LMFDB - Embedded newform 546.2.ch.a.137.16

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			137.16
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.52325 + 0.824446i) q^{3} -1.00000i q^{4} +(2.39134 + 0.640759i) q^{5} +(-1.66007 + 0.494128i) q^{6} +(-0.703385 - 2.55054i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.64058 + 2.51167i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52325 + 0.824446i) q^{3} -1.00000i q^{4} +(2.39134 + 0.640759i) q^{5} +(-1.66007 + 0.494128i) q^{6} +(-0.703385 - 2.55054i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.64058 + 2.51167i) q^{9} +(-2.14402 + 1.23785i) q^{10} +(1.48111 - 5.52759i) q^{11} +(0.824446 - 1.52325i) q^{12} +(-1.32815 + 3.35202i) q^{13} +(2.30087 + 1.30613i) q^{14} +(3.11434 + 2.94757i) q^{15} -1.00000 q^{16} +7.78434 q^{17} +(-2.93608 - 0.615960i) q^{18} +(0.0409293 - 0.0109670i) q^{19} +(0.640759 - 2.39134i) q^{20} +(1.03135 - 4.46501i) q^{21} +(2.86129 + 4.95590i) q^{22} -3.92816 q^{23} +(0.494128 + 1.66007i) q^{24} +(0.977829 + 0.564550i) q^{25} +(-1.43109 - 3.30938i) q^{26} +(0.428265 + 5.17847i) q^{27} +(-2.55054 + 0.703385i) q^{28} +(-0.496669 - 0.286752i) q^{29} +(-4.28642 + 0.117925i) q^{30} +(-5.21337 + 1.39692i) q^{31} +(0.707107 - 0.707107i) q^{32} +(6.81331 - 7.19880i) q^{33} +(-5.50436 + 5.50436i) q^{34} +(-0.0477563 - 6.54992i) q^{35} +(2.51167 - 1.64058i) q^{36} +(6.33367 - 6.33367i) q^{37} +(-0.0211866 + 0.0366962i) q^{38} +(-4.78666 + 4.01097i) q^{39} +(1.23785 + 2.14402i) q^{40} +(1.41205 + 5.26984i) q^{41} +(2.42796 + 3.88651i) q^{42} +(-4.42948 + 2.55736i) q^{43} +(-5.52759 - 1.48111i) q^{44} +(2.31380 + 7.05749i) q^{45} +(2.77763 - 2.77763i) q^{46} +(-1.80603 + 6.74019i) q^{47} +(-1.52325 - 0.824446i) q^{48} +(-6.01050 + 3.58802i) q^{49} +(-1.09063 + 0.292232i) q^{50} +(11.8575 + 6.41777i) q^{51} +(3.35202 + 1.32815i) q^{52} +(-3.45966 - 1.99744i) q^{53} +(-3.96456 - 3.35890i) q^{54} +(7.08370 - 12.2693i) q^{55} +(1.30613 - 2.30087i) q^{56} +(0.0713872 + 0.0170386i) q^{57} +(0.553963 - 0.148434i) q^{58} +(-1.36857 - 1.36857i) q^{59} +(2.94757 - 3.11434i) q^{60} +(-5.77032 + 9.99448i) q^{61} +(2.69864 - 4.67418i) q^{62} +(5.25217 - 5.95103i) q^{63} +1.00000i q^{64} +(-5.32389 + 7.16481i) q^{65} +(0.272584 + 9.90805i) q^{66} +(1.84292 - 6.87786i) q^{67} -7.78434i q^{68} +(-5.98356 - 3.23855i) q^{69} +(4.66526 + 4.59772i) q^{70} +(1.41008 + 0.377829i) q^{71} +(-0.615960 + 2.93608i) q^{72} +(3.90570 + 14.5763i) q^{73} +8.95716i q^{74} +(1.02404 + 1.66612i) q^{75} +(-0.0109670 - 0.0409293i) q^{76} +(-15.1401 + 0.110389i) q^{77} +(0.548493 - 6.22086i) q^{78} +(0.0358923 + 0.0621672i) q^{79} +(-2.39134 - 0.640759i) q^{80} +(-3.61702 + 8.24119i) q^{81} +(-4.72481 - 2.72787i) q^{82} +(-0.675019 + 0.675019i) q^{83} +(-4.46501 - 1.03135i) q^{84} +(18.6150 + 4.98788i) q^{85} +(1.32379 - 4.94045i) q^{86} +(-0.520139 - 0.846272i) q^{87} +(4.95590 - 2.86129i) q^{88} +(-6.95723 - 6.95723i) q^{89} +(-6.62651 - 3.35429i) q^{90} +(9.48365 + 1.02973i) q^{91} +3.92816i q^{92} +(-9.09294 - 2.17029i) q^{93} +(-3.48898 - 6.04309i) q^{94} +0.104903 q^{95} +(1.66007 - 0.494128i) q^{96} +(3.14895 - 11.7521i) q^{97} +(1.71295 - 6.78718i) q^{98} +(16.3134 - 5.34836i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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
$3$	1.52325	+	0.824446i	0.879448	+	0.475994i
$3$	1.52325	+	0.824446i	0.879448	+	0.475994i
$4$		−	1.00000i		−	0.500000i
$5$	2.39134	+	0.640759i	1.06944	+	0.286556i	0.750264	−	0.661139i	$-0.229927\pi$
$5$	2.39134	+	0.640759i	1.06944	+	0.286556i	0.319178	+	0.947695i	$0.396593\pi$
$6$	−1.66007	+	0.494128i	−0.677721	+	0.201727i
$7$	−0.703385	−	2.55054i	−0.265855	−	0.964013i
$7$	−0.703385	−	2.55054i	−0.265855	−	0.964013i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.64058	+	2.51167i	0.546859	+	0.837225i
$10$	−2.14402	+	1.23785i	−0.677999	+	0.391443i
$11$	1.48111	−	5.52759i	0.446572	−	1.66663i	−0.265179	−	0.964199i	$-0.585431\pi$
$11$	1.48111	−	5.52759i	0.446572	−	1.66663i	0.711751	−	0.702432i	$-0.247902\pi$
$12$	0.824446	−	1.52325i	0.237997	−	0.439724i
$13$	−1.32815	+	3.35202i	−0.368362	+	0.929683i
$13$	−1.32815	+	3.35202i	−0.368362	+	0.929683i
$14$	2.30087	+	1.30613i	0.614934	+	0.349079i
$15$	3.11434	+	2.94757i	0.804120	+	0.761059i
$16$	−1.00000			−0.250000
$17$	7.78434			1.88798			0.943990	−	0.329975i	$-0.107040\pi$
$17$	7.78434			1.88798			0.943990	+	0.329975i	$0.107040\pi$
$18$	−2.93608	−	0.615960i	−0.692042	−	0.145183i
$19$	0.0409293	−	0.0109670i	0.00938982	−	0.00251599i	−0.254121	−	0.967172i	$-0.581786\pi$
$19$	0.0409293	−	0.0109670i	0.00938982	−	0.00251599i	0.263511	+	0.964656i	$0.415120\pi$
$20$	0.640759	−	2.39134i	0.143278	−	0.534721i
$21$	1.03135	−	4.46501i	0.225059	−	0.974345i
$22$	2.86129	+	4.95590i	0.610029	+	1.05660i
$23$	−3.92816			−0.819077			−0.409539	−	0.912293i	$-0.634310\pi$
$23$	−3.92816			−0.819077			−0.409539	+	0.912293i	$0.634310\pi$
$24$	0.494128	+	1.66007i	0.100863	+	0.338861i
$25$	0.977829	+	0.564550i	0.195566	+	0.112910i
$26$	−1.43109	−	3.30938i	−0.280660	−	0.649022i
$27$	0.428265	+	5.17847i	0.0824196	+	0.996598i
$28$	−2.55054	+	0.703385i	−0.482007	+	0.132927i
$29$	−0.496669	−	0.286752i	−0.0922292	−	0.0532486i	0.453176	−	0.891421i	$-0.350291\pi$
$29$	−0.496669	−	0.286752i	−0.0922292	−	0.0532486i	−0.545405	+	0.838172i	$0.683624\pi$
$30$	−4.28642	+	0.117925i	−0.782590	+	0.0215301i
$31$	−5.21337	+	1.39692i	−0.936349	+	0.250894i	−0.694560	−	0.719435i	$-0.744401\pi$
$31$	−5.21337	+	1.39692i	−0.936349	+	0.250894i	−0.241789	+	0.970329i	$0.577734\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	6.81331	−	7.19880i	1.18604	−	1.25315i
$34$	−5.50436	+	5.50436i	−0.943990	+	0.943990i
$35$	−0.0477563	−	6.54992i	−0.00807230	−	1.10714i
$36$	2.51167	−	1.64058i	0.418612	−	0.273429i
$37$	6.33367	−	6.33367i	1.04125	−	1.04125i	0.0421367	−	0.999112i	$-0.486583\pi$
$37$	6.33367	−	6.33367i	1.04125	−	1.04125i	0.999112	−	0.0421367i	$-0.0134165\pi$
$38$	−0.0211866	+	0.0366962i	−0.00343691	+	0.00595291i
$39$	−4.78666	+	4.01097i	−0.766479	+	0.642270i
$40$	1.23785	+	2.14402i	0.195721	+	0.338999i
$41$	1.41205	+	5.26984i	0.220525	+	0.823011i	0.984148	+	0.177349i	$0.0567520\pi$
$41$	1.41205	+	5.26984i	0.220525	+	0.823011i	−0.763623	+	0.645662i	$0.776581\pi$
$42$	2.42796	+	3.88651i	0.374643	+	0.599702i
$43$	−4.42948	+	2.55736i	−0.675490	+	0.389994i	−0.798154	−	0.602454i	$-0.794190\pi$
$43$	−4.42948	+	2.55736i	−0.675490	+	0.389994i	0.122664	+	0.992448i	$0.460856\pi$
$44$	−5.52759	−	1.48111i	−0.833316	−	0.223286i
$45$	2.31380	+	7.05749i	0.344922	+	1.05207i
$46$	2.77763	−	2.77763i	0.409539	−	0.409539i
$47$	−1.80603	+	6.74019i	−0.263436	+	0.983158i	0.699764	+	0.714374i	$0.253288\pi$
$47$	−1.80603	+	6.74019i	−0.263436	+	0.983158i	−0.963200	+	0.268784i	$0.913378\pi$
$48$	−1.52325	−	0.824446i	−0.219862	−	0.118999i
$49$	−6.01050	+	3.58802i	−0.858643	+	0.512575i
$50$	−1.09063	+	0.292232i	−0.154238	+	0.0413279i
$51$	11.8575	+	6.41777i	1.66038	+	0.898668i
$52$	3.35202	+	1.32815i	0.464841	+	0.184181i
$53$	−3.45966	−	1.99744i	−0.475221	−	0.274369i	0.243202	−	0.969976i	$-0.421802\pi$
$53$	−3.45966	−	1.99744i	−0.475221	−	0.274369i	−0.718423	+	0.695607i	$0.755136\pi$
$54$	−3.96456	−	3.35890i	−0.539509	−	0.457089i
$55$	7.08370	−	12.2693i	0.955166	−	1.65440i
$56$	1.30613	−	2.30087i	0.174540	−	0.307467i
$57$	0.0713872	+	0.0170386i	0.00945546	+	0.00225681i
$58$	0.553963	−	0.148434i	0.0727389	−	0.0194903i
$59$	−1.36857	−	1.36857i	−0.178173	−	0.178173i	0.612386	−	0.790559i	$-0.290210\pi$
$59$	−1.36857	−	1.36857i	−0.178173	−	0.178173i	−0.790559	+	0.612386i	$0.790210\pi$
$60$	2.94757	−	3.11434i	0.380530	−	0.402060i
$61$	−5.77032	+	9.99448i	−0.738813	+	1.27966i	0.214217	+	0.976786i	$0.431280\pi$
$61$	−5.77032	+	9.99448i	−0.738813	+	1.27966i	−0.953030	+	0.302876i	$0.902053\pi$
$62$	2.69864	−	4.67418i	0.342727	−	0.593621i
$63$	5.25217	−	5.95103i	0.661711	−	0.749759i
$64$			1.00000i			0.125000i
$65$	−5.32389	+	7.16481i	−0.660348	+	0.888685i
$66$	0.272584	+	9.90805i	0.0335528	+	1.21960i
$67$	1.84292	−	6.87786i	0.225148	−	0.840264i	−0.757197	−	0.653186i	$-0.773432\pi$
$67$	1.84292	−	6.87786i	0.225148	−	0.840264i	0.982345	−	0.187078i	$-0.0599016\pi$
$68$		−	7.78434i		−	0.943990i
$69$	−5.98356	−	3.23855i	−0.720336	−	0.389876i
$70$	4.66526	+	4.59772i	0.557605	+	0.549533i
$71$	1.41008	+	0.377829i	0.167346	+	0.0448401i	0.341519	−	0.939875i	$-0.389059\pi$
$71$	1.41008	+	0.377829i	0.167346	+	0.0448401i	−0.174173	+	0.984715i	$0.555725\pi$
$72$	−0.615960	+	2.93608i	−0.0725916	+	0.346021i
$73$	3.90570	+	14.5763i	0.457127	+	1.70602i	0.681758	+	0.731578i	$0.261216\pi$
$73$	3.90570	+	14.5763i	0.457127	+	1.70602i	−0.224630	+	0.974444i	$0.572117\pi$
$74$			8.95716i			1.04125i
$75$	1.02404	+	1.66612i	0.118245	+	0.192387i
$76$	−0.0109670	−	0.0409293i	−0.00125800	−	0.00469491i
$77$	−15.1401	+	0.110389i	−1.72538	+	0.0125800i
$78$	0.548493	−	6.22086i	0.0621046	−	0.704374i
$79$	0.0358923	+	0.0621672i	0.00403820	+	0.00699436i	0.868037	−	0.496499i	$-0.165381\pi$
$79$	0.0358923	+	0.0621672i	0.00403820	+	0.00699436i	−0.863999	+	0.503493i	$0.832048\pi$
$80$	−2.39134	−	0.640759i	−0.267360	−	0.0716390i
