LMFDB - Embedded newform 546.2.bm.b.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.5
Root			$3.31964i$ of defining polynomial
Character	$\chi$	$=$	546.277
Dual form			546.2.bm.b.205.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.744278 + 2.53891i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.744278 + 2.53891i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.65982 - 2.87489i) q^{10} +(4.19183 - 2.42015i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.96948 - 2.04504i) q^{13} +(2.53891 + 0.744278i) q^{14} +(-2.87489 - 1.65982i) q^{15} +1.00000 q^{16} +5.42123 q^{17} +(0.866025 + 0.500000i) q^{18} +(-6.03917 - 3.48672i) q^{19} +(-2.87489 + 1.65982i) q^{20} +(2.57090 - 0.624890i) q^{21} +(-2.42015 - 4.19183i) q^{22} -6.23820 q^{23} +(0.866025 - 0.500000i) q^{24} +(3.01000 - 5.21347i) q^{25} +(-2.04504 - 2.96948i) q^{26} +1.00000 q^{27} +(0.744278 - 2.53891i) q^{28} +(-0.459279 + 0.795495i) q^{29} +(-1.65982 + 2.87489i) q^{30} +(4.25364 + 2.45584i) q^{31} -1.00000i q^{32} +(-4.19183 - 2.42015i) q^{33} -5.42123i q^{34} +(2.07441 + 8.53445i) q^{35} +(0.500000 - 0.866025i) q^{36} +7.81686i q^{37} +(-3.48672 + 6.03917i) q^{38} +(-3.25580 - 1.54912i) q^{39} +(1.65982 + 2.87489i) q^{40} +(-6.91006 - 3.98953i) q^{41} +(-0.624890 - 2.57090i) q^{42} +(-2.86888 - 4.96904i) q^{43} +(-4.19183 + 2.42015i) q^{44} +3.31964i q^{45} +6.23820i q^{46} +(1.99396 - 1.15121i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-5.89210 - 3.77931i) q^{49} +(-5.21347 - 3.01000i) q^{50} +(-2.71061 - 4.69492i) q^{51} +(-2.96948 + 2.04504i) q^{52} +(2.54507 - 4.40819i) q^{53} -1.00000i q^{54} +(8.03403 - 13.9153i) q^{55} +(-2.53891 - 0.744278i) q^{56} +6.97343i q^{57} +(0.795495 + 0.459279i) q^{58} +8.43334i q^{59} +(2.87489 + 1.65982i) q^{60} +(1.82308 - 3.15766i) q^{61} +(2.45584 - 4.25364i) q^{62} +(-1.82662 - 1.91402i) q^{63} -1.00000 q^{64} +(5.14253 - 10.8081i) q^{65} +(-2.42015 + 4.19183i) q^{66} +(7.62461 - 4.40207i) q^{67} -5.42123 q^{68} +(3.11910 + 5.40244i) q^{69} +(8.53445 - 2.07441i) q^{70} +(-6.84209 + 3.95028i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.61061 + 0.929885i) q^{73} +7.81686 q^{74} -6.01999 q^{75} +(6.03917 + 3.48672i) q^{76} +(3.02466 + 12.4439i) q^{77} +(-1.54912 + 3.25580i) q^{78} +(-1.39270 - 2.41222i) q^{79} +(2.87489 - 1.65982i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.98953 + 6.91006i) q^{82} +5.97886i q^{83} +(-2.57090 + 0.624890i) q^{84} +(15.5854 - 8.99826i) q^{85} +(-4.96904 + 2.86888i) q^{86} +0.918558 q^{87} +(2.42015 + 4.19183i) q^{88} +6.22313i q^{89} +3.31964 q^{90} +(2.98205 + 9.06131i) q^{91} +6.23820 q^{92} -4.91168i q^{93} +(-1.15121 - 1.99396i) q^{94} -23.1493 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-0.466544 + 0.269360i) q^{97} +(-3.77931 + 5.89210i) q^{98} +4.84030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	$ 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) $ 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	2.87489	−	1.65982i	1.28569	−	0.742293i	0.307808	−	0.951449i	$-0.400405\pi$
$5$	2.87489	−	1.65982i	1.28569	−	0.742293i	0.977882	+	0.209155i	$0.0670714\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.744278	+	2.53891i	−0.281311	+	0.959617i
$7$	−0.744278	+	2.53891i	−0.281311	+	0.959617i
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.65982	−	2.87489i	−0.524881	−	0.909120i
$11$	4.19183	−	2.42015i	1.26388	−	0.729703i	0.290060	−	0.957009i	$-0.406325\pi$
$11$	4.19183	−	2.42015i	1.26388	−	0.729703i	0.973824	+	0.227305i	$0.0729915\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.96948	−	2.04504i	0.823585	−	0.567192i
$13$	2.96948	−	2.04504i	0.823585	−	0.567192i
$14$	2.53891	+	0.744278i	0.678551	+	0.198917i
$15$	−2.87489	−	1.65982i	−0.742293	−	0.428563i
$16$	1.00000			0.250000
$17$	5.42123			1.31484			0.657421	−	0.753524i	$-0.271647\pi$
$17$	5.42123			1.31484			0.657421	+	0.753524i	$0.271647\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−6.03917	−	3.48672i	−1.38548	−	0.799908i	−0.392679	−	0.919676i	$-0.628452\pi$
$19$	−6.03917	−	3.48672i	−1.38548	−	0.799908i	−0.992802	+	0.119768i	$0.961785\pi$
$20$	−2.87489	+	1.65982i	−0.642845	+	0.371147i
$21$	2.57090	−	0.624890i	0.561016	−	0.136362i
$22$	−2.42015	−	4.19183i	−0.515978	−	0.893700i
$23$	−6.23820			−1.30075			−0.650377	−	0.759612i	$-0.725389\pi$
$23$	−6.23820			−1.30075			−0.650377	+	0.759612i	$0.725389\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	3.01000	−	5.21347i	0.601999	−	1.04269i
$26$	−2.04504	−	2.96948i	−0.401066	−	0.582363i
$27$	1.00000			0.192450
$28$	0.744278	−	2.53891i	0.140655	−	0.479808i
$29$	−0.459279	+	0.795495i	−0.0852860	+	0.147720i	−0.905513	−	0.424318i	$-0.860514\pi$
$29$	−0.459279	+	0.795495i	−0.0852860	+	0.147720i	0.820227	+	0.572038i	$0.193847\pi$
$30$	−1.65982	+	2.87489i	−0.303040	+	0.524881i
$31$	4.25364	+	2.45584i	0.763976	+	0.441082i	0.830722	−	0.556688i	$-0.187928\pi$
$31$	4.25364	+	2.45584i	0.763976	+	0.441082i	−0.0667452	+	0.997770i	$0.521261\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.19183	−	2.42015i	−0.729703	−	0.421294i
$34$		−	5.42123i		−	0.929733i
$35$	2.07441	+	8.53445i	0.350639	+	1.44258i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$			7.81686i			1.28508i	0.766251	+	0.642542i	$0.222120\pi$
$37$			7.81686i			1.28508i	−0.766251	+	0.642542i	$0.777880\pi$
$38$	−3.48672	+	6.03917i	−0.565620	+	0.979683i
$39$	−3.25580	−	1.54912i	−0.521345	−	0.248058i
$40$	1.65982	+	2.87489i	0.262440	+	0.454560i
$41$	−6.91006	−	3.98953i	−1.07917	−	0.623059i	−0.148498	−	0.988913i	$-0.547444\pi$
$41$	−6.91006	−	3.98953i	−1.07917	−	0.623059i	−0.930673	+	0.365853i	$0.880777\pi$
$42$	−0.624890	−	2.57090i	−0.0964225	−	0.396698i
$43$	−2.86888	−	4.96904i	−0.437500	−	0.757772i	0.559996	−	0.828495i	$-0.310803\pi$
$43$	−2.86888	−	4.96904i	−0.437500	−	0.757772i	−0.997496	+	0.0707235i	$0.977469\pi$
$44$	−4.19183	+	2.42015i	−0.631942	+	0.364852i
$45$			3.31964i			0.494862i
$46$			6.23820i			0.919772i
$47$	1.99396	−	1.15121i	0.290849	−	0.167922i	−0.347476	−	0.937689i	$-0.612961\pi$
$47$	1.99396	−	1.15121i	0.290849	−	0.167922i	0.638325	+	0.769767i	$0.279628\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−5.89210	−	3.77931i	−0.841728	−	0.539901i
$50$	−5.21347	−	3.01000i	−0.737295	−	0.425678i
$51$	−2.71061	−	4.69492i	−0.379562	−	0.657421i
$52$	−2.96948	+	2.04504i	−0.411793	+	0.283596i
$53$	2.54507	−	4.40819i	0.349592	−	0.605512i	−0.636585	−	0.771207i	$-0.719653\pi$
$53$	2.54507	−	4.40819i	0.349592	−	0.605512i	0.986177	+	0.165695i	$0.0529868\pi$
$54$		−	1.00000i		−	0.136083i
$55$	8.03403	−	13.9153i	1.08331	−	1.87634i
$56$	−2.53891	−	0.744278i	−0.339276	−	0.0994584i
$57$			6.97343i			0.923654i
$58$	0.795495	+	0.459279i	0.104454	+	0.0603063i
$59$			8.43334i			1.09793i	0.835846	+	0.548964i	$0.184977\pi$
$59$			8.43334i			1.09793i	−0.835846	+	0.548964i	$0.815023\pi$
$60$	2.87489	+	1.65982i	0.371147	+	0.214282i
$61$	1.82308	−	3.15766i	0.233421	−	0.404297i	−0.725392	−	0.688336i	$-0.758341\pi$
$61$	1.82308	−	3.15766i	0.233421	−	0.404297i	0.958813	+	0.284039i	$0.0916747\pi$
$62$	2.45584	−	4.25364i	0.311892	−	0.540213i
$63$	−1.82662	−	1.91402i	−0.230132	−	0.241144i
$64$	−1.00000			−0.125000
$65$	5.14253	−	10.8081i	0.637852	−	1.34058i
$66$	−2.42015	+	4.19183i	−0.297900	+	0.515978i
$67$	7.62461	−	4.40207i	0.931494	−	0.537798i	0.0442103	−	0.999022i	$-0.485923\pi$
$67$	7.62461	−	4.40207i	0.931494	−	0.537798i	0.887284	+	0.461224i	$0.152590\pi$
$68$	−5.42123			−0.657421
$69$	3.11910	+	5.40244i	0.375495	+	0.650377i
$70$	8.53445	−	2.07441i	1.02006	−	0.247939i
$71$	−6.84209	+	3.95028i	−0.812007	+	0.468812i	−0.847652	−	0.530552i	$-0.821985\pi$
$71$	−6.84209	+	3.95028i	−0.812007	+	0.468812i	0.0356457	+	0.999364i	$0.488651\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	1.61061	+	0.929885i	0.188507	+	0.108835i	0.591284	−	0.806464i	$-0.298621\pi$
$73$	1.61061	+	0.929885i	0.188507	+	0.108835i	−0.402776	+	0.915298i	$0.631955\pi$
$74$	7.81686			0.908691
$75$	−6.01999			−0.695129
$76$	6.03917	+	3.48672i	0.692740	+	0.399954i
$77$	3.02466	+	12.4439i	0.344691	+	1.41812i
$78$	−1.54912	+	3.25580i	−0.175404	+	0.368646i
$79$	−1.39270	−	2.41222i	−0.156691	−	0.271396i	0.776983	−	0.629522i	$-0.216749\pi$
$79$	−1.39270	−	2.41222i	−0.156691	−	0.271396i	−0.933673	+	0.358126i	$0.883416\pi$
$80$	2.87489	−	1.65982i	0.321423	−	0.185573i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.98953	+	6.91006i	−0.440570	+	0.763089i
$83$			5.97886i			0.656265i	0.944632	+	0.328132i	$0.106419\pi$
$83$			5.97886i			0.656265i	−0.944632	+	0.328132i	$0.893581\pi$
$84$	−2.57090	+	0.624890i	−0.280508	+	0.0681810i
$85$	15.5854	−	8.99826i	1.69048	−	0.975998i
