LMFDB - Embedded newform 570.2.bh.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	570.127
Dual form			570.2.bh.a.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 + 0.996195i) q^{2} +(-0.422618 - 0.906308i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-2.20941 + 0.344270i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.04704 - 0.280552i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.642788 + 0.766044i) q^{9} +O(q^{10})$	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.422618 - 0.906308i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-2.20941 + 0.344270i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.04704 - 0.280552i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.642788 + 0.766044i) q^{9} +(-0.150397 - 2.23100i) q^{10} +(0.117008 + 0.202663i) q^{11} +(0.258819 + 0.965926i) q^{12} +(1.99368 + 0.929669i) q^{13} +(0.188230 + 1.06750i) q^{14} +(1.24575 + 1.85691i) q^{15} +(0.939693 + 0.342020i) q^{16} +(1.87289 + 0.163857i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(4.35241 - 0.237722i) q^{19} +(2.23562 + 0.0446200i) q^{20} +(-0.696763 - 0.830370i) q^{21} +(-0.212090 + 0.0988992i) q^{22} +(2.16110 + 3.08637i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(4.76296 - 1.52126i) q^{25} +(-1.09989 + 1.90507i) q^{26} +(0.965926 + 0.258819i) q^{27} +(-1.07985 + 0.0944743i) q^{28} +(0.821087 + 0.688973i) q^{29} +(-1.95842 + 1.07917i) q^{30} +(4.21298 + 2.43236i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(0.134226 - 0.191694i) q^{33} +(-0.326466 + 1.85148i) q^{34} +(-2.21674 + 0.980317i) q^{35} +(0.766044 - 0.642788i) q^{36} +(3.32063 - 3.32063i) q^{37} +(-0.142520 + 4.35657i) q^{38} -2.19978i q^{39} +(-0.239298 + 2.22323i) q^{40} +(-1.70610 + 4.68746i) q^{41} +(0.887937 - 0.621740i) q^{42} +(6.80597 + 4.76559i) q^{43} +(-0.0800380 - 0.219902i) q^{44} +(1.15645 - 1.91380i) q^{45} +(-3.26298 + 1.88388i) q^{46} +(-0.0782572 - 0.894484i) q^{47} +(-0.0871557 - 0.996195i) q^{48} +(-5.04460 + 2.91250i) q^{49} +(1.10036 + 4.87742i) q^{50} +(-0.643013 - 1.76666i) q^{51} +(-1.80196 - 1.26174i) q^{52} +(5.90623 - 4.13559i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-0.328288 - 0.407483i) q^{55} -1.08397i q^{56} +(-2.05486 - 3.84416i) q^{57} +(-0.757914 + 0.757914i) q^{58} +(0.887152 - 0.744409i) q^{59} +(-0.904376 - 2.04502i) q^{60} +(1.01701 - 5.76777i) q^{61} +(-2.79029 + 3.98495i) q^{62} +(-0.458106 + 0.982411i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-4.72491 - 1.36765i) q^{65} +(0.179266 + 0.150422i) q^{66} +(10.8162 - 0.946295i) q^{67} +(-1.81598 - 0.486591i) q^{68} +(1.88388 - 3.26298i) q^{69} +(-0.783385 - 2.29375i) q^{70} +(-15.2795 + 2.69418i) q^{71} +(0.573576 + 0.819152i) q^{72} +(1.05671 - 0.492751i) q^{73} +(3.01858 + 3.59740i) q^{74} +(-3.39165 - 3.67379i) q^{75} +(-4.32757 - 0.521678i) q^{76} +(0.179369 + 0.179369i) q^{77} +(2.19141 + 0.191724i) q^{78} +(-13.7007 - 4.98666i) q^{79} +(-2.19391 - 0.432154i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.52093 - 2.10814i) q^{82} +(1.08213 + 4.03855i) q^{83} +(0.541985 + 0.938746i) q^{84} +(-4.19439 + 0.282753i) q^{85} +(-5.34064 + 6.36472i) q^{86} +(0.277416 - 1.03533i) q^{87} +(0.226041 - 0.0605676i) q^{88} +(2.14016 - 0.778954i) q^{89} +(1.80572 + 1.31885i) q^{90} +(2.34828 + 0.414065i) q^{91} +(-1.59233 - 3.41476i) q^{92} +(0.423989 - 4.84622i) q^{93} +0.897901 q^{94} +(-9.53441 + 2.02363i) q^{95} +1.00000 q^{96} +(0.0196120 - 0.224166i) q^{97} +(-2.46175 - 5.27925i) q^{98} +(-0.230460 - 0.0406363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.0871557	+	0.996195i	−0.0616284	+	0.704416i
$2$	−0.0871557	+	0.996195i	−0.0616284	+	0.704416i
$3$	−0.422618	−	0.906308i	−0.243999	−	0.523257i
$3$	−0.422618	−	0.906308i	−0.243999	−	0.523257i
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	−2.20941	+	0.344270i	−0.988077	+	0.153962i
$5$	−2.20941	+	0.344270i	−0.988077	+	0.153962i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	1.04704	−	0.280552i	0.395742	−	0.106039i	−0.0554592	−	0.998461i	$-0.517662\pi$
$7$	1.04704	−	0.280552i	0.395742	−	0.106039i	0.451201	+	0.892422i	$0.350996\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	−0.642788	+	0.766044i	−0.214263	+	0.255348i
$10$	−0.150397	−	2.23100i	−0.0475598	−	0.705506i
$11$	0.117008	+	0.202663i	0.0352791	+	0.0611053i	0.883126	−	0.469136i	$-0.155435\pi$
$11$	0.117008	+	0.202663i	0.0352791	+	0.0611053i	−0.847847	+	0.530241i	$0.822101\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	1.99368	+	0.929669i	0.552948	+	0.257844i	0.678948	−	0.734186i	$-0.262436\pi$
$13$	1.99368	+	0.929669i	0.552948	+	0.257844i	−0.126000	+	0.992030i	$0.540214\pi$
$14$	0.188230	+	1.06750i	0.0503065	+	0.285302i
$15$	1.24575	+	1.85691i	0.321651	+	0.479452i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	1.87289	+	0.163857i	0.454243	+	0.0397411i	0.311982	−	0.950088i	$-0.399007\pi$
$17$	1.87289	+	0.163857i	0.454243	+	0.0397411i	0.142261	+	0.989829i	$0.454563\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	4.35241	−	0.237722i	0.998512	−	0.0545372i
$19$	4.35241	−	0.237722i	0.998512	−	0.0545372i
$20$	2.23562	+	0.0446200i	0.499900	+	0.00997734i
$21$	−0.696763	−	0.830370i	−0.152046	−	0.181202i
$22$	−0.212090	+	0.0988992i	−0.0452177	+	0.0210854i
$23$	2.16110	+	3.08637i	0.450621	+	0.643554i	0.978616	−	0.205694i	$-0.0659451\pi$
$23$	2.16110	+	3.08637i	0.450621	+	0.643554i	−0.527995	+	0.849247i	$0.677056\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	4.76296	−	1.52126i	0.952591	−	0.304253i
$26$	−1.09989	+	1.90507i	−0.215707	+	0.373615i
$27$	0.965926	+	0.258819i	0.185893	+	0.0498097i
$28$	−1.07985	+	0.0944743i	−0.204072	+	0.0178540i
$29$	0.821087	+	0.688973i	0.152472	+	0.127939i	0.715833	−	0.698272i	$-0.246047\pi$
$29$	0.821087	+	0.688973i	0.152472	+	0.127939i	−0.563361	+	0.826211i	$0.690492\pi$
$30$	−1.95842	+	1.07917i	−0.357556	+	0.197028i
$31$	4.21298	+	2.43236i	0.756673	+	0.436866i	0.828100	−	0.560580i	$-0.189422\pi$
$31$	4.21298	+	2.43236i	0.756673	+	0.436866i	−0.0714267	+	0.997446i	$0.522755\pi$
$32$	−0.422618	+	0.906308i	−0.0747091	+	0.160214i
$33$	0.134226	−	0.191694i	0.0233657	−	0.0333697i
$34$	−0.326466	+	1.85148i	−0.0559885	+	0.317527i
$35$	−2.21674	+	0.980317i	−0.374698	+	0.165704i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	3.32063	−	3.32063i	0.545908	−	0.545908i	−0.379347	−	0.925255i	$-0.623851\pi$
$37$	3.32063	−	3.32063i	0.545908	−	0.545908i	0.925255	+	0.379347i	$0.123851\pi$
$38$	−0.142520	+	4.35657i	−0.0231198	+	0.706729i
$39$		−	2.19978i		−	0.352247i
$40$	−0.239298	+	2.22323i	−0.0378363	+	0.351523i
$41$	−1.70610	+	4.68746i	−0.266447	+	0.732058i	0.732250	+	0.681036i	$0.238470\pi$
$41$	−1.70610	+	4.68746i	−0.266447	+	0.732058i	−0.998698	+	0.0510224i	$0.983752\pi$
$42$	0.887937	−	0.621740i	0.137012	−	0.0959366i
$43$	6.80597	+	4.76559i	1.03790	+	0.726746i	0.962741	−	0.270425i	$-0.0871644\pi$
$43$	6.80597	+	4.76559i	1.03790	+	0.726746i	0.0751599	+	0.997171i	$0.476053\pi$
$44$	−0.0800380	−	0.219902i	−0.0120662	−	0.0331515i
$45$	1.15645	−	1.91380i	0.172394	−	0.285292i
$46$	−3.26298	+	1.88388i	−0.481100	+	0.277763i
$47$	−0.0782572	−	0.894484i	−0.0114150	−	0.130474i	0.988349	−	0.152206i	$-0.0486376\pi$
$47$	−0.0782572	−	0.894484i	−0.0114150	−	0.130474i	−0.999764	+	0.0217317i	$0.993082\pi$
$48$	−0.0871557	−	0.996195i	−0.0125798	−	0.143788i
$49$	−5.04460	+	2.91250i	−0.720658	+	0.416072i
$50$	1.10036	+	4.87742i	0.155614	+	0.689771i
$51$	−0.643013	−	1.76666i	−0.0900398	−	0.247382i
$52$	−1.80196	−	1.26174i	−0.249887	−	0.174973i
$53$	5.90623	−	4.13559i	0.811283	−	0.568066i	−0.0926707	−	0.995697i	$-0.529540\pi$
$53$	5.90623	−	4.13559i	0.811283	−	0.568066i	0.903954	+	0.427630i	$0.140652\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	−0.328288	−	0.407483i	−0.0442664	−	0.0549450i
$56$		−	1.08397i		−	0.144852i
$57$	−2.05486	−	3.84416i	−0.272173	−	0.509171i
$58$	−0.757914	+	0.757914i	−0.0995190	+	0.0995190i
$59$	0.887152	−	0.744409i	0.115497	−	0.0969138i	−0.583210	−	0.812322i	$-0.698203\pi$
$59$	0.887152	−	0.744409i	0.115497	−	0.0969138i	0.698707	+	0.715408i	$0.253759\pi$
$60$	−0.904376	−	2.04502i	−0.116754	−	0.264011i
$61$	1.01701	−	5.76777i	0.130215	−	0.738487i	−0.847858	−	0.530224i	$-0.822108\pi$
$61$	1.01701	−	5.76777i	0.130215	−	0.738487i	0.978073	−	0.208263i	$-0.0667811\pi$
$62$	−2.79029	+	3.98495i	−0.354368	+	0.506090i
$63$	−0.458106	+	0.982411i	−0.0577159	+	0.123772i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−4.72491	−	1.36765i	−0.586053	−	0.169636i
$66$	0.179266	+	0.150422i	0.0220661	+	0.0185157i
$67$	10.8162	−	0.946295i	1.32141	−	0.115608i	0.595476	−	0.803373i	$-0.296964\pi$
$67$	10.8162	−	0.946295i	1.32141	−	0.115608i	0.725933	+	0.687765i	$0.241408\pi$
$68$	−1.81598	−	0.486591i	−0.220220	−	0.0590079i
$69$	1.88388	−	3.26298i	0.226793	−	0.392817i
$70$	−0.783385	−	2.29375i	−0.0936324	−	0.274155i
$71$	−15.2795	+	2.69418i	−1.81334	+	0.319741i	−0.974457	−	0.224572i	$-0.927901\pi$
$71$	−15.2795	+	2.69418i	−1.81334	+	0.319741i	−0.838882	+	0.544313i	$0.816790\pi$
$72$	0.573576	+	0.819152i	0.0675966	+	0.0965380i
$73$	1.05671	−	0.492751i	0.123678	−	0.0576721i	−0.359794	−	0.933032i	$-0.617153\pi$
$73$	1.05671	−	0.492751i	0.123678	−	0.0576721i	0.483472	+	0.875360i	$0.339375\pi$
$74$	3.01858	+	3.59740i	0.350903	+	0.418190i
$75$	−3.39165	−	3.67379i	−0.391633	−	0.424213i
$76$	−4.32757	−	0.521678i	−0.496406	−	0.0598405i
