LMFDB - Embedded newform 80.2.j.b.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.9
Root			$1.41303 - 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	80.43
Dual form			80.2.j.b.67.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29521 - 0.567819i) q^{2} +1.96251i q^{3} +(1.35516 - 1.47090i) q^{4} +(-1.72581 - 1.42182i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 + 1.60205i) q^{7} +(0.920026 - 2.67461i) q^{8} -0.851447 q^{9} +O(q^{10})$	\(q+(1.29521 - 0.567819i) q^{2} +1.96251i q^{3} +(1.35516 - 1.47090i) q^{4} +(-1.72581 - 1.42182i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 + 1.60205i) q^{7} +(0.920026 - 2.67461i) q^{8} -0.851447 q^{9} +(-3.04263 - 0.861621i) q^{10} +(0.754587 - 0.754587i) q^{11} +(2.88665 + 2.65952i) q^{12} -5.94580 q^{13} +(-1.16532 + 2.98467i) q^{14} +(2.79034 - 3.38692i) q^{15} +(-0.327065 - 3.98661i) q^{16} +(1.95574 - 1.95574i) q^{17} +(-1.10281 + 0.483468i) q^{18} +(-0.780680 + 0.780680i) q^{19} +(-4.43011 + 0.611680i) q^{20} +(-3.14404 - 3.14404i) q^{21} +(0.548884 - 1.40582i) q^{22} +(4.93121 + 4.93121i) q^{23} +(5.24896 + 1.80556i) q^{24} +(0.956833 + 4.90759i) q^{25} +(-7.70109 + 3.37614i) q^{26} +4.21656i q^{27} +(0.185408 + 4.52748i) q^{28} +(1.44802 + 1.44802i) q^{29} +(1.69094 - 5.97120i) q^{30} -3.60859i q^{31} +(-2.68729 - 4.97780i) q^{32} +(1.48089 + 1.48089i) q^{33} +(1.42260 - 3.64361i) q^{34} +(5.04266 - 0.486998i) q^{35} +(-1.15385 + 1.25239i) q^{36} +10.2364 q^{37} +(-0.567864 + 1.45443i) q^{38} -11.6687i q^{39} +(-5.39062 + 3.30776i) q^{40} -6.93334i q^{41} +(-5.85745 - 2.28696i) q^{42} -9.91344 q^{43} +(-0.0873298 - 2.13251i) q^{44} +(1.46944 + 1.21061i) q^{45} +(9.18700 + 3.58694i) q^{46} +(-0.104270 - 0.104270i) q^{47} +(7.82376 - 0.641868i) q^{48} +1.86688i q^{49} +(4.02593 + 5.81308i) q^{50} +(3.83816 + 3.83816i) q^{51} +(-8.05753 + 8.74565i) q^{52} -4.03213i q^{53} +(2.39424 + 5.46135i) q^{54} +(-2.37516 + 0.229383i) q^{55} +(2.81093 + 5.75878i) q^{56} +(-1.53209 - 1.53209i) q^{57} +(2.69771 + 1.05328i) q^{58} +(3.46736 + 3.46736i) q^{59} +(-1.20043 - 8.69413i) q^{60} +(0.680578 - 0.680578i) q^{61} +(-2.04902 - 4.67390i) q^{62} +(1.36406 - 1.36406i) q^{63} +(-6.30711 - 4.92142i) q^{64} +(10.2613 + 8.45388i) q^{65} +(2.75894 + 1.07719i) q^{66} -9.04721 q^{67} +(-0.226341 - 5.52703i) q^{68} +(-9.67754 + 9.67754i) q^{69} +(6.25480 - 3.49408i) q^{70} -3.64007 q^{71} +(-0.783353 + 2.27729i) q^{72} +(2.94030 - 2.94030i) q^{73} +(13.2583 - 5.81242i) q^{74} +(-9.63120 + 1.87779i) q^{75} +(0.0903496 + 2.20625i) q^{76} +2.41777i q^{77} +(-6.62570 - 15.1135i) q^{78} -10.7140 q^{79} +(-5.10380 + 7.34515i) q^{80} -10.8294 q^{81} +(-3.93688 - 8.98016i) q^{82} -4.23845i q^{83} +(-8.88523 + 0.363865i) q^{84} +(-6.15595 + 0.594515i) q^{85} +(-12.8400 + 5.62904i) q^{86} +(-2.84176 + 2.84176i) q^{87} +(-1.32399 - 2.71247i) q^{88} -0.0426256 q^{89} +(2.59064 + 0.733625i) q^{90} +(9.52546 - 9.52546i) q^{91} +(13.9359 - 0.570698i) q^{92} +7.08189 q^{93} +(-0.194258 - 0.0758455i) q^{94} +(2.45730 - 0.237315i) q^{95} +(9.76898 - 5.27383i) q^{96} +(-1.91173 + 1.91173i) q^{97} +(1.06005 + 2.41802i) q^{98} +(-0.642491 + 0.642491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.29521	−	0.567819i	0.915855	−	0.401509i
$2$	1.29521	−	0.567819i	0.915855	−	0.401509i
$3$			1.96251i			1.13306i	0.824043	+	0.566528i	$0.191714\pi$
$3$			1.96251i			1.13306i	−0.824043	+	0.566528i	$0.808286\pi$
$4$	1.35516	−	1.47090i	0.677582	−	0.735448i
$5$	−1.72581	−	1.42182i	−0.771805	−	0.635859i
$5$	−1.72581	−	1.42182i	−0.771805	−	0.635859i
$6$	1.11435	+	2.54187i	0.454932	+	1.03772i
$7$	−1.60205	+	1.60205i	−0.605517	+	0.605517i	−0.941771	−	0.336254i	$-0.890840\pi$
$7$	−1.60205	+	1.60205i	−0.605517	+	0.605517i	0.336254	+	0.941771i	$0.390840\pi$
$8$	0.920026	−	2.67461i	0.325278	−	0.945618i
$9$	−0.851447			−0.283816
$10$	−3.04263	−	0.861621i	−0.962165	−	0.272468i
$11$	0.754587	−	0.754587i	0.227517	−	0.227517i	−0.584138	−	0.811654i	$-0.698567\pi$
$11$	0.754587	−	0.754587i	0.227517	−	0.227517i	0.811654	+	0.584138i	$0.198567\pi$
$12$	2.88665	+	2.65952i	0.833303	+	0.767738i
$13$	−5.94580			−1.64907			−0.824534	−	0.565812i	$-0.808563\pi$
$13$	−5.94580			−1.64907			−0.824534	+	0.565812i	$0.808563\pi$
$14$	−1.16532	+	2.98467i	−0.311446	+	0.797687i
$15$	2.79034	−	3.38692i	0.720464	−	0.874498i
$16$	−0.327065	−	3.98661i	−0.0817662	−	0.996652i
$17$	1.95574	−	1.95574i	0.474336	−	0.474336i	−0.428978	−	0.903315i	$-0.641126\pi$
$17$	1.95574	−	1.95574i	0.474336	−	0.474336i	0.903315	+	0.428978i	$0.141126\pi$
$18$	−1.10281	+	0.483468i	−0.259934	+	0.113954i
$19$	−0.780680	+	0.780680i	−0.179100	+	0.179100i	−0.790964	−	0.611863i	$-0.790420\pi$
$19$	−0.780680	+	0.780680i	−0.179100	+	0.179100i	0.611863	+	0.790964i	$0.290420\pi$
$20$	−4.43011	+	0.611680i	−0.990602	+	0.136776i
$21$	−3.14404	−	3.14404i	−0.686085	−	0.686085i
$22$	0.548884	−	1.40582i	0.117022	−	0.299722i
$23$	4.93121	+	4.93121i	1.02823	+	1.02823i	0.999590	+	0.0286378i	$0.00911693\pi$
$23$	4.93121	+	4.93121i	1.02823	+	1.02823i	0.0286378	+	0.999590i	$0.490883\pi$
$24$	5.24896	+	1.80556i	1.07144	+	0.368558i
$25$	0.956833	+	4.90759i	0.191367	+	0.981519i
$26$	−7.70109	+	3.37614i	−1.51031	+	0.662115i
$27$			4.21656i			0.811477i
$28$	0.185408	+	4.52748i	0.0350388	+	0.855614i
$29$	1.44802	+	1.44802i	0.268891	+	0.268891i	0.828653	−	0.559762i	$-0.189108\pi$
$29$	1.44802	+	1.44802i	0.268891	+	0.268891i	−0.559762	+	0.828653i	$0.689108\pi$
$30$	1.69094	−	5.97120i	0.308722	−	1.09019i
$31$		−	3.60859i		−	0.648121i	−0.946036	−	0.324061i	$-0.894952\pi$
$31$		−	3.60859i		−	0.648121i	0.946036	−	0.324061i	$-0.105048\pi$
$32$	−2.68729	−	4.97780i	−0.475050	−	0.879959i
$33$	1.48089	+	1.48089i	0.257789	+	0.257789i
$34$	1.42260	−	3.64361i	0.243973	−	0.624874i
$35$	5.04266	−	0.486998i	0.852365	−	0.0823177i
$36$	−1.15385	+	1.25239i	−0.192308	+	0.208732i
$37$	10.2364			1.68285			0.841427	−	0.540371i	$-0.181716\pi$
$37$	10.2364			1.68285			0.841427	+	0.540371i	$0.181716\pi$
$38$	−0.567864	+	1.45443i	−0.0921197	+	0.235940i
$39$		−	11.6687i		−	1.86849i
$40$	−5.39062	+	3.30776i	−0.852331	+	0.523002i
$41$		−	6.93334i		−	1.08281i	−0.840763	−	0.541403i	$-0.817893\pi$
$41$		−	6.93334i		−	1.08281i	0.840763	−	0.541403i	$-0.182107\pi$
$42$	−5.85745	−	2.28696i	−0.903823	−	0.352885i
$43$	−9.91344			−1.51179			−0.755893	−	0.654695i	$-0.772797\pi$
$43$	−9.91344			−1.51179			−0.755893	+	0.654695i	$0.772797\pi$
$44$	−0.0873298	−	2.13251i	−0.0131655	−	0.321488i
$45$	1.46944	+	1.21061i	0.219050	+	0.180467i
$46$	9.18700	+	3.58694i	1.35455	+	0.528865i
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	0.699461	−	0.714671i	$-0.253423\pi$
$47$	−0.104270	−	0.104270i	−0.0152093	−	0.0152093i	−0.714671	+	0.699461i	$0.753423\pi$
$48$	7.82376	−	0.641868i	1.12926	−	0.0926457i
$49$			1.86688i			0.266698i
$50$	4.02593	+	5.81308i	0.569352	+	0.822094i
$51$	3.83816	+	3.83816i	0.537450	+	0.537450i
$52$	−8.05753	+	8.74565i	−1.11738	+	1.21280i
$53$		−	4.03213i		−	0.553856i	−0.960891	−	0.276928i	$-0.910684\pi$
$53$		−	4.03213i		−	0.553856i	0.960891	−	0.276928i	$-0.0893164\pi$
$54$	2.39424	+	5.46135i	0.325815	+	0.743195i
$55$	−2.37516	+	0.229383i	−0.320267	+	0.0309300i
$56$	2.81093	+	5.75878i	0.375627	+	0.769550i
$57$	−1.53209	−	1.53209i	−0.202931	−	0.202931i
$58$	2.69771	+	1.05328i	0.354227	+	0.138303i
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	0.895823	−	0.444411i	$-0.146587\pi$
$59$	3.46736	+	3.46736i	0.451412	+	0.451412i	−0.444411	+	0.895823i	$0.646587\pi$
$60$	−1.20043	−	8.69413i	−0.154975	−	1.12241i
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	−0.662194	−	0.749333i	$-0.730374\pi$
$61$	0.680578	−	0.680578i	0.0871391	−	0.0871391i	0.749333	+	0.662194i	$0.230374\pi$
$62$	−2.04902	−	4.67390i	−0.260226	−	0.593585i
$63$	1.36406	−	1.36406i	0.171855	−	0.171855i
$64$	−6.30711	−	4.92142i	−0.788388	−	0.615178i
$65$	10.2613	+	8.45388i	1.27276	+	1.04857i
$66$	2.75894	+	1.07719i	0.339602	+	0.132593i
$67$	−9.04721			−1.10529			−0.552646	−	0.833416i	$-0.686382\pi$
$67$	−9.04721			−1.10529			−0.552646	+	0.833416i	$0.686382\pi$
$68$	−0.226341	−	5.52703i	−0.0274479	−	0.670251i
$69$	−9.67754	+	9.67754i	−1.16504	+	1.16504i
$70$	6.25480	−	3.49408i	0.747592	−	0.417623i
$71$	−3.64007			−0.431997			−0.215998	−	0.976394i	$-0.569301\pi$
$71$	−3.64007			−0.431997			−0.215998	+	0.976394i	$0.569301\pi$
$72$	−0.783353	+	2.27729i	−0.0923191	+	0.268381i
$73$	2.94030	−	2.94030i	0.344136	−	0.344136i	−0.513784	−	0.857920i	$-0.671757\pi$
$73$	2.94030	−	2.94030i	0.344136	−	0.344136i	0.857920	+	0.513784i	$0.171757\pi$
$74$	13.2583	−	5.81242i	1.54125	−	0.675681i
$75$	−9.63120	+	1.87779i	−1.11212	+	0.216829i
$76$	0.0903496	+	2.20625i	0.0103638	+	0.253074i
$77$			2.41777i			0.275530i
$78$	−6.62570	−	15.1135i	−0.750213	−	1.71126i
$79$	−10.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$79$	−10.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$80$	−5.10380	+	7.34515i	−0.570622	+	0.821213i
