LMFDB - Embedded newform 504.2.y.a.173.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (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:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.18
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14306 - 0.832711i) q^{2} +(1.10317 + 1.33530i) q^{3} +(0.613184 + 1.90368i) q^{4} +4.07380i q^{5} +(-0.149078 - 2.44495i) q^{6} +(-1.75571 + 1.97926i) q^{7} +(0.884310 - 2.68663i) q^{8} +(-0.566029 + 2.94612i) q^{9} +O(q^{10})$	\(q+(-1.14306 - 0.832711i) q^{2} +(1.10317 + 1.33530i) q^{3} +(0.613184 + 1.90368i) q^{4} +4.07380i q^{5} +(-0.149078 - 2.44495i) q^{6} +(-1.75571 + 1.97926i) q^{7} +(0.884310 - 2.68663i) q^{8} +(-0.566029 + 2.94612i) q^{9} +(3.39230 - 4.65661i) q^{10} +2.74034 q^{11} +(-1.86553 + 2.91887i) q^{12} +(-1.95290 - 3.38252i) q^{13} +(3.65504 - 0.800414i) q^{14} +(-5.43973 + 4.49410i) q^{15} +(-3.24801 + 2.33461i) q^{16} +(1.43584 + 2.48695i) q^{17} +(3.10027 - 2.89626i) q^{18} +(3.11606 - 5.39718i) q^{19} +(-7.75522 + 2.49799i) q^{20} +(-4.57975 - 0.160937i) q^{21} +(-3.13238 - 2.28191i) q^{22} +1.81864i q^{23} +(4.56299 - 1.78300i) q^{24} -11.5958 q^{25} +(-0.584376 + 5.49263i) q^{26} +(-4.55836 + 2.49426i) q^{27} +(-4.84446 - 2.12867i) q^{28} +(1.34231 - 2.32495i) q^{29} +(9.96023 - 0.607312i) q^{30} +(-2.37517 - 1.37130i) q^{31} +(5.65674 + 0.0360438i) q^{32} +(3.02306 + 3.65917i) q^{33} +(0.429655 - 4.03838i) q^{34} +(-8.06311 - 7.15243i) q^{35} +(-5.95555 + 0.728974i) q^{36} +(-1.81115 - 1.04567i) q^{37} +(-8.05614 + 3.57453i) q^{38} +(2.36228 - 6.33919i) q^{39} +(10.9448 + 3.60250i) q^{40} +(-1.48536 - 2.57272i) q^{41} +(5.10093 + 3.99757i) q^{42} +(6.12162 + 3.53432i) q^{43} +(1.68033 + 5.21674i) q^{44} +(-12.0019 - 2.30589i) q^{45} +(1.51440 - 2.07882i) q^{46} +(2.16004 + 3.74131i) q^{47} +(-6.70051 - 1.76158i) q^{48} +(-0.834935 - 6.95003i) q^{49} +(13.2548 + 9.65599i) q^{50} +(-1.73684 + 4.66081i) q^{51} +(5.24175 - 5.79180i) q^{52} +(6.25109 + 10.8272i) q^{53} +(7.28749 + 0.944712i) q^{54} +11.1636i q^{55} +(3.76495 + 6.46724i) q^{56} +(10.6444 - 1.79314i) q^{57} +(-3.47036 + 1.53981i) q^{58} +(2.59806 + 1.49999i) q^{59} +(-11.8909 - 7.59980i) q^{60} +(-3.22201 - 5.58068i) q^{61} +(1.57307 + 3.54531i) q^{62} +(-4.83735 - 6.29286i) q^{63} +(-6.43599 - 4.75163i) q^{64} +(13.7797 - 7.95571i) q^{65} +(-0.408523 - 6.70000i) q^{66} +(10.0657 + 5.81145i) q^{67} +(-3.85393 + 4.25835i) q^{68} +(-2.42842 + 2.00627i) q^{69} +(3.26073 + 14.8899i) q^{70} +10.7001i q^{71} +(7.41459 + 4.12599i) q^{72} +(-8.82742 + 5.09652i) q^{73} +(1.19952 + 2.70343i) q^{74} +(-12.7922 - 15.4839i) q^{75} +(12.1852 + 2.62253i) q^{76} +(-4.81126 + 5.42385i) q^{77} +(-7.97895 + 5.27899i) q^{78} +(5.08828 + 8.81316i) q^{79} +(-9.51076 - 13.2317i) q^{80} +(-8.35922 - 3.33518i) q^{81} +(-0.444474 + 4.17766i) q^{82} +(-1.49623 - 0.863849i) q^{83} +(-2.50186 - 8.81707i) q^{84} +(-10.1313 + 5.84934i) q^{85} +(-4.05433 - 9.13750i) q^{86} +(4.58530 - 0.772437i) q^{87} +(2.42331 - 7.36229i) q^{88} +(4.99319 - 8.64846i) q^{89} +(11.7988 + 12.6299i) q^{90} +(10.1236 + 2.07344i) q^{91} +(-3.46211 + 1.11516i) q^{92} +(-0.789119 - 4.68433i) q^{93} +(0.646362 - 6.07524i) q^{94} +(21.9870 + 12.6942i) q^{95} +(6.19222 + 7.59318i) q^{96} +(3.84317 + 2.21886i) q^{97} +(-4.83298 + 8.63958i) q^{98} +(-1.55111 + 8.07337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.14306	−	0.832711i	−0.808267	−	0.588816i
$2$	−1.14306	−	0.832711i	−0.808267	−	0.588816i
$3$	1.10317	+	1.33530i	0.636916	+	0.770933i
$3$	1.10317	+	1.33530i	0.636916	+	0.770933i
$4$	0.613184	+	1.90368i	0.306592	+	0.951841i
$5$			4.07380i			1.82186i	0.412562	+	0.910929i	$0.364634\pi$
$5$			4.07380i			1.82186i	−0.412562	+	0.910929i	$0.635366\pi$
$6$	−0.149078	−	2.44495i	−0.0608606	−	0.998146i
$7$	−1.75571	+	1.97926i	−0.663598	+	0.748090i
$7$	−1.75571	+	1.97926i	−0.663598	+	0.748090i
$8$	0.884310	−	2.68663i	0.312651	−	0.949868i
$9$	−0.566029	+	2.94612i	−0.188676	+	0.982039i
$10$	3.39230	−	4.65661i	1.07274	−	1.47255i
$11$	2.74034			0.826244			0.413122	−	0.910676i	$-0.364438\pi$
$11$	2.74034			0.826244			0.413122	+	0.910676i	$0.364438\pi$
$12$	−1.86553	+	2.91887i	−0.538533	+	0.842605i
$13$	−1.95290	−	3.38252i	−0.541636	−	0.938142i	−0.998810	−	0.0487644i	$-0.984472\pi$
$13$	−1.95290	−	3.38252i	−0.541636	−	0.938142i	0.457174	−	0.889377i	$-0.348862\pi$
$14$	3.65504	−	0.800414i	0.976851	−	0.213920i
$15$	−5.43973	+	4.49410i	−1.40453	+	1.16037i
$16$	−3.24801	+	2.33461i	−0.812003	+	0.583654i
$17$	1.43584	+	2.48695i	0.348243	+	0.603175i	0.985937	−	0.167115i	$-0.0534451\pi$
$17$	1.43584	+	2.48695i	0.348243	+	0.603175i	−0.637694	+	0.770289i	$0.720112\pi$
$18$	3.10027	−	2.89626i	0.730741	−	0.682655i
$19$	3.11606	−	5.39718i	0.714874	−	1.23820i	−0.248135	−	0.968726i	$-0.579818\pi$
$19$	3.11606	−	5.39718i	0.714874	−	1.23820i	0.963008	−	0.269472i	$-0.0868491\pi$
$20$	−7.75522	+	2.49799i	−1.73412	+	0.558567i
$21$	−4.57975	−	0.160937i	−0.999383	−	0.0351193i
$22$	−3.13238	−	2.28191i	−0.667826	−	0.486506i
$23$			1.81864i			0.379212i	0.981860	+	0.189606i	$0.0607211\pi$
$23$			1.81864i			0.379212i	−0.981860	+	0.189606i	$0.939279\pi$
$24$	4.56299	−	1.78300i	0.931417	−	0.363953i
$25$	−11.5958			−2.31917
$26$	−0.584376	+	5.49263i	−0.114606	+	1.07719i
$27$	−4.55836	+	2.49426i	−0.877258	+	0.480020i
$28$	−4.84446	−	2.12867i	−0.915516	−	0.402281i
$29$	1.34231	−	2.32495i	0.249261	−	0.431733i	−0.714060	−	0.700085i	$-0.753146\pi$
$29$	1.34231	−	2.32495i	0.249261	−	0.431733i	0.963321	+	0.268352i	$0.0864789\pi$
$30$	9.96023	−	0.607312i	1.81848	−	0.110879i
$31$	−2.37517	−	1.37130i	−0.426593	−	0.246293i	0.271301	−	0.962494i	$-0.412546\pi$
$31$	−2.37517	−	1.37130i	−0.426593	−	0.246293i	−0.697894	+	0.716201i	$0.745879\pi$
$32$	5.65674	+	0.0360438i	0.999980	+	0.00637171i
$33$	3.02306	+	3.65917i	0.526248	+	0.636979i
$34$	0.429655	−	4.03838i	0.0736853	−	0.692577i
$35$	−8.06311	−	7.15243i	−1.36291	−	1.20898i
$36$	−5.95555	+	0.728974i	−0.992592	+	0.121496i
$37$	−1.81115	−	1.04567i	−0.297752	−	0.171907i	0.343681	−	0.939087i	$-0.388326\pi$
$37$	−1.81115	−	1.04567i	−0.297752	−	0.171907i	−0.641432	+	0.767179i	$0.721660\pi$
$38$	−8.05614	+	3.57453i	−1.30688	+	0.579866i
$39$	2.36228	−	6.33919i	0.378268	−	1.01508i
$40$	10.9448	+	3.60250i	1.73053	+	0.569605i
$41$	−1.48536	−	2.57272i	−0.231975	−	0.401792i	0.726414	−	0.687257i	$-0.241185\pi$
$41$	−1.48536	−	2.57272i	−0.231975	−	0.401792i	−0.958389	+	0.285465i	$0.907852\pi$
$42$	5.10093	+	3.99757i	0.787090	+	0.616838i
$43$	6.12162	+	3.53432i	0.933539	+	0.538979i	0.887929	−	0.459980i	$-0.152144\pi$
$43$	6.12162	+	3.53432i	0.933539	+	0.538979i	0.0456099	+	0.998959i	$0.485477\pi$
$44$	1.68033	+	5.21674i	0.253320	+	0.786453i
$45$	−12.0019	−	2.30589i	−1.78914	−	0.343742i
$46$	1.51440	−	2.07882i	0.223286	−	0.306505i
$47$	2.16004	+	3.74131i	0.315075	+	0.545726i	0.979453	−	0.201671i	$-0.0646370\pi$
$47$	2.16004	+	3.74131i	0.315075	+	0.545726i	−0.664378	+	0.747396i	$0.731304\pi$
$48$	−6.70051	−	1.76158i	−0.967136	−	0.254262i
$49$	−0.834935	−	6.95003i	−0.119276	−	0.992861i
$50$	13.2548	+	9.65599i	1.87451	+	1.36556i
$51$	−1.73684	+	4.66081i	−0.243206	+	0.652644i
$52$	5.24175	−	5.79180i	0.726900	−	0.803178i
$53$	6.25109	+	10.8272i	0.858653	+	1.48723i	0.873214	+	0.487337i	$0.162031\pi$
$53$	6.25109	+	10.8272i	0.858653	+	1.48723i	−0.0145613	+	0.999894i	$0.504635\pi$
$54$	7.28749	+	0.944712i	0.991702	+	0.128559i
$55$			11.1636i			1.50530i
$56$	3.76495	+	6.46724i	0.503112	+	0.864221i
$57$	10.6444	−	1.79314i	1.40988	−	0.237508i
$58$	−3.47036	+	1.53981i	−0.455681	+	0.202187i
$59$	2.59806	+	1.49999i	0.338238	+	0.195282i	0.659493	−	0.751711i	$-0.270771\pi$
$59$	2.59806	+	1.49999i	0.338238	+	0.195282i	−0.321255	+	0.946993i	$0.604105\pi$
$60$	−11.8909	−	7.59980i	−1.53511	−	0.981130i
$61$	−3.22201	−	5.58068i	−0.412536	−	0.714533i	0.582630	−	0.812737i	$-0.302024\pi$
$61$	−3.22201	−	5.58068i	−0.412536	−	0.714533i	−0.995166	+	0.0982042i	$0.968690\pi$
$62$	1.57307	+	3.54531i	0.199779	+	0.450255i
$63$	−4.83735	−	6.29286i	−0.609448	−	0.792826i
$64$	−6.43599	−	4.75163i	−0.804499	−	0.593954i
$65$	13.7797	−	7.95571i	1.70916	−	0.986785i
$66$	−0.408523	−	6.70000i	−0.0502857	−	0.824713i
$67$	10.0657	+	5.81145i	1.22972	+	0.709982i	0.966972	−	0.254881i	$-0.0820364\pi$
$67$	10.0657	+	5.81145i	1.22972	+	0.709982i	0.262753	+	0.964863i	$0.415370\pi$
$68$	−3.85393	+	4.25835i	−0.467358	+	0.516400i
$69$	−2.42842	+	2.00627i	−0.292347	+	0.241526i
$70$	3.26073	+	14.8899i	0.389732	+	1.77969i
$71$			10.7001i			1.26986i	0.772568	+	0.634932i	$0.218972\pi$
$71$			10.7001i			1.26986i	−0.772568	+	0.634932i	$0.781028\pi$
$72$	7.41459	+	4.12599i	0.873818	+	0.486253i
$73$	−8.82742	+	5.09652i	−1.03317	+	0.596502i	−0.917892	−	0.396831i	$-0.870110\pi$
$73$	−8.82742	+	5.09652i	−1.03317	+	0.596502i	−0.115280	+	0.993333i	$0.536777\pi$
$74$	1.19952	+	2.70343i	0.139441	+	0.314268i
$75$	−12.7922	−	15.4839i	−1.47712	−	1.78793i
$76$	12.1852	+	2.62253i	1.39774	+	0.300825i
$77$	−4.81126	+	5.42385i	−0.548294	+	0.618105i