$81$	−3.61702	+	8.24119i	−0.401891	+	0.915687i
$82$	−4.72481	−	2.72787i	−0.521768	−	0.301243i
$83$	−0.675019	+	0.675019i	−0.0740930	+	0.0740930i	−0.743182	−	0.669089i	$-0.766684\pi$
$83$	−0.675019	+	0.675019i	−0.0740930	+	0.0740930i	0.669089	+	0.743182i	$0.266684\pi$
$84$	−4.46501	−	1.03135i	−0.487173	−	0.112530i
$85$	18.6150	+	4.98788i	2.01908	+	0.541012i
$86$	1.32379	−	4.94045i	0.142748	−	0.532742i
$87$	−0.520139	−	0.846272i	−0.0557648	−	0.0907299i
$88$	4.95590	−	2.86129i	0.528301	−	0.305015i
$89$	−6.95723	−	6.95723i	−0.737465	−	0.737465i	0.234622	−	0.972087i	$-0.424615\pi$
$89$	−6.95723	−	6.95723i	−0.737465	−	0.737465i	−0.972087	+	0.234622i	$0.924615\pi$
$90$	−6.62651	−	3.35429i	−0.698495	−	0.353574i
$91$	9.48365	+	1.02973i	0.994157	+	0.107945i
$92$			3.92816i			0.409539i
$93$	−9.09294	−	2.17029i	−0.942894	−	0.225048i
$94$	−3.48898	−	6.04309i	−0.359861	−	0.623297i
$95$	0.104903			0.0107628
$96$	1.66007	−	0.494128i	0.169430	−	0.0504317i
$97$	3.14895	−	11.7521i	0.319728	−	1.19324i	−0.599779	−	0.800166i	$-0.704745\pi$
$97$	3.14895	−	11.7521i	0.319728	−	1.19324i	0.919507	−	0.393075i	$-0.128589\pi$
$98$	1.71295	−	6.78718i	0.173034	−	0.685609i
$99$	16.3134	−	5.34836i	1.63956	−	0.537530i
$100$	0.564550	−	0.977829i	0.0564550	−	0.0977829i
$101$	−0.178616	−	0.309372i	−0.0177730	−	0.0307837i	0.857002	−	0.515313i	$-0.172324\pi$
$101$	−0.178616	−	0.309372i	−0.0177730	−	0.0307837i	−0.874775	+	0.484529i	$0.838991\pi$
$102$	−12.9226	+	3.84646i	−1.27952	+	0.380856i
$103$	−10.1527	+	5.86169i	−1.00038	+	0.577570i	−0.908361	−	0.418188i	$-0.862665\pi$
$103$	−10.1527	+	5.86169i	−1.00038	+	0.577570i	−0.0920193	+	0.995757i	$0.529332\pi$
$104$	−3.30938	+	1.43109i	−0.324511	+	0.140330i
$105$	5.32731	−	10.0165i	0.519892	−	0.977513i
$106$	3.85875	−	1.03395i	0.374795	−	0.100426i
$107$		−	2.43878i		−	0.235765i	−0.993028	−	0.117883i	$-0.962389\pi$
$107$		−	2.43878i		−	0.235765i	0.993028	−	0.117883i	$-0.0376107\pi$
$108$	5.17847	−	0.428265i	0.498299	−	0.0412098i
$109$	−0.934204	+	0.250319i	−0.0894805	+	0.0239762i	−0.303282	−	0.952901i	$-0.598082\pi$
$109$	−0.934204	+	0.250319i	−0.0894805	+	0.0239762i	0.213801	+	0.976877i	$0.431416\pi$
$110$	3.66679	+	13.6847i	0.349615	+	1.30478i
$111$	14.8695	−	4.42598i	1.41135	−	0.420096i
$112$	0.703385	+	2.55054i	0.0664637	+	0.241003i
$113$	10.6463	−	6.14663i	1.00152	−	0.578227i	0.0928209	−	0.995683i	$-0.470412\pi$
$113$	10.6463	−	6.14663i	1.00152	−	0.578227i	0.908697	+	0.417456i	$0.137078\pi$
$114$	−0.0625264	+	0.0384303i	−0.00585614	+	0.00359932i
$115$	−9.39357	−	2.51700i	−0.875955	−	0.234711i
$116$	−0.286752	+	0.496669i	−0.0266243	+	0.0461146i
$117$	−10.5981	+	2.16337i	−0.979795	+	0.200003i
$118$	1.93546			0.178173
$119$	−5.47539	−	19.8543i	−0.501928	−	1.82004i
$120$	0.117925	+	4.28642i	0.0107650	+	0.391295i
$121$	−18.8343	−	10.8740i	−1.71221	−	0.988543i
$122$	−2.98694	−	11.1474i	−0.270424	−	1.00924i
$123$	−2.19380	+	9.19144i	−0.197808	+	0.828764i
$124$	1.39692	+	5.21337i	0.125447	+	0.468174i
$125$	−6.77634	−	6.77634i	−0.606095	−	0.606095i
$126$	0.494170	+	7.92186i	0.0440241	+	0.705735i
$127$	−6.58830	−	3.80376i	−0.584618	−	0.337529i	0.178349	−	0.983967i	$-0.442924\pi$
$127$	−6.58830	−	3.80376i	−0.584618	−	0.337529i	−0.762966	+	0.646438i	$0.776258\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.85561	+	0.243630i	−0.779693	+	0.0214504i
$130$	−1.30172	−	8.83084i	−0.114169	−	0.774516i
$131$	6.29363	−	3.63363i	0.549877	−	0.317472i	−0.199195	−	0.979960i	$-0.563833\pi$
$131$	6.29363	−	3.63363i	0.549877	−	0.317472i	0.749072	+	0.662488i	$0.230500\pi$
$132$	−7.19880	−	6.81331i	−0.626575	−	0.593022i
$133$	−0.0567607	−	0.0966777i	−0.00492178	−	0.00838302i
$134$	3.56024	+	6.16652i	0.307558	+	0.532706i
$135$	−2.29402	+	12.6579i	−0.197438	+	1.08942i
$136$	5.50436	+	5.50436i	0.471995	+	0.471995i
$137$	−10.1389	−	10.1389i	−0.866221	−	0.866221i	0.125831	−	0.992052i	$-0.459840\pi$
$137$	−10.1389	−	10.1389i	−0.866221	−	0.866221i	−0.992052	+	0.125831i	$0.959840\pi$
$138$	6.52102	−	1.94101i	0.555106	−	0.165230i
$139$	−9.26030	−	16.0393i	−0.785448	−	1.36044i	−0.928731	−	0.370754i	$-0.879099\pi$
$139$	−9.26030	−	16.0393i	−0.785448	−	1.36044i	0.143283	−	0.989682i	$-0.454234\pi$
$140$	−6.54992	+	0.0477563i	−0.553569	+	0.00403615i
$141$	−8.30796	+	8.77802i	−0.699656	+	0.739243i
$142$	−1.26424	+	0.729910i	−0.106093	+	0.0612527i
$143$	16.5614	+	12.3062i	1.38494	+	1.02909i
$144$	−1.64058	−	2.51167i	−0.136715	−	0.209306i
$145$	−1.00397	−	1.00397i	−0.0833751	−	0.0833751i
$146$	−13.0687	−	7.54523i	−1.08157	−	0.624447i
$147$	−12.1136	+	0.510120i	−0.999114	+	0.0420740i
$148$	−6.33367	−	6.33367i	−0.520624	−	0.520624i
$149$	0.405922	+	1.51492i	0.0332545	+	0.124107i	0.980558	−	0.196231i	$-0.0628702\pi$
$149$	0.405922	+	1.51492i	0.0332545	+	0.124107i	−0.947303	+	0.320338i	$0.896203\pi$
$150$	−1.90223	−	0.454020i	−0.155316	−	0.0370706i
$151$	−0.820601	−	3.06252i	−0.0667795	−	0.249225i	0.924464	−	0.381269i	$-0.124513\pi$
$151$	−0.820601	−	3.06252i	−0.0667795	−	0.249225i	−0.991244	+	0.132044i	$0.957846\pi$
$152$	0.0366962	+	0.0211866i	0.00297645	+	0.00171846i
$153$	12.7708	+	19.5517i	1.03246	+	1.58066i
$154$	10.6276	−	10.7837i	0.856399	−	0.868979i
$155$	−13.3620			−1.07327
$156$	4.01097	+	4.78666i	0.321135	+	0.383239i
$157$	−4.62867	+	8.01710i	−0.369408	+	0.639834i	−0.989473	−	0.144717i	$-0.953773\pi$
$157$	−4.62867	+	8.01710i	−0.369408	+	0.639834i	0.620065	+	0.784551i	$0.287106\pi$
$158$	−0.0693386	−	0.0185792i	−0.00551628	−	0.00147808i
$159$	−3.62315	−	5.89490i	−0.287334	−	0.467496i
$160$	2.14402	−	1.23785i	0.169500	−	0.0978607i
$161$	2.76301	+	10.0189i	0.217755	+	0.789601i
$162$	−3.26978	−	8.38502i	−0.256898	−	0.658789i
$163$	−0.541593	−	2.02125i	−0.0424208	−	0.158317i	0.941466	−	0.337107i	$-0.109448\pi$
$163$	−0.541593	−	2.02125i	−0.0424208	−	0.158317i	−0.983887	+	0.178790i	$0.942782\pi$
$164$	5.26984	−	1.41205i	0.411505	−	0.110263i
$165$	20.9057	−	12.8491i	1.62750	−	1.00030i
$166$		−	0.954621i		−	0.0740930i
$167$	19.2306	−	5.15284i	1.48811	−	0.398738i	0.579013	−	0.815318i	$-0.303438\pi$
$167$	19.2306	−	5.15284i	1.48811	−	0.398738i	0.909099	+	0.416580i	$0.136771\pi$
$168$	3.88651	−	2.42796i	0.299851	−	0.187321i
$169$	−9.47205	−	8.90395i	−0.728619	−	0.684919i
$170$	−16.6898	+	9.63585i	−1.28005	+	0.739036i
$171$	0.0946930	+	0.0848089i	0.00724136	+	0.00648550i
$172$	2.55736	+	4.42948i	0.194997	+	0.337745i
$173$	−1.87505	+	3.24769i	−0.142558	+	0.246917i	−0.928459	−	0.371435i	$-0.878866\pi$
$173$	−1.87505	+	3.24769i	−0.142558	+	0.246917i	0.785901	+	0.618352i	$0.212199\pi$
$174$	0.966199	+	0.230611i	0.0732474	+	0.0174826i
$175$	0.752115	−	2.89109i	0.0568546	−	0.218546i
$176$	−1.48111	+	5.52759i	−0.111643	+	0.416658i
$177$	−0.956363	−	3.21300i	−0.0718847	−	0.241504i
$178$	9.83900			0.737465
$179$	4.77595	+	8.27218i	0.356971	+	0.618292i	0.987453	−	0.157912i	$-0.0504762\pi$
$179$	4.77595	+	8.27218i	0.356971	+	0.618292i	−0.630482	+	0.776204i	$0.717143\pi$
$180$	7.05749	−	2.31380i	0.526034	−	0.172461i
$181$			1.46463i			0.108865i	0.998517	+	0.0544324i	$0.0173349\pi$
$181$			1.46463i			0.108865i	−0.998517	+	0.0544324i	$0.982665\pi$
$182$	−7.43408	+	5.97783i	−0.551051	+	0.443106i
$183$	−17.0295	+	10.4668i	−1.25886	+	0.773726i
$184$	−2.77763	−	2.77763i	−0.204769	−	0.204769i
$185$	19.2043	−	11.0876i	1.41193	−	0.815179i
$186$	7.96431	−	4.89506i	0.583971	−	0.358923i
$187$	11.5295	−	43.0286i	0.843120	−	3.14657i
$188$	6.74019	+	1.80603i	0.491579	+	0.131718i
$189$	12.9067	−	4.73477i	0.938822	−	0.344404i
$190$	−0.0741777	+	0.0741777i	−0.00538142	+	0.00538142i
$191$	−5.48746	−	3.16819i	−0.397059	−	0.229242i	0.288155	−	0.957584i	$-0.406958\pi$
$191$	−5.48746	−	3.16819i	−0.397059	−	0.229242i	−0.685214	+	0.728342i	$0.740291\pi$
$192$	−0.824446	+	1.52325i	−0.0594993	+	0.109931i
$193$	−4.89481	−	1.31156i	−0.352336	−	0.0944081i	0.0783100	−	0.996929i	$-0.475048\pi$
$193$	−4.89481	−	1.31156i	−0.352336	−	0.0944081i	−0.430646	+	0.902521i	$0.641714\pi$
$194$	6.08331	+	10.5366i	0.436756	+	0.756484i
$195$	−14.0166	+	6.52452i	−1.00375	+	0.467231i
$196$	3.58802	+	6.01050i	0.256287	+	0.429321i
$197$	−0.215514	−	0.804307i	−0.0153547	−	0.0573045i	0.957823	−	0.287357i	$-0.0927767\pi$
$197$	−0.215514	−	0.804307i	−0.0153547	−	0.0573045i	−0.973178	+	0.230053i	$0.926110\pi$
$198$	−7.75345	+	15.3172i	−0.551014	+	1.08854i
$199$		−	0.839174i		−	0.0594875i	−0.999558	−	0.0297437i	$-0.990531\pi$
$199$		−	0.839174i		−	0.0594875i	0.999558	−	0.0297437i	$-0.00946912\pi$
$200$	0.292232	+	1.09063i	0.0206639	+	0.0771189i
$201$	8.47765	−	8.95730i	0.597967	−	0.631800i
$202$	0.345060	+	0.0924584i	0.0242783	+	0.00650535i
$203$	−0.382023	+	1.46847i	−0.0268127	+	0.103067i
$204$	6.41777	−	11.8575i	0.449334	−	0.830190i
$205$			13.5068i			0.943355i
$206$	3.03423	−	11.3239i	0.211405	−	0.788975i
$207$	−6.44444	−	9.86625i	−0.447919	−	0.685752i
$208$	1.32815	−	3.35202i	0.0920904	−	0.232421i
$209$		−	0.242484i		−	0.0167729i
$210$	3.31578	+	10.8497i	0.228810	+	0.748703i
$211$	−13.4074	+	23.2222i	−0.923001	+	1.59868i	−0.128255	+	0.991741i	$0.540938\pi$
$211$	−13.4074	+	23.2222i	−0.923001	+	1.59868i	−0.794745	+	0.606943i	$0.792396\pi$
$212$	−1.99744	+	3.45966i	−0.137185	+	0.237611i
