LMFDB - Embedded newform 315.2.k.c.16.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(16,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.12
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.588830 + 1.01988i) q^{2} +(-0.114571 + 1.72826i) q^{3} +(0.306558 - 0.530973i) q^{4} +1.00000 q^{5} +(-1.83009 + 0.900802i) q^{6} +(-1.15510 + 2.38028i) q^{7} +3.07736 q^{8} +(-2.97375 - 0.396015i) q^{9} +(0.588830 + 1.01988i) q^{10} -1.60736 q^{11} +(0.882536 + 0.590644i) q^{12} +(2.48616 + 4.30615i) q^{13} +(-3.10777 + 0.223512i) q^{14} +(-0.114571 + 1.72826i) q^{15} +(1.19893 + 2.07661i) q^{16} +(0.876227 + 1.51767i) q^{17} +(-1.34714 - 3.26606i) q^{18} +(3.57754 - 6.19648i) q^{19} +(0.306558 - 0.530973i) q^{20} +(-3.98140 - 2.26902i) q^{21} +(-0.946464 - 1.63932i) q^{22} -7.47750 q^{23} +(-0.352576 + 5.31848i) q^{24} +1.00000 q^{25} +(-2.92785 + 5.07118i) q^{26} +(1.02512 - 5.09403i) q^{27} +(0.909761 + 1.34302i) q^{28} +(-1.18010 + 2.04400i) q^{29} +(-1.83009 + 0.900802i) q^{30} +(2.01920 - 3.49736i) q^{31} +(1.66543 - 2.88461i) q^{32} +(0.184157 - 2.77794i) q^{33} +(-1.03190 + 1.78730i) q^{34} +(-1.15510 + 2.38028i) q^{35} +(-1.12190 + 1.45758i) q^{36} +(4.22323 - 7.31485i) q^{37} +8.42626 q^{38} +(-7.72698 + 3.80336i) q^{39} +3.07736 q^{40} +(2.20143 + 3.81300i) q^{41} +(-0.0302268 - 5.39664i) q^{42} +(-0.404008 + 0.699762i) q^{43} +(-0.492749 + 0.853467i) q^{44} +(-2.97375 - 0.396015i) q^{45} +(-4.40298 - 7.62618i) q^{46} +(-4.23300 - 7.33177i) q^{47} +(-3.72627 + 1.83414i) q^{48} +(-4.33148 - 5.49893i) q^{49} +(0.588830 + 1.01988i) q^{50} +(-2.72331 + 1.34046i) q^{51} +3.04860 q^{52} +(1.44386 + 2.50083i) q^{53} +(5.79894 - 1.95401i) q^{54} -1.60736 q^{55} +(-3.55467 + 7.32499i) q^{56} +(10.2992 + 6.89284i) q^{57} -2.77952 q^{58} +(6.69929 - 11.6035i) q^{59} +(0.882536 + 0.590644i) q^{60} +(5.44467 + 9.43045i) q^{61} +4.75587 q^{62} +(4.37761 - 6.62092i) q^{63} +8.71834 q^{64} +(2.48616 + 4.30615i) q^{65} +(2.94161 - 1.44792i) q^{66} +(4.05970 - 7.03161i) q^{67} +1.07446 q^{68} +(0.856702 - 12.9230i) q^{69} +(-3.10777 + 0.223512i) q^{70} -2.85904 q^{71} +(-9.15130 - 1.21868i) q^{72} +(5.87110 + 10.1690i) q^{73} +9.94706 q^{74} +(-0.114571 + 1.72826i) q^{75} +(-2.19344 - 3.79916i) q^{76} +(1.85667 - 3.82598i) q^{77} +(-8.42887 - 5.64109i) q^{78} +(-0.958875 - 1.66082i) q^{79} +(1.19893 + 2.07661i) q^{80} +(8.68634 + 2.35530i) q^{81} +(-2.59254 + 4.49042i) q^{82} +(0.628986 - 1.08944i) q^{83} +(-2.42532 + 1.41843i) q^{84} +(0.876227 + 1.51767i) q^{85} -0.951568 q^{86} +(-3.39735 - 2.27370i) q^{87} -4.94644 q^{88} +(-3.79432 + 6.57195i) q^{89} +(-1.34714 - 3.26606i) q^{90} +(-13.1216 + 0.943711i) q^{91} +(-2.29228 + 3.97035i) q^{92} +(5.81299 + 3.89039i) q^{93} +(4.98503 - 8.63433i) q^{94} +(3.57754 - 6.19648i) q^{95} +(4.79454 + 3.20878i) q^{96} +(5.89502 - 10.2105i) q^{97} +(3.05777 - 7.65555i) q^{98} +(4.77989 + 0.636540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.588830	+	1.01988i	0.416366	+	0.721167i	0.995571	−	0.0940150i	$-0.0299702\pi$
$2$	0.588830	+	1.01988i	0.416366	+	0.721167i	−0.579205	+	0.815182i	$0.696637\pi$
$3$	−0.114571	+	1.72826i	−0.0661474	+	0.997810i
$3$	−0.114571	+	1.72826i	−0.0661474	+	0.997810i
$4$	0.306558	−	0.530973i	0.153279	−	0.265487i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.83009	+	0.900802i	−0.747129	+	0.367751i
$7$	−1.15510	+	2.38028i	−0.436587	+	0.899662i
$7$	−1.15510	+	2.38028i	−0.436587	+	0.899662i
$8$	3.07736			1.08801
$9$	−2.97375	−	0.396015i	−0.991249	−	0.132005i
$10$	0.588830	+	1.01988i	0.186205	+	0.322516i
$11$	−1.60736			−0.484638			−0.242319	−	0.970197i	$-0.577908\pi$
$11$	−1.60736			−0.484638			−0.242319	+	0.970197i	$0.577908\pi$
$12$	0.882536	+	0.590644i	0.254766	+	0.170504i
$13$	2.48616	+	4.30615i	0.689536	+	1.19431i	0.971988	+	0.235030i	$0.0755188\pi$
$13$	2.48616	+	4.30615i	0.689536	+	1.19431i	−0.282452	+	0.959281i	$0.591148\pi$
$14$	−3.10777	+	0.223512i	−0.830587	+	0.0597361i
$15$	−0.114571	+	1.72826i	−0.0295820	+	0.446234i
$16$	1.19893	+	2.07661i	0.299732	+	0.519152i
$17$	0.876227	+	1.51767i	0.212516	+	0.368089i	0.952501	−	0.304534i	$-0.0985008\pi$
$17$	0.876227	+	1.51767i	0.212516	+	0.368089i	−0.739985	+	0.672623i	$0.765168\pi$
$18$	−1.34714	−	3.26606i	−0.317525	−	0.769819i
$19$	3.57754	−	6.19648i	0.820744	−	1.42157i	−0.0843851	−	0.996433i	$-0.526893\pi$
$19$	3.57754	−	6.19648i	0.820744	−	1.42157i	0.905129	−	0.425137i	$-0.139774\pi$
$20$	0.306558	−	0.530973i	0.0685483	−	0.118729i
$21$	−3.98140	−	2.26902i	−0.868812	−	0.495142i
$22$	−0.946464	−	1.63932i	−0.201787	−	0.349505i
$23$	−7.47750			−1.55917			−0.779583	−	0.626299i	$-0.784569\pi$
$23$	−7.47750			−1.55917			−0.779583	+	0.626299i	$0.784569\pi$
$24$	−0.352576	+	5.31848i	−0.0719692	+	1.08563i
$25$	1.00000			0.200000
$26$	−2.92785	+	5.07118i	−0.574199	+	0.994541i
$27$	1.02512	−	5.09403i	0.197285	−	0.980346i
$28$	0.909761	+	1.34302i	0.171929	+	0.253807i
$29$	−1.18010	+	2.04400i	−0.219140	+	0.379561i	−0.954545	−	0.298066i	$-0.903658\pi$
$29$	−1.18010	+	2.04400i	−0.219140	+	0.379561i	0.735406	+	0.677627i	$0.236992\pi$
$30$	−1.83009	+	0.900802i	−0.334126	+	0.164463i
$31$	2.01920	−	3.49736i	0.362659	−	0.628144i	−0.625738	−	0.780033i	$-0.715202\pi$
$31$	2.01920	−	3.49736i	0.362659	−	0.628144i	0.988398	+	0.151889i	$0.0485356\pi$
$32$	1.66543	−	2.88461i	0.294409	−	0.509932i
$33$	0.184157	−	2.77794i	0.0320576	−	0.483577i
$34$	−1.03190	+	1.78730i	−0.176969	+	0.306519i
$35$	−1.15510	+	2.38028i	−0.195248	+	0.402341i
$36$	−1.12190	+	1.45758i	−0.186983	+	0.242930i
$37$	4.22323	−	7.31485i	0.694295	−	1.20255i	−0.276123	−	0.961122i	$-0.589050\pi$
$37$	4.22323	−	7.31485i	0.694295	−	1.20255i	0.970418	−	0.241431i	$-0.0776169\pi$
$38$	8.42626			1.36692
$39$	−7.72698	+	3.80336i	−1.23731	+	0.609025i
$40$	3.07736			0.486574
$41$	2.20143	+	3.81300i	0.343806	+	0.595490i	0.985136	−	0.171775i	$-0.0549503\pi$
$41$	2.20143	+	3.81300i	0.343806	+	0.595490i	−0.641330	+	0.767265i	$0.721617\pi$
$42$	−0.0302268	−	5.39664i	−0.00466409	−	0.832719i
$43$	−0.404008	+	0.699762i	−0.0616106	+	0.106713i	−0.895185	−	0.445694i	$-0.852957\pi$
$43$	−0.404008	+	0.699762i	−0.0616106	+	0.106713i	0.833575	+	0.552406i	$0.186290\pi$
$44$	−0.492749	+	0.853467i	−0.0742847	+	0.128665i
$45$	−2.97375	−	0.396015i	−0.443300	−	0.0590345i
$46$	−4.40298	−	7.62618i	−0.649184	−	1.12442i
$47$	−4.23300	−	7.33177i	−0.617446	−	1.06945i	−0.989950	−	0.141417i	$-0.954834\pi$
$47$	−4.23300	−	7.33177i	−0.617446	−	1.06945i	0.372504	−	0.928031i	$-0.378499\pi$
$48$	−3.72627	+	1.83414i	−0.537841	+	0.264735i
$49$	−4.33148	−	5.49893i	−0.618783	−	0.785562i
$50$	0.588830	+	1.01988i	0.0832732	+	0.144233i
$51$	−2.72331	+	1.34046i	−0.381340	+	0.187703i
$52$	3.04860			0.422765
$53$	1.44386	+	2.50083i	0.198329	+	0.343516i	0.947987	−	0.318310i	$-0.103115\pi$
$53$	1.44386	+	2.50083i	0.198329	+	0.343516i	−0.749658	+	0.661826i	$0.769782\pi$
$54$	5.79894	−	1.95401i	0.789136	−	0.265908i
$55$	−1.60736			−0.216737
$56$	−3.55467	+	7.32499i	−0.475012	+	0.978843i
$57$	10.2992	+	6.89284i	1.36417	+	0.912980i
$58$	−2.77952			−0.364969
$59$	6.69929	−	11.6035i	0.872173	−	1.51065i	0.0124286	−	0.999923i	$-0.496044\pi$
$59$	6.69929	−	11.6035i	0.872173	−	1.51065i	0.859744	−	0.510725i	$-0.170623\pi$
$60$	0.882536	+	0.590644i	0.113935	+	0.0762518i
$61$	5.44467	+	9.43045i	0.697119	+	1.20745i	0.969461	+	0.245245i	$0.0788684\pi$
$61$	5.44467	+	9.43045i	0.697119	+	1.20745i	−0.272342	+	0.962200i	$0.587798\pi$
$62$	4.75587			0.603996
$63$	4.37761	−	6.62092i	0.551527	−	0.834157i
$64$	8.71834			1.08979
$65$	2.48616	+	4.30615i	0.308370	+	0.534112i
$66$	2.94161	−	1.44792i	0.362087	−	0.178226i
$67$	4.05970	−	7.03161i	0.495972	−	0.859048i	−0.504017	−	0.863693i	$-0.668145\pi$
$67$	4.05970	−	7.03161i	0.495972	−	0.859048i	0.999989	+	0.00464514i	$0.00147860\pi$
$68$	1.07446			0.130297
$69$	0.856702	−	12.9230i	0.103135	−	1.55575i
$70$	−3.10777	+	0.223512i	−0.371450	+	0.0267148i
$71$	−2.85904			−0.339306			−0.169653	−	0.985504i	$-0.554265\pi$
$71$	−2.85904			−0.339306			−0.169653	+	0.985504i	$0.554265\pi$
$72$	−9.15130	−	1.21868i	−1.07849	−	0.143623i
$73$	5.87110	+	10.1690i	0.687160	+	1.19020i	0.972753	+	0.231845i	$0.0744762\pi$
$73$	5.87110	+	10.1690i	0.687160	+	1.19020i	−0.285593	+	0.958351i	$0.592191\pi$
$74$	9.94706			1.15632
$75$	−0.114571	+	1.72826i	−0.0132295	+	0.199562i
$76$	−2.19344	−	3.79916i	−0.251605	−	0.435793i
$77$	1.85667	−	3.82598i	0.211587	−	0.436010i
$78$	−8.42887	−	5.64109i	−0.954381	−	0.638727i
$79$	−0.958875	−	1.66082i	−0.107882	−	0.186857i	0.807030	−	0.590510i	$-0.201073\pi$
$79$	−0.958875	−	1.66082i	−0.107882	−	0.186857i	−0.914912	+	0.403653i	$0.867740\pi$