$78$	−7.97895	+	5.27899i	−0.903438	+	0.597728i
$79$	5.08828	+	8.81316i	0.572476	+	0.991558i	0.996311	+	0.0858184i	$0.0273505\pi$
$79$	5.08828	+	8.81316i	0.572476	+	0.991558i	−0.423835	+	0.905740i	$0.639316\pi$
$80$	−9.51076	−	13.2317i	−1.06333	−	1.47935i
$81$	−8.35922	−	3.33518i	−0.928803	−	0.370575i
$82$	−0.444474	+	4.17766i	−0.0490839	+	0.461346i
$83$	−1.49623	−	0.863849i	−0.164233	−	0.0948198i	0.415631	−	0.909533i	$-0.363561\pi$
$83$	−1.49623	−	0.863849i	−0.164233	−	0.0948198i	−0.579864	+	0.814714i	$0.696894\pi$
$84$	−2.50186	−	8.81707i	−0.272975	−	0.962021i
$85$	−10.1313	+	5.84934i	−1.09890	+	0.634450i
$86$	−4.05433	−	9.13750i	−0.437190	−	0.985322i
$87$	4.58530	−	0.772437i	0.491596	−	0.0828139i
$88$	2.42331	−	7.36229i	0.258326	−	0.784823i
$89$	4.99319	−	8.64846i	0.529277	−	0.916735i	−0.470140	−	0.882592i	$-0.655796\pi$
$89$	4.99319	−	8.64846i	0.529277	−	0.916735i	0.999417	−	0.0341433i	$-0.0108703\pi$
$90$	11.7988	+	12.6299i	1.24370	+	1.33131i
$91$	10.1236	+	2.07344i	1.06124	+	0.217356i
$92$	−3.46211	+	1.11516i	−0.360950	+	0.116263i
$93$	−0.789119	−	4.68433i	−0.0818279	−	0.485743i
$94$	0.646362	−	6.07524i	0.0666672	−	0.626613i
$95$	21.9870	+	12.6942i	2.25582	+	1.30240i
$96$	6.19222	+	7.59318i	0.631991	+	0.774976i
$97$	3.84317	+	2.21886i	0.390215	+	0.225291i	0.682253	−	0.731116i	$-0.261000\pi$
$97$	3.84317	+	2.21886i	0.390215	+	0.225291i	−0.292038	+	0.956407i	$0.594333\pi$
$98$	−4.83298	+	8.63958i	−0.488205	+	0.872729i
$99$	−1.55111	+	8.07337i	−0.155893	+	0.811404i
$100$	−7.11039	−	22.0748i	−0.711039	−	2.20748i
$101$		−	1.55370i		−	0.154599i	−0.997008	−	0.0772995i	$-0.975370\pi$
$101$		−	1.55370i		−	0.154599i	0.997008	−	0.0772995i	$-0.0246298\pi$
$102$	5.86642	−	3.88131i	0.580862	−	0.384307i
$103$		−	5.92155i		−	0.583467i	−0.956500	−	0.291734i	$-0.905768\pi$
$103$		−	5.92155i		−	0.583467i	0.956500	−	0.291734i	$-0.0942321\pi$
$104$	−10.8145	+	2.25553i	−1.06045	+	0.221173i
$105$	0.655624	−	18.6570i	0.0639823	−	1.82073i
$106$	1.87055	−	17.5815i	0.181684	−	1.70767i
$107$	9.26250	−	16.0431i	0.895440	−	1.55095i	0.0621811	−	0.998065i	$-0.480194\pi$
$107$	9.26250	−	16.0431i	0.895440	−	1.55095i	0.833259	−	0.552883i	$-0.186472\pi$
$108$	−7.54339	−	7.14824i	−0.725863	−	0.687840i
$109$	8.74600	−	5.04951i	0.837715	−	0.483655i	−0.0187719	−	0.999824i	$-0.505976\pi$
$109$	8.74600	−	5.04951i	0.837715	−	0.483655i	0.856487	+	0.516169i	$0.172642\pi$
$110$	9.29606	−	12.7607i	0.886344	−	1.21668i
$111$	−0.601733	−	3.57198i	−0.0571140	−	0.339037i
$112$	1.08177	−	10.5276i	0.102218	−	0.994762i
$113$	−14.2884	+	8.24942i	−1.34414	+	0.776040i	−0.987412	−	0.158168i	$-0.949441\pi$
$113$	−14.2884	+	8.24942i	−1.34414	+	0.776040i	−0.356729	+	0.934208i	$0.616108\pi$
$114$	−13.6604	−	6.81401i	−1.27941	−	0.638191i
$115$	−7.40877			−0.690871
$116$	5.24906	+	1.12971i	0.487363	+	0.104891i
$117$	11.0707	−	3.83886i	1.02349	−	0.354903i
$118$	−1.72068	−	3.87801i	−0.158402	−	0.357000i
$119$	−7.44325	−	1.52447i	−0.682322	−	0.139748i
$120$	7.26359	+	18.5887i	0.663072	+	1.69691i
$121$	−3.49053			−0.317321
$122$	−0.964139	+	9.06207i	−0.0872891	+	0.820441i
$123$	1.79674	−	4.82155i	0.162006	−	0.434745i
$124$	1.15411	−	5.36242i	0.103642	−	0.481560i
$125$		−	26.8702i		−	2.40334i
$126$	0.289256	+	11.2212i	0.0257689	+	0.999668i
$127$	−3.87388			−0.343752			−0.171876	−	0.985119i	$-0.554983\pi$
$127$	−3.87388			−0.343752			−0.171876	+	0.985119i	$0.554983\pi$
$128$	3.40001	+	10.7907i	0.300521	+	0.953775i
$129$	2.03383	+	12.0731i	0.179069	+	1.06298i
$130$	−22.3759	−	2.38063i	−1.96249	−	0.208795i
$131$			11.5102i			1.00565i	0.864388	+	0.502826i	$0.167706\pi$
$131$			11.5102i			1.00565i	−0.864388	+	0.502826i	$0.832294\pi$
$132$	−5.11219	+	7.99870i	−0.444959	+	0.696197i
$133$	5.21150	+	15.6434i	0.451894	+	1.35645i
$134$	−6.66650	−	15.0247i	−0.575898	−	1.29794i
$135$	−10.1611	−	18.5699i	−0.874528	−	1.59824i
$136$	7.95126	−	1.65835i	0.681815	−	0.142202i
$137$		−	1.18194i		−	0.100980i	−0.998725	−	0.0504901i	$-0.983922\pi$
$137$		−	1.18194i		−	0.100980i	0.998725	−	0.0504901i	$-0.0160783\pi$
$138$	4.44648	−	0.271118i	0.378509	−	0.0230791i
$139$	−3.44266	−	5.96286i	−0.292002	−	0.505763i	0.682281	−	0.731090i	$-0.260988\pi$
$139$	−3.44266	−	5.96286i	−0.292002	−	0.505763i	−0.974283	+	0.225327i	$0.927655\pi$
$140$	8.67178	−	19.7353i	0.732899	−	1.66794i
$141$	−2.61285	+	7.01160i	−0.220042	+	0.590483i
$142$	8.91007	−	12.2309i	0.747716	−	1.02639i
$143$	−5.35161	−	9.26926i	−0.447524	−	0.775134i
$144$	−5.03958	−	10.8905i	−0.419965	−	0.907540i
$145$	9.47140	+	5.46831i	0.786557	+	0.454119i
$146$	14.3342	+	1.52506i	1.18631	+	0.126215i
$147$	8.35927	−	8.78195i	0.689461	−	0.724323i
$148$	0.880053	−	4.08905i	0.0723399	−	0.336118i
$149$	−18.0648			−1.47993			−0.739964	−	0.672646i	$-0.765157\pi$
$149$	−18.0648			−1.47993			−0.739964	+	0.672646i	$0.765157\pi$
$150$	1.72868	+	28.3513i	0.141146	+	2.31487i
$151$	10.4233			0.848239			0.424120	−	0.905606i	$-0.360584\pi$
$151$	10.4233			0.848239			0.424120	+	0.905606i	$0.360584\pi$
$152$	−11.7447	−	13.1445i	−0.952619	−	1.06616i
$153$	−8.13958	+	2.82248i	−0.658046	+	0.228184i
$154$	10.0161	−	2.19341i	0.807118	−	0.176750i
$155$	5.58642	−	9.67596i	0.448712	−	0.777192i
$156$	13.5163	+	0.609943i	1.08217	+	0.0488345i
$157$	0.574868	−	0.995701i	0.0458795	−	0.0794656i	−0.842174	−	0.539206i	$-0.818724\pi$
$157$	0.574868	−	0.995701i	0.0458795	−	0.0794656i	0.888053	+	0.459741i	$0.152058\pi$
$158$	1.52259	−	14.3111i	0.121131	−	1.13853i
$159$	−7.56150	+	20.2913i	−0.599666	+	1.60920i
$160$	−0.146835	+	23.0444i	−0.0116084	+	1.82182i
$161$	−3.59956	−	3.19301i	−0.283685	−	0.251644i
$162$	6.77788	+	10.7731i	0.532520	+	0.846417i
$163$	18.1351	+	10.4703i	1.42045	+	0.820097i	0.996337	−	0.0855122i	$-0.0272527\pi$
$163$	18.1351	+	10.4703i	1.42045	+	0.820097i	0.424113	+	0.905609i	$0.360586\pi$
$164$	3.98685	−	4.40521i	0.311321	−	0.343989i
$165$	−14.9067	+	12.3154i	−1.16049	+	0.958750i
$166$	0.990949	+	2.23336i	0.0769125	+	0.173343i
$167$	−5.59391	−	9.68893i	−0.432869	−	0.749752i	0.564250	−	0.825604i	$-0.309166\pi$
$167$	−5.59391	−	9.68893i	−0.432869	−	0.749752i	−0.997119	+	0.0758524i	$0.975832\pi$
$168$	−4.48229	+	12.1618i	−0.345816	+	0.938302i
$169$	−1.12762	+	1.95309i	−0.0867398	+	0.150238i
$170$	16.4516	+	1.75033i	1.26178	+	0.134244i
$171$	14.1369	+	12.2352i	1.08108	+	0.935652i
$172$	−2.97454	+	13.8208i	−0.226807	+	1.05383i
$173$	−9.17272	+	5.29587i	−0.697389	+	0.402638i	−0.806374	−	0.591406i	$-0.798573\pi$
$173$	−9.17272	+	5.29587i	−0.697389	+	0.402638i	0.108985	+	0.994043i	$0.465240\pi$
$174$	−5.88450	−	2.93529i	−0.446103	−	0.222524i
$175$	20.3590	−	22.9512i	1.53900	−	1.73495i
$176$	−8.90066	+	6.39764i	−0.670912	+	0.482241i
$177$	0.863172	+	5.12392i	0.0648799	+	0.385137i
$178$	−12.9092	+	5.72785i	−0.967586	+	0.429320i
$179$	3.10851	+	5.38410i	0.232341	+	0.402427i	0.958497	−	0.285104i	$-0.0920280\pi$
$179$	3.10851	+	5.38410i	0.232341	+	0.402427i	−0.726155	+	0.687531i	$0.758695\pi$
$180$	−2.96969	−	24.2617i	−0.221348	−	1.80836i
$181$	−16.2136			−1.20515			−0.602573	−	0.798064i	$-0.705858\pi$
$181$	−16.2136			−1.20515			−0.602573	+	0.798064i	$0.705858\pi$
$182$	−9.84534	−	10.8001i	−0.729785	−	0.800558i
$183$	3.89743	−	10.4588i	0.288107	−	0.773135i
$184$	4.88601	+	1.60824i	0.360202	+	0.118561i
$185$	4.25985	−	7.37828i	0.313190	−	0.542462i
$186$	−2.99868	+	6.01159i	−0.219874	+	0.440791i
$187$	3.93470	+	6.81510i	0.287734	+	0.498369i
$188$	−5.79775	+	6.40615i	−0.422845	+	0.467216i
$189$	3.06641	−	13.4014i	0.223048	−	0.974807i
$190$	−14.5619	−	32.8191i	−1.05643	−	2.38095i
$191$	13.9598	−	8.05968i	1.01009	−	0.583178i	0.0988745	−	0.995100i	$-0.468476\pi$
$191$	13.9598	−	8.05968i	1.01009	−	0.583178i	0.911219	+	0.411922i	$0.135142\pi$
$192$	−0.755167	−	13.8358i	−0.0544995	−	0.998514i
$193$	−5.58191	+	9.66815i	−0.401795	+	0.695929i	−0.993943	−	0.109901i	$-0.964947\pi$
$193$	−5.58191	+	9.66815i	−0.401795	+	0.695929i	0.592148	+	0.805829i	$0.298280\pi$
$194$	−2.54532	−	5.73654i	−0.182743	−	0.411860i
$195$	25.8246	+	9.62346i	1.84934	+	0.689151i
$196$	12.7187	−	5.85110i	0.908477	−	0.417935i
$197$	5.22777			0.372463			0.186231	−	0.982506i	$-0.440373\pi$
$197$	5.22777			0.372463			0.186231	+	0.982506i	$0.440373\pi$
$198$	8.49580	−	7.93674i	0.603771	−	0.564039i
$199$	14.4846	−	8.36269i	1.02679	−	0.592815i	0.110724	−	0.993851i	$-0.464683\pi$
$199$	14.4846	−	8.36269i	1.02679	−	0.592815i	0.916062	+	0.401036i	$0.131350\pi$
$200$	−10.2543	+	31.1538i	−0.725090	+	2.20291i
$201$	3.34421	+	19.8518i	0.235883	+	1.40023i
$202$	−1.29378	+	1.77598i	−0.0910304	+	0.124957i
$203$	2.24497	+	6.73874i	0.157566	+	0.472967i
$204$	−9.93770	−	0.448453i	−0.695778	−	0.0313980i
$205$	10.4808	−	6.05107i	0.732008	−	0.422625i
$206$	−4.93094	+	6.76870i	−0.343555	+	0.471598i
$207$	−5.35792	−	1.02940i	−0.372401	−	0.0715483i
$208$	14.2399	+	6.42719i	0.987360	+	0.445645i
$209$	8.53907	−	14.7901i	0.590660	−	1.02305i
$210$	−16.2853	+	20.7802i	−1.12379	+	1.43397i
$211$	−9.01244	+	5.20333i	−0.620442	+	0.358212i	−0.777041	−	0.629450i	$-0.783280\pi$
