LMFDB - Embedded newform 462.2.bc.b.107.8

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			107.8
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.b.95.8

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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	−0.630497	−	0.776192i	$-0.717149\pi$
$5$	−1.75629	−	3.94468i	−0.785435	−	1.76412i	−0.154938	−	0.987924i	$-0.549518\pi$
$6$	−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	0.374066	−	0.927402i	$-0.377963\pi$
$13$	−2.24820	−	3.09438i	−0.623538	−	0.858227i	−0.997605	+	0.0691750i	$0.977963\pi$
$14$	−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	0.944874	+	0.327435i	$0.106184\pi$
$17$	−0.195558	+	1.86061i	−0.0474299	+	0.451265i	−0.992303	+	0.123830i	$0.960482\pi$
$18$	−0.0696043	+	2.99919i	−0.0164059	+	0.706916i
$19$	0.385005	−	1.81130i	0.0883261	−	0.415542i	−0.911663	−	0.410938i	$-0.865201\pi$
$19$	0.385005	−	1.81130i	0.0883261	−	0.415542i	0.999989	−	0.00460363i	$-0.00146539\pi$
$20$	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	0.961151	−	0.276022i	$-0.0890163\pi$
$23$	5.76787	+	3.33008i	1.20268	+	0.694370i	0.241534	+	0.970392i	$0.422350\pi$
$24$	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	0.685323	+	0.728239i	$0.259661\pi$
$29$	−1.60027	+	4.92514i	−0.297163	+	0.914575i	−0.982486	+	0.186335i	$0.940339\pi$
$30$	3.31785	+	6.70277i	0.605754	+	1.22375i
$31$	1.16659	+	0.519398i	0.209525	+	0.0932866i	0.508816	−	0.860875i	$-0.330083\pi$
$31$	1.16659	+	0.519398i	0.209525	+	0.0932866i	−0.299291	+	0.954162i	$0.596750\pi$
$32$	−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	0.942414	−	0.334447i	$-0.108550\pi$
$37$	3.11006	+	3.45407i	0.511290	+	0.567845i	−0.431124	+	0.902292i	$0.641883\pi$
$38$	−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	−0.872151	−	0.489237i	$-0.837275\pi$
$41$	−2.90786	−	8.94949i	−0.454132	−	1.39768i	0.418019	−	0.908438i	$-0.362725\pi$
$42$	−4.57279	+	0.299298i	−0.705597	+	0.0461827i
$43$		−	2.90165i		−	0.442498i	−0.975217	−	0.221249i	$-0.928987\pi$
$43$		−	2.90165i		−	0.442498i	0.975217	−	0.221249i	$-0.0710134\pi$
$44$	−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	0.778751	+	0.627333i	$0.215854\pi$
$47$	−1.28772	+	6.05823i	−0.187833	+	0.883684i	−0.966584	+	0.256351i	$0.917480\pi$
$48$	−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	−0.0937353	−	0.995597i	$-0.529881\pi$
$53$	5.16057	−	11.5908i	0.708859	−	1.59212i	0.802594	−	0.596526i	$-0.203453\pi$
$54$	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	0.981813	−	0.189852i	$-0.0608007\pi$
$59$	0.0588568	+	0.276899i	0.00766250	+	0.0360492i	−0.974150	+	0.225901i	$0.927467\pi$
$60$	6.31924	−	4.00030i	0.815810	−	0.516437i
$61$	−3.90556	−	8.77203i	−0.500055	−	1.12314i	−0.970585	−	0.240759i	$-0.922604\pi$
$61$	−3.90556	−	8.77203i	−0.500055	−	1.12314i	0.470530	−	0.882384i	$-0.344063\pi$
$62$	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	0.532377	−	0.846507i	$-0.321299\pi$
$67$	−3.82181	−	6.61957i	−0.466908	−	0.808709i	−0.999285	+	0.0377985i	$0.987966\pi$
$68$	−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	−0.753713	−	0.657204i	$-0.771739\pi$
$71$	0.878299	−	1.20888i	0.104235	−	0.143467i	0.857948	+	0.513737i	$0.171739\pi$
$72$	−0.555484	−	2.94812i	−0.0654644	−	0.347440i
$73$	1.25945	+	5.92524i	0.147407	+	0.693496i	0.988328	+	0.152339i	$0.0486805\pi$
$73$	1.25945	+	5.92524i	0.147407	+	0.693496i	−0.840921	+	0.541158i	$0.817986\pi$
$74$	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	0.130167	−	0.991492i	$-0.458449\pi$
$79$	4.12085	−	0.433118i	0.463631	−	0.0487296i	0.333465	+	0.942763i	$0.391782\pi$
$80$	−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	0.329427	−	0.944181i	$-0.393144\pi$
$83$	−4.25224	−	3.08943i	−0.466744	−	0.339109i	−0.796171	+	0.605072i	$0.793144\pi$
