LMFDB - Embedded newform 287.2.h.d.78.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.8
Character	$\chi$	$=$	287.78
Dual form			287.2.h.d.92.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45435 - 1.05664i) q^{2} -0.241537 q^{3} +(0.380592 - 1.17134i) q^{4} +(1.25760 - 3.87050i) q^{5} +(-0.351279 + 0.255219i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.426843 + 1.31369i) q^{8} -2.94166 q^{9} +O(q^{10})$	\(q+(1.45435 - 1.05664i) q^{2} -0.241537 q^{3} +(0.380592 - 1.17134i) q^{4} +(1.25760 - 3.87050i) q^{5} +(-0.351279 + 0.255219i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.426843 + 1.31369i) q^{8} -2.94166 q^{9} +(-2.26075 - 6.95788i) q^{10} +(-0.339751 - 1.04564i) q^{11} +(-0.0919270 + 0.282922i) q^{12} +(0.0510485 - 0.0370889i) q^{13} +1.79767 q^{14} +(-0.303757 + 0.934868i) q^{15} +(4.00168 + 2.90739i) q^{16} +(-0.00984317 - 0.0302942i) q^{17} +(-4.27819 + 3.10829i) q^{18} +(3.48788 + 2.53410i) q^{19} +(-4.05504 - 2.94616i) q^{20} +(-0.195408 - 0.141972i) q^{21} +(-1.59899 - 1.16173i) q^{22} +(0.423162 - 0.307445i) q^{23} +(-0.103098 - 0.317304i) q^{24} +(-9.35409 - 6.79615i) q^{25} +(0.0350524 - 0.107880i) q^{26} +1.43513 q^{27} +(0.996402 - 0.723929i) q^{28} +(0.123161 - 0.379051i) q^{29} +(0.546055 + 1.68059i) q^{30} +(0.900425 + 2.77122i) q^{31} +6.12933 q^{32} +(0.0820624 + 0.252562i) q^{33} +(-0.0463255 - 0.0336575i) q^{34} +(3.29244 - 2.39210i) q^{35} +(-1.11957 + 3.44569i) q^{36} +(-2.89195 + 8.90049i) q^{37} +7.75023 q^{38} +(-0.0123301 + 0.00895835i) q^{39} +5.62142 q^{40} +(4.17210 + 4.85733i) q^{41} -0.434204 q^{42} +(-7.33409 + 5.32852i) q^{43} -1.35411 q^{44} +(-3.69943 + 11.3857i) q^{45} +(0.290564 - 0.894264i) q^{46} +(9.11532 - 6.62267i) q^{47} +(-0.966555 - 0.702243i) q^{48} +(0.309017 + 0.951057i) q^{49} -20.7852 q^{50} +(0.00237749 + 0.00731717i) q^{51} +(-0.0240151 - 0.0739109i) q^{52} +(-1.50408 + 4.62907i) q^{53} +(2.08718 - 1.51642i) q^{54} -4.47443 q^{55} +(-0.426843 + 1.31369i) q^{56} +(-0.842453 - 0.612078i) q^{57} +(-0.221403 - 0.681409i) q^{58} +(-2.89964 + 2.10671i) q^{59} +(0.979442 + 0.711606i) q^{60} +(-5.59033 - 4.06161i) q^{61} +(4.23773 + 3.07889i) q^{62} +(-2.37985 - 1.72906i) q^{63} +(0.910798 - 0.661734i) q^{64} +(-0.0793539 - 0.244226i) q^{65} +(0.386215 + 0.280602i) q^{66} +(2.40645 - 7.40629i) q^{67} -0.0392310 q^{68} +(-0.102209 + 0.0742594i) q^{69} +(2.26075 - 6.95788i) q^{70} +(1.51073 + 4.64954i) q^{71} +(-1.25563 - 3.86442i) q^{72} -8.37743 q^{73} +(5.19877 + 16.0002i) q^{74} +(2.25936 + 1.64152i) q^{75} +(4.29575 - 3.12104i) q^{76} +(0.339751 - 1.04564i) q^{77} +(-0.00846646 + 0.0260571i) q^{78} -3.65872 q^{79} +(16.2856 - 11.8322i) q^{80} +8.47834 q^{81} +(11.2001 + 2.65581i) q^{82} +10.2230 q^{83} +(-0.240668 + 0.174856i) q^{84} -0.129632 q^{85} +(-5.03594 + 15.4990i) q^{86} +(-0.0297480 + 0.0915549i) q^{87} +(1.22863 - 0.892652i) q^{88} +(-10.7758 - 7.82907i) q^{89} +(6.65036 + 20.4677i) q^{90} +0.0630994 q^{91} +(-0.199071 - 0.612678i) q^{92} +(-0.217486 - 0.669353i) q^{93} +(6.25903 - 19.2633i) q^{94} +(14.1946 - 10.3130i) q^{95} -1.48046 q^{96} +(3.02983 - 9.32485i) q^{97} +(1.45435 + 1.05664i) q^{98} +(0.999431 + 3.07593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.45435	−	1.05664i	1.02838	−	0.747160i	0.0603947	−	0.998175i	$-0.480764\pi$
$2$	1.45435	−	1.05664i	1.02838	−	0.747160i	0.967983	+	0.251014i	$0.0807641\pi$
$3$	−0.241537			−0.139451			−0.0697257	−	0.997566i	$-0.522212\pi$
$3$	−0.241537			−0.139451			−0.0697257	+	0.997566i	$0.522212\pi$
$4$	0.380592	−	1.17134i	0.190296	−	0.585670i
$5$	1.25760	−	3.87050i	0.562416	−	1.73094i	−0.113091	−	0.993585i	$-0.536075\pi$
$5$	1.25760	−	3.87050i	0.562416	−	1.73094i	0.675507	−	0.737354i	$-0.263925\pi$
$6$	−0.351279	+	0.255219i	−0.143409	+	0.104193i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	0.426843	+	1.31369i	0.150912	+	0.464459i
$9$	−2.94166			−0.980553
$10$	−2.26075	−	6.95788i	−0.714912	−	2.20027i
$11$	−0.339751	−	1.04564i	−0.102439	−	0.315274i	0.886682	−	0.462380i	$-0.153004\pi$
$11$	−0.339751	−	1.04564i	−0.102439	−	0.315274i	−0.989121	+	0.147106i	$0.953004\pi$
$12$	−0.0919270	+	0.282922i	−0.0265370	+	0.0816726i
$13$	0.0510485	−	0.0370889i	0.0141583	−	0.0102866i	−0.580684	−	0.814129i	$-0.697215\pi$
$13$	0.0510485	−	0.0370889i	0.0141583	−	0.0102866i	0.594842	+	0.803843i	$0.297215\pi$
$14$	1.79767			0.480448
$15$	−0.303757	+	0.934868i	−0.0784297	+	0.241382i
$16$	4.00168	+	2.90739i	1.00042	+	0.726848i
$17$	−0.00984317	−	0.0302942i	−0.00238732	−	0.00734742i	0.949856	−	0.312688i	$-0.101230\pi$
$17$	−0.00984317	−	0.0302942i	−0.00238732	−	0.00734742i	−0.952243	+	0.305341i	$0.901230\pi$
$18$	−4.27819	+	3.10829i	−1.00838	+	0.732631i
$19$	3.48788	+	2.53410i	0.800175	+	0.581361i	0.910966	−	0.412483i	$-0.135338\pi$
$19$	3.48788	+	2.53410i	0.800175	+	0.581361i	−0.110790	+	0.993844i	$0.535338\pi$
$20$	−4.05504	−	2.94616i	−0.906734	−	0.658781i
$21$	−0.195408	−	0.141972i	−0.0426414	−	0.0309808i
$22$	−1.59899	−	1.16173i	−0.340906	−	0.247683i
$23$	0.423162	−	0.307445i	0.0882354	−	0.0641068i	−0.542793	−	0.839867i	$-0.682633\pi$
$23$	0.423162	−	0.307445i	0.0882354	−	0.0641068i	0.631028	+	0.775760i	$0.282633\pi$
$24$	−0.103098	−	0.317304i	−0.0210449	−	0.0647695i
$25$	−9.35409	−	6.79615i	−1.87082	−	1.35923i
$26$	0.0350524	−	0.107880i	0.00687434	−	0.0211571i
$27$	1.43513			0.276191
$28$	0.996402	−	0.723929i	0.188302	−	0.136810i
$29$	0.123161	−	0.379051i	0.0228704	−	0.0703880i	−0.938970	−	0.343999i	$-0.888218\pi$
$29$	0.123161	−	0.379051i	0.0228704	−	0.0703880i	0.961840	+	0.273611i	$0.0882182\pi$
$30$	0.546055	+	1.68059i	0.0996956	+	0.306832i
$31$	0.900425	+	2.77122i	0.161721	+	0.497726i	0.998780	−	0.0493868i	$-0.0157267\pi$
$31$	0.900425	+	2.77122i	0.161721	+	0.497726i	−0.837059	+	0.547113i	$0.815727\pi$
$32$	6.12933			1.08352
$33$	0.0820624	+	0.252562i	0.0142852	+	0.0439654i
$34$	−0.0463255	−	0.0336575i	−0.00794477	−	0.00577221i
$35$	3.29244	−	2.39210i	0.556524	−	0.404338i
$36$	−1.11957	+	3.44569i	−0.186595	+	0.574281i
$37$	−2.89195	+	8.90049i	−0.475433	+	1.46323i	0.369940	+	0.929056i	$0.379378\pi$
$37$	−2.89195	+	8.90049i	−0.475433	+	1.46323i	−0.845373	+	0.534176i	$0.820622\pi$
$38$	7.75023			1.25725
$39$	−0.0123301	+	0.00895835i	−0.00197440	+	0.00143448i
$40$	5.62142			0.888825
$41$	4.17210	+	4.85733i	0.651572	+	0.758587i
$41$	4.17210	+	4.85733i	0.651572	+	0.758587i
$42$	−0.434204			−0.0669992
$43$	−7.33409	+	5.32852i	−1.11844	+	0.812592i	−0.983971	−	0.178326i	$-0.942932\pi$
$43$	−7.33409	+	5.32852i	−1.11844	+	0.812592i	−0.134466	+	0.990918i	$0.542932\pi$
$44$	−1.35411			−0.204140
$45$	−3.69943	+	11.3857i	−0.551479	+	1.69728i
$46$	0.290564	−	0.894264i	0.0428413	−	0.131852i
$47$	9.11532	−	6.62267i	1.32961	−	0.966016i	0.329848	−	0.944034i	$-0.393002\pi$
$47$	9.11532	−	6.62267i	1.32961	−	0.966016i	0.999758	−	0.0219818i	$-0.00699760\pi$
$48$	−0.966555	−	0.702243i	−0.139510	−	0.101360i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−20.7852			−2.93947
$51$	0.00237749	+	0.00731717i	0.000332915	+	0.00102461i
$52$	−0.0240151	−	0.0739109i	−0.00333030	−	0.0102496i
$53$	−1.50408	+	4.62907i	−0.206601	+	0.635852i	0.793043	+	0.609166i	$0.208496\pi$
$53$	−1.50408	+	4.62907i	−0.206601	+	0.635852i	−0.999644	+	0.0266864i	$0.991504\pi$
$54$	2.08718	−	1.51642i	0.284029	−	0.206359i
$55$	−4.47443			−0.603333
$56$	−0.426843	+	1.31369i	−0.0570393	+	0.175549i
$57$	−0.842453	−	0.612078i	−0.111586	−	0.0810717i
$58$	−0.221403	−	0.681409i	−0.0290717	−	0.0894734i
$59$	−2.89964	+	2.10671i	−0.377500	+	0.274270i	−0.760314	−	0.649555i	$-0.774955\pi$
$59$	−2.89964	+	2.10671i	−0.377500	+	0.274270i	0.382814	+	0.923826i	$0.374955\pi$