$77$	0.179369	+	0.179369i	0.0204410	+	0.0204410i
$78$	2.19141	+	0.191724i	0.248129	+	0.0217085i
$79$	−13.7007	−	4.98666i	−1.54145	−	0.561043i	−0.575061	−	0.818111i	$-0.695022\pi$
$79$	−13.7007	−	4.98666i	−1.54145	−	0.561043i	−0.966394	+	0.257067i	$0.917244\pi$
$80$	−2.19391	−	0.432154i	−0.245287	−	0.0483163i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−4.52093	−	2.10814i	−0.499253	−	0.232805i
$83$	1.08213	+	4.03855i	0.118779	+	0.443288i	0.999542	−	0.0302690i	$-0.00963639\pi$
$83$	1.08213	+	4.03855i	0.118779	+	0.443288i	−0.880763	+	0.473557i	$0.842970\pi$
$84$	0.541985	+	0.938746i	0.0591355	+	0.102426i
$85$	−4.19439	+	0.282753i	−0.454945	+	0.0306689i
$86$	−5.34064	+	6.36472i	−0.575896	+	0.686326i
$87$	0.277416	−	1.03533i	0.0297421	−	0.110999i
$88$	0.226041	−	0.0605676i	0.0240961	−	0.00645653i
$89$	2.14016	−	0.778954i	0.226856	−	0.0825690i	−0.226091	−	0.974106i	$-0.572595\pi$
$89$	2.14016	−	0.778954i	0.226856	−	0.0825690i	0.452948	+	0.891537i	$0.350372\pi$
$90$	1.80572	+	1.31885i	0.190340	+	0.139019i
$91$	2.34828	+	0.414065i	0.246166	+	0.0434058i
$92$	−1.59233	−	3.41476i	−0.166012	−	0.356013i
$93$	0.423989	−	4.84622i	0.0439656	−	0.502529i
$94$	0.897901			0.0926114
$95$	−9.53441	+	2.02363i	−0.978210	+	0.207620i
$96$	1.00000			0.102062
$97$	0.0196120	−	0.224166i	0.00199130	−	0.0227606i	−0.995134	−	0.0985304i	$-0.968586\pi$
$97$	0.0196120	−	0.224166i	0.00199130	−	0.0227606i	0.997125	+	0.0757697i	$0.0241414\pi$
$98$	−2.46175	−	5.27925i	−0.248675	−	0.533285i
$99$	−0.230460	−	0.0406363i	−0.0231621	−	0.00408411i
$100$	−4.95476	+	0.671073i	−0.495476	+	0.0671073i
$101$	−0.465899	+	0.169573i	−0.0463587	+	0.0168732i	−0.365095	−	0.930970i	$-0.618964\pi$
$101$	−0.465899	+	0.169573i	−0.0463587	+	0.0168732i	0.318737	+	0.947843i	$0.396741\pi$
$102$	1.81598	−	0.486591i	0.179809	−	0.0481797i
$103$	−2.02618	+	7.56180i	−0.199645	+	0.745087i	0.791370	+	0.611338i	$0.209368\pi$
$103$	−2.02618	+	7.56180i	−0.199645	+	0.745087i	−0.991015	+	0.133749i	$0.957298\pi$
$104$	1.41399	−	1.68513i	0.138654	−	0.165241i
$105$	1.82530	+	1.59475i	0.178131	+	0.155632i
$106$	3.60509	+	6.24419i	0.350157	+	0.606490i
$107$	−1.26790	−	4.73187i	−0.122573	−	0.457447i	0.877169	−	0.480182i	$-0.159429\pi$
$107$	−1.26790	−	4.73187i	−0.122573	−	0.457447i	−0.999742	+	0.0227348i	$0.992763\pi$
$108$	−0.906308	−	0.422618i	−0.0872095	−	0.0406665i
$109$	−0.796296	−	4.51602i	−0.0762713	−	0.432556i	−0.998901	−	0.0468692i	$-0.985076\pi$
$109$	−0.796296	−	4.51602i	−0.0762713	−	0.432556i	0.922630	−	0.385687i	$-0.126035\pi$
$110$	0.434545	−	0.291525i	0.0414322	−	0.0277958i
$111$	−4.41287	−	1.60615i	−0.418851	−	0.152449i
$112$	1.07985	+	0.0944743i	0.102036	+	0.00892698i
$113$	9.48876	+	9.48876i	0.892628	+	0.892628i	0.994770	−	0.102142i	$-0.0325696\pi$
$113$	9.48876	+	9.48876i	0.892628	+	0.892628i	−0.102142	+	0.994770i	$0.532570\pi$
$114$	4.00862	−	1.71200i	0.375442	−	0.160343i
$115$	−5.83730	−	6.07505i	−0.544331	−	0.566502i
$116$	−0.688973	−	0.821087i	−0.0639696	−	0.0762360i
$117$	−1.99368	+	0.929669i	−0.184316	+	0.0859479i
$118$	0.664256	+	0.948656i	0.0611497	+	0.0873308i
$119$	2.00695	−	0.353880i	0.183977	−	0.0324401i
$120$	2.11606	−	0.722699i	0.193169	−	0.0659731i
$121$	5.47262	−	9.47885i	0.497511	−	0.861714i
$122$	5.65718	+	1.51584i	0.512177	+	0.137237i
$123$	4.96931	−	0.434758i	0.448067	−	0.0392008i
$124$	−3.72660	−	3.12699i	−0.334658	−	0.280812i
$125$	−9.99958	+	5.00083i	−0.894390	+	0.447288i
$126$	−0.938746	−	0.541985i	−0.0836302	−	0.0482839i
$127$	3.59026	−	7.69933i	0.318584	−	0.683205i	−0.680173	−	0.733051i	$-0.738095\pi$
$127$	3.59026	−	7.69933i	0.318584	−	0.683205i	0.998757	+	0.0498464i	$0.0158732\pi$
$128$	0.573576	−	0.819152i	0.0506975	−	0.0724035i
$129$	1.44277	−	8.18233i	0.127028	−	0.720414i
$130$	1.77425	−	4.58773i	0.155612	−	0.402371i
$131$	−9.94463	+	8.34453i	−0.868866	+	0.729065i	−0.963859	−	0.266413i	$-0.914162\pi$
$131$	−9.94463	+	8.34453i	−0.868866	+	0.729065i	0.0949930	+	0.995478i	$0.469717\pi$
$132$	−0.165474	+	0.165474i	−0.0144026	+	0.0144026i
$133$	4.49044	−	1.46998i	0.389370	−	0.127464i
$134$			10.8575i			0.937947i
$135$	−2.22323	−	0.239298i	−0.191345	−	0.0205955i
$136$	0.643013	−	1.76666i	0.0551379	−	0.151490i
$137$	9.93909	−	6.95943i	0.849154	−	0.594584i	−0.0659404	−	0.997824i	$-0.521005\pi$
$137$	9.93909	−	6.95943i	0.849154	−	0.594584i	0.915094	+	0.403239i	$0.132116\pi$
$138$	3.08637	+	2.16110i	0.262730	+	0.183965i
$139$	1.44972	+	3.98308i	0.122964	+	0.337840i	0.985867	−	0.167529i	$-0.0535787\pi$
$139$	1.44972	+	3.98308i	0.122964	+	0.337840i	−0.862903	+	0.505369i	$0.831356\pi$
$140$	2.35329	−	0.580490i	0.198890	−	0.0490604i
$141$	−0.777605	+	0.448950i	−0.0654861	+	0.0378084i
$142$	−1.35224	−	15.4561i	−0.113477	−	1.29705i
$143$	0.0448663	+	0.512824i	0.00375191	+	0.0428845i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−2.05131	−	1.23955i	−0.170352	−	0.102939i
$146$	0.398778	+	1.09563i	0.0330031	+	0.0906752i
$147$	4.77157	+	3.34109i	0.393552	+	0.275568i
$148$	−3.84680	+	2.69356i	−0.316205	+	0.221409i
$149$	2.14254	−	5.88659i	0.175524	−	0.482248i	−0.820468	−	0.571693i	$-0.806287\pi$
$149$	2.14254	−	5.88659i	0.175524	−	0.482248i	0.995992	+	0.0894444i	$0.0285091\pi$
$150$	3.95541	−	3.05855i	0.322958	−	0.249729i
$151$			9.93789i			0.808734i	0.914597	+	0.404367i	$0.132508\pi$
$151$			9.93789i			0.808734i	−0.914597	+	0.404367i	$0.867492\pi$
$152$	0.896865	−	4.26563i	0.0727454	−	0.345989i
$153$	−1.32939	+	1.32939i	−0.107475	+	0.107475i
$154$	−0.194319	+	0.163053i	−0.0156587	+	0.0131392i
$155$	−10.1456	−	3.92368i	−0.814912	−	0.315158i
$156$	−0.381989	+	2.16637i	−0.0305836	+	0.173448i
$157$	−1.20390	+	1.71935i	−0.0960820	+	0.137219i	−0.864315	−	0.502951i	$-0.832247\pi$
$157$	−1.20390	+	1.71935i	−0.0960820	+	0.137219i	0.768233	+	0.640171i	$0.221136\pi$
$158$	6.16179	−	13.2140i	0.490205	−	1.05125i
$159$	−6.24419	−	3.60509i	−0.495197	−	0.285902i
$160$	0.621721	−	2.14790i	0.0491514	−	0.169806i
$161$	3.12864	+	2.62524i	0.246571	+	0.206898i
$162$	0.996195	−	0.0871557i	0.0782684	−	0.00684760i
$163$	−20.1916	−	5.41033i	−1.58153	−	0.423770i	−0.642131	−	0.766595i	$-0.721949\pi$
$163$	−20.1916	−	5.41033i	−1.58153	−	0.423770i	−0.939399	+	0.342826i	$0.888616\pi$
$164$	2.49415	−	4.31999i	0.194760	−	0.337334i
$165$	−0.230565	+	0.469740i	−0.0179494	+	0.0365692i
$166$	−4.11749	+	0.726025i	−0.319579	+	0.0563505i
$167$	4.72740	+	6.75143i	0.365818	+	0.522442i	0.959294	−	0.282410i	$-0.0911338\pi$
$167$	4.72740	+	6.75143i	0.365818	+	0.522442i	−0.593476	+	0.804851i	$0.702245\pi$
$168$	−0.982411	+	0.458106i	−0.0757947	+	0.0353436i
$169$	−5.24576	−	6.25165i	−0.403520	−	0.480896i
$170$	0.0838876	−	4.20307i	0.00643388	−	0.322361i
$171$	−2.61557	+	3.48695i	−0.200018	+	0.266653i
$172$	−5.87504	−	5.87504i	−0.447967	−	0.447967i
$173$	7.45247	+	0.652007i	0.566601	+	0.0495711i	0.366858	−	0.930277i	$-0.380434\pi$
$173$	7.45247	+	0.652007i	0.566601	+	0.0495711i	0.199743	+	0.979848i	$0.435989\pi$
$174$	1.00721	+	0.366595i	0.0763565	+	0.0277915i
$175$	4.56019	−	2.92908i	0.344718	−	0.221417i
$176$	0.0406363	+	0.230460i	0.00306308	+	0.0173716i
$177$	−1.04959	−	0.489432i	−0.0788921	−	0.0367880i
$178$	0.589463	+	2.19991i	0.0441821	+	0.164890i
$179$	−5.19978	−	9.00629i	−0.388650	−	0.673162i	0.603618	−	0.797274i	$-0.293725\pi$
$179$	−5.19978	−	9.00629i	−0.388650	−	0.673162i	−0.992268	+	0.124112i	$0.960392\pi$
$180$	−1.47121	+	1.68391i	−0.109658	+	0.125511i
$181$	16.3874	−	19.5297i	1.21807	−	1.45163i	0.364056	−	0.931377i	$-0.381392\pi$
$181$	16.3874	−	19.5297i	1.21807	−	1.45163i	0.854010	−	0.520257i	$-0.174164\pi$
$182$	−0.617155	+	2.30325i	−0.0457465	+	0.170728i
$183$	−5.65718	+	1.51584i	−0.418191	+	0.112054i
$184$	3.54054	−	1.28865i	0.261012	−	0.0950007i
$185$	−6.19342	+	8.47981i	−0.455350	+	0.623448i
$186$	4.79082	+	0.844751i	0.351280	+	0.0619402i
$187$	0.185935	+	0.398738i	0.0135969	+	0.0291586i
$188$	−0.0782572	+	0.894484i	−0.00570749	+	0.0652370i
$189$	1.08397			0.0788473
$190$	−1.18495	−	9.67450i	−0.0859653	−	0.701862i
$191$	1.28827			0.0932160			0.0466080	−	0.998913i	$-0.485159\pi$
$191$	1.28827			0.0932160			0.0466080	+	0.998913i	$0.485159\pi$
$192$	−0.0871557	+	0.996195i	−0.00628992	+	0.0718942i
$193$	−4.01258	−	8.60501i	−0.288832	−	0.619402i	0.707335	−	0.706879i	$-0.249897\pi$
$193$	−4.01258	−	8.60501i	−0.288832	−	0.619402i	−0.996167	+	0.0874768i	$0.972120\pi$
$194$	0.221604	+	0.0390747i	0.0159102	+	0.00280540i
$195$	0.757319	+	4.86022i	0.0542328	+	0.348048i
$196$	5.47372	−	1.99227i	0.390980	−	0.142305i
$197$	13.4304	−	3.59866i	0.956874	−	0.256394i	0.253597	−	0.967310i	$-0.418386\pi$
$197$	13.4304	−	3.59866i	0.956874	−	0.256394i	0.703277	+	0.710916i	$0.251719\pi$
$198$	0.0605676	−	0.226041i	0.00430435	−	0.0160641i
$199$	−11.4373	+	13.6304i	−0.810766	+	0.966233i	−0.999876	−	0.0157226i	$-0.994995\pi$
$199$	−11.4373	+	13.6304i	−0.810766	+	0.966233i	0.189110	+	0.981956i	$0.439440\pi$
$200$	−0.236684	−	4.99439i	−0.0167361	−	0.353157i
$201$	−5.42876	−	9.40289i	−0.382915	−	0.663228i
$202$	−0.128322	−	0.478905i	−0.00902873	−	0.0336957i
$203$	1.05300	+	0.491022i	0.0739061	+	0.0344630i
$204$	0.326466	+	1.85148i	0.0228572	+	0.129630i
$205$	2.15571	−	10.9439i	0.150561	−	0.764352i
$206$	−7.35643	−	2.67752i	−0.512547	−	0.186552i
$207$	−3.75343	−	0.328383i	−0.260881	−	0.0228242i
$208$	1.55548	+	1.55548i	0.107853	+	0.107853i
$209$	0.557443	+	0.854258i	0.0385591	+	0.0590903i