$81$	−10.8294			−1.20326
$82$	−3.93688	−	8.98016i	−0.434756	−	0.991693i
$83$		−	4.23845i		−	0.465230i	−0.972569	−	0.232615i	$-0.925272\pi$
$83$		−	4.23845i		−	0.465230i	0.972569	−	0.232615i	$-0.0747282\pi$
$84$	−8.88523	+	0.363865i	−0.969458	+	0.0397009i
$85$	−6.15595	+	0.594515i	−0.667707	+	0.0644842i
$86$	−12.8400	+	5.62904i	−1.38458	+	0.606995i
$87$	−2.84176	+	2.84176i	−0.304668	+	0.304668i
$88$	−1.32399	−	2.71247i	−0.141138	−	0.289150i
$89$	−0.0426256			−0.00451831			−0.00225915	−	0.999997i	$-0.500719\pi$
$89$	−0.0426256			−0.00451831			−0.00225915	+	0.999997i	$0.500719\pi$
$90$	2.59064	+	0.733625i	0.273078	+	0.0773308i
$91$	9.52546	−	9.52546i	0.998539	−	0.998539i
$92$	13.9359	−	0.570698i	1.45292	−	0.0594993i
$93$	7.08189			0.734358
$94$	−0.194258	−	0.0758455i	−0.0200362	−	0.00782287i
$95$	2.45730	−	0.237315i	0.252113	−	0.0243480i
$96$	9.76898	−	5.27383i	0.997042	−	0.538258i
$97$	−1.91173	+	1.91173i	−0.194106	+	0.194106i	−0.797468	−	0.603362i	$-0.793828\pi$
$97$	−1.91173	+	1.91173i	−0.194106	+	0.194106i	0.603362	+	0.797468i	$0.293828\pi$
$98$	1.06005	+	2.41802i	0.107081	+	0.244257i
$99$	−0.642491	+	0.642491i	−0.0645728	+	0.0645728i
$100$	8.51522	+	5.24319i	0.851522	+	0.524319i
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	0.909587	−	0.415514i	$-0.136398\pi$
$101$	4.96537	+	4.96537i	0.494073	+	0.494073i	−0.415514	+	0.909587i	$0.636398\pi$
$102$	7.15062	+	2.79186i	0.708017	+	0.276435i
$103$	0.442220	+	0.442220i	0.0435733	+	0.0435733i	0.728558	−	0.684984i	$-0.240191\pi$
$103$	0.442220	+	0.442220i	0.0435733	+	0.0435733i	−0.684984	+	0.728558i	$0.740191\pi$
$104$	−5.47029	+	15.9027i	−0.536406	+	1.55939i
$105$	0.955739	+	9.89627i	0.0932706	+	0.965777i
$106$	−2.28952	−	5.22248i	−0.222378	−	0.507252i
$107$		−	17.5924i		−	1.70072i	−0.526204	−	0.850359i	$-0.676385\pi$
$107$		−	17.5924i		−	1.70072i	0.526204	−	0.850359i	$-0.323615\pi$
$108$	6.20211	+	5.71412i	0.596799	+	0.549842i
$109$	−0.345161	−	0.345161i	−0.0330605	−	0.0330605i	0.690383	−	0.723444i	$-0.257442\pi$
$109$	−0.345161	−	0.345161i	−0.0330605	−	0.0330605i	−0.723444	+	0.690383i	$0.757442\pi$
$110$	−2.94610	+	1.64576i	−0.280900	+	0.156917i
$111$			20.0890i			1.90677i
$112$	6.91071	+	5.86276i	0.653001	+	0.553979i
$113$	−5.43662	−	5.43662i	−0.511435	−	0.511435i	0.403531	−	0.914966i	$-0.367783\pi$
$113$	−5.43662	−	5.43662i	−0.511435	−	0.511435i	−0.914966	+	0.403531i	$0.867783\pi$
$114$	−2.85434	−	1.11444i	−0.267334	−	0.104377i
$115$	−1.49901	−	15.5216i	−0.139784	−	1.44740i
$116$	4.09219	−	0.167582i	0.379950	−	0.0155596i
$117$	5.06253			0.468031
$118$	6.45981	+	2.52214i	0.594673	+	0.232182i
$119$			6.26638i			0.574438i
$120$	−6.49151	−	10.5791i	−0.592591	−	0.965739i
$121$			9.86120i			0.896472i
$122$	0.495050	−	1.26794i	0.0448197	−	0.114794i
$123$	13.6067			1.22688
$124$	−5.30785	−	4.89023i	−0.476659	−	0.439155i
$125$	5.32642	−	9.83002i	0.476410	−	0.879223i
$126$	0.992211	−	2.54129i	0.0883932	−	0.226396i
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	0.928311	−	0.371805i	$-0.121261\pi$
$127$	6.27150	+	6.27150i	0.556505	+	0.556505i	−0.371805	+	0.928311i	$0.621261\pi$
$128$	−10.9635	−	2.79301i	−0.969049	−	0.246869i
$129$		−	19.4552i		−	1.71294i
$130$	18.0909	+	5.12302i	1.58667	+	0.449319i
$131$	1.61521	+	1.61521i	0.141122	+	0.141122i	0.774138	−	0.633017i	$-0.218184\pi$
$131$	1.61521	+	1.61521i	0.141122	+	0.141122i	−0.633017	+	0.774138i	$0.718184\pi$
$132$	4.18507	−	0.171386i	0.364263	−	0.0149172i
$133$		−	2.50138i		−	0.216897i
$134$	−11.7181	+	5.13718i	−1.01229	+	0.443785i
$135$	5.99520	−	7.27697i	0.515985	−	0.626302i
$136$	−3.43152	−	7.03018i	−0.294250	−	0.602833i
$137$	−6.83585	−	6.83585i	−0.584026	−	0.584026i	0.351981	−	0.936007i	$-0.385508\pi$
$137$	−6.83585	−	6.83585i	−0.584026	−	0.584026i	−0.936007	+	0.351981i	$0.885508\pi$
$138$	−7.03941	+	18.0296i	−0.599234	+	1.53478i
$139$	13.7427	+	13.7427i	1.16564	+	1.16564i	0.983220	+	0.182423i	$0.0583940\pi$
$139$	13.7427	+	13.7427i	1.16564	+	1.16564i	0.182423	+	0.983220i	$0.441606\pi$
$140$	6.11730	−	8.07718i	0.517006	−	0.682647i
$141$	0.204631	−	0.204631i	0.0172330	−	0.0172330i
$142$	−4.71467	+	2.06690i	−0.395647	+	0.173450i
$143$	−4.48662	+	4.48662i	−0.375190	+	0.375190i
$144$	0.278479	+	3.39439i	0.0232066	+	0.282865i
$145$	−0.440176	−	4.55784i	−0.0365547	−	0.378508i
$146$	2.13876	−	5.47788i	0.177005	−	0.453353i
$147$	−3.66378			−0.302184
$148$	13.8720	−	15.0567i	1.14027	−	1.23765i
$149$	1.73811	−	1.73811i	0.142391	−	0.142391i	−0.632318	−	0.774709i	$-0.717896\pi$
$149$	1.73811	−	1.73811i	0.142391	−	0.142391i	0.774709	+	0.632318i	$0.217896\pi$
$150$	−11.4082	+	7.90093i	−0.931478	+	0.645108i
$151$	5.83522			0.474864			0.237432	−	0.971404i	$-0.423694\pi$
$151$	5.83522			0.474864			0.237432	+	0.971404i	$0.423694\pi$
$152$	1.36977	+	2.80626i	0.111103	+	0.227618i
$153$	−1.66521	+	1.66521i	−0.134624	+	0.134624i
$154$	1.37286	+	3.13153i	0.110628	+	0.252346i
$155$	−5.13078	+	6.22773i	−0.412114	+	0.500223i
$156$	−17.1634	−	15.8130i	−1.37417	−	1.26605i
$157$		−	3.14732i		−	0.251183i	−0.992082	−	0.125592i	$-0.959917\pi$
$157$		−	3.14732i		−	0.251183i	0.992082	−	0.125592i	$-0.0400829\pi$
$158$	−13.8770	+	6.08363i	−1.10399	+	0.483987i
$159$	7.91310			0.627550
$160$	−2.43980	+	12.4116i	−0.192883	+	0.981222i
$161$	−15.8001			−1.24522
$162$	−14.0264	+	6.14913i	−1.10202	+	0.483121i
$163$			7.82117i			0.612601i	0.951935	+	0.306301i	$0.0990913\pi$
$163$			7.82117i			0.612601i	−0.951935	+	0.306301i	$0.900909\pi$
$164$	−10.1982	−	9.39580i	−0.796347	−	0.733689i
$165$	−0.450167	−	4.66128i	−0.0350454	−	0.362880i
$166$	−2.40667	−	5.48970i	−0.186794	−	0.426083i
$167$	−9.88460	+	9.88460i	−0.764893	+	0.764893i	−0.977203	−	0.212309i	$-0.931902\pi$
$167$	−9.88460	+	9.88460i	−0.764893	+	0.764893i	0.212309	+	0.977203i	$0.431902\pi$
$168$	−11.3017	+	5.51649i	−0.871943	+	0.425606i
$169$	22.3525			1.71942
$170$	−7.63570	+	4.26549i	−0.585632	+	0.327148i
$171$	0.664708	−	0.664708i	0.0508315	−	0.0508315i
$172$	−13.4343	+	14.5816i	−1.02436	+	1.11184i
$173$	3.49245			0.265526			0.132763	−	0.991148i	$-0.457615\pi$
$173$	3.49245			0.265526			0.132763	+	0.991148i	$0.457615\pi$
$174$	−2.06708	+	5.29429i	−0.156705	+	0.401359i
$175$	−9.39509	−	6.32931i	−0.710202	−	0.478451i
$176$	−3.25504	−	2.76144i	−0.245358	−	0.208152i
$177$	−6.80473	+	6.80473i	−0.511475	+	0.511475i
$178$	−0.0552094	+	0.0242036i	−0.00413812	+	0.00181414i
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	−0.0220444	−	0.999757i	$-0.507018\pi$
$179$	13.0809	−	13.0809i	0.977713	−	0.977713i	0.999757	+	0.0220444i	$0.00701753\pi$
$180$	3.77200	−	0.520813i	0.281148	−	0.0388191i
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.999903	+	0.0138952i	$0.00442312\pi$
$181$	13.6393	+	13.6393i	1.01380	+	1.01380i	0.0138952	+	0.999903i	$0.495577\pi$
$182$	6.92878	−	17.7462i	0.513595	−	1.31544i
$183$	1.33564	+	1.33564i	0.0987335	+	0.0987335i
$184$	17.7259	−	8.65223i	1.30677	−	0.637851i
$185$	−17.6661	−	14.5544i	−1.29884	−	1.07006i
$186$	9.17257	−	4.02123i	0.672565	−	0.294851i
$187$		−	2.95155i		−	0.215839i
$188$	−0.294673	+	0.0120674i	−0.0214912	+	0.000880102i
$189$	−6.75513	−	6.75513i	−0.491363	−	0.491363i
$190$	3.04797	−	1.70267i	0.221123	−	0.123525i
$191$			2.92523i			0.211662i	0.994384	+	0.105831i	$0.0337503\pi$
$191$			2.92523i			0.211662i	−0.994384	+	0.105831i	$0.966250\pi$
$192$	9.65835	−	12.3778i	0.697031	−	0.893288i
$193$	0.0830702	+	0.0830702i	0.00597953	+	0.00597953i	0.710090	−	0.704111i	$-0.248654\pi$
$193$	0.0830702	+	0.0830702i	0.00597953	+	0.00597953i	−0.704111	+	0.710090i	$0.748654\pi$
$194$	−1.39058	+	3.56161i	−0.0998379	+	0.255709i
$195$	−16.5908	+	20.1379i	−1.18809	+	1.44211i
$196$	2.74599	+	2.52993i	0.196142	+	0.180710i
$197$	7.80487			0.556074			0.278037	−	0.960570i	$-0.410316\pi$
$197$	7.80487			0.556074			0.278037	+	0.960570i	$0.410316\pi$
$198$	−0.467346	+	1.19698i	−0.0332128	+	0.0850659i
$199$		−	10.9740i		−	0.777924i	−0.921254	−	0.388962i	$-0.872834\pi$
$199$		−	10.9740i		−	0.777924i	0.921254	−	0.388962i	$-0.127166\pi$
$200$	14.0062	+	1.95595i	0.990389	+	0.138307i
$201$		−	17.7552i		−	1.25236i
$202$	9.25065	+	3.61179i	0.650873	+	0.254125i
$203$	−4.63960			−0.325636
$204$	10.8469	−	0.444197i	0.759432	−	0.0311000i
$205$	−9.85799	+	11.9656i	−0.688512	+	0.835715i
$206$	0.823871	+	0.321669i	0.0574018	+	0.0224118i
$207$	−4.19866	−	4.19866i	−0.291827	−	0.291827i
$208$	1.94466	+	23.7036i	0.134838	+	1.64355i
$209$			1.17818i			0.0814966i
$210$	6.85718	+	12.2751i	0.473190	+	0.847063i
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	0.329824	−	0.944042i	$-0.393011\pi$
$211$	−8.92204	−	8.92204i	−0.614218	−	0.614218i	−0.944042	+	0.329824i	$0.893011\pi$
$212$	−5.93085	−	5.46420i	−0.407332	−	0.375283i
$213$		−	7.14367i		−	0.489477i
$214$	−9.98927	−	22.7859i	−0.682853	−	1.55761i
