LMFDB - Embedded newform 570.2.bh.a.13.10

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			13.10
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.a.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.19391 - 0.432154i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.280552 - 1.04704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.19391 - 0.432154i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.280552 - 1.04704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(2.22323 - 0.239298i) q^{10} +(0.117008 + 0.202663i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-0.929669 + 1.99368i) q^{13} +(-0.188230 - 1.06750i) q^{14} +(1.80572 - 1.31885i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.163857 - 1.87289i) 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} +(0.0988992 + 0.212090i) q^{22} +(-3.08637 + 2.16110i) q^{23} +(0.984808 - 0.173648i) q^{24} +(4.62649 - 1.89621i) q^{25} +(-1.09989 + 1.90507i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-0.0944743 - 1.07985i) q^{28} +(-0.821087 - 0.688973i) q^{29} +(1.91380 - 1.15645i) q^{30} +(4.21298 + 2.43236i) q^{31} +(0.906308 + 0.422618i) q^{32} +(0.191694 + 0.134226i) q^{33} +(0.326466 - 1.85148i) q^{34} +(-1.06799 - 2.17586i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-3.32063 - 3.32063i) q^{37} +(-4.35657 - 0.142520i) q^{38} +2.19978i q^{39} +(2.23100 + 0.150397i) q^{40} +(-1.70610 + 4.68746i) q^{41} +(-0.621740 - 0.887937i) q^{42} +(-4.76559 + 6.80597i) q^{43} +(0.0800380 + 0.219902i) q^{44} +(1.07917 - 1.95842i) q^{45} +(-3.26298 + 1.88388i) q^{46} +(-0.894484 + 0.0782572i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(5.04460 - 2.91250i) q^{49} +(4.77415 - 1.48577i) q^{50} +(-0.643013 - 1.76666i) q^{51} +(-1.26174 + 1.80196i) q^{52} +(4.13559 + 5.90623i) q^{53} +(0.342020 - 0.939693i) q^{54} +(0.344286 + 0.394060i) q^{55} -1.08397i q^{56} +(-3.84416 + 2.05486i) q^{57} +(-0.757914 - 0.757914i) q^{58} +(-0.887152 + 0.744409i) q^{59} +(2.00731 - 0.985254i) q^{60} +(1.01701 - 5.76777i) q^{61} +(3.98495 + 2.79029i) q^{62} +(-0.982411 - 0.458106i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.17803 + 4.77572i) q^{65} +(0.179266 + 0.150422i) q^{66} +(-0.946295 - 10.8162i) q^{67} +(0.486591 - 1.81598i) q^{68} +(-1.88388 + 3.26298i) q^{69} +(-0.874284 - 2.26066i) q^{70} +(-15.2795 + 2.69418i) q^{71} +(0.819152 - 0.573576i) q^{72} +(0.492751 + 1.05671i) 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} +(-0.191724 + 2.19141i) q^{78} +(13.7007 + 4.98666i) q^{79} +(2.20941 + 0.344270i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-2.10814 + 4.52093i) q^{82} +(-4.03855 + 1.08213i) q^{83} +(-0.541985 - 0.938746i) q^{84} +(-0.449890 - 4.17976i) q^{85} +(-5.34064 + 6.36472i) q^{86} +(-1.03533 - 0.277416i) q^{87} +(0.0605676 + 0.226041i) q^{88} +(-2.14016 + 0.778954i) q^{89} +(1.24575 - 1.85691i) q^{90} +(2.34828 + 0.414065i) q^{91} +(-3.41476 + 1.59233i) q^{92} +(4.84622 + 0.423989i) q^{93} -0.897901 q^{94} +(-9.44607 + 2.40245i) q^{95} +1.00000 q^{96} +(-0.224166 - 0.0196120i) q^{97} +(5.27925 - 2.46175i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	2.19391	−	0.432154i	0.981147	−	0.193265i
$5$	2.19391	−	0.432154i	0.981147	−	0.193265i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−0.280552	−	1.04704i	−0.106039	−	0.395742i	0.892422	−	0.451201i	$-0.149004\pi$
$7$	−0.280552	−	1.04704i	−0.106039	−	0.395742i	−0.998461	+	0.0554592i	$0.982338\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	2.22323	−	0.239298i	0.703046	−	0.0756725i
$11$	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	$0.822101\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	−0.929669	+	1.99368i	−0.257844	+	0.552948i	−0.992030	−	0.126000i	$-0.959786\pi$
$13$	−0.929669	+	1.99368i	−0.257844	+	0.552948i	0.734186	+	0.678948i	$0.237564\pi$
$14$	−0.188230	−	1.06750i	−0.0503065	−	0.285302i
$15$	1.80572	−	1.31885i	0.466235	−	0.340526i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.163857	−	1.87289i	0.0397411	−	0.454243i	−0.950088	−	0.311982i	$-0.899007\pi$
$17$	0.163857	−	1.87289i	0.0397411	−	0.454243i	0.989829	−	0.142261i	$-0.0454372\pi$
$18$	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
$22$	0.0988992	+	0.212090i	0.0210854	+	0.0452177i
$23$	−3.08637	+	2.16110i	−0.643554	+	0.450621i	−0.849247	−	0.527995i	$-0.822944\pi$
$23$	−3.08637	+	2.16110i	−0.643554	+	0.450621i	0.205694	+	0.978616i	$0.434055\pi$
$24$	0.984808	−	0.173648i	0.201023	−	0.0354458i
$25$	4.62649	−	1.89621i	0.925297	−	0.379243i
$26$	−1.09989	+	1.90507i	−0.215707	+	0.373615i
$27$	0.258819	−	0.965926i	0.0498097	−	0.185893i
$28$	−0.0944743	−	1.07985i	−0.0178540	−	0.204072i
$29$	−0.821087	−	0.688973i	−0.152472	−	0.127939i	0.563361	−	0.826211i	$-0.309508\pi$
$29$	−0.821087	−	0.688973i	−0.152472	−	0.127939i	−0.715833	+	0.698272i	$0.753953\pi$
$30$	1.91380	−	1.15645i	0.349410	−	0.211139i
$31$	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	$0.522755\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	0.191694	+	0.134226i	0.0333697	+	0.0233657i
$34$	0.326466	−	1.85148i	0.0559885	−	0.317527i
$35$	−1.06799	−	2.17586i	−0.180523	−	0.367788i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−3.32063	−	3.32063i	−0.545908	−	0.545908i	0.379347	−	0.925255i	$-0.376149\pi$
$37$	−3.32063	−	3.32063i	−0.545908	−	0.545908i	−0.925255	+	0.379347i	$0.876149\pi$
$38$	−4.35657	−	0.142520i	−0.706729	−	0.0231198i
$39$			2.19978i			0.352247i
$40$	2.23100	+	0.150397i	0.352753	+	0.0237799i
$41$	−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	$0.983752\pi$
$42$	−0.621740	−	0.887937i	−0.0959366	−	0.137012i
$43$	−4.76559	+	6.80597i	−0.726746	+	1.03790i	0.270425	+	0.962741i	$0.412836\pi$
$43$	−4.76559	+	6.80597i	−0.726746	+	1.03790i	−0.997171	+	0.0751599i	$0.976053\pi$
$44$	0.0800380	+	0.219902i	0.0120662	+	0.0331515i
$45$	1.07917	−	1.95842i	0.160873	−	0.291943i
$46$	−3.26298	+	1.88388i	−0.481100	+	0.277763i
$47$	−0.894484	+	0.0782572i	−0.130474	+	0.0114150i	−0.152206	−	0.988349i	$-0.548638\pi$
$47$	−0.894484	+	0.0782572i	−0.130474	+	0.0114150i	0.0217317	+	0.999764i	$0.493082\pi$
$48$	0.996195	−	0.0871557i	0.143788	−	0.0125798i
$49$	5.04460	−	2.91250i	0.720658	−	0.416072i
$50$	4.77415	−	1.48577i	0.675166	−	0.210120i
$51$	−0.643013	−	1.76666i	−0.0900398	−	0.247382i
$52$	−1.26174	+	1.80196i	−0.174973	+	0.249887i
$53$	4.13559	+	5.90623i	0.568066	+	0.811283i	0.995697	−	0.0926707i	$-0.0295404\pi$
$53$	4.13559	+	5.90623i	0.568066	+	0.811283i	−0.427630	+	0.903954i	$0.640652\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	0.344286	+	0.394060i	0.0464235	+	0.0531350i
$56$		−	1.08397i		−	0.144852i
$57$	−3.84416	+	2.05486i	−0.509171	+	0.272173i
$58$	−0.757914	−	0.757914i	−0.0995190	−	0.0995190i
$59$	−0.887152	+	0.744409i	−0.115497	+	0.0969138i	−0.698707	−	0.715408i	$-0.746241\pi$
$59$	−0.887152	+	0.744409i	−0.115497	+	0.0969138i	0.583210	+	0.812322i	$0.301797\pi$
$60$	2.00731	−	0.985254i	0.259142	−	0.127196i
$61$	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	$-0.0667811\pi$
$62$	3.98495	+	2.79029i	0.506090	+	0.354368i
$63$	−0.982411	−	0.458106i	−0.123772	−	0.0577159i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−1.17803	+	4.77572i	−0.146117	+	0.592355i
$66$	0.179266	+	0.150422i	0.0220661	+	0.0185157i
$67$	−0.946295	−	10.8162i	−0.115608	−	1.32141i	−0.803373	−	0.595476i	$-0.796964\pi$
$67$	−0.946295	−	10.8162i	−0.115608	−	1.32141i	0.687765	−	0.725933i	$-0.258592\pi$
$68$	0.486591	−	1.81598i	0.0590079	−	0.220220i
$69$	−1.88388	+	3.26298i	−0.226793	+	0.392817i
$70$	−0.874284	−	2.26066i	−0.104497	−	0.270201i
$71$	−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	$0.816790\pi$
$72$	0.819152	−	0.573576i	0.0965380	−	0.0675966i
$73$	0.492751	+	1.05671i	0.0576721	+	0.123678i	0.933032	−	0.359794i	$-0.117153\pi$
$73$	0.492751	+	1.05671i	0.0576721	+	0.123678i	−0.875360	+	0.483472i	$0.839375\pi$
$74$	−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
$78$	−0.191724	+	2.19141i	−0.0217085	+	0.248129i
$79$	13.7007	+	4.98666i	1.54145	+	0.561043i	0.966394	−	0.257067i	$-0.0827562\pi$
$79$	13.7007	+	4.98666i	1.54145	+	0.561043i	0.575061	+	0.818111i	$0.304978\pi$
$80$	2.20941	+	0.344270i	0.247019	+	0.0384905i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−2.10814	+	4.52093i	−0.232805	+	0.499253i
$83$	−4.03855	+	1.08213i	−0.443288	+	0.118779i	−0.473557	−	0.880763i	$-0.657030\pi$
$83$	−4.03855	+	1.08213i	−0.443288	+	0.118779i	0.0302690	+	0.999542i	$0.490364\pi$
$84$	−0.541985	−	0.938746i	−0.0591355	−	0.102426i
