LMFDB - Embedded newform 462.2.bc.b.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.8
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(0.110709 + 1.72851i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.75629 + 3.94468i) q^{5} +(-1.73061 - 0.0705756i) q^{6} +(2.64495 + 0.0650804i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97549 + 0.382724i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(0.110709 + 1.72851i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.75629 + 3.94468i) q^{5} +(-1.73061 - 0.0705756i) q^{6} +(2.64495 + 0.0650804i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97549 + 0.382724i) q^{9} +(-3.73949 - 2.15900i) q^{10} +(3.29397 + 0.387016i) q^{11} +(0.251087 - 1.71375i) q^{12} +(-2.24820 + 3.09438i) q^{13} +(-0.341197 + 2.62366i) q^{14} +(-7.01286 - 2.59904i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.195558 - 1.86061i) q^{17} +(-0.0696043 - 2.99919i) q^{18} +(0.385005 + 1.81130i) q^{19} +(2.53805 - 3.49333i) q^{20} +(0.180329 + 4.57903i) q^{21} +(-0.729209 + 3.23547i) q^{22} +(5.76787 - 3.33008i) q^{23} +(1.67812 + 0.428848i) q^{24} +(-9.13033 - 10.1403i) q^{25} +(-2.84243 - 2.55934i) q^{26} +(-0.990956 - 5.10078i) q^{27} +(-2.57362 - 0.613574i) q^{28} +(-1.60027 - 4.92514i) q^{29} +(3.31785 - 6.70277i) q^{30} +(1.16659 - 0.519398i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.304288 + 5.73650i) q^{33} +1.87086 q^{34} +(-4.90201 + 10.3192i) q^{35} +(2.99004 + 0.244278i) q^{36} +(3.11006 - 3.45407i) q^{37} +(-1.84163 + 0.193563i) q^{38} +(-5.59756 - 3.54346i) q^{39} +(3.20889 + 2.88930i) q^{40} +(-2.90786 + 8.94949i) q^{41} +(-4.57279 - 0.299298i) q^{42} +2.90165i q^{43} +(-3.14152 - 1.06341i) q^{44} +(3.71608 - 12.4095i) q^{45} +(2.70893 + 6.08437i) q^{46} +(-1.28772 - 6.05823i) q^{47} +(-0.601910 + 1.62410i) q^{48} +(6.99153 + 0.344269i) q^{49} +(11.0391 - 8.02037i) q^{50} +(3.19444 - 0.544012i) q^{51} +(2.84243 - 2.55934i) q^{52} +(5.16057 + 11.5908i) q^{53} +(5.17643 - 0.452350i) q^{54} +(-7.31180 + 12.3139i) q^{55} +(0.879230 - 2.49539i) q^{56} +(-3.08823 + 0.866012i) q^{57} +(5.06543 - 1.07669i) q^{58} +(0.0588568 - 0.276899i) q^{59} +(6.31924 + 4.00030i) q^{60} +(-3.90556 + 8.77203i) q^{61} +(0.394611 + 1.21449i) q^{62} +(-7.89492 + 0.818640i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-8.25787 - 14.3031i) q^{65} +(-5.67327 - 0.902248i) q^{66} +(-3.82181 + 6.61957i) q^{67} +(-0.195558 + 1.86061i) q^{68} +(6.39464 + 9.60115i) q^{69} +(-9.75026 - 5.95381i) q^{70} +(0.878299 + 1.20888i) q^{71} +(-0.555484 + 2.94812i) q^{72} +(1.25945 - 5.92524i) q^{73} +(3.11006 + 3.45407i) q^{74} +(16.5167 - 16.9045i) q^{75} -1.85177i q^{76} +(8.68719 + 1.23801i) q^{77} +(4.10915 - 5.19651i) q^{78} +(4.12085 + 0.433118i) q^{79} +(-3.20889 + 2.88930i) q^{80} +(8.70704 - 2.27758i) q^{81} +(-8.59651 - 3.82741i) q^{82} +(-4.25224 + 3.08943i) q^{83} +(0.775645 - 4.51646i) q^{84} +(7.68299 + 2.49635i) q^{85} +(-2.88576 - 0.303305i) q^{86} +(8.33598 - 3.31135i) q^{87} +(1.38597 - 3.01315i) q^{88} +(0.326895 - 0.188733i) q^{89} +(11.9531 + 4.99287i) q^{90} +(-6.14776 + 8.03817i) q^{91} +(-6.33420 + 2.05810i) q^{92} +(1.02694 + 1.95895i) q^{93} +(6.15965 - 0.647405i) q^{94} +(-7.82120 - 1.66245i) q^{95} +(-1.55229 - 0.768377i) q^{96} +(-3.32691 - 2.41714i) q^{97} +(-1.07320 + 6.91724i) q^{98} +(-9.94928 + 0.109119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	0.110709	+	1.72851i	0.0639180	+	0.997955i
$3$	0.110709	+	1.72851i	0.0639180	+	0.997955i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−1.75629	+	3.94468i	−0.785435	+	1.76412i	−0.154938	+	0.987924i	$0.549518\pi$
$5$	−1.75629	+	3.94468i	−0.785435	+	1.76412i	−0.630497	+	0.776192i	$0.717149\pi$
$6$	−1.73061	−	0.0705756i	−0.706520	−	0.0288124i
$7$	2.64495	+	0.0650804i	0.999697	+	0.0245981i
$7$	2.64495	+	0.0650804i	0.999697	+	0.0245981i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−2.97549	+	0.382724i	−0.991829	+	0.127575i
$10$	−3.73949	−	2.15900i	−1.18253	−	0.682735i
$11$	3.29397	+	0.387016i	0.993168	+	0.116690i
$11$	3.29397	+	0.387016i	0.993168	+	0.116690i
$12$	0.251087	−	1.71375i	0.0724826	−	0.494718i
$13$	−2.24820	+	3.09438i	−0.623538	+	0.858227i	−0.997605	−	0.0691750i	$-0.977963\pi$
$13$	−2.24820	+	3.09438i	−0.623538	+	0.858227i	0.374066	+	0.927402i	$0.377963\pi$
$14$	−0.341197	+	2.62366i	−0.0911886	+	0.701202i
$15$	−7.01286	−	2.59904i	−1.81071	−	0.671070i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.195558	−	1.86061i	−0.0474299	−	0.451265i	−0.992303	−	0.123830i	$-0.960482\pi$
$17$	−0.195558	−	1.86061i	−0.0474299	−	0.451265i	0.944874	−	0.327435i	$-0.106184\pi$
$18$	−0.0696043	−	2.99919i	−0.0164059	−	0.706916i
$19$	0.385005	+	1.81130i	0.0883261	+	0.415542i	0.999989	+	0.00460363i	$0.00146539\pi$
$19$	0.385005	+	1.81130i	0.0883261	+	0.415542i	−0.911663	+	0.410938i	$0.865201\pi$
$20$	2.53805	−	3.49333i	0.567526	−	0.781132i
$21$	0.180329	+	4.57903i	0.0393509	+	0.999225i
$22$	−0.729209	+	3.23547i	−0.155468	+	0.689804i
$23$	5.76787	−	3.33008i	1.20268	−	0.694370i	0.241534	−	0.970392i	$-0.422350\pi$
$23$	5.76787	−	3.33008i	1.20268	−	0.694370i	0.961151	+	0.276022i	$0.0890163\pi$
$24$	1.67812	+	0.428848i	0.342545	+	0.0875382i
$25$	−9.13033	−	10.1403i	−1.82607	−	2.02805i
$26$	−2.84243	−	2.55934i	−0.557446	−	0.501927i
$27$	−0.990956	−	5.10078i	−0.190710	−	0.981647i
$28$	−2.57362	−	0.613574i	−0.486369	−	0.115955i
$29$	−1.60027	−	4.92514i	−0.297163	−	0.914575i	−0.982486	−	0.186335i	$-0.940339\pi$
$29$	−1.60027	−	4.92514i	−0.297163	−	0.914575i	0.685323	−	0.728239i	$-0.259661\pi$
$30$	3.31785	−	6.70277i	0.605754	−	1.22375i
$31$	1.16659	−	0.519398i	0.209525	−	0.0932866i	−0.299291	−	0.954162i	$-0.596750\pi$
$31$	1.16659	−	0.519398i	0.209525	−	0.0932866i	0.508816	+	0.860875i	$0.330083\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.304288	+	5.73650i	−0.0529697	+	0.998596i
$34$	1.87086			0.320850
$35$	−4.90201	+	10.3192i	−0.828591	+	1.74426i
$36$	2.99004	+	0.244278i	0.498340	+	0.0407130i
$37$	3.11006	−	3.45407i	0.511290	−	0.567845i	−0.431124	−	0.902292i	$-0.641883\pi$
$37$	3.11006	−	3.45407i	0.511290	−	0.567845i	0.942414	+	0.334447i	$0.108550\pi$
$38$	−1.84163	+	0.193563i	−0.298751	+	0.0314000i
$39$	−5.59756	−	3.54346i	−0.896327	−	0.567407i
$40$	3.20889	+	2.88930i	0.507371	+	0.456839i
$41$	−2.90786	+	8.94949i	−0.454132	+	1.39768i	0.418019	+	0.908438i	$0.362725\pi$
$41$	−2.90786	+	8.94949i	−0.454132	+	1.39768i	−0.872151	+	0.489237i	$0.837275\pi$
$42$	−4.57279	−	0.299298i	−0.705597	−	0.0461827i
$43$			2.90165i			0.442498i	0.975217	+	0.221249i	$0.0710134\pi$
$43$			2.90165i			0.442498i	−0.975217	+	0.221249i	$0.928987\pi$
$44$	−3.14152	−	1.06341i	−0.473602	−	0.160316i
$45$	3.71608	−	12.4095i	0.553961	−	1.84990i
$46$	2.70893	+	6.08437i	0.399411	+	0.897091i
$47$	−1.28772	−	6.05823i	−0.187833	−	0.883684i	−0.966584	−	0.256351i	$-0.917480\pi$
$47$	−1.28772	−	6.05823i	−0.187833	−	0.883684i	0.778751	−	0.627333i	$-0.215854\pi$
$48$	−0.601910	+	1.62410i	−0.0868782	+	0.234419i
$49$	6.99153	+	0.344269i	0.998790	+	0.0491813i
$50$	11.0391	−	8.02037i	1.56116	−	1.13425i
$51$	3.19444	−	0.544012i	0.447311	−	0.0761769i
$52$	2.84243	−	2.55934i	0.394174	−	0.354916i
$53$	5.16057	+	11.5908i	0.708859	+	1.59212i	0.802594	+	0.596526i	$0.203453\pi$
$53$	5.16057	+	11.5908i	0.708859	+	1.59212i	−0.0937353	+	0.995597i	$0.529881\pi$
$54$	5.17643	−	0.452350i	0.704422	−	0.0615570i
$55$	−7.31180	+	12.3139i	−0.985923	+	1.66041i
$56$	0.879230	−	2.49539i	0.117492	−	0.333460i
$57$	−3.08823	+	0.866012i	−0.409046	+	0.114706i
$58$	5.06543	−	1.07669i	0.665124	−	0.141376i
$59$	0.0588568	−	0.276899i	0.00766250	−	0.0360492i	−0.974150	−	0.225901i	$-0.927467\pi$
$59$	0.0588568	−	0.276899i	0.00766250	−	0.0360492i	0.981813	+	0.189852i	$0.0608007\pi$
$60$	6.31924	+	4.00030i	0.815810	+	0.516437i
$61$	−3.90556	+	8.77203i	−0.500055	+	1.12314i	0.470530	+	0.882384i	$0.344063\pi$
$61$	−3.90556	+	8.77203i	−0.500055	+	1.12314i	−0.970585	+	0.240759i	$0.922604\pi$
$62$	0.394611	+	1.21449i	0.0501157	+	0.154240i
$63$	−7.89492	+	0.818640i	−0.994667	+	0.103139i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−8.25787	−	14.3031i	−1.02426	−	1.77408i
$66$	−5.67327	−	0.902248i	−0.698331	−	0.111059i
$67$	−3.82181	+	6.61957i	−0.466908	+	0.808709i	−0.999285	−	0.0377985i	$-0.987966\pi$
$67$	−3.82181	+	6.61957i	−0.466908	+	0.808709i	0.532377	+	0.846507i	$0.321299\pi$
$68$	−0.195558	+	1.86061i	−0.0237149	+	0.225633i
$69$	6.39464	+	9.60115i	0.769824	+	1.15584i
$70$	−9.75026	−	5.95381i	−1.16538	−	0.711616i
$71$	0.878299	+	1.20888i	0.104235	+	0.143467i	0.857948	−	0.513737i	$-0.171739\pi$
$71$	0.878299	+	1.20888i	0.104235	+	0.143467i	−0.753713	+	0.657204i	$0.771739\pi$
$72$	−0.555484	+	2.94812i	−0.0654644	+	0.347440i
$73$	1.25945	−	5.92524i	0.147407	−	0.693496i	−0.840921	−	0.541158i	$-0.817986\pi$
$73$	1.25945	−	5.92524i	0.147407	−	0.693496i	0.988328	−	0.152339i	$-0.0486805\pi$
$74$	3.11006	+	3.45407i	0.361537	+	0.401527i
$75$	16.5167	−	16.9045i	1.90719	−	1.95196i
$76$		−	1.85177i		−	0.212413i
$77$	8.68719	+	1.23801i	0.989998	+	0.141084i
$78$	4.10915	−	5.19651i	0.465270	−	0.588389i
$79$	4.12085	+	0.433118i	0.463631	+	0.0487296i	0.333465	−	0.942763i	$-0.391782\pi$
$79$	4.12085	+	0.433118i	0.463631	+	0.0487296i	0.130167	+	0.991492i	$0.458449\pi$
$80$	−3.20889	+	2.88930i	−0.358765	+	0.323034i