$215$	17.1087	+	14.0952i	1.16680	+	0.961283i
$216$	11.2777	+	3.87934i	0.767347	+	0.263956i
$217$	5.78113	+	5.78113i	0.392449	+	0.392449i
$218$	−0.643047	−	0.251069i	−0.0435527	−	0.0170045i
$219$	5.77037	+	5.77037i	0.389926	+	0.389926i
$220$	−2.88134	+	3.80447i	−0.194260	+	0.256497i
$221$	−11.6284	+	11.6284i	−0.782213	+	0.782213i
$222$	11.4069	+	26.0196i	0.765584	+	1.74632i
$223$	13.1678	−	13.1678i	0.881784	−	0.881784i	−0.111931	−	0.993716i	$-0.535704\pi$
$223$	13.1678	−	13.1678i	0.881784	−	0.881784i	0.993716	+	0.111931i	$0.0357037\pi$
$224$	12.2798	+	3.66950i	0.820481	+	0.245179i
$225$	−0.814693	−	4.17856i	−0.0543129	−	0.278570i
$226$	−10.1286	−	3.95458i	−0.673745	−	0.263055i
$227$	19.3432			1.28385			0.641927	−	0.766766i	$-0.278135\pi$
$227$	19.3432			1.28385			0.641927	+	0.766766i	$0.278135\pi$
$228$	−4.32979	+	0.177312i	−0.286747	+	0.0117428i
$229$	−13.2143	+	13.2143i	−0.873223	+	0.873223i	−0.992822	−	0.119599i	$-0.961839\pi$
$229$	−13.2143	+	13.2143i	−0.873223	+	0.873223i	0.119599	+	0.992822i	$0.461839\pi$
$230$	−10.7550	−	19.2527i	−0.709165	−	1.26948i
$231$	−4.74490			−0.312191
$232$	5.20511	−	2.54068i	0.341732	−	0.166804i
$233$	−20.6884	+	20.6884i	−1.35534	+	1.35534i	−0.475769	+	0.879570i	$0.657830\pi$
$233$	−20.6884	+	20.6884i	−1.35534	+	1.35534i	−0.879570	+	0.475769i	$0.842170\pi$
$234$	6.55707	−	2.87460i	0.428649	−	0.187919i
$235$	0.0316965	+	0.328204i	0.00206765	+	0.0214096i
$236$	9.79896	−	0.401284i	0.637858	−	0.0261214i
$237$		−	21.0264i		−	1.36581i
$238$	3.55817	+	8.11630i	0.230642	+	0.526102i
$239$	−14.1053			−0.912395			−0.456198	−	0.889878i	$-0.650789\pi$
$239$	−14.1053			−0.912395			−0.456198	+	0.889878i	$0.650789\pi$
$240$	−14.4149	−	10.0163i	−0.930480	−	0.646547i
$241$	12.8011			0.824592			0.412296	−	0.911050i	$-0.364727\pi$
$241$	12.8011			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$242$	5.59937	+	12.7724i	0.359941	+	0.821039i
$243$		−	8.60310i		−	0.551889i
$244$	−0.0787646	−	1.92335i	−0.00504238	−	0.123130i
$245$	2.65438	−	3.22189i	0.169582	−	0.205839i
$246$	17.6237	−	7.72617i	1.12364	−	0.492603i
$247$	4.64177	−	4.64177i	0.295349	−	0.295349i
$248$	−9.65157	−	3.31999i	−0.612876	−	0.210820i
$249$	8.31800			0.527132
$250$	1.31719	−	15.7564i	0.0833066	−	0.996524i
$251$	−6.84118	+	6.84118i	−0.431812	+	0.431812i	−0.889244	−	0.457433i	$-0.848769\pi$
$251$	−6.84118	+	6.84118i	−0.431812	+	0.431812i	0.457433	+	0.889244i	$0.348769\pi$
$252$	−0.157865	−	3.85491i	−0.00994457	−	0.242837i
$253$	7.44205			0.467878
$254$	11.6840	+	4.56186i	0.733120	+	0.286237i
$255$	−1.16674	−	12.0811i	−0.0730642	−	0.756549i
$256$	−15.7861	+	2.60776i	−0.986629	+	0.162985i
$257$	−6.66524	+	6.66524i	−0.415766	+	0.415766i	−0.883742	−	0.467975i	$-0.844984\pi$
$257$	−6.66524	+	6.66524i	−0.415766	+	0.415766i	0.467975	+	0.883742i	$0.344984\pi$
$258$	−11.0471	−	25.1987i	−0.687759	−	1.56880i
$259$	−16.3992	+	16.3992i	−1.01900	+	1.01900i
$260$	26.3405	−	3.63693i	1.63357	−	0.225553i
$261$	−1.23291	−	1.23291i	−0.0763154	−	0.0763154i
$262$	3.00919	+	1.17490i	0.185908	+	0.0725854i
$263$	−7.32015	−	7.32015i	−0.451380	−	0.451380i	0.444432	−	0.895812i	$-0.353405\pi$
$263$	−7.32015	−	7.32015i	−0.451380	−	0.451380i	−0.895812	+	0.444432i	$0.853405\pi$
$264$	5.32325	−	2.59834i	0.327623	−	0.159917i
$265$	−5.73298	+	6.95869i	−0.352174	+	0.427469i
$266$	−1.42033	−	3.23982i	−0.0870859	−	0.198646i
$267$		−	0.0836533i		−	0.00511950i
$268$	−12.2604	+	13.3075i	−0.748926	+	0.812885i
$269$	15.9801	+	15.9801i	0.974321	+	0.974321i	0.999678	−	0.0253576i	$-0.00807242\pi$
$269$	15.9801	+	15.9801i	0.974321	+	0.974321i	−0.0253576	+	0.999678i	$0.508072\pi$
$270$	3.63307	−	12.8294i	0.221102	−	0.780774i
$271$		−	3.59684i		−	0.218492i	−0.994015	−	0.109246i	$-0.965156\pi$
$271$		−	3.59684i		−	0.218492i	0.994015	−	0.109246i	$-0.0348437\pi$
$272$	−8.43642	−	7.15711i	−0.511533	−	0.433963i
$273$	18.6938	+	18.6938i	1.13140	+	1.13140i
$274$	−12.7354	−	4.97237i	−0.769375	−	0.300392i
$275$	4.42522	+	2.98119i	0.266851	+	0.179773i
$276$	1.12000	+	27.3493i	0.0674161	+	1.64623i
$277$	−20.9416			−1.25826			−0.629131	−	0.777300i	$-0.716589\pi$
$277$	−20.9416			−1.25826			−0.629131	+	0.777300i	$0.716589\pi$
$278$	25.6032	+	9.99640i	1.53558	+	0.599545i
$279$			3.07252i			0.183947i
$280$	3.33684	−	13.9352i	0.199415	−	0.832788i
$281$		−	3.26699i		−	0.194892i	−0.995241	−	0.0974462i	$-0.968933\pi$
$281$		−	3.26699i		−	0.194892i	0.995241	−	0.0974462i	$-0.0310674\pi$
$282$	0.148848	−	0.381234i	0.00886375	−	0.0227022i
$283$	0.000151619	0		9.01279e−6	0		4.50640e−6	−	1.00000i	$-0.499999\pi$
$283$	0.000151619	0		9.01279e−6	0		4.50640e−6		1.00000i	$0.499999\pi$
$284$	−4.93289	+	5.35416i	−0.292713	+	0.317711i
$285$	0.465733	+	4.82247i	0.0275877	+	0.285658i
$286$	−3.26355	+	8.35873i	−0.192978	+	0.494262i
$287$	11.1075	+	11.1075i	0.655657	+	0.655657i
$288$	2.28809	+	4.23833i	0.134827	+	0.249746i
$289$			9.35017i			0.550010i
$290$	−3.15815	−	5.65344i	−0.185453	−	0.331981i
$291$	−3.75178	−	3.75178i	−0.219933	−	0.219933i
$292$	−0.340287	−	8.30947i	−0.0199138	−	0.486275i
$293$		−	11.0593i		−	0.646091i	−0.946384	−	0.323045i	$-0.895293\pi$
$293$		−	11.0593i		−	0.646091i	0.946384	−	0.323045i	$-0.104707\pi$
$294$	−4.74538	+	2.08036i	−0.276756	+	0.121329i
$295$	−1.05402	−	10.9140i	−0.0613677	−	0.635436i
$296$	9.41775	−	27.3784i	0.547396	−	1.59134i
$297$	3.18176	+	3.18176i	0.184624	+	0.184624i
$298$	1.26429	−	3.23815i	0.0732384	−	0.187581i
$299$	−29.3200	−	29.3200i	−1.69562	−	1.69562i
$300$	−10.2898	+	16.7112i	−0.594083	+	0.964822i
$301$	15.8818	−	15.8818i	0.915413	−	0.915413i
$302$	7.55787	−	3.31335i	0.434906	−	0.190662i
$303$	−9.74459	+	9.74459i	−0.559812	+	0.559812i
$304$	3.36760	+	2.85693i	0.193145	+	0.163856i
$305$	−2.14221	+	0.206885i	−0.122663	+	0.0118462i
$306$	−1.21127	+	3.10234i	−0.0692435	+	0.177349i
$307$	15.1317			0.863613			0.431806	−	0.901966i	$-0.357876\pi$
$307$	15.1317			0.863613			0.431806	+	0.901966i	$0.357876\pi$
$308$	3.55629	+	3.27647i	0.202638	+	0.186694i
$309$	−0.867862	+	0.867862i	−0.0493709	+	0.0493709i
$310$	−3.10923	+	10.9796i	−0.176593	+	0.623600i
$311$	−27.1556			−1.53985			−0.769925	−	0.638134i	$-0.779707\pi$
$311$	−27.1556			−1.53985			−0.769925	+	0.638134i	$0.779707\pi$
$312$	−31.2092	−	10.7355i	−1.76687	−	0.607778i
$313$	13.6695	−	13.6695i	0.772646	−	0.772646i	−0.205922	−	0.978568i	$-0.566019\pi$
$313$	13.6695	−	13.6695i	0.772646	−	0.772646i	0.978568	+	0.205922i	$0.0660194\pi$
$314$	−1.78711	−	4.07645i	−0.100852	−	0.230048i
$315$	−4.29356	+	0.414653i	−0.241915	+	0.0233631i
$316$	−14.5193	+	15.7592i	−0.816772	+	0.886525i
$317$			25.8314i			1.45084i	0.688307	+	0.725419i	$0.258354\pi$
$317$			25.8314i			1.45084i	−0.688307	+	0.725419i	$0.741646\pi$
$318$	10.2492	−	4.49321i	0.574745	−	0.251967i
$319$	2.18532			0.122354
$320$	3.88746	+	17.4610i	0.217316	+	0.976101i
$321$	34.5252			1.92701
$322$	−20.4645	+	8.97157i	−1.14044	+	0.499966i
$323$			3.05361i			0.169908i
$324$	−14.6756	+	15.9289i	−0.815310	+	0.884938i
$325$	−5.68914	−	29.1796i	−0.315576	−	1.61859i
$326$	4.44101	+	10.1301i	0.245965	+	0.561054i
$327$	0.677383	−	0.677383i	0.0374594	−	0.0374594i
$328$	−18.5440	−	6.37885i	−1.02392	−	0.352213i
$329$	0.334091			0.0184190
$330$	−3.22983	−	5.78175i	−0.177796	−	0.318275i
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	−0.974227	−	0.225568i	$-0.927576\pi$
$331$	−13.6207	+	13.6207i	−0.748659	+	0.748659i	0.225568	+	0.974227i	$0.427576\pi$
$332$	−6.23431	−	5.74379i	−0.342152	−	0.315231i
$333$	−8.71576			−0.477621
$334$	−7.19002	+	18.4153i	−0.393420	+	1.00764i
$335$	15.6138	+	12.8635i	0.853071	+	0.702810i
$336$	−11.5057	+	13.5623i	−0.627689	+	0.739886i
$337$	16.0911	−	16.0911i	0.876536	−	0.876536i	−0.116638	−	0.993174i	$-0.537212\pi$
$337$	16.0911	−	16.0911i	0.876536	−	0.876536i	0.993174	+	0.116638i	$0.0372119\pi$
$338$	28.9513	−	12.6922i	1.57474	−	0.690364i
$339$	10.6694	−	10.6694i	0.579484	−	0.579484i
$340$	−7.46785	+	9.86042i	−0.405001	+	0.534756i
$341$	−2.72299	−	2.72299i	−0.147458	−	0.147458i
$342$	0.483506	−	1.23837i	0.0261450	−	0.0669636i
$343$	−14.2052	−	14.2052i	−0.767007	−	0.767007i
$344$	−9.12062	+	26.5146i	−0.491751	+	1.42957i
$345$	30.4614	−	2.94183i	1.63998	−	0.158383i
$346$	4.52347	−	1.98308i	0.243183	−	0.106611i
$347$		−	5.57562i		−	0.299315i	−0.988738	−	0.149658i	$-0.952183\pi$
$347$		−	5.57562i		−	0.299315i	0.988738	−	0.149658i	$-0.0478171\pi$
$348$	0.328882	+	8.03097i	0.0176299	+	0.430505i
$349$	−15.0811	−	15.0811i	−0.807273	−	0.807273i	0.176947	−	0.984220i	$-0.443378\pi$
$349$	−15.0811	−	15.0811i	−0.807273	−	0.807273i	−0.984220	+	0.176947i	$0.943378\pi$
$350$	−15.7626	−	2.86310i	−0.842544	−	0.153039i
$351$		−	25.0708i		−	1.33818i
$352$	−5.78398	−	1.72839i	−0.308287	−	0.0921234i
$353$	2.57880	+	2.57880i	0.137256	+	0.137256i	0.772397	−	0.635141i	$-0.219058\pi$
$353$	2.57880	+	2.57880i	0.137256	+	0.137256i	−0.635141	+	0.772397i	$0.719058\pi$
