LMFDB - Embedded newform 105.2.q.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(4,105)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 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			4.5
Root			$2.07845 + 0.556918i$ of defining polynomial
Character	$\chi$	$=$	105.4
Dual form			105.2.q.a.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248840 - 0.143668i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(0.717839 + 2.11771i) q^{5} +0.287336 q^{6} +(-1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.248840 - 0.143668i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(0.717839 + 2.11771i) q^{5} +0.287336 q^{6} +(-1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.482874 + 0.423842i) 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} +(-3.96942 + 3.04035i) q^{25} +(-0.653336 - 1.13161i) q^{26} +1.00000i q^{27} +(5.05315 + 0.449051i) q^{28} +0.118657 q^{29} +(0.206261 + 0.608495i) q^{30} +(3.13010 - 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +(2.88421 - 1.66520i) q^{33} +1.59401 q^{34} +(4.28093 - 4.08334i) q^{35} -1.91744 q^{36} +(-6.71665 + 3.87786i) q^{37} +(-0.412386 - 0.238091i) q^{38} +(2.27377 - 3.93829i) q^{39} +(-2.38374 + 0.808014i) q^{40} +0.0701896 q^{41} +(-0.320341 - 0.689431i) q^{42} +2.92981i q^{43} +(3.19291 + 5.53029i) q^{44} +(-1.47507 + 1.68052i) 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} +(-3.22230 - 2.82836i) q^{60} +(3.65901 + 6.33759i) q^{61} -1.79878i q^{62} +(1.52050 - 2.16520i) q^{63} +6.08612 q^{64} +(9.63038 - 3.26440i) q^{65} +(0.478471 - 0.828736i) q^{66} +(2.62934 + 1.51805i) q^{67} +(-9.21197 + 5.31853i) q^{68} -7.63366 q^{69} +(0.478621 - 1.63113i) q^{70} -3.77048 q^{71} +(-0.974816 + 0.562810i) q^{72} +(-2.03961 - 1.17757i) q^{73} +(-1.11425 + 1.92993i) q^{74} +(-4.95779 + 0.648315i) q^{75} +3.17764 q^{76} +(-8.77681 - 0.779956i) q^{77} -1.30667i q^{78} +(-5.97016 - 10.3406i) q^{79} +(5.17964 - 5.90106i) 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} +(2.44454 - 2.78502i) 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}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.634274\pi$
$2$	0.248840	−	0.143668i	0.175957	−	0.101589i	0.585392	+	0.810751i	$0.300941\pi$
$3$	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
$5$	0.717839	+	2.11771i	0.321027	+	0.947070i
$5$	0.717839	+	2.11771i	0.321027	+	0.947070i
$6$	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
$10$	0.482874	+	0.423842i	0.152698	+	0.134030i
$11$	1.66520	−	2.88421i	0.502076	−	0.869621i	−0.497921	−	0.867222i	$-0.665903\pi$
$11$	1.66520	−	2.88421i	0.502076	−	0.869621i	0.999997	−	0.00239862i	$-0.000763504\pi$
$12$	−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	$-0.0984514\pi$
$17$	4.80431	+	2.77377i	1.16522	+	0.672738i	0.212668	+	0.977125i	$0.431785\pi$
$18$	0.248840	+	0.143668i	0.0586522	+	0.0338629i
$19$	−0.828617	−	1.43521i	−0.190098	−	0.329259i	0.755185	−	0.655512i	$-0.227547\pi$
$19$	−0.828617	−	1.43521i	−0.190098	−	0.329259i	−0.945282	+	0.326253i	$0.894214\pi$
$20$	−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	$-0.959650\pi$
$23$	−6.61094	+	3.81683i	−1.37848	+	0.795864i	−0.386500	+	0.922289i	$0.626316\pi$
$24$	−0.562810	+	0.974816i	−0.114883	+	0.198983i
$25$	−3.96942	+	3.04035i	−0.793883	+	0.608070i
$26$	−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	$0.496493\pi$
$30$	0.206261	+	0.608495i	0.0376579	+	0.111095i
$31$	3.13010	−	5.42150i	0.562183	−	0.973729i	−0.435123	−	0.900371i	$-0.643295\pi$
$31$	3.13010	−	5.42150i	0.562183	−	0.973729i	0.997306	−	0.0733583i	$-0.0233717\pi$
$32$	−2.82342	−	1.63010i	−0.499115	−	0.288164i
$33$	2.88421	−	1.66520i	0.502076	−	0.289874i
$34$	1.59401			0.273370
$35$	4.28093	−	4.08334i	0.723609	−	0.690211i
$36$	−1.91744			−0.319573
$37$	−6.71665	+	3.87786i	−1.10421	+	0.637516i	−0.937324	−	0.348460i	$-0.886705\pi$
$37$	−6.71665	+	3.87786i	−1.10421	+	0.637516i	−0.166887	+	0.985976i	$0.553372\pi$
$38$	−0.412386	−	0.238091i	−0.0668979	−	0.0386235i
$39$	2.27377	−	3.93829i	0.364095	−	0.630630i
$40$	−2.38374	+	0.808014i	−0.376902	+	0.127758i
$41$	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
$45$	−1.47507	+	1.68052i	−0.219891	+	0.250518i
$46$	−1.09671	+	1.89956i	−0.161701	+	0.280075i
$47$	5.53029	−	3.19291i	0.806675	−	0.465734i	−0.0391247	−	0.999234i	$-0.512457\pi$
$47$	5.53029	−	3.19291i	0.806675	−	0.465734i	0.845800	+	0.533500i	$0.179124\pi$
$48$		−	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	$-0.349513\pi$
$53$	−0.640682	−	0.369898i	−0.0880044	−	0.0508094i	−0.543356	+	0.839502i	$0.682847\pi$
$54$	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	−0.914191	−	0.405283i	$-0.867173\pi$
$59$	−0.815051	+	1.41171i	−0.106111	+	0.183789i	0.808081	+	0.589072i	$0.200506\pi$
$60$	−3.22230	−	2.82836i	−0.415997	−	0.365140i
$61$	3.65901	+	6.33759i	0.468488	+	0.811446i	0.999351	−	0.0360120i	$-0.0114655\pi$
$61$	3.65901	+	6.33759i	0.468488	+	0.811446i	−0.530863	+	0.847458i	$0.678132\pi$
$62$		−	1.79878i		−	0.228445i
$63$	1.52050	−	2.16520i	0.191565	−	0.272789i
$64$	6.08612			0.760765
$65$	9.63038	−	3.26440i	1.19450	−	0.404899i
$66$	0.478471	−	0.828736i	0.0588957	−	0.102010i
$67$	2.62934	+	1.51805i	0.321224	+	0.185459i	0.651938	−	0.758272i	$-0.273956\pi$
