LMFDB - Embedded newform 550.2.ba.c.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(49,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("550.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	550.499
Dual form			550.2.ba.c.399.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.363271 - 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(1.90211 - 0.618034i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.363271 - 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(1.90211 - 0.618034i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(0.309017 - 3.30220i) q^{11} +0.381966i q^{12} +(-0.726543 + 1.00000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.363271 + 0.500000i) q^{17} +(-2.71441 + 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} -0.763932 q^{21} +(-2.48990 - 2.19098i) q^{22} -1.23607i q^{23} +(0.309017 + 0.224514i) q^{24} +(0.381966 + 1.17557i) q^{26} +(1.31433 + 1.80902i) q^{27} +(-1.17557 - 1.61803i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} +1.00000i q^{32} +(-0.502029 + 1.16312i) q^{33} +0.618034 q^{34} +(-0.881966 + 2.71441i) q^{36} +(3.52671 - 1.14590i) q^{37} +(-3.44095 - 4.73607i) q^{38} +(0.381966 - 0.277515i) q^{39} +(1.73607 - 5.34307i) q^{41} +(-0.449028 + 0.618034i) q^{42} +8.56231i q^{43} +(-3.23607 + 0.726543i) q^{44} +(-1.00000 - 0.726543i) q^{46} +(-6.15537 - 2.00000i) q^{47} +(0.363271 - 0.118034i) q^{48} +(-2.42705 + 1.76336i) q^{49} +(-0.0729490 - 0.224514i) q^{51} +(1.17557 + 0.381966i) q^{52} +(0.898056 - 1.23607i) q^{53} +2.23607 q^{54} -2.00000 q^{56} +(-1.31433 + 1.80902i) q^{57} +(-4.25325 - 1.38197i) q^{58} +(2.66312 + 8.19624i) q^{59} +(2.00000 - 1.45309i) q^{61} +(-1.90211 + 0.618034i) q^{62} +(-5.42882 - 1.76393i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.645898 + 1.08981i) q^{66} +11.0902i q^{67} +(0.363271 - 0.500000i) q^{68} +(-0.145898 + 0.449028i) q^{69} +(4.23607 - 3.07768i) q^{71} +(1.67760 + 2.30902i) q^{72} +(9.87384 - 3.20820i) q^{73} +(1.14590 - 3.52671i) q^{74} -5.85410 q^{76} +(-1.45309 - 6.47214i) q^{77} -0.472136i q^{78} +(10.8541 + 7.88597i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-3.30220 - 4.54508i) q^{82} +(5.48183 + 7.54508i) q^{83} +(0.236068 + 0.726543i) q^{84} +(6.92705 + 5.03280i) q^{86} +1.70820i q^{87} +(-1.31433 + 3.04508i) q^{88} +8.09017 q^{89} +(-0.763932 + 2.35114i) q^{91} +(-1.17557 + 0.381966i) q^{92} +(0.449028 + 0.618034i) q^{93} +(-5.23607 + 3.80423i) q^{94} +(0.118034 - 0.363271i) q^{96} +(4.20025 - 5.78115i) q^{97} +3.00000i q^{98} +(-6.25329 + 7.10642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 10 q^{19} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 20 q^{29} - 4 q^{31} - 4 q^{34} - 16 q^{36} + 12 q^{39} - 4 q^{41} - 8 q^{44} - 8 q^{46} - 6 q^{49} - 14 q^{51} - 16 q^{56} - 10 q^{59} + 16 q^{61} + 2 q^{64} + 32 q^{66} - 28 q^{69} + 16 q^{71} + 36 q^{74} - 20 q^{76} + 60 q^{79} + 28 q^{81} - 16 q^{84} + 42 q^{86} + 20 q^{89} - 24 q^{91} - 24 q^{94} - 8 q^{96} + 26 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 10 * q^19 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 20 * q^29 - 4 * q^31 - 4 * q^34 - 16 * q^36 + 12 * q^39 - 4 * q^41 - 8 * q^44 - 8 * q^46 - 6 * q^49 - 14 * q^51 - 16 * q^56 - 10 * q^59 + 16 * q^61 + 2 * q^64 + 32 * q^66 - 28 * q^69 + 16 * q^71 + 36 * q^74 - 20 * q^76 + 60 * q^79 + 28 * q^81 - 16 * q^84 + 42 * q^86 + 20 * q^89 - 24 * q^91 - 24 * q^94 - 8 * q^96 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−0.363271	−	0.118034i	−0.209735	−	0.0681470i	0.202265	−	0.979331i	$-0.435170\pi$
$3$	−0.363271	−	0.118034i	−0.209735	−	0.0681470i	−0.412000	+	0.911184i	$0.635170\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	1.90211	−	0.618034i	0.718931	−	0.233595i	0.0733714	−	0.997305i	$-0.476624\pi$
$7$	1.90211	−	0.618034i	0.718931	−	0.233595i	0.645560	+	0.763710i	$0.276624\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−2.30902	−	1.67760i	−0.769672	−	0.559200i
$10$		0			0
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$			0.381966i			0.110264i
$13$	−0.726543	+	1.00000i	−0.201507	+	0.277350i	−0.897796	−	0.440411i	$-0.854833\pi$
$13$	−0.726543	+	1.00000i	−0.201507	+	0.277350i	0.696290	+	0.717761i	$0.254833\pi$
$14$	0.618034	−	1.90211i	0.165177	−	0.508361i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.363271	+	0.500000i	0.0881062	+	0.121268i	0.850795	−	0.525498i	$-0.176121\pi$
$17$	0.363271	+	0.500000i	0.0881062	+	0.121268i	−0.762688	+	0.646766i	$0.776121\pi$
$18$	−2.71441	+	0.881966i	−0.639793	+	0.207881i
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	−0.497219	−	0.867625i	$-0.665645\pi$
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	0.912236	−	0.409666i	$-0.134355\pi$
$20$		0			0
$21$	−0.763932			−0.166704
$22$	−2.48990	−	2.19098i	−0.530848	−	0.467119i
$23$		−	1.23607i		−	0.257738i	−0.991662	−	0.128869i	$-0.958865\pi$
$23$		−	1.23607i		−	0.257738i	0.991662	−	0.128869i	$-0.0411347\pi$
$24$	0.309017	+	0.224514i	0.0630778	+	0.0458287i
$25$		0			0
$26$	0.381966	+	1.17557i	0.0749097	+	0.230548i
$27$	1.31433	+	1.80902i	0.252942	+	0.348145i
$28$	−1.17557	−	1.61803i	−0.222162	−	0.305780i
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$		0			0
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$			1.00000i			0.176777i
$33$	−0.502029	+	1.16312i	−0.0873920	+	0.202473i
$34$	0.618034			0.105992
$35$		0			0
$36$	−0.881966	+	2.71441i	−0.146994	+	0.452402i
$37$	3.52671	−	1.14590i	0.579788	−	0.188384i	−0.00441771	−	0.999990i	$-0.501406\pi$
$37$	3.52671	−	1.14590i	0.579788	−	0.188384i	0.584206	+	0.811606i	$0.301406\pi$
$38$	−3.44095	−	4.73607i	−0.558197	−	0.768292i
$39$	0.381966	−	0.277515i	0.0611635	−	0.0444379i
$40$		0			0
$41$	1.73607	−	5.34307i	0.271128	−	0.834447i	−0.719090	−	0.694917i	$-0.755441\pi$
$41$	1.73607	−	5.34307i	0.271128	−	0.834447i	0.990218	−	0.139530i	$-0.0445591\pi$
$42$	−0.449028	+	0.618034i	−0.0692865	+	0.0953647i
$43$			8.56231i			1.30574i	0.757470	+	0.652870i	$0.226435\pi$
$43$			8.56231i			1.30574i	−0.757470	+	0.652870i	$0.773565\pi$
$44$	−3.23607	+	0.726543i	−0.487856	+	0.109530i
$45$		0			0
$46$	−1.00000	−	0.726543i	−0.147442	−	0.107123i
$47$	−6.15537	−	2.00000i	−0.897853	−	0.291730i	−0.176502	−	0.984300i	$-0.556478\pi$
$47$	−6.15537	−	2.00000i	−0.897853	−	0.291730i	−0.721350	+	0.692570i	$0.756478\pi$
$48$	0.363271	−	0.118034i	0.0524337	−	0.0170367i
$49$	−2.42705	+	1.76336i	−0.346722	+	0.251908i
$50$		0			0
$51$	−0.0729490	−	0.224514i	−0.0102149	−	0.0314382i
$52$	1.17557	+	0.381966i	0.163022	+	0.0529692i
$53$	0.898056	−	1.23607i	0.123357	−	0.169787i	−0.742872	−	0.669434i	$-0.766537\pi$
$53$	0.898056	−	1.23607i	0.123357	−	0.169787i	0.866229	+	0.499647i	$0.166537\pi$
$54$	2.23607			0.304290
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−1.31433	+	1.80902i	−0.174087	+	0.239610i
$58$	−4.25325	−	1.38197i	−0.558480	−	0.181461i
$59$	2.66312	+	8.19624i	0.346709	+	1.06706i	0.960663	+	0.277718i	$0.0895779\pi$
$59$	2.66312	+	8.19624i	0.346709	+	1.06706i	−0.613954	+	0.789342i	$0.710422\pi$
$60$		0			0
$61$	2.00000	−	1.45309i	0.256074	−	0.186048i	−0.452341	−	0.891845i	$-0.649411\pi$
$61$	2.00000	−	1.45309i	0.256074	−	0.186048i	0.708414	+	0.705797i	$0.249411\pi$
$62$	−1.90211	+	0.618034i	−0.241569	+	0.0784904i
$63$	−5.42882	−	1.76393i	−0.683968	−	0.222235i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	0.645898	+	1.08981i	0.0795046	+	0.134147i
$67$			11.0902i			1.35488i	0.735578	+	0.677440i	$0.236911\pi$
$67$			11.0902i			1.35488i	−0.735578	+	0.677440i	$0.763089\pi$
$68$	0.363271	−	0.500000i	0.0440531	−	0.0606339i
$69$	−0.145898	+	0.449028i	−0.0175641	+	0.0540566i
$70$		0			0
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	−0.307330	−	0.951603i	$-0.599435\pi$
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	0.810058	+	0.586349i	$0.199435\pi$
$72$	1.67760	+	2.30902i	0.197707	+	0.272120i
$73$	9.87384	−	3.20820i	1.15565	−	0.375492i	0.332378	−	0.943146i	$-0.392149\pi$
$73$	9.87384	−	3.20820i	1.15565	−	0.375492i	0.823267	+	0.567654i	$0.192149\pi$
$74$	1.14590	−	3.52671i	0.133208	−	0.409972i
$75$		0			0
$76$	−5.85410			−0.671512
$77$	−1.45309	−	6.47214i	−0.165594	−	0.737568i
$78$		−	0.472136i		−	0.0534589i
$79$	10.8541	+	7.88597i	1.22118	+	0.887241i	0.996198	−	0.0871218i	$-0.0277669\pi$