$80$	1.19893	+	2.07661i	0.134044	+	0.232172i
$81$	8.68634	+	2.35530i	0.965149	+	0.261700i
$82$	−2.59254	+	4.49042i	−0.286298	+	0.495883i
$83$	0.628986	−	1.08944i	0.0690402	−	0.119581i	−0.829439	−	0.558598i	$-0.811340\pi$
$83$	0.628986	−	1.08944i	0.0690402	−	0.119581i	0.898479	+	0.439016i	$0.144673\pi$
$84$	−2.42532	+	1.41843i	−0.264624	+	0.154763i
$85$	0.876227	+	1.51767i	0.0950401	+	0.164614i
$86$	−0.951568			−0.102610
$87$	−3.39735	−	2.27370i	−0.364234	−	0.243767i
$88$	−4.94644			−0.527292
$89$	−3.79432	+	6.57195i	−0.402197	+	0.696625i	−0.993991	−	0.109464i	$-0.965087\pi$
$89$	−3.79432	+	6.57195i	−0.402197	+	0.696625i	0.591794	+	0.806089i	$0.298420\pi$
$90$	−1.34714	−	3.26606i	−0.142001	−	0.344273i
$91$	−13.1216	+	0.943711i	−1.37552	+	0.0989278i
$92$	−2.29228	+	3.97035i	−0.238987	+	0.413938i
$93$	5.81299	+	3.89039i	0.602779	+	0.403415i
$94$	4.98503	−	8.63433i	0.514167	−	0.890563i
$95$	3.57754	−	6.19648i	0.367048	−	0.635746i
$96$	4.79454	+	3.20878i	0.489341	+	0.327495i
$97$	5.89502	−	10.2105i	0.598549	−	1.03672i	−0.394487	−	0.918902i	$-0.629078\pi$
$97$	5.89502	−	10.2105i	0.598549	−	1.03672i	0.993036	−	0.117815i	$-0.0375890\pi$
$98$	3.05777	−	7.65555i	0.308881	−	0.773327i
$99$	4.77989	+	0.636540i	0.480397	+	0.0639747i
$100$	0.306558	−	0.530973i	0.0306558	−	0.0530973i
$101$	−12.4801			−1.24181			−0.620907	−	0.783885i	$-0.713235\pi$
$101$	−12.4801			−1.24181			−0.620907	+	0.783885i	$0.713235\pi$
$102$	−2.97069	−	1.98816i	−0.294142	−	0.196857i
$103$	−4.61850			−0.455074			−0.227537	−	0.973769i	$-0.573067\pi$
$103$	−4.61850			−0.455074			−0.227537	+	0.973769i	$0.573067\pi$
$104$	7.65081	+	13.2516i	0.750224	+	1.29943i
$105$	−3.98140	−	2.26902i	−0.388545	−	0.221434i
$106$	−1.70037	+	2.94513i	−0.165155	+	0.286057i
$107$	−7.72051	+	13.3723i	−0.746370	+	1.29275i	0.203183	+	0.979141i	$0.434871\pi$
$107$	−7.72051	+	13.3723i	−0.746370	+	1.29275i	−0.949552	+	0.313609i	$0.898462\pi$
$108$	−2.39053	−	2.10592i	−0.230029	−	0.202643i
$109$	−5.86738	−	10.1626i	−0.561993	−	0.973401i	−0.997322	−	0.0731296i	$-0.976701\pi$
$109$	−5.86738	−	10.1626i	−0.561993	−	0.973401i	0.435329	−	0.900271i	$-0.356632\pi$
$110$	−0.946464	−	1.63932i	−0.0902418	−	0.156303i
$111$	12.1581	+	8.13689i	1.15399	+	0.772320i
$112$	−6.32780	+	0.455097i	−0.597921	+	0.0430027i
$113$	−4.92553	−	8.53126i	−0.463355	−	0.802554i	0.535771	−	0.844363i	$-0.320021\pi$
$113$	−4.92553	−	8.53126i	−0.463355	−	0.802554i	−0.999126	+	0.0418097i	$0.986688\pi$
$114$	−0.965402	+	14.5627i	−0.0904182	+	1.36393i
$115$	−7.47750			−0.697280
$116$	0.723539	+	1.25321i	0.0671789	+	0.116357i
$117$	−5.68790	−	13.7900i	−0.525847	−	1.27488i
$118$	15.7790			1.45257
$119$	−4.62461	+	0.332604i	−0.423937	+	0.0304897i
$120$	−0.352576	+	5.31848i	−0.0321856	+	0.485508i
$121$	−8.41638			−0.765126
$122$	−6.41198	+	11.1059i	−0.580513	+	1.00548i
$123$	−6.84206	+	3.36779i	−0.616928	+	0.303663i
$124$	−1.23800	−	2.14428i	−0.111176	−	0.192562i
$125$	1.00000			0.0894427
$126$	9.33024	+	0.566057i	0.831204	+	0.0504283i
$127$	−8.26362			−0.733278			−0.366639	−	0.930363i	$-0.619492\pi$
$127$	−8.26362			−0.733278			−0.366639	+	0.930363i	$0.619492\pi$
$128$	1.80277	+	3.12248i	0.159343	+	0.275991i
$129$	−1.16308	−	0.778401i	−0.102404	−	0.0685344i
$130$	−2.92785	+	5.07118i	−0.256789	+	0.444772i
$131$	−6.59573			−0.576272			−0.288136	−	0.957589i	$-0.593036\pi$
$131$	−6.59573			−0.576272			−0.288136	+	0.957589i	$0.593036\pi$
$132$	−1.41856	−	0.949380i	−0.123469	−	0.0826329i
$133$	10.6169	+	15.6731i	0.920606	+	1.35903i
$134$	9.56191			0.826023
$135$	1.02512	−	5.09403i	0.0882284	−	0.438424i
$136$	2.69647	+	4.67042i	0.231220	+	0.400485i
$137$	−7.16732			−0.612345			−0.306173	−	0.951976i	$-0.599048\pi$
$137$	−7.16732			−0.612345			−0.306173	+	0.951976i	$0.599048\pi$
$138$	13.6845	−	6.73574i	1.16490	−	0.573385i
$139$	4.12443	+	7.14371i	0.349829	+	0.605922i	0.986219	−	0.165446i	$-0.0529063\pi$
$139$	4.12443	+	7.14371i	0.349829	+	0.605922i	−0.636390	+	0.771368i	$0.719573\pi$
$140$	0.909761	+	1.34302i	0.0768888	+	0.113506i
$141$	13.1562	−	6.47570i	1.10795	−	0.545352i
$142$	−1.68349	−	2.91589i	−0.141275	−	0.244696i
$143$	−3.99616	−	6.92155i	−0.334175	−	0.578809i
$144$	−2.74295	−	6.65010i	−0.228579	−	0.554175i
$145$	−1.18010	+	2.04400i	−0.0980022	+	0.169745i
$146$	−6.91416	+	11.9757i	−0.572220	+	0.991114i
$147$	9.99984	−	6.85589i	0.824773	−	0.565465i
$148$	−2.58933	−	4.48484i	−0.212841	−	0.368652i
$149$	−5.98896			−0.490635			−0.245317	−	0.969443i	$-0.578892\pi$
$149$	−5.98896			−0.490635			−0.245317	+	0.969443i	$0.578892\pi$
$150$	−1.83009	+	0.900802i	−0.149426	+	0.0735501i
$151$	1.46476			0.119200			0.0596001	−	0.998222i	$-0.481017\pi$
$151$	1.46476			0.119200			0.0596001	+	0.998222i	$0.481017\pi$
$152$	11.0094	−	19.0688i	0.892979	−	1.54669i
$153$	−2.00466	−	4.86016i	−0.162067	−	0.392921i
$154$	4.99531	−	0.359265i	0.402534	−	0.0289504i
$155$	2.01920	−	3.49736i	0.162186	−	0.280915i
$156$	−0.349280	+	5.26877i	−0.0279648	+	0.421839i
$157$	−7.57099	+	13.1133i	−0.604231	+	1.04656i	0.387942	+	0.921684i	$0.373186\pi$
$157$	−7.57099	+	13.1133i	−0.604231	+	1.04656i	−0.992173	+	0.124875i	$0.960147\pi$
$158$	1.12923	−	1.95588i	0.0898367	−	0.155602i
$159$	−4.48751	+	2.20883i	−0.355882	+	0.175172i
$160$	1.66543	−	2.88461i	0.131664	−	0.228048i
$161$	8.63727	−	17.7986i	0.680712	−	1.40272i
$162$	2.71265	+	10.2459i	0.213126	+	0.804997i
$163$	−1.99957	+	3.46336i	−0.156619	+	0.271271i	−0.933647	−	0.358194i	$-0.883393\pi$
$163$	−1.99957	+	3.46336i	−0.156619	+	0.271271i	0.777029	+	0.629465i	$0.216726\pi$
$164$	2.69946			0.210793
$165$	0.184157	−	2.77794i	0.0143366	−	0.216262i
$166$	1.48146			0.114984
$167$	8.07580	+	13.9877i	0.624924	+	1.08240i	0.988556	+	0.150857i	$0.0482034\pi$
$167$	8.07580	+	13.9877i	0.624924	+	1.08240i	−0.363631	+	0.931543i	$0.618463\pi$
$168$	−12.2522	−	6.98261i	−0.945278	−	0.538720i
$169$	−5.86196	+	10.1532i	−0.450920	+	0.781016i
$170$	−1.03190	+	1.78730i	−0.0791429	+	0.137080i
$171$	−13.0926	+	17.0100i	−1.00122	+	1.30079i
$172$	0.247703	+	0.429034i	0.0188872	+	0.0327136i
$173$	−5.41672	−	9.38204i	−0.411826	−	0.713303i	0.583264	−	0.812283i	$-0.301775\pi$
$173$	−5.41672	−	9.38204i	−0.411826	−	0.713303i	−0.995089	+	0.0989796i	$0.968442\pi$
$174$	0.318452	−	4.80373i	0.0241418	−	0.364170i
$175$	−1.15510	+	2.38028i	−0.0873175	+	0.179932i
$176$	−1.92712	−	3.33786i	−0.145262	−	0.251601i
$177$	19.2863	+	12.9075i	1.44965	+	0.970188i
$178$	−8.93684			−0.669844
$179$	1.14877	+	1.98973i	0.0858634	+	0.148720i	0.905759	−	0.423794i	$-0.139302\pi$
$179$	1.14877	+	1.98973i	0.0858634	+	0.148720i	−0.819895	+	0.572513i	$0.805968\pi$
$180$	−1.12190	+	1.45758i	−0.0836213	+	0.108641i
$181$	21.2841			1.58204			0.791019	−	0.611792i	$-0.209551\pi$
$181$	21.2841			1.58204			0.791019	+	0.611792i	$0.209551\pi$
$182$	−8.68888	−	12.8268i	−0.644063	−	0.950789i
$183$	−16.9220	+	8.32934i	−1.25091	+	0.615723i
$184$	−23.0110			−1.69639
$185$	4.22323	−	7.31485i	0.310498	−	0.537798i
$186$	−0.544883	+	8.21936i	−0.0399528	+	0.602673i
$187$	−1.40841	−	2.43944i	−0.102993	−	0.178390i
$188$	−5.19063			−0.378565
$189$	10.9411	+	8.32420i	0.795848	+	0.605496i
$190$	8.42626			0.611305
$191$	3.63533	+	6.29657i	0.263043	+	0.455604i	0.967049	−	0.254590i	$-0.0819406\pi$
$191$	3.63533	+	6.29657i	0.263043	+	0.455604i	−0.704006	+	0.710194i	$0.748607\pi$
$192$	−0.998867	+	15.0675i	−0.0720870	+	1.08741i
$193$	−7.95510	+	13.7786i	−0.572620	+	0.991808i	0.423675	+	0.905814i	$0.360740\pi$
$193$	−7.95510	+	13.7786i	−0.572620	+	0.991808i	−0.996296	+	0.0859936i	$0.972594\pi$
$194$	13.8847			0.996861
$195$	−7.72698	+	3.80336i	−0.553340	+	0.272364i
$196$	−4.24763	+	0.614160i	−0.303402	+	0.0438686i
$197$	−10.9249			−0.778364			−0.389182	−	0.921161i	$-0.627242\pi$
$197$	−10.9249			−0.778364			−0.389182	+	0.921161i	$0.627242\pi$
$198$	2.16535	+	5.24975i	0.153885	+	0.373083i
$199$	1.63900	+	2.83882i	0.116185	+	0.201239i	0.918253	−	0.395994i	$-0.129600\pi$
$199$	1.63900	+	2.83882i	0.116185	+	0.201239i	−0.802068	+	0.597233i	$0.796267\pi$
$200$	3.07736			0.217602
$201$	11.6873	+	7.82183i	0.824360	+	0.551709i
$202$	−7.34864	−	12.7282i	−0.517049	−	0.895555i
$203$	−3.50215	−	5.17000i	−0.245803	−	0.362863i
$204$	−0.123101	+	1.85694i	−0.00861880	+	0.130011i
$205$	2.20143	+	3.81300i	0.153755	+	0.266311i
$206$	−2.71951	−	4.71033i	−0.189477	−	0.328184i
$207$	22.2362	+	2.96120i	1.54552	+	0.205818i
$208$	−5.96146	+	10.3255i	−0.413353	+	0.715948i
$209$	−5.75040	+	9.95999i	−0.397764	+	0.688947i
$210$	−0.0302268	−	5.39664i	−0.00208585	−	0.372403i
$211$	−9.44405	−	16.3576i	−0.650155	−	1.12610i	−0.983085	−	0.183150i	$-0.941371\pi$
$211$	−9.44405	−	16.3576i	−0.650155	−	1.12610i	0.332930	−	0.942952i	$-0.391963\pi$