$81$	8.70704	−	2.27758i	0.967449	−	0.253064i
$82$	−8.59651	−	3.82741i	−0.949325	−	0.422667i
$83$	−4.25224	+	3.08943i	−0.466744	+	0.339109i	−0.796171	−	0.605072i	$-0.793144\pi$
$83$	−4.25224	+	3.08943i	−0.466744	+	0.339109i	0.329427	+	0.944181i	$0.393144\pi$
$84$	0.775645	−	4.51646i	0.0846298	−	0.492786i
$85$	7.68299	+	2.49635i	0.833337	+	0.270768i
$86$	−2.88576	−	0.303305i	−0.311179	−	0.0327063i
$87$	8.33598	−	3.31135i	0.893711	−	0.355014i
$88$	1.38597	−	3.01315i	0.147744	−	0.321203i
$89$	0.326895	−	0.188733i	0.0346508	−	0.0200056i	−0.482575	−	0.875855i	$-0.660298\pi$
$89$	0.326895	−	0.188733i	0.0346508	−	0.0200056i	0.517225	+	0.855849i	$0.326965\pi$
$90$	11.9531	+	4.99287i	1.25997	+	0.526295i
$91$	−6.14776	+	8.03817i	−0.644461	+	0.842630i
$92$	−6.33420	+	2.05810i	−0.660386	+	0.214572i
$93$	1.02694	+	1.95895i	0.106488	+	0.203134i
$94$	6.15965	−	0.647405i	0.635319	−	0.0667748i
$95$	−7.82120	−	1.66245i	−0.802438	−	0.170563i
$96$	−1.55229	−	0.768377i	−0.158430	−	0.0784222i
$97$	−3.32691	−	2.41714i	−0.337797	−	0.245424i	0.405935	−	0.913902i	$-0.366946\pi$
$97$	−3.32691	−	2.41714i	−0.337797	−	0.245424i	−0.743732	+	0.668478i	$0.766946\pi$
$98$	−1.07320	+	6.91724i	−0.108409	+	0.698747i
$99$	−9.94928	+	0.109119i	−0.999940	+	0.0109669i
$100$	6.82253	+	11.8170i	0.682253	+	1.18170i
$101$	18.2429	−	8.12225i	1.81523	−	0.808194i	0.861354	−	0.508006i	$-0.169617\pi$
$101$	18.2429	−	8.12225i	1.81523	−	0.808194i	0.953880	−	0.300188i	$-0.0970496\pi$
$102$	0.207122	+	3.23380i	0.0205081	+	0.320194i
$103$	−6.69173	+	7.43192i	−0.659356	+	0.732289i	−0.976364	−	0.216134i	$-0.930655\pi$
$103$	−6.69173	+	7.43192i	−0.659356	+	0.732289i	0.317008	+	0.948423i	$0.397322\pi$
$104$	2.24820	+	3.09438i	0.220454	+	0.303429i
$105$	−18.3795	−	7.33074i	−1.79366	−	0.715407i
$106$	−12.0668	+	3.92073i	−1.17203	+	0.380815i
$107$	−8.33745	+	1.77218i	−0.806012	+	0.171323i	−0.592451	−	0.805607i	$-0.701840\pi$
$107$	−8.33745	+	1.77218i	−0.806012	+	0.171323i	−0.213561	+	0.976930i	$0.568506\pi$
$108$	−0.0912118	+	5.19535i	−0.00877686	+	0.499923i
$109$	0.521271	+	0.300956i	0.0499287	+	0.0288263i	0.524757	−	0.851252i	$-0.324156\pi$
$109$	0.521271	+	0.300956i	0.0499287	+	0.0288263i	−0.474828	+	0.880079i	$0.657490\pi$
$110$	−11.4822	−	8.55891i	−1.09478	−	0.816060i
$111$	6.31470	+	4.99336i	0.599364	+	0.473949i
$112$	2.38981	+	1.13525i	0.225816	+	0.107271i
$113$	2.79358	+	0.907689i	0.262798	+	0.0853882i	0.437452	−	0.899242i	$-0.355881\pi$
$113$	2.79358	+	0.907689i	0.262798	+	0.0853882i	−0.174655	+	0.984630i	$0.555881\pi$
$114$	−0.538460	−	3.16184i	−0.0504314	−	0.296133i
$115$	3.00609	+	28.6010i	0.280319	+	2.66706i
$116$	0.541311	+	5.15023i	0.0502594	+	0.478186i
$117$	5.50520	−	10.0677i	0.508955	−	0.930762i
$118$	0.269230	+	0.0874782i	0.0247846	+	0.00805302i
$119$	−0.396153	−	4.93396i	−0.0363153	−	0.452295i
$120$	−4.63893	+	5.86648i	−0.423474	+	0.535533i
$121$	10.7004	+	2.54964i	0.972767	+	0.231785i
$122$	−8.31573	−	4.80109i	−0.752871	−	0.434670i
$123$	−15.7912	−	4.03548i	−1.42384	−	0.363867i
$124$	−1.24908	+	0.265501i	−0.112171	+	0.0238427i
$125$	35.5023	−	11.5354i	3.17542	−	1.03176i
$126$	0.0110887	−	7.93725i	0.000987859	−	0.707106i
$127$	4.41242	+	6.07317i	0.391539	+	0.538907i	0.958595	−	0.284772i	$-0.0919179\pi$
$127$	4.41242	+	6.07317i	0.391539	+	0.538907i	−0.567057	+	0.823679i	$0.691918\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−5.01553	+	0.321240i	−0.441593	+	0.0282836i
$130$	15.0879	−	6.71756i	1.32330	−	0.589169i
$131$	2.19833	+	3.80762i	0.192069	+	0.332673i	0.945936	−	0.324354i	$-0.105147\pi$
$131$	2.19833	+	3.80762i	0.192069	+	0.332673i	−0.753867	+	0.657027i	$0.771814\pi$
$132$	1.49032	−	5.54788i	0.129716	−	0.482881i
$133$	0.900438	+	4.81587i	0.0780778	+	0.417589i
$134$	−6.18382	−	4.49281i	−0.534200	−	0.388119i
$135$	21.8614	+	5.04943i	1.88153	+	0.434586i
$136$	−1.82998	−	0.388974i	−0.156919	−	0.0333543i
$137$	−13.2270	+	1.39021i	−1.13006	+	0.118774i	−0.651047	−	0.759037i	$-0.725670\pi$
$137$	−13.2270	+	1.39021i	−1.13006	+	0.118774i	−0.479008	+	0.877811i	$0.659003\pi$
$138$	−10.2170	+	5.35601i	−0.869727	+	0.455934i
$139$	8.53433	−	2.77297i	0.723873	−	0.235200i	0.0761713	−	0.997095i	$-0.475730\pi$
$139$	8.53433	−	2.77297i	0.723873	−	0.235200i	0.647701	+	0.761894i	$0.275730\pi$
$140$	6.94037	−	9.07451i	0.586568	−	0.766936i
$141$	10.3292	−	2.89653i	0.869871	−	0.243932i
$142$	−1.29406	+	0.747126i	−0.108595	+	0.0626974i
$143$	−8.60307	+	9.32270i	−0.719425	+	0.779604i
$144$	−2.87391	−	0.860604i	−0.239493	−	0.0717170i
$145$	22.2386	+	2.33738i	1.84682	+	0.194108i
$146$	5.76113	+	1.87190i	0.476794	+	0.154920i
$147$	0.178955	+	12.1230i	0.0147600	+	0.999891i
$148$	−3.76023	+	2.73197i	−0.309089	+	0.224567i
$149$	−4.03330	−	1.79574i	−0.330421	−	0.147113i	0.234820	−	0.972039i	$-0.424550\pi$
$149$	−4.03330	−	1.79574i	−0.330421	−	0.147113i	−0.565241	+	0.824926i	$0.691217\pi$
$150$	15.0854	+	18.1932i	1.23172	+	1.48547i
$151$	4.14869	−	3.73550i	0.337616	−	0.303991i	−0.482831	−	0.875714i	$-0.660391\pi$
$151$	4.14869	−	3.73550i	0.337616	−	0.303991i	0.820447	+	0.571723i	$0.193725\pi$
$152$	1.84163	+	0.193563i	0.149376	+	0.0157000i
$153$	1.29398	+	5.46139i	0.104612	+	0.441527i
$154$	−2.13929	+	8.51020i	−0.172389	+	0.685771i
$155$			5.51403i			0.442897i
$156$	4.73852	+	4.62982i	0.379385	+	0.370682i
$157$	−6.00875	−	6.67339i	−0.479551	−	0.532595i	0.454019	−	0.890992i	$-0.349990\pi$
$157$	−6.00875	−	6.67339i	−0.479551	−	0.532595i	−0.933569	+	0.358397i	$0.883323\pi$
$158$	−0.861491	+	4.05300i	−0.0685366	+	0.322439i
$159$	−19.4635	+	10.2033i	−1.54356	+	0.809175i
$160$	−2.53805	−	3.49333i	−0.200651	−	0.276172i
$161$	15.4725	−	8.43253i	1.21940	−	0.664577i
$162$	1.35497	+	8.89742i	0.106456	+	0.699047i
$163$	1.73933	−	16.5486i	0.136234	−	1.29618i	−0.686237	−	0.727378i	$-0.740739\pi$
$163$	1.73933	−	16.5486i	0.136234	−	1.29618i	0.822471	−	0.568806i	$-0.192595\pi$
$164$	4.70502	−	8.14934i	0.367401	−	0.636357i
$165$	−22.0942	−	11.2753i	−1.72003	−	0.877777i
$166$	−2.62803	−	4.55188i	−0.203975	−	0.353294i
$167$	−3.93748	−	2.86075i	−0.304691	−	0.221371i	0.424924	−	0.905229i	$-0.360301\pi$
$167$	−3.93748	−	2.86075i	−0.304691	−	0.221371i	−0.729615	+	0.683858i	$0.760301\pi$
$168$	4.41064	+	1.24349i	0.340288	+	0.0959377i
$169$	−0.503574	−	1.54984i	−0.0387365	−	0.119219i
$170$	−3.28577	+	7.37996i	−0.252007	+	0.566017i
$171$	−1.83881	−	5.24216i	−0.140617	−	0.400878i
$172$	0.603288	−	2.83825i	0.0460003	−	0.216414i
$173$	14.1785	−	3.01373i	1.07797	−	0.229130i	0.365485	−	0.930817i	$-0.380903\pi$
$173$	14.1785	−	3.01373i	1.07797	−	0.229130i	0.712485	+	0.701688i	$0.247570\pi$
$174$	2.42186	+	8.63644i	0.183601	+	0.654727i
$175$	−23.4893	−	27.4147i	−1.77563	−	2.07236i
$176$	2.85178	+	1.69333i	0.214961	+	0.127640i
$177$	0.485139	+	0.0710791i	0.0364653	+	0.00534263i
$178$	0.153529	+	0.344832i	0.0115075	+	0.0258462i
$179$	1.69852	−	1.52935i	0.126953	−	0.114309i	−0.603209	−	0.797584i	$-0.706111\pi$
$179$	1.69852	−	1.52935i	0.126953	−	0.114309i	0.730162	+	0.683274i	$0.239445\pi$
$180$	−6.21496	+	11.3657i	−0.463236	+	0.847152i
$181$	1.13997	−	0.828240i	0.0847337	−	0.0615626i	−0.544612	−	0.838688i	$-0.683323\pi$
$181$	1.13997	−	0.828240i	0.0847337	−	0.0615626i	0.629346	+	0.777126i	$0.283323\pi$
$182$	−7.35152	−	6.95430i	−0.544931	−	0.515487i
$183$	−15.5949	−	5.77965i	−1.15281	−	0.427244i
$184$	−1.38473	−	6.51463i	−0.102083	−	0.480265i
$185$	8.16305	+	18.3345i	0.600159	+	1.34798i
$186$	−2.05557	+	0.816544i	−0.150721	+	0.0598719i
$187$	0.0759244	−	6.20449i	0.00555214	−	0.453717i
$188$			6.19358i			0.451713i
$189$	−2.28907	−	13.5558i	−0.166505	−	0.986041i
$190$	2.47088	−	7.60458i	0.179256	−	0.551694i
$191$	3.21681	+	2.89643i	0.232760	+	0.209578i	0.777254	−	0.629186i	$-0.216612\pi$
$191$	3.21681	+	2.89643i	0.232760	+	0.209578i	−0.544494	+	0.838764i	$0.683278\pi$
$192$	0.926426	−	1.46347i	0.0668591	−	0.105617i
$193$	−17.6146	+	1.85137i	−1.26793	+	0.133264i	−0.714501	−	0.699634i	$-0.753346\pi$
$193$	−17.6146	+	1.85137i	−1.26793	+	0.133264i	−0.553425	+	0.832899i	$0.686680\pi$
$194$	2.75166	−	3.05603i	0.197558	−	0.219410i
$195$	23.8087	−	15.8573i	1.70498	−	1.13556i
$196$	−6.76717	−	1.79037i	−0.483369	−	0.127883i
$197$	−20.8535			−1.48575			−0.742873	−	0.669432i	$-0.766538\pi$
$197$	−20.8535			−1.48575			−0.742873	+	0.669432i	$0.766538\pi$
$198$	0.931461	−	9.90618i	0.0661961	−	0.704001i
$199$	8.32060	−	14.4117i	0.589831	−	1.02162i	−0.404423	−	0.914572i	$-0.632528\pi$
$199$	8.32060	−	14.4117i	0.589831	−	1.02162i	0.994254	−	0.107046i	$-0.0341391\pi$
$200$	−12.4654	+	5.54995i	−0.881436	+	0.392441i
$201$	−11.8651	−	5.87318i	−0.836899	−	0.414262i
$202$	6.17086	+	18.9919i	0.434180	+	1.33627i
$203$	−3.91212	−	13.1309i	−0.274577	−	0.921608i
$204$	−3.23774	−	0.132037i	−0.226687	−	0.00924446i
$205$	−30.1958	−	27.1885i	−2.10897	−	1.89892i
$206$	−6.69173	−	7.43192i	−0.466235	−	0.517807i
$207$	−15.8877	+	12.1161i	−1.10427	+	0.842129i
$208$	−3.31243	+	1.91243i	−0.229676	+	0.132603i
$209$	0.567189	+	6.11538i	0.0392333	+	0.423010i
$210$	9.21176	−	17.5126i	0.635672	−	1.20848i
$211$	−7.10704	+	9.78201i	−0.489269	+	0.673421i	−0.980253	−	0.197748i	$-0.936637\pi$
$211$	−7.10704	+	9.78201i	−0.489269	+	0.673421i	0.490984	+	0.871169i	$0.336637\pi$
$212$	−2.63793	−	12.4105i	−0.181174	−	0.852356i
$213$	−1.99232	+	1.65198i	−0.136511	+	0.113192i
