LMFDB - Embedded newform 403.2.v.a.36.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(36,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("403.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.v (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.4
Character	$\chi$	$=$	403.36
Dual form			403.2.v.a.56.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01769 + 1.16491i) q^{2} +2.06545 q^{3} +(1.71404 - 2.96880i) q^{4} +(-0.697719 + 0.402828i) q^{5} +(-4.16742 + 2.40606i) q^{6} +(-3.06444 + 1.76926i) q^{7} +3.32715i q^{8} +1.26608 q^{9} +O(q^{10})$	\(q+(-2.01769 + 1.16491i) q^{2} +2.06545 q^{3} +(1.71404 - 2.96880i) q^{4} +(-0.697719 + 0.402828i) q^{5} +(-4.16742 + 2.40606i) q^{6} +(-3.06444 + 1.76926i) q^{7} +3.32715i q^{8} +1.26608 q^{9} +(0.938518 - 1.62556i) q^{10} +(-2.36827 - 1.36732i) q^{11} +(3.54025 - 6.13190i) q^{12} +(-2.60889 + 2.48871i) q^{13} +(4.12205 - 7.13960i) q^{14} +(-1.44110 + 0.832021i) q^{15} +(-0.447763 - 0.775548i) q^{16} +(-2.93982 - 5.09192i) q^{17} +(-2.55455 + 1.47487i) q^{18} +(-1.53113 + 0.883997i) q^{19} +2.76185i q^{20} +(-6.32945 + 3.65431i) q^{21} +6.37124 q^{22} +(0.351079 + 0.608087i) q^{23} +6.87206i q^{24} +(-2.17546 + 3.76800i) q^{25} +(2.36479 - 8.06056i) q^{26} -3.58133 q^{27} +12.1303i q^{28} +(4.10411 + 7.10853i) q^{29} +(1.93846 - 3.35751i) q^{30} +(0.598037 + 5.53555i) q^{31} +(-3.95590 - 2.28394i) q^{32} +(-4.89154 - 2.82413i) q^{33} +(11.8633 + 6.84926i) q^{34} +(1.42541 - 2.46889i) q^{35} +(2.17010 - 3.75873i) q^{36} -2.38216i q^{37} +(2.05956 - 3.56725i) q^{38} +(-5.38853 + 5.14031i) q^{39} +(-1.34027 - 2.32142i) q^{40} +(-0.418594 - 0.241675i) q^{41} +(8.51389 - 14.7465i) q^{42} +(-2.03967 - 3.53280i) q^{43} +(-8.11860 + 4.68728i) q^{44} +(-0.883367 + 0.510012i) q^{45} +(-1.41673 - 0.817952i) q^{46} -9.08357i q^{47} +(-0.924831 - 1.60185i) q^{48} +(2.76054 - 4.78139i) q^{49} -10.1369i q^{50} +(-6.07205 - 10.5171i) q^{51} +(2.91675 + 12.0110i) q^{52} +(-3.69225 - 6.39516i) q^{53} +(7.22599 - 4.17193i) q^{54} +2.20318 q^{55} +(-5.88658 - 10.1959i) q^{56} +(-3.16246 + 1.82585i) q^{57} +(-16.5616 - 9.56184i) q^{58} +(5.50412 - 3.17780i) q^{59} +5.70445i q^{60} +(-6.21086 + 10.7575i) q^{61} +(-7.65508 - 10.4723i) q^{62} +(-3.87982 + 2.24002i) q^{63} +12.4334 q^{64} +(0.817750 - 2.78736i) q^{65} +13.1595 q^{66} +(8.65854 + 4.99901i) q^{67} -20.1558 q^{68} +(0.725136 + 1.25597i) q^{69} +6.64192i q^{70} +3.95870i q^{71} +4.21243i q^{72} +(4.67556 - 2.69944i) q^{73} +(2.77500 + 4.80645i) q^{74} +(-4.49330 + 7.78262i) q^{75} +6.06081i q^{76} +9.67658 q^{77} +(4.88436 - 16.6487i) q^{78} +(1.97766 - 3.42541i) q^{79} +(0.624825 + 0.360743i) q^{80} -11.1953 q^{81} +1.12612 q^{82} +(-11.8553 + 6.84466i) q^{83} +25.0545i q^{84} +(4.10234 + 2.36849i) q^{85} +(8.23080 + 4.75206i) q^{86} +(8.47683 + 14.6823i) q^{87} +(4.54929 - 7.87960i) q^{88} +(-3.76741 + 2.17512i) q^{89} +(1.18824 - 2.05809i) q^{90} +(3.59163 - 12.2423i) q^{91} +2.40705 q^{92} +(1.23522 + 11.4334i) q^{93} +(10.5815 + 18.3278i) q^{94} +(0.712198 - 1.23356i) q^{95} +(-8.17072 - 4.71736i) q^{96} +(12.4981 + 7.21579i) q^{97} +12.8631i q^{98} +(-2.99842 - 1.73114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.01769	+	1.16491i	−1.42672	+	0.823716i	−0.996860	−	0.0791799i	$-0.974770\pi$
$2$	−2.01769	+	1.16491i	−1.42672	+	0.823716i	−0.429858	+	0.902896i	$0.641437\pi$
$3$	2.06545			1.19249			0.596244	−	0.802804i	$-0.296659\pi$
$3$	2.06545			1.19249			0.596244	+	0.802804i	$0.296659\pi$
$4$	1.71404	−	2.96880i	0.857018	−	1.48440i
$5$	−0.697719	+	0.402828i	−0.312029	+	0.180150i	−0.647834	−	0.761781i	$-0.724325\pi$
$5$	−0.697719	+	0.402828i	−0.312029	+	0.180150i	0.335805	+	0.941932i	$0.390992\pi$
$6$	−4.16742	+	2.40606i	−1.70134	+	0.982271i
$7$	−3.06444	+	1.76926i	−1.15825	+	0.668716i	−0.950884	−	0.309547i	$-0.899822\pi$
$7$	−3.06444	+	1.76926i	−1.15825	+	0.668716i	−0.207366	+	0.978263i	$0.566489\pi$
$8$			3.32715i			1.17633i
$9$	1.26608			0.422026
$10$	0.938518	−	1.62556i	0.296786	−	0.514048i
$11$	−2.36827	−	1.36732i	−0.714061	−	0.412263i	0.0985020	−	0.995137i	$-0.468595\pi$
$11$	−2.36827	−	1.36732i	−0.714061	−	0.412263i	−0.812563	+	0.582874i	$0.801928\pi$
$12$	3.54025	−	6.13190i	1.02198	−	1.77013i
$13$	−2.60889	+	2.48871i	−0.723576	+	0.690245i
$13$	−2.60889	+	2.48871i	−0.723576	+	0.690245i
$14$	4.12205	−	7.13960i	1.10166	−	1.90814i
$15$	−1.44110	+	0.832021i	−0.372091	+	0.214827i
$16$	−0.447763	−	0.775548i	−0.111941	−	0.193887i
$17$	−2.93982	−	5.09192i	−0.713012	−	1.23497i	−0.963721	−	0.266910i	$-0.913997\pi$
$17$	−2.93982	−	5.09192i	−0.713012	−	1.23497i	0.250710	−	0.968062i	$-0.419336\pi$
$18$	−2.55455	+	1.47487i	−0.602113	+	0.347630i
$19$	−1.53113	+	0.883997i	−0.351265	+	0.202803i	−0.665242	−	0.746628i	$-0.731672\pi$
$19$	−1.53113	+	0.883997i	−0.351265	+	0.202803i	0.313977	+	0.949430i	$0.398338\pi$
$20$			2.76185i			0.617568i
$21$	−6.32945	+	3.65431i	−1.38120	+	0.797435i
$22$	6.37124			1.35835
$23$	0.351079	+	0.608087i	0.0732051	+	0.126795i	0.900304	−	0.435261i	$-0.143344\pi$
$23$	0.351079	+	0.608087i	0.0732051	+	0.126795i	−0.827099	+	0.562056i	$0.810011\pi$
$24$			6.87206i			1.40275i
$25$	−2.17546	+	3.76800i	−0.435092	+	0.753601i
$26$	2.36479	−	8.06056i	0.463774	−	1.58081i
$27$	−3.58133			−0.689227
$28$			12.1303i			2.29241i
$29$	4.10411	+	7.10853i	0.762114	+	1.32002i	0.941759	+	0.336289i	$0.109172\pi$
$29$	4.10411	+	7.10853i	0.762114	+	1.32002i	−0.179645	+	0.983732i	$0.557495\pi$
$30$	1.93846	−	3.35751i	0.353913	−	0.612995i
$31$	0.598037	+	5.53555i	0.107411	+	0.994215i
$31$	0.598037	+	5.53555i	0.107411	+	0.994215i
$32$	−3.95590	−	2.28394i	−0.699312	−	0.403748i
$33$	−4.89154	−	2.82413i	−0.851509	−	0.491619i
$34$	11.8633	+	6.84926i	2.03453	+	1.17464i
$35$	1.42541	−	2.46889i	0.240939	−	0.417318i
$36$	2.17010	−	3.75873i	0.361684	−	0.626455i
$37$		−	2.38216i		−	0.391625i	−0.980641	−	0.195812i	$-0.937266\pi$
$37$		−	2.38216i		−	0.391625i	0.980641	−	0.195812i	$-0.0627343\pi$
$38$	2.05956	−	3.56725i	0.334104	−	0.578685i
$39$	−5.38853	+	5.14031i	−0.862855	+	0.823108i
$40$	−1.34027	−	2.32142i	−0.211915	−	0.367048i
$41$	−0.418594	−	0.241675i	−0.0653734	−	0.0377433i	0.466957	−	0.884280i	$-0.345350\pi$
$41$	−0.418594	−	0.241675i	−0.0653734	−	0.0377433i	−0.532330	+	0.846537i	$0.678684\pi$
$42$	8.51389	−	14.7465i	1.31372	−	2.27543i
$43$	−2.03967	−	3.53280i	−0.311046	−	0.538748i	0.667543	−	0.744571i	$-0.267346\pi$
$43$	−2.03967	−	3.53280i	−0.311046	−	0.538748i	−0.978589	+	0.205824i	$0.934013\pi$
$44$	−8.11860	+	4.68728i	−1.22393	+	0.706634i
$45$	−0.883367	+	0.510012i	−0.131685	+	0.0760281i
$46$	−1.41673	−	0.817952i	−0.208886	−	0.120600i
$47$		−	9.08357i		−	1.32497i	−0.749073	−	0.662487i	$-0.769501\pi$
$47$		−	9.08357i		−	1.32497i	0.749073	−	0.662487i	$-0.230499\pi$
$48$	−0.924831	−	1.60185i	−0.133488	−	0.231208i
$49$	2.76054	−	4.78139i	0.394362	−	0.683056i
$50$		−	10.1369i		−	1.43357i
$51$	−6.07205	−	10.5171i	−0.850258	−	1.47269i
$52$	2.91675	+	12.0110i	0.404480	+	1.66563i
$53$	−3.69225	−	6.39516i	−0.507170	−	0.878443i	−0.999966	−	0.00829857i	$-0.997358\pi$
$53$	−3.69225	−	6.39516i	−0.507170	−	0.878443i	0.492796	−	0.870145i	$-0.335975\pi$
$54$	7.22599	−	4.17193i	0.983333	−	0.567727i
$55$	2.20318			0.297077
$56$	−5.88658	−	10.1959i	−0.786627	−	1.36248i
$57$	−3.16246	+	1.82585i	−0.418879	+	0.241840i
$58$	−16.5616	−	9.56184i	−2.17464	−	1.25553i
$59$	5.50412	−	3.17780i	0.716575	−	0.413715i	−0.0969157	−	0.995293i	$-0.530898\pi$
$59$	5.50412	−	3.17780i	0.716575	−	0.413715i	0.813491	+	0.581578i	$0.197564\pi$
$60$			5.70445i			0.736442i
$61$	−6.21086	+	10.7575i	−0.795219	+	1.37736i	0.127481	+	0.991841i	$0.459311\pi$
$61$	−6.21086	+	10.7575i	−0.795219	+	1.37736i	−0.922700	+	0.385519i	$0.874022\pi$
$62$	−7.65508	−	10.4723i	−0.972196	−	1.32999i
$63$	−3.87982	+	2.24002i	−0.488812	+	0.282216i
$64$	12.4334			1.55418
$65$	0.817750	−	2.78736i	0.101429	−	0.345729i
$66$	13.1595			1.61982
$67$	8.65854	+	4.99901i	1.05781	+	0.610726i	0.924825	−	0.380392i	$-0.124211\pi$
$67$	8.65854	+	4.99901i	1.05781	+	0.610726i	0.132983	+	0.991118i	$0.457544\pi$
$68$	−20.1558			−2.44425
$69$	0.725136	+	1.25597i	0.0872961	+	0.151201i
$70$			6.64192i			0.793861i
$71$			3.95870i			0.469811i	0.972018	+	0.234906i	$0.0754781\pi$
$71$			3.95870i			0.469811i	−0.972018	+	0.234906i	$0.924522\pi$
$72$			4.21243i			0.496440i
$73$	4.67556	−	2.69944i	0.547233	−	0.315945i	−0.200772	−	0.979638i	$-0.564345\pi$
