LMFDB - Embedded newform 82.2.g.b.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,2,Mod(5,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	82.g (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.654773296574$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 13 x^{14} - 24 x^{13} + 58 x^{12} - 66 x^{11} + 75 x^{10} - 430 x^{9} + 1721 x^{8} + \cdots + 32761 $ x^16 - 6x^15 + 13x^14 - 24x^13 + 58x^12 - 66x^11 + 75x^10 - 430x^9 + 1721x^8 - 6000x^7 + 16245x^6 - 33054x^5 + 53998x^4 - 71746x^3 + 73383x^2 - 55024*x + 32761
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			61.1
Root			$-0.913545 + 2.08351i$ of defining polynomial
Character	$\chi$	$=$	82.61
Dual form			82.2.g.b.39.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.724993 + 0.724993i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.49825 - 2.06217i) q^{5} +(0.913545 - 0.465474i) q^{6} +(4.04724 + 2.06217i) q^{7} +(-0.587785 - 0.809017i) q^{8} +1.94877i q^{9} +(-2.06217 + 1.49825i) q^{10} +(0.171416 - 1.08228i) q^{11} +(-1.01267 + 0.160391i) q^{12} +(-2.69279 - 5.28490i) q^{13} +(-3.21191 - 3.21191i) q^{14} +(0.408835 + 2.58128i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.76224 - 0.437495i) q^{17} +(0.602203 - 1.85339i) q^{18} +(-3.48583 + 6.84132i) q^{19} +(2.42423 - 0.787679i) q^{20} +(-4.42928 + 1.43916i) q^{21} +(-0.497469 + 0.976337i) q^{22} +(0.672378 - 2.06937i) q^{23} +(1.01267 + 0.160391i) q^{24} +(-0.462695 - 1.42403i) q^{25} +(0.927873 + 5.85836i) q^{26} +(-3.58782 - 3.58782i) q^{27} +(2.06217 + 4.04724i) q^{28} +(0.819364 - 0.129775i) q^{29} +(0.408835 - 2.58128i) q^{30} +(1.80687 - 1.31276i) q^{31} -1.00000i q^{32} +(0.660369 + 0.908920i) q^{33} +(2.49185 + 1.26966i) q^{34} +(10.3163 - 5.25644i) q^{35} +(-1.14546 + 1.57659i) q^{36} +(-3.54101 - 2.57269i) q^{37} +(5.42930 - 5.42930i) q^{38} +(5.78377 + 1.87926i) q^{39} -2.54898 q^{40} +(-5.90059 - 2.48656i) q^{41} +4.65722 q^{42} +(-0.952111 - 0.309360i) q^{43} +(0.774826 - 0.774826i) q^{44} +(4.01870 + 2.91975i) q^{45} +(-1.27894 + 1.76031i) q^{46} +(-9.51562 + 4.84845i) q^{47} +(-0.913545 - 0.465474i) q^{48} +(8.01308 + 11.0291i) q^{49} +1.49731i q^{50} +(2.31978 - 1.68542i) q^{51} +(0.927873 - 5.85836i) q^{52} +(3.68486 - 0.583625i) q^{53} +(2.30352 + 4.52092i) q^{54} +(-1.97502 - 1.97502i) q^{55} +(-0.710575 - 4.48640i) q^{56} +(-2.43271 - 7.48711i) q^{57} +(-0.819364 - 0.129775i) q^{58} +(-0.297378 + 0.915234i) q^{59} +(-1.18649 + 2.32861i) q^{60} +(8.84292 - 2.87324i) q^{61} +(-2.12410 + 0.690161i) q^{62} +(-4.01870 + 7.88713i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-14.9329 - 2.36513i) q^{65} +(-0.347176 - 1.06850i) q^{66} +(-0.228398 - 1.44205i) q^{67} +(-1.97754 - 1.97754i) q^{68} +(1.01281 + 1.98775i) q^{69} +(-11.4357 + 1.81124i) q^{70} +(-0.410577 + 2.59228i) q^{71} +(1.57659 - 1.14546i) q^{72} -4.69360i q^{73} +(2.57269 + 3.54101i) q^{74} +(1.36786 + 0.696960i) q^{75} +(-6.84132 + 3.48583i) q^{76} +(2.92560 - 4.02675i) q^{77} +(-4.91997 - 3.57457i) q^{78} +(-3.38526 + 3.38526i) q^{79} +(2.42423 + 0.787679i) q^{80} -0.644013 q^{81} +(4.84341 + 4.18824i) q^{82} -1.32381 q^{83} +(-4.42928 - 1.43916i) q^{84} +(-5.04072 + 5.04072i) q^{85} +(0.809914 + 0.588437i) q^{86} +(-0.499948 + 0.688119i) q^{87} +(-0.976337 + 0.497469i) q^{88} +(9.68450 + 4.93450i) q^{89} +(-2.91975 - 4.01870i) q^{90} -26.9422i q^{91} +(1.76031 - 1.27894i) q^{92} +(-0.358220 + 2.26171i) q^{93} +(10.5482 - 1.67066i) q^{94} +(8.88531 + 17.4384i) q^{95} +(0.724993 + 0.724993i) q^{96} +(-2.53723 - 16.0194i) q^{97} +(-4.21273 - 12.9654i) q^{98} +(2.10911 + 0.334050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 4 q^{4} - 6 q^{6} + 12 q^{11} + 4 q^{12} - 18 q^{13} - 10 q^{14} - 18 q^{15} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 16 q^{19} + 10 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 4 q^{25} - 2 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 + 4 * q^4 - 6 * q^6 + 12 * q^11 + 4 * q^12 - 18 * q^13 - 10 * q^14 - 18 * q^15 - 4 * q^16 - 4 * q^17 + 4 * q^18 - 16 * q^19 + 10 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 - 10 * q^29 - 18 * q^30 + 40 * q^31 - 60 * q^33 + 26 * q^34 + 44 * q^35 + 10 * q^36 - 16 * q^37 + 14 * q^38 + 80 * q^39 - 4 * q^41 + 16 * q^42 - 40 * q^43 - 2 * q^44 + 58 * q^45 + 10 * q^46 + 6 * q^48 + 20 * q^49 - 6 * q^51 - 2 * q^52 + 46 * q^53 + 18 * q^54 - 18 * q^55 - 60 * q^57 + 10 * q^58 - 2 * q^59 - 42 * q^60 - 60 * q^61 - 58 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 + 50 * q^67 - 16 * q^68 + 48 * q^69 - 26 * q^70 - 38 * q^71 - 4 * q^72 - 10 * q^74 + 6 * q^75 - 4 * q^76 - 38 * q^78 - 20 * q^79 + 10 * q^80 + 40 * q^81 + 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^86 - 70 * q^87 - 18 * q^88 + 36 * q^89 - 6 * q^92 - 12 * q^93 + 20 * q^94 - 72 * q^95 + 4 * q^96 - 10 * q^97 - 36 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.724993	+	0.724993i	−0.418575	+	0.418575i	−0.884712	−	0.466137i	$-0.845645\pi$
$3$	−0.724993	+	0.724993i	−0.418575	+	0.418575i	0.466137	+	0.884712i	$0.345645\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	1.49825	−	2.06217i	0.670040	−	0.922231i	−0.329722	−	0.944078i	$-0.606955\pi$
$5$	1.49825	−	2.06217i	0.670040	−	0.922231i	0.999761	+	0.0218477i	$0.00695488\pi$
$6$	0.913545	−	0.465474i	0.372953	−	0.190029i
$7$	4.04724	+	2.06217i	1.52971	+	0.779427i	0.997731	−	0.0673293i	$-0.0214478\pi$
$7$	4.04724	+	2.06217i	1.52971	+	0.779427i	0.531981	+	0.846756i	$0.321448\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$			1.94877i			0.649590i
$10$	−2.06217	+	1.49825i	−0.652115	+	0.473790i
$11$	0.171416	−	1.08228i	0.0516839	−	0.326319i	−0.948277	−	0.317445i	$-0.897175\pi$
$11$	0.171416	−	1.08228i	0.0516839	−	0.326319i	0.999961	−	0.00887433i	$-0.00282482\pi$
$12$	−1.01267	+	0.160391i	−0.292333	+	0.0463010i
$13$	−2.69279	−	5.28490i	−0.746846	−	1.46577i	−0.880151	−	0.474693i	$-0.842559\pi$
$13$	−2.69279	−	5.28490i	−0.746846	−	1.46577i	0.133305	−	0.991075i	$-0.457441\pi$
$14$	−3.21191	−	3.21191i	−0.858418	−	0.858418i
$15$	0.408835	+	2.58128i	0.105561	+	0.666485i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.76224	−	0.437495i	−0.669941	−	0.106108i	−0.187807	−	0.982206i	$-0.560138\pi$
$17$	−2.76224	−	0.437495i	−0.669941	−	0.106108i	−0.482134	+	0.876098i	$0.660138\pi$
$18$	0.602203	−	1.85339i	0.141941	−	0.436848i
$19$	−3.48583	+	6.84132i	−0.799704	+	1.56951i	0.0221138	+	0.999755i	$0.492960\pi$
$19$	−3.48583	+	6.84132i	−0.799704	+	1.56951i	−0.821817	+	0.569751i	$0.807040\pi$
$20$	2.42423	−	0.787679i	0.542074	−	0.176130i
$21$	−4.42928	+	1.43916i	−0.966548	+	0.314050i
$22$	−0.497469	+	0.976337i	−0.106061	+	0.208156i
$23$	0.672378	−	2.06937i	0.140200	−	0.431493i	−0.856162	−	0.516707i	$-0.827158\pi$
$23$	0.672378	−	2.06937i	0.140200	−	0.431493i	0.996363	+	0.0852146i	$0.0271576\pi$
$24$	1.01267	+	0.160391i	0.206711	+	0.0327398i
$25$	−0.462695	−	1.42403i	−0.0925390	−	0.284806i
$26$	0.927873	+	5.85836i	0.181971	+	1.14892i
$27$	−3.58782	−	3.58782i	−0.690477	−	0.690477i
$28$	2.06217	+	4.04724i	0.389714	+	0.764856i
$29$	0.819364	−	0.129775i	0.152152	−	0.0240985i	−0.0798937	−	0.996803i	$-0.525458\pi$
$29$	0.819364	−	0.129775i	0.152152	−	0.0240985i	0.232046	+	0.972705i	$0.425458\pi$
$30$	0.408835	−	2.58128i	0.0746427	−	0.471276i
$31$	1.80687	−	1.31276i	0.324523	−	0.235779i	−0.413580	−	0.910468i	$-0.635722\pi$
$31$	1.80687	−	1.31276i	0.324523	−	0.235779i	0.738103	+	0.674688i	$0.235722\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.660369	+	0.908920i	0.114955	+	0.158223i
$34$	2.49185	+	1.26966i	0.427349	+	0.217745i
$35$	10.3163	−	5.25644i	1.74378	−	0.888500i
$36$	−1.14546	+	1.57659i	−0.190910	+	0.262765i
$37$	−3.54101	−	2.57269i	−0.582138	−	0.422948i	0.257356	−	0.966317i	$-0.417149\pi$
$37$	−3.54101	−	2.57269i	−0.582138	−	0.422948i	−0.839494	+	0.543369i	$0.817149\pi$
$38$	5.42930	−	5.42930i	0.880749	−	0.880749i
$39$	5.78377	+	1.87926i	0.926145	+	0.300923i
$40$	−2.54898			−0.403030
$41$	−5.90059	−	2.48656i	−0.921518	−	0.388336i
$41$	−5.90059	−	2.48656i	−0.921518	−	0.388336i
$42$	4.65722			0.718624
$43$	−0.952111	−	0.309360i	−0.145196	−	0.0471769i	0.235518	−	0.971870i	$-0.424321\pi$
$43$	−0.952111	−	0.309360i	−0.145196	−	0.0471769i	−0.380713	+	0.924693i	$0.624321\pi$
$44$	0.774826	−	0.774826i	0.116809	−	0.116809i
$45$	4.01870	+	2.91975i	0.599072	+	0.435251i
$46$	−1.27894	+	1.76031i	−0.188569	+	0.259543i
$47$	−9.51562	+	4.84845i	−1.38800	+	0.707220i	−0.978722	−	0.205192i	$-0.934218\pi$
$47$	−9.51562	+	4.84845i	−1.38800	+	0.707220i	−0.409275	+	0.912411i	$0.634218\pi$
$48$	−0.913545	−	0.465474i	−0.131859	−	0.0671854i
$49$	8.01308	+	11.0291i	1.14473	+	1.57558i
$50$			1.49731i			0.211752i
$51$	2.31978	−	1.68542i	0.324835	−	0.236006i
$52$	0.927873	−	5.85836i	0.128673	−	0.812408i
$53$	3.68486	−	0.583625i	0.506155	−	0.0801670i	0.101865	−	0.994798i	$-0.467519\pi$
$53$	3.68486	−	0.583625i	0.506155	−	0.0801670i	0.404289	+	0.914631i	$0.367519\pi$
$54$	2.30352	+	4.52092i	0.313470	+	0.615220i
$55$	−1.97502	−	1.97502i	−0.266311	−	0.266311i
$56$	−0.710575	−	4.48640i	−0.0949546	−	0.599520i
$57$	−2.43271	−	7.48711i	−0.322220	−	0.991692i
$58$	−0.819364	−	0.129775i	−0.107588	−	0.0170402i
$59$	−0.297378	+	0.915234i	−0.0387153	+	0.119153i	−0.968546	−	0.248833i	$-0.919953\pi$
$59$	−0.297378	+	0.915234i	−0.0387153	+	0.119153i	0.929831	+	0.367987i	$0.119953\pi$
$60$	−1.18649	+	2.32861i	−0.153175	+	0.300622i
$61$	8.84292	−	2.87324i	1.13222	−	0.367881i	0.317801	−	0.948157i	$-0.397056\pi$