$354$	−4.94973	+	12.6774i	−0.263075	+	0.673798i
$355$	6.28206	+	5.17554i	0.333417	+	0.274689i
$356$	−0.0577647	+	0.0626979i	−0.00306152	+	0.00332298i
$357$	−12.2978			−0.650870
$358$	9.51500	−	24.3702i	0.502883	−	1.28800i
$359$			5.77227i			0.304649i	0.988331	+	0.152324i	$0.0486758\pi$
$359$			5.77227i			0.304649i	−0.988331	+	0.152324i	$0.951324\pi$
$360$	4.58983	−	2.81638i	0.241905	−	0.148436i
$361$			17.7811i			0.935846i
$362$	25.4104	+	9.92115i	1.33554	+	0.521444i
$363$	−19.3527			−1.01575
$364$	−1.10240	−	26.9195i	−0.0577814	−	1.41096i
$365$	−9.25499	+	0.893807i	−0.484428	+	0.0467840i
$366$	2.48835	+	0.971540i	0.130068	+	0.0507832i
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	0.456307	−	0.889822i	$-0.349172\pi$
$367$	−8.30496	−	8.30496i	−0.433516	−	0.433516i	−0.889822	+	0.456307i	$0.849172\pi$
$368$	18.0460	−	21.2716i	0.940710	−	1.10886i
$369$			5.90337i			0.307317i
$370$	−31.1456	−	8.81990i	−1.61918	−	0.458525i
$371$	6.45967	+	6.45967i	0.335369	+	0.335369i
$372$	9.59712	−	10.4167i	0.497587	−	0.540082i
$373$			16.0484i			0.830953i	0.909604	+	0.415477i	$0.136385\pi$
$373$			16.0484i			0.830953i	−0.909604	+	0.415477i	$0.863615\pi$
$374$	−1.67595	−	3.82289i	−0.0866612	−	0.197677i
$375$	19.2915	+	10.4532i	0.996209	+	0.539799i
$376$	−0.374813	+	0.182951i	−0.0193295	+	0.00943496i
$377$	−8.60964	−	8.60964i	−0.443419	−	0.443419i
$378$	−12.5850	−	4.91365i	−0.647304	−	0.252731i
$379$	8.91367	+	8.91367i	0.457865	+	0.457865i	0.897954	−	0.440089i	$-0.145053\pi$
$379$	8.91367	+	8.91367i	0.457865	+	0.457865i	−0.440089	+	0.897954i	$0.645053\pi$
$380$	2.98097	−	3.93602i	0.152921	−	0.201914i
$381$	−12.3079	+	12.3079i	−0.630552	+	0.630552i
$382$	1.66100	+	3.78880i	0.0849841	+	0.193852i
$383$	24.8928	−	24.8928i	1.27196	−	1.27196i	0.326904	−	0.945057i	$-0.393995\pi$
$383$	24.8928	−	24.8928i	1.27196	−	1.27196i	0.945057	−	0.326904i	$-0.106005\pi$
$384$	5.48131	−	21.5161i	0.279717	−	1.09799i
$385$	3.43764	−	4.17261i	0.175199	−	0.212656i
$386$	0.154763	+	0.0604250i	0.00787721	+	0.00307555i
$387$	8.44078			0.429069
$388$	0.221247	+	5.40265i	0.0112321	+	0.274278i
$389$	16.5819	−	16.5819i	0.840738	−	0.840738i	−0.148217	−	0.988955i	$-0.547353\pi$
$389$	16.5819	−	16.5819i	0.840738	−	0.840738i	0.988955	+	0.148217i	$0.0473534\pi$
$390$	−10.0540	+	35.5035i	−0.509103	+	1.79779i
$391$	19.2883			0.975452
$392$	4.99319	+	1.71758i	0.252194	+	0.0867510i
$393$	−3.16987	+	3.16987i	−0.159899	+	0.159899i
$394$	10.1090	−	4.43176i	0.509284	−	0.223269i
$395$	18.4904	+	15.2335i	0.930351	+	0.766478i
$396$	0.0743567	+	1.81572i	0.00373656	+	0.0912432i
$397$			8.62531i			0.432892i	0.976295	+	0.216446i	$0.0694465\pi$
$397$			8.62531i			0.432892i	−0.976295	+	0.216446i	$0.930553\pi$
$398$	−6.23123	−	14.2137i	−0.312343	−	0.712466i
$399$	4.90897			0.245756
$400$	19.2517	−	5.41962i	0.962585	−	0.270981i
$401$	19.7107			0.984307			0.492153	−	0.870508i	$-0.336210\pi$
$401$	19.7107			0.984307			0.492153	+	0.870508i	$0.336210\pi$
$402$	−10.0818	−	22.9969i	−0.502833	−	1.14698i
$403$			21.4559i			1.06880i
$404$	14.0324	−	0.574651i	0.698139	−	0.0285900i
$405$	18.6894	+	15.3975i	0.928686	+	0.765107i
$406$	−6.00928	+	2.63445i	−0.298235	+	0.130746i
$407$	7.72426	−	7.72426i	0.382877	−	0.382877i
$408$	13.7968	−	6.73438i	0.683043	−	0.333402i
$409$	−26.7930			−1.32483			−0.662414	−	0.749138i	$-0.730468\pi$
$409$	−26.7930			−1.32483			−0.662414	+	0.749138i	$0.730468\pi$
$410$	−5.97391	+	21.0956i	−0.295030	+	1.04184i
$411$	13.4154	−	13.4154i	0.661734	−	0.661734i
$412$	1.24974	−	0.0511790i	0.0615703	−	0.00252141i
$413$	−11.1098			−0.546675
$414$	−7.82225	−	3.05409i	−0.384443	−	0.150100i
$415$	−6.02633	+	7.31475i	−0.295821	+	0.359067i
$416$	15.9781	+	29.5970i	0.783390	+	1.45111i
$417$	−26.9702	+	26.9702i	−1.32074	+	1.32074i
$418$	0.668995	+	1.52600i	0.0327216	+	0.0746391i
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	−0.923840	−	0.382779i	$-0.874967\pi$
$419$	−11.0752	+	11.0752i	−0.541061	+	0.541061i	0.382779	+	0.923840i	$0.374967\pi$
$420$	15.8516	+	12.0053i	0.773477	+	0.585797i
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	0.701158	−	0.713006i	$-0.252667\pi$
$421$	−0.243092	−	0.243092i	−0.0118476	−	0.0118476i	−0.713006	+	0.701158i	$0.752667\pi$
$422$	−16.6221	−	6.48985i	−0.809149	−	0.315921i
$423$	0.0887804	+	0.0887804i	0.00431665	+	0.00431665i
$424$	−10.7844	−	3.70967i	−0.523737	−	0.180157i
$425$	11.4693	+	7.72666i	0.556342	+	0.374798i
$426$	−4.05631	−	9.25259i	−0.196529	−	0.448290i
$427$			2.18064i			0.105528i
$428$	−25.8765	−	23.8405i	−1.25079	−	1.15237i
$429$	−8.80505	−	8.80505i	−0.425112	−	0.425112i
$430$	30.1630	+	8.54163i	1.45459	+	0.411914i
$431$		−	20.7024i		−	0.997200i	−0.866832	−	0.498600i	$-0.833848\pi$
$431$		−	20.7024i		−	0.997200i	0.866832	−	0.498600i	$-0.166152\pi$
$432$	16.8098	−	1.37909i	0.808760	−	0.0663514i
$433$	−5.68221	−	5.68221i	−0.273069	−	0.273069i	0.557265	−	0.830335i	$-0.311851\pi$
$433$	−5.68221	−	5.68221i	−0.273069	−	0.273069i	−0.830335	+	0.557265i	$0.811851\pi$
$434$	10.7704	+	4.20517i	0.516998	+	0.201855i
$435$	8.94480	−	0.863851i	0.428871	−	0.0414185i
$436$	−0.975446	+	0.0399462i	−0.0467154	+	0.00191307i
$437$	−7.69939			−0.368312
$438$	10.7504	+	4.19735i	0.513674	+	0.200557i
$439$			18.7902i			0.896808i	0.893831	+	0.448404i	$0.148007\pi$
$439$			18.7902i			0.896808i	−0.893831	+	0.448404i	$0.851993\pi$
$440$	−1.57170	+	6.56368i	−0.0749279	+	0.312911i
$441$		−	1.58955i		−	0.0756930i
$442$	−8.45848	+	21.6642i	−0.402329	+	1.03046i
$443$	12.1641			0.577934			0.288967	−	0.957339i	$-0.406688\pi$
$443$	12.1641			0.577934			0.288967	+	0.957339i	$0.406688\pi$
$444$	29.5489	+	27.2239i	1.40233	+	1.29199i
$445$	0.0735637	+	0.0606062i	0.00348725	+	0.00287301i
$446$	9.57824	−	24.5321i	0.453543	−	1.16163i
$447$	3.41105	+	3.41105i	0.161337	+	0.161337i
$448$	17.9886	−	2.21993i	0.849884	−	0.104882i
$449$		−	27.2708i		−	1.28699i	−0.765452	−	0.643493i	$-0.777484\pi$
$449$		−	27.2708i		−	1.28699i	0.765452	−	0.643493i	$-0.222516\pi$
$450$	−3.42787	−	4.94953i	−0.161591	−	0.233323i
$451$	−5.23181	−	5.23181i	−0.246356	−	0.246356i
$452$	−15.3642	+	0.629191i	−0.722672	+	0.0295946i
$453$			11.4517i			0.538047i
$454$	25.0536	−	10.9834i	1.17582	−	0.515479i
$455$	−29.9826	+	2.89559i	−1.40561	+	0.135748i
$456$	−5.50732	+	2.68819i	−0.257904	+	0.125886i
$457$	−19.7514	−	19.7514i	−0.923933	−	0.923933i	0.0733714	−	0.997305i	$-0.476624\pi$
$457$	−19.7514	−	19.7514i	−0.923933	−	0.923933i	−0.997305	+	0.0733714i	$0.976624\pi$
$458$	−9.61200	+	24.6186i	−0.449139	+	1.15035i
$459$	8.24649	+	8.24649i	0.384913	+	0.384913i
$460$	−24.8621	−	18.8295i	−1.15920	−	0.877928i
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	−0.338818	−	0.940852i	$-0.610027\pi$
$461$	12.9262	−	12.9262i	0.602035	−	0.602035i	0.940852	+	0.338818i	$0.110027\pi$
$462$	−6.14566	+	2.69424i	−0.285922	+	0.125348i
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	−0.959293	−	0.282414i	$-0.908865\pi$
$463$	−14.5647	+	14.5647i	−0.676879	+	0.676879i	0.282414	+	0.959293i	$0.408865\pi$
$464$	5.29909	−	6.24629i	0.246004	−	0.289977i
$465$	−12.2220	−	10.0692i	−0.566781	−	0.466948i
$466$	−15.0486	+	38.5431i	−0.697114	+	1.78547i
$467$	−42.3556			−1.95998			−0.979991	−	0.199040i	$-0.936218\pi$
$467$	−42.3556			−1.95998			−0.979991	+	0.199040i	$0.936218\pi$
$468$	6.86056	−	7.44646i	0.317130	−	0.344213i
$469$	14.4941	−	14.4941i	0.669274	−	0.669274i
$470$	0.227414	+	0.407096i	0.0104898	+	0.0187779i
$471$	6.17665			0.284605
$472$	12.4639	−	6.08378i	0.573698	−	0.280029i
$473$	−7.48056	+	7.48056i	−0.343956	+	0.343956i
$474$	−11.9392	−	27.2337i	−0.548385	−	1.25088i
$475$	−4.57824	−	3.08428i	−0.210064	−	0.141517i
$476$	9.21718	+	8.49196i	0.422469	+	0.389229i
$477$			3.43315i			0.157193i
$478$	−18.2694	+	8.00925i	−0.835622	+	0.366335i
$479$	−27.0905			−1.23780			−0.618899	−	0.785470i	$-0.712421\pi$
$479$	−27.0905			−1.23780			−0.618899	+	0.785470i	$0.712421\pi$
$480$	−24.3579	−	4.78814i	−1.11178	−	0.218548i
$481$	−60.8636			−2.77514
$482$	16.5802	−	7.26871i	0.755207	−	0.331081i
$483$		−	31.0078i		−	1.41090i
$484$	14.5048	+	13.3635i	0.659308	+	0.607433i
$485$	6.01741	−	0.581136i	0.273236	−	0.0263880i
$486$	−4.88500	−	11.1429i	−0.221588	−	0.505450i
$487$	21.9674	−	21.9674i	0.995436	−	0.995436i	−0.00455390	−	0.999990i	$-0.501450\pi$
$487$	21.9674	−	21.9674i	0.995436	−	0.995436i	0.999990	+	0.00455390i	$0.00144956\pi$
$488$	−1.19413	−	2.44643i	−0.0540559	−	0.110745i
$489$	−15.3491			−0.694111
$490$	1.60855	−	5.68024i	0.0726667	−	0.256607i
$491$	−6.11955	+	6.11955i	−0.276171	+	0.276171i	−0.831579	−	0.555407i	$-0.812562\pi$
$491$	−6.11955	+	6.11955i	−0.276171	+	0.276171i	0.555407	+	0.831579i	$0.312562\pi$
$492$	18.4394	−	20.0141i	0.831311	−	0.902305i
$493$	5.66390			0.255089
$494$	3.37640	−	8.64777i	0.151912	−	0.389082i
$495$	2.02233	−	0.195308i	0.0908968	−	0.00877842i
$496$	−14.3860	+	1.18024i	−0.645951	+	0.0529945i
