LMFDB - Embedded newform 95.2.e.c.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(11,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$0.689667 - 1.19454i$ of defining polynomial
Character	$\chi$	$=$	95.11
Dual form			95.2.e.c.26.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.548719 + 0.950409i) q^{2} +(0.189667 - 0.328513i) q^{3} +(0.397815 + 0.689035i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.208148 + 0.360522i) q^{6} +1.89307 q^{7} -3.06803 q^{8} +(1.42805 + 2.47346i) q^{9} +(-0.548719 - 0.950409i) q^{10} +0.134400 q^{11} +0.301809 q^{12} +(-1.75687 - 3.04298i) q^{13} +(-1.03876 + 1.79919i) q^{14} +(0.189667 + 0.328513i) q^{15} +(0.887858 - 1.53781i) q^{16} +(0.830615 - 1.43867i) q^{17} -3.13440 q^{18} +(2.10596 - 3.81640i) q^{19} -0.795629 q^{20} +(0.359052 - 0.621897i) q^{21} +(-0.0737478 + 0.127735i) q^{22} +(-2.68492 - 4.65042i) q^{23} +(-0.581904 + 1.00789i) q^{24} +(-0.500000 - 0.866025i) q^{25} +3.85611 q^{26} +2.22142 q^{27} +(0.753090 + 1.30439i) q^{28} +(-2.48530 - 4.30466i) q^{29} -0.416295 q^{30} +6.56472 q^{31} +(-2.09366 - 3.62633i) q^{32} +(0.0254912 - 0.0441521i) q^{33} +(0.911548 + 1.57885i) q^{34} +(-0.946534 + 1.63944i) q^{35} +(-1.13620 + 1.96796i) q^{36} -1.69819 q^{37} +(2.47156 + 4.09566i) q^{38} -1.33288 q^{39} +(1.53402 - 2.65699i) q^{40} +(-5.31637 + 9.20823i) q^{41} +(0.394038 + 0.682493i) q^{42} +(-4.25392 + 7.36801i) q^{43} +(0.0534662 + 0.0926063i) q^{44} -2.85611 q^{45} +5.89307 q^{46} +(5.55771 + 9.62623i) q^{47} +(-0.336794 - 0.583345i) q^{48} -3.41630 q^{49} +1.09744 q^{50} +(-0.315080 - 0.545735i) q^{51} +(1.39781 - 2.42109i) q^{52} +(0.132424 + 0.229365i) q^{53} +(-1.21894 + 2.11126i) q^{54} +(-0.0672000 + 0.116394i) q^{55} -5.80799 q^{56} +(-0.854305 - 1.41568i) q^{57} +5.45492 q^{58} +(3.44833 - 5.97269i) q^{59} +(-0.150905 + 0.261374i) q^{60} +(-4.58794 - 7.94655i) q^{61} +(-3.60219 + 6.23917i) q^{62} +(2.70340 + 4.68243i) q^{63} +8.14676 q^{64} +3.51373 q^{65} +(0.0279750 + 0.0484542i) q^{66} +(1.47677 + 2.55784i) q^{67} +1.32172 q^{68} -2.03696 q^{69} +(-1.03876 - 1.79919i) q^{70} +(-0.664176 + 1.15039i) q^{71} +(-4.38131 - 7.58865i) q^{72} +(3.17119 - 5.49266i) q^{73} +(0.931830 - 1.61398i) q^{74} -0.379334 q^{75} +(3.46742 - 0.0671384i) q^{76} +0.254428 q^{77} +(0.731376 - 1.26678i) q^{78} +(0.733639 - 1.27070i) q^{79} +(0.887858 + 1.53781i) q^{80} +(-3.86283 + 6.69062i) q^{81} +(-5.83439 - 10.1055i) q^{82} +7.44736 q^{83} +0.571345 q^{84} +(0.830615 + 1.43867i) q^{85} +(-4.66842 - 8.08593i) q^{86} -1.88551 q^{87} -0.412343 q^{88} +(-4.86804 - 8.43169i) q^{89} +(1.56720 - 2.71447i) q^{90} +(-3.32587 - 5.76057i) q^{91} +(2.13620 - 3.70001i) q^{92} +(1.24511 - 2.15659i) q^{93} -12.1985 q^{94} +(2.25212 + 3.73202i) q^{95} -1.58839 q^{96} +(-8.73447 + 15.1285i) q^{97} +(1.87459 - 3.24688i) q^{98} +(0.191930 + 0.332433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20}+ \cdots - 38 q^{99}+O(q^{100}) $ 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9 - q^10 - 4 * q^11 + 12 * q^12 - 7 * q^13 + q^14 - 3 * q^15 - 7 * q^16 + q^17 - 20 * q^18 + 5 * q^19 + 10 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 - 23 * q^24 - 4 * q^25 + 6 * q^26 + 24 * q^27 + 19 * q^28 + q^29 + 4 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 + 4 * q^35 + 7 * q^36 - 4 * q^37 + 13 * q^38 + 30 * q^39 - 12 * q^40 + 8 * q^41 + 15 * q^42 - q^43 + 12 * q^44 + 2 * q^45 + 24 * q^46 + 12 * q^47 - 23 * q^48 - 20 * q^49 + 2 * q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 + 34 * q^54 + 2 * q^55 - 82 * q^56 + 7 * q^57 - 54 * q^58 + 5 * q^59 - 6 * q^60 - 37 * q^62 + 3 * q^63 + 112 * q^64 + 14 * q^65 + 31 * q^66 - 4 * q^67 + 32 * q^68 - 18 * q^69 + q^70 - 20 * q^71 - 17 * q^72 + 20 * q^73 - 25 * q^74 + 6 * q^75 + 63 * q^76 + 28 * q^77 + 18 * q^78 - 17 * q^79 - 7 * q^80 - 12 * q^81 - 21 * q^82 + 2 * q^83 - 40 * q^84 + q^85 - 8 * q^86 - 32 * q^87 - 14 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 + q^92 + 8 * q^93 - 62 * q^94 - 4 * q^95 + 42 * q^96 - q^97 - 9 * q^98 - 38 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.548719	+	0.950409i	−0.388003	+	0.672041i	−0.992181	−	0.124809i	$-0.960168\pi$
$2$	−0.548719	+	0.950409i	−0.388003	+	0.672041i	0.604178	+	0.796850i	$0.293502\pi$
$3$	0.189667	−	0.328513i	0.109504	−	0.189667i	−0.806065	−	0.591827i	$-0.798407\pi$
$3$	0.189667	−	0.328513i	0.109504	−	0.189667i	0.915570	+	0.402160i	$0.131740\pi$
$4$	0.397815	+	0.689035i	0.198907	+	0.344518i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.208148	+	0.360522i	0.0849759	+	0.147183i
$7$	1.89307			0.715512			0.357756	−	0.933815i	$-0.383542\pi$
$7$	1.89307			0.715512			0.357756	+	0.933815i	$0.383542\pi$
$8$	−3.06803			−1.08471
$9$	1.42805	+	2.47346i	0.476018	+	0.824487i
$10$	−0.548719	−	0.950409i	−0.173520	−	0.300546i
$11$	0.134400			0.0405231			0.0202615	−	0.999795i	$-0.493550\pi$
$11$	0.134400			0.0405231			0.0202615	+	0.999795i	$0.493550\pi$
$12$	0.301809			0.0871248
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	0.512626	−	0.858612i	$-0.328673\pi$
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	−0.999893	+	0.0146407i	$0.995340\pi$
$14$	−1.03876	+	1.79919i	−0.277621	+	0.480854i
$15$	0.189667	+	0.328513i	0.0489718	+	0.0848216i
$16$	0.887858	−	1.53781i	0.221964	−	0.384454i
$17$	0.830615	−	1.43867i	0.201454	−	0.348928i	−0.747543	−	0.664213i	$-0.768767\pi$
$17$	0.830615	−	1.43867i	0.201454	−	0.348928i	0.948997	+	0.315285i	$0.102100\pi$
$18$	−3.13440			−0.738785
$19$	2.10596	−	3.81640i	0.483141	−	0.875543i
$19$	2.10596	−	3.81640i	0.483141	−	0.875543i
$20$	−0.795629			−0.177908
$21$	0.359052	−	0.621897i	0.0783516	−	0.135709i
$22$	−0.0737478	+	0.127735i	−0.0157231	+	0.0272332i
$23$	−2.68492	−	4.65042i	−0.559844	−	0.969679i	−0.997509	−	0.0705407i	$-0.977528\pi$
$23$	−2.68492	−	4.65042i	−0.559844	−	0.969679i	0.437664	−	0.899138i	$-0.355806\pi$
$24$	−0.581904	+	1.00789i	−0.118781	+	0.205734i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.85611			0.756245
$27$	2.22142			0.427512
$28$	0.753090	+	1.30439i	0.142321	+	0.246507i
$29$	−2.48530	−	4.30466i	−0.461508	−	0.799355i	0.537528	−	0.843246i	$-0.319358\pi$
$29$	−2.48530	−	4.30466i	−0.461508	−	0.799355i	−0.999036	+	0.0438905i	$0.986025\pi$
$30$	−0.416295			−0.0760048
$31$	6.56472			1.17906			0.589529	−	0.807747i	$-0.299313\pi$
$31$	6.56472			1.17906			0.589529	+	0.807747i	$0.299313\pi$
$32$	−2.09366	−	3.62633i	−0.370111	−	0.641050i
$33$	0.0254912	−	0.0441521i	0.00443745	−	0.00768589i
$34$	0.911548	+	1.57885i	0.156329	+	0.270770i
$35$	−0.946534	+	1.63944i	−0.159993	+	0.277117i
$36$	−1.13620	+	1.96796i	−0.189367	+	0.327993i
$37$	−1.69819			−0.279181			−0.139590	−	0.990209i	$-0.544579\pi$
$37$	−1.69819			−0.279181			−0.139590	+	0.990209i	$0.544579\pi$
$38$	2.47156	+	4.09566i	0.400940	+	0.664404i
$39$	−1.33288			−0.213431
$40$	1.53402	−	2.65699i	0.242549	−	0.420107i
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	0.0675398	+	0.997717i	$0.478485\pi$
$41$	−5.31637	+	9.20823i	−0.830278	+	1.43808i	−0.897818	+	0.440367i	$0.854848\pi$
$42$	0.394038	+	0.682493i	0.0608013	+	0.105311i
$43$	−4.25392	+	7.36801i	−0.648717	+	1.12361i	0.334713	+	0.942320i	$0.391361\pi$
$43$	−4.25392	+	7.36801i	−0.648717	+	1.12361i	−0.983430	+	0.181290i	$0.941973\pi$
$44$	0.0534662	+	0.0926063i	0.00806034	+	0.0139609i
$45$	−2.85611			−0.425763
$46$	5.89307			0.868885
$47$	5.55771	+	9.62623i	0.810675	+	1.40413i	0.912392	+	0.409316i	$0.134233\pi$
$47$	5.55771	+	9.62623i	0.810675	+	1.40413i	−0.101718	+	0.994813i	$0.532434\pi$
$48$	−0.336794	−	0.583345i	−0.0486121	−	0.0841986i
$49$	−3.41630			−0.488042
$50$	1.09744			0.155201
$51$	−0.315080	−	0.545735i	−0.0441201	−	0.0764182i
$52$	1.39781	−	2.42109i	0.193842	−	0.335744i
$53$	0.132424	+	0.229365i	0.0181898	+	0.0315057i	0.874977	−	0.484164i	$-0.160876\pi$
$53$	0.132424	+	0.229365i	0.0181898	+	0.0315057i	−0.856787	+	0.515670i	$0.827543\pi$
$54$	−1.21894	+	2.11126i	−0.165876	+	0.287306i
$55$	−0.0672000	+	0.116394i	−0.00906124	+	0.0156945i
$56$	−5.80799			−0.776125
$57$	−0.854305	−	1.41568i	−0.113155	−	0.187511i
$58$	5.45492			0.716266
$59$	3.44833	−	5.97269i	0.448935	−	0.777578i	−0.549382	−	0.835571i	$-0.685137\pi$
$59$	3.44833	−	5.97269i	0.448935	−	0.777578i	0.998317	+	0.0579932i	$0.0184702\pi$
$60$	−0.150905	+	0.261374i	−0.0194817	+	0.0337433i
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	−0.994568	−	0.104087i	$-0.966808\pi$
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	0.407142	−	0.913365i	$-0.366525\pi$
$62$	−3.60219	+	6.23917i	−0.457478	+	0.792375i
$63$	2.70340	+	4.68243i	0.340596	+	0.589930i
$64$	8.14676			1.01834
$65$	3.51373			0.435825
$66$	0.0279750	+	0.0484542i	0.00344349	+	0.00596430i
$67$	1.47677	+	2.55784i	0.180416	+	0.312490i	0.942022	−	0.335550i	$-0.108922\pi$
