+	0.0603984i
$186$	5.14393	−	2.96985i	0.377171	−	0.217760i
$187$	0.724969	+	8.61267i	0.0530150	+	0.629821i
$188$		−	0.975023i		−	0.0711109i
$189$	1.99118	−	1.74218i	0.144837	−	0.126725i
$190$	0.0665739	+	0.0483688i	0.00482978	+	0.00350904i
$191$	−1.64393	−	15.6410i	−0.118951	−	1.13174i	−0.877316	−	0.479912i	$-0.840668\pi$
$191$	−1.64393	−	15.6410i	−0.118951	−	1.13174i	0.758366	−	0.651829i	$-0.225998\pi$
$192$	0.207912	+	0.978148i	0.0150047	+	0.0705917i
$193$	−4.23890	−	19.9424i	−0.305123	−	1.43549i	−0.817103	−	0.576492i	$-0.804421\pi$
$193$	−4.23890	−	19.9424i	−0.305123	−	1.43549i	0.511981	−	0.858997i	$-0.328912\pi$
$194$	0.178835	+	1.70150i	0.0128396	+	0.122160i
$195$	−0.658897	−	0.478717i	−0.0471846	−	0.0342816i
$196$	0.533210	+	6.97966i	0.0380865	+	0.498547i
$197$			1.55101i			0.110505i	0.998472	+	0.0552525i	$0.0175964\pi$
$197$			1.55101i			0.110505i	−0.998472	+	0.0552525i	$0.982404\pi$
$198$	2.83727	+	1.71753i	0.201636	+	0.122060i
$199$	8.55221	−	4.93762i	0.606250	−	0.350019i	−0.165246	−	0.986252i	$-0.552842\pi$
$199$	8.55221	−	4.93762i	0.606250	−	0.350019i	0.771497	+	0.636234i	$0.219509\pi$
$200$	−3.66603	−	3.30091i	−0.259228	−	0.233410i
$201$	3.34397	+	7.51068i	0.235865	+	0.529762i
$202$	−6.36740	−	8.76397i	−0.448009	−	0.616631i
$203$	−19.6317	+	1.78121i	−1.37788	+	0.125016i
$204$	2.47845	+	0.805298i	0.173526	+	0.0563822i
$205$	1.14349	−	0.120186i	0.0798651	−	0.00839416i
$206$	−1.06777	+	10.1592i	−0.0743952	+	0.707823i
$207$	1.80133	−	2.00058i	0.125201	−	0.139050i
$208$	−1.57477	+	2.72758i	−0.109191	+	0.189124i
$209$	−0.305257	−	1.01032i	−0.0211150	−	0.0698856i
$210$	−0.679331	−	0.0811940i	−0.0468783	−	0.00560292i
$211$	20.3003	−	6.59598i	1.39753	−	0.454086i	0.489141	−	0.872205i	$-0.337310\pi$
$211$	20.3003	−	6.59598i	1.39753	−	0.454086i	0.908393	+	0.418118i	$0.137310\pi$
$212$	−9.72847	+	4.33139i	−0.668154	+	0.297481i
$213$	5.78807	−	13.0002i	0.396592	−	0.890760i
$214$	2.51324	−	0.534205i	0.171801	−	0.0365175i
$215$	1.03685	+	1.15154i	0.0707128	+	0.0785346i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	15.0134	−	4.64293i	1.01918	−	0.315183i
$218$	−2.13530	−	6.57178i	−0.144621	−	0.445097i
$219$	12.2477	+	7.07121i	0.827622	+	0.477828i
$220$	−0.160876	−	0.842424i	−0.0108463	−	0.0567962i
$221$	4.10385	+	7.10808i	0.276055	+	0.478141i
$222$	−4.64400	−	0.987114i	−0.311685	−	0.0662507i
$223$	7.36255	−	10.1337i	0.493033	−	0.678602i	−0.487911	−	0.872893i	$-0.662241\pi$
$223$	7.36255	−	10.1337i	0.493033	−	0.678602i	0.980944	+	0.194292i	$0.0622409\pi$
$224$	−0.0376649	+	2.64548i	−0.00251660	+	0.176759i
$225$	−1.52442	+	4.69169i	−0.101628	+	0.312779i
$226$	5.67926	−	5.11363i	0.377779	−	0.340153i
$227$	−11.0551	−	4.92205i	−0.733753	−	0.326688i	0.00561955	−	0.999984i	$-0.498211\pi$
$227$	−11.0551	−	4.92205i	−0.733753	−	0.326688i	−0.739373	+	0.673296i	$0.764878\pi$
$228$	−0.316482	−	0.0332636i	−0.0209595	−	0.00220293i
$229$	−4.65887	+	21.9183i	−0.307867	+	1.44840i	0.503567	+	0.863956i	$0.332021\pi$
$229$	−4.65887	+	21.9183i	−0.307867	+	1.44840i	−0.811434	+	0.584444i	$0.801313\pi$
$230$	−0.696136			−0.0459018
$231$	6.31174	+	6.09606i	0.415282	+	0.401091i
$232$	−7.45057			−0.489154
$233$	1.71639	−	8.07499i	0.112445	−	0.529010i	−0.885484	−	0.464671i	$-0.846173\pi$
$233$	1.71639	−	8.07499i	0.112445	−	0.529010i	0.997928	−	0.0643393i	$-0.0204940\pi$
$234$	3.13229	+	0.329217i	0.204764	+	0.0215216i
$235$	0.230334	+	0.102551i	0.0150253	+	0.00668970i
$236$	8.38398	−	7.54897i	0.545751	−	0.491396i
$237$	3.76975	−	11.6021i	0.244872	−	0.753638i
$238$	5.92141	+	3.53207i	0.383828	+	0.228950i
$239$	−4.44476	+	6.11768i	−0.287507	+	0.395720i	−0.928202	−	0.372075i	$-0.878646\pi$
$239$	−4.44476	+	6.11768i	−0.287507	+	0.395720i	0.640695	+	0.767795i	$0.278646\pi$
$240$	−0.252940	−	0.0537640i	−0.0163272	−	0.00347045i
$241$	7.46665	+	12.9326i	0.480969	+	0.833063i	0.999762	−	0.0218370i	$-0.00695149\pi$
$241$	7.46665	+	12.9326i	0.480969	+	0.833063i	−0.518792	+	0.854900i	$0.673618\pi$
$242$	−4.88703	+	9.85479i	−0.314150	+	0.633490i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.71984	+	5.29311i	0.110101	+	0.338857i
$245$	−1.70492	−	0.608146i	−0.108923	−	0.0388530i
$246$	−3.59720	+	2.61352i	−0.229349	+	0.166632i
$247$	−0.670644	−	0.744826i	−0.0426721	−	0.0473921i
$248$	5.80990	−	1.23493i	0.368929	−	0.0784183i
$249$	−6.58703	+	14.7947i	−0.417436	+	0.937576i
$250$	2.34654	−	1.04475i	0.148409	−	0.0660757i
$251$	23.1588	−	7.52475i	1.46177	−	0.474958i	0.533160	−	0.846015i	$-0.321004\pi$
$251$	23.1588	−	7.52475i	1.46177	−	0.474958i	0.928610	+	0.371057i	$0.121004\pi$
$252$	2.43209	−	1.04161i	0.153207	−	0.0656150i
$253$	7.11289	+	5.39672i	0.447184	+	0.339289i
$254$	4.04942	−	7.01380i	0.254083	−	0.440085i
$255$	−0.450918	+	0.500795i	−0.0282376	+	0.0313610i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−14.8646	+	1.56233i	−0.927229	+	0.0974557i	−0.556090	−	0.831122i	$-0.687699\pi$
$257$	−14.8646	+	1.56233i	−0.927229	+	0.0974557i	−0.371138	+	0.928578i	$0.621032\pi$
$258$	−5.69902	−	1.85172i	−0.354806	−	0.115283i
$259$	−11.4015	−	5.27202i	−0.708454	−	0.327587i
$260$	−0.478717	−	0.658897i	−0.0296887	−	0.0408631i
$261$	3.03042	+	6.80644i	0.187578	+	0.421308i
$262$	−4.47828	−	4.03226i	−0.276669	−	0.249114i
$263$	15.7608	−	9.09949i	0.971851	−	0.561099i	0.0720511	−	0.997401i	$-0.477046\pi$
$263$	15.7608	−	9.09949i	0.971851	−	0.561099i	0.899800	+	0.436302i	$0.143712\pi$
$264$	2.16766	+	2.51023i	0.133410	+	0.154494i
$265$		−	2.75376i		−	0.169162i
$266$	−0.796951	−	0.271548i	−0.0488642	−	0.0166497i
$267$	−1.01234	−	0.735504i	−0.0619539	−	0.0450121i
$268$	0.859377	+	8.17642i	0.0524948	+	0.499455i
$269$	−1.06224	−	4.99746i	−0.0647661	−	0.304700i	0.933827	−	0.357725i	$-0.116447\pi$
$269$	−1.06224	−	4.99746i	−0.0647661	−	0.304700i	−0.998593	+	0.0530241i	$0.983114\pi$
$270$	0.0537640	+	0.252940i	0.00327197	+	0.0153934i
$271$	2.92064	+	27.7880i	0.177416	+	1.68800i	0.614764	+	0.788711i	$0.289251\pi$
$271$	2.92064	+	27.7880i	0.177416	+	1.68800i	−0.437348	+	0.899292i	$0.644082\pi$
$272$	2.10830	+	1.53177i	0.127834	+	0.0928771i
$273$	7.88760	+	2.68757i	0.477379	+	0.162659i
$274$			4.56883i			0.276013i
$275$	−15.9298	−	3.73293i	−0.960604	−	0.225104i
$276$	2.33137	−	1.34602i	0.140332	−	0.0810209i
$277$	20.0810	+	18.0810i	1.20655	+	1.08638i	0.994016	+	0.109231i	$0.0348388\pi$
$277$	20.0810	+	18.0810i	1.20655	+	1.08638i	0.212536	+	0.977153i	$0.431828\pi$
$278$	1.64051	+	3.68464i	0.0983912	+	0.220990i
$279$	−3.49127	−	4.80532i	−0.209017	−	0.287687i
$280$	−0.620992	−	0.287145i	−0.0371114	−	0.0171602i
$281$	7.02548	+	2.28272i	0.419105	+	0.136175i	0.510975	−	0.859596i	$-0.329284\pi$
$281$	7.02548	+	2.28272i	0.419105	+	0.136175i	−0.0918701	+	0.995771i	$0.529284\pi$
$282$	−0.969682	+	0.101918i	−0.0577437	+	0.00606911i
$283$	0.675099	−	6.42314i	0.0401305	−	0.381816i	−0.955961	−	0.293493i	$-0.905182\pi$
$283$	0.675099	−	6.42314i	0.0401305	−	0.381816i	0.996092	−	0.0883236i	$-0.0281509\pi$
$284$	9.52207	−	10.5753i	0.565031	−	0.627530i
$285$	0.0411450	−	0.0712651i	0.00243722	−	0.00422138i
$286$	−0.216663	+	10.4436i	−0.0128115	+	0.617543i
$287$	−10.8140	+	4.63138i	−0.638331	+	0.273382i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	−9.32617	+	4.15228i	−0.548598	+	0.244252i
$290$	0.783638	−	1.76008i	0.0460168	−	0.103355i
$291$	1.67348	−	0.355710i	0.0981014	−	0.0208521i
$292$	9.46312	+	10.5099i	0.553787	+	0.615043i
$293$	15.6385	−	11.3620i	0.913608	−	0.663775i	−0.0283165	−	0.999599i	$-0.509015\pi$
