LMFDB - Embedded newform 400.2.bm.a.227.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(67,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 15, 13]))

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

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

chi := DirichletCharacter("400.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bm (of order $20$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$58$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			227.27
Character	$\chi$	$=$	400.227
Dual form			400.2.bm.a.363.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.265938 + 1.38898i) q^{2} +(2.91719 + 0.947853i) q^{3} +(-1.85855 - 0.738766i) q^{4} +(-0.815404 - 2.08209i) q^{5} +(-2.09234 + 3.79986i) q^{6} +(2.13068 + 2.13068i) q^{7} +(1.52039 - 2.38504i) q^{8} +(5.18453 + 3.76678i) q^{9} +O(q^{10})$	\(q+(-0.265938 + 1.38898i) q^{2} +(2.91719 + 0.947853i) q^{3} +(-1.85855 - 0.738766i) q^{4} +(-0.815404 - 2.08209i) q^{5} +(-2.09234 + 3.79986i) q^{6} +(2.13068 + 2.13068i) q^{7} +(1.52039 - 2.38504i) q^{8} +(5.18453 + 3.76678i) q^{9} +(3.10884 - 0.578876i) q^{10} +(1.86799 + 0.295860i) q^{11} +(-4.72152 - 3.91676i) q^{12} +(-2.19177 - 1.59242i) q^{13} +(-3.52610 + 2.39285i) q^{14} +(-0.405170 - 6.84675i) q^{15} +(2.90845 + 2.74607i) q^{16} +(-2.61405 + 5.13036i) q^{17} +(-6.61076 + 6.19950i) q^{18} +(2.86516 - 5.62320i) q^{19} +(-0.0227085 + 4.47208i) q^{20} +(4.19602 + 8.23516i) q^{21} +(-0.907714 + 2.51593i) q^{22} +(-0.777021 + 4.90592i) q^{23} +(6.69595 - 5.51650i) q^{24} +(-3.67023 + 3.39549i) q^{25} +(2.79472 - 2.62085i) q^{26} +(6.14515 + 8.45807i) q^{27} +(-2.38591 - 5.53405i) q^{28} +(-2.71486 - 5.32821i) q^{29} +(9.61778 + 1.25803i) q^{30} +(-0.552358 + 0.179472i) q^{31} +(-4.58772 + 3.30951i) q^{32} +(5.16885 + 2.63366i) q^{33} +(-6.43081 - 4.99523i) q^{34} +(2.69891 - 6.17363i) q^{35} +(-6.85296 - 10.8309i) q^{36} +(-4.77149 - 3.46669i) q^{37} +(7.04858 + 5.47508i) q^{38} +(-4.88444 - 6.72286i) q^{39} +(-6.20561 - 1.22084i) q^{40} +(1.55176 - 2.13581i) q^{41} +(-12.5544 + 3.63817i) q^{42} +2.00825 q^{43} +(-3.25319 - 1.92988i) q^{44} +(3.61531 - 13.8661i) q^{45} +(-6.60761 - 2.38394i) q^{46} +(-3.37142 - 6.61678i) q^{47} +(5.88163 + 10.7676i) q^{48} +2.07955i q^{49} +(-3.74024 - 6.00089i) q^{50} +(-12.4885 + 12.4885i) q^{51} +(2.89711 + 4.57880i) q^{52} +(-7.29703 - 2.37095i) q^{53} +(-13.3823 + 6.28619i) q^{54} +(-0.907156 - 4.13057i) q^{55} +(8.32121 - 1.84227i) q^{56} +(13.6882 - 13.6882i) q^{57} +(8.12278 - 2.35392i) q^{58} +(-3.08394 + 0.488448i) q^{59} +(-4.30512 + 13.0244i) q^{60} +(14.2512 + 2.25717i) q^{61} +(-0.102391 - 0.814945i) q^{62} +(3.02076 + 19.0723i) q^{63} +(-3.37680 - 7.25239i) q^{64} +(-1.52838 + 5.86194i) q^{65} +(-5.03270 + 6.47906i) q^{66} +(1.33320 + 4.10317i) q^{67} +(8.64849 - 7.60388i) q^{68} +(-6.91681 + 13.5750i) q^{69} +(7.85733 + 5.39054i) q^{70} +(0.503455 - 1.54948i) q^{71} +(16.8664 - 6.63831i) q^{72} +(-6.88778 - 1.09092i) q^{73} +(6.08410 - 5.70560i) q^{74} +(-13.9252 + 6.42647i) q^{75} +(-9.47929 + 8.33433i) q^{76} +(3.34970 + 4.61046i) q^{77} +(10.6369 - 4.99655i) q^{78} +(3.44016 - 10.5877i) q^{79} +(3.34602 - 8.29482i) q^{80} +(3.96862 + 12.2142i) q^{81} +(2.55394 + 2.72336i) q^{82} +(-14.6610 + 4.76365i) q^{83} +(-1.71468 - 18.4054i) q^{84} +(12.8134 + 1.25938i) q^{85} +(-0.534068 + 2.78942i) q^{86} +(-2.86940 - 18.1167i) q^{87} +(3.54572 - 4.00540i) q^{88} +(-5.42146 + 3.93892i) q^{89} +(18.2984 + 8.70913i) q^{90} +(-1.27703 - 8.06288i) q^{91} +(5.06846 - 8.54388i) q^{92} -1.78145 q^{93} +(10.0872 - 2.92320i) q^{94} +(-14.0443 - 1.38036i) q^{95} +(-16.5202 + 5.30598i) q^{96} +(16.1691 - 8.23856i) q^{97} +(-2.88847 - 0.553032i) q^{98} +(8.57021 + 8.57021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9}+O(q^{10}) $ 464 * q - 8 * q^2 - 10 * q^3 - 10 * q^4 - 8 * q^5 - 6 * q^6 - 16 * q^7 - 2 * q^8 + 108 * q^9	\( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9} - 4 q^{10} - 6 q^{11} - 22 q^{12} - 6 q^{13} - 10 q^{14} - 12 q^{15} + 34 q^{16} - 16 q^{17} - 24 q^{18} - 10 q^{19} - 14 q^{20} - 36 q^{21} - 60 q^{22} - 16 q^{23} - 12 q^{24} - 16 q^{26} - 10 q^{27} + 6 q^{28} - 10 q^{29} - 106 q^{30} + 2 q^{32} - 16 q^{33} - 10 q^{34} - 60 q^{35} + 10 q^{36} - 6 q^{37} - 38 q^{38} - 20 q^{39} + 16 q^{40} - 38 q^{42} + 16 q^{43} - 80 q^{44} - 4 q^{45} - 6 q^{46} + 24 q^{47} + 60 q^{48} + 38 q^{50} - 16 q^{51} - 160 q^{52} - 10 q^{53} - 16 q^{55} - 6 q^{56} - 12 q^{57} - 110 q^{58} - 10 q^{59} - 50 q^{60} - 6 q^{61} - 14 q^{62} - 12 q^{63} + 20 q^{64} - 16 q^{65} - 6 q^{66} + 30 q^{67} - 50 q^{68} - 22 q^{69} + 38 q^{70} - 12 q^{71} + 172 q^{72} - 8 q^{73} + 8 q^{74} - 58 q^{75} - 16 q^{76} + 60 q^{77} - 48 q^{78} + 208 q^{80} - 96 q^{81} - 14 q^{82} - 10 q^{83} - 22 q^{84} + 2 q^{85} - 126 q^{86} - 72 q^{87} + 86 q^{88} + 110 q^{90} + 64 q^{91} - 66 q^{92} - 28 q^{93} - 10 q^{94} - 160 q^{95} - 36 q^{96} - 16 q^{97} - 44 q^{98} - 12 q^{99}+O(q^{100}) \) 464 * q - 8 * q^2 - 10 * q^3 - 10 * q^4 - 8 * q^5 - 6 * q^6 - 16 * q^7 - 2 * q^8 + 108 * q^9 - 4 * q^10 - 6 * q^11 - 22 * q^12 - 6 * q^13 - 10 * q^14 - 12 * q^15 + 34 * q^16 - 16 * q^17 - 24 * q^18 - 10 * q^19 - 14 * q^20 - 36 * q^21 - 60 * q^22 - 16 * q^23 - 12 * q^24 - 16 * q^26 - 10 * q^27 + 6 * q^28 - 10 * q^29 - 106 * q^30 + 2 * q^32 - 16 * q^33 - 10 * q^34 - 60 * q^35 + 10 * q^36 - 6 * q^37 - 38 * q^38 - 20 * q^39 + 16 * q^40 - 38 * q^42 + 16 * q^43 - 80 * q^44 - 4 * q^45 - 6 * q^46 + 24 * q^47 + 60 * q^48 + 38 * q^50 - 16 * q^51 - 160 * q^52 - 10 * q^53 - 16 * q^55 - 6 * q^56 - 12 * q^57 - 110 * q^58 - 10 * q^59 - 50 * q^60 - 6 * q^61 - 14 * q^62 - 12 * q^63 + 20 * q^64 - 16 * q^65 - 6 * q^66 + 30 * q^67 - 50 * q^68 - 22 * q^69 + 38 * q^70 - 12 * q^71 + 172 * q^72 - 8 * q^73 + 8 * q^74 - 58 * q^75 - 16 * q^76 + 60 * q^77 - 48 * q^78 + 208 * q^80 - 96 * q^81 - 14 * q^82 - 10 * q^83 - 22 * q^84 + 2 * q^85 - 126 * q^86 - 72 * q^87 + 86 * q^88 + 110 * q^90 + 64 * q^91 - 66 * q^92 - 28 * q^93 - 10 * q^94 - 160 * q^95 - 36 * q^96 - 16 * q^97 - 44 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{20}\right)$	$-1$

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 $

$2$	−0.265938	+	1.38898i	−0.188046	+	0.982160i
$2$	−0.265938	+	1.38898i	−0.188046	+	0.982160i
$3$	2.91719	+	0.947853i	1.68424	+	0.547243i	0.985727	−	0.168353i	$-0.0538447\pi$
$3$	2.91719	+	0.947853i	1.68424	+	0.547243i	0.698515	+	0.715596i	$0.253845\pi$
$4$	−1.85855	−	0.738766i	−0.929277	−	0.369383i
$5$	−0.815404	−	2.08209i	−0.364660	−	0.931141i
$5$	−0.815404	−	2.08209i	−0.364660	−	0.931141i
$6$	−2.09234	+	3.79986i	−0.854196	+	1.55129i
$7$	2.13068	+	2.13068i	0.805320	+	0.805320i	0.983921	−	0.178602i	$-0.0571574\pi$
$7$	2.13068	+	2.13068i	0.805320	+	0.805320i	−0.178602	+	0.983921i	$0.557157\pi$
$8$	1.52039	−	2.38504i	0.537540	−	0.843238i
$9$	5.18453	+	3.76678i	1.72818	+	1.25559i
$10$	3.10884	−	0.578876i	0.983102	−	0.183057i
$11$	1.86799	+	0.295860i	0.563220	+	0.0892053i	0.431551	−	0.902089i	$-0.357966\pi$
$11$	1.86799	+	0.295860i	0.563220	+	0.0892053i	0.131669	+	0.991294i	$0.457966\pi$
$12$	−4.72152	−	3.91676i	−1.36298	−	1.13067i
$13$	−2.19177	−	1.59242i	−0.607888	−	0.441657i	0.240782	−	0.970579i	$-0.422596\pi$
$13$	−2.19177	−	1.59242i	−0.607888	−	0.441657i	−0.848670	+	0.528923i	$0.822596\pi$
$14$	−3.52610	+	2.39285i	−0.942390	+	0.639516i
$15$	−0.405170	−	6.84675i	−0.104614	−	1.76782i
$16$	2.90845	+	2.74607i	0.727112	+	0.686519i
$17$	−2.61405	+	5.13036i	−0.634000	+	1.24429i	0.320829	+	0.947137i	$0.396039\pi$
$17$	−2.61405	+	5.13036i	−0.634000	+	1.24429i	−0.954828	+	0.297157i	$0.903961\pi$
$18$	−6.61076	+	6.19950i	−1.55817	+	1.46124i
$19$	2.86516	−	5.62320i	0.657313	−	1.29005i	−0.286027	−	0.958222i	$-0.592335\pi$
$19$	2.86516	−	5.62320i	0.657313	−	1.29005i	0.943340	−	0.331828i	$-0.107665\pi$
$20$	−0.0227085	+	4.47208i	−0.00507778	+	0.999987i
$21$	4.19602	+	8.23516i	0.915647	+	1.79706i
$22$	−0.907714	+	2.51593i	−0.193525	+	0.536397i
$23$	−0.777021	+	4.90592i	−0.162020	+	1.02296i	0.763927	+	0.645302i	$0.223269\pi$
$23$	−0.777021	+	4.90592i	−0.162020	+	1.02296i	−0.925947	+	0.377653i	$0.876731\pi$
$24$	6.69595	−	5.51650i	1.36680	−	1.12605i
$25$	−3.67023	+	3.39549i	−0.734047	+	0.679099i
$26$	2.79472	−	2.62085i	0.548089	−	0.513992i
$27$	6.14515	+	8.45807i	1.18263	+	1.62776i
$28$	−2.38591	−	5.53405i	−0.450894	−	1.04584i
$29$	−2.71486	−	5.32821i	−0.504136	−	0.989423i	−0.993117	−	0.117129i	$-0.962631\pi$
$29$	−2.71486	−	5.32821i	−0.504136	−	0.989423i	0.488980	−	0.872295i	$-0.337369\pi$
$30$	9.61778	+	1.25803i	1.75596	+	0.229685i
$31$	−0.552358	+	0.179472i	−0.0992064	+	0.0322341i	−0.358200	−	0.933645i	$-0.616609\pi$
$31$	−0.552358	+	0.179472i	−0.0992064	+	0.0322341i	0.258993	+	0.965879i	$0.416609\pi$
$32$	−4.58772	+	3.30951i	−0.811002	+	0.585044i
$33$	5.16885	+	2.63366i	0.899781	+	0.458461i
$34$	−6.43081	−	4.99523i	−1.10288	−	0.856674i
$35$	2.69891	−	6.17363i	0.456198	−	1.04353i
$36$	−6.85296	−	10.8309i	−1.14216	−	1.80515i
$37$	−4.77149	−	3.46669i	−0.784428	−	0.569920i	0.121877	−	0.992545i	$-0.461109\pi$
$37$	−4.77149	−	3.46669i	−0.784428	−	0.569920i	−0.906305	+	0.422625i	$0.861109\pi$
$38$	7.04858	+	5.47508i	1.14343	+	0.888176i
$39$	−4.88444	−	6.72286i	−0.782137	−	1.07652i
$40$	−6.20561	−	1.22084i	−0.981193	−	0.193031i
$41$	1.55176	−	2.13581i	0.242344	−	0.333558i	−0.670467	−	0.741939i	$-0.733906\pi$
$41$	1.55176	−	2.13581i	0.242344	−	0.333558i	0.912812	+	0.408381i	$0.133906\pi$
$42$	−12.5544	+	3.63817i	−1.93718	+	0.561382i
$43$	2.00825			0.306255			0.153127	−	0.988206i	$-0.451066\pi$
$43$	2.00825			0.306255			0.153127	+	0.988206i	$0.451066\pi$
$44$	−3.25319	−	1.92988i	−0.490436	−	0.290940i
$45$	3.61531	−	13.8661i	0.538939	−	2.06704i
$46$	−6.60761	−	2.38394i	−0.974239	−	0.351493i
$47$	−3.37142	−	6.61678i	−0.491772	−	0.965157i	−0.994892	−	0.100941i	$-0.967815\pi$