$85$	−0.449890	−	4.17976i	−0.0487974	−	0.453359i
$86$	−5.34064	+	6.36472i	−0.575896	+	0.686326i
$87$	−1.03533	−	0.277416i	−0.110999	−	0.0297421i
$88$	0.0605676	+	0.226041i	0.00645653	+	0.0240961i
$89$	−2.14016	+	0.778954i	−0.226856	+	0.0825690i	−0.452948	−	0.891537i	$-0.649628\pi$
$89$	−2.14016	+	0.778954i	−0.226856	+	0.0825690i	0.226091	+	0.974106i	$0.427405\pi$
$90$	1.24575	−	1.85691i	0.131314	−	0.195735i
$91$	2.34828	+	0.414065i	0.246166	+	0.0434058i
$92$	−3.41476	+	1.59233i	−0.356013	+	0.166012i
$93$	4.84622	+	0.423989i	0.502529	+	0.0439656i
$94$	−0.897901			−0.0926114
$95$	−9.44607	+	2.40245i	−0.969146	+	0.246486i
$96$	1.00000			0.102062
$97$	−0.224166	−	0.0196120i	−0.0227606	−	0.00199130i	0.0757697	−	0.997125i	$-0.475859\pi$
$97$	−0.224166	−	0.0196120i	−0.0227606	−	0.00199130i	−0.0985304	+	0.995134i	$0.531414\pi$
$98$	5.27925	−	2.46175i	0.533285	−	0.248675i
$99$	0.230460	+	0.0406363i	0.0231621	+	0.00408411i
$100$	4.88547	−	1.06403i	0.488547	−	0.106403i
$101$	−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	$0.396741\pi$
$102$	−0.486591	−	1.81598i	−0.0481797	−	0.179809i
$103$	−7.56180	−	2.02618i	−0.745087	−	0.199645i	−0.133749	−	0.991015i	$-0.542702\pi$
$103$	−7.56180	−	2.02618i	−0.745087	−	0.199645i	−0.611338	+	0.791370i	$0.709368\pi$
$104$	−1.41399	+	1.68513i	−0.138654	+	0.165241i
$105$	−1.88748	−	1.52065i	−0.184200	−	0.148400i
$106$	3.60509	+	6.24419i	0.350157	+	0.606490i
$107$	−4.73187	+	1.26790i	−0.457447	+	0.122573i	−0.480182	−	0.877169i	$-0.659429\pi$
$107$	−4.73187	+	1.26790i	−0.457447	+	0.122573i	0.0227348	+	0.999742i	$0.492763\pi$
$108$	0.422618	−	0.906308i	0.0406665	−	0.0872095i
$109$	0.796296	+	4.51602i	0.0762713	+	0.432556i	0.998901	+	0.0468692i	$0.0149244\pi$
$109$	0.796296	+	4.51602i	0.0762713	+	0.432556i	−0.922630	+	0.385687i	$0.873965\pi$
$110$	0.308631	+	0.422567i	0.0294268	+	0.0402901i
$111$	−4.41287	−	1.60615i	−0.418851	−	0.152449i
$112$	0.0944743	−	1.07985i	0.00892698	−	0.102036i
$113$	−9.48876	+	9.48876i	−0.892628	+	0.892628i	−0.994770	−	0.102142i	$-0.967430\pi$
$113$	−9.48876	+	9.48876i	−0.892628	+	0.892628i	0.102142	+	0.994770i	$0.467430\pi$
$114$	−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
$117$	0.929669	+	1.99368i	0.0859479	+	0.184316i
$118$	−0.948656	+	0.664256i	−0.0873308	+	0.0611497i
$119$	−2.00695	+	0.353880i	−0.183977	+	0.0324401i
$120$	2.08554	−	0.806557i	0.190383	−	0.0736283i
$121$	5.47262	−	9.47885i	0.497511	−	0.861714i
$122$	1.51584	−	5.65718i	0.137237	−	0.512177i
$123$	0.434758	+	4.96931i	0.0392008	+	0.448067i
$124$	3.72660	+	3.12699i	0.334658	+	0.280812i
$125$	9.33064	−	6.15948i	0.834558	−	0.550920i
$126$	−0.938746	−	0.541985i	−0.0836302	−	0.0482839i
$127$	−7.69933	−	3.59026i	−0.683205	−	0.318584i	0.0498464	−	0.998757i	$-0.484127\pi$
$127$	−7.69933	−	3.59026i	−0.683205	−	0.318584i	−0.733051	+	0.680173i	$0.761905\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	−1.44277	+	8.18233i	−0.127028	+	0.720414i
$130$	−1.58978	+	4.65487i	−0.139433	+	0.408259i
$131$	−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
$133$	1.46998	+	4.49044i	0.127464	+	0.389370i
$134$		−	10.8575i		−	0.937947i
$135$	0.150397	−	2.23100i	0.0129441	−	0.192014i
$136$	0.643013	−	1.76666i	0.0551379	−	0.151490i
$137$	−6.95943	−	9.93909i	−0.594584	−	0.849154i	0.403239	−	0.915094i	$-0.367884\pi$
$137$	−6.95943	−	9.93909i	−0.594584	−	0.849154i	−0.997824	+	0.0659404i	$0.978995\pi$
$138$	−2.16110	+	3.08637i	−0.183965	+	0.262730i
$139$	−1.44972	−	3.98308i	−0.122964	−	0.337840i	0.862903	−	0.505369i	$-0.168644\pi$
$139$	−1.44972	−	3.98308i	−0.122964	−	0.337840i	−0.985867	+	0.167529i	$0.946421\pi$
$140$	−0.673928	−	2.32826i	−0.0569573	−	0.196774i
$141$	−0.777605	+	0.448950i	−0.0654861	+	0.0378084i
$142$	−15.4561	+	1.35224i	−1.29705	+	0.113477i
$143$	−0.512824	+	0.0448663i	−0.0428845	+	0.00375191i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−2.09913	−	1.15671i	−0.174324	−	0.0960596i
$146$	0.398778	+	1.09563i	0.0330031	+	0.0906752i
$147$	3.34109	−	4.77157i	0.275568	−	0.393552i
$148$	−2.69356	−	3.84680i	−0.221409	−	0.316205i
$149$	−2.14254	+	5.88659i	−0.175524	+	0.482248i	−0.995992	−	0.0894444i	$-0.971491\pi$
$149$	−2.14254	+	5.88659i	−0.175524	+	0.482248i	0.820468	+	0.571693i	$0.193713\pi$
$150$	3.69893	−	3.36421i	0.302016	−	0.274687i
$151$			9.93789i			0.808734i	0.914597	+	0.404367i	$0.132508\pi$
$151$			9.93789i			0.808734i	−0.914597	+	0.404367i	$0.867492\pi$
$152$	−4.26563	−	0.896865i	−0.345989	−	0.0727454i
$153$	−1.32939	−	1.32939i	−0.107475	−	0.107475i
$154$	0.194319	−	0.163053i	0.0156587	−	0.0131392i
$155$	10.2941	+	3.51573i	0.826838	+	0.282391i
$156$	−0.381989	+	2.16637i	−0.0305836	+	0.173448i
$157$	1.71935	+	1.20390i	0.137219	+	0.0960820i	0.640171	−	0.768233i	$-0.278864\pi$
$157$	1.71935	+	1.20390i	0.137219	+	0.0960820i	−0.502951	+	0.864315i	$0.667753\pi$
$158$	13.2140	+	6.16179i	1.05125	+	0.490205i
$159$	6.24419	+	3.60509i	0.495197	+	0.285902i
$160$	2.17099	+	0.535522i	0.171632	+	0.0423367i
$161$	3.12864	+	2.62524i	0.246571	+	0.206898i
$162$	−0.0871557	−	0.996195i	−0.00684760	−	0.0782684i
$163$	5.41033	−	20.1916i	0.423770	−	1.58153i	−0.342826	−	0.939399i	$-0.611384\pi$
$163$	5.41033	−	20.1916i	0.423770	−	1.58153i	0.766595	−	0.642131i	$-0.221949\pi$
$164$	−2.49415	+	4.31999i	−0.194760	+	0.337334i
$165$	0.478566	+	0.211638i	0.0372563	+	0.0164760i
$166$	−4.11749	+	0.726025i	−0.319579	+	0.0563505i
$167$	6.75143	−	4.72740i	0.522442	−	0.365818i	−0.282410	−	0.959294i	$-0.591134\pi$
$167$	6.75143	−	4.72740i	0.522442	−	0.365818i	0.804851	+	0.593476i	$0.202245\pi$
$168$	−0.458106	−	0.982411i	−0.0353436	−	0.0757947i
$169$	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
$173$	−0.652007	+	7.45247i	−0.0495711	+	0.566601i	0.930277	+	0.366858i	$0.119566\pi$
$173$	−0.652007	+	7.45247i	−0.0495711	+	0.566601i	−0.979848	+	0.199743i	$0.935989\pi$
$174$	−1.00721	−	0.366595i	−0.0763565	−	0.0277915i
$175$	−3.28337	−	4.31211i	−0.248200	−	0.325965i
$176$	0.0406363	+	0.230460i	0.00306308	+	0.0173716i
$177$	−0.489432	+	1.04959i	−0.0367880	+	0.0788921i
$178$	−2.19991	+	0.589463i	−0.164890	+	0.0441821i
$179$	5.19978	+	9.00629i	0.388650	+	0.673162i	0.992268	−	0.124112i	$-0.0396082\pi$
$179$	5.19978	+	9.00629i	0.388650	+	0.673162i	−0.603618	+	0.797274i	$0.706275\pi$
$180$	1.40285	−	1.74127i	0.104562	−	0.129786i
$181$	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	$-0.174164\pi$
$182$	2.30325	+	0.617155i	0.170728	+	0.0457465i
$183$	−1.51584	−	5.65718i	−0.112054	−	0.418191i
$184$	−3.54054	+	1.28865i	−0.261012	+	0.0950007i
$185$	−8.72018	−	5.85014i	−0.641120	−	0.430111i
$186$	4.79082	+	0.844751i	0.351280	+	0.0619402i
$187$	0.398738	−	0.185935i	0.0291586	−	0.0135969i
$188$	−0.894484	−	0.0782572i	−0.0652370	−	0.00570749i
$189$	−1.08397			−0.0788473
$190$	−9.61951	+	1.57003i	−0.697873	+	0.113902i
$191$	1.28827			0.0932160			0.0466080	−	0.998913i	$-0.485159\pi$
$191$	1.28827			0.0932160			0.0466080	+	0.998913i	$0.485159\pi$
$192$	0.996195	+	0.0871557i	0.0718942	+	0.00628992i
$193$	8.60501	−	4.01258i	0.619402	−	0.288832i	−0.0874768	−	0.996167i	$-0.527880\pi$
$193$	8.60501	−	4.01258i	0.619402	−	0.288832i	0.706879	+	0.707335i	$0.250103\pi$
$194$	−0.221604	−	0.0390747i	−0.0159102	−	0.00280540i
$195$	0.950646	+	4.82613i	0.0680771	+	0.345606i
$196$	5.47372	−	1.99227i	0.390980	−	0.142305i
$197$	−3.59866	−	13.4304i	−0.256394	−	0.956874i	−0.967310	−	0.253597i	$-0.918386\pi$
$197$	−3.59866	−	13.4304i	−0.256394	−	0.956874i	0.710916	−	0.703277i	$-0.248281\pi$
$198$	0.226041	+	0.0605676i	0.0160641	+	0.00430435i
$199$	11.4373	−	13.6304i	0.810766	−	0.966233i	−0.189110	−	0.981956i	$-0.560560\pi$
$199$	11.4373	−	13.6304i	0.810766	−	0.966233i	0.999876	+	0.0157226i	$0.00500487\pi$
$200$	4.95962	−	0.634179i	0.350698	−	0.0448433i
$201$	−5.42876	−	9.40289i	−0.382915	−	0.663228i
$202$	−0.478905	+	0.128322i	−0.0336957	+	0.00902873i
$203$	−0.491022	+	1.05300i	−0.0344630	+	0.0739061i
$204$	−0.326466	−	1.85148i	−0.0228572	−	0.129630i
$205$	−1.71732	+	11.0212i	−0.119943	+	0.769751i
$206$	−7.35643	−	2.67752i	−0.512547	−	0.186552i
$207$	−0.328383	+	3.75343i	−0.0228242	+	0.260881i
$208$	−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	$0.511585\pi$
$212$	3.04715	+	6.53464i	0.209279	+	0.448801i
$213$	−12.7093	+	8.89914i	−0.870826	+	0.609759i
$214$	−4.82437	+	0.850666i	−0.329787	+	0.0581503i
$215$	−7.51406	+	16.9912i	−0.512454	+	1.15879i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	1.36481	−	5.09354i	0.0926494	−	0.345772i
