LMFDB - Embedded newform 429.2.bq.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.159737 + 1.51979i) q^{2} +(-1.11400 - 1.32627i) q^{3} +(-0.327964 - 0.0697108i) q^{4} +(-0.0308880 - 0.0425136i) q^{5} +(2.19361 - 1.48120i) q^{6} +(0.593356 - 2.79152i) q^{7} +(-0.786124 + 2.41944i) q^{8} +(-0.517989 + 2.95494i) q^{9} +O(q^{10})$	\(q+(-0.159737 + 1.51979i) q^{2} +(-1.11400 - 1.32627i) q^{3} +(-0.327964 - 0.0697108i) q^{4} +(-0.0308880 - 0.0425136i) q^{5} +(2.19361 - 1.48120i) q^{6} +(0.593356 - 2.79152i) q^{7} +(-0.786124 + 2.41944i) q^{8} +(-0.517989 + 2.95494i) q^{9} +(0.0695459 - 0.0401523i) q^{10} +(-1.36326 - 3.02349i) q^{11} +(0.272897 + 0.512627i) q^{12} +(3.59860 + 0.223749i) q^{13} +(4.14775 + 1.34769i) q^{14} +(-0.0219753 + 0.0883261i) q^{15} +(-4.16409 - 1.85397i) q^{16} +(-0.257042 - 2.44559i) q^{17} +(-4.40816 - 1.25925i) q^{18} +(5.52856 - 4.97793i) q^{19} +(0.00716646 + 0.0160961i) q^{20} +(-4.36331 + 2.32281i) q^{21} +(4.81285 - 1.58891i) q^{22} +(3.85605 - 2.22629i) q^{23} +(4.08458 - 1.65266i) q^{24} +(1.54423 - 4.75266i) q^{25} +(-0.914881 + 5.43339i) q^{26} +(4.49610 - 2.60483i) q^{27} +(-0.389198 + 0.874153i) q^{28} +(-4.11347 + 4.56848i) q^{29} +(-0.130727 - 0.0475068i) q^{30} +(3.67715 + 2.67161i) q^{31} +(0.938861 - 1.62615i) q^{32} +(-2.49129 + 5.17624i) q^{33} +3.75785 q^{34} +(-0.137005 + 0.0609986i) q^{35} +(0.375873 - 0.933004i) q^{36} +(-3.07469 + 3.41479i) q^{37} +(6.68232 + 9.19743i) q^{38} +(-3.71211 - 5.02198i) q^{39} +(0.127141 - 0.0413106i) q^{40} +(4.96085 - 1.05446i) q^{41} +(-2.83322 - 7.00238i) q^{42} +(-0.528770 - 0.305286i) q^{43} +(0.236330 + 1.08663i) q^{44} +(0.141625 - 0.0692506i) q^{45} +(2.76755 + 6.21602i) q^{46} +(-1.86212 - 0.605038i) q^{47} +(2.17994 + 7.58804i) q^{48} +(-1.04569 - 0.465572i) q^{49} +(6.97639 + 3.10609i) q^{50} +(-2.95716 + 3.06530i) q^{51} +(-1.16461 - 0.324243i) q^{52} +(5.56039 - 7.65322i) q^{53} +(3.24061 + 7.24923i) q^{54} +(-0.0864313 + 0.151347i) q^{55} +(6.28747 + 3.63007i) q^{56} +(-12.7609 - 1.78692i) q^{57} +(-6.28607 - 6.98139i) q^{58} +(-0.151087 + 0.710810i) q^{59} +(0.0133644 - 0.0274358i) q^{60} +(-9.90275 + 1.04082i) q^{61} +(-4.64767 + 5.16176i) q^{62} +(7.94143 + 3.19931i) q^{63} +(-5.05381 - 3.67181i) q^{64} +(-0.101641 - 0.159901i) q^{65} +(-7.46887 - 4.61309i) q^{66} +(2.02560 + 3.50845i) q^{67} +(-0.0861836 + 0.819982i) q^{68} +(-7.24831 - 2.63407i) q^{69} +(-0.0708206 - 0.217963i) q^{70} +(-1.54242 + 0.162115i) q^{71} +(-6.74211 - 3.57620i) q^{72} +(-8.77633 + 2.85160i) q^{73} +(-4.69864 - 5.21837i) q^{74} +(-8.02359 + 3.24641i) q^{75} +(-2.16018 + 1.24718i) q^{76} +(-9.24904 + 2.01157i) q^{77} +(8.22533 - 4.83944i) q^{78} +(-8.11346 + 11.1672i) q^{79} +(0.0498011 + 0.234296i) q^{80} +(-8.46338 - 3.06125i) q^{81} +(0.810134 + 7.70791i) q^{82} +(11.5025 - 8.35703i) q^{83} +(1.59293 - 0.457628i) q^{84} +(-0.0960312 + 0.0864669i) q^{85} +(0.548436 - 0.754857i) q^{86} +(10.6415 + 0.366279i) q^{87} +(8.38686 - 0.921491i) q^{88} +(-2.78116 + 1.60571i) q^{89} +(0.0826239 + 0.226303i) q^{90} +(2.75985 - 9.91281i) q^{91} +(-1.41984 + 0.461334i) q^{92} +(-0.553089 - 7.85309i) q^{93} +(1.21698 - 2.73339i) q^{94} +(-0.382396 - 0.0812807i) q^{95} +(-3.20262 + 0.566359i) q^{96} +(2.50578 - 1.11565i) q^{97} +(0.874609 - 1.51487i) q^{98} +(9.64041 - 2.46223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.159737	+	1.51979i	−0.112951	+	1.07466i	0.780395	+	0.625287i	$0.215018\pi$
$2$	−0.159737	+	1.51979i	−0.112951	+	1.07466i	−0.893346	+	0.449370i	$0.851649\pi$
$3$	−1.11400	−	1.32627i	−0.643171	−	0.765723i
$3$	−1.11400	−	1.32627i	−0.643171	−	0.765723i
$4$	−0.327964	−	0.0697108i	−0.163982	−	0.0348554i
$5$	−0.0308880	−	0.0425136i	−0.0138135	−	0.0190127i	0.802054	−	0.597251i	$-0.203740\pi$
$5$	−0.0308880	−	0.0425136i	−0.0138135	−	0.0190127i	−0.815868	+	0.578238i	$0.803740\pi$
$6$	2.19361	−	1.48120i	0.895536	−	0.604699i
$7$	0.593356	−	2.79152i	0.224267	−	1.05510i	−0.711557	−	0.702628i	$-0.752010\pi$
$7$	0.593356	−	2.79152i	0.224267	−	1.05510i	0.935824	−	0.352467i	$-0.114657\pi$
$8$	−0.786124	+	2.41944i	−0.277937	+	0.855402i
$9$	−0.517989	+	2.95494i	−0.172663	+	0.984981i
$10$	0.0695459	−	0.0401523i	0.0219923	−	0.0126973i
$11$	−1.36326	−	3.02349i	−0.411039	−	0.911618i
$11$	−1.36326	−	3.02349i	−0.411039	−	0.911618i
$12$	0.272897	+	0.512627i	0.0787787	+	0.147983i
$13$	3.59860	+	0.223749i	0.998073	+	0.0620567i
$13$	3.59860	+	0.223749i	0.998073	+	0.0620567i
$14$	4.14775	+	1.34769i	1.10853	+	0.360185i
$15$	−0.0219753	+	0.0883261i	−0.00567399	+	0.0228057i
$16$	−4.16409	−	1.85397i	−1.04102	−	0.463493i
$17$	−0.257042	−	2.44559i	−0.0623417	−	0.593142i	−0.980444	−	0.196798i	$-0.936946\pi$
$17$	−0.257042	−	2.44559i	−0.0623417	−	0.593142i	0.918102	−	0.396344i	$-0.129721\pi$
$18$	−4.40816	−	1.25925i	−1.03901	−	0.296808i
$19$	5.52856	−	4.97793i	1.26834	−	1.14202i	0.285335	−	0.958428i	$-0.407895\pi$
$19$	5.52856	−	4.97793i	1.26834	−	1.14202i	0.983003	−	0.183588i	$-0.0587714\pi$
$20$	0.00716646	+	0.0160961i	0.00160247	+	0.00359921i
$21$	−4.36331	+	2.32281i	−0.952153	+	0.506880i
$22$	4.81285	−	1.58891i	1.02610	−	0.338758i
$23$	3.85605	−	2.22629i	0.804041	−	0.464213i	−0.0408412	−	0.999166i	$-0.513004\pi$
$23$	3.85605	−	2.22629i	0.804041	−	0.464213i	0.844882	+	0.534952i	$0.179670\pi$
$24$	4.08458	−	1.65266i	0.833762	−	0.337347i
$25$	1.54423	−	4.75266i	0.308846	−	0.950531i
$26$	−0.914881	+	5.43339i	−0.179423	+	1.06558i
$27$	4.49610	−	2.60483i	0.865274	−	0.501299i
$28$	−0.389198	+	0.874153i	−0.0735515	+	0.165199i
$29$	−4.11347	+	4.56848i	−0.763853	+	0.848345i	−0.992125	−	0.125253i	$-0.960026\pi$
$29$	−4.11347	+	4.56848i	−0.763853	+	0.848345i	0.228272	+	0.973597i	$0.426692\pi$
$30$	−0.130727	−	0.0475068i	−0.0238674	−	0.00867352i
$31$	3.67715	+	2.67161i	0.660437	+	0.479835i	0.866810	−	0.498638i	$-0.166166\pi$
$31$	3.67715	+	2.67161i	0.660437	+	0.479835i	−0.206374	+	0.978473i	$0.566166\pi$
$32$	0.938861	−	1.62615i	0.165969	−	0.287466i
$33$	−2.49129	+	5.17624i	−0.433678	+	0.901068i
$34$	3.75785			0.644466
$35$	−0.137005	+	0.0609986i	−0.0231581	+	0.0103106i
$36$	0.375873	−	0.933004i	0.0626455	−	0.155501i
$37$	−3.07469	+	3.41479i	−0.505476	+	0.561388i	−0.940833	−	0.338869i	$-0.889956\pi$
$37$	−3.07469	+	3.41479i	−0.505476	+	0.561388i	0.435357	+	0.900258i	$0.356622\pi$
$38$	6.68232	+	9.19743i	1.08402	+	1.49202i
$39$	−3.71211	−	5.02198i	−0.594413	−	0.804160i
$40$	0.127141	−	0.0413106i	0.0201028	−	0.00653178i
$41$	4.96085	−	1.05446i	0.774755	−	0.164679i	0.196465	−	0.980511i	$-0.437054\pi$
$41$	4.96085	−	1.05446i	0.774755	−	0.164679i	0.578290	+	0.815832i	$0.303720\pi$
$42$	−2.83322	−	7.00238i	−0.437175	−	1.08049i
$43$	−0.528770	−	0.305286i	−0.0806367	−	0.0465556i	0.459139	−	0.888364i	$-0.348158\pi$
$43$	−0.528770	−	0.305286i	−0.0806367	−	0.0465556i	−0.539776	+	0.841809i	$0.681491\pi$
$44$	0.236330	+	1.08663i	0.0356281	+	0.163816i
$45$	0.141625	−	0.0692506i	0.0211122	−	0.0103233i
$46$	2.76755	+	6.21602i	0.408053	+	0.916502i
$47$	−1.86212	−	0.605038i	−0.271618	−	0.0882539i	0.170041	−	0.985437i	$-0.445610\pi$
$47$	−1.86212	−	0.605038i	−0.271618	−	0.0882539i	−0.441659	+	0.897183i	$0.645610\pi$
$48$	2.17994	+	7.58804i	0.314648	+	1.09524i
$49$	−1.04569	−	0.465572i	−0.149385	−	0.0665103i
$50$	6.97639	+	3.10609i	0.986610	+	0.439267i
$51$	−2.95716	+	3.06530i	−0.414086	+	0.429228i
$52$	−1.16461	−	0.324243i	−0.161503	−	0.0449644i
$53$	5.56039	−	7.65322i	0.763778	−	1.05125i	−0.233112	−	0.972450i	$-0.574891\pi$
$53$	5.56039	−	7.65322i	0.763778	−	1.05125i	0.996890	−	0.0788005i	$-0.0251090\pi$
$54$	3.24061	+	7.24923i	0.440991	+	0.986495i
$55$	−0.0864313	+	0.151347i	−0.0116544	+	0.0204076i
$56$	6.28747	+	3.63007i	0.840198	+	0.485089i
$57$	−12.7609	−	1.78692i	−1.69023	−	0.236684i
$58$	−6.28607	−	6.98139i	−0.825401	−	0.916701i
$59$	−0.151087	+	0.710810i	−0.0196699	+	0.0925395i	−0.986888	−	0.161409i	$-0.948396\pi$
$59$	−0.151087	+	0.710810i	−0.0196699	+	0.0925395i	0.967218	+	0.253949i	$0.0817294\pi$
$60$	0.0133644	−	0.0274358i	0.00172533	−	0.00354195i
$61$	−9.90275	+	1.04082i	−1.26792	+	0.133264i	−0.714497	−	0.699638i	$-0.753344\pi$
$61$	−9.90275	+	1.04082i	−1.26792	+	0.133264i	−0.553421	+	0.832902i	$0.686678\pi$
$62$	−4.64767	+	5.16176i	−0.590255	+	0.655545i
$63$	7.94143	+	3.19931i	1.00053	+	0.403075i
$64$	−5.05381	−	3.67181i	−0.631726	−	0.458976i
$65$	−0.101641	−	0.159901i	−0.0126070	−	0.0198332i
$66$	−7.46887	−	4.61309i	−0.919354	−	0.567832i
$67$	2.02560	+	3.50845i	0.247467	+	0.428625i	0.962822	−	0.270135i	$-0.0870685\pi$
$67$	2.02560	+	3.50845i	0.247467	+	0.428625i	−0.715355	+	0.698761i	$0.753735\pi$
$68$	−0.0861836	+	0.819982i	−0.0104513	+	0.0994374i
$69$	−7.24831	−	2.63407i	−0.872594	−	0.317104i
$70$	−0.0708206	−	0.217963i	−0.00846468	−	0.0260516i
$71$	−1.54242	+	0.162115i	−0.183052	+	0.0192395i	−0.195611	−	0.980682i	$-0.562669\pi$
$71$	−1.54242	+	0.162115i	−0.183052	+	0.0192395i	0.0125589	+	0.999921i	$0.496002\pi$
$72$	−6.74211	−	3.57620i	−0.794565	−	0.421459i
$73$	−8.77633	+	2.85160i	−1.02719	+	0.333755i	−0.773679	−	0.633578i	$-0.781586\pi$
$73$	−8.77633	+	2.85160i	−1.02719	+	0.333755i	−0.253512	+	0.967332i	$0.581586\pi$
$74$	−4.69864	−	5.21837i	−0.546206	−	0.606623i
$75$	−8.02359	+	3.24641i	−0.926484	+	0.374863i
$76$	−2.16018	+	1.24718i	−0.247790	+	0.143061i
$77$	−9.24904	+	2.01157i	−1.05403	+	0.229239i
$78$	8.22533	−	4.83944i	0.931336	−	0.547959i
$79$	−8.11346	+	11.1672i	−0.912836	+	1.25641i	0.0533531	+	0.998576i	$0.483009\pi$
