LMFDB - Embedded newform 462.2.y.c.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	462.163
Dual form			462.2.y.c.445.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 - 0.743145i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.87534 + 0.398616i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(1.79574 + 1.94302i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.669131 - 0.743145i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.87534 + 0.398616i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(1.79574 + 1.94302i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.958617 - 1.66037i) q^{10} +(-1.73626 + 2.82585i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.60011 - 4.92462i) q^{13} +(0.242362 - 2.63463i) q^{14} +(1.55108 + 1.12692i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-4.54632 + 5.04920i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.694683 + 6.60946i) q^{19} +(-0.592458 + 1.82340i) q^{20} +(0.850191 + 2.50543i) q^{21} +(3.26180 - 0.600568i) q^{22} +(2.85828 - 4.95068i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-1.20973 - 0.538605i) q^{25} +(-4.73039 + 2.10610i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.12008 + 1.58280i) q^{28} +(-3.63924 - 2.64406i) q^{29} +(-0.200406 - 1.90673i) q^{30} +(9.24191 - 1.96443i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.73553 + 1.87534i) q^{33} +6.79437 q^{34} +(2.59310 + 4.35963i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(3.66491 - 1.63172i) q^{37} +(4.44696 - 4.93884i) q^{38} +(3.46479 - 3.84804i) q^{39} +(1.75148 - 0.779810i) q^{40} +(-1.53107 + 1.11239i) q^{41} +(1.29301 - 2.30827i) q^{42} -0.609071 q^{43} +(-2.62888 - 2.02213i) q^{44} +(0.958617 + 1.66037i) q^{45} +(-5.59163 + 1.18854i) q^{46} +(-0.613200 - 5.83421i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.550652 + 6.97831i) q^{49} +(0.409204 + 1.25940i) q^{50} +(-6.20696 + 2.76352i) q^{51} +(4.73039 + 2.10610i) q^{52} +(2.43769 - 0.518147i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.38250 + 4.60732i) q^{55} +(2.59486 + 0.516428i) q^{56} +(-2.05369 + 6.32060i) q^{57} +(0.470206 + 4.47371i) q^{58} +(1.37262 - 13.0596i) q^{59} +(-1.28288 + 1.42478i) q^{60} +(6.34514 + 1.34870i) q^{61} +(-7.64390 - 5.55362i) q^{62} +(-0.242362 + 2.63463i) q^{63} +(0.309017 - 0.951057i) q^{64} +(4.96377 - 8.59751i) q^{65} +(3.22407 + 0.778046i) q^{66} +(2.15852 + 3.73867i) q^{67} +(-4.54632 - 5.04920i) q^{68} +(4.62479 - 3.36010i) q^{69} +(1.50471 - 4.84421i) q^{70} +(1.23121 + 3.78928i) q^{71} +(0.978148 + 0.207912i) q^{72} +(1.52535 - 14.5128i) q^{73} +(-3.66491 - 1.63172i) q^{74} +(-0.886070 - 0.984080i) q^{75} -6.64587 q^{76} +(-8.60854 + 1.70089i) q^{77} -5.17805 q^{78} +(-4.72313 - 5.24557i) q^{79} +(-1.75148 - 0.779810i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.85115 + 0.393475i) q^{82} +(-2.12639 - 6.54437i) q^{83} +(-2.58057 + 0.583645i) q^{84} +(-10.5386 + 7.65673i) q^{85} +(0.407548 + 0.452628i) q^{86} +(-2.24918 - 3.89569i) q^{87} +(0.256328 + 3.30670i) q^{88} +(-3.97357 + 6.88242i) q^{89} +(0.592458 - 1.82340i) q^{90} +(12.4420 - 5.73429i) q^{91} +(4.62479 + 3.36010i) q^{92} +(9.24191 + 1.96443i) q^{93} +(-3.92535 + 4.35954i) q^{94} +(-1.33187 + 12.6719i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-1.48574 + 4.57265i) q^{97} +(5.55435 - 4.26018i) q^{98} +(-3.26180 + 0.600568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	1.87534	+	0.398616i	0.838677	+	0.178266i	0.607175	−	0.794568i	$-0.292303\pi$
$5$	1.87534	+	0.398616i	0.838677	+	0.178266i	0.231502	+	0.972834i	$0.425636\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	1.79574	+	1.94302i	0.678725	+	0.734392i
$7$	1.79574	+	1.94302i	0.678725	+	0.734392i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.958617	−	1.66037i	−0.303141	−	0.525056i
$11$	−1.73626	+	2.82585i	−0.523502	+	0.852025i
$11$	−1.73626	+	2.82585i	−0.523502	+	0.852025i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.60011	−	4.92462i	0.443790	−	1.36584i	−0.440016	−	0.897990i	$-0.645027\pi$
$13$	1.60011	−	4.92462i	0.443790	−	1.36584i	0.883806	−	0.467854i	$-0.154973\pi$
$14$	0.242362	−	2.63463i	0.0647740	−	0.704134i
$15$	1.55108	+	1.12692i	0.400486	+	0.290970i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−4.54632	+	5.04920i	−1.10264	+	1.22461i	−0.130197	+	0.991488i	$0.541561\pi$
$17$	−4.54632	+	5.04920i	−1.10264	+	1.22461i	−0.972447	+	0.233123i	$0.925106\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	0.694683	+	6.60946i	0.159371	+	1.51632i	0.723324	+	0.690508i	$0.242613\pi$
$19$	0.694683	+	6.60946i	0.159371	+	1.51632i	−0.563953	+	0.825807i	$0.690720\pi$
$20$	−0.592458	+	1.82340i	−0.132478	+	0.407724i
$21$	0.850191	+	2.50543i	0.185527	+	0.546729i
$22$	3.26180	−	0.600568i	0.695417	−	0.128042i
$23$	2.85828	−	4.95068i	0.595992	−	1.03229i	−0.397414	−	0.917639i	$-0.630092\pi$
$23$	2.85828	−	4.95068i	0.595992	−	1.03229i	0.993406	−	0.114649i	$-0.0365742\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−1.20973	−	0.538605i	−0.241945	−	0.107721i
$26$	−4.73039	+	2.10610i	−0.927705	+	0.413041i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.12008	+	1.58280i	−0.400658	+	0.299121i
$29$	−3.63924	−	2.64406i	−0.675790	−	0.490991i	0.196168	−	0.980570i	$-0.437150\pi$
$29$	−3.63924	−	2.64406i	−0.675790	−	0.490991i	−0.871959	+	0.489580i	$0.837150\pi$
$30$	−0.200406	−	1.90673i	−0.0365889	−	0.348120i
$31$	9.24191	−	1.96443i	1.65990	−	0.352822i	0.719918	−	0.694059i	$-0.244179\pi$
$31$	9.24191	−	1.96443i	1.65990	−	0.352822i	0.939977	+	0.341237i	$0.110846\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.73553	+	1.87534i	−0.476194	+	0.326455i
$34$	6.79437			1.16522
$35$	2.59310	+	4.35963i	0.438314	+	0.736912i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	3.66491	−	1.63172i	0.602508	−	0.268254i	−0.0827314	−	0.996572i	$-0.526364\pi$
$37$	3.66491	−	1.63172i	0.602508	−	0.268254i	0.685239	+	0.728318i	$0.259698\pi$
$38$	4.44696	−	4.93884i	0.721391	−	0.801186i
$39$	3.46479	−	3.84804i	0.554811	−	0.616180i
$40$	1.75148	−	0.779810i	0.276933	−	0.123299i
$41$	−1.53107	+	1.11239i	−0.239113	+	0.173726i	−0.700888	−	0.713271i	$-0.747213\pi$
$41$	−1.53107	+	1.11239i	−0.239113	+	0.173726i	0.461775	+	0.886997i	$0.347213\pi$
$42$	1.29301	−	2.30827i	0.199516	−	0.356174i
$43$	−0.609071			−0.0928824			−0.0464412	−	0.998921i	$-0.514788\pi$
$43$	−0.609071			−0.0928824			−0.0464412	+	0.998921i	$0.514788\pi$
$44$	−2.62888	−	2.02213i	−0.396318	−	0.304847i
$45$	0.958617	+	1.66037i	0.142902	+	0.247514i
$46$	−5.59163	+	1.18854i	−0.824441	+	0.175240i
$47$	−0.613200	−	5.83421i	−0.0894444	−	0.851006i	−0.943622	−	0.331025i	$-0.892606\pi$
$47$	−0.613200	−	5.83421i	−0.0894444	−	0.851006i	0.854178	−	0.519981i	$-0.174061\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−0.550652	+	6.97831i	−0.0786646	+	0.996901i
$50$	0.409204	+	1.25940i	0.0578701	+	0.178106i
$51$	−6.20696	+	2.76352i	−0.869149	+	0.386970i
$52$	4.73039	+	2.10610i	0.655987	+	0.292064i
$53$	2.43769	−	0.518147i	0.334843	−	0.0711730i	−0.0374222	−	0.999300i	$-0.511915\pi$
$53$	2.43769	−	0.518147i	0.334843	−	0.0711730i	0.372265	+	0.928127i	$0.378581\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−4.38250	+	4.60732i	−0.590936	+	0.621251i
$56$	2.59486	+	0.516428i	0.346753	+	0.0690106i
$57$	−2.05369	+	6.32060i	−0.272018	+	0.837184i
$58$	0.470206	+	4.47371i	0.0617410	+	0.587427i
$59$	1.37262	−	13.0596i	0.178700	−	1.70022i	−0.426778	−	0.904357i	$-0.640351\pi$
$59$	1.37262	−	13.0596i	0.178700	−	1.70022i	0.605478	−	0.795862i	$-0.292982\pi$
$60$	−1.28288	+	1.42478i	−0.165619	+	0.183939i
$61$	6.34514	+	1.34870i	0.812412	+	0.172683i	0.595342	−	0.803473i	$-0.297017\pi$
$61$	6.34514	+	1.34870i	0.812412	+	0.172683i	0.217070	+	0.976156i	$0.430350\pi$
$62$	−7.64390	−	5.55362i	−0.970776	−	0.705310i
$63$	−0.242362	+	2.63463i	−0.0305348	+	0.331932i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.96377	−	8.59751i	0.615680	−	1.06639i
$66$	3.22407	+	0.778046i	0.396856	+	0.0957708i
$67$	2.15852	+	3.73867i	0.263705	+	0.456751i	0.967224	−	0.253926i	$-0.0817220\pi$
$67$	2.15852	+	3.73867i	0.263705	+	0.456751i	−0.703518	+	0.710677i	$0.748389\pi$
$68$	−4.54632	−	5.04920i	−0.551322	−	0.612305i
$69$	4.62479	−	3.36010i	0.556759	−	0.404509i
$70$	1.50471	−	4.84421i	0.179848	−	0.578994i
$71$	1.23121	+	3.78928i	0.146118	+	0.449705i	0.997153	−	0.0754040i	$-0.0240246\pi$
$71$	1.23121	+	3.78928i	0.146118	+	0.449705i	−0.851035	+	0.525109i	$0.824025\pi$
$72$	0.978148	+	0.207912i	0.115276	+	0.0245026i
$73$	1.52535	−	14.5128i	0.178529	−	1.69859i	−0.428203	−	0.903683i	$-0.640853\pi$
$73$	1.52535	−	14.5128i	0.178529	−	1.69859i	0.606732	−	0.794907i	$-0.292480\pi$
$74$	−3.66491	−	1.63172i	−0.426037	−	0.189684i
$75$	−0.886070	−	0.984080i	−0.102315	−	0.113632i
$76$	−6.64587			−0.762334
$77$	−8.60854	+	1.70089i	−0.981034	+	0.193835i
$78$	−5.17805			−0.586299
$79$	−4.72313	−	5.24557i	−0.531393	−	0.590172i	0.416351	−	0.909204i	$-0.363309\pi$
$79$	−4.72313	−	5.24557i	−0.531393	−	0.590172i	−0.947744	+	0.319032i	$0.896642\pi$
$80$	−1.75148	−	0.779810i	−0.195822	−	0.0871854i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	1.85115	+	0.393475i	0.204426	+	0.0434520i