$61$	8.84292	−	2.87324i	1.13222	−	0.367881i	0.814419	+	0.580277i	$0.197056\pi$
$62$	−2.12410	+	0.690161i	−0.269761	+	0.0876505i
$63$	−4.01870	+	7.88713i	−0.506308	+	0.993685i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−14.9329	−	2.36513i	−1.85219	−	0.293359i
$66$	−0.347176	−	1.06850i	−0.0427345	−	0.131523i
$67$	−0.228398	−	1.44205i	−0.0279032	−	0.176174i	0.969801	−	0.243898i	$-0.0784262\pi$
$67$	−0.228398	−	1.44205i	−0.0279032	−	0.176174i	−0.997704	+	0.0677241i	$0.978426\pi$
$68$	−1.97754	−	1.97754i	−0.239812	−	0.239812i
$69$	1.01281	+	1.98775i	0.121928	+	0.239296i
$70$	−11.4357	+	1.81124i	−1.36683	+	0.216485i
$71$	−0.410577	+	2.59228i	−0.0487266	+	0.307647i	−1.00000		0.000701924i	$-0.999777\pi$
$71$	−0.410577	+	2.59228i	−0.0487266	+	0.307647i	0.951273	+	0.308349i	$0.0997766\pi$
$72$	1.57659	−	1.14546i	0.185803	−	0.134994i
$73$		−	4.69360i		−	0.549344i	−0.961538	−	0.274672i	$-0.911431\pi$
$73$		−	4.69360i		−	0.549344i	0.961538	−	0.274672i	$-0.0885693\pi$
$74$	2.57269	+	3.54101i	0.299069	+	0.411634i
$75$	1.36786	+	0.696960i	0.157947	+	0.0804780i
$76$	−6.84132	+	3.48583i	−0.784753	+	0.399852i
$77$	2.92560	−	4.02675i	0.333403	−	0.458890i
$78$	−4.91997	−	3.57457i	−0.557077	−	0.404740i
$79$	−3.38526	+	3.38526i	−0.380872	+	0.380872i	−0.871416	−	0.490545i	$-0.836798\pi$
$79$	−3.38526	+	3.38526i	−0.380872	+	0.380872i	0.490545	+	0.871416i	$0.336798\pi$
$80$	2.42423	+	0.787679i	0.271037	+	0.0880652i
$81$	−0.644013			−0.0715570
$82$	4.84341	+	4.18824i	0.534865	+	0.462514i
$83$	−1.32381			−0.145307			−0.0726534	−	0.997357i	$-0.523147\pi$
$83$	−1.32381			−0.145307			−0.0726534	+	0.997357i	$0.523147\pi$
$84$	−4.42928	−	1.43916i	−0.483274	−	0.157025i
$85$	−5.04072	+	5.04072i	−0.546743	+	0.546743i
$86$	0.809914	+	0.588437i	0.0873353	+	0.0634528i
$87$	−0.499948	+	0.688119i	−0.0536000	+	0.0737741i
$88$	−0.976337	+	0.497469i	−0.104078	+	0.0530303i
$89$	9.68450	+	4.93450i	1.02655	+	0.523056i	0.884371	−	0.466785i	$-0.154588\pi$
$89$	9.68450	+	4.93450i	1.02655	+	0.523056i	0.142184	+	0.989840i	$0.454588\pi$
$90$	−2.91975	−	4.01870i	−0.307769	−	0.423608i
$91$		−	26.9422i		−	2.82431i
$92$	1.76031	−	1.27894i	0.183525	−	0.133339i
$93$	−0.358220	+	2.26171i	−0.0371457	+	0.234528i
$94$	10.5482	−	1.67066i	1.08796	−	0.172316i
$95$	8.88531	+	17.4384i	0.911614	+	1.78914i
$96$	0.724993	+	0.724993i	0.0739943	+	0.0739943i
$97$	−2.53723	−	16.0194i	−0.257616	−	1.62653i	−0.689283	−	0.724492i	$-0.742074\pi$
$97$	−2.53723	−	16.0194i	−0.257616	−	1.62653i	0.431667	−	0.902033i	$-0.357926\pi$
$98$	−4.21273	−	12.9654i	−0.425550	−	1.30971i
$99$	2.10911	+	0.334050i	0.211974	+	0.0335733i
$100$	0.462695	−	1.42403i	0.0462695	−	0.142403i
$101$	−6.58865	+	12.9310i	−0.655596	+	1.28668i	0.288649	+	0.957435i	$0.406794\pi$
$101$	−6.58865	+	12.9310i	−0.655596	+	1.28668i	−0.944245	+	0.329244i	$0.893206\pi$
$102$	−2.72707	+	0.886079i	−0.270020	+	0.0877349i
$103$	8.29946	−	2.69666i	0.817770	−	0.265710i	0.129885	−	0.991529i	$-0.458539\pi$
$103$	8.29946	−	2.69666i	0.817770	−	0.265710i	0.687885	+	0.725819i	$0.258539\pi$
$104$	−2.69279	+	5.28490i	−0.264050	+	0.518227i
$105$	−3.66839	+	11.2902i	−0.357999	+	1.10181i
$106$	−3.68486	−	0.583625i	−0.357905	−	0.0566867i
$107$	3.38067	+	10.4046i	0.326822	+	1.00585i	0.970612	+	0.240652i	$0.0773612\pi$
$107$	3.38067	+	10.4046i	0.326822	+	1.00585i	−0.643790	+	0.765203i	$0.722639\pi$
$108$	−0.793741	−	5.01148i	−0.0763777	−	0.482230i
$109$	2.36170	+	2.36170i	0.226210	+	0.226210i	0.811107	−	0.584898i	$-0.198865\pi$
$109$	2.36170	+	2.36170i	0.226210	+	0.226210i	−0.584898	+	0.811107i	$0.698865\pi$
$110$	1.26804	+	2.48867i	0.120903	+	0.237285i
$111$	4.43239	−	0.702021i	0.420704	−	0.0666329i
$112$	−0.710575	+	4.48640i	−0.0671431	+	0.423925i
$113$	7.45541	−	5.41667i	0.701346	−	0.509558i	−0.179024	−	0.983845i	$-0.557294\pi$
$113$	7.45541	−	5.41667i	0.701346	−	0.509558i	0.880370	+	0.474287i	$0.157294\pi$
$114$			7.87241i			0.737319i
$115$	−3.25999	−	4.48699i	−0.303996	−	0.418414i
$116$	0.739159	+	0.376620i	0.0686292	+	0.0349683i
$117$	10.2991	−	5.24763i	0.952148	−	0.485144i
$118$	0.565646	−	0.778545i	0.0520719	−	0.0716709i
$119$	−10.2772	−	7.46685i	−0.942113	−	0.684485i
$120$	1.84799	−	1.84799i	0.168698	−	0.168698i
$121$	9.31968	+	3.02815i	0.847244	+	0.275286i
$122$	−9.29800			−0.841801
$123$	6.08063	−	2.47515i	0.548272	−	0.223177i
$124$	2.23341			0.200566
$125$	8.49131	+	2.75899i	0.759486	+	0.246772i
$126$	6.25926	−	6.25926i	0.557620	−	0.557620i
$127$	2.73754	+	1.98894i	0.242917	+	0.176490i	0.702582	−	0.711603i	$-0.252030\pi$
$127$	2.73754	+	1.98894i	0.242917	+	0.176490i	−0.459665	+	0.888092i	$0.652030\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.914558	−	0.465991i	0.0805223	−	0.0410282i
$130$	13.4711	+	6.86388i	1.18150	+	0.602002i
$131$	−9.85985	−	13.5709i	−0.861459	−	1.18570i	−0.981220	−	0.192894i	$-0.938213\pi$
$131$	−9.85985	−	13.5709i	−0.861459	−	1.18570i	0.119760	−	0.992803i	$-0.461787\pi$
$132$			1.12349i			0.0977870i
$133$	−28.2159	+	20.5001i	−2.44663	+	1.77758i
$134$	−0.228398	+	1.44205i	−0.0197306	+	0.124574i
$135$	−12.7742	+	2.02323i	−1.09943	+	0.174132i
$136$	1.26966	+	2.49185i	0.108873	+	0.213674i
$137$	14.5443	+	14.5443i	1.24260	+	1.24260i	0.958917	+	0.283688i	$0.0915581\pi$
$137$	14.5443	+	14.5443i	1.24260	+	1.24260i	0.283688	+	0.958917i	$0.408442\pi$
$138$	−0.348989	−	2.20343i	−0.0297080	−	0.187569i
$139$	−5.66519	−	17.4357i	−0.480515	−	1.47887i	−0.838373	−	0.545097i	$-0.816493\pi$
$139$	−5.66519	−	17.4357i	−0.480515	−	1.47887i	0.357858	−	0.933776i	$-0.383507\pi$
$140$	11.4357	+	1.81124i	0.966497	+	0.153078i
$141$	3.38367	−	10.4139i	0.284956	−	0.877005i
$142$	1.19154	−	2.33853i	0.0999920	−	0.196245i
$143$	−6.18132	+	2.00843i	−0.516908	+	0.167954i
$144$	−1.85339	+	0.602203i	−0.154449	+	0.0501836i
$145$	0.959999	−	1.88410i	0.0797236	−	0.156466i
$146$	−1.45040	+	4.46388i	−0.120036	+	0.369433i
$147$	−13.8054	−	2.18656i	−1.13865	−	0.180345i
$148$	−1.35254	−	4.16270i	−0.111178	−	0.342172i
$149$	−1.82819	−	11.5427i	−0.149771	−	0.945617i	−0.942054	−	0.335463i	$-0.891107\pi$
$149$	−1.82819	−	11.5427i	−0.149771	−	0.945617i	0.792283	−	0.610154i	$-0.208893\pi$
$150$	−1.08554	−	1.08554i	−0.0886340	−	0.0886340i
$151$	2.01851	+	3.96156i	0.164264	+	0.322387i	0.958436	−	0.285306i	$-0.0920952\pi$
$151$	2.01851	+	3.96156i	0.164264	+	0.322387i	−0.794172	+	0.607693i	$0.792095\pi$
$152$	7.58366	−	1.20113i	0.615116	−	0.0974248i
$153$	0.852578	−	5.38297i	0.0689268	−	0.435187i
$154$	−4.02675	+	2.92560i	−0.324485	+	0.235752i
$155$		−	5.69292i		−	0.457266i
$156$	3.57457	+	4.91997i	0.286195	+	0.393913i
$157$	14.4903	+	7.38317i	1.15645	+	0.589242i	0.923633	−	0.383279i	$-0.125205\pi$
$157$	14.4903	+	7.38317i	1.15645	+	0.589242i	0.232819	+	0.972520i	$0.425205\pi$
$158$	4.26568	−	2.17347i	0.339359	−	0.172912i
$159$	−2.24838	+	3.09462i	−0.178308	+	0.245420i
$160$	−2.06217	−	1.49825i	−0.163029	−	0.118447i
$161$	6.98866	−	6.98866i	0.550783	−	0.550783i
$162$	0.612493	+	0.199011i	0.0481220	+	0.0156358i
$163$	11.8312			0.926695			0.463348	−	0.886177i	$-0.346648\pi$
$163$	11.8312			0.926695			0.463348	+	0.886177i	$0.346648\pi$
$164$	−3.31212	−	5.47995i	−0.258633	−	0.427912i
$165$	2.86375			0.222942
$166$	1.25902	+	0.409079i	0.0977186	+	0.0317507i
$167$	−7.40168	+	7.40168i	−0.572759	+	0.572759i	−0.932899	−	0.360139i	$-0.882729\pi$
$167$	−7.40168	+	7.40168i	−0.572759	+	0.572759i	0.360139	+	0.932899i	$0.382729\pi$
$168$	3.76777	+	2.73744i	0.290690	+	0.211198i
$169$	−13.0379	+	17.9451i	−1.00291	+	1.38039i
$170$	6.35168	−	3.23634i	0.487152	−	0.248216i
$171$	−13.3322	−	6.79307i	−1.01954	−	0.519479i
$172$	−0.588437	−	0.809914i	−0.0448679	−	0.0617554i
$173$			3.10902i			0.236374i	0.992991	+	0.118187i	$0.0377083\pi$
$173$			3.10902i			0.236374i	−0.992991	+	0.118187i	$0.962292\pi$
$174$	0.688119	−	0.499948i	0.0521662	−	0.0379010i
$175$	1.06395	−	6.71753i	0.0804273	−	0.507798i
$176$	1.08228	−	0.171416i	0.0815798	−	0.0129210i
$177$	−0.447942	−	0.879135i	−0.0336694	−	0.0660799i
$178$	−7.68566	−	7.68566i	−0.576065	−	0.576065i
$179$	2.65552	+	16.7663i	0.198483	+	1.25317i	0.862733	+	0.505660i	$0.168751\pi$
$179$	2.65552	+	16.7663i	0.198483	+	1.25317i	−0.664250	+	0.747511i	$0.731249\pi$
$180$	1.53500	+	4.72426i	0.114413	+	0.352126i
$181$	−7.28529	−	1.15388i	−0.541511	−	0.0857669i	−0.120314	−	0.992736i	$-0.538390\pi$
$181$	−7.28529	−	1.15388i	−0.541511	−	0.0857669i	−0.421197	+	0.906969i	$0.638390\pi$
$182$	−8.32561	+	25.6236i	−0.617135	+	1.89935i
$183$	−4.32798	+	8.49414i	−0.319933	+	0.627905i
$184$	−2.06937	+	0.672378i	−0.152556	+	0.0495683i
$185$	−10.6107	+	3.44761i	−0.780111	+	0.253473i
$186$	1.03959	−	2.04032i	0.0762267	−	0.149603i
$187$	−0.946984	+	2.91452i	−0.0692503	+	0.213131i
$188$	−10.5482	−	1.67066i	−0.769303	−	0.121846i
$189$	−7.12207	−	21.9195i	−0.518054	−	1.59441i
$190$	−3.06167	−	19.3306i	−0.222117	−	1.40239i
$191$	−12.0477	−	12.0477i	−0.871744	−	0.871744i	0.120918	−	0.992662i	$-0.461416\pi$
$191$	−12.0477	−	12.0477i	−0.871744	−	0.871744i	−0.992662	+	0.120918i	$0.961416\pi$
$192$	−0.465474	−	0.913545i	−0.0335927	−	0.0659294i
$193$	−12.8697	+	2.03836i	−0.926383	+	0.146725i	−0.601357	−	0.798981i	$-0.705373\pi$
$193$	−12.8697	+	2.03836i	−0.926383	+	0.146725i	−0.325026	+	0.945705i	$0.605373\pi$
$194$	−2.53723	+	16.0194i	−0.182162	+	1.15013i
$195$	12.5409	−	9.11151i	0.898074	−	0.652489i
$196$			13.6327i			0.973762i
$197$	−5.95146	−	8.19149i	−0.424024	−	0.583619i	0.542544	−	0.840027i	$-0.317461\pi$
