LMFDB - Embedded newform 105.2.q.a.79.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,2,Mod(4,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.27814731656356152999936.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$-0.556918 - 2.07845i$ of defining polynomial
Character	$\chi$	$=$	105.79
Dual form			105.2.q.a.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.248840 - 0.143668i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.958719 - 1.66055i) q^{4} +(1.47507 - 1.68052i) q^{5} +0.287336 q^{6} +(1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.608495 + 0.206261i) q^{10} +(1.66520 + 2.88421i) q^{11} +(1.66055 + 0.958719i) q^{12} -4.54754i q^{13} +(-0.622139 + 0.436894i) q^{14} +(-0.437190 + 2.19291i) q^{15} +(-1.75572 + 3.04100i) q^{16} +(-4.80431 + 2.77377i) q^{17} +(-0.248840 + 0.143668i) q^{18} +(-0.828617 + 1.43521i) q^{19} +(-4.20477 - 0.838284i) q^{20} +(0.234193 + 2.63537i) q^{21} -0.956942i q^{22} +(6.61094 + 3.81683i) q^{23} +(-0.562810 - 0.974816i) q^{24} +(-0.648315 - 4.95779i) q^{25} +(-0.653336 + 1.13161i) q^{26} +1.00000i q^{27} +(-5.05315 + 0.449051i) q^{28} +0.118657 q^{29} +(0.423842 - 0.482874i) q^{30} +(3.13010 + 5.42150i) q^{31} +(2.82342 - 1.63010i) q^{32} +(-2.88421 - 1.66520i) q^{33} +1.59401 q^{34} +(-2.38772 - 5.41284i) q^{35} -1.91744 q^{36} +(6.71665 + 3.87786i) q^{37} +(0.412386 - 0.238091i) q^{38} +(2.27377 + 3.93829i) q^{39} +(1.89163 + 1.66037i) q^{40} +0.0701896 q^{41} +(0.320341 - 0.689431i) q^{42} +2.92981i q^{43} +(3.19291 - 5.53029i) q^{44} +(-0.717839 - 2.11771i) q^{45} +(-1.09671 - 1.89956i) q^{46} +(-5.53029 - 3.19291i) q^{47} -3.51145i q^{48} +(-4.51415 - 5.35000i) q^{49} +(-0.550949 + 1.32684i) q^{50} +(2.77377 - 4.80431i) q^{51} +(-7.55142 + 4.35981i) q^{52} +(0.640682 - 0.369898i) q^{53} +(0.143668 - 0.248840i) q^{54} +(7.30326 + 1.45601i) q^{55} +(2.70080 + 1.25492i) q^{56} -1.65723i q^{57} +(-0.0295266 - 0.0170472i) q^{58} +(-0.815051 - 1.41171i) q^{59} +(4.06058 - 1.37641i) q^{60} +(3.65901 - 6.33759i) q^{61} -1.79878i q^{62} +(-1.52050 - 2.16520i) q^{63} +6.08612 q^{64} +(-7.64225 - 6.70796i) q^{65} +(0.478471 + 0.828736i) q^{66} +(-2.62934 + 1.51805i) q^{67} +(9.21197 + 5.31853i) q^{68} -7.63366 q^{69} +(-0.183490 + 1.68997i) q^{70} -3.77048 q^{71} +(0.974816 + 0.562810i) q^{72} +(2.03961 - 1.17757i) q^{73} +(-1.11425 - 1.92993i) q^{74} +(3.04035 + 3.96942i) q^{75} +3.17764 q^{76} +(8.77681 - 0.779956i) q^{77} -1.30667i q^{78} +(-5.97016 + 10.3406i) q^{79} +(2.52065 + 7.43623i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0174660 - 0.0100840i) q^{82} +1.22411i q^{83} +(4.15163 - 2.91547i) q^{84} +(-2.42533 + 12.1653i) q^{85} +(0.420920 - 0.729054i) q^{86} +(-0.102760 + 0.0593285i) q^{87} +(-3.24652 + 1.87438i) q^{88} +(-6.50007 + 11.2585i) q^{89} +(-0.125620 + 0.630102i) q^{90} +(-10.9113 - 5.06990i) q^{91} -14.6371i q^{92} +(-5.42150 - 3.13010i) q^{93} +(0.917438 + 1.58905i) q^{94} +(1.18963 + 3.50954i) q^{95} +(-1.63010 + 2.82342i) q^{96} +3.04306i q^{97} +(0.354679 + 1.97983i) q^{98} +3.33039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35}+ \cdots + 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9 - 4 * q^10 - 24 * q^14 - 4 * q^15 - 24 * q^19 - 8 * q^20 - 4 * q^21 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 24 * q^29 - 12 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 + 16 * q^36 - 4 * q^39 + 32 * q^40 + 16 * q^41 + 20 * q^44 - 2 * q^45 - 32 * q^46 - 40 * q^49 - 40 * q^50 + 4 * q^51 - 4 * q^54 + 8 * q^55 + 84 * q^56 + 4 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^64 + 30 * q^65 + 28 * q^66 + 40 * q^69 + 16 * q^70 - 56 * q^71 + 40 * q^74 + 8 * q^75 - 64 * q^76 - 16 * q^79 + 52 * q^80 - 8 * q^81 + 12 * q^84 - 64 * q^85 - 48 * q^86 + 16 * q^89 - 8 * q^90 + 8 * q^91 - 32 * q^94 - 22 * q^95 + 8 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.248840	−	0.143668i	−0.175957	−	0.101589i	0.409435	−	0.912339i	$-0.365726\pi$
$2$	−0.248840	−	0.143668i	−0.175957	−	0.101589i	−0.585392	+	0.810751i	$0.699059\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.958719	−	1.66055i	−0.479360	−	0.830275i
$5$	1.47507	−	1.68052i	0.659673	−	0.751553i
$5$	1.47507	−	1.68052i	0.659673	−	0.751553i
$6$	0.287336			0.117304
$7$	1.11487	−	2.39939i	0.421380	−	0.906884i
$7$	1.11487	−	2.39939i	0.421380	−	0.906884i
$8$			1.12562i			0.397967i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.608495	+	0.206261i	−0.192423	+	0.0652254i
$11$	1.66520	+	2.88421i	0.502076	+	0.869621i	0.999997	+	0.00239862i	$0.000763504\pi$
$11$	1.66520	+	2.88421i	0.502076	+	0.869621i	−0.497921	+	0.867222i	$0.665903\pi$
$12$	1.66055	+	0.958719i	0.479360	+	0.276758i
$13$		−	4.54754i		−	1.26126i	−0.776083	−	0.630630i	$-0.782796\pi$
$13$		−	4.54754i		−	1.26126i	0.776083	−	0.630630i	$-0.217204\pi$
$14$	−0.622139	+	0.436894i	−0.166274	+	0.116765i
$15$	−0.437190	+	2.19291i	−0.112882	+	0.566208i
$16$	−1.75572	+	3.04100i	−0.438931	+	0.760250i
$17$	−4.80431	+	2.77377i	−1.16522	+	0.672738i	−0.952549	−	0.304386i	$-0.901549\pi$
$17$	−4.80431	+	2.77377i	−1.16522	+	0.672738i	−0.212668	+	0.977125i	$0.568215\pi$
$18$	−0.248840	+	0.143668i	−0.0586522	+	0.0338629i
$19$	−0.828617	+	1.43521i	−0.190098	+	0.329259i	−0.945282	−	0.326253i	$-0.894214\pi$
$19$	−0.828617	+	1.43521i	−0.190098	+	0.329259i	0.755185	+	0.655512i	$0.227547\pi$
$20$	−4.20477	−	0.838284i	−0.940216	−	0.187446i
$21$	0.234193	+	2.63537i	0.0511052	+	0.575084i
$22$		−	0.956942i		−	0.204021i
$23$	6.61094	+	3.81683i	1.37848	+	0.795864i	0.991976	−	0.126425i	$-0.0403505\pi$
$23$	6.61094	+	3.81683i	1.37848	+	0.795864i	0.386500	+	0.922289i	$0.373684\pi$
$24$	−0.562810	−	0.974816i	−0.114883	−	0.198983i
$25$	−0.648315	−	4.95779i	−0.129663	−	0.991558i
$26$	−0.653336	+	1.13161i	−0.128130	+	0.221927i
$27$			1.00000i			0.192450i
$28$	−5.05315	+	0.449051i	−0.954956	+	0.0848627i
$29$	0.118657			0.0220341			0.0110170	−	0.999939i	$-0.496493\pi$
$29$	0.118657			0.0220341			0.0110170	+	0.999939i	$0.496493\pi$
$30$	0.423842	−	0.482874i	0.0773825	−	0.0881604i
$31$	3.13010	+	5.42150i	0.562183	+	0.973729i	0.997306	+	0.0733583i	$0.0233717\pi$
$31$	3.13010	+	5.42150i	0.562183	+	0.973729i	−0.435123	+	0.900371i	$0.643295\pi$
$32$	2.82342	−	1.63010i	0.499115	−	0.288164i
$33$	−2.88421	−	1.66520i	−0.502076	−	0.289874i
$34$	1.59401			0.273370
$35$	−2.38772	−	5.41284i	−0.403599	−	0.914936i
$36$	−1.91744			−0.319573
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.937324	−	0.348460i	$-0.113295\pi$
$37$	6.71665	+	3.87786i	1.10421	+	0.637516i	0.166887	+	0.985976i	$0.446628\pi$
$38$	0.412386	−	0.238091i	0.0668979	−	0.0386235i
$39$	2.27377	+	3.93829i	0.364095	+	0.630630i
$40$	1.89163	+	1.66037i	0.299093	+	0.262528i
$41$	0.0701896			0.0109618			0.00548089	−	0.999985i	$-0.498255\pi$
$41$	0.0701896			0.0109618			0.00548089	+	0.999985i	$0.498255\pi$
$42$	0.320341	−	0.689431i	0.0494297	−	0.106381i
$43$			2.92981i			0.446792i	0.974728	+	0.223396i	$0.0717143\pi$
$43$			2.92981i			0.446792i	−0.974728	+	0.223396i	$0.928286\pi$
$44$	3.19291	−	5.53029i	0.481350	−	0.833722i
$45$	−0.717839	−	2.11771i	−0.107009	−	0.315690i
$46$	−1.09671	−	1.89956i	−0.161701	−	0.280075i
$47$	−5.53029	−	3.19291i	−0.806675	−	0.465734i	0.0391247	−	0.999234i	$-0.487543\pi$
$47$	−5.53029	−	3.19291i	−0.806675	−	0.465734i	−0.845800	+	0.533500i	$0.820876\pi$
$48$		−	3.51145i		−	0.506833i
$49$	−4.51415	−	5.35000i	−0.644879	−	0.764285i
$50$	−0.550949	+	1.32684i	−0.0779159	+	0.187643i
$51$	2.77377	−	4.80431i	0.388406	−	0.672738i
$52$	−7.55142	+	4.35981i	−1.04719	+	0.604597i
$53$	0.640682	−	0.369898i	0.0880044	−	0.0508094i	−0.455352	−	0.890311i	$-0.650487\pi$
$53$	0.640682	−	0.369898i	0.0880044	−	0.0508094i	0.543356	+	0.839502i	$0.317153\pi$
$54$	0.143668	−	0.248840i	0.0195507	−	0.0338629i
$55$	7.30326	+	1.45601i	0.984772	+	0.196329i
$56$	2.70080	+	1.25492i	0.360910	+	0.167695i
$57$		−	1.65723i		−	0.219506i
$58$	−0.0295266	−	0.0170472i	−0.00387704	−	0.00223841i
$59$	−0.815051	−	1.41171i	−0.106111	−	0.183789i	0.808081	−	0.589072i	$-0.200506\pi$
$59$	−0.815051	−	1.41171i	−0.106111	−	0.183789i	−0.914191	+	0.405283i	$0.867173\pi$
$60$	4.06058	−	1.37641i	0.524219	−	0.177694i
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	−0.530863	−	0.847458i	$-0.678132\pi$
$61$	3.65901	−	6.33759i	0.468488	−	0.811446i	0.999351	+	0.0360120i	$0.0114655\pi$
$62$		−	1.79878i		−	0.228445i
$63$	−1.52050	−	2.16520i	−0.191565	−	0.272789i
$64$	6.08612			0.760765
$65$	−7.64225	−	6.70796i	−0.947904	−	0.832020i
$66$	0.478471	+	0.828736i	0.0588957	+	0.102010i
$67$	−2.62934	+	1.51805i	−0.321224	+	0.185459i	−0.651938	−	0.758272i	$-0.726044\pi$
$67$	−2.62934	+	1.51805i	−0.321224	+	0.185459i	0.330714	+	0.943731i	$0.392711\pi$
$68$	9.21197	+	5.31853i	1.11712	+	0.644967i
$69$	−7.63366			−0.918984
$70$	−0.183490	+	1.68997i	−0.0219312	+	0.201990i
$71$	−3.77048			−0.447474			−0.223737	−	0.974650i	$-0.571826\pi$
$71$	−3.77048			−0.447474			−0.223737	+	0.974650i	$0.571826\pi$
$72$	0.974816	+	0.562810i	0.114883	+	0.0663278i
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	−0.375869	−	0.926673i	$-0.622656\pi$