$47$	−3.37142	−	6.61678i	−0.491772	−	0.965157i	0.503120	−	0.864216i	$-0.332185\pi$
$48$	5.88163	+	10.7676i	0.848940	+	1.55417i
$49$			2.07955i			0.297079i
$50$	−3.74024	−	6.00089i	−0.528949	−	0.848653i
$51$	−12.4885	+	12.4885i	−1.74874	+	1.74874i
$52$	2.89711	+	4.57880i	0.401756	+	0.634965i
$53$	−7.29703	−	2.37095i	−1.00232	−	0.325675i	−0.238531	−	0.971135i	$-0.576666\pi$
$53$	−7.29703	−	2.37095i	−1.00232	−	0.325675i	−0.763794	+	0.645460i	$0.776666\pi$
$54$	−13.3823	+	6.28619i	−1.82111	+	0.855442i
$55$	−0.907156	−	4.13057i	−0.122321	−	0.556967i
$56$	8.32121	−	1.84227i	1.11197	−	0.246184i
$57$	13.6882	−	13.6882i	1.81305	−	1.81305i
$58$	8.12278	−	2.35392i	1.06657	−	0.309085i
$59$	−3.08394	+	0.488448i	−0.401494	+	0.0635905i	−0.353916	−	0.935277i	$-0.615150\pi$
$59$	−3.08394	+	0.488448i	−0.401494	+	0.0635905i	−0.0475780	+	0.998868i	$0.515150\pi$
$60$	−4.30512	+	13.0244i	−0.555788	+	1.68144i
$61$	14.2512	+	2.25717i	1.82468	+	0.289001i	0.972267	−	0.233873i	$-0.0751399\pi$
$61$	14.2512	+	2.25717i	1.82468	+	0.289001i	0.852410	+	0.522873i	$0.175140\pi$
$62$	−0.102391	−	0.814945i	−0.0130037	−	0.103498i
$63$	3.02076	+	19.0723i	0.380580	+	2.40289i
$64$	−3.37680	−	7.25239i	−0.422101	−	0.906549i
$65$	−1.52838	+	5.86194i	−0.189572	+	0.727084i
$66$	−5.03270	+	6.47906i	−0.619483	+	0.797517i
$67$	1.33320	+	4.10317i	0.162876	+	0.501282i	0.998874	−	0.0474517i	$-0.0151100\pi$
$67$	1.33320	+	4.10317i	0.162876	+	0.501282i	−0.835997	+	0.548734i	$0.815110\pi$
$68$	8.64849	−	7.60388i	1.04878	−	0.922106i
$69$	−6.91681	+	13.5750i	−0.832686	+	1.63424i
$70$	7.85733	+	5.39054i	0.939131	+	0.644293i
$71$	0.503455	−	1.54948i	0.0597491	−	0.183889i	−0.916727	−	0.399514i	$-0.869179\pi$
$71$	0.503455	−	1.54948i	0.0597491	−	0.183889i	0.976476	+	0.215625i	$0.0691789\pi$
$72$	16.8664	−	6.63831i	1.98773	−	0.782332i
$73$	−6.88778	−	1.09092i	−0.806153	−	0.127682i	−0.260262	−	0.965538i	$-0.583809\pi$
$73$	−6.88778	−	1.09092i	−0.806153	−	0.127682i	−0.545891	+	0.837856i	$0.683809\pi$
$74$	6.08410	−	5.70560i	0.707262	−	0.663263i
$75$	−13.9252	+	6.42647i	−1.60794	+	0.742065i
$76$	−9.47929	+	8.33433i	−1.08735	+	0.956014i
$77$	3.34970	+	4.61046i	0.381733	+	0.525411i
$78$	10.6369	−	4.99655i	1.20439	−	0.565748i
$79$	3.44016	−	10.5877i	0.387048	−	1.19121i	−0.547936	−	0.836521i	$-0.684586\pi$
$79$	3.44016	−	10.5877i	0.387048	−	1.19121i	0.934984	−	0.354691i	$-0.115414\pi$
$80$	3.34602	−	8.29482i	0.374097	−	0.927390i
$81$	3.96862	+	12.2142i	0.440958	+	1.35713i
$82$	2.55394	+	2.72336i	0.282036	+	0.300745i
$83$	−14.6610	+	4.76365i	−1.60925	+	0.522878i	−0.969372	−	0.245596i	$-0.921016\pi$
$83$	−14.6610	+	4.76365i	−1.60925	+	0.522878i	−0.639881	+	0.768474i	$0.721016\pi$
$84$	−1.71468	−	18.4054i	−0.187087	−	2.00819i
$85$	12.8134	+	1.25938i	1.38981	+	0.136599i
$86$	−0.534068	+	2.78942i	−0.0575901	+	0.300791i
$87$	−2.86940	−	18.1167i	−0.307632	−	1.94231i
$88$	3.54572	−	4.00540i	0.377975	−	0.426977i
$89$	−5.42146	+	3.93892i	−0.574674	+	0.417525i	−0.836800	−	0.547509i	$-0.815576\pi$
$89$	−5.42146	+	3.93892i	−0.574674	+	0.417525i	0.262126	+	0.965034i	$0.415576\pi$
$90$	18.2984	+	8.70913i	1.92882	+	0.918023i
$91$	−1.27703	−	8.06288i	−0.133870	−	0.845219i
$92$	5.06846	−	8.54388i	0.528424	−	0.890761i
$93$	−1.78145			−0.184727
$94$	10.0872	−	2.92320i	1.04041	−	0.301505i
$95$	−14.0443	−	1.38036i	−1.44091	−	0.141622i
$96$	−16.5202	+	5.30598i	−1.68608	+	0.541539i
$97$	16.1691	−	8.23856i	1.64172	−	0.836499i	0.644296	−	0.764776i	$-0.277150\pi$
$97$	16.1691	−	8.23856i	1.64172	−	0.836499i	0.997425	−	0.0717224i	$-0.0228496\pi$
$98$	−2.88847	−	0.553032i	−0.291779	−	0.0558646i
$99$	8.57021	+	8.57021i	0.861338	+	0.861338i
$100$	9.32981	−	3.59927i	0.932981	−	0.359927i
$101$	−5.46814	+	5.46814i	−0.544100	+	0.544100i	−0.924728	−	0.380628i	$-0.875708\pi$
$101$	−5.46814	+	5.46814i	−0.544100	+	0.544100i	0.380628	+	0.924728i	$0.375708\pi$
$102$	−14.0252	−	20.6675i	−1.38870	−	2.04639i
$103$	1.65972	+	3.25738i	0.163537	+	0.320959i	0.958204	−	0.286086i	$-0.0923544\pi$
$103$	1.65972	+	3.25738i	0.163537	+	0.320959i	−0.794667	+	0.607046i	$0.792354\pi$
$104$	−7.13033	+	2.80636i	−0.699186	+	0.275186i
$105$	13.7249	−	15.4515i	1.33942	−	1.50791i
$106$	5.23377	−	9.50494i	0.508348	−	0.923201i
$107$		−	7.23409i		−	0.699346i	−0.936872	−	0.349673i	$-0.886293\pi$
$107$		−	7.23409i		−	0.699346i	0.936872	−	0.349673i	$-0.113707\pi$
$108$	−5.17255	−	20.2596i	−0.497729	−	1.94948i
$109$	7.52270	−	1.19148i	0.720544	−	0.114123i	0.214616	−	0.976699i	$-0.431150\pi$
$109$	7.52270	−	1.19148i	0.720544	−	0.114123i	0.505928	+	0.862576i	$0.331150\pi$
$110$	5.97855	−	0.161550i	0.570032	−	0.0154032i
$111$	−10.6334	−	14.6357i	−1.00928	−	1.38916i
$112$	0.345969	+	12.0480i	0.0326910	+	1.13842i
$113$	0.175586	−	0.0278101i	0.0165177	−	0.00261615i	−0.148170	−	0.988962i	$-0.547338\pi$
$113$	0.175586	−	0.0278101i	0.0165177	−	0.00261615i	0.164688	+	0.986346i	$0.447338\pi$
$114$	15.3725	+	22.6529i	1.43976	+	2.12164i
$115$	10.8482	−	2.38247i	1.01160	−	0.222167i
$116$	1.10941	+	11.9084i	0.103006	+	1.10567i
$117$	−5.36503	−	16.5119i	−0.495997	−	1.52652i
$118$	0.141689	−	4.41344i	0.0130435	−	0.406290i
$119$	−16.5008	+	5.36144i	−1.51263	+	0.491482i
$120$	−16.9458	−	9.44341i	−1.54693	−	0.862062i
$121$	−7.05977	−	2.29386i	−0.641798	−	0.208533i
$122$	−6.92509	+	19.1944i	−0.626969	+	1.73778i
$123$	6.55122	−	4.75974i	0.590704	−	0.429171i
$124$	1.15917	+	0.0745049i	0.104097	+	0.00669074i
$125$	10.0625	+	4.87307i	0.900014	+	0.435861i
$126$	−27.2945	−	0.876261i	−2.43159	−	0.0780635i
$127$	−3.10750	+	19.6200i	−0.275746	+	1.74099i	0.328781	+	0.944406i	$0.393362\pi$
$127$	−3.10750	+	19.6200i	−0.275746	+	1.74099i	−0.604527	+	0.796585i	$0.706638\pi$
$128$	10.9715	−	2.76165i	0.969751	−	0.244097i
$129$	5.85844	+	1.90352i	0.515807	+	0.167596i
$130$	−7.73569	−	3.68181i	−0.678465	−	0.322916i
$131$	−4.45018	−	2.26748i	−0.388814	−	0.198111i	0.248645	−	0.968595i	$-0.420015\pi$
$131$	−4.45018	−	2.26748i	−0.388814	−	0.198111i	−0.637460	+	0.770484i	$0.720015\pi$
$132$	−7.66093	−	8.71337i	−0.666798	−	0.758402i
$133$	18.0859	−	5.87648i	1.56825	−	0.509555i
$134$	−6.05379	+	0.760608i	−0.522968	+	0.0657065i
$135$	12.5997	−	19.6915i	1.08441	−	1.69478i
$136$	8.26171	+	14.0348i	0.708436	+	1.20347i
$137$	19.8591	−	3.14538i	1.69668	−	0.268728i	0.768228	−	0.640177i	$-0.221139\pi$
$137$	19.8591	−	3.14538i	1.69668	−	0.268728i	0.928454	+	0.371449i	$0.121139\pi$
$138$	−17.0160	−	13.2174i	−1.44850	−	1.12514i
$139$	−2.42437	+	15.3069i	−0.205633	+	1.29831i	0.641578	+	0.767058i	$0.278280\pi$
$139$	−2.42437	+	15.3069i	−0.205633	+	1.29831i	−0.847211	+	0.531257i	$0.821720\pi$
$140$	−9.57693	+	9.48016i	−0.809398	+	0.801220i
$141$	−3.56334	−	22.4980i	−0.300087	−	1.89468i
$142$	2.01831	+	1.11136i	0.169373	+	0.0932628i
$143$	−3.62307	−	3.62307i	−0.302977	−	0.302977i
$144$	4.73508	+	25.1926i	0.394590	+	2.09938i
$145$	−8.88013	+	9.99723i	−0.737454	+	0.830225i
$146$	3.34698	−	9.27690i	0.276998	−	0.767762i
$147$	−1.97111	+	6.06646i	−0.162575	+	0.500353i
$148$	6.30700	+	9.96805i	0.518432	+	0.819368i
$149$	−7.95923	−	7.95923i	−0.652046	−	0.652046i	0.301440	−	0.953485i	$-0.402533\pi$
$149$	−7.95923	−	7.95923i	−0.652046	−	0.652046i	−0.953485	+	0.301440i	$0.902533\pi$
$150$	−5.22303	−	21.0509i	−0.426458	−	1.71880i
$151$	−6.00738			−0.488874			−0.244437	−	0.969665i	$-0.578603\pi$
$151$	−6.00738			−0.488874			−0.244437	+	0.969665i	$0.578603\pi$
$152$	−9.05536	−	15.3830i	−0.734487	−	1.24773i
$153$	−32.8776	+	16.7520i	−2.65799	+	1.35432i
$154$	−7.29467	+	3.42658i	−0.587821	+	0.276122i
$155$	0.824072	+	1.00372i	0.0661911	+	0.0806206i
$156$	4.11138	+	16.1033i	0.329174	+	1.28929i
$157$			8.20881i			0.655134i	0.944828	+	0.327567i	$0.106229\pi$
$157$			8.20881i			0.655134i	−0.944828	+	0.327567i	$0.893771\pi$
$158$	13.7913	+	7.59400i	1.09718	+	0.604146i
$159$	−19.0395	−	13.8330i	−1.50993	−	1.09703i
$160$	10.6315	+	6.85348i	0.840498	+	0.541815i
$161$	−12.1085	+	8.79734i	−0.954284	+	0.693328i
$162$	−18.0207	+	2.26415i	−1.41584	+	0.177888i
$163$	10.6812	−	14.7014i	0.836617	−	1.15151i	−0.150038	−	0.988680i	$-0.547939\pi$
$163$	10.6812	−	14.7014i	0.836617	−	1.15151i	0.986655	−	0.162825i	$-0.0520606\pi$
$164$	−4.46190	+	2.82314i	−0.348416	+	0.220450i
$165$	1.26883	−	12.9095i	0.0987783	−	1.00501i
$166$	−2.71772	−	21.6307i	−0.210936	−	1.67887i
$167$	0.822281	−	1.61382i	0.0636300	−	0.124881i	−0.857001	−	0.515315i	$-0.827675\pi$
$167$	0.822281	−	1.61382i	0.0636300	−	0.124881i	0.920631	+	0.390434i	$0.127675\pi$
$168$	26.0208	+	2.51301i	2.00755	+	0.193883i
$169$	−1.74914	−	5.38331i	−0.134549	−	0.414101i
$170$	−5.15682	+	17.4627i	−0.395510	+	1.33933i
$171$	36.0359	−	18.3612i	2.75573	−	1.40412i
$172$	−3.73244	−	1.48362i	−0.284596	−	0.113125i
$173$	−8.49470	+	6.17176i	−0.645840	+	0.469230i	−0.861852	−	0.507160i	$-0.830695\pi$
$173$	−8.49470	+	6.17176i	−0.645840	+	0.469230i	0.216011	+	0.976391i	$0.430695\pi$
$174$	25.9269	+	0.832354i	1.96551	+	0.0631006i
$175$	−15.0548	−	0.585379i	−1.13803	−	0.0442505i
$176$	4.62050	+	5.99013i	0.348283	+	0.451523i
$177$	−9.45941	−	1.49822i	−0.711013	−	0.112613i
$178$	−4.02933	−	8.57783i	−0.302011	−	0.642936i
$179$	8.71088	−	4.43842i	0.651082	−	0.331743i	−0.0970629	−	0.995278i	$-0.530945\pi$
$179$	8.71088	−	4.43842i	0.651082	−	0.331743i	0.748145	+	0.663535i	$0.230945\pi$
$180$	−16.9631	+	23.1001i	−1.26435	+	1.72178i
$181$	15.7746	+	8.03754i	1.17251	+	0.597426i	0.928131	−	0.372253i	$-0.121415\pi$
$181$	15.7746	+	8.03754i	1.17251	+	0.597426i	0.244383	+	0.969679i	$0.421415\pi$
$182$	11.5388	+	0.370441i	0.855314	+	0.0274589i
$183$	39.4340	+	20.0926i	2.91504	+	1.48529i
$184$	10.5194	+	9.31216i	0.775502	+	0.686501i
$185$	−3.32728	+	12.7614i	−0.244627	+	0.938240i
$186$	0.473754	−	2.47440i	0.0347373	−	0.181432i
$187$	−6.40088	+	8.81006i	−0.468079	+	0.644255i
$188$	1.37771	+	14.7883i	0.100480	+	1.07855i