$197$	−5.95146	−	8.19149i	−0.424024	−	0.583619i	−0.966569	+	0.256408i	$0.917461\pi$
$198$	−1.90266	−	0.969452i	−0.135216	−	0.0688959i
$199$	7.85406	−	4.00184i	0.556760	−	0.283683i	−0.152884	−	0.988244i	$-0.548856\pi$
$199$	7.85406	−	4.00184i	0.556760	−	0.283683i	0.709643	+	0.704561i	$0.248856\pi$
$200$	−0.880098	+	1.21135i	−0.0622323	+	0.0856554i
$201$	1.21106	+	0.879887i	0.0854216	+	0.0620625i
$202$	10.2621	−	10.2621i	0.722037	−	0.722037i
$203$	3.58378	+	1.16444i	0.251532	+	0.0817277i
$204$	2.86741			0.200759
$205$	−13.9683	+	8.44253i	−0.975589	+	0.589652i
$206$	−8.72657			−0.608009
$207$	4.03272	+	1.31031i	0.280293	+	0.0910728i
$208$	4.19412	−	4.19412i	0.290810	−	0.290810i
$209$	6.80669	+	4.94535i	0.470828	+	0.342077i
$210$	6.97770	−	9.60398i	0.481507	−	0.662737i
$211$	6.01660	−	3.06561i	0.414200	−	0.211045i	−0.234457	−	0.972127i	$-0.575331\pi$
$211$	6.01660	−	3.06561i	0.414200	−	0.211045i	0.648657	+	0.761081i	$0.275331\pi$
$212$	3.32416	+	1.69375i	0.228304	+	0.116327i
$213$	−1.58172	−	2.17705i	−0.108378	−	0.149169i
$214$		−	10.9401i		−	0.747849i
$215$	−2.06446	+	1.49992i	−0.140795	+	0.102293i
$216$	−0.793741	+	5.01148i	−0.0540072	+	0.340988i
$217$	10.0200	−	1.58700i	0.680199	−	0.107733i
$218$	−1.51630	−	2.97591i	−0.102697	−	0.201554i
$219$	3.40283	+	3.40283i	0.229942	+	0.229942i
$220$	−0.436936	−	2.75871i	−0.0294582	−	0.185992i
$221$	5.12601	+	15.7762i	0.344813	+	1.06122i
$222$	−4.43239	−	0.702021i	−0.297482	−	0.0471166i
$223$	1.64382	−	5.05915i	0.110078	−	0.338786i	−0.880811	−	0.473469i	$-0.843002\pi$
$223$	1.64382	−	5.05915i	0.110078	−	0.338786i	0.990889	+	0.134683i	$0.0430017\pi$
$224$	2.06217	−	4.04724i	0.137785	−	0.270417i
$225$	2.77510	−	0.901686i	0.185007	−	0.0601124i
$226$	−8.76436	+	2.84771i	−0.582996	+	0.189427i
$227$	0.277576	−	0.544773i	0.0184233	−	0.0361579i	−0.881611	−	0.471976i	$-0.843541\pi$
$227$	0.277576	−	0.544773i	0.0184233	−	0.0361579i	0.900035	+	0.435818i	$0.143541\pi$
$228$	2.43271	−	7.48711i	0.161110	−	0.495846i
$229$	9.56759	+	1.51536i	0.632244	+	0.100138i	0.464328	−	0.885664i	$-0.346296\pi$
$229$	9.56759	+	1.51536i	0.632244	+	0.100138i	0.167917	+	0.985801i	$0.446296\pi$
$230$	1.71388	+	5.27478i	0.113010	+	0.347809i
$231$	0.798322	+	5.04041i	0.0525257	+	0.331634i
$232$	−0.586600	−	0.586600i	−0.0385122	−	0.0385122i
$233$	5.70275	+	11.1923i	0.373600	+	0.733231i	0.998887	−	0.0471637i	$-0.0150182\pi$
$233$	5.70275	+	11.1923i	0.373600	+	0.733231i	−0.625287	+	0.780395i	$0.715018\pi$
$234$	−11.4166	+	1.80821i	−0.746326	+	0.118206i
$235$	−4.25849	+	26.8871i	−0.277793	+	1.75392i
$236$	−0.778545	+	0.565646i	−0.0506790	+	0.0368204i
$237$		−	4.90858i		−	0.318847i
$238$	7.46685	+	10.2772i	0.484004	+	0.666175i
$239$	12.2608	+	6.24717i	0.793082	+	0.404096i	0.803093	−	0.595854i	$-0.203186\pi$
$239$	12.2608	+	6.24717i	0.793082	+	0.404096i	−0.0100103	+	0.999950i	$0.503186\pi$
$240$	−2.32861	+	1.18649i	−0.150311	+	0.0765873i
$241$	4.77171	−	6.56770i	0.307373	−	0.423063i	−0.627187	−	0.778869i	$-0.715794\pi$
$241$	4.77171	−	6.56770i	0.307373	−	0.423063i	0.934560	+	0.355806i	$0.115794\pi$
$242$	−7.92779	−	5.75988i	−0.509618	−	0.370259i
$243$	11.2304	−	11.2304i	0.720429	−	0.720429i
$244$	8.84292	+	2.87324i	0.566110	+	0.183940i
$245$	34.7494			2.22006
$246$	−6.54789	+	0.474990i	−0.417478	+	0.0302843i
$247$	45.5423			2.89779
$248$	−2.12410	−	0.690161i	−0.134880	−	0.0438253i
$249$	0.959751	−	0.959751i	0.0608218	−	0.0608218i
$250$	−7.22314	−	5.24792i	−0.456831	−	0.331907i
$251$	−6.41377	+	8.82779i	−0.404833	+	0.557205i	−0.961949	−	0.273230i	$-0.911908\pi$
$251$	−6.41377	+	8.82779i	−0.404833	+	0.557205i	0.557115	+	0.830435i	$0.311908\pi$
$252$	−7.88713	+	4.01870i	−0.496843	+	0.253154i
$253$	−2.12437	−	1.08242i	−0.133558	−	0.0680513i
$254$	−1.98894	−	2.73754i	−0.124797	−	0.171768i
$255$		−	7.30898i		−	0.457706i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.51269	−	22.1783i	0.219116	−	1.38344i	−0.595460	−	0.803385i	$-0.703030\pi$
$257$	3.51269	−	22.1783i	0.219116	−	1.38344i	0.814576	−	0.580057i	$-0.196970\pi$
$258$	−1.01380	+	0.160569i	−0.0631161	+	0.00999661i
$259$	−9.02596	−	17.7144i	−0.560846	−	1.10072i
$260$	−10.6907	−	10.6907i	−0.663012	−	0.663012i
$261$	0.252901	+	1.59675i	0.0156542	+	0.0988365i
$262$	5.18363	+	15.9536i	0.320246	+	0.985615i
$263$	−19.6044	−	3.10503i	−1.20886	−	0.191464i	−0.480706	−	0.876882i	$-0.659620\pi$
$263$	−19.6044	−	3.10503i	−1.20886	−	0.191464i	−0.728150	+	0.685418i	$0.759620\pi$
$264$	0.347176	−	1.06850i	0.0213672	−	0.0657616i
$265$	4.31733	−	8.47323i	0.265211	−	0.520506i
$266$	33.1698	−	10.7775i	2.03377	−	0.660813i
$267$	−10.5987	+	3.44372i	−0.648628	+	0.210752i
$268$	0.662836	−	1.30089i	0.0404892	−	0.0794644i
$269$	3.68176	−	11.3313i	0.224481	−	0.690882i	−0.773863	−	0.633353i	$-0.781678\pi$
$269$	3.68176	−	11.3313i	0.224481	−	0.690882i	0.998344	−	0.0575284i	$-0.0183220\pi$
$270$	12.7742	+	2.02323i	0.777412	+	0.123130i
$271$	2.42041	+	7.44926i	0.147030	+	0.452511i	0.997266	−	0.0738898i	$-0.0235413\pi$
$271$	2.42041	+	7.44926i	0.147030	+	0.452511i	−0.850237	+	0.526400i	$0.823541\pi$
$272$	−0.437495	−	2.76224i	−0.0265271	−	0.167485i
$273$	19.5329	+	19.5329i	1.18219	+	1.18219i
$274$	−9.33803	−	18.3269i	−0.564131	−	1.10717i
$275$	−1.62051	+	0.256663i	−0.0977203	+	0.0154774i
$276$	−0.348989	+	2.20343i	−0.0210067	+	0.132631i
$277$	−22.2666	+	16.1776i	−1.33787	+	0.972019i	−0.338350	+	0.941020i	$0.609869\pi$
$277$	−22.2666	+	16.1776i	−1.33787	+	0.972019i	−0.999519	+	0.0309991i	$0.990131\pi$
$278$			18.3329i			1.09954i
$279$	2.55828	+	3.52116i	0.153160	+	0.210807i
$280$	−10.3163	−	5.25644i	−0.616519	−	0.314132i
$281$	−5.50390	+	2.80438i	−0.328335	+	0.167295i	−0.610386	−	0.792104i	$-0.708985\pi$
$281$	−5.50390	+	2.80438i	−0.328335	+	0.167295i	0.282050	+	0.959400i	$0.408985\pi$
$282$	−6.43612	+	8.85856i	−0.383265	+	0.527519i
$283$	2.75353	+	2.00056i	0.163680	+	0.118921i	0.666610	−	0.745406i	$-0.267745\pi$
$283$	2.75353	+	2.00056i	0.163680	+	0.118921i	−0.502930	+	0.864327i	$0.667745\pi$
$284$	−1.85587	+	1.85587i	−0.110126	+	0.110126i
$285$	−19.0845	−	6.20094i	−1.13047	−	0.367312i
$286$	6.49943			0.384319
$287$	−18.7534	−	22.2317i	−1.10698	−	1.31230i
$288$	1.94877			0.114832
$289$	−8.72941	−	2.83636i	−0.513494	−	0.166844i
$290$	−1.49523	+	1.49523i	−0.0878031	+	0.0878031i
$291$	13.4534	+	9.77449i	0.788655	+	0.572991i
$292$	2.75883	−	3.79720i	0.161448	−	0.222214i
$293$	−13.2465	+	6.74944i	−0.773870	+	0.394306i	−0.795882	−	0.605451i	$-0.792993\pi$
$293$	−13.2465	+	6.74944i	−0.773870	+	0.394306i	0.0220125	+	0.999758i	$0.492993\pi$
$294$	12.4541	+	6.34566i	0.726335	+	0.370086i
$295$	1.44182	+	1.98450i	0.0839461	+	0.115542i
$296$			4.37692i			0.254404i
$297$	−4.49803	+	3.26801i	−0.261002	+	0.189629i
$298$	−1.82819	+	11.5427i	−0.105904	+	0.668652i
$299$	−12.7470	+	2.01892i	−0.737176	+	0.116757i
$300$	0.696960	+	1.36786i	0.0402390	+	0.0789735i
$301$	−3.21547	−	3.21547i	−0.185336	−	0.185336i
$302$	−0.695532	−	4.39142i	−0.0400234	−	0.252698i
$303$	−4.59813	−	14.1516i	−0.264156	−	0.812988i
$304$	−7.58366	−	1.20113i	−0.434953	−	0.0688898i
$305$	7.32384	−	22.5405i	0.419362	−	1.29066i
$306$	−2.47428	+	4.85604i	−0.141445	+	0.277602i
$307$	−29.9143	+	9.71976i	−1.70730	+	0.554736i	−0.989880	−	0.141904i	$-0.954678\pi$
$307$	−29.9143	+	9.71976i	−1.70730	+	0.554736i	−0.717421	+	0.696640i	$0.754678\pi$
$308$	4.73373	−	1.53808i	0.269729	−	0.0876403i
$309$	−4.06199	+	7.97211i	−0.231079	+	0.453518i
$310$	−1.75921	+	5.41429i	−0.0999163	+	0.307511i
$311$	28.6347	+	4.53529i	1.62372	+	0.257172i	0.900953	−	0.433916i	$-0.142869\pi$
$311$	28.6347	+	4.53529i	1.62372	+	0.257172i	0.722770	+	0.691089i	$0.242869\pi$
$312$	−1.87926	−	5.78377i	−0.106392	−	0.327442i
$313$	1.22753	+	7.75030i	0.0693839	+	0.438073i	0.997787	+	0.0664973i	$0.0211824\pi$
$313$	1.22753	+	7.75030i	0.0693839	+	0.438073i	−0.928403	+	0.371576i	$0.878818\pi$
$314$	−11.4996	−	11.4996i	−0.648958	−	0.648958i
$315$	10.2436	+	20.1042i	0.577161	+	1.13274i
$316$	−4.72854	+	0.748927i	−0.266001	+	0.0421304i
$317$	1.56250	−	9.86523i	0.0877587	−	0.554087i	−0.904158	−	0.427198i	$-0.859501\pi$
$317$	1.56250	−	9.86523i	0.0877587	−	0.554087i	0.991917	−	0.126889i	$-0.0404992\pi$
$318$	3.09462	−	2.24838i	0.173538	−	0.126083i
$319$		−	0.909026i		−	0.0508957i
$320$	1.49825	+	2.06217i	0.0837550	+	0.115279i
$321$	−9.99425	−	5.09233i	−0.557825	−	0.284226i
$322$	−8.80622	+	4.48699i	−0.490752	+	0.250050i
$323$	12.6217	−	17.3723i	0.702292	−	0.966622i
$324$	−0.521018	−	0.378542i	−0.0289454	−	0.0210301i
$325$	−6.27991	+	6.27991i	−0.348347	+	0.348347i
$326$	−11.2522	−	3.65606i	−0.623201	−	0.202490i
$327$	−3.42443			−0.189371
$328$	1.45661	+	6.23525i	0.0804279	+	0.344284i
$329$	−48.5103			−2.67446
$330$	−2.72359	−	0.884947i	−0.149928	−	0.0487147i
$331$	−0.577987	+	0.577987i	−0.0317691	+	0.0317691i	−0.722813	−	0.691044i	$-0.757151\pi$
$331$	−0.577987	+	0.577987i	−0.0317691	+	0.0317691i	0.691044	+	0.722813i	$0.257151\pi$
$332$	−1.07098	−	0.778114i	−0.0587778	−	0.0427046i
$333$	5.01358	−	6.90061i	0.274743	−	0.378151i
$334$	9.32666	−	4.75217i	0.510332	−	0.260027i
$335$	−3.31594	−	1.68956i	−0.181169	−	0.0923104i
$336$	−2.73744	−	3.76777i	−0.149340	−	0.205549i
$337$			0.325565i			0.0177346i	0.999961	+	0.00886731i	$0.00282259\pi$
$337$			0.325565i			0.0177346i	−0.999961	+	0.00886731i	$0.997177\pi$
$338$	17.9451	−	13.0379i	0.976083	−	0.709166i
$339$	−1.47807	+	9.33217i	−0.0802778	+	0.506854i