$79$	10.8541	+	7.88597i	1.22118	+	0.887241i	0.224984	+	0.974362i	$0.427767\pi$
$80$		0			0
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$	−3.30220	−	4.54508i	−0.364667	−	0.501921i
$83$	5.48183	+	7.54508i	0.601708	+	0.828181i	0.995863	−	0.0908634i	$-0.0289627\pi$
$83$	5.48183	+	7.54508i	0.601708	+	0.828181i	−0.394155	+	0.919044i	$0.628963\pi$
$84$	0.236068	+	0.726543i	0.0257571	+	0.0792723i
$85$		0			0
$86$	6.92705	+	5.03280i	0.746963	+	0.542700i
$87$			1.70820i			0.183139i
$88$	−1.31433	+	3.04508i	−0.140108	+	0.324607i
$89$	8.09017			0.857556			0.428778	−	0.903410i	$-0.358944\pi$
$89$	8.09017			0.857556			0.428778	+	0.903410i	$0.358944\pi$
$90$		0			0
$91$	−0.763932	+	2.35114i	−0.0800818	+	0.246467i
$92$	−1.17557	+	0.381966i	−0.122562	+	0.0398227i
$93$	0.449028	+	0.618034i	0.0465620	+	0.0640871i
$94$	−5.23607	+	3.80423i	−0.540059	+	0.392376i
$95$		0			0
$96$	0.118034	−	0.363271i	0.0120468	−	0.0370762i
$97$	4.20025	−	5.78115i	0.426471	−	0.586987i	−0.540668	−	0.841236i	$-0.681828\pi$
$97$	4.20025	−	5.78115i	0.426471	−	0.586987i	0.967139	+	0.254249i	$0.0818283\pi$
$98$			3.00000i			0.303046i
$99$	−6.25329	+	7.10642i	−0.628479	+	0.714222i
$100$		0			0
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	0.743191	−	0.669079i	$-0.233311\pi$
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	−0.406673	+	0.913574i	$0.633311\pi$
$102$	−0.224514	−	0.0729490i	−0.0222302	−	0.00722303i
$103$	14.9394	−	4.85410i	1.47202	−	0.478289i	0.540303	−	0.841470i	$-0.318309\pi$
$103$	14.9394	−	4.85410i	1.47202	−	0.478289i	0.931718	+	0.363181i	$0.118309\pi$
$104$	1.00000	−	0.726543i	0.0980581	−	0.0712434i
$105$		0			0
$106$	−0.472136	−	1.45309i	−0.0458579	−	0.141136i
$107$	−1.08981	−	0.354102i	−0.105356	−	0.0342323i	0.255864	−	0.966713i	$-0.417640\pi$
$107$	−1.08981	−	0.354102i	−0.105356	−	0.0342323i	−0.361221	+	0.932480i	$0.617640\pi$
$108$	1.31433	−	1.80902i	0.126471	−	0.174073i
$109$	−18.9443			−1.81453			−0.907266	−	0.420557i	$-0.861835\pi$
$109$	−18.9443			−1.81453			−0.907266	+	0.420557i	$0.861835\pi$
$110$		0			0
$111$	−1.41641			−0.134439
$112$	−1.17557	+	1.61803i	−0.111081	+	0.152890i
$113$	1.76336	+	0.572949i	0.165883	+	0.0538985i	0.390781	−	0.920484i	$-0.372205\pi$
$113$	1.76336	+	0.572949i	0.165883	+	0.0538985i	−0.224898	+	0.974382i	$0.572205\pi$
$114$	0.690983	+	2.12663i	0.0647165	+	0.199177i
$115$		0			0
$116$	−3.61803	+	2.62866i	−0.335926	+	0.244065i
$117$	3.35520	−	1.09017i	0.310188	−	0.100786i
$118$	8.19624	+	2.66312i	0.754525	+	0.245160i
$119$	1.00000	+	0.726543i	0.0916698	+	0.0666020i
$120$		0			0
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$		−	2.47214i		−	0.223817i
$123$	−1.26133	+	1.73607i	−0.113730	+	0.156536i
$124$	−0.618034	+	1.90211i	−0.0555011	+	0.170815i
$125$		0			0
$126$	−4.61803	+	3.35520i	−0.411407	+	0.298905i
$127$	6.43288	+	8.85410i	0.570826	+	0.785675i	0.992652	−	0.121002i	$-0.0386108\pi$
$127$	6.43288	+	8.85410i	0.570826	+	0.785675i	−0.421826	+	0.906677i	$0.638611\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	1.01064	−	3.11044i	0.0889822	−	0.273859i
$130$		0			0
$131$	6.79837			0.593977			0.296988	−	0.954881i	$-0.404018\pi$
$131$	6.79837			0.593977			0.296988	+	0.954881i	$0.404018\pi$
$132$	1.26133	+	0.118034i	0.109784	+	0.0102735i
$133$		−	11.7082i		−	1.01523i
$134$	8.97214	+	6.51864i	0.775074	+	0.563125i
$135$		0			0
$136$	−0.190983	−	0.587785i	−0.0163767	−	0.0504022i
$137$	−9.45756	−	13.0172i	−0.808014	−	1.11214i	−0.991627	−	0.129138i	$-0.958779\pi$
$137$	−9.45756	−	13.0172i	−0.808014	−	1.11214i	0.183612	−	0.982999i	$-0.441221\pi$
$138$	0.277515	+	0.381966i	0.0236236	+	0.0325151i
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$		0			0
$141$	2.00000	+	1.45309i	0.168430	+	0.122372i
$142$		−	5.23607i		−	0.439401i
$143$	3.07768	+	2.70820i	0.257369	+	0.226471i
$144$	2.85410			0.237842
$145$		0			0
$146$	3.20820	−	9.87384i	0.265513	−	0.817165i
$147$	1.08981	−	0.354102i	0.0898863	−	0.0292058i
$148$	−2.17963	−	3.00000i	−0.179164	−	0.246598i
$149$	−5.00000	+	3.63271i	−0.409616	+	0.297603i	−0.773446	−	0.633862i	$-0.781469\pi$
$149$	−5.00000	+	3.63271i	−0.409616	+	0.297603i	0.363830	+	0.931465i	$0.381469\pi$
$150$		0			0
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	0.798669	+	0.601770i	$0.205538\pi$
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	−0.999849	+	0.0173966i	$0.994462\pi$
$152$	−3.44095	+	4.73607i	−0.279098	+	0.384146i
$153$		−	1.76393i		−	0.142605i
$154$	−6.09017	−	2.62866i	−0.490760	−	0.211823i
$155$		0			0
$156$	−0.381966	−	0.277515i	−0.0305818	−	0.0222189i
$157$	9.23305	+	3.00000i	0.736878	+	0.239426i	0.653325	−	0.757077i	$-0.273373\pi$
$157$	9.23305	+	3.00000i	0.736878	+	0.239426i	0.0835524	+	0.996503i	$0.473373\pi$
$158$	12.7598	−	4.14590i	1.01511	−	0.329830i
$159$	−0.472136	+	0.343027i	−0.0374428	+	0.0272038i
$160$		0			0
$161$	−0.763932	−	2.35114i	−0.0602063	−	0.185296i
$162$	7.33094	+	2.38197i	0.575973	+	0.187145i
$163$	−0.534785	+	0.736068i	−0.0418876	+	0.0576533i	−0.829447	−	0.558585i	$-0.811344\pi$
$163$	−0.534785	+	0.736068i	−0.0418876	+	0.0576533i	0.787559	+	0.616239i	$0.211344\pi$
$164$	−5.61803			−0.438695
$165$		0			0
$166$	9.32624			0.723856
$167$	−8.67802	+	11.9443i	−0.671525	+	0.924276i	−0.999794	−	0.0203090i	$-0.993535\pi$
$167$	−8.67802	+	11.9443i	−0.671525	+	0.924276i	0.328268	+	0.944585i	$0.393535\pi$
$168$	0.726543	+	0.236068i	0.0560540	+	0.0182130i
$169$	3.54508	+	10.9106i	0.272699	+	0.839281i
$170$		0			0
$171$	−13.5172	+	9.82084i	−1.03369	+	0.751018i
$172$	8.14324	−	2.64590i	0.620916	−	0.201748i
$173$	−20.8172	−	6.76393i	−1.58271	−	0.514252i	−0.619954	−	0.784638i	$-0.712849\pi$
$173$	−20.8172	−	6.76393i	−1.58271	−	0.514252i	−0.962752	+	0.270386i	$0.912849\pi$
$174$	1.38197	+	1.00406i	0.104767	+	0.0761174i
$175$		0			0
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$		−	3.29180i		−	0.247427i
$178$	4.75528	−	6.54508i	0.356423	−	0.490575i
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	−0.800855	−	0.598859i	$-0.795621\pi$
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	0.999905	−	0.0137566i	$-0.00437900\pi$
$180$		0			0
$181$	3.38197	−	2.45714i	0.251380	−	0.182638i	−0.454958	−	0.890513i	$-0.650346\pi$
$181$	3.38197	−	2.45714i	0.251380	−	0.182638i	0.706338	+	0.707875i	$0.250346\pi$
$182$	1.45309	+	2.00000i	0.107710	+	0.148250i
$183$	−0.898056	+	0.291796i	−0.0663862	+	0.0215702i
$184$	−0.381966	+	1.17557i	−0.0281589	+	0.0866642i
$185$		0			0
$186$	0.763932			0.0560142
$187$	1.76336	−	1.04508i	0.128949	−	0.0764242i
$188$			6.47214i			0.472029i
$189$	3.61803	+	2.62866i	0.263173	+	0.191207i
$190$		0			0
$191$	1.47214	+	4.53077i	0.106520	+	0.327835i	0.990084	−	0.140475i	$-0.0448630\pi$
$191$	1.47214	+	4.53077i	0.106520	+	0.327835i	−0.883564	+	0.468310i	$0.844863\pi$
$192$	−0.224514	−	0.309017i	−0.0162029	−	0.0223014i
$193$	10.2371	+	14.0902i	0.736883	+	1.01423i	0.998792	+	0.0491400i	$0.0156480\pi$
$193$	10.2371	+	14.0902i	0.736883	+	1.01423i	−0.261909	+	0.965093i	$0.584352\pi$
$194$	−2.20820	−	6.79615i	−0.158540	−	0.487935i
$195$		0			0
$196$	2.42705	+	1.76336i	0.173361	+	0.125954i
$197$		−	20.9443i		−	1.49222i	−0.665824	−	0.746109i	$-0.731920\pi$
$197$		−	20.9443i		−	1.49222i	0.665824	−	0.746109i	$-0.268080\pi$
$198$	2.07363	+	9.23607i	0.147366	+	0.656379i
$199$	18.9443			1.34292			0.671462	−	0.741039i	$-0.265667\pi$
$199$	18.9443			1.34292			0.671462	+	0.741039i	$0.265667\pi$
$200$		0			0
$201$	1.30902	−	4.02874i	0.0923309	−	0.284165i
$202$	3.97574	−	1.29180i	0.279732	−	0.0908905i
$203$	−5.25731	−	7.23607i	−0.368991	−	0.507872i
$204$	−0.190983	+	0.138757i	−0.0133715	+	0.00971495i
$205$		0			0
$206$	4.85410	−	14.9394i	0.338201	−	1.04088i
$207$	−2.07363	+	2.85410i	−0.144127	+	0.198374i
$208$		−	1.23607i		−	0.0857059i
$209$	−17.8262	−	7.69421i	−1.23307	−	0.532220i
$210$		0			0
$211$	4.92705	+	3.57971i	0.339192	+	0.246438i	0.744321	−	0.667822i	$-0.232773\pi$
$211$	4.92705	+	3.57971i	0.339192	+	0.246438i	−0.405129	+	0.914260i	$0.632773\pi$
$212$	−1.45309	−	0.472136i	−0.0997983	−	0.0324264i
$213$	−1.90211	+	0.618034i	−0.130331	+	0.0423470i
$214$	−0.927051	+	0.673542i	−0.0633719	+	0.0460424i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−3.80423	−	1.23607i	−0.258248	−	0.0839098i
$218$	−11.1352	+	15.3262i	−0.754168	+	1.03802i