$189$	−4.92809	+	31.1147i	−0.358465	+	2.26326i
$190$	5.65220	−	19.1402i	0.410054	−	1.38858i
$191$	−6.55015	+	9.01551i	−0.473953	+	0.652340i	−0.977329	−	0.211728i	$-0.932091\pi$
$191$	−6.55015	+	9.01551i	−0.473953	+	0.652340i	0.503376	+	0.864067i	$0.332091\pi$
$192$	−2.97659	−	24.3573i	−0.214817	−	1.75784i
$193$	−13.5952	+	13.5952i	−0.978605	+	0.978605i	−0.999776	−	0.0211707i	$-0.993261\pi$
$193$	−13.5952	+	13.5952i	−0.978605	+	0.978605i	0.0211707	+	0.999776i	$0.493261\pi$
$194$	7.14326	+	24.6495i	0.512856	+	1.76973i
$195$	−10.0148	+	15.6517i	−0.717177	+	1.12084i
$196$	1.53630	−	3.86497i	0.109736	−	0.276069i
$197$	−0.307259	+	0.945645i	−0.0218913	+	0.0673744i	−0.961405	−	0.275136i	$-0.911277\pi$
$197$	−0.307259	+	0.945645i	−0.0218913	+	0.0673744i	0.939514	+	0.342510i	$0.111277\pi$
$198$	−14.1830	+	9.62474i	−1.00794	+	0.684001i
$199$			1.98228i			0.140520i	0.997529	+	0.0702602i	$0.0223830\pi$
$199$			1.98228i			0.140520i	−0.997529	+	0.0702602i	$0.977617\pi$
$200$	2.51818	+	13.9161i	0.178062	+	0.984019i
$201$			13.2334i			0.933413i
$202$	−6.14098	−	9.04934i	−0.432078	−	0.636710i
$203$	5.56820	−	17.1372i	0.390811	−	1.20279i
$204$	32.4367	−	13.9845i	2.27102	−	0.979110i
$205$	−5.71228	−	1.48936i	−0.398963	−	0.104021i
$206$	−4.96583	+	1.43906i	−0.345986	+	0.100264i
$207$	−22.5080	+	22.5080i	−1.56442	+	1.56442i
$208$	−2.00177	−	10.6502i	−0.138798	−	0.738461i
$209$	7.01577	−	9.65638i	0.485291	−	0.667946i
$210$	17.8119	+	23.1728i	1.22914	+	1.59908i
$211$	0.199143	−	1.25734i	0.0137096	−	0.0865589i	−0.979885	−	0.199564i	$-0.936048\pi$
$211$	0.199143	−	1.25734i	0.0137096	−	0.0865589i	0.993594	+	0.113005i	$0.0360475\pi$
$212$	11.8104	+	9.79734i	0.811139	+	0.672884i
$213$	2.93735	−	4.04292i	0.201264	−	0.277016i
$214$	10.0480	+	1.92382i	0.686870	+	0.131509i
$215$	−1.63753	−	4.18136i	−0.111679	−	0.285166i
$216$	29.5158	−	1.79681i	2.00830	−	0.122257i
$217$	−1.55929	−	0.794499i	−0.105852	−	0.0539341i
$218$	−0.345623	+	10.7658i	−0.0234086	+	0.729150i
$219$	−19.0589	−	9.71101i	−1.28788	−	0.656210i
$220$	−1.36553	+	8.34707i	−0.0920640	+	0.562760i
$221$	13.8991	−	7.08193i	0.934952	−	0.476382i
$222$	23.1565	−	10.8775i	1.55417	−	0.730050i
$223$	18.8587	+	2.98692i	1.26287	+	0.200019i	0.751726	−	0.659475i	$-0.229221\pi$
$223$	18.8587	+	2.98692i	1.26287	+	0.200019i	0.511145	+	0.859494i	$0.329221\pi$
$224$	−16.8264	−	2.72346i	−1.12426	−	0.181969i
$225$	−31.8185	+	3.77908i	−2.12124	+	0.251939i
$226$	−0.00806713	+	0.251282i	−0.000536618	+	0.0167150i
$227$	−10.9986	+	7.99095i	−0.730003	+	0.530378i	−0.889564	−	0.456810i	$-0.848992\pi$
$227$	−10.9986	+	7.99095i	−0.730003	+	0.530378i	0.159561	+	0.987188i	$0.448992\pi$
$228$	−35.5526	+	15.3279i	−2.35453	+	1.01511i
$229$	−16.7577	+	8.53847i	−1.10738	+	0.564238i	−0.909381	−	0.415964i	$-0.863444\pi$
$229$	−16.7577	+	8.53847i	−1.10738	+	0.564238i	−0.197999	+	0.980202i	$0.563444\pi$
$230$	0.424282	+	15.7015i	0.0279763	+	1.03533i
$231$	5.40166	+	16.6246i	0.355403	+	1.09382i
$232$	−16.8356	−	1.62594i	−1.10531	−	0.106748i
$233$	−1.96671	+	3.85990i	−0.128844	+	0.252870i	−0.946412	−	0.322961i	$-0.895322\pi$
$233$	−1.96671	+	3.85990i	−0.128844	+	0.252870i	0.817568	+	0.575832i	$0.195322\pi$
$234$	24.3615	−	3.06082i	1.59256	−	0.200092i
$235$	−11.0277	+	12.4150i	−0.719368	+	0.809863i
$236$	6.09251	+	1.37050i	0.396589	+	0.0892121i
$237$	20.0712	−	27.6256i	1.30376	−	1.79448i
$238$	−3.05877	−	24.3452i	−0.198271	−	1.57806i
$239$	−2.29470	+	1.66720i	−0.148432	+	0.107842i	−0.659523	−	0.751685i	$-0.729242\pi$
$239$	−2.29470	+	1.66720i	−0.148432	+	0.107842i	0.511091	+	0.859527i	$0.329242\pi$
$240$	17.6233	−	21.0261i	1.13758	−	1.35723i
$241$	−14.1159	−	10.2558i	−0.909284	−	0.660633i	0.0315498	−	0.999502i	$-0.489956\pi$
$241$	−14.1159	−	10.2558i	−0.909284	−	0.660633i	−0.940834	+	0.338869i	$0.889956\pi$
$242$	5.06359	−	9.19589i	0.325500	−	0.591134i
$243$			8.02846i			0.515026i
$244$	−24.8191	−	14.7234i	−1.58888	−	0.942567i
$245$	4.32983	−	1.69568i	0.276623	−	0.108333i
$246$	4.86899	+	10.3653i	0.310435	+	0.660870i
$247$	−15.2343	+	7.76224i	−0.969332	+	0.493899i
$248$	−0.411754	+	1.59026i	−0.0261464	+	0.100982i
$249$	−47.2842			−2.99651
$250$	−9.44461	+	12.6807i	−0.597329	+	0.801996i
$251$	−3.80608	−	3.80608i	−0.240238	−	0.240238i	0.576711	−	0.816948i	$-0.304336\pi$
$251$	−3.80608	−	3.80608i	−0.240238	−	0.240238i	−0.816948	+	0.576711i	$0.804336\pi$
$252$	8.47575	−	37.6786i	0.533922	−	2.37353i
$253$	−2.90293	+	8.93431i	−0.182506	+	0.561696i
$254$	−26.4254	−	9.53395i	−1.65808	−	0.598213i
$255$	36.1854	+	15.8191i	2.26602	+	0.990629i
$256$	0.918154	+	15.9736i	0.0573846	+	0.998352i
$257$	16.6616	+	16.6616i	1.03932	+	1.03932i	0.999195	+	0.0401284i	$0.0127767\pi$
$257$	16.6616	+	16.6616i	1.03932	+	1.03932i	0.0401284	+	0.999195i	$0.487223\pi$
$258$	−4.20194	+	7.63106i	−0.261602	+	0.475089i
$259$	−2.78010	−	17.5529i	−0.172747	−	1.09068i
$260$	7.17118	−	9.76562i	0.444738	−	0.605638i
$261$	5.99494	−	37.8505i	0.371077	−	2.34289i
$262$	4.33297	−	5.57823i	0.267692	−	0.344624i
$263$	−13.1426	+	2.08158i	−0.810406	+	0.128356i	−0.547867	−	0.836566i	$-0.684560\pi$
$263$	−13.1426	+	2.08158i	−0.810406	+	0.128356i	−0.262539	+	0.964921i	$0.584560\pi$
$264$	14.1401	−	8.32370i	0.870261	−	0.512288i
$265$	1.01349	+	17.1264i	0.0622580	+	1.05207i
$266$	3.35260	+	26.6839i	0.205561	+	1.63609i
$267$	−19.5490	+	6.35184i	−1.19638	+	0.388727i
$268$	0.553457	−	8.61089i	0.0338078	−	0.525994i
$269$	17.0196	+	8.67192i	1.03770	+	0.528736i	0.887927	−	0.459984i	$-0.152145\pi$
$269$	17.0196	+	8.67192i	1.03770	+	0.528736i	0.149776	+	0.988720i	$0.452145\pi$
$270$	24.0005	+	22.7375i	1.46062	+	1.38376i
$271$	3.30052	+	1.07240i	0.200492	+	0.0651439i	0.407542	−	0.913187i	$-0.366386\pi$
$271$	3.30052	+	1.07240i	0.200492	+	0.0651439i	−0.207049	+	0.978330i	$0.566386\pi$
$272$	−21.6912	+	7.74302i	−1.31522	+	0.469489i
$273$	3.91707	−	24.7314i	0.237072	−	1.49681i
$274$	−0.912410	+	28.4205i	−0.0551207	+	1.71695i
$275$	−7.86055	+	5.25687i	−0.474009	+	0.317001i
$276$	22.8840	−	20.1200i	1.37746	−	1.21108i
$277$	−7.80271	+	5.66900i	−0.468820	+	0.340617i	−0.796981	−	0.604004i	$-0.793571\pi$
$277$	−7.80271	+	5.66900i	−0.468820	+	0.340617i	0.328161	+	0.944622i	$0.393571\pi$
$278$	−20.6163	−	7.43810i	−1.23648	−	0.446107i
$279$	−3.53975	−	1.15013i	−0.211919	−	0.0688567i
$280$	−10.6209	−	15.8233i	−0.634722	−	0.945625i
$281$	−7.96879	+	2.58922i	−0.475378	+	0.154460i	−0.536900	−	0.843646i	$-0.680405\pi$
$281$	−7.96879	+	2.58922i	−0.475378	+	0.154460i	0.0615218	+	0.998106i	$0.480405\pi$
$282$	32.1970	+	1.03365i	1.91731	+	0.0615530i
$283$	−6.15262	−	18.9358i	−0.365735	−	1.12562i	−0.949520	−	0.313708i	$-0.898429\pi$
$283$	−6.15262	−	18.9358i	−0.365735	−	1.12562i	0.583785	−	0.811909i	$-0.301571\pi$
$284$	−2.08040	+	2.50785i	−0.123449	+	0.148813i
$285$	−39.6615	−	17.3387i	−2.34935	−	1.02706i
$286$	5.99590	−	4.06888i	0.354545	−	0.240598i
$287$	7.85702	−	1.24443i	0.463785	−	0.0734564i
$288$	−36.2514	−	0.122704i	−2.13613	−	0.00723041i
$289$	−9.49498	−	13.0687i	−0.558528	−	0.768748i
$290$	−11.5244	−	14.9930i	−0.676738	−	0.880419i
$291$	54.9772	−	8.70754i	3.22282	−	0.510445i
$292$	11.9954	+	7.11598i	0.701976	+	0.416432i
$293$			24.0445i			1.40470i	0.711833	+	0.702348i	$0.247865\pi$
$293$			24.0445i			1.40470i	−0.711833	+	0.702348i	$0.752135\pi$
$294$	−7.90203	−	4.35114i	−0.460855	−	0.253764i
$295$	3.53165	+	6.02277i	0.205621	+	0.350659i
$296$	−15.5227	+	6.10944i	−0.902240	+	0.355104i
$297$	8.97666	+	17.6177i	0.520878	+	1.02228i
$298$	13.1719	−	8.93859i	0.763028	−	0.517799i
$299$	9.51532	−	9.51532i	0.550285	−	0.550285i
$300$	30.6284	−	1.65647i	1.76833	−	0.0956364i
$301$	4.27892	+	4.27892i	0.246633	+	0.246633i
$302$	1.59759	−	8.34416i	0.0919308	−	0.480152i
$303$	−21.1346	+	10.7686i	−1.21415	+	0.618641i
$304$	23.7749	−	8.48684i	1.36358	−	0.486753i
$305$	−6.92084	−	31.5128i	−0.396286	−	1.80442i
$306$	−14.5248	−	50.1214i	−0.830329	−	2.86525i
$307$	33.6839			1.92244			0.961222	−	0.275777i	$-0.0889351\pi$
$307$	33.6839			1.92244			0.961222	+	0.275777i	$0.0889351\pi$
$308$	−2.81954	−	11.0434i	−0.160658	−	0.629258i
$309$	1.75420	+	11.0756i	0.0997929	+	0.630068i
$310$	−1.61330	+	0.877697i	−0.0916294	+	0.0498498i
$311$	−11.3287	+	8.23077i	−0.642390	+	0.466724i	−0.860671	−	0.509162i	$-0.829955\pi$
$311$	−11.3287	+	8.23077i	−0.642390	+	0.466724i	0.218280	+	0.975886i	$0.429955\pi$
$312$	−23.4606	+	1.42818i	−1.32819	+	0.0808550i
$313$	−2.40292	−	15.1715i	−0.135821	−	0.857541i	−0.957677	−	0.287846i	$-0.907061\pi$
$313$	−2.40292	−	15.1715i	−0.135821	−	0.857541i	0.821856	−	0.569696i	$-0.192939\pi$
$314$	−11.4019	−	2.18303i	−0.643447	−	0.123196i
$315$	37.2473	−	21.8412i	2.09865	−	1.23061i
$316$	−14.2156	+	17.1364i	−0.799688	+	0.963997i
$317$	6.01667	−	1.95494i	0.337930	−	0.109800i	−0.135136	−	0.990827i	$-0.543147\pi$
$317$	6.01667	−	1.95494i	0.337930	−	0.109800i	0.473066	+	0.881027i	$0.343147\pi$
$318$	24.2772	−	22.7669i	1.36140	−	1.27670i
$319$	−3.49492	−	10.7562i	−0.195678	−	0.602234i
$320$	−12.3467	+	12.9445i	−0.690202	+	0.723617i
$321$	6.85686	−	21.1032i	0.382713	−	1.17787i
$322$	−8.99927	−	19.1581i	−0.501509	−	1.06764i
$323$	21.3593	+	29.3986i	1.18847	+	1.63578i
$324$	1.64751	−	25.6325i	0.0915282	−	1.42403i
$325$	13.4514	−	1.59761i	0.746147	−	0.0886197i
$326$	17.5795	+	18.7457i	0.973640	+	1.03823i
$327$	23.0745	+	3.65464i	1.27602	+	0.202102i
$328$	−2.73471	−	6.94828i	−0.150999	−	0.383655i
$329$	6.91482	−	21.2816i	0.381226	−	1.17329i
$330$	17.5937	+	5.19551i	0.968501	+	0.286004i
$331$	4.47354	−	8.77981i	0.245888	−	0.482582i	−0.734769	−	0.678318i	$-0.762709\pi$
$331$	4.47354	−	8.77981i	0.245888	−	0.482582i	0.980657	+	0.195735i	$0.0627094\pi$
$332$	30.7675	+	1.97755i	1.68858	+	0.108532i
$333$	−11.6797	−	35.9463i	−0.640042	−	1.96985i
$334$	2.02289	+	1.57131i	0.110688	+	0.0859783i
$335$	7.45609	−	6.12159i	0.407370	−	0.334458i
