LMFDB - Embedded newform 80.2.j.b.67.9

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			67.9
Root			$1.41303 + 0.0578659i$ of defining polynomial
Character	$\chi$	$=$	80.67
Dual form			80.2.j.b.43.9

$q$-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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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	$-0.808286\pi$
$3$		−	1.96251i		−	1.13306i	0.824043	−	0.566528i	$-0.191714\pi$
$4$	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	0.336254	−	0.941771i	$-0.390840\pi$
$7$	−1.60205	−	1.60205i	−0.605517	−	0.605517i	−0.941771	+	0.336254i	$0.890840\pi$
$8$	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	0.811654	−	0.584138i	$-0.198567\pi$
$11$	0.754587	+	0.754587i	0.227517	+	0.227517i	−0.584138	+	0.811654i	$0.698567\pi$
$12$	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	0.903315	−	0.428978i	$-0.141126\pi$
$17$	1.95574	+	1.95574i	0.474336	+	0.474336i	−0.428978	+	0.903315i	$0.641126\pi$
$18$	−1.10281	−	0.483468i	−0.259934	−	0.113954i
$19$	−0.780680	−	0.780680i	−0.179100	−	0.179100i	0.611863	−	0.790964i	$-0.290420\pi$
$19$	−0.780680	−	0.780680i	−0.179100	−	0.179100i	−0.790964	+	0.611863i	$0.790420\pi$
$20$	−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	0.0286378	−	0.999590i	$-0.490883\pi$
$23$	4.93121	−	4.93121i	1.02823	−	1.02823i	0.999590	−	0.0286378i	$-0.00911693\pi$
$24$	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	−0.559762	−	0.828653i	$-0.689108\pi$
$29$	1.44802	−	1.44802i	0.268891	−	0.268891i	0.828653	+	0.559762i	$0.189108\pi$
$30$	1.69094	+	5.97120i	0.308722	+	1.09019i
$31$			3.60859i			0.648121i	0.946036	+	0.324061i	$0.105048\pi$
$31$			3.60859i			0.648121i	−0.946036	+	0.324061i	$0.894952\pi$
$32$	−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	$0.182107\pi$
$41$			6.93334i			1.08281i	−0.840763	+	0.541403i	$0.817893\pi$
$42$	−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	−0.714671	−	0.699461i	$-0.753423\pi$
$47$	−0.104270	+	0.104270i	−0.0152093	+	0.0152093i	0.699461	+	0.714671i	$0.253423\pi$
$48$	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	$0.0893164\pi$
$53$			4.03213i			0.553856i	−0.960891	+	0.276928i	$0.910684\pi$
$54$	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	−0.444411	−	0.895823i	$-0.646587\pi$
$59$	3.46736	−	3.46736i	0.451412	−	0.451412i	0.895823	+	0.444411i	$0.146587\pi$
$60$	−1.20043	+	8.69413i	−0.154975	+	1.12241i
$61$	0.680578	+	0.680578i	0.0871391	+	0.0871391i	0.749333	−	0.662194i	$-0.230374\pi$
$61$	0.680578	+	0.680578i	0.0871391	+	0.0871391i	−0.662194	+	0.749333i	$0.730374\pi$
$62$	−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	0.857920	−	0.513784i	$-0.171757\pi$
$73$	2.94030	+	2.94030i	0.344136	+	0.344136i	−0.513784	+	0.857920i	$0.671757\pi$
$74$	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	$0.0747282\pi$
$83$			4.23845i			0.465230i	−0.972569	+	0.232615i	$0.925272\pi$
$84$	−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	0.603362	−	0.797468i	$-0.293828\pi$
$97$	−1.91173	−	1.91173i	−0.194106	−	0.194106i	−0.797468	+	0.603362i	$0.793828\pi$
$98$	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	−0.415514	−	0.909587i	$-0.636398\pi$
$101$	4.96537	−	4.96537i	0.494073	−	0.494073i	0.909587	+	0.415514i	$0.136398\pi$
$102$	7.15062	−	2.79186i	0.708017	−	0.276435i
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	−0.684984	−	0.728558i	$-0.740191\pi$
$103$	0.442220	−	0.442220i	0.0435733	−	0.0435733i	0.728558	+	0.684984i	$0.240191\pi$