$67$	2.62934	+	1.51805i	0.321224	+	0.185459i	−0.330714	+	0.943731i	$0.607289\pi$
$68$	−9.21197	+	5.31853i	−1.11712	+	0.644967i
$69$	−7.63366			−0.918984
$70$	0.478621	−	1.63113i	0.0572062	−	0.194957i
$71$	−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	$-0.377344\pi$
$73$	−2.03961	−	1.17757i	−0.238718	−	0.137824i	−0.614588	+	0.788849i	$0.710678\pi$
$74$	−1.11425	+	1.92993i	−0.129529	+	0.224350i
$75$	−4.95779	+	0.648315i	−0.572476	+	0.0748610i
$76$	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	−0.977423	−	0.211292i	$-0.932233\pi$
$79$	−5.97016	−	10.3406i	−0.671696	−	1.16341i	0.305727	−	0.952119i	$-0.401101\pi$
$80$	5.17964	−	5.90106i	0.579101	−	0.659759i
$81$	−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	−0.972160	−	0.234319i	$-0.924714\pi$
$89$	−6.50007	−	11.2585i	−0.689006	−	1.19339i	0.283153	−	0.959075i	$-0.408619\pi$
$90$	−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
$95$	2.44454	−	2.78502i	0.250805	−	0.285737i
$96$	−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
$100$	−1.24310	−	9.50626i	−0.124310	−	0.950626i
$101$	−8.01983	+	13.8907i	−0.798002	+	1.38218i	0.122913	+	0.992417i	$0.460776\pi$
$101$	−8.01983	+	13.8907i	−0.798002	+	1.38218i	−0.920915	+	0.389763i	$0.872557\pi$
$102$	1.38045	+	0.797004i	0.136685	+	0.0789151i
$103$	4.58293	−	2.64596i	0.451570	−	0.260714i	−0.256923	−	0.966432i	$-0.582709\pi$
$103$	4.58293	−	2.64596i	0.451570	−	0.260714i	0.708493	+	0.705718i	$0.249375\pi$
$104$	5.11880			0.501940
$105$	5.74906	−	1.39581i	0.561051	−	0.136217i
$106$	−0.212570			−0.0206466
$107$	−4.47018	+	2.58086i	−0.432148	+	0.249501i	−0.700261	−	0.713886i	$-0.746933\pi$
$107$	−4.47018	+	2.58086i	−0.432148	+	0.249501i	0.268113	+	0.963387i	$0.413600\pi$
$108$	−1.66055	−	0.958719i	−0.159787	−	0.0922528i
$109$	1.62043	−	2.80668i	0.155209	−	0.268831i	−0.777926	−	0.628356i	$-0.783728\pi$
$109$	1.62043	−	2.80668i	0.155209	−	0.268831i	0.933135	+	0.359525i	$0.117061\pi$
$110$	2.02653	−	0.686930i	0.193222	−	0.0654962i
$111$	−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
$115$	−12.8285	−	11.2602i	−1.19627	−	1.05002i
$116$	−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
$130$	1.92744	−	2.19589i	0.169047	−	0.192592i
$131$	2.64893	+	4.58808i	0.231438	+	0.400862i	0.958231	−	0.285994i	$-0.0923237\pi$
$131$	2.64893	+	4.58808i	0.231438	+	0.400862i	−0.726794	+	0.686856i	$0.758990\pi$
$132$			6.38582i			0.555815i
$133$	−2.51982	+	3.58824i	−0.218496	+	0.311140i
$134$	0.872379			0.0753621
$135$	−2.11771	+	0.717839i	−0.182264	+	0.0617817i
$136$	−3.12221	+	5.40783i	−0.267727	+	0.463718i
$137$	12.8779	+	7.43507i	1.10023	+	0.635221i	0.936283	−	0.351247i	$-0.114242\pi$
$137$	12.8779	+	7.43507i	1.10023	+	0.635221i	0.163952	+	0.986468i	$0.447576\pi$
$138$	−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	$0.367757\pi$
$140$	2.67639	+	11.0235i	0.226196	+	0.931653i
$141$	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
$145$	0.0851767	+	0.251282i	0.00707354	+	0.0208678i
$146$	−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	0.999234	−	0.0391236i	$-0.0124566\pi$
$149$	5.68502	+	9.84675i	0.465735	+	0.806677i	−0.533499	+	0.845801i	$0.679123\pi$
$150$	−1.14056	+	0.873602i	−0.0931259	+	0.0713293i
$151$	−4.47016	+	7.74255i	−0.363777	+	0.630080i	−0.988579	−	0.150703i	$-0.951846\pi$
$151$	−4.47016	+	7.74255i	−0.363777	+	0.630080i	0.624802	+	0.780783i	$0.285180\pi$
$152$	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	$-0.375965\pi$
$157$	−2.89800	−	1.67316i	−0.231286	−	0.133533i	−0.611165	+	0.791503i	$0.709299\pi$
$158$	−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	$-0.454995\pi$
$163$	13.6450	−	7.87793i	1.06876	−	0.617047i	0.927842	+	0.372974i	$0.121662\pi$
$164$	−0.0672922	+	0.116553i	−0.00525463	+	0.00910129i
$165$	5.59680	+	4.91258i	0.435711	+	0.382444i
$166$	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
$170$	1.14424	+	3.37565i	0.0877592	+	0.258900i
$171$	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	$-0.561599\pi$
$173$	7.38391	−	4.26310i	0.561388	−	0.324118i	0.753703	+	0.657216i	$0.228266\pi$
$174$	0.0340944			0.00258469
$175$	11.7204	+	6.13459i	0.885976	+	0.463732i
$176$	−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	−0.997709	−	0.0676564i	$-0.978448\pi$
$179$	−5.89031	+	10.2023i	−0.440262	+	0.762557i	0.557446	+	0.830213i	$0.311781\pi$
$180$	−1.37641	−	4.06058i	−0.102592	−	0.302658i
$181$	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
$185$	−13.0337	−	11.4403i	−0.958254	−	0.841105i
$186$	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	−0.951809	−	0.306692i	$-0.900778\pi$
$191$	−10.2478	−	17.7498i	−0.741507	−	1.28433i	0.210302	−	0.977637i	$-0.432555\pi$
$192$	5.27073	+	3.04306i	0.380382	+	0.219614i
$193$	−7.39842	−	4.27148i	−0.532550	−	0.307468i	0.209504	−	0.977808i	$-0.432815\pi$
$193$	−7.39842	−	4.27148i	−0.532550	−	0.307468i	−0.742054	+	0.670340i	$0.766148\pi$
$194$	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	−0.790988	−	0.611832i	$-0.790433\pi$
$199$	1.89549	−	3.28309i	0.134368	−	0.232732i	0.925356	+	0.379100i	$0.123766\pi$
$200$	−3.42228	−	4.46805i	−0.241992	−	0.315939i
$201$	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
$205$	0.0503848	+	0.148642i	0.00351903	+	0.0103816i
