LMFDB - Embedded newform 125.2.h.a.104.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			104.5
Character	$\chi$	$=$	125.104
Dual form			125.2.h.a.119.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190125 - 0.740487i) q^{2} +(1.27736 - 0.243669i) q^{3} +(1.24044 - 0.681938i) q^{4} +(1.11923 + 1.93580i) q^{5} +(-0.423291 - 0.899540i) q^{6} +(-1.40937 + 1.93983i) q^{7} +(-1.78748 - 1.90348i) q^{8} +(-1.21706 + 0.481867i) q^{9} +O(q^{10})$	\(q+(-0.190125 - 0.740487i) q^{2} +(1.27736 - 0.243669i) q^{3} +(1.24044 - 0.681938i) q^{4} +(1.11923 + 1.93580i) q^{5} +(-0.423291 - 0.899540i) q^{6} +(-1.40937 + 1.93983i) q^{7} +(-1.78748 - 1.90348i) q^{8} +(-1.21706 + 0.481867i) q^{9} +(1.22064 - 1.19682i) q^{10} +(-0.424635 + 0.109028i) q^{11} +(1.41832 - 1.17334i) q^{12} +(-1.96830 - 4.97136i) q^{13} +(1.70438 + 0.674810i) q^{14} +(1.90135 + 2.19999i) q^{15} +(0.447306 - 0.704842i) q^{16} +(-1.77096 + 3.22136i) q^{17} +(0.588209 + 0.809600i) q^{18} +(0.953375 - 4.99777i) q^{19} +(2.70843 + 1.63800i) q^{20} +(-1.32760 + 2.82128i) q^{21} +(0.161467 + 0.293708i) q^{22} +(-3.97654 - 0.250183i) q^{23} +(-2.74708 - 1.99587i) q^{24} +(-2.49466 + 4.33321i) q^{25} +(-3.30700 + 2.40268i) q^{26} +(-4.73108 + 3.00243i) q^{27} +(-0.425395 + 3.36735i) q^{28} +(8.71338 + 1.10076i) q^{29} +(1.26757 - 1.82620i) q^{30} +(0.739916 + 0.406772i) q^{31} +(-5.57375 - 1.81102i) q^{32} +(-0.515845 + 0.242738i) q^{33} +(2.72208 + 0.698910i) q^{34} +(-5.33254 - 0.557148i) q^{35} +(-1.18108 + 1.42769i) q^{36} +(1.87503 + 1.18993i) q^{37} +(-3.88204 + 0.244237i) q^{38} +(-3.72560 - 5.87060i) q^{39} +(1.68415 - 5.59064i) q^{40} +(0.550798 + 8.75468i) q^{41} +(2.34153 + 0.446671i) q^{42} +(7.96661 - 2.58851i) q^{43} +(-0.452384 + 0.424817i) q^{44} +(-2.29497 - 1.81666i) q^{45} +(0.570782 + 2.99214i) q^{46} +(1.44504 - 1.53881i) q^{47} +(0.399622 - 1.00933i) q^{48} +(0.386494 + 1.18951i) q^{49} +(3.68298 + 1.02341i) q^{50} +(-1.47720 + 4.54636i) q^{51} +(-5.83172 - 4.82442i) q^{52} +(0.907174 + 0.426884i) q^{53} +(3.12276 + 2.93246i) q^{54} +(-0.686320 - 0.699983i) q^{55} +(6.21165 - 0.784714i) q^{56} -6.61625i q^{57} +(-0.841533 - 6.66142i) q^{58} +(2.53945 + 3.06967i) q^{59} +(3.85877 + 1.43236i) q^{60} +(0.719696 - 11.4392i) q^{61} +(0.160533 - 0.625235i) q^{62} +(0.780544 - 3.04002i) q^{63} +(-0.176495 + 2.80531i) q^{64} +(7.42059 - 9.37433i) q^{65} +(0.277819 + 0.335826i) q^{66} +(-0.358552 - 2.83823i) q^{67} +5.20359i q^{68} +(-5.14044 + 0.649388i) q^{69} +(0.601287 + 4.05460i) q^{70} +(2.63411 + 2.47359i) q^{71} +(3.09269 + 1.45531i) q^{72} +(5.86297 + 4.85027i) q^{73} +(0.524639 - 1.61467i) q^{74} +(-2.13070 + 6.14293i) q^{75} +(-2.22556 - 6.84957i) q^{76} +(0.386973 - 0.977382i) q^{77} +(-3.63877 + 3.87490i) q^{78} +(-3.20949 - 16.8248i) q^{79} +(1.86507 + 0.0770174i) q^{80} +(-2.44907 + 2.29983i) q^{81} +(6.37800 - 2.07234i) q^{82} +(-6.03472 - 1.15118i) q^{83} +(0.277137 + 4.40497i) q^{84} +(-8.21802 + 0.177213i) q^{85} +(-3.43141 - 5.40703i) q^{86} +(11.3983 - 0.717123i) q^{87} +(0.966560 + 0.613398i) q^{88} +(-8.43845 + 10.2003i) q^{89} +(-0.908886 + 2.04478i) q^{90} +(12.4177 + 3.18832i) q^{91} +(-5.10328 + 2.40142i) q^{92} +(1.04426 + 0.339299i) q^{93} +(-1.41421 - 0.777466i) q^{94} +(10.7417 - 3.74810i) q^{95} +(-7.56097 - 0.955173i) q^{96} +(-2.08420 + 16.4982i) q^{97} +(0.807331 - 0.512348i) q^{98} +(0.464269 - 0.337311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.190125	−	0.740487i	−0.134438	−	0.523603i	−0.999750	−	0.0223684i	$-0.992879\pi$
$2$	−0.190125	−	0.740487i	−0.134438	−	0.523603i	0.865311	−	0.501235i	$-0.167121\pi$
$3$	1.27736	−	0.243669i	0.737484	−	0.140683i	0.195064	−	0.980790i	$-0.437508\pi$
$3$	1.27736	−	0.243669i	0.737484	−	0.140683i	0.542419	+	0.840108i	$0.317508\pi$
$4$	1.24044	−	0.681938i	0.620220	−	0.340969i
$5$	1.11923	+	1.93580i	0.500534	+	0.865717i
$5$	1.11923	+	1.93580i	0.500534	+	0.865717i
$6$	−0.423291	−	0.899540i	−0.172808	−	0.367236i
$7$	−1.40937	+	1.93983i	−0.532692	+	0.733188i	−0.987538	−	0.157382i	$-0.949694\pi$
$7$	−1.40937	+	1.93983i	−0.532692	+	0.733188i	0.454845	+	0.890570i	$0.349694\pi$
$8$	−1.78748	−	1.90348i	−0.631971	−	0.672981i
$9$	−1.21706	+	0.481867i	−0.405686	+	0.160622i
$10$	1.22064	−	1.19682i	0.386001	−	0.378467i
$11$	−0.424635	+	0.109028i	−0.128032	+	0.0328731i	−0.312162	−	0.950029i	$-0.601053\pi$
$11$	−0.424635	+	0.109028i	−0.128032	+	0.0328731i	0.184130	+	0.982902i	$0.441053\pi$
$12$	1.41832	−	1.17334i	0.409434	−	0.338713i
$13$	−1.96830	−	4.97136i	−0.545909	−	1.37881i	−0.896819	−	0.442398i	$-0.854128\pi$
$13$	−1.96830	−	4.97136i	−0.545909	−	1.37881i	0.350910	−	0.936409i	$-0.385872\pi$
$14$	1.70438	+	0.674810i	0.455514	+	0.180351i
$15$	1.90135	+	2.19999i	0.490927	+	0.568036i
$16$	0.447306	−	0.704842i	0.111827	−	0.176210i
$17$	−1.77096	+	3.22136i	−0.429520	+	0.781294i	−0.999176	−	0.0405892i	$-0.987077\pi$
$17$	−1.77096	+	3.22136i	−0.429520	+	0.781294i	0.569656	+	0.821883i	$0.307077\pi$
$18$	0.588209	+	0.809600i	0.138642	+	0.190825i
$19$	0.953375	−	4.99777i	0.218719	−	1.14657i	−0.688284	−	0.725442i	$-0.741635\pi$
$19$	0.953375	−	4.99777i	0.218719	−	1.14657i	0.907003	−	0.421125i	$-0.138365\pi$
$20$	2.70843	+	1.63800i	0.605624	+	0.366269i
$21$	−1.32760	+	2.82128i	−0.289705	+	0.615655i
$22$	0.161467	+	0.293708i	0.0344249	+	0.0626187i
$23$	−3.97654	−	0.250183i	−0.829167	−	0.0521668i	−0.357467	−	0.933926i	$-0.616359\pi$
$23$	−3.97654	−	0.250183i	−0.829167	−	0.0521668i	−0.471700	+	0.881759i	$0.656359\pi$
$24$	−2.74708	−	1.99587i	−0.560745	−	0.407405i
$25$	−2.49466	+	4.33321i	−0.498931	+	0.866641i
$26$	−3.30700	+	2.40268i	−0.648557	+	0.471204i
$27$	−4.73108	+	3.00243i	−0.910496	+	0.577818i
$28$	−0.425395	+	3.36735i	−0.0803922	+	0.636369i
$29$	8.71338	+	1.10076i	1.61803	+	0.204405i	0.881564	−	0.472065i	$-0.156491\pi$
$29$	8.71338	+	1.10076i	1.61803	+	0.204405i	0.736470	+	0.676470i	$0.236491\pi$
$30$	1.26757	−	1.82620i	0.231426	−	0.333417i
$31$	0.739916	+	0.406772i	0.132893	+	0.0730584i	0.546813	−	0.837255i	$-0.315841\pi$
$31$	0.739916	+	0.406772i	0.132893	+	0.0730584i	−0.413920	+	0.910313i	$0.635841\pi$
$32$	−5.57375	−	1.81102i	−0.985309	−	0.320146i
$33$	−0.515845	+	0.242738i	−0.0897971	+	0.0422553i
$34$	2.72208	+	0.698910i	0.466832	+	0.119862i
$35$	−5.33254	−	0.557148i	−0.901364	−	0.0941752i
$36$	−1.18108	+	1.42769i	−0.196847	+	0.237948i
$37$	1.87503	+	1.18993i	0.308253	+	0.195624i	0.680950	−	0.732330i	$-0.261567\pi$
$37$	1.87503	+	1.18993i	0.308253	+	0.195624i	−0.372697	+	0.927953i	$0.621567\pi$
$38$	−3.88204	+	0.244237i	−0.629750	+	0.0396205i
$39$	−3.72560	−	5.87060i	−0.596573	−	0.940048i
$40$	1.68415	−	5.59064i	0.266288	−	0.883957i
$41$	0.550798	+	8.75468i	0.0860202	+	1.36725i	0.770137	+	0.637879i	$0.220188\pi$
$41$	0.550798	+	8.75468i	0.0860202	+	1.36725i	−0.684117	+	0.729373i	$0.739812\pi$
$42$	2.34153	+	0.446671i	0.361306	+	0.0689228i
$43$	7.96661	−	2.58851i	1.21490	−	0.394744i	0.369676	−	0.929161i	$-0.379469\pi$
$43$	7.96661	−	2.58851i	1.21490	−	0.394744i	0.845221	+	0.534417i	$0.179469\pi$
$44$	−0.452384	+	0.424817i	−0.0681995	+	0.0640436i
$45$	−2.29497	−	1.81666i	−0.342113	−	0.270812i
$46$	0.570782	+	2.99214i	0.0841572	+	0.441168i
$47$	1.44504	−	1.53881i	0.210781	−	0.224459i	−0.614887	−	0.788615i	$-0.710799\pi$
$47$	1.44504	−	1.53881i	0.210781	−	0.224459i	0.825668	+	0.564156i	$0.190799\pi$
$48$	0.399622	−	1.00933i	0.0576805	−	0.145684i
$49$	0.386494	+	1.18951i	0.0552134	+	0.169929i
$50$	3.68298	+	1.02341i	0.520852	+	0.144732i
$51$	−1.47720	+	4.54636i	−0.206850	+	0.636618i
$52$	−5.83172	−	4.82442i	−0.808714	−	0.669026i
$53$	0.907174	+	0.426884i	0.124610	+	0.0586370i	0.487074	−	0.873361i	$-0.338064\pi$
$53$	0.907174	+	0.426884i	0.124610	+	0.0586370i	−0.362464	+	0.931998i	$0.618064\pi$
$54$	3.12276	+	2.93246i	0.424953	+	0.399058i
$55$	−0.686320	−	0.699983i	−0.0925433	−	0.0943856i
$56$	6.21165	−	0.784714i	0.830067	−	0.104862i
$57$		−	6.61625i		−	0.876344i
$58$	−0.841533	−	6.66142i	−0.110499	−	0.874688i
$59$	2.53945	+	3.06967i	0.330608	+	0.399637i	0.909457	−	0.415798i	$-0.136498\pi$
$59$	2.53945	+	3.06967i	0.330608	+	0.399637i	−0.578849	+	0.815435i	$0.696498\pi$
$60$	3.85877	+	1.43236i	0.498165	+	0.184916i
$61$	0.719696	−	11.4392i	0.0921477	−	1.46465i	−0.631983	−	0.774982i	$-0.717759\pi$
$61$	0.719696	−	11.4392i	0.0921477	−	1.46465i	0.724130	−	0.689663i	$-0.242241\pi$
$62$	0.160533	−	0.625235i	0.0203877	−	0.0794049i
$63$	0.780544	−	3.04002i	0.0983393	−	0.383006i
$64$	−0.176495	+	2.80531i	−0.0220619	+	0.350664i
$65$	7.42059	−	9.37433i	0.920411	−	1.16274i
$66$	0.277819	+	0.335826i	0.0341972	+	0.0413373i
$67$	−0.358552	−	2.83823i	−0.0438041	−	0.346745i	−0.998751	−	0.0499678i	$-0.984088\pi$
$67$	−0.358552	−	2.83823i	−0.0438041	−	0.346745i	0.954947	−	0.296777i	$-0.0959119\pi$
$68$			5.20359i			0.631027i
$69$	−5.14044	+	0.649388i	−0.618836	+	0.0781772i
$70$	0.601287	+	4.05460i	0.0718675	+	0.484618i
$71$	2.63411	+	2.47359i	0.312611	+	0.293561i	0.824931	−	0.565233i	$-0.191214\pi$
$71$	2.63411	+	2.47359i	0.312611	+	0.293561i	−0.512320	+	0.858795i	$0.671214\pi$
$72$	3.09269	+	1.45531i	0.364478	+	0.171510i
$73$	5.86297	+	4.85027i	0.686209	+	0.567681i	0.913844	−	0.406065i	$-0.133099\pi$
$73$	5.86297	+	4.85027i	0.686209	+	0.567681i	−0.227635	+	0.973746i	$0.573099\pi$
$74$	0.524639	−	1.61467i	0.0609880	−	0.187702i
$75$	−2.13070	+	6.14293i	−0.246032	+	0.709325i
$76$	−2.22556	−	6.84957i	−0.255289	−	0.785700i