$86$	−4.96904	+	2.86888i	−0.535825	+	0.309359i
$87$	0.918558			0.0984798
$88$	2.42015	+	4.19183i	0.257989	+	0.446850i
$89$			6.22313i			0.659650i	0.944042	+	0.329825i	$0.106990\pi$
$89$			6.22313i			0.659650i	−0.944042	+	0.329825i	$0.893010\pi$
$90$	3.31964			0.349921
$91$	2.98205	+	9.06131i	0.312604	+	0.949884i
$92$	6.23820			0.650377
$93$		−	4.91168i		−	0.509318i
$94$	−1.15121	−	1.99396i	−0.118738	−	0.205661i
$95$	−23.1493			−2.37507
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−0.466544	+	0.269360i	−0.0473704	+	0.0273493i	−0.523498	−	0.852027i	$-0.675373\pi$
$97$	−0.466544	+	0.269360i	−0.0473704	+	0.0273493i	0.476128	+	0.879376i	$0.342040\pi$
$98$	−3.77931	+	5.89210i	−0.381768	+	0.595192i
$99$			4.84030i			0.486469i
$100$	−3.01000	+	5.21347i	−0.301000	+	0.521347i
$101$	7.98541	+	13.8311i	0.794578	+	1.37625i	0.923107	+	0.384543i	$0.125641\pi$
$101$	7.98541	+	13.8311i	0.794578	+	1.37625i	−0.128529	+	0.991706i	$0.541026\pi$
$102$	−4.69492	+	2.71061i	−0.464867	+	0.268391i
$103$	1.31241	+	2.27316i	0.129316	+	0.223981i	0.923412	−	0.383811i	$-0.125389\pi$
$103$	1.31241	+	2.27316i	0.129316	+	0.223981i	−0.794096	+	0.607792i	$0.792055\pi$
$104$	2.04504	+	2.96948i	0.200533	+	0.291181i
$105$	6.35384	−	6.06371i	0.620072	−	0.591758i
$106$	−4.40819	−	2.54507i	−0.428161	−	0.247199i
$107$	6.98183			0.674959			0.337479	−	0.941333i	$-0.390426\pi$
$107$	6.98183			0.674959			0.337479	+	0.941333i	$0.390426\pi$
$108$	−1.00000			−0.0962250
$109$	7.17312	+	4.14140i	0.687060	+	0.396674i	0.802510	−	0.596639i	$-0.203498\pi$
$109$	7.17312	+	4.14140i	0.687060	+	0.396674i	−0.115450	+	0.993313i	$0.536831\pi$
$110$	−13.9153	−	8.03403i	−1.32678	−	0.766014i
$111$	6.76960	−	3.90843i	0.642542	−	0.370972i
$112$	−0.744278	+	2.53891i	−0.0703277	+	0.239904i
$113$	2.78680	+	4.82688i	0.262160	+	0.454075i	0.966816	−	0.255475i	$-0.0822318\pi$
$113$	2.78680	+	4.82688i	0.262160	+	0.454075i	−0.704655	+	0.709550i	$0.748898\pi$
$114$	6.97343			0.653122
$115$	−17.9341	+	10.3543i	−1.67237	+	0.965541i
$116$	0.459279	−	0.795495i	0.0426430	−	0.0738598i
$117$	0.286318	+	3.59416i	0.0264701	+	0.332281i
$118$	8.43334			0.776352
$119$	−4.03490	+	13.7640i	−0.369879	+	1.26174i
$120$	1.65982	−	2.87489i	0.151520	−	0.262440i
$121$	6.21427	−	10.7634i	0.564934	−	0.978494i
$122$	−3.15766	−	1.82308i	−0.285881	−	0.165054i
$123$			7.97905i			0.719447i
$124$	−4.25364	−	2.45584i	−0.381988	−	0.220541i
$125$		−	3.38601i		−	0.302854i
$126$	−1.91402	+	1.82662i	−0.170514	+	0.162728i
$127$	−5.35058	+	9.26748i	−0.474787	+	0.822356i	−0.999583	−	0.0288723i	$-0.990808\pi$
$127$	−5.35058	+	9.26748i	−0.474787	+	0.822356i	0.524796	+	0.851228i	$0.324142\pi$
$128$			1.00000i			0.0883883i
$129$	−2.86888	+	4.96904i	−0.252591	+	0.437500i
$130$	−10.8081	−	5.14253i	−0.947930	−	0.451030i
$131$	8.39711	+	14.5442i	0.733659	+	1.27073i	0.955309	+	0.295608i	$0.0955224\pi$
$131$	8.39711	+	14.5442i	0.733659	+	1.27073i	−0.221650	+	0.975126i	$0.571144\pi$
$132$	4.19183	+	2.42015i	0.364852	+	0.210647i
$133$	13.3473	−	12.7378i	1.15736	−	1.10451i
$134$	−4.40207	−	7.62461i	−0.380281	−	0.658666i
$135$	2.87489	−	1.65982i	0.247431	−	0.142854i
$136$			5.42123i			0.464867i
$137$		−	16.1077i		−	1.37617i	−0.725629	−	0.688086i	$-0.758451\pi$
$137$		−	16.1077i		−	1.37617i	0.725629	−	0.688086i	$-0.241549\pi$
$138$	5.40244	−	3.11910i	0.459886	−	0.265515i
$139$	5.04105	+	8.73136i	0.427577	+	0.740584i	0.996657	−	0.0816975i	$-0.0260341\pi$
$139$	5.04105	+	8.73136i	0.427577	+	0.740584i	−0.569081	+	0.822282i	$0.692701\pi$
$140$	−2.07441	−	8.53445i	−0.175319	−	0.721292i
$141$	−1.99396	−	1.15121i	−0.167922	−	0.0969496i
$142$	3.95028	+	6.84209i	0.331500	+	0.574175i
$143$	7.49823	−	15.7590i	0.627033	−	1.31784i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$			3.04928i			0.253229i
$146$	0.929885	−	1.61061i	0.0769578	−	0.133295i
$147$	−0.326927	+	6.99236i	−0.0269645	+	0.576720i
$148$		−	7.81686i		−	0.642542i
$149$	6.73965	+	3.89114i	0.552134	+	0.318775i	0.749982	−	0.661458i	$-0.230062\pi$
$149$	6.73965	+	3.89114i	0.552134	+	0.318775i	−0.197848	+	0.980233i	$0.563395\pi$
$150$			6.01999i			0.491530i
$151$	−12.2591	−	7.07781i	−0.997634	−	0.575984i	−0.0900867	−	0.995934i	$-0.528714\pi$
$151$	−12.2591	−	7.07781i	−0.997634	−	0.575984i	−0.907547	+	0.419950i	$0.862048\pi$
$152$	3.48672	−	6.03917i	0.282810	−	0.489841i
$153$	−2.71061	+	4.69492i	−0.219140	+	0.379562i
$154$	12.4439	−	3.02466i	1.00276	−	0.243734i
$155$	16.3050			1.30965
$156$	3.25580	+	1.54912i	0.260672	+	0.124029i
$157$	0.648559	−	1.12334i	0.0517606	−	0.0896520i	−0.838984	−	0.544156i	$-0.816850\pi$
$157$	0.648559	−	1.12334i	0.0517606	−	0.0896520i	0.890745	+	0.454504i	$0.150183\pi$
$158$	−2.41222	+	1.39270i	−0.191906	+	0.110797i
$159$	−5.09014			−0.403674
$160$	−1.65982	−	2.87489i	−0.131220	−	0.227280i
$161$	4.64295	−	15.8382i	0.365916	−	1.24823i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−18.7290	−	10.8132i	−1.46696	−	0.846953i	−0.467648	−	0.883915i	$-0.654899\pi$
$163$	−18.7290	−	10.8132i	−1.46696	−	0.846953i	−0.999317	+	0.0369622i	$0.988232\pi$
$164$	6.91006	+	3.98953i	0.539585	+	0.311530i
$165$	−16.0681			−1.25090
$166$	5.97886			0.464049
$167$	11.2333	+	6.48557i	0.869261	+	0.501868i	0.867103	−	0.498130i	$-0.165980\pi$
$167$	11.2333	+	6.48557i	0.869261	+	0.501868i	0.00215851	+	0.999998i	$0.499313\pi$
$168$	0.624890	+	2.57090i	0.0482113	+	0.198349i
$169$	4.63561	−	12.1454i	0.356585	−	0.934263i
$170$	−8.99826	−	15.5854i	−0.690135	−	1.19535i
$171$	6.03917	−	3.48672i	0.461827	−	0.266636i
$172$	2.86888	+	4.96904i	0.218750	+	0.378886i
$173$	−6.72607	+	11.6499i	−0.511374	+	0.885725i	0.488539	+	0.872542i	$0.337530\pi$
$173$	−6.72607	+	11.6499i	−0.511374	+	0.885725i	−0.999913	+	0.0131835i	$0.995803\pi$
$174$		−	0.918558i		−	0.0696357i
$175$	10.9962	+	11.5224i	0.831237	+	0.871009i
$176$	4.19183	−	2.42015i	0.315971	−	0.182426i
$177$	7.30349	−	4.21667i	0.548964	−	0.316944i
$178$	6.22313			0.466443
$179$	−2.36998	−	4.10493i	−0.177141	−	0.306817i	0.763759	−	0.645501i	$-0.223352\pi$
$179$	−2.36998	−	4.10493i	−0.177141	−	0.306817i	−0.940900	+	0.338684i	$0.890018\pi$
$180$		−	3.31964i		−	0.247431i
$181$	−16.7842			−1.24756			−0.623780	−	0.781600i	$-0.714404\pi$
$181$	−16.7842			−1.24756			−0.623780	+	0.781600i	$0.714404\pi$
$182$	9.06131	−	2.98205i	0.671669	−	0.221044i
$183$	−3.64615			−0.269531
$184$		−	6.23820i		−	0.459886i
$185$	12.9746	+	22.4726i	0.953909	+	1.65222i
$186$	−4.91168			−0.360142
$187$	22.7249	−	13.1202i	1.66181	−	0.959444i
$188$	−1.99396	+	1.15121i	−0.145424	+	0.0839608i
$189$	−0.744278	+	2.53891i	−0.0541383	+	0.184678i
$190$			23.1493i			1.67942i
$191$	−6.99350	+	12.1131i	−0.506032	+	0.876473i	0.493944	+	0.869494i	$0.335555\pi$
$191$	−6.99350	+	12.1131i	−0.506032	+	0.876473i	−0.999976	+	0.00697916i	$0.997778\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−10.0487	+	5.80159i	−0.723318	+	0.417608i	−0.815973	−	0.578091i	$-0.803798\pi$
$193$	−10.0487	+	5.80159i	−0.723318	+	0.417608i	0.0926548	+	0.995698i	$0.470465\pi$
$194$	0.269360	+	0.466544i	0.0193389	+	0.0334959i
$195$	−11.9313	+	0.950473i	−0.854420	+	0.0680648i
$196$	5.89210	+	3.77931i	0.420864	+	0.269951i
$197$	−16.7733	−	9.68409i	−1.19505	−	0.689963i	−0.235603	−	0.971849i	$-0.575706\pi$
$197$	−16.7733	−	9.68409i	−1.19505	−	0.689963i	−0.959448	+	0.281887i	$0.909040\pi$
$198$	4.84030			0.343985
$199$	−15.9597			−1.13135			−0.565677	−	0.824627i	$-0.691385\pi$
$199$	−15.9597			−1.13135			−0.565677	+	0.824627i	$0.691385\pi$
$200$	5.21347	+	3.01000i	0.368648	+	0.212839i
$201$	−7.62461	−	4.40207i	−0.537798	−	0.310498i
$202$	13.8311	−	7.98541i	0.973155	−	0.561851i
$203$	−1.67786	−	1.75814i	−0.117762	−	0.123397i
$204$	2.71061	+	4.69492i	0.189781	+	0.328710i
$205$	−26.4876			−1.84997
$206$	2.27316	−	1.31241i	0.158379	−	0.0914400i
$207$	3.11910	−	5.40244i	0.216792	−	0.375495i
$208$	2.96948	−	2.04504i	0.205896	−	0.141798i
$209$	−33.7535			−2.33478
$210$	−6.06371	−	6.35384i	−0.418436	−	0.438457i
$211$	−7.94467	+	13.7606i	−0.546934	+	0.947317i	0.451549	+	0.892247i	$0.350872\pi$
$211$	−7.94467	+	13.7606i	−0.546934	+	0.947317i	−0.998482	+	0.0550706i	$0.982462\pi$
$212$	−2.54507	+	4.40819i	−0.174796	+	0.302756i
$213$	6.84209	+	3.95028i	0.468812	+	0.270669i
$214$		−	6.98183i		−	0.477268i
$215$	−16.4954	−	9.52363i	−1.12498	−	0.649506i
$216$			1.00000i			0.0680414i
$217$	−9.40105	+	8.97177i	−0.638185	+	0.609043i
$218$	4.14140	−	7.17312i	0.280491	−	0.485825i
$219$		−	1.85977i		−	0.125672i
$220$	−8.03403	+	13.9153i	−0.541654	+	0.938172i
$221$	16.0982	−	11.0866i	1.08288	−	0.745768i
$222$	−3.90843	−	6.76960i	−0.262317	−	0.454346i
$223$	21.3888	+	12.3488i	1.43230	+	0.826940i	0.997296	−	0.0734882i	$-0.0234131\pi$