$497$	5.83157	−	5.83157i	0.261581	−	0.261581i
$498$	10.7736	−	4.72312i	0.482776	−	0.211648i
$499$	−15.4115	+	15.4115i	−0.689914	+	0.689914i	−0.962213	−	0.272298i	$-0.912216\pi$
$499$	−15.4115	+	15.4115i	−0.689914	+	0.689914i	0.272298	+	0.962213i	$0.412216\pi$
$500$	−7.24075	−	21.1559i	−0.323816	−	0.946120i
$501$	−19.3986	−	19.3986i	−0.866667	−	0.866667i
$502$	−4.97625	+	12.7454i	−0.222101	+	0.568853i
$503$	26.4312	+	26.4312i	1.17851	+	1.17851i	0.980124	+	0.198387i	$0.0635704\pi$
$503$	26.4312	+	26.4312i	1.17851	+	1.17851i	0.198387	+	0.980124i	$0.436430\pi$
$504$	−2.39336	−	4.90330i	−0.106609	−	0.218410i
$505$	−1.50940	−	15.6292i	−0.0671673	−	0.695488i
$506$	9.63905	−	4.22574i	0.428508	−	0.187857i
$507$			43.8671i			1.94820i
$508$	17.7236	−	0.725812i	0.786358	−	0.0322027i
$509$	0.233714	+	0.233714i	0.0103592	+	0.0103592i	0.712267	−	0.701908i	$-0.247668\pi$
$509$	0.233714	+	0.233714i	0.0103592	+	0.0103592i	−0.701908	+	0.712267i	$0.747668\pi$
$510$	−8.37107	−	14.9851i	−0.370677	−	0.663553i
$511$			9.42101i			0.416761i
$512$	−18.9656	+	12.3412i	−0.838169	+	0.545410i
$513$	−3.29178	−	3.29178i	−0.145336	−	0.145336i
$514$	−4.84827	+	12.4176i	−0.213848	+	0.547716i
$515$	−0.134428	−	1.39195i	−0.00592362	−	0.0613365i
$516$	−28.6166	−	26.3650i	−1.25978	−	1.16066i
$517$	−0.157362			−0.00692075
$518$	−11.9287	+	30.5523i	−0.524118	+	1.34239i
$519$			6.85397i			0.300856i
$520$	32.0515	−	19.6673i	1.40555	−	0.862466i
$521$		−	4.50147i		−	0.197213i	−0.995127	−	0.0986064i	$-0.968562\pi$
$521$		−	4.50147i		−	0.197213i	0.995127	−	0.0986064i	$-0.0314385\pi$
$522$	−2.29696	−	0.896816i	−0.100535	−	0.0392526i
$523$	−12.6042			−0.551141			−0.275571	−	0.961281i	$-0.588867\pi$
$523$	−12.6042			−0.551141			−0.275571	+	0.961281i	$0.588867\pi$
$524$	4.56468	−	0.186931i	0.199409	−	0.00816613i
$525$	12.4213	−	18.4380i	0.542111	−	0.804699i
$526$	−13.6377	−	5.32465i	−0.594632	−	0.232166i
$527$	−7.05746	−	7.05746i	−0.307428	−	0.307428i
$528$	5.41936	−	6.38805i	0.235847	−	0.278004i
$529$			25.6336i			1.11450i
$530$	−3.47417	+	12.2683i	−0.150908	+	0.532901i
$531$	−2.95227	−	2.95227i	−0.128118	−	0.128118i
$532$	−3.67926	−	3.38977i	−0.159516	−	0.146965i
$533$			41.2242i			1.78562i
$534$	−0.0474999	−	0.108349i	−0.00205552	−	0.00468872i
$535$	−25.0132	+	30.3610i	−1.08142	+	1.31262i
$536$	−8.32367	+	24.1978i	−0.359528	+	1.04519i
$537$	25.6714	+	25.6714i	1.10780	+	1.10780i
$538$	29.7714	+	11.6238i	1.28354	+	0.501139i
$539$	1.40873	+	1.40873i	0.0606782	+	0.0606782i
$540$	−2.57918	−	18.6798i	−0.110990	−	0.803851i
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	−0.322955	−	0.946414i	$-0.604676\pi$
$541$	14.5013	−	14.5013i	0.623459	−	0.623459i	0.946414	+	0.322955i	$0.104676\pi$
$542$	−2.04235	−	4.65868i	−0.0877266	−	0.200107i
$543$	−26.7672	+	26.7672i	−1.14869	+	1.14869i
$544$	−14.9909	−	4.47964i	−0.642730	−	0.192063i
$545$	0.104924	+	1.08644i	0.00449444	+	0.0465380i
$546$	34.8272	+	13.5978i	1.49047	+	0.581932i
$547$	30.2936			1.29526			0.647630	−	0.761955i	$-0.275760\pi$
$547$	30.2936			1.29526			0.647630	+	0.761955i	$0.275760\pi$
$548$	−19.3185	+	0.791125i	−0.825246	+	0.0337952i
$549$	−0.579476	+	0.579476i	−0.0247314	+	0.0247314i
$550$	7.42439	+	1.34856i	0.316577	+	0.0575029i
$551$	−2.26088			−0.0963169
$552$	16.9801	+	34.7873i	0.722721	+	1.48064i
$553$	17.1644	−	17.1644i	0.729904	−	0.729904i
$554$	−27.1239	+	11.8911i	−1.15239	+	0.505203i
$555$	28.5631	−	34.6699i	1.21244	−	1.47165i
$556$	38.8378	−	1.59047i	1.64709	−	0.0674510i
$557$			9.72758i			0.412171i	0.978534	+	0.206085i	$0.0660725\pi$
$557$			9.72758i			0.412171i	−0.978534	+	0.206085i	$0.933928\pi$
$558$	1.74464	+	3.97958i	0.0738563	+	0.168469i
$559$	58.9433			2.49304
$560$	−3.59075	−	19.9438i	−0.151737	−	0.842780i
$561$	5.79245			0.244557
$562$	−1.85506	−	4.23146i	−0.0782510	−	0.178493i
$563$		−	17.7853i		−	0.749562i	−0.927113	−	0.374781i	$-0.877718\pi$
$563$		−	17.7853i		−	0.749562i	0.927113	−	0.374781i	$-0.122282\pi$
$564$	−0.0236823	−	0.578299i	−0.000997205	−	0.0243508i
$565$	1.65265	+	17.1125i	0.0695276	+	0.719928i
$566$	0.000196379	0	8.60919e-5i	8.25441e−6	0	3.61871e-6i
$567$	17.3492	−	17.3492i	0.728597	−	0.728597i
$568$	−3.34896	+	9.73578i	−0.140519	+	0.408504i
$569$	−15.7897			−0.661938			−0.330969	−	0.943642i	$-0.607376\pi$
$569$	−15.7897			−0.661938			−0.330969	+	0.943642i	$0.607376\pi$
$570$	3.34151	+	5.98168i	0.139961	+	0.250545i
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	−0.0241793	−	0.999708i	$-0.507697\pi$
$571$	23.3108	−	23.3108i	0.975528	−	0.975528i	0.999708	+	0.0241793i	$0.00769727\pi$
$572$	0.519245	+	12.6795i	0.0217107	+	0.530155i
$573$	−5.74079			−0.239825
$574$	20.6937	+	8.07958i	0.863739	+	0.337235i
$575$	−19.4820	+	28.9187i	−0.812456	+	1.20599i
$576$	5.37017	+	4.19033i	0.223757	+	0.174597i
$577$	25.7383	−	25.7383i	1.07150	−	1.07150i	0.0742597	−	0.997239i	$-0.476341\pi$
$577$	25.7383	−	25.7383i	1.07150	−	1.07150i	0.997239	−	0.0742597i	$-0.0236594\pi$
$578$	5.30920	+	12.1105i	0.220834	+	0.503729i
$579$	−0.163026	+	0.163026i	−0.00677514	+	0.00677514i
$580$	−7.30061	−	5.52916i	−0.303141	−	0.229586i
$581$	6.79020	+	6.79020i	0.281705	+	0.281705i
$582$	−6.98969	−	2.72903i	−0.289732	−	0.113122i
$583$	−3.04260	−	3.04260i	−0.126011	−	0.126011i
$584$	−5.15902	−	10.5693i	−0.213482	−	0.437362i
$585$	−8.73697	−	7.19803i	−0.361229	−	0.297602i
$586$	−6.27967	−	14.3242i	−0.259411	−	0.591725i
$587$		−	23.1327i		−	0.954790i	−0.878689	−	0.477395i	$-0.841581\pi$
$587$		−	23.1327i		−	0.954790i	0.878689	−	0.477395i	$-0.158419\pi$
$588$	−4.96502	+	5.38904i	−0.204754	+	0.222240i
$589$	2.81715	+	2.81715i	0.116079	+	0.116079i
$590$	−7.56235	−	13.5374i	−0.311337	−	0.557328i
$591$			15.3171i			0.630063i
$592$	−3.34797	−	40.8085i	−0.137601	−	1.67722i
$593$	−25.5047	−	25.5047i	−1.04735	−	1.04735i	−0.998822	−	0.0485322i	$-0.984546\pi$
$593$	−25.5047	−	25.5047i	−1.04735	−	1.04735i	−0.0485322	−	0.998822i	$-0.515454\pi$
$594$	5.92773	+	2.31440i	0.243218	+	0.0949609i
$595$	8.90969	−	10.8146i	0.365261	−	0.443354i
$596$	−0.201154	−	4.91199i	−0.00823960	−	0.201203i
$597$	21.5365			0.881432
$598$	−54.6241	−	21.3272i	−2.23374	−	0.872135i
$599$		−	11.0699i		−	0.452304i	−0.974092	−	0.226152i	$-0.927385\pi$
$599$		−	11.0699i		−	0.452304i	0.974092	−	0.226152i	$-0.0726146\pi$
$600$	−3.83858	+	27.4874i	−0.156709	+	1.12217i
$601$			13.7579i			0.561197i	0.959825	+	0.280599i	$0.0905330\pi$
$601$			13.7579i			0.561197i	−0.959825	+	0.280599i	$0.909467\pi$
$602$	11.5524	−	29.5884i	0.470839	−	1.20593i
$603$	7.70322			0.313700
$604$	7.90768	−	8.58300i	0.321759	−	0.349237i
$605$	14.0209	−	17.0185i	0.570030	−	0.691902i
$606$	−7.08817	+	18.1545i	−0.287937	+	0.737476i
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	0.974399	−	0.224826i	$-0.0721813\pi$
$607$	18.4675	+	18.4675i	0.749573	+	0.749573i	−0.224826	+	0.974399i	$0.572181\pi$
$608$	5.98398	+	1.78815i	0.242683	+	0.0725193i
$609$		−	9.10526i		−	0.368964i
$610$	−2.65715	+	1.48435i	−0.107585	+	0.0600995i
$611$	0.619968	+	0.619968i	0.0250812	+	0.0250812i
$612$	0.192718	+	4.70598i	0.00779015	+	0.190228i
$613$		−	11.6810i		−	0.471790i	−0.971779	−	0.235895i	$-0.924198\pi$
$613$		−	11.6810i		−	0.471790i	0.971779	−	0.235895i	$-0.0758021\pi$
$614$	19.5988	−	8.59208i	0.790944	−	0.346748i
$615$	−23.4826	−	19.3464i	−0.946912	−	0.780122i
$616$	6.46660	+	2.22441i	0.260547	+	0.0896240i
$617$	29.1000	+	29.1000i	1.17152	+	1.17152i	0.981847	+	0.189677i	$0.0607441\pi$
$617$	29.1000	+	29.1000i	1.17152	+	1.17152i	0.189677	+	0.981847i	$0.439256\pi$
$618$	−0.631279	+	1.61686i	−0.0253938	+	0.0650395i
$619$	−4.23279	−	4.23279i	−0.170130	−	0.170130i	0.616906	−	0.787036i	$-0.288386\pi$
$619$	−4.23279	−	4.23279i	−0.170130	−	0.170130i	−0.787036	+	0.616906i	$0.788386\pi$
$620$	2.20730	+	15.9864i	0.0886474	+	0.642030i
$621$	−20.7927	+	20.7927i	−0.834383	+	0.834383i
$622$	−35.1723	+	15.4194i	−1.41028	+	0.618263i
$623$	0.0682883	−	0.0682883i	0.00273591	−	0.00273591i
$624$	−46.5185	+	3.81642i	−1.86223	+	0.152779i
$625$	−23.1689	+	9.39149i	−0.926758	+	0.375660i
$626$	9.94314	−	25.4668i	0.397408	−	1.01786i
$627$	−2.31220			−0.0923402
$628$	−4.62938	−	4.26513i	−0.184732	−	0.170197i
$629$	20.0197	−	20.0197i	0.798239	−	0.798239i
$630$	−5.32563	+	2.97503i	−0.212178	+	0.118528i
$631$	−1.33886			−0.0532991			−0.0266496	−	0.999645i	$-0.508484\pi$
$631$	−1.33886			−0.0532991			−0.0266496	+	0.999645i	$0.508484\pi$
$632$	−9.85718	+	28.6559i	−0.392097	+	1.13987i
$633$	17.5096	−	17.5096i	0.695944	−	0.695944i
$634$	14.6676	+	33.4573i	0.582524	+	1.32876i
$635$	−1.90644	−	19.7404i	−0.0756548	−	0.783373i
$636$	10.7235	−	11.6393i	0.425216	−	0.461530i
$637$		−	11.1001i		−	0.439803i
$638$	2.83045	−	1.24086i	0.112059	−	0.0491263i
$639$	3.09933			0.122608
$640$	14.9498	+	20.4084i	0.590943	+	0.806713i
$641$	24.5069			0.967965			0.483982	−	0.875078i	$-0.339190\pi$
$641$	24.5069			0.967965			0.483982	+	0.875078i	$0.339190\pi$