$210$	−1.74777	+	1.67937i	−0.120607	+	0.115887i
$211$	13.8589	+	16.5164i	0.954087	+	1.13704i	0.990474	+	0.137698i	$0.0439705\pi$
$211$	13.8589	+	16.5164i	0.954087	+	1.13704i	−0.0363875	+	0.999338i	$0.511585\pi$
$212$	−6.53464	+	3.04715i	−0.448801	+	0.209279i
$213$	8.89914	+	12.7093i	0.609759	+	0.870826i
$214$	4.82437	−	0.850666i	0.329787	−	0.0581503i
$215$	−16.6778	−	8.18604i	−1.13742	−	0.558283i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	5.09354	+	1.36481i	0.345772	+	0.0926494i
$218$	4.56823	−	0.399669i	0.309400	−	0.0270690i
$219$	−0.893168	−	0.749457i	−0.0603547	−	0.0506436i
$220$	0.252542	+	0.458299i	0.0170264	+	0.0308985i
$221$	3.58162	+	2.06785i	0.240926	+	0.139098i
$222$	1.98465	−	4.25609i	0.133201	−	0.285650i
$223$	−8.53863	+	12.1944i	−0.571789	+	0.816600i	−0.996036	−	0.0889468i	$-0.971650\pi$
$223$	−8.53863	+	12.1944i	−0.571789	+	0.816600i	0.424247	+	0.905546i	$0.360539\pi$
$224$	−0.188230	+	1.06750i	−0.0125766	+	0.0713255i
$225$	−1.89621	+	4.62649i	−0.126414	+	0.308432i
$226$	−10.2797	+	8.62566i	−0.683793	+	0.573770i
$227$	11.0794	−	11.0794i	0.735365	−	0.735365i	−0.236312	−	0.971677i	$-0.575939\pi$
$227$	11.0794	−	11.0794i	0.735365	−	0.735365i	0.971677	+	0.236312i	$0.0759387\pi$
$228$	1.35611	+	4.14258i	0.0898105	+	0.274349i
$229$			19.1457i			1.26518i	0.774487	+	0.632590i	$0.218008\pi$
$229$			19.1457i			1.26518i	−0.774487	+	0.632590i	$0.781992\pi$
$230$	6.56069	−	5.28561i	0.432599	−	0.348523i
$231$	0.0867588	−	0.238368i	0.00570831	−	0.0156835i
$232$	0.878010	−	0.614789i	0.0576442	−	0.0403629i
$233$	7.45632	+	5.22097i	0.488480	+	0.342037i	0.791727	−	0.610875i	$-0.209182\pi$
$233$	7.45632	+	5.22097i	0.488480	+	0.342037i	−0.303248	+	0.952912i	$0.598071\pi$
$234$	−0.752371	−	2.06712i	−0.0491840	−	0.135132i
$235$	0.480846	+	1.94934i	0.0313669	+	0.127161i
$236$	−1.00294	+	0.579047i	−0.0652858	+	0.0376928i
$237$	1.27073	+	14.5245i	0.0825430	+	0.943471i
$238$	0.177616	+	2.03016i	0.0115131	+	0.131596i
$239$	−16.5640	+	9.56321i	−1.07143	+	0.618593i	−0.928573	−	0.371150i	$-0.878964\pi$
$239$	−16.5640	+	9.56321i	−1.07143	+	0.618593i	−0.142861	+	0.989743i	$0.545630\pi$
$240$	0.535522	+	2.17099i	0.0345678	+	0.140137i
$241$	6.14096	+	16.8721i	0.395574	+	1.08683i	0.964417	+	0.264384i	$0.0851687\pi$
$241$	6.14096	+	16.8721i	0.395574	+	1.08683i	−0.568844	+	0.822446i	$0.692609\pi$
$242$	8.96581	+	6.27793i	0.576344	+	0.403561i
$243$	−0.819152	+	0.573576i	−0.0525486	+	0.0367949i
$244$	−2.00313	+	5.50354i	−0.128237	+	0.352328i
$245$	10.1429	−	8.17161i	0.648006	−	0.522065i
$246$			4.98829i			0.318042i
$247$	8.89833	+	3.57236i	0.566187	+	0.227304i
$248$	3.43988	−	3.43988i	0.218433	−	0.218433i
$249$	3.20284	−	2.68750i	0.202972	−	0.170314i
$250$	−4.11028	−	10.3974i	−0.259957	−	0.657588i
$251$	−0.233241	+	1.32278i	−0.0147221	+	0.0834930i	−0.991284	−	0.131746i	$-0.957942\pi$
$251$	−0.233241	+	1.32278i	−0.0147221	+	0.0834930i	0.976561	+	0.215239i	$0.0690529\pi$
$252$	0.621740	−	0.887937i	0.0391659	−	0.0559348i
$253$	−0.372629	+	0.799105i	−0.0234270	+	0.0502393i
$254$	7.35712	+	4.24764i	0.461627	+	0.266520i
$255$	2.02889	+	3.68191i	0.127054	+	0.230570i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.89611	−	0.253377i	0.180655	−	0.0158052i	0.00353054	−	0.999994i	$-0.498876\pi$
$257$	2.89611	−	0.253377i	0.180655	−	0.0158052i	0.177124	+	0.984189i	$0.443321\pi$
$258$	8.02545	+	2.15041i	0.499643	+	0.133879i
$259$	2.54520	−	4.40842i	0.158151	−	0.273926i
$260$	4.41564	+	2.16735i	0.273846	+	0.134413i
$261$	−1.05557	+	0.186125i	−0.0653381	+	0.0115209i
$262$	−7.44605	−	10.6341i	−0.460018	−	0.656974i
$263$	−8.44661	+	3.93872i	−0.520840	+	0.242872i	−0.665216	−	0.746651i	$-0.731660\pi$
$263$	−8.44661	+	3.93872i	−0.520840	+	0.242872i	0.144376	+	0.989523i	$0.453883\pi$
$264$	−0.150422	−	0.179266i	−0.00925784	−	0.0110331i
$265$	−11.6255	+	11.1705i	−0.714149	+	0.686200i
$266$	1.07302	+	4.60147i	0.0657912	+	0.282134i
$267$	−1.61044	−	1.61044i	−0.0985575	−	0.0985575i
$268$	−10.8162	−	0.946295i	−0.660705	−	0.0578042i
$269$	−21.9302	−	7.98193i	−1.33711	−	0.486667i	−0.428206	−	0.903681i	$-0.640854\pi$
$269$	−21.9302	−	7.98193i	−1.33711	−	0.486667i	−0.908900	+	0.417014i	$0.863077\pi$
$270$	0.432154	−	2.19391i	0.0263001	−	0.133517i
$271$	3.43176	+	19.4625i	0.208465	+	1.18226i	0.891894	+	0.452245i	$0.149377\pi$
$271$	3.43176	+	19.4625i	0.208465	+	1.18226i	−0.683429	+	0.730017i	$0.739512\pi$
$272$	1.70390	+	0.794541i	0.103314	+	0.0481761i
$273$	−0.617155	−	2.30325i	−0.0373519	−	0.139399i
$274$	6.06670	+	10.5078i	0.366503	+	0.634801i
$275$	0.865607	+	0.787277i	0.0521980	+	0.0474746i
$276$	−2.42187	+	2.88628i	−0.145780	+	0.173733i
$277$	−3.30684	+	12.3413i	−0.198689	+	0.741516i	0.792592	+	0.609752i	$0.208731\pi$
$277$	−3.30684	+	12.3413i	−0.198689	+	0.741516i	−0.991281	+	0.131764i	$0.957936\pi$
$278$	−4.09427	+	1.09706i	−0.245558	+	0.0657971i
$279$	−4.57135	+	1.66384i	−0.273680	+	0.0996112i
$280$	0.373178	+	2.39493i	0.0223017	+	0.143125i
$281$	21.6460	+	3.81678i	1.29129	+	0.227690i	0.776769	−	0.629786i	$-0.216857\pi$
$281$	21.6460	+	3.81678i	1.29129	+	0.227690i	0.514525	+	0.857476i	$0.327968\pi$
$282$	−0.379469	−	0.813775i	−0.0225971	−	0.0484596i
$283$	−1.64113	+	18.7582i	−0.0975551	+	1.11506i	0.776792	+	0.629758i	$0.216846\pi$
$283$	−1.64113	+	18.7582i	−0.0975551	+	1.11506i	−0.874347	+	0.485302i	$0.838710\pi$
$284$	15.5152			0.920657
$285$	5.86345	+	7.78589i	0.347321	+	0.461196i
$286$	−0.514783			−0.0304398
$287$	−0.471265	+	5.38659i	−0.0278179	+	0.317960i
$288$	−0.422618	−	0.906308i	−0.0249030	−	0.0534047i
$289$	−13.2609	−	2.33825i	−0.780051	−	0.137544i
$290$	1.41361	−	1.93547i	0.0830103	−	0.113655i
$291$	−0.211452	+	0.0769622i	−0.0123955	+	0.00451160i
$292$	−1.12622	+	0.301770i	−0.0659070	+	0.0176597i
$293$	6.11640	−	22.8267i	0.357324	−	1.33355i	−0.520211	−	0.854038i	$-0.674147\pi$
$293$	6.11640	−	22.8267i	0.357324	−	1.33355i	0.877535	−	0.479513i	$-0.159186\pi$
$294$	−3.74424	+	4.46221i	−0.218369	+	0.260242i
$295$	−1.70380	+	1.95012i	−0.0991992	+	0.113540i
$296$	−2.34804	−	4.06692i	−0.136477	−	0.236385i
$297$	0.0605676	+	0.226041i	0.00351449	+	0.0131163i
$298$	5.67746	+	2.64744i	0.328886	+	0.153362i
$299$	1.43924	+	8.16236i	0.0832336	+	0.472041i
$300$	2.70217	+	4.20693i	0.156010	+	0.242887i
$301$	8.46309	+	3.08031i	0.487804	+	0.177546i
$302$	−9.90007	−	0.866144i	−0.569685	−	0.0498410i
$303$	0.350583	+	0.350583i	0.0201405	+	0.0201405i
$304$	4.17124	+	1.26523i	0.239237	+	0.0725657i
$305$	−0.261328	+	13.0935i	−0.0149636	+	0.749730i
$306$	−1.20847	−	1.44020i	−0.0690836	−	0.0823306i
$307$	2.90363	−	1.35399i	0.165719	−	0.0772761i	−0.337989	−	0.941150i	$-0.609747\pi$
$307$	2.90363	−	1.35399i	0.165719	−	0.0772761i	0.503708	+	0.863874i	$0.331969\pi$
$308$	−0.145497	−	0.207791i	−0.00829045	−	0.0118400i
$309$	7.70962	−	1.35941i	0.438585	−	0.0773344i
$310$	4.79300	−	9.76500i	0.272224	−	0.554615i
$311$	7.98421	−	13.8291i	0.452743	−	0.784174i	−0.545812	−	0.837908i	$-0.683779\pi$
$311$	7.98421	−	13.8291i	0.452743	−	0.784174i	0.998555	+	0.0537334i	$0.0171121\pi$
$312$	−2.12483	−	0.569346i	−0.120295	−	0.0322329i
$313$	−29.1394	+	2.54937i	−1.64706	+	0.144099i	−0.872569	−	0.488490i	$-0.837548\pi$
$313$	−29.1394	+	2.54937i	−1.64706	+	0.144099i	−0.774488	+	0.632589i	$0.781992\pi$
$314$	−1.60788	−	1.34917i	−0.0907381	−	0.0761383i
$315$	0.673928	−	2.32826i	0.0379715	−	0.131182i
$316$	12.6267	+	7.29001i	0.710306	+	0.410095i
$317$	−5.74190	+	12.3135i	−0.322497	+	0.691597i	−0.998994	−	0.0448484i	$-0.985720\pi$
$317$	−5.74190	+	12.3135i	−0.322497	+	0.691597i	0.676497	+	0.736446i	$0.263497\pi$
$318$	4.13559	−	5.90623i	0.231912	−	0.331205i
$319$	−0.0435562	+	0.247019i	−0.00243868	+	0.0138304i
$320$	2.08554	+	0.806557i	0.116585	+	0.0450879i
$321$	−3.75269	+	3.14888i	−0.209455	+	0.175753i
$322$	−2.88793	+	2.88793i	−0.160938	+	0.160938i
$323$	8.19054	+	0.267944i	0.455734	+	0.0149088i
$324$			1.00000i			0.0555556i
$325$	10.9101	+	1.39506i	0.605183	+	0.0773839i
$326$	7.14956	−	19.6432i	0.395977	−	1.08794i
$327$	−3.75637	+	2.63024i	−0.207728	+	0.145453i
$328$	4.08617	+	2.86117i	0.225621	+	0.157981i
$329$	−0.332888	−	0.914601i	−0.0183527	−	0.0504236i
$330$	−0.447858	−	0.270628i	−0.0246538	−	0.0148976i
$331$	3.54746	−	2.04812i	0.194986	−	0.112575i	−0.399329	−	0.916808i	$-0.630757\pi$
$331$	3.54746	−	2.04812i	0.194986	−	0.112575i	0.594315	+	0.804233i	$0.297423\pi$
$332$	−0.364399	−	4.16510i	−0.0199990	−	0.228590i
$333$	0.409290	+	4.67821i	0.0224289	+	0.256364i
$334$	−7.13776	+	4.12099i	−0.390561	+	0.225490i
$335$	−23.5716	+	5.81444i	−1.28785	+	0.317677i
$336$	−0.370740	−	1.01860i	−0.0202255	−	0.0555692i
$337$	19.7356	+	13.8190i	1.07507	+	0.752770i	0.970343	−	0.241732i	$-0.0777154\pi$
$337$	19.7356	+	13.8190i	1.07507	+	0.752770i	0.104723	+	0.994501i	$0.466604\pi$
$338$	6.68506	−	4.68093i	0.363619	−	0.254609i
$339$	4.58962	−	12.6099i	0.249274	−	0.684874i
$340$	4.17976	+	0.449890i	0.226680	+	0.0243987i
$341$			1.13842i			0.0616490i
$342$	−3.24571	−	2.90952i	−0.175508	−	0.157329i
$343$	−9.83015	+	9.83015i	−0.530778	+	0.530778i
$344$	6.36472	−	5.34064i	0.343163	−	0.287948i
$345$	−3.03892	+	7.85782i	−0.163610	+	0.423051i
$346$	−1.29905	+	7.36729i	−0.0698374	+	0.396068i
$347$	10.7931	−	15.4142i	0.579406	−	0.827478i	−0.417283	−	0.908776i	$-0.637018\pi$
$347$	10.7931	−	15.4142i	0.579406	−	0.827478i	0.996690	+	0.0812983i	$0.0259066\pi$
$348$	−0.452984	+	0.971428i	−0.0242825	+	0.0520740i