$211$	−9.01244	+	5.20333i	−0.620442	+	0.358212i	0.156599	+	0.987662i	$0.449947\pi$
$212$	−16.7785	+	18.5392i	−1.15235	+	1.27327i
$213$	−14.2878	+	11.8040i	−0.978981	+	0.808797i
$214$	−23.9469	+	10.6253i	−1.63698	+	0.726331i
$215$	−14.3981	+	24.9383i	−0.981944	+	1.70078i
$216$	2.67014	+	14.4523i	0.181680	+	0.983358i
$217$	6.88428	−	2.29345i	0.467335	−	0.155690i
$218$	−14.2020	−	1.51099i	−0.961881	−	0.102337i
$219$	−16.5435	−	6.16489i	−1.11791	−	0.416585i
$220$	−21.2520	+	6.84534i	−1.43281	+	0.461513i
$221$	5.60811	−	9.71353i	0.377242	−	0.653402i
$222$	−2.28661	+	4.58406i	−0.153467	+	0.307662i
$223$	5.16110	+	2.97976i	0.345613	+	0.199540i	0.662751	−	0.748840i	$-0.269389\pi$
$223$	5.16110	+	2.97976i	0.345613	+	0.199540i	−0.317139	+	0.948379i	$0.602722\pi$
$224$	−10.0030	+	11.1329i	−0.668351	+	0.743846i
$225$	6.56358	−	34.1627i	0.437572	−	2.27752i
$226$	23.2019	+	2.46852i	1.54337	+	0.164204i
$227$			11.2442i			0.746302i	0.927771	+	0.373151i	$0.121723\pi$
$227$			11.2442i			0.746302i	−0.927771	+	0.373151i	$0.878277\pi$
$228$	9.94054	+	19.1640i	0.658328	+	1.26917i
$229$	27.1955			1.79713			0.898565	−	0.438840i	$-0.144611\pi$
$229$	27.1955			1.79713			0.898565	+	0.438840i	$0.144611\pi$
$230$	8.46868	+	6.16936i	0.558408	+	0.406796i
$231$	−12.5501	−	0.441022i	−0.825734	−	0.0290171i
$232$	−5.05928	−	5.66228i	−0.332158	−	0.371747i
$233$	0.534499	+	0.308593i	0.0350162	+	0.0202166i	0.517406	−	0.855740i	$-0.326898\pi$
$233$	0.534499	+	0.308593i	0.0350162	+	0.0202166i	−0.482390	+	0.875957i	$0.660231\pi$
$234$	−15.8512	−	4.83063i	−1.03622	−	0.315788i
$235$	−15.2413	+	8.79959i	−0.994235	+	0.574022i
$236$	−1.26241	+	5.86564i	−0.0821762	+	0.381821i
$237$	−6.15493	+	16.5168i	−0.399806	+	1.07288i
$238$	7.23866	+	7.94065i	0.469213	+	0.514716i
$239$	4.41712	−	2.55022i	0.285720	−	0.164960i	−0.350290	−	0.936641i	$-0.613917\pi$
$239$	4.41712	−	2.55022i	0.285720	−	0.164960i	0.636010	+	0.771681i	$0.280584\pi$
$240$	7.17631	−	27.2965i	0.463229	−	1.76198i
$241$			12.8484i			0.827638i	0.910359	+	0.413819i	$0.135805\pi$
$241$			12.8484i			0.827638i	−0.910359	+	0.413819i	$0.864195\pi$
$242$	3.98989	+	2.90660i	0.256480	+	0.186843i
$243$	−4.76820	−	14.8413i	−0.305880	−	0.952070i
$244$	8.64816	−	9.55566i	0.553642	−	0.611739i
$245$	28.3130	−	3.40136i	1.80885	−	0.217305i
$246$	−6.06875	+	4.01517i	−0.386929	+	0.255998i
$247$	−24.3414			−1.54881
$248$	−5.78457	+	5.16855i	−0.367321	+	0.328203i
$249$	−0.497104	−	2.95088i	−0.0315027	−	0.187005i
$250$	−22.3751	+	30.7143i	−1.41512	+	1.94254i
$251$		−	4.27582i		−	0.269887i	−0.990853	−	0.134944i	$-0.956915\pi$
$251$		−	4.27582i		−	0.269887i	0.990853	−	0.134944i	$-0.0430854\pi$
$252$	9.01342	−	13.0675i	0.567792	−	0.823172i
$253$			4.98369i			0.313322i
$254$	4.42809	+	3.22583i	0.277843	+	0.202406i
$255$	−18.9872	−	7.07553i	−1.18902	−	0.443087i
$256$	5.09915	−	15.1657i	0.318697	−	0.947857i
$257$	−7.91365			−0.493640			−0.246820	−	0.969061i	$-0.579386\pi$
$257$	−7.91365			−0.493640			−0.246820	+	0.969061i	$0.579386\pi$
$258$	7.72864	−	15.4939i	0.481164	−	0.964611i
$259$	5.24952	−	1.74884i	0.326189	−	0.108668i
$260$	23.5946	+	21.3539i	1.46328	+	1.32431i
$261$	6.08980	+	5.27060i	0.376949	+	0.326242i
$262$	9.58468	−	13.1569i	0.592143	−	0.812835i
$263$		−	9.24857i		−	0.570291i	−0.958484	−	0.285146i	$-0.907958\pi$
$263$		−	9.24857i		−	0.570291i	0.958484	−	0.285146i	$-0.0920419\pi$
$264$	12.5042	−	4.88603i	0.769578	−	0.300714i
$265$	−44.1079	+	25.4657i	−2.70952	+	1.56434i
$266$	7.06936	−	22.2211i	0.433450	−	1.36246i
$267$	17.0566	−	2.87334i	1.04385	−	0.175846i
$268$	−4.89101	+	22.7254i	−0.298766	+	1.38818i
$269$	5.30069	−	3.06036i	0.323189	−	0.186593i	−0.329624	−	0.944112i	$-0.606922\pi$
$269$	5.30069	−	3.06036i	0.323189	−	0.186593i	0.652813	+	0.757519i	$0.273589\pi$
$270$	−3.84857	+	29.6878i	−0.234216	+	1.80674i
$271$	−11.0687	−	6.39053i	−0.672377	−	0.388197i	0.124600	−	0.992207i	$-0.460235\pi$
$271$	−11.0687	−	6.39053i	−0.672377	−	0.388197i	−0.796977	+	0.604010i	$0.793569\pi$
$272$	−10.4697	−	4.72551i	−0.634819	−	0.286526i
$273$	8.39941	+	15.8054i	0.508355	+	0.956585i
$274$	−0.984216	+	1.35103i	−0.0594587	+	0.0816189i
$275$	−31.7766			−1.91620
$276$	−5.30836	−	3.39273i	−0.319526	−	0.204218i
$277$		−	14.4824i		−	0.870160i	−0.900392	−	0.435080i	$-0.856720\pi$
$277$		−	14.4824i		−	0.870160i	0.900392	−	0.435080i	$-0.143280\pi$
$278$	−1.03017	+	9.68266i	−0.0617852	+	0.580727i
$279$	5.38444	−	6.22133i	0.322358	−	0.372461i
$280$	−26.3462	+	15.3376i	−1.57449	+	0.916600i
$281$	9.67392	+	5.58524i	0.577098	+	0.333188i	0.759979	−	0.649947i	$-0.225209\pi$
$281$	9.67392	+	5.58524i	0.577098	+	0.333188i	−0.182881	+	0.983135i	$0.558542\pi$
$282$	8.82529	−	5.83894i	0.525538	−	0.347704i
$283$	−4.40020	+	7.62137i	−0.261565	+	0.453043i	−0.966658	−	0.256071i	$-0.917572\pi$
$283$	−4.40020	+	7.62137i	−0.261565	+	0.453043i	0.705093	+	0.709115i	$0.250905\pi$
$284$	−20.3695	+	6.56111i	−1.20871	+	0.389330i
$285$	7.30491	+	43.3631i	0.432706	+	2.56861i
$286$	−1.60139	+	15.0517i	−0.0946922	+	0.890025i
$287$	7.69996	+	1.57705i	0.454514	+	0.0930903i
$288$	−3.30807	+	16.6450i	−0.194930	+	0.980817i
$289$	4.37671	−	7.58069i	0.257454	−	0.445923i
$290$	−6.27287	−	14.1376i	−0.368356	−	0.830186i
$291$	1.27685	+	7.57955i	0.0748500	+	0.444321i
$292$	−15.1150	−	13.6795i	−0.884537	−	0.800532i
$293$	26.7134	−	15.4230i	1.56061	−	0.901021i	0.563420	−	0.826171i	$-0.309485\pi$
$293$	26.7134	−	15.4230i	1.56061	−	0.901021i	0.997195	−	0.0748505i	$-0.0238480\pi$
$294$	−16.8680	+	3.07747i	−0.983761	+	0.179481i
$295$	−6.11065	+	10.5840i	−0.355776	+	0.616222i
$296$	−4.41095	+	3.94121i	−0.256381	+	0.229078i
$297$	−12.4915	+	6.83511i	−0.724829	+	0.396613i
$298$	20.6492	+	15.0428i	1.19618	+	0.871405i
$299$	6.15157	−	3.55161i	0.355755	−	0.205395i
$300$	21.6324	−	33.8468i	1.24895	−	1.95414i
$301$	−17.7432	+	5.91102i	−1.02270	+	0.340706i
$302$	−11.9145	−	8.67963i	−0.685604	−	0.499457i
$303$	2.07465	−	1.71400i	0.119186	−	0.0984666i
$304$	2.47933	+	24.8049i	0.142199	+	1.42266i
$305$	22.7346	−	13.1258i	1.30178	−	0.751582i
$306$	11.6544	+	3.55166i	0.666235	+	0.203035i
$307$	−21.5749			−1.23135			−0.615673	−	0.788002i	$-0.711116\pi$
$307$	−21.5749			−1.23135			−0.615673	+	0.788002i	$0.711116\pi$
$308$	−13.2755	−	5.83329i	−0.756440	−	0.332382i
$309$	7.90702	−	6.53248i	0.449814	−	0.371620i
$310$	−14.4429	+	6.40835i	−0.820302	+	0.363970i
$311$	−2.71247	+	4.69813i	−0.153810	+	0.266406i	−0.932625	−	0.360847i	$-0.882488\pi$
$311$	−2.71247	+	4.69813i	−0.153810	+	0.266406i	0.778815	+	0.627253i	$0.215821\pi$
$312$	−14.9421	−	11.9524i	−0.845929	−	0.676671i
$313$	−2.30013	+	1.32798i	−0.130011	+	0.0750618i	−0.563595	−	0.826051i	$-0.690582\pi$
$313$	−2.30013	+	1.32798i	−0.130011	+	0.0750618i	0.433584	+	0.901113i	$0.357249\pi$
$314$	−1.48624	+	0.659449i	−0.0838735	+	0.0372149i
$315$	25.6359	−	19.7064i	1.44442	−	1.11033i
$316$	−13.6574	+	15.0906i	−0.768289	+	0.848910i
$317$	13.4759	+	23.3409i	0.756882	+	1.31096i	0.944433	+	0.328703i	$0.106612\pi$
$317$	13.4759	+	23.3409i	0.756882	+	1.31096i	−0.187551	+	0.982255i	$0.560055\pi$
$318$	25.5401	−	16.8977i	1.43222	−	0.947575i
$319$	3.67840	−	6.37117i	0.205951	−	0.356717i
$320$	19.3572	−	26.2189i	1.08210	−	1.46568i
$321$	31.6404	−	5.33013i	1.76600	−	0.297499i
$322$	1.45566	+	6.64720i	0.0811210	+	0.370434i
$323$	17.8967			0.995799
$324$	1.22337	−	17.9584i	0.0679651	−	0.997688i
$325$	22.6455	+	39.2232i	1.25615	+	2.17571i
$326$	−12.0108	−	27.0695i	−0.665217	−	1.49924i
$327$	16.3909	+	6.10803i	0.906420	+	0.337775i
$328$	−8.22549	+	1.71554i	−0.454177	+	0.0947249i
$329$	−11.1974	−	2.29338i	−0.617335	−	0.126438i
$330$	27.2944	−	1.66424i	1.50251	−	0.0916135i
$331$	18.1229	−	10.4633i	0.996127	−	0.575114i	0.0890271	−	0.996029i	$-0.471624\pi$
$331$	18.1229	−	10.4633i	0.996127	−	0.575114i	0.907100	+	0.420915i	$0.138291\pi$
$332$	0.727029	−	3.37805i	0.0399009	−	0.185394i
$333$	4.10583	−	4.74399i	0.224998	−	0.259969i
$334$	−1.67390	+	15.7332i	−0.0915915	+	0.860880i
$335$	−23.6747	+	41.0058i	−1.29349	+	2.24039i
$336$	15.2508	−	10.1692i	0.831999	−	0.554777i
$337$	1.05277	+	1.82344i	0.0573478	+	0.0993293i	0.893274	−	0.449512i	$-0.148402\pi$
$337$	1.05277	+	1.82344i	0.0573478	+	0.0993293i	−0.835926	+	0.548842i	$0.815069\pi$
$338$	2.91530	−	1.29353i	0.158571	−	0.0703585i
$339$	−26.7780	−	9.97874i	−1.45438	−	0.541971i
$340$	−17.3477	−	15.7001i	−0.940809	−	0.851460i
$341$	−6.50877	−	3.75784i	−0.352470	−	0.203498i
$342$	−5.97098	−	25.7576i	−0.322874	−	1.39281i
$343$	15.2218	+	10.5497i	0.821901	+	0.569631i
$344$	14.9088	−	13.3211i	0.803831	−	0.718227i
$345$	−8.17313	−	9.89289i	−0.440027	−	0.532616i
$346$	14.8949	+	1.58471i	0.800756	+	0.0851947i
$347$	0.513957	−	0.890200i	0.0275907	−	0.0477885i	−0.851900	−	0.523704i	$-0.824550\pi$
$347$	0.513957	−	0.890200i	0.0275907	−	0.0477885i	0.879491	+	0.475915i	$0.157883\pi$
$348$	4.28211	+	8.25531i	0.229545	+	0.442531i
$349$	13.2244	−	22.9054i	0.707887	−	1.22610i	−0.257752	−	0.966211i	$-0.582982\pi$