$293$	15.6385	−	11.3620i	0.913608	−	0.663775i	0.941925	+	0.335824i	$0.109015\pi$
$294$	6.88569	−	1.25986i	0.401582	−	0.0734767i
$295$	0.901512	+	2.77457i	0.0524881	+	0.161542i
$296$	−4.11168	−	2.37388i	−0.238986	−	0.137979i
$297$	1.41155	−	3.00126i	0.0819063	−	0.174151i
$298$	0.785421	+	1.36039i	0.0454982	+	0.0788052i
$299$	8.29341	+	1.76282i	0.479620	+	0.101946i
$300$	−2.89962	+	3.99099i	−0.167410	+	0.230420i
$301$	−13.6159	−	8.12174i	−0.784805	−	0.468129i
$302$	3.98822	−	12.2745i	0.229496	−	0.706317i
$303$	−8.05039	+	7.24860i	−0.462483	+	0.416421i
$304$	−0.290713	−	0.129434i	−0.0166735	−	0.00742353i
$305$	−1.43130	−	0.150436i	−0.0819562	−	0.00861394i
$306$	0.541818	−	2.54905i	0.0309737	−	0.145720i
$307$	−7.35898			−0.419999			−0.210000	−	0.977701i	$-0.567346\pi$
$307$	−7.35898			−0.419999			−0.210000	+	0.977701i	$0.567346\pi$
$308$	4.11903	+	7.74813i	0.234704	+	0.441491i
$309$	10.2151			0.581119
$310$	−0.319342	+	1.50239i	−0.0181374	+	0.0853298i
$311$	−5.08753	−	0.534721i	−0.288488	−	0.0303213i	−0.0408206	−	0.999166i	$-0.512997\pi$
$311$	−5.08753	−	0.534721i	−0.288488	−	0.0303213i	−0.247667	+	0.968845i	$0.579664\pi$
$312$	2.87725	+	1.28103i	0.162892	+	0.0725243i
$313$	−10.8499	+	9.76926i	−0.613270	+	0.552191i	−0.916149	−	0.400838i	$-0.868719\pi$
$313$	−10.8499	+	9.76926i	−0.613270	+	0.552191i	0.302879	+	0.953029i	$0.402052\pi$
$314$	0.227233	−	0.699350i	0.0128235	−	0.0394666i
$315$	−0.00973980	+	0.684097i	−0.000548775	+	0.0385445i
$316$	7.17049	−	9.86934i	0.403372	−	0.555194i
$317$	−22.2389	−	4.72702i	−1.24906	−	0.265496i	−0.464513	−	0.885566i	$-0.653771\pi$
$317$	−22.2389	−	4.72702i	−1.24906	−	0.265496i	−0.784546	+	0.620071i	$0.787104\pi$
$318$	5.32457	+	9.22242i	0.298587	+	0.517168i
$319$	−21.6518	+	11.9088i	−1.21227	+	0.666767i
$320$	−0.223946	−	0.129295i	−0.0125190	−	0.00722782i
$321$	−0.793984	−	2.44363i	−0.0443158	−	0.136390i
$322$	6.80452	−	2.10431i	0.379201	−	0.117268i
$323$	−0.670913	+	0.487447i	−0.0373306	+	0.0271223i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	−15.1976	+	3.23034i	−0.843010	+	0.179187i
$326$	5.00609	−	11.2439i	0.277261	−	0.622739i
$327$	−6.31258	+	2.81054i	−0.349086	+	0.155423i
$328$	−4.22877	+	1.37401i	−0.233495	+	0.0758670i
$329$	−2.56144	−	0.306144i	−0.141217	−	0.0168783i
$330$	−0.820993	+	0.248052i	−0.0451942	+	0.0136548i
$331$	12.1420	−	21.0305i	0.667384	−	1.15594i	−0.311249	−	0.950328i	$-0.600747\pi$
$331$	12.1420	−	21.0305i	0.667384	−	1.15594i	0.978633	−	0.205615i	$-0.0659194\pi$
$332$	−10.8364	+	12.0351i	−0.594727	+	0.660512i
$333$	−0.496275	+	4.72175i	−0.0271957	+	0.258750i
$334$	−7.21001	+	0.757803i	−0.394514	+	0.0414651i
$335$	−2.02194	−	0.656967i	−0.110470	−	0.0358940i
$336$	2.63493	−	0.239070i	0.143747	−	0.0130423i
$337$	−4.80260	−	6.61020i	−0.261614	−	0.360081i	0.657922	−	0.753086i	$-0.271436\pi$
$337$	−4.80260	−	6.61020i	−0.261614	−	0.360081i	−0.919536	+	0.393005i	$0.871436\pi$
$338$	−1.25291	−	2.81407i	−0.0681491	−	0.153065i
$339$	−5.67926	−	5.11363i	−0.308455	−	0.277734i
$340$	−0.583603	+	0.336943i	−0.0316503	+	0.0182733i
$341$	14.9100	−	12.8752i	0.807423	−	0.697232i
$342$			0.318225i			0.0172076i
$343$	18.5034	+	0.790750i	0.999088	+	0.0426965i
$344$	−4.84788	−	3.52219i	−0.261380	−	0.189904i
$345$	0.0727660	+	0.692322i	0.00391759	+	0.0372734i
$346$	−5.37965	−	25.3093i	−0.289212	−	1.36064i
$347$	−1.65135	−	7.76900i	−0.0886493	−	0.417062i	−0.999985	−	0.00539905i	$-0.998281\pi$
$347$	−1.65135	−	7.76900i	−0.0886493	−	0.417062i	0.911336	−	0.411663i	$-0.135052\pi$
$348$	0.778797	+	7.40976i	0.0417479	+	0.397205i
$349$	26.2552	+	19.0755i	1.40541	+	1.02109i	0.993970	+	0.109651i	$0.0349734\pi$
$349$	26.2552	+	19.0755i	1.40541	+	1.02109i	0.411438	+	0.911438i	$0.365027\pi$
$350$	−9.82275	+	8.59442i	−0.525048	+	0.459391i
$351$		−	3.14954i		−	0.168110i
$352$	1.28586	+	3.05722i	0.0685365	+	0.162950i
$353$	1.65943	−	0.958072i	0.0883225	−	0.0509930i	−0.455188	−	0.890395i	$-0.650428\pi$
$353$	1.65943	−	0.958072i	0.0883225	−	0.0509930i	0.543511	+	0.839402i	$0.317095\pi$
$354$	−8.38398	−	7.54897i	−0.445604	−	0.401223i
$355$	1.49674	+	3.36173i	0.0794387	+	0.178422i
$356$	−0.735504	−	1.01234i	−0.0389817	−	0.0536537i
$357$	2.89376	−	6.25818i	0.153154	−	0.331218i
$358$	−0.874076	−	0.284005i	−0.0461964	−	0.0150101i
$359$	−28.0002	+	2.94294i	−1.47780	+	0.155323i	−0.808862	−	0.587999i	$-0.799916\pi$
$359$	−28.0002	+	2.94294i	−1.47780	+	0.155323i	−0.668934	+	0.743321i	$0.733249\pi$
$360$	−0.0270301	+	0.257174i	−0.00142461	+	0.0135543i
$361$	−12.6457	+	14.0445i	−0.665564	+	0.739184i
$362$	3.33165	−	5.77058i	0.175107	−	0.303295i
$363$	10.3116	+	3.83015i	0.541221	+	0.201031i
$364$	6.67105	+	4.99343i	0.349658	+	0.261727i
$365$	−3.47810	+	1.13010i	−0.182052	+	0.0591524i
$366$	5.08434	−	2.26370i	0.265763	−	0.118325i
$367$	−5.00694	+	11.2458i	−0.261360	+	0.587025i	−0.995790	−	0.0916594i	$-0.970783\pi$
$367$	−5.00694	+	11.2458i	−0.261360	+	0.587025i	0.734430	+	0.678684i	$0.237450\pi$
$368$	2.63321	−	0.559706i	0.137266	−	0.0291767i
$369$	2.97521	+	3.30431i	0.154883	+	0.172015i
$370$	0.993250	−	0.721638i	0.0516366	−	0.0375162i
$371$	8.32419	+	26.9172i	0.432171	+	1.39747i
$372$	−1.83547	−	5.64899i	−0.0951646	−	0.292886i
$373$	12.1782	+	7.03107i	0.630562	+	0.364055i	0.780970	−	0.624569i	$-0.214725\pi$
$373$	12.1782	+	7.03107i	0.630562	+	0.364055i	−0.150408	+	0.988624i	$0.548059\pi$
$374$	8.57519	+	1.08155i	0.443412	+	0.0559255i
$375$	−1.28431	−	2.22448i	−0.0663213	−	0.114872i
$376$	−0.953716	−	0.202719i	−0.0491842	−	0.0104544i
$377$	−13.7929	+	18.9843i	−0.710371	+	0.977741i
$378$	−1.29012	−	2.30989i	−0.0663568	−	0.118808i
$379$	−8.33121	+	25.6408i	−0.427946	+	1.31708i	0.472200	+	0.881491i	$0.343460\pi$
$379$	−8.33121	+	25.6408i	−0.427946	+	1.31708i	−0.900145	+	0.435589i	$0.856540\pi$
$380$	0.0611533	−	0.0550627i	0.00313710	−	0.00282466i
$381$	−7.39866	−	3.29409i	−0.379045	−	0.168762i
$382$	−15.6410	−	1.64393i	−0.800262	−	0.0841109i
$383$	6.77919	−	31.8936i	0.346400	−	1.62969i	−0.367914	−	0.929860i	$-0.619928\pi$
$383$	6.77919	−	31.8936i	0.346400	−	1.62969i	0.714314	−	0.699825i	$-0.246739\pi$
$384$	1.00000			0.0510310
$385$	−2.26361	+	0.158121i	−0.115364	+	0.00805859i
$386$	−20.3880			−1.03772
$387$	−1.24587	+	5.86136i	−0.0633312	+	0.297950i
$388$	1.70150	+	0.178835i	0.0863805	+	0.00907895i
$389$	15.1046	+	6.72501i	0.765835	+	0.340972i	0.752200	−	0.658935i	$-0.228993\pi$
$389$	15.1046	+	6.72501i	0.765835	+	0.340972i	0.0136354	+	0.999907i	$0.495660\pi$
$390$	−0.605248	+	0.544968i	−0.0306479	+	0.0275955i
$391$	2.16789	−	6.67209i	0.109635	−	0.337422i
$392$	6.93800	+	0.929595i	0.350422	+	0.0469516i
$393$	−3.54206	+	4.87523i	−0.178673	+	0.245923i
$394$	1.51712	+	0.322473i	0.0764313	+	0.0162460i
$395$	1.57730	+	2.73196i	0.0793623	+	0.137460i
$396$	2.26990	−	2.41817i	0.114067	−	0.121518i
$397$	−30.5632	−	17.6457i	−1.53392	−	0.885611i	−0.999176	−	0.0405988i	$-0.987073\pi$
$397$	−30.5632	−	17.6457i	−1.53392	−	0.885611i	−0.534747	−	0.845012i	$-0.679593\pi$
$398$	−3.05162	−	9.39192i	−0.152964	−	0.470774i
$399$	−0.186756	+	0.820970i	−0.00934950	+	0.0410999i
$400$	−3.99099	+	2.89962i	−0.199549	+	0.144981i
$401$	−7.61606	−	8.45849i	−0.380328	−	0.422397i	0.522338	−	0.852738i	$-0.325060\pi$
$401$	−7.61606	−	8.45849i	−0.380328	−	0.422397i	−0.902666	+	0.430341i	$0.858393\pi$
$402$	8.04180	−	1.70934i	0.401089	−	0.0852540i
$403$	7.60896	−	17.0900i	0.379029	−	0.851313i