$67$	1.47677	+	2.55784i	0.180416	+	0.312490i	−0.761606	+	0.648040i	$0.775589\pi$
$68$	1.32172			0.160282
$69$	−2.03696			−0.245221
$70$	−1.03876	−	1.79919i	−0.124156	−	0.215044i
$71$	−0.664176	+	1.15039i	−0.0788232	+	0.136526i	−0.902742	−	0.430181i	$-0.858450\pi$
$71$	−0.664176	+	1.15039i	−0.0788232	+	0.136526i	0.823919	+	0.566707i	$0.191783\pi$
$72$	−4.38131	−	7.58865i	−0.516342	−	0.894331i
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	−0.618585	−	0.785718i	$-0.712294\pi$
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	0.989744	+	0.142851i	$0.0456271\pi$
$74$	0.931830	−	1.61398i	0.108323	−	0.187621i
$75$	−0.379334			−0.0438017
$76$	3.46742	−	0.0671384i	0.397740	−	0.00770130i
$77$	0.254428			0.0289948
$78$	0.731376	−	1.26678i	0.0828120	−	0.143435i
$79$	0.733639	−	1.27070i	0.0825408	−	0.142965i	−0.821800	−	0.569776i	$-0.807030\pi$
$79$	0.733639	−	1.27070i	0.0825408	−	0.142965i	0.904341	+	0.426811i	$0.140363\pi$
$80$	0.887858	+	1.53781i	0.0992655	+	0.171933i
$81$	−3.86283	+	6.69062i	−0.429203	+	0.743402i
$82$	−5.83439	−	10.1055i	−0.644301	−	1.11596i
$83$	7.44736			0.817454			0.408727	−	0.912657i	$-0.365973\pi$
$83$	7.44736			0.817454			0.408727	+	0.912657i	$0.365973\pi$
$84$	0.571345			0.0623388
$85$	0.830615	+	1.43867i	0.0900928	+	0.156045i
$86$	−4.66842	−	8.08593i	−0.503408	−	0.871929i
$87$	−1.88551			−0.202148
$88$	−0.412343			−0.0439559
$89$	−4.86804	−	8.43169i	−0.516011	−	0.893757i	−0.999827	−	0.0185878i	$-0.994083\pi$
$89$	−4.86804	−	8.43169i	−0.516011	−	0.893757i	0.483816	−	0.875170i	$-0.339250\pi$
$90$	1.56720	−	2.71447i	0.165197	−	0.286130i
$91$	−3.32587	−	5.76057i	−0.348646	−	0.603872i
$92$	2.13620	−	3.70001i	0.222714	−	0.385753i
$93$	1.24511	−	2.15659i	0.129112	−	0.223628i
$94$	−12.1985			−1.25818
$95$	2.25212	+	3.73202i	0.231063	+	0.382897i
$96$	−1.58839			−0.162115
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.0432737	+	0.999063i	$0.513779\pi$
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.843577	+	0.537008i	$0.819555\pi$
$98$	1.87459	−	3.24688i	0.189362	−	0.327984i
$99$	0.191930	+	0.332433i	0.0192897	+	0.0334108i
$100$	0.397815	−	0.689035i	0.0397815	−	0.0689035i
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	0.699955	−	0.714187i	$-0.253203\pi$
$101$	−2.69865	−	4.67420i	−0.268526	−	0.465101i	−0.968481	+	0.249086i	$0.919870\pi$
$102$	0.691562			0.0684749
$103$	2.14750			0.211599			0.105800	−	0.994387i	$-0.466260\pi$
$103$	2.14750			0.211599			0.105800	+	0.994387i	$0.466260\pi$
$104$	5.39012	+	9.33596i	0.528545	+	0.915467i
$105$	0.359052	+	0.621897i	0.0350399	+	0.0606909i
$106$	−0.290654			−0.0282308
$107$	−1.00093			−0.0967631			−0.0483815	−	0.998829i	$-0.515406\pi$
$107$	−1.00093			−0.0967631			−0.0483815	+	0.998829i	$0.515406\pi$
$108$	0.883713	+	1.53064i	0.0850353	+	0.147285i
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	0.153752	+	0.988109i	$0.450864\pi$
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	−0.932604	+	0.360902i	$0.882469\pi$
$110$	−0.0737478	−	0.127735i	−0.00703158	−	0.0121790i
$111$	−0.322091	+	0.557877i	−0.0305715	+	0.0529514i
$112$	1.68077	−	2.91119i	0.158818	−	0.275081i
$113$	0.843010			0.0793037			0.0396519	−	0.999214i	$-0.487375\pi$
$113$	0.843010			0.0793037			0.0396519	+	0.999214i	$0.487375\pi$
$114$	1.81425	−	0.0351287i	0.169920	−	0.00329010i
$115$	5.36984			0.500740
$116$	1.97737	−	3.42491i	0.183595	−	0.317995i
$117$	5.01780	−	8.69108i	0.463896	−	0.803491i
$118$	3.78433	+	6.55466i	0.348376	+	0.603405i
$119$	1.57241	−	2.72349i	0.144143	−	0.249662i
$120$	−0.581904	−	1.00789i	−0.0531203	−	0.0920071i
$121$	−10.9819			−0.998358
$122$	10.0700			0.911692
$123$	2.01668	+	3.49299i	0.181838	+	0.314953i
$124$	2.61154	+	4.52332i	0.234523	+	0.406206i
$125$	1.00000			0.0894427
$126$	−5.93363			−0.528610
$127$	−9.36984	−	16.2290i	−0.831439	−	1.44009i	−0.896897	−	0.442239i	$-0.854184\pi$
$127$	−9.36984	−	16.2290i	−0.831439	−	1.44009i	0.0654584	−	0.997855i	$-0.479149\pi$
$128$	−0.282960	+	0.490101i	−0.0250104	+	0.0433193i
$129$	1.61366	+	2.79493i	0.142074	+	0.246080i
$130$	−1.92805	+	3.33949i	−0.169101	+	0.292892i
$131$	−1.44322	+	2.49973i	−0.126095	+	0.218402i	−0.922160	−	0.386808i	$-0.873578\pi$
$131$	−1.44322	+	2.49973i	−0.126095	+	0.218402i	0.796066	+	0.605210i	$0.206911\pi$
$132$	0.0405631			0.00353057
$133$	3.98673	−	7.22471i	0.345693	−	0.626461i
$134$	−3.24133			−0.280008
$135$	−1.11071	+	1.92381i	−0.0955946	+	0.165575i
$136$	−2.54835	+	4.41387i	−0.218519	+	0.378487i
$137$	9.41579	+	16.3086i	0.804445	+	1.39334i	0.916665	+	0.399656i	$0.130871\pi$
$137$	9.41579	+	16.3086i	0.804445	+	1.39334i	−0.112220	+	0.993683i	$0.535796\pi$
$138$	1.11772	−	1.93595i	0.0951466	−	0.164799i
$139$	9.08974	+	15.7439i	0.770982	+	1.33538i	0.937025	+	0.349262i	$0.113568\pi$
$139$	9.08974	+	15.7439i	0.770982	+	1.33538i	−0.166043	+	0.986118i	$0.553099\pi$
$140$	−1.50618			−0.127295
$141$	4.21645			0.355089
$142$	−0.728892	−	1.26248i	−0.0611672	−	0.105945i
$143$	−0.236123	−	0.408977i	−0.0197456	−	0.0342003i
$144$	5.07163			0.422636
$145$	4.97059			0.412785
$146$	3.48018	+	6.02785i	0.288022	+	0.498868i
$147$	−0.647958	+	1.12230i	−0.0534427	+	0.0925655i
$148$	−0.675565	−	1.17011i	−0.0555311	−	0.0961827i
$149$	11.1272	−	19.2728i	0.911573	−	1.57889i	0.0997308	−	0.995014i	$-0.468202\pi$
$149$	11.1272	−	19.2728i	0.911573	−	1.57889i	0.811842	−	0.583877i	$-0.198465\pi$
$150$	0.208148	−	0.360522i	0.0169952	−	0.0294365i
$151$	3.33482			0.271384			0.135692	−	0.990751i	$-0.456674\pi$
$151$	3.33482			0.271384			0.135692	+	0.990751i	$0.456674\pi$
$152$	−6.46116	+	11.7088i	−0.524069	+	0.949712i
$153$	4.74465			0.383582
$154$	−0.139610	+	0.241811i	−0.0112501	+	0.0194857i
$155$	−3.28236	+	5.68521i	−0.263645	+	0.456647i
$156$	−0.530238	−	0.918400i	−0.0424530	−	0.0735308i
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	−0.973767	−	0.227548i	$-0.926929\pi$
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	0.683945	+	0.729533i	$0.260263\pi$
$158$	0.805123	+	1.39451i	0.0640522	+	0.110942i
$159$	0.100466			0.00796744
$160$	4.18732			0.331037
$161$	−5.08273	−	8.80355i	−0.400576	−	0.693817i
$162$	−4.23922	−	7.34254i	−0.333064	−	0.576884i
$163$	−19.7783			−1.54916			−0.774578	−	0.632478i	$-0.782038\pi$
$163$	−19.7783			−1.54916			−0.774578	+	0.632478i	$0.782038\pi$
$164$	−8.45972			−0.660593
$165$	0.0254912	+	0.0441521i	0.00198449	+	0.00343723i
$166$	−4.08651	+	7.07805i	−0.317175	+	0.549363i
$167$	1.70160	+	2.94726i	0.131674	+	0.228066i	0.924322	−	0.381614i	$-0.124632\pi$
$167$	1.70160	+	2.94726i	0.131674	+	0.228066i	−0.792648	+	0.609679i	$0.791298\pi$
$168$	−1.10158	+	1.90800i	−0.0849890	+	0.147205i
$169$	0.326838	−	0.566100i	0.0251414	−	0.0435461i
$170$	−1.82310			−0.139825
$171$	12.4471	−	0.241010i	0.951857	−	0.0184305i
$172$	−6.76909			−0.516138
$173$	5.29286	−	9.16750i	0.402409	−	0.696992i	−0.591607	−	0.806226i	$-0.701506\pi$
$173$	5.29286	−	9.16750i	0.402409	−	0.696992i	0.994016	+	0.109234i	$0.0348398\pi$
$174$	1.03462	−	1.79201i	0.0784341	−	0.135852i
$175$	−0.946534	−	1.63944i	−0.0715512	−	0.123930i
$176$	0.119328	−	0.206682i	0.00899469	−	0.0155793i
$177$	−1.30807	−	2.26564i	−0.0983205	−	0.170296i
$178$	10.6847			0.800855
$179$	−14.6024			−1.09144			−0.545718	−	0.837969i	$-0.683743\pi$
$179$	−14.6024			−1.09144			−0.545718	+	0.837969i	$0.683743\pi$
$180$	−1.13620	−	1.96796i	−0.0846874	−	0.146683i
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	0.949141	−	0.314851i	$-0.101955\pi$
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	−0.747240	+	0.664555i	$0.768621\pi$
$182$	7.29987			0.541102
$183$	−3.48072			−0.257303
$184$	8.23742	+	14.2676i	0.607270	+	1.05182i
$185$	0.849095	−	1.47068i	0.0624267	−	0.108126i
$186$	1.36643	+	2.36673i	0.100192	+	0.173537i
$187$	0.111635	−	0.193357i	0.00816353	−	0.0141396i
$188$	−4.42187	+	7.65891i	−0.322498	+	0.558583i
$189$	4.20530			0.305890
$190$	−4.78273	+	0.0926063i	−0.346975	+	0.00671836i
$191$	20.4758			1.48157			0.740787	−	0.671740i	$-0.234453\pi$
$191$	20.4758			1.48157			0.740787	+	0.671740i	$0.234453\pi$
$192$	1.54517	−	2.67631i	0.111513	−	0.193146i
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	−0.993322	−	0.115373i	$-0.963194\pi$
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	0.596577	+	0.802556i	$0.296527\pi$
$194$	−9.58554	−	16.6026i	−0.688202	−	1.19200i
$195$	0.666439	−	1.15431i	0.0477247	−	0.0826616i
$196$	−1.35905	−	2.35395i	−0.0970752	−	0.168139i
$197$	−19.8532			−1.41448			−0.707242	−	0.706971i	$-0.750061\pi$
$197$	−19.8532			−1.41448			−0.707242	+	0.706971i	$0.750061\pi$
$198$	−0.421263			−0.0299379
$199$	−10.5013	−	18.1888i	−0.744417	−	1.28937i	−0.950467	−	0.310826i	$-0.899394\pi$
$199$	−10.5013	−	18.1888i	−0.744417	−	1.28937i	0.206050	−	0.978542i	$-0.433939\pi$
$200$	1.53402	+	2.65699i	0.108471	+	0.187878i