$60$	0.979442	+	0.711606i	0.126445	+	0.0918680i
$61$	−5.59033	−	4.06161i	−0.715769	−	0.520036i	0.169261	−	0.985571i	$-0.445862\pi$
$61$	−5.59033	−	4.06161i	−0.715769	−	0.520036i	−0.885030	+	0.465535i	$0.845862\pi$
$62$	4.23773	+	3.07889i	0.538192	+	0.391019i
$63$	−2.37985	−	1.72906i	−0.299833	−	0.217842i
$64$	0.910798	−	0.661734i	0.113850	−	0.0827167i
$65$	−0.0793539	−	0.244226i	−0.00984264	−	0.0302925i
$66$	0.386215	+	0.280602i	0.0475398	+	0.0345397i
$67$	2.40645	−	7.40629i	0.293995	−	0.904822i	−0.689563	−	0.724226i	$-0.742197\pi$
$67$	2.40645	−	7.40629i	0.293995	−	0.904822i	0.983557	−	0.180596i	$-0.0578027\pi$
$68$	−0.0392310			−0.00475746
$69$	−0.102209	+	0.0742594i	−0.0123046	+	0.00893979i
$70$	2.26075	−	6.95788i	0.270211	−	0.831625i
$71$	1.51073	+	4.64954i	0.179290	+	0.551799i	0.999803	−	0.0198289i	$-0.00631215\pi$
$71$	1.51073	+	4.64954i	0.179290	+	0.551799i	−0.820513	+	0.571628i	$0.806312\pi$
$72$	−1.25563	−	3.86442i	−0.147977	−	0.455427i
$73$	−8.37743			−0.980504			−0.490252	−	0.871581i	$-0.663095\pi$
$73$	−8.37743			−0.980504			−0.490252	+	0.871581i	$0.663095\pi$
$74$	5.19877	+	16.0002i	0.604344	+	1.85998i
$75$	2.25936	+	1.64152i	0.260888	+	0.189547i
$76$	4.29575	−	3.12104i	0.492756	−	0.358008i
$77$	0.339751	−	1.04564i	0.0387182	−	0.119162i
$78$	−0.00846646	+	0.0260571i	−0.000958638	+	0.00295038i
$79$	−3.65872			−0.411638			−0.205819	−	0.978590i	$-0.565986\pi$
$79$	−3.65872			−0.411638			−0.205819	+	0.978590i	$0.565986\pi$
$80$	16.2856	−	11.8322i	1.82078	−	1.32288i
$81$	8.47834			0.942038
$82$	11.2001	+	2.65581i	1.23685	+	0.293285i
$83$	10.2230			1.12212			0.561061	−	0.827774i	$-0.310393\pi$
$83$	10.2230			1.12212			0.561061	+	0.827774i	$0.310393\pi$
$84$	−0.240668	+	0.174856i	−0.0262590	+	0.0190783i
$85$	−0.129632			−0.0140606
$86$	−5.03594	+	15.4990i	−0.543040	+	1.67130i
$87$	−0.0297480	+	0.0915549i	−0.00318932	+	0.00981571i
$88$	1.22863	−	0.892652i	0.130972	−	0.0951571i
$89$	−10.7758	−	7.82907i	−1.14223	−	0.829880i	−0.154803	−	0.987945i	$-0.549474\pi$
$89$	−10.7758	−	7.82907i	−1.14223	−	0.829880i	−0.987429	+	0.158065i	$0.949474\pi$
$90$	6.65036	+	20.4677i	0.701010	+	2.15749i
$91$	0.0630994			0.00661462
$92$	−0.199071	−	0.612678i	−0.0207546	−	0.0638761i
$93$	−0.217486	−	0.669353i	−0.0225523	−	0.0694087i
$94$	6.25903	−	19.2633i	0.645570	−	1.98686i
$95$	14.1946	−	10.3130i	1.45633	−	1.05809i
$96$	−1.48046			−0.151099
$97$	3.02983	−	9.32485i	0.307632	−	0.946795i	−0.671050	−	0.741412i	$-0.734156\pi$
$97$	3.02983	−	9.32485i	0.307632	−	0.946795i	0.978682	−	0.205382i	$-0.0658437\pi$
$98$	1.45435	+	1.05664i	0.146911	+	0.106737i
$99$	0.999431	+	3.07593i	0.100447	+	0.309143i
$100$	−11.5207	+	8.37028i	−1.15207	+	0.837028i
$101$	−4.86293	−	3.53313i	−0.483880	−	0.351559i	0.318946	−	0.947773i	$-0.396671\pi$
$101$	−4.86293	−	3.53313i	−0.483880	−	0.351559i	−0.802826	+	0.596214i	$0.796671\pi$
$102$	0.0111893	+	0.00812953i	0.00110791	+	0.000804943i
$103$	−0.341900	−	0.248405i	−0.0336884	−	0.0244761i	0.570814	−	0.821080i	$-0.306628\pi$
$103$	−0.341900	−	0.248405i	−0.0336884	−	0.0244761i	−0.604502	+	0.796604i	$0.706628\pi$
$104$	0.0705130	+	0.0512307i	0.00691436	+	0.00502358i
$105$	−0.795246	+	0.577780i	−0.0776081	+	0.0563856i
$106$	2.70384	+	8.32155i	0.262620	+	0.808260i
$107$	−14.5176	−	10.5476i	−1.40346	−	1.01968i	−0.994232	−	0.107246i	$-0.965797\pi$
$107$	−14.5176	−	10.5476i	−1.40346	−	1.01968i	−0.409232	−	0.912430i	$-0.634203\pi$
$108$	0.546199	−	1.68103i	0.0525580	−	0.161757i
$109$	−9.62665			−0.922066			−0.461033	−	0.887383i	$-0.652521\pi$
$109$	−9.62665			−0.922066			−0.461033	+	0.887383i	$0.652521\pi$
$110$	−6.50738	+	4.72789i	−0.620454	+	0.450786i
$111$	0.698512	−	2.14980i	0.0662998	−	0.204050i
$112$	1.52851	+	4.70426i	0.144430	+	0.444511i
$113$	−2.51240	−	7.73237i	−0.236347	−	0.727400i	−0.996940	−	0.0781716i	$-0.975092\pi$
$113$	−2.51240	−	7.73237i	−0.236347	−	0.727400i	0.760593	−	0.649229i	$-0.224908\pi$
$114$	−1.87197			−0.175326
$115$	−0.657797	−	2.02449i	−0.0613399	−	0.188785i
$116$	−0.397124	−	0.288527i	−0.0368720	−	0.0267891i
$117$	−0.150167	+	0.109103i	−0.0138830	+	0.0100866i
$118$	−1.99103	+	6.12777i	−0.183289	+	0.564107i
$119$	0.00984317	−	0.0302942i	0.000902322	−	0.00277706i
$120$	−1.35778			−0.123948
$121$	7.92124	−	5.75512i	0.720113	−	0.523193i
$122$	−12.4220			−1.12463
$123$	−1.00772	−	1.17322i	−0.0908627	−	0.105786i
$124$	3.58874			0.322279
$125$	−21.6060	+	15.6977i	−1.93250	+	1.40404i
$126$	−5.28814			−0.471105
$127$	2.48529	−	7.64894i	0.220534	−	0.678734i	−0.778180	−	0.628041i	$-0.783857\pi$
$127$	2.48529	−	7.64894i	0.220534	−	0.678734i	0.998714	−	0.0506930i	$-0.0161430\pi$
$128$	−3.16273	+	9.73389i	−0.279549	+	0.860363i
$129$	1.77145	−	1.28704i	0.155968	−	0.113317i
$130$	−0.373468	−	0.271340i	−0.0327553	−	0.0237981i
$131$	−3.12529	−	9.61867i	−0.273058	−	0.840387i	−0.989727	−	0.142973i	$-0.954334\pi$
$131$	−3.12529	−	9.61867i	−0.273058	−	0.840387i	0.716668	−	0.697414i	$-0.245666\pi$
$132$	0.327068			0.0284677
$133$	1.33225	+	4.10025i	0.115521	+	0.355537i
$134$	−4.32600	−	13.3141i	−0.373710	−	1.15016i
$135$	1.80482	−	5.55467i	0.155334	−	0.478070i
$136$	0.0355956	−	0.0258617i	0.00305230	−	0.00221762i
$137$	22.4248			1.91588			0.957942	−	0.286962i	$-0.0926453\pi$
$137$	22.4248			1.91588			0.957942	+	0.286962i	$0.0926453\pi$
$138$	−0.0701820	+	0.215998i	−0.00597429	+	0.0183870i
$139$	3.40242	+	2.47200i	0.288589	+	0.209672i	0.722655	−	0.691209i	$-0.242921\pi$
$139$	3.40242	+	2.47200i	0.288589	+	0.209672i	−0.434066	+	0.900881i	$0.642921\pi$
$140$	−1.54889	−	4.76698i	−0.130905	−	0.402884i
$141$	−2.20169	+	1.59962i	−0.185416	+	0.134712i
$142$	7.11003	+	5.16574i	0.596661	+	0.433499i
$143$	−0.0561256	−	0.0407776i	−0.00469346	−	0.00341000i
$144$	−11.7716	−	8.55256i	−0.980966	−	0.712713i
$145$	−1.31223	−	0.953389i	−0.108975	−	0.0791747i
$146$	−12.1837	+	8.85196i	−1.00833	+	0.732594i
$147$	−0.0746391	−	0.229715i	−0.00615613	−	0.0189466i
$148$	9.32486	+	6.77491i	0.766499	+	0.556894i
$149$	−6.38604	+	19.6542i	−0.523165	+	1.61014i	0.244751	+	0.969586i	$0.421294\pi$
$149$	−6.38604	+	19.6542i	−0.523165	+	1.61014i	−0.767916	+	0.640551i	$0.778706\pi$
$150$	5.02040			0.409914
$151$	0.101414	−	0.0736818i	0.00825298	−	0.00599614i	−0.583651	−	0.812005i	$-0.698376\pi$
$151$	0.101414	−	0.0736818i	0.00825298	−	0.00599614i	0.591904	+	0.806008i	$0.298376\pi$
$152$	−1.84023	+	5.66365i	−0.149262	+	0.459383i
$153$	0.0289553	+	0.0891151i	0.00234089	+	0.00720453i
$154$	−0.610760	−	1.87973i	−0.0492164	−	0.151473i
$155$	11.8584			0.952488
$156$	0.00580054	+	0.0178522i	0.000464415	+	0.00142932i
$157$	9.80990	+	7.12731i	0.782915	+	0.568821i	0.905852	−	0.423593i	$-0.139231\pi$
$157$	9.80990	+	7.12731i	0.782915	+	0.568821i	−0.122937	+	0.992414i	$0.539231\pi$
$158$	−5.32105	+	3.86597i	−0.423320	+	0.307560i
$159$	0.363290	−	1.11809i	0.0288108	−	0.0886705i
$160$	7.70824	−	23.7235i	0.609390	−	1.87551i
$161$	0.523057			0.0412227
$162$	12.3304	−	8.95859i	0.968771	−	0.703854i
$163$	−10.9892			−0.860738			−0.430369	−	0.902653i	$-0.641617\pi$
$163$	−10.9892			−0.860738			−0.430369	+	0.902653i	$0.641617\pi$
$164$	7.27745	−	3.03829i	0.568273	−	0.237251i
$165$	1.08074			0.0841356
$166$	14.8678	−	10.8021i	1.15397	−	0.838406i
$167$	−25.2772			−1.95601			−0.978006	−	0.208579i	$-0.933116\pi$
$167$	−25.2772			−1.95601			−0.978006	+	0.208579i	$0.933116\pi$
$168$	0.103098	−	0.317304i	0.00795422	−	0.0244806i
$169$	−4.01599	+	12.3599i	−0.308922	+	0.950765i
$170$	−0.188530	+	0.136975i	−0.0144596	+	0.0105055i
$171$	−10.2602	−	7.45445i	−0.784614	−	0.570056i
$172$	3.45023	+	10.6187i	0.263077	+	0.809669i
$173$	−13.2763			−1.00938			−0.504688	−	0.863302i	$-0.668392\pi$