$340$	−7.04090	+	1.11517i	−0.381846	+	0.0604785i
$341$	−1.11105	−	2.18056i	−0.0601668	−	0.118084i
$342$	10.5805	+	10.5805i	0.572126	+	0.572126i
$343$	4.71301	+	29.7568i	0.254479	+	1.60672i
$344$	0.309360	+	0.952111i	0.0166796	+	0.0513344i
$345$	5.61651	+	0.889568i	0.302383	+	0.0478927i
$346$	0.960740	−	2.95685i	0.0516497	−	0.158961i
$347$	−3.88879	+	7.63219i	−0.208761	+	0.409717i	−0.971517	−	0.236969i	$-0.923846\pi$
$347$	−3.88879	+	7.63219i	−0.208761	+	0.409717i	0.762756	+	0.646687i	$0.223846\pi$
$348$	−0.808933	+	0.262838i	−0.0433633	+	0.0140896i
$349$	9.28725	−	3.01761i	0.497135	−	0.161529i	−0.0497086	−	0.998764i	$-0.515829\pi$
$349$	9.28725	−	3.01761i	0.497135	−	0.161529i	0.546843	+	0.837235i	$0.315829\pi$
$350$	−3.08771	+	6.05998i	−0.165045	+	0.323919i
$351$	−9.30004	+	28.6226i	−0.496399	+	1.52776i
$352$	−1.08228	−	0.171416i	−0.0576856	−	0.00913650i
$353$	−4.96815	−	15.2904i	−0.264428	−	0.813825i	−0.991825	−	0.127608i	$-0.959270\pi$
$353$	−4.96815	−	15.2904i	−0.264428	−	0.813825i	0.727397	−	0.686217i	$-0.240730\pi$
$354$	0.154350	+	0.974529i	0.00820362	+	0.0517956i
$355$	4.73058	+	4.73058i	0.251073	+	0.251073i
$356$	4.93450	+	9.68450i	0.261528	+	0.513277i
$357$	12.8643	−	2.03751i	0.680853	−	0.107837i
$358$	2.65552	−	16.7663i	0.140349	−	0.886126i
$359$	14.2141	−	10.3272i	0.750192	−	0.545046i	−0.145694	−	0.989330i	$-0.546542\pi$
$359$	14.2141	−	10.3272i	0.750192	−	0.545046i	0.895886	+	0.444283i	$0.146542\pi$
$360$		−	4.96738i		−	0.261804i
$361$	−23.4848	−	32.3240i	−1.23604	−	1.70126i
$362$	6.57215	+	3.34868i	0.345425	+	0.176003i
$363$	−8.95209	+	4.56132i	−0.469863	+	0.239407i
$364$	15.8363	−	21.7967i	0.830045	−	1.14246i
$365$	−9.67900	−	7.03220i	−0.506622	−	0.368082i
$366$	6.74099	−	6.74099i	0.352357	−	0.352357i
$367$	−3.08411	−	1.00209i	−0.160989	−	0.0523085i	0.227414	−	0.973798i	$-0.426973\pi$
$367$	−3.08411	−	1.00209i	−0.160989	−	0.0523085i	−0.388403	+	0.921490i	$0.626973\pi$
$368$	2.17586			0.113425
$369$	4.84574	−	11.4989i	0.252259	−	0.598609i
$370$	11.1567			0.580009
$371$	16.1170	+	5.23674i	0.836755	+	0.271878i
$372$	−1.61921	+	1.61921i	−0.0839519	+	0.0839519i
$373$	11.0962	+	8.06187i	0.574540	+	0.417428i	0.836752	−	0.547583i	$-0.184452\pi$
$373$	11.0962	+	8.06187i	0.574540	+	0.417428i	−0.262212	+	0.965010i	$0.584452\pi$
$374$	1.80127	−	2.47924i	0.0931414	−	0.128198i
$375$	−8.15639	+	4.15589i	−0.421194	+	0.214609i
$376$	9.51562	+	4.84845i	0.490731	+	0.250040i
$377$	−2.89222	−	3.98080i	−0.148957	−	0.205022i
$378$			23.0475i			1.18544i
$379$	13.8818	−	10.0857i	0.713062	−	0.518070i	−0.171098	−	0.985254i	$-0.554732\pi$
$379$	13.8818	−	10.0857i	0.713062	−	0.518070i	0.884160	+	0.467184i	$0.154732\pi$
$380$	−3.06167	+	19.3306i	−0.157060	+	0.991640i
$381$	−3.42666	+	0.542730i	−0.175553	+	0.0278049i
$382$	7.73513	+	15.1810i	0.395764	+	0.776730i
$383$	12.4262	+	12.4262i	0.634947	+	0.634947i	0.949305	−	0.314358i	$-0.101789\pi$
$383$	12.4262	+	12.4262i	0.634947	+	0.634947i	−0.314358	+	0.949305i	$0.601789\pi$
$384$	0.160391	+	1.01267i	0.00818494	+	0.0516777i
$385$	−3.92054	−	12.0662i	−0.199809	−	0.614950i
$386$	12.8697	+	2.03836i	0.655052	+	0.103750i
$387$	0.602871	−	1.85545i	0.0306457	−	0.0943176i
$388$	7.36332	−	14.4513i	0.373816	−	0.733655i
$389$	23.6635	−	7.68874i	1.19979	−	0.389834i	0.360105	−	0.932912i	$-0.382741\pi$
$389$	23.6635	−	7.68874i	1.19979	−	0.389834i	0.839683	+	0.543077i	$0.182741\pi$
$390$	−14.7427	+	4.79021i	−0.746528	+	0.242562i
$391$	−2.76261	+	5.42192i	−0.139711	+	0.274198i
$392$	4.21273	−	12.9654i	0.212775	−	0.654854i
$393$	16.9872	+	2.69050i	0.856888	+	0.135718i
$394$	3.12887	+	9.62967i	0.157630	+	0.485136i
$395$	1.90900	+	12.0530i	0.0960523	+	0.606451i
$396$	1.50996	+	1.50996i	0.0758782	+	0.0758782i
$397$	−6.31023	−	12.3845i	−0.316702	−	0.621562i	0.676699	−	0.736260i	$-0.263410\pi$
$397$	−6.31023	−	12.3845i	−0.316702	−	0.621562i	−0.993400	+	0.114698i	$0.963410\pi$
$398$	−8.70629	+	1.37894i	−0.436407	+	0.0691201i
$399$	5.59394	−	35.3188i	0.280047	−	1.76815i
$400$	1.21135	−	0.880098i	0.0605675	−	0.0440049i
$401$		−	7.05439i		−	0.352279i	−0.984365	−	0.176140i	$-0.943639\pi$
$401$		−	7.05439i		−	0.352279i	0.984365	−	0.176140i	$-0.0563610\pi$
$402$	−0.879887	−	1.21106i	−0.0438848	−	0.0604022i
$403$	−11.8033	−	6.01410i	−0.587966	−	0.299584i
$404$	−12.9310	+	6.58865i	−0.643339	+	0.327798i
$405$	−0.964896	+	1.32807i	−0.0479461	+	0.0659921i
$406$	−3.04854	−	2.21490i	−0.151297	−	0.109924i
$407$	−3.39135	+	3.39135i	−0.168103	+	0.168103i
$408$	−2.72707	−	0.886079i	−0.135010	−	0.0438674i
$409$	−32.2084			−1.59260			−0.796301	−	0.604900i	$-0.793213\pi$
$409$	−32.2084			−1.59260			−0.796301	+	0.604900i	$0.793213\pi$
$410$	15.8935	−	3.71288i	0.784926	−	0.183366i
$411$	−21.0891			−1.04025
$412$	8.29946	+	2.69666i	0.408885	+	0.132855i
$413$	−3.09093	+	3.09093i	−0.152095	+	0.152095i
$414$	−3.43043	−	2.49236i	−0.168597	−	0.122493i
$415$	−1.98340	+	2.72992i	−0.0973613	+	0.134006i
$416$	−5.28490	+	2.69279i	−0.259114	+	0.132025i
$417$	16.7480	+	8.53351i	0.820151	+	0.417888i
$418$	−4.94535	−	6.80669i	−0.241885	−	0.332926i
$419$			0.665263i			0.0325002i	0.999868	+	0.0162501i	$0.00517280\pi$
$419$			0.665263i			0.0325002i	−0.999868	+	0.0162501i	$0.994827\pi$
$420$	−9.60398	+	6.97770i	−0.468626	+	0.340477i
$421$	−3.78470	+	23.8956i	−0.184455	+	1.16460i	0.705553	+	0.708657i	$0.250699\pi$
$421$	−3.78470	+	23.8956i	−0.184455	+	1.16460i	−0.890008	+	0.455945i	$0.849301\pi$
$422$	−6.66945	+	1.05634i	−0.324664	+	0.0514217i
$423$	−9.44852	−	18.5438i	−0.459403	−	0.901629i
$424$	−2.63807	−	2.63807i	−0.128116	−	0.128116i
$425$	0.655067	+	4.13593i	0.0317754	+	0.200622i
$426$	0.831560	+	2.55928i	0.0402892	+	0.123998i
$427$	41.7145	+	6.60693i	2.01871	+	0.319732i
$428$	−3.38067	+	10.4046i	−0.163411	+	0.502927i
$429$	3.02532	−	5.93752i	0.146064	−	0.286666i
$430$	2.42692	−	0.788553i	0.117036	−	0.0380274i
$431$	30.1041	−	9.78141i	1.45006	−	0.471154i	0.525044	−	0.851075i	$-0.324049\pi$
$431$	30.1041	−	9.78141i	1.45006	−	0.471154i	0.925019	+	0.379921i	$0.124049\pi$
$432$	2.30352	−	4.52092i	0.110828	−	0.217513i
$433$	−8.05564	+	24.7927i	−0.387129	+	1.19146i	0.547795	+	0.836613i	$0.315467\pi$
$433$	−8.05564	+	24.7927i	−0.387129	+	1.19146i	−0.934924	+	0.354848i	$0.884533\pi$
$434$	−10.0200	−	1.58700i	−0.480973	−	0.0761787i
$435$	0.669970	+	2.06196i	0.0321226	+	0.0988632i
$436$	0.522483	+	3.29882i	0.0250224	+	0.157985i
$437$	11.8134	+	11.8134i	0.565112	+	0.565112i
$438$	−2.18475	−	4.28781i	−0.104391	−	0.204880i
$439$	−1.93917	+	0.307134i	−0.0925514	+	0.0146587i	−0.202538	−	0.979274i	$-0.564919\pi$
$439$	−1.93917	+	0.307134i	−0.0925514	+	0.0146587i	0.109987	+	0.993933i	$0.464919\pi$
$440$	−0.436936	+	2.75871i	−0.0208301	+	0.131516i
$441$	−21.4931	+	15.6157i	−1.02348	+	0.743603i
$442$		−	16.5881i		−	0.789016i
$443$	12.8871	+	17.7375i	0.612282	+	0.842734i	0.996763	−	0.0803988i	$-0.0256194\pi$
$443$	12.8871	+	17.7375i	0.612282	+	0.842734i	−0.384480	+	0.923133i	$0.625619\pi$
$444$	3.99852	+	2.03735i	0.189761	+	0.0966881i
$445$	24.6856	−	12.5779i	1.17021	−	0.596252i
$446$	−3.12673	+	4.30357i	−0.148055	+	0.203780i
$447$	9.69382	+	7.04297i	0.458502	+	0.333121i
$448$	−3.21191	+	3.21191i	−0.151748	+	0.151748i
$449$	29.0347	+	9.43394i	1.37023	+	0.445215i	0.899446	−	0.437033i	$-0.143971\pi$
$449$	29.0347	+	9.43394i	1.37023	+	0.445215i	0.470786	+	0.882248i	$0.343971\pi$
$450$	−2.91792			−0.137552
$451$	−3.70261	+	5.95985i	−0.174349	+	0.280638i
$452$	9.21539			0.433456
$453$	−4.33551	−	1.40869i	−0.203700	−	0.0661861i
$454$	−0.432334	+	0.432334i	−0.0202905	+	0.0202905i
$455$	−55.5595	−	40.3663i	−2.60467	−	1.89240i
$456$	−4.62729	+	6.36892i	−0.216693	+	0.298252i
$457$	7.12311	−	3.62941i	0.333205	−	0.169777i	−0.279381	−	0.960180i	$-0.590129\pi$
$457$	7.12311	−	3.62941i	0.333205	−	0.169777i	0.612586	+	0.790404i	$0.290129\pi$
$458$	−8.63105	−	4.39774i	−0.403302	−	0.205493i
$459$	8.34077	+	11.4801i	0.389314	+	0.535844i
$460$		−	5.54623i		−	0.258594i
$461$	25.4999	−	18.5267i	1.18765	−	0.862876i	0.194634	−	0.980876i	$-0.437648\pi$
$461$	25.4999	−	18.5267i	1.18765	−	0.862876i	0.993014	+	0.118000i	$0.0376481\pi$
$462$	0.798322	−	5.04041i	0.0371413	−	0.234501i
$463$	−3.02643	+	0.479340i	−0.140650	+	0.0222768i	−0.226363	−	0.974043i	$-0.572683\pi$
$463$	−3.02643	+	0.479340i	−0.140650	+	0.0222768i	0.0857123	+	0.996320i	$0.472683\pi$
$464$	0.376620	+	0.739159i	0.0174842	+	0.0343146i
$465$	4.12733	+	4.12733i	0.191400	+	0.191400i
$466$	−1.96504	−	12.4067i	−0.0910285	−	0.574731i
$467$	8.15470	+	25.0976i	0.377354	+	1.16138i	0.941876	+	0.335960i	$0.109061\pi$
$467$	8.15470	+	25.0976i	0.377354	+	1.16138i	−0.564522	+	0.825418i	$0.690939\pi$
$468$	11.4166	+	1.80821i	0.527732	+	0.0835846i
$469$	2.04937	−	6.30730i	0.0946309	−	0.291244i
$470$	12.3586	−	24.2552i	0.570061	−	1.11881i
$471$	−15.8581	+	5.15261i	−0.730703	+	0.237420i
$472$	0.915234	−	0.297378i	0.0421271	−	0.0136879i
$473$	−0.498020	+	0.977420i	−0.0228990	+	0.0449418i
$474$	−1.51684	+	4.66834i	−0.0696706	+	0.214424i
$475$	11.3551	+	1.79847i	0.521008	+	0.0825196i
$476$	−3.92556	−	12.0816i	−0.179928	−	0.553760i
$477$	1.13735	+	7.18095i	0.0520757	+	0.328793i
$478$	−9.73019	−	9.73019i	−0.445049	−	0.445049i
$479$	−18.1117	−	35.5461i	−0.827542	−	1.62414i	−0.780421	−	0.625254i	$-0.784995\pi$
$479$	−18.1117	−	35.5461i	−0.827542	−	1.62414i	−0.0471215	−	0.998889i	$-0.515005\pi$
$480$	2.58128	−	0.408835i	0.117819	−	0.0186607i
$481$	−4.06123	+	25.6416i	−0.185176	+	1.16916i
