LMFDB - Embedded newform 504.2.cz.b.187.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.2
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40798 - 0.132660i) q^{2} +(1.55918 - 0.754290i) q^{3} +(1.96480 + 0.373564i) q^{4} +0.987364 q^{5} +(-2.29536 + 0.855183i) q^{6} +(1.42351 + 2.23016i) q^{7} +(-2.71684 - 0.786619i) q^{8} +(1.86209 - 2.35215i) q^{9} +O(q^{10})$	\(q+(-1.40798 - 0.132660i) q^{2} +(1.55918 - 0.754290i) q^{3} +(1.96480 + 0.373564i) q^{4} +0.987364 q^{5} +(-2.29536 + 0.855183i) q^{6} +(1.42351 + 2.23016i) q^{7} +(-2.71684 - 0.786619i) q^{8} +(1.86209 - 2.35215i) q^{9} +(-1.39019 - 0.130983i) q^{10} +0.596462 q^{11} +(3.34526 - 0.899578i) q^{12} +(0.909546 + 1.57538i) q^{13} +(-1.70842 - 3.32886i) q^{14} +(1.53948 - 0.744759i) q^{15} +(3.72090 + 1.46796i) q^{16} +(0.0458635 - 0.0264793i) q^{17} +(-2.93382 + 3.06475i) q^{18} +(2.88749 + 1.66709i) q^{19} +(1.93998 + 0.368843i) q^{20} +(3.90170 + 2.40349i) q^{21} +(-0.839806 - 0.0791264i) q^{22} +1.11839i q^{23} +(-4.82939 + 0.822805i) q^{24} -4.02511 q^{25} +(-1.07163 - 2.33876i) q^{26} +(1.12914 - 5.07199i) q^{27} +(1.96381 + 4.91360i) q^{28} +(-2.55834 - 1.47706i) q^{29} +(-2.26635 + 0.844377i) q^{30} +(-1.72807 + 2.99311i) q^{31} +(-5.04421 - 2.56046i) q^{32} +(0.929993 - 0.449905i) q^{33} +(-0.0680875 + 0.0311980i) q^{34} +(1.40552 + 2.20198i) q^{35} +(4.53732 - 3.92590i) q^{36} +(2.36629 + 1.36618i) q^{37} +(-3.84437 - 2.73029i) q^{38} +(2.60644 + 1.77024i) q^{39} +(-2.68251 - 0.776680i) q^{40} +(5.17811 - 2.98959i) q^{41} +(-5.17466 - 3.90165i) q^{42} +(4.04280 - 7.00233i) q^{43} +(1.17193 + 0.222817i) q^{44} +(1.83856 - 2.32243i) q^{45} +(0.148365 - 1.57466i) q^{46} +(-5.20424 - 9.01400i) q^{47} +(6.90882 - 0.517826i) q^{48} +(-2.94724 + 6.34931i) q^{49} +(5.66727 + 0.533970i) q^{50} +(0.0515365 - 0.0758804i) q^{51} +(1.19857 + 3.43508i) q^{52} +(-7.99715 + 4.61716i) q^{53} +(-2.26265 + 6.99145i) q^{54} +0.588925 q^{55} +(-2.11316 - 7.17876i) q^{56} +(5.75960 + 0.421296i) q^{57} +(3.40614 + 2.41905i) q^{58} +(6.26402 + 3.61653i) q^{59} +(3.30299 - 0.888211i) q^{60} +(-0.202338 - 0.350460i) q^{61} +(2.83015 - 3.98498i) q^{62} +(7.89638 + 0.804461i) q^{63} +(6.76246 + 4.27424i) q^{64} +(0.898053 + 1.55547i) q^{65} +(-1.36909 + 0.510084i) q^{66} +(1.88318 - 3.26177i) q^{67} +(0.100004 - 0.0348937i) q^{68} +(0.843588 + 1.74377i) q^{69} +(-1.68683 - 3.28680i) q^{70} -6.24780i q^{71} +(-6.90926 + 4.92566i) q^{72} +(1.72344 - 0.995030i) q^{73} +(-3.15044 - 2.23746i) q^{74} +(-6.27588 + 3.03610i) q^{75} +(5.05059 + 4.35417i) q^{76} +(0.849070 + 1.33021i) q^{77} +(-3.43497 - 2.83823i) q^{78} +(14.2015 - 8.19924i) q^{79} +(3.67388 + 1.44941i) q^{80} +(-2.06522 - 8.75984i) q^{81} +(-7.68727 + 3.52234i) q^{82} +(11.3718 + 6.56551i) q^{83} +(6.76821 + 6.17991i) q^{84} +(0.0452840 - 0.0261447i) q^{85} +(-6.62110 + 9.32281i) q^{86} +(-5.10305 - 0.373272i) q^{87} +(-1.62049 - 0.469189i) q^{88} +(-8.46840 - 4.88923i) q^{89} +(-2.89675 + 3.02602i) q^{90} +(-2.21860 + 4.27100i) q^{91} +(-0.417789 + 2.19741i) q^{92} +(-0.436706 + 5.97026i) q^{93} +(6.13166 + 13.3819i) q^{94} +(2.85101 + 1.64603i) q^{95} +(-9.79617 - 0.187435i) q^{96} +(-15.2566 - 8.80839i) q^{97} +(4.99195 - 8.54871i) q^{98} +(1.11067 - 1.40297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40798	−	0.132660i	−0.995591	−	0.0938045i
$2$	−1.40798	−	0.132660i	−0.995591	−	0.0938045i
$3$	1.55918	−	0.754290i	0.900194	−	0.435489i
$3$	1.55918	−	0.754290i	0.900194	−	0.435489i
$4$	1.96480	+	0.373564i	0.982401	+	0.186782i
$5$	0.987364			0.441563			0.220781	−	0.975323i	$-0.429139\pi$
$5$	0.987364			0.441563			0.220781	+	0.975323i	$0.429139\pi$
$6$	−2.29536	+	0.855183i	−0.937075	+	0.349127i
$7$	1.42351	+	2.23016i	0.538036	+	0.842922i
$7$	1.42351	+	2.23016i	0.538036	+	0.842922i
$8$	−2.71684	−	0.786619i	−0.960549	−	0.278112i
$9$	1.86209	−	2.35215i	0.620698	−	0.784050i
$10$	−1.39019	−	0.130983i	−0.439616	−	0.0414206i
$11$	0.596462			0.179840			0.0899201	−	0.995949i	$-0.471339\pi$
$11$	0.596462			0.179840			0.0899201	+	0.995949i	$0.471339\pi$
$12$	3.34526	−	0.899578i	0.965693	−	0.259686i
$13$	0.909546	+	1.57538i	0.252263	+	0.436932i	0.964148	−	0.265363i	$-0.0854920\pi$
$13$	0.909546	+	1.57538i	0.252263	+	0.436932i	−0.711886	+	0.702295i	$0.752159\pi$
$14$	−1.70842	−	3.32886i	−0.456594	−	0.889675i
$15$	1.53948	−	0.744759i	0.397492	−	0.192296i
$16$	3.72090	+	1.46796i	0.930225	+	0.366989i
$17$	0.0458635	−	0.0264793i	0.0111235	−	0.00642218i	−0.494428	−	0.869219i	$-0.664622\pi$
$17$	0.0458635	−	0.0264793i	0.0111235	−	0.00642218i	0.505551	+	0.862796i	$0.331289\pi$
$18$	−2.93382	+	3.06475i	−0.691508	+	0.722368i
$19$	2.88749	+	1.66709i	0.662436	+	0.382458i	0.793205	−	0.608955i	$-0.208411\pi$
$19$	2.88749	+	1.66709i	0.662436	+	0.382458i	−0.130768	+	0.991413i	$0.541744\pi$
$20$	1.93998	+	0.368843i	0.433792	+	0.0824759i
$21$	3.90170	+	2.40349i	0.851420	+	0.524484i
$22$	−0.839806	−	0.0791264i	−0.179047	−	0.0168698i
$23$			1.11839i			0.233200i	0.993179	+	0.116600i	$0.0371995\pi$
$23$			1.11839i			0.233200i	−0.993179	+	0.116600i	$0.962800\pi$
$24$	−4.82939	+	0.822805i	−0.985795	+	0.167954i
$25$	−4.02511			−0.805022
$26$	−1.07163	−	2.33876i	−0.210164	−	0.458669i
$27$	1.12914	−	5.07199i	0.217303	−	0.976104i
$28$	1.96381	+	4.91360i	0.371125	+	0.928583i
$29$	−2.55834	−	1.47706i	−0.475072	−	0.274283i	0.243289	−	0.969954i	$-0.421774\pi$
$29$	−2.55834	−	1.47706i	−0.475072	−	0.274283i	−0.718361	+	0.695671i	$0.755107\pi$
$30$	−2.26635	+	0.844377i	−0.413778	+	0.154161i
$31$	−1.72807	+	2.99311i	−0.310371	+	0.537578i	−0.978443	−	0.206519i	$-0.933787\pi$
$31$	−1.72807	+	2.99311i	−0.310371	+	0.537578i	0.668072	+	0.744097i	$0.267120\pi$
$32$	−5.04421	−	2.56046i	−0.891698	−	0.452630i
$33$	0.929993	−	0.449905i	0.161891	−	0.0783185i
$34$	−0.0680875	+	0.0311980i	−0.0116769	+	0.00535042i
$35$	1.40552	+	2.20198i	0.237577	+	0.372203i
$36$	4.53732	−	3.92590i	0.756221	−	0.654317i
$37$	2.36629	+	1.36618i	0.389015	+	0.224598i	0.681733	−	0.731601i	$-0.261226\pi$
$37$	2.36629	+	1.36618i	0.389015	+	0.224598i	−0.292718	+	0.956199i	$0.594560\pi$
$38$	−3.84437	−	2.73029i	−0.623639	−	0.442911i
$39$	2.60644	+	1.77024i	0.417365	+	0.283466i
$40$	−2.68251	−	0.776680i	−0.424142	−	0.122804i
$41$	5.17811	−	2.98959i	0.808686	−	0.466895i	−0.0378137	−	0.999285i	$-0.512039\pi$
$41$	5.17811	−	2.98959i	0.808686	−	0.466895i	0.846499	+	0.532390i	$0.178706\pi$
$42$	−5.17466	−	3.90165i	−0.798467	−	0.602038i
$43$	4.04280	−	7.00233i	0.616521	−	1.06785i	−0.373594	−	0.927592i	$-0.621875\pi$
$43$	4.04280	−	7.00233i	0.616521	−	1.06785i	0.990116	−	0.140254i	$-0.0447918\pi$
$44$	1.17193	+	0.222817i	0.176675	+	0.0335909i
$45$	1.83856	−	2.32243i	0.274077	−	0.346207i
$46$	0.148365	−	1.57466i	0.0218752	−	0.232172i
$47$	−5.20424	−	9.01400i	−0.759116	−	1.31483i	−0.943302	−	0.331936i	$-0.892298\pi$
$47$	−5.20424	−	9.01400i	−0.759116	−	1.31483i	0.184186	−	0.982891i	$-0.441035\pi$
$48$	6.90882	−	0.517826i	0.997203	−	0.0747417i
$49$	−2.94724	+	6.34931i	−0.421034	+	0.907045i
$50$	5.66727	+	0.533970i	0.801473	+	0.0755147i
$51$	0.0515365	−	0.0758804i	0.00721655	−	0.0106254i
$52$	1.19857	+	3.43508i	0.166212	+	0.476361i
$53$	−7.99715	+	4.61716i	−1.09849	+	0.634216i	−0.935825	−	0.352465i	$-0.885343\pi$
$53$	−7.99715	+	4.61716i	−1.09849	+	0.634216i	−0.162669	+	0.986681i	$0.552010\pi$
$54$	−2.26265	+	6.99145i	−0.307908	+	0.951416i
$55$	0.588925			0.0794107
$56$	−2.11316	−	7.17876i	−0.282383	−	0.959302i
$57$	5.75960	+	0.421296i	0.762877	+	0.0558021i
$58$	3.40614	+	2.41905i	0.447248	+	0.317637i
$59$	6.26402	+	3.61653i	0.815506	+	0.470832i	0.848864	−	0.528611i	$-0.177287\pi$
$59$	6.26402	+	3.61653i	0.815506	+	0.470832i	−0.0333585	+	0.999443i	$0.510620\pi$
$60$	3.30299	−	0.888211i	0.426414	−	0.114668i
$61$	−0.202338	−	0.350460i	−0.0259068	−	0.0448718i	0.852781	−	0.522268i	$-0.174914\pi$
$61$	−0.202338	−	0.350460i	−0.0259068	−	0.0448718i	−0.878688	+	0.477396i	$0.841581\pi$
$62$	2.83015	−	3.98498i	0.359429	−	0.506093i
$63$	7.89638	+	0.804461i	0.994851	+	0.101353i
$64$	6.76246	+	4.27424i	0.845308	+	0.534280i
$65$	0.898053	+	1.55547i	0.111390	+	0.192933i
$66$	−1.36909	+	0.510084i	−0.168524	+	0.0627870i
$67$	1.88318	−	3.26177i	0.230068	−	0.398489i	−0.727760	−	0.685832i	$-0.759439\pi$
$67$	1.88318	−	3.26177i	0.230068	−	0.398489i	0.957828	+	0.287343i	$0.0927719\pi$
$68$	0.100004	−	0.0348937i	0.0121273	−	0.00423148i
$69$	0.843588	+	1.74377i	0.101556	+	0.209925i
$70$	−1.68683	−	3.28680i	−0.201615	−	0.392847i
$71$		−	6.24780i		−	0.741478i	−0.928737	−	0.370739i	$-0.879105\pi$
$71$		−	6.24780i		−	0.741478i	0.928737	−	0.370739i	$-0.120895\pi$
$72$	−6.90926	+	4.92566i	−0.814264	+	0.580495i
$73$	1.72344	−	0.995030i	0.201714	−	0.116459i	−0.395741	−	0.918362i	$-0.629512\pi$
$73$	1.72344	−	0.995030i	0.201714	−	0.116459i	0.597455	+	0.801903i	$0.296179\pi$
$74$	−3.15044	−	2.23746i	−0.366232	−	0.260099i
$75$	−6.27588	+	3.03610i	−0.724676	+	0.350579i
$76$	5.05059	+	4.35417i	0.579342	+	0.499458i
$77$	0.849070	+	1.33021i	0.0967605	+	0.151591i
$78$	−3.43497	−	2.83823i	−0.388934	−	0.321366i