$73$	4.67556	−	2.69944i	0.547233	−	0.315945i	0.748005	+	0.663693i	$0.231012\pi$
$74$	2.77500	+	4.80645i	0.322588	+	0.558738i
$75$	−4.49330	+	7.78262i	−0.518841	+	0.898660i
$76$			6.06081i			0.695222i
$77$	9.67658			1.10275
$78$	4.88436	−	16.6487i	0.553045	−	1.88509i
$79$	1.97766	−	3.42541i	0.222504	−	0.385388i	−0.733064	−	0.680160i	$-0.761910\pi$
$79$	1.97766	−	3.42541i	0.222504	−	0.385388i	0.955568	+	0.294772i	$0.0952436\pi$
$80$	0.624825	+	0.360743i	0.0698576	+	0.0403323i
$81$	−11.1953			−1.24392
$82$	1.12612			0.124359
$83$	−11.8553	+	6.84466i	−1.30129	+	0.751299i	−0.980625	−	0.195894i	$-0.937239\pi$
$83$	−11.8553	+	6.84466i	−1.30129	+	0.751299i	−0.320663	+	0.947193i	$0.603906\pi$
$84$			25.0545i			2.73366i
$85$	4.10234	+	2.36849i	0.444961	+	0.256899i
$86$	8.23080	+	4.75206i	0.887550	+	0.512427i
$87$	8.47683	+	14.6823i	0.908811	+	1.57411i
$88$	4.54929	−	7.87960i	0.484956	−	0.839968i
$89$	−3.76741	+	2.17512i	−0.399345	+	0.230562i	−0.686201	−	0.727412i	$-0.740723\pi$
$89$	−3.76741	+	2.17512i	−0.399345	+	0.230562i	0.286856	+	0.957974i	$0.407390\pi$
$90$	1.18824	−	2.05809i	0.125251	−	0.216942i
$91$	3.59163	−	12.2423i	0.376505	−	1.28334i
$92$	2.40705			0.250952
$93$	1.23522	+	11.4334i	0.128086	+	1.18559i
$94$	10.5815	+	18.3278i	1.09140	+	1.89037i
$95$	0.712198	−	1.23356i	0.0730700	−	0.126561i
$96$	−8.17072	−	4.71736i	−0.833920	−	0.481464i
$97$	12.4981	+	7.21579i	1.26899	+	0.732652i	0.974797	−	0.223093i	$-0.0716155\pi$
$97$	12.4981	+	7.21579i	1.26899	+	0.732652i	0.294194	+	0.955746i	$0.404949\pi$
$98$			12.8631i			1.29937i
$99$	−2.99842	−	1.73114i	−0.301352	−	0.173986i
$100$	7.45763	+	12.9170i	0.745763	+	1.29170i
$101$	8.08689	+	14.0069i	0.804676	+	1.39374i	0.916510	+	0.400012i	$0.130994\pi$
$101$	8.08689	+	14.0069i	0.804676	+	1.39374i	−0.111834	+	0.993727i	$0.535673\pi$
$102$	24.5030	+	14.1468i	2.42616	+	1.40074i
$103$	−3.73123	−	6.46268i	−0.367649	−	0.636787i	0.621548	−	0.783376i	$-0.286504\pi$
$103$	−3.73123	−	6.46268i	−0.367649	−	0.636787i	−0.989198	+	0.146589i	$0.953171\pi$
$104$	−8.28032	−	8.68017i	−0.811952	−	0.851161i
$105$	2.94412	−	5.09936i	0.287316	−	0.497647i
$106$	14.8996	+	8.60229i	1.44718	+	0.835528i
$107$	5.11246			0.494241			0.247120	−	0.968985i	$-0.420516\pi$
$107$	5.11246			0.494241			0.247120	+	0.968985i	$0.420516\pi$
$108$	−6.13852	+	10.6322i	−0.590679	+	1.02309i
$109$		−	9.88416i		−	0.946731i	−0.880866	−	0.473366i	$-0.843039\pi$
$109$		−	9.88416i		−	0.946731i	0.880866	−	0.473366i	$-0.156961\pi$
$110$	−4.44533	+	2.56651i	−0.423846	+	0.244708i
$111$		−	4.92023i		−	0.467007i
$112$	2.74429	+	1.58441i	0.259311	+	0.149713i
$113$	−5.51465			−0.518774			−0.259387	−	0.965773i	$-0.583521\pi$
$113$	−5.51465			−0.518774			−0.259387	+	0.965773i	$0.583521\pi$
$114$	4.25391	−	7.36798i	0.398415	−	0.690075i
$115$	−0.489909	−	0.282849i	−0.0456843	−	0.0263758i
$116$	28.1384			2.61258
$117$	−3.30306	+	3.15090i	−0.305368	+	0.291301i
$118$	−7.40372	+	12.8236i	−0.681567	+	1.18051i
$119$	18.0178	+	10.4026i	1.65169	+	0.953605i
$120$	−2.76826	−	4.79477i	−0.252706	−	0.437700i
$121$	−1.76086	−	3.04990i	−0.160078	−	0.277263i
$122$		−	28.9404i		−	2.62014i
$123$	−0.864584	−	0.499168i	−0.0779569	−	0.0450084i
$124$	17.4590	+	7.71268i	1.56786	+	0.692619i
$125$		−	7.53363i		−	0.673828i
$126$	5.21884	−	9.03930i	0.464931	−	0.805285i
$127$	−5.85647			−0.519678			−0.259839	−	0.965652i	$-0.583669\pi$
$127$	−5.85647			−0.519678			−0.259839	+	0.965652i	$0.583669\pi$
$128$	−17.1749	+	9.91593i	−1.51806	+	0.876453i
$129$	−4.21282	−	7.29682i	−0.370918	−	0.642450i
$130$	1.59706	+	6.57661i	0.140072	+	0.576807i
$131$	−2.37843	+	4.11956i	−0.207804	+	0.359928i	−0.951023	−	0.309121i	$-0.899965\pi$
$131$	−2.37843	+	4.11956i	−0.207804	+	0.359928i	0.743218	+	0.669049i	$0.233298\pi$
$132$	−16.7686	+	9.68133i	−1.45952	+	0.842652i
$133$	3.12803	−	5.41791i	0.271235	−	0.469793i
$134$	−23.2936			−2.01226
$135$	2.49876	−	1.44266i	0.215059	−	0.124164i
$136$	16.9416	−	9.78123i	1.45273	−	0.838734i
$137$			1.94034i			0.165774i	0.996559	+	0.0828872i	$0.0264141\pi$
$137$			1.94034i			0.165774i	−0.996559	+	0.0828872i	$0.973586\pi$
$138$	−2.92619	−	1.68944i	−0.249094	−	0.143815i
$139$	−6.94174	+	12.0234i	−0.588791	+	1.01982i	0.405600	+	0.914050i	$0.367062\pi$
$139$	−6.94174	+	12.0234i	−0.588791	+	1.01982i	−0.994391	+	0.105765i	$0.966271\pi$
$140$	−4.88642	−	8.46352i	−0.412978	−	0.715298i
$141$		−	18.7616i		−	1.58002i
$142$	−4.61153	−	7.98741i	−0.386991	−	0.670289i
$143$	9.58144	−	2.32675i	0.801240	−	0.194573i
$144$	−0.566903	−	0.981904i	−0.0472419	−	0.0818254i
$145$	−5.72703	−	3.30650i	−0.475604	−	0.274590i
$146$	−6.28921	+	10.8932i	−0.520498	+	0.901530i
$147$	5.70175	−	9.87571i	0.470272	−	0.814535i
$148$	−7.07215	−	4.08311i	−0.581327	−	0.335629i
$149$	−11.0996	+	6.40838i	−0.909318	+	0.524995i	−0.880212	−	0.474581i	$-0.842599\pi$
$149$	−11.0996	+	6.40838i	−0.909318	+	0.524995i	−0.0291064	+	0.999576i	$0.509266\pi$
$150$		−	20.9372i		−	1.70951i
$151$			10.1405i			0.825225i	0.910907	+	0.412612i	$0.135384\pi$
$151$			10.1405i			0.825225i	−0.910907	+	0.412612i	$0.864616\pi$
$152$	−2.94119	−	5.09429i	−0.238562	−	0.413201i
$153$	−3.72205	−	6.44677i	−0.300910	−	0.521191i
$154$	−19.5243	+	11.2723i	−1.57331	+	0.908352i
$155$	−2.64714	−	3.62136i	−0.212623	−	0.290874i
$156$	6.02439	+	24.8081i	0.482337	+	1.98624i
$157$	7.50882			0.599269			0.299634	−	0.954054i	$-0.403135\pi$
$157$	7.50882			0.599269			0.299634	+	0.954054i	$0.403135\pi$
$158$			9.21519i			0.733121i
$159$	−7.62615	−	13.2089i	−0.604793	−	1.04753i
$160$	3.68015			0.290941
$161$	−2.15172	−	1.24230i	−0.169580	−	0.0979068i
$162$	22.5885	−	13.0415i	1.77472	−	1.02464i
$163$	−1.99452	−	1.15154i	−0.156223	−	0.0901954i	0.419851	−	0.907593i	$-0.362082\pi$
$163$	−1.99452	−	1.15154i	−0.156223	−	0.0901954i	−0.576074	+	0.817398i	$0.695416\pi$
$164$	−1.43497	+	0.828480i	−0.112052	+	0.0646934i
$165$	4.55057			0.354261
$166$	15.9468	−	27.6207i	1.23771	−	2.14378i
$167$			12.3354i			0.954538i	0.878757	+	0.477269i	$0.158373\pi$
$167$			12.3354i			0.954538i	−0.878757	+	0.477269i	$0.841627\pi$
$168$	−12.1584	−	21.0590i	−0.938043	−	1.62474i
$169$	0.612625	−	12.9856i	0.0471250	−	0.998889i
$170$	−11.0363			−0.846446
$171$	−1.93853	+	1.11921i	−0.148243	+	0.0855881i
$172$	−13.9842			−1.06629
$173$	3.78841			0.288027			0.144014	−	0.989576i	$-0.453999\pi$
$173$	3.78841			0.288027			0.144014	+	0.989576i	$0.453999\pi$
$174$	−34.2071	−	19.7495i	−2.59324	−	1.49721i
$175$		−	15.3958i		−	1.16381i
$176$			2.44894i			0.184596i
$177$	11.3685	−	6.56359i	0.854507	−	0.493350i
$178$	5.06763	−	8.77740i	0.379835	−	0.657894i
$179$	13.7027			1.02419			0.512093	−	0.858930i	$-0.328870\pi$
$179$	13.7027			1.02419			0.512093	+	0.858930i	$0.328870\pi$
$180$			3.49672i			0.260630i
$181$	9.18766	+	15.9135i	0.682913	+	1.18284i	0.974088	+	0.226170i	$0.0726206\pi$
$181$	9.18766	+	15.9135i	0.682913	+	1.18284i	−0.291175	+	0.956670i	$0.594046\pi$
$182$	7.01443	+	28.8850i	0.519944	+	2.14110i
$183$	−12.8282	+	22.2191i	−0.948289	+	1.64248i
$184$	−2.02320	+	1.16809i	−0.149152	+	0.0861130i
$185$	0.959602	+	1.66208i	0.0705513	+	0.122198i
$186$	−15.8112	−	21.6301i	−1.15933	−	1.58599i
$187$			16.0787i			1.17579i
$188$	−26.9673	−	15.5696i	−1.96679	−	1.13553i
$189$	10.9748	−	6.33628i	0.798297	−	0.460897i
$190$			3.31859i			0.240756i
$191$	3.99548			0.289103			0.144552	−	0.989497i	$-0.453826\pi$
$191$	3.99548			0.289103			0.144552	+	0.989497i	$0.453826\pi$
$192$	25.6806			1.85334
$193$			5.99785i			0.431734i	0.976423	+	0.215867i	$0.0692578\pi$
$193$			5.99785i			0.431734i	−0.976423	+	0.215867i	$0.930742\pi$
$194$	−33.6230			−2.41399
$195$	1.68902	−	5.75714i	0.120953	−	0.412278i
$196$	−9.46331	−	16.3909i	−0.675951	−	1.17078i
$197$	6.92526	+	3.99830i	0.493404	+	0.284867i	0.725986	−	0.687710i	$-0.241384\pi$
$197$	6.92526	+	3.99830i	0.493404	+	0.284867i	−0.232581	+	0.972577i	$0.574717\pi$
$198$	8.06648			0.573260
$199$	24.3971			1.72946			0.864732	−	0.502234i	$-0.167488\pi$
$199$	24.3971			1.72946			0.864732	+	0.502234i	$0.167488\pi$
$200$	−12.5367	−	7.23808i	−0.886480	−	0.511809i
$201$	17.8838	+	10.3252i	1.26142	+	0.728283i
$202$	−32.6336	−	18.8410i	−2.29609	−	1.32565i
$203$	−25.1536	−	14.5224i	−1.76544	−	1.01928i
$204$	−41.6309			−2.91474
$205$	0.389415			0.0271979
$206$	15.0569	+	8.69310i	1.04906	+	0.605677i
$207$	0.444494	+	0.769886i	0.0308945	+	0.0535108i
