LMFDB - Embedded newform 546.2.ch.a.305.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.24
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.31731 - 1.12458i) q^{3} +1.00000i q^{4} +(-0.258772 + 0.965749i) q^{5} +(-0.136279 - 1.72668i) q^{6} +(-0.443687 - 2.60828i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.470622 + 2.96286i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.31731 - 1.12458i) q^{3} +1.00000i q^{4} +(-0.258772 + 0.965749i) q^{5} +(-0.136279 - 1.72668i) q^{6} +(-0.443687 - 2.60828i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.470622 + 2.96286i) q^{9} +(-0.865867 + 0.499908i) q^{10} +(2.62764 + 0.704074i) q^{11} +(1.12458 - 1.31731i) q^{12} +(3.59766 - 0.238399i) q^{13} +(1.53060 - 2.15807i) q^{14} +(1.42695 - 0.981182i) q^{15} -1.00000 q^{16} +2.39192 q^{17} +(-1.76228 + 2.42784i) q^{18} +(-0.807382 - 3.01319i) q^{19} +(-0.965749 - 0.258772i) q^{20} +(-2.34876 + 3.93489i) q^{21} +(1.36017 + 2.35588i) q^{22} +6.02053 q^{23} +(1.72668 - 0.136279i) q^{24} +(3.46442 + 2.00018i) q^{25} +(2.71250 + 2.37536i) q^{26} +(2.71202 - 4.43226i) q^{27} +(2.60828 - 0.443687i) q^{28} +(2.49077 + 1.43804i) q^{29} +(1.70281 + 0.315204i) q^{30} +(-0.354443 - 1.32280i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.66963 - 3.88249i) q^{33} +(1.69134 + 1.69134i) q^{34} +(2.63376 + 0.246460i) q^{35} +(-2.96286 + 0.470622i) q^{36} +(0.770187 + 0.770187i) q^{37} +(1.55974 - 2.70155i) q^{38} +(-5.00734 - 3.73183i) q^{39} +(-0.499908 - 0.865867i) q^{40} +(-0.406096 + 0.108813i) q^{41} +(-4.44321 + 1.12156i) q^{42} +(-3.05357 + 1.76298i) q^{43} +(-0.704074 + 2.62764i) q^{44} +(-2.98316 - 0.312200i) q^{45} +(4.25716 + 4.25716i) q^{46} +(0.717315 + 0.192204i) q^{47} +(1.31731 + 1.12458i) q^{48} +(-6.60628 + 2.31452i) q^{49} +(1.03537 + 3.86406i) q^{50} +(-3.15090 - 2.68991i) q^{51} +(0.238399 + 3.59766i) q^{52} +(-2.12547 - 1.22714i) q^{53} +(5.05177 - 1.21639i) q^{54} +(-1.35992 + 2.35545i) q^{55} +(2.15807 + 1.53060i) q^{56} +(-2.32501 + 4.87728i) q^{57} +(0.744387 + 2.77809i) q^{58} +(7.69807 - 7.69807i) q^{59} +(0.981182 + 1.42695i) q^{60} +(-0.903521 + 1.56494i) q^{61} +(0.684731 - 1.18599i) q^{62} +(7.51916 - 2.54210i) q^{63} -1.00000i q^{64} +(-0.700739 + 3.53613i) q^{65} +(0.857618 - 4.63305i) q^{66} +(-0.116226 - 0.0311427i) q^{67} +2.39192i q^{68} +(-7.93091 - 6.77059i) q^{69} +(1.68808 + 2.03662i) q^{70} +(-3.68364 + 13.7475i) q^{71} +(-2.42784 - 1.76228i) q^{72} +(4.19031 - 1.12279i) q^{73} +1.08921i q^{74} +(-2.31435 - 6.53089i) q^{75} +(3.01319 - 0.807382i) q^{76} +(0.670575 - 7.16601i) q^{77} +(-0.901926 - 6.17953i) q^{78} +(-5.71760 - 9.90318i) q^{79} +(0.258772 - 0.965749i) q^{80} +(-8.55703 + 2.78877i) q^{81} +(-0.364096 - 0.210211i) q^{82} +(-7.50388 - 7.50388i) q^{83} +(-3.93489 - 2.34876i) q^{84} +(-0.618961 + 2.30999i) q^{85} +(-3.40581 - 0.912585i) q^{86} +(-1.66391 - 4.69543i) q^{87} +(-2.35588 + 1.36017i) q^{88} +(-7.22489 + 7.22489i) q^{89} +(-1.88865 - 2.33017i) q^{90} +(-2.21805 - 9.27795i) q^{91} +6.02053i q^{92} +(-1.02069 + 2.14114i) q^{93} +(0.371309 + 0.643127i) q^{94} +3.11891 q^{95} +(0.136279 + 1.72668i) q^{96} +(-4.73874 - 1.26974i) q^{97} +(-6.30796 - 3.03473i) q^{98} +(-0.849444 + 8.11667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.31731	−	1.12458i	−0.760550	−	0.649279i
$3$	−1.31731	−	1.12458i	−0.760550	−	0.649279i
$4$			1.00000i			0.500000i
$5$	−0.258772	+	0.965749i	−0.115726	+	0.431896i	−0.999340	−	0.0363200i	$-0.988436\pi$
$5$	−0.258772	+	0.965749i	−0.115726	+	0.431896i	0.883614	+	0.468216i	$0.155103\pi$
$6$	−0.136279	−	1.72668i	−0.0556358	−	0.704915i
$7$	−0.443687	−	2.60828i	−0.167698	−	0.985838i
$7$	−0.443687	−	2.60828i	−0.167698	−	0.985838i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.470622	+	2.96286i	0.156874	+	0.987619i
$10$	−0.865867	+	0.499908i	−0.273811	+	0.158085i
$11$	2.62764	+	0.704074i	0.792263	+	0.212286i	0.632184	−	0.774818i	$-0.282159\pi$
$11$	2.62764	+	0.704074i	0.792263	+	0.212286i	0.160079	+	0.987104i	$0.448825\pi$
$12$	1.12458	−	1.31731i	0.324639	−	0.380275i
$13$	3.59766	−	0.238399i	0.997812	−	0.0661200i
$13$	3.59766	−	0.238399i	0.997812	−	0.0661200i
$14$	1.53060	−	2.15807i	0.409070	−	0.576768i
$15$	1.42695	−	0.981182i	0.368437	−	0.253340i
$16$	−1.00000			−0.250000
$17$	2.39192			0.580126			0.290063	−	0.957008i	$-0.406324\pi$
$17$	2.39192			0.580126			0.290063	+	0.957008i	$0.406324\pi$
$18$	−1.76228	+	2.42784i	−0.415372	+	0.572246i
$19$	−0.807382	−	3.01319i	−0.185226	−	0.691273i	−0.994582	−	0.103955i	$-0.966850\pi$
$19$	−0.807382	−	3.01319i	−0.185226	−	0.691273i	0.809356	−	0.587319i	$-0.199816\pi$
$20$	−0.965749	−	0.258772i	−0.215948	−	0.0578631i
$21$	−2.34876	+	3.93489i	−0.512541	+	0.858663i
$22$	1.36017	+	2.35588i	0.289988	+	0.502275i
$23$	6.02053			1.25537			0.627683	−	0.778469i	$-0.284003\pi$
$23$	6.02053			1.25537			0.627683	+	0.778469i	$0.284003\pi$
$24$	1.72668	−	0.136279i	0.352457	−	0.0278179i
$25$	3.46442	+	2.00018i	0.692884	+	0.400037i
$26$	2.71250	+	2.37536i	0.531966	+	0.465846i
$27$	2.71202	−	4.43226i	0.521929	−	0.852989i
$28$	2.60828	−	0.443687i	0.492919	−	0.0838489i
$29$	2.49077	+	1.43804i	0.462524	+	0.267038i	0.713105	−	0.701057i	$-0.247288\pi$
$29$	2.49077	+	1.43804i	0.462524	+	0.267038i	−0.250581	+	0.968096i	$0.580622\pi$
$30$	1.70281	+	0.315204i	0.310888	+	0.0575482i
$31$	−0.354443	−	1.32280i	−0.0636598	−	0.237582i	0.926764	−	0.375645i	$-0.122579\pi$
$31$	−0.354443	−	1.32280i	−0.0636598	−	0.237582i	−0.990423	+	0.138064i	$0.955912\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.66963	−	3.88249i	−0.464723	−	0.675854i
$34$	1.69134	+	1.69134i	0.290063	+	0.290063i
$35$	2.63376	+	0.246460i	0.445187	+	0.0416593i
$36$	−2.96286	+	0.470622i	−0.493809	+	0.0784370i
$37$	0.770187	+	0.770187i	0.126618	+	0.126618i	0.767576	−	0.640958i	$-0.221463\pi$
$37$	0.770187	+	0.770187i	0.126618	+	0.126618i	−0.640958	+	0.767576i	$0.721463\pi$
$38$	1.55974	−	2.70155i	0.253024	−	0.438250i
$39$	−5.00734	−	3.73183i	−0.801816	−	0.597570i
$40$	−0.499908	−	0.865867i	−0.0790425	−	0.136906i
$41$	−0.406096	+	0.108813i	−0.0634216	+	0.0169938i	−0.290390	−	0.956908i	$-0.593785\pi$
$41$	−0.406096	+	0.108813i	−0.0634216	+	0.0169938i	0.226969	+	0.973902i	$0.427118\pi$
$42$	−4.44321	+	1.12156i	−0.685602	+	0.173061i
$43$	−3.05357	+	1.76298i	−0.465665	+	0.268852i	−0.714423	−	0.699714i	$-0.753311\pi$
$43$	−3.05357	+	1.76298i	−0.465665	+	0.268852i	0.248758	+	0.968566i	$0.419978\pi$
$44$	−0.704074	+	2.62764i	−0.106143	+	0.396131i
$45$	−2.98316	−	0.312200i	−0.444703	−	0.0465401i
$46$	4.25716	+	4.25716i	0.627683	+	0.627683i
$47$	0.717315	+	0.192204i	0.104631	+	0.0280358i	0.310755	−	0.950490i	$-0.399418\pi$
$47$	0.717315	+	0.192204i	0.104631	+	0.0280358i	−0.206124	+	0.978526i	$0.566085\pi$
$48$	1.31731	+	1.12458i	0.190138	+	0.162320i
$49$	−6.60628	+	2.31452i	−0.943755	+	0.330646i
$50$	1.03537	+	3.86406i	0.146424	+	0.546460i
$51$	−3.15090	−	2.68991i	−0.441215	−	0.376663i
$52$	0.238399	+	3.59766i	0.0330600	+	0.498906i
$53$	−2.12547	−	1.22714i	−0.291956	−	0.168561i	0.346867	−	0.937914i	$-0.387245\pi$
$53$	−2.12547	−	1.22714i	−0.291956	−	0.168561i	−0.638824	+	0.769353i	$0.720579\pi$
$54$	5.05177	−	1.21639i	0.687459	−	0.165530i
$55$	−1.35992	+	2.35545i	−0.183371	+	0.317608i
$56$	2.15807	+	1.53060i	0.288384	+	0.204535i
$57$	−2.32501	+	4.87728i	−0.307955	+	0.646012i
$58$	0.744387	+	2.77809i	0.0977428	+	0.364781i
$59$	7.69807	−	7.69807i	1.00220	−	1.00220i	0.00220530	−	0.999998i	$-0.499298\pi$
$59$	7.69807	−	7.69807i	1.00220	−	1.00220i	0.999998	−	0.00220530i	$-0.000701968\pi$
$60$	0.981182	+	1.42695i	0.126670	+	0.184218i
$61$	−0.903521	+	1.56494i	−0.115684	+	0.200371i	−0.918053	−	0.396458i	$-0.870239\pi$
$61$	−0.903521	+	1.56494i	−0.115684	+	0.200371i	0.802369	+	0.596828i	$0.203573\pi$
$62$	0.684731	−	1.18599i	0.0869609	−	0.150621i
$63$	7.51916	−	2.54210i	0.947325	−	0.320274i
$64$		−	1.00000i		−	0.125000i
$65$	−0.700739	+	3.53613i	−0.0869160	+	0.438603i
$66$	0.857618	−	4.63305i	0.105565	−	0.570288i
$67$	−0.116226	−	0.0311427i	−0.0141993	−	0.00380469i	0.251712	−	0.967802i	$-0.419006\pi$
$67$	−0.116226	−	0.0311427i	−0.0141993	−	0.00380469i	−0.265912	+	0.963997i	$0.585673\pi$
$68$			2.39192i			0.290063i
$69$	−7.93091	−	6.77059i	−0.954770	−	0.815083i
$70$	1.68808	+	2.03662i	0.201764	+	0.243423i
$71$	−3.68364	+	13.7475i	−0.437168	+	1.63153i	0.298657	+	0.954361i	$0.403461\pi$
$71$	−3.68364	+	13.7475i	−0.437168	+	1.63153i	−0.735825	+	0.677172i	$0.763205\pi$
$72$	−2.42784	−	1.76228i	−0.286123	−	0.207686i
$73$	4.19031	−	1.12279i	0.490439	−	0.131413i	−0.00512035	−	0.999987i	$-0.501630\pi$
$73$	4.19031	−	1.12279i	0.490439	−	0.131413i	0.495559	+	0.868574i	$0.334963\pi$
$74$			1.08921i			0.126618i
$75$	−2.31435	−	6.53089i	−0.267238	−	0.754123i
$76$	3.01319	−	0.807382i	0.345637	−	0.0926131i
$77$	0.670575	−	7.16601i	0.0764191	−	0.816643i
$78$	−0.901926	−	6.17953i	−0.102123	−	0.699693i
$79$	−5.71760	−	9.90318i	−0.643281	−	1.11419i	−0.984696	−	0.174282i	$-0.944240\pi$
$79$	−5.71760	−	9.90318i	−0.643281	−	1.11419i	0.341415	−	0.939913i	$-0.389094\pi$
$80$	0.258772	−	0.965749i	0.0289315	−	0.107974i