$213$	1.83640	+	1.73806i	0.125828	+	0.119090i
$214$	1.72448	+	1.72448i	0.117883	+	0.117883i
$215$	−12.2311	+	3.27731i	−0.834152	+	0.223510i
$216$	−3.35890	+	3.96456i	−0.228545	+	0.269754i
$217$	7.22990	+	12.3143i	0.490798	+	0.835951i
$218$	0.483580	−	0.837585i	0.0327521	−	0.0567284i
$219$	−6.06800	+	25.4233i	−0.410037	+	1.71795i
$220$	−12.2693	−	7.08370i	−0.827198	−	0.477583i
$221$	−10.3387	+	26.0932i	−0.695459	+	1.75522i
$222$	−7.38470	+	13.6440i	−0.495628	+	0.915724i
$223$	23.0072	−	6.16476i	1.54068	−	0.412823i	0.614192	−	0.789157i	$-0.289482\pi$
$223$	23.0072	−	6.16476i	1.54068	−	0.412823i	0.926484	+	0.376334i	$0.122816\pi$
$224$	−2.30087	−	1.30613i	−0.153733	−	0.0872698i
$225$	0.186237	+	3.38217i	0.0124158	+	0.225478i
$226$	−3.18173	+	11.8744i	−0.211646	+	0.789872i
$227$	−3.50350	+	3.50350i	−0.232535	+	0.232535i	−0.813750	−	0.581215i	$-0.802578\pi$
$227$	−3.50350	+	3.50350i	−0.232535	+	0.232535i	0.581215	+	0.813750i	$0.302578\pi$
$228$	0.0170386	−	0.0713872i	0.00112841	−	0.00472773i
$229$	−8.33396	−	2.23308i	−0.550723	−	0.147566i	−0.0272823	−	0.999628i	$-0.508685\pi$
$229$	−8.33396	−	2.23308i	−0.550723	−	0.147566i	−0.523441	+	0.852062i	$0.675352\pi$
$230$	8.42205	−	4.86247i	0.555333	−	0.320622i
$231$	−23.1532	−	12.3141i	−1.52337	−	0.810207i
$232$	−0.148434	−	0.553963i	−0.00974516	−	0.0363694i
$233$	−4.33158	−	7.50251i	−0.283771	−	0.491506i	0.688539	−	0.725199i	$-0.258252\pi$
$233$	−4.33158	−	7.50251i	−0.283771	−	0.491506i	−0.972310	+	0.233693i	$0.924919\pi$
$234$	5.96426	−	9.02372i	0.389896	−	0.589899i
$235$	−8.63768	+	14.9609i	−0.563460	+	0.975941i
$236$	−1.36857	+	1.36857i	−0.0890866	+	0.0890866i
$237$	0.00341931	+	0.124287i	0.000222108	+	0.00807334i
$238$	17.9108	+	10.1674i	1.16098	+	0.659054i
$239$	3.07238	−	3.07238i	0.198736	−	0.198736i	−0.600722	−	0.799458i	$-0.705120\pi$
$239$	3.07238	−	3.07238i	0.198736	−	0.198736i	0.799458	+	0.600722i	$0.205120\pi$
$240$	−3.11434	−	2.94757i	−0.201030	−	0.190265i
$241$	12.0272	−	12.0272i	0.774741	−	0.774741i	−0.204190	−	0.978931i	$-0.565456\pi$
$241$	12.0272	−	12.0272i	0.774741	−	0.774741i	0.978931	+	0.204190i	$0.0654561\pi$
$242$	21.0069	−	5.62878i	1.35038	−	0.361832i
$243$	−12.3040	+	9.57134i	−0.789305	+	0.614002i
$244$	9.99448	+	5.77032i	0.639831	+	0.369407i
$245$	−16.6722	+	4.72892i	−1.06515	+	0.302120i
$246$	−4.94808	−	8.05058i	−0.315478	−	0.513286i
$247$	−0.0175986	+	0.151761i	−0.00111977	+	0.00965635i
$248$	−4.67418	−	2.69864i	−0.296811	−	0.171364i
$249$	−1.58474	+	0.471705i	−0.100429	+	0.0298931i
$250$	9.58320			0.606095
$251$	12.6415	+	21.8958i	0.797926	+	1.38205i	0.920964	+	0.389647i	$0.127403\pi$
$251$	12.6415	+	21.8958i	0.797926	+	1.38205i	−0.123038	+	0.992402i	$0.539264\pi$
$252$	−5.95103	−	5.25217i	−0.374880	−	0.330855i
$253$	−5.81804	+	21.7132i	−0.365777	+	1.36510i
$254$	7.34830	−	1.96897i	0.461073	−	0.123544i
$255$	24.2431	+	22.9449i	1.51816	+	1.43686i
$256$	1.00000			0.0625000
$257$	0.853029			0.0532105			0.0266053	−	0.999646i	$-0.491530\pi$
$257$	0.853029			0.0532105			0.0266053	+	0.999646i	$0.491530\pi$
$258$	6.08959	−	6.43414i	0.379121	−	0.400572i
$259$	−20.6093	−	11.6993i	−1.28060	−	0.726956i
$260$	7.16481	+	5.32389i	0.444342	+	0.330174i
$261$	−0.0945957	−	1.71791i	−0.00585532	−	0.106336i
$262$	−1.88090	+	7.01963i	−0.116203	+	0.433674i
$263$	2.80809	−	1.62125i	0.173154	−	0.0999705i	−0.410918	−	0.911672i	$-0.634792\pi$
$263$	2.80809	−	1.62125i	0.173154	−	0.0999705i	0.584072	+	0.811702i	$0.301458\pi$
$264$	9.90805	−	0.272584i	0.609799	−	0.0167764i
$265$	−6.99337	−	6.99337i	−0.429599	−	0.429599i
$266$	0.108497	+	0.0282256i	0.00665240	+	0.00173062i
$267$	−4.86173	−	16.3335i	−0.297533	−	0.999591i
$268$	−6.87786	−	1.84292i	−0.420132	−	0.112574i
$269$		−	2.96347i		−	0.180686i	−0.995911	−	0.0903429i	$-0.971204\pi$
$269$		−	2.96347i		−	0.180686i	0.995911	−	0.0903429i	$-0.0287963\pi$
$270$	−7.32839	−	10.5726i	−0.445991	−	0.643430i
$271$	−17.1536	+	17.1536i	−1.04201	+	1.04201i	−0.0429287	+	0.999078i	$0.513669\pi$
$271$	−17.1536	+	17.1536i	−1.04201	+	1.04201i	−0.999078	+	0.0429287i	$0.986331\pi$
$272$	−7.78434			−0.471995
$273$	13.5970	+	9.38730i	0.822928	+	0.568145i
$274$	14.3385			0.866221
$275$	4.56887	−	4.56887i	0.275513	−	0.275513i
$276$	−3.23855	+	5.98356i	−0.194938	+	0.360168i
$277$			28.9470i			1.73926i	0.493707	+	0.869628i	$0.335641\pi$
$277$			28.9470i			1.73926i	−0.493707	+	0.869628i	$0.664359\pi$
$278$	17.8895	+	4.79348i	1.07294	+	0.287494i
$279$	−12.0615	−	10.8025i	−0.722105	−	0.646731i
$280$	4.59772	−	4.66526i	0.274766	−	0.278803i
$281$	22.0807	+	22.0807i	1.31722	+	1.31722i	0.915965	+	0.401258i	$0.131427\pi$
$281$	22.0807	+	22.0807i	1.31722	+	1.31722i	0.401258	+	0.915965i	$0.368573\pi$
$282$	−0.332381	−	12.0816i	−0.0197930	−	0.719449i
$283$	10.7216	−	6.19011i	0.637332	−	0.367964i	−0.146254	−	0.989247i	$-0.546722\pi$
$283$	10.7216	−	6.19011i	0.637332	−	0.367964i	0.783586	+	0.621283i	$0.213388\pi$
$284$	0.377829	−	1.41008i	0.0224201	−	0.0836728i
$285$	0.159794	+	0.0864870i	0.00946536	+	0.00512305i
$286$	−20.4125	+	3.00893i	−1.20702	+	0.177922i
$287$	12.4477	−	7.30822i	0.734766	−	0.431390i
$288$	2.93608	+	0.615960i	0.173010	+	0.0362958i
$289$	43.5959			2.56447
$290$	1.41983			0.0833751
$291$	14.4856	−	15.3052i	0.849160	−	0.897205i
$292$	14.5763	−	3.90570i	0.853011	−	0.228564i
$293$	6.53976	−	24.4067i	0.382057	−	1.42586i	−0.460697	−	0.887558i	$-0.652400\pi$
$293$	6.53976	−	24.4067i	0.382057	−	1.42586i	0.842754	−	0.538299i	$-0.180933\pi$
$294$	8.20491	−	8.92633i	0.478520	−	0.520594i
$295$	−2.39581	−	4.14966i	−0.139489	−	0.241602i
$296$	8.95716			0.520624
$297$	29.2588	+	5.30263i	1.69777	+	0.307690i
$298$	−1.35824	−	0.784182i	−0.0786809	−	0.0454264i
$299$	5.21717	−	13.1672i	0.301717	−	0.761482i
$300$	1.66612	−	1.02404i	0.0961933	−	0.0591227i
$301$	9.63829	+	9.49876i	0.555542	+	0.547499i
$302$	2.74578	+	1.58528i	0.158002	+	0.0912225i
$303$	−0.0170160	−	0.618510i	−0.000977546	−	0.0355325i
$304$	−0.0409293	+	0.0109670i	−0.00234745	+	0.000628999i
$305$	−20.2029	+	20.2029i	−1.15681	+	1.15681i
$306$	−22.8555	−	4.79484i	−1.30656	−	0.274103i
$307$	2.47641	−	2.47641i	0.141336	−	0.141336i	−0.632899	−	0.774235i	$-0.718135\pi$
$307$	2.47641	−	2.47641i	0.141336	−	0.141336i	0.774235	+	0.632899i	$0.218135\pi$
$308$	0.110389	+	15.1401i	0.00628998	+	0.862689i
$309$	−20.2978	+	0.558420i	−1.15470	+	0.0317674i
$310$	9.44839	−	9.44839i	0.536633	−	0.536633i
$311$	10.4287	−	18.0630i	0.591356	−	1.02426i	−0.402694	−	0.915335i	$-0.631926\pi$
$311$	10.4287	−	18.0630i	0.591356	−	1.02426i	0.994050	−	0.108924i	$-0.0347406\pi$
$312$	−6.22086	−	0.548493i	−0.352187	−	0.0310523i
$313$	−0.995941	−	1.72502i	−0.0562939	−	0.0975039i	0.836505	−	0.547959i	$-0.184595\pi$
$313$	−0.995941	−	1.72502i	−0.0562939	−	0.0975039i	−0.892799	+	0.450455i	$0.851262\pi$
$314$	−2.39598	−	8.94191i	−0.135213	−	0.504621i
$315$	16.3729	−	10.8656i	0.922509	−	0.612206i
$316$	0.0621672	−	0.0358923i	0.00349718	−	0.00201910i
$317$	6.77720	+	1.81594i	0.380645	+	0.101994i	0.444068	−	0.895993i	$-0.353535\pi$
$317$	6.77720	+	1.81594i	0.380645	+	0.101994i	−0.0634225	+	0.997987i	$0.520202\pi$
$318$	6.73028	+	1.60637i	0.377415	+	0.0900809i
$319$	−2.32067	+	2.32067i	−0.129933	+	0.129933i
$320$	−0.640759	+	2.39134i	−0.0358195	+	0.133680i
$321$	2.01064	−	3.71487i	0.112223	−	0.207344i
$322$	−9.03818	−	5.13070i	−0.503678	−	0.285923i
$323$	0.318607	−	0.0853706i	0.0177278	−	0.00475015i
$324$	8.24119	+	3.61702i	0.457844	+	0.200946i
$325$	−3.19108	+	2.52789i	−0.177009	+	0.140222i
$326$	1.81220	+	1.04628i	0.100369	+	0.0579479i
$327$	−1.62940	−	0.388903i	−0.0901061	−	0.0215064i
$328$	−2.72787	+	4.72481i	−0.150621	+	0.260884i
$329$	18.4615	−	0.134605i	1.01781	−	0.00742102i
$330$	−5.69683	+	23.8682i	−0.313600	+	1.31390i
$331$	−10.9650	+	2.93806i	−0.602690	+	0.161490i	−0.547246	−	0.836972i	$-0.684324\pi$
$331$	−10.9650	+	2.93806i	−0.602690	+	0.161490i	−0.0554436	+	0.998462i	$0.517657\pi$
$332$	0.675019	+	0.675019i	0.0370465	+	0.0370465i
$333$	26.2990	+	5.51725i	1.44118	+	0.302343i
$334$	−9.95452	+	17.2417i	−0.544687	+	0.943425i
$335$	8.81409	−	15.2665i	0.481565	−	0.834096i
$336$	−1.03135	+	4.46501i	−0.0562648	+	0.243586i
$337$			22.2939i			1.21442i	0.794540	+	0.607212i	$0.207712\pi$
$337$			22.2939i			1.21442i	−0.794540	+	0.607212i	$0.792288\pi$
$338$	12.9938	−	0.401710i	0.706769	−	0.0218502i
$339$	21.2845	−	0.585565i	1.15602	−	0.0318035i
$340$	4.98788	−	18.6150i	0.270506	−	1.00954i
$341$			30.8864i			1.67259i
$342$	−0.126927	+	0.00698915i	−0.00686343	+	0.000377930i
$343$	13.3791	+	12.8062i	0.722403	+	0.691472i
$344$	−4.94045	−	1.32379i	−0.266371	−	0.0713739i
$345$	−12.2336	−	11.5785i	−0.658636	−	0.623366i
$346$	−0.970598	−	3.62232i	−0.0521797	−	0.194737i
$347$		−	13.8722i		−	0.744700i	−0.928092	−	0.372350i	$-0.878552\pi$
$347$		−	13.8722i		−	0.744700i	0.928092	−	0.372350i	$-0.121448\pi$
$348$	−0.846272	+	0.520139i	−0.0453650	+	0.0278824i
$349$	7.81705	+	29.1736i	0.418437	+	1.56163i	0.777851	+	0.628449i	$0.216310\pi$
$349$	7.81705	+	29.1736i	0.418437	+	1.56163i	−0.359414	+	0.933178i	$0.617023\pi$
$350$	1.51248	+	2.57613i	0.0808455	+	0.137700i
$351$	−17.9271	−	5.44222i	−0.956880	−	0.290484i