$642$	44.7175	−	19.6041i	1.76486	−	0.773710i
$643$		−	10.8979i		−	0.429771i	−0.976639	−	0.214885i	$-0.931062\pi$
$643$		−	10.8979i		−	0.429771i	0.976639	−	0.214885i	$-0.0689378\pi$
$644$	−21.4117	+	23.2402i	−0.843738	+	0.915793i
$645$	−27.6619	+	33.5760i	−1.08919	+	1.32205i
$646$	1.73390	+	3.95509i	0.0682194	+	0.155611i
$647$	−11.6612	+	11.6612i	−0.458448	+	0.458448i	−0.898146	−	0.439698i	$-0.855085\pi$
$647$	−11.6612	+	11.6612i	−0.458448	+	0.458448i	0.439698	+	0.898146i	$0.355085\pi$
$648$	−9.96331	+	28.9644i	−0.391396	+	1.13783i
$649$	5.23285			0.205407
$650$	−23.9374	−	34.5634i	−0.938901	−	1.35569i
$651$	−11.3455	+	11.3455i	−0.444666	+	0.444666i
$652$	11.5041	+	10.5990i	0.450536	+	0.415087i
$653$	5.28393			0.206776			0.103388	−	0.994641i	$-0.467032\pi$
$653$	5.28393			0.206776			0.103388	+	0.994641i	$0.467032\pi$
$654$	0.492726	−	1.26199i	0.0192671	−	0.0493476i
$655$	−0.491000	−	5.08409i	−0.0191849	−	0.198652i
$656$	−27.6405	+	2.26765i	−1.07918	+	0.0885369i
$657$	−2.50351	+	2.50351i	−0.0976713	+	0.0976713i
$658$	0.432720	−	0.189703i	0.0168692	−	0.00739540i
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	−0.314635	−	0.949213i	$-0.601882\pi$
$659$	16.2902	−	16.2902i	0.634578	−	0.634578i	0.949213	+	0.314635i	$0.101882\pi$
$660$	−7.46631	−	5.65465i	−0.290626	−	0.220107i
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	0.413114	−	0.910679i	$-0.364441\pi$
$661$	−12.7924	−	12.7924i	−0.497566	−	0.497566i	−0.910679	+	0.413114i	$0.864441\pi$
$662$	−9.90761	+	25.3757i	−0.385070	+	0.986256i
$663$	−22.8209	−	22.8209i	−0.886291	−	0.886291i
$664$	−11.3362	−	3.89948i	−0.439930	−	0.151329i
$665$	−3.55652	+	4.31690i	−0.137916	+	0.167402i
$666$	−11.2888	+	4.94897i	−0.437431	+	0.191769i
$667$			14.2810i			0.552962i
$668$	1.14396	+	27.9344i	0.0442613	+	1.08082i
$669$	25.8420	+	25.8420i	0.999111	+	0.999111i
$670$	27.5273	+	7.79526i	1.06347	+	0.301157i
$671$		−	1.02711i		−	0.0396512i
$672$	−7.20144	+	24.0993i	−0.277802	+	0.929651i
$673$	11.9553	+	11.9553i	0.460841	+	0.460841i	0.898931	−	0.438090i	$-0.144345\pi$
$673$	11.9553	+	11.9553i	0.460841	+	0.460841i	−0.438090	+	0.898931i	$0.644345\pi$
$674$	11.7046	−	29.9782i	0.450843	−	1.15472i
$675$	−20.6931	+	4.03454i	−0.796480	+	0.155290i
$676$	30.2913	−	32.8782i	1.16505	−	1.26455i
$677$	−3.18699			−0.122486			−0.0612430	−	0.998123i	$-0.519506\pi$
$677$	−3.18699			−0.122486			−0.0612430	+	0.998123i	$0.519506\pi$
$678$	7.76090	−	19.8775i	0.298056	−	0.763391i
$679$		−	6.12535i		−	0.235069i
$680$	−4.07353	+	17.0118i	−0.156213	+	0.652371i
$681$			37.9613i			1.45468i
$682$	−5.07303	−	1.98069i	−0.194256	−	0.0758447i
$683$	35.1661			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$683$	35.1661			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$684$	−0.0769279	−	1.87850i	−0.00294141	−	0.0718264i
$685$	2.07799	+	21.5167i	0.0793961	+	0.822112i
$686$	−26.4647	−	10.3328i	−1.01043	−	0.394508i
$687$	−25.9331	−	25.9331i	−0.989410	−	0.989410i
$688$	3.24234	+	39.5210i	0.123613	+	1.50672i
$689$			23.9743i			0.913346i
$690$	37.7836	−	21.1068i	1.43840	−	0.803523i
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	0.760134	−	0.649767i	$-0.225133\pi$
$691$	2.90121	+	2.90121i	0.110367	+	0.110367i	−0.649767	+	0.760134i	$0.725133\pi$
$692$	4.73284	−	5.13703i	0.179916	−	0.195280i
$693$		−	2.05860i		−	0.0781999i
$694$	−3.16594	−	7.22163i	−0.120178	−	0.274129i
$695$	−4.17758	−	43.2571i	−0.158465	−	1.64083i
$696$	4.98611	+	10.2151i	0.188998	+	0.387202i
$697$	−13.5598	−	13.5598i	−0.513614	−	0.513614i
$698$	−28.0966	−	10.9699i	−1.06347	−	0.415218i
$699$	−40.6011	−	40.6011i	−1.53568	−	1.53568i
$700$	−22.0416	+	5.24195i	−0.833095	+	0.198127i
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	−0.344358	−	0.938839i	$-0.611903\pi$
$701$	15.7397	−	15.7397i	0.594481	−	0.594481i	0.938839	+	0.344358i	$0.111903\pi$
$702$	−14.2357	−	32.4721i	−0.537291	−	1.22558i
$703$	−7.99136	+	7.99136i	−0.301400	+	0.301400i
$704$	−8.47290	+	1.04562i	−0.319335	+	0.0394082i
$705$	−0.644103	+	0.0622047i	−0.0242583	+	0.00234276i
$706$	4.80440	+	1.87581i	0.180816	+	0.0705971i
$707$	−15.9095			−0.598339
$708$	0.787524	+	19.2306i	0.0295970	+	0.722729i
$709$	−1.95755	+	1.95755i	−0.0735172	+	0.0735172i	−0.742909	−	0.669392i	$-0.766555\pi$
$709$	−1.95755	+	1.95755i	−0.0735172	+	0.0735172i	0.669392	+	0.742909i	$0.266555\pi$
$710$	11.0754	+	3.13636i	0.415652	+	0.117705i
$711$	9.12243			0.342118
$712$	−0.0392167	+	0.114007i	−0.00146971	+	0.00427260i
$713$	17.7947	−	17.7947i	0.666416	−	0.666416i
$714$	−15.9283	+	6.98294i	−0.596103	+	0.261330i
$715$	14.1222	−	1.36387i	0.528142	−	0.0510057i
$716$	−1.51388	−	36.9674i	−0.0565762	−	1.38154i
$717$		−	27.6818i		−	1.03379i
$718$	3.27760	+	7.47633i	0.122319	+	0.279014i
$719$	−0.0658604			−0.00245618			−0.00122809	−	0.999999i	$-0.500391\pi$
$719$	−0.0658604			−0.00245618			−0.00122809	+	0.999999i	$0.500391\pi$
$720$	4.34562	−	6.25401i	0.161952	−	0.233073i
$721$	−1.41692			−0.0527687
$722$	10.0964	+	23.0303i	0.375750	+	0.857100i
$723$			25.1223i			0.934309i
$724$	38.5454	−	1.57850i	1.43253	−	0.0586644i
$725$	−5.72078	+	8.49181i	−0.212465	+	0.315378i
$726$	−25.0659	+	10.9888i	−0.930283	+	0.407834i
$727$	−16.2286	+	16.2286i	−0.601885	+	0.601885i	−0.940813	−	0.338927i	$-0.889936\pi$
$727$	−16.2286	+	16.2286i	−0.601885	+	0.601885i	0.338927	+	0.940813i	$0.389936\pi$
$728$	−16.7132	−	34.2406i	−0.619434	−	1.26904i
$729$	−15.6045			−0.577943
$730$	−11.4797	+	6.41283i	−0.424882	+	0.237350i
$731$	−19.3881	+	19.3881i	−0.717095	+	0.717095i
$732$	3.77460	−	0.154576i	0.139513	−	0.00571330i
$733$	−0.669106			−0.0247140			−0.0123570	−	0.999924i	$-0.503933\pi$
$733$	−0.669106			−0.0247140			−0.0123570	+	0.999924i	$0.503933\pi$
$734$	−15.4724	−	6.04100i	−0.571098	−	0.222977i
$735$	6.32298	+	5.20925i	0.233227	+	0.192146i
$736$	11.2950	−	37.7981i	0.416338	−	1.39326i
$737$	−6.82691	+	6.82691i	−0.251472	+	0.251472i
$738$	3.35205	+	7.64614i	0.123391	+	0.281458i
$739$	23.4183	−	23.4183i	0.861454	−	0.861454i	−0.130053	−	0.991507i	$-0.541515\pi$
$739$	23.4183	−	23.4183i	0.861454	−	0.861454i	0.991507	+	0.130053i	$0.0415147\pi$
$740$	−45.3484	+	6.26141i	−1.66704	+	0.230174i
$741$	9.10952	+	9.10952i	0.334647	+	0.334647i
$742$	12.0346	+	4.69874i	0.441804	+	0.172496i
$743$	30.0968	+	30.0968i	1.10414	+	1.10414i	0.993905	+	0.110238i	$0.0351614\pi$
$743$	30.0968	+	30.0968i	1.10414	+	1.10414i	0.110238	+	0.993905i	$0.464839\pi$
$744$	6.51552	−	18.9413i	0.238871	−	0.694422i
$745$	−5.47092	+	0.528358i	−0.200439	+	0.0193575i
$746$	9.11257	+	20.7861i	0.333635	+	0.761033i
$747$			3.60882i			0.132040i
$748$	−4.34142	−	3.99983i	−0.158738	−	0.146248i
$749$	28.1838	+	28.1838i	1.02981	+	1.02981i
$750$	30.9222	+	2.58501i	1.12912	+	0.0943911i
$751$			53.2724i			1.94394i	0.235107	+	0.971970i	$0.424456\pi$
$751$			53.2724i			1.94394i	−0.235107	+	0.971970i	$0.575544\pi$
$752$	−0.381580	+	0.449786i	−0.0139148	+	0.0164020i
$753$	−13.4259	−	13.4259i	−0.489267	−	0.489267i
$754$	−16.0401	−	6.26262i	−0.584144	−	0.228071i
$755$	−10.0705	−	8.29666i	−0.366502	−	0.301946i
$756$	−19.0904	+	0.781783i	−0.694311	+	0.0284332i
$757$	−27.1717			−0.987574			−0.493787	−	0.869583i	$-0.664388\pi$
$757$	−27.1717			−0.987574			−0.493787	+	0.869583i	$0.664388\pi$
$758$	16.6065	+	6.48377i	0.603174	+	0.235501i
$759$			14.6051i			0.530132i
$760$	1.62605	−	6.79065i	0.0589830	−	0.246323i
$761$		−	12.9068i		−	0.467870i	−0.972252	−	0.233935i	$-0.924840\pi$
$761$		−	12.9068i		−	0.467870i	0.972252	−	0.233935i	$-0.0751604\pi$
$762$	−8.95270	+	22.9300i	−0.324322	+	0.830666i
$763$	1.10593			0.0400374
$764$	4.30270	+	3.96416i	0.155666	+	0.143418i
$765$	5.24147	−	0.506198i	0.189506	−	0.0183016i
$766$	18.1069	−	46.3761i	0.654229	−	1.67564i
$767$	−20.6162	−	20.6162i	−0.744409	−	0.744409i
$768$	−5.11775	−	30.9803i	−0.184671	−	1.11791i
$769$			34.4858i			1.24359i	0.783180	+	0.621795i	$0.213596\pi$
$769$			34.4858i			1.24359i	−0.783180	+	0.621795i	$0.786404\pi$
$770$	2.08320	−	7.35638i	0.0750733	−	0.265106i
$771$	−13.0806	−	13.0806i	−0.471087	−	0.471087i
$772$	0.234761	−	0.00961387i	0.00844925	−	0.000346011i
$773$			26.6789i			0.959574i	0.877385	+	0.479787i	$0.159286\pi$
$773$			26.6789i			0.959574i	−0.877385	+	0.479787i	$0.840714\pi$
$774$	10.9326	−	4.79283i	0.392965	−	0.172275i
$775$	17.7095	−	3.45281i	0.636143	−	0.124029i
$776$	3.35429	+	6.87196i	0.120412	+	0.246689i
$777$	−32.1836	−	32.1836i	−1.15458	−	1.15458i
$778$	12.0616	−	30.8927i	0.432431	−	1.10756i
$779$	5.41272	+	5.41272i	0.193931	+	0.193931i
$780$	7.13751	+	51.6936i	0.255564	+	1.85093i
$781$	−2.74675	+	2.74675i	−0.0982864	+	0.0982864i
$782$	24.9825	−	10.9523i	0.893373	−	0.391652i
$783$	−6.10566	+	6.10566i	−0.218199	+	0.218199i
$784$	7.44253	−	0.610593i	0.265805	−	0.0218069i
$785$	−4.47493	+	5.43167i	−0.159717	+	0.193865i
$786$	−2.30575	+	5.90557i	−0.0822433	+	0.210645i
$787$	−33.2611			−1.18563			−0.592815	−	0.805338i	$-0.701984\pi$