$81$	−8.55703	+	2.78877i	−0.950781	+	0.309864i
$82$	−0.364096	−	0.210211i	−0.0402077	−	0.0232139i
$83$	−7.50388	−	7.50388i	−0.823658	−	0.823658i	0.162972	−	0.986631i	$-0.447892\pi$
$83$	−7.50388	−	7.50388i	−0.823658	−	0.823658i	−0.986631	+	0.162972i	$0.947892\pi$
$84$	−3.93489	−	2.34876i	−0.429331	−	0.256271i
$85$	−0.618961	+	2.30999i	−0.0671357	+	0.250554i
$86$	−3.40581	−	0.912585i	−0.367258	−	0.0984066i
$87$	−1.66391	−	4.69543i	−0.178390	−	0.503403i
$88$	−2.35588	+	1.36017i	−0.251137	+	0.144994i
$89$	−7.22489	+	7.22489i	−0.765836	+	0.765836i	−0.977371	−	0.211534i	$-0.932154\pi$
$89$	−7.22489	+	7.22489i	−0.765836	+	0.765836i	0.211534	+	0.977371i	$0.432154\pi$
$90$	−1.88865	−	2.33017i	−0.199081	−	0.245622i
$91$	−2.21805	−	9.27795i	−0.232514	−	0.972593i
$92$			6.02053i			0.627683i
$93$	−1.02069	+	2.14114i	−0.105840	+	0.222026i
$94$	0.371309	+	0.643127i	0.0382977	+	0.0663335i
$95$	3.11891			0.319994
$96$	0.136279	+	1.72668i	0.0139090	+	0.176229i
$97$	−4.73874	−	1.26974i	−0.481146	−	0.128923i	0.0100903	−	0.999949i	$-0.496788\pi$
$97$	−4.73874	−	1.26974i	−0.481146	−	0.128923i	−0.491236	+	0.871026i	$0.663455\pi$
$98$	−6.30796	−	3.03473i	−0.637200	−	0.306554i
$99$	−0.849444	+	8.11667i	−0.0853723	+	0.815756i
$100$	−2.00018	+	3.46442i	−0.200018	+	0.346442i
$101$	2.21803	+	3.84175i	0.220703	+	0.382268i	0.955022	−	0.296537i	$-0.0958316\pi$
$101$	2.21803	+	3.84175i	0.220703	+	0.382268i	−0.734319	+	0.678805i	$0.762498\pi$
$102$	−0.325969	−	4.13008i	−0.0322758	−	0.408939i
$103$	6.30061	−	3.63766i	0.620817	−	0.358429i	−0.156370	−	0.987699i	$-0.549979\pi$
$103$	6.30061	−	3.63766i	0.620817	−	0.358429i	0.777187	+	0.629270i	$0.216646\pi$
$104$	−2.37536	+	2.71250i	−0.232923	+	0.265983i
$105$	−3.19232	−	3.28655i	−0.311539	−	0.320734i
$106$	−0.635216	−	2.37066i	−0.0616976	−	0.230259i
$107$			19.8288i			1.91692i	0.285230	+	0.958459i	$0.407930\pi$
$107$			19.8288i			1.91692i	−0.285230	+	0.958459i	$0.592070\pi$
$108$	4.43226	+	2.71202i	0.426494	+	0.260965i
$109$	−3.83882	−	14.3267i	−0.367693	−	1.37225i	−0.863734	−	0.503948i	$-0.831880\pi$
$109$	−3.83882	−	14.3267i	−0.367693	−	1.37225i	0.496041	−	0.868299i	$-0.334786\pi$
$110$	−2.62716	+	0.703945i	−0.250490	+	0.0671185i
$111$	−0.148437	−	1.88072i	−0.0140890	−	0.178510i
$112$	0.443687	+	2.60828i	0.0419245	+	0.246460i
$113$	−3.61436	+	2.08675i	−0.340010	+	0.196305i	−0.660277	−	0.751022i	$-0.729561\pi$
$113$	−3.61436	+	2.08675i	−0.340010	+	0.196305i	0.320266	+	0.947328i	$0.396228\pi$
$114$	−5.09279	+	1.80473i	−0.476983	+	0.169028i
$115$	−1.55794	+	5.81432i	−0.145279	+	0.542188i
$116$	−1.43804	+	2.49077i	−0.133519	+	0.231262i
$117$	2.39948	+	10.5472i	0.221832	+	0.975085i
$118$	10.8867			1.00220
$119$	−1.06126	−	6.23880i	−0.0972858	−	0.571910i
$120$	−0.315204	+	1.70281i	−0.0287741	+	0.155444i
$121$	−3.11751	−	1.79990i	−0.283410	−	0.163627i
$122$	−1.74547	+	0.467697i	−0.158027	+	0.0423433i
$123$	0.657325	+	0.313348i	0.0592690	+	0.0282537i
$124$	1.32280	−	0.354443i	0.118791	−	0.0318299i
$125$	−6.36305	+	6.36305i	−0.569129	+	0.569129i
$126$	7.11438	+	3.51931i	0.633799	+	0.313525i
$127$	2.36521	+	1.36556i	0.209879	+	0.121173i	0.601255	−	0.799057i	$-0.294668\pi$
$127$	2.36521	+	1.36556i	0.209879	+	0.121173i	−0.391376	+	0.920231i	$0.628001\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	6.00512	+	1.11160i	0.528721	+	0.0978710i
$130$	−2.99592	+	2.00492i	−0.262759	+	0.175843i
$131$	−12.6239	+	7.28842i	−1.10296	+	0.636793i	−0.936996	−	0.349340i	$-0.886406\pi$
$131$	−12.6239	+	7.28842i	−1.10296	+	0.636793i	−0.165961	+	0.986132i	$0.553073\pi$
$132$	3.88249	−	2.66963i	0.337927	−	0.232362i
$133$	−7.50103	+	3.44279i	−0.650422	+	0.298528i
$134$	−0.0601631	−	0.104205i	−0.00519730	−	0.00900198i
$135$	3.57866	+	3.76608i	0.308002	+	0.324132i
$136$	−1.69134	+	1.69134i	−0.145031	+	0.145031i
$137$	6.26105	−	6.26105i	0.534917	−	0.534917i	−0.387114	−	0.922032i	$-0.626528\pi$
$137$	6.26105	−	6.26105i	0.534917	−	0.534917i	0.922032	+	0.387114i	$0.126528\pi$
$138$	−0.820474	−	10.3955i	−0.0698434	−	0.884926i
$139$	−11.2557	−	19.4954i	−0.954695	−	1.65358i	−0.735065	−	0.677996i	$-0.762849\pi$
$139$	−11.2557	−	19.4954i	−0.954695	−	1.65358i	−0.219629	−	0.975583i	$-0.570485\pi$
$140$	−0.246460	+	2.63376i	−0.0208296	+	0.222593i
$141$	−0.728778	−	1.05987i	−0.0613742	−	0.0892574i
$142$	−12.3257	+	7.11625i	−1.03435	+	0.597182i
$143$	9.62120	+	1.90659i	0.804566	+	0.159437i
$144$	−0.470622	−	2.96286i	−0.0392185	−	0.246905i
$145$	−2.03333	+	2.03333i	−0.168859	+	0.168859i
$146$	3.75693	+	2.16906i	0.310926	+	0.179513i
$147$	11.3054	+	4.38037i	0.932455	+	0.361287i
$148$	−0.770187	+	0.770187i	−0.0633090	+	0.0633090i
$149$	−21.6763	+	5.80816i	−1.77580	+	0.475823i	−0.989807	−	0.142418i	$-0.954512\pi$
$149$	−21.6763	+	5.80816i	−1.77580	+	0.475823i	−0.785989	+	0.618241i	$0.787846\pi$
$150$	2.98155	−	6.25453i	0.243443	−	0.510680i
$151$	11.9716	−	3.20779i	0.974237	−	0.261046i	0.263621	−	0.964626i	$-0.415083\pi$
$151$	11.9716	−	3.20779i	0.974237	−	0.261046i	0.710616	+	0.703580i	$0.248416\pi$
$152$	2.70155	+	1.55974i	0.219125	+	0.126512i
$153$	1.12569	+	7.08691i	0.0910067	+	0.572943i
$154$	5.54131	−	4.59297i	0.446531	−	0.370112i
$155$	1.36921			0.109978
$156$	3.73183	−	5.00734i	0.298785	−	0.400908i
$157$	−2.86148	+	4.95622i	−0.228371	+	0.395550i	−0.957325	−	0.289012i	$-0.906673\pi$
$157$	−2.86148	+	4.95622i	−0.228371	+	0.395550i	0.728955	+	0.684562i	$0.240007\pi$
$158$	2.95965	−	11.0456i	0.235457	−	0.878738i
$159$	1.41989	+	4.00680i	0.112604	+	0.317760i
$160$	0.865867	−	0.499908i	0.0684528	−	0.0395212i
$161$	−2.67123	−	15.7032i	−0.210522	−	1.23759i
$162$	−8.02269	−	4.07877i	−0.630322	−	0.320459i
$163$	22.5241	−	6.03532i	1.76422	−	0.472723i	0.776658	−	0.629923i	$-0.216913\pi$
$163$	22.5241	−	6.03532i	1.76422	−	0.472723i	0.987567	+	0.157200i	$0.0502468\pi$
$164$	−0.108813	−	0.406096i	−0.00849688	−	0.0317108i
$165$	4.44033	−	1.57352i	0.345679	−	0.122498i
$166$		−	10.6121i		−	0.823658i
$167$	1.91833	+	7.15930i	0.148445	+	0.554003i	0.999578	+	0.0290533i	$0.00924925\pi$
$167$	1.91833	+	7.15930i	0.148445	+	0.554003i	−0.851133	+	0.524950i	$0.824084\pi$
$168$	−1.12156	−	4.44321i	−0.0865303	−	0.342801i
$169$	12.8863	−	1.71536i	0.991256	−	0.131951i
$170$	−2.07108	+	1.19574i	−0.158845	+	0.0917091i
$171$	8.54768	−	3.81023i	0.653657	−	0.291376i
$172$	−1.76298	−	3.05357i	−0.134426	−	0.232832i
$173$	8.83631	−	15.3049i	0.671812	−	1.16361i	−0.305577	−	0.952167i	$-0.598849\pi$
$173$	8.83631	−	15.3049i	0.671812	−	1.16361i	0.977390	−	0.211446i	$-0.0678172\pi$
$174$	2.14360	−	4.49673i	0.162506	−	0.340897i
$175$	3.67993	−	9.92364i	0.278176	−	0.750157i
$176$	−2.62764	−	0.704074i	−0.198066	−	0.0530716i
$177$	−18.7979	+	1.48363i	−1.41293	+	0.111517i
$178$	−10.2175			−0.765836
$179$	−4.83492	−	8.37432i	−0.361379	−	0.625926i	0.626809	−	0.779173i	$-0.284360\pi$
$179$	−4.83492	−	8.37432i	−0.361379	−	0.625926i	−0.988188	+	0.153247i	$0.951027\pi$
$180$	0.312200	−	2.98316i	0.0232700	−	0.222352i
$181$			5.02844i			0.373761i	0.982383	+	0.186880i	$0.0598377\pi$
$181$			5.02844i			0.373761i	−0.982383	+	0.186880i	$0.940162\pi$
$182$	4.99210	−	8.12889i	0.370039	−	0.602554i
$183$	2.95013	−	1.04544i	0.218080	−	0.0772808i
$184$	−4.25716	+	4.25716i	−0.313842	+	0.313842i
$185$	−0.943109	+	0.544504i	−0.0693388	+	0.0400328i
$186$	−2.23575	+	0.792280i	−0.163933	+	0.0580928i
$187$	6.28510	+	1.68409i	0.459612	+	0.123153i
$188$	−0.192204	+	0.717315i	−0.0140179	+	0.0523156i
$189$	−12.7639	−	5.10719i	−0.928436	−	0.371493i
$190$	2.20540	+	2.20540i	0.159997	+	0.159997i
$191$	19.9816	+	11.5364i	1.44582	+	0.834745i	0.998229	−	0.0594925i	$-0.0189482\pi$
$191$	19.9816	+	11.5364i	1.44582	+	0.834745i	0.447592	+	0.894238i	$0.352282\pi$
$192$	−1.12458	+	1.31731i	−0.0811599	+	0.0950688i
$193$	−0.188846	+	0.704783i	−0.0135934	+	0.0507314i	−0.972389	−	0.233364i	$-0.925027\pi$
$193$	−0.188846	+	0.704783i	−0.0135934	+	0.0507314i	0.958796	+	0.284095i	$0.0916933\pi$
$194$	−2.45295	−	4.24863i	−0.176112	−	0.305034i
$195$	4.89977	−	3.87014i	0.350879	−	0.277147i
$196$	−2.31452	−	6.60628i	−0.165323	−	0.471877i
$197$	12.8434	−	3.44137i	0.915051	−	0.245187i	0.229582	−	0.973289i	$-0.426264\pi$
$197$	12.8434	−	3.44137i	0.915051	−	0.245187i	0.685469	+	0.728102i	$0.259597\pi$
$198$	−6.34000	+	5.13870i	−0.450564	+	0.365192i
$199$			8.74434i			0.619870i	0.950758	+	0.309935i	$0.100307\pi$
$199$			8.74434i			0.619870i	−0.950758	+	0.309935i	$0.899693\pi$
$200$	−3.86406	+	1.03537i	−0.273230	+	0.0732118i
$201$	0.118083	+	0.171731i	0.00832897	+	0.0121129i
$202$	−1.14814	+	4.28491i	−0.0807828	+	0.301485i
$203$	2.64571	−	7.13467i	0.185692	−	0.500755i
$204$	2.68991	−	3.15090i	0.188332	−	0.220607i
$205$		−	0.420345i		−	0.0293581i
$206$	7.02742	+	1.88299i	0.489623	+	0.131194i
$207$	2.83339	+	17.8380i	0.196935	+	1.23982i
$208$	−3.59766	+	0.238399i	−0.249453	+	0.0165300i
$209$		−	8.48603i		−	0.586991i
$210$	0.0666300	−	4.58125i	0.00459791	−	0.316136i
$211$	−8.87901	+	15.3789i	−0.611256	+	1.05873i	0.379773	+	0.925080i	$0.376002\pi$
$211$	−8.87901	+	15.3789i	−0.611256	+	1.05873i	−0.991029	+	0.133647i	$0.957331\pi$
$212$	1.22714	−	2.12547i	0.0842805	−	0.145978i
$213$	20.3128	−	13.9672i	1.39181	−	0.957019i