$352$	−2.86129	−	4.95590i	−0.152507	−	0.264150i
$353$	−25.4363	−	6.81565i	−1.35384	−	0.362760i	−0.492289	−	0.870432i	$-0.663840\pi$
$353$	−25.4363	−	6.81565i	−1.35384	−	0.362760i	−0.861551	+	0.507672i	$0.830506\pi$
$354$	2.94818	+	1.59568i	0.156694	+	0.0848094i
$355$	3.12989	+	1.80704i	0.166117	+	0.0959078i
$356$	−6.95723	+	6.95723i	−0.368732	+	0.368732i
$357$	8.02839	−	34.7571i	0.424907	−	1.83954i
$358$	−9.22642	−	2.47221i	−0.487631	−	0.130660i
$359$	−9.23430	+	34.4629i	−0.487368	+	1.81888i	0.0817854	+	0.996650i	$0.473938\pi$
$359$	−9.23430	+	34.4629i	−0.487368	+	1.81888i	−0.569153	+	0.822231i	$0.692729\pi$
$360$	−3.35429	+	6.62651i	−0.176787	+	0.349248i
$361$	−16.4529	+	9.49910i	−0.865944	+	0.499953i
$362$	−1.03565	−	1.03565i	−0.0544324	−	0.0544324i
$363$	−19.7243	−	32.0916i	−1.03526	−	1.68437i
$364$	1.02973	−	9.48365i	0.0539725	−	0.497078i
$365$			37.3595i			1.95548i
$366$	4.64058	−	19.4428i	0.242567	−	1.01629i
$367$	1.12567	+	1.94972i	0.0587597	+	0.101775i	0.893909	−	0.448249i	$-0.147952\pi$
$367$	1.12567	+	1.94972i	0.0587597	+	0.101775i	−0.835149	+	0.550023i	$0.814619\pi$
$368$	3.92816			0.204769
$369$	−10.9196	+	12.1922i	−0.568449	+	0.634700i
$370$	−5.73938	+	21.4197i	−0.298376	+	1.11355i
$371$	−2.66107	+	10.2290i	−0.138156	+	0.531062i
$372$	−2.17029	+	9.09294i	−0.112524	+	0.471447i
$373$	7.42142	−	12.8543i	0.384267	−	0.665569i	−0.607401	−	0.794396i	$-0.707788\pi$
$373$	7.42142	−	12.8543i	0.384267	−	0.665569i	0.991667	+	0.128826i	$0.0411210\pi$
$374$	22.2733	+	38.5784i	1.15172	+	1.99484i
$375$	−4.73533	−	15.9088i	−0.244531	−	0.821526i
$376$	−6.04309	+	3.48898i	−0.311649	+	0.179930i
$377$	1.62085	−	1.28400i	0.0834780	−	0.0661291i
$378$	−5.77840	+	12.4744i	−0.297209	+	0.641613i
$379$	1.05885	−	0.283718i	0.0543895	−	0.0145736i	−0.231522	−	0.972830i	$-0.574370\pi$
$379$	1.05885	−	0.283718i	0.0543895	−	0.0145736i	0.285911	+	0.958256i	$0.407704\pi$
$380$		−	0.104903i		−	0.00538142i
$381$	−6.89963	−	11.2258i	−0.353479	−	0.575114i
$382$	6.12047	−	1.63997i	0.313150	−	0.0839084i
$383$	−1.41649	−	5.28643i	−0.0723795	−	0.270124i	0.920247	−	0.391338i	$-0.127988\pi$
$383$	−1.41649	−	5.28643i	−0.0723795	−	0.270124i	−0.992626	+	0.121214i	$0.961321\pi$
$384$	−0.494128	−	1.66007i	−0.0252159	−	0.0847152i
$385$	−36.2760	−	9.43719i	−1.84880	−	0.480964i
$386$	4.38856	−	2.53374i	0.223372	−	0.128964i
$387$	−13.6902	−	6.92987i	−0.695910	−	0.352265i
$388$	−11.7521	−	3.14895i	−0.596620	−	0.159864i
$389$	−14.5496	+	25.2006i	−0.737693	+	1.27772i	0.215839	+	0.976429i	$0.430751\pi$
$389$	−14.5496	+	25.2006i	−0.737693	+	1.27772i	−0.953532	+	0.301293i	$0.902582\pi$
$390$	5.29771	−	14.5248i	0.268260	−	0.735491i
$391$	−30.5781			−1.54640
$392$	−6.78718	−	1.71295i	−0.342804	−	0.0865169i
$393$	12.5825	−	0.346161i	0.634703	−	0.0174615i
$394$	0.721122	+	0.416340i	0.0363296	+	0.0209749i
$395$	0.0459966	+	0.171662i	0.00231434	+	0.00863723i
$396$	−5.34836	−	16.3134i	−0.268765	−	0.819779i
$397$	−1.65429	−	6.17388i	−0.0830262	−	0.309858i	0.911907	−	0.410397i	$-0.134610\pi$
$397$	−1.65429	−	6.17388i	−0.0830262	−	0.309858i	−0.994933	+	0.100539i	$0.967943\pi$
$398$	0.593386	+	0.593386i	0.0297437	+	0.0297437i
$399$	−0.00675514	−	0.194060i	−0.000338180	−	0.00971517i
$400$	−0.977829	−	0.564550i	−0.0488914	−	0.0282275i
$401$	−8.86439	−	8.86439i	−0.442667	−	0.442667i	0.450241	−	0.892907i	$-0.351338\pi$
$401$	−8.86439	−	8.86439i	−0.442667	−	0.442667i	−0.892907	+	0.450241i	$0.851338\pi$
$402$	0.339170	+	12.3284i	0.0169163	+	0.614883i
$403$	2.24163	−	19.3306i	0.111663	−	0.962927i
$404$	−0.309372	+	0.178616i	−0.0153918	+	0.00888648i
$405$	−13.9302	+	17.3899i	−0.692195	+	0.864110i
$406$	−0.768236	−	1.30850i	−0.0381269	−	0.0649396i
$407$	−25.6290	−	44.3908i	−1.27038	−	2.20037i
$408$	3.84646	+	12.9226i	0.190428	+	0.639762i
$409$	−18.8531	−	18.8531i	−0.932224	−	0.932224i	0.0656208	−	0.997845i	$-0.479097\pi$
$409$	−18.8531	−	18.8531i	−0.932224	−	0.932224i	−0.997845	+	0.0656208i	$0.979097\pi$
$410$	−9.55074	−	9.55074i	−0.471678	−	0.471678i
$411$	−7.08506	−	23.8030i	−0.349480	−	1.17411i
$412$	5.86169	+	10.1527i	0.288785	+	0.500190i
$413$	−2.52797	+	4.45324i	−0.124393	+	0.219129i
$414$	11.5334	+	2.41959i	0.566836	+	0.118916i
$415$	−2.04673	+	1.18168i	−0.100470	+	0.0580063i
$416$	1.43109	+	3.30938i	0.0701651	+	0.162256i
$417$	−0.882192	−	32.0665i	−0.0432011	−	1.57030i
$418$	0.171462	+	0.171462i	0.00838647	+	0.00838647i
$419$	16.1591	+	9.32948i	0.789425	+	0.455775i	0.839760	−	0.542958i	$-0.182696\pi$
$419$	16.1591	+	9.32948i	0.789425	+	0.455775i	−0.0503351	+	0.998732i	$0.516029\pi$
$420$	−10.0165	−	5.32731i	−0.488757	−	0.259946i
$421$	−21.5756	−	21.5756i	−1.05153	−	1.05153i	−0.998598	−	0.0529334i	$-0.983143\pi$
$421$	−21.5756	−	21.5756i	−1.05153	−	1.05153i	−0.0529334	−	0.998598i	$-0.516857\pi$
$422$	−6.94016	−	25.9010i	−0.337842	−	1.26084i
$423$	−19.8921	+	6.52164i	−0.967187	+	0.317093i
$424$	−1.03395	−	3.85875i	−0.0502130	−	0.187398i
$425$	7.61175	+	4.39465i	0.369224	+	0.213172i
$426$	−2.52753	+	0.0695357i	−0.122459	+	0.00336901i
$427$	29.5501	+	7.68744i	1.43003	+	0.372022i
$428$	−2.43878			−0.117883
$429$	15.0814	+	32.3994i	0.728138	+	1.56426i
$430$	6.33127	−	10.9661i	0.305321	−	0.528831i
$431$	−10.7745	−	2.88702i	−0.518990	−	0.139063i	−0.0101904	−	0.999948i	$-0.503244\pi$
$431$	−10.7745	−	2.88702i	−0.518990	−	0.139063i	−0.508799	+	0.860885i	$0.669910\pi$
$432$	−0.428265	−	5.17847i	−0.0206049	−	0.249149i
$433$	24.9227	−	14.3891i	1.19771	−	0.691497i	0.237664	−	0.971347i	$-0.423618\pi$
$433$	24.9227	−	14.3891i	1.19771	−	0.691497i	0.960044	+	0.279850i	$0.0902849\pi$
$434$	−13.8199	−	3.59523i	−0.663374	−	0.172577i
$435$	−0.701576	−	2.35701i	−0.0336380	−	0.113010i
$436$	0.250319	+	0.934204i	0.0119881	+	0.0447403i
$437$	−0.160777	+	0.0430799i	−0.00769099	+	0.00206079i
$438$	−13.6863	−	22.2677i	−0.653956	−	1.06399i
$439$		−	7.21511i		−	0.344358i	−0.985066	−	0.172179i	$-0.944919\pi$
$439$		−	7.21511i		−	0.344358i	0.985066	−	0.172179i	$-0.0550808\pi$
$440$	13.6847	−	3.66679i	0.652391	−	0.174808i
$441$	−18.8726	−	9.20999i	−0.898697	−	0.438571i
$442$	−11.1401	−	25.7613i	−0.529881	−	1.22534i
$443$	17.9991	−	10.3918i	0.855161	−	0.493728i	−0.00722759	−	0.999974i	$-0.502301\pi$
$443$	17.9991	−	10.3918i	0.855161	−	0.493728i	0.862389	+	0.506246i	$0.168967\pi$
$444$	−4.42598	−	14.8695i	−0.210048	−	0.705676i
$445$	−12.1792	−	21.0950i	−0.577350	−	1.00000i
$446$	−11.9094	+	20.6277i	−0.563926	+	0.976749i
$447$	−0.630652	+	2.64227i	−0.0298288	+	0.124975i
$448$	2.55054	−	0.703385i	0.120502	−	0.0332318i
$449$	5.60390	−	20.9140i	0.264465	−	0.986995i	−0.698113	−	0.715988i	$-0.745977\pi$
$449$	5.60390	−	20.9140i	0.264465	−	0.986995i	0.962577	−	0.271007i	$-0.0873567\pi$
$450$	−2.52325	−	2.25987i	−0.118947	−	0.106531i
$451$	31.2209			1.47014
$452$	−6.14663	−	10.6463i	−0.289113	−	0.500759i
$453$	1.27491	−	5.34153i	0.0599004	−	0.250967i
$454$		−	4.95469i		−	0.232535i
$455$	22.0189	+	8.53917i	1.03226	+	0.400323i
$456$	0.0384303	+	0.0625264i	0.00179966	+	0.00292807i
$457$	4.27974	+	4.27974i	0.200198	+	0.200198i	0.800085	−	0.599887i	$-0.204788\pi$
$457$	4.27974	+	4.27974i	0.200198	+	0.200198i	−0.599887	+	0.800085i	$0.704788\pi$
$458$	7.47202	−	4.31397i	0.349145	−	0.201579i
$459$	3.33376	+	40.3110i	0.155607	+	1.88156i
$460$	−2.51700	+	9.39357i	−0.117356	+	0.437978i
$461$	−13.3236	−	3.57005i	−0.620543	−	0.166274i	−0.0651682	−	0.997874i	$-0.520758\pi$
$461$	−13.3236	−	3.57005i	−0.620543	−	0.166274i	−0.555374	+	0.831600i	$0.687425\pi$
$462$	25.0791	−	7.66442i	1.16679	−	0.356581i
$463$	−4.62243	+	4.62243i	−0.214822	+	0.214822i	−0.806312	−	0.591490i	$-0.798540\pi$
$463$	−4.62243	+	4.62243i	−0.214822	+	0.214822i	0.591490	+	0.806312i	$0.298540\pi$
$464$	0.496669	+	0.286752i	0.0230573	+	0.0133121i
$465$	−20.3537	−	11.0163i	−0.943881	−	0.510868i
$466$	8.36796	+	2.24219i	0.387638	+	0.103867i
$467$	4.81509	+	8.33997i	0.222816	+	0.385928i	0.955662	−	0.294466i	$-0.0951419\pi$
$467$	4.81509	+	8.33997i	0.222816	+	0.385928i	−0.732846	+	0.680394i	$0.761809\pi$
$468$	2.16337	+	10.5981i	0.100002	+	0.489898i
$469$	−18.8385	+	0.137354i	−0.869882	+	0.00634243i
$470$	−4.47119	−	16.6867i	−0.206241	−	0.769700i
$471$	−13.6603	+	8.39594i	−0.629433	+	0.386865i
$472$		−	1.93546i		−	0.0890866i
$473$	7.57549	+	28.2721i	0.348321	+	1.29995i
$474$	−0.0903023	−	0.0854667i	−0.00414772	−	0.00392561i
$475$	0.0462132	+	0.0123828i	0.00212041	+	0.000568161i
$476$	−19.8543	+	5.47539i	−0.910018	+	0.250964i
$477$	−0.658927	−	11.9665i	−0.0301702	−	0.547908i
$478$			4.34501i			0.198736i
$479$	−5.58674	+	20.8500i	−0.255265	+	0.952661i	0.712678	+	0.701491i	$0.247482\pi$
$479$	−5.58674	+	20.8500i	−0.255265	+	0.952661i	−0.967943	+	0.251170i	$0.919185\pi$
$480$	4.28642	−	0.117925i	0.195647	−	0.00538252i
$481$	12.8185	+	29.6426i	0.584475	+	1.35159i
$482$			17.0091i			0.774741i
$483$	−4.05131	+	17.5393i	−0.184341	+	0.798064i
$484$	−10.8740	+	18.8343i	−0.494272	+	0.856104i
$485$	15.0605	−	26.0855i	0.683861	−	1.18448i
$486$	1.93231	−	15.4682i	0.0876513	−	0.701653i
$487$	−21.1129	−	21.1129i	−0.956716	−	0.956716i	0.0423849	−	0.999101i	$-0.486504\pi$
$487$	−21.1129	−	21.1129i	−0.956716	−	0.956716i	−0.999101	+	0.0423849i	$0.986504\pi$