$219$	−3.96556			−0.267968
$220$		0			0
$221$	−0.763932			−0.0513876
$222$	−0.832544	+	1.14590i	−0.0558767	+	0.0769076i
$223$	−24.4500	−	7.94427i	−1.63729	−	0.531988i	−0.661359	−	0.750069i	$-0.730020\pi$
$223$	−24.4500	−	7.94427i	−1.63729	−	0.531988i	−0.975931	+	0.218081i	$0.930020\pi$
$224$	0.618034	+	1.90211i	0.0412941	+	0.127090i
$225$		0			0
$226$	1.50000	−	1.08981i	0.0997785	−	0.0724933i
$227$	−13.7966	+	4.48278i	−0.915711	+	0.297532i	−0.728706	−	0.684827i	$-0.759878\pi$
$227$	−13.7966	+	4.48278i	−0.915711	+	0.297532i	−0.187005	+	0.982359i	$0.559878\pi$
$228$	2.12663	+	0.690983i	0.140839	+	0.0457615i
$229$	1.38197	+	1.00406i	0.0913229	+	0.0663500i	0.632510	−	0.774552i	$-0.282025\pi$
$229$	1.38197	+	1.00406i	0.0913229	+	0.0663500i	−0.541187	+	0.840902i	$0.682025\pi$
$230$		0			0
$231$	−0.236068	+	2.52265i	−0.0155321	+	0.165978i
$232$			4.47214i			0.293610i
$233$	5.65334	−	7.78115i	0.370363	−	0.509760i	−0.582637	−	0.812733i	$-0.697979\pi$
$233$	5.65334	−	7.78115i	0.370363	−	0.509760i	0.952999	+	0.302972i	$0.0979790\pi$
$234$	1.09017	−	3.35520i	0.0712666	−	0.219336i
$235$		0			0
$236$	6.97214	−	5.06555i	0.453847	−	0.329739i
$237$	−3.01217	−	4.14590i	−0.195662	−	0.269305i
$238$	1.17557	−	0.381966i	0.0762009	−	0.0247592i
$239$	6.70820	−	20.6457i	0.433918	−	1.33546i	−0.460274	−	0.887777i	$-0.652249\pi$
$239$	6.70820	−	20.6457i	0.433918	−	1.33546i	0.894192	−	0.447684i	$-0.147751\pi$
$240$		0			0
$241$	−11.0902			−0.714381			−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902			−0.714381			−0.357190	+	0.934032i	$0.616265\pi$
$242$	−8.00448	+	7.54508i	−0.514547	+	0.485016i
$243$		−	9.65248i		−	0.619207i
$244$	−2.00000	−	1.45309i	−0.128037	−	0.0930242i
$245$		0			0
$246$	0.663119	+	2.04087i	0.0422789	+	0.130121i
$247$	4.25325	+	5.85410i	0.270628	+	0.372488i
$248$	1.17557	+	1.61803i	0.0746488	+	0.102745i
$249$	−1.10081	−	3.38795i	−0.0697612	−	0.214703i
$250$		0			0
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.0936883	−	0.995602i	$-0.529866\pi$
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.975825	+	0.218555i	$0.929866\pi$
$252$			5.70820i			0.359583i
$253$	−4.08174	−	0.381966i	−0.256617	−	0.0240140i
$254$	10.9443			0.686705
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.34307	−	1.73607i	0.333291	−	0.108293i	−0.137590	−	0.990489i	$-0.543936\pi$
$257$	5.34307	−	1.73607i	0.333291	−	0.108293i	0.470882	+	0.882196i	$0.343936\pi$
$258$	−1.92236	−	2.64590i	−0.119681	−	0.164726i
$259$	6.00000	−	4.35926i	0.372822	−	0.270871i
$260$		0			0
$261$	−3.94427	+	12.1392i	−0.244144	+	0.751399i
$262$	3.99598	−	5.50000i	0.246873	−	0.339791i
$263$			23.2361i			1.43280i	0.697691	+	0.716399i	$0.254211\pi$
$263$			23.2361i			1.43280i	−0.697691	+	0.716399i	$0.745789\pi$
$264$	0.836881	−	0.951057i	0.0515065	−	0.0585335i
$265$		0			0
$266$	−9.47214	−	6.88191i	−0.580774	−	0.421957i
$267$	−2.93893	−	0.954915i	−0.179859	−	0.0584399i
$268$	10.5474	−	3.42705i	0.644284	−	0.209340i
$269$	5.00000	−	3.63271i	0.304855	−	0.221490i	−0.424830	−	0.905273i	$-0.639666\pi$
$269$	5.00000	−	3.63271i	0.304855	−	0.221490i	0.729686	+	0.683783i	$0.239666\pi$
$270$		0			0
$271$	0.618034	+	1.90211i	0.0375429	+	0.115545i	0.968072	−	0.250674i	$-0.0806521\pi$
$271$	0.618034	+	1.90211i	0.0375429	+	0.115545i	−0.930529	+	0.366219i	$0.880652\pi$
$272$	−0.587785	−	0.190983i	−0.0356397	−	0.0115800i
$273$	0.555029	−	0.763932i	0.0335919	−	0.0462353i
$274$	−16.0902			−0.972043
$275$		0			0
$276$	0.472136			0.0284192
$277$	−13.9353	+	19.1803i	−0.837293	+	1.15243i	0.149228	+	0.988803i	$0.452321\pi$
$277$	−13.9353	+	19.1803i	−0.837293	+	1.15243i	−0.986521	+	0.163632i	$0.947679\pi$
$278$		0			0
$279$	1.76393	+	5.42882i	0.105604	+	0.325015i
$280$		0			0
$281$	13.0172	−	9.45756i	0.776542	−	0.564191i	−0.127397	−	0.991852i	$-0.540662\pi$
$281$	13.0172	−	9.45756i	0.776542	−	0.564191i	0.903939	+	0.427661i	$0.140662\pi$
$282$	2.35114	−	0.763932i	0.140008	−	0.0454915i
$283$	−22.8254	−	7.41641i	−1.35683	−	0.440860i	−0.461844	−	0.886961i	$-0.652812\pi$
$283$	−22.8254	−	7.41641i	−1.35683	−	0.440860i	−0.894982	+	0.446101i	$0.852812\pi$
$284$	−4.23607	−	3.07768i	−0.251364	−	0.182627i
$285$		0			0
$286$	4.00000	−	0.898056i	0.236525	−	0.0531032i
$287$		−	11.2361i		−	0.663244i
$288$	1.67760	−	2.30902i	0.0988535	−	0.136060i
$289$	5.13525	−	15.8047i	0.302074	−	0.929688i
$290$		0			0
$291$	−2.20820	+	1.60435i	−0.129447	+	0.0940489i
$292$	−6.10237	−	8.39919i	−0.357114	−	0.491525i
$293$	−26.9726	+	8.76393i	−1.57576	+	0.511994i	−0.960959	−	0.276691i	$-0.910762\pi$
$293$	−26.9726	+	8.76393i	−1.57576	+	0.511994i	−0.614798	+	0.788685i	$0.710762\pi$
$294$	0.354102	−	1.08981i	0.0206516	−	0.0635592i
$295$		0			0
$296$	−3.70820			−0.215535
$297$	6.37988	−	3.78115i	0.370198	−	0.219405i
$298$			6.18034i			0.358017i
$299$	1.23607	+	0.898056i	0.0714837	+	0.0519359i
$300$		0			0
$301$	5.29180	+	16.2865i	0.305014	+	0.938737i
$302$	4.70228	+	6.47214i	0.270586	+	0.372430i
$303$	−0.938545	−	1.29180i	−0.0539180	−	0.0742117i
$304$	1.80902	+	5.56758i	0.103754	+	0.319323i
$305$		0			0
$306$	−1.42705	−	1.03681i	−0.0815791	−	0.0592707i
$307$			27.7984i			1.58654i	0.608872	+	0.793268i	$0.291622\pi$
$307$			27.7984i			1.58654i	−0.608872	+	0.793268i	$0.708378\pi$
$308$	−5.70634	+	3.38197i	−0.325149	+	0.192705i
$309$	−6.00000			−0.341328
$310$		0			0
$311$	8.05573	−	24.7930i	0.456798	−	1.40588i	−0.412212	−	0.911088i	$-0.635244\pi$
$311$	8.05573	−	24.7930i	0.456798	−	1.40588i	0.869011	−	0.494793i	$-0.164756\pi$
$312$	−0.449028	+	0.145898i	−0.0254212	+	0.00825985i
$313$	2.54290	+	3.50000i	0.143733	+	0.197832i	0.874814	−	0.484459i	$-0.160984\pi$
$313$	2.54290	+	3.50000i	0.143733	+	0.197832i	−0.731081	+	0.682291i	$0.760984\pi$
$314$	7.85410	−	5.70634i	0.443233	−	0.322027i
$315$		0			0
$316$	4.14590	−	12.7598i	0.233225	−	0.717793i
$317$	−2.17963	+	3.00000i	−0.122420	+	0.168497i	−0.865828	−	0.500341i	$-0.833208\pi$
$317$	−2.17963	+	3.00000i	−0.122420	+	0.168497i	0.743408	+	0.668838i	$0.233208\pi$
$318$			0.583592i			0.0327262i
$319$	−14.4721	+	3.24920i	−0.810284	+	0.181920i
$320$		0			0
$321$	0.354102	+	0.257270i	0.0197640	+	0.0143594i
$322$	−2.35114	−	0.763932i	−0.131024	−	0.0425723i
$323$	3.44095	−	1.11803i	0.191460	−	0.0622091i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$		0			0
$326$	0.281153	+	0.865300i	0.0155716	+	0.0479245i
$327$	6.88191	+	2.23607i	0.380570	+	0.123655i
$328$	−3.30220	+	4.54508i	−0.182333	+	0.250960i
$329$	−12.9443			−0.713641
$330$		0			0
$331$	6.27051			0.344658			0.172329	−	0.985039i	$-0.444871\pi$
$331$	6.27051			0.344658			0.172329	+	0.985039i	$0.444871\pi$
$332$	5.48183	−	7.54508i	0.300854	−	0.414090i
$333$	−10.0656	−	3.27051i	−0.551591	−	0.179223i
$334$	4.56231	+	14.0413i	0.249638	+	0.768308i
$335$		0			0
$336$	0.618034	−	0.449028i	0.0337165	−	0.0244965i
$337$	25.4868	−	8.28115i	1.38835	−	0.451103i	0.482947	−	0.875650i	$-0.339567\pi$
$337$	25.4868	−	8.28115i	1.38835	−	0.451103i	0.905406	+	0.424547i	$0.139567\pi$
$338$	10.9106	+	3.54508i	0.593461	+	0.192827i
$339$	−0.572949	−	0.416272i	−0.0311183	−	0.0226088i
$340$		0			0
$341$	−4.38197	+	4.97980i	−0.237297	+	0.269671i
$342$			16.7082i			0.903476i
$343$	−11.7557	+	16.1803i	−0.634748	+	0.873656i
$344$	2.64590	−	8.14324i	0.142657	−	0.439054i
$345$		0			0
$346$	−17.7082	+	12.8658i	−0.951999	+	0.691668i
$347$	−9.76784	−	13.4443i	−0.524365	−	0.721726i	0.461894	−	0.886935i	$-0.347170\pi$
$347$	−9.76784	−	13.4443i	−0.524365	−	0.721726i	−0.986259	+	0.165209i	$0.947170\pi$
$348$	1.62460	−	0.527864i	0.0870876	−	0.0282965i
$349$	6.05573	−	18.6376i	0.324156	−	0.997649i	−0.647665	−	0.761926i	$-0.724254\pi$
$349$	6.05573	−	18.6376i	0.324156	−	0.997649i	0.971820	−	0.235723i	$-0.0757458\pi$
$350$		0			0
$351$	−2.76393			−0.147528
$352$	3.30220	+	0.309017i	0.176008	+	0.0164707i
$353$		−	32.6180i		−	1.73608i	−0.496492	−	0.868041i	$-0.665379\pi$
$353$		−	32.6180i		−	1.73608i	0.496492	−	0.868041i	$-0.334621\pi$
$354$	−2.66312	−	1.93487i	−0.141543	−	0.102837i
$355$		0			0
$356$	−2.50000	−	7.69421i	−0.132500	−	0.407792i
$357$	−0.277515	−	0.381966i	−0.0146876	−	0.0202158i
$358$	−5.06555	−	6.97214i	−0.267723	−	0.368489i
$359$	−1.58359	−	4.87380i	−0.0835788	−	0.257229i	0.900531	−	0.434793i	$-0.143178\pi$
