LMFDB - Embedded newform 153.2.s.a.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.424498 - 0.0558863i) q^{2} +(0.159139 + 1.72472i) q^{3} +(-1.75478 + 0.470191i) q^{4} +(0.651116 + 1.32033i) q^{5} +(0.163943 + 0.723249i) q^{6} +(0.282318 + 0.139224i) q^{7} +(-1.50976 + 0.625364i) q^{8} +(-2.94935 + 0.548943i) q^{9} +O(q^{10})$	\(q+(0.424498 - 0.0558863i) q^{2} +(0.159139 + 1.72472i) q^{3} +(-1.75478 + 0.470191i) q^{4} +(0.651116 + 1.32033i) q^{5} +(0.163943 + 0.723249i) q^{6} +(0.282318 + 0.139224i) q^{7} +(-1.50976 + 0.625364i) q^{8} +(-2.94935 + 0.548943i) q^{9} +(0.350186 + 0.524091i) q^{10} +(1.64668 - 0.558972i) q^{11} +(-1.09020 - 2.95168i) q^{12} +(1.19285 + 4.45178i) q^{13} +(0.127624 + 0.0433227i) q^{14} +(-2.17359 + 1.33311i) q^{15} +(2.54064 - 1.46684i) q^{16} +(0.980810 - 4.00475i) q^{17} +(-1.22132 + 0.397854i) q^{18} +(2.71326 + 1.12387i) q^{19} +(-1.76337 - 2.01074i) q^{20} +(-0.195195 + 0.509078i) q^{21} +(0.667774 - 0.329310i) q^{22} +(2.37437 - 2.70745i) q^{23} +(-1.31884 - 2.50440i) q^{24} +(1.72448 - 2.24739i) q^{25} +(0.755157 + 1.82311i) q^{26} +(-1.41613 - 4.99946i) q^{27} +(-0.560867 - 0.111563i) q^{28} +(0.470444 - 7.17759i) q^{29} +(-0.848184 + 0.687379i) q^{30} +(-2.94918 + 8.68799i) q^{31} +(3.58944 - 2.75428i) q^{32} +(1.22612 + 2.75111i) q^{33} +(0.192542 - 1.75482i) q^{34} +0.463405i q^{35} +(4.91734 - 2.35003i) q^{36} +(0.433080 + 2.17724i) q^{37} +(1.21458 + 0.325446i) q^{38} +(-7.48827 + 2.76579i) q^{39} +(-1.80872 - 1.58620i) q^{40} +(-4.44987 + 0.291660i) q^{41} +(-0.0544096 + 0.227011i) q^{42} +(2.28110 + 1.75035i) q^{43} +(-2.62673 + 1.75512i) q^{44} +(-2.64516 - 3.53670i) q^{45} +(0.856606 - 1.28200i) q^{46} +(-1.24615 + 4.65071i) q^{47} +(2.93420 + 4.14847i) q^{48} +(-4.20101 - 5.47486i) q^{49} +(0.606441 - 1.05039i) q^{50} +(7.06317 + 1.05431i) q^{51} +(-4.18637 - 7.25101i) q^{52} +(4.06143 - 9.80516i) q^{53} +(-0.880547 - 2.04312i) q^{54} +(1.81021 + 1.81021i) q^{55} +(-0.513299 - 0.0336434i) q^{56} +(-1.50658 + 4.85847i) q^{57} +(-0.201426 - 3.07317i) q^{58} +(-0.857092 + 6.51026i) q^{59} +(3.18735 - 3.36132i) q^{60} +(1.69302 - 3.43311i) q^{61} +(-0.766381 + 3.85286i) q^{62} +(-0.909082 - 0.255644i) q^{63} +(-2.77905 + 2.77905i) q^{64} +(-5.10115 + 4.47359i) q^{65} +(0.674237 + 1.09932i) q^{66} +(-4.04083 - 2.33298i) q^{67} +(0.161894 + 7.48860i) q^{68} +(5.04746 + 3.66427i) q^{69} +(0.0258980 + 0.196715i) q^{70} +(-5.89482 + 1.17255i) q^{71} +(4.10953 - 2.67319i) q^{72} +(6.74041 + 4.50380i) q^{73} +(0.305519 + 0.900031i) q^{74} +(4.15055 + 2.61660i) q^{75} +(-5.28959 - 0.696388i) q^{76} +(0.542710 + 0.0714492i) q^{77} +(-3.02419 + 1.59257i) q^{78} +(2.46684 + 7.26708i) q^{79} +(3.59096 + 2.39940i) q^{80} +(8.39732 - 3.23805i) q^{81} +(-1.87266 + 0.372496i) q^{82} +(0.542874 + 4.12354i) q^{83} +(0.103160 - 0.985096i) q^{84} +(5.92622 - 1.31256i) q^{85} +(1.06615 + 0.615539i) q^{86} +(12.4542 - 0.330850i) q^{87} +(-2.13653 + 1.87369i) q^{88} +(2.40264 - 2.40264i) q^{89} +(-1.32052 - 1.35350i) q^{90} +(-0.283031 + 1.42289i) q^{91} +(-2.89347 + 5.86737i) q^{92} +(-15.4537 - 3.70391i) q^{93} +(-0.269080 + 2.04386i) q^{94} +(0.282766 + 4.31417i) q^{95} +(5.32159 + 5.75249i) q^{96} +(-18.6989 - 1.22559i) q^{97} +(-2.08929 - 2.08929i) q^{98} +(-4.54979 + 2.55254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.424498	−	0.0558863i	0.300166	−	0.0395176i	0.0210609	−	0.999778i	$-0.493296\pi$
$2$	0.424498	−	0.0558863i	0.300166	−	0.0395176i	0.279105	+	0.960261i	$0.409962\pi$
$3$	0.159139	+	1.72472i	0.0918791	+	0.995770i
$3$	0.159139	+	1.72472i	0.0918791	+	0.995770i
$4$	−1.75478	+	0.470191i	−0.877388	+	0.235095i
$5$	0.651116	+	1.32033i	0.291188	+	0.590471i	0.992481	−	0.122403i	$-0.0390599\pi$
$5$	0.651116	+	1.32033i	0.291188	+	0.590471i	−0.701292	+	0.712874i	$0.747393\pi$
$6$	0.163943	+	0.723249i	0.0669294	+	0.295265i
$7$	0.282318	+	0.139224i	0.106706	+	0.0526217i	0.494859	−	0.868974i	$-0.335220\pi$
$7$	0.282318	+	0.139224i	0.106706	+	0.0526217i	−0.388152	+	0.921595i	$0.626887\pi$
$8$	−1.50976	+	0.625364i	−0.533781	+	0.221099i
$9$	−2.94935	+	0.548943i	−0.983116	+	0.182981i
$10$	0.350186	+	0.524091i	0.110739	+	0.165732i
$11$	1.64668	−	0.558972i	0.496492	−	0.168536i	−0.0619508	−	0.998079i	$-0.519732\pi$
$11$	1.64668	−	0.558972i	0.496492	−	0.168536i	0.558443	+	0.829543i	$0.311399\pi$
$12$	−1.09020	−	2.95168i	−0.314715	−	0.852076i
$13$	1.19285	+	4.45178i	0.330837	+	1.23470i	0.908312	+	0.418294i	$0.137372\pi$
$13$	1.19285	+	4.45178i	0.330837	+	1.23470i	−0.577474	+	0.816409i	$0.695962\pi$
$14$	0.127624	+	0.0433227i	0.0341091	+	0.0115785i
$15$	−2.17359	+	1.33311i	−0.561219	+	0.344208i
$16$	2.54064	−	1.46684i	0.635159	−	0.366709i
$17$	0.980810	−	4.00475i	0.237881	−	0.971294i
$17$	0.980810	−	4.00475i	0.237881	−	0.971294i
$18$	−1.22132	+	0.397854i	−0.287867	+	0.0937750i
$19$	2.71326	+	1.12387i	0.622464	+	0.257833i	0.671547	−	0.740962i	$-0.265630\pi$
$19$	2.71326	+	1.12387i	0.622464	+	0.257833i	−0.0490835	+	0.998795i	$0.515630\pi$
$20$	−1.76337	−	2.01074i	−0.394302	−	0.449615i
$21$	−0.195195	+	0.509078i	−0.0425951	+	0.111090i
$22$	0.667774	−	0.329310i	0.142370	−	0.0702091i
$23$	2.37437	−	2.70745i	0.495090	−	0.564542i	−0.449295	−	0.893383i	$-0.648325\pi$
$23$	2.37437	−	2.70745i	0.495090	−	0.564542i	0.944385	+	0.328842i	$0.106658\pi$
$24$	−1.31884	−	2.50440i	−0.269208	−	0.511209i
$25$	1.72448	−	2.24739i	0.344896	−	0.449477i
$26$	0.755157	+	1.82311i	0.148099	+	0.357541i
$27$	−1.41613	−	4.99946i	−0.272535	−	0.962146i
$28$	−0.560867	−	0.111563i	−0.105994	−	0.0210835i
$29$	0.470444	−	7.17759i	0.0873593	−	1.33285i	−0.699020	−	0.715102i	$-0.746380\pi$
$29$	0.470444	−	7.17759i	0.0873593	−	1.33285i	0.786379	−	0.617744i	$-0.211953\pi$
$30$	−0.848184	+	0.687379i	−0.154857	+	0.125498i
$31$	−2.94918	+	8.68799i	−0.529688	+	1.56041i	0.271773	+	0.962361i	$0.412390\pi$
$31$	−2.94918	+	8.68799i	−0.529688	+	1.56041i	−0.801460	+	0.598048i	$0.795943\pi$
$32$	3.58944	−	2.75428i	0.634530	−	0.486892i
$33$	1.22612	+	2.75111i	0.213441	+	0.478907i
$34$	0.192542	−	1.75482i	0.0330206	−	0.300950i
$35$			0.463405i			0.0783298i
$36$	4.91734	−	2.35003i	0.819557	−	0.391671i
$37$	0.433080	+	2.17724i	0.0711978	+	0.357936i	0.999917	−	0.0128470i	$-0.00408945\pi$
$37$	0.433080	+	2.17724i	0.0711978	+	0.357936i	−0.928720	+	0.370783i	$0.879089\pi$
$38$	1.21458	+	0.325446i	0.197031	+	0.0527944i
$39$	−7.48827	+	2.76579i	−1.19908	+	0.442881i
$40$	−1.80872	−	1.58620i	−0.285984	−	0.250801i
$41$	−4.44987	+	0.291660i	−0.694953	+	0.0455496i	−0.408786	−	0.912630i	$-0.634048\pi$
$41$	−4.44987	+	0.291660i	−0.694953	+	0.0455496i	−0.286167	+	0.958180i	$0.592381\pi$
$42$	−0.0544096	+	0.227011i	−0.00839558	+	0.0350286i
$43$	2.28110	+	1.75035i	0.347865	+	0.266926i	0.767884	−	0.640589i	$-0.221310\pi$
$43$	2.28110	+	1.75035i	0.347865	+	0.266926i	−0.420019	+	0.907515i	$0.637977\pi$
$44$	−2.62673	+	1.75512i	−0.395994	+	0.264595i
$45$	−2.64516	−	3.53670i	−0.394317	−	0.527220i
$46$	0.856606	−	1.28200i	0.126300	−	0.189021i
$47$	−1.24615	+	4.65071i	−0.181770	+	0.678376i	0.813528	+	0.581525i	$0.197544\pi$
$47$	−1.24615	+	4.65071i	−0.181770	+	0.678376i	−0.995299	+	0.0968512i	$0.969123\pi$
$48$	2.93420	+	4.14847i	0.423516	+	0.598779i
$49$	−4.20101	−	5.47486i	−0.600144	−	0.782123i
$50$	0.606441	−	1.05039i	0.0857637	−	0.148547i
$51$	7.06317	+	1.05431i	0.989042	+	0.147634i
$52$	−4.18637	−	7.25101i	−0.580546	−	1.00553i
$53$	4.06143	−	9.80516i	0.557881	−	1.34684i	−0.353560	−	0.935412i	$-0.615029\pi$
$53$	4.06143	−	9.80516i	0.557881	−	1.34684i	0.911441	−	0.411431i	$-0.134971\pi$
$54$	−0.880547	−	2.04312i	−0.119827	−	0.278033i
$55$	1.81021	+	1.81021i	0.244089	+	0.244089i
$56$	−0.513299	−	0.0336434i	−0.0685925	−	0.00449579i
$57$	−1.50658	+	4.85847i	−0.199551	+	0.643520i
$58$	−0.201426	−	3.07317i	−0.0264485	−	0.403527i
$59$	−0.857092	+	6.51026i	−0.111584	+	0.847564i	0.840518	+	0.541783i	$0.182251\pi$
$59$	−0.857092	+	6.51026i	−0.111584	+	0.847564i	−0.952102	+	0.305780i	$0.901083\pi$
$60$	3.18735	−	3.36132i	0.411485	−	0.433944i
$61$	1.69302	−	3.43311i	0.216769	−	0.439565i	−0.761142	−	0.648585i	$-0.775361\pi$
$61$	1.69302	−	3.43311i	0.216769	−	0.439565i	0.977911	+	0.209021i	$0.0670276\pi$
$62$	−0.766381	+	3.85286i	−0.0973305	+	0.489313i
$63$	−0.909082	−	0.255644i	−0.114534	−	0.0322081i
$64$	−2.77905	+	2.77905i	−0.347382	+	0.347382i
$65$	−5.10115	+	4.47359i	−0.632720	+	0.554881i
$66$	0.674237	+	1.09932i	0.0829929	+	0.135317i
$67$	−4.04083	−	2.33298i	−0.493666	−	0.285018i	0.232428	−	0.972614i	$-0.425333\pi$
$67$	−4.04083	−	2.33298i	−0.493666	−	0.285018i	−0.726094	+	0.687595i	$0.758666\pi$
$68$	0.161894	+	7.48860i	0.0196326	+	0.908127i
$69$	5.04746	+	3.66427i	0.607642	+	0.441126i
$70$	0.0258980	+	0.196715i	0.00309540	+	0.0235119i
$71$	−5.89482	+	1.17255i	−0.699586	+	0.139156i	−0.532054	−	0.846710i	$-0.678580\pi$
$71$	−5.89482	+	1.17255i	−0.699586	+	0.139156i	−0.167532	+	0.985867i	$0.553580\pi$
$72$	4.10953	−	2.67319i	0.484312	−	0.315038i
$73$	6.74041	+	4.50380i	0.788905	+	0.527130i	0.883525	−	0.468384i	$-0.155164\pi$
$73$	6.74041	+	4.50380i	0.788905	+	0.527130i	−0.0946199	+	0.995513i	$0.530164\pi$
$74$	0.305519	+	0.900031i	0.0355159	+	0.104626i
$75$	4.15055	+	2.61660i	0.479265	+	0.302139i
$76$	−5.28959	−	0.696388i	−0.606758	−	0.0798812i
$77$	0.542710	+	0.0714492i	0.0618476	+	0.00814239i
$78$	−3.02419	+	1.59257i	−0.342422	+	0.180323i