$79$	14.2015	−	8.19924i	1.59779	−	0.922487i	0.605883	−	0.795554i	$-0.292820\pi$
$79$	14.2015	−	8.19924i	1.59779	−	0.922487i	0.991911	−	0.126933i	$-0.0405134\pi$
$80$	3.67388	+	1.44941i	0.410753	+	0.162049i
$81$	−2.06522	−	8.75984i	−0.229468	−	0.973316i
$82$	−7.68727	+	3.52234i	−0.848917	+	0.388978i
$83$	11.3718	+	6.56551i	1.24822	+	0.720658i	0.970754	−	0.240078i	$-0.0771731\pi$
$83$	11.3718	+	6.56551i	1.24822	+	0.720658i	0.277463	+	0.960736i	$0.410506\pi$
$84$	6.76821	+	6.17991i	0.738473	+	0.674284i
$85$	0.0452840	−	0.0261447i	0.00491174	−	0.00283579i
$86$	−6.62110	+	9.32281i	−0.713971	+	1.00530i
$87$	−5.10305	−	0.373272i	−0.547104	−	0.0400189i
$88$	−1.62049	−	0.469189i	−0.172745	−	0.0500157i
$89$	−8.46840	−	4.88923i	−0.897648	−	0.518258i	−0.0212119	−	0.999775i	$-0.506752\pi$
$89$	−8.46840	−	4.88923i	−0.897648	−	0.518258i	−0.876437	+	0.481517i	$0.840086\pi$
$90$	−2.89675	+	3.02602i	−0.305344	+	0.318971i
$91$	−2.21860	+	4.27100i	−0.232573	+	0.447723i
$92$	−0.417789	+	2.19741i	−0.0435575	+	0.229096i
$93$	−0.436706	+	5.97026i	−0.0452843	+	0.619088i
$94$	6.13166	+	13.3819i	0.632432	+	1.38024i
$95$	2.85101	+	1.64603i	0.292507	+	0.168879i
$96$	−9.79617	−	0.187435i	−0.999817	−	0.0191300i
$97$	−15.2566	−	8.80839i	−1.54907	−	0.894357i	−0.998213	−	0.0597581i	$-0.980967\pi$
$97$	−15.2566	−	8.80839i	−1.54907	−	0.894357i	−0.550859	−	0.834599i	$-0.685700\pi$
$98$	4.99195	−	8.54871i	0.504263	−	0.863550i
$99$	1.11067	−	1.40297i	0.111626	−	0.141004i
$100$	−7.90855	−	1.50364i	−0.790855	−	0.150364i
$101$	−10.5058			−1.04537			−0.522683	−	0.852527i	$-0.675069\pi$
$101$	−10.5058			−1.04537			−0.522683	+	0.852527i	$0.675069\pi$
$102$	−0.0826285	+	0.100001i	−0.00818144	+	0.00990159i
$103$	−19.5085			−1.92223			−0.961116	−	0.276145i	$-0.910943\pi$
$103$	−19.5085			−1.92223			−0.961116	+	0.276145i	$0.910943\pi$
$104$	−1.23187	−	4.99553i	−0.120795	−	0.489852i
$105$	3.85240	+	2.37312i	0.375955	+	0.231593i
$106$	11.8723	−	5.43996i	1.15314	−	0.528375i
$107$	−9.11269	+	15.7837i	−0.880957	+	1.52586i	−0.0306794	+	0.999529i	$0.509767\pi$
$107$	−9.11269	+	15.7837i	−0.880957	+	1.52586i	−0.850278	+	0.526334i	$0.823566\pi$
$108$	4.11324	−	9.54365i	0.395797	−	0.918338i
$109$	−4.63639	+	2.67682i	−0.444085	+	0.256393i	−0.705329	−	0.708880i	$-0.749201\pi$
$109$	−4.63639	+	2.67682i	−0.444085	+	0.256393i	0.261244	+	0.965273i	$0.415867\pi$
$110$	−0.829194	−	0.0781266i	−0.0790605	−	0.00744908i
$111$	4.71997	+	0.345251i	0.447999	+	0.0327697i
$112$	2.02296	+	10.3879i	0.191151	+	0.981561i
$113$	1.12161	+	1.94269i	0.105512	+	0.182753i	0.913947	−	0.405833i	$-0.133018\pi$
$113$	1.12161	+	1.94269i	0.105512	+	0.182753i	−0.808435	+	0.588585i	$0.799685\pi$
$114$	−8.05350	−	1.35724i	−0.754279	−	0.127117i
$115$			1.10426i			0.102972i
$116$	−4.47486	−	3.85783i	−0.415480	−	0.358191i
$117$	5.39919	+	0.794116i	0.499155	+	0.0734161i
$118$	−8.33983	−	5.92298i	−0.767744	−	0.545254i
$119$	0.124340	+	0.0645895i	0.0113983	+	0.00592091i
$120$	−4.76837	+	0.812408i	−0.435290	+	0.0741623i
$121$	−10.6442			−0.967658
$122$	0.238396	+	0.520282i	0.0215834	+	0.0471041i
$123$	5.81860	−	8.56711i	0.524646	−	0.772470i
$124$	−4.51344	+	5.23532i	−0.405318	+	0.470146i
$125$	−8.91107			−0.797031
$126$	−11.0112	−	2.18019i	−0.980957	−	0.194227i
$127$		−	0.334561i		−	0.0296875i	−0.999890	−	0.0148437i	$-0.995275\pi$
$127$		−	0.334561i		−	0.0296875i	0.999890	−	0.0148437i	$-0.00472508\pi$
$128$	−8.95438	−	6.91514i	−0.791462	−	0.611218i
$129$	1.02167	−	13.9674i	0.0899528	−	1.22976i
$130$	−1.05809	−	2.30921i	−0.0928007	−	0.202531i
$131$			7.05300i			0.616223i	0.951350	+	0.308112i	$0.0996971\pi$
$131$			7.05300i			0.616223i	−0.951350	+	0.308112i	$0.900303\pi$
$132$	1.99532	−	0.536564i	0.173670	−	0.0467019i
$133$	0.392484	+	8.81270i	0.0340326	+	0.764158i
$134$	−3.08419	+	4.34268i	−0.266433	+	0.375150i
$135$	1.11487	−	5.00790i	0.0959528	−	0.431011i
$136$	−0.145433	+	0.0358630i	−0.0124708	+	0.00307523i
$137$	−12.6891			−1.08410			−0.542052	−	0.840345i	$-0.682353\pi$
$137$	−12.6891			−1.08410			−0.542052	+	0.840345i	$0.682353\pi$
$138$	−0.956425	−	2.56710i	−0.0814163	−	0.218526i
$139$	6.27084	−	3.62047i	0.531885	−	0.307084i	−0.209899	−	0.977723i	$-0.567313\pi$
$139$	6.27084	−	3.62047i	0.531885	−	0.307084i	0.741784	+	0.670639i	$0.233980\pi$
$140$	1.93899	+	4.85151i	0.163875	+	0.410028i
$141$	−14.9135	−	10.1290i	−1.25595	−	0.853013i
$142$	−0.828831	+	8.79677i	−0.0695539	+	0.738208i
$143$	0.542510	+	0.939655i	0.0453670	+	0.0785779i
$144$	10.3815	−	6.01864i	0.865127	−	0.501553i
$145$	−2.52601	−	1.45840i	−0.209774	−	0.121113i
$146$	−2.55857	+	1.17235i	−0.211749	+	0.0970242i
$147$	0.193940	+	12.1228i	0.0159959	+	0.999872i
$148$	4.13893	+	3.56823i	0.340218	+	0.293306i
$149$			2.18170i			0.178732i	0.995999	+	0.0893658i	$0.0284840\pi$
$149$			2.18170i			0.178732i	−0.995999	+	0.0893658i	$0.971516\pi$
$150$	9.23907	−	3.44221i	0.754367	−	0.281055i
$151$		−	1.99673i		−	0.162492i	−0.996694	−	0.0812458i	$-0.974110\pi$
$151$		−	1.99673i		−	0.162492i	0.996694	−	0.0812458i	$-0.0258899\pi$
$152$	−6.53349	−	6.80059i	−0.529936	−	0.551601i
$153$	0.0231188	−	0.157185i	0.00186905	−	0.0127076i
$154$	−1.01901	−	1.98554i	−0.0821139	−	0.159999i
$155$	−1.70624	+	2.95529i	−0.137048	+	0.237374i
$156$	4.45984	+	4.45185i	0.357073	+	0.356433i
$157$	−2.19450	+	3.80098i	−0.175140	+	0.303351i	−0.940210	−	0.340596i	$-0.889371\pi$
$157$	−2.19450	+	3.80098i	−0.175140	+	0.303351i	0.765070	+	0.643947i	$0.222704\pi$
$158$	−21.0831	+	9.66039i	−1.67728	+	0.768539i
$159$	−8.98634	+	13.2312i	−0.712663	+	1.04930i
$160$	−4.98047	−	2.52811i	−0.393741	−	0.199865i
$161$	−2.49418	+	1.59203i	−0.196569	+	0.125470i
$162$	1.74570	+	12.6076i	0.137155	+	0.990550i
$163$	−6.37092	+	11.0348i	−0.499009	+	0.864309i	−0.999999	−	0.00114404i	$-0.999636\pi$
$163$	−6.37092	+	11.0348i	−0.499009	+	0.864309i	0.500990	+	0.865453i	$0.332969\pi$
$164$	11.2908	−	3.93959i	0.881661	−	0.307630i
$165$	0.918242	−	0.444221i	0.0714850	−	0.0345825i
$166$	−15.1403	−	10.7527i	−1.17511	−	0.834569i
$167$	6.90384	+	11.9578i	0.534235	+	0.925322i	0.999200	+	0.0399932i	$0.0127336\pi$
$167$	6.90384	+	11.9578i	0.534235	+	0.925322i	−0.464965	+	0.885329i	$0.653933\pi$
$168$	−8.70967	−	9.59905i	−0.671965	−	0.740582i
$169$	4.84545	−	8.39257i	0.372727	−	0.645582i
$170$	−0.0672272	+	0.0308038i	−0.00515609	+	0.00236255i
$171$	9.29804	−	3.68753i	0.711039	−	0.281992i
$172$	10.5591	−	12.2480i	0.805125	−	0.933898i
$173$	1.56982	+	2.71901i	0.119352	+	0.206723i	0.919511	−	0.393065i	$-0.128585\pi$
$173$	1.56982	+	2.71901i	0.119352	+	0.206723i	−0.800159	+	0.599787i	$0.795252\pi$
$174$	7.13546	+	1.20253i	0.540938	+	0.0911633i
$175$	−5.72979	−	8.97665i	−0.433131	−	0.678571i
$176$	2.21938	+	0.875581i	0.167292	+	0.0659994i
$177$	12.4947	+	0.913944i	0.939156	+	0.0686963i
$178$	11.2747	+	8.00734i	0.845075	+	0.600176i
$179$	10.7917	+	18.6918i	0.806610	+	1.39709i	0.915199	+	0.403003i	$0.132033\pi$
$179$	10.7917	+	18.6918i	0.806610	+	1.39709i	−0.108589	+	0.994087i	$0.534633\pi$
$180$	4.47999	−	3.87629i	0.333919	−	0.288922i
$181$	−12.4662			−0.926607			−0.463303	−	0.886200i	$-0.653336\pi$
$181$	−12.4662			−0.926607			−0.463303	+	0.886200i	$0.653336\pi$
$182$	3.69034	−	5.71916i	0.273546	−	0.423932i
$183$	−0.579831	−	0.393809i	−0.0428623	−	0.0291112i
$184$	0.879744	−	3.03848i	0.0648556	−	0.224000i
$185$	2.33639	+	1.34891i	0.171775	+	0.0991741i
$186$	1.40689	−	8.34807i	0.103158	−	0.612110i
$187$	0.0273559	−	0.0157939i	0.00200046	−	0.00115496i
$188$	−6.85800	−	19.6549i	−0.500171	−	1.43348i
$189$	12.9187	−	4.70186i	0.939696	−	0.342010i
$190$	−3.79579	−	2.69579i	−0.275376	−	0.195573i
$191$	9.85151	−	5.68777i	0.712830	−	0.411553i	−0.0992778	−	0.995060i	$-0.531653\pi$
$191$	9.85151	−	5.68777i	0.712830	−	0.411553i	0.812108	+	0.583507i	$0.198320\pi$
$192$	13.7679	+	1.56346i	0.993614	+	0.112833i
$193$	−8.87562	+	15.3730i	−0.638881	+	1.10657i	0.346797	+	0.937940i	$0.387269\pi$
$193$	−8.87562	+	15.3730i	−0.638881	+	1.10657i	−0.985679	+	0.168635i	$0.946064\pi$
$194$	20.3124	+	14.4260i	1.45835	+	1.03572i
$195$	2.57351	+	1.74787i	0.184293	+	0.125168i
$196$	−8.16262	+	11.3742i	−0.583044	+	0.812440i
$197$			6.17600i			0.440021i	0.975497	+	0.220011i	$0.0706092\pi$
$197$			6.17600i			0.440021i	−0.975497	+	0.220011i	$0.929391\pi$
$198$	−1.74991	+	1.82801i	−0.124361	+	0.129911i
$199$	−10.0075	−	17.3336i	−0.709415	−	1.22874i	−0.965074	−	0.261977i	$-0.915626\pi$
$199$	−10.0075	−	17.3336i	−0.709415	−	1.22874i	0.255659	−	0.966767i	$-0.417708\pi$
$200$	10.9356	+	3.16623i	0.773263	+	0.223886i
$201$	0.475905	−	6.50616i	0.0335678	−	0.458909i
$202$	14.7919	+	1.39369i	1.04076	+	0.0980600i
$203$	−0.347743	−	7.80812i	−0.0244068	−	0.548023i
$204$	0.129605	−	0.129838i	0.00907417	−	0.00909047i
$205$	5.11268	−	2.95181i	0.357085	−	0.206163i
$206$	27.4676	+	2.58799i	1.91376	+	0.180314i
$207$	2.63061	+	2.08254i	0.182840	+	0.144747i
$208$	1.07174	+	7.19701i	0.0743118	+	0.499023i
$209$	1.72228	+	0.994359i	0.119133	+	0.0687812i
$210$	−5.10927	−	3.85235i	−0.352573	−	0.265838i
$211$	−11.1360	−	19.2881i	−0.766633	−	1.32785i	−0.939379	−	0.342881i	$-0.888597\pi$