$359$	−1.58359	−	4.87380i	−0.0835788	−	0.257229i	−0.984109	+	0.177564i	$0.943178\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$		−	4.18034i		−	0.219714i
$363$	3.68571	+	2.01722i	0.193450	+	0.105877i
$364$	2.47214			0.129575
$365$		0			0
$366$	−0.291796	+	0.898056i	−0.0152524	+	0.0469421i
$367$	−18.7436	+	6.09017i	−0.978409	+	0.317904i	−0.754206	−	0.656638i	$-0.771978\pi$
$367$	−18.7436	+	6.09017i	−0.978409	+	0.317904i	−0.224203	+	0.974542i	$0.571978\pi$
$368$	0.726543	+	1.00000i	0.0378736	+	0.0521286i
$369$	−12.9721	+	9.42481i	−0.675302	+	0.490636i
$370$		0			0
$371$	0.944272	−	2.90617i	0.0490242	−	0.150881i
$372$	0.449028	−	0.618034i	0.0232810	−	0.0320436i
$373$			4.29180i			0.222221i	0.993808	+	0.111110i	$0.0354407\pi$
$373$			4.29180i			0.222221i	−0.993808	+	0.111110i	$0.964559\pi$
$374$	0.190983	−	2.04087i	0.00987550	−	0.105531i
$375$		0			0
$376$	5.23607	+	3.80423i	0.270030	+	0.196188i
$377$	5.25731	+	1.70820i	0.270765	+	0.0879770i
$378$	4.25325	−	1.38197i	0.218764	−	0.0710807i
$379$	11.5451	−	8.38800i	0.593031	−	0.430862i	−0.250367	−	0.968151i	$-0.580551\pi$
$379$	11.5451	−	8.38800i	0.593031	−	0.430862i	0.843398	+	0.537289i	$0.180551\pi$
$380$		0			0
$381$	−1.29180	−	3.97574i	−0.0661807	−	0.203683i
$382$	4.53077	+	1.47214i	0.231814	+	0.0753210i
$383$	16.6700	−	22.9443i	0.851797	−	1.17240i	−0.131667	−	0.991294i	$-0.542033\pi$
$383$	16.6700	−	22.9443i	0.851797	−	1.17240i	0.983464	−	0.181104i	$-0.0579669\pi$
$384$	−0.381966			−0.0194921
$385$		0			0
$386$	17.4164			0.886472
$387$	14.3641	−	19.7705i	0.730169	−	1.00499i
$388$	−6.79615	−	2.20820i	−0.345022	−	0.112105i
$389$	3.29180	+	10.1311i	0.166901	+	0.513667i	0.999171	−	0.0407020i	$-0.0129594\pi$
$389$	3.29180	+	10.1311i	0.166901	+	0.513667i	−0.832271	+	0.554370i	$0.812959\pi$
$390$		0			0
$391$	0.618034	−	0.449028i	0.0312553	−	0.0227083i
$392$	2.85317	−	0.927051i	0.144107	−	0.0468231i
$393$	−2.46965	−	0.802439i	−0.124578	−	0.0404777i
$394$	−16.9443	−	12.3107i	−0.853640	−	0.620206i
$395$		0			0
$396$	8.69098	+	3.75123i	0.436738	+	0.188506i
$397$		−	17.1246i		−	0.859460i	−0.902958	−	0.429730i	$-0.858609\pi$
$397$		−	17.1246i		−	0.859460i	0.902958	−	0.429730i	$-0.141391\pi$
$398$	11.1352	−	15.3262i	0.558155	−	0.768235i
$399$	−1.38197	+	4.25325i	−0.0691848	+	0.212929i
$400$		0			0
$401$	14.3992	−	10.4616i	0.719061	−	0.522428i	−0.167023	−	0.985953i	$-0.553415\pi$
$401$	14.3992	−	10.4616i	0.719061	−	0.522428i	0.886084	+	0.463525i	$0.153415\pi$
$402$	−2.48990	−	3.42705i	−0.124185	−	0.170926i
$403$	2.35114	−	0.763932i	0.117119	−	0.0380542i
$404$	1.29180	−	3.97574i	0.0642693	−	0.197800i
$405$		0			0
$406$	−8.94427			−0.443897
$407$	−2.69417	−	12.0000i	−0.133545	−	0.594818i
$408$			0.236068i			0.0116871i
$409$	−10.8541	−	7.88597i	−0.536701	−	0.389936i	0.286157	−	0.958183i	$-0.407622\pi$
$409$	−10.8541	−	7.88597i	−0.536701	−	0.389936i	−0.822858	+	0.568247i	$0.807622\pi$
$410$		0			0
$411$	1.89919	+	5.84510i	0.0936800	+	0.288317i
$412$	−9.23305	−	12.7082i	−0.454880	−	0.626088i
$413$	10.1311	+	13.9443i	0.498519	+	0.686153i
$414$	1.09017	+	3.35520i	0.0535789	+	0.164899i
$415$		0			0
$416$	−1.00000	−	0.726543i	−0.0490290	−	0.0356217i
$417$		0			0
$418$	−16.7027	+	9.89919i	−0.816958	+	0.484185i
$419$	10.8541			0.530258			0.265129	−	0.964213i	$-0.414586\pi$
$419$	10.8541			0.530258			0.265129	+	0.964213i	$0.414586\pi$
$420$		0			0
$421$	−9.70820	+	29.8788i	−0.473149	+	1.45620i	0.375289	+	0.926908i	$0.377543\pi$
$421$	−9.70820	+	29.8788i	−0.473149	+	1.45620i	−0.848438	+	0.529295i	$0.822457\pi$
$422$	5.79210	−	1.88197i	0.281955	−	0.0916127i
$423$	10.8576	+	14.9443i	0.527917	+	0.726615i
$424$	−1.23607	+	0.898056i	−0.0600288	+	0.0436135i
$425$		0			0
$426$	−0.618034	+	1.90211i	−0.0299438	+	0.0921577i
$427$	2.90617	−	4.00000i	0.140639	−	0.193574i
$428$			1.14590i			0.0553891i
$429$	−0.798374	−	1.34708i	−0.0385459	−	0.0650378i
$430$		0			0
$431$	13.7082	+	9.95959i	0.660301	+	0.479737i	0.866765	−	0.498718i	$-0.166196\pi$
$431$	13.7082	+	9.95959i	0.660301	+	0.479737i	−0.206464	+	0.978454i	$0.566196\pi$
$432$	−2.12663	−	0.690983i	−0.102317	−	0.0332449i
$433$	26.3848	−	8.57295i	1.26797	−	0.411990i	0.403644	−	0.914916i	$-0.367743\pi$
$433$	26.3848	−	8.57295i	1.26797	−	0.411990i	0.864329	+	0.502926i	$0.167743\pi$
$434$	−3.23607	+	2.35114i	−0.155336	+	0.112858i
$435$		0			0
$436$	5.85410	+	18.0171i	0.280361	+	0.862861i
$437$	−6.88191	−	2.23607i	−0.329206	−	0.106966i
$438$	−2.33090	+	3.20820i	−0.111375	+	0.153294i
$439$	6.58359			0.314218			0.157109	−	0.987581i	$-0.449783\pi$
$439$	6.58359			0.314218			0.157109	+	0.987581i	$0.449783\pi$
$440$		0			0
$441$	8.56231			0.407729
$442$	−0.449028	+	0.618034i	−0.0213581	+	0.0293969i
$443$	8.14324	+	2.64590i	0.386897	+	0.125710i	0.496005	−	0.868319i	$-0.334800\pi$
$443$	8.14324	+	2.64590i	0.386897	+	0.125710i	−0.109109	+	0.994030i	$0.534800\pi$
$444$	0.437694	+	1.34708i	0.0207720	+	0.0639298i
$445$		0			0
$446$	−20.7984	+	15.1109i	−0.984832	+	0.715522i
$447$	2.24514	−	0.729490i	0.106191	−	0.0345037i
$448$	1.90211	+	0.618034i	0.0898664	+	0.0291994i
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	0.750523	−	0.660844i	$-0.229802\pi$
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	−0.396576	+	0.918002i	$0.629802\pi$
$450$		0			0
$451$	−17.1074	−	7.38394i	−0.805556	−	0.347696i
$452$		−	1.85410i		−	0.0872096i
$453$	1.79611	−	2.47214i	0.0843887	−	0.116151i
$454$	−4.48278	+	13.7966i	−0.210387	+	0.647505i
$455$		0			0
$456$	1.80902	−	1.31433i	0.0847150	−	0.0615490i
$457$	5.54734	+	7.63525i	0.259493	+	0.357162i	0.918808	−	0.394705i	$-0.129153\pi$
$457$	5.54734	+	7.63525i	0.259493	+	0.357162i	−0.659314	+	0.751867i	$0.729153\pi$
$458$	1.62460	−	0.527864i	0.0759125	−	0.0246655i
$459$	−0.427051	+	1.31433i	−0.0199330	+	0.0613476i
$460$		0			0
$461$	1.34752			0.0627605			0.0313802	−	0.999508i	$-0.490010\pi$
$461$	1.34752			0.0627605			0.0313802	+	0.999508i	$0.490010\pi$
$462$	1.90211	+	1.67376i	0.0884943	+	0.0778705i
$463$			19.4164i			0.902357i	0.892434	+	0.451178i	$0.148996\pi$
$463$			19.4164i			0.902357i	−0.892434	+	0.451178i	$0.851004\pi$
$464$	3.61803	+	2.62866i	0.167963	+	0.122032i
$465$		0			0
$466$	−2.97214	−	9.14729i	−0.137682	−	0.423740i
$467$	19.5762	+	26.9443i	0.905877	+	1.24683i	0.968555	+	0.248798i	$0.0800357\pi$
$467$	19.5762	+	26.9443i	0.905877	+	1.24683i	−0.0626787	+	0.998034i	$0.519964\pi$
$468$	−2.07363	−	2.85410i	−0.0958534	−	0.131931i
$469$	6.85410	+	21.0948i	0.316493	+	0.974065i
$470$		0			0
$471$	−3.00000	−	2.17963i	−0.138233	−	0.100432i
$472$		−	8.61803i		−	0.396677i
$473$	28.2744	+	2.64590i	1.30006	+	0.121659i
$474$	−5.12461			−0.235381
$475$		0			0
$476$	0.381966	−	1.17557i	0.0175074	−	0.0538822i
$477$	−4.14725	+	1.34752i	−0.189890	+	0.0616989i
$478$	−12.7598	−	17.5623i	−0.583618	−	0.803281i
$479$	−27.8885	+	20.2622i	−1.27426	+	0.925804i	−0.999364	−	0.0356697i	$-0.988644\pi$
$479$	−27.8885	+	20.2622i	−1.27426	+	0.925804i	−0.274896	+	0.961474i	$0.588644\pi$
$480$		0			0
$481$	−1.41641	+	4.35926i	−0.0645826	+	0.198765i
$482$	−6.51864	+	8.97214i	−0.296916	+	0.408670i
$483$			0.944272i			0.0429659i
$484$	1.39919	+	10.9106i	0.0635994	+	0.495939i
$485$		0			0
$486$	−7.80902	−	5.67358i	−0.354224	−	0.257359i
$487$	−1.28157	−	0.416408i	−0.0580736	−	0.0188692i	0.279836	−	0.960048i	$-0.409720\pi$
$487$	−1.28157	−	0.416408i	−0.0580736	−	0.0188692i	−0.337910	+	0.941179i	$0.609720\pi$
$488$	−2.35114	+	0.763932i	−0.106431	+	0.0345816i
$489$	0.281153	−	0.204270i	0.0127142	−	0.00923739i
$490$		0			0
$491$	7.06231	+	21.7355i	0.318717	+	0.980911i	0.974197	+	0.225699i	$0.0724664\pi$
$491$	7.06231	+	21.7355i	0.318717	+	0.980911i	−0.655480	+	0.755213i	$0.727534\pi$
$492$	2.04087	+	0.663119i	0.0920095	+	0.0298957i
$493$	1.62460	−	2.23607i	0.0731682	−	0.100707i
$494$	7.23607			0.325566
$495$		0			0
$496$	2.00000			0.0898027
$497$	6.15537	−	8.47214i	0.276106	−	0.380027i
$498$	−3.38795	−	1.10081i	−0.151818	−	0.0493286i
$499$	9.53444	+	29.3440i	0.426820	+	1.31362i	0.901241	+	0.433319i	$0.142658\pi$
$499$	9.53444	+	29.3440i	0.426820	+	1.31362i	−0.474420	+	0.880298i	$0.657342\pi$
$500$		0			0
$501$	4.56231	−	3.31471i	0.203829	−	0.148090i
$502$	−19.9192	+	6.47214i	−0.889037	+	0.288866i
$503$	3.07768	+	1.00000i	0.137227	+	0.0445878i	0.376825	−	0.926284i	$-0.377016\pi$
$503$	3.07768	+	1.00000i	0.137227	+	0.0445878i	−0.239598	+	0.970872i	$0.577016\pi$