$79$	2.46684	+	7.26708i	0.277541	+	0.817610i	0.992911	+	0.118864i	$0.0379252\pi$
$79$	2.46684	+	7.26708i	0.277541	+	0.817610i	−0.715369	+	0.698747i	$0.753742\pi$
$80$	3.59096	+	2.39940i	0.401482	+	0.268262i
$81$	8.39732	−	3.23805i	0.933036	−	0.359783i
$82$	−1.87266	+	0.372496i	−0.206801	+	0.0411353i
$83$	0.542874	+	4.12354i	0.0595882	+	0.452617i	0.995065	+	0.0992282i	$0.0316374\pi$
$83$	0.542874	+	4.12354i	0.0595882	+	0.452617i	−0.935477	+	0.353389i	$0.885029\pi$
$84$	0.103160	−	0.985096i	0.0112557	−	0.107483i
$85$	5.92622	−	1.31256i	0.642789	−	0.142367i
$86$	1.06615	+	0.615539i	0.114965	+	0.0663753i
$87$	12.4542	−	0.330850i	1.33523	−	0.0354709i
$88$	−2.13653	+	1.87369i	−0.227755	+	0.199736i
$89$	2.40264	−	2.40264i	0.254680	−	0.254680i	−0.568206	−	0.822886i	$-0.692363\pi$
$89$	2.40264	−	2.40264i	0.254680	−	0.254680i	0.822886	+	0.568206i	$0.192363\pi$
$90$	−1.32052	−	1.35350i	−0.139195	−	0.142671i
$91$	−0.283031	+	1.42289i	−0.0296697	+	0.149160i
$92$	−2.89347	+	5.86737i	−0.301665	+	0.611716i
$93$	−15.4537	−	3.70391i	−1.60248	−	0.384078i
$94$	−0.269080	+	2.04386i	−0.0277535	+	0.210808i
$95$	0.282766	+	4.31417i	0.0290112	+	0.442625i
$96$	5.32159	+	5.75249i	0.543133	+	0.587111i
$97$	−18.6989	−	1.22559i	−1.89858	−	0.124440i	−0.929137	−	0.369736i	$-0.879448\pi$
$97$	−18.6989	−	1.22559i	−1.89858	−	0.124440i	−0.969448	+	0.245296i	$0.921115\pi$
$98$	−2.08929	−	2.08929i	−0.211050	−	0.211050i
$99$	−4.54979	+	2.55254i	−0.457271	+	0.256540i
$100$	−1.96938	+	4.75449i	−0.196938	+	0.475449i
$101$	1.81085	+	3.13649i	0.180187	+	0.312092i	0.941944	−	0.335770i	$-0.108996\pi$
$101$	1.81085	+	3.13649i	0.180187	+	0.312092i	−0.761757	+	0.647862i	$0.775663\pi$
$102$	3.05723	+	0.0528202i	0.302711	+	0.00522998i
$103$	6.75574	−	11.7013i	0.665663	−	1.15296i	−0.313442	−	0.949607i	$-0.601482\pi$
$103$	6.75574	−	11.7013i	0.665663	−	1.15296i	0.979105	−	0.203355i	$-0.0651844\pi$
$104$	−4.58490	−	5.97516i	−0.449587	−	0.585913i
$105$	−0.799247	+	0.0737460i	−0.0779985	+	0.00719687i
$106$	1.17610	−	4.38926i	0.114233	−	0.426322i
$107$	−2.01958	+	3.02251i	−0.195240	+	0.292197i	−0.916153	−	0.400828i	$-0.868723\pi$
$107$	−2.01958	+	3.02251i	−0.195240	+	0.292197i	0.720913	+	0.693025i	$0.243723\pi$
$108$	4.83569	+	8.10707i	0.465315	+	0.780104i
$109$	6.81952	−	4.55666i	0.653192	−	0.436449i	−0.184321	−	0.982866i	$-0.559009\pi$
$109$	6.81952	−	4.55666i	0.653192	−	0.436449i	0.837513	+	0.546417i	$0.184009\pi$
$110$	0.869597	+	0.667265i	0.0829128	+	0.0636212i
$111$	−3.68622	+	1.09343i	−0.349880	+	0.103784i
$112$	0.921487	−	0.0603975i	0.0870724	−	0.00570702i
$113$	−14.1582	−	12.4164i	−1.33189	−	1.16804i	−0.971983	−	0.235052i	$-0.924474\pi$
$113$	−14.1582	−	12.4164i	−1.33189	−	1.16804i	−0.359910	−	0.932987i	$-0.617193\pi$
$114$	−0.368017	+	2.14661i	−0.0344680	+	0.201049i
$115$	5.12072	+	1.37209i	0.477510	+	0.127948i
$116$	2.54931	+	12.8163i	0.236698	+	1.18996i
$117$	−5.96191	−	12.4751i	−0.551179	−	1.15332i
$118$			2.81149i			0.258819i
$119$	0.834458	−	0.994062i	0.0764946	−	0.0911255i
$120$	2.44793	−	3.37197i	0.223464	−	0.307817i
$121$	−6.32778	+	4.85548i	−0.575253	+	0.441407i
$122$	0.526822	−	1.55197i	0.0476962	−	0.140508i
$123$	−1.21118	−	7.62839i	−0.109209	−	0.687829i
$124$	1.09013	−	16.6322i	0.0978965	−	1.49361i
$125$	11.3095	+	2.24959i	1.01155	+	0.201210i
$126$	−0.400191	−	0.0577151i	−0.0356518	−	0.00514167i
$127$	−6.18204	−	14.9248i	−0.548568	−	1.32436i	−0.918544	−	0.395318i	$-0.870634\pi$
$127$	−6.18204	−	14.9248i	−0.548568	−	1.32436i	0.369977	−	0.929041i	$-0.379366\pi$
$128$	−6.53295	+	8.51390i	−0.577436	+	0.752530i
$129$	−2.65586	+	4.21282i	−0.233836	+	0.370919i
$130$	−1.91542	+	2.18412i	−0.167993	+	0.191560i
$131$	6.46251	−	3.18696i	0.564632	−	0.278446i	−0.137489	−	0.990503i	$-0.543903\pi$
$131$	6.46251	−	3.18696i	0.564632	−	0.278446i	0.702121	+	0.712058i	$0.252237\pi$
$132$	−3.44512	−	4.25108i	−0.299859	−	0.370009i
$133$	0.609533	+	0.695039i	0.0528532	+	0.0602675i
$134$	−1.84571	−	0.764518i	−0.159445	−	0.0660443i
$135$	5.67888	−	5.12500i	0.488760	−	0.441089i
$136$	1.02364	+	6.65958i	0.0877760	+	0.571054i
$137$	16.9099	−	9.76295i	1.44471	−	0.834105i	0.446553	−	0.894757i	$-0.352651\pi$
$137$	16.9099	−	9.76295i	1.44471	−	0.834105i	0.998159	+	0.0606525i	$0.0193182\pi$
$138$	2.34742	+	1.27339i	0.199826	+	0.108398i
$139$	−9.93763	−	3.37337i	−0.842899	−	0.286126i	−0.133602	−	0.991035i	$-0.542654\pi$
$139$	−9.93763	−	3.37337i	−0.842899	−	0.286126i	−0.709297	+	0.704909i	$0.750988\pi$
$140$	−0.217889	−	0.813173i	−0.0184150	−	0.0687256i
$141$	−8.21951	−	1.40916i	−0.692208	−	0.118673i
$142$	−2.43681	+	0.827186i	−0.204493	+	0.0694159i
$143$	4.45267	+	6.66389i	0.372351	+	0.557262i
$144$	−6.68801	+	5.72088i	−0.557334	+	0.476740i
$145$	9.78313	−	4.05231i	0.812445	−	0.336526i
$146$	3.11299	+	1.53516i	0.257633	+	0.127051i
$147$	8.77408	−	8.11685i	0.723674	−	0.669467i
$148$	−1.78367	−	3.61693i	−0.146617	−	0.297310i
$149$	−2.83710	+	0.760197i	−0.232424	+	0.0622778i	−0.373151	−	0.927771i	$-0.621723\pi$
$149$	−2.83710	+	0.760197i	−0.232424	+	0.0622778i	0.140727	+	0.990048i	$0.455056\pi$
$150$	1.90814	+	0.878786i	0.155799	+	0.0717526i
$151$	3.90142	−	0.513632i	0.317493	−	0.0417988i	0.0299044	−	0.999553i	$-0.490480\pi$
$151$	3.90142	−	0.513632i	0.317493	−	0.0417988i	0.287589	+	0.957754i	$0.407146\pi$
$152$	−4.79920			−0.389266
$153$	−0.694373	+	12.3498i	−0.0561367	+	0.998423i
$154$	0.234373			0.0188863
$155$	−13.3913	+	1.76300i	−1.07562	+	0.141607i
$156$	11.8398	−	8.37426i	0.947941	−	0.670478i
$157$	5.62181	−	1.50636i	0.448669	−	0.120221i	−0.0274075	−	0.999624i	$-0.508725\pi$
$157$	5.62181	−	1.50636i	0.448669	−	0.120221i	0.476077	+	0.879404i	$0.342059\pi$
$158$	1.45330	+	2.94700i	0.115618	+	0.234451i
$159$	17.5575	+	5.44446i	1.39240	+	0.431774i
$160$	5.97371	+	2.94591i	0.472263	+	0.232894i
$161$	1.04727	−	0.433793i	0.0825364	−	0.0341877i
$162$	3.38369	−	1.84384i	0.265848	−	0.144866i
$163$	−4.31689	−	6.46068i	−0.338125	−	0.506039i	0.622975	−	0.782242i	$-0.285924\pi$
$163$	−4.31689	−	6.46068i	−0.338125	−	0.506039i	−0.961099	+	0.276203i	$0.910924\pi$
$164$	7.67139	−	2.60409i	0.599035	−	0.203345i
$165$	−2.83404	+	3.41019i	−0.220629	+	0.265483i
$166$	0.460898	+	1.72010i	0.0357727	+	0.133505i
$167$	−2.85280	−	0.968395i	−0.220756	−	0.0749367i	0.208870	−	0.977943i	$-0.433021\pi$
$167$	−2.85280	−	0.968395i	−0.220756	−	0.0749367i	−0.429626	+	0.903007i	$0.641355\pi$
$168$	−0.0236605	−	0.890654i	−0.00182544	−	0.0687154i
$169$	−7.13714	+	4.12063i	−0.549011	+	0.316972i
$170$	2.44232	−	0.888375i	0.187317	−	0.0681352i
$171$	−8.61928	−	1.82526i	−0.659133	−	0.139581i
$172$	−4.82582	−	1.99892i	−0.367966	−	0.152416i
$173$	−16.4031	−	18.7041i	−1.24710	−	1.42205i	−0.867903	−	0.496733i	$-0.834533\pi$
$173$	−16.4031	−	18.7041i	−1.24710	−	1.42205i	−0.379199	−	0.925315i	$-0.623801\pi$
$174$	5.26832	−	0.836467i	0.399390	−	0.0634124i
$175$	0.799742	−	0.394389i	0.0604548	−	0.0298130i
$176$	3.36369	−	3.83555i	0.253548	−	0.289116i
$177$	−11.3648	−	0.442209i	−0.854231	−	0.0332385i
$178$	0.885643	−	1.15419i	0.0663818	−	0.0865104i
$179$	−5.98135	−	14.4403i	−0.447067	−	1.07932i	−0.973415	−	0.229047i	$-0.926439\pi$
$179$	−5.98135	−	14.4403i	−0.447067	−	1.07932i	0.526348	−	0.850269i	$-0.323561\pi$
$180$	6.30458	+	4.96239i	0.469916	+	0.369874i
$181$	−0.871620	−	0.173376i	−0.0647870	−	0.0128869i	0.162590	−	0.986694i	$-0.448015\pi$
$181$	−0.871620	−	0.173376i	−0.0647870	−	0.0128869i	−0.227377	+	0.973807i	$0.573015\pi$
$182$	−0.0406261	+	0.619834i	−0.00301140	+	0.0459451i
$183$	6.19060	+	2.37365i	0.457622	+	0.175466i
$184$	−1.89159	+	5.57244i	−0.139450	+	0.410806i
$185$	−2.59269	+	1.98944i	−0.190619	+	0.146267i
$186$	−6.76708	−	0.708655i	−0.496186	−	0.0519611i
$187$	−0.623464	−	7.14278i	−0.0455922	−	0.522332i
$188$		−	8.74689i		−	0.637933i
$189$	0.296244	−	1.60860i	0.0215486	−	0.117008i
$190$	0.361137	+	1.81556i	0.0261996	+	0.131714i
$191$	20.5887	+	5.51673i	1.48975	+	0.399177i	0.909652	−	0.415372i	$-0.136349\pi$
$191$	20.5887	+	5.51673i	1.48975	+	0.399177i	0.580096	+	0.814548i	$0.303015\pi$
$192$	−5.23536	−	4.35085i	−0.377830	−	0.313995i
$193$	5.51459	+	4.83617i	0.396949	+	0.348115i	0.834431	−	0.551112i	$-0.185796\pi$
$193$	5.51459	+	4.83617i	0.396949	+	0.348115i	−0.437482	+	0.899227i	$0.644130\pi$
$194$	−8.00615	+	0.524750i	−0.574808	+	0.0376749i
$195$	−8.52750	−	8.08616i	−0.610667	−	0.579062i
$196$	9.94606	+	7.63188i	0.710433	+	0.545134i
$197$	−17.8237	+	11.9094i	−1.26988	+	0.848509i	−0.993643	−	0.112579i	$-0.964089\pi$
$197$	−17.8237	+	11.9094i	−1.26988	+	0.848509i	−0.276241	+	0.961088i	$0.589089\pi$
$198$	−1.78873	+	1.33782i	−0.127119	+	0.0950747i
$199$	−1.58466	+	2.37161i	−0.112333	+	0.168119i	−0.883376	−	0.468664i	$-0.844735\pi$
$199$	−1.58466	+	2.37161i	−0.112333	+	0.168119i	0.771043	+	0.636783i	$0.219735\pi$
$200$	−1.19812	+	4.47144i	−0.0847199	+	0.316179i
$201$	3.38069	−	7.34059i	0.238455	−	0.517766i
$202$	0.943991	+	1.23023i	0.0664190	+	0.0865589i
$203$	1.13211	−	1.96087i	0.0794585	−	0.137626i
$204$	−12.8900	+	1.47095i	−0.902482	+	0.102987i
$205$	−3.28247	−	5.68541i	−0.229258	−	0.397086i
$206$	2.21386	−	5.34473i	0.154247	−	0.372385i
$207$	−5.51661	+	9.28860i	−0.383431	+	0.645602i
$208$	9.56064	+	9.56064i	0.662911	+	0.662911i
$209$	5.09607	+	0.334014i	0.352503	+	0.0231043i
$210$	−0.335158	+	0.0759720i	−0.0231281	+	0.00524257i
$211$	1.46224	+	22.3095i	0.100665	+	1.53585i	0.687525	+	0.726160i	$0.258697\pi$