$211$	−11.1360	−	19.2881i	−0.766633	−	1.32785i	0.172745	−	0.984967i	$-0.444736\pi$
$212$	−17.4376	+	6.08436i	−1.19762	+	0.417876i
$213$	−4.71265	−	9.74146i	−0.322906	−	0.667474i
$214$	14.9243	−	21.0141i	1.02021	−	1.43650i
$215$	3.99172	−	6.91385i	0.272233	−	0.471521i
$216$	−7.05741	+	12.8916i	−0.480196	+	0.877161i
$217$	−9.13504	+	0.406839i	−0.620127	+	0.0276180i
$218$	6.88304	−	3.15384i	0.466178	−	0.213605i
$219$	1.93662	−	2.85141i	0.130864	−	0.192680i
$220$	1.15712	+	0.220001i	0.0780132	+	0.0148325i
$221$	0.0834300	+	0.0481683i	0.00561211	+	0.00324015i
$222$	−6.59981	−	1.11225i	−0.442950	−	0.0746496i
$223$	0.766027	−	1.32680i	0.0512969	−	0.0888489i	−0.839237	−	0.543766i	$-0.816998\pi$
$223$	0.766027	−	1.32680i	0.0512969	−	0.0888489i	0.890534	+	0.454917i	$0.150331\pi$
$224$	−1.47023	−	14.8942i	−0.0982337	−	0.995163i
$225$	−7.49513	+	9.46767i	−0.499676	+	0.631178i
$226$	−1.32149	−	2.88405i	−0.0879041	−	0.191844i
$227$		−	6.32468i		−	0.419784i	−0.977725	−	0.209892i	$-0.932689\pi$
$227$		−	6.32468i		−	0.419784i	0.977725	−	0.209892i	$-0.0673112\pi$
$228$	11.1591	+	2.97934i	0.739029	+	0.197312i
$229$	23.4328			1.54848			0.774241	−	0.632891i	$-0.218132\pi$
$229$	23.4328			1.54848			0.774241	+	0.632891i	$0.218132\pi$
$230$	0.146490	−	1.55477i	0.00965927	−	0.102518i
$231$	2.32722	+	1.43359i	0.153120	+	0.0943233i
$232$	5.78873	+	6.02538i	0.380048	+	0.395585i
$233$	−7.87513	+	13.6401i	−0.515917	+	0.893594i	0.483913	+	0.875116i	$0.339215\pi$
$233$	−7.87513	+	13.6401i	−0.515917	+	0.893594i	−0.999829	+	0.0184777i	$0.994118\pi$
$234$	−7.49659	−	1.83435i	−0.490068	−	0.119915i
$235$	−5.13848	−	8.90011i	−0.335197	−	0.580579i
$236$	10.9566	+	9.44578i	0.713211	+	0.614868i
$237$	15.9581	−	23.4962i	1.03659	−	1.52624i
$238$	−0.166500	−	0.107435i	−0.0107926	−	0.00696401i
$239$	18.4765	−	10.6674i	1.19514	−	0.690016i	0.235675	−	0.971832i	$-0.424270\pi$
$239$	18.4765	−	10.6674i	1.19514	−	0.690016i	0.959468	+	0.281816i	$0.0909367\pi$
$240$	6.82153	−	0.511283i	0.440328	−	0.0330032i
$241$			7.85610i			0.506056i	0.967459	+	0.253028i	$0.0814264\pi$
$241$			7.85610i			0.506056i	−0.967459	+	0.253028i	$0.918574\pi$
$242$	14.9868	+	1.41206i	0.963391	+	0.0907706i
$243$	−9.82751	−	12.1004i	−0.630435	−	0.776242i
$244$	−0.266636	−	0.764171i	−0.0170696	−	0.0489211i
$245$	−2.91000	+	6.26908i	−0.185913	+	0.400517i
$246$	−9.32897	+	11.2904i	−0.594794	+	0.719850i
$247$			6.06520i			0.385919i
$248$	7.04933	−	6.77247i	0.447633	−	0.430052i
$249$	22.6830	+	1.65919i	1.43748	+	0.105147i
$250$	12.5466	+	1.18214i	0.793516	+	0.0747651i
$251$			10.4715i			0.660953i	0.943814	+	0.330476i	$0.107209\pi$
$251$			10.4715i			0.660953i	−0.943814	+	0.330476i	$0.892791\pi$
$252$	15.2143	+	4.53041i	0.958412	+	0.285389i
$253$			0.667075i			0.0419387i
$254$	−0.0443827	+	0.471054i	−0.00278482	+	0.0295566i
$255$	0.0508853	−	0.0749216i	0.00318656	−	0.00469177i
$256$	11.6902	+	10.9242i	0.730638	+	0.682765i
$257$		−	25.1508i		−	1.56886i	−0.620216	−	0.784431i	$-0.712955\pi$
$257$		−	25.1508i		−	1.56886i	0.620216	−	0.784431i	$-0.287045\pi$
$258$	−3.29139	+	19.5302i	−0.204913	+	1.21590i
$259$	0.321639	+	7.22197i	0.0199856	+	0.448751i
$260$	1.18343	+	3.39168i	0.0733932	+	0.210343i
$261$	−8.23813	+	3.26718i	−0.509928	+	0.202233i
$262$	0.935648	−	9.93047i	0.0578045	−	0.613506i
$263$			23.3838i			1.44190i	0.692985	+	0.720952i	$0.256295\pi$
$263$			23.3838i			1.44190i	−0.692985	+	0.720952i	$0.743705\pi$
$264$	−2.88055	+	0.490772i	−0.177285	+	0.0302049i
$265$	−7.89610	+	4.55882i	−0.485054	+	0.280046i
$266$	0.616481	−	12.4602i	0.0377989	−	0.763981i
$267$	−16.8917	−	1.23557i	−1.03375	−	0.0756158i
$268$	4.91857	−	5.70525i	0.300449	−	0.348504i
$269$	−1.38696	−	2.40229i	−0.0845646	−	0.146470i	0.820641	−	0.571444i	$-0.193617\pi$
$269$	−1.38696	−	2.40229i	−0.0845646	−	0.146470i	−0.905206	+	0.424974i	$0.860283\pi$
$270$	−2.23406	+	6.90311i	−0.135961	+	0.420110i
$271$	12.0898	−	20.9401i	0.734401	−	1.27202i	−0.220584	−	0.975368i	$-0.570796\pi$
$271$	12.0898	−	20.9401i	0.734401	−	1.27202i	0.954985	−	0.296653i	$-0.0958704\pi$
$272$	0.209524	−	0.0312012i	0.0127043	−	0.00189185i
$273$	−0.237632	+	8.33274i	−0.0143821	+	0.504320i
$274$	17.8660	+	1.68333i	1.07932	+	0.101694i
$275$	−2.40083			−0.144775
$276$	1.00608	+	3.74129i	0.0605586	+	0.225199i
$277$			11.9194i			0.716168i	0.933689	+	0.358084i	$0.116570\pi$
$277$			11.9194i			0.716168i	−0.933689	+	0.358084i	$0.883430\pi$
$278$	−9.30949	+	4.26565i	−0.558346	+	0.255837i
$279$	3.82241	+	9.63813i	0.228841	+	0.577020i
$280$	−2.08646	−	7.08805i	−0.124690	−	0.423592i
$281$	−7.49842	+	12.9876i	−0.447318	+	0.774778i	−0.998210	−	0.0597984i	$-0.980954\pi$
$281$	−7.49842	+	12.9876i	−0.447318	+	0.774778i	0.550892	+	0.834576i	$0.314288\pi$
$282$	19.6542	+	16.2398i	1.17039	+	0.967065i
$283$	−10.9844	−	6.34182i	−0.652952	−	0.376982i	0.136634	−	0.990622i	$-0.456372\pi$
$283$	−10.9844	−	6.34182i	−0.652952	−	0.376982i	−0.789586	+	0.613639i	$0.789705\pi$
$284$	2.33395	−	12.2757i	0.138495	−	0.728429i
$285$	5.68682	+	0.415973i	0.336858	+	0.0246401i
$286$	−0.639188	−	1.39498i	−0.0377960	−	0.0824870i
$287$	14.0384	+	7.29233i	0.828658	+	0.430452i
$288$	−15.4154	+	7.09690i	−0.908360	+	0.418189i
$289$	−8.49860	+	14.7200i	−0.499918	+	0.865883i
$290$	3.36310	+	2.38849i	0.197488	+	0.140257i
$291$	−30.4319	−	2.22599i	−1.78395	−	0.130490i
$292$	3.75793	−	1.31122i	0.219916	−	0.0767335i
$293$	−8.97645	−	15.5477i	−0.524410	−	0.908304i	−0.999596	−	0.0284192i	$-0.990953\pi$
$293$	−8.97645	−	15.5477i	−0.524410	−	0.908304i	0.475186	−	0.879885i	$-0.342381\pi$
$294$	1.33514	−	17.0944i	0.0778671	−	0.996964i
$295$	6.18487	+	3.57083i	0.360097	+	0.207902i
$296$	−5.35417	−	5.57305i	−0.311205	−	0.323927i
$297$	0.673488	−	3.02525i	0.0390798	−	0.175543i
$298$	0.289423	−	3.07178i	0.0167658	−	0.177944i
$299$	−1.76188	+	1.01722i	−0.101892	+	0.0588276i
$300$	−13.4650	+	3.62090i	−0.777405	+	0.209053i
$301$	21.3713	−	0.951795i	1.23182	−	0.0548605i
$302$	−0.264885	+	2.81135i	−0.0152424	+	0.161775i
$303$	−16.3804	+	7.92442i	−0.941032	+	0.455246i
$304$	8.29685	+	10.4418i	0.475857	+	0.598879i
$305$	−0.199782	−	0.346032i	−0.0114395	−	0.0198137i
$306$	−0.0534029	+	0.218246i	−0.00305284	+	0.0124763i
$307$		−	16.8133i		−	0.959586i	−0.877382	−	0.479793i	$-0.840712\pi$
$307$		−	16.8133i		−	0.959586i	0.877382	−	0.479793i	$-0.159288\pi$
$308$	1.17134	+	2.93078i	0.0667432	+	0.166996i
$309$	−30.4173	+	14.7151i	−1.73038	+	0.837112i
$310$	2.79439	−	3.93463i	0.158711	−	0.223472i
$311$	−2.52996	+	4.38202i	−0.143461	+	0.248482i	−0.928798	−	0.370587i	$-0.879156\pi$
$311$	−2.52996	+	4.38202i	−0.143461	+	0.248482i	0.785337	+	0.619069i	$0.212490\pi$
$312$	−5.68878	−	6.85974i	−0.322064	−	0.388357i
$313$	11.7469	−	6.78206i	0.663973	−	0.383345i	−0.129816	−	0.991538i	$-0.541439\pi$
$313$	11.7469	−	6.78206i	0.663973	−	0.383345i	0.793789	+	0.608193i	$0.208105\pi$
$314$	3.59404	−	5.06057i	0.202823	−	0.285584i
$315$	7.79660	+	0.794296i	0.439289	+	0.0447535i
$316$	30.9661	−	10.8047i	1.74198	−	0.607814i
$317$	22.0589	−	12.7357i	1.23895	−	0.715310i	0.270073	−	0.962840i	$-0.412952\pi$
$317$	22.0589	−	12.7357i	1.23895	−	0.715310i	0.968880	+	0.247530i	$0.0796188\pi$
$318$	14.4078	−	17.4371i	0.807949	−	0.977822i
$319$	−1.52595	−	0.881010i	−0.0854370	−	0.0493271i
$320$	6.67701	+	4.22023i	0.373256	+	0.235918i
$321$	−2.30290	+	31.4832i	−0.128535	+	1.75722i
$322$	3.72295	−	1.91067i	0.207472	−	0.106478i
$323$	0.176574			0.00982484
$324$	−0.785384	−	17.9829i	−0.0436325	−	0.999048i
$325$	−3.66102	−	6.34108i	−0.203077	−	0.351740i
$326$	10.4340	−	14.6915i	0.577885	−	0.813688i
$327$	−5.20987	+	7.67083i	−0.288107	+	0.424198i
$328$	−16.4198	+	4.04903i	−0.906631	+	0.223570i
$329$	12.6944	−	24.4378i	0.699865	−	1.34730i
$330$	−1.35179	+	0.503639i	−0.0744138	+	0.0277244i
$331$	1.68300	+	2.91505i	0.0925062	+	0.160225i	0.908565	−	0.417743i	$-0.137179\pi$
$331$	1.68300	+	2.91505i	0.0925062	+	0.160225i	−0.816059	+	0.577969i	$0.803846\pi$
$332$	19.8907	+	17.1480i	1.09164	+	0.941120i
$333$	7.61970	−	3.02191i	0.417557	−	0.165600i
$334$	−8.13414	−	17.7522i	−0.445080	−	0.971356i
$335$	1.85939	−	3.22056i	0.101589	−	0.175958i
$336$	10.9896	+	14.6707i	0.599533	+	0.800350i
$337$	12.3135	+	21.3276i	0.670759	+	1.16179i	0.977689	+	0.210056i	$0.0673648\pi$
$337$	12.3135	+	21.3276i	0.670759	+	1.16179i	−0.306930	+	0.951732i	$0.599302\pi$
$338$	−7.93564	+	11.1738i	−0.431642	+	0.607772i
$339$	3.21415	+	2.18298i	0.174568	+	0.118563i
$340$	0.0987408	−	0.0344528i	0.00535497	−	0.00186846i
$341$	−1.03073	+	1.78528i	−0.0558171	+	0.0966781i
$342$	−13.5806	+	3.95848i	−0.734356	+	0.214050i
$343$	−18.3554	+	2.46549i	−0.991099	+	0.133124i
$344$	−16.4918	+	15.8441i	−0.889179	+	0.854256i
$345$	0.832929	+	1.72173i	0.0448434	+	0.0926950i
$346$	−1.84957	−	4.03656i	−0.0994337	−	0.217007i
$347$	−6.36125	+	11.0180i	−0.341490	+	0.591477i	−0.984710	−	0.174204i	$-0.944265\pi$
$347$	−6.36125	+	11.0180i	−0.341490	+	0.591477i	0.643220	+	0.765681i	$0.277598\pi$
$348$	−9.88704	−	2.63972i	−0.530001	−	0.141504i
$349$	15.8919	−	27.5256i	0.850674	−	1.47341i	−0.0299270	−	0.999552i	$-0.509527\pi$