$349$	−25.4677	−	14.7038i	−1.36326	−	0.787077i	−0.373201	−	0.927750i	$-0.621740\pi$
$349$	−25.4677	−	14.7038i	−1.36326	−	0.787077i	−0.990056	+	0.140674i	$0.955073\pi$
$350$	2.52048	+	4.79812i	0.134725	+	0.256470i
$351$	1.68513	+	1.41399i	0.0899457	+	0.0754734i
$352$	−0.233125	+	0.0203958i	−0.0124256	+	0.00108710i
$353$	−15.0744	−	4.03918i	−0.802332	−	0.214984i	−0.165724	−	0.986172i	$-0.552996\pi$
$353$	−15.0744	−	4.03918i	−0.802332	−	0.214984i	−0.636607	+	0.771188i	$0.719663\pi$
$354$	0.579047	−	1.00294i	0.0307760	−	0.0533056i
$355$	32.8310	−	11.2128i	1.74249	−	0.595114i
$356$	−2.24291	+	0.395486i	−0.118874	+	0.0209607i
$357$	−1.16890	−	1.66936i	−0.0618647	−	0.0883519i
$358$	9.42521	−	4.39505i	0.498138	−	0.232285i
$359$	−9.92110	−	11.8235i	−0.523616	−	0.624021i	0.437816	−	0.899065i	$-0.355752\pi$
$359$	−9.92110	−	11.8235i	−0.523616	−	0.624021i	−0.961432	+	0.275044i	$0.911308\pi$
$360$	−1.54927	−	1.61238i	−0.0816539	−	0.0849796i
$361$	18.8870	−	2.06933i	0.994051	−	0.108912i
$362$	18.0272	+	18.0272i	0.947487	+	0.947487i
$363$	−10.9036	−	0.953940i	−0.572290	−	0.0500689i
$364$	−2.24070	−	0.815548i	−0.117445	−	0.0427463i
$365$	−2.16506	+	1.45248i	−0.113324	+	0.0760263i
$366$	−1.01701	−	5.76777i	−0.0531601	−	0.301486i
$367$	−21.0067	−	9.79558i	−1.09654	−	0.511325i	−0.211754	−	0.977323i	$-0.567918\pi$
$367$	−21.0067	−	9.79558i	−1.09654	−	0.511325i	−0.884786	+	0.465998i	$0.845696\pi$
$368$	0.975170	+	3.63938i	0.0508342	+	0.189716i
$369$	−2.49415	−	4.31999i	−0.129840	−	0.224889i
$370$	−7.90775	−	6.90892i	−0.411104	−	0.359178i
$371$	5.02378	−	5.98711i	0.260822	−	0.310835i
$372$	−1.25908	+	4.69897i	−0.0652805	+	0.243630i
$373$	−8.15046	+	2.18391i	−0.422015	+	0.113079i	−0.463575	−	0.886057i	$-0.653434\pi$
$373$	−8.15046	+	2.18391i	−0.422015	+	0.113079i	0.0415606	+	0.999136i	$0.486767\pi$
$374$	−0.413426	+	0.150475i	−0.0213778	+	0.00778087i
$375$	8.75830	+	6.94926i	0.452277	+	0.358858i
$376$	−0.884260	−	0.155919i	−0.0456022	−	0.00804090i
$377$	0.996468	+	2.13693i	0.0513207	+	0.110058i
$378$	−0.0944743	+	1.07985i	−0.00485923	+	0.0555413i
$379$	17.1950			0.883249			0.441625	−	0.897200i	$-0.354402\pi$
$379$	17.1950			0.883249			0.441625	+	0.897200i	$0.354402\pi$
$380$	9.74096	−	0.337253i	0.499701	−	0.0173007i
$381$	−8.49527			−0.435226
$382$	−0.112280	+	1.28337i	−0.00574475	+	0.0656628i
$383$	−15.7178	−	33.7069i	−0.803142	−	1.72234i	−0.684020	−	0.729463i	$-0.739770\pi$
$383$	−15.7178	−	33.7069i	−0.803142	−	1.72234i	−0.119121	−	0.992880i	$-0.538008\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	−0.458050	−	0.334547i	−0.0233444	−	0.0170501i
$386$	8.92198	−	3.24734i	0.454117	−	0.165285i
$387$	−8.02545	+	2.15041i	−0.407957	+	0.109312i
$388$	−0.0582401	+	0.217355i	−0.00295669	+	0.0110345i
$389$	6.24938	−	7.44773i	0.316856	−	0.377615i	−0.583984	−	0.811765i	$-0.698507\pi$
$389$	6.24938	−	7.44773i	0.316856	−	0.377615i	0.900840	+	0.434150i	$0.142951\pi$
$390$	−4.90773	+	0.330841i	−0.248513	+	0.0167528i
$391$	3.54179	+	6.13455i	0.179116	+	0.310238i
$392$	1.50762	+	5.62652i	0.0761464	+	0.284182i
$393$	11.7655	+	5.48634i	0.593491	+	0.276749i
$394$	2.41443	+	13.6929i	0.121637	+	0.689839i
$395$	31.9873	+	6.30082i	1.60945	+	0.317029i
$396$	0.219902	+	0.0800380i	0.0110505	+	0.00402206i
$397$	−23.5486	−	2.06024i	−1.18187	−	0.103400i	−0.520770	−	0.853697i	$-0.674355\pi$
$397$	−23.5486	−	2.06024i	−1.18187	−	0.103400i	−0.661101	+	0.750297i	$0.729911\pi$
$398$	−12.5817	−	12.5817i	−0.630664	−	0.630664i
$399$	−3.23000	−	3.44848i	−0.161702	−	0.172640i
$400$	4.99602	+	0.199507i	0.249801	+	0.00997535i
$401$	−8.57713	−	10.2218i	−0.428321	−	0.510454i	0.508116	−	0.861289i	$-0.330342\pi$
$401$	−8.57713	−	10.2218i	−0.428321	−	0.510454i	−0.936437	+	0.350835i	$0.885898\pi$
$402$	9.84025	−	4.58859i	0.490787	−	0.228858i
$403$	6.13805	+	8.76604i	0.305758	+	0.436667i
$404$	0.488267	−	0.0860947i	0.0242922	−	0.00428337i
$405$	0.722699	+	2.11606i	0.0359112	+	0.105148i
$406$	−0.580928	+	1.00620i	−0.0288310	+	0.0499367i
$407$	1.06151	+	0.284430i	0.0526170	+	0.0140987i
$408$	−1.87289	+	0.163857i	−0.0927219	+	0.00811211i
$409$	20.6985	+	17.3681i	1.02347	+	0.858797i	0.990060	−	0.140645i	$-0.0449175\pi$
$409$	20.6985	+	17.3681i	1.02347	+	0.858797i	0.0334141	+	0.999442i	$0.489362\pi$
$410$	10.7143	+	3.10133i	0.529143	+	0.153164i
$411$	−10.5078	−	6.06670i	−0.518313	−	0.299248i
$412$	3.30849	−	7.09508i	0.162998	−	0.349550i
$413$	0.720034	−	1.02832i	0.0354306	−	0.0506001i
$414$	0.654266	−	3.71053i	0.0321554	−	0.182362i
$415$	−3.78121	−	8.55025i	−0.185612	−	0.419715i
$416$	−1.68513	+	1.41399i	−0.0826204	+	0.0693268i
$417$	2.99722	−	2.99722i	0.146774	−	0.146774i
$418$	−0.899592	+	0.480868i	−0.0440005	+	0.0235200i
$419$			31.8456i			1.55576i	0.628412	+	0.777881i	$0.283705\pi$
$419$			31.8456i			1.55576i	−0.628412	+	0.777881i	$0.716295\pi$
$420$	−1.52065	−	1.88748i	−0.0742000	−	0.0920998i
$421$	2.73386	−	7.51123i	0.133240	−	0.366075i	−0.855074	−	0.518507i	$-0.826488\pi$
$421$	2.73386	−	7.51123i	0.133240	−	0.366075i	0.988314	+	0.152432i	$0.0487104\pi$
$422$	−17.6614	+	12.3667i	−0.859745	+	0.602000i
$423$	0.735517	+	0.515015i	0.0357621	+	0.0250409i
$424$	−2.46602	−	6.77535i	−0.119761	−	0.329040i
$425$	9.16976	−	2.06872i	0.444799	−	0.100348i
$426$	−13.4365	+	7.75759i	−0.651003	+	0.375856i
$427$	−0.553312	−	6.32438i	−0.0267766	−	0.306058i
$428$	0.426958	+	4.88015i	0.0206378	+	0.235891i
$429$	0.445815	−	0.257392i	0.0215242	−	0.0124270i
$430$	9.60846	−	15.9009i	0.463361	−	0.766809i
$431$	3.90248	+	10.7220i	0.187976	+	0.516459i	0.997503	−	0.0706230i	$-0.0224987\pi$
$431$	3.90248	+	10.7220i	0.187976	+	0.516459i	−0.809527	+	0.587082i	$0.800276\pi$
$432$	0.819152	+	0.573576i	0.0394115	+	0.0275962i
$433$	10.5466	−	7.38483i	0.506839	−	0.354893i	−0.292019	−	0.956413i	$-0.594327\pi$
$433$	10.5466	−	7.38483i	0.506839	−	0.354893i	0.798858	+	0.601520i	$0.205438\pi$
$434$	−1.80355	+	4.95521i	−0.0865731	+	0.237858i
$435$	−0.256492	+	2.38297i	−0.0122978	+	0.114255i
$436$			4.58568i			0.219614i
$437$	10.1397	+	12.9194i	0.485048	+	0.618020i
$438$	0.824450	−	0.824450i	0.0393937	−	0.0393937i
$439$	12.6627	−	10.6253i	0.604357	−	0.507116i	−0.288486	−	0.957484i	$-0.593152\pi$
$439$	12.6627	−	10.6253i	0.604357	−	0.507116i	0.892843	+	0.450368i	$0.148707\pi$
$440$	−0.478566	+	0.211638i	−0.0228147	+	0.0100894i
$441$	1.01150	−	5.73651i	0.0481668	−	0.273167i
$442$	−2.37214	+	3.38776i	−0.112831	+	0.161139i
$443$	7.98062	−	17.1145i	0.379171	−	0.813134i	−0.620413	−	0.784276i	$-0.713035\pi$
$443$	7.98062	−	17.1145i	0.379171	−	0.813134i	0.999583	−	0.0288589i	$-0.00918736\pi$
$444$	4.06692	+	2.34804i	0.193008	+	0.111433i
$445$	−4.46031	+	2.45782i	−0.211439	+	0.116512i
$446$	−11.4038	−	9.56896i	−0.539987	−	0.453103i
$447$	−6.24054	+	0.545977i	−0.295168	+	0.0258238i
$448$	−1.04704	−	0.280552i	−0.0494678	−	0.0132549i
$449$	7.77854	−	13.4728i	0.367092	−	0.635822i	−0.622018	−	0.783003i	$-0.713687\pi$
$449$	7.77854	−	13.4728i	0.367092	−	0.635822i	0.989110	+	0.147181i	$0.0470201\pi$
$450$	−4.44361	−	2.29222i	−0.209474	−	0.108056i
$451$	−1.14960	+	0.202706i	−0.0541326	+	0.00954504i
$452$	−7.69690	−	10.9923i	−0.362032	−	0.517035i
$453$	9.00678	−	4.19993i	0.423176	−	0.197330i
$454$	10.0716	+	12.0029i	0.472684	+	0.563323i
$455$	−5.33085	−	0.106397i	−0.249914	−	0.00498795i
$456$	−4.24501	+	0.989899i	−0.198791	+	0.0463563i
$457$	−18.9072	−	18.9072i	−0.884440	−	0.884440i	0.109542	−	0.993982i	$-0.465062\pi$
$457$	−18.9072	−	18.9072i	−0.884440	−	0.884440i	−0.993982	+	0.109542i	$0.965062\pi$
$458$	−19.0728	−	1.66865i	−0.891213	−	0.0779711i
$459$	1.76666	+	0.643013i	0.0824608	+	0.0300133i
$460$	4.69370	+	6.99640i	0.218845	+	0.326209i
$461$	−6.83448	−	38.7603i	−0.318314	−	1.80525i	−0.553007	−	0.833176i	$-0.686520\pi$
$461$	−6.83448	−	38.7603i	−0.318314	−	1.80525i	0.234694	−	0.972069i	$-0.424591\pi$
$462$	0.229899	+	0.107204i	0.0106959	+	0.00498757i
$463$	1.35848	+	5.06992i	0.0631339	+	0.235619i	0.990282	−	0.139077i	$-0.0444136\pi$
$463$	1.35848	+	5.06992i	0.0631339	+	0.235619i	−0.927148	+	0.374696i	$0.877747\pi$
$464$	0.535926	+	0.928251i	0.0248797	+	0.0430930i
$465$	0.731641	+	10.8532i	0.0339291	+	0.503307i
$466$	−5.85097	+	6.97291i	−0.271041	+	0.323014i
$467$	6.64972	−	24.8171i	0.307712	−	1.14840i	−0.622873	−	0.782323i	$-0.714035\pi$
$467$	6.64972	−	24.8171i	0.307712	−	1.14840i	0.930585	−	0.366075i	$-0.119299\pi$
$468$	2.12483	−	0.569346i	0.0982202	−	0.0263180i
$469$	11.0595	−	4.02531i	0.510678	−	0.185872i
$470$	−1.98383	+	0.309120i	−0.0915072	+	0.0142586i
$471$	2.06705	+	0.364477i	0.0952448	+	0.0167942i
$472$	−0.489432	−	1.04959i	−0.0225279	−	0.0483113i
$473$	−0.169459	+	1.93693i	−0.00779176	+	0.0890602i
$474$	−14.5800			−0.669683
$475$	20.3687	−	7.75343i	0.934581	−	0.355752i
$476$	−2.03791			−0.0934076
$477$	−0.628408	+	7.18274i	−0.0287728	+	0.328875i
$478$	−8.08317	−	17.3344i	−0.369716	−	0.792858i
$479$	−6.91347	−	1.21903i	−0.315885	−	0.0556990i	0.0134581	−	0.999909i	$-0.495716\pi$
$479$	−6.91347	−	1.21903i	−0.315885	−	0.0556990i	−0.329343	+	0.944210i	$0.606827\pi$
$480$	−2.20941	+	0.344270i	−0.100845	+	0.0157137i
$481$	9.70736	−	3.53319i	0.442617	−	0.161100i
$482$	−17.3432	+	4.64708i	−0.789959	+	0.211669i
$483$	1.05706	−	3.94499i	0.0480977	−	0.179503i
$484$	−7.03546	+	8.38454i	−0.319794	+	0.381115i
$485$	0.0338427	+	0.502026i	0.00153672	+	0.0227958i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.31235	−	8.62980i	−0.104782	−	0.391054i	0.893538	−	0.448988i	$-0.148215\pi$