$79$	−8.11346	+	11.1672i	−0.912836	+	1.25641i	−0.966189	+	0.257835i	$0.916991\pi$
$80$	0.0498011	+	0.234296i	0.00556793	+	0.0261951i
$81$	−8.46338	−	3.06125i	−0.940375	−	0.340139i
$82$	0.810134	+	7.70791i	0.0894643	+	0.851196i
$83$	11.5025	−	8.35703i	1.26256	−	0.917303i	0.263679	−	0.964610i	$-0.415064\pi$
$83$	11.5025	−	8.35703i	1.26256	−	0.917303i	0.998880	+	0.0473069i	$0.0150639\pi$
$84$	1.59293	−	0.457628i	0.173803	−	0.0499314i
$85$	−0.0960312	+	0.0864669i	−0.0104161	+	0.00937865i
$86$	0.548436	−	0.754857i	0.0591393	−	0.0813983i
$87$	10.6415	+	0.366279i	1.14088	+	0.0392692i
$88$	8.38686	−	0.921491i	0.894043	−	0.0982313i
$89$	−2.78116	+	1.60571i	−0.294803	+	0.170204i	−0.640106	−	0.768287i	$-0.721109\pi$
$89$	−2.78116	+	1.60571i	−0.294803	+	0.170204i	0.345303	+	0.938491i	$0.387776\pi$
$90$	0.0826239	+	0.226303i	0.00870932	+	0.0238544i
$91$	2.75985	−	9.91281i	0.289311	−	1.03914i
$92$	−1.41984	+	0.461334i	−0.148028	+	0.0480973i
$93$	−0.553089	−	7.85309i	−0.0573526	−	0.814327i
$94$	1.21698	−	2.73339i	0.125522	−	0.281927i
$95$	−0.382396	−	0.0812807i	−0.0392330	−	0.00833923i
$96$	−3.20262	+	0.566359i	−0.326866	+	0.0578038i
$97$	2.50578	−	1.11565i	0.254424	−	0.113277i	−0.275562	−	0.961283i	$-0.588864\pi$
$97$	2.50578	−	1.11565i	0.254424	−	0.113277i	0.529986	+	0.848007i	$0.322197\pi$
$98$	0.874609	−	1.51487i	0.0883489	−	0.153025i
$99$	9.64041	−	2.46223i	0.968897	−	0.247463i
$100$	−0.837763	+	1.45105i	−0.0837763	+	0.145105i
$101$	−1.76066	+	16.7516i	−0.175193	+	1.66685i	0.455063	+	0.890459i	$0.349617\pi$
$101$	−1.76066	+	16.7516i	−0.175193	+	1.66685i	−0.630256	+	0.776388i	$0.717050\pi$
$102$	−4.18626	−	4.98392i	−0.414501	−	0.493482i
$103$	−2.55671	−	7.86874i	−0.251920	−	0.775330i	−0.994421	−	0.105485i	$-0.966360\pi$
$103$	−2.55671	−	7.86874i	−0.251920	−	0.775330i	0.742501	−	0.669845i	$-0.233640\pi$
$104$	−3.37030	+	8.53072i	−0.330485	+	0.836505i
$105$	0.233525	+	0.113753i	0.0227897	+	0.0111012i
$106$	10.7431	+	9.67315i	1.04346	+	0.939539i
$107$	−14.7556	+	3.13641i	−1.42648	+	0.303208i	−0.855520	−	0.517770i	$-0.826762\pi$
$107$	−14.7556	+	3.13641i	−1.42648	+	0.303208i	−0.570961	+	0.820977i	$0.693429\pi$
$108$	−1.65614	+	0.540861i	−0.159362	+	0.0520444i
$109$		−	1.71447i		−	0.164216i	−0.996623	−	0.0821080i	$-0.973835\pi$
$109$		−	1.71447i		−	0.164216i	0.996623	−	0.0821080i	$-0.0261652\pi$
$110$	−0.216210	−	0.155533i	−0.0206148	−	0.0148295i
$111$	7.95416	+	0.273782i	0.754976	+	0.0259862i
$112$	−7.64618	+	10.5241i	−0.722496	+	0.994431i
$113$	9.06928	−	8.16602i	0.853166	−	0.768194i	−0.121327	−	0.992613i	$-0.538715\pi$
$113$	9.06928	−	8.16602i	0.853166	−	0.768194i	0.974493	+	0.224418i	$0.0720482\pi$
$114$	4.75414	−	19.1085i	0.445266	−	1.78968i
$115$	−0.213753	−	0.0951689i	−0.0199326	−	0.00887455i
$116$	1.66754	−	1.21154i	0.154827	−	0.112489i
$117$	−2.52520	+	10.5178i	−0.233455	+	0.972368i
$118$	−1.05615	−	0.343164i	−0.0972265	−	0.0315908i
$119$	−6.97942	−	0.733567i	−0.639802	−	0.0672459i
$120$	−0.196425	−	0.122603i	−0.0179310	−	0.0111921i
$121$	−7.28303	+	8.24363i	−0.662094	+	0.749421i
$122$		−	15.2164i		−	1.37763i
$123$	−6.92491	−	5.40476i	−0.624398	−	0.487330i
$124$	−1.01973	−	1.13253i	−0.0915747	−	0.101704i
$125$	−0.499640	+	0.162343i	−0.0446891	+	0.0145204i
$126$	−6.13083	+	11.5583i	−0.546178	+	1.02969i
$127$	−0.335627	+	0.753832i	−0.0297821	+	0.0668917i	−0.927824	−	0.373018i	$-0.878323\pi$
$127$	−0.335627	+	0.753832i	−0.0297821	+	0.0668917i	0.898042	+	0.439910i	$0.144990\pi$
$128$	8.90055	−	9.88507i	0.786705	−	0.873725i
$129$	0.184161	+	1.04138i	0.0162145	+	0.0916886i
$130$	0.259252	−	0.128932i	0.0227379	−	0.0113080i
$131$	−15.0453			−1.31451			−0.657257	−	0.753667i	$-0.728283\pi$
$131$	−15.0453			−1.31451			−0.657257	+	0.753667i	$0.728283\pi$
$132$	1.17789	−	1.52395i	0.102522	−	0.132643i
$133$	−10.6156	−	18.3868i	−0.920489	−	1.59433i
$134$	−5.65569	+	2.51807i	−0.488577	+	0.217528i
$135$	−0.249616	−	0.110688i	−0.0214835	−	0.00952647i
$136$	6.11902	+	1.30064i	0.524702	+	0.111529i
$137$	19.2209	−	2.02020i	1.64216	−	0.172597i	0.762097	−	0.647463i	$-0.224170\pi$
$137$	19.2209	−	2.02020i	1.64216	−	0.172597i	0.880058	+	0.474865i	$0.157503\pi$
$138$	5.16106	−	10.5952i	0.439339	−	0.901922i
$139$	−4.18009	+	19.6658i	−0.354551	+	1.66803i	0.333793	+	0.942646i	$0.391671\pi$
$139$	−4.18009	+	19.6658i	−0.354551	+	1.66803i	−0.688344	+	0.725385i	$0.741662\pi$
$140$	0.0491849	−	0.0104546i	0.00415689	−	0.000883574i
$141$	1.27196	+	3.14369i	0.107118	+	0.264746i
$142$		−	2.37006i		−	0.198891i
$143$	−4.22934	−	11.1854i	−0.353675	−	0.935368i
$144$	7.63533	−	11.3443i	0.636277	−	0.945359i
$145$	0.321279	+	0.0337678i	0.0266808	+	0.00280426i
$146$	−2.93194	−	13.7937i	−0.242649	−	1.14158i
$147$	0.547431	+	1.90552i	0.0451513	+	0.157165i
$148$	1.24644	−	0.905588i	0.102456	−	0.0744389i
$149$	−1.54898	−	14.7376i	−0.126898	−	1.20735i	−0.853797	−	0.520606i	$-0.825706\pi$
$149$	−1.54898	−	14.7376i	−0.126898	−	1.20735i	0.726900	−	0.686744i	$-0.240961\pi$
$150$	−3.65221	−	12.7128i	−0.298202	−	1.03799i
$151$	8.35775	+	2.71560i	0.680144	+	0.220992i	0.628658	−	0.777682i	$-0.283604\pi$
$151$	8.35775	+	2.71560i	0.680144	+	0.220992i	0.0514855	+	0.998674i	$0.483604\pi$
$152$	7.69769	+	17.2893i	0.624365	+	1.40235i
$153$	7.35971	+	0.507243i	0.594998	+	0.0410082i
$154$	−1.57975	−	14.3780i	−0.127300	−	1.15861i
$155$		−	0.238850i		−	0.0191849i
$156$	0.867350	+	1.90580i	0.0694435	+	0.152586i
$157$	−2.14416	+	6.59904i	−0.171122	+	0.526660i	−0.999435	−	0.0336055i	$-0.989301\pi$
$157$	−2.14416	+	6.59904i	−0.171122	+	0.526660i	0.828313	+	0.560266i	$0.189301\pi$
$158$	−15.6759	−	14.1146i	−1.24710	−	1.12290i
$159$	−16.3445	+	1.15114i	−1.29621	+	0.0912911i
$160$	−0.0981332	+	0.0103142i	−0.00775811	+	0.000815410i
$161$	−3.92672	−	12.0852i	−0.309469	−	0.952448i
$162$	6.00439	−	12.3736i	0.471749	−	0.972161i
$163$	10.2836	−	4.57856i	0.805474	−	0.358620i	0.0376584	−	0.999291i	$-0.488010\pi$
$163$	10.2836	−	4.57856i	0.805474	−	0.358620i	0.767816	+	0.640670i	$0.221343\pi$
$164$	−1.70049			−0.132786
$165$	0.297012	−	0.0539696i	0.0231223	−	0.00420153i
$166$	10.8636	+	18.8163i	0.843179	+	1.46043i
$167$	−0.822790	+	7.82832i	−0.0636694	+	0.605774i	0.915442	+	0.402450i	$0.131841\pi$
$167$	−0.822790	+	7.82832i	−0.0636694	+	0.605774i	−0.979112	+	0.203324i	$0.934826\pi$
$168$	−2.18981	−	12.3828i	−0.168947	−	0.955354i
$169$	12.8999	+	1.61036i	0.992298	+	0.123874i
$170$	−0.116072	−	0.159760i	−0.00890233	−	0.0122530i
$171$	11.8458	+	18.9151i	0.905870	+	1.44647i
$172$	0.152136	+	0.136984i	0.0116002	+	0.0104449i
$173$	12.6404	+	14.0386i	0.961033	+	1.06734i	0.997685	+	0.0680072i	$0.0216641\pi$
$173$	12.6404	+	14.0386i	0.961033	+	1.06734i	−0.0366518	+	0.999328i	$0.511669\pi$
$174$	−2.25650	+	16.1143i	−0.171065	+	1.22162i
$175$	−12.3509	−	7.13077i	−0.933637	−	0.539035i
$176$	0.0712718	+	15.1175i	0.00537232	+	1.13953i
$177$	1.11104	−	0.591462i	0.0835107	−	0.0444570i
$178$	−1.99609	−	4.48329i	−0.149613	−	0.336037i
$179$	2.39515	+	11.2683i	0.179022	+	0.842233i	0.972366	+	0.233460i	$0.0750048\pi$
$179$	2.39515	+	11.2683i	0.179022	+	0.842233i	−0.793344	+	0.608773i	$0.791662\pi$
$180$	−0.0512753	+	0.0128389i	−0.00382184	+	0.000956953i
$181$	−16.3518	+	11.8803i	−1.21542	+	0.883054i	−0.995712	−	0.0925115i	$-0.970511\pi$
$181$	−16.3518	+	11.8803i	−1.21542	+	0.883054i	−0.219708	+	0.975566i	$0.570511\pi$
$182$	14.6246	+	5.77784i	1.08405	+	0.428282i
$183$	12.4121	+	11.9743i	0.917530	+	0.885162i
$184$	2.35505	+	11.0796i	0.173616	+	0.816800i
$185$	0.240146	+	0.0252404i	0.0176559	+	0.00185571i
$186$	12.0234	+	0.413846i	0.881600	+	0.0303447i
$187$	−7.04380	+	4.11114i	−0.515094	+	0.300636i
$188$	0.568529	+	0.328240i	0.0414642	+	0.0239394i
$189$	−4.60364	−	14.0965i	−0.334865	−	1.02537i
$190$	0.184613	−	0.568179i	0.0133932	−	0.0412201i
$191$	−1.77552	+	8.35317i	−0.128472	+	0.604414i	0.866056	+	0.499947i	$0.166647\pi$
$191$	−1.77552	+	8.35317i	−0.128472	+	0.604414i	−0.994528	+	0.104467i	$0.966686\pi$
$192$	0.760154	+	10.7931i	0.0548594	+	0.778927i
$193$	−9.92857	+	22.2999i	−0.714674	+	1.60518i	0.0790242	+	0.996873i	$0.474820\pi$
$193$	−9.92857	+	22.2999i	−0.714674	+	1.60518i	−0.793698	+	0.608312i	$0.791847\pi$
$194$	1.29529	+	3.98649i	0.0929963	+	0.286213i
$195$	−0.0988431	+	0.312934i	−0.00707830	+	0.0224096i
$196$	0.310493	+	0.225587i	0.0221781	+	0.0161133i
$197$	4.13328	+	7.15905i	0.294484	+	0.510061i	0.974865	−	0.222797i	$-0.0715189\pi$
$197$	4.13328	+	7.15905i	0.294484	+	0.510061i	−0.680381	+	0.732859i	$0.738186\pi$
$198$	2.20215	+	15.0447i	0.156500	+	1.06918i
$199$	8.74845	−	15.1528i	0.620161	−	1.07415i	−0.369294	−	0.929313i	$-0.620400\pi$
$199$	8.74845	−	15.1528i	0.620161	−	1.07415i	0.989455	−	0.144838i	$-0.0462662\pi$
$200$	10.2848	+	7.47236i	0.727247	+	0.528376i
$201$	2.39662	−	6.59493i	0.169045	−	0.465170i
$202$	−25.1778	−	5.35170i	−1.77150	−	0.376544i
$203$	10.3122	+	14.1936i	0.723777	+	0.996194i
$204$	1.18353	−	0.799160i	0.0828634	−	0.0559524i
$205$	−0.198059	−	0.178334i	−0.0138331	−	0.0124554i
$206$	12.3673	−	2.62874i	0.861669	−	0.183153i
$207$	4.58117	+	12.5476i	0.318413	+	0.872118i
$208$	−14.5701	−	7.60341i	−1.01025	−	0.527202i
$209$	−22.5876	−	9.92933i	−1.56242	−	0.686826i
$210$	−0.210184	+	0.336739i	−0.0145041	+	0.0232372i
$211$	9.97872	+	1.04881i	0.686964	+	0.0722028i	0.441578	−	0.897223i	$-0.354419\pi$
$211$	9.97872	+	1.04881i	0.686964	+	0.0722028i	0.245385	+	0.969426i	$0.421085\pi$