$73$	2.03961	−	1.17757i	0.238718	−	0.137824i	0.614588	+	0.788849i	$0.289322\pi$
$74$	−1.11425	−	1.92993i	−0.129529	−	0.224350i
$75$	3.04035	+	3.96942i	0.351070	+	0.458349i
$76$	3.17764			0.364501
$77$	8.77681	−	0.779956i	1.00021	−	0.0888843i
$78$		−	1.30667i		−	0.147951i
$79$	−5.97016	+	10.3406i	−0.671696	+	1.16341i	0.305727	+	0.952119i	$0.401101\pi$
$79$	−5.97016	+	10.3406i	−0.671696	+	1.16341i	−0.977423	+	0.211292i	$0.932233\pi$
$80$	2.52065	+	7.43623i	0.281817	+	0.831396i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.0174660	−	0.0100840i	−0.00192880	−	0.00111359i
$83$			1.22411i			0.134363i	0.997741	+	0.0671817i	$0.0214007\pi$
$83$			1.22411i			0.134363i	−0.997741	+	0.0671817i	$0.978599\pi$
$84$	4.15163	−	2.91547i	0.452980	−	0.318103i
$85$	−2.42533	+	12.1653i	−0.263064	+	1.31951i
$86$	0.420920	−	0.729054i	0.0453889	−	0.0786160i
$87$	−0.102760	+	0.0593285i	−0.0110170	+	0.00636069i
$88$	−3.24652	+	1.87438i	−0.346080	+	0.199810i
$89$	−6.50007	+	11.2585i	−0.689006	+	1.19339i	0.283153	+	0.959075i	$0.408619\pi$
$89$	−6.50007	+	11.2585i	−0.689006	+	1.19339i	−0.972160	+	0.234319i	$0.924714\pi$
$90$	−0.125620	+	0.630102i	−0.0132415	+	0.0664186i
$91$	−10.9113	−	5.06990i	−1.14382	−	0.531470i
$92$		−	14.6371i		−	1.52602i
$93$	−5.42150	−	3.13010i	−0.562183	−	0.324576i
$94$	0.917438	+	1.58905i	0.0946265	+	0.163898i
$95$	1.18963	+	3.50954i	0.122053	+	0.360072i
$96$	−1.63010	+	2.82342i	−0.166372	+	0.288164i
$97$			3.04306i			0.308976i	0.987995	+	0.154488i	$0.0493728\pi$
$97$			3.04306i			0.308976i	−0.987995	+	0.154488i	$0.950627\pi$
$98$	0.354679	+	1.97983i	0.0358280	+	0.199993i
$99$	3.33039			0.334717
$100$	−7.61111	+	5.82969i	−0.761111	+	0.582969i
$101$	−8.01983	−	13.8907i	−0.798002	−	1.38218i	−0.920915	−	0.389763i	$-0.872557\pi$
$101$	−8.01983	−	13.8907i	−0.798002	−	1.38218i	0.122913	−	0.992417i	$-0.460776\pi$
$102$	−1.38045	+	0.797004i	−0.136685	+	0.0789151i
$103$	−4.58293	−	2.64596i	−0.451570	−	0.260714i	0.256923	−	0.966432i	$-0.417291\pi$
$103$	−4.58293	−	2.64596i	−0.451570	−	0.260714i	−0.708493	+	0.705718i	$0.750625\pi$
$104$	5.11880			0.501940
$105$	4.77425	+	3.49379i	0.465919	+	0.340959i
$106$	−0.212570			−0.0206466
$107$	4.47018	+	2.58086i	0.432148	+	0.249501i	0.700261	−	0.713886i	$-0.253067\pi$
$107$	4.47018	+	2.58086i	0.432148	+	0.249501i	−0.268113	+	0.963387i	$0.586400\pi$
$108$	1.66055	−	0.958719i	0.159787	−	0.0922528i
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	0.933135	−	0.359525i	$-0.117061\pi$
$109$	1.62043	+	2.80668i	0.155209	+	0.268831i	−0.777926	+	0.628356i	$0.783728\pi$
$110$	−1.60816	−	1.41156i	−0.153332	−	0.134587i
$111$	−7.75572			−0.736141
$112$	5.33915	+	7.60297i	0.504503	+	0.718413i
$113$			12.6608i			1.19103i	0.803345	+	0.595513i	$0.203051\pi$
$113$			12.6608i			1.19103i	−0.803345	+	0.595513i	$0.796949\pi$
$114$	−0.238091	+	0.412386i	−0.0222993	+	0.0386235i
$115$	16.1659	−	5.47973i	1.50748	−	0.510988i
$116$	−0.113759	−	0.197036i	−0.0105622	−	0.0182943i
$117$	−3.93829	−	2.27377i	−0.364095	−	0.210210i
$118$			0.468387i			0.0431185i
$119$	1.29920	+	14.6198i	0.119097	+	1.34019i
$120$	−2.46839	−	0.492110i	−0.225332	−	0.0449233i
$121$	−0.0457629	+	0.0792637i	−0.00416027	+	0.00720579i
$122$	−1.82102	+	1.05136i	−0.164867	+	0.0951861i
$123$	−0.0607860	+	0.0350948i	−0.00548089	+	0.00316439i
$124$	6.00178	−	10.3954i	0.538976	−	0.933533i
$125$	−9.28799	−	6.22360i	−0.830743	−	0.556656i
$126$	0.0672922	+	0.757235i	0.00599486	+	0.0674599i
$127$		−	16.5475i		−	1.46836i	−0.678957	−	0.734178i	$-0.737568\pi$
$127$		−	16.5475i		−	1.46836i	0.678957	−	0.734178i	$-0.262432\pi$
$128$	−7.16131	−	4.13458i	−0.632976	−	0.365449i
$129$	−1.46491	−	2.53729i	−0.128978	−	0.223396i
$130$	0.937979	+	2.76715i	0.0822662	+	0.242696i
$131$	2.64893	−	4.58808i	0.231438	−	0.400862i	−0.726794	−	0.686856i	$-0.758990\pi$
$131$	2.64893	−	4.58808i	0.231438	−	0.400862i	0.958231	+	0.285994i	$0.0923237\pi$
$132$			6.38582i			0.555815i
$133$	2.51982	+	3.58824i	0.218496	+	0.311140i
$134$	0.872379			0.0753621
$135$	1.68052	+	1.47507i	0.144636	+	0.126954i
$136$	−3.12221	−	5.40783i	−0.267727	−	0.463718i
$137$	−12.8779	+	7.43507i	−1.10023	+	0.635221i	−0.936283	−	0.351247i	$-0.885758\pi$
$137$	−12.8779	+	7.43507i	−1.10023	+	0.635221i	−0.163952	+	0.986468i	$0.552424\pi$
$138$	1.89956	+	1.09671i	0.161701	+	0.0933583i
$139$	9.51685			0.807209			0.403605	−	0.914934i	$-0.367757\pi$
$139$	9.51685			0.807209			0.403605	+	0.914934i	$0.367757\pi$
$140$	−6.69913	+	9.15432i	−0.566180	+	0.773681i
$141$	6.38582			0.537783
$142$	0.938247	+	0.541697i	0.0787359	+	0.0454582i
$143$	13.1160	−	7.57255i	1.09682	−	0.633249i
$144$	1.75572	+	3.04100i	0.146310	+	0.253417i
$145$	0.175028	−	0.199406i	0.0145353	−	0.0165598i
$146$	−0.676716			−0.0560054
$147$	6.58437	+	2.37616i	0.543069	+	0.195982i
$148$		−	14.8711i		−	1.22240i
$149$	5.68502	−	9.84675i	0.465735	−	0.806677i	−0.533499	−	0.845801i	$-0.679123\pi$
$149$	5.68502	−	9.84675i	0.465735	−	0.806677i	0.999234	+	0.0391236i	$0.0124566\pi$
$150$	−0.186284	−	1.42455i	−0.0152100	−	0.116314i
$151$	−4.47016	−	7.74255i	−0.363777	−	0.630080i	0.624802	−	0.780783i	$-0.285180\pi$
$151$	−4.47016	−	7.74255i	−0.363777	−	0.630080i	−0.988579	+	0.150703i	$0.951846\pi$
$152$	−1.61550	−	0.932708i	−0.131034	−	0.0756526i
$153$			5.54754i			0.448492i
$154$	−2.29608	−	1.06686i	−0.185023	−	0.0859701i
$155$	13.7281	+	2.73690i	1.10267	+	0.219833i
$156$	4.35981	−	7.55142i	0.349064	−	0.604597i
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	−0.379879	−	0.925036i	$-0.624035\pi$
$157$	2.89800	−	1.67316i	0.231286	−	0.133533i	0.611165	+	0.791503i	$0.290701\pi$
$158$	2.97123	−	1.71544i	0.236379	−	0.136473i
$159$	−0.369898	+	0.640682i	−0.0293348	+	0.0508094i
$160$	1.42533	−	7.14934i	0.112682	−	0.565205i
$161$	16.5284	−	11.6070i	1.30262	−	0.914758i
$162$			0.287336i			0.0225752i
$163$	−13.6450	−	7.87793i	−1.06876	−	0.617047i	−0.140916	−	0.990022i	$-0.545005\pi$
$163$	−13.6450	−	7.87793i	−1.06876	−	0.617047i	−0.927842	+	0.372974i	$0.878338\pi$
$164$	−0.0672922	−	0.116553i	−0.00525463	−	0.00910129i
$165$	−7.05282	+	2.39069i	−0.549061	+	0.186115i
$166$	0.175865	−	0.304608i	0.0136498	−	0.0236421i
$167$			22.5942i			1.74839i	0.485577	+	0.874194i	$0.338610\pi$
$167$			22.5942i			1.74839i	−0.485577	+	0.874194i	$0.661390\pi$
$168$	−2.96642	+	0.263613i	−0.228864	+	0.0203382i
$169$	−7.68012			−0.590779
$170$	2.35128	−	2.67877i	0.180335	−	0.205452i
$171$	0.828617	+	1.43521i	0.0633659	+	0.109753i
$172$	4.86510	−	2.80887i	0.370960	−	0.214174i
$173$	−7.38391	−	4.26310i	−0.561388	−	0.324118i	0.192314	−	0.981333i	$-0.438401\pi$
$173$	−7.38391	−	4.26310i	−0.561388	−	0.324118i	−0.753703	+	0.657216i	$0.771734\pi$
$174$	0.0340944			0.00258469
$175$	−12.6185	−	3.97171i	−0.953866	−	0.300233i
$176$	−11.6945			−0.881506
$177$	1.41171	+	0.815051i	0.106111	+	0.0612630i
$178$	3.23496	−	1.86770i	0.242470	−	0.139990i
$179$	−5.89031	−	10.2023i	−0.440262	−	0.762557i	0.557446	−	0.830213i	$-0.311781\pi$
$179$	−5.89031	−	10.2023i	−0.440262	−	0.762557i	−0.997709	+	0.0676564i	$0.978448\pi$
$180$	−2.82836	+	3.22230i	−0.210814	+	0.240176i
$181$	9.08967			0.675630			0.337815	−	0.941213i	$-0.390312\pi$
$181$	9.08967			0.675630			0.337815	+	0.941213i	$0.390312\pi$
$182$	1.98679	+	2.82920i	0.147271	+	0.209714i
$183$			7.31802i			0.540964i
$184$	−4.29630	+	7.44141i	−0.316727	+	0.548588i
$185$	16.4244	−	5.56736i	1.20755	−	0.409320i
$186$	0.899391	+	1.55779i	0.0659465	+	0.114223i
$187$	−16.0002	−	9.23775i	−1.17005	−	0.675531i
$188$			12.2444i			0.893016i
$189$	2.39939	+	1.11487i	0.174530	+	0.0810945i
$190$	0.208182	−	1.04423i	0.0151031	−	0.0757562i
$191$	−10.2478	+	17.7498i	−0.741507	+	1.28433i	0.210302	+	0.977637i	$0.432555\pi$
$191$	−10.2478	+	17.7498i	−0.741507	+	1.28433i	−0.951809	+	0.306692i	$0.900778\pi$
$192$	−5.27073	+	3.04306i	−0.380382	+	0.219614i
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	−0.209504	−	0.977808i	$-0.567185\pi$
$193$	7.39842	−	4.27148i	0.532550	−	0.307468i	0.742054	+	0.670340i	$0.233852\pi$
$194$	0.437190	−	0.757235i	0.0313884	−	0.0543663i
$195$	9.97236	+	1.98814i	0.714135	+	0.142374i
$196$	−4.55613	+	12.6251i	−0.325438	+	0.901794i
$197$		−	13.8086i		−	0.983820i	−0.870646	−	0.491910i	$-0.836299\pi$
$197$		−	13.8086i		−	0.983820i	0.870646	−	0.491910i	$-0.163701\pi$
$198$	−0.828736	−	0.478471i	−0.0588957	−	0.0340034i
$199$	1.89549	+	3.28309i	0.134368	+	0.232732i	0.925356	−	0.379100i	$-0.123766\pi$
$199$	1.89549	+	3.28309i	0.134368	+	0.232732i	−0.790988	+	0.611832i	$0.790433\pi$
$200$	5.58059	−	0.729756i	0.394607	−	0.0516016i
$201$	1.51805	−	2.62934i	0.107075	−	0.185459i
$202$			4.60877i			0.324272i
$203$	0.132287	−	0.284705i	0.00928471	−	0.0199824i
$204$	−10.6371			−0.744744
$205$	0.103535	−	0.117955i	0.00723119	−	0.00823836i
$206$	0.760278	+	1.31684i	0.0529711	+	0.0917486i
$207$	6.61094	−	3.81683i	0.459492	−	0.265288i
$208$	13.8291	+	7.98422i	0.958874	+	0.553606i
$209$	−5.51924			−0.381774
$210$	−0.686078	−	1.55530i	−0.0473439	−	0.107326i
$211$	−0.114416			−0.00787674			−0.00393837	−	0.999992i	$-0.501254\pi$
$211$	−0.114416			−0.00787674			−0.00393837	+	0.999992i	$0.501254\pi$