$77$	0.386973	−	0.977382i	0.0440997	−	0.111383i
$78$	−3.63877	+	3.87490i	−0.412010	+	0.438746i
$79$	−3.20949	−	16.8248i	−0.361096	−	1.89293i	−0.443397	−	0.896325i	$-0.646227\pi$
$79$	−3.20949	−	16.8248i	−0.361096	−	1.89293i	0.0823006	−	0.996608i	$-0.473773\pi$
$80$	1.86507	+	0.0770174i	0.208521	+	0.00861081i
$81$	−2.44907	+	2.29983i	−0.272119	+	0.255537i
$82$	6.37800	−	2.07234i	0.704333	−	0.228852i
$83$	−6.03472	−	1.15118i	−0.662396	−	0.126359i	−0.154789	−	0.987948i	$-0.549470\pi$
$83$	−6.03472	−	1.15118i	−0.662396	−	0.126359i	−0.507607	+	0.861589i	$0.669470\pi$
$84$	0.277137	+	4.40497i	0.0302382	+	0.480622i
$85$	−8.21802	+	0.177213i	−0.891369	+	0.0192215i
$86$	−3.43141	−	5.40703i	−0.370018	−	0.583055i
$87$	11.3983	−	0.717123i	1.22203	−	0.0768836i
$88$	0.966560	+	0.613398i	0.103036	+	0.0653884i
$89$	−8.43845	+	10.2003i	−0.894474	+	1.08123i	0.101784	+	0.994807i	$0.467545\pi$
$89$	−8.43845	+	10.2003i	−0.894474	+	1.08123i	−0.996258	+	0.0864273i	$0.972455\pi$
$90$	−0.908886	+	2.04478i	−0.0958050	+	0.215539i
$91$	12.4177	+	3.18832i	1.30173	+	0.334227i
$92$	−5.10328	+	2.40142i	−0.532053	+	0.250365i
$93$	1.04426	+	0.339299i	0.108284	+	0.0351837i
$94$	−1.41421	−	0.777466i	−0.145864	−	0.0801895i
$95$	10.7417	−	3.74810i	1.10208	−	0.384547i
$96$	−7.56097	−	0.955173i	−0.771688	−	0.0974869i
$97$	−2.08420	+	16.4982i	−0.211619	+	1.67513i	0.425954	+	0.904745i	$0.359939\pi$
$97$	−2.08420	+	16.4982i	−0.211619	+	1.67513i	−0.637573	+	0.770390i	$0.720061\pi$
$98$	0.807331	−	0.512348i	0.0815528	−	0.0517550i
$99$	0.464269	−	0.337311i	0.0466608	−	0.0339010i
$100$	−0.139495	+	7.07629i	−0.0139495	+	0.707629i
$101$	−6.34341	−	4.60876i	−0.631193	−	0.458588i	0.225620	−	0.974215i	$-0.427559\pi$
$101$	−6.34341	−	4.60876i	−0.631193	−	0.458588i	−0.856813	+	0.515627i	$0.827559\pi$
$102$	3.64737	+	0.229473i	0.361143	+	0.0227212i
$103$	1.46435	+	2.66365i	0.144287	+	0.262457i	0.938569	−	0.345093i	$-0.112153\pi$
$103$	1.46435	+	2.66365i	0.144287	+	0.262457i	−0.794282	+	0.607550i	$0.792153\pi$
$104$	−5.94456	+	12.6328i	−0.582912	+	1.23875i
$105$	−6.94733	+	0.587698i	−0.677990	+	0.0573535i
$106$	0.143626	−	0.752911i	0.0139501	−	0.0731292i
$107$	−6.03692	−	8.30911i	−0.583611	−	0.803272i	0.410474	−	0.911872i	$-0.365363\pi$
$107$	−6.03692	−	8.30911i	−0.583611	−	0.803272i	−0.994085	+	0.108600i	$0.965363\pi$
$108$	−3.82115	+	6.95064i	−0.367690	+	0.668826i
$109$	−5.37276	+	8.46611i	−0.514617	+	0.810906i	−0.997914	−	0.0645499i	$-0.979439\pi$
$109$	−5.37276	+	8.46611i	−0.514617	+	0.810906i	0.483298	+	0.875456i	$0.339439\pi$
$110$	−0.387841	+	0.641294i	−0.0369792	+	0.0611450i
$111$	2.68504	+	1.06308i	0.254853	+	0.100903i
$112$	0.736855	+	1.86108i	0.0696262	+	0.175856i
$113$	12.8361	−	10.6189i	1.20752	−	0.998945i	0.207732	−	0.978186i	$-0.433392\pi$
$113$	12.8361	−	10.6189i	1.20752	−	0.998945i	0.999785	−	0.0207591i	$-0.00660829\pi$
$114$	−4.89925	+	1.25791i	−0.458856	+	0.117814i
$115$	−3.96636	−	7.97781i	−0.369865	−	0.743935i
$116$	11.5591	−	4.57656i	1.07323	−	0.424923i
$117$	4.79107	+	5.10198i	0.442935	+	0.471678i
$118$	1.79024	−	2.46405i	0.164805	−	0.226834i
$119$	−3.75296	−	7.97545i	−0.344033	−	0.731108i
$120$	0.789000	−	7.55163i	0.0720255	−	0.689366i
$121$	−9.47095	+	5.20670i	−0.860995	+	0.473336i
$122$	−8.60744	+	1.64196i	−0.779281	+	0.148656i
$123$	2.83681	+	11.0487i	0.255787	+	0.996224i
$124$	1.19521			0.107333
$125$	−11.1803	+	0.0206852i	−0.999998	+	0.00185014i
$126$	−2.39949			−0.213764
$127$	−0.714694	−	2.78355i	−0.0634188	−	0.247000i	0.928968	−	0.370160i	$-0.120697\pi$
$127$	−0.714694	−	2.78355i	−0.0634188	−	0.247000i	−0.992387	+	0.123160i	$0.960697\pi$
$128$	−9.40271	+	1.79366i	−0.831090	+	0.158539i
$129$	9.54549	−	5.24768i	0.840433	−	0.462032i
$130$	−8.35240	−	3.71256i	−0.732554	−	0.325613i
$131$	−7.29257	−	15.4975i	−0.637155	−	1.35402i	−0.918884	−	0.394529i	$-0.870908\pi$
$131$	−7.29257	−	15.4975i	−0.637155	−	1.35402i	0.281729	−	0.959494i	$-0.409092\pi$
$132$	−0.474342	+	0.652876i	−0.0412862	+	0.0568256i
$133$	8.35117	+	8.89310i	0.724139	+	0.771129i
$134$	−2.03350	+	0.805120i	−0.175668	+	0.0695518i
$135$	−11.1073	−	5.79802i	−0.955962	−	0.499014i
$136$	9.29734	−	2.38715i	0.797240	−	0.204696i
$137$	7.93364	−	6.56328i	0.677816	−	0.560738i	−0.233545	−	0.972346i	$-0.575033\pi$
$137$	7.93364	−	6.56328i	0.677816	−	0.560738i	0.911361	+	0.411608i	$0.135033\pi$
$138$	1.45819	+	3.68296i	0.124129	+	0.313514i
$139$	−0.532385	−	0.210786i	−0.0451563	−	0.0178786i	0.345438	−	0.938442i	$-0.387730\pi$
$139$	−0.532385	−	0.210786i	−0.0451563	−	0.0178786i	−0.390594	+	0.920563i	$0.627730\pi$
$140$	−6.99464	+	2.94535i	−0.591155	+	0.248928i
$141$	1.47087	−	2.31773i	0.123870	−	0.195188i
$142$	1.33085	−	2.42081i	0.111683	−	0.203150i
$143$	1.37783	+	1.89642i	0.115220	+	0.158586i
$144$	−0.204757	+	1.07338i	−0.0170631	+	0.0894479i
$145$	7.62142	+	18.0994i	0.632924	+	1.50307i
$146$	2.47687	−	5.26361i	0.204987	−	0.435619i
$147$	0.783538	+	1.42525i	0.0646251	+	0.117553i
$148$	3.13733	+	0.197384i	0.257887	+	0.0162248i
$149$	0.662571	+	0.481386i	0.0542799	+	0.0394367i	0.614594	−	0.788843i	$-0.289320\pi$
$149$	0.662571	+	0.481386i	0.0542799	+	0.0394367i	−0.560314	+	0.828280i	$0.689320\pi$
$150$	4.95386	+	0.409834i	0.404481	+	0.0334628i
$151$	0.346884	−	0.252026i	0.0282290	−	0.0205096i	−0.573581	−	0.819149i	$-0.694446\pi$
$151$	0.346884	−	0.252026i	0.0282290	−	0.0205096i	0.601810	+	0.798639i	$0.294446\pi$
$152$	−11.2173	+	7.11870i	−0.909841	+	0.577403i
$153$	0.603090	−	4.77395i	0.0487569	−	0.385951i
$154$	−0.797311	−	0.100724i	−0.0642492	−	0.00811656i
$155$	0.0407042	+	1.88760i	0.00326944	+	0.151616i
$156$	−8.62476	−	4.74150i	−0.690534	−	0.379624i
$157$	16.4545	+	5.34640i	1.31321	+	0.426689i	0.880159	−	0.474679i	$-0.157436\pi$
$157$	16.4545	+	5.34640i	1.31321	+	0.426689i	0.433055	+	0.901368i	$0.357436\pi$
$158$	−11.8483	+	5.57539i	−0.942600	+	0.443554i
$159$	1.26281	+	0.324233i	0.100147	+	0.0257134i
$160$	−2.73252	−	12.8166i	−0.216025	−	1.01324i
$161$	6.08974	−	7.36123i	0.479939	−	0.580146i
$162$	2.16862	+	1.37625i	0.170383	+	0.108128i
$163$	−6.16522	+	0.387883i	−0.482897	+	0.0303813i	−0.302374	−	0.953189i	$-0.597779\pi$
$163$	−6.16522	+	0.387883i	−0.482897	+	0.0303813i	−0.180523	+	0.983571i	$0.557779\pi$
$164$	6.65338	+	10.4841i	0.519542	+	0.818667i
$165$	−1.04724	−	0.726894i	−0.0815276	−	0.0565886i
$166$	0.294912	+	4.68749i	0.0228896	+	0.363820i
$167$	17.8432	+	3.40377i	1.38075	+	0.263391i	0.823669	−	0.567070i	$-0.191923\pi$
$167$	17.8432	+	3.40377i	1.38075	+	0.263391i	0.557076	+	0.830462i	$0.311923\pi$
$168$	7.74330	−	2.51595i	0.597409	−	0.194110i
$169$	−11.3636	+	10.6712i	−0.874126	+	0.820859i
$170$	1.69367	+	6.05164i	0.129899	+	0.464139i
$171$	1.24795	+	6.54197i	0.0954330	+	0.500277i
$172$	8.11691	−	8.64363i	0.618908	−	0.659070i
$173$	0.464801	−	1.17395i	0.0353382	−	0.0892540i	−0.911036	−	0.412327i	$-0.864716\pi$
$173$	0.464801	−	1.17395i	0.0353382	−	0.0892540i	0.946374	+	0.323073i	$0.104716\pi$
$174$	−2.69812	−	8.30397i	−0.204544	−	0.629523i
$175$	−4.88980	−	10.9463i	−0.369634	−	0.827464i
$176$	−0.113095	+	0.348069i	−0.00852482	+	0.0262367i
$177$	3.99177	+	3.30228i	0.300040	+	0.248215i
$178$	9.15757	+	4.30923i	0.686389	+	0.322990i
$179$	5.05238	+	4.74450i	0.377633	+	0.354621i	0.850002	−	0.526780i	$-0.176601\pi$
$179$	5.05238	+	4.74450i	0.377633	+	0.354621i	−0.472369	+	0.881401i	$0.656601\pi$
$180$	−4.08562	−	0.688439i	−0.304524	−	0.0513132i
$181$	−6.63103	+	0.837694i	−0.492881	+	0.0622653i	−0.367845	−	0.929887i	$-0.619904\pi$
$181$	−6.63103	+	0.837694i	−0.492881	+	0.0622653i	−0.125035	+	0.992152i	$0.539904\pi$
$182$		−	9.80130i		−	0.726521i
$183$	−1.86808	−	14.7874i	−0.138093	−	1.09312i
$184$	6.63179	+	8.01646i	0.488902	+	0.590981i
$185$	−0.204883	+	4.96150i	−0.0150633	+	0.364777i
$186$	0.0527078	−	0.837767i	0.00386472	−	0.0614280i
$187$	0.400793	−	1.56099i	0.0293089	−	0.114151i
$188$	0.743112	−	2.89423i	0.0541970	−	0.211083i
$189$	0.843625	−	13.4090i	0.0613647	−	0.975364i
$190$	−4.81768	−	7.24150i	−0.349511	−	0.525354i
$191$	−12.3363	−	14.9120i	−0.892623	−	1.07900i	−0.996432	−	0.0843985i	$-0.973103\pi$
$191$	−12.3363	−	14.9120i	−0.892623	−	1.07900i	0.103809	−	0.994597i	$-0.466897\pi$
$192$	0.458120	+	3.62639i	0.0330620	+	0.261712i
$193$		−	2.28327i		−	0.164353i	−0.996618	−	0.0821766i	$-0.973813\pi$
$193$		−	2.28327i		−	0.164353i	0.996618	−	0.0821766i	$-0.0261872\pi$
$194$	12.6129	−	1.59338i	0.905556	−	0.114398i
$195$	7.19453	−	13.7826i	0.515211	−	0.986989i
$196$	1.29059	+	1.21195i	0.0921851	+	0.0865676i
$197$	−1.80100	−	0.847485i	−0.128316	−	0.0603808i	0.360550	−	0.932740i	$-0.382589\pi$
$197$	−1.80100	−	0.847485i	−0.128316	−	0.0603808i	−0.488865	+	0.872359i	$0.662589\pi$
$198$	−0.338043	−	0.279654i	−0.0240237	−	0.0198741i
$199$	6.34746	−	19.5355i	0.449960	−	1.38483i	−0.426992	−	0.904255i	$-0.640427\pi$
$199$	6.34746	−	19.5355i	0.449960	−	1.38483i	0.876952	−	0.480578i	$-0.159573\pi$
$200$	12.7073	−	2.99701i	0.898543	−	0.211921i
$201$	−1.14959	−	3.53807i	−0.0810857	−	0.249556i
$202$	−2.20668	+	5.57345i	−0.155262	+	0.392146i
$203$	−14.4157	+	15.3511i	−1.01178	+	1.07744i
$204$	1.26795	+	6.64685i	0.0887745	+	0.465372i
$205$	−16.3309	+	10.8647i	−1.14060	+	0.758825i
$206$	1.69399	−	1.59076i	0.118026	−	0.110833i
$207$	4.96024	−	1.61168i	0.344761	−	0.112019i
$208$	−4.38446	−	0.836380i	−0.304007	−	0.0579925i
$209$	0.140059	+	2.22617i	0.00968807	+	0.153988i