$84$	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	0.517225	−	0.855849i	$-0.326965\pi$
$89$	0.326895	+	0.188733i	0.0346508	+	0.0200056i	−0.482575	+	0.875855i	$0.660298\pi$
$90$	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	−0.743732	−	0.668478i	$-0.766946\pi$
$97$	−3.32691	+	2.41714i	−0.337797	+	0.245424i	0.405935	+	0.913902i	$0.366946\pi$
$98$	−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	0.953880	+	0.300188i	$0.0970496\pi$
$101$	18.2429	+	8.12225i	1.81523	+	0.808194i	0.861354	+	0.508006i	$0.169617\pi$
$102$	0.207122	−	3.23380i	0.0205081	−	0.320194i
$103$	−6.69173	−	7.43192i	−0.659356	−	0.732289i	0.317008	−	0.948423i	$-0.397322\pi$
$103$	−6.69173	−	7.43192i	−0.659356	−	0.732289i	−0.976364	+	0.216134i	$0.930655\pi$
$104$	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	−0.213561	−	0.976930i	$-0.568506\pi$
$107$	−8.33745	−	1.77218i	−0.806012	−	0.171323i	−0.592451	+	0.805607i	$0.701840\pi$
$108$	−0.0912118	−	5.19535i	−0.00877686	−	0.499923i
$109$	0.521271	−	0.300956i	0.0499287	−	0.0288263i	−0.474828	−	0.880079i	$-0.657490\pi$
$109$	0.521271	−	0.300956i	0.0499287	−	0.0288263i	0.524757	+	0.851252i	$0.324156\pi$
$110$	−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	−0.174655	−	0.984630i	$-0.555881\pi$
$113$	2.79358	−	0.907689i	0.262798	−	0.0853882i	0.437452	+	0.899242i	$0.355881\pi$
$114$	−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	−0.567057	−	0.823679i	$-0.691918\pi$
$127$	4.41242	−	6.07317i	0.391539	−	0.538907i	0.958595	+	0.284772i	$0.0919179\pi$
$128$	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	−0.753867	−	0.657027i	$-0.771814\pi$
$131$	2.19833	−	3.80762i	0.192069	−	0.332673i	0.945936	+	0.324354i	$0.105147\pi$
$132$	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	−0.479008	−	0.877811i	$-0.659003\pi$
$137$	−13.2270	−	1.39021i	−1.13006	−	0.118774i	−0.651047	+	0.759037i	$0.725670\pi$
$138$	−10.2170	−	5.35601i	−0.869727	−	0.455934i
$139$	8.53433	+	2.77297i	0.723873	+	0.235200i	0.647701	−	0.761894i	$-0.275730\pi$
$139$	8.53433	+	2.77297i	0.723873	+	0.235200i	0.0761713	+	0.997095i	$0.475730\pi$
$140$	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	−0.565241	−	0.824926i	$-0.691217\pi$
$149$	−4.03330	+	1.79574i	−0.330421	+	0.147113i	0.234820	+	0.972039i	$0.424550\pi$
$150$	15.0854	−	18.1932i	1.23172	−	1.48547i
$151$	4.14869	+	3.73550i	0.337616	+	0.303991i	0.820447	−	0.571723i	$-0.193725\pi$
$151$	4.14869	+	3.73550i	0.337616	+	0.303991i	−0.482831	+	0.875714i	$0.660391\pi$
$152$	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	−0.933569	−	0.358397i	$-0.883323\pi$
$157$	−6.00875	+	6.67339i	−0.479551	+	0.532595i	0.454019	+	0.890992i	$0.349990\pi$
$158$	−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	0.822471	+	0.568806i	$0.192595\pi$
$163$	1.73933	+	16.5486i	0.136234	+	1.29618i	−0.686237	+	0.727378i	$0.740739\pi$
$164$	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	−0.729615	−	0.683858i	$-0.760301\pi$
$167$	−3.93748	+	2.86075i	−0.304691	+	0.221371i	0.424924	+	0.905229i	$0.360301\pi$
$168$	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	0.712485	−	0.701688i	$-0.247570\pi$
$173$	14.1785	+	3.01373i	1.07797	+	0.229130i	0.365485	+	0.930817i	$0.380903\pi$
$174$	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	0.730162	−	0.683274i	$-0.239445\pi$
$179$	1.69852	+	1.52935i	0.126953	+	0.114309i	−0.603209	+	0.797584i	$0.706111\pi$
$180$	−6.21496	−	11.3657i	−0.463236	−	0.847152i
$181$	1.13997	+	0.828240i	0.0847337	+	0.0615626i	0.629346	−	0.777126i	$-0.283323\pi$
$181$	1.13997	+	0.828240i	0.0847337	+	0.0615626i	−0.544612	+	0.838688i	$0.683323\pi$
$182$	−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	−0.544494	−	0.838764i	$-0.683278\pi$
$191$	3.21681	−	2.89643i	0.232760	−	0.209578i	0.777254	+	0.629186i	$0.216612\pi$
$192$	0.926426	+	1.46347i	0.0668591	+	0.105617i