$218$	0.399669	+	4.56823i	0.0270690	+	0.309400i
$219$	0.893168	+	0.749457i	0.0603547	+	0.0506436i
$220$	0.270628	+	0.447858i	0.0182457	+	0.0301946i
$221$	3.58162	+	2.06785i	0.240926	+	0.139098i
$222$	−4.25609	−	1.98465i	−0.285650	−	0.133201i
$223$	−12.1944	−	8.53863i	−0.816600	−	0.571789i	0.0889468	−	0.996036i	$-0.471650\pi$
$223$	−12.1944	−	8.53863i	−0.816600	−	0.571789i	−0.905546	+	0.424247i	$0.860539\pi$
$224$	0.188230	−	1.06750i	0.0125766	−	0.0713255i
$225$	1.52126	−	4.76296i	0.101418	−	0.317530i
$226$	−10.2797	+	8.62566i	−0.683793	+	0.573770i
$227$	−11.0794	−	11.0794i	−0.735365	−	0.735365i	0.236312	−	0.971677i	$-0.424061\pi$
$227$	−11.0794	−	11.0794i	−0.735365	−	0.735365i	−0.971677	+	0.236312i	$0.924061\pi$
$228$	−4.14258	+	1.35611i	−0.274349	+	0.0898105i
$229$		−	19.1457i		−	1.26518i	−0.774487	−	0.632590i	$-0.781992\pi$
$229$		−	19.1457i		−	1.26518i	0.774487	−	0.632590i	$-0.218008\pi$
$230$	−6.34456	+	5.54318i	−0.418348	+	0.365507i
$231$	0.0867588	−	0.238368i	0.00570831	−	0.0156835i
$232$	−0.614789	−	0.878010i	−0.0403629	−	0.0576442i
$233$	−5.22097	+	7.45632i	−0.342037	+	0.488480i	−0.952912	−	0.303248i	$-0.901929\pi$
$233$	−5.22097	+	7.45632i	−0.342037	+	0.488480i	0.610875	+	0.791727i	$0.290818\pi$
$234$	0.752371	+	2.06712i	0.0491840	+	0.135132i
$235$	−1.92860	+	0.558244i	−0.125808	+	0.0364158i
$236$	−1.00294	+	0.579047i	−0.0652858	+	0.0376928i
$237$	14.5245	−	1.27073i	0.943471	−	0.0825430i
$238$	−2.03016	+	0.177616i	−0.131596	+	0.0115131i
$239$	16.5640	−	9.56321i	1.07143	−	0.618593i	0.142861	−	0.989743i	$-0.454370\pi$
$239$	16.5640	−	9.56321i	1.07143	−	0.618593i	0.928573	+	0.371150i	$0.121036\pi$
$240$	2.14790	−	0.621721i	0.138646	−	0.0401319i
$241$	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	$0.692609\pi$
$242$	6.27793	−	8.96581i	0.403561	−	0.576344i
$243$	−0.573576	−	0.819152i	−0.0367949	−	0.0525486i
$244$	2.00313	−	5.50354i	0.128237	−	0.352328i
$245$	9.80876	−	8.56982i	0.626659	−	0.547506i
$246$			4.98829i			0.318042i
$247$	3.57236	−	8.89833i	0.227304	−	0.566187i
$248$	3.43988	+	3.43988i	0.218433	+	0.218433i
$249$	−3.20284	+	2.68750i	−0.202972	+	0.170314i
$250$	9.83197	−	5.32282i	0.621828	−	0.336645i
$251$	−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	$0.0690529\pi$
$252$	−0.887937	−	0.621740i	−0.0559348	−	0.0391659i
$253$	−0.799105	−	0.372629i	−0.0502393	−	0.0234270i
$254$	−7.35712	−	4.24764i	−0.461627	−	0.266520i
$255$	−2.17418	−	3.59802i	−0.136153	−	0.225317i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.253377	−	2.89611i	−0.0158052	−	0.180655i	−0.999994	−	0.00353054i	$-0.998876\pi$
$257$	−0.253377	−	2.89611i	−0.0158052	−	0.180655i	0.984189	−	0.177124i	$-0.0566794\pi$
$258$	−2.15041	+	8.02545i	−0.133879	+	0.499643i
$259$	−2.54520	+	4.40842i	−0.158151	+	0.273926i
$260$	−1.98943	+	4.49860i	−0.123379	+	0.278991i
$261$	−1.05557	+	0.186125i	−0.0653381	+	0.0115209i
$262$	−10.6341	+	7.44605i	−0.656974	+	0.460018i
$263$	−3.93872	−	8.44661i	−0.242872	−	0.520840i	0.746651	−	0.665216i	$-0.231660\pi$
$263$	−3.93872	−	8.44661i	−0.242872	−	0.520840i	−0.989523	+	0.144376i	$0.953883\pi$
$264$	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
$268$	0.946295	−	10.8162i	0.0578042	−	0.660705i
$269$	21.9302	+	7.98193i	1.33711	+	0.486667i	0.908900	−	0.417014i	$-0.136923\pi$
$269$	21.9302	+	7.98193i	1.33711	+	0.486667i	0.428206	+	0.903681i	$0.359146\pi$
$270$	0.344270	−	2.20941i	0.0209516	−	0.134460i
$271$	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	$0.739512\pi$
$272$	0.794541	−	1.70390i	0.0481761	−	0.103314i
$273$	2.30325	−	0.617155i	0.139399	−	0.0373519i
$274$	−6.06670	−	10.5078i	−0.366503	−	0.634801i
$275$	0.925627	+	0.715747i	0.0558174	+	0.0431612i
$276$	−2.42187	+	2.88628i	−0.145780	+	0.173733i
$277$	12.3413	+	3.30684i	0.741516	+	0.198689i	0.609752	−	0.792592i	$-0.291269\pi$
$277$	12.3413	+	3.30684i	0.741516	+	0.198689i	0.131764	+	0.991281i	$0.457936\pi$
$278$	−1.09706	−	4.09427i	−0.0657971	−	0.245558i
$279$	4.57135	−	1.66384i	0.273680	−	0.0996112i
$280$	−0.468442	−	2.37813i	−0.0279948	−	0.142121i
$281$	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	$0.327968\pi$
$282$	−0.813775	+	0.379469i	−0.0484596	+	0.0225971i
$283$	−18.7582	−	1.64113i	−1.11506	−	0.0975551i	−0.485302	−	0.874347i	$-0.661290\pi$
$283$	−18.7582	−	1.64113i	−1.11506	−	0.0975551i	−0.629758	+	0.776792i	$0.716846\pi$
$284$	−15.5152			−0.920657
$285$	−7.54573	+	6.16944i	−0.446970	+	0.365446i
$286$	−0.514783			−0.0304398
$287$	5.38659	+	0.471265i	0.317960	+	0.0278179i
$288$	0.906308	−	0.422618i	0.0534047	−	0.0249030i
$289$	13.2609	+	2.33825i	0.780051	+	0.137544i
$290$	−1.99033	−	1.33526i	−0.116876	−	0.0784092i
$291$	−0.211452	+	0.0769622i	−0.0123955	+	0.00451160i
$292$	0.301770	+	1.12622i	0.0176597	+	0.0659070i
$293$	22.8267	+	6.11640i	1.33355	+	0.357324i	0.854038	−	0.520211i	$-0.174147\pi$
$293$	22.8267	+	6.11640i	1.33355	+	0.357324i	0.479513	+	0.877535i	$0.340814\pi$
$294$	3.74424	−	4.46221i	0.218369	−	0.260242i
$295$	−1.62463	+	2.01655i	−0.0945898	+	0.117408i
$296$	−2.34804	−	4.06692i	−0.136477	−	0.236385i
$297$	0.226041	−	0.0605676i	0.0131163	−	0.00351449i
$298$	−2.64744	+	5.67746i	−0.153362	+	0.328886i
$299$	−1.43924	−	8.16236i	−0.0832336	−	0.472041i
$300$	3.97807	−	3.02902i	0.229674	−	0.174881i
$301$	8.46309	+	3.08031i	0.487804	+	0.177546i
$302$	−0.866144	+	9.90007i	−0.0498410	+	0.569685i
$303$	−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
$307$	−1.35399	−	2.90363i	−0.0772761	−	0.165719i	0.863874	−	0.503708i	$-0.168031\pi$
$307$	−1.35399	−	2.90363i	−0.0772761	−	0.165719i	−0.941150	+	0.337989i	$0.890253\pi$
$308$	0.207791	−	0.145497i	0.0118400	−	0.00829045i
$309$	−7.70962	+	1.35941i	−0.438585	+	0.0773344i
$310$	9.94847	+	4.39954i	0.565035	+	0.249877i
$311$	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	$0.0171121\pi$
$312$	−0.569346	+	2.12483i	−0.0322329	+	0.120295i
$313$	−2.54937	−	29.1394i	−0.144099	−	1.64706i	−0.632589	−	0.774488i	$-0.718008\pi$
$313$	−2.54937	−	29.1394i	−0.144099	−	1.64706i	0.488490	−	0.872569i	$-0.337548\pi$
$314$	1.60788	+	1.34917i	0.0907381	+	0.0761383i
$315$	−2.35329	−	0.580490i	−0.132593	−	0.0327069i
$316$	12.6267	+	7.29001i	0.710306	+	0.410095i
$317$	12.3135	+	5.74190i	0.691597	+	0.322497i	0.736446	−	0.676497i	$-0.236503\pi$
$317$	12.3135	+	5.74190i	0.691597	+	0.322497i	−0.0448484	+	0.998994i	$0.514280\pi$
$318$	5.90623	+	4.13559i	0.331205	+	0.231912i
$319$	0.0435562	−	0.247019i	0.00243868	−	0.0138304i
$320$	2.11606	+	0.722699i	0.118291	+	0.0404001i
$321$	−3.75269	+	3.14888i	−0.209455	+	0.175753i
$322$	2.88793	+	2.88793i	0.160938	+	0.160938i
$323$	−0.267944	+	8.19054i	−0.0149088	+	0.455734i
$324$		−	1.00000i		−	0.0555556i
$325$	−0.520654	+	10.9866i	−0.0288807	+	0.609427i
$326$	7.14956	−	19.6432i	0.395977	−	1.08794i
$327$	2.63024	+	3.75637i	0.145453	+	0.207728i
$328$	−2.86117	+	4.08617i	−0.157981	+	0.225621i
$329$	0.332888	+	0.914601i	0.0183527	+	0.0504236i
$330$	0.458299	+	0.252542i	0.0252286	+	0.0139020i
$331$	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	$0.297423\pi$
$332$	−4.16510	+	0.364399i	−0.228590	+	0.0199990i
$333$	−4.67821	+	0.409290i	−0.256364	+	0.0224289i
$334$	7.13776	−	4.12099i	0.390561	−	0.225490i
$335$	−6.75035	−	23.3208i	−0.368811	−	1.27415i
$336$	−0.370740	−	1.01860i	−0.0202255	−	0.0555692i
$337$	13.8190	−	19.7356i	0.752770	−	1.07507i	−0.241732	−	0.970343i	$-0.577715\pi$
$337$	13.8190	−	19.7356i	0.752770	−	1.07507i	0.994501	−	0.104723i	$-0.0333957\pi$
$338$	4.68093	+	6.68506i	0.254609	+	0.363619i
$339$	−4.58962	+	12.6099i	−0.249274	+	0.684874i
$340$	0.282753	−	4.19439i	0.0153345	−	0.227473i
$341$			1.13842i			0.0616490i
$342$	−2.90952	+	3.24571i	−0.157329	+	0.175508i
$343$	−9.83015	−	9.83015i	−0.530778	−	0.530778i
$344$	−6.36472	+	5.34064i	−0.343163	+	0.287948i
$345$	−2.72296	+	7.97282i	−0.146599	+	0.429242i
$346$	−1.29905	+	7.36729i	−0.0698374	+	0.396068i
$347$	−15.4142	−	10.7931i	−0.827478	−	0.579406i	0.0812983	−	0.996690i	$-0.474093\pi$
$347$	−15.4142	−	10.7931i	−0.827478	−	0.579406i	−0.908776	+	0.417283i	$0.862982\pi$
$348$	−0.971428	−	0.452984i	−0.0520740	−	0.0242825i
$349$	25.4677	+	14.7038i	1.36326	+	0.787077i	0.990056	−	0.140674i	$-0.0449268\pi$
$349$	25.4677	+	14.7038i	1.36326	+	0.787077i	0.373201	+	0.927750i	$0.378260\pi$
$350$	−2.89506	−	4.58186i	−0.154747	−	0.244911i
$351$	1.68513	+	1.41399i	0.0899457	+	0.0754734i
$352$	0.0203958	+	0.233125i	0.00108710	+	0.0124256i
$353$	4.03918	−	15.0744i	0.214984	−	0.802332i	−0.771188	−	0.636607i	$-0.780337\pi$