$83$	−2.12639	−	6.54437i	−0.233402	−	0.718338i	−0.997329	−	0.0730354i	$-0.976731\pi$
$83$	−2.12639	−	6.54437i	−0.233402	−	0.718338i	0.763927	−	0.645302i	$-0.223269\pi$
$84$	−2.58057	+	0.583645i	−0.281564	+	0.0636808i
$85$	−10.5386	+	7.65673i	−1.14307	+	0.830489i
$86$	0.407548	+	0.452628i	0.0439470	+	0.0488081i
$87$	−2.24918	−	3.89569i	−0.241137	−	0.417661i
$88$	0.256328	+	3.30670i	0.0273246	+	0.352496i
$89$	−3.97357	+	6.88242i	−0.421197	+	0.729535i	−0.996057	−	0.0887168i	$-0.971723\pi$
$89$	−3.97357	+	6.88242i	−0.421197	+	0.729535i	0.574859	+	0.818252i	$0.305057\pi$
$90$	0.592458	−	1.82340i	0.0624506	−	0.192203i
$91$	12.4420	−	5.73429i	1.30428	−	0.601117i
$92$	4.62479	+	3.36010i	0.482167	+	0.350315i
$93$	9.24191	+	1.96443i	0.958341	+	0.203702i
$94$	−3.92535	+	4.35954i	−0.404869	+	0.449652i
$95$	−1.33187	+	12.6719i	−0.136647	+	1.30011i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	−1.48574	+	4.57265i	−0.150854	+	0.464282i	−0.997717	−	0.0675291i	$-0.978488\pi$
$97$	−1.48574	+	4.57265i	−0.150854	+	0.464282i	0.846863	+	0.531811i	$0.178488\pi$
$98$	5.55435	−	4.26018i	0.561074	−	0.430344i
$99$	−3.26180	+	0.600568i	−0.327823	+	0.0603594i
$100$	0.662105	−	1.14680i	0.0662105	−	0.114680i
$101$	−16.8659	+	3.58495i	−1.67822	+	0.356716i	−0.945953	−	0.324305i	$-0.894870\pi$
$101$	−16.8659	+	3.58495i	−1.67822	+	0.356716i	−0.732264	+	0.681021i	$0.761536\pi$
$102$	6.20696	+	2.76352i	0.614581	+	0.273629i
$103$	−9.48987	+	4.22516i	−0.935065	+	0.416318i	−0.816967	−	0.576684i	$-0.804346\pi$
$103$	−9.48987	+	4.22516i	−0.935065	+	0.416318i	−0.118098	+	0.993002i	$0.537680\pi$
$104$	−1.60011	−	4.92462i	−0.156903	−	0.482899i
$105$	0.595692	+	5.03743i	0.0581336	+	0.491603i
$106$	−2.01619	−	1.46485i	−0.195830	−	0.142279i
$107$	0.563633	+	5.36261i	0.0544885	+	0.518423i	0.987392	+	0.158296i	$0.0506000\pi$
$107$	0.563633	+	5.36261i	0.0544885	+	0.518423i	−0.932903	+	0.360127i	$0.882733\pi$
$108$	−0.978148	+	0.207912i	−0.0941223	+	0.0200063i
$109$	0.489092	+	0.847133i	0.0468466	+	0.0811406i	0.888498	−	0.458881i	$-0.151749\pi$
$109$	0.489092	+	0.847133i	0.0468466	+	0.0811406i	−0.841651	+	0.540021i	$0.818416\pi$
$110$	6.35637	+	0.173934i	0.606056	+	0.0165839i
$111$	4.01175			0.380778
$112$	−1.35252	−	2.27392i	−0.127801	−	0.214865i
$113$	−14.8835	+	10.8135i	−1.40012	+	1.01725i	−0.405457	+	0.914114i	$0.632888\pi$
$113$	−14.8835	+	10.8135i	−1.40012	+	1.01725i	−0.994667	+	0.103136i	$0.967112\pi$
$114$	6.07131	−	2.70312i	0.568630	−	0.253170i
$115$	7.33365	−	8.14485i	0.683867	−	0.759511i
$116$	3.00998	−	3.34293i	0.279470	−	0.310383i
$117$	4.73039	−	2.10610i	0.437325	−	0.194709i
$118$	−10.6237	+	7.71854i	−0.977987	+	0.710549i
$119$	−17.9747	+	0.233448i	−1.64774	+	0.0214002i
$120$	1.91723			0.175019
$121$	−4.97081	−	9.81280i	−0.451892	−	0.892073i
$122$	−3.24345	−	5.61782i	−0.293648	−	0.508613i
$123$	−1.85115	+	0.393475i	−0.166913	+	0.0354784i
$124$	0.987624	+	9.39662i	0.0886913	+	0.843841i
$125$	−9.80933	−	7.12689i	−0.877373	−	0.637449i
$126$	2.12008	−	1.58280i	0.188872	−	0.141007i
$127$	−6.50098	−	20.0080i	−0.576869	−	1.77542i	−0.629725	−	0.776818i	$-0.716832\pi$
$127$	−6.50098	−	20.0080i	−0.576869	−	1.77542i	0.0528555	−	0.998602i	$-0.483168\pi$
$128$	−0.913545	+	0.406737i	−0.0807468	+	0.0359508i
$129$	−0.556414	−	0.247731i	−0.0489895	−	0.0218115i
$130$	−9.71061	+	2.06405i	−0.851676	+	0.181029i
$131$	2.73650	−	4.73976i	0.239089	−	0.414115i	−0.721364	−	0.692556i	$-0.756484\pi$
$131$	2.73650	−	4.73976i	0.239089	−	0.414115i	0.960453	+	0.278441i	$0.0898178\pi$
$132$	−1.57913	−	2.91657i	−0.137445	−	0.253855i
$133$	−11.5949	+	13.2186i	−1.00540	+	1.14620i
$134$	1.33404	−	4.10575i	0.115244	−	0.354683i
$135$	0.200406	+	1.90673i	0.0172482	+	0.164105i
$136$	−0.710205	+	6.75715i	−0.0608996	+	0.579421i
$137$	11.6413	−	12.9290i	0.994586	−	1.10460i	7.18224e−5	−	1.00000i	$-0.499977\pi$
$137$	11.6413	−	12.9290i	0.994586	−	1.10460i	0.994514	−	0.104600i	$-0.0333562\pi$
$138$	−5.59163	−	1.18854i	−0.475991	−	0.101175i
$139$	−4.12045	−	2.99368i	−0.349492	−	0.253921i	0.399164	−	0.916880i	$-0.369300\pi$
$139$	−4.12045	−	2.99368i	−0.349492	−	0.253921i	−0.748656	+	0.662959i	$0.769300\pi$
$140$	−4.60680	+	2.12319i	−0.389346	+	0.179442i
$141$	1.81280	−	5.57922i	0.152665	−	0.469855i
$142$	1.99214	−	3.45049i	0.167177	−	0.289559i
$143$	11.1380	+	13.0721i	0.931408	+	1.09314i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−5.77085	−	6.40918i	−0.479243	−	0.532253i
$146$	−11.8057	+	8.57737i	−0.977050	+	0.709868i
$147$	−3.34138	+	6.15103i	−0.275592	+	0.507328i
$148$	1.23970	+	3.81540i	0.101903	+	0.313624i
$149$	−2.04413	−	0.434493i	−0.167461	−	0.0355950i	0.123418	−	0.992355i	$-0.460614\pi$
$149$	−2.04413	−	0.434493i	−0.167461	−	0.0355950i	−0.290879	+	0.956760i	$0.593948\pi$
$150$	−0.138418	+	1.31696i	−0.0113018	+	0.107529i
$151$	7.49255	+	3.33590i	0.609735	+	0.271471i	0.688287	−	0.725439i	$-0.258363\pi$
$151$	7.49255	+	3.33590i	0.609735	+	0.271471i	−0.0785522	+	0.996910i	$0.525030\pi$
$152$	4.44696	+	4.93884i	0.360696	+	0.400593i
$153$	−6.79437			−0.549292
$154$	7.02425	+	5.25927i	0.566030	+	0.423804i
$155$	18.1148			1.45501
$156$	3.46479	+	3.84804i	0.277406	+	0.308090i
$157$	0.918291	+	0.408850i	0.0732876	+	0.0326297i	0.443053	−	0.896495i	$-0.353895\pi$
$157$	0.918291	+	0.408850i	0.0732876	+	0.0326297i	−0.369765	+	0.929125i	$0.620562\pi$
$158$	−0.737825	+	7.01994i	−0.0586982	+	0.558476i
$159$	2.43769	+	0.518147i	0.193321	+	0.0410917i
$160$	0.592458	+	1.82340i	0.0468379	+	0.144152i
$161$	14.7520	−	3.33643i	1.16262	−	0.262948i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	3.97039	+	4.40956i	0.310985	+	0.345384i	0.878294	−	0.478121i	$-0.158682\pi$
$163$	3.97039	+	4.40956i	0.310985	+	0.345384i	−0.567309	+	0.823505i	$0.692015\pi$
$164$	−0.946254	−	1.63896i	−0.0738900	−	0.127981i
$165$	−5.87758	+	2.42647i	−0.457569	+	0.188901i
$166$	−3.44058	+	5.95926i	−0.267041	+	0.462528i
$167$	−2.06205	+	6.34632i	−0.159566	+	0.491093i	−0.998595	−	0.0529935i	$-0.983124\pi$
$167$	−2.06205	+	6.34632i	−0.159566	+	0.491093i	0.839029	+	0.544087i	$0.183124\pi$
$168$	2.16047	+	1.52721i	0.166684	+	0.117826i
$169$	−11.1743	−	8.11863i	−0.859565	−	0.624510i
$170$	12.7417	+	2.70834i	0.977247	+	0.207720i
$171$	−4.44696	+	4.93884i	−0.340067	+	0.377683i
$172$	0.0636652	−	0.605734i	0.00485443	−	0.0461868i
$173$	−0.745184	−	7.08995i	−0.0566553	−	0.539039i	−0.985633	−	0.168903i	$-0.945978\pi$
$173$	−0.745184	−	7.08995i	−0.0566553	−	0.539039i	0.928977	−	0.370136i	$-0.120689\pi$
$174$	−1.39007	+	4.27819i	−0.105381	+	0.324328i
$175$	−1.12583	−	3.31772i	−0.0851048	−	0.250796i
$176$	2.28584	−	2.40311i	0.172302	−	0.181141i
$177$	6.56578	−	11.3723i	0.493514	−	0.854792i
$178$	7.77347	−	1.65230i	0.582646	−	0.123845i
$179$	10.5415	+	4.69339i	0.787911	+	0.350801i	0.760929	−	0.648835i	$-0.224744\pi$
$179$	10.5415	+	4.69339i	0.787911	+	0.350801i	0.0269822	+	0.999636i	$0.491410\pi$
$180$	−1.75148	+	0.779810i	−0.130548	+	0.0581236i
$181$	−3.44494	−	10.6024i	−0.256060	−	0.788072i	−0.993619	−	0.112789i	$-0.964022\pi$
$181$	−3.44494	−	10.6024i	−0.256060	−	0.788072i	0.737559	−	0.675283i	$-0.235978\pi$
$182$	−12.5867	−	5.40923i	−0.932991	−	0.400959i
$183$	5.24801	+	3.81290i	0.387944	+	0.281858i
$184$	−0.597542	−	5.68524i	−0.0440514	−	0.419121i
$185$	7.52338	−	1.59914i	0.553130	−	0.117571i
$186$	−4.72419	−	8.18253i	−0.346394	−	0.599972i
$187$	−6.37467	−	21.6139i	−0.466162	−	1.58057i
$188$	5.86634			0.427847
$189$	−1.29301	+	2.30827i	−0.0940525	+	0.167902i
$190$	10.3082	−	7.48938i	0.747839	−	0.543337i
$191$	10.4054	−	4.63278i	0.752908	−	0.335216i	0.00585669	−	0.999983i	$-0.498136\pi$
$191$	10.4054	−	4.63278i	0.752908	−	0.335216i	0.747051	+	0.664767i	$0.231469\pi$
$192$	0.669131	−	0.743145i	0.0482903	−	0.0536319i
$193$	−14.4631	+	16.0629i	−1.04108	+	1.15624i	−0.0535886	+	0.998563i	$0.517066\pi$
$193$	−14.4631	+	16.0629i	−1.04108	+	1.15624i	−0.987491	+	0.157673i	$0.949601\pi$
$194$	4.39230	−	1.95558i	0.315349	−	0.140402i
$195$	8.03155	−	5.83527i	0.575151	−	0.417872i
$196$	−6.88252	−	1.27707i	−0.491609	−	0.0912191i
$197$	14.0693			1.00240			0.501198	−	0.865333i	$-0.332893\pi$
$197$	14.0693			1.00240			0.501198	+	0.865333i	$0.332893\pi$
$198$	2.62888	+	2.02213i	0.186826	+	0.143706i
$199$	−2.98877	−	5.17670i	−0.211868	−	0.366966i	0.740431	−	0.672132i	$-0.234621\pi$
$199$	−2.98877	−	5.17670i	−0.211868	−	0.366966i	−0.952299	+	0.305166i	$0.901288\pi$
$200$	−1.29527	+	0.275319i	−0.0915896	+	0.0194680i
$201$	0.451254	+	4.29340i	0.0318290	+	0.302833i
$202$	13.9496	+	10.1350i	0.981491	+	0.713095i
$203$	−1.39766	−	11.8192i	−0.0980962	−	0.829543i
$204$	−2.09958	−	6.46183i	−0.147000	−	0.452419i
$205$	−3.31469	+	1.47580i	−0.231508	+	0.103074i
$206$	9.48987	+	4.22516i	0.661191	+	0.294381i
$207$	5.59163	−	1.18854i	0.388645	−	0.0826091i
$208$	−2.58903	+	4.48433i	−0.179517	+	0.310932i
$209$	−19.8835	−	9.51267i	−1.37537	−	0.658005i
$210$	3.34494	−	3.81338i	0.230823	−	0.263148i
$211$	−6.94970	+	21.3890i	−0.478437	+	1.47248i	0.362828	+	0.931856i	$0.381811\pi$
$211$	−6.94970	+	21.3890i	−0.478437	+	1.47248i	−0.841265	+	0.540622i	$0.818189\pi$
$212$	0.260501	+	2.47850i	0.0178913	+	0.170224i
$213$	−0.416471	+	3.96246i	−0.0285361	+	0.271503i
$214$	3.60805	−	4.00715i	0.246641	−	0.273923i