$193$	−17.6146	−	1.85137i	−1.26793	−	0.133264i	−0.553425	−	0.832899i	$-0.686680\pi$
$193$	−17.6146	−	1.85137i	−1.26793	−	0.133264i	−0.714501	+	0.699634i	$0.753346\pi$
$194$	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	0.994254	+	0.107046i	$0.0341391\pi$
$199$	8.32060	+	14.4117i	0.589831	+	1.02162i	−0.404423	+	0.914572i	$0.632528\pi$
$200$	−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	0.490984	−	0.871169i	$-0.336637\pi$
$211$	−7.10704	−	9.78201i	−0.489269	−	0.673421i	−0.980253	+	0.197748i	$0.936637\pi$
$212$	−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	0.977704	+	0.209988i	$0.0673426\pi$
$223$	4.63157	+	14.2545i	0.310153	+	0.954552i	−0.667551	+	0.744564i	$0.732657\pi$
$224$	−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	0.0363419	−	0.999339i	$-0.488429\pi$
$227$	7.17181	−	1.52442i	0.476010	−	0.101179i	0.439668	+	0.898160i	$0.355096\pi$
$228$	3.20080	+	0.205008i	0.211978	+	0.0135770i
$229$	1.63005	+	15.5088i	0.107716	+	1.02485i	0.906204	+	0.422842i	$0.138967\pi$
$229$	1.63005	+	15.5088i	0.107716	+	1.02485i	−0.798487	+	0.602012i	$0.794366\pi$
$230$	−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	−0.943918	−	0.330179i	$-0.892891\pi$
$233$	−1.36272	−	12.9655i	−0.0892750	−	0.849395i	0.854643	−	0.519216i	$-0.173776\pi$
$234$	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	0.865516	−	0.500881i	$-0.166991\pi$
$239$	−1.99602	−	6.14310i	−0.129111	−	0.397364i	−0.994628	+	0.103517i	$0.966991\pi$
$240$	−5.34944	+	5.22673i	−0.345305	+	0.337384i
$241$	−13.3575	+	7.71194i	−0.860430	+	0.496770i	−0.864156	−	0.503223i	$-0.832147\pi$
$241$	−13.3575	+	7.71194i	−0.860430	+	0.496770i	0.00372601	+	0.999993i	$0.498814\pi$
$242$	−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	0.979507	−	0.201410i	$-0.0645524\pi$
$251$	7.68813	+	10.5818i	0.485270	+	0.667917i	−0.494237	+	0.869327i	$0.664552\pi$
$252$	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	−0.198294	−	0.980143i	$-0.563540\pi$
$257$	12.1156	−	10.9090i	0.755752	−	0.680482i	0.954046	+	0.299660i	$0.0968734\pi$
$258$	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	0.988366	+	0.152094i	$0.0486017\pi$
$263$	10.1504	+	17.5810i	0.625901	+	1.08409i	−0.362465	+	0.931997i	$0.618065\pi$
$264$	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	0.423348	−	0.905967i	$-0.360855\pi$
$269$	10.6458	+	1.11891i	0.649084	+	0.0682215i	0.225736	+	0.974189i	$0.427521\pi$
$270$	−7.30691	−	21.2138i	−0.444684	−	1.29103i
$271$	−3.10292	+	2.79389i	−0.188489	+	0.169716i	−0.757973	−	0.652286i	$-0.773810\pi$
$271$	−3.10292	+	2.79389i	−0.188489	+	0.169716i	0.569483	+	0.822003i	$0.307143\pi$
$272$	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	−0.999013	−	0.0444150i	$-0.985858\pi$
$277$	−4.95199	+	11.1223i	−0.297536	+	0.668277i	0.701477	+	0.712692i	$0.252524\pi$
$278$	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	0.662513	−	0.749050i	$-0.269490\pi$
$281$	2.59579	+	1.88595i	0.154852	+	0.112507i	−0.507661	+	0.861557i	$0.669490\pi$
$282$	1.80098	−	10.5753i	0.107247	−	0.629752i
$283$	−14.9341	−	13.4467i	−0.887738	−	0.799323i	0.0927932	−	0.995685i	$-0.470420\pi$
$283$	−14.9341	−	13.4467i	−0.887738	−	0.799323i	−0.980531	+	0.196362i	$0.937087\pi$
$284$	−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	−0.991057	−	0.133436i	$-0.957399\pi$
$293$	−1.89733	+	5.83938i	−0.110843	+	0.341141i	0.880214	+	0.474577i	$0.157399\pi$
$294$	−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	$-0.804044\pi$
$307$		−	20.2358i		−	1.15492i	0.816419	−	0.577460i	$-0.195956\pi$
$308$	−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	0.395277	−	0.918562i	$-0.370649\pi$
$311$	−8.41084	−	7.57316i	−0.476935	−	0.429434i	−0.872212	+	0.489128i	$0.837315\pi$
$312$	−5.09977	−	4.22861i	−0.288718	−	0.239398i
$313$	7.01174	−	3.12183i	0.396327	−	0.176456i	−0.198889	−	0.980022i	$-0.563733\pi$