$214$	−0.890971	−	8.47702i	−0.0609055	−	0.579477i
$215$	−11.4461	−	5.09613i	−0.780618	−	0.347553i
$216$	−5.15736	−	0.633774i	−0.350914	−	0.0431229i
$217$	3.11937	−	1.29786i	0.211756	−	0.0881045i
$218$	−0.353795	+	0.486957i	−0.0239620	+	0.0329809i
$219$	10.3813	+	1.52099i	0.701500	+	0.102779i
$220$	9.71224	−	10.5246i	0.654799	−	0.709572i
$221$	6.19710	+	3.57790i	0.416862	+	0.240676i
$222$	−5.62607	+	5.75816i	−0.377597	+	0.386462i
$223$	4.63157	−	14.2545i	0.310153	−	0.954552i	−0.667551	−	0.744564i	$-0.732657\pi$
$223$	4.63157	−	14.2545i	0.310153	−	0.954552i	0.977704	−	0.209988i	$-0.0673426\pi$
$224$	−1.37884	+	2.25805i	−0.0921274	+	0.150873i
$225$	31.0481	+	26.6778i	2.06987	+	1.77852i
$226$	−1.19472	+	2.68340i	−0.0794719	+	0.178497i
$227$	7.17181	+	1.52442i	0.476010	+	0.101179i	0.439668	−	0.898160i	$-0.355096\pi$
$227$	7.17181	+	1.52442i	0.476010	+	0.101179i	0.0363419	+	0.999339i	$0.488429\pi$
$228$	3.20080	−	0.205008i	0.211978	−	0.0135770i
$229$	1.63005	−	15.5088i	0.107716	−	1.02485i	−0.798487	−	0.602012i	$-0.794366\pi$
$229$	1.63005	−	15.5088i	0.107716	−	1.02485i	0.906204	−	0.422842i	$-0.138967\pi$
$230$	−28.7586			−1.89628
$231$	−1.17816	+	15.1530i	−0.0775172	+	0.996991i
$232$	−5.17859			−0.339991
$233$	−1.36272	+	12.9655i	−0.0892750	+	0.849395i	0.854643	+	0.519216i	$0.173776\pi$
$233$	−1.36272	+	12.9655i	−0.0892750	+	0.849395i	−0.943918	+	0.330179i	$0.892891\pi$
$234$	9.43713	+	6.52740i	0.616925	+	0.426710i
$235$	26.1594	+	5.56036i	1.70645	+	0.362718i
$236$	−0.115141	+	0.258611i	−0.00749505	+	0.0168342i
$237$	−0.292433	+	7.17087i	−0.0189956	+	0.465798i
$238$	4.94834	+	0.121756i	0.320753	+	0.00789230i
$239$	−1.99602	+	6.14310i	−0.129111	+	0.397364i	−0.994628	−	0.103517i	$-0.966991\pi$
$239$	−1.99602	+	6.14310i	−0.129111	+	0.397364i	0.865516	+	0.500881i	$0.166991\pi$
$240$	−5.34944	−	5.22673i	−0.345305	−	0.337384i
$241$	−13.3575	−	7.71194i	−0.860430	−	0.496770i	0.00372601	−	0.999993i	$-0.498814\pi$
$241$	−13.3575	−	7.71194i	−0.860430	−	0.496770i	−0.864156	+	0.503223i	$0.832147\pi$
$242$	−3.65417	+	10.3753i	−0.234899	+	0.666950i
$243$	4.90077	+	14.7981i	0.314384	+	0.949296i
$244$	5.64402	−	7.76833i	0.361321	−	0.497316i
$245$	−13.6372	+	26.9747i	−0.871246	+	1.72335i
$246$	5.66400	−	15.2829i	0.361124	−	0.974400i
$247$	−6.47043	−	2.88082i	−0.411704	−	0.183302i
$248$	−0.133482	−	1.26999i	−0.00847609	−	0.0806446i
$249$	−5.81087	−	7.00800i	−0.368249	−	0.444114i
$250$	7.76120	+	36.5136i	0.490862	+	2.30932i
$251$	7.68813	−	10.5818i	0.485270	−	0.667917i	−0.494237	−	0.869327i	$-0.664552\pi$
$251$	7.68813	−	10.5818i	0.485270	−	0.667917i	0.979507	+	0.201410i	$0.0645524\pi$
$252$	7.89261	+	0.840696i	0.497187	+	0.0529589i
$253$	20.2880	−	8.73693i	1.27549	−	0.549286i
$254$	−6.50113	+	3.75343i	−0.407917	+	0.235511i
$255$	−3.46439	+	13.5565i	−0.216949	+	0.848940i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	12.1156	+	10.9090i	0.755752	+	0.680482i	0.954046	−	0.299660i	$-0.0968734\pi$
$257$	12.1156	+	10.9090i	0.755752	+	0.680482i	−0.198294	+	0.980143i	$0.563540\pi$
$258$	0.204786	−	5.02164i	0.0127494	−	0.312634i
$259$	8.45073	−	8.93343i	0.525103	−	0.555096i
$260$	5.10365	+	15.7074i	0.316515	+	0.974132i
$261$	6.64656	+	14.0422i	0.411412	+	0.869191i
$262$	−4.01655	+	1.78828i	−0.248143	+	0.110481i
$263$	10.1504	−	17.5810i	0.625901	−	1.08409i	−0.362465	−	0.931997i	$-0.618065\pi$
$263$	10.1504	−	17.5810i	0.625901	−	1.08409i	0.988366	−	0.152094i	$-0.0486017\pi$
$264$	5.36170	+	2.06207i	0.329990	+	0.126912i
$265$	−54.7856			−3.36545
$266$	−4.88361	+	0.392110i	−0.299433	+	0.0240418i
$267$	0.362417	+	0.544146i	0.0221795	+	0.0333012i
$268$	5.11458	−	5.68031i	0.312423	−	0.346980i
$269$	10.6458	−	1.11891i	0.649084	−	0.0682215i	0.225736	−	0.974189i	$-0.427521\pi$
$269$	10.6458	−	1.11891i	0.649084	−	0.0682215i	0.423348	+	0.905967i	$0.360855\pi$
$270$	−7.30691	+	21.2138i	−0.444684	+	1.29103i
$271$	−3.10292	−	2.79389i	−0.188489	−	0.169716i	0.569483	−	0.822003i	$-0.307143\pi$
$271$	−3.10292	−	2.79389i	−0.188489	−	0.169716i	−0.757973	+	0.652286i	$0.773810\pi$
$272$	0.578128	−	1.77930i	0.0350542	−	0.107886i
$273$	−14.5747	−	9.73656i	−0.882099	−	0.589283i
$274$		−	13.2998i		−	0.803471i
$275$	−26.1506	−	36.9353i	−1.57694	−	2.22728i
$276$	−4.25871	−	10.7209i	−0.256344	−	0.645320i
$277$	−4.95199	−	11.1223i	−0.297536	−	0.668277i	0.701477	−	0.712692i	$-0.252524\pi$
$277$	−4.95199	−	11.1223i	−0.297536	−	0.668277i	−0.999013	+	0.0444150i	$0.985858\pi$
$278$	1.86570	+	8.77744i	0.111897	+	0.526436i
$279$	−3.27238	+	1.99194i	−0.195912	+	0.119254i
$280$	8.29933	+	7.85090i	0.495980	+	0.469181i
$281$	2.59579	−	1.88595i	0.154852	−	0.112507i	−0.507661	−	0.861557i	$-0.669490\pi$
$281$	2.59579	−	1.88595i	0.154852	−	0.112507i	0.662513	+	0.749050i	$0.269490\pi$
$282$	1.80098	+	10.5753i	0.107247	+	0.629752i
$283$	−14.9341	+	13.4467i	−0.887738	+	0.799323i	−0.980531	−	0.196362i	$-0.937087\pi$
$283$	−14.9341	+	13.4467i	−0.887738	+	0.799323i	0.0927932	+	0.995685i	$0.470420\pi$
$284$	−0.607767	−	1.36507i	−0.0360643	−	0.0810018i
$285$	2.00768	−	13.7031i	0.118924	−	0.811699i
$286$	−8.37237	−	9.53043i	−0.495068	−	0.563546i
$287$	−8.27360	+	23.4817i	−0.488375	+	1.38608i
$288$	1.15629	−	2.76821i	0.0681353	−	0.163118i
$289$	13.2049	−	2.80678i	0.776757	−	0.165105i
$290$	−4.64914	+	21.8725i	−0.273007	+	1.28440i
$291$	3.80973	−	6.01820i	0.223331	−	0.352793i
$292$	−2.46385	+	5.53390i	−0.144186	+	0.323847i
$293$	−1.89733	−	5.83938i	−0.110843	−	0.341141i	0.880214	−	0.474577i	$-0.157399\pi$
$293$	−1.89733	−	5.83938i	−0.110843	−	0.341141i	−0.991057	+	0.133436i	$0.957399\pi$
$294$	−12.0753	−	1.08923i	−0.704248	−	0.0635250i
$295$	0.988911	+	0.718486i	0.0575766	+	0.0418318i
$296$	−2.32395	−	4.02520i	−0.135077	−	0.233960i
$297$	−1.29009	−	17.1853i	−0.0748586	−	0.997194i
$298$	2.20750	−	3.82350i	0.127877	−	0.221490i
$299$	−2.66278	+	25.3347i	−0.153993	+	1.46514i
$300$	−19.6704	+	13.1011i	−1.13567	+	0.756390i
$301$	−0.188841	+	7.67473i	−0.0108846	+	0.442364i
$302$	3.28138	+	4.51643i	0.188822	+	0.259891i
$303$	16.0590	+	30.6338i	0.922568	+	1.75986i
$304$	−0.385005	+	1.81130i	−0.0220815	+	0.103885i
$305$	−27.7436	−	30.8124i	−1.58859	−	1.76431i
$306$	−5.56673	+	0.716024i	−0.318229	+	0.0409324i
$307$			20.2358i			1.15492i	0.816419	+	0.577460i	$0.195956\pi$
$307$			20.2358i			1.15492i	−0.816419	+	0.577460i	$0.804044\pi$
$308$	−8.23996	−	3.01713i	−0.469515	−	0.171917i
$309$	−13.5870	−	10.7439i	−0.772936	−	0.611201i
$310$	−5.48382	−	0.576373i	−0.311460	−	0.0327358i
$311$	−8.41084	+	7.57316i	−0.476935	+	0.429434i	−0.872212	−	0.489128i	$-0.837315\pi$
$311$	−8.41084	+	7.57316i	−0.476935	+	0.429434i	0.395277	+	0.918562i	$0.370649\pi$
$312$	−5.09977	+	4.22861i	−0.288718	+	0.239398i
$313$	7.01174	+	3.12183i	0.396327	+	0.176456i	0.595216	−	0.803566i	$-0.297067\pi$
$313$	7.01174	+	3.12183i	0.396327	+	0.176456i	−0.198889	+	0.980022i	$0.563733\pi$
$314$	7.26492	−	5.27827i	0.409983	−	0.297870i
$315$	10.6365	−	32.5807i	0.599297	−	1.83572i
$316$	−3.94075	−	1.28043i	−0.221684	−	0.0720296i
$317$	29.0730	+	3.05569i	1.63290	+	0.171625i	0.876137	−	0.482063i	$-0.160112\pi$
$317$	29.0730	+	3.05569i	1.63290	+	0.171625i	0.756765	+	0.653688i	$0.226779\pi$
$318$	−8.11292	−	20.4234i	−0.454950	−	1.14529i
$319$	−3.36514	−	16.8426i	−0.188412	−	0.943003i
$320$	3.73949	−	2.15900i	0.209044	−	0.120692i
$321$	−3.98626	−	14.2152i	−0.222491	−	0.793413i
$322$	6.76902	+	16.2691i	0.377223	+	0.906644i
$323$	3.29485	−	1.07056i	0.183330	−	0.0595676i
$324$	−8.99031	+	0.417513i	−0.499462	+	0.0231952i
$325$	51.9046	−	5.45540i	2.87915	−	0.302611i
$326$	16.2761	+	3.45959i	0.901450	+	0.191609i
$327$	−0.462495	+	0.934340i	−0.0255761	+	0.0516691i
$328$	7.61289	+	5.53109i	0.420351	+	0.305403i
$329$	−3.01168	−	16.1075i	−0.166039	−	0.888037i
$330$	13.5230	−	20.7946i	0.744415	−	1.14471i
$331$	8.06414	+	13.9675i	0.443245	+	0.767723i	0.997928	−	0.0643388i	$-0.0204938\pi$
$331$	8.06414	+	13.9675i	0.443245	+	0.767723i	−0.554683	+	0.832062i	$0.687161\pi$
$332$	4.80165	−	2.13783i	0.263525	−	0.117329i
$333$	−7.93197	+	11.4678i	−0.434670	+	0.628433i
$334$	3.25665	−	3.61688i	0.178196	−	0.197907i
$335$	−19.3999	−	26.7017i	−1.05993	−	1.45887i
$336$	−1.69772	+	4.25649i	−0.0926182	+	0.232211i
$337$	17.8788	−	5.80917i	0.973920	−	0.316446i	0.221523	−	0.975155i	$-0.428897\pi$
$337$	17.8788	−	5.80917i	0.973920	−	0.316446i	0.752397	+	0.658709i	$0.228897\pi$
$338$	1.59399	−	0.338813i	0.0867017	−	0.0184290i
$339$	−1.25967	+	4.92921i	−0.0684160	+	0.267718i
$340$	−6.99608	−	4.03919i	−0.379415	−	0.219056i
$341$	4.04371	−	1.25939i	0.218979	−	0.0681999i
$342$	5.40565	−	1.28078i	0.292304	−	0.0692565i
$343$	18.4698	+	1.36559i	0.997278	+	0.0737347i
$344$	2.75964	+	0.896660i	0.148790	+	0.0483447i
$345$	−49.1043	+	8.36245i	−2.64369	+	0.450219i
$346$	1.51516	+	14.4158i	0.0814557	+	0.775000i
$347$	−0.842256	−	8.01353i	−0.0452147	−	0.430189i	−0.993590	−	0.113040i	$-0.963941\pi$
$347$	−0.842256	−	8.01353i	−0.0452147	−	0.430189i	0.948376	−	0.317149i	$-0.102726\pi$
$348$	−8.84228	+	1.50584i	−0.473996	+	0.0807214i
$349$	−29.0378	−	9.43496i	−1.55436	−	0.505042i	−0.599065	−	0.800701i	$-0.704461\pi$
$349$	−29.0378	−	9.43496i	−1.55436	−	0.505042i	−0.955294	+	0.295659i	$0.904461\pi$
$350$	29.7198	−	20.4950i	1.58859	−	1.09551i
$351$	18.0116	+	8.40119i	0.961390	+	0.448422i
$352$	−1.98215	+	2.65915i	−0.105649	+	0.141733i