$349$	13.2244	−	22.9054i	0.707887	−	1.22610i	0.965639	−	0.259885i	$-0.0836848\pi$
$350$	−42.3833	+	9.28148i	−2.26548	+	0.496116i
$351$	17.3389	+	10.5477i	0.925481	+	0.562996i
$352$	15.5014	+	0.0987724i	0.826227	+	0.00526459i
$353$	27.3509			1.45574			0.727872	−	0.685713i	$-0.240510\pi$
$353$	27.3509			1.45574			0.727872	+	0.685713i	$0.240510\pi$
$354$	3.28008	−	6.57573i	0.174334	−	0.349496i
$355$	−43.5900			−2.31351
$356$	19.5257	+	4.20235i	1.03486	+	0.222724i
$357$	−6.17556	−	11.6207i	−0.326845	−	0.615032i
$358$	0.930178	−	8.74286i	0.0491614	−	0.462075i
$359$	−9.73162	−	5.61855i	−0.513615	−	0.296536i	0.220703	−	0.975341i	$-0.429165\pi$
$359$	−9.73162	−	5.61855i	−0.513615	−	0.296536i	−0.734318	+	0.678805i	$0.762498\pi$
$360$	−16.8085	+	30.2056i	−0.885884	+	1.59197i
$361$	−9.91968	−	17.1814i	−0.522088	−	0.904283i
$362$	18.5331	+	13.5012i	0.974080	+	0.709609i
$363$	−3.85065	−	4.66088i	−0.202107	−	0.244633i
$364$	2.26046	+	20.5435i	0.118480	+	1.07677i
$365$	−20.7622	−	35.9612i	−1.08674	−	1.88229i
$366$	−13.1642	+	8.70960i	−0.688101	+	0.455258i
$367$			4.92031i			0.256838i	0.991720	+	0.128419i	$0.0409902\pi$
$367$			4.92031i			0.256838i	−0.991720	+	0.128419i	$0.959010\pi$
$368$	−4.24582	−	5.90695i	−0.221329	−	0.307921i
$369$	8.42031	−	2.91982i	0.438344	−	0.152000i
$370$	−11.0133	+	4.88661i	−0.572552	+	0.254043i
$371$	−32.4050	−	6.63695i	−1.68238	−	0.344573i
$372$	8.43360	−	4.37459i	0.437262	−	0.226812i
$373$		−	20.0278i		−	1.03700i	−0.855078	−	0.518500i	$-0.826491\pi$
$373$		−	20.0278i		−	1.03700i	0.855078	−	0.518500i	$-0.173509\pi$
$374$	1.17740	−	11.0666i	0.0608820	−	0.572238i
$375$	35.8796	−	29.6424i	1.85282	−	1.53073i
$376$	11.9617	−	2.49477i	0.616876	−	0.128658i
$377$	−10.4856			−0.540036
$378$	−14.6646	+	12.7652i	−0.754265	+	0.656571i
$379$		−	37.5940i		−	1.93107i	−0.260266	−	0.965537i	$-0.583810\pi$
$379$		−	37.5940i		−	1.93107i	0.260266	−	0.965537i	$-0.416190\pi$
$380$	−10.6837	+	49.6402i	−0.548060	+	2.54649i
$381$	−4.27355	−	5.17278i	−0.218941	−	0.265010i
$382$	−22.6683	−	2.41174i	−1.15981	−	0.123395i
$383$	19.8436			1.01396			0.506979	−	0.861958i	$-0.330762\pi$
$383$	19.8436			1.01396			0.506979	+	0.861958i	$0.330762\pi$
$384$	−10.6580	+	16.4440i	−0.543890	+	0.839156i
$385$	−22.0957	−	19.6001i	−1.12610	−	0.998914i
$386$	14.4312	−	6.40318i	0.734531	−	0.325913i
$387$	−13.8775	+	16.0345i	−0.705435	+	0.815079i
$388$	−1.86742	+	8.67674i	−0.0948041	+	0.440495i
$389$	0.180583			0.00915592			0.00457796	−	0.999990i	$-0.498543\pi$
$389$	0.180583			0.00915592			0.00457796	+	0.999990i	$0.498543\pi$
$390$	−21.5056	−	32.5047i	−1.08898	−	1.64594i
$391$	−4.52287	+	2.61128i	−0.228731	+	0.132058i
$392$	−19.4105	−	3.90281i	−0.980379	−	0.197122i
$393$	−15.3695	+	12.6977i	−0.775290	+	0.640515i
$394$	−5.97566	−	4.35322i	−0.301050	−	0.219312i
$395$	−35.9031	+	20.7286i	−1.80648	+	1.04297i
$396$	−16.3202	+	1.99764i	−0.820123	+	0.100385i
$397$	4.66006	−	8.07146i	0.233882	−	0.405095i	−0.725065	−	0.688680i	$-0.758191\pi$
$397$	4.66006	−	8.07146i	0.233882	−	0.405095i	0.958947	+	0.283585i	$0.0915239\pi$
$398$	−23.5205	−	2.50241i	−1.17898	−	0.125435i
$399$	−15.1394	+	24.2162i	−0.757917	+	1.21233i
$400$	37.6634	−	27.0718i	1.88317	−	1.35359i
$401$			9.97636i			0.498196i	0.968478	+	0.249098i	$0.0801341\pi$
$401$			9.97636i			0.498196i	−0.968478	+	0.249098i	$0.919866\pi$
$402$	12.7081	−	25.4766i	0.633824	−	1.27066i
$403$			10.7121i			0.533606i
$404$	2.95775	−	0.952705i	0.147154	−	0.0473989i
$405$	13.5868	−	34.0538i	0.675135	−	1.69215i
$406$	3.04528	−	9.57221i	0.151135	−	0.475061i
$407$	−4.96318	−	2.86549i	−0.246016	−	0.142037i
$408$	10.9860	+	8.78784i	0.543887	+	0.435063i
$409$	16.5345	+	9.54620i	0.817579	+	0.472029i	0.849581	−	0.527458i	$-0.176855\pi$
$409$	16.5345	+	9.54620i	0.817579	+	0.472029i	−0.0320019	+	0.999488i	$0.510188\pi$
$410$	−17.0190	−	1.81070i	−0.840507	−	0.0894239i
$411$	1.57824	−	1.30388i	0.0778489	−	0.0643158i
$412$	11.2727	−	3.63100i	0.555368	−	0.178886i
$413$	−7.53031	+	2.50868i	−0.370542	+	0.123444i
$414$	5.26725	+	5.63827i	0.258871	+	0.277106i
$415$	3.51915	−	6.09535i	0.172748	−	0.299209i
$416$	−10.9251	−	19.2044i	−0.535648	−	0.941574i
$417$	4.16434	−	11.1750i	0.203929	−	0.547243i
$418$	−22.0766	+	9.79544i	−1.07980	+	0.479111i
$419$	6.45468	−	3.72661i	0.315332	−	0.182057i	−0.333978	−	0.942581i	$-0.608391\pi$
$419$	6.45468	−	3.72661i	0.315332	−	0.182057i	0.649310	+	0.760524i	$0.275058\pi$
$420$	35.9190	−	10.1921i	1.75267	−	0.497322i
$421$	−28.9696	−	16.7256i	−1.41189	−	0.815156i	−0.416325	−	0.909216i	$-0.636682\pi$
$421$	−28.9696	−	16.7256i	−1.41189	−	0.815156i	−0.995567	+	0.0940603i	$0.970015\pi$
$422$	14.6347	+	1.55702i	0.712404	+	0.0757947i
$423$	−12.2450	+	4.24606i	−0.595371	+	0.206450i
$424$	34.6166	−	7.21978i	1.68113	−	0.350623i
$425$	−16.6498	−	28.8383i	−0.807635	−	1.39886i
$426$	26.1611	−	1.59514i	1.26751	−	0.0772848i
$427$	16.7025	+	3.42089i	0.808293	+	0.165549i
$428$	36.2206	+	7.79547i	1.75079	+	0.376808i
$429$	6.47346	−	17.3715i	0.312542	−	0.838706i
$430$	37.2243	−	16.5165i	1.79512	−	0.796498i
$431$	−12.1762	+	7.02996i	−0.586509	+	0.338621i	−0.763716	−	0.645552i	$-0.776627\pi$
$431$	−12.1762	+	7.02996i	−0.586509	+	0.338621i	0.177207	+	0.984174i	$0.443294\pi$
$432$	8.98249	−	18.7434i	0.432170	−	0.901792i
$433$		−	21.7475i		−	1.04512i	−0.852603	−	0.522559i	$-0.824978\pi$
$433$		−	21.7475i		−	1.04512i	0.852603	−	0.522559i	$-0.175022\pi$
$434$	−9.77895	−	3.11106i	−0.469405	−	0.149335i
$435$	3.14675	+	18.6796i	0.150875	+	0.895618i
$436$	14.9756	+	13.5533i	0.717199	+	0.649087i
$437$	9.81551	+	5.66699i	0.469539	+	0.271089i
$438$	13.7767	+	20.8228i	0.658276	+	0.994953i
$439$	13.5080	−	7.79885i	0.644702	−	0.372219i	−0.141722	−	0.989907i	$-0.545264\pi$
$439$	13.5080	−	7.79885i	0.644702	−	0.372219i	0.786423	+	0.617688i	$0.211930\pi$
$440$	29.9925	+	9.87208i	1.42984	+	0.470633i
$441$	20.9482	+	1.47410i	0.997533	+	0.0701952i
$442$	−14.4990	+	6.43323i	−0.689646	+	0.305998i
$443$	−0.996398	−	1.72581i	−0.0473403	−	0.0819958i	0.841384	−	0.540437i	$-0.181741\pi$
$443$	−0.996398	−	1.72581i	−0.0473403	−	0.0819958i	−0.888725	+	0.458441i	$0.848408\pi$
$444$	6.43094	−	3.33579i	0.305199	−	0.158310i
$445$	35.2321	+	20.3413i	1.67016	+	0.964269i
$446$	−3.41818	−	7.70375i	−0.161855	−	0.364783i
$447$	−19.9286	−	24.1219i	−0.942590	−	1.14093i
$448$	20.7045	−	4.39599i	0.978194	−	0.207691i
$449$		−	21.7790i		−	1.02781i	−0.857846	−	0.513907i	$-0.828198\pi$
$449$		−	21.7790i		−	1.02781i	0.857846	−	0.513907i	$-0.171802\pi$
$450$	−35.9503	+	33.5846i	−1.69471	+	1.58319i
$451$	−4.07040	−	7.05015i	−0.191668	−	0.331978i
$452$	−24.4657	−	22.1422i	−1.15077	−	1.04148i
$453$	11.4987	+	13.9182i	0.540257	+	0.653936i
$454$	9.36314	−	12.8528i	0.439434	−	0.603211i
$455$	−8.44680	+	41.2416i	−0.395992	+	1.93343i
$456$	4.59540	−	30.1832i	0.215199	−	1.41346i
$457$	1.34647	+	2.33216i	0.0629854	+	0.109094i	0.895799	−	0.444460i	$-0.146605\pi$
$457$	1.34647	+	2.33216i	0.0629854	+	0.109094i	−0.832813	+	0.553554i	$0.813271\pi$
$458$	−31.0862	−	22.6460i	−1.45256	−	1.05818i
$459$	−12.7482	−	7.75508i	−0.595034	−	0.361976i
$460$	−4.54294	−	14.1039i	−0.211816	−	0.657599i
$461$	−6.53523	−	3.77312i	−0.304376	−	0.175732i	0.340031	−	0.940414i	$-0.389562\pi$
$461$	−6.53523	−	3.77312i	−0.304376	−	0.175732i	−0.644407	+	0.764683i	$0.722896\pi$
$462$	13.9783	+	10.9547i	0.650328	+	0.509659i
$463$	−6.86381	−	11.8885i	−0.318988	−	0.552504i	0.661289	−	0.750131i	$-0.270010\pi$
$463$	−6.86381	−	11.8885i	−0.318988	−	0.552504i	−0.980277	+	0.197628i	$0.936676\pi$
$464$	1.06803	+	10.6853i	0.0495819	+	0.496051i
$465$	19.0830	−	3.21472i	0.884955	−	0.149079i
$466$	−0.353997	−	0.797824i	−0.0163986	−	0.0369585i
$467$	−2.35625	−	1.36038i	−0.109034	−	0.0629510i	0.444491	−	0.895783i	$-0.353385\pi$
$467$	−2.35625	−	1.36038i	−0.109034	−	0.0629510i	−0.553525	+	0.832832i	$0.686718\pi$
$468$	14.0963	+	18.7211i	0.651604	+	0.865385i
$469$	−29.1749	+	9.71944i	−1.34717	+	0.448802i
$470$	24.7493	+	2.63315i	1.14160	+	0.121458i
$471$	1.96373	−	0.330809i	0.0904840	−	0.0152429i
$472$	6.32740	−	5.65357i	0.291242	−	0.260227i
$473$	16.7753	+	9.68525i	0.771331	+	0.445328i
$474$	20.7892	−	13.7544i	0.954879	−	0.631762i
$475$	−36.1334	+	62.5848i	−1.65791	+	2.87159i
$476$	−1.66197	−	15.1044i	−0.0761764	−	0.692308i
$477$	−35.4365	+	12.2879i	−1.62253	+	0.562626i
$478$	−7.17264	−	0.763118i	−0.328069	−	0.0349042i
$479$	15.0299			0.686733			0.343367	−	0.939201i	$-0.388433\pi$
$479$	15.0299			0.686733			0.343367	+	0.939201i	$0.388433\pi$
$480$	−30.9331	+	25.2259i	−1.41190	+	1.15140i
$481$			8.16835i			0.372445i
$482$	10.6990	−	14.6865i	0.487326	−	0.668953i
$483$	0.292686	−	8.32890i	0.0133177	−	0.378978i
$484$	−2.14034	−	6.64485i	−0.0972880	−	0.302039i
$485$	−9.03917	+	15.6563i	−0.410448	+	0.710916i
$486$	−6.90816	+	20.9351i	−0.313361	+	0.949634i
$487$	5.11438	+	8.85837i	0.231755	+	0.401411i	0.958325	−	0.285682i	$-0.0922200\pi$
$487$	5.11438	+	8.85837i	0.231755	+	0.401411i	−0.726570	+	0.687093i	$0.758887\pi$
$488$	−17.8425	+	3.72130i	−0.807692	+	0.168455i