$482$	−6.56770	+	4.77171i	−0.299150	+	0.217346i
$483$			10.1335i			0.461088i
$484$	5.75988	+	7.92779i	0.261813	+	0.360354i
$485$	−36.8362	−	18.7690i	−1.67264	−	0.852255i
$486$	−14.1511	+	7.21035i	−0.641907	+	0.327068i
$487$	−6.80971	+	9.37277i	−0.308578	+	0.424721i	−0.934937	−	0.354814i	$-0.884544\pi$
$487$	−6.80971	+	9.37277i	−0.308578	+	0.424721i	0.626359	+	0.779534i	$0.284544\pi$
$488$	−7.52224	−	5.46523i	−0.340516	−	0.247399i
$489$	−8.57758	+	8.57758i	−0.387891	+	0.387891i
$490$	−33.0487	−	10.7382i	−1.49299	−	0.485101i
$491$	−10.7931			−0.487087			−0.243543	−	0.969890i	$-0.578310\pi$
$491$	−10.7931			−0.487087			−0.243543	+	0.969890i	$0.578310\pi$
$492$	6.37419	+	1.57167i	0.287371	+	0.0708562i
$493$	−2.32005			−0.104490
$494$	−43.3133	−	14.0733i	−1.94876	−	0.633190i
$495$	3.84885	−	3.84885i	0.172993	−	0.172993i
$496$	1.80687	+	1.31276i	0.0811306	+	0.0589449i
$497$	−7.00743	+	9.64490i	−0.314326	+	0.432633i
$498$	−1.20936	+	0.616198i	−0.0541926	+	0.0276125i
$499$	−21.4382	−	10.9233i	−0.959705	−	0.488994i	−0.0973235	−	0.995253i	$-0.531028\pi$
$499$	−21.4382	−	10.9233i	−0.959705	−	0.488994i	−0.862382	+	0.506259i	$0.831028\pi$
$500$	5.24792	+	7.22314i	0.234694	+	0.323029i
$501$		−	10.7323i		−	0.479485i
$502$	8.82779	−	6.41377i	0.394004	−	0.286260i
$503$	1.09071	−	6.88646i	0.0486323	−	0.307052i	−0.951367	−	0.308059i	$-0.900321\pi$
$503$	1.09071	−	6.88646i	0.0486323	−	0.307052i	0.999999	+	0.00100699i	$0.000320535\pi$
$504$	8.74295	−	1.38475i	0.389442	−	0.0616816i
$505$	16.7944	+	32.9608i	0.747339	+	1.46674i
$506$	1.68591	+	1.68591i	0.0749479	+	0.0749479i
$507$	−3.55770	−	22.4624i	−0.158003	−	0.997590i
$508$	1.04565	+	3.21817i	0.0463930	+	0.142783i
$509$	−26.6613	−	4.22274i	−1.18174	−	0.187170i	−0.465518	−	0.885039i	$-0.654132\pi$
$509$	−26.6613	−	4.22274i	−1.18174	−	0.187170i	−0.716225	+	0.697869i	$0.754132\pi$
$510$	−2.25860	+	6.95125i	−0.100012	+	0.307807i
$511$	9.67900	−	18.9961i	0.428174	−	0.840338i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	37.0520	−	12.0389i	1.63589	−	0.531531i
$514$	−10.1942	+	20.0073i	−0.449648	+	0.882484i
$515$	6.87373	−	21.1552i	0.302893	−	0.932209i
$516$	1.01380	+	0.160569i	0.0446299	+	0.00706867i
$517$	3.61624	+	11.1297i	0.159042	+	0.489482i
$518$	3.11013	+	19.6366i	0.136651	+	0.862783i
$519$	−2.25402	−	2.25402i	−0.0989404	−	0.0989404i
$520$	6.86388	+	13.4711i	0.301001	+	0.590748i
$521$	18.1983	−	2.88233i	0.797283	−	0.126277i	0.255515	−	0.966805i	$-0.417755\pi$
$521$	18.1983	−	2.88233i	0.797283	−	0.126277i	0.541768	+	0.840528i	$0.317755\pi$
$522$	0.252901	−	1.59675i	0.0110692	−	0.0698880i
$523$	3.77265	−	2.74099i	0.164967	−	0.119855i	−0.502239	−	0.864729i	$-0.667490\pi$
$523$	3.77265	−	2.74099i	0.164967	−	0.119855i	0.667206	+	0.744874i	$0.267490\pi$
$524$		−	16.7746i		−	0.732801i
$525$	4.09881	+	5.64153i	0.178887	+	0.246216i
$526$	17.6853	+	9.01113i	0.771118	+	0.392904i
$527$	−5.56532	+	2.83567i	−0.242429	+	0.123524i
$528$	−0.660369	+	0.908920i	−0.0287389	+	0.0395557i
$529$	14.7772	+	10.7363i	0.642487	+	0.466794i
$530$	−6.72439	+	6.72439i	−0.292089	+	0.292089i
$531$	−1.78358	−	0.579521i	−0.0774008	−	0.0251491i
$532$	−34.8768			−1.51210
$533$	2.74784	+	37.8799i	0.119022	+	1.64076i
$534$	11.1441			0.482253
$535$	26.5212	+	8.61727i	1.14661	+	0.372557i
$536$	−1.03239	+	1.03239i	−0.0445925	+	0.0445925i
$537$	−14.0807	−	10.2302i	−0.607626	−	0.441466i
$538$	−7.00313	+	9.63898i	−0.301926	+	0.415566i
$539$	13.3101	−	6.78183i	0.573306	−	0.292114i
$540$	−11.5238	−	5.87164i	−0.495903	−	0.252675i
$541$	−0.258470	−	0.355753i	−0.0111125	−	0.0152950i	0.803425	−	0.595406i	$-0.203009\pi$
$541$	−0.258470	−	0.355753i	−0.0111125	−	0.0152950i	−0.814537	+	0.580111i	$0.803009\pi$
$542$		−	7.83262i		−	0.336440i
$543$	6.11834	−	4.44523i	0.262563	−	0.190763i
$544$	−0.437495	+	2.76224i	−0.0187575	+	0.118430i
$545$	8.40865	−	1.33180i	0.360187	−	0.0570480i
$546$	−12.5409	−	24.6129i	−0.536702	−	1.05334i
$547$	−8.70852	−	8.70852i	−0.372350	−	0.372350i	0.495983	−	0.868332i	$-0.334808\pi$
$547$	−8.70852	−	8.70852i	−0.372350	−	0.372350i	−0.868332	+	0.495983i	$0.834808\pi$
$548$	3.21766	+	20.3155i	0.137452	+	0.867837i
$549$	5.59928	+	17.2328i	0.238972	+	0.735479i
$550$	1.62051	+	0.256663i	0.0690987	+	0.0109442i
$551$	−1.96833	+	6.05791i	−0.0838538	+	0.258075i
$552$	1.01281	−	1.98775i	0.0431079	−	0.0846041i
$553$	−20.6819	+	6.71997i	−0.879485	+	0.285762i
$554$	26.1759	−	8.50508i	1.11211	−	0.361346i
$555$	5.19316	−	10.1921i	0.220437	−	0.432633i
$556$	5.66519	−	17.4357i	0.240258	−	0.739437i
$557$	−45.9773	−	7.28208i	−1.94812	−	0.308552i	−0.948162	−	0.317787i	$-0.897060\pi$
$557$	−45.9773	−	7.28208i	−1.94812	−	0.308552i	−0.999957	+	0.00923483i	$0.997060\pi$
$558$	−1.34497	−	4.13938i	−0.0569369	−	0.175234i
$559$	0.928902	+	5.86486i	0.0392884	+	0.248057i
$560$	8.18709	+	8.18709i	0.345968	+	0.345968i
$561$	−1.42645	−	2.79956i	−0.0602247	−	0.118198i
$562$	6.10112	−	0.966323i	0.257360	−	0.0407619i
$563$	−3.25464	+	20.5490i	−0.137167	+	0.866038i	0.819123	+	0.573618i	$0.194461\pi$
$563$	−3.25464	+	20.5490i	−0.137167	+	0.866038i	−0.956290	+	0.292420i	$0.905539\pi$
$564$	8.85856	−	6.43612i	0.373013	−	0.271009i
$565$		−	23.4899i		−	0.988226i
$566$	−2.00056	−	2.75353i	−0.0840897	−	0.115740i
$567$	−2.60647	−	1.32807i	−0.109462	−	0.0557735i
$568$	2.33853	−	1.19154i	0.0981226	−	0.0499960i
$569$	−17.1758	+	23.6404i	−0.720046	+	0.991059i	0.279476	+	0.960153i	$0.409839\pi$
$569$	−17.1758	+	23.6404i	−0.720046	+	0.991059i	−0.999522	+	0.0309061i	$0.990161\pi$
$570$	16.2343	+	11.7949i	0.679978	+	0.494033i
$571$	−21.9985	+	21.9985i	−0.920607	+	0.920607i	−0.997072	−	0.0764655i	$-0.975637\pi$
$571$	−21.9985	+	21.9985i	−0.920607	+	0.920607i	0.0764655	+	0.997072i	$0.475637\pi$
$572$	−6.18132	−	2.00843i	−0.258454	−	0.0839768i
$573$	17.4691			0.729781
$574$	10.9656	+	26.9387i	0.457693	+	1.12440i
$575$	−3.25794			−0.135866
$576$	−1.85339	−	0.602203i	−0.0772246	−	0.0250918i
$577$	0.585639	−	0.585639i	0.0243805	−	0.0243805i	−0.694811	−	0.719192i	$-0.744512\pi$
$577$	0.585639	−	0.585639i	0.0243805	−	0.0243805i	0.719192	+	0.694811i	$0.244512\pi$
$578$	7.42568	+	5.39507i	0.308867	+	0.224405i
$579$	7.85266	−	10.8083i	0.326345	−	0.449176i
$580$	1.88410	−	0.959999i	0.0782332	−	0.0398618i
$581$	−5.35776	−	2.72992i	−0.222277	−	0.113256i
$582$	−9.77449	−	13.4534i	−0.405166	−	0.557663i
$583$		−	4.08809i		−	0.169311i
$584$	−3.79720	+	2.75883i	−0.157129	+	0.114161i
$585$	4.60910	−	29.1007i	0.190563	−	1.20317i
$586$	14.6839	−	2.32570i	0.606585	−	0.0960737i
$587$	−15.3553	−	30.1365i	−0.633782	−	1.24387i	−0.954928	−	0.296837i	$-0.904068\pi$
$587$	−15.3553	−	30.1365i	−0.633782	−	1.24387i	0.321147	−	0.947030i	$-0.395932\pi$
$588$	−9.88359	−	9.88359i	−0.407593	−	0.407593i
$589$	2.68262	+	16.9374i	0.110536	+	0.697894i
$590$	−0.758011	−	2.33292i	−0.0312068	−	0.0960447i
$591$	10.2535	+	1.62400i	0.421774	+	0.0668025i
$592$	1.35254	−	4.16270i	0.0555892	−	0.171086i
$593$	5.39521	−	10.5887i	0.221555	−	0.434826i	−0.753297	−	0.657681i	$-0.771538\pi$
$593$	5.39521	−	10.5887i	0.221555	−	0.434826i	0.974852	+	0.222855i	$0.0715376\pi$
$594$	5.28776	−	1.71810i	0.216959	−	0.0704943i
$595$	−30.7958	+	10.0062i	−1.26251	+	0.410213i
$596$	5.30561	−	10.4128i	0.217326	−	0.426527i
$597$	−2.79283	+	8.59545i	−0.114303	+	0.351788i
$598$	12.7470	+	2.01892i	0.521262	+	0.0825598i
$599$	−1.43996	−	4.43174i	−0.0588351	−	0.181076i	0.917320	−	0.398151i	$-0.130348\pi$
$599$	−1.43996	−	4.43174i	−0.0588351	−	0.181076i	−0.976155	+	0.217076i	$0.930348\pi$
$600$	−0.240156	−	1.51629i	−0.00980433	−	0.0619021i
$601$	4.16468	+	4.16468i	0.169881	+	0.169881i	0.786927	−	0.617046i	$-0.211671\pi$
$601$	4.16468	+	4.16468i	0.169881	+	0.169881i	−0.617046	+	0.786927i	$0.711671\pi$
$602$	2.06446	+	4.05173i	0.0841410	+	0.165136i
$603$	2.81022	−	0.445095i	0.114441	−	0.0181257i
$604$	−0.695532	+	4.39142i	−0.0283008	+	0.178684i
$605$	20.2078	−	14.6818i	0.821564	−	0.596901i
$606$			14.8799i			0.604453i
$607$	−18.2711	−	25.1480i	−0.741602	−	1.02073i	−0.998525	−	0.0542956i	$-0.982709\pi$
$607$	−18.2711	−	25.1480i	−0.741602	−	1.02073i	0.256923	−	0.966432i	$-0.417291\pi$
$608$	6.84132	+	3.48583i	0.277452	+	0.141369i
$609$	−3.44243	+	1.75400i	−0.139494	+	0.0710758i
$610$	−13.9308	+	19.1741i	−0.564040	+	0.776335i
$611$	51.2472	+	37.2333i	2.07324	+	1.50630i
$612$	3.85378	−	3.85378i	0.155780	−	0.155780i
$613$	−7.48982	−	2.43359i	−0.302511	−	0.0982917i	0.153828	−	0.988098i	$-0.450840\pi$
$613$	−7.48982	−	2.43359i	−0.302511	−	0.0982917i	−0.456339	+	0.889806i	$0.650840\pi$
$614$	31.4538			1.26937
$615$	4.00615	−	16.2477i	0.161544	−	0.655170i
$616$	−4.97733			−0.200542
$617$	5.75004	+	1.86830i	0.231488	+	0.0752149i	0.422464	−	0.906380i	$-0.361165\pi$
$617$	5.75004	+	1.86830i	0.231488	+	0.0752149i	−0.190976	+	0.981595i	$0.561165\pi$
$618$	6.32670	−	6.32670i	0.254497	−	0.254497i
$619$	8.25456	+	5.99729i	0.331779	+	0.241051i	0.741185	−	0.671301i	$-0.234264\pi$
$619$	8.25456	+	5.99729i	0.331779	+	0.241051i	−0.409406	+	0.912352i	$0.634264\pi$
$620$	3.34621	−	4.60567i	0.134387	−	0.184968i
$621$	−9.83689	+	5.01215i	−0.394741	+	0.201131i
$622$	−25.8317	−	13.1619i	−1.03576	−	0.527745i
$623$	29.0197	+	39.9422i	1.16265	+	1.60025i
$624$			6.08142i			0.243452i
$625$	24.4684	−	17.7773i	0.978736	−	0.711094i
$626$	1.22753	−	7.75030i	0.0490619	−	0.309764i
$627$	−8.52014	+	1.34946i	−0.340262	+	0.0538922i
$628$	7.38317	+	14.4903i	0.294621	+	0.578226i
$629$	8.65556	+	8.65556i	0.345120	+	0.345120i