$212$	1.77050			0.121598
$213$	0.327562	−	4.94116i	0.0224442	−	0.338563i
$214$	−18.1843			−1.24305
$215$	−0.404008	+	0.699762i	−0.0275531	+	0.0477234i
$216$	3.15467	−	15.6762i	0.214648	−	1.06663i
$217$	5.99232	+	8.84607i	0.406785	+	0.600511i
$218$	6.90979	−	11.9681i	0.467990	−	0.810582i
$219$	−18.2474	+	8.98169i	−1.23304	+	0.606927i
$220$	−0.492749	+	0.853467i	−0.0332211	+	0.0575407i
$221$	−4.35687	+	7.54633i	−0.293075	+	0.507621i
$222$	−1.13964	+	17.1911i	−0.0764878	+	1.15379i
$223$	−6.01501	+	10.4183i	−0.402795	+	0.697662i	−0.994062	−	0.108814i	$-0.965295\pi$
$223$	−6.01501	+	10.4183i	−0.402795	+	0.697662i	0.591267	+	0.806476i	$0.298628\pi$
$224$	4.94244	+	7.29621i	0.330231	+	0.487499i
$225$	−2.97375	−	0.396015i	−0.198250	−	0.0264010i
$226$	5.80060	−	10.0469i	0.385850	−	0.668312i
$227$	13.9879			0.928412			0.464206	−	0.885727i	$-0.346340\pi$
$227$	13.9879			0.928412			0.464206	+	0.885727i	$0.346340\pi$
$228$	6.81722	−	3.35556i	0.451482	−	0.222228i
$229$	−4.09285			−0.270463			−0.135232	−	0.990814i	$-0.543178\pi$
$229$	−4.09285			−0.270463			−0.135232	+	0.990814i	$0.543178\pi$
$230$	−4.40298	−	7.62618i	−0.290324	−	0.502856i
$231$	6.39955	+	3.64714i	0.421060	+	0.239964i
$232$	−3.63160	+	6.29012i	−0.238426	+	0.412967i
$233$	6.24685	−	10.8199i	0.409244	−	0.708832i	−0.585561	−	0.810628i	$-0.699126\pi$
$233$	6.24685	−	10.8199i	0.409244	−	0.708832i	0.994805	+	0.101796i	$0.0324590\pi$
$234$	10.7150	−	13.9209i	0.700458	−	0.910041i
$235$	−4.23300	−	7.33177i	−0.276130	−	0.478272i
$236$	−4.10743	−	7.11428i	−0.267371	−	0.463100i
$237$	2.98018	−	1.46690i	0.193584	−	0.0952855i
$238$	−3.06233	−	4.52072i	−0.198501	−	0.293035i
$239$	−6.07011	−	10.5137i	−0.392643	−	0.680077i	0.600155	−	0.799884i	$-0.295106\pi$
$239$	−6.07011	−	10.5137i	−0.392643	−	0.680077i	−0.992797	+	0.119807i	$0.961772\pi$
$240$	−3.72627	+	1.83414i	−0.240530	+	0.118393i
$241$	7.56726			0.487450			0.243725	−	0.969844i	$-0.421631\pi$
$241$	7.56726			0.487450			0.243725	+	0.969844i	$0.421631\pi$
$242$	−4.95582	−	8.58374i	−0.318572	−	0.551784i
$243$	−5.06576	+	14.7424i	−0.324969	+	0.945725i
$244$	6.67642			0.427414
$245$	−4.33148	−	5.49893i	−0.276728	−	0.351314i
$246$	−7.46356	−	4.99505i	−0.475859	−	0.318473i
$247$	35.5773			2.26373
$248$	6.21381	−	10.7626i	0.394578	−	0.683429i
$249$	1.81076	+	1.21187i	0.114752	+	0.0767990i
$250$	0.588830	+	1.01988i	0.0372409	+	0.0645031i
$251$	−2.11183			−0.133298			−0.0666488	−	0.997776i	$-0.521231\pi$
$251$	−2.11183			−0.133298			−0.0666488	+	0.997776i	$0.521231\pi$
$252$	−2.17354	−	4.35408i	−0.136920	−	0.274282i
$253$	12.0191			0.755631
$254$	−4.86587	−	8.42794i	−0.305312	−	0.528816i
$255$	−2.72331	+	1.34046i	−0.170540	+	0.0839432i
$256$	6.59530	−	11.4234i	0.412206	−	0.713962i
$257$	−14.0321			−0.875301			−0.437651	−	0.899145i	$-0.644189\pi$
$257$	−14.0321			−0.875301			−0.437651	+	0.899145i	$0.644189\pi$
$258$	0.109022	−	1.64455i	0.00678740	−	0.102385i
$259$	12.5331	+	18.5019i	0.778771	+	1.14965i
$260$	3.04860			0.189066
$261$	4.31878	−	5.61099i	0.267326	−	0.347312i
$262$	−3.88377	−	6.72689i	−0.239940	−	0.415588i
$263$	30.0166			1.85090			0.925451	−	0.378866i	$-0.123686\pi$
$263$	30.0166			1.85090			0.925451	+	0.378866i	$0.123686\pi$
$264$	0.566717	−	8.54872i	0.0348790	−	0.526137i
$265$	1.44386	+	2.50083i	0.0886954	+	0.153625i
$266$	−9.73318	+	20.0569i	−0.596780	+	1.22977i
$267$	−10.9233	−	7.31051i	−0.668495	−	0.447396i
$268$	−2.48907	−	4.31119i	−0.152044	−	0.263348i
$269$	−7.46179	−	12.9242i	−0.454953	−	0.788002i	0.543732	−	0.839259i	$-0.317011\pi$
$269$	−7.46179	−	12.9242i	−0.454953	−	0.788002i	−0.998686	+	0.0512568i	$0.983677\pi$
$270$	5.79894	−	1.95401i	0.352912	−	0.118918i
$271$	−8.77299	+	15.1953i	−0.532921	+	0.923046i	0.466340	+	0.884606i	$0.345572\pi$
$271$	−8.77299	+	15.1953i	−0.532921	+	0.923046i	−0.999261	+	0.0384405i	$0.987761\pi$
$272$	−2.10107	+	3.63916i	−0.127396	+	0.220656i
$273$	−0.127623	−	22.7857i	−0.00772412	−	1.37905i
$274$	−4.22034	−	7.30984i	−0.254960	−	0.441603i
$275$	−1.60736			−0.0969276
$276$	−6.59916	−	4.41654i	−0.397223	−	0.265845i
$277$	−3.96084			−0.237984			−0.118992	−	0.992895i	$-0.537966\pi$
$277$	−3.96084			−0.237984			−0.118992	+	0.992895i	$0.537966\pi$
$278$	−4.85717	+	8.41287i	−0.291314	+	0.504571i
$279$	−7.38960	+	9.60063i	−0.442404	+	0.574774i
$280$	−3.55467	+	7.32499i	−0.212432	+	0.437752i
$281$	11.1885	−	19.3791i	0.667451	−	1.15606i	−0.311163	−	0.950357i	$-0.600719\pi$
$281$	11.1885	−	19.3791i	0.667451	−	1.15606i	0.978614	−	0.205703i	$-0.0659481\pi$
$282$	14.3512	+	9.60466i	0.854602	+	0.571949i
$283$	−14.8004	+	25.6351i	−0.879794	+	1.52385i	−0.0282282	+	0.999602i	$0.508987\pi$
$283$	−14.8004	+	25.6351i	−0.879794	+	1.52385i	−0.851566	+	0.524247i	$0.824347\pi$
$284$	−0.876461	+	1.51807i	−0.0520084	+	0.0900811i
$285$	10.2992	+	6.89284i	0.610074	+	0.408297i
$286$	4.70612	−	8.15123i	0.278279	−	0.481993i
$287$	−11.6189	+	0.835634i	−0.685841	+	0.0493259i
$288$	−6.09492	+	7.91856i	−0.359147	+	0.466606i
$289$	6.96445	−	12.0628i	0.409674	−	0.709576i
$290$	−2.77952			−0.163219
$291$	16.9709	+	11.3579i	0.994853	+	0.665814i
$292$	7.19932			0.421308
$293$	7.62430	+	13.2057i	0.445416	+	0.771483i	0.998081	−	0.0619201i	$-0.0197224\pi$
$293$	7.62430	+	13.2057i	0.445416	+	0.771483i	−0.552665	+	0.833404i	$0.686389\pi$
$294$	12.8804	+	6.16171i	0.751202	+	0.359359i
$295$	6.69929	−	11.6035i	0.390048	−	0.675582i
$296$	12.9964	−	22.5104i	0.755401	−	1.30839i
$297$	−1.64774	+	8.18795i	−0.0956116	+	0.475113i
$298$	−3.52648	−	6.10805i	−0.204284	−	0.353830i
$299$	−18.5902	−	32.1992i	−1.07510	−	1.86213i
$300$	0.882536	+	0.590644i	0.0509532	+	0.0341009i
$301$	−1.19896	−	1.76995i	−0.0691069	−	0.102018i
$302$	0.862493	+	1.49388i	0.0496309	+	0.0859632i
$303$	1.42985	−	21.5688i	0.0821428	−	1.23909i
$304$	17.1569			0.984014
$305$	5.44467	+	9.43045i	0.311761	+	0.539986i
$306$	3.77640	−	4.90633i	0.215882	−	0.280476i
$307$	−26.9708			−1.53931			−0.769653	−	0.638463i	$-0.779571\pi$
$307$	−26.9708			−1.53931			−0.769653	+	0.638463i	$0.779571\pi$
$308$	−1.46232	−	2.15872i	−0.0833231	−	0.123005i
$309$	0.529144	−	7.98195i	0.0301020	−	0.454077i
$310$	4.75587			0.270115
$311$	−6.91102	+	11.9702i	−0.391888	+	0.678770i	−0.992699	−	0.120621i	$-0.961511\pi$
$311$	−6.91102	+	11.9702i	−0.391888	+	0.678770i	0.600810	+	0.799392i	$0.294845\pi$
$312$	−23.7787	+	11.7043i	−1.34620	+	0.662627i
$313$	−7.22385	−	12.5121i	−0.408316	−	0.707224i	0.586385	−	0.810032i	$-0.300551\pi$
$313$	−7.22385	−	12.5121i	−0.408316	−	0.707224i	−0.994701	+	0.102808i	$0.967217\pi$
$314$	−17.8321			−1.00632
$315$	4.37761	−	6.62092i	0.246650	−	0.373046i
$316$	−1.17580			−0.0661440
$317$	12.6683	+	21.9421i	0.711523	+	1.23239i	0.964285	+	0.264865i	$0.0853275\pi$
$317$	12.6683	+	21.9421i	0.711523	+	1.23239i	−0.252763	+	0.967528i	$0.581339\pi$
$318$	−4.89514	−	3.27611i	−0.274506	−	0.183715i
$319$	1.89685	−	3.28545i	0.106203	−	0.183950i
$320$	8.71834			0.487370
$321$	−22.2262	−	14.8751i	−1.24055	−	0.830247i
$322$	23.2384	−	1.67131i	1.29502	−	0.0931385i
$323$	12.5389			0.697685
$324$	3.91346	−	3.89018i	0.217415	−	0.216121i
$325$	2.48616	+	4.30615i	0.137907	+	0.238862i
$326$	−4.70964			−0.260843
$327$	18.2358	−	8.97601i	1.00844	−	0.496374i
$328$	6.77461	+	11.7340i	0.374065	+	0.647900i
$329$	22.3412	−	1.60679i	1.23171	−	0.0885851i
$330$	2.94161	−	1.44792i	0.161930	−	0.0797051i
$331$	−3.82670	−	6.62803i	−0.210334	−	0.364310i	0.741485	−	0.670970i	$-0.234122\pi$
$331$	−3.82670	−	6.62803i	−0.210334	−	0.364310i	−0.951819	+	0.306660i	$0.900789\pi$
$332$	−0.385641	−	0.667950i	−0.0211648	−	0.0366585i
$333$	−15.4556	+	20.0800i	−0.846962	+	1.10038i
$334$	−9.51055	+	16.4728i	−0.520394	+	0.901349i
$335$	4.05970	−	7.03161i	0.221805	−	0.384178i
$336$	−0.0615454	−	10.9882i	−0.00335758	−	0.599456i
$337$	9.51431	+	16.4793i	0.518278	+	0.897683i	0.999775	+	0.0212354i	$0.00675996\pi$
$337$	9.51431	+	16.4793i	0.518278	+	0.897683i	−0.481497	+	0.876448i	$0.659907\pi$
$338$	−13.8068			−0.750990
$339$	15.3085	−	7.53514i	0.831446	−	0.409253i
$340$	1.07446			0.0582705
$341$	−3.24559	+	5.62152i	−0.175758	+	0.304423i
$342$	−25.0576	−	3.33693i	−1.35496	−	0.180440i
$343$	18.0923	−	3.95831i	0.976893	−	0.213729i
$344$	−1.24328	+	2.15342i	−0.0670331	+	0.116105i
$345$	0.856702	−	12.9230i	0.0461233	−	0.695753i
$346$	6.37906	−	11.0489i	0.342941	−	0.593990i
$347$	13.1453	−	22.7683i	0.705675	−	1.22227i	−0.260772	−	0.965400i	$-0.583977\pi$
$347$	13.1453	−	22.7683i	0.705675	−	1.22227i	0.966447	−	0.256865i	$-0.0826895\pi$
$348$	−2.24876	+	1.10688i	−0.120546	+	0.0593350i
$349$	1.95792	−	3.39122i	0.104805	−	0.181528i	−0.808853	−	0.588010i	$-0.799911\pi$