$215$	−1.14221	−	0.242785i	−0.0778983	−	0.0165578i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	20.4130	+	14.4296i	1.38572	+	0.979546i
$218$	0.302276	−	0.930309i	0.0204727	−	0.0630085i
$219$	7.29635	−	12.6376i	0.493041	−	0.853973i
$220$	−4.12398	−	4.84009i	−0.278039	−	0.326319i
$221$	17.5908	+	30.4682i	1.18329	+	2.04951i
$222$	−2.68438	−	2.98131i	−0.180164	−	0.200092i
$223$	17.8871	−	12.9958i	1.19781	−	0.870261i	0.203743	−	0.979024i	$-0.434689\pi$
$223$	17.8871	−	12.9958i	1.19781	−	0.870261i	0.994068	+	0.108764i	$0.0346891\pi$
$224$	−0.784836	+	2.52666i	−0.0524390	+	0.168820i
$225$	−0.409204	−	1.25940i	−0.0272802	−	0.0839599i
$226$	17.9950	+	3.82496i	1.19701	+	0.254433i
$227$	−0.596972	+	5.67981i	−0.0396224	+	0.376982i	0.956685	+	0.291125i	$0.0940296\pi$
$227$	−0.596972	+	5.67981i	−0.0396224	+	0.376982i	−0.996307	+	0.0858572i	$0.972637\pi$
$228$	−6.07131	−	2.70312i	−0.402082	−	0.179018i
$229$	−12.3165	−	13.6789i	−0.813900	−	0.903927i	0.182960	−	0.983120i	$-0.441432\pi$
$229$	−12.3165	−	13.6789i	−0.813900	−	0.903927i	−0.996859	+	0.0791934i	$0.974766\pi$
$230$	−10.9600			−0.722679
$231$	−8.55611	−	1.94757i	−0.562951	−	0.128140i
$232$	−4.49835			−0.295331
$233$	6.78081	+	7.53085i	0.444225	+	0.493362i	0.923121	−	0.384510i	$-0.125629\pi$
$233$	6.78081	+	7.53085i	0.444225	+	0.493362i	−0.478896	+	0.877872i	$0.658963\pi$
$234$	−4.73039	−	2.10610i	−0.309235	−	0.137680i
$235$	1.17565	−	11.1855i	0.0766908	−	0.729664i
$236$	12.8446	+	2.73021i	0.836113	+	0.177721i
$237$	−2.18123	−	6.71313i	−0.141686	−	0.436065i
$238$	12.2009	+	13.2016i	0.790867	+	0.855732i
$239$	5.24020	−	3.80723i	0.338961	−	0.246269i	−0.405263	−	0.914200i	$-0.632820\pi$
$239$	5.24020	−	3.80723i	0.338961	−	0.246269i	0.744223	+	0.667931i	$0.232820\pi$
$240$	−1.28288	−	1.42478i	−0.0828096	−	0.0919694i
$241$	−11.7414	−	20.3367i	−0.756329	−	1.31000i	−0.944711	−	0.327904i	$-0.893658\pi$
$241$	−11.7414	−	20.3367i	−0.756329	−	1.31000i	0.188383	−	0.982096i	$-0.439676\pi$
$242$	−3.96621	+	10.2601i	−0.254958	+	0.659543i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.00456	+	6.16940i	−0.128329	+	0.394956i
$245$	−3.81432	+	12.8672i	−0.243688	+	0.822055i
$246$	1.53107	+	1.11239i	0.0976175	+	0.0709233i
$247$	33.6607	+	7.15480i	2.14178	+	0.455249i
$248$	6.32220	−	7.02151i	0.401460	−	0.445866i
$249$	0.719277	−	6.84346i	0.0455823	−	0.433687i
$250$	1.26741	+	12.0586i	0.0801579	+	0.762651i
$251$	3.83626	−	11.8068i	0.242143	−	0.745239i	−0.753950	−	0.656931i	$-0.771854\pi$
$251$	3.83626	−	11.8068i	0.242143	−	0.745239i	0.996093	−	0.0883078i	$-0.0281459\pi$
$252$	−2.59486	−	0.516428i	−0.163461	−	0.0325319i
$253$	9.02715	+	16.6727i	0.567532	+	1.04820i
$254$	−10.5188	+	18.2191i	−0.660009	+	1.14317i
$255$	−12.7417	+	2.70834i	−0.797919	+	0.169603i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	20.7012	−	9.21677i	1.29131	−	0.574926i	0.357903	−	0.933759i	$-0.383492\pi$
$257$	20.7012	−	9.21677i	1.29131	−	0.574926i	0.933402	+	0.358833i	$0.116825\pi$
$258$	0.188213	+	0.579261i	0.0117176	+	0.0360632i
$259$	9.75169	+	4.19085i	0.605941	+	0.260407i
$260$	8.03155	+	5.83527i	0.498096	+	0.361888i
$261$	−0.470206	−	4.47371i	−0.0291050	−	0.276916i
$262$	−5.35341	+	1.13790i	−0.330735	+	0.0702998i
$263$	7.83814	+	13.5761i	0.483321	+	0.837136i	0.999817	−	0.0191539i	$-0.00609723\pi$
$263$	7.83814	+	13.5761i	0.483321	+	0.837136i	−0.516496	+	0.856290i	$0.672764\pi$
$264$	−1.11079	+	3.12508i	−0.0683645	+	0.192336i
$265$	4.77804			0.293513
$266$	17.5818	−	0.228346i	1.07801	−	0.0140008i
$267$	−6.42937	+	4.67121i	−0.393471	+	0.285873i
$268$	−3.94382	+	1.75590i	−0.240907	+	0.107259i
$269$	−15.2785	+	16.9685i	−0.931545	+	1.03459i	0.0677746	+	0.997701i	$0.478410\pi$
$269$	−15.2785	+	16.9685i	−0.931545	+	1.03459i	−0.999320	+	0.0368848i	$0.988257\pi$
$270$	1.28288	−	1.42478i	0.0780736	−	0.0867095i
$271$	−10.4052	+	4.63270i	−0.632072	+	0.281417i	−0.697659	−	0.716430i	$-0.745775\pi$
$271$	−10.4052	+	4.63270i	−0.632072	+	0.281417i	0.0655866	+	0.997847i	$0.479108\pi$
$272$	5.49676	−	3.99363i	0.333290	−	0.242149i
$273$	13.6987	−	0.177913i	0.829082	−	0.0107678i
$274$	−17.3977			−1.05103
$275$	3.62241	−	2.48334i	0.218440	−	0.149751i
$276$	2.85828	+	4.95068i	0.172048	+	0.297996i
$277$	−7.49380	+	1.59286i	−0.450259	+	0.0957055i	−0.427459	−	0.904035i	$-0.640591\pi$
$277$	−7.49380	+	1.59286i	−0.450259	+	0.0957055i	−0.0227995	+	0.999740i	$0.507258\pi$
$278$	0.532380	+	5.06526i	0.0319300	+	0.303794i
$279$	7.64390	+	5.55362i	0.457628	+	0.332486i
$280$	4.66039	+	2.00283i	0.278511	+	0.119692i
$281$	1.04523	+	3.21688i	0.0623530	+	0.191903i	0.977380	−	0.211489i	$-0.0678312\pi$
$281$	1.04523	+	3.21688i	0.0623530	+	0.191903i	−0.915027	+	0.403392i	$0.867831\pi$
$282$	−5.35917	+	2.38606i	−0.319134	+	0.142088i
$283$	12.2266	+	5.44363i	0.726796	+	0.323590i	0.736569	−	0.676362i	$-0.236444\pi$
$283$	12.2266	+	5.44363i	0.726796	+	0.323590i	−0.00977378	+	0.999952i	$0.503111\pi$
$284$	−3.89722	+	0.828379i	−0.231257	+	0.0491553i
$285$	−6.37085	+	11.0346i	−0.377376	+	0.653635i
$286$	2.26165	−	17.0241i	0.133734	−	1.00666i
$287$	−4.91080	−	0.977344i	−0.289875	−	0.0576908i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−3.04841	−	29.0037i	−0.179318	−	1.70610i
$290$	−0.901495	+	8.57715i	−0.0529376	+	0.503668i
$291$	−3.21716	+	3.57302i	−0.188593	+	0.209454i
$292$	14.2738	+	3.03399i	0.835312	+	0.177551i
$293$	1.05956	+	0.769816i	0.0619002	+	0.0449732i	0.618305	−	0.785938i	$-0.287820\pi$
$293$	1.05956	+	0.769816i	0.0619002	+	0.0449732i	−0.556405	+	0.830911i	$0.687820\pi$
$294$	6.80693	−	1.63271i	0.396988	−	0.0952218i
$295$	7.77990	−	23.9441i	0.452963	−	1.39408i
$296$	2.00587	−	3.47427i	0.116589	−	0.201938i
$297$	−3.22407	−	0.778046i	−0.187080	−	0.0451468i
$298$	1.04490	+	1.80981i	0.0605293	+	0.104840i
$299$	−19.8067	−	21.9975i	−1.14545	−	1.27215i
$300$	1.07131	−	0.778351i	0.0618520	−	0.0449381i
$301$	−1.09373	−	1.18344i	−0.0630416	−	0.0682121i
$302$	−2.53444	−	7.80020i	−0.145840	−	0.448851i
$303$	−16.8659	−	3.58495i	−0.968919	−	0.205950i
$304$	0.694683	−	6.60946i	0.0398428	−	0.379079i
$305$	11.3617	+	5.05854i	0.650568	+	0.289651i
$306$	4.54632	+	5.04920i	0.259896	+	0.288644i
$307$	26.5258			1.51390			0.756952	−	0.653470i	$-0.226687\pi$
$307$	26.5258			1.51390			0.756952	+	0.653470i	$0.226687\pi$
$308$	−0.791738	−	8.73917i	−0.0451134	−	0.497961i
$309$	−10.3880			−0.590950
$310$	−12.1211	−	13.4619i	−0.688434	−	0.764584i
$311$	−4.89169	−	2.17792i	−0.277382	−	0.123499i	0.263331	−	0.964706i	$-0.415179\pi$
$311$	−4.89169	−	2.17792i	−0.277382	−	0.123499i	−0.540713	+	0.841207i	$0.681846\pi$
$312$	0.541254	−	5.14969i	0.0306425	−	0.291544i
$313$	−12.9104	−	2.74418i	−0.729737	−	0.155110i	−0.171963	−	0.985103i	$-0.555011\pi$
$313$	−12.9104	−	2.74418i	−0.729737	−	0.155110i	−0.557774	+	0.829993i	$0.688344\pi$
$314$	−0.310622	−	0.955997i	−0.0175294	−	0.0539500i
$315$	−1.50471	+	4.84421i	−0.0847811	+	0.272940i
$316$	5.71053	−	4.14894i	0.321242	−	0.233396i
$317$	8.44249	+	9.37634i	0.474178	+	0.526628i	0.932021	−	0.362406i	$-0.118044\pi$
$317$	8.44249	+	9.37634i	0.474178	+	0.526628i	−0.457843	+	0.889033i	$0.651378\pi$
$318$	−1.24608	−	2.15827i	−0.0698764	−	0.121030i
$319$	13.7904	−	5.69316i	0.772113	−	0.318756i
$320$	0.958617	−	1.66037i	0.0535883	−	0.0928177i
$321$	−1.66627	+	5.12824i	−0.0930019	+	0.286230i
$322$	−12.3505	−	8.73035i	−0.688264	−	0.486523i
$323$	−36.5308	−	26.5411i	−2.03263	−	1.47679i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−4.58812	+	5.09562i	−0.254503	+	0.282654i
$326$	0.620235	−	5.90115i	0.0343517	−	0.326834i
$327$	0.102248	+	0.972826i	0.00565434	+	0.0537974i
$328$	−0.584817	+	1.79988i	−0.0322911	+	0.0993819i
$329$	10.2348	−	11.6682i	0.564264	−	0.643287i
$330$	5.73609	+	2.74426i	0.315761	+	0.151067i
$331$	−16.6320	+	28.8075i	−0.914178	+	1.58340i	−0.106077	+	0.994358i	$0.533829\pi$
$331$	−16.6320	+	28.8075i	−0.914178	+	1.58340i	−0.808101	+	0.589044i	$0.799504\pi$
$332$	6.73079	−	1.43067i	0.369400	−	0.0785184i
$333$	3.66491	+	1.63172i	0.200836	+	0.0894179i
$334$	6.09601	−	2.71412i	0.333559	−	0.148510i
$335$	2.55767	+	7.87169i	0.139740	+	0.430077i
$336$	−0.310704	−	2.62744i	−0.0169503	−	0.143339i
$337$	15.4742	+	11.2427i	0.842933	+	0.612427i	0.923188	−	0.384347i	$-0.125574\pi$
$337$	15.4742	+	11.2427i	0.842933	+	0.612427i	−0.0802553	+	0.996774i	$0.525574\pi$
$338$	1.44377	+	13.7366i	0.0785309	+	0.747171i
$339$	−17.9950	+	3.82496i	−0.977356	+	0.207743i
$340$	−6.51320	−	11.2812i	−0.353228	−	0.611809i
$341$	−10.4952	+	29.5270i	−0.568345	+	1.59897i
$342$	6.64587			0.359368
$343$	−14.5478	+	11.4613i	−0.785508	+	0.618851i
$344$	−0.492748	+	0.358003i	−0.0265672	+	0.0193022i
$345$	10.0124	−	4.45782i	0.539051	−	0.240001i
$346$	−4.77023	+	5.29788i	−0.256449	+	0.284816i
$347$	−1.78757	+	1.98529i	−0.0959615	+	0.106576i	−0.789213	−	0.614120i	$-0.789511\pi$
$347$	−1.78757	+	1.98529i	−0.0959615	+	0.106576i	0.693251	+	0.720696i	$0.256178\pi$
$348$	4.10945	−	1.82964i	0.220290	−	0.0980792i
$349$	−11.3477	+	8.24461i	−0.607430	+	0.441324i	−0.848509	−	0.529182i	$-0.822499\pi$
$349$	−11.3477	+	8.24461i	−0.607430	+	0.441324i	0.241078	+	0.970506i	$0.422499\pi$
$350$	−1.71221	+	3.05664i	−0.0915217	+	0.163384i
$351$	5.17805			0.276384