$210$	1.75604	+	5.03267i	0.121178	+	0.347287i
$211$	14.1792	+	22.3429i	0.976137	+	1.53815i	0.836517	+	0.547941i	$0.184588\pi$
$211$	14.1792	+	22.3429i	0.976137	+	1.53815i	0.139620	+	0.990205i	$0.455412\pi$
$212$	1.41640	−	0.0891126i	0.0972790	−	0.00612028i
$213$	3.96744	+	2.51781i	0.271845	+	0.172518i
$214$	−5.00502	+	6.05002i	−0.342136	+	0.413571i
$215$	13.9273	+	12.5247i	0.949834	+	0.854174i
$216$	14.1718	+	3.63870i	0.964268	+	0.247582i
$217$	−1.83189	+	0.862020i	−0.124357	+	0.0585177i
$218$	7.29053	+	2.36884i	0.493777	+	0.160438i
$219$	8.67098	+	4.76691i	0.585930	+	0.322118i
$220$	−1.32868	−	0.400259i	−0.0895798	−	0.0269855i
$221$	19.5003	+	2.46346i	1.31173	+	0.165710i
$222$	0.276706	−	2.19035i	0.0185713	−	0.147007i
$223$	−12.5422	+	7.95950i	−0.839886	+	0.533008i	−0.884793	−	0.465984i	$-0.845701\pi$
$223$	−12.5422	+	7.95950i	−0.839886	+	0.533008i	0.0449078	+	0.998991i	$0.485701\pi$
$224$	11.3686	−	8.25974i	0.759594	−	0.551877i
$225$	0.948111	−	6.47586i	0.0632074	−	0.431724i
$226$	−10.3036	−	7.48602i	−0.685387	−	0.497963i
$227$	3.08996	+	0.194404i	0.205088	+	0.0129030i	0.165002	−	0.986293i	$-0.447237\pi$
$227$	3.08996	+	0.194404i	0.205088	+	0.0129030i	0.0400857	+	0.999196i	$0.487237\pi$
$228$	−4.51187	−	8.20707i	−0.298806	−	0.543526i
$229$	1.14443	−	2.43205i	0.0756263	−	0.160714i	−0.863439	−	0.504454i	$-0.831694\pi$
$229$	1.14443	−	2.43205i	0.0756263	−	0.160714i	0.939065	+	0.343740i	$0.111694\pi$
$230$	−5.15336	+	4.45381i	−0.339803	+	0.293676i
$231$	0.256145	−	1.34276i	0.0168531	−	0.0883472i
$232$	−13.4798	−	18.5533i	−0.884990	−	1.21808i
$233$	−4.83045	+	8.78655i	−0.316453	+	0.575626i	−0.985920	−	0.167216i	$-0.946522\pi$
$233$	−4.83045	+	8.78655i	−0.316453	+	0.575626i	0.669467	+	0.742842i	$0.266522\pi$
$234$	2.86704	−	4.51774i	0.187424	−	0.295334i
$235$	4.59616	+	1.07503i	0.299820	+	0.0701272i
$236$	5.24336	+	2.07599i	0.341314	+	0.135136i
$237$	−8.19935	−	20.7092i	−0.532605	−	1.34521i
$238$	−5.19218	+	4.29535i	−0.336559	+	0.278426i
$239$	−23.8116	+	6.11379i	−1.54025	+	0.395468i	−0.920947	−	0.389687i	$-0.872583\pi$
$239$	−23.8116	+	6.11379i	−1.54025	+	0.395468i	−0.619299	+	0.785155i	$0.712583\pi$
$240$	2.40113	−	0.356082i	0.154992	−	0.0229850i
$241$	−16.6756	+	6.60234i	−1.07417	+	0.425294i	−0.837580	−	0.546315i	$-0.816030\pi$
$241$	−16.6756	+	6.60234i	−1.07417	+	0.425294i	−0.236591	+	0.971609i	$0.576030\pi$
$242$	5.65615	+	6.02319i	0.363591	+	0.387185i
$243$	7.31278	−	10.0652i	0.469115	−	0.645682i
$244$	−6.90812	−	14.6805i	−0.442247	−	0.939822i
$245$	−1.87007	+	2.07950i	−0.119475	+	0.132855i
$246$	7.64204	−	4.20124i	0.487238	−	0.267862i
$247$	−26.7222	+	5.09754i	−1.70030	+	0.324349i
$248$	−0.548306	−	2.13551i	−0.0348175	−	0.135605i
$249$	−7.98901			−0.506283
$250$	2.14097	+	8.27494i	0.135407	+	0.523353i
$251$	7.88642			0.497786			0.248893	−	0.968531i	$-0.419933\pi$
$251$	7.88642			0.497786			0.248893	+	0.968531i	$0.419933\pi$
$252$	−1.10489	−	4.30325i	−0.0696013	−	0.271079i
$253$	1.71586	−	0.327317i	0.107875	−	0.0205783i
$254$	−1.92530	+	1.05844i	−0.120804	+	0.0664126i
$255$	−10.4542	+	2.22884i	−0.654666	+	0.139576i
$256$	5.50948	+	11.7082i	0.344342	+	0.731765i
$257$	0.927696	−	1.27686i	0.0578681	−	0.0796486i	−0.779102	−	0.626897i	$-0.784325\pi$
$257$	0.927696	−	1.27686i	0.0578681	−	0.0796486i	0.836970	+	0.547248i	$0.184325\pi$
$258$	−5.70067	−	6.07059i	−0.354908	−	0.377939i
$259$	−4.95089	+	1.96019i	−0.307633	+	0.121801i
$260$	2.81209	−	16.6887i	0.174399	−	1.03499i
$261$	−11.1351	+	2.85901i	−0.689246	+	0.176968i
$262$	−10.0892	+	8.34651i	−0.623312	+	0.515649i
$263$	−6.52664	−	16.4844i	−0.402450	−	1.01647i	−0.979801	−	0.199976i	$-0.935914\pi$
$263$	−6.52664	−	16.4844i	−0.402450	−	1.01647i	0.577351	−	0.816496i	$-0.304086\pi$
$264$	1.38411	+	0.548008i	0.0851861	+	0.0337276i
$265$	0.188972	+	2.23389i	0.0116085	+	0.137227i
$266$	4.99746	−	7.87473i	0.306414	−	0.482831i
$267$	−8.29343	+	15.0857i	−0.507550	+	0.923229i
$268$	−2.38026	−	3.27614i	−0.145397	−	0.200122i
$269$	−2.27377	+	11.9195i	−0.138635	+	0.726748i	0.843288	+	0.537462i	$0.180617\pi$
$269$	−2.27377	+	11.9195i	−0.138635	+	0.726748i	−0.981922	+	0.189285i	$0.939383\pi$
$270$	−2.18159	+	9.32713i	−0.132767	+	0.567631i
$271$	−13.4707	+	28.6267i	−0.818286	+	1.73895i	−0.158686	+	0.987329i	$0.550726\pi$
$271$	−13.4707	+	28.6267i	−0.818286	+	1.73895i	−0.659600	+	0.751617i	$0.729274\pi$
$272$	1.47839	+	2.68918i	0.0896404	+	0.163055i
$273$	16.6387	+	1.04682i	1.00702	+	0.0633564i
$274$	−6.36840	−	4.62691i	−0.384729	−	0.279522i
$275$	0.586879	−	2.11202i	0.0353901	−	0.127360i
$276$	−5.93356	+	4.31099i	−0.357159	+	0.259491i
$277$	−1.96346	+	1.24605i	−0.117973	+	0.0748680i	−0.593504	−	0.804831i	$-0.702256\pi$
$277$	−1.96346	+	1.24605i	−0.117973	+	0.0748680i	0.475531	+	0.879699i	$0.342256\pi$
$278$	−0.0548648	+	0.434299i	−0.00329057	+	0.0260476i
$279$	−1.09653	−	0.138524i	−0.0656476	−	0.00829322i
$280$	8.47131	+	11.1463i	0.506258	+	0.666116i
$281$	−14.7075	−	8.08552i	−0.877377	−	0.482342i	−0.0216473	−	0.999766i	$-0.506891\pi$
$281$	−14.7075	−	8.08552i	−0.877377	−	0.482342i	−0.855729	+	0.517424i	$0.826891\pi$
$282$	−1.99589	−	0.648505i	−0.118854	−	0.0386179i
$283$	9.16111	−	4.31089i	0.544571	−	0.256256i	−0.133758	−	0.991014i	$-0.542704\pi$
$283$	9.16111	−	4.31089i	0.544571	−	0.256256i	0.678329	+	0.734758i	$0.262704\pi$
$284$	4.95429	+	1.27205i	0.293983	+	0.0754820i
$285$	12.8078	−	7.40509i	0.758666	−	0.438640i
$286$	1.14231	−	1.38082i	0.0675463	−	0.0816494i
$287$	−17.7589	−	11.2701i	−1.04827	−	0.665255i
$288$	7.65625	−	0.481690i	0.451149	−	0.0283839i
$289$	1.86819	+	2.94380i	0.109894	+	0.173165i
$290$	11.9533	−	9.08469i	0.701924	−	0.533472i
$291$	1.35782	+	21.5819i	0.0795968	+	1.26516i
$292$	10.5802	+	2.01829i	0.619162	+	0.118111i
$293$	−11.8075	+	3.83648i	−0.689801	+	0.224130i	−0.632881	−	0.774249i	$-0.718128\pi$
$293$	−11.8075	+	3.83648i	−0.689801	+	0.224130i	−0.0569195	+	0.998379i	$0.518128\pi$
$294$	0.906408	−	0.851174i	0.0528628	−	0.0496415i
$295$	−3.10005	+	8.35153i	−0.180492	+	0.486245i
$296$	−1.08658	−	5.69606i	−0.0631563	−	0.331077i
$297$	1.68163	−	1.79076i	0.0975782	−	0.103910i
$298$	0.230489	−	0.582148i	0.0133519	−	0.0337229i
$299$	6.58329	+	20.2613i	0.380721	+	1.17174i
$300$	1.54609	+	9.07295i	0.0892634	+	0.523827i
$301$	−6.20664	+	19.1021i	−0.357745	+	1.10103i
$302$	−0.252573	−	0.208947i	−0.0145340	−	0.0120235i
$303$	−9.22582	−	4.34134i	−0.530010	−	0.249404i
$304$	−3.09618	−	2.90751i	−0.177578	−	0.166757i
$305$	22.9496	−	11.4099i	1.31409	−	0.653331i
$306$	−3.64971	+	0.461065i	−0.208640	+	0.0263573i
$307$			31.5212i			1.79901i	0.436911	+	0.899505i	$0.356072\pi$
$307$			31.5212i			1.79901i	−0.436911	+	0.899505i	$0.643928\pi$
$308$	−0.186497	−	1.47628i	−0.0106267	−	0.0841186i
$309$	2.51955	+	3.04562i	0.143332	+	0.173259i
$310$	1.39000	−	0.389020i	0.0789469	−	0.0220949i
$311$	0.00198664	−	0.0315768i	0.000112652	−	0.00179056i	−0.997970	−	0.0636858i	$-0.979714\pi$
$311$	0.00198664	−	0.0315768i	0.000112652	−	0.00179056i	0.998083	+	0.0618952i	$0.0197145\pi$
$312$	−4.51511	+	17.5852i	−0.255618	+	0.995565i
$313$	4.30436	−	16.7644i	0.243297	−	0.947578i	−0.723146	−	0.690695i	$-0.757305\pi$
$313$	4.30436	−	16.7644i	0.243297	−	0.947578i	0.966443	−	0.256883i	$-0.0826955\pi$
$314$	0.830526	−	13.2008i	0.0468693	−	0.744966i
$315$	6.75848	−	1.89150i	0.380797	−	0.106574i
$316$	−15.4546	−	18.6814i	−0.869391	−	1.05091i
$317$	−3.27455	−	25.9208i	−0.183917	−	1.45586i	−0.766060	−	0.642769i	$-0.777786\pi$
$317$	−3.27455	−	25.9208i	−0.183917	−	1.45586i	0.582143	−	0.813086i	$-0.302214\pi$
$318$		−	0.996735i		−	0.0558941i
$319$	−3.82002	+	0.482581i	−0.213880	+	0.0270193i
$320$	−5.62806	+	2.79812i	−0.314618	+	0.156420i
$321$	−9.73599	−	9.14270i	−0.543410	−	0.510296i
$322$	−6.60870	−	3.10982i	−0.368289	−	0.173303i
$323$	14.4112	+	11.9220i	0.801861	+	0.663357i
$324$	−1.46958	+	4.52291i	−0.0816435	+	0.251273i
$325$	26.4522	+	3.87279i	1.46730	+	0.214823i
$326$	1.45938	+	4.49151i	0.0808277	+	0.248762i
$327$	−4.80001	+	12.1234i	−0.265441	+	0.670427i
$328$	15.6798	−	16.6973i	0.865771	−	0.921953i
$329$	0.948439	+	4.97189i	0.0522891	+	0.274109i
$330$	−0.339149	+	0.913668i	−0.0186695	+	0.0502958i
$331$	15.6935	−	14.7372i	0.862593	−	0.810029i	−0.120580	−	0.992704i	$-0.538476\pi$
$331$	15.6935	−	14.7372i	0.862593	−	0.810029i	0.983173	+	0.182675i	$0.0584756\pi$
$332$	−8.27074	+	2.68733i	−0.453916	+	0.147486i
$333$	−2.85541	−	0.544699i	−0.156476	−	0.0298493i
$334$	−0.871982	−	13.8598i	−0.0477127	−	0.758372i
$335$	5.09295	−	3.87071i	0.278258	−	0.211480i
$336$	1.39472	+	2.19772i	0.0760880	+	0.119896i
$337$	20.9350	−	1.31712i	1.14040	−	0.0717480i	0.518667	−	0.854976i	$-0.326428\pi$
$337$	20.9350	−	1.31712i	1.14040	−	0.0717480i	0.621734	+	0.783228i	$0.286428\pi$
$338$	10.0624	+	6.38577i	0.547320	+	0.347340i
$339$	13.8088	−	16.6919i	0.749990	−	0.906582i
$340$	−10.0731	+	5.82400i	−0.546291	+	0.315851i
$341$	−0.358544	−	0.0920584i	−0.0194162	−	0.00498524i
$342$	4.60698	−	2.16788i	0.249117	−	0.117225i
$343$	−18.8150	−	6.11337i	−1.01592	−	0.330091i
$344$	−19.1674	−	10.5373i	−1.03343	−	0.568136i
$345$	−7.01041	−	9.22405i	−0.377428	−	0.496606i
$346$	−0.957667	−	0.120981i	−0.0514845	−	0.00650400i
$347$	−2.02238	+	16.0088i	−0.108567	+	0.859398i	0.839948	+	0.542667i	$0.182585\pi$
$347$	−2.02238	+	16.0088i	−0.108567	+	0.859398i	−0.948515	+	0.316731i	$0.897415\pi$
$348$	13.6499	−	8.66251i	0.731713	−	0.464359i