$212$	−1.22847	−	0.709256i	−0.0843715	−	0.0487119i
$213$	3.26533	−	1.88524i	0.223737	−	0.129175i
$214$	−0.741573	−	1.28444i	−0.0506929	−	0.0878026i
$215$	4.92361	+	4.32169i	0.335788	+	0.294737i
$216$	−1.12562			−0.0765888
$217$	16.4979	−	1.46610i	1.11995	−	0.0995253i
$218$		−	0.931218i		−	0.0630700i
$219$	−1.17757	+	2.03961i	−0.0795728	+	0.137824i
$220$	−4.58399	−	13.5233i	−0.309053	−	0.911744i
$221$	12.6138	+	21.8478i	0.848498	+	1.46964i
$222$	1.92993	+	1.11425i	0.129529	+	0.0747835i
$223$			7.86673i			0.526795i	0.964687	+	0.263398i	$0.0848431\pi$
$223$			7.86673i			0.526795i	−0.964687	+	0.263398i	$0.915157\pi$
$224$	−0.763518	−	8.59183i	−0.0510147	−	0.574066i
$225$	−4.61773	−	1.91744i	−0.307849	−	0.127829i
$226$	1.81895	−	3.15051i	0.120995	−	0.209569i
$227$	−7.77575	+	4.48933i	−0.516095	+	0.297967i	−0.735335	−	0.677703i	$-0.762975\pi$
$227$	−7.77575	+	4.48933i	−0.516095	+	0.297967i	0.219241	+	0.975671i	$0.429642\pi$
$228$	−2.75192	+	1.58882i	−0.182250	+	0.105222i
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	−0.937734	−	0.347354i	$-0.887080\pi$
$229$	−2.54306	+	4.40471i	−0.168050	+	0.291071i	0.769684	+	0.638425i	$0.220414\pi$
$230$	−4.80999	−	0.958942i	−0.317161	−	0.0632308i
$231$	−7.21096	+	5.06387i	−0.474446	+	0.333178i
$232$			0.133563i			0.00876883i
$233$	−18.8952	−	10.9091i	−1.23786	−	0.714681i	−0.269207	−	0.963082i	$-0.586761\pi$
$233$	−18.8952	−	10.9091i	−1.23786	−	0.714681i	−0.968657	+	0.248401i	$0.920095\pi$
$234$	0.653336	+	1.13161i	0.0427099	+	0.0739757i
$235$	−13.5233	+	4.58399i	−0.882166	+	0.299027i
$236$	−1.56281	+	2.70687i	−0.101730	+	0.176202i
$237$		−	11.9403i		−	0.775608i
$238$	1.77710	−	3.82465i	0.115193	−	0.247915i
$239$	−7.44905			−0.481839			−0.240920	−	0.970545i	$-0.577449\pi$
$239$	−7.44905			−0.481839			−0.240920	+	0.970545i	$0.577449\pi$
$240$	−5.90106	−	5.17964i	−0.380912	−	0.334344i
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	0.932720	+	0.360601i	$0.117428\pi$
$241$	12.0879	+	20.9368i	0.778650	+	1.34866i	−0.154070	+	0.988060i	$0.549238\pi$
$242$	0.0227753	−	0.0131493i	0.00146405	−	0.000845271i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−14.0319			−0.898297
$245$	−15.6495	−	0.305506i	−0.999810	−	0.0195180i
$246$	0.0201680			0.00128586
$247$	6.52666	+	3.76817i	0.415281	+	0.239763i
$248$	−6.10255	+	3.52331i	−0.387512	+	0.223730i
$249$	−0.612055	−	1.06011i	−0.0387874	−	0.0671817i
$250$	1.41709	+	2.88307i	0.0896249	+	0.182341i
$251$	6.00200			0.378843			0.189421	−	0.981896i	$-0.439339\pi$
$251$	6.00200			0.378843			0.189421	+	0.981896i	$0.439339\pi$
$252$	−2.13769	+	4.60068i	−0.134662	+	0.289816i
$253$			25.4231i			1.59834i
$254$	−2.37735	+	4.11769i	−0.149168	+	0.258367i
$255$	−3.98224	−	11.7481i	−0.249377	−	0.735694i
$256$	−4.89810	−	8.48376i	−0.306131	−	0.530235i
$257$	6.35139	+	3.66697i	0.396189	+	0.228740i	0.684838	−	0.728695i	$-0.259873\pi$
$257$	6.35139	+	3.66697i	0.396189	+	0.228740i	−0.288650	+	0.957435i	$0.593206\pi$
$258$			0.841839i			0.0524106i
$259$	16.7927	−	11.7926i	1.04345	−	0.732755i
$260$	−3.81213	+	19.1214i	−0.236418	+	1.18586i
$261$	0.0593285	−	0.102760i	0.00367234	−	0.00636069i
$262$	−1.31832	+	0.761132i	−0.0814460	+	0.0470229i
$263$	8.21661	−	4.74386i	0.506658	−	0.292519i	−0.224801	−	0.974405i	$-0.572173\pi$
$263$	8.21661	−	4.74386i	0.506658	−	0.292519i	0.731459	+	0.681886i	$0.238840\pi$
$264$	1.87438	−	3.24652i	0.115360	−	0.199810i
$265$	0.323431	−	1.62231i	0.0198682	−	0.0996575i
$266$	−0.111519	−	1.25492i	−0.00683766	−	0.0769438i
$267$		−	13.0001i		−	0.795596i
$268$	5.04159	+	2.91076i	0.307964	+	0.177803i
$269$	8.02423	+	13.8984i	0.489246	+	0.847399i	0.999923	−	0.0123733i	$-0.00393863\pi$
$269$	8.02423	+	13.8984i	0.489246	+	0.847399i	−0.510677	+	0.859772i	$0.670605\pi$
$270$	−0.206261	−	0.608495i	−0.0125526	−	0.0370318i
$271$	−12.0845	+	20.9309i	−0.734080	+	1.27146i	0.221045	+	0.975264i	$0.429053\pi$
$271$	−12.0845	+	20.9309i	−0.734080	+	1.27146i	−0.955126	+	0.296201i	$0.904280\pi$
$272$		−	19.4799i		−	1.18114i
$273$	11.9844	−	1.06500i	0.725331	−	0.0644570i
$274$	4.27272			0.258125
$275$	13.2197	−	10.1256i	0.797179	−	0.610595i
$276$	7.31853	+	12.6761i	0.440524	+	0.763010i
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.962348	−	0.271820i	$-0.912374\pi$
$277$	−20.1071	+	11.6088i	−1.20812	+	0.697508i	−0.245771	+	0.969328i	$0.579041\pi$
$278$	−2.36818	−	1.36727i	−0.142034	−	0.0820032i
$279$	6.26020			0.374789
$280$	6.09280	−	2.68767i	0.364114	−	0.160619i
$281$	12.4472			0.742538			0.371269	−	0.928525i	$-0.378923\pi$
$281$	12.4472			0.742538			0.371269	+	0.928525i	$0.378923\pi$
$282$	−1.58905	−	0.917438i	−0.0946265	−	0.0546326i
$283$	−7.50649	+	4.33388i	−0.446215	+	0.257622i	−0.706230	−	0.707982i	$-0.749606\pi$
$283$	−7.50649	+	4.33388i	−0.446215	+	0.257622i	0.260016	+	0.965604i	$0.416272\pi$
$284$	3.61483	+	6.26107i	0.214501	+	0.371526i
$285$	−2.78502	−	2.44454i	−0.164970	−	0.144802i
$286$	−4.35173			−0.257323
$287$	0.0782520	−	0.168412i	0.00461907	−	0.00994107i
$288$		−	3.26020i		−	0.192109i
$289$	6.88760	−	11.9297i	0.405153	−	0.701746i
$290$	−0.0722022	+	0.0244743i	−0.00423986	+	0.00143718i
$291$	−1.52153	−	2.63537i	−0.0891936	−	0.154488i
$292$	−3.91083	−	2.25792i	−0.228864	−	0.132135i
$293$		−	27.0063i		−	1.57772i	−0.614571	−	0.788862i	$-0.710671\pi$
$293$		−	27.0063i		−	1.57772i	0.614571	−	0.788862i	$-0.289329\pi$
$294$	−1.29708	−	1.53725i	−0.0756471	−	0.0896540i
$295$	−3.57467	−	0.712664i	−0.208125	−	0.0414929i
$296$	−4.36500	+	7.56040i	−0.253710	+	0.439439i
$297$	−2.88421	+	1.66520i	−0.167359	+	0.0966245i
$298$	−2.82932	+	1.63351i	−0.163898	+	0.0946267i
$299$	17.3572	−	30.0635i	1.00379	−	1.73862i
$300$	3.67657	−	8.85421i	0.212267	−	0.511198i
$301$	7.02976	+	3.26634i	0.405189	+	0.188269i
$302$			2.56888i			0.147822i
$303$	13.8907	+	8.01983i	0.798002	+	0.460727i
$304$	−2.90964	−	5.03965i	−0.166879	−	0.289044i
$305$	−5.25316	−	15.4975i	−0.300795	−	0.887382i
$306$	0.797004	−	1.38045i	0.0455617	−	0.0789151i
$307$		−	2.24681i		−	0.128232i	−0.997942	−	0.0641161i	$-0.979577\pi$
$307$		−	2.24681i		−	0.128232i	0.997942	−	0.0641161i	$-0.0204228\pi$
$308$	−9.70965	−	13.8266i	−0.553259	−	0.787842i
$309$	5.29191			0.301046
$310$	−3.02289	−	2.65333i	−0.171689	−	0.150699i
$311$	−14.2994	−	24.7672i	−0.810843	−	1.40442i	−0.912275	−	0.409578i	$-0.865676\pi$
$311$	−14.2994	−	24.7672i	−0.810843	−	1.40442i	0.101432	−	0.994842i	$-0.467657\pi$
$312$	−4.43301	+	2.55940i	−0.250970	+	0.144898i
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	0.789391	−	0.613891i	$-0.210397\pi$
$313$	11.5429	+	6.66427i	0.652441	+	0.376687i	−0.136950	+	0.990578i	$0.543730\pi$
$314$	−0.961518			−0.0542616
$315$	−5.88151	−	0.638590i	−0.331386	−	0.0359804i
$316$	22.8948			1.28794
$317$	25.2815	+	14.5963i	1.41995	+	0.819808i	0.996294	−	0.0860147i	$-0.0274132\pi$
$317$	25.2815	+	14.5963i	1.41995	+	0.819808i	0.423656	+	0.905823i	$0.360747\pi$
$318$	0.184091	−	0.106285i	0.0103233	−	0.00596016i
$319$	0.197587	+	0.342231i	0.0110628	+	0.0191613i
$320$	8.97747	−	10.2279i	0.501856	−	0.571755i
$321$	−5.16172			−0.288099
$322$	−5.78047	+	0.513685i	−0.322133	+	0.0286266i
$323$		−	9.19357i		−	0.511544i
$324$	−0.958719	+	1.66055i	−0.0532622	+	0.0922528i
$325$	−22.5458	+	2.94824i	−1.25061	+	0.163539i
$326$	2.26361	+	3.92069i	0.125370	+	0.217147i
$327$	−2.80668	−	1.62043i	−0.155209	−	0.0896102i
$328$			0.0790069i			0.00436243i
$329$	−13.8266	+	9.70965i	−0.762283	+	0.535310i
$330$	2.09849	+	0.418365i	0.115518	+	0.0230302i
$331$	12.4457	−	21.5566i	0.684080	−	1.18486i	−0.289646	−	0.957134i	$-0.593537\pi$
$331$	12.4457	−	21.5566i	0.684080	−	1.18486i	0.973725	−	0.227727i	$-0.0731293\pi$
$332$	2.03270	−	1.17358i	0.111559	−	0.0644084i
$333$	6.71665	−	3.87786i	0.368070	−	0.212505i
$334$	3.24605	−	5.62233i	0.177616	−	0.307640i
$335$	−1.32735	+	6.65789i	−0.0725209	+	0.363759i
$336$	−8.42533	−	3.91479i	−0.459639	−	0.213569i
$337$		−	4.72659i		−	0.257474i	−0.991679	−	0.128737i	$-0.958908\pi$
$337$		−	4.72659i		−	0.257474i	0.991679	−	0.128737i	$-0.0410923\pi$
$338$	1.91112	+	1.10339i	0.103951	+	0.0600164i
$339$	−6.33039	−	10.9646i	−0.343820	−	0.595513i
$340$	22.5263	−	7.63570i	1.22166	−	0.414104i
$341$	−10.4245	+	18.0557i	−0.564517	+	0.977772i
$342$		−	0.476183i		−	0.0257490i
$343$	−17.8694	+	4.86668i	−0.964857	+	0.262776i
$344$	−3.29785			−0.177808
$345$	−11.2602	+	12.8285i	−0.606229	+	0.690665i
$346$	1.22494	+	2.12166i	0.0658533	+	0.114061i
$347$	12.2615	−	7.07915i	0.658229	−	0.380029i	−0.133373	−	0.991066i	$-0.542581\pi$
$347$	12.2615	−	7.07915i	0.658229	−	0.380029i	0.791602	+	0.611037i	$0.209247\pi$
$348$	0.197036	+	0.113759i	0.0105622	+	0.00609811i
$349$	−5.04930			−0.270283			−0.135141	−	0.990826i	$-0.543149\pi$
$349$	−5.04930			−0.270283			−0.135141	+	0.990826i	$0.543149\pi$
$350$	2.56937	+	2.80119i	0.137339	+	0.149730i
$351$	4.54754			0.242730
$352$	9.40310	+	5.42888i	0.501187	+	0.289360i
$353$	−13.9417	+	8.04924i	−0.742042	+	0.428418i	−0.822811	−	0.568315i	$-0.807596\pi$
$353$	−13.9417	+	8.04924i	−0.742042	+	0.428418i	0.0807694	+	0.996733i	$0.474262\pi$