$206$	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
$210$	1.23006	−	1.17329i	0.0848824	−	0.0809647i
$211$	−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
$215$	−6.20450	+	2.10313i	−0.423143	+	0.143432i
$216$	−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
$220$	−9.41956	+	10.7315i	−0.635067	+	0.723519i
$221$	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	$-0.237025\pi$
$227$	7.77575	+	4.48933i	0.516095	+	0.297967i	−0.219241	+	0.975671i	$0.570358\pi$
$228$	2.75192	+	1.58882i	0.182250	+	0.105222i
$229$	−2.54306	−	4.40471i	−0.168050	−	0.291071i	0.769684	−	0.638425i	$-0.220414\pi$
$229$	−2.54306	−	4.40471i	−0.168050	−	0.291071i	−0.937734	+	0.347354i	$0.887080\pi$
$230$	−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	$-0.413239\pi$
$233$	18.8952	−	10.9091i	1.23786	−	0.714681i	0.968657	+	0.248401i	$0.0799052\pi$
$234$	0.653336	−	1.13161i	0.0427099	−	0.0739757i
$235$	10.7315	+	9.41956i	0.700048	+	0.614465i
$236$	−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	$0.577449\pi$
$240$	7.43623	−	2.52065i	0.480007	−	0.162707i
$241$	12.0879	−	20.9368i	0.778650	−	1.34866i	−0.154070	−	0.988060i	$-0.549238\pi$
$241$	12.0879	−	20.9368i	0.778650	−	1.34866i	0.932720	−	0.360601i	$-0.117428\pi$
$242$	−0.0227753	−	0.0131493i	−0.00146405	−	0.000845271i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−14.0319			−0.898297
$245$	−14.5702	−	5.71924i	−0.930855	−	0.365389i
$246$	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
$250$	−3.20536	−	0.214294i	−0.202725	−	0.0135532i
$251$	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
$255$	−8.18303	+	9.32277i	−0.512441	+	0.583814i
$256$	−4.89810	+	8.48376i	−0.306131	+	0.530235i
$257$	−6.35139	+	3.66697i	−0.396189	+	0.228740i	−0.684838	−	0.728695i	$-0.740127\pi$
$257$	−6.35139	+	3.66697i	−0.396189	+	0.228740i	0.288650	+	0.957435i	$0.406794\pi$
$258$			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	$-0.427827\pi$
$263$	−8.21661	−	4.74386i	−0.506658	−	0.292519i	−0.731459	+	0.681886i	$0.761160\pi$
$264$	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	−0.510677	−	0.859772i	$-0.670605\pi$
$269$	8.02423	−	13.8984i	0.489246	−	0.847399i	0.999923	+	0.0123733i	$0.00393863\pi$
$270$	−0.423842	+	0.482874i	−0.0257942	+	0.0293868i
$271$	−12.0845	−	20.9309i	−0.734080	−	1.27146i	−0.955126	−	0.296201i	$-0.904280\pi$
$271$	−12.0845	−	20.9309i	−0.734080	−	1.27146i	0.221045	−	0.975264i	$-0.429053\pi$
$272$		−	19.4799i		−	1.18114i
$273$	−11.9844	−	1.06500i	−0.725331	−	0.0644570i
$274$	4.27272			0.258125
$275$	2.15914	+	16.5114i	0.130201	+	0.995675i
$276$	7.31853	−	12.6761i	0.440524	−	0.763010i
$277$	20.1071	+	11.6088i	1.20812	+	0.697508i	0.962348	−	0.271820i	$-0.0876257\pi$
$277$	20.1071	+	11.6088i	1.20812	+	0.697508i	0.245771	+	0.969328i	$0.420959\pi$
$278$	2.36818	−	1.36727i	0.142034	−	0.0820032i
$279$	6.26020			0.374789
$280$	4.59629	+	4.81870i	0.274681	+	0.287972i
$281$	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	$-0.250394\pi$
$283$	7.50649	+	4.33388i	0.446215	+	0.257622i	−0.260016	+	0.965604i	$0.583728\pi$
$284$	3.61483	−	6.26107i	0.214501	−	0.371526i
$285$	3.50954	−	1.18963i	0.207887	−	0.0704674i
$286$	−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
$290$	0.0572965	+	0.0502918i	0.00336456	+	0.00295324i
$291$	−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
$305$	−10.7946	+	12.2981i	−0.618098	+	0.704187i
$306$	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
$310$	3.80930	−	1.29123i	0.216354	−	0.0733372i
$311$	−14.2994	+	24.7672i	−0.810843	+	1.40442i	0.101432	+	0.994842i	$0.467657\pi$
$311$	−14.2994	+	24.7672i	−0.810843	+	1.40442i	−0.912275	+	0.409578i	$0.865676\pi$
$312$	4.43301	+	2.55940i	0.250970	+	0.144898i
$313$	−11.5429	+	6.66427i	−0.652441	+	0.376687i	−0.789391	−	0.613891i	$-0.789603\pi$
$313$	−11.5429	+	6.66427i	−0.652441	+	0.376687i	0.136950	+	0.990578i	$0.456270\pi$
$314$	−0.961518			−0.0542616
$315$	5.67674	+	1.66572i	0.319848	+	0.0938527i
$316$	22.8948			1.28794
$317$	−25.2815	+	14.5963i	−1.41995	+	0.819808i	−0.996294	−	0.0860147i	$-0.972587\pi$
$317$	−25.2815	+	14.5963i	−1.41995	+	0.819808i	−0.423656	+	0.905823i	$0.639253\pi$
$318$	−0.184091	−	0.106285i	−0.0103233	−	0.00596016i
$319$	0.197587	−	0.342231i	0.0110628	−	0.0191613i
$320$	4.36885	+	12.8886i	0.244226	+	0.720497i
$321$	−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
$325$	13.8261	+	18.0511i	0.766935	+	1.00129i
$326$	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	0.973725	+	0.227727i	$0.0731293\pi$
$331$	12.4457	+	21.5566i	0.684080	+	1.18486i	−0.289646	+	0.957134i	$0.593537\pi$
$332$	−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
$340$	−17.8758	−	15.6905i	−0.969453	−	0.850934i
$341$	−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
$345$	−5.47973	−	16.1659i	−0.295019	−	0.870342i
$346$	1.22494	−	2.12166i	0.0658533	−	0.114061i
$347$	−12.2615	−	7.07915i	−0.658229	−	0.380029i	0.133373	−	0.991066i	$-0.457419\pi$
$347$	−12.2615	−	7.07915i	−0.658229	−	0.380029i	−0.791602	+	0.611037i	$0.790753\pi$
$348$	−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	$0.543149\pi$
$350$	3.79784	−	0.157306i	0.203003	−	0.00840838i
$351$	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	$-0.192404\pi$