$201$	1.12038			0.0790254
$202$	5.92321			0.416756
$203$	−4.70483	−	8.14901i	−0.330215	−	0.571948i
$204$	0.250687	−	0.434203i	0.0175516	−	0.0304003i
$205$	−5.31637	−	9.20823i	−0.371312	−	0.643131i
$206$	−1.17837	+	2.04100i	−0.0821011	+	0.142203i
$207$	7.66842	−	13.2821i	0.532992	−	0.923169i
$208$	−6.23939			−0.432624
$209$	0.283041	−	0.512924i	0.0195784	−	0.0354797i
$210$	−0.788075			−0.0543824
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	−0.556321	−	0.830967i	$-0.687788\pi$
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	0.997799	+	0.0663046i	$0.0211209\pi$
$212$	−0.105360	+	0.182489i	−0.00723617	+	0.0125334i
$213$	0.251944	+	0.436380i	0.0172629	+	0.0299003i
$214$	0.549227	−	0.951289i	0.0375444	−	0.0650288i
$215$	−4.25392	−	7.36801i	−0.290115	−	0.502494i
$216$	−6.81538			−0.463728
$217$	12.4275			0.843630
$218$	−8.92377	−	15.4564i	−0.604394	−	1.04684i
$219$	−1.20294	−	2.08355i	−0.0812870	−	0.140793i
$220$	−0.106932			−0.00720939
$221$	−5.83712			−0.392647
$222$	−0.353475	−	0.612236i	−0.0237237	−	0.0410906i
$223$	−10.1972	+	17.6621i	−0.682856	+	1.18274i	0.291249	+	0.956647i	$0.405929\pi$
$223$	−10.1972	+	17.6621i	−0.682856	+	1.18274i	−0.974105	+	0.226095i	$0.927404\pi$
$224$	−3.96344	−	6.86488i	−0.264819	−	0.458679i
$225$	1.42805	−	2.47346i	0.0952035	−	0.164897i
$226$	−0.462576	+	0.801205i	−0.0307701	+	0.0532954i
$227$	25.4172			1.68700			0.843500	−	0.537129i	$-0.180491\pi$
$227$	25.4172			1.68700			0.843500	+	0.537129i	$0.180491\pi$
$228$	0.635598	−	1.15182i	0.0420935	−	0.0762814i
$229$	2.21553			0.146406			0.0732030	−	0.997317i	$-0.476678\pi$
$229$	2.21553			0.146406			0.0732030	+	0.997317i	$0.476678\pi$
$230$	−2.94653	+	5.10355i	−0.194289	+	0.336518i
$231$	0.0482566	−	0.0835829i	0.00317505	−	0.00549935i
$232$	7.62496	+	13.2068i	0.500603	+	0.867071i
$233$	7.07882	−	12.2609i	0.463749	−	0.803236i	−0.535395	−	0.844602i	$-0.679837\pi$
$233$	7.07882	−	12.2609i	0.463749	−	0.803236i	0.999144	+	0.0413652i	$0.0131707\pi$
$234$	5.50672	+	9.53792i	0.359986	+	0.623514i
$235$	−11.1154			−0.725089
$236$	5.48719			0.357186
$237$	−0.278294	−	0.482019i	−0.0180771	−	0.0313105i
$238$	1.72562	+	2.98887i	0.111855	+	0.193739i
$239$	3.01476			0.195008			0.0975042	−	0.995235i	$-0.468914\pi$
$239$	3.01476			0.195008			0.0975042	+	0.995235i	$0.468914\pi$
$240$	0.673589			0.0434800
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	0.939781	+	0.341776i	$0.111028\pi$
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	−0.173904	+	0.984763i	$0.555638\pi$
$242$	6.02600	−	10.4373i	0.387366	−	0.670937i
$243$	4.79743	+	8.30939i	0.307755	+	0.533048i
$244$	3.65030	−	6.32251i	0.233687	−	0.404757i
$245$	1.70815	−	2.95860i	0.109130	−	0.189018i
$246$	−4.42636			−0.282215
$247$	−15.3131	+	0.296503i	−0.974352	+	0.0188660i
$248$	−20.1407			−1.27894
$249$	1.41252	−	2.44655i	0.0895147	−	0.155044i
$250$	−0.548719	+	0.950409i	−0.0347040	+	0.0601092i
$251$	−8.59495	−	14.8869i	−0.542509	−	0.939653i	−0.998759	−	0.0498012i	$-0.984141\pi$
$251$	−8.59495	−	14.8869i	−0.542509	−	0.939653i	0.456250	−	0.889851i	$-0.349192\pi$
$252$	−2.15090	+	3.72548i	−0.135494	+	0.234683i
$253$	−0.360853	−	0.625016i	−0.0226866	−	0.0392944i
$254$	20.5656			1.29040
$255$	0.630160			0.0394622
$256$	7.83623	+	13.5727i	0.489764	+	0.848297i
$257$	9.77143	+	16.9246i	0.609525	+	1.05573i	0.991319	+	0.131481i	$0.0419732\pi$
$257$	9.77143	+	16.9246i	0.609525	+	1.05573i	−0.381794	+	0.924248i	$0.624693\pi$
$258$	−3.54178			−0.220501
$259$	−3.21479			−0.199757
$260$	1.39781	+	2.42109i	0.0866888	+	0.150149i
$261$	7.09827	−	12.2946i	0.439372	−	0.761014i
$262$	−1.58384	−	2.74330i	−0.0978502	−	0.169482i
$263$	−4.40680	+	7.63280i	−0.271735	+	0.470659i	−0.969306	−	0.245857i	$-0.920931\pi$
$263$	−4.40680	+	7.63280i	−0.271735	+	0.470659i	0.697571	+	0.716515i	$0.254264\pi$
$264$	−0.0782078	+	0.135460i	−0.00481336	+	0.00833698i
$265$	−0.264847			−0.0162694
$266$	4.67883	+	7.75336i	0.286878	+	0.475389i
$267$	−3.69322			−0.226022
$268$	−1.17496	+	2.03510i	−0.0717723	+	0.124313i
$269$	−0.144181	+	0.249729i	−0.00879088	+	0.0152263i	−0.870387	−	0.492368i	$-0.836132\pi$
$269$	−0.144181	+	0.249729i	−0.00879088	+	0.0152263i	0.861596	+	0.507594i	$0.169465\pi$
$270$	−1.21894	−	2.11126i	−0.0741820	−	0.128487i
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	−0.189761	−	0.981830i	$-0.560771\pi$
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	0.945171	−	0.326577i	$-0.105895\pi$
$272$	−1.47494	−	2.55466i	−0.0894311	−	0.154899i
$273$	−2.52323			−0.152713
$274$	−20.6665			−1.24851
$275$	−0.0672000	−	0.116394i	−0.00405231	−	0.00701881i
$276$	−0.810333	−	1.40354i	−0.0487763	−	0.0844831i
$277$	−4.40486			−0.264662			−0.132331	−	0.991206i	$-0.542246\pi$
$277$	−4.40486			−0.264662			−0.132331	+	0.991206i	$0.542246\pi$
$278$	−19.9509			−1.19657
$279$	9.37476	+	16.2376i	0.561252	+	0.972118i
$280$	2.90399	−	5.02987i	0.173547	−	0.300592i
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.676600	+	0.736350i	$0.263452\pi$
$281$	16.3607	+	28.3376i	0.975998	+	1.69048i	0.299398	+	0.954128i	$0.403214\pi$
$282$	−2.31365	+	4.00736i	−0.137776	+	0.238635i
$283$	0.664463	−	1.15088i	0.0394982	−	0.0684129i	−0.845600	−	0.533816i	$-0.820757\pi$
$283$	0.664463	−	1.15088i	0.0394982	−	0.0684129i	0.885099	+	0.465403i	$0.154091\pi$
$284$	−1.05688			−0.0627140
$285$	1.65317	−	0.0320097i	0.0979252	−	0.00189609i
$286$	0.518260			0.0306454
$287$	−10.0643	+	17.4318i	−0.594074	+	1.02897i
$288$	5.97972	−	10.3572i	0.352358	−	0.610302i
$289$	7.12016	+	12.3325i	0.418833	+	0.725440i
$290$	−2.72746	+	4.72410i	−0.160162	+	0.277409i
$291$	3.31328	+	5.73877i	0.194228	+	0.336413i
$292$	5.04618			0.295305
$293$	−7.72365			−0.451220			−0.225610	−	0.974218i	$-0.572438\pi$
$293$	−7.72365			−0.451220			−0.225610	+	0.974218i	$0.572438\pi$
$294$	−0.711094	−	1.23165i	−0.0414718	−	0.0718313i
$295$	3.44833	+	5.97269i	0.200770	+	0.347743i
$296$	5.21010			0.302831
$297$	0.298558			0.0173241
$298$	12.2114	+	21.1507i	0.707386	+	1.22523i
$299$	−9.43409	+	16.3403i	−0.545588	+	0.944986i
$300$	−0.150905	−	0.261374i	−0.00871248	−	0.0150905i
$301$	−8.05296	+	13.9481i	−0.464165	+	0.803957i
$302$	−1.82988	+	3.16944i	−0.105298	+	0.182381i
$303$	−2.04738			−0.117619
$304$	−3.99912	−	6.62700i	−0.229366	−	0.380085i
$305$	9.17589			0.525410
$306$	−2.60348	+	4.50936i	−0.148831	+	0.257783i
$307$	4.55001	−	7.88085i	0.259683	−	0.449784i	−0.706474	−	0.707739i	$-0.749715\pi$
$307$	4.55001	−	7.88085i	0.259683	−	0.449784i	0.966157	+	0.257955i	$0.0830486\pi$
$308$	0.101215	+	0.175310i	0.00576727	+	0.00998921i
$309$	0.407309	−	0.705480i	0.0231710	−	0.0401333i
$310$	−3.60219	−	6.23917i	−0.204590	−	0.354361i
$311$	−12.4569			−0.706364			−0.353182	−	0.935555i	$-0.614900\pi$
$311$	−12.4569			−0.706364			−0.353182	+	0.935555i	$0.614900\pi$
$312$	4.08931			0.231512
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	0.835672	−	0.549229i	$-0.185078\pi$
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	−0.893482	+	0.449099i	$0.851745\pi$
$314$	−3.98530	−	6.90274i	−0.224903	−	0.389544i
$315$	−5.40680			−0.304639
$316$	1.16741			0.0656719
$317$	−11.7856	−	20.4133i	−0.661947	−	1.14653i	−0.980103	−	0.198487i	$-0.936397\pi$
$317$	−11.7856	−	20.4133i	−0.661947	−	1.14653i	0.318157	−	0.948038i	$-0.396936\pi$
$318$	−0.0551274	+	0.0954834i	−0.00309139	+	0.00535445i
$319$	−0.334024	−	0.578546i	−0.0187017	−	0.0323923i
$320$	−4.07338	+	7.05530i	−0.227709	+	0.394403i
$321$	−0.189842	+	0.328817i	−0.0105960	+	0.0183528i
$322$	11.1560			0.621698
$323$	−3.74129	−	6.19974i	−0.208171	−	0.344963i
$324$	−6.14676			−0.341487
$325$	−1.75687	+	3.04298i	−0.0974534	+	0.168794i
$326$	10.8527	−	18.7975i	0.601077	−	1.04110i
$327$	3.08454	+	5.34257i	0.170575	+	0.295445i
$328$	16.3108	−	28.2511i	0.900613	−	1.55991i
$329$	10.5211	+	18.2231i	0.580048	+	1.00467i
$330$	−0.0559501			−0.00307995
$331$	−18.7175			−1.02881			−0.514403	−	0.857549i	$-0.671986\pi$
$331$	−18.7175			−1.02881			−0.514403	+	0.857549i	$0.671986\pi$
$332$	2.96267	+	5.13150i	0.162598	+	0.281627i
$333$	−2.42511	−	4.20041i	−0.132895	−	0.230181i
$334$	−3.73480			−0.204359
$335$	−2.95354			−0.161369
$336$	−0.637575	−	1.10431i	−0.0347826	−	0.0602451i
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.0508197	−	0.998708i	$-0.483817\pi$
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.839497	−	0.543365i	$-0.182850\pi$
$338$	0.358684	+	0.621259i	0.0195098	+	0.0337921i
$339$	0.159891	−	0.276940i	0.00868409	−	0.0150413i
$340$	−0.660861	+	1.14465i	−0.0358402	+	0.0620771i
$341$	0.882297			0.0477791
$342$	−6.60093	+	11.9621i	−0.356937	+	0.646838i
$343$	−19.7188			−1.06471
$344$	13.0512	−	22.6053i	0.703671	−	1.21879i
$345$	1.01848	−	1.76406i	0.0548332	−	0.0949738i
$346$	5.80859	+	10.0608i	0.312271	+	0.540870i