$349$	23.7166	−	17.2311i	1.26952	−	0.922359i	0.270335	−	0.962766i	$-0.412865\pi$
$349$	23.7166	−	17.2311i	1.26952	−	0.922359i	0.999183	+	0.0404070i	$0.0128655\pi$
$350$	−7.17593	+	5.70200i	−0.383570	+	0.304785i
$351$	24.2384	+	17.6102i	1.29375	+	0.939963i
$352$	2.56426	+	0.161330i	0.136676	+	0.00859890i
$353$	0.0443327	+	0.0806409i	0.00235959	+	0.00429208i	0.877484	−	0.479606i	$-0.159220\pi$
$353$	0.0443327	+	0.0806409i	0.00235959	+	0.00429208i	−0.875124	+	0.483898i	$0.839220\pi$
$354$	1.68636	−	3.58370i	0.0896291	−	0.190472i
$355$	−1.84022	+	7.86763i	−0.0976686	+	0.417570i
$356$	−3.51140	+	18.4074i	−0.186104	+	0.975591i
$357$	−6.73725	−	9.27303i	−0.356573	−	0.490781i
$358$	2.55266	−	4.64327i	0.134912	−	0.245404i
$359$	12.3900	−	19.5236i	0.653921	−	1.03042i	−0.341957	−	0.939716i	$-0.611090\pi$
$359$	12.3900	−	19.5236i	0.653921	−	1.03042i	0.995878	−	0.0906995i	$-0.0289103\pi$
$360$	0.644236	+	7.61567i	0.0339542	+	0.401381i
$361$	−6.40300	−	2.53513i	−0.337000	−	0.133428i
$362$	1.88102	+	4.75093i	0.0988645	+	0.249703i
$363$	−10.8291	+	8.95860i	−0.568380	+	0.470205i
$364$	17.5776	−	4.51317i	0.921318	−	0.236554i
$365$	−2.82716	+	16.7781i	−0.147980	+	0.878206i
$366$	−10.5947	+	4.19474i	−0.553794	+	0.219262i
$367$	−6.34641	−	6.75824i	−0.331280	−	0.352777i	0.541666	−	0.840594i	$-0.317794\pi$
$367$	−6.34641	−	6.75824i	−0.331280	−	0.352777i	−0.872946	+	0.487816i	$0.837794\pi$
$368$	−1.95507	+	2.69093i	−0.101915	+	0.140274i
$369$	−4.88895	−	10.3895i	−0.254508	−	0.540858i
$370$	3.71288	−	0.791590i	0.193023	−	0.0411528i
$371$	−2.10663	+	1.15813i	−0.109371	+	0.0601271i
$372$	1.52672	−	0.291237i	0.0791567	−	0.0150999i
$373$	−1.40284	−	5.46370i	−0.0726362	−	0.282899i	0.921881	−	0.387473i	$-0.126652\pi$
$373$	−1.40284	−	5.46370i	−0.0726362	−	0.282899i	−0.994517	+	0.104574i	$0.966652\pi$
$374$	−1.23209			−0.0637098
$375$	−14.2762	+	2.75072i	−0.737222	+	0.142047i
$376$	−5.51207			−0.284263
$377$	−11.6783	−	45.4840i	−0.601463	−	2.34254i
$378$	−10.0896	+	1.92470i	−0.518954	+	0.0989957i
$379$	2.01687	−	1.10878i	0.103599	−	0.0569543i	−0.429112	−	0.903252i	$-0.641173\pi$
$379$	2.01687	−	1.10878i	0.103599	−	0.0569543i	0.532711	+	0.846297i	$0.321173\pi$
$380$	10.7685	−	11.9745i	0.552413	−	0.614278i
$381$	−1.59119	−	3.38144i	−0.0815189	−	0.173237i
$382$	−8.69672	+	11.9700i	−0.444963	+	0.612439i
$383$	8.63182	+	9.19195i	0.441065	+	0.469687i	0.910637	−	0.413208i	$-0.135592\pi$
$383$	8.63182	+	9.19195i	0.441065	+	0.469687i	−0.469572	+	0.882894i	$0.655592\pi$
$384$	−11.5736	+	4.58230i	−0.590612	+	0.233840i
$385$	2.32513	−	0.344810i	0.118500	−	0.0175732i
$386$	−1.69073	+	0.434105i	−0.0860558	+	0.0220954i
$387$	−8.44851	+	6.98922i	−0.429462	+	0.355282i
$388$	8.66539	+	21.8863i	0.439919	+	1.11111i
$389$	14.6798	+	5.81215i	0.744296	+	0.294688i	0.709499	−	0.704707i	$-0.248921\pi$
$389$	14.6798	+	5.81215i	0.744296	+	0.294688i	0.0347973	+	0.999394i	$0.488921\pi$
$390$	−11.5737	−	2.70705i	−0.586055	−	0.137077i
$391$	7.84822	−	12.3668i	0.396901	−	0.625417i
$392$	1.57335	−	2.86190i	0.0794659	−	0.144548i
$393$	−13.0915	−	18.0189i	−0.660378	−	0.908933i
$394$	−0.285137	+	1.49474i	−0.0143650	+	0.0753040i
$395$	28.9772	−	25.0437i	1.45800	−	1.26008i
$396$	0.345873	−	0.735017i	0.0173807	−	0.0369360i
$397$	4.85846	+	8.83750i	0.243839	+	0.443541i	0.969700	−	0.244300i	$-0.0785583\pi$
$397$	4.85846	+	8.83750i	0.243839	+	0.443541i	−0.725861	+	0.687842i	$0.758558\pi$
$398$	−15.6726	−	0.986034i	−0.785595	−	0.0494254i
$399$	12.8344	+	9.32475i	0.642525	+	0.466822i
$400$	1.93835	+	3.69661i	0.0969175	+	0.184830i
$401$	2.26478	−	1.64546i	0.113098	−	0.0821704i	−0.529799	−	0.848123i	$-0.677733\pi$
$401$	2.26478	−	1.64546i	0.113098	−	0.0821704i	0.642897	+	0.765953i	$0.277733\pi$
$402$	−2.40133	+	1.52393i	−0.119767	+	0.0760067i
$403$	0.565834	−	4.47904i	0.0281862	−	0.223117i
$404$	−11.0115	−	1.39108i	−0.547843	−	0.0692086i
$405$	−7.19308	−	2.16688i	−0.357427	−	0.107673i
$406$	14.1081	+	7.75598i	0.700172	+	0.384923i
$407$	−0.925940	−	0.300856i	−0.0458972	−	0.0149129i
$408$	11.2944	−	5.31472i	0.559154	−	0.263118i
$409$	6.90885	+	1.77389i	0.341621	+	0.0877133i	0.415603	−	0.909546i	$-0.363571\pi$
$409$	6.90885	+	1.77389i	0.341621	+	0.0877133i	−0.0739818	+	0.997260i	$0.523571\pi$
$410$	11.1501	+	10.0271i	0.550663	+	0.495205i
$411$	8.53483	−	10.3168i	0.420992	−	0.508892i
$412$	3.63288	+	2.30550i	0.178979	+	0.113584i
$413$	−9.53367	+	0.599808i	−0.469121	+	0.0295146i
$414$	−2.13649	−	3.36657i	−0.105003	−	0.165458i
$415$	−4.52576	−	12.9705i	−0.222161	−	0.636694i
$416$	1.96758	+	31.2738i	0.0964685	+	1.53332i
$417$	−0.731409	−	0.139524i	−0.0358172	−	0.00683250i
$418$	1.62182	−	0.526962i	0.0793259	−	0.0257745i
$419$	2.22820	−	2.09242i	0.108855	−	0.102221i	−0.628209	−	0.778045i	$-0.716212\pi$
$419$	2.22820	−	2.09242i	0.108855	−	0.102221i	0.737064	+	0.675823i	$0.236212\pi$
$420$	−8.21697	+	5.46665i	−0.400947	+	0.266745i
$421$	−4.55317	−	23.8685i	−0.221908	−	1.16328i	−0.902523	−	0.430641i	$-0.858288\pi$
$421$	−4.55317	−	23.8685i	−0.221908	−	1.16328i	0.680616	−	0.732641i	$-0.261712\pi$
$422$	13.8488	−	14.7474i	0.674148	−	0.717894i
$423$	−1.01719	+	2.56914i	−0.0494577	+	0.124916i
$424$	−0.808996	−	2.48983i	−0.0392883	−	0.120917i
$425$	−9.54088	−	15.7101i	−0.462801	−	0.762052i
$426$	1.11010	−	3.41653i	0.0537845	−	0.165532i
$427$	21.1759	+	17.5182i	1.02477	+	0.847767i
$428$	−13.1547	−	6.19015i	−0.635858	−	0.299212i
$429$	2.22208	+	2.08667i	0.107283	+	0.100745i
$430$	6.62641	−	12.6942i	0.319554	−	0.612170i
$431$	21.3566	−	2.69796i	1.02871	−	0.129956i	0.407181	−	0.913347i	$-0.366512\pi$
$431$	21.3566	−	2.69796i	1.02871	−	0.129956i	0.621529	+	0.783391i	$0.286512\pi$
$432$			4.67767i			0.225054i
$433$	−0.585967	−	4.63840i	−0.0281598	−	0.222908i	0.971755	−	0.235994i	$-0.0758344\pi$
$433$	−0.585967	−	4.63840i	−0.0281598	−	0.222908i	−0.999914	+	0.0130861i	$0.995834\pi$
$434$	0.986601	+	1.19260i	0.0473584	+	0.0572464i
$435$	14.1455	+	21.2623i	0.678227	+	1.01945i
$436$	−0.891223	+	14.1656i	−0.0426818	+	0.678409i
$437$	−5.04149	+	19.6353i	−0.241167	+	0.939285i
$438$	1.88127	−	7.32705i	0.0898904	−	0.350100i
$439$	−1.76929	+	28.1220i	−0.0844436	+	1.34219i	0.696485	+	0.717571i	$0.254746\pi$
$439$	−1.76929	+	28.1220i	−0.0844436	+	1.34219i	−0.780928	+	0.624621i	$0.785254\pi$
$440$	−0.105615	+	2.55760i	−0.00503501	+	0.121929i
$441$	−1.04357	−	1.26146i	−0.0496938	−	0.0600695i
$442$	−1.88333	−	14.9081i	−0.0895808	−	0.709105i
$443$			7.72655i			0.367100i	0.983010	+	0.183550i	$0.0587589\pi$
$443$			7.72655i			0.367100i	−0.983010	+	0.183550i	$0.941241\pi$
$444$	4.05559	−	0.512340i	0.192470	−	0.0243146i
$445$	−29.1904	−	4.91867i	−1.38376	−	0.233167i
$446$	8.27848	+	7.77401i	0.391997	+	0.368110i
$447$	0.963640	+	0.453454i	0.0455786	+	0.0214477i
$448$	−5.19309	−	4.29609i	−0.245350	−	0.202971i
$449$	−9.85181	+	30.3208i	−0.464936	+	1.43092i	0.394128	+	0.919056i	$0.371047\pi$
$449$	−9.85181	+	30.3208i	−0.464936	+	1.43092i	−0.859063	+	0.511869i	$0.828953\pi$
$450$	−4.97555	+	0.529157i	−0.234549	+	0.0249447i
$451$	−1.18839	−	3.65749i	−0.0559592	−	0.172225i
$452$	8.68094	−	21.9256i	0.408317	−	1.03129i
$453$	0.381685	−	0.406453i	0.0179331	−	0.0190968i
$454$	−0.443524	−	2.32503i	−0.0208156	−	0.109119i
$455$	7.72626	+	27.6066i	0.362213	+	1.29422i
$456$	−12.5939	+	11.8264i	−0.589762	+	0.553824i
$457$	22.8872	−	7.43649i	1.07062	−	0.347864i	0.279889	−	0.960032i	$-0.409702\pi$
$457$	22.8872	−	7.43649i	1.07062	−	0.347864i	0.790728	+	0.612168i	$0.209702\pi$
$458$	−2.01848	−	0.385046i	−0.0943175	−	0.0179920i
$459$	−1.29338	−	20.5577i	−0.0603698	−	0.959550i
$460$	−10.3604	−	7.19119i	−0.483056	−	0.335291i
$461$	−12.2186	−	19.2534i	−0.569075	−	0.896719i	0.430909	−	0.902396i	$-0.358193\pi$
$461$	−12.2186	−	19.2534i	−0.569075	−	0.896719i	−0.999984	+	0.00567645i	$0.998193\pi$
$462$	−1.04300	+	0.0656197i	−0.0485246	+	0.00305291i
$463$	−24.6253	−	15.6277i	−1.14443	−	0.726280i	−0.178213	−	0.983992i	$-0.557032\pi$
$463$	−24.6253	−	15.6277i	−1.14443	−	0.726280i	−0.966222	+	0.257712i	$0.917032\pi$
$464$	4.67341	−	5.64918i	0.216957	−	0.262257i
$465$	0.511944	+	2.40123i	0.0237408	+	0.111354i
$466$	7.42471	+	1.90634i	0.343943	+	0.0883096i
$467$	−26.6246	+	12.5286i	−1.23204	+	0.579753i	−0.927884	−	0.372870i	$-0.878374\pi$
$467$	−26.6246	+	12.5286i	−1.23204	+	0.579753i	−0.304154	+	0.952623i	$0.598374\pi$
$468$	9.42227	+	3.06148i	0.435545	+	0.141517i
$469$	6.01102	+	3.30459i	0.277563	+	0.152592i
$470$	−0.0777983	−	3.60778i	−0.00358857	−	0.166415i
$471$	22.3211	+	2.81981i	1.02850	+	0.129930i
$472$	1.30382	−	10.3208i	0.0600130	−	0.475052i
$473$	−3.10068	+	1.96775i	−0.142570	+	0.0904774i
$474$	−13.7760	+	10.0088i	−0.632752	+	0.459721i
$475$	19.2780	+	16.5989i	0.884536	+	0.761609i
$476$	−10.0941	−	7.33378i	−0.462662	−	0.336143i
$477$	−1.30979	−	0.0824047i	−0.0599709	−	0.00377305i
$478$	9.05435	+	16.4698i	0.414137	+	0.753312i
$479$	−7.10123	+	15.0909i	−0.324464	+	0.689520i	−0.998804	−	0.0489007i	$-0.984428\pi$
$479$	−7.10123	+	15.0909i	−0.324464	+	0.689520i	0.674340	+	0.738421i	$0.264428\pi$
$480$	−6.61343	−	15.7056i	−0.301860	−	0.716859i
$481$	2.22495	−	11.6636i	0.101449	−	0.531815i
$482$	8.05939	+	11.0928i	0.367095	+	0.505263i
$483$	5.98508	−	10.8868i	0.272331	−	0.495367i
$484$	−8.19750	+	12.9172i	−0.372614	+	0.587145i
$485$	−34.2699	+	14.4306i	−1.55612	+	0.655260i
$486$	−8.84347	−	3.50138i	−0.401148	−	0.158826i
$487$	−10.9231	−	27.5885i	−0.494972	−	1.25016i	−0.935790	−	0.352559i	$-0.885312\pi$