$349$	1.95792	−	3.39122i	0.104805	−	0.181528i	0.913659	+	0.406482i	$0.133245\pi$
$350$	−3.10777	+	0.223512i	−0.166117	+	0.0119472i
$351$	24.4843	−	8.25023i	1.30687	−	0.440365i
$352$	−2.67695	+	4.63662i	−0.142682	+	0.247132i
$353$	21.7990			1.16024			0.580121	−	0.814530i	$-0.303005\pi$
$353$	21.7990			1.16024			0.580121	+	0.814530i	$0.303005\pi$
$354$	−1.80781	+	27.2701i	−0.0960839	+	1.44939i
$355$	−2.85904			−0.151742
$356$	2.32635	+	4.02936i	0.123296	+	0.213556i
$357$	−0.0449799	−	8.03062i	−0.00238059	−	0.425026i
$358$	−1.35287	+	2.34323i	−0.0715012	+	0.123844i
$359$	−7.67176	+	13.2879i	−0.404900	+	0.701308i	−0.994310	−	0.106527i	$-0.966027\pi$
$359$	−7.67176	+	13.2879i	−0.404900	+	0.701308i	0.589410	+	0.807834i	$0.299360\pi$
$360$	−9.15130	−	1.21868i	−0.482316	−	0.0642302i
$361$	−16.0976	−	27.8818i	−0.847241	−	1.46746i
$362$	12.5327	+	21.7074i	0.658706	+	1.14091i
$363$	0.964271	−	14.5457i	0.0506111	−	0.763450i
$364$	−3.52144	+	7.25653i	−0.184574	+	0.380345i
$365$	5.87110	+	10.1690i	0.307307	+	0.532272i
$366$	−18.4592	−	12.3540i	−0.964877	−	0.645752i
$367$	−11.6145			−0.606273			−0.303136	−	0.952947i	$-0.598034\pi$
$367$	−11.6145			−0.606273			−0.303136	+	0.952947i	$0.598034\pi$
$368$	−8.96500	−	15.5278i	−0.467333	−	0.809444i
$369$	−5.03650	−	12.2107i	−0.262190	−	0.635663i
$370$	9.94706			0.517123
$371$	−7.62049	+	0.548068i	−0.395636	+	0.0284543i
$372$	3.84771	−	1.89391i	0.199495	−	0.0981949i
$373$	21.8711			1.13244			0.566221	−	0.824254i	$-0.308405\pi$
$373$	21.8711			1.13244			0.566221	+	0.824254i	$0.308405\pi$
$374$	1.65863	−	2.87284i	0.0857659	−	0.148551i
$375$	−0.114571	+	1.72826i	−0.00591641	+	0.0892468i
$376$	−13.0265	−	22.5625i	−0.671789	−	1.16357i
$377$	−11.7357			−0.604418
$378$	−2.04726	+	16.0602i	−0.105300	+	0.826047i
$379$	−18.8100			−0.966207			−0.483103	−	0.875563i	$-0.660490\pi$
$379$	−18.8100			−0.966207			−0.483103	+	0.875563i	$0.660490\pi$
$380$	−2.19344	−	3.79916i	−0.112521	−	0.194893i
$381$	0.946769	−	14.2817i	0.0485045	−	0.731672i
$382$	−4.28118	+	7.41522i	−0.219044	+	0.379396i
$383$	−8.66187			−0.442601			−0.221300	−	0.975206i	$-0.571030\pi$
$383$	−8.66187			−0.442601			−0.221300	+	0.975206i	$0.571030\pi$
$384$	−5.60299	+	2.75790i	−0.285927	+	0.140738i
$385$	1.85667	−	3.82598i	0.0946246	−	0.194990i
$386$	−18.7368			−0.953679
$387$	1.47853	−	1.92092i	0.0751581	−	0.0976459i
$388$	−3.61433	−	6.26019i	−0.183490	−	0.317813i
$389$	−20.3809			−1.03335			−0.516676	−	0.856181i	$-0.672831\pi$
$389$	−20.3809			−1.03335			−0.516676	+	0.856181i	$0.672831\pi$
$390$	−8.42887	−	5.64109i	−0.426812	−	0.285648i
$391$	−6.55198	−	11.3484i	−0.331348	−	0.573912i
$392$	−13.3295	−	16.9222i	−0.673243	−	0.854701i
$393$	0.755678	−	11.3991i	0.0381189	−	0.575010i
$394$	−6.43289	−	11.1421i	−0.324084	−	0.561331i
$395$	−0.958875	−	1.66082i	−0.0482462	−	0.0835649i
$396$	1.80330	−	2.34286i	0.0906191	−	0.117733i
$397$	−5.35451	+	9.27428i	−0.268735	+	0.465463i	−0.968535	−	0.248876i	$-0.919939\pi$
$397$	−5.35451	+	9.27428i	−0.268735	+	0.465463i	0.699800	+	0.714339i	$0.253272\pi$
$398$	−1.93018	+	3.34317i	−0.0967512	+	0.167578i
$399$	−28.3036	+	16.5531i	−1.41695	+	0.828693i
$400$	1.19893	+	2.07661i	0.0599465	+	0.103830i
$401$	24.9398			1.24544			0.622718	−	0.782446i	$-0.286028\pi$
$401$	24.9398			1.24544			0.622718	+	0.782446i	$0.286028\pi$
$402$	−1.09551	+	16.5254i	−0.0546393	+	0.824214i
$403$	20.0802			1.00027
$404$	−3.82586	+	6.62658i	−0.190344	+	0.329685i
$405$	8.68634	+	2.35530i	0.431628	+	0.117036i
$406$	3.21063	−	6.61604i	0.159341	−	0.328349i
$407$	−6.78826	+	11.7576i	−0.336482	+	0.582803i
$408$	−8.38062	+	4.12510i	−0.414903	+	0.204223i
$409$	11.1739	−	19.3538i	0.552516	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$409$	11.1739	−	19.3538i	0.552516	−	0.956985i	0.998092	−	0.0617413i	$-0.0196654\pi$
$410$	−2.59254	+	4.49042i	−0.128037	+	0.221766i
$411$	0.821165	−	12.3870i	0.0405051	−	0.611004i
$412$	−1.41583	+	2.45230i	−0.0697532	+	0.120816i
$413$	19.8812	+	29.3494i	0.978292	+	1.44419i
$414$	10.0733	+	24.4220i	0.495074	+	1.20028i
$415$	0.628986	−	1.08944i	0.0308757	−	0.0534783i
$416$	16.5621			0.812023
$417$	−12.8187	+	6.30961i	−0.627735	+	0.308983i
$418$	−13.5441			−0.662461
$419$	9.93735	+	17.2120i	0.485471	+	0.840861i	0.999861	−	0.0166960i	$-0.00531475\pi$
$419$	9.93735	+	17.2120i	0.485471	+	0.840861i	−0.514389	+	0.857557i	$0.671981\pi$
$420$	−2.42532	+	1.41843i	−0.118343	+	0.0692123i
$421$	1.00473	−	1.74024i	0.0489674	−	0.0848141i	−0.840503	−	0.541807i	$-0.817740\pi$
$421$	1.00473	−	1.74024i	0.0489674	−	0.0848141i	0.889470	+	0.456993i	$0.151074\pi$
$422$	11.1219	−	19.2637i	0.541405	−	0.937741i
$423$	9.68437	+	23.4791i	0.470870	+	1.14160i
$424$	4.44327	+	7.69597i	0.215784	+	0.373749i
$425$	0.876227	+	1.51767i	0.0425032	+	0.0736178i
$426$	5.23229	−	2.57543i	0.253505	−	0.124780i
$427$	−28.7363	+	2.06672i	−1.39065	+	0.100016i
$428$	4.73356	+	8.19876i	0.228805	+	0.396302i
$429$	12.4201	−	6.11338i	0.599646	−	0.295157i
$430$	−0.951568			−0.0458887
$431$	14.1006	+	24.4229i	0.679201	+	1.17641i	0.975222	+	0.221229i	$0.0710069\pi$
$431$	14.1006	+	24.4229i	0.679201	+	1.17641i	−0.296021	+	0.955181i	$0.595660\pi$
$432$	11.8073	−	3.97861i	0.568081	−	0.191421i
$433$	−9.44136			−0.453723			−0.226861	−	0.973927i	$-0.572846\pi$
$433$	−9.44136			−0.453723			−0.226861	+	0.973927i	$0.572846\pi$
$434$	−5.49351	+	11.3203i	−0.263697	+	0.543392i
$435$	−3.39735	−	2.27370i	−0.162890	−	0.109016i
$436$	−7.19476			−0.344567
$437$	−26.7511	+	46.3342i	−1.27968	+	2.21646i
$438$	−19.9049	−	13.3215i	−0.951093	−	0.636526i
$439$	13.9061	+	24.0861i	0.663702	+	1.14957i	0.979636	+	0.200784i	$0.0643489\pi$
$439$	13.9061	+	24.0861i	0.663702	+	1.14957i	−0.315934	+	0.948781i	$0.602318\pi$
$440$	−4.94644			−0.235812
$441$	10.7031	+	18.0678i	0.509670	+	0.860370i
$442$	−10.2618			−0.488106
$443$	17.1164	+	29.6466i	0.813227	+	1.40855i	0.910594	+	0.413302i	$0.135625\pi$
$443$	17.1164	+	29.6466i	0.813227	+	1.40855i	−0.0973670	+	0.995249i	$0.531042\pi$
$444$	8.04762	−	3.96119i	0.381923	−	0.187990i
$445$	−3.79432	+	6.57195i	−0.179868	+	0.311540i
$446$	−14.1673			−0.670841
$447$	0.686159	−	10.3505i	0.0324542	−	0.489560i
$448$	−10.0706	+	20.7521i	−0.475790	+	0.980445i
$449$	−23.5806			−1.11284			−0.556418	−	0.830903i	$-0.687824\pi$
$449$	−23.5806			−1.11284			−0.556418	+	0.830903i	$0.687824\pi$
$450$	−1.34714	−	3.26606i	−0.0635049	−	0.153964i
$451$	−3.53850	−	6.12887i	−0.166622	−	0.288597i
$452$	−6.03983			−0.284090
$453$	−0.167818	+	2.53147i	−0.00788478	+	0.118939i
$454$	8.23652	+	14.2661i	0.386559	+	0.669540i
$455$	−13.1216	+	0.943711i	−0.615151	+	0.0442419i
$456$	31.6945	+	21.2118i	1.48423	+	0.993333i
$457$	−15.9577	−	27.6396i	−0.746471	−	1.29293i	−0.949504	−	0.313754i	$-0.898413\pi$
$457$	−15.9577	−	27.6396i	−0.746471	−	1.29293i	0.203034	−	0.979172i	$-0.434920\pi$
$458$	−2.41000	−	4.17424i	−0.112612	−	0.195049i
$459$	8.62929	−	2.90773i	0.402781	−	0.135721i
$460$	−2.29228	+	3.97035i	−0.106878	+	0.185119i
$461$	2.51227	−	4.35138i	0.117008	−	0.202664i	−0.801573	−	0.597897i	$-0.796003\pi$
$461$	2.51227	−	4.35138i	0.117008	−	0.202664i	0.918581	+	0.395234i	$0.129336\pi$
$462$	0.0485854	+	8.67435i	0.00226040	+	0.403567i
$463$	−2.74525	−	4.75491i	−0.127582	−	0.220979i	0.795157	−	0.606404i	$-0.207388\pi$
$463$	−2.74525	−	4.75491i	−0.127582	−	0.220979i	−0.922739	+	0.385424i	$0.874055\pi$
$464$	−5.65944			−0.262733
$465$	5.81299	+	3.89039i	0.269571	+	0.180413i
$466$	14.7133			0.681582
$467$	−5.54814	+	9.60965i	−0.256737	+	0.444682i	−0.965366	−	0.260900i	$-0.915981\pi$
$467$	−5.54814	+	9.60965i	−0.256737	+	0.444682i	0.708629	+	0.705582i	$0.249314\pi$
$468$	−9.06577	−	1.20729i	−0.419065	−	0.0558071i
$469$	12.0478	+	17.7855i	0.556318	+	0.821257i
$470$	4.98503	−	8.63433i	0.229942	−	0.398272i
$471$	−21.7958	−	14.5870i	−1.00430	−	0.672135i
$472$	20.6161	−	35.7082i	0.948935	−	1.64360i
$473$	0.649387	−	1.12477i	0.0298588	−	0.0517170i
$474$	3.25089	+	2.17569i	0.149318	+	0.0999326i
$475$	3.57754	−	6.19648i	0.164149	−	0.284314i
$476$	−1.24111	+	2.55751i	−0.0568860	+	0.117223i
$477$	−3.30330	−	8.00864i	−0.151248	−	0.366690i
$478$	7.14853	−	12.3816i	0.326966	−	0.566322i
$479$	5.44508			0.248792			0.124396	−	0.992233i	$-0.460301\pi$
$479$	5.44508			0.248792			0.124396	+	0.992233i	$0.460301\pi$
$480$	4.79454	+	3.20878i	0.218840	+	0.146460i
$481$	41.9984			1.91496
$482$	4.45583	+	7.71773i	0.202958	+	0.351533i
$483$	29.7709	+	16.9666i	1.35462	+	0.772008i
$484$	−2.58011	+	4.46887i	−0.117278	+	0.203131i
$485$	5.89502	−	10.2105i	0.267679	−	0.463634i
$486$	−18.0184	+	3.51427i	−0.817331	+	0.159411i
$487$	−7.59443	−	13.1539i	−0.344136	−	0.596062i	0.641060	−	0.767491i	$-0.278495\pi$