$336$	−10.4104	+	35.4741i	−0.567936	+	1.93527i
$337$	0.348433	+	2.19992i	0.0189804	+	0.119837i	0.995359	−	0.0962277i	$-0.0306777\pi$
$337$	0.348433	+	2.19992i	0.0189804	+	0.119837i	−0.976379	+	0.216065i	$0.930678\pi$
$338$	7.94249	−	0.997908i	0.432015	−	0.0542790i
$339$	0.538578	+	0.0853024i	0.0292515	+	0.00463299i
$340$	−22.8840	−	11.8067i	−1.24106	−	0.640310i
$341$	−1.08490	+	0.171831i	−0.0587505	+	0.00930516i
$342$	15.9201	+	54.9362i	0.860862	+	2.97061i
$343$	10.4839	−	10.4839i	0.566076	−	0.566076i
$344$	3.05333	−	4.78974i	0.164624	−	0.258246i
$345$	33.9044	+	3.33234i	1.82535	+	0.179407i
$346$	−6.31342	−	13.4403i	−0.339412	−	0.722556i
$347$	−9.58203	−	3.11339i	−0.514390	−	0.167135i	0.0403078	−	0.999187i	$-0.487166\pi$
$347$	−9.58203	−	3.11339i	−0.514390	−	0.167135i	−0.554698	+	0.832052i	$0.687166\pi$
$348$	−8.05106	+	35.7907i	−0.431582	+	1.91858i
$349$	−6.97492	+	6.97492i	−0.373359	+	0.373359i	−0.868699	−	0.495340i	$-0.835043\pi$
$349$	−6.97492	+	6.97492i	−0.373359	+	0.373359i	0.495340	+	0.868699i	$0.335043\pi$
$350$	4.81671	−	20.7552i	0.257464	−	1.10941i
$351$		−	28.3238i		−	1.51181i
$352$	−9.54896	+	4.82480i	−0.508961	+	0.257162i
$353$	14.1515	+	27.7740i	0.753210	+	1.47826i	0.874180	+	0.485602i	$0.161400\pi$
$353$	14.1515	+	27.7740i	0.753210	+	1.47826i	−0.120969	+	0.992656i	$0.538600\pi$
$354$	4.59662	−	12.7405i	0.244308	−	0.677152i
$355$	−3.63667	+	0.215207i	−0.193015	+	0.0114220i
$356$	12.9860	−	3.31551i	0.688258	−	0.175722i
$357$	−53.2179			−2.81659
$358$	3.84834	+	13.2796i	0.203391	+	0.701850i
$359$	7.00140	−	9.63660i	0.369520	−	0.508600i	−0.583251	−	0.812292i	$-0.698219\pi$
$359$	7.00140	−	9.63660i	0.369520	−	0.508600i	0.952770	+	0.303692i	$0.0982194\pi$
$360$	−27.5745	−	29.7046i	−1.45331	−	1.56557i
$361$	−12.2433	−	16.8514i	−0.644383	−	0.886917i
$362$	−15.3591	+	19.7731i	−0.807255	+	1.03925i
$363$	−18.4205	−	13.3833i	−0.966824	−	0.702439i
$364$	−3.58314	+	15.9287i	−0.187808	+	0.834892i
$365$	3.34493	+	15.2305i	0.175082	+	0.797203i
$366$	−38.3953	+	49.4298i	−2.00696	+	2.58374i
$367$	−1.26293	−	0.643494i	−0.0659243	−	0.0335901i	0.420718	−	0.907192i	$-0.361778\pi$
$367$	−1.26293	−	0.643494i	−0.0659243	−	0.0335901i	−0.486642	+	0.873602i	$0.661778\pi$
$368$	−15.7319	+	12.1349i	−0.820085	+	0.632573i
$369$	16.0903	−	5.22805i	0.837627	−	0.272162i
$370$	−16.8406	−	8.01529i	−0.875501	−	0.416695i
$371$	−10.4959	−	20.5993i	−0.544919	−	1.06946i
$372$	3.31092	+	1.31607i	0.171663	+	0.0682352i
$373$	−5.26570	−	7.24761i	−0.272647	−	0.375267i	0.650634	−	0.759392i	$-0.274503\pi$
$373$	−5.26570	−	7.24761i	−0.272647	−	0.375267i	−0.923281	+	0.384125i	$0.874503\pi$
$374$	−10.5348	−	11.2337i	−0.544741	−	0.580878i
$375$	24.7352	+	23.7534i	1.27732	+	1.22662i
$376$	−20.9072	−	2.01916i	−1.07820	−	0.104130i
$377$	−2.53437	+	16.0014i	−0.130527	+	0.824114i
$378$	−41.9073	−	15.1196i	−2.15548	−	0.777668i
$379$	11.6046	+	22.7752i	0.596086	+	1.16988i	0.970155	+	0.242484i	$0.0779621\pi$
$379$	11.6046	+	22.7752i	0.596086	+	1.16988i	−0.374070	+	0.927401i	$0.622038\pi$
$380$	25.0823	+	12.9409i	1.28670	+	0.663855i
$381$	−27.6620	+	54.2898i	−1.41717	+	2.78135i
$382$	−10.7805	−	11.4956i	−0.551577	−	0.588167i
$383$	−3.17331	+	6.22796i	−0.162148	+	0.318234i	−0.957758	−	0.287576i	$-0.907151\pi$
$383$	−3.17331	+	6.22796i	−0.162148	+	0.318234i	0.795610	+	0.605810i	$0.207151\pi$
$384$	34.6235	+	2.34310i	1.76688	+	0.119571i
$385$	6.86806	−	10.7338i	0.350029	−	0.547043i
$386$	−15.2681	−	22.4990i	−0.777124	−	1.14517i
$387$	10.4118	+	7.56463i	0.529263	+	0.384532i
$388$	−36.1375	+	3.36664i	−1.83460	+	0.170915i
$389$	8.99851	+	1.42522i	0.456243	+	0.0722617i	0.380326	−	0.924852i	$-0.375812\pi$
$389$	8.99851	+	1.42522i	0.456243	+	0.0722617i	0.0759166	+	0.997114i	$0.475812\pi$
$390$	−19.0767	−	18.0728i	−0.965985	−	0.915153i
$391$	−23.1380	−	16.8107i	−1.17014	−	0.850154i
$392$	4.95982	+	3.16174i	0.250509	+	0.159692i
$393$	−10.8328	−	10.8328i	−0.546442	−	0.546442i
$394$	−1.23177	−	0.678260i	−0.0620559	−	0.0341702i
$395$	−24.8497	+	1.47053i	−1.25033	+	0.0739905i
$396$	−9.59682	−	22.2596i	−0.482258	−	1.11859i
$397$	18.7758	+	6.10063i	0.942331	+	0.306182i	0.739596	−	0.673052i	$-0.235017\pi$
$397$	18.7758	+	6.10063i	0.942331	+	0.306182i	0.202736	+	0.979234i	$0.435017\pi$
$398$	−2.75336	−	0.527164i	−0.138014	−	0.0264243i
$399$	58.3302			2.92016
$400$	−19.9990	−	0.203108i	−0.999948	−	0.0101554i
$401$	23.2772			1.16241			0.581204	−	0.813758i	$-0.302582\pi$
$401$	23.2772			1.16241			0.581204	+	0.813758i	$0.302582\pi$
$402$	−18.3810	−	3.51926i	−0.916761	−	0.175525i
$403$	1.49644	+	0.486222i	0.0745428	+	0.0242204i
$404$	14.2025	−	6.12316i	0.706601	−	0.304639i
$405$	22.1950	−	18.2225i	1.10288	−	0.905484i
$406$	22.3225	+	12.2916i	1.10784	+	0.610020i
$407$	−7.88743	−	7.88743i	−0.390965	−	0.390965i
$408$	10.7981	+	48.7730i	0.534586	+	2.41462i
$409$	13.4659	+	9.78355i	0.665846	+	0.483765i	0.868632	−	0.495458i	$-0.165000\pi$
$409$	13.4659	+	9.78355i	0.665846	+	0.483765i	−0.202786	+	0.979223i	$0.565000\pi$
$410$	3.58781	−	7.53819i	0.177189	−	0.372285i
$411$	60.9143	+	9.64788i	3.00468	+	0.475895i
$412$	−0.678235	−	7.28017i	−0.0334142	−	0.358668i
$413$	−7.61159	−	5.53015i	−0.374542	−	0.272121i
$414$	−25.2776	−	37.2490i	−1.24232	−	1.83069i
$415$	21.8730	+	26.6413i	1.07370	+	1.30777i
$416$	15.3253	+	0.0518734i	0.751387	+	0.00254330i
$417$	−21.5811	+	42.3552i	−1.05683	+	2.07414i
$418$	11.5468	+	12.3128i	0.564773	+	0.602238i
$419$	0.378515	−	0.742878i	0.0184917	−	0.0362920i	−0.881576	−	0.472042i	$-0.843517\pi$
$419$	0.378515	−	0.742878i	0.0184917	−	0.0362920i	0.900068	+	0.435750i	$0.143517\pi$
$420$	−36.9235	+	18.5779i	−1.80168	+	0.906510i
$421$	−1.49053	−	2.92532i	−0.0726438	−	0.142572i	0.851828	−	0.523821i	$-0.175494\pi$
$421$	−1.49053	−	2.92532i	−0.0726438	−	0.142572i	−0.924472	+	0.381249i	$0.875494\pi$
$422$	1.69347	+	0.610981i	0.0824367	+	0.0297421i
$423$	7.44475	−	47.0043i	0.361976	−	2.28543i
$424$	−16.7492	+	13.7989i	−0.813412	+	0.670135i
$425$	−7.82594	−	27.7056i	−0.379614	−	1.34392i
$426$	4.83439	+	5.15510i	0.234227	+	0.249765i
$427$	25.5554	+	35.1739i	1.23671	+	1.70219i
$428$	−5.34430	+	13.4450i	−0.258327	+	0.649887i
$429$	−7.13506	−	14.0033i	−0.344484	−	0.676088i
$430$	6.24332	−	1.16253i	0.301080	−	0.0560620i
$431$	33.0774	−	10.7475i	1.59328	−	0.517688i	0.627846	−	0.778337i	$-0.283937\pi$
$431$	33.0774	−	10.7475i	1.59328	−	0.517688i	0.965434	+	0.260649i	$0.0839366\pi$
$432$	−5.35364	+	41.4749i	−0.257577	+	1.99546i
$433$	−15.7001	−	7.99960i	−0.754499	−	0.384436i	0.0340408	−	0.999420i	$-0.489162\pi$
$433$	−15.7001	−	7.99960i	−0.754499	−	0.384436i	−0.788539	+	0.614984i	$0.789162\pi$
$434$	1.51822	−	1.95454i	0.0728769	−	0.0938211i
$435$	−35.3809	+	20.7468i	−1.69639	+	0.994732i
$436$	−14.8616	−	3.34309i	−0.711740	−	0.160105i
$437$	25.3607	+	18.4256i	1.21317	+	0.881416i
$438$	18.5569	−	23.8900i	0.886685	−	1.14151i
$439$	0.683934	+	0.941354i	0.0326424	+	0.0449284i	0.825026	−	0.565094i	$-0.191160\pi$
$439$	0.683934	+	0.941354i	0.0326424	+	0.0449284i	−0.792384	+	0.610023i	$0.791160\pi$
$440$	−11.2308	−	4.11650i	−0.535408	−	0.196246i
$441$	−7.83323	+	10.7815i	−0.373011	+	0.513406i
$442$	6.14040	+	21.1889i	0.292069	+	1.00785i
$443$	13.8226			0.656734			0.328367	−	0.944550i	$-0.393502\pi$
$443$	13.8226			0.656734			0.328367	+	0.944550i	$0.393502\pi$
$444$	8.95048	+	35.0568i	0.424771	+	1.66372i
$445$	12.6219	+	8.07618i	0.598335	+	0.382848i
$446$	−9.16402	+	25.4001i	−0.433929	+	1.20273i
$447$	−15.6744	−	30.7628i	−0.741375	−	1.45503i
$448$	8.25762	−	22.6474i	0.390136	−	1.06999i
$449$			10.2551i			0.483968i	0.970280	+	0.241984i	$0.0777982\pi$
$449$			10.2551i			0.483968i	−0.970280	+	0.241984i	$0.922202\pi$
$450$	3.21266	−	45.2004i	0.151446	−	2.13077i
$451$	3.53057	−	3.53057i	0.166248	−	0.166248i
$452$	−0.346881	−	0.0780304i	−0.0163159	−	0.00367024i
$453$	−17.5247	−	5.69411i	−0.823381	−	0.267533i
$454$	−8.17437	−	17.4020i	−0.383642	−	0.816715i
$455$	−15.7464	+	9.23341i	−0.738201	+	0.432869i
$456$	−11.8354	−	53.4583i	−0.554244	−	2.50341i
$457$	−6.65254	+	6.65254i	−0.311193	+	0.311193i	−0.845372	−	0.534179i	$-0.820621\pi$
$457$	−6.65254	+	6.65254i	−0.311193	+	0.311193i	0.534179	+	0.845372i	$0.320621\pi$
$458$	−7.40330	−	25.5469i	−0.345934	−	1.19373i
$459$	−59.4566	+	9.41700i	−2.77520	+	0.439548i
$460$	−21.9220	−	3.58631i	−1.02212	−	0.167212i
$461$	28.4006	+	4.49822i	1.32275	+	0.209503i	0.777559	−	0.628810i	$-0.216458\pi$
$461$	28.4006	+	4.49822i	1.32275	+	0.209503i	0.545190	+	0.838313i	$0.316458\pi$
$462$	−24.5278	+	3.08172i	−1.14114	+	0.143375i
$463$	1.86349	+	11.7656i	0.0866039	+	0.546795i	0.992397	+	0.123076i	$0.0392758\pi$
$463$	1.86349	+	11.7656i	0.0866039	+	0.546795i	−0.905793	+	0.423720i	$0.860724\pi$
$464$	6.73563	−	22.9520i	0.312694	−	1.06552i
$465$	1.45260	+	3.70914i	0.0673626	+	0.172007i
$466$	−4.83831	−	3.75823i	−0.224130	−	0.174097i
$467$	−4.43650	−	13.6542i	−0.205297	−	0.631839i	−0.999701	−	0.0244493i	$-0.992217\pi$
$467$	−4.43650	−	13.6542i	−0.205297	−	0.631839i	0.794404	−	0.607389i	$-0.207783\pi$
$468$	−2.22721	+	34.6517i	−0.102953	+	1.60178i
$469$	−5.90191	+	11.5831i	−0.272525	+	0.534860i
$470$	−14.3115	−	18.6189i	−0.660141	−	0.858826i
$471$	−7.78075	+	23.9467i	−0.358518	+	1.10340i
$472$	−3.52383	+	8.09794i	−0.162198	+	0.372738i
$473$	3.75138	+	0.594161i	0.172489	+	0.0273195i
$474$	33.0339	+	35.2253i	1.51730	+	1.61795i
$475$	8.57772	+	30.3671i	0.393573	+	1.39334i
$476$	34.6285	+	2.22572i	1.58720	+	0.102016i
$477$	−28.9008	−	39.7786i	−1.32328	−	1.82134i
$478$	−1.70546	−	3.63067i	−0.0780061	−	0.166063i
$479$	−0.493619	+	1.51920i	−0.0225540	+	0.0694142i	−0.961700	−	0.274104i	$-0.911619\pi$
$479$	−0.493619	+	1.51920i	−0.0225540	+	0.0694142i	0.939146	+	0.343518i	$0.111619\pi$
$480$	24.5182	+	30.0701i	1.11910	+	1.37250i
$481$	4.93761	+	15.1964i	0.225135	+	0.692896i