$208$	3.09828	+	0.908967i	0.214827	+	0.0630256i
$209$	4.83483			0.334433
$210$			13.7185i			0.946669i
$211$	−16.5976			−1.14262			−0.571311	−	0.820733i	$-0.693565\pi$
$211$	−16.5976			−1.14262			−0.571311	+	0.820733i	$0.693565\pi$
$212$	−25.3146			−1.73861
$213$			8.17649i			0.560244i
$214$	−10.3153	+	5.95557i	−0.705142	+	0.407114i
$215$	2.84623	+	1.64327i	0.194111	+	0.112070i
$216$		−	11.9156i		−	0.810755i
$217$	−11.6265	−	15.9053i	−0.789256	−	1.07972i
$218$	11.5142	+	19.9431i	0.779838	+	1.35072i
$219$	9.65713	−	5.57555i	0.652569	−	0.376761i
$220$	3.77634	−	6.54081i	0.254601	−	0.440981i
$221$	20.3420	+	5.96790i	1.36835	+	0.401444i
$222$	5.73163	+	9.92747i	0.384682	+	0.666288i
$223$			6.07807i			0.407018i	0.979073	+	0.203509i	$0.0652346\pi$
$223$			6.07807i			0.407018i	−0.979073	+	0.203509i	$0.934765\pi$
$224$	16.1635			1.07997
$225$	−2.75430	+	4.77059i	−0.183620	+	0.318039i
$226$	11.1268	−	6.42407i	0.740145	−	0.427323i
$227$		−	21.2918i		−	1.41319i	−0.707620	−	0.706594i	$-0.750231\pi$
$227$		−	21.2918i		−	1.41319i	0.707620	−	0.706594i	$-0.249769\pi$
$228$			12.5183i			0.829044i
$229$	−21.3189	−	12.3084i	−1.40879	−	0.813365i	−0.413518	−	0.910496i	$-0.635700\pi$
$229$	−21.3189	−	12.3084i	−1.40879	−	0.813365i	−0.995272	+	0.0971311i	$0.969033\pi$
$230$	1.31798			0.0869048
$231$	19.9865			1.31501
$232$	−23.6511	+	13.6550i	−1.55277	+	0.896494i
$233$	−23.3202			−1.52776			−0.763878	−	0.645360i	$-0.776707\pi$
$233$	−23.3202			−1.52776			−0.763878	+	0.645360i	$0.776707\pi$
$234$	2.99401	−	10.2053i	0.195725	−	0.667142i
$235$	3.65912	+	6.33778i	0.238695	+	0.413431i
$236$		−	21.7875i		−	1.41824i
$237$	4.08475	−	7.07500i	0.265333	−	0.459571i
$238$	−48.4724			−3.14200
$239$	16.0766	−	9.28182i	1.03991	−	0.600391i	0.120101	−	0.992762i	$-0.461678\pi$
$239$	16.0766	−	9.28182i	1.03991	−	0.600391i	0.919807	+	0.392370i	$0.128345\pi$
$240$	1.29054	+	0.745096i	0.0833043	+	0.0480958i
$241$	−11.6897	+	6.74907i	−0.753002	+	0.434746i	−0.826778	−	0.562529i	$-0.809829\pi$
$241$	−11.6897	+	6.74907i	−0.753002	+	0.434746i	0.0737754	+	0.997275i	$0.476495\pi$
$242$	7.10572	+	4.10249i	0.456773	+	0.263718i
$243$	−12.3793			−0.794132
$244$	21.2913	+	36.8776i	1.36303	+	2.36084i
$245$			4.44809i			0.284178i
$246$	2.32594			0.148297
$247$	1.79453	−	6.11679i	0.114183	−	0.389202i
$248$	−18.4176	+	1.98976i	−1.16952	+	0.126350i
$249$	−24.4865	+	14.1373i	−1.55177	+	0.895915i
$250$	8.77601	+	15.2005i	0.555043	+	0.961363i
$251$	−15.1667	−	26.2695i	−0.957315	−	1.65812i	−0.728978	−	0.684537i	$-0.760005\pi$
$251$	−15.1667	−	26.2695i	−0.957315	−	1.65812i	−0.228337	−	0.973582i	$-0.573329\pi$
$252$			15.3579i			0.967455i
$253$		−	1.92015i		−	0.120719i
$254$	11.8165	−	6.82227i	0.741434	−	0.428067i
$255$	8.47318	+	4.89199i	0.530611	+	0.306348i
$256$	10.6689	−	18.4791i	0.666809	−	1.15495i
$257$	−9.39107	+	16.2658i	−0.585799	+	1.01463i	0.408977	+	0.912545i	$0.365886\pi$
$257$	−9.39107	+	16.2658i	−0.585799	+	1.01463i	−0.994775	+	0.102088i	$0.967448\pi$
$258$	17.0003	+	9.81513i	1.05839	+	0.611063i
$259$	4.21465	+	7.29999i	0.261886	+	0.453599i
$260$	−6.87344	−	7.20536i	−0.426273	−	0.446857i
$261$	5.19612	+	8.99995i	0.321632	+	0.557083i
$262$		−	11.0826i		−	0.684688i
$263$	−7.15072	−	12.3854i	−0.440932	−	0.763717i	0.556826	−	0.830629i	$-0.312019\pi$
$263$	−7.15072	−	12.3854i	−0.440932	−	0.763717i	−0.997759	+	0.0669115i	$0.978685\pi$
$264$	9.39632	−	16.2749i	0.578303	−	1.00165i
$265$	5.15231	+	2.97469i	0.316504	+	0.182733i
$266$			14.5755i			0.893683i
$267$	−7.78140	+	4.49259i	−0.476214	+	0.274942i
$268$	29.6821	−	17.1370i	1.81312	−	1.04681i
$269$	16.9523			1.03360			0.516801	−	0.856106i	$-0.327123\pi$
$269$	16.9523			1.03360			0.516801	+	0.856106i	$0.327123\pi$
$270$	−3.36114	+	5.82167i	−0.204552	+	0.354295i
$271$	8.85495	−	5.11241i	0.537900	−	0.310557i	−0.206328	−	0.978483i	$-0.566151\pi$
$271$	8.85495	−	5.11241i	0.537900	−	0.310557i	0.744227	+	0.667926i	$0.232818\pi$
$272$	−2.63269	+	4.55995i	−0.159630	+	0.276487i
$273$	7.41832	−	25.2859i	0.448977	−	1.53037i
$274$	−2.26032	−	3.91499i	−0.136551	−	0.236513i
$275$	10.3042	−	5.94911i	0.621364	−	0.358745i
$276$	4.97164			0.299257
$277$	−8.72500	+	15.1121i	−0.524234	+	0.908001i	0.475367	+	0.879787i	$0.342315\pi$
$277$	−8.72500	+	15.1121i	−0.524234	+	0.908001i	−0.999602	+	0.0282134i	$0.991018\pi$
$278$		−	32.3460i		−	1.93999i
$279$	0.757162	+	7.00844i	0.0453301	+	0.419585i
$280$	8.21436	+	4.74256i	0.490902	+	0.283422i
$281$			8.85673i			0.528348i	0.964475	+	0.264174i	$0.0850994\pi$
$281$			8.85673i			0.528348i	−0.964475	+	0.264174i	$0.914901\pi$
$282$	21.8556	+	37.8551i	1.30148	+	2.25424i
$283$	−7.30420	−	12.6512i	−0.434189	−	0.752038i	0.563040	−	0.826430i	$-0.309632\pi$
$283$	−7.30420	−	12.6512i	−0.434189	−	0.752038i	−0.997229	+	0.0743918i	$0.976298\pi$
$284$	11.7526	+	6.78535i	0.697387	+	0.402637i
$285$	1.47101	−	2.54786i	0.0871350	−	0.150922i
$286$	−16.6219	+	15.8562i	−0.982871	+	0.937595i
$287$	1.71034			0.100958
$288$	−5.00848	−	2.89165i	−0.295128	−	0.170392i
$289$	−8.78512	+	15.2163i	−0.516772	+	0.895075i
$290$	15.4071			0.904738
$291$	25.8142	+	14.9038i	1.51326	+	0.873679i
$292$		−	18.5077i		−	1.08308i
$293$	−5.51079	+	3.18166i	−0.321944	+	0.185874i	−0.652259	−	0.757996i	$-0.726178\pi$
$293$	−5.51079	+	3.18166i	−0.321944	+	0.185874i	0.330315	+	0.943871i	$0.392845\pi$
$294$			26.5681i			1.54948i
$295$	−2.56022	+	4.43443i	−0.149062	+	0.258182i
$296$	7.92580			0.460678
$297$	8.48156	+	4.89683i	0.492150	+	0.284143i
$298$	14.9304	−	25.8602i	0.864894	−	1.49804i
$299$	−2.42928	−	0.712698i	−0.140489	−	0.0412164i
$300$	15.4033	+	26.6794i	0.889312	+	1.54033i
$301$	12.5009	+	7.21738i	0.720538	+	0.416003i
$302$	−11.8128	−	20.4604i	−0.679751	−	1.17736i
$303$	16.7031	+	28.9305i	0.959565	+	1.66202i
$304$	1.37116	+	0.791642i	0.0786416	+	0.0454038i
$305$		−	10.0076i		−	0.573036i
$306$	15.0198	+	8.67170i	0.858627	+	0.495728i
$307$	−29.3809	−	16.9631i	−1.67686	−	0.968133i	−0.963646	−	0.267183i	$-0.913907\pi$
$307$	−29.3809	−	16.9631i	−1.67686	−	0.968133i	−0.713210	−	0.700950i	$-0.752760\pi$
$308$	16.5860	−	28.7278i	0.945075	−	1.63692i
$309$	−7.70667	−	13.3483i	−0.438417	−	0.759360i
$310$	9.55965	+	4.22307i	0.542952	+	0.239854i
$311$	−27.7741			−1.57492			−0.787462	−	0.616363i	$-0.788605\pi$
$311$	−27.7741			−1.57492			−0.787462	+	0.616363i	$0.788605\pi$
$312$	−17.1026	−	17.9284i	−0.968242	−	1.01500i
$313$	−8.11192	+	14.0503i	−0.458513	+	0.794167i	−0.998883	−	0.0472602i	$-0.984951\pi$
$313$	−8.11192	+	14.0503i	−0.458513	+	0.794167i	0.540370	+	0.841428i	$0.318284\pi$
$314$	−15.1504	+	8.74710i	−0.854988	+	0.493628i
$315$	1.80468	−	3.12581i	0.101682	−	0.176119i
$316$	−6.77955	−	11.7425i	−0.381380	−	0.660569i
$317$	26.9183	+	15.5413i	1.51188	+	0.872886i	0.999904	+	0.0138883i	$0.00442094\pi$
$317$	26.9183	+	15.5413i	1.51188	+	0.872886i	0.511979	+	0.858998i	$0.328912\pi$
$318$	30.7743	+	17.7676i	1.72574	+	0.996356i
$319$		−	22.4466i		−	1.25677i
$320$	−8.67503	+	5.00853i	−0.484949	+	0.279985i
$321$	10.5595			0.589376
$322$	5.78867			0.322590
$323$	9.00249	+	5.19759i	0.500912	+	0.289202i
$324$	−19.1891	+	33.2365i	−1.06606	+	1.84647i
$325$	−3.70194	−	15.2444i	−0.205347	−	0.845607i
$326$	5.36575			0.297182
$327$		−	20.4152i		−	1.12897i
$328$	0.804090	−	1.39272i	0.0443984	−	0.0769003i
$329$	16.0712	+	27.8361i	0.886032	+	1.53465i
$330$	−9.18161	+	5.30100i	−0.505431	+	0.291811i
$331$		−	24.3269i		−	1.33713i	−0.743656	−	0.668563i	$-0.766910\pi$
$331$		−	24.3269i		−	1.33713i	0.743656	−	0.668563i	$-0.233090\pi$
$332$			46.9280i			2.57551i
$333$		−	3.01600i		−	0.165276i
$334$	−14.3696	−	24.8889i	−0.786269	−	1.36186i
$335$	−8.05497			−0.440090
$336$	5.66818	+	3.27253i	0.309225	+	0.178531i
$337$	28.4683			1.55077			0.775385	−	0.631489i	$-0.217556\pi$
$337$	28.4683			1.55077			0.775385	+	0.631489i	$0.217556\pi$
$338$	13.8909	+	26.9144i	0.755567	+	1.46395i
$339$	−11.3902			−0.618632
$340$	14.0631	−	8.11934i	0.762680	−	0.440333i
$341$	6.15257	−	13.9274i	0.333180	−	0.754211i
$342$	2.60756	−	4.51642i	0.141001	−	0.244220i
$343$		−	5.23321i		−	0.282567i
$344$	11.7542	−	6.78627i	0.633742	−	0.365891i
$345$	−1.01188	−	0.584211i	−0.0544779	−	0.0314528i
$346$	−7.64381	+	4.41316i	−0.410934	+	0.237253i
$347$	−11.6100	−	20.1091i	−0.623257	−	1.07951i	−0.988875	−	0.148748i	$-0.952476\pi$
$347$	−11.6100	−	20.1091i	−0.623257	−	1.07951i	0.365618	−	0.930765i	$-0.380858\pi$
$348$	58.1183			3.11547