$353$	4.03918	−	15.0744i	0.214984	−	0.802332i	0.986172	−	0.165724i	$-0.0529961\pi$
$354$	−0.579047	+	1.00294i	−0.0307760	+	0.0533056i
$355$	−32.3575	+	12.5139i	−1.71736	+	0.664168i
$356$	−2.24291	+	0.395486i	−0.118874	+	0.0209607i
$357$	−1.66936	+	1.16890i	−0.0883519	+	0.0618647i
$358$	4.39505	+	9.42521i	0.232285	+	0.498138i
$359$	9.92110	+	11.8235i	0.523616	+	0.624021i	0.961432	−	0.275044i	$-0.0886923\pi$
$359$	9.92110	+	11.8235i	0.523616	+	0.624021i	−0.437816	+	0.899065i	$0.644248\pi$
$360$	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
$363$	0.953940	−	10.9036i	0.0500689	−	0.572290i
$364$	2.24070	+	0.815548i	0.117445	+	0.0427463i
$365$	1.53771	+	2.10538i	0.0804875	+	0.110201i
$366$	−1.01701	−	5.76777i	−0.0531601	−	0.301486i
$367$	−9.79558	+	21.0067i	−0.511325	+	1.09654i	0.465998	+	0.884786i	$0.345696\pi$
$367$	−9.79558	+	21.0067i	−0.511325	+	1.09654i	−0.977323	+	0.211754i	$0.932082\pi$
$368$	−3.63938	+	0.975170i	−0.189716	+	0.0508342i
$369$	2.49415	+	4.31999i	0.129840	+	0.224889i
$370$	−8.17712	−	6.58789i	−0.425108	−	0.342488i
$371$	5.02378	−	5.98711i	0.260822	−	0.310835i
$372$	4.69897	+	1.25908i	0.243630	+	0.0652805i
$373$	−2.18391	−	8.15046i	−0.113079	−	0.422015i	0.886057	−	0.463575i	$-0.153434\pi$
$373$	−2.18391	−	8.15046i	−0.113079	−	0.422015i	−0.999136	+	0.0415606i	$0.986767\pi$
$374$	0.413426	−	0.150475i	0.0213778	−	0.00778087i
$375$	5.85332	−	9.52568i	0.302264	−	0.491904i
$376$	−0.884260	−	0.155919i	−0.0456022	−	0.00804090i
$377$	2.13693	−	0.996468i	0.110058	−	0.0513207i
$378$	−1.07985	−	0.0944743i	−0.0555413	−	0.00485923i
$379$	−17.1950			−0.883249			−0.441625	−	0.897200i	$-0.645598\pi$
$379$	−17.1950			−0.883249			−0.441625	+	0.897200i	$0.645598\pi$
$380$	−9.71974	+	0.725662i	−0.498612	+	0.0372257i
$381$	−8.49527			−0.435226
$382$	1.28337	+	0.112280i	0.0656628	+	0.00574475i
$383$	33.7069	−	15.7178i	1.72234	−	0.803142i	0.729463	−	0.684020i	$-0.239770\pi$
$383$	33.7069	−	15.7178i	1.72234	−	0.803142i	0.992880	−	0.119121i	$-0.0380078\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	0.316004	−	0.471034i	0.0161051	−	0.0240061i
$386$	8.92198	−	3.24734i	0.454117	−	0.165285i
$387$	2.15041	+	8.02545i	0.109312	+	0.407957i
$388$	−0.217355	−	0.0582401i	−0.0110345	−	0.00295669i
$389$	−6.24938	+	7.44773i	−0.316856	+	0.377615i	−0.900840	−	0.434150i	$-0.857049\pi$
$389$	−6.24938	+	7.44773i	−0.316856	+	0.377615i	0.583984	+	0.811765i	$0.301493\pi$
$390$	0.526403	+	4.89062i	0.0266555	+	0.247646i
$391$	3.54179	+	6.13455i	0.179116	+	0.310238i
$392$	5.62652	−	1.50762i	0.284182	−	0.0761464i
$393$	−5.48634	+	11.7655i	−0.276749	+	0.593491i
$394$	−2.41443	−	13.6929i	−0.121637	−	0.689839i
$395$	32.2132	+	5.01946i	1.62082	+	0.252557i
$396$	0.219902	+	0.0800380i	0.0110505	+	0.00402206i
$397$	−2.06024	+	23.5486i	−0.103400	+	1.18187i	0.750297	+	0.661101i	$0.229911\pi$
$397$	−2.06024	+	23.5486i	−0.103400	+	1.18187i	−0.853697	+	0.520770i	$0.825645\pi$
$398$	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	$0.885898\pi$
$402$	−4.58859	−	9.84025i	−0.228858	−	0.490787i
$403$	−8.76604	+	6.13805i	−0.436667	+	0.305758i
$404$	−0.488267	+	0.0860947i	−0.0242922	+	0.00428337i
$405$	−0.806557	−	2.08554i	−0.0400781	−	0.103631i
$406$	−0.580928	+	1.00620i	−0.0288310	+	0.0499367i
$407$	0.284430	−	1.06151i	0.0140987	−	0.0526170i
$408$	−0.163857	−	1.87289i	−0.00811211	−	0.0927219i
$409$	−20.6985	−	17.3681i	−1.02347	−	0.858797i	−0.0334141	−	0.999442i	$-0.510638\pi$
$409$	−20.6985	−	17.3681i	−1.02347	−	0.858797i	−0.990060	+	0.140645i	$0.955082\pi$
$410$	−2.67134	+	10.8295i	−0.131928	+	0.534833i
$411$	−10.5078	−	6.06670i	−0.518313	−	0.299248i
$412$	−7.09508	−	3.30849i	−0.349550	−	0.162998i
$413$	1.02832	+	0.720034i	0.0506001	+	0.0354306i
$414$	−0.654266	+	3.71053i	−0.0321554	+	0.182362i
$415$	−8.39257	+	4.11936i	−0.411975	+	0.202211i
$416$	−1.68513	+	1.41399i	−0.0826204	+	0.0693268i
$417$	−2.99722	−	2.99722i	−0.146774	−	0.146774i
$418$	−0.480868	−	0.899592i	−0.0235200	−	0.0440005i
$419$		−	31.8456i		−	1.55576i	−0.628412	−	0.777881i	$-0.716295\pi$
$419$		−	31.8456i		−	1.55576i	0.628412	−	0.777881i	$-0.283705\pi$
$420$	−1.59475	−	1.82530i	−0.0778159	−	0.0890657i
$421$	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	$0.0487104\pi$
$422$	12.3667	+	17.6614i	0.602000	+	0.859745i
$423$	−0.515015	+	0.735517i	−0.0250409	+	0.0357621i
$424$	2.46602	+	6.77535i	0.119761	+	0.329040i
$425$	−2.79332	−	8.97561i	−0.135496	−	0.435381i
$426$	−13.4365	+	7.75759i	−0.651003	+	0.375856i
$427$	−6.32438	+	0.553312i	−0.306058	+	0.0267766i
$428$	−4.88015	+	0.426958i	−0.235891	+	0.0206378i
$429$	−0.445815	+	0.257392i	−0.0215242	+	0.0124270i
$430$	−8.96634	+	16.2716i	−0.432395	+	0.784687i
$431$	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	$0.800276\pi$
$432$	0.573576	−	0.819152i	0.0275962	−	0.0394115i
$433$	7.38483	+	10.5466i	0.354893	+	0.506839i	0.956413	−	0.292019i	$-0.0943269\pi$
$433$	7.38483	+	10.5466i	0.354893	+	0.506839i	−0.601520	+	0.798858i	$0.705438\pi$
$434$	1.80355	−	4.95521i	0.0865731	−	0.237858i
$435$	−2.39131	−	0.161204i	−0.114654	−	0.00772912i
$436$			4.58568i			0.219614i
$437$	12.9194	−	10.1397i	0.618020	−	0.485048i
$438$	0.824450	+	0.824450i	0.0393937	+	0.0393937i
$439$	−12.6627	+	10.6253i	−0.604357	+	0.507116i	−0.892843	−	0.450368i	$-0.851293\pi$
$439$	−12.6627	+	10.6253i	−0.604357	+	0.507116i	0.288486	+	0.957484i	$0.406848\pi$
$440$	0.230565	+	0.469740i	0.0109917	+	0.0223940i
$441$	1.01150	−	5.73651i	0.0481668	−	0.273167i
$442$	3.38776	+	2.37214i	0.161139	+	0.112831i
$443$	17.1145	+	7.98062i	0.813134	+	0.379171i	0.784276	−	0.620413i	$-0.213035\pi$
$443$	17.1145	+	7.98062i	0.813134	+	0.379171i	0.0288589	+	0.999583i	$0.490813\pi$
$444$	−4.06692	−	2.34804i	−0.193008	−	0.111433i
$445$	−4.35869	+	2.63383i	−0.206622	+	0.124856i
$446$	−11.4038	−	9.56896i	−0.539987	−	0.453103i
$447$	0.545977	+	6.24054i	0.0258238	+	0.295168i
$448$	0.280552	−	1.04704i	0.0132549	−	0.0494678i
$449$	−7.77854	+	13.4728i	−0.367092	+	0.635822i	−0.989110	−	0.147181i	$-0.952980\pi$
$449$	−7.77854	+	13.4728i	−0.367092	+	0.635822i	0.622018	+	0.783003i	$0.286313\pi$
$450$	1.93059	−	4.61225i	0.0910091	−	0.217423i
$451$	−1.14960	+	0.202706i	−0.0541326	+	0.00954504i
$452$	−10.9923	+	7.69690i	−0.517035	+	0.362032i
$453$	4.19993	+	9.00678i	0.197330	+	0.423176i
$454$	−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	−0.993982	−	0.109542i	$-0.965062\pi$
$457$	−18.9072	+	18.9072i	−0.884440	+	0.884440i	0.109542	+	0.993982i	$0.465062\pi$
$458$	1.66865	−	19.0728i	0.0779711	−	0.891213i
$459$	−1.76666	−	0.643013i	−0.0824608	−	0.0300133i
$460$	−6.80354	+	4.96912i	−0.317217	+	0.231687i
$461$	−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	$-0.424591\pi$
$462$	0.107204	−	0.229899i	0.00498757	−	0.0106959i
$463$	−5.06992	+	1.35848i	−0.235619	+	0.0631339i	−0.374696	−	0.927148i	$-0.622253\pi$
$463$	−5.06992	+	1.35848i	−0.235619	+	0.0631339i	0.139077	+	0.990282i	$0.455586\pi$
$464$	−0.535926	−	0.928251i	−0.0248797	−	0.0430930i
$465$	10.8154	−	1.16412i	0.501552	−	0.0539847i
$466$	−5.85097	+	6.97291i	−0.271041	+	0.323014i
$467$	−24.8171	−	6.64972i	−1.14840	−	0.307712i	−0.366075	−	0.930585i	$-0.619299\pi$
$467$	−24.8171	−	6.64972i	−1.14840	−	0.307712i	−0.782323	+	0.622873i	$0.785965\pi$
$468$	0.569346	+	2.12483i	0.0263180	+	0.0982202i
$469$	−11.0595	+	4.02531i	−0.510678	+	0.185872i
$470$	−1.96991	+	0.388031i	−0.0908654	+	0.0178986i
$471$	2.06705	+	0.364477i	0.0952448	+	0.0167942i
$472$	−1.04959	+	0.489432i	−0.0483113	+	0.0225279i
$473$	−1.93693	−	0.169459i	−0.0890602	−	0.00779176i
$474$	14.5800			0.669683
$475$	−19.6856	+	9.35292i	−0.903237	+	0.429142i
$476$	−2.03791			−0.0934076
$477$	7.18274	+	0.628408i	0.328875	+	0.0287728i
$478$	17.3344	−	8.08317i	0.792858	−	0.369716i
$479$	6.91347	+	1.21903i	0.315885	+	0.0556990i	0.329343	−	0.944210i	$-0.393173\pi$
$479$	6.91347	+	1.21903i	0.315885	+	0.0556990i	−0.0134581	+	0.999909i	$0.504284\pi$
$480$	2.19391	−	0.432154i	0.100138	−	0.0197250i
$481$	9.70736	−	3.53319i	0.442617	−	0.161100i
$482$	4.64708	+	17.3432i	0.211669	+	0.789959i
$483$	3.94499	+	1.05706i	0.179503	+	0.0480977i
$484$	7.03546	−	8.38454i	0.319794	−	0.381115i
$485$	−0.500276	+	0.0538473i	−0.0227164	+	0.00244508i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−8.62980	+	2.31235i	−0.391054	+	0.104782i	−0.448988	−	0.893538i	$-0.648215\pi$
$487$	−8.62980	+	2.31235i	−0.391054	+	0.104782i	0.0579342	+	0.998320i	$0.481549\pi$
$488$	2.47517	−	5.30802i	0.112046	−	0.240283i
$489$	−3.62992	−	20.5863i	−0.164151	−	0.930946i