$347$	1.28333	−	2.22279i	0.0688927	−	0.119326i	−0.829521	−	0.558475i	$-0.811387\pi$
$347$	1.28333	−	2.22279i	0.0688927	−	0.119326i	0.898414	+	0.439149i	$0.144720\pi$
$348$	−0.750085	−	1.29919i	−0.0402088	−	0.0696436i
$349$	16.6195			0.889619			0.444810	−	0.895625i	$-0.353271\pi$
$349$	16.6195			0.889619			0.444810	+	0.895625i	$0.353271\pi$
$350$	2.07752			0.111048
$351$	−3.90274	−	6.75974i	−0.208313	−	0.360808i
$352$	−0.281388	−	0.487378i	−0.0149980	−	0.0259773i
$353$	28.3629			1.50961			0.754803	−	0.655951i	$-0.227732\pi$
$353$	28.3629			1.50961			0.754803	+	0.655951i	$0.227732\pi$
$354$	2.87105			0.152595
$355$	−0.664176	−	1.15039i	−0.0352508	−	0.0610562i
$356$	3.87315	−	6.70850i	0.205277	−	0.355550i
$357$	−0.596468	−	1.03311i	−0.0315684	−	0.0546781i
$358$	8.01262	−	13.8783i	0.423480	−	0.733489i
$359$	−8.69427	+	15.0589i	−0.458866	+	0.794780i	−0.998901	−	0.0468628i	$-0.985078\pi$
$359$	−8.69427	+	15.0589i	−0.458866	+	0.794780i	0.540035	+	0.841643i	$0.318411\pi$
$360$	8.76262			0.461831
$361$	−10.1298	−	16.0744i	−0.533150	−	0.846021i
$362$	−5.96195			−0.313353
$363$	−2.08291	+	3.60771i	−0.109324	+	0.189355i
$364$	2.64616	−	4.58328i	0.138696	−	0.240229i
$365$	3.17119	+	5.49266i	0.165987	+	0.287499i
$366$	1.90994	−	3.30811i	0.0998342	−	0.172918i
$367$	−12.9024	−	22.3477i	−0.673501	−	1.16654i	−0.976905	−	0.213676i	$-0.931456\pi$
$367$	−12.9024	−	22.3477i	−0.673501	−	1.16654i	0.303404	−	0.952862i	$-0.401877\pi$
$368$	−9.53531			−0.497062
$369$	−30.3683			−1.58091
$370$	0.931830	+	1.61398i	0.0484435	+	0.0839067i
$371$	0.250687	+	0.434203i	0.0130150	+	0.0225427i
$372$	1.98129			0.102725
$373$	27.0663			1.40144			0.700719	−	0.713437i	$-0.252862\pi$
$373$	27.0663			1.40144			0.700719	+	0.713437i	$0.252862\pi$
$374$	0.122512	+	0.212197i	0.00633495	+	0.0109724i
$375$	0.189667	−	0.328513i	0.00979436	−	0.0169643i
$376$	−17.0512	−	29.5336i	−0.879349	−	1.52308i
$377$	−8.73267	+	15.1254i	−0.449755	+	0.778999i
$378$	−2.30753	+	3.99675i	−0.118686	+	0.205571i
$379$	12.4028			0.637092			0.318546	−	0.947907i	$-0.396806\pi$
$379$	12.4028			0.637092			0.318546	+	0.947907i	$0.396806\pi$
$380$	−1.67557	+	3.03644i	−0.0859547	+	0.155766i
$381$	−7.10859			−0.364184
$382$	−11.2354	+	19.4604i	−0.574855	+	0.995678i
$383$	2.67971	−	4.64139i	0.136927	−	0.237164i	−0.789405	−	0.613873i	$-0.789611\pi$
$383$	2.67971	−	4.64139i	0.136927	−	0.237164i	0.926332	+	0.376709i	$0.122944\pi$
$384$	0.107336	+	0.185912i	0.00547749	+	0.00948728i
$385$	−0.127214	+	0.220341i	−0.00648343	+	0.0112296i
$386$	−6.04881	−	10.4769i	−0.307877	−	0.533258i
$387$	−24.2993			−1.23520
$388$	−13.8988			−0.705605
$389$	−4.28467	−	7.42126i	−0.217241	−	0.376273i	0.736722	−	0.676195i	$-0.236372\pi$
$389$	−4.28467	−	7.42126i	−0.217241	−	0.376273i	−0.953964	+	0.299923i	$0.903039\pi$
$390$	0.731376	+	1.26678i	0.0370346	+	0.0641459i
$391$	−8.92053			−0.451131
$392$	10.4813			0.529386
$393$	0.547462	+	0.948232i	0.0276158	+	0.0478320i
$394$	10.8939	−	18.8687i	0.548824	−	0.950592i
$395$	0.733639	+	1.27070i	0.0369134	+	0.0639359i
$396$	−0.152705	+	0.264493i	−0.00767373	+	0.0132913i
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	−0.700999	−	0.713162i	$-0.747262\pi$
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	0.968116	+	0.250502i	$0.0805957\pi$
$398$	23.0490			1.15534
$399$	−1.61726	−	2.67998i	−0.0809641	−	0.134167i
$400$	−1.77572			−0.0887858
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	−0.945603	−	0.325323i	$-0.894527\pi$
$401$	−3.82604	+	6.62690i	−0.191063	+	0.330932i	0.754539	+	0.656255i	$0.227860\pi$
$402$	−0.614773	+	1.06482i	−0.0306621	+	0.0531083i
$403$	−11.5333	−	19.9763i	−0.574516	−	0.995091i
$404$	2.14713	−	3.71893i	0.106824	−	0.185024i
$405$	−3.86283	−	6.69062i	−0.191946	−	0.332459i
$406$	10.3265			0.512497
$407$	−0.228237			−0.0113133
$408$	0.966676	+	1.67433i	0.0478576	+	0.0828918i
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	0.997482	−	0.0709173i	$-0.0225927\pi$
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	−0.560157	+	0.828386i	$0.689259\pi$
$410$	11.6688			0.576280
$411$	7.14345			0.352361
$412$	0.854305	+	1.47970i	0.0420886	+	0.0728996i
$413$	6.52793	−	11.3067i	0.321218	−	0.556367i
$414$	8.41561	+	14.5763i	0.413605	+	0.716384i
$415$	−3.72368	+	6.44961i	−0.182788	+	0.316599i
$416$	−7.35657	+	12.7420i	−0.360685	+	0.624726i
$417$	6.89609			0.337703
$418$	0.332178	+	0.550456i	0.0162473	+	0.0269237i
$419$	1.18732			0.0580045			0.0290023	−	0.999579i	$-0.490767\pi$
$419$	1.18732			0.0580045			0.0290023	+	0.999579i	$0.490767\pi$
$420$	−0.285672	+	0.494799i	−0.0139394	+	0.0241437i
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	0.0975661	+	0.995229i	$0.468894\pi$
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	−0.910677	+	0.413120i	$0.864439\pi$
$422$	7.03770	+	12.1896i	0.342590	+	0.593383i
$423$	−15.8734	+	27.4935i	−0.771791	+	1.33678i
$424$	−0.406280	−	0.703698i	−0.0197307	−	0.0341746i
$425$	−1.66123			−0.0805815
$426$	−0.552987			−0.0267923
$427$	−8.68529	−	15.0434i	−0.420311	−	0.727999i
$428$	−0.398183	−	0.689673i	−0.0192469	−	0.0333366i
$429$	−0.179139			−0.00864890
$430$	9.33683			0.450262
$431$	3.08799	+	5.34855i	0.148743	+	0.257631i	0.930763	−	0.365623i	$-0.119144\pi$
$431$	3.08799	+	5.34855i	0.148743	+	0.257631i	−0.782020	+	0.623253i	$0.785811\pi$
$432$	1.97230	−	3.41613i	0.0948925	−	0.164359i
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	0.998111	−	0.0614325i	$-0.0195669\pi$
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	−0.552258	+	0.833673i	$0.686234\pi$
$434$	−6.81918	+	11.8112i	−0.327331	+	0.566954i
$435$	0.942757	−	1.63290i	0.0452017	−	0.0782917i
$436$	−12.9392			−0.619677
$437$	−23.4022	+	0.453129i	−1.11948	+	0.0216761i
$438$	2.64030			0.126158
$439$	0.113656	−	0.196858i	0.00542450	−	0.00939550i	−0.863300	−	0.504690i	$-0.831607\pi$
$439$	0.113656	−	0.196858i	0.00542450	−	0.00939550i	0.868725	+	0.495295i	$0.164940\pi$
$440$	0.206172	−	0.357100i	0.00982884	−	0.0170241i
$441$	−4.87865	−	8.45007i	−0.232317	−	0.402384i
$442$	3.20294	−	5.54765i	0.152348	−	0.263875i
$443$	17.4913	+	30.2959i	0.831038	+	1.43940i	0.897216	+	0.441593i	$0.145586\pi$
$443$	17.4913	+	30.2959i	0.831038	+	1.43940i	−0.0661770	+	0.997808i	$0.521080\pi$
$444$	−0.512529			−0.0243236
$445$	9.73608			0.461534
$446$	−11.1908	−	19.3831i	−0.529901	−	0.917815i
$447$	−4.22091	−	7.31083i	−0.199642	−	0.345791i
$448$	15.4224			0.728638
$449$	−16.9509			−0.799961			−0.399980	−	0.916524i	$-0.630983\pi$
$449$	−16.9509			−0.799961			−0.399980	+	0.916524i	$0.630983\pi$
$450$	1.56720	+	2.71447i	0.0738785	+	0.127961i
$451$	−0.714520	+	1.23759i	−0.0336454	+	0.0582756i
$452$	0.335362	+	0.580864i	0.0157741	+	0.0273215i
$453$	0.632505	−	1.09553i	0.0297177	−	0.0514725i
$454$	−13.9469	+	24.1568i	−0.654561	+	1.13373i
$455$	6.65174			0.311838
$456$	2.62103	+	4.34335i	0.122741	+	0.203396i
$457$	1.60241			0.0749578			0.0374789	−	0.999297i	$-0.488067\pi$
$457$	1.60241			0.0749578			0.0374789	+	0.999297i	$0.488067\pi$
$458$	−1.21570	+	2.10566i	−0.0568060	+	0.0983909i
$459$	1.84514	−	3.19588i	0.0861239	−	0.149171i
$460$	2.13620	+	3.70001i	0.0996009	+	0.172514i
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	−0.746107	−	0.665826i	$-0.768079\pi$
$461$	4.37081	−	7.57046i	0.203569	−	0.352592i	0.949676	+	0.313234i	$0.101413\pi$
$462$	0.0529586	+	0.0917270i	0.00246386	+	0.00426753i
$463$	21.1886			0.984718			0.492359	−	0.870392i	$-0.336135\pi$
$463$	21.1886			0.984718			0.492359	+	0.870392i	$0.336135\pi$
$464$	−8.82636			−0.409753
$465$	1.24511	+	2.15659i	0.0577406	+	0.100010i
$466$	7.76857	+	13.4556i	0.359872	+	0.623316i
$467$	20.4516			0.946388			0.473194	−	0.880958i	$-0.343101\pi$
$467$	20.4516			0.946388			0.473194	+	0.880958i	$0.343101\pi$
$468$	7.98461			0.369089
$469$	2.79563	+	4.84217i	0.129090	+	0.223591i
$470$	6.09924	−	10.5642i	0.281337	−	0.487290i
$471$	1.37753	+	2.38596i	0.0634734	+	0.109939i
$472$	−10.5796	+	18.3244i	−0.486965	+	0.843449i
$473$	−0.571727	+	0.990259i	−0.0262880	+	0.0455322i
$474$	0.610821			0.0280559
$475$	−4.35808	+	0.0843840i	−0.199963	+	0.00387180i
$476$	2.50211			0.114684
$477$	−0.378216	+	0.655090i	−0.0173173	+	0.0299945i
$478$	−1.65425	+	2.86525i	−0.0756639	+	0.131054i
$479$	−11.7746	−	20.3942i	−0.537994	−	0.931833i	−0.999012	−	0.0444419i	$-0.985849\pi$
$479$	−11.7746	−	20.3942i	−0.537994	−	0.931833i	0.461018	−	0.887391i	$-0.347484\pi$
$480$	0.794197	−	1.37559i	0.0362499	−	0.0627867i
$481$	2.98350	+	5.16757i	0.136036	+	0.235621i
$482$	−26.0962			−1.18865
$483$	−3.85611			−0.175459
$484$	−4.36877	−	7.56694i	−0.198581	−	0.343952i
$485$	−8.73447	−	15.1285i	−0.396612	−	0.686952i
$486$	−10.5298			−0.477640
$487$	36.0392			1.63309			0.816546	−	0.577280i	$-0.195886\pi$
$487$	36.0392			1.63309			0.816546	+	0.577280i	$0.195886\pi$
$488$	14.0760	+	24.3803i	0.637188	+	1.10364i