$482$	17.9991	−	16.8793i	0.819835	−	0.768833i
$483$	−43.6614	+	14.1865i	−1.98666	+	0.645506i
$484$	11.4263	+	9.47878i	0.519379	+	0.430854i
$485$	−30.3378	−	26.9478i	−1.37757	−	1.22364i
$486$	−11.1514	−	2.13507i	−0.505838	−	0.0968486i
$487$	−0.0775144	−	0.489407i	−0.00351251	−	0.0221771i	0.985870	−	0.167513i	$-0.0535737\pi$
$487$	−0.0775144	−	0.489407i	−0.00351251	−	0.0221771i	−0.989382	+	0.145336i	$0.953574\pi$
$488$	27.0508	−	30.5578i	1.22453	−	1.38329i
$489$	45.0940	−	32.7627i	2.03922	−	1.48158i
$490$	1.20380	+	6.46501i	0.0543823	+	0.292059i
$491$	−3.91057	−	24.6903i	−0.176481	−	1.11426i	−0.903798	−	0.427958i	$-0.859233\pi$
$491$	−3.91057	−	24.6903i	−0.176481	−	1.11426i	0.727317	−	0.686302i	$-0.240767\pi$
$492$	−15.6921	+	4.00642i	−0.707456	+	0.180623i
$493$	34.4324			1.55076
$494$	−6.73027	−	23.2244i	−0.302809	−	1.04492i
$495$	10.8558	−	24.8322i	0.487932	−	1.11612i
$496$	−2.09935	−	0.994830i	−0.0942635	−	0.0446692i
$497$	4.37413	−	2.22873i	0.196206	−	0.0999722i
$498$	12.5746	−	65.6770i	0.563483	−	2.94306i
$499$	−16.1637	−	16.1637i	−0.723588	−	0.723588i	0.245746	−	0.969334i	$-0.420967\pi$
$499$	−16.1637	−	16.1637i	−0.723588	−	0.723588i	−0.969334	+	0.245746i	$0.920967\pi$
$500$	−15.1016	−	16.4907i	−0.675363	−	0.737486i
$501$	3.92842	−	3.92842i	0.175509	−	0.175509i
$502$	6.29877	−	4.27441i	0.281128	−	0.190776i
$503$	−1.62532	−	3.18987i	−0.0724695	−	0.142229i	0.851929	−	0.523657i	$-0.175433\pi$
$503$	−1.62532	−	3.18987i	−0.0724695	−	0.142229i	−0.924399	+	0.381427i	$0.875433\pi$
$504$	50.0810	+	21.7928i	2.23079	+	0.970730i
$505$	15.8439	+	6.92644i	0.705045	+	0.308223i
$506$	−11.6376	−	6.40810i	−0.517355	−	0.284875i
$507$		−	17.3621i		−	0.771077i
$508$	20.2700	−	34.1691i	0.899337	−	1.51601i
$509$	6.86823	−	1.08782i	0.304429	−	0.0482168i	−0.00235110	−	0.999997i	$-0.500748\pi$
$509$	6.86823	−	1.08782i	0.304429	−	0.0482168i	0.306780	+	0.951780i	$0.400748\pi$
$510$	−31.5955	+	46.0541i	−1.39907	+	2.03931i
$511$	−12.3512	−	17.0000i	−0.546386	−	0.752036i
$512$	−22.4313	−	2.97269i	−0.991333	−	0.131375i
$513$	65.1682	−	10.3216i	2.87725	−	0.455711i
$514$	−27.5737	+	18.7118i	−1.21622	+	0.825341i
$515$	5.42884	−	6.11177i	0.239223	−	0.269317i
$516$	−9.48197	−	7.86582i	−0.417421	−	0.346273i
$517$	−4.34013	−	13.3575i	−0.190879	−	0.587464i
$518$	25.1200	+	0.806451i	1.10371	+	0.0354334i
$519$	−30.6306	+	9.95249i	−1.34453	+	0.436866i
$520$	11.6572	+	12.5577i	0.511202	+	0.550692i
$521$	−1.19111	−	0.387015i	−0.0521835	−	0.0169555i	0.282809	−	0.959176i	$-0.408734\pi$
$521$	−1.19111	−	0.387015i	−0.0521835	−	0.0169555i	−0.334992	+	0.942221i	$0.608734\pi$
$522$	50.9795	+	18.3928i	2.23131	+	0.805029i
$523$	−20.7904	+	15.1051i	−0.909099	+	0.660499i	−0.940787	−	0.338999i	$-0.889912\pi$
$523$	−20.7904	+	15.1051i	−0.909099	+	0.660499i	0.0316879	+	0.999498i	$0.489912\pi$
$524$	6.59577	+	7.50188i	0.288138	+	0.327721i
$525$	−43.3628	−	15.9774i	−1.89251	−	0.697310i
$526$	0.603823	−	18.8084i	0.0263279	−	0.820085i
$527$	0.523135	−	3.30294i	0.0227881	−	0.143878i
$528$	7.80111	+	21.8539i	0.339500	+	0.951069i
$529$	−1.58999	−	0.516620i	−0.0691301	−	0.0224617i
$530$	−24.0578	−	3.14683i	−1.04500	−	0.136690i
$531$	−17.8286	−	9.08415i	−0.773697	−	0.394219i
$532$	−37.9550	−	2.43952i	−1.64556	−	0.105767i
$533$	−6.80221	+	2.21017i	−0.294636	+	0.0957332i
$534$	−3.62381	−	28.8424i	−0.156817	−	1.24813i
$535$	−15.0621	+	5.89871i	−0.651190	+	0.255023i
$536$	11.8132	+	3.05870i	0.510253	+	0.132116i
$537$	29.6183	−	4.69108i	1.27812	−	0.202435i
$538$	−16.5713	+	21.3338i	−0.714440	+	0.919764i
$539$	−0.615258	+	3.88459i	−0.0265010	+	0.167321i
$540$	−37.9647	+	27.2895i	−1.63374	+	1.17435i
$541$	−1.18506	−	7.48216i	−0.0509496	−	0.321683i	−0.999979	−	0.00649535i	$-0.997932\pi$
$541$	−1.18506	−	7.48216i	−0.0509496	−	0.321683i	0.949029	−	0.315188i	$-0.102068\pi$
$542$	−2.36728	+	4.29918i	−0.101684	+	0.184665i
$543$	38.3990	+	38.3990i	1.64786	+	1.64786i
$544$	−4.98643	−	32.1879i	−0.213792	−	1.38004i
$545$	−8.61481	−	14.6914i	−0.369018	−	0.629312i
$546$	33.3098	+	12.0178i	1.42553	+	0.514312i
$547$	1.27034	−	3.90969i	0.0543157	−	0.167166i	−0.920219	−	0.391405i	$-0.871989\pi$
$547$	1.27034	−	3.90969i	0.0543157	−	0.167166i	0.974534	+	0.224238i	$0.0719893\pi$
$548$	−39.2330	−	8.82540i	−1.67595	−	0.377003i
$549$	65.3835	+	65.3835i	2.79050	+	2.79050i
$550$	−5.21129	−	12.3162i	−0.222210	−	0.525163i
$551$	−37.7401			−1.60778
$552$	21.8606	+	37.1362i	0.930450	+	1.58062i
$553$	29.8889	−	15.2291i	1.27100	−	0.647609i
$554$	−5.79912	−	12.3454i	−0.246381	−	0.524508i
$555$	−21.8023	+	34.0738i	−0.925456	+	1.44635i
$556$	15.8141	−	26.6577i	0.670665	−	1.13054i
$557$			22.0519i			0.934368i	0.884160	+	0.467184i	$0.154731\pi$
$557$			22.0519i			0.934368i	−0.884160	+	0.467184i	$0.845269\pi$
$558$	2.53887	−	4.61079i	0.107479	−	0.195190i
$559$	−4.40162	−	3.19796i	−0.186169	−	0.135259i
$560$	24.8029	−	10.5443i	1.04811	−	0.445577i
$561$	−27.0232	+	19.6335i	−1.14092	+	0.828929i
$562$	−1.47718	−	11.7571i	−0.0623111	−	0.495943i
$563$	20.8530	−	28.7017i	0.878850	−	1.20963i	−0.0978886	−	0.995197i	$-0.531209\pi$
$563$	20.8530	−	28.7017i	0.878850	−	1.20963i	0.976738	−	0.214435i	$-0.0687911\pi$
$564$	−9.99813	+	44.4463i	−0.420997	+	1.87153i
$565$	−0.201077	−	0.342910i	−0.00845936	−	0.0144263i
$566$	27.9377	−	3.51014i	1.17431	−	0.147542i
$567$	−17.5686	+	34.4802i	−0.737810	+	1.44803i
$568$	−2.93011	−	3.55657i	−0.122945	−	0.149230i
$569$	−0.366257	−	1.12722i	−0.0153543	−	0.0472557i	0.943086	−	0.332549i	$-0.107909\pi$
$569$	−0.366257	−	1.12722i	−0.0153543	−	0.0472557i	−0.958440	+	0.285294i	$0.907909\pi$
$570$	34.6307	−	50.4782i	1.45052	−	2.11430i
$571$	−29.5296	+	15.0461i	−1.23578	+	0.629659i	−0.944981	−	0.327126i	$-0.893920\pi$
$571$	−29.5296	+	15.0461i	−1.23578	+	0.629659i	−0.290795	+	0.956785i	$0.593920\pi$
$572$	4.05708	+	9.41028i	0.169635	+	0.393464i
$573$	−27.6534	+	20.0914i	−1.15524	+	0.839330i
$574$	−0.360984	+	11.2442i	−0.0150672	+	0.469325i
$575$	−13.8062	−	20.6442i	−0.575757	−	0.860925i
$576$	9.81103	−	50.3199i	0.408793	−	2.09666i
$577$	40.6082	+	6.43171i	1.69054	+	0.267755i	0.926193	−	0.377049i	$-0.123061\pi$
$577$	40.6082	+	6.43171i	1.69054	+	0.267755i	0.764348	+	0.644804i	$0.223061\pi$
$578$	20.6773	−	9.71292i	0.860063	−	0.404004i
$579$	−52.5461	+	26.7736i	−2.18374	+	1.11267i
$580$	23.8898	−	12.0201i	0.991970	−	0.499106i
$581$	−41.3876	−	21.0880i	−1.71705	−	0.874879i
$582$	−2.52588	+	78.6782i	−0.104701	+	3.26132i
$583$	−12.9293	−	6.58781i	−0.535477	−	0.272839i
$584$	−13.0740	+	14.7690i	−0.541006	+	0.611145i
$585$	−30.0046	+	24.6343i	−1.24054	+	1.01850i
$586$	−33.3975	−	6.39435i	−1.37964	−	0.264148i
$587$	15.7008	−	21.6104i	0.648043	−	0.891955i	−0.350969	−	0.936387i	$-0.614148\pi$
$587$	15.7008	−	21.6104i	0.648043	−	0.891955i	0.999012	+	0.0444318i	$0.0141478\pi$
$588$	8.14512	−	9.81866i	0.335899	−	0.404915i
$589$	−0.573389	+	3.62023i	−0.0236261	+	0.149169i
$590$	−9.30473	+	3.30372i	−0.383070	+	0.136012i
$591$	−1.79266	+	2.46739i	−0.0737404	+	0.101495i
$592$	−4.35785	−	23.1856i	−0.179106	−	0.952920i
$593$	−16.4505	+	16.4505i	−0.675543	+	0.675543i	−0.958988	−	0.283445i	$-0.908522\pi$
$593$	−16.4505	+	16.4505i	−0.675543	+	0.675543i	0.283445	+	0.958988i	$0.408522\pi$
$594$	−26.8579	+	7.78323i	−1.10199	+	0.319350i
$595$	24.6179	+	29.9845i	1.00923	+	1.22925i
$596$	8.91265	+	20.6727i	0.365077	+	0.846786i
$597$	−1.87891	+	5.78270i	−0.0768989	+	0.236670i
$598$	10.6861	+	15.7471i	0.436989	+	0.643947i
$599$		−	23.3489i		−	0.954010i	−0.878900	−	0.477005i	$-0.841722\pi$
$599$		−	23.3489i		−	0.954010i	0.878900	−	0.477005i	$-0.158278\pi$
$600$	−5.84443	+	42.9829i	−0.238598	+	1.75477i
$601$			15.1516i			0.618045i	0.951055	+	0.309022i	$0.100002\pi$
$601$			15.1516i			0.618045i	−0.951055	+	0.309022i	$0.899998\pi$
$602$	−7.08128	+	4.80543i	−0.288611	+	0.195855i
$603$	−8.54373	+	26.2949i	−0.347928	+	1.07081i
$604$	11.1650	+	4.43805i	0.454299	+	0.180582i
$605$	0.980534	+	16.5695i	0.0398644	+	0.673647i
$606$	−9.33696	−	32.2194i	−0.379288	−	1.30882i
$607$	26.9658	−	26.9658i	1.09451	−	1.09451i	0.0994658	−	0.995041i	$-0.468287\pi$
$607$	26.9658	−	26.9658i	1.09451	−	1.09451i	0.995041	−	0.0994658i	$-0.0317134\pi$
$608$	5.46544	+	35.2799i	0.221653	+	1.43079i
$609$	32.4870	−	44.7145i	1.31644	−	1.81192i
$610$	45.6113	−	1.23249i	1.84675	−	0.0499022i
$611$	−3.14729	+	19.8712i	−0.127326	+	0.803902i
$612$	73.4805	−	6.84559i	2.97027	−	0.276717i
$613$	−10.3904	+	14.3011i	−0.419664	+	0.577617i	−0.965542	−	0.260247i	$-0.916196\pi$
$613$	−10.3904	+	14.3011i	−0.419664	+	0.577617i	0.545878	+	0.837864i	$0.316196\pi$
$614$	−8.95782	+	46.7864i	−0.361508	+	1.88815i
$615$	−15.2521	−	9.75915i	−0.615025	−	0.393527i
$616$	16.0890	−	0.979433i	0.648243	−	0.0394625i
$617$	3.77594	+	1.92394i	0.152014	+	0.0774548i	0.528342	−	0.849031i	$-0.322814\pi$
$617$	3.77594	+	1.92394i	0.152014	+	0.0774548i	−0.376329	+	0.926486i	$0.622814\pi$
$618$	−15.8503	−	0.508857i	−0.637593	−	0.0204692i
$619$	36.5563	+	18.6263i	1.46932	+	0.748656i	0.991537	−	0.129822i	$-0.0414406\pi$
$619$	36.5563	+	18.6263i	1.46932	+	0.748656i	0.477783	+	0.878478i	$0.341441\pi$
$620$	−0.790069	−	2.47426i	−0.0317299	−	0.0993688i
$621$	−46.2695	+	23.5755i	−1.85673	+	0.946052i
$622$	−8.41968	−	17.9242i	−0.337599	−	0.718696i
$623$	−19.9439	−	3.15881i	−0.799037	−	0.126555i
$624$	4.25532	−	32.9661i	0.170349	−	1.31970i
$625$	1.94123	−	24.9245i	0.0776491	−	0.996981i
$626$	21.7119	+	0.697038i	0.867784	+	0.0278592i
$627$	29.6192	−	21.5196i	1.18288	−	0.859410i
$628$	6.06439	−	15.2565i	0.241996	−	0.608801i
$629$	30.2583	−	15.4174i	1.20648	−	0.614730i
$630$	20.4316	+	57.5443i	0.814014	+	2.29262i
$631$	8.06752	+	24.8293i	0.321163	+	0.988437i	0.973143	+	0.230201i	$0.0739385\pi$
$631$	8.06752	+	24.8293i	0.321163	+	0.988437i	−0.651980	+	0.758236i	$0.726062\pi$
$632$	−20.0217	−	24.3024i	−0.796421	−	0.966698i