$313$	7.01174	−	3.12183i	0.396327	−	0.176456i	0.595216	+	0.803566i	$0.297067\pi$
$314$	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	0.756765	−	0.653688i	$-0.226779\pi$
$317$	29.0730	−	3.05569i	1.63290	−	0.171625i	0.876137	+	0.482063i	$0.160112\pi$
$318$	−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	−0.554683	−	0.832062i	$-0.687161\pi$
$331$	8.06414	−	13.9675i	0.443245	−	0.767723i	0.997928	+	0.0643388i	$0.0204938\pi$
$332$	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	0.752397	−	0.658709i	$-0.228897\pi$
$337$	17.8788	+	5.80917i	0.973920	+	0.316446i	0.221523	+	0.975155i	$0.428897\pi$
$338$	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	0.948376	+	0.317149i	$0.102726\pi$
$347$	−0.842256	+	8.01353i	−0.0452147	+	0.430189i	−0.993590	+	0.113040i	$0.963941\pi$
$348$	−8.84228	−	1.50584i	−0.473996	−	0.0807214i
$349$	−29.0378	+	9.43496i	−1.55436	+	0.505042i	−0.955294	−	0.295659i	$-0.904461\pi$
$349$	−29.0378	+	9.43496i	−1.55436	+	0.505042i	−0.599065	+	0.800701i	$0.704461\pi$
$350$	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	−0.782133	−	0.623112i	$-0.785868\pi$
$353$	−11.9037	+	6.87258i	−0.633568	+	0.365791i	0.148565	+	0.988903i	$0.452535\pi$
$354$	−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	0.695846	−	0.718191i	$-0.255030\pi$
$359$	−1.72698	−	1.91800i	−0.0911463	−	0.101228i	−0.786992	+	0.616963i	$0.788363\pi$
$360$	−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	−0.211702	−	0.977334i	$-0.567901\pi$
$367$	−0.145281	+	0.0308803i	−0.00758358	+	0.00161194i	0.204118	+	0.978946i	$0.434567\pi$
$368$	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	0.576628	−	0.817007i	$-0.304368\pi$
$373$	3.03976	+	1.75501i	0.157393	+	0.0908707i	−0.419235	+	0.907878i	$0.637702\pi$
$374$	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	0.821537	−	0.570156i	$-0.193117\pi$
$379$	10.3794	+	7.54109i	0.533155	+	0.387360i	−0.288382	+	0.957516i	$0.593117\pi$
$380$	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	0.275917	−	0.961181i	$-0.411019\pi$
$383$	14.5926	−	1.53374i	0.745645	−	0.0783705i	0.469728	+	0.882811i	$0.344352\pi$
$384$	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	0.999537	+	0.0304306i	$0.00968786\pi$
$389$	1.94848	+	9.16687i	0.0987917	+	0.464779i	−0.900745	+	0.434348i	$0.856979\pi$
$390$	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	−0.884836	−	0.465903i	$-0.845730\pi$
$397$	−0.775753	+	1.34364i	−0.0389339	+	0.0674356i	0.845902	+	0.533339i	$0.179063\pi$
$398$	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	0.979202	−	0.202890i	$-0.0650333\pi$
$401$	3.46856	+	7.79050i	0.173211	+	0.389039i	−0.805990	+	0.591929i	$0.798367\pi$
$402$	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	−0.926200	−	0.377032i	$-0.876945\pi$
$409$	−0.531107	+	1.19289i	−0.0262615	+	0.0589844i	0.899939	+	0.436017i	$0.143611\pi$
$410$	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	$0.110183\pi$
$419$			13.8898i			0.678560i	−0.940685	+	0.339280i	$0.889817\pi$
$420$	16.4537	−	10.9919i	0.802860	−	0.536348i
$421$	2.64867	+	8.15177i	0.129088	+	0.397293i	0.994624	−	0.103555i	$-0.0330217\pi$
$421$	2.64867	+	8.15177i	0.129088	+	0.397293i	−0.865535	+	0.500848i	$0.833022\pi$
$422$	−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	0.329649	−	0.944103i	$-0.393070\pi$
$431$	−3.14269	−	1.39921i	−0.151378	−	0.0673978i	−0.481027	+	0.876706i	$0.659736\pi$
$432$	1.16939	+	5.06286i	0.0562624	+	0.243587i
$433$	2.61109	−	8.03611i	0.125481	−	0.386191i	−0.868507	−	0.495676i	$-0.834920\pi$
$433$	2.61109	−	8.03611i	0.125481	−	0.386191i	0.993988	+	0.109485i	$0.0349203\pi$
$434$	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	0.799918	−	0.600109i	$-0.204876\pi$
$439$	14.2511	+	8.22787i	0.680168	+	0.392695i	−0.119751	+	0.992804i	$0.538209\pi$