$211$	1.46224	+	22.3095i	0.100665	+	1.53585i	−0.586861	+	0.809688i	$0.699636\pi$
$212$	−2.51661	+	19.1155i	−0.172841	+	1.31286i
$213$	−2.96043	−	9.98034i	−0.202845	−	0.683842i
$214$	−0.688391	+	1.39592i	−0.0470575	+	0.0954231i
$215$	−0.825785	+	4.15150i	−0.0563180	+	0.283130i
$216$	5.26450	+	6.66239i	0.358204	+	0.453318i
$217$	−2.04218	+	2.04218i	−0.138632	+	0.138632i
$218$	2.64022	−	2.31541i	0.178818	−	0.156820i
$219$	−6.69515	+	12.3421i	−0.452416	+	0.834000i
$220$	−4.02766	−	2.32537i	−0.271545	−	0.156776i
$221$	18.9982	−	0.410718i	1.27796	−	0.0276279i
$222$	−1.50369	+	0.670167i	−0.100921	+	0.0449787i
$223$	2.68845	+	20.4208i	0.180032	+	1.36748i	0.807973	+	0.589220i	$0.200565\pi$
$223$	2.68845	+	20.4208i	0.180032	+	1.36748i	−0.627941	+	0.778261i	$0.716102\pi$
$224$	1.39683	−	0.277846i	0.0933295	−	0.0185644i
$225$	−3.85241	+	7.57497i	−0.256827	+	0.504998i
$226$	−6.70405	−	4.47950i	−0.445947	−	0.297972i
$227$	−4.12043	−	12.1384i	−0.273482	−	0.805653i	−0.993717	−	0.111922i	$-0.964299\pi$
$227$	−4.12043	−	12.1384i	−0.273482	−	0.805653i	0.720235	−	0.693730i	$-0.244034\pi$
$228$	0.359295	−	9.23391i	0.0237949	−	0.611531i
$229$	27.2041	+	3.58149i	1.79770	+	0.236672i	0.953929	−	0.300033i	$-0.0969978\pi$
$229$	27.2041	+	3.58149i	1.79770	+	0.236672i	0.843770	+	0.536705i	$0.180331\pi$
$230$	2.25042	+	0.296273i	0.148388	+	0.0195357i
$231$	−0.0368636	+	0.947396i	−0.00242545	+	0.0623341i
$232$	3.77835	+	11.1307i	0.248061	+	0.730763i
$233$	−7.36408	−	4.92052i	−0.482437	−	0.322354i	0.290458	−	0.956888i	$-0.406192\pi$
$233$	−7.36408	−	4.92052i	−0.482437	−	0.322354i	−0.772895	+	0.634533i	$0.781192\pi$
$234$	−3.22801	−	4.96245i	−0.211021	−	0.324406i
$235$	−6.95188	+	1.38282i	−0.453491	+	0.0902049i
$236$	−1.55706	−	11.8270i	−0.101356	−	0.769875i
$237$	−12.1411	+	5.41110i	−0.788652	+	0.351489i
$238$	0.298672	−	0.468613i	0.0193600	−	0.0303756i
$239$	17.0123	+	9.82203i	1.10043	+	0.635334i	0.936334	−	0.351110i	$-0.114196\pi$
$239$	17.0123	+	9.82203i	1.10043	+	0.635334i	0.164097	+	0.986444i	$0.447529\pi$
$240$	−3.56685	+	6.57526i	−0.230239	+	0.424431i
$241$	−13.7982	+	12.1007i	−0.888822	+	0.779476i	−0.976239	−	0.216696i	$-0.930472\pi$
$241$	−13.7982	+	12.1007i	−0.888822	+	0.779476i	0.0874174	+	0.996172i	$0.472139\pi$
$242$	−2.41478	+	2.41478i	−0.155228	+	0.155228i
$243$	6.92109	+	13.9678i	0.443988	+	0.896033i
$244$	−1.35666	+	6.82038i	−0.0868512	+	0.436630i
$245$	4.49330	−	9.11151i	0.287066	−	0.582113i
$246$	−0.940467	−	3.17055i	−0.0599620	−	0.202147i
$247$	−1.76670	+	13.4194i	−0.112413	+	0.853858i
$248$	−0.980603	−	14.9611i	−0.0622683	−	0.950031i
$249$	−7.02557	+	1.59252i	−0.445228	+	0.100922i
$250$	4.92657	+	0.322904i	0.311584	+	0.0204223i
$251$	8.88797	+	8.88797i	0.561004	+	0.561004i	0.929593	−	0.368589i	$-0.120159\pi$
$251$	8.88797	+	8.88797i	0.561004	+	0.561004i	−0.368589	+	0.929593i	$0.620159\pi$
$252$	1.71544	+	0.0211555i	0.108062	+	0.00133267i
$253$	2.39643	−	5.78550i	0.150663	−	0.363731i
$254$	−3.45836	−	5.99005i	−0.216997	−	0.375849i
$255$	3.20690	+	10.0122i	0.200824	+	0.626990i
$256$	1.63276	−	2.82802i	0.102048	−	0.176751i
$257$	3.18159	+	4.14632i	0.198462	+	0.258641i	0.881973	−	0.471299i	$-0.156215\pi$
$257$	3.18159	+	4.14632i	0.198462	+	0.258641i	−0.683512	+	0.729940i	$0.739548\pi$
$258$	−0.891970	+	1.93676i	−0.0555316	+	0.120578i
$259$	−0.180858	+	0.674969i	−0.0112379	+	0.0419406i
$260$	6.84794	−	10.2487i	0.424691	−	0.635595i
$261$	2.55258	+	21.4275i	0.158001	+	1.32633i
$262$	2.56522	−	1.71402i	0.158480	−	0.105893i
$263$	8.15412	+	6.25688i	0.502805	+	0.385816i	0.828791	−	0.559559i	$-0.189029\pi$
$263$	8.15412	+	6.25688i	0.502805	+	0.385816i	−0.325986	+	0.945375i	$0.605696\pi$
$264$	−3.57160	−	3.38675i	−0.219817	−	0.208440i
$265$	15.5905	−	1.02186i	0.957720	−	0.0627723i
$266$	0.297589	+	0.260979i	0.0182464	+	0.0160016i
$267$	4.52625	+	3.76154i	0.277002	+	0.230203i
$268$	8.18770	+	2.19389i	0.500144	+	0.134013i
$269$	−2.69186	−	13.5329i	−0.164126	−	0.825116i	−0.971858	−	0.235567i	$-0.924305\pi$
$269$	−2.69186	−	13.5329i	−0.164126	−	0.825116i	0.807733	−	0.589549i	$-0.200695\pi$
$270$	2.12426	−	2.49292i	0.129278	−	0.151715i
$271$		−	9.45664i		−	0.574450i	−0.957863	−	0.287225i	$-0.907267\pi$
$271$		−	9.45664i		−	0.574450i	0.957863	−	0.287225i	$-0.0927327\pi$
$272$	−3.38243	−	11.6133i	−0.205090	−	0.704160i
$273$	−2.49914	−	0.261713i	−0.151255	−	0.0158396i
$274$	6.63262	−	5.08939i	0.400691	−	0.307461i
$275$	1.58344	−	4.66466i	0.0954849	−	0.281290i
$276$	−10.5801	−	4.05670i	−0.636845	−	0.244185i
$277$	−0.580947	+	8.86353i	−0.0349057	+	0.532558i	0.944222	+	0.329310i	$0.106816\pi$
$277$	−0.580947	+	8.86353i	−0.0349057	+	0.532558i	−0.979127	+	0.203248i	$0.934850\pi$
$278$	−4.40703	−	0.876614i	−0.264316	−	0.0525758i
$279$	3.92894	−	27.2429i	0.235219	−	1.63099i
$280$	−0.289797	−	0.699632i	−0.0173187	−	0.0418110i
$281$	−18.3180	+	23.8725i	−1.09276	+	1.42411i	−0.196543	+	0.980495i	$0.562972\pi$
$281$	−18.3180	+	23.8725i	−1.09276	+	1.42411i	−0.896217	+	0.443617i	$0.853695\pi$
$282$	−3.56792	−	0.138829i	−0.212467	−	0.00826717i
$283$	9.37146	−	10.6861i	0.557075	−	0.635223i	−0.402921	−	0.915235i	$-0.632005\pi$
$283$	9.37146	−	10.6861i	0.557075	−	0.635223i	0.959997	+	0.280012i	$0.0903384\pi$
$284$	9.79276	−	4.82926i	0.581094	−	0.286564i
$285$	−7.39576	+	1.17425i	−0.438087	+	0.0695564i
$286$	2.26257	+	2.57997i	0.133789	+	0.152557i
$287$	−1.29689	−	0.537188i	−0.0765528	−	0.0317092i
$288$	−9.07458	+	10.0937i	−0.534725	+	0.594778i
$289$	−15.0760	−	7.85579i	−0.886825	−	0.462106i
$290$	3.92646	−	2.26694i	0.230569	−	0.133119i
$291$	−0.861923	−	32.4455i	−0.0505268	−	1.90199i
$292$	−13.9456	−	4.73388i	−0.816102	−	0.277029i
$293$	−8.12175	−	30.3108i	−0.474478	−	1.77078i	−0.623375	−	0.781923i	$-0.714239\pi$
$293$	−8.12175	−	30.3108i	−0.474478	−	1.77078i	0.148897	−	0.988853i	$-0.452428\pi$
$294$	3.27096	−	3.93594i	0.190767	−	0.229549i
$295$	−9.15378	+	3.10729i	−0.532954	+	0.180913i
$296$	−2.01541	−	3.01628i	−0.117143	−	0.175318i
$297$	−5.12647	−	7.44092i	−0.297468	−	0.431766i
$298$	−1.16186	+	0.481257i	−0.0673046	+	0.0278785i
$299$	14.8852	+	7.34059i	0.860835	+	0.424517i
$300$	−8.51359	−	2.64000i	−0.491533	−	0.152421i
$301$	0.400306	+	0.811741i	0.0230733	+	0.0467880i
$302$	1.62744	−	0.436072i	0.0936488	−	0.0250931i
$303$	−5.12140	+	3.62236i	−0.294217	+	0.208099i
$304$	8.54193	−	1.12457i	0.489913	−	0.0644983i
$305$	5.63520			0.322671
$306$	0.395425	+	5.28128i	0.0226049	+	0.301911i
$307$	−31.8168			−1.81588			−0.907940	−	0.419101i	$-0.862345\pi$
$307$	−31.8168			−1.81588			−0.907940	+	0.419101i	$0.862345\pi$
$308$	−0.985930	+	0.129800i	−0.0561786	+	0.00739605i
$309$	21.2566	+	9.78966i	1.20925	+	0.556914i
$310$	−5.58606	+	1.49678i	−0.317267	+	0.0850114i
$311$	14.2534	+	28.9031i	0.808239	+	1.63895i	0.768598	+	0.639732i	$0.220955\pi$
$311$	14.2534	+	28.9031i	0.808239	+	1.63895i	0.0396406	+	0.999214i	$0.487379\pi$
$312$	9.57587	−	8.85858i	0.542127	−	0.501518i
$313$	11.7102	+	5.77482i	0.661899	+	0.326412i	0.742025	−	0.670372i	$-0.233866\pi$
$313$	11.7102	+	5.77482i	0.661899	+	0.326412i	−0.0801262	+	0.996785i	$0.525532\pi$
$314$	2.30226	−	0.953629i	0.129924	−	0.0538164i
$315$	−0.254383	−	1.36674i	−0.0143329	−	0.0770073i
$316$	−7.74567	−	11.5922i	−0.435728	−	0.652113i
$317$	−18.2026	+	6.17895i	−1.02236	+	0.347044i	−0.781760	−	0.623580i	$-0.785678\pi$
$317$	−18.2026	+	6.17895i	−1.02236	+	0.347044i	−0.240600	+	0.970624i	$0.577344\pi$
$318$	7.75742	+	1.32994i	0.435014	+	0.0745794i
$319$	−3.23740	−	12.0822i	−0.181260	−	0.676471i
$320$	−5.47877	−	1.85979i	−0.306272	−	0.103965i
$321$	−5.53440	−	3.00222i	−0.308900	−	0.167567i
$322$	0.420321	−	0.242673i	0.0234236	−	0.0135236i
$323$	7.16200	−	9.76361i	0.398504	−	0.543262i
$324$	−13.2129	+	9.63039i	−0.734051	+	0.535022i
$325$	12.0619	+	4.99621i	0.669075	+	0.277140i
$326$	−2.19358	−	2.50129i	−0.121491	−	0.138534i
$327$	8.94424	+	11.0367i	0.494618	+	0.610329i
$328$	6.53585	−	3.22313i	0.360882	−	0.177967i
$329$	−0.999304	+	1.13949i	−0.0550934	+	0.0628220i
$330$	−1.01246	+	1.60600i	−0.0557342	+	0.0884076i
$331$	16.9562	−	22.0978i	0.932000	−	1.21461i	−0.0444831	−	0.999010i	$-0.514164\pi$
$331$	16.9562	−	22.0978i	0.932000	−	1.21461i	0.976483	−	0.215595i	$-0.0691692\pi$
$332$	−2.89147	−	6.98063i	−0.158690	−	0.383112i
$333$	−2.47248	−	6.18370i	−0.135491	−	0.338865i
$334$	−1.26513	−	0.251650i	−0.0692248	−	0.0137697i
$335$	0.449254	−	6.85429i	0.0245454	−	0.374490i
$336$	0.250814	+	1.57970i	0.0136830	+	0.0861797i
$337$	4.08691	−	12.0397i	0.222628	−	0.655842i	−0.777024	−	0.629471i	$-0.783272\pi$
$337$	4.08691	−	12.0397i	0.222628	−	0.655842i	0.999652	−	0.0263709i	$-0.00839510\pi$
$338$	−2.79942	+	2.14807i	−0.152268	+	0.116840i
$339$	19.1618	−	26.3950i	1.04072	−	1.43358i
$340$	−9.78204	+	5.08971i	−0.530506	+	0.276028i
$341$			15.9548i			0.864003i
$342$	−3.76088	−	0.293119i	−0.203365	−	0.0158500i
$343$	−0.853665	−	4.29166i	−0.0460936	−	0.231728i
$344$	−4.53853	−	1.21610i	−0.244701	−	0.0655675i
$345$	−1.55158	+	9.05019i	−0.0835340	+	0.487246i
$346$	−8.00838	−	7.02316i	−0.430533	−	0.377568i
$347$	−30.3920	+	1.99199i	−1.63153	+	0.106936i	−0.853429	−	0.521209i	$-0.825481\pi$
$347$	−30.3920	+	1.99199i	−1.63153	+	0.106936i	−0.778097	+	0.628145i	$0.783815\pi$
$348$	−21.6988	+	6.43644i	−1.16318	+	0.345029i
$349$	15.4559	+	11.8597i	0.827336	+	0.634837i	0.933125	−	0.359551i	$-0.117070\pi$
$349$	15.4559	+	11.8597i	0.827336	+	0.634837i	−0.105789	+	0.994389i	$0.533737\pi$