$487$	−2.31235	−	8.62980i	−0.104782	−	0.391054i	−0.998320	+	0.0579342i	$0.981549\pi$
$488$	−5.30802	−	2.47517i	−0.240283	−	0.112046i
$489$	3.62992	+	20.5863i	0.164151	+	0.930946i
$490$	7.25650	+	10.8165i	0.327815	+	0.488640i
$491$	−15.9223	−	5.79526i	−0.718566	−	0.261536i	−0.0432488	−	0.999064i	$-0.513771\pi$
$491$	−15.9223	−	5.79526i	−0.718566	−	0.261536i	−0.675317	+	0.737528i	$0.735993\pi$
$492$	−4.96931	−	0.434758i	−0.224034	−	0.0196004i
$493$	1.42491	+	1.42491i	0.0641748	+	0.0641748i
$494$	−4.33431	+	8.55312i	−0.195010	+	0.384823i
$495$	0.523170	+	0.0104418i	0.0235147	+	0.000469322i
$496$	3.12699	+	3.72660i	0.140406	+	0.167329i
$497$	−15.2423	+	7.10760i	−0.683710	+	0.318819i
$498$	2.39813	+	3.42488i	0.107463	+	0.153473i
$499$	6.70806	−	1.18281i	0.300294	−	0.0529500i	−0.0214710	−	0.999769i	$-0.506835\pi$
$499$	6.70806	−	1.18281i	0.300294	−	0.0529500i	0.321765	+	0.946820i	$0.395724\pi$
$500$	10.7161	−	3.18845i	0.479236	−	0.142592i
$501$	4.12099	−	7.13776i	0.184112	−	0.318892i
$502$	−1.29742	−	0.347642i	−0.0579065	−	0.0155160i
$503$	13.4523	−	1.17693i	0.599810	−	0.0524765i	0.216792	−	0.976218i	$-0.430441\pi$
$503$	13.4523	−	1.17693i	0.599810	−	0.0524765i	0.383017	+	0.923741i	$0.374885\pi$
$504$	0.830370	+	0.696763i	0.0369876	+	0.0310363i
$505$	0.970982	−	0.535052i	0.0432081	−	0.0238095i
$506$	−0.763588	−	0.440858i	−0.0339456	−	0.0195985i
$507$	−3.44897	+	7.39633i	−0.153174	+	0.328483i
$508$	−4.87269	+	6.95892i	−0.216191	+	0.308752i
$509$	1.88162	−	10.6712i	0.0834013	−	0.472992i	−0.914289	−	0.405063i	$-0.867250\pi$
$509$	1.88162	−	10.6712i	0.0834013	−	0.472992i	0.997690	−	0.0679293i	$-0.0216392\pi$
$510$	−3.84473	+	1.70027i	−0.170247	+	0.0752891i
$511$	0.968168	−	0.812390i	0.0428292	−	0.0359380i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.26563	+	0.896865i	0.188332	+	0.0395976i
$514$			2.90718i			0.128230i
$515$	1.87335	−	17.4047i	0.0825498	−	0.766941i
$516$	−2.84169	+	7.80749i	−0.125099	+	0.343706i
$517$	0.172122	−	0.120521i	0.00756993	−	0.00530052i
$518$	4.16982	+	2.91974i	0.183211	+	0.128286i
$519$	−2.55863	−	7.02978i	−0.112311	−	0.308573i
$520$	−2.54395	+	4.20994i	−0.111560	+	0.184618i
$521$	−11.1186	+	6.41932i	−0.487115	+	0.281236i	−0.723377	−	0.690454i	$-0.757411\pi$
$521$	−11.1186	+	6.41932i	−0.487115	+	0.281236i	0.236262	+	0.971689i	$0.424078\pi$
$522$	−0.0934181	−	1.06777i	−0.00408880	−	0.0467352i
$523$	−1.03521	−	11.8325i	−0.0452667	−	0.517401i	−0.984651	−	0.174535i	$-0.944158\pi$
$523$	−1.03521	−	11.8325i	−0.0452667	−	0.517401i	0.939384	−	0.342866i	$-0.111398\pi$
$524$	11.2426	−	6.49089i	0.491133	−	0.283556i
$525$	−4.58186	−	2.89506i	−0.199969	−	0.126351i
$526$	−3.18756	−	8.75775i	−0.138984	−	0.381856i
$527$	7.49189	+	5.24588i	0.326352	+	0.228514i
$528$	0.191694	−	0.134226i	0.00834242	−	0.00584142i
$529$	3.01112	−	8.27299i	0.130918	−	0.359695i
$530$	−10.1148	−	12.5548i	−0.439358	−	0.545348i
$531$			1.15809i			0.0502570i
$532$	−4.67748	+	0.667894i	−0.202794	+	0.0289569i
$533$	−7.75920	+	7.75920i	−0.336088	+	0.336088i
$534$	1.74467	−	1.46396i	0.0754994	−	0.0633516i
$535$	4.43035	+	10.0181i	0.191541	+	0.433121i
$536$	1.88539	−	10.6926i	0.0814364	−	0.461849i
$537$	−5.96495	+	8.51883i	−0.257406	+	0.367615i
$538$	9.86290	−	21.1510i	0.425220	−	0.911886i
$539$	−1.18051	−	0.681570i	−0.0508484	−	0.0293573i
$540$	2.14790	+	0.621721i	0.0924308	+	0.0267546i
$541$	−20.0702	−	16.8409i	−0.862887	−	0.724048i	0.0997011	−	0.995017i	$-0.468211\pi$
$541$	−20.0702	−	16.8409i	−0.862887	−	0.724048i	−0.962588	+	0.270969i	$0.912656\pi$
$542$	−19.6875	+	1.72243i	−0.845651	+	0.0739849i
$543$	−24.6256	−	6.59840i	−1.05678	−	0.283164i
$544$	−0.940022	+	1.62817i	−0.0403031	+	0.0698071i
$545$	3.31407	+	9.70358i	0.141959	+	0.415656i
$546$	2.34828	−	0.414065i	0.100497	−	0.0177203i
$547$	−15.3497	−	21.9216i	−0.656305	−	0.937301i	0.343693	−	0.939082i	$-0.388322\pi$
$547$	−15.3497	−	21.9216i	−0.656305	−	0.937301i	−0.999998	+	0.00178108i	$0.999433\pi$
$548$	−10.9966	+	5.12779i	−0.469751	+	0.219048i
$549$	3.76464	+	4.48653i	0.160671	+	0.191480i
$550$	−0.859723	+	0.793697i	−0.0366587	+	0.0338434i
$551$	3.73749	+	2.80351i	0.159222	+	0.119433i
$552$	−2.66421	−	2.66421i	−0.113396	−	0.113396i
$553$	−15.7442	−	1.37744i	−0.669511	−	0.0585746i
$554$	−12.0061	−	4.36987i	−0.510091	−	0.185658i
$555$	10.3028	+	2.02943i	0.437328	+	0.0861444i
$556$	−0.736043	−	4.17431i	−0.0312152	−	0.177030i
$557$	−28.9209	−	13.4861i	−1.22542	−	0.571422i	−0.301301	−	0.953529i	$-0.597421\pi$
$557$	−28.9209	−	13.4861i	−1.22542	−	0.571422i	−0.924118	+	0.382107i	$0.875199\pi$
$558$	−1.25908	−	4.69897i	−0.0533013	−	0.198923i
$559$	9.13852	+	15.8284i	0.386518	+	0.669469i
$560$	−2.41834	+	0.163026i	−0.102194	+	0.00688911i
$561$	0.282800	−	0.337028i	0.0119398	−	0.0142293i
$562$	−5.68883	+	21.2310i	−0.239969	+	0.895576i
$563$	−9.05866	+	2.42726i	−0.381777	+	0.102297i	−0.444603	−	0.895728i	$-0.646655\pi$
$563$	−9.05866	+	2.42726i	−0.381777	+	0.102297i	0.0628262	+	0.998024i	$0.479989\pi$
$564$	0.843751	−	0.307100i	0.0355283	−	0.0129313i
$565$	−24.2312	−	17.6978i	−1.01942	−	0.744554i
$566$	−18.5438	−	3.26977i	−0.779454	−	0.137439i
$567$	−0.458106	−	0.982411i	−0.0192386	−	0.0412574i
$568$	−1.35224	+	15.4561i	−0.0567386	+	0.648525i
$569$	42.6967			1.78994			0.894969	−	0.446129i	$-0.147198\pi$
$569$	42.6967			1.78994			0.894969	+	0.446129i	$0.147198\pi$
$570$	−8.26729	+	5.16255i	−0.346279	+	0.216235i
$571$	−5.49505			−0.229961			−0.114980	−	0.993368i	$-0.536681\pi$
$571$	−5.49505			−0.229961			−0.114980	+	0.993368i	$0.536681\pi$
$572$	0.0448663	−	0.512824i	0.00187596	−	0.0214423i
$573$	−0.544446	−	1.16757i	−0.0227446	−	0.0487759i
$574$	−5.32501	−	0.938944i	−0.222262	−	0.0391908i
$575$	14.9884	+	11.4127i	0.625061	+	0.475941i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	−30.0705	+	8.05737i	−1.25185	+	0.335433i	−0.823052	−	0.567967i	$-0.807730\pi$
$577$	−30.0705	+	8.05737i	−1.25185	+	0.335433i	−0.428800	+	0.903399i	$0.641064\pi$
$578$	3.48511	−	13.0066i	0.144961	−	0.541004i
$579$	−6.10300	+	7.27327i	−0.253632	+	0.302267i
$580$	1.80490	+	1.57692i	0.0749443	+	0.0654781i
$581$	2.26605	+	3.92491i	0.0940115	+	0.162833i
$582$	−0.0582401	−	0.217355i	−0.00241413	−	0.00900965i
$583$	1.52921	+	0.713080i	0.0633332	+	0.0295328i
$584$	−0.202465	−	1.14823i	−0.00837805	−	0.0475143i
$585$	4.08480	−	2.74038i	0.168886	−	0.113301i
$586$	22.2068	+	8.08260i	0.917353	+	0.333889i
$587$	−1.14810	−	0.100445i	−0.0473870	−	0.00414582i	0.0634376	−	0.997986i	$-0.479794\pi$
$587$	−1.14810	−	0.100445i	−0.0473870	−	0.00414582i	−0.110825	+	0.993840i	$0.535349\pi$
$588$	−4.11890	−	4.11890i	−0.169861	−	0.169861i
$589$	18.9148	+	9.58513i	0.779373	+	0.394949i
$590$	−1.79421	−	1.86728i	−0.0738663	−	0.0768748i
$591$	−8.93741	−	10.6512i	−0.367636	−	0.438131i
$592$	4.25609	−	1.98465i	0.174924	−	0.0815685i
$593$	5.40540	+	7.71971i	0.221973	+	0.317011i	0.914657	−	0.404231i	$-0.132461\pi$
$593$	5.40540	+	7.71971i	0.221973	+	0.317011i	−0.692684	+	0.721241i	$0.743572\pi$
$594$	−0.230460	+	0.0406363i	−0.00945589	+	0.00166733i
$595$	−4.31235	+	1.47280i	−0.176789	+	0.0603788i
$596$	−3.13219	+	5.42511i	−0.128300	+	0.222221i
$597$	17.1869	+	4.60522i	0.703414	+	0.188479i
$598$	−8.25674	+	0.722371i	−0.337643	+	0.0295399i
$599$	−33.9043	−	28.4491i	−1.38529	−	1.16240i	−0.967207	−	0.253991i	$-0.918257\pi$
$599$	−33.9043	−	28.4491i	−1.38529	−	1.16240i	−0.418086	−	0.908408i	$-0.637299\pi$
$600$	−4.42643	+	2.32523i	−0.180708	+	0.0949272i
$601$	−27.1935	−	15.7002i	−1.10925	−	0.640423i	−0.170612	−	0.985338i	$-0.554574\pi$
$601$	−27.1935	−	15.7002i	−1.10925	−	0.640423i	−0.938634	+	0.344915i	$0.887908\pi$
$602$	−3.80620	+	8.16242i	−0.155129	+	0.332675i
$603$	−6.22762	+	8.89396i	−0.253608	+	0.362190i
$604$	1.72570	−	9.78691i	0.0702176	−	0.398224i
$605$	−8.82796	+	22.8267i	−0.358908	+	0.928037i
$606$	−0.379804	+	0.318694i	−0.0154285	+	0.0129460i
$607$	−14.5898	+	14.5898i	−0.592183	+	0.592183i	−0.938221	−	0.346038i	$-0.887527\pi$
$607$	−14.5898	+	14.5898i	−0.592183	+	0.592183i	0.346038	+	0.938221i	$0.387527\pi$
$608$	−1.62396	+	4.04509i	−0.0658602	+	0.164050i
$609$		−	1.16186i		−	0.0470808i
$610$	−13.0209	−	1.40151i	−0.527200	−	0.0567453i
$611$	0.675554	−	1.85607i	0.0273300	−	0.0750886i
$612$	1.54004	−	1.07835i	0.0622525	−	0.0435897i
$613$	12.6665	+	8.86919i	0.511596	+	0.358223i	0.800691	−	0.599077i	$-0.204466\pi$
$613$	12.6665	+	8.86919i	0.511596	+	0.358223i	−0.289096	+	0.957300i	$0.593355\pi$
$614$	1.09577	+	3.01059i	0.0442215	+	0.121498i
$615$	−10.8295	+	2.67134i	−0.436690	+	0.107719i
$616$	0.219681	−	0.126833i	0.00885120	−	0.00511024i
$617$	−2.54589	−	29.0996i	−0.102494	−	1.17151i	−0.857036	−	0.515256i	$-0.827697\pi$
$617$	−2.54589	−	29.0996i	−0.102494	−	1.17151i	0.754543	−	0.656251i	$-0.227859\pi$
$618$	0.682303	+	7.79876i	0.0274463	+	0.313712i
$619$	3.59996	−	2.07844i	0.144694	−	0.0835394i	−0.425905	−	0.904768i	$-0.640044\pi$
$619$	3.59996	−	2.07844i	0.144694	−	0.0835394i	0.570599	+	0.821229i	$0.306711\pi$
$620$	9.31010	+	5.62583i	0.373903	+	0.225939i
$621$	1.28865	+	3.54054i	0.0517118	+	0.142077i
$622$	13.0806	+	9.15911i	0.524483	+	0.367247i
$623$	2.02229	−	1.41602i	0.0810212	−	0.0567316i
$624$	0.752371	−	2.06712i	0.0301189	−	0.0827511i
$625$	20.3715	−	14.4914i	0.814861	−	0.579657i
$626$		−	29.2507i		−	1.16909i