$787$	−33.2611			−1.18563			−0.592815	+	0.805338i	$0.701984\pi$
$788$	10.5769	−	11.4802i	0.376786	−	0.408963i
$789$	14.3659	−	14.3659i	0.511439	−	0.511439i
$790$	32.5988	+	9.23142i	1.15981	+	0.328439i
$791$	17.4195			0.619365
$792$	1.12731	+	2.30952i	0.0400571	+	0.0820653i
$793$	−4.04658	+	4.04658i	−0.143698	+	0.143698i
$794$	4.89762	+	11.1716i	0.173810	+	0.396466i
$795$	−13.6565	−	11.2510i	−0.484346	−	0.399033i
$796$	−16.1416	−	14.8715i	−0.572122	−	0.527107i
$797$		−	15.9072i		−	0.563461i	−0.959494	−	0.281730i	$-0.909092\pi$
$797$		−	15.9072i		−	0.563461i	0.959494	−	0.281730i	$-0.0909084\pi$
$798$	6.35818	−	2.78741i	0.225077	−	0.0986732i
$799$	−0.407850			−0.0144287
$800$	21.8577	−	17.9510i	0.772787	−	0.634665i
$801$	0.0362935			0.00128237
$802$	25.5296	−	11.1921i	0.901483	−	0.395208i
$803$		−	4.43743i		−	0.156593i
$804$	−26.1161	−	24.0613i	−0.921044	−	0.848575i
$805$	27.2679	+	22.4649i	0.961067	+	0.791784i
$806$	12.1831	+	27.7900i	0.429131	+	0.978863i
$807$	−31.3610	+	31.3610i	−1.10396	+	1.10396i
$808$	17.8487	−	8.71217i	0.627915	−	0.306493i
$809$	12.4922			0.439204			0.219602	−	0.975590i	$-0.429524\pi$
$809$	12.4922			0.439204			0.219602	+	0.975590i	$0.429524\pi$
$810$	32.9498	+	9.33082i	1.15774	+	0.327851i
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.288777	+	0.957396i	$0.593249\pi$
$811$	−35.4886	+	35.4886i	−1.24617	+	1.24617i	−0.957396	+	0.288777i	$0.906751\pi$
$812$	−6.28741	+	6.82436i	−0.220645	+	0.239488i
$813$	7.05884			0.247564
$814$	5.61859	−	14.3906i	0.196932	−	0.504389i
$815$	11.1203	−	13.4978i	0.389528	−	0.472809i
$816$	14.0459	−	16.5566i	0.491705	−	0.579595i
$817$	7.73923	−	7.73923i	0.270761	−	0.270761i
$818$	−34.7027	+	15.2136i	−1.21335	+	0.531930i
$819$	−8.11042	+	8.11042i	−0.283401	+	0.283401i
$820$	4.24099	+	30.7154i	0.148102	+	1.07263i
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	0.371239	−	0.928537i	$-0.378933\pi$
$821$	−15.9683	−	15.9683i	−0.557299	−	0.557299i	−0.928537	+	0.371239i	$0.878933\pi$
$822$	9.75833	−	24.9934i	0.340361	−	0.871745i
$823$	−21.7278	−	21.7278i	−0.757384	−	0.757384i	0.218462	−	0.975846i	$-0.429896\pi$
$823$	−21.7278	−	21.7278i	−0.757384	−	0.757384i	−0.975846	+	0.218462i	$0.929896\pi$
$824$	1.58962	−	0.775914i	0.0553771	−	0.0270302i
$825$	−5.85062	+	8.68454i	−0.203693	+	0.302357i
$826$	−14.3895	+	6.30833i	−0.500675	+	0.219495i
$827$			39.2381i			1.36444i	0.731146	+	0.682221i	$0.238986\pi$
$827$			39.2381i			1.36444i	−0.731146	+	0.682221i	$0.761014\pi$
$828$	−11.8657	+	0.485919i	−0.412360	+	0.0168869i
$829$	−18.6072	−	18.6072i	−0.646254	−	0.646254i	0.305831	−	0.952086i	$-0.401066\pi$
$829$	−18.6072	−	18.6072i	−0.646254	−	0.646254i	−0.952086	+	0.305831i	$0.901066\pi$
$830$	−3.65193	+	12.8960i	−0.126760	+	0.447628i
$831$		−	41.0982i		−	1.42568i
$832$	37.5008	+	29.2618i	1.30011	+	1.01447i
$833$	3.65114	+	3.65114i	0.126504	+	0.126504i
$834$	−19.6180	+	50.2465i	−0.679317	+	1.73989i
$835$	31.1131	−	3.00477i	1.07671	−	0.103984i
$836$	1.73298	+	1.59663i	0.0599365	+	0.0552206i
$837$	15.2158			0.525935
$838$	−8.05608	+	20.6335i	−0.278293	+	0.712774i
$839$		−	12.5955i		−	0.434845i	−0.976078	−	0.217422i	$-0.930235\pi$
$839$		−	12.5955i		−	0.434845i	0.976078	−	0.217422i	$-0.0697649\pi$
$840$	27.3480	+	6.54859i	0.943596	+	0.225948i
$841$		−	24.8065i		−	0.855396i
$842$	−0.452889	−	0.176824i	−0.0156076	−	0.00609377i
$843$	6.41151			0.220824
$844$	−25.2142	+	1.03256i	−0.867909	+	0.0355423i
$845$	−38.5762	−	31.7814i	−1.32706	−	1.09331i
$846$	0.165401	+	0.0645785i	0.00568660	+	0.00222025i
$847$	−15.7981	−	15.7981i	−0.542829	−	0.542829i
$848$	−16.0745	+	1.31877i	−0.552002	+	0.0452867i
$849$		0	0.000297553i		0	1.02120e-5i
$850$	19.2425	+	3.49520i	0.660014	+	0.119884i
$851$	50.4778	+	50.4778i	1.73036	+	1.73036i
$852$	−10.5076	−	9.68085i	−0.359984	−	0.331660i
$853$		−	43.6914i		−	1.49597i	−0.663718	−	0.747983i	$-0.731022\pi$
$853$		−	43.6914i		−	1.49597i	0.663718	−	0.747983i	$-0.268978\pi$
$854$	1.23821	+	2.82439i	0.0423706	+	0.0966488i
$855$	−2.09226	+	0.202061i	−0.0715537	+	0.00691035i
$856$	−47.0527	−	16.1854i	−1.60823	−	0.553206i
$857$	28.9373	+	28.9373i	0.988478	+	0.988478i	0.999934	−	0.0114561i	$-0.00364668\pi$
$857$	28.9373	+	28.9373i	0.988478	+	0.988478i	−0.0114561	+	0.999934i	$0.503647\pi$
$858$	−16.4041	−	6.40475i	−0.560027	−	0.218655i
$859$	−28.1247	−	28.1247i	−0.959602	−	0.959602i	0.0396134	−	0.999215i	$-0.487387\pi$
$859$	−28.1247	−	28.1247i	−0.959602	−	0.959602i	−0.999215	+	0.0396134i	$0.987387\pi$
$860$	43.9176	−	6.06386i	1.49758	−	0.206776i
$861$	−21.7987	+	21.7987i	−0.742896	+	0.742896i
$862$	−11.7552	−	26.8141i	−0.400384	−	0.913291i
$863$	22.2144	−	22.2144i	0.756186	−	0.756186i	−0.219440	−	0.975626i	$-0.570423\pi$
$863$	22.2144	−	22.2144i	0.756186	−	0.756186i	0.975626	+	0.219440i	$0.0704229\pi$
$864$	20.9892	−	11.3311i	0.714066	−	0.385492i
$865$	−6.02730	−	4.96565i	−0.204934	−	0.168837i
$866$	−10.5861	−	4.13322i	−0.359732	−	0.140452i
$867$	−18.3498			−0.623192
$868$	16.3378	−	0.669061i	0.554541	−	0.0227094i
$869$	−8.08466	+	8.08466i	−0.274253	+	0.274253i
$870$	11.0949	−	6.19790i	0.376153	−	0.210129i
$871$	53.7929			1.82270
$872$	−1.24073	+	0.605616i	−0.0420164	+	0.0205087i
$873$	1.62773	−	1.62773i	0.0550904	−	0.0550904i
$874$	−9.97237	+	4.37186i	−0.337320	+	0.147880i
$875$	7.21497	+	24.2813i	0.243911	+	0.820859i
$876$	16.3074	−	0.667816i	0.550976	−	0.0225634i
$877$			5.13889i			0.173528i	0.996229	+	0.0867640i	$0.0276526\pi$
$877$			5.13889i			0.173528i	−0.996229	+	0.0867640i	$0.972347\pi$
$878$	10.6694	+	24.3374i	0.360076	+	0.821346i
$879$	21.7040			0.732057
$880$	1.69129	+	9.39382i	0.0570135	+	0.316666i
$881$	−4.34528			−0.146396			−0.0731982	−	0.997317i	$-0.523321\pi$
$881$	−4.34528			−0.146396			−0.0731982	+	0.997317i	$0.523321\pi$
$882$	−0.902579	−	2.05881i	−0.0303914	−	0.0693239i
$883$			35.4317i			1.19237i	0.802846	+	0.596186i	$0.203318\pi$
$883$			35.4317i			1.19237i	−0.802846	+	0.596186i	$0.796682\pi$
$884$	1.34578	+	32.8626i	0.0452635	+	1.10529i
$885$	21.4188	−	2.06853i	0.719985	−	0.0695330i
$886$	15.7551	−	6.90701i	0.529304	−	0.232046i
$887$	37.4644	−	37.4644i	1.25793	−	1.25793i	0.305855	−	0.952078i	$-0.401058\pi$
$887$	37.4644	−	37.4644i	1.25793	−	1.25793i	0.952078	−	0.305855i	$-0.0989422\pi$
$888$	53.7304	+	18.4824i	1.80307	+	0.620230i
$889$	−20.0945			−0.673947
$890$	0.129694	+	0.0367271i	0.00434736	+	0.00123110i
$891$	−8.17171	+	8.17171i	−0.273763	+	0.273763i
$892$	−1.52394	−	37.2131i	−0.0510253	−	1.24599i
$893$	0.162803			0.00544799
$894$	6.35491	+	2.48119i	0.212540	+	0.0829833i
$895$	−41.1739	+	3.97640i	−1.37629	+	0.132916i
$896$	22.0386	−	13.0896i	0.736259	−	0.437292i
$897$	57.5407	−	57.5407i	1.92123	−	1.92123i
$898$	−15.4849	−	35.3215i	−0.516736	−	1.17869i
$899$	5.22531	−	5.22531i	0.174274	−	0.174274i
$900$	−7.25026	−	4.46430i	−0.241675	−	0.148810i
$901$	−7.88580	−	7.88580i	−0.262714	−	0.262714i
$902$	−9.74703	−	3.80560i	−0.324541	−	0.126712i
$903$	31.1682	+	31.1682i	1.03721	+	1.03721i
$904$	−19.5427	+	9.53903i	−0.649980	+	0.317263i
$905$	−4.14613	−	42.9314i	−0.137822	−	1.42709i
$906$	6.50248	+	14.8324i	0.216031	+	0.492773i
$907$		−	0.181405i		−	0.00602345i	−0.999995	−	0.00301173i	$-0.999041\pi$
$907$		−	0.181405i		−	0.00602345i	0.999995	−	0.00301173i	$-0.000958664\pi$
$908$	26.2132	−	28.4518i	0.869916	−	0.944208i
$909$	−4.22775	−	4.22775i	−0.140226	−	0.140226i
$910$	−37.1898	+	20.7751i	−1.23283	+	0.688689i
$911$		−	23.4249i		−	0.776101i	−0.921638	−	0.388050i	$-0.873149\pi$
$911$		−	23.4249i		−	0.776101i	0.921638	−	0.388050i	$-0.126851\pi$
$912$	−5.60676	+	6.60895i	−0.185658	+	0.218844i
$913$	−3.19828	−	3.19828i	−0.105848	−	0.105848i
$914$	−36.7976	−	14.3671i	−1.21716	−	0.475222i
$915$	−0.406015	−	4.20411i	−0.0134224	−	0.138984i
$916$	1.52931	+	37.3443i	0.0505299	+	1.23389i
$917$	−5.17529			−0.170903
$918$	15.3635	+	5.99846i	0.507071	+	0.197979i
$919$			3.05885i			0.100902i	0.998727	+	0.0504511i	$0.0160659\pi$
$919$			3.05885i			0.100902i	−0.998727	+	0.0504511i	$0.983934\pi$
$920$	−42.8935	−	10.2710i	−1.41416	−	0.338625i
$921$			29.6962i			0.978522i
$922$	9.40249	−	24.0820i	0.309654	−	0.793099i
$923$	21.6431			0.712392
$924$	−6.43011	+	6.97925i	−0.211535	+	0.229600i
$925$	9.79453	+	50.2361i	0.322042	+	1.65175i
$926$	−10.5943	+	27.1345i	−0.348150	+	0.891696i
$927$	−0.376527	−	0.376527i	−0.0123668	−	0.0123668i
$928$	3.31670	−	11.0992i	0.108876	−	0.364349i
$929$			59.9772i			1.96779i	0.178752	+	0.983894i	$0.442794\pi$
$929$			59.9772i			1.96779i	−0.178752	+	0.983894i	$0.557206\pi$
$930$	−21.5476	−	6.10190i	−0.706573	−	0.200089i
$931$	−1.45744	−	1.45744i	−0.0477657	−	0.0477657i
$932$	2.39430	+	58.4665i	0.0784280	+	1.91513i
$933$		−	53.2931i		−	1.74474i
$934$	−54.8596	+	24.0503i	−1.79506	+	0.786950i
$935$	−4.19659	+	5.09381i	−0.137243	+	0.166586i
$936$	4.65766	−	13.5403i	0.152240	−	0.442579i