$214$	−14.0210	+	14.0210i	−0.958459	+	0.958459i
$215$	−0.912418	−	3.40519i	−0.0622264	−	0.232232i
$216$	1.21639	+	5.05177i	0.0827649	+	0.343730i
$217$	−3.29297	+	1.51140i	−0.223542	+	0.102600i
$218$	7.41604	−	12.8450i	0.502277	−	0.869970i
$219$	−6.78262	−	3.23329i	−0.458327	−	0.218486i
$220$	−2.35545	−	1.35992i	−0.158804	−	0.0916856i
$221$	8.60532	−	0.570231i	0.578856	−	0.0383579i
$222$	1.22491	−	1.43483i	0.0822103	−	0.0962993i
$223$	0.888970	+	3.31768i	0.0595299	+	0.222168i	0.989282	−	0.146018i	$-0.0466456\pi$
$223$	0.888970	+	3.31768i	0.0595299	+	0.222168i	−0.929752	+	0.368186i	$0.879979\pi$
$224$	−1.53060	+	2.15807i	−0.102268	+	0.144192i
$225$	−4.29582	+	11.2059i	−0.286388	+	0.747060i
$226$	−4.03129	−	1.08018i	−0.268158	−	0.0718526i
$227$	12.3677	+	12.3677i	0.820873	+	0.820873i	0.986233	−	0.165360i	$-0.0528787\pi$
$227$	12.3677	+	12.3677i	0.820873	+	0.820873i	−0.165360	+	0.986233i	$0.552879\pi$
$228$	−4.87728	−	2.32501i	−0.323006	−	0.153978i
$229$	−1.31243	+	4.89806i	−0.0867279	+	0.323673i	−0.995636	−	0.0933240i	$-0.970251\pi$
$229$	−1.31243	+	4.89806i	−0.0867279	+	0.323673i	0.908908	+	0.416997i	$0.136917\pi$
$230$	−5.21298	+	3.00971i	−0.343733	+	0.198455i
$231$	−8.94214	+	8.68576i	−0.588350	+	0.571481i
$232$	−2.77809	+	0.744387i	−0.182390	+	0.0488714i
$233$	12.0628	+	20.8933i	0.790258	+	1.36877i	0.925807	+	0.377996i	$0.123387\pi$
$233$	12.0628	+	20.8933i	0.790258	+	1.36877i	−0.135549	+	0.990771i	$0.543280\pi$
$234$	−5.76128	+	9.15465i	−0.376626	+	0.598458i
$235$	−0.371241	+	0.643009i	−0.0242171	+	0.0419453i
$236$	7.69807	+	7.69807i	0.501101	+	0.501101i
$237$	−3.60509	+	19.4755i	−0.234176	+	1.26507i
$238$	3.66107	−	5.16193i	0.237312	−	0.334598i
$239$	−13.7771	−	13.7771i	−0.891170	−	0.891170i	0.103464	−	0.994633i	$-0.467007\pi$
$239$	−13.7771	−	13.7771i	−0.891170	−	0.891170i	−0.994633	+	0.103464i	$0.967007\pi$
$240$	−1.42695	+	0.981182i	−0.0921091	+	0.0633350i
$241$	6.68381	+	6.68381i	0.430542	+	0.430542i	0.888813	−	0.458270i	$-0.151531\pi$
$241$	6.68381	+	6.68381i	0.430542	+	0.430542i	−0.458270	+	0.888813i	$0.651531\pi$
$242$	−0.931695	−	3.47713i	−0.0598916	−	0.223519i
$243$	14.4085	+	5.94941i	0.924305	+	0.381655i
$244$	−1.56494	−	0.903521i	−0.100185	−	0.0578420i
$245$	−0.525728	−	6.97894i	−0.0335875	−	0.445868i
$246$	0.243228	+	0.686370i	0.0155077	+	0.0437613i
$247$	−3.62303	−	10.6480i	−0.230528	−	0.677513i
$248$	1.18599	+	0.684731i	0.0753104	+	0.0434805i
$249$	1.44621	+	18.3237i	0.0916499	+	1.16122i
$250$	−8.99872			−0.569129
$251$	−11.7459	−	20.3444i	−0.741393	−	1.28413i	−0.951861	−	0.306529i	$-0.900832\pi$
$251$	−11.7459	−	20.3444i	−0.741393	−	1.28413i	0.210468	−	0.977601i	$-0.432501\pi$
$252$	2.54210	+	7.51916i	0.160137	+	0.473662i
$253$	15.8198	+	4.23890i	0.994581	+	0.266497i
$254$	0.706864	+	2.63805i	0.0443526	+	0.165526i
$255$	3.41315	−	2.34691i	0.213740	−	0.146969i
$256$	1.00000			0.0625000
$257$	−2.71554			−0.169390			−0.0846952	−	0.996407i	$-0.526992\pi$
$257$	−2.71554			−0.169390			−0.0846952	+	0.996407i	$0.526992\pi$
$258$	3.46024	+	5.03228i	0.215425	+	0.313296i
$259$	1.66714	−	2.35059i	0.103591	−	0.146058i
$260$	−3.53613	−	0.700739i	−0.219301	−	0.0434580i
$261$	−3.08851	+	8.05656i	−0.191174	+	0.498688i
$262$	−14.0802	−	3.77277i	−0.869875	−	0.233082i
$263$	−23.2354	+	13.4150i	−1.43276	+	0.827202i	−0.997330	−	0.0730218i	$-0.976736\pi$
$263$	−23.2354	+	13.4150i	−1.43276	+	0.827202i	−0.435426	+	0.900224i	$0.643402\pi$
$264$	4.63305	+	0.857618i	0.285144	+	0.0527827i
$265$	1.73512	−	1.73512i	0.106588	−	0.106588i
$266$	−7.73845	−	2.86961i	−0.474475	−	0.175947i
$267$	17.6424	−	1.39244i	1.07970	−	0.0852159i
$268$	0.0311427	−	0.116226i	0.00190234	−	0.00709964i
$269$			14.3365i			0.874109i	0.899435	+	0.437055i	$0.143978\pi$
$269$			14.3365i			0.874109i	−0.899435	+	0.437055i	$0.856022\pi$
$270$	−0.132527	+	5.19351i	−0.00806534	+	0.316067i
$271$	11.0330	+	11.0330i	0.670208	+	0.670208i	0.957764	−	0.287556i	$-0.0928428\pi$
$271$	11.0330	+	11.0330i	0.670208	+	0.670208i	−0.287556	+	0.957764i	$0.592843\pi$
$272$	−2.39192			−0.145031
$273$	−7.51197	+	14.7163i	−0.454645	+	0.890673i
$274$	8.85446			0.534917
$275$	7.69497	+	7.69497i	0.464024	+	0.464024i
$276$	6.77059	−	7.93091i	0.407542	−	0.477385i
$277$		−	6.79670i		−	0.408374i	−0.978932	−	0.204187i	$-0.934545\pi$
$277$		−	6.79670i		−	0.408374i	0.978932	−	0.204187i	$-0.0654551\pi$
$278$	5.82637	−	21.7443i	0.349442	−	1.30414i
$279$	3.75245	−	1.67270i	0.224653	−	0.100142i
$280$	−2.03662	+	1.68808i	−0.121712	+	0.100882i
$281$	13.1459	−	13.1459i	0.784217	−	0.784217i	−0.196322	−	0.980539i	$-0.562900\pi$
$281$	13.1459	−	13.1459i	0.784217	−	0.784217i	0.980539	+	0.196322i	$0.0628999\pi$
$282$	0.234120	−	1.26477i	0.0139416	−	0.0753158i
$283$	−27.7672	+	16.0314i	−1.65059	+	0.952968i	−0.673760	+	0.738950i	$0.735322\pi$
$283$	−27.7672	+	16.0314i	−1.65059	+	0.952968i	−0.976830	+	0.214018i	$0.931345\pi$
$284$	−13.7475	−	3.68364i	−0.815766	−	0.218584i
$285$	−4.10858	−	3.50748i	−0.243371	−	0.207765i
$286$	5.45505	+	8.15138i	0.322564	+	0.482001i
$287$	0.463995	+	1.01093i	0.0273888	+	0.0596736i
$288$	1.76228	−	2.42784i	0.103843	−	0.143062i
$289$	−11.2787			−0.663454
$290$	−2.87556			−0.168859
$291$	4.81446	+	7.00175i	0.282229	+	0.410450i
$292$	1.12279	+	4.19031i	0.0657063	+	0.245219i
$293$	−29.4602	−	7.89384i	−1.72108	−	0.461163i	−0.742985	−	0.669308i	$-0.766591\pi$
$293$	−29.4602	−	7.89384i	−1.72108	−	0.461163i	−0.978098	+	0.208145i	$0.933257\pi$
$294$	4.89674	+	11.0915i	0.285584	+	0.646871i
$295$	5.44236	+	9.42644i	0.316866	+	0.548829i
$296$	−1.08921			−0.0633090
$297$	10.2469	−	9.73691i	0.594583	−	0.564993i
$298$	−19.4345	−	11.2205i	−1.12581	−	0.649986i
$299$	21.6598	−	1.43529i	1.25262	−	0.0830048i
$300$	6.53089	−	2.31435i	0.377061	−	0.133619i
$301$	5.95318	+	7.18236i	0.343135	+	0.413984i
$302$	10.7335	+	6.19697i	0.617641	+	0.356595i
$303$	1.39852	−	7.55515i	0.0803431	−	0.434032i
$304$	0.807382	+	3.01319i	0.0463065	+	0.172818i
$305$	−1.27754	−	1.27754i	−0.0731516	−	0.0731516i
$306$	−4.21522	+	5.80719i	−0.240968	+	0.331975i
$307$	−19.5251	−	19.5251i	−1.11436	−	1.11436i	−0.992554	−	0.121801i	$-0.961133\pi$
$307$	−19.5251	−	19.5251i	−1.11436	−	1.11436i	−0.121801	−	0.992554i	$-0.538867\pi$
$308$	7.16601	+	0.670575i	0.408322	+	0.0382096i
$309$	−12.3907	−	2.29363i	−0.704883	−	0.130480i
$310$	0.968179	+	0.968179i	0.0549888	+	0.0549888i
$311$	−0.849686	+	1.47170i	−0.0481813	+	0.0834525i	−0.889110	−	0.457693i	$-0.848676\pi$
$311$	−0.849686	+	1.47170i	−0.0481813	+	0.0834525i	0.840929	+	0.541146i	$0.182009\pi$
$312$	6.17953	−	0.901926i	0.349847	−	0.0510615i
$313$	13.0269	+	22.5633i	0.736325	+	1.27535i	0.954140	+	0.299362i	$0.0967737\pi$
$313$	13.0269	+	22.5633i	0.736325	+	1.27535i	−0.217815	+	0.975990i	$0.569893\pi$
$314$	−5.52795	+	1.48121i	−0.311960	+	0.0835895i
$315$	0.509282	+	7.91944i	0.0286948	+	0.446210i
$316$	9.90318	−	5.71760i	0.557097	−	0.321640i
$317$	1.99671	−	7.45184i	0.112147	−	0.418537i	−0.886911	−	0.461940i	$-0.847153\pi$
$317$	1.99671	−	7.45184i	0.112147	−	0.418537i	0.999058	+	0.0434034i	$0.0138201\pi$
$318$	−1.82923	+	3.83725i	−0.102578	+	0.215182i
$319$	5.53234	+	5.53234i	0.309752	+	0.309752i
$320$	0.965749	+	0.258772i	0.0539870	+	0.0144658i
$321$	22.2991	−	26.1207i	1.24461	−	1.45791i
$322$	9.21503	−	12.9927i	0.513533	−	0.724056i
$323$	−1.93119	−	7.20731i	−0.107454	−	0.401025i
$324$	−2.78877	−	8.55703i	−0.154932	−	0.475391i
$325$	12.9406	+	6.37007i	0.717818	+	0.353348i
$326$	20.1946	+	11.6593i	1.11847	+	0.645751i
$327$	−11.0546	+	23.1898i	−0.611322	+	1.28240i
$328$	0.210211	−	0.364096i	0.0116070	−	0.0201038i
$329$	0.183059	−	1.95624i	0.0100924	−	0.107851i
$330$	4.25243	+	2.02714i	0.234089	+	0.111591i
$331$	−8.83538	−	32.9741i	−0.485636	−	1.81242i	−0.577178	−	0.816618i	$-0.695846\pi$
$331$	−8.83538	−	32.9741i	−0.485636	−	1.81242i	0.0915418	−	0.995801i	$-0.470820\pi$
$332$	7.50388	−	7.50388i	0.411829	−	0.411829i
$333$	−1.91949	+	2.64442i	−0.105187	+	0.144913i
$334$	−3.70593	+	6.41885i	−0.202779	+	0.351224i
$335$	0.0601520	−	0.104186i	0.00328646	−	0.00569231i
$336$	2.34876	−	3.93489i	0.128135	−	0.214666i
$337$		−	10.9669i		−	0.597406i	−0.954346	−	0.298703i	$-0.903446\pi$
$337$		−	10.9669i		−	0.597406i	0.954346	−	0.298703i	$-0.0965539\pi$
$338$	10.3250	+	7.89907i	0.561603	+	0.429653i
$339$	7.10797	+	1.31575i	0.386052	+	0.0714616i
$340$	−2.30999	−	0.618961i	−0.125277	−	0.0335679i
$341$		−	3.72539i		−	0.201741i
$342$	8.73836	+	3.34988i	0.472516	+	0.181141i
$343$	8.96805	+	16.2041i	0.484229	+	0.874941i
$344$	0.912585	−	3.40581i	0.0492033	−	0.183629i
$345$	8.59098	−	5.90724i	0.462523	−	0.318035i
$346$	17.0704	−	4.57401i	0.917713	−	0.245900i
$347$		−	25.9795i		−	1.39465i	−0.716754	−	0.697327i	$-0.754373\pi$
$347$		−	25.9795i		−	1.39465i	0.716754	−	0.697327i	$-0.245627\pi$
$348$	4.69543	−	1.66391i	0.251701	−	0.0891952i
$349$	−22.9606	+	6.15227i	−1.22905	+	0.329324i	−0.814210	−	0.580570i	$-0.802830\pi$
$349$	−22.9606	+	6.15227i	−1.22905	+	0.329324i	−0.414842	+	0.909893i	$0.636163\pi$
$350$	9.61918	−	4.41497i	0.514167	−	0.235990i
$351$	8.70030	−	16.5923i	0.464387	−	0.885632i
$352$	−1.36017	−	2.35588i	−0.0724971	−	0.125569i