$490$	10.5183	−	7.68232i	0.475170	−	0.347052i
$491$	−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	$0.735993\pi$
$492$	−0.434758	+	4.96931i	−0.0196004	+	0.224034i
$493$	−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
$497$	7.10760	+	15.2423i	0.318819	+	0.683710i
$498$	−3.42488	+	2.39813i	−0.153473	+	0.107463i
$499$	−6.70806	+	1.18281i	−0.300294	+	0.0529500i	−0.321765	−	0.946820i	$-0.604276\pi$
$499$	−6.70806	+	1.18281i	−0.300294	+	0.0529500i	0.0214710	+	0.999769i	$0.493165\pi$
$500$	10.2585	−	4.44565i	0.458773	−	0.198816i
$501$	4.12099	−	7.13776i	0.184112	−	0.318892i
$502$	−0.347642	+	1.29742i	−0.0155160	+	0.0579065i
$503$	1.17693	+	13.4523i	0.0524765	+	0.599810i	0.976218	+	0.216792i	$0.0695595\pi$
$503$	1.17693	+	13.4523i	0.0524765	+	0.599810i	−0.923741	+	0.383017i	$0.874885\pi$
$504$	−0.830370	−	0.696763i	−0.0369876	−	0.0310363i
$505$	−0.948859	+	0.573369i	−0.0422237	+	0.0255146i
$506$	−0.763588	−	0.440858i	−0.0339456	−	0.0195985i
$507$	7.39633	+	3.44897i	0.328483	+	0.153174i
$508$	−6.95892	−	4.87269i	−0.308752	−	0.216191i
$509$	−1.88162	+	10.6712i	−0.0834013	+	0.472992i	0.914289	+	0.405063i	$0.132750\pi$
$509$	−1.88162	+	10.6712i	−0.0834013	+	0.472992i	−0.997690	+	0.0679293i	$0.978361\pi$
$510$	−1.85232	−	3.77382i	−0.0820222	−	0.167108i
$511$	0.968168	−	0.812390i	0.0428292	−	0.0359380i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.896865	+	4.26563i	−0.0395976	+	0.188332i
$514$		−	2.90718i		−	0.128230i
$515$	−17.4655	−	1.17739i	−0.769624	−	0.0518821i
$516$	−2.84169	+	7.80749i	−0.125099	+	0.343706i
$517$	−0.120521	−	0.172122i	−0.00530052	−	0.00756993i
$518$	−2.91974	+	4.16982i	−0.128286	+	0.183211i
$519$	2.55863	+	7.02978i	0.112311	+	0.308573i
$520$	−2.37394	+	4.30809i	−0.104104	+	0.188922i
$521$	−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	$0.424078\pi$
$522$	−1.06777	+	0.0934181i	−0.0467352	+	0.00408880i
$523$	11.8325	−	1.03521i	0.517401	−	0.0452667i	0.174535	−	0.984651i	$-0.444158\pi$
$523$	11.8325	−	1.03521i	0.517401	−	0.0452667i	0.342866	+	0.939384i	$0.388602\pi$
$524$	−11.2426	+	6.49089i	−0.491133	+	0.283556i
$525$	−4.79812	−	2.52048i	−0.209407	−	0.110003i
$526$	−3.18756	−	8.75775i	−0.138984	−	0.381856i
$527$	5.24588	−	7.49189i	0.228514	−	0.326352i
$528$	0.134226	+	0.191694i	0.00584142	+	0.00834242i
$529$	−3.01112	+	8.27299i	−0.130918	+	0.359695i
$530$	10.6077	+	12.1413i	0.460769	+	0.527382i
$531$			1.15809i			0.0502570i
$532$	0.667894	+	4.67748i	0.0289569	+	0.202794i
$533$	−7.75920	−	7.75920i	−0.336088	−	0.336088i
$534$	−1.74467	+	1.46396i	−0.0754994	+	0.0633516i
$535$	−9.83337	+	4.82656i	−0.425134	+	0.208670i
$536$	1.88539	−	10.6926i	0.0814364	−	0.461849i
$537$	8.51883	+	5.96495i	0.367615	+	0.257406i
$538$	21.1510	+	9.86290i	0.911886	+	0.425220i
$539$	1.18051	+	0.681570i	0.0508484	+	0.0293573i
$540$	0.535522	−	2.17099i	0.0230452	−	0.0934247i
$541$	−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	$0.912656\pi$
$542$	1.72243	+	19.6875i	0.0739849	+	0.845651i
$543$	6.59840	−	24.6256i	0.283164	−	1.05678i
$544$	0.940022	−	1.62817i	0.0403031	−	0.0698071i
$545$	3.69862	+	9.56362i	0.158431	+	0.409660i
$546$	2.34828	−	0.414065i	0.100497	−	0.0177203i
$547$	−21.9216	+	15.3497i	−0.937301	+	0.656305i	−0.939082	−	0.343693i	$-0.888322\pi$
$547$	−21.9216	+	15.3497i	−0.937301	+	0.656305i	0.00178108	+	0.999998i	$0.499433\pi$
$548$	−5.12779	−	10.9966i	−0.219048	−	0.469751i
$549$	−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
$553$	1.37744	−	15.7442i	0.0585746	−	0.669511i
$554$	12.0061	+	4.36987i	0.510091	+	0.185658i
$555$	−10.3755	−	1.61672i	−0.440417	−	0.0686258i
$556$	−0.736043	−	4.17431i	−0.0312152	−	0.177030i
$557$	−13.4861	+	28.9209i	−0.571422	+	1.22542i	0.382107	+	0.924118i	$0.375199\pi$
$557$	−13.4861	+	28.9209i	−0.571422	+	1.22542i	−0.953529	+	0.301301i	$0.902579\pi$
$558$	4.69897	−	1.25908i	0.198923	−	0.0533013i
$559$	−9.13852	−	15.8284i	−0.386518	−	0.669469i
$560$	−0.259392	−	2.40991i	−0.0109613	−	0.101837i
$561$	0.282800	−	0.337028i	0.0119398	−	0.0142293i
$562$	21.2310	+	5.68883i	0.895576	+	0.239969i
$563$	−2.42726	−	9.05866i	−0.102297	−	0.381777i	0.895728	−	0.444603i	$-0.146655\pi$
$563$	−2.42726	−	9.05866i	−0.102297	−	0.381777i	−0.998024	+	0.0628262i	$0.979989\pi$
$564$	−0.843751	+	0.307100i	−0.0355283	+	0.0129313i
$565$	−16.7169	+	24.9181i	−0.703285	+	1.04831i
$566$	−18.5438	−	3.26977i	−0.779454	−	0.137439i
$567$	−0.982411	+	0.458106i	−0.0412574	+	0.0192386i
$568$	−15.4561	−	1.35224i	−0.648525	−	0.0567386i
$569$	−42.6967			−1.78994			−0.894969	−	0.446129i	$-0.852802\pi$
$569$	−42.6967			−1.78994			−0.894969	+	0.446129i	$0.852802\pi$
$570$	−8.05471	+	5.48831i	−0.337375	+	0.229880i
$571$	−5.49505			−0.229961			−0.114980	−	0.993368i	$-0.536681\pi$
$571$	−5.49505			−0.229961			−0.114980	+	0.993368i	$0.536681\pi$
$572$	−0.512824	−	0.0448663i	−0.0214423	−	0.00187596i
$573$	1.16757	−	0.544446i	0.0487759	−	0.0227446i
$574$	5.32501	+	0.938944i	0.222262	+	0.0391908i
$575$	−10.1812	+	15.8507i	−0.424583	+	0.661021i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	8.05737	+	30.0705i	0.335433	+	1.25185i	0.903399	+	0.428800i	$0.141064\pi$
$577$	8.05737	+	30.0705i	0.335433	+	1.25185i	−0.567967	+	0.823052i	$0.692270\pi$
$578$	13.0066	+	3.48511i	0.541004	+	0.144961i
$579$	6.10300	−	7.27327i	0.253632	−	0.302267i
$580$	−1.86638	−	1.50365i	−0.0774973	−	0.0624356i
$581$	2.26605	+	3.92491i	0.0940115	+	0.162833i
$582$	−0.217355	+	0.0582401i	−0.00900965	+	0.00241413i
$583$	−0.713080	+	1.52921i	−0.0295328	+	0.0633332i
$584$	0.202465	+	1.14823i	0.00837805	+	0.0475143i
$585$	2.90119	+	3.97220i	0.119949	+	0.164230i
$586$	22.2068	+	8.08260i	0.917353	+	0.333889i
$587$	−0.100445	+	1.14810i	−0.00414582	+	0.0473870i	−0.997986	−	0.0634376i	$-0.979794\pi$
$587$	−0.100445	+	1.14810i	−0.00414582	+	0.0473870i	0.993840	+	0.110825i	$0.0353492\pi$
$588$	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
$592$	−1.98465	−	4.25609i	−0.0815685	−	0.174924i
$593$	−7.71971	+	5.40540i	−0.317011	+	0.221973i	−0.721241	−	0.692684i	$-0.756428\pi$
$593$	−7.71971	+	5.40540i	−0.317011	+	0.221973i	0.404231	+	0.914657i	$0.367539\pi$
$594$	0.230460	−	0.0406363i	0.00945589	−	0.00166733i
$595$	−4.25014	+	1.64369i	−0.174239	+	0.0673849i
$596$	−3.13219	+	5.42511i	−0.128300	+	0.222221i
$597$	4.60522	−	17.1869i	0.188479	−	0.703414i
$598$	−0.722371	−	8.25674i	−0.0295399	−	0.337643i
$599$	33.9043	+	28.4491i	1.38529	+	1.16240i	0.967207	+	0.253991i	$0.0817432\pi$
$599$	33.9043	+	28.4491i	1.38529	+	1.16240i	0.418086	+	0.908408i	$0.362701\pi$
$600$	4.22693	−	2.67079i	0.172563	−	0.109034i
$601$	−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	$0.887908\pi$
$602$	8.16242	+	3.80620i	0.332675	+	0.155129i
$603$	−8.89396	−	6.22762i	−0.362190	−	0.253608i
$604$	−1.72570	+	9.78691i	−0.0702176	+	0.398224i
$605$	7.91011	−	23.1608i	0.321592	−	0.941619i
$606$	−0.379804	+	0.318694i	−0.0154285	+	0.0129460i
$607$	14.5898	+	14.5898i	0.592183	+	0.592183i	0.938221	−	0.346038i	$-0.112473\pi$
$607$	14.5898	+	14.5898i	0.592183	+	0.592183i	−0.346038	+	0.938221i	$0.612473\pi$
$608$	−4.04509	−	1.62396i	−0.164050	−	0.0658602i
$609$			1.16186i			0.0470808i
$610$	0.880838	−	13.0664i	0.0356641	−	0.529044i
$611$	0.675554	−	1.85607i	0.0273300	−	0.0750886i
$612$	−1.07835	−	1.54004i	−0.0435897	−	0.0622525i
$613$	−8.86919	+	12.6665i	−0.358223	+	0.511596i	−0.957300	−	0.289096i	$-0.906645\pi$
$613$	−8.86919	+	12.6665i	−0.358223	+	0.511596i	0.599077	+	0.800691i	$0.295534\pi$
$614$	−1.09577	−	3.01059i	−0.0442215	−	0.121498i
$615$	3.10133	+	10.7143i	0.125058	+	0.432044i
$616$	0.219681	−	0.126833i	0.00885120	−	0.00511024i
$617$	−29.0996	+	2.54589i	−1.17151	+	0.102494i	−0.656251	−	0.754543i	$-0.727859\pi$
$617$	−29.0996	+	2.54589i	−1.17151	+	0.102494i	−0.515256	+	0.857036i	$0.672303\pi$
$618$	−7.79876	+	0.682303i	−0.313712	+	0.0274463i
$619$	−3.59996	+	2.07844i	−0.144694	+	0.0835394i	−0.570599	−	0.821229i	$-0.693289\pi$
$619$	−3.59996	+	2.07844i	−0.144694	+	0.0835394i	0.425905	+	0.904768i	$0.359956\pi$
$620$	9.52716	+	5.24987i	0.382620	+	0.210840i
$621$	1.28865	+	3.54054i	0.0517118	+	0.142077i
$622$	9.15911	−	13.0806i	0.367247	−	0.524483i
$623$	1.41602	+	2.02229i	0.0567316	+	0.0810212i
$624$	−0.752371	+	2.06712i	−0.0301189	+	0.0827511i
$625$	17.8087	−	17.5456i	0.712350	−	0.701825i
$626$		−	29.2507i		−	1.16909i
$627$	−0.866240	−	0.538635i	−0.0345943	−	0.0215110i
$628$	1.48418	+	1.48418i	0.0592251	+	0.0592251i
$629$	−6.76328	+	5.67506i	−0.269669	+	0.226280i
$630$	−2.29375	−	0.783385i	−0.0913850	−	0.0312108i