$487$	−7.59443	−	13.1539i	−0.344136	−	0.596062i	−0.985196	+	0.171429i	$0.945162\pi$
$488$	16.7552	+	29.0209i	0.758474	+	1.31372i
$489$	−5.75649	−	3.85258i	−0.260317	−	0.174220i
$490$	3.05777	−	7.65555i	0.138136	−	0.345842i
$491$	−9.81633	−	17.0024i	−0.443005	−	0.767307i	0.554906	−	0.831913i	$-0.312754\pi$
$491$	−9.81633	−	17.0024i	−0.443005	−	0.767307i	−0.997911	+	0.0646062i	$0.979421\pi$
$492$	−0.309280	+	4.66537i	−0.0139434	+	0.210331i
$493$	−4.13615			−0.186283
$494$	20.9490	+	36.2847i	0.942540	+	1.63253i
$495$	4.77989	+	0.636540i	0.214840	+	0.0286104i
$496$	9.68352			0.434803
$497$	3.30248	−	6.80532i	0.148137	−	0.305260i
$498$	−0.169732	+	2.56035i	−0.00760589	+	0.114732i
$499$	9.06442			0.405779			0.202890	−	0.979202i	$-0.434967\pi$
$499$	9.06442			0.405779			0.202890	+	0.979202i	$0.434967\pi$
$500$	0.306558	−	0.530973i	0.0137097	−	0.0237458i
$501$	−25.0996	+	12.3545i	−1.12137	+	0.551957i
$502$	−1.24351	−	2.15382i	−0.0555006	−	0.0961298i
$503$	−7.65457			−0.341300			−0.170650	−	0.985332i	$-0.554587\pi$
$503$	−7.65457			−0.341300			−0.170650	+	0.985332i	$0.554587\pi$
$504$	13.4715	−	20.3750i	0.600068	−	0.907573i
$505$	−12.4801			−0.555356
$506$	7.07718	+	12.2580i	0.314619	+	0.544937i
$507$	−16.8757	−	11.2942i	−0.749478	−	0.501594i
$508$	−2.53328	+	4.38776i	−0.112396	+	0.194675i
$509$	7.55193			0.334734			0.167367	−	0.985895i	$-0.446474\pi$
$509$	7.55193			0.334734			0.167367	+	0.985895i	$0.446474\pi$
$510$	−2.97069	−	1.98816i	−0.131544	−	0.0880371i
$511$	−30.9869	+	2.22859i	−1.37078	+	0.0985869i
$512$	22.7451			1.00520
$513$	−27.8976	−	24.5762i	−1.23171	−	1.08507i
$514$	−8.26255	−	14.3112i	−0.364446	−	0.631238i
$515$	−4.61850			−0.203515
$516$	−0.769861	+	0.378940i	−0.0338913	+	0.0166819i
$517$	6.80396	+	11.7848i	0.299238	+	0.518295i
$518$	−11.4899	+	23.6768i	−0.504836	+	1.04030i
$519$	16.8352	−	8.28659i	0.738982	−	0.363741i
$520$	7.65081	+	13.2516i	0.335510	+	0.581121i
$521$	1.88176	+	3.25930i	0.0824412	+	0.142792i	0.904298	−	0.426902i	$-0.140395\pi$
$521$	1.88176	+	3.25930i	0.0824412	+	0.142792i	−0.821857	+	0.569694i	$0.807062\pi$
$522$	8.26559	+	1.10073i	0.361775	+	0.0481778i
$523$	11.0026	−	19.0571i	0.481111	−	0.833309i	−0.518654	−	0.854984i	$-0.673567\pi$
$523$	11.0026	−	19.0571i	0.481111	−	0.833309i	0.999765	+	0.0216752i	$0.00689997\pi$
$524$	−2.02197	+	3.50216i	−0.0883303	+	0.152992i
$525$	−3.98140	−	2.26902i	−0.173762	−	0.0990283i
$526$	17.6747	+	30.6135i	0.770653	+	1.33481i
$527$	7.07711			0.308284
$528$	5.98948	−	2.94813i	0.260658	−	0.128301i
$529$	32.9130			1.43100
$530$	−1.70037	+	2.94513i	−0.0738595	+	0.127928i
$531$	−24.5172	+	31.8529i	−1.06395	+	1.38230i
$532$	11.5767	−	0.832601i	0.501914	−	0.0360978i
$533$	−10.9462	+	18.9594i	−0.474134	+	0.821223i
$534$	1.02390	−	15.4452i	0.0443085	−	0.668377i
$535$	−7.72051	+	13.3723i	−0.333787	+	0.578135i
$536$	12.4932	−	21.6388i	0.539623	−	0.934655i
$537$	−3.57039	+	1.75741i	−0.154074	+	0.0758379i
$538$	8.78745	−	15.2203i	0.378854	−	0.656194i
$539$	6.96226	+	8.83878i	0.299886	+	0.380713i
$540$	−2.39053	−	2.10592i	−0.102872	−	0.0906246i
$541$	−11.5596	+	20.0217i	−0.496984	+	0.860802i	−0.999994	−	0.00347895i	$-0.998893\pi$
$541$	−11.5596	+	20.0217i	−0.496984	+	0.860802i	0.503010	+	0.864281i	$0.332226\pi$
$542$	−20.6632			−0.887560
$543$	−2.43854	+	36.7845i	−0.104648	+	1.57857i
$544$	5.83718			0.250267
$545$	−5.86738	−	10.1626i	−0.251331	−	0.435318i
$546$	23.1636	−	13.5470i	0.991310	−	0.579760i
$547$	−14.6676	+	25.4049i	−0.627139	+	1.08624i	0.360984	+	0.932572i	$0.382441\pi$
$547$	−14.6676	+	25.4049i	−0.627139	+	1.08624i	−0.988123	+	0.153665i	$0.950892\pi$
$548$	−2.19720	+	3.80565i	−0.0938595	+	0.162569i
$549$	−12.4565	−	30.1999i	−0.531629	−	1.28890i
$550$	−0.946464	−	1.63932i	−0.0403574	−	0.0699010i
$551$	8.44373	+	14.6250i	0.359715	+	0.623044i
$552$	2.63638	−	39.7689i	0.112212	−	1.69268i
$553$	5.06082	−	0.363976i	0.215208	−	0.0154778i
$554$	−2.33226	−	4.03959i	−0.0990883	−	0.171626i
$555$	12.1581	+	8.13689i	0.516082	+	0.345392i
$556$	5.05749			0.214486
$557$	15.0497	+	26.0668i	0.637674	+	1.10448i	0.985942	+	0.167089i	$0.0534367\pi$
$557$	15.0497	+	26.0668i	0.637674	+	1.10448i	−0.348268	+	0.937395i	$0.613230\pi$
$558$	−14.1427	−	1.88340i	−0.598710	−	0.0797305i
$559$	−4.01771			−0.169931
$560$	−6.32780	+	0.455097i	−0.267398	+	0.0192314i
$561$	4.37735	−	2.15461i	0.184812	−	0.0909678i
$562$	26.3526			1.11162
$563$	10.8960	−	18.8724i	0.459212	−	0.795378i	−0.539708	−	0.841852i	$-0.681465\pi$
$563$	10.8960	−	18.8724i	0.459212	−	0.795378i	0.998919	+	0.0464746i	$0.0147986\pi$
$564$	0.594694	−	8.97074i	0.0250411	−	0.377736i
$565$	−4.92553	−	8.53126i	−0.207218	−	0.358913i
$566$	−34.8598			−1.46527
$567$	−15.6399	+	17.9553i	−0.656813	+	0.754053i
$568$	−8.79831			−0.369169
$569$	−15.5848	−	26.9936i	−0.653348	−	1.13163i	−0.982305	−	0.187287i	$-0.940031\pi$
$569$	−15.5848	−	26.9936i	−0.653348	−	1.13163i	0.328958	−	0.944345i	$-0.393303\pi$
$570$	−0.965402	+	14.5627i	−0.0404363	+	0.609966i
$571$	−11.9278	+	20.6596i	−0.499164	+	0.864577i	−1.00000		0.000965379i	$-0.999693\pi$
$571$	−11.9278	+	20.6596i	−0.499164	+	0.864577i	0.500836	+	0.865542i	$0.333026\pi$
$572$	−4.90021			−0.204888
$573$	−11.2986	+	5.56138i	−0.472006	+	0.232330i
$574$	−7.69380	−	11.3579i	−0.321133	−	0.474068i
$575$	−7.47750			−0.311833
$576$	−25.9261	−	3.45260i	−1.08026	−	0.143858i
$577$	5.84044	+	10.1159i	0.243141	+	0.421132i	0.961607	−	0.274429i	$-0.0884889\pi$
$577$	5.84044	+	10.1159i	0.243141	+	0.421132i	−0.718466	+	0.695562i	$0.755156\pi$
$578$	16.4035			0.682297
$579$	−22.9016	−	15.3271i	−0.951758	−	0.636972i
$580$	0.723539	+	1.25321i	0.0300433	+	0.0520365i
$581$	1.86662	+	2.75557i	0.0774405	+	0.114320i
$582$	−1.59078	+	23.9963i	−0.0659398	+	0.994678i
$583$	−2.32080	−	4.01975i	−0.0961178	−	0.166481i
$584$	18.0675	+	31.2938i	0.747638	+	1.29495i
$585$	−5.68790	−	13.7900i	−0.235166	−	0.570145i
$586$	−8.97883	+	15.5518i	−0.370912	+	0.642439i
$587$	2.39441	−	4.14725i	0.0988280	−	0.171175i	−0.812372	−	0.583140i	$-0.801824\pi$
$587$	2.39441	−	4.14725i	0.0988280	−	0.171175i	0.911200	+	0.411965i	$0.135157\pi$
$588$	−0.574771	−	7.41137i	−0.0237032	−	0.305640i
$589$	−14.4475	−	25.0239i	−0.595301	−	1.03109i
$590$	15.7790			0.649610
$591$	1.25167	−	18.8810i	0.0514868	−	0.776660i
$592$	20.2534			0.832411
$593$	21.0432	−	36.4480i	0.864142	−	1.49674i	−0.00375417	−	0.999993i	$-0.501195\pi$
$593$	21.0432	−	36.4480i	0.864142	−	1.49674i	0.867896	−	0.496745i	$-0.165472\pi$
$594$	−9.32100	+	3.14081i	−0.382445	+	0.128869i
$595$	−4.62461	+	0.332604i	−0.189591	+	0.0136354i
$596$	−1.83596	+	3.17998i	−0.0752039	+	0.130257i
$597$	−5.09400	+	2.50736i	−0.208484	+	0.102619i
$598$	21.8930	−	37.9198i	0.895271	−	1.55066i
$599$	16.5033	−	28.5846i	0.674308	−	1.16794i	−0.302362	−	0.953193i	$-0.597775\pi$
$599$	16.5033	−	28.5846i	0.674308	−	1.16794i	0.976671	−	0.214743i	$-0.0688915\pi$
$600$	−0.352576	+	5.31848i	−0.0143938	+	0.217126i
$601$	14.2290	−	24.6453i	0.580412	−	1.00530i	−0.415018	−	0.909813i	$-0.636225\pi$
$601$	14.2290	−	24.6453i	0.580412	−	1.00530i	0.995430	−	0.0954900i	$-0.0304418\pi$
$602$	1.09916	−	2.26500i	0.0447983	−	0.0923145i
$603$	−14.8572	+	19.3025i	−0.605030	+	0.786060i
$604$	0.449032	−	0.777746i	0.0182708	−	0.0316460i
$605$	−8.41638			−0.342175
$606$	22.8396	−	11.2421i	0.927795	−	0.456678i
$607$	7.05638			0.286410			0.143205	−	0.989693i	$-0.454259\pi$
$607$	7.05638			0.286410			0.143205	+	0.989693i	$0.454259\pi$
$608$	−11.9163	−	20.6396i	−0.483269	−	0.837047i
$609$	9.33634	−	5.46029i	0.378327	−	0.221262i
$610$	−6.41198	+	11.1059i	−0.259613	+	0.449664i
$611$	21.0478	−	36.4558i	0.851502	−	1.47485i
$612$	−3.19516	−	0.425501i	−0.129157	−	0.0171999i
$613$	−9.36330	−	16.2177i	−0.378180	−	0.655027i	0.612618	−	0.790379i	$-0.290117\pi$
$613$	−9.36330	−	16.2177i	−0.378180	−	0.655027i	−0.990797	+	0.135353i	$0.956783\pi$
$614$	−15.8812	−	27.5071i	−0.640914	−	1.11010i
$615$	−6.84206	+	3.36779i	−0.275898	+	0.135802i
$616$	5.71364	−	11.7739i	0.230209	−	0.474385i
$617$	5.18057	+	8.97300i	0.208562	+	0.361240i	0.951262	−	0.308385i	$-0.0997884\pi$
$617$	5.18057	+	8.97300i	0.208562	+	0.361240i	−0.742700	+	0.669624i	$0.766455\pi$
$618$	8.45224	−	4.16035i	0.339999	−	0.167354i
$619$	−37.9385			−1.52488			−0.762438	−	0.647061i	$-0.775998\pi$
$619$	−37.9385			−1.52488			−0.762438	+	0.647061i	$0.775998\pi$
$620$	−1.23800	−	2.14428i	−0.0497194	−	0.0861165i
$621$	−7.66534	+	38.0906i	−0.307600	+	1.52852i
$622$	−16.2777			−0.652676
$623$	−11.2603	−	16.6228i	−0.451133	−	0.665979i
$624$	−17.1622	−	11.4859i	−0.687038	−	0.459805i
$625$	1.00000			0.0400000
$626$	8.50724	−	14.7350i	0.340018	−	0.588928i