$349$	15.8919	−	27.5256i	0.850674	−	1.47341i	0.880601	−	0.473859i	$-0.157139\pi$
$350$	6.87657	+	13.3990i	0.367568	+	0.716208i
$351$	9.01731	−	2.83438i	0.481308	−	0.151288i
$352$	−3.00868	−	1.52722i	−0.160363	−	0.0814011i
$353$		−	7.75100i		−	0.412544i	−0.978495	−	0.206272i	$-0.933867\pi$
$353$		−	7.75100i		−	0.412544i	0.978495	−	0.206272i	$-0.0661332\pi$
$354$	−17.4710	−	2.94435i	−0.928571	−	0.156490i
$355$		−	6.16886i		−	0.327409i
$356$	−14.8123	−	12.7699i	−0.785050	−	0.676801i
$357$	0.242588	+	0.00691809i	0.0128391	+	0.000366144i
$358$	−12.7148	−	27.7492i	−0.672000	−	1.46659i
$359$	−17.2667	−	9.96893i	−0.911302	−	0.526140i	−0.0304519	−	0.999536i	$-0.509695\pi$
$359$	−17.2667	−	9.96893i	−0.911302	−	0.526140i	−0.880850	+	0.473396i	$0.843028\pi$
$360$	−6.82196	+	4.86342i	−0.359549	+	0.256325i
$361$	−3.94159	−	6.82704i	−0.207452	−	0.359318i
$362$	17.5522	+	1.65376i	0.922521	+	0.0869199i
$363$	−16.5963	+	8.02884i	−0.871079	+	0.421405i
$364$	−5.95461	+	7.56289i	−0.312106	+	0.396403i
$365$	1.70166	−	0.982457i	0.0890692	−	0.0514241i
$366$	0.764146	+	0.631395i	0.0399426	+	0.0330035i
$367$	−14.2007			−0.741273			−0.370636	−	0.928778i	$-0.620860\pi$
$367$	−14.2007			−0.741273			−0.370636	+	0.928778i	$0.620860\pi$
$368$	−1.64174	+	4.16141i	−0.0855818	+	0.216928i
$369$	2.61018	−	17.7466i	0.135880	−	0.923850i
$370$	−3.11064	−	2.20919i	−0.161714	−	0.114850i
$371$	−21.6810	−	11.2624i	−1.12562	−	0.584713i
$372$	−3.08831	+	11.5673i	−0.160122	+	0.599734i
$373$			18.9154i			0.979404i	0.871890	+	0.489702i	$0.162894\pi$
$373$			18.9154i			0.979404i	−0.871890	+	0.489702i	$0.837106\pi$
$374$	−0.0406116	+	0.0186085i	−0.00209998	+	0.000962220i
$375$	−13.8940	+	6.72153i	−0.717482	+	0.347098i
$376$	7.04850	+	28.5834i	0.363499	+	1.47408i
$377$		−	5.37381i		−	0.276765i
$378$	−18.8130	+	4.90633i	−0.967635	+	0.252354i
$379$	21.2622			1.09217			0.546083	−	0.837731i	$-0.316118\pi$
$379$	21.2622			1.09217			0.546083	+	0.837731i	$0.316118\pi$
$380$	4.98677	+	4.29916i	0.255816	+	0.220542i
$381$	−0.252356	−	0.521641i	−0.0129286	−	0.0267245i
$382$	−14.6252	+	6.70136i	−0.748293	+	0.342871i
$383$	−35.4166			−1.80971			−0.904853	−	0.425725i	$-0.860019\pi$
$383$	−35.4166			−1.80971			−0.904853	+	0.425725i	$0.860019\pi$
$384$	−19.1775	−	4.02776i	−0.978649	−	0.205541i
$385$	0.838341	+	1.31340i	0.0427258	+	0.0669370i
$386$	14.5361	−	20.4674i	0.739866	−	1.04177i
$387$	−8.94247	−	22.5483i	−0.454571	−	1.14619i
$388$	−26.6857	−	23.0061i	−1.35476	−	1.16796i
$389$			26.1451i			1.32561i	0.748793	+	0.662804i	$0.230634\pi$
$389$			26.1451i			1.32561i	−0.748793	+	0.662804i	$0.769366\pi$
$390$	−3.39157	−	2.80237i	−0.171739	−	0.141903i
$391$	0.0296141	+	0.0512931i	0.00149765	+	0.00259401i
$392$	13.0017	−	14.9317i	0.656684	−	0.754166i
$393$	5.32001	+	10.9969i	0.268359	+	0.554721i
$394$	0.819305	−	8.69566i	0.0412760	−	0.438081i
$395$	14.0221	−	8.09564i	0.705526	−	0.407336i
$396$	2.70634	−	2.34165i	0.135999	−	0.117672i
$397$	13.2348	−	22.9234i	0.664238	−	1.15049i	−0.315254	−	0.949007i	$-0.602090\pi$
$397$	13.2348	−	22.9234i	0.664238	−	1.15049i	0.979491	−	0.201486i	$-0.0645770\pi$
$398$	11.7909	+	25.7329i	0.591026	+	1.28987i
$399$	7.25928	+	13.4446i	0.363419	+	0.673069i
$400$	−14.9770	−	5.90869i	−0.748852	−	0.295435i
$401$	20.2019			1.00883			0.504417	−	0.863460i	$-0.331708\pi$
$401$	20.2019			1.00883			0.504417	+	0.863460i	$0.331708\pi$
$402$	−1.53317	+	9.09740i	−0.0764675	+	0.453737i
$403$	−6.28704			−0.313180
$404$	−20.6418	−	3.92458i	−1.02697	−	0.195255i
$405$	−2.03912	−	8.64916i	−0.101325	−	0.429780i
$406$	−0.546207	+	11.0398i	−0.0271078	+	0.547896i
$407$	1.41140	+	0.814873i	0.0699606	+	0.0403917i
$408$	−0.199705	+	0.165616i	−0.00988689	+	0.00819919i
$409$	2.71698	+	1.56865i	0.134346	+	0.0775648i	0.565667	−	0.824634i	$-0.308619\pi$
$409$	2.71698	+	1.56865i	0.134346	+	0.0775648i	−0.431321	+	0.902199i	$0.641952\pi$
$410$	−7.59013	+	3.47784i	−0.374850	+	0.171758i
$411$	−19.7846	+	9.57128i	−0.975904	+	0.472116i
$412$	−38.3304	−	7.28767i	−1.88840	−	0.359038i
$413$	0.851439	+	19.1179i	0.0418966	+	0.940732i
$414$	−3.42758	−	3.28115i	−0.168456	−	0.161260i
$415$	11.2281	+	6.48255i	0.551166	+	0.318216i
$416$	−0.554233	−	10.2754i	−0.0271735	−	0.503793i
$417$	7.04649	−	10.3750i	0.345068	−	0.508066i
$418$	−2.29302	−	1.62851i	−0.112155	−	0.0796531i
$419$	24.0865	−	13.9063i	1.17670	−	0.679369i	0.221453	−	0.975171i	$-0.428920\pi$
$419$	24.0865	−	13.9063i	1.17670	−	0.679369i	0.955249	+	0.295802i	$0.0955868\pi$
$420$	6.68269	+	6.10182i	0.326082	+	0.297738i
$421$	−15.8011	−	9.12277i	−0.770099	−	0.444617i	0.0628110	−	0.998025i	$-0.479993\pi$
$421$	−15.8011	−	9.12277i	−0.770099	−	0.444617i	−0.832910	+	0.553409i	$0.813327\pi$
$422$	13.1205	+	28.6345i	0.638695	+	1.39391i
$423$	−30.8931	−	4.54377i	−1.50207	−	0.220926i
$424$	25.3589	−	6.25338i	1.23154	−	0.303691i
$425$	−0.184606	+	0.106582i	−0.00895469	+	0.00517000i
$426$	5.34301	+	14.3409i	0.258870	+	0.694820i
$427$	0.493552	−	0.950131i	0.0238847	−	0.0459800i
$428$	−23.8008	+	27.6076i	−1.15046	+	1.33446i
$429$	1.55464	+	1.05588i	0.0750589	+	0.0509785i
$430$	−6.53744	+	9.20501i	−0.315263	+	0.443905i
$431$	−10.6958	+	6.17520i	−0.515197	+	0.297449i	−0.734967	−	0.678103i	$-0.762802\pi$
$431$	−10.6958	+	6.17520i	−0.515197	+	0.297449i	0.219771	+	0.975552i	$0.429469\pi$
$432$	11.6469	−	17.2148i	0.560360	−	0.828249i
$433$			2.34665i			0.112773i	0.998409	+	0.0563865i	$0.0179579\pi$
$433$			2.34665i			0.112773i	−0.998409	+	0.0563865i	$0.982042\pi$
$434$	12.9159	+	0.639030i	0.619983	+	0.0306744i
$435$	−5.03857	−	0.368555i	−0.241581	−	0.0176709i
$436$	−10.1096	+	3.52744i	−0.484160	+	0.168934i
$437$	−1.86446	+	3.22933i	−0.0891891	+	0.154480i
$438$	−3.10498	+	3.75781i	−0.148362	+	0.179555i
$439$	2.37122	+	4.10708i	0.113172	+	0.196020i	0.917048	−	0.398778i	$-0.130565\pi$
$439$	2.37122	+	4.10708i	0.113172	+	0.196020i	−0.803875	+	0.594798i	$0.797232\pi$
$440$	−1.60002	−	0.463260i	−0.0762778	−	0.0220851i
$441$	9.44650	+	18.7554i	0.449833	+	0.893113i
$442$	−0.111078	−	0.0788877i	−0.00528342	−	0.00375230i
$443$	−13.8305	−	23.9551i	−0.657105	−	1.13814i	−0.981362	−	0.192170i	$-0.938447\pi$
$443$	−13.8305	−	23.9551i	−0.657105	−	1.13814i	0.324257	−	0.945969i	$-0.394886\pi$
$444$	9.14483	+	2.44156i	0.433994	+	0.115871i
$445$	−8.36139	−	4.82745i	−0.396368	−	0.228843i
$446$	−1.25456	+	1.76648i	−0.0594052	+	0.0836453i
$447$	1.64563	+	3.40166i	0.0778357	+	0.160893i
$448$	0.0941829	+	21.1658i	0.00444973	+	0.999990i
$449$	16.3923			0.773599			0.386800	−	0.922164i	$-0.373580\pi$
$449$	16.3923			0.773599			0.386800	+	0.922164i	$0.373580\pi$
$450$	11.8090	−	12.3360i	0.556680	−	0.581523i
$451$	3.08855	−	1.78317i	0.145434	−	0.0839664i
$452$	1.47803	+	4.23599i	0.0695206	+	0.199244i
$453$	−1.50611	−	3.11326i	−0.0707634	−	0.146274i
$454$	−0.839029	+	8.90501i	−0.0393776	+	0.417933i
$455$	−2.19057	+	4.21704i	−0.102696	+	0.197698i
$456$	−15.3165	−	5.67521i	−0.717262	−	0.265766i
$457$	4.26536	+	7.38783i	0.199525	+	0.345588i	0.948375	−	0.317152i	$-0.102727\pi$
$457$	4.26536	+	7.38783i	0.199525	+	0.345588i	−0.748849	+	0.662740i	$0.769393\pi$
$458$	−32.9928	−	3.10858i	−1.54165	−	0.145255i
$459$	−0.0825164	−	0.262518i	−0.00385154	−	0.0122533i
$460$	−0.412509	+	2.16964i	−0.0192334	+	0.101160i
$461$	21.3803	−	37.0317i	0.995779	−	1.72474i	0.418405	−	0.908261i	$-0.362589\pi$
$461$	21.3803	−	37.0317i	0.995779	−	1.72474i	0.577375	−	0.816479i	$-0.304077\pi$
$462$	−3.08649	−	2.32719i	−0.143596	−	0.108271i
$463$	1.14233	−	0.659523i	0.0530885	−	0.0306506i	−0.473221	−	0.880944i	$-0.656909\pi$
$463$	1.14233	−	0.659523i	0.0530885	−	0.0306506i	0.526309	+	0.850293i	$0.323575\pi$
$464$	−7.35107	−	9.25153i	−0.341265	−	0.429491i
$465$	−0.431188	+	5.89482i	−0.0199959	+	0.273366i
$466$	12.8975	−	18.1603i	0.597465	−	0.841259i
$467$	17.7502	+	10.2481i	0.821379	+	0.474223i	0.850892	−	0.525341i	$-0.176062\pi$
$467$	17.7502	+	10.2481i	0.821379	+	0.474223i	−0.0295128	+	0.999564i	$0.509396\pi$
$468$	10.3117	+	3.57722i	0.476658	+	0.165357i
$469$	9.95501	−	0.443357i	0.459680	−	0.0204723i
$470$	6.05418	+	13.2128i	0.279258	+	0.609462i
$471$	−0.554577	+	7.58170i	−0.0255536	+	0.349346i
$472$	−14.1735	−	14.7529i	−0.652389	−	0.679059i
$473$	2.41138	−	4.17663i	0.110875	−	0.192042i
$474$	−25.5857	+	30.9651i	−1.17519	+	1.42227i
$475$	−11.6225	−	6.71024i	−0.533276	−	0.307887i
$476$	0.220176	+	0.173355i	0.0100917	+	0.00794569i
$477$	−4.03120	+	27.4081i	−0.184576	+	1.25493i
$478$	−27.4296	+	12.5684i	−1.25460	+	0.574864i
$479$	5.43687			0.248417			0.124209	−	0.992256i	$-0.460361\pi$
$479$	5.43687			0.248417			0.124209	+	0.992256i	$0.460361\pi$
$480$	−9.67238	−	0.185066i	−0.441482	−	0.00844709i
$481$			4.97040i			0.226631i
$482$	1.04219	−	11.0612i	0.0474703	−	0.503824i
$483$	−2.68803	+	4.36361i	−0.122310	+	0.198551i
$484$	−20.9138	−	3.97630i	−0.950628	−	0.180741i
$485$	−15.0638	−	8.69709i	−0.684012	−	0.394915i
$486$	12.2317	+	18.3408i	0.554840	+	0.831957i
$487$	−13.9989	+	8.08226i	−0.634350	+	0.366242i	−0.782435	−	0.622732i	$-0.786023\pi$
$487$	−13.9989	+	8.08226i	−0.634350	+	0.366242i	0.148085	+	0.988975i	$0.452689\pi$