$937$	23.7463	+	23.7463i	0.775759	+	0.775759i	0.979107	−	0.203347i	$-0.0651821\pi$
$937$	23.7463	+	23.7463i	0.775759	+	0.775759i	−0.203347	+	0.979107i	$0.565182\pi$
$938$	10.5429	−	27.0029i	0.344239	−	0.881677i
$939$	26.8266	+	26.8266i	0.875451	+	0.875451i
$940$	0.525707	+	0.398147i	0.0171467	+	0.0129861i
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.163278	+	0.986580i	$0.552207\pi$
$941$	−35.2727	+	35.2727i	−1.14986	+	1.14986i	−0.986580	+	0.163278i	$0.947793\pi$
$942$	8.00008	−	3.50722i	0.260657	−	0.114271i
$943$	34.1897	−	34.1897i	1.11337	−	1.11337i
$944$	12.6889	−	14.9570i	0.412990	−	0.486810i
$945$	2.05346	+	21.2627i	0.0667989	+	0.691674i
$946$	−5.44133	+	13.9365i	−0.176913	+	0.453116i
$947$	−19.9140			−0.647118			−0.323559	−	0.946208i	$-0.604879\pi$
$947$	−19.9140			−0.647118			−0.323559	+	0.946208i	$0.604879\pi$
$948$	−30.9276	−	28.4942i	−1.00448	−	0.925448i
$949$	−17.4824	+	17.4824i	−0.567504	+	0.567504i
$950$	−7.68112	−	1.39519i	−0.249208	−	0.0452661i
$951$	−50.6945			−1.64388
$952$	16.7601	+	5.76523i	0.543199	+	0.186852i
$953$	−23.1060	+	23.1060i	−0.748477	+	0.748477i	−0.974193	−	0.225716i	$-0.927528\pi$
$953$	−23.1060	+	23.1060i	−0.748477	+	0.748477i	0.225716	+	0.974193i	$0.427528\pi$
$954$	1.94941	+	4.44667i	0.0631144	+	0.143966i
$955$	4.15916	−	5.04838i	0.134587	−	0.163362i
$956$	−19.1150	+	20.7474i	−0.618222	+	0.671019i
$957$			4.28871i			0.138634i
$958$	−35.0881	+	15.3825i	−1.13364	+	0.496987i
$959$	21.9027			0.707276
$960$	−34.2675	+	7.62918i	−1.10598	+	0.246231i
$961$	17.9781			0.579939
$962$	−78.8314	+	34.5595i	−2.54163	+	1.11424i
$963$			14.9790i			0.482690i
$964$	17.3476	−	18.8291i	0.558728	−	0.606444i
$965$	−0.0252521	−	0.261475i	−0.000812894	−	0.00841717i
$966$	−17.6068	−	40.1617i	−0.566490	−	1.29218i
$967$	−41.7332	+	41.7332i	−1.34205	+	1.34205i	−0.448030	+	0.894018i	$0.647874\pi$
$967$	−41.7332	+	41.7332i	−1.34205	+	1.34205i	−0.894018	+	0.448030i	$0.852126\pi$
$968$	26.3749	+	9.07255i	0.847721	+	0.291603i
$969$	−5.99275			−0.192515
$970$	7.46386	−	4.16949i	0.239650	−	0.133874i
$971$	33.5030	−	33.5030i	1.07516	−	1.07516i	0.0782268	−	0.996936i	$-0.475074\pi$
$971$	33.5030	−	33.5030i	1.07516	−	1.07516i	0.996936	−	0.0782268i	$-0.0249258\pi$
$972$	−12.6543	−	11.6586i	−0.405885	−	0.373950i
$973$	−44.0330			−1.41163
$974$	15.9790	−	40.9259i	0.511999	−	1.31135i
$975$	57.2652	−	11.1650i	1.83395	−	0.357566i
$976$	−2.93579	−	2.49060i	−0.0939723	−	0.0797223i
$977$	9.16848	−	9.16848i	0.293326	−	0.293326i	−0.545067	−	0.838393i	$-0.683496\pi$
$977$	9.16848	−	9.16848i	0.293326	−	0.293326i	0.838393	+	0.545067i	$0.183496\pi$
$978$	−19.8804	+	8.71552i	−0.635706	+	0.278692i
$979$	−0.0321648	+	0.0321648i	−0.00102799	+	0.00102799i
$980$	−1.14194	−	8.27050i	−0.0364778	−	0.264191i
$981$	0.293887	+	0.293887i	0.00938308	+	0.00938308i
$982$	−4.45134	+	11.4009i	−0.142048	+	0.363818i
$983$	−39.1183	−	39.1183i	−1.24768	−	1.24768i	−0.956742	−	0.290936i	$-0.906033\pi$
$983$	−39.1183	−	39.1183i	−1.24768	−	1.24768i	−0.290936	−	0.956742i	$-0.593967\pi$
$984$	12.5186	−	36.3928i	0.399077	−	1.16016i
$985$	−13.4697	−	11.0972i	−0.429181	−	0.353585i
$986$	7.33597	−	3.21607i	0.233625	−	0.102421i
$987$			0.655657i			0.0208698i
$988$	−0.537201	−	13.1179i	−0.0170906	−	0.417336i
$989$	−48.8852	−	48.8852i	−1.55446	−	1.55446i
$990$	2.50845	−	1.40128i	0.0797237	−	0.0445356i
$991$		−	12.9925i		−	0.412722i	−0.978476	−	0.206361i	$-0.933838\pi$
$991$		−	12.9925i		−	0.412722i	0.978476	−	0.206361i	$-0.0661621\pi$
$992$	−17.9628	+	9.69732i	−0.570320	+	0.307890i
$993$	−26.7307	−	26.7307i	−0.848273	−	0.848273i
$994$	4.24186	−	10.8644i	0.134544	−	0.344598i
$995$	−15.6031	+	18.9390i	−0.494650	+	0.600406i
$996$	11.2722	−	12.2349i	0.357175	−	0.387678i
$997$	−8.89509			−0.281710			−0.140855	−	0.990030i	$-0.544985\pi$
$997$	−8.89509			−0.281710			−0.140855	+	0.990030i	$0.544985\pi$
$998$	−11.2103	+	28.7122i	−0.354855	+	0.908868i
$999$			43.1624i			1.36560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.j.b.43.9	✓	18
3.2	odd	2		720.2.bd.g.523.1		18
4.3	odd	2		320.2.j.b.143.2		18
5.2	odd	4		80.2.s.b.27.6	yes	18
5.3	odd	4		400.2.s.d.107.4		18
5.4	even	2		400.2.j.d.43.1		18
8.3	odd	2		640.2.j.c.543.8		18
8.5	even	2		640.2.j.d.543.2		18
15.2	even	4		720.2.z.g.667.4		18
16.3	odd	4		80.2.s.b.3.6	yes	18
16.5	even	4		640.2.s.c.223.8		18
16.11	odd	4		640.2.s.d.223.2		18
16.13	even	4		320.2.s.b.303.2		18
20.3	even	4		1600.2.s.d.207.8		18
20.7	even	4		320.2.s.b.207.2		18
20.19	odd	2		1600.2.j.d.143.8		18
40.27	even	4		640.2.s.c.287.8		18
40.37	odd	4		640.2.s.d.287.2		18
48.35	even	4		720.2.z.g.163.4		18
80.3	even	4		400.2.j.d.307.1		18
80.13	odd	4		1600.2.j.d.1007.2		18
80.19	odd	4		400.2.s.d.243.4		18
80.27	even	4		640.2.j.d.607.8		18
80.29	even	4		1600.2.s.d.943.8		18
80.37	odd	4		640.2.j.c.607.2		18
80.67	even	4	inner	80.2.j.b.67.9	yes	18
80.77	odd	4		320.2.j.b.47.8		18
240.227	odd	4		720.2.bd.g.307.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	1.1	even	1	trivial
80.2.j.b.67.9	yes	18	80.67	even	4	inner
80.2.s.b.3.6	yes	18	16.3	odd	4
80.2.s.b.27.6	yes	18	5.2	odd	4
320.2.j.b.47.8		18	80.77	odd	4
320.2.j.b.143.2		18	4.3	odd	2
320.2.s.b.207.2		18	20.7	even	4
320.2.s.b.303.2		18	16.13	even	4
400.2.j.d.43.1		18	5.4	even	2
400.2.j.d.307.1		18	80.3	even	4
400.2.s.d.107.4		18	5.3	odd	4
400.2.s.d.243.4		18	80.19	odd	4
640.2.j.c.543.8		18	8.3	odd	2
640.2.j.c.607.2		18	80.37	odd	4
640.2.j.d.543.2		18	8.5	even	2
640.2.j.d.607.8		18	80.27	even	4
640.2.s.c.223.8		18	16.5	even	4
640.2.s.c.287.8		18	40.27	even	4
640.2.s.d.223.2		18	16.11	odd	4
640.2.s.d.287.2		18	40.37	odd	4
720.2.z.g.163.4		18	48.35	even	4
720.2.z.g.667.4		18	15.2	even	4
720.2.bd.g.307.1		18	240.227	odd	4
720.2.bd.g.523.1		18	3.2	odd	2
1600.2.j.d.143.8		18	20.19	odd	2
1600.2.j.d.1007.2		18	80.13	odd	4
1600.2.s.d.207.8		18	20.3	even	4
1600.2.s.d.943.8		18	80.29	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29521 - 0.567819i) q^{2} +1.96251i q^{3} +(1.35516 - 1.47090i) q^{4} +(-1.72581 - 1.42182i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 + 1.60205i) q^{7} +(0.920026 - 2.67461i) q^{8} -0.851447 q^{9} +O(q^{10})\)	\(q+(1.29521 - 0.567819i) q^{2} +1.96251i q^{3} +(1.35516 - 1.47090i) q^{4} +(-1.72581 - 1.42182i) q^{5} +(1.11435 + 2.54187i) q^{6} +(-1.60205 + 1.60205i) q^{7} +(0.920026 - 2.67461i) q^{8} -0.851447 q^{9} +(-3.04263 - 0.861621i) q^{10} +(0.754587 - 0.754587i) q^{11} +(2.88665 + 2.65952i) q^{12} -5.94580 q^{13} +(-1.16532 + 2.98467i) q^{14} +(2.79034 - 3.38692i) q^{15} +(-0.327065 - 3.98661i) q^{16} +(1.95574 - 1.95574i) q^{17} +(-1.10281 + 0.483468i) q^{18} +(-0.780680 + 0.780680i) q^{19} +(-4.43011 + 0.611680i) q^{20} +(-3.14404 - 3.14404i) q^{21} +(0.548884 - 1.40582i) q^{22} +(4.93121 + 4.93121i) q^{23} +(5.24896 + 1.80556i) q^{24} +(0.956833 + 4.90759i) q^{25} +(-7.70109 + 3.37614i) q^{26} +4.21656i q^{27} +(0.185408 + 4.52748i) q^{28} +(1.44802 + 1.44802i) q^{29} +(1.69094 - 5.97120i) q^{30} -3.60859i q^{31} +(-2.68729 - 4.97780i) q^{32} +(1.48089 + 1.48089i) q^{33} +(1.42260 - 3.64361i) q^{34} +(5.04266 - 0.486998i) q^{35} +(-1.15385 + 1.25239i) q^{36} +10.2364 q^{37} +(-0.567864 + 1.45443i) q^{38} -11.6687i q^{39} +(-5.39062 + 3.30776i) q^{40} -6.93334i q^{41} +(-5.85745 - 2.28696i) q^{42} -9.91344 q^{43} +(-0.0873298 - 2.13251i) q^{44} +(1.46944 + 1.21061i) q^{45} +(9.18700 + 3.58694i) q^{46} +(-0.104270 - 0.104270i) q^{47} +(7.82376 - 0.641868i) q^{48} +1.86688i q^{49} +(4.02593 + 5.81308i) q^{50} +(3.83816 + 3.83816i) q^{51} +(-8.05753 + 8.74565i) q^{52} -4.03213i q^{53} +(2.39424 + 5.46135i) q^{54} +(-2.37516 + 0.229383i) q^{55} +(2.81093 + 5.75878i) q^{56} +(-1.53209 - 1.53209i) q^{57} +(2.69771 + 1.05328i) q^{58} +(3.46736 + 3.46736i) q^{59} +(-1.20043 - 8.69413i) q^{60} +(0.680578 - 0.680578i) q^{61} +(-2.04902 - 4.67390i) q^{62} +(1.36406 - 1.36406i) q^{63} +(-6.30711 - 4.92142i) q^{64} +(10.2613 + 8.45388i) q^{65} +(2.75894 + 1.07719i) q^{66} -9.04721 q^{67} +(-0.226341 - 5.52703i) q^{68} +(-9.67754 + 9.67754i) q^{69} +(6.25480 - 3.49408i) q^{70} -3.64007 q^{71} +(-0.783353 + 2.27729i) q^{72} +(2.94030 - 2.94030i) q^{73} +(13.2583 - 5.81242i) q^{74} +(-9.63120 + 1.87779i) q^{75} +(0.0903496 + 2.20625i) q^{76} +2.41777i q^{77} +(-6.62570 - 15.1135i) q^{78} -10.7140 q^{79} +(-5.10380 + 7.34515i) q^{80} -10.8294 q^{81} +(-3.93688 - 8.98016i) q^{82} -4.23845i q^{83} +(-8.88523 + 0.363865i) q^{84} +(-6.15595 + 0.594515i) q^{85} +(-12.8400 + 5.62904i) q^{86} +(-2.84176 + 2.84176i) q^{87} +(-1.32399 - 2.71247i) q^{88} -0.0426256 q^{89} +(2.59064 + 0.733625i) q^{90} +(9.52546 - 9.52546i) q^{91} +(13.9359 - 0.570698i) q^{92} +7.08189 q^{93} +(-0.194258 - 0.0758455i) q^{94} +(2.45730 - 0.237315i) q^{95} +(9.76898 - 5.27383i) q^{96} +(-1.91173 + 1.91173i) q^{97} +(1.06005 + 2.41802i) q^{98} +(-0.642491 + 0.642491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more