$352$	−3.31538	−	0.0907212i	−0.176711	−	0.00483545i
$353$	−3.34076	−	5.78636i	−0.177811	−	0.307977i	0.763320	−	0.646021i	$-0.223568\pi$
$353$	−3.34076	−	5.78636i	−0.177811	−	0.307977i	−0.941130	+	0.338044i	$0.890235\pi$
$354$	−12.8446	+	2.73021i	−0.682683	+	0.145109i
$355$	0.798473	+	7.59696i	0.0423786	+	0.403205i
$356$	−6.42937	−	4.67121i	−0.340756	−	0.247574i
$357$	−16.5157	−	7.09770i	−0.874101	−	0.375650i
$358$	−3.56579	−	10.9744i	−0.188458	−	0.580014i
$359$	−5.97720	+	2.66122i	−0.315465	+	0.140454i	−0.558360	−	0.829598i	$-0.688569\pi$
$359$	−5.97720	+	2.66122i	−0.315465	+	0.140454i	0.242896	+	0.970052i	$0.421903\pi$
$360$	1.75148	+	0.779810i	0.0923112	+	0.0410996i
$361$	−24.6176	+	5.23264i	−1.29566	+	0.275402i
$362$	−5.57402	+	9.65449i	−0.292964	+	0.507429i
$363$	−0.549837	−	10.9862i	−0.0288590	−	0.576629i
$364$	4.40233	+	12.9732i	0.230745	+	0.679983i
$365$	8.64556	−	26.6083i	0.452529	−	1.39274i
$366$	−0.678065	−	6.45136i	−0.0354430	−	0.337218i
$367$	−0.583002	+	5.54689i	−0.0304325	+	0.289546i	0.968712	+	0.248188i	$0.0798350\pi$
$367$	−0.583002	+	5.54689i	−0.0304325	+	0.289546i	−0.999144	+	0.0413577i	$0.986832\pi$
$368$	−3.82512	+	4.24823i	−0.199398	+	0.221454i
$369$	−1.85115	−	0.393475i	−0.0963672	−	0.0204835i
$370$	−6.22252	−	4.52093i	−0.323493	−	0.235032i
$371$	5.38422	+	3.80603i	0.279535	+	0.197599i
$372$	−2.91971	+	8.98594i	−0.151380	+	0.465899i
$373$	4.20548	−	7.28411i	0.217752	−	0.377157i	−0.736369	−	0.676581i	$-0.763461\pi$
$373$	4.20548	−	7.28411i	0.217752	−	0.377157i	0.954120	+	0.299424i	$0.0967944\pi$
$374$	−11.7968	+	19.1998i	−0.609997	+	0.992800i
$375$	−6.06250	−	10.5006i	−0.313066	−	0.542246i
$376$	−3.92535	−	4.35954i	−0.202434	−	0.224826i
$377$	−18.8442	+	13.6911i	−0.970526	+	0.705128i
$378$	2.58057	−	0.583645i	0.132730	−	0.0300194i
$379$	3.95373	+	12.1683i	0.203090	+	0.625046i	0.999786	+	0.0206665i	$0.00657881\pi$
$379$	3.95373	+	12.1683i	0.203090	+	0.625046i	−0.796697	+	0.604379i	$0.793421\pi$
$380$	−12.4633	−	2.64915i	−0.639352	−	0.135898i
$381$	2.19903	−	20.9224i	0.112660	−	1.07189i
$382$	−10.4054	−	4.63278i	−0.532386	−	0.237034i
$383$	11.7321	+	13.0299i	0.599485	+	0.665795i	0.964154	−	0.265342i	$-0.0854847\pi$
$383$	11.7321	+	13.0299i	0.599485	+	0.665795i	−0.364670	+	0.931137i	$0.618818\pi$
$384$	−1.00000			−0.0510310
$385$	−16.8219	−	0.241748i	−0.857325	−	0.0123206i
$386$	21.6148			1.10017
$387$	−0.407548	−	0.452628i	−0.0207168	−	0.0230084i
$388$	−4.39230	−	1.95558i	−0.222985	−	0.0992794i
$389$	0.157291	−	1.49652i	0.00797496	−	0.0758767i	−0.989811	−	0.142391i	$-0.954521\pi$
$389$	0.157291	−	1.49652i	0.00797496	−	0.0758767i	0.997785	+	0.0665140i	$0.0211877\pi$
$390$	−9.71061	−	2.06405i	−0.491716	−	0.104517i
$391$	12.0023	+	36.9394i	0.606984	+	1.86810i
$392$	3.65626	+	5.96924i	0.184669	+	0.301492i
$393$	4.42775	−	3.21695i	0.223351	−	0.162274i
$394$	−9.41420	−	10.4555i	−0.474281	−	0.526742i
$395$	−6.76650	−	11.7199i	−0.340460	−	0.589693i
$396$	−0.256328	−	3.30670i	−0.0128810	−	0.166168i
$397$	−1.97282	+	3.41702i	−0.0990128	+	0.171495i	−0.911276	−	0.411796i	$-0.864902\pi$
$397$	−1.97282	+	3.41702i	−0.0990128	+	0.171495i	0.812264	+	0.583291i	$0.198235\pi$
$398$	−1.84716	+	5.68497i	−0.0925897	+	0.284962i
$399$	−15.9689	+	7.35978i	−0.799447	+	0.368450i
$400$	1.07131	+	0.778351i	0.0535654	+	0.0389176i
$401$	−9.89855	−	2.10400i	−0.494310	−	0.105069i	−0.0459897	−	0.998942i	$-0.514644\pi$
$401$	−9.89855	−	2.10400i	−0.494310	−	0.105069i	−0.448320	+	0.893873i	$0.647977\pi$
$402$	2.88867	−	3.20819i	0.144074	−	0.160010i
$403$	5.11397	−	48.6562i	0.254745	−	2.42374i
$404$	−1.80235	−	17.1482i	−0.0896702	−	0.853155i
$405$	−0.592458	+	1.82340i	−0.0294395	+	0.0906054i
$406$	−7.84814	+	8.94723i	−0.389497	+	0.444043i
$407$	−1.75223	+	13.1896i	−0.0868550	+	0.653783i
$408$	−3.39718	+	5.88410i	−0.168186	+	0.291306i
$409$	−24.4547	+	5.19800i	−1.20921	+	0.257025i	−0.768041	−	0.640401i	$-0.778768\pi$
$409$	−24.4547	+	5.19800i	−1.20921	+	0.257025i	−0.441165	+	0.897426i	$0.645435\pi$
$410$	3.31469	+	1.47580i	0.163701	+	0.0728844i
$411$	15.8936	−	7.07628i	0.783973	−	0.349047i
$412$	−3.21006	−	9.87953i	−0.158148	−	0.486730i
$413$	27.8400	−	20.7846i	1.36992	−	1.02275i
$414$	−4.62479	−	3.36010i	−0.227296	−	0.165140i
$415$	−1.37902	−	13.1205i	−0.0676936	−	0.644061i
$416$	5.06490	−	1.07658i	0.248327	−	0.0527836i
$417$	−2.54658	−	4.41080i	−0.124707	−	0.215998i
$418$	6.23535	+	21.1415i	0.304981	+	1.03407i
$419$	−15.5673			−0.760511			−0.380256	−	0.924881i	$-0.624164\pi$
$419$	−15.5673			−0.760511			−0.380256	+	0.924881i	$0.624164\pi$
$420$	−5.07210	+	0.0658745i	−0.247493	+	0.00321434i
$421$	−8.08182	+	5.87179i	−0.393884	+	0.286173i	−0.767045	−	0.641593i	$-0.778274\pi$
$421$	−8.08182	+	5.87179i	−0.393884	+	0.286173i	0.373161	+	0.927766i	$0.378274\pi$
$422$	20.5454	−	9.14739i	1.00013	−	0.445288i
$423$	3.92535	−	4.35954i	0.190857	−	0.211968i
$424$	1.66757	−	1.85203i	0.0809846	−	0.0899425i
$425$	8.21933	−	3.65948i	0.398696	−	0.177511i
$426$	3.22335	−	2.34190i	0.156172	−	0.113466i
$427$	8.77365	+	14.7506i	0.424587	+	0.713834i
$428$	−5.39215			−0.260639
$429$	4.85820	+	16.4722i	0.234556	+	0.795284i
$430$	0.583866	+	1.01129i	0.0281565	+	0.0487685i
$431$	5.33500	−	1.13399i	0.256978	−	0.0546224i	−0.0776210	−	0.996983i	$-0.524732\pi$
$431$	5.33500	−	1.13399i	0.256978	−	0.0546224i	0.334599	+	0.942361i	$0.391399\pi$
$432$	−0.104528	−	0.994522i	−0.00502913	−	0.0478490i
$433$	−13.6775	−	9.93726i	−0.657297	−	0.477554i	0.208452	−	0.978033i	$-0.433157\pi$
$433$	−13.6775	−	9.93726i	−0.657297	−	0.477554i	−0.865749	+	0.500479i	$0.833157\pi$
$434$	−2.93565	−	24.8251i	−0.140916	−	1.19164i
$435$	−2.66509	−	8.20229i	−0.127781	−	0.393270i
$436$	−0.893616	+	0.397864i	−0.0427965	+	0.0190542i
$437$	34.7069	+	15.4525i	1.66026	+	0.739194i
$438$	−14.2738	+	3.03399i	−0.682029	+	0.144970i
$439$	7.31193	−	12.6646i	0.348979	−	0.604450i	−0.637089	−	0.770790i	$-0.719862\pi$
$439$	7.31193	−	12.6646i	0.348979	−	0.604450i	0.986068	+	0.166340i	$0.0531951\pi$
$440$	−0.837402	+	6.30337i	−0.0399216	+	0.300501i
$441$	−5.55435	+	4.26018i	−0.264493	+	0.202866i
$442$	10.8717	−	33.4597i	0.517115	−	1.59152i
$443$	3.06103	+	29.1238i	0.145434	+	1.38371i	0.787146	+	0.616767i	$0.211558\pi$
$443$	3.06103	+	29.1238i	0.145434	+	1.38371i	−0.641712	+	0.766946i	$0.721775\pi$
$444$	−0.419342	+	3.98977i	−0.0199011	+	0.189346i
$445$	−10.1952	+	11.3229i	−0.483300	+	0.536759i
$446$	−21.6266	−	4.59687i	−1.02405	−	0.217668i
$447$	−1.69068	−	1.22835i	−0.0799664	−	0.0580990i
$448$	2.40284	−	1.10742i	0.113523	−	0.0523208i
$449$	−1.88389	+	5.79800i	−0.0889061	+	0.273625i	−0.985618	−	0.168991i	$-0.945949\pi$
$449$	−1.88389	+	5.79800i	−0.0889061	+	0.273625i	0.896712	+	0.442615i	$0.145949\pi$
$450$	−0.662105	+	1.14680i	−0.0312119	+	0.0540607i
$451$	−0.485102	−	6.25797i	−0.0228426	−	0.294676i
$452$	−9.19852	−	15.9323i	−0.432662	−	0.749393i
$453$	5.48795	+	6.09499i	0.257846	+	0.286367i
$454$	4.62037	−	3.35690i	0.216845	−	0.157547i
$455$	25.6188	−	5.79416i	1.20103	−	0.271634i
$456$	2.05369	+	6.32060i	0.0961727	+	0.295989i
$457$	7.00258	+	1.48844i	0.327567	+	0.0696265i	0.368760	−	0.929525i	$-0.379782\pi$
$457$	7.00258	+	1.48844i	0.327567	+	0.0696265i	−0.0411929	+	0.999151i	$0.513116\pi$
$458$	−1.92403	+	18.3059i	−0.0899041	+	0.855380i
$459$	−6.20696	−	2.76352i	−0.289716	−	0.128990i
$460$	7.33365	+	8.14485i	0.341933	+	0.379755i
$461$	−17.5082			−0.815437			−0.407718	−	0.913108i	$-0.633675\pi$
$461$	−17.5082			−0.815437			−0.407718	+	0.913108i	$0.633675\pi$
$462$	4.27783	+	7.66160i	0.199023	+	0.356450i
$463$	4.75603			0.221031			0.110516	−	0.993874i	$-0.464750\pi$
$463$	4.75603			0.221031			0.110516	+	0.993874i	$0.464750\pi$
$464$	3.00998	+	3.34293i	0.139735	+	0.155191i
$465$	16.5487	+	7.36793i	0.767425	+	0.341680i
$466$	1.05927	−	10.0782i	0.0490696	−	0.466866i
$467$	5.66857	+	1.20489i	0.262310	+	0.0557557i	0.337189	−	0.941437i	$-0.390524\pi$
$467$	5.66857	+	1.20489i	0.262310	+	0.0557557i	−0.0748792	+	0.997193i	$0.523857\pi$
$468$	1.60011	+	4.92462i	0.0739650	+	0.227641i
$469$	−3.38817	+	10.9077i	−0.156451	+	0.503672i
$470$	−9.09914	+	6.61091i	−0.419712	+	0.304939i
$471$	0.672607	+	0.747005i	0.0309921	+	0.0344202i
$472$	−6.56578	−	11.3723i	−0.302215	−	0.523451i
$473$	1.05750	−	1.72114i	0.0486241	−	0.0791381i
$474$	−3.52930	+	6.11293i	−0.162106	+	0.280776i
$475$	2.71951	−	8.36980i	0.124780	−	0.384033i
$476$	1.64670	−	17.9006i	0.0754763	−	0.820474i
$477$	2.01619	+	1.46485i	0.0923151	+	0.0670708i
$478$	−6.33570	−	1.34670i	−0.289788	−	0.0615964i
$479$	2.72835	−	3.03014i	0.124662	−	0.138451i	−0.677583	−	0.735447i	$-0.736972\pi$
$479$	2.72835	−	3.03014i	0.124662	−	0.138451i	0.802244	+	0.596996i	$0.203639\pi$
$480$	−0.200406	+	1.90673i	−0.00914722	+	0.0870300i
$481$	−2.17137	−	20.6592i	−0.0990061	−	0.941980i
$482$	−7.25657	+	22.3334i	−0.330528	+	1.01726i
$483$	14.8337	+	2.95219i	0.674955	+	0.134329i
$484$	10.2786	−	3.91786i	0.467211	−	0.178085i
$485$	−4.60900	+	7.98303i	−0.209284	+	0.362491i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	16.9767	+	7.55852i	0.769288	+	0.342509i	0.753570	−	0.657367i	$-0.228330\pi$
$487$	16.9767	+	7.55852i	0.769288	+	0.342509i	0.0157177	+	0.999876i	$0.494997\pi$