$353$	13.9417	+	8.04924i	0.742042	+	0.428418i	−0.0807694	+	0.996733i	$0.525738\pi$
$354$	−0.234193	+	0.405635i	−0.0124472	+	0.0215592i
$355$	−2.70660	−	7.98480i	−0.143651	−	0.423789i
$356$	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	0.870041	−	0.492979i	$-0.164092\pi$
$359$	0.153241	+	0.265421i	0.00808776	+	0.0140084i	−0.861953	+	0.506988i	$0.830759\pi$
$360$	−1.89163	−	1.66037i	−0.0996977	−	0.0875093i
$361$	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	$-0.121579\pi$
$367$	20.4813	+	11.8249i	1.06911	+	0.617253i	0.141174	+	0.989985i	$0.454912\pi$
$368$	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	$-0.828827\pi$
$373$	−16.3140	+	9.41887i	−0.844705	+	0.487691i	0.0141557	+	0.999900i	$0.495494\pi$
$374$	2.65434	−	4.59744i	0.137252	−	0.237728i
$375$	−4.93184	−	10.0338i	−0.254679	−	0.518143i
$376$	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	$0.619298\pi$
$380$	2.28103	+	6.72933i	0.117015	+	0.345208i
$381$	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	$-0.445534\pi$
$383$	21.6995	−	12.5282i	1.10879	−	0.640161i	0.938516	+	0.345235i	$0.112201\pi$
$384$	8.26917			0.421984
$385$	−4.64861	−	19.1466i	−0.236915	−	0.975803i
$386$	−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	−0.984716	−	0.174169i	$-0.944276\pi$
$389$	−6.73590	+	11.6669i	−0.341524	+	0.591536i	0.643192	+	0.765705i	$0.277610\pi$
$390$	2.76715	−	0.937979i	0.140120	−	0.0474964i
$391$	−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
$395$	17.6129	−	20.0660i	0.886199	−	1.00963i
$396$	−3.19291	+	5.53029i	−0.160450	+	0.277907i
$397$	−15.9768	+	9.22418i	−0.801850	+	0.462948i	−0.844118	−	0.536158i	$-0.819875\pi$
$397$	−15.9768	+	9.22418i	−0.801850	+	0.462948i	0.0422675	+	0.999106i	$0.486542\pi$
$398$		−	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	−0.986585	−	0.163249i	$-0.947803\pi$
$401$	−12.7093	−	22.0131i	−0.634670	−	1.09928i	0.351915	−	0.936032i	$-0.385531\pi$
$402$	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	−0.999113	−	0.0420997i	$-0.986595\pi$
$409$	−9.36556	+	16.2216i	−0.463097	+	0.802108i	0.536016	+	0.844208i	$0.319929\pi$
$410$	0.0338928	+	0.0297493i	0.00167385	+	0.00146921i
$411$	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
$415$	−2.59231	+	0.878713i	−0.127252	+	0.0431343i
$416$	−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	$0.515926\pi$
$420$	−3.19392	+	10.8848i	−0.155847	+	0.531124i
$421$	−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
$425$	−27.5035	+	3.59655i	−1.33412	+	0.174458i
$426$	−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
$430$	−1.24178	+	1.41473i	−0.0598837	+	0.0682244i
$431$	−18.3063	+	31.7075i	−0.881784	+	1.52729i	−0.0324277	+	0.999474i	$0.510324\pi$
$431$	−18.3063	+	31.7075i	−0.881784	+	1.52729i	−0.849356	+	0.527820i	$0.823009\pi$
$432$	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	0.536727	−	0.843756i	$-0.319660\pi$
$439$	−9.68731	−	16.7789i	−0.462350	−	0.800814i	−0.999078	+	0.0429418i	$0.986327\pi$
$440$	−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	$-0.794400\pi$
$443$	−14.2396	+	8.22121i	−0.676542	+	0.390602i	0.122009	+	0.992529i	$0.461066\pi$
$444$	7.43556	−	12.8788i	0.352876	−	0.611199i
$445$	19.1762	−	21.8470i	0.909038	−	1.03565i
$446$	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	$0.219165\pi$
$450$	−1.42455	+	0.186284i	−0.0671540	+	0.00878152i
$451$	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
$455$	−18.5692	−	19.4677i	−0.870535	−	0.912659i
$456$	1.86542			0.0873561
$457$	32.4156	−	18.7152i	1.51634	−	0.875459i	0.516523	−	0.856273i	$-0.327226\pi$
$457$	32.4156	−	18.7152i	1.51634	−	0.875459i	0.999816	−	0.0191857i	$-0.00610737\pi$
$458$	−1.26563	−	0.730712i	−0.0591390	−	0.0341439i
$459$	−2.77377	+	4.80431i	−0.129469	+	0.224246i
$460$	30.9971	−	10.5071i	1.44525	−	0.489894i
$461$	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
$465$	10.5204	+	9.23426i	0.487873	+	0.428229i
$466$	3.13458	−	5.42926i	0.145207	−	0.251506i
$467$	−10.4607	+	6.03950i	−0.484065	+	0.279475i	−0.722109	−	0.691779i	$-0.756827\pi$
$467$	−10.4607	+	6.03950i	−0.484065	+	0.279475i	0.238044	+	0.971254i	$0.423494\pi$
$468$			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	−0.538819	−	0.842421i	$-0.681129\pi$
$479$	10.0708	−	17.4432i	0.460149	−	0.797001i	0.998968	+	0.0454204i	$0.0144627\pi$
$480$	4.80904	−	5.47885i	0.219502	−	0.250074i
$481$	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
$485$	−6.44432	+	2.18443i	−0.292622	+	0.0991896i
$486$	−0.143668	+	0.248840i	−0.00651691	+	0.0112876i
$487$	−34.5887	−	19.9698i	−1.56737	−	0.904919i	−0.996475	−	0.0838930i	$-0.973265\pi$
$487$	−34.5887	−	19.9698i	−1.56737	−	0.904919i	−0.570891	−	0.821026i	$-0.693402\pi$
$488$	−7.13372	+	4.11866i	−0.322928	+	0.186443i
$489$	15.7559			0.712505
$490$	−4.44732	+	0.670092i	−0.200909	+	0.0302717i
$491$	−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
$495$	2.39069	+	7.05282i	0.107453	+	0.317001i
$496$	−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	0.839241	+	0.543759i	$0.183000\pi$
$499$	19.8929	+	34.4556i	0.890530	+	1.54244i	0.0512890	+	0.998684i	$0.483667\pi$
$500$	19.2392	−	9.45650i	0.860402	−	0.422907i
$501$	−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	0.952437	+	0.304737i	$0.0985685\pi$