$489$	6.02516	+	35.7662i	0.272467	+	1.61741i
$490$	−35.1959	−	19.6886i	−1.58999	−	0.889441i
$491$	1.88058	+	3.25726i	0.0848695	+	0.146998i	0.905336	−	0.424697i	$-0.139619\pi$
$491$	1.88058	+	3.25726i	0.0848695	+	0.146998i	−0.820466	+	0.571695i	$0.806286\pi$
$492$	10.2804	+	0.463919i	0.463478	+	0.0209151i
$493$	7.70940			0.347214
$494$	27.8237	+	20.2694i	1.25185	+	0.911961i
$495$	−32.8893	−	6.31892i	−1.47826	−	0.284014i
$496$	10.9160	−	1.09109i	0.490144	−	0.0489915i
$497$	−21.1782	−	18.7863i	−0.949973	−	0.842679i
$498$	−1.88901	+	3.78699i	−0.0846487	+	0.169699i
$499$			2.53938i			0.113678i	0.998383	+	0.0568391i	$0.0181022\pi$
$499$			2.53938i			0.113678i	−0.998383	+	0.0568391i	$0.981898\pi$
$500$	51.1523	−	16.4764i	2.28760	−	0.736845i
$501$	6.76655	−	18.1581i	0.302307	−	0.811242i
$502$	−3.56052	+	4.88753i	−0.158914	+	0.218141i
$503$	−23.1423			−1.03186			−0.515932	−	0.856630i	$-0.672554\pi$
$503$	−23.1423			−1.03186			−0.515932	+	0.856630i	$0.672554\pi$
$504$	−21.1843	+	7.43134i	−0.943624	+	0.331018i
$505$	6.32947			0.281658
$506$	4.14997	−	5.69667i	0.184489	−	0.253248i
$507$	−3.85191	+	0.648890i	−0.171069	+	0.0288182i
$508$	−2.37540	−	7.37464i	−0.105391	−	0.327197i
$509$			38.1542i			1.69116i	0.533852	+	0.845578i	$0.320744\pi$
$509$			38.1542i			1.69116i	−0.533852	+	0.845578i	$0.679256\pi$
$510$	15.8117	+	23.8986i	0.700153	+	1.05825i
$511$	5.41111	−	26.4198i	0.239373	−	1.16874i
$512$	−18.4573	+	13.0892i	−0.815705	+	0.578468i
$513$	−0.742208	+	32.3746i	−0.0327693	+	1.42937i
$514$	9.04579	+	6.58978i	0.398993	+	0.290663i
$515$	24.1232			1.06300
$516$	−21.7363	+	11.2748i	−0.956887	+	0.496347i
$517$	5.91926	+	10.2525i	0.260329	+	0.450903i
$518$	−7.45681	−	2.37230i	−0.327634	−	0.104233i
$519$	−17.1906	−	6.40604i	−0.754585	−	0.281194i
$520$	−9.18856	−	44.0563i	−0.402945	−	1.93200i
$521$	0.924081	+	1.60056i	0.0404847	+	0.0701216i	0.885558	−	0.464529i	$-0.153776\pi$
$521$	0.924081	+	1.60056i	0.0404847	+	0.0701216i	−0.845073	+	0.534651i	$0.820443\pi$
$522$	−2.57213	−	11.0957i	−0.112579	−	0.485644i
$523$	0.254312	−	0.440482i	0.0111203	−	0.0192609i	−0.860412	−	0.509600i	$-0.829794\pi$
$523$	0.254312	−	0.440482i	0.0111203	−	0.0192609i	0.871532	+	0.490339i	$0.163127\pi$
$524$	−21.9118	+	7.05788i	−0.957220	+	0.308325i
$525$	53.1061	+	1.86620i	2.31774	+	0.0814475i
$526$	−7.70139	+	10.5717i	−0.335796	+	0.460948i
$527$		−	7.87590i		−	0.343080i
$528$	−18.3617	−	4.82732i	−0.799090	−	0.210082i
$529$	19.6926			0.856198
$530$	71.6236	+	7.62024i	3.11113	+	0.331002i
$531$	−5.88972	+	6.80514i	−0.255592	+	0.295318i
$532$	−26.5844	+	19.5133i	−1.15258	+	0.846010i
$533$	−5.80152	+	10.0485i	−0.251292	+	0.435250i
$534$	−21.8894	−	10.9188i	−0.947248	−	0.472503i
$535$	65.3565	+	37.7336i	2.82561	+	1.63137i
$536$	24.5145	−	21.9038i	1.05886	−	0.946100i
$537$	−3.76015	+	10.0904i	−0.162262	+	0.435432i
$538$	−8.60742	−	0.915768i	−0.371092	−	0.0394816i
$539$	−2.28801	−	19.0455i	−0.0985514	−	0.820346i
$540$	29.1205	−	30.7302i	1.25315	−	1.32242i
$541$	−20.6621	−	11.9293i	−0.888334	−	0.512880i	−0.0149369	−	0.999888i	$-0.504755\pi$
$541$	−20.6621	−	11.9293i	−0.888334	−	0.512880i	−0.873397	+	0.487008i	$0.838088\pi$
$542$	7.33078	+	16.5218i	0.314884	+	0.709673i
$543$	−17.8863	−	21.6499i	−0.767576	−	0.929087i
$544$	8.03255	+	14.1198i	0.344393	+	0.605381i
$545$	20.5707	+	35.6295i	0.881151	+	1.52620i
$546$	3.56026	−	25.0608i	0.152365	−	1.07250i
$547$	27.4132	+	15.8270i	1.17211	+	0.676715i	0.954175	−	0.299249i	$-0.0967361\pi$
$547$	27.4132	+	15.8270i	1.17211	+	0.676715i	0.217930	+	0.975964i	$0.430069\pi$
$548$	2.25004	−	0.724748i	0.0961170	−	0.0309597i
$549$	18.2651	−	6.33359i	0.779535	−	0.270311i
$550$	36.3226	+	26.4607i	1.54880	+	1.12829i
$551$	−8.36546	−	14.4894i	−0.356380	−	0.617269i
$552$	3.24263	+	8.29843i	0.138016	+	0.353205i
$553$	−26.3771	−	5.40236i	−1.12167	−	0.229732i
$554$	−12.0596	+	16.5542i	−0.512364	+	0.703322i
$555$	14.5515	−	2.45134i	0.617678	−	0.104054i
$556$	9.24040	−	10.2101i	0.391880	−	0.433003i
$557$	9.85092	+	17.0623i	0.417397	+	0.722953i	0.995677	−	0.0928859i	$-0.0296092\pi$
$557$	9.85092	+	17.0623i	0.417397	+	0.722953i	−0.578280	+	0.815838i	$0.696276\pi$
$558$	−11.3353	+	2.62769i	−0.479862	+	0.111239i
$559$		−	27.6087i		−	1.16772i
$560$	42.8872	+	4.40692i	1.81232	+	0.186226i
$561$	−4.75953	+	12.7722i	−0.200947	+	0.539243i
$562$	−6.40700	−	14.4399i	−0.270263	−	0.609109i
$563$	−32.1405	−	18.5563i	−1.35456	−	0.782057i	−0.365677	−	0.930742i	$-0.619163\pi$
$563$	−32.1405	−	18.5563i	−1.35456	−	0.782057i	−0.988885	+	0.148685i	$0.952496\pi$
$564$	−14.9500	−	0.674641i	−0.629509	−	0.0284075i
$565$	−33.6065	−	58.2082i	−1.41384	−	2.44884i
$566$	11.3761	−	5.04760i	0.478173	−	0.212167i
$567$	21.2776	−	10.6895i	0.893575	−	0.448915i
$568$	28.7472	+	9.46218i	1.20620	+	0.397024i
$569$	−33.6384	+	19.4211i	−1.41019	+	0.814176i	−0.995406	−	0.0957428i	$-0.969477\pi$
$569$	−33.6384	+	19.4211i	−1.41019	+	0.814176i	−0.414787	+	0.909918i	$0.636144\pi$
$570$	27.7589	−	55.6496i	1.16269	−	2.33090i
$571$	−11.9862	−	6.92026i	−0.501609	−	0.289604i	0.227769	−	0.973715i	$-0.426857\pi$
$571$	−11.9862	−	6.92026i	−0.501609	−	0.289604i	−0.729378	+	0.684111i	$0.760190\pi$
$572$	14.3642	−	15.8715i	0.600597	−	0.663621i
$573$	26.1621	+	9.74922i	1.09294	+	0.407280i
$574$	−7.48831	−	8.21451i	−0.312556	−	0.342867i
$575$		−	21.0886i		−	0.879457i
$576$	17.6418	−	16.2716i	0.735076	−	0.677985i
$577$	−33.2555	+	19.2001i	−1.38445	+	0.799310i	−0.992682	−	0.120756i	$-0.961468\pi$
$577$	−33.2555	+	19.2001i	−1.38445	+	0.799310i	−0.391763	+	0.920066i	$0.628135\pi$
$578$	−11.3154	+	5.02066i	−0.470658	+	0.208832i
$579$	−19.0676	+	3.21212i	−0.792424	+	0.133491i
$580$	−4.60222	+	21.3836i	−0.191097	+	0.887906i
$581$	4.33674	−	1.44476i	0.179918	−	0.0599386i
$582$	4.85206	−	9.72714i	0.201124	−	0.403203i
$583$	17.1301	+	29.6702i	0.709457	+	1.22882i
$584$	5.88629	+	28.2229i	0.243576	+	1.16787i
$585$	15.6388	+	45.0998i	0.646583	+	1.86465i
$586$	−43.3780	−	4.61511i	−1.79193	−	0.190648i
$587$	−0.101386	−	0.0585350i	−0.00418463	−	0.00241600i	0.497906	−	0.867231i	$-0.334102\pi$
$587$	−0.101386	−	0.0585350i	−0.00418463	−	0.00241600i	−0.502091	+	0.864815i	$0.667436\pi$
$588$	21.8438	+	10.5284i	0.900824	+	0.434185i
$589$	−14.8023	+	8.54613i	−0.609920	+	0.352137i
$590$	15.7982	−	7.00972i	0.650403	−	0.288586i
$591$	5.76712	+	6.98061i	0.237228	+	0.287144i
$592$	8.32388	−	0.831999i	0.342109	−	0.0341950i
$593$	−21.4369	+	37.1298i	−0.880309	+	1.52474i	−0.0293113	+	0.999570i	$0.509331\pi$
$593$	−21.4369	+	37.1298i	−0.880309	+	1.52474i	−0.850998	+	0.525170i	$0.824002\pi$
$594$	19.9702	+	2.58883i	0.819388	+	0.106221i
$595$	6.21040	−	30.3223i	0.254601	−	1.24309i
$596$	−11.0771	−	34.3897i	−0.453734	−	1.40866i
$597$	27.1457	+	10.1158i	1.11100	+	0.414010i
$598$	−9.98910	−	1.06277i	−0.408485	−	0.0434599i
$599$	−23.8725	−	13.7828i	−0.975404	−	0.563150i	−0.0745243	−	0.997219i	$-0.523744\pi$
$599$	−23.8725	−	13.7828i	−0.975404	−	0.563150i	−0.900879	+	0.434070i	$0.857077\pi$
$600$	−52.9118	+	20.6754i	−2.16011	+	0.844070i
$601$	24.2296	+	13.9890i	0.988345	+	0.570621i	0.904779	−	0.425881i	$-0.140036\pi$
$601$	24.2296	+	13.9890i	0.988345	+	0.570621i	0.0835659	+	0.996502i	$0.473369\pi$
$602$	25.2037	+	8.01826i	1.02723	+	0.326800i
$603$	−22.8187	+	26.3654i	−0.929250	+	1.07368i
$604$	6.39142	+	19.8427i	0.260063	+	0.807389i
$605$		−	14.2197i		−	0.578113i
$606$	−3.79872	+	0.231622i	−0.154313	+	0.00940900i
$607$		−	40.9855i		−	1.66355i	−0.555113	−	0.831775i	$-0.687325\pi$
$607$		−	40.9855i		−	1.66355i	0.555113	−	0.831775i	$-0.312675\pi$
$608$	17.8213	−	30.4181i	0.722748	−	1.23362i
$609$	−6.52163	+	10.4317i	−0.264270	+	0.422713i
$610$	−36.9171	−	3.92771i	−1.49473	−	0.159028i
$611$	8.43669	−	14.6128i	0.341312	−	0.591170i
$612$	−10.3642	−	13.7645i	−0.418946	−	0.556396i
$613$	−32.3663	+	18.6867i	−1.30726	+	0.754748i	−0.981638	−	0.190751i	$-0.938908\pi$
$613$	−32.3663	+	18.6867i	−1.30726	+	0.754748i	−0.325624	+	0.945499i	$0.605574\pi$
$614$	24.6615	+	17.9657i	0.995256	+	0.725035i
$615$	19.6420	+	7.31955i	0.792044	+	0.295153i
$616$	10.3172	+	17.7224i	0.415694	+	0.714058i
$617$	−15.2736	+	8.81820i	−0.614891	+	0.355008i	−0.774877	−	0.632112i	$-0.782188\pi$
$617$	−15.2736	+	8.81820i	−0.614891	+	0.355008i	0.159986	+	0.987119i	$0.448855\pi$
$618$	−14.4779	+	0.882770i	−0.582386	+	0.0355102i
$619$	−23.2026			−0.932591			−0.466296	−	0.884629i	$-0.654412\pi$
$619$	−23.2026			−0.932591			−0.466296	+	0.884629i	$0.654412\pi$
$620$	21.8454	+	4.70162i	0.877334	+	0.188822i
$621$	−4.53615	−	8.29001i	−0.182029	−	0.332667i
$622$	7.01270	−	3.11155i	0.281184	−	0.124762i
$623$	8.35093	+	25.0671i	0.334573	+	1.00429i
$624$	7.12685	+	26.1048i	0.285302	+	1.04503i
$625$	51.4844			2.05938
$626$	3.73501	+	0.397379i	0.149281	+	0.0158824i
$627$	29.1692	−	4.91383i	1.16491	−	0.196239i
$628$	2.24800	+	0.483818i	0.0897049	+	0.0193064i
$629$		−	6.00567i		−	0.239462i
$630$	−45.7131	+	1.17837i	−1.82125	+	0.0469473i
$631$	2.53810			0.101040			0.0505201	−	0.998723i	$-0.483912\pi$