$212$	−2.35712	+	2.12236i	−0.161887	+	0.145764i
$213$	1.93327	+	1.86507i	0.132466	+	0.127793i
$214$	−2.40967	−	22.9265i	−0.164722	−	1.56722i
$215$	0.00335383	+	0.0319096i	0.000228730	+	0.00217622i
$216$	2.76773	+	12.9258i	0.188320	+	0.879487i
$217$	9.63971	−	8.67963i	0.654386	−	0.589212i
$218$	2.60563	+	0.273863i	0.176476	+	0.0185484i
$219$	13.5589	+	8.46309i	0.916223	+	0.571883i
$220$	0.0388968	−	0.0436110i	0.00262242	−	0.00294025i
$221$	−0.377794	−	8.85821i	−0.0254132	−	0.595867i
$222$	−1.68666	+	12.0450i	−0.113202	+	0.808405i
$223$	24.4679	−	5.20081i	1.63849	−	0.348272i	0.705650	−	0.708561i	$-0.250655\pi$
$223$	24.4679	−	5.20081i	1.63849	−	0.348272i	0.932841	+	0.360289i	$0.117322\pi$
$224$	−3.98236	−	3.58574i	−0.266083	−	0.239582i
$225$	13.2439	+	7.02494i	0.882929	+	0.468329i
$226$	10.9620	+	15.0879i	0.729179	+	1.00363i
$227$	1.35605	+	0.288237i	0.0900040	+	0.0191309i	0.252694	−	0.967546i	$-0.418684\pi$
$227$	1.35605	+	0.288237i	0.0900040	+	0.0191309i	−0.162690	+	0.986677i	$0.552017\pi$
$228$	4.06055	+	1.47562i	0.268916	+	0.0977253i
$229$	−8.08179	−	5.87176i	−0.534059	−	0.388017i	0.287815	−	0.957686i	$-0.407071\pi$
$229$	−8.08179	−	5.87176i	−0.534059	−	0.388017i	−0.821874	+	0.569669i	$0.807071\pi$
$230$	0.178781	−	0.309659i	0.0117885	−	0.0204183i
$231$	12.9714	+	10.0258i	0.853452	+	0.659652i
$232$	−7.81946	−	13.5437i	−0.513373	−	0.889188i
$233$	−9.11143	−	6.61984i	−0.596909	−	0.433680i	0.247871	−	0.968793i	$-0.420269\pi$
$233$	−9.11143	−	6.61984i	−0.596909	−	0.433680i	−0.844780	+	0.535113i	$0.820269\pi$
$234$	−15.5815	−	5.51786i	−1.01859	−	0.360714i
$235$	0.0317946	+	0.0978537i	0.00207405	+	0.00638327i
$236$	0.0991022	−	0.222587i	0.00645100	−	0.0144892i
$237$	23.8492	−	1.67969i	1.54917	−	0.109107i
$238$	2.22974	−	10.4901i	0.144533	−	0.679972i
$239$	0.964473	−	2.96834i	0.0623866	−	0.192006i	−0.915005	−	0.403442i	$-0.867814\pi$
$239$	0.964473	−	2.96834i	0.0623866	−	0.192006i	0.977392	+	0.211436i	$0.0678138\pi$
$240$	0.255261	−	0.327056i	0.0164770	−	0.0211114i
$241$	22.5477	+	13.0179i	1.45243	+	0.838558i	0.998619	−	0.0525422i	$-0.0167324\pi$
$241$	22.5477	+	13.0179i	1.45243	+	0.838558i	0.453806	+	0.891100i	$0.350066\pi$
$242$	−11.3653	−	12.3855i	−0.730586	−	0.796172i
$243$	5.36818	+	14.6350i	0.344369	+	0.938834i
$244$	3.32030	+	0.348977i	0.212560	+	0.0223410i
$245$	0.0125061	+	0.0588367i	0.000798987	+	0.00375894i
$246$	9.32028	−	9.66110i	0.594239	−	0.615969i
$247$	21.0089	−	16.6766i	1.33676	−	1.06111i
$248$	−9.35451	+	6.79645i	−0.594012	+	0.431575i
$249$	−23.8975	−	5.94562i	−1.51444	−	0.376788i
$250$	−0.166917	−	0.785281i	−0.0105567	−	0.0496656i
$251$	−3.12068	−	7.00917i	−0.196976	−	0.442415i	0.787871	−	0.615840i	$-0.211183\pi$
$251$	−3.12068	−	7.00917i	−0.196976	−	0.442415i	−0.984847	+	0.173425i	$0.944517\pi$
$252$	−2.38147	−	1.60286i	−0.150019	−	0.100971i
$253$	−11.9880	−	8.62372i	−0.753677	−	0.542168i
$254$	−1.09206	−	0.630499i	−0.0685217	−	0.0395610i
$255$	0.221658	+	0.0310389i	0.0138807	+	0.00194373i
$256$	5.24160	+	5.82139i	0.327600	+	0.363837i
$257$	9.59192	+	8.63660i	0.598328	+	0.538737i	0.911680	−	0.410900i	$-0.134786\pi$
$257$	9.59192	+	8.63660i	0.598328	+	0.538737i	−0.313353	+	0.949637i	$0.601452\pi$
$258$	−1.61210	+	0.113540i	−0.100365	+	0.00706867i
$259$	7.70807	+	10.6093i	0.478956	+	0.659227i
$260$	0.0221878	+	0.0595271i	0.00137603	+	0.00369171i
$261$	−11.3689	−	14.5215i	−0.703714	−	0.898858i
$262$	2.40329	−	22.8657i	0.148476	−	1.41265i
$263$	−2.10302	−	3.64253i	−0.129678	−	0.224608i	0.793874	−	0.608082i	$-0.208061\pi$
$263$	−2.10302	−	3.64253i	−0.129678	−	0.224608i	−0.923552	+	0.383474i	$0.874728\pi$
$264$	−10.5651	−	10.0967i	−0.650240	−	0.621409i
$265$	−0.497115			−0.0305375
$266$	29.6398	−	13.1965i	1.81733	−	0.809128i
$267$	5.22783	+	1.89981i	0.319938	+	0.116267i
$268$	−0.419747	−	1.29185i	−0.0256402	−	0.0789123i
$269$	−21.3640	+	2.24545i	−1.30259	+	0.136907i	−0.730289	−	0.683138i	$-0.760615\pi$
$269$	−21.3640	+	2.24545i	−1.30259	+	0.136907i	−0.572298	+	0.820045i	$0.693948\pi$
$270$	0.208095	−	0.361684i	0.0126643	−	0.0220114i
$271$	2.87082	+	2.58490i	0.174390	+	0.157022i	0.751704	−	0.659501i	$-0.229232\pi$
$271$	2.87082	+	2.58490i	0.174390	+	0.157022i	−0.577314	+	0.816522i	$0.695899\pi$
$272$	−3.46370	+	10.6602i	−0.210018	+	0.646369i
$273$	−16.2215	+	7.38260i	−0.981773	+	0.446815i
$274$			29.5346i			1.78425i
$275$	−16.4748	+	1.81014i	−0.993469	+	0.109156i
$276$	2.19356	+	1.36916i	0.132037	+	0.0824139i
$277$	−9.89756	−	22.2303i	−0.594687	−	1.33569i	−0.920681	−	0.390316i	$-0.872366\pi$
$277$	−9.89756	−	22.2303i	−0.594687	−	1.33569i	0.325994	−	0.945372i	$-0.394301\pi$
$278$	−29.2203	−	9.49423i	−1.75251	−	0.569426i
$279$	−9.79918	+	9.48192i	−0.586661	+	0.567668i
$280$	−0.0398795	−	0.379429i	−0.00238326	−	0.0226752i
$281$	−9.41195	+	6.83818i	−0.561470	+	0.407932i	−0.831997	−	0.554781i	$-0.812802\pi$
$281$	−9.41195	+	6.83818i	−0.561470	+	0.407932i	0.270527	+	0.962712i	$0.412802\pi$
$282$	−4.98094	+	1.43096i	−0.296610	+	0.0852123i
$283$	0.454283	+	2.13723i	0.0270043	+	0.127045i	0.989585	−	0.143950i	$-0.0459805\pi$
$283$	0.454283	+	2.13723i	0.0270043	+	0.127045i	−0.962581	+	0.270995i	$0.912647\pi$
$284$	0.517159	+	0.0543556i	0.0306878	+	0.00322541i
$285$	0.318190	+	0.597707i	0.0188480	+	0.0354051i
$286$	17.6751	−	4.64100i	1.04515	−	0.274428i
$287$		−	14.4740i		−	0.854372i
$288$	4.31887	+	3.61661i	0.254492	+	0.213111i
$289$	10.7137	−	2.27726i	0.630217	−	0.133957i
$290$	−0.102640	+	0.482884i	−0.00602724	+	0.0283559i
$291$	−4.27110	−	2.08051i	−0.250377	−	0.121962i
$292$	3.07710	−	0.323416i	0.180074	−	0.0189265i
$293$	6.90951	+	1.46866i	0.403658	+	0.0858002i	0.405267	−	0.914199i	$-0.367179\pi$
$293$	6.90951	+	1.46866i	0.403658	+	0.0858002i	−0.00160861	+	0.999999i	$0.500512\pi$
$294$	−2.98344	+	0.527600i	−0.173998	+	0.0307703i
$295$	0.0348859	−	0.0155322i	0.00203113	−	0.000904319i
$296$	−5.84480	−	10.1235i	−0.339722	−	0.588416i
$297$	−14.0050	−	10.0429i	−0.812654	−	0.582746i
$298$	22.6455			1.31182
$299$	14.3745	−	7.14874i	0.831299	−	0.413423i
$300$	2.85775	−	0.505373i	0.164993	−	0.0291777i
$301$	−1.16596	+	1.29493i	−0.0672048	+	0.0746385i
$302$	−5.46219	+	12.2683i	−0.314314	+	0.705960i
$303$	24.1786	−	16.3262i	1.38902	−	0.937918i
$304$	−32.2503	+	10.4788i	−1.84968	+	0.600999i
$305$	0.350125	+	0.388853i	0.0200481	+	0.0222657i
$306$	−1.94652	+	11.1042i	−0.111275	+	0.634786i
$307$		−	11.2971i		−	0.644762i	−0.946610	−	0.322381i	$-0.895517\pi$
$307$		−	11.2971i		−	0.644762i	0.946610	−	0.322381i	$-0.104483\pi$
$308$	3.17358	−	0.0149619i	0.180831	−	0.000852531i
$309$	−7.58790	+	12.1567i	−0.431660	+	0.691571i
$310$	0.363002	+	0.0381531i	0.0206172	+	0.00216695i
$311$	7.12145	+	2.31390i	0.403820	+	0.131209i	0.503883	−	0.863772i	$-0.331904\pi$
$311$	7.12145	+	2.31390i	0.403820	+	0.131209i	−0.100063	+	0.994981i	$0.531904\pi$
$312$	15.0686	−	5.03333i	0.853089	−	0.284956i
$313$	−13.4440	+	9.76761i	−0.759898	+	0.552098i	−0.898879	−	0.438197i	$-0.855617\pi$
$313$	−13.4440	+	9.76761i	−0.759898	+	0.552098i	0.138981	+	0.990295i	$0.455617\pi$
$314$	−9.68668	−	4.31279i	−0.546651	−	0.243385i
$315$	−0.109280	−	0.436439i	−0.00615725	−	0.0245905i
$316$	3.43940	−	3.09685i	0.193481	−	0.174211i
$317$	11.6973	−	16.0999i	0.656985	−	0.904262i	−0.342392	−	0.939557i	$-0.611237\pi$
$317$	11.6973	−	16.0999i	0.656985	−	0.904262i	0.999377	+	0.0352948i	$0.0112370\pi$
$318$	0.861333	−	25.0242i	0.0483011	−	1.40329i
$319$	19.4205	+	6.20903i	1.08734	+	0.347639i
$320$			0.328270i			0.0183509i
$321$	20.5976	+	16.0760i	1.14964	+	0.897274i
$322$	18.9943	−	4.03736i	1.05851	−	0.224993i
$323$	−13.5950	−	12.2410i	−0.756448	−	0.681109i
$324$	2.56228	+	1.59397i	0.142349	+	0.0885538i
$325$	6.62047	−	16.7574i	0.367238	−	0.929533i
$326$	5.31579	+	16.3603i	0.294415	+	0.906115i
$327$	−2.27385	+	1.90992i	−0.125744	+	0.105619i
$328$	−1.34864	+	12.8314i	−0.0744660	+	0.708497i
$329$	−2.79387	+	4.83913i	−0.154031	+	0.266790i
$330$	0.0345790	+	0.460017i	0.00190351	+	0.0253231i
$331$	−3.02866	+	5.24578i	−0.166470	+	0.288334i	−0.937176	−	0.348856i	$-0.886570\pi$
$331$	−3.02866	+	5.24578i	−0.166470	+	0.288334i	0.770706	+	0.637190i	$0.219904\pi$
$332$	−4.35497	+	1.93896i	−0.239010	+	0.106414i
$333$	−8.49786	−	10.8544i	−0.465680	−	0.594816i
$334$	−11.7660	−	2.50094i	−0.643807	−	0.136845i
$335$	0.0865901	−	0.194485i	0.00473092	−	0.0106258i
$336$	22.4756	−	1.58295i	1.22615	−	0.0863569i
$337$	19.4118	−	6.30729i	1.05743	−	0.343580i	0.271850	−	0.962340i	$-0.412365\pi$
$337$	19.4118	−	6.30729i	1.05743	−	0.343580i	0.785580	+	0.618760i	$0.212365\pi$
$338$	−4.50801	+	19.3479i	−0.245203	+	1.05239i
$339$	−20.9336	−	2.93134i	−1.13696	−	0.159209i
$340$	0.0375224	−	0.0216636i	0.00203494	−	0.00117487i
$341$	3.06467	−	14.7600i	0.165961	−	0.799297i
$342$	−30.6392	+	14.9817i	−1.65678	+	0.810118i
$343$	9.82217	−	13.5191i	0.530348	−	0.729961i
$344$	1.15430	−	1.03934i	0.0622357	−	0.0560373i
$345$	0.111902	+	0.389513i	0.00602460	+	0.0209707i
$346$	−23.3549	+	16.9684i	−1.25557	+	0.912224i
$347$	−0.816640	−	7.76981i	−0.0438395	−	0.417105i	−0.994329	−	0.106348i	$-0.966084\pi$
$347$	−0.816640	−	7.76981i	−0.0438395	−	0.417105i	0.950489	−	0.310757i	$-0.100583\pi$
$348$	−3.46448	−	0.861951i	−0.185716	−	0.0462054i
$349$	−2.00372	−	9.42677i	−0.107257	−	0.504604i	−0.998677	−	0.0514255i	$-0.983624\pi$
$349$	−2.00372	−	9.42677i	−0.107257	−	0.504604i	0.891420	−	0.453178i	$-0.149710\pi$
$350$	12.8102	−	17.6317i	0.684733	−	0.942455i
$351$	16.7625	−	8.36774i	0.894715	−	0.446637i