$489$	−3.75129	+	6.49742i	−0.169639	+	0.293824i
$490$	1.87459	+	3.24688i	0.0846852	+	0.146679i
$491$	−10.0297	+	17.3720i	−0.452635	+	0.783988i	−0.998549	−	0.0538541i	$-0.982849\pi$
$491$	−10.0297	+	17.3720i	−0.452635	+	0.783988i	0.545913	+	0.837842i	$0.316183\pi$
$492$	−1.60453	+	2.77913i	−0.0723378	+	0.125293i
$493$	−8.25729			−0.371890
$494$	8.12081	−	14.7164i	0.365373	−	0.662124i
$495$	−0.383860			−0.0172532
$496$	5.82853	−	10.0953i	0.261709	−	0.453293i
$497$	−1.25733	+	2.17776i	−0.0563989	+	0.0976858i
$498$	1.55015	+	2.68494i	0.0694640	+	0.120315i
$499$	18.4364	−	31.9328i	0.825328	−	1.42951i	−0.0763399	−	0.997082i	$-0.524323\pi$
$499$	18.4364	−	31.9328i	0.825328	−	1.42951i	0.901668	−	0.432429i	$-0.142343\pi$
$500$	0.397815	+	0.689035i	0.0177908	+	0.0308146i
$501$	1.29095			0.0576753
$502$	18.8649			0.841980
$503$	10.8244	+	18.7483i	0.482634	+	0.835947i	0.999801	−	0.0199377i	$-0.00634678\pi$
$503$	10.8244	+	18.7483i	0.482634	+	0.835947i	−0.517167	+	0.855884i	$0.673013\pi$
$504$	−8.29412	−	14.3658i	−0.369449	−	0.639905i
$505$	5.39731			0.240177
$506$	0.792028			0.0352099
$507$	−0.123981	−	0.214741i	−0.00550617	−	0.00953697i
$508$	7.45492	−	12.9123i	0.330759	−	0.572891i
$509$	18.2279	+	31.5717i	0.807938	+	1.39939i	0.914289	+	0.405062i	$0.132750\pi$
$509$	18.2279	+	31.5717i	0.807938	+	1.39939i	−0.106351	+	0.994329i	$0.533917\pi$
$510$	−0.345781	+	0.598910i	−0.0153114	+	0.0265202i
$511$	6.00327	−	10.3980i	0.265569	−	0.459979i
$512$	−18.3314			−0.810141
$513$	4.67822	−	8.47783i	0.206549	−	0.374305i
$514$	−21.4471			−0.945990
$515$	−1.07375	+	1.85979i	−0.0473150	+	0.0819520i
$516$	−1.28387	+	2.22373i	−0.0565193	+	0.0978943i
$517$	0.746955	+	1.29376i	0.0328511	+	0.0568997i
$518$	1.76402	−	3.05537i	0.0775065	−	0.134245i
$519$	−2.00776	−	3.47754i	−0.0881309	−	0.152647i
$520$	−10.7802			−0.472745
$521$	−22.6092			−0.990528			−0.495264	−	0.868742i	$-0.664929\pi$
$521$	−22.6092			−0.990528			−0.495264	+	0.868742i	$0.664929\pi$
$522$	7.78991	+	13.4925i	0.340955	+	0.590552i
$523$	−0.266456	−	0.461515i	−0.0116513	−	0.0201806i	0.860141	−	0.510056i	$-0.170375\pi$
$523$	−0.266456	−	0.461515i	−0.0116513	−	0.0201806i	−0.871792	+	0.489876i	$0.837042\pi$
$524$	−2.29654			−0.100325
$525$	−0.718104			−0.0313406
$526$	−4.83619	−	8.37653i	−0.210868	−	0.365234i
$527$	5.45275	−	9.44444i	0.237525	−	0.411406i
$528$	−0.0452651	−	0.0784015i	−0.00196991	−	0.00341199i
$529$	−2.91759	+	5.05341i	−0.126852	+	0.219714i
$530$	0.145327	−	0.251713i	0.00631259	−	0.0109337i
$531$	19.6976			0.854804
$532$	6.56406	−	0.127098i	0.284588	−	0.00551038i
$533$	37.3606			1.61827
$534$	2.02654	−	3.51007i	0.0876971	−	0.151896i
$535$	0.500463	−	0.866827i	0.0216369	−	0.0374762i
$536$	−4.53078	−	7.84754i	−0.195700	−	0.338962i
$537$	−2.76959	+	4.79708i	−0.119517	+	0.207009i
$538$	−0.158230	−	0.274062i	−0.00682178	−	0.0118157i
$539$	−0.459150			−0.0197770
$540$	−1.76743			−0.0760579
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	0.807057	−	0.590473i	$-0.201059\pi$
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	−0.914893	+	0.403696i	$0.867725\pi$
$542$	13.6473	+	23.6378i	0.586202	+	1.01533i
$543$	2.06077			0.0884362
$544$	−6.95610			−0.298240
$545$	−8.13145	−	14.0841i	−0.348313	−	0.603296i
$546$	1.38454	−	2.39810i	0.0592530	−	0.102629i
$547$	−11.3149	−	19.5981i	−0.483792	−	0.837952i	0.516035	−	0.856568i	$-0.327408\pi$
$547$	−11.3149	−	19.5981i	−0.483792	−	0.837952i	−0.999827	+	0.0186154i	$0.994074\pi$
$548$	−7.49148	+	12.9756i	−0.320020	+	0.554291i
$549$	13.1037	−	22.6962i	0.559250	−	0.968650i
$550$	0.147496			0.00628923
$551$	−21.6622	+	0.419439i	−0.922843	+	0.0178687i
$552$	6.24946			0.265995
$553$	1.38883	−	2.40552i	0.0590590	−	0.102293i
$554$	2.41703	−	4.18642i	0.102690	−	0.177864i
$555$	−0.322091	−	0.557877i	−0.0136720	−	0.0236806i
$556$	−7.23207	+	12.5263i	−0.306708	+	0.531234i
$557$	−17.6277	−	30.5321i	−0.746910	−	1.29369i	−0.949297	−	0.314381i	$-0.898203\pi$
$557$	−17.6277	−	30.5321i	−0.746910	−	1.29369i	0.202387	−	0.979306i	$-0.435130\pi$
$558$	−20.5764			−0.871070
$559$	29.8943			1.26439
$560$	1.68077	+	2.91119i	0.0710257	+	0.123020i
$561$	−0.0423468	−	0.0733467i	−0.00178788	−	0.00309670i
$562$	−35.9097			−1.51476
$563$	−24.6295			−1.03801			−0.519005	−	0.854771i	$-0.673698\pi$
$563$	−24.6295			−1.03801			−0.519005	+	0.854771i	$0.673698\pi$
$564$	1.67737	+	2.90528i	0.0706298	+	0.122334i
$565$	−0.421505	+	0.730068i	−0.0177329	+	0.0307142i
$566$	0.729207	+	1.26302i	0.0306509	+	0.0530888i
$567$	−7.31260	+	12.6658i	−0.307100	+	0.531913i
$568$	2.03771	−	3.52942i	0.0855005	−	0.148091i
$569$	−20.0193			−0.839252			−0.419626	−	0.907697i	$-0.637839\pi$
$569$	−20.0193			−0.839252			−0.419626	+	0.907697i	$0.637839\pi$
$570$	−0.876702	+	1.58875i	−0.0367210	+	0.0665454i
$571$	−16.6121			−0.695195			−0.347597	−	0.937644i	$-0.613002\pi$
$571$	−16.6121			−0.695195			−0.347597	+	0.937644i	$0.613002\pi$
$572$	0.187866	−	0.325394i	0.00785508	−	0.0136054i
$573$	3.88357	−	6.72655i	0.162239	−	0.281006i
$574$	−11.0449	−	19.1303i	−0.461005	−	0.798484i
$575$	−2.68492	+	4.65042i	−0.111969	+	0.193936i
$576$	11.6340	+	20.1507i	0.484750	+	0.839612i
$577$	12.4486			0.518244			0.259122	−	0.965845i	$-0.416567\pi$
$577$	12.4486			0.518244			0.259122	+	0.965845i	$0.416567\pi$
$578$	−15.6279			−0.650034
$579$	2.09080	+	3.62136i	0.0868905	+	0.150499i
$580$	1.97737	+	3.42491i	0.0821060	+	0.142212i
$581$	14.0984			0.584899
$582$	−7.27224			−0.301444
$583$	0.0177977	+	0.0308266i	0.000737107	+	0.00127671i
$584$	−9.72930	+	16.8516i	−0.402601	+	0.697326i
$585$	5.01780	+	8.69108i	0.207460	+	0.359332i
$586$	4.23811	−	7.34063i	0.175075	−	0.303238i
$587$	−2.25572	+	3.90702i	−0.0931036	+	0.161260i	−0.908816	−	0.417198i	$-0.863012\pi$
$587$	−2.25572	+	3.90702i	−0.0931036	+	0.161260i	0.815712	+	0.578458i	$0.196345\pi$
$588$	−1.03107			−0.0425206
$589$	13.8250	−	25.0536i	0.569651	−	1.03232i
$590$	−7.56867			−0.311597
$591$	−3.76550	+	6.52204i	−0.154892	+	0.268281i
$592$	−1.50775	+	2.61150i	−0.0619682	+	0.107332i
$593$	−9.80411	−	16.9812i	−0.402606	−	0.697335i	0.591433	−	0.806354i	$-0.298562\pi$
$593$	−9.80411	−	16.9812i	−0.402606	−	0.697335i	−0.994040	+	0.109019i	$0.965229\pi$
$594$	−0.163825	+	0.283753i	−0.00672181	+	0.0116425i
$595$	1.57241	+	2.72349i	0.0644625	+	0.111652i
$596$	17.7062			0.725274
$597$	−7.96699			−0.326067
$598$	−10.3533	−	17.9325i	−0.423379	−	0.733315i
$599$	−5.38795	−	9.33221i	−0.220146	−	0.381304i	0.734706	−	0.678385i	$-0.237320\pi$
$599$	−5.38795	−	9.33221i	−0.220146	−	0.381304i	−0.954852	+	0.297082i	$0.903987\pi$
$600$	1.16381			0.0475122
$601$	15.0244			0.612860			0.306430	−	0.951893i	$-0.400866\pi$
$601$	15.0244			0.612860			0.306430	+	0.951893i	$0.400866\pi$
$602$	−8.83763	−	15.3072i	−0.360195	−	0.623876i
$603$	−4.21782	+	7.30547i	−0.171763	+	0.297502i
$604$	1.32664	+	2.29781i	0.0539802	+	0.0934964i
$605$	5.49097	−	9.51064i	0.223240	−	0.386662i
$606$	1.12344	−	1.94585i	0.0456365	−	0.0790448i
$607$	25.1901			1.02243			0.511217	−	0.859452i	$-0.329195\pi$
$607$	25.1901			1.02243			0.511217	+	0.859452i	$0.329195\pi$
$608$	−18.2487	+	0.353343i	−0.740082	+	0.0143300i
$609$	−3.56940			−0.144640
$610$	−5.03499	+	8.72085i	−0.203861	+	0.353097i
$611$	19.5283	−	33.8240i	0.790030	−	1.36837i
$612$	1.88749	+	3.26923i	0.0762973	+	0.132151i
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	−0.982088	−	0.188424i	$-0.939662\pi$
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	0.654224	+	0.756301i	$0.272995\pi$
$614$	4.99336	+	8.64875i	0.201516	+	0.349035i
$615$	−4.03336			−0.162641
$616$	−0.780593			−0.0314510
$617$	−3.25913	−	5.64498i	−0.131208	−	0.227258i	0.792935	−	0.609307i	$-0.208552\pi$
$617$	−3.25913	−	5.64498i	−0.131208	−	0.227258i	−0.924142	+	0.382048i	$0.875219\pi$
$618$	0.446996	+	0.774220i	0.0179808	+	0.0311437i
$619$	−4.39112			−0.176494			−0.0882470	−	0.996099i	$-0.528126\pi$
$619$	−4.39112			−0.176494			−0.0882470	+	0.996099i	$0.528126\pi$
$620$	−5.22308			−0.209764
$621$	−5.96433	−	10.3305i	−0.239340	−	0.414550i
$622$	6.83532	−	11.8391i	0.274071	−	0.474705i
$623$	−9.21553	−	15.9618i	−0.369212	−	0.639494i
$624$	−1.18341	+	2.04972i	−0.0473742	+	0.0820545i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.24484			0.0897220
$627$	−0.114819	−	0.190267i	−0.00458541	−	0.00759855i
$628$	−5.77858			−0.230590
$629$	−1.41054	+	2.44313i	−0.0562420	+	0.0974140i
$630$	2.96682	−	5.13867i	0.118201	−	0.204730i
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	0.972124	+	0.234469i	$0.0753350\pi$
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	−0.283006	+	0.959118i	$0.591332\pi$
$632$	−2.25083	+	3.89855i	−0.0895331	+	0.155076i
$633$	−2.43261	−	4.21340i	−0.0966875	−	0.167468i
$634$	25.8680			1.02735
$635$	18.7397			0.743661
$636$	0.0399667	+	0.0692243i	0.00158478	+	0.00274492i