$631$	2.53810			0.101040			0.0505201	+	0.998723i	$0.483912\pi$
$632$	28.1773	−	5.87678i	1.12083	−	0.233766i
$633$	−16.8902	−	6.29410i	−0.671327	−	0.250168i
$634$	4.03247	−	37.9017i	0.160150	−	1.50527i
$635$		−	15.7814i		−	0.626267i
$636$	−43.2648	−	1.95238i	−1.71556	−	0.0774171i
$637$	−21.8781	+	16.3969i	−0.866840	+	0.649668i
$638$	−9.50998	+	4.21960i	−0.376504	+	0.167056i
$639$	−31.5237	−	6.05655i	−1.24706	−	0.239593i
$640$	−43.9593	+	13.8509i	−1.73764	+	0.547507i
$641$			2.85567i			0.112792i	0.998408	+	0.0563961i	$0.0179610\pi$
$641$			2.85567i			0.112792i	−0.998408	+	0.0563961i	$0.982039\pi$
$642$	−40.6055	−	20.2547i	−1.60257	−	0.799389i
$643$	6.65938	+	11.5344i	0.262620	+	0.454872i	0.966937	−	0.255014i	$-0.0820800\pi$
$643$	6.65938	+	11.5344i	0.262620	+	0.454872i	−0.704317	+	0.709885i	$0.748747\pi$
$644$	3.87128	−	8.81031i	0.152550	−	0.347175i
$645$	−49.1836	+	8.28543i	−1.93660	+	0.326238i
$646$	−20.4570	−	14.9028i	−0.804872	−	0.586342i
$647$	−1.08557	−	1.88026i	−0.0426780	−	0.0739205i	0.843897	−	0.536505i	$-0.180256\pi$
$647$	−1.08557	−	1.88026i	−0.0426780	−	0.0739205i	−0.886575	+	0.462584i	$0.846922\pi$
$648$	−16.3525	+	19.5088i	−0.642388	+	0.766379i
$649$	7.11956	+	4.11048i	0.279467	+	0.161351i
$650$	6.77634	−	63.6917i	0.265790	−	2.49819i
$651$	10.6570	+	6.66248i	0.417680	+	0.261123i
$652$	−8.81197	+	40.9437i	−0.345103	+	1.60348i
$653$	−2.61269			−0.102243			−0.0511213	−	0.998692i	$-0.516280\pi$
$653$	−2.61269			−0.102243			−0.0511213	+	0.998692i	$0.516280\pi$
$654$	−13.6496	−	20.6308i	−0.533742	−	0.806727i
$655$	−46.8903			−1.83215
$656$	10.8308	+	4.88849i	0.422872	+	0.190863i
$657$	−10.0184	−	28.8914i	−0.390853	−	1.12716i
$658$	10.8897	+	11.9457i	0.424523	+	0.465692i
$659$	−17.3447	+	30.0419i	−0.675652	+	1.17026i	0.300625	+	0.953742i	$0.402805\pi$
$659$	−17.3447	+	30.0419i	−0.675652	+	1.17026i	−0.976278	+	0.216522i	$0.930529\pi$
$660$	−32.5851	−	20.8261i	−1.26837	−	0.810653i
$661$	17.3986	−	30.1352i	0.676725	−	1.17212i	−0.299236	−	0.954179i	$-0.596732\pi$
$661$	17.3986	−	30.1352i	0.676725	−	1.17212i	0.975961	−	0.217944i	$-0.0699349\pi$
$662$	−29.4286	−	3.13099i	−1.14377	−	0.121689i
$663$	19.1571	−	3.22720i	0.744001	−	0.125334i
$664$	−3.64398	+	3.25591i	−0.141414	+	0.126354i
$665$	−63.7281	+	21.2306i	−2.47127	+	0.823288i
$666$	−8.64360	+	2.00371i	−0.334933	+	0.0776421i
$667$	4.22825	+	2.44118i	0.163718	+	0.0945229i
$668$	15.0145	−	16.5901i	0.580930	−	0.641891i
$669$	1.71471	+	10.1788i	0.0662945	+	0.393534i
$670$	61.2076	−	27.1580i	2.36466	−	1.04920i
$671$	−8.82940	−	15.2930i	−0.340855	−	0.590379i
$672$	−25.9006	−	1.07545i	−0.999139	−	0.0414863i
$673$	−13.8678	+	24.0198i	−0.534565	+	0.925895i	0.464619	+	0.885511i	$0.346191\pi$
$673$	−13.8678	+	24.0198i	−0.534565	+	0.925895i	−0.999184	+	0.0403837i	$0.987142\pi$
$674$	0.315025	−	2.96096i	0.0121343	−	0.114052i
$675$	52.8581	−	28.9230i	2.03451	−	1.11325i
$676$	−4.40950	−	0.949021i	−0.169596	−	0.0365008i
$677$	2.96317	−	1.71079i	0.113884	−	0.0657508i	−0.441976	−	0.897027i	$-0.645722\pi$
$677$	2.96317	−	1.71079i	0.113884	−	0.0657508i	0.555860	+	0.831276i	$0.312389\pi$
$678$	22.2995	+	33.7046i	0.856407	+	1.29442i
$679$	−11.1392	+	3.71096i	−0.427483	+	0.142413i
$680$	6.75577	+	32.3918i	0.259072	+	1.24217i
$681$	−15.0143	+	12.4042i	−0.575349	+	0.475331i
$682$	4.31074	+	9.71537i	0.165067	+	0.372021i
$683$	−10.8234	−	18.7467i	−0.414146	−	0.717321i	0.581193	−	0.813766i	$-0.302586\pi$
$683$	−10.8234	−	18.7467i	−0.414146	−	0.717321i	−0.995338	+	0.0964447i	$0.969253\pi$
$684$	−14.6235	+	34.4147i	−0.559142	+	1.31588i
$685$	4.81500			0.183972
$686$	−8.61462	−	24.7344i	−0.328908	−	0.944362i
$687$	30.0013	+	36.3140i	1.14462	+	1.38547i
$688$	−28.1344	+	2.81212i	−1.07261	+	0.107211i
$689$	24.4155	−	42.2888i	0.930155	−	1.61108i
$690$	1.10448	+	18.1141i	0.0420469	+	0.689590i
$691$	−8.96469	−	15.5273i	−0.341033	−	0.590686i	0.643592	−	0.765369i	$-0.277443\pi$
$691$	−8.96469	−	15.5273i	−0.341033	−	0.590686i	−0.984625	+	0.174683i	$0.944110\pi$
$692$	−15.7062	−	14.2146i	−0.597061	−	0.540358i
$693$	−13.2560	−	17.2446i	−0.503553	−	0.655068i
$694$	−1.32877	+	0.589577i	−0.0504392	+	0.0223800i
$695$	24.2915	−	14.0247i	0.921429	−	0.531987i
$696$	1.97957	−	13.0021i	0.0750355	−	0.492843i
$697$	4.26550	−	7.38806i	0.161567	−	0.279843i
$698$	−34.1899	+	15.1701i	−1.29411	+	0.574199i
$699$	0.177581	+	1.05414i	0.00671671	+	0.0398714i
$700$	56.1756	+	24.6838i	2.12324	+	0.932958i
$701$	20.2367			0.764329			0.382165	−	0.924094i	$-0.375179\pi$
$701$	20.2367			0.764329			0.382165	+	0.924094i	$0.375179\pi$
$702$	−11.0362	−	26.4950i	−0.416535	−	0.999989i
$703$	−11.2873	+	6.51674i	−0.425710	+	0.245784i
$704$	−17.6368	−	13.0211i	−0.664713	−	0.490751i
$705$	−28.5639	−	10.6442i	−1.07578	−	0.400885i
$706$	−31.2638	−	22.7754i	−1.17663	−	0.857165i
$707$	3.07518	+	2.72786i	0.115654	+	0.102592i
$708$	−9.22502	+	4.78511i	−0.346698	+	0.179835i
$709$	28.1032	−	16.2254i	1.05544	−	0.609357i	0.131271	−	0.991347i	$-0.458094\pi$
$709$	28.1032	−	16.2254i	1.05544	−	0.609357i	0.924167	+	0.381990i	$0.124761\pi$
$710$	49.8260	+	36.2978i	1.86994	+	1.36223i
$711$	−28.8447	+	10.0022i	−1.08176	+	0.375111i
$712$	−18.8197	−	21.0628i	−0.705299	−	0.789362i
$713$	2.49390	−	4.31957i	0.0933975	−	0.161769i
$714$	−2.61764	+	18.4256i	−0.0979626	+	0.689562i
$715$	37.7611	−	21.8014i	1.41218	−	0.815325i
$716$	−8.34353	+	9.21907i	−0.311812	+	0.344533i
$717$	8.27814	+	3.08483i	0.309153	+	0.115205i
$718$	6.44522	+	14.5260i	0.240533	+	0.542105i
$719$	23.6058	−	40.8864i	0.880347	−	1.52481i	0.0293921	−	0.999568i	$-0.490643\pi$
$719$	23.6058	−	40.8864i	0.880347	−	1.52481i	0.850955	−	0.525238i	$-0.176024\pi$
$720$	44.3656	−	20.5303i	1.65341	−	0.765118i
$721$	11.7203	+	10.3965i	0.436486	+	0.387188i
$722$	−2.96832	+	27.8996i	−0.110469	+	1.03832i
$723$	−17.1564	+	14.1740i	−0.638054	+	0.527136i
$724$	−9.94191	−	30.8655i	−0.369488	−	1.14711i
$725$	−15.5653	+	26.9598i	−0.578079	+	1.00126i
$726$	0.520359	+	8.53416i	0.0193123	+	0.316732i
$727$	−31.7188	−	18.3129i	−1.17639	−	0.679187i	−0.221210	−	0.975226i	$-0.571001\pi$
$727$	−31.7188	−	18.3129i	−1.17639	−	0.679187i	−0.955176	+	0.296039i	$0.904334\pi$
$728$	14.5230	−	25.3649i	0.538258	−	0.940084i
$729$	14.5574	−	22.7395i	0.539162	−	0.842202i
$730$	−6.21278	+	58.3948i	−0.229945	+	2.16129i
$731$			20.2989i			0.750783i
$732$	22.3000	+	1.00632i	0.824233	+	0.0371947i
$733$	−1.50220			−0.0554852			−0.0277426	−	0.999615i	$-0.508832\pi$
$733$	−1.50220			−0.0554852			−0.0277426	+	0.999615i	$0.508832\pi$
$734$	4.09720	−	5.62422i	0.151230	−	0.207594i
$735$	35.7759	+	34.0540i	1.31961	+	1.25610i
$736$	−0.0655507	+	10.2876i	−0.00241623	+	0.379204i
$737$	27.5835	+	15.9254i	1.01605	+	0.586619i
$738$	−12.0563	−	3.67415i	−0.443799	−	0.135247i
$739$	43.8655	−	25.3257i	1.61362	−	0.931622i	0.625094	−	0.780549i	$-0.285060\pi$
$739$	43.8655	−	25.3257i	1.61362	−	0.931622i	0.988523	−	0.151073i	$-0.0482728\pi$
$740$	16.6580	+	3.58516i	0.612359	+	0.131793i
$741$	−26.8527	−	32.5030i	−0.986459	−	1.19403i
$742$	31.5142	+	34.5704i	1.15692	+	1.26912i
$743$	42.1176	−	24.3166i	1.54515	−	0.892090i	0.546644	−	0.837365i	$-0.315905\pi$
$743$	42.1176	−	24.3166i	1.54515	−	0.892090i	0.998501	−	0.0547246i	$-0.0174281\pi$
$744$	−13.2829	−	2.02233i	−0.486975	−	0.0741421i
$745$		−	73.5925i		−	2.69622i
$746$	−16.6774	+	22.8930i	−0.610601	+	0.838173i
$747$	3.39191	−	3.91911i	0.124104	−	0.143393i
$748$	−10.5611	+	11.6693i	−0.386152	+	0.426673i
$749$	15.4912	+	46.5000i	0.566036	+	1.69907i
$750$	−65.6962	+	4.00574i	−2.39889	+	0.146269i
$751$	6.32891			0.230945			0.115473	−	0.993311i	$-0.463162\pi$
$751$	6.32891			0.230945			0.115473	+	0.993311i	$0.463162\pi$
$752$	−15.7504	−	7.10893i	−0.574357	−	0.259236i
$753$	5.70949	−	4.71696i	0.208065	−	0.171896i
$754$	11.9857	+	8.73147i	0.436493	+	0.317982i
$755$			42.4626i			1.54537i
$756$	27.3923	−	2.38005i	0.996247	−	0.0865616i
$757$		−	12.0691i		−	0.438660i	−0.975651	−	0.219330i	$-0.929613\pi$
$757$		−	12.0691i		−	0.438660i	0.975651	−	0.219330i	$-0.0703872\pi$
$758$	−31.3049	+	42.9723i	−1.13705	+	1.56082i
$759$	−6.65470	+	5.49786i	−0.241550	+	0.199560i
$760$	53.5480	−	47.8454i	1.94239	−	1.73554i
$761$	−17.7280			−0.642639			−0.321319	−	0.946971i	$-0.604126\pi$
$761$	−17.7280			−0.642639			−0.321319	+	0.946971i	$0.604126\pi$
$762$	0.577509	+	9.47145i	0.0209209	+	0.343114i
$763$	−5.36120	+	26.1761i	−0.194088	+	0.947638i
$764$	23.9030	+	21.6329i	0.864779	+	0.782651i
$765$	−11.4982	−	33.1590i	−0.415718	−	1.19887i
$766$	−22.6824	−	16.5239i	−0.819549	−	0.597035i
$767$		−	11.7173i		−	0.423087i
$768$	25.8759	−	9.92150i	0.933717	−	0.358011i
$769$	32.9917	−	19.0478i	1.18971	−	0.686881i	0.231471	−	0.972842i	$-0.425646\pi$
$769$	32.9917	−	19.0478i	1.18971	−	0.686881i	0.958241	+	0.285961i	$0.0923129\pi$
$770$	8.93551	+	40.8035i	0.322013	+	1.47045i
$771$	−8.73010	−	10.5671i	−0.314407	−	0.380563i
$772$	−21.8278	−	4.69782i	−0.785600	−	0.169078i
$773$	7.71732	−	4.45560i	0.277573	−	0.160257i	−0.354751	−	0.934961i	$-0.615434\pi$