$404$	−9.89631	+	4.40612i	−0.492360	+	0.219213i
$405$	0.245934	−	0.0799088i	0.0122206	−	0.00397070i
$406$	−2.33938	+	19.5731i	−0.116102	+	0.971394i
$407$	−15.7431	−	0.326607i	−0.780358	−	0.0161893i
$408$	1.30300	−	2.25686i	0.0645081	−	0.111731i
$409$	11.3250	−	12.5776i	0.559983	−	0.621924i	−0.394965	−	0.918696i	$-0.629243\pi$
$409$	11.3250	−	12.5776i	0.559983	−	0.621924i	0.954948	+	0.296772i	$0.0959100\pi$
$410$	0.120186	−	1.14349i	0.00593557	−	0.0564732i
$411$	4.54381	−	0.477573i	0.224129	−	0.0235569i
$412$	9.71517	+	3.15665i	0.478632	+	0.155517i
$413$	−17.1991	−	24.3955i	−0.846312	−	1.20042i
$414$	−1.58234	−	2.17791i	−0.0777678	−	0.107038i
$415$	−1.70334	−	3.82577i	−0.0836138	−	0.187800i
$416$	2.34057	+	2.10745i	0.114756	+	0.103326i
$417$	3.49298	−	2.01667i	0.171052	−	0.0987569i
$418$	−1.05171	+	0.0885277i	−0.0514410	+	0.00433003i
$419$			34.1305i			1.66738i	0.552231	+	0.833691i	$0.313777\pi$
$419$			34.1305i			1.66738i	−0.552231	+	0.833691i	$0.686223\pi$
$420$	−0.220661	+	0.647605i	−0.0107671	+	0.0315999i
$421$	−26.0524	−	18.9282i	−1.26972	−	0.922503i	−0.270525	−	0.962713i	$-0.587197\pi$
$421$	−26.0524	−	18.9282i	−1.26972	−	0.922503i	−0.999191	+	0.0402099i	$0.987197\pi$
$422$	−2.23117	−	21.2281i	−0.108611	−	1.03337i
$423$	0.202719	+	0.953716i	0.00985652	+	0.0463713i
$424$	2.21408	+	10.4164i	0.107525	+	0.505866i
$425$	1.34379	+	12.7853i	0.0651834	+	0.620179i
$426$	−11.5127	−	8.36448i	−0.557793	−	0.405260i
$427$	14.4453	−	2.85613i	0.699057	−	0.138218i
$428$		−	2.56938i		−	0.124196i
$429$	10.4090	−	0.876178i	0.502553	−	0.0423023i
$430$	1.34195	−	0.774777i	0.0647147	−	0.0373631i
$431$	−2.94253	−	2.64947i	−0.141737	−	0.127620i	0.595213	−	0.803568i	$-0.297068\pi$
$431$	−2.94253	−	2.64947i	−0.141737	−	0.127620i	−0.736950	+	0.675948i	$0.763734\pi$
$432$	−0.406737	−	0.913545i	−0.0195691	−	0.0439530i
$433$	−15.8550	−	21.8226i	−0.761944	−	1.04873i	−0.997050	−	0.0767567i	$-0.975544\pi$
$433$	−15.8550	−	21.8226i	−0.761944	−	1.04873i	0.235105	−	0.971970i	$-0.424456\pi$
$434$	−1.42000	−	15.6507i	−0.0681623	−	0.751257i
$435$	−1.83235	−	0.595367i	−0.0878545	−	0.0285456i
$436$	−6.87213	+	0.722290i	−0.329115	+	0.0345914i
$437$	−0.0895468	+	0.851981i	−0.00428360	+	0.0407558i
$438$	9.46312	−	10.5099i	0.452166	−	0.502181i
$439$	5.42858	−	9.40258i	0.259092	−	0.448761i	−0.706907	−	0.707307i	$-0.749910\pi$
$439$	5.42858	−	9.40258i	0.259092	−	0.448761i	0.965999	+	0.258546i	$0.0832434\pi$
$440$	−0.857463	−	0.0177889i	−0.0408779	−	0.000848053i
$441$	−1.97271	−	6.71628i	−0.0939387	−	0.319823i
$442$	7.80599	−	2.53632i	0.371293	−	0.120640i
$443$	3.14962	−	1.40230i	0.149643	−	0.0666253i	−0.330549	−	0.943789i	$-0.607234\pi$
$443$	3.14962	−	1.40230i	0.149643	−	0.0666253i	0.480192	+	0.877164i	$0.340567\pi$
$444$	−1.93109	+	4.33729i	−0.0916453	+	0.205839i
$445$	0.316507	−	0.0672757i	0.0150039	−	0.00318917i
$446$	−8.38148	−	9.30857i	−0.396874	−	0.440774i
$447$	1.27084	−	0.923318i	0.0601086	−	0.0436714i
$448$	2.57984	+	0.586869i	0.121886	+	0.0277269i
$449$	−4.51994	−	13.9109i	−0.213309	−	0.656498i	−0.999269	−	0.0382208i	$-0.987831\pi$
$449$	−4.51994	−	13.9109i	−0.213309	−	0.656498i	0.785960	−	0.618277i	$-0.212169\pi$
$450$	4.27222	+	2.46657i	0.201394	+	0.116275i
$451$	−10.0929	+	10.7521i	−0.475254	+	0.506298i
$452$	−3.82110	−	6.61833i	−0.179729	−	0.311300i
$453$	−12.6241	−	2.68334i	−0.593133	−	0.126074i
$454$	−7.11298	+	9.79018i	−0.333829	+	0.459476i
$455$	−1.88127	+	1.05073i	−0.0881952	+	0.0492590i
$456$	−0.0983369	+	0.302650i	−0.00460505	+	0.0141729i
$457$	−26.1923	+	23.5836i	−1.22522	+	1.10320i	−0.233829	+	0.972278i	$0.575126\pi$
$457$	−26.1923	+	23.5836i	−1.22522	+	1.10320i	−0.991393	+	0.130918i	$0.958208\pi$
$458$	20.4707	+	9.11413i	0.956532	+	0.425875i
$459$	−2.59172	−	0.272401i	−0.120971	−	0.0127146i
$460$	−0.144735	+	0.680924i	−0.00674829	+	0.0317482i
$461$	8.90379			0.414691			0.207345	−	0.978268i	$-0.433518\pi$
$461$	8.90379			0.414691			0.207345	+	0.978268i	$0.433518\pi$
$462$	7.27513	−	4.90637i	0.338470	−	0.228265i
$463$	7.09357			0.329666			0.164833	−	0.986321i	$-0.447291\pi$
$463$	7.09357			0.329666			0.164833	+	0.986321i	$0.447291\pi$
$464$	−1.54906	+	7.28776i	−0.0719134	+	0.338326i
$465$	1.52754	+	0.160550i	0.0708378	+	0.00744535i
$466$	−7.54167	−	3.35777i	−0.349361	−	0.155546i
$467$	−7.69542	+	6.92899i	−0.356102	+	0.320635i	−0.827692	−	0.561182i	$-0.810347\pi$
$467$	−7.69542	+	6.92899i	−0.356102	+	0.320635i	0.471591	+	0.881818i	$0.343680\pi$
$468$	0.973262	−	2.99539i	0.0449890	−	0.138462i
$469$	21.7497	+	0.309661i	1.00431	+	0.0142988i
$470$	0.148199	−	0.203979i	0.00683592	−	0.00940884i
$471$	−0.719271	−	0.152886i	−0.0331423	−	0.00704460i
$472$	−5.64088	−	9.77029i	−0.259643	−	0.449714i
$473$	−19.7180	−	2.48694i	−0.906635	−	0.114350i
$474$	−10.5648	−	6.09959i	−0.485257	−	0.280163i
$475$	−0.485109	−	1.49301i	−0.0222583	−	0.0685040i
$476$	4.68602	−	5.05766i	0.214783	−	0.231817i
$477$	8.61533	−	6.25940i	0.394469	−	0.286598i
$478$	5.05988	+	5.61956i	0.231433	+	0.257033i
$479$	−12.1118	+	2.57444i	−0.553401	+	0.117629i	−0.476120	−	0.879380i	$-0.657957\pi$
$479$	−12.1118	+	2.57444i	−0.553401	+	0.117629i	−0.0772810	+	0.997009i	$0.524624\pi$
$480$	−0.105178	+	0.236234i	−0.00480071	+	0.0107826i
$481$	−13.6605	+	6.08203i	−0.622864	+	0.277317i
$482$	14.2024	−	4.61464i	0.646902	−	0.210191i
$483$	−2.80405	−	6.54728i	−0.127588	−	0.297912i
$484$	8.62337	+	6.82916i	0.391972	+	0.310416i
$485$	−0.221207	+	0.383142i	−0.0100445	+	0.0173976i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	3.47243	−	33.0380i	0.157351	−	1.49710i	−0.576115	−	0.817369i	$-0.695432\pi$
$487$	3.47243	−	33.0380i	0.157351	−	1.49710i	0.733466	−	0.679726i	$-0.237901\pi$
$488$	5.53502	−	0.581754i	0.250558	−	0.0263348i
$489$	−11.7055	−	3.80336i	−0.529343	−	0.171994i
$490$	−0.949329	+	1.54122i	−0.0428863	+	0.0696252i
$491$	5.37255	+	7.39468i	0.242460	+	0.333717i	0.912853	−	0.408289i	$-0.133874\pi$
$491$	5.37255	+	7.39468i	0.242460	+	0.333717i	−0.670393	+	0.742006i	$0.733874\pi$
$492$	1.80851	+	4.06198i	0.0815339	+	0.183128i
$493$	14.4290	+	12.9920i	0.649851	+	0.585129i
$494$	−0.867985	+	0.501131i	−0.0390525	+	0.0225470i
$495$	0.332511	+	0.790567i	0.0149452	+	0.0355333i
$496$		−	5.93970i		−	0.266700i
$497$	−24.7921	−	28.3355i	−1.11208	−	1.27102i
$498$	13.1019	+	9.51908i	0.587109	+	0.426560i
$499$	−4.57819	−	43.5586i	−0.204948	−	1.94995i	−0.298682	−	0.954353i	$-0.596547\pi$
$499$	−4.57819	−	43.5586i	−0.204948	−	1.94995i	0.0937336	−	0.995597i	$-0.470120\pi$
$500$	−0.534045	−	2.51248i	−0.0238832	−	0.112362i
$501$	1.50730	+	7.09130i	0.0673413	+	0.316816i
$502$	−2.54533	−	24.2172i	−0.113604	−	1.08087i
$503$	11.0196	+	8.00623i	0.491341	+	0.356980i	0.805700	−	0.592324i	$-0.201790\pi$
$503$	11.0196	+	8.00623i	0.491341	+	0.356980i	−0.314359	+	0.949304i	$0.601790\pi$
$504$	−0.513185	−	2.59550i	−0.0228591	−	0.115613i
$505$		−	2.80128i		−	0.124655i
$506$	6.75765	−	5.83541i	0.300414	−	0.259416i
$507$	−2.66769	+	1.54019i	−0.118476	+	0.0684024i
$508$	−6.01861	−	5.41918i	−0.267033	−	0.240437i
$509$	−0.699314	−	1.57068i	−0.0309965	−	0.0696194i	0.897384	−	0.441251i	$-0.145465\pi$
$509$	−0.699314	−	1.57068i	−0.0309965	−	0.0696194i	−0.928380	+	0.371632i	$0.878798\pi$
$510$	0.396101	+	0.545186i	0.0175396	+	0.0241412i
$511$	30.5813	−	21.5602i	1.35284	−	0.953766i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	0.316482	−	0.0332636i	0.0139730	−	0.00146862i
$514$	−1.56233	+	14.8646i	−0.0689116	+	0.655650i