$353$	−11.9037	−	6.87258i	−0.633568	−	0.365791i	0.148565	−	0.988903i	$-0.452535\pi$
$353$	−11.9037	−	6.87258i	−0.633568	−	0.365791i	−0.782133	+	0.623112i	$0.785868\pi$
$354$	−0.121401	+	0.475051i	−0.00645237	+	0.0252487i
$355$	−6.31117	+	1.34148i	−0.334962	+	0.0711984i
$356$	−0.358991	+	0.116643i	−0.0190265	+	0.00618208i
$357$	8.48454	−	1.23099i	0.449049	−	0.0651508i
$358$	1.34343	+	1.84908i	0.0710026	+	0.0977267i
$359$	−1.72698	+	1.91800i	−0.0911463	+	0.101228i	−0.786992	−	0.616963i	$-0.788363\pi$
$359$	−1.72698	+	1.91800i	−0.0911463	+	0.101228i	0.695846	+	0.718191i	$0.255030\pi$
$360$	−10.6538	−	7.36896i	−0.561506	−	0.388378i
$361$	14.2248	−	6.33328i	0.748672	−	0.333330i
$362$	0.704543	+	1.22030i	0.0370300	+	0.0641378i
$363$	−3.22243	+	18.7781i	−0.169134	+	0.985593i
$364$	7.68465	−	6.58433i	0.402785	−	0.345113i
$365$	21.1612	+	15.3745i	1.10763	+	0.804740i
$366$	7.37810	−	14.9053i	0.385659	−	0.779115i
$367$	−0.145281	−	0.0308803i	−0.00758358	−	0.00161194i	0.204118	−	0.978946i	$-0.434567\pi$
$367$	−0.145281	−	0.0308803i	−0.00758358	−	0.00161194i	−0.211702	+	0.977334i	$0.567901\pi$
$368$	6.62368	−	0.696177i	0.345283	−	0.0362907i
$369$	5.22713	−	27.7420i	0.272114	−	1.44419i
$370$	−19.0873	+	6.20185i	−0.992304	+	0.322419i
$371$	12.8951	+	30.9930i	0.669481	+	1.60908i
$372$	−0.597206	−	2.12966i	−0.0309637	−	0.110418i
$373$	3.03976	−	1.75501i	0.157393	−	0.0908707i	−0.419235	−	0.907878i	$-0.637702\pi$
$373$	3.03976	−	1.75501i	0.157393	−	0.0908707i	0.576628	+	0.817007i	$0.304368\pi$
$374$	6.16256	+	0.724054i	0.318658	+	0.0374399i
$375$	23.8695	+	60.0890i	1.23261	+	3.10298i
$376$	−6.15965	−	0.647405i	−0.317660	−	0.0333874i
$377$	18.8380	+	6.12083i	0.970206	+	0.315239i
$378$	13.7208	−	0.859560i	0.705723	−	0.0442110i
$379$	10.3794	−	7.54109i	0.533155	−	0.387360i	−0.288382	−	0.957516i	$-0.593117\pi$
$379$	10.3794	−	7.54109i	0.533155	−	0.387360i	0.821537	+	0.570156i	$0.193117\pi$
$380$	7.30464	+	3.25224i	0.374720	+	0.166836i
$381$	−10.0090	+	8.29926i	−0.512779	+	0.425184i
$382$	−3.21681	+	2.89643i	−0.164586	+	0.148194i
$383$	14.5926	+	1.53374i	0.745645	+	0.0783705i	0.469728	−	0.882811i	$-0.344352\pi$
$383$	14.5926	+	1.53374i	0.745645	+	0.0783705i	0.275917	+	0.961181i	$0.411019\pi$
$384$	1.35861	+	1.07433i	0.0693314	+	0.0548239i
$385$	−20.1408	+	32.0939i	−1.02647	+	1.63566i
$386$		−	17.7116i		−	0.901498i
$387$	−1.11053	−	8.63383i	−0.0564515	−	0.438882i
$388$	2.75166	+	3.05603i	0.139694	+	0.155146i
$389$	1.94848	−	9.16687i	0.0987917	−	0.464779i	−0.900745	−	0.434348i	$-0.856979\pi$
$389$	1.94848	−	9.16687i	0.0987917	−	0.464779i	0.999537	−	0.0304306i	$-0.00968786\pi$
$390$	13.2817	+	25.3358i	0.672547	+	1.28293i
$391$	−7.32396	−	10.0806i	−0.370388	−	0.509796i
$392$	2.48792	−	6.54295i	0.125659	−	0.330469i
$393$	−6.33813	+	4.22137i	−0.319716	+	0.212940i
$394$	2.17978	−	20.7392i	0.109816	−	1.04483i
$395$	−8.94590	+	15.4948i	−0.450117	+	0.779626i
$396$	9.75455	+	1.96184i	0.490184	+	0.0985860i
$397$	−0.775753	−	1.34364i	−0.0389339	−	0.0674356i	0.845902	−	0.533339i	$-0.179063\pi$
$397$	−0.775753	−	1.34364i	−0.0389339	−	0.0674356i	−0.884836	+	0.465903i	$0.845730\pi$
$398$	13.4630	+	9.78145i	0.674839	+	0.490300i
$399$	−8.22458	+	2.08958i	−0.411744	+	0.104610i
$400$	−4.21656	−	12.9772i	−0.210828	−	0.648861i
$401$	3.46856	−	7.79050i	0.173211	−	0.389039i	−0.805990	−	0.591929i	$-0.798367\pi$
$401$	3.46856	−	7.79050i	0.173211	−	0.389039i	0.979202	+	0.202890i	$0.0650333\pi$
$402$	7.08125	−	11.1862i	0.353181	−	0.557916i
$403$	−1.01550	+	4.77758i	−0.0505859	+	0.237988i
$404$	−19.5329	+	4.15185i	−0.971800	+	0.206562i
$405$	−6.30773	+	38.3466i	−0.313434	+	1.90546i
$406$	13.4679	−	2.51813i	0.668400	−	0.124973i
$407$	11.5812	−	10.1739i	0.574059	−	0.504303i
$408$	0.469750	−	3.20620i	0.0232561	−	0.158731i
$409$	−0.531107	−	1.19289i	−0.0262615	−	0.0589844i	0.899939	−	0.436017i	$-0.143611\pi$
$409$	−0.531107	−	1.19289i	−0.0262615	−	0.0589844i	−0.926200	+	0.377032i	$0.876945\pi$
$410$	30.1958	−	27.1885i	1.49127	−	1.34274i
$411$	−3.86734	−	22.7090i	−0.190762	−	1.12015i
$412$	8.09069	−	5.87823i	0.398599	−	0.289599i
$413$	0.173694	−	0.728554i	0.00854692	−	0.0358498i
$414$	−10.3890	−	17.0672i	−0.510593	−	0.838806i
$415$	−4.71868	−	22.1997i	−0.231631	−	1.08974i
$416$	−1.55571	−	3.49419i	−0.0762751	−	0.171317i
$417$	5.73794	+	14.4447i	0.280988	+	0.707359i
$418$	−6.14116	−	0.0751495i	−0.300374	−	0.00367568i
$419$		−	13.8898i		−	0.678560i	−0.940685	−	0.339280i	$-0.889817\pi$
$419$		−	13.8898i		−	0.678560i	0.940685	−	0.339280i	$-0.110183\pi$
$420$	16.4537	+	10.9919i	0.802860	+	0.536348i
$421$	2.64867	−	8.15177i	0.129088	−	0.397293i	−0.865535	−	0.500848i	$-0.833022\pi$
$421$	2.64867	−	8.15177i	0.129088	−	0.397293i	0.994624	+	0.103555i	$0.0330217\pi$
$422$	−8.98553	−	8.09061i	−0.437409	−	0.393845i
$423$	6.15022	+	17.5334i	0.299034	+	0.852501i
$424$	12.6182	−	1.32623i	0.612796	−	0.0644074i
$425$	−17.0816	+	18.9710i	−0.828579	+	0.920230i
$426$	−1.43468	−	2.15408i	−0.0695104	−	0.104366i
$427$	−10.9009	+	22.9474i	−0.527531	+	1.11050i
$428$	8.52371			0.412009
$429$	−17.0668	−	13.8384i	−0.823994	−	0.668123i
$430$	6.26466	−	10.8507i	0.302109	−	0.523268i
$431$	−3.14269	+	1.39921i	−0.151378	+	0.0673978i	−0.481027	−	0.876706i	$-0.659736\pi$
$431$	−3.14269	+	1.39921i	−0.151378	+	0.0673978i	0.329649	+	0.944103i	$0.393070\pi$
$432$	1.16939	−	5.06286i	0.0562624	−	0.243587i
$433$	2.61109	+	8.03611i	0.125481	+	0.386191i	0.993988	−	0.109485i	$-0.0349203\pi$
$433$	2.61109	+	8.03611i	0.125481	+	0.386191i	−0.868507	+	0.495676i	$0.834920\pi$
$434$	0.964688	+	3.23794i	0.0463065	+	0.155426i
$435$	−1.57815	+	38.6985i	−0.0756665	+	1.85545i
$436$	−0.447308	−	0.402758i	−0.0214221	−	0.0192886i
$437$	8.25245	+	9.16528i	0.394768	+	0.438435i
$438$	−2.59779	+	10.1654i	−0.124127	+	0.485722i
$439$	14.2511	−	8.22787i	0.680168	−	0.392695i	−0.119751	−	0.992804i	$-0.538209\pi$
$439$	14.2511	−	8.22787i	0.680168	−	0.392695i	0.799918	+	0.600109i	$0.204876\pi$
$440$	9.45179	+	10.7592i	0.450596	+	0.512923i
$441$	−20.9350	+	1.65146i	−0.996903	+	0.0786409i
$442$	−4.20607	+	5.78916i	−0.200063	+	0.275362i
$443$	5.48140	+	25.7880i	0.260429	+	1.22522i	0.892763	+	0.450527i	$0.148764\pi$
$443$	5.48140	+	25.7880i	0.260429	+	1.22522i	−0.632334	+	0.774696i	$0.717903\pi$
$444$	−5.13853	−	6.19714i	−0.243864	−	0.294103i
$445$	0.170370	+	1.62096i	0.00807632	+	0.0768411i
$446$	13.6923	+	6.09620i	0.648348	+	0.288663i
$447$	2.65743	−	7.17041i	0.125692	−	0.339149i
$448$	−2.10156	−	1.60731i	−0.0992892	−	0.0759385i
$449$	−18.2425	+	25.1086i	−0.860917	+	1.18495i	0.120433	+	0.992721i	$0.461572\pi$
$449$	−18.2425	+	25.1086i	−0.860917	+	1.18495i	−0.981350	+	0.192229i	$0.938428\pi$
$450$	−29.7771	+	28.0894i	−1.40370	+	1.32415i
$451$	−13.0420	+	28.3539i	−0.614124	+	1.33513i
$452$	−2.54381	−	1.46867i	−0.119651	−	0.0690805i
$453$	6.91614	+	6.75750i	0.324949	+	0.317495i
$454$	−2.26572	+	6.97318i	−0.106336	+	0.327267i
$455$	−20.9108	−	38.3683i	−0.980314	−	1.79873i
$456$	−0.130690	+	3.20469i	−0.00612011	+	0.150074i
$457$	−2.98129	+	6.69610i	−0.139459	+	0.313230i	−0.969750	−	0.244100i	$-0.921508\pi$
$457$	−2.98129	+	6.69610i	−0.139459	+	0.313230i	0.830291	+	0.557330i	$0.188174\pi$
$458$	15.2535	+	3.24223i	0.712749	+	0.151500i
$459$	−9.29680	+	2.84129i	−0.433938	+	0.132620i
$460$	3.00609	−	28.6010i	0.140160	−	1.33353i
$461$	15.0082			0.699002			0.349501	−	0.936936i	$-0.386351\pi$
$461$	15.0082			0.699002			0.349501	+	0.936936i	$0.386351\pi$
$462$	−14.9468	−	2.75562i	−0.695388	−	0.128203i
$463$	26.8294			1.24687			0.623434	−	0.781876i	$-0.285737\pi$
$463$	26.8294			1.24687			0.623434	+	0.781876i	$0.285737\pi$
$464$	0.541311	−	5.15023i	0.0251297	−	0.239093i
$465$	−9.53104	+	0.610454i	−0.441992	+	0.0283091i
$466$	−12.7520	−	2.71052i	−0.590724	−	0.125562i
$467$	0.289655	−	0.650576i	0.0134036	−	0.0301051i	−0.906720	−	0.421734i	$-0.861422\pi$
$467$	0.289655	−	0.650576i	0.0134036	−	0.0301051i	0.920123	+	0.391629i	$0.128088\pi$
$468$	−7.47809	+	8.70313i	−0.345675	+	0.402302i
$469$	−10.5393	+	17.2597i	−0.486660	+	0.796979i
$470$	−8.26430	+	25.4349i	−0.381204	+	1.17322i
$471$	10.8698	−	11.1250i	0.500854	−	0.512612i
$472$	−0.245159	−	0.141543i	−0.0112844	−	0.00651503i
$473$	−1.12299	+	9.55795i	−0.0516350	+	0.439475i
$474$	−7.10102	−	1.04039i	−0.326161	−	0.0477867i
$475$	14.8519	−	20.4418i	0.681451	−	0.937936i
$476$	−0.638332	+	4.90851i	−0.0292579	+	0.224981i
$477$	−19.7913	−	32.5133i	−0.906181	−	1.48868i
$478$	−5.90081	−	2.62721i	−0.269897	−	0.120166i
$479$	−2.82997	−	26.9253i	−0.129305	−	1.23025i	−0.846122	−	0.532989i	$-0.821069\pi$
$479$	−2.82997	−	26.9253i	−0.129305	−	1.23025i	0.716817	−	0.697261i	$-0.245598\pi$
$480$	5.75727	−	4.77379i	0.262782	−	0.217893i
$481$	3.69617	+	17.3891i	0.168531	+	0.792876i
$482$	9.06593	−	12.4782i	0.412942	−	0.568366i
$483$	16.2887	+	25.8107i	0.741159	+	1.17443i
$484$	−9.93651	−	4.71867i	−0.451659	−	0.214485i
$485$	15.3779	−	8.87842i	0.698273	−	0.403148i
$486$	−15.2293	+	3.32710i	−0.690813	+	0.150920i
$487$	24.2545	+	26.9374i	1.09908	+	1.22065i	0.973530	+	0.228561i	$0.0734019\pi$
$487$	24.2545	+	26.9374i	1.09908	+	1.22065i	0.125547	+	0.992088i	$0.459931\pi$
$488$	7.13581	+	6.42511i	0.323023	+	0.290851i
$489$	28.7969	+	1.17436i	1.30224	+	0.0531063i
$490$	−25.4015	−	16.3821i	−1.14752	−	0.740067i