$488$	−11.1474	+	2.98694i	−0.504619	+	0.135212i
$489$	0.841433	−	3.52538i	0.0380509	−	0.159423i
$490$	8.44519	−	15.1329i	0.381515	−	0.683635i
$491$	6.57987	−	11.3967i	0.296946	−	0.514325i	−0.678490	−	0.734610i	$-0.737365\pi$
$491$	6.57987	−	11.3967i	0.296946	−	0.514325i	0.975436	+	0.220285i	$0.0706987\pi$
$492$	9.19144	+	2.19380i	0.414382	+	0.0989041i
$493$	−3.86624	−	2.23218i	−0.174127	−	0.100532i
$494$	−0.0948674	−	0.119756i	−0.00426829	−	0.00538806i
$495$	42.4379	−	2.33682i	1.90744	−	0.105032i
$496$	5.21337	−	1.39692i	0.234087	−	0.0627235i
$497$	−0.0281600	−	3.86222i	−0.00126315	−	0.173244i
$498$	0.787034	−	1.45413i	0.0352678	−	0.0651610i
$499$	−1.81756	+	6.78322i	−0.0813651	+	0.303659i	−0.994601	−	0.103772i	$-0.966909\pi$
$499$	−1.81756	+	6.78322i	−0.0813651	+	0.303659i	0.913236	+	0.407431i	$0.133575\pi$
$500$	−6.77634	+	6.77634i	−0.303047	+	0.303047i
$501$	33.5413	+	8.00559i	1.49851	+	0.357663i
$502$	−24.4216	−	6.54374i	−1.08999	−	0.292061i
$503$	−29.4294	+	16.9911i	−1.31219	+	0.757593i	−0.982459	−	0.186481i	$-0.940292\pi$
$503$	−29.4294	+	16.9911i	−1.31219	+	0.757593i	−0.329732	+	0.944075i	$0.606958\pi$
$504$	7.92186	−	0.494170i	0.352867	−	0.0220121i
$505$	−0.228900	−	0.854265i	−0.0101859	−	0.0380143i
$506$	−11.2396	−	19.4676i	−0.499661	−	0.865438i
$507$	−7.08747	−	21.3721i	−0.314765	−	0.949169i
$508$	−3.80376	+	6.58830i	−0.168765	+	0.292309i
$509$	11.5175	−	11.5175i	0.510502	−	0.510502i	−0.404178	−	0.914680i	$-0.632442\pi$
$509$	11.5175	−	11.5175i	0.510502	−	0.510502i	0.914680	+	0.404178i	$0.132442\pi$
$510$	−33.3669	+	0.917969i	−1.47751	+	0.0406484i
$511$	34.4301	−	20.2144i	1.52310	−	0.894231i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.0743207	+	0.207254i	0.00328134	+	0.00915051i
$514$	−0.603183	+	0.603183i	−0.0266053	+	0.0266053i
$515$	−28.0346	+	7.51186i	−1.23535	+	0.331012i
$516$	0.243630	+	8.85561i	0.0107252	+	0.389847i
$517$	34.5821	+	19.9660i	1.52092	+	0.878103i
$518$	22.8456	−	6.30033i	1.00378	−	0.276821i
$519$	−5.53371	+	3.40115i	−0.242903	+	0.149294i
$520$	−8.83084	+	1.30172i	−0.387258	+	0.0570844i
$521$	16.3419	+	9.43501i	0.715952	+	0.413355i	0.813261	−	0.581899i	$-0.197690\pi$
$521$	16.3419	+	9.43501i	0.715952	+	0.413355i	−0.0973088	+	0.995254i	$0.531023\pi$
$522$	1.28164	+	1.14786i	0.0560957	+	0.0502403i
$523$	11.7336			0.513077			0.256538	−	0.966534i	$-0.417418\pi$
$523$	11.7336			0.513077			0.256538	+	0.966534i	$0.417418\pi$
$524$	−3.63363	−	6.29363i	−0.158736	−	0.274938i
$525$	3.52920	−	3.78377i	0.154027	−	0.165137i
$526$	−0.839220	+	3.13201i	−0.0365917	+	0.136562i
$527$	−40.5826	+	10.8741i	−1.76781	+	0.473682i
$528$	−6.81331	+	7.19880i	−0.296511	+	0.313288i
$529$	−7.56959			−0.329113
$530$	9.89012			0.429599
$531$	1.19216	−	5.68266i	0.0517355	−	0.246607i
$532$	−0.0966777	+	0.0567607i	−0.00419151	+	0.00246089i
$533$	−19.5400	−	2.26591i	−0.846372	−	0.0981474i
$534$	14.9873	+	8.11173i	0.648562	+	0.351029i
$535$	1.56267	−	5.83196i	0.0675600	−	0.252137i
$536$	6.16652	−	3.56024i	0.266353	−	0.153779i
$537$	0.454985	+	16.5381i	0.0196341	+	0.713672i
$538$	2.09549	+	2.09549i	0.0903429	+	0.0903429i
$539$	10.9309	+	38.5378i	0.470827	+	1.65994i
$540$	12.6579	+	2.29402i	0.544710	+	0.0987191i
$541$	33.2829	+	8.91812i	1.43094	+	0.383420i	0.889352	−	0.457223i	$-0.151156\pi$
$541$	33.2829	+	8.91812i	1.43094	+	0.383420i	0.541590	+	0.840643i	$0.317822\pi$
$542$		−	24.2589i		−	1.04201i
$543$	−1.20751	+	2.23099i	−0.0518190	+	0.0957410i
$544$	5.50436	−	5.50436i	0.235997	−	0.235997i
$545$	−2.39440			−0.102565
$546$	−16.2524	+	2.97671i	−0.695537	+	0.127392i
$547$	6.84016			0.292464			0.146232	−	0.989250i	$-0.453285\pi$
$547$	6.84016			0.292464			0.146232	+	0.989250i	$0.453285\pi$
$548$	−10.1389	+	10.1389i	−0.433111	+	0.433111i
$549$	−34.5695	+	1.90355i	−1.47539	+	0.0812415i
$550$			6.46136i			0.275513i
$551$	−0.0234731	−	0.00628960i	−0.000999989	−	0.000267946i
$552$	−1.94101	−	6.52102i	−0.0826150	−	0.277553i
$553$	0.133314	−	0.135272i	0.00566908	−	0.00575236i
$554$	−20.4686	−	20.4686i	−0.869628	−	0.869628i
$555$	38.3941	−	1.05627i	1.62974	−	0.0448363i
$556$	−16.0393	+	9.26030i	−0.680218	+	0.392724i
$557$	5.89761	−	22.0102i	0.249890	−	0.932602i	−0.720972	−	0.692964i	$-0.756305\pi$
$557$	5.89761	−	22.0102i	0.249890	−	0.932602i	0.970862	−	0.239638i	$-0.0770288\pi$
$558$	16.1673	−	0.890244i	0.684418	−	0.0376870i
$559$	−2.68932	−	18.2443i	−0.113746	−	0.771650i
$560$	0.0477563	+	6.54992i	0.00201807	+	0.276785i
$561$	53.0371	−	56.0379i	2.23923	−	2.36592i
$562$	−31.2268			−1.31722
$563$	−3.69803			−0.155853			−0.0779267	−	0.996959i	$-0.524830\pi$
$563$	−3.69803			−0.155853			−0.0779267	+	0.996959i	$0.524830\pi$
$564$	8.77802	+	8.30796i	0.369621	+	0.349828i
$565$	29.3974	−	7.87702i	1.23676	−	0.331389i
$566$	−3.20424	+	11.9584i	−0.134684	+	0.502648i
$567$	23.5636	+	3.42862i	0.989579	+	0.143989i
$568$	0.729910	+	1.26424i	0.0306264	+	0.0530464i
$569$	20.2398			0.848495			0.424248	−	0.905546i	$-0.360539\pi$
$569$	20.2398			0.848495			0.424248	+	0.905546i	$0.360539\pi$
$570$	−0.174147	+	0.0518356i	−0.00729420	+	0.00217115i
$571$	33.5986	+	19.3982i	1.40606	+	0.811788i	0.995005	−	0.0998230i	$-0.0318277\pi$
$571$	33.5986	+	19.3982i	1.40606	+	0.811788i	0.411053	+	0.911611i	$0.365161\pi$
$572$	12.3062	−	16.5614i	0.514547	−	0.692469i
$573$	−5.74677	−	9.35006i	−0.240075	−	0.390604i
$574$	−3.63418	+	13.9696i	−0.151688	+	0.583078i
$575$	−3.84106	−	2.21764i	−0.160183	−	0.0924819i
$576$	−2.51167	+	1.64058i	−0.104653	+	0.0683573i
$577$	−30.0124	+	8.04180i	−1.24943	+	0.334784i	−0.822117	−	0.569319i	$-0.807207\pi$
$577$	−30.0124	+	8.04180i	−1.24943	+	0.334784i	−0.427315	+	0.904103i	$0.640540\pi$
$578$	−30.8270	+	30.8270i	−1.28223	+	1.28223i
$579$	−6.37470	−	6.03334i	−0.264924	−	0.250737i
$580$	−1.00397	+	1.00397i	−0.0416875	+	0.0416875i
$581$	2.19646	+	1.24686i	0.0911246	+	0.0517286i
$582$	0.579533	+	21.0652i	0.0240224	+	0.873182i
$583$	−16.1652	+	16.1652i	−0.669493	+	0.669493i
$584$	−7.54523	+	13.0687i	−0.312224	+	0.540787i
$585$	−26.7299	−	1.61747i	−1.10515	−	0.0668743i
$586$	12.6339	+	21.8825i	0.521900	+	0.903957i
$587$	6.66042	+	24.8570i	0.274905	+	1.02596i	0.955905	+	0.293676i	$0.0948788\pi$
$587$	6.66042	+	24.8570i	0.274905	+	1.02596i	−0.681000	+	0.732284i	$0.738455\pi$
$588$	0.510120	+	12.1136i	0.0210370	+	0.499557i
$589$	−0.198059	+	0.114350i	−0.00816090	+	0.00471170i
$590$	4.62834	+	1.24016i	0.190546	+	0.0510566i
$591$	0.334828	−	1.40284i	0.0137730	−	0.0577051i
$592$	−6.33367	+	6.33367i	−0.260312	+	0.260312i
$593$	1.58779	−	5.92573i	0.0652029	−	0.243340i	−0.925631	−	0.378428i	$-0.876465\pi$
$593$	1.58779	−	5.92573i	0.0652029	−	0.243340i	0.990834	+	0.135087i	$0.0431315\pi$
$594$	−24.4386	+	16.9396i	−1.00273	+	0.695039i
$595$	−0.371752	−	50.9868i	−0.0152403	−	2.09025i
$596$	1.51492	−	0.405922i	0.0620536	−	0.0166272i
$597$	0.691854	−	1.27827i	0.0283157	−	0.0523162i
$598$	5.62156	+	12.9997i	0.229883	+	0.531599i
$599$	−19.4626	−	11.2368i	−0.795222	−	0.459122i	0.0465758	−	0.998915i	$-0.485169\pi$
$599$	−19.4626	−	11.2368i	−0.795222	−	0.459122i	−0.841798	+	0.539793i	$0.818502\pi$
$600$	−0.454020	+	1.90223i	−0.0185353	+	0.0776580i
$601$	−16.0680	+	27.8305i	−0.655426	+	1.13523i	0.326361	+	0.945245i	$0.394178\pi$
$601$	−16.0680	+	27.8305i	−0.655426	+	1.13523i	−0.981787	+	0.189986i	$0.939156\pi$
$602$	−13.5319	+	0.0986632i	−0.551520	+	0.00402121i
$603$	20.2984	−	6.65484i	0.826614	−	0.271006i
$604$	−3.06252	+	0.820601i	−0.124612	+	0.0333898i
$605$	−38.0716	−	38.0716i	−1.54783	−	1.54783i
$606$	0.449385	+	0.425320i	0.0182550	+	0.0172775i
$607$	11.2263	−	19.4445i	0.455662	−	0.789229i	−0.543064	−	0.839691i	$-0.682736\pi$
$607$	11.2263	−	19.4445i	0.455662	−	0.789229i	0.998726	+	0.0504618i	$0.0160693\pi$
$608$	0.0211866	−	0.0366962i	0.000859228	−	0.00148823i
$609$	−1.79259	+	1.92189i	−0.0726395	+	0.0778790i
$610$		−	28.5712i		−	1.15681i
$611$	−20.1946	−	15.0058i	−0.816985	−	0.607070i
$612$	19.5517	−	12.7708i	0.790332	−	0.516229i
$613$	0.0481476	−	0.179689i	0.00194466	−	0.00725758i	−0.964947	−	0.262446i	$-0.915471\pi$
$613$	0.0481476	−	0.179689i	0.00194466	−	0.00725758i	0.966891	+	0.255188i	$0.0821375\pi$
$614$			3.50217i			0.141336i
$615$	−11.1356	+	20.5742i	−0.449032	+	0.829632i
$616$	−10.7837	−	10.6276i	−0.434489	−	0.428199i
$617$	35.5899	+	9.53628i	1.43279	+	0.383916i	0.890004	−	0.455952i	$-0.150701\pi$
$617$	35.5899	+	9.53628i	1.43279	+	0.383916i	0.542790	+	0.839868i	$0.317368\pi$
$618$	13.9579	−	14.7476i	0.561467	−	0.593235i
$619$	6.52704	+	24.3592i	0.262344	+	0.979081i	0.963856	+	0.266423i	$0.0858419\pi$
$619$	6.52704	+	24.3592i	0.262344	+	0.979081i	−0.701512	+	0.712657i	$0.747491\pi$
$620$			13.3620i			0.536633i
$621$	−1.68229	−	20.3419i	−0.0675080	−	0.816290i
$622$	5.39828	+	20.1467i	0.216451	+	0.807808i
$623$	−12.8511	+	22.6383i	−0.514867	+	0.906984i
$624$	4.78666	−	4.01097i	0.191620	−	0.160567i
$625$	−14.6853	−	25.4357i	−0.587413	−	1.01743i
$626$	1.92401	+	0.515537i	0.0768989	+	0.0206050i
$627$	0.199915	−	0.369363i	0.00798382	−	0.0147509i
$628$	8.01710	+	4.62867i	0.319917	+	0.184704i
$629$	49.3034	−	49.3034i	1.96586	−	1.96586i
$630$	−3.89427	+	19.2605i	−0.155151	+	0.767358i