$515$	−1.76753	+	1.96304i	−0.0778868	+	0.0865021i
$516$	−2.99615	+	5.18949i	−0.131898	+	0.228455i
$517$	−3.09558	+	0.935289i	−0.136143	+	0.0411340i
$518$	−7.52732	+	10.0562i	−0.330731	+	0.441845i
$519$	−24.6083	+	7.99572i	−1.08018	+	0.350973i
$520$	−0.744029	+	0.331263i	−0.0326278	+	0.0145269i
$521$	−8.40395	+	18.8756i	−0.368184	+	0.826954i	0.630526	+	0.776168i	$0.282839\pi$
$521$	−8.40395	+	18.8756i	−0.368184	+	0.826954i	−0.998710	+	0.0507858i	$0.983827\pi$
$522$	7.28776	−	1.54906i	0.318977	−	0.0678006i
$523$	0.783659	+	0.870342i	0.0342670	+	0.0380574i	0.760035	−	0.649883i	$-0.225182\pi$
$523$	0.783659	+	0.870342i	0.0342670	+	0.0380574i	−0.725768	+	0.687940i	$0.758515\pi$
$524$	−4.87523	+	3.54206i	−0.212975	+	0.154736i
$525$	9.57409	+	8.87058i	0.417848	+	0.387144i
$526$	−5.62379	−	17.3083i	−0.245209	−	0.754676i
$527$	−13.4051	−	7.73943i	−0.583935	−	0.337135i
$528$	2.90606	−	1.59838i	0.126470	−	0.0695606i
$529$	7.87646	+	13.6424i	0.342455	+	0.593149i
$530$	−2.69359	−	0.572540i	−0.117002	−	0.0248695i
$531$	−6.63125	+	9.12714i	−0.287772	+	0.396084i
$532$	−0.431309	+	0.723078i	−0.0186996	+	0.0313494i
$533$	−4.32750	+	13.3187i	−0.187445	+	0.576896i
$534$	−0.929908	+	0.837293i	−0.0402411	+	0.0362332i
$535$	0.606976	+	0.270243i	0.0262419	+	0.0116836i
$536$	8.17642	+	0.859377i	0.353168	+	0.0371194i
$537$	−0.191083	+	0.898974i	−0.00824584	+	0.0387936i
$538$	−5.10910			−0.220269
$539$	21.6481	−	8.38810i	0.932449	−	0.361301i
$540$	0.258590			0.0111280
$541$	−6.45455	+	30.3663i	−0.277503	+	1.30555i	0.589712	+	0.807614i	$0.299241\pi$
$541$	−6.45455	+	30.3663i	−0.277503	+	1.30555i	−0.867215	+	0.497934i	$0.834092\pi$
$542$	27.7880	+	2.92064i	1.19360	+	0.125452i
$543$	−6.08722	−	2.71020i	−0.261228	−	0.116306i
$544$	1.93664	−	1.74375i	0.0830326	−	0.0747629i
$545$	0.552168	−	1.69940i	0.0236523	−	0.0727943i
$546$	4.26876	−	7.15646i	0.182686	−	0.306268i
$547$	7.49930	−	10.3219i	0.320647	−	0.441333i	−0.618018	−	0.786164i	$-0.712064\pi$
$547$	7.49930	−	10.3219i	0.320647	−	0.441333i	0.938665	+	0.344832i	$0.112064\pi$
$548$	4.46899	+	0.949914i	0.190906	+	0.0405783i
$549$	−2.78275	−	4.81987i	−0.118765	−	0.205707i
$550$	−6.96335	+	14.8056i	−0.296918	+	0.631312i
$551$	−2.05331	−	1.18548i	−0.0874739	−	0.0505031i
$552$	−0.831886	−	2.56028i	−0.0354074	−	0.108973i
$553$	−23.6758	−	21.9361i	−1.00680	−	0.932819i
$554$	21.8610	−	15.8829i	0.928785	−	0.674802i
$555$	−0.821508	−	0.912377i	−0.0348711	−	0.0387282i
$556$	3.94521	−	0.838579i	0.167314	−	0.0355637i
$557$	1.08061	−	2.42708i	0.0457867	−	0.102839i	−0.889204	−	0.457511i	$-0.848741\pi$
$557$	1.08061	−	2.42708i	0.0457867	−	0.102839i	0.934991	+	0.354673i	$0.115408\pi$
$558$	−5.42619	+	2.41589i	−0.229709	+	0.102273i
$559$	−17.9493	+	5.83208i	−0.759175	+	0.246671i
$560$	−0.409982	+	0.547721i	−0.0173249	+	0.0231454i
$561$	0.179271	−	8.64126i	0.00756884	−	0.364834i
$562$	3.69351	−	6.39735i	0.155801	−	0.269856i
$563$	−1.95264	+	2.16862i	−0.0822938	+	0.0913965i	−0.782885	−	0.622166i	$-0.786253\pi$
$563$	−1.95264	+	2.16862i	−0.0822938	+	0.0913965i	0.700592	+	0.713563i	$0.252920\pi$
$564$	−0.101918	+	0.969682i	−0.00429151	+	0.0408310i
$565$	1.96537	−	0.206569i	0.0826839	−	0.00869042i
$566$	−6.14242	−	1.99579i	−0.258185	−	0.0838894i
$567$	−2.16238	+	1.52450i	−0.0908114	+	0.0640232i
$568$	−8.36448	−	11.5127i	−0.350966	−	0.483063i
$569$	−11.3396	−	25.4692i	−0.475381	−	1.06772i	−0.979012	−	0.203804i	$-0.934670\pi$
$569$	−11.3396	−	25.4692i	−0.475381	−	1.06772i	0.503631	−	0.863919i	$-0.331997\pi$
$570$	−0.0611533	−	0.0550627i	−0.00256143	−	0.00230632i
$571$	−12.5183	+	7.22745i	−0.523875	+	0.302459i	−0.738519	−	0.674233i	$-0.764474\pi$
$571$	−12.5183	+	7.22745i	−0.523875	+	0.302459i	0.214644	+	0.976692i	$0.431141\pi$
$572$	10.1703	+	2.38327i	0.425243	+	0.0996497i
$573$			15.7271i			0.657011i
$574$	2.28182	+	11.5406i	0.0952413	+	0.481696i
$575$	10.7439	+	7.80590i	0.448051	+	0.325528i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	5.17942	+	24.3673i	0.215622	+	1.01442i	0.944178	+	0.329436i	$0.106858\pi$
$577$	5.17942	+	24.3673i	0.215622	+	1.01442i	−0.728556	+	0.684986i	$0.759808\pi$
$578$	2.12252	+	9.98568i	0.0882853	+	0.415349i
$579$	2.13112	+	20.2763i	0.0885665	+	0.842654i
$580$	−1.55869	−	1.13245i	−0.0647211	−	0.0470226i
$581$	28.2143	+	32.2468i	1.17053	+	1.33782i
$582$		−	1.71087i		−	0.0709179i
$583$	23.0837	+	26.7318i	0.956027	+	1.10712i
$584$	12.2477	−	7.07121i	0.506813	−	0.292609i
$585$	0.605248	+	0.544968i	0.0250239	+	0.0225316i
$586$	−7.86230	−	17.6590i	−0.324789	−	0.729487i
$587$	−5.40866	−	7.44438i	−0.223239	−	0.307263i	0.682676	−	0.730721i	$-0.260816\pi$
$587$	−5.40866	−	7.44438i	−0.223239	−	0.307263i	−0.905916	+	0.423458i	$0.860816\pi$
$588$	0.199284	−	6.99716i	0.00821833	−	0.288558i
$589$	1.79765	+	0.584091i	0.0740708	+	0.0240671i
$590$	2.90137	−	0.304947i	0.119448	−	0.0125545i
$591$	0.162125	−	1.54251i	0.00666892	−	0.0634506i
$592$	−3.17687	+	3.52827i	−0.130568	+	0.145011i
$593$	19.9910	−	34.6254i	0.820931	−	1.42190i	−0.0840579	−	0.996461i	$-0.526788\pi$
$593$	19.9910	−	34.6254i	0.820931	−	1.42190i	0.904989	−	0.425434i	$-0.139879\pi$
$594$	−2.64219	−	2.00470i	−0.108411	−	0.0822537i
$595$	0.701925	+	1.63895i	0.0287761	+	0.0671905i
$596$	1.49396	−	0.485417i	0.0611950	−	0.0198834i
$597$	−9.02149	+	4.01662i	−0.369225	+	0.164390i
$598$	3.44859	−	7.74567i	0.141023	−	0.316744i
$599$	−39.4209	+	8.37917i	−1.61069	+	0.342364i	−0.923347	−	0.383966i	$-0.874558\pi$
$599$	−39.4209	+	8.37917i	−1.61069	+	0.342364i	−0.687346	+	0.726330i	$0.741225\pi$
$600$	3.30091	+	3.66603i	0.134759	+	0.149665i
$601$	13.3425	−	9.69389i	0.544252	−	0.395422i	−0.281410	−	0.959588i	$-0.590802\pi$
$601$	13.3425	−	9.69389i	0.544252	−	0.395422i	0.825662	+	0.564166i	$0.190802\pi$
$602$	−10.7752	+	11.6297i	−0.439162	+	0.473992i
$603$	−2.54057	−	7.81907i	−0.103460	−	0.318417i
$604$	−11.1771	−	6.45308i	−0.454788	−	0.262572i
$605$	−2.52027	+	1.31886i	−0.102464	+	0.0536191i
$606$	5.41643	+	9.38154i	0.220028	+	0.381099i
$607$	43.3464	+	9.21355i	1.75937	+	0.373967i	0.970597	−	0.240712i	$-0.0773810\pi$
$607$	43.3464	+	9.21355i	1.75937	+	0.373967i	0.788778	+	0.614679i	$0.210714\pi$
$608$	−0.187048	+	0.257449i	−0.00758579	+	0.0104409i
$609$	19.7104	+	0.280625i	0.798704	+	0.0113715i
$610$	−0.444733	+	1.36875i	−0.0180067	+	0.0554190i
$611$	−2.28211	+	2.05482i	−0.0923241	+	0.0831290i
$612$	−2.38070	−	1.05996i	−0.0962341	−	0.0428462i
$613$	22.1621	+	2.32934i	0.895120	+	0.0940810i	0.540906	−	0.841083i	$-0.318082\pi$
$613$	22.1621	+	2.32934i	0.895120	+	0.0940810i	0.354215	+	0.935164i	$0.384748\pi$
$614$	−1.53002	+	7.19817i	−0.0617465	+	0.290495i
$615$	−1.14979			−0.0463641
$616$	8.43521	−	2.41809i	0.339864	−	0.0974277i
$617$	20.2027			0.813332			0.406666	−	0.913577i	$-0.366691\pi$
$617$	20.2027			0.813332			0.406666	+	0.913577i	$0.366691\pi$
$618$	2.12385	−	9.99191i	0.0854336	−	0.401934i
$619$	13.8578	+	1.45651i	0.556992	+	0.0585422i	0.378842	−	0.925461i	$-0.376322\pi$
$619$	13.8578	+	1.45651i	0.556992	+	0.0585422i	0.178149	+	0.984003i	$0.442989\pi$
$620$	1.40316	+	0.624727i	0.0563522	+	0.0250896i
$621$	−2.00058	+	1.80133i	−0.0802803	+	0.0722847i
$622$	−1.58079	+	4.86519i	−0.0633841	+	0.195076i
$623$	−2.89040	+	1.61435i	−0.115801	+	0.0646776i
$624$	1.85125	−	2.54803i	0.0741095	−	0.102003i
$625$	−23.4769	−	4.99018i	−0.939078	−	0.199607i
$626$	7.29996	+	12.6439i	0.291765	+	0.505352i
$627$	0.197977	+	1.03670i	0.00790643	+	0.0414017i