$349$	−2.88824	+	1.66753i	−0.154604	+	0.0892606i	−0.575306	−	0.817938i	$-0.695117\pi$
$349$	−2.88824	+	1.66753i	−0.154604	+	0.0892606i	0.420702	+	0.907199i	$0.361784\pi$
$350$	17.9347	+	31.0638i	0.958651	+	1.66043i
$351$	9.34329	−	8.91289i	0.498708	−	0.475735i
$352$	6.24577	+	10.8180i	0.332901	+	0.576601i
$353$			22.3414i			1.18911i	0.804055	+	0.594556i	$0.202672\pi$
$353$			22.3414i			1.18911i	−0.804055	+	0.594556i	$0.797328\pi$
$354$	−15.2920	+	26.4865i	−0.812761	+	1.40774i
$355$	−1.59468	−	2.76206i	−0.0846367	−	0.146595i
$356$			14.9129i			0.790382i
$357$	37.2149	+	21.4860i	1.96962	+	1.13716i
$358$	−27.6477	+	15.9624i	−1.46123	+	0.843639i
$359$	−10.1347	+	5.85126i	−0.534888	+	0.308818i	−0.743005	−	0.669286i	$-0.766600\pi$
$359$	−10.1347	+	5.85126i	−0.534888	+	0.308818i	0.208117	+	0.978104i	$0.433267\pi$
$360$	−1.69689	−	2.93909i	−0.0894338	−	0.154904i
$361$	−7.93710	+	13.7475i	−0.417742	+	0.723550i
$362$	−37.0756	−	21.4056i	−1.94865	−	1.12505i
$363$	−3.63696	−	6.29940i	−0.190891	−	0.330633i
$364$	−30.1887	−	31.6466i	−1.58232	−	1.65873i
$365$	−2.17482	+	3.76690i	−0.113835	+	0.197168i
$366$		−	59.7749i		−	3.12448i
$367$	−12.8971	+	22.3384i	−0.673221	+	1.16605i	0.303764	+	0.952747i	$0.401756\pi$
$367$	−12.8971	+	22.3384i	−0.673221	+	1.16605i	−0.976985	+	0.213306i	$0.931577\pi$
$368$	0.314400	−	0.544558i	0.0163893	−	0.0283870i
$369$	−0.529972	−	0.305980i	−0.0275893	−	0.0159287i
$370$	−3.87235	−	2.23570i	−0.201314	−	0.116229i
$371$	22.6294	+	13.0651i	1.17486	+	0.678305i
$372$	36.0606	+	15.9302i	1.86966	+	0.825940i
$373$	0.300172	−	0.519913i	0.0155423	−	0.0269201i	−0.858150	−	0.513400i	$-0.828386\pi$
$373$	0.300172	−	0.519913i	0.0155423	−	0.0269201i	0.873692	+	0.486480i	$0.161719\pi$
$374$	−18.7303	−	32.4418i	−0.968521	−	1.67753i
$375$		−	15.5603i		−	0.803532i
$376$	30.2224			1.55860
$377$	−28.3982	−	8.33142i	−1.46258	−	0.429090i
$378$	−14.7624	+	25.5693i	−0.759297	+	1.31514i
$379$			2.97164i			0.152643i	0.997083	+	0.0763215i	$0.0243175\pi$
$379$			2.97164i			0.152643i	−0.997083	+	0.0763215i	$0.975682\pi$
$380$	−2.44146	−	4.22874i	−0.125244	−	0.216930i
$381$	−12.0962			−0.619709
$382$	−8.06163	+	4.65438i	−0.412469	+	0.238139i
$383$			18.4750i			0.944028i	0.881591	+	0.472014i	$0.156473\pi$
$383$			18.4750i			0.944028i	−0.881591	+	0.472014i	$0.843527\pi$
$384$	−35.4739	+	20.4808i	−1.81027	+	1.04516i
$385$	−6.75153	+	3.89800i	−0.344090	+	0.198660i
$386$	−6.98696	−	12.1018i	−0.355627	−	0.615964i
$387$	−2.58238	−	4.47281i	−0.131270	−	0.227365i
$388$	42.8444	−	24.7362i	2.17510	−	1.25579i
$389$	−5.26744	+	9.12347i	−0.267070	+	0.462578i	−0.968104	−	0.250549i	$-0.919389\pi$
$389$	−5.26744	+	9.12347i	−0.267070	+	0.462578i	0.701034	+	0.713128i	$0.252722\pi$
$390$	3.29865	+	13.5837i	0.167034	+	0.687835i
$391$	2.06422	−	3.57534i	0.104392	−	0.180813i
$392$	15.9084	+	9.18472i	0.803495	+	0.463898i
$393$	−4.91252	+	8.50874i	−0.247804	+	0.429209i
$394$	−18.6307			−0.938599
$395$			3.18663i			0.160337i
$396$	−10.2788	+	5.93446i	−0.516528	+	0.298218i
$397$	−14.1744	+	8.18360i	−0.711393	+	0.410723i	−0.811577	−	0.584246i	$-0.801390\pi$
$397$	−14.1744	+	8.18360i	−0.711393	+	0.410723i	0.100183	+	0.994969i	$0.468057\pi$
$398$	−49.2256	+	28.4204i	−2.46746	+	1.42459i
$399$	6.46079	−	11.1904i	0.323444	−	0.560222i
$400$	3.89636			0.194818
$401$	−7.41943	+	4.28361i	−0.370509	+	0.213913i	−0.673681	−	0.739023i	$-0.735288\pi$
$401$	−7.41943	+	4.28361i	−0.370509	+	0.213913i	0.303172	+	0.952936i	$0.401954\pi$
$402$	−48.1117			−2.39960
$403$	−15.3366	−	12.9533i	−0.763971	−	0.645251i
$404$	55.4449			2.75848
$405$	7.81116	−	4.50978i	0.388140	−	0.224093i
$406$	67.6694			3.35838
$407$	−3.25718	+	5.64160i	−0.161452	+	0.279644i
$408$	34.9920	−	20.2026i	1.73236	−	1.00018i
$409$	21.4781	−	12.4004i	1.06202	−	0.613159i	0.136032	−	0.990705i	$-0.456565\pi$
$409$	21.4781	−	12.4004i	1.06202	−	0.613159i	0.925991	+	0.377546i	$0.123232\pi$
$410$	−0.785716	+	0.453633i	−0.0388037	+	0.0224034i
$411$			4.00767i			0.197684i
$412$	−25.5818			−1.26033
$413$	−11.2447	+	19.4764i	−0.553315	+	0.958371i
$414$	−1.79370	−	1.03559i	−0.0881554	−	0.0508965i
$415$	5.51445	−	9.55130i	0.270694	−	0.468855i
$416$	16.0046	−	3.88655i	0.784690	−	0.190554i
$417$	−14.3378	+	24.8338i	−0.702125	+	1.21612i
$418$	−9.75517	+	5.63215i	−0.477141	+	0.275478i
$419$	−13.4278	−	23.2576i	−0.655990	−	1.13621i	−0.981645	−	0.190719i	$-0.938918\pi$
$419$	−13.4278	−	23.2576i	−0.655990	−	1.13621i	0.325654	−	0.945489i	$-0.394415\pi$
$420$	−10.0926	−	17.4810i	−0.492471	−	0.852984i
$421$	−24.9930	+	14.4297i	−1.21808	+	0.703261i	−0.964508	−	0.264055i	$-0.914940\pi$
$421$	−24.9930	+	14.4297i	−1.21808	+	0.703261i	−0.253576	+	0.967316i	$0.581607\pi$
$422$	33.4886	−	19.3347i	1.63020	−	0.941197i
$423$		−	11.5005i		−	0.559174i
$424$	21.2777	−	12.2847i	1.03334	−	0.596596i
$425$	25.5819			1.24090
$426$	−9.52489	−	16.4976i	−0.461482	−	0.799311i
$427$		−	43.9544i		−	2.12710i
$428$	8.76294	−	15.1779i	0.423573	−	0.733650i
$429$	19.7900	−	4.80579i	0.955468	−	0.232026i
$430$	−7.65705			−0.369256
$431$		−	19.8066i		−	0.954050i	−0.878890	−	0.477025i	$-0.841715\pi$
$431$		−	19.8066i		−	0.954050i	0.878890	−	0.477025i	$-0.158285\pi$
$432$	1.60358	+	2.77749i	0.0771525	+	0.133632i
$433$	14.7264	−	25.5068i	0.707704	−	1.22578i	−0.258003	−	0.966144i	$-0.583064\pi$
$433$	14.7264	−	25.5068i	0.707704	−	1.22578i	0.965707	−	0.259635i	$-0.0836023\pi$
$434$	41.9868	+	18.5481i	2.01543	+	0.890337i
$435$	−11.8289	−	6.82941i	−0.567152	−	0.327445i
$436$	−29.3441	−	16.9418i	−1.40533	−	0.811365i
$437$	−1.07509	−	0.620706i	−0.0514287	−	0.0296924i
$438$	−12.9900	+	22.4994i	−0.620688	+	1.07506i
$439$	12.7416	−	22.0691i	0.608124	−	1.05330i	−0.383425	−	0.923572i	$-0.625256\pi$
$439$	12.7416	−	22.0691i	0.608124	−	1.05330i	0.991549	−	0.129730i	$-0.0414110\pi$
$440$			7.33033i			0.349460i
$441$	3.49505	−	6.05361i	0.166431	−	0.288267i
$442$	−47.9958	+	11.6553i	−2.28293	+	0.554385i
$443$	−6.13857	−	10.6323i	−0.291652	−	0.505156i	0.682548	−	0.730840i	$-0.260872\pi$
$443$	−6.13857	−	10.6323i	−0.291652	−	0.505156i	−0.974201	+	0.225684i	$0.927538\pi$
$444$	−14.6072	−	8.43345i	−0.693225	−	0.400234i
$445$	1.75240	−	3.03524i	0.0830716	−	0.143884i
$446$	−7.08041	−	12.2636i	−0.335267	−	0.580700i
$447$	−22.9257	+	13.2362i	−1.08435	+	0.626050i
$448$	−38.1015	+	21.9979i	−1.80012	+	1.03930i
$449$	−12.7887	−	7.38357i	−0.603537	−	0.348452i	0.166895	−	0.985975i	$-0.446626\pi$
$449$	−12.7887	−	7.38357i	−0.603537	−	0.348452i	−0.770432	+	0.637522i	$0.779959\pi$
$450$		−	12.8341i		−	0.605003i
$451$	0.660896	+	1.14471i	0.0311204	+	0.0539021i
$452$	−9.45230	+	16.3719i	−0.444599	+	0.770068i
$453$			20.9447i			0.984070i
$454$	24.8031	+	42.9602i	1.16407	+	2.01622i
$455$	2.42560	+	9.98850i	0.113714	+	0.468268i
$456$	−6.07488	−	10.5220i	−0.284482	−	0.492738i
$457$	−18.0941	+	10.4467i	−0.846408	+	0.488674i	−0.859437	−	0.511241i	$-0.829186\pi$
$457$	−18.0941	+	10.4467i	−0.846408	+	0.488674i	0.0130294	+	0.999915i	$0.495853\pi$
$458$	57.3530			2.67993
$459$	10.5285	+	18.2358i	0.491427	+	0.851176i
$460$	−1.67944	+	0.969627i	−0.0783045	+	0.0452091i
$461$	−22.2598	−	12.8517i	−1.03674	−	0.598563i	−0.117833	−	0.993033i	$-0.537595\pi$
$461$	−22.2598	−	12.8517i	−1.03674	−	0.598563i	−0.918909	+	0.394470i	$0.870928\pi$
$462$	−40.3264	+	23.2825i	−1.87615	+	1.08320i
$463$			5.55846i			0.258323i	0.991624	+	0.129162i	$0.0412286\pi$
$463$			5.55846i			0.258323i	−0.991624	+	0.129162i	$0.958771\pi$
$464$	3.67534	−	6.36587i	0.170623	−	0.295528i
$465$	−5.46753	−	7.47972i	−0.253551	−	0.346864i
$466$	47.0528	−	27.1660i	2.17968	−	1.25844i
$467$	−26.9951			−1.24918			−0.624592	−	0.780951i	$-0.714735\pi$
$467$	−26.9951			−1.24918			−0.624592	+	0.780951i	$0.714735\pi$
$468$	3.69283	+	15.2069i	0.170701	+	0.702938i
$469$	−35.3781			−1.63361
$470$	−14.7659	−	8.52510i	−0.681100	−	0.393233i
$471$	15.5091			0.714621
$472$	10.5730	+	18.3130i	0.486663	+	0.842925i
$473$			11.1555i			0.512931i
$474$			19.0335i			0.874237i
$475$		−	7.69239i		−	0.352951i
$476$	61.7664	−	35.6608i	2.83106	−	1.63451i
$477$	−4.67468	−	8.09678i	−0.214039	−	0.370726i
$478$	−21.6250	+	37.4556i	−0.989104	+	1.71318i
$479$		−	38.8051i		−	1.77305i	−0.462680	−	0.886526i	$-0.653112\pi$
$479$		−	38.8051i		−	1.77305i	0.462680	−	0.886526i	$-0.346888\pi$
$480$	7.60115			0.346944
$481$	5.92851	+	6.21480i	0.270317	+	0.283370i
$482$	15.7241	−	27.2350i	0.716215	−	1.24052i