$352$	−6.19658	−	0.621765i	−0.330279	−	0.0331402i
$353$	11.6933	−	6.75112i	0.622371	−	0.359326i	−0.155421	−	0.987848i	$-0.549673\pi$
$353$	11.6933	−	6.75112i	0.622371	−	0.359326i	0.777791	+	0.628522i	$0.216340\pi$
$354$	0.721427	+	1.78303i	0.0383434	+	0.0947668i
$355$	0.0545344	+	0.0605666i	0.00289438	+	0.00321454i
$356$	1.02406	−	0.332736i	0.0542748	−	0.0176350i
$357$	6.80220	+	10.0738i	0.360010	+	0.533162i
$358$	−17.5081	+	1.84018i	−0.925332	+	0.0972564i
$359$	−6.67287	−	20.5370i	−0.352181	−	1.08390i	−0.957626	−	0.288014i	$-0.907005\pi$
$359$	−6.67287	−	20.5370i	−0.352181	−	1.08390i	0.605445	−	0.795887i	$-0.292995\pi$
$360$	0.0562129	+	0.397093i	0.00296268	+	0.0209286i
$361$	3.79906	−	36.1457i	0.199951	−	1.90240i
$362$	−15.4436	−	26.7491i	−0.811697	−	1.40590i
$363$	19.0466	+	0.475835i	0.999688	+	0.0249748i
$364$	−1.59616	+	3.05865i	−0.0836615	+	0.160317i
$365$	0.392315	+	0.285033i	0.0205347	+	0.0149193i
$366$	−20.1811	+	16.9511i	−1.05488	+	0.886050i
$367$	−15.2330	+	16.9179i	−0.795155	+	0.883110i	−0.995318	−	0.0966531i	$-0.969186\pi$
$367$	−15.2330	+	16.9179i	−0.795155	+	0.883110i	0.200163	+	0.979763i	$0.435853\pi$
$368$	−20.1844	+	2.12146i	−1.05218	+	0.110589i
$369$	0.546208	+	15.2052i	0.0284345	+	0.791553i
$370$	−0.0767204	+	0.360941i	−0.00398850	+	0.0187644i
$371$	−18.0648	−	20.0630i	−0.937879	−	1.04162i
$372$	−0.366052	+	2.61408i	−0.0189789	+	0.135534i
$373$	−8.18735	−	4.72697i	−0.423925	−	0.244753i	0.272830	−	0.962062i	$-0.412040\pi$
$373$	−8.18735	−	4.72697i	−0.423925	−	0.244753i	−0.696755	+	0.717309i	$0.745374\pi$
$374$	−5.12293	−	11.3618i	−0.264900	−	0.587506i
$375$	0.771911	+	0.481807i	0.0398613	+	0.0248804i
$376$	2.92771	−	4.02965i	0.150985	−	0.207813i
$377$	−15.8249	+	15.5197i	−0.815026	+	0.799307i
$378$	22.1592	−	4.74485i	1.13975	−	0.244049i
$379$	−0.488407	−	0.217453i	−0.0250878	−	0.0111698i	0.394154	−	0.919044i	$-0.371038\pi$
$379$	−0.488407	−	0.217453i	−0.0250878	−	0.0111698i	−0.419242	+	0.907874i	$0.637704\pi$
$380$	0.119746	+	0.0533142i	0.00614283	+	0.00273496i
$381$	1.37368	−	0.394639i	0.0703755	−	0.0202180i
$382$	−12.4115	−	4.03274i	−0.635027	−	0.206333i
$383$	11.5605	+	25.9654i	0.590716	+	1.32677i	0.923439	+	0.383745i	$0.125366\pi$
$383$	11.5605	+	25.9654i	0.590716	+	1.32677i	−0.332724	+	0.943024i	$0.607968\pi$
$384$	−23.0255	−	0.792538i	−1.17502	−	0.0404441i
$385$	0.371203	+	0.331077i	0.0189182	+	0.0168733i
$386$	−32.3054	−	18.6515i	−1.64430	−	0.949337i
$387$	1.17600	−	1.40435i	0.0597794	−	0.0713872i
$388$	−0.899579	+	0.191211i	−0.0456692	+	0.00970728i
$389$	0.206020	−	0.0669401i	0.0104456	−	0.00339400i	−0.303790	−	0.952739i	$-0.598252\pi$
$389$	0.206020	−	0.0669401i	0.0104456	−	0.00339400i	0.314235	+	0.949345i	$0.398252\pi$
$390$	−0.459806	−	0.200208i	−0.0232832	−	0.0101379i
$391$	−6.43575	−	8.85804i	−0.325470	−	0.447971i
$392$	1.94847	−	2.16399i	0.0984125	−	0.109298i
$393$	16.7605	+	19.9541i	0.845456	+	1.00655i
$394$	−11.5405	+	5.13817i	−0.581403	+	0.258857i
$395$	0.725367			0.0364972
$396$	−3.33335	+	0.135480i	−0.167507	+	0.00680812i
$397$	−8.84027	+	15.3118i	−0.443681	+	0.768477i	−0.997959	−	0.0638537i	$-0.979661\pi$
$397$	−8.84027	+	15.3118i	−0.443681	+	0.768477i	0.554279	+	0.832331i	$0.312994\pi$
$398$	21.6316	+	15.7163i	1.08430	+	0.787787i
$399$	−12.5600	+	34.5621i	−0.628786	+	1.73027i
$400$	−15.2416	+	16.9275i	−0.762080	+	0.846376i
$401$	−3.39553	+	7.62648i	−0.169565	+	0.380848i	−0.978261	−	0.207378i	$-0.933507\pi$
$401$	−3.39553	+	7.62648i	−0.169565	+	0.380848i	0.808696	+	0.588226i	$0.200174\pi$
$402$	9.64010	+	4.69583i	0.480805	+	0.234207i
$403$	12.6348	+	10.4368i	0.629387	+	0.519895i
$404$	1.74520	−	5.37118i	0.0868270	−	0.267226i
$405$	0.131271	+	0.454365i	0.00652292	+	0.0225776i
$406$	−23.2186	+	13.4052i	−1.15232	+	0.665291i
$407$	14.5162	+	4.64106i	0.719542	+	0.230049i
$408$	−5.09162	−	9.56440i	−0.252073	−	0.473508i
$409$	−1.30659	−	2.93464i	−0.0646065	−	0.145109i	0.878357	−	0.478006i	$-0.158640\pi$
$409$	−1.30659	−	2.93464i	−0.0646065	−	0.145109i	−0.942963	+	0.332898i	$0.891974\pi$
$410$	0.302668	−	0.272523i	0.0149477	−	0.0134590i
$411$	−24.0915	−	23.2417i	−1.18835	−	1.14643i
$412$	0.289971	+	2.75889i	0.0142859	+	0.135921i
$413$	1.89459	+	0.843526i	0.0932267	+	0.0415072i
$414$	−19.8015	+	4.95812i	−0.973192	+	0.243678i
$415$	−0.710575	−	0.230880i	−0.0348808	−	0.0113334i
$416$	3.74244	−	5.64181i	0.183488	−	0.276613i
$417$	30.7388	−	16.3638i	1.50529	−	0.801341i
$418$	18.6986	−	32.7425i	0.914579	−	1.60149i
$419$	27.3952	−	15.8166i	1.33834	−	0.772693i	0.351782	−	0.936082i	$-0.385576\pi$
$419$	27.3952	−	15.8166i	1.33834	−	0.772693i	0.986562	+	0.163389i	$0.0522426\pi$
$420$	−0.0686579	−	0.0535861i	−0.00335016	−	0.00261473i
$421$	−9.81469	+	30.2065i	−0.478339	+	1.47217i	0.363063	+	0.931765i	$0.381731\pi$
$421$	−9.81469	+	30.2065i	−0.478339	+	1.47217i	−0.841402	+	0.540410i	$0.818269\pi$
$422$	−3.18794	+	14.9981i	−0.155186	+	0.730095i
$423$	2.75241	−	5.18905i	0.133827	−	0.252300i
$424$	14.1454	+	19.4694i	0.686959	+	0.945519i
$425$	−12.0200	−	2.55492i	−0.583054	−	0.123932i
$426$	−3.14334	+	2.64026i	−0.152295	+	0.127921i
$427$	−2.97038	+	28.2613i	−0.143747	+	1.36766i
$428$	5.05795			0.244485
$429$	−10.1233	+	18.0698i	−0.488760	+	0.872418i
$430$	−0.0490318			−0.00236452
$431$	−0.875315	+	8.32807i	−0.0421624	+	0.401149i	0.953005	+	0.302955i	$0.0979732\pi$
$431$	−0.875315	+	8.32807i	−0.0421624	+	0.401149i	−0.995167	+	0.0981938i	$0.968693\pi$
$432$	−23.5514	+	2.51109i	−1.13312	+	0.120815i
$433$	−12.8492	−	2.73118i	−0.617492	−	0.131252i	−0.111463	−	0.993769i	$-0.535554\pi$
$433$	−12.8492	−	2.73118i	−0.617492	−	0.131252i	−0.506029	+	0.862517i	$0.668887\pi$
$434$	11.6514	+	16.0368i	0.559287	+	0.769793i
$435$	−0.313121	−	0.463721i	−0.0150130	−	0.0222337i
$436$	−0.119517	+	0.562282i	−0.00572381	+	0.0269284i
$437$	10.2360	−	31.5033i	0.489656	−	1.50701i
$438$	−15.0280	+	19.2548i	−0.718066	+	0.920031i
$439$	−2.27093	+	1.31112i	−0.108386	+	0.0625764i	−0.553213	−	0.833040i	$-0.686598\pi$
$439$	−2.27093	+	1.31112i	−0.108386	+	0.0625764i	0.444827	+	0.895616i	$0.353265\pi$
$440$	−0.298229	−	0.328093i	−0.0142175	−	0.0156412i
$441$	1.91740	−	2.84880i	0.0913045	−	0.135657i
$442$	13.5230	+	0.840813i	0.643223	+	0.0399934i
$443$	−2.11058	−	0.685770i	−0.100277	−	0.0325819i	0.258449	−	0.966025i	$-0.416789\pi$
$443$	−2.11058	−	0.685770i	−0.100277	−	0.0325819i	−0.358726	+	0.933443i	$0.616789\pi$
$444$	−2.58959	−	0.644281i	−0.122896	−	0.0305762i
$445$	0.154169	+	0.0686404i	0.00730830	+	0.00325387i
$446$	3.99574	+	38.0169i	0.189204	+	1.80015i
$447$	−17.8205	+	18.4721i	−0.842878	+	0.873700i
$448$	−13.2486	+	11.9291i	−0.625939	+	0.563598i
$449$	−8.62088	−	19.3628i	−0.406844	−	0.913787i	−0.994506	−	0.104680i	$-0.966618\pi$
$449$	−8.62088	−	19.3628i	−0.406844	−	0.913787i	0.587662	−	0.809107i	$-0.300049\pi$
$450$	−12.7920	+	19.0059i	−0.603021	+	0.895947i
$451$	−9.95110	−	13.5616i	−0.468579	−	0.638591i
$452$	−3.54365	+	2.04593i	−0.166679	+	0.0962324i
$453$	−5.70895	−	14.1098i	−0.268230	−	0.662937i
$454$	−0.654671	+	2.01487i	−0.0307252	+	0.0945626i
$455$	−0.506675	+	0.188855i	−0.0237533	+	0.00885366i
$456$	14.3550	−	29.4696i	0.672236	−	1.38004i
$457$	−0.794108	+	1.78360i	−0.0371468	+	0.0834331i	−0.931166	−	0.364596i	$-0.881207\pi$
$457$	−0.794108	+	1.78360i	−0.0371468	+	0.0834331i	0.894019	+	0.448029i	$0.147874\pi$
$458$	10.2148	−	11.3447i	0.477308	−	0.530104i
$459$	−7.52601	−	10.3260i	−0.351284	−	0.481978i
$460$	0.0634689	+	0.0461128i	0.00295925	+	0.00215002i
$461$	−19.4303	+	33.6543i	−0.904961	+	1.56744i	−0.0839910	+	0.996467i	$0.526767\pi$
$461$	−19.4303	+	33.6543i	−0.904961	+	1.56744i	−0.820970	+	0.570972i	$0.806567\pi$
$462$	−17.3092	+	18.1123i	−0.805298	+	0.842660i
$463$	9.49669			0.441348			0.220674	−	0.975348i	$-0.429174\pi$
$463$	9.49669			0.441348			0.220674	+	0.975348i	$0.429174\pi$
$464$	25.5987	−	11.3973i	1.18839	−	0.529105i
$465$	−0.316779	+	0.266080i	−0.0146903	+	0.0123391i
$466$	11.5162	−	12.7901i	0.533479	−	0.592488i
$467$	4.34077	+	5.97456i	0.200867	+	0.276470i	0.897553	−	0.440906i	$-0.145343\pi$
$467$	4.34077	+	5.97456i	0.200867	+	0.276470i	−0.696686	+	0.717376i	$0.745343\pi$
$468$	1.56138	−	3.27341i	0.0721746	−	0.151313i
$469$	10.9958	−	3.57276i	0.507739	−	0.164975i
$470$	−0.153796	+	0.0326904i	−0.00709409	+	0.00150790i
$471$	11.1407	−	4.50762i	0.513337	−	0.207700i
$472$	−1.60099	−	0.924332i	−0.0736915	−	0.0425458i
$473$	−0.202177	+	2.01492i	−0.00929611	+	0.0926461i
$474$	−1.25682	+	36.5142i	−0.0577275	+	1.67715i
$475$	−15.1210	−	33.9624i	−0.693801	−	1.55830i
$476$	2.23786	+	0.727124i	0.102572	+	0.0333277i
$477$	19.7346	+	20.3949i	0.903585	+	0.933819i
$478$	4.35721	+	1.93995i	0.199294	+	0.0887314i
$479$	−11.1643	−	4.97066i	−0.510109	−	0.227115i	0.135508	−	0.990776i	$-0.456733\pi$
$479$	−11.1643	−	4.97066i	−0.510109	−	0.227115i	−0.645618	+	0.763661i	$0.723400\pi$
$480$	0.123000	+	0.118661i	0.00561417	+	0.00541611i
$481$	−11.8287	+	11.6005i	−0.539340	+	0.528938i
$482$	−23.3863	+	32.1884i	−1.06521	+	1.46614i
$483$	−11.6539	+	18.6709i	−0.530270	+	0.849554i
$484$	2.96324	−	2.19590i	0.134693	−	0.0998138i
$485$	−0.124829	−	0.0720699i	−0.00566818	−	0.00327253i
$486$	−23.0997	+	5.82079i	−1.04782	+	0.264036i
$487$	17.3609	+	19.2813i	0.786698	+	0.873717i	0.994530	−	0.104447i	$-0.0333074\pi$
$487$	17.3609	+	19.2813i	0.786698	+	0.873717i	−0.207832	+	0.978165i	$0.566641\pi$
$488$	5.26659	−	24.7774i	0.238407	−	1.12162i