$628$	−0.636823	−	0.367670i	−0.0254120	−	0.0146716i
$629$	3.82336	+	11.7671i	0.152447	+	0.469184i
$630$	0.667123	+	0.151759i	0.0265788	+	0.00604621i
$631$	33.7516	−	24.5220i	1.34363	−	0.976204i	0.344327	−	0.938850i	$-0.388107\pi$
$631$	33.7516	−	24.5220i	1.34363	−	0.976204i	0.999302	−	0.0373544i	$-0.0118930\pi$
$632$	−8.16284	−	9.06575i	−0.324700	−	0.360616i
$633$	−20.8786	+	4.43789i	−0.829850	+	0.176390i
$634$	−9.24744	+	20.7701i	−0.367263	+	0.824886i
$635$	1.91322	−	0.851821i	0.0759239	−	0.0338035i
$636$	10.1279	−	3.29076i	0.401599	−	0.130487i
$637$	15.2126	−	15.9573i	0.602747	−	0.632253i
$638$	7.14695	+	23.6547i	0.282950	+	0.936497i
$639$	−7.11525	+	12.3240i	−0.281475	+	0.487529i
$640$	−0.173031	+	0.192170i	−0.00683964	+	0.00759619i
$641$	−5.14207	+	48.9236i	−0.203100	+	1.93236i	0.134174	+	0.990958i	$0.457162\pi$
$641$	−5.14207	+	48.9236i	−0.203100	+	1.93236i	−0.337273	+	0.941407i	$0.609505\pi$
$642$	−2.55531	+	0.268574i	−0.100850	+	0.0105998i
$643$	−21.2034	−	6.88940i	−0.836180	−	0.271692i	−0.140534	−	0.990076i	$-0.544882\pi$
$643$	−21.2034	−	6.88940i	−0.836180	−	0.271692i	−0.695646	+	0.718384i	$0.744882\pi$
$644$	−0.643585	−	7.09333i	−0.0253608	−	0.279516i
$645$	−0.910805	−	1.25362i	−0.0358629	−	0.0493610i
$646$	0.337304	+	0.757598i	0.0132711	+	0.0298073i
$647$	27.4375	+	24.7048i	1.07868	+	0.971246i	0.999672	−	0.0256286i	$-0.00815872\pi$
$647$	27.4375	+	24.7048i	1.07868	+	0.971246i	0.0790059	+	0.996874i	$0.474825\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−32.0094	−	19.3768i	−1.25648	−	0.760605i
$650$			15.5371i			0.609415i
$651$	−15.4165	+	3.04816i	−0.604221	+	0.119467i
$652$	−9.95732	−	7.23442i	−0.389959	−	0.283322i
$653$	2.77891	+	26.4396i	0.108747	+	1.03466i	0.903752	+	0.428057i	$0.140802\pi$
$653$	2.77891	+	26.4396i	0.108747	+	1.03466i	−0.795005	+	0.606603i	$0.792532\pi$
$654$	1.43667	+	6.75898i	0.0561781	+	0.264297i
$655$	−0.323988	−	1.52424i	−0.0126593	−	0.0595571i
$656$	0.464774	+	4.42203i	0.0181464	+	0.172651i
$657$	−11.4415	−	8.31270i	−0.446374	−	0.324309i
$658$	−0.832007	+	2.44181i	−0.0324350	+	0.0951918i
$659$			3.16463i			0.123277i	0.998099	+	0.0616383i	$0.0196325\pi$
$659$			3.16463i			0.123277i	−0.998099	+	0.0616383i	$0.980367\pi$
$660$	0.0719378	+	0.854625i	0.00280018	+	0.0332662i
$661$	23.4909	−	13.5625i	0.913689	−	0.527519i	0.0320727	−	0.999486i	$-0.489789\pi$
$661$	23.4909	−	13.5625i	0.913689	−	0.527519i	0.881616	+	0.471967i	$0.156456\pi$
$662$	−18.0465	−	16.2492i	−0.701398	−	0.631541i
$663$	−3.33837	−	7.49811i	−0.129652	−	0.291203i
$664$	9.51908	+	13.1019i	0.369412	+	0.508452i
$665$	−0.125451	−	0.177942i	−0.00486479	−	0.00690030i
$666$	4.51538	+	1.46714i	0.174968	+	0.0568504i
$667$	19.9474	−	2.09655i	0.772365	−	0.0811788i
$668$	−0.757803	+	7.21001i	−0.0293203	+	0.278964i
$669$	−8.38148	+	9.30857i	−0.324047	+	0.359890i
$670$	−1.06300	+	1.84116i	−0.0410671	+	0.0711303i
$671$	15.1552	−	10.5377i	0.585061	−	0.406802i
$672$	0.313987	−	2.62705i	0.0121123	−	0.101341i
$673$	−16.2429	+	5.27765i	−0.626119	+	0.203438i	−0.604855	−	0.796336i	$-0.706769\pi$
$673$	−16.2429	+	5.27765i	−0.626119	+	0.203438i	−0.0212638	+	0.999774i	$0.506769\pi$
$674$	−7.46427	+	3.32331i	−0.287513	+	0.128009i
$675$	2.00649	−	4.50664i	0.0772296	−	0.173461i
$676$	−3.01307	+	0.640449i	−0.115887	+	0.0246326i
$677$	32.1025	+	35.6534i	1.23380	+	1.37027i	0.904741	+	0.425962i	$0.140064\pi$
$677$	32.1025	+	35.6534i	1.23380	+	1.37027i	0.329057	+	0.944310i	$0.393269\pi$
$678$	−6.18267	+	4.49197i	−0.237444	+	0.172513i
$679$	1.00406	−	4.41378i	0.0385322	−	0.169385i
$680$	0.208242	+	0.640904i	0.00798573	+	0.0245776i
$681$	10.4801	+	6.05066i	0.401597	+	0.231862i
$682$	−9.49390	−	17.2611i	−0.363540	−	0.660962i
$683$	11.0765	+	19.1850i	0.423829	+	0.734093i	0.996310	−	0.0858248i	$-0.0273525\pi$
$683$	11.0765	+	19.1850i	0.423829	+	0.734093i	−0.572482	+	0.819918i	$0.694019\pi$
$684$	0.311271	+	0.0661627i	0.0119017	+	0.00252979i
$685$	−0.694443	+	0.955819i	−0.0265333	+	0.0365200i
$686$	4.62054	−	17.9346i	0.176413	−	0.684747i
$687$	6.92443	−	21.3112i	0.264184	−	0.813074i
$688$	−4.45315	+	4.00964i	−0.169775	+	0.152866i
$689$	30.6402	+	13.6419i	1.16730	+	0.519715i
$690$	0.692322	+	0.0727660i	0.0263563	+	0.00277015i
$691$	−9.25346	+	43.5341i	−0.352018	+	1.65612i	0.344657	+	0.938729i	$0.387995\pi$
$691$	−9.25346	+	43.5341i	−0.352018	+	1.65612i	−0.696675	+	0.717387i	$0.745338\pi$
$692$	−25.8747			−0.983609
$693$	−5.63995	−	6.72242i	−0.214244	−	0.255364i
$694$	−7.94257			−0.301496
$695$	−0.216849	+	1.02019i	−0.00822554	+	0.0386981i
$696$	7.40976	+	0.778797i	0.280866	+	0.0295202i
$697$	10.5855	+	4.71297i	0.400955	+	0.178517i
$698$	24.1174	−	21.7154i	0.912858	−	0.821941i
$699$	−2.55106	+	7.85134i	−0.0964898	+	0.296965i
$700$	6.36434	+	11.3950i	0.240550	+	0.430690i
$701$	2.99207	−	4.11823i	0.113009	−	0.155543i	−0.748766	−	0.662835i	$-0.769353\pi$
$701$	2.99207	−	4.11823i	0.113009	−	0.155543i	0.861775	+	0.507291i	$0.169353\pi$
$702$	−3.08072	−	0.654827i	−0.116274	−	0.0247148i
$703$	−0.755427	−	1.30844i	−0.0284915	−	0.0493486i
$704$	3.25775	−	0.622128i	0.122781	−	0.0234473i
$705$	−0.218352	−	0.126066i	−0.00822363	−	0.00474791i
$706$	−0.592121	−	1.82236i	−0.0222848	−	0.0685855i
$707$	8.46781	+	27.3816i	0.318465	+	1.02979i
$708$	−9.12714	+	6.63125i	−0.343019	+	0.249218i
$709$	3.44359	+	3.82449i	0.129327	+	0.143632i	0.804330	−	0.594183i	$-0.202525\pi$
$709$	3.44359	+	3.82449i	0.129327	+	0.143632i	−0.675003	+	0.737815i	$0.735858\pi$
$710$	3.59946	−	0.765089i	0.135085	−	0.0287133i
$711$	−4.96185	+	11.1445i	−0.186084	+	0.417951i
$712$	−1.14313	+	0.508956i	−0.0428407	+	0.0190739i
$713$	−15.2073	+	4.94115i	−0.569518	+	0.185048i
$714$	−5.51977	−	4.13168i	−0.206572	−	0.154624i
$715$	−1.63271	+	2.15191i	−0.0610598	+	0.0804769i
$716$	−0.459529	+	0.795928i	−0.0171734	+	0.0297452i
$717$	5.05988	−	5.61956i	0.188965	−	0.209866i
$718$	−2.94294	+	28.0002i	−0.109830	+	1.04496i
$719$	26.6990	−	2.80617i	0.995704	−	0.104653i	0.407363	−	0.913266i	$-0.366448\pi$
$719$	26.6990	−	2.80617i	0.995704	−	0.104653i	0.588340	+	0.808613i	$0.299782\pi$
$720$	0.245934	+	0.0799088i	0.00916542	+	0.00297803i
$721$	11.3431	−	24.5311i	0.422440	−	0.913587i
$722$	11.1084	+	15.2894i	0.413412	+	0.569012i
$723$	−6.07392	−	13.6423i	−0.225892	−	0.507361i
$724$	−4.95179	−	4.45861i	−0.184032	−	0.165703i
$725$	−31.8305	+	18.3773i	−1.18215	+	0.682517i
$726$	5.89036	−	9.28998i	0.218612	−	0.344783i
$727$			0.277821i			0.0103038i	0.999987	+	0.00515190i	$0.00163991\pi$
$727$			0.277821i			0.0103038i	−0.999987	+	0.00515190i	$0.998360\pi$
$728$	6.27130	−	5.48708i	0.232430	−	0.203365i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	0.382270	+	3.63706i	0.0141485	+	0.134614i
$731$	3.24674	+	15.2747i	0.120085	+	0.564955i
$732$	−1.15713	−	5.44389i	−0.0427689	−	0.201212i
$733$	−4.26297	−	40.5595i	−0.157456	−	1.49810i	−0.732945	−	0.680288i	$-0.761855\pi$
$733$	−4.26297	−	40.5595i	−0.157456	−	1.49810i	0.575488	−	0.817810i	$-0.304812\pi$
$734$	9.95903	+	7.23566i	0.367595	+	0.267073i
$735$	1.63201	+	0.783027i	0.0601975	+	0.0288824i
$736$		−	2.69204i		−	0.0992299i
$737$	25.1348	−	10.5716i	0.925852	−	0.389411i
$738$	3.85068	−	2.22319i	0.141746	−	0.0818369i
$739$	18.1712	+	16.3615i	0.668440	+	0.601866i	0.931861	−	0.362815i	$-0.118184\pi$
$739$	18.1712	+	16.3615i	0.668440	+	0.601866i	−0.263421	+	0.964681i	$0.584851\pi$
$740$	−0.499360	−	1.12158i	−0.0183569	−	0.0412302i
$741$	0.589115	+	0.810847i	0.0216417	+	0.0297872i