$350$	0.317448	−	0.212112i	0.0169683	−	0.0113379i
$351$	20.5673	−	12.2679i	1.09780	−	0.654813i
$352$	4.37110	−	6.54181i	0.232980	−	0.348680i
$353$	−1.44138	+	5.37930i	−0.0767169	+	0.286311i	−0.993617	−	0.112805i	$-0.964016\pi$
$353$	−1.44138	+	5.37930i	−0.0767169	+	0.286311i	0.916900	+	0.399116i	$0.130683\pi$
$354$	−4.84905	+	0.447419i	−0.257724	+	0.0237801i
$355$	−5.38637	−	7.01966i	−0.285879	−	0.372565i
$356$	−3.08640	+	5.34580i	−0.163579	+	0.283327i
$357$	1.84728	+	1.28102i	0.0977683	+	0.0677986i
$358$	−3.34609	−	5.79559i	−0.176846	−	0.306307i
$359$	−12.0601	+	29.1158i	−0.636510	+	1.53667i	0.194789	+	0.980845i	$0.437598\pi$
$359$	−12.0601	+	29.1158i	−0.636510	+	1.53667i	−0.831299	+	0.555826i	$0.812402\pi$
$360$	6.20528	+	3.68539i	0.327047	+	0.194237i
$361$	−7.33635	−	7.33635i	−0.386123	−	0.386123i
$362$	−0.379691	−	0.0248862i	−0.0199561	−	0.00130799i
$363$	−9.38136	−	10.1410i	−0.492394	−	0.532264i
$364$	−0.172375	−	2.62994i	−0.00903492	−	0.137846i
$365$	−1.55772	+	11.8321i	−0.0815350	+	0.619319i
$366$	2.76055	+	0.661643i	0.144296	+	0.0345847i
$367$	−4.38649	+	8.89492i	−0.228973	+	0.464311i	−0.980792	−	0.195059i	$-0.937510\pi$
$367$	−4.38649	+	8.89492i	−0.228973	+	0.464311i	0.751819	+	0.659370i	$0.229177\pi$
$368$	2.06102	−	10.3614i	0.107438	−	0.540128i
$369$	12.9641	−	3.30293i	0.674885	−	0.171944i
$370$	−0.989412	+	0.989412i	−0.0514371	+	0.0514371i
$371$	2.51173	−	2.20273i	0.130403	−	0.114360i
$372$	28.8594	−	0.766657i	1.49629	−	0.0397493i
$373$	24.3815	+	14.0767i	1.26243	+	0.728863i	0.973544	−	0.228501i	$-0.0733823\pi$
$373$	24.3815	+	14.0767i	1.26243	+	0.728863i	0.288884	+	0.957364i	$0.406716\pi$
$374$	−0.663843	−	2.99726i	−0.0343265	−	0.154984i
$375$	−2.08015	+	19.8637i	−0.107418	+	1.02576i
$376$	−1.02699	−	7.80077i	−0.0529630	−	0.402294i
$377$	32.5143	−	6.46749i	1.67457	−	0.333093i
$378$	0.0358566	−	0.699404i	0.00184427	−	0.0359734i
$379$	−19.3719	−	12.9439i	−0.995067	−	0.664883i	−0.0524031	−	0.998626i	$-0.516688\pi$
$379$	−19.3719	−	12.9439i	−0.995067	−	0.664883i	−0.942664	+	0.333743i	$0.891688\pi$
$380$	−2.52467	−	7.43745i	−0.129513	−	0.381533i
$381$	24.7573	−	13.0374i	1.26836	−	0.667928i
$382$	9.04819	+	1.19122i	0.462946	+	0.0609479i
$383$	−20.2001	−	2.65939i	−1.03218	−	0.135889i	−0.404641	−	0.914476i	$-0.632603\pi$
$383$	−20.2001	−	2.65939i	−1.03218	−	0.135889i	−0.627537	+	0.778587i	$0.715937\pi$
$384$	−15.7238	−	9.91264i	−0.802401	−	0.505852i
$385$	0.259031	+	0.763080i	0.0132014	+	0.0388902i
$386$	2.61121	+	1.74476i	0.132907	+	0.0888057i
$387$	−7.68861	−	3.91020i	−0.390834	−	0.198767i
$388$	33.3886	−	6.64141i	1.69505	−	0.337167i
$389$	3.27044	+	24.8415i	0.165818	+	1.25951i	0.848657	+	0.528944i	$0.177412\pi$
$389$	3.27044	+	24.8415i	0.165818	+	1.25951i	−0.682839	+	0.730569i	$0.739255\pi$
$390$	−4.07182	−	2.95599i	−0.206185	−	0.149682i
$391$	−8.51384	−	12.1642i	−0.430564	−	0.615172i
$392$	9.76630	+	5.63858i	0.493273	+	0.284791i
$393$	6.52506	+	10.6389i	0.329146	+	0.536660i
$394$	−6.90055	+	6.05162i	−0.347645	+	0.304876i
$395$	−7.98877	+	7.98877i	−0.401958	+	0.401958i
$396$	6.78368	−	6.61840i	0.340893	−	0.332587i
$397$	−0.535806	+	2.69368i	−0.0268914	+	0.135192i	−0.991899	−	0.127030i	$-0.959455\pi$
$397$	−0.535806	+	2.69368i	−0.0268914	+	0.135192i	0.965007	+	0.262222i	$0.0844554\pi$
$398$	−0.540144	+	1.09530i	−0.0270750	+	0.0549026i
$399$	−1.10175	+	1.16188i	−0.0551565	+	0.0581670i
$400$	1.08473	−	8.23932i	0.0542363	−	0.411966i
$401$	−1.04529	−	15.9480i	−0.0521991	−	0.796405i	−0.941063	−	0.338233i	$-0.890171\pi$
$401$	−1.04529	−	15.9480i	−0.0521991	−	0.796405i	0.888863	−	0.458172i	$-0.151496\pi$
$402$	1.02486	−	3.30500i	0.0511153	−	0.164839i
$403$	−42.1950	−	2.76560i	−2.10188	−	0.137765i
$404$	−4.65239	−	4.65239i	−0.231465	−	0.231465i
$405$	9.74294	+	8.97892i	0.484130	+	0.446166i
$406$	0.370993	−	0.895656i	0.0184121	−	0.0444506i
$407$	1.93016	+	3.34313i	0.0956744	+	0.165713i
$408$	−11.3230	+	2.82529i	−0.560574	+	0.139873i
$409$	4.21393	−	7.29874i	0.208365	−	0.360899i	−0.742834	−	0.669475i	$-0.766519\pi$
$409$	4.21393	−	7.29874i	0.208365	−	0.360899i	0.951200	+	0.308576i	$0.0998523\pi$
$410$	−1.71114	−	2.23000i	−0.0845072	−	0.110132i
$411$	19.5294	+	27.6113i	0.963315	+	1.36196i
$412$	−6.35297	+	23.7096i	−0.312989	+	1.16809i
$413$	−1.14836	+	1.71864i	−0.0565070	+	0.0845687i
$414$	−1.82269	+	4.25130i	−0.0895801	+	0.208940i
$415$	−5.09097	+	3.40168i	−0.249906	+	0.166982i
$416$	16.5431	+	12.6940i	0.811093	+	0.622373i
$417$	4.23667	−	17.6765i	0.207471	−	0.865623i
$418$	2.18194	−	0.143012i	0.106722	−	0.00699495i
$419$	8.61354	+	7.55387i	0.420799	+	0.369031i	0.843401	−	0.537285i	$-0.180550\pi$
$419$	8.61354	+	7.55387i	0.420799	+	0.369031i	−0.422602	+	0.906315i	$0.638883\pi$
$420$	1.36782	−	0.505206i	0.0667430	−	0.0246515i
$421$	−11.2172	−	3.00563i	−0.546691	−	0.146485i	−0.0251059	−	0.999685i	$-0.507992\pi$
$421$	−11.2172	−	3.00563i	−0.546691	−	0.146485i	−0.521585	+	0.853199i	$0.674659\pi$
$422$	1.86751	+	9.38862i	0.0909091	+	0.457031i
$423$	1.12237	−	14.4006i	0.0545715	−	0.700183i
$424$			17.3433i			0.842267i
$425$	−7.30883	−	9.11037i	−0.354530	−	0.441918i
$426$	−1.81446	−	4.07119i	−0.0879109	−	0.197250i
$427$	0.955943	−	0.733521i	0.0462613	−	0.0354976i
$428$	2.12275	−	6.25342i	0.102607	−	0.302271i
$429$	−10.7848	+	8.74011i	−0.520694	+	0.421976i
$430$	−0.118532	+	1.80846i	−0.00571614	+	0.0872115i
$431$	−16.3546	−	3.25313i	−0.787772	−	0.156698i	−0.215220	−	0.976566i	$-0.569047\pi$
$431$	−16.3546	−	3.25313i	−0.787772	−	0.156698i	−0.572552	+	0.819868i	$0.694047\pi$
$432$	−10.9313	−	10.6246i	−0.525931	−	0.511175i
$433$	2.99292	+	7.22556i	0.143831	+	0.347238i	0.979335	−	0.202246i	$-0.0648242\pi$
$433$	2.99292	+	7.22556i	0.143831	+	0.347238i	−0.835504	+	0.549484i	$0.814824\pi$
$434$	−0.752774	+	0.981034i	−0.0361343	+	0.0470911i
$435$	8.54599	+	16.2283i	0.409749	+	0.778089i
$436$	−9.82424	+	11.2024i	−0.470496	+	0.536497i
$437$	9.48508	−	4.67752i	0.453733	−	0.223756i
$438$	−2.15233	+	5.61336i	−0.102842	+	0.268217i
$439$	−13.1609	−	15.0071i	−0.628135	−	0.716250i	0.347000	−	0.937865i	$-0.387201\pi$
$439$	−13.1609	−	15.0071i	−0.628135	−	0.716250i	−0.975134	+	0.221615i	$0.928867\pi$
$440$	−3.86502	−	1.60095i	−0.184258	−	0.0763221i
$441$	15.3956	+	13.8412i	0.733125	+	0.659103i
$442$	8.04177	−	1.23609i	0.382508	−	0.0587948i
$443$	−23.4193	+	13.5212i	−1.11269	+	0.642410i	−0.939524	−	0.342483i	$-0.888732\pi$
$443$	−23.4193	+	13.5212i	−1.11269	+	0.642410i	−0.173163	+	0.984893i	$0.555399\pi$
$444$	5.95436	−	3.65194i	0.282582	−	0.173314i
$445$	4.73669	+	1.60789i	0.224541	+	0.0762212i
$446$	2.28249	+	8.51837i	0.108079	+	0.403356i
$447$	−1.76262	−	4.77223i	−0.0833693	−	0.225719i
$448$	−1.17149	+	0.397667i	−0.0553477	+	0.0187880i
$449$	19.2189	+	28.7631i	0.906996	+	1.35741i	0.933808	+	0.357774i	$0.116464\pi$
$449$	19.2189	+	28.7631i	0.906996	+	1.35741i	−0.0268124	+	0.999640i	$0.508536\pi$
$450$	−1.21200	+	3.43086i	−0.0571344	+	0.161732i
$451$	−7.16448	+	2.96762i	−0.337362	+	0.139740i
$452$	30.6826	+	15.1310i	1.44319	+	0.711701i
$453$	1.50674	+	6.64714i	0.0707929	+	0.312310i
$454$	−2.42748	−	4.92245i	−0.113927	−	0.231022i
$455$	−2.06298	+	0.552774i	−0.0967140	+	0.0259144i
$456$	−0.763741	−	8.27729i	−0.0357654	−	0.387620i
$457$	0.698830	−	0.0920028i	0.0326899	−	0.00430371i	−0.114163	−	0.993462i	$-0.536419\pi$
$457$	0.698830	−	0.0920028i	0.0326899	−	0.00430371i	0.146853	+	0.989158i	$0.453085\pi$
$458$	11.7483			0.548960
$459$	−21.4105	+	0.767738i	−0.999358	+	0.0358349i
$460$	−9.63087			−0.449041
$461$	−14.9569	+	1.96911i	−0.696612	+	0.0917107i	−0.470512	−	0.882393i	$-0.655931\pi$
$461$	−14.9569	+	1.96911i	−0.696612	+	0.0917107i	−0.226100	+	0.974104i	$0.572598\pi$
$462$	0.0372979	+	0.404228i	0.00173526	+	0.0188064i
$463$	−1.60507	+	0.430077i	−0.0745938	+	0.0199874i	−0.295923	−	0.955212i	$-0.595627\pi$
$463$	−1.60507	+	0.430077i	−0.0745938	+	0.0199874i	0.221329	+	0.975199i	$0.428960\pi$
$464$	−9.33313	−	18.9257i	−0.433280	−	0.878604i
$465$	−5.17177	−	22.8157i	−0.239835	−	1.05805i
$466$	−3.40103	−	1.67720i	−0.157550	−	0.0776949i
$467$	−7.68148	+	3.18177i	−0.355457	+	0.147235i	−0.553264	−	0.833006i	$-0.686618\pi$
$467$	−7.68148	+	3.18177i	−0.355457	+	0.147235i	0.197807	+	0.980241i	$0.436618\pi$
$468$	16.3275	+	19.0877i	0.754738	+	0.882329i
$469$	−0.815995	−	1.22122i	−0.0376792	−	0.0563909i
$470$	−2.87378	+	0.975518i	−0.132558	+	0.0449973i
$471$	3.49270	+	9.45635i	0.160935	+	0.435726i
$472$	−2.77728	−	10.3649i	−0.127834	−	0.477085i
$473$	4.73464	+	1.60719i	0.217699	+	0.0738989i
$474$	−4.85149	+	2.97553i	−0.222836	+	0.136670i
$475$	7.20472	−	4.15965i	0.330575	−	0.190858i
$476$	−0.996888	+	2.13671i	−0.0456923	+	0.0979360i
$477$	−6.59611	+	31.1483i	−0.302015	+	1.42618i
$478$	7.77059	+	3.21868i	0.355419	+	0.147219i
$479$	−9.12309	−	10.4029i	−0.416844	−	0.475320i	0.504866	−	0.863197i	$-0.331542\pi$
$479$	−9.12309	−	10.4029i	−0.416844	−	0.475320i	−0.921711	+	0.387877i	$0.873208\pi$
$480$	−4.13023	+	10.7718i	−0.188518	+	0.491664i
$481$	−9.17599	+	4.52510i	−0.418389	+	0.206327i
$482$	−5.18106	+	5.90787i	−0.235991	+	0.269096i
$483$	0.914836	+	1.73722i	0.0416265	+	0.0790462i
$484$	8.82084	−	11.4955i	0.400947	−	0.522525i
$485$	−10.5570	−	25.4868i	−0.479367	−	1.15729i
$486$	3.71860	+	5.54250i	0.168679	+	0.251413i
$487$	23.3311	+	4.64084i	1.05723	+	0.210296i	0.692945	−	0.720991i	$-0.256313\pi$