$627$	0.538635	−	0.866240i	0.0215110	−	0.0345943i
$628$	1.48418	−	1.48418i	0.0592251	−	0.0592251i
$629$	6.76328	−	5.67506i	0.269669	−	0.226280i
$630$	2.26066	+	0.874284i	0.0900669	+	0.0348323i
$631$	−3.77553	+	21.4121i	−0.150301	+	0.852402i	0.812655	+	0.582745i	$0.198021\pi$
$631$	−3.77553	+	21.4121i	−0.150301	+	0.852402i	−0.962956	+	0.269657i	$0.913090\pi$
$632$	−8.36276	+	11.9433i	−0.332653	+	0.475077i
$633$	9.11192	−	19.5406i	0.362166	−	0.776668i
$634$	−11.7662	−	6.79324i	−0.467297	−	0.269794i
$635$	−5.28169	+	18.2470i	−0.209598	+	0.724109i
$636$	5.52331	+	4.63461i	0.219014	+	0.183774i
$637$	−12.7650	+	1.11679i	−0.505768	+	0.0442489i
$638$	−0.242283	−	0.0649196i	−0.00959208	−	0.00257019i
$639$	7.75759	−	13.4365i	0.306886	−	0.531541i
$640$	−0.985254	+	2.00731i	−0.0389456	+	0.0793457i
$641$	−2.53741	+	0.447414i	−0.100222	+	0.0176718i	−0.223534	−	0.974696i	$-0.571759\pi$
$641$	−2.53741	+	0.447414i	−0.100222	+	0.0176718i	0.123312	+	0.992368i	$0.460648\pi$
$642$	−2.80983	−	4.01286i	−0.110895	−	0.158375i
$643$	−32.5887	+	15.1964i	−1.28517	+	0.599286i	−0.940614	−	0.339478i	$-0.889749\pi$
$643$	−32.5887	+	15.1964i	−1.28517	+	0.599286i	−0.344559	+	0.938765i	$0.611972\pi$
$644$	−2.62524	−	3.12864i	−0.103449	−	0.123286i
$645$	−0.370728	+	18.5748i	−0.0145974	+	0.731382i
$646$	−0.980777	+	8.13602i	−0.0385882	+	0.320107i
$647$	27.5500	+	27.5500i	1.08310	+	1.08310i	0.996218	+	0.0868843i	$0.0276910\pi$
$647$	27.5500	+	27.5500i	1.08310	+	1.08310i	0.0868843	+	0.996218i	$0.472309\pi$
$648$	−0.996195	−	0.0871557i	−0.0391342	−	0.00342380i
$649$	0.254668	+	0.0926916i	0.00999659	+	0.00363846i
$650$	−2.34063	+	10.7470i	−0.0918069	+	0.421532i
$651$	−0.915686	−	5.19311i	−0.0358886	−	0.203534i
$652$	18.9454	+	8.83437i	0.741958	+	0.345981i
$653$	6.07061	+	22.6558i	0.237561	+	0.886590i	0.976978	+	0.213342i	$0.0684349\pi$
$653$	6.07061	+	22.6558i	0.237561	+	0.886590i	−0.739416	+	0.673248i	$0.764898\pi$
$654$	−2.29284	−	3.97132i	−0.0896572	−	0.155291i
$655$	19.0990	−	21.8601i	0.746258	−	0.854145i
$656$	−3.20641	+	3.82125i	−0.125189	+	0.149195i
$657$	−0.301770	+	1.12622i	−0.0117732	+	0.0439380i
$658$	0.940134	−	0.251908i	0.0366502	−	0.00982040i
$659$	37.7578	−	13.7427i	1.47083	−	0.535340i	0.522507	−	0.852635i	$-0.324997\pi$
$659$	37.7578	−	13.7427i	1.47083	−	0.535340i	0.948327	+	0.317296i	$0.102775\pi$
$660$	0.308631	−	0.422567i	0.0120135	−	0.0164484i
$661$	−32.2462	−	5.68588i	−1.25423	−	0.221155i	−0.493228	−	0.869900i	$-0.664183\pi$
$661$	−32.2462	−	5.68588i	−1.25423	−	0.221155i	−0.761006	+	0.648745i	$0.775294\pi$
$662$	1.73115	+	3.71246i	0.0672830	+	0.144289i
$663$	0.360449	−	4.11996i	0.0139987	−	0.160006i
$664$	4.18101			0.162255
$665$	−9.41513	+	4.79371i	−0.365103	+	0.185892i
$666$	−4.69608			−0.181969
$667$	−0.351978	+	4.02312i	−0.0136286	+	0.155776i
$668$	−3.48321	−	7.46977i	−0.134769	−	0.289014i
$669$	14.6605	+	2.58504i	0.566807	+	0.0999434i
$670$	−3.73791	−	23.9887i	−0.144408	−	0.926763i
$671$	1.28791	−	0.468762i	0.0497193	−	0.0180964i
$672$	1.04704	−	0.280552i	0.0403903	−	0.0108225i
$673$	11.4467	−	42.7196i	0.441238	−	1.64672i	−0.284446	−	0.958692i	$-0.591809\pi$
$673$	11.4467	−	42.7196i	0.441238	−	1.64672i	0.725683	−	0.688029i	$-0.241524\pi$
$674$	−15.4865	+	18.4561i	−0.596518	+	0.710902i
$675$	4.99439	−	0.236684i	0.192234	−	0.00910997i
$676$	4.08047	+	7.06759i	0.156941	+	0.271830i
$677$	1.22076	+	4.55594i	0.0469176	+	0.175099i	0.985409	−	0.170204i	$-0.0544427\pi$
$677$	1.22076	+	4.55594i	0.0469176	+	0.175099i	−0.938491	+	0.345303i	$0.887776\pi$
$678$	12.1619	+	5.67117i	0.467074	+	0.217800i
$679$	−0.0423559	−	0.240212i	−0.00162547	−	0.00921849i
$680$	−0.812469	+	4.12465i	−0.0311567	+	0.158173i
$681$	−14.7237	−	5.35899i	−0.564213	−	0.205357i
$682$	−1.13409	−	0.0992199i	−0.0434265	−	0.00379933i
$683$	17.5698	+	17.5698i	0.672288	+	0.672288i	0.958243	−	0.285955i	$-0.0923108\pi$
$683$	17.5698	+	17.5698i	0.672288	+	0.672288i	−0.285955	+	0.958243i	$0.592311\pi$
$684$	3.18134	−	2.97978i	0.121641	−	0.113935i
$685$	−19.5636	+	18.7979i	−0.747486	+	0.718232i
$686$	−8.93599	−	10.6495i	−0.341178	−	0.406600i
$687$	17.3519	−	8.09130i	0.662015	−	0.308702i
$688$	4.76559	+	6.80597i	0.181686	+	0.259475i
$689$	15.6199	−	2.75420i	0.595070	−	0.104927i
$690$	−7.56306	−	3.71221i	−0.287921	−	0.141321i
$691$	9.95589	−	17.2441i	0.378740	−	0.655997i	−0.612139	−	0.790750i	$-0.709691\pi$
$691$	9.95589	−	17.2441i	0.378740	−	0.655997i	0.990879	+	0.134753i	$0.0430242\pi$
$692$	−7.22603	−	1.93621i	−0.274692	−	0.0736036i
$693$	−0.252701	+	0.0221084i	−0.00959930	+	0.000839830i
$694$	14.4149	+	12.0955i	0.547181	+	0.459139i
$695$	−4.57428	−	8.30114i	−0.173512	−	0.314880i
$696$	−0.928251	−	0.535926i	−0.0351853	−	0.0203142i
$697$	−3.96340	+	8.49954i	−0.150125	+	0.321943i
$698$	16.8675	−	24.0893i	0.638445	−	0.911794i
$699$	1.58063	−	8.96420i	0.0597849	−	0.339057i
$700$	−4.99954	+	2.09271i	−0.188965	+	0.0790969i
$701$	−6.42294	+	5.38949i	−0.242591	+	0.203558i	−0.755974	−	0.654601i	$-0.772836\pi$
$701$	−6.42294	+	5.38949i	−0.242591	+	0.203558i	0.513383	+	0.858160i	$0.328392\pi$
$702$	−1.55548	+	1.55548i	−0.0587079	+	0.0587079i
$703$	13.6633	−	15.2421i	0.515323	−	0.574867i
$704$		−	0.234015i		−	0.00881978i
$705$	1.56349	−	1.25962i	0.0588843	−	0.0474400i
$706$	5.33764	−	14.6650i	0.200885	−	0.551926i
$707$	−0.440239	+	0.308258i	−0.0165569	+	0.0115933i
$708$	0.948656	+	0.664256i	0.0356527	+	0.0249643i
$709$	−1.76613	−	4.85240i	−0.0663283	−	0.182236i	0.902100	−	0.431526i	$-0.142025\pi$
$709$	−1.76613	−	4.85240i	−0.0663283	−	0.182236i	−0.968429	+	0.249291i	$0.919803\pi$
$710$	8.30872	+	33.6834i	0.311821	+	1.26411i
$711$	12.6267	−	7.29001i	0.473537	−	0.273397i
$712$	−0.198498	−	2.26884i	−0.00743903	−	0.0850285i
$713$	1.59749	+	18.2594i	0.0598266	+	0.683821i
$714$	1.76488	−	1.01896i	0.0660492	−	0.0381335i
$715$	−0.275678	−	1.11759i	−0.0103098	−	0.0417956i
$716$	3.55686	+	9.77240i	0.132926	+	0.365212i
$717$	15.6674	+	10.9705i	0.585112	+	0.409700i
$718$	12.6432	−	8.85286i	0.471840	−	0.330386i
$719$	−12.7619	+	35.0631i	−0.475940	+	1.30763i	0.436972	+	0.899475i	$0.356051\pi$
$719$	−12.7619	+	35.0631i	−0.475940	+	1.30763i	−0.912911	+	0.408158i	$0.866171\pi$
$720$	1.74127	−	1.40285i	0.0648932	−	0.0522811i
$721$			8.48593i			0.316032i
$722$	0.415347	+	18.9955i	0.0154576	+	0.706938i
$723$	12.6961	−	12.6961i	0.472172	−	0.472172i
$724$	−19.5297	+	16.3874i	−0.725817	+	0.609033i
$725$	4.95891	+	2.03246i	0.184169	+	0.0754837i
$726$	1.90062	−	10.7790i	0.0705386	−	0.400045i
$727$	−27.3724	+	39.0918i	−1.01519	+	1.44984i	−0.126142	+	0.992012i	$0.540260\pi$
$727$	−27.3724	+	39.0918i	−1.01519	+	1.44984i	−0.889043	+	0.457823i	$0.848629\pi$
$728$	1.00773	−	2.16109i	0.0373491	−	0.0800954i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	−1.25826	−	2.28341i	−0.0465701	−	0.0845129i
$731$	11.9660	+	10.0406i	0.442577	+	0.371366i
$732$	5.83446	−	0.510449i	0.215648	−	0.0188667i
$733$	−42.3053	−	11.3357i	−1.56258	−	0.418693i	−0.629103	−	0.777322i	$-0.716578\pi$
$733$	−42.3053	−	11.3357i	−1.56258	−	0.418693i	−0.933480	+	0.358629i	$0.883244\pi$
$734$	11.5892	−	20.0730i	0.427764	−	0.740908i
$735$	−11.6926	−	5.73911i	−0.431287	−	0.211690i
$736$	−3.71053	+	0.654266i	−0.136772	+	0.0241166i
$737$	1.45736	+	2.08132i	0.0536825	+	0.0766665i
$738$	4.52093	−	2.10814i	0.166418	−	0.0776018i
$739$	10.7828	+	12.8504i	0.396652	+	0.472711i	0.926996	−	0.375071i	$-0.122382\pi$
$739$	10.7828	+	12.8504i	0.396652	+	0.472711i	−0.530344	+	0.847782i	$0.677937\pi$
$740$	7.57183	−	7.27550i	0.278346	−	0.267453i
$741$	−0.522938	−	9.57437i	−0.0192106	−	0.351723i
$742$	5.52648	+	5.52648i	0.202883	+	0.202883i
$743$	8.41112	+	0.735878i	0.308574	+	0.0269967i	0.240391	−	0.970676i	$-0.422724\pi$
$743$	8.41112	+	0.735878i	0.308574	+	0.0269967i	0.0681829	+	0.997673i	$0.478280\pi$
$744$	−4.57135	−	1.66384i	−0.167594	−	0.0609992i
$745$	−2.70718	+	13.7435i	−0.0991833	+	0.503522i
$746$	−1.46524	−	8.30979i	−0.0536462	−	0.304243i
$747$	−3.78928	−	1.76697i	−0.138643	−	0.0646501i
$748$	−0.113870	−	0.424968i	−0.00416349	−	0.0155384i
$749$	−2.65507	−	4.59872i	−0.0970143	−	0.168034i
$750$	−7.68615	+	8.11930i	−0.280659	+	0.296475i
$751$	32.7096	−	38.9817i	1.19359	−	1.42246i	0.312237	−	0.950004i	$-0.398922\pi$
$751$	32.7096	−	38.9817i	1.19359	−	1.42246i	0.881352	−	0.472460i	$-0.156634\pi$
$752$	0.232394	−	0.867306i	0.00847453	−	0.0316274i
$753$	1.29742	−	0.347642i	0.0472805	−	0.0126688i
$754$	−2.21565	+	0.806430i	−0.0806892	+	0.0293685i
$755$	−3.42131	−	21.9568i	−0.124514	−	0.799091i
$756$	−1.06750	−	0.188230i	−0.0388247	−	0.00684584i
$757$	−2.74217	−	5.88061i	−0.0996659	−	0.213734i	0.850152	−	0.526537i	$-0.176510\pi$
$757$	−2.74217	−	5.88061i	−0.0996659	−	0.213734i	−0.949818	+	0.312803i	$0.898732\pi$
$758$	−1.49865	+	17.1296i	−0.0544332	+	0.622175i
$759$	0.881715			0.0320042
$760$	−0.513011	+	9.73328i	−0.0186089	+	0.353063i
$761$	−39.3024			−1.42471			−0.712355	−	0.701820i	$-0.752371\pi$
$761$	−39.3024			−1.42471			−0.712355	+	0.701820i	$0.752371\pi$
$762$	0.740412	−	8.46294i	0.0268223	−	0.306580i
$763$	−2.10073	−	4.50503i	−0.0760515	−	0.163093i
$764$	−1.26870	−	0.223706i	−0.0458999	−	0.00809339i
$765$	2.47950	−	3.39484i	0.0896465	−	0.122741i
$766$	34.9485	−	12.7202i	1.26274	−	0.459601i
$767$	2.46075	−	0.659357i	0.0888527	−	0.0238080i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−30.4116	+	36.2432i	−1.09667	+	1.30696i	−0.148602	+	0.988897i	$0.547477\pi$