$489$	−17.5284	−	8.53832i	−0.792661	−	0.386116i
$490$	−0.0914174	+	0.00960835i	−0.00412982	+	0.000434061i
$491$	6.09468	−	6.76883i	0.275049	−	0.305473i	−0.589755	−	0.807582i	$-0.700776\pi$
$491$	6.09468	−	6.76883i	0.275049	−	0.305473i	0.864804	+	0.502109i	$0.167442\pi$
$492$	1.89435	+	2.25530i	0.0854038	+	0.101677i
$493$	12.2299	+	8.88557i	0.550809	+	0.400186i
$494$	21.9891	+	34.5930i	0.989337	+	1.55641i
$495$	−0.402451	−	0.333795i	−0.0180888	−	0.0150030i
$496$	−10.3589	−	17.9422i	−0.465129	−	0.805627i
$497$	−0.462658	+	4.40189i	−0.0207530	+	0.197452i
$498$	12.8534	−	35.3695i	0.575976	−	1.58495i
$499$	−4.92897	−	15.1698i	−0.220651	−	0.679094i	−0.998704	−	0.0508954i	$-0.983793\pi$
$499$	−4.92897	−	15.1698i	−0.220651	−	0.679094i	0.778053	−	0.628199i	$-0.216207\pi$
$500$	0.175181	−	0.0184122i	0.00783431	−	0.000823420i
$501$	11.2991	−	7.62954i	0.504805	−	0.340863i
$502$	11.1510	−	3.62317i	0.497693	−	0.161710i
$503$	14.7874	+	16.4230i	0.659335	+	0.732266i	0.976360	−	0.216151i	$-0.0693504\pi$
$503$	14.7874	+	16.4230i	0.659335	+	0.732266i	−0.317024	+	0.948417i	$0.602684\pi$
$504$	−13.9835	+	16.6988i	−0.622874	+	0.743823i
$505$	0.766555	−	0.442571i	0.0341112	−	0.0196941i
$506$	15.0212	−	16.8417i	0.667774	−	0.748706i
$507$	−12.2347	−	18.9027i	−0.543364	−	0.839497i
$508$	0.162624	−	0.223832i	0.00721526	−	0.00993096i
$509$	4.87026	+	22.9128i	0.215871	+	1.01559i	0.943948	+	0.330096i	$0.107081\pi$
$509$	4.87026	+	22.9128i	0.215871	+	1.01559i	−0.728077	+	0.685495i	$0.759586\pi$
$510$	−0.0825797	+	0.331916i	−0.00365669	+	0.0146975i
$511$	2.75282	+	26.1913i	0.121777	+	1.15863i
$512$	11.8380	−	8.60079i	0.523169	−	0.380105i
$513$	11.8903	−	36.7822i	0.524968	−	1.62397i
$514$	−14.6580	+	13.1982i	−0.646539	+	0.582146i
$515$	−0.255557	+	0.351744i	−0.0112612	+	0.0154997i
$516$	0.0121975	−	0.354373i	0.000536966	−	0.0156004i
$517$	0.709223	+	6.45493i	0.0311916	+	0.283887i
$518$	−17.3551	+	10.0200i	−0.762541	+	0.440253i
$519$	4.53751	−	32.4037i	0.199175	−	1.42236i
$520$	0.466773	−	0.120213i	0.0204694	−	0.00527168i
$521$	−0.455193	+	0.147901i	−0.0199424	+	0.00647967i	−0.318971	−	0.947764i	$-0.603337\pi$
$521$	−0.455193	+	0.147901i	−0.0199424	+	0.00647967i	0.299029	+	0.954244i	$0.403337\pi$
$522$	23.8857	−	14.9587i	1.04545	−	0.654724i
$523$	4.07927	−	9.16218i	0.178374	−	0.400634i	−0.802126	−	0.597155i	$-0.796298\pi$
$523$	4.07927	−	9.16218i	0.178374	−	0.400634i	0.980500	+	0.196521i	$0.0629643\pi$
$524$	4.93431	+	1.04882i	0.215556	+	0.0458179i
$525$	4.30157	+	24.3243i	0.187736	+	1.06160i
$526$	5.87183	−	2.61431i	0.256024	−	0.113989i
$527$	5.58847	−	9.67952i	0.243438	−	0.421646i
$528$	19.9706	−	16.9355i	0.869107	−	0.737024i
$529$	−1.58728	+	2.74924i	−0.0690120	+	0.119532i
$530$	0.0794076	−	0.755512i	0.00344924	−	0.0328174i
$531$	−2.02214	−	0.814646i	−0.0877534	−	0.0353526i
$532$	2.19977	+	6.77021i	0.0953723	+	0.293526i
$533$	18.0881	−	2.68460i	0.783481	−	0.116283i
$534$	−3.72240	+	7.64176i	−0.161084	+	0.330691i
$535$	0.589111	+	0.530438i	0.0254695	+	0.0229328i
$536$	−10.0809	+	2.14275i	−0.435427	+	0.0925529i
$537$	12.2766	−	15.7296i	0.529775	−	0.678781i
$538$		−	32.8276i		−	1.41530i
$539$	0.0178979	+	3.79634i	0.000770917	+	0.163520i
$540$	0.0741487	+	0.0537024i	0.00319085	+	0.00231098i
$541$	−15.7922	+	21.7361i	−0.678960	+	0.934508i	−0.999921	−	0.0125841i	$-0.995994\pi$
$541$	−15.7922	+	21.7361i	−0.678960	+	0.934508i	0.320961	+	0.947093i	$0.395994\pi$
$542$	−4.38709	+	3.95016i	−0.188442	+	0.169674i
$543$	33.9724	+	8.45223i	1.45790	+	0.362720i
$544$	−4.21823	−	1.87808i	−0.180855	−	0.0805218i
$545$	−0.0728881	+	0.0529563i	−0.00312218	+	0.00226840i
$546$	−8.62885	−	25.8327i	−0.369281	−	1.10554i
$547$	−42.0171	−	13.6522i	−1.79652	−	0.583725i	−0.796735	−	0.604329i	$-0.793441\pi$
$547$	−42.0171	−	13.6522i	−1.79652	−	0.583725i	−0.999788	+	0.0206039i	$0.993441\pi$
$548$	−6.44460	−	0.677354i	−0.275299	−	0.0289351i
$549$	2.05395	−	29.8012i	0.0876603	−	1.27188i
$550$	−0.119407	−	25.3275i	−0.00509152	−	1.07997i
$551$			45.7337i			1.94832i
$552$	12.0710	−	15.4662i	0.513778	−	0.658284i
$553$	26.3594	+	29.2750i	1.12091	+	1.24490i
$554$	35.3664	−	11.4913i	1.50258	−	0.488217i
$555$	−0.234048	−	0.346617i	−0.00993480	−	0.0147131i
$556$	2.74184	−	6.15827i	0.116280	−	0.261169i
$557$	−21.5565	+	23.9409i	−0.913379	+	1.01441i	0.0864560	+	0.996256i	$0.472446\pi$
$557$	−21.5565	+	23.9409i	−0.913379	+	1.01441i	−0.999835	+	0.0181547i	$0.994221\pi$
$558$	−12.8453	−	16.4073i	−0.543784	−	0.694578i
$559$	−1.83453	−	1.21691i	−0.0775922	−	0.0514700i
$560$	0.683591			0.0288870
$561$	13.2993	+	4.76216i	0.561497	+	0.201059i
$562$	−8.88919	−	15.3965i	−0.374968	−	0.649463i
$563$	−30.9483	+	13.7791i	−1.30431	+	0.580718i	−0.936984	−	0.349372i	$-0.886395\pi$
$563$	−30.9483	+	13.7791i	−1.30431	+	0.580718i	−0.367330	+	0.930091i	$0.619728\pi$
$564$	−0.198008	−	1.11968i	−0.00833764	−	0.0471472i
$565$	−0.627298	−	0.133336i	−0.0263906	−	0.00560950i
$566$	−3.32072	+	0.349022i	−0.139580	+	0.0146705i
$567$	−13.5673	+	21.8093i	−0.569775	+	0.915903i
$568$	0.820308	−	3.85924i	0.0344193	−	0.161930i
$569$	2.02808	−	0.431082i	0.0850217	−	0.0180719i	−0.165204	−	0.986259i	$-0.552828\pi$
$569$	2.02808	−	0.431082i	0.0850217	−	0.0180719i	0.250226	+	0.968187i	$0.419495\pi$
$570$	−0.959219	+	0.388108i	−0.0401773	+	0.0162560i
$571$			3.26576i			0.136668i	0.997663	+	0.0683340i	$0.0217683\pi$
$571$			3.26576i			0.136668i	−0.997663	+	0.0683340i	$0.978232\pi$
$572$	0.607326	+	3.96323i	0.0253936	+	0.165711i
$573$	13.0565	−	6.95065i	0.545443	−	0.290367i
$574$	21.9975	+	2.31203i	0.918157	+	0.0965022i
$575$	−4.62616	−	21.7644i	−0.192924	−	0.907637i
$576$	13.4678	−	13.0318i	0.561158	−	0.542990i
$577$	−7.13010	+	5.18032i	−0.296830	+	0.215660i	−0.726225	−	0.687457i	$-0.758727\pi$
$577$	−7.13010	+	5.18032i	−0.296830	+	0.215660i	0.429395	+	0.903117i	$0.358727\pi$
$578$	1.74960	+	16.6464i	0.0727739	+	0.692397i
$579$	40.6362	−	11.6742i	1.68878	−	0.485165i
$580$	−0.103014	−	0.0334712i	−0.00427742	−	0.00138982i
$581$	−16.5038	−	37.0681i	−0.684691	−	1.53784i
$582$	3.84420	−	6.15887i	0.159347	−	0.255293i
$583$	−30.7197	−	6.37846i	−1.27228	−	0.264169i
$584$		−	23.4755i		−	0.971424i
$585$	0.525146	−	0.217517i	0.0217121	−	0.00899321i
$586$	−3.33577	+	10.2664i	−0.137799	+	0.424103i
$587$	−21.6147	−	19.4620i	−0.892135	−	0.803282i	0.0891152	−	0.996021i	$-0.471596\pi$
$587$	−21.6147	−	19.4620i	−0.892135	−	0.803282i	−0.981250	+	0.192740i	$0.938263\pi$
$588$	−0.0467020	−	0.663103i	−0.00192596	−	0.0273459i
$589$	33.6285	−	3.53449i	1.38564	−	0.145636i
$590$	0.0180332	+	0.0555004i	0.000742414	+	0.00228492i
$591$	4.89035	−	13.4571i	0.201162	−	0.553550i
$592$	19.1342	−	8.51910i	0.786412	−	0.350133i
$593$	16.9869			0.697569			0.348784	−	0.937203i	$-0.386595\pi$
$593$	16.9869			0.697569			0.348784	+	0.937203i	$0.386595\pi$
$594$	17.5002	−	19.6806i	0.718042	−	0.807503i
$595$	0.184393	+	0.319379i	0.00755939	+	0.0130933i
$596$	−0.519359	+	4.94137i	−0.0212738	+	0.202406i
$597$	−29.8425	+	5.27743i	−1.22137	+	0.215991i
$598$	8.56848	+	22.9882i	0.350391	+	0.940058i
$599$	7.74682	+	10.6626i	0.316527	+	0.435661i	0.937403	−	0.348247i	$-0.113223\pi$
$599$	7.74682	+	10.6626i	0.316527	+	0.435661i	−0.620876	+	0.783909i	$0.713223\pi$
$600$	−1.54696	−	21.9647i	−0.0631544	−	0.896705i
$601$	34.0999	+	30.7037i	1.39096	+	1.25243i	0.931260	+	0.364356i	$0.118711\pi$
$601$	34.0999	+	30.7037i	1.39096	+	1.25243i	0.459703	+	0.888073i	$0.347956\pi$
$602$	−1.78178	−	1.97887i	−0.0726200	−	0.0806526i
$603$	−11.4165	+	4.16821i	−0.464916	+	0.169743i
$604$	−2.55173	−	1.47324i	−0.103828	−	0.0599454i
$605$	0.575424	+	0.0549992i	0.0233943	+	0.00223604i
$606$	20.9503	+	39.3543i	0.851049	+	1.59866i
$607$	−2.68804	−	6.03744i	−0.109104	−	0.245052i	0.850739	−	0.525588i	$-0.176155\pi$
$607$	−2.68804	−	6.03744i	−0.109104	−	0.245052i	−0.959844	+	0.280536i	$0.909488\pi$
$608$	−2.90435	−	13.6639i	−0.117787	−	0.554143i
$609$	7.33665	−	29.4885i	0.297296	−	1.19494i
$610$	−0.646904	+	0.470004i	−0.0261924	+	0.0190299i
$611$	−6.56564	−	2.59394i	−0.265617	−	0.104940i
$612$	−2.37836	−	0.679409i	−0.0961394	−	0.0274635i
$613$	6.56254	+	30.8743i	0.265058	+	1.24700i	0.886200	+	0.463303i	$0.153336\pi$
$613$	6.56254	+	30.8743i	0.265058	+	1.24700i	−0.621141	+	0.783699i	$0.713331\pi$
$614$	17.1693	+	1.80457i	0.692898	+	0.0728265i
$615$	−0.0158795	+	0.461345i	−0.000640322	+	0.0186032i
$616$	2.40403	−	23.9589i	0.0968612	−	0.965330i
$617$	28.0280	+	16.1820i	1.12837	+	0.651462i	0.943523	−	0.331306i	$-0.107489\pi$
$617$	28.0280	+	16.1820i	1.12837	+	0.651462i	0.184843	+	0.982768i	$0.440822\pi$
$618$	−17.2636	−	13.4739i	−0.694445	−	0.542000i
$619$	2.47895	−	7.62943i	0.0996375	−	0.306653i	−0.888797	−	0.458301i	$-0.848458\pi$
$619$	2.47895	−	7.62943i	0.0996375	−	0.306653i	0.988434	+	0.151648i	$0.0484581\pi$
$620$	−0.0166504	+	0.0783340i	−0.000668696	+	0.00314597i
$621$	11.5381	−	20.0539i	0.463006	−	0.804737i
$622$	−4.65421	+	10.4535i	−0.186617	+	0.419148i
$623$	2.83214	+	8.71643i	0.113467	+	0.349216i
$624$	6.14694	+	27.7941i	0.246074	+	1.11265i
$625$	−20.1919	−	14.6703i	−0.807677	−	0.586812i
$626$	−12.6973	−	21.9923i	−0.507485	−	0.878989i
$627$	11.9937	+	41.0186i	0.478984	+	1.63813i
$628$	1.16323	−	2.01477i	0.0464179	−	0.0803982i
$629$	9.14150	+	6.64168i	0.364495	+	0.264821i
$630$	0.680753	−	0.0963682i	0.0271219	−	0.00383940i
$631$	14.2018	+	3.01868i	0.565364	+	0.120172i	0.481722	−	0.876324i	$-0.340011\pi$