$742$	28.0597	−	2.54589i	1.03010	−	0.0934624i
$743$	7.75760	+	2.52060i	0.284599	+	0.0924717i	0.447838	−	0.894115i	$-0.352194\pi$
$743$	7.75760	+	2.52060i	0.284599	+	0.0924717i	−0.163239	+	0.986587i	$0.552194\pi$
$744$	−5.90716	+	0.620868i	−0.216567	+	0.0227621i
$745$	−0.0424600	+	0.403980i	−0.00155561	+	0.0148007i
$746$	9.40941	−	10.4502i	0.344503	−	0.382609i
$747$	8.09741	−	14.0251i	0.296269	−	0.513152i
$748$	2.84079	−	8.16293i	0.103870	−	0.298466i
$749$	−6.74991	−	0.806753i	−0.246636	−	0.0294781i
$750$	−2.44290	+	0.793745i	−0.0892020	+	0.0289835i
$751$	18.6842	−	8.31873i	0.681795	−	0.303555i	−0.0364594	−	0.999335i	$-0.511608\pi$
$751$	18.6842	−	8.31873i	0.681795	−	0.303555i	0.718255	+	0.695780i	$0.244941\pi$
$752$	−0.396578	+	0.890728i	−0.0144617	+	0.0324815i
$753$	−23.8185	+	5.06277i	−0.867993	+	0.184498i
$754$	15.7017	+	17.4386i	0.571824	+	0.635075i
$755$	2.70002	−	1.96168i	0.0982638	−	0.0713928i
$756$	−2.52764	+	0.781678i	−0.0919295	+	0.0284293i
$757$	−0.269730	−	0.830144i	−0.00980351	−	0.0301721i	0.946035	−	0.324064i	$-0.105049\pi$
$757$	−0.269730	−	0.830144i	−0.00980351	−	0.0301721i	−0.955839	+	0.293892i	$0.905049\pi$
$758$	23.3484	+	13.4802i	0.848051	+	0.489622i
$759$	−6.50981	−	6.11066i	−0.236291	−	0.221803i
$760$	−0.0411450	−	0.0712651i	−0.00149248	−	0.00258506i
$761$	−23.1038	−	4.91086i	−0.837512	−	0.178019i	−0.230861	−	0.972987i	$-0.574154\pi$
$761$	−23.1038	−	4.91086i	−0.837512	−	0.178019i	−0.606651	+	0.794968i	$0.707488\pi$
$762$	−4.76038	+	6.55210i	−0.172450	+	0.237357i
$763$	−0.260264	+	18.2802i	−0.00942219	+	0.661789i
$764$	−4.85995	+	14.9574i	−0.175827	+	0.541140i
$765$	0.500795	−	0.450918i	0.0181063	−	0.0163030i
$766$	−29.7872	−	13.2621i	−1.07625	−	0.479179i
$767$	−35.3377	−	3.71414i	−1.27597	−	0.134110i
$768$	0.207912	−	0.978148i	0.00750237	−	0.0352959i
$769$	−54.3911			−1.96139			−0.980696	−	0.195537i	$-0.937355\pi$
$769$	−54.3911			−1.96139			−0.980696	+	0.195537i	$0.937355\pi$
$770$	−0.315965	+	2.24702i	−0.0113866	+	0.0809768i
$771$	14.9465			0.538284
$772$	−4.23890	+	19.9424i	−0.152561	+	0.717744i
$773$	23.1483	+	2.43298i	0.832585	+	0.0875082i	0.511223	−	0.859448i	$-0.329193\pi$
$773$	23.1483	+	2.43298i	0.832585	+	0.0875082i	0.321362	+	0.946956i	$0.395859\pi$
$774$	5.47424	+	2.43729i	0.196768	+	0.0876066i
$775$	21.7751	−	19.6064i	0.782185	−	0.704283i
$776$	0.528688	−	1.62713i	0.0189788	−	0.0584107i
$777$	10.7880	+	6.43492i	0.387016	+	0.230851i
$778$	9.71848	−	13.3763i	0.348425	−	0.479565i
$779$	−1.38403	−	0.294185i	−0.0495880	−	0.0105403i
$780$	0.407221	+	0.705327i	0.0145808	+	0.0252548i
$781$	−42.7094	−	20.0870i	−1.52826	−	0.718770i
$782$	−6.07556	−	3.50773i	−0.217262	−	0.125436i
$783$	−2.30235	−	7.08592i	−0.0822794	−	0.253230i
$784$	2.35177	−	6.59312i	0.0839919	−	0.235468i
$785$	0.153836	−	0.111768i	0.00549065	−	0.00398919i
$786$	4.03226	+	4.47828i	0.143826	+	0.159735i
$787$	−1.45107	+	0.308433i	−0.0517249	+	0.0109945i	−0.233701	−	0.972308i	$-0.575084\pi$
$787$	−1.45107	+	0.308433i	−0.0517249	+	0.0109945i	0.181977	+	0.983303i	$0.441751\pi$
$788$	0.630853	−	1.41692i	0.0224732	−	0.0504756i
$789$	−16.6256	+	7.40219i	−0.591887	+	0.263525i
$790$	3.00019	−	0.974822i	0.106742	−	0.0346826i
$791$	−18.5865	+	7.96016i	−0.660860	+	0.283031i
$792$	−1.89339	−	2.72306i	−0.0672787	−	0.0967598i
$793$	8.76440	−	15.1804i	0.311233	−	0.539071i
$794$	−23.6145	+	26.2266i	−0.838048	+	0.930746i
$795$	−0.287847	+	2.73868i	−0.0102089	+	0.0971309i
$796$	−9.82115	+	1.03224i	−0.348101	+	0.0365869i
$797$	38.2199	+	12.4184i	1.35382	+	0.439883i	0.893975	−	0.448117i	$-0.147905\pi$
$797$	38.2199	+	12.4184i	1.35382	+	0.439883i	0.459845	+	0.887999i	$0.347905\pi$
$798$	0.764201	+	0.353364i	0.0270524	+	0.0125090i
$799$	1.49351	+	2.05564i	0.0528366	+	0.0727233i
$800$	2.00649	+	4.50664i	0.0709400	+	0.159334i
$801$	0.929908	+	0.837293i	0.0328567	+	0.0295843i
$802$	−9.85712	+	5.69101i	−0.348067	+	0.200957i
$803$	24.2900	−	40.1258i	0.857177	−	1.41601i
$804$		−	8.22146i		−	0.289949i
$805$	1.74338	+	0.594027i	0.0614460	+	0.0209367i
$806$	−15.1345	−	10.9959i	−0.533092	−	0.387314i
$807$	0.534047	+	5.08112i	0.0187993	+	0.178864i
$808$	2.25228	+	10.5961i	0.0792349	+	0.372771i
$809$	0.528269	+	2.48531i	0.0185730	+	0.0873789i	0.986458	−	0.164015i	$-0.0524445\pi$
$809$	0.528269	+	2.48531i	0.0185730	+	0.0873789i	−0.967885	+	0.251394i	$0.919111\pi$
$810$	−0.0270301	−	0.257174i	−0.000949740	−	0.00903617i
$811$	−17.7240	−	12.8772i	−0.622373	−	0.452181i	0.231377	−	0.972864i	$-0.425677\pi$
$811$	−17.7240	−	12.8772i	−0.622373	−	0.452181i	−0.853750	+	0.520684i	$0.825677\pi$
$812$	18.6590	+	6.35773i	0.654801	+	0.223113i
$813$		−	27.9411i		−	0.979937i
$814$	−3.59265	+	15.3312i	−0.125922	+	0.537358i
$815$	2.75631	−	1.59136i	0.0965494	−	0.0557428i
$816$	−1.93664	−	1.74375i	−0.0677958	−	0.0610436i
$817$	−0.775606	−	1.74204i	−0.0271350	−	0.0609463i
$818$	−9.94820	−	13.6925i	−0.347831	−	0.478748i
$819$	−7.56346	−	3.49733i	−0.264289	−	0.122206i
$820$	−1.09352	−	0.355306i	−0.0381873	−	0.0124078i
$821$	9.45006	−	0.993241i	0.329809	−	0.0346644i	0.0618232	−	0.998087i	$-0.480309\pi$
$821$	9.45006	−	0.993241i	0.329809	−	0.0346644i	0.267986	+	0.963423i	$0.413642\pi$
$822$	0.477573	−	4.54381i	0.0166573	−	0.158483i
$823$	11.3558	−	12.6119i	0.395838	−	0.439623i	−0.511973	−	0.859001i	$-0.671085\pi$
$823$	11.3558	−	12.6119i	0.395838	−	0.439623i	0.907812	+	0.419378i	$0.137752\pi$
$824$	5.10757	−	8.84657i	0.177931	−	0.308185i
$825$	15.4523	+	5.37760i	0.537982	+	0.187224i
$826$	−27.4382	+	11.7512i	−0.954699	+	0.408875i
$827$	24.8456	−	8.07282i	0.863965	−	0.280719i	0.156682	−	0.987649i	$-0.449920\pi$
$827$	24.8456	−	8.07282i	0.863965	−	0.280719i	0.707284	+	0.706930i	$0.249920\pi$
$828$	−2.45930	+	1.09495i	−0.0854666	+	0.0380522i
$829$	−8.78371	+	19.7285i	−0.305071	+	0.685200i	−0.999406	−	0.0344512i	$-0.989032\pi$
$829$	−8.78371	+	19.7285i	−0.305071	+	0.685200i	0.694336	+	0.719651i	$0.255698\pi$
$830$	−4.09631	+	0.870698i	−0.142185	+	0.0302224i
$831$	−18.0810	−	20.0810i	−0.627224	−	0.696603i
$832$	2.54803	−	1.85125i	0.0883371	−	0.0641807i
$833$	−11.8154	−	13.8985i	−0.409379	−	0.481553i
$834$	−1.24637	−	3.83594i	−0.0431583	−	0.132828i
$835$	−1.62355	−	0.937355i	−0.0561851	−	0.0324385i
$836$	−0.132070	+	1.04714i	−0.00456775	+	0.0362160i
$837$	2.96985	+	5.14393i	0.102653	+	0.177800i
$838$	33.3846	+	7.09612i	1.15325	+	0.245132i
$839$	20.3378	−	27.9926i	0.702138	−	0.966411i	−0.297792	−	0.954631i	$-0.596250\pi$
$839$	20.3378	−	27.9926i	0.702138	−	0.966411i	0.999931	−	0.0117798i	$-0.00374972\pi$
$840$	0.587575	+	0.350483i	0.0202733	+	0.0120928i
$841$	−8.19236	+	25.2135i	−0.282495	+	0.869431i
$842$	−23.9312	+	21.5477i	−0.824722	+	0.742583i
$843$	−6.74838	−	3.00457i	−0.232427	−	0.103483i
$844$	−21.2281	−	2.23117i	−0.730702	−	0.0767999i
$845$	0.165614	−	0.779152i	0.00569729	−	0.0268037i
$846$	0.975023			0.0335220
$847$	20.6482	−	20.5098i	0.709480	−	0.704725i
$848$	10.6491			0.365693
$849$	−1.34280	+	6.31739i	−0.0460849	+	0.216812i
$850$	12.7853	+	1.34379i	0.438533	+	0.0460916i
$851$	11.6762	+	5.19856i	0.400253	+	0.178204i
$852$	−10.5753	+	9.52207i	−0.362305	+	0.326221i
$853$	−6.54416	+	20.1409i	−0.224068	+	0.689610i	0.774317	+	0.632798i	$0.218094\pi$
$853$	−6.54416	+	20.1409i	−0.224068	+	0.689610i	−0.998385	+	0.0568121i	$0.981906\pi$
$854$	0.209624	−	14.7235i	0.00717320	−	0.503826i
$855$	−0.0483688	+	0.0665739i	−0.00165418	+	0.00227678i
$856$	−2.51324	−	0.534205i	−0.0859007	−	0.0182588i