$483$	−4.44427	−	2.56590i	−0.202222	−	0.116753i
$484$	−12.0727			−0.548759
$485$	−11.6269			−0.527950
$486$	24.9775	−	14.4208i	1.13300	−	0.654140i
$487$		−	31.3794i		−	1.42194i	−0.703224	−	0.710969i	$-0.748257\pi$
$487$		−	31.3794i		−	1.42194i	0.703224	−	0.710969i	$-0.251743\pi$
$488$	−35.7919	−	20.6645i	−1.62022	−	0.935436i
$489$	−4.11958	−	2.37844i	−0.186294	−	0.107557i
$490$	−5.18163	−	8.97484i	−0.234082	−	0.405442i
$491$	−1.64511	+	2.84942i	−0.0742428	+	0.128592i	−0.900757	−	0.434324i	$-0.856987\pi$
$491$	−1.64511	+	2.84942i	−0.0742428	+	0.128592i	0.826514	+	0.562916i	$0.190321\pi$
$492$	−2.96385	+	1.71118i	−0.133621	+	0.0771461i
$493$	24.1307	−	41.7956i	1.08679	−	1.88238i
$494$	3.50471	+	14.4322i	0.157684	+	0.649336i
$495$	2.78940			0.125374
$496$	4.02531	−	2.94242i	0.180742	−	0.132119i
$497$	−7.00396	−	12.1312i	−0.314170	−	0.544159i
$498$	32.9374	−	57.0492i	1.47596	−	2.55644i
$499$	23.5878	+	13.6184i	1.05593	+	0.609644i	0.924305	−	0.381655i	$-0.124646\pi$
$499$	23.5878	+	13.6184i	1.05593	+	0.609644i	0.131629	+	0.991299i	$0.457979\pi$
$500$	−22.3658	−	12.9129i	−1.00023	−	0.577483i
$501$			25.4780i			1.13827i
$502$	61.2034	+	35.3358i	2.73164	+	1.57711i
$503$	5.15524	+	8.92914i	0.229861	+	0.398131i	0.957767	−	0.287546i	$-0.0928395\pi$
$503$	5.15524	+	8.92914i	0.229861	+	0.398131i	−0.727906	+	0.685677i	$0.759506\pi$
$504$	−7.45287	−	12.9088i	−0.331977	−	0.575002i
$505$	−11.2848	−	6.51526i	−0.502165	−	0.289925i
$506$	2.23681	+	3.87427i	0.0994383	+	0.172232i
$507$	1.26535	−	26.8210i	0.0561960	−	1.19116i
$508$	−10.0382	+	17.3867i	−0.445373	+	0.771409i
$509$	5.07895	+	2.93233i	0.225120	+	0.129973i	0.608319	−	0.793693i	$-0.291844\pi$
$509$	5.07895	+	2.93233i	0.225120	+	0.129973i	−0.383199	+	0.923666i	$0.625177\pi$
$510$	−22.7949			−1.00938
$511$	−9.55199	+	16.5445i	−0.422555	+	0.731887i
$512$			10.0498i			0.444141i
$513$	5.48347	−	3.16588i	0.242101	−	0.139777i
$514$		−	43.7590i		−	1.93013i
$515$	5.20670	+	3.00609i	0.229435	+	0.132464i
$516$	−28.8837			−1.27153
$517$	−12.4202	+	21.5124i	−0.546238	+	0.946113i
$518$	−17.0077	−	9.81939i	−0.747275	−	0.431439i
$519$	7.82476			0.343469
$520$	9.27395	+	2.72078i	0.406690	+	0.119314i
$521$	−11.7060	+	20.2754i	−0.512850	+	0.888282i	0.487039	+	0.873380i	$0.338077\pi$
$521$	−11.7060	+	20.2754i	−0.512850	+	0.888282i	−0.999889	+	0.0149016i	$0.995257\pi$
$522$	−20.9683	−	12.1060i	−0.917757	−	0.529867i
$523$	14.6248	+	25.3308i	0.639496	+	1.10764i	0.985543	+	0.169423i	$0.0541904\pi$
$523$	14.6248	+	25.3308i	0.639496	+	1.10764i	−0.346047	+	0.938217i	$0.612476\pi$
$524$	8.15342	+	14.1221i	0.356184	+	0.616929i
$525$		−	31.7992i		−	1.38783i
$526$	28.8558	+	16.6599i	1.25817	+	0.726407i
$527$	26.4285	−	19.3187i	1.15124	−	0.841536i
$528$			5.05817i			0.220129i
$529$	11.2535	−	19.4916i	0.489282	−	0.847461i
$530$	−13.8610			−0.602082
$531$	6.96864	−	4.02335i	0.302413	−	0.174598i
$532$	−10.7231	−	18.5730i	−0.464906	−	0.805241i
$533$	1.69353	−	0.411255i	0.0733547	−	0.0178134i
$534$	10.4669	−	18.1293i	0.452949	−	0.784530i
$535$	−3.56706	+	2.05945i	−0.154218	+	0.0890376i
$536$	−16.6325	+	28.8082i	−0.718412	+	1.24433i
$537$	28.3022			1.22133
$538$	−34.2045	+	19.7480i	−1.47466	+	0.851395i
$539$	−13.0754	+	7.54909i	−0.563197	+	0.325162i
$540$		−	9.89108i		−	0.425644i
$541$	17.4401	+	10.0690i	0.749807	+	0.432901i	0.825624	−	0.564221i	$-0.190823\pi$
$541$	17.4401	+	10.0690i	0.749807	+	0.432901i	−0.0758173	+	0.997122i	$0.524157\pi$
$542$	−11.9110	+	20.6305i	−0.511621	+	0.886154i
$543$	18.9766	+	32.8685i	0.814365	+	1.41052i
$544$			26.8575i			1.15151i
$545$	3.98162	+	6.89637i	0.170554	+	0.295408i
$546$	14.4880	+	59.6606i	0.620027	+	2.55324i
$547$	11.0420	+	19.1252i	0.472120	+	0.817737i	0.999491	−	0.0318987i	$-0.0101554\pi$
$547$	11.0420	+	19.1252i	0.472120	+	0.817737i	−0.527371	+	0.849635i	$0.676822\pi$
$548$	5.76047	+	3.32581i	0.246075	+	0.142072i
$549$	−7.86344	+	13.6199i	−0.335603	+	0.581282i
$550$	−13.8604	+	24.0068i	−0.591008	+	1.02366i
$551$	−12.5678	−	7.25604i	−0.535408	−	0.309118i
$552$	−4.17881	+	2.41264i	−0.177862	+	0.102689i
$553$			13.9959i			0.595168i
$554$		−	40.6554i		−	1.72728i
$555$	1.98201	+	3.43294i	0.0841315	+	0.145720i
$556$	23.7968	+	41.2172i	1.00921	+	1.74800i
$557$	−38.0285	+	21.9558i	−1.61132	+	0.930296i	−0.622254	+	0.782815i	$0.713783\pi$
$557$	−38.0285	+	21.9558i	−1.61132	+	0.930296i	−0.989065	+	0.147481i	$0.952884\pi$
$558$	−9.69193	−	13.2588i	−0.410292	−	0.561290i
$559$	14.1134	+	4.14056i	0.596933	+	0.175127i
$560$	−2.55299			−0.107883
$561$			33.2098i			1.40212i
$562$	−10.3173	−	17.8701i	−0.435209	−	0.753804i
$563$	29.3966			1.23892			0.619459	−	0.785029i	$-0.287352\pi$
$563$	29.3966			1.23892			0.619459	+	0.785029i	$0.287352\pi$
$564$	−55.6995	−	32.1581i	−2.34537	−	1.35410i
$565$	3.84767	−	2.22146i	0.161873	−	0.0934573i
$566$	29.4751	+	17.0175i	1.23893	+	0.715298i
$567$	34.3073	−	19.8073i	1.44077	−	0.831829i
$568$	−13.1712			−0.552651
$569$	2.90157	−	5.02567i	0.121640	−	0.210687i	−0.798774	−	0.601631i	$-0.794518\pi$
$569$	2.90157	−	5.02567i	0.121640	−	0.210687i	0.920415	+	0.390944i	$0.127851\pi$
$570$			6.85437i			0.287098i
$571$	6.65113	+	11.5201i	0.278341	+	0.482101i	0.970973	−	0.239191i	$-0.0768821\pi$
$571$	6.65113	+	11.5201i	0.278341	+	0.482101i	−0.692631	+	0.721292i	$0.743549\pi$
$572$	9.51527	−	32.4335i	0.397853	−	1.35611i
$573$	8.25247			0.344752
$574$	−3.45093	+	1.99240i	−0.144039	+	0.0831610i
$575$	−3.05503			−0.127404
$576$	15.7417			0.655903
$577$	−18.5691	−	10.7209i	−0.773043	−	0.446316i	0.0609163	−	0.998143i	$-0.480598\pi$
$577$	−18.5691	−	10.7209i	−0.773043	−	0.446316i	−0.833959	+	0.551827i	$0.813931\pi$
$578$		−	40.9355i		−	1.70269i
$579$			12.3882i			0.514838i
$580$	−19.6327	+	11.3349i	−0.815202	+	0.470657i
$581$	24.2199	−	41.9501i	1.00481	−	1.74038i
$582$	−69.4466			−2.87865
$583$			20.1940i			0.836349i
$584$	8.98143	+	15.5563i	0.371654	+	0.643724i
$585$	1.03533	−	3.52901i	0.0428058	−	0.145907i
$586$	7.41269	−	12.8392i	0.306215	−	0.530381i
$587$	−0.657786	+	0.379773i	−0.0271497	+	0.0156749i	−0.513513	−	0.858082i	$-0.671656\pi$
$587$	−0.657786	+	0.379773i	−0.0271497	+	0.0156749i	0.486364	+	0.873756i	$0.338323\pi$
$588$	−19.5460	−	33.8546i	−0.806063	−	1.39614i
$589$	−5.80908	−	7.94697i	−0.239359	−	0.327449i
$590$		−	11.9297i		−	0.491138i
$591$	14.3038	+	8.25829i	0.588379	+	0.339701i
$592$	−1.84748	+	1.06664i	−0.0759309	+	0.0438387i
$593$			24.4852i			1.00549i	0.864436	+	0.502743i	$0.167676\pi$
$593$			24.4852i			1.00549i	−0.864436	+	0.502743i	$0.832324\pi$
$594$	−22.8175			−0.936212
$595$	−16.7618			−0.687169
$596$			43.9368i			1.79972i
$597$	50.3909			2.06236
$598$	5.73175	−	1.39190i	0.234389	−	0.0569189i
$599$	−16.5872	−	28.7299i	−0.677734	−	1.17387i	−0.975662	−	0.219282i	$-0.929629\pi$
$599$	−16.5872	−	28.7299i	−0.677734	−	1.17387i	0.297927	−	0.954589i	$-0.403705\pi$
$600$	−25.8939	−	14.9499i	−1.05712	−	0.610326i
$601$	28.2738			1.15331			0.576655	−	0.816987i	$-0.304357\pi$
$601$	28.2738			1.15331			0.576655	+	0.816987i	$0.304357\pi$
$602$	−33.6304			−1.37067
$603$	10.9624	+	6.32914i	0.446423	+	0.257742i
$604$	30.1052	+	17.3812i	1.22496	+	0.707232i
$605$	2.45717	+	1.41865i	0.0998981	+	0.0576762i
$606$	−67.4030	−	38.9151i	−2.73806	−	1.58082i
$607$	−7.96826			−0.323422			−0.161711	−	0.986838i	$-0.551701\pi$
$607$	−7.96826			−0.323422			−0.161711	+	0.986838i	$0.551701\pi$
$608$	8.07599			0.327525
$609$	−51.9535	−	29.9954i	−2.10526	−	1.21547i
$610$	11.6580	+	20.1923i	0.472019	+	0.817561i
$611$	22.6064	+	23.6980i	0.914556	+	0.958720i
$612$	−25.5189			−1.03154
$613$			25.6086i			1.03432i	0.855889	+	0.517160i	$0.173011\pi$
$613$			25.6086i			1.03432i	−0.855889	+	0.517160i	$0.826989\pi$
$614$	79.0418			3.18987
$615$	0.804316			0.0324331
$616$			32.1954i			1.29719i
$617$	−10.4382	+	6.02651i	−0.420227	+	0.242618i	−0.695174	−	0.718841i	$-0.744673\pi$
$617$	−10.4382	+	6.02651i	−0.420227	+	0.242618i	0.274947	+	0.961459i	$0.411340\pi$
$618$	31.0992	+	17.9552i	1.25100	+	0.722262i
$619$			22.4603i			0.902754i	0.892333	+	0.451377i	$0.149067\pi$
$619$			22.4603i			0.902754i	−0.892333	+	0.451377i	$0.850933\pi$
$620$	−15.2884	+	1.65169i	−0.613995	+	0.0663334i
$621$	−1.25733	−	2.17776i	−0.0504549	−	0.0873904i
$622$	56.0394	−	32.3543i	2.24697	−	1.29729i
$623$	7.69668	−	13.3310i	0.308361	−	0.534097i
$624$	6.39934	+	1.87743i	0.256179	+	0.0751572i
$625$	−7.84253	−	13.5837i	−0.313701	−	0.543347i
$626$		−	37.7987i		−	1.51074i