$504$	4.61803	+	3.35520i	0.205704	+	0.149452i
$505$		0			0
$506$	−2.70820	+	3.07768i	−0.120394	+	0.136820i
$507$		−	4.38197i		−	0.194610i
$508$	6.43288	−	8.85410i	0.285413	−	0.392837i
$509$	2.56231	−	7.88597i	0.113572	−	0.349539i	−0.878074	−	0.478524i	$-0.841172\pi$
$509$	2.56231	−	7.88597i	0.113572	−	0.349539i	0.991647	+	0.128985i	$0.0411719\pi$
$510$		0			0
$511$	16.7984	−	12.2047i	0.743116	−	0.539906i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	12.4495	−	4.04508i	0.549658	−	0.178595i
$514$	1.73607	−	5.34307i	0.0765747	−	0.235673i
$515$		0			0
$516$	−3.27051			−0.143976
$517$	−8.50651	+	19.7082i	−0.374116	+	0.866766i
$518$		−	7.41641i		−	0.325858i
$519$	6.76393	+	4.91428i	0.296904	+	0.215713i
$520$		0			0
$521$	−6.19098	−	19.0539i	−0.271232	−	0.834766i	−0.990192	−	0.139714i	$-0.955382\pi$
$521$	−6.19098	−	19.0539i	−0.271232	−	0.834766i	0.718960	−	0.695052i	$-0.244618\pi$
$522$	7.50245	+	10.3262i	0.328373	+	0.451967i
$523$	5.40858	+	7.44427i	0.236501	+	0.325515i	0.910726	−	0.413010i	$-0.135523\pi$
$523$	5.40858	+	7.44427i	0.236501	+	0.325515i	−0.674226	+	0.738525i	$0.735523\pi$
$524$	−2.10081	−	6.46564i	−0.0917744	−	0.282453i
$525$		0			0
$526$	18.7984	+	13.6578i	0.819648	+	0.595509i
$527$		−	1.23607i		−	0.0538440i
$528$	−0.277515	−	1.23607i	−0.0120773	−	0.0537930i
$529$	21.4721			0.933571
$530$		0			0
$531$	7.60081	−	23.3929i	0.329847	−	1.01517i
$532$	−11.1352	+	3.61803i	−0.482771	+	0.156862i
$533$	4.08174	+	5.61803i	0.176800	+	0.243344i
$534$	−2.50000	+	1.81636i	−0.108186	+	0.0786014i
$535$		0			0
$536$	3.42705	−	10.5474i	0.148026	−	0.455577i
$537$	−1.93487	+	2.66312i	−0.0834958	+	0.114922i
$538$		−	6.18034i		−	0.266453i
$539$	5.07295	+	8.55951i	0.218507	+	0.368684i
$540$		0			0
$541$	2.52786	+	1.83660i	0.108681	+	0.0789616i	0.640798	−	0.767709i	$-0.278603\pi$
$541$	2.52786	+	1.83660i	0.108681	+	0.0789616i	−0.532117	+	0.846671i	$0.678603\pi$
$542$	1.90211	+	0.618034i	0.0817028	+	0.0265468i
$543$	−1.51860	+	0.493422i	−0.0651693	+	0.0211748i
$544$	−0.500000	+	0.363271i	−0.0214373	+	0.0155751i
$545$		0			0
$546$	−0.291796	−	0.898056i	−0.0124877	−	0.0384332i
$547$	7.91872	+	2.57295i	0.338580	+	0.110011i	0.473372	−	0.880863i	$-0.343037\pi$
$547$	7.91872	+	2.57295i	0.338580	+	0.110011i	−0.134792	+	0.990874i	$0.543037\pi$
$548$	−9.45756	+	13.0172i	−0.404007	+	0.556068i
$549$	−7.05573			−0.301131
$550$		0			0
$551$	−26.1803			−1.11532
$552$	0.277515	−	0.381966i	0.0118118	−	0.0162576i
$553$	25.5195	+	8.29180i	1.08520	+	0.352603i
$554$	7.32624	+	22.5478i	0.311262	+	0.957966i
$555$		0			0
$556$		0			0
$557$	−33.5115	+	10.8885i	−1.41993	+	0.461362i	−0.915579	−	0.402138i	$-0.868267\pi$
$557$	−33.5115	+	10.8885i	−1.41993	+	0.461362i	−0.504348	+	0.863500i	$0.668267\pi$
$558$	5.42882	+	1.76393i	0.229820	+	0.0746732i
$559$	−8.56231	−	6.22088i	−0.362147	−	0.263115i
$560$		0			0
$561$	−0.763932	+	0.171513i	−0.0322532	+	0.00724130i
$562$		−	16.0902i		−	0.678723i
$563$	−0.224514	+	0.309017i	−0.00946214	+	0.0130235i	−0.813722	−	0.581254i	$-0.802562\pi$
$563$	−0.224514	+	0.309017i	−0.00946214	+	0.0130235i	0.804260	+	0.594278i	$0.202562\pi$
$564$	0.763932	−	2.35114i	0.0321673	−	0.0990009i
$565$		0			0
$566$	−19.4164	+	14.1068i	−0.816132	+	0.592955i
$567$	9.06154	+	12.4721i	0.380549	+	0.523780i
$568$	−4.97980	+	1.61803i	−0.208948	+	0.0678912i
$569$	−11.8090	+	36.3444i	−0.495060	+	1.52364i	0.321804	+	0.946806i	$0.395711\pi$
$569$	−11.8090	+	36.3444i	−0.495060	+	1.52364i	−0.816864	+	0.576831i	$0.804289\pi$
$570$		0			0
$571$	−2.47214			−0.103456			−0.0517278	−	0.998661i	$-0.516473\pi$
$571$	−2.47214			−0.103456			−0.0517278	+	0.998661i	$0.516473\pi$
$572$	1.62460	−	3.76393i	0.0679279	−	0.157378i
$573$		−	1.81966i		−	0.0760174i
$574$	−9.09017	−	6.60440i	−0.379416	−	0.275662i
$575$		0			0
$576$	−0.881966	−	2.71441i	−0.0367486	−	0.113101i
$577$	3.99598	+	5.50000i	0.166355	+	0.228968i	0.884053	−	0.467386i	$-0.154804\pi$
$577$	3.99598	+	5.50000i	0.166355	+	0.228968i	−0.717698	+	0.696354i	$0.754804\pi$
$578$	−9.76784	−	13.4443i	−0.406288	−	0.559208i
$579$	−2.05573	−	6.32688i	−0.0854331	−	0.262936i
$580$		0			0
$581$	15.0902	+	10.9637i	0.626046	+	0.454849i
$582$			2.72949i			0.113141i
$583$	−3.80423	−	3.34752i	−0.157555	−	0.138640i
$584$	−10.3820			−0.429609
$585$		0			0
$586$	−8.76393	+	26.9726i	−0.362035	+	1.11423i
$587$	−21.0620	+	6.84346i	−0.869322	+	0.282460i	−0.709517	−	0.704689i	$-0.751087\pi$
$587$	−21.0620	+	6.84346i	−0.869322	+	0.282460i	−0.159805	+	0.987149i	$0.551087\pi$
$588$	−0.673542	−	0.927051i	−0.0277764	−	0.0382309i
$589$	−9.47214	+	6.88191i	−0.390293	+	0.283564i
$590$		0			0
$591$	−2.47214	+	7.60845i	−0.101690	+	0.312970i
$592$	−2.17963	+	3.00000i	−0.0895821	+	0.123299i
$593$			28.6869i			1.17803i	0.808122	+	0.589015i	$0.200484\pi$
$593$			28.6869i			1.17803i	−0.808122	+	0.589015i	$0.799516\pi$
$594$	0.690983	−	7.38394i	0.0283514	−	0.302967i
$595$		0			0
$596$	5.00000	+	3.63271i	0.204808	+	0.148802i
$597$	−6.88191	−	2.23607i	−0.281658	−	0.0915162i
$598$	1.45309	−	0.472136i	0.0594211	−	0.0193071i
$599$	−10.8541	+	7.88597i	−0.443487	+	0.322212i	−0.787019	−	0.616929i	$-0.788377\pi$
$599$	−10.8541	+	7.88597i	−0.443487	+	0.322212i	0.343532	+	0.939141i	$0.388377\pi$
$600$		0			0
$601$	−8.38854	−	25.8173i	−0.342176	−	1.05311i	−0.963078	−	0.269221i	$-0.913234\pi$
$601$	−8.38854	−	25.8173i	−0.342176	−	1.05311i	0.620903	−	0.783888i	$-0.286766\pi$
$602$	16.2865	+	5.29180i	0.663787	+	0.215678i
$603$	18.6049	−	25.6074i	0.757648	−	1.04281i
$604$	8.00000			0.325515
$605$		0			0
$606$	−1.59675			−0.0648634
$607$	13.5923	−	18.7082i	0.551695	−	0.759343i	−0.438546	−	0.898709i	$-0.644506\pi$
$607$	13.5923	−	18.7082i	0.551695	−	0.759343i	0.990241	+	0.139366i	$0.0445065\pi$
$608$	5.56758	+	1.80902i	0.225795	+	0.0733653i
$609$	1.05573	+	3.24920i	0.0427803	+	0.131664i
$610$		0			0
$611$	6.47214	−	4.70228i	0.261835	−	0.190234i
$612$	−1.67760	+	0.545085i	−0.0678129	+	0.0220338i
$613$	−33.9605	−	11.0344i	−1.37165	−	0.445677i	−0.471736	−	0.881740i	$-0.656373\pi$
$613$	−33.9605	−	11.0344i	−1.37165	−	0.445677i	−0.899916	+	0.436063i	$0.856373\pi$
$614$	22.4894	+	16.3395i	0.907597	+	0.659408i
$615$		0			0
$616$	−0.618034	+	6.60440i	−0.0249013	+	0.266099i
$617$			23.4508i			0.944096i	0.881573	+	0.472048i	$0.156485\pi$
$617$			23.4508i			0.944096i	−0.881573	+	0.472048i	$0.843515\pi$
$618$	−3.52671	+	4.85410i	−0.141865	+	0.195261i
$619$	−1.60739	+	4.94704i	−0.0646065	+	0.198838i	−0.978149	−	0.207905i	$-0.933336\pi$
$619$	−1.60739	+	4.94704i	−0.0646065	+	0.198838i	0.913543	+	0.406743i	$0.133336\pi$
$620$		0			0
$621$	2.23607	−	1.62460i	0.0897303	−	0.0651929i
$622$	−15.3229	−	21.0902i	−0.614393	−	0.845639i
$623$	15.3884	−	5.00000i	0.616524	−	0.200321i
$624$	−0.145898	+	0.449028i	−0.00584060	+	0.0179755i
$625$		0			0
$626$	4.32624			0.172911
$627$	5.56758	+	4.89919i	0.222348	+	0.195655i
$628$		−	9.70820i		−	0.387400i
$629$	1.85410	+	1.34708i	0.0739279	+	0.0537118i
$630$		0			0
$631$	7.32624	+	22.5478i	0.291653	+	0.897615i	0.984325	+	0.176363i	$0.0564332\pi$
$631$	7.32624	+	22.5478i	0.291653	+	0.897615i	−0.692672	+	0.721252i	$0.743567\pi$
$632$	−7.88597	−	10.8541i	−0.313687	−	0.431753i
$633$	−1.36733	−	1.88197i	−0.0543464	−	0.0748014i
$634$	1.14590	+	3.52671i	0.0455094	+	0.140064i
$635$		0			0
$636$	0.472136	+	0.343027i	0.0187214	+	0.0136019i
$637$		−	3.70820i		−	0.146924i
$638$	−5.87785	+	13.6180i	−0.232706	+	0.539143i
$639$	−14.9443			−0.591186
$640$		0			0
$641$	5.15248	−	15.8577i	0.203511	−	0.626341i	−0.796261	−	0.604954i	$-0.793192\pi$
$641$	5.15248	−	15.8577i	0.203511	−	0.626341i	0.999771	−	0.0213875i	$-0.00680836\pi$
$642$	0.416272	−	0.135255i	0.0164289	−	0.00533809i
$643$	23.4989	+	32.3435i	0.926706	+	1.27550i	0.961131	+	0.276094i	$0.0890402\pi$
$643$	23.4989	+	32.3435i	0.926706	+	1.27550i	−0.0344245	+	0.999407i	$0.510960\pi$
$644$	−2.00000	+	1.45309i	−0.0788110	+	0.0572596i
$645$		0			0
$646$	1.11803	−	3.44095i	0.0439885	−	0.135383i
$647$	17.0785	−	23.5066i	0.671426	−	0.924139i	−0.328365	−	0.944551i	$-0.606498\pi$
$647$	17.0785	−	23.5066i	0.671426	−	0.924139i	0.999792	+	0.0204118i	$0.00649774\pi$
$648$		−	7.70820i		−	0.302807i
$649$	27.8885	−	6.26137i	1.09472	−	0.245780i
$650$		0			0
$651$	1.23607	+	0.898056i	0.0484453	+	0.0351976i