$630$	−3.52970	−	22.2856i	−0.140627	−	0.887881i
$631$	−5.60513	−	17.2508i	−0.223137	−	0.686744i	−0.998475	−	0.0551982i	$-0.982421\pi$
$631$	−5.60513	−	17.2508i	−0.223137	−	0.686744i	0.775339	−	0.631545i	$-0.217579\pi$
$632$	4.72854	+	0.748927i	0.188091	+	0.0297907i
$633$	−2.13945	+	6.58454i	−0.0850354	+	0.261712i
$634$	−4.53455	+	8.89955i	−0.180090	+	0.353446i
$635$	8.20305	−	2.66533i	0.325528	−	0.105771i
$636$	−3.63795	+	1.18204i	−0.144254	+	0.0468710i
$637$	36.7100	−	72.0473i	1.45450	−	2.85462i
$638$	−0.280904	+	0.864535i	−0.0111211	+	0.0342273i
$639$	−5.05176	−	0.800121i	−0.199845	−	0.0316523i
$640$	−0.787679	−	2.42423i	−0.0311357	−	0.0958260i
$641$	−2.14644	−	13.5521i	−0.0847794	−	0.535276i	−0.993125	−	0.117056i	$-0.962654\pi$
$641$	−2.14644	−	13.5521i	−0.0847794	−	0.535276i	0.908346	−	0.418220i	$-0.137346\pi$
$642$	7.93149	+	7.93149i	0.313031	+	0.313031i
$643$	−5.19500	−	10.1958i	−0.204871	−	0.402082i	0.765594	−	0.643324i	$-0.222445\pi$
$643$	−5.19500	−	10.1958i	−0.204871	−	0.402082i	−0.970465	+	0.241242i	$0.922445\pi$
$644$	9.76177	−	1.54611i	0.384668	−	0.0609254i
$645$	0.409289	−	2.58415i	0.0161157	−	0.101751i
$646$	−17.3723	+	12.6217i	−0.683505	+	0.496595i
$647$			48.2350i			1.89631i	0.317805	+	0.948156i	$0.397054\pi$
$647$			48.2350i			1.89631i	−0.317805	+	0.948156i	$0.602946\pi$
$648$	0.378542	+	0.521018i	0.0148705	+	0.0204675i
$649$	0.939563	+	0.478731i	0.0368811	+	0.0187918i
$650$	7.91315	−	4.03195i	0.310379	−	0.158146i
$651$	−6.11383	+	8.41497i	−0.239620	+	0.329809i
$652$	9.57168	+	6.95423i	0.374856	+	0.272349i
$653$	−9.51860	+	9.51860i	−0.372492	+	0.372492i	−0.868384	−	0.495892i	$-0.834841\pi$
$653$	−9.51860	+	9.51860i	−0.372492	+	0.372492i	0.495892	+	0.868384i	$0.334841\pi$
$654$	3.25683	+	1.05821i	0.127352	+	0.0413792i
$655$	−42.7581			−1.67070
$656$	0.541476	−	6.38019i	0.0211411	−	0.249105i
$657$	9.14674			0.356848
$658$	46.1361	+	14.9905i	1.79857	+	0.584391i
$659$	−4.06726	+	4.06726i	−0.158438	+	0.158438i	−0.781874	−	0.623436i	$-0.785736\pi$
$659$	−4.06726	+	4.06726i	−0.158438	+	0.158438i	0.623436	+	0.781874i	$0.285736\pi$
$660$	2.31682	+	1.68327i	0.0901821	+	0.0655211i
$661$	7.03556	−	9.68362i	0.273652	−	0.376649i	−0.649967	−	0.759963i	$-0.725217\pi$
$661$	7.03556	−	9.68362i	0.273652	−	0.376649i	0.923618	+	0.383314i	$0.125217\pi$
$662$	0.728307	−	0.371091i	0.0283064	−	0.0144229i
$663$	−15.1540	−	7.72134i	−0.588532	−	0.299872i
$664$	0.778114	+	1.07098i	0.0301967	+	0.0415622i
$665$			88.9004i			3.44741i
$666$	−6.90061	+	5.01358i	−0.267393	+	0.194272i
$667$	0.282371	−	1.78282i	0.0109335	−	0.0690312i
$668$	−10.3387	+	1.63749i	−0.400016	+	0.0633562i
$669$	2.47609	+	4.85960i	0.0957312	+	0.187883i
$670$	2.63155	+	2.63155i	0.101666	+	0.101666i
$671$	−1.59383	−	10.0630i	−0.0615290	−	0.388479i
$672$	1.43916	+	4.42928i	0.0555168	+	0.170863i
$673$	−35.2932	−	5.58989i	−1.36045	−	0.215474i	−0.566804	−	0.823853i	$-0.691820\pi$
$673$	−35.2932	−	5.58989i	−1.36045	−	0.215474i	−0.793647	+	0.608378i	$0.791820\pi$
$674$	0.100605	−	0.309630i	0.00387516	−	0.0119265i
$675$	−3.44910	+	6.76923i	−0.132756	+	0.260548i
$676$	−21.0957	+	6.85440i	−0.811373	+	0.263631i
$677$	−0.954446	+	0.310118i	−0.0366823	+	0.0119188i	−0.327301	−	0.944920i	$-0.606139\pi$
$677$	−0.954446	+	0.310118i	−0.0366823	+	0.0119188i	0.290618	+	0.956839i	$0.406139\pi$
$678$	4.28953	−	8.41867i	0.164738	−	0.323317i
$679$	22.7660	−	70.0666i	0.873679	−	2.68891i
$680$	7.04090	+	1.11517i	0.270006	+	0.0427648i
$681$	0.193716	+	0.596197i	0.00742322	+	0.0228463i
$682$	0.382842	+	2.41717i	0.0146598	+	0.0925582i
$683$	−16.9042	−	16.9042i	−0.646821	−	0.646821i	0.305402	−	0.952223i	$-0.401209\pi$
$683$	−16.9042	−	16.9042i	−0.646821	−	0.646821i	−0.952223	+	0.305402i	$0.901209\pi$
$684$	−6.79307	−	13.3322i	−0.259740	−	0.509768i
$685$	51.7839	−	8.20177i	1.97856	−	0.313374i
$686$	4.71301	−	29.7568i	0.179944	−	1.13612i
$687$	−8.03506	+	5.83781i	−0.306557	+	0.222726i
$688$		−	1.00111i		−	0.0381669i
$689$	−13.0070	−	17.9026i	−0.495526	−	0.682033i
$690$	−5.06673	−	2.58163i	−0.192887	−	0.0982809i
$691$	−2.21661	+	1.12942i	−0.0843236	+	0.0429650i	−0.495644	−	0.868526i	$-0.665068\pi$
$691$	−2.21661	+	1.12942i	−0.0843236	+	0.0429650i	0.411320	+	0.911491i	$0.365068\pi$
$692$	−1.82744	+	2.51525i	−0.0694687	+	0.0956154i
$693$	7.84720	+	5.70133i	0.298091	+	0.216575i
$694$	6.05694	−	6.05694i	0.229918	−	0.229918i
$695$	−44.4432	−	14.4405i	−1.68583	−	0.547758i
$696$	0.850562			0.0322405
$697$	15.2110	+	9.44996i	0.576157	+	0.357943i
$698$	−9.76519			−0.369618
$699$	−12.2488	−	3.97987i	−0.463292	−	0.150533i
$700$	4.80922	−	4.80922i	0.181772	−	0.181772i
$701$	15.7086	+	11.4129i	0.593304	+	0.431061i	0.843496	−	0.537136i	$-0.180494\pi$
$701$	15.7086	+	11.4129i	0.593304	+	0.431061i	−0.250192	+	0.968196i	$0.580494\pi$
$702$	17.6897	−	24.3478i	0.667655	−	0.918949i
$703$	29.9439	−	15.2572i	1.12936	−	0.575436i
$704$	0.976337	+	0.497469i	0.0367971	+	0.0187491i
$705$	−16.4056	−	22.5803i	−0.617869	−	0.850424i
$706$			16.0773i			0.605076i
$707$	−53.3317	+	38.7477i	−2.00574	+	1.45726i
$708$	0.154350	−	0.974529i	0.00580084	−	0.0366250i
$709$	−21.5002	+	3.40529i	−0.807456	+	0.127888i	−0.546497	−	0.837461i	$-0.684039\pi$
$709$	−21.5002	+	3.40529i	−0.807456	+	0.127888i	−0.260959	+	0.965350i	$0.584039\pi$
$710$	−3.03722	−	5.96088i	−0.113985	−	0.223708i
$711$	−6.59709	−	6.59709i	−0.247410	−	0.247410i
$712$	−1.70031	−	10.7353i	−0.0637219	−	0.402324i
$713$	−1.50169	−	4.62174i	−0.0562389	−	0.173085i
$714$	−12.8643	−	2.03751i	−0.481436	−	0.0762520i
$715$	−5.11946	+	15.7561i	−0.191457	+	0.589244i
$716$	−7.70662	+	15.1251i	−0.288010	+	0.565251i
$717$	−13.4181	+	4.35981i	−0.501109	+	0.162820i
$718$	−16.7097	+	5.42931i	−0.623600	+	0.202620i
$719$	−12.9174	+	25.3518i	−0.481738	+	0.945463i	0.514391	+	0.857556i	$0.328018\pi$
$719$	−12.9174	+	25.3518i	−0.481738	+	0.945463i	−0.996129	+	0.0879076i	$0.971982\pi$
$720$	−1.53500	+	4.72426i	−0.0572063	+	0.176063i
$721$	39.1508	+	6.20089i	1.45805	+	0.230933i
$722$	12.3467	+	37.9991i	0.459495	+	1.41418i
$723$	1.30208	+	8.22099i	0.0484248	+	0.305742i
$724$	−5.21569	−	5.21569i	−0.193840	−	0.193840i
$725$	−0.563918	−	1.10675i	−0.0209434	−	0.0411037i
$726$	9.92347	−	1.57172i	0.368294	−	0.0583321i
$727$	5.52299	−	34.8708i	0.204836	−	1.29328i	−0.644162	−	0.764889i	$-0.722794\pi$
$727$	5.52299	−	34.8708i	0.204836	−	1.29328i	0.848998	−	0.528396i	$-0.177206\pi$
$728$	−21.7967	+	15.8363i	−0.807841	+	0.586931i
$729$			14.3519i			0.531550i
$730$	7.03220	+	9.67900i	0.260274	+	0.358236i
$731$	2.49461	+	1.27107i	0.0922667	+	0.0470122i
$732$	−8.49414	+	4.32798i	−0.313952	+	0.159967i
$733$	−15.3832	+	21.1731i	−0.568191	+	0.782048i	−0.992339	−	0.123545i	$-0.960574\pi$
$733$	−15.3832	+	21.1731i	−0.568191	+	0.782048i	0.424148	+	0.905593i	$0.360574\pi$
$734$	2.62350	+	1.90608i	0.0968351	+	0.0703548i
$735$	−25.1931	+	25.1931i	−0.929262	+	0.929262i
$736$	−2.06937	−	0.672378i	−0.0762778	−	0.0247842i
$737$	−1.59985			−0.0589311
$738$	−8.16192	+	9.43869i	−0.300445	+	0.347443i
$739$	−35.7982			−1.31686			−0.658430	−	0.752642i	$-0.728779\pi$
$739$	−35.7982			−1.31686			−0.658430	+	0.752642i	$0.728779\pi$
$740$	−10.6107	−	3.44761i	−0.390055	−	0.126737i
$741$	−33.0179	+	33.0179i	−1.21294	+	1.21294i
$742$	−13.7100	−	9.96088i	−0.503309	−	0.365675i
$743$	21.9293	−	30.1830i	0.804507	−	1.10731i	−0.187641	−	0.982238i	$-0.560084\pi$
$743$	21.9293	−	30.1830i	0.804507	−	1.10731i	0.992148	−	0.125071i	$-0.0399157\pi$
$744$	2.04032	−	1.03959i	0.0748017	−	0.0381134i
$745$	−26.5422	−	13.5239i	−0.972429	−	0.495478i
$746$	−8.06187	−	11.0962i	−0.295166	−	0.406261i
$747$		−	2.57980i		−	0.0943898i
$748$	−2.47924	+	1.80127i	−0.0906498	+	0.0658609i
$749$	−7.77375	+	49.0816i	−0.284047	+	1.79340i
$750$	9.04143	−	1.43202i	0.330146	−	0.0522900i
$751$	1.76436	+	3.46276i	0.0643825	+	0.126358i	0.920955	−	0.389669i	$-0.127411\pi$
$751$	1.76436	+	3.46276i	0.0643825	+	0.126358i	−0.856573	+	0.516027i	$0.827411\pi$
$752$	−7.55164	−	7.55164i	−0.275380	−	0.275380i
$753$	−1.75015	−	11.0500i	−0.0637791	−	0.402685i
$754$	1.52053	+	4.67972i	0.0553745	+	0.170425i
$755$	11.1936	+	1.77290i	0.407379	+	0.0645224i
$756$	7.12207	−	21.9195i	0.259027	−	0.797204i
$757$	8.13083	−	15.9577i	0.295520	−	0.579991i	−0.694733	−	0.719267i	$-0.744478\pi$
$757$	8.13083	−	15.9577i	0.295520	−	0.579991i	0.990254	+	0.139276i	$0.0444777\pi$
$758$	−16.3191	+	5.30239i	−0.592735	+	0.192591i
$759$	2.32490	−	0.755407i	0.0843887	−	0.0274196i
$760$	8.88531	−	17.4384i	0.322304	−	0.632557i
$761$	15.2643	−	46.9786i	0.553329	−	1.70297i	−0.146986	−	0.989139i	$-0.546957\pi$
$761$	15.2643	−	46.9786i	0.553329	−	1.70297i	0.700315	−	0.713834i	$-0.253043\pi$
$762$	3.42666	+	0.542730i	0.124135	+	0.0196610i
$763$	4.68813	+	14.4286i	0.169722	+	0.522349i
$764$	−2.66534	−	16.8283i	−0.0964288	−	0.608827i
$765$	−9.82321	−	9.82321i	−0.355159	−	0.355159i
$766$	−7.97809	−	15.6579i	−0.288260	−	0.565742i
$767$	5.63770	−	0.892924i	0.203566	−	0.0322416i
$768$	0.160391	−	1.01267i	0.00578763	−	0.0365417i
$769$	4.62442	−	3.35984i	0.166761	−	0.121159i	−0.501275	−	0.865288i	$-0.667135\pi$
$769$	4.62442	−	3.35984i	0.166761	−	0.121159i	0.668036	+	0.744129i	$0.267135\pi$
$770$			12.6871i			0.457213i
$771$	13.5324	+	18.6258i	0.487358	+	0.670791i
$772$	−11.6099	−	5.91556i	−0.417851	−	0.212906i
$773$	−30.5356	+	15.5587i	−1.09829	+	0.559606i	−0.906660	−	0.421862i	$-0.861377\pi$
$773$	−30.5356	+	15.5587i	−1.09829	+	0.559606i	−0.191628	+	0.981468i	$0.561377\pi$