$487$	23.3311	+	4.64084i	1.05723	+	0.210296i	0.364286	+	0.931287i	$0.381313\pi$
$488$	−0.409118	+	6.24193i	−0.0185199	+	0.282559i
$489$	10.4559	−	8.47359i	0.472832	−	0.383189i
$490$	1.39819	−	4.11893i	0.0631638	−	0.186074i
$491$	−20.9795	+	16.0981i	−0.946792	+	0.726499i	−0.961904	−	0.273387i	$-0.911856\pi$
$491$	−20.9795	+	16.0981i	−0.946792	+	0.726499i	0.0151123	+	0.999886i	$0.495189\pi$
$492$	5.71215	+	12.8166i	0.257524	+	0.577818i
$493$	−28.2830	−	8.92387i	−1.27380	−	0.401911i
$494$			5.79526i			0.260741i
$495$	−6.33264	−	4.34524i	−0.284631	−	0.195304i
$496$	5.25108	+	26.3990i	0.235781	+	1.18535i
$497$	−1.82746	−	0.489667i	−0.0819730	−	0.0219646i
$498$	−2.89335	+	1.06866i	−0.129654	+	0.0478877i
$499$	−22.9464	−	20.1234i	−1.02722	−	0.900848i	−0.0320966	−	0.999485i	$-0.510218\pi$
$499$	−22.9464	−	20.1234i	−1.02722	−	0.900848i	−0.995123	+	0.0986370i	$0.968552\pi$
$500$	−20.9033	+	1.37008i	−0.934824	+	0.0612716i
$501$	1.21622	−	5.07440i	0.0543368	−	0.226708i
$502$	4.26964	+	3.27621i	0.190564	+	0.146225i
$503$	10.6641	−	7.12553i	0.475489	−	0.317712i	−0.294630	−	0.955611i	$-0.595197\pi$
$503$	10.6641	−	7.12553i	0.475489	−	0.317712i	0.770119	+	0.637900i	$0.220197\pi$
$504$	1.53237	−	0.182546i	0.0682571	−	0.00813124i
$505$	−2.96214	+	4.43315i	−0.131813	+	0.197273i
$506$	0.693952	−	2.58987i	0.0308499	−	0.115134i
$507$	−8.24275	−	11.6538i	−0.366073	−	0.517566i
$508$	17.8656	+	23.2829i	0.792657	+	1.03301i
$509$	4.49484	−	7.78528i	0.199230	−	0.345077i	−0.749049	−	0.662515i	$-0.769489\pi$
$509$	4.49484	−	7.78528i	0.199230	−	0.345077i	0.948279	+	0.317438i	$0.102823\pi$
$510$	1.92087	+	4.07095i	0.0850576	+	0.180265i
$511$	1.27590	+	2.20993i	0.0564427	+	0.0977616i
$512$	8.74862	−	21.1210i	0.386638	−	0.933427i
$513$	1.77640	−	15.1564i	0.0784298	−	0.669169i
$514$	1.58230	+	1.58230i	0.0697923	+	0.0697923i
$515$	19.8484	+	1.30093i	0.874624	+	0.0573259i
$516$	2.67961	−	8.64132i	0.117963	−	0.380413i
$517$	0.547602	+	8.35480i	0.0240835	+	0.367444i
$518$	−0.0390522	+	0.296631i	−0.00171586	+	0.0130332i
$519$	29.6491	−	31.2673i	1.30145	−	1.37248i
$520$	4.90390	−	9.94413i	0.215050	−	0.436079i
$521$	−2.27564	+	11.4404i	−0.0996976	+	0.501214i	0.898379	+	0.439221i	$0.144745\pi$
$521$	−2.27564	+	11.4404i	−0.0996976	+	0.501214i	−0.998077	+	0.0619925i	$0.980255\pi$
$522$	2.28107	+	8.95328i	0.0998397	+	0.391874i
$523$	12.3418	−	12.3418i	0.539671	−	0.539671i	−0.383761	−	0.923432i	$-0.625371\pi$
$523$	12.3418	−	12.3418i	0.539671	−	0.539671i	0.923432	+	0.383761i	$0.125371\pi$
$524$	−9.84178	+	8.63101i	−0.429940	+	0.377047i
$525$	0.807483	+	1.31657i	0.0352415	+	0.0574599i
$526$	3.81109	+	2.20033i	0.166171	+	0.0959390i
$527$	31.9006	+	20.3320i	1.38961	+	0.885675i
$528$	7.15057	+	5.19105i	0.311189	+	0.225912i
$529$	1.30945	+	9.94628i	0.0569327	+	0.432447i
$530$	6.56106	−	1.30508i	0.284994	−	0.0566888i
$531$	−1.04590	−	19.6715i	−0.0453881	−	0.853671i
$532$	−1.39639	−	0.933041i	−0.0605414	−	0.0404525i
$533$	−6.60644	−	19.4620i	−0.286157	−	0.842991i
$534$	2.13160	+	1.34381i	0.0922436	+	0.0581525i
$535$	−5.30571	−	0.698509i	−0.229386	−	0.0301992i
$536$	7.55966	+	0.995247i	0.326527	+	0.0429881i
$537$	23.9536	−	12.6142i	1.03367	−	0.544343i
$538$	−1.89899	−	5.59426i	−0.0818715	−	0.241186i
$539$	−9.97801	−	6.66709i	−0.429783	−	0.287172i
$540$	−7.55544	+	11.6634i	−0.325134	+	0.501912i
$541$	−4.00985	+	0.797608i	−0.172397	+	0.0342918i	−0.280534	−	0.959844i	$-0.590511\pi$
$541$	−4.00985	+	0.797608i	−0.172397	+	0.0342918i	0.108137	+	0.994136i	$0.465511\pi$
$542$	−0.528496	−	4.01433i	−0.0227009	−	0.172430i
$543$	0.160317	−	1.53090i	0.00687985	−	0.0656970i
$544$	−7.50962	−	17.0762i	−0.321973	−	0.732138i
$545$	10.4566	+	6.03713i	0.447912	+	0.258602i
$546$	−1.07551	+	0.0285712i	−0.0460275	+	0.00122273i
$547$	14.5589	−	12.7678i	0.622493	−	0.545911i	−0.288947	−	0.957345i	$-0.593305\pi$
$547$	14.5589	−	12.7678i	0.622493	−	0.545911i	0.911440	+	0.411434i	$0.134972\pi$
$548$	−25.0827	+	25.0827i	−1.07148	+	1.07148i
$549$	−3.10873	+	11.0548i	−0.132678	+	0.471808i
$550$	0.411477	−	2.06863i	0.0175454	−	0.0882068i
$551$	9.34310	−	18.9459i	0.398030	−	0.807124i
$552$	−9.91196	−	2.37568i	−0.421881	−	0.101116i
$553$	−0.315317	+	2.39507i	−0.0134087	+	0.101849i
$554$	0.248739	+	3.79502i	0.0105679	+	0.161235i
$555$	−3.84384	−	4.15509i	−0.163162	−	0.176374i
$556$	19.0244	+	1.24693i	0.806816	+	0.0528815i
$557$	−2.32543	−	2.32543i	−0.0985316	−	0.0985316i	0.656123	−	0.754654i	$-0.272195\pi$
$557$	−2.32543	−	2.32543i	−0.0985316	−	0.0985316i	−0.754654	+	0.656123i	$0.772195\pi$
$558$	0.145327	−	11.7841i	0.00615217	−	0.498862i
$559$	−5.07117	+	12.2429i	−0.214488	+	0.517819i
$560$	0.679740	+	1.17734i	0.0287243	+	0.0497519i
$561$	12.2201	−	2.21200i	0.515934	−	0.0933908i
$562$	−6.44181	+	11.1575i	−0.271732	+	0.470653i
$563$	−6.12618	−	7.98379i	−0.258188	−	0.336477i	0.646216	−	0.763155i	$-0.276351\pi$
$563$	−6.12618	−	7.98379i	−0.258188	−	0.336477i	−0.904404	+	0.426678i	$0.859684\pi$
$564$	15.0860	−	1.39197i	0.635234	−	0.0586127i
$565$	7.17517	−	26.7781i	0.301862	−	1.12656i
$566$	3.38096	−	5.05997i	0.142113	−	0.212686i
$567$	2.82153	+	0.254949i	0.118493	+	0.0107068i
$568$	8.16650	−	5.45668i	0.342659	−	0.228957i
$569$	18.9335	+	14.5282i	0.793734	+	0.609054i	0.923986	−	0.382427i	$-0.124912\pi$
$569$	18.9335	+	14.5282i	0.793734	+	0.609054i	−0.130251	+	0.991481i	$0.541578\pi$
$570$	−3.07386	+	0.911788i	−0.128750	+	0.0381906i
$571$	−18.2351	+	1.19519i	−0.763115	+	0.0500172i	−0.441990	−	0.897020i	$-0.645727\pi$
$571$	−18.2351	+	1.19519i	−0.763115	+	0.0500172i	−0.321124	+	0.947037i	$0.604061\pi$
$572$	−10.9467	−	9.60003i	−0.457706	−	0.401397i
$573$	−6.23837	+	36.3878i	−0.260611	+	1.52012i
$574$	−0.580548	−	0.155557i	−0.0242316	−	0.00649284i
$575$	−1.99013	−	10.0051i	−0.0829941	−	0.417240i
$576$	6.67086	−	9.72194i	0.277952	−	0.405081i
$577$		−	22.3597i		−	0.930846i	−0.885088	−	0.465423i	$-0.845902\pi$
$577$		−	22.3597i		−	0.930846i	0.885088	−	0.465423i	$-0.154098\pi$
$578$	−6.83878	−	2.49223i	−0.284456	−	0.103663i
$579$	−7.46347	+	10.2808i	−0.310171	+	0.427255i
$580$	−15.2618	+	11.7108i	−0.633714	+	0.486266i
$581$	−0.420832	+	1.23973i	−0.0174591	+	0.0514327i
$582$	−2.17914	−	13.7249i	−0.0903284	−	0.568915i
$583$	1.20706	−	18.4162i	0.0499913	−	0.762720i
$584$	−12.9929	−	2.58445i	−0.537651	−	0.106945i
$585$	12.5893	−	15.9944i	0.520505	−	0.661288i
$586$	−5.14163	−	12.4130i	−0.212399	−	0.512776i
$587$	−15.5520	+	20.2678i	−0.641902	+	0.836542i	−0.995086	−	0.0990112i	$-0.968432\pi$
$587$	−15.5520	+	20.2678i	−0.641902	+	0.836542i	0.353185	+	0.935554i	$0.385099\pi$
$588$	−11.5801	+	18.3687i	−0.477555	+	0.757514i
$589$	−17.7660	+	20.2583i	−0.732036	+	0.834727i
$590$	−3.71211	+	1.83061i	−0.152825	+	0.0753650i
$591$	−23.3769	−	28.8457i	−0.961596	−	1.18655i
$592$	4.29395	+	4.89631i	0.176480	+	0.201237i
$593$	8.60925	+	3.56607i	0.353539	+	0.146441i	0.552383	−	0.833590i	$-0.313719\pi$
$593$	8.60925	+	3.56607i	0.353539	+	0.146441i	−0.198844	+	0.980031i	$0.563719\pi$
$594$	−2.59203	−	2.87216i	−0.106352	−	0.117846i
$595$	1.85582	+	0.454513i	0.0760813	+	0.0186332i
$596$	4.62103	−	2.66795i	0.189285	−	0.109284i
$597$	−4.34255	−	2.35568i	−0.177729	−	0.0964116i
$598$	6.72900	+	2.28419i	0.275169	+	0.0934073i
$599$	−4.75389	−	17.7417i	−0.194239	−	0.724908i	−0.992463	−	0.122548i	$-0.960894\pi$
$599$	−4.75389	−	17.7417i	−0.194239	−	0.724908i	0.798224	−	0.602361i	$-0.205773\pi$
$600$	−7.90268	−	1.35484i	−0.322625	−	0.0553113i
$601$	−25.0795	+	8.51334i	−1.02301	+	0.347267i	−0.782016	−	0.623259i	$-0.785808\pi$
$601$	−25.0795	+	8.51334i	−1.02301	+	0.347267i	−0.240999	+	0.970525i	$0.577475\pi$
$602$	0.215295	+	0.322211i	0.00877475	+	0.0131323i
$603$	13.1985	+	4.66258i	0.537485	+	0.189875i
$604$	−6.60461	+	2.73572i	−0.268738	+	0.111315i
$605$	−10.5310	−	5.19330i	−0.428145	−	0.211138i
$606$	−1.97159	+	1.82390i	−0.0800903	+	0.0740910i
$607$	11.3219	+	22.9585i	0.459541	+	0.931858i	0.996120	+	0.0880073i	$0.0280499\pi$
$607$	11.3219	+	22.9585i	0.459541	+	0.931858i	−0.536578	+	0.843850i	$0.680283\pi$
$608$	12.8345	−	3.43900i	0.520509	−	0.139470i
$609$	3.56212	+	1.64052i	0.144345	+	0.0664774i
$610$	2.39214	−	0.314931i	0.0968547	−	0.0127512i
$611$	−22.1904			−0.897729
$612$	−4.58830	−	21.9976i	−0.185471	−	0.889202i
$613$	30.5459			1.23374			0.616869	−	0.787066i	$-0.288401\pi$
$613$	30.5459			1.23374			0.616869	+	0.787066i	$0.288401\pi$
$614$	−13.5062	+	1.77812i	−0.545065	+	0.0717591i
$615$	9.28339	−	6.56613i	0.374343	−	0.264772i
$616$	−0.864045	+	0.231520i	−0.0348134	+	0.00932821i
$617$	−3.17966	−	6.44771i	−0.128008	−	0.259575i	0.823428	−	0.567421i	$-0.192059\pi$
$617$	−3.17966	−	6.44771i	−0.128008	−	0.259575i	−0.951436	+	0.307846i	$0.900392\pi$
$618$	9.57050	+	2.96774i	0.384982	+	0.119380i
$619$	22.0935	+	10.8953i	0.888011	+	0.437918i	0.828292	−	0.560297i	$-0.189313\pi$
$619$	22.0935	+	10.8953i	0.888011	+	0.437918i	0.0597188	+	0.998215i	$0.480980\pi$
$620$	22.6698	−	9.39013i	0.910441	−	0.377117i
$621$	−16.8982	−	8.03644i	−0.678101	−	0.322491i
$622$	7.66585	+	11.4728i	0.307373	+	0.460016i
$623$	1.01282	−	0.343805i	0.0405776	−	0.0137742i
$624$	−14.9680	+	18.0109i	−0.599199	+	0.721015i
$625$	0.727694	+	2.71579i	0.0291077	+	0.108632i
$626$	5.29369	+	1.79696i	0.211578	+	0.0718212i
$627$	0.234903	+	8.84248i	0.00938112	+	0.353135i
$628$	−9.15674	+	5.28664i	−0.365394	+	0.210960i
$629$	9.14406	+	0.401082i	0.364598	+	0.0159922i
$630$	−0.184368	−	0.565964i	−0.00734538	−	0.0225486i