$173$	−13.2763			−1.00938			−0.504688	+	0.863302i	$0.668392\pi$
$174$	0.0534771	+	0.164585i	0.00405409	+	0.0124772i
$175$	−3.57295	−	10.9964i	−0.270089	−	0.831250i
$176$	1.68053	−	5.17213i	0.126674	−	0.389864i
$177$	0.700370	−	0.508848i	0.0526430	−	0.0382474i
$178$	−23.9443			−1.79470
$179$	6.52763	−	20.0900i	0.487898	−	1.50160i	−0.339842	−	0.940483i	$-0.610373\pi$
$179$	6.52763	−	20.0900i	0.487898	−	1.50160i	0.827740	−	0.561113i	$-0.189627\pi$
$180$	11.9285	+	8.66659i	0.889101	+	0.645970i
$181$	−6.54492	−	20.1432i	−0.486480	−	1.49723i	−0.829826	−	0.558023i	$-0.811560\pi$
$181$	−6.54492	−	20.1432i	−0.486480	−	1.49723i	0.343345	−	0.939209i	$-0.388440\pi$
$182$	0.0917684	−	0.0666737i	0.00680233	−	0.00494218i
$183$	1.35027	+	0.981030i	0.0998150	+	0.0725199i
$184$	0.584511	+	0.424672i	0.0430907	+	0.0313072i
$185$	30.8124	+	22.3865i	2.26537	+	1.64589i
$186$	−1.02357	−	0.743666i	−0.0750517	−	0.0545282i
$187$	−0.0283327	+	0.0205849i	−0.00207189	+	0.00150532i
$188$	−4.28819	−	13.1977i	−0.312748	−	0.962540i
$189$	1.16105	+	0.843549i	0.0844536	+	0.0613592i
$190$	9.74669	−	29.9972i	0.707099	−	2.17623i
$191$	12.3197			0.891423			0.445711	−	0.895177i	$-0.352951\pi$
$191$	12.3197			0.891423			0.445711	+	0.895177i	$0.352951\pi$
$192$	−0.219992	+	0.159833i	−0.0158765	+	0.0115350i
$193$	−6.02163	+	18.5327i	−0.433447	+	1.33401i	0.461223	+	0.887284i	$0.347411\pi$
$193$	−6.02163	+	18.5327i	−0.433447	+	1.33401i	−0.894670	+	0.446728i	$0.852589\pi$
$194$	−5.44663	−	16.7630i	−0.391045	−	1.20351i
$195$	0.0191669	+	0.0589897i	0.00137257	+	0.00422434i
$196$	1.23162			0.0879729
$197$	3.23976	+	9.97094i	0.230823	+	0.710400i	0.997648	+	0.0685440i	$0.0218354\pi$
$197$	3.23976	+	9.97094i	0.230823	+	0.710400i	−0.766825	+	0.641856i	$0.778165\pi$
$198$	4.70368	+	3.41743i	0.334276	+	0.242866i
$199$	14.8434	−	10.7844i	1.05222	−	0.764484i	0.0795881	−	0.996828i	$-0.474639\pi$
$199$	14.8434	−	10.7844i	1.05222	−	0.764484i	0.972634	+	0.232344i	$0.0746395\pi$
$200$	4.93529	−	15.1892i	0.348977	−	1.07404i
$201$	−0.581247	+	1.78889i	−0.0409980	+	0.126179i
$202$	−10.8056			−0.760283
$203$	0.322440	−	0.234266i	0.0226308	−	0.0164423i
$204$	0.00947575			0.000663435
$205$	24.0471	−	10.0395i	1.67952	−	0.701190i
$206$	−0.759717			−0.0529320
$207$	−1.24480	+	0.904399i	−0.0865195	+	0.0628601i
$208$	0.312112			0.0216411
$209$	1.46475	−	4.50805i	0.101319	−	0.311828i
$210$	−0.546055	+	1.68059i	−0.0376814	+	0.115971i
$211$	3.57295	−	2.59590i	0.245972	−	0.178709i	−0.457968	−	0.888969i	$-0.651422\pi$
$211$	3.57295	−	2.59590i	0.245972	−	0.178709i	0.703940	+	0.710260i	$0.251422\pi$
$212$	4.84978	+	3.52357i	0.333084	+	0.242000i
$213$	−0.364897	−	1.12304i	−0.0250023	−	0.0769492i
$214$	−32.2586			−2.20515
$215$	11.4007	+	35.0877i	0.777520	+	2.39296i
$216$	0.612576	+	1.88531i	0.0416805	+	0.128279i
$217$	−0.900425	+	2.77122i	−0.0611248	+	0.188123i
$218$	−14.0005	+	10.1719i	−0.948233	+	0.688931i
$219$	2.02346			0.136733
$220$	−1.70293	+	5.24109i	−0.114812	+	0.353354i
$221$	−0.00162606	−	0.00118140i	−0.000109380	−	7.94695e-5i
$222$	−1.25569	−	3.86463i	−0.0842767	−	0.259377i
$223$	−2.73379	+	1.98622i	−0.183068	+	0.133007i	−0.675545	−	0.737319i	$-0.736092\pi$
$223$	−2.73379	+	1.98622i	−0.183068	+	0.133007i	0.492477	+	0.870326i	$0.336092\pi$
$224$	4.95873	+	3.60273i	0.331319	+	0.240717i
$225$	27.5166	+	19.9920i	1.83444	+	1.33280i
$226$	−11.8243	−	8.59083i	−0.786539	−	0.571454i
$227$	18.5618	+	13.4860i	1.23199	+	0.895094i	0.997038	−	0.0769121i	$-0.0245061\pi$
$227$	18.5618	+	13.4860i	1.23199	+	0.895094i	0.234954	+	0.972007i	$0.424506\pi$
$228$	−1.03758	+	0.753848i	−0.0687156	+	0.0499248i
$229$	−5.78828	−	17.8145i	−0.382501	−	1.17722i	−0.938277	−	0.345884i	$-0.887579\pi$
$229$	−5.78828	−	17.8145i	−0.382501	−	1.17722i	0.555777	−	0.831332i	$-0.312421\pi$
$230$	−3.09583	−	2.24925i	−0.204133	−	0.148311i
$231$	−0.0820624	+	0.252562i	−0.00539931	+	0.0166174i
$232$	0.550525			0.0361437
$233$	−9.06303	+	6.58468i	−0.593739	+	0.431377i	−0.843651	−	0.536892i	$-0.819598\pi$
$233$	−9.06303	+	6.58468i	−0.593739	+	0.431377i	0.249912	+	0.968269i	$0.419598\pi$
$234$	−0.103112	+	0.317347i	−0.00674066	+	0.0207456i
$235$	−14.1696	−	43.6095i	−0.924322	−	2.84477i
$236$	1.36410	+	4.19826i	0.0887951	+	0.273283i
$237$	0.883717			0.0574036
$238$	−0.0176948	−	0.0544589i	−0.00114698	−	0.00353005i
$239$	14.3950	+	10.4586i	0.931137	+	0.676511i	0.946271	−	0.323375i	$-0.104817\pi$
$239$	14.3950	+	10.4586i	0.931137	+	0.676511i	−0.0151340	+	0.999885i	$0.504817\pi$
$240$	−3.93357	+	2.85790i	−0.253911	+	0.184477i
$241$	−0.860787	+	2.64923i	−0.0554482	+	0.170652i	−0.974945	−	0.222445i	$-0.928596\pi$
$241$	−0.860787	+	2.64923i	−0.0554482	+	0.170652i	0.919497	+	0.393097i	$0.128596\pi$
$242$	5.43912	−	16.7399i	0.349640	−	1.07608i
$243$	−6.35323			−0.407560
$244$	−6.88517	+	5.00237i	−0.440778	+	0.320244i
$245$	4.06968			0.260002
$246$	−2.70525	−	0.641477i	−0.172480	−	0.0408991i
$247$	0.272038			0.0173094
$248$	−3.25618	+	2.36576i	−0.206768	+	0.150226i
$249$	−2.46924			−0.156482
$250$	−14.8357	+	45.6597i	−0.938293	+	2.88777i
$251$	−7.15501	+	22.0209i	−0.451620	+	1.38994i	0.423437	+	0.905925i	$0.360823\pi$
$251$	−7.15501	+	22.0209i	−0.451620	+	1.38994i	−0.875058	+	0.484019i	$0.839177\pi$
$252$	−2.93108	+	2.12955i	−0.184640	+	0.134149i
$253$	−0.465248	−	0.338023i	−0.0292499	−	0.0212513i
$254$	−4.46774	−	13.7503i	−0.280331	−	0.862769i
$255$	0.0313110			0.00196077
$256$	6.38134	+	19.6398i	0.398834	+	1.22748i
$257$	−6.31074	−	19.4225i	−0.393653	−	1.21154i	−0.930005	−	0.367546i	$-0.880198\pi$
$257$	−6.31074	−	19.4225i	−0.393653	−	1.21154i	0.536352	−	0.843994i	$-0.319802\pi$
$258$	1.21637	−	3.74359i	0.0757277	−	0.233066i
$259$	−7.57121	+	5.50081i	−0.470452	+	0.341804i
$260$	−0.316273			−0.0196144
$261$	−0.362298	+	1.11504i	−0.0224257	+	0.0690192i
$262$	−14.7088	−	10.6865i	−0.908711	−	0.660217i
$263$	9.17448	+	28.2361i	0.565723	+	1.74111i	0.665795	+	0.746135i	$0.268093\pi$
$263$	9.17448	+	28.2361i	0.565723	+	1.74111i	−0.100072	+	0.994980i	$0.531907\pi$
$264$	−0.296760	+	0.215609i	−0.0182643	+	0.0132698i
$265$	16.0253	+	11.6430i	0.984425	+	0.715227i
$266$	6.27007	+	4.55547i	0.384442	+	0.279314i
$267$	2.60275	+	1.89101i	0.159286	+	0.115728i
$268$	−7.75941	−	5.63754i	−0.473982	−	0.344368i
$269$	−8.22726	+	5.97746i	−0.501625	+	0.364452i	−0.809637	−	0.586930i	$-0.800336\pi$
$269$	−8.22726	+	5.97746i	−0.501625	+	0.364452i	0.308012	+	0.951382i	$0.400336\pi$
$270$	−3.24447	−	9.98547i	−0.197452	−	0.607696i
$271$	−18.7853	−	13.6483i	−1.14113	−	0.829077i	−0.153851	−	0.988094i	$-0.549167\pi$
$271$	−18.7853	−	13.6483i	−1.14113	−	0.829077i	−0.987276	+	0.159017i	$0.949167\pi$
$272$	0.0486878	−	0.149846i	0.00295213	−	0.00908573i
$273$	−0.0152409			−0.000922418
$274$	32.6135	−	23.6951i	1.97025	−	1.43147i
$275$	−3.92830	+	12.0901i	−0.236885	+	0.729058i
$276$	0.0480831	+	0.147985i	0.00289426	+	0.00890762i
$277$	6.94575	+	21.3768i	0.417330	+	1.28441i	0.910150	+	0.414278i	$0.135966\pi$
$277$	6.94575	+	21.3768i	0.417330	+	1.28441i	−0.492821	+	0.870131i	$0.664034\pi$
$278$	7.56032			0.453438
$279$	−2.64874	−	8.15200i	−0.158576	−	0.488047i
$280$	4.54783	+	3.30419i	0.271785	+	0.197463i
$281$	13.0907	−	9.51094i	0.780925	−	0.567375i	−0.124332	−	0.992241i	$-0.539679\pi$
$281$	13.0907	−	9.51094i	0.780925	−	0.567375i	0.905256	+	0.424866i	$0.139679\pi$
$282$	−1.51179	+	4.65280i	−0.0900256	+	0.277070i
$283$	5.21437	−	16.0482i	0.309962	−	0.953965i	−0.667817	−	0.744326i	$-0.732771\pi$
$283$	5.21437	−	16.0482i	0.309962	−	0.953965i	0.977779	−	0.209640i	$-0.0672291\pi$
$284$	6.02117			0.357291
$285$	−3.42851	+	2.49096i	−0.203088	+	0.147552i