$104$	−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	$0.323615\pi$
$107$			17.5924i			1.70072i	−0.526204	+	0.850359i	$0.676385\pi$
$108$	6.20211	−	5.71412i	0.596799	−	0.549842i
$109$	−0.345161	+	0.345161i	−0.0330605	+	0.0330605i	−0.723444	−	0.690383i	$-0.757442\pi$
$109$	−0.345161	+	0.345161i	−0.0330605	+	0.0330605i	0.690383	+	0.723444i	$0.257442\pi$
$110$	−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	−0.914966	−	0.403531i	$-0.867783\pi$
$113$	−5.43662	+	5.43662i	−0.511435	+	0.511435i	0.403531	+	0.914966i	$0.367783\pi$
$114$	−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	−0.371805	−	0.928311i	$-0.621261\pi$
$127$	6.27150	−	6.27150i	0.556505	−	0.556505i	0.928311	+	0.371805i	$0.121261\pi$
$128$	−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	−0.633017	−	0.774138i	$-0.718184\pi$
$131$	1.61521	−	1.61521i	0.141122	−	0.141122i	0.774138	+	0.633017i	$0.218184\pi$
$132$	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	−0.936007	−	0.351981i	$-0.885508\pi$
$137$	−6.83585	+	6.83585i	−0.584026	+	0.584026i	0.351981	+	0.936007i	$0.385508\pi$
$138$	−7.03941	−	18.0296i	−0.599234	−	1.53478i
$139$	13.7427	−	13.7427i	1.16564	−	1.16564i	0.182423	−	0.983220i	$-0.441606\pi$
$139$	13.7427	−	13.7427i	1.16564	−	1.16564i	0.983220	−	0.182423i	$-0.0583940\pi$
$140$	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	0.774709	−	0.632318i	$-0.217896\pi$
$149$	1.73811	+	1.73811i	0.142391	+	0.142391i	−0.632318	+	0.774709i	$0.717896\pi$
$150$	−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	$0.0400829\pi$
$157$			3.14732i			0.251183i	−0.992082	+	0.125592i	$0.959917\pi$
$158$	−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	$-0.900909\pi$
$163$		−	7.82117i		−	0.612601i	0.951935	−	0.306301i	$-0.0990913\pi$
$164$	−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	0.212309	−	0.977203i	$-0.431902\pi$
$167$	−9.88460	−	9.88460i	−0.764893	−	0.764893i	−0.977203	+	0.212309i	$0.931902\pi$
$168$	−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	0.999757	−	0.0220444i	$-0.00701753\pi$
$179$	13.0809	+	13.0809i	0.977713	+	0.977713i	−0.0220444	+	0.999757i	$0.507018\pi$
$180$	3.77200	+	0.520813i	0.281148	+	0.0388191i
$181$	13.6393	−	13.6393i	1.01380	−	1.01380i	0.0138952	−	0.999903i	$-0.495577\pi$
$181$	13.6393	−	13.6393i	1.01380	−	1.01380i	0.999903	−	0.0138952i	$-0.00442312\pi$
$182$	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	$-0.966250\pi$
$191$		−	2.92523i		−	0.211662i	0.994384	−	0.105831i	$-0.0337503\pi$
$192$	9.65835	+	12.3778i	0.697031	+	0.893288i
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	−0.704111	−	0.710090i	$-0.748654\pi$
$193$	0.0830702	−	0.0830702i	0.00597953	−	0.00597953i	0.710090	+	0.704111i	$0.248654\pi$
$194$	−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	$0.127166\pi$
$199$			10.9740i			0.777924i	−0.921254	+	0.388962i	$0.872834\pi$
$200$	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	−0.944042	−	0.329824i	$-0.893011\pi$
$211$	−8.92204	+	8.92204i	−0.614218	+	0.614218i	0.329824	+	0.944042i	$0.393011\pi$
$212$	−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	0.993716	−	0.111931i	$-0.0357037\pi$
$223$	13.1678	+	13.1678i	0.881784	+	0.881784i	−0.111931	+	0.993716i	$0.535704\pi$
$224$	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	0.119599	−	0.992822i	$-0.461839\pi$
$229$	−13.2143	−	13.2143i	−0.873223	−	0.873223i	−0.992822	+	0.119599i	$0.961839\pi$
$230$	−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	−0.879570	−	0.475769i	$-0.842170\pi$