$631$	−4.23320	−	1.75345i	−0.168521	−	0.0698036i	0.296828	−	0.954931i	$-0.404071\pi$
$631$	−4.23320	−	1.75345i	−0.168521	−	0.0698036i	−0.465349	+	0.885127i	$0.654071\pi$
$632$	−8.26891	−	9.42888i	−0.328920	−	0.375061i
$633$	−38.2450	+	6.07228i	−1.52010	+	0.241351i
$634$	−7.38166	+	3.64023i	−0.293163	+	0.144572i
$635$	15.6804	−	17.8801i	0.622259	−	0.709551i
$636$	−33.3695	−	1.29842i	−1.32319	−	0.0514858i
$637$	19.3617	−	25.2327i	0.767139	−	0.999755i
$638$	−2.04950	−	4.94793i	−0.0811405	−	0.195890i
$639$	16.7422	−	6.69419i	0.662312	−	0.264818i
$640$	−15.4949	−	3.08213i	−0.612490	−	0.121832i
$641$	0.700297	−	10.6845i	0.0276601	−	0.422011i	−0.961464	−	0.274930i	$-0.911345\pi$
$641$	0.700297	−	10.6845i	0.0276601	−	0.422011i	0.989124	−	0.147081i	$-0.0469879\pi$
$642$	−2.51713	−	0.965140i	−0.0993430	−	0.0380910i
$643$	8.02090	−	23.6288i	0.316313	−	0.931829i	−0.666222	−	0.745753i	$-0.732090\pi$
$643$	8.02090	−	23.6288i	0.316313	−	0.931829i	0.982535	−	0.186075i	$-0.0595769\pi$
$644$	−1.63376	+	1.25363i	−0.0643791	+	0.0493998i
$645$	−7.29161	−	0.763584i	−0.287107	−	0.0300661i
$646$	2.49460	−	4.54490i	0.0981489	−	0.178817i
$647$		−	23.7610i		−	0.934140i	−0.884220	−	0.467070i	$-0.845310\pi$
$647$		−	23.7610i		−	0.934140i	0.884220	−	0.467070i	$-0.154690\pi$
$648$	−10.6530	+	10.1401i	−0.418489	+	0.398339i
$649$	2.22770	+	11.1994i	0.0874448	+	0.439615i
$650$	5.39949	+	1.44679i	0.211785	+	0.0567477i
$651$	−3.84720	−	3.19721i	−0.150784	−	0.125309i
$652$	10.6129	+	9.30728i	0.415634	+	0.364501i
$653$	−19.5004	+	1.27812i	−0.763109	+	0.0500168i	−0.441987	−	0.897021i	$-0.645726\pi$
$653$	−19.5004	+	1.27812i	−0.763109	+	0.0500168i	−0.321121	+	0.947038i	$0.604060\pi$
$654$	4.41361	+	4.18518i	0.172586	+	0.163654i
$655$	8.41569	+	6.45759i	0.328828	+	0.252319i
$656$	−10.8777	+	7.26824i	−0.424702	+	0.283777i
$657$	−22.3521	−	9.58317i	−0.872040	−	0.373875i
$658$	−0.360521	+	0.539558i	−0.0140546	+	0.0210342i
$659$	8.87097	−	33.1069i	0.345564	−	1.28966i	−0.546388	−	0.837532i	$-0.683997\pi$
$659$	8.87097	−	33.1069i	0.345564	−	1.28966i	0.891952	−	0.452130i	$-0.149336\pi$
$660$	3.36966	−	7.31665i	0.131164	−	0.284800i
$661$	11.4006	+	14.8575i	0.443431	+	0.577891i	0.960580	−	0.278005i	$-0.0896732\pi$
$661$	11.4006	+	14.8575i	0.443431	+	0.577891i	−0.517149	+	0.855896i	$0.673007\pi$
$662$	5.96294	−	10.3281i	0.231756	−	0.401413i
$663$	3.73174	+	32.7014i	0.144929	+	1.27002i
$664$	−3.39832	−	5.88607i	−0.131880	−	0.228424i
$665$	−0.520806	+	1.25734i	−0.0201960	+	0.0487575i
$666$	−1.39515	−	2.48679i	−0.0540609	−	0.0963613i
$667$	−18.3160	−	18.3160i	−0.709196	−	0.709196i
$668$	5.46136	+	0.357956i	0.211306	+	0.0138497i
$669$	−34.7925	+	7.88660i	−1.34516	+	0.304914i
$670$	−0.192353	−	2.93474i	−0.00743125	−	0.113379i
$671$	0.868852	−	6.59958i	0.0335416	−	0.254774i
$672$	0.701498	+	2.36493i	0.0270609	+	0.0912290i
$673$	1.50963	−	3.06122i	0.0581918	−	0.118001i	−0.865834	−	0.500331i	$-0.833212\pi$
$673$	1.50963	−	3.06122i	0.0581918	−	0.118001i	0.924026	+	0.382330i	$0.124878\pi$
$674$	1.06204	−	5.33922i	0.0409081	−	0.205659i
$675$	−13.6778	−	5.43887i	−0.526459	−	0.209342i
$676$	10.5866	−	10.5866i	0.407177	−	0.407177i
$677$	38.0369	−	33.3575i	1.46188	−	1.28203i	0.576553	−	0.817060i	$-0.304398\pi$
$677$	38.0369	−	33.3575i	1.46188	−	1.28203i	0.885325	−	0.464973i	$-0.153936\pi$
$678$	6.65903	−	12.2755i	0.255738	−	0.471438i
$679$	−5.10841	−	2.94934i	−0.196043	−	0.113185i
$680$	−8.12636	+	5.68770i	−0.311632	+	0.218113i
$681$	20.2796	−	9.03829i	0.777118	−	0.346348i
$682$	0.891657	+	6.77281i	0.0341433	+	0.259344i
$683$	25.0946	−	4.99162i	0.960218	−	0.190999i	0.309991	−	0.950739i	$-0.399674\pi$
$683$	25.0946	−	4.99162i	0.960218	−	0.190999i	0.650227	+	0.759740i	$0.274674\pi$
$684$	15.9831	−	0.849792i	0.611130	−	0.0324926i
$685$	23.9007	+	15.9699i	0.913198	+	0.610179i
$686$	−0.602225	−	1.77410i	−0.0229930	−	0.0677353i
$687$	−1.84784	+	47.4896i	−0.0704995	+	1.81184i
$688$	8.36293	+	1.10100i	0.318834	+	0.0419753i
$689$	48.4951	+	6.38451i	1.84752	+	0.243230i
$690$	−0.152860	+	3.92850i	−0.00581927	+	0.149556i
$691$	4.16476	+	12.2690i	0.158435	+	0.466734i	0.996941	−	0.0781581i	$-0.0249039\pi$
$691$	4.16476	+	12.2690i	0.158435	+	0.466734i	−0.838506	+	0.544892i	$0.816571\pi$
$692$	37.5782	+	25.1090i	1.42851	+	0.954500i
$693$	−1.63986	+	0.0871884i	−0.0622933	+	0.00331201i
$694$	−12.7900	+	2.54409i	−0.485502	+	0.0965724i
$695$	−2.01658	−	15.3174i	−0.0764932	−	0.581024i
$696$	−18.5960	+	8.28793i	−0.704881	+	0.314153i
$697$	−3.19645	+	18.1067i	−0.121074	+	0.685839i
$698$	7.22381	+	4.17067i	0.273425	+	0.157862i
$699$	7.31463	−	13.4841i	0.276665	−	0.510014i
$700$	−1.21793	+	1.06810i	−0.0460334	+	0.0403703i
$701$	−11.6445	+	11.6445i	−0.439808	+	0.439808i	−0.891947	−	0.452139i	$-0.850661\pi$
$701$	−11.6445	+	11.6445i	−0.439808	+	0.439808i	0.452139	+	0.891947i	$0.350661\pi$
$702$	8.04516	−	6.35714i	0.303645	−	0.239935i
$703$	−1.27187	+	6.39413i	−0.0479695	+	0.241159i
$704$	−3.02280	+	6.12962i	−0.113926	+	0.231019i
$705$	−3.49129	−	11.7700i	−0.131490	−	0.443285i
$706$	−0.311234	+	2.36406i	−0.0117135	+	0.0889725i
$707$	0.0745625	+	1.13760i	0.00280421	+	0.0427840i
$708$	20.1506	−	4.56765i	0.757306	−	0.171663i
$709$	22.5988	+	1.48120i	0.848715	+	0.0556277i	0.483552	−	0.875316i	$-0.339347\pi$
$709$	22.5988	+	1.48120i	0.848715	+	0.0556277i	0.365163	+	0.930944i	$0.381013\pi$
$710$	−2.67881	−	2.67881i	−0.100534	−	0.100534i
$711$	−11.2648	−	20.0790i	−0.422463	−	0.753021i
$712$	−2.12489	+	5.12994i	−0.0796337	+	0.192253i
$713$	16.5199	+	28.6132i	0.618673	+	1.07157i
$714$	0.855758	+	0.440552i	0.0320259	+	0.0164872i
$715$	−5.89935	+	10.2180i	−0.220623	+	0.382130i
$716$	17.2856	+	22.5270i	0.645994	+	0.841875i
$717$	−14.2330	+	30.9045i	−0.531540	+	1.15415i
$718$	−3.49234	+	13.0336i	−0.130333	+	0.486409i
$719$	−6.76012	+	10.1172i	−0.252110	+	0.377309i	−0.935840	−	0.352426i	$-0.885357\pi$
$719$	−6.76012	+	10.1172i	−0.252110	+	0.377309i	0.683730	+	0.729735i	$0.260357\pi$
$720$	−11.9081	−	5.10545i	−0.443790	−	0.190269i
$721$	3.53637	−	2.36293i	0.131701	−	0.0880000i
$722$	−3.52427	−	2.70427i	−0.131160	−	0.100642i
$723$	−23.0662	−	21.8724i	−0.857843	−	0.813445i
$724$	1.61102	−	0.105592i	0.0598730	−	0.00392428i
$725$	−15.3195	−	13.4349i	−0.568954	−	0.498959i
$726$	−4.54912	−	3.78054i	−0.168834	−	0.140309i
$727$	28.5310	+	7.64487i	1.05816	+	0.283533i	0.745619	−	0.666372i	$-0.232154\pi$
$727$	28.5310	+	7.64487i	1.05816	+	0.283533i	0.312539	+	0.949905i	$0.398821\pi$
$728$	−0.462517	−	2.32523i	−0.0171420	−	0.0861787i
$729$	−22.9891	+	14.1598i	−0.851450	+	0.524437i
$730$			5.10976i			0.189121i
$731$	9.24705	−	7.41848i	0.342014	−	0.274382i
$732$	−11.9792	−	1.25447i	−0.442763	−	0.0463666i
$733$	−10.8761	+	8.34555i	−0.401719	+	0.308250i	−0.789787	−	0.613381i	$-0.789809\pi$
$733$	−10.8761	+	8.34555i	−0.401719	+	0.308250i	0.388068	+	0.921631i	$0.373142\pi$
$734$	−1.36495	+	4.02102i	−0.0503814	+	0.148419i
$735$	16.4299	+	6.29970i	0.606026	+	0.232368i
$736$	1.06560	−	16.2579i	0.0392785	−	0.599274i
$737$	−7.95803	−	1.58295i	−0.293138	−	0.0583087i
$738$	5.31866	−	2.12661i	0.195783	−	0.0782815i
$739$	18.6853	+	45.1102i	0.687349	+	1.65941i	0.750055	+	0.661375i	$0.230027\pi$
$739$	18.6853	+	45.1102i	0.687349	+	1.65941i	−0.0627066	+	0.998032i	$0.519973\pi$
$740$	3.61418	−	4.71009i	0.132860	−	0.173146i
$741$	−23.4260	−	0.911515i	−0.860575	−	0.0334853i
$742$	0.943124	−	1.07543i	0.0346232	−	0.0394802i
$743$	−1.29635	+	0.639289i	−0.0475585	+	0.0234532i	−0.465912	−	0.884831i	$-0.654274\pi$
$743$	−1.29635	+	0.639289i	−0.0475585	+	0.0234532i	0.418354	+	0.908284i	$0.362607\pi$
$744$	25.6477	−	4.07217i	0.940291	−	0.149293i
$745$	−2.85099	−	3.25093i	−0.104452	−	0.119105i
$746$	11.1366	+	4.61294i	0.407741	+	0.168892i
$747$	−3.86471	−	11.8637i	−0.141402	−	0.434072i
$748$	4.45251	+	12.2408i	0.162800	+	0.447569i
$749$	−0.990971	+	0.572137i	−0.0362093	+	0.0209054i
$750$	0.227090	+	8.54836i	0.00829214	+	0.312142i
$751$	−25.7381	−	8.73692i	−0.939198	−	0.318815i	−0.190470	−	0.981693i	$-0.561001\pi$
$751$	−25.7381	−	8.73692i	−0.939198	−	0.318815i	−0.748727	+	0.662878i	$0.769335\pi$
$752$	3.65581	+	13.6437i	0.133314	+	0.497534i
$753$	−13.9149	+	16.7437i	−0.507086	+	0.610175i
$754$	13.4408	−	4.56254i	0.489485	−	0.166158i
$755$	3.21844	+	4.81674i	0.117131	+	0.175299i
$756$	0.236506	+	2.96202i	0.00860164	+	0.107728i
$757$	17.6756	−	7.32147i	0.642430	−	0.266103i	−0.0375938	−	0.999293i	$-0.511969\pi$
$757$	17.6756	−	7.32147i	0.642430	−	0.266103i	0.680024	+	0.733190i	$0.261969\pi$
$758$	−8.94672	−	4.41204i	−0.324960	−	0.160252i
$759$	10.3598	+	3.21249i	0.376036	+	0.116606i
$760$	−3.12484	−	6.33654i	−0.113350	−	0.229850i
$761$	−32.5721	+	8.72766i	−1.18074	+	0.316377i	−0.795218	−	0.606323i	$-0.792644\pi$
$761$	−32.5721	+	8.72766i	−1.18074	+	0.316377i	−0.385518	+	0.922700i	$0.625977\pi$
$762$	9.78083	−	6.91797i	0.354322	−	0.250611i
$763$	2.55967	−	0.336987i	0.0926664	−	0.0121998i
$764$	−38.7225			−1.40093
$765$	−16.7580	+	7.12436i	−0.605886	+	0.257582i
$766$	−8.72354			−0.315194
$767$	−30.0046	+	3.95019i	−1.08340	+	0.142633i
$768$	5.13740	+	2.36601i	0.185380	+	0.0853761i
$769$	−23.7420	+	6.36164i	−0.856157	+	0.229407i	−0.660093	−	0.751184i	$-0.729483\pi$
$769$	−23.7420	+	6.36164i	−0.856157	+	0.229407i	−0.196065	+	0.980591i	$0.562816\pi$
$770$	0.152604	+	0.309450i	0.00549946	+	0.0111518i
$771$	−6.64495	+	6.14720i	−0.239312	+	0.221386i