$652$	0.865300	+	0.281153i	0.0338878	+	0.0110108i
$653$	−14.5964	+	4.74265i	−0.571200	+	0.185594i	−0.580354	−	0.814364i	$-0.697086\pi$
$653$	−14.5964	+	4.74265i	−0.571200	+	0.185594i	0.00915459	+	0.999958i	$0.497086\pi$
$654$	5.85410	−	4.25325i	0.228914	−	0.166315i
$655$		0			0
$656$	1.73607	+	5.34307i	0.0677821	+	0.208612i
$657$	−28.1809	−	9.15654i	−1.09944	−	0.357231i
$658$	−7.60845	+	10.4721i	−0.296608	+	0.408246i
$659$	16.9098			0.658713			0.329357	−	0.944206i	$-0.393168\pi$
$659$	16.9098			0.658713			0.329357	+	0.944206i	$0.393168\pi$
$660$		0			0
$661$	−3.52786			−0.137218			−0.0686090	−	0.997644i	$-0.521856\pi$
$661$	−3.52786			−0.137218			−0.0686090	+	0.997644i	$0.521856\pi$
$662$	3.68571	−	5.07295i	0.143249	−	0.197166i
$663$	0.277515	+	0.0901699i	0.0107778	+	0.00350191i
$664$	−2.88197	−	8.86978i	−0.111842	−	0.344214i
$665$		0			0
$666$	−8.56231	+	6.22088i	−0.331783	+	0.241054i
$667$	−5.25731	+	1.70820i	−0.203564	+	0.0661419i
$668$	14.0413	+	4.56231i	0.543276	+	0.176521i
$669$	7.94427	+	5.77185i	0.307143	+	0.223153i
$670$		0			0
$671$	−4.18034	−	7.05342i	−0.161380	−	0.272294i
$672$		−	0.763932i		−	0.0294693i
$673$	−5.79210	+	7.97214i	−0.223269	+	0.307303i	−0.905926	−	0.423435i	$-0.860824\pi$
$673$	−5.79210	+	7.97214i	−0.223269	+	0.307303i	0.682657	+	0.730738i	$0.260824\pi$
$674$	8.28115	−	25.4868i	0.318978	−	0.981714i
$675$		0			0
$676$	9.28115	−	6.74315i	0.356967	−	0.259352i
$677$	8.44100	+	11.6180i	0.324414	+	0.446517i	0.939808	−	0.341702i	$-0.111003\pi$
$677$	8.44100	+	11.6180i	0.324414	+	0.446517i	−0.615395	+	0.788219i	$0.711003\pi$
$678$	−0.673542	+	0.218847i	−0.0258672	+	0.00840477i
$679$	4.41641	−	13.5923i	0.169486	−	0.521625i
$680$		0			0
$681$	5.54102			0.212332
$682$	1.45309	+	6.47214i	0.0556415	+	0.247831i
$683$		−	18.4721i		−	0.706817i	−0.935469	−	0.353408i	$-0.885023\pi$
$683$		−	18.4721i		−	0.706817i	0.935469	−	0.353408i	$-0.114977\pi$
$684$	13.5172	+	9.82084i	0.516844	+	0.375509i
$685$		0			0
$686$	6.18034	+	19.0211i	0.235966	+	0.726230i
$687$	−0.383516	−	0.527864i	−0.0146320	−	0.0201393i
$688$	−5.03280	−	6.92705i	−0.191874	−	0.264091i
$689$	0.583592	+	1.79611i	0.0222331	+	0.0684264i
$690$		0			0
$691$	21.2082	+	15.4087i	0.806798	+	0.586173i	0.912901	−	0.408182i	$-0.133837\pi$
$691$	21.2082	+	15.4087i	0.806798	+	0.586173i	−0.106102	+	0.994355i	$0.533837\pi$
$692$			21.8885i			0.832078i
$693$	−7.50245	+	17.3820i	−0.284995	+	0.660286i
$694$	−16.6180			−0.630812
$695$		0			0
$696$	0.527864	−	1.62460i	0.0200086	−	0.0615802i
$697$	3.30220	−	1.07295i	0.125080	−	0.0406408i
$698$	−11.5187	−	15.8541i	−0.435988	−	0.600087i
$699$	−2.97214	+	2.15938i	−0.112417	+	0.0816754i
$700$		0			0
$701$	−4.58359	+	14.1068i	−0.173120	+	0.532808i	−0.999543	−	0.0302419i	$-0.990372\pi$
$701$	−4.58359	+	14.1068i	−0.173120	+	0.532808i	0.826423	+	0.563050i	$0.190372\pi$
$702$	−1.62460	+	2.23607i	−0.0613165	+	0.0843949i
$703$		−	21.7082i		−	0.818740i
$704$	2.19098	−	2.48990i	0.0825758	−	0.0938416i
$705$		0			0
$706$	−26.3885	−	19.1724i	−0.993146	−	0.721563i
$707$	7.95148	+	2.58359i	0.299046	+	0.0971660i
$708$	−3.13068	+	1.01722i	−0.117658	+	0.0382295i
$709$	19.7984	−	14.3844i	0.743544	−	0.540216i	−0.150275	−	0.988644i	$-0.548016\pi$
$709$	19.7984	−	14.3844i	0.743544	−	0.540216i	0.893819	+	0.448428i	$0.148016\pi$
$710$		0			0
$711$	−11.8328	−	36.4177i	−0.443765	−	1.36577i
$712$	−7.69421	−	2.50000i	−0.288353	−	0.0936915i
$713$	−1.45309	+	2.00000i	−0.0544185	+	0.0749006i
$714$	−0.472136			−0.0176692
$715$		0			0
$716$	−8.61803			−0.322071
$717$	−4.87380	+	6.70820i	−0.182015	+	0.250522i
$718$	−4.87380	−	1.58359i	−0.181888	−	0.0590991i
$719$	−8.29180	−	25.5195i	−0.309232	−	0.951718i	−0.978064	−	0.208304i	$-0.933206\pi$
$719$	−8.29180	−	25.5195i	−0.309232	−	0.951718i	0.668832	−	0.743413i	$-0.266794\pi$
$720$		0			0
$721$	25.4164	−	18.4661i	0.946556	−	0.687714i
$722$	−14.5231	+	4.71885i	−0.540494	+	0.175617i
$723$	4.02874	+	1.30902i	0.149830	+	0.0486829i
$724$	−3.38197	−	2.45714i	−0.125690	−	0.0913190i
$725$		0			0
$726$	3.79837	−	1.79611i	0.140971	−	0.0666600i
$727$			2.87539i			0.106642i	0.998577	+	0.0533211i	$0.0169807\pi$
$727$			2.87539i			0.106642i	−0.998577	+	0.0533211i	$0.983019\pi$
$728$	1.45309	−	2.00000i	0.0538549	−	0.0741249i
$729$	6.00658	−	18.4863i	0.222466	−	0.684679i
$730$		0			0
$731$	−4.28115	+	3.11044i	−0.158344	+	0.115044i
$732$	0.555029	+	0.763932i	0.0205145	+	0.0282357i
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	−0.469699	−	0.882827i	$-0.655637\pi$
$733$	−8.95554	+	2.90983i	−0.330780	+	0.107477i	0.138918	+	0.990304i	$0.455637\pi$
$734$	−6.09017	+	18.7436i	−0.224792	+	0.691839i
$735$		0			0
$736$	1.23607			0.0455621
$737$	36.6219	+	3.42705i	1.34899	+	0.126237i
$738$			16.0344i			0.590236i
$739$	−30.3885	−	22.0786i	−1.11786	−	0.812173i	−0.133977	−	0.990984i	$-0.542775\pi$
$739$	−30.3885	−	22.0786i	−1.11786	−	0.812173i	−0.983883	+	0.178811i	$0.942775\pi$
$740$		0			0
$741$	−0.854102	−	2.62866i	−0.0313762	−	0.0965661i
$742$	−1.79611	−	2.47214i	−0.0659373	−	0.0907550i
$743$	−5.15131	−	7.09017i	−0.188983	−	0.260113i	0.704003	−	0.710197i	$-0.251394\pi$
$743$	−5.15131	−	7.09017i	−0.188983	−	0.260113i	−0.892986	+	0.450084i	$0.851394\pi$
$744$	−0.236068	−	0.726543i	−0.00865467	−	0.0266363i
$745$		0			0
$746$	3.47214	+	2.52265i	0.127124	+	0.0923609i
$747$		−	26.6180i		−	0.973903i
$748$	−1.53884	−	1.35410i	−0.0562656	−	0.0495109i
$749$	−2.29180			−0.0837404
$750$		0			0
$751$	−10.4377	+	32.1239i	−0.380877	+	1.17222i	0.558551	+	0.829470i	$0.311358\pi$
$751$	−10.4377	+	32.1239i	−0.380877	+	1.17222i	−0.939427	+	0.342748i	$0.888642\pi$
$752$	6.15537	−	2.00000i	0.224463	−	0.0729325i
$753$	4.70228	+	6.47214i	0.171361	+	0.235858i
$754$	4.47214	−	3.24920i	0.162866	−	0.118329i
$755$		0			0
$756$	1.38197	−	4.25325i	0.0502616	−	0.154689i
$757$	−1.55909	+	2.14590i	−0.0566660	+	0.0779940i	−0.836410	−	0.548105i	$-0.815349\pi$
$757$	−1.55909	+	2.14590i	−0.0566660	+	0.0779940i	0.779744	+	0.626099i	$0.215349\pi$
$758$		−	14.2705i		−	0.518328i
$759$	1.43769	+	0.620541i	0.0521850	+	0.0225242i
$760$		0			0
$761$	3.44427	+	2.50241i	0.124855	+	0.0907123i	0.648460	−	0.761249i	$-0.275413\pi$
$761$	3.44427	+	2.50241i	0.124855	+	0.0907123i	−0.523605	+	0.851961i	$0.675413\pi$
$762$	−3.97574	−	1.29180i	−0.144026	−	0.0467968i
$763$	−36.0341	+	11.7082i	−1.30452	+	0.423865i
$764$	3.85410	−	2.80017i	0.139437	−	0.101307i
$765$		0			0
$766$	−8.76393	−	26.9726i	−0.316654	−	0.974560i
$767$	−10.1311	−	3.29180i	−0.365813	−	0.118860i
$768$	−0.224514	+	0.309017i	−0.00810145	+	0.0111507i
$769$	−13.4164			−0.483808			−0.241904	−	0.970300i	$-0.577772\pi$
$769$	−13.4164			−0.483808			−0.241904	+	0.970300i	$0.577772\pi$
$770$		0			0
$771$	−2.14590			−0.0772826
$772$	10.2371	−	14.0902i	0.368442	−	0.507116i
$773$	3.69822	+	1.20163i	0.133016	+	0.0432195i	0.374768	−	0.927118i	$-0.377722\pi$
$773$	3.69822	+	1.20163i	0.133016	+	0.0432195i	−0.241753	+	0.970338i	$0.577722\pi$
$774$	−7.55166	−	23.2416i	−0.271439	−	0.835403i
$775$		0			0
$776$	−5.78115	+	4.20025i	−0.207531	+	0.150780i
$777$	−2.69417	+	0.875388i	−0.0966527	+	0.0314044i
$778$	10.1311	+	3.29180i	0.363218	+	0.118017i
$779$	−26.6074	−	19.3314i	−0.953309	−	0.692619i
$780$		0			0
$781$	−8.85410	−	14.9394i	−0.316825	−	0.534573i
$782$		−	0.763932i		−	0.0273182i
$783$	5.87785	−	8.09017i	0.210057	−	0.289119i
$784$	0.927051	−	2.85317i	0.0331090	−	0.101899i
$785$		0			0
$786$	−2.10081	+	1.52633i	−0.0749335	+	0.0544424i
$787$	−15.4087	−	21.2082i	−0.549259	−	0.755991i	0.440652	−	0.897678i	$-0.354747\pi$
$787$	−15.4087	−	21.2082i	−0.549259	−	0.755991i	−0.989911	+	0.141687i	$0.954747\pi$
$788$	−19.9192	+	6.47214i	−0.709592	+	0.230560i
$789$	2.74265	−	8.44100i	0.0976408	−	0.300507i
$790$		0			0
$791$	3.70820			0.131849
$792$	8.14324	−	4.82624i	0.289357	−	0.171493i
$793$			3.05573i			0.108512i
$794$	−13.8541	−	10.0656i	−0.491664	−	0.357215i
$795$		0			0
$796$	−5.85410	−	18.0171i	−0.207493	−	0.638598i
$797$	14.5559	+	20.0344i	0.515596	+	0.709656i	0.984850	−	0.173406i	$-0.0554774\pi$
$797$	14.5559	+	20.0344i	0.515596	+	0.709656i	−0.469255	+	0.883063i	$0.655477\pi$
$798$	2.62866	+	3.61803i	0.0930534	+	0.128077i
$799$	−1.23607	−	3.80423i	−0.0437289	−	0.134584i
$800$		0			0
$801$	−18.6803	−	13.5721i	−0.660037	−	0.479545i