$631$	14.2018	+	3.01868i	0.565364	+	0.120172i	0.0836419	+	0.996496i	$0.473345\pi$
$632$	−20.6403	−	28.4089i	−0.821025	−	1.13004i
$633$	−9.72534	−	14.4029i	−0.386548	−	0.572462i
$634$	22.6001	+	20.3492i	0.897565	+	0.808171i
$635$	0.0424149	−	0.00901558i	0.00168319	−	0.000357772i
$636$	5.44066	+	0.761860i	0.215736	+	0.0302097i
$637$	−3.65886	−	1.90938i	−0.144969	−	0.0756524i
$638$	−12.5386	+	28.5234i	−0.496409	+	1.12925i
$639$	0.319917	−	4.64174i	0.0126557	−	0.183625i
$640$	−0.695170	−	0.0730653i	−0.0274790	−	0.00288816i
$641$	5.78185	−	5.20600i	0.228369	−	0.205625i	−0.547000	−	0.837132i	$-0.684230\pi$
$641$	5.78185	−	5.20600i	0.228369	−	0.205625i	0.775369	+	0.631508i	$0.217564\pi$
$642$	−27.7224	+	28.7361i	−1.09412	+	1.13412i
$643$	−3.27492	−	31.1587i	−0.129150	−	1.22878i	−0.846622	−	0.532194i	$-0.821368\pi$
$643$	−3.27492	−	31.1587i	−0.129150	−	1.22878i	0.717472	−	0.696587i	$-0.245299\pi$
$644$	0.445352	+	4.23724i	0.0175493	+	0.166971i
$645$	0.0385846	−	0.0399955i	0.00151927	−	0.00157482i
$646$	20.7755	−	18.7063i	0.817400	−	0.735990i
$647$	11.3485	+	1.19277i	0.446155	+	0.0468928i	0.324943	−	0.945734i	$-0.394655\pi$
$647$	11.3485	+	1.19277i	0.446155	+	0.0468928i	0.121213	+	0.992627i	$0.461322\pi$
$648$	14.0598	−	18.0701i	0.552321	−	0.709861i
$649$	2.35510	−	0.512208i	0.0924458	−	0.0201059i
$650$	24.4103	+	12.7385i	0.957449	+	0.499646i
$651$	−22.2502	−	3.11572i	−0.872055	−	0.122115i
$652$	−3.69182	+	0.784721i	−0.144583	+	0.0307321i
$653$	−14.1970	−	12.7830i	−0.555572	−	0.500239i	0.342840	−	0.939394i	$-0.388611\pi$
$653$	−14.1970	−	12.7830i	−0.555572	−	0.500239i	−0.898411	+	0.439155i	$0.855278\pi$
$654$	−2.53947	−	3.76086i	−0.0993012	−	0.147061i
$655$	0.464718	+	0.639630i	0.0181580	+	0.0249924i
$656$	−22.6124	−	4.80640i	−0.882864	−	0.187659i
$657$	−3.88028	−	27.4106i	−0.151384	−	1.06939i
$658$	−6.90820	−	5.01910i	−0.269310	−	0.195665i
$659$	12.8196	−	22.2042i	0.499380	−	0.864951i	−0.500620	−	0.865667i	$-0.666895\pi$
$659$	12.8196	−	22.2042i	0.499380	−	0.864951i	1.00000		0.000716157i	$0.000227960\pi$
$660$	−0.101171	−	0.00300485i	−0.00393808	−	0.000116964i
$661$	−18.3069	−	31.7084i	−0.712054	−	1.23331i	−0.964085	−	0.265594i	$-0.914432\pi$
$661$	−18.3069	−	31.7084i	−0.712054	−	1.23331i	0.252031	−	0.967719i	$-0.418902\pi$
$662$	−7.48873	−	5.44088i	−0.291058	−	0.211466i
$663$	−11.3275	+	10.3691i	−0.439924	+	0.402704i
$664$	11.1770	+	34.3992i	0.433751	+	1.33495i
$665$	−0.453793	+	1.01924i	−0.0175974	+	0.0395243i
$666$	17.8538	−	11.1812i	0.691822	−	0.433261i
$667$	−5.69100	+	26.7740i	−0.220356	+	1.03669i
$668$	0.815563	−	2.51005i	0.0315551	−	0.0971166i
$669$	−34.1550	−	26.6573i	−1.32051	−	1.03063i
$670$	0.281745	+	0.162666i	0.0108848	+	0.00628432i
$671$	16.6470	+	28.5220i	0.642649	+	1.10108i
$672$	−0.319287	+	9.27622i	−0.0123168	+	0.357838i
$673$	−49.5419	−	5.20707i	−1.90970	−	0.200718i	−0.925622	−	0.378449i	$-0.876458\pi$
$673$	−49.5419	−	5.20707i	−1.90970	−	0.200718i	−0.984079	+	0.177731i	$0.943124\pi$
$674$	6.48499	+	30.5095i	0.249793	+	1.17518i
$675$	−5.43683	−	25.3909i	−0.209264	−	0.977294i
$676$	−4.11843	−	1.42740i	−0.158401	−	0.0549000i
$677$	−0.177353	+	0.128854i	−0.00681621	+	0.00495227i	−0.591188	−	0.806534i	$-0.701341\pi$
$677$	−0.177353	+	0.128854i	−0.00681621	+	0.00495227i	0.584372	+	0.811486i	$0.301341\pi$
$678$	7.79890	−	31.3465i	0.299515	−	1.20385i
$679$	−1.62753	−	7.65692i	−0.0624588	−	0.293846i
$680$	−0.133709	−	0.300316i	−0.00512751	−	0.0115166i
$681$	−1.12836	−	2.11958i	−0.0432389	−	0.0812226i
$682$	21.9426	+	7.01538i	0.840224	+	0.268633i
$683$	−26.7368	−	15.4365i	−1.02306	−	0.590662i	−0.108069	−	0.994143i	$-0.534467\pi$
$683$	−26.7368	−	15.4365i	−1.02306	−	0.590662i	−0.914988	+	0.403481i	$0.867800\pi$
$684$	−2.56640	−	7.02924i	−0.0981287	−	0.268770i
$685$	−0.679581	−	0.754752i	−0.0259655	−	0.0288376i
$686$	18.9772	+	17.0872i	0.724554	+	0.652391i
$687$	1.21560	+	17.2598i	0.0463780	+	0.658503i
$688$	1.63586	+	2.25156i	0.0623664	+	0.0858400i
$689$	21.7220	−	26.2968i	0.827543	−	1.00183i
$690$	−0.609854	+	0.107848i	−0.0232168	+	0.00410572i
$691$	−1.80033	+	17.1290i	−0.0684879	+	0.651619i	0.905395	+	0.424569i	$0.139575\pi$
$691$	−1.80033	+	17.1290i	−0.0684879	+	0.651619i	−0.973883	+	0.227049i	$0.927092\pi$
$692$	−3.16695	−	5.48532i	−0.120389	−	0.208521i
$693$	−1.15316	−	28.3724i	−0.0438049	−	1.07778i
$694$	11.9390			0.453197
$695$	0.965179	−	0.429725i	0.0366113	−	0.0163004i
$696$	−9.25170	+	25.4585i	−0.350685	+	0.965001i
$697$	−3.85392	−	11.8611i	−0.145978	−	0.449273i
$698$	14.6468	−	1.53944i	0.554390	−	0.0582688i
$699$	1.37047	+	19.4587i	0.0518359	+	0.735997i
$700$	3.55354	+	3.19962i	0.134311	+	0.120934i
$701$	−11.6320	+	35.7995i	−0.439333	+	1.35213i	0.449248	+	0.893407i	$0.351692\pi$
$701$	−11.6320	+	35.7995i	−0.439333	+	1.35213i	−0.888581	+	0.458721i	$0.848308\pi$
$702$	10.0397	+	26.8122i	0.378922	+	1.01196i
$703$			34.1845i			1.28929i
$704$	−4.21202	+	20.2858i	−0.158747	+	0.764550i
$705$	0.0943612	−	0.151178i	0.00355385	−	0.00569368i
$706$	8.39247	+	18.8498i	0.315855	+	0.709421i
$707$	45.7177	+	14.8546i	1.71939	+	0.558664i
$708$	−0.405611	+	0.116527i	−0.0152438	+	0.00437934i
$709$	−4.28213	−	40.7418i	−0.160819	−	1.53009i	−0.715846	−	0.698258i	$-0.753959\pi$
$709$	−4.28213	−	40.7418i	−0.160819	−	1.53009i	0.555028	−	0.831832i	$-0.312708\pi$
$710$	−0.100760	+	0.0732063i	−0.00378145	+	0.00274738i
$711$	−28.7958	−	29.7593i	−1.07993	−	1.11606i
$712$	−1.69857	−	7.99115i	−0.0636567	−	0.299481i
$713$	20.1271	+	2.11544i	0.753764	+	0.0792238i
$714$	−16.3967	+	8.72878i	−0.613630	+	0.326666i
$715$	−0.344895	+	0.525298i	−0.0128984	+	0.0196450i
$716$		−	3.86256i		−	0.144351i
$717$	−5.01125	+	2.02759i	−0.187149	+	0.0757219i
$718$	32.2779	−	6.86088i	1.20460	−	0.256046i
$719$	−8.78574	+	41.3336i	−0.327653	+	1.54148i	0.438443	+	0.898759i	$0.355530\pi$
$719$	−8.78574	+	41.3336i	−0.327653	+	1.54148i	−0.766096	+	0.642726i	$0.777803\pi$
$720$	−0.718127	+	0.0257968i	−0.0267630	+	0.000961392i
$721$	−23.4828	+	2.46814i	−0.874545	+	0.0919184i
$722$	54.3271	+	11.5476i	2.02185	+	0.429757i
$723$	−7.85295	−	44.4064i	−0.292054	−	1.65149i
$724$	6.19098	−	2.75640i	0.230086	−	0.102441i
$725$	15.3602	+	26.6047i	0.570465	+	0.988074i
$726$	−3.76562	+	28.8709i	−0.139755	+	1.07150i
$727$	13.2304			0.490687			0.245343	−	0.969436i	$-0.421099\pi$
$727$	13.2304			0.490687			0.245343	+	0.969436i	$0.421099\pi$
$728$	21.8139	+	14.4700i	0.808476	+	0.536294i
$729$	13.4298	−	23.4231i	0.497399	−	0.867522i
$730$	−0.495859	+	0.550707i	−0.0183526	+	0.0203826i
$731$	−0.610687	+	1.37163i	−0.0225871	+	0.0507314i
$732$	−3.23599	−	4.79238i	−0.119606	−	0.177131i
$733$	28.6806	−	9.31891i	1.05934	−	0.344202i	0.273015	−	0.962010i	$-0.411979\pi$
$733$	28.6806	−	9.31891i	1.05934	−	0.344202i	0.786329	+	0.617808i	$0.211979\pi$
$734$	−23.2785	−	25.8534i	−0.859226	−	0.954267i
$735$	0.0641015	−	0.0821309i	0.00236442	−	0.00302944i
$736$		−	8.36070i		−	0.308180i
$737$	7.84635	−	10.9073i	0.289024	−	0.401777i
$738$	−23.1961	−	1.59871i	−0.853859	−	0.0588493i
$739$	1.31190	+	0.137887i	0.0482591	+	0.00507224i	0.128627	−	0.991693i	$-0.458943\pi$
$739$	1.31190	+	0.137887i	0.0482591	+	0.00507224i	−0.0803681	+	0.996765i	$0.525610\pi$
$740$	−0.0769997	−	0.0250187i	−0.00283056	−	0.000919706i
$741$	−45.5217	−	9.28566i	−1.67228	−	0.341117i
$742$	33.3773	−	24.2500i	1.22532	−	0.890246i
$743$	−19.1669	−	8.53368i	−0.703167	−	0.313070i	0.0238248	−	0.999716i	$-0.492416\pi$
$743$	−19.1669	−	8.53368i	−0.703167	−	0.313070i	−0.726992	+	0.686646i	$0.759082\pi$
$744$	19.4349	+	4.83534i	0.712518	+	0.177272i
$745$	−0.578703	+	0.521067i	−0.0212020	+	0.0190904i
$746$	8.49184	−	11.6880i	0.310908	−	0.427929i
$747$	18.7364	+	38.3180i	0.685529	+	1.40198i
$748$	2.59670	−	0.857275i	0.0949448	−	0.0313451i
$749$			43.0516i			1.57307i
$750$	−0.855550	+	1.09618i	−0.0312403	+	0.0400270i
$751$	5.63220	−	1.19716i	0.205522	−	0.0436850i	−0.104000	−	0.994577i	$-0.533164\pi$
$751$	5.63220	−	1.19716i	0.205522	−	0.0436850i	0.309522	+	0.950892i	$0.399831\pi$
$752$	6.63229	+	5.97174i	0.241855	+	0.217767i
$753$	−5.81960	+	11.9471i	−0.212078	+	0.435377i
$754$	−21.0590	−	26.5297i	−0.766923	−	0.966156i
$755$	−0.142704	−	0.439197i	−0.00519353	−	0.0159840i
$756$	0.527145	+	4.94407i	0.0191721	+	0.179814i
$757$	−2.24737	+	21.3823i	−0.0816819	+	0.777151i	0.874628	+	0.484795i	$0.161106\pi$
$757$	−2.24737	+	21.3823i	−0.0816819	+	0.777151i	−0.956310	+	0.292356i	$0.905561\pi$
$758$	0.408500	−	0.707543i	0.0148374	−	0.0256991i
$759$	1.91727	+	25.5062i	0.0695925	+	0.925815i
$760$	0.497265	−	0.861288i	0.0180377	−	0.0312422i
$761$	−43.9517	+	19.5686i	−1.59325	+	0.709360i	−0.995714	−	0.0924838i	$-0.970519\pi$
$761$	−43.9517	+	19.5686i	−1.59325	+	0.709360i	−0.597534	+	0.801844i	$0.703853\pi$
$762$	0.380343	+	2.15074i	0.0137784	+	0.0779132i
$763$	−4.78596	−	1.01729i	−0.173263	−	0.0368283i
$764$	1.16461	−	2.61576i	0.0421342	−	0.0946349i
$765$	−0.205762	−	0.328556i	−0.00743933	−	0.0118790i
$766$	−41.3087	+	13.4220i	−1.49254	+	0.484957i
$767$	−0.702745	+	2.52412i	−0.0253747	+	0.0911405i
$768$	1.88157	−	13.4368i	0.0678953	−	0.484860i
$769$	7.84234	−	4.52778i	0.282802	−	0.163276i	−0.351889	−	0.936042i	$-0.614461\pi$
$769$	7.84234	−	4.52778i	0.282802	−	0.163276i	0.634691	+	0.772766i	$0.281127\pi$
$770$	−0.562464	+	0.511267i	−0.0202698	+	0.0184248i
$771$	0.769035	−	22.3427i	0.0276961	−	0.804653i
$772$	4.81075	−	6.62144i	0.173143	−	0.238311i
$773$	2.82434	−	2.54305i	0.101584	−	0.0914671i	−0.616774	−	0.787141i	$-0.711561\pi$