$440$	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	−0.632334	−	0.774696i	$-0.717903\pi$
$443$	5.48140	−	25.7880i	0.260429	−	1.22522i	0.892763	−	0.450527i	$-0.148764\pi$
$444$	−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	−0.981350	−	0.192229i	$-0.938428\pi$
$449$	−18.2425	−	25.1086i	−0.860917	−	1.18495i	0.120433	−	0.992721i	$-0.461572\pi$
$450$	−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	0.830291	−	0.557330i	$-0.188174\pi$
$457$	−2.98129	−	6.69610i	−0.139459	−	0.313230i	−0.969750	+	0.244100i	$0.921508\pi$
$458$	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	0.920123	−	0.391629i	$-0.128088\pi$
$467$	0.289655	+	0.650576i	0.0134036	+	0.0301051i	−0.906720	+	0.421734i	$0.861422\pi$
$468$	−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	0.716817	+	0.697261i	$0.245598\pi$
$479$	−2.82997	+	26.9253i	−0.129305	+	1.23025i	−0.846122	+	0.532989i	$0.821069\pi$
$480$	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	0.125547	−	0.992088i	$-0.459931\pi$
$487$	24.2545	−	26.9374i	1.09908	−	1.22065i	0.973530	−	0.228561i	$-0.0734019\pi$
$488$	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	−0.708250	−	0.705961i	$-0.750515\pi$
$491$	6.19751	−	19.0740i	0.279690	−	0.860797i	0.987940	−	0.154836i	$-0.0494848\pi$
$492$	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	0.804537	+	0.593902i	$0.202413\pi$
$499$	29.2875	+	32.5271i	1.31109	+	1.45611i	0.506551	+	0.862210i	$0.330920\pi$
$500$	−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	−0.979756	−	0.200193i	$-0.935843\pi$
$503$	−6.83567	−	21.0380i	−0.304788	−	0.938040i	0.674969	−	0.737846i	$-0.264157\pi$
$504$	−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	−0.999992	−	0.00397414i	$-0.998735\pi$
$509$	−1.91402	+	9.00475i	−0.0848374	+	0.399129i	0.915155	+	0.403103i	$0.132068\pi$
$510$	−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	−0.995134	−	0.0985349i	$-0.968584\pi$
$521$	−2.87855	−	13.5425i	−0.126112	−	0.593308i	0.869022	−	0.494773i	$-0.164749\pi$
$522$	−14.6600	−	5.14234i	−0.641653	−	0.225074i
$523$	−8.12513	−	18.2494i	−0.355287	−	0.797988i	−0.999452	−	0.0331016i	$-0.989462\pi$
$523$	−8.12513	−	18.2494i	−0.355287	−	0.797988i	0.644165	−	0.764887i	$-0.277205\pi$
$524$	−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	−0.551769	−	0.833997i	$-0.686047\pi$
$541$	−21.3541	+	2.24440i	−0.918082	+	0.0964944i	−0.366314	+	0.930491i	$0.619380\pi$
$542$	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	−0.859434	−	0.511247i	$-0.829184\pi$
$547$	−29.3339	+	9.53116i	−1.25423	+	0.407523i	−0.394793	+	0.918770i	$0.629184\pi$
$548$	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	0.128672	−	0.991687i	$-0.458929\pi$
$557$	15.3305	−	3.25860i	0.649575	−	0.138071i	0.520903	+	0.853616i	$0.325595\pi$
$558$	−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	0.510088	−	0.860122i	$-0.329613\pi$
$563$	5.03519	+	2.24181i	0.212208	+	0.0944811i	−0.297880	+	0.954603i	$0.596279\pi$
$564$	−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	0.533002	−	0.846114i	$-0.321064\pi$
$569$	16.1198	+	3.42637i	0.675778	+	0.143641i	0.142776	+	0.989755i	$0.454397\pi$
$570$	13.4181	−	3.42904i	0.562024	−	0.143627i
$571$	12.5956	−	7.27209i	0.527111	−	0.304328i	−0.212728	−	0.977111i	$-0.568235\pi$
$571$	12.5956	−	7.27209i	0.527111	−	0.304328i	0.739839	+	0.672784i	$0.234902\pi$
$572$	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	−0.835610	−	0.549323i	$-0.814886\pi$
$577$	2.30481	−	21.9288i	0.0959507	−	0.912910i	0.931561	−	0.363586i	$-0.118448\pi$
$578$	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	−0.240762	−	0.970584i	$-0.577397\pi$
$587$	−24.3744	−	7.91972i	−1.00604	−	0.326882i	−0.765276	+	0.643702i	$0.777397\pi$
$588$	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	−0.956791	−	0.290777i	$-0.906086\pi$