$223$	21.3888	+	12.3488i	1.43230	+	0.826940i	0.435005	+	0.900428i	$0.356746\pi$
$224$	2.53891	+	0.744278i	0.169638	+	0.0497292i
$225$	3.01000	+	5.21347i	0.200666	+	0.347564i
$226$	4.82688	−	2.78680i	0.321079	−	0.185375i
$227$		−	15.9659i		−	1.05970i	−0.848093	−	0.529848i	$-0.822249\pi$
$227$		−	15.9659i		−	1.05970i	0.848093	−	0.529848i	$-0.177751\pi$
$228$		−	6.97343i		−	0.461827i
$229$	−5.05038	+	2.91584i	−0.333738	+	0.192684i	−0.657500	−	0.753455i	$-0.728386\pi$
$229$	−5.05038	+	2.91584i	−0.333738	+	0.192684i	0.323761	+	0.946139i	$0.395053\pi$
$230$	10.3543	+	17.9341i	0.682741	+	1.18254i
$231$	9.26443	−	8.84139i	0.609555	−	0.581721i
$232$	−0.795495	−	0.459279i	−0.0522268	−	0.0301532i
$233$	−5.79484	−	10.0370i	−0.379632	−	0.657543i	0.611376	−	0.791340i	$-0.290616\pi$
$233$	−5.79484	−	10.0370i	−0.379632	−	0.657543i	−0.991009	+	0.133797i	$0.957283\pi$
$234$	3.59416	−	0.286318i	0.234958	−	0.0187172i
$235$	3.82161	−	6.61922i	0.249294	−	0.431790i
$236$		−	8.43334i		−	0.548964i
$237$	−1.39270	+	2.41222i	−0.0904654	+	0.156691i
$238$	13.7640	+	4.03490i	0.892188	+	0.261544i
$239$		−	21.8120i		−	1.41090i	−0.708760	−	0.705450i	$-0.750745\pi$
$239$		−	21.8120i		−	1.41090i	0.708760	−	0.705450i	$-0.249255\pi$
$240$	−2.87489	−	1.65982i	−0.185573	−	0.107141i
$241$			20.3132i			1.30849i	0.756282	+	0.654246i	$0.227014\pi$
$241$			20.3132i			1.30849i	−0.756282	+	0.654246i	$0.772986\pi$
$242$	−10.7634	−	6.21427i	−0.691900	−	0.399468i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.82308	+	3.15766i	−0.116710	+	0.202148i
$245$	−23.2121	−	1.08528i	−1.48297	−	0.0693360i
$246$	7.97905			0.508726
$247$	−25.0637	+	1.99662i	−1.59476	+	0.127042i
$248$	−2.45584	+	4.25364i	−0.155946	+	0.270106i
$249$	5.17784	−	2.98943i	0.328132	−	0.189447i
$250$	−3.38601			−0.214150
$251$	9.39667	+	16.2755i	0.593112	+	1.02730i	0.993810	+	0.111091i	$0.0354344\pi$
$251$	9.39667	+	16.2755i	0.593112	+	1.02730i	−0.400698	+	0.916210i	$0.631232\pi$
$252$	1.82662	+	1.91402i	0.115066	+	0.120572i
$253$	−26.1494	+	15.0974i	−1.64400	+	0.949164i
$254$	9.26748	+	5.35058i	0.581493	+	0.335725i
$255$	−15.5854	−	8.99826i	−0.975998	−	0.563493i
$256$	1.00000			0.0625000
$257$	19.0185			1.18634			0.593170	−	0.805077i	$-0.297876\pi$
$257$	19.0185			1.18634			0.593170	+	0.805077i	$0.297876\pi$
$258$	4.96904	+	2.86888i	0.309359	+	0.178608i
$259$	−19.8463	−	5.81792i	−1.23319	−	0.361508i
$260$	−5.14253	+	10.8081i	−0.318926	+	0.670288i
$261$	−0.459279	−	0.795495i	−0.0284287	−	0.0492399i
$262$	14.5442	−	8.39711i	0.898545	−	0.518775i
$263$	10.1573	+	17.5930i	0.626327	+	1.08483i	0.988283	+	0.152635i	$0.0487759\pi$
$263$	10.1573	+	17.5930i	0.626327	+	1.08483i	−0.361956	+	0.932195i	$0.617891\pi$
$264$	2.42015	−	4.19183i	0.148950	−	0.257989i
$265$		−	16.8974i		−	1.03800i
$266$	−12.7378	−	13.3473i	−0.781005	−	0.818374i
$267$	5.38939	−	3.11156i	0.329825	−	0.190425i
$268$	−7.62461	+	4.40207i	−0.465747	+	0.268899i
$269$	−12.3202			−0.751175			−0.375588	−	0.926787i	$-0.622559\pi$
$269$	−12.3202			−0.751175			−0.375588	+	0.926787i	$0.622559\pi$
$270$	−1.65982	−	2.87489i	−0.101013	−	0.174960i
$271$			11.8163i			0.717790i	0.933378	+	0.358895i	$0.116846\pi$
$271$			11.8163i			0.717790i	−0.933378	+	0.358895i	$0.883154\pi$
$272$	5.42123			0.328710
$273$	6.35630	−	7.11319i	0.384701	−	0.430510i
$274$	−16.1077			−0.973100
$275$		−	29.1386i		−	1.75712i
$276$	−3.11910	−	5.40244i	−0.187748	−	0.325188i
$277$	32.3313			1.94260			0.971299	−	0.237863i	$-0.0764470\pi$
$277$	32.3313			1.94260			0.971299	+	0.237863i	$0.0764470\pi$
$278$	8.73136	−	5.04105i	0.523672	−	0.302342i
$279$	−4.25364	+	2.45584i	−0.254659	+	0.147027i
$280$	−8.53445	+	2.07441i	−0.510031	+	0.123970i
$281$			0.624762i			0.0372702i	0.999826	+	0.0186351i	$0.00593208\pi$
$281$			0.624762i			0.0372702i	−0.999826	+	0.0186351i	$0.994068\pi$
$282$	−1.15121	+	1.99396i	−0.0685537	+	0.118738i
$283$	6.28688	+	10.8892i	0.373716	+	0.647295i	0.990134	−	0.140124i	$-0.0447501\pi$
$283$	6.28688	+	10.8892i	0.373716	+	0.647295i	−0.616418	+	0.787419i	$0.711417\pi$
$284$	6.84209	−	3.95028i	0.406003	−	0.234406i
$285$	11.5746	+	20.0479i	0.685622	+	1.18753i
$286$	−15.7590	−	7.49823i	−0.931852	−	0.443380i
$287$	15.2720	−	14.5747i	0.901481	−	0.860317i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	12.3897			0.728808
$290$	3.04928			0.179060
$291$	0.466544	+	0.269360i	0.0273493	+	0.0157901i
$292$	−1.61061	−	0.929885i	−0.0942537	−	0.0544174i
$293$	17.5615	−	10.1391i	1.02595	−	0.592334i	0.110129	−	0.993917i	$-0.464873\pi$
$293$	17.5615	−	10.1391i	1.02595	−	0.592334i	0.915822	+	0.401584i	$0.131540\pi$
$294$	6.99236	+	0.326927i	0.407803	+	0.0190668i
$295$	13.9978	+	24.2449i	0.814984	+	1.41159i
$296$	−7.81686			−0.454346
$297$	4.19183	−	2.42015i	0.243234	−	0.140431i
$298$	3.89114	−	6.73965i	0.225408	−	0.390417i
$299$	−18.5242	+	12.7574i	−1.07128	+	0.737778i
$300$	6.01999			0.347564
$301$	14.7512	−	3.58546i	0.850244	−	0.206663i
$302$	−7.07781	+	12.2591i	−0.407282	+	0.705434i
$303$	7.98541	−	13.8311i	0.458750	−	0.794578i
$304$	−6.03917	−	3.48672i	−0.346370	−	0.199977i
$305$		−	12.1039i		−	0.693067i
$306$	4.69492	+	2.71061i	0.268391	+	0.154956i
$307$		−	23.8860i		−	1.36325i	−0.731703	−	0.681624i	$-0.761274\pi$
$307$		−	23.8860i		−	1.36325i	0.731703	−	0.681624i	$-0.238726\pi$
$308$	−3.02466	−	12.4439i	−0.172346	−	0.709058i
$309$	1.31241	−	2.27316i	0.0746605	−	0.129316i
$310$		−	16.3050i		−	0.926062i
$311$	−14.1582	+	24.5227i	−0.802837	+	1.39055i	0.114905	+	0.993376i	$0.463344\pi$
$311$	−14.1582	+	24.5227i	−0.802837	+	1.39055i	−0.917742	+	0.397177i	$0.869990\pi$
$312$	1.54912	−	3.25580i	0.0877019	−	0.184323i
$313$	−15.7533	−	27.2855i	−0.890427	−	1.54226i	−0.839364	−	0.543569i	$-0.817072\pi$
$313$	−15.7533	−	27.2855i	−0.890427	−	1.54226i	−0.0510628	−	0.998695i	$-0.516261\pi$
$314$	−1.12334	−	0.648559i	−0.0633935	−	0.0366003i
$315$	−8.42825	−	2.47073i	−0.474878	−	0.139210i
$316$	1.39270	+	2.41222i	0.0783454	+	0.135698i
$317$	−2.06314	+	1.19116i	−0.115878	+	0.0669020i	−0.556819	−	0.830634i	$-0.687978\pi$
$317$	−2.06314	+	1.19116i	−0.115878	+	0.0669020i	0.440941	+	0.897536i	$0.354645\pi$
$318$			5.09014i			0.285441i
$319$			4.44610i			0.248934i
$320$	−2.87489	+	1.65982i	−0.160711	+	0.0927867i
$321$	−3.49091	−	6.04644i	−0.194844	−	0.337479i
$322$	−15.8382	−	4.64295i	−0.882628	−	0.258742i
$323$	−32.7397	−	18.9023i	−1.82169	−	1.05175i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−1.72363	−	21.6368i	−0.0956100	−	1.20020i
$326$	−10.8132	+	18.7290i	−0.598886	+	1.03730i
$327$		−	8.28280i		−	0.458040i
$328$	3.98953	−	6.91006i	0.220285	−	0.381544i
$329$	1.43876	+	5.91930i	0.0793215	+	0.326341i
$330$			16.0681i			0.884517i
$331$	−26.2737	−	15.1691i	−1.44413	−	0.833769i	−0.446009	−	0.895029i	$-0.647155\pi$
$331$	−26.2737	−	15.1691i	−1.44413	−	0.833769i	−0.998122	+	0.0612593i	$0.980488\pi$
$332$		−	5.97886i		−	0.328132i
$333$	−6.76960	−	3.90843i	−0.370972	−	0.214181i
$334$	6.48557	−	11.2333i	0.354874	−	0.614660i
$335$	14.6133	−	25.3109i	0.798408	−	1.38288i
$336$	2.57090	−	0.624890i	0.140254	−	0.0340905i
$337$	16.6355			0.906194			0.453097	−	0.891461i	$-0.350319\pi$
$337$	16.6355			0.906194			0.453097	+	0.891461i	$0.350319\pi$
$338$	−12.1454	−	4.63561i	−0.660623	−	0.252144i
$339$	2.78680	−	4.82688i	0.151358	−	0.262160i
$340$	−15.5854	+	8.99826i	−0.845239	+	0.487999i
$341$	23.7740			1.28744
$342$	−3.48672	−	6.03917i	−0.188540	−	0.326561i
$343$	13.9807	−	12.1466i	0.754885	−	0.655857i
$344$	4.96904	−	2.86888i	0.267913	−	0.154679i
$345$	17.9341	+	10.3543i	0.965541	+	0.557455i
$346$	11.6499	+	6.72607i	0.626302	+	0.361596i
$347$	−6.00937			−0.322600			−0.161300	−	0.986905i	$-0.551569\pi$
$347$	−6.00937			−0.322600			−0.161300	+	0.986905i	$0.551569\pi$
$348$	−0.918558			−0.0492399
$349$	−8.66674	−	5.00374i	−0.463920	−	0.267844i	0.249771	−	0.968305i	$-0.419645\pi$
$349$	−8.66674	−	5.00374i	−0.463920	−	0.267844i	−0.713691	+	0.700461i	$0.752978\pi$
$350$	11.5224	−	10.9962i	0.615897	−	0.587773i
$351$	2.96948	−	2.04504i	0.158499	−	0.109156i
$352$	−2.42015	−	4.19183i	−0.128995	−	0.223425i
$353$	−18.9488	+	10.9401i	−1.00854	+	0.582283i	−0.910765	−	0.412925i	$-0.864507\pi$
$353$	−18.9488	+	10.9401i	−1.00854	+	0.582283i	−0.0977792	+	0.995208i	$0.531174\pi$
$354$	−4.21667	−	7.30349i	−0.224113	−	0.388176i
$355$	−13.1135	+	22.7133i	−0.695992	+	1.20549i
$356$		−	6.22313i		−	0.329825i
$357$	13.9374	−	3.38767i	0.737647	−	0.179294i
$358$	−4.10493	+	2.36998i	−0.216952	+	0.125258i
$359$	3.97403	−	2.29441i	0.209741	−	0.121094i	−0.391450	−	0.920199i	$-0.628026\pi$
$359$	3.97403	−	2.29441i	0.209741	−	0.121094i	0.601191	+	0.799105i	$0.294693\pi$
$360$	−3.31964			−0.174960
$361$	14.8144	+	25.6593i	0.779705	+	1.35049i
$362$			16.7842i			0.882158i