$627$	−16.5546	−	11.0793i	−0.661127	−	0.442465i
$628$	4.64189	+	8.03999i	0.185232	+	0.320830i
$629$	14.8020			0.590195
$630$	9.33024	+	0.566057i	0.371726	+	0.0225522i
$631$	−6.06904			−0.241605			−0.120802	−	0.992677i	$-0.538547\pi$
$631$	−6.06904			−0.241605			−0.120802	+	0.992677i	$0.538547\pi$
$632$	−2.95081	−	5.11095i	−0.117377	−	0.203303i
$633$	29.3521	−	14.4476i	1.16664	−	0.574242i
$634$	−14.9190	+	25.8404i	−0.592508	+	1.02625i
$635$	−8.26362			−0.327932
$636$	−0.202848	+	3.05988i	−0.00804343	+	0.121332i
$637$	12.9105	−	32.3232i	0.511533	−	1.28069i
$638$	4.46770			0.176878
$639$	8.50207	+	1.13222i	0.336337	+	0.0447901i
$640$	1.80277	+	3.12248i	0.0712605	+	0.123427i
$641$	−9.27333			−0.366275			−0.183137	−	0.983087i	$-0.558625\pi$
$641$	−9.27333			−0.366275			−0.183137	+	0.983087i	$0.558625\pi$
$642$	2.08339	−	31.4271i	0.0822247	−	1.24033i
$643$	−3.82825	−	6.63073i	−0.150972	−	0.261490i	0.780613	−	0.625014i	$-0.214907\pi$
$643$	−3.82825	−	6.63073i	−0.150972	−	0.261490i	−0.931585	+	0.363524i	$0.881574\pi$
$644$	−6.80273	−	10.0424i	−0.268065	−	0.395728i
$645$	−1.16308	−	0.778401i	−0.0457963	−	0.0306495i
$646$	7.38331	+	12.7883i	0.290492	+	0.503148i
$647$	−0.663635	−	1.14945i	−0.0260902	−	0.0451895i	0.852686	−	0.522425i	$-0.174972\pi$
$647$	−0.663635	−	1.14945i	−0.0260902	−	0.0451895i	−0.878776	+	0.477235i	$0.841639\pi$
$648$	26.7310	+	7.24811i	1.05009	+	0.284733i
$649$	−10.7682	+	18.6510i	−0.422688	+	0.732117i
$650$	−2.92785	+	5.07118i	−0.114840	+	0.198908i
$651$	−15.9748	+	9.34276i	−0.626103	+	0.366172i
$652$	1.22597	+	2.12344i	0.0480126	+	0.0831603i
$653$	−44.1050			−1.72596			−0.862981	−	0.505236i	$-0.831405\pi$
$653$	−44.1050			−1.72596			−0.862981	+	0.505236i	$0.831405\pi$
$654$	19.8923	+	13.3131i	0.777850	+	0.520583i
$655$	−6.59573			−0.257717
$656$	−5.27873	+	9.14303i	−0.206100	+	0.356975i
$657$	−13.4321	−	32.5652i	−0.524035	−	1.27049i
$658$	14.7939	+	21.8393i	0.576727	+	0.851385i
$659$	0.473550	−	0.820212i	0.0184469	−	0.0319509i	−0.856655	−	0.515890i	$-0.827461\pi$
$659$	0.473550	−	0.820212i	0.0184469	−	0.0319509i	0.875101	+	0.483939i	$0.160795\pi$
$660$	−1.41856	−	0.949380i	−0.0552172	−	0.0369546i
$661$	−3.32749	+	5.76338i	−0.129424	+	0.224169i	−0.923454	−	0.383710i	$-0.874646\pi$
$661$	−3.32749	+	5.76338i	−0.129424	+	0.224169i	0.794029	+	0.607879i	$0.207980\pi$
$662$	4.50655	−	7.80557i	0.175152	−	0.303372i
$663$	−12.5428	−	8.39439i	−0.487123	−	0.326011i
$664$	1.93562	−	3.35259i	0.0751166	−	0.130106i
$665$	10.6169	+	15.6731i	0.411707	+	0.607777i
$666$	−29.5801	−	3.93919i	−1.14620	−	0.152641i
$667$	8.82422	−	15.2840i	0.341675	−	0.591798i
$668$	9.90279			0.383150
$669$	−17.3164	−	11.5891i	−0.669490	−	0.448061i
$670$	9.56191			0.369409
$671$	−8.75156	−	15.1582i	−0.337850	−	0.585174i
$672$	−13.1760	+	7.70588i	−0.508275	+	0.297261i
$673$	21.6445	−	37.4894i	0.834336	−	1.44511i	−0.0602342	−	0.998184i	$-0.519185\pi$
$673$	21.6445	−	37.4894i	0.834336	−	1.44511i	0.894570	−	0.446928i	$-0.147482\pi$
$674$	−11.2046	+	19.4070i	−0.431586	+	0.747530i
$675$	1.02512	−	5.09403i	0.0394569	−	0.196069i
$676$	3.59405	+	6.22508i	0.138233	+	0.239426i
$677$	0.740320	+	1.28227i	0.0284528	+	0.0492817i	0.879901	−	0.475157i	$-0.157609\pi$
$677$	0.740320	+	1.28227i	0.0284528	+	0.0492817i	−0.851448	+	0.524438i	$0.824275\pi$
$678$	16.6991	+	11.1760i	0.641325	+	0.429212i
$679$	17.4945	+	25.8259i	0.671375	+	0.991109i
$680$	2.69647	+	4.67042i	0.103405	+	0.179102i
$681$	−1.60261	+	24.1748i	−0.0614121	+	0.926379i
$682$	−7.64441			−0.292719
$683$	−14.0585	−	24.3500i	−0.537932	−	0.931726i	−0.999015	−	0.0443687i	$-0.985872\pi$
$683$	−14.0585	−	24.3500i	−0.537932	−	0.931726i	0.461083	−	0.887357i	$-0.347461\pi$
$684$	5.01822	+	12.1664i	0.191877	+	0.465193i
$685$	−7.16732			−0.273849
$686$	14.6903	+	16.1213i	0.560879	+	0.615514i
$687$	0.468921	−	7.07351i	0.0178905	−	0.269871i
$688$	−1.93751			−0.0738668
$689$	−7.17931	+	12.4349i	−0.273510	+	0.473733i
$690$	13.6845	−	6.73574i	0.520958	−	0.256425i
$691$	−8.13779	−	14.0951i	−0.309576	−	0.536202i	0.668693	−	0.743538i	$-0.266854\pi$
$691$	−8.13779	−	14.0951i	−0.309576	−	0.536202i	−0.978270	+	0.207336i	$0.933521\pi$
$692$	−6.64215			−0.252497
$693$	−7.03641	+	10.6422i	−0.267291	+	0.404264i
$694$	30.9613			1.17528
$695$	4.12443	+	7.14371i	0.156448	+	0.270977i
$696$	−10.4549	−	6.99701i	−0.396291	−	0.265221i
$697$	−3.85791	+	6.68210i	−0.146129	+	0.253102i
$698$	4.61154			0.174549
$699$	17.9838	+	12.0358i	0.680209	+	0.455236i
$700$	0.909761	+	1.34302i	0.0343857	+	0.0507614i
$701$	0.626032			0.0236449			0.0118225	−	0.999930i	$-0.496237\pi$
$701$	0.626032			0.0236449			0.0118225	+	0.999930i	$0.496237\pi$
$702$	22.8314	+	20.1131i	0.861714	+	0.759121i
$703$	−30.2175	−	52.3383i	−1.13968	−	1.97398i
$704$	−14.0135			−0.528155
$705$	13.1562	−	6.47570i	0.495489	−	0.243889i
$706$	12.8359	+	22.2324i	0.483085	+	0.836729i
$707$	14.4158	−	29.7061i	0.542160	−	1.11721i
$708$	12.7659	−	6.28361i	0.479772	−	0.236153i
$709$	4.65206	+	8.05761i	0.174712	+	0.302610i	0.940062	−	0.341005i	$-0.110767\pi$
$709$	4.65206	+	8.05761i	0.174712	+	0.302610i	−0.765350	+	0.643615i	$0.777434\pi$
$710$	−1.68349	−	2.91589i	−0.0631803	−	0.109431i
$711$	2.19374	+	5.31859i	0.0822717	+	0.199463i
$712$	−11.6765	+	20.2243i	−0.437595	+	0.757937i
$713$	−15.0986	+	26.1515i	−0.565446	+	0.979381i
$714$	8.16382	−	4.77455i	0.305523	−	0.178683i
$715$	−3.99616	−	6.92155i	−0.149448	−	0.258851i
$716$	1.40866			0.0526441
$717$	18.8659	−	9.28614i	0.704560	−	0.346797i
$718$	−18.0695			−0.674347
$719$	5.22955	−	9.05785i	0.195029	−	0.337801i	−0.751881	−	0.659299i	$-0.770853\pi$
$719$	5.22955	−	9.05785i	0.195029	−	0.337801i	0.946910	+	0.321498i	$0.104186\pi$
$720$	−2.74295	−	6.65010i	−0.102224	−	0.247835i
$721$	5.33483	−	10.9933i	0.198680	−	0.409413i
$722$	18.9575	−	32.8353i	0.705525	−	1.22200i
$723$	−0.866986	+	13.0782i	−0.0322436	+	0.486382i
$724$	6.52481	−	11.3013i	0.242493	−	0.420010i
$725$	−1.18010	+	2.04400i	−0.0438279	+	0.0759122i
$726$	15.4027	−	7.58149i	0.571648	−	0.281376i
$727$	24.3299	−	42.1406i	0.902346	−	1.56291i	0.0779060	−	0.996961i	$-0.475177\pi$
$727$	24.3299	−	42.1406i	0.902346	−	1.56291i	0.824440	−	0.565949i	$-0.191490\pi$
$728$	−40.3800	+	2.90414i	−1.49658	+	0.107635i
$729$	−24.8983	−	10.4440i	−0.922158	−	0.386814i
$730$	−6.91416	+	11.9757i	−0.255905	+	0.443240i
$731$	−1.41601			−0.0523730
$732$	−0.764922	+	11.5386i	−0.0282723	+	0.426478i
$733$	26.2629			0.970044			0.485022	−	0.874502i	$-0.338812\pi$
$733$	26.2629			0.970044			0.485022	+	0.874502i	$0.338812\pi$
$734$	−6.83898	−	11.8455i	−0.252431	−	0.437224i
$735$	9.99984	−	6.85589i	0.368849	−	0.252883i
$736$	−12.4533	+	21.5697i	−0.459033	+	0.795069i
$737$	−6.52542	+	11.3024i	−0.240367	+	0.416328i
$738$	9.48784	−	12.3267i	0.349252	−	0.453751i
$739$	0.240735	+	0.416966i	0.00885560	+	0.0153383i	0.870419	−	0.492311i	$-0.163848\pi$
$739$	0.240735	+	0.416966i	0.00885560	+	0.0153383i	−0.861564	+	0.507650i	$0.830514\pi$
$740$	−2.58933	−	4.48484i	−0.0951855	−	0.164866i
$741$	−4.07612	+	61.4867i	−0.149740	+	2.25877i
$742$	−5.04614	−	7.44930i	−0.185250	−	0.273472i
$743$	22.4502	+	38.8849i	0.823618	+	1.42655i	0.902971	+	0.429702i	$0.141381\pi$
$743$	22.4502	+	38.8849i	0.823618	+	1.42655i	−0.0793529	+	0.996847i	$0.525285\pi$
$744$	17.8887	+	11.9722i	0.655831	+	0.438921i
$745$	−5.98896			−0.219419
$746$	12.8784	+	22.3060i	0.471510	+	0.816679i
$747$	−2.30188	+	2.99062i	−0.0842214	+	0.109421i
$748$	−1.72704			−0.0631468
$749$	−22.9119	−	33.8234i	−0.837182	−	1.23588i
$750$	−1.83009	+	0.900802i	−0.0668253	+	0.0328926i
$751$	−12.5538			−0.458096			−0.229048	−	0.973415i	$-0.573561\pi$
$751$	−12.5538			−0.458096			−0.229048	+	0.973415i	$0.573561\pi$
$752$	10.1501	−	17.5805i	0.370137	−	0.641097i
$753$	0.241954	−	3.64979i	0.00881729	−	0.133006i
$754$	−6.91033	−	11.9690i	−0.251659	−	0.435887i
$755$	1.46476			0.0533079
$756$	7.77400	−	3.25759i	0.282738	−	0.118477i
$757$	19.1344			0.695453			0.347727	−	0.937596i	$-0.386954\pi$
$757$	19.1344			0.695453			0.347727	+	0.937596i	$0.386954\pi$
$758$	−11.0759	−	19.1841i	−0.402296	−	0.696796i
$759$	−1.37703	+	20.7720i	−0.0499831	+	0.753977i
$760$	11.0094	−	19.0688i	0.399353	−	0.691699i
$761$	−11.9685			−0.433858			−0.216929	−	0.976187i	$-0.569604\pi$
$761$	−11.9685			−0.433858			−0.216929	+	0.976187i	$0.569604\pi$
$762$	15.1231	−	7.44388i	0.547853	−	0.269663i
$763$	30.9673	−	2.22718i	1.12109	−	0.0806293i
$764$	4.45775			0.161276
$765$	−2.00466	−	4.86016i	−0.0724785	−	0.175720i
$766$	−5.10037	−	8.83410i	−0.184284	−	0.319189i
$767$	66.6219			2.40558
$768$	18.9869	+	12.7072i	0.685132	+	0.458530i
$769$	3.00699	+	5.20826i	0.108435	+	0.187815i	0.915136	−	0.403144i	$-0.132083\pi$