$286$	−0.124713			−0.00737446
$287$	0.520233	+	6.38196i	0.0307084	+	0.376715i
$288$	−18.0304			−1.06245
$289$	13.7525	−	9.99175i	0.808969	−	0.587750i
$290$	−2.91583			−0.171223
$291$	−0.731815	+	2.25230i	−0.0428998	+	0.132032i
$292$	−3.18838	+	9.81282i	−0.186586	+	0.574252i
$293$	−7.36183	+	5.34868i	−0.430083	+	0.312473i	−0.781682	−	0.623677i	$-0.785638\pi$
$293$	−7.36183	+	5.34868i	−0.430083	+	0.312473i	0.351599	+	0.936151i	$0.385638\pi$
$294$	−0.351279	−	0.255219i	−0.0204870	−	0.0148847i
$295$	4.50743	+	13.8724i	0.262432	+	0.807684i
$296$	−12.9269			−0.751359
$297$	−0.487587	−	1.50064i	−0.0282926	−	0.0870758i
$298$	11.4800	+	35.3318i	0.665019	+	2.04672i
$299$	0.0101990	−	0.0313892i	0.000589823	−	0.00181529i
$300$	2.78268	−	2.02173i	0.160658	−	0.116725i
$301$	−9.06543			−0.522523
$302$	0.0696360	−	0.214318i	0.00400710	−	0.0123326i
$303$	1.17458	+	0.853381i	0.0674778	+	0.0490255i
$304$	6.58979	+	20.2813i	0.377950	+	1.16321i
$305$	−22.7509	+	16.5295i	−1.30271	+	0.946475i
$306$	0.136274	+	0.0990089i	0.00779027	+	0.00565996i
$307$	25.6668	+	18.6480i	1.46488	+	1.06430i	0.982057	+	0.188582i	$0.0603892\pi$
$307$	25.6668	+	18.6480i	1.46488	+	1.06430i	0.482825	+	0.875717i	$0.339611\pi$
$308$	−1.09550	−	0.795927i	−0.0624219	−	0.0453522i
$309$	0.0825815	+	0.0599990i	0.00469790	+	0.00341322i
$310$	17.2462	−	12.5301i	0.979518	−	0.711662i
$311$	−3.11988	−	9.60200i	−0.176912	−	0.544480i	0.822803	−	0.568326i	$-0.192409\pi$
$311$	−3.11988	−	9.60200i	−0.176912	−	0.544480i	−0.999716	+	0.0238464i	$0.992409\pi$
$312$	−0.0170315	−	0.0123741i	−0.000964218	−	0.000700546i
$313$	−2.92538	+	9.00339i	−0.165352	+	0.508902i	−0.999062	−	0.0433009i	$-0.986213\pi$
$313$	−2.92538	+	9.00339i	−0.165352	+	0.508902i	0.833710	+	0.552203i	$0.186213\pi$
$314$	21.7980			1.23013
$315$	−9.68524	+	7.03674i	−0.545701	+	0.396475i
$316$	−1.39248	+	4.28561i	−0.0783331	+	0.241084i
$317$	−2.97920	−	9.16902i	−0.167328	−	0.514984i	0.831872	−	0.554968i	$-0.187269\pi$
$317$	−2.97920	−	9.16902i	−0.167328	−	0.514984i	−0.999200	+	0.0399839i	$0.987269\pi$
$318$	−0.653076	−	2.00996i	−0.0366227	−	0.112713i
$319$	−0.438197			−0.0245343
$320$	−1.41582	−	4.35744i	−0.0791466	−	0.243588i
$321$	3.50653	+	2.54764i	0.195715	+	0.142195i
$322$	0.760706	−	0.552685i	0.0423925	−	0.0308000i
$323$	0.0424365	−	0.130606i	0.00236123	−	0.00726711i
$324$	3.22679	−	9.93103i	0.179266	−	0.551724i
$325$	−0.729574			−0.0404695
$326$	−15.9821	+	11.6116i	−0.885164	+	0.643110i
$327$	2.32519			0.128583
$328$	−4.60018	+	7.55415i	−0.254002	+	0.417108i
$329$	11.2672			0.621179
$330$	1.57177	−	1.14196i	0.0865232	−	0.0628628i
$331$	−18.7879			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$331$	−18.7879			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$332$	3.89080	−	11.9746i	0.213535	−	0.657194i
$333$	8.50712	−	26.1822i	0.466187	−	1.43478i
$334$	−36.7619	+	26.7091i	−2.01152	+	1.46145i
$335$	−25.6397	−	18.6283i	−1.40084	−	1.01777i
$336$	−0.369191	−	1.13625i	−0.0201410	−	0.0619877i
$337$	−20.7661			−1.13120			−0.565601	−	0.824679i	$-0.691356\pi$
$337$	−20.7661			−1.13120			−0.565601	+	0.824679i	$0.691356\pi$
$338$	7.21943	+	22.2191i	0.392685	+	1.20856i
$339$	0.606838	+	1.86765i	0.0329589	+	0.101437i
$340$	−0.0493370	+	0.151844i	−0.00267567	+	0.00823487i
$341$	2.59180	−	1.88305i	0.140354	−	0.101973i
$342$	−22.7985			−1.23280
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−10.1305	−	7.36025i	−0.546201	−	0.396838i
$345$	0.158882	+	0.488990i	0.00855394	+	0.0263263i
$346$	−19.3083	+	14.0283i	−1.03802	+	0.754166i
$347$	18.6347	+	13.5389i	1.00036	+	0.726806i	0.962166	−	0.272464i	$-0.0878387\pi$
$347$	18.6347	+	13.5389i	1.00036	+	0.726806i	0.0381967	+	0.999270i	$0.487839\pi$
$348$	0.0959201	+	0.0696900i	0.00514186	+	0.00373578i
$349$	20.3805	+	14.8073i	1.09094	+	0.792617i	0.979558	−	0.201160i	$-0.0644711\pi$
$349$	20.3805	+	14.8073i	1.09094	+	0.792617i	0.111386	+	0.993777i	$0.464471\pi$
$350$	−16.8156	−	12.2172i	−0.898831	−	0.653039i
$351$	0.0732613	−	0.0532275i	0.00391040	−	0.00284107i
$352$	−2.08244	−	6.40910i	−0.110995	−	0.341606i
$353$	4.61991	+	3.35656i	0.245893	+	0.178652i	0.703905	−	0.710295i	$-0.251438\pi$
$353$	4.61991	+	3.35656i	0.245893	+	0.178652i	−0.458012	+	0.888946i	$0.651438\pi$
$354$	0.480908	−	1.48008i	0.0255600	−	0.0786655i
$355$	19.8959			1.05597
$356$	−13.2717	+	9.64245i	−0.703398	+	0.511049i
$357$	−0.00237749	+	0.00731717i	−0.000125830	+	0.000387265i
$358$	−11.7345	−	36.1152i	−0.620189	−	1.90875i
$359$	−4.81244	−	14.8112i	−0.253991	−	0.781703i	−0.994027	−	0.109136i	$-0.965192\pi$
$359$	−4.81244	−	14.8112i	−0.253991	−	0.781703i	0.740036	−	0.672567i	$-0.234808\pi$
$360$	−16.5363			−0.871540
$361$	−0.127636	−	0.392822i	−0.00671766	−	0.0206748i
$362$	−30.8028	−	22.3795i	−1.61896	−	1.17624i
$363$	−1.91327	+	1.39008i	−0.100421	+	0.0729600i
$364$	0.0240151	−	0.0739109i	0.00125873	−	0.00387399i
$365$	−10.5355	+	32.4248i	−0.551451	+	1.69719i
$366$	3.00036			0.156832
$367$	10.0018	−	7.26672i	0.522089	−	0.379320i	−0.295301	−	0.955404i	$-0.595420\pi$
$367$	10.0018	−	7.26672i	0.522089	−	0.379320i	0.817390	+	0.576084i	$0.195420\pi$
$368$	2.58722			0.134868
$369$	−12.2729	−	14.2886i	−0.638901	−	0.743835i
$370$	68.4665			3.55940
$371$	−3.93772	+	2.86092i	−0.204436	+	0.148532i
$372$	−0.866814			−0.0449422
$373$	2.25111	−	6.92822i	0.116558	−	0.358730i	−0.875711	−	0.482836i	$-0.839607\pi$
$373$	2.25111	−	6.92822i	0.116558	−	0.358730i	0.992269	+	0.124107i	$0.0396066\pi$
$374$	−0.0194546	+	0.0598752i	−0.00100598	+	0.00309607i
$375$	5.21864	−	3.79157i	0.269490	−	0.195796i
$376$	12.5909	+	9.14785i	0.649328	+	0.471764i
$377$	−0.00777140	−	0.0239179i	−0.000400247	−	0.00123183i
$378$	2.57989			0.132695
$379$	3.26799	+	10.0578i	0.167865	+	0.516636i	0.999236	−	0.0390821i	$-0.0124434\pi$
$379$	3.26799	+	10.0578i	0.167865	+	0.516636i	−0.831371	+	0.555718i	$0.812443\pi$
$380$	−6.67765	−	20.5517i	−0.342556	−	1.05428i
$381$	−0.600290	+	1.84750i	−0.0307538	+	0.0946505i
$382$	17.9171	−	13.0176i	0.916720	−	0.666036i
$383$	33.2111			1.69701			0.848504	−	0.529189i	$-0.177504\pi$
$383$	33.2111			1.69701			0.848504	+	0.529189i	$0.177504\pi$
$384$	0.763917	−	2.35110i	0.0389835	−	0.119979i
$385$	−3.61989	−	2.63001i	−0.184487	−	0.134038i
$386$	10.8249	+	33.3157i	0.550974	+	1.69572i
$387$	21.5744	−	15.6747i	1.09669	−	0.796790i
$388$	−9.76945	−	7.09792i	−0.495968	−	0.360342i
$389$	−15.6208	−	11.3492i	−0.792009	−	0.575428i	0.116550	−	0.993185i	$-0.462816\pi$
$389$	−15.6208	−	11.3492i	−0.792009	−	0.575428i	−0.908559	+	0.417757i	$0.862816\pi$
$390$	0.0902064	+	0.0655388i	0.00456778	+	0.00331869i
$391$	−0.0134791	−	0.00979311i	−0.000681665	−	0.000495259i
$392$	−1.11749	+	0.811904i	−0.0564417	+	0.0410073i
$393$	0.754874	+	2.32326i	0.0380784	+	0.117193i
$394$	15.2475	+	11.0779i	0.768156	+	0.558098i
$395$	−4.60121	+	14.1611i	−0.231512	+	0.712520i
$396$	3.98334			0.200170
$397$	−0.786377	+	0.571336i	−0.0394671	+	0.0286746i	−0.607344	−	0.794439i	$-0.707765\pi$
$397$	−0.786377	+	0.571336i	−0.0394671	+	0.0286746i	0.567877	+	0.823114i	$0.307765\pi$
$398$	10.1922	−	31.3684i	0.510890	−	1.57236i
$399$	−0.321788	−	0.990363i	−0.0161096	−	0.0495802i
$400$	−17.6730	−	54.3921i	−0.883652	−	2.71960i
$401$	3.52756			0.176158			0.0880790	−	0.996113i	$-0.471927\pi$
$401$	3.52756			0.176158			0.0880790	+	0.996113i	$0.471927\pi$
$402$	1.04489	+	3.21584i	0.0521144	+	0.160392i
$403$	0.148747	+	0.108071i	0.00740962	+	0.00538340i
$404$	−5.98929	+	4.35147i	−0.297978	+	0.216494i
$405$	10.6624	−	32.8154i	0.529817	−	1.63061i
$406$	0.221403	−	0.681409i	0.0109881	−	0.0338178i
$407$	10.2893			0.510021
$408$	−0.00859765	+	0.00624656i	−0.000425647	+	0.000309251i