$802$		−	17.7984i		−	0.628482i
$803$	−7.54294	−	33.5967i	−0.266185	−	1.18560i
$804$	−4.23607			−0.149395
$805$		0			0
$806$	0.763932	−	2.35114i	0.0269084	−	0.0828154i
$807$	−2.24514	+	0.729490i	−0.0790327	+	0.0256793i
$808$	−2.45714	−	3.38197i	−0.0864420	−	0.118977i
$809$	13.6803	−	9.93935i	0.480975	−	0.349449i	−0.320728	−	0.947171i	$-0.603928\pi$
$809$	13.6803	−	9.93935i	0.480975	−	0.349449i	0.801703	+	0.597722i	$0.203928\pi$
$810$		0			0
$811$	2.59017	−	7.97172i	0.0909532	−	0.279925i	−0.895225	−	0.445615i	$-0.852985\pi$
$811$	2.59017	−	7.97172i	0.0909532	−	0.279925i	0.986178	+	0.165690i	$0.0529851\pi$
$812$	−5.25731	+	7.23607i	−0.184495	+	0.253936i
$813$		−	0.763932i		−	0.0267923i
$814$	−11.2918	−	4.87380i	−0.395777	−	0.170826i
$815$		0			0
$816$	0.190983	+	0.138757i	0.00668574	+	0.00485748i
$817$	47.6713	+	15.4894i	1.66781	+	0.541904i
$818$	−12.7598	+	4.14590i	−0.446135	+	0.144958i
$819$	5.70820	−	4.14725i	0.199461	−	0.144917i
$820$		0			0
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	0.969426	+	0.245386i	$0.0789145\pi$
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	−0.640048	+	0.768335i	$0.721085\pi$
$822$	5.84510	+	1.89919i	0.203871	+	0.0662418i
$823$	−13.8698	+	19.0902i	−0.483472	+	0.665441i	−0.979167	−	0.203055i	$-0.934913\pi$
$823$	−13.8698	+	19.0902i	−0.483472	+	0.665441i	0.495696	+	0.868496i	$0.334913\pi$
$824$	−15.7082			−0.547221
$825$		0			0
$826$	17.2361			0.599720
$827$	23.1481	−	31.8607i	0.804940	−	1.10790i	−0.187145	−	0.982332i	$-0.559923\pi$
$827$	23.1481	−	31.8607i	0.804940	−	1.10790i	0.992085	−	0.125572i	$-0.0400766\pi$
$828$	3.35520	+	1.09017i	0.116601	+	0.0378860i
$829$	−9.59675	−	29.5358i	−0.333309	−	1.02582i	−0.967549	−	0.252683i	$-0.918687\pi$
$829$	−9.59675	−	29.5358i	−0.333309	−	1.02582i	0.634240	−	0.773136i	$-0.281313\pi$
$830$		0			0
$831$	7.32624	−	5.32282i	0.254144	−	0.184647i
$832$	−1.17557	+	0.381966i	−0.0407556	+	0.0132423i
$833$	−1.76336	−	0.572949i	−0.0610967	−	0.0198515i
$834$		0			0
$835$		0			0
$836$	−1.80902	+	19.3314i	−0.0625662	+	0.668590i
$837$		−	4.47214i		−	0.154580i
$838$	6.37988	−	8.78115i	0.220389	−	0.303340i
$839$	−3.74265	+	11.5187i	−0.129210	+	0.397669i	−0.994645	−	0.103354i	$-0.967043\pi$
$839$	−3.74265	+	11.5187i	−0.129210	+	0.397669i	0.865434	+	0.501023i	$0.167043\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	18.4661	+	25.4164i	0.636384	+	0.875907i
$843$	−5.84510	+	1.89919i	−0.201316	+	0.0654115i
$844$	1.88197	−	5.79210i	0.0647799	−	0.199372i
$845$		0			0
$846$	18.4721			0.635085
$847$	−21.8213	+	2.79837i	−0.749789	+	0.0961533i
$848$			1.52786i			0.0524671i
$849$	7.41641	+	5.38834i	0.254530	+	0.184927i
$850$		0			0
$851$	−1.41641	−	4.35926i	−0.0485538	−	0.149433i
$852$	1.17557	+	1.61803i	0.0402744	+	0.0554329i
$853$	−17.9111	−	24.6525i	−0.613263	−	0.844085i	0.383577	−	0.923509i	$-0.374692\pi$
$853$	−17.9111	−	24.6525i	−0.613263	−	0.844085i	−0.996841	+	0.0794240i	$0.974692\pi$
$854$	−1.52786	−	4.70228i	−0.0522824	−	0.160909i
$855$		0			0
$856$	0.927051	+	0.673542i	0.0316860	+	0.0230212i
$857$		−	10.7426i		−	0.366962i	−0.983023	−	0.183481i	$-0.941263\pi$
$857$		−	10.7426i		−	0.366962i	0.983023	−	0.183481i	$-0.0587365\pi$
$858$	−1.55909	−	0.145898i	−0.0532263	−	0.00498088i
$859$	−46.5066			−1.58678			−0.793392	−	0.608711i	$-0.791687\pi$
$859$	−46.5066			−1.58678			−0.793392	+	0.608711i	$0.791687\pi$
$860$		0			0
$861$	−1.32624	+	4.08174i	−0.0451981	+	0.139105i
$862$	16.1150	−	5.23607i	0.548878	−	0.178341i
$863$	−19.5357	−	26.8885i	−0.665002	−	0.915297i	0.334632	−	0.942349i	$-0.391388\pi$
$863$	−19.5357	−	26.8885i	−0.665002	−	0.915297i	−0.999634	+	0.0270522i	$0.991388\pi$
$864$	−1.80902	+	1.31433i	−0.0615440	+	0.0447143i
$865$		0			0
$866$	8.57295	−	26.3848i	0.291321	−	0.896593i
$867$	−3.73098	+	5.13525i	−0.126711	+	0.174402i
$868$			4.00000i			0.135769i
$869$	29.3951	−	33.4055i	0.997161	−	1.13320i
$870$		0			0
$871$	−11.0902	−	8.05748i	−0.375776	−	0.273017i
$872$	18.0171	+	5.85410i	0.610135	+	0.198245i
$873$	−19.3969	+	6.30244i	−0.656486	+	0.213305i
$874$	−5.85410	+	4.25325i	−0.198018	+	0.143868i
$875$		0			0
$876$	1.22542	+	3.77147i	0.0414033	+	0.127426i
$877$	−26.8011	−	8.70820i	−0.905009	−	0.294055i	−0.180706	−	0.983537i	$-0.557838\pi$
$877$	−26.8011	−	8.70820i	−0.905009	−	0.294055i	−0.724303	+	0.689482i	$0.757838\pi$
$878$	3.86974	−	5.32624i	0.130597	−	0.179752i
$879$	10.8328			0.365382
$880$		0			0
$881$	−46.3394			−1.56121			−0.780607	−	0.625022i	$-0.785090\pi$
$881$	−46.3394			−1.56121			−0.780607	+	0.625022i	$0.785090\pi$
$882$	5.03280	−	6.92705i	0.169463	−	0.233246i
$883$	3.26944	+	1.06231i	0.110025	+	0.0357494i	0.363512	−	0.931589i	$-0.381577\pi$
$883$	3.26944	+	1.06231i	0.110025	+	0.0357494i	−0.253487	+	0.967339i	$0.581577\pi$
$884$	0.236068	+	0.726543i	0.00793983	+	0.0244363i
$885$		0			0
$886$	6.92705	−	5.03280i	0.232719	−	0.169080i
$887$	35.9281	−	11.6738i	1.20635	−	0.391967i	0.364256	−	0.931299i	$-0.381323\pi$
$887$	35.9281	−	11.6738i	1.20635	−	0.391967i	0.842093	+	0.539332i	$0.181323\pi$
$888$	1.34708	+	0.437694i	0.0452052	+	0.0146881i
$889$	17.7082	+	12.8658i	0.593914	+	0.431504i
$890$		0			0
$891$	24.9443	−	5.60034i	0.835665	−	0.187618i
$892$			25.7082i			0.860774i
$893$	−22.2703	+	30.6525i	−0.745248	+	1.02575i
$894$	0.729490	−	2.24514i	0.0243978	−	0.0750887i
$895$		0			0
$896$	1.61803	−	1.17557i	0.0540547	−	0.0392731i
$897$	−0.343027	−	0.472136i	−0.0114533	−	0.0157642i
$898$	8.81678	−	2.86475i	0.294220	−	0.0955978i
$899$	−2.76393	+	8.50651i	−0.0921823	+	0.283708i
$900$		0			0
$901$	0.944272			0.0314583
$902$	−16.0292	+	9.50000i	−0.533714	+	0.316315i
$903$		−	6.54102i		−	0.217672i
$904$	−1.50000	−	1.08981i	−0.0498893	−	0.0362467i
$905$		0			0
$906$	−0.944272	−	2.90617i	−0.0313713	−	0.0965510i
$907$	−6.13512	−	8.44427i	−0.203713	−	0.280387i	0.694921	−	0.719086i	$-0.255439\pi$
$907$	−6.13512	−	8.44427i	−0.203713	−	0.280387i	−0.898634	+	0.438699i	$0.855439\pi$
$908$	8.52675	+	11.7361i	0.282970	+	0.389475i
$909$	−3.68692	−	11.3472i	−0.122287	−	0.376362i
$910$		0			0
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	0.316842	−	0.948478i	$-0.397377\pi$
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	−0.804147	+	0.594431i	$0.797377\pi$
$912$		−	2.23607i		−	0.0740436i
$913$	26.6093	−	15.7705i	0.880641	−	0.521928i
$914$	9.43769			0.312171
$915$		0			0
$916$	0.527864	−	1.62460i	0.0174411	−	0.0536782i
$917$	12.9313	−	4.20163i	0.427028	−	0.138750i
$918$	0.812299	+	1.11803i	0.0268099	+	0.0369006i
$919$	35.1246	−	25.5195i	1.15865	−	0.841811i	0.169047	−	0.985608i	$-0.445931\pi$
$919$	35.1246	−	25.5195i	1.15865	−	0.841811i	0.989607	+	0.143797i	$0.0459311\pi$
$920$		0			0
$921$	3.28115	−	10.0984i	0.108118	−	0.332752i
$922$	0.792055	−	1.09017i	0.0260849	−	0.0359028i
$923$			6.47214i			0.213033i
$924$	2.47214	−	0.555029i	0.0813273	−	0.0182591i
$925$		0			0
$926$	15.7082	+	11.4127i	0.516204	+	0.375044i
$927$	−42.6385	−	13.8541i	−1.40043	−	0.455028i
$928$	4.25325	−	1.38197i	0.139620	−	0.0453653i
$929$	−13.1525	+	9.55583i	−0.431519	+	0.313517i	−0.782256	−	0.622957i	$-0.785931\pi$
$929$	−13.1525	+	9.55583i	−0.431519	+	0.313517i	0.350737	+	0.936474i	$0.385931\pi$
$930$		0			0
$931$	5.42705	+	16.7027i	0.177864	+	0.547410i
$932$	−9.14729	−	2.97214i	−0.299630	−	0.0973556i
$933$	−5.85283	+	8.05573i	−0.191613	+	0.263733i
$934$	33.3050			1.08977
$935$		0			0
$936$	−3.52786			−0.115312
$937$	−22.2501	+	30.6246i	−0.726879	+	1.00046i	0.272389	+	0.962187i	$0.412186\pi$
$937$	−22.2501	+	30.6246i	−0.726879	+	1.00046i	−0.999267	+	0.0382752i	$0.987814\pi$
$938$	21.0948	+	6.85410i	0.688768	+	0.223794i
$939$	−0.510643	−	1.57160i	−0.0166642	−	0.0512872i
$940$		0			0
$941$	−38.9787	+	28.3197i	−1.27067	+	0.923196i	−0.999229	−	0.0392595i	$-0.987500\pi$
$941$	−38.9787	+	28.3197i	−1.27067	+	0.923196i	−0.271441	+	0.962455i	$0.587500\pi$
$942$	−3.52671	+	1.14590i	−0.114906	+	0.0373354i
$943$	−6.60440	−	2.14590i	−0.215069	−	0.0698801i
$944$	−6.97214	−	5.06555i	−0.226924	−	0.164870i
$945$		0			0
$946$	18.7599	−	21.3193i	0.609936	−	0.693149i
$947$		−	30.2148i		−	0.981848i	−0.871202	−	0.490924i	$-0.836659\pi$
$947$		−	30.2148i		−	0.981848i	0.871202	−	0.490924i	$-0.163341\pi$
$948$	−3.01217	+	4.14590i	−0.0978308	+	0.134653i
$949$	−3.96556	+	12.2047i	−0.128727	+	0.396182i
$950$		0			0