$633$	1.77271	−	3.47915i	0.0704590	−	0.138284i
$634$	1.11532	+	8.87695i	0.0442948	+	0.352549i
$635$	43.3845	−	9.52809i	1.72166	−	0.378111i
$636$	25.1666	+	39.7752i	0.997922	+	1.57719i
$637$	3.31152	−	4.55791i	0.131207	−	0.180591i
$638$	15.8697	−	1.99389i	0.628287	−	0.0789390i
$639$	8.44672	−	6.13690i	0.334147	−	0.242772i
$640$	−14.6962	−	20.5918i	−0.580918	−	0.813962i
$641$	15.7481	+	11.4417i	0.622014	+	0.451919i	0.853624	−	0.520889i	$-0.174400\pi$
$641$	15.7481	+	11.4417i	0.622014	+	0.451919i	−0.231611	+	0.972809i	$0.574400\pi$
$642$	27.4886	+	15.1362i	1.08489	+	0.597379i
$643$		−	16.8366i		−	0.663972i	−0.943284	−	0.331986i	$-0.892281\pi$
$643$		−	16.8366i		−	0.663972i	0.943284	−	0.331986i	$-0.107719\pi$
$644$	29.0035	−	7.40499i	1.14290	−	0.291797i
$645$	−0.813681	−	13.7500i	−0.0320386	−	0.541404i
$646$	−46.5145	+	21.8496i	−1.83009	+	0.859661i
$647$	7.74234	−	3.94492i	0.304383	−	0.155091i	−0.295127	−	0.955458i	$-0.595362\pi$
$647$	7.74234	−	3.94492i	0.304383	−	0.155091i	0.599510	+	0.800367i	$0.295362\pi$
$648$	35.1651	+	9.10502i	1.38141	+	0.357679i
$649$	−5.90527			−0.231802
$650$	−1.35816	+	19.1086i	−0.0532714	+	0.749500i
$651$	−3.79568	−	3.79568i	−0.148765	−	0.148765i
$652$	−30.7125	+	19.4325i	−1.20280	+	0.761035i
$653$	−7.00299	+	21.5530i	−0.274048	+	0.843434i	0.715421	+	0.698693i	$0.246235\pi$
$653$	−7.00299	+	21.5530i	−0.274048	+	0.843434i	−0.989470	+	0.144741i	$0.953765\pi$
$654$	−11.2126	+	31.0782i	−0.438448	+	1.21525i
$655$	−1.09241	+	11.1146i	−0.0426842	+	0.434284i
$656$	10.3783	−	1.95066i	0.405205	−	0.0761605i
$657$	−31.6007	−	31.6007i	−1.23286	−	1.23286i
$658$	27.7209	+	15.2642i	1.08067	+	0.595059i
$659$	−3.69535	−	23.3315i	−0.143950	−	0.908866i	−0.948912	−	0.315540i	$-0.897814\pi$
$659$	−3.69535	−	23.3315i	−0.143950	−	0.908866i	0.804962	−	0.593326i	$-0.202186\pi$
$660$	−11.8953	+	23.0557i	−0.463024	+	0.897442i
$661$	−4.32159	+	27.2854i	−0.168090	+	1.06128i	0.748991	+	0.662580i	$0.230539\pi$
$661$	−4.32159	+	27.2854i	−0.168090	+	1.06128i	−0.917081	+	0.398701i	$0.869461\pi$
$662$	11.0053	+	8.54855i	0.427735	+	0.332249i
$663$	47.2589	−	7.48507i	1.83538	−	0.290696i
$664$	−10.9290	+	42.2096i	−0.424128	+	1.63805i
$665$	−26.9827	−	32.8649i	−1.04635	−	1.27445i
$666$	53.0349	−	6.66340i	2.05506	−	0.258201i
$667$	28.2493	−	9.17874i	1.09382	−	0.355402i
$668$	−2.72049	+	2.39190i	−0.105259	+	0.0925452i
$669$	52.1833	+	26.5887i	2.01752	+	1.02798i
$670$	6.51994	+	11.9844i	0.251887	+	0.462996i
$671$	25.9533	+	8.43272i	1.00191	+	0.325542i
$672$	−46.5045	−	23.8938i	−1.79395	−	0.921724i
$673$	6.06969	−	38.3225i	0.233969	−	1.47722i	−0.538744	−	0.842469i	$-0.681101\pi$
$673$	6.06969	−	38.3225i	0.233969	−	1.47722i	0.772714	−	0.634755i	$-0.218899\pi$
$674$	−3.14832	−	0.101073i	−0.121269	−	0.00389320i
$675$	−51.2734	−	10.1773i	−1.97352	−	0.391723i
$676$	−0.726128	+	11.2974i	−0.0279280	+	0.434515i
$677$	−15.7426	+	11.4377i	−0.605037	+	0.439585i	−0.847663	−	0.530534i	$-0.821991\pi$
$677$	−15.7426	+	11.4377i	−0.605037	+	0.439585i	0.242626	+	0.970120i	$0.421991\pi$
$678$	−0.261712	+	0.725391i	−0.0100510	+	0.0278585i
$679$	52.0047	+	16.8974i	1.99576	+	0.648461i
$680$	22.4851	−	28.6457i	0.862263	−	1.09851i
$681$	−39.6593	+	12.8861i	−1.51975	+	0.493796i
$682$	0.0498446	−	1.55260i	0.00190865	−	0.0594522i
$683$	−6.53679	−	20.1182i	−0.250123	−	0.769800i	−0.994751	−	0.102321i	$-0.967373\pi$
$683$	−6.53679	−	20.1182i	−0.250123	−	0.769800i	0.744628	−	0.667480i	$-0.232627\pi$
$684$	−80.5393	+	7.50320i	−3.07950	+	0.286892i
$685$	−22.7422	−	38.7839i	−0.868935	−	1.48186i
$686$	11.7739	+	17.3500i	0.449529	+	0.662426i
$687$	−56.9786	+	9.02453i	−2.17387	+	0.344307i
$688$	5.84088	+	5.51479i	0.222682	+	0.210250i
$689$	12.2179	+	16.8165i	0.465465	+	0.640657i
$690$	−13.6450	+	46.2065i	−0.519458	+	1.75905i
$691$	−26.5444	+	4.20423i	−1.00980	+	0.159936i	−0.639349	−	0.768917i	$-0.720796\pi$
$691$	−26.5444	+	4.20423i	−1.00980	+	0.159936i	−0.370449	+	0.928853i	$0.620796\pi$
$692$	20.3474	−	5.19496i	0.773490	−	0.197483i
$693$			36.5206i			1.38730i
$694$	6.87267	−	12.4813i	0.260883	−	0.473784i
$695$	33.8473	−	7.43353i	1.28390	−	0.281970i
$696$	−47.5716	−	20.7009i	−1.80320	−	0.784665i
$697$	6.90112	+	13.5442i	0.261399	+	0.513023i
$698$	−7.83316	−	11.5429i	−0.296490	−	0.436907i
$699$	−9.39590	+	9.39590i	−0.355386	+	0.355386i
$700$	27.5477	+	12.2099i	1.04120	+	0.461491i
$701$	5.07989	+	5.07989i	0.191865	+	0.191865i	0.796501	−	0.604637i	$-0.206682\pi$
$701$	5.07989	+	5.07989i	0.191865	+	0.191865i	−0.604637	+	0.796501i	$0.706682\pi$
$702$	39.3413	+	7.53236i	1.48484	+	0.284291i
$703$	−33.1650	+	16.8984i	−1.25084	+	0.637335i
$704$	−4.16214	−	14.5464i	−0.156866	−	0.548240i
$705$	−43.9375	+	25.7642i	−1.65478	+	0.970336i
$706$	−42.3410	+	12.2701i	−1.59353	+	0.461792i
$707$	−23.3017			−0.876349
$708$	16.4740	+	9.77283i	0.619131	+	0.367285i
$709$	−2.86676	−	18.1000i	−0.107663	−	0.679760i	−0.981199	−	0.192999i	$-0.938178\pi$
$709$	−2.86676	−	18.1000i	−0.107663	−	0.679760i	0.873535	−	0.486760i	$-0.161822\pi$
$710$	0.668209	−	5.10851i	0.0250774	−	0.191719i
$711$	57.7173	−	41.9340i	2.16457	−	1.57265i
$712$	1.15172	+	18.9191i	0.0431625	+	0.709023i
$713$	−0.451281	−	2.84928i	−0.0169006	−	0.106706i
$714$	14.1526	−	73.9188i	0.529649	−	2.76634i
$715$	−4.58931	+	10.4978i	−0.171631	+	0.392597i
$716$	−19.4686	+	1.81373i	−0.727576	+	0.0677824i
$717$	−8.27434	+	2.68850i	−0.309011	+	0.100404i
$718$	11.5232	+	12.2876i	0.430040	+	0.458568i
$719$	5.35087	+	16.4683i	0.199554	+	0.614164i	0.999893	+	0.0146163i	$0.00465268\pi$
$719$	5.35087	+	16.4683i	0.199554	+	0.614164i	−0.800339	+	0.599547i	$0.795347\pi$
$720$	48.5924	−	30.4010i	1.81093	−	1.13298i
$721$	−3.40410	+	10.4767i	−0.126775	+	0.390174i
$722$	26.6623	−	12.5243i	0.992268	−	0.466106i
$723$	−31.4578	−	43.2979i	−1.16993	−	1.61027i
$724$	−23.3800	−	26.5919i	−0.868912	−	0.988281i
$725$	28.0561	+	10.3375i	1.04198	+	0.383924i
$726$	23.4878	−	22.0266i	0.871715	−	0.817485i
$727$	8.01269	+	1.26908i	0.297174	+	0.0470678i	0.303241	−	0.952914i	$-0.401931\pi$
$727$	8.01269	+	1.26908i	0.297174	+	0.0470678i	−0.00606707	+	0.999982i	$0.501931\pi$
$728$	−21.1719	−	9.21297i	−0.784681	−	0.341456i
$729$	4.29606	−	13.2219i	0.159113	−	0.489701i
$730$	−22.0445	+	0.595680i	−0.815904	+	0.0220471i
$731$	−5.24965	+	10.3030i	−0.194165	+	0.381071i
$732$	−58.4465	−	66.4757i	−2.16024	−	2.45701i
$733$	−11.7101	−	36.0399i	−0.432521	−	1.33116i	−0.895606	−	0.444849i	$-0.853257\pi$
$733$	−11.7101	−	36.0399i	−0.432521	−	1.33116i	0.463085	−	0.886314i	$-0.346743\pi$
$734$	1.22966	−	1.58306i	0.0453877	−	0.0584318i
$735$	14.2382	−	0.842572i	0.525184	−	0.0310787i
$736$	−12.6714	−	25.0785i	−0.467075	−	0.924407i
$737$	1.27644	+	8.05912i	0.0470182	+	0.296862i
$738$	2.98267	+	23.7395i	0.109794	+	0.873863i
$739$	16.4612	+	2.60719i	0.605533	+	0.0959071i	0.451670	−	0.892185i	$-0.350828\pi$
$739$	16.4612	+	2.60719i	0.605533	+	0.0959071i	0.153863	+	0.988092i	$0.450828\pi$
$740$	15.6117	−	21.2597i	0.573896	−	0.781524i
$741$	−51.7987	+	8.20411i	−1.90287	+	0.301385i
$742$	31.4034	−	9.10048i	1.15286	−	0.334089i
$743$	−33.4793	+	33.4793i	−1.22824	+	1.22824i	−0.263604	+	0.964631i	$0.584911\pi$
$743$	−33.4793	+	33.4793i	−1.22824	+	1.22824i	−0.964631	+	0.263604i	$0.915089\pi$
$744$	−2.70850	+	4.24882i	−0.0992984	+	0.155769i
$745$	−10.0819	+	23.0619i	−0.369372	+	0.844921i
$746$	11.4672	−	5.38656i	0.419843	−	0.197216i
$747$	−93.9540	−	30.5275i	−3.43760	−	1.11694i
$748$	18.4050	−	11.6452i	0.672952	−	0.425791i
$749$	15.4135	−	15.4135i	0.563197	−	0.563197i
$750$	−39.5711	+	28.0398i	−1.44493	+	1.02387i
$751$		−	4.53824i		−	0.165603i	−0.996566	−	0.0828014i	$-0.973613\pi$
$751$		−	4.53824i		−	0.165603i	0.996566	−	0.0828014i	$-0.0263867\pi$
$752$	8.36457	−	28.5027i	0.305025	−	1.03939i
$753$	−7.49546	−	14.7107i	−0.273150	−	0.536087i
$754$	−21.5517	−	7.77558i	−0.784867	−	0.283170i
$755$	4.89844	+	12.5079i	0.178272	+	0.455210i
$756$	32.1456	−	54.1877i	1.16912	−	1.97079i
$757$	26.9824			0.980694			0.490347	−	0.871527i	$-0.336870\pi$
$757$	26.9824			0.980694			0.490347	+	0.871527i	$0.336870\pi$
$758$	−34.7205	+	10.0618i	−1.26111	+	0.365459i
$759$	−16.9368	+	23.3116i	−0.614768	+	0.846156i
$760$	−24.6451	+	31.3975i	−0.893971	+	1.13891i
$761$	6.52572	+	8.98188i	0.236557	+	0.325593i	0.910747	−	0.412965i	$-0.135507\pi$
$761$	6.52572	+	8.98188i	0.236557	+	0.325593i	−0.674190	+	0.738558i	$0.735507\pi$
$762$	−68.0513	−	52.8598i	−2.46524	−	1.91491i
$763$	18.5671	+	13.4898i	0.672174	+	0.488363i
$764$	18.8342	−	11.9168i	0.681397	−	0.431134i
$765$	61.6876	+	54.7946i	2.23032	+	1.98110i
$766$	−7.80664	−	6.06392i	−0.282066	−	0.219098i
$767$	7.53710	+	3.84034i	0.272149	+	0.138667i
$768$	−12.4622	+	47.4684i	−0.449692	+	1.71287i
$769$	−20.0944	+	6.52906i	−0.724622	+	0.235444i	−0.648026	−	0.761618i	$-0.724405\pi$
$769$	−20.0944	+	6.52906i	−0.724622	+	0.235444i	−0.0765959	+	0.997062i	$0.524405\pi$
$770$	13.0826	+	12.3941i	0.471463	+	0.446654i
$771$	32.8124	+	64.3979i	1.18171	+	2.31923i
$772$	35.3111	−	15.2238i	1.27088	−	0.547915i
$773$	17.3316	+	23.8549i	0.623374	+	0.858001i	0.997593	−	0.0693395i	$-0.0220892\pi$
$773$	17.3316	+	23.8549i	0.623374	+	0.858001i	−0.374219	+	0.927340i	$0.622089\pi$
$774$	−13.2760	+	12.4501i	−0.477198	+	0.447511i
$775$	1.41789	−	2.53423i	0.0509320	−	0.0910323i
$776$	4.93410	−	51.0897i	0.177124	−	1.83401i
$777$	8.52746	−	53.8403i	0.305921	−	1.93151i
$778$	−4.37266	+	12.1198i	−0.156767	+	0.434515i
$779$	−7.56406	−	14.8453i	−0.271011	−	0.531888i
$780$	30.1761	−	21.6910i	1.08048	−	0.776661i
$781$	1.39888	−	2.74545i	0.0500558	−	0.0982399i
$782$	29.5031	−	27.6677i	1.05503	−	0.989394i
$783$	28.3831	−	55.7051i	1.01433	−	1.99074i
$784$	−5.71061	+	6.04828i	−0.203950	+	0.216010i
$785$	17.0915	−	6.69349i	0.610022	−	0.238901i
$786$	17.9274	−	12.1657i	0.639451	−	0.433938i
$787$	−31.3374	−	22.7679i	−1.11706	−	0.811589i	−0.133296	−	0.991076i	$-0.542556\pi$