$233$	−20.6884	−	20.6884i	−1.35534	−	1.35534i	−0.475769	−	0.879570i	$-0.657830\pi$
$234$	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	0.457433	−	0.889244i	$-0.348769\pi$
$251$	−6.84118	−	6.84118i	−0.431812	−	0.431812i	−0.889244	+	0.457433i	$0.848769\pi$
$252$	−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	0.467975	−	0.883742i	$-0.344984\pi$
$257$	−6.66524	−	6.66524i	−0.415766	−	0.415766i	−0.883742	+	0.467975i	$0.844984\pi$
$258$	−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	−0.895812	−	0.444432i	$-0.853405\pi$
$263$	−7.32015	+	7.32015i	−0.451380	+	0.451380i	0.444432	+	0.895812i	$0.353405\pi$
$264$	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	−0.0253576	−	0.999678i	$-0.508072\pi$
$269$	15.9801	−	15.9801i	0.974321	−	0.974321i	0.999678	+	0.0253576i	$0.00807242\pi$
$270$	3.63307	+	12.8294i	0.221102	+	0.780774i
$271$			3.59684i			0.218492i	0.994015	+	0.109246i	$0.0348437\pi$
$271$			3.59684i			0.218492i	−0.994015	+	0.109246i	$0.965156\pi$
$272$	−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	$0.0310674\pi$
$281$			3.26699i			0.194892i	−0.995241	+	0.0974462i	$0.968933\pi$
$282$	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	$0.104707\pi$
$293$			11.0593i			0.646091i	−0.946384	+	0.323045i	$0.895293\pi$
$294$	−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	0.978568	−	0.205922i	$-0.0660194\pi$
$313$	13.6695	+	13.6695i	0.772646	+	0.772646i	−0.205922	+	0.978568i	$0.566019\pi$
$314$	−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	$-0.741646\pi$
$317$		−	25.8314i		−	1.45084i	0.688307	−	0.725419i	$-0.258354\pi$
$318$	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	0.225568	−	0.974227i	$-0.427576\pi$
$331$	−13.6207	−	13.6207i	−0.748659	−	0.748659i	−0.974227	+	0.225568i	$0.927576\pi$
$332$	−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	0.993174	−	0.116638i	$-0.0372119\pi$
$337$	16.0911	+	16.0911i	0.876536	+	0.876536i	−0.116638	+	0.993174i	$0.537212\pi$
$338$	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	$0.0478171\pi$
$347$			5.57562i			0.299315i	−0.988738	+	0.149658i	$0.952183\pi$
$348$	0.328882	−	8.03097i	0.0176299	−	0.430505i
$349$	−15.0811	+	15.0811i	−0.807273	+	0.807273i	−0.984220	−	0.176947i	$-0.943378\pi$
$349$	−15.0811	+	15.0811i	−0.807273	+	0.807273i	0.176947	+	0.984220i	$0.443378\pi$
$350$	−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	−0.635141	−	0.772397i	$-0.719058\pi$
$353$	2.57880	−	2.57880i	0.137256	−	0.137256i	0.772397	+	0.635141i	$0.219058\pi$
$354$	−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	$-0.951324\pi$
$359$		−	5.77227i		−	0.304649i	0.988331	−	0.152324i	$-0.0486758\pi$
$360$	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	−0.889822	−	0.456307i	$-0.849172\pi$
$367$	−8.30496	+	8.30496i	−0.433516	+	0.433516i	0.456307	+	0.889822i	$0.349172\pi$
$368$	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	$-0.863615\pi$
$373$		−	16.0484i		−	0.830953i	0.909604	−	0.415477i	$-0.136385\pi$
$374$	−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	−0.440089	−	0.897954i	$-0.645053\pi$
$379$	8.91367	−	8.91367i	0.457865	−	0.457865i	0.897954	+	0.440089i	$0.145053\pi$
$380$	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	0.945057	+	0.326904i	$0.106005\pi$
$383$	24.8928	+	24.8928i	1.27196	+	1.27196i	0.326904	+	0.945057i	$0.393995\pi$
$384$	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	0.988955	−	0.148217i	$-0.0473534\pi$
$389$	16.5819	+	16.5819i	0.840738	+	0.840738i	−0.148217	+	0.988955i	$0.547353\pi$