$773$	7.71732	−	4.45560i	0.277573	−	0.160257i	0.632324	+	0.774704i	$0.282101\pi$
$774$	29.2150	−	6.77245i	1.05011	−	0.243431i
$775$	27.5421	+	15.9014i	0.989341	+	0.571196i
$776$	9.35980	−	8.36303i	0.335997	−	0.300215i
$777$	8.12634	+	5.08039i	0.291531	+	0.182258i
$778$	−0.206418	−	0.150373i	−0.00740043	−	0.00539115i
$779$	−18.5139			−0.663330
$780$	−2.48479	+	55.0628i	−0.0889696	+	1.97156i
$781$			29.3219i			1.04922i
$782$	7.34436	+	0.781387i	0.262634	+	0.0279423i
$783$	−0.319723	+	13.9461i	−0.0114260	+	0.498391i
$784$	18.9375	+	20.6245i	0.676340	+	0.736590i
$785$	4.05629	+	2.34190i	0.144775	+	0.0835859i
$786$	28.1419	−	1.71591i	1.00379	−	0.0612046i
$787$	21.3211	−	36.9292i	0.760015	−	1.31638i	−0.182827	−	0.983145i	$-0.558525\pi$
$787$	21.3211	−	36.9292i	0.760015	−	1.31638i	0.942842	−	0.333240i	$-0.108142\pi$
$788$	3.20558	+	9.95200i	0.114194	+	0.354525i
$789$	12.3496	−	10.2027i	0.439656	−	0.363227i
$790$	58.3004	+	6.20275i	2.07424	+	0.220684i
$791$	8.75863	−	42.7641i	0.311421	−	1.52052i
$792$	20.3185	+	11.3066i	0.721987	+	0.401764i
$793$	−12.5845	+	21.7970i	−0.446889	+	0.774034i
$794$	−12.0479	+	5.34570i	−0.427565	+	0.189712i
$795$	−82.6627	−	30.8040i	−2.93174	−	1.09251i
$796$	24.8016	+	22.4462i	0.879070	+	0.795585i
$797$	−36.6795	+	21.1769i	−1.29925	+	0.750124i	−0.980275	−	0.197638i	$-0.936673\pi$
$797$	−36.6795	+	21.1769i	−1.29925	+	0.750124i	−0.318978	+	0.947762i	$0.603340\pi$
$798$	37.4704	−	15.0739i	1.32644	−	0.533611i
$799$	−6.20297	+	10.7439i	−0.219445	+	0.380090i
$800$	−65.5947	−	0.417959i	−2.31912	−	0.0147771i
$801$	22.6531	+	19.6058i	0.800408	+	0.692737i
$802$	8.30743	−	11.4036i	0.293345	−	0.402675i
$803$	−24.1902	+	13.9662i	−0.853652	+	0.492856i
$804$	−35.7408	+	18.5391i	−1.26048	+	0.653824i
$805$	13.0077	−	14.6639i	0.458460	−	0.516834i
$806$	8.92005	−	12.2446i	0.314195	−	0.431296i
$807$	9.93405	+	3.70190i	0.349695	+	0.130313i
$808$	−4.17423	−	1.37395i	−0.146849	−	0.0483355i
$809$	5.56524	−	3.21310i	0.195664	−	0.112966i	−0.398968	−	0.916965i	$-0.630631\pi$
$809$	5.56524	−	3.21310i	0.195664	−	0.112966i	0.594631	+	0.803999i	$0.297298\pi$
$810$	−43.8876	+	27.6117i	−1.54205	+	0.970177i
$811$	−5.81983			−0.204362			−0.102181	−	0.994766i	$-0.532582\pi$
$811$	−5.81983			−0.204362			−0.102181	+	0.994766i	$0.532582\pi$
$812$	−11.4518	+	8.40579i	−0.401881	+	0.294986i
$813$	−3.67745	−	21.8299i	−0.128974	−	0.765607i
$814$	3.28710	+	7.40833i	0.115213	+	0.259662i
$815$	−42.6539	+	73.8787i	−1.49410	+	2.58786i
$816$	−5.23993	−	19.1932i	−0.183434	−	0.671896i
$817$	38.1507	−	22.0263i	1.33472	−	0.770604i
$818$	−10.9507	−	24.6804i	−0.382884	−	0.862929i
$819$	−11.8389	+	28.6517i	−0.413683	+	1.00117i
$820$	17.9460	+	16.2416i	0.626700	+	0.567182i
$821$	6.20321	+	10.7443i	0.216494	+	0.374978i	0.953734	−	0.300653i	$-0.0972046\pi$
$821$	6.20321	+	10.7443i	0.216494	+	0.374978i	−0.737240	+	0.675631i	$0.763871\pi$
$822$	−2.88979	+	0.176201i	−0.100793	+	0.00614571i
$823$	−9.92319	+	17.1875i	−0.345901	+	0.599117i	−0.985517	−	0.169577i	$-0.945760\pi$
$823$	−9.92319	+	17.1875i	−0.345901	+	0.599117i	0.639616	+	0.768694i	$0.279093\pi$
$824$	−15.9090	−	5.23648i	−0.554217	−	0.182421i
$825$	−35.0550	−	42.4311i	−1.22046	−	1.47726i
$826$	10.6966	+	3.40300i	0.372183	+	0.118406i
$827$	47.7986			1.66212			0.831059	−	0.556184i	$-0.187735\pi$
$827$	47.7986			1.66212			0.831059	+	0.556184i	$0.187735\pi$
$828$	−1.32574	−	10.8310i	−0.0460726	−	0.376403i
$829$	−22.8767	−	39.6237i	−0.794542	−	1.37619i	−0.923130	−	0.384488i	$-0.874378\pi$
$829$	−22.8767	−	39.6237i	−0.794542	−	1.37619i	0.128588	−	0.991698i	$-0.458955\pi$
$830$	−9.09827	+	4.03693i	−0.315806	+	0.140124i
$831$	19.3382	−	15.9765i	0.670836	−	0.554219i
$832$	−3.50364	+	31.0493i	−0.121467	+	1.07644i
$833$	16.0856	−	12.0556i	0.557331	−	0.417701i
$834$	−14.0657	+	9.30605i	−0.487054	+	0.322242i
$835$	39.4708	−	22.7885i	1.36594	−	0.788627i
$836$	33.3917	+	7.18662i	1.15488	+	0.248555i
$837$	14.2473	+	0.326628i	0.492457	+	0.0112899i
$838$	−10.4813	−	1.11513i	−0.362070	−	0.0385217i
$839$	3.42718	−	5.93605i	0.118319	−	0.204935i	−0.800782	−	0.598955i	$-0.795583\pi$
$839$	3.42718	−	5.93605i	0.118319	−	0.204935i	0.919102	+	0.394020i	$0.128916\pi$
$840$	−49.5447	−	18.2600i	−1.70945	−	0.630029i
$841$	10.8964	+	18.8731i	0.375738	+	0.650797i
$842$	19.1865	+	43.2417i	0.661209	+	1.49021i
$843$	3.21404	+	19.0790i	0.110697	+	0.657116i
$844$	−15.4318	−	13.9662i	−0.531184	−	0.480737i
$845$	−7.95650	−	4.59369i	−0.273712	−	0.158028i
$846$	17.5325	+	5.34302i	0.602780	+	0.183697i
$847$	6.12837	−	6.90866i	0.210573	−	0.237384i
$848$	−45.5809	−	20.5730i	−1.56526	−	0.706479i
$849$	−15.0309	+	2.53210i	−0.515861	+	0.0869015i
$850$	−4.98222	+	46.8285i	−0.170889	+	1.60620i
$851$	1.90170	−	3.29383i	0.0651893	−	0.112911i
$852$	−31.2321	−	19.9613i	−1.06999	−	0.683864i
$853$	−3.05627	+	5.29361i	−0.104645	+	0.181250i	−0.913593	−	0.406630i	$-0.866704\pi$
$853$	−3.05627	+	5.29361i	−0.104645	+	0.181250i	0.808948	+	0.587880i	$0.200037\pi$
$854$	−16.2434	−	17.8187i	−0.555839	−	0.609743i
$855$	−49.8439	+	57.5911i	−1.70463	+	1.96957i
$856$	−34.9111	−	39.0720i	−1.19324	−	1.33545i
$857$	−21.2319			−0.725267			−0.362634	−	0.931932i	$-0.618122\pi$
$857$	−21.2319			−0.725267			−0.362634	+	0.931932i	$0.618122\pi$
$858$	−21.8651	+	14.4662i	−0.746461	+	0.493869i
$859$	−33.1672			−1.13165			−0.565825	−	0.824525i	$-0.691442\pi$
$859$	−33.1672			−1.13165			−0.565825	+	0.824525i	$0.691442\pi$
$860$	−56.3032	−	12.1177i	−1.91992	−	0.413210i
$861$	6.38854	+	12.0215i	0.217721	+	0.409691i
$862$	19.7721	+	2.10361i	0.673442	+	0.0716494i
$863$	−29.6428	−	17.1143i	−1.00905	−	0.582577i	−0.0981387	−	0.995173i	$-0.531289\pi$
$863$	−29.6428	−	17.1143i	−1.00905	−	0.582577i	−0.910914	+	0.412596i	$0.864622\pi$
$864$	−25.8754	+	13.9451i	−0.880298	+	0.474420i
$865$	−21.5743	−	37.3678i	−0.733549	−	1.27054i
$866$	−18.1094	+	24.8587i	−0.615382	+	0.844734i
$867$	14.9507	−	2.51859i	0.507753	−	0.0855357i
$868$	8.58734	+	11.6992i	0.291473	+	0.397096i
$869$	13.9436	+	24.1511i	0.473005	+	0.819269i
$870$	11.9578	−	23.9723i	0.405407	−	0.812737i
$871$		−	45.3967i		−	1.53821i
$872$	−5.83200	−	27.9626i	−0.197496	−	0.946934i
$873$	−8.71236	+	10.0665i	−0.294869	+	0.340699i
$874$	−6.50078	−	14.6512i	−0.219892	−	0.495584i
$875$	53.1830	+	47.1763i	1.79791	+	1.59485i
$876$	1.59178	−	35.2738i	0.0537813	−	1.19179i
$877$			2.17833i			0.0735570i	0.999323	+	0.0367785i	$0.0117096\pi$
$877$			2.17833i			0.0735570i	−0.999323	+	0.0367785i	$0.988290\pi$
$878$	−21.9347	−	2.33369i	−0.740260	−	0.0787583i
$879$	50.0637	+	18.6561i	1.68861	+	0.629255i
$880$	−26.0627	−	36.2595i	−0.878574	−	1.22231i
$881$	−35.1960			−1.18578			−0.592891	−	0.805283i	$-0.702014\pi$
$881$	−35.1960			−1.18578			−0.592891	+	0.805283i	$0.702014\pi$
$882$	−22.7176	−	19.1288i	−0.764941	−	0.644100i
$883$		−	27.8372i		−	0.936796i	−0.883518	−	0.468398i	$-0.844831\pi$
$883$		−	27.8372i		−	0.936796i	0.883518	−	0.468398i	$-0.155169\pi$
$884$	21.9303	+	4.71987i	0.737595	+	0.158747i
$885$	−20.8738	+	3.51639i	−0.701666	+	0.118202i
$886$	−0.298158	+	2.80242i	−0.0100168	+	0.0941493i
$887$	−14.0372			−0.471321			−0.235661	−	0.971835i	$-0.575725\pi$
$887$	−14.0372			−0.471321			−0.235661	+	0.971835i	$0.575725\pi$
$888$	−10.1287	−	1.54210i	−0.339897	−	0.0517495i
$889$	6.80143	−	7.66742i	0.228113	−	0.257157i
$890$	−23.3341	−	52.5895i	−0.782161	−	1.76280i
$891$	−22.9071	−	9.13952i	−0.767418	−	0.306185i
$892$	−2.50781	+	11.6522i	−0.0839678	+	0.390145i
$893$	26.9233			0.900955
$894$	2.69306	+	44.1676i	0.0900694	+	1.47718i
$895$	−21.9338	+	12.6635i	−0.733165	+	0.423293i
$896$	−27.3271	−	12.2160i	−0.912934	−	0.408106i
$897$	11.5287	+	4.29613i	0.384932	+	0.143444i
$898$	−18.1356	+	24.8948i	−0.605193	+	0.830749i
$899$	−6.37643	+	3.68144i	−0.212666	+	0.122783i
$900$	69.0597	−	8.45307i	2.30199	−	0.281769i
$901$	−17.9512	+	31.0923i	−0.598040	+	1.03584i
$902$	−1.21801	+	11.4482i	−0.0405553	+	0.381184i
$903$	−27.4667	−	17.1715i	−0.914035	−	0.571432i
$904$	9.52778	+	45.6828i	0.316889	+	1.51939i
$905$		−	66.0509i		−	2.19561i
$906$	−1.55388	−	25.4845i	−0.0516244	−	0.846667i
$907$			15.0820i			0.500790i	0.968144	+	0.250395i	$0.0805605\pi$
$907$			15.0820i			0.500790i	−0.968144	+	0.250395i	$0.919440\pi$
$908$	−21.4053	+	6.89474i	−0.710360	+	0.228810i
$909$	4.57739	+	0.879440i	0.151822	+	0.0291692i
$910$	43.9975	−	40.1079i	1.45850	−	1.32957i
$911$	39.9026	+	23.0378i	1.32203	+	0.763277i	0.984053	−	0.177876i	$-0.0569227\pi$
$911$	39.9026	+	23.0378i	1.32203	+	0.763277i	0.337981	+	0.941153i	$0.390256\pi$
$912$	−30.3867	+	30.6747i	−1.00621	+	1.01574i
$913$	−4.10018	−	2.36724i	−0.135696	−	0.0783443i
$914$	0.402913	−	3.78703i	0.0133272	−	0.125264i
$915$	42.6070	+	15.8774i	1.40854	+	0.524890i
$916$	16.6759	+	51.7716i	0.550986	+	1.71058i
$917$	−22.7817	−	20.2086i	−0.752317	−	0.667348i
$918$	8.11424	+	19.4801i	0.267810	+	0.642939i
$919$	−9.96012	+	17.2514i	−0.328554	+	0.569072i	−0.982225	−	0.187706i	$-0.939895\pi$
$919$	−9.96012	+	17.2514i	−0.328554	+	0.569072i	0.653671	+	0.756779i	$0.273228\pi$