$488$	5.92607	−	2.63846i	0.268261	−	0.119437i
$489$	1.83360	+	5.64324i	0.0829182	+	0.255196i
$490$	12.1145	−	5.77524i	0.547276	−	0.260899i
$491$	12.3631	+	8.98229i	0.557937	+	0.405365i	0.830703	−	0.556715i	$-0.187939\pi$
$491$	12.3631	+	8.98229i	0.557937	+	0.405365i	−0.272766	+	0.962080i	$0.587939\pi$
$492$	−0.197821	−	1.88214i	−0.00891846	−	0.0848535i
$493$	29.8956	−	6.35450i	1.34643	−	0.286192i
$494$	−17.2063	−	29.8023i	−0.774150	−	1.34087i
$495$	−6.35637	−	0.173934i	−0.285698	−	0.00781774i
$496$	−9.44838			−0.424245
$497$	−5.15171	+	9.19682i	−0.231086	+	0.412534i
$498$	−5.56697	+	4.04464i	−0.249462	+	0.181245i
$499$	−30.0054	+	13.3593i	−1.34323	+	0.598043i	−0.947332	−	0.320253i	$-0.896232\pi$
$499$	−30.0054	+	13.3593i	−1.34323	+	0.598043i	−0.395894	+	0.918296i	$0.629565\pi$
$500$	8.11321	−	9.01063i	0.362834	−	0.402968i
$501$	−4.46505	+	4.95895i	−0.199484	+	0.221549i
$502$	−11.3411	+	5.04940i	−0.506179	+	0.225366i
$503$	−4.06678	+	2.95469i	−0.181329	+	0.131743i	−0.674747	−	0.738049i	$-0.735747\pi$
$503$	−4.06678	+	2.95469i	−0.181329	+	0.131743i	0.493418	+	0.869792i	$0.335747\pi$
$504$	1.35252	+	2.27392i	0.0602460	+	0.101288i
$505$	−33.0582			−1.47107
$506$	6.34989	−	17.8647i	0.282287	−	0.794183i
$507$	−6.90612	−	11.9618i	−0.306712	−	0.531240i
$508$	20.5779	−	4.37397i	0.912997	−	0.194063i
$509$	−2.68924	−	25.5865i	−0.119199	−	1.13410i	−0.876623	−	0.481177i	$-0.840209\pi$
$509$	−2.68924	−	25.5865i	−0.119199	−	1.13410i	0.757425	−	0.652922i	$-0.226457\pi$
$510$	10.5386	+	7.65673i	0.466656	+	0.339046i
$511$	30.9377	−	23.0973i	1.36860	−	1.02176i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−6.07131	+	2.70312i	−0.268055	+	0.119346i
$514$	−20.7012	−	9.21677i	−0.913091	−	0.406534i
$515$	−19.4809	+	4.14080i	−0.858433	+	0.182466i
$516$	0.304535	−	0.527471i	0.0134064	−	0.0232206i
$517$	17.5512	+	8.39688i	0.771903	+	0.369294i
$518$	−3.41075	−	10.0511i	−0.149860	−	0.441622i
$519$	2.20298	−	6.78009i	0.0967002	−	0.297613i
$520$	−1.03771	−	9.87316i	−0.0455066	−	0.432967i
$521$	−0.387137	+	3.68336i	−0.0169608	+	0.161371i	−0.999724	−	0.0234984i	$-0.992520\pi$
$521$	−0.387137	+	3.68336i	−0.0169608	+	0.161371i	0.982763	+	0.184869i	$0.0591862\pi$
$522$	−3.00998	+	3.34293i	−0.131743	+	0.146316i
$523$	38.0964	+	8.09763i	1.66584	+	0.354085i	0.941929	−	0.335811i	$-0.109010\pi$
$523$	38.0964	+	8.09763i	1.66584	+	0.354085i	0.723909	+	0.689896i	$0.242344\pi$
$524$	4.42775	+	3.21695i	0.193427	+	0.140533i
$525$	0.320938	−	3.48880i	0.0140069	−	0.152264i
$526$	4.84424	−	14.9090i	0.211219	−	0.650065i
$527$	−32.0979	+	55.5951i	−1.39821	+	2.42176i
$528$	3.06565	−	1.26561i	0.133415	−	0.0550786i
$529$	−4.83948	−	8.38222i	−0.210412	−	0.364444i
$530$	−3.19713	−	3.55077i	−0.138875	−	0.154236i
$531$	10.6237	−	7.71854i	0.461028	−	0.334956i
$532$	−11.9342	−	12.9131i	−0.517415	−	0.559852i
$533$	3.02822	+	9.31989i	0.131167	+	0.403689i
$534$	7.77347	+	1.65230i	0.336391	+	0.0715021i
$535$	−1.08062	+	10.2814i	−0.0467191	+	0.444503i
$536$	3.94382	+	1.75590i	0.170347	+	0.0758433i
$537$	7.72119	+	8.57525i	0.333194	+	0.370050i
$538$	22.8333			0.984414
$539$	−18.7635	−	13.6722i	−0.808203	−	0.588904i
$540$	−1.91723			−0.0825047
$541$	10.2096	+	11.3390i	0.438947	+	0.487500i	0.921506	−	0.388363i	$-0.126959\pi$
$541$	10.2096	+	11.3390i	0.438947	+	0.487500i	−0.482560	+	0.875863i	$0.660293\pi$
$542$	10.4052	+	4.63270i	0.446943	+	0.198992i
$543$	1.16529	−	11.0870i	0.0500073	−	0.475788i
$544$	−6.64590	−	1.41263i	−0.284940	−	0.0605660i
$545$	0.579534	+	1.78362i	0.0248245	+	0.0764019i
$546$	−9.29843	−	10.0611i	−0.397936	−	0.430574i
$547$	−24.3755	+	17.7099i	−1.04222	+	0.757219i	−0.970718	−	0.240221i	$-0.922780\pi$
$547$	−24.3755	+	17.7099i	−1.04222	+	0.757219i	−0.0715044	+	0.997440i	$0.522780\pi$
$548$	11.6413	+	12.9290i	0.497293	+	0.552300i
$549$	3.24345	+	5.61782i	0.138427	+	0.239763i
$550$	−4.26935	−	1.03030i	−0.182046	−	0.0439320i
$551$	14.9477	−	25.8902i	0.636795	−	1.10296i
$552$	1.76651	−	5.43676i	0.0751877	−	0.231404i
$553$	1.71074	−	18.5968i	0.0727480	−	0.790816i
$554$	6.19805	+	4.50315i	0.263330	+	0.191320i
$555$	7.52338	+	1.59914i	0.319350	+	0.0678799i
$556$	3.40799	−	3.78495i	0.144531	−	0.160518i
$557$	1.89014	−	17.9835i	0.0800877	−	0.761983i	−0.878607	−	0.477546i	$-0.841526\pi$
$557$	1.89014	−	17.9835i	0.0800877	−	0.761983i	0.958695	−	0.284438i	$-0.0918068\pi$
$558$	−0.987624	−	9.39662i	−0.0418095	−	0.397790i
$559$	−0.974578	+	2.99944i	−0.0412203	+	0.126863i
$560$	−1.63002	−	4.80350i	−0.0688807	−	0.202985i
$561$	2.96762	−	22.3381i	0.125293	−	0.943116i
$562$	1.69121	−	2.92927i	0.0713395	−	0.123564i
$563$	−21.3861	+	4.54577i	−0.901319	+	0.191581i	−0.635190	−	0.772356i	$-0.719078\pi$
$563$	−21.3861	+	4.54577i	−0.901319	+	0.191581i	−0.266129	+	0.963937i	$0.585745\pi$
$564$	5.35917	+	2.38606i	0.225662	+	0.100471i
$565$	−32.2221	+	14.3462i	−1.35559	+	0.603549i
$566$	−4.13578	−	12.7286i	−0.173840	−	0.535024i
$567$	−2.12008	+	1.58280i	−0.0890351	+	0.0664713i
$568$	3.22335	+	2.34190i	0.135249	+	0.0982641i
$569$	−4.25653	−	40.4982i	−0.178443	−	1.69777i	−0.607359	−	0.794427i	$-0.707771\pi$
$569$	−4.25653	−	40.4982i	−0.178443	−	1.69777i	0.428916	−	0.903344i	$-0.358896\pi$
$570$	12.4633	−	2.64915i	0.522028	−	0.110961i
$571$	12.1909	+	21.1152i	0.510172	+	0.883643i	0.999931	+	0.0117853i	$0.00375146\pi$
$571$	12.1909	+	21.1152i	0.510172	+	0.883643i	−0.489759	+	0.871858i	$0.662915\pi$
$572$	−14.1647	+	9.71061i	−0.592256	+	0.406021i
$573$	11.3901			0.475829
$574$	2.55966	+	4.30340i	0.106838	+	0.179621i
$575$	−6.12419	+	4.44949i	−0.255396	+	0.185556i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−10.6933	+	11.8761i	−0.445166	+	0.494407i	−0.923407	−	0.383821i	$-0.874608\pi$
$577$	−10.6933	+	11.8761i	−0.445166	+	0.494407i	0.478241	+	0.878229i	$0.341275\pi$
$578$	−19.5142	+	21.6727i	−0.811682	+	0.901464i
$579$	−19.7461	+	8.79154i	−0.820621	+	0.365364i
$580$	6.97728	−	5.06929i	0.289716	−	0.210491i
$581$	8.89739	−	15.8836i	0.369126	−	0.658963i
$582$	4.80797			0.199297
$583$	−2.76826	+	7.78818i	−0.114650	+	0.322553i
$584$	−7.29635	−	12.6376i	−0.301925	−	0.522949i
$585$	9.71061	−	2.06405i	0.401484	−	0.0853381i
$586$	−0.136900	−	1.30252i	−0.00565528	−	0.0538064i
$587$	6.20045	+	4.50489i	0.255920	+	0.185937i	0.708346	−	0.705865i	$-0.249442\pi$
$587$	6.20045	+	4.50489i	0.255920	+	0.185937i	−0.452426	+	0.891802i	$0.649442\pi$
$588$	−5.76807	−	3.96603i	−0.237871	−	0.163556i
$589$	19.4040	+	59.7194i	0.799528	+	2.46069i
$590$	−22.9997	+	10.2401i	−0.946882	+	0.421579i
$591$	12.8529	+	5.72250i	0.528700	+	0.235392i
$592$	−3.92408	+	0.834089i	−0.161279	+	0.0342808i
$593$	13.7460	−	23.8088i	0.564482	−	0.977711i	−0.432616	−	0.901578i	$-0.642409\pi$
$593$	13.7460	−	23.8088i	0.564482	−	0.977711i	0.997098	−	0.0761330i	$-0.0242574\pi$
$594$	1.57913	+	2.91657i	0.0647923	+	0.119668i
$595$	−33.8017	−	6.72720i	−1.38573	−	0.275788i
$596$	0.645782	−	1.98751i	0.0264523	−	0.0814117i
$597$	−0.624822	−	5.94479i	−0.0255723	−	0.243304i
$598$	−3.09411	+	29.4385i	−0.126527	+	1.20383i
$599$	−2.69568	+	2.99386i	−0.110143	+	0.122326i	−0.795695	−	0.605698i	$-0.792894\pi$
$599$	−2.69568	+	2.99386i	−0.110143	+	0.122326i	0.685552	+	0.728023i	$0.259561\pi$
$600$	−1.29527	−	0.275319i	−0.0528793	−	0.0112398i
$601$	22.8549	+	16.6050i	0.932270	+	0.677334i	0.946548	−	0.322564i	$-0.104545\pi$
$601$	22.8549	+	16.6050i	0.932270	+	0.677334i	−0.0142777	+	0.999898i	$0.504545\pi$
$602$	−0.147616	+	1.60467i	−0.00601636	+	0.0654016i
$603$	−1.33404	+	4.10575i	−0.0543263	+	0.167199i
$604$	−4.10081	+	7.10280i	−0.166859	+	0.289009i
$605$	−5.41042	−	20.3838i	−0.219965	−	0.828718i
$606$	8.62133	+	14.9326i	0.350218	+	0.606595i
$607$	−29.4019	−	32.6542i	−1.19339	−	1.32539i	−0.932995	−	0.359889i	$-0.882815\pi$
$607$	−29.4019	−	32.6542i	−1.19339	−	1.32539i	−0.260393	−	0.965503i	$-0.583852\pi$
$608$	−5.37662	+	3.90634i	−0.218051	+	0.158423i
$609$	3.53047	−	11.3658i	0.143062	−	0.460566i
$610$	−3.84321	−	11.8282i	−0.155607	−	0.478910i
$611$	−29.7124	−	6.31557i	−1.20204	−	0.255501i
$612$	0.710205	−	6.75715i	0.0287083	−	0.273142i
$613$	36.6321	+	16.3097i	1.47956	+	0.658741i	0.978420	−	0.206626i	$-0.0662484\pi$
$613$	36.6321	+	16.3097i	1.47956	+	0.658741i	0.501138	+	0.865368i	$0.332915\pi$
$614$	−17.7492	−	19.7125i	−0.716299	−	0.795531i
$615$	−3.62838			−0.146311
$616$	−5.96470	+	6.43602i	−0.240324	+	0.259315i
$617$	3.76368			0.151520			0.0757600	−	0.997126i	$-0.475862\pi$
$617$	3.76368			0.151520			0.0757600	+	0.997126i	$0.475862\pi$
$618$	6.95090	+	7.71976i	0.279606	+	0.310534i
$619$	10.0421	+	4.47104i	0.403626	+	0.179706i	0.598501	−	0.801122i	$-0.295763\pi$
$619$	10.0421	+	4.47104i	0.403626	+	0.179706i	−0.194874	+	0.980828i	$0.562430\pi$
$620$	−1.89351	+	18.0155i	−0.0760451	+	0.723521i
$621$	5.59163	+	1.18854i	0.224384	+	0.0476944i
$622$	1.65467	+	5.09255i	0.0663462	+	0.204193i
$623$	−20.5082	+	4.63830i	−0.821643	+	0.185830i
$624$	−4.18913	+	3.04358i	−0.167700	+	0.121841i
$625$	−11.1246	−	12.3551i	−0.444983	−	0.494204i
$626$	6.59939	+	11.4305i	0.263765	+	0.456854i
$627$	−14.2953	−	16.7776i	−0.570900	−	0.670033i
$628$	−0.502597	+	0.870524i	−0.0200558	+	0.0347377i
$629$	−8.42296	+	25.9232i	−0.335845	+	1.03363i
$630$	4.60680	−	2.12319i	0.183539	−	0.0845898i