$487$	−10.9231	−	27.5885i	−0.494972	−	1.25016i	0.440818	−	0.897596i	$-0.354688\pi$
$488$	−23.0608	+	19.0775i	−1.04391	+	0.863600i
$489$	−7.78068	+	1.99774i	−0.351855	+	0.0903409i
$490$	1.89539	+	0.989399i	0.0856251	+	0.0446965i
$491$	−28.4489	+	11.2637i	−1.28388	+	0.508324i	−0.908243	−	0.418444i	$-0.862576\pi$
$491$	−28.4489	+	11.2637i	−1.28388	+	0.508324i	−0.375636	+	0.926767i	$0.622576\pi$
$492$	11.0534	+	11.7707i	0.498326	+	0.530663i
$493$	−18.9770	+	26.1195i	−0.854679	+	1.17636i
$494$	8.85522	+	18.8183i	0.398415	+	0.846675i
$495$	1.17259	+	0.521204i	0.0527040	+	0.0234264i
$496$	0.617679	−	0.339572i	0.0277346	−	0.0152472i
$497$	−8.51079	+	1.62352i	−0.381761	+	0.0728248i
$498$	1.51891	+	5.91575i	0.0680639	+	0.265091i
$499$	−4.66942			−0.209032			−0.104516	−	0.994523i	$-0.533329\pi$
$499$	−4.66942			−0.209032			−0.104516	+	0.994523i	$0.533329\pi$
$500$	−13.8544	+	7.64994i	−0.619588	+	0.342116i
$501$	23.6215			1.05533
$502$	−1.49940	−	5.83979i	−0.0669216	−	0.260642i
$503$	5.50034	−	1.04925i	0.245248	−	0.0467835i	−0.0632916	−	0.997995i	$-0.520160\pi$
$503$	5.50034	−	1.04925i	0.245248	−	0.0467835i	0.308539	+	0.951212i	$0.400160\pi$
$504$	−7.18182	+	3.94824i	−0.319903	+	0.175868i
$505$	1.82192	−	17.4378i	0.0810743	−	0.775973i
$506$	−0.568601	−	1.20834i	−0.0252774	−	0.0537172i
$507$	−11.9152	+	16.3999i	−0.529173	+	0.728344i
$508$	−2.78474	−	2.96545i	−0.123553	−	0.131571i
$509$	15.8524	−	6.27641i	0.702645	−	0.278197i	0.0104892	−	0.999945i	$-0.496661\pi$
$509$	15.8524	−	6.27641i	0.702645	−	0.278197i	0.692156	+	0.721748i	$0.256661\pi$
$510$	3.63802	+	7.31742i	0.161094	+	0.324021i
$511$	−17.6718	+	4.53735i	−0.781755	+	0.200721i
$512$	−7.12880	+	5.89746i	−0.315052	+	0.260633i
$513$	10.4950	+	26.5073i	0.463364	+	1.17032i
$514$	−1.12188	−	0.444183i	−0.0494839	−	0.0195921i
$515$	−3.51735	+	5.81593i	−0.154993	+	0.256280i
$516$	8.26202	−	13.0189i	0.363715	−	0.573123i
$517$	−0.445841	+	0.810982i	−0.0196081	+	0.0356670i
$518$	2.39278	+	3.29338i	0.105133	+	0.144703i
$519$	0.307661	−	1.61282i	0.0135048	−	0.0707948i
$520$	−31.1080	+	2.63153i	−1.36418	+	0.115400i
$521$	4.42174	−	9.39668i	0.193720	−	0.411676i	−0.784243	−	0.620454i	$-0.786948\pi$
$521$	4.42174	−	9.39668i	0.193720	−	0.411676i	0.977963	+	0.208778i	$0.0669485\pi$
$522$	4.23412	+	7.70183i	0.185322	+	0.337100i
$523$	−23.8758	−	1.50214i	−1.04401	−	0.0656838i	−0.468491	−	0.883469i	$-0.655202\pi$
$523$	−23.8758	−	1.50214i	−1.04401	−	0.0656838i	−0.575524	+	0.817785i	$0.695202\pi$
$524$	−19.6143	−	14.2506i	−0.856856	−	0.622542i
$525$	−8.91331	−	12.7909i	−0.389009	−	0.558240i
$526$	−10.9656	+	7.96698i	−0.478123	+	0.347377i
$527$	−2.62072	+	1.66316i	−0.114160	+	0.0724483i
$528$	−0.0596486	+	0.472167i	−0.00259587	+	0.0205484i
$529$	−7.06832	−	0.892937i	−0.307318	−	0.0388233i
$530$	1.61824	−	0.564649i	0.0702917	−	0.0245268i
$531$	−4.56983	−	2.51229i	−0.198314	−	0.109024i
$532$	16.4237	+	5.33638i	0.712057	+	0.231361i
$533$	42.4386	−	19.9701i	1.83822	−	0.865000i
$534$	12.7475	+	3.27301i	0.551640	+	0.141637i
$535$	9.32809	−	20.9861i	0.403289	−	0.907307i
$536$	−4.76160	+	5.75578i	−0.205670	+	0.248612i
$537$	7.60980	+	4.82933i	0.328387	+	0.208401i
$538$	9.25856	−	0.582499i	0.399165	−	0.0251133i
$539$	−0.293808	−	0.462967i	−0.0126552	−	0.0199414i
$540$	−17.7318	+	0.382369i	−0.763055	+	0.0164545i
$541$	−0.758937	−	12.0630i	−0.0326292	−	0.518627i	−0.980065	−	0.198680i	$-0.936335\pi$
$541$	−0.758937	−	12.0630i	−0.0326292	−	0.518627i	0.947435	−	0.319948i	$-0.103665\pi$
$542$	23.7588	+	4.53223i	1.02053	+	0.194676i
$543$	−8.26609	+	2.68582i	−0.354732	+	0.115259i
$544$	15.7048	−	14.7478i	0.673339	−	0.632307i
$545$	−22.4020	−	0.925084i	−0.959598	−	0.0396263i
$546$	−2.38828	−	12.5198i	−0.102209	−	0.535797i
$547$	31.2112	−	33.2366i	1.33449	−	1.42109i	0.504399	−	0.863470i	$-0.331714\pi$
$547$	31.2112	−	33.2366i	1.33449	−	1.42109i	0.830095	−	0.557622i	$-0.188286\pi$
$548$	5.36546	−	13.5516i	0.229201	−	0.578896i
$549$	4.63629	+	14.2690i	0.197872	+	0.608987i
$550$	−1.67550	−	0.0330293i	−0.0714436	−	0.00140837i
$551$	13.8084	−	42.4980i	0.588259	−	1.81048i
$552$	10.4245	+	8.62393i	0.443698	+	0.367059i
$553$	37.1606	+	17.4864i	1.58023	+	0.743599i
$554$	1.29599	+	1.21701i	0.0550613	+	0.0517060i
$555$	0.947255	+	6.38754i	0.0402087	+	0.271136i
$556$	−0.804135	+	0.101586i	−0.0341029	+	0.00430820i
$557$		−	6.97153i		−	0.295393i	−0.989033	−	0.147697i	$-0.952814\pi$
$557$		−	6.97153i		−	0.295393i	0.989033	−	0.147697i	$-0.0471859\pi$
$558$	0.105902	+	0.838303i	0.00448320	+	0.0354882i
$559$	−28.5491	−	34.5100i	−1.20750	−	1.45962i
$560$	−2.77798	+	3.50938i	−0.117391	+	0.148298i
$561$	0.131592	−	2.09160i	0.00555583	−	0.0883074i
$562$	−3.19096	+	12.4280i	−0.134603	+	0.524242i
$563$	−10.6422	+	41.4487i	−0.448516	+	1.74685i	0.194404	+	0.980921i	$0.437723\pi$
$563$	−10.6422	+	41.4487i	−0.448516	+	1.74685i	−0.642920	+	0.765933i	$0.722277\pi$
$564$	0.243986	−	3.87804i	0.0102737	−	0.163295i
$565$	34.9226	+	12.9631i	1.46921	+	0.545362i
$566$	−4.93391	−	5.96407i	−0.207388	−	0.250689i
$567$	−1.00964	−	7.99210i	−0.0424008	−	0.335637i
$568$		−	9.43547i		−	0.395903i
$569$	7.24738	−	0.915557i	0.303826	−	0.0383822i	0.0280578	−	0.999606i	$-0.491068\pi$
$569$	7.24738	−	0.915557i	0.303826	−	0.0383822i	0.275768	+	0.961224i	$0.411068\pi$
$570$	−7.91844	−	8.07608i	−0.331667	−	0.338270i
$571$	−18.1512	−	17.0451i	−0.759605	−	0.713317i	0.204492	−	0.978868i	$-0.434446\pi$
$571$	−18.1512	−	17.0451i	−0.759605	−	0.713317i	−0.964097	+	0.265552i	$0.914446\pi$
$572$	3.00235	+	1.41280i	0.125535	+	0.0590721i
$573$	−19.3915	−	16.0420i	−0.810091	−	0.670165i
$574$	−4.96898	+	15.2930i	−0.207401	+	0.638316i
$575$	11.0042	−	16.6071i	0.458907	−	0.692563i
$576$	−1.13698	−	3.49927i	−0.0473743	−	0.145803i
$577$	−4.57018	+	11.5430i	−0.190259	+	0.480539i	−0.993325	−	0.115351i	$-0.963201\pi$
$577$	−4.57018	+	11.5430i	−0.190259	+	0.480539i	0.803066	+	0.595890i	$0.203201\pi$
$578$	1.82466	−	1.94306i	0.0758957	−	0.0808207i
$579$	−0.556362	−	2.91655i	−0.0231216	−	0.121208i
$580$	21.7966	+	17.2539i	0.905053	+	0.716428i
$581$	10.7383	−	10.0839i	0.445498	−	0.418351i
$582$	15.7230	−	5.10871i	0.651739	−	0.211763i
$583$	−0.431760	−	0.0823627i	−0.0178817	−	0.00341111i
$584$	−1.24759	−	19.8298i	−0.0516255	−	0.820563i
$585$	−4.51411	+	14.9848i	−0.186635	+	0.619547i
$586$	5.08576	+	8.01387i	0.210091	+	0.331050i
$587$	11.1402	−	0.700885i	0.459807	−	0.0289286i	0.168802	−	0.985650i	$-0.446010\pi$
$587$	11.1402	−	0.700885i	0.459807	−	0.0289286i	0.291005	+	0.956721i	$0.406010\pi$
$588$	1.94386	+	1.23361i	0.0801636	+	0.0508733i
$589$	2.73837	−	3.31012i	0.112833	−	0.136391i
$590$	6.77359	+	0.707710i	0.278864	+	0.0291360i
$591$	−2.50703	−	0.643695i	−0.103125	−	0.0264781i
$592$	1.67743	−	0.789337i	0.0689418	−	0.0324416i
$593$	11.6461	+	3.78406i	0.478250	+	0.155393i	0.538215	−	0.842808i	$-0.319099\pi$
$593$	11.6461	+	3.78406i	0.478250	+	0.155393i	−0.0599651	+	0.998200i	$0.519099\pi$
$594$	−1.64575	−	0.904760i	−0.0675260	−	0.0371227i
$595$	11.2385	−	16.1913i	0.460732	−	0.663780i
$596$	1.15015	+	0.145298i	0.0471122	+	0.00595165i
$597$	3.34779	−	26.5005i	0.137016	−	1.08459i
$598$	13.7516	−	8.72700i	0.562343	−	0.356874i
$599$	−27.2425	+	19.7928i	−1.11310	+	0.808713i	−0.983149	−	0.182808i	$-0.941481\pi$
$599$	−27.2425	+	19.7928i	−1.11310	+	0.808713i	−0.129949	+	0.991521i	$0.541481\pi$
$600$	15.5015	−	6.92465i	0.632847	−	0.282697i
$601$	16.4504	+	11.9519i	0.671026	+	0.487529i	0.870369	−	0.492401i	$-0.163881\pi$
$601$	16.4504	+	11.9519i	0.671026	+	0.487529i	−0.199342	+	0.979930i	$0.563881\pi$
$602$	15.3249	+	0.964159i	0.624595	+	0.0392962i
$603$	1.80403	+	3.28152i	0.0734657	+	0.133634i
$604$	0.258423	−	0.549177i	0.0105151	−	0.0223457i
$605$	−20.6793	−	12.5064i	−0.840732	−	0.508457i
$606$	−1.46065	+	7.65699i	−0.0593348	+	0.311044i
$607$	12.7282	+	17.5189i	0.516622	+	0.711069i	0.985018	−	0.172449i	$-0.0551680\pi$
$607$	12.7282	+	17.5189i	0.516622	+	0.711069i	−0.468396	+	0.883518i	$0.655168\pi$
$608$	−14.3649	+	26.1297i	−0.582575	+	1.05970i
$609$	−14.6734	+	23.1216i	−0.594596	+	0.936933i
$610$	−12.8122	−	14.8246i	−0.518751	−	0.600230i
$611$	−10.4943	−	4.15497i	−0.424552	−	0.168092i
$612$	−2.50744	−	6.33307i	−0.101357	−	0.255999i
$613$	12.0336	−	9.95504i	0.486032	−	0.402080i	−0.361874	−	0.932227i	$-0.617863\pi$
$613$	12.0336	−	9.95504i	0.486032	−	0.402080i	0.847906	+	0.530147i	$0.177863\pi$
$614$	23.3410	−	5.99296i	0.941967	−	0.241856i
$615$	−18.2130	+	17.8575i	−0.734418	+	0.720083i
$616$	−2.55213	+	1.01046i	−0.102828	+	0.0407126i
$617$	−27.1080	−	28.8670i	−1.09133	−	1.16214i	−0.985834	−	0.167723i	$-0.946359\pi$
$617$	−27.1080	−	28.8670i	−1.09133	−	1.16214i	−0.105491	−	0.994420i	$-0.533641\pi$
$618$	1.77621	−	2.44474i	0.0714496	−	0.0983420i
$619$	17.8171	+	37.8633i	0.716131	+	1.52186i	0.847658	+	0.530543i	$0.178012\pi$
$619$	17.8171	+	37.8633i	0.716131	+	1.52186i	−0.131527	+	0.991313i	$0.541988\pi$
$620$	1.33772	+	2.31370i	0.0537240	+	0.0929204i
$621$	19.5645	−	10.7557i	0.785096	−	0.431610i
$622$	−0.0237599	+	0.00453245i	−0.000952686	+	0.000181734i
$623$	−7.89404	−	30.7453i	−0.316268	−	1.23178i
$624$	−5.80432			−0.232359
$625$	−12.5534	−	21.6197i	−0.502135	−	0.864789i
$626$	−13.2322			−0.528863
$627$	0.721355	+	2.80949i	0.0288082	+	0.112200i
$628$	24.0568	−	4.58907i	0.959970	−	0.183124i
$629$	−7.15380	+	3.93283i	−0.285241	+	0.156812i
$630$	−2.68558	−	4.64495i	−0.106996	−	0.185059i