$363$	−12.4285			−0.652329
$364$	−2.98205	−	9.06131i	−0.156302	−	0.474942i
$365$	6.17376			0.323149
$366$			3.64615i			0.190587i
$367$	−18.7030	−	32.3945i	−0.976289	−	1.69098i	−0.675615	−	0.737254i	$-0.736122\pi$
$367$	−18.7030	−	32.3945i	−0.976289	−	1.69098i	−0.300673	−	0.953727i	$-0.597211\pi$
$368$	−6.23820			−0.325188
$369$	6.91006	−	3.98953i	0.359724	−	0.207686i
$370$	22.4726	−	12.9746i	1.16830	−	0.674516i
$371$	9.29775	+	9.74262i	0.482715	+	0.505812i
$372$			4.91168i			0.254659i
$373$	−7.90570	+	13.6931i	−0.409341	+	0.709000i	−0.994816	−	0.101690i	$-0.967575\pi$
$373$	−7.90570	+	13.6931i	−0.409341	+	0.709000i	0.585475	+	0.810691i	$0.300908\pi$
$374$	−13.1202	−	22.7249i	−0.678429	−	1.17507i
$375$	−2.93237	+	1.69300i	−0.151427	+	0.0874263i
$376$	1.15121	+	1.99396i	0.0593692	+	0.102831i
$377$	0.263000	+	3.30145i	0.0135452	+	0.170033i
$378$	2.53891	+	0.744278i	0.130587	+	0.0382816i
$379$	−4.44021	−	2.56356i	−0.228078	−	0.131681i	0.381607	−	0.924325i	$-0.375371\pi$
$379$	−4.44021	−	2.56356i	−0.228078	−	0.131681i	−0.609685	+	0.792644i	$0.708704\pi$
$380$	23.1493			1.18753
$381$	10.7012			0.548237
$382$	12.1131	+	6.99350i	0.619760	+	0.357819i
$383$	17.5182	+	10.1141i	0.895136	+	0.516807i	0.875619	−	0.483003i	$-0.160454\pi$
$383$	17.5182	+	10.1141i	0.895136	+	0.516807i	0.0195170	+	0.999810i	$0.493787\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	29.3502	+	30.7545i	1.49583	+	1.56740i
$386$	5.80159	+	10.0487i	0.295293	+	0.511463i
$387$	5.73775			0.291666
$388$	0.466544	−	0.269360i	0.0236852	−	0.0136747i
$389$	−3.08894	+	5.35019i	−0.156615	+	0.271266i	−0.933646	−	0.358197i	$-0.883392\pi$
$389$	−3.08894	+	5.35019i	−0.156615	+	0.271266i	0.777031	+	0.629463i	$0.216725\pi$
$390$	0.950473	+	11.9313i	0.0481291	+	0.604166i
$391$	−33.8187			−1.71028
$392$	3.77931	−	5.89210i	0.190884	−	0.297596i
$393$	8.39711	−	14.5442i	0.423578	−	0.733659i
$394$	−9.68409	+	16.7733i	−0.487877	+	0.845028i
$395$	−8.00771	−	4.62325i	−0.402911	−	0.232621i
$396$		−	4.84030i		−	0.243234i
$397$	−29.2439	−	16.8840i	−1.46771	−	0.847384i	−0.468365	−	0.883535i	$-0.655157\pi$
$397$	−29.2439	−	16.8840i	−1.46771	−	0.847384i	−0.999346	+	0.0361514i	$0.988490\pi$
$398$			15.9597i			0.799988i
$399$	−17.7049	−	5.19018i	−0.886354	−	0.259834i
$400$	3.01000	−	5.21347i	0.150500	−	0.260673i
$401$			23.9683i			1.19692i	0.801153	+	0.598460i	$0.204220\pi$
$401$			23.9683i			1.19692i	−0.801153	+	0.598460i	$0.795780\pi$
$402$	−4.40207	+	7.62461i	−0.219555	+	0.380281i
$403$	17.6534	−	1.40630i	0.879378	−	0.0700530i
$404$	−7.98541	−	13.8311i	−0.397289	−	0.688124i
$405$	−2.87489	−	1.65982i	−0.142854	−	0.0824771i
$406$	−1.75814	+	1.67786i	−0.0872549	+	0.0832706i
$407$	18.9180	+	32.7669i	0.937730	+	1.62420i
$408$	4.69492	−	2.71061i	0.232433	−	0.134195i
$409$			1.38201i			0.0683361i	0.999416	+	0.0341680i	$0.0108781\pi$
$409$			1.38201i			0.0683361i	−0.999416	+	0.0341680i	$0.989122\pi$
$410$			26.4876i			1.30813i
$411$	−13.9497	+	8.05384i	−0.688086	+	0.397267i
$412$	−1.31241	−	2.27316i	−0.0646579	−	0.111991i
$413$	−21.4115	−	6.27675i	−1.05359	−	0.308859i
$414$	−5.40244	−	3.11910i	−0.265515	−	0.153295i
$415$	9.92382	+	17.1886i	0.487141	+	0.843753i
$416$	−2.04504	−	2.96948i	−0.100266	−	0.145591i
$417$	5.04105	−	8.73136i	0.246861	−	0.427577i
$418$			33.7535i			1.65094i
$419$	−10.2059	+	17.6771i	−0.498590	+	0.863584i	−0.999999	−	0.00162717i	$-0.999482\pi$
$419$	−10.2059	+	17.6771i	−0.498590	+	0.863584i	0.501409	+	0.865211i	$0.332815\pi$
$420$	−6.35384	+	6.06371i	−0.310036	+	0.295879i
$421$			8.53522i			0.415981i	0.978131	+	0.207991i	$0.0666923\pi$
$421$			8.53522i			0.415981i	−0.978131	+	0.207991i	$0.933308\pi$
$422$	13.7606	+	7.94467i	0.669854	+	0.386741i
$423$			2.30242i			0.111948i
$424$	4.40819	+	2.54507i	0.214081	+	0.123600i
$425$	16.3179	−	28.2634i	0.791534	−	1.37098i
$426$	3.95028	−	6.84209i	0.191392	−	0.331500i
$427$	6.66013	+	6.97880i	0.322306	+	0.337728i
$428$	−6.98183			−0.337479
$429$	−17.3969	+	1.38587i	−0.839928	+	0.0669103i
$430$	−9.52363	+	16.4954i	−0.459270	+	0.795479i
$431$	25.3676	−	14.6460i	1.22192	−	0.705473i	0.256589	−	0.966520i	$-0.417401\pi$
$431$	25.3676	−	14.6460i	1.22192	−	0.705473i	0.965326	+	0.261047i	$0.0840679\pi$
$432$	1.00000			0.0481125
$433$	−7.92957	−	13.7344i	−0.381071	−	0.660034i	0.610145	−	0.792290i	$-0.291111\pi$
$433$	−7.92957	−	13.7344i	−0.381071	−	0.660034i	−0.991216	+	0.132256i	$0.957778\pi$
$434$	8.97177	+	9.40105i	0.430659	+	0.451265i
$435$	2.64075	−	1.52464i	0.126614	−	0.0731009i
$436$	−7.17312	−	4.14140i	−0.343530	−	0.198337i
$437$	37.6735	+	21.7508i	1.80217	+	1.04048i
$438$	−1.85977			−0.0888632
$439$	11.1343			0.531410			0.265705	−	0.964054i	$-0.414395\pi$
$439$	11.1343			0.531410			0.265705	+	0.964054i	$0.414395\pi$
$440$	13.9153	+	8.03403i	0.663388	+	0.383007i
$441$	6.21903	−	3.21305i	0.296144	−	0.153003i
$442$	−11.0866	−	16.0982i	−0.527338	−	0.765715i
$443$	−1.87317	−	3.24442i	−0.0889970	−	0.154147i	0.818090	−	0.575090i	$-0.195033\pi$
$443$	−1.87317	−	3.24442i	−0.0889970	−	0.154147i	−0.907087	+	0.420942i	$0.861699\pi$
$444$	−6.76960	+	3.90843i	−0.321271	+	0.185486i
$445$	10.3293	+	17.8908i	0.489654	+	0.848106i
$446$	12.3488	−	21.3888i	0.584735	−	1.01279i
$447$		−	7.78228i		−	0.368089i
$448$	0.744278	−	2.53891i	0.0351639	−	0.119952i
$449$	10.4838	−	6.05280i	0.494759	−	0.285649i	−0.231788	−	0.972766i	$-0.574457\pi$
$449$	10.4838	−	6.05280i	0.494759	−	0.285649i	0.726547	+	0.687117i	$0.241124\pi$
$450$	5.21347	−	3.01000i	0.245765	−	0.141893i
$451$	−38.6210			−1.81859
$452$	−2.78680	−	4.82688i	−0.131080	−	0.227037i
$453$			14.1556i			0.665089i
$454$	−15.9659			−0.749318
$455$	23.6132	+	21.1006i	1.10700	+	0.989212i
$456$	−6.97343			−0.326561
$457$			36.6836i			1.71599i	0.513660	+	0.857994i	$0.328289\pi$
$457$			36.6836i			1.71599i	−0.513660	+	0.857994i	$0.671711\pi$
$458$	2.91584	+	5.05038i	0.136248	+	0.235989i
$459$	5.42123			0.253041
$460$	17.9341	−	10.3543i	0.836183	−	0.482771i
$461$	−1.86597	+	1.07732i	−0.0869071	+	0.0501758i	−0.542824	−	0.839847i	$-0.682645\pi$
$461$	−1.86597	+	1.07732i	−0.0869071	+	0.0501758i	0.455917	+	0.890022i	$0.349312\pi$
$462$	−8.84139	−	9.26443i	−0.411339	−	0.431020i
$463$		−	38.0453i		−	1.76811i	−0.467379	−	0.884057i	$-0.654802\pi$
$463$		−	38.0453i		−	1.76811i	0.467379	−	0.884057i	$-0.345198\pi$
$464$	−0.459279	+	0.795495i	−0.0213215	+	0.0369299i
$465$	−8.15250	−	14.1205i	−0.378063	−	0.654825i
$466$	−10.0370	+	5.79484i	−0.464953	+	0.268441i
$467$	−2.78062	−	4.81618i	−0.128672	−	0.222866i	0.794490	−	0.607277i	$-0.207738\pi$
$467$	−2.78062	−	4.81618i	−0.128672	−	0.222866i	−0.923162	+	0.384410i	$0.874405\pi$
$468$	−0.286318	−	3.59416i	−0.0132351	−	0.166140i
$469$	5.50161	+	22.6345i	0.254041	+	1.04517i
$470$	−6.61922	−	3.82161i	−0.305322	−	0.176278i
$471$	−1.29712			−0.0597680
$472$	−8.43334			−0.388176
$473$	−24.0517	−	13.8862i	−1.10590	−	0.638490i
$474$	2.41222	+	1.39270i	0.110797	+	0.0639687i
$475$	−36.3558	+	20.9900i	−1.66812	+	0.963088i
$476$	4.03490	−	13.7640i	0.184940	−	0.630872i
$477$	2.54507	+	4.40819i	0.116531	+	0.201837i
$478$	−21.8120			−0.997657
$479$	30.7829	−	17.7725i	1.40651	−	0.812048i	0.411459	−	0.911428i	$-0.365019\pi$
$479$	30.7829	−	17.7725i	1.40651	−	0.812048i	0.995050	+	0.0993800i	$0.0316859\pi$
$480$	−1.65982	+	2.87489i	−0.0757600	+	0.131220i
$481$	15.9858	+	23.2120i	0.728890	+	1.05838i
$482$	20.3132			0.925243
$483$	−16.0378	+	3.89818i	−0.729743	+	0.177373i
$484$	−6.21427	+	10.7634i	−0.282467	+	0.489247i
$485$	−0.894176	+	1.54876i	−0.0406024	+	0.0703255i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$		−	22.1134i		−	1.00206i	−0.865431	−	0.501028i	$-0.832955\pi$
$487$		−	22.1134i		−	1.00206i	0.865431	−	0.501028i	$-0.167045\pi$
$488$	3.15766	+	1.82308i	0.142941	+	0.0825268i
$489$			21.6263i			0.977977i
$490$	−1.08528	+	23.2121i	−0.0490279	+	1.04862i
$491$	−0.690710	+	1.19635i	−0.0311713	+	0.0539903i	−0.881190	−	0.472762i	$-0.843257\pi$
$491$	−0.690710	+	1.19635i	−0.0311713	+	0.0539903i	0.850019	+	0.526752i	$0.176590\pi$
$492$		−	7.97905i		−	0.359724i
$493$	−2.48986	+	4.31256i	−0.112138	+	0.194228i
$494$	1.99662	+	25.0637i	0.0898323	+	1.12767i
$495$	8.03403	+	13.9153i	0.361103	+	0.625448i
$496$	4.25364	+	2.45584i	0.190994	+	0.110271i
$497$	−4.93698	−	20.3115i	−0.221454	−	0.911097i
$498$	−2.98943	−	5.17784i	−0.133960	−	0.232025i
$499$	−5.74809	+	3.31866i	−0.257320	+	0.148564i	−0.623111	−	0.782133i	$-0.714132\pi$
$499$	−5.74809	+	3.31866i	−0.257320	+	0.148564i	0.365792	+	0.930697i	$0.380798\pi$
$500$			3.38601i			0.151427i
$501$		−	12.9711i		−	0.579507i
$502$	16.2755	−	9.39667i	0.726411	−	0.419394i
$503$	−3.41926	−	5.92234i	−0.152457	−	0.264064i	0.779673	−	0.626187i	$-0.215385\pi$