$772$	−11.9508	−	5.89348i	−0.430119	−	0.212111i
$773$	−14.8745	+	6.16122i	−0.534999	+	0.221604i	−0.633791	−	0.773504i	$-0.718502\pi$
$773$	−14.8745	+	6.16122i	−0.534999	+	0.221604i	0.0987921	+	0.995108i	$0.468502\pi$
$774$	−3.48233	−	1.23019i	−0.125170	−	0.0442182i
$775$	14.4395	+	21.6102i	0.518681	+	0.776261i
$776$	28.9973	−	9.84326i	1.04094	−	0.353352i
$777$	−1.19292	−	0.204515i	−0.0427957	−	0.00733694i
$778$	2.77659	+	10.3624i	0.0995457	+	0.371510i
$779$	−12.4014	−	4.20972i	−0.444327	−	0.150829i
$780$	18.7659	+	10.1798i	0.671927	+	0.364497i
$781$	−9.05145	+	5.22586i	−0.323886	+	0.186996i
$782$	−4.29393	−	4.68789i	−0.153551	−	0.167639i
$783$	−36.5503	+	7.81246i	−1.30620	+	0.279194i
$784$	−18.7040	−	7.74744i	−0.667999	−	0.276694i
$785$	5.64935	+	6.44185i	0.201634	+	0.229919i
$786$	3.36445	+	4.15153i	0.120006	+	0.148080i
$787$	14.3216	−	7.06264i	0.510510	−	0.251756i	−0.168743	−	0.985660i	$-0.553971\pi$
$787$	14.3216	−	7.06264i	0.510510	−	0.251756i	0.679253	+	0.733904i	$0.262304\pi$
$788$	25.6769	−	29.2789i	0.914700	−	1.04302i
$789$	−9.49375	+	15.0593i	−0.337987	+	0.536126i
$790$	−2.94476	+	3.83768i	−0.104770	+	0.136539i
$791$	−2.26846	−	5.47655i	−0.0806572	−	0.194724i
$792$	5.27283	−	6.69900i	0.187362	−	0.238038i
$793$	17.3030	+	3.44178i	0.614447	+	0.122221i
$794$	−0.0769092	+	1.17341i	−0.00272941	+	0.0416427i
$795$	4.24349	+	26.7268i	0.150501	+	0.947901i
$796$	1.66561	−	4.90673i	0.0590360	−	0.173914i
$797$	6.71176	−	5.15011i	0.237743	−	0.182426i	−0.483018	−	0.875610i	$-0.660459\pi$
$797$	6.71176	−	5.15011i	0.237743	−	0.182426i	0.720761	+	0.693184i	$0.243793\pi$
$798$	−0.402758	+	0.554791i	−0.0142575	+	0.0196394i
$799$	17.4027	+	9.55200i	0.615663	+	0.337926i
$800$		−	12.8166i		−	0.453134i
$801$	−5.76732	+	8.40514i	−0.203778	+	0.296981i
$802$	−1.33500	−	6.71148i	−0.0471404	−	0.236991i
$803$	13.6168	+	3.64861i	0.480526	+	0.128757i
$804$	−2.48087	+	14.4707i	−0.0874935	+	0.510341i
$805$	1.25465	+	1.10030i	0.0442205	+	0.0387803i
$806$	−18.0663	+	1.18413i	−0.636357	+	0.0417090i
$807$	22.9122	−	6.79634i	0.806546	−	0.239242i
$808$	−4.69540	−	3.60291i	−0.165184	−	0.126750i
$809$	−6.98362	+	4.66631i	−0.245531	+	0.164059i	−0.672247	−	0.740327i	$-0.734671\pi$
$809$	−6.98362	+	4.66631i	−0.245531	+	0.164059i	0.426716	+	0.904386i	$0.359671\pi$
$810$	4.63766	+	3.26704i	0.162951	+	0.114792i
$811$	−19.3160	+	28.9084i	−0.678276	+	1.01511i	0.319443	+	0.947606i	$0.396504\pi$
$811$	−19.3160	+	28.9084i	−0.678276	+	1.01511i	−0.997719	+	0.0675061i	$0.978496\pi$
$812$	−1.06461	+	3.97319i	−0.0373606	+	0.139432i
$813$	16.3101	−	1.50492i	0.572020	−	0.0527799i
$814$	1.00618	+	1.31129i	0.0352668	+	0.0459605i
$815$	5.71945	−	9.90638i	0.200344	−	0.347005i
$816$	19.4915	−	7.68189i	0.682338	−	0.268920i
$817$	4.22205	+	7.31281i	0.147711	+	0.255843i
$818$	1.38091	−	3.33380i	0.0482823	−	0.116564i
$819$	0.0536704	−	4.35198i	0.00187540	−	0.152070i
$820$	8.43323	+	8.43323i	0.294501	+	0.294501i
$821$	−6.99294	−	0.458342i	−0.244055	−	0.0159962i	−0.0571154	−	0.998368i	$-0.518190\pi$
$821$	−6.99294	−	0.458342i	−0.244055	−	0.0159962i	−0.186940	+	0.982371i	$0.559857\pi$
$822$	9.83330	+	10.6295i	0.342976	+	0.370747i
$823$	0.301901	+	4.60612i	0.0105236	+	0.160559i	0.999886	+	0.0150884i	$0.00480298\pi$
$823$	0.301901	+	4.60612i	0.0105236	+	0.160559i	−0.989363	+	0.145471i	$0.953530\pi$
$824$	−2.88200	+	21.8909i	−0.100399	+	0.762607i
$825$	8.29724	+	1.98866i	0.288873	+	0.0692364i
$826$	−0.391428	+	0.793737i	−0.0136195	+	0.0276176i
$827$	−4.28494	+	21.5419i	−0.149002	+	0.749084i	0.831953	+	0.554847i	$0.187223\pi$
$827$	−4.28494	+	21.5419i	−0.149002	+	0.749084i	−0.980955	+	0.194237i	$0.937777\pi$
$828$	5.31299	−	18.8933i	0.184639	−	0.656587i
$829$	−23.5987	+	23.5987i	−0.819616	+	0.819616i	−0.986052	−	0.166437i	$-0.946774\pi$
$829$	−23.5987	+	23.5987i	−0.819616	+	0.819616i	0.166437	+	0.986052i	$0.446774\pi$
$830$	−1.97100	+	1.72852i	−0.0684145	+	0.0599979i
$831$	−15.3796	+	0.408563i	−0.533512	+	0.0141729i
$832$	−15.6867	−	9.05675i	−0.543840	−	0.313986i
$833$	−26.0458	+	11.4542i	−0.902435	+	0.396864i
$834$	0.810585	−	7.74042i	0.0280683	−	0.268029i
$835$	−0.578900	−	4.39718i	−0.0200337	−	0.152171i
$836$	−9.09952	+	1.81001i	−0.314713	+	0.0626004i
$837$	47.6117	+	2.44093i	1.64570	+	0.0843708i
$838$	4.07859	+	2.72523i	0.140893	+	0.0941414i
$839$	16.5614	+	48.7884i	0.571765	+	1.68436i	0.718786	+	0.695231i	$0.244698\pi$
$839$	16.5614	+	48.7884i	0.571765	+	1.68436i	−0.147022	+	0.989133i	$0.546969\pi$
$840$	1.16055	−	0.611159i	0.0400429	−	0.0210870i
$841$	−22.5446	−	2.96806i	−0.777401	−	0.102347i
$842$	−4.92964	−	0.648999i	−0.169887	−	0.0223660i
$843$	−44.0885	−	27.7944i	−1.51849	−	0.957291i
$844$	−13.0556	−	38.4606i	−0.449393	−	1.32387i
$845$	−10.0877	−	6.74040i	−0.347028	−	0.231877i
$846$	−0.328354	−	6.17578i	−0.0112890	−	0.212328i
$847$	−2.46245	+	0.489812i	−0.0846108	+	0.0168301i
$848$	−4.06396	−	30.8688i	−0.139557	−	1.06004i
$849$	19.9219	+	14.4626i	0.683720	+	0.496355i
$850$	−3.61173	−	3.45887i	−0.123881	−	0.118638i
$851$	6.92305	+	3.99702i	0.237319	+	0.137016i
$852$	9.88755	+	16.1213i	0.338742	+	0.552307i
$853$	−5.29504	+	4.64363i	−0.181299	+	0.158995i	−0.745185	−	0.666858i	$-0.767639\pi$
$853$	−5.29504	+	4.64363i	−0.181299	+	0.158995i	0.563886	+	0.825852i	$0.309306\pi$
$854$	0.364803	−	0.364803i	0.0124833	−	0.0124833i
$855$	−3.20221	−	12.5688i	−0.109513	−	0.429843i
$856$	1.15891	−	5.82625i	0.0396108	−	0.199137i
$857$	9.43767	−	19.1377i	0.322385	−	0.653731i	−0.673996	−	0.738735i	$-0.735424\pi$
$857$	9.43767	−	19.1377i	0.322385	−	0.653731i	0.996381	+	0.0850037i	$0.0270902\pi$
$858$	−4.08967	+	4.31288i	−0.139619	+	0.147239i
$859$	2.65570	−	20.1721i	0.0906114	−	0.688262i	−0.884499	−	0.466542i	$-0.845500\pi$
$859$	2.65570	−	20.1721i	0.0906114	−	0.688262i	0.975110	−	0.221720i	$-0.0711671\pi$
$860$	−0.502930	−	7.67323i	−0.0171498	−	0.261655i
$861$	0.720116	−	2.32226i	0.0245415	−	0.0791424i
$862$	−7.12430	−	0.466951i	−0.242654	−	0.0159044i
$863$	−8.04291	−	8.04291i	−0.273784	−	0.273784i	0.556837	−	0.830621i	$-0.312015\pi$
$863$	−8.04291	−	8.04291i	−0.273784	−	0.273784i	−0.830621	+	0.556837i	$0.812015\pi$
$864$	−18.8530	−	14.0448i	−0.641393	−	0.477815i
$865$	14.0154	−	33.8361i	0.476537	−	1.15046i
$866$	1.67430	+	2.89997i	0.0568951	+	0.0985452i
$867$	11.1499	−	27.2522i	0.378670	−	0.925532i
$868$	2.62336	−	4.54379i	0.0890426	−	0.154226i
$869$	8.12419	+	10.5877i	0.275594	+	0.359162i
$870$	4.53470	+	6.41130i	0.153741	+	0.217363i
$871$	5.56579	−	20.7718i	0.188590	−	0.703826i
$872$	−7.44629	+	11.1442i	−0.252163	+	0.377389i
$873$	55.8223	−	6.64993i	1.88930	−	0.225066i
$874$	3.76499	−	2.51569i	0.127353	−	0.0850944i
$875$	2.87967	+	2.20965i	0.0973507	+	0.0746998i
$876$	5.94535	−	24.8056i	0.200875	−	0.838103i
$877$	11.9857	−	0.785586i	0.404729	−	0.0265273i	0.138320	−	0.990388i	$-0.455830\pi$
$877$	11.9857	−	0.785586i	0.404729	−	0.0265273i	0.266409	+	0.963860i	$0.414163\pi$
$878$	−6.42547	−	5.63498i	−0.216849	−	0.190171i
$879$	50.9853	−	18.8314i	1.71969	−	0.635168i
$880$	7.25436	+	1.94380i	0.244545	+	0.0655255i
$881$	−9.38269	−	47.1700i	−0.316111	−	1.58920i	−0.732993	−	0.680236i	$-0.761877\pi$
$881$	−9.38269	−	47.1700i	−0.316111	−	1.58920i	0.416882	−	0.908960i	$-0.363123\pi$
$882$	7.30895	+	5.01515i	0.246105	+	0.168869i
$883$		−	20.2173i		−	0.680366i	−0.940359	−	0.340183i	$-0.889511\pi$
$883$		−	20.2173i		−	0.680366i	0.940359	−	0.340183i	$-0.110489\pi$
$884$	−33.1445	+	9.65351i	−1.11477	+	0.324683i
$885$	−6.81594	−	15.2933i	−0.229115	−	0.514077i
$886$	−9.18583	+	7.04853i	−0.308604	+	0.236800i
$887$	−7.80991	+	23.0072i	−0.262231	+	0.772508i	0.733456	+	0.679737i	$0.237906\pi$
$887$	−7.80991	+	23.0072i	−0.262231	+	0.772508i	−0.995687	+	0.0927713i	$0.970427\pi$
$888$	4.88152	−	3.95604i	0.163813	−	0.132756i
$889$	0.332582	−	5.07423i	0.0111545	−	0.170184i
$890$	2.10058	+	0.417830i	0.0704114	+	0.0140057i
$891$	12.0177	−	10.0259i	0.402609	−	0.335880i
$892$	−14.3193	−	34.5699i	−0.479447	−	1.15749i
$893$	−8.60793	+	11.2181i	−0.288053	+	0.375398i
$894$	−1.01493	−	1.92730i	−0.0339445	−	0.0644585i
$895$	15.1714	−	17.2997i	0.507124	−	0.578264i
$896$	−3.02971	+	1.49409i	−0.101216	+	0.0499140i
$897$	−10.2917	+	26.8411i	−0.343629	+	0.896198i
$898$	9.76585	+	11.1358i	0.325891	+	0.371607i
$899$	60.9715	+	25.2552i	2.03351	+	0.842308i
$900$	3.19843	−	15.1037i	0.106614	−	0.503458i
$901$	−35.2837	−	25.8820i	−1.17547	−	0.862255i
$902$	−2.87546	+	1.66015i	−0.0957424	+	0.0552769i
$903$	−1.33633	+	0.819598i	−0.0444701	+	0.0272745i
$904$	29.1403	+	9.89180i	0.969192	+	0.328996i
$905$	−0.338612	−	1.26372i	−0.0112558	−	0.0420074i
$906$	1.01109	+	2.73749i	0.0335913	+	0.0909471i
$907$	2.94670	−	1.00027i	0.0978436	−	0.0332134i	−0.272088	−	0.962272i	$-0.587714\pi$
$907$	2.94670	−	1.00027i	0.0978436	−	0.0332134i	0.369932	+	0.929059i	$0.379381\pi$
$908$	12.9378	+	19.3628i	0.429355	+	0.642576i
$909$	−7.06259	−	8.25655i	−0.234251	−	0.273852i
$910$	−0.844840	+	0.349944i	−0.0280062	+	0.0116005i
$911$	11.9546	+	5.89534i	0.396072	+	0.195321i	0.629408	−	0.777075i	$-0.283297\pi$
$911$	11.9546	+	5.89534i	0.396072	+	0.195321i	−0.233336	+	0.972396i	$0.574964\pi$
$912$	3.29892	+	14.5535i	0.109238	+	0.481915i
$913$	3.19888	+	6.48669i	0.105868	+	0.214678i
$914$	0.291511	−	0.0781101i	0.00964232	−	0.00258365i
$915$	0.896782	+	9.71918i	0.0296467	+	0.321306i
$916$	−49.4211	+	6.50641i	−1.63292	+	0.214978i
$917$	2.26819			0.0749021