$390$	−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	$-0.930553\pi$
$397$		−	8.62531i		−	0.432892i	0.976295	−	0.216446i	$-0.0694465\pi$
$398$	−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	0.382779	−	0.923840i	$-0.374967\pi$
$419$	−11.0752	−	11.0752i	−0.541061	−	0.541061i	−0.923840	+	0.382779i	$0.874967\pi$
$420$	15.8516	−	12.0053i	0.773477	−	0.585797i
$421$	−0.243092	+	0.243092i	−0.0118476	+	0.0118476i	−0.713006	−	0.701158i	$-0.752667\pi$
$421$	−0.243092	+	0.243092i	−0.0118476	+	0.0118476i	0.701158	+	0.713006i	$0.252667\pi$
$422$	−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	$0.166152\pi$
$431$			20.7024i			0.997200i	−0.866832	+	0.498600i	$0.833848\pi$
$432$	16.8098	+	1.37909i	0.808760	+	0.0663514i
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	−0.830335	−	0.557265i	$-0.811851\pi$
$433$	−5.68221	+	5.68221i	−0.273069	+	0.273069i	0.557265	+	0.830335i	$0.311851\pi$
$434$	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	$-0.851993\pi$
$439$		−	18.7902i		−	0.896808i	0.893831	−	0.448404i	$-0.148007\pi$
$440$	−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	$0.222516\pi$
$449$			27.2708i			1.28699i	−0.765452	+	0.643493i	$0.777484\pi$
$450$	−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	−0.997305	−	0.0733714i	$-0.976624\pi$
$457$	−19.7514	+	19.7514i	−0.923933	+	0.923933i	0.0733714	+	0.997305i	$0.476624\pi$
$458$	−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	0.940852	−	0.338818i	$-0.110027\pi$
$461$	12.9262	+	12.9262i	0.602035	+	0.602035i	−0.338818	+	0.940852i	$0.610027\pi$
$462$	−6.14566	−	2.69424i	−0.285922	−	0.125348i
$463$	−14.5647	−	14.5647i	−0.676879	−	0.676879i	0.282414	−	0.959293i	$-0.408865\pi$
$463$	−14.5647	−	14.5647i	−0.676879	−	0.676879i	−0.959293	+	0.282414i	$0.908865\pi$
$464$	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	0.999990	−	0.00455390i	$-0.00144956\pi$
$487$	21.9674	+	21.9674i	0.995436	+	0.995436i	−0.00455390	+	0.999990i	$0.501450\pi$
$488$	−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	0.555407	−	0.831579i	$-0.312562\pi$
$491$	−6.11955	−	6.11955i	−0.276171	−	0.276171i	−0.831579	+	0.555407i	$0.812562\pi$
$492$	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	0.272298	−	0.962213i	$-0.412216\pi$
$499$	−15.4115	−	15.4115i	−0.689914	−	0.689914i	−0.962213	+	0.272298i	$0.912216\pi$
$500$	−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	0.198387	−	0.980124i	$-0.436430\pi$
$503$	26.4312	−	26.4312i	1.17851	−	1.17851i	0.980124	−	0.198387i	$-0.0635704\pi$
$504$	−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	−0.701908	−	0.712267i	$-0.747668\pi$
$509$	0.233714	−	0.233714i	0.0103592	−	0.0103592i	0.712267	+	0.701908i	$0.247668\pi$
$510$	−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	$0.0314385\pi$
$521$			4.50147i			0.197213i	−0.995127	+	0.0986064i	$0.968562\pi$
$522$	−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	0.946414	−	0.322955i	$-0.104676\pi$
$541$	14.5013	+	14.5013i	0.623459	+	0.623459i	−0.322955	+	0.946414i	$0.604676\pi$
$542$	−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	$-0.933928\pi$
$557$		−	9.72758i		−	0.412171i	0.978534	−	0.206085i	$-0.0660725\pi$
$558$	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	$0.122282\pi$
$563$			17.7853i			0.749562i	−0.927113	+	0.374781i	$0.877718\pi$
$564$	−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	0.999708	−	0.0241793i	$-0.00769727\pi$
$571$	23.3108	+	23.3108i	0.975528	+	0.975528i	−0.0241793	+	0.999708i	$0.507697\pi$