$631$	14.5516	+	30.9237i	0.579290	+	1.23105i	0.952848	+	0.303448i	$0.0981377\pi$
$631$	14.5516	+	30.9237i	0.579290	+	1.23105i	−0.373558	+	0.927607i	$0.621862\pi$
$632$	−26.2886	+	36.1832i	−1.04570	+	1.43929i
$633$	23.5562	+	25.0848i	0.936276	+	0.997032i
$634$	−18.5714	+	7.35294i	−0.737565	+	0.292023i
$635$	4.58849	−	4.49893i	0.182089	−	0.178535i
$636$	1.78754	−	0.458963i	0.0708807	−	0.0181991i
$637$	5.15273	−	4.26271i	0.204159	−	0.168895i
$638$	1.08362	+	2.73692i	0.0429011	+	0.108356i
$639$	−4.39781	−	1.74121i	−0.173975	−	0.0688814i
$640$	−13.9960	−	16.1943i	−0.553239	−	0.640135i
$641$	19.7900	−	31.1840i	0.781656	−	1.23169i	−0.186773	−	0.982403i	$-0.559803\pi$
$641$	19.7900	−	31.1840i	0.781656	−	1.23169i	0.968429	−	0.249290i	$-0.0801972\pi$
$642$	−4.91900	+	8.94762i	−0.194137	+	0.353134i
$643$	17.2789	+	23.7824i	0.681413	+	0.937885i	0.999950	−	0.0100259i	$-0.00319139\pi$
$643$	17.2789	+	23.7824i	0.681413	+	0.937885i	−0.318537	+	0.947911i	$0.603191\pi$
$644$	2.53406	−	13.2840i	0.0998558	−	0.523463i
$645$	20.8420	+	12.6048i	0.820654	+	0.496314i
$646$	6.08815	−	12.9380i	0.239535	−	0.509038i
$647$	16.8066	+	30.5712i	0.660737	+	1.20188i	0.968167	+	0.250306i	$0.0805312\pi$
$647$	16.8066	+	30.5712i	0.660737	+	1.20188i	−0.307429	+	0.951571i	$0.599469\pi$
$648$	8.75534	+	0.550839i	0.343942	+	0.0216390i
$649$	−1.41302	−	1.02662i	−0.0554659	−	0.0402983i
$650$	−2.16146	−	20.3238i	−0.0847796	−	0.797165i
$651$	−2.12993	+	1.54748i	−0.0834785	+	0.0606507i
$652$	−7.38307	+	4.68544i	−0.289143	+	0.183496i
$653$	−0.0842199	+	0.666669i	−0.00329578	+	0.0260888i	−0.993677	−	0.112278i	$-0.964185\pi$
$653$	−0.0842199	+	0.666669i	−0.00329578	+	0.0260888i	0.990381	+	0.138367i	$0.0441853\pi$
$654$	9.88984	+	1.24938i	0.386723	+	0.0488545i
$655$	21.8380	−	31.4622i	0.853283	−	1.22933i
$656$	6.41704	+	3.52780i	0.250543	+	0.137737i
$657$	−9.47276	−	3.07789i	−0.369568	−	0.120080i
$658$	3.50130	−	1.64759i	0.136495	−	0.0642296i
$659$	−38.4962	−	9.88414i	−1.49960	−	0.385032i	−0.592369	−	0.805667i	$-0.701807\pi$
$659$	−38.4962	−	9.88414i	−1.49960	−	0.385032i	−0.907230	+	0.420635i	$0.861807\pi$
$660$	−1.79474	−	0.187515i	−0.0698600	−	0.00729903i
$661$	2.61310	−	3.15870i	0.101638	−	0.122859i	−0.717242	−	0.696825i	$-0.754596\pi$
$661$	2.61310	−	3.15870i	0.101638	−	0.122859i	0.818880	+	0.573965i	$0.194596\pi$
$662$	−13.8964	−	8.81893i	−0.540099	−	0.342757i
$663$	25.5092	−	1.60490i	0.990694	−	0.0623292i
$664$	8.59570	+	13.5447i	0.333578	+	0.525635i
$665$	−7.86841	+	26.1196i	−0.305124	+	1.01288i
$666$	0.139542	+	2.21796i	0.00540714	+	0.0859440i
$667$	−34.3738	−	6.55715i	−1.33096	−	0.253894i
$668$	24.4545	−	7.94576i	0.946174	−	0.307431i
$669$	−14.0814	+	13.2233i	−0.544417	+	0.511242i
$670$	−3.83451	−	3.03534i	−0.148140	−	0.117266i
$671$	0.941587	+	4.93597i	0.0363496	+	0.190551i
$672$	12.5091	−	13.3208i	0.482549	−	0.513862i
$673$	−8.66757	+	21.8918i	−0.334110	+	0.843866i	0.661472	+	0.749970i	$0.269932\pi$
$673$	−8.66757	+	21.8918i	−0.334110	+	0.843866i	−0.995582	+	0.0938962i	$0.970068\pi$
$674$	−4.95556	−	15.2517i	−0.190881	−	0.587472i
$675$	−1.20775	−	27.9908i	−0.0464863	−	1.07737i
$676$	−6.81884	+	20.9862i	−0.262263	+	0.807163i
$677$	24.1194	+	19.9533i	0.926982	+	0.766867i	0.972695	−	0.232088i	$-0.0745558\pi$
$677$	24.1194	+	19.9533i	0.926982	+	0.766867i	−0.0457123	+	0.998955i	$0.514556\pi$
$678$	−14.9855	−	7.05166i	−0.575516	−	0.270818i
$679$	−29.0663	−	27.2950i	−1.11546	−	1.04749i
$680$	15.0269	+	15.3260i	0.576255	+	0.587727i
$681$	3.99436	−	0.504605i	0.153064	−	0.0193365i
$682$			0.282999i			0.0108366i
$683$	2.90320	+	22.9812i	0.111088	+	0.879351i	0.944913	+	0.327322i	$0.106146\pi$
$683$	2.90320	+	22.9812i	0.111088	+	0.879351i	−0.833825	+	0.552029i	$0.813854\pi$
$684$	6.00922	+	7.26390i	0.229768	+	0.277742i
$685$	21.5847	+	8.01215i	0.824711	+	0.306128i
$686$	−0.949670	+	15.0946i	−0.0362586	+	0.576314i
$687$	0.869238	−	3.38546i	0.0331635	−	0.129163i
$688$	1.73903	−	6.77306i	0.0662997	−	0.258220i
$689$	0.336601	−	5.35013i	0.0128235	−	0.203824i
$690$	−5.49744	+	6.94483i	−0.209284	+	0.264385i
$691$	−28.6159	−	34.5907i	−1.08860	−	1.31589i	−0.945297	−	0.326211i	$-0.894228\pi$
$691$	−28.6159	−	34.5907i	−1.08860	−	1.31589i	−0.143302	−	0.989679i	$-0.545772\pi$
$692$	−0.224005	−	1.77318i	−0.00851540	−	0.0674063i
$693$			1.37600i			0.0522699i
$694$	12.2388	−	1.54612i	0.464579	−	0.0586900i
$695$	−0.187820	−	1.26651i	−0.00712442	−	0.0480414i
$696$	−21.7394	−	20.4146i	−0.824028	−	0.773814i
$697$	−29.1774	−	13.7298i	−1.10517	−	0.520055i
$698$	−17.2685	−	14.2857i	−0.653622	−	0.540723i
$699$	−4.02920	+	12.4006i	−0.152398	+	0.469034i
$700$	−13.5302	−	10.2437i	−0.511394	−	0.387176i
$701$	0.716710	+	2.20581i	0.0270697	+	0.0833121i	0.963679	−	0.267064i	$-0.0860536\pi$
$701$	0.716710	+	2.20581i	0.0270697	+	0.0833121i	−0.936609	+	0.350376i	$0.886054\pi$
$702$	8.43181	−	21.2963i	0.318238	−	0.803778i
$703$	7.73461	−	8.23653i	0.291716	−	0.310646i
$704$	−0.230911	−	1.21048i	−0.00870277	−	0.0456215i
$705$	6.13290	+	0.253256i	0.230978	+	0.00953817i
$706$	0.0512847	−	0.0481596i	0.00193013	−	0.00181251i
$707$	17.8804	−	5.80971i	0.672463	−	0.218496i
$708$	7.20351	+	1.37414i	0.270724	+	0.0516435i
$709$	1.37419	+	21.8421i	0.0516088	+	0.820298i	0.935659	+	0.352906i	$0.114806\pi$
$709$	1.37419	+	21.8421i	0.0516088	+	0.820298i	−0.884050	+	0.467392i	$0.845194\pi$
$710$	6.17574	−	0.133174i	0.231771	−	0.00499792i
$711$	12.0134	+	18.9302i	0.450539	+	0.709936i
$712$	34.4997	−	2.17054i	1.29293	−	0.0813443i
$713$	−2.84054	−	1.80266i	−0.106379	−	0.0675102i
$714$	−5.58564	+	6.75188i	−0.209037	+	0.252683i
$715$	−2.12898	+	4.78972i	−0.0796194	+	0.179125i
$716$	9.50264	+	2.43986i	0.355130	+	0.0911820i
$717$	−28.9263	+	13.6117i	−1.08027	+	0.508337i
$718$	−16.8126	−	5.46274i	−0.627441	−	0.203868i
$719$	9.66372	+	5.31268i	0.360396	+	0.198129i	0.651656	−	0.758515i	$-0.274075\pi$
$719$	9.66372	+	5.31268i	0.360396	+	0.198129i	−0.291260	+	0.956644i	$0.594075\pi$
$720$	−2.30701	+	0.804982i	−0.0859773	+	0.0299999i
$721$	−7.23085	−	0.913469i	−0.269291	−	0.0340194i
$722$	−0.659859	+	5.22332i	−0.0245574	+	0.194392i
$723$	−19.6920	+	12.4969i	−0.732352	+	0.464764i
$724$	−7.65415	+	5.56106i	−0.284464	+	0.206675i
$725$	−26.5067	+	35.0109i	−0.984434	+	1.30027i
$726$	8.69260	+	6.31554i	0.322613	+	0.234392i
$727$	40.1806	+	2.52795i	1.49021	+	0.0937564i	0.786882	−	0.617104i	$-0.211694\pi$
$727$	40.1806	+	2.52795i	1.49021	+	0.0937564i	0.703333	+	0.710860i	$0.251694\pi$
$728$	−16.1275	−	29.3358i	−0.597725	−	1.08726i
$729$	11.1799	−	23.7584i	0.414069	−	0.879941i
$730$	12.9615	−	1.09646i	0.479726	−	0.0405817i
$731$	−5.77001	+	30.2475i	−0.213412	+	1.11874i
$732$	−12.4013	−	17.0690i	−0.458366	−	0.630887i
$733$	−1.13244	+	2.05990i	−0.0418275	+	0.0760840i	−0.896394	−	0.443258i	$-0.853823\pi$
$733$	−1.13244	+	2.05990i	−0.0418275	+	0.0760840i	0.854567	+	0.519341i	$0.173823\pi$
$734$	−3.79778	+	5.98434i	−0.140179	+	0.220886i
$735$	−1.88204	+	3.11195i	−0.0694202	+	0.114786i
$736$	21.7112	+	8.59606i	0.800285	+	0.316855i
$737$	0.461700	+	1.16612i	0.0170069	+	0.0429546i
$738$	−6.76381	+	5.59551i	−0.248979	+	0.205974i
$739$	19.6198	−	5.03751i	0.721726	−	0.185308i	0.130078	−	0.991504i	$-0.458477\pi$
$739$	19.6198	−	5.03751i	0.721726	−	0.185308i	0.591649	+	0.806196i	$0.298477\pi$
$740$	3.12929	+	6.29416i	0.115035	+	0.231378i
$741$	−32.8918	+	13.0228i	−1.20831	+	0.478404i
$742$	1.25810	+	1.33974i	0.0461863	+	0.0491835i
$743$	2.26332	−	3.11520i	0.0830333	−	0.114286i	−0.765480	−	0.643460i	$-0.777498\pi$
$743$	2.26332	−	3.11520i	0.0830333	−	0.114286i	0.848513	+	0.529174i	$0.177498\pi$
$744$	−1.22074	−	2.59421i	−0.0447546	−	0.0951083i
$745$	−0.190300	+	1.82139i	−0.00697205	+	0.0667304i
$746$	−3.77908	+	2.07757i	−0.138362	+	0.0760651i
$747$	7.89932	−	1.50688i	0.289021	−	0.0551337i
$748$	−0.567335	−	2.20963i	−0.0207438	−	0.0807919i
$749$	24.6265			0.899834
$750$	4.75114	+	10.0484i	0.173487	+	0.366915i
$751$	8.34327			0.304450			0.152225	−	0.988346i	$-0.451356\pi$
$751$	8.34327			0.304450			0.152225	+	0.988346i	$0.451356\pi$
$752$	−0.438243	−	1.70684i	−0.0159811	−	0.0622422i
$753$	10.0738	−	1.92168i	0.367109	−	0.0700298i
$754$	−31.4600	+	17.2953i	−1.14570	+	0.629856i
$755$	0.876115	+	0.389424i	0.0318851	+	0.0141726i
$756$	−8.09767	−	17.2084i	−0.294509	−	0.625864i
$757$	−0.340371	+	0.468480i	−0.0123710	+	0.0170272i	−0.815158	−	0.579239i	$-0.803350\pi$
$757$	−0.340371	+	0.468480i	−0.0123710	+	0.0170272i	0.802787	+	0.596266i	$0.203350\pi$
$758$	−1.20449	−	1.28266i	−0.0437492	−	0.0465882i
$759$	2.11201	−	0.836203i	0.0766611	−	0.0303523i
$760$	−26.3351	−	13.7470i	−0.955274	−	0.498655i
$761$	−49.9907	+	12.8354i	−1.81216	+	0.465284i	−0.993969	−	0.109658i	$-0.965024\pi$
$761$	−49.9907	+	12.8354i	−1.81216	+	0.465284i	−0.818194	+	0.574943i	$0.805024\pi$
$762$	−2.20139	+	1.82115i	−0.0797479	+	0.0659732i
$763$	−8.85063	−	22.3541i	−0.320414	−	0.809274i
$764$	−25.4715	−	10.0849i	−0.921527	−	0.364858i
$765$	9.91641	−	4.17567i	0.358529	−	0.150972i
$766$	5.16540	−	8.13936i	0.186633	−	0.294087i
$767$	10.2620	−	18.6666i	0.370540	−	0.674010i
$768$	9.89052	+	13.6131i	0.356893	+	0.491222i
$769$	−3.77778	+	19.8038i	−0.136230	+	0.714145i	0.846974	+	0.531635i	$0.178422\pi$
$769$	−3.77778	+	19.8038i	−0.136230	+	0.714145i	−0.983204	+	0.182510i	$0.941578\pi$
$770$	−0.697392	−	1.65617i	−0.0251323	−	0.0596842i
$771$	0.873868	−	1.85706i	0.0314716	−	0.0668806i