$631$	−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	$0.913090\pi$
$632$	11.9433	+	8.36276i	0.475077	+	0.332653i
$633$	19.5406	+	9.11192i	0.776668	+	0.362166i
$634$	11.7662	+	6.79324i	0.467297	+	0.269794i
$635$	−18.4432	−	4.54941i	−0.731895	−	0.180538i
$636$	5.52331	+	4.63461i	0.219014	+	0.183774i
$637$	1.11679	+	12.7650i	0.0442489	+	0.505768i
$638$	0.0649196	−	0.242283i	0.00257019	−	0.00959208i
$639$	−7.75759	+	13.4365i	−0.306886	+	0.531541i
$640$	2.04502	+	0.904376i	0.0808365	+	0.0357486i
$641$	−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	$0.460648\pi$
$642$	−4.01286	+	2.80983i	−0.158375	+	0.110895i
$643$	−15.1964	−	32.5887i	−0.599286	−	1.28517i	−0.938765	−	0.344559i	$-0.888028\pi$
$643$	−15.1964	−	32.5887i	−0.599286	−	1.28517i	0.339478	−	0.940614i	$-0.389749\pi$
$644$	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	0.0868843	−	0.996218i	$-0.472309\pi$
$647$	27.5500	−	27.5500i	1.08310	−	1.08310i	0.996218	−	0.0868843i	$-0.0276910\pi$
$648$	0.0871557	−	0.996195i	0.00342380	−	0.0391342i
$649$	−0.254668	−	0.0926916i	−0.00999659	−	0.00363846i
$650$	−1.47622	+	10.8994i	−0.0579020	+	0.427510i
$651$	−0.915686	−	5.19311i	−0.0358886	−	0.203534i
$652$	8.83437	−	18.9454i	0.345981	−	0.741958i
$653$	−22.6558	+	6.07061i	−0.886590	+	0.237561i	−0.673248	−	0.739416i	$-0.735102\pi$
$653$	−22.6558	+	6.07061i	−0.886590	+	0.237561i	−0.213342	+	0.976978i	$0.568435\pi$
$654$	2.29284	+	3.97132i	0.0896572	+	0.155291i
$655$	−18.2115	+	22.6048i	−0.711582	+	0.883241i
$656$	−3.20641	+	3.82125i	−0.125189	+	0.149195i
$657$	1.12622	+	0.301770i	0.0439380	+	0.0117732i
$658$	0.251908	+	0.940134i	0.00982040	+	0.0366502i
$659$	−37.7578	+	13.7427i	−1.47083	+	0.535340i	−0.948327	−	0.317296i	$-0.897225\pi$
$659$	−37.7578	+	13.7427i	−1.47083	+	0.535340i	−0.522507	+	0.852635i	$0.675003\pi$
$660$	0.434545	+	0.291525i	0.0169146	+	0.0113476i
$661$	−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	$0.775294\pi$
$662$	3.71246	−	1.73115i	0.144289	−	0.0672830i
$663$	4.11996	+	0.360449i	0.160006	+	0.0139987i
$664$	−4.18101			−0.162255
$665$	5.16557	+	9.21636i	0.200312	+	0.357395i
$666$	−4.69608			−0.181969
$667$	4.02312	+	0.351978i	0.155776	+	0.0136286i
$668$	7.46977	−	3.48321i	0.289014	−	0.134769i
$669$	−14.6605	−	2.58504i	−0.566807	−	0.0999434i
$670$	−4.69212	−	23.8204i	−0.181272	−	0.920263i
$671$	1.28791	−	0.468762i	0.0497193	−	0.0180964i
$672$	−0.280552	−	1.04704i	−0.0108225	−	0.0403903i
$673$	42.7196	+	11.4467i	1.64672	+	0.441238i	0.958692	−	0.284446i	$-0.0918095\pi$
$673$	42.7196	+	11.4467i	1.64672	+	0.441238i	0.688029	+	0.725683i	$0.258476\pi$
$674$	15.4865	−	18.4561i	0.596518	−	0.710902i
$675$	−0.634179	−	4.95962i	−0.0244096	−	0.190896i
$676$	4.08047	+	7.06759i	0.156941	+	0.271830i
$677$	4.55594	−	1.22076i	0.175099	−	0.0469176i	−0.170204	−	0.985409i	$-0.554443\pi$
$677$	4.55594	−	1.22076i	0.175099	−	0.0469176i	0.345303	+	0.938491i	$0.387776\pi$
$678$	−5.67117	+	12.1619i	−0.217800	+	0.467074i
$679$	0.0423559	+	0.240212i	0.00162547	+	0.00921849i
$680$	0.647242	−	4.15378i	0.0248206	−	0.159290i
$681$	−14.7237	−	5.35899i	−0.564213	−	0.205357i
$682$	−0.0992199	+	1.13409i	−0.00379933	+	0.0434265i
$683$	−17.5698	+	17.5698i	−0.672288	+	0.672288i	−0.958243	−	0.285955i	$-0.907689\pi$
$683$	−17.5698	+	17.5698i	−0.672288	+	0.672288i	0.285955	+	0.958243i	$0.407689\pi$
$684$	−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
$687$	−8.09130	−	17.3519i	−0.308702	−	0.662015i
$688$	−6.80597	+	4.76559i	−0.259475	+	0.181686i
$689$	−15.6199	+	2.75420i	−0.595070	+	0.104927i
$690$	−3.40748	+	7.70516i	−0.129720	+	0.293330i
$691$	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	$0.0430242\pi$
$692$	−1.93621	+	7.22603i	−0.0736036	+	0.274692i
$693$	−0.0221084	−	0.252701i	−0.000839830	−	0.00959930i
$694$	−14.4149	−	12.0955i	−0.547181	−	0.459139i
$695$	−4.90186	−	8.11201i	−0.185938	−	0.307706i
$696$	−0.928251	−	0.535926i	−0.0351853	−	0.0203142i
$697$	8.49954	+	3.96340i	0.321943	+	0.150125i
$698$	24.0893	+	16.8675i	0.911794	+	0.638445i
$699$	−1.58063	+	8.96420i	−0.0597849	+	0.339057i
$700$	−2.48470	−	4.81675i	−0.0939130	−	0.182056i
$701$	−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
$703$	15.2421	+	13.6633i	0.574867	+	0.515323i
$704$			0.234015i			0.00881978i
$705$	−1.51198	+	1.32100i	−0.0569445	+	0.0497518i
$706$	5.33764	−	14.6650i	0.200885	−	0.551926i
$707$	0.308258	+	0.440239i	0.0115933	+	0.0165569i
$708$	−0.664256	+	0.948656i	−0.0249643	+	0.0356527i
$709$	1.76613	+	4.85240i	0.0663283	+	0.182236i	0.968429	−	0.249291i	$-0.0801974\pi$
$709$	1.76613	+	4.85240i	0.0663283	+	0.182236i	−0.902100	+	0.431526i	$0.857975\pi$
$710$	−33.3250	+	9.64612i	−1.25067	+	0.362012i
$711$	12.6267	−	7.29001i	0.473537	−	0.273397i
$712$	−2.26884	+	0.198498i	−0.0850285	+	0.00743903i
$713$	−18.2594	+	1.59749i	−0.683821	+	0.0598266i
$714$	−1.76488	+	1.01896i	−0.0660492	+	0.0381335i
$715$	−1.10570	+	0.320052i	−0.0413509	+	0.0119693i
$716$	3.55686	+	9.77240i	0.132926	+	0.365212i
$717$	10.9705	−	15.6674i	0.409700	−	0.585112i
$718$	8.85286	+	12.6432i	0.330386	+	0.471840i
$719$	12.7619	−	35.0631i	0.475940	−	1.30763i	−0.436972	−	0.899475i	$-0.643949\pi$
$719$	12.7619	−	35.0631i	0.475940	−	1.30763i	0.912911	−	0.408158i	$-0.133829\pi$
$720$	1.68391	−	1.47121i	0.0627554	−	0.0548288i
$721$			8.48593i			0.316032i
$722$	18.9955	−	0.415347i	0.706938	−	0.0154576i
$723$	12.6961	+	12.6961i	0.472172	+	0.472172i
$724$	19.5297	−	16.3874i	0.725817	−	0.609033i
$725$	−5.10519	−	1.63057i	−0.189602	−	0.0605578i
$726$	1.90062	−	10.7790i	0.0705386	−	0.400045i
$727$	39.0918	+	27.3724i	1.44984	+	1.01519i	0.992012	+	0.126142i	$0.0402596\pi$
$727$	39.0918	+	27.3724i	1.44984	+	1.01519i	0.457823	+	0.889043i	$0.348629\pi$
$728$	2.16109	+	1.00773i	0.0800954	+	0.0373491i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	1.34836	+	2.23139i	0.0499052	+	0.0825873i
$731$	11.9660	+	10.0406i	0.442577	+	0.371366i
$732$	−0.510449	−	5.83446i	−0.0188667	−	0.215648i
$733$	11.3357	−	42.3053i	0.418693	−	1.56258i	−0.358629	−	0.933480i	$-0.616756\pi$
$733$	11.3357	−	42.3053i	0.418693	−	1.56258i	0.777322	−	0.629103i	$-0.216578\pi$
$734$	−11.5892	+	20.0730i	−0.427764	+	0.740908i
$735$	5.26799	−	11.9123i	0.194313	−	0.439390i
$736$	−3.71053	+	0.654266i	−0.136772	+	0.0241166i
$737$	2.08132	−	1.45736i	0.0766665	−	0.0536825i
$738$	2.10814	+	4.52093i	0.0776018	+	0.166418i
$739$	−10.7828	−	12.8504i	−0.396652	−	0.472711i	0.530344	−	0.847782i	$-0.322063\pi$
$739$	−10.7828	−	12.8504i	−0.396652	−	0.472711i	−0.926996	+	0.375071i	$0.877618\pi$
$740$	−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
$743$	−0.735878	+	8.41112i	−0.0269967	+	0.308574i	0.970676	+	0.240391i	$0.0772757\pi$
$743$	−0.735878	+	8.41112i	−0.0269967	+	0.308574i	−0.997673	+	0.0681829i	$0.978280\pi$
$744$	4.57135	+	1.66384i	0.167594	+	0.0609992i
$745$	−2.15664	+	13.8406i	−0.0790130	+	0.507079i
$746$	−1.46524	−	8.30979i	−0.0536462	−	0.304243i
$747$	−1.76697	+	3.78928i	−0.0646501	+	0.138643i
$748$	0.424968	−	0.113870i	0.0155384	−	0.00416349i
$749$	2.65507	+	4.59872i	0.0970143	+	0.168034i
$750$	6.66127	−	8.97928i	0.243235	−	0.327877i
$751$	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	$-0.156634\pi$
$752$	−0.867306	−	0.232394i	−0.0316274	−	0.00847453i
$753$	0.347642	+	1.29742i	0.0126688	+	0.0472805i
$754$	2.21565	−	0.806430i	0.0806892	−	0.0293685i
$755$	4.29470	+	21.8028i	0.156300	+	0.793486i
$756$	−1.06750	−	0.188230i	−0.0388247	−	0.00684584i
$757$	−5.88061	+	2.74217i	−0.213734	+	0.0996659i	−0.526537	−	0.850152i	$-0.676510\pi$
$757$	−5.88061	+	2.74217i	−0.213734	+	0.0996659i	0.312803	+	0.949818i	$0.398732\pi$
$758$	−17.1296	−	1.49865i	−0.622175	−	0.0544332i
$759$	−0.881715			−0.0320042
$760$	−9.74600	−	0.124231i	−0.353525	−	0.00450633i
$761$	−39.3024			−1.42471			−0.712355	−	0.701820i	$-0.752371\pi$
$761$	−39.3024			−1.42471			−0.712355	+	0.701820i	$0.752371\pi$
$762$	−8.46294	−	0.740412i	−0.306580	−	0.0268223i
$763$	4.50503	−	2.10073i	0.163093	−	0.0760515i
$764$	1.26870	+	0.223706i	0.0458999	+	0.00809339i
$765$	−3.49107	−	2.34207i	−0.126220	−	0.0846775i
$766$	34.9485	−	12.7202i	1.26274	−	0.459601i
$767$	−0.659357	−	2.46075i	−0.0238080	−	0.0888527i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	30.4116	−	36.2432i	1.09667	−	1.30696i	0.148602	−	0.988897i	$-0.452523\pi$
$769$	30.4116	−	36.2432i	1.09667	−	1.30696i	0.948069	−	0.318064i	$-0.103033\pi$
$770$	0.355855	−	0.441700i	0.0128241	−	0.0159178i
$771$	−1.45359	−	2.51769i	−0.0523497	−	0.0906723i
$772$	9.17106	−	2.45738i	0.330074	−	0.0884429i