$491$	6.19751	+	19.0740i	0.279690	+	0.860797i	0.987940	+	0.154836i	$0.0494848\pi$
$491$	6.19751	+	19.0740i	0.279690	+	0.860797i	−0.708250	+	0.705961i	$0.750515\pi$
$492$	14.6071	+	7.23047i	0.658539	+	0.325975i
$493$	−8.85083	+	3.94064i	−0.398621	+	0.177478i
$494$	3.54139	−	6.13386i	0.159334	−	0.275975i
$495$	17.0433	−	39.4384i	0.766041	−	1.77262i
$496$	1.27699			0.0573385
$497$	2.24438	+	3.25457i	0.100674	+	0.145988i
$498$	7.57701	−	5.04650i	0.339534	−	0.226139i
$499$	29.2875	−	32.5271i	1.31109	−	1.45611i	0.506551	−	0.862210i	$-0.330920\pi$
$499$	29.2875	−	32.5271i	1.31109	−	1.45611i	0.804537	−	0.593902i	$-0.202413\pi$
$500$	−37.1248	+	3.90198i	−1.66027	+	0.174502i
$501$	4.50891	−	7.12268i	0.201443	−	0.318218i
$502$	9.72020	+	8.75211i	0.433834	+	0.390626i
$503$	−6.83567	+	21.0380i	−0.304788	+	0.938040i	0.674969	+	0.737846i	$0.264157\pi$
$503$	−6.83567	+	21.0380i	−0.304788	+	0.938040i	−0.979756	+	0.200193i	$0.935843\pi$
$504$	−1.66109	+	7.76149i	−0.0739909	+	0.345724i
$505$			86.2273i			3.83707i
$506$	6.56839	+	21.0901i	0.292001	+	0.937569i
$507$	2.62317	−	1.04201i	0.116499	−	0.0462775i
$508$	−3.05331	−	6.85785i	−0.135469	−	0.304268i
$509$	−1.91402	−	9.00475i	−0.0848374	−	0.399129i	0.915155	−	0.403103i	$-0.132068\pi$
$509$	−1.91402	−	9.00475i	−0.0848374	−	0.399129i	−0.999992	+	0.00397414i	$0.998735\pi$
$510$	−13.1201	−	4.86245i	−0.580967	−	0.215313i
$511$	3.71679	−	15.5900i	0.164421	−	0.689661i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	8.85755	−	3.75875i	0.391070	−	0.165953i
$514$	−12.1156	+	10.9090i	−0.534397	+	0.481174i
$515$	−17.5640	−	39.4493i	−0.773961	−	1.73835i
$516$	4.97272	+	0.728568i	0.218912	+	0.0320734i
$517$	−1.89707	−	20.4540i	−0.0834328	−	0.899566i
$518$	8.00115	+	9.33824i	0.351550	+	0.410299i
$519$	6.77895	+	24.1740i	0.297563	+	1.06112i
$520$	−16.1548	+	3.43382i	−0.708436	+	0.150583i
$521$	−2.87855	+	13.5425i	−0.126112	+	0.593308i	0.869022	+	0.494773i	$0.164749\pi$
$521$	−2.87855	+	13.5425i	−0.126112	+	0.593308i	−0.995134	+	0.0985349i	$0.968584\pi$
$522$	−14.6600	+	5.14234i	−0.641653	+	0.225074i
$523$	−8.12513	+	18.2494i	−0.355287	+	0.797988i	0.644165	+	0.764887i	$0.277205\pi$
$523$	−8.12513	+	18.2494i	−0.355287	+	0.797988i	−0.999452	+	0.0331016i	$0.989462\pi$
$524$	−1.35864	−	4.18147i	−0.0593526	−	0.182669i
$525$	44.7861	−	43.6366i	1.95462	−	1.90446i
$526$	16.4237	+	11.9325i	0.716107	+	0.520282i
$527$	−1.19453	−	2.06900i	−0.0520348	−	0.0901268i
$528$	−2.61122	+	5.11679i	−0.113639	+	0.222680i
$529$	10.6789	−	18.4964i	0.464301	−	0.804192i
$530$	5.72665	−	54.4855i	0.248750	−	2.36670i
$531$	−0.0691515	+	0.846436i	−0.00300092	+	0.0367322i
$532$	0.120514	−	4.89784i	0.00522494	−	0.212348i
$533$	−21.1557	−	29.1183i	−0.916354	−	1.26125i
$534$	−0.579048	+	0.303552i	−0.0250579	+	0.0131360i
$535$	7.65226	−	36.0010i	0.330836	−	1.55646i
$536$	5.11458	+	5.68031i	0.220916	+	0.245352i
$537$	2.83154	+	2.76659i	0.122190	+	0.119387i
$538$			10.7044i			0.461500i
$539$	22.8966	+	3.83984i	0.986228	+	0.165394i
$540$	−20.3338	−	9.48433i	−0.875028	−	0.408140i
$541$	−21.3541	−	2.24440i	−0.918082	−	0.0964944i	−0.366314	−	0.930491i	$-0.619380\pi$
$541$	−21.3541	−	2.24440i	−0.918082	−	0.0964944i	−0.551769	+	0.833997i	$0.686047\pi$
$542$	3.10292	−	2.79389i	0.133282	−	0.120008i
$543$	1.55783	+	1.87876i	0.0668527	+	0.0806254i
$544$	1.70912	+	0.760948i	0.0732778	+	0.0326254i
$545$	−2.10268	+	1.52768i	−0.0900687	+	0.0654388i
$546$	11.2067	−	13.4771i	0.479602	−	0.576766i
$547$	−29.3339	−	9.53116i	−1.25423	−	0.407523i	−0.394793	−	0.918770i	$-0.629184\pi$
$547$	−29.3339	−	9.53116i	−1.25423	−	0.407523i	−0.859434	+	0.511247i	$0.829184\pi$
$548$	13.2270	+	1.39021i	0.565028	+	0.0593868i
$549$	8.26367	−	27.5958i	0.352685	−	1.17776i
$550$	39.4664	−	22.1465i	1.68285	−	0.944331i
$551$	8.30481	−	4.79478i	0.353797	−	0.204265i
$552$	11.1073	−	3.11474i	0.472758	−	0.132572i
$553$	10.8712	+	1.41376i	0.462292	+	0.0601193i
$554$	11.5790	−	3.76226i	0.491946	−	0.159843i
$555$	−30.7876	+	16.1397i	−1.30686	+	0.685092i
$556$	−8.92437	+	0.937989i	−0.378478	+	0.0397796i
$557$	15.3305	+	3.25860i	0.649575	+	0.138071i	0.520903	−	0.853616i	$-0.325595\pi$
$557$	15.3305	+	3.25860i	0.649575	+	0.138071i	0.128672	+	0.991687i	$0.458929\pi$
$558$	−1.63897	−	3.46267i	−0.0693833	−	0.146586i
$559$	−8.97882	−	6.52350i	−0.379764	−	0.275915i
$560$	−8.67540	+	7.43322i	−0.366603	+	0.314111i
$561$	10.7329	−	0.555658i	0.453144	−	0.0234599i
$562$	1.60429	+	2.77871i	0.0676728	+	0.117213i
$563$	5.03519	−	2.24181i	0.212208	−	0.0944811i	−0.297880	−	0.954603i	$-0.596279\pi$
$563$	5.03519	−	2.24181i	0.212208	−	0.0944811i	0.510088	+	0.860122i	$0.329613\pi$
$564$	−10.7057	+	0.685687i	−0.450789	+	0.0288726i
$565$	−8.48687	+	9.42562i	−0.357045	+	0.396539i
$566$	−11.8120	−	16.2578i	−0.496495	−	0.683367i
$567$	23.1779	−	5.45743i	0.973382	−	0.229191i
$568$	1.42112	−	0.461749i	0.0596288	−	0.0193746i
$569$	16.1198	−	3.42637i	0.675778	−	0.143641i	0.142776	−	0.989755i	$-0.454397\pi$
$569$	16.1198	−	3.42637i	0.675778	−	0.143641i	0.533002	+	0.846114i	$0.321064\pi$
$570$	13.4181	+	3.42904i	0.562024	+	0.143627i
$571$	12.5956	+	7.27209i	0.527111	+	0.304328i	0.739839	−	0.672784i	$-0.234902\pi$
$571$	12.5956	+	7.27209i	0.527111	+	0.304328i	−0.212728	+	0.977111i	$0.568235\pi$
$572$	10.3534	−	7.33030i	0.432896	−	0.306495i
$573$	−4.65037	+	5.88094i	−0.194272	+	0.245680i
$574$	−22.4882	−	10.6828i	−0.938641	−	0.445891i
$575$	−86.4305	−	28.0830i	−3.60440	−	1.17114i
$576$	2.63218	+	1.43932i	0.109674	+	0.0599715i
$577$	2.30481	+	21.9288i	0.0959507	+	0.912910i	0.931561	+	0.363586i	$0.118448\pi$
$577$	2.30481	+	21.9288i	0.0959507	+	0.912910i	−0.835610	+	0.549323i	$0.814886\pi$
$578$	1.41112	+	13.4259i	0.0586949	+	0.558445i
$579$	−5.15021	−	30.2420i	−0.214035	−	1.25682i
$580$	−21.2667	−	6.90997i	−0.883052	−	0.286921i
$581$	−11.4480	+	7.89466i	−0.474944	+	0.327526i
$582$	5.58700	+	4.41794i	0.231589	+	0.183129i
$583$	12.5129	+	40.1770i	0.518232	+	1.66396i
$584$	−5.24604	−	3.02880i	−0.217083	−	0.125333i
$585$	30.0453	+	39.3981i	1.24222	+	1.62891i
$586$	6.00572	−	1.27656i	0.248094	−	0.0527340i
$587$	−24.3744	+	7.91972i	−1.00604	+	0.326882i	−0.765276	−	0.643702i	$-0.777397\pi$
$587$	−24.3744	+	7.91972i	−1.00604	+	0.326882i	−0.240762	+	0.970584i	$0.577397\pi$
$588$	2.34548	−	11.8953i	0.0967258	−	0.490555i
$589$	1.38993	+	1.91307i	0.0572710	+	0.0788268i
$590$	−0.817919	+	0.908391i	−0.0336732	+	0.0373979i
$591$	−2.30867	−	36.0454i	−0.0949660	−	1.48271i
$592$	4.24607	−	1.89047i	0.174512	−	0.0776980i
$593$	−5.51747	−	9.55654i	−0.226575	−	0.392440i	0.730215	−	0.683217i	$-0.239420\pi$
$593$	−5.51747	−	9.55654i	−0.226575	−	0.392440i	−0.956791	+	0.290777i	$0.906086\pi$
$594$	17.2260	+	0.513333i	0.706793	+	0.0210623i
$595$	20.1587	+	7.10275i	0.826425	+	0.291184i
$596$	3.57181	+	2.59507i	0.146307	+	0.106298i
$597$	25.8319	+	12.7867i	1.05723	+	0.523325i
$598$	−24.9176	−	5.29639i	−1.01896	−	0.216586i
$599$	24.6888	−	2.59489i	1.00876	−	0.106025i	0.414290	−	0.910145i	$-0.364030\pi$
$599$	24.6888	−	2.59489i	1.00876	−	0.106025i	0.594466	+	0.804121i	$0.297363\pi$
$600$	−10.9732	−	20.9321i	−0.447978	−	0.854550i
$601$	36.2245	−	11.7701i	1.47763	−	0.480111i	0.544226	−	0.838939i	$-0.316823\pi$
$601$	36.2245	−	11.7701i	1.47763	−	0.480111i	0.933404	+	0.358828i	$0.116823\pi$
$602$	−7.61295	−	0.990034i	−0.310281	−	0.0403508i
$603$	8.83828	−	21.1591i	0.359922	−	0.861667i
$604$	−4.83469	+	2.79131i	−0.196721	+	0.113577i
$605$	−28.8505	+	37.7319i	−1.17294	+	1.53402i
$606$	−32.1446	+	12.7690i	−1.30578	+	0.518704i
$607$	−43.5289	−	4.57507i	−1.76678	−	0.185696i	−0.835377	−	0.549677i	$-0.814751\pi$
$607$	−43.5289	−	4.57507i	−1.76678	−	0.185696i	−0.931406	+	0.363981i	$0.881417\pi$
$608$	−1.76114	−	0.572228i	−0.0714236	−	0.0232069i
$609$	22.2638	−	8.21584i	0.902173	−	0.332923i
$610$	33.5436	−	24.3708i	1.35814	−	0.986746i
$611$	21.6415	+	9.63543i	0.875523	+	0.389808i
$612$	−0.130220	−	5.61108i	−0.00526383	−	0.226814i
$613$	−22.1356	+	19.9310i	−0.894047	+	0.805004i	−0.981559	−	0.191160i	$-0.938775\pi$
$613$	−22.1356	+	19.9310i	−0.894047	+	0.805004i	0.0875119	+	0.996163i	$0.472108\pi$
$614$	−20.1250	−	2.11522i	−0.812178	−	0.0853633i
$615$	43.6525	−	55.2038i	1.76024	−	2.22603i
$616$	3.86191	−	7.87945i	0.155601	−	0.317472i
$617$		−	39.8641i		−	1.60487i	−0.596742	−	0.802433i	$-0.703538\pi$
$617$		−	39.8641i		−	1.60487i	0.596742	−	0.802433i	$-0.296462\pi$
$618$	12.1053	−	12.3895i	0.486947	−	0.498379i
$619$	−18.3614	−	20.3924i	−0.738006	−	0.819639i	0.250926	−	0.968006i	$-0.419265\pi$
$619$	−18.3614	−	20.3924i	−0.738006	−	0.819639i	−0.988932	+	0.148367i	$0.952598\pi$
$620$	1.14643	−	5.39353i	0.0460418	−	0.216609i
$621$	−22.7017	−	26.1207i	−0.910990	−	1.04819i
$622$	−6.65250	−	9.15638i	−0.266741	−	0.367137i
$623$	0.876903	−	0.477914i	0.0351324	−	0.0191472i
$624$	−3.67237	−	5.51384i	−0.147013	−	0.220730i
$625$	−9.71722	+	92.4532i	−0.388689	+	3.69813i
$626$	−3.83765	+	6.64701i	−0.153383	+	0.265668i
$627$	−10.5077	+	1.65742i	−0.419637	+	0.0661910i
$628$	4.48997	+	7.77685i	0.179169	+	0.310330i
$629$	−7.03488	−	5.11114i	−0.280499	−	0.203795i
$630$	31.2904	+	13.9838i	1.24664	+	0.557129i
$631$	−5.16165	−	15.8859i	−0.205482	−	0.632409i	−0.999693	−	0.0247669i	$-0.992116\pi$
$631$	−5.16165	−	15.8859i	−0.205482	−	0.632409i	0.794211	−	0.607642i	$-0.207884\pi$
$632$	1.68533	−	3.78532i	0.0670389	−	0.150572i