$787$	−31.3374	−	22.7679i	−1.11706	−	0.811589i	−0.983760	+	0.179487i	$0.942556\pi$
$788$	1.26967	−	1.53054i	0.0452300	−	0.0545232i
$789$	−40.3124	−	6.38486i	−1.43516	−	0.227307i
$790$	4.56594	−	34.9070i	0.162449	−	1.24193i
$791$	0.433371	+	0.314863i	0.0154089	+	0.0111952i
$792$	33.4703	−	7.41017i	1.18932	−	0.263309i
$793$	−27.6410	−	27.6410i	−0.981561	−	0.981561i
$794$	−13.4669	+	24.4569i	−0.477922	+	0.867944i
$795$	−13.2768	+	50.9216i	−0.470878	+	1.80600i
$796$	1.46444	−	3.68418i	0.0519059	−	0.130582i
$797$	−8.89181	−	2.88912i	−0.314964	−	0.102338i	0.147269	−	0.989096i	$-0.452952\pi$
$797$	−8.89181	−	2.88912i	−0.314964	−	0.102338i	−0.462233	+	0.886758i	$0.652952\pi$
$798$	−15.5122	+	81.0197i	−0.549125	+	2.86807i
$799$	42.7595			1.51272
$800$	5.60059	−	27.7242i	0.198011	−	0.980200i
$801$	−42.9448			−1.51738
$802$	−6.19028	+	32.3316i	−0.218586	+	1.14167i
$803$	−12.5435	−	4.07564i	−0.442652	−	0.143826i
$804$	9.77640	−	24.5950i	0.344787	−	0.867400i
$805$	28.1902	+	18.0377i	0.993575	+	0.635744i
$806$	−1.07331	+	1.94922i	−0.0378058	+	0.0686584i
$807$	41.4297	+	41.4297i	1.45840	+	1.45840i
$808$	4.72799	+	21.3554i	0.166330	+	0.751282i
$809$	24.8580	+	18.0604i	0.873962	+	0.634971i	0.931647	−	0.363364i	$-0.118372\pi$
$809$	24.8580	+	18.0604i	0.873962	+	0.634971i	−0.0576848	+	0.998335i	$0.518372\pi$
$810$	19.4083	+	35.6745i	0.681938	+	1.25348i
$811$	3.79220	+	0.600625i	0.133162	+	0.0210908i	0.222660	−	0.974896i	$-0.428526\pi$
$811$	3.79220	+	0.600625i	0.133162	+	0.0210908i	−0.0894976	+	0.995987i	$0.528526\pi$
$812$	−23.0092	+	27.7367i	−0.807463	+	0.973369i
$813$	8.61177	+	6.25681i	0.302028	+	0.219436i
$814$	13.0531	−	8.85795i	0.457510	−	0.310471i
$815$	−39.3193	−	10.2517i	−1.37729	−	0.359101i
$816$	−70.6166	+	2.02782i	−2.47207	+	0.0709880i
$817$	5.75395	−	11.2928i	0.201305	−	0.395084i
$818$	−17.1703	+	16.1021i	−0.600345	+	0.562997i
$819$	23.7503	−	46.6125i	0.829902	−	1.62877i
$820$	9.51629	+	6.98809i	0.332323	+	0.244035i
$821$	−19.6303	−	38.5267i	−0.685103	−	1.34459i	−0.927284	−	0.374360i	$-0.877862\pi$
$821$	−19.6303	−	38.5267i	−0.685103	−	1.34459i	0.242180	−	0.970231i	$-0.422138\pi$
$822$	−29.6001	+	82.0433i	−1.03242	+	2.86159i
$823$	5.24982	−	33.1460i	0.182997	−	1.15540i	−0.709621	−	0.704584i	$-0.751134\pi$
$823$	5.24982	−	33.1460i	0.182997	−	1.15540i	0.892618	−	0.450814i	$-0.148866\pi$
$824$	10.2924	+	0.994012i	0.358553	+	0.0346281i
$825$	−27.9135	+	7.88465i	−0.971822	+	0.274508i
$826$	9.70549	−	9.10171i	0.337697	−	0.316689i
$827$	−24.9189	−	34.2979i	−0.866515	−	1.19266i	−0.979976	−	0.199114i	$-0.936194\pi$
$827$	−24.9189	−	34.2979i	−0.866515	−	1.19266i	0.113461	−	0.993542i	$-0.463806\pi$
$828$	58.4606	−	25.2042i	2.03165	−	0.875907i
$829$	−24.9830	−	49.0320i	−0.867697	−	1.70295i	−0.696303	−	0.717748i	$-0.745173\pi$
$829$	−24.9830	−	49.0320i	−0.867697	−	1.70295i	−0.171393	−	0.985203i	$-0.554827\pi$
$830$	−42.8212	+	23.2963i	−1.48634	+	0.808627i
$831$	−28.1354	+	9.14174i	−0.976006	+	0.317124i
$832$	−4.14764	+	21.2729i	−0.143793	+	0.737504i
$833$	−10.6689	−	5.43606i	−0.369654	−	0.188348i
$834$	−53.0915	−	41.2396i	−1.83841	−	1.42801i
$835$	−4.03061	−	0.396154i	−0.139485	−	0.0137095i
$836$	−20.1730	+	12.7639i	−0.697698	+	0.441449i
$837$	−4.91230	−	3.56900i	−0.169794	−	0.123363i
$838$	0.931185	+	0.723311i	0.0321672	+	0.0249864i
$839$	−4.55856	−	6.27432i	−0.157379	−	0.216614i	0.723045	−	0.690801i	$-0.242742\pi$
$839$	−4.55856	−	6.27432i	−0.157379	−	0.216614i	−0.880424	+	0.474187i	$0.842742\pi$
$840$	−15.9851	−	56.2268i	−0.551538	−	1.94001i
$841$	−3.97357	+	5.46915i	−0.137020	+	0.188591i
$842$	4.45962	−	1.29237i	0.153689	−	0.0445378i
$843$	−25.7007			−0.885178
$844$	−1.29900	+	2.18972i	−0.0447134	+	0.0753731i
$845$	−9.78230	+	8.03145i	−0.336521	+	0.276290i
$846$	63.3084	+	22.8409i	2.17659	+	0.785285i
$847$	−10.1546	−	19.9296i	−0.348917	−	0.684788i
$848$	−14.7122	−	26.9340i	−0.505221	−	0.924917i
$849$		−	61.0711i		−	2.09596i
$850$	40.5639	−	3.50215i	1.39133	−	0.120123i
$851$	20.7149	−	20.7149i	0.710096	−	0.710096i
$852$	−8.44600	+	5.34396i	−0.289355	+	0.183081i
$853$	25.3339	+	8.23147i	0.867415	+	0.281840i	0.708722	−	0.705488i	$-0.249272\pi$
$853$	25.3339	+	8.23147i	0.867415	+	0.281840i	0.158693	+	0.987328i	$0.449272\pi$
$854$	−55.6522	+	26.1419i	−1.90438	+	0.894558i
$855$	−67.6135	−	60.0583i	−2.31233	−	2.05395i
$856$	−17.2536	−	10.9987i	−0.589715	−	0.375927i
$857$	10.3941	−	10.3941i	0.355057	−	0.355057i	−0.506930	−	0.861987i	$-0.669220\pi$
$857$	10.3941	−	10.3941i	0.355057	−	0.355057i	0.861987	+	0.506930i	$0.169220\pi$
$858$	21.3479	−	6.18647i	0.728805	−	0.211203i
$859$	−22.9076	+	3.62822i	−0.781599	+	0.123793i	−0.534468	−	0.845189i	$-0.679488\pi$
$859$	−22.9076	+	3.62822i	−0.781599	+	0.123793i	−0.247131	+	0.968982i	$0.579488\pi$
$860$	−0.0456043	+	8.98104i	−0.00155509	+	0.306251i
$861$	24.1000	+	3.81706i	0.821325	+	0.130085i
$862$	6.13157	+	48.8021i	0.208842	+	1.66221i
$863$	3.16396	+	19.9765i	0.107703	+	0.680008i	0.981173	+	0.193130i	$0.0618640\pi$
$863$	3.16396	+	19.9765i	0.107703	+	0.680008i	−0.873470	+	0.486877i	$0.838136\pi$
$864$	−56.1842	−	18.4658i	−1.91143	−	0.628221i
$865$	19.7768	+	12.6543i	0.672432	+	0.430259i
$866$	15.2866	−	19.6798i	0.519459	−	0.668747i
$867$	−15.3115	−	47.1238i	−0.520004	−	1.60041i
$868$	2.31108	+	2.62857i	0.0784431	+	0.0892195i
$869$	9.55866	−	18.7599i	0.324255	−	0.636387i
$870$	−19.4078	−	54.6609i	−0.657987	−	1.85318i
$871$	3.61188	−	11.1162i	0.122384	−	0.376659i
$872$	8.59575	−	19.7534i	0.291089	−	0.668936i
$873$	114.862	+	18.1923i	3.88749	+	0.615717i
$874$	−32.3372	+	30.3255i	−1.09382	+	1.02578i
$875$	11.0569	+	31.8228i	0.373792	+	1.07581i
$876$	28.2479	+	32.1285i	0.954408	+	1.08552i
$877$	−6.51158	−	8.96242i	−0.219880	−	0.302639i	0.684799	−	0.728732i	$-0.259890\pi$
$877$	−6.51158	−	8.96242i	−0.219880	−	0.302639i	−0.904680	+	0.426092i	$0.859890\pi$
$878$	−1.48941	+	0.699632i	−0.0502651	+	0.0236114i
$879$	−22.7907	+	70.1425i	−0.768711	+	2.36585i
$880$	8.70445	−	14.5047i	0.293427	−	0.488953i
$881$	−6.23665	−	19.1944i	−0.210118	−	0.646677i	−0.999464	−	0.0327288i	$-0.989580\pi$
$881$	−6.23665	−	19.1944i	−0.210118	−	0.646677i	0.789346	−	0.613948i	$-0.210420\pi$
$882$	−12.8922	−	13.7474i	−0.434103	−	0.462901i
$883$	8.52353	−	2.76946i	0.286840	−	0.0931998i	−0.162063	−	0.986780i	$-0.551815\pi$
$883$	8.52353	−	2.76946i	0.286840	−	0.0931998i	0.448903	+	0.893581i	$0.351815\pi$
$884$	−31.0641	+	2.89399i	−1.04480	+	0.0973354i
$885$	4.59380	+	20.9171i	0.154419	+	0.703119i
$886$	−3.67596	+	19.1994i	−0.123496	+	0.645018i
$887$	5.35861	+	33.8329i	0.179925	+	1.13600i	0.897987	+	0.440021i	$0.145029\pi$
$887$	5.35861	+	33.8329i	0.179925	+	1.13600i	−0.718063	+	0.695978i	$0.754971\pi$
$888$	−51.0736	+	3.10916i	−1.71392	+	0.104337i
$889$	−48.4249	+	35.1827i	−1.62412	+	1.17999i
$890$	−14.5743	+	15.3838i	−0.488533	+	0.515668i
$891$	3.79965	+	23.9901i	0.127293	+	0.803697i
$892$	−32.8433	−	19.4835i	−1.09967	−	0.652357i
$893$	−46.8671			−1.56835
$894$	46.8974	−	13.5905i	1.56849	−	0.454536i
$895$	−16.3441	−	14.5178i	−0.546323	−	0.485276i
$896$	29.2608	+	17.4925i	0.977536	+	0.584383i
$897$	36.7771	−	18.7389i	1.22795	−	0.625673i
$898$	−14.2442	−	2.72722i	−0.475334	−	0.0910084i
$899$	2.45584	+	2.45584i	0.0819067	+	0.0819067i
$900$	61.9283	+	16.4828i	2.06428	+	0.549428i
$901$	31.2386	−	31.2386i	1.04071	−	1.04071i
$902$	3.96500	+	5.84282i	0.132020	+	0.194545i
$903$	8.42665	+	16.5382i	0.280421	+	0.550358i
$904$	0.200632	−	0.461062i	0.00667292	−	0.0153347i
$905$	3.87228	−	39.3980i	0.128719	−	1.30963i
$906$	12.5695	−	22.8272i	0.417594	−	0.758384i
$907$		−	4.94754i		−	0.164280i	−0.996621	−	0.0821402i	$-0.973824\pi$
$907$		−	4.94754i		−	0.164280i	0.996621	−	0.0821402i	$-0.0261755\pi$
$908$	26.3449	−	6.72623i	0.874288	−	0.223218i
$909$	−48.9470	+	7.75245i	−1.62347	+	0.257133i
$910$	−8.63750	−	24.3270i	−0.286330	−	0.806431i
$911$	−1.54477	−	2.12619i	−0.0511805	−	0.0704439i	0.782660	−	0.622450i	$-0.213863\pi$
$911$	−1.54477	−	2.12619i	−0.0511805	−	0.0704439i	−0.833840	+	0.552006i	$0.813863\pi$
$912$	77.4002	−	2.22262i	2.56298	−	0.0735984i
$913$	−28.7959	+	4.56083i	−0.953007	+	0.150941i
$914$	−7.47112	−	11.0094i	−0.247123	−	0.364160i
$915$	9.68011	−	98.4889i	0.320015	−	3.25594i
$916$	37.4530	−	3.48920i	1.23748	−	0.115286i
$917$	−4.65063	−	14.3132i	−0.153577	−	0.472662i
$918$	2.73168	−	85.0887i	0.0901588	−	2.80834i
$919$	−37.7745	+	12.2737i	−1.24607	+	0.404872i	−0.856510	−	0.516131i	$-0.827372\pi$
$919$	−37.7745	+	12.2737i	−1.24607	+	0.404872i	−0.389557	+	0.921002i	$0.627372\pi$
$920$	10.8112	−	29.4956i	0.356435	−	0.972441i
$921$	98.2625	+	31.9274i	3.23786	+	1.05204i
$922$	−13.8007	+	38.2518i	−0.454503	+	1.25976i
$923$	−3.57087	+	2.59439i	−0.117537	+	0.0853953i
$924$	2.24241	−	34.8883i	0.0737700	−	1.14774i
$925$	29.2836	−	3.47801i	0.962839	−	0.114356i
$926$	−16.8378	−	0.540561i	−0.553326	−	0.0177639i
$927$	−3.66499	+	23.1398i	−0.120374	+	0.760011i
$928$	30.0887	+	15.4595i	0.987711	+	0.507482i
$929$	−12.3637	−	4.01720i	−0.405639	−	0.131800i	0.0990888	−	0.995079i	$-0.468407\pi$
$929$	−12.3637	−	4.01720i	−0.405639	−	0.131800i	−0.504728	+	0.863278i	$0.668407\pi$
$930$	−5.53824	+	1.03124i	−0.181606	+	0.0338156i
$931$	11.6937	+	5.95826i	0.383247	+	0.195274i
$932$	6.50681	−	5.72088i	0.213138	−	0.187394i
$933$	−40.8495	+	13.2728i	−1.33735	+	0.434532i
$934$	20.1452	−	2.53108i	0.659172	−	0.0828195i
$935$	23.5627	+	6.14349i	0.770582	+	0.200913i
$936$	−47.5384	−	12.3087i	−1.55384	−	0.402324i
$937$	−55.9030	+	8.85417i	−1.82627	+	0.289253i	−0.972759	−	0.231818i	$-0.925533\pi$
$937$	−55.9030	+	8.85417i	−1.82627	+	0.289253i	−0.853513	+	0.521071i	$0.825533\pi$
$938$	−14.5193	−	11.2781i	−0.474071	−	0.368241i
$939$	7.37053	−	46.5357i	0.240528	−	1.51863i
$940$	29.6673	−	14.9270i	0.967642	−	0.486865i