$631$	13.3102	+	3.56646i	0.529871	+	0.141979i	0.513829	−	0.857893i	$-0.328227\pi$
$631$	13.3102	+	3.56646i	0.529871	+	0.141979i	0.0160424	+	0.999871i	$0.494893\pi$
$632$	−0.0185792	+	0.0693386i	−0.000739041	+	0.00275814i
$633$	−39.5682	+	24.3196i	−1.57270	+	0.966617i
$634$	−6.07627	+	3.50814i	−0.241319	+	0.139326i
$635$	−13.3176	−	13.3176i	−0.528493	−	0.528493i
$636$	−5.89490	+	3.62315i	−0.233748	+	0.143667i
$637$	−4.04429	−	24.9127i	−0.160241	−	0.987078i
$638$		−	3.28193i		−	0.129933i
$639$	1.36436	+	4.16152i	0.0539731	+	0.164627i
$640$	−1.23785	−	2.14402i	−0.0489304	−	0.0847499i
$641$	31.6508			1.25013			0.625065	−	0.780573i	$-0.285073\pi$
$641$	31.6508			1.25013			0.625065	+	0.780573i	$0.285073\pi$
$642$	1.20507	+	4.04854i	0.0475603	+	0.159783i
$643$	6.31792	−	23.5788i	0.249154	−	0.929856i	−0.722095	−	0.691793i	$-0.756821\pi$
$643$	6.31792	−	23.5788i	0.249154	−	0.929856i	0.971250	−	0.238063i	$-0.0765125\pi$
$644$	10.0189	−	2.76301i	0.394801	−	0.108878i
$645$	−21.3329	−	5.09171i	−0.839983	−	0.200486i
$646$	−0.164923	+	0.285655i	−0.00648882	+	0.0112390i
$647$	2.75059	+	4.76415i	0.108137	+	0.187298i	0.915015	−	0.403419i	$-0.132178\pi$
$647$	2.75059	+	4.76415i	0.108137	+	0.187298i	−0.806879	+	0.590717i	$0.798845\pi$
$648$	−8.38502	+	3.26978i	−0.329395	+	0.128449i
$649$	−9.59193	+	5.53790i	−0.376516	+	0.217382i
$650$	0.468944	−	4.04393i	0.0183935	−	0.158616i
$651$	0.860436	+	24.7185i	0.0337231	+	0.968793i
$652$	−2.02125	+	0.541593i	−0.0791583	+	0.0212104i
$653$		−	28.5936i		−	1.11895i	−0.828846	−	0.559476i	$-0.811002\pi$
$653$		−	28.5936i		−	1.11895i	0.828846	−	0.559476i	$-0.188998\pi$
$654$	1.42716	−	0.877164i	0.0558062	−	0.0342998i
$655$	17.3785	−	4.65656i	0.679035	−	0.181947i
$656$	−1.41205	−	5.26984i	−0.0551313	−	0.205753i
$657$	−30.2032	+	33.7233i	−1.17834	+	1.31567i
$658$	−12.9590	+	13.1494i	−0.505196	+	0.512617i
$659$	18.6398	−	10.7617i	0.726103	−	0.419216i	−0.0908917	−	0.995861i	$-0.528972\pi$
$659$	18.6398	−	10.7617i	0.726103	−	0.419216i	0.816995	+	0.576645i	$0.195638\pi$
$660$	−12.8491	−	20.9057i	−0.500151	−	0.813752i
$661$	−17.1317	−	4.59043i	−0.666347	−	0.178547i	−0.0902382	−	0.995920i	$-0.528763\pi$
$661$	−17.1317	−	4.59043i	−0.666347	−	0.178547i	−0.576109	+	0.817373i	$0.695429\pi$
$662$	5.67589	−	9.83094i	0.220600	−	0.382090i
$663$	−37.2610	+	31.2228i	−1.44710	+	1.21259i
$664$	−0.954621			−0.0370465
$665$	−0.0737873	−	0.267560i	−0.00286135	−	0.0103755i
$666$	−22.4975	+	14.6949i	−0.871759	+	0.569416i
$667$	1.95099	+	1.12641i	0.0755428	+	0.0436147i
$668$	−5.15284	−	19.2306i	−0.199369	−	0.744056i
$669$	40.1282	+	9.57773i	1.55145	+	0.370297i
$670$	4.56251	+	17.0275i	0.176265	+	0.657831i
$671$	46.6989	+	46.6989i	1.80279	+	1.80279i
$672$	−2.42796	−	3.88651i	−0.0936607	−	0.149926i
$673$	31.2748	+	18.0565i	1.20555	+	0.696027i	0.961785	−	0.273806i	$-0.0882828\pi$
$673$	31.2748	+	18.0565i	1.20555	+	0.696027i	0.243769	+	0.969833i	$0.421616\pi$
$674$	−15.7641	−	15.7641i	−0.607212	−	0.607212i
$675$	−2.50474	+	5.30544i	−0.0964073	+	0.204206i
$676$	−8.90395	+	9.47205i	−0.342459	+	0.364310i
$677$	−24.7294	+	14.2775i	−0.950428	+	0.548730i	−0.893214	−	0.449632i	$-0.851555\pi$
$677$	−24.7294	+	14.2775i	−0.950428	+	0.548730i	−0.0572142	+	0.998362i	$0.518222\pi$
$678$	−14.6364	+	15.4645i	−0.562106	+	0.593910i
$679$	−32.1890	+	0.234694i	−1.23530	+	0.00900675i
$680$	9.63585	+	16.6898i	0.369518	+	0.640024i
$681$	−8.22515	+	2.44825i	−0.315188	+	0.0938173i
$682$	−21.8400	−	21.8400i	−0.836295	−	0.836295i
$683$	30.5769	+	30.5769i	1.16999	+	1.16999i	0.982211	+	0.187782i	$0.0601300\pi$
$683$	30.5769	+	30.5769i	1.16999	+	1.16999i	0.187782	+	0.982211i	$0.439870\pi$
$684$	0.0848089	−	0.0946930i	0.00324275	−	0.00362068i
$685$	−17.7489	−	30.7421i	−0.678152	−	1.17459i
$686$	−18.5158	+	0.405062i	−0.706938	+	0.0154653i
$687$	−10.8536	−	10.2724i	−0.414092	−	0.391918i
$688$	4.42948	−	2.55736i	0.168872	−	0.0974985i
$689$	11.2904	−	8.94396i	0.430129	−	0.340738i
$690$	16.8377	−	0.463228i	0.641001	−	0.0176348i
$691$	5.19603	+	5.19603i	0.197666	+	0.197666i	0.798999	−	0.601333i	$-0.205363\pi$
$691$	5.19603	+	5.19603i	0.197666	+	0.197666i	−0.601333	+	0.798999i	$0.705363\pi$
$692$	3.24769	+	1.87505i	0.123458	+	0.0712788i
$693$	−25.1158	−	37.8460i	−0.954070	−	1.43765i
$694$	9.80914	+	9.80914i	0.372350	+	0.372350i
$695$	−11.8672	−	44.2891i	−0.450150	−	1.67998i
$696$	0.230611	−	0.966199i	0.00874128	−	0.0366237i
$697$	10.9919	+	41.0222i	0.416347	+	1.55383i
$698$	−26.1563	−	15.1014i	−0.990032	−	0.571595i
$699$	−0.412652	−	14.9993i	−0.0156079	−	0.567327i
$700$	−2.89109	−	0.752115i	−0.109273	−	0.0284273i
$701$	1.20413			0.0454794			0.0227397	−	0.999741i	$-0.492761\pi$
$701$	1.20413			0.0454794			0.0227397	+	0.999741i	$0.492761\pi$
$702$	16.5246	−	8.82817i	0.623682	−	0.333198i
$703$	0.189771	−	0.328694i	0.00715736	−	0.0123969i
$704$	5.52759	+	1.48111i	0.208329	+	0.0558216i
$705$	−25.4918	+	15.6679i	−0.960076	+	0.590086i
$706$	22.8056	−	13.1668i	0.858300	−	0.495540i
$707$	−0.663429	+	0.673175i	−0.0249508	+	0.0253173i
$708$	−3.21300	+	0.956363i	−0.120752	+	0.0359423i
$709$	9.56860	+	35.7105i	0.359356	+	1.34114i	0.874913	+	0.484281i	$0.160919\pi$
$709$	9.56860	+	35.7105i	0.359356	+	1.34114i	−0.515556	+	0.856856i	$0.672415\pi$
$710$	−3.49093	+	0.935393i	−0.131012	+	0.0351047i
$711$	−0.0972599	+	0.192140i	−0.00364753	+	0.00720581i
$712$		−	9.83900i		−	0.368732i
$713$	20.4789	−	5.48731i	0.766942	−	0.205501i
$714$	18.9001	+	30.2539i	0.707318	+	1.13223i
$715$	31.7188	+	40.0402i	1.18622	+	1.49742i
$716$	8.27218	−	4.77595i	0.309146	−	0.178485i
$717$	7.21302	−	2.14699i	0.269375	−	0.0801808i
$718$	−17.8393	−	30.8986i	−0.665757	−	1.15312i
$719$	−15.3736	+	26.6278i	−0.573338	+	0.993050i	0.422882	+	0.906185i	$0.361018\pi$
$719$	−15.3736	+	26.6278i	−0.573338	+	0.993050i	−0.996220	+	0.0868654i	$0.972315\pi$
$720$	−2.31380	−	7.05749i	−0.0862304	−	0.263017i
$721$	22.0918	+	21.7720i	0.822740	+	0.810830i
$722$	4.91710	−	18.3509i	0.182995	−	0.682948i
$723$	28.2362	−	8.40465i	1.05012	−	0.312572i
$724$	1.46463			0.0544324
$725$	−0.323772	−	0.560789i	−0.0120246	−	0.0208272i
$726$	36.6394	+	8.74503i	1.35982	+	0.324559i
$727$		−	27.2848i		−	1.01194i	−0.862552	−	0.505968i	$-0.831135\pi$
$727$		−	27.2848i		−	1.01194i	0.862552	−	0.505968i	$-0.168865\pi$
$728$	5.97783	+	7.43408i	0.221553	+	0.275525i
$729$	−26.6332	+	4.43552i	−0.986414	+	0.164278i
$730$	−26.4171	−	26.4171i	−0.977742	−	0.977742i
$731$	−34.4806	+	19.9074i	−1.27531	+	0.736301i
$732$	10.4668	+	17.0295i	0.386863	+	0.629430i
$733$	1.50653	−	5.62244i	0.0556449	−	0.207670i	−0.932506	−	0.361154i	$-0.882383\pi$
$733$	1.50653	−	5.62244i	0.0556449	−	0.207670i	0.988151	+	0.153485i	$0.0490495\pi$
$734$	−2.17463	−	0.582691i	−0.0802672	−	0.0215075i
$735$	−29.2947	−	6.54204i	−1.08055	−	0.241307i
$736$	−2.77763	+	2.77763i	−0.102385	+	0.102385i
$737$	−35.2884	−	20.3738i	−1.29987	−	0.750478i
$738$	−0.899887	−	16.3425i	−0.0331253	−	0.601575i
$739$	10.8425	+	2.90524i	0.398848	+	0.106871i	0.452667	−	0.891680i	$-0.350473\pi$
$739$	10.8425	+	2.90524i	0.398848	+	0.106871i	−0.0538189	+	0.998551i	$0.517139\pi$
$740$	−11.0876	−	19.2043i	−0.407589	−	0.705965i
$741$	−0.151926	+	0.216661i	−0.00558115	+	0.00795925i
$742$	−5.35132	−	9.11463i	−0.196453	−	0.334609i
$743$	9.63444	+	35.9562i	0.353453	+	1.31911i	0.882420	+	0.470463i	$0.155913\pi$
$743$	9.63444	+	35.9562i	0.353453	+	1.31911i	−0.528967	+	0.848643i	$0.677420\pi$
$744$	−4.89506	−	7.96431i	−0.179461	−	0.291986i
$745$			3.88280i			0.142255i
$746$	3.84161	+	14.3371i	0.140651	+	0.524918i
$747$	−2.80285	−	0.588008i	−0.102551	−	0.0215141i
$748$	−43.0286	−	11.5295i	−1.57328	−	0.421560i
$749$	−6.22020	+	1.71540i	−0.227281	+	0.0626794i
$750$	14.5976	+	7.90083i	0.533029	+	0.288498i
$751$		−	12.2730i		−	0.447847i	−0.974607	−	0.223924i	$-0.928113\pi$
$751$		−	12.2730i		−	0.447847i	0.974607	−	0.223924i	$-0.0718866\pi$
$752$	1.80603	−	6.74019i	0.0658591	−	0.245790i
$753$	1.20431	+	43.7750i	0.0438874	+	1.59525i
$754$	−0.238191	+	2.05404i	−0.00867441	+	0.0748036i
$755$		−	7.84935i		−	0.285667i
$756$	−4.73477	−	12.9067i	−0.172202	−	0.469411i
$757$	26.7153	−	46.2723i	0.970984	−	1.68179i	0.278388	−	0.960469i	$-0.410200\pi$
$757$	26.7153	−	46.2723i	0.970984	−	1.68179i	0.692596	−	0.721326i	$-0.256467\pi$
$758$	−0.548101	+	0.949339i	−0.0199079	+	0.0344815i
$759$	−26.7637	+	28.2780i	−0.971462	+	1.02643i
$760$	0.0741777	+	0.0741777i	0.00269071	+	0.00269071i
$761$	24.7062	−	6.62002i	0.895601	−	0.239975i	0.218475	−	0.975843i	$-0.429892\pi$
$761$	24.7062	−	6.62002i	0.895601	−	0.239975i	0.677126	+	0.735867i	$0.263225\pi$
$762$	12.8166	+	3.05905i	0.464296	+	0.110818i
$763$	1.29555	+	2.20665i	0.0469022	+	0.0798862i
$764$	−3.16819	+	5.48746i	−0.114621	+	0.198529i
$765$	18.0114	+	54.9379i	0.651205	+	1.98628i
$766$	4.73968	+	2.73646i	0.171252	+	0.0988722i
$767$	6.40515	−	2.76982i	0.231277	−	0.100012i
$768$	1.52325	+	0.824446i	0.0549655	+	0.0297496i
$769$	−22.0110	+	5.89784i	−0.793739	+	0.212682i	−0.632833	−	0.774288i	$-0.718108\pi$
$769$	−22.0110	+	5.89784i	−0.793739	+	0.212682i	−0.160905	+	0.986970i	$0.551441\pi$
$770$	32.3241	−	18.9779i	1.16488	−	0.683916i
$771$	1.29938	+	0.703277i	0.0467959	+	0.0253279i