$774$	−1.14673	+	1.57834i	−0.0412183	+	0.0567321i
$775$	−2.70544	−	1.96562i	−0.0971823	−	0.0706071i
$776$	−11.4686	+	11.4686i	−0.411700	+	0.411700i
$777$	19.3866	+	6.29909i	0.695491	+	0.225979i
$778$	−24.8813			−0.892037
$779$	37.5798	−	31.7001i	1.34644	−	1.13578i
$780$	15.5014			0.555040
$781$	2.73519	+	0.888718i	0.0978729	+	0.0318008i
$782$	4.30286	−	4.30286i	0.153870	−	0.153870i
$783$	−3.40534	−	2.47413i	−0.121697	−	0.0884181i
$784$	−8.01308	+	11.0291i	−0.286182	+	0.393895i
$785$	36.9355	−	18.8196i	1.31828	−	0.671700i
$786$	−15.3243	−	7.80814i	−0.546601	−	0.278507i
$787$	17.2951	+	23.8047i	0.616505	+	0.848546i	0.997093	−	0.0761987i	$-0.0242783\pi$
$787$	17.2951	+	23.8047i	0.616505	+	0.848546i	−0.380588	+	0.924745i	$0.624278\pi$
$788$		−	10.1252i		−	0.360697i
$789$	16.4641	−	11.9619i	0.586139	−	0.425855i
$790$	1.90900	−	12.0530i	0.0679193	−	0.428825i
$791$	41.3439	−	6.54823i	1.47002	−	0.232828i
$792$	−0.969452	−	1.90266i	−0.0344480	−	0.0676080i
$793$	−38.9969	−	38.9969i	−1.38482	−	1.38482i
$794$	2.17436	+	13.7284i	0.0771651	+	0.487201i
$795$	3.01300	+	9.27307i	0.106860	+	0.328882i
$796$	8.70629	+	1.37894i	0.308586	+	0.0488753i
$797$	−12.9355	+	39.8112i	−0.458197	+	1.41019i	0.409143	+	0.912470i	$0.365828\pi$
$797$	−12.9355	+	39.8112i	−0.458197	+	1.41019i	−0.867340	+	0.497716i	$0.834172\pi$
$798$	−16.2343	+	31.8615i	−0.574687	+	1.12789i
$799$	28.4056	−	9.22954i	1.00492	−	0.326518i
$800$	−1.42403	+	0.462695i	−0.0503470	+	0.0163587i
$801$	−9.61620	+	18.8729i	−0.339772	+	0.666840i
$802$	−2.17993	+	6.70912i	−0.0769759	+	0.236907i
$803$	−5.07978	−	0.804558i	−0.179261	−	0.0283922i
$804$	0.462584	+	1.42369i	0.0163141	+	0.0502096i
$805$	−3.94101	−	24.8826i	−0.138903	−	0.876996i
$806$	9.36719	+	9.36719i	0.329945	+	0.329945i
$807$	5.54586	+	10.8844i	0.195224	+	0.383148i
$808$	14.3341	−	2.27030i	0.504271	−	0.0798687i
$809$	−0.205606	+	1.29814i	−0.00722871	+	0.0456403i	−0.991039	−	0.133573i	$-0.957355\pi$
$809$	−0.205606	+	1.29814i	−0.00722871	+	0.0456403i	0.983810	+	0.179213i	$0.0573551\pi$
$810$	1.32807	−	0.964896i	0.0466635	−	0.0339030i
$811$		−	16.9841i		−	0.596394i	−0.954504	−	0.298197i	$-0.903615\pi$
$811$		−	16.9841i		−	0.596394i	0.954504	−	0.298197i	$-0.0963853\pi$
$812$	2.21490	+	3.04854i	0.0777277	+	0.106983i
$813$	−7.15545	−	3.64588i	−0.250953	−	0.127867i
$814$	4.27335	−	2.17738i	0.149781	−	0.0763172i
$815$	17.7262	−	24.3981i	0.620922	−	0.854626i
$816$	2.31978	+	1.68542i	0.0812087	+	0.0590016i
$817$	5.43533	−	5.43533i	0.190158	−	0.190158i
$818$	30.6320	+	9.95294i	1.07102	+	0.347996i
$819$	52.5042			1.83465
$820$	−16.2630	−	1.38021i	−0.567928	−	0.0481992i
$821$	26.8880			0.938397			0.469198	−	0.883093i	$-0.344543\pi$
$821$	26.8880			0.938397			0.469198	+	0.883093i	$0.344543\pi$
$822$	20.0569	+	6.51688i	0.699564	+	0.227302i
$823$	40.3027	−	40.3027i	1.40487	−	1.40487i	0.621265	−	0.783601i	$-0.286619\pi$
$823$	40.3027	−	40.3027i	1.40487	−	1.40487i	0.783601	−	0.621265i	$-0.213381\pi$
$824$	−7.05994	−	5.12935i	−0.245945	−	0.178689i
$825$	0.988778	−	1.36094i	0.0344248	−	0.0473817i
$826$	3.89480	−	1.98450i	0.135517	−	0.0690495i
$827$	10.1607	+	5.17716i	0.353324	+	0.180027i	0.621639	−	0.783304i	$-0.286467\pi$
$827$	10.1607	+	5.17716i	0.353324	+	0.180027i	−0.268315	+	0.963331i	$0.586467\pi$
$828$	2.49236	+	3.43043i	0.0866154	+	0.119216i
$829$			39.8026i			1.38240i	0.722663	+	0.691200i	$0.242918\pi$
$829$			39.8026i			1.38240i	−0.722663	+	0.691200i	$0.757082\pi$
$830$	2.72992	−	1.98340i	0.0947568	−	0.0688448i
$831$	4.41446	−	27.8718i	0.153136	−	0.966862i
$832$	5.85836	−	0.927873i	0.203102	−	0.0321682i
$833$	−17.3089	−	33.9706i	−0.599717	−	1.17701i
$834$	−13.2913	−	13.2913i	−0.460238	−	0.460238i
$835$	4.17392	+	26.3531i	0.144445	+	0.911987i
$836$	2.59992	+	8.00174i	0.0899202	+	0.276746i
$837$	−11.1927	−	1.77275i	−0.386876	−	0.0612751i
$838$	0.205577	−	0.632702i	0.00710155	−	0.0218563i
$839$	−10.9830	+	21.5553i	−0.379175	+	0.744172i	−0.999183	−	0.0404235i	$-0.987129\pi$
$839$	−10.9830	+	21.5553i	−0.379175	+	0.744172i	0.620008	+	0.784595i	$0.287129\pi$
$840$	11.2902	−	3.66839i	0.389547	−	0.126572i
$841$	−26.9261	+	8.74883i	−0.928487	+	0.301684i
$842$	10.9836	−	21.5566i	0.378520	−	0.742888i
$843$	1.95714	−	6.02345i	0.0674074	−	0.207459i
$844$	6.66945	+	1.05634i	0.229572	+	0.0363606i
$845$	17.4718	+	53.7725i	0.601047	+	1.84983i
$846$	3.25574	+	20.5559i	0.111935	+	0.706727i
$847$	31.4744	+	31.4744i	1.08147	+	1.08147i
$848$	1.69375	+	3.32416i	0.0581634	+	0.114152i
$849$	−3.44668	+	0.545901i	−0.118290	+	0.0187353i
$850$	0.655067	−	4.13593i	0.0224686	−	0.141861i
$851$	−7.70473	+	5.59782i	−0.264115	+	0.191891i
$852$		−	2.69099i		−	0.0921917i
$853$	10.6445	+	14.6509i	0.364461	+	0.501638i	0.951385	−	0.308004i	$-0.0996611\pi$
$853$	10.6445	+	14.6509i	0.364461	+	0.501638i	−0.586924	+	0.809642i	$0.699661\pi$
$854$	−37.6312	−	19.1741i	−1.28771	−	0.656123i
$855$	−33.9834	+	17.3154i	−1.16221	+	0.592175i
$856$	6.43042	−	8.85071i	0.219787	−	0.302511i
$857$	24.9677	+	18.1401i	0.852879	+	0.619653i	0.925938	−	0.377674i	$-0.123276\pi$
$857$	24.9677	+	18.1401i	0.852879	+	0.619653i	−0.0730590	+	0.997328i	$0.523276\pi$
$858$	−4.71204	+	4.71204i	−0.160866	+	0.160866i
$859$	−27.1071	−	8.80762i	−0.924881	−	0.300512i	−0.192414	−	0.981314i	$-0.561632\pi$
$859$	−27.1071	−	8.80762i	−0.924881	−	0.300512i	−0.732468	+	0.680802i	$0.761632\pi$
$860$	−2.55181			−0.0870160
$861$	29.7139	+	2.52177i	1.01265	+	0.0859418i
$862$	−31.6533			−1.07812
$863$	−52.0783	−	16.9213i	−1.77276	−	0.576006i	−0.774374	−	0.632728i	$-0.781935\pi$
$863$	−52.0783	−	16.9213i	−1.77276	−	0.576006i	−0.998390	+	0.0567216i	$0.981935\pi$
$864$	−3.58782	+	3.58782i	−0.122060	+	0.122060i
$865$	6.41133	+	4.65810i	0.217992	+	0.158380i
$866$	15.3227	−	21.0899i	0.520688	−	0.716665i
$867$	8.38510	−	4.27242i	0.284773	−	0.145099i
$868$	9.03913	+	4.60567i	0.306808	+	0.156327i
$869$	3.08351	+	4.24408i	0.104601	+	0.143971i
$870$		−	2.16807i		−	0.0735044i
$871$	−7.00605	+	5.09019i	−0.237391	+	0.172475i
$872$	0.522483	−	3.29882i	0.0176935	−	0.111712i
$873$	31.2182	−	4.94447i	1.05657	−	0.167345i
$874$	−7.58467	−	14.8858i	−0.256555	−	0.503518i
$875$	28.6768	+	28.6768i	0.969454	+	0.969454i
$876$	0.752813	+	4.75308i	0.0254352	+	0.160592i
$877$	3.79878	+	11.6914i	0.128276	+	0.394792i	0.994484	−	0.104892i	$-0.0334496\pi$
$877$	3.79878	+	11.6914i	0.128276	+	0.394792i	−0.866208	+	0.499684i	$0.833450\pi$
$878$	1.93917	+	0.307134i	0.0654437	+	0.0103653i
$879$	4.71034	−	14.4969i	0.158876	−	0.488969i
$880$	1.26804	−	2.48867i	0.0427456	−	0.0838929i
$881$	−27.3418	+	8.88388i	−0.921168	+	0.299306i	−0.730946	−	0.682435i	$-0.760921\pi$
$881$	−27.3418	+	8.88388i	−0.921168	+	0.299306i	−0.190222	+	0.981741i	$0.560921\pi$
$882$	25.2667	−	8.20964i	0.850773	−	0.276433i
$883$	22.8545	−	44.8545i	0.769115	−	1.50947i	−0.0890094	−	0.996031i	$-0.528370\pi$
$883$	22.8545	−	44.8545i	0.769115	−	1.50947i	0.858124	−	0.513442i	$-0.171630\pi$
$884$	−5.12601	+	15.7762i	−0.172406	+	0.530612i
$885$	−2.48406	−	0.393436i	−0.0835007	−	0.0132252i
$886$	−6.77512	−	20.8517i	−0.227615	−	0.700526i
$887$	4.82487	+	30.4630i	0.162003	+	1.02285i	0.925971	+	0.377594i	$0.123248\pi$
$887$	4.82487	+	30.4630i	0.162003	+	1.02285i	−0.763968	+	0.645254i	$0.776752\pi$
$888$	−3.17324	−	3.17324i	−0.106487	−	0.106487i
$889$	6.97793	+	13.6950i	0.234032	+	0.459314i
$890$	−27.3642	+	4.33407i	−0.917251	+	0.145278i
$891$	−0.110394	+	0.697002i	−0.00369835	+	0.0233504i
$892$	4.30357	−	3.12673i	0.144094	−	0.104691i
$893$		−	82.0003i		−	2.74404i
$894$	−7.04297	−	9.69382i	−0.235552	−	0.324210i
$895$	38.5536	+	19.6440i	1.28870	+	0.656628i
$896$	4.04724	−	2.06217i	0.135209	−	0.0688923i
$897$	7.77776	−	10.7052i	0.259692	−	0.357435i
$898$	−24.6984	−	17.9444i	−0.824195	−	0.598813i
$899$	1.31012	−	1.31012i	0.0436949	−	0.0436949i
$900$	2.77510	+	0.901686i	0.0925034	+	0.0300562i
$901$	−10.4338			−0.347600
$902$	5.36308	−	4.52398i	0.178571	−	0.150632i
$903$	4.66238			0.155154
$904$	−8.76436	−	2.84771i	−0.291498	−	0.0947135i
$905$	−13.2947	+	13.2947i	−0.441931	+	0.441931i
$906$	3.68800	+	2.67949i	0.122526	+	0.0890202i
$907$	−18.1449	+	24.9743i	−0.602492	+	0.829259i	−0.995934	−	0.0900903i	$-0.971284\pi$
$907$	−18.1449	+	24.9743i	−0.602492	+	0.829259i	0.393441	+	0.919350i	$0.371284\pi$
$908$	0.544773	−	0.277576i	0.0180789	−	0.00921167i
$909$	−25.1995	−	12.8398i	−0.835814	−	0.425868i
$910$	40.3663	+	55.5595i	1.33813	+	1.84178i
$911$		−	10.8554i		−	0.359656i	−0.983698	−	0.179828i	$-0.942446\pi$
$911$		−	10.8554i		−	0.359656i	0.983698	−	0.179828i	$-0.0575541\pi$
$912$	6.36892	−	4.62729i	0.210896	−	0.153225i
$913$	−0.226922	+	1.43273i	−0.00751002	+	0.0474164i
$914$	−7.89603	+	1.25061i	−0.261177	+	0.0413665i
$915$	11.0319	+	21.6514i	0.364705	+	0.715774i
$916$	6.84964	+	6.84964i	0.226318	+	0.226318i
$917$	−11.9196	−	75.2574i	−0.393620	−	2.48522i
$918$	−4.38500	−	13.4956i	−0.144727	−	0.445423i
$919$	8.86840	+	1.40462i	0.292542	+	0.0463340i	0.300980	−	0.953630i	$-0.402686\pi$
$919$	8.86840	+	1.40462i	0.292542	+	0.0463340i	−0.00843871	+	0.999964i	$0.502686\pi$
$920$	−1.71388	+	5.27478i	−0.0565049	+	0.173904i
$921$	14.6409	−	28.7345i	0.482435	−	0.946832i
$922$	−29.9769	+	9.74009i	−0.987237	+	0.320773i
$923$	14.8056	−	4.81062i	0.487331	−	0.158343i
$924$	−2.31682	+	4.54702i	−0.0762178	+	0.149586i
$925$	−2.02518	+	6.23286i	−0.0665875	+	0.204935i
$926$	3.02643	+	0.479340i	0.0994548	+	0.0157521i
$927$	5.25517	+	16.1737i	0.172602	+	0.531215i
$928$	−0.129775	−	0.819364i	−0.00426006	−	0.0268970i