$509$	16.6981	+	28.9219i	0.740128	+	1.28194i	−0.212308	+	0.977203i	$0.568098\pi$
$510$	−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
$515$	8.89318	+	7.80596i	0.391880	+	0.343972i
$516$	−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
$520$	3.67448	+	10.8402i	0.161136	+	0.475372i
$521$	−6.77589	+	11.7362i	−0.296857	+	0.514172i	−0.975415	−	0.220375i	$-0.929272\pi$
$521$	−6.77589	+	11.7362i	−0.296857	+	0.514172i	0.678558	+	0.734547i	$0.262605\pi$
$522$	0.0295266	+	0.0170472i	0.00129235	+	0.000746136i
$523$	17.5052	−	10.1066i	0.765450	−	0.441933i	−0.0657991	−	0.997833i	$-0.520960\pi$
$523$	17.5052	−	10.1066i	0.765450	−	0.441933i	0.831249	+	0.555900i	$0.187626\pi$
$524$	−10.1583			−0.443768
$525$	7.08283	+	11.1729i	0.309120	+	0.487625i
$526$	−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
$530$	−0.152591	−	0.450162i	−0.00662812	−	0.0195538i
$531$	−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
$535$	−8.67438	−	7.61391i	−0.375026	−	0.329178i
$536$	−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	0.965317	+	0.261082i	$0.0840794\pi$
$541$	16.4854	+	28.5535i	0.708762	+	1.22761i	−0.256554	+	0.966530i	$0.582587\pi$
$542$	−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
$550$	2.90944	+	3.79850i	0.124059	+	0.161969i
$551$	−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
$555$	−5.56736	−	16.4244i	−0.236321	−	0.697177i
$556$	−9.12399	+	15.8032i	−0.386943	+	0.670206i
$557$	20.7796	+	11.9971i	0.880460	+	0.508334i	0.870810	−	0.491620i	$-0.163595\pi$
$557$	20.7796	+	11.9971i	0.880460	+	0.508334i	0.00964963	+	0.999953i	$0.496928\pi$
$558$	1.55779	−	0.899391i	0.0659465	−	0.0380742i
$559$	13.3234			0.563521
$560$	−19.9336	−	5.84909i	−0.842347	−	0.247169i
$561$	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	$-0.334853\pi$
$563$	−0.196151	−	0.113248i	−0.00826680	−	0.00477284i	−0.504128	+	0.863629i	$0.668186\pi$
$564$	−6.12221	+	10.6040i	−0.257792	+	0.446508i
$565$	−26.8119	+	9.08840i	−1.12799	+	0.382352i
$566$	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	0.700036	−	0.714108i	$-0.253167\pi$
$569$	−6.40275	−	11.0899i	−0.268417	−	0.464912i	−0.968453	+	0.249195i	$0.919834\pi$
$570$	0.702404	−	0.800236i	0.0294205	−	0.0335182i
$571$	0.780149	−	1.35126i	0.0326482	−	0.0565484i	−0.849240	−	0.528008i	$-0.822939\pi$
$571$	0.780149	−	1.35126i	0.0326482	−	0.0565484i	0.881888	+	0.471459i	$0.156273\pi$
$572$	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	−0.995709	−	0.0925443i	$-0.970500\pi$
$577$	−37.8018	−	21.8249i	−1.57371	−	0.908581i	−0.578000	−	0.816037i	$-0.696167\pi$
$578$	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
$585$	7.64225	+	6.70796i	0.315968	+	0.277340i
$586$	−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
$590$	−0.991909	+	0.336226i	−0.0408362	+	0.0138422i
$591$	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	$-0.726859\pi$
$593$	−7.92838	+	4.57745i	−0.325579	+	0.187973i	0.328297	+	0.944574i	$0.393525\pi$
$594$	0.956942			0.0392638
$595$	31.8931	−	7.74333i	1.30749	−	0.317446i
$596$	−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	−0.0808467	−	0.996727i	$-0.525762\pi$
$599$	20.1368	−	34.8780i	0.822767	−	1.42507i	0.903614	−	0.428348i	$-0.140904\pi$
$600$	−0.729756	−	5.58059i	−0.0297922	−	0.227827i
$601$	−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
$605$	0.135007	−	0.153811i	0.00548883	−	0.00625332i
$606$	−2.30438	+	3.99131i	−0.0936092	+	0.162136i
$607$	−24.3409	+	14.0532i	−0.987966	+	0.570402i	−0.904666	−	0.426122i	$-0.859879\pi$
$607$	−24.3409	+	14.0532i	−0.987966	+	0.570402i	−0.0833003	+	0.996524i	$0.526546\pi$
$608$			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	$-0.319744\pi$
$613$	1.83025	+	1.05670i	0.0739232	+	0.0426796i	−0.462583	+	0.886576i	$0.653077\pi$
$614$	−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	−0.974792	−	0.223114i	$-0.928378\pi$
$619$	−7.31895	+	12.6768i	−0.294173	+	0.509523i	0.680619	+	0.732638i	$0.261711\pi$
$620$	−17.7061	+	20.1722i	−0.711095	+	0.810137i
$621$	−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
$625$	6.51251	−	24.1368i	0.260501	−	0.965474i
$626$	−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
$630$	1.65191	−	0.401067i	0.0658137	−	0.0159789i
$631$	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
$635$	35.0429	−	11.8785i	1.39064	−	0.471383i
$636$	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
$640$	13.8965	+	12.1976i	0.549308	+	0.482154i
$641$	6.52024	−	11.2934i	0.257534	−	0.446062i	−0.708047	−	0.706166i	$-0.750423\pi$
$641$	6.52024	−	11.2934i	0.257534	−	0.446062i	0.965581	+	0.260104i	$0.0837567\pi$
$642$	−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	$-0.574661\pi$
$647$	−30.2927	−	17.4895i	−1.19093	−	0.687582i	−0.958517	+	0.285035i	$0.907995\pi$
$648$	−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	$-0.448491\pi$
$653$	28.0168	−	16.1755i	1.09638	−	0.632997i	0.935269	+	0.353939i	$0.115158\pi$
$654$	0.465609	−	0.806458i	0.0182067	−	0.0315350i
$655$	−7.81473	+	8.90317i	−0.305347	+	0.347875i
$656$	−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	$0.553211\pi$
$660$	−13.5233	+	4.58399i	−0.526395	+	0.178432i
$661$	15.1715	−	26.2779i	0.590104	−	1.02209i	−0.404114	−	0.914709i	$-0.632420\pi$