$941$	3.91205	+	24.6997i	0.127529	+	0.805188i	0.965677	+	0.259745i	$0.0836385\pi$
$941$	3.91205	+	24.6997i	0.127529	+	0.805188i	−0.838148	+	0.545443i	$0.816362\pi$
$942$	−31.1924	−	17.1757i	−1.01630	−	0.559613i
$943$	9.27239	+	9.27239i	0.301950	+	0.301950i
$944$	−10.3108	−	7.04810i	−0.335588	−	0.229396i
$945$	68.8021	−	15.1103i	2.23813	−	0.491538i
$946$	−1.82291	+	5.05260i	−0.0592680	+	0.164274i
$947$	−7.54840	+	23.2316i	−0.245290	+	0.754925i	0.750298	+	0.661099i	$0.229910\pi$
$947$	−7.54840	+	23.2316i	−0.245290	+	0.754925i	−0.995589	+	0.0938261i	$0.970090\pi$
$948$	−57.7123	+	36.5158i	−1.87441	+	1.18598i
$949$	13.3592	+	13.3592i	0.433660	+	0.433660i
$950$	−44.4605	+	3.83857i	−1.44249	+	0.124540i
$951$	19.4048			0.629243
$952$	−12.3005	+	47.5066i	−0.398662	+	1.53970i
$953$	22.2202	−	11.3218i	0.719783	−	0.366748i	−0.0554170	−	0.998463i	$-0.517649\pi$
$953$	22.2202	−	11.3218i	0.719783	−	0.366748i	0.775200	+	0.631715i	$0.217649\pi$
$954$	62.9377	−	29.5642i	2.03768	−	0.957176i
$955$	24.1122	+	6.28676i	0.780252	+	0.203435i
$956$	5.49649	−	1.40333i	0.177769	−	0.0453869i
$957$		−	34.6907i		−	1.12139i
$958$	−1.97888	−	1.08964i	−0.0639347	−	0.0352048i
$959$	49.0152	+	35.6116i	1.58278	+	1.14996i
$960$	−48.2871	+	26.0586i	−1.55846	+	0.841037i
$961$	−24.8066	+	18.0231i	−0.800214	+	0.581390i
$962$	−22.4206	+	2.81697i	−0.722870	+	0.0908227i
$963$	27.2493	−	37.5054i	0.878095	−	1.20859i
$964$	18.6585	+	29.4893i	0.600950	+	0.949786i
$965$	39.3921	+	17.2209i	1.26808	+	0.554362i
$966$	−8.09355	−	64.4177i	−0.260406	−	2.07261i
$967$	8.68337	−	17.0421i	0.279238	−	0.548036i	−0.708206	−	0.706006i	$-0.750495\pi$
$967$	8.68337	−	17.0421i	0.279238	−	0.548036i	0.987444	+	0.157970i	$0.0504950\pi$
$968$	−16.2046	+	13.3503i	−0.520835	+	0.429093i
$969$	34.4437	+	106.007i	1.10649	+	3.40543i
$970$	45.4980	−	34.9723i	1.46085	−	1.12289i
$971$	−13.8306	+	7.04703i	−0.443844	+	0.226150i	−0.661606	−	0.749852i	$-0.730125\pi$
$971$	−13.8306	+	7.04703i	−0.443844	+	0.226150i	0.217761	+	0.976002i	$0.430125\pi$
$972$	5.93115	−	14.9213i	0.190242	−	0.478602i
$973$	−37.7796	+	27.4485i	−1.21116	+	0.879958i
$974$	0.700392	+	0.0224853i	0.0224420	+	0.000720476i
$975$	40.7545	+	8.08936i	1.30519	+	0.259067i
$976$	35.2505	+	45.6997i	1.12834	+	1.46281i
$977$	−41.7734	−	6.61626i	−1.33645	−	0.211673i	−0.553028	−	0.833163i	$-0.686528\pi$
$977$	−41.7734	−	6.61626i	−1.33645	−	0.211673i	−0.783422	+	0.621490i	$0.786528\pi$
$978$	33.5147	+	71.3476i	1.07168	+	2.28145i
$979$	−11.2926	+	5.75387i	−0.360913	+	0.183894i
$980$	−9.29993	−	0.0472236i	−0.297075	−	0.00150850i
$981$	43.4897	+	22.1591i	1.38852	+	0.707486i
$982$	35.3345	+	1.13437i	1.12757	+	0.0361994i
$983$	−7.67178	−	3.90897i	−0.244692	−	0.124677i	0.327344	−	0.944905i	$-0.393846\pi$
$983$	−7.67178	−	3.90897i	−0.244692	−	0.124677i	−0.572036	+	0.820228i	$0.693846\pi$
$984$	−1.39172	−	22.8616i	−0.0443665	−	0.728801i
$985$	2.21946	−	0.131341i	0.0707179	−	0.00418487i
$986$	−9.15686	+	47.8260i	−0.291614	+	1.52309i
$987$	40.3437	−	55.5283i	1.28415	−	1.76749i
$988$	34.0482	−	3.17199i	1.08322	−	0.100915i
$989$	−1.56045	+	9.85230i	−0.0496195	+	0.313285i
$990$	31.6045	+	21.6823i	1.00446	+	0.689110i
$991$	5.42976	−	7.47343i	0.172482	−	0.237401i	−0.714021	−	0.700125i	$-0.753128\pi$
$991$	5.42976	−	7.47343i	0.172482	−	0.237401i	0.886503	+	0.462724i	$0.153128\pi$
$992$	1.94010	−	2.65140i	0.0615982	−	0.0841820i
$993$	21.3721	−	21.3721i	0.678224	−	0.678224i
$994$	1.93243	+	6.66830i	0.0612928	+	0.211506i
$995$	4.12730	−	1.61636i	0.130844	−	0.0512421i
$996$	87.8802	+	34.9319i	2.78459	+	1.10686i
$997$	−2.94614	+	9.06730i	−0.0933053	+	0.287164i	−0.986808	−	0.161893i	$-0.948240\pi$
$997$	−2.94614	+	9.06730i	−0.0933053	+	0.287164i	0.893503	+	0.449057i	$0.148240\pi$
$998$	26.7497	−	18.1526i	0.846748	−	0.574612i
$999$		−	61.6609i		−	1.95086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bm.a.227.27	yes	464
16.11	odd	4		400.2.bd.a.27.33	✓	464
25.13	odd	20		400.2.bd.a.163.33	yes	464
400.363	even	20	inner	400.2.bm.a.363.27	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bd.a.27.33	✓	464	16.11	odd	4
400.2.bd.a.163.33	yes	464	25.13	odd	20
400.2.bm.a.227.27	yes	464	1.1	even	1	trivial
400.2.bm.a.363.27	yes	464	400.363	even	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.265938 + 1.38898i) q^{2} +(2.91719 + 0.947853i) q^{3} +(-1.85855 - 0.738766i) q^{4} +(-0.815404 - 2.08209i) q^{5} +(-2.09234 + 3.79986i) q^{6} +(2.13068 + 2.13068i) q^{7} +(1.52039 - 2.38504i) q^{8} +(5.18453 + 3.76678i) q^{9} +O(q^{10})\)	\(q+(-0.265938 + 1.38898i) q^{2} +(2.91719 + 0.947853i) q^{3} +(-1.85855 - 0.738766i) q^{4} +(-0.815404 - 2.08209i) q^{5} +(-2.09234 + 3.79986i) q^{6} +(2.13068 + 2.13068i) q^{7} +(1.52039 - 2.38504i) q^{8} +(5.18453 + 3.76678i) q^{9} +(3.10884 - 0.578876i) q^{10} +(1.86799 + 0.295860i) q^{11} +(-4.72152 - 3.91676i) q^{12} +(-2.19177 - 1.59242i) q^{13} +(-3.52610 + 2.39285i) q^{14} +(-0.405170 - 6.84675i) q^{15} +(2.90845 + 2.74607i) q^{16} +(-2.61405 + 5.13036i) q^{17} +(-6.61076 + 6.19950i) q^{18} +(2.86516 - 5.62320i) q^{19} +(-0.0227085 + 4.47208i) q^{20} +(4.19602 + 8.23516i) q^{21} +(-0.907714 + 2.51593i) q^{22} +(-0.777021 + 4.90592i) q^{23} +(6.69595 - 5.51650i) q^{24} +(-3.67023 + 3.39549i) q^{25} +(2.79472 - 2.62085i) q^{26} +(6.14515 + 8.45807i) q^{27} +(-2.38591 - 5.53405i) q^{28} +(-2.71486 - 5.32821i) q^{29} +(9.61778 + 1.25803i) q^{30} +(-0.552358 + 0.179472i) q^{31} +(-4.58772 + 3.30951i) q^{32} +(5.16885 + 2.63366i) q^{33} +(-6.43081 - 4.99523i) q^{34} +(2.69891 - 6.17363i) q^{35} +(-6.85296 - 10.8309i) q^{36} +(-4.77149 - 3.46669i) q^{37} +(7.04858 + 5.47508i) q^{38} +(-4.88444 - 6.72286i) q^{39} +(-6.20561 - 1.22084i) q^{40} +(1.55176 - 2.13581i) q^{41} +(-12.5544 + 3.63817i) q^{42} +2.00825 q^{43} +(-3.25319 - 1.92988i) q^{44} +(3.61531 - 13.8661i) q^{45} +(-6.60761 - 2.38394i) q^{46} +(-3.37142 - 6.61678i) q^{47} +(5.88163 + 10.7676i) q^{48} +2.07955i q^{49} +(-3.74024 - 6.00089i) q^{50} +(-12.4885 + 12.4885i) q^{51} +(2.89711 + 4.57880i) q^{52} +(-7.29703 - 2.37095i) q^{53} +(-13.3823 + 6.28619i) q^{54} +(-0.907156 - 4.13057i) q^{55} +(8.32121 - 1.84227i) q^{56} +(13.6882 - 13.6882i) q^{57} +(8.12278 - 2.35392i) q^{58} +(-3.08394 + 0.488448i) q^{59} +(-4.30512 + 13.0244i) q^{60} +(14.2512 + 2.25717i) q^{61} +(-0.102391 - 0.814945i) q^{62} +(3.02076 + 19.0723i) q^{63} +(-3.37680 - 7.25239i) q^{64} +(-1.52838 + 5.86194i) q^{65} +(-5.03270 + 6.47906i) q^{66} +(1.33320 + 4.10317i) q^{67} +(8.64849 - 7.60388i) q^{68} +(-6.91681 + 13.5750i) q^{69} +(7.85733 + 5.39054i) q^{70} +(0.503455 - 1.54948i) q^{71} +(16.8664 - 6.63831i) q^{72} +(-6.88778 - 1.09092i) q^{73} +(6.08410 - 5.70560i) q^{74} +(-13.9252 + 6.42647i) q^{75} +(-9.47929 + 8.33433i) q^{76} +(3.34970 + 4.61046i) q^{77} +(10.6369 - 4.99655i) q^{78} +(3.44016 - 10.5877i) q^{79} +(3.34602 - 8.29482i) q^{80} +(3.96862 + 12.2142i) q^{81} +(2.55394 + 2.72336i) q^{82} +(-14.6610 + 4.76365i) q^{83} +(-1.71468 - 18.4054i) q^{84} +(12.8134 + 1.25938i) q^{85} +(-0.534068 + 2.78942i) q^{86} +(-2.86940 - 18.1167i) q^{87} +(3.54572 - 4.00540i) q^{88} +(-5.42146 + 3.93892i) q^{89} +(18.2984 + 8.70913i) q^{90} +(-1.27703 - 8.06288i) q^{91} +(5.06846 - 8.54388i) q^{92} -1.78145 q^{93} +(10.0872 - 2.92320i) q^{94} +(-14.0443 - 1.38036i) q^{95} +(-16.5202 + 5.30598i) q^{96} +(16.1691 - 8.23856i) q^{97} +(-2.88847 - 0.553032i) q^{98} +(8.57021 + 8.57021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9}+O(q^{10}) \) 464 * q - 8 * q^2 - 10 * q^3 - 10 * q^4 - 8 * q^5 - 6 * q^6 - 16 * q^7 - 2 * q^8 + 108 * q^9	\( 464 q - 8 q^{2} - 10 q^{3} - 10 q^{4} - 8 q^{5} - 6 q^{6} - 16 q^{7} - 2 q^{8} + 108 q^{9} - 4 q^{10} - 6 q^{11} - 22 q^{12} - 6 q^{13} - 10 q^{14} - 12 q^{15} + 34 q^{16} - 16 q^{17} - 24 q^{18} - 10 q^{19} - 14 q^{20} - 36 q^{21} - 60 q^{22} - 16 q^{23} - 12 q^{24} - 16 q^{26} - 10 q^{27} + 6 q^{28} - 10 q^{29} - 106 q^{30} + 2 q^{32} - 16 q^{33} - 10 q^{34} - 60 q^{35} + 10 q^{36} - 6 q^{37} - 38 q^{38} - 20 q^{39} + 16 q^{40} - 38 q^{42} + 16 q^{43} - 80 q^{44} - 4 q^{45} - 6 q^{46} + 24 q^{47} + 60 q^{48} + 38 q^{50} - 16 q^{51} - 160 q^{52} - 10 q^{53} - 16 q^{55} - 6 q^{56} - 12 q^{57} - 110 q^{58} - 10 q^{59} - 50 q^{60} - 6 q^{61} - 14 q^{62} - 12 q^{63} + 20 q^{64} - 16 q^{65} - 6 q^{66} + 30 q^{67} - 50 q^{68} - 22 q^{69} + 38 q^{70} - 12 q^{71} + 172 q^{72} - 8 q^{73} + 8 q^{74} - 58 q^{75} - 16 q^{76} + 60 q^{77} - 48 q^{78} + 208 q^{80} - 96 q^{81} - 14 q^{82} - 10 q^{83} - 22 q^{84} + 2 q^{85} - 126 q^{86} - 72 q^{87} + 86 q^{88} + 110 q^{90} + 64 q^{91} - 66 q^{92} - 28 q^{93} - 10 q^{94} - 160 q^{95} - 36 q^{96} - 16 q^{97} - 44 q^{98} - 12 q^{99}+O(q^{100}) \) 464 * q - 8 * q^2 - 10 * q^3 - 10 * q^4 - 8 * q^5 - 6 * q^6 - 16 * q^7 - 2 * q^8 + 108 * q^9 - 4 * q^10 - 6 * q^11 - 22 * q^12 - 6 * q^13 - 10 * q^14 - 12 * q^15 + 34 * q^16 - 16 * q^17 - 24 * q^18 - 10 * q^19 - 14 * q^20 - 36 * q^21 - 60 * q^22 - 16 * q^23 - 12 * q^24 - 16 * q^26 - 10 * q^27 + 6 * q^28 - 10 * q^29 - 106 * q^30 + 2 * q^32 - 16 * q^33 - 10 * q^34 - 60 * q^35 + 10 * q^36 - 6 * q^37 - 38 * q^38 - 20 * q^39 + 16 * q^40 - 38 * q^42 + 16 * q^43 - 80 * q^44 - 4 * q^45 - 6 * q^46 + 24 * q^47 + 60 * q^48 + 38 * q^50 - 16 * q^51 - 160 * q^52 - 10 * q^53 - 16 * q^55 - 6 * q^56 - 12 * q^57 - 110 * q^58 - 10 * q^59 - 50 * q^60 - 6 * q^61 - 14 * q^62 - 12 * q^63 + 20 * q^64 - 16 * q^65 - 6 * q^66 + 30 * q^67 - 50 * q^68 - 22 * q^69 + 38 * q^70 - 12 * q^71 + 172 * q^72 - 8 * q^73 + 8 * q^74 - 58 * q^75 - 16 * q^76 + 60 * q^77 - 48 * q^78 + 208 * q^80 - 96 * q^81 - 14 * q^82 - 10 * q^83 - 22 * q^84 + 2 * q^85 - 126 * q^86 - 72 * q^87 + 86 * q^88 + 110 * q^90 + 64 * q^91 - 66 * q^92 - 28 * q^93 - 10 * q^94 - 160 * q^95 - 36 * q^96 - 16 * q^97 - 44 * q^98 - 12 * q^99

Introduction

L-functions

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