$503$	−3.41926	−	5.92234i	−0.152457	−	0.264064i	−0.932130	+	0.362123i	$0.882052\pi$
$504$	1.91402	−	1.82662i	0.0852571	−	0.0813641i
$505$	45.9143	+	26.5087i	2.04316	+	1.17962i
$506$	15.0974	+	26.1494i	0.671160	+	1.16248i
$507$	−12.8360	+	2.05815i	−0.570069	+	0.0914057i
$508$	5.35058	−	9.26748i	0.237394	−	0.411178i
$509$		−	26.6906i		−	1.18304i	−0.806291	−	0.591519i	$-0.798528\pi$
$509$		−	26.6906i		−	1.18304i	0.806291	−	0.591519i	$-0.201472\pi$
$510$	−8.99826	+	15.5854i	−0.398450	+	0.690135i
$511$	−3.55963	+	3.39709i	−0.157469	+	0.150278i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.03917	−	3.48672i	−0.266636	−	0.153942i
$514$		−	19.0185i		−	0.838869i
$515$	7.54608	+	4.35673i	0.332520	+	0.191980i
$516$	2.86888	−	4.96904i	0.126295	−	0.218750i
$517$	5.57222	−	9.65136i	0.245066	−	0.424466i
$518$	−5.81792	+	19.8463i	−0.255625	+	0.871995i
$519$	13.4521			0.590484
$520$	10.8081	+	5.14253i	0.473965	+	0.225515i
$521$	5.45450	−	9.44747i	0.238966	−	0.413901i	−0.721452	−	0.692465i	$-0.756525\pi$
$521$	5.45450	−	9.44747i	0.238966	−	0.413901i	0.960418	+	0.278563i	$0.0898582\pi$
$522$	−0.795495	+	0.459279i	−0.0348179	+	0.0201021i
$523$	18.7920			0.821715			0.410857	−	0.911700i	$-0.365229\pi$
$523$	18.7920			0.821715			0.410857	+	0.911700i	$0.365229\pi$
$524$	−8.39711	−	14.5442i	−0.366830	−	0.635367i
$525$	4.48055	−	15.2842i	0.195547	−	0.667057i
$526$	17.5930	−	10.1573i	0.767091	−	0.442880i
$527$	23.0600	+	13.3137i	1.00451	+	0.579953i
$528$	−4.19183	−	2.42015i	−0.182426	−	0.105324i
$529$	15.9151			0.691960
$530$	−16.8974			−0.733977
$531$	−7.30349	−	4.21667i	−0.316944	−	0.182988i
$532$	−13.3473	+	12.7378i	−0.578678	+	0.552254i
$533$	−28.6780	+	2.28455i	−1.24218	+	0.0989548i
$534$	−3.11156	−	5.38939i	−0.134651	−	0.233222i
$535$	20.0720	−	11.5886i	0.867788	−	0.501018i
$536$	4.40207	+	7.62461i	0.190140	+	0.329333i
$537$	−2.36998	+	4.10493i	−0.102272	+	0.177141i
$538$			12.3202i			0.531161i
$539$	−33.8452	−	1.58243i	−1.45781	−	0.0681599i
$540$	−2.87489	+	1.65982i	−0.123716	+	0.0714272i
$541$	−2.95325	+	1.70506i	−0.126970	+	0.0733061i	−0.562140	−	0.827042i	$-0.690022\pi$
$541$	−2.95325	+	1.70506i	−0.126970	+	0.0733061i	0.435170	+	0.900348i	$0.356688\pi$
$542$	11.8163			0.507554
$543$	8.39210	+	14.5355i	0.360140	+	0.623780i
$544$		−	5.42123i		−	0.232433i
$545$	27.4959			1.17780
$546$	−7.11319	−	6.35630i	−0.304416	−	0.272025i
$547$	13.6809			0.584953			0.292476	−	0.956273i	$-0.405521\pi$
$547$	13.6809			0.584953			0.292476	+	0.956273i	$0.405521\pi$
$548$			16.1077i			0.688086i
$549$	1.82308	+	3.15766i	0.0778070	+	0.134766i
$550$	−29.1386			−1.24247
$551$	5.54733	−	3.20275i	0.236324	−	0.136442i
$552$	−5.40244	+	3.11910i	−0.229943	+	0.132758i
$553$	7.16097	−	1.74056i	0.304515	−	0.0740163i
$554$		−	32.3313i		−	1.37362i
$555$	12.9746	−	22.4726i	0.550740	−	0.953909i
$556$	−5.04105	−	8.73136i	−0.213788	−	0.370292i
$557$	−19.5186	+	11.2691i	−0.827031	+	0.477487i	−0.852835	−	0.522180i	$-0.825119\pi$
$557$	−19.5186	+	11.2691i	−0.827031	+	0.477487i	0.0258039	+	0.999667i	$0.491785\pi$
$558$	2.45584	+	4.25364i	0.103964	+	0.180071i
$559$	−18.6810	−	8.88849i	−0.790121	−	0.375943i
$560$	2.07441	+	8.53445i	0.0876597	+	0.360646i
$561$	−22.7249	−	13.1202i	−0.959444	−	0.553935i
$562$	0.624762			0.0263540
$563$	23.2517			0.979942			0.489971	−	0.871739i	$-0.337007\pi$
$563$	23.2517			0.979942			0.489971	+	0.871739i	$0.337007\pi$
$564$	1.99396	+	1.15121i	0.0839608	+	0.0484748i
$565$	16.0235	+	9.25117i	0.674114	+	0.389200i
$566$	10.8892	−	6.28688i	0.457707	−	0.264257i
$567$	2.57090	−	0.624890i	0.107968	−	0.0262429i
$568$	−3.95028	−	6.84209i	−0.165750	−	0.287088i
$569$	−35.5594			−1.49073			−0.745364	−	0.666658i	$-0.767724\pi$
$569$	−35.5594			−1.49073			−0.745364	+	0.666658i	$0.767724\pi$
$570$	20.0479	−	11.5746i	0.839712	−	0.484808i
$571$	−0.735579	+	1.27406i	−0.0307830	+	0.0533178i	−0.881006	−	0.473104i	$-0.843133\pi$
$571$	−0.735579	+	1.27406i	−0.0307830	+	0.0533178i	0.850223	+	0.526422i	$0.176467\pi$
$572$	−7.49823	+	15.7590i	−0.313517	+	0.658919i
$573$	13.9870			0.584315
$574$	−14.5747	−	15.2720i	−0.608336	−	0.637443i
$575$	−18.7769	+	32.5226i	−0.783053	+	1.35629i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−14.0755	−	8.12650i	−0.585971	−	0.338311i	0.177532	−	0.984115i	$-0.443189\pi$
$577$	−14.0755	−	8.12650i	−0.585971	−	0.338311i	−0.763503	+	0.645804i	$0.776522\pi$
$578$		−	12.3897i		−	0.515345i
$579$	10.0487	+	5.80159i	0.417608	+	0.241106i
$580$		−	3.04928i		−	0.126614i
$581$	−15.1798	−	4.44994i	−0.629763	−	0.184614i
$582$	0.269360	−	0.466544i	0.0111653	−	0.0193389i
$583$		−	24.6378i		−	1.02039i
$584$	−0.929885	+	1.61061i	−0.0384789	+	0.0666474i
$585$	6.78880	+	9.85759i	0.280682	+	0.407561i
$586$	−10.1391	−	17.5615i	−0.418843	−	0.725457i
$587$	16.9203	+	9.76894i	0.698376	+	0.403207i	0.806742	−	0.590904i	$-0.201229\pi$
$587$	16.9203	+	9.76894i	0.698376	+	0.403207i	−0.108366	+	0.994111i	$0.534562\pi$
$588$	0.326927	−	6.99236i	0.0134822	−	0.288360i
$589$	−17.1256	−	29.6625i	−0.705650	−	1.22222i
$590$	24.2449	−	13.9978i	0.998148	−	0.576281i
$591$			19.3682i			0.796700i
$592$			7.81686i			0.321271i
$593$	−5.59347	+	3.22939i	−0.229696	+	0.132615i	−0.610432	−	0.792069i	$-0.709004\pi$
$593$	−5.59347	+	3.22939i	−0.229696	+	0.132615i	0.380736	+	0.924684i	$0.375671\pi$
$594$	−2.42015	−	4.19183i	−0.0993000	−	0.171993i
$595$	11.2458	+	46.2672i	0.461034	+	1.89677i
$596$	−6.73965	−	3.89114i	−0.276067	−	0.159387i
$597$	7.97985	+	13.8215i	0.326594	+	0.565677i
$598$	12.7574	+	18.5242i	0.521688	+	0.757511i
$599$	−1.33645	+	2.31480i	−0.0546058	+	0.0945800i	−0.892036	−	0.451964i	$-0.850724\pi$
$599$	−1.33645	+	2.31480i	−0.0546058	+	0.0945800i	0.837430	+	0.546544i	$0.184057\pi$
$600$		−	6.01999i		−	0.245765i
$601$	−11.2155	+	19.4258i	−0.457489	+	0.792394i	−0.998828	−	0.0484108i	$-0.984584\pi$
$601$	−11.2155	+	19.4258i	−0.457489	+	0.792394i	0.541339	+	0.840805i	$0.317918\pi$
$602$	−3.58546	−	14.7512i	−0.146133	−	0.601213i
$603$			8.80414i			0.358532i
$604$	12.2591	+	7.07781i	0.498817	+	0.287992i
$605$		−	41.2582i		−	1.67739i
$606$	−13.8311	−	7.98541i	−0.561851	−	0.324385i
$607$	4.46601	−	7.73536i	0.181270	−	0.313969i	−0.761043	−	0.648701i	$-0.775313\pi$
$607$	4.46601	−	7.73536i	0.181270	−	0.313969i	0.942313	+	0.334732i	$0.108646\pi$
$608$	−3.48672	+	6.03917i	−0.141405	+	0.244921i
$609$	−0.683663	+	2.33213i	−0.0277034	+	0.0945029i
$610$	−12.1039			−0.490073
$611$	3.56674	−	7.49623i	0.144295	−	0.303265i
$612$	2.71061	−	4.69492i	0.109570	−	0.189781i
$613$	7.11962	−	4.11052i	0.287559	−	0.166022i	−0.349282	−	0.937018i	$-0.613574\pi$
$613$	7.11962	−	4.11052i	0.287559	−	0.166022i	0.636840	+	0.770996i	$0.280241\pi$
$614$	−23.8860			−0.963962
$615$	13.2438	+	22.9389i	0.534041	+	0.924986i
$616$	−12.4439	+	3.02466i	−0.501380	+	0.121867i
$617$	−12.8168	+	7.39980i	−0.515986	+	0.297905i	−0.735291	−	0.677752i	$-0.762955\pi$
$617$	−12.8168	+	7.39980i	−0.515986	+	0.297905i	0.219305	+	0.975656i	$0.429621\pi$
$618$	−2.27316	−	1.31241i	−0.0914400	−	0.0527929i
$619$	−25.6395	−	14.8030i	−1.03054	−	0.594981i	−0.113399	−	0.993550i	$-0.536174\pi$
$619$	−25.6395	−	14.8030i	−1.03054	−	0.594981i	−0.917139	+	0.398568i	$0.869507\pi$
$620$	−16.3050			−0.654825
$621$	−6.23820			−0.250330
$622$	24.5227	+	14.1582i	0.983270	+	0.567691i
$623$	−15.7999	−	4.63174i	−0.633012	−	0.185567i
$624$	−3.25580	−	1.54912i	−0.130336	−	0.0620146i
$625$	9.42983	+	16.3329i	0.377193	+	0.653318i
$626$	−27.2855	+	15.7533i	−1.09055	+	0.629627i
$627$	16.8768	+	29.2314i	0.673993	+	1.16739i
$628$	−0.648559	+	1.12334i	−0.0258803	+	0.0448260i
$629$			42.3770i			1.68968i
$630$	−2.47073	+	8.42825i	−0.0984364	+	0.335790i
$631$	−5.80637	+	3.35231i	−0.231148	+	0.133453i	−0.611101	−	0.791552i	$-0.709273\pi$
$631$	−5.80637	+	3.35231i	−0.231148	+	0.133453i	0.379954	+	0.925006i	$0.375940\pi$
$632$	2.41222	−	1.39270i	0.0959531	−	0.0553985i
$633$	15.8893			0.631545
$634$	1.19116	+	2.06314i	0.0473068	+	0.0819378i
$635$			35.5240i			1.40973i
$636$	5.09014			0.201837
$637$	−25.2253	+	0.827011i	−0.999463	+	0.0327674i
$638$	4.44610			0.176023
$639$		−	7.90056i		−	0.312541i
$640$	1.65982	+	2.87489i	0.0656101	+	0.113640i
$641$	−47.1384			−1.86185			−0.930927	−	0.365206i	$-0.880998\pi$
$641$	−47.1384			−1.86185			−0.930927	+	0.365206i	$0.880998\pi$
$642$	−6.04644	+	3.49091i	−0.238634	+	0.137775i
$643$	22.7365	−	13.1269i	0.896641	−	0.517676i	0.0205324	−	0.999789i	$-0.493464\pi$
$643$	22.7365	−	13.1269i	0.896641	−	0.517676i	0.876109	+	0.482113i	$0.160131\pi$
$644$	−4.64295	+	15.8382i	−0.182958	+	0.624113i
$645$			19.0473i			0.749985i
$646$	−18.9023	+	32.7397i	−0.743701	+	1.28813i
$647$	19.0713	+	33.0325i	0.749772	+	1.29864i	0.947932	+	0.318473i	$0.103170\pi$