$769$	−30.4116	+	36.2432i	−1.09667	+	1.30696i	−0.948069	+	0.318064i	$0.896967\pi$
$770$	0.373196	−	0.427149i	0.0134491	−	0.0153934i
$771$	−1.45359	−	2.51769i	−0.0523497	−	0.0906723i
$772$	2.45738	+	9.17106i	0.0884429	+	0.330074i
$773$	37.7911	+	17.6223i	1.35925	+	0.633829i	0.959217	−	0.282672i	$-0.0912208\pi$
$773$	37.7911	+	17.6223i	1.35925	+	0.633829i	0.400033	+	0.916501i	$0.368999\pi$
$774$	−1.44277	−	8.18233i	−0.0518591	−	0.294108i
$775$	23.7665	+	5.17620i	0.853718	+	0.185934i
$776$	−0.211452	−	0.0769622i	−0.00759068	−	0.00276278i
$777$	−5.07104	−	0.443658i	−0.181922	−	0.0159162i
$778$	6.87471	+	6.87471i	0.246470	+	0.246470i
$779$	−6.31132	+	20.8073i	−0.226126	+	0.745500i
$780$	0.0981544	−	4.91789i	0.00351449	−	0.176089i
$781$	−2.33383	−	2.78135i	−0.0835109	−	0.0995244i
$782$	−6.41989	+	2.99365i	−0.229575	+	0.107053i
$783$	0.614789	+	0.878010i	0.0219708	+	0.0313775i
$784$	−5.73651	+	1.01150i	−0.204875	+	0.0361251i
$785$	2.06799	−	4.21322i	0.0738098	−	0.150376i
$786$	−6.49089	+	11.2426i	−0.231523	+	0.401009i
$787$	38.0235	+	10.1884i	1.35539	+	0.363176i	0.862122	−	0.506701i	$-0.169135\pi$
$787$	38.0235	+	10.1884i	1.35539	+	0.363176i	0.493269	+	0.869877i	$0.335802\pi$
$788$	−13.8512	+	1.21183i	−0.493430	+	0.0431695i
$789$	7.13938	+	5.99065i	0.254169	+	0.213273i
$790$	−9.06472	+	31.3164i	−0.322508	+	1.11419i
$791$	12.5972	+	7.27298i	0.447904	+	0.258597i
$792$	−0.0988992	+	0.212090i	−0.00351423	+	0.00753629i
$793$	7.38972	−	10.5536i	0.262417	−	0.374770i
$794$	4.10479	−	23.2794i	0.145674	−	0.826156i
$795$	15.0371	+	5.81542i	0.533311	+	0.206252i
$796$	13.6304	−	11.4373i	0.483117	−	0.405383i
$797$	5.69075	−	5.69075i	0.201577	−	0.201577i	−0.599099	−	0.800675i	$-0.704474\pi$
$797$	5.69075	−	5.69075i	0.201577	−	0.201577i	0.800675	+	0.599099i	$0.204474\pi$
$798$	3.71687	−	2.91715i	0.131576	−	0.103266i
$799$		−	1.68809i		−	0.0597205i
$800$	−0.634179	+	4.95962i	−0.0224216	+	0.175349i
$801$	−0.778954	+	2.14016i	−0.0275230	+	0.0756188i
$802$	10.9305	−	7.65360i	0.385968	−	0.270258i
$803$	0.223505	+	0.156500i	0.00788734	+	0.00552277i
$804$	3.71349	+	10.2027i	0.130965	+	0.359823i
$805$	−7.81623	−	4.72313i	−0.275486	−	0.166468i
$806$	−9.26765	+	5.35068i	−0.326439	+	0.188470i
$807$	2.03401	+	23.2488i	0.0716004	+	0.818396i
$808$	0.0432118	+	0.493913i	0.00152018	+	0.0173758i
$809$	33.4535	−	19.3144i	1.17616	−	0.679058i	0.221040	−	0.975265i	$-0.429055\pi$
$809$	33.4535	−	19.3144i	1.17616	−	0.679058i	0.955124	+	0.296206i	$0.0957216\pi$
$810$	−2.17099	+	0.535522i	−0.0762810	+	0.0188163i
$811$	−2.03469	−	5.59025i	−0.0714475	−	0.196300i	0.898829	−	0.438300i	$-0.144419\pi$
$811$	−2.03469	−	5.59025i	−0.0714475	−	0.196300i	−0.970276	+	0.241999i	$0.922197\pi$
$812$	−0.951737	−	0.666414i	−0.0333994	−	0.0233865i
$813$	16.1887	−	11.3354i	0.567761	−	0.397551i
$814$	−0.375864	+	1.03268i	−0.0131740	+	0.0361954i
$815$	46.4741	+	5.00225i	1.62792	+	0.175221i
$816$		−	1.88004i		−	0.0658147i
$817$	30.7553	+	19.1239i	1.07599	+	0.669060i
$818$	−19.1060	+	19.1060i	−0.668025	+	0.668025i
$819$	−1.82663	+	1.53273i	−0.0638278	+	0.0535579i
$820$	−4.02334	+	10.4033i	−0.140501	+	0.363298i
$821$	0.672695	−	3.81504i	0.0234772	−	0.133146i	−0.970816	−	0.239824i	$-0.922910\pi$
$821$	0.672695	−	3.81504i	0.0234772	−	0.133146i	0.994294	+	0.106678i	$0.0340214\pi$
$822$	6.95943	−	9.93909i	0.242738	−	0.346666i
$823$	−1.78090	+	3.81915i	−0.0620782	+	0.133127i	−0.934899	−	0.354913i	$-0.884510\pi$
$823$	−1.78090	+	3.81915i	−0.0620782	+	0.133127i	0.872821	+	0.488040i	$0.162288\pi$
$824$	6.77973	+	3.91428i	0.236183	+	0.136360i
$825$	0.347694	−	1.11722i	0.0121051	−	0.0388967i
$826$	0.961647	+	0.806918i	0.0334600	+	0.0280763i
$827$	−26.7585	+	2.34106i	−0.930484	+	0.0814068i	−0.542309	−	0.840179i	$-0.682450\pi$
$827$	−26.7585	+	2.34106i	−0.930484	+	0.0814068i	−0.388175	+	0.921586i	$0.626894\pi$
$828$	3.63938	+	0.975170i	0.126477	+	0.0338895i
$829$	7.34894	−	12.7287i	0.255239	−	0.442087i	−0.709721	−	0.704483i	$-0.751179\pi$
$829$	7.34894	−	12.7287i	0.255239	−	0.442087i	0.964960	+	0.262395i	$0.0845124\pi$
$830$	8.84727	−	3.02161i	0.307093	−	0.104882i
$831$	12.5825	−	2.21864i	0.436483	−	0.0769638i
$832$	−1.26174	−	1.80196i	−0.0437431	−	0.0624717i
$833$	−9.92522	+	4.62821i	−0.343889	+	0.160358i
$834$	2.72459	+	3.24703i	0.0943447	+	0.112436i
$835$	−12.7691	−	13.2892i	−0.441892	−	0.459890i
$836$	−0.400634	−	0.938079i	−0.0138562	−	0.0324442i
$837$	3.43988	+	3.43988i	0.118900	+	0.118900i
$838$	−31.7245	−	2.77553i	−1.09590	−	0.0958791i
$839$	−50.6062	−	18.4191i	−1.74712	−	0.635899i	−0.747521	−	0.664238i	$-0.768756\pi$
$839$	−50.6062	−	18.4191i	−1.74712	−	0.635899i	−0.999598	+	0.0283386i	$0.990978\pi$
$840$	2.01283	−	1.35036i	0.0694494	−	0.0465917i
$841$	−4.83630	−	27.4280i	−0.166769	−	0.945793i
$842$	7.24437	+	3.37811i	0.249658	+	0.116417i
$843$	−5.68883	−	21.2310i	−0.195934	−	0.731235i
$844$	−10.7803	−	18.6721i	−0.371074	−	0.642719i
$845$	13.7423	+	12.0065i	0.472748	+	0.413035i
$846$	−0.577160	+	0.687832i	−0.0198432	+	0.0236481i
$847$	3.07071	−	11.4601i	0.105511	−	0.393772i
$848$	6.96449	−	1.86613i	0.239162	−	0.0640832i
$849$	17.6943	−	6.44019i	0.607266	−	0.221027i
$850$	1.26165	+	9.31517i	0.0432742	+	0.319508i
$851$	17.4249	+	3.07248i	0.597318	+	0.105323i
$852$	−6.55700	−	14.0615i	−0.224639	−	0.481740i
$853$	2.93088	−	33.5001i	0.100351	−	1.14702i	−0.764372	−	0.644775i	$-0.776951\pi$
$853$	2.93088	−	33.5001i	0.100351	−	1.14702i	0.864724	−	0.502247i	$-0.167493\pi$
$854$	6.34854			0.217243
$855$	4.57841	−	8.60454i	0.156578	−	0.294269i
$856$	−4.89879			−0.167437
$857$	−1.47749	+	16.8878i	−0.0504700	+	0.576875i	0.928289	+	0.371860i	$0.121280\pi$
$857$	−1.47749	+	16.8878i	−0.0504700	+	0.576875i	−0.978759	+	0.205015i	$0.934276\pi$
$858$	0.217557	+	0.466552i	0.00742727	+	0.0159278i
$859$	1.30286	+	0.229730i	0.0444531	+	0.00783827i	0.195830	−	0.980638i	$-0.437260\pi$
$859$	1.30286	+	0.229730i	0.0444531	+	0.00783827i	−0.151377	+	0.988476i	$0.548371\pi$
$860$	15.0029	+	10.9577i	0.511596	+	0.373656i
$861$	5.08107	−	1.84936i	0.173162	−	0.0630260i
$862$	−11.0213	+	2.95315i	−0.375387	+	0.100585i
$863$	10.8668	−	40.5556i	0.369912	−	1.38053i	−0.490727	−	0.871313i	$-0.663269\pi$
$863$	10.8668	−	40.5556i	0.369912	−	1.38053i	0.860639	−	0.509216i	$-0.170065\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−16.6900	+	1.12511i	−0.567477	+	0.0382549i
$866$	6.43753	+	11.1501i	0.218756	+	0.378897i
$867$	3.48511	+	13.0066i	0.118361	+	0.441728i
$868$	−4.77916	−	2.22856i	−0.162215	−	0.0756423i
$869$	−0.592479	−	3.36012i	−0.0200985	−	0.113984i
$870$	−2.35155	−	0.463205i	−0.0797249	−	0.0157041i
$871$	22.4438	+	8.16888i	0.760479	+	0.276792i
$872$	−4.56823	−	0.399669i	−0.154700	−	0.0135345i
$873$	0.159115	+	0.159115i	0.00538522	+	0.00538522i
$874$	−13.7540	+	8.97512i	−0.465236	+	0.303588i
$875$	−9.06692	+	8.04145i	−0.306518	+	0.271851i
$876$	0.749457	+	0.893168i	0.0253218	+	0.0301774i
$877$	−5.27914	+	2.46170i	−0.178264	+	0.0831258i	−0.509701	−	0.860351i	$-0.670244\pi$
$877$	−5.27914	+	2.46170i	−0.178264	+	0.0831258i	0.331438	+	0.943477i	$0.392466\pi$
$878$	9.48120	+	13.5406i	0.319975	+	0.456972i
$879$	−23.2729	+	4.10364i	−0.784976	+	0.138412i
$880$	−0.169123	−	0.495190i	−0.00570112	−	0.0166929i
$881$	20.8210	−	36.0631i	0.701478	−	1.21500i	−0.266470	−	0.963843i	$-0.585857\pi$
$881$	20.8210	−	36.0631i	0.701478	−	1.21500i	0.967948	−	0.251152i	$-0.0808094\pi$
$882$	5.62652	+	1.50762i	0.189455	+	0.0507643i
$883$	33.8245	−	2.95926i	1.13828	−	0.0995870i	0.497611	−	0.867400i	$-0.334211\pi$
$883$	33.8245	−	2.95926i	1.13828	−	0.0995870i	0.640674	+	0.767813i	$0.278655\pi$
$884$	−3.16812	−	2.65837i	−0.106556	−	0.0894107i
$885$	2.48747	+	0.720012i	0.0836154	+	0.0242030i
$886$	16.3538	+	9.44188i	0.549417	+	0.317206i
$887$	−16.4094	+	35.1900i	−0.550973	+	1.18156i	0.411806	+	0.911272i	$0.364898\pi$
$887$	−16.4094	+	35.1900i	−0.550973	+	1.18156i	−0.962778	+	0.270293i	$0.912880\pi$
$888$	−2.69356	+	3.84680i	−0.0903899	+	0.129090i
$889$	1.59906	−	9.06873i	0.0536308	−	0.304155i
$890$	−2.05972	−	4.65755i	−0.0690421	−	0.156122i
$891$	0.179266	−	0.150422i	0.00600564	−	0.00503933i
$892$	10.5265	−	10.5265i	0.352452	−	0.352452i
$893$	−0.553246	−	3.87456i	−0.0185137	−	0.129657i
$894$		−	6.26438i		−	0.209512i
$895$	14.5890	+	18.1084i	0.487657	+	0.605298i
$896$	0.370740	−	1.01860i	0.0123855	−	0.0340290i
$897$	6.78936	−	4.75396i	0.226690	−	0.158730i
$898$	12.7436	+	8.92317i	0.425260	+	0.297770i
$899$	1.78339	+	4.89981i	0.0594793	+	0.163418i
$900$	2.67079	−	4.22693i	0.0890262	−	0.140898i
$901$	11.7394	−	6.77772i	0.391095	−	0.225799i
$902$	−0.101740	−	1.16289i	−0.00338757	−	0.0387201i
$903$	−0.784945	−	8.97196i	−0.0261213	−	0.298568i
$904$	11.6213	−	6.70957i	0.386519	−	0.223157i
$905$	−29.4829	+	48.7908i	−0.980046	+	1.62186i
$906$	3.39896	+	9.33856i	0.112923	+	0.310253i
$907$	−20.7860	−	14.5545i	−0.690186	−	0.483274i	0.175101	−	0.984551i	$-0.443975\pi$
$907$	−20.7860	−	14.5545i	−0.690186	−	0.483274i	−0.865287	+	0.501277i	$0.832864\pi$
$908$	−12.8350	+	8.98716i	−0.425944	+	0.298249i
$909$	0.169573	−	0.465899i	0.00562439	−	0.0154529i
$910$	0.570606	−	5.30129i	0.0189154	−	0.175736i
$911$			49.5498i			1.64166i	0.571175	+	0.820829i	$0.306488\pi$
$911$			49.5498i			1.64166i	−0.571175	+	0.820829i	$0.693512\pi$
$912$	−0.616155	−	4.31513i	−0.0204029	−	0.142888i
$913$	−0.691848	+	0.691848i	−0.0228968	+	0.0228968i
$914$	20.4831	−	17.1874i	0.677520	−	0.568507i