$661$	15.1715	−	26.2779i	0.590104	−	1.02209i	0.994218	−	0.107382i	$-0.0342467\pi$
$662$	6.19400	+	3.57611i	0.240737	+	0.138989i
$663$	21.8478	−	12.6138i	0.848498	−	0.489881i
$664$	−1.37788			−0.0534722
$665$	−9.40768	−	2.76049i	−0.364814	−	0.107047i
$666$	−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
$670$	0.626227	+	1.84745i	0.0241933	+	0.0713731i
$671$	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
$675$	−3.04035	−	3.96942i	−0.117023	−	0.152783i
$676$	7.36308	−	12.7532i	0.283195	−	0.490509i
$677$	−20.2833	+	11.7105i	−0.779549	+	0.450073i	−0.836270	−	0.548317i	$-0.815269\pi$
$677$	−20.2833	+	11.7105i	−0.779549	+	0.450073i	0.0567215	+	0.998390i	$0.481935\pi$
$678$			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	−0.953845	−	0.300299i	$-0.902913\pi$
$683$	−44.1887	−	25.5124i	−1.69083	−	0.976204i	−0.736989	−	0.675904i	$-0.763753\pi$
$684$	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
$690$	−3.68610	−	3.23546i	−0.140327	−	0.123172i
$691$	−12.3057	−	21.3142i	−0.468133	−	0.810829i	0.531204	−	0.847244i	$-0.321740\pi$
$691$	−12.3057	−	21.3142i	−0.468133	−	0.810829i	−0.999337	+	0.0364144i	$0.988406\pi$
$692$			16.3485i			0.621476i
$693$	−3.71294	−	7.99092i	−0.141043	−	0.303550i
$694$	−4.06819			−0.154426
$695$	6.83157	+	20.1540i	0.259136	+	0.764483i
$696$	−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
$700$	−21.4233	+	13.5809i	−0.809726	+	0.513309i
$701$	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
$705$	4.58399	+	13.5233i	0.172643	+	0.509319i
$706$	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	0.954772	−	0.297339i	$-0.0960993\pi$
$709$	5.85482	+	10.1408i	0.219882	+	0.380848i	−0.734889	+	0.678187i	$0.762766\pi$
$710$	−1.82067	−	1.59809i	−0.0683285	−	0.0599751i
$711$	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	0.727989	−	0.685589i	$-0.240455\pi$
$719$	−6.16037	−	10.6701i	−0.229743	−	0.397927i	−0.957732	+	0.287662i	$0.907122\pi$
$720$	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
$725$	−0.470999	+	0.360759i	−0.0174925	+	0.0133983i
$726$	−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
$730$	−0.485773	−	1.43309i	−0.0179793	−	0.0530410i
$731$	−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	$-0.607327\pi$
$733$	8.69135	−	5.01795i	0.321022	−	0.185342i	0.651848	+	0.758349i	$0.273994\pi$
$734$	6.79541			0.250823
$735$	−9.75853	−	12.2381i	−0.359949	−	0.451409i
$736$	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	0.424910	+	0.905235i	$0.360306\pi$
$739$	−15.5360	+	26.9092i	−0.571502	+	0.989870i	−0.996412	+	0.0846345i	$0.973028\pi$
$740$	31.4928	−	10.6751i	1.15770	−	0.392423i
$741$	−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
$745$	−16.7717	+	19.1076i	−0.614466	+	0.700049i
$746$	−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	0.700268	−	0.713881i	$-0.253064\pi$
$751$	−7.34725	−	12.7258i	−0.268105	−	0.464371i	−0.968372	+	0.249509i	$0.919731\pi$
$752$	−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
$760$	3.13487	+	2.75163i	0.113714	+	0.0998120i
$761$	7.12611	+	12.3428i	0.258321	+	0.447426i	0.965792	−	0.259317i	$-0.0834974\pi$
$761$	7.12611	+	12.3428i	0.258321	+	0.447426i	−0.707471	+	0.706742i	$0.750164\pi$
$762$		−	4.75470i		−	0.172245i
$763$	−8.54088	−	0.758990i	−0.309200	−	0.0274773i
$764$	39.2992			1.42179
$765$	−11.7481	+	3.98224i	−0.424753	+	0.143978i
$766$	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	$0.378642\pi$
$770$	−3.90752	−	4.09660i	−0.140817	−	0.147631i
$771$	−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	$-0.0558811\pi$
$773$	36.8580	+	21.2800i	1.32569	+	0.765387i	0.341059	+	0.940042i	$0.389214\pi$
$774$	−0.420920	+	0.729054i	−0.0151296	+	0.0262053i
$775$	4.05858	+	31.0368i	0.145789	+	1.11487i
$776$	−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
$780$	−12.8621	+	14.6535i	−0.460537	+	0.524681i
$781$	−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	$-0.481598\pi$
$787$	−21.8231	−	12.5996i	−0.777909	−	0.449126i	−0.835689	+	0.549203i	$0.814931\pi$
$788$	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
$795$	1.09125	−	1.24324i	0.0387027	−	0.0440933i
$796$	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
$800$	16.1634	−	2.11364i	0.571463	−	0.0747284i
$801$	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
$805$	−12.7155	+	43.3343i	−0.448164	+	1.52733i
$806$	−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	−0.0964371	+	0.995339i	$0.530745\pi$
$809$	−25.8890	+	44.8410i	−0.910207	+	1.57653i	−0.813770	+	0.581187i	$0.802589\pi$
$810$	−0.608495	+	0.206261i	−0.0213803	+	0.00724726i
$811$	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
$815$	26.4781	+	23.2411i	0.927487	+	0.814099i
$816$	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	0.786882	−	0.617103i	$-0.211694\pi$
$821$	−4.03967	−	6.99692i	−0.140985	−	0.244194i	−0.927868	+	0.372909i	$0.878360\pi$
$822$	3.70029	+	2.13636i	0.129062	+	0.0745142i
$823$	4.42994	+	2.55762i	0.154418	+	0.0891532i	0.575218	−	0.818000i	$-0.304917\pi$
$823$	4.42994	+	2.55762i	0.154418	+	0.0891532i	−0.420800	+	0.907153i	$0.638251\pi$
$824$	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	−0.563750	−	0.825945i	$-0.690642\pi$
$829$	12.4790	−	21.6143i	0.433415	−	0.750696i	0.997165	+	0.0752491i	$0.0239752\pi$