$647$	19.0713	+	33.0325i	0.749772	+	1.29864i	−0.198160	+	0.980170i	$0.563497\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	20.4100	+	35.3511i	0.801161	+	1.38765i
$650$	−21.6368	+	1.72363i	−0.848667	+	0.0676065i
$651$	12.4703	+	3.65566i	0.488750	+	0.143277i
$652$	18.7290	+	10.8132i	0.733482	+	0.423476i
$653$	14.4215			0.564358			0.282179	−	0.959362i	$-0.408943\pi$
$653$	14.4215			0.564358			0.282179	+	0.959362i	$0.408943\pi$
$654$	−8.28280			−0.323883
$655$	48.2815	+	27.8754i	1.88652	+	1.08918i
$656$	−6.91006	−	3.98953i	−0.269793	−	0.155765i
$657$	−1.61061	+	0.929885i	−0.0628358	+	0.0362783i
$658$	5.91930	−	1.43876i	0.230758	−	0.0560887i
$659$	2.67525	+	4.63366i	0.104213	+	0.180502i	0.913416	−	0.407027i	$-0.133434\pi$
$659$	2.67525	+	4.63366i	0.104213	+	0.180502i	−0.809204	+	0.587528i	$0.800101\pi$
$660$	16.0681			0.625448
$661$	39.4262	−	22.7627i	1.53350	−	0.885366i	0.534303	−	0.845293i	$-0.320574\pi$
$661$	39.4262	−	22.7627i	1.53350	−	0.885366i	0.999197	−	0.0400733i	$-0.0127592\pi$
$662$	−15.1691	+	26.2737i	−0.589564	+	1.02115i
$663$	−17.6504	−	8.39815i	−0.685486	−	0.326157i
$664$	−5.97886			−0.232025
$665$	17.2295	−	58.7738i	0.668132	−	2.27915i
$666$	−3.90843	+	6.76960i	−0.151449	+	0.262317i
$667$	2.86507	−	4.96245i	0.110936	−	0.192147i
$668$	−11.2333	−	6.48557i	−0.434631	−	0.250934i
$669$		−	24.6977i		−	0.954868i
$670$	−25.3109	−	14.6133i	−0.977847	−	0.564560i
$671$		−	17.6485i		−	0.681312i
$672$	−0.624890	−	2.57090i	−0.0241056	−	0.0991745i
$673$	−21.3333	+	36.9503i	−0.822337	+	1.42433i	0.0815998	+	0.996665i	$0.473997\pi$
$673$	−21.3333	+	36.9503i	−0.822337	+	1.42433i	−0.903937	+	0.427665i	$0.859336\pi$
$674$		−	16.6355i		−	0.640776i
$675$	3.01000	−	5.21347i	0.115855	−	0.200666i
$676$	−4.63561	+	12.1454i	−0.178293	+	0.467131i
$677$	16.4015	+	28.4082i	0.630361	+	1.09182i	0.987478	+	0.157758i	$0.0504264\pi$
$677$	16.4015	+	28.4082i	0.630361	+	1.09182i	−0.357117	+	0.934060i	$0.616240\pi$
$678$	−4.82688	−	2.78680i	−0.185375	−	0.107026i
$679$	−0.336640	−	1.38499i	−0.0129191	−	0.0531511i
$680$	8.99826	+	15.5854i	0.345067	+	0.597674i
$681$	−13.8269	+	7.98297i	−0.529848	+	0.305908i
$682$		−	23.7740i		−	0.910355i
$683$		−	16.1649i		−	0.618531i	−0.950976	−	0.309266i	$-0.899917\pi$
$683$		−	16.1649i		−	0.618531i	0.950976	−	0.309266i	$-0.100083\pi$
$684$	−6.03917	+	3.48672i	−0.230913	+	0.133318i
$685$	−26.7358	−	46.3078i	−1.02152	−	1.76933i
$686$	−12.1466	−	13.9807i	−0.463761	−	0.533785i
$687$	5.05038	+	2.91584i	0.192684	+	0.111246i
$688$	−2.86888	−	4.96904i	−0.109375	−	0.189443i
$689$	−1.45740	−	18.2948i	−0.0555225	−	0.696977i
$690$	10.3543	−	17.9341i	0.394180	−	0.682741i
$691$		−	22.2081i		−	0.844834i	−0.906402	−	0.422417i	$-0.861182\pi$
$691$		−	22.2081i		−	0.844834i	0.906402	−	0.422417i	$-0.138818\pi$
$692$	6.72607	−	11.6499i	0.255687	−	0.442863i
$693$	−12.2891	−	3.60253i	−0.466824	−	0.136849i
$694$			6.00937i			0.228113i
$695$	28.9849	+	16.7345i	1.09946	+	0.634775i
$696$			0.918558i			0.0348179i
$697$	−37.4610	−	21.6281i	−1.41894	−	0.819224i
$698$	−5.00374	+	8.66674i	−0.189394	+	0.328041i
$699$	−5.79484	+	10.0370i	−0.219181	+	0.379632i
$700$	−10.9962	−	11.5224i	−0.415618	−	0.435505i
$701$	−0.442053			−0.0166961			−0.00834805	−	0.999965i	$-0.502657\pi$
$701$	−0.442053			−0.0166961			−0.00834805	+	0.999965i	$0.502657\pi$
$702$	−2.04504	−	2.96948i	−0.0771851	−	0.112076i
$703$	27.2552	−	47.2073i	1.02795	−	1.78046i
$704$	−4.19183	+	2.42015i	−0.157985	+	0.0912129i
$705$	−7.64322			−0.287860
$706$	10.9401	+	18.9488i	0.411736	+	0.713149i
$707$	−41.0593	+	9.97999i	−1.54419	+	0.375336i
$708$	−7.30349	+	4.21667i	−0.274482	+	0.158472i
$709$	−20.6065	−	11.8972i	−0.773895	−	0.446809i	0.0603673	−	0.998176i	$-0.480773\pi$
$709$	−20.6065	−	11.8972i	−0.773895	−	0.446809i	−0.834262	+	0.551368i	$0.814106\pi$
$710$	22.7133	+	13.1135i	0.852413	+	0.492141i
$711$	2.78540			0.104460
$712$	−6.22313			−0.233222
$713$	−26.5350	−	15.3200i	−0.993745	−	0.573739i
$714$	−3.38767	−	13.9374i	−0.126780	−	0.521595i
$715$	−4.60058	−	57.7512i	−0.172052	−	2.15977i
$716$	2.36998	+	4.10493i	0.0885705	+	0.153409i
$717$	−18.8897	+	10.9060i	−0.705450	+	0.407292i
$718$	−2.29441	−	3.97403i	−0.0856265	−	0.148309i
$719$	14.6548	−	25.3829i	0.546532	−	0.946621i	−0.451977	−	0.892030i	$-0.649281\pi$
$719$	14.6548	−	25.3829i	0.546532	−	0.946621i	0.998509	−	0.0545911i	$-0.0173855\pi$
$720$			3.31964i			0.123716i
$721$	−6.74815	+	1.64022i	−0.251314	+	0.0610851i
$722$	25.6593	−	14.8144i	0.954939	−	0.551334i
$723$	17.5918	−	10.1566i	0.654246	−	0.377729i
$724$	16.7842			0.623780
$725$	2.76486	+	4.78887i	0.102684	+	0.177854i
$726$			12.4285i			0.461266i
$727$	41.1850			1.52747			0.763734	−	0.645531i	$-0.223364\pi$
$727$	41.1850			1.52747			0.763734	+	0.645531i	$0.223364\pi$
$728$	−9.06131	+	2.98205i	−0.335835	+	0.110522i
$729$	1.00000			0.0370370
$730$		−	6.17376i		−	0.228501i
$731$	−15.5528	−	26.9383i	−0.575243	−	0.996349i
$732$	3.64615			0.134766
$733$	0.0649817	−	0.0375172i	0.00240015	−	0.00138573i	−0.498799	−	0.866717i	$-0.666226\pi$
$733$	0.0649817	−	0.0375172i	0.00240015	−	0.00138573i	0.501200	+	0.865332i	$0.332892\pi$
$734$	−32.3945	+	18.7030i	−1.19570	+	0.690340i
$735$	10.6662	+	20.6449i	0.393428	+	0.761499i
$736$			6.23820i			0.229943i
$737$	21.3074	−	36.9054i	0.784866	−	1.35943i
$738$	−3.98953	−	6.91006i	−0.146857	−	0.254363i
$739$	−19.3552	+	11.1748i	−0.711994	+	0.411070i	−0.811799	−	0.583937i	$-0.801511\pi$
$739$	−19.3552	+	11.1748i	−0.711994	+	0.411070i	0.0998049	+	0.995007i	$0.468178\pi$
$740$	−12.9746	−	22.4726i	−0.476955	−	0.826110i
$741$	14.2610	+	20.7075i	0.523889	+	0.760708i
$742$	9.74262	−	9.29775i	0.357663	−	0.341331i
$743$	28.6927	+	16.5658i	1.05263	+	0.607738i	0.923386	−	0.383874i	$-0.125410\pi$
$743$	28.6927	+	16.5658i	1.05263	+	0.607738i	0.129248	+	0.991612i	$0.458744\pi$
$744$	4.91168			0.180071
$745$	25.8343			0.946497
$746$	13.6931	+	7.90570i	0.501339	+	0.289448i
$747$	−5.17784	−	2.98943i	−0.189447	−	0.109377i
$748$	−22.7249	+	13.1202i	−0.830903	+	0.479722i
$749$	−5.19643	+	17.7262i	−0.189873	+	0.647702i
$750$	1.69300	+	2.93237i	0.0618197	+	0.107075i
$751$	9.68697			0.353483			0.176741	−	0.984257i	$-0.443444\pi$
$751$	9.68697			0.353483			0.176741	+	0.984257i	$0.443444\pi$
$752$	1.99396	−	1.15121i	0.0727122	−	0.0419804i
$753$	9.39667	−	16.2755i	0.342434	−	0.593112i
$754$	3.30145	−	0.263000i	0.120232	−	0.00957790i
$755$	−46.9916			−1.71020
$756$	0.744278	−	2.53891i	0.0270691	−	0.0923392i
$757$	19.4924	−	33.7618i	0.708462	−	1.22709i	−0.256966	−	0.966421i	$-0.582723\pi$
$757$	19.4924	−	33.7618i	0.708462	−	1.22709i	0.965428	−	0.260672i	$-0.0839440\pi$
$758$	−2.56356	+	4.44021i	−0.0931126	+	0.161276i
$759$	26.1494	+	15.0974i	0.949164	+	0.548000i
$760$		−	23.1493i		−	0.839712i
$761$	−37.7899	−	21.8180i	−1.36988	−	0.790902i	−0.378970	−	0.925409i	$-0.623722\pi$
$761$	−37.7899	−	21.8180i	−1.36988	−	0.790902i	−0.990913	+	0.134507i	$0.957055\pi$
$762$		−	10.7012i		−	0.387662i
$763$	−15.8534	+	15.1295i	−0.573933	+	0.547726i
$764$	6.99350	−	12.1131i	0.253016	−	0.438237i
$765$			17.9965i			0.650665i
$766$	10.1141	−	17.5182i	0.365438	−	0.632957i
$767$	17.2465	+	25.0426i	0.622736	+	0.904237i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−0.826746	−	0.477322i	−0.0298132	−	0.0172127i	0.485019	−	0.874503i	$-0.338813\pi$
$769$	−0.826746	−	0.477322i	−0.0298132	−	0.0172127i	−0.514833	+	0.857291i	$0.672146\pi$
$770$	30.7545	−	29.3502i	1.10832	−	1.05771i
$771$	−9.50923	−	16.4705i	−0.342467	−	0.593170i
$772$	10.0487	−	5.80159i	0.361659	−	0.208804i
$773$		−	22.1822i		−	0.797838i	−0.916986	−	0.398919i	$-0.869385\pi$
$773$		−	22.1822i		−	0.797838i	0.916986	−	0.398919i	$-0.130615\pi$
$774$		−	5.73775i		−	0.206239i
$775$	25.6069	−	14.7841i	0.919827	−	0.531062i
$776$	−0.269360	−	0.466544i	−0.00966945	−	0.0167480i
$777$	4.88467	+	20.0963i	0.175237	+	0.720952i
$778$	5.35019	+	3.08894i	0.191814	+	0.110744i
$779$	27.8207	+	48.1869i	0.996780	+	1.72647i
$780$	11.9313	−	0.950473i	0.427210	−	0.0340324i
$781$	−19.1206	+	33.1178i	−0.684188	+	1.18505i
$782$			33.8187i			1.20935i
$783$	−0.459279	+	0.795495i	−0.0164133	+	0.0284287i
$784$	−5.89210	−	3.77931i	−0.210432	−	0.134975i
$785$		−	4.30596i		−	0.153686i
$786$	−14.5442	−	8.39711i	−0.518775	−	0.299515i
$787$		−	9.38696i		−	0.334609i	−0.985905	−	0.167304i	$-0.946494\pi$
$787$		−	9.38696i		−	0.334609i	0.985905	−	0.167304i	$-0.0535063\pi$
$788$	16.7733	+	9.68409i	0.597525	+	0.344981i
$789$	10.1573	−	17.5930i	0.361610	−	0.626327i
$790$	−4.62325	+	8.00771i	−0.164488	+	0.284901i
$791$	−14.3292	+	3.48289i	−0.509486	+	0.123837i
$792$	−4.84030			−0.171993
$793$	−1.04396	−	13.1049i	−0.0370721	−	0.465368i