$773$	−17.6223	+	37.7911i	−0.633829	+	1.35925i	0.282672	+	0.959217i	$0.408779\pi$
$773$	−17.6223	+	37.7911i	−0.633829	+	1.35925i	−0.916501	+	0.400033i	$0.868999\pi$
$774$	1.44277	+	8.18233i	0.0518591	+	0.294108i
$775$	24.1036	+	3.26459i	0.865826	+	0.117268i
$776$	−0.211452	−	0.0769622i	−0.00759068	−	0.00276278i
$777$	−0.443658	+	5.07104i	−0.0159162	+	0.181922i
$778$	−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
$782$	2.99365	+	6.41989i	0.107053	+	0.229575i
$783$	−0.878010	+	0.614789i	−0.0313775	+	0.0219708i
$784$	5.73651	−	1.01150i	0.204875	−	0.0361251i
$785$	4.29238	+	1.89823i	0.153202	+	0.0677508i
$786$	−6.49089	+	11.2426i	−0.231523	+	0.401009i
$787$	10.1884	−	38.0235i	0.363176	−	1.35539i	−0.506701	−	0.862122i	$-0.669135\pi$
$787$	10.1884	−	38.0235i	0.363176	−	1.35539i	0.869877	−	0.493269i	$-0.164198\pi$
$788$	−1.21183	−	13.8512i	−0.0431695	−	0.493430i
$789$	−7.13938	−	5.99065i	−0.254169	−	0.213273i
$790$	31.6532	+	7.80793i	1.12617	+	0.277794i
$791$	12.5972	+	7.27298i	0.447904	+	0.258597i
$792$	0.212090	+	0.0988992i	0.00753629	+	0.00351423i
$793$	10.5536	+	7.38972i	0.374770	+	0.262417i
$794$	−4.10479	+	23.2794i	−0.145674	+	0.826156i
$795$	15.2572	+	5.21079i	0.541116	+	0.184808i
$796$	13.6304	−	11.4373i	0.483117	−	0.405383i
$797$	−5.69075	−	5.69075i	−0.201577	−	0.201577i	0.599099	−	0.800675i	$-0.295526\pi$
$797$	−5.69075	−	5.69075i	−0.201577	−	0.201577i	−0.800675	+	0.599099i	$0.795526\pi$
$798$	2.91715	+	3.71687i	0.103266	+	0.131576i
$799$			1.68809i			0.0597205i
$800$	4.99439	+	0.236684i	0.176579	+	0.00836804i
$801$	−0.778954	+	2.14016i	−0.0275230	+	0.0756188i
$802$	−7.65360	−	10.9305i	−0.270258	−	0.385968i
$803$	−0.156500	+	0.223505i	−0.00552277	+	0.00788734i
$804$	−3.71349	−	10.2027i	−0.130965	−	0.359823i
$805$	7.99847	+	4.40749i	0.281909	+	0.155344i
$806$	−9.26765	+	5.35068i	−0.326439	+	0.188470i
$807$	23.2488	−	2.03401i	0.818396	−	0.0716004i
$808$	−0.493913	+	0.0432118i	−0.0173758	+	0.00152018i
$809$	−33.4535	+	19.3144i	−1.17616	+	0.679058i	−0.955124	−	0.296206i	$-0.904278\pi$
$809$	−33.4535	+	19.3144i	−1.17616	+	0.679058i	−0.221040	+	0.975265i	$0.570945\pi$
$810$	−0.621721	−	2.14790i	−0.0218451	−	0.0754694i
$811$	−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	$0.922197\pi$
$812$	−0.666414	+	0.951737i	−0.0233865	+	0.0333994i
$813$	11.3354	+	16.1887i	0.397551	+	0.567761i
$814$	0.375864	−	1.03268i	0.0131740	−	0.0361954i
$815$	3.14389	−	46.6367i	0.110126	−	1.63361i
$816$		−	1.88004i		−	0.0658147i
$817$	19.1239	−	30.7553i	0.669060	−	1.07599i
$818$	−19.1060	−	19.1060i	−0.668025	−	0.668025i
$819$	1.82663	−	1.53273i	0.0638278	−	0.0535579i
$820$	−3.60503	+	10.5555i	−0.125893	+	0.368615i
$821$	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	$0.0340214\pi$
$822$	−9.93909	−	6.95943i	−0.346666	−	0.242738i
$823$	−3.81915	−	1.78090i	−0.133127	−	0.0620782i	0.354913	−	0.934899i	$-0.384510\pi$
$823$	−3.81915	−	1.78090i	−0.133127	−	0.0620782i	−0.488040	+	0.872821i	$0.662288\pi$
$824$	−6.77973	−	3.91428i	−0.236183	−	0.136360i
$825$	1.14139	+	0.257500i	0.0397381	+	0.00896500i
$826$	0.961647	+	0.806918i	0.0334600	+	0.0280763i
$827$	2.34106	+	26.7585i	0.0814068	+	0.930484i	0.921586	+	0.388175i	$0.126894\pi$
$827$	2.34106	+	26.7585i	0.0814068	+	0.930484i	−0.840179	+	0.542309i	$0.817550\pi$
$828$	−0.975170	+	3.63938i	−0.0338895	+	0.126477i
$829$	−7.34894	+	12.7287i	−0.255239	+	0.442087i	−0.964960	−	0.262395i	$-0.915488\pi$
$829$	−7.34894	+	12.7287i	−0.255239	+	0.442087i	0.709721	+	0.704483i	$0.248821\pi$
$830$	−8.71966	+	3.37223i	−0.302664	+	0.117052i
$831$	12.5825	−	2.21864i	0.436483	−	0.0769638i
$832$	−1.80196	+	1.26174i	−0.0624717	+	0.0437431i
$833$	−4.62821	−	9.92522i	−0.160358	−	0.343889i
$834$	−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
$838$	2.77553	−	31.7245i	0.0958791	−	1.09590i
$839$	50.6062	+	18.4191i	1.74712	+	0.635899i	0.999598	−	0.0283386i	$-0.00902168\pi$
$839$	50.6062	+	18.4191i	1.74712	+	0.635899i	0.747521	+	0.664238i	$0.231244\pi$
$840$	−1.42960	−	1.95735i	−0.0493258	−	0.0675350i
$841$	−4.83630	−	27.4280i	−0.166769	−	0.945793i
$842$	3.37811	−	7.24437i	0.116417	−	0.249658i
$843$	21.2310	−	5.68883i	0.731235	−	0.195934i
$844$	10.7803	+	18.6721i	0.371074	+	0.642719i
$845$	14.2104	+	11.4486i	0.488852	+	0.393843i
$846$	−0.577160	+	0.687832i	−0.0198432	+	0.0236481i
$847$	−11.4601	−	3.07071i	−0.393772	−	0.105511i
$848$	1.86613	+	6.96449i	0.0640832	+	0.239162i
$849$	−17.6943	+	6.44019i	−0.607266	+	0.221027i
$850$	−2.00042	−	9.18491i	−0.0686137	−	0.315040i
$851$	17.4249	+	3.07248i	0.597318	+	0.105323i
$852$	−14.0615	+	6.55700i	−0.481740	+	0.224639i
$853$	33.5001	+	2.93088i	1.14702	+	0.100351i	0.644775	−	0.764372i	$-0.276951\pi$
$853$	33.5001	+	2.93088i	1.14702	+	0.100351i	0.502247	+	0.864724i	$0.332507\pi$
$854$	−6.34854			−0.217243
$855$	−4.23143	+	8.78038i	−0.144712	+	0.300283i
$856$	−4.89879			−0.167437
$857$	16.8878	+	1.47749i	0.576875	+	0.0504700i	0.371860	−	0.928289i	$-0.378720\pi$
$857$	16.8878	+	1.47749i	0.576875	+	0.0504700i	0.205015	+	0.978759i	$0.434276\pi$
$858$	−0.466552	+	0.217557i	−0.0159278	+	0.00742727i
$859$	−1.30286	−	0.229730i	−0.0444531	−	0.00783827i	0.151377	−	0.988476i	$-0.451629\pi$
$859$	−1.30286	−	0.229730i	−0.0444531	−	0.00783827i	−0.195830	+	0.980638i	$0.562740\pi$
$860$	−10.3504	+	15.4282i	−0.352945	+	0.526098i
$861$	5.08107	−	1.84936i	0.173162	−	0.0630260i
$862$	2.95315	+	11.0213i	0.100585	+	0.375387i
$863$	40.5556	+	10.8668i	1.38053	+	0.369912i	0.871313	−	0.490727i	$-0.163269\pi$
$863$	40.5556	+	10.8668i	1.38053	+	0.369912i	0.509216	+	0.860639i	$0.329935\pi$
$864$	0.642788	−	0.766044i	0.0218681	−	0.0260614i
$865$	1.79017	+	16.6318i	0.0608676	+	0.565499i
$866$	6.43753	+	11.1501i	0.218756	+	0.378897i
$867$	13.0066	−	3.48511i	0.441728	−	0.118361i
$868$	2.22856	−	4.77916i	0.0756423	−	0.162215i
$869$	0.592479	+	3.36012i	0.0200985	+	0.113984i
$870$	−2.36816	−	0.369006i	−0.0802881	−	0.0125105i
$871$	22.4438	+	8.16888i	0.760479	+	0.276792i
$872$	−0.399669	+	4.56823i	−0.0135345	+	0.154700i
$873$	−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
$877$	2.46170	+	5.27914i	0.0831258	+	0.178264i	0.943477	−	0.331438i	$-0.107534\pi$
$877$	2.46170	+	5.27914i	0.0831258	+	0.178264i	−0.860351	+	0.509701i	$0.829756\pi$
$878$	−13.5406	+	9.48120i	−0.456972	+	0.319975i
$879$	23.2729	−	4.10364i	0.784976	−	0.138412i
$880$	0.188747	+	0.488048i	0.00636265	+	0.0164521i
$881$	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	$-0.0808094\pi$
$882$	1.50762	−	5.62652i	0.0507643	−	0.189455i
$883$	2.95926	+	33.8245i	0.0995870	+	1.13828i	0.867400	+	0.497611i	$0.165789\pi$
$883$	2.95926	+	33.8245i	0.0995870	+	1.13828i	−0.767813	+	0.640674i	$0.778655\pi$
$884$	3.16812	+	2.65837i	0.106556	+	0.0894107i
$885$	−0.620185	+	2.51422i	−0.0208473	+	0.0845145i
$886$	16.3538	+	9.44188i	0.549417	+	0.317206i
$887$	35.1900	+	16.4094i	1.18156	+	0.550973i	0.911272	−	0.411806i	$-0.135102\pi$
$887$	35.1900	+	16.4094i	1.18156	+	0.550973i	0.270293	+	0.962778i	$0.412880\pi$
$888$	−3.84680	−	2.69356i	−0.129090	−	0.0903899i
$889$	−1.59906	+	9.06873i	−0.0536308	+	0.304155i
$890$	−4.57166	+	2.24393i	−0.153242	+	0.0752166i
$891$	0.179266	−	0.150422i	0.00600564	−	0.00503933i
$892$	−10.5265	−	10.5265i	−0.352452	−	0.352452i
$893$	3.87456	−	0.553246i	0.129657	−	0.0185137i
$894$			6.26438i			0.209512i
$895$	15.3000	+	17.5119i	0.511421	+	0.585358i
$896$	0.370740	−	1.01860i	0.0123855	−	0.0340290i
$897$	−4.75396	−	6.78936i	−0.158730	−	0.226690i
$898$	−8.92317	+	12.7436i	−0.297770	+	0.425260i
$899$	−1.78339	−	4.89981i	−0.0594793	−	0.163418i
$900$	2.32523	−	4.42643i	0.0775077	−	0.147548i
$901$	11.7394	−	6.77772i	0.391095	−	0.225799i
$902$	−1.16289	+	0.101740i	−0.0387201	+	0.00338757i
$903$	8.97196	−	0.784945i	0.298568	−	0.0261213i
$904$	−11.6213	+	6.70957i	−0.386519	+	0.223157i
$905$	27.5126	−	49.9284i	0.914551	−	1.65968i
$906$	3.39896	+	9.33856i	0.112923	+	0.310253i
$907$	−14.5545	+	20.7860i	−0.483274	+	0.690186i	−0.984551	−	0.175101i	$-0.943975\pi$
$907$	−14.5545	+	20.7860i	−0.483274	+	0.690186i	0.501277	+	0.865287i	$0.332864\pi$
$908$	−8.98716	−	12.8350i	−0.298249	−	0.425944i
$909$	−0.169573	+	0.465899i	−0.00562439	+	0.0154529i
$910$	5.31984	+	0.358622i	0.176351	+	0.0118882i
$911$			49.5498i			1.64166i	0.571175	+	0.820829i	$0.306488\pi$
$911$			49.5498i			1.64166i	−0.571175	+	0.820829i	$0.693512\pi$
$912$	−4.31513	+	0.616155i	−0.142888	+	0.0204029i
$913$	−0.691848	−	0.691848i	−0.0228968	−	0.0228968i
$914$	−20.4831	+	17.1874i	−0.677520	+	0.568507i