$354$	−0.234193	−	0.405635i	−0.0124472	−	0.0215592i
$355$	−5.56174	+	6.33638i	−0.295186	+	0.336300i
$356$	24.9270			1.32113
$357$	−8.43504	−	12.0115i	−0.446430	−	0.635717i
$358$			3.38499i			0.178902i
$359$	0.153241	−	0.265421i	0.00808776	−	0.0140084i	−0.861953	−	0.506988i	$-0.830759\pi$
$359$	0.153241	−	0.265421i	0.00808776	−	0.0140084i	0.870041	+	0.492979i	$0.164092\pi$
$360$	2.38374	−	0.808014i	0.125634	−	0.0425861i
$361$	8.12679	+	14.0760i	0.427726	+	0.740843i
$362$	−2.26188	−	1.30589i	−0.118882	−	0.0686363i
$363$		−	0.0915259i		−	0.00480386i
$364$	2.04208	+	22.9794i	0.107034	+	1.20445i
$365$	1.02964	−	5.16461i	0.0538940	−	0.270328i
$366$	1.05136	−	1.82102i	0.0549557	−	0.0951861i
$367$	−20.4813	+	11.8249i	−1.06911	+	0.617253i	−0.927939	−	0.372732i	$-0.878421\pi$
$367$	−20.4813	+	11.8249i	−1.06911	+	0.617253i	−0.141174	+	0.989985i	$0.545088\pi$
$368$	−23.2140	+	13.4026i	−1.21011	+	0.698658i
$369$	0.0350948	−	0.0607860i	0.00182696	−	0.00316439i
$370$	−4.88690	−	0.974276i	−0.254058	−	0.0506502i
$371$	−0.173255	−	1.94963i	−0.00899496	−	0.101220i
$372$			12.0036i			0.622355i
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	0.858861	−	0.512209i	$-0.171173\pi$
$373$	16.3140	+	9.41887i	0.844705	+	0.487691i	−0.0141557	+	0.999900i	$0.504506\pi$
$374$	2.65434	+	4.59744i	0.137252	+	0.237728i
$375$	11.1554	+	0.745798i	0.576064	+	0.0385128i
$376$	3.59401	−	6.22500i	0.185347	−	0.321030i
$377$		−	0.539598i		−	0.0277907i
$378$	−0.436894	−	0.622139i	−0.0224714	−	0.0319994i
$379$	−14.2534			−0.732147			−0.366074	−	0.930586i	$-0.619298\pi$
$379$	−14.2534			−0.732147			−0.366074	+	0.930586i	$0.619298\pi$
$380$	4.68726	−	5.34010i	0.240451	−	0.273941i
$381$	8.27377	+	14.3306i	0.423878	+	0.734178i
$382$	5.10014	−	2.94457i	0.260946	−	0.150657i
$383$	−21.6995	−	12.5282i	−1.10879	−	0.640161i	−0.170276	−	0.985396i	$-0.554466\pi$
$383$	−21.6995	−	12.5282i	−1.10879	−	0.640161i	−0.938516	+	0.345235i	$0.887799\pi$
$384$	8.26917			0.421984
$385$	11.6357	−	15.9001i	0.593010	−	0.810345i
$386$	−2.45470			−0.124941
$387$	2.53729	+	1.46491i	0.128978	+	0.0744653i
$388$	5.05315	−	2.91744i	0.256535	−	0.148110i
$389$	−6.73590	−	11.6669i	−0.341524	−	0.591536i	0.643192	−	0.765705i	$-0.277610\pi$
$389$	−6.73590	−	11.6669i	−0.341524	−	0.591536i	−0.984716	+	0.174169i	$0.944276\pi$
$390$	−2.19589	−	1.92744i	−0.111193	−	0.0975995i
$391$	−42.3480			−2.14163
$392$	6.02206	−	5.08122i	0.304160	−	0.256640i
$393$			5.29785i			0.267241i
$394$	−1.98385	+	3.43613i	−0.0999449	+	0.173110i
$395$	8.57123	+	25.2862i	0.431265	+	1.27229i
$396$	−3.19291	−	5.53029i	−0.160450	−	0.277907i
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	0.844118	−	0.536158i	$-0.180125\pi$
$397$	15.9768	+	9.22418i	0.801850	+	0.462948i	−0.0422675	+	0.999106i	$0.513458\pi$
$398$		−	1.08929i		−	0.0546010i
$399$	−3.97635	−	1.84759i	−0.199067	−	0.0924953i
$400$	16.2149	+	6.73298i	0.810745	+	0.336649i
$401$	−12.7093	+	22.0131i	−0.634670	+	1.09928i	0.351915	+	0.936032i	$0.385531\pi$
$401$	−12.7093	+	22.0131i	−0.634670	+	1.09928i	−0.986585	+	0.163249i	$0.947803\pi$
$402$	−0.755502	+	0.436189i	−0.0376810	+	0.0217552i
$403$	24.6545	−	14.2343i	1.22813	−	0.709059i
$404$	−15.3775	+	26.6346i	−0.765060	+	1.32512i
$405$	−2.19291	−	0.437190i	−0.108967	−	0.0217241i
$406$	−0.0738212	+	0.0518406i	−0.00366368	+	0.00257281i
$407$			25.8296i			1.28033i
$408$	5.40783	+	3.12221i	0.267727	+	0.154573i
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	0.536016	−	0.844208i	$-0.319929\pi$
$409$	−9.36556	−	16.2216i	−0.463097	−	0.802108i	−0.999113	+	0.0420997i	$0.986595\pi$
$410$	−0.0427100	+	0.0144774i	−0.00210930	+	0.000714986i
$411$	7.43507	−	12.8779i	0.366745	−	0.635221i
$412$			10.1469i			0.499903i
$413$	−4.29592	+	0.381759i	−0.211388	+	0.0187851i
$414$	−2.19342			−0.107801
$415$	2.05714	+	1.80565i	0.100981	+	0.0886360i
$416$	−7.41296	−	12.8396i	−0.363450	−	0.629514i
$417$	−8.24184	+	4.75843i	−0.403605	+	0.233021i
$418$	1.37341	+	0.792938i	0.0671756	+	0.0387839i
$419$	−2.04745			−0.100024			−0.0500121	−	0.998749i	$-0.515926\pi$
$419$	−2.04745			−0.100024			−0.0500121	+	0.998749i	$0.515926\pi$
$420$	1.22446	−	11.2774i	0.0597473	−	0.550283i
$421$	−16.0512			−0.782287			−0.391144	−	0.920330i	$-0.627920\pi$
$421$	−16.0512			−0.782287			−0.391144	+	0.920330i	$0.627920\pi$
$422$	0.0284714	+	0.0164380i	0.00138596	+	0.000800187i
$423$	−5.53029	+	3.19291i	−0.268892	+	0.155245i
$424$	0.416364	+	0.721164i	0.0202204	+	0.0350228i
$425$	16.8665	+	22.0205i	0.818144	+	1.06815i
$426$	−1.08339			−0.0524906
$427$	−11.1271	−	15.8450i	−0.538476	−	0.766791i
$428$		−	9.89727i		−	0.478403i
$429$	−7.57255	+	13.1160i	−0.365606	+	0.633249i
$430$	−0.604305	−	1.78277i	−0.0291422	−	0.0859730i
$431$	−18.3063	−	31.7075i	−0.881784	−	1.52729i	−0.849356	−	0.527820i	$-0.823009\pi$
$431$	−18.3063	−	31.7075i	−0.881784	−	1.52729i	−0.0324277	−	0.999474i	$-0.510324\pi$
$432$	−3.04100	−	1.75572i	−0.146310	−	0.0844722i
$433$		−	18.0047i		−	0.865252i	−0.901574	−	0.432626i	$-0.857587\pi$
$433$		−	18.0047i		−	0.865252i	0.901574	−	0.432626i	$-0.142413\pi$
$434$	−4.31598	−	2.00540i	−0.207174	−	0.0962622i
$435$	−0.0518757	+	0.260205i	−0.00248725	+	0.0124759i
$436$	3.10708	−	5.38163i	0.148802	−	0.257733i
$437$	−10.9559	+	6.32538i	−0.524090	+	0.302584i
$438$	0.586053	−	0.338358i	0.0280027	−	0.0161674i
$439$	−9.68731	+	16.7789i	−0.462350	+	0.800814i	−0.999078	−	0.0429418i	$-0.986327\pi$
$439$	−9.68731	+	16.7789i	−0.462350	+	0.800814i	0.536727	+	0.843756i	$0.319660\pi$
$440$	−1.63892	+	8.22070i	−0.0781324	+	0.391907i
$441$	−6.89031	+	1.23437i	−0.328110	+	0.0587796i
$442$		−	7.24881i		−	0.344791i
$443$	14.2396	+	8.22121i	0.676542	+	0.390602i	0.798551	−	0.601927i	$-0.205600\pi$
$443$	14.2396	+	8.22121i	0.676542	+	0.390602i	−0.122009	+	0.992529i	$0.538934\pi$
$444$	7.43556	+	12.8788i	0.352876	+	0.611199i
$445$	9.33201	+	27.5306i	0.442380	+	1.30507i
$446$	1.13020	−	1.95756i	0.0535164	−	0.0926931i
$447$			11.3700i			0.537785i
$448$	6.78520	−	14.6030i	0.320571	−	0.689926i
$449$	32.7245			1.54436			0.772182	−	0.635401i	$-0.219165\pi$
$449$	32.7245			1.54436			0.772182	+	0.635401i	$0.219165\pi$
$450$	0.873602	+	1.14056i	0.0411820	+	0.0537663i
$451$	0.116880	+	0.202441i	0.00550365	+	0.00953259i
$452$	21.0239	−	12.1381i	0.988880	−	0.570930i
$453$	7.74255	+	4.47016i	0.363777	+	0.210027i
$454$	2.57989			0.121080
$455$	−24.6151	+	10.8583i	−1.15397	+	0.509043i
$456$	1.86542			0.0873561
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.999816	−	0.0191857i	$-0.993893\pi$
$457$	−32.4156	−	18.7152i	−1.51634	−	0.875459i	−0.516523	−	0.856273i	$-0.672774\pi$
$458$	1.26563	−	0.730712i	0.0591390	−	0.0341439i
$459$	−2.77377	−	4.80431i	−0.129469	−	0.224246i
$460$	−24.5979	−	21.5908i	−1.14688	−	1.00667i
$461$	28.3604			1.32088			0.660438	−	0.750881i	$-0.270371\pi$
$461$	28.3604			1.32088			0.660438	+	0.750881i	$0.270371\pi$
$462$	2.52189	−	0.224109i	0.117329	−	0.0104265i
$463$		−	7.20833i		−	0.334999i	−0.985872	−	0.167500i	$-0.946431\pi$
$463$		−	7.20833i		−	0.334999i	0.985872	−	0.167500i	$-0.0535693\pi$
$464$	−0.208329	+	0.360836i	−0.00967143	+	0.0167514i
$465$	−13.2573	+	4.49382i	−0.614793	+	0.208396i
$466$	3.13458	+	5.42926i	0.145207	+	0.251506i
$467$	10.4607	+	6.03950i	0.484065	+	0.279475i	0.722109	−	0.691779i	$-0.243173\pi$
$467$	10.4607	+	6.03950i	0.484065	+	0.279475i	−0.238044	+	0.971254i	$0.576506\pi$
$468$			8.71963i			0.403065i
$469$	0.711033	+	8.00122i	0.0328325	+	0.369462i
$470$	4.02372	+	0.802189i	0.185601	+	0.0370022i
$471$	−1.67316	+	2.89800i	−0.0770952	+	0.133533i
$472$	1.58905	−	0.917438i	0.0731419	−	0.0422285i
$473$	−8.45018	+	4.87871i	−0.388540	+	0.224323i
$474$	−1.71544	+	2.97123i	−0.0787929	+	0.136473i
$475$	7.65266	+	3.17764i	0.351128	+	0.145800i
$476$	23.0313	−	16.1737i	1.05564	−	0.741319i
$477$		−	0.739795i		−	0.0338729i
$478$	1.85362	+	1.07019i	0.0847827	+	0.0489493i
$479$	10.0708	+	17.4432i	0.460149	+	0.797001i	0.998968	−	0.0454204i	$-0.0144627\pi$
$479$	10.0708	+	17.4432i	0.460149	+	0.797001i	−0.538819	+	0.842421i	$0.681129\pi$
$480$	2.34030	+	6.90418i	0.106820	+	0.315131i
$481$	17.6347	−	30.5443i	0.804075	−	1.39270i
$482$		−	6.94657i		−	0.316408i
$483$	−8.51050	+	18.3161i	−0.387241	+	0.833413i
$484$	0.175495			0.00797705
$485$	5.11393	+	4.48874i	0.232212	+	0.203823i
$486$	−0.143668	−	0.248840i	−0.00651691	−	0.0112876i
$487$	34.5887	−	19.9698i	1.56737	−	0.904919i	0.570891	−	0.821026i	$-0.306598\pi$
$487$	34.5887	−	19.9698i	1.56737	−	0.904919i	0.996475	−	0.0838930i	$-0.0267354\pi$
$488$	7.13372	+	4.11866i	0.322928	+	0.186443i
$489$	15.7559			0.712505
$490$	3.85033	+	2.32435i	0.173940	+	0.105004i
$491$	−31.5989			−1.42604			−0.713019	−	0.701145i	$-0.752673\pi$
$491$	−31.5989			−1.42604			−0.713019	+	0.701145i	$0.752673\pi$
$492$	0.116553	+	0.0672922i	0.00525463	+	0.00303376i
$493$	−0.570066	+	0.329127i	−0.0256745	+	0.0148232i
$494$	−1.08273	−	1.87534i	−0.0487143	−	0.0843757i
$495$	4.91258	−	5.59680i	0.220804	−	0.251558i
$496$	−21.9824			−0.987037
$497$	−4.20358	+	9.04686i	−0.188556	+	0.405807i
$498$			0.351730i			0.0157614i
$499$	19.8929	−	34.4556i	0.890530	−	1.54244i	0.0512890	−	0.998684i	$-0.483667\pi$