$830$	−0.518828	+	0.591091i	−0.0180088	+	0.0205171i
$831$	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
$835$	−47.8479	+	16.2190i	−1.65585	+	0.561280i
$836$	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	$0.435610\pi$
$840$	1.57116	+	6.47126i	0.0542100	+	0.223280i
$841$	−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
$845$	−5.51309	−	16.2643i	−0.189656	−	0.559509i
$846$	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
$850$	−6.32728	+	4.84634i	−0.217024	+	0.166228i
$851$	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	$-0.515392\pi$
$857$	−27.4455	−	15.8456i	−0.937519	−	0.541277i	−0.889182	+	0.457554i	$0.848726\pi$
$858$	−3.76871	−	2.17587i	−0.128662	−	0.0742828i
$859$	−21.8456	−	37.8377i	−0.745363	−	1.29101i	−0.950025	−	0.312174i	$-0.898943\pi$
$859$	−21.8456	−	37.8377i	−0.745363	−	1.29101i	0.204662	−	0.978833i	$-0.434390\pi$
$860$	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	$-0.896262\pi$
$863$	−33.6005	+	19.3992i	−1.14377	+	0.660358i	−0.196411	+	0.980522i	$0.562929\pi$
$864$	1.63010	−	2.82342i	0.0554572	−	0.0960547i
$865$	14.3285	+	12.5768i	0.487183	+	0.427623i
$866$	−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
$870$	0.0244743	+	0.0722022i	0.000829757	+	0.00244788i
$871$	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
$875$	−4.57798	+	29.2240i	−0.154764	+	0.987951i
$876$	4.51583			0.152576
$877$	−3.72454	+	2.15036i	−0.125769	+	0.0726127i	−0.561565	−	0.827433i	$-0.689800\pi$
$877$	−3.72454	+	2.15036i	−0.125769	+	0.0726127i	0.435796	+	0.900046i	$0.356467\pi$
$878$	−4.82118	−	2.78351i	−0.162707	−	0.0939390i
$879$	13.5031	−	23.3881i	0.455450	−	0.788862i
$880$	−8.39476	−	24.7656i	−0.282987	−	0.834848i
$881$	−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
$885$	−2.73942	−	2.40452i	−0.0920847	−	0.0808271i
$886$	−2.36225	+	4.09153i	−0.0793613	+	0.137458i
$887$	−8.73964	+	5.04584i	−0.293449	+	0.169423i	−0.639496	−	0.768794i	$-0.720857\pi$
$887$	−8.73964	+	5.04584i	−0.293449	+	0.169423i	0.346047	+	0.938217i	$0.387524\pi$
$888$		−	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
$900$	7.61111	−	5.82969i	0.253704	−	0.194323i
$901$	−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
$905$	6.52492	+	19.2493i	0.216896	+	0.639869i
$906$	−1.28444	+	2.22471i	−0.0426726	+	0.0739111i
$907$	3.69531	+	2.13349i	0.122701	+	0.0708414i	0.560094	−	0.828429i	$-0.310765\pi$
$907$	3.69531	+	2.13349i	0.122701	+	0.0708414i	−0.437393	+	0.899270i	$0.644098\pi$
$908$	−14.9095	+	8.60802i	−0.494790	+	0.285667i
$909$	−16.0397			−0.532002
$910$	−7.41763	−	2.17655i	−0.245892	−	0.0721519i
$911$	−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
$915$	−15.4975	+	5.25316i	−0.512331	+	0.173664i
$916$	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	−0.938642	−	0.344894i	$-0.887915\pi$
$919$	−23.2822	−	40.3259i	−0.768008	−	1.33023i	0.170634	−	0.985335i	$-0.445419\pi$
$920$	12.6747	−	14.4401i	0.417873	−	0.476075i
$921$	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	0.920288	−	0.391242i	$-0.127954\pi$
$929$	3.69774	+	6.40467i	0.121319	+	0.210130i	−0.798969	+	0.601372i	$0.794621\pi$
$930$	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
$935$	31.0485	+	27.2527i	1.01539	+	0.891259i
$936$	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
$940$	−25.9302	+	8.78952i	−0.845749	+	0.286683i
$941$	−18.0180	+	31.2080i	−0.587369	+	1.01735i	0.407206	+	0.913336i	$0.366503\pi$
$941$	−18.0180	+	31.2080i	−0.587369	+	1.01735i	−0.994576	+	0.104017i	$0.966830\pi$
$942$	−0.832699	−	0.480759i	−0.0271308	−	0.0156640i
$943$	−0.464020	+	0.267902i	−0.0151106	+	0.00872408i
$944$	5.72401			0.186301
$945$	4.08334	+	4.28093i	0.132831	+	0.139259i
$946$	2.80366			0.0911548
$947$	29.6476	−	17.1170i	0.963417	−	0.556229i	0.0661943	−	0.997807i	$-0.478914\pi$
$947$	29.6476	−	17.1170i	0.963417	−	0.556229i	0.897223	+	0.441577i	$0.145581\pi$
$948$	19.8275	+	11.4474i	0.643968	+	0.371795i
$949$	−5.35504	+	9.27521i	−0.173832	+	0.301086i
$950$	2.36081	−	0.308716i	0.0765949	−	0.0100161i
$951$	−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
$955$	30.2326	−	34.4434i	0.978305	−	1.11456i
$956$	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
$970$	−1.28977	+	1.46942i	−0.0414122	+	0.0471801i
$971$	−22.3468	−	38.7058i	−0.717144	−	1.24213i	−0.962127	−	0.272602i	$-0.912116\pi$
$971$	−22.3468	−	38.7058i	−0.717144	−	1.24213i	0.244983	−	0.969527i	$-0.421218\pi$
$972$		−	1.91744i		−	0.0615019i
$973$	−10.6100	−	22.8346i	−0.340141	−	0.732045i
$974$	−11.4761			−0.367718
$975$	2.94824	+	22.5458i	0.0944192	+	0.722042i
$976$	12.8484	−	22.2541i	0.411268	−	0.712337i
$977$	−12.5029	−	7.21858i	−0.400005	−	0.230943i	0.286481	−	0.958086i	$-0.407514\pi$
$977$	−12.5029	−	7.21858i	−0.400005	−	0.230943i	−0.686486	+	0.727143i	$0.740848\pi$
$978$	3.92069	−	2.26361i	0.125370	−	0.0723824i
$979$	−43.2956			−1.38373
$980$	23.4658	−	18.7114i	0.749587	−	0.597713i
$981$	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	$-0.247061\pi$
$983$	14.5389	+	8.39401i	0.463717	+	0.267727i	−0.249889	+	0.968275i	$0.580394\pi$
$984$	−0.0395034	+	0.0684220i	−0.00125932	+	0.00218121i
$985$	29.2426	−	9.91233i	0.931747	−	0.315833i
$986$	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