$772$	−1.31156	+	4.89481i	−0.0472041	+	0.176168i
$773$	17.5332	−	17.5332i	0.630626	−	0.630626i	−0.317599	−	0.948225i	$-0.602877\pi$
$773$	17.5332	−	17.5332i	0.630626	−	0.630626i	0.948225	+	0.317599i	$0.102877\pi$
$774$	14.5806	−	4.78025i	0.524088	−	0.171823i
$775$	−5.88641	−	1.57726i	−0.211446	−	0.0566568i
$776$	10.5366	−	6.08331i	0.378242	−	0.218378i
$777$	−21.7477	−	34.8121i	−0.780193	−	1.24888i
$778$	−7.53142	−	28.1076i	−0.270014	−	1.00771i
$779$	0.115588	+	0.200205i	0.00414138	+	0.00717308i
$780$	6.52452	+	14.0166i	0.233615	+	0.501875i
$781$	4.17697	−	7.23473i	0.149464	−	0.258879i
$782$	21.6220	−	21.6220i	0.773200	−	0.773200i
$783$	1.27223	−	2.69480i	0.0454659	−	0.0963041i
$784$	6.01050	−	3.58802i	0.214661	−	0.128144i
$785$	−16.2058	+	16.2058i	−0.578409	+	0.578409i
$786$	−8.65240	+	9.14194i	−0.308621	+	0.326082i
$787$	22.8023	−	22.8023i	0.812815	−	0.812815i	−0.172240	−	0.985055i	$-0.555100\pi$
$787$	22.8023	−	22.8023i	0.812815	−	0.812815i	0.985055	+	0.172240i	$0.0551005\pi$
$788$	−0.804307	+	0.215514i	−0.0286523	+	0.00767735i
$789$	5.61405	−	0.154450i	0.199865	−	0.00549856i
$790$	−0.153908	−	0.0888586i	−0.00547579	−	0.00316145i
$791$	−23.1657	−	22.8303i	−0.823676	−	0.811752i
$792$	15.3172	+	7.75345i	0.544272	+	0.275507i
$793$	−25.8379	−	32.6163i	−0.917529	−	1.15824i
$794$	5.53535	+	3.19583i	0.196442	+	0.113416i
$795$	−4.88699	−	16.4183i	−0.173324	−	0.582297i
$796$	−0.839174			−0.0297437
$797$	−3.20767	−	5.55586i	−0.113622	−	0.196798i	0.803606	−	0.595161i	$-0.202912\pi$
$797$	−3.20767	−	5.55586i	−0.113622	−	0.196798i	−0.917228	+	0.398363i	$0.869579\pi$
$798$	0.141998	+	0.132445i	0.00502668	+	0.00468850i
$799$	−14.0587	+	52.4679i	−0.497363	+	1.85618i
$800$	1.09063	−	0.292232i	0.0385595	−	0.0103320i
$801$	6.06043	−	28.8882i	0.214135	−	1.02071i
$802$	12.5361			0.442667
$803$	86.3564			3.04745
$804$	−8.95730	−	8.47765i	−0.315900	−	0.298983i
$805$	0.187594	+	25.7291i	0.00661183	+	0.906831i
$806$	12.0837	+	15.2539i	0.425632	+	0.537295i
$807$	2.44322	−	4.51410i	0.0860055	−	0.158904i
$808$	0.0924584	−	0.345060i	0.00325268	−	0.0121392i
$809$	39.2125	−	22.6393i	1.37864	−	0.795957i	0.386642	−	0.922230i	$-0.373635\pi$
$809$	39.2125	−	22.6393i	1.37864	−	0.795957i	0.991995	+	0.126273i	$0.0403016\pi$
$810$	−2.44639	−	22.1466i	−0.0859576	−	0.778152i
$811$	11.6485	+	11.6485i	0.409035	+	0.409035i	0.881402	−	0.472367i	$-0.156600\pi$
$811$	11.6485	+	11.6485i	0.409035	+	0.409035i	−0.472367	+	0.881402i	$0.656600\pi$
$812$	1.46847	+	0.382023i	0.0515333	+	0.0134064i
$813$	−40.2714	+	11.9870i	−1.41238	+	0.420402i
$814$	49.5115	+	13.2666i	1.73538	+	0.464993i
$815$		−	5.18054i		−	0.181466i
$816$	−11.8575	−	6.41777i	−0.415095	−	0.224667i
$817$	−0.153249	+	0.153249i	−0.00536150	+	0.00536150i
$818$	26.6623			0.932224
$819$	12.9723	+	25.5092i	0.453289	+	0.891364i
$820$	13.5068			0.471678
$821$	−5.07374	+	5.07374i	−0.177075	+	0.177075i	−0.790079	−	0.613005i	$-0.789961\pi$
$821$	−5.07374	+	5.07374i	−0.177075	+	0.177075i	0.613005	+	0.790079i	$0.289961\pi$
$822$	21.8411	+	11.8213i	0.761797	+	0.412316i
$823$			16.1118i			0.561623i	0.959763	+	0.280812i	$0.0906036\pi$
$823$			16.1118i			0.561623i	−0.959763	+	0.280812i	$0.909396\pi$
$824$	−11.3239	−	3.03423i	−0.394487	−	0.105703i
$825$	10.7263	−	3.19274i	0.373443	−	0.111157i
$826$	−1.36137	−	4.93646i	−0.0473682	−	0.171761i
$827$	−15.0026	−	15.0026i	−0.521691	−	0.521691i	0.396391	−	0.918082i	$-0.370263\pi$
$827$	−15.0026	−	15.0026i	−0.521691	−	0.521691i	−0.918082	+	0.396391i	$0.870263\pi$
$828$	−9.86625	+	6.44444i	−0.342876	+	0.223960i
$829$	9.10656	−	5.25767i	0.316284	−	0.182607i	−0.333451	−	0.942767i	$-0.608213\pi$
$829$	9.10656	−	5.25767i	0.316284	−	0.182607i	0.649735	+	0.760161i	$0.274880\pi$
$830$	0.611682	−	2.28283i	0.0212318	−	0.0792381i
$831$	−23.8652	+	44.0935i	−0.827876	+	1.52959i
$832$	−3.35202	−	1.32815i	−0.116210	−	0.0460452i
$833$	−46.7878	+	27.9304i	−1.62110	+	0.967731i
$834$	23.2982	+	22.0506i	0.806752	+	0.763551i
$835$	49.2888			1.70571
$836$	−0.242484			−0.00838647
$837$	−9.46660	−	26.3990i	−0.327214	−	0.912484i
$838$	−18.0232	+	4.82929i	−0.622600	+	0.166825i
$839$	1.06107	−	3.95999i	0.0366324	−	0.136714i	−0.945188	−	0.326527i	$-0.894122\pi$
$839$	1.06107	−	3.95999i	0.0366324	−	0.136714i	0.981820	+	0.189813i	$0.0607882\pi$
$840$	10.8497	−	3.31578i	0.374351	−	0.114405i
$841$	−14.3355	−	24.8299i	−0.494329	−	0.856203i
$842$	30.5125			1.05153
$843$	15.4300	+	51.8387i	0.531439	+	1.78542i
$844$	23.2222	+	13.4074i	0.799342	+	0.461500i
$845$	−16.9457	−	27.3617i	−0.582948	−	0.941271i
$846$	9.45434	−	18.6773i	0.325047	−	0.642140i
$847$	−14.4867	+	55.6862i	−0.497770	+	1.91340i
$848$	3.45966	+	1.99744i	0.118805	+	0.0685923i
$849$	21.4351	−	0.589707i	0.735649	−	0.0202387i
$850$	−8.48980	+	2.27484i	−0.291198	+	0.0780262i
$851$	−24.8796	+	24.8796i	−0.852863	+	0.852863i
$852$	1.73806	−	1.83640i	0.0595451	−	0.0629141i
$853$	12.0814	−	12.0814i	0.413660	−	0.413660i	−0.469352	−	0.883011i	$-0.655512\pi$
$853$	12.0814	−	12.0814i	0.413660	−	0.413660i	0.883011	+	0.469352i	$0.155512\pi$
$854$	−26.3309	+	15.4592i	−0.901025	+	0.529003i
$855$	0.172102	+	0.263483i	0.00588575	+	0.00901092i
$856$	1.72448	−	1.72448i	0.0589414	−	0.0589414i
$857$	−10.9200	+	18.9141i	−0.373021	+	0.646092i	−0.990029	−	0.140866i	$-0.955011\pi$
$857$	−10.9200	+	18.9141i	−0.373021	+	0.646092i	0.617007	+	0.786957i	$0.288345\pi$
$858$	−33.5740	−	12.2456i	−1.14620	−	0.418060i
$859$	−15.3913	−	26.6586i	−0.525145	−	0.909578i	−0.999571	−	0.0292827i	$-0.990678\pi$
$859$	−15.3913	−	26.6586i	−0.525145	−	0.909578i	0.474426	−	0.880295i	$-0.342656\pi$
$860$	3.27731	+	12.2311i	0.111755	+	0.417076i
$861$	24.9862	−	0.869757i	0.851528	−	0.0296412i
$862$	9.66016	−	5.57729i	0.329026	−	0.189963i
$863$	−18.5892	−	4.98097i	−0.632784	−	0.169554i	−0.0718515	−	0.997415i	$-0.522891\pi$
$863$	−18.5892	−	4.98097i	−0.632784	−	0.169554i	−0.560933	+	0.827861i	$0.689557\pi$
$864$	3.96456	+	3.35890i	0.134877	+	0.114272i
$865$	−6.56488	+	6.56488i	−0.223213	+	0.223213i
$866$	−7.44836	+	27.7976i	−0.253105	+	0.944602i
$867$	66.4075	+	35.9425i	2.25532	+	1.22067i
$868$	12.3143	−	7.22990i	0.417975	−	0.245399i
$869$	0.396796	−	0.106321i	0.0134604	−	0.00360669i
$870$	2.16275	+	1.17057i	0.0733241	+	0.0396861i
$871$	20.6070	+	15.3123i	0.698243	+	0.518837i
$872$	−0.837585	−	0.483580i	−0.0283642	−	0.0163761i
$873$	34.6834	−	11.3710i	1.17386	−	0.384850i
$874$	0.0832241	−	0.144148i	0.00281510	−	0.00487589i
$875$	−12.5169	+	22.0497i	−0.423150	+	0.745416i
$876$	25.4233	+	6.06800i	0.858974	+	0.205019i
$877$	−3.06519	+	0.821315i	−0.103504	+	0.0277339i	−0.310199	−	0.950672i	$-0.600396\pi$
$877$	−3.06519	+	0.821315i	−0.103504	+	0.0277339i	0.206695	+	0.978405i	$0.433729\pi$
$878$	5.10185	+	5.10185i	0.172179	+	0.172179i
$879$	30.0837	−	31.7858i	1.01470	−	1.07211i
$880$	−7.08370	+	12.2693i	−0.238792	+	0.413599i
$881$	−11.7122	+	20.2861i	−0.394594	+	0.683456i	−0.993049	−	0.117700i	$-0.962448\pi$
$881$	−11.7122	+	20.2861i	−0.394594	+	0.683456i	0.598456	+	0.801156i	$0.295781\pi$
$882$	19.8574	−	6.83252i	0.668634	−	0.230063i
$883$		−	22.3093i		−	0.750767i	−0.926870	−	0.375383i	$-0.877511\pi$
$883$		−	22.3093i		−	0.750767i	0.926870	−	0.375383i	$-0.122489\pi$
$884$	26.0932	+	10.3387i	0.877611	+	0.347730i
$885$	−0.228239	−	8.29618i	−0.00767217	−	0.278873i
$886$	−5.37917	+	20.0753i	−0.180717	+	0.674445i
$887$		−	51.8983i		−	1.74258i	−0.490772	−	0.871288i	$-0.663285\pi$
$887$		−	51.8983i		−	1.74258i	0.490772	−	0.871288i	$-0.336715\pi$
$888$	13.6440	+	7.38470i	0.457862	+	0.247814i
$889$	−5.06752	+	19.4792i	−0.169959	+	0.653313i
$890$	23.5284	+	6.30443i	0.788675	+	0.211325i
$891$	40.1967	+	32.1995i	1.34664	+	1.07873i
$892$	−6.16476	−	23.0072i	−0.206411	−	0.770338i
$893$			0.295678i			0.00989448i
$894$	−1.42243	−	2.31430i	−0.0475730	−	0.0774018i
$895$	6.12046	+	22.8419i	0.204584	+	0.763519i
$896$	−1.30613	+	2.30087i	−0.0436349	+	0.0768667i
$897$	18.8027	−	15.7557i	0.627805	−	0.526068i
$898$	10.8259	+	18.7510i	0.361265	+	0.625730i
$899$	2.98989	+	0.801139i	0.0997184	+	0.0267195i
$900$	3.38217	−	0.186237i	0.112739	−	0.00620791i
$901$	−26.9312	−	15.5487i	−0.897208	−	0.518003i
$902$	−22.0765	+	22.0765i	−0.735068	+	0.735068i
$903$	6.85030	+	22.4152i	0.227964	+	0.745932i
$904$	11.8744	+	3.18173i	0.394936	+	0.105823i
$905$	−0.938472	+	3.50242i	−0.0311959	+	0.116425i
$906$	2.87553	+	4.67853i	0.0955332	+	0.155434i
$907$	−1.54805	+	0.893767i	−0.0514022	+	0.0296770i	−0.525481	−	0.850805i	$-0.676115\pi$
$907$	−1.54805	+	0.893767i	−0.0514022	+	0.0296770i	0.474079	+	0.880482i	$0.342781\pi$
$908$	3.50350	+	3.50350i	0.116268	+	0.116268i
$909$	0.484009	−	0.956174i	0.0160536	−	0.0317143i
$910$	−21.6078	+	9.53158i	−0.716292	+	0.315969i
$911$		−	23.6770i		−	0.784454i	−0.919868	−	0.392227i	$-0.871705\pi$
$911$		−	23.6770i		−	0.784454i	0.919868	−	0.392227i	$-0.128295\pi$
$912$	−0.0713872	−	0.0170386i	−0.00236386	−	0.000564204i
$913$	2.73145	+	4.73101i	0.0903978	+	0.156574i
$914$	−6.05246			−0.200198
$915$	−47.4302	+	14.1178i	−1.56799	+	0.466721i
$916$	−2.23308	+	8.33396i	−0.0737829	+	0.275362i
$917$	−13.6946	−	13.4963i	−0.452234	−	0.445687i
$918$	−30.8615	−	26.1469i	−1.01858	−	0.862975i