$572$	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	0.997239	+	0.0742597i	$0.0236594\pi$
$577$	25.7383	+	25.7383i	1.07150	+	1.07150i	0.0742597	+	0.997239i	$0.476341\pi$
$578$	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	$0.158419\pi$
$587$			23.1327i			0.954790i	−0.878689	+	0.477395i	$0.841581\pi$
$588$	−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	−0.0485322	+	0.998822i	$0.515454\pi$
$593$	−25.5047	+	25.5047i	−1.04735	+	1.04735i	−0.998822	+	0.0485322i	$0.984546\pi$
$594$	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	$0.0726146\pi$
$599$			11.0699i			0.452304i	−0.974092	+	0.226152i	$0.927385\pi$
$600$	−3.83858	−	27.4874i	−0.156709	−	1.12217i
$601$		−	13.7579i		−	0.561197i	−0.959825	−	0.280599i	$-0.909467\pi$
$601$		−	13.7579i		−	0.561197i	0.959825	−	0.280599i	$-0.0905330\pi$
$602$	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	−0.224826	−	0.974399i	$-0.572181\pi$
$607$	18.4675	−	18.4675i	0.749573	−	0.749573i	0.974399	+	0.224826i	$0.0721813\pi$
$608$	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	$0.0758021\pi$
$613$			11.6810i			0.471790i	−0.971779	+	0.235895i	$0.924198\pi$
$614$	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	0.189677	−	0.981847i	$-0.439256\pi$
$617$	29.1000	−	29.1000i	1.17152	−	1.17152i	0.981847	−	0.189677i	$-0.0607441\pi$
$618$	−0.631279	−	1.61686i	−0.0253938	−	0.0650395i
$619$	−4.23279	+	4.23279i	−0.170130	+	0.170130i	−0.787036	−	0.616906i	$-0.788386\pi$
$619$	−4.23279	+	4.23279i	−0.170130	+	0.170130i	0.616906	+	0.787036i	$0.288386\pi$
$620$	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	$0.0689378\pi$
$643$			10.8979i			0.429771i	−0.976639	+	0.214885i	$0.931062\pi$
$644$	−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	0.439698	−	0.898146i	$-0.355085\pi$
$647$	−11.6612	−	11.6612i	−0.458448	−	0.458448i	−0.898146	+	0.439698i	$0.855085\pi$
$648$	−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	0.949213	−	0.314635i	$-0.101882\pi$
$659$	16.2902	+	16.2902i	0.634578	+	0.634578i	−0.314635	+	0.949213i	$0.601882\pi$
$660$	−7.46631	+	5.65465i	−0.290626	+	0.220107i
$661$	−12.7924	+	12.7924i	−0.497566	+	0.497566i	−0.910679	−	0.413114i	$-0.864441\pi$
$661$	−12.7924	+	12.7924i	−0.497566	+	0.497566i	0.413114	+	0.910679i	$0.364441\pi$
$662$	−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	−0.438090	−	0.898931i	$-0.644345\pi$
$673$	11.9553	−	11.9553i	0.460841	−	0.460841i	0.898931	+	0.438090i	$0.144345\pi$
$674$	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	−0.649767	−	0.760134i	$-0.725133\pi$
$691$	2.90121	−	2.90121i	0.110367	−	0.110367i	0.760134	+	0.649767i	$0.225133\pi$
$692$	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	0.938839	−	0.344358i	$-0.111903\pi$
$701$	15.7397	+	15.7397i	0.594481	+	0.594481i	−0.344358	+	0.938839i	$0.611903\pi$
$702$	−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	0.669392	−	0.742909i	$-0.266555\pi$
$709$	−1.95755	−	1.95755i	−0.0735172	−	0.0735172i	−0.742909	+	0.669392i	$0.766555\pi$
$710$	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	0.338927	−	0.940813i	$-0.389936\pi$
$727$	−16.2286	−	16.2286i	−0.601885	−	0.601885i	−0.940813	+	0.338927i	$0.889936\pi$
$728$	−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	0.991507	−	0.130053i	$-0.0415147\pi$
$739$	23.4183	+	23.4183i	0.861454	+	0.861454i	−0.130053	+	0.991507i	$0.541515\pi$
$740$	−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	0.110238	−	0.993905i	$-0.464839\pi$