$627$	9.98610			0.398807
$628$	12.8704	−	22.2921i	0.513584	−	0.889554i
$629$	−12.1298	+	7.00313i	−0.483646	+	0.279233i
$630$			8.40919i			0.335030i
$631$			12.8073i			0.509849i	0.966961	+	0.254925i	$0.0820507\pi$
$631$			12.8073i			0.509849i	−0.966961	+	0.254925i	$0.917949\pi$
$632$	11.3968	+	6.57997i	0.453342	+	0.261737i
$633$	−34.2814			−1.36256
$634$	−72.4169			−2.87604
$635$	4.08617	−	2.35915i	0.162155	−	0.0936201i
$636$	−52.2860			−2.07327
$637$	4.69756	+	19.3443i	0.186124	+	0.766449i
$638$	26.1483	+	45.2901i	1.03522	+	1.79305i
$639$			5.01202i			0.198273i
$640$	7.98883	−	13.8371i	0.315786	−	0.546958i
$641$	−7.18083			−0.283626			−0.141813	−	0.989893i	$-0.545293\pi$
$641$	−7.18083			−0.283626			−0.141813	+	0.989893i	$0.545293\pi$
$642$	−21.3058	+	12.3009i	−0.840873	+	0.485478i
$643$	−16.6168	−	9.59371i	−0.655302	−	0.378339i	0.135182	−	0.990821i	$-0.456838\pi$
$643$	−16.6168	−	9.59371i	−0.655302	−	0.378339i	−0.790485	+	0.612482i	$0.790171\pi$
$644$	−7.37626	+	4.25869i	−0.290665	+	0.167816i
$645$	5.87874	+	3.39409i	0.231475	+	0.133642i
$646$	−24.2189			−0.952880
$647$	−9.21699	−	15.9643i	−0.362357	−	0.627621i	0.625991	−	0.779830i	$-0.284695\pi$
$647$	−9.21699	−	15.9643i	−0.362357	−	0.627621i	−0.988348	+	0.152209i	$0.951361\pi$
$648$		−	37.2484i		−	1.46325i
$649$	−17.3803			−0.682238
$650$	25.2277	+	26.4460i	0.989513	+	1.03730i
$651$	−24.0139	−	32.8516i	−0.941177	−	1.28756i
$652$	−6.83736	+	3.94755i	−0.267772	+	0.154598i
$653$	17.1717	+	29.7422i	0.671980	+	1.16390i	0.977342	+	0.211668i	$0.0678894\pi$
$653$	17.1717	+	29.7422i	0.671980	+	1.16390i	−0.305361	+	0.952237i	$0.598777\pi$
$654$	23.7819	+	41.1915i	0.929947	+	1.61072i
$655$		−	3.83240i		−	0.149744i
$656$			0.432853i			0.0169001i
$657$	5.91963	−	3.41770i	0.230947	−	0.133337i
$658$	−64.8531	−	37.4429i	−2.52824	−	1.45968i
$659$	8.72805	−	15.1174i	0.339997	−	0.588891i	−0.644435	−	0.764659i	$-0.722907\pi$
$659$	8.72805	−	15.1174i	0.339997	−	0.588891i	0.984432	+	0.175768i	$0.0562407\pi$
$660$	7.79983	−	13.5097i	0.303608	−	0.525864i
$661$	37.0848	+	21.4109i	1.44243	+	0.832788i	0.998012	−	0.0630307i	$-0.0200766\pi$
$661$	37.0848	+	21.4109i	1.44243	+	0.832788i	0.444420	+	0.895819i	$0.353410\pi$
$662$	28.3386	+	49.0840i	1.10141	+	1.90770i
$663$	42.0154	+	12.3264i	1.63174	+	0.478717i
$664$	−22.7732	−	39.4444i	−0.883772	−	1.53074i
$665$			5.04024i			0.195452i
$666$	3.51337	+	6.08534i	0.136140	+	0.235802i
$667$	−2.88174	+	4.99131i	−0.111581	+	0.193264i
$668$	36.6211	+	21.1432i	1.41691	+	0.818056i
$669$			12.5539i			0.485364i
$670$	16.2524	−	9.38332i	0.627885	−	0.362509i
$671$	29.4180	−	16.9845i	1.13567	−	0.655679i
$672$	33.3849			1.28785
$673$	12.1021	−	20.9614i	0.466501	−	0.808003i	−0.532767	−	0.846262i	$-0.678848\pi$
$673$	12.1021	−	20.9614i	0.466501	−	0.808003i	0.999268	+	0.0382591i	$0.0121812\pi$
$674$	−57.4401	+	33.1631i	−2.21251	+	1.27739i
$675$	7.79103	−	13.4945i	0.299877	−	0.519402i
$676$	−37.5014	−	24.0765i	−1.44236	−	0.926018i
$677$	22.3881	+	38.7773i	0.860443	+	1.49033i	0.871502	+	0.490392i	$0.163147\pi$
$677$	22.3881	+	38.7773i	0.860443	+	1.49033i	−0.0110586	+	0.999939i	$0.503520\pi$
$678$	22.9819	−	13.2686i	0.882614	−	0.509577i
$679$	−51.0663			−1.95975
$680$	−7.88031	+	13.6491i	−0.302196	+	0.523419i
$681$		−	43.9771i		−	1.68521i
$682$	3.81024	+	35.2683i	0.145901	+	1.35049i
$683$	31.0552	+	17.9298i	1.18830	+	0.686063i	0.957919	−	0.287038i	$-0.0926708\pi$
$683$	31.0552	+	17.9298i	1.18830	+	0.686063i	0.230377	+	0.973101i	$0.426004\pi$
$684$			7.67345i			0.293402i
$685$	−0.781624	−	1.35381i	−0.0298643	−	0.0517265i
$686$	6.09622	+	10.5590i	0.232755	+	0.403143i
$687$	−44.0330	−	25.4225i	−1.67996	−	0.969927i
$688$	−1.82657	+	3.16372i	−0.0696374	+	0.120616i
$689$	25.5484	+	7.49534i	0.973317	+	0.285550i
$690$	2.72221			0.103633
$691$	−14.0807	−	8.12947i	−0.535653	−	0.309260i	0.207662	−	0.978201i	$-0.433415\pi$
$691$	−14.0807	−	8.12947i	−0.535653	−	0.309260i	−0.743315	+	0.668941i	$0.766748\pi$
$692$	6.49346	−	11.2470i	0.246844	−	0.427547i
$693$	12.2513			0.465388
$694$	46.8506	+	27.0492i	1.77842	+	1.02677i
$695$		−	11.1853i		−	0.424283i
$696$	−48.8502	+	28.2037i	−1.85166	+	1.06906i
$697$			2.84193i			0.107646i
$698$	3.88504	−	6.72908i	0.147051	−	0.254699i
$699$	−48.1667			−1.82183
$700$	−45.7069	−	26.3889i	−1.72756	−	0.997407i
$701$	−13.6269	+	23.6025i	−0.514682	+	0.891456i	0.485173	+	0.874418i	$0.338757\pi$
$701$	−13.6269	+	23.6025i	−0.514682	+	0.891456i	−0.999855	+	0.0170374i	$0.994577\pi$
$702$	−8.46909	+	28.8675i	−0.319645	+	1.08953i
$703$	2.10582	+	3.64739i	0.0794226	+	0.137564i
$704$	−29.4457	−	17.0005i	−1.10978	−	0.640730i
$705$	7.55772	+	13.0904i	0.284640	+	0.493011i
$706$	−26.0257	−	45.0778i	−0.979490	−	1.69653i
$707$	−49.5636	−	28.6156i	−1.86403	−	1.07620i
$708$		−	45.0009i		−	1.69124i
$709$	−29.5944	−	17.0863i	−1.11144	−	0.641690i	−0.172238	−	0.985055i	$-0.555100\pi$
$709$	−29.5944	−	17.0863i	−1.11144	−	0.641690i	−0.939202	+	0.343365i	$0.888433\pi$
$710$	6.43511	+	3.71531i	0.241505	+	0.139433i
$711$	2.50387	−	4.33683i	0.0939025	−	0.162644i
$712$	−7.23694	−	12.5347i	−0.271216	−	0.469759i
$713$	−3.15614	+	2.30708i	−0.118198	+	0.0864007i
$714$	−100.117			−3.74680
$715$	−5.74787	+	5.48309i	−0.214958	+	0.205056i
$716$	23.4869	−	40.6805i	0.877746	−	1.52030i
$717$	33.2054	−	19.1711i	1.24008	−	0.715959i
$718$	13.6324	−	23.6120i	0.508756	−	0.881192i
$719$	26.1406	+	45.2769i	0.974881	+	1.68854i	0.680327	+	0.732908i	$0.261838\pi$
$719$	26.1406	+	45.2769i	0.974881	+	1.68854i	0.294554	+	0.955635i	$0.404829\pi$
$720$	0.791078	+	0.456729i	0.0294817	+	0.0170213i
$721$	22.8683	+	13.2030i	0.851659	+	0.491706i
$722$		−	36.9841i		−	1.37640i
$723$	−24.1446	+	13.9399i	−0.897946	+	0.518429i
$724$	62.9919			2.34107
$725$	−35.7133			−1.32636
$726$	14.6765	+	8.47348i	0.544696	+	0.314480i
$727$	4.77504	−	8.27060i	0.177096	−	0.306740i	−0.763788	−	0.645467i	$-0.776663\pi$
$727$	4.77504	−	8.27060i	0.177096	−	0.306740i	0.940885	+	0.338727i	$0.109996\pi$
$728$	40.7320	+	11.9499i	1.50963	+	0.442892i
$729$	8.01704			0.296927
$730$		−	10.1339i		−	0.375072i
$731$	−11.9925	+	20.7716i	−0.443559	+	0.768267i
$732$	43.9760	+	76.1687i	1.62540	+	2.81528i
$733$	37.8692	−	21.8638i	1.39873	−	0.807558i	0.404472	−	0.914550i	$-0.367455\pi$
$733$	37.8692	−	21.8638i	1.39873	−	0.807558i	0.994260	+	0.106992i	$0.0341220\pi$
$734$		−	60.0957i		−	2.21817i
$735$			9.18730i			0.338879i
$736$		−	3.20738i		−	0.118226i
$737$	−13.6705	−	23.6780i	−0.503560	−	0.872191i
$738$	1.42576			0.0524828
$739$	21.8672	+	12.6250i	0.804398	+	0.464419i	0.845007	−	0.534756i	$-0.179596\pi$
$739$	21.8672	+	12.6250i	0.804398	+	0.464419i	−0.0406086	+	0.999175i	$0.512930\pi$
$740$	6.57916			0.241855
$741$	3.70651	−	12.6339i	0.136162	−	0.464118i
$742$	−60.8786			−2.23492
$743$	−0.413644	+	0.238817i	−0.0151751	+	0.00876136i	−0.507568	−	0.861611i	$-0.669456\pi$
$743$	−0.413644	+	0.238817i	−0.0151751	+	0.00876136i	0.492393	+	0.870373i	$0.336122\pi$
$744$	−38.0406	+	4.10975i	−1.39464	+	0.150671i
$745$	5.16295	−	8.94250i	0.189156	−	0.327628i
$746$			1.39869i			0.0512098i
$747$	−15.0097	+	8.66588i	−0.549178	+	0.317068i
$748$	47.7345	+	27.5595i	1.74535	+	1.00768i
$749$	−15.6669	+	9.04526i	−0.572454	+	0.330507i
$750$	18.1264	+	31.3958i	0.661882	+	1.14641i
$751$	−31.7774			−1.15957			−0.579786	−	0.814769i	$-0.696864\pi$
$751$	−31.7774			−1.15957			−0.579786	+	0.814769i	$0.696864\pi$
$752$	−7.04474	+	4.06728i	−0.256895	+	0.148319i
$753$	−31.3261	−	54.2584i	−1.14159	−	1.97729i
$754$	67.0041	−	16.2712i	2.44015	−	0.592564i
$755$	−4.08489	−	7.07524i	−0.148664	−	0.257494i
$756$		−	43.4425i		−	1.57999i
$757$	11.0337	−	19.1109i	0.401026	−	0.694598i	−0.592824	−	0.805332i	$-0.701987\pi$
$757$	11.0337	−	19.1109i	0.401026	−	0.694598i	0.993850	+	0.110734i	$0.0353202\pi$
$758$	−3.46170	−	5.99584i	−0.125735	−	0.217779i
$759$		−	3.96598i		−	0.143956i
$760$	4.10425	+	2.36959i	0.148877	+	0.0859540i
$761$	−19.7284	+	11.3902i	−0.715154	+	0.412894i	−0.812966	−	0.582310i	$-0.802149\pi$
$761$	−19.7284	+	11.3902i	−0.715154	+	0.412894i	0.0978124	+	0.995205i	$0.468815\pi$
$762$	24.4064	−	14.0910i	0.884151	−	0.510465i
$763$	17.4876	+	30.2894i	0.633094	+	1.09655i
$764$	6.84840	−	11.8618i	0.247766	−	0.429144i
$765$	5.19389	+	2.99869i	0.187785	+	0.108418i
$766$	−21.5217	−	37.2767i	−0.777611	−	1.34686i
$767$	−6.45101	+	21.9887i	−0.232932	+	0.793966i
$768$	22.0362	−	38.1677i	0.795161	−	1.37726i