$633$	−17.6951	−	11.2016i	−0.703317	−	0.445225i
$634$	−6.07791	+	28.5943i	−0.241385	+	1.13563i
$635$	−31.7062	+	6.73936i	−1.25822	+	0.267443i
$636$	21.1596	−	5.93364i	0.839032	−	0.235284i
$637$	−16.7837	+	20.8605i	−0.664993	+	0.826522i
$638$	17.1021	−	1.58618i	0.677077	−	0.0627975i
$639$	−3.07603	−	3.26085i	−0.121686	−	0.128997i
$640$	1.75629	+	3.94468i	0.0694233	+	0.155927i
$641$	−19.4621	+	17.5237i	−0.768706	+	0.692146i	−0.957039	−	0.289959i	$-0.906358\pi$
$641$	−19.4621	+	17.5237i	−0.768706	+	0.692146i	0.188333	+	0.982105i	$0.439692\pi$
$642$	14.5540	−	2.47854i	0.574399	−	0.0978200i
$643$	−32.7834	+	23.8185i	−1.29285	+	0.939310i	−0.999859	−	0.0168053i	$-0.994650\pi$
$643$	−32.7834	+	23.8185i	−1.29285	+	0.939310i	−0.292991	+	0.956115i	$0.594650\pi$
$644$	−16.8876	+	5.03135i	−0.665464	+	0.198263i
$645$	7.54152	−	20.3489i	0.296947	−	0.801237i
$646$	0.720291	+	3.38870i	0.0283395	+	0.133327i
$647$	−9.93730	−	22.3195i	−0.390676	−	0.877472i	−0.996634	−	0.0819756i	$-0.973877\pi$
$647$	−9.93730	−	22.3195i	−0.390676	−	0.877472i	0.605959	−	0.795496i	$-0.292790\pi$
$648$	0.524517	−	8.98470i	0.0206050	−	0.352952i
$649$	0.301037	−	0.889319i	0.0118167	−	0.0349088i
$650$			52.1905i			2.04708i
$651$	2.58871	+	5.24817i	0.101459	+	0.205692i
$652$	−5.14196	+	15.8253i	−0.201375	+	0.619767i
$653$	−7.12248	−	6.41311i	−0.278724	−	0.250965i	0.517897	−	0.855443i	$-0.326715\pi$
$653$	−7.12248	−	6.41311i	−0.278724	−	0.250965i	−0.796622	+	0.604478i	$0.793382\pi$
$654$	−0.880877	−	0.557627i	−0.0344450	−	0.0218049i
$655$	−18.8808	+	1.98445i	−0.737732	+	0.0775388i
$656$	−6.29655	+	6.99303i	−0.245839	+	0.273032i
$657$	−1.47974	+	18.1125i	−0.0577302	+	0.706635i
$658$	16.3341	−	1.31148i	0.636770	−	0.0511269i
$659$	−20.2379			−0.788355			−0.394177	−	0.919034i	$-0.628970\pi$
$659$	−20.2379			−0.788355			−0.394177	+	0.919034i	$0.628970\pi$
$660$	19.2672	+	15.6225i	0.749974	+	0.608105i
$661$	18.5004	−	32.0436i	0.719582	−	1.24635i	−0.241583	−	0.970380i	$-0.577667\pi$
$661$	18.5004	−	32.0436i	0.719582	−	1.24635i	0.961165	−	0.275973i	$-0.0890000\pi$
$662$	−14.7339	+	6.55996i	−0.572650	+	0.254960i
$663$	−5.49836	+	11.1079i	−0.213538	+	0.431393i
$664$	1.62421	+	4.99881i	0.0630316	+	0.193991i
$665$	−20.5785	−	4.90610i	−0.798000	−	0.190250i
$666$	−10.5759	−	9.08724i	−0.409807	−	0.352123i
$667$	−25.6313	−	23.0785i	−0.992448	−	0.893604i
$668$	3.25665	+	3.61688i	0.126004	+	0.139941i
$669$	25.1518	+	6.42760i	0.972425	+	0.248505i
$670$	28.5832	−	16.5025i	1.10427	−	0.637549i
$671$	−16.2597	+	27.3833i	−0.627699	+	1.05712i
$672$	−4.05572	−	2.13334i	−0.156453	−	0.0822955i
$673$	18.7665	−	25.8299i	0.723396	−	0.995669i	−0.276008	−	0.961155i	$-0.589012\pi$
$673$	18.7665	−	25.8299i	0.723396	−	0.995669i	0.999404	−	0.0345139i	$-0.0109883\pi$
$674$	3.90851	+	18.3881i	0.150550	+	0.708282i
$675$	−42.6755	+	56.6204i	−1.64258	+	2.17932i
$676$	0.170340	+	1.62067i	0.00655153	+	0.0623336i
$677$	24.1465	+	10.7507i	0.928027	+	0.413184i	0.814377	−	0.580337i	$-0.197079\pi$
$677$	24.1465	+	10.7507i	0.928027	+	0.413184i	0.113650	+	0.993521i	$0.463746\pi$
$678$	−4.77054	−	1.76802i	−0.183211	−	0.0679002i
$679$	−8.64221	−	6.60974i	−0.331658	−	0.253659i
$680$	4.74835	−	6.53554i	0.182091	−	0.250627i
$681$	−1.84098	+	12.5653i	−0.0705465	+	0.481504i
$682$	0.829810	+	4.15320i	0.0317751	+	0.159034i
$683$	−17.5805	−	10.1501i	−0.672698	−	0.388383i	0.124400	−	0.992232i	$-0.460299\pi$
$683$	−17.5805	−	10.1501i	−0.672698	−	0.388383i	−0.797098	+	0.603850i	$0.793633\pi$
$684$	0.708717	+	5.50992i	0.0270985	+	0.210677i
$685$	17.7464	−	54.6178i	0.678055	−	2.08684i
$686$	−3.28873	+	18.2259i	−0.125564	+	0.695869i
$687$	26.9876	+	1.10058i	1.02964	+	0.0419896i
$688$	−1.18021	+	2.65079i	−0.0449950	+	0.101061i
$689$	−47.4684	−	10.0897i	−1.80840	−	0.384388i
$690$	−3.18384	−	49.7094i	−0.121207	−	1.89241i
$691$	−2.04034	+	19.4126i	−0.0776183	+	0.738489i	0.884626	+	0.466301i	$0.154414\pi$
$691$	−2.04034	+	19.4126i	−0.0776183	+	0.738489i	−0.962244	+	0.272188i	$0.912253\pi$
$692$	−14.4952			−0.551026
$693$	−26.3224	−	0.358888i	−0.999907	−	0.0136330i
$694$	8.05767			0.305865
$695$	−4.05023	+	38.5354i	−0.153634	+	1.46173i
$696$	−0.573318	−	8.95125i	−0.0217316	−	0.339296i
$697$	17.2202	+	3.66027i	0.652262	+	0.138642i
$698$	12.4185	−	27.8925i	0.470049	−	1.05575i
$699$	−22.5618	−	0.920085i	−0.853365	−	0.0348008i
$700$	17.2762	+	31.6993i	0.652979	+	1.19812i
$701$	−13.7758	+	42.3975i	−0.520305	+	1.60133i	0.253114	+	0.967437i	$0.418545\pi$
$701$	−13.7758	+	42.3975i	−0.520305	+	1.60133i	−0.773418	+	0.633896i	$0.781455\pi$
$702$	−10.2379	+	17.0348i	−0.386404	+	0.642937i
$703$	7.45375	+	4.30342i	0.281123	+	0.162307i
$704$	−2.43739	−	2.24925i	−0.0918627	−	0.0847717i
$705$	−6.71503	+	45.8324i	−0.252903	+	1.72615i
$706$	8.07920	−	11.1201i	0.304065	−	0.418509i
$707$	48.7801	−	20.2957i	1.83456	−	0.763298i
$708$	−0.459759	−	0.170392i	−0.0172788	−	0.00640372i
$709$	26.8623	+	11.9599i	1.00884	+	0.449162i	0.843531	−	0.537080i	$-0.180473\pi$
$709$	26.8623	+	11.9599i	1.00884	+	0.449162i	0.165304	+	0.986243i	$0.447139\pi$
$710$	−0.674435	−	6.41682i	−0.0253111	−	0.240819i
$711$	−12.4273	+	0.288408i	−0.466060	+	0.0108162i
$712$	−0.0784795	−	0.369217i	−0.00294114	−	0.0138370i
$713$	4.99909	−	6.88065i	0.187217	−	0.257683i
$714$	0.337370	+	8.56673i	0.0126258	+	0.320602i
$715$	−21.6656	−	50.3097i	−0.810249	−	1.88148i
$716$	−1.97937	+	1.14279i	−0.0739726	+	0.0427081i
$717$	−10.8394	−	2.77003i	−0.404804	−	0.103449i
$718$	−1.72698	−	1.91800i	−0.0644502	−	0.0715792i
$719$	21.2977	+	19.1765i	0.794269	+	0.715163i	0.962706	−	0.270550i	$-0.0872055\pi$
$719$	21.2977	+	19.1765i	0.794269	+	0.715163i	−0.168437	+	0.985712i	$0.553872\pi$
$720$	8.44222	−	9.82520i	0.314623	−	0.366164i
$721$	−18.1830	+	19.2216i	−0.677169	+	0.715849i
$722$	4.81169	+	14.8089i	0.179072	+	0.551128i
$723$	11.8514	−	23.9423i	0.440757	−	0.890423i
$724$	−1.28726	+	0.573127i	−0.0478408	+	0.0213001i
$725$	−35.3311	+	61.1953i	−1.31217	+	2.27274i
$726$	−18.3384	−	5.16762i	−0.680601	−	0.191788i
$727$	−14.7463			−0.546910			−0.273455	−	0.961885i	$-0.588166\pi$
$727$	−14.7463			−0.546910			−0.273455	+	0.961885i	$0.588166\pi$
$728$	5.74499	+	8.33080i	0.212924	+	0.308760i
$729$	−25.0360	+	10.1093i	−0.927260	+	0.374419i
$730$	−17.5023	+	19.4382i	−0.647788	+	0.719441i
$731$	5.39886	−	0.567443i	0.199684	−	0.0209876i
$732$	14.0525	+	8.89571i	0.519394	+	0.328795i
$733$	15.9877	+	14.3954i	0.590519	+	0.531706i	0.909310	−	0.416119i	$-0.136610\pi$
$733$	15.9877	+	14.3954i	0.590519	+	0.531706i	−0.318791	+	0.947825i	$0.603277\pi$
$734$	0.0458971	−	0.141257i	0.00169409	−	0.00521388i
$735$	−48.1358	−	20.5856i	−1.77552	−	0.759311i
$736$			6.66017i			0.245497i
$737$	−15.1508	+	20.3255i	−0.558087	+	0.748701i
$738$	27.0436	+	8.09832i	0.995490	+	0.298103i
$739$	−20.7536	−	46.6133i	−0.763433	−	1.71470i	−0.697180	−	0.716896i	$-0.745562\pi$
$739$	−20.7536	−	46.6133i	−0.763433	−	1.71470i	−0.0662536	−	0.997803i	$-0.521105\pi$
$740$	−4.17271	−	19.6311i	−0.153392	−	0.721652i
$741$	4.26319	−	11.5031i	0.156612	−	0.422578i
$742$	−32.1711	+	9.58482i	−1.18104	+	0.351870i
$743$	38.3659	−	27.8744i	1.40751	−	1.02261i	0.413827	−	0.910355i	$-0.364192\pi$
$743$	38.3659	−	27.8744i	1.40751	−	1.02261i	0.993679	−	0.112258i	$-0.0358083\pi$
$744$	2.18042	−	0.371324i	0.0799379	−	0.0136134i
$745$	14.1673	−	12.7563i	0.519049	−	0.467354i
$746$	1.42765	+	3.20655i	0.0522700	+	0.117400i
$747$	11.4701	−	10.8200i	0.419668	−	0.395883i
$748$	−1.36425	+	6.05312i	−0.0498819	+	0.221324i
$749$	−22.1675	+	4.14472i	−0.809982	+	0.151445i
$750$	−62.2548	+	17.4577i	−2.27323	+	0.637465i
$751$	−37.0996	+	7.88576i	−1.35378	+	0.287755i	−0.826980	−	0.562232i	$-0.809943\pi$
$751$	−37.0996	+	7.88576i	−1.35378	+	0.287755i	−0.526803	+	0.849987i	$0.676610\pi$
$752$	1.28772	−	6.05823i	0.0469582	−	0.220921i
$753$	19.1419	+	12.1175i	0.697569	+	0.441586i
$754$	−8.05641	+	18.0950i	−0.293397	+	0.658981i
$755$	7.44907	+	22.9259i	0.271099	+	0.834358i
$756$	−0.579366	+	13.7355i	−0.0210713	+	0.499556i
$757$	−39.1289	−	28.4288i	−1.42216	−	1.03326i	−0.991410	−	0.130793i	$-0.958248\pi$
$757$	−39.1289	−	28.4288i	−1.42216	−	1.03326i	−0.430754	−	0.902469i	$-0.641752\pi$
$758$	6.41483	+	11.1108i	0.232997	+	0.403563i
$759$	17.3479	+	34.1007i	0.629690	+	1.23778i
$760$	−3.99796	+	6.92468i	−0.145021	+	0.251184i
$761$	1.35625	−	12.9038i	0.0491640	−	0.467764i	−0.942048	−	0.335479i	$-0.891102\pi$
$761$	1.35625	−	12.9038i	0.0491640	−	0.467764i	0.991212	−	0.132285i	$-0.0422315\pi$
$762$	−7.20757	−	10.8217i	−0.261103	−	0.392029i
$763$	1.35915	+	0.829938i	0.0492045	+	0.0300458i
$764$	−2.54431	−	3.50194i	−0.0920499	−	0.126696i
$765$	−23.8160	−	4.48741i	−0.861071	−	0.162242i
$766$	−3.05068	+	14.3523i	−0.110225	+	0.518570i
$767$	0.724510	+	0.804650i	0.0261605	+	0.0290542i
$768$	−1.21045	+	1.23887i	−0.0436785	+	0.0447039i
$769$		−	23.5374i		−	0.848781i	−0.905479	−	0.424390i	$-0.860488\pi$
$769$		−	23.5374i		−	0.848781i	0.905479	−	0.424390i	$-0.139512\pi$
$770$	−29.8128	−	23.3852i	−1.07438	−	0.842742i
$771$	−17.5149	+	22.1497i	−0.630785	+	0.797702i
$772$	17.6146	+	1.85137i	0.633963	+	0.0666322i
$773$	36.5925	−	32.9480i	1.31614	−	1.18506i	0.347192	−	0.937794i	$-0.387135\pi$
$773$	36.5925	−	32.9480i	1.31614	−	1.18506i	0.968948	−	0.247264i	$-0.0795315\pi$
$774$	8.70262	−	0.201968i	0.312809	−	0.00725957i