$857$	13.0623	+	22.6246i	0.446200	+	0.772842i	0.998135	−	0.0610458i	$-0.0194436\pi$
$857$	13.0623	+	22.6246i	0.446200	+	0.772842i	−0.551935	+	0.833887i	$0.686110\pi$
$858$	1.30713	−	10.3637i	0.0446247	−	0.353812i
$859$	−10.8888	−	6.28664i	−0.371521	−	0.214498i	0.302602	−	0.953117i	$-0.402145\pi$
$859$	−10.8888	−	6.28664i	−0.371521	−	0.214498i	−0.674123	+	0.738620i	$0.735478\pi$
$860$	−0.478838	−	1.47371i	−0.0163283	−	0.0502532i
$861$	11.2389	−	3.47564i	0.383020	−	0.118450i
$862$	−3.20336	+	2.32738i	−0.109107	+	0.0792707i
$863$	13.6407	+	15.1495i	0.464334	+	0.515695i	0.929145	−	0.369715i	$-0.120545\pi$
$863$	13.6407	+	15.1495i	0.464334	+	0.515695i	−0.464812	+	0.885410i	$0.653878\pi$
$864$	−0.978148	+	0.207912i	−0.0332773	+	0.00707330i
$865$	2.72146	−	6.11249i	0.0925323	−	0.207831i
$866$	−24.6422	+	10.9714i	−0.837375	+	0.372823i
$867$	9.70911	−	3.15468i	0.329739	−	0.107139i
$868$	−15.6039	−	1.86499i	−0.529631	−	0.0633018i
$869$	−38.2122	−	13.2983i	−1.29626	−	0.451114i
$870$	−0.963324	+	1.66853i	−0.0326597	+	0.0565683i
$871$	17.3264	−	19.2429i	0.587081	−	0.652020i
$872$	−0.722290	+	6.87213i	−0.0244598	+	0.232720i
$873$	−1.70150	+	0.178835i	−0.0575870	+	0.00605264i
$874$	0.814745	+	0.264727i	0.0275592	+	0.00895452i
$875$	−6.76811	+	0.614077i	−0.228804	+	0.0207596i
$876$	−8.31270	−	11.4415i	−0.280860	−	0.386571i
$877$	−11.6313	−	26.1243i	−0.392761	−	0.882156i	−0.996390	−	0.0848905i	$-0.972946\pi$
$877$	−11.6313	−	26.1243i	−0.392761	−	0.882156i	0.603629	−	0.797265i	$-0.293721\pi$
$878$	−8.06845	−	7.26486i	−0.272297	−	0.245177i
$879$	−16.7404	+	9.66510i	−0.564641	+	0.325996i
$880$	−0.195677	+	0.835027i	−0.00659626	+	0.0281488i
$881$		−	4.04742i		−	0.136361i	−0.997673	−	0.0681805i	$-0.978281\pi$
$881$		−	4.04742i		−	0.136361i	0.997673	−	0.0681805i	$-0.0217194\pi$
$882$	−6.97966	+	0.533210i	−0.235017	+	0.0179541i
$883$	−36.1691	−	26.2784i	−1.21719	−	0.884337i	−0.221322	−	0.975201i	$-0.571037\pi$
$883$	−36.1691	−	26.2784i	−1.21719	−	0.884337i	−0.995863	+	0.0908635i	$0.971037\pi$
$884$	−0.857939	−	8.16274i	−0.0288556	−	0.274543i
$885$	−0.606552	−	2.85360i	−0.0203890	−	0.0959229i
$886$	−0.716814	−	3.37234i	−0.0240818	−	0.113296i
$887$	4.44139	+	42.2570i	0.149127	+	1.41885i	0.771549	+	0.636170i	$0.219482\pi$
$887$	4.44139	+	42.2570i	0.149127	+	1.41885i	−0.622422	+	0.782682i	$0.713851\pi$
$888$	3.84101	+	2.79066i	0.128896	+	0.0936484i
$889$	−16.1262	+	14.1097i	−0.540857	+	0.473223i
$890$		−	0.323578i		−	0.0108464i
$891$	−1.71753	+	2.83727i	−0.0575395	+	0.0950520i
$892$	−10.8478	+	6.26296i	−0.363210	+	0.209699i
$893$	−0.230580	−	0.207616i	−0.00771608	−	0.00694759i
$894$	−0.638919	−	1.43504i	−0.0213686	−	0.0479948i
$895$	−0.139693	−	0.192271i	−0.00466942	−	0.00642690i
$896$	1.11042	−	2.40145i	0.0370966	−	0.0802268i
$897$	−8.06371	−	2.62006i	−0.269240	−	0.0874812i
$898$	−14.5467	+	1.52892i	−0.485430	+	0.0510207i
$899$	4.62582	−	44.0117i	0.154280	−	1.46787i
$900$	3.30091	−	3.66603i	0.110030	−	0.122201i
$901$	13.8758	−	24.0336i	0.462271	−	0.800676i
$902$	8.41874	+	12.1078i	0.280314	+	0.403145i
$903$	12.6923	+	9.50049i	0.422374	+	0.316156i
$904$	−7.26816	+	2.36157i	−0.241735	+	0.0785446i
$905$	1.57410	−	0.700833i	0.0523247	−	0.0232965i
$906$	−5.24940	+	11.7904i	−0.174400	+	0.391708i
$907$	32.4675	−	6.90119i	1.07807	−	0.229150i	0.365540	−	0.930795i	$-0.380884\pi$
$907$	32.4675	−	6.90119i	1.07807	−	0.229150i	0.712526	+	0.701645i	$0.247551\pi$
$908$	8.09737	+	8.99304i	0.268721	+	0.298444i
$909$	8.76397	−	6.36740i	0.290683	−	0.211193i
$910$	0.636631	+	2.05862i	0.0211041	+	0.0682425i
$911$	−10.6870	−	32.8913i	−0.354077	−	1.08974i	−0.956543	−	0.291592i	$-0.905815\pi$
$911$	−10.6870	−	32.8913i	−0.354077	−	1.08974i	0.602466	−	0.798145i	$-0.294185\pi$
$912$	0.275591	+	0.159112i	0.00912572	+	0.00526874i
$913$	48.6048	+	22.8597i	1.60858	+	0.756547i
$914$	17.6226	+	30.5232i	0.582903	+	1.00962i
$915$	1.40774	+	0.299224i	0.0465384	+	0.00989203i
$916$	13.1711	−	18.1284i	0.435184	−	0.598979i
$917$	7.77443	+	13.9197i	0.256734	+	0.459667i
$918$	−0.805298	+	2.47845i	−0.0265788	+	0.0818011i
$919$	0.644092	−	0.579943i	0.0212466	−	0.0191306i	−0.658439	−	0.752634i	$-0.728783\pi$
$919$	0.644092	−	0.579943i	0.0212466	−	0.0191306i	0.679686	+	0.733504i	$0.262116\pi$
$920$	0.635952	+	0.283144i	0.0209667	+	0.00933498i
$921$	7.31867	+	0.769223i	0.241158	+	0.0253468i
$922$	1.85120	−	8.70922i	0.0609661	−	0.286823i
$923$	−44.8196			−1.47525
$924$	−3.28657	−	8.13624i	−0.108120	−	0.267663i
$925$	−23.4213			−0.770087
$926$	1.47484	−	6.93856i	0.0484661	−	0.228015i
$927$	−10.1592	−	1.06777i	−0.333671	−	0.0350702i
$928$	6.80644	+	3.03042i	0.223432	+	0.0994784i
$929$	−6.84854	+	6.16645i	−0.224693	+	0.202315i	−0.773787	−	0.633446i	$-0.781640\pi$
$929$	−6.84854	+	6.16645i	−0.224693	+	0.202315i	0.549093	+	0.835761i	$0.314973\pi$
$930$	0.474635	−	1.46077i	0.0155639	−	0.0479007i
$931$	1.76414	+	1.36011i	0.0578173	+	0.0445758i
$932$	−4.85240	+	6.67875i	−0.158946	+	0.218770i
$933$	5.00377	+	1.06358i	0.163816	+	0.0348202i
$934$	5.17761	+	8.96788i	0.169416	+	0.293438i
$935$	1.62957	+	1.52966i	0.0532928	+	0.0500251i
$936$	−2.72758	−	1.57477i	−0.0891538	−	0.0514730i
$937$	−11.3471	−	34.9228i	−0.370694	−	1.14088i	−0.946338	−	0.323178i	$-0.895249\pi$
$937$	−11.3471	−	34.9228i	−0.370694	−	1.14088i	0.575644	−	0.817700i	$-0.304751\pi$
$938$	4.82492	−	21.2101i	0.157539	−	0.692533i
$939$	11.8116	−	8.58162i	0.385457	−	0.280051i
$940$	−0.168709	−	0.187370i	−0.00550268	−	0.00611135i
$941$	50.2525	−	10.6815i	1.63819	−	0.348207i	0.705447	−	0.708762i	$-0.250746\pi$
$941$	50.2525	−	10.6815i	1.63819	−	0.348207i	0.932738	+	0.360555i	$0.117413\pi$
$942$	−0.299090	+	0.671766i	−0.00974487	+	0.0218873i
$943$	10.9350	−	4.86858i	0.356093	−	0.158543i
$944$	−10.7296	+	3.48626i	−0.349218	+	0.113468i
$945$	0.0811940	−	0.679331i	0.00264124	−	0.0220986i
$946$	−6.53220	+	18.7701i	−0.212380	+	0.610268i
$947$	26.9261	−	46.6373i	0.874980	−	1.51551i	0.0181955	−	0.999834i	$-0.494208\pi$
$947$	26.9261	−	46.6373i	0.874980	−	1.51551i	0.856784	−	0.515675i	$-0.172459\pi$
$948$	−8.16284	+	9.06575i	−0.265117	+	0.294442i
$949$	4.65592	−	44.2981i	0.151138	−	1.43798i
$950$	−1.56124	+	0.164093i	−0.0506535	+	0.00532389i
$951$	21.6229	+	7.02572i	0.701171	+	0.227824i
$952$	−3.97286	−	5.63516i	−0.128761	−	0.182637i
$953$	−34.5095	−	47.4983i	−1.11787	−	1.53862i	−0.809277	−	0.587427i	$-0.800141\pi$
$953$	−34.5095	−	47.4983i	−1.11787	−	1.53862i	−0.308596	−	0.951193i	$-0.599859\pi$
$954$	−4.33139	−	9.72847i	−0.140234	−	0.314971i
$955$	−3.02229	−	2.72128i	−0.0977989	−	0.0880585i
$956$	6.54877	−	3.78093i	0.211802	−	0.122284i
$957$	22.7780	−	9.58038i	0.736308	−	0.309690i
$958$			12.3824i			0.400056i
$959$	3.89868	−	11.4420i	0.125895	−	0.369482i
$960$	0.209204	+	0.151996i	0.00675203	+	0.00490564i
$961$	0.447384	+	4.25658i	0.0144318	+	0.137309i
$962$	3.10896	+	14.6265i	0.100237	+	0.471577i
$963$	0.534205	+	2.51324i	0.0172145	+	0.0809879i
$964$	−1.56096	−	14.8515i	−0.0502750	−	0.478335i
$965$	−4.26525	−	3.09888i	−0.137303	−	0.0997566i
$966$	−6.98720	+	1.38151i	−0.224809	+	0.0444495i
$967$			17.2008i			0.553140i	0.960994	+	0.276570i	$0.0891978\pi$
$967$			17.2008i			0.553140i	−0.960994	+	0.276570i	$0.910802\pi$
$968$	8.47283	−	7.01507i	0.272327	−	0.225473i
$969$	0.718190	−	0.414647i	0.0230716	−	0.0133204i
$970$	0.328778	+	0.296033i	0.0105564	+	0.00950506i
$971$	−15.8722	−	35.6495i	−0.509362	−	1.14405i	−0.966969	−	0.254892i	$-0.917960\pi$