$353$	−5.04647	+	18.8337i	−0.268596	+	1.00242i	0.691416	+	0.722457i	$0.256987\pi$
$353$	−5.04647	+	18.8337i	−0.268596	+	1.00242i	−0.960012	+	0.279958i	$0.909679\pi$
$354$	−14.3412	−	12.2430i	−0.762226	−	0.650709i
$355$	−12.3234	−	7.11495i	−0.654061	−	0.377622i
$356$	−7.22489	−	7.22489i	−0.382918	−	0.382918i
$357$	−5.61804	+	9.41193i	−0.297338	+	0.498132i
$358$	2.50274	−	9.34034i	0.132274	−	0.493652i
$359$	−14.5356	−	3.89480i	−0.767160	−	0.205560i	−0.146043	−	0.989278i	$-0.546654\pi$
$359$	−14.5356	−	3.89480i	−0.767160	−	0.205560i	−0.621116	+	0.783718i	$0.713321\pi$
$360$	2.33017	−	1.88865i	0.122811	−	0.0995407i
$361$	8.02703	−	4.63441i	0.422475	−	0.243916i
$362$	−3.55564	+	3.55564i	−0.186880	+	0.186880i
$363$	2.08260	+	5.87693i	0.109308	+	0.308459i
$364$	9.27795	−	2.21805i	0.486296	−	0.116257i
$365$			4.33733i			0.227026i
$366$	2.82529	+	1.34682i	0.147680	+	0.0703996i
$367$	11.9462	+	20.6914i	0.623585	+	1.08008i	0.988813	+	0.149162i	$0.0476578\pi$
$367$	11.9462	+	20.6914i	0.623585	+	1.08008i	−0.365228	+	0.930918i	$0.619009\pi$
$368$	−6.02053			−0.313842
$369$	−0.513516	−	1.15199i	−0.0267326	−	0.0599704i
$370$	−1.05190	−	0.281856i	−0.0546858	−	0.0146530i
$371$	−2.25769	+	6.08831i	−0.117214	+	0.316089i
$372$	−2.14114	−	1.02069i	−0.111013	−	0.0529201i
$373$	−9.33247	+	16.1643i	−0.483217	+	0.836956i	−0.999814	−	0.0192724i	$-0.993865\pi$
$373$	−9.33247	+	16.1643i	−0.483217	+	0.836956i	0.516598	+	0.856228i	$0.327198\pi$
$374$	3.25341	+	5.63507i	0.168230	+	0.291382i
$375$	15.5379	−	1.22634i	0.802375	−	0.0633279i
$376$	−0.643127	+	0.371309i	−0.0331667	+	0.0191488i
$377$	9.30376	+	4.57980i	0.479168	+	0.235872i
$378$	−5.41410	−	12.6368i	−0.278471	−	0.649965i
$379$	−6.24281	−	23.2985i	−0.320672	−	1.19676i	−0.918592	−	0.395207i	$-0.870673\pi$
$379$	−6.24281	−	23.2985i	−0.320672	−	1.19676i	0.597921	−	0.801555i	$-0.295994\pi$
$380$			3.11891i			0.159997i
$381$	−1.58004	−	4.45874i	−0.0809479	−	0.228428i
$382$	5.97168	+	22.2866i	0.305538	+	1.14028i
$383$	−33.3679	+	8.94090i	−1.70502	+	0.456859i	−0.974195	−	0.225707i	$-0.927531\pi$
$383$	−33.3679	+	8.94090i	−1.70502	+	0.456859i	−0.730825	+	0.682565i	$0.760864\pi$
$384$	−1.72668	+	0.136279i	−0.0881143	+	0.00695448i
$385$	6.74705	+	2.50197i	0.343861	+	0.127512i
$386$	−0.631891	+	0.364823i	−0.0321624	+	0.0185690i
$387$	−6.66053	−	8.21759i	−0.338574	−	0.417723i
$388$	1.26974	−	4.73874i	0.0644613	−	0.240573i
$389$	2.31745	−	4.01394i	0.117499	−	0.203515i	−0.801277	−	0.598294i	$-0.795846\pi$
$389$	2.31745	−	4.01394i	0.117499	−	0.203515i	0.918776	+	0.394779i	$0.129179\pi$
$390$	6.20126	+	0.728052i	0.314013	+	0.0368663i
$391$	14.4006			0.728271
$392$	3.03473	−	6.30796i	0.153277	−	0.318600i
$393$	24.8261	+	4.59553i	1.25231	+	0.231814i
$394$	11.5150	+	6.64821i	0.580119	+	0.334932i
$395$	11.0435	−	2.95911i	0.555661	−	0.148889i
$396$	−8.11667	−	0.849444i	−0.407878	−	0.0426862i
$397$	−25.0585	+	6.71440i	−1.25765	+	0.336986i	−0.825287	−	0.564713i	$-0.808987\pi$
$397$	−25.0585	+	6.71440i	−1.25765	+	0.336986i	−0.432363	+	0.901700i	$0.642320\pi$
$398$	−6.18318	+	6.18318i	−0.309935	+	0.309935i
$399$	13.7529	+	3.90030i	0.688507	+	0.195259i
$400$	−3.46442	−	2.00018i	−0.173221	−	0.100009i
$401$	3.93609	−	3.93609i	0.196559	−	0.196559i	−0.601964	−	0.798523i	$-0.705615\pi$
$401$	3.93609	−	3.93609i	0.196559	−	0.196559i	0.798523	+	0.601964i	$0.205615\pi$
$402$	−0.0379343	+	0.204930i	−0.00189199	+	0.0102210i
$403$	−1.59052	−	4.67448i	−0.0792294	−	0.232853i
$404$	−3.84175	+	2.21803i	−0.191134	+	0.110351i
$405$	−0.478937	−	8.98560i	−0.0237986	−	0.446498i
$406$	6.91577	−	3.17417i	0.343224	−	0.157532i
$407$	1.48150	+	2.56604i	0.0734354	+	0.127194i
$408$	4.13008	−	0.325969i	0.204470	−	0.0161379i
$409$	28.0275	−	28.0275i	1.38587	−	1.38587i	0.552083	−	0.833789i	$-0.313833\pi$
$409$	28.0275	−	28.0275i	1.38587	−	1.38587i	0.833789	−	0.552083i	$-0.186167\pi$
$410$	0.297229	−	0.297229i	0.0146791	−	0.0146791i
$411$	−15.2888	+	1.20668i	−0.754142	+	0.0595212i
$412$	3.63766	+	6.30061i	0.179215	+	0.310409i
$413$	−23.4943	−	16.6632i	−1.15608	−	0.819943i
$414$	−10.6098	+	14.6169i	−0.521445	+	0.718379i
$415$	9.18866	−	5.30508i	0.451054	−	0.260416i
$416$	−2.71250	−	2.37536i	−0.132991	−	0.116461i
$417$	−7.09698	+	38.3395i	−0.347541	+	1.87749i
$418$	6.00053	−	6.00053i	0.293496	−	0.293496i
$419$	−0.209157	−	0.120757i	−0.0102180	−	0.00589935i	0.494882	−	0.868960i	$-0.335211\pi$
$419$	−0.209157	−	0.120757i	−0.0102180	−	0.00589935i	−0.505100	+	0.863061i	$0.668544\pi$
$420$	3.28655	−	3.19232i	0.160367	−	0.155769i
$421$	6.40219	−	6.40219i	0.312024	−	0.312024i	−0.533669	−	0.845693i	$-0.679187\pi$
$421$	6.40219	−	6.40219i	0.312024	−	0.312024i	0.845693	+	0.533669i	$0.179187\pi$
$422$	−17.1529	+	4.59611i	−0.834992	+	0.223735i
$423$	−0.231888	+	2.21576i	−0.0112748	+	0.107734i
$424$	2.37066	−	0.635216i	0.115129	−	0.0308488i
$425$	8.28661	+	4.78428i	0.401960	+	0.232072i
$426$	24.2396	+	4.48697i	1.17441	+	0.217394i
$427$	4.48270	+	1.66229i	0.216933	+	0.0804441i
$428$	−19.8288			−0.958459
$429$	−10.5300	−	13.3314i	−0.508393	−	0.643647i
$430$	1.76266	−	3.05301i	0.0850028	−	0.147229i
$431$	0.795097	−	2.96734i	0.0382985	−	0.142932i	−0.944129	−	0.329576i	$-0.893094\pi$
$431$	0.795097	−	2.96734i	0.0382985	−	0.142932i	0.982428	+	0.186644i	$0.0597610\pi$
$432$	−2.71202	+	4.43226i	−0.130482	+	0.213247i
$433$	17.7654	−	10.2569i	0.853750	−	0.492913i	−0.00816416	−	0.999967i	$-0.502599\pi$
$433$	17.7654	−	10.2569i	0.853750	−	0.492913i	0.861914	+	0.507054i	$0.169265\pi$
$434$	−3.39720	−	1.25976i	−0.163071	−	0.0604706i
$435$	4.96518	−	0.391880i	0.238062	−	0.0187892i
$436$	14.3267	−	3.83882i	0.686124	−	0.183846i
$437$	−4.86087	−	18.1410i	−0.232527	−	0.867802i
$438$	−2.50975	−	7.08232i	−0.119921	−	0.338406i
$439$			20.2834i			0.968075i	0.875047	+	0.484038i	$0.160830\pi$
$439$			20.2834i			0.968075i	−0.875047	+	0.484038i	$0.839170\pi$
$440$	−0.703945	−	2.62716i	−0.0335593	−	0.125245i
$441$	−9.96666	−	18.4842i	−0.474603	−	0.880200i
$442$	6.48809	+	5.68166i	0.308607	+	0.270249i
$443$	26.0451	−	15.0372i	1.23744	−	0.714437i	0.268870	−	0.963176i	$-0.413350\pi$
$443$	26.0451	−	15.0372i	1.23744	−	0.714437i	0.968570	+	0.248740i	$0.0800164\pi$
$444$	1.88072	−	0.148437i	0.0892548	−	0.00704449i
$445$	−5.10783	−	8.84702i	−0.242134	−	0.419389i
$446$	−1.71736	+	2.97455i	−0.0813193	+	0.140849i
$447$	35.0863	+	16.7257i	1.65952	+	0.791099i
$448$	−2.60828	+	0.443687i	−0.123230	+	0.0209622i
$449$	−25.8278	−	6.92055i	−1.21889	−	0.326601i	−0.408646	−	0.912693i	$-0.633999\pi$
$449$	−25.8278	−	6.92055i	−1.21889	−	0.326601i	−0.810244	+	0.586092i	$0.800666\pi$
$450$	−10.9614	+	4.88617i	−0.516724	+	0.230336i
$451$	−1.14369			−0.0538541
$452$	−2.08675	−	3.61436i	−0.0981525	−	0.170005i
$453$	−19.3778	−	9.23744i	−0.910448	−	0.434013i
$454$			17.4906i			0.820873i
$455$	9.53413	+	0.258793i	0.446967	+	0.0121324i
$456$	−1.80473	−	5.09279i	−0.0845141	−	0.238492i
$457$	−1.89243	+	1.89243i	−0.0885243	+	0.0885243i	−0.749982	−	0.661458i	$-0.769938\pi$
$457$	−1.89243	+	1.89243i	−0.0885243	+	0.0885243i	0.661458	+	0.749982i	$0.269938\pi$
$458$	−4.39148	+	2.53542i	−0.205200	+	0.118473i
$459$	6.48694	−	10.6016i	0.302785	−	0.494841i
$460$	−5.81432	−	1.55794i	−0.271094	−	0.0726394i
$461$	0.317785	−	1.18599i	0.0148007	−	0.0552371i	−0.958131	−	0.286332i	$-0.907564\pi$
$461$	0.317785	−	1.18599i	0.0148007	−	0.0552371i	0.972931	+	0.231095i	$0.0742307\pi$
$462$	−12.4648	−	0.181289i	−0.579915	−	0.00843432i
$463$	0.583009	+	0.583009i	0.0270947	+	0.0270947i	0.720524	−	0.693430i	$-0.243901\pi$
$463$	0.583009	+	0.583009i	0.0270947	+	0.0270947i	−0.693430	+	0.720524i	$0.743901\pi$
$464$	−2.49077	−	1.43804i	−0.115631	−	0.0667595i
$465$	−1.80368	−	1.53979i	−0.0836436	−	0.0714062i
$466$	−6.24415	+	23.3035i	−0.289254	+	1.07951i
$467$	−12.3655	−	21.4176i	−0.572206	−	0.991089i	−0.996339	−	0.0854895i	$-0.972755\pi$
$467$	−12.3655	−	21.4176i	−0.572206	−	0.991089i	0.424133	−	0.905600i	$-0.360579\pi$
$468$	−10.5472	+	2.39948i	−0.487542	+	0.110916i
$469$	−0.0296610	+	0.316968i	−0.00136962	+	0.0146362i
$470$	−0.717183	+	0.192169i	−0.0330812	+	0.00886408i
$471$	9.34315	−	3.31092i	0.430510	−	0.152559i
$472$			10.8867i			0.501101i
$473$	−9.26494	+	2.48253i	−0.426003	+	0.114147i
$474$	−16.3204	+	11.2221i	−0.749623	+	0.515447i
$475$	3.22982	−	12.0539i	0.148194	−	0.553069i
$476$	6.23880	−	1.06126i	0.285955	−	0.0486429i
$477$	2.63555	−	6.87500i	0.120674	−	0.314784i
$478$		−	19.4838i		−	0.891170i
$479$	−33.5692	−	8.99484i	−1.53382	−	0.410985i	−0.609554	−	0.792745i	$-0.708651\pi$
$479$	−33.5692	−	8.99484i	−1.53382	−	0.410985i	−0.924261	+	0.381760i	$0.875318\pi$
$480$	−1.70281	−	0.315204i	−0.0777221	−	0.0143870i
$481$	2.95448	+	2.58726i	0.134713	+	0.117969i
$482$			9.45234i			0.430542i
$483$	−14.1408	+	23.6901i	−0.643427	+	1.07794i
$484$	1.79990	−	3.11751i	0.0818135	−	0.141705i
$485$	2.45250	−	4.24786i	0.111362	−	0.192885i
$486$	5.98147	+	14.3952i	0.271325	+	0.652980i
$487$	14.4968	−	14.4968i	0.656912	−	0.656912i	−0.297736	−	0.954648i	$-0.596231\pi$
$487$	14.4968	−	14.4968i	0.656912	−	0.656912i	0.954648	+	0.297736i	$0.0962315\pi$
$488$	−0.467697	−	1.74547i	−0.0211717	−	0.0790137i