$794$	−16.8840	+	29.2439i	−0.599191	+	1.03783i
$795$	−14.6336	+	8.44871i	−0.519000	+	0.299645i
$796$	15.9597			0.565677
$797$	4.13426	+	7.16075i	0.146443	+	0.253647i	0.929910	−	0.367786i	$-0.119884\pi$
$797$	4.13426	+	7.16075i	0.146443	+	0.253647i	−0.783467	+	0.621433i	$0.786551\pi$
$798$	−5.19018	+	17.7049i	−0.183730	+	0.626747i
$799$	10.8097	−	6.24099i	0.382420	−	0.220790i
$800$	−5.21347	−	3.01000i	−0.184324	−	0.106419i
$801$	−5.38939	−	3.11156i	−0.190425	−	0.109942i
$802$	23.9683			0.846350
$803$	9.00185			0.317668
$804$	7.62461	+	4.40207i	0.268899	+	0.155249i
$805$	−12.9406	−	53.2396i	−0.456095	−	1.87645i
$806$	−1.40630	−	17.6534i	−0.0495350	−	0.621814i
$807$	6.16010	+	10.6696i	0.216846	+	0.375588i
$808$	−13.8311	+	7.98541i	−0.486577	+	0.280926i
$809$	−26.2317	−	45.4346i	−0.922256	−	1.59739i	−0.795915	−	0.605408i	$-0.793010\pi$
$809$	−26.2317	−	45.4346i	−0.922256	−	1.59739i	−0.126341	−	0.991987i	$-0.540323\pi$
$810$	−1.65982	+	2.87489i	−0.0583201	+	0.101013i
$811$		−	11.2172i		−	0.393890i	−0.980415	−	0.196945i	$-0.936898\pi$
$811$		−	11.2172i		−	0.393890i	0.980415	−	0.196945i	$-0.0631020\pi$
$812$	1.67786	+	1.75814i	0.0588812	+	0.0616985i
$813$	10.2332	−	5.90816i	0.358895	−	0.207208i
$814$	32.7669	−	18.9180i	1.14848	−	0.663075i
$815$	−71.7916			−2.51475
$816$	−2.71061	−	4.69492i	−0.0948905	−	0.164355i
$817$			40.0118i			1.39984i
$818$	1.38201			0.0483209
$819$	−9.33835	−	1.94812i	−0.326308	−	0.0680730i
$820$	26.4876			0.924986
$821$		−	43.8725i		−	1.53116i	−0.643340	−	0.765580i	$-0.722452\pi$
$821$		−	43.8725i		−	1.53116i	0.643340	−	0.765580i	$-0.277548\pi$
$822$	8.05384	+	13.9497i	0.280910	+	0.486550i
$823$	−28.8460			−1.00551			−0.502755	−	0.864429i	$-0.667680\pi$
$823$	−28.8460			−1.00551			−0.502755	+	0.864429i	$0.667680\pi$
$824$	−2.27316	+	1.31241i	−0.0791894	+	0.0457200i
$825$	−25.2348	+	14.5693i	−0.878562	+	0.507238i
$826$	−6.27675	+	21.4115i	−0.218396	+	0.745000i
$827$		−	14.3678i		−	0.499618i	−0.968295	−	0.249809i	$-0.919632\pi$
$827$		−	14.3678i		−	0.499618i	0.968295	−	0.249809i	$-0.0803678\pi$
$828$	−3.11910	+	5.40244i	−0.108396	+	0.187748i
$829$	−1.63987	−	2.84034i	−0.0569550	−	0.0986490i	0.836142	−	0.548513i	$-0.184806\pi$
$829$	−1.63987	−	2.84034i	−0.0569550	−	0.0986490i	−0.893097	+	0.449864i	$0.851472\pi$
$830$	17.1886	−	9.92382i	0.596624	−	0.344461i
$831$	−16.1656	−	27.9997i	−0.560780	−	0.971299i
$832$	−2.96948	+	2.04504i	−0.102948	+	0.0708991i
$833$	−31.9424	−	20.4885i	−1.10674	−	0.709884i
$834$	−8.73136	−	5.04105i	−0.302342	−	0.174557i
$835$	43.0595			1.49013
$836$	33.7535			1.16739
$837$	4.25364	+	2.45584i	0.147027	+	0.0848863i
$838$	17.6771	+	10.2059i	0.610646	+	0.352556i
$839$	24.9564	−	14.4086i	0.861590	−	0.497439i	−0.00295444	−	0.999996i	$-0.500940\pi$
$839$	24.9564	−	14.4086i	0.861590	−	0.497439i	0.864544	+	0.502556i	$0.167607\pi$
$840$	6.06371	+	6.35384i	0.209218	+	0.219228i
$841$	14.0781	+	24.3840i	0.485453	+	0.840829i
$842$	8.53522			0.294143
$843$	0.541060	−	0.312381i	0.0186351	−	0.0107590i
$844$	7.94467	−	13.7606i	0.273467	−	0.473659i
$845$	−6.83231	−	42.6110i	−0.235039	−	1.46586i
$846$	2.30242			0.0791590
$847$	22.7022	+	23.7884i	0.780057	+	0.817381i
$848$	2.54507	−	4.40819i	0.0873981	−	0.151378i
$849$	6.28688	−	10.8892i	0.215765	−	0.373716i
$850$	−28.2634	−	16.3179i	−0.969427	−	0.559699i
$851$		−	48.7631i		−	1.67158i
$852$	−6.84209	−	3.95028i	−0.234406	−	0.135334i
$853$		−	12.2038i		−	0.417851i	−0.977932	−	0.208926i	$-0.933003\pi$
$853$		−	12.2038i		−	0.417851i	0.977932	−	0.208926i	$-0.0669966\pi$
$854$	6.97880	−	6.66013i	0.238810	−	0.227905i
$855$	11.5746	−	20.0479i	0.395844	−	0.685622i
$856$			6.98183i			0.238634i
$857$	7.44836	−	12.9009i	0.254431	−	0.440688i	−0.710310	−	0.703889i	$-0.751445\pi$
$857$	7.44836	−	12.9009i	0.254431	−	0.440688i	0.964741	+	0.263202i	$0.0847784\pi$
$858$	1.38587	+	17.3969i	0.0473127	+	0.593919i
$859$	−24.2792	−	42.0527i	−0.828394	−	1.43482i	−0.899298	−	0.437337i	$-0.855922\pi$
$859$	−24.2792	−	42.0527i	−0.828394	−	1.43482i	0.0709036	−	0.997483i	$-0.477412\pi$
$860$	16.4954	+	9.52363i	0.562489	+	0.324753i
$861$	−20.2581	−	5.93864i	−0.690393	−	0.202388i
$862$	−14.6460	−	25.3676i	−0.498845	−	0.864025i
$863$	−8.26166	+	4.76987i	−0.281230	+	0.162368i	−0.633980	−	0.773349i	$-0.718580\pi$
$863$	−8.26166	+	4.76987i	−0.281230	+	0.162368i	0.352750	+	0.935718i	$0.385247\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			44.6562i			1.51836i
$866$	−13.7344	+	7.92957i	−0.466714	+	0.269458i
$867$	−6.19487	−	10.7298i	−0.210389	−	0.364404i
$868$	9.40105	−	8.97177i	0.319092	−	0.304522i
$869$	−11.6759	−	6.74108i	−0.396078	−	0.228675i
$870$	−1.52464	−	2.64075i	−0.0516902	−	0.0895300i
$871$	13.6387	−	28.6645i	0.462130	−	0.971259i
$872$	−4.14140	+	7.17312i	−0.140246	+	0.242912i
$873$		−	0.538719i		−	0.0182329i
$874$	21.7508	−	37.6735i	0.735733	−	1.27433i
$875$	8.59675	+	2.52013i	0.290623	+	0.0851960i
$876$			1.85977i			0.0628358i
$877$	36.9438	+	21.3295i	1.24750	+	0.720246i	0.970611	−	0.240656i	$-0.0773625\pi$
$877$	36.9438	+	21.3295i	1.24750	+	0.720246i	0.276891	+	0.960901i	$0.410696\pi$
$878$		−	11.1343i		−	0.375764i
$879$	−17.5615	−	10.1391i	−0.592334	−	0.341984i
$880$	8.03403	−	13.9153i	0.270827	−	0.469086i
$881$	−8.12329	+	14.0700i	−0.273681	+	0.474029i	−0.969801	−	0.243896i	$-0.921574\pi$
$881$	−8.12329	+	14.0700i	−0.273681	+	0.474029i	0.696121	+	0.717925i	$0.254908\pi$
$882$	−3.21305	−	6.21903i	−0.108189	−	0.209406i
$883$	−4.99907			−0.168232			−0.0841160	−	0.996456i	$-0.526807\pi$
$883$	−4.99907			−0.168232			−0.0841160	+	0.996456i	$0.526807\pi$
$884$	−16.0982	+	11.0866i	−0.541442	+	0.372884i
$885$	13.9978	−	24.2449i	0.470531	−	0.814984i
$886$	−3.24442	+	1.87317i	−0.108999	+	0.0629304i
$887$	−54.1502			−1.81819			−0.909093	−	0.416593i	$-0.863224\pi$
$887$	−54.1502			−1.81819			−0.909093	+	0.416593i	$0.863224\pi$
$888$	3.90843	+	6.76960i	0.131158	+	0.227173i
$889$	−19.5469	−	20.4822i	−0.655584	−	0.686951i
$890$	17.8908	−	10.3293i	0.599701	−	0.346238i
$891$	−4.19183	−	2.42015i	−0.140431	−	0.0810781i
$892$	−21.3888	−	12.3488i	−0.716151	−	0.413470i
$893$	−16.0558			−0.537287
$894$	−7.78228			−0.260278
$895$	−13.6269	−	7.86749i	−0.455497	−	0.262981i
$896$	−2.53891	−	0.744278i	−0.0848189	−	0.0248646i
$897$	20.3103	+	9.66374i	0.678141	+	0.322663i
$898$	−6.05280	−	10.4838i	−0.201984	−	0.349847i
$899$	−3.90722	+	2.25583i	−0.130313	+	0.0752362i
$900$	−3.01000	−	5.21347i	−0.100333	−	0.173782i
$901$	13.7974	−	23.8978i	0.459658	−	0.796152i
$902$			38.6210i			1.28594i
$903$	−10.4807	−	10.9822i	−0.348776	−	0.365463i
$904$	−4.82688	+	2.78680i	−0.160540	+	0.0926877i
$905$	−48.2528	+	27.8587i	−1.60398	+	0.926056i
$906$	14.1556			0.470289
$907$	4.67111	+	8.09059i	0.155102	+	0.268644i	0.933096	−	0.359627i	$-0.117096\pi$
$907$	4.67111	+	8.09059i	0.155102	+	0.268644i	−0.777994	+	0.628271i	$0.783763\pi$
$908$			15.9659i			0.529848i
$909$	−15.9708			−0.529718
$910$	21.1006	−	23.6132i	0.699479	−	0.782770i
$911$	28.5910			0.947262			0.473631	−	0.880723i	$-0.342943\pi$
$911$	28.5910			0.947262			0.473631	+	0.880723i	$0.342943\pi$
$912$			6.97343i			0.230913i
$913$	14.4697	+	25.0623i	0.478879	+	0.829442i
$914$	36.6836			1.21339
$915$	−10.4823	+	6.05195i	−0.346534	+	0.200071i
$916$	5.05038	−	2.91584i	0.166869	−	0.0963420i
$917$	−43.1762	+	10.4945i	−1.42580	+	0.346560i
$918$		−	5.42123i		−	0.178927i
$919$	12.5064	−	21.6617i	0.412548	−	0.714554i	−0.582620	−	0.812745i	$-0.697972\pi$
$919$	12.5064	−	21.6617i	0.412548	−	0.714554i	0.995168	+	0.0981909i	$0.0313056\pi$
$920$	−10.3543	−	17.9341i	−0.341370	−	0.591271i
$921$	−20.6859	+	11.9430i	−0.681624	+	0.393536i
$922$	1.07732	+	1.86597i	0.0354797	+	0.0614526i
$923$	−12.2389	+	25.7226i	−0.402850	+	0.846671i
$924$	−9.26443	+	8.84139i	−0.304777	+	0.290860i
$925$	40.7529	+	23.5287i	1.33995	+	0.773619i
$926$	−38.0453			−1.25025
$927$	−2.62482			−0.0862105
$928$	0.795495	+	0.459279i	0.0261134	+	0.0150766i
$929$	9.62656	+	5.55790i	0.315837	+	0.182349i	0.649536	−	0.760331i	$-0.274963\pi$
$929$	9.62656	+	5.55790i	0.315837	+	0.182349i	−0.333698	+	0.942680i	$0.608297\pi$
$930$	−14.1205	+	8.15250i	−0.463031	+	0.267331i
$931$	22.4060	+	43.3680i	0.734328	+	1.42133i
$932$	5.79484	+	10.0370i	0.189816	+	0.328771i
$933$	28.3164			0.927036
$934$	−4.81618	+	2.78062i	−0.157590	+	0.0909848i
$935$	43.5543	−	75.4383i	1.42438	−	2.46710i
$936$	−3.59416	+	0.286318i	−0.117479	+	0.00935861i
$937$	33.2870			1.08744			0.543719	−	0.839267i	$-0.317016\pi$
$937$	33.2870			1.08744			0.543719	+	0.839267i	$0.317016\pi$
$938$	22.6345	−	5.50161i	0.739044	−	0.179634i
$939$	−15.7533	+	27.2855i	−0.514088	+	0.890427i
$940$	−3.82161	+	6.61922i	−0.124647	+	0.215895i