$488$	0.274042	+	1.11131i	0.0124053	+	0.0503066i
$489$	−1.61001	+	22.0107i	−0.0728073	+	0.995359i
$490$	4.92887	−	8.44069i	0.222664	−	0.381312i
$491$	11.0080	+	19.0664i	0.496784	+	0.860454i	0.999993	−	0.00371008i	$-0.00118096\pi$
$491$	11.0080	+	19.0664i	0.496784	+	0.860454i	−0.503210	+	0.864164i	$0.667848\pi$
$492$	14.6328	−	14.6591i	0.659696	−	0.660881i
$493$	−0.156446			−0.00704597
$494$	0.804607	−	8.53966i	0.0362010	−	0.384218i
$495$	1.09663	−	1.38524i	0.0492900	−	0.0622619i
$496$	−10.8237	+	8.60032i	−0.486000	+	0.386166i
$497$	13.9336	−	8.89381i	0.625008	−	0.398942i
$498$	−31.7170	−	5.34522i	−1.42127	−	0.239525i
$499$	32.0091			1.43292			0.716461	−	0.697627i	$-0.245761\pi$
$499$	32.0091			1.43292			0.716461	+	0.697627i	$0.245761\pi$
$500$	−17.5085	−	3.32885i	−0.783004	−	0.148871i
$501$	19.7840	+	13.4369i	0.883883	+	0.600316i
$502$	1.38914	−	14.7436i	0.0620003	−	0.658038i
$503$	20.2947			0.904898			0.452449	−	0.891790i	$-0.350551\pi$
$503$	20.2947			0.904898			0.452449	+	0.891790i	$0.350551\pi$
$504$	−20.8204	−	8.39704i	−0.927415	−	0.374034i
$505$	−10.3730			−0.461595
$506$	0.0884940	−	0.939227i	0.00393404	−	0.0417538i
$507$	1.22451	−	16.7404i	0.0543823	−	0.743468i
$508$	0.124980	−	0.657346i	0.00554508	−	0.0291650i
$509$	−19.6266			−0.869934			−0.434967	−	0.900446i	$-0.643240\pi$
$509$	−19.6266			−0.869934			−0.434967	+	0.900446i	$0.643240\pi$
$510$	−0.0815844	+	0.0987376i	−0.00361262	+	0.00437217i
$511$	4.67241	+	2.42712i	0.206695	+	0.107369i
$512$	−15.0103	−	16.9319i	−0.663369	−	0.748292i
$513$	11.7159	−	12.7629i	0.517268	−	0.563498i
$514$	−3.33649	+	35.4117i	−0.147166	+	1.56194i
$515$	−19.2620			−0.848786
$516$	7.22507	−	27.0614i	0.318066	−	1.19131i
$517$	−3.10413	−	5.37651i	−0.136520	−	0.236459i
$518$	0.505204	−	10.2110i	0.0221974	−	0.448647i
$519$	4.49857	+	3.05533i	0.197465	+	0.134114i
$520$	−1.21630	−	4.93240i	−0.0533384	−	0.216300i
$521$	2.25095	−	1.29959i	0.0986160	−	0.0569359i	−0.449881	−	0.893089i	$-0.648534\pi$
$521$	2.25095	−	1.29959i	0.0986160	−	0.0569359i	0.548497	+	0.836153i	$0.315200\pi$
$522$	12.0325	−	3.50725i	0.526650	−	0.153508i
$523$	30.0038	+	17.3227i	1.31198	+	0.757469i	0.982423	−	0.186668i	$-0.0597688\pi$
$523$	30.0038	+	17.3227i	1.31198	+	0.757469i	0.329552	+	0.944137i	$0.393102\pi$
$524$	−2.63474	+	13.8578i	−0.115099	+	0.605379i
$525$	−15.7048	−	9.67431i	−0.685412	−	0.422221i
$526$	3.10208	−	32.9238i	0.135257	−	1.43555i
$527$			0.183033i			0.00797302i
$528$	4.12085	−	0.308863i	0.179337	−	0.0134416i
$529$	21.7492			0.945618
$530$	11.7223	−	5.37122i	0.509185	−	0.233311i
$531$	20.1708	−	7.99959i	0.875339	−	0.347152i
$532$	−2.52095	+	17.4618i	−0.109297	+	0.757067i
$533$	9.41947	+	5.43833i	0.408002	+	0.235560i
$534$	23.6192	+	3.98050i	1.02210	+	0.172253i
$535$	−8.99755	+	15.5842i	−0.388998	+	0.673764i
$536$	−7.68209	+	7.38037i	−0.331816	+	0.318783i
$537$	30.9253	+	21.0038i	1.33452	+	0.906381i
$538$	1.63412	+	3.56636i	0.0704521	+	0.153757i
$539$	−1.75792	+	3.78713i	−0.0757189	+	0.163123i
$540$	4.06127	−	9.42306i	0.174769	−	0.405504i
$541$	22.8775	+	13.2083i	0.983581	+	0.567871i	0.903349	−	0.428905i	$-0.141101\pi$
$541$	22.8775	+	13.2083i	0.983581	+	0.567871i	0.0802317	+	0.996776i	$0.474434\pi$
$542$	−19.8000	+	27.8794i	−0.850485	+	1.19752i
$543$	−19.4371	+	9.40314i	−0.834126	+	0.403527i
$544$	−0.299144	+	0.0161352i	−0.0128257	+	0.000691791i
$545$	−4.57780	+	2.64300i	−0.196092	+	0.113214i
$546$	1.44000	−	11.7008i	0.0616262	−	0.500748i
$547$	8.53028	−	14.7749i	0.364728	−	0.631728i	−0.624004	−	0.781421i	$-0.714495\pi$
$547$	8.53028	−	14.7749i	0.364728	−	0.631728i	0.988733	+	0.149693i	$0.0478286\pi$
$548$	−24.9316	−	4.74019i	−1.06503	−	0.202491i
$549$	−1.20111	−	0.176660i	−0.0512620	−	0.00753965i
$550$	3.38031	+	0.318493i	0.144137	+	0.0135806i
$551$	−4.92479	−	8.52999i	−0.209803	−	0.363390i
$552$	−0.920214	−	5.40112i	−0.0391669	−	0.229887i
$553$	38.5016	+	20.0000i	1.63726	+	0.850484i
$554$	1.58122	−	16.7823i	0.0671798	−	0.713010i
$555$	4.66032	+	0.340888i	0.197820	+	0.0144699i
$556$	13.6734	−	4.77095i	0.579883	−	0.202333i
$557$	27.2075	−	15.7083i	1.15282	−	0.665581i	0.203248	−	0.979127i	$-0.434850\pi$
$557$	27.2075	−	15.7083i	1.15282	−	0.665581i	0.949573	+	0.313546i	$0.101517\pi$
$558$	−4.10327	−	14.0773i	−0.173705	−	0.595942i
$559$	14.7084			0.622101
$560$	1.99739	+	10.2566i	0.0844053	+	0.433421i
$561$	0.0307395	−	0.0452598i	0.00129782	−	0.00191087i
$562$	12.2805	−	17.2916i	0.518024	−	0.729401i
$563$	−21.4356	−	12.3758i	−0.903403	−	0.521580i	−0.0251002	−	0.999685i	$-0.507990\pi$
$563$	−21.4356	−	12.3758i	−0.903403	−	0.521580i	−0.878303	+	0.478105i	$0.841324\pi$
$564$	−25.5183	−	25.4726i	−1.07452	−	1.07259i
$565$	1.10744	+	1.91814i	0.0465903	+	0.0806968i
$566$	14.6244	+	10.3863i	0.614711	+	0.436570i
$567$	16.5960	−	17.0755i	0.696967	−	0.717103i
$568$	−4.91464	+	16.9743i	−0.206214	+	0.712225i
$569$	−22.5509	−	39.0594i	−0.945385	−	1.63745i	−0.754979	−	0.655749i	$-0.772353\pi$
$569$	−22.5509	−	39.0594i	−0.945385	−	1.63745i	−0.190406	−	0.981706i	$-0.560980\pi$
$570$	−7.95173	−	1.34009i	−0.333061	−	0.0561303i
$571$	15.3350	−	26.5610i	0.641750	−	1.11154i	−0.343292	−	0.939229i	$-0.611542\pi$
$571$	15.3350	−	26.5610i	0.641750	−	1.11154i	0.985042	−	0.172315i	$-0.0551248\pi$
$572$	0.714904	+	2.04890i	0.0298916	+	0.0856687i
$573$	11.0701	−	16.2992i	0.462458	−	0.680907i
$574$	−18.7983	−	12.1298i	−0.784626	−	0.506286i
$575$		−	4.50163i		−	0.187731i
$576$	22.6460	−	7.94729i	0.943583	−	0.331137i
$577$	9.54217	−	5.50918i	0.397246	−	0.229350i	−0.288049	−	0.957616i	$-0.593007\pi$
$577$	9.54217	−	5.50918i	0.397246	−	0.229350i	0.685295	+	0.728266i	$0.259673\pi$
$578$	13.9186	−	19.5980i	0.578937	−	0.815170i
$579$	−2.24298	+	30.6641i	−0.0932152	+	1.27436i
$580$	−4.41832	−	3.80909i	−0.183461	−	0.158164i
$581$	1.54572	+	34.7070i	0.0641271	+	1.43989i
$582$	42.5521	+	7.17123i	1.76384	+	0.297257i
$583$	−4.77000	+	2.75396i	−0.197553	+	0.114057i
$584$	−5.46503	+	1.34765i	−0.226144	+	0.0557660i
$585$	5.33097	+	0.784082i	0.220408	+	0.0324178i
$586$	10.5761	+	23.0816i	0.436894	+	0.953491i
$587$	−5.13008	−	2.96185i	−0.211741	−	0.122249i	0.390379	−	0.920654i	$-0.372344\pi$
$587$	−5.13008	−	2.96185i	−0.211741	−	0.122249i	−0.602120	+	0.798405i	$0.705677\pi$
$588$	−4.14758	+	23.8914i	−0.171043	+	0.985263i
$589$	−9.97959	+	5.76172i	−0.411202	+	0.237407i
$590$	−8.23445	−	5.84814i	−0.339007	−	0.240764i
$591$	4.65849	+	9.62950i	0.191625	+	0.396105i
$592$	6.79923	+	8.55702i	0.279447	+	0.351691i
$593$	4.85575	+	2.80347i	0.199402	+	0.115125i	0.596376	−	0.802705i	$-0.296607\pi$
$593$	4.85575	+	2.80347i	0.199402	+	0.115125i	−0.396975	+	0.917830i	$0.629940\pi$
$594$	−1.34959	+	4.17014i	−0.0553741	+	0.171103i
$595$	0.122769	+	0.0637733i	0.00503304	+	0.00261445i
$596$	−0.815003	+	4.28661i	−0.0333838	+	0.175586i
$597$	−28.6781	−	19.4776i	−1.17372	−	0.797164i
$598$	2.61564	−	1.19850i	0.106961	−	0.0490102i
$599$	37.6894	+	21.7600i	1.53995	+	0.889088i	0.998841	+	0.0481332i	$0.0153272\pi$
$599$	37.6894	+	21.7600i	1.53995	+	0.889088i	0.541105	+	0.840955i	$0.318006\pi$
$600$	19.4388	−	3.31188i	0.793587	−	0.135207i
$601$	−4.01127	−	2.31591i	−0.163623	−	0.0944679i	0.415952	−	0.909386i	$-0.363448\pi$
$601$	−4.01127	−	2.31591i	−0.163623	−	0.0944679i	−0.579576	+	0.814919i	$0.696782\pi$
$602$	−30.2166	−	1.49500i	−1.23154	−	0.0609317i
$603$	−4.16551	−	10.5033i	−0.169633	−	0.427726i
$604$	0.745906	−	3.92318i	0.0303505	−	0.159632i
$605$	−10.5097			−0.427281
$606$	24.1145	−	8.98438i	0.979587	−	0.364965i
$607$	4.94356			0.200653			0.100327	−	0.994955i	$-0.468011\pi$
$607$	4.94356			0.200653			0.100327	+	0.994955i	$0.468011\pi$
$608$	−10.2966	−	15.8025i	−0.417581	−	0.640876i
$609$	−6.43178	−	11.9120i	−0.260629	−	0.482698i
$610$	0.235384	+	0.513708i	0.00953040	+	0.0207994i
$611$	9.46699	−	16.3973i	0.382993	−	0.663364i
$612$	0.104142	−	0.300201i	0.00420971	−	0.0121349i
$613$	−41.1560	+	23.7614i	−1.66227	+	0.959714i	−0.690648	+	0.723191i	$0.742675\pi$
$613$	−41.1560	+	23.7614i	−1.66227	+	0.959714i	−0.971626	+	0.236523i	$0.923992\pi$
$614$	−2.23045	+	23.6728i	−0.0900135	+	0.955355i
$615$	5.74508	−	8.45885i	0.231664	−	0.341094i
$616$	−1.26042	−	4.28186i	−0.0507838	−	0.172521i
$617$	8.64692	+	14.9769i	0.348112	+	0.602947i	0.985914	−	0.167253i	$-0.0534896\pi$
$617$	8.64692	+	14.9769i	0.348112	+	0.602947i	−0.637802	+	0.770200i	$0.720156\pi$
$618$	44.7790	−	16.6834i	1.80128	−	0.671103i
$619$			49.5916i			1.99325i	0.0820681	+	0.996627i	$0.473848\pi$
$619$			49.5916i			1.99325i	−0.0820681	+	0.996627i	$0.526152\pi$
$620$	−4.45640	+	5.16917i	−0.178974	+	0.207599i
$621$	5.67244	+	1.26281i	0.227627	+	0.0506750i
$622$	4.14345	−	5.83417i	0.166137	−	0.233929i
$623$	−1.15107	−	25.8458i	−0.0461167	−	1.03549i
$624$	7.09967	+	10.4130i	0.284214	+	0.416855i
$625$	11.3271			0.453083
$626$	−17.4390	+	7.99066i	−0.697005	+	0.319371i
$627$	3.43538	+	0.251287i	0.137196	+	0.0100355i
$628$	−5.73166	+	6.64839i	−0.228718	+	0.265300i
$629$	0.144702			0.00576963
$630$	−10.8721	−	2.15265i	−0.433154	−	0.0857635i