$489$	−36.4585	−	17.3799i	−1.64871	−	0.785944i
$490$	4.56311	−	5.30660i	0.206140	−	0.239728i
$491$	−9.58871	+	16.6081i	−0.432732	+	0.749514i	−0.997107	−	0.0760042i	$-0.975784\pi$
$491$	−9.58871	+	16.6081i	−0.432732	+	0.749514i	0.564375	+	0.825518i	$0.309117\pi$
$492$	−0.313348	+	0.657325i	−0.0141268	+	0.0296345i
$493$	5.95771	+	3.43969i	0.268322	+	0.154916i
$494$	4.96738	−	10.0911i	0.223493	−	0.454021i
$495$	−7.61885	−	2.92071i	−0.342442	−	0.131276i
$496$	0.354443	+	1.32280i	0.0159150	+	0.0593954i
$497$	37.4919	+	3.50838i	1.68174	+	0.157372i
$498$	−11.9342	+	13.9794i	−0.534784	+	0.626434i
$499$	−19.3527	−	5.18555i	−0.866348	−	0.232137i	−0.201840	−	0.979418i	$-0.564692\pi$
$499$	−19.3527	−	5.18555i	−0.866348	−	0.232137i	−0.664508	+	0.747281i	$0.731359\pi$
$500$	−6.36305	−	6.36305i	−0.284564	−	0.284564i
$501$	5.52419	−	11.5884i	0.246803	−	0.517729i
$502$	6.08011	−	22.6913i	0.271369	−	1.01276i
$503$	−28.1802	+	16.2699i	−1.25649	+	0.725437i	−0.972391	−	0.233357i	$-0.925029\pi$
$503$	−28.1802	+	16.2699i	−1.25649	+	0.725437i	−0.284103	+	0.958794i	$0.591696\pi$
$504$	−3.51931	+	7.11438i	−0.156763	+	0.316900i
$505$	−4.28413	+	1.14793i	−0.190641	+	0.0510821i
$506$	8.18892	+	14.1836i	0.364042	+	0.630539i
$507$	−18.9044	−	12.2321i	−0.839573	−	0.543247i
$508$	−1.36556	+	2.36521i	−0.0605867	+	0.104939i
$509$	7.11266	+	7.11266i	0.315263	+	0.315263i	0.846944	−	0.531681i	$-0.178440\pi$
$509$	7.11266	+	7.11266i	0.315263	+	0.315263i	−0.531681	+	0.846944i	$0.678440\pi$
$510$	4.07297	+	0.753944i	0.180354	+	0.0333852i
$511$	−4.78774	−	10.4313i	−0.211797	−	0.461456i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−15.5449	−	4.59332i	−0.686323	−	0.202800i
$514$	−1.92017	−	1.92017i	−0.0846952	−	0.0846952i
$515$	1.88265	+	7.02613i	0.0829593	+	0.309608i
$516$	−1.11160	+	6.00512i	−0.0489355	+	0.264361i
$517$	1.74952	+	1.01009i	0.0769437	+	0.0444235i
$518$	2.84096	−	0.483267i	0.124825	−	0.0212336i
$519$	−28.8519	+	10.2242i	−1.26646	+	0.448793i
$520$	−2.00492	−	2.99592i	−0.0879217	−	0.131380i
$521$	9.70219	+	5.60156i	0.425060	+	0.245409i	0.697240	−	0.716838i	$-0.254411\pi$
$521$	9.70219	+	5.60156i	0.425060	+	0.245409i	−0.272180	+	0.962246i	$0.587744\pi$
$522$	−7.88075	+	3.51294i	−0.344931	+	0.153757i
$523$	25.7922			1.12781			0.563906	−	0.825839i	$-0.309298\pi$
$523$	25.7922			1.12781			0.563906	+	0.825839i	$0.309298\pi$
$524$	−7.28842	−	12.6239i	−0.318396	−	0.551479i
$525$	−16.0076	+	8.93414i	−0.698628	+	0.389918i
$526$	−25.9157	−	6.94410i	−1.12998	−	0.302777i
$527$	−0.847799	−	3.16403i	−0.0369307	−	0.137827i
$528$	2.66963	+	3.88249i	0.116181	+	0.168963i
$529$	13.2468			0.575946
$530$	2.45384			0.106588
$531$	26.4311	+	19.1854i	1.14701	+	0.832575i
$532$	−3.44279	−	7.50103i	−0.149264	−	0.325211i
$533$	−1.43506	+	0.488286i	−0.0621592	+	0.0211500i
$534$	13.4597	+	11.4905i	0.582457	+	0.497241i
$535$	−19.1496	−	5.13112i	−0.827909	−	0.221838i
$536$	0.104205	−	0.0601631i	0.00450099	−	0.00259865i
$537$	−3.04853	+	16.4689i	−0.131554	+	0.710684i
$538$	−10.1374	+	10.1374i	−0.437055	+	0.437055i
$539$	−18.9885	+	1.43042i	−0.817894	+	0.0616124i
$540$	−3.76608	+	3.57866i	−0.162066	+	0.154001i
$541$	−8.11996	+	30.3041i	−0.349104	+	1.30288i	0.538639	+	0.842537i	$0.318939\pi$
$541$	−8.11996	+	30.3041i	−0.349104	+	1.30288i	−0.887743	+	0.460339i	$0.847728\pi$
$542$			15.6030i			0.670208i
$543$	5.65490	−	6.62402i	0.242675	−	0.284264i
$544$	−1.69134	−	1.69134i	−0.0725157	−	0.0725157i
$545$	14.8294			0.635220
$546$	−15.7178	+	5.09425i	−0.672659	+	0.218014i
$547$	−34.3963			−1.47068			−0.735340	−	0.677699i	$-0.762977\pi$
$547$	−34.3963			−1.47068			−0.735340	+	0.677699i	$0.762977\pi$
$548$	6.26105	+	6.26105i	0.267459	+	0.267459i
$549$	−5.06192	−	1.94051i	−0.216038	−	0.0828188i
$550$			10.8823i			0.464024i
$551$	2.32210	−	8.66620i	0.0989249	−	0.369193i
$552$	10.3955	−	0.820474i	0.442463	−	0.0349217i
$553$	−23.2935	+	19.3070i	−0.990539	+	0.821019i
$554$	4.80600	−	4.80600i	0.204187	−	0.204187i
$555$	1.85471	+	0.343323i	0.0787281	+	0.0145733i
$556$	19.4954	−	11.2557i	0.826790	−	0.477347i
$557$	−5.45470	−	1.46158i	−0.231123	−	0.0619293i	0.141398	−	0.989953i	$-0.454840\pi$
$557$	−5.45470	−	1.46158i	−0.231123	−	0.0619293i	−0.372522	+	0.928023i	$0.621507\pi$
$558$	3.83616	+	1.47061i	0.162398	+	0.0622557i
$559$	−10.5654	+	7.07057i	−0.446869	+	0.299053i
$560$	−2.63376	−	0.246460i	−0.111297	−	0.0104148i
$561$	−6.38554	−	9.28659i	−0.269598	−	0.392080i
$562$	18.5911			0.784217
$563$	−33.6191			−1.41688			−0.708438	−	0.705773i	$-0.750600\pi$
$563$	−33.6191			−1.41688			−0.708438	+	0.705773i	$0.750600\pi$
$564$	1.05987	−	0.728778i	0.0446287	−	0.0306871i
$565$	−1.07998	−	4.03056i	−0.0454353	−	0.169567i
$566$	−30.9703	−	8.29847i	−1.30178	−	0.348811i
$567$	11.0705	+	21.0818i	0.464919	+	0.885353i
$568$	−7.11625	−	12.3257i	−0.298591	−	0.517175i
$569$	17.5200			0.734475			0.367237	−	0.930127i	$-0.380304\pi$
$569$	17.5200			0.734475			0.367237	+	0.930127i	$0.380304\pi$
$570$	−0.425044	−	5.38537i	−0.0178031	−	0.225568i
$571$	−26.9908	−	15.5831i	−1.12953	−	0.652134i	−0.185712	−	0.982604i	$-0.559459\pi$
$571$	−26.9908	−	15.5831i	−1.12953	−	0.652134i	−0.943816	+	0.330470i	$0.892793\pi$
$572$	−1.90659	+	9.62120i	−0.0797186	+	0.402283i
$573$	−13.3484	−	37.6681i	−0.557638	−	1.57361i
$574$	−0.386745	+	1.04293i	−0.0161424	+	0.0435312i
$575$	20.8576	+	12.0422i	0.869823	+	0.502193i
$576$	2.96286	−	0.470622i	0.123452	−	0.0196093i
$577$	−7.26401	−	27.1097i	−0.302405	−	1.12859i	−0.935156	−	0.354235i	$-0.884741\pi$
$577$	−7.26401	−	27.1097i	−0.302405	−	1.12859i	0.632752	−	0.774355i	$-0.281925\pi$
$578$	−7.97526	−	7.97526i	−0.331727	−	0.331727i
$579$	1.04136	−	0.716046i	0.0432773	−	0.0297579i
$580$	−2.03333	−	2.03333i	−0.0844294	−	0.0844294i
$581$	−16.2429	+	22.9016i	−0.673868	+	0.950120i
$582$	−1.54664	+	8.35533i	−0.0641105	+	0.346339i
$583$	−4.72098	−	4.72098i	−0.195523	−	0.195523i
$584$	−2.16906	+	3.75693i	−0.0897565	+	0.155463i
$585$	−10.8068	−	0.412009i	−0.446807	−	0.0170345i
$586$	−15.2497	−	26.4133i	−0.629960	−	1.09112i
$587$	31.1188	−	8.33825i	1.28441	−	0.344156i	0.448875	−	0.893595i	$-0.351825\pi$
$587$	31.1188	−	8.33825i	1.28441	−	0.344156i	0.835534	+	0.549438i	$0.185158\pi$
$588$	−4.38037	+	11.3054i	−0.180644	+	0.466227i
$589$	−3.69967	+	2.13601i	−0.152442	+	0.0880127i
$590$	−2.81717	+	10.5138i	−0.115981	+	0.432847i
$591$	−20.7888	−	9.91008i	−0.855137	−	0.407646i
$592$	−0.770187	−	0.770187i	−0.0316545	−	0.0316545i
$593$	−35.2590	−	9.44763i	−1.44791	−	0.387967i	−0.552617	−	0.833436i	$-0.686371\pi$
$593$	−35.2590	−	9.44763i	−1.44791	−	0.387967i	−0.895298	+	0.445468i	$0.853037\pi$
$594$	14.1307	+	0.360584i	0.579788	+	0.0147949i
$595$	6.29974	+	0.589512i	0.258264	+	0.0241676i
$596$	−5.80816	−	21.6763i	−0.237911	−	0.887898i
$597$	9.83375	−	11.5190i	0.402468	−	0.471442i
$598$	16.3307	+	14.3009i	0.667812	+	0.584807i
$599$	33.3012	+	19.2265i	1.36065	+	0.785572i	0.989711	−	0.143084i	$-0.0457019\pi$
$599$	33.3012	+	19.2265i	1.36065	+	0.785572i	0.370941	+	0.928656i	$0.379035\pi$
$600$	6.25453	+	2.98155i	0.255340	+	0.121721i
$601$	3.79158	−	6.56721i	0.154662	−	0.267882i	−0.778274	−	0.627925i	$-0.783905\pi$
$601$	3.79158	−	6.56721i	0.154662	−	0.267882i	0.932936	+	0.360043i	$0.117238\pi$
$602$	−0.869166	+	9.28823i	−0.0354245	+	0.378560i
$603$	0.0375727	−	0.359018i	0.00153008	−	0.0146203i
$604$	3.20779	+	11.9716i	0.130523	+	0.487118i
$605$	2.54497	−	2.54497i	0.103468	−	0.103468i
$606$	6.33120	−	4.35339i	0.257187	−	0.176844i
$607$	−12.8583	+	22.2711i	−0.521900	+	0.903958i	0.477775	+	0.878482i	$0.341443\pi$
$607$	−12.8583	+	22.2711i	−0.521900	+	0.903958i	−0.999675	+	0.0254758i	$0.991890\pi$
$608$	−1.55974	+	2.70155i	−0.0632559	+	0.109562i
$609$	−11.5088	+	6.42326i	−0.466358	+	0.260284i
$610$		−	1.80671i		−	0.0731516i
$611$	2.62648	+	0.520478i	0.106256	+	0.0210563i
$612$	−7.08691	+	1.12569i	−0.286471	+	0.0455033i
$613$	16.8054	+	4.50299i	0.678763	+	0.181874i	0.581699	−	0.813404i	$-0.302388\pi$
$613$	16.8054	+	4.50299i	0.678763	+	0.181874i	0.0970638	+	0.995278i	$0.469055\pi$
$614$		−	27.6127i		−	1.11436i
$615$	−0.472713	+	0.553725i	−0.0190616	+	0.0223284i
$616$	4.59297	+	5.54131i	0.185056	+	0.223266i
$617$	−6.86571	+	25.6232i	−0.276403	+	1.03155i	0.678492	+	0.734607i	$0.262634\pi$
$617$	−6.86571	+	25.6232i	−0.276403	+	1.03155i	−0.954895	+	0.296942i	$0.904033\pi$
$618$	−7.13972	−	10.3834i	−0.287202	−	0.417682i
$619$	−34.5242	+	9.25074i	−1.38765	+	0.371819i	−0.873892	−	0.486119i	$-0.838412\pi$
$619$	−34.5242	+	9.25074i	−1.38765	+	0.371819i	−0.513753	+	0.857938i	$0.671745\pi$
$620$			1.36921i			0.0549888i
$621$	16.3278	−	26.6845i	0.655213	−	1.07081i
$622$	−1.64147	+	0.439830i	−0.0658169	+	0.0176356i
$623$	22.0501	+	15.6390i	0.883420	+	0.626562i
$624$	5.00734	+	3.73183i	0.200454	+	0.149393i
$625$	5.50238	+	9.53040i	0.220095	+	0.381216i
$626$	−6.74323	+	25.1661i	−0.269514	+	1.00584i
$627$	−9.54326	+	11.1788i	−0.381121	+	0.446436i
$628$	−4.95622	−	2.86148i	−0.197775	−	0.114185i
$629$	1.84222	+	1.84222i	0.0734543	+	0.0734543i
$630$	−5.23977	+	5.96001i	−0.208758	+	0.237452i
$631$	−1.50154	+	5.60383i	−0.0597754	+	0.223085i	−0.989352	−	0.145545i	$-0.953506\pi$