$773$	2.82434	−	2.54305i	0.101584	−	0.0914671i	0.718358	+	0.695673i	$0.244894\pi$
$774$	1.94648	+	2.01160i	0.0699646	+	0.0723056i
$775$	18.3756	−	13.3507i	0.660072	−	0.479570i
$776$	0.729385	+	6.93964i	0.0261834	+	0.249118i
$777$	5.48392	−	22.0417i	0.196734	−	0.790743i
$778$	0.0688261	+	0.323801i	0.00246753	+	0.0116088i
$779$	22.1773	−	30.5244i	0.794584	−	1.09365i
$780$	0.0542318	−	0.0957404i	0.00194181	−	0.00342806i
$781$	2.59288	+	4.44250i	0.0927805	+	0.158965i
$782$	14.4904	−	8.36605i	0.518177	−	0.299169i
$783$	−6.59449	+	31.2552i	−0.235668	+	1.11697i
$784$	3.49119	+	3.87736i	0.124686	+	0.138477i
$785$	0.346777	−	0.112675i	0.0123770	−	0.00402154i
$786$	−33.0034	+	22.2851i	−1.17719	+	0.794884i
$787$	−40.1305	+	4.21789i	−1.43050	+	0.150352i	−0.787877	−	0.615832i	$-0.788820\pi$
$787$	−40.1305	+	4.21789i	−1.43050	+	0.150352i	−0.642622	+	0.766184i	$0.722153\pi$
$788$	−0.856502	−	2.63604i	−0.0305116	−	0.0939051i
$789$	−2.48821	+	6.84697i	−0.0885828	+	0.243759i
$790$	−0.115868	+	1.10241i	−0.00412239	+	0.0392220i
$791$	−17.4143	−	30.1624i	−0.619181	−	1.07245i
$792$	−1.62135	+	25.2600i	−0.0576120	+	0.897576i
$793$	−35.8690	+	1.52978i	−1.27374	+	0.0543239i
$794$	−21.8587	−	15.8813i	−0.775735	−	0.563605i
$795$	0.553788	+	0.659309i	0.0196408	+	0.0233833i
$796$	−3.92548	+	4.35969i	−0.139135	+	0.154525i
$797$	28.4878	−	2.99419i	1.00909	−	0.106059i	0.414466	−	0.910065i	$-0.363968\pi$
$797$	28.4878	−	2.99419i	1.00909	−	0.106059i	0.594622	+	0.804005i	$0.297302\pi$
$798$	−50.5210	−	24.6095i	−1.78842	−	0.871165i
$799$	−1.00103	+	4.70949i	−0.0354140	+	0.166610i
$800$	−6.27873	−	6.97324i	−0.221987	−	0.246541i
$801$	−3.30416	−	9.04992i	−0.116747	−	0.319763i
$802$	−11.0483	−	6.37874i	−0.390129	−	0.225241i
$803$	20.5862	+	22.6477i	0.726472	+	0.799220i
$804$	−1.24574	+	1.99583i	−0.0439339	+	0.0703873i
$805$	−0.392497	+	0.540226i	−0.0138337	+	0.0190405i
$806$	−17.8801	+	17.5352i	−0.629798	+	0.617652i
$807$	26.7777	+	25.8330i	0.942619	+	0.909366i
$808$	−39.1454	−	17.4287i	−1.37713	−	0.613139i
$809$	27.4843	+	12.2368i	0.966297	+	0.430223i	0.828347	−	0.560216i	$-0.189282\pi$
$809$	27.4843	+	12.2368i	0.966297	+	0.430223i	0.137951	+	0.990439i	$0.455948\pi$
$810$	−0.711510	+	0.126927i	−0.0249999	+	0.00445975i
$811$	14.5373	+	4.72345i	0.510473	+	0.165863i	0.552917	−	0.833236i	$-0.313515\pi$
$811$	14.5373	+	4.72345i	0.510473	+	0.165863i	−0.0424443	+	0.999099i	$0.513515\pi$
$812$	−2.39259	−	5.37385i	−0.0839635	−	0.188585i
$813$	0.230169	−	6.68708i	0.00807238	−	0.234526i
$814$	−9.37223	+	21.3203i	−0.328496	+	0.747277i
$815$	−0.512291	−	0.295771i	−0.0179448	−	0.0103604i
$816$	17.9969	−	7.28168i	0.630017	−	0.254910i
$817$	−4.44303	+	0.944395i	−0.155442	+	0.0330402i
$818$	4.66876	−	1.51697i	0.163239	−	0.0530396i
$819$	27.8622	+	13.2899i	0.973584	+	0.464387i
$820$	0.0525245	+	0.0722938i	0.00183424	+	0.00252461i
$821$	14.7360	−	16.3660i	0.514290	−	0.571177i	−0.428933	−	0.903336i	$-0.641110\pi$
$821$	14.7360	−	16.3660i	0.514290	−	0.571177i	0.943223	+	0.332159i	$0.107777\pi$
$822$	39.1708	−	32.9016i	1.36624	−	1.14758i
$823$	4.96259	−	2.20949i	0.172985	−	0.0770179i	−0.318417	−	0.947951i	$-0.603151\pi$
$823$	4.96259	−	2.20949i	0.172985	−	0.0770179i	0.491402	+	0.870933i	$0.336485\pi$
$824$	21.0479			0.733237
$825$	20.7538	+	19.8336i	0.722553	+	0.690516i
$826$	−1.58462	+	2.74465i	−0.0551360	+	0.0954984i
$827$	−18.8217	−	13.6747i	−0.654494	−	0.475518i	0.210305	−	0.977636i	$-0.432554\pi$
$827$	−18.8217	−	13.6747i	−0.654494	−	0.475518i	−0.864799	+	0.502118i	$0.832554\pi$
$828$	−0.627754	−	4.43451i	−0.0218160	−	0.154110i
$829$	−5.03747	+	5.59468i	−0.174959	+	0.194311i	−0.824246	−	0.566232i	$-0.808401\pi$
$829$	−5.03747	+	5.59468i	−0.174959	+	0.194311i	0.649287	+	0.760543i	$0.275067\pi$
$830$	0.464395	−	1.04305i	0.0161194	−	0.0362047i
$831$	−18.4574	+	37.8915i	−0.640282	+	1.31444i
$832$	−17.3651	−	14.3442i	−0.602026	−	0.497294i
$833$	−0.869810	+	2.67700i	−0.0301371	+	0.0927526i
$834$	19.9596	+	49.3306i	0.691143	+	1.70818i
$835$	0.358224	−	0.206821i	0.0123969	−	0.00715734i
$836$	6.71574	+	4.83106i	0.232269	+	0.167086i
$837$	23.4919	+	2.43347i	0.812000	+	0.0841129i
$838$	19.6620	+	44.1616i	0.679212	+	1.52554i
$839$	21.0549	−	18.9579i	0.726897	−	0.654501i	−0.220198	−	0.975455i	$-0.570670\pi$
$839$	21.0549	−	18.9579i	0.726897	−	0.654501i	0.947095	+	0.320954i	$0.104004\pi$
$840$	−0.458799	+	0.475576i	−0.0158301	+	0.0164089i
$841$	−0.918976	−	8.74347i	−0.0316888	−	0.301499i
$842$	−44.3399	−	19.7414i	−1.52805	−	0.680333i
$843$	19.5542	+	4.86503i	0.673483	+	0.167560i
$844$	−3.19954	−	1.03959i	−0.110133	−	0.0357843i
$845$	−0.329988	−	0.598161i	−0.0113519	−	0.0205774i
$846$	7.44662	+	5.01198i	0.256020	+	0.172315i
$847$	18.6908	+	25.2221i	0.642224	+	0.866643i
$848$	−37.3428	+	21.5599i	−1.28236	+	0.740369i
$849$	2.32848	−	2.98339i	0.0799131	−	0.102390i
$850$	5.80299	−	17.8598i	0.199041	−	0.612585i
$851$	−4.25384	+	20.0128i	−0.145820	+	0.686028i
$852$	−0.504028	−	0.746446i	−0.0172677	−	0.0255728i
$853$	22.2695	+	30.6513i	0.762492	+	1.04948i	0.997003	+	0.0773669i	$0.0246513\pi$
$853$	22.2695	+	30.6513i	0.762492	+	1.04948i	−0.234510	+	0.972114i	$0.575349\pi$
$854$	−42.4769	−	9.02874i	−1.45353	−	0.308957i
$855$	0.438257	−	1.08786i	0.0149881	−	0.0372039i
$856$	4.01141	−	38.1660i	0.137107	−	1.30449i
$857$	−3.72803			−0.127347			−0.0636735	−	0.997971i	$-0.520282\pi$
$857$	−3.72803			−0.127347			−0.0636735	+	0.997971i	$0.520282\pi$
$858$	−25.8453	−	18.2718i	−0.882345	−	0.623789i
$859$	−24.4580			−0.834498			−0.417249	−	0.908792i	$-0.637006\pi$
$859$	−24.4580			−0.834498			−0.417249	+	0.908792i	$0.637006\pi$
$860$	0.00112451	−	0.0106990i	3.83454e−5	−	0.000364832i
$861$	−19.1964	+	16.1241i	−0.654212	+	0.549507i
$862$	−12.5171	−	2.66060i	−0.426335	−	0.0906203i
$863$	−16.3883	−	22.5566i	−0.557865	−	0.767835i	0.433188	−	0.901303i	$-0.357389\pi$
$863$	−16.3883	−	22.5566i	−0.557865	−	0.767835i	−0.991053	+	0.133468i	$0.957389\pi$
$864$	−0.0146408	−	9.75692i	−0.000498092	−	0.331937i
$865$	0.206395	−	0.971014i	0.00701765	−	0.0330155i
$866$	6.20332	−	19.0918i	0.210797	−	0.648767i
$867$	−14.9554	−	11.6724i	−0.507911	−	0.396414i
$868$	−3.76654	+	2.17461i	−0.127845	+	0.0738111i
$869$	44.8248	+	9.30715i	1.52058	+	0.315724i
$870$	0.754777	−	0.401806i	0.0255893	−	0.0136225i
$871$	6.50433	+	13.0787i	0.220391	+	0.443156i
$872$	4.14805	+	1.34778i	0.140471	+	0.0456417i
$873$	1.99871	+	7.98234i	0.0676459	+	0.270161i
$874$	46.2435	+	20.5889i	1.56421	+	0.696431i
$875$	0.156719	+	1.49108i	0.00529806	+	0.0504077i
$876$	−3.85684	−	3.72078i	−0.130311	−	0.125714i
$877$	−19.6055	+	17.6529i	−0.662030	+	0.596094i	−0.930101	−	0.367305i	$-0.880281\pi$
$877$	−19.6055	+	17.6529i	−0.662030	+	0.596094i	0.268071	+	0.963399i	$0.413614\pi$
$878$	−1.62988	−	3.66078i	−0.0550059	−	0.123545i
$879$	−5.74938	−	10.8000i	−0.193922	−	0.364274i
$880$	0.640500	−	0.469980i	0.0215912	−	0.0158430i
$881$	−14.0896	+	8.13461i	−0.474689	+	0.274062i	−0.718201	−	0.695836i	$-0.755034\pi$
$881$	−14.0896	+	8.13461i	−0.474689	+	0.274062i	0.243511	+	0.969898i	$0.421701\pi$
$882$	4.02331	+	3.36910i	0.135472	+	0.113444i
$883$	5.00113	−	15.3919i	0.168302	−	0.517979i	−0.830963	−	0.556328i	$-0.812210\pi$
$883$	5.00113	−	15.3919i	0.168302	−	0.517979i	0.999264	+	0.0383490i	$0.0122099\pi$
$884$	−0.493610	+	2.93150i	−0.0166019	+	0.0985972i
$885$	−0.0594629	−	0.0289652i	−0.00199882	−	0.000973654i
$886$	1.37937	−	3.09811i	0.0463408	−	0.104083i
$887$	−5.63793	+	6.26156i	−0.189303	+	0.210243i	−0.830324	−	0.557281i	$-0.811845\pi$
$887$	−5.63793	+	6.26156i	−0.189303	+	0.210243i	0.641021	+	0.767524i	$0.278511\pi$
$888$	−6.91536	+	19.0294i	−0.232064	+	0.638585i
$889$	1.90519	+	1.38420i	0.0638980	+	0.0464246i
$890$	−0.128946	+	0.223341i	−0.00432227	+	0.00748639i
$891$	2.28211	+	29.7623i	0.0764537	+	0.997073i
$892$	−8.38713			−0.280822
$893$	−13.3067	+	5.92451i	−0.445290	+	0.198256i
$894$	−25.2272	−	30.0341i	−0.843724	−	1.00449i
$895$	0.405075	−	0.449882i	0.0135402	−	0.0150379i
$896$	−22.3132	−	30.7114i	−0.745430	−	1.02600i
$897$	−25.4944	−	11.1008i	−0.851234	−	0.370643i
$898$	30.8046	−	10.0090i	1.02796	−	0.334005i
$899$	−27.3311	+	5.80940i	−0.911542	+	0.193754i
$900$	−3.85381	−	3.22717i	−0.128460	−	0.107572i
$901$	−20.1459	−	11.6312i	−0.671156	−	0.387492i
$902$	22.2004	−	12.9573i	0.739192	−	0.431432i
$903$	3.01631	+	0.103821i	0.100377	+	0.00345496i
$904$	12.6276	+	28.3621i	0.419988	+	0.943309i
$905$	1.01015	+	0.328217i	0.0335784	+	0.0109103i
$906$	22.3560	−	6.42257i	0.742727	−	0.213376i
$907$	−1.47771	−	0.657919i	−0.0490665	−	0.0218458i	0.382057	−	0.924139i	$-0.375216\pi$
$907$	−1.47771	−	0.657919i	−0.0490665	−	0.0218458i	−0.431123	+	0.902293i	$0.641883\pi$
$908$	−0.424641	−	0.189062i	−0.0140922	−	0.00627425i
$909$	−48.5880	−	13.8798i	−1.61156	−	0.460364i
$910$	−0.206086	−	0.800209i	−0.00683169	−	0.0265267i
$911$	−16.7365	+	23.0359i	−0.554506	+	0.763212i	−0.990615	−	0.136682i	$-0.956356\pi$
$911$	−16.7365	+	23.0359i	−0.554506	+	0.763212i	0.436109	+	0.899894i	$0.356356\pi$
$912$	49.8247	+	31.0993i	1.64986	+	1.02980i
$913$	−40.9483	−	23.3848i	−1.35519	−	0.773925i
$914$	−2.58385	−	1.49179i	−0.0854662	−	0.0493439i
$915$	0.125684	−	0.897544i	0.00415498	−	0.0296719i
$916$	2.24121	+	2.48911i	0.0740515	+	0.0822425i
$917$	−8.92721	+	41.9992i	−0.294802	+	1.38694i
$918$	16.8956	−	9.78854i	0.557639	−	0.323070i
$919$	−2.19555	+	0.230762i	−0.0724246	+	0.00761213i	−0.140671	−	0.990056i	$-0.544926\pi$