$409$	4.29868			0.212556			0.106278	−	0.994336i	$-0.466107\pi$
$409$	4.29868			0.212556			0.106278	+	0.994336i	$0.466107\pi$
$410$	24.3646	−	40.0101i	1.20328	−	1.97596i
$411$	−5.41643			−0.267173
$412$	−0.421091	+	0.305941i	−0.0207457	+	0.0150726i
$413$	−3.58415			−0.176364
$414$	−0.854740	+	2.63062i	−0.0420082	+	0.129288i
$415$	12.8565	−	39.5682i	0.631100	−	1.94233i
$416$	0.312893	−	0.227330i	0.0153408	−	0.0111458i
$417$	−0.821810	−	0.597080i	−0.0402442	−	0.0292391i
$418$	−2.63314	−	8.10398i	−0.128791	−	0.396379i
$419$	25.7277			1.25688			0.628441	−	0.777857i	$-0.283693\pi$
$419$	25.7277			1.25688			0.628441	+	0.777857i	$0.283693\pi$
$420$	0.374114	+	1.15140i	0.0182549	+	0.0561827i
$421$	−8.96855	−	27.6024i	−0.437100	−	1.34526i	−0.890919	−	0.454163i	$-0.849939\pi$
$421$	−8.96855	−	27.6024i	−0.437100	−	1.34526i	0.453818	−	0.891094i	$-0.350061\pi$
$422$	2.45336	−	7.55067i	0.119428	−	0.367561i
$423$	−26.8142	+	19.4816i	−1.30375	+	0.947230i
$424$	−6.72316			−0.326506
$425$	−0.113810	+	0.350270i	−0.00552058	+	0.0169906i
$426$	−1.71734	−	1.24772i	−0.0832052	−	0.0604521i
$427$	−2.13532	−	6.57183i	−0.103335	−	0.318033i
$428$	−17.8801	+	12.9907i	−0.864268	+	0.627927i
$429$	0.0135564	+	0.00984931i	0.000654510	+	0.000475529i
$430$	53.6558	+	38.9832i	2.58751	+	1.87994i
$431$	−7.59178	−	5.51575i	−0.365683	−	0.265685i	0.389735	−	0.920927i	$-0.372566\pi$
$431$	−7.59178	−	5.51575i	−0.365683	−	0.265685i	−0.755419	+	0.655242i	$0.772566\pi$
$432$	5.74294	+	4.17249i	0.276307	+	0.200749i
$433$	−5.89875	+	4.28569i	−0.283476	+	0.205957i	−0.720432	−	0.693526i	$-0.756056\pi$
$433$	−5.89875	+	4.28569i	−0.283476	+	0.205957i	0.436956	+	0.899483i	$0.356056\pi$
$434$	1.61867	+	4.98175i	0.0776986	+	0.239132i
$435$	0.316952	+	0.230279i	0.0151967	+	0.0110410i
$436$	−3.66382	+	11.2761i	−0.175465	+	0.540027i
$437$	2.25504			0.107873
$438$	2.94281	−	2.13808i	0.140613	−	0.102161i
$439$	6.45026	−	19.8518i	0.307854	−	0.947477i	−0.670743	−	0.741690i	$-0.734025\pi$
$439$	6.45026	−	19.8518i	0.307854	−	0.947477i	0.978597	−	0.205787i	$-0.0659754\pi$
$440$	−1.90988	−	5.87801i	−0.0910500	−	0.280223i
$441$	−0.909023	−	2.79768i	−0.0432868	−	0.133223i
$442$	−0.00361317			−0.000171861
$443$	−1.97927	−	6.09156i	−0.0940378	−	0.289419i	0.892964	−	0.450128i	$-0.148622\pi$
$443$	−1.97927	−	6.09156i	−0.0940378	−	0.289419i	−0.987002	+	0.160710i	$0.948622\pi$
$444$	−2.25230	−	1.63639i	−0.106889	−	0.0776597i
$445$	−43.8540	+	31.8618i	−2.07888	+	1.51039i
$446$	−1.87716	+	5.77729i	−0.0888859	+	0.273563i
$447$	1.54247	−	4.74722i	0.0729562	−	0.224536i
$448$	1.12581			0.0531895
$449$	10.4391	−	7.58443i	0.492650	−	0.357932i	−0.313552	−	0.949571i	$-0.601519\pi$
$449$	10.4391	−	7.58443i	0.492650	−	0.357932i	0.806203	+	0.591639i	$0.201519\pi$
$450$	61.1430			2.88231
$451$	3.66156	−	6.01281i	0.172416	−	0.283132i
$452$	−10.0134			−0.470993
$453$	−0.0244953	+	0.0177969i	−0.00115089	+	0.000836171i
$454$	41.2452			1.93573
$455$	0.0793539	−	0.244226i	0.00372017	−	0.0114495i
$456$	0.444484	−	1.36798i	0.0208149	−	0.0640616i
$457$	−16.7888	+	12.1978i	−0.785348	+	0.570589i	−0.906579	−	0.422036i	$-0.861316\pi$
$457$	−16.7888	+	12.1978i	−0.785348	+	0.570589i	0.121231	+	0.992624i	$0.461316\pi$
$458$	−27.2418	−	19.7923i	−1.27292	−	0.924834i
$459$	−0.0141262	−	0.0434761i	−0.000659357	−	0.00202929i
$460$	−2.62172			−0.122238
$461$	−9.46625	−	29.1341i	−0.440887	−	1.35691i	−0.886932	−	0.461901i	$-0.847168\pi$
$461$	−9.46625	−	29.1341i	−0.440887	−	1.35691i	0.446044	−	0.895011i	$-0.352832\pi$
$462$	0.147521	+	0.454023i	0.00686330	+	0.0211231i
$463$	−6.23680	+	19.1949i	−0.289849	+	0.892063i	0.695055	+	0.718957i	$0.255380\pi$
$463$	−6.23680	+	19.1949i	−0.289849	+	0.892063i	−0.984903	+	0.173106i	$0.944620\pi$
$464$	1.59490	−	1.15876i	0.0740414	−	0.0537943i
$465$	−2.86424			−0.132826
$466$	−6.22312	+	19.1528i	−0.288281	+	0.887237i
$467$	31.2029	+	22.6702i	1.44390	+	1.04905i	0.987210	+	0.159427i	$0.0509645\pi$
$467$	31.2029	+	22.6702i	1.44390	+	1.04905i	0.456688	+	0.889627i	$0.349035\pi$
$468$	0.0706443	+	0.217421i	0.00326553	+	0.0100503i
$469$	6.30017	−	4.57734i	0.290915	−	0.211362i
$470$	−66.6872	−	48.4511i	−3.07605	−	2.23488i
$471$	−2.36945	−	1.72151i	−0.109179	−	0.0793230i
$472$	−4.00525	−	2.90998i	−0.184356	−	0.133943i
$473$	8.06350	+	5.85848i	0.370760	+	0.269373i
$474$	1.28523	−	0.933774i	0.0590326	−	0.0428897i
$475$	−15.4039	−	47.4083i	−0.706779	−	2.17524i
$476$	−0.0317386	−	0.0230594i	−0.00145473	−	0.00105693i
$477$	4.42448	−	13.6172i	0.202583	−	0.623487i
$478$	31.9864			1.46302
$479$	6.29935	−	4.57675i	0.287825	−	0.209117i	−0.434498	−	0.900673i	$-0.643074\pi$
$479$	6.29935	−	4.57675i	0.287825	−	0.209117i	0.722323	+	0.691556i	$0.243074\pi$
$480$	−1.86183	+	5.73011i	−0.0849804	+	0.261543i
$481$	0.182480	+	0.561616i	0.00832038	+	0.0256075i
$482$	1.54741	+	4.76244i	0.0704827	+	0.216923i
$483$	−0.126338			−0.00574856
$484$	−3.72645	−	11.4688i	−0.169384	−	0.521310i
$485$	−32.2815	−	23.4539i	−1.46583	−	1.06498i
$486$	−9.23979	+	6.71310i	−0.419126	+	0.304513i
$487$	−5.11573	+	15.7446i	−0.231816	+	0.713456i	0.765712	+	0.643184i	$0.222387\pi$
$487$	−5.11573	+	15.7446i	−0.231816	+	0.713456i	−0.997528	+	0.0702724i	$0.977613\pi$
$488$	2.94950	−	9.07762i	0.133518	−	0.410925i
$489$	2.65429			0.120031
$490$	5.91872	−	4.30021i	0.267381	−	0.194263i
$491$	−34.9163			−1.57575			−0.787875	−	0.615835i	$-0.788819\pi$
$491$	−34.9163			−1.57575			−0.787875	+	0.615835i	$0.788819\pi$
$492$	−1.75777	+	0.733860i	−0.0792466	+	0.0330849i
$493$	−0.0126953			−0.000571769
$494$	0.395638	−	0.287447i	0.0178006	−	0.0129329i
$495$	13.1623			0.591600
$496$	−4.45382	+	13.7074i	−0.199982	+	0.615483i
$497$	−1.51073	+	4.64954i	−0.0677654	+	0.208560i
$498$	−3.59113	+	2.60911i	−0.160922	+	0.116917i
$499$	14.6084	+	10.6136i	0.653960	+	0.475130i	0.864618	−	0.502430i	$-0.167561\pi$
$499$	14.6084	+	10.6136i	0.653960	+	0.475130i	−0.210658	+	0.977560i	$0.567561\pi$
$500$	10.1643	+	31.2824i	0.454559	+	1.39899i
$501$	6.10539			0.272769
$502$	12.8624	+	39.5863i	0.574075	+	1.76682i
$503$	5.26445	+	16.2023i	0.234730	+	0.722425i	0.997157	+	0.0753506i	$0.0240076\pi$
$503$	5.26445	+	16.2023i	0.234730	+	0.722425i	−0.762427	+	0.647074i	$0.775992\pi$
$504$	1.25563	−	3.86442i	0.0559301	−	0.172135i
$505$	−19.7906	+	14.3787i	−0.880669	+	0.639844i
$506$	−1.03380			−0.0459581
$507$	0.970011	−	2.98539i	0.0430797	−	0.132586i
$508$	−8.01364	−	5.82225i	−0.355548	−	0.258321i
$509$	−5.35225	−	16.4725i	−0.237234	−	0.730133i	−0.996817	−	0.0797219i	$-0.974597\pi$
$509$	−5.35225	−	16.4725i	−0.237234	−	0.730133i	0.759583	−	0.650411i	$-0.225403\pi$
$510$	0.0455370	−	0.0330846i	0.00201641	−	0.00146501i
$511$	−6.77748	−	4.92413i	−0.299818	−	0.217831i
$512$	13.4726	+	9.78844i	0.595412	+	0.432592i
$513$	5.00557	+	3.63676i	0.221001	+	0.160567i
$514$	−29.7006	−	21.5788i	−1.31004	−	0.951799i
$515$	−1.39142	+	1.01093i	−0.0613135	+	0.0445468i
$516$	−0.833358	−	2.56481i	−0.0366865	−	0.112910i
$517$	−10.0219	−	7.28133i	−0.440763	−	0.320233i
$518$	−5.19877	+	16.0002i	−0.228421	+	0.703007i
$519$	3.20671			0.140759
$520$	0.286965	−	0.208492i	0.0125843	−	0.00914300i
$521$	2.21338	−	6.81208i	0.0969699	−	0.298443i	−0.890792	−	0.454411i	$-0.849850\pi$
$521$	2.21338	−	6.81208i	0.0969699	−	0.298443i	0.987762	+	0.155968i	$0.0498498\pi$
$522$	0.651293	+	2.00447i	0.0285063	+	0.0877334i
$523$	−2.03734	−	6.27028i	−0.0890865	−	0.274180i	0.896581	−	0.442880i	$-0.146043\pi$
$523$	−2.03734	−	6.27028i	−0.0890865	−	0.274180i	−0.985667	+	0.168700i	$0.946043\pi$
$524$	−12.4562			−0.544152
$525$	0.862999	+	2.65604i	0.0376644	+	0.115919i
$526$	43.1784	+	31.3710i	1.88267	+	1.36784i