$631$	−1.50154	+	5.60383i	−0.0597754	+	0.223085i	0.929576	+	0.368630i	$0.120173\pi$
$632$	11.0456	+	2.95965i	0.439369	+	0.117729i
$633$	28.9913	−	10.2736i	1.15230	−	0.408340i
$634$	6.68113	−	3.85735i	0.265342	−	0.153195i
$635$	−1.93083	+	1.93083i	−0.0766228	+	0.0766228i
$636$	−4.00680	+	1.41989i	−0.158880	+	0.0563022i
$637$	−23.2154	+	9.90180i	−0.919827	+	0.392323i
$638$			7.82392i			0.309752i
$639$	−42.4656	−	4.44420i	−1.67991	−	0.175810i
$640$	0.499908	+	0.865867i	0.0197606	+	0.0342264i
$641$	3.15937			0.124787			0.0623937	−	0.998052i	$-0.480127\pi$
$641$	3.15937			0.124787			0.0623937	+	0.998052i	$0.480127\pi$
$642$	34.2379	−	2.70225i	1.35126	−	0.106649i
$643$	−6.54863	−	1.75470i	−0.258253	−	0.0691986i	0.127370	−	0.991855i	$-0.459347\pi$
$643$	−6.54863	−	1.75470i	−0.258253	−	0.0691986i	−0.385622	+	0.922657i	$0.626013\pi$
$644$	15.7032	−	2.67123i	0.618794	−	0.105261i
$645$	−2.62748	+	5.51179i	−0.103457	+	0.217026i
$646$	3.73078	−	6.46190i	0.146785	−	0.254240i
$647$	−12.2604	−	21.2357i	−0.482008	−	0.834861i	0.517779	−	0.855514i	$-0.326759\pi$
$647$	−12.2604	−	21.2357i	−0.482008	−	0.834861i	−0.999787	+	0.0206528i	$0.993426\pi$
$648$	4.07877	−	8.02269i	0.160229	−	0.315161i
$649$	25.6477	−	14.8077i	1.00676	−	0.581254i
$650$	4.64610	+	13.6547i	0.182235	+	0.535583i
$651$	6.03756	+	1.71224i	0.236631	+	0.0671081i
$652$	6.03532	+	22.5241i	0.236361	+	0.882112i
$653$		−	16.0114i		−	0.626573i	−0.949659	−	0.313287i	$-0.898570\pi$
$653$		−	16.0114i		−	0.626573i	0.949659	−	0.313287i	$-0.101430\pi$
$654$	−24.2145	+	8.58086i	−0.946860	+	0.335538i
$655$	−3.77207	−	14.0776i	−0.147387	−	0.550056i
$656$	0.406096	−	0.108813i	0.0158554	−	0.00424844i
$657$	5.29872	+	11.8869i	0.206723	+	0.463751i
$658$	1.51271	−	1.25383i	0.0589717	−	0.0488793i
$659$	−20.1690	+	11.6446i	−0.785671	+	0.453608i	−0.838436	−	0.544999i	$-0.816530\pi$
$659$	−20.1690	+	11.6446i	−0.785671	+	0.453608i	0.0527651	+	0.998607i	$0.483197\pi$
$660$	1.57352	+	4.44033i	0.0612490	+	0.172840i
$661$	2.84919	−	10.6333i	0.110821	−	0.413588i	−0.888120	−	0.459612i	$-0.847988\pi$
$661$	2.84919	−	10.6333i	0.110821	−	0.413588i	0.998940	+	0.0460240i	$0.0146551\pi$
$662$	17.0686	−	29.5638i	0.663392	−	1.14903i
$663$	−11.9772	−	8.92623i	−0.465154	−	0.346666i
$664$	10.6121			0.411829
$665$	−1.38382	−	8.13501i	−0.0536623	−	0.315462i
$666$	−3.22717	+	0.512606i	−0.125050	+	0.0198631i
$667$	14.9957	+	8.65779i	0.580637	+	0.335231i
$668$	−7.15930	+	1.91833i	−0.277002	+	0.0742223i
$669$	2.55996	−	5.37014i	0.0989738	−	0.207622i
$670$	0.116205	−	0.0311370i	0.00448938	−	0.00120293i
$671$	−3.47596	+	3.47596i	−0.134188	+	0.134188i
$672$	4.44321	−	1.12156i	0.171400	−	0.0432652i
$673$	18.9312	+	10.9299i	0.729745	+	0.421318i	0.818329	−	0.574750i	$-0.194901\pi$
$673$	18.9312	+	10.9299i	0.729745	+	0.421318i	−0.0885839	+	0.996069i	$0.528234\pi$
$674$	7.75478	−	7.75478i	0.298703	−	0.298703i
$675$	18.2609	−	9.93066i	0.702863	−	0.382231i
$676$	1.71536	+	12.8863i	0.0659753	+	0.495628i
$677$	−23.4518	+	13.5399i	−0.901327	+	0.520381i	−0.877630	−	0.479338i	$-0.840877\pi$
$677$	−23.4518	+	13.5399i	−0.901327	+	0.520381i	−0.0236963	+	0.999719i	$0.507543\pi$
$678$	4.09572	+	5.95647i	0.157295	+	0.228757i
$679$	−1.20933	+	12.9233i	−0.0464098	+	0.495952i
$680$	−1.19574	−	2.07108i	−0.0458546	−	0.0794224i
$681$	−2.38360	−	30.2006i	−0.0913399	−	1.15729i
$682$	2.63425	−	2.63425i	0.100871	−	0.100871i
$683$	14.0948	−	14.0948i	0.539324	−	0.539324i	−0.384006	−	0.923331i	$-0.625456\pi$
$683$	14.0948	−	14.0948i	0.539324	−	0.539324i	0.923331	+	0.384006i	$0.125456\pi$
$684$	3.81023	+	8.54768i	0.145688	+	0.326829i
$685$	4.42642	+	7.66678i	0.169125	+	0.292933i
$686$	−5.11669	+	17.7994i	−0.195356	+	0.679585i
$687$	7.23716	−	4.97634i	0.276115	−	0.189859i
$688$	3.05357	−	1.76298i	0.116416	−	0.0672129i
$689$	−7.93929	−	3.90813i	−0.302463	−	0.148888i
$690$	10.2518	+	1.89770i	0.390279	+	0.0722441i
$691$	−20.3155	+	20.3155i	−0.772839	+	0.772839i	−0.978602	−	0.205763i	$-0.934032\pi$
$691$	−20.3155	+	20.3155i	−0.772839	+	0.772839i	0.205763	+	0.978602i	$0.434032\pi$
$692$	15.3049	+	8.83631i	0.581807	+	0.335906i
$693$	21.5475	−	1.38567i	0.818520	−	0.0526372i
$694$	18.3703	−	18.3703i	0.697327	−	0.697327i
$695$	21.7403	−	5.82530i	0.824658	−	0.220966i
$696$	4.49673	+	2.14360i	0.170448	+	0.0812531i
$697$	−0.971349	+	0.260272i	−0.0367925	+	0.00985852i
$698$	−20.5859	−	11.8853i	−0.779188	−	0.449864i
$699$	7.60587	−	41.0886i	0.287680	−	1.55411i
$700$	9.92364	+	3.67993i	0.375078	+	0.139088i
$701$	7.84194			0.296186			0.148093	−	0.988973i	$-0.452687\pi$
$701$	7.84194			0.296186			0.148093	+	0.988973i	$0.452687\pi$
$702$	17.8846	−	5.58050i	0.675010	−	0.210622i
$703$	1.69888	−	2.94255i	0.0640746	−	0.110981i
$704$	0.704074	−	2.62764i	0.0265358	−	0.0990329i
$705$	1.21216	−	0.429551i	0.0456525	−	0.0161778i
$706$	−16.8858	+	9.74903i	−0.635506	+	0.366909i
$707$	9.03625	−	7.48979i	0.339843	−	0.281683i
$708$	−1.48363	−	18.7979i	−0.0557584	−	0.706467i
$709$	32.2135	−	8.63157i	1.20980	−	0.324166i	0.403118	−	0.915148i	$-0.367926\pi$
$709$	32.2135	−	8.63157i	1.20980	−	0.324166i	0.806684	+	0.590982i	$0.201260\pi$
$710$	−3.68297	−	13.7450i	−0.138219	−	0.515841i
$711$	26.6509	−	21.6011i	0.999485	−	0.810104i
$712$		−	10.2175i		−	0.382918i
$713$	−2.13393	−	7.96395i	−0.0799164	−	0.298252i
$714$	−10.6278	+	2.68268i	−0.397735	+	0.100397i
$715$	−4.33098	+	8.79830i	−0.161970	+	0.329038i
$716$	8.37432	−	4.83492i	0.312963	−	0.180689i
$717$	2.65525	+	33.6424i	0.0991619	+	1.25640i
$718$	−7.52418	−	13.0323i	−0.280800	−	0.486360i
$719$	19.1095	−	33.0985i	0.712662	−	1.23437i	−0.251192	−	0.967937i	$-0.580822\pi$
$719$	19.1095	−	33.0985i	0.712662	−	1.23437i	0.963854	−	0.266430i	$-0.0858442\pi$
$720$	2.98316	+	0.312200i	0.111176	+	0.0116350i
$721$	−12.2835	−	14.8198i	−0.457463	−	0.551918i
$722$	8.95299	+	2.39895i	0.333196	+	0.0892795i
$723$	−1.28816	−	16.3212i	−0.0479072	−	0.606991i
$724$	−5.02844			−0.186880
$725$	5.75270	+	9.96398i	0.213650	+	0.370053i
$726$	−2.68300	+	5.62824i	−0.0995753	+	0.208884i
$727$			39.4219i			1.46208i	0.682337	+	0.731038i	$0.260964\pi$
$727$			39.4219i			1.46208i	−0.682337	+	0.731038i	$0.739036\pi$
$728$	8.12889	+	4.99210i	0.301277	+	0.185020i
$729$	−12.2899	−	24.0408i	−0.455180	−	0.890400i
$730$	−3.06696	+	3.06696i	−0.113513	+	0.113513i
$731$	−7.30389	+	4.21690i	−0.270144	+	0.155968i
$732$	1.04544	+	2.95013i	0.0386404	+	0.109040i
$733$	42.0320	+	11.2625i	1.55249	+	0.415988i	0.930276	−	0.366860i	$-0.119567\pi$
$733$	42.0320	+	11.2625i	1.55249	+	0.415988i	0.622213	+	0.782848i	$0.286234\pi$
$734$	−6.18379	+	23.0782i	−0.228248	+	0.851833i
$735$	−7.15586	+	9.78467i	−0.263948	+	0.360913i
$736$	−4.25716	−	4.25716i	−0.156921	−	0.156921i
$737$	−0.283474	−	0.163664i	−0.0104419	−	0.00602862i
$738$	0.451473	−	1.17769i	0.0166189	−	0.0433515i
$739$	−0.950364	+	3.54681i	−0.0349597	+	0.130471i	−0.981200	−	0.192992i	$-0.938181\pi$
$739$	−0.950364	+	3.54681i	−0.0349597	+	0.130471i	0.946241	+	0.323464i	$0.104847\pi$
$740$	−0.544504	−	0.943109i	−0.0200164	−	0.0346694i
$741$	−7.20187	+	18.1011i	−0.264567	+	0.664960i
$742$	−5.90151	+	2.70865i	−0.216651	+	0.0994378i
$743$	17.5705	−	4.70799i	0.644598	−	0.172720i	0.0783128	−	0.996929i	$-0.475047\pi$
$743$	17.5705	−	4.70799i	0.644598	−	0.172720i	0.566285	+	0.824209i	$0.308380\pi$
$744$	−0.792280	−	2.23575i	−0.0290464	−	0.0819665i
$745$		−	22.4369i		−	0.822024i
$746$	−18.0289	+	4.83084i	−0.660086	+	0.176870i
$747$	18.7014	−	25.7644i	0.684250	−	0.942671i
$748$	−1.68409	+	6.28510i	−0.0615763	+	0.229806i
$749$	51.7190	−	8.79776i	1.88977	−	0.321463i
$750$	11.8541	+	10.1198i	0.432851	+	0.369523i
$751$			21.9597i			0.801322i	0.916226	+	0.400661i	$0.131220\pi$
$751$			21.9597i			0.801322i	−0.916226	+	0.400661i	$0.868780\pi$
$752$	−0.717315	−	0.192204i	−0.0261578	−	0.00700896i
$753$	−7.40606	+	40.0092i	−0.269892	+	1.45802i
$754$	3.34034	+	9.81716i	0.121648	+	0.357520i
$755$			12.3917i			0.450979i
$756$	5.10719	−	12.7639i	0.185747	−	0.464218i
$757$	7.52013	−	13.0252i	0.273324	−	0.473411i	−0.696387	−	0.717666i	$-0.745210\pi$
$757$	7.52013	−	13.0252i	0.273324	−	0.473411i	0.969711	+	0.244256i	$0.0785436\pi$
$758$	12.0602	−	20.8888i	0.438045	−	0.758717i
$759$	−16.0726	−	23.3746i	−0.583398	−	0.848445i
$760$	−2.20540	+	2.20540i	−0.0799984	+	0.0799984i
$761$	5.89968	+	22.0179i	0.213863	+	0.798149i	0.986564	+	0.163378i	$0.0522389\pi$
$761$	5.89968	+	22.0179i	0.213863	+	0.798149i	−0.772700	+	0.634771i	$0.781094\pi$
$762$	2.03555	−	4.27006i	0.0737402	−	0.154688i
$763$	−35.6648	+	16.3693i	−1.29115	+	0.592608i
$764$	−11.5364	+	19.9816i	−0.417373	+	0.722911i
$765$	−7.13548	−	0.746758i	−0.257984	−	0.0269991i
$766$	−29.9168	−	17.2725i	−1.08094	−	0.624081i
$767$	25.8598	−	29.5302i	0.933744	−	1.06628i
$768$	−1.31731	−	1.12458i	−0.0475344	−	0.0405799i
$769$	−2.22659	−	8.30976i	−0.0802930	−	0.299658i	0.914088	−	0.405515i	$-0.132908\pi$
$769$	−2.22659	−	8.30976i	−0.0802930	−	0.299658i	−0.994381	+	0.105858i	$0.966241\pi$
$770$	3.00172	+	6.54004i	0.108175	+	0.235687i
$771$	3.57721	+	3.05385i	0.128830	+	0.109982i
$772$	−0.704783	−	0.188846i	−0.0253657	−	0.00679672i