$743$	30.0968	−	30.0968i	1.10414	−	1.10414i	0.993905	−	0.110238i	$-0.0351614\pi$
$744$	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	$-0.575544\pi$
$751$		−	53.2724i		−	1.94394i	0.235107	−	0.971970i	$-0.424456\pi$
$752$	−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	$0.0751604\pi$
$761$			12.9068i			0.467870i	−0.972252	+	0.233935i	$0.924840\pi$
$762$	−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	$-0.786404\pi$
$769$		−	34.4858i		−	1.24359i	0.783180	−	0.621795i	$-0.213596\pi$
$770$	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	$-0.840714\pi$
$773$		−	26.6789i		−	0.959574i	0.877385	−	0.479787i	$-0.159286\pi$
$774$	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	$0.0909084\pi$
$797$			15.9072i			0.563461i	−0.959494	+	0.281730i	$0.909092\pi$
$798$	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	−0.957396	−	0.288777i	$-0.906751\pi$
$811$	−35.4886	−	35.4886i	−1.24617	−	1.24617i	−0.288777	−	0.957396i	$-0.593249\pi$
$812$	−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	−0.928537	−	0.371239i	$-0.878933\pi$
$821$	−15.9683	+	15.9683i	−0.557299	+	0.557299i	0.371239	+	0.928537i	$0.378933\pi$
$822$	9.75833	+	24.9934i	0.340361	+	0.871745i
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	−0.975846	−	0.218462i	$-0.929896\pi$
$823$	−21.7278	+	21.7278i	−0.757384	+	0.757384i	0.218462	+	0.975846i	$0.429896\pi$
$824$	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	$-0.761014\pi$
$827$		−	39.2381i		−	1.36444i	0.731146	−	0.682221i	$-0.238986\pi$
$828$	−11.8657	−	0.485919i	−0.412360	−	0.0168869i
$829$	−18.6072	+	18.6072i	−0.646254	+	0.646254i	−0.952086	−	0.305831i	$-0.901066\pi$
$829$	−18.6072	+	18.6072i	−0.646254	+	0.646254i	0.305831	+	0.952086i	$0.401066\pi$
$830$	−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	$0.0697649\pi$
$839$			12.5955i			0.434845i	−0.976078	+	0.217422i	$0.930235\pi$
$840$	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	$0.268978\pi$
$853$			43.6914i			1.49597i	−0.663718	+	0.747983i	$0.731022\pi$
$854$	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	−0.0114561	−	0.999934i	$-0.503647\pi$
$857$	28.9373	−	28.9373i	0.988478	−	0.988478i	0.999934	+	0.0114561i	$0.00364668\pi$
$858$	−16.4041	+	6.40475i	−0.560027	+	0.218655i
$859$	−28.1247	+	28.1247i	−0.959602	+	0.959602i	−0.999215	−	0.0396134i	$-0.987387\pi$
$859$	−28.1247	+	28.1247i	−0.959602	+	0.959602i	0.0396134	+	0.999215i	$0.487387\pi$
$860$	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	0.975626	−	0.219440i	$-0.0704229\pi$
$863$	22.2144	+	22.2144i	0.756186	+	0.756186i	−0.219440	+	0.975626i	$0.570423\pi$
$864$	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	$-0.972347\pi$
$877$		−	5.13889i		−	0.173528i	0.996229	−	0.0867640i	$-0.0276526\pi$
$878$	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	$-0.796682\pi$
$883$		−	35.4317i		−	1.19237i	0.802846	−	0.596186i	$-0.203318\pi$
$884$	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	0.952078	+	0.305855i	$0.0989422\pi$
$887$	37.4644	+	37.4644i	1.25793	+	1.25793i	0.305855	+	0.952078i	$0.401058\pi$
$888$	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	$0.000958664\pi$
$907$			0.181405i			0.00602345i	−0.999995	+	0.00301173i	$0.999041\pi$
$908$	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	$0.126851\pi$
$911$			23.4249i			0.776101i	−0.921638	+	0.388050i	$0.873149\pi$
$912$	−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	$-0.983934\pi$
$919$		−	3.05885i		−	0.100902i	0.998727	−	0.0504511i	$-0.0160659\pi$