$990$	1.60816	+	1.41156i	0.0511108	+	0.0448623i
$991$	−20.0539	+	34.7344i	−0.637033	+	1.10337i	0.349048	+	0.937105i	$0.386505\pi$
$991$	−20.0539	+	34.7344i	−0.637033	+	1.10337i	−0.986081	+	0.166268i	$0.946828\pi$
$992$	−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	$-0.0313488\pi$
$997$	44.4447	+	25.6602i	1.40758	+	0.812666i	0.412424	+	0.910992i	$0.364682\pi$
$998$	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.4.5	yes	16
3.2	odd	2		315.2.bf.b.109.4		16
4.3	odd	2		1680.2.di.d.529.3		16
5.2	odd	4		525.2.i.h.151.3		8
5.3	odd	4		525.2.i.k.151.2		8
5.4	even	2	inner	105.2.q.a.4.4	✓	16
7.2	even	3	inner	105.2.q.a.79.4	yes	16
7.3	odd	6		735.2.d.e.589.5		8
7.4	even	3		735.2.d.d.589.5		8
7.5	odd	6		735.2.q.g.79.4		16
7.6	odd	2		735.2.q.g.214.5		16
15.14	odd	2		315.2.bf.b.109.5		16
20.19	odd	2		1680.2.di.d.529.7		16
21.2	odd	6		315.2.bf.b.289.5		16
21.11	odd	6		2205.2.d.s.1324.4		8
21.17	even	6		2205.2.d.o.1324.4		8
28.23	odd	6		1680.2.di.d.289.7		16
35.2	odd	12		525.2.i.h.226.3		8
35.3	even	12		3675.2.a.bn.1.3		4
35.4	even	6		735.2.d.d.589.4		8
35.9	even	6	inner	105.2.q.a.79.5	yes	16
35.17	even	12		3675.2.a.cb.1.2		4
35.18	odd	12		3675.2.a.bp.1.3		4
35.19	odd	6		735.2.q.g.79.5		16
35.23	odd	12		525.2.i.k.226.2		8
35.24	odd	6		735.2.d.e.589.4		8
35.32	odd	12		3675.2.a.bz.1.2		4
35.34	odd	2		735.2.q.g.214.4		16
105.44	odd	6		315.2.bf.b.289.4		16
105.59	even	6		2205.2.d.o.1324.5		8
105.74	odd	6		2205.2.d.s.1324.5		8
140.79	odd	6		1680.2.di.d.289.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	5.4	even	2	inner
105.2.q.a.4.5	yes	16	1.1	even	1	trivial
105.2.q.a.79.4	yes	16	7.2	even	3	inner
105.2.q.a.79.5	yes	16	35.9	even	6	inner
315.2.bf.b.109.4		16	3.2	odd	2
315.2.bf.b.109.5		16	15.14	odd	2
315.2.bf.b.289.4		16	105.44	odd	6
315.2.bf.b.289.5		16	21.2	odd	6
525.2.i.h.151.3		8	5.2	odd	4
525.2.i.h.226.3		8	35.2	odd	12
525.2.i.k.151.2		8	5.3	odd	4
525.2.i.k.226.2		8	35.23	odd	12
735.2.d.d.589.4		8	35.4	even	6
735.2.d.d.589.5		8	7.4	even	3
735.2.d.e.589.4		8	35.24	odd	6
735.2.d.e.589.5		8	7.3	odd	6
735.2.q.g.79.4		16	7.5	odd	6
735.2.q.g.79.5		16	35.19	odd	6
735.2.q.g.214.4		16	35.34	odd	2
735.2.q.g.214.5		16	7.6	odd	2
1680.2.di.d.289.3		16	140.79	odd	6
1680.2.di.d.289.7		16	28.23	odd	6
1680.2.di.d.529.3		16	4.3	odd	2
1680.2.di.d.529.7		16	20.19	odd	2
2205.2.d.o.1324.4		8	21.17	even	6
2205.2.d.o.1324.5		8	105.59	even	6
2205.2.d.s.1324.4		8	21.11	odd	6
2205.2.d.s.1324.5		8	105.74	odd	6
3675.2.a.bn.1.3		4	35.3	even	12
3675.2.a.bp.1.3		4	35.18	odd	12
3675.2.a.bz.1.2		4	35.32	odd	12
3675.2.a.cb.1.2		4	35.17	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.248840 - 0.143668i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(0.717839 + 2.11771i) q^{5} +0.287336 q^{6} +(-1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.248840 - 0.143668i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.958719 + 1.66055i) q^{4} +(0.717839 + 2.11771i) q^{5} +0.287336 q^{6} +(-1.11487 - 2.39939i) q^{7} +1.12562i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.482874 + 0.423842i) 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} +(-3.96942 + 3.04035i) q^{25} +(-0.653336 - 1.13161i) q^{26} +1.00000i q^{27} +(5.05315 + 0.449051i) q^{28} +0.118657 q^{29} +(0.206261 + 0.608495i) q^{30} +(3.13010 - 5.42150i) q^{31} +(-2.82342 - 1.63010i) q^{32} +(2.88421 - 1.66520i) q^{33} +1.59401 q^{34} +(4.28093 - 4.08334i) q^{35} -1.91744 q^{36} +(-6.71665 + 3.87786i) q^{37} +(-0.412386 - 0.238091i) q^{38} +(2.27377 - 3.93829i) q^{39} +(-2.38374 + 0.808014i) q^{40} +0.0701896 q^{41} +(-0.320341 - 0.689431i) q^{42} +2.92981i q^{43} +(3.19291 + 5.53029i) q^{44} +(-1.47507 + 1.68052i) 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} +(-3.22230 - 2.82836i) q^{60} +(3.65901 + 6.33759i) q^{61} -1.79878i q^{62} +(1.52050 - 2.16520i) q^{63} +6.08612 q^{64} +(9.63038 - 3.26440i) q^{65} +(0.478471 - 0.828736i) q^{66} +(2.62934 + 1.51805i) q^{67} +(-9.21197 + 5.31853i) q^{68} -7.63366 q^{69} +(0.478621 - 1.63113i) q^{70} -3.77048 q^{71} +(-0.974816 + 0.562810i) q^{72} +(-2.03961 - 1.17757i) q^{73} +(-1.11425 + 1.92993i) q^{74} +(-4.95779 + 0.648315i) q^{75} +3.17764 q^{76} +(-8.77681 - 0.779956i) q^{77} -1.30667i q^{78} +(-5.97016 - 10.3406i) q^{79} +(5.17964 - 5.90106i) 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} +(2.44454 - 2.78502i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^5 - 8 * q^6 + 8 * q^9	\( 16 q + 8 q^{4} + 2 q^{5} - 8 q^{6} + 8 q^{9} - 4 q^{10} - 24 q^{14} - 4 q^{15} - 24 q^{19} - 8 q^{20} - 4 q^{21} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 24 q^{29} - 12 q^{30} + 16 q^{31} + 16 q^{34} - 10 q^{35} + 16 q^{36} - 4 q^{39} + 32 q^{40} + 16 q^{41} + 20 q^{44} - 2 q^{45} - 32 q^{46} - 40 q^{49} - 40 q^{50} + 4 q^{51} - 4 q^{54} + 8 q^{55} + 84 q^{56} + 4 q^{59} + 16 q^{60} + 16 q^{61} + 16 q^{64} + 30 q^{65} + 28 q^{66} + 40 q^{69} + 16 q^{70} - 56 q^{71} + 40 q^{74} + 8 q^{75} - 64 q^{76} - 16 q^{79} + 52 q^{80} - 8 q^{81} + 12 q^{84} - 64 q^{85} - 48 q^{86} + 16 q^{89} - 8 q^{90} + 8 q^{91} - 32 q^{94} - 22 q^{95} + 8 q^{96}+O(q^{100}) \) 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

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