$769$	3.00699	+	5.20826i	0.108435	+	0.187815i	−0.806702	+	0.590959i	$0.798749\pi$
$770$	4.99531	−	0.359265i	0.180019	−	0.0129470i
$771$	1.60767	−	24.2512i	0.0578989	−	0.873384i
$772$	4.87739	+	8.44789i	0.175541	+	0.304046i
$773$	−19.6799	−	34.0866i	−0.707837	−	1.22601i	−0.965658	−	0.259817i	$-0.916338\pi$
$773$	−19.6799	−	34.0866i	−0.707837	−	1.22601i	0.257821	−	0.966193i	$-0.416996\pi$
$774$	2.82972	+	0.376836i	0.101712	+	0.0135451i
$775$	2.01920	−	3.49736i	0.0725318	−	0.125629i
$776$	18.1411	−	31.4213i	0.651228	−	1.12796i
$777$	−33.4119	+	19.5407i	−1.19865	+	0.701019i
$778$	−12.0009	−	20.7861i	−0.430252	−	0.745219i
$779$	31.5029			1.12871
$780$	−0.349280	+	5.26877i	−0.0125062	+	0.188652i
$781$	4.59552			0.164441
$782$	7.71601	−	13.3645i	0.275924	−	0.477915i
$783$	9.20243	+	8.10682i	0.328868	+	0.289714i
$784$	6.22599	−	15.5876i	0.222357	−	0.556701i
$785$	−7.57099	+	13.1133i	−0.270220	+	0.468035i
$786$	12.0708	−	5.94145i	0.430550	−	0.211924i
$787$	−24.6270	+	42.6552i	−0.877856	+	1.52049i	−0.0241681	+	0.999708i	$0.507694\pi$
$787$	−24.6270	+	42.6552i	−0.877856	+	1.52049i	−0.853688	+	0.520784i	$0.825640\pi$
$788$	−3.34910	+	5.80081i	−0.119307	+	0.206645i
$789$	−3.43902	+	51.8764i	−0.122432	+	1.84685i
$790$	1.12923	−	1.95588i	0.0401762	−	0.0695872i
$791$	25.9963	−	1.86966i	0.924322	−	0.0664776i
$792$	14.7095	+	1.95887i	0.522678	+	0.0696053i
$793$	−27.0726	+	46.8912i	−0.961377	+	1.66515i
$794$	−12.6116			−0.447569
$795$	−4.48751	+	2.20883i	−0.159155	+	0.0783393i
$796$	2.00979			0.0712350
$797$	−6.82813	−	11.8267i	−0.241865	−	0.418922i	0.719381	−	0.694616i	$-0.244426\pi$
$797$	−6.82813	−	11.8267i	−0.241865	−	0.418922i	−0.961245	+	0.275694i	$0.911092\pi$
$798$	−33.5483	−	19.1194i	−1.18760	−	0.676819i
$799$	7.41813	−	12.8486i	0.262435	−	0.454550i
$800$	1.66543	−	2.88461i	0.0588819	−	0.101986i
$801$	13.8859	−	18.0407i	0.490635	−	0.637437i
$802$	14.6853	+	25.4357i	0.518557	+	0.898167i
$803$	−9.43698	−	16.3453i	−0.333024	−	0.576814i
$804$	7.73602	−	3.80781i	0.272828	−	0.134291i
$805$	8.63727	−	17.7986i	0.304424	−	0.627317i
$806$	11.8238	+	20.4795i	0.416477	+	0.721359i
$807$	23.1912	−	11.4152i	0.816370	−	0.401832i
$808$	−38.4057			−1.35111
$809$	−12.7564	−	22.0948i	−0.448492	−	0.776811i	0.549796	−	0.835299i	$-0.314705\pi$
$809$	−12.7564	−	22.0948i	−0.448492	−	0.776811i	−0.998288	+	0.0584877i	$0.981372\pi$
$810$	2.71265	+	10.2459i	0.0953128	+	0.360005i
$811$	37.9267			1.33179			0.665893	−	0.746047i	$-0.268051\pi$
$811$	37.9267			1.33179			0.665893	+	0.746047i	$0.268051\pi$
$812$	−3.81874	+	0.274645i	−0.134012	+	0.00963816i
$813$	−25.2562	−	16.9029i	−0.885773	−	0.592811i
$814$	−15.9885			−0.560398
$815$	−1.99957	+	3.46336i	−0.0700420	+	0.121316i
$816$	−6.04868	−	4.04813i	−0.211746	−	0.141713i
$817$	2.89071	+	5.00685i	0.101133	+	0.175168i
$818$	26.3182			0.920195
$819$	39.3941	+	2.39000i	1.37654	+	0.0835134i
$820$	2.69946			0.0942694
$821$	22.6790	+	39.2811i	0.791501	+	1.37092i	0.925037	+	0.379876i	$0.124033\pi$
$821$	22.6790	+	39.2811i	0.791501	+	1.37092i	−0.133536	+	0.991044i	$0.542633\pi$
$822$	13.1168	−	6.45633i	0.457501	−	0.225190i
$823$	3.62695	−	6.28206i	0.126427	−	0.218979i	−0.795863	−	0.605477i	$-0.792982\pi$
$823$	3.62695	−	6.28206i	0.126427	−	0.218979i	0.922290	+	0.386499i	$0.126316\pi$
$824$	−14.2128			−0.495126
$825$	0.184157	−	2.77794i	0.00641151	−	0.0967153i
$826$	−18.2263	+	37.5584i	−0.634175	+	1.30682i
$827$	15.2005			0.528572			0.264286	−	0.964444i	$-0.414864\pi$
$827$	15.2005			0.528572			0.264286	+	0.964444i	$0.414864\pi$
$828$	8.38899	−	10.8990i	0.291538	−	0.378768i
$829$	26.6868	+	46.2229i	0.926872	+	1.60539i	0.788523	+	0.615005i	$0.210846\pi$
$829$	26.6868	+	46.2229i	0.926872	+	1.60539i	0.138349	+	0.990384i	$0.455821\pi$
$830$	1.48146			0.0514224
$831$	0.453796	−	6.84535i	0.0157420	−	0.237462i
$832$	21.6752	+	37.5425i	0.751451	+	1.30155i
$833$	4.55021	−	11.3921i	0.157655	−	0.394712i
$834$	−13.9831	−	9.35831i	−0.484196	−	0.324052i
$835$	8.07580	+	13.9877i	0.279475	+	0.484064i
$836$	3.52566	+	6.10662i	0.121937	+	0.211202i
$837$	−15.7457	−	13.8711i	−0.544252	−	0.479455i
$838$	−11.7028	+	20.2699i	−0.404267	+	0.700212i
$839$	12.9952	−	22.5083i	0.448644	−	0.777073i	−0.549654	−	0.835392i	$-0.685241\pi$
$839$	12.9952	−	22.5083i	0.448644	−	0.777073i	0.998298	+	0.0583187i	$0.0185739\pi$
$840$	−12.2522	−	6.98261i	−0.422741	−	0.240923i
$841$	11.7147	+	20.2905i	0.403956	+	0.699672i
$842$	2.36646			0.0815535
$843$	32.2102	+	21.5569i	1.10938	+	0.742460i
$844$	−11.5806			−0.398620
$845$	−5.86196	+	10.1532i	−0.201657	+	0.349281i
$846$	−18.2436	+	23.7022i	−0.627226	+	0.814897i
$847$	9.72178	−	20.0334i	0.334044	−	0.688355i
$848$	−3.46217	+	5.99665i	−0.118891	+	0.205926i
$849$	−42.6084	−	28.5160i	−1.46232	−	0.978666i
$850$	−1.03190	+	1.78730i	−0.0353938	+	0.0613039i
$851$	−31.5792	+	54.6968i	−1.08252	+	1.87498i
$852$	−2.52321	−	1.68868i	−0.0864436	−	0.0578531i
$853$	−5.33160	+	9.23460i	−0.182550	+	0.316187i	−0.942748	−	0.333505i	$-0.891769\pi$
$853$	−5.33160	+	9.23460i	−0.182550	+	0.316187i	0.760198	+	0.649692i	$0.225102\pi$
$854$	−19.0286	−	28.0907i	−0.651146	−	0.961245i
$855$	−13.0926	+	17.0100i	−0.447757	+	0.581730i
$856$	−23.7588	+	41.1515i	−0.812059	+	1.40653i
$857$	−51.5864			−1.76216			−0.881079	−	0.472970i	$-0.843182\pi$
$857$	−51.5864			−1.76216			−0.881079	+	0.472970i	$0.843182\pi$
$858$	13.5482	+	9.06727i	0.462530	+	0.309552i
$859$	0.433804			0.0148012			0.00740060	−	0.999973i	$-0.497644\pi$
$859$	0.433804			0.0148012			0.00740060	+	0.999973i	$0.497644\pi$
$860$	0.247703	+	0.429034i	0.00844661	+	0.0146300i
$861$	−0.113008	−	20.1762i	−0.00385129	−	0.687602i
$862$	−16.6057	+	28.7619i	−0.565592	+	0.979635i
$863$	−3.30629	+	5.72666i	−0.112547	+	0.194938i	−0.916797	−	0.399354i	$-0.869234\pi$
$863$	−3.30629	+	5.72666i	−0.112547	+	0.194938i	0.804249	+	0.594292i	$0.202568\pi$
$864$	−12.9870	−	11.4408i	−0.441827	−	0.389225i
$865$	−5.41672	−	9.38204i	−0.184174	−	0.318999i
$866$	−5.55936	−	9.62910i	−0.188915	−	0.327210i
$867$	20.0497	+	13.4184i	0.680923	+	0.455713i
$868$	6.53402	−	0.469929i	0.221779	−	0.0159504i
$869$	1.54126	+	2.66954i	0.0522837	+	0.0905580i
$870$	0.318452	−	4.80373i	0.0107965	−	0.162862i
$871$	40.3723			1.36796
$872$	−18.0561	−	31.2740i	−0.611456	−	1.05907i
$873$	−21.5738	+	28.0288i	−0.730163	+	0.948633i
$874$	−63.0073			−2.13125
$875$	−1.15510	+	2.38028i	−0.0390496	+	0.0804682i
$876$	−0.824831	+	12.4423i	−0.0278684	+	0.420385i
$877$	−47.9270			−1.61838			−0.809190	−	0.587547i	$-0.800094\pi$
$877$	−47.9270			−1.61838			−0.809190	+	0.587547i	$0.800094\pi$
$878$	−16.3767	+	28.3652i	−0.552686	+	0.957280i
$879$	−23.6963	+	11.6638i	−0.799257	+	0.393409i
$880$	−1.92712	−	3.33786i	−0.0649630	−	0.112519i
$881$	−15.2584			−0.514068			−0.257034	−	0.966402i	$-0.582745\pi$
$881$	−15.2584			−0.514068			−0.257034	+	0.966402i	$0.582745\pi$
$882$	−12.1247	+	21.5547i	−0.408262	+	0.725786i
$883$	−20.3889			−0.686141			−0.343071	−	0.939310i	$-0.611467\pi$
$883$	−20.3889			−0.686141			−0.343071	+	0.939310i	$0.611467\pi$
$884$	2.67127	+	4.62677i	0.0898444	+	0.155615i
$885$	19.2863	+	12.9075i	0.648302	+	0.433881i
$886$	−20.1574	+	34.9136i	−0.677200	+	1.17295i
$887$	12.2117			0.410030			0.205015	−	0.978759i	$-0.434276\pi$
$887$	12.2117			0.410030			0.205015	+	0.978759i	$0.434276\pi$
$888$	37.4148	+	25.0402i	1.25556	+	0.840293i
$889$	9.54533	−	19.6697i	0.320140	−	0.659702i
$890$	−8.93684			−0.299563
$891$	−13.9621	−	3.78582i	−0.467748	−	0.126830i
$892$	3.68790	+	6.38762i	0.123480	+	0.213873i
$893$	−60.5749			−2.02706
$894$	10.9603	−	5.39486i	0.366567	−	0.180431i
$895$	1.14877	+	1.98973i	0.0383993	+	0.0665095i
$896$	−9.51476	+	0.684305i	−0.317866	+	0.0228610i
$897$	57.7785	−	28.4396i	1.92917	−	0.949572i
$898$	−13.8849	−	24.0494i	−0.463347	−	0.802540i
$899$	4.76573	+	8.25448i	0.158946	+	0.275302i
$900$	−1.12190	+	1.45758i	−0.0373966	+	0.0485860i
$901$	−2.53029	+	4.38259i	−0.0842962	+	0.146005i
$902$	4.16716	−	7.21773i	0.138751	−	0.240324i
$903$	3.19629	−	1.86933i	0.106366	−	0.0622073i
$904$	−15.1576	−	26.2538i	−0.504135	−	0.873188i
$905$	21.2841			0.707509
$906$	−2.68063	+	1.31945i	−0.0890579	+	0.0438359i
$907$	25.4436			0.844840			0.422420	−	0.906400i	$-0.361181\pi$
$907$	25.4436			0.844840			0.422420	+	0.906400i	$0.361181\pi$
$908$	4.28811	−	7.42722i	0.142306	−	0.246481i
$909$	37.1126	+	4.94230i	1.23095	+	0.163926i
$910$	−8.68888	−	12.8268i	−0.288034	−	0.425206i
$911$	−3.03816	+	5.26226i	−0.100659	+	0.174346i	−0.911956	−	0.410287i	$-0.865428\pi$
$911$	−3.03816	+	5.26226i	−0.100659	+	0.174346i	0.811297	+	0.584634i	$0.198762\pi$
$912$	−1.96568	+	29.6515i	−0.0650900	+	0.981859i