$920$	−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	$-0.557206\pi$
$929$		−	59.9772i		−	1.96779i	0.178752	−	0.983894i	$-0.442794\pi$
$930$	−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	−0.203347	−	0.979107i	$-0.565182\pi$
$937$	23.7463	−	23.7463i	0.775759	−	0.775759i	0.979107	+	0.203347i	$0.0651821\pi$
$938$	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	−0.986580	−	0.163278i	$-0.947793\pi$
$941$	−35.2727	−	35.2727i	−1.14986	−	1.14986i	−0.163278	−	0.986580i	$-0.552207\pi$
$942$	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	0.225716	−	0.974193i	$-0.427528\pi$
$953$	−23.1060	−	23.1060i	−0.748477	−	0.748477i	−0.974193	+	0.225716i	$0.927528\pi$
$954$	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	−0.894018	−	0.448030i	$-0.852126\pi$
$967$	−41.7332	−	41.7332i	−1.34205	−	1.34205i	−0.448030	−	0.894018i	$-0.647874\pi$
$968$	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	0.996936	+	0.0782268i	$0.0249258\pi$
$971$	33.5030	+	33.5030i	1.07516	+	1.07516i	0.0782268	+	0.996936i	$0.475074\pi$
$972$	−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	0.838393	−	0.545067i	$-0.183496\pi$
$977$	9.16848	+	9.16848i	0.293326	+	0.293326i	−0.545067	+	0.838393i	$0.683496\pi$
$978$	−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	−0.290936	+	0.956742i	$0.593967\pi$
$983$	−39.1183	+	39.1183i	−1.24768	+	1.24768i	−0.956742	+	0.290936i	$0.906033\pi$
$984$	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	$0.0661621\pi$
$991$			12.9925i			0.412722i	−0.978476	+	0.206361i	$0.933838\pi$
$992$	−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.67.9	yes	18
3.2	odd	2		720.2.bd.g.307.1		18
4.3	odd	2		320.2.j.b.47.8		18
5.2	odd	4		400.2.s.d.243.4		18
5.3	odd	4		80.2.s.b.3.6	yes	18
5.4	even	2		400.2.j.d.307.1		18
8.3	odd	2		640.2.j.c.607.2		18
8.5	even	2		640.2.j.d.607.8		18
15.8	even	4		720.2.z.g.163.4		18
16.3	odd	4		640.2.s.d.287.2		18
16.5	even	4		320.2.s.b.207.2		18
16.11	odd	4		80.2.s.b.27.6	yes	18
16.13	even	4		640.2.s.c.287.8		18
20.3	even	4		320.2.s.b.303.2		18
20.7	even	4		1600.2.s.d.943.8		18
20.19	odd	2		1600.2.j.d.1007.2		18
40.3	even	4		640.2.s.c.223.8		18
40.13	odd	4		640.2.s.d.223.2		18
48.11	even	4		720.2.z.g.667.4		18
80.3	even	4		640.2.j.d.543.2		18
80.13	odd	4		640.2.j.c.543.8		18
80.27	even	4		400.2.j.d.43.1		18
80.37	odd	4		1600.2.j.d.143.8		18
80.43	even	4	inner	80.2.j.b.43.9	✓	18
80.53	odd	4		320.2.j.b.143.2		18
80.59	odd	4		400.2.s.d.107.4		18
80.69	even	4		1600.2.s.d.207.8		18
240.203	odd	4		720.2.bd.g.523.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.9	✓	18	80.43	even	4	inner
80.2.j.b.67.9	yes	18	1.1	even	1	trivial
80.2.s.b.3.6	yes	18	5.3	odd	4
80.2.s.b.27.6	yes	18	16.11	odd	4
320.2.j.b.47.8		18	4.3	odd	2
320.2.j.b.143.2		18	80.53	odd	4
320.2.s.b.207.2		18	16.5	even	4
320.2.s.b.303.2		18	20.3	even	4
400.2.j.d.43.1		18	80.27	even	4
400.2.j.d.307.1		18	5.4	even	2
400.2.s.d.107.4		18	80.59	odd	4
400.2.s.d.243.4		18	5.2	odd	4
640.2.j.c.543.8		18	80.13	odd	4
640.2.j.c.607.2		18	8.3	odd	2
640.2.j.d.543.2		18	80.3	even	4
640.2.j.d.607.8		18	8.5	even	2
640.2.s.c.223.8		18	40.3	even	4
640.2.s.c.287.8		18	16.13	even	4
640.2.s.d.223.2		18	40.13	odd	4
640.2.s.d.287.2		18	16.3	odd	4
720.2.z.g.163.4		18	15.8	even	4
720.2.z.g.667.4		18	48.11	even	4
720.2.bd.g.307.1		18	3.2	odd	2
720.2.bd.g.523.1		18	240.203	odd	4
1600.2.j.d.143.8		18	80.37	odd	4
1600.2.j.d.1007.2		18	20.19	odd	2
1600.2.s.d.207.8		18	80.69	even	4
1600.2.s.d.943.8		18	20.7	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