$593$	−5.51747	+	9.55654i	−0.226575	+	0.392440i	0.730215	+	0.683217i	$0.239420\pi$
$594$	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	0.594466	−	0.804121i	$-0.297363\pi$
$599$	24.6888	+	2.59489i	1.00876	+	0.106025i	0.414290	+	0.910145i	$0.364030\pi$
$600$	−10.9732	+	20.9321i	−0.447978	+	0.854550i
$601$	36.2245	+	11.7701i	1.47763	+	0.480111i	0.933404	−	0.358828i	$-0.116823\pi$
$601$	36.2245	+	11.7701i	1.47763	+	0.480111i	0.544226	+	0.838939i	$0.316823\pi$
$602$	−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	−0.931406	−	0.363981i	$-0.881417\pi$
$607$	−43.5289	+	4.57507i	−1.76678	+	0.185696i	−0.835377	+	0.549677i	$0.814751\pi$
$608$	−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	0.0875119	−	0.996163i	$-0.472108\pi$
$613$	−22.1356	−	19.9310i	−0.894047	−	0.805004i	−0.981559	+	0.191160i	$0.938775\pi$
$614$	−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	$0.296462\pi$
$617$			39.8641i			1.60487i	−0.596742	+	0.802433i	$0.703538\pi$
$618$	12.1053	+	12.3895i	0.486947	+	0.498379i
$619$	−18.3614	+	20.3924i	−0.738006	+	0.819639i	−0.988932	−	0.148367i	$-0.952598\pi$
$619$	−18.3614	+	20.3924i	−0.738006	+	0.819639i	0.250926	+	0.968006i	$0.419265\pi$
$620$	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	0.794211	+	0.607642i	$0.207884\pi$
$631$	−5.16165	+	15.8859i	−0.205482	+	0.632409i	−0.999693	+	0.0247669i	$0.992116\pi$
$632$	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	0.188333	−	0.982105i	$-0.439692\pi$
$641$	−19.4621	−	17.5237i	−0.768706	−	0.692146i	−0.957039	+	0.289959i	$0.906358\pi$
$642$	14.5540	+	2.47854i	0.574399	+	0.0978200i
$643$	−32.7834	−	23.8185i	−1.29285	−	0.939310i	−0.292991	−	0.956115i	$-0.594650\pi$
$643$	−32.7834	−	23.8185i	−1.29285	−	0.939310i	−0.999859	+	0.0168053i	$0.994650\pi$
$644$	−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	0.605959	+	0.795496i	$0.292790\pi$
$647$	−9.93730	+	22.3195i	−0.390676	+	0.877472i	−0.996634	+	0.0819756i	$0.973877\pi$
$648$	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	−0.796622	−	0.604478i	$-0.793382\pi$
$653$	−7.12248	+	6.41311i	−0.278724	+	0.250965i	0.517897	+	0.855443i	$0.326715\pi$
$654$	−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	0.961165	+	0.275973i	$0.0890000\pi$
$661$	18.5004	+	32.0436i	0.719582	+	1.24635i	−0.241583	+	0.970380i	$0.577667\pi$
$662$	−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	0.999404	+	0.0345139i	$0.0109883\pi$
$673$	18.7665	+	25.8299i	0.723396	+	0.995669i	−0.276008	+	0.961155i	$0.589012\pi$
$674$	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	0.113650	−	0.993521i	$-0.463746\pi$
$677$	24.1465	−	10.7507i	0.928027	−	0.413184i	0.814377	+	0.580337i	$0.197079\pi$
$678$	−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	−0.797098	−	0.603850i	$-0.793633\pi$
$683$	−17.5805	+	10.1501i	−0.672698	+	0.388383i	0.124400	+	0.992232i	$0.460299\pi$
$684$	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	−0.962244	−	0.272188i	$-0.912253\pi$
$691$	−2.04034	−	19.4126i	−0.0776183	−	0.738489i	0.884626	−	0.466301i	$-0.154414\pi$
$692$	−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	−0.773418	−	0.633896i	$-0.781455\pi$
$701$	−13.7758	−	42.3975i	−0.520305	−	1.60133i	0.253114	−	0.967437i	$-0.418545\pi$
$702$	−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	0.165304	−	0.986243i	$-0.447139\pi$
$709$	26.8623	−	11.9599i	1.00884	−	0.449162i	0.843531	+	0.537080i	$0.180473\pi$
$710$	−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	−0.168437	−	0.985712i	$-0.553872\pi$
$719$	21.2977	−	19.1765i	0.794269	−	0.715163i	0.962706	+	0.270550i	$0.0872055\pi$
$720$	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	−0.318791	−	0.947825i	$-0.603277\pi$
$733$	15.9877	−	14.3954i	0.590519	−	0.531706i	0.909310	+	0.416119i	$0.136610\pi$
$734$	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	−0.0662536	+	0.997803i	$0.521105\pi$