$915$	11.9772	−	5.29670i	0.395953	−	0.175103i
$916$	3.32461	−	18.8548i	0.109848	−	0.622980i
$917$	−8.07130	+	11.5270i	−0.266538	+	0.380655i
$918$	−0.794541	+	1.70390i	−0.0262238	+	0.0562370i
$919$	−48.9189	−	28.2433i	−1.61369	−	0.931662i	−0.988506	−	0.151180i	$-0.951693\pi$
$919$	−48.9189	−	28.2433i	−1.61369	−	0.931662i	−0.625179	−	0.780481i	$-0.714974\pi$
$920$	−7.37886	+	4.06606i	−0.243274	+	0.134054i
$921$	−2.45426	−	2.05937i	−0.0808705	−	0.0678584i
$922$	39.2084	−	3.43029i	1.29126	−	0.112971i
$923$	−32.9671	−	8.83351i	−1.08513	−	0.290758i
$924$	−0.126833	+	0.219681i	−0.00417250	+	0.00722698i
$925$	10.7645	−	20.8675i	0.353933	−	0.686121i
$926$	−5.16902	+	0.911438i	−0.169865	+	0.0299517i
$927$	−4.49027	−	6.41278i	−0.147480	−	0.210623i
$928$	−0.971428	+	0.452984i	−0.0318887	+	0.0148699i
$929$	4.35904	+	5.19490i	0.143015	+	0.170439i	0.832797	−	0.553578i	$-0.186738\pi$
$929$	4.35904	+	5.19490i	0.143015	+	0.170439i	−0.689782	+	0.724017i	$0.742294\pi$
$930$	−10.8757	−	0.217064i	−0.356628	−	0.00711782i
$931$	−21.2638	+	13.8756i	−0.696894	+	0.454755i
$932$	−6.43643	−	6.43643i	−0.210832	−	0.210832i
$933$	−15.9077	−	1.39174i	−0.520793	−	0.0455635i
$934$	24.1431	+	8.78737i	0.789986	+	0.287531i
$935$	−0.548079	−	0.816964i	−0.0179241	−	0.0267176i
$936$	0.381989	+	2.16637i	0.0124857	+	0.0708099i
$937$	26.0075	+	12.1275i	0.849629	+	0.396189i	0.798131	−	0.602484i	$-0.205822\pi$
$937$	26.0075	+	12.1275i	0.849629	+	0.396189i	0.0514987	+	0.998673i	$0.483600\pi$
$938$	3.04610	+	11.3682i	0.0994587	+	0.371185i
$939$	14.6254	+	25.3319i	0.477281	+	0.826674i
$940$	−0.135042	−	2.00322i	−0.00440458	−	0.0653379i
$941$	−3.11137	+	3.70799i	−0.101428	+	0.120877i	−0.814370	−	0.580345i	$-0.802918\pi$
$941$	−3.11137	+	3.70799i	−0.101428	+	0.120877i	0.712943	+	0.701222i	$0.247362\pi$
$942$	−0.543246	+	2.02742i	−0.0176999	+	0.0660570i
$943$	−18.1543	+	4.86443i	−0.591185	+	0.158408i
$944$	1.08825	−	0.396092i	0.0354196	−	0.0128917i
$945$	−2.39493	+	0.373178i	−0.0779072	+	0.0121395i
$946$	−1.91479	−	0.337629i	−0.0622552	−	0.0109773i
$947$	11.2302	+	24.0832i	0.364932	+	0.782600i	0.999949	+	0.0101015i	$0.00321545\pi$
$947$	11.2302	+	24.0832i	0.364932	+	0.782600i	−0.635017	+	0.772498i	$0.719007\pi$
$948$	1.27073	−	14.5245i	0.0412715	−	0.471735i
$949$	2.56483			0.0832581
$950$	5.94867	+	20.9670i	0.193000	+	0.680258i
$951$	13.5865			0.440572
$952$	0.177616	−	2.03016i	0.00575656	−	0.0657978i
$953$	22.4991	+	48.2494i	0.728817	+	1.56295i	0.823417	+	0.567437i	$0.192065\pi$
$953$	22.4991	+	48.2494i	0.728817	+	1.56295i	−0.0946001	+	0.995515i	$0.530157\pi$
$954$	−7.10064	−	1.25203i	−0.229892	−	0.0405361i
$955$	−2.84631	+	0.443512i	−0.0921045	+	0.0143517i
$956$	17.9730	−	6.54162i	0.581287	−	0.211571i
$957$	0.242283	−	0.0649196i	0.00783190	−	0.00209855i
$958$	1.81694	−	6.78092i	0.0587027	−	0.219082i
$959$	8.45410	−	10.0752i	0.272997	−	0.325345i
$960$	−0.150397	−	2.23100i	−0.00485405	−	0.0720054i
$961$	−3.66720	−	6.35178i	−0.118297	−	0.204896i
$962$	2.67369	+	9.97836i	0.0862033	+	0.321715i
$963$	4.43981	+	2.07032i	0.143071	+	0.0667151i
$964$	−3.11784	−	17.6822i	−0.100419	−	0.569505i
$965$	11.8279	+	17.6306i	0.380753	+	0.567548i
$966$	3.83785	+	1.39686i	0.123481	+	0.0449433i
$967$	34.2036	+	2.99243i	1.09991	+	0.0962300i	0.622628	−	0.782518i	$-0.286065\pi$
$967$	34.2036	+	2.99243i	1.09991	+	0.0962300i	0.477286	+	0.878748i	$0.341621\pi$
$968$	−7.73945	−	7.73945i	−0.248755	−	0.248755i
$969$	−3.21863	−	7.53639i	−0.103397	−	0.242104i
$970$	−0.503065	−	0.0100405i	−0.0161525	−	0.000322381i
$971$	24.5509	+	29.2587i	0.787877	+	0.938955i	0.999261	−	0.0384480i	$-0.0122414\pi$
$971$	24.5509	+	29.2587i	0.787877	+	0.938955i	−0.211384	+	0.977403i	$0.567797\pi$
$972$	0.906308	−	0.422618i	0.0290698	−	0.0135555i
$973$	2.63537	+	3.76370i	0.0844861	+	0.120659i
$974$	8.79850	−	1.55141i	0.281922	−	0.0497105i
$975$	−3.34645	−	10.4775i	−0.107172	−	0.335548i
$976$	2.92837	−	5.07209i	0.0937349	−	0.162354i
$977$	−55.1221	−	14.7699i	−1.76351	−	0.472531i	−0.776087	−	0.630626i	$-0.782798\pi$
$977$	−55.1221	−	14.7699i	−1.76351	−	0.472531i	−0.987424	+	0.158094i	$0.949465\pi$
$978$	−20.8244	+	1.82190i	−0.665889	+	0.0582578i
$979$	0.408281	+	0.342588i	0.0130487	+	0.0109492i
$980$	−11.4078	+	6.28617i	−0.364408	+	0.200804i
$981$	3.97132	+	2.29284i	0.126794	+	0.0732048i
$982$	7.16093	−	15.3567i	0.228515	−	0.490051i
$983$	−11.5751	+	16.5309i	−0.369188	+	0.527254i	−0.960165	−	0.279434i	$-0.909853\pi$
$983$	−11.5751	+	16.5309i	−0.369188	+	0.527254i	0.590977	+	0.806688i	$0.298742\pi$
$984$	0.866207	−	4.91251i	0.0276137	−	0.156605i
$985$	−28.4342	+	12.5746i	−0.905990	+	0.400659i
$986$	−1.54368	+	1.29530i	−0.0491608	+	0.0412508i
$987$	−0.688226	+	0.688226i	−0.0219065	+	0.0219065i
$988$	−8.14281	−	5.06327i	−0.259057	−	0.161084i
$989$			31.3047i			0.995432i
$990$	−0.0559993	+	0.520269i	−0.00177977	+	0.0165352i
$991$	−3.65237	+	10.0348i	−0.116021	+	0.318766i	−0.984088	−	0.177682i	$-0.943140\pi$
$991$	−3.65237	+	10.0348i	−0.116021	+	0.318766i	0.868067	+	0.496448i	$0.165362\pi$
$992$	−3.98495	+	2.79029i	−0.126522	+	0.0885919i
$993$	−3.35545	−	2.34951i	−0.106482	−	0.0745595i
$994$	−5.75210	−	15.8038i	−0.182445	−	0.501265i
$995$	20.5770	−	34.0526i	0.652336	−	1.07954i
$996$	−3.62086	+	2.09051i	−0.114731	+	0.0662402i
$997$	2.71428	+	31.0243i	0.0859620	+	0.982550i	0.909614	+	0.415455i	$0.136377\pi$
$997$	2.71428	+	31.0243i	0.0859620	+	0.982550i	−0.823652	+	0.567096i	$0.808067\pi$
$998$	0.593665	+	6.78563i	0.0187922	+	0.214795i
$999$	4.06692	−	2.34804i	0.128672	−	0.0742886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.127.1	yes	120
5.3	odd	4	inner	570.2.bh.a.13.10	✓	120
19.3	odd	18	inner	570.2.bh.a.307.10	yes	120
95.3	even	36	inner	570.2.bh.a.193.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.13.10	✓	120	5.3	odd	4	inner
570.2.bh.a.127.1	yes	120	1.1	even	1	trivial
570.2.bh.a.193.1	yes	120	95.3	even	36	inner
570.2.bh.a.307.10	yes	120	19.3	odd	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.422618 - 0.906308i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-2.20941 + 0.344270i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.04704 - 0.280552i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.642788 + 0.766044i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 + 0.996195i) q^{2} +(-0.422618 - 0.906308i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(-2.20941 + 0.344270i) q^{5} +(0.939693 - 0.342020i) q^{6} +(1.04704 - 0.280552i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-0.642788 + 0.766044i) q^{9} +(-0.150397 - 2.23100i) q^{10} +(0.117008 + 0.202663i) q^{11} +(0.258819 + 0.965926i) q^{12} +(1.99368 + 0.929669i) q^{13} +(0.188230 + 1.06750i) q^{14} +(1.24575 + 1.85691i) q^{15} +(0.939693 + 0.342020i) q^{16} +(1.87289 + 0.163857i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(4.35241 - 0.237722i) q^{19} +(2.23562 + 0.0446200i) q^{20} +(-0.696763 - 0.830370i) q^{21} +(-0.212090 + 0.0988992i) q^{22} +(2.16110 + 3.08637i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(4.76296 - 1.52126i) q^{25} +(-1.09989 + 1.90507i) q^{26} +(0.965926 + 0.258819i) q^{27} +(-1.07985 + 0.0944743i) q^{28} +(0.821087 + 0.688973i) q^{29} +(-1.95842 + 1.07917i) q^{30} +(4.21298 + 2.43236i) q^{31} +(-0.422618 + 0.906308i) q^{32} +(0.134226 - 0.191694i) q^{33} +(-0.326466 + 1.85148i) q^{34} +(-2.21674 + 0.980317i) q^{35} +(0.766044 - 0.642788i) q^{36} +(3.32063 - 3.32063i) q^{37} +(-0.142520 + 4.35657i) q^{38} -2.19978i q^{39} +(-0.239298 + 2.22323i) q^{40} +(-1.70610 + 4.68746i) q^{41} +(0.887937 - 0.621740i) q^{42} +(6.80597 + 4.76559i) q^{43} +(-0.0800380 - 0.219902i) q^{44} +(1.15645 - 1.91380i) q^{45} +(-3.26298 + 1.88388i) q^{46} +(-0.0782572 - 0.894484i) q^{47} +(-0.0871557 - 0.996195i) q^{48} +(-5.04460 + 2.91250i) q^{49} +(1.10036 + 4.87742i) q^{50} +(-0.643013 - 1.76666i) q^{51} +(-1.80196 - 1.26174i) q^{52} +(5.90623 - 4.13559i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-0.328288 - 0.407483i) q^{55} -1.08397i q^{56} +(-2.05486 - 3.84416i) q^{57} +(-0.757914 + 0.757914i) q^{58} +(0.887152 - 0.744409i) q^{59} +(-0.904376 - 2.04502i) q^{60} +(1.01701 - 5.76777i) q^{61} +(-2.79029 + 3.98495i) q^{62} +(-0.458106 + 0.982411i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-4.72491 - 1.36765i) q^{65} +(0.179266 + 0.150422i) q^{66} +(10.8162 - 0.946295i) q^{67} +(-1.81598 - 0.486591i) q^{68} +(1.88388 - 3.26298i) q^{69} +(-0.783385 - 2.29375i) q^{70} +(-15.2795 + 2.69418i) q^{71} +(0.573576 + 0.819152i) q^{72} +(1.05671 - 0.492751i) q^{73} +(3.01858 + 3.59740i) q^{74} +(-3.39165 - 3.67379i) q^{75} +(-4.32757 - 0.521678i) q^{76} +(0.179369 + 0.179369i) q^{77} +(2.19141 + 0.191724i) q^{78} +(-13.7007 - 4.98666i) q^{79} +(-2.19391 - 0.432154i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.52093 - 2.10814i) q^{82} +(1.08213 + 4.03855i) q^{83} +(0.541985 + 0.938746i) q^{84} +(-4.19439 + 0.282753i) q^{85} +(-5.34064 + 6.36472i) q^{86} +(0.277416 - 1.03533i) q^{87} +(0.226041 - 0.0605676i) q^{88} +(2.14016 - 0.778954i) q^{89} +(1.80572 + 1.31885i) q^{90} +(2.34828 + 0.414065i) q^{91} +(-1.59233 - 3.41476i) q^{92} +(0.423989 - 4.84622i) q^{93} +0.897901 q^{94} +(-9.53441 + 2.02363i) q^{95} +1.00000 q^{96} +(0.0196120 - 0.224166i) q^{97} +(-2.46175 - 5.27925i) q^{98} +(-0.230460 - 0.0406363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more