$919$	−15.2596	+	26.4303i	−0.503366	+	0.871856i	0.496626	+	0.867965i	$0.334572\pi$
$919$	−15.2596	+	26.4303i	−0.503366	+	0.871856i	−0.999992	+	0.00389145i	$0.998761\pi$
$920$	−4.86247	−	8.42205i	−0.160311	−	0.277667i
$921$	5.81385	−	1.73052i	0.191573	−	0.0570225i
$922$	11.9456	−	6.89681i	0.393408	−	0.227134i
$923$	−3.13928	+	4.22480i	−0.103331	+	0.139061i
$924$	−12.3141	+	23.1532i	−0.405103	+	0.761684i
$925$	9.76891	−	2.61757i	0.321200	−	0.0860652i
$926$		−	6.53710i		−	0.214822i
$927$	−31.3790	−	15.8838i	−1.03062	−	0.521694i
$928$	−0.553963	+	0.148434i	−0.0181847	+	0.00487258i
$929$	−9.14047	−	34.1127i	−0.299889	−	1.11920i	−0.937256	−	0.348641i	$-0.886643\pi$
$929$	−9.14047	−	34.1127i	−0.299889	−	1.11920i	0.637367	−	0.770560i	$-0.280023\pi$
$930$	22.1820	−	6.60256i	0.727375	−	0.216507i
$931$	−0.206656	+	0.212772i	−0.00677286	+	0.00697332i
$932$	−7.50251	+	4.33158i	−0.245753	+	0.141885i
$933$	30.7775	−	18.9166i	1.00761	−	0.619301i
$934$	−9.30203	−	2.49247i	−0.304372	−	0.0815562i
$935$	55.1419	−	95.5087i	1.80333	−	3.12347i
$936$	−9.02372	−	5.96426i	−0.294950	−	0.194948i
$937$	−3.28868			−0.107437			−0.0537183	−	0.998556i	$-0.517107\pi$
$937$	−3.28868			−0.107437			−0.0537183	+	0.998556i	$0.517107\pi$
$938$	13.2237	−	13.4180i	0.431770	−	0.438112i
$939$	−0.0948793	−	3.44874i	−0.00309627	−	0.112545i
$940$	14.9609	+	8.63768i	0.487970	+	0.281730i
$941$	−11.8870	−	44.3627i	−0.387504	−	1.44618i	−0.834182	−	0.551489i	$-0.814060\pi$
$941$	−11.8870	−	44.3627i	−0.387504	−	1.44618i	0.446679	−	0.894694i	$-0.352607\pi$
$942$	3.72246	−	15.5961i	0.121284	−	0.508149i
$943$	−5.54675	−	20.7008i	−0.180627	−	0.674109i
$944$	1.36857	+	1.36857i	0.0445433	+	0.0445433i
$945$	33.8981	−	3.05240i	1.10271	−	0.0992947i
$946$	−25.3481	−	14.6347i	−0.824137	−	0.475816i
$947$	−34.6075	−	34.6075i	−1.12459	−	1.12459i	−0.991042	−	0.133550i	$-0.957362\pi$
$947$	−34.6075	−	34.6075i	−1.12459	−	1.12459i	−0.133550	−	0.991042i	$-0.542638\pi$
$948$	0.124287	−	0.00341931i	0.00403667	−	0.000111054i
$949$	−54.0472	−	6.26745i	−1.75445	−	0.203450i
$950$	−0.0414336	+	0.0239217i	−0.00134428	+	0.000776123i
$951$	8.82621	+	8.35357i	0.286209	+	0.270883i
$952$	10.1674	−	17.9108i	0.329527	−	0.580491i
$953$	−18.5153	−	32.0695i	−0.599770	−	1.03883i	−0.992855	−	0.119329i	$-0.961926\pi$
$953$	−18.5153	−	32.0695i	−0.599770	−	1.03883i	0.393085	−	0.919502i	$-0.371408\pi$
$954$	8.92752	+	7.99566i	0.289039	+	0.258869i
$955$	−11.0924	−	11.0924i	−0.358941	−	0.358941i
$956$	−3.07238	−	3.07238i	−0.0993680	−	0.0993680i
$957$	−5.44823	+	1.62169i	−0.176116	+	0.0524219i
$958$	−10.7928	−	18.6936i	−0.348698	−	0.603963i
$959$	−18.7280	+	32.9911i	−0.604760	+	1.06534i
$960$	−2.94757	+	3.11434i	−0.0951324	+	0.100515i
$961$	−1.61896	+	0.934707i	−0.0522245	+	0.0301518i
$962$	−30.0246	−	11.8964i	−0.968031	−	0.383556i
$963$	6.12541	−	4.00100i	0.197389	−	0.128930i
$964$	−12.0272	−	12.0272i	−0.387371	−	0.387371i
$965$	−10.8648	−	6.27278i	−0.349750	−	0.201928i
$966$	−9.53742	−	15.2668i	−0.306861	−	0.491202i
$967$	−5.01374	−	5.01374i	−0.161231	−	0.161231i	0.621881	−	0.783112i	$-0.286369\pi$
$967$	−5.01374	−	5.01374i	−0.161231	−	0.161231i	−0.783112	+	0.621881i	$0.786369\pi$
$968$	−5.62878	−	21.0069i	−0.180916	−	0.675188i
$969$	0.555702	+	0.132634i	0.0178517	+	0.00426082i
$970$	7.79587	+	29.0946i	0.250310	+	0.934171i
$971$	31.5042	+	18.1890i	1.01102	+	0.583712i	0.911490	−	0.411323i	$-0.134933\pi$
$971$	31.5042	+	18.1890i	1.01102	+	0.583712i	0.0995286	+	0.995035i	$0.468267\pi$
$972$	9.57134	+	12.3040i	0.307001	+	0.394652i
$973$	−34.3953	+	34.9006i	−1.10266	+	1.11886i
$974$	29.8581			0.956716
$975$	−6.94492	+	1.21974i	−0.222416	+	0.0390629i
$976$	5.77032	−	9.99448i	0.184703	−	0.319916i
$977$	−8.49686	−	2.27673i	−0.271839	−	0.0728390i	0.120325	−	0.992735i	$-0.461606\pi$
$977$	−8.49686	−	2.27673i	−0.271839	−	0.0728390i	−0.392163	+	0.919896i	$0.628273\pi$
$978$	1.89784	+	3.08781i	0.0606862	+	0.0987371i
$979$	−48.7611	+	28.1523i	−1.55841	+	0.899750i
$980$	4.72892	+	16.6722i	0.151060	+	0.532575i
$981$	−2.16135	−	1.93575i	−0.0690067	−	0.0618037i
$982$	3.40599	+	12.7113i	0.108690	+	0.405635i
$983$	−17.3212	+	4.64120i	−0.552461	+	0.148031i	−0.524240	−	0.851570i	$-0.675651\pi$
$983$	−17.3212	+	4.64120i	−0.552461	+	0.148031i	−0.0282204	+	0.999602i	$0.508984\pi$
$984$	−8.05058	+	4.94808i	−0.256643	+	0.157739i
$985$		−	2.06147i		−	0.0656838i
$986$	4.31223	−	1.15546i	0.137329	−	0.0367973i
$987$	28.2324	+	15.0154i	0.898646	+	0.477947i
$988$	0.151761	+	0.0175986i	0.00482817	+	0.000559887i
$989$	17.3997	−	10.0457i	0.553278	−	0.319435i
$990$	−28.3558	+	31.6605i	−0.901206	+	1.00624i
$991$	−2.69363	−	4.66550i	−0.0855660	−	0.148205i	0.820066	−	0.572269i	$-0.193937\pi$
$991$	−2.69363	−	4.66550i	−0.0855660	−	0.148205i	−0.905632	+	0.424064i	$0.860603\pi$
$992$	−2.69864	+	4.67418i	−0.0856818	+	0.148405i
$993$	−19.1247	−	4.56465i	−0.606903	−	0.144855i
$994$	2.75091	+	2.71109i	0.0872537	+	0.0859906i
$995$	0.537708	−	2.00675i	0.0170465	−	0.0636184i
$996$	0.471705	+	1.58474i	0.0149466	+	0.0502144i
$997$	−6.25625			−0.198137			−0.0990687	−	0.995081i	$-0.531586\pi$
$997$	−6.25625			−0.198137			−0.0990687	+	0.995081i	$0.531586\pi$
$998$	−3.51126	−	6.08167i	−0.111147	−	0.192512i
$999$	35.5112	+	30.0862i	1.12353	+	0.951887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.16	yes	152
3.2	odd	2	inner	546.2.ch.a.137.30	yes	152
7.2	even	3		546.2.bw.a.527.23	yes	152
13.2	odd	12		546.2.bw.a.431.4	✓	152
21.2	odd	6		546.2.bw.a.527.4	yes	152
39.2	even	12		546.2.bw.a.431.23	yes	152
91.2	odd	12	inner	546.2.ch.a.275.30	yes	152
273.2	even	12	inner	546.2.ch.a.275.16	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.4	✓	152	13.2	odd	12
546.2.bw.a.431.23	yes	152	39.2	even	12
546.2.bw.a.527.4	yes	152	21.2	odd	6
546.2.bw.a.527.23	yes	152	7.2	even	3
546.2.ch.a.137.16	yes	152	1.1	even	1	trivial
546.2.ch.a.137.30	yes	152	3.2	odd	2	inner
546.2.ch.a.275.16	yes	152	273.2	even	12	inner
546.2.ch.a.275.30	yes	152	91.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52325 + 0.824446i) q^{3} -1.00000i q^{4} +(2.39134 + 0.640759i) q^{5} +(-1.66007 + 0.494128i) q^{6} +(-0.703385 - 2.55054i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.64058 + 2.51167i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52325 + 0.824446i) q^{3} -1.00000i q^{4} +(2.39134 + 0.640759i) q^{5} +(-1.66007 + 0.494128i) q^{6} +(-0.703385 - 2.55054i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.64058 + 2.51167i) q^{9} +(-2.14402 + 1.23785i) q^{10} +(1.48111 - 5.52759i) q^{11} +(0.824446 - 1.52325i) q^{12} +(-1.32815 + 3.35202i) q^{13} +(2.30087 + 1.30613i) q^{14} +(3.11434 + 2.94757i) q^{15} -1.00000 q^{16} +7.78434 q^{17} +(-2.93608 - 0.615960i) q^{18} +(0.0409293 - 0.0109670i) q^{19} +(0.640759 - 2.39134i) q^{20} +(1.03135 - 4.46501i) q^{21} +(2.86129 + 4.95590i) q^{22} -3.92816 q^{23} +(0.494128 + 1.66007i) q^{24} +(0.977829 + 0.564550i) q^{25} +(-1.43109 - 3.30938i) q^{26} +(0.428265 + 5.17847i) q^{27} +(-2.55054 + 0.703385i) q^{28} +(-0.496669 - 0.286752i) q^{29} +(-4.28642 + 0.117925i) q^{30} +(-5.21337 + 1.39692i) q^{31} +(0.707107 - 0.707107i) q^{32} +(6.81331 - 7.19880i) q^{33} +(-5.50436 + 5.50436i) q^{34} +(-0.0477563 - 6.54992i) q^{35} +(2.51167 - 1.64058i) q^{36} +(6.33367 - 6.33367i) q^{37} +(-0.0211866 + 0.0366962i) q^{38} +(-4.78666 + 4.01097i) q^{39} +(1.23785 + 2.14402i) q^{40} +(1.41205 + 5.26984i) q^{41} +(2.42796 + 3.88651i) q^{42} +(-4.42948 + 2.55736i) q^{43} +(-5.52759 - 1.48111i) q^{44} +(2.31380 + 7.05749i) q^{45} +(2.77763 - 2.77763i) q^{46} +(-1.80603 + 6.74019i) q^{47} +(-1.52325 - 0.824446i) q^{48} +(-6.01050 + 3.58802i) q^{49} +(-1.09063 + 0.292232i) q^{50} +(11.8575 + 6.41777i) q^{51} +(3.35202 + 1.32815i) q^{52} +(-3.45966 - 1.99744i) q^{53} +(-3.96456 - 3.35890i) q^{54} +(7.08370 - 12.2693i) q^{55} +(1.30613 - 2.30087i) q^{56} +(0.0713872 + 0.0170386i) q^{57} +(0.553963 - 0.148434i) q^{58} +(-1.36857 - 1.36857i) q^{59} +(2.94757 - 3.11434i) q^{60} +(-5.77032 + 9.99448i) q^{61} +(2.69864 - 4.67418i) q^{62} +(5.25217 - 5.95103i) q^{63} +1.00000i q^{64} +(-5.32389 + 7.16481i) q^{65} +(0.272584 + 9.90805i) q^{66} +(1.84292 - 6.87786i) q^{67} -7.78434i q^{68} +(-5.98356 - 3.23855i) q^{69} +(4.66526 + 4.59772i) q^{70} +(1.41008 + 0.377829i) q^{71} +(-0.615960 + 2.93608i) q^{72} +(3.90570 + 14.5763i) q^{73} +8.95716i q^{74} +(1.02404 + 1.66612i) q^{75} +(-0.0109670 - 0.0409293i) q^{76} +(-15.1401 + 0.110389i) q^{77} +(0.548493 - 6.22086i) q^{78} +(0.0358923 + 0.0621672i) q^{79} +(-2.39134 - 0.640759i) q^{80} +(-3.61702 + 8.24119i) q^{81} +(-4.72481 - 2.72787i) q^{82} +(-0.675019 + 0.675019i) q^{83} +(-4.46501 - 1.03135i) q^{84} +(18.6150 + 4.98788i) q^{85} +(1.32379 - 4.94045i) q^{86} +(-0.520139 - 0.846272i) q^{87} +(4.95590 - 2.86129i) q^{88} +(-6.95723 - 6.95723i) q^{89} +(-6.62651 - 3.35429i) q^{90} +(9.48365 + 1.02973i) q^{91} +3.92816i q^{92} +(-9.09294 - 2.17029i) q^{93} +(-3.48898 - 6.04309i) q^{94} +0.104903 q^{95} +(1.66007 - 0.494128i) q^{96} +(3.14895 - 11.7521i) q^{97} +(1.71295 - 6.78718i) q^{98} +(16.3134 - 5.34836i) 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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