$913$	−1.01101	+	1.75112i	−0.0334595	+	0.0579536i
$914$	18.7928	−	32.5501i	0.621610	−	1.07666i
$915$	−16.9220	+	8.32934i	−0.559425	+	0.275360i
$916$	−1.25470	+	2.17320i	−0.0414563	+	0.0718044i
$917$	7.61875	−	15.6997i	0.251593	−	0.518450i
$918$	8.04673	+	7.08871i	0.265582	+	0.233962i
$919$	13.9957	−	24.2412i	0.461674	−	0.799643i	−0.537371	−	0.843346i	$-0.680582\pi$
$919$	13.9957	−	24.2412i	0.461674	−	0.799643i	0.999045	+	0.0437034i	$0.0139157\pi$
$920$	−23.0110			−0.758650
$921$	3.09007	−	46.6125i	0.101821	−	1.53593i
$922$	5.91720			0.194873
$923$	−7.10803	−	12.3115i	−0.233964	−	0.405237i
$924$	3.89837	−	2.27993i	0.128247	−	0.0750042i
$925$	4.22323	−	7.31485i	0.138859	−	0.240511i
$926$	3.23297	−	5.59967i	0.106242	−	0.184017i
$927$	13.7342	+	1.82900i	0.451092	+	0.0600721i
$928$	3.93076	+	6.80827i	0.129033	+	0.223492i
$929$	29.6232	+	51.3090i	0.971907	+	1.68339i	0.689786	+	0.724013i	$0.257705\pi$
$929$	29.6232	+	51.3090i	0.971907	+	1.68339i	0.282121	+	0.959379i	$0.408962\pi$
$930$	−0.544883	+	8.21936i	−0.0178674	+	0.269524i
$931$	−49.5701	+	7.16727i	−1.62459	+	0.234898i
$932$	−3.83003	−	6.63382i	−0.125457	−	0.217298i
$933$	−19.8959	−	13.3155i	−0.651361	−	0.435929i
$934$	−13.0676			−0.427586
$935$	−1.40841	−	2.43944i	−0.0460601	−	0.0797784i
$936$	−17.5037	−	42.4367i	−0.572128	−	1.38709i
$937$	−19.9446			−0.651560			−0.325780	−	0.945446i	$-0.605627\pi$
$937$	−19.9446			−0.651560			−0.325780	+	0.945446i	$0.605627\pi$
$938$	−11.0450	+	22.7600i	−0.360631	+	0.743141i
$939$	22.4517	−	11.0512i	0.732684	−	0.360641i
$940$	−5.19063			−0.169300
$941$	10.7113	−	18.5526i	0.349179	−	0.604796i	−0.636925	−	0.770926i	$-0.719794\pi$
$941$	10.7113	−	18.5526i	0.349179	−	0.604796i	0.986104	+	0.166130i	$0.0531271\pi$
$942$	2.04304	−	30.8185i	0.0665658	−	1.00412i
$943$	−16.4612	−	28.5117i	−0.536051	−	0.928468i
$944$	32.1279			1.04567
$945$	10.9411	+	8.32420i	0.355914	+	0.270786i
$946$	1.52951			0.0497288
$947$	−21.7745	−	37.7145i	−0.707575	−	1.22556i	−0.965754	−	0.259459i	$-0.916456\pi$
$947$	−21.7745	−	37.7145i	−0.707575	−	1.22556i	0.258179	−	0.966097i	$-0.416878\pi$
$948$	0.134712	−	2.03209i	0.00437525	−	0.0659991i
$949$	−29.1929	+	50.5637i	−0.947643	+	1.64137i
$950$	8.42626			0.273384
$951$	−39.3731	+	19.3802i	−1.27676	+	0.628445i
$952$	−14.2316	+	1.02354i	−0.461249	+	0.0331732i
$953$	14.1810			0.459368			0.229684	−	0.973265i	$-0.426231\pi$
$953$	14.1810			0.459368			0.229684	+	0.973265i	$0.426231\pi$
$954$	6.22280	−	8.08471i	0.201471	−	0.261752i
$955$	3.63533	+	6.29657i	0.117636	+	0.203752i
$956$	−7.44335			−0.240735
$957$	5.46077	+	3.65467i	0.176522	+	0.118139i
$958$	3.20623	+	5.55335i	0.103589	+	0.179421i
$959$	8.27898	−	17.0602i	0.267342	−	0.550904i
$960$	−0.998867	+	15.0675i	−0.0322383	+	0.486303i
$961$	7.34565	+	12.7230i	0.236957	+	0.410421i
$962$	24.7300	+	42.8336i	0.797326	+	1.38101i
$963$	28.2545	−	36.7084i	0.910488	−	1.18291i
$964$	2.31980	−	4.01801i	0.0747157	−	0.129411i
$965$	−7.95510	+	13.7786i	−0.256084	+	0.443550i
$966$	0.226021	+	40.3533i	0.00727210	+	1.29835i
$967$	−13.7181	−	23.7605i	−0.441145	−	0.764086i	0.556630	−	0.830761i	$-0.312094\pi$
$967$	−13.7181	−	23.7605i	−0.441145	−	0.764086i	−0.997775	+	0.0666752i	$0.978761\pi$
$968$	−25.9003			−0.832466
$969$	−1.43660	+	21.6705i	−0.0461501	+	0.696157i
$970$	13.8847			0.445810
$971$	17.4646	−	30.2495i	0.560465	−	0.970753i	−0.436991	−	0.899466i	$-0.643956\pi$
$971$	17.4646	−	30.2495i	0.560465	−	0.970753i	0.997456	−	0.0712874i	$-0.0227108\pi$
$972$	6.27487	+	7.20918i	0.201266	+	0.231234i
$973$	−21.7682	+	1.56558i	−0.697856	+	0.0501900i
$974$	8.94366	−	15.4909i	0.286573	−	0.496360i
$975$	−7.72698	+	3.80336i	−0.247461	+	0.121805i
$976$	−13.0556	+	22.6129i	−0.417898	+	0.723821i
$977$	4.74862	−	8.22485i	0.151922	−	0.263136i	−0.780012	−	0.625764i	$-0.784787\pi$
$977$	4.74862	−	8.22485i	0.151922	−	0.263136i	0.931934	+	0.362628i	$0.118121\pi$
$978$	0.539586	−	8.13946i	0.0172541	−	0.260271i
$979$	6.09885	−	10.5635i	0.194920	−	0.337611i
$980$	−4.24763	+	0.614160i	−0.135686	+	0.0196186i
$981$	13.4236	+	32.5446i	0.428581	+	1.03907i
$982$	11.5603	−	20.0230i	0.368904	−	0.638961i
$983$	−2.58750			−0.0825284			−0.0412642	−	0.999148i	$-0.513139\pi$
$983$	−2.58750			−0.0825284			−0.0412642	+	0.999148i	$0.513139\pi$
$984$	−21.0555	+	10.3639i	−0.671225	+	0.330389i
$985$	−10.9249			−0.348095
$986$	−2.43549	−	4.21839i	−0.0775618	−	0.134341i
$987$	0.217295	+	38.7954i	0.00691657	+	1.23487i
$988$	10.9065	−	18.8906i	0.346982	−	0.600990i
$989$	3.02097	−	5.23247i	0.0960612	−	0.166383i
$990$	2.16535	+	5.24975i	0.0688193	+	0.166848i
$991$	−18.2359	−	31.5855i	−0.579282	−	1.00335i	−0.995562	−	0.0941096i	$-0.970000\pi$
$991$	−18.2359	−	31.5855i	−0.579282	−	1.00335i	0.416280	−	0.909237i	$-0.363334\pi$
$992$	−6.72568	−	11.6492i	−0.213540	−	0.369863i
$993$	11.8934	−	5.85414i	0.377425	−	0.185775i
$994$	8.88524	−	0.639030i	0.281823	−	0.0202688i
$995$	1.63900	+	2.83882i	0.0519597	+	0.0899968i
$996$	1.19857	−	0.589959i	0.0379782	−	0.0186936i
$997$	−54.1449			−1.71479			−0.857393	−	0.514662i	$-0.827917\pi$
$997$	−54.1449			−1.71479			−0.857393	+	0.514662i	$0.827917\pi$
$998$	5.33741	+	9.24466i	0.168953	+	0.292635i
$999$	−32.9327	−	29.0119i	−1.04195	−	0.917894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.12	✓	36
3.2	odd	2		945.2.k.c.856.7		36
7.4	even	3		315.2.l.c.151.7	yes	36
9.4	even	3		315.2.l.c.121.7	yes	36
9.5	odd	6		945.2.l.c.226.12		36
21.11	odd	6		945.2.l.c.46.12		36
63.4	even	3	inner	315.2.k.c.256.12	yes	36
63.32	odd	6		945.2.k.c.361.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.12	✓	36	1.1	even	1	trivial
315.2.k.c.256.12	yes	36	63.4	even	3	inner
315.2.l.c.121.7	yes	36	9.4	even	3
315.2.l.c.151.7	yes	36	7.4	even	3
945.2.k.c.361.7		36	63.32	odd	6
945.2.k.c.856.7		36	3.2	odd	2
945.2.l.c.46.12		36	21.11	odd	6
945.2.l.c.226.12		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.588830 + 1.01988i) q^{2} +(-0.114571 + 1.72826i) q^{3} +(0.306558 - 0.530973i) q^{4} +1.00000 q^{5} +(-1.83009 + 0.900802i) q^{6} +(-1.15510 + 2.38028i) q^{7} +3.07736 q^{8} +(-2.97375 - 0.396015i) q^{9} +(0.588830 + 1.01988i) q^{10} -1.60736 q^{11} +(0.882536 + 0.590644i) q^{12} +(2.48616 + 4.30615i) q^{13} +(-3.10777 + 0.223512i) q^{14} +(-0.114571 + 1.72826i) q^{15} +(1.19893 + 2.07661i) q^{16} +(0.876227 + 1.51767i) q^{17} +(-1.34714 - 3.26606i) q^{18} +(3.57754 - 6.19648i) q^{19} +(0.306558 - 0.530973i) q^{20} +(-3.98140 - 2.26902i) q^{21} +(-0.946464 - 1.63932i) q^{22} -7.47750 q^{23} +(-0.352576 + 5.31848i) q^{24} +1.00000 q^{25} +(-2.92785 + 5.07118i) q^{26} +(1.02512 - 5.09403i) q^{27} +(0.909761 + 1.34302i) q^{28} +(-1.18010 + 2.04400i) q^{29} +(-1.83009 + 0.900802i) q^{30} +(2.01920 - 3.49736i) q^{31} +(1.66543 - 2.88461i) q^{32} +(0.184157 - 2.77794i) q^{33} +(-1.03190 + 1.78730i) q^{34} +(-1.15510 + 2.38028i) q^{35} +(-1.12190 + 1.45758i) q^{36} +(4.22323 - 7.31485i) q^{37} +8.42626 q^{38} +(-7.72698 + 3.80336i) q^{39} +3.07736 q^{40} +(2.20143 + 3.81300i) q^{41} +(-0.0302268 - 5.39664i) q^{42} +(-0.404008 + 0.699762i) q^{43} +(-0.492749 + 0.853467i) q^{44} +(-2.97375 - 0.396015i) q^{45} +(-4.40298 - 7.62618i) q^{46} +(-4.23300 - 7.33177i) q^{47} +(-3.72627 + 1.83414i) q^{48} +(-4.33148 - 5.49893i) q^{49} +(0.588830 + 1.01988i) q^{50} +(-2.72331 + 1.34046i) q^{51} +3.04860 q^{52} +(1.44386 + 2.50083i) q^{53} +(5.79894 - 1.95401i) q^{54} -1.60736 q^{55} +(-3.55467 + 7.32499i) q^{56} +(10.2992 + 6.89284i) q^{57} -2.77952 q^{58} +(6.69929 - 11.6035i) q^{59} +(0.882536 + 0.590644i) q^{60} +(5.44467 + 9.43045i) q^{61} +4.75587 q^{62} +(4.37761 - 6.62092i) q^{63} +8.71834 q^{64} +(2.48616 + 4.30615i) q^{65} +(2.94161 - 1.44792i) q^{66} +(4.05970 - 7.03161i) q^{67} +1.07446 q^{68} +(0.856702 - 12.9230i) q^{69} +(-3.10777 + 0.223512i) q^{70} -2.85904 q^{71} +(-9.15130 - 1.21868i) q^{72} +(5.87110 + 10.1690i) q^{73} +9.94706 q^{74} +(-0.114571 + 1.72826i) q^{75} +(-2.19344 - 3.79916i) q^{76} +(1.85667 - 3.82598i) q^{77} +(-8.42887 - 5.64109i) q^{78} +(-0.958875 - 1.66082i) q^{79} +(1.19893 + 2.07661i) q^{80} +(8.68634 + 2.35530i) q^{81} +(-2.59254 + 4.49042i) q^{82} +(0.628986 - 1.08944i) q^{83} +(-2.42532 + 1.41843i) q^{84} +(0.876227 + 1.51767i) q^{85} -0.951568 q^{86} +(-3.39735 - 2.27370i) q^{87} -4.94644 q^{88} +(-3.79432 + 6.57195i) q^{89} +(-1.34714 - 3.26606i) q^{90} +(-13.1216 + 0.943711i) q^{91} +(-2.29228 + 3.97035i) q^{92} +(5.81299 + 3.89039i) q^{93} +(4.98503 - 8.63433i) q^{94} +(3.57754 - 6.19648i) q^{95} +(4.79454 + 3.20878i) q^{96} +(5.89502 - 10.2105i) q^{97} +(3.05777 - 7.65555i) q^{98} +(4.77989 + 0.636540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more