$527$	0.0750889	−	0.0545553i	0.00327092	−	0.00237646i
$528$	−0.405909	+	1.24926i	−0.0176649	+	0.0543671i
$529$	−7.02285	+	21.6141i	−0.305341	+	0.939744i
$530$	35.6089			1.54675
$531$	8.52974	−	6.19722i	0.370159	−	0.268936i
$532$	5.30984			0.230211
$533$	0.393132	+	0.0932207i	0.0170284	+	0.00403784i
$534$	5.78343			0.250274
$535$	−59.0818	+	42.9254i	−2.55433	+	1.85583i
$536$	10.7567			0.464620
$537$	−1.57666	+	4.85247i	−0.0680381	+	0.209400i
$538$	−5.64924	+	17.3866i	−0.243556	+	0.749589i
$539$	0.889479	−	0.646244i	0.0383126	−	0.0278357i
$540$	−5.81951	−	4.22812i	−0.250432	−	0.181949i
$541$	0.241550	+	0.743413i	0.0103850	+	0.0319618i	0.956115	−	0.292992i	$-0.0946511\pi$
$541$	0.241550	+	0.743413i	0.0103850	+	0.0319618i	−0.945730	+	0.324954i	$0.894651\pi$
$542$	−41.7418			−1.79296
$543$	1.58084	+	4.86533i	0.0678404	+	0.208791i
$544$	−0.0603320	−	0.185683i	−0.00258671	−	0.00796109i
$545$	−12.1065	+	37.2599i	−0.518585	+	1.59604i
$546$	−0.0221655	+	0.0161042i	−0.000948595	+	0.000689194i
$547$	−16.9129			−0.723143			−0.361571	−	0.932344i	$-0.617760\pi$
$547$	−16.9129			−0.723143			−0.361571	+	0.932344i	$0.617760\pi$
$548$	8.53471	−	26.2671i	0.364585	−	1.12208i
$549$	16.4449	+	11.9479i	0.701849	+	0.509923i
$550$	7.06178	+	21.7339i	0.301116	+	0.926738i
$551$	1.39012	−	1.00998i	0.0592212	−	0.0430267i
$552$	−0.141181	−	0.102574i	−0.00600906	−	0.00436584i
$553$	−2.95997	−	2.15054i	−0.125871	−	0.0914503i
$554$	32.6892	+	23.7501i	1.38883	+	1.00905i
$555$	−7.44234	−	5.40718i	−0.315910	−	0.229522i
$556$	4.19049	−	3.04457i	0.177716	−	0.129118i
$557$	−7.68517	−	23.6525i	−0.325631	−	1.00219i	−0.971155	−	0.238449i	$-0.923361\pi$
$557$	−7.68517	−	23.6525i	−0.325631	−	1.00219i	0.645524	−	0.763740i	$-0.276639\pi$
$558$	−12.4660	−	9.05705i	−0.527726	−	0.383415i
$559$	−0.176765	+	0.544027i	−0.00747636	+	0.0230099i
$560$	20.1301			0.850651
$561$	0.00684340	−	0.00497202i	0.000288929	−	0.000209919i
$562$	8.98871	−	27.6644i	0.379166	−	1.16695i
$563$	4.54119	+	13.9764i	0.191388	+	0.589033i	1.00000		0.000689856i	$0.000219588\pi$
$563$	4.54119	+	13.9764i	0.191388	+	0.589033i	−0.808611	+	0.588343i	$0.799780\pi$
$564$	1.03576	+	3.18773i	0.0436132	+	0.134228i
$565$	−33.0877			−1.39201
$566$	−9.37372	−	28.8494i	−0.394007	−	1.21263i
$567$	6.85912	+	4.98344i	0.288056	+	0.209285i
$568$	−5.46320	+	3.96925i	−0.229231	+	0.166546i
$569$	1.40559	−	4.32597i	0.0589255	−	0.181354i	−0.917261	−	0.398286i	$-0.869605\pi$
$569$	1.40559	−	4.32597i	0.0589255	−	0.181354i	0.976187	+	0.216932i	$0.0696051\pi$
$570$	−2.35419	+	7.24544i	−0.0986060	+	0.303478i
$571$	35.2700			1.47600			0.738001	−	0.674800i	$-0.235770\pi$
$571$	35.2700			1.47600			0.738001	+	0.674800i	$0.235770\pi$
$572$	−0.0691254	+	0.0502226i	−0.00289028	+	0.00209991i
$573$	−2.97567			−0.124310
$574$	7.50006	+	8.73187i	0.313046	+	0.364461i
$575$	−6.04774			−0.252208
$576$	−2.67926	+	1.94660i	−0.111636	+	0.0811082i
$577$	−30.9945			−1.29032			−0.645159	−	0.764048i	$-0.723209\pi$
$577$	−30.9945			−1.29032			−0.645159	+	0.764048i	$0.723209\pi$
$578$	9.44312	−	29.0629i	0.392782	−	1.20886i
$579$	1.45445	−	4.47633i	0.0604448	−	0.186030i
$580$	−1.61617	+	1.17421i	−0.0671077	+	0.0487566i
$581$	8.27060	+	6.00894i	0.343122	+	0.249293i
$582$	1.31556	+	4.04889i	0.0545318	+	0.167832i
$583$	5.35138			0.221631
$584$	−3.57585	−	11.0053i	−0.147970	−	0.455404i
$585$	0.233432	+	0.718430i	0.00965123	+	0.0297034i
$586$	−5.05500	+	15.5577i	−0.208820	+	0.642682i
$587$	2.32639	−	1.69022i	0.0960203	−	0.0697628i	−0.538739	−	0.842473i	$-0.681099\pi$
$587$	2.32639	−	1.69022i	0.0960203	−	0.0697628i	0.634759	+	0.772710i	$0.281099\pi$
$588$	−0.297482			−0.0122680
$589$	−3.88197	+	11.9475i	−0.159954	+	0.492287i
$590$	21.2136	+	15.4126i	0.873349	+	0.634525i
$591$	−0.782521	−	2.40835i	−0.0321886	−	0.0990664i
$592$	−37.4499	+	27.2089i	−1.53918	+	1.11828i
$593$	17.4733	+	12.6951i	0.717543	+	0.521325i	0.885598	−	0.464452i	$-0.153749\pi$
$593$	17.4733	+	12.6951i	0.717543	+	0.521325i	−0.168055	+	0.985778i	$0.553749\pi$
$594$	−2.29476	−	1.66724i	−0.0941551	−	0.0684077i
$595$	−0.104875	−	0.0761959i	−0.00429944	−	0.00312373i
$596$	20.5913	+	14.9605i	0.843453	+	0.612805i
$597$	−3.58524	+	2.60483i	−0.146734	+	0.106608i
$598$	−0.0183344	−	0.0564275i	−0.000749750	−	0.00230749i
$599$	−17.6902	−	12.8527i	−0.722804	−	0.525148i	0.164475	−	0.986381i	$-0.447407\pi$
$599$	−17.6902	−	12.8527i	−0.722804	−	0.525148i	−0.887279	+	0.461234i	$0.847407\pi$
$600$	−1.19205	+	3.66877i	−0.0486654	+	0.149777i
$601$	−22.9758			−0.937204			−0.468602	−	0.883409i	$-0.655242\pi$
$601$	−22.9758			−0.937204			−0.468602	+	0.883409i	$0.655242\pi$
$602$	−13.1843	+	9.57893i	−0.537351	+	0.390408i
$603$	−7.07895	+	21.7868i	−0.288277	+	0.887226i
$604$	−0.0477091	−	0.146833i	−0.00194125	−	0.00597457i
$605$	−12.3134	−	37.8968i	−0.500611	−	1.54072i
$606$	2.60996			0.106023
$607$	3.20521	+	9.86463i	0.130096	+	0.400393i	0.994795	−	0.101897i	$-0.0324911\pi$
$607$	3.20521	+	9.86463i	0.130096	+	0.400393i	−0.864699	+	0.502290i	$0.832491\pi$
$608$	21.3784	+	15.5323i	0.867007	+	0.629918i
$609$	−0.0778812	+	0.0565840i	−0.00315591	+	0.00229290i
$610$	−15.6219	+	48.0791i	−0.632511	+	1.94667i
$611$	0.219696	−	0.676155i	0.00888795	−	0.0273543i
$612$	0.115404			0.00466494
$613$	2.94621	−	2.14054i	0.118996	−	0.0864558i	−0.526695	−	0.850054i	$-0.676569\pi$
$613$	2.94621	−	2.14054i	0.118996	−	0.0864558i	0.645692	+	0.763598i	$0.276569\pi$
$614$	57.0328			2.30166
$615$	−5.80826	+	2.42491i	−0.234212	+	0.0977819i
$616$	1.51867			0.0611890
$617$	13.1768	−	9.57353i	0.530479	−	0.385416i	−0.290058	−	0.957009i	$-0.593675\pi$
$617$	13.1768	−	9.57353i	0.530479	−	0.385416i	0.820537	+	0.571593i	$0.193675\pi$
$618$	0.183500			0.00738144
$619$	10.3443	−	31.8365i	0.415772	−	1.27962i	−0.495786	−	0.868445i	$-0.665120\pi$
$619$	10.3443	−	31.8365i	0.415772	−	1.27962i	0.911558	−	0.411171i	$-0.134880\pi$
$620$	4.51320	−	13.8902i	0.181255	−	0.557844i
$621$	0.607293	−	0.441224i	0.0243698	−	0.0177057i
$622$	−14.6833	−	10.6680i	−0.588746	−	0.427749i
$623$	−4.11599	−	12.6677i	−0.164904	−	0.507521i
$624$	−0.0753866			−0.00301788
$625$	15.7213	+	48.3852i	0.628852	+	1.93541i
$626$	5.25887	+	16.1851i	0.210187	+	0.646888i
$627$	−0.353792	+	1.08886i	−0.0141291	+	0.0434849i
$628$	12.0821	−	8.77814i	0.482127	−	0.350286i
$629$	0.298099			0.0118860
$630$	−6.65036	+	20.4677i	−0.264957	+	0.815453i
$631$	16.7790	+	12.1906i	0.667961	+	0.485302i	0.869342	−	0.494211i	$-0.164543\pi$
$631$	16.7790	+	12.1906i	0.667961	+	0.485302i	−0.201381	+	0.979513i	$0.564543\pi$
$632$	−1.56170	−	4.80642i	−0.0621211	−	0.191189i
$633$	−0.863000	+	0.627006i	−0.0343012	+	0.0249213i
$634$	−14.0212	−	10.1870i	−0.556852	−	0.404577i
$635$	−26.4797	−	19.2386i	−1.05081	−	0.763462i
$636$	−1.17140	−	0.851074i	−0.0464491	−	0.0337473i
$637$	0.0510485	+	0.0370889i	0.00202262	+	0.00146952i
$638$	−0.637290	+	0.463018i	−0.0252305	+	0.0183311i
$639$	−4.44405	−	13.6774i	−0.175804	−	0.541068i
$640$	33.6975	+	24.4827i	1.33201	+	0.967763i
$641$	−3.01806	+	9.28864i	−0.119206	+	0.366879i	−0.992801	−	0.119775i	$-0.961783\pi$
$641$	−3.01806	+	9.28864i	−0.119206	+	0.366879i	0.873595	+	0.486654i	$0.161783\pi$
$642$	7.79165			0.307512
$643$	−15.1995	+	11.0431i	−0.599409	+	0.435496i	−0.845669	−	0.533708i	$-0.820798\pi$
$643$	−15.1995	+	11.0431i	−0.599409	+	0.435496i	0.246260	+	0.969204i	$0.420798\pi$
$644$	0.199071	−	0.612678i	0.00784451	−	0.0241429i
$645$	−2.75369	−	8.47498i	−0.108426	−	0.333702i
$646$	−0.0762868	−	0.234787i	−0.00300146	−	0.00923756i
$647$	−4.03262			−0.158539			−0.0792693	−	0.996853i	$-0.525259\pi$
$647$	−4.03262			−0.158539			−0.0792693	+	0.996853i	$0.525259\pi$
$648$	3.61892	+	11.1379i	0.142165	+	0.437538i