$631$	−22.2118	−	16.1378i	−0.884238	−	0.642436i	0.0501314	−	0.998743i	$-0.484036\pi$
$631$	−22.2118	−	16.1378i	−0.884238	−	0.642436i	−0.934369	+	0.356306i	$0.884036\pi$
$632$	−6.90436	−	1.46757i	−0.274641	−	0.0583767i
$633$	−15.0486	+	16.7131i	−0.598126	+	0.664286i
$634$	1.31885	−	12.5480i	0.0523781	−	0.498344i
$635$	−4.21606	−	40.1131i	−0.167309	−	1.59184i
$636$	−0.770117	+	2.37018i	−0.0305371	+	0.0939836i
$637$	33.4844	+	13.8778i	1.32670	+	0.549858i
$638$	−13.4584	−	6.43879i	−0.532824	−	0.254914i
$639$	−1.99214	+	3.45049i	−0.0788079	+	0.136499i
$640$	−1.87534	+	0.398616i	−0.0741293	+	0.0157567i
$641$	32.3215	+	14.3904i	1.27662	+	0.568389i	0.929289	−	0.369354i	$-0.120421\pi$
$641$	32.3215	+	14.3904i	1.27662	+	0.568389i	0.347333	+	0.937742i	$0.387088\pi$
$642$	4.92597	−	2.19318i	0.194413	−	0.0865581i
$643$	7.08619	+	21.8091i	0.279452	+	0.860065i	0.988007	+	0.154410i	$0.0493475\pi$
$643$	7.08619	+	21.8091i	0.279452	+	0.860065i	−0.708555	+	0.705656i	$0.750652\pi$
$644$	1.77615	+	15.0199i	0.0699903	+	0.591868i
$645$	−0.944715	−	0.686375i	−0.0371981	−	0.0270260i
$646$	4.71993	+	44.9071i	0.185703	+	1.76685i
$647$	8.12114	−	1.72620i	0.319275	−	0.0678640i	−0.0454866	−	0.998965i	$-0.514484\pi$
$647$	8.12114	−	1.72620i	0.319275	−	0.0678640i	0.364762	+	0.931101i	$0.381151\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	34.5213	+	26.5537i	1.35508	+	1.04232i
$650$	6.85683			0.268947
$651$	12.7791	+	21.4848i	0.500853	+	0.842056i
$652$	−4.80042	+	3.48771i	−0.187999	+	0.136589i
$653$	13.3322	−	5.93587i	0.521729	−	0.232289i	−0.128937	−	0.991653i	$-0.541157\pi$
$653$	13.3322	−	5.93587i	0.521729	−	0.232289i	0.650666	+	0.759364i	$0.274490\pi$
$654$	0.654533	−	0.726933i	0.0255943	−	0.0284253i
$655$	7.02121	−	7.79785i	0.274341	−	0.304687i
$656$	1.72889	−	0.769752i	0.0675019	−	0.0300538i
$657$	11.8057	−	8.57737i	0.460586	−	0.334635i
$658$	−15.5196	+	0.201562i	−0.605016	+	0.00785771i
$659$	37.7131			1.46910			0.734548	−	0.678557i	$-0.237394\pi$
$659$	37.7131			1.46910			0.734548	+	0.678557i	$0.237394\pi$
$660$	−1.79881	−	6.09902i	−0.0700184	−	0.237404i
$661$	−1.39393	−	2.41436i	−0.0542176	−	0.0939076i	0.837643	−	0.546218i	$-0.183933\pi$
$661$	−1.39393	−	2.41436i	−0.0542176	−	0.0939076i	−0.891860	+	0.452311i	$0.850600\pi$
$662$	32.5371	−	6.91598i	1.26459	−	0.268797i
$663$	3.67748	+	34.9889i	0.142821	+	1.35886i
$664$	−5.56697	−	4.04464i	−0.216040	−	0.156963i
$665$	−27.0134	+	20.1676i	−1.04754	+	0.782064i
$666$	−1.23970	−	3.81540i	−0.0480373	−	0.147844i
$667$	−23.4919	+	10.4593i	−0.909609	+	0.404984i
$668$	−6.09601	−	2.71412i	−0.235862	−	0.105012i
$669$	21.6266	−	4.59687i	0.836131	−	0.177725i
$670$	4.13839	−	7.16791i	0.159880	−	0.276920i
$671$	−14.8280	+	15.5887i	−0.572430	+	0.601795i
$672$	−1.74467	+	1.98900i	−0.0673021	+	0.0767274i
$673$	11.2481	−	34.6182i	0.433584	−	1.33443i	−0.460947	−	0.887428i	$-0.652490\pi$
$673$	11.2481	−	34.6182i	0.433584	−	1.33443i	0.894531	−	0.447007i	$-0.147510\pi$
$674$	−1.99933	−	19.0224i	−0.0770114	−	0.732715i
$675$	0.138418	−	1.31696i	0.00532770	−	0.0506897i
$676$	9.24220	−	10.2645i	0.355469	−	0.394788i
$677$	33.3247	+	7.08339i	1.28077	+	0.272237i	0.797546	−	0.603258i	$-0.206131\pi$
$677$	33.3247	+	7.08339i	1.28077	+	0.272237i	0.483228	+	0.875495i	$0.339464\pi$
$678$	14.8835	+	10.8135i	0.571598	+	0.415291i
$679$	−11.5528	+	5.32445i	−0.443354	+	0.204334i
$680$	−4.02538	+	12.3888i	−0.154366	+	0.475090i
$681$	−2.85555	+	4.94595i	−0.109425	+	0.189529i
$682$	28.9654	−	11.9580i	1.10914	−	0.457894i
$683$	19.9450	+	34.5458i	0.763175	+	1.32186i	0.941206	+	0.337834i	$0.109694\pi$
$683$	19.9450	+	34.5458i	0.763175	+	1.32186i	−0.178030	+	0.984025i	$0.556973\pi$
$684$	−4.44696	−	4.93884i	−0.170034	−	0.188841i
$685$	26.9851	−	19.6059i	1.03105	−	0.749101i
$686$	18.2518	+	3.14204i	0.696856	+	0.119964i
$687$	−5.68801	−	17.5059i	−0.217011	−	0.667891i
$688$	0.595761	+	0.126633i	0.0227132	+	0.00482783i
$689$	1.34889	−	12.8338i	0.0513885	−	0.488929i
$690$	−10.0124	−	4.45782i	−0.381167	−	0.169706i
$691$	5.37124	+	5.96537i	0.204332	+	0.226933i	0.836597	−	0.547818i	$-0.184542\pi$
$691$	5.37124	+	5.96537i	0.204332	+	0.226933i	−0.632266	+	0.774752i	$0.717875\pi$
$692$	7.12900			0.271004
$693$	−7.02425	−	5.25927i	−0.266829	−	0.199783i
$694$	2.67147			0.101408
$695$	−6.53391	−	7.25665i	−0.247845	−	0.275260i
$696$	−4.10945	−	1.82964i	−0.155768	−	0.0693525i
$697$	1.34407	−	12.7880i	0.0509102	−	0.484379i
$698$	13.7201	+	2.91629i	0.519312	+	0.110383i
$699$	3.13150	+	9.63778i	0.118444	+	0.364534i
$700$	3.41722	−	0.772868i	0.129159	−	0.0292117i
$701$	12.5540	−	9.12104i	0.474159	−	0.344497i	−0.324901	−	0.945748i	$-0.605331\pi$
$701$	12.5540	−	9.12104i	0.474159	−	0.344497i	0.799060	+	0.601251i	$0.205331\pi$
$702$	−3.46479	−	3.84804i	−0.130770	−	0.145235i
$703$	13.3308	+	23.0896i	0.502780	+	0.870840i
$704$	2.15101	+	2.52451i	0.0810691	+	0.0951462i
$705$	5.62358	−	9.74032i	0.211796	−	0.366842i
$706$	−2.06470	+	6.35450i	−0.0777061	+	0.239155i
$707$	−37.2523	−	26.3331i	−1.40102	−	0.990358i
$708$	10.6237	+	7.71854i	0.399262	+	0.290081i
$709$	−13.0264	−	2.76884i	−0.489215	−	0.103986i	−0.0433019	−	0.999062i	$-0.513788\pi$
$709$	−13.0264	−	2.76884i	−0.489215	−	0.103986i	−0.445913	+	0.895076i	$0.647121\pi$
$710$	5.11136	−	5.67674i	0.191826	−	0.213044i
$711$	0.737825	−	7.01994i	0.0276706	−	0.263268i
$712$	0.830702	+	7.90360i	0.0311319	+	0.296200i
$713$	16.6907	−	51.3686i	0.625070	−	1.92377i
$714$	5.77651	+	17.0228i	0.216180	+	0.637063i
$715$	15.6768	+	28.9544i	0.586280	+	1.08283i
$716$	−5.76957	+	9.99319i	−0.215619	+	0.373463i
$717$	6.33570	−	1.34670i	0.236611	−	0.0502933i
$718$	5.97720	+	2.66122i	0.223067	+	0.0993160i
$719$	4.47101	−	1.99062i	0.166741	−	0.0742377i	−0.321669	−	0.946852i	$-0.604244\pi$
$719$	4.47101	−	1.99062i	0.166741	−	0.0742377i	0.488410	+	0.872614i	$0.337577\pi$
$720$	−0.592458	−	1.82340i	−0.0220796	−	0.0679541i
$721$	−25.2509	−	10.8517i	−0.940392	−	0.404139i
$722$	20.3610	+	14.7931i	0.757759	+	0.550544i
$723$	−2.45462	−	23.3541i	−0.0912882	−	0.868549i
$724$	10.9044	−	2.31781i	0.405260	−	0.0861407i
$725$	2.97838	+	5.15871i	0.110614	+	0.191590i
$726$	−7.79646	+	7.75984i	−0.289354	+	0.287995i
$727$	−15.7037			−0.582419			−0.291209	−	0.956659i	$-0.594058\pi$
$727$	−15.7037			−0.582419			−0.291209	+	0.956659i	$0.594058\pi$
$728$	6.69527	−	11.9524i	0.248143	−	0.442984i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−25.5588	+	11.3795i	−0.945975	+	0.421175i
$731$	2.76903	−	3.07532i	0.102416	−	0.113745i
$732$	−4.34058	+	4.82070i	−0.160432	+	0.178178i
$733$	−19.3667	+	8.62259i	−0.715324	+	0.318483i	−0.731930	−	0.681379i	$-0.761380\pi$
$733$	−19.3667	+	8.62259i	−0.715324	+	0.318483i	0.0166066	+	0.999862i	$0.494714\pi$
$734$	4.51225	−	3.27834i	0.166550	−	0.121006i
$735$	−8.71812	+	10.2033i	−0.321573	+	0.376356i
$736$	5.71655			0.210715
$737$	−14.3127	−	0.391647i	−0.527214	−	0.0144265i
$738$	0.946254	+	1.63896i	0.0348321	+	0.0603310i
$739$	−12.1028	+	2.57254i	−0.445210	+	0.0946323i	−0.425061	−	0.905165i	$-0.639747\pi$
$739$	−12.1028	+	2.57254i	−0.445210	+	0.0946323i	−0.0201490	+	0.999797i	$0.506414\pi$
$740$	0.803976	+	7.64932i	0.0295548	+	0.281195i
$741$	27.8404	+	20.2273i	1.02274	+	0.743067i
$742$	−0.774321	−	6.54799i	−0.0284262	−	0.240384i
$743$	−11.8665	−	36.5213i	−0.435339	−	1.33984i	−0.892739	−	0.450575i	$-0.851219\pi$
$743$	−11.8665	−	36.5213i	−0.435339	−	1.33984i	0.457400	−	0.889261i	$-0.348781\pi$
$744$	8.63152	−	3.84300i	0.316447	−	0.140891i
$745$	−3.66023	−	1.62964i	−0.134101	−	0.0597054i
$746$	−8.22717	+	1.74874i	−0.301218	+	0.0640259i
$747$	3.44058	−	5.95926i	0.125884	−	0.218038i
$748$	22.1618	−	4.08048i	0.810317	−	0.149197i
$749$	−9.40752	+	10.7250i	−0.343743	+	0.391883i
$750$	−3.74683	+	11.5316i	−0.136815	+	0.421073i
$751$	0.117717	+	1.12000i	0.00429554	+	0.0408693i	0.996460	−	0.0840717i	$-0.0267925\pi$
$751$	0.117717	+	1.12000i	0.00429554	+	0.0408693i	−0.992164	+	0.124941i	$0.960126\pi$
$752$	−0.613200	+	5.83421i	−0.0223611	+	0.212752i
$753$	8.30686	−	9.22571i	0.302719	−	0.336203i
$754$	22.7837	+	4.84283i	0.829734	+	0.176365i
$755$	12.7213	+	9.24258i	0.462976	+	0.336372i
$756$	−2.16047	−	1.52721i	−0.0785756	−	0.0555439i
$757$	4.58962	−	14.1254i	0.166813	−	0.513396i	−0.832353	−	0.554246i	$-0.813007\pi$
$757$	4.58962	−	14.1254i	0.166813	−	0.513396i	0.999165	+	0.0408501i	$0.0130066\pi$
$758$	6.39728	−	11.0804i	0.232360	−	0.402458i
$759$	1.46531	+	18.9029i	0.0531874	+	0.686133i
$760$	6.37085	+	11.0346i	0.231095	+	0.400268i
$761$	2.99444	+	3.32566i	0.108548	+	0.120555i	0.794970	−	0.606648i	$-0.207486\pi$
$761$	2.99444	+	3.32566i	0.108548	+	0.120555i	−0.686422	+	0.727203i	$0.740820\pi$
$762$	−17.0198	+	12.3656i	−0.616562	+	0.447959i
$763$	−0.767714	+	2.47155i	−0.0277931	+	0.0894759i
$764$	3.51974	+	10.8326i	0.127340	+	0.391911i
$765$	−12.7417	−	2.70834i	−0.460679	−	0.0979203i
$766$	1.83274	−	17.4374i	0.0662196	−	0.630038i
$767$	−62.1174	−	27.6564i	−2.24293	−	0.998616i
$768$	0.669131	+	0.743145i	0.0241452	+	0.0268159i
$769$	−14.7272			−0.531078			−0.265539	−	0.964100i	$-0.585550\pi$
$769$	−14.7272			−0.531078			−0.265539	+	0.964100i	$0.585550\pi$
$770$	11.0764	+	12.6629i	0.399166	+	0.456339i
$771$	22.6603			0.816090