$631$			29.8258i			1.18735i	0.804706	+	0.593673i	$0.202323\pi$
$631$			29.8258i			1.18735i	−0.804706	+	0.593673i	$0.797677\pi$
$632$	−45.0329	+	11.1049i	−1.79131	+	0.441728i
$633$	−31.9119	−	21.6739i	−1.26838	−	0.861460i
$634$	−32.7480	+	15.0053i	−1.30059	+	0.595937i
$635$		−	0.330334i		−	0.0131089i
$636$	−22.5991	+	22.6397i	−0.896111	+	0.897721i
$637$	−12.6832	+	1.13197i	−0.502528	+	0.0448503i
$638$	2.03163	+	1.44287i	0.0804332	+	0.0571240i
$639$	−14.6958	−	11.6340i	−0.581355	−	0.460234i
$640$	−8.84123	−	6.82776i	−0.349480	−	0.269891i
$641$	−33.4164			−1.31987			−0.659934	−	0.751323i	$-0.729416\pi$
$641$	−33.4164			−1.31987			−0.659934	+	0.751323i	$0.729416\pi$
$642$	7.41897	−	44.0221i	0.292804	−	1.73741i
$643$	27.9288	−	16.1247i	1.10140	−	0.635895i	0.164814	−	0.986325i	$-0.447298\pi$
$643$	27.9288	−	16.1247i	1.10140	−	0.635895i	0.936589	+	0.350429i	$0.113964\pi$
$644$	−5.49530	+	2.19630i	−0.216545	+	0.0865463i
$645$	1.00876	−	13.7909i	0.0397198	−	0.543015i
$646$	−0.248612	−	0.0234242i	−0.00978152	−	0.000921615i
$647$	4.28702	+	7.42533i	0.168540	+	0.291920i	0.937907	−	0.346888i	$-0.112761\pi$
$647$	4.28702	+	7.42533i	0.168540	+	0.291920i	−0.769367	+	0.638807i	$0.779428\pi$
$648$	−1.27980	+	25.4237i	−0.0502751	+	0.998735i
$649$	3.73625	+	2.15712i	0.146661	+	0.0846746i
$650$	4.31344	+	9.41377i	0.169187	+	0.369238i
$651$	−13.9363	+	7.52480i	−0.546207	+	0.294920i
$652$	−16.6398	+	19.3012i	−0.651664	+	0.755892i
$653$		−	27.8214i		−	1.08874i	−0.838846	−	0.544368i	$-0.816769\pi$
$653$		−	27.8214i		−	1.08874i	0.838846	−	0.544368i	$-0.183231\pi$
$654$	8.35299	−	10.1092i	0.326628	−	0.395302i
$655$			6.96388i			0.272101i
$656$	23.6558	−	3.52270i	0.923605	−	0.137538i
$657$	0.868751	−	5.90663i	0.0338932	−	0.230440i
$658$	−21.1153	+	32.7239i	−0.823162	+	1.27571i
$659$	−4.36264	+	7.55632i	−0.169944	+	0.294352i	−0.938400	−	0.345551i	$-0.887692\pi$
$659$	−4.36264	+	7.55632i	−0.169944	+	0.294352i	0.768456	+	0.639903i	$0.221025\pi$
$660$	1.97011	−	0.529784i	0.0766864	−	0.0206218i
$661$	−5.10008	+	8.83360i	−0.198370	+	0.343587i	−0.948000	−	0.318270i	$-0.896898\pi$
$661$	−5.10008	+	8.83360i	−0.198370	+	0.343587i	0.749630	+	0.661857i	$0.230231\pi$
$662$	−1.98292	−	4.32759i	−0.0770684	−	0.168196i
$663$	0.166415	+	0.0121728i	0.00646303	+	0.000472751i
$664$	−25.7308	−	26.7827i	−0.998549	−	1.03937i
$665$	0.387524	+	8.70134i	0.0150275	+	0.337424i
$666$	−11.1293	+	3.24396i	−0.431250	+	0.125701i
$667$	1.65192	−	2.86121i	0.0639627	−	0.110787i
$668$	9.09768	+	26.0737i	0.352000	+	1.00882i
$669$	0.193585	−	2.64652i	0.00748442	−	0.102321i
$670$	−3.04522	+	4.28781i	−0.117647	+	0.165652i
$671$	−0.120687	−	0.209036i	−0.00465908	−	0.00806976i
$672$	−13.5269	−	22.1138i	−0.521813	−	0.853060i
$673$	4.62525	−	8.01117i	0.178290	−	0.308808i	−0.763005	−	0.646393i	$-0.776277\pi$
$673$	4.62525	−	8.01117i	0.178290	−	0.308808i	0.941295	+	0.337585i	$0.109610\pi$
$674$	−14.5078	−	31.6623i	−0.558820	−	1.21959i
$675$	−4.54491	+	20.4153i	−0.174934	+	0.785786i
$676$	12.6555	−	14.6797i	0.486751	−	0.564602i
$677$	4.99926	+	8.65897i	0.192137	+	0.332791i	0.945958	−	0.324288i	$-0.105125\pi$
$677$	4.99926	+	8.65897i	0.192137	+	0.332791i	−0.753821	+	0.657080i	$0.771791\pi$
$678$	−4.23585	−	3.49998i	−0.162677	−	0.134416i
$679$	−2.07376	−	46.5635i	−0.0795835	−	1.78694i
$680$	−0.143595	+	0.0354098i	−0.00550663	+	0.00135790i
$681$	−4.77064	−	9.86132i	−0.182811	−	0.377887i
$682$	1.68808	−	2.37689i	0.0646398	−	0.0910159i
$683$	−2.71974	−	4.71073i	−0.104068	−	0.180251i	0.809289	−	0.587411i	$-0.199853\pi$
$683$	−2.71974	−	4.71073i	−0.104068	−	0.180251i	−0.913357	+	0.407159i	$0.866519\pi$
$684$	19.6463	−	3.77186i	0.751196	−	0.144221i
$685$	−12.5288			−0.478700
$686$	26.1711	−	1.03633i	0.999217	−	0.0395672i
$687$	36.5360	−	17.6751i	1.39393	−	0.674348i
$688$	25.3220	−	20.1203i	0.965392	−	0.767080i
$689$	−14.5476	−	8.39904i	−0.554218	−	0.319978i
$690$	−0.944340	−	2.53466i	−0.0359504	−	0.0964928i
$691$	−28.7551	+	16.6018i	−1.09390	+	0.631561i	−0.934611	−	0.355671i	$-0.884252\pi$
$691$	−28.7551	+	16.6018i	−1.09390	+	0.631561i	−0.159285	+	0.987233i	$0.550919\pi$
$692$	2.06867	+	5.92876i	0.0786390	+	0.225378i
$693$	4.70989	+	0.479831i	0.178914	+	0.0182273i
$694$	10.4181	−	14.6692i	0.395467	−	0.556836i
$695$	6.19160	−	3.57472i	0.234861	−	0.135597i
$696$	13.5706	+	5.02828i	0.514391	+	0.190596i
$697$	0.158324	−	0.274226i	0.00599696	−	0.0103870i
$698$	−26.0270	+	36.6472i	−0.985136	+	1.38712i
$699$	−1.99015	+	27.2076i	−0.0752743	+	1.02908i
$700$	−7.90455	−	19.7778i	−0.298764	−	0.747530i
$701$			23.0342i			0.869990i	0.900433	+	0.434995i	$0.143250\pi$
$701$			23.0342i			0.869990i	−0.900433	+	0.434995i	$0.856750\pi$
$702$	−13.0722	+	2.79452i	−0.493378	+	0.105472i
$703$	4.55509	+	7.88965i	0.171799	+	0.297564i
$704$	4.03355	+	2.54942i	0.152020	+	0.0960850i
$705$	−14.7251	−	10.0010i	−0.554579	−	0.376659i
$706$	−1.02824	+	10.9132i	−0.0386985	+	0.410725i
$707$	−14.9551	−	23.4296i	−0.562445	−	0.881162i
$708$	24.2081	+	6.46327i	0.909797	+	0.242904i
$709$	−9.18454	+	5.30269i	−0.344932	+	0.199147i	−0.662451	−	0.749105i	$-0.730484\pi$
$709$	−9.18454	+	5.30269i	−0.344932	+	0.199147i	0.317519	+	0.948252i	$0.397150\pi$
$710$	−0.818358	+	8.68561i	−0.0307124	+	0.325965i
$711$	7.15868	−	48.6718i	0.268472	−	1.82534i
$712$	19.1613	+	19.9447i	0.718101	+	0.747458i
$713$	−3.34745	−	1.93265i	−0.125363	−	0.0723784i
$714$	−0.340641	−	0.0419222i	−0.0127482	−	0.00156890i
$715$	0.535655	+	0.927781i	0.0200324	+	0.0346971i
$716$	14.2210	+	40.7571i	0.531464	+	1.52316i
$717$	20.7619	−	30.5690i	0.775366	−	1.14162i
$718$	22.9887	+	16.3266i	0.857929	+	0.609305i
$719$	4.09327	−	7.08976i	0.152653	−	0.264403i	−0.779549	−	0.626342i	$-0.784552\pi$
$719$	4.09327	−	7.08976i	0.152653	−	0.264403i	0.932202	+	0.361938i	$0.117885\pi$
$720$	10.2503	−	5.94259i	0.382008	−	0.221467i
$721$	−27.7706	−	43.5072i	−1.03423	−	1.62029i
$722$	4.64400	+	10.1352i	0.172832	+	0.377193i
$723$	5.92577	+	12.2491i	0.220382	+	0.455548i
$724$	−24.4937	−	4.65692i	−0.910300	−	0.173073i
$725$	10.2976	+	5.94533i	0.382444	+	0.220804i
$726$	24.4323	−	9.10277i	0.906768	−	0.337835i
$727$	−13.2393	+	22.9312i	−0.491019	+	0.850470i	−0.999947	−	0.0103394i	$-0.996709\pi$
$727$	−13.2393	+	22.9312i	−0.491019	+	0.850470i	0.508927	+	0.860809i	$0.330042\pi$
$728$	9.38725	−	9.85844i	0.347915	−	0.365378i
$729$	−24.4501	−	11.4540i	−0.905559	−	0.424220i
$730$	−2.52624	+	1.15753i	−0.0935003	+	0.0428423i
$731$		−	0.428202i		−	0.0158376i
$732$	−0.992140	−	0.990361i	−0.0366706	−	0.0366048i
$733$	28.9483			1.06923			0.534614	−	0.845096i	$-0.320457\pi$
$733$	28.9483			1.06923			0.534614	+	0.845096i	$0.320457\pi$
$734$	19.9943	+	1.88386i	0.738004	+	0.0695347i
$735$	0.191490	+	11.9696i	0.00706321	+	0.441506i
$736$	2.86359	−	5.64137i	0.105553	−	0.207944i
$737$	1.12325	−	1.94552i	0.0413754	−	0.0716643i
$738$	−6.02933	+	24.6405i	−0.221943	+	0.907031i
$739$	−2.87702	−	4.98314i	−0.105833	−	0.183308i	0.808245	−	0.588846i	$-0.200417\pi$
$739$	−2.87702	−	4.98314i	−0.105833	−	0.183308i	−0.914078	+	0.405538i	$0.867084\pi$
$740$	4.08664	+	3.52314i	0.150228	+	0.129513i
$741$	4.57492	+	9.45674i	0.168064	+	0.347402i
$742$	29.0324	+	18.7334i	1.06581	+	0.687724i
$743$	42.7660	−	24.6910i	1.56893	−	0.905824i	0.572639	−	0.819808i	$-0.305920\pi$
$743$	42.7660	−	24.6910i	1.56893	−	0.905824i	0.996294	−	0.0860161i	$-0.0274137\pi$
$744$	5.88279	−	15.8767i	0.215673	−	0.582070i
$745$			2.15413i			0.0789212i
$746$	2.50931	−	26.6325i	0.0918725	−	0.975085i
$747$	36.6184	−	14.5226i	1.33980	−	0.531353i
$748$	0.0596489	−	0.0208128i	0.00218098	−	0.000760990i
$749$	−48.1721	+	2.14540i	−1.76017	+	0.0783912i
$750$	20.4541	−	7.62060i	0.746878	−	0.278265i
$751$			39.1399i			1.42824i	0.700025	+	0.714118i	$0.253172\pi$
$751$			39.1399i			1.42824i	−0.700025	+	0.714118i	$0.746828\pi$
$752$	−6.13228	−	41.1798i	−0.223621	−	1.50167i
$753$	7.89852	+	16.3269i	0.287838	+	0.594986i
$754$	−0.712888	+	7.56621i	−0.0259618	+	0.275545i
$755$		−	1.97150i		−	0.0717502i
$756$	27.1391	−	4.41228i	0.987040	−	0.160473i
$757$			14.0726i			0.511476i	0.966746	+	0.255738i	$0.0823184\pi$
$757$			14.0726i			0.511476i	−0.966746	+	0.255738i	$0.917682\pi$
$758$	−29.9367	−	2.82063i	−1.08735	−	0.102450i
$759$	0.503168	+	1.04009i	0.0182639	+	0.0377529i
$760$	−6.45094	−	6.71466i	−0.234000	−	0.243566i
$761$			21.4162i			0.776335i	0.921589	+	0.388167i	$0.126892\pi$
$761$			21.4162i			0.776335i	−0.921589	+	0.388167i	$0.873108\pi$
$762$	0.286111	+	0.767937i	0.0103647	+	0.0278194i
$763$	−12.5697	−	6.52942i	−0.455053	−	0.236381i
$764$	21.4810	−	7.49519i	0.777156	−	0.271166i
$765$	0.0228267	−	0.155199i	0.000825302	−	0.00561122i
$766$	49.8658	+	4.69836i	1.80173	+	0.169759i
$767$			13.1576i			0.475094i
$768$	26.4672	+	8.21508i	0.955053	+	0.296436i
$769$	1.93709	−	1.11838i	0.0698531	−	0.0403297i	−0.464667	−	0.885486i	$-0.653826\pi$
$769$	1.93709	−	1.11838i	0.0698531	−	0.0403297i	0.534520	+	0.845156i	$0.320493\pi$
$770$	−1.00613	−	1.96045i	−0.0362584	−	0.0706497i
$771$	−18.9710	−	39.2146i	−0.683223	−	1.41228i
$772$	−23.1816	+	26.8894i	−0.834326	+	0.967769i