$951$	1.14590	−	0.832544i	0.0371583	−	0.0269971i
$952$	−0.726543	−	1.00000i	−0.0235474	−	0.0324102i
$953$	−10.7719	+	3.50000i	−0.348936	+	0.113376i	−0.478241	−	0.878229i	$-0.658725\pi$
$953$	−10.7719	+	3.50000i	−0.348936	+	0.113376i	0.129305	+	0.991605i	$0.458725\pi$
$954$	−1.34752	+	4.14725i	−0.0436277	+	0.134272i
$955$		0			0
$956$	−21.7082			−0.702093
$957$	5.64083	+	0.527864i	0.182342	+	0.0170634i
$958$			34.4721i			1.11374i
$959$	−26.0344	−	18.9151i	−0.840696	−	0.610801i
$960$		0			0
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	2.69417	+	3.70820i	0.0868635	+	0.119557i
$963$	1.92236	+	2.64590i	0.0619471	+	0.0852629i
$964$	3.42705	+	10.5474i	0.110378	+	0.339708i
$965$		0			0
$966$	0.763932	+	0.555029i	0.0245791	+	0.0178578i
$967$			38.0000i			1.22200i	0.791632	+	0.610999i	$0.209232\pi$
$967$			38.0000i			1.22200i	−0.791632	+	0.610999i	$0.790768\pi$
$968$	9.64932	+	5.28115i	0.310141	+	0.169743i
$969$	−1.38197			−0.0443951
$970$		0			0
$971$	−3.12461	+	9.61657i	−0.100274	+	0.308610i	−0.988592	−	0.150617i	$-0.951874\pi$
$971$	−3.12461	+	9.61657i	−0.100274	+	0.308610i	0.888319	+	0.459228i	$0.151874\pi$
$972$	−9.18005	+	2.98278i	−0.294450	+	0.0956727i
$973$		0			0
$974$	−1.09017	+	0.792055i	−0.0349313	+	0.0253791i
$975$		0			0
$976$	−0.763932	+	2.35114i	−0.0244529	+	0.0752582i
$977$	−25.4540	+	35.0344i	−0.814346	+	1.12085i	0.176292	+	0.984338i	$0.443590\pi$
$977$	−25.4540	+	35.0344i	−0.814346	+	1.12085i	−0.990638	+	0.136513i	$0.956410\pi$
$978$		−	0.347524i		−	0.0111126i
$979$	2.50000	−	26.7153i	0.0799003	−	0.853826i
$980$		0			0
$981$	43.7426	+	31.7809i	1.39660	+	1.01469i
$982$	21.7355	+	7.06231i	0.693609	+	0.225367i
$983$	−5.70634	+	1.85410i	−0.182004	+	0.0591367i	−0.398601	−	0.917124i	$-0.630504\pi$
$983$	−5.70634	+	1.85410i	−0.182004	+	0.0591367i	0.216597	+	0.976261i	$0.430504\pi$
$984$	1.73607	−	1.26133i	0.0553438	−	0.0402096i
$985$		0			0
$986$	−0.854102	−	2.62866i	−0.0272001	−	0.0837134i
$987$	4.70228	+	1.52786i	0.149675	+	0.0486324i
$988$	4.25325	−	5.85410i	0.135314	−	0.186244i
$989$	10.5836			0.336539
$990$		0			0
$991$	30.5410			0.970167			0.485084	−	0.874468i	$-0.338789\pi$
$991$	30.5410			0.970167			0.485084	+	0.874468i	$0.338789\pi$
$992$	1.17557	−	1.61803i	0.0373244	−	0.0513726i
$993$	−2.27790	−	0.740133i	−0.0722868	−	0.0234874i
$994$	−3.23607	−	9.95959i	−0.102642	−	0.315899i
$995$		0			0
$996$	−2.88197	+	2.09387i	−0.0913186	+	0.0663468i
$997$	−8.22899	+	2.67376i	−0.260615	+	0.0846789i	−0.436410	−	0.899748i	$-0.643750\pi$
$997$	−8.22899	+	2.67376i	−0.260615	+	0.0846789i	0.175795	+	0.984427i	$0.443750\pi$
$998$	29.3440	+	9.53444i	0.928868	+	0.301807i
$999$	6.70820	+	4.87380i	0.212238	+	0.154200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.c.499.2		8
5.2	odd	4		550.2.h.h.301.1		4
5.3	odd	4		22.2.c.a.15.1	yes	4
5.4	even	2	inner	550.2.ba.c.499.1		8
11.3	even	5	inner	550.2.ba.c.399.1		8
15.8	even	4		198.2.f.e.37.1		4
20.3	even	4		176.2.m.c.81.1		4
40.3	even	4		704.2.m.a.257.1		4
40.13	odd	4		704.2.m.h.257.1		4
55.3	odd	20		22.2.c.a.3.1	✓	4
55.8	even	20		242.2.c.c.3.1		4
55.13	even	20		242.2.c.d.27.1		4
55.14	even	10	inner	550.2.ba.c.399.2		8
55.17	even	20		6050.2.a.ci.1.2		2
55.18	even	20		242.2.c.d.9.1		4
55.27	odd	20		6050.2.a.bs.1.2		2
55.28	even	20		242.2.a.d.1.1		2
55.38	odd	20		242.2.a.f.1.1		2
55.43	even	4		242.2.c.c.81.1		4
55.47	odd	20		550.2.h.h.201.1		4
55.48	odd	20		242.2.c.a.9.1		4
55.53	odd	20		242.2.c.a.27.1		4
165.38	even	20		2178.2.a.p.1.1		2
165.83	odd	20		2178.2.a.x.1.1		2
165.113	even	20		198.2.f.e.91.1		4
220.3	even	20		176.2.m.c.113.1		4
220.83	odd	20		1936.2.a.n.1.2		2
220.203	even	20		1936.2.a.o.1.2		2
440.3	even	20		704.2.m.a.641.1		4
440.83	odd	20		7744.2.a.cy.1.1		2
440.93	odd	20		7744.2.a.bm.1.2		2
440.203	even	20		7744.2.a.cz.1.1		2
440.333	odd	20		704.2.m.h.641.1		4
440.413	even	20		7744.2.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.3.1	✓	4	55.3	odd	20
22.2.c.a.15.1	yes	4	5.3	odd	4
176.2.m.c.81.1		4	20.3	even	4
176.2.m.c.113.1		4	220.3	even	20
198.2.f.e.37.1		4	15.8	even	4
198.2.f.e.91.1		4	165.113	even	20
242.2.a.d.1.1		2	55.28	even	20
242.2.a.f.1.1		2	55.38	odd	20
242.2.c.a.9.1		4	55.48	odd	20
242.2.c.a.27.1		4	55.53	odd	20
242.2.c.c.3.1		4	55.8	even	20
242.2.c.c.81.1		4	55.43	even	4
242.2.c.d.9.1		4	55.18	even	20
242.2.c.d.27.1		4	55.13	even	20
550.2.h.h.201.1		4	55.47	odd	20
550.2.h.h.301.1		4	5.2	odd	4
550.2.ba.c.399.1		8	11.3	even	5	inner
550.2.ba.c.399.2		8	55.14	even	10	inner
550.2.ba.c.499.1		8	5.4	even	2	inner
550.2.ba.c.499.2		8	1.1	even	1	trivial
704.2.m.a.257.1		4	40.3	even	4
704.2.m.a.641.1		4	440.3	even	20
704.2.m.h.257.1		4	40.13	odd	4
704.2.m.h.641.1		4	440.333	odd	20
1936.2.a.n.1.2		2	220.83	odd	20
1936.2.a.o.1.2		2	220.203	even	20
2178.2.a.p.1.1		2	165.38	even	20
2178.2.a.x.1.1		2	165.83	odd	20
6050.2.a.bs.1.2		2	55.27	odd	20
6050.2.a.ci.1.2		2	55.17	even	20
7744.2.a.bm.1.2		2	440.93	odd	20
7744.2.a.bn.1.2		2	440.413	even	20
7744.2.a.cy.1.1		2	440.83	odd	20
7744.2.a.cz.1.1		2	440.203	even	20

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.363271 - 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(1.90211 - 0.618034i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.363271 - 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(1.90211 - 0.618034i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(0.309017 - 3.30220i) q^{11} +0.381966i q^{12} +(-0.726543 + 1.00000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.363271 + 0.500000i) q^{17} +(-2.71441 + 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} -0.763932 q^{21} +(-2.48990 - 2.19098i) q^{22} -1.23607i q^{23} +(0.309017 + 0.224514i) q^{24} +(0.381966 + 1.17557i) q^{26} +(1.31433 + 1.80902i) q^{27} +(-1.17557 - 1.61803i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} +1.00000i q^{32} +(-0.502029 + 1.16312i) q^{33} +0.618034 q^{34} +(-0.881966 + 2.71441i) q^{36} +(3.52671 - 1.14590i) q^{37} +(-3.44095 - 4.73607i) q^{38} +(0.381966 - 0.277515i) q^{39} +(1.73607 - 5.34307i) q^{41} +(-0.449028 + 0.618034i) q^{42} +8.56231i q^{43} +(-3.23607 + 0.726543i) q^{44} +(-1.00000 - 0.726543i) q^{46} +(-6.15537 - 2.00000i) q^{47} +(0.363271 - 0.118034i) q^{48} +(-2.42705 + 1.76336i) q^{49} +(-0.0729490 - 0.224514i) q^{51} +(1.17557 + 0.381966i) q^{52} +(0.898056 - 1.23607i) q^{53} +2.23607 q^{54} -2.00000 q^{56} +(-1.31433 + 1.80902i) q^{57} +(-4.25325 - 1.38197i) q^{58} +(2.66312 + 8.19624i) q^{59} +(2.00000 - 1.45309i) q^{61} +(-1.90211 + 0.618034i) q^{62} +(-5.42882 - 1.76393i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.645898 + 1.08981i) q^{66} +11.0902i q^{67} +(0.363271 - 0.500000i) q^{68} +(-0.145898 + 0.449028i) q^{69} +(4.23607 - 3.07768i) q^{71} +(1.67760 + 2.30902i) q^{72} +(9.87384 - 3.20820i) q^{73} +(1.14590 - 3.52671i) q^{74} -5.85410 q^{76} +(-1.45309 - 6.47214i) q^{77} -0.472136i q^{78} +(10.8541 + 7.88597i) q^{79} +(2.38197 + 7.33094i) q^{81} +(-3.30220 - 4.54508i) q^{82} +(5.48183 + 7.54508i) q^{83} +(0.236068 + 0.726543i) q^{84} +(6.92705 + 5.03280i) q^{86} +1.70820i q^{87} +(-1.31433 + 3.04508i) q^{88} +8.09017 q^{89} +(-0.763932 + 2.35114i) q^{91} +(-1.17557 + 0.381966i) q^{92} +(0.449028 + 0.618034i) q^{93} +(-5.23607 + 3.80423i) q^{94} +(0.118034 - 0.363271i) q^{96} +(4.20025 - 5.78115i) q^{97} +3.00000i q^{98} +(-6.25329 + 7.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 10 q^{19} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 20 q^{29} - 4 q^{31} - 4 q^{34} - 16 q^{36} + 12 q^{39} - 4 q^{41} - 8 q^{44} - 8 q^{46} - 6 q^{49} - 14 q^{51} - 16 q^{56} - 10 q^{59} + 16 q^{61} + 2 q^{64} + 32 q^{66} - 28 q^{69} + 16 q^{71} + 36 q^{74} - 20 q^{76} + 60 q^{79} + 28 q^{81} - 16 q^{84} + 42 q^{86} + 20 q^{89} - 24 q^{91} - 24 q^{94} - 8 q^{96} + 26 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 10 * q^19 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 20 * q^29 - 4 * q^31 - 4 * q^34 - 16 * q^36 + 12 * q^39 - 4 * q^41 - 8 * q^44 - 8 * q^46 - 6 * q^49 - 14 * q^51 - 16 * q^56 - 10 * q^59 + 16 * q^61 + 2 * q^64 + 32 * q^66 - 28 * q^69 + 16 * q^71 + 36 * q^74 - 20 * q^76 + 60 * q^79 + 28 * q^81 - 16 * q^84 + 42 * q^86 + 20 * q^89 - 24 * q^91 - 24 * q^94 - 8 * q^96 + 26 * q^99

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