$637$	6.00198	+	10.3957i	0.237807	+	0.411894i
$638$	0.733141			0.0290253
$639$	−3.79391			−0.150085
$640$	−0.282960	−	0.490101i	−0.0111850	−	0.0193730i
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	−0.929889	−	0.367839i	$-0.880098\pi$
$641$	−3.70621	+	6.41934i	−0.146386	+	0.253549i	0.783503	+	0.621388i	$0.213431\pi$
$642$	−0.208340	−	0.360856i	−0.00822253	−	0.0142418i
$643$	8.27294	−	14.3292i	0.326253	−	0.565087i	−0.655512	−	0.755185i	$-0.727547\pi$
$643$	8.27294	−	14.3292i	0.326253	−	0.565087i	0.981765	+	0.190098i	$0.0608805\pi$
$644$	4.04397	−	7.00437i	0.159355	−	0.276011i
$645$	−3.22731			−0.127075
$646$	7.94520	−	0.153840i	0.312600	−	0.00605276i
$647$	29.4822			1.15907			0.579533	−	0.814949i	$-0.303235\pi$
$647$	29.4822			1.15907			0.579533	+	0.814949i	$0.303235\pi$
$648$	11.8513	−	20.5270i	0.465562	−	0.806377i
$649$	0.463456	−	0.802729i	0.0181922	−	0.0315099i
$650$	−1.92805	−	3.33949i	−0.0756245	−	0.130985i
$651$	2.35708	−	4.08258i	0.0923811	−	0.160009i
$652$	−7.86810	−	13.6279i	−0.308138	−	0.533712i
$653$	6.57421			0.257269			0.128634	−	0.991692i	$-0.458941\pi$
$653$	6.57421			0.257269			0.128634	+	0.991692i	$0.458941\pi$
$654$	−6.77017			−0.264735
$655$	−1.44322	−	2.49973i	−0.0563912	−	0.0976725i
$656$	9.44037	+	16.3512i	0.368584	+	0.638407i
$657$	18.1145			0.706713
$658$	−23.0925			−0.900241
$659$	13.1685	+	22.8085i	0.512972	+	0.888494i	0.999887	+	0.0150445i	$0.00478898\pi$
$659$	13.1685	+	22.8085i	0.512972	+	0.888494i	−0.486915	+	0.873450i	$0.661878\pi$
$660$	−0.0202816	+	0.0351287i	−0.000789458	+	0.00136738i
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	0.826880	−	0.562378i	$-0.190114\pi$
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	−0.900474	+	0.434910i	$0.856780\pi$
$662$	10.2706	−	17.7893i	0.399180	−	0.691399i
$663$	−1.10711	+	1.91757i	−0.0429965	+	0.0744721i
$664$	−22.8487			−0.886703
$665$	4.26341	+	7.06496i	0.165328	+	0.273967i
$666$	5.32281			0.206255
$667$	−13.3456	+	23.1153i	−0.516745	+	0.895029i
$668$	−1.35384	+	2.34492i	−0.0523817	+	0.0907278i
$669$	3.86815	+	6.69983i	0.149551	+	0.259031i
$670$	1.62067	−	2.80708i	0.0626118	−	0.108447i
$671$	−0.616619	−	1.06802i	−0.0238043	−	0.0412303i
$672$	−3.00694			−0.115995
$673$	−21.0431			−0.811150			−0.405575	−	0.914062i	$-0.632929\pi$
$673$	−21.0431			−0.811150			−0.405575	+	0.914062i	$0.632929\pi$
$674$	17.9366	+	31.0670i	0.690891	+	1.19666i
$675$	−1.11071	−	1.92381i	−0.0427512	−	0.0740473i
$676$	0.520083			0.0200032
$677$	−15.2744			−0.587043			−0.293522	−	0.955952i	$-0.594827\pi$
$677$	−15.2744			−0.587043			−0.293522	+	0.955952i	$0.594827\pi$
$678$	0.175471	+	0.303924i	0.00673891	+	0.0116721i
$679$	−16.5349	+	28.6394i	−0.634553	+	1.09908i
$680$	−2.54835	−	4.41387i	−0.0977248	−	0.169264i
$681$	4.82081	−	8.34988i	0.184734	−	0.319968i
$682$	−0.484133	+	0.838544i	−0.0185384	+	0.0321095i
$683$	−8.60225			−0.329156			−0.164578	−	0.986364i	$-0.552626\pi$
$683$	−8.60225			−0.329156			−0.164578	+	0.986364i	$0.552626\pi$
$684$	5.11772	+	8.48064i	0.195681	+	0.324265i
$685$	−18.8316			−0.719518
$686$	10.8201	−	18.7409i	0.413112	−	0.715530i
$687$	0.420212	−	0.727828i	0.0160321	−	0.0277684i
$688$	7.55375	+	13.0835i	0.287984	+	0.498803i
$689$	0.465302	−	0.805926i	0.0177266	−	0.0307033i
$690$	1.11772	+	1.93595i	0.0425509	+	0.0737003i
$691$	34.1079			1.29753			0.648763	−	0.760990i	$-0.275286\pi$
$691$	34.1079			1.29753			0.648763	+	0.760990i	$0.275286\pi$
$692$	8.42231			0.320168
$693$	0.363337	+	0.629318i	0.0138020	+	0.0239058i
$694$	1.40837	+	2.43937i	0.0534611	+	0.0925974i
$695$	−18.1795			−0.689587
$696$	5.78481			0.219273
$697$	8.83172	+	15.2970i	0.334525	+	0.579414i
$698$	−9.11942	+	15.7953i	−0.345175	+	0.597861i
$699$	−2.68523	−	4.65096i	−0.101565	−	0.175916i
$700$	0.753090	−	1.30439i	0.0284641	−	0.0493013i
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	−0.949372	−	0.314155i	$-0.898279\pi$
$701$	−5.36463	+	9.29181i	−0.202619	+	0.350947i	0.746752	+	0.665102i	$0.231612\pi$
$702$	8.56603			0.323304
$703$	−3.57633	+	6.48098i	−0.134884	+	0.244435i
$704$	1.09492			0.0412665
$705$	−2.10823	+	3.65155i	−0.0794004	+	0.137525i
$706$	−15.5633	+	26.9564i	−0.585732	+	1.01452i
$707$	−5.10873	−	8.84859i	−0.192134	−	0.332785i
$708$	1.04074	−	1.80261i	0.0391134	−	0.0677463i
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	0.998807	+	0.0488369i	$0.0155514\pi$
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	−0.457109	+	0.889410i	$0.651115\pi$
$710$	1.45778			0.0547096
$711$	4.19070			0.157164
$712$	14.9353	+	25.8687i	0.559724	+	0.969470i
$713$	−17.6257	−	30.5287i	−0.660089	−	1.14331i
$714$	1.30917			0.0489946
$715$	0.472245			0.0176610
$716$	−5.80905	−	10.0616i	−0.217095	−	0.376019i
$717$	0.571800	−	0.990386i	0.0213542	−	0.0369866i
$718$	−9.54143	−	16.5262i	−0.356083	−	0.616754i
$719$	10.0278	−	17.3686i	0.373972	−	0.647739i	−0.616200	−	0.787589i	$-0.711329\pi$
$719$	10.0278	−	17.3686i	0.373972	−	0.647739i	0.990173	+	0.139851i	$0.0446622\pi$
$720$	−2.53582	+	4.39216i	−0.0945043	+	0.163686i
$721$	4.06535			0.151402
$722$	20.8357	−	0.807171i	0.775424	−	0.0300398i
$723$	9.02026			0.335467
$724$	−2.16117	+	3.74326i	−0.0803193	+	0.139117i
$725$	−2.48530	+	4.30466i	−0.0923016	+	0.159871i
$726$	−2.28587	−	3.95923i	−0.0848364	−	0.146941i
$727$	0.390261	−	0.675951i	0.0144740	−	0.0250697i	−0.858698	−	0.512482i	$-0.828726\pi$
$727$	0.390261	−	0.675951i	0.0144740	−	0.0250697i	0.873172	+	0.487413i	$0.162059\pi$
$728$	10.2039	+	17.6736i	0.378180	+	0.655028i
$729$	−19.5373			−0.723604
$730$	−6.96036			−0.257615
$731$	7.06674	+	12.2399i	0.261373	+	0.452711i
$732$	−1.38468	−	2.39834i	−0.0511794	−	0.0886452i
$733$	−26.8391			−0.991326			−0.495663	−	0.868515i	$-0.665075\pi$
$733$	−26.8391			−0.991326			−0.495663	+	0.868515i	$0.665075\pi$
$734$	28.3192			1.04528
$735$	−0.647958	−	1.12230i	−0.0239003	−	0.0413965i
$736$	−11.2426	+	19.4728i	−0.414409	+	0.717777i
$737$	0.198478	+	0.343774i	0.00731103	+	0.0126631i
$738$	16.6636	−	28.8623i	0.613397	−	1.06243i
$739$	−10.3265	+	17.8861i	−0.379867	+	0.657949i	−0.991043	−	0.133546i	$-0.957364\pi$
$739$	−10.3265	+	17.8861i	−0.379867	+	0.657949i	0.611175	+	0.791495i	$0.290697\pi$
$740$	1.35113			0.0496685
$741$	−2.80699	+	5.08680i	−0.103117	+	0.186868i
$742$	−0.550227			−0.0201995
$743$	−0.736585	+	1.27580i	−0.0270227	+	0.0468047i	−0.879220	−	0.476415i	$-0.841936\pi$
$743$	−0.736585	+	1.27580i	−0.0270227	+	0.0468047i	0.852198	+	0.523220i	$0.175269\pi$
$744$	−3.82003	+	6.61649i	−0.140049	+	0.242572i
$745$	11.1272	+	19.2728i	0.407668	+	0.706102i
$746$	−14.8518	+	25.7240i	−0.543762	+	0.941824i
$747$	10.6352	+	18.4208i	0.389123	+	0.673980i
$748$	0.177639			0.00649514
$749$	−1.89482			−0.0692352
$750$	0.208148	+	0.360522i	0.00760048	+	0.0131644i
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	0.688411	−	0.725321i	$-0.258308\pi$
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	−0.972352	+	0.233521i	$0.924975\pi$
$752$	19.7378			0.719764
$753$	−6.52071			−0.237628
$754$	−9.58356	−	16.5992i	−0.349013	−	0.604508i
$755$	−1.66741	+	2.88804i	−0.0606832	+	0.105106i
$756$	1.67293	+	2.89760i	0.0608438	+	0.105385i
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	−0.989039	−	0.147654i	$-0.952828\pi$
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	0.622392	+	0.782706i	$0.286161\pi$
$758$	−6.80568	+	11.7878i	−0.247193	+	0.428152i
$759$	−0.273767			−0.00993713
$760$	−6.90957	−	11.4499i	−0.250637	−	0.415333i
$761$	−15.1076			−0.547649			−0.273825	−	0.961780i	$-0.588289\pi$
$761$	−15.1076			−0.547649			−0.273825	+	0.961780i	$0.588289\pi$
$762$	3.90062	−	6.75607i	0.141305	−	0.244747i
$763$	−15.3934	+	26.6621i	−0.557278	+	0.965234i
$764$	8.14556	+	14.1085i	0.294696	+	0.510428i
$765$	−2.37232	+	4.10898i	−0.0857715	+	0.148561i
$766$	2.94082	+	5.09364i	0.106256	+	0.184041i
$767$	−24.2331			−0.875005
$768$	5.94509			0.214525
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.780900	−	0.624656i	$-0.785239\pi$
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.150518	−	0.988607i	$-0.548094\pi$
$770$	−0.139610	−	0.241811i	−0.00503118	−	0.00871426i
$771$	7.41327			0.266982
$772$	−8.77063			−0.315662
$773$	−15.0779	−	26.1157i	−0.542314	−	0.939316i	−0.998771	−	0.0495699i	$-0.984215\pi$
$773$	−15.0779	−	26.1157i	−0.542314	−	0.939316i	0.456457	−	0.889746i	$-0.349118\pi$
$774$	13.3335	−	23.0943i	0.479262	−	0.830107i
$775$	−3.28236	−	5.68521i	−0.117906	−	0.204219i
$776$	26.7976	−	46.4148i	0.961978	−	1.66620i
$777$	−0.609739	+	1.05610i	−0.0218743	+	0.0378874i
$778$	9.40431			0.337161
$779$	23.9462	+	39.6816i	0.857962	+	1.42174i
$780$	1.06048			0.0379712
$781$	−0.0892652	+	0.154612i	−0.00319416	+	0.00553244i
$782$	4.89487	−	8.47816i	0.175040	−	0.303178i
$783$	−5.52088	−	9.56245i	−0.197300	−	0.341734i