$941$	39.3672	+	22.7287i	1.28333	+	0.740934i	0.977457	−	0.211137i	$-0.0677166\pi$
$941$	39.3672	+	22.7287i	1.28333	+	0.740934i	0.305878	+	0.952071i	$0.401050\pi$
$942$			1.29712i			0.0422624i
$943$	43.1063	+	24.8874i	1.40374	+	0.810447i
$944$			8.43334i			0.274482i
$945$	2.07441	+	8.53445i	0.0674805	+	0.277626i
$946$	−13.8862	+	24.0517i	−0.451480	+	0.781987i
$947$		−	32.4398i		−	1.05415i	−0.849818	−	0.527077i	$-0.823288\pi$
$947$		−	32.4398i		−	1.05415i	0.849818	−	0.527077i	$-0.176712\pi$
$948$	1.39270	−	2.41222i	0.0452327	−	0.0783454i
$949$	6.68432	−	0.532486i	0.216982	−	0.0172852i
$950$	20.9900	+	36.3558i	0.681006	+	1.17954i
$951$	2.06314	+	1.19116i	0.0669020	+	0.0386259i
$952$	−13.7640	−	4.03490i	−0.446094	−	0.130772i
$953$	11.1179	+	19.2568i	0.360144	+	0.623788i	0.987984	−	0.154554i	$-0.0493941\pi$
$953$	11.1179	+	19.2568i	0.360144	+	0.623788i	−0.627840	+	0.778342i	$0.716061\pi$
$954$	4.40819	−	2.54507i	0.142720	−	0.0823997i
$955$			46.4318i			1.50250i
$956$			21.8120i			0.705450i
$957$	3.85044	−	2.22305i	0.124467	−	0.0718610i
$958$	−17.7725	−	30.7829i	−0.574205	−	0.994552i
$959$	40.8959	+	11.9886i	1.32060	+	0.387132i
$960$	2.87489	+	1.65982i	0.0927867	+	0.0535704i
$961$	−3.43769	−	5.95426i	−0.110893	−	0.192073i
$962$	23.2120	−	15.9858i	0.748385	−	0.515403i
$963$	−3.49091	+	6.04644i	−0.112493	+	0.194844i
$964$		−	20.3132i		−	0.654246i
$965$	−19.2592	+	33.3579i	−0.619975	+	1.07383i
$966$	3.89818	+	16.0378i	0.125422	+	0.516007i
$967$		−	48.5963i		−	1.56275i	−0.624061	−	0.781376i	$-0.714518\pi$
$967$		−	48.5963i		−	1.56275i	0.624061	−	0.781376i	$-0.285482\pi$
$968$	10.7634	+	6.21427i	0.345950	+	0.199734i
$969$			37.8046i			1.21446i
$970$	1.54876	+	0.894176i	0.0497276	+	0.0287103i
$971$	13.1755	−	22.8207i	0.422823	−	0.732350i	−0.573392	−	0.819281i	$-0.694373\pi$
$971$	13.1755	−	22.8207i	0.422823	−	0.732350i	0.996214	+	0.0869311i	$0.0277060\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−25.9201	+	6.30020i	−0.830959	+	0.201975i
$974$	−22.1134			−0.708560
$975$	−17.8762	+	12.3111i	−0.572498	+	0.394272i
$976$	1.82308	−	3.15766i	0.0583552	−	0.101074i
$977$	−30.3578	+	17.5271i	−0.971233	+	0.560742i	−0.899612	−	0.436690i	$-0.856151\pi$
$977$	−30.3578	+	17.5271i	−0.971233	+	0.560742i	−0.0716210	+	0.997432i	$0.522817\pi$
$978$	21.6263			0.691534
$979$	15.0609	+	26.0863i	0.481349	+	0.833721i
$980$	23.2121	+	1.08528i	0.741483	+	0.0346680i
$981$	−7.17312	+	4.14140i	−0.229020	+	0.132225i
$982$	1.19635	+	0.690710i	0.0381769	+	0.0220415i
$983$	−5.98021	−	3.45268i	−0.190739	−	0.110123i	0.401589	−	0.915820i	$-0.368458\pi$
$983$	−5.98021	−	3.45268i	−0.190739	−	0.110123i	−0.592329	+	0.805697i	$0.701791\pi$
$984$	−7.97905			−0.254363
$985$	−64.2953			−2.04862
$986$	4.31256	+	2.48986i	0.137340	+	0.0792932i
$987$	4.40688	−	4.20565i	0.140273	−	0.133867i
$988$	25.0637	−	1.99662i	0.797382	−	0.0635210i
$989$	17.8966	+	30.9978i	0.569079	+	0.985674i
$990$	13.9153	−	8.03403i	0.442259	−	0.255338i
$991$	−2.37336	−	4.11079i	−0.0753924	−	0.130583i	0.825864	−	0.563869i	$-0.190688\pi$
$991$	−2.37336	−	4.11079i	−0.0753924	−	0.130583i	−0.901257	+	0.433285i	$0.857354\pi$
$992$	2.45584	−	4.25364i	0.0779730	−	0.135053i
$993$			30.3382i			0.962754i
$994$	−20.3115	+	4.93698i	−0.644243	+	0.156591i
$995$	−45.8824	+	26.4902i	−1.45457	+	0.839796i
$996$	−5.17784	+	2.98943i	−0.164066	+	0.0947237i
$997$	39.6702			1.25637			0.628184	−	0.778065i	$-0.283799\pi$
$997$	39.6702			1.25637			0.628184	+	0.778065i	$0.283799\pi$
$998$	3.31866	+	5.74809i	0.105050	+	0.181953i
$999$			7.81686i			0.247314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.b.277.5	yes	20
3.2	odd	2		1638.2.dt.b.1369.6		20
7.2	even	3		546.2.bd.b.121.1	✓	20
13.10	even	6		546.2.bd.b.361.1	yes	20
21.2	odd	6		1638.2.cr.b.667.10		20
39.23	odd	6		1638.2.cr.b.361.10		20
91.23	even	6	inner	546.2.bm.b.205.10	yes	20
273.23	odd	6		1638.2.dt.b.1297.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.1	✓	20	7.2	even	3
546.2.bd.b.361.1	yes	20	13.10	even	6
546.2.bm.b.205.10	yes	20	91.23	even	6	inner
546.2.bm.b.277.5	yes	20	1.1	even	1	trivial
1638.2.cr.b.361.10		20	39.23	odd	6
1638.2.cr.b.667.10		20	21.2	odd	6
1638.2.dt.b.1297.1		20	273.23	odd	6
1638.2.dt.b.1369.6		20	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.744278 + 2.53891i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(2.87489 - 1.65982i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.744278 + 2.53891i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.65982 - 2.87489i) q^{10} +(4.19183 - 2.42015i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.96948 - 2.04504i) q^{13} +(2.53891 + 0.744278i) q^{14} +(-2.87489 - 1.65982i) q^{15} +1.00000 q^{16} +5.42123 q^{17} +(0.866025 + 0.500000i) q^{18} +(-6.03917 - 3.48672i) q^{19} +(-2.87489 + 1.65982i) q^{20} +(2.57090 - 0.624890i) q^{21} +(-2.42015 - 4.19183i) q^{22} -6.23820 q^{23} +(0.866025 - 0.500000i) q^{24} +(3.01000 - 5.21347i) q^{25} +(-2.04504 - 2.96948i) q^{26} +1.00000 q^{27} +(0.744278 - 2.53891i) q^{28} +(-0.459279 + 0.795495i) q^{29} +(-1.65982 + 2.87489i) q^{30} +(4.25364 + 2.45584i) q^{31} -1.00000i q^{32} +(-4.19183 - 2.42015i) q^{33} -5.42123i q^{34} +(2.07441 + 8.53445i) q^{35} +(0.500000 - 0.866025i) q^{36} +7.81686i q^{37} +(-3.48672 + 6.03917i) q^{38} +(-3.25580 - 1.54912i) q^{39} +(1.65982 + 2.87489i) q^{40} +(-6.91006 - 3.98953i) q^{41} +(-0.624890 - 2.57090i) q^{42} +(-2.86888 - 4.96904i) q^{43} +(-4.19183 + 2.42015i) q^{44} +3.31964i q^{45} +6.23820i q^{46} +(1.99396 - 1.15121i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-5.89210 - 3.77931i) q^{49} +(-5.21347 - 3.01000i) q^{50} +(-2.71061 - 4.69492i) q^{51} +(-2.96948 + 2.04504i) q^{52} +(2.54507 - 4.40819i) q^{53} -1.00000i q^{54} +(8.03403 - 13.9153i) q^{55} +(-2.53891 - 0.744278i) q^{56} +6.97343i q^{57} +(0.795495 + 0.459279i) q^{58} +8.43334i q^{59} +(2.87489 + 1.65982i) q^{60} +(1.82308 - 3.15766i) q^{61} +(2.45584 - 4.25364i) q^{62} +(-1.82662 - 1.91402i) q^{63} -1.00000 q^{64} +(5.14253 - 10.8081i) q^{65} +(-2.42015 + 4.19183i) q^{66} +(7.62461 - 4.40207i) q^{67} -5.42123 q^{68} +(3.11910 + 5.40244i) q^{69} +(8.53445 - 2.07441i) q^{70} +(-6.84209 + 3.95028i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(1.61061 + 0.929885i) q^{73} +7.81686 q^{74} -6.01999 q^{75} +(6.03917 + 3.48672i) q^{76} +(3.02466 + 12.4439i) q^{77} +(-1.54912 + 3.25580i) q^{78} +(-1.39270 - 2.41222i) q^{79} +(2.87489 - 1.65982i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.98953 + 6.91006i) q^{82} +5.97886i q^{83} +(-2.57090 + 0.624890i) q^{84} +(15.5854 - 8.99826i) q^{85} +(-4.96904 + 2.86888i) q^{86} +0.918558 q^{87} +(2.42015 + 4.19183i) q^{88} +6.22313i q^{89} +3.31964 q^{90} +(2.98205 + 9.06131i) q^{91} +6.23820 q^{92} -4.91168i q^{93} +(-1.15121 - 1.99396i) q^{94} -23.1493 q^{95} +(-0.866025 + 0.500000i) q^{96} +(-0.466544 + 0.269360i) q^{97} +(-3.77931 + 5.89210i) q^{98} +4.84030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9	\( 20 q - 10 q^{3} - 20 q^{4} - 10 q^{9} + 4 q^{10} + 6 q^{11} + 10 q^{12} + 8 q^{13} + 4 q^{14} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{21} - 10 q^{22} - 16 q^{23} + 6 q^{25} + 8 q^{26} + 20 q^{27} + 8 q^{29} + 4 q^{30} + 12 q^{31} - 6 q^{33} + 10 q^{35} + 10 q^{36} + 6 q^{38} - 10 q^{39} - 4 q^{40} - 18 q^{41} - 2 q^{42} + 18 q^{43} - 6 q^{44} - 6 q^{47} - 10 q^{48} - 20 q^{49} + 12 q^{50} + 4 q^{51} - 8 q^{52} + 18 q^{53} - 12 q^{55} - 4 q^{56} + 24 q^{58} - 6 q^{61} - 6 q^{63} - 20 q^{64} - 6 q^{65} - 10 q^{66} + 24 q^{67} + 8 q^{68} + 8 q^{69} + 42 q^{70} - 6 q^{71} + 24 q^{73} + 36 q^{74} - 12 q^{75} + 12 q^{76} - 34 q^{77} + 2 q^{78} - 10 q^{81} + 18 q^{82} - 6 q^{84} - 36 q^{86} - 16 q^{87} + 10 q^{88} - 8 q^{90} - 10 q^{91} + 16 q^{92} - 16 q^{94} - 80 q^{95} - 96 q^{97} - 12 q^{98}+O(q^{100}) \) 20 * q - 10 * q^3 - 20 * q^4 - 10 * q^9 + 4 * q^10 + 6 * q^11 + 10 * q^12 + 8 * q^13 + 4 * q^14 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^21 - 10 * q^22 - 16 * q^23 + 6 * q^25 + 8 * q^26 + 20 * q^27 + 8 * q^29 + 4 * q^30 + 12 * q^31 - 6 * q^33 + 10 * q^35 + 10 * q^36 + 6 * q^38 - 10 * q^39 - 4 * q^40 - 18 * q^41 - 2 * q^42 + 18 * q^43 - 6 * q^44 - 6 * q^47 - 10 * q^48 - 20 * q^49 + 12 * q^50 + 4 * q^51 - 8 * q^52 + 18 * q^53 - 12 * q^55 - 4 * q^56 + 24 * q^58 - 6 * q^61 - 6 * q^63 - 20 * q^64 - 6 * q^65 - 10 * q^66 + 24 * q^67 + 8 * q^68 + 8 * q^69 + 42 * q^70 - 6 * q^71 + 24 * q^73 + 36 * q^74 - 12 * q^75 + 12 * q^76 - 34 * q^77 + 2 * q^78 - 10 * q^81 + 18 * q^82 - 6 * q^84 - 36 * q^86 - 16 * q^87 + 10 * q^88 - 8 * q^90 - 10 * q^91 + 16 * q^92 - 16 * q^94 - 80 * q^95 - 96 * q^97 - 12 * q^98

Introduction

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