$775$	−15.9182	−	7.08722i	−0.571797	−	0.254580i
$776$	−3.32691	+	2.41714i	−0.119429	+	0.0867704i
$777$	16.3771	+	13.6182i	0.587525	+	0.488549i
$778$	8.91298	+	2.89600i	0.319546	+	0.103827i
$779$	−17.3298	−	1.82143i	−0.620904	−	0.0652596i
$780$	−26.5854	+	10.5607i	−0.951909	+	0.378132i
$781$	2.42523	+	4.32191i	0.0867817	+	0.154650i
$782$	10.7909	−	6.23013i	0.385882	−	0.222789i
$783$	−23.5363	+	13.0432i	−0.841117	+	0.466128i
$784$	6.24705	+	3.15822i	0.223109	+	0.112793i
$785$	36.8775	−	11.9822i	1.31621	−	0.427664i
$786$	−3.53573	−	6.74467i	−0.126115	−	0.240574i
$787$	−28.3147	+	2.97600i	−1.00931	+	0.106083i	−0.594726	−	0.803928i	$-0.702740\pi$
$787$	−28.3147	+	2.97600i	−1.00931	+	0.106083i	−0.414584	+	0.910011i	$0.636073\pi$
$788$	20.3978	+	4.33568i	0.726640	+	0.154452i
$789$	31.5127	+	15.5987i	1.12188	+	0.555328i
$790$	−14.4748	−	10.5165i	−0.514989	−	0.374162i
$791$	7.32980	+	2.58260i	0.260618	+	0.0918266i
$792$	−2.97072	+	9.49604i	−0.105560	+	0.337427i
$793$	−18.3635	−	31.8066i	−0.652108	−	1.12948i
$794$	1.41737	−	0.631055i	0.0503007	−	0.0223953i
$795$	−6.06527	−	94.6974i	−0.215113	−	3.35857i
$796$	−11.1351	+	12.3668i	−0.394674	+	0.438330i
$797$	−28.4681	−	39.1830i	−1.00839	−	1.38793i	−0.920032	−	0.391843i	$-0.871838\pi$
$797$	−28.4681	−	39.1830i	−1.00839	−	1.38793i	−0.0883592	−	0.996089i	$-0.528162\pi$
$798$	−1.21843	−	8.39795i	−0.0431318	−	0.297284i
$799$	−11.0202	+	3.58068i	−0.389867	+	0.126675i
$800$	13.3469	−	2.83697i	0.471884	−	0.100302i
$801$	−0.900438	+	0.686682i	−0.0318154	+	0.0242627i
$802$	7.38526	+	4.26388i	0.260783	+	0.150563i
$803$	6.44174	−	19.0301i	0.227324	−	0.671558i
$804$	10.3847	+	8.21173i	0.366240	+	0.289605i
$805$	6.08959	+	75.8439i	0.214630	+	2.67315i
$806$	−4.64525	−	1.50933i	−0.163622	−	0.0531640i
$807$	3.11264	+	18.2774i	0.109570	+	0.643396i
$808$	−2.08736	−	19.8599i	−0.0734331	−	0.698669i
$809$	−1.33421	−	12.6942i	−0.0469083	−	0.446303i	−0.992617	−	0.121288i	$-0.961297\pi$
$809$	−1.33421	−	12.6942i	−0.0469083	−	0.446303i	0.945709	−	0.325014i	$-0.105369\pi$
$810$	−37.4772	−	10.2815i	−1.31681	−	0.361255i
$811$	45.8517	+	14.8981i	1.61007	+	0.523143i	0.969570	−	0.244815i	$-0.0787271\pi$
$811$	45.8517	+	14.8981i	1.61007	+	0.523143i	0.640500	+	0.767958i	$0.278727\pi$
$812$	1.09656	+	13.6573i	0.0384817	+	0.479278i
$813$	4.48573	−	5.67274i	0.157322	−	0.198952i
$814$	8.90764	+	12.5812i	0.312213	+	0.440972i
$815$	62.2241	+	35.9251i	2.17962	+	1.25840i
$816$	3.13953	+	0.802316i	0.109906	+	0.0280867i
$817$	−5.25578	+	1.11715i	−0.183876	+	0.0390841i
$818$	1.24187	−	0.403507i	0.0434209	−	0.0141083i
$819$	15.2162	−	26.2704i	0.531696	−	0.917961i
$820$	23.8832	+	32.8724i	0.834037	+	1.14795i
$821$	7.62406	−	8.46737i	0.266081	−	0.295513i	−0.595267	−	0.803528i	$-0.702954\pi$
$821$	7.62406	−	8.46737i	0.266081	−	0.295513i	0.861348	+	0.508015i	$0.169620\pi$
$822$	22.9889	−	1.47241i	0.801828	−	0.0513563i
$823$	51.3158	−	22.8473i	1.78876	−	0.796406i	0.811499	−	0.584354i	$-0.198652\pi$
$823$	51.3158	−	22.8473i	1.78876	−	0.796406i	0.977258	−	0.212052i	$-0.0680145\pi$
$824$	5.00032	+	8.66081i	0.174194	+	0.301713i
$825$	60.9478	−	49.2906i	2.12193	−	1.71608i
$826$	0.706407	+	0.248897i	0.0245791	+	0.00866024i
$827$	−32.4296	−	23.5615i	−1.12769	−	0.819313i	−0.142331	−	0.989819i	$-0.545460\pi$
$827$	−32.4296	−	23.5615i	−1.12769	−	0.819313i	−0.985357	+	0.170506i	$0.945460\pi$
$828$	18.0596	−	8.54811i	0.627616	−	0.297067i
$829$	45.9785	+	9.77303i	1.59690	+	0.339432i	0.918549	−	0.395307i	$-0.129362\pi$
$829$	45.9785	+	9.77303i	1.59690	+	0.339432i	0.678351	+	0.734738i	$0.262695\pi$
$830$	22.5713	−	2.37234i	0.783461	−	0.0823450i
$831$	18.6768	−	9.79090i	0.647893	−	0.339643i
$832$	3.63766	−	1.18195i	0.126113	−	0.0409767i
$833$	−0.726701	−	13.0759i	−0.0251787	−	0.453052i
$834$	−14.9653	+	4.19663i	−0.518207	+	0.145317i
$835$	18.2001	−	10.5078i	0.629840	−	0.363638i
$836$	0.716664	−	6.09967i	0.0247864	−	0.210961i
$837$	−3.80537	−	5.43581i	−0.131533	−	0.187889i
$838$	13.8137	+	1.45188i	0.477186	+	0.0501543i
$839$	−13.3373	−	4.33355i	−0.460455	−	0.149611i	0.0695986	−	0.997575i	$-0.477828\pi$
$839$	−13.3373	−	4.33355i	−0.460455	−	0.149611i	−0.530053	+	0.847964i	$0.677828\pi$
$840$	−12.6515	+	15.2146i	−0.436519	+	0.524955i
$841$	1.76540	−	1.28264i	0.0608759	−	0.0442290i
$842$	7.83025	+	3.48625i	0.269848	+	0.120144i
$843$	3.54727	+	4.27806i	0.122174	+	0.147344i
$844$	8.98553	−	8.09061i	0.309295	−	0.278490i
$845$	6.99806	+	0.735526i	0.240741	+	0.0253029i
$846$	−18.0802	+	4.28379i	−0.621609	+	0.147280i
$847$	28.1362	+	7.44005i	0.966771	+	0.255643i
$848$			12.6877i			0.435699i
$849$	−24.8961	−	24.3250i	−0.854431	−	0.834832i
$850$	−17.0816	−	18.9710i	−0.585894	−	0.650701i
$851$	6.43608	−	30.2794i	0.220626	−	1.03796i
$852$	2.29224	−	1.20166i	0.0785310	−	0.0411681i
$853$	−11.7929	−	16.2316i	−0.403783	−	0.555759i	0.557906	−	0.829904i	$-0.311605\pi$
$853$	−11.7929	−	16.2316i	−0.403783	−	0.555759i	−0.961688	+	0.274145i	$0.911605\pi$
$854$	−21.6822	−	13.2398i	−0.741951	−	0.453058i
$855$	23.9081	+	1.95323i	0.817641	+	0.0667990i
$856$	−0.890971	+	8.47702i	−0.0304527	+	0.289739i
$857$	14.7710	−	25.5842i	0.504568	−	0.873938i	−0.495418	−	0.868655i	$-0.664985\pi$
$857$	14.7710	−	25.5842i	0.504568	−	0.873938i	0.999986	−	0.00528309i	$-0.00168167\pi$
$858$	15.5465	−	15.5268i	0.530750	−	0.530077i
$859$	0.316537	+	0.548259i	0.0108001	+	0.0187063i	0.871375	−	0.490618i	$-0.163229\pi$
$859$	0.316537	+	0.548259i	0.0108001	+	0.0187063i	−0.860575	+	0.509324i	$0.829895\pi$
$860$	10.1364	+	7.36455i	0.345650	+	0.251129i
$861$	−41.5043	−	11.7013i	−1.41446	−	0.398781i
$862$	−1.06305	−	3.27173i	−0.0362076	−	0.111436i
$863$	2.94457	−	6.61362i	0.100234	−	0.225130i	−0.856467	−	0.516202i	$-0.827345\pi$
$863$	2.94457	−	6.61362i	0.100234	−	0.225130i	0.956701	+	0.291072i	$0.0940119\pi$
$864$	4.91289	+	1.69220i	0.167140	+	0.0575698i
$865$	−13.0133	+	61.2226i	−0.442464	+	2.08163i
$866$	−8.26502	+	1.75678i	−0.280857	+	0.0596980i
$867$	6.31345	+	22.5140i	0.214416	+	0.764615i
$868$	−3.32104	+	0.620946i	−0.112724	+	0.0210763i
$869$	13.4063	+	3.02151i	0.454778	+	0.102498i
$870$	−38.3215	−	5.61460i	−1.29922	−	0.190353i
$871$	−11.8913	−	26.7082i	−0.402921	−	0.904974i
$872$	0.447308	−	0.402758i	0.0151477	−	0.0136391i
$873$	10.8243	+	5.91889i	0.366346	+	0.200324i
$874$	−9.97768	+	7.24921i	−0.337500	+	0.245208i
$875$	94.6526	−	28.2001i	3.19984	−	0.953336i
$876$	−9.83817	−	3.64614i	−0.332401	−	0.123191i
$877$	−5.53107	−	26.0217i	−0.186771	−	0.878689i	−0.967313	−	0.253585i	$-0.918390\pi$
$877$	−5.53107	−	26.0217i	−0.186771	−	0.878689i	0.780542	−	0.625103i	$-0.214943\pi$
$878$	6.69316	+	15.0331i	0.225883	+	0.507342i
$879$	9.88338	−	3.92603i	0.333358	−	0.132422i
$880$	−11.6882	+	8.27537i	−0.394009	+	0.278963i
$881$			7.71388i			0.259887i	0.991521	+	0.129944i	$0.0414796\pi$
$881$			7.71388i			0.259887i	−0.991521	+	0.129944i	$0.958520\pi$
$882$	0.545888	−	20.9929i	0.0183810	−	0.706868i
$883$	−4.37770	+	13.4732i	−0.147321	+	0.453408i	−0.997302	−	0.0734053i	$-0.976613\pi$
$883$	−4.37770	+	13.4732i	−0.147321	+	0.453408i	0.849981	+	0.526813i	$0.176613\pi$
$884$	−5.31780	−	4.78816i	−0.178857	−	0.161043i
$885$	−1.13243	+	1.78888i	−0.0380661	+	0.0601327i
$886$	−26.2197	+	2.75580i	−0.880867	+	0.0925828i
$887$	−31.4042	+	34.8779i	−1.05445	+	1.17109i	−0.0696188	+	0.997574i	$0.522178\pi$
$887$	−31.4042	+	34.8779i	−1.05445	+	1.17109i	−0.984832	+	0.173512i	$0.944488\pi$
$888$	6.70032	−	4.46260i	0.224848	−	0.149755i
$889$	11.2754	+	16.3504i	0.378164	+	0.548375i
$890$	−1.62989			−0.0546342
$891$	29.5622	−	4.13251i	0.990370	−	0.138444i
$892$	−7.49404	+	12.9801i	−0.250919	+	0.434604i
$893$	10.4775	−	4.66490i	0.350617	−	0.156105i
$894$	6.85335	+	3.39239i	0.229210	+	0.113458i
$895$	3.04973	+	9.38610i	0.101941	+	0.313743i
$896$	1.81818	−	1.92203i	0.0607412	−	0.0642107i
$897$	−44.0860	−	1.79786i	−1.47199	−	0.0600288i
$898$	−23.0642	−	20.7671i	−0.769664	−	0.693008i
$899$	−4.42496	−	4.91442i	−0.147581	−	0.163905i
$900$	−24.8230	−	32.5501i	−0.827433	−	1.08500i
$901$	20.5569	−	11.8685i	0.684848	−	0.395397i
$902$	−26.8353	−	15.9344i	−0.893519	−	0.530556i
$903$	−13.2867	+	0.523251i	−0.442155	+	0.0174127i
$904$	1.72653	−	2.37636i	0.0574234	−	0.0790365i
$905$	1.26502	+	5.95147i	0.0420508	+	0.197833i
$906$	−7.44341	+	6.17190i	−0.247291	+	0.205048i
$907$	−2.54162	−	24.1819i	−0.0843930	−	0.802946i	−0.952083	−	0.305840i	$-0.901063\pi$
$907$	−2.54162	−	24.1819i	−0.0843930	−	0.802946i	0.867690	−	0.497106i	$-0.165604\pi$
$908$	−6.69815	−	2.98221i	−0.222286	−	0.0989680i
$909$	−51.1728	+	31.1496i	−1.69730	+	1.03317i
$910$	40.3439	−	16.7857i	1.33739	−	0.556440i
$911$	25.8939	−	35.6399i	0.857904	−	1.18080i	−0.124161	−	0.992262i	$-0.539624\pi$
$911$	25.8939	−	35.6399i	0.857904	−	1.18080i	0.982065	−	0.188541i	$-0.0603759\pi$
$912$	−3.17348	−	0.464956i	−0.105084	−	0.0153962i
$913$	−15.2024	+	8.53080i	−0.503126	+	0.282328i
$914$	−6.34778	−	3.66489i	−0.209966	−	0.121224i
$915$	50.1880	−	51.3663i	1.65916	−	1.69812i
$916$	−4.81890	+	14.8310i	−0.159221	+	0.490031i
$917$	5.56668	+	10.2140i	0.183828	+	0.337297i
$918$	−1.85394	−	9.54287i	−0.0611892	−	0.314962i
$919$	−7.58142	+	17.0282i	−0.250088	+	0.561707i	−0.994346	−	0.106185i	$-0.966136\pi$
$919$	−7.58142	+	17.0282i	−0.250088	+	0.561707i	0.744258	+	0.667892i	$0.232803\pi$
$920$	28.1301	+	5.97924i	0.927422	+	0.197130i