$739$	−20.7536	+	46.6133i	−0.763433	+	1.71470i	−0.697180	+	0.716896i	$0.745562\pi$
$740$	−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	0.993679	+	0.112258i	$0.0358083\pi$
$743$	38.3659	+	27.8744i	1.40751	+	1.02261i	0.413827	+	0.910355i	$0.364192\pi$
$744$	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	−0.526803	−	0.849987i	$-0.676610\pi$
$751$	−37.0996	−	7.88576i	−1.35378	−	0.287755i	−0.826980	+	0.562232i	$0.809943\pi$
$752$	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	−0.430754	+	0.902469i	$0.641752\pi$
$757$	−39.1289	+	28.4288i	−1.42216	+	1.03326i	−0.991410	+	0.130793i	$0.958248\pi$
$758$	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	0.991212	+	0.132285i	$0.0422315\pi$
$761$	1.35625	+	12.9038i	0.0491640	+	0.467764i	−0.942048	+	0.335479i	$0.891102\pi$
$762$	−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	$0.139512\pi$
$769$			23.5374i			0.848781i	−0.905479	+	0.424390i	$0.860488\pi$
$770$	−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	0.968948	+	0.247264i	$0.0795315\pi$
$773$	36.5925	+	32.9480i	1.31614	+	1.18506i	0.347192	+	0.937794i	$0.387135\pi$
$774$	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	−0.414584	−	0.910011i	$-0.636073\pi$
$787$	−28.3147	−	2.97600i	−1.00931	−	0.106083i	−0.594726	+	0.803928i	$0.702740\pi$
$788$	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	−0.0883592	+	0.996089i	$0.528162\pi$
$797$	−28.4681	+	39.1830i	−1.00839	+	1.38793i	−0.920032	+	0.391843i	$0.871838\pi$
$798$	−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	0.945709	+	0.325014i	$0.105369\pi$
$809$	−1.33421	+	12.6942i	−0.0469083	+	0.446303i	−0.992617	+	0.121288i	$0.961297\pi$
$810$	−37.4772	+	10.2815i	−1.31681	+	0.361255i
$811$	45.8517	−	14.8981i	1.61007	−	0.523143i	0.640500	−	0.767958i	$-0.278727\pi$
$811$	45.8517	−	14.8981i	1.61007	−	0.523143i	0.969570	+	0.244815i	$0.0787271\pi$
$812$	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	0.861348	−	0.508015i	$-0.169620\pi$
$821$	7.62406	+	8.46737i	0.266081	+	0.295513i	−0.595267	+	0.803528i	$0.702954\pi$
$822$	22.9889	+	1.47241i	0.801828	+	0.0513563i
$823$	51.3158	+	22.8473i	1.78876	+	0.796406i	0.977258	+	0.212052i	$0.0680145\pi$
$823$	51.3158	+	22.8473i	1.78876	+	0.796406i	0.811499	+	0.584354i	$0.198652\pi$
$824$	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	−0.985357	−	0.170506i	$-0.945460\pi$
$827$	−32.4296	+	23.5615i	−1.12769	+	0.819313i	−0.142331	+	0.989819i	$0.545460\pi$
$828$	18.0596	+	8.54811i	0.627616	+	0.297067i
$829$	45.9785	−	9.77303i	1.59690	−	0.339432i	0.678351	−	0.734738i	$-0.262695\pi$
$829$	45.9785	−	9.77303i	1.59690	−	0.339432i	0.918549	+	0.395307i	$0.129362\pi$
$830$	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	−0.530053	−	0.847964i	$-0.677828\pi$
$839$	−13.3373	+	4.33355i	−0.460455	+	0.149611i	0.0695986	+	0.997575i	$0.477828\pi$
$840$	−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	−0.961688	−	0.274145i	$-0.911605\pi$
$853$	−11.7929	+	16.2316i	−0.403783	+	0.555759i	0.557906	+	0.829904i	$0.311605\pi$
$854$	−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	0.999986	+	0.00528309i	$0.00168167\pi$
$857$	14.7710	+	25.5842i	0.504568	+	0.873938i	−0.495418	+	0.868655i	$0.664985\pi$
$858$	15.5465	+	15.5268i	0.530750	+	0.530077i
$859$	0.316537	−	0.548259i	0.0108001	−	0.0187063i	−0.860575	−	0.509324i	$-0.829895\pi$
$859$	0.316537	−	0.548259i	0.0108001	−	0.0187063i	0.871375	+	0.490618i	$0.163229\pi$
$860$	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	0.956701	−	0.291072i	$-0.0940119\pi$
$863$	2.94457	+	6.61362i	0.100234	+	0.225130i	−0.856467	+	0.516202i	$0.827345\pi$
$864$	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	0.780542	+	0.625103i	$0.214943\pi$
$877$	−5.53107	+	26.0217i	−0.186771	+	0.878689i	−0.967313	+	0.253585i	$0.918390\pi$