$784$	−3.03318	+	5.25363i	−0.108328	+	0.187630i
$785$	−3.63145	−	6.28986i	−0.129612	−	0.224495i
$786$	−1.20161			−0.0428601
$787$	43.0969			1.53624			0.768119	−	0.640307i	$-0.221193\pi$
$787$	43.0969			1.53624			0.768119	+	0.640307i	$0.221193\pi$
$788$	−7.89791	−	13.6796i	−0.281351	−	0.487315i
$789$	1.67165	+	2.89538i	0.0595123	+	0.103078i
$790$	−1.61025			−0.0572900
$791$	1.59588			0.0567428
$792$	−0.588848	−	1.01991i	−0.0209238	−	0.0362411i
$793$	−16.1208	+	27.9221i	−0.572467	+	0.991542i
$794$	5.84086	+	10.1167i	0.207284	+	0.359027i
$795$	−0.0502328	+	0.0870057i	−0.00178157	+	0.00308578i
$796$	8.35514	−	14.4715i	0.296140	−	0.512929i
$797$	−50.5062			−1.78902			−0.894510	−	0.447048i	$-0.852475\pi$
$797$	−50.5062			−1.78902			−0.894510	+	0.447048i	$0.852475\pi$
$798$	3.43450	−	0.0665010i	0.121580	−	0.00235411i
$799$	18.4652			0.653253
$800$	−2.09366	+	3.62633i	−0.0740221	+	0.128210i
$801$	13.9036	−	24.0818i	0.491261	−	0.850889i
$802$	−4.19885	−	7.27261i	−0.148266	−	0.256805i
$803$	0.426207	−	0.738212i	0.0150405	−	0.0260509i
$804$	0.445703	+	0.771981i	0.0157187	+	0.0272257i
$805$	10.1655			0.358286
$806$	25.3142			0.891656
$807$	0.0546928	+	0.0947307i	0.00192528	+	0.00333468i
$808$	8.27955	+	14.3406i	0.291274	+	0.504501i
$809$	−30.0872			−1.05781			−0.528905	−	0.848681i	$-0.677397\pi$
$809$	−30.0872			−1.05781			−0.528905	+	0.848681i	$0.677397\pi$
$810$	8.47843			0.297902
$811$	−11.4755	−	19.8761i	−0.402958	−	0.697944i	0.591123	−	0.806581i	$-0.298685\pi$
$811$	−11.4755	−	19.8761i	−0.402958	−	0.697944i	−0.994081	+	0.108637i	$0.965351\pi$
$812$	3.74330	−	6.48359i	0.131364	−	0.227529i
$813$	−4.71725	−	8.17051i	−0.165441	−	0.286552i
$814$	0.125238	−	0.216918i	0.00438958	−	0.00760298i
$815$	9.88915	−	17.1285i	0.346402	−	0.599986i
$816$	−1.11899			−0.0391723
$817$	19.1607	+	31.7514i	0.670347	+	1.11084i
$818$	−19.4123			−0.678734
$819$	9.49903	−	16.4528i	0.331923	−	0.574907i
$820$	4.22986	−	7.32634i	0.147713	−	0.255847i
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	0.979417	+	0.201846i	$0.0646941\pi$
$821$	19.0403	+	32.9788i	0.664513	+	1.15097i	−0.314905	+	0.949123i	$0.601973\pi$
$822$	−3.91975	+	6.78921i	−0.136717	+	0.236801i
$823$	−26.8966	−	46.5862i	−0.937556	−	1.62389i	−0.770012	−	0.638030i	$-0.779750\pi$
$823$	−26.8966	−	46.5862i	−0.937556	−	1.62389i	−0.167544	−	0.985865i	$-0.553584\pi$
$824$	−6.58858			−0.229524
$825$	−0.0509824			−0.00177498
$826$	7.16400	+	12.4084i	0.249267	+	0.431744i
$827$	−16.2046	−	28.0672i	−0.563490	−	0.975993i	−0.997188	−	0.0749347i	$-0.976125\pi$
$827$	−16.2046	−	28.0672i	−0.563490	−	0.975993i	0.433699	−	0.901058i	$-0.357208\pi$
$828$	12.2024			0.424064
$829$	−18.5305			−0.643592			−0.321796	−	0.946809i	$-0.604287\pi$
$829$	−18.5305			−0.643592			−0.321796	+	0.946809i	$0.604287\pi$
$830$	−4.08651	−	7.07805i	−0.141845	−	0.245683i
$831$	−0.835456	+	1.44705i	−0.0289817	+	0.0501977i
$832$	−14.3128	−	24.7904i	−0.496206	−	0.859454i
$833$	−2.83763	+	4.91491i	−0.0983179	+	0.170292i
$834$	−3.78402	+	6.55411i	−0.131030	+	0.226950i
$835$	−3.40320			−0.117773
$836$	0.466021	−	0.00902339i	0.0161177	−	0.000312081i
$837$	14.5830			0.504062
$838$	−0.651507	+	1.12844i	−0.0225059	+	0.0389814i
$839$	−0.413304	+	0.715864i	−0.0142688	+	0.0247144i	−0.873072	−	0.487592i	$-0.837875\pi$
$839$	−0.413304	+	0.715864i	−0.0142688	+	0.0247144i	0.858803	+	0.512306i	$0.171209\pi$
$840$	−1.10158	−	1.90800i	−0.0380082	−	0.0658322i
$841$	2.14661	−	3.71803i	0.0740209	−	0.128208i
$842$	−18.3093	−	31.7126i	−0.630979	−	1.09289i
$843$	12.4123			0.427504
$844$	10.2045			0.351253
$845$	0.326838	+	0.566100i	0.0112436	+	0.0194744i
$846$	−17.4201	−	30.1725i	−0.598914	−	1.03735i
$847$	−20.7895			−0.714337
$848$	0.470294			0.0161500
$849$	−0.252053	−	0.436569i	−0.00865044	−	0.0149830i
$850$	0.911548	−	1.57885i	0.0312658	−	0.0541540i
$851$	4.55951	+	7.89730i	0.156298	+	0.270716i
$852$	−0.200454	+	0.347197i	−0.00686745	+	0.0118948i
$853$	3.67469	−	6.36475i	0.125819	−	0.217925i	−0.796234	−	0.604989i	$-0.793177\pi$
$853$	3.67469	−	6.36475i	0.125819	−	0.217925i	0.922053	+	0.387064i	$0.126511\pi$
$854$	19.0631			0.652327
$855$	−6.01485	+	10.9000i	−0.205704	+	0.372774i
$856$	3.07087			0.104960
$857$	22.6748	−	39.2739i	0.774556	−	1.34157i	−0.160488	−	0.987038i	$-0.551307\pi$
$857$	22.6748	−	39.2739i	0.774556	−	1.34157i	0.935044	−	0.354532i	$-0.115360\pi$
$858$	0.0982968	−	0.170255i	0.00335580	−	0.00581241i
$859$	−14.8143	−	25.6590i	−0.505456	−	0.875475i	−0.999980	−	0.00631148i	$-0.997991\pi$
$859$	−14.8143	−	25.6590i	−0.505456	−	0.875475i	0.494524	−	0.869164i	$-0.335342\pi$
$860$	3.38454	−	5.86220i	0.115412	−	0.199899i
$861$	3.81771	+	6.61247i	0.130107	+	0.225352i
$862$	−6.77775			−0.230851
$863$	41.0807			1.39840			0.699201	−	0.714925i	$-0.253539\pi$
$863$	41.0807			1.39840			0.699201	+	0.714925i	$0.253539\pi$
$864$	−4.65090	−	8.05559i	−0.158227	−	0.274057i
$865$	5.29286	+	9.16750i	0.179963	+	0.311704i
$866$	−20.3632			−0.691970
$867$	5.40183			0.183456
$868$	4.94382	+	8.56295i	0.167804	+	0.290645i
$869$	0.0986010	−	0.170782i	0.00334481	−	0.00579338i
$870$	1.03462	+	1.79201i	0.0350768	+	0.0607548i
$871$	5.18898	−	8.98758i	0.175822	−	0.304533i
$872$	24.9475	−	43.2104i	0.844831	−	1.46329i
$873$	−49.8931			−1.68863
$874$	12.4106	−	22.4903i	0.419794	−	0.760746i
$875$	1.89307			0.0639974
$876$	0.957093	−	1.65773i	0.0323372	−	0.0560096i
$877$	−27.3154	+	47.3116i	−0.922374	+	1.59760i	−0.126643	+	0.991948i	$0.540420\pi$
$877$	−27.3154	+	47.3116i	−0.922374	+	1.59760i	−0.795731	+	0.605650i	$0.792913\pi$
$878$	0.124730	+	0.216039i	0.00420944	+	0.00729097i
$879$	−1.46492	+	2.53732i	−0.0494105	+	0.0855815i
$880$	0.119328	+	0.206682i	0.00402255	+	0.00696726i
$881$	−15.4805			−0.521552			−0.260776	−	0.965399i	$-0.583978\pi$
$881$	−15.4805			−0.521552			−0.260776	+	0.965399i	$0.583978\pi$
$882$	10.7080			0.360558
$883$	22.6747	+	39.2738i	0.763066	+	1.32167i	0.941263	+	0.337674i	$0.109640\pi$
$883$	22.6747	+	39.2738i	0.763066	+	1.32167i	−0.178197	+	0.983995i	$0.557027\pi$
$884$	−2.32209	−	4.02198i	−0.0781004	−	0.135274i
$885$	2.61614			0.0879406
$886$	−38.3913			−1.28978
$887$	15.5700	+	26.9680i	0.522788	+	0.905496i	0.999648	+	0.0265165i	$0.00844145\pi$
$887$	15.5700	+	26.9680i	0.522788	+	0.905496i	−0.476860	+	0.878979i	$0.658225\pi$
$888$	0.988184	−	1.71158i	0.0331613	−	0.0574370i
$889$	−17.7377	−	30.7227i	−0.594905	−	1.03041i
$890$	−5.34237	+	9.25326i	−0.179077	+	0.310170i
$891$	−0.519164	+	0.899218i	−0.0173926	+	0.0301249i
$892$	−16.2264			−0.543301
$893$	48.4419	−	0.937963i	1.62105	−	0.0313877i
$894$	9.26438			0.309847
$895$	7.30121	−	12.6461i	0.244052	−	0.422711i
$896$	−0.535663	+	0.927795i	−0.0178952	+	0.0309955i
$897$	3.57867	+	6.19844i	0.119488	+	0.206960i
$898$	9.30127	−	16.1103i	0.310387	−	0.537606i
$899$	−16.3153	−	28.2589i	−0.544145	−	0.942486i
$900$	2.27240			0.0757467
$901$	0.439972			0.0146576
$902$	−0.784142	−	1.35817i	−0.0261091	−	0.0452222i
$903$	3.05476	+	5.29100i	0.101656	+	0.176073i
$904$	−2.58638			−0.0860218
$905$	−5.43261			−0.180586
$906$	0.694135	+	1.20228i	0.0230611	+	0.0399430i
$907$	−21.7707	+	37.7080i	−0.722886	+	1.25207i	0.236952	+	0.971521i	$0.423851\pi$
$907$	−21.7707	+	37.7080i	−0.722886	+	1.25207i	−0.959838	+	0.280554i	$0.909482\pi$
$908$	10.1113	+	17.5134i	0.335557	+	0.581201i
$909$	7.70764	−	13.3500i	0.255646	−	0.442792i
$910$	−3.64993	+	6.32187i	−0.120994	+	0.209568i
$911$	5.72789			0.189774			0.0948868	−	0.995488i	$-0.469751\pi$
$911$	5.72789			0.189774			0.0948868	+	0.995488i	$0.469751\pi$
$912$	−2.93556	+	0.0568401i	−0.0972060	+	0.00188217i
$913$	1.00093			0.0331258
$914$	−0.879275	+	1.52295i	−0.0290838	+	0.0503747i
$915$	1.74036	−	3.01440i	0.0575346	−	0.0996529i
$916$	0.881369	+	1.52658i	0.0291212	+	0.0504395i
$917$	−2.73211	+	4.73216i	−0.0902223	+	0.156270i
$918$	2.02493	+	3.50728i	0.0668327	+	0.115758i
$919$	7.93860			0.261870			0.130935	−	0.991391i	$-0.458202\pi$
$919$	7.93860			0.261870			0.130935	+	0.991391i	$0.458202\pi$
$920$	−16.4748			−0.543159
$921$	−1.72597	−	2.98947i	−0.0568728	−	0.0985065i
$922$	4.79669	+	8.30812i	0.157971	+	0.273613i
$923$	4.66747			0.153632
$924$	0.0767887			0.00252616
$925$	0.849095	+	1.47068i	0.0279181	+	0.0483555i
$926$	−11.6266	+	20.1378i	−0.382073	+	0.661771i
$927$	3.06674	+	5.31174i	0.100725	+	0.174461i
$928$	−10.4067	+	18.0250i	−0.341618	+	0.591700i
$929$	14.4784	−	25.0772i	0.475019	−	0.822758i	−0.524571	−	0.851366i	$-0.675774\pi$
$929$	14.4784	−	25.0772i	0.475019	−	0.822758i	0.999591	+	0.0286089i	$0.00910773\pi$
$930$	−2.73286			−0.0896141
$931$	−7.19459	+	13.0380i	−0.235793	+	0.427302i
$932$	11.2642			0.368972
$933$	−2.36265	+	4.09224i	−0.0773498	+	0.133974i
$934$	−11.2222	+	19.4374i	−0.367201	+	0.636011i
$935$	0.111635	+	0.193357i	0.00365084	+	0.00632344i
$936$	−15.3948	+	26.6645i	−0.503193	+	0.871556i