$499$	19.8929	−	34.4556i	0.890530	−	1.54244i	0.839241	−	0.543759i	$-0.183000\pi$
$500$	−1.43002	+	21.3899i	−0.0639525	+	0.956584i
$501$	−11.2971	−	19.5671i	−0.504716	−	0.874194i
$502$	−1.49354	−	0.862295i	−0.0666599	−	0.0384861i
$503$		−	12.8734i		−	0.573995i	−0.957931	−	0.286997i	$-0.907343\pi$
$503$		−	12.8734i		−	0.573995i	0.957931	−	0.286997i	$-0.0926571\pi$
$504$	2.43719	−	1.71151i	0.108561	−	0.0762365i
$505$	−35.1735	−	7.01237i	−1.56520	−	0.312046i
$506$	3.65248	−	6.32628i	0.162373	−	0.281238i
$507$	6.65118	−	3.84006i	0.295389	−	0.170543i
$508$	−27.4780	+	15.8644i	−1.21914	+	0.703871i
$509$	16.6981	−	28.9219i	0.740128	−	1.28194i	−0.212308	−	0.977203i	$-0.568098\pi$
$509$	16.6981	−	28.9219i	0.740128	−	1.28194i	0.952437	−	0.304737i	$-0.0985685\pi$
$510$	−0.696884	+	3.49552i	−0.0308585	+	0.154784i
$511$	−0.551558	−	6.20665i	−0.0243995	−	0.274566i
$512$			19.3531i			0.855296i
$513$	−1.43521	−	0.828617i	−0.0633659	−	0.0365843i
$514$	−1.05365	−	1.82498i	−0.0464746	−	0.0804965i
$515$	−11.2068	+	3.79874i	−0.493828	+	0.167392i
$516$	−2.80887	+	4.86510i	−0.123653	+	0.214174i
$517$		−	21.2673i		−	0.935335i
$518$	−5.87290	+	0.521899i	−0.258041	+	0.0229309i
$519$	8.52620			0.374259
$520$	7.55061	−	8.60227i	0.331116	−	0.377234i
$521$	−6.77589	−	11.7362i	−0.296857	−	0.514172i	0.678558	−	0.734547i	$-0.262605\pi$
$521$	−6.77589	−	11.7362i	−0.296857	−	0.514172i	−0.975415	+	0.220375i	$0.929272\pi$
$522$	−0.0295266	+	0.0170472i	−0.00129235	+	0.000746136i
$523$	−17.5052	−	10.1066i	−0.765450	−	0.441933i	0.0657991	−	0.997833i	$-0.479040\pi$
$523$	−17.5052	−	10.1066i	−0.765450	−	0.441933i	−0.831249	+	0.555900i	$0.812374\pi$
$524$	−10.1583			−0.443768
$525$	12.9138	−	2.86963i	0.563603	−	0.125241i
$526$	−2.72616			−0.118866
$527$	−30.0760	−	17.3644i	−1.31013	−	0.756404i
$528$	10.1277	−	5.84725i	0.440753	−	0.254469i
$529$	17.6364	+	30.5471i	0.766798	+	1.32813i
$530$	−0.313556	+	0.357228i	−0.0136200	+	0.0155170i
$531$	−1.63010			−0.0707404
$532$	3.54264	−	7.62441i	0.153593	−	0.330560i
$533$		−	0.319190i		−	0.0138257i
$534$	−1.86770	+	3.23496i	−0.0808235	+	0.139990i
$535$	10.9310	−	3.70528i	0.472590	−	0.160193i
$536$	−1.70875	−	2.95963i	−0.0738066	−	0.127837i
$537$	10.2023	+	5.89031i	0.440262	+	0.254186i
$538$		−	4.61130i		−	0.198807i
$539$	7.91354	−	21.9285i	0.340860	−	0.944529i
$540$	0.838284	−	4.20477i	0.0360740	−	0.180945i
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	−0.256554	−	0.966530i	$-0.582587\pi$
$541$	16.4854	−	28.5535i	0.708762	−	1.22761i	0.965317	−	0.261082i	$-0.0840794\pi$
$542$	6.01421	−	3.47231i	0.258332	−	0.149148i
$543$	−7.87189	+	4.54484i	−0.337815	+	0.195038i
$544$	−9.04306	+	15.6630i	−0.387718	+	0.671547i
$545$	7.10694	+	1.41688i	0.304428	+	0.0606923i
$546$	−3.13521	−	1.45676i	−0.134175	−	0.0623437i
$547$			24.6221i			1.05277i	0.850248	+	0.526383i	$0.176452\pi$
$547$			24.6221i			1.05277i	−0.850248	+	0.526383i	$0.823548\pi$
$548$	24.6926	+	14.2563i	1.05482	+	0.608998i
$549$	−3.65901	−	6.33759i	−0.156163	−	0.270482i
$550$	−4.74432	+	0.620399i	−0.202298	+	0.0264539i
$551$	−0.0983213	+	0.170297i	−0.00418863	+	0.00725491i
$552$		−	8.59260i		−	0.365725i
$553$	18.1553	+	25.8532i	0.772041	+	1.09939i
$554$	6.67127			0.283435
$555$	−11.4403	+	13.0337i	−0.485612	+	0.553248i
$556$	−9.12399	−	15.8032i	−0.386943	−	0.670206i
$557$	−20.7796	+	11.9971i	−0.880460	+	0.508334i	−0.870810	−	0.491620i	$-0.836405\pi$
$557$	−20.7796	+	11.9971i	−0.880460	+	0.508334i	−0.00964963	+	0.999953i	$0.503072\pi$
$558$	−1.55779	−	0.899391i	−0.0659465	−	0.0380742i
$559$	13.3234			0.563521
$560$	20.6526	+	2.24237i	0.872732	+	0.0947575i
$561$	18.4755			0.780036
$562$	−3.09736	−	1.78826i	−0.130654	−	0.0754333i
$563$	0.196151	−	0.113248i	0.00826680	−	0.00477284i	−0.495861	−	0.868402i	$-0.665147\pi$
$563$	0.196151	−	0.113248i	0.00826680	−	0.00477284i	0.504128	+	0.863629i	$0.331814\pi$
$564$	−6.12221	−	10.6040i	−0.257792	−	0.446508i
$565$	21.2767	+	18.6756i	0.895119	+	0.785688i
$566$	2.49056			0.104686
$567$	−2.63537	+	0.234193i	−0.110675	+	0.00983520i
$568$		−	4.24413i		−	0.178080i
$569$	−6.40275	+	11.0899i	−0.268417	+	0.464912i	−0.968453	−	0.249195i	$-0.919834\pi$
$569$	−6.40275	+	11.0899i	−0.268417	+	0.464912i	0.700036	+	0.714108i	$0.253167\pi$
$570$	0.341822	+	1.00842i	0.0143174	+	0.0422380i
$571$	0.780149	+	1.35126i	0.0326482	+	0.0565484i	0.881888	−	0.471459i	$-0.156273\pi$
$571$	0.780149	+	1.35126i	0.0326482	+	0.0565484i	−0.849240	+	0.528008i	$0.822939\pi$
$572$	−25.1492	−	14.5199i	−1.05154	−	0.607107i
$573$		−	20.4957i		−	0.856219i
$574$	−0.0436677	+	0.0306655i	−0.00182265	+	0.00127995i
$575$	14.6371	−	35.2502i	0.610408	−	1.47003i
$576$	3.04306	−	5.27073i	0.126794	−	0.219614i
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.578000	−	0.816037i	$-0.303833\pi$
$577$	37.8018	−	21.8249i	1.57371	−	0.908581i	0.995709	−	0.0925443i	$-0.0295000\pi$
$578$	−3.42782	+	1.97905i	−0.142579	+	0.0823178i
$579$	−4.27148	+	7.39842i	−0.177517	+	0.307468i
$580$	−0.498926	−	0.0994684i	−0.0207168	−	0.00413020i
$581$	2.93712	+	1.36472i	0.121852	+	0.0566180i
$582$			0.874380i			0.0362442i
$583$	2.13372	+	1.23191i	0.0883697	+	0.0510203i
$584$	1.32550	+	2.29583i	0.0548494	+	0.0950020i
$585$	−9.63038	+	3.26440i	−0.398167	+	0.134966i
$586$	−3.87994	+	6.72025i	−0.160279	+	0.277611i
$587$			13.6961i			0.565297i	0.959224	+	0.282648i	$0.0912129\pi$
$587$			13.6961i			0.565297i	−0.959224	+	0.282648i	$0.908787\pi$
$588$	−2.36683	−	13.2117i	−0.0976064	−	0.544843i
$589$	−10.3746			−0.427479
$590$	0.787135	+	0.690905i	0.0324058	+	0.0284441i
$591$	6.90429	+	11.9586i	0.284004	+	0.491910i
$592$	−23.5852	+	13.6169i	−0.969344	+	0.559651i
$593$	7.92838	+	4.57745i	0.325579	+	0.187973i	0.653877	−	0.756601i	$-0.273141\pi$
$593$	7.92838	+	4.57745i	0.325579	+	0.187973i	−0.328297	+	0.944574i	$0.606475\pi$
$594$	0.956942			0.0392638
$595$	26.4853	+	19.3820i	1.08579	+	0.794583i
$596$	−21.8014			−0.893018
$597$	−3.28309	−	1.89549i	−0.134368	−	0.0775773i
$598$	−8.63833	+	4.98734i	−0.353247	+	0.203948i
$599$	20.1368	+	34.8780i	0.822767	+	1.42507i	0.903614	+	0.428348i	$0.140904\pi$
$599$	20.1368	+	34.8780i	0.822767	+	1.42507i	−0.0808467	+	0.996727i	$0.525762\pi$
$600$	−4.46805	+	3.42228i	−0.182408	+	0.139714i
$601$	−8.82450			−0.359959			−0.179980	−	0.983670i	$-0.557603\pi$
$601$	−8.82450			−0.359959			−0.179980	+	0.983670i	$0.557603\pi$
$602$	−1.28002	−	1.82275i	−0.0521696	−	0.0742897i
$603$			3.03610i			0.123639i
$604$	−8.57126	+	14.8459i	−0.348760	+	0.604070i
$605$	0.0657008	+	0.193826i	0.00267112	+	0.00788013i
$606$	−2.30438	−	3.99131i	−0.0936092	−	0.162136i
$607$	24.3409	+	14.0532i	0.987966	+	0.570402i	0.904666	−	0.426122i	$-0.140121\pi$
$607$	24.3409	+	14.0532i	0.987966	+	0.570402i	0.0833003	+	0.996524i	$0.473454\pi$
$608$			5.40292i			0.219117i
$609$	0.0277887	+	0.312705i	0.00112606	+	0.0126714i
$610$	−0.919292	+	4.61110i	−0.0372211	+	0.186698i
$611$	−14.5199	+	25.1492i	−0.587412	+	1.01743i
$612$	9.21197	−	5.31853i	0.372372	−	0.214989i
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	−0.536506	−	0.843896i	$-0.680256\pi$
$613$	−1.83025	+	1.05670i	−0.0739232	+	0.0426796i	0.462583	+	0.886576i	$0.346923\pi$
$614$	−0.322795	+	0.559097i	−0.0130269	+	0.0225633i
$615$	−0.0306862	+	0.153920i	−0.00123739	+	0.00620664i
$616$	0.877935	+	9.87935i	0.0353730	+	0.398050i
$617$		−	18.0390i		−	0.726221i	−0.931746	−	0.363111i	$-0.881715\pi$
$617$		−	18.0390i		−	0.726221i	0.931746	−	0.363111i	$-0.118285\pi$
$618$	−1.31684	−	0.760278i	−0.0529711	−	0.0305829i
$619$	−7.31895	−	12.6768i	−0.294173	−	0.509523i	0.680619	−	0.732638i	$-0.261711\pi$
$619$	−7.31895	−	12.6768i	−0.294173	−	0.509523i	−0.974792	+	0.223114i	$0.928378\pi$
$620$	−8.61662	−	25.4201i	−0.346052	−	1.02090i
$621$	−3.81683	+	6.61094i	−0.153164	+	0.265288i
$622$			8.21744i			0.329489i
$623$	19.7667	+	28.1479i	0.791937	+	1.12772i
$624$	−15.9684			−0.639249
$625$	−24.1594	+	6.42842i	−0.966375	+	0.257137i
$626$	−1.91488	−	3.31668i	−0.0765341	−	0.132561i
$627$	4.77980	−	2.75962i	0.190887	−	0.110209i
$628$	−5.55673	−	3.20818i	−0.221738	−	0.128020i
$629$	−43.0252			−1.71553
$630$	1.37181	+	1.00389i	0.0546543	+	0.0399960i
$631$	12.1251			0.482692			0.241346	−	0.970439i	$-0.422411\pi$
$631$	12.1251			0.482692			0.241346	+	0.970439i	$0.422411\pi$
$632$	−11.6396	−	6.72014i	−0.462999	−	0.267313i
$633$	0.0990874	−	0.0572082i	0.00393837	−	0.00227382i
$634$	−4.19403	−	7.26428i	−0.166566	−	0.288501i
$635$	−27.8085	−	24.4088i	−1.10355	−	0.968635i
$636$	1.41851			0.0562477
$637$	−24.3293	+	20.5283i	−0.963963	+	0.813360i
$638$		−	0.113548i		−	0.00449540i
$639$	−1.88524	+	3.26533i	−0.0745790	+	0.129175i
$640$	−17.5117	+	5.93593i	−0.692212	+	0.234638i
$641$	6.52024	+	11.2934i	0.257534	+	0.446062i	0.965581	−	0.260104i	$-0.0837567\pi$
$641$	6.52024	+	11.2934i	0.257534	+	0.446062i	−0.708047	+	0.706166i	$0.750423\pi$
$642$	1.28444	+	0.741573i	0.0506929	+	0.0292675i
$643$			27.0185i			1.06550i	0.846271	+	0.532752i	$0.178842\pi$
$643$			27.0185i			1.06550i	−0.846271	+	0.532752i	$0.821158\pi$
$644$	−35.1200	−	16.3184i	−1.38392	−	0.643033i