$772$	−14.4631	−	16.0629i	−0.520540	−	0.578118i
$773$	31.0197	+	13.8109i	1.11570	+	0.496742i	0.879948	−	0.475070i	$-0.157577\pi$
$773$	31.0197	+	13.8109i	1.11570	+	0.496742i	0.235754	+	0.971813i	$0.424244\pi$
$774$	−0.0636652	+	0.605734i	−0.00228840	+	0.0217727i
$775$	−12.2382	−	2.60132i	−0.439610	−	0.0934420i
$776$	1.48574	+	4.57265i	0.0533351	+	0.164149i
$777$	7.20404	+	7.79490i	0.258444	+	0.279641i
$778$	−1.21738	+	0.884479i	−0.0436452	+	0.0317101i
$779$	−8.41590	−	9.34680i	−0.301531	−	0.334884i
$780$	4.96377	+	8.59751i	0.177732	+	0.307840i
$781$	−12.8456	−	3.09996i	−0.459653	−	0.110925i
$782$	19.4202	−	33.6367i	0.694464	−	1.20285i
$783$	1.39007	−	4.27819i	0.0496769	−	0.152890i
$784$	1.98949	−	6.71133i	0.0710533	−	0.239690i
$785$	1.55913	+	1.13278i	0.0556478	+	0.0404305i
$786$	−5.35341	−	1.13790i	−0.190950	−	0.0405876i
$787$	−16.2557	+	18.0537i	−0.579452	+	0.643546i	−0.959596	−	0.281381i	$-0.909208\pi$
$787$	−16.2557	+	18.0537i	−0.579452	+	0.643546i	0.380145	+	0.924927i	$0.375874\pi$
$788$	−1.47064	+	13.9922i	−0.0523895	+	0.498452i
$789$	1.63862	+	15.5904i	0.0583363	+	0.555033i
$790$	−4.18193	+	12.8706i	−0.148786	+	0.457917i
$791$	−47.7378	−	9.50075i	−1.69736	−	0.337808i
$792$	−2.28584	+	2.40311i	−0.0812239	+	0.0853907i
$793$	16.7947	−	29.0894i	0.596399	−	1.03299i
$794$	3.85941	−	0.820343i	0.136965	−	0.0291129i
$795$	4.36495	+	1.94340i	0.154809	+	0.0689254i
$796$	5.46075	−	2.43128i	0.193551	−	0.0861745i
$797$	4.42817	+	13.6285i	0.156854	+	0.482746i	0.998344	−	0.0575259i	$-0.0183212\pi$
$797$	4.42817	+	13.6285i	0.156854	+	0.482746i	−0.841490	+	0.540272i	$0.818321\pi$
$798$	16.1547	+	6.94257i	0.571870	+	0.245764i
$799$	32.2459	+	23.4280i	1.14078	+	0.828823i
$800$	−0.138418	−	1.31696i	−0.00489380	−	0.0465614i
$801$	−7.77347	+	1.65230i	−0.274662	+	0.0583813i
$802$	5.05984	+	8.76390i	0.178669	+	0.309464i
$803$	38.3624	+	29.5083i	1.35378	+	1.04133i
$804$	−4.31704			−0.152250
$805$	28.9949	−	0.376575i	1.02194	−	0.0132725i
$806$	−39.5805	+	28.7569i	−1.39416	+	1.01292i
$807$	−20.8593	+	9.28715i	−0.734281	+	0.326923i
$808$	−11.5376	+	12.8138i	−0.405891	+	0.450788i
$809$	21.6258	−	24.0179i	0.760323	−	0.844424i	−0.231395	−	0.972860i	$-0.574329\pi$
$809$	21.6258	−	24.0179i	0.760323	−	0.844424i	0.991718	+	0.128436i	$0.0409956\pi$
$810$	1.75148	−	0.779810i	0.0615408	−	0.0273997i
$811$	−2.51847	+	1.82977i	−0.0884354	+	0.0642520i	−0.631124	−	0.775682i	$-0.717406\pi$
$811$	−2.51847	+	1.82977i	−0.0884354	+	0.0642520i	0.542689	+	0.839934i	$0.317406\pi$
$812$	11.9005	−	0.154559i	0.417626	−	0.00542397i
$813$	−11.3899			−0.399462
$814$	10.9742	−	7.52338i	0.384647	−	0.263694i
$815$	5.68810	+	9.85208i	0.199245	+	0.345103i
$816$	6.64590	−	1.41263i	0.232653	−	0.0494519i
$817$	−0.423111	−	4.02563i	−0.0148028	−	0.140839i
$818$	20.2262	+	14.6952i	0.707194	+	0.513806i
$819$	12.5867	+	5.40923i	0.439816	+	0.189014i
$820$	−1.12123	−	3.45080i	−0.0391551	−	0.120507i
$821$	−15.5356	+	6.91691i	−0.542197	+	0.241402i	−0.659513	−	0.751693i	$-0.729238\pi$
$821$	−15.5356	+	6.91691i	−0.542197	+	0.241402i	0.117316	+	0.993095i	$0.462571\pi$
$822$	−15.8936	−	7.07628i	−0.554353	−	0.246814i
$823$	−30.5314	+	6.48966i	−1.06426	+	0.226215i	−0.706583	−	0.707630i	$-0.749764\pi$
$823$	−30.5314	+	6.48966i	−1.06426	+	0.226215i	−0.357676	+	0.933846i	$0.616431\pi$
$824$	−5.19398	+	8.99623i	−0.180941	+	0.313399i
$825$	4.31931	−	0.795279i	0.150379	−	0.0276881i
$826$	−34.0746	−	6.78151i	−1.18561	−	0.235959i
$827$	−10.5134	+	32.3570i	−0.365587	+	1.12516i	0.584025	+	0.811736i	$0.301477\pi$
$827$	−10.5134	+	32.3570i	−0.365587	+	1.12516i	−0.949612	+	0.313427i	$0.898523\pi$
$828$	0.597542	+	5.68524i	0.0207660	+	0.197576i
$829$	−3.44660	+	32.7922i	−0.119705	+	1.13892i	0.755493	+	0.655157i	$0.227397\pi$
$829$	−3.44660	+	32.7922i	−0.119705	+	1.13892i	−0.875198	+	0.483764i	$0.839269\pi$
$830$	−8.82770	+	9.80416i	−0.306414	+	0.340307i
$831$	−7.49380	−	1.59286i	−0.259957	−	0.0552556i
$832$	−4.18913	−	3.04358i	−0.145232	−	0.105517i
$833$	−32.7314	−	34.5060i	−1.13408	−	1.19556i
$834$	−1.57387	+	4.84388i	−0.0544987	+	0.167730i
$835$	−6.39678	+	11.0795i	−0.221370	+	0.383423i
$836$	11.5390	−	18.7802i	0.399083	−	0.649527i
$837$	4.72419	+	8.18253i	0.163292	+	0.282830i
$838$	10.4165	+	11.5687i	0.359833	+	0.399636i
$839$	35.8087	−	26.0166i	1.23625	−	0.898192i	0.238912	−	0.971041i	$-0.423209\pi$
$839$	35.8087	−	26.0166i	1.23625	−	0.898192i	0.997343	+	0.0728496i	$0.0232093\pi$
$840$	3.44285	+	3.72523i	0.118790	+	0.128532i
$841$	−2.70848	−	8.33585i	−0.0933959	−	0.287443i
$842$	9.77138	+	2.07697i	0.336744	+	0.0715771i
$843$	−0.353560	+	3.36389i	−0.0121772	+	0.115859i
$844$	−20.5454	−	9.14739i	−0.707201	−	0.314866i
$845$	−17.7195	−	19.6795i	−0.609568	−	0.676994i
$846$	−5.86634			−0.201689
$847$	10.1402	−	27.2796i	0.348421	−	0.937338i
$848$	−2.49215			−0.0855808
$849$	8.95543	+	9.94601i	0.307349	+	0.341346i
$850$	−8.21933	−	3.65948i	−0.281921	−	0.125519i
$851$	2.39719	−	22.8077i	0.0821745	−	0.781838i
$852$	−3.89722	−	0.828379i	−0.133517	−	0.0283798i
$853$	−7.97460	−	24.5433i	−0.273045	−	0.840346i	−0.989730	−	0.142949i	$-0.954341\pi$
$853$	−7.97460	−	24.5433i	−0.273045	−	0.840346i	0.716685	−	0.697397i	$-0.245659\pi$
$854$	5.09115	−	16.3902i	0.174215	−	0.560861i
$855$	−10.3082	+	7.48938i	−0.352535	+	0.256131i
$856$	3.60805	+	4.00715i	0.123321	+	0.136961i
$857$	−9.48755	−	16.4329i	−0.324089	−	0.561338i	0.657239	−	0.753682i	$-0.271724\pi$
$857$	−9.48755	−	16.4329i	−0.324089	−	0.561338i	−0.981327	+	0.192344i	$0.938391\pi$
$858$	8.99044	−	14.6324i	0.306929	−	0.499541i
$859$	9.24176	−	16.0072i	0.315325	−	0.546158i	−0.664182	−	0.747571i	$-0.731220\pi$
$859$	9.24176	−	16.0072i	0.315325	−	0.546158i	0.979506	+	0.201413i	$0.0645533\pi$
$860$	0.360849	−	1.11058i	0.0123048	−	0.0378704i
$861$	−4.08871	−	2.89025i	−0.139343	−	0.0984994i
$862$	−4.41253	−	3.20589i	−0.150291	−	0.109193i
$863$	−38.3902	−	8.16009i	−1.30682	−	0.277773i	−0.498690	−	0.866780i	$-0.666185\pi$
$863$	−38.3902	−	8.16009i	−1.30682	−	0.277773i	−0.808127	+	0.589008i	$0.799519\pi$
$864$	−0.669131	+	0.743145i	−0.0227643	+	0.0252823i
$865$	1.42869	−	13.5931i	0.0485770	−	0.462179i
$866$	1.76719	+	16.8137i	0.0600514	+	0.571351i
$867$	9.01200	−	27.7361i	0.306064	−	0.941967i
$868$	−16.4843	+	18.7928i	−0.559514	+	0.637870i
$869$	23.0237	−	4.23917i	0.781027	−	0.143804i
$870$	−4.31220	+	7.46895i	−0.146197	+	0.253221i
$871$	21.8654	−	4.64764i	0.740881	−	0.157479i
$872$	0.893616	+	0.397864i	0.0302617	+	0.0134734i
$873$	−4.39230	+	1.95558i	−0.148657	+	0.0661862i
$874$	−11.7400	−	36.1320i	−0.397112	−	1.22218i
$875$	−3.76728	−	31.8578i	−0.127357	−	1.07699i
$876$	11.8057	+	8.57737i	0.398879	+	0.289803i
$877$	3.88489	+	36.9623i	0.131183	+	1.24813i	0.839942	+	0.542676i	$0.182589\pi$
$877$	3.88489	+	36.9623i	0.131183	+	1.24813i	−0.708759	+	0.705451i	$0.750744\pi$
$878$	−14.3043	+	3.04047i	−0.482746	+	0.102611i
$879$	0.654845	+	1.13422i	0.0220874	+	0.0382565i
$880$	5.24465	−	3.59546i	0.176797	−	0.121203i
$881$	4.53086			0.152649			0.0763243	−	0.997083i	$-0.475682\pi$
$881$	4.53086			0.152649			0.0763243	+	0.997083i	$0.475682\pi$
$882$	6.88252	+	1.27707i	0.231747	+	0.0430011i
$883$	−22.8341	+	16.5899i	−0.768428	+	0.558296i	−0.901484	−	0.432813i	$-0.857521\pi$
$883$	−22.8341	+	16.5899i	−0.768428	+	0.558296i	0.133056	+	0.991109i	$0.457521\pi$
$884$	−32.1400	+	14.3096i	−1.08099	+	0.481286i
$885$	16.8462	−	18.7096i	0.566280	−	0.628917i
$886$	19.5950	−	21.7624i	0.658306	−	0.731122i
$887$	25.3332	−	11.2791i	0.850607	−	0.378715i	0.0653333	−	0.997864i	$-0.479189\pi$
$887$	25.3332	−	11.2791i	0.850607	−	0.378715i	0.785274	+	0.619149i	$0.212522\pi$
$888$	3.24557	−	2.35804i	0.108914	−	0.0791308i
$889$	27.2018	−	48.5606i	0.912320	−	1.62867i
$890$	15.2365			0.510730
$891$	−2.62888	−	2.02213i	−0.0880707	−	0.0677439i
$892$	11.0549	+	19.1476i	0.370144	+	0.641108i
$893$	38.1350	−	8.10584i	1.27614	−	0.271252i
$894$	0.218443	+	2.07835i	0.00730582	+	0.0695103i
$895$	17.8981	+	13.0037i	0.598267	+	0.434666i
$896$	−2.43079	−	1.04464i	−0.0812068	−	0.0348991i
$897$	−9.14709	−	28.1519i	−0.305412	−	0.939963i
$898$	5.56932	−	2.47962i	0.185851	−	0.0827461i
$899$	−38.8276	−	17.2872i	−1.29497	−	0.576559i
$900$	1.29527	−	0.275319i	0.0431758	−	0.00917729i
$901$	−8.46629	+	14.6641i	−0.282053	+	0.488530i
$902$	−4.32598	+	4.54790i	−0.144039	+	0.151428i
$903$	−0.517826	−	1.52598i	−0.0172322	−	0.0507815i
$904$	−5.68500	+	17.4966i	−0.189080	+	0.581929i
$905$	−2.23413	−	21.2563i	−0.0742650	−	0.706584i
$906$	0.857302	−	8.15668i	0.0284819	−	0.270988i
$907$	−20.8745	+	23.1835i	−0.693126	+	0.769794i	−0.982266	−	0.187493i	$-0.939964\pi$
$907$	−20.8745	+	23.1835i	−0.693126	+	0.769794i	0.289140	+	0.957287i	$0.406631\pi$
$908$	−5.58629	−	1.18740i	−0.185388	−	0.0394054i
$909$	−13.9496	−	10.1350i	−0.462679	−	0.336156i
$910$	−21.4482	−	15.1614i	−0.711001	−	0.502596i
$911$	−5.85479	+	18.0192i	−0.193978	+	0.597002i	0.806009	+	0.591903i	$0.201623\pi$
$911$	−5.85479	+	18.0192i	−0.193978	+	0.597002i	−0.999987	+	0.00509937i	$0.998377\pi$
$912$	3.32294	−	5.75549i	0.110033	−	0.190583i
$913$	22.1853	+	5.35385i	0.734228	+	0.177187i
$914$	−3.57951	−	6.19990i	−0.118400	−	0.205074i
$915$	8.32191	+	9.24242i	0.275114	+	0.305545i