$929$	−5.07660	−	5.07660i	−0.166558	−	0.166558i	0.618907	−	0.785465i	$-0.287576\pi$
$929$	−5.07660	−	5.07660i	−0.166558	−	0.166558i	−0.785465	+	0.618907i	$0.787576\pi$
$930$	−2.64991	−	5.20074i	−0.0868939	−	0.170539i
$931$	−103.386	+	16.3747i	−3.38833	+	0.536658i
$932$	−1.96504	+	12.4067i	−0.0643669	+	0.406396i
$933$	−24.0480	+	17.4719i	−0.787296	+	0.572004i
$934$		−	26.3892i		−	0.863480i
$935$	4.59141	+	6.31953i	0.150155	+	0.206671i
$936$	−10.2991	−	5.24763i	−0.336635	−	0.171524i
$937$	35.2956	−	17.9840i	1.15306	−	0.587511i	0.230385	−	0.973100i	$-0.426001\pi$
$937$	35.2956	−	17.9840i	1.15306	−	0.587511i	0.922671	+	0.385588i	$0.126001\pi$
$938$	−3.89813	+	5.36531i	−0.127278	+	0.175184i
$939$	−6.50886	−	4.72897i	−0.212409	−	0.154324i
$940$	−19.2490	+	19.2490i	−0.627833	+	0.627833i
$941$	25.0280	+	8.13209i	0.815889	+	0.265098i	0.687090	−	0.726572i	$-0.258888\pi$
$941$	25.0280	+	8.13209i	0.815889	+	0.265098i	0.128799	+	0.991671i	$0.458888\pi$
$942$	16.6742			0.543275
$943$	−9.11303	+	10.5386i	−0.296761	+	0.343183i
$944$	−0.962334			−0.0313213
$945$	−55.8724	−	18.1540i	−1.81753	−	0.590551i
$946$	0.775685	−	0.775685i	0.0252197	−	0.0252197i
$947$	−26.1301	−	18.9846i	−0.849113	−	0.616917i	0.0757885	−	0.997124i	$-0.475853\pi$
$947$	−26.1301	−	18.9846i	−0.849113	−	0.616917i	−0.924901	+	0.380207i	$0.875853\pi$
$948$	2.88519	−	3.97113i	0.0937067	−	0.128976i
$949$	−24.8052	+	12.6389i	−0.805211	+	0.410276i
$950$	−10.2436	−	5.21937i	−0.332346	−	0.169339i
$951$	6.01942	+	8.28503i	0.195193	+	0.268660i
$952$			12.7034i			0.411718i
$953$	35.9498	−	26.1191i	1.16453	−	0.846079i	0.174185	−	0.984713i	$-0.444271\pi$
$953$	35.9498	−	26.1191i	1.16453	−	0.846079i	0.990344	+	0.138634i	$0.0442711\pi$
$954$	1.13735	−	7.18095i	0.0368231	−	0.232492i
$955$	−42.8951	+	6.79392i	−1.38805	+	0.219846i
$956$	6.24717	+	12.2608i	0.202048	+	0.396541i
$957$	0.659037	+	0.659037i	0.0213037	+	0.0213037i
$958$	6.24085	+	39.4032i	0.201633	+	1.27306i
$959$	28.8714	+	88.8572i	0.932307	+	2.86935i
$960$	−2.58128	−	0.408835i	−0.0833106	−	0.0131951i
$961$	−8.03812	+	24.7388i	−0.259294	+	0.798025i
$962$	11.7861	−	23.1316i	0.380001	−	0.745793i
$963$	−20.2762	+	6.58815i	−0.653393	+	0.212300i
$964$	7.72079	−	2.50864i	0.248670	−	0.0807978i
$965$	−15.0787	+	29.5935i	−0.485399	+	0.952650i
$966$	3.13141	−	9.63749i	0.100751	−	0.310081i
$967$	−20.2590	−	3.20872i	−0.651487	−	0.103185i	−0.178062	−	0.984019i	$-0.556983\pi$
$967$	−20.2590	−	3.20872i	−0.651487	−	0.103185i	−0.473425	+	0.880834i	$0.656983\pi$
$968$	−3.02815	−	9.31968i	−0.0973283	−	0.299546i
$969$	3.44415	+	21.7455i	0.110642	+	0.698565i
$970$	29.2334	+	29.2334i	0.938626	+	0.938626i
$971$	−22.2919	−	43.7503i	−0.715380	−	1.40401i	−0.906398	−	0.422426i	$-0.861179\pi$
$971$	−22.2919	−	43.7503i	−0.715380	−	1.40401i	0.191017	−	0.981587i	$-0.438821\pi$
$972$	15.6866	−	2.48452i	0.503148	−	0.0796909i
$973$	13.0269	−	82.2488i	0.417624	−	2.63678i
$974$	9.37277	−	6.80971i	0.300323	−	0.218197i
$975$		−	9.10578i		−	0.291618i
$976$	5.46523	+	7.52224i	0.174938	+	0.240781i
$977$	−29.0108	−	14.7817i	−0.928137	−	0.472909i	−0.0765164	−	0.997068i	$-0.524380\pi$
$977$	−29.0108	−	14.7817i	−0.928137	−	0.472909i	−0.851620	+	0.524159i	$0.824380\pi$
$978$	10.8084	−	5.50714i	0.345614	−	0.176099i
$979$	7.00058	−	9.63547i	0.223739	−	0.307951i
$980$	28.1129	+	20.4252i	0.898033	+	0.652459i
$981$	−4.60241	+	4.60241i	−0.146943	+	0.146943i
$982$	10.2649	+	3.33526i	0.327565	+	0.106432i
$983$	−25.5895			−0.816180			−0.408090	−	0.912942i	$-0.633805\pi$
$983$	−25.5895			−0.816180			−0.408090	+	0.912942i	$0.633805\pi$
$984$	−5.57654	−	3.46448i	−0.177774	−	0.110443i
$985$	−25.8090			−0.822345
$986$	2.20650	+	0.716936i	0.0702694	+	0.0228319i
$987$	35.1697	−	35.1697i	1.11946	−	1.11946i
$988$	36.8445	+	26.7691i	1.17218	+	0.851639i
$989$	−1.28036	+	1.76226i	−0.0407130	+	0.0560366i
$990$	−4.84984	+	2.47112i	−0.154138	+	0.0785372i
$991$	10.0425	+	5.11692i	0.319011	+	0.162544i	0.606162	−	0.795341i	$-0.292708\pi$
$991$	10.0425	+	5.11692i	0.319011	+	0.162544i	−0.287151	+	0.957885i	$0.592708\pi$
$992$	−1.31276	−	1.80687i	−0.0416803	−	0.0573680i
$993$		−	0.838074i		−	0.0265955i
$994$	9.64490	−	7.00743i	0.305918	−	0.222262i
$995$	3.51490	−	22.1922i	0.111430	−	0.703540i
$996$	1.34058	−	0.212327i	0.0424780	−	0.00672785i
$997$	17.1364	+	33.6322i	0.542717	+	1.06514i	0.985684	+	0.168604i	$0.0539258\pi$
$997$	17.1364	+	33.6322i	0.542717	+	1.06514i	−0.442967	+	0.896538i	$0.646074\pi$
$998$	17.0134	+	17.0134i	0.538551	+	0.538551i
$999$	3.47414	+	21.9349i	0.109917	+	0.693989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.2.g.b.61.1	yes	16
3.2	odd	2		738.2.u.b.307.1		16
4.3	odd	2		656.2.bs.b.225.2		16
41.11	odd	40		3362.2.a.bd.1.6		16
41.30	odd	40		3362.2.a.bd.1.11		16
41.39	even	20	inner	82.2.g.b.39.1	✓	16
123.80	odd	20		738.2.u.b.613.1		16
164.39	odd	20		656.2.bs.b.449.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.g.b.39.1	✓	16	41.39	even	20	inner
82.2.g.b.61.1	yes	16	1.1	even	1	trivial
656.2.bs.b.225.2		16	4.3	odd	2
656.2.bs.b.449.2		16	164.39	odd	20
738.2.u.b.307.1		16	3.2	odd	2
738.2.u.b.613.1		16	123.80	odd	20
3362.2.a.bd.1.6		16	41.11	odd	40
3362.2.a.bd.1.11		16	41.30	odd	40

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.724993 + 0.724993i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.49825 - 2.06217i) q^{5} +(0.913545 - 0.465474i) q^{6} +(4.04724 + 2.06217i) q^{7} +(-0.587785 - 0.809017i) q^{8} +1.94877i q^{9} +(-2.06217 + 1.49825i) q^{10} +(0.171416 - 1.08228i) q^{11} +(-1.01267 + 0.160391i) q^{12} +(-2.69279 - 5.28490i) q^{13} +(-3.21191 - 3.21191i) q^{14} +(0.408835 + 2.58128i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.76224 - 0.437495i) q^{17} +(0.602203 - 1.85339i) q^{18} +(-3.48583 + 6.84132i) q^{19} +(2.42423 - 0.787679i) q^{20} +(-4.42928 + 1.43916i) q^{21} +(-0.497469 + 0.976337i) q^{22} +(0.672378 - 2.06937i) q^{23} +(1.01267 + 0.160391i) q^{24} +(-0.462695 - 1.42403i) q^{25} +(0.927873 + 5.85836i) q^{26} +(-3.58782 - 3.58782i) q^{27} +(2.06217 + 4.04724i) q^{28} +(0.819364 - 0.129775i) q^{29} +(0.408835 - 2.58128i) q^{30} +(1.80687 - 1.31276i) q^{31} -1.00000i q^{32} +(0.660369 + 0.908920i) q^{33} +(2.49185 + 1.26966i) q^{34} +(10.3163 - 5.25644i) q^{35} +(-1.14546 + 1.57659i) q^{36} +(-3.54101 - 2.57269i) q^{37} +(5.42930 - 5.42930i) q^{38} +(5.78377 + 1.87926i) q^{39} -2.54898 q^{40} +(-5.90059 - 2.48656i) q^{41} +4.65722 q^{42} +(-0.952111 - 0.309360i) q^{43} +(0.774826 - 0.774826i) q^{44} +(4.01870 + 2.91975i) q^{45} +(-1.27894 + 1.76031i) q^{46} +(-9.51562 + 4.84845i) q^{47} +(-0.913545 - 0.465474i) q^{48} +(8.01308 + 11.0291i) q^{49} +1.49731i q^{50} +(2.31978 - 1.68542i) q^{51} +(0.927873 - 5.85836i) q^{52} +(3.68486 - 0.583625i) q^{53} +(2.30352 + 4.52092i) q^{54} +(-1.97502 - 1.97502i) q^{55} +(-0.710575 - 4.48640i) q^{56} +(-2.43271 - 7.48711i) q^{57} +(-0.819364 - 0.129775i) q^{58} +(-0.297378 + 0.915234i) q^{59} +(-1.18649 + 2.32861i) q^{60} +(8.84292 - 2.87324i) q^{61} +(-2.12410 + 0.690161i) q^{62} +(-4.01870 + 7.88713i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-14.9329 - 2.36513i) q^{65} +(-0.347176 - 1.06850i) q^{66} +(-0.228398 - 1.44205i) q^{67} +(-1.97754 - 1.97754i) q^{68} +(1.01281 + 1.98775i) q^{69} +(-11.4357 + 1.81124i) q^{70} +(-0.410577 + 2.59228i) q^{71} +(1.57659 - 1.14546i) q^{72} -4.69360i q^{73} +(2.57269 + 3.54101i) q^{74} +(1.36786 + 0.696960i) q^{75} +(-6.84132 + 3.48583i) q^{76} +(2.92560 - 4.02675i) q^{77} +(-4.91997 - 3.57457i) q^{78} +(-3.38526 + 3.38526i) q^{79} +(2.42423 + 0.787679i) q^{80} -0.644013 q^{81} +(4.84341 + 4.18824i) q^{82} -1.32381 q^{83} +(-4.42928 - 1.43916i) q^{84} +(-5.04072 + 5.04072i) q^{85} +(0.809914 + 0.588437i) q^{86} +(-0.499948 + 0.688119i) q^{87} +(-0.976337 + 0.497469i) q^{88} +(9.68450 + 4.93450i) q^{89} +(-2.91975 - 4.01870i) q^{90} -26.9422i q^{91} +(1.76031 - 1.27894i) q^{92} +(-0.358220 + 2.26171i) q^{93} +(10.5482 - 1.67066i) q^{94} +(8.88531 + 17.4384i) q^{95} +(0.724993 + 0.724993i) q^{96} +(-2.53723 - 16.0194i) q^{97} +(-4.21273 - 12.9654i) q^{98} +(2.10911 + 0.334050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 4 q^{4} - 6 q^{6} + 12 q^{11} + 4 q^{12} - 18 q^{13} - 10 q^{14} - 18 q^{15} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 16 q^{19} + 10 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 4 q^{25} - 2 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 + 4 * q^4 - 6 * q^6 + 12 * q^11 + 4 * q^12 - 18 * q^13 - 10 * q^14 - 18 * q^15 - 4 * q^16 - 4 * q^17 + 4 * q^18 - 16 * q^19 + 10 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 - 10 * q^29 - 18 * q^30 + 40 * q^31 - 60 * q^33 + 26 * q^34 + 44 * q^35 + 10 * q^36 - 16 * q^37 + 14 * q^38 + 80 * q^39 - 4 * q^41 + 16 * q^42 - 40 * q^43 - 2 * q^44 + 58 * q^45 + 10 * q^46 + 6 * q^48 + 20 * q^49 - 6 * q^51 - 2 * q^52 + 46 * q^53 + 18 * q^54 - 18 * q^55 - 60 * q^57 + 10 * q^58 - 2 * q^59 - 42 * q^60 - 60 * q^61 - 58 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 + 50 * q^67 - 16 * q^68 + 48 * q^69 - 26 * q^70 - 38 * q^71 - 4 * q^72 - 10 * q^74 + 6 * q^75 - 4 * q^76 - 38 * q^78 - 20 * q^79 + 10 * q^80 + 40 * q^81 + 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^86 - 70 * q^87 - 18 * q^88 + 36 * q^89 - 6 * q^92 - 12 * q^93 + 20 * q^94 - 72 * q^95 + 4 * q^96 - 10 * q^97 - 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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