$645$	−6.42482	−	1.28088i	−0.252977	−	0.0504347i
$646$	−1.32082	+	2.28773i	−0.0519670	+	0.0900095i
$647$	30.2927	−	17.4895i	1.19093	−	0.687582i	0.232411	−	0.972618i	$-0.425339\pi$
$647$	30.2927	−	17.4895i	1.19093	−	0.687582i	0.958517	+	0.285035i	$0.0920054\pi$
$648$	0.974816	−	0.562810i	0.0382944	−	0.0221093i
$649$	2.71444	−	4.70155i	0.106551	−	0.184552i
$650$	6.03386	+	2.50546i	0.236667	+	0.0982723i
$651$	−13.5546	+	9.51864i	−0.531246	+	0.373065i
$652$			30.2109i			1.18315i
$653$	−28.0168	−	16.1755i	−1.09638	−	0.632997i	−0.161114	−	0.986936i	$-0.551509\pi$
$653$	−28.0168	−	16.1755i	−1.09638	−	0.632997i	−0.935269	+	0.353939i	$0.884842\pi$
$654$	0.465609	+	0.806458i	0.0182067	+	0.0315350i
$655$	−3.80300	−	11.2193i	−0.148596	−	0.438376i
$656$	−0.123234	+	0.213447i	−0.00481146	+	0.00833370i
$657$		−	2.35514i		−	0.0918827i
$658$	4.83557	−	0.429716i	0.188510	−	0.0167521i
$659$	−8.54282			−0.332781			−0.166390	−	0.986060i	$-0.553211\pi$
$659$	−8.54282			−0.332781			−0.166390	+	0.986060i	$0.553211\pi$
$660$	10.7315	+	9.41956i	0.417724	+	0.366656i
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	0.994218	+	0.107382i	$0.0342467\pi$
$661$	15.1715	+	26.2779i	0.590104	+	1.02209i	−0.404114	+	0.914709i	$0.632420\pi$
$662$	−6.19400	+	3.57611i	−0.240737	+	0.138989i
$663$	−21.8478	−	12.6138i	−0.848498	−	0.489881i
$664$	−1.37788			−0.0534722
$665$	9.74704	+	1.05829i	0.377974	+	0.0410388i
$666$	−2.22850			−0.0863525
$667$	0.784435	+	0.452894i	0.0303734	+	0.0175361i
$668$	37.5187	−	21.6614i	1.45164	−	0.838107i
$669$	−3.93337	−	6.81279i	−0.152073	−	0.263398i
$670$	1.28682	−	1.46605i	0.0497143	−	0.0566386i
$671$	24.3719			0.940867
$672$	4.95714	+	7.05899i	0.191226	+	0.272306i
$673$		−	40.5075i		−	1.56145i	−0.624875	−	0.780725i	$-0.714850\pi$
$673$		−	40.5075i		−	1.56145i	0.624875	−	0.780725i	$-0.285150\pi$
$674$	−0.679059	+	1.17617i	−0.0261564	+	0.0453042i
$675$	4.95779	−	0.648315i	0.190825	−	0.0249537i
$676$	7.36308	+	12.7532i	0.283195	+	0.490509i
$677$	20.2833	+	11.7105i	0.779549	+	0.450073i	0.836270	−	0.548317i	$-0.184731\pi$
$677$	20.2833	+	11.7105i	0.779549	+	0.450073i	−0.0567215	+	0.998390i	$0.518065\pi$
$678$			3.63790i			0.139713i
$679$	7.30149	+	3.39260i	0.280205	+	0.130196i
$680$	−13.6935	−	2.73000i	−0.525121	−	0.104691i
$681$	4.48933	−	7.77575i	0.172032	−	0.297967i
$682$	5.18806	−	2.99533i	0.198661	−	0.114697i
$683$	44.1887	−	25.5124i	1.69083	−	0.976204i	0.736989	−	0.675904i	$-0.236247\pi$
$683$	44.1887	−	25.5124i	1.69083	−	0.976204i	0.953845	−	0.300299i	$-0.0970866\pi$
$684$	1.58882	−	2.75192i	0.0607501	−	0.105222i
$685$	−6.50107	+	32.6089i	−0.248393	+	1.24592i
$686$	5.14581	+	1.35623i	0.196468	+	0.0517812i
$687$		−	5.08612i		−	0.194047i
$688$	−8.90956	−	5.14393i	−0.339674	−	0.196111i
$689$	−1.68212	−	2.91353i	−0.0640838	−	0.110996i
$690$	4.64504	−	1.57452i	0.176834	−	0.0599411i
$691$	−12.3057	+	21.3142i	−0.468133	+	0.810829i	−0.999337	−	0.0364144i	$-0.988406\pi$
$691$	−12.3057	+	21.3142i	−0.468133	+	0.810829i	0.531204	+	0.847244i	$0.321740\pi$
$692$			16.3485i			0.621476i
$693$	3.71294	−	7.99092i	0.141043	−	0.303550i
$694$	−4.06819			−0.154426
$695$	14.0381	−	15.9933i	0.532494	−	0.606660i
$696$	−0.0667814	−	0.115669i	−0.00253134	−	0.00438441i
$697$	−0.337213	+	0.194690i	−0.0127728	+	0.00737441i
$698$	1.25647	+	0.725422i	0.0475580	+	0.0274576i
$699$	21.8183			0.825243
$700$	5.50234	+	24.7613i	0.207969	+	0.935891i
$701$	25.7244			0.971595			0.485798	−	0.874071i	$-0.338529\pi$
$701$	25.7244			0.971595			0.485798	+	0.874071i	$0.338529\pi$
$702$	−1.13161	−	0.653336i	−0.0427099	−	0.0246586i
$703$	−11.1311	+	6.42652i	−0.419816	+	0.242381i
$704$	10.1346	+	17.5536i	0.381962	+	0.661577i
$705$	9.41956	−	10.7315i	0.354761	−	0.404173i
$706$	4.62567			0.174089
$707$	−42.2703	+	3.75638i	−1.58974	+	0.141273i
$708$		−	3.12562i		−	0.117468i
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	−0.734889	−	0.678187i	$-0.762766\pi$
$709$	5.85482	−	10.1408i	0.219882	−	0.380848i	0.954772	+	0.297339i	$0.0960993\pi$
$710$	2.29432	−	0.777702i	0.0861042	−	0.0291867i
$711$	5.97016	+	10.3406i	0.223899	+	0.387804i
$712$	−12.6727	−	7.31661i	−0.474931	−	0.274202i
$713$			47.7883i			1.78968i
$714$	0.373306	+	4.20079i	0.0139706	+	0.157211i
$715$	6.62129	−	33.2119i	0.247622	−	1.24205i
$716$	−11.2943	+	19.5623i	−0.422088	+	0.731077i
$717$	6.45107	−	3.72453i	0.240920	−	0.139095i
$718$	−0.0762651	+	0.0440317i	−0.00284619	+	0.00164325i
$719$	−6.16037	+	10.6701i	−0.229743	+	0.397927i	−0.957732	−	0.287662i	$-0.907122\pi$
$719$	−6.16037	+	10.6701i	−0.229743	+	0.397927i	0.727989	+	0.685589i	$0.240455\pi$
$720$	7.70029	+	1.53517i	0.286973	+	0.0572123i
$721$	−11.4580	+	8.04635i	−0.426719	+	0.299662i
$722$		−	4.67023i		−	0.173808i
$723$	−20.9368	−	12.0879i	−0.778650	−	0.449554i
$724$	−8.71444	−	15.0939i	−0.323870	−	0.560959i
$725$	−0.0769272	−	0.588277i	−0.00285700	−	0.0218481i
$726$	−0.0131493	+	0.0227753i	−0.000488017	+	0.000845271i
$727$			17.6540i			0.654751i	0.944894	+	0.327376i	$0.106164\pi$
$727$			17.6540i			0.654751i	−0.944894	+	0.327376i	$0.893836\pi$
$728$	5.70678	−	12.2820i	0.211507	−	0.455202i
$729$	−1.00000			−0.0370370
$730$	−0.998206	+	1.13724i	−0.0369452	+	0.0420910i
$731$	−8.12662	−	14.0757i	−0.300574	−	0.520609i
$732$	12.1519	−	7.01593i	0.449149	−	0.259316i
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	0.330826	−	0.943692i	$-0.392673\pi$
$733$	−8.69135	−	5.01795i	−0.321022	−	0.185342i	−0.651848	+	0.758349i	$0.726006\pi$
$734$	6.79541			0.250823
$735$	13.7056	−	7.56017i	0.505539	−	0.278861i
$736$	24.8873			0.917357
$737$	−8.75672	−	5.05570i	−0.322558	−	0.186229i
$738$	−0.0174660	+	0.0100840i	−0.000642932	+	0.000371197i
$739$	−15.5360	−	26.9092i	−0.571502	−	0.989870i	−0.996412	−	0.0846345i	$-0.973028\pi$
$739$	−15.5360	−	26.9092i	−0.571502	−	0.989870i	0.424910	−	0.905235i	$-0.360306\pi$
$740$	−24.9913	−	21.9360i	−0.918697	−	0.806383i
$741$	−7.53634			−0.276854
$742$	−0.236987	+	0.510038i	−0.00870005	+	0.0187241i
$743$		−	4.04189i		−	0.148283i	−0.997248	−	0.0741413i	$-0.976378\pi$
$743$		−	4.04189i		−	0.148283i	0.997248	−	0.0741413i	$-0.0236216\pi$
$744$	3.52331	−	6.10255i	0.129171	−	0.223730i
$745$	−8.16186	−	24.0785i	−0.299027	−	0.882168i
$746$	−2.70638	−	4.68759i	−0.0990876	−	0.171625i
$747$	1.06011	+	0.612055i	0.0387874	+	0.0223939i
$748$			35.4256i			1.29529i
$749$	11.1761	−	7.84839i	0.408367	−	0.286774i
$750$	−2.66877	−	1.78826i	−0.0974498	−	0.0652981i
$751$	−7.34725	+	12.7258i	−0.268105	+	0.464371i	−0.968372	−	0.249509i	$-0.919731\pi$
$751$	−7.34725	+	12.7258i	−0.268105	+	0.464371i	0.700268	+	0.713881i	$0.253064\pi$
$752$	19.4193	−	11.2117i	0.708149	−	0.408850i
$753$	−5.19789	+	3.00100i	−0.189421	+	0.109363i
$754$	−0.0775229	+	0.134274i	−0.00282322	+	0.00488996i
$755$	−19.6054	−	3.90862i	−0.713512	−	0.142249i
$756$	−0.449051	−	5.05315i	−0.0163318	−	0.183781i
$757$			29.6087i			1.07615i	0.842898	+	0.538073i	$0.180847\pi$
$757$			29.6087i			1.07615i	−0.842898	+	0.538073i	$0.819153\pi$
$758$	3.54681	+	2.04775i	0.128826	+	0.0743778i
$759$	−12.7115	−	22.0170i	−0.461400	−	0.799168i
$760$	−3.95041	+	1.33907i	−0.143297	+	0.0485731i
$761$	7.12611	−	12.3428i	0.258321	−	0.447426i	−0.707471	−	0.706742i	$-0.750164\pi$
$761$	7.12611	−	12.3428i	0.258321	−	0.447426i	0.965792	+	0.259317i	$0.0834974\pi$
$762$		−	4.75470i		−	0.172245i
$763$	8.54088	−	0.758990i	0.309200	−	0.0274773i
$764$	39.2992			1.42179
$765$	9.32277	+	8.18303i	0.337065	+	0.295858i
$766$	3.59980	+	6.23504i	0.130066	+	0.225281i
$767$	−6.41981	+	3.70648i	−0.231806	+	0.133833i
$768$	8.48376	+	4.89810i	0.306131	+	0.176745i
$769$	20.6367			0.744178			0.372089	−	0.928197i	$-0.378642\pi$
$769$	20.6367			0.744178			0.372089	+	0.928197i	$0.378642\pi$
$770$	−5.17977	+	2.28491i	−0.186666	+	0.0823425i
$771$	−7.33395			−0.264126
$772$	−14.1860	−	8.19030i	−0.510566	−	0.294775i
$773$	−36.8580	+	21.2800i	−1.32569	+	0.765387i	−0.984630	−	0.174655i	$-0.944119\pi$
$773$	−36.8580	+	21.2800i	−1.32569	+	0.765387i	−0.341059	+	0.940042i	$0.610786\pi$
$774$	−0.420920	−	0.729054i	−0.0151296	−	0.0262053i
$775$	24.8494	−	19.0332i	0.892615	−	0.683694i
$776$	−3.42533			−0.122962
$777$	−8.64659	+	18.6090i	−0.310195	+	0.667594i
$778$			3.87093i			0.138780i
$779$	−0.0581603	+	0.100737i	−0.00208381	+	0.00360926i
$780$	−6.25929	−	18.4657i	−0.224118	−	0.661177i
$781$	−6.27860	−	10.8748i	−0.224666	−	0.389133i
$782$	10.5379	+	6.08405i	0.376834	+	0.217565i
$783$			0.118657i			0.00424046i
$784$	24.1949	−	4.33442i	0.864105	−	0.154801i
$785$	1.46298	−	7.33819i	0.0522159	−	0.261911i
$786$	0.761132	−	1.31832i	0.0271487	−	0.0470229i
$787$	21.8231	−	12.5996i	0.777909	−	0.449126i	−0.0577798	−	0.998329i	$-0.518402\pi$
$787$	21.8231	−	12.5996i	0.777909	−	0.449126i	0.835689	+	0.549203i	$0.185069\pi$
$788$	−22.9298	+	13.2385i	−0.816842	+	0.471604i
$789$	−4.74386	+	8.21661i	−0.168886	+	0.292519i
$790$	1.49995	−	7.52363i	0.0533657	−	0.267679i
$791$	30.3782	+	14.1151i	1.08012	+	0.501874i
$792$			3.74876i			0.133206i
$793$	−28.8205	−	16.6395i	−1.02344	−	0.590886i
$794$	−2.65044	−	4.59069i	−0.0940605	−	0.162918i