$773$	18.6176	+	18.6176i	0.669627	+	0.669627i	0.957630	−	0.288002i	$-0.0929911\pi$
$773$	18.6176	+	18.6176i	0.669627	+	0.669627i	−0.288002	+	0.957630i	$0.592991\pi$
$774$	1.10101	−	10.5204i	0.0395749	−	0.378149i
$775$	1.41790	−	5.29168i	0.0509325	−	0.190083i
$776$	4.24863	−	2.45295i	0.152517	−	0.0880558i
$777$	−4.83958	+	1.22161i	−0.173619	+	0.0438251i
$778$	4.47697	−	1.19960i	0.160507	−	0.0430077i
$779$	0.655750	+	1.13579i	0.0234947	+	0.0406940i
$780$	3.87014	+	4.89977i	0.138573	+	0.175440i
$781$	−19.3586	+	33.5300i	−0.692704	+	1.19980i
$782$	10.1828	+	10.1828i	0.364135	+	0.364135i
$783$	13.1288	−	7.13971i	0.469185	−	0.255153i
$784$	6.60628	−	2.31452i	0.235939	−	0.0826615i
$785$	−4.04600	−	4.04600i	−0.144408	−	0.144408i
$786$	14.3052	+	20.8042i	0.510248	+	0.742062i
$787$	−6.12245	−	6.12245i	−0.218242	−	0.218242i	0.589515	−	0.807757i	$-0.299319\pi$
$787$	−6.12245	−	6.12245i	−0.218242	−	0.218242i	−0.807757	+	0.589515i	$0.799319\pi$
$788$	3.44137	+	12.8434i	0.122594	+	0.457526i
$789$	45.6945	+	8.45846i	1.62677	+	0.301129i
$790$	9.90137	+	5.71656i	0.352275	+	0.203386i
$791$	7.04648	+	8.50141i	0.250544	+	0.302275i
$792$	−5.13870	−	6.34000i	−0.182596	−	0.225282i
$793$	−2.87748	+	5.84554i	−0.102182	+	0.207581i
$794$	−22.4668	−	12.9712i	−0.797318	−	0.460332i
$795$	−4.23699	+	0.334407i	−0.150271	+	0.0118602i
$796$	−8.74434			−0.309935
$797$	10.9178	+	18.9102i	0.386729	+	0.669834i	0.992007	−	0.126180i	$-0.0402717\pi$
$797$	10.9178	+	18.9102i	0.386729	+	0.669834i	−0.605279	+	0.796014i	$0.706938\pi$
$798$	6.96684	+	12.4827i	0.246624	+	0.441883i
$799$	1.71576	+	0.459736i	0.0606992	+	0.0162643i
$800$	−1.03537	−	3.86406i	−0.0366059	−	0.136615i
$801$	−24.8065	−	18.0061i	−0.876494	−	0.636214i
$802$	5.56648			0.196559
$803$	11.8011			0.416454
$804$	−0.171731	+	0.118083i	−0.00605647	+	0.00416448i
$805$	15.8566	+	1.48382i	0.558873	+	0.0522977i
$806$	2.18069	−	4.43003i	0.0768116	−	0.156041i
$807$	16.1226	−	18.8856i	0.567541	−	0.664804i
$808$	−4.28491	−	1.14814i	−0.150743	−	0.0403914i
$809$	−25.7086	+	14.8429i	−0.903866	+	0.521847i	−0.878452	−	0.477830i	$-0.841423\pi$
$809$	−25.7086	+	14.8429i	−0.903866	+	0.521847i	−0.0254133	+	0.999677i	$0.508090\pi$
$810$	6.01512	−	6.69244i	0.211350	−	0.235148i
$811$	6.15669	−	6.15669i	0.216190	−	0.216190i	−0.590700	−	0.806891i	$-0.701148\pi$
$811$	6.15669	−	6.15669i	0.216190	−	0.216190i	0.806891	+	0.590700i	$0.201148\pi$
$812$	7.13467	+	2.64571i	0.250378	+	0.0928461i
$813$	−2.12637	−	26.9415i	−0.0745751	−	0.944879i
$814$	−0.766883	+	2.86205i	−0.0268792	+	0.100315i
$815$			23.3144i			0.816668i
$816$	3.15090	+	2.68991i	0.110304	+	0.0941658i
$817$	7.77759	+	7.77759i	0.272103	+	0.272103i
$818$	39.6369			1.38587
$819$	26.4454	−	10.9382i	0.924075	−	0.382210i
$820$	0.420345			0.0146791
$821$	14.4417	+	14.4417i	0.504017	+	0.504017i	0.912684	−	0.408667i	$-0.134006\pi$
$821$	14.4417	+	14.4417i	0.504017	+	0.504017i	−0.408667	+	0.912684i	$0.634006\pi$
$822$	−11.6641	−	9.95758i	−0.406832	−	0.347311i
$823$		−	56.0176i		−	1.95265i	−0.216304	−	0.976326i	$-0.569400\pi$
$823$		−	56.0176i		−	1.95265i	0.216304	−	0.976326i	$-0.430600\pi$
$824$	−1.88299	+	7.02742i	−0.0655971	+	0.244812i
$825$	−1.48304	−	18.7903i	−0.0516327	−	0.654194i
$826$	−4.83029	−	28.3956i	−0.168067	−	0.988010i
$827$	22.2898	−	22.2898i	0.775093	−	0.775093i	−0.203899	−	0.978992i	$-0.565361\pi$
$827$	22.2898	−	22.2898i	0.775093	−	0.775093i	0.978992	+	0.203899i	$0.0653614\pi$
$828$	−17.8380	+	2.83339i	−0.619912	+	0.0984673i
$829$	3.84389	−	2.21927i	0.133504	−	0.0770785i	−0.431761	−	0.901988i	$-0.642107\pi$
$829$	3.84389	−	2.21927i	0.133504	−	0.0770785i	0.565264	+	0.824910i	$0.308774\pi$
$830$	10.2486	+	2.74611i	0.355735	+	0.0953189i
$831$	−7.64346	+	8.95338i	−0.265149	+	0.310589i
$832$	−0.238399	−	3.59766i	−0.00826499	−	0.124726i
$833$	−15.8017	+	5.53615i	−0.547496	+	0.191816i
$834$	−32.1285	+	22.0918i	−1.11252	+	0.764977i
$835$	−7.41049			−0.256451
$836$	8.48603			0.293496
$837$	−6.82425	−	2.01648i	−0.235880	−	0.0696997i
$838$	−0.0625082	−	0.233284i	−0.00215931	−	0.00805866i
$839$	−3.32216	−	0.890169i	−0.114694	−	0.0307320i	0.201016	−	0.979588i	$-0.435576\pi$
$839$	−3.32216	−	0.890169i	−0.114694	−	0.0307320i	−0.315709	+	0.948856i	$0.602242\pi$
$840$	4.58125	+	0.0666300i	0.158068	+	0.00229895i
$841$	−10.3641	−	17.9511i	−0.357381	−	0.619002i
$842$	9.05407			0.312024
$843$	−32.1009	+	2.53358i	−1.10561	+	0.0872612i
$844$	−15.3789	−	8.87901i	−0.529363	−	0.305628i
$845$	−1.67801	+	12.8888i	−0.0577254	+	0.443390i
$846$	−1.73075	+	1.40281i	−0.0595043	+	0.0482295i
$847$	−3.31144	+	8.92995i	−0.113782	+	0.306837i
$848$	2.12547	+	1.22714i	0.0729891	+	0.0421403i
$849$	54.6068	+	10.1082i	1.87410	+	0.346912i
$850$	2.47652	+	9.24251i	0.0849441	+	0.317016i
$851$	4.63693	+	4.63693i	0.158952	+	0.158952i
$852$	13.9672	+	20.3128i	0.478510	+	0.695904i
$853$	−13.9504	−	13.9504i	−0.477651	−	0.477651i	0.426728	−	0.904380i	$-0.359666\pi$
$853$	−13.9504	−	13.9504i	−0.477651	−	0.477651i	−0.904380	+	0.426728i	$0.859666\pi$
$854$	1.99433	+	4.34517i	0.0682445	+	0.148689i
$855$	1.46783	+	9.24089i	0.0501987	+	0.316032i
$856$	−14.0210	−	14.0210i	−0.479230	−	0.479230i
$857$	−11.0508	+	19.1405i	−0.377487	+	0.653827i	−0.990696	−	0.136094i	$-0.956545\pi$
$857$	−11.0508	+	19.1405i	−0.377487	+	0.653827i	0.613209	+	0.789921i	$0.289878\pi$
$858$	1.98091	−	16.8726i	0.0676270	−	0.576020i
$859$	−17.9237	−	31.0447i	−0.611548	−	1.05923i	−0.990980	−	0.134013i	$-0.957214\pi$
$859$	−17.9237	−	31.0447i	−0.611548	−	1.05923i	0.379431	−	0.925220i	$-0.376120\pi$
$860$	3.40519	−	0.912418i	0.116116	−	0.0311132i
$861$	0.525655	−	1.85352i	0.0179143	−	0.0631677i
$862$	2.66045	−	1.53601i	0.0906152	−	0.0523167i
$863$	1.69524	−	6.32672i	0.0577067	−	0.215364i	−0.931051	−	0.364888i	$-0.881107\pi$
$863$	1.69524	−	6.32672i	0.0577067	−	0.215364i	0.988758	+	0.149524i	$0.0477740\pi$
$864$	−5.05177	+	1.21639i	−0.171865	+	0.0413825i
$865$	12.4941	+	12.4941i	0.424814	+	0.424814i
$866$	19.8147	+	5.30934i	0.673332	+	0.180419i
$867$	14.8576	+	12.6839i	0.504590	+	0.430767i
$868$	−1.51140	−	3.29297i	−0.0513001	−	0.111771i
$869$	−8.05123	−	30.0476i	−0.273119	−	1.01929i
$870$	3.78801	+	3.23381i	0.128426	+	0.109636i
$871$	−0.425567	−	0.0843327i	−0.0144198	−	0.00285750i
$872$	12.8450	+	7.41604i	0.434985	+	0.251139i
$873$	1.53190	−	14.6378i	0.0518471	−	0.495413i
$874$	9.39047	−	16.2648i	0.317637	−	0.550164i
$875$	19.4199	+	13.7734i	0.656511	+	0.465627i
$876$	3.23329	−	6.78262i	0.109243	−	0.229163i
$877$	12.5521	+	46.8449i	0.423853	+	1.58184i	0.766415	+	0.642345i	$0.222039\pi$
$877$	12.5521	+	46.8449i	0.423853	+	1.58184i	−0.342562	+	0.939495i	$0.611295\pi$
$878$	−14.3426	+	14.3426i	−0.484038	+	0.484038i
$879$	29.9310	+	43.5291i	1.00955	+	1.46820i
$880$	1.35992	−	2.35545i	0.0458428	−	0.0794020i
$881$	−9.72164	+	16.8384i	−0.327530	+	0.567299i	−0.982021	−	0.188771i	$-0.939550\pi$
$881$	−9.72164	+	16.8384i	−0.327530	+	0.567299i	0.654491	+	0.756070i	$0.272883\pi$
$882$	6.02281	−	20.1178i	0.202799	−	0.677401i
$883$			39.2848i			1.32204i	0.750369	+	0.661020i	$0.229876\pi$
$883$			39.2848i			1.32204i	−0.750369	+	0.661020i	$0.770124\pi$
$884$	0.570231	+	8.60532i	0.0191789	+	0.289428i
$885$	3.43154	−	18.5380i	0.115350	−	0.623146i
$886$	29.0495	+	7.78380i	0.975939	+	0.261502i
$887$		−	17.8606i		−	0.599700i	−0.953986	−	0.299850i	$-0.903063\pi$
$887$		−	17.8606i		−	0.599700i	0.953986	−	0.299850i	$-0.0969366\pi$
$888$	1.43483	+	1.22491i	0.0481497	+	0.0411052i
$889$	2.51234	−	6.77502i	0.0842613	−	0.227227i
$890$	2.64401	−	9.86757i	0.0886273	−	0.330762i
$891$	−24.4483	+	1.30311i	−0.819048	+	0.0436557i
$892$	−3.31768	+	0.888970i	−0.111084	+	0.0297649i
$893$		−	2.31659i		−	0.0775217i
$894$	12.9829	+	36.6366i	0.434212	+	1.22531i
$895$	9.33863	−	2.50228i	0.312156	−	0.0836419i
$896$	−2.15807	−	1.53060i	−0.0720960	−	0.0511338i
$897$	−30.1468	−	22.4676i	−1.00657	−	0.750170i
$898$	−13.3695	−	23.1566i	−0.446145	−	0.772746i
$899$	1.01941	−	3.80449i	0.0339992	−	0.126887i
$900$	−11.2059	−	4.29582i	−0.373530	−	0.143194i
$901$	−5.08396	−	2.93523i	−0.169371	−	0.0977866i
$902$	−0.808709	−	0.808709i	−0.0269270	−	0.0269270i
$903$	0.234978	−	16.1563i	0.00781956	−	0.537647i
$904$	1.08018	−	4.03129i	0.0359263	−	0.134079i
$905$	−4.85621	−	1.30122i	−0.161426	−	0.0432539i
$906$	−7.17031	−	20.2340i	−0.238218	−	0.672230i
$907$	−23.0932	+	13.3329i	−0.766797	+	0.442710i	−0.831731	−	0.555179i	$-0.812650\pi$
$907$	−23.0932	+	13.3329i	−0.766797	+	0.442710i	0.0649338	+	0.997890i	$0.479316\pi$
$908$	−12.3677	+	12.3677i	−0.410436	+	0.410436i
$909$	−10.3387	+	8.37973i	−0.342913	+	0.277938i
$910$	6.55866	+	6.92464i	0.217417	+	0.229550i
$911$			24.7584i			0.820283i	0.912022	+	0.410142i	$0.134521\pi$
$911$			24.7584i			0.820283i	−0.912022	+	0.410142i	$0.865479\pi$
$912$	2.32501	−	4.87728i	0.0769888	−	0.161503i
$913$	−14.4342	−	25.0008i	−0.477703	−	0.827405i
$914$	−2.67630			−0.0885243
$915$	0.246218	+	3.11962i	0.00813970	+	0.103131i
$916$	−4.89806	−	1.31243i	−0.161836	−	0.0433640i
$917$	24.6113	+	29.6930i	0.812738	+	0.980549i
$918$	12.0834	−	2.90951i	0.398813	−	0.0960281i
$919$	−19.2368	+	33.3191i	−0.634563	+	1.09910i	0.352045	+	0.935983i	$0.385487\pi$