$971$	−15.8722	−	35.6495i	−0.509362	−	1.14405i	0.457607	−	0.889155i	$-0.348707\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	−0.964250	−	10.6276i	−0.0309124	−	0.340704i
$974$	−31.5941	−	10.2655i	−1.01234	−	0.328929i
$975$	15.4520	−	1.62407i	0.494860	−	0.0520118i
$976$	0.581754	−	5.53502i	0.0186215	−	0.177172i
$977$	−13.5999	+	15.1042i	−0.435100	+	0.483227i	−0.920321	−	0.391164i	$-0.872072\pi$
$977$	−13.5999	+	15.1042i	−0.435100	+	0.483227i	0.485221	+	0.874392i	$0.338739\pi$
$978$	−6.15397	+	10.6590i	−0.196782	+	0.340837i
$979$	−2.50851	+	3.30622i	−0.0801723	+	0.105667i
$980$	1.31016	+	1.24902i	0.0418516	+	0.0398985i
$981$	6.57178	−	2.13530i	0.209821	−	0.0681749i
$982$	8.35010	−	3.71771i	0.266463	−	0.118637i
$983$	−20.1154	+	45.1800i	−0.641582	+	1.44102i	0.240843	+	0.970564i	$0.422576\pi$
$983$	−20.1154	+	45.1800i	−0.641582	+	1.44102i	−0.882425	+	0.470453i	$0.844090\pi$
$984$	4.34922	−	0.924456i	0.138648	−	0.0294706i
$985$	0.268373	+	0.298058i	0.00855106	+	0.00949692i
$986$	15.7080	−	11.4126i	0.500246	−	0.363450i
$987$	2.51541	+	0.572211i	0.0800662	+	0.0182137i
$988$	0.309716	+	0.953208i	0.00985338	+	0.0303256i
$989$	13.9703	+	8.06576i	0.444230	+	0.256476i
$990$	0.842424	−	0.160876i	0.0267740	−	0.00511299i
$991$	23.9443	+	41.4727i	0.760615	+	1.31742i	0.942534	+	0.334110i	$0.108436\pi$
$991$	23.9443	+	41.4727i	0.760615	+	1.31742i	−0.181919	+	0.983314i	$0.558231\pi$
$992$	−5.80990	−	1.23493i	−0.184465	−	0.0392092i
$993$	−14.2738	+	19.6462i	−0.452964	+	0.623452i
$994$	−32.8709	+	18.3591i	−1.04260	+	0.582315i
$995$	0.789120	−	2.42866i	0.0250168	−	0.0769937i
$996$	12.0351	−	10.8364i	0.381347	−	0.343366i
$997$	25.2177	+	11.2276i	0.798651	+	0.355582i	0.765147	−	0.643856i	$-0.222666\pi$
$997$	25.2177	+	11.2276i	0.798651	+	0.355582i	0.0335046	+	0.999439i	$0.489333\pi$
$998$	−43.5586	−	4.57819i	−1.37882	−	0.144920i
$999$	0.987114	−	4.64400i	0.0312309	−	0.146930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.b.61.7	yes	64
7.3	odd	6		462.2.ba.a.325.6	yes	64
11.2	odd	10		462.2.ba.a.145.6	✓	64
77.24	even	30	inner	462.2.ba.b.409.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.145.6	✓	64	11.2	odd	10
462.2.ba.a.325.6	yes	64	7.3	odd	6
462.2.ba.b.61.7	yes	64	1.1	even	1	trivial
462.2.ba.b.409.7	yes	64	77.24	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.192170 - 0.173031i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.35536 + 2.27222i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(-0.994522 - 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.192170 - 0.173031i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.35536 + 2.27222i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.129295 - 0.223946i) q^{10} +(-0.415022 + 3.29056i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.973262 + 2.99539i) q^{13} +(1.94077 + 1.79816i) q^{14} +(-0.209204 + 0.151996i) q^{15} +(0.669131 + 0.743145i) q^{16} +(2.54905 - 0.541818i) q^{17} +(0.406737 - 0.913545i) q^{18} +(-0.290713 + 0.129434i) q^{19} +(-0.245934 + 0.0799088i) q^{20} +(1.58545 - 2.11810i) q^{21} +(3.13236 + 1.09010i) q^{22} +(1.34602 - 2.33137i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.515653 + 4.90611i) q^{25} +(3.13229 - 0.329217i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(2.16238 - 1.52450i) q^{28} +(4.37934 + 6.02764i) q^{29} +(0.105178 + 0.236234i) q^{30} +(-4.41406 - 3.97443i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.756705 - 3.22915i) q^{33} -2.60600i q^{34} +(0.132705 + 0.671173i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.496275 + 4.72175i) q^{37} +(0.0661627 + 0.311271i) q^{38} +(-0.654827 - 3.08072i) q^{39} +(0.0270301 + 0.257174i) q^{40} +(3.59720 + 2.61352i) q^{41} +(-1.74218 - 1.99118i) q^{42} +5.99231i q^{43} +(1.71753 - 2.83727i) q^{44} +(0.223946 - 0.129295i) q^{45} +(-2.00058 - 1.80133i) q^{46} +(0.396578 + 0.890728i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-3.32600 - 6.15936i) q^{49} +(4.69169 + 1.52442i) q^{50} +(-2.59172 + 0.272401i) q^{51} +(0.329217 - 3.13229i) q^{52} +(7.12566 - 7.91385i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.489613 + 0.704158i) q^{55} +(-1.04161 - 2.43209i) q^{56} +(0.302650 - 0.0983369i) q^{57} +(6.80644 - 3.03042i) q^{58} +(-4.58871 + 10.3064i) q^{59} +(0.252940 - 0.0537640i) q^{60} +(-3.72405 - 4.13598i) q^{61} +(-4.80532 + 3.49127i) q^{62} +(-1.79816 + 1.94077i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.705327 + 0.407221i) q^{65} +(-3.00126 - 1.41155i) q^{66} +(-4.11073 - 7.11999i) q^{67} +(-2.54905 - 0.541818i) q^{68} +(-1.58234 + 2.17791i) q^{69} +(0.684097 + 0.00973980i) q^{70} +(-4.39747 + 13.5340i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-12.9197 - 5.75224i) q^{73} +(4.72175 + 0.496275i) q^{74} +(1.02566 - 4.82533i) q^{75} +0.318225 q^{76} +(-6.91437 - 5.40291i) q^{77} -3.14954 q^{78} +(-2.53635 + 11.9326i) q^{79} +(0.257174 + 0.0270301i) q^{80} +(0.913545 + 0.406737i) q^{81} +(3.30431 - 2.97521i) q^{82} +(5.00447 - 15.4022i) q^{83} +(-2.30989 + 1.29012i) q^{84} +(0.396101 - 0.545186i) q^{85} +(5.86136 + 1.24587i) q^{86} +(-3.72529 - 6.45239i) q^{87} +(-2.41817 - 2.26990i) q^{88} +(1.08367 + 0.625657i) q^{89} +(-0.0799088 - 0.245934i) q^{90} +(-8.12532 - 1.84837i) q^{91} +(-2.17791 + 1.58234i) q^{92} +(3.97443 + 4.41406i) q^{93} +(0.953716 - 0.202719i) q^{94} +(-0.0334703 + 0.0751756i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-1.62713 + 0.528688i) q^{97} +(-6.71628 + 1.97271i) q^{98} +(-1.09010 + 3.13236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 2 q^{5} + 16 q^{6} + 16 q^{7} - 8 q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} - 10 q^{19} - 20 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 8 q^{24} - 12 q^{26} - 20 q^{29} - 18 q^{30} + 34 q^{31} + 8 q^{33} - 2 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} - 18 q^{39} + 12 q^{40} + 28 q^{41} + 4 q^{42} + 6 q^{44} - 12 q^{45} + 42 q^{46} + 24 q^{47} - 44 q^{49} + 14 q^{51} - 32 q^{54} + 14 q^{55} - 4 q^{56} - 10 q^{58} - 30 q^{59} + 2 q^{60} - 28 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{64} - 12 q^{65} - 4 q^{66} + 16 q^{67} - 30 q^{68} - 30 q^{70} - 24 q^{71} - 116 q^{73} - 44 q^{74} + 12 q^{75} - 32 q^{77} - 18 q^{80} + 8 q^{81} - 28 q^{82} - 8 q^{83} - 2 q^{84} - 80 q^{85} - 18 q^{86} - 10 q^{87} - 14 q^{88} - 24 q^{89} - 4 q^{90} + 48 q^{91} + 8 q^{92} + 76 q^{93} + 6 q^{94} + 98 q^{95} - 8 q^{96} - 120 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 2 * q^5 + 16 * q^6 + 16 * q^7 - 8 * q^9 - 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 - 10 * q^19 - 20 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 8 * q^24 - 12 * q^26 - 20 * q^29 - 18 * q^30 + 34 * q^31 + 8 * q^33 - 2 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 - 18 * q^39 + 12 * q^40 + 28 * q^41 + 4 * q^42 + 6 * q^44 - 12 * q^45 + 42 * q^46 + 24 * q^47 - 44 * q^49 + 14 * q^51 - 32 * q^54 + 14 * q^55 - 4 * q^56 - 10 * q^58 - 30 * q^59 + 2 * q^60 - 28 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^64 - 12 * q^65 - 4 * q^66 + 16 * q^67 - 30 * q^68 - 30 * q^70 - 24 * q^71 - 116 * q^73 - 44 * q^74 + 12 * q^75 - 32 * q^77 - 18 * q^80 + 8 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 80 * q^85 - 18 * q^86 - 10 * q^87 - 14 * q^88 - 24 * q^89 - 4 * q^90 + 48 * q^91 + 8 * q^92 + 76 * q^93 + 6 * q^94 + 98 * q^95 - 8 * q^96 - 120 * q^97 - 40 * q^98 + 8 * q^99

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