$795$	0.531054	+	1.56667i	0.0188345	+	0.0555642i
$796$	3.63449	−	6.29512i	0.128821	−	0.223125i
$797$		−	51.7211i		−	1.83205i	−0.401116	−	0.916027i	$-0.631377\pi$
$797$		−	51.7211i		−	1.83205i	0.401116	−	0.916027i	$-0.368623\pi$
$798$	0.724036	+	1.03103i	0.0256306	+	0.0364980i
$799$	35.4256			1.25327
$800$	−9.91217	−	12.9411i	−0.350448	−	0.457537i
$801$	6.50007	+	11.2585i	0.229669	+	0.397798i
$802$	6.32515	−	3.65182i	0.223349	−	0.128950i
$803$	6.79271	+	3.92177i	0.239709	+	0.138396i
$804$	−5.82152			−0.205309
$805$	4.87477	−	44.8975i	0.171813	−	1.58243i
$806$	−8.18003			−0.288129
$807$	−13.8984	−	8.02423i	−0.489246	−	0.282466i
$808$	15.6357	−	9.02728i	0.550062	−	0.317579i
$809$	−25.8890	−	44.8410i	−0.910207	−	1.57653i	−0.813770	−	0.581187i	$-0.802589\pi$
$809$	−25.8890	−	44.8410i	−0.910207	−	1.57653i	−0.0964371	−	0.995339i	$-0.530745\pi$
$810$	0.482874	+	0.423842i	0.0169665	+	0.0148923i
$811$	12.0263			0.422299			0.211149	−	0.977454i	$-0.432279\pi$
$811$	12.0263			0.422299			0.211149	+	0.977454i	$0.432279\pi$
$812$	−0.599592	+	0.0532831i	−0.0210416	+	0.00186987i
$813$		−	24.1690i		−	0.847643i
$814$	3.71089	−	6.42744i	0.130067	−	0.225282i
$815$	−33.3664	+	11.3102i	−1.16877	+	0.396178i
$816$	9.73994	+	16.8701i	0.340966	+	0.590571i
$817$	−4.20488	−	2.42769i	−0.147110	−	0.0849341i
$818$			5.38212i			0.188182i
$819$	−9.84632	+	6.91454i	−0.344058	+	0.241613i
$820$	−0.295132	−	0.0588389i	−0.0103064	−	0.00205474i
$821$	−4.03967	+	6.99692i	−0.140985	+	0.244194i	−0.927868	−	0.372909i	$-0.878360\pi$
$821$	−4.03967	+	6.99692i	−0.140985	+	0.244194i	0.786882	+	0.617103i	$0.211694\pi$
$822$	−3.70029	+	2.13636i	−0.129062	+	0.0745142i
$823$	−4.42994	+	2.55762i	−0.154418	+	0.0891532i	−0.575218	−	0.818000i	$-0.695083\pi$
$823$	−4.42994	+	2.55762i	−0.154418	+	0.0891532i	0.420800	+	0.907153i	$0.361749\pi$
$824$	2.97834	−	5.15864i	0.103755	−	0.179710i
$825$	−6.38582	+	15.3789i	−0.222326	+	0.535423i
$826$	1.12384	+	0.522188i	0.0391035	+	0.0181693i
$827$		−	0.705254i		−	0.0245241i	−0.999925	−	0.0122620i	$-0.996097\pi$
$827$		−	0.705254i		−	0.0245241i	0.999925	−	0.0122620i	$-0.00390323\pi$
$828$	−12.6761	−	7.31853i	−0.440524	−	0.254337i
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	0.997165	−	0.0752491i	$-0.0239752\pi$
$829$	12.4790	+	21.6143i	0.433415	+	0.750696i	−0.563750	+	0.825945i	$0.690642\pi$
$830$	−0.252486	−	0.744864i	−0.00876391	−	0.0258546i
$831$	11.6088	−	20.1071i	0.402706	−	0.697508i
$832$		−	27.6769i		−	0.959523i
$833$	36.5270	+	13.1818i	1.26559	+	0.456723i
$834$	2.73453			0.0946891
$835$	37.9700	+	33.3280i	1.31401	+	1.15336i
$836$	5.29140	+	9.16498i	0.183007	+	0.316977i
$837$	−5.42150	+	3.13010i	−0.187394	+	0.108192i
$838$	0.509487	+	0.294152i	0.0175999	+	0.0101613i
$839$	11.6389			0.401819			0.200909	−	0.979610i	$-0.435610\pi$
$839$	11.6389			0.401819			0.200909	+	0.979610i	$0.435610\pi$
$840$	−3.93268	+	5.37399i	−0.135690	+	0.185420i
$841$	−28.9859			−0.999514
$842$	3.99418	+	2.30604i	0.137649	+	0.0794714i
$843$	−10.7796	+	6.22360i	−0.371269	+	0.214352i
$844$	0.109693	+	0.189994i	0.00377579	+	0.00653986i
$845$	−11.3287	+	12.9066i	−0.389721	+	0.444001i
$846$	1.83488			0.0630843
$847$	0.139165	+	0.198172i	0.00478177	+	0.00680926i
$848$			2.59775i			0.0892071i
$849$	4.33388	−	7.50649i	0.148738	−	0.257622i
$850$	−1.03342	−	7.90275i	−0.0354460	−	0.271062i
$851$	29.6023	+	51.2726i	1.01475	+	1.75760i
$852$	−6.26107	−	3.61483i	−0.214501	−	0.123842i
$853$		−	32.5996i		−	1.11619i	−0.829778	−	0.558094i	$-0.811533\pi$
$853$		−	32.5996i		−	1.11619i	0.829778	−	0.558094i	$-0.188467\pi$
$854$	0.492445	+	5.54146i	0.0168511	+	0.189625i
$855$	3.63417	+	0.724526i	0.124286	+	0.0247783i
$856$	−2.90507	+	5.03172i	−0.0992931	+	0.171981i
$857$	27.4455	−	15.8456i	0.937519	−	0.541277i	0.0483371	−	0.998831i	$-0.484608\pi$
$857$	27.4455	−	15.8456i	0.937519	−	0.541277i	0.889182	+	0.457554i	$0.151274\pi$
$858$	3.76871	−	2.17587i	0.128662	−	0.0742828i
$859$	−21.8456	+	37.8377i	−0.745363	+	1.29101i	0.204662	+	0.978833i	$0.434390\pi$
$859$	−21.8456	+	37.8377i	−0.745363	+	1.29101i	−0.950025	+	0.312174i	$0.898943\pi$
$860$	2.45601	−	12.3192i	0.0837494	−	0.420081i
$861$	0.0164380	+	0.184975i	0.000560204	+	0.00630394i
$862$			10.5201i			0.358317i
$863$	33.6005	+	19.3992i	1.14377	+	0.660358i	0.947362	−	0.320164i	$-0.103738\pi$
$863$	33.6005	+	19.3992i	1.14377	+	0.660358i	0.196411	+	0.980522i	$0.437071\pi$
$864$	1.63010	+	2.82342i	0.0554572	+	0.0960547i
$865$	−18.0561	+	6.12044i	−0.613924	+	0.208101i
$866$	−2.58670	+	4.48030i	−0.0878997	+	0.152247i
$867$			13.7752i			0.467830i
$868$	−18.2514	−	25.9901i	−0.619493	−	0.882160i
$869$	−39.7660			−1.34897
$870$	0.0502918	−	0.0572965i	0.00170505	−	0.00194253i
$871$	6.90338	+	11.9570i	0.233912	+	0.405148i
$872$	−3.15925	+	1.82399i	−0.106986	+	0.0617682i
$873$	2.63537	+	1.52153i	0.0891936	+	0.0514960i
$874$	3.63501			0.122956
$875$	−25.2877	+	15.3470i	−0.854881	+	0.518825i
$876$	4.51583			0.152576
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	0.561565	−	0.827433i	$-0.310200\pi$
$877$	3.72454	+	2.15036i	0.125769	+	0.0726127i	−0.435796	+	0.900046i	$0.643533\pi$
$878$	4.82118	−	2.78351i	0.162707	−	0.0939390i
$879$	13.5031	+	23.3881i	0.455450	+	0.788862i
$880$	−17.2502	+	19.6529i	−0.581506	+	0.662498i
$881$	−1.29308			−0.0435650			−0.0217825	−	0.999763i	$-0.506934\pi$
$881$	−1.29308			−0.0435650			−0.0217825	+	0.999763i	$0.506934\pi$
$882$	1.89192	+	0.682755i	0.0637044	+	0.0229896i
$883$			1.49533i			0.0503218i	0.999683	+	0.0251609i	$0.00800981\pi$
$883$			1.49533i			0.0503218i	−0.999683	+	0.0251609i	$0.991990\pi$
$884$	24.1862	−	41.8918i	0.813471	−	1.40897i
$885$	3.45209	−	1.17015i	0.116041	−	0.0393342i
$886$	−2.36225	−	4.09153i	−0.0793613	−	0.137458i
$887$	8.73964	+	5.04584i	0.293449	+	0.169423i	0.639496	−	0.768794i	$-0.279143\pi$
$887$	8.73964	+	5.04584i	0.293449	+	0.169423i	−0.346047	+	0.938217i	$0.612476\pi$
$888$		−	8.73000i		−	0.292960i
$889$	−39.7040	−	18.4483i	−1.33163	−	0.618736i
$890$	1.63308	−	8.19142i	0.0547410	−	0.274577i
$891$	1.66520	−	2.88421i	0.0557862	−	0.0966245i
$892$	13.0631	−	7.54198i	0.437385	−	0.252524i
$893$	9.16498	−	5.29140i	0.306694	−	0.177070i
$894$	1.63351	−	2.82932i	0.0546328	−	0.0946267i
$895$	−25.8339	−	5.15036i	−0.863531	−	0.172158i
$896$	−17.9044	+	12.5733i	−0.598143	+	0.420044i
$897$			34.7144i			1.15908i
$898$	−8.14317	−	4.70146i	−0.271741	−	0.156890i
$899$	0.371409	+	0.643299i	0.0123872	+	0.0214552i
$900$	1.24310	+	9.50626i	0.0414368	+	0.316875i
$901$	−2.05202	+	3.55421i	−0.0683628	+	0.118408i
$902$		−	0.0671674i		−	0.00223643i
$903$	−7.72112	+	0.686142i	−0.256943	+	0.0228334i
$904$	−14.2512			−0.473989
$905$	13.4079	−	15.2754i	0.445695	−	0.507772i
$906$	−1.28444	−	2.22471i	−0.0426726	−	0.0739111i
$907$	−3.69531	+	2.13349i	−0.122701	+	0.0708414i	−0.560094	−	0.828429i	$-0.689235\pi$
$907$	−3.69531	+	2.13349i	−0.122701	+	0.0708414i	0.437393	+	0.899270i	$0.355902\pi$
$908$	14.9095	+	8.60802i	0.494790	+	0.285667i
$909$	−16.0397			−0.532002
$910$	7.68520	+	0.834427i	0.254762	+	0.0276610i
$911$	−28.5451			−0.945742			−0.472871	−	0.881132i	$-0.656782\pi$
$911$	−28.5451			−0.945742			−0.472871	+	0.881132i	$0.656782\pi$
$912$	5.03965	+	2.90964i	0.166879	+	0.0963479i
$913$	−3.53058	+	2.03838i	−0.116845	+	0.0674606i
$914$	5.37754	+	9.31417i	0.177873	+	0.308085i
$915$	12.2981	+	10.7946i	0.406563	+	0.356859i
$916$	9.75231			0.322226
$917$	−8.05539	−	11.4709i	−0.266012	−	0.378802i
$918$			1.59401i			0.0526101i
$919$	−23.2822	+	40.3259i	−0.768008	+	1.33023i	0.170634	+	0.985335i	$0.445419\pi$
$919$	−23.2822	+	40.3259i	−0.768008	+	1.33023i	−0.938642	+	0.344894i	$0.887915\pi$
$920$	6.16810	+	18.1967i	0.203356	+	0.599926i
$921$	1.12341	+	1.94580i	0.0370175	+	0.0641161i
$922$	−7.05720	−	4.07448i	−0.232417	−	0.134186i
$923$			17.1464i			0.564381i
$924$	15.3221	+	7.11934i	0.504060	+	0.234209i
$925$	14.8711	−	35.8138i	0.488959	−	1.17755i
$926$	−1.03561	+	1.79372i	−0.0340321	+	0.0589453i
$927$	−4.58293	+	2.64596i	−0.150523	+	0.0869046i
$928$	0.335019	−	0.193423i	0.0109975	−	0.00634943i
$929$	3.69774	−	6.40467i	0.121319	−	0.210130i	−0.798969	−	0.601372i	$-0.794621\pi$
$929$	3.69774	−	6.40467i	0.121319	−	0.210130i	0.920288	+	0.391242i	$0.127954\pi$
$930$	3.94457	+	0.786409i	0.129348	+	0.0257874i
$931$	11.4188	−	2.04564i	0.374238	−	0.0670432i
$932$			41.8352i			1.37036i
$933$	24.7672	+	14.2994i	0.810843	+	0.468140i
$934$	−1.73537	−	3.00574i	−0.0567829	−	0.0983509i
$935$	−39.1258	+	13.2624i	−1.27955	+	0.433728i
$936$	2.55940	−	4.43301i	0.0836567	−	0.144898i
$937$		−	44.1988i		−	1.44391i	−0.691939	−	0.721956i	$-0.743243\pi$
$937$		−	44.1988i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$938$	0.972585	−	2.09318i	0.0317560	−	0.0683447i
$939$	−13.3285			−0.434960
$940$	20.5770	+	18.0614i	0.671149	+	0.589099i
$941$	−18.0180	−	31.2080i	−0.587369	−	1.01735i	−0.994576	−	0.104017i	$-0.966830\pi$
$941$	−18.0180	−	31.2080i	−0.587369	−	1.01735i	0.407206	−	0.913336i	$-0.366503\pi$
$942$	0.832699	−	0.480759i	0.0271308	−	0.0156640i
$943$	0.464020	+	0.267902i	0.0151106	+	0.00872408i
$944$	5.72401			0.186301