$878$	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	$-0.958520\pi$
$881$		−	7.71388i		−	0.259887i	0.991521	−	0.129944i	$-0.0414796\pi$
$882$	0.545888	+	20.9929i	0.0183810	+	0.706868i
$883$	−4.37770	−	13.4732i	−0.147321	−	0.453408i	0.849981	−	0.526813i	$-0.176613\pi$
$883$	−4.37770	−	13.4732i	−0.147321	−	0.453408i	−0.997302	+	0.0734053i	$0.976613\pi$
$884$	−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	−0.984832	−	0.173512i	$-0.944488\pi$
$887$	−31.4042	−	34.8779i	−1.05445	−	1.17109i	−0.0696188	−	0.997574i	$-0.522178\pi$
$888$	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	0.867690	+	0.497106i	$0.165604\pi$
$907$	−2.54162	+	24.1819i	−0.0843930	+	0.802946i	−0.952083	+	0.305840i	$0.901063\pi$
$908$	−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	0.982065	+	0.188541i	$0.0603759\pi$
$911$	25.8939	+	35.6399i	0.857904	+	1.18080i	−0.124161	+	0.992262i	$0.539624\pi$
$912$	−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	0.744258	−	0.667892i	$-0.232803\pi$
$919$	−7.58142	−	17.0282i	−0.250088	−	0.561707i	−0.994346	+	0.106185i	$0.966136\pi$
$920$	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	−0.814380	−	0.580332i	$-0.802923\pi$
$929$	−21.3577	−	47.9702i	−0.700724	−	1.57385i	0.113656	−	0.993520i	$-0.463744\pi$
$930$	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	0.866365	−	0.499411i	$-0.166450\pi$
$937$	3.78576	+	5.21065i	0.123675	+	0.170224i	−0.742690	+	0.669636i	$0.766450\pi$
$938$	−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	−0.706980	−	0.707233i	$-0.749943\pi$
$941$	4.03671	−	38.4067i	0.131593	−	1.25202i	0.838573	−	0.544789i	$-0.183390\pi$
$942$	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	0.260321	−	0.965522i	$-0.416172\pi$
$947$	−13.7152	−	7.91848i	−0.445685	−	0.257316i	−0.706006	+	0.708206i	$0.749505\pi$
$948$	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	−0.982089	−	0.188419i	$-0.939664\pi$
$953$	−2.37126	+	7.29798i	−0.0768126	+	0.236405i	0.905276	+	0.424823i	$0.139664\pi$
$954$	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	$-0.902236\pi$
$967$		−	18.8028i		−	0.604656i	0.953204	−	0.302328i	$-0.0977638\pi$
$968$	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	0.622937	+	0.782272i	$0.285939\pi$
$971$	−8.23654	+	38.7499i	−0.264323	+	1.24354i	−0.887260	+	0.461270i	$0.847394\pi$
$972$	−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	−0.812714	−	0.582663i	$-0.802011\pi$
$977$	5.12931	−	11.5206i	0.164101	−	0.368577i	0.976815	+	0.214086i	$0.0686773\pi$
$978$	−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	0.344674	+	0.938722i	$0.387989\pi$
$983$	12.9052	+	60.7141i	0.411611	+	1.93648i	0.0669372	+	0.997757i	$0.478677\pi$
$984$	−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	0.981252	+	0.192727i	$0.0617332\pi$
$991$	20.6992	+	35.8521i	0.657533	+	1.13888i	−0.323720	+	0.946153i	$0.604933\pi$
$992$	−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	0.968612	−	0.248578i	$-0.0799634\pi$
$997$	−0.548307	−	2.57958i	−0.0173651	−	0.0816962i	−0.985977	+	0.166882i	$0.946630\pi$
$998$	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.107.8	yes	128
3.2	odd	2		462.2.bc.a.107.16	yes	128
7.4	even	3	inner	462.2.bc.b.305.4	yes	128
11.7	odd	10		462.2.bc.a.359.5	yes	128
21.11	odd	6		462.2.bc.a.305.5	yes	128
33.29	even	10	inner	462.2.bc.b.359.4	yes	128
77.18	odd	30		462.2.bc.a.95.16	✓	128
231.95	even	30	inner	462.2.bc.b.95.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.16	✓	128	77.18	odd	30
462.2.bc.a.107.16	yes	128	3.2	odd	2
462.2.bc.a.305.5	yes	128	21.11	odd	6
462.2.bc.a.359.5	yes	128	11.7	odd	10
462.2.bc.b.95.8	yes	128	231.95	even	30	inner
462.2.bc.b.107.8	yes	128	1.1	even	1	trivial
462.2.bc.b.305.4	yes	128	7.4	even	3	inner
462.2.bc.b.359.4	yes	128	33.29	even	10	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more