$915$	−5.77039	−	11.7563i	−0.190763	−	0.388651i
$916$	3.32461	−	18.8548i	0.109848	−	0.622980i
$917$	11.5270	+	8.07130i	0.380655	+	0.266538i
$918$	−1.70390	−	0.794541i	−0.0562370	−	0.0262238i
$919$	48.9189	+	28.2433i	1.61369	+	0.931662i	0.988506	+	0.151180i	$0.0483073\pi$
$919$	48.9189	+	28.2433i	1.61369	+	0.931662i	0.625179	+	0.780481i	$0.285026\pi$
$920$	−7.21074	+	4.35725i	−0.237731	+	0.143654i
$921$	−2.45426	−	2.05937i	−0.0808705	−	0.0678584i
$922$	−3.43029	−	39.2084i	−0.112971	−	1.29126i
$923$	8.83351	−	32.9671i	0.290758	−	1.08513i
$924$	0.126833	−	0.219681i	0.00417250	−	0.00722698i
$925$	−21.6595	−	9.06621i	−0.712158	−	0.298095i
$926$	−5.16902	+	0.911438i	−0.169865	+	0.0299517i
$927$	−6.41278	+	4.49027i	−0.210623	+	0.147480i
$928$	−0.452984	−	0.971428i	−0.0148699	−	0.0318887i
$929$	−4.35904	−	5.19490i	−0.143015	−	0.170439i	0.689782	−	0.724017i	$-0.257706\pi$
$929$	−4.35904	−	5.19490i	−0.143015	−	0.170439i	−0.832797	+	0.553578i	$0.813262\pi$
$930$	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
$933$	1.39174	−	15.9077i	0.0455635	−	0.520793i
$934$	−24.1431	−	8.78737i	−0.789986	−	0.287531i
$935$	0.794444	−	0.580241i	0.0259811	−	0.0189759i
$936$	0.381989	+	2.16637i	0.0124857	+	0.0708099i
$937$	12.1275	−	26.0075i	0.396189	−	0.849629i	−0.602484	−	0.798131i	$-0.705822\pi$
$937$	12.1275	−	26.0075i	0.396189	−	0.849629i	0.998673	−	0.0514987i	$-0.0163998\pi$
$938$	−11.3682	+	3.04610i	−0.371185	+	0.0994587i
$939$	−14.6254	−	25.3319i	−0.477281	−	0.826674i
$940$	−1.99624	+	0.214865i	−0.0651101	+	0.00700814i
$941$	−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	$0.247362\pi$
$942$	2.02742	+	0.543246i	0.0660570	+	0.0176999i
$943$	−4.86443	−	18.1543i	−0.158408	−	0.591185i
$944$	−1.08825	+	0.396092i	−0.0354196	+	0.0128917i
$945$	−2.37813	+	0.468442i	−0.0773607	+	0.0152384i
$946$	−1.91479	−	0.337629i	−0.0622552	−	0.0109773i
$947$	24.0832	−	11.2302i	0.782600	−	0.364932i	0.0101015	−	0.999949i	$-0.496785\pi$
$947$	24.0832	−	11.2302i	0.782600	−	0.364932i	0.772498	+	0.635017i	$0.219007\pi$
$948$	14.5245	+	1.27073i	0.471735	+	0.0412715i
$949$	−2.56483			−0.0832581
$950$	−20.4259	+	7.60162i	−0.662702	+	0.246629i
$951$	13.5865			0.440572
$952$	−2.03016	−	0.177616i	−0.0657978	−	0.00575656i
$953$	−48.2494	+	22.4991i	−1.56295	+	0.728817i	−0.995515	−	0.0946001i	$-0.969843\pi$
$953$	−48.2494	+	22.4991i	−1.56295	+	0.728817i	−0.567437	+	0.823417i	$0.692065\pi$
$954$	7.10064	+	1.25203i	0.229892	+	0.0405361i
$955$	2.82635	−	0.556731i	0.0914585	−	0.0180154i
$956$	17.9730	−	6.54162i	0.581287	−	0.211571i
$957$	−0.0649196	−	0.242283i	−0.00209855	−	0.00783190i
$958$	6.78092	+	1.81694i	0.219082	+	0.0587027i
$959$	−8.45410	+	10.0752i	−0.272997	+	0.325345i
$960$	2.22323	−	0.239298i	0.0717543	−	0.00772330i
$961$	−3.66720	−	6.35178i	−0.118297	−	0.204896i
$962$	9.97836	−	2.67369i	0.321715	−	0.0862033i
$963$	−2.07032	+	4.43981i	−0.0667151	+	0.143071i
$964$	3.11784	+	17.6822i	0.100419	+	0.569505i
$965$	17.1446	−	12.5219i	0.551903	−	0.403095i
$966$	3.83785	+	1.39686i	0.123481	+	0.0449433i
$967$	2.99243	−	34.2036i	0.0962300	−	1.09991i	−0.782518	−	0.622628i	$-0.786065\pi$
$967$	2.99243	−	34.2036i	0.0962300	−	1.09991i	0.878748	−	0.477286i	$-0.158379\pi$
$968$	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	$0.567797\pi$
$972$	−0.422618	−	0.906308i	−0.0135555	−	0.0290698i
$973$	−3.76370	+	2.63537i	−0.120659	+	0.0844861i
$974$	−8.79850	+	1.55141i	−0.281922	+	0.0497105i
$975$	4.17126	+	10.1773i	0.133587	+	0.325934i
$976$	2.92837	−	5.07209i	0.0937349	−	0.162354i
$977$	−14.7699	+	55.1221i	−0.472531	+	1.76351i	0.158094	+	0.987424i	$0.449465\pi$
$977$	−14.7699	+	55.1221i	−0.472531	+	1.76351i	−0.630626	+	0.776087i	$0.717202\pi$
$978$	−1.82190	−	20.8244i	−0.0582578	−	0.665889i
$979$	−0.408281	−	0.342588i	−0.0130487	−	0.0109492i
$980$	11.1479	−	6.73635i	0.356106	−	0.215185i
$981$	3.97132	+	2.29284i	0.126794	+	0.0732048i
$982$	−15.3567	−	7.16093i	−0.490051	−	0.228515i
$983$	−16.5309	−	11.5751i	−0.527254	−	0.369188i	0.279434	−	0.960165i	$-0.409853\pi$
$983$	−16.5309	−	11.5751i	−0.527254	−	0.369188i	−0.806688	+	0.590977i	$0.798742\pi$
$984$	−0.866207	+	4.91251i	−0.0276137	+	0.156605i
$985$	−13.6991	−	27.9099i	−0.436490	−	0.889282i
$986$	−1.54368	+	1.29530i	−0.0491608	+	0.0412508i
$987$	0.688226	+	0.688226i	0.0219065	+	0.0219065i
$988$	5.06327	−	8.14281i	0.161084	−	0.259057i
$989$		−	31.3047i		−	0.995432i
$990$	0.522089	+	0.0351952i	0.0165931	+	0.00111858i
$991$	−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	$0.165362\pi$
$992$	2.79029	+	3.98495i	0.0885919	+	0.126522i
$993$	2.34951	−	3.35545i	0.0745595	−	0.106482i
$994$	5.75210	+	15.8038i	0.182445	+	0.501265i
$995$	19.2019	−	34.8465i	0.608741	−	1.10471i
$996$	−3.62086	+	2.09051i	−0.114731	+	0.0662402i
$997$	31.0243	−	2.71428i	0.982550	−	0.0859620i	0.415455	−	0.909614i	$-0.363623\pi$
$997$	31.0243	−	2.71428i	0.982550	−	0.0859620i	0.567096	+	0.823652i	$0.308067\pi$
$998$	−6.78563	+	0.593665i	−0.214795	+	0.0187922i
$999$	−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.13.10	✓	120
5.2	odd	4	inner	570.2.bh.a.127.1	yes	120
19.3	odd	18	inner	570.2.bh.a.193.1	yes	120
95.22	even	36	inner	570.2.bh.a.307.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.13.10	✓	120	1.1	even	1	trivial
570.2.bh.a.127.1	yes	120	5.2	odd	4	inner
570.2.bh.a.193.1	yes	120	19.3	odd	18	inner
570.2.bh.a.307.10	yes	120	95.22	even	36	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)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.19391 - 0.432154i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.280552 - 1.04704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.19391 - 0.432154i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.280552 - 1.04704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(2.22323 - 0.239298i) q^{10} +(0.117008 + 0.202663i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-0.929669 + 1.99368i) q^{13} +(-0.188230 - 1.06750i) q^{14} +(1.80572 - 1.31885i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.163857 - 1.87289i) 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} +(0.0988992 + 0.212090i) q^{22} +(-3.08637 + 2.16110i) q^{23} +(0.984808 - 0.173648i) q^{24} +(4.62649 - 1.89621i) q^{25} +(-1.09989 + 1.90507i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-0.0944743 - 1.07985i) q^{28} +(-0.821087 - 0.688973i) q^{29} +(1.91380 - 1.15645i) q^{30} +(4.21298 + 2.43236i) q^{31} +(0.906308 + 0.422618i) q^{32} +(0.191694 + 0.134226i) q^{33} +(0.326466 - 1.85148i) q^{34} +(-1.06799 - 2.17586i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-3.32063 - 3.32063i) q^{37} +(-4.35657 - 0.142520i) q^{38} +2.19978i q^{39} +(2.23100 + 0.150397i) q^{40} +(-1.70610 + 4.68746i) q^{41} +(-0.621740 - 0.887937i) q^{42} +(-4.76559 + 6.80597i) q^{43} +(0.0800380 + 0.219902i) q^{44} +(1.07917 - 1.95842i) q^{45} +(-3.26298 + 1.88388i) q^{46} +(-0.894484 + 0.0782572i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(5.04460 - 2.91250i) q^{49} +(4.77415 - 1.48577i) q^{50} +(-0.643013 - 1.76666i) q^{51} +(-1.26174 + 1.80196i) q^{52} +(4.13559 + 5.90623i) q^{53} +(0.342020 - 0.939693i) q^{54} +(0.344286 + 0.394060i) q^{55} -1.08397i q^{56} +(-3.84416 + 2.05486i) q^{57} +(-0.757914 - 0.757914i) q^{58} +(-0.887152 + 0.744409i) q^{59} +(2.00731 - 0.985254i) q^{60} +(1.01701 - 5.76777i) q^{61} +(3.98495 + 2.79029i) q^{62} +(-0.982411 - 0.458106i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.17803 + 4.77572i) q^{65} +(0.179266 + 0.150422i) q^{66} +(-0.946295 - 10.8162i) q^{67} +(0.486591 - 1.81598i) q^{68} +(-1.88388 + 3.26298i) q^{69} +(-0.874284 - 2.26066i) q^{70} +(-15.2795 + 2.69418i) q^{71} +(0.819152 - 0.573576i) q^{72} +(0.492751 + 1.05671i) 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} +(-0.191724 + 2.19141i) q^{78} +(13.7007 + 4.98666i) q^{79} +(2.20941 + 0.344270i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-2.10814 + 4.52093i) q^{82} +(-4.03855 + 1.08213i) q^{83} +(-0.541985 - 0.938746i) q^{84} +(-0.449890 - 4.17976i) q^{85} +(-5.34064 + 6.36472i) q^{86} +(-1.03533 - 0.277416i) q^{87} +(0.0605676 + 0.226041i) q^{88} +(-2.14016 + 0.778954i) q^{89} +(1.24575 - 1.85691i) q^{90} +(2.34828 + 0.414065i) q^{91} +(-3.41476 + 1.59233i) q^{92} +(4.84622 + 0.423989i) q^{93} -0.897901 q^{94} +(-9.44607 + 2.40245i) q^{95} +1.00000 q^{96} +(-0.224166 - 0.0196120i) q^{97} +(5.27925 - 2.46175i) 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

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