$945$	5.41284	−	2.38772i	0.176080	−	0.0776726i
$946$	2.80366			0.0911548
$947$	−29.6476	−	17.1170i	−0.963417	−	0.556229i	−0.0661943	−	0.997807i	$-0.521086\pi$
$947$	−29.6476	−	17.1170i	−0.963417	−	0.556229i	−0.897223	+	0.441577i	$0.854419\pi$
$948$	−19.8275	+	11.4474i	−0.643968	+	0.371795i
$949$	−5.35504	−	9.27521i	−0.173832	−	0.301086i
$950$	−1.44776	−	1.89017i	−0.0469716	−	0.0613251i
$951$	−29.1925			−0.946633
$952$	−16.4563	+	1.46240i	−0.533353	+	0.0473967i
$953$			30.9689i			1.00318i	0.865105	+	0.501591i	$0.167252\pi$
$953$			30.9689i			1.00318i	−0.865105	+	0.501591i	$0.832748\pi$
$954$	−0.106285	+	0.184091i	−0.00344110	+	0.00596016i
$955$	14.7126	+	43.4039i	0.476088	+	1.40452i
$956$	7.14155	+	12.3695i	0.230974	+	0.400059i
$957$	−0.342231	−	0.197587i	−0.0110628	−	0.00638709i
$958$		−	5.78743i		−	0.186983i
$959$	3.48249	+	39.1883i	0.112455	+	1.26545i
$960$	−2.66079	+	13.3463i	−0.0858766	+	0.430751i
$961$	−4.09508	+	7.09289i	−0.132099	+	0.228803i
$962$	−8.77646	+	5.06709i	−0.282964	+	0.163370i
$963$	4.47018	−	2.58086i	0.144049	−	0.0831670i
$964$	23.1778	−	40.1451i	0.746506	−	1.29299i
$965$	3.73490	−	18.7340i	0.120231	−	0.603068i
$966$	4.74919	−	3.33510i	0.152803	−	0.107305i
$967$		−	21.0270i		−	0.676184i	−0.941113	−	0.338092i	$-0.890218\pi$
$967$		−	21.0270i		−	0.676184i	0.941113	−	0.338092i	$-0.109782\pi$
$968$	−0.0892209	−	0.0515117i	−0.00286767	−	0.00165565i
$969$	4.59678	+	7.96187i	0.147670	+	0.255772i
$970$	−0.627664	−	1.85169i	−0.0201531	−	0.0594540i
$971$	−22.3468	+	38.7058i	−0.717144	+	1.24213i	0.244983	+	0.969527i	$0.421218\pi$
$971$	−22.3468	+	38.7058i	−0.717144	+	1.24213i	−0.962127	+	0.272602i	$0.912116\pi$
$972$		−	1.91744i		−	0.0615019i
$973$	10.6100	−	22.8346i	0.340141	−	0.732045i
$974$	−11.4761			−0.367718
$975$	18.0511	−	13.8261i	0.578097	−	0.442790i
$976$	12.8484	+	22.2541i	0.411268	+	0.712337i
$977$	12.5029	−	7.21858i	0.400005	−	0.230943i	−0.286481	−	0.958086i	$-0.592486\pi$
$977$	12.5029	−	7.21858i	0.400005	−	0.230943i	0.686486	+	0.727143i	$0.259152\pi$
$978$	−3.92069	−	2.26361i	−0.125370	−	0.0723824i
$979$	−43.2956			−1.38373
$980$	14.4962	+	26.2797i	0.463063	+	0.839473i
$981$	3.24087			0.103473
$982$	7.86307	+	4.53974i	0.250921	+	0.144869i
$983$	−14.5389	+	8.39401i	−0.463717	+	0.267727i	−0.713606	−	0.700547i	$-0.752939\pi$
$983$	−14.5389	+	8.39401i	−0.463717	+	0.267727i	0.249889	+	0.968275i	$0.419606\pi$
$984$	−0.0395034	−	0.0684220i	−0.00125932	−	0.00218121i
$985$	−23.2056	−	20.3687i	−0.739393	−	0.649000i
$986$	0.189140			0.00602345
$987$	7.11934	−	15.3221i	0.226611	−	0.487707i
$988$		−	14.4505i		−	0.459730i
$989$	−11.1826	+	19.3688i	−0.355585	+	0.615892i
$990$	−2.02653	+	0.686930i	−0.0644073	+	0.0218321i
$991$	−20.0539	−	34.7344i	−0.637033	−	1.10337i	−0.986081	−	0.166268i	$-0.946828\pi$
$991$	−20.0539	−	34.7344i	−0.637033	−	1.10337i	0.349048	−	0.937105i	$-0.386505\pi$
$992$	17.6752	+	10.2048i	0.561188	+	0.324002i
$993$			24.8915i			0.789907i
$994$	2.34576	−	1.64730i	0.0744031	−	0.0522492i
$995$	8.31330	+	1.65738i	0.263549	+	0.0525425i
$996$	−1.17358	+	2.03270i	−0.0371862	+	0.0644084i
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.995154	−	0.0983259i	$-0.968651\pi$
$997$	−44.4447	+	25.6602i	−1.40758	+	0.812666i	−0.412424	+	0.910992i	$0.635318\pi$
$998$	−9.90032	+	5.71595i	−0.313389	+	0.180935i
$999$	−3.87786	+	6.71665i	−0.122690	+	0.212505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.q.a.79.4	yes	16
3.2	odd	2		315.2.bf.b.289.5		16
4.3	odd	2		1680.2.di.d.289.7		16
5.2	odd	4		525.2.i.h.226.3		8
5.3	odd	4		525.2.i.k.226.2		8
5.4	even	2	inner	105.2.q.a.79.5	yes	16
7.2	even	3		735.2.d.d.589.5		8
7.3	odd	6		735.2.q.g.214.5		16
7.4	even	3	inner	105.2.q.a.4.5	yes	16
7.5	odd	6		735.2.d.e.589.5		8
7.6	odd	2		735.2.q.g.79.4		16
15.14	odd	2		315.2.bf.b.289.4		16
20.19	odd	2		1680.2.di.d.289.3		16
21.2	odd	6		2205.2.d.s.1324.4		8
21.5	even	6		2205.2.d.o.1324.4		8
21.11	odd	6		315.2.bf.b.109.4		16
28.11	odd	6		1680.2.di.d.529.3		16
35.2	odd	12		3675.2.a.bz.1.2		4
35.4	even	6	inner	105.2.q.a.4.4	✓	16
35.9	even	6		735.2.d.d.589.4		8
35.12	even	12		3675.2.a.cb.1.2		4
35.18	odd	12		525.2.i.k.151.2		8
35.19	odd	6		735.2.d.e.589.4		8
35.23	odd	12		3675.2.a.bp.1.3		4
35.24	odd	6		735.2.q.g.214.4		16
35.32	odd	12		525.2.i.h.151.3		8
35.33	even	12		3675.2.a.bn.1.3		4
35.34	odd	2		735.2.q.g.79.5		16
105.44	odd	6		2205.2.d.s.1324.5		8
105.74	odd	6		315.2.bf.b.109.5		16
105.89	even	6		2205.2.d.o.1324.5		8
140.39	odd	6		1680.2.di.d.529.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	35.4	even	6	inner
105.2.q.a.4.5	yes	16	7.4	even	3	inner
105.2.q.a.79.4	yes	16	1.1	even	1	trivial
105.2.q.a.79.5	yes	16	5.4	even	2	inner
315.2.bf.b.109.4		16	21.11	odd	6
315.2.bf.b.109.5		16	105.74	odd	6
315.2.bf.b.289.4		16	15.14	odd	2
315.2.bf.b.289.5		16	3.2	odd	2
525.2.i.h.151.3		8	35.32	odd	12
525.2.i.h.226.3		8	5.2	odd	4
525.2.i.k.151.2		8	35.18	odd	12
525.2.i.k.226.2		8	5.3	odd	4
735.2.d.d.589.4		8	35.9	even	6
735.2.d.d.589.5		8	7.2	even	3
735.2.d.e.589.4		8	35.19	odd	6
735.2.d.e.589.5		8	7.5	odd	6
735.2.q.g.79.4		16	7.6	odd	2
735.2.q.g.79.5		16	35.34	odd	2
735.2.q.g.214.4		16	35.24	odd	6
735.2.q.g.214.5		16	7.3	odd	6
1680.2.di.d.289.3		16	20.19	odd	2
1680.2.di.d.289.7		16	4.3	odd	2
1680.2.di.d.529.3		16	28.11	odd	6
1680.2.di.d.529.7		16	140.39	odd	6
2205.2.d.o.1324.4		8	21.5	even	6
2205.2.d.o.1324.5		8	105.89	even	6
2205.2.d.s.1324.4		8	21.2	odd	6
2205.2.d.s.1324.5		8	105.44	odd	6
3675.2.a.bn.1.3		4	35.33	even	12
3675.2.a.bp.1.3		4	35.23	odd	12
3675.2.a.bz.1.2		4	35.2	odd	12
3675.2.a.cb.1.2		4	35.12	even	12

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248840 - 0.143668i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.958719 - 1.66055i) q^{4} +(1.47507 - 1.68052i) q^{5} +0.287336 q^{6} +(1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.608495 + 0.206261i) q^{10} +(1.66520 + 2.88421i) q^{11} +(1.66055 + 0.958719i) q^{12} -4.54754i q^{13} +(-0.622139 + 0.436894i) q^{14} +(-0.437190 + 2.19291i) q^{15} +(-1.75572 + 3.04100i) q^{16} +(-4.80431 + 2.77377i) q^{17} +(-0.248840 + 0.143668i) q^{18} +(-0.828617 + 1.43521i) q^{19} +(-4.20477 - 0.838284i) q^{20} +(0.234193 + 2.63537i) q^{21} -0.956942i q^{22} +(6.61094 + 3.81683i) q^{23} +(-0.562810 - 0.974816i) q^{24} +(-0.648315 - 4.95779i) q^{25} +(-0.653336 + 1.13161i) q^{26} +1.00000i q^{27} +(-5.05315 + 0.449051i) q^{28} +0.118657 q^{29} +(0.423842 - 0.482874i) q^{30} +(3.13010 + 5.42150i) q^{31} +(2.82342 - 1.63010i) q^{32} +(-2.88421 - 1.66520i) q^{33} +1.59401 q^{34} +(-2.38772 - 5.41284i) q^{35} -1.91744 q^{36} +(6.71665 + 3.87786i) q^{37} +(0.412386 - 0.238091i) q^{38} +(2.27377 + 3.93829i) q^{39} +(1.89163 + 1.66037i) q^{40} +0.0701896 q^{41} +(0.320341 - 0.689431i) q^{42} +2.92981i q^{43} +(3.19291 - 5.53029i) q^{44} +(-0.717839 - 2.11771i) q^{45} +(-1.09671 - 1.89956i) q^{46} +(-5.53029 - 3.19291i) q^{47} -3.51145i q^{48} +(-4.51415 - 5.35000i) q^{49} +(-0.550949 + 1.32684i) q^{50} +(2.77377 - 4.80431i) q^{51} +(-7.55142 + 4.35981i) q^{52} +(0.640682 - 0.369898i) q^{53} +(0.143668 - 0.248840i) q^{54} +(7.30326 + 1.45601i) q^{55} +(2.70080 + 1.25492i) q^{56} -1.65723i q^{57} +(-0.0295266 - 0.0170472i) q^{58} +(-0.815051 - 1.41171i) q^{59} +(4.06058 - 1.37641i) q^{60} +(3.65901 - 6.33759i) q^{61} -1.79878i q^{62} +(-1.52050 - 2.16520i) q^{63} +6.08612 q^{64} +(-7.64225 - 6.70796i) q^{65} +(0.478471 + 0.828736i) q^{66} +(-2.62934 + 1.51805i) q^{67} +(9.21197 + 5.31853i) q^{68} -7.63366 q^{69} +(-0.183490 + 1.68997i) q^{70} -3.77048 q^{71} +(0.974816 + 0.562810i) q^{72} +(2.03961 - 1.17757i) q^{73} +(-1.11425 - 1.92993i) q^{74} +(3.04035 + 3.96942i) q^{75} +3.17764 q^{76} +(8.77681 - 0.779956i) q^{77} -1.30667i q^{78} +(-5.97016 + 10.3406i) q^{79} +(2.52065 + 7.43623i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0174660 - 0.0100840i) q^{82} +1.22411i q^{83} +(4.15163 - 2.91547i) q^{84} +(-2.42533 + 12.1653i) q^{85} +(0.420920 - 0.729054i) q^{86} +(-0.102760 + 0.0593285i) q^{87} +(-3.24652 + 1.87438i) q^{88} +(-6.50007 + 11.2585i) q^{89} +(-0.125620 + 0.630102i) q^{90} +(-10.9113 - 5.06990i) q^{91} -14.6371i q^{92} +(-5.42150 - 3.13010i) q^{93} +(0.917438 + 1.58905i) q^{94} +(1.18963 + 3.50954i) q^{95} +(-1.63010 + 2.82342i) q^{96} +3.04306i q^{97} +(0.354679 + 1.97983i) q^{98} +3.33039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35}+ \cdots + 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9 - 4 * q^10 - 24 * q^14 - 4 * q^15 - 24 * q^19 - 8 * q^20 - 4 * q^21 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 24 * q^29 - 12 * q^30 + 16 * q^31 + 16 * q^34 - 10 * q^35 + 16 * q^36 - 4 * q^39 + 32 * q^40 + 16 * q^41 + 20 * q^44 - 2 * q^45 - 32 * q^46 - 40 * q^49 - 40 * q^50 + 4 * q^51 - 4 * q^54 + 8 * q^55 + 84 * q^56 + 4 * q^59 + 16 * q^60 + 16 * q^61 + 16 * q^64 + 30 * q^65 + 28 * q^66 + 40 * q^69 + 16 * q^70 - 56 * q^71 + 40 * q^74 + 8 * q^75 - 64 * q^76 - 16 * q^79 + 52 * q^80 - 8 * q^81 + 12 * q^84 - 64 * q^85 - 48 * q^86 + 16 * q^89 - 8 * q^90 + 8 * q^91 - 32 * q^94 - 22 * q^95 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more