$773$	−20.9625	−	36.3081i	−0.753969	−	1.30591i	−0.945885	−	0.324501i	$-0.894804\pi$
$773$	−20.9625	−	36.3081i	−0.753969	−	1.30591i	0.191917	−	0.981411i	$-0.438530\pi$
$774$	9.59955	+	32.9338i	0.345049	+	1.18378i
$775$	6.95568	−	12.0476i	0.249855	−	0.432762i
$776$	34.5209	+	35.9321i	1.23923	+	1.28989i
$777$	5.94895	+	11.0178i	0.213417	+	0.395260i
$778$	3.46839	−	36.8117i	0.124348	−	1.31976i
$779$	19.9357			0.714270
$780$	4.40349	+	4.39559i	0.157670	+	0.157388i
$781$		−	3.72658i		−	0.133347i
$782$	−0.0348915	−	0.0761482i	−0.00124772	−	0.00272305i
$783$	−10.3803	+	11.3081i	−0.370963	+	0.404117i
$784$	−20.2869	+	19.2987i	−0.724532	+	0.689241i
$785$	−2.16677	+	3.75295i	−0.0773352	+	0.133948i
$786$	−6.03161	−	16.1891i	−0.215140	−	0.577448i
$787$	−33.7398	−	19.4797i	−1.20269	−	0.694375i	−0.241540	−	0.970391i	$-0.577652\pi$
$787$	−33.7398	−	19.4797i	−1.20269	−	0.694375i	−0.961153	+	0.276016i	$0.910986\pi$
$788$	−2.30713	+	12.1346i	−0.0821880	+	0.432278i
$789$	17.6381	+	36.4595i	0.627934	+	1.29799i
$790$	−20.8167	+	9.53832i	−0.740625	+	0.339358i
$791$	−2.73588	+	5.26681i	−0.0972768	+	0.187266i
$792$	−4.12111	+	2.93797i	−0.146437	+	0.104396i
$793$	0.368072	−	0.637519i	0.0130706	−	0.0226390i
$794$	−21.6754	+	30.5199i	−0.769230	+	1.08311i
$795$	−8.87279	+	13.0640i	−0.314685	+	0.463331i
$796$	−13.1876	−	37.7955i	−0.467424	−	1.33963i
$797$	16.1678	+	28.0035i	0.572694	+	0.991936i	0.996288	+	0.0860834i	$0.0274351\pi$
$797$	16.1678	+	28.0035i	0.572694	+	0.991936i	−0.423594	+	0.905852i	$0.639232\pi$
$798$	−8.43736	−	19.8926i	−0.298679	−	0.704192i
$799$	−0.477369	−	0.275609i	−0.0168881	−	0.00975036i
$800$	20.3035	+	10.3062i	0.717837	+	0.364378i
$801$	−27.2692	+	10.8147i	−0.963508	+	0.382120i
$802$	−28.4438	−	2.67997i	−1.00439	−	0.0946331i
$803$	1.02797	−	0.593498i	0.0362762	−	0.0209441i
$804$	3.36552	−	12.6055i	0.118693	−	0.444563i
$805$	−2.46267	+	1.57192i	−0.0867976	+	0.0554028i
$806$	8.85202	+	0.834036i	0.311799	+	0.0293777i
$807$	−3.97455	−	2.69943i	−0.139911	−	0.0950245i
$808$	28.5426	+	8.26406i	1.00412	+	0.290729i
$809$	−3.92445	−	6.79736i	−0.137976	−	0.238982i	0.788754	−	0.614709i	$-0.210727\pi$
$809$	−3.92445	−	6.79736i	−0.137976	−	0.238982i	−0.926731	+	0.375727i	$0.877393\pi$
$810$	1.72364	+	12.4483i	0.0605626	+	0.437390i
$811$			19.5316i			0.685849i	0.939363	+	0.342924i	$0.111417\pi$
$811$			19.5316i			0.685849i	−0.939363	+	0.342924i	$0.888583\pi$
$812$	2.23358	−	15.4713i	0.0783834	−	0.542937i
$813$	3.05524	−	41.7686i	0.107152	−	1.46489i
$814$	−1.87912	−	1.33456i	−0.0658631	−	0.0467763i
$815$	−6.29042	+	10.8953i	−0.220344	+	0.381647i
$816$	0.303151	−	0.206690i	0.0106124	−	0.00723560i
$817$	23.3471	−	13.4795i	0.816812	−	0.471587i
$818$	−3.61735	−	2.56906i	−0.126478	−	0.0898250i
$819$	5.91479	+	13.1715i	0.206680	+	0.460249i
$820$	11.1481	−	3.88981i	0.389309	−	0.135838i
$821$	18.7192	−	10.8075i	0.653304	−	0.377185i	−0.136417	−	0.990651i	$-0.543559\pi$
$821$	18.7192	−	10.8075i	0.653304	−	0.377185i	0.789721	+	0.613466i	$0.210225\pi$
$822$	29.1261	−	10.8515i	1.01589	−	0.378490i
$823$	−22.1783	−	12.8047i	−0.773088	−	0.446343i	0.0608870	−	0.998145i	$-0.480607\pi$
$823$	−22.1783	−	12.8047i	−0.773088	−	0.446343i	−0.833975	+	0.551802i	$0.813940\pi$
$824$	53.0016	+	15.3458i	1.84640	+	0.534596i
$825$	−3.74332	+	1.81092i	−0.130326	+	0.0630481i
$826$	1.33737	−	27.0306i	0.0465331	−	0.940514i
$827$	−26.8088			−0.932233			−0.466116	−	0.884723i	$-0.654347\pi$
$827$	−26.8088			−0.932233			−0.466116	+	0.884723i	$0.654347\pi$
$828$	4.39067	+	5.07448i	0.152587	+	0.176350i
$829$	23.5626	+	40.8116i	0.818363	+	1.41745i	0.906888	+	0.421373i	$0.138452\pi$
$829$	23.5626	+	40.8116i	0.818363	+	1.41745i	−0.0885244	+	0.996074i	$0.528215\pi$
$830$	−14.9489	−	10.6168i	−0.518885	−	0.368514i
$831$	8.99069	+	18.5845i	0.311883	+	0.644690i
$832$	−0.582783	+	14.5411i	−0.0202044	+	0.504121i
$833$	0.0329546	+	0.369243i	0.00114181	+	0.0127935i
$834$	−11.2976	+	13.6730i	−0.391205	+	0.473457i
$835$	6.81660	+	11.8067i	0.235898	+	0.408588i
$836$	3.01248	+	2.59710i	0.104189	+	0.0898226i
$837$	13.2298	+	12.1444i	0.457288	+	0.419771i
$838$	−35.7581	+	16.3845i	−1.23524	+	0.565994i
$839$	−8.69175	+	15.0545i	−0.300072	+	0.519741i	−0.976152	−	0.217088i	$-0.930344\pi$
$839$	−8.69175	+	15.0545i	−0.300072	+	0.519741i	0.676080	+	0.736829i	$0.263678\pi$
$840$	−8.59961	−	9.47775i	−0.296715	−	0.327014i
$841$	−10.1366	−	17.5571i	−0.349538	−	0.605417i
$842$	21.0374	+	14.9408i	0.724996	+	0.514895i
$843$	−1.89495	+	25.9061i	−0.0652655	+	0.892253i
$844$	−14.6747	−	42.0573i	−0.505124	−	1.44767i
$845$	4.78423	−	8.28652i	0.164582	−	0.285065i
$846$	42.8940	+	10.4958i	1.47473	+	0.360853i
$847$	−15.1522	−	23.7384i	−0.520635	−	0.815660i
$848$	−36.5344	+	5.44051i	−1.25460	+	0.186828i
$849$	−21.9102	−	1.60266i	−0.751956	−	0.0550032i
$850$	0.274060	−	0.125576i	0.00940018	−	0.00430721i
$851$	−1.52791	+	2.64642i	−0.0523762	+	0.0907183i
$852$	−5.62038	−	20.9005i	−0.192551	−	0.716040i
$853$	−15.7848	+	27.3400i	−0.540460	+	0.936105i	0.458417	+	0.888737i	$0.348417\pi$
$853$	−15.7848	+	27.3400i	−0.540460	+	0.936105i	−0.998878	+	0.0473675i	$0.984917\pi$
$854$	−0.820955	+	1.27229i	−0.0280925	+	0.0435368i
$855$	9.18055	−	3.64093i	0.313968	−	0.124517i
$856$	37.1735	−	35.7135i	1.27056	−	1.22066i
$857$			19.5475i			0.667730i	0.942621	+	0.333865i	$0.108353\pi$
$857$			19.5475i			0.667730i	−0.942621	+	0.333865i	$0.891647\pi$
$858$	−2.04883	−	1.69290i	−0.0699459	−	0.0577946i
$859$			10.6567i			0.363603i	0.983335	+	0.181802i	$0.0581929\pi$
$859$			10.6567i			0.363603i	−0.983335	+	0.181802i	$0.941807\pi$
$860$	10.4257	−	12.0932i	0.355513	−	0.412375i
$861$	27.3889	+	0.781071i	0.933410	+	0.0266188i
$862$	15.8786	−	7.27565i	0.540827	−	0.247810i
$863$	−20.0336	−	11.5664i	−0.681953	−	0.393726i	0.118638	−	0.992938i	$-0.462147\pi$
$863$	−20.0336	−	11.5664i	−0.681953	−	0.393726i	−0.800590	+	0.599212i	$0.795481\pi$
$864$	−18.6823	+	22.6930i	−0.635583	+	0.772032i
$865$	1.54999	+	2.68466i	0.0527012	+	0.0912811i
$866$	0.311306	−	3.30404i	0.0105786	−	0.112276i
$867$	−2.14771	+	29.3616i	−0.0729399	+	0.997171i
$868$	−18.1005	−	2.61316i	−0.614372	−	0.0886964i
$869$	8.47066	−	4.89054i	0.287348	−	0.165900i
$870$	7.04530	+	1.18733i	0.238858	+	0.0402543i
$871$	6.85137			0.232150
$872$	14.7020	−	3.62543i	0.497872	−	0.122772i
$873$	−49.1278	+	19.4837i	−1.66273	+	0.659424i
$874$	3.05352	−	4.29949i	0.103287	−	0.145432i
$875$	−12.6850	−	19.8731i	−0.428831	−	0.671834i
$876$	4.87025	−	4.87900i	0.164551	−	0.164846i
$877$		−	24.7109i		−	0.834427i	−0.908809	−	0.417213i	$-0.863007\pi$
$877$		−	24.7109i		−	0.834427i	0.908809	−	0.417213i	$-0.136993\pi$
$878$	−2.79379	−	6.09725i	−0.0942858	−	0.205772i
$879$	−25.7234	−	17.4708i	−0.867627	−	0.589275i
$880$	2.19133	+	0.864518i	0.0738698	+	0.0291429i
$881$		−	13.4387i		−	0.452760i	−0.974039	−	0.226380i	$-0.927311\pi$
$881$		−	13.4387i		−	0.452760i	0.974039	−	0.226380i	$-0.0726891\pi$
$882$	−10.8124	−	27.6603i	−0.364072	−	0.931371i
$883$	22.0989			0.743687			0.371843	−	0.928296i	$-0.378726\pi$
$883$	22.0989			0.743687			0.371843	+	0.928296i	$0.378726\pi$
$884$	0.145929	+	0.125808i	0.00490814	+	0.00423137i
$885$	12.3368	+	0.902396i	0.414696	+	0.0303337i
$886$	16.2951	+	35.5629i	0.547445	+	1.19476i
$887$	−36.0760			−1.21131			−0.605657	−	0.795726i	$-0.707090\pi$
$887$	−36.0760			−1.21131			−0.605657	+	0.795726i	$0.707090\pi$
$888$	−12.5518	−	4.65081i	−0.421211	−	0.156071i
$889$	0.746125	−	0.476251i	0.0250242	−	0.0159729i
$890$	11.1322	+	7.90617i	0.373154	+	0.265015i
$891$	−1.23182	−	5.22492i	−0.0412676	−	0.175041i
$892$	2.00073	−	2.32073i	0.0669895	−	0.0777040i
$893$		−	34.7038i		−	1.16132i
$894$	−1.86575	−	5.00777i	−0.0624000	−	0.167485i
$895$	10.6553	+	18.4556i	0.356169	+	0.616903i
$896$	2.67524	−	29.8135i	0.0893735	−	0.995998i
$897$	−1.97982	+	2.91501i	−0.0661041	+	0.0973293i
$898$	−23.0800	−	2.17459i	−0.770188	−	0.0725671i
$899$	8.84199	−	5.10493i	0.294897	−	0.170259i
$900$	−18.2632	+	15.8022i	−0.608775	+	0.526740i
$901$	−0.244518	+	0.423518i	−0.00814609	+	0.0141094i
$902$	−4.58516	+	2.10094i	−0.152669	+	0.0699538i
$903$	32.6038	−	17.6042i	1.08499	−	0.585830i
$904$	−1.51909	−	6.16026i	−0.0505240	−	0.204887i
$905$	−12.3087			−0.409155
$906$	1.70757	+	4.58321i	0.0567302	+	0.152267i
$907$	11.6898			0.388154			0.194077	−	0.980986i	$-0.437829\pi$
$907$	11.6898			0.388154			0.194077	+	0.980986i	$0.437829\pi$
$908$	2.36267	−	12.4267i	0.0784079	−	0.412396i
$909$	−19.5628	+	24.7112i	−0.648856	+	0.819619i
$910$	3.64370	−	5.64689i	0.120788	−	0.187193i
$911$	−32.9219	−	19.0075i	−1.09075	−	0.629745i	−0.156975	−	0.987603i	$-0.550174\pi$
$911$	−32.9219	−	19.0075i	−1.09075	−	0.629745i	−0.933776	+	0.357857i	$0.883507\pi$
$912$	20.8124	+	10.0224i	0.689169	+	0.331876i
$913$	6.78284	+	3.91608i	0.224479	+	0.129603i
$914$	−5.02547	−	10.9677i	−0.166228	−	0.362780i
$915$	−0.572504	−	0.388833i	−0.0189264	−	0.0128544i
$916$	46.0408	+	8.75364i	1.52123	+	0.289228i
$917$	−15.7293	+	10.0400i	−0.519428	+	0.331550i
$918$	0.0813558	+	0.380566i	0.00268514	+	0.0125605i
$919$	37.9408	+	21.9051i	1.25155	+	0.722583i	0.971417	−	0.237378i	$-0.0762881\pi$