$937$	7.34080	+	12.7146i	0.239813	+	0.415369i	0.960661	−	0.277725i	$-0.0895804\pi$
$937$	7.34080	+	12.7146i	0.239813	+	0.415369i	−0.720847	+	0.693094i	$0.756247\pi$
$938$	−6.13606			−0.200349
$939$	−0.775939			−0.0253218
$940$	−4.42187	−	7.65891i	−0.144226	−	0.249806i
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	0.867284	−	0.497814i	$-0.165864\pi$
$941$	0.0773773	+	0.134021i	0.00252243	+	0.00436897i	−0.864761	+	0.502183i	$0.832530\pi$
$942$	−3.02352			−0.0985114
$943$	57.0961			1.85931
$944$	−6.12326	−	10.6058i	−0.199295	−	0.345189i
$945$	−2.10265	+	3.64189i	−0.0683991	+	0.118471i
$946$	−0.627435	−	1.08675i	−0.0203997	−	0.0353332i
$947$	3.75904	−	6.51084i	0.122152	−	0.211574i	−0.798464	−	0.602043i	$-0.794354\pi$
$947$	3.75904	−	6.51084i	0.122152	−	0.211574i	0.920616	+	0.390469i	$0.127687\pi$
$948$	0.221419	−	0.383509i	0.00719135	−	0.0124558i
$949$	−22.2854			−0.723415
$950$	2.31116	−	4.18827i	0.0749841	−	0.135885i
$951$	−8.94137			−0.289944
$952$	−4.82420	+	8.35576i	−0.156353	+	0.270812i
$953$	−11.3372	+	19.6365i	−0.367247	+	0.636090i	−0.989134	−	0.147017i	$-0.953033\pi$
$953$	−11.3372	+	19.6365i	−0.367247	+	0.636090i	0.621887	+	0.783107i	$0.286366\pi$
$954$	−0.415069	−	0.718920i	−0.0134384	−	0.0232759i
$955$	−10.2379	+	17.7325i	−0.331290	+	0.573811i
$956$	1.19931	+	2.07727i	0.0387886	+	0.0671838i
$957$	−0.253413			−0.00819167
$958$	25.8437			0.834973
$959$	17.8247	+	30.8733i	0.575590	+	0.996952i
$960$	1.54517	+	2.67631i	0.0498702	+	0.0863777i
$961$	12.0955			0.390177
$962$	−6.54840			−0.211129
$963$	−1.42937	−	2.47575i	−0.0460609	−	0.0797799i
$964$	−9.45972	+	16.3847i	−0.304677	+	0.527716i
$965$	−5.51176	−	9.54664i	−0.177430	−	0.307317i
$966$	2.11592	−	3.66488i	0.0680786	−	0.117916i
$967$	−14.4172	+	24.9714i	−0.463627	+	0.803025i	−0.999138	−	0.0415030i	$-0.986785\pi$
$967$	−14.4172	+	24.9714i	−0.463627	+	0.803025i	0.535512	+	0.844528i	$0.320119\pi$
$968$	33.6929			1.08293
$969$	−2.74629	+	0.0531755i	−0.0882236	+	0.00170824i
$970$	19.1711			0.615546
$971$	−13.1831	+	22.8338i	−0.423065	+	0.732770i	−0.996238	−	0.0866647i	$-0.972379\pi$
$971$	−13.1831	+	22.8338i	−0.423065	+	0.732770i	0.573173	+	0.819435i	$0.305712\pi$
$972$	−3.81698	+	6.61120i	−0.122430	+	0.212054i
$973$	17.2075	+	29.8043i	0.551647	+	0.955481i
$974$	−19.7754	+	34.2520i	−0.633645	+	1.09750i
$975$	0.666439	+	1.15431i	0.0213431	+	0.0369674i
$976$	−16.2938			−0.521551
$977$	4.59218			0.146917			0.0734585	−	0.997298i	$-0.476596\pi$
$977$	4.59218			0.146917			0.0734585	+	0.997298i	$0.476596\pi$
$978$	−4.11681	−	7.13052i	−0.131641	−	0.228009i
$979$	−0.654264	−	1.13322i	−0.0209104	−	0.0362178i
$980$	2.71810			0.0868267
$981$	−46.4486			−1.48299
$982$	−11.0070	−	19.0647i	−0.351248	−	0.608379i
$983$	−3.45737	+	5.98833i	−0.110273	+	0.190998i	−0.915880	−	0.401452i	$-0.868506\pi$
$983$	−3.45737	+	5.98833i	−0.110273	+	0.190998i	0.805607	+	0.592450i	$0.201839\pi$
$984$	−6.18724	−	10.7166i	−0.197242	−	0.341633i
$985$	9.92662	−	17.1934i	0.316288	−	0.547828i
$986$	4.53094	−	7.84781i	0.144294	−	0.249925i
$987$	7.98203			0.254071
$988$	−6.29609	−	10.4333i	−0.200305	−	0.331929i
$989$	45.6857			1.45272
$990$	0.210632	−	0.364825i	0.00669431	−	0.0115949i
$991$	19.0035	−	32.9150i	0.603666	−	1.04558i	−0.388594	−	0.921409i	$-0.627039\pi$
$991$	19.0035	−	32.9150i	0.603666	−	1.04558i	0.992261	−	0.124172i	$-0.0396274\pi$
$992$	−13.7443	−	23.8058i	−0.436382	−	0.755835i
$993$	−3.55009	+	6.14893i	−0.112659	+	0.195130i
$994$	−1.37984	−	2.38996i	−0.0437659	−	0.0758048i
$995$	21.0026			0.665827
$996$	2.24768			0.0712205
$997$	−8.11326	−	14.0526i	−0.256950	−	0.445050i	0.708474	−	0.705737i	$-0.249384\pi$
$997$	−8.11326	−	14.0526i	−0.256950	−	0.445050i	−0.965423	+	0.260688i	$0.916051\pi$
$998$	20.2329	+	35.0443i	0.640460	+	1.10931i
$999$	−3.77239			−0.119353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.e.c.11.2	✓	8
3.2	odd	2		855.2.k.h.676.3		8
4.3	odd	2		1520.2.q.o.961.2		8
5.2	odd	4		475.2.j.c.49.4		16
5.3	odd	4		475.2.j.c.49.5		16
5.4	even	2		475.2.e.e.201.3		8
19.7	even	3	inner	95.2.e.c.26.2	yes	8
19.8	odd	6		1805.2.a.i.1.2		4
19.11	even	3		1805.2.a.o.1.3		4
57.26	odd	6		855.2.k.h.406.3		8
76.7	odd	6		1520.2.q.o.881.2		8
95.7	odd	12		475.2.j.c.349.5		16
95.49	even	6		9025.2.a.bg.1.2		4
95.64	even	6		475.2.e.e.26.3		8
95.83	odd	12		475.2.j.c.349.4		16
95.84	odd	6		9025.2.a.bp.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.2	✓	8	1.1	even	1	trivial
95.2.e.c.26.2	yes	8	19.7	even	3	inner
475.2.e.e.26.3		8	95.64	even	6
475.2.e.e.201.3		8	5.4	even	2
475.2.j.c.49.4		16	5.2	odd	4
475.2.j.c.49.5		16	5.3	odd	4
475.2.j.c.349.4		16	95.83	odd	12
475.2.j.c.349.5		16	95.7	odd	12
855.2.k.h.406.3		8	57.26	odd	6
855.2.k.h.676.3		8	3.2	odd	2
1520.2.q.o.881.2		8	76.7	odd	6
1520.2.q.o.961.2		8	4.3	odd	2
1805.2.a.i.1.2		4	19.8	odd	6
1805.2.a.o.1.3		4	19.11	even	3
9025.2.a.bg.1.2		4	95.49	even	6
9025.2.a.bp.1.3		4	95.84	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.548719 + 0.950409i) q^{2} +(0.189667 - 0.328513i) q^{3} +(0.397815 + 0.689035i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.208148 + 0.360522i) q^{6} +1.89307 q^{7} -3.06803 q^{8} +(1.42805 + 2.47346i) q^{9} +(-0.548719 - 0.950409i) q^{10} +0.134400 q^{11} +0.301809 q^{12} +(-1.75687 - 3.04298i) q^{13} +(-1.03876 + 1.79919i) q^{14} +(0.189667 + 0.328513i) q^{15} +(0.887858 - 1.53781i) q^{16} +(0.830615 - 1.43867i) q^{17} -3.13440 q^{18} +(2.10596 - 3.81640i) q^{19} -0.795629 q^{20} +(0.359052 - 0.621897i) q^{21} +(-0.0737478 + 0.127735i) q^{22} +(-2.68492 - 4.65042i) q^{23} +(-0.581904 + 1.00789i) q^{24} +(-0.500000 - 0.866025i) q^{25} +3.85611 q^{26} +2.22142 q^{27} +(0.753090 + 1.30439i) q^{28} +(-2.48530 - 4.30466i) q^{29} -0.416295 q^{30} +6.56472 q^{31} +(-2.09366 - 3.62633i) q^{32} +(0.0254912 - 0.0441521i) q^{33} +(0.911548 + 1.57885i) q^{34} +(-0.946534 + 1.63944i) q^{35} +(-1.13620 + 1.96796i) q^{36} -1.69819 q^{37} +(2.47156 + 4.09566i) q^{38} -1.33288 q^{39} +(1.53402 - 2.65699i) q^{40} +(-5.31637 + 9.20823i) q^{41} +(0.394038 + 0.682493i) q^{42} +(-4.25392 + 7.36801i) q^{43} +(0.0534662 + 0.0926063i) q^{44} -2.85611 q^{45} +5.89307 q^{46} +(5.55771 + 9.62623i) q^{47} +(-0.336794 - 0.583345i) q^{48} -3.41630 q^{49} +1.09744 q^{50} +(-0.315080 - 0.545735i) q^{51} +(1.39781 - 2.42109i) q^{52} +(0.132424 + 0.229365i) q^{53} +(-1.21894 + 2.11126i) q^{54} +(-0.0672000 + 0.116394i) q^{55} -5.80799 q^{56} +(-0.854305 - 1.41568i) q^{57} +5.45492 q^{58} +(3.44833 - 5.97269i) q^{59} +(-0.150905 + 0.261374i) q^{60} +(-4.58794 - 7.94655i) q^{61} +(-3.60219 + 6.23917i) q^{62} +(2.70340 + 4.68243i) q^{63} +8.14676 q^{64} +3.51373 q^{65} +(0.0279750 + 0.0484542i) q^{66} +(1.47677 + 2.55784i) q^{67} +1.32172 q^{68} -2.03696 q^{69} +(-1.03876 - 1.79919i) q^{70} +(-0.664176 + 1.15039i) q^{71} +(-4.38131 - 7.58865i) q^{72} +(3.17119 - 5.49266i) q^{73} +(0.931830 - 1.61398i) q^{74} -0.379334 q^{75} +(3.46742 - 0.0671384i) q^{76} +0.254428 q^{77} +(0.731376 - 1.26678i) q^{78} +(0.733639 - 1.27070i) q^{79} +(0.887858 + 1.53781i) q^{80} +(-3.86283 + 6.69062i) q^{81} +(-5.83439 - 10.1055i) q^{82} +7.44736 q^{83} +0.571345 q^{84} +(0.830615 + 1.43867i) q^{85} +(-4.66842 - 8.08593i) q^{86} -1.88551 q^{87} -0.412343 q^{88} +(-4.86804 - 8.43169i) q^{89} +(1.56720 - 2.71447i) q^{90} +(-3.32587 - 5.76057i) q^{91} +(2.13620 - 3.70001i) q^{92} +(1.24511 - 2.15659i) q^{93} -12.1985 q^{94} +(2.25212 + 3.73202i) q^{95} -1.58839 q^{96} +(-8.73447 + 15.1285i) q^{97} +(1.87459 - 3.24688i) q^{98} +(0.191930 + 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20}+ \cdots - 38 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9 - q^10 - 4 * q^11 + 12 * q^12 - 7 * q^13 + q^14 - 3 * q^15 - 7 * q^16 + q^17 - 20 * q^18 + 5 * q^19 + 10 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 - 23 * q^24 - 4 * q^25 + 6 * q^26 + 24 * q^27 + 19 * q^28 + q^29 + 4 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 + 4 * q^35 + 7 * q^36 - 4 * q^37 + 13 * q^38 + 30 * q^39 - 12 * q^40 + 8 * q^41 + 15 * q^42 - q^43 + 12 * q^44 + 2 * q^45 + 24 * q^46 + 12 * q^47 - 23 * q^48 - 20 * q^49 + 2 * q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 + 34 * q^54 + 2 * q^55 - 82 * q^56 + 7 * q^57 - 54 * q^58 + 5 * q^59 - 6 * q^60 - 37 * q^62 + 3 * q^63 + 112 * q^64 + 14 * q^65 + 31 * q^66 - 4 * q^67 + 32 * q^68 - 18 * q^69 + q^70 - 20 * q^71 - 17 * q^72 + 20 * q^73 - 25 * q^74 + 6 * q^75 + 63 * q^76 + 28 * q^77 + 18 * q^78 - 17 * q^79 - 7 * q^80 - 12 * q^81 - 21 * q^82 + 2 * q^83 - 40 * q^84 + q^85 - 8 * q^86 - 32 * q^87 - 14 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 + q^92 + 8 * q^93 - 62 * q^94 - 4 * q^95 + 42 * q^96 - q^97 - 9 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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