$649$	3.18802	+	2.31623i	0.125141	+	0.0909201i
$650$	−1.06105	+	0.770901i	−0.0416180	+	0.0302372i
$651$	0.217486	−	0.669353i	0.00852395	−	0.0262340i
$652$	−4.18239	+	12.8721i	−0.163795	+	0.504109i
$653$	43.7890			1.71360			0.856798	−	0.515653i	$-0.172451\pi$
$653$	43.7890			1.71360			0.856798	+	0.515653i	$0.172451\pi$
$654$	3.38164	−	2.45690i	0.132232	−	0.0960725i
$655$	−41.1594			−1.60823
$656$	2.57325	+	31.5674i	0.100469	+	1.23250i
$657$	24.6435			0.961436
$658$	16.3864	−	11.9054i	0.638807	−	0.464120i
$659$	11.4826			0.447299			0.223650	−	0.974670i	$-0.428203\pi$
$659$	11.4826			0.447299			0.223650	+	0.974670i	$0.428203\pi$
$660$	0.411321	−	1.26592i	0.0160107	−	0.0492757i
$661$	12.8321	−	39.4931i	0.499111	−	1.53610i	−0.311340	−	0.950298i	$-0.600778\pi$
$661$	12.8321	−	39.4931i	0.499111	−	1.53610i	0.810451	−	0.585806i	$-0.199222\pi$
$662$	−27.3241	+	19.8521i	−1.06198	+	0.771575i
$663$	0.000392753	0	0.000285352i	1.52533e−5	0	1.10821e-5i
$664$	4.36363	+	13.4299i	0.169342	+	0.521180i
$665$	17.5454			0.680383
$666$	−15.2930	−	47.0670i	−0.592592	−	1.82381i
$667$	−0.0644203	−	0.198265i	−0.00249436	−	0.00767686i
$668$	−9.62031	+	29.6083i	−0.372221	+	1.14558i
$669$	0.660312	−	0.479745i	0.0255291	−	0.0185480i
$670$	−56.9724			−2.20104
$671$	−2.34769	+	7.22544i	−0.0906314	+	0.278935i
$672$	−1.19772	−	0.870192i	−0.0462029	−	0.0335684i
$673$	2.07165	+	6.37588i	0.0798562	+	0.245772i	0.983012	−	0.183541i	$-0.0587559\pi$
$673$	2.07165	+	6.37588i	0.0798562	+	0.245772i	−0.903156	+	0.429313i	$0.858756\pi$
$674$	−30.2011	+	21.9424i	−1.16330	+	0.845189i
$675$	−13.4244	−	9.75336i	−0.516704	−	0.375407i
$676$	12.9493	+	9.40819i	0.498048	+	0.361853i
$677$	−14.7221	−	10.6962i	−0.565817	−	0.411090i	0.267766	−	0.963484i	$-0.413715\pi$
$677$	−14.7221	−	10.6962i	−0.565817	−	0.411090i	−0.833583	+	0.552394i	$0.813715\pi$
$678$	2.85600	+	2.07500i	0.109684	+	0.0796901i
$679$	7.93219	−	5.76307i	0.304409	−	0.221166i
$680$	−0.0553326	−	0.170296i	−0.00212191	−	0.00653056i
$681$	−4.48337	−	3.25736i	−0.171803	−	0.124822i
$682$	1.77965	−	5.47721i	0.0681465	−	0.209733i
$683$	15.4801			0.592330			0.296165	−	0.955137i	$-0.404292\pi$
$683$	15.4801			0.592330			0.296165	+	0.955137i	$0.404292\pi$
$684$	−12.6366	+	9.18105i	−0.483174	+	0.351046i
$685$	28.2015	−	86.7953i	1.07752	−	3.31628i
$686$	0.555511	+	1.70969i	0.0212095	+	0.0652761i
$687$	1.39809	+	4.30286i	0.0533403	+	0.164164i
$688$	−44.8408			−1.70954
$689$	0.0949064	+	0.292092i	0.00361565	+	0.0111278i
$690$	0.747758	+	0.543278i	0.0284667	+	0.0206822i
$691$	−33.8220	+	24.5731i	−1.28665	+	0.934804i	−0.999732	−	0.0231513i	$-0.992630\pi$
$691$	−33.8220	+	24.5731i	−1.28665	+	0.934804i	−0.286916	+	0.957956i	$0.592630\pi$
$692$	−5.05284	+	15.5510i	−0.192080	+	0.591161i
$693$	−0.999431	+	3.07593i	−0.0379652	+	0.116845i
$694$	41.4071			1.57179
$695$	13.8468	−	10.0603i	0.525237	−	0.381607i
$696$	−0.132972			−0.00504030
$697$	0.106082	−	0.174202i	0.00401814	−	0.00659836i
$698$	45.2864			1.71412
$699$	2.18906	−	1.59044i	0.0827978	−	0.0601561i
$700$	−14.2404			−0.538235
$701$	14.7406	−	45.3669i	0.556745	−	1.71348i	−0.134546	−	0.990907i	$-0.542958\pi$
$701$	14.7406	−	45.3669i	0.556745	−	1.71348i	0.691291	−	0.722577i	$-0.257042\pi$
$702$	0.0503048	−	0.154822i	0.00189863	−	0.00584339i
$703$	−32.6415	+	23.7154i	−1.23110	+	0.894444i
$704$	−1.00138	−	0.727547i	−0.0377410	−	0.0274205i
$705$	3.42248	+	10.5333i	0.128898	+	0.396707i
$706$	10.2656			0.386352
$707$	−1.85747	−	5.71672i	−0.0698575	−	0.214999i
$708$	−0.329480	−	1.01404i	−0.0123826	−	0.0381098i
$709$	−0.757765	+	2.33216i	−0.0284585	+	0.0875861i	−0.964277	−	0.264896i	$-0.914662\pi$
$709$	−0.757765	+	2.33216i	−0.0284585	+	0.0875861i	0.935818	+	0.352482i	$0.114662\pi$
$710$	28.9356	−	21.0229i	1.08593	−	0.788976i
$711$	10.7627			0.403633
$712$	5.68538	−	17.4978i	0.213069	−	0.655758i
$713$	1.23303	+	0.895845i	0.0461772	+	0.0335497i
$714$	0.00427395	+	0.0131539i	0.000159948	+	0.000492271i
$715$	−0.228413	+	0.165952i	−0.00854217	+	0.00620625i
$716$	−21.0478	−	15.2922i	−0.786595	−	0.571495i
$717$	−3.47693	−	2.52614i	−0.129848	−	0.0943404i
$718$	−22.6491	−	16.4555i	−0.845256	−	0.614114i
$719$	−8.02040	−	5.82716i	−0.299111	−	0.217317i	0.428099	−	0.903732i	$-0.359183\pi$
$719$	−8.02040	−	5.82716i	−0.299111	−	0.217317i	−0.727210	+	0.686415i	$0.759183\pi$
$720$	−47.9066	+	34.8062i	−1.78537	+	1.29715i
$721$	−0.130594	−	0.401928i	−0.00486358	−	0.0149686i
$722$	−0.600699	−	0.436434i	−0.0223557	−	0.0162424i
$723$	0.207912	−	0.639887i	0.00773233	−	0.0237977i
$724$	−26.0855			−0.969460
$725$	−3.72815	+	2.70866i	−0.138460	+	0.100597i
$726$	−1.31375	+	4.04330i	−0.0487578	+	0.150061i
$727$	−2.61414	−	8.04549i	−0.0969530	−	0.298391i	0.890805	−	0.454386i	$-0.150141\pi$
$727$	−2.61414	−	8.04549i	−0.0969530	−	0.298391i	−0.987758	+	0.155996i	$0.950141\pi$
$728$	0.0269336	+	0.0828929i	0.000998224	+	0.00307222i
$729$	−23.9005			−0.885203
$730$	18.9393	+	58.2891i	0.700974	+	2.15738i
$731$	0.233614	+	0.169730i	0.00864052	+	0.00627771i
$732$	1.66302	−	1.20826i	0.0614671	−	0.0446585i
$733$	−9.74287	+	29.9855i	−0.359861	+	1.10754i	0.593276	+	0.804999i	$0.297834\pi$
$733$	−9.74287	+	29.9855i	−0.359861	+	1.10754i	−0.953137	+	0.302539i	$0.902166\pi$
$734$	6.86772	−	21.1367i	0.253492	−	0.780168i
$735$	−0.982979			−0.0362577
$736$	2.59370	−	1.88443i	0.0956050	−	0.0694611i
$737$	−8.56194			−0.315383
$738$	−32.9470	−	7.81249i	−1.21280	−	0.287582i
$739$	13.5580			0.498740			0.249370	−	0.968408i	$-0.419776\pi$
$739$	13.5580			0.498740			0.249370	+	0.968408i	$0.419776\pi$
$740$	37.9492	−	27.5717i	1.39504	−	1.01356i
$741$	−0.0657073			−0.00241382
$742$	−2.70384	+	8.32155i	−0.0992609	+	0.305494i
$743$	10.9122	−	33.5843i	0.400330	−	1.23209i	−0.524402	−	0.851471i	$-0.675711\pi$
$743$	10.9122	−	33.5843i	0.400330	−	1.23209i	0.924732	−	0.380619i	$-0.124289\pi$
$744$	0.786489	−	0.571418i	0.0288341	−	0.0209492i
$745$	68.0405	+	49.4343i	2.49281	+	1.81113i
$746$	−4.04676	−	12.4547i	−0.148163	−	0.455997i
$747$	−30.0727			−1.10030
$748$	0.0133288	+	0.0410217i	0.000487348	+	0.00149990i
$749$	−5.54521	−	17.0664i	−0.202618	−	0.623593i
$750$	3.58338	−	11.0285i	0.130846	−	0.402704i
$751$	11.4445	−	8.31489i	0.417615	−	0.303415i	−0.359063	−	0.933313i	$-0.616904\pi$
$751$	11.4445	−	8.31489i	0.417615	−	0.303415i	0.776677	+	0.629899i	$0.216904\pi$
$752$	55.7313			2.03231
$753$	1.72820	−	5.31885i	0.0629791	−	0.193830i
$754$	−0.0365750	−	0.0265733i	−0.00133198	−	0.000967743i
$755$	−0.157646	−	0.485186i	−0.00573734	−	0.0176577i
$756$	1.42997	−	1.03893i	0.0520074	−	0.0377856i
$757$	2.89408	+	2.10267i	0.105187	+	0.0764230i	0.639135	−	0.769094i	$-0.279292\pi$
$757$	2.89408	+	2.10267i	0.105187	+	0.0764230i	−0.533948	+	0.845517i	$0.679292\pi$
$758$	15.3803	+	11.1745i	0.558639	+	0.405875i
$759$	0.112375	+	0.0816450i	0.00407894	+	0.00296352i
$760$	19.6069	+	14.2452i	0.711215	+	0.516728i
$761$	14.3418	−	10.4199i	0.519889	−	0.377722i	−0.296673	−	0.954979i	$-0.595877\pi$
$761$	14.3418	−	10.4199i	0.519889	−	0.377722i	0.816562	+	0.577257i	$0.195877\pi$
$762$	1.07912	+	3.32120i	0.0390925	+	0.120314i
$763$	−7.78813	−	5.65840i	−0.281949	−	0.204848i
$764$	4.68878	−	14.4306i	0.169634	−	0.522080i
$765$	0.381334			0.0137872
$766$	48.3004	−	35.0923i	1.74517	−	1.26794i
$767$	−0.0698866	+	0.215089i	−0.00252346	+	0.00776640i
$768$	−1.54133	−	4.74373i	−0.0556180	−	0.171175i
$769$	4.24172	+	13.0547i	0.152960	+	0.470764i	0.997949	−	0.0640214i	$-0.0203926\pi$
$769$	4.24172	+	13.0547i	0.152960	+	0.470764i	−0.844988	+	0.534785i	$0.820393\pi$
$770$	−8.04356			−0.289870
$771$	1.52428	+	4.69125i	0.0548955	+	0.168951i
$772$	19.4163	+	14.1068i	0.698808	+	0.507714i