$769$		−	36.6977i		−	1.32335i	−0.749789	−	0.661677i	$-0.769845\pi$
$769$		−	36.6977i		−	1.32335i	0.749789	−	0.661677i	$-0.230155\pi$
$770$	9.08164	−	15.7299i	0.327280	−	0.566865i
$771$	−19.3968	+	33.5962i	−0.698557	+	1.20994i
$772$	17.8064	+	10.2805i	0.640866	+	0.370004i
$773$	−10.7203	−	6.18937i	−0.385582	−	0.222616i	0.294662	−	0.955602i	$-0.404793\pi$
$773$	−10.7203	−	6.18937i	−0.385582	−	0.222616i	−0.680244	+	0.732986i	$0.738126\pi$
$774$	10.4208	+	6.01648i	0.374569	+	0.216258i
$775$	−22.1590	−	9.78896i	−0.795975	−	0.351630i
$776$	−24.0080	+	41.5831i	−0.861837	+	1.49275i
$777$	8.70515	+	15.0778i	0.312295	+	0.540912i
$778$		−	24.5444i		−	0.879959i
$779$	0.854561			0.0306178
$780$	−14.1967	−	14.8823i	−0.508325	−	0.532872i
$781$	5.41282	−	9.37528i	0.193686	−	0.335474i
$782$			9.61854i			0.343958i
$783$	−14.6982	−	25.4580i	−0.525269	−	0.909793i
$784$	−4.94426			−0.176581
$785$	−5.23905	+	3.02476i	−0.186990	+	0.107958i
$786$		−	22.8906i		−	0.816481i
$787$	−3.69093	+	2.13096i	−0.131568	+	0.0759606i	−0.564339	−	0.825543i	$-0.690869\pi$
$787$	−3.69093	+	2.13096i	−0.131568	+	0.0759606i	0.432772	+	0.901504i	$0.357536\pi$
$788$	23.7403	−	13.7065i	0.845713	−	0.488272i
$789$	−14.7695	−	25.5814i	−0.525806	−	0.910723i
$790$	−3.71214	−	6.42961i	−0.132072	−	0.228755i
$791$	16.8993	−	9.75682i	0.600870	−	0.346913i
$792$	5.75975	−	9.97618i	0.204664	−	0.354488i
$793$	−10.5689	−	43.5223i	−0.375314	−	1.54552i
$794$	19.0663	−	33.0238i	0.676639	−	1.17197i
$795$	10.6418	+	6.14406i	0.377427	+	0.217907i
$796$	41.8175	−	72.4300i	1.48218	−	2.56721i
$797$	11.9580			0.423575			0.211788	−	0.977316i	$-0.432072\pi$
$797$	11.9580			0.423575			0.211788	+	0.977316i	$0.432072\pi$
$798$			30.1050i			1.06571i
$799$	−46.2528	+	26.7041i	−1.63631	+	0.944723i
$800$	17.2118	−	9.93724i	0.608529	−	0.351335i
$801$	−4.76984	+	2.75387i	−0.168534	+	0.0973031i
$802$	9.98005	−	17.2860i	0.352408	−	0.610388i
$803$	−14.7640			−0.521010
$804$	61.3068	−	35.3955i	2.16212	−	1.24830i
$805$	2.00173			0.0705518
$806$	46.0339	+	8.26992i	1.62148	+	0.291295i
$807$	35.0142			1.23256
$808$	−46.6031	+	26.9063i	−1.63949	+	0.946560i
$809$	−5.08466			−0.178767			−0.0893835	−	0.995997i	$-0.528490\pi$
$809$	−5.08466			−0.178767			−0.0893835	+	0.995997i	$0.528490\pi$
$810$	−10.5070	+	18.1986i	−0.369177	+	0.639434i
$811$	8.91611	−	5.14772i	0.313087	−	0.180761i	−0.335220	−	0.942140i	$-0.608811\pi$
$811$	8.91611	−	5.14772i	0.313087	−	0.180761i	0.648307	+	0.761379i	$0.275477\pi$
$812$	−86.2283	+	49.7840i	−3.02602	+	1.74707i
$813$	18.2894	−	10.5594i	0.641439	−	0.370335i
$814$		−	15.1773i		−	0.531964i
$815$	1.85549			0.0649949
$816$	−5.43768	+	9.41834i	−0.190357	+	0.329708i
$817$	6.24597	+	3.60611i	0.218519	+	0.126162i
$818$	−28.8907	+	50.0401i	−1.01014	+	1.74961i
$819$	4.54728	−	15.4997i	0.158895	−	0.541604i
$820$	0.667470	−	1.15609i	0.0233091	−	0.0403725i
$821$	19.8038	−	11.4337i	0.691156	−	0.399039i	−0.112889	−	0.993608i	$-0.536010\pi$
$821$	19.8038	−	11.4337i	0.691156	−	0.399039i	0.804045	+	0.594569i	$0.202677\pi$
$822$	−4.66858	−	8.08622i	−0.162835	−	0.282039i
$823$	−3.95218	−	6.84537i	−0.137764	−	0.238615i	0.788886	−	0.614540i	$-0.210658\pi$
$823$	−3.95218	−	6.84537i	−0.137764	−	0.238615i	−0.926650	+	0.375925i	$0.877325\pi$
$824$	21.5023	−	12.4144i	0.749068	−	0.432475i
$825$	21.2827	−	12.2876i	0.740969	−	0.427798i
$826$		−	52.3963i		−	1.82310i
$827$	34.9966	−	20.2053i	1.21695	−	0.702606i	0.252685	−	0.967549i	$-0.418686\pi$
$827$	34.9966	−	20.2053i	1.21695	−	0.702606i	0.964264	+	0.264943i	$0.0853530\pi$
$828$	3.04751			0.105908
$829$	25.7408	+	44.5844i	0.894016	+	1.54848i	0.835018	+	0.550223i	$0.185457\pi$
$829$	25.7408	+	44.5844i	0.894016	+	1.54848i	0.0589981	+	0.998258i	$0.481209\pi$
$830$			25.6954i			0.891899i
$831$	−18.0210	+	31.2134i	−0.625143	+	1.08278i
$832$	−32.4374	+	30.9432i	−1.12456	+	1.07276i
$833$	−32.4619			−1.12474
$834$		−	66.8091i		−	2.31341i
$835$	−4.96903	−	8.60661i	−0.171960	−	0.297844i
$836$	8.28708	−	14.3536i	0.286615	−	0.496431i
$837$	−2.14177	−	19.8246i	−0.0740303	−	0.685239i
$838$	54.1861	+	31.2843i	1.87183	+	1.08070i
$839$	22.8087	+	13.1686i	0.787443	+	0.454631i	0.839062	−	0.544036i	$-0.183105\pi$
$839$	22.8087	+	13.1686i	0.787443	+	0.454631i	−0.0516185	+	0.998667i	$0.516438\pi$
$840$	16.9663	+	9.79552i	0.585394	+	0.337978i
$841$	−19.1874	+	33.2336i	−0.661636	+	1.14599i
$842$	33.6186	−	58.2292i	1.15857	−	2.00671i
$843$			18.2931i			0.630049i
$844$	−28.4488	+	49.2748i	−0.979248	+	1.69611i
$845$	4.80351	+	9.30705i	0.165246	+	0.320172i
$846$	13.3971	+	23.2044i	0.460601	+	0.797784i
$847$	10.7921	+	6.23082i	0.370821	+	0.214094i
$848$	−3.30650	+	5.72703i	−0.113546	+	0.196667i
$849$	−15.0864	−	26.1305i	−0.517765	−	0.896796i
$850$	−51.6161	+	29.8006i	−1.77042	+	1.02215i
$851$	1.44856	−	0.836327i	0.0496560	−	0.0286689i
$852$	24.2743	+	14.0148i	0.831625	+	0.480139i
$853$			15.4511i			0.529035i	0.964381	+	0.264517i	$0.0852127\pi$
$853$			15.4511i			0.529035i	−0.964381	+	0.264517i	$0.914787\pi$
$854$	51.2030	+	88.6862i	1.75213	+	3.03478i
$855$	0.901698	−	1.56179i	0.0308374	−	0.0534120i
$856$			17.0099i			0.581388i
$857$	17.9399	+	31.0728i	0.612814	+	1.06142i	0.990764	+	0.135599i	$0.0432958\pi$
$857$	17.9399	+	31.0728i	0.612814	+	1.06142i	−0.377950	+	0.925826i	$0.623371\pi$
$858$	−34.3316	+	32.7501i	−1.17206	+	1.11807i
$859$	17.4324	+	30.1938i	0.594786	+	1.03020i	0.993577	+	0.113157i	$0.0360964\pi$
$859$	17.4324	+	30.1938i	0.594786	+	1.03020i	−0.398792	+	0.917042i	$0.630570\pi$
$860$	9.75707	−	5.63324i	0.332713	−	0.192092i
$861$	3.53262			0.120391
$862$	23.0729	+	39.9635i	0.785867	+	1.36116i
$863$	−40.5249	+	23.3970i	−1.37948	+	0.796445i	−0.992097	−	0.125473i	$-0.959955\pi$
$863$	−40.5249	+	23.3970i	−1.37948	+	0.796445i	−0.387386	+	0.921918i	$0.626622\pi$
$864$	14.1674	+	8.17954i	0.481984	+	0.278274i
$865$	−2.64324	+	1.52608i	−0.0898730	+	0.0518882i
$866$			68.6196i			2.33179i
$867$	−18.1452	+	31.4284i	−0.616244	+	1.06737i
$868$	−67.1478	+	7.25435i	−2.27914	+	0.246229i
$869$	−9.36727	+	5.40820i	−0.317763	+	0.183460i
$870$	31.8226			1.07889
$871$	−35.0303	+	8.50674i	−1.18696	+	0.288240i
$872$	32.8861			1.11366
$873$	15.8236	+	9.13575i	0.535547	+	0.309198i
$874$	2.89227			0.0978324
$875$	13.3289	+	23.0864i	0.450600	+	0.780462i
$876$		−	38.2267i		−	1.29156i
$877$		−	16.5376i		−	0.558436i	−0.960228	−	0.279218i	$-0.909925\pi$
$877$		−	16.5376i		−	0.558436i	0.960228	−	0.279218i	$-0.0900752\pi$
$878$			59.3714i			2.00369i
$879$	−11.3823	+	6.57155i	−0.383914	+	0.221653i
$880$	−0.986504	−	1.70868i	−0.0332551	−	0.0575994i
$881$	−5.37876	+	9.31629i	−0.181215	+	0.313874i	−0.942295	−	0.334785i	$-0.891336\pi$
$881$	−5.37876	+	9.31629i	−0.181215	+	0.313874i	0.761079	+	0.648659i	$0.224670\pi$
$882$			16.2857i			0.548368i
$883$	44.8606			1.50968			0.754840	−	0.655909i	$-0.227714\pi$
$883$	44.8606			1.50968			0.754840	+	0.655909i	$0.227714\pi$
$884$	52.5844	−	50.1621i	1.76860	−	1.68713i
$885$	−5.28800	+	9.15909i	−0.177754	+	0.307879i
$886$	24.7714	+	14.3018i	0.832211	+	0.480477i
$887$	−39.3658			−1.32177			−0.660886	−	0.750486i	$-0.729820\pi$
$887$	−39.3658			−1.32177			−0.660886	+	0.750486i	$0.729820\pi$
$888$	16.3703			0.549353
$889$	17.9468	−	10.3616i	0.601917	−	0.347517i
$890$			8.16554i			0.273710i
$891$	26.5135	+	15.3076i	0.888235	+	0.512823i
$892$	18.0446	+	10.4180i	0.604176	+	0.348821i
$893$	8.02985	+	13.9081i	0.268709	+	0.465417i
$894$	30.8379	−	53.4129i	1.03138	−	1.78639i
$895$	−9.56062	+	5.51983i	−0.319576	+	0.184508i
$896$	35.0876	−	60.7736i	1.17220	−	2.03030i
$897$	−5.01755	−	1.47204i	−0.167531	−	0.0491500i
$898$	34.4048			1.14810
$899$	−36.8952	+	26.9697i	−1.23052	+	0.899489i
$900$	9.44194	+	16.3539i	0.314731	+	0.545130i
$901$	−21.7091	+	37.6013i	−0.723236	+	1.25268i
$902$	−2.66696	−	1.53977i	−0.0888000	−	0.0512687i
$903$	25.8199	+	14.9071i	0.859233	+	0.496078i
$904$		−	18.3481i		−	0.610247i
$905$	−12.8208	−	7.40210i	−0.426178	−	0.246054i
$906$	−24.3988	−	42.2599i	−0.810595	−	1.40399i
$907$	−2.78603	−	4.82555i	−0.0925087	−	0.160230i	0.816057	−	0.577971i	$-0.196155\pi$
$907$	−2.78603	−	4.82555i	−0.0925087	−	0.160230i	−0.908566	+	0.417741i	$0.862822\pi$
$908$	−63.2110	−	36.4949i	−2.09773	−	1.21113i
$909$	10.2386	+	17.7338i	0.339594	+	0.588194i
$910$	−16.5298	−	17.3280i	−0.547958	−	0.574419i
$911$	−2.61537	+	4.52995i	−0.0866510	+	0.150084i	−0.906094	−	0.423077i	$-0.860950\pi$