$772$	−1.55705	−	2.83226i	−0.0560393	−	0.101935i
$773$	10.9066	+	0.686183i	0.392282	+	0.0246803i	0.257707	−	0.966223i	$-0.417033\pi$
$773$	10.9066	+	0.686183i	0.392282	+	0.0246803i	0.134575	+	0.990903i	$0.457033\pi$
$774$	6.78169	+	4.92719i	0.243763	+	0.177104i
$775$	−3.60846	+	2.19145i	−0.129620	+	0.0787193i
$776$	35.1293	−	25.5230i	1.26107	−	0.916221i
$777$	−5.84642	+	3.71025i	−0.209739	+	0.133105i
$778$	1.51282	−	11.9752i	0.0542374	−	0.429333i
$779$	44.2790	+	5.59374i	1.58646	+	0.200416i
$780$	−0.474465	−	22.0027i	−0.0169886	−	0.787821i
$781$	−1.38823	−	0.763183i	−0.0496746	−	0.0273088i
$782$	−10.6496	−	3.46026i	−0.380829	−	0.123739i
$783$	−44.5286	+	20.9536i	−1.59132	+	0.748820i
$784$	1.01129	+	0.259656i	0.0361177	+	0.00927344i
$785$	8.06680	+	37.8365i	0.287916	+	1.35044i
$786$	−10.8537	+	13.1199i	−0.387140	+	0.467972i
$787$	−29.5971	−	18.7829i	−1.05502	−	0.669537i	−0.109133	−	0.994027i	$-0.534807\pi$
$787$	−29.5971	−	18.7829i	−1.05502	−	0.669537i	−0.945889	+	0.324490i	$0.894807\pi$
$788$	−2.81196	+	0.176914i	−0.100172	+	0.00630229i
$789$	−12.3536	−	19.4662i	−0.439800	−	0.693014i
$790$	−24.0538	−	16.6958i	−0.855796	−	0.594011i
$791$	2.50815	+	39.8659i	0.0891795	+	1.41747i
$792$	−1.47194	−	0.280787i	−0.0523030	−	0.00997733i
$793$	−58.2852	+	18.9380i	−2.06977	+	0.672509i
$794$	5.62034	−	5.27785i	0.199458	−	0.187304i
$795$	0.785716	+	2.80743i	0.0278665	+	0.0995694i
$796$	−5.44833	−	28.5612i	−0.193111	−	1.01232i
$797$	−6.21668	+	6.62009i	−0.220206	+	0.234496i	−0.829581	−	0.558387i	$-0.811421\pi$
$797$	−6.21668	+	6.62009i	−0.220206	+	0.234496i	0.609375	+	0.792882i	$0.291421\pi$
$798$	4.46472	−	11.2766i	0.158049	−	0.399187i
$799$	2.39796	+	7.38016i	0.0848337	+	0.261091i
$800$	21.7521	−	19.6343i	0.769054	−	0.694179i
$801$	5.35488	−	16.4806i	0.189205	−	0.582314i
$802$	−1.64903	−	1.36420i	−0.0582294	−	0.0481715i
$803$	−3.01844	−	1.42037i	−0.106518	−	0.0501237i
$804$	−3.83874	−	3.60482i	−0.135382	−	0.127132i
$805$	21.0657	+	3.54963i	0.742468	+	0.125108i
$806$	−3.42425	+	0.432583i	−0.120614	+	0.0152371i
$807$			15.7796i			0.555468i
$808$	2.56608	+	20.3126i	0.0902743	+	0.714595i
$809$	−9.39916	−	11.3616i	−0.330457	−	0.399454i	0.578949	−	0.815364i	$-0.303463\pi$
$809$	−9.39916	−	11.3616i	−0.330457	−	0.399454i	−0.909406	+	0.415910i	$0.863463\pi$
$810$	−0.236963	+	5.73836i	−0.00832604	+	0.201625i
$811$	0.179268	−	2.84938i	0.00629494	−	0.100055i	−0.993625	−	0.112739i	$-0.964038\pi$
$811$	0.179268	−	2.84938i	0.00629494	−	0.100055i	0.999920	+	0.0126840i	$0.00403755\pi$
$812$	−7.41326	+	28.8728i	−0.260155	+	1.01324i
$813$	−10.2315	+	39.8489i	−0.358833	+	1.39756i
$814$	−0.0467360	+	0.742847i	−0.00163809	+	0.0260368i
$815$	−7.65115	−	11.5005i	−0.268008	−	0.402845i
$816$	2.54370	+	3.07481i	0.0890474	+	0.107640i
$817$	−5.34160	−	42.2831i	−0.186879	−	1.47930i
$818$		−	5.45317i		−	0.190666i
$819$	−16.6494	+	2.10331i	−0.581776	+	0.0734955i
$820$	−12.8484	+	24.6137i	−0.448685	+	0.859547i
$821$	25.1734	+	23.6394i	0.878559	+	0.825022i	0.985576	−	0.169235i	$-0.0541298\pi$
$821$	25.1734	+	23.6394i	0.878559	+	0.825022i	−0.107016	+	0.994257i	$0.534130\pi$
$822$	−9.26217	−	4.35844i	−0.323055	−	0.152018i
$823$	−4.34190	−	3.59194i	−0.151349	−	0.125207i	0.558668	−	0.829392i	$-0.311313\pi$
$823$	−4.34190	−	3.59194i	−0.151349	−	0.125207i	−0.710017	+	0.704185i	$0.751313\pi$
$824$	2.45268	−	7.54859i	0.0854433	−	0.262968i
$825$	0.235021	−	2.84081i	0.00818239	−	0.0989043i
$826$	2.25674	+	6.94552i	0.0785219	+	0.241666i
$827$	−8.94773	+	22.5994i	−0.311143	+	0.785857i	0.687098	+	0.726565i	$0.258884\pi$
$827$	−8.94773	+	22.5994i	−0.311143	+	0.785857i	−0.998241	+	0.0592924i	$0.981116\pi$
$828$	5.05382	−	5.38177i	0.175632	−	0.187029i
$829$	1.97178	+	10.3364i	0.0684827	+	0.358999i	0.999989	−	0.00472665i	$-0.00150454\pi$
$829$	1.97178	+	10.3364i	0.0684827	+	0.358999i	−0.931506	+	0.363726i	$0.881505\pi$
$830$	−8.74399	+	5.81727i	−0.303508	+	0.201920i
$831$	−2.20442	+	2.07009i	−0.0764706	+	0.0718107i
$832$	14.2936	−	4.64427i	0.495542	−	0.161011i
$833$	−4.51629	−	0.861528i	−0.156480	−	0.0298502i
$834$	0.0357434	+	0.568125i	0.00123769	+	0.0196726i
$835$	13.3816	+	38.3504i	0.463088	+	1.32717i
$836$	1.69185	+	2.66592i	0.0585137	+	0.0922028i
$837$	−4.72190	+	0.297077i	−0.163213	+	0.0102685i
$838$	−1.97304	−	1.25213i	−0.0681577	−	0.0432542i
$839$	12.5946	−	15.2243i	0.434815	−	0.525600i	−0.506904	−	0.862003i	$-0.669210\pi$
$839$	12.5946	−	15.2243i	0.434815	−	0.525600i	0.941718	+	0.336402i	$0.109210\pi$
$840$	13.5369	+	12.1736i	0.467068	+	0.420028i
$841$	46.6224	+	11.9706i	1.60767	+	0.412780i
$842$	−16.8087	+	7.90956i	−0.579265	+	0.272581i
$843$	−20.7570	−	6.74435i	−0.714908	−	0.232288i
$844$	32.8249	+	18.0456i	1.12988	+	0.621157i
$845$	−33.3758	−	10.0543i	−1.14816	−	0.345878i
$846$	2.09581	+	0.264762i	0.0720553	+	0.00910270i
$847$	3.24796	−	25.7102i	0.111601	−	0.883414i
$848$	0.706670	−	0.448466i	0.0242671	−	0.0154004i
$849$	10.6516	−	7.73883i	0.365562	−	0.265596i
$850$	−9.81917	+	10.0518i	−0.336795	+	0.344773i
$851$	−7.15845	−	5.20092i	−0.245389	−	0.178285i
$852$	6.63837	+	0.417651i	0.227427	+	0.0143085i
$853$	−2.92007	−	5.31159i	−0.0999814	−	0.181866i	0.821585	−	0.570086i	$-0.193090\pi$
$853$	−2.92007	−	5.31159i	−0.0999814	−	0.181866i	−0.921567	+	0.388220i	$0.873090\pi$
$854$	8.94596	−	19.0111i	0.306124	−	0.650547i
$855$	−11.2672	+	9.73774i	−0.385331	+	0.333024i
$856$	−5.02530	+	26.3435i	−0.171761	+	0.900403i
$857$	−33.5662	−	46.1999i	−1.14660	−	1.57816i	−0.751802	−	0.659388i	$-0.770815\pi$
$857$	−33.5662	−	46.1999i	−1.14660	−	1.57816i	−0.394796	−	0.918769i	$-0.629185\pi$
$858$	1.12268	−	2.04215i	0.0383276	−	0.0697177i
$859$	20.2524	−	31.9126i	0.691002	−	1.08884i	−0.299863	−	0.953982i	$-0.596941\pi$
$859$	20.2524	−	31.9126i	0.691002	−	1.08884i	0.990864	−	0.134862i	$-0.0430591\pi$
$860$	25.8170	+	6.03853i	0.880353	+	0.205912i
$861$	−25.4307	−	10.0687i	−0.866675	−	0.343141i
$862$	−6.05822	−	15.3013i	−0.206344	−	0.521165i
$863$	42.1584	−	34.8764i	1.43509	−	1.18721i	0.485286	−	0.874355i	$-0.338715\pi$
$863$	42.1584	−	34.8764i	1.43509	−	1.18721i	0.949802	−	0.312853i	$-0.101285\pi$
$864$	31.8073	−	8.16673i	1.08211	−	0.277838i
$865$	2.79276	−	0.414159i	0.0949566	−	0.0140818i
$866$	−3.32327	+	1.31578i	−0.112929	+	0.0447119i
$867$	3.10367	+	3.30507i	0.105406	+	0.112246i
$868$	−1.68450	+	2.31852i	−0.0571757	+	0.0786956i
$869$	3.19723	+	6.79446i	0.108459	+	0.230486i
$870$	13.0550	−	14.5171i	0.442607	−	0.492175i
$871$	−13.4041	+	7.36898i	−0.454182	+	0.249688i
$872$	25.7187	−	4.90611i	0.870947	−	0.166142i
$873$	−5.41333	−	21.0835i	−0.183214	−	0.713570i
$874$	15.4982			0.524235
$875$	15.7171	−	21.7171i	0.531335	−	0.734172i
$876$	14.0066			0.473238
$877$	4.04083	+	15.7380i	0.136449	+	0.531434i	0.999647	+	0.0265685i	$0.00845801\pi$
$877$	4.04083	+	15.7380i	0.136449	+	0.531434i	−0.863198	+	0.504866i	$0.831542\pi$
$878$	21.1604	−	4.03656i	0.714128	−	0.136227i
$879$	−14.1476	+	7.77769i	−0.477185	+	0.262335i
$880$	−0.800372	+	0.170640i	−0.0269805	+	0.00575228i
$881$	22.8935	+	48.6512i	0.771302	+	1.63910i	0.769121	+	0.639103i	$0.220694\pi$
$881$	22.8935	+	48.6512i	0.771302	+	1.63910i	0.00218091	+	0.999998i	$0.499306\pi$
$882$	−0.735685	+	1.01258i	−0.0247718	+	0.0340955i
$883$	−11.4938	−	12.2397i	−0.386799	−	0.411899i	0.505872	−	0.862609i	$-0.331171\pi$
$883$	−11.4938	−	12.2397i	−0.386799	−	0.411899i	−0.892670	+	0.450710i	$0.851171\pi$
$884$	25.8689	−	10.2422i	0.870065	−	0.344483i
$885$	−1.92486	+	11.4233i	−0.0647034	+	0.383990i
$886$	5.72141	−	1.46901i	0.192214	−	0.0493523i
$887$	−37.7187	+	31.2036i	−1.26647	+	1.04771i	−0.270077	+	0.962839i	$0.587049\pi$
$887$	−37.7187	+	31.2036i	−1.26647	+	1.04771i	−0.996392	+	0.0848755i	$0.972951\pi$
$888$	−2.77591	−	7.01115i	−0.0931535	−	0.235279i
$889$	6.40689	+	2.53667i	0.214880	+	0.0850771i
$890$	1.90760	+	22.5503i	0.0639430	+	0.755886i
$891$	0.789216	−	1.24360i	0.0264397	−	0.0416623i
$892$	−10.1299	+	18.4263i	−0.339175	+	0.616957i
$893$	−6.31295	−	8.68903i	−0.211255	−	0.290767i
$894$	0.152565	−	0.799775i	0.00510255	−	0.0267485i
$895$	−3.52965	+	15.0906i	−0.117983	+	0.504423i
$896$	9.77250	−	20.7676i	0.326476	−	0.693798i
$897$	13.3463	+	24.2768i	0.445619	+	0.810578i
$898$	24.3252	+	1.53041i	0.811742	+	0.0510705i
$899$	5.99941	+	4.35883i	0.200092	+	0.145375i
$900$	−3.24006	−	8.67947i	−0.108002	−	0.289316i
$901$	−2.98171	+	2.16634i	−0.0993352	+	0.0721713i
$902$	−2.48238	+	1.57537i	−0.0826543	+	0.0524540i
$903$	−3.27352	+	25.9126i	−0.108936	+	0.862316i
$904$	−43.1572	−	5.45202i	−1.43539	−	0.181331i
$905$	−9.04325	−	11.8988i	−0.300608	−	0.395529i
$906$	−0.373541	−	0.205356i	−0.0124101	−	0.00682249i
$907$	36.6570	+	11.9106i	1.21717	+	0.395484i	0.846052	−	0.533100i	$-0.178973\pi$
$907$	36.6570	+	11.9106i	1.21717	+	0.395484i	0.371122	+	0.928584i	$0.378973\pi$
$908$	3.96548	−	1.86601i	0.131599	−	0.0619259i
$909$	9.94111	+	2.55244i	0.329726	+	0.0846592i
$910$	18.9734	−	10.9699i	0.628961	−	0.363648i
$911$	−0.480995	+	0.581423i	−0.0159361	+	0.0192634i	−0.778421	−	0.627742i	$-0.783979\pi$
$911$	−0.480995	+	0.581423i	−0.0159361	+	0.0192634i	0.762485	+	0.647006i	$0.223979\pi$
$912$	−4.66341	−	2.95949i	−0.154421	−	0.0979985i
$913$	2.68806	−	0.169119i	0.0889619	−	0.00559701i
$914$	−9.85804	−	15.5338i	−0.326075	−	0.513812i
$915$	26.5347	−	20.1667i	0.877209	−	0.666691i
$916$	−0.238902	−	3.79724i	−0.00789355	−	0.125464i
$917$	40.3405	+	7.69536i	1.33216	+	0.254123i