$916$	14.8914	−	10.8192i	0.492025	−	0.357477i
$917$	14.1235	−	3.19429i	0.466399	−	0.105485i
$918$	2.09958	+	6.46183i	0.0692963	+	0.213272i
$919$	46.4880	+	9.88133i	1.53350	+	0.325955i	0.895844	−	0.444369i	$-0.146572\pi$
$919$	46.4880	+	9.88133i	1.53350	+	0.325955i	0.637653	+	0.770324i	$0.279905\pi$
$920$	1.14563	−	10.8999i	0.0377703	−	0.359360i
$921$	24.2325	+	10.7890i	0.798488	+	0.355510i
$922$	11.7153	+	13.0111i	0.385821	+	0.428498i
$923$	20.6308			0.679072
$924$	2.83125	−	8.30566i	0.0931414	−	0.273236i
$925$	−5.31239			−0.174670
$926$	−3.18240	−	3.53442i	−0.104580	−	0.116148i
$927$	−9.48987	−	4.22516i	−0.311688	−	0.138773i
$928$	0.470206	−	4.47371i	0.0154353	−	0.146857i
$929$	−32.2827	−	6.86189i	−1.05916	−	0.225131i	−0.354777	−	0.934951i	$-0.615443\pi$
$929$	−32.2827	−	6.86189i	−1.05916	−	0.225131i	−0.704383	+	0.709820i	$0.748776\pi$
$930$	−5.59777	−	17.2282i	−0.183558	−	0.564933i
$931$	−46.5054	+	1.20819i	−1.52415	+	0.0395969i
$932$	−8.19838	+	5.95647i	−0.268547	+	0.195111i
$933$	−3.58294	−	3.97926i	−0.117300	−	0.130275i
$934$	−2.89760	−	5.01880i	−0.0948125	−	0.164220i
$935$	−3.33903	−	43.0745i	−0.109198	−	1.40869i
$936$	2.58903	−	4.48433i	0.0846250	−	0.146575i
$937$	6.53084	−	20.0999i	0.213353	−	0.656634i	−0.785913	−	0.618337i	$-0.787807\pi$
$937$	6.53084	−	20.0999i	0.213353	−	0.656634i	0.999266	−	0.0382968i	$-0.0121932\pi$
$938$	10.3731	−	4.78079i	0.338695	−	0.156098i
$939$	−10.6780	−	7.75805i	−0.348465	−	0.253174i
$940$	11.0014	+	2.33841i	0.358825	+	0.0762707i
$941$	−23.5750	+	26.1827i	−0.768523	+	0.853531i	−0.992649	−	0.121029i	$-0.961381\pi$
$941$	−23.5750	+	26.1827i	−0.768523	+	0.853531i	0.224126	+	0.974560i	$0.428047\pi$
$942$	0.105071	−	0.999688i	0.00342341	−	0.0325716i
$943$	1.13085	+	10.7594i	0.0368257	+	0.350373i
$944$	−4.05788	+	12.4889i	−0.132073	+	0.406478i
$945$	−3.34494	+	3.81338i	−0.108811	+	0.124049i
$946$	−1.98666	+	0.365789i	−0.0645920	+	0.0118928i
$947$	−18.2859	+	31.6721i	−0.594211	+	1.02920i	0.399447	+	0.916756i	$0.369202\pi$
$947$	−18.2859	+	31.6721i	−0.594211	+	1.02920i	−0.993658	+	0.112447i	$0.964131\pi$
$948$	6.90436	−	1.46757i	0.224243	−	0.0476643i
$949$	−69.0291	−	30.7337i	−2.24078	−	0.997659i
$950$	−8.03969	+	3.57950i	−0.260842	+	0.116134i
$951$	3.89890	+	11.9996i	0.126431	+	0.389113i
$952$	−14.4046	+	10.7541i	−0.466856	+	0.348543i
$953$	−8.16558	−	5.93264i	−0.264509	−	0.192177i	0.447623	−	0.894222i	$-0.352271\pi$
$953$	−8.16558	−	5.93264i	−0.264509	−	0.192177i	−0.712133	+	0.702045i	$0.752271\pi$
$954$	−0.260501	−	2.47850i	−0.00843402	−	0.0802443i
$955$	21.3603	−	4.54028i	0.691204	−	0.146920i
$956$	3.23862	+	5.60946i	0.104745	+	0.181423i
$957$	14.9138	+	0.408096i	0.482093	+	0.0131919i
$958$	−4.07746			−0.131737
$959$	46.0261	−	0.597769i	1.48626	−	0.0193030i
$960$	1.55108	−	1.12692i	0.0500607	−	0.0363713i
$961$	53.2339	−	23.7013i	1.71722	−	0.764557i
$962$	−13.8999	+	15.4374i	−0.448150	+	0.497721i
$963$	−3.60805	+	4.00715i	−0.116268	+	0.129129i
$964$	21.4526	−	9.55130i	0.690941	−	0.307627i
$965$	−33.5262	+	24.3582i	−1.07925	+	0.784119i
$966$	−7.73175	−	12.9990i	−0.248765	−	0.418234i
$967$	9.45364			0.304009			0.152004	−	0.988380i	$-0.451427\pi$
$967$	9.45364			0.304009			0.152004	+	0.988380i	$0.451427\pi$
$968$	−9.78929	−	5.01695i	−0.314640	−	0.161251i
$969$	−22.5772	−	39.1049i	−0.725286	−	1.25623i
$970$	9.01657	−	1.91653i	0.289505	−	0.0615361i
$971$	3.82600	+	36.4020i	0.122782	+	1.16820i	0.866316	+	0.499497i	$0.166482\pi$
$971$	3.82600	+	36.4020i	0.122782	+	1.16820i	−0.743533	+	0.668699i	$0.766852\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−1.58246	−	13.3820i	−0.0507315	−	0.429007i
$974$	−5.74256	−	17.6738i	−0.184004	−	0.566305i
$975$	−6.26403	+	2.78893i	−0.200609	+	0.0893171i
$976$	−5.92607	−	2.63846i	−0.189689	−	0.0844550i
$977$	−8.38540	+	1.78237i	−0.268273	+	0.0570231i	−0.340084	−	0.940395i	$-0.610455\pi$
$977$	−8.38540	+	1.78237i	−0.268273	+	0.0570231i	0.0718111	+	0.997418i	$0.477122\pi$
$978$	2.96683	−	5.13869i	0.0948686	−	0.164317i
$979$	−12.5495	−	23.1784i	−0.401085	−	0.740784i
$980$	−12.3980	−	5.13841i	−0.396040	−	0.164141i
$981$	−0.302276	+	0.930309i	−0.00965092	+	0.0297025i
$982$	−1.59736	−	15.1979i	−0.0509738	−	0.484983i
$983$	−4.39030	+	41.7709i	−0.140029	+	1.33229i	0.668448	+	0.743758i	$0.266959\pi$
$983$	−4.39030	+	41.7709i	−0.140029	+	1.33229i	−0.808477	+	0.588527i	$0.799708\pi$
$984$	−1.26634	+	1.40641i	−0.0403693	+	0.0448346i
$985$	26.3847	+	5.60824i	0.840687	+	0.178693i
$986$	−24.7264	−	17.9648i	−0.787448	−	0.572114i
$987$	14.0959	−	6.49651i	0.448676	−	0.206786i
$988$	−10.6341	+	32.7284i	−0.338316	+	1.04123i
$989$	−1.74089	+	3.01531i	−0.0553571	+	0.0958814i
$990$	4.12398	+	4.84009i	0.131069	+	0.153828i
$991$	−22.5545	−	39.0655i	−0.716467	−	1.24096i	−0.962391	−	0.271668i	$-0.912425\pi$
$991$	−22.5545	−	39.0655i	−0.716467	−	1.24096i	0.245924	−	0.969289i	$-0.420909\pi$
$992$	6.32220	+	7.02151i	0.200730	+	0.222933i
$993$	−26.9112	+	19.5521i	−0.854000	+	0.620467i
$994$	10.2817	−	2.32541i	0.326117	−	0.0737574i
$995$	−3.54144	−	10.8994i	−0.112271	−	0.345535i
$996$	6.73079	+	1.43067i	0.213273	+	0.0453326i
$997$	0.105006	−	0.999062i	0.00332556	−	0.0316406i	−0.992733	−	0.120336i	$-0.961603\pi$
$997$	0.105006	−	0.999062i	0.00332556	−	0.0316406i	0.996059	+	0.0886949i	$0.0282696\pi$
$998$	30.0054	+	13.3593i	0.949804	+	0.422880i
$999$	2.68438	+	2.98131i	0.0849301	+	0.0943244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.163.4	✓	40
7.4	even	3	inner	462.2.y.c.361.2	yes	40
11.5	even	5	inner	462.2.y.c.247.2	yes	40
77.60	even	15	inner	462.2.y.c.445.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.163.4	✓	40	1.1	even	1	trivial
462.2.y.c.247.2	yes	40	11.5	even	5	inner
462.2.y.c.361.2	yes	40	7.4	even	3	inner
462.2.y.c.445.4	yes	40	77.60	even	15	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.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 - 0.743145i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.87534 + 0.398616i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(1.79574 + 1.94302i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.669131 - 0.743145i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(1.87534 + 0.398616i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(1.79574 + 1.94302i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.958617 - 1.66037i) q^{10} +(-1.73626 + 2.82585i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.60011 - 4.92462i) q^{13} +(0.242362 - 2.63463i) q^{14} +(1.55108 + 1.12692i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-4.54632 + 5.04920i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.694683 + 6.60946i) q^{19} +(-0.592458 + 1.82340i) q^{20} +(0.850191 + 2.50543i) q^{21} +(3.26180 - 0.600568i) q^{22} +(2.85828 - 4.95068i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-1.20973 - 0.538605i) q^{25} +(-4.73039 + 2.10610i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.12008 + 1.58280i) q^{28} +(-3.63924 - 2.64406i) q^{29} +(-0.200406 - 1.90673i) q^{30} +(9.24191 - 1.96443i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.73553 + 1.87534i) q^{33} +6.79437 q^{34} +(2.59310 + 4.35963i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(3.66491 - 1.63172i) q^{37} +(4.44696 - 4.93884i) q^{38} +(3.46479 - 3.84804i) q^{39} +(1.75148 - 0.779810i) q^{40} +(-1.53107 + 1.11239i) q^{41} +(1.29301 - 2.30827i) q^{42} -0.609071 q^{43} +(-2.62888 - 2.02213i) q^{44} +(0.958617 + 1.66037i) q^{45} +(-5.59163 + 1.18854i) q^{46} +(-0.613200 - 5.83421i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-0.550652 + 6.97831i) q^{49} +(0.409204 + 1.25940i) q^{50} +(-6.20696 + 2.76352i) q^{51} +(4.73039 + 2.10610i) q^{52} +(2.43769 - 0.518147i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-4.38250 + 4.60732i) q^{55} +(2.59486 + 0.516428i) q^{56} +(-2.05369 + 6.32060i) q^{57} +(0.470206 + 4.47371i) q^{58} +(1.37262 - 13.0596i) q^{59} +(-1.28288 + 1.42478i) q^{60} +(6.34514 + 1.34870i) q^{61} +(-7.64390 - 5.55362i) q^{62} +(-0.242362 + 2.63463i) q^{63} +(0.309017 - 0.951057i) q^{64} +(4.96377 - 8.59751i) q^{65} +(3.22407 + 0.778046i) q^{66} +(2.15852 + 3.73867i) q^{67} +(-4.54632 - 5.04920i) q^{68} +(4.62479 - 3.36010i) q^{69} +(1.50471 - 4.84421i) q^{70} +(1.23121 + 3.78928i) q^{71} +(0.978148 + 0.207912i) q^{72} +(1.52535 - 14.5128i) q^{73} +(-3.66491 - 1.63172i) q^{74} +(-0.886070 - 0.984080i) q^{75} -6.64587 q^{76} +(-8.60854 + 1.70089i) q^{77} -5.17805 q^{78} +(-4.72313 - 5.24557i) q^{79} +(-1.75148 - 0.779810i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.85115 + 0.393475i) q^{82} +(-2.12639 - 6.54437i) q^{83} +(-2.58057 + 0.583645i) q^{84} +(-10.5386 + 7.65673i) q^{85} +(0.407548 + 0.452628i) q^{86} +(-2.24918 - 3.89569i) q^{87} +(0.256328 + 3.30670i) q^{88} +(-3.97357 + 6.88242i) q^{89} +(0.592458 - 1.82340i) q^{90} +(12.4420 - 5.73429i) q^{91} +(4.62479 + 3.36010i) q^{92} +(9.24191 + 1.96443i) q^{93} +(-3.92535 + 4.35954i) q^{94} +(-1.33187 + 12.6719i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-1.48574 + 4.57265i) q^{97} +(5.55435 - 4.26018i) q^{98} +(-3.26180 + 0.600568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

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