$920$	−6.55164	+	19.9046i	−0.216001	+	0.656236i
$921$	−23.8008	−	28.8089i	−0.784263	−	0.949285i
$922$	4.32826	+	9.75487i	0.142544	+	0.321260i
$923$	36.1932	−	20.8961i	1.19131	−	0.687805i
$924$	−6.85594	−	24.1618i	−0.225544	−	0.794864i
$925$	21.0019	+	12.1254i	0.690537	+	0.398682i
$926$	−2.05389	+	19.3048i	−0.0674952	+	0.634396i
$927$	17.4456	+	3.35177i	0.572988	+	0.110086i
$928$	7.67691	−	13.1033i	0.252007	−	0.430136i
$929$	−21.8574	−	37.8581i	−0.717117	−	1.24208i	−0.962137	−	0.272566i	$-0.912128\pi$
$929$	−21.8574	−	37.8581i	−0.717117	−	1.24208i	0.245020	−	0.969518i	$-0.421206\pi$
$930$	−24.4900	−	12.2160i	−0.803060	−	0.400580i
$931$	−40.1122	−	17.1504i	−1.31463	−	0.562082i
$932$	−0.259717	+	1.20674i	−0.00850731	+	0.0395281i
$933$	−9.26570	+	1.56089i	−0.303346	+	0.0511014i
$934$	1.56054	+	3.51708i	0.0510624	+	0.115082i
$935$	−27.7634	+	16.0292i	−0.907959	+	0.524210i
$936$	−0.523699	−	33.1376i	−0.0171176	−	1.08314i
$937$		−	35.6517i		−	1.16469i	−0.812942	−	0.582345i	$-0.802135\pi$
$937$		−	35.6517i		−	1.16469i	0.812942	−	0.582345i	$-0.197865\pi$
$938$	41.4423	+	13.1844i	1.35314	+	0.430484i
$939$	−4.31068	−	1.60636i	−0.140674	−	0.0524217i
$940$	−26.0974	−	23.6189i	−0.851202	−	0.770363i
$941$	24.8080	+	14.3229i	0.808717	+	0.466913i	0.846510	−	0.532373i	$-0.178699\pi$
$941$	24.8080	+	14.3229i	0.808717	+	0.466913i	−0.0377931	+	0.999286i	$0.512033\pi$
$942$	−2.52014	−	1.25709i	−0.0821105	−	0.0409581i
$943$	4.67885	−	2.70134i	0.152364	−	0.0879677i
$944$	−11.9404	+	1.19348i	−0.388627	+	0.0388446i
$945$	54.5946	+	12.4919i	1.77596	+	0.406363i
$946$	−11.1103	−	25.0399i	−0.361225	−	0.814116i
$947$	10.0075	+	17.3335i	0.325199	+	0.563262i	0.981553	−	0.191192i	$-0.0612353\pi$
$947$	10.0075	+	17.3335i	0.325199	+	0.563262i	−0.656353	+	0.754454i	$0.727902\pi$
$948$	−35.2168	−	1.58921i	−1.14379	−	0.0516151i
$949$	34.4781	+	19.9059i	1.11921	+	0.646174i
$950$	93.4178	−	41.4497i	3.03087	−	1.34481i
$951$	−16.3008	+	43.7434i	−0.528591	+	1.41848i
$952$	−10.6778	+	18.6492i	−0.346071	+	0.604423i
$953$		−	31.6668i		−	1.02579i	−0.858452	−	0.512893i	$-0.828574\pi$
$953$		−	31.6668i		−	1.02579i	0.858452	−	0.512893i	$-0.171426\pi$
$954$	50.7384	+	15.4625i	1.64272	+	0.500617i
$955$	32.8335	+	56.8693i	1.06247	+	1.84025i
$956$	7.56332	+	6.84503i	0.244615	+	0.221384i
$957$	12.5653	−	2.11674i	0.406178	−	0.0684245i
$958$	−17.1801	−	12.5156i	−0.555064	−	0.404359i
$959$	2.33937	+	2.07515i	0.0755422	+	0.0670102i
$960$	56.3643	−	3.07640i	1.81915	−	0.0992904i
$961$	−11.7391	−	20.3326i	−0.378679	−	0.655892i
$962$	6.80187	−	9.33693i	0.219301	−	0.301035i
$963$	42.0221	+	36.3693i	1.35414	+	1.17198i
$964$	−24.4593	+	7.87844i	−0.787780	+	0.253747i
$965$	−39.3861	−	22.7396i	−1.26788	−	0.732013i
$966$	−7.27013	+	9.27674i	−0.233913	+	0.298474i
$967$	−13.3950	−	23.2007i	−0.430753	−	0.746085i	0.566186	−	0.824278i	$-0.308419\pi$
$967$	−13.3950	−	23.2007i	−0.430753	−	0.746085i	−0.996938	+	0.0781923i	$0.975085\pi$
$968$	−3.08671	+	9.37776i	−0.0992105	+	0.301413i
$969$	19.7431	+	23.8974i	0.634240	+	0.767694i
$970$	23.3695	−	10.3691i	0.750350	−	0.332932i
$971$	12.8786	+	7.43546i	0.413294	+	0.238615i	0.692204	−	0.721702i	$-0.256640\pi$
$971$	12.8786	+	7.43546i	0.413294	+	0.238615i	−0.278910	+	0.960317i	$0.589973\pi$
$972$	25.3293	−	18.1776i	0.812439	−	0.583047i
$973$	17.8464	+	3.65516i	0.572128	+	0.117179i
$974$	1.53041	−	14.3845i	0.0490373	−	0.460908i
$975$	−27.3927	+	73.5083i	−0.877267	+	2.35415i
$976$	23.4939	+	10.6040i	0.752020	+	0.339425i
$977$	38.3461	+	22.1391i	1.22680	+	0.708294i	0.966359	−	0.257196i	$-0.0827986\pi$
$977$	38.3461	+	22.1391i	1.22680	+	0.708294i	0.260441	+	0.965490i	$0.416132\pi$
$978$	22.8958	−	45.9003i	0.732127	−	1.46773i
$979$	13.6831	−	23.6997i	0.437312	−	0.757447i
$980$	23.8362	+	51.8133i	0.761419	+	1.65512i
$981$	9.92595	+	28.6249i	0.316911	+	0.913923i
$982$	0.562737	−	5.28924i	0.0179577	−	0.168786i
$983$	−24.7730			−0.790135			−0.395068	−	0.918652i	$-0.629279\pi$
$983$	−24.7730			−0.790135			−0.395068	+	0.918652i	$0.629279\pi$
$984$	−11.3649	−	9.09092i	−0.362299	−	0.289808i
$985$			21.2969i			0.678575i
$986$	−8.81233	−	6.41970i	−0.280642	−	0.204445i
$987$	−9.29035	−	17.4819i	−0.295715	−	0.556454i
$988$	−14.9258	−	46.3383i	−0.474852	−	1.47422i
$989$	−6.42765	+	11.1330i	−0.204387	+	0.354009i
$990$	32.3327	+	34.6102i	1.02760	+	1.09998i
$991$	19.4064	+	33.6129i	0.616466	+	1.06775i	0.990125	+	0.140184i	$0.0447695\pi$
$991$	19.4064	+	33.6129i	0.616466	+	1.06775i	−0.373660	+	0.927566i	$0.621897\pi$
$992$	−13.3863	−	7.84272i	−0.425015	−	0.249007i
$993$	33.9643	+	12.6567i	1.07782	+	0.401648i
$994$	8.56449	+	39.1092i	0.271649	+	1.24047i
$995$	34.0679	+	59.0074i	1.08003	+	1.87066i
$996$	5.31273	−	2.75576i	0.168340	−	0.0873197i
$997$	−23.7026			−0.750668			−0.375334	−	0.926890i	$-0.622472\pi$
$997$	−23.7026			−0.750668			−0.375334	+	0.926890i	$0.622472\pi$
$998$	2.11457	−	2.90267i	0.0669355	−	0.0918823i
$999$	10.8641	+	0.249066i	0.343724	+	0.00788010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.18	✓	184
7.3	odd	6		504.2.ca.a.101.80	yes	184
8.5	even	2	inner	504.2.y.a.173.50	yes	184
9.5	odd	6		504.2.ca.a.5.13	yes	184
56.45	odd	6		504.2.ca.a.101.13	yes	184
63.59	even	6	inner	504.2.y.a.437.50	yes	184
72.5	odd	6		504.2.ca.a.5.80	yes	184
504.437	even	6	inner	504.2.y.a.437.18	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.18	✓	184	1.1	even	1	trivial
504.2.y.a.173.50	yes	184	8.5	even	2	inner
504.2.y.a.437.18	yes	184	504.437	even	6	inner
504.2.y.a.437.50	yes	184	63.59	even	6	inner
504.2.ca.a.5.13	yes	184	9.5	odd	6
504.2.ca.a.5.80	yes	184	72.5	odd	6
504.2.ca.a.101.13	yes	184	56.45	odd	6
504.2.ca.a.101.80	yes	184	7.3	odd	6

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.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14306 - 0.832711i) q^{2} +(1.10317 + 1.33530i) q^{3} +(0.613184 + 1.90368i) q^{4} +4.07380i q^{5} +(-0.149078 - 2.44495i) q^{6} +(-1.75571 + 1.97926i) q^{7} +(0.884310 - 2.68663i) q^{8} +(-0.566029 + 2.94612i) q^{9} +O(q^{10})\)	\(q+(-1.14306 - 0.832711i) q^{2} +(1.10317 + 1.33530i) q^{3} +(0.613184 + 1.90368i) q^{4} +4.07380i q^{5} +(-0.149078 - 2.44495i) q^{6} +(-1.75571 + 1.97926i) q^{7} +(0.884310 - 2.68663i) q^{8} +(-0.566029 + 2.94612i) q^{9} +(3.39230 - 4.65661i) q^{10} +2.74034 q^{11} +(-1.86553 + 2.91887i) q^{12} +(-1.95290 - 3.38252i) q^{13} +(3.65504 - 0.800414i) q^{14} +(-5.43973 + 4.49410i) q^{15} +(-3.24801 + 2.33461i) q^{16} +(1.43584 + 2.48695i) q^{17} +(3.10027 - 2.89626i) q^{18} +(3.11606 - 5.39718i) q^{19} +(-7.75522 + 2.49799i) q^{20} +(-4.57975 - 0.160937i) q^{21} +(-3.13238 - 2.28191i) q^{22} +1.81864i q^{23} +(4.56299 - 1.78300i) q^{24} -11.5958 q^{25} +(-0.584376 + 5.49263i) q^{26} +(-4.55836 + 2.49426i) q^{27} +(-4.84446 - 2.12867i) q^{28} +(1.34231 - 2.32495i) q^{29} +(9.96023 - 0.607312i) q^{30} +(-2.37517 - 1.37130i) q^{31} +(5.65674 + 0.0360438i) q^{32} +(3.02306 + 3.65917i) q^{33} +(0.429655 - 4.03838i) q^{34} +(-8.06311 - 7.15243i) q^{35} +(-5.95555 + 0.728974i) q^{36} +(-1.81115 - 1.04567i) q^{37} +(-8.05614 + 3.57453i) q^{38} +(2.36228 - 6.33919i) q^{39} +(10.9448 + 3.60250i) q^{40} +(-1.48536 - 2.57272i) q^{41} +(5.10093 + 3.99757i) q^{42} +(6.12162 + 3.53432i) q^{43} +(1.68033 + 5.21674i) q^{44} +(-12.0019 - 2.30589i) q^{45} +(1.51440 - 2.07882i) q^{46} +(2.16004 + 3.74131i) q^{47} +(-6.70051 - 1.76158i) q^{48} +(-0.834935 - 6.95003i) q^{49} +(13.2548 + 9.65599i) q^{50} +(-1.73684 + 4.66081i) q^{51} +(5.24175 - 5.79180i) q^{52} +(6.25109 + 10.8272i) q^{53} +(7.28749 + 0.944712i) q^{54} +11.1636i q^{55} +(3.76495 + 6.46724i) q^{56} +(10.6444 - 1.79314i) q^{57} +(-3.47036 + 1.53981i) q^{58} +(2.59806 + 1.49999i) q^{59} +(-11.8909 - 7.59980i) q^{60} +(-3.22201 - 5.58068i) q^{61} +(1.57307 + 3.54531i) q^{62} +(-4.83735 - 6.29286i) q^{63} +(-6.43599 - 4.75163i) q^{64} +(13.7797 - 7.95571i) q^{65} +(-0.408523 - 6.70000i) q^{66} +(10.0657 + 5.81145i) q^{67} +(-3.85393 + 4.25835i) q^{68} +(-2.42842 + 2.00627i) q^{69} +(3.26073 + 14.8899i) q^{70} +10.7001i q^{71} +(7.41459 + 4.12599i) q^{72} +(-8.82742 + 5.09652i) q^{73} +(1.19952 + 2.70343i) q^{74} +(-12.7922 - 15.4839i) q^{75} +(12.1852 + 2.62253i) q^{76} +(-4.81126 + 5.42385i) q^{77} +(-7.97895 + 5.27899i) q^{78} +(5.08828 + 8.81316i) q^{79} +(-9.51076 - 13.2317i) q^{80} +(-8.35922 - 3.33518i) q^{81} +(-0.444474 + 4.17766i) q^{82} +(-1.49623 - 0.863849i) q^{83} +(-2.50186 - 8.81707i) q^{84} +(-10.1313 + 5.84934i) q^{85} +(-4.05433 - 9.13750i) q^{86} +(4.58530 - 0.772437i) q^{87} +(2.42331 - 7.36229i) q^{88} +(4.99319 - 8.64846i) q^{89} +(11.7988 + 12.6299i) q^{90} +(10.1236 + 2.07344i) q^{91} +(-3.46211 + 1.11516i) q^{92} +(-0.789119 - 4.68433i) q^{93} +(0.646362 - 6.07524i) q^{94} +(21.9870 + 12.6942i) q^{95} +(6.19222 + 7.59318i) q^{96} +(3.84317 + 2.21886i) q^{97} +(-4.83298 + 8.63958i) q^{98} +(-1.55111 + 8.07337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

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