$919$	−2.19555	+	0.230762i	−0.0724246	+	0.00761213i	0.0682468	+	0.997668i	$0.478259\pi$
$920$	0.398292	−	0.442348i	0.0131313	−	0.0145838i
$921$	−14.9831	+	12.5851i	−0.493709	+	0.414692i
$922$	−48.0439	−	34.9059i	−1.58224	−	1.14957i
$923$	−5.58684	+	0.238273i	−0.183893	+	0.00784285i
$924$	−3.55522	−	4.19235i	−0.116958	−	0.137918i
$925$	11.4813	+	19.8862i	0.377503	+	0.653854i
$926$	−1.51697	+	14.4330i	−0.0498507	+	0.474298i
$927$	24.5760	−	3.47901i	0.807183	−	0.114266i
$928$	3.56707	+	10.9783i	0.117095	+	0.360381i
$929$	31.5861	−	3.31984i	1.03631	−	0.108920i	0.428933	−	0.903336i	$-0.358889\pi$
$929$	31.5861	−	3.31984i	1.03631	−	0.108920i	0.607374	+	0.794416i	$0.292223\pi$
$930$	−0.353785	−	0.523942i	−0.0116011	−	0.0171807i
$931$	−8.09875	+	2.63144i	−0.265426	+	0.0862421i
$932$	2.52674	+	2.80623i	0.0827661	+	0.0919211i
$933$	−4.86447	−	12.0227i	−0.159256	−	0.393604i
$934$	−9.77348	+	5.64272i	−0.319798	+	0.184635i
$935$	0.392348	+	0.172473i	0.0128312	+	0.00564046i
$936$	−23.4620	−	14.3778i	−0.766880	−	0.469955i
$937$	29.9207	−	41.1823i	0.977466	−	1.34537i	0.0392830	−	0.999228i	$-0.487493\pi$
$937$	29.9207	−	41.1823i	0.977466	−	1.34537i	0.938183	−	0.346139i	$-0.112507\pi$
$938$	3.67342	+	17.2821i	0.119941	+	0.564280i
$939$	27.9311	+	6.94917i	0.911498	+	0.226778i
$940$	−0.00360601	−	0.0343089i	−0.000117615	−	0.00111903i
$941$	−8.63767	+	6.27563i	−0.281580	+	0.204580i	−0.719606	−	0.694382i	$-0.755678\pi$
$941$	−8.63767	+	6.27563i	−0.281580	+	0.204580i	0.438026	+	0.898962i	$0.355678\pi$
$942$	5.07108	+	17.6516i	0.165225	+	0.575121i
$943$	16.7817	−	15.1103i	0.546488	−	0.492060i
$944$	1.94696	−	2.67976i	0.0633682	−	0.0872188i
$945$	−0.457098	+	0.631130i	−0.0148694	+	0.0205307i
$946$	−3.02997	−	0.629124i	−0.0985127	−	0.0204546i
$947$	−31.5704	+	18.2272i	−1.02590	+	0.592304i	−0.915808	−	0.401617i	$-0.868448\pi$
$947$	−31.5704	+	18.2272i	−1.02590	+	0.592304i	−0.110093	+	0.993921i	$0.535115\pi$
$948$	−7.93876	−	1.11167i	−0.257839	−	0.0361054i
$949$	−32.2205	+	8.29809i	−1.04592	+	0.269367i
$950$	54.0313	−	17.5558i	1.75301	−	0.569586i
$951$	−34.3837	+	2.42163i	−1.11497	+	0.0785266i
$952$	7.26151	−	16.3096i	0.235347	−	0.528598i
$953$	−38.8524	−	8.25833i	−1.25855	−	0.267514i	−0.470102	−	0.882612i	$-0.655783\pi$
$953$	−38.8524	−	8.25833i	−1.25855	−	0.267514i	−0.788450	+	0.615099i	$0.789116\pi$
$954$	−34.1484	+	26.7347i	−1.10560	+	0.865568i
$955$	0.409966	−	0.182528i	0.0132662	−	0.00590648i
$956$	−0.523237	+	0.906274i	−0.0169227	+	0.0293110i
$957$	−13.3997	−	32.6737i	−0.433150	−	1.05619i
$958$	9.33773	−	16.1734i	0.301688	−	0.522539i
$959$	5.76542	−	54.8543i	0.186175	−	1.77134i
$960$	0.435375	−	0.365695i	0.0140517	−	0.0118027i
$961$	−3.19556	−	9.83491i	−0.103082	−	0.317255i
$962$	−15.7409	−	19.8301i	−0.507508	−	0.639350i
$963$	−1.62465	−	45.2267i	−0.0523536	−	1.45741i
$964$	−6.48733	−	5.84122i	−0.208943	−	0.188133i
$965$	1.25472	−	0.266700i	0.0403910	−	0.00858537i
$966$	−26.5143	−	20.6939i	−0.853085	−	0.665816i
$967$			15.4478i			0.496769i	0.968662	+	0.248384i	$0.0798996\pi$
$967$			15.4478i			0.496769i	−0.968662	+	0.248384i	$0.920100\pi$
$968$	−14.2196	−	24.1014i	−0.457036	−	0.774648i
$969$	−1.08999	+	31.6673i	−0.0350154	+	1.01730i
$970$	0.129471	−	0.178202i	0.00415707	−	0.00572171i
$971$	30.6703	−	27.6157i	0.984257	−	0.886229i	−0.00925524	−	0.999957i	$-0.502946\pi$
$971$	30.6703	−	27.6157i	0.984257	−	0.886229i	0.993512	+	0.113729i	$0.0362794\pi$
$972$	−0.740353	−	5.17396i	−0.0237468	−	0.165955i
$973$	52.4172	+	23.3376i	1.68042	+	0.748170i
$974$	−32.0767	+	23.3051i	−1.02780	+	0.746744i
$975$	−29.6001	+	9.88727i	−0.947961	+	0.316646i
$976$	43.1656	+	14.0253i	1.38170	+	0.448940i
$977$	8.37161	+	0.879892i	0.267832	+	0.0281502i	0.237492	−	0.971389i	$-0.423675\pi$
$977$	8.37161	+	0.879892i	0.267832	+	0.0281502i	0.0303393	+	0.999540i	$0.490341\pi$
$978$	15.7764	−	25.2757i	0.504474	−	0.808227i
$979$	8.64630	+	6.21984i	0.276337	+	0.198787i
$980$		−	0.0201681i		−	0.000644246i
$981$	5.06615	+	0.888074i	0.161750	+	0.0283540i
$982$	9.31368	+	10.3439i	0.297212	+	0.330087i
$983$	50.4865	−	16.4041i	1.61027	−	0.523209i	0.640652	−	0.767831i	$-0.278664\pi$
$983$	50.4865	−	16.4041i	1.61027	−	0.523209i	0.969618	+	0.244623i	$0.0786641\pi$
$984$	18.5203	−	12.5056i	0.590407	−	0.398664i
$985$	0.176689	−	0.396849i	0.00562977	−	0.0126447i
$986$	−15.4578	+	17.1676i	−0.492277	+	0.546729i
$987$	9.53039	−	1.68538i	0.303356	−	0.0536462i
$988$	−8.05268	+	4.00477i	−0.256190	+	0.127409i
$989$	−2.71862			−0.0864470
$990$	0.571587	−	0.558323i	0.0181662	−	0.0177447i
$991$	−28.8827	−	50.0263i	−0.917489	−	1.58914i	−0.803215	−	0.595689i	$-0.796879\pi$
$991$	−28.8827	−	50.0263i	−0.917489	−	1.58914i	−0.114274	−	0.993449i	$-0.536454\pi$
$992$	7.79679	−	3.47135i	0.247548	−	0.110216i
$993$	10.3313	−	1.82701i	0.327853	−	0.0579784i
$994$	−6.61607	−	1.40629i	−0.209849	−	0.0446048i
$995$	−0.914420	+	0.0961095i	−0.0289891	+	0.00304687i
$996$	7.42303	+	3.61586i	0.235208	+	0.114573i
$997$	−0.518471	+	2.43921i	−0.0164201	+	0.0772507i	−0.985595	−	0.169124i	$-0.945906\pi$
$997$	−0.518471	+	2.43921i	−0.0164201	+	0.0772507i	0.969175	+	0.246375i	$0.0792394\pi$
$998$	23.8423	−	5.06784i	0.754716	−	0.160420i
$999$	−4.92918	+	23.3623i	−0.155952	+	0.739150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.14	✓	416
3.2	odd	2	inner	429.2.bq.a.29.39	yes	416
11.8	odd	10	inner	429.2.bq.a.107.14	yes	416
13.9	even	3	inner	429.2.bq.a.425.39	yes	416
33.8	even	10	inner	429.2.bq.a.107.39	yes	416
39.35	odd	6	inner	429.2.bq.a.425.14	yes	416
143.74	odd	30	inner	429.2.bq.a.74.39	yes	416
429.74	even	30	inner	429.2.bq.a.74.14	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.14	✓	416	1.1	even	1	trivial
429.2.bq.a.29.39	yes	416	3.2	odd	2	inner
429.2.bq.a.74.14	yes	416	429.74	even	30	inner
429.2.bq.a.74.39	yes	416	143.74	odd	30	inner
429.2.bq.a.107.14	yes	416	11.8	odd	10	inner
429.2.bq.a.107.39	yes	416	33.8	even	10	inner
429.2.bq.a.425.14	yes	416	39.35	odd	6	inner
429.2.bq.a.425.39	yes	416	13.9	even	3	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.159737 + 1.51979i) q^{2} +(-1.11400 - 1.32627i) q^{3} +(-0.327964 - 0.0697108i) q^{4} +(-0.0308880 - 0.0425136i) q^{5} +(2.19361 - 1.48120i) q^{6} +(0.593356 - 2.79152i) q^{7} +(-0.786124 + 2.41944i) q^{8} +(-0.517989 + 2.95494i) q^{9} +O(q^{10})\)	\(q+(-0.159737 + 1.51979i) q^{2} +(-1.11400 - 1.32627i) q^{3} +(-0.327964 - 0.0697108i) q^{4} +(-0.0308880 - 0.0425136i) q^{5} +(2.19361 - 1.48120i) q^{6} +(0.593356 - 2.79152i) q^{7} +(-0.786124 + 2.41944i) q^{8} +(-0.517989 + 2.95494i) q^{9} +(0.0695459 - 0.0401523i) q^{10} +(-1.36326 - 3.02349i) q^{11} +(0.272897 + 0.512627i) q^{12} +(3.59860 + 0.223749i) q^{13} +(4.14775 + 1.34769i) q^{14} +(-0.0219753 + 0.0883261i) q^{15} +(-4.16409 - 1.85397i) q^{16} +(-0.257042 - 2.44559i) q^{17} +(-4.40816 - 1.25925i) q^{18} +(5.52856 - 4.97793i) q^{19} +(0.00716646 + 0.0160961i) q^{20} +(-4.36331 + 2.32281i) q^{21} +(4.81285 - 1.58891i) q^{22} +(3.85605 - 2.22629i) q^{23} +(4.08458 - 1.65266i) q^{24} +(1.54423 - 4.75266i) q^{25} +(-0.914881 + 5.43339i) q^{26} +(4.49610 - 2.60483i) q^{27} +(-0.389198 + 0.874153i) q^{28} +(-4.11347 + 4.56848i) q^{29} +(-0.130727 - 0.0475068i) q^{30} +(3.67715 + 2.67161i) q^{31} +(0.938861 - 1.62615i) q^{32} +(-2.49129 + 5.17624i) q^{33} +3.75785 q^{34} +(-0.137005 + 0.0609986i) q^{35} +(0.375873 - 0.933004i) q^{36} +(-3.07469 + 3.41479i) q^{37} +(6.68232 + 9.19743i) q^{38} +(-3.71211 - 5.02198i) q^{39} +(0.127141 - 0.0413106i) q^{40} +(4.96085 - 1.05446i) q^{41} +(-2.83322 - 7.00238i) q^{42} +(-0.528770 - 0.305286i) q^{43} +(0.236330 + 1.08663i) q^{44} +(0.141625 - 0.0692506i) q^{45} +(2.76755 + 6.21602i) q^{46} +(-1.86212 - 0.605038i) q^{47} +(2.17994 + 7.58804i) q^{48} +(-1.04569 - 0.465572i) q^{49} +(6.97639 + 3.10609i) q^{50} +(-2.95716 + 3.06530i) q^{51} +(-1.16461 - 0.324243i) q^{52} +(5.56039 - 7.65322i) q^{53} +(3.24061 + 7.24923i) q^{54} +(-0.0864313 + 0.151347i) q^{55} +(6.28747 + 3.63007i) q^{56} +(-12.7609 - 1.78692i) q^{57} +(-6.28607 - 6.98139i) q^{58} +(-0.151087 + 0.710810i) q^{59} +(0.0133644 - 0.0274358i) q^{60} +(-9.90275 + 1.04082i) q^{61} +(-4.64767 + 5.16176i) q^{62} +(7.94143 + 3.19931i) q^{63} +(-5.05381 - 3.67181i) q^{64} +(-0.101641 - 0.159901i) q^{65} +(-7.46887 - 4.61309i) q^{66} +(2.02560 + 3.50845i) q^{67} +(-0.0861836 + 0.819982i) q^{68} +(-7.24831 - 2.63407i) q^{69} +(-0.0708206 - 0.217963i) q^{70} +(-1.54242 + 0.162115i) q^{71} +(-6.74211 - 3.57620i) q^{72} +(-8.77633 + 2.85160i) q^{73} +(-4.69864 - 5.21837i) q^{74} +(-8.02359 + 3.24641i) q^{75} +(-2.16018 + 1.24718i) q^{76} +(-9.24904 + 2.01157i) q^{77} +(8.22533 - 4.83944i) q^{78} +(-8.11346 + 11.1672i) q^{79} +(0.0498011 + 0.234296i) q^{80} +(-8.46338 - 3.06125i) q^{81} +(0.810134 + 7.70791i) q^{82} +(11.5025 - 8.35703i) q^{83} +(1.59293 - 0.457628i) q^{84} +(-0.0960312 + 0.0864669i) q^{85} +(0.548436 - 0.754857i) q^{86} +(10.6415 + 0.366279i) q^{87} +(8.38686 - 0.921491i) q^{88} +(-2.78116 + 1.60571i) q^{89} +(0.0826239 + 0.226303i) q^{90} +(2.75985 - 9.91281i) q^{91} +(-1.41984 + 0.461334i) q^{92} +(-0.553089 - 7.85309i) q^{93} +(1.21698 - 2.73339i) q^{94} +(-0.382396 - 0.0812807i) q^{95} +(-3.20262 + 0.566359i) q^{96} +(2.50578 - 1.11565i) q^{97} +(0.874609 - 1.51487i) q^{98} +(9.64041 - 2.46223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Introduction

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