$919$	37.9408	+	21.9051i	1.25155	+	0.722583i	0.280133	+	0.959961i	$0.409621\pi$
$920$	0.868628	−	3.00009i	0.0286378	−	0.0989099i
$921$	−12.6821	−	26.2150i	−0.417890	−	0.863813i
$922$	−35.0156	+	49.3036i	−1.15318	+	1.62373i
$923$	9.84266	−	5.68266i	0.323975	−	0.187047i
$924$	4.03698	+	3.68608i	0.132807	+	0.121263i
$925$	−9.52457	−	5.49901i	−0.313166	−	0.180806i
$926$	−1.69586	+	0.777053i	−0.0557295	+	0.0255356i
$927$	−36.3267	+	45.8870i	−1.19313	+	1.50713i
$928$	9.12284	+	14.0011i	0.299472	+	0.459610i
$929$	18.1459	−	10.4765i	0.595348	−	0.343724i	−0.171862	−	0.985121i	$-0.554978\pi$
$929$	18.1459	−	10.4765i	0.595348	−	0.343724i	0.767209	+	0.641397i	$0.221645\pi$
$930$	1.38911	−	8.24258i	0.0455506	−	0.270285i
$931$	−19.0950	+	13.4203i	−0.625815	+	0.439831i
$932$	−20.5685	+	23.8583i	−0.673744	+	0.781504i
$933$	−0.639354	+	8.74069i	−0.0209315	+	0.286157i
$934$	−23.6323	−	16.7838i	−0.773273	−	0.549181i
$935$	0.0270102	−	0.0155943i	0.000883328	−	0.000509989i
$936$	−14.0441	−	6.40459i	−0.459045	−	0.209341i
$937$			4.89020i			0.159756i	0.996805	+	0.0798779i	$0.0254530\pi$
$937$			4.89020i			0.159756i	−0.996805	+	0.0798779i	$0.974547\pi$
$938$	−14.0752	−	0.696390i	−0.459573	−	0.0227379i
$939$	13.1999	−	19.4350i	0.430762	−	0.634238i
$940$	−6.77134	−	19.4065i	−0.220857	−	0.632970i
$941$	11.7139	−	20.2891i	0.381863	−	0.661406i	−0.609465	−	0.792813i	$-0.708616\pi$
$941$	11.7139	−	20.2891i	0.381863	−	0.661406i	0.991329	+	0.131406i	$0.0419492\pi$
$942$	1.78662	−	10.6013i	0.0582111	−	0.345409i
$943$	3.34351	+	5.79113i	0.108880	+	0.188585i
$944$	17.9989	+	22.6521i	0.585813	+	0.737262i
$945$	12.7555	−	4.64245i	0.414935	−	0.151019i
$946$	−3.94923	+	5.56071i	−0.128401	+	0.180794i
$947$	16.1533	+	27.9784i	0.524912	+	0.909174i	0.999579	+	0.0290090i	$0.00923514\pi$
$947$	16.1533	+	27.9784i	0.524912	+	0.909174i	−0.474667	+	0.880165i	$0.657432\pi$
$948$	40.1319	−	40.2040i	1.30342	−	1.30576i
$949$	3.13510	+	1.81005i	0.101770	+	0.0587567i
$950$	15.4740	+	10.9897i	0.502043	+	0.356553i
$951$	24.7875	−	36.4962i	0.803788	−	1.18347i
$952$	−0.287006	−	0.273288i	−0.00930190	−	0.00885731i
$953$	5.93791			0.192348			0.0961739	−	0.995365i	$-0.469340\pi$
$953$	5.93791			0.192348			0.0961739	+	0.995365i	$0.469340\pi$
$954$	9.31178	−	38.0552i	0.301480	−	1.23208i
$955$	9.72703	−	5.61590i	0.314759	−	0.181726i
$956$	40.2876	−	14.0572i	1.30299	−	0.454642i
$957$	−3.04378	−	0.222643i	−0.0983913	−	0.00719701i
$958$	−7.65500	−	0.721254i	−0.247322	−	0.0233026i
$959$	−18.0631	−	28.2988i	−0.583287	−	0.913815i
$960$	13.5940	+	1.54370i	0.438743	+	0.0498228i
$961$	9.52754	+	16.5022i	0.307340	+	0.532328i
$962$	0.659372	−	6.99822i	0.0212590	−	0.225632i
$963$	20.1568	+	50.8251i	0.649544	+	1.63781i
$964$	−2.93475	+	15.4357i	−0.0945220	+	0.497150i
$965$	−8.76347	+	15.1788i	−0.282106	+	0.488622i
$966$	4.36356	−	5.78727i	0.140395	−	0.186202i
$967$	−28.6842	+	16.5608i	−0.922422	+	0.532560i	−0.884407	−	0.466717i	$-0.845437\pi$
$967$	−28.6842	+	16.5608i	−0.922422	+	0.532560i	−0.0380148	+	0.999277i	$0.512103\pi$
$968$	28.9187	+	8.37296i	0.929482	+	0.269117i
$969$	0.275311	−	0.133188i	0.00884426	−	0.00427862i
$970$	20.0558	+	14.2437i	0.643951	+	0.457337i
$971$	−28.1254	−	16.2382i	−0.902589	−	0.521110i	−0.0245494	−	0.999699i	$-0.507815\pi$
$971$	−28.1254	−	16.2382i	−0.902589	−	0.521110i	−0.878039	+	0.478589i	$0.841148\pi$
$972$	−14.7888	−	27.4461i	−0.474352	−	0.880335i
$973$	17.0008	+	8.83120i	0.545021	+	0.283115i
$974$	20.7823	−	9.52256i	0.665908	−	0.305122i
$975$	−10.4912	−	7.12542i	−0.335988	−	0.228196i
$976$	−0.238420	−	1.60105i	−0.00763164	−	0.0512484i
$977$	−10.1902	+	17.6500i	−0.326014	+	0.564673i	−0.981717	−	0.190346i	$-0.939039\pi$
$977$	−10.1902	+	17.6500i	−0.326014	+	0.564673i	0.655703	+	0.755019i	$0.272372\pi$
$978$	5.18680	−	30.7770i	0.165855	−	0.984140i
$979$	−5.05108	−	2.91624i	−0.161433	−	0.0932035i
$980$	−8.05948	+	11.2304i	−0.257451	+	0.358743i
$981$	−2.33711	+	15.8900i	−0.0746181	+	0.507328i
$982$	−12.9697	−	28.3054i	−0.413879	−	0.903261i
$983$	36.0299			1.14918			0.574588	−	0.818443i	$-0.305162\pi$
$983$	36.0299			1.14918			0.574588	+	0.818443i	$0.305162\pi$
$984$	−22.5473	+	18.6984i	−0.718781	+	0.596085i
$985$			6.09796i			0.194297i
$986$	0.220273	+	0.0207541i	0.00701491	+	0.000660944i
$987$	1.35968	−	47.6782i	0.0432791	−	1.51762i
$988$	−2.26574	+	11.9169i	−0.0720827	+	0.379128i
$989$	7.83132	+	4.52141i	0.249021	+	0.143773i
$990$	−1.72780	+	1.80491i	−0.0549132	+	0.0573638i
$991$	44.5588	−	25.7261i	1.41546	−	0.817215i	0.419563	−	0.907726i	$-0.362183\pi$
$991$	44.5588	−	25.7261i	1.41546	−	0.817215i	0.995895	+	0.0905109i	$0.0288500\pi$
$992$	16.3805	−	10.6732i	0.520081	−	0.338874i
$993$	4.82290	+	3.27561i	0.153050	+	0.103948i
$994$	−20.7981	+	10.6739i	−0.659674	+	0.338554i
$995$	−9.88108	−	17.1145i	−0.313251	−	0.542567i
$996$	43.9478	+	11.7335i	1.39254	+	0.371791i
$997$	23.1742			0.733935			0.366967	−	0.930234i	$-0.380396\pi$
$997$	23.1742			0.733935			0.366967	+	0.930234i	$0.380396\pi$
$998$	−45.0680	−	4.24631i	−1.42660	−	0.134415i
$999$	9.60110	−	10.4592i	0.303765	−	0.330914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.2	yes	180
7.3	odd	6		504.2.bf.b.115.63	✓	180
8.3	odd	2	inner	504.2.cz.b.187.57	yes	180
9.4	even	3		504.2.bf.b.355.63	yes	180
56.3	even	6		504.2.bf.b.115.64	yes	180
63.31	odd	6	inner	504.2.cz.b.283.57	yes	180
72.67	odd	6		504.2.bf.b.355.64	yes	180
504.283	even	6	inner	504.2.cz.b.283.2	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.63	✓	180	7.3	odd	6
504.2.bf.b.115.64	yes	180	56.3	even	6
504.2.bf.b.355.63	yes	180	9.4	even	3
504.2.bf.b.355.64	yes	180	72.67	odd	6
504.2.cz.b.187.2	yes	180	1.1	even	1	trivial
504.2.cz.b.187.57	yes	180	8.3	odd	2	inner
504.2.cz.b.283.2	yes	180	504.283	even	6	inner
504.2.cz.b.283.57	yes	180	63.31	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40798 - 0.132660i) q^{2} +(1.55918 - 0.754290i) q^{3} +(1.96480 + 0.373564i) q^{4} +0.987364 q^{5} +(-2.29536 + 0.855183i) q^{6} +(1.42351 + 2.23016i) q^{7} +(-2.71684 - 0.786619i) q^{8} +(1.86209 - 2.35215i) q^{9} +O(q^{10})\)	\(q+(-1.40798 - 0.132660i) q^{2} +(1.55918 - 0.754290i) q^{3} +(1.96480 + 0.373564i) q^{4} +0.987364 q^{5} +(-2.29536 + 0.855183i) q^{6} +(1.42351 + 2.23016i) q^{7} +(-2.71684 - 0.786619i) q^{8} +(1.86209 - 2.35215i) q^{9} +(-1.39019 - 0.130983i) q^{10} +0.596462 q^{11} +(3.34526 - 0.899578i) q^{12} +(0.909546 + 1.57538i) q^{13} +(-1.70842 - 3.32886i) q^{14} +(1.53948 - 0.744759i) q^{15} +(3.72090 + 1.46796i) q^{16} +(0.0458635 - 0.0264793i) q^{17} +(-2.93382 + 3.06475i) q^{18} +(2.88749 + 1.66709i) q^{19} +(1.93998 + 0.368843i) q^{20} +(3.90170 + 2.40349i) q^{21} +(-0.839806 - 0.0791264i) q^{22} +1.11839i q^{23} +(-4.82939 + 0.822805i) q^{24} -4.02511 q^{25} +(-1.07163 - 2.33876i) q^{26} +(1.12914 - 5.07199i) q^{27} +(1.96381 + 4.91360i) q^{28} +(-2.55834 - 1.47706i) q^{29} +(-2.26635 + 0.844377i) q^{30} +(-1.72807 + 2.99311i) q^{31} +(-5.04421 - 2.56046i) q^{32} +(0.929993 - 0.449905i) q^{33} +(-0.0680875 + 0.0311980i) q^{34} +(1.40552 + 2.20198i) q^{35} +(4.53732 - 3.92590i) q^{36} +(2.36629 + 1.36618i) q^{37} +(-3.84437 - 2.73029i) q^{38} +(2.60644 + 1.77024i) q^{39} +(-2.68251 - 0.776680i) q^{40} +(5.17811 - 2.98959i) q^{41} +(-5.17466 - 3.90165i) q^{42} +(4.04280 - 7.00233i) q^{43} +(1.17193 + 0.222817i) q^{44} +(1.83856 - 2.32243i) q^{45} +(0.148365 - 1.57466i) q^{46} +(-5.20424 - 9.01400i) q^{47} +(6.90882 - 0.517826i) q^{48} +(-2.94724 + 6.34931i) q^{49} +(5.66727 + 0.533970i) q^{50} +(0.0515365 - 0.0758804i) q^{51} +(1.19857 + 3.43508i) q^{52} +(-7.99715 + 4.61716i) q^{53} +(-2.26265 + 6.99145i) q^{54} +0.588925 q^{55} +(-2.11316 - 7.17876i) q^{56} +(5.75960 + 0.421296i) q^{57} +(3.40614 + 2.41905i) q^{58} +(6.26402 + 3.61653i) q^{59} +(3.30299 - 0.888211i) q^{60} +(-0.202338 - 0.350460i) q^{61} +(2.83015 - 3.98498i) q^{62} +(7.89638 + 0.804461i) q^{63} +(6.76246 + 4.27424i) q^{64} +(0.898053 + 1.55547i) q^{65} +(-1.36909 + 0.510084i) q^{66} +(1.88318 - 3.26177i) q^{67} +(0.100004 - 0.0348937i) q^{68} +(0.843588 + 1.74377i) q^{69} +(-1.68683 - 3.28680i) q^{70} -6.24780i q^{71} +(-6.90926 + 4.92566i) q^{72} +(1.72344 - 0.995030i) q^{73} +(-3.15044 - 2.23746i) q^{74} +(-6.27588 + 3.03610i) q^{75} +(5.05059 + 4.35417i) q^{76} +(0.849070 + 1.33021i) q^{77} +(-3.43497 - 2.83823i) q^{78} +(14.2015 - 8.19924i) q^{79} +(3.67388 + 1.44941i) q^{80} +(-2.06522 - 8.75984i) q^{81} +(-7.68727 + 3.52234i) q^{82} +(11.3718 + 6.56551i) q^{83} +(6.76821 + 6.17991i) q^{84} +(0.0452840 - 0.0261447i) q^{85} +(-6.62110 + 9.32281i) q^{86} +(-5.10305 - 0.373272i) q^{87} +(-1.62049 - 0.469189i) q^{88} +(-8.46840 - 4.88923i) q^{89} +(-2.89675 + 3.02602i) q^{90} +(-2.21860 + 4.27100i) q^{91} +(-0.417789 + 2.19741i) q^{92} +(-0.436706 + 5.97026i) q^{93} +(6.13166 + 13.3819i) q^{94} +(2.85101 + 1.64603i) q^{95} +(-9.79617 - 0.187435i) q^{96} +(-15.2566 - 8.80839i) q^{97} +(4.99195 - 8.54871i) q^{98} +(1.11067 - 1.40297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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