$921$	−34.9778	+	2.24029i	−1.15256	+	0.0738202i
$922$	−1.56879	+	14.9260i	−0.0516652	+	0.491562i
$923$	−5.71531			−0.188122
$924$	4.30289	−	14.5769i	0.141555	−	0.479544i
$925$	−63.4210			−2.08527
$926$	−2.80444	+	26.6824i	−0.0921596	+	0.876840i
$927$	17.0668	−	24.6747i	0.560547	−	0.810423i
$928$	5.06543	+	1.07669i	0.166281	+	0.0353441i
$929$	−21.3577	+	47.9702i	−0.700724	+	1.57385i	0.113656	+	0.993520i	$0.463744\pi$
$929$	−21.3577	+	47.9702i	−0.700724	+	1.57385i	−0.814380	+	0.580332i	$0.802923\pi$
$930$	0.389156	−	9.54264i	0.0127609	−	0.312916i
$931$	2.06819	+	12.7963i	0.0677823	+	0.419383i
$932$	4.02862	−	12.3988i	0.131962	−	0.406136i
$933$	−14.0214	−	13.6998i	−0.459041	−	0.448511i
$934$	0.616735	+	0.356072i	0.0201802	+	0.0116510i
$935$	24.3414	+	11.1963i	0.796048	+	0.366160i
$936$	−7.87378	−	8.34685i	−0.257363	−	0.272825i
$937$	3.78576	−	5.21065i	0.123675	−	0.170224i	−0.742690	−	0.669636i	$-0.766450\pi$
$937$	3.78576	−	5.21065i	0.123675	−	0.170224i	0.866365	+	0.499411i	$0.166450\pi$
$938$	−16.0635	−	12.2857i	−0.524492	−	0.401142i
$939$	−4.61984	+	12.4655i	−0.150763	+	0.406795i
$940$	−24.4317	−	10.8777i	−0.796874	−	0.354791i
$941$	4.03671	+	38.4067i	0.131593	+	1.25202i	0.838573	+	0.544789i	$0.183390\pi$
$941$	4.03671	+	38.4067i	0.131593	+	1.25202i	−0.706980	+	0.707233i	$0.749943\pi$
$942$	9.92784	+	11.9731i	0.323467	+	0.390106i
$943$	13.0303	+	61.3030i	0.424326	+	1.99630i
$944$	0.166393	−	0.229021i	0.00541564	−	0.00745399i
$945$	57.4937	+	14.7782i	1.87027	+	0.480736i
$946$	−9.38821	−	2.11591i	−0.305237	−	0.0687943i
$947$	−13.7152	+	7.91848i	−0.445685	+	0.257316i	−0.706006	−	0.708206i	$-0.749505\pi$
$947$	−13.7152	+	7.91848i	−0.445685	+	0.257316i	0.260321	+	0.965522i	$0.416172\pi$
$948$	1.77695	−	6.95337i	0.0577127	−	0.225835i
$949$	15.5035	+	17.2183i	0.503263	+	0.558931i
$950$	18.7774	+	16.9073i	0.609220	+	0.548544i
$951$	−2.06315	+	50.5912i	−0.0669021	+	1.64053i
$952$	−4.81489	−	1.14791i	−0.156052	−	0.0372041i
$953$	−2.37126	−	7.29798i	−0.0768126	−	0.236405i	0.905276	−	0.424823i	$-0.139664\pi$
$953$	−2.37126	−	7.29798i	−0.0768126	−	0.236405i	−0.982089	+	0.188419i	$0.939664\pi$
$954$	34.4039	−	16.2843i	1.11387	−	0.527224i
$955$	−17.0751	+	7.60233i	−0.552538	+	0.246006i
$956$	3.22962	−	5.59387i	0.104453	−	0.180919i
$957$	28.7400	−	7.68131i	0.929032	−	0.248301i
$958$	27.0737			0.874710
$959$	−35.0751	+	2.81622i	−1.13263	+	0.0909405i
$960$	4.14584	+	6.22472i	0.133806	+	0.200902i
$961$	−19.6519	+	21.8256i	−0.633932	+	0.704053i
$962$	−17.6802	+	1.85827i	−0.570033	+	0.0599129i
$963$	24.1297	−	8.46404i	0.777569	−	0.272750i
$964$	11.4622	+	10.3206i	0.369172	+	0.332404i
$965$	23.6332	−	72.7355i	0.760780	−	2.34144i
$966$	−27.3720	+	13.5015i	−0.880679	+	0.434403i
$967$			18.8028i			0.604656i	0.953204	+	0.302328i	$0.0977638\pi$
$967$			18.8028i			0.604656i	−0.953204	+	0.302328i	$0.902236\pi$
$968$	5.73146	−	9.38884i	0.184216	−	0.301769i
$969$	2.21524	+	5.57665i	0.0711639	+	0.179148i
$970$	7.22236	+	16.2217i	0.231896	+	0.520847i
$971$	−8.23654	−	38.7499i	−0.264323	−	1.24354i	−0.887260	−	0.461270i	$-0.847394\pi$
$971$	−8.23654	−	38.7499i	−0.264323	−	1.24354i	0.622937	−	0.782272i	$-0.285939\pi$
$972$	−1.71699	−	15.4936i	−0.0550724	−	0.496958i
$973$	22.7534	−	6.77896i	0.729439	−	0.217323i
$974$	−29.3251	+	21.3059i	−0.939636	+	0.682686i
$975$	15.1760	+	89.1137i	0.486022	+	2.85392i
$976$	−7.13581	+	6.42511i	−0.228412	+	0.205663i
$977$	5.12931	+	11.5206i	0.164101	+	0.368577i	0.976815	−	0.214086i	$-0.0686773\pi$
$977$	5.12931	+	11.5206i	0.164101	+	0.368577i	−0.812714	+	0.582663i	$0.802011\pi$
$978$	−4.17802	+	28.5164i	−0.133598	+	0.911854i
$979$	1.14982	−	0.495166i	0.0367485	−	0.0158256i
$980$	18.9475	−	23.5499i	0.605256	−	0.752275i
$981$	−1.66622	−	0.695987i	−0.0531982	−	0.0222212i
$982$	−19.6173	+	4.16979i	−0.626014	+	0.133063i
$983$	12.9052	−	60.7141i	0.411611	−	1.93648i	0.0669372	−	0.997757i	$-0.478677\pi$
$983$	12.9052	−	60.7141i	0.411611	−	1.93648i	0.344674	−	0.938722i	$-0.387989\pi$
$984$	−8.71772	+	13.7713i	−0.277911	+	0.439013i
$985$	36.6246	−	82.2603i	1.16696	−	2.62103i
$986$	−2.99389	−	9.21425i	−0.0953450	−	0.293442i
$987$	27.5086	−	6.98896i	0.875608	−	0.222461i
$988$	5.73008	+	4.16315i	0.182298	+	0.132447i
$989$	9.66275	+	16.7364i	0.307258	+	0.532186i
$990$	37.4408	+	21.0724i	1.18995	+	0.669725i
$991$	20.6992	−	35.8521i	0.657533	−	1.13888i	−0.323720	−	0.946153i	$-0.604933\pi$
$991$	20.6992	−	35.8521i	0.657533	−	1.13888i	0.981252	−	0.192727i	$-0.0617332\pi$
$992$	−0.133482	+	1.26999i	−0.00423805	+	0.0403223i
$993$	−23.2502	+	15.4853i	−0.737822	+	0.491410i
$994$	−3.47135	+	1.89189i	−0.110104	+	0.0600072i
$995$	42.2362	+	58.1332i	1.33898	+	1.84295i
$996$	4.22685	+	8.06301i	0.133933	+	0.255486i
$997$	−0.548307	+	2.57958i	−0.0173651	+	0.0816962i	−0.985977	−	0.166882i	$-0.946630\pi$
$997$	−0.548307	+	2.57958i	−0.0173651	+	0.0816962i	0.968612	+	0.248578i	$0.0799634\pi$
$998$	29.2875	+	32.5271i	0.927080	+	1.02963i
$999$	−20.7004	−	12.4409i	−0.654931	−	0.393613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.b.95.8	yes	128
3.2	odd	2		462.2.bc.a.95.16	✓	128
7.2	even	3	inner	462.2.bc.b.359.4	yes	128
11.8	odd	10		462.2.bc.a.305.5	yes	128
21.2	odd	6		462.2.bc.a.359.5	yes	128
33.8	even	10	inner	462.2.bc.b.305.4	yes	128
77.30	odd	30		462.2.bc.a.107.16	yes	128
231.107	even	30	inner	462.2.bc.b.107.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.16	✓	128	3.2	odd	2
462.2.bc.a.107.16	yes	128	77.30	odd	30
462.2.bc.a.305.5	yes	128	11.8	odd	10
462.2.bc.a.359.5	yes	128	21.2	odd	6
462.2.bc.b.95.8	yes	128	1.1	even	1	trivial
462.2.bc.b.107.8	yes	128	231.107	even	30	inner
462.2.bc.b.305.4	yes	128	33.8	even	10	inner
462.2.bc.b.359.4	yes	128	7.2	even	3	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.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.110709 + 1.72851i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.75629 + 3.94468i) q^{5} +(-1.73061 - 0.0705756i) q^{6} +(2.64495 + 0.0650804i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97549 + 0.382724i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(0.110709 + 1.72851i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-1.75629 + 3.94468i) q^{5} +(-1.73061 - 0.0705756i) q^{6} +(2.64495 + 0.0650804i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.97549 + 0.382724i) q^{9} +(-3.73949 - 2.15900i) q^{10} +(3.29397 + 0.387016i) q^{11} +(0.251087 - 1.71375i) q^{12} +(-2.24820 + 3.09438i) q^{13} +(-0.341197 + 2.62366i) q^{14} +(-7.01286 - 2.59904i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.195558 - 1.86061i) q^{17} +(-0.0696043 - 2.99919i) q^{18} +(0.385005 + 1.81130i) q^{19} +(2.53805 - 3.49333i) q^{20} +(0.180329 + 4.57903i) q^{21} +(-0.729209 + 3.23547i) q^{22} +(5.76787 - 3.33008i) q^{23} +(1.67812 + 0.428848i) q^{24} +(-9.13033 - 10.1403i) q^{25} +(-2.84243 - 2.55934i) q^{26} +(-0.990956 - 5.10078i) q^{27} +(-2.57362 - 0.613574i) q^{28} +(-1.60027 - 4.92514i) q^{29} +(3.31785 - 6.70277i) q^{30} +(1.16659 - 0.519398i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.304288 + 5.73650i) q^{33} +1.87086 q^{34} +(-4.90201 + 10.3192i) q^{35} +(2.99004 + 0.244278i) q^{36} +(3.11006 - 3.45407i) q^{37} +(-1.84163 + 0.193563i) q^{38} +(-5.59756 - 3.54346i) q^{39} +(3.20889 + 2.88930i) q^{40} +(-2.90786 + 8.94949i) q^{41} +(-4.57279 - 0.299298i) q^{42} +2.90165i q^{43} +(-3.14152 - 1.06341i) q^{44} +(3.71608 - 12.4095i) q^{45} +(2.70893 + 6.08437i) q^{46} +(-1.28772 - 6.05823i) q^{47} +(-0.601910 + 1.62410i) q^{48} +(6.99153 + 0.344269i) q^{49} +(11.0391 - 8.02037i) q^{50} +(3.19444 - 0.544012i) q^{51} +(2.84243 - 2.55934i) q^{52} +(5.16057 + 11.5908i) q^{53} +(5.17643 - 0.452350i) q^{54} +(-7.31180 + 12.3139i) q^{55} +(0.879230 - 2.49539i) q^{56} +(-3.08823 + 0.866012i) q^{57} +(5.06543 - 1.07669i) q^{58} +(0.0588568 - 0.276899i) q^{59} +(6.31924 + 4.00030i) q^{60} +(-3.90556 + 8.77203i) q^{61} +(0.394611 + 1.21449i) q^{62} +(-7.89492 + 0.818640i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-8.25787 - 14.3031i) q^{65} +(-5.67327 - 0.902248i) q^{66} +(-3.82181 + 6.61957i) q^{67} +(-0.195558 + 1.86061i) q^{68} +(6.39464 + 9.60115i) q^{69} +(-9.75026 - 5.95381i) q^{70} +(0.878299 + 1.20888i) q^{71} +(-0.555484 + 2.94812i) q^{72} +(1.25945 - 5.92524i) q^{73} +(3.11006 + 3.45407i) q^{74} +(16.5167 - 16.9045i) q^{75} -1.85177i q^{76} +(8.68719 + 1.23801i) q^{77} +(4.10915 - 5.19651i) q^{78} +(4.12085 + 0.433118i) q^{79} +(-3.20889 + 2.88930i) q^{80} +(8.70704 - 2.27758i) q^{81} +(-8.59651 - 3.82741i) q^{82} +(-4.25224 + 3.08943i) q^{83} +(0.775645 - 4.51646i) q^{84} +(7.68299 + 2.49635i) q^{85} +(-2.88576 - 0.303305i) q^{86} +(8.33598 - 3.31135i) q^{87} +(1.38597 - 3.01315i) q^{88} +(0.326895 - 0.188733i) q^{89} +(11.9531 + 4.99287i) q^{90} +(-6.14776 + 8.03817i) q^{91} +(-6.33420 + 2.05810i) q^{92} +(1.02694 + 1.95895i) q^{93} +(6.15965 - 0.647405i) q^{94} +(-7.82120 - 1.66245i) q^{95} +(-1.55229 - 0.768377i) q^{96} +(-3.32691 - 2.41714i) q^{97} +(-1.07320 + 6.91724i) q^{98} +(-9.94928 + 0.109119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^16 - 2 * q^17 - 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 + 38 * q^29 + 6 * q^30 - 3 * q^31 - 64 * q^32 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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