$918$	−9.04583	+	1.52246i	−0.298557	+	0.0502486i
$919$	23.5802			0.777841			0.388920	−	0.921271i	$-0.372848\pi$
$919$	23.5802			0.777841			0.388920	+	0.921271i	$0.372848\pi$
$920$	−8.58913	+	1.13078i	−0.283175	+	0.0372807i
$921$	−5.06330	−	54.8752i	−0.166841	−	1.80820i
$922$	−6.23913	+	1.67177i	−0.205475	+	0.0550568i
$923$	−12.2516	−	24.8438i	−0.403266	−	0.817743i
$924$	−0.380770	−	1.67980i	−0.0125264	−	0.0552614i
$925$	5.63993	+	2.78131i	0.185440	+	0.0914488i
$926$	−0.657313	+	0.272268i	−0.0216007	+	0.00894729i
$927$	−13.5017	+	38.2197i	−0.443454	+	1.25530i
$928$	−18.0804	−	27.0593i	−0.593520	−	0.888265i
$929$	−16.5760	+	5.62680i	−0.543842	+	0.184609i	−0.579822	−	0.814743i	$-0.696878\pi$
$929$	−16.5760	+	5.62680i	−0.543842	+	0.184609i	0.0359804	+	0.999352i	$0.488545\pi$
$930$	−3.47049	−	9.39622i	−0.113802	−	0.308114i
$931$	−5.24540	−	19.5761i	−0.171911	−	0.641580i
$932$	15.2359	+	5.17189i	0.499069	+	0.169411i
$933$	−47.5816	+	29.1829i	−1.55775	+	0.955405i
$934$	−3.08296	+	1.77995i	−0.100878	+	0.0582417i
$935$	9.02491	−	5.47396i	0.295146	−	0.179018i
$936$	16.8025	+	15.1060i	0.549207	+	0.493755i
$937$	38.3879	+	15.9008i	1.25408	+	0.519456i	0.908087	−	0.418782i	$-0.137543\pi$
$937$	38.3879	+	15.9008i	1.25408	+	0.519456i	0.345991	+	0.938238i	$0.387543\pi$
$938$	−0.414638	−	0.472805i	−0.0135384	−	0.0154376i
$939$	−8.09643	+	21.1158i	−0.264217	+	0.689089i
$940$	11.5488	−	5.69524i	0.376681	−	0.185758i
$941$	10.1862	−	11.6152i	0.332062	−	0.378644i	−0.561582	−	0.827421i	$-0.689807\pi$
$941$	10.1862	−	11.6152i	0.332062	−	0.378644i	0.893644	+	0.448777i	$0.148140\pi$
$942$	2.01113	+	3.81901i	0.0655261	+	0.124430i
$943$	−9.77598	+	12.7403i	−0.318350	+	0.414881i
$944$	7.37193	+	17.7974i	0.239936	+	0.579256i
$945$	2.31678	−	0.656244i	0.0753647	−	0.0213476i
$946$	2.09967	+	0.417650i	0.0682661	+	0.0135790i
$947$	0.363107	−	5.53995i	0.0117994	−	0.180024i	−0.987891	−	0.155149i	$-0.950414\pi$
$947$	0.363107	−	5.53995i	0.0117994	−	0.180024i	0.999691	−	0.0248756i	$-0.00791896\pi$
$948$	18.7607	−	15.2039i	0.609320	−	0.493800i
$949$	−12.0096	+	35.3792i	−0.389849	+	1.14846i
$950$	2.82593	−	2.16841i	0.0916851	−	0.0703525i
$951$	−13.5537	−	30.4112i	−0.439510	−	0.986149i
$952$	−0.638182	+	2.02264i	−0.0206836	+	0.0655540i
$953$		−	15.3612i		−	0.497600i	−0.968555	−	0.248800i	$-0.919964\pi$
$953$		−	15.3612i		−	0.497600i	0.968555	−	0.248800i	$-0.0800361\pi$
$954$	−1.05927	+	13.5911i	−0.0342952	+	0.440027i
$955$	6.12173	+	30.7760i	0.198094	+	0.995888i
$956$	−34.4709	−	9.23645i	−1.11487	−	0.298728i
$957$	20.3232	−	7.50638i	0.656956	−	0.242647i
$958$	−4.45412	−	3.90615i	−0.143906	−	0.126202i
$959$	6.13322	−	0.401992i	0.198052	−	0.0129810i
$960$	2.33574	−	9.74533i	0.0753857	−	0.314529i
$961$	−42.1896	−	32.3732i	−1.36095	−	1.04430i
$962$	−3.64230	+	2.43371i	−0.117433	+	0.0784659i
$963$	4.29726	−	10.0231i	0.138477	−	0.322989i
$964$	18.5231	−	27.7218i	0.596590	−	0.892861i
$965$	−2.79471	+	10.4300i	−0.0899650	+	0.335754i
$966$	0.485433	+	0.686320i	0.0156185	+	0.0220820i
$967$	−16.6461	−	21.6936i	−0.535301	−	0.697618i	0.444909	−	0.895576i	$-0.353236\pi$
$967$	−16.6461	−	21.6936i	−0.535301	−	0.697618i	−0.980211	+	0.197957i	$0.936569\pi$
$968$	6.51701	−	11.2878i	0.209464	−	0.362803i
$969$	17.9793	+	10.7987i	0.577578	+	0.346904i
$970$	−5.90578	−	10.2291i	−0.189623	−	0.328437i
$971$	15.7860	−	38.1109i	0.506598	−	1.22304i	−0.439232	−	0.898374i	$-0.644749\pi$
$971$	15.7860	−	38.1109i	0.506598	−	1.22304i	0.945830	−	0.324662i	$-0.105251\pi$
$972$	−18.7125	−	21.2561i	−0.600203	−	0.681789i
$973$	−2.33592	−	2.33592i	−0.0748862	−	0.0748862i
$974$	10.1634	+	0.666142i	0.325655	+	0.0213446i
$975$	−6.69756	+	21.5986i	−0.214494	+	0.691708i
$976$	−0.734458	−	11.2057i	−0.0235094	−	0.358685i
$977$	2.97193	−	22.5741i	0.0950805	−	0.722208i	−0.875805	−	0.482665i	$-0.839669\pi$
$977$	2.97193	−	22.5741i	0.0950805	−	0.722208i	0.970886	−	0.239543i	$-0.0769978\pi$
$978$	3.96496	−	4.18137i	0.126785	−	0.133705i
$979$	2.61337	−	5.29939i	0.0835237	−	0.169369i
$980$	−3.60058	+	18.1014i	−0.115016	+	0.578227i
$981$	−17.6118	+	17.1827i	−0.562302	+	0.548602i
$982$	−8.00610	+	8.00610i	−0.255485	+	0.255485i
$983$	−28.0545	+	24.6031i	−0.894798	+	0.784717i	−0.977297	−	0.211874i	$-0.932043\pi$
$983$	−28.0545	+	24.6031i	−0.894798	+	0.784717i	0.0824986	+	0.996591i	$0.473710\pi$
$984$	6.59911	+	10.7596i	0.210372	+	0.343004i
$985$	−27.3297	−	15.7788i	−0.870795	−	0.502754i
$986$	−12.5048	−	2.20753i	−0.398235	−	0.0703022i
$987$	−2.12433	−	1.54219i	−0.0676182	−	0.0490883i
$988$	−3.20953	−	24.3788i	−0.102109	−	0.775593i
$989$	10.1552	−	2.01999i	0.322915	−	0.0642319i
$990$	−2.93104	−	1.49064i	−0.0931544	−	0.0473756i
$991$	30.8345	+	20.6029i	0.979489	+	0.654474i	0.938715	−	0.344695i	$-0.112018\pi$
$991$	30.8345	+	20.6029i	0.979489	+	0.654474i	0.0407744	+	0.999168i	$0.487018\pi$
$992$	13.3432	+	39.3079i	0.423648	+	1.24803i
$993$	40.8110	+	25.7282i	1.29510	+	0.816461i
$994$	−0.803121	−	0.105733i	−0.0254735	−	0.00335364i
$995$	−4.16311	−	0.548084i	−0.131979	−	0.0173754i
$996$	11.5795	−	6.09788i	0.366911	−	0.193219i
$997$	−3.42621	−	10.0933i	−0.108509	−	0.319658i	0.879090	−	0.476656i	$-0.158151\pi$
$997$	−3.42621	−	10.0933i	−0.108509	−	0.319658i	−0.987599	+	0.156999i	$0.949818\pi$
$998$	−10.8653	−	7.25997i	−0.343936	−	0.229810i
$999$	10.2717	−	5.24842i	0.324982	−	0.166053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.11	yes	256
3.2	odd	2		459.2.y.a.368.6		256
9.2	odd	6	inner	153.2.s.a.11.11	✓	256
9.7	even	3		459.2.y.a.62.6		256
17.14	odd	16	inner	153.2.s.a.14.11	yes	256
51.14	even	16		459.2.y.a.422.6		256
153.65	even	48	inner	153.2.s.a.65.11	yes	256
153.133	odd	48		459.2.y.a.116.6		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.11	✓	256	9.2	odd	6	inner
153.2.s.a.14.11	yes	256	17.14	odd	16	inner
153.2.s.a.65.11	yes	256	153.65	even	48	inner
153.2.s.a.113.11	yes	256	1.1	even	1	trivial
459.2.y.a.62.6		256	9.7	even	3
459.2.y.a.116.6		256	153.133	odd	48
459.2.y.a.368.6		256	3.2	odd	2
459.2.y.a.422.6		256	51.14	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.424498 - 0.0558863i) q^{2} +(0.159139 + 1.72472i) q^{3} +(-1.75478 + 0.470191i) q^{4} +(0.651116 + 1.32033i) q^{5} +(0.163943 + 0.723249i) q^{6} +(0.282318 + 0.139224i) q^{7} +(-1.50976 + 0.625364i) q^{8} +(-2.94935 + 0.548943i) q^{9} +O(q^{10})\)	\(q+(0.424498 - 0.0558863i) q^{2} +(0.159139 + 1.72472i) q^{3} +(-1.75478 + 0.470191i) q^{4} +(0.651116 + 1.32033i) q^{5} +(0.163943 + 0.723249i) q^{6} +(0.282318 + 0.139224i) q^{7} +(-1.50976 + 0.625364i) q^{8} +(-2.94935 + 0.548943i) q^{9} +(0.350186 + 0.524091i) q^{10} +(1.64668 - 0.558972i) q^{11} +(-1.09020 - 2.95168i) q^{12} +(1.19285 + 4.45178i) q^{13} +(0.127624 + 0.0433227i) q^{14} +(-2.17359 + 1.33311i) q^{15} +(2.54064 - 1.46684i) q^{16} +(0.980810 - 4.00475i) q^{17} +(-1.22132 + 0.397854i) q^{18} +(2.71326 + 1.12387i) q^{19} +(-1.76337 - 2.01074i) q^{20} +(-0.195195 + 0.509078i) q^{21} +(0.667774 - 0.329310i) q^{22} +(2.37437 - 2.70745i) q^{23} +(-1.31884 - 2.50440i) q^{24} +(1.72448 - 2.24739i) q^{25} +(0.755157 + 1.82311i) q^{26} +(-1.41613 - 4.99946i) q^{27} +(-0.560867 - 0.111563i) q^{28} +(0.470444 - 7.17759i) q^{29} +(-0.848184 + 0.687379i) q^{30} +(-2.94918 + 8.68799i) q^{31} +(3.58944 - 2.75428i) q^{32} +(1.22612 + 2.75111i) q^{33} +(0.192542 - 1.75482i) q^{34} +0.463405i q^{35} +(4.91734 - 2.35003i) q^{36} +(0.433080 + 2.17724i) q^{37} +(1.21458 + 0.325446i) q^{38} +(-7.48827 + 2.76579i) q^{39} +(-1.80872 - 1.58620i) q^{40} +(-4.44987 + 0.291660i) q^{41} +(-0.0544096 + 0.227011i) q^{42} +(2.28110 + 1.75035i) q^{43} +(-2.62673 + 1.75512i) q^{44} +(-2.64516 - 3.53670i) q^{45} +(0.856606 - 1.28200i) q^{46} +(-1.24615 + 4.65071i) q^{47} +(2.93420 + 4.14847i) q^{48} +(-4.20101 - 5.47486i) q^{49} +(0.606441 - 1.05039i) q^{50} +(7.06317 + 1.05431i) q^{51} +(-4.18637 - 7.25101i) q^{52} +(4.06143 - 9.80516i) q^{53} +(-0.880547 - 2.04312i) q^{54} +(1.81021 + 1.81021i) q^{55} +(-0.513299 - 0.0336434i) q^{56} +(-1.50658 + 4.85847i) q^{57} +(-0.201426 - 3.07317i) q^{58} +(-0.857092 + 6.51026i) q^{59} +(3.18735 - 3.36132i) q^{60} +(1.69302 - 3.43311i) q^{61} +(-0.766381 + 3.85286i) q^{62} +(-0.909082 - 0.255644i) q^{63} +(-2.77905 + 2.77905i) q^{64} +(-5.10115 + 4.47359i) q^{65} +(0.674237 + 1.09932i) q^{66} +(-4.04083 - 2.33298i) q^{67} +(0.161894 + 7.48860i) q^{68} +(5.04746 + 3.66427i) q^{69} +(0.0258980 + 0.196715i) q^{70} +(-5.89482 + 1.17255i) q^{71} +(4.10953 - 2.67319i) q^{72} +(6.74041 + 4.50380i) q^{73} +(0.305519 + 0.900031i) q^{74} +(4.15055 + 2.61660i) q^{75} +(-5.28959 - 0.696388i) q^{76} +(0.542710 + 0.0714492i) q^{77} +(-3.02419 + 1.59257i) q^{78} +(2.46684 + 7.26708i) q^{79} +(3.59096 + 2.39940i) q^{80} +(8.39732 - 3.23805i) q^{81} +(-1.87266 + 0.372496i) q^{82} +(0.542874 + 4.12354i) q^{83} +(0.103160 - 0.985096i) q^{84} +(5.92622 - 1.31256i) q^{85} +(1.06615 + 0.615539i) q^{86} +(12.4542 - 0.330850i) q^{87} +(-2.13653 + 1.87369i) q^{88} +(2.40264 - 2.40264i) q^{89} +(-1.32052 - 1.35350i) q^{90} +(-0.283031 + 1.42289i) q^{91} +(-2.89347 + 5.86737i) q^{92} +(-15.4537 - 3.70391i) q^{93} +(-0.269080 + 2.04386i) q^{94} +(0.282766 + 4.31417i) q^{95} +(5.32159 + 5.75249i) q^{96} +(-18.6989 - 1.22559i) q^{97} +(-2.08929 - 2.08929i) q^{98} +(-4.54979 + 2.55254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

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