$911$	−2.61537	+	4.52995i	−0.0866510	+	0.150084i	0.819443	+	0.573161i	$0.194283\pi$
$912$	2.83207	+	1.63510i	0.0937792	+	0.0541434i
$913$	37.4354			1.23893
$914$	24.3388	−	42.1561i	0.805057	−	1.39440i
$915$		−	20.6703i		−	0.683338i
$916$	−73.0825	+	42.1942i	−2.41471	+	1.39414i
$917$		−	16.8322i		−	0.555848i
$918$	−42.4863	−	24.5295i	−1.40226	−	0.809593i
$919$	−22.5674			−0.744429			−0.372214	−	0.928147i	$-0.621401\pi$
$919$	−22.5674			−0.744429			−0.372214	+	0.928147i	$0.621401\pi$
$920$	0.941082	−	1.63000i	0.0310266	−	0.0537396i
$921$	−60.6847	−	35.0363i	−1.99963	−	1.15449i
$922$	59.8844			1.97219
$923$	−9.85207	−	10.3278i	−0.324285	−	0.339944i
$924$	34.2575	−	59.3358i	1.12699	−	1.95200i
$925$	8.97599	+	5.18229i	0.295129	+	0.170393i
$926$	−6.47511	−	11.2152i	−0.212785	−	0.368555i
$927$	−4.72403	−	8.18226i	−0.155158	−	0.268741i
$928$		−	37.4942i		−	1.23081i
$929$	27.2880	+	15.7547i	0.895289	+	0.516896i	0.875669	−	0.482912i	$-0.160421\pi$
$929$	27.2880	+	15.7547i	0.895289	+	0.516896i	0.0196204	+	0.999808i	$0.493754\pi$
$930$	19.7450	+	8.72254i	0.647463	+	0.286023i
$931$			9.76122i			0.319911i
$932$	−39.9716	+	69.2329i	−1.30931	+	2.26780i
$933$	−57.3659			−1.87808
$934$	54.4676	−	31.4469i	1.78223	−	1.02897i
$935$	−6.47697	−	11.2184i	−0.211820	−	0.366882i
$936$	−10.4835	−	10.9898i	−0.342665	−	0.359212i
$937$	8.73034	−	15.1214i	0.285208	−	0.493994i	−0.687452	−	0.726230i	$-0.741271\pi$
$937$	8.73034	−	15.1214i	0.285208	−	0.493994i	0.972660	+	0.232236i	$0.0746040\pi$
$938$	71.3819	−	41.2124i	2.33070	−	1.34563i
$939$	−16.7548	+	29.0201i	−0.546771	+	0.947035i
$940$	25.0874			0.818262
$941$	25.5062	−	14.7260i	0.831477	−	0.480054i	−0.0228811	−	0.999738i	$-0.507284\pi$
$941$	25.5062	−	14.7260i	0.831477	−	0.480054i	0.854358	+	0.519685i	$0.173951\pi$
$942$	−31.2924	+	18.0667i	−1.01956	+	0.588645i
$943$		−	0.339389i		−	0.0110520i
$944$	−4.92908	−	2.84581i	−0.160428	−	0.0926231i
$945$	−5.10487	+	8.84189i	−0.166061	+	0.287627i
$946$	−12.9952	−	22.5083i	−0.422510	−	0.731809i
$947$			17.1334i			0.556760i	0.960471	+	0.278380i	$0.0897975\pi$
$947$			17.1334i			0.556760i	−0.960471	+	0.278380i	$0.910203\pi$
$948$	−14.0028	−	24.2536i	−0.454791	−	0.787720i
$949$	−5.47991	+	18.6787i	−0.177885	+	0.606335i
$950$	8.96095	+	15.5208i	0.290732	+	0.503562i
$951$	55.5984	+	32.0997i	1.80290	+	1.04091i
$952$	−34.6110	+	59.9480i	−1.12175	+	1.94293i
$953$	−2.88125	+	4.99048i	−0.0933329	+	0.161657i	−0.908912	−	0.416989i	$-0.863085\pi$
$953$	−2.88125	+	4.99048i	−0.0933329	+	0.161657i	0.815579	+	0.578646i	$0.196419\pi$
$954$	18.8641	+	10.8912i	0.610746	+	0.352615i
$955$	−2.78773	+	1.60949i	−0.0902087	+	0.0520820i
$956$		−	63.6375i		−	2.05818i
$957$		−	46.3622i		−	1.49868i
$958$	45.2045	+	78.2965i	1.46049	+	2.52965i
$959$	−3.43296	−	5.94606i	−0.110856	−	0.192008i
$960$	−17.9178	+	10.3449i	−0.578295	+	0.333879i
$961$	−30.2847	+	6.62093i	−0.976926	+	0.213579i
$962$	−19.2016	−	5.63331i	−0.619083	−	0.181625i
$963$	6.47278			0.208582
$964$			46.2726i			1.49034i
$965$	−2.41610	−	4.18481i	−0.0777771	−	0.134714i
$966$	11.9562			0.384684
$967$	33.0380	+	19.0745i	1.06243	+	0.613395i	0.926104	−	0.377269i	$-0.123137\pi$
$967$	33.0380	+	19.0745i	1.06243	+	0.613395i	0.136328	+	0.990664i	$0.456470\pi$
$968$	10.1475	−	5.85864i	0.326152	−	0.188304i
$969$	18.5942	+	10.7354i	0.597331	+	0.344869i
$970$	23.4594	−	13.5443i	0.753236	−	0.434881i
$971$	−7.76766			−0.249276			−0.124638	−	0.992202i	$-0.539777\pi$
$971$	−7.76766			−0.249276			−0.124638	+	0.992202i	$0.539777\pi$
$972$	−21.2186	+	36.7516i	−0.680585	+	1.17881i
$973$		−	49.1269i		−	1.57494i
$974$	36.5542	+	63.3138i	1.17127	+	2.02870i
$975$	−7.64618	−	31.4865i	−0.244874	−	1.00838i
$976$	11.1240			0.356070
$977$	−1.90298	+	1.09869i	−0.0608817	+	0.0351501i	−0.530132	−	0.847915i	$-0.677858\pi$
$977$	−1.90298	+	1.09869i	−0.0608817	+	0.0351501i	0.469250	+	0.883065i	$0.344524\pi$
$978$	11.0827			0.354385
$979$	11.8963			0.380209
$980$	13.2055	+	7.62418i	0.421833	+	0.243545i
$981$		−	12.5141i		−	0.399545i
$982$		−	7.66563i		−	0.244620i
$983$	−51.6018	+	29.7923i	−1.64584	+	0.950227i	−0.667142	+	0.744930i	$0.732483\pi$
$983$	−51.6018	+	29.7923i	−1.64584	+	0.950227i	−0.978700	+	0.205297i	$0.934184\pi$
$984$	1.66081	−	2.87660i	0.0529446	−	0.0917027i
$985$	−6.44252			−0.205276
$986$			112.441i			3.58084i
$987$	33.1942	+	57.4940i	1.05658	+	1.83005i
$988$	−15.0836	−	15.8120i	−0.479873	−	0.503046i
$989$	1.43217	−	2.48059i	0.0455403	−	0.0788781i
$990$	−5.62814	+	3.24941i	−0.178874	+	0.103273i
$991$	−11.8187	−	20.4706i	−0.375434	−	0.650270i	0.614958	−	0.788560i	$-0.289173\pi$
$991$	−11.8187	−	20.4706i	−0.375434	−	0.650270i	−0.990392	+	0.138290i	$0.955840\pi$
$992$	10.2771	−	23.2640i	0.326298	−	0.738633i
$993$		−	50.2459i		−	1.59451i
$994$	28.2636	+	16.3180i	0.896466	+	0.517575i
$995$	−17.0223	+	9.82784i	−0.539644	+	0.311563i
$996$			96.9273i			3.07126i
$997$	13.7677			0.436027			0.218014	−	0.975946i	$-0.430042\pi$
$997$	13.7677			0.436027			0.218014	+	0.975946i	$0.430042\pi$
$998$	−63.4570			−2.00870
$999$			8.53129i			0.269918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.v.a.36.4	yes	70
13.4	even	6		403.2.s.a.160.4	✓	70
31.25	even	3		403.2.s.a.335.4	yes	70
403.56	even	6	inner	403.2.v.a.56.4	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.4	✓	70	13.4	even	6
403.2.s.a.335.4	yes	70	31.25	even	3
403.2.v.a.36.4	yes	70	1.1	even	1	trivial
403.2.v.a.56.4	yes	70	403.56	even	6	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.01769 + 1.16491i) q^{2} +2.06545 q^{3} +(1.71404 - 2.96880i) q^{4} +(-0.697719 + 0.402828i) q^{5} +(-4.16742 + 2.40606i) q^{6} +(-3.06444 + 1.76926i) q^{7} +3.32715i q^{8} +1.26608 q^{9} +O(q^{10})\)	\(q+(-2.01769 + 1.16491i) q^{2} +2.06545 q^{3} +(1.71404 - 2.96880i) q^{4} +(-0.697719 + 0.402828i) q^{5} +(-4.16742 + 2.40606i) q^{6} +(-3.06444 + 1.76926i) q^{7} +3.32715i q^{8} +1.26608 q^{9} +(0.938518 - 1.62556i) q^{10} +(-2.36827 - 1.36732i) q^{11} +(3.54025 - 6.13190i) q^{12} +(-2.60889 + 2.48871i) q^{13} +(4.12205 - 7.13960i) q^{14} +(-1.44110 + 0.832021i) q^{15} +(-0.447763 - 0.775548i) q^{16} +(-2.93982 - 5.09192i) q^{17} +(-2.55455 + 1.47487i) q^{18} +(-1.53113 + 0.883997i) q^{19} +2.76185i q^{20} +(-6.32945 + 3.65431i) q^{21} +6.37124 q^{22} +(0.351079 + 0.608087i) q^{23} +6.87206i q^{24} +(-2.17546 + 3.76800i) q^{25} +(2.36479 - 8.06056i) q^{26} -3.58133 q^{27} +12.1303i q^{28} +(4.10411 + 7.10853i) q^{29} +(1.93846 - 3.35751i) q^{30} +(0.598037 + 5.53555i) q^{31} +(-3.95590 - 2.28394i) q^{32} +(-4.89154 - 2.82413i) q^{33} +(11.8633 + 6.84926i) q^{34} +(1.42541 - 2.46889i) q^{35} +(2.17010 - 3.75873i) q^{36} -2.38216i q^{37} +(2.05956 - 3.56725i) q^{38} +(-5.38853 + 5.14031i) q^{39} +(-1.34027 - 2.32142i) q^{40} +(-0.418594 - 0.241675i) q^{41} +(8.51389 - 14.7465i) q^{42} +(-2.03967 - 3.53280i) q^{43} +(-8.11860 + 4.68728i) q^{44} +(-0.883367 + 0.510012i) q^{45} +(-1.41673 - 0.817952i) q^{46} -9.08357i q^{47} +(-0.924831 - 1.60185i) q^{48} +(2.76054 - 4.78139i) q^{49} -10.1369i q^{50} +(-6.07205 - 10.5171i) q^{51} +(2.91675 + 12.0110i) q^{52} +(-3.69225 - 6.39516i) q^{53} +(7.22599 - 4.17193i) q^{54} +2.20318 q^{55} +(-5.88658 - 10.1959i) q^{56} +(-3.16246 + 1.82585i) q^{57} +(-16.5616 - 9.56184i) q^{58} +(5.50412 - 3.17780i) q^{59} +5.70445i q^{60} +(-6.21086 + 10.7575i) q^{61} +(-7.65508 - 10.4723i) q^{62} +(-3.87982 + 2.24002i) q^{63} +12.4334 q^{64} +(0.817750 - 2.78736i) q^{65} +13.1595 q^{66} +(8.65854 + 4.99901i) q^{67} -20.1558 q^{68} +(0.725136 + 1.25597i) q^{69} +6.64192i q^{70} +3.95870i q^{71} +4.21243i q^{72} +(4.67556 - 2.69944i) q^{73} +(2.77500 + 4.80645i) q^{74} +(-4.49330 + 7.78262i) q^{75} +6.06081i q^{76} +9.67658 q^{77} +(4.88436 - 16.6487i) q^{78} +(1.97766 - 3.42541i) q^{79} +(0.624825 + 0.360743i) q^{80} -11.1953 q^{81} +1.12612 q^{82} +(-11.8553 + 6.84466i) q^{83} +25.0545i q^{84} +(4.10234 + 2.36849i) q^{85} +(8.23080 + 4.75206i) q^{86} +(8.47683 + 14.6823i) q^{87} +(4.54929 - 7.87960i) q^{88} +(-3.76741 + 2.17512i) q^{89} +(1.18824 - 2.05809i) q^{90} +(3.59163 - 12.2423i) q^{91} +2.40705 q^{92} +(1.23522 + 11.4334i) q^{93} +(10.5815 + 18.3278i) q^{94} +(0.712198 - 1.23356i) q^{95} +(-8.17072 - 4.71736i) q^{96} +(12.4981 + 7.21579i) q^{97} +12.8631i q^{98} +(-2.99842 - 1.73114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Introduction

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