$918$	−14.9768	+	4.86625i	−0.494307	+	0.160610i
$919$	30.5959	−	28.7315i	1.00927	−	0.947765i	0.0106293	−	0.999944i	$-0.496617\pi$
$919$	30.5959	−	28.7315i	1.00927	−	0.947765i	0.998638	+	0.0521787i	$0.0166165\pi$
$920$	−8.09579	+	21.8101i	−0.266910	+	0.719057i
$921$	7.68075	+	40.2639i	0.253089	+	1.32674i
$922$	−11.9338	+	12.7082i	−0.393019	+	0.418523i
$923$	7.11240	−	17.9639i	0.234108	−	0.591288i
$924$	−0.597947	−	1.84029i	−0.0196710	−	0.0605411i
$925$	−9.83379	+	5.15643i	−0.323333	+	0.169542i
$926$	−6.89022	+	21.2059i	−0.226427	+	0.696870i
$927$	−3.06573	−	2.53619i	−0.100692	−	0.0832994i
$928$	−46.5727	−	21.9155i	−1.52882	−	0.719410i
$929$	−12.0393	−	11.3056i	−0.394995	−	0.370925i	0.461447	−	0.887168i	$-0.347330\pi$
$929$	−12.0393	−	11.3056i	−0.394995	−	0.370925i	−0.856443	+	0.516242i	$0.827330\pi$
$930$	1.68074	−	0.835620i	0.0551137	−	0.0274011i
$931$	6.31335	−	0.797561i	0.206912	−	0.0261390i
$932$			14.1933i			0.464916i
$933$	−0.00515664	−	0.0408190i	−0.000168821	−	0.00133635i
$934$	14.3392	+	17.3331i	0.469194	+	0.567158i
$935$	3.47034	−	0.971243i	0.113492	−	0.0317630i
$936$	1.14753	−	18.2394i	0.0375080	−	0.596173i
$937$	−8.84462	+	34.4475i	−0.288941	+	1.12535i	0.643913	+	0.765098i	$0.277310\pi$
$937$	−8.84462	+	34.4475i	−0.288941	+	1.12535i	−0.932855	+	0.360253i	$0.882690\pi$
$938$	1.30416	−	5.07937i	0.0425823	−	0.165847i
$939$	1.41325	−	22.4630i	0.0461197	−	0.733051i
$940$	6.43437	−	1.80079i	0.209866	−	0.0587352i
$941$	−21.7724	−	26.3183i	−0.709760	−	0.857952i	0.285175	−	0.958475i	$-0.407948\pi$
$941$	−21.7724	−	26.3183i	−0.709760	−	0.857952i	−0.994935	+	0.100523i	$0.967948\pi$
$942$	−2.15576	−	17.0646i	−0.0702384	−	0.555994i
$943$		−	34.9512i		−	1.13817i
$944$	3.29954	−	0.416829i	0.107391	−	0.0135666i
$945$	26.9015	−	13.3747i	0.875104	−	0.435079i
$946$	2.04661	+	1.92190i	0.0665411	+	0.0624863i
$947$	−28.0925	−	13.2193i	−0.912882	−	0.429570i	−0.0888060	−	0.996049i	$-0.528305\pi$
$947$	−28.0925	−	13.2193i	−0.912882	−	0.429570i	−0.824076	+	0.566479i	$0.808305\pi$
$948$	−24.2932	−	20.0971i	−0.789006	−	0.652723i
$949$	12.5724	−	38.6937i	0.408116	−	1.25605i
$950$	8.62603	−	17.4310i	0.279865	−	0.565535i
$951$	−10.4989	−	32.3122i	−0.340449	−	1.04780i
$952$	−8.47272	+	21.3997i	−0.274603	+	0.693567i
$953$	23.9563	−	25.5109i	0.776022	−	0.826379i	−0.212547	−	0.977151i	$-0.568176\pi$
$953$	23.9563	−	25.5109i	0.776022	−	0.826379i	0.988569	+	0.150772i	$0.0481759\pi$
$954$	0.188003	+	0.985545i	0.00608682	+	0.0319082i
$955$	15.0596	−	40.5706i	0.487317	−	1.31283i
$956$	−25.3677	+	23.8218i	−0.820449	+	0.770453i
$957$	−4.76195	+	1.54725i	−0.153932	+	0.0500155i
$958$	12.5247	+	2.38922i	0.404655	+	0.0771921i
$959$	1.55022	+	24.6400i	0.0500592	+	0.795668i
$960$	−6.50724	+	4.94559i	−0.210020	+	0.159618i
$961$	−16.2286	−	25.5722i	−0.523504	−	0.824910i
$962$	−9.05977	+	0.569992i	−0.292099	+	0.0183773i
$963$	11.3512	+	7.20367i	0.365786	+	0.232135i
$964$	−16.1827	+	19.5615i	−0.521210	+	0.630035i
$965$	4.41995	−	2.55550i	0.142283	−	0.0822644i
$966$	−9.19945	−	2.36202i	−0.295988	−	0.0759967i
$967$	4.41434	−	2.07723i	0.141956	−	0.0667992i	−0.353490	−	0.935438i	$-0.615005\pi$
$967$	4.41434	−	2.07723i	0.141956	−	0.0667992i	0.495445	+	0.868639i	$0.335005\pi$
$968$	26.8400	+	8.72084i	0.862670	+	0.280298i
$969$	21.3133	+	11.7171i	0.684682	+	0.376407i
$970$	17.2012	+	22.6328i	0.552298	+	0.726694i
$971$	−31.0982	−	3.92862i	−0.997989	−	0.126075i	−0.390668	−	0.920532i	$-0.627756\pi$
$971$	−31.0982	−	3.92862i	−0.997989	−	0.126075i	−0.607321	+	0.794456i	$0.707756\pi$
$972$	2.20724	−	17.4721i	0.0707973	−	0.560418i
$973$	1.15922	−	0.735662i	0.0371628	−	0.0235842i
$974$	−18.3522	+	13.3336i	−0.588042	+	0.427238i
$975$	34.7326	−	1.49865i	1.11233	−	0.0479951i
$976$	−7.74093	−	5.62412i	−0.247781	−	0.180024i
$977$	41.2986	+	2.59829i	1.32126	+	0.0831266i	0.707695	−	0.706518i	$-0.249735\pi$
$977$	41.2986	+	2.59829i	1.32126	+	0.0831266i	0.613564	+	0.789645i	$0.289735\pi$
$978$	2.95860	+	5.38167i	0.0946055	+	0.172087i
$979$	2.47114	−	5.25145i	0.0789781	−	0.167837i
$980$	−0.901621	+	3.85477i	−0.0288012	+	0.123136i
$981$	2.45941	−	12.8927i	0.0785230	−	0.411632i
$982$	13.7494	+	18.9245i	0.438762	+	0.603905i
$983$	20.4563	−	37.2098i	0.652454	−	1.18681i	−0.318586	−	0.947894i	$-0.603208\pi$
$983$	20.4563	−	37.2098i	0.652454	−	1.18681i	0.971040	−	0.238916i	$-0.0767920\pi$
$984$	15.9601	−	25.1491i	0.508790	−	0.801724i
$985$	−0.375164	−	4.43490i	−0.0119537	−	0.141308i
$986$	22.9491	+	9.08621i	0.730850	+	0.289364i
$987$	2.42299	+	6.11978i	0.0771247	+	0.194795i
$988$	−29.6711	+	24.5461i	−0.943965	+	0.780915i
$989$	−32.3272	+	8.30021i	−1.02795	+	0.263931i
$990$	0.163007	−	0.967381i	0.00518069	−	0.0307454i
$991$	0.537405	−	0.212774i	0.0170712	−	0.00675898i	−0.359573	−	0.933117i	$-0.617078\pi$
$991$	0.537405	−	0.212774i	0.0170712	−	0.00675898i	0.376645	+	0.926358i	$0.377078\pi$
$992$	−3.38743	−	3.60725i	−0.107551	−	0.114530i
$993$	16.4552	−	22.6487i	0.522191	−	0.718735i
$994$	2.82031	+	5.99346i	0.0894547	+	0.190101i
$995$	44.9211	−	9.57723i	1.42409	−	0.303618i
$996$	−9.90989	+	5.44801i	−0.314007	+	0.172627i
$997$	−39.6674	+	7.56695i	−1.25628	+	0.239648i	−0.772201	−	0.635378i	$-0.780844\pi$
$997$	−39.6674	+	7.56695i	−1.25628	+	0.239648i	−0.484076	+	0.875026i	$0.660844\pi$
$998$	0.887771	+	3.45764i	0.0281019	+	0.109450i
$999$	−12.4436			−0.393699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.104.5	✓	240
5.2	odd	4		625.2.g.b.351.16		480
5.3	odd	4		625.2.g.b.351.9		480
5.4	even	2		625.2.h.a.274.8		240
125.6	even	25		625.2.h.a.349.8		240
125.33	odd	100		625.2.g.b.276.9		480
125.92	odd	100		625.2.g.b.276.16		480
125.119	even	50	inner	125.2.h.a.119.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.104.5	✓	240	1.1	even	1	trivial
125.2.h.a.119.5	yes	240	125.119	even	50	inner
625.2.g.b.276.9		480	125.33	odd	100
625.2.g.b.276.16		480	125.92	odd	100
625.2.g.b.351.9		480	5.3	odd	4
625.2.g.b.351.16		480	5.2	odd	4
625.2.h.a.274.8		240	5.4	even	2
625.2.h.a.349.8		240	125.6	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190125 - 0.740487i) q^{2} +(1.27736 - 0.243669i) q^{3} +(1.24044 - 0.681938i) q^{4} +(1.11923 + 1.93580i) q^{5} +(-0.423291 - 0.899540i) q^{6} +(-1.40937 + 1.93983i) q^{7} +(-1.78748 - 1.90348i) q^{8} +(-1.21706 + 0.481867i) q^{9} +O(q^{10})\)	\(q+(-0.190125 - 0.740487i) q^{2} +(1.27736 - 0.243669i) q^{3} +(1.24044 - 0.681938i) q^{4} +(1.11923 + 1.93580i) q^{5} +(-0.423291 - 0.899540i) q^{6} +(-1.40937 + 1.93983i) q^{7} +(-1.78748 - 1.90348i) q^{8} +(-1.21706 + 0.481867i) q^{9} +(1.22064 - 1.19682i) q^{10} +(-0.424635 + 0.109028i) q^{11} +(1.41832 - 1.17334i) q^{12} +(-1.96830 - 4.97136i) q^{13} +(1.70438 + 0.674810i) q^{14} +(1.90135 + 2.19999i) q^{15} +(0.447306 - 0.704842i) q^{16} +(-1.77096 + 3.22136i) q^{17} +(0.588209 + 0.809600i) q^{18} +(0.953375 - 4.99777i) q^{19} +(2.70843 + 1.63800i) q^{20} +(-1.32760 + 2.82128i) q^{21} +(0.161467 + 0.293708i) q^{22} +(-3.97654 - 0.250183i) q^{23} +(-2.74708 - 1.99587i) q^{24} +(-2.49466 + 4.33321i) q^{25} +(-3.30700 + 2.40268i) q^{26} +(-4.73108 + 3.00243i) q^{27} +(-0.425395 + 3.36735i) q^{28} +(8.71338 + 1.10076i) q^{29} +(1.26757 - 1.82620i) q^{30} +(0.739916 + 0.406772i) q^{31} +(-5.57375 - 1.81102i) q^{32} +(-0.515845 + 0.242738i) q^{33} +(2.72208 + 0.698910i) q^{34} +(-5.33254 - 0.557148i) q^{35} +(-1.18108 + 1.42769i) q^{36} +(1.87503 + 1.18993i) q^{37} +(-3.88204 + 0.244237i) q^{38} +(-3.72560 - 5.87060i) q^{39} +(1.68415 - 5.59064i) q^{40} +(0.550798 + 8.75468i) q^{41} +(2.34153 + 0.446671i) q^{42} +(7.96661 - 2.58851i) q^{43} +(-0.452384 + 0.424817i) q^{44} +(-2.29497 - 1.81666i) q^{45} +(0.570782 + 2.99214i) q^{46} +(1.44504 - 1.53881i) q^{47} +(0.399622 - 1.00933i) q^{48} +(0.386494 + 1.18951i) q^{49} +(3.68298 + 1.02341i) q^{50} +(-1.47720 + 4.54636i) q^{51} +(-5.83172 - 4.82442i) q^{52} +(0.907174 + 0.426884i) q^{53} +(3.12276 + 2.93246i) q^{54} +(-0.686320 - 0.699983i) q^{55} +(6.21165 - 0.784714i) q^{56} -6.61625i q^{57} +(-0.841533 - 6.66142i) q^{58} +(2.53945 + 3.06967i) q^{59} +(3.85877 + 1.43236i) q^{60} +(0.719696 - 11.4392i) q^{61} +(0.160533 - 0.625235i) q^{62} +(0.780544 - 3.04002i) q^{63} +(-0.176495 + 2.80531i) q^{64} +(7.42059 - 9.37433i) q^{65} +(0.277819 + 0.335826i) q^{66} +(-0.358552 - 2.83823i) q^{67} +5.20359i q^{68} +(-5.14044 + 0.649388i) q^{69} +(0.601287 + 4.05460i) q^{70} +(2.63411 + 2.47359i) q^{71} +(3.09269 + 1.45531i) q^{72} +(5.86297 + 4.85027i) q^{73} +(0.524639 - 1.61467i) q^{74} +(-2.13070 + 6.14293i) q^{75} +(-2.22556 - 6.84957i) q^{76} +(0.386973 - 0.977382i) q^{77} +(-3.63877 + 3.87490i) q^{78} +(-3.20949 - 16.8248i) q^{79} +(1.86507 + 0.0770174i) q^{80} +(-2.44907 + 2.29983i) q^{81} +(6.37800 - 2.07234i) q^{82} +(-6.03472 - 1.15118i) q^{83} +(0.277137 + 4.40497i) q^{84} +(-8.21802 + 0.177213i) q^{85} +(-3.43141 - 5.40703i) q^{86} +(11.3983 - 0.717123i) q^{87} +(0.966560 + 0.613398i) q^{88} +(-8.43845 + 10.2003i) q^{89} +(-0.908886 + 2.04478i) q^{90} +(12.4177 + 3.18832i) q^{91} +(-5.10328 + 2.40142i) q^{92} +(1.04426 + 0.339299i) q^{93} +(-1.41421 - 0.777466i) q^{94} +(10.7417 - 3.74810i) q^{95} +(-7.56097 - 0.955173i) q^{96} +(-2.08420 + 16.4982i) q^{97} +(0.807331 - 0.512348i) q^{98} +(0.464269 - 0.337311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

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Database

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