$919$	−19.2368	+	33.3191i	−0.634563	+	1.09910i	−0.986608	+	0.163112i	$0.947847\pi$
$920$	−3.00971	−	5.21298i	−0.0992273	−	0.171867i
$921$	3.76304	+	47.6782i	0.123996	+	1.57105i
$922$	1.06333	−	0.613914i	0.0350189	−	0.0202182i
$923$	−9.97510	+	50.3372i	−0.328334	+	1.65687i
$924$	−8.68576	−	8.94214i	−0.285741	−	0.294175i
$925$	1.12773	+	4.20876i	0.0370797	+	0.138383i
$926$			0.824500i			0.0270947i
$927$	13.7431	+	16.9558i	0.451381	+	0.556903i
$928$	−0.744387	−	2.77809i	−0.0244357	−	0.0911952i
$929$	58.5090	−	15.6774i	1.91962	−	0.514360i	0.930728	−	0.365713i	$-0.119175\pi$
$929$	58.5090	−	15.6774i	1.91962	−	0.514360i	0.988890	−	0.148647i	$-0.0474920\pi$
$930$	−0.186595	−	2.36419i	−0.00611870	−	0.0775249i
$931$	12.3079	+	18.0373i	0.403375	+	0.591148i
$932$	−20.8933	+	12.0628i	−0.684383	+	0.395129i
$933$	2.77435	−	0.983145i	0.0908282	−	0.0321867i
$934$	6.40084	−	23.8882i	0.209442	−	0.781647i
$935$	−3.25281	+	5.63404i	−0.106378	+	0.184253i
$936$	−9.15465	−	5.76128i	−0.299229	−	0.188313i
$937$	22.4479			0.733342			0.366671	−	0.930351i	$-0.380497\pi$
$937$	22.4479			0.733342			0.366671	+	0.930351i	$0.380497\pi$
$938$	−0.245104	+	0.203157i	−0.00800293	+	0.00663331i
$939$	8.21379	−	44.3727i	0.268047	−	1.44805i
$940$	−0.643009	−	0.371241i	−0.0209726	−	0.0121086i
$941$	−33.3503	+	8.93620i	−1.08719	+	0.291312i	−0.757538	−	0.652791i	$-0.773598\pi$
$941$	−33.3503	+	8.93620i	−1.08719	+	0.291312i	−0.329652	+	0.944103i	$0.606931\pi$
$942$	8.94778	+	4.26543i	0.291534	+	0.138975i
$943$	−2.44491	+	0.655113i	−0.0796173	+	0.0213334i
$944$	−7.69807	+	7.69807i	−0.250551	+	0.250551i
$945$	8.23519	−	11.0051i	0.267891	−	0.357996i
$946$	−8.30672	−	4.79589i	−0.270075	−	0.155928i
$947$	12.5695	−	12.5695i	0.408454	−	0.408454i	−0.472745	−	0.881199i	$-0.656737\pi$
$947$	12.5695	−	12.5695i	0.408454	−	0.408454i	0.881199	+	0.472745i	$0.156737\pi$
$948$	−19.4755	−	3.60509i	−0.632535	−	0.117088i
$949$	14.8076	−	5.03838i	0.480677	−	0.163553i
$950$	10.8072	−	6.23954i	0.350632	−	0.202437i
$951$	−11.0105	+	7.57092i	−0.357040	+	0.245504i
$952$	5.16193	+	3.66107i	0.167299	+	0.118656i
$953$	12.0178	+	20.8154i	0.389294	+	0.674277i	0.992355	−	0.123418i	$-0.0393857\pi$
$953$	12.0178	+	20.8154i	0.389294	+	0.674277i	−0.603061	+	0.797695i	$0.706052\pi$
$954$	6.72497	−	2.99774i	0.217729	−	0.0970554i
$955$	−16.3120	+	16.3120i	−0.527843	+	0.527843i
$956$	13.7771	−	13.7771i	0.445585	−	0.445585i
$957$	−1.06624	−	13.5094i	−0.0344666	−	0.436697i
$958$	−17.3767	−	30.0973i	−0.561415	−	0.972400i
$959$	−19.1085	−	13.5526i	−0.617047	−	0.437638i
$960$	−0.981182	−	1.42695i	−0.0316675	−	0.0460546i
$961$	25.2226	−	14.5623i	0.813633	−	0.469751i
$962$	0.259666	+	3.91860i	0.00837197	+	0.126341i
$963$	−58.7498	+	9.33185i	−1.89318	+	0.300715i
$964$	−6.68381	+	6.68381i	−0.215271	+	0.215271i
$965$	−0.631776	−	0.364756i	−0.0203376	−	0.0117419i
$966$	−26.7505	+	6.75239i	−0.860682	+	0.217255i
$967$	−17.5794	+	17.5794i	−0.565315	+	0.565315i	−0.930813	−	0.365497i	$-0.880899\pi$
$967$	−17.5794	+	17.5794i	−0.565315	+	0.565315i	0.365497	+	0.930813i	$0.380899\pi$
$968$	3.47713	−	0.931695i	0.111759	−	0.0299458i
$969$	−5.56124	+	11.6661i	−0.178653	+	0.374768i
$970$	4.73787	−	1.26951i	0.152124	−	0.0407614i
$971$	0.844055	+	0.487315i	0.0270870	+	0.0156387i	0.513482	−	0.858100i	$-0.328355\pi$
$971$	0.844055	+	0.487315i	0.0270870	+	0.0156387i	−0.486395	+	0.873739i	$0.661689\pi$
$972$	−5.94941	+	14.4085i	−0.190828	+	0.462152i
$973$	−45.8556	+	38.0079i	−1.47006	+	1.21848i
$974$	20.5016			0.656912
$975$	−9.88319	−	22.9442i	−0.316516	−	0.734803i
$976$	0.903521	−	1.56494i	0.0289210	−	0.0500927i
$977$	12.0858	−	45.1047i	0.386658	−	1.44303i	−0.448879	−	0.893593i	$-0.648176\pi$
$977$	12.0858	−	45.1047i	0.386658	−	1.44303i	0.835537	−	0.549435i	$-0.185157\pi$
$978$	−13.4906	−	38.0695i	−0.431383	−	1.21733i
$979$	−24.0712	+	13.8975i	−0.769320	+	0.444167i
$980$	6.97894	−	0.525728i	0.222934	−	0.0167938i
$981$	40.6413	−	18.1163i	1.29758	−	0.578410i
$982$	−18.5240	+	4.96348i	−0.591123	+	0.158391i
$983$	−3.84942	−	14.3662i	−0.122777	−	0.458212i	0.876973	−	0.480539i	$-0.159559\pi$
$983$	−3.84942	−	14.3662i	−0.122777	−	0.458212i	−0.999751	+	0.0223274i	$0.992892\pi$
$984$	−0.686370	+	0.243228i	−0.0218807	+	0.00775383i
$985$			13.2940i			0.423582i
$986$	1.78051	+	6.64496i	0.0567031	+	0.211619i
$987$	−2.44110	+	2.37111i	−0.0777011	+	0.0754733i
$988$	10.6480	−	3.62303i	0.338757	−	0.115264i
$989$	−18.3841	+	10.6141i	−0.584580	+	0.337508i
$990$	−3.32209	−	7.45260i	−0.105583	−	0.236859i
$991$	7.92573	+	13.7278i	0.251769	+	0.436077i	0.964013	−	0.265855i	$-0.0856543\pi$
$991$	7.92573	+	13.7278i	0.251769	+	0.436077i	−0.712244	+	0.701932i	$0.752321\pi$
$992$	−0.684731	+	1.18599i	−0.0217402	+	0.0376552i
$993$	−25.4432	+	53.3733i	−0.807415	+	1.69375i
$994$	24.0299	+	28.9915i	0.762184	+	0.919556i
$995$	−8.44484	−	2.26279i	−0.267719	−	0.0717352i
$996$	−18.3237	+	1.44621i	−0.580609	+	0.0458249i
$997$	49.4284			1.56541			0.782707	−	0.622390i	$-0.213838\pi$
$997$	49.4284			1.56541			0.782707	+	0.622390i	$0.213838\pi$
$998$	−10.0177	−	17.3512i	−0.317105	−	0.549243i
$999$	5.50243	−	1.32490i	0.174089	−	0.0419181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.305.24	yes	152
3.2	odd	2	inner	546.2.ch.a.305.9	yes	152
7.2	even	3		546.2.bw.a.149.36	yes	152
13.11	odd	12		546.2.bw.a.11.17	✓	152
21.2	odd	6		546.2.bw.a.149.17	yes	152
39.11	even	12		546.2.bw.a.11.36	yes	152
91.37	odd	12	inner	546.2.ch.a.401.9	yes	152
273.128	even	12	inner	546.2.ch.a.401.24	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.17	✓	152	13.11	odd	12
546.2.bw.a.11.36	yes	152	39.11	even	12
546.2.bw.a.149.17	yes	152	21.2	odd	6
546.2.bw.a.149.36	yes	152	7.2	even	3
546.2.ch.a.305.9	yes	152	3.2	odd	2	inner
546.2.ch.a.305.24	yes	152	1.1	even	1	trivial
546.2.ch.a.401.9	yes	152	91.37	odd	12	inner
546.2.ch.a.401.24	yes	152	273.128	even	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.31731 - 1.12458i) q^{3} +1.00000i q^{4} +(-0.258772 + 0.965749i) q^{5} +(-0.136279 - 1.72668i) q^{6} +(-0.443687 - 2.60828i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.470622 + 2.96286i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.31731 - 1.12458i) q^{3} +1.00000i q^{4} +(-0.258772 + 0.965749i) q^{5} +(-0.136279 - 1.72668i) q^{6} +(-0.443687 - 2.60828i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.470622 + 2.96286i) q^{9} +(-0.865867 + 0.499908i) q^{10} +(2.62764 + 0.704074i) q^{11} +(1.12458 - 1.31731i) q^{12} +(3.59766 - 0.238399i) q^{13} +(1.53060 - 2.15807i) q^{14} +(1.42695 - 0.981182i) q^{15} -1.00000 q^{16} +2.39192 q^{17} +(-1.76228 + 2.42784i) q^{18} +(-0.807382 - 3.01319i) q^{19} +(-0.965749 - 0.258772i) q^{20} +(-2.34876 + 3.93489i) q^{21} +(1.36017 + 2.35588i) q^{22} +6.02053 q^{23} +(1.72668 - 0.136279i) q^{24} +(3.46442 + 2.00018i) q^{25} +(2.71250 + 2.37536i) q^{26} +(2.71202 - 4.43226i) q^{27} +(2.60828 - 0.443687i) q^{28} +(2.49077 + 1.43804i) q^{29} +(1.70281 + 0.315204i) q^{30} +(-0.354443 - 1.32280i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.66963 - 3.88249i) q^{33} +(1.69134 + 1.69134i) q^{34} +(2.63376 + 0.246460i) q^{35} +(-2.96286 + 0.470622i) q^{36} +(0.770187 + 0.770187i) q^{37} +(1.55974 - 2.70155i) q^{38} +(-5.00734 - 3.73183i) q^{39} +(-0.499908 - 0.865867i) q^{40} +(-0.406096 + 0.108813i) q^{41} +(-4.44321 + 1.12156i) q^{42} +(-3.05357 + 1.76298i) q^{43} +(-0.704074 + 2.62764i) q^{44} +(-2.98316 - 0.312200i) q^{45} +(4.25716 + 4.25716i) q^{46} +(0.717315 + 0.192204i) q^{47} +(1.31731 + 1.12458i) q^{48} +(-6.60628 + 2.31452i) q^{49} +(1.03537 + 3.86406i) q^{50} +(-3.15090 - 2.68991i) q^{51} +(0.238399 + 3.59766i) q^{52} +(-2.12547 - 1.22714i) q^{53} +(5.05177 - 1.21639i) q^{54} +(-1.35992 + 2.35545i) q^{55} +(2.15807 + 1.53060i) q^{56} +(-2.32501 + 4.87728i) q^{57} +(0.744387 + 2.77809i) q^{58} +(7.69807 - 7.69807i) q^{59} +(0.981182 + 1.42695i) q^{60} +(-0.903521 + 1.56494i) q^{61} +(0.684731 - 1.18599i) q^{62} +(7.51916 - 2.54210i) q^{63} -1.00000i q^{64} +(-0.700739 + 3.53613i) q^{65} +(0.857618 - 4.63305i) q^{66} +(-0.116226 - 0.0311427i) q^{67} +2.39192i q^{68} +(-7.93091 - 6.77059i) q^{69} +(1.68808 + 2.03662i) q^{70} +(-3.68364 + 13.7475i) q^{71} +(-2.42784 - 1.76228i) q^{72} +(4.19031 - 1.12279i) q^{73} +1.08921i q^{74} +(-2.31435 - 6.53089i) q^{75} +(3.01319 - 0.807382i) q^{76} +(0.670575 - 7.16601i) q^{77} +(-0.901926 - 6.17953i) q^{78} +(-5.71760 - 9.90318i) q^{79} +(0.258772 - 0.965749i) q^{80} +(-8.55703 + 2.78877i) q^{81} +(-0.364096 - 0.210211i) q^{82} +(-7.50388 - 7.50388i) q^{83} +(-3.93489 - 2.34876i) q^{84} +(-0.618961 + 2.30999i) q^{85} +(-3.40581 - 0.912585i) q^{86} +(-1.66391 - 4.69543i) q^{87} +(-2.35588 + 1.36017i) q^{88} +(-7.22489 + 7.22489i) q^{89} +(-1.88865 - 2.33017i) q^{90} +(-2.21805 - 9.27795i) q^{91} +6.02053i q^{92} +(-1.02069 + 2.14114i) q^{93} +(0.371309 + 0.643127i) q^{94} +3.11891 q^{95} +(0.136279 + 1.72668i) q^{96} +(-4.73874 - 1.26974i) q^{97} +(-6.30796 - 3.03473i) q^{98} +(-0.849444 + 8.11667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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