$773$	29.3245	−	21.3055i	1.05473	−	0.766306i	0.0816234	−	0.996663i	$-0.473990\pi$
$773$	29.3245	−	21.3055i	1.05473	−	0.766306i	0.973106	+	0.230357i	$0.0739895\pi$
$774$	14.8140	−	45.5929i	0.532479	−	1.63880i
$775$	10.4110	−	32.0417i	0.373974	−	1.15097i
$776$	13.5432			0.486172
$777$	1.82873	−	1.32865i	0.0656053	−	0.0476650i
$778$	−34.7102			−1.24442
$779$	2.24286	+	27.5143i	0.0803587	+	0.985801i
$780$	0.0763918			0.00273526
$781$	4.34850	−	3.15937i	0.155601	−	0.113051i
$782$	−0.0299511			−0.00107105
$783$	0.176752	−	0.543988i	0.00631661	−	0.0194405i
$784$	−1.52851	+	4.70426i	−0.0545895	+	0.168009i
$785$	39.9232	−	29.0059i	1.42492	−	1.03526i
$786$	3.55271	+	2.58120i	0.126721	+	0.0920683i
$787$	0.00886218	+	0.0272750i	0.000315903	+	0.000972248i	0.951214	−	0.308531i	$-0.0998373\pi$
$787$	0.00886218	+	0.0272750i	0.000315903	+	0.000972248i	−0.950898	+	0.309503i	$0.899837\pi$
$788$	12.9124			0.459985
$789$	−2.21598	−	6.82007i	−0.0788908	−	0.242801i
$790$	8.27146	+	25.4569i	0.294285	+	0.905717i
$791$	2.51240	−	7.73237i	0.0893306	−	0.274931i
$792$	−3.61421	+	2.62588i	−0.128425	+	0.0933066i
$793$	−0.436019			−0.0154835
$794$	−0.539965	+	1.66184i	−0.0191626	+	0.0589766i
$795$	−3.87070	−	2.81223i	−0.137280	−	0.0997394i
$796$	−6.98290	−	21.4911i	−0.247502	−	0.761733i
$797$	−32.2460	+	23.4281i	−1.14221	+	0.829864i	−0.987426	−	0.158084i	$-0.949468\pi$
$797$	−32.2460	+	23.4281i	−1.14221	+	0.829864i	−0.154785	+	0.987948i	$0.549468\pi$
$798$	−1.51445	−	1.10031i	−0.0536111	−	0.0389507i
$799$	−0.290352	−	0.210953i	−0.0102719	−	0.00746298i
$800$	−57.3343	−	41.6558i	−2.02707	−	1.47276i
$801$	31.6987	+	23.0305i	1.12002	+	0.813741i
$802$	5.13029	−	3.72738i	0.181157	−	0.131618i
$803$	2.84624	+	8.75981i	0.100441	+	0.309127i
$804$	1.87419	+	1.36168i	0.0660975	+	0.0480226i
$805$	0.657797	−	2.02449i	0.0231843	−	0.0713539i
$806$	0.330522			0.0116422
$807$	1.98719	−	1.44378i	0.0699524	−	0.0508234i
$808$	2.56572	−	7.89646i	0.0902616	−	0.277797i
$809$	−8.29548	−	25.5308i	−0.291653	−	0.897617i	−0.984325	−	0.176364i	$-0.943566\pi$
$809$	−8.29548	−	25.5308i	−0.291653	−	0.897617i	0.692672	−	0.721253i	$-0.256434\pi$
$810$	−19.1674	−	58.9913i	−0.673475	−	2.07274i
$811$	10.5124			0.369140			0.184570	−	0.982819i	$-0.440911\pi$
$811$	10.5124			0.369140			0.184570	+	0.982819i	$0.440911\pi$
$812$	−0.151688	−	0.466847i	−0.00532320	−	0.0163831i
$813$	4.53735	+	3.29658i	0.159132	+	0.115616i
$814$	14.9642	−	10.8721i	0.524495	−	0.381068i
$815$	−13.8200	+	42.5335i	−0.484093	+	1.48988i
$816$	−0.0117599	+	0.0361933i	−0.000411679	+	0.00126702i
$817$	−39.0834			−1.36736
$818$	6.25177	−	4.54218i	0.218588	−	0.158813i
$819$	−0.185617			−0.00648598
$820$	−2.60756	−	31.9883i	−0.0910601	−	1.11708i
$821$	−33.6187			−1.17330			−0.586651	−	0.809840i	$-0.699554\pi$
$821$	−33.6187			−1.17330			−0.586651	+	0.809840i	$0.699554\pi$
$822$	−7.87737	+	5.72324i	−0.274755	+	0.199621i
$823$	36.0307			1.25595			0.627975	−	0.778233i	$-0.283884\pi$
$823$	36.0307			1.25595			0.627975	+	0.778233i	$0.283884\pi$
$824$	0.180389	−	0.555180i	0.00628414	−	0.0193406i
$825$	0.948829	−	2.92020i	0.0330340	−	0.101668i
$826$	−5.21259	+	3.78717i	−0.181369	+	0.131772i
$827$	−30.7164	−	22.3168i	−1.06812	−	0.776031i	−0.0925426	−	0.995709i	$-0.529499\pi$
$827$	−30.7164	−	22.3168i	−1.06812	−	0.776031i	−0.975572	+	0.219678i	$0.929499\pi$
$828$	0.585600	+	1.80229i	0.0203510	+	0.0626339i
$829$	−10.5044			−0.364833			−0.182417	−	0.983221i	$-0.558392\pi$
$829$	−10.5044			−0.364833			−0.182417	+	0.983221i	$0.558392\pi$
$830$	−23.1117	−	71.1305i	−0.802219	−	2.46898i
$831$	−1.67766	−	5.16330i	−0.0581973	−	0.179113i
$832$	0.0219519	−	0.0675610i	0.000761046	−	0.00234226i
$833$	0.0257698	−	0.0187228i	0.000892869	−	0.000648707i
$834$	−1.82610			−0.0632326
$835$	−31.7887	+	97.8354i	−1.10009	+	3.38573i
$836$	−4.72299	−	3.43145i	−0.163348	−	0.118679i
$837$	1.29223	+	3.97707i	0.0446659	+	0.137468i
$838$	37.4170	−	27.1851i	1.29255	−	0.939093i
$839$	38.8588	+	28.2326i	1.34156	+	0.974698i	0.999385	+	0.0350600i	$0.0111622\pi$
$839$	38.8588	+	28.2326i	1.34156	+	0.974698i	0.342171	+	0.939638i	$0.388838\pi$
$840$	−1.09847	−	0.798084i	−0.0379008	−	0.0275365i
$841$	23.3330	+	16.9524i	0.804586	+	0.584566i
$842$	−42.2093	−	30.6668i	−1.45463	−	1.05685i
$843$	−3.16189	+	2.29724i	−0.108901	+	0.0791213i
$844$	−1.68085	−	5.17312i	−0.0578572	−	0.178066i
$845$	42.7886	+	31.0877i	1.47197	+	1.06945i
$846$	−18.4119	+	56.6661i	−0.633015	+	1.94822i
$847$	9.79120			0.336430
$848$	−19.4774	+	14.1511i	−0.668856	+	0.485952i
$849$	−1.25946	+	3.87623i	−0.0432247	+	0.133032i
$850$	0.204592	+	0.629671i	0.00701746	+	0.0215975i
$851$	1.51265	+	4.65547i	0.0518531	+	0.159587i
$852$	−1.45433			−0.0498247
$853$	−1.50843	−	4.64246i	−0.0516475	−	0.158955i	0.921906	−	0.387413i	$-0.126631\pi$
$853$	−1.50843	−	4.64246i	−0.0516475	−	0.158955i	−0.973554	+	0.228459i	$0.926631\pi$
$854$	−10.0496	−	7.30145i	−0.343889	−	0.249850i
$855$	−41.7556	+	30.3372i	−1.42801	+	1.03751i
$856$	7.65956	−	23.5737i	0.261798	−	0.805733i
$857$	6.52431	−	20.0798i	0.222866	−	0.685911i	−0.775635	−	0.631182i	$-0.782570\pi$
$857$	6.52431	−	20.0798i	0.222866	−	0.685911i	0.998501	−	0.0547297i	$-0.0174297\pi$
$858$	0.0301229			0.00102838
$859$	−43.0261	+	31.2603i	−1.46803	+	1.06659i	−0.486854	+	0.873483i	$0.661856\pi$
$859$	−43.0261	+	31.2603i	−1.46803	+	1.06659i	−0.981178	+	0.193104i	$0.938144\pi$
$860$	45.4387			1.54945
$861$	−0.125655	−	1.54148i	−0.00428233	−	0.0525335i
$862$	−16.8693			−0.574570
$863$	18.8412	−	13.6890i	0.641363	−	0.465977i	−0.218955	−	0.975735i	$-0.570265\pi$
$863$	18.8412	−	13.6890i	0.641363	−	0.465977i	0.860318	+	0.509757i	$0.170265\pi$
$864$	8.79639			0.299259
$865$	−16.6962	+	51.3857i	−0.567689	+	1.74717i
$866$	−4.05037	+	12.4658i	−0.137637	+	0.423604i
$867$	−3.32173	+	2.41338i	−0.112812	+	0.0819626i
$868$	2.90335	+	2.10941i	0.0985462	+	0.0715980i
$869$	1.24305	+	3.82572i	0.0421677	+	0.129779i
$870$	0.704280			0.0238773
$871$	−0.151846	−	0.467333i	−0.00514509	−	0.0158350i
$872$	−4.10907	−	12.6464i	−0.139151	−	0.428262i
$873$	−8.91272	+	27.4305i	−0.301650	+	0.928383i
$874$	3.27960	−	2.38277i	0.110934	−	0.0805984i
$875$	−26.7064			−0.902843
$876$	0.770112	−	2.37016i	0.0260197	−	0.0800803i
$877$	−25.1234	−	18.2532i	−0.848358	−	0.616368i	0.0763350	−	0.997082i	$-0.475678\pi$
$877$	−25.1234	−	18.2532i	−0.848358	−	0.616368i	−0.924693	+	0.380714i	$0.875678\pi$
$878$	−11.5954	−	35.6871i	−0.391327	−	1.20438i
$879$	1.77815	−	1.29191i	0.0599757	−	0.0435749i
$880$	−17.9053	−	13.0089i	−0.603586	−	0.438531i
$881$	−7.71344	−	5.60414i	−0.259872	−	0.188808i	0.450218	−	0.892918i	$-0.351346\pi$
$881$	−7.71344	−	5.60414i	−0.259872	−	0.188808i	−0.710091	+	0.704110i	$0.751346\pi$
$882$	−4.27819	−	3.10829i	−0.144054	−	0.104662i
$883$	2.64031	+	1.91830i	0.0888536	+	0.0645559i	0.631325	−	0.775518i	$-0.282511\pi$
$883$	2.64031	+	1.91830i	0.0888536	+	0.0645559i	−0.542472	+	0.840074i	$0.682511\pi$
$884$	−0.00200269	+	0.00145504i	−6.73576e−5	+	4.89382e-5i
$885$	−1.08871	−	3.35071i	−0.0365966	−	0.112633i
$886$	−9.31515	−	6.76785i	−0.312948	−	0.227370i
$887$	−12.2388	+	37.6673i	−0.410940	+	1.26474i	0.504892	+	0.863183i	$0.331532\pi$
$887$	−12.2388	+	37.6673i	−0.410940	+	1.26474i	−0.915832	+	0.401561i	$0.868468\pi$
$888$	3.12232			0.104778
$889$	6.50658	−	4.72731i	0.218224	−	0.158549i
$890$	−30.1123	+	92.6762i	−1.00937	+	3.10651i
$891$	−2.88052	−	8.86533i	−0.0965011	−	0.297000i
$892$	1.28608	+	3.95814i	0.0430610	+	0.132528i
$893$	48.5757			1.62552
$894$	−2.77285	−	8.53394i	−0.0927379	−	0.285418i
$895$	−69.5490	−	50.5303i	−2.32477	−	1.68904i
$896$	−8.28014	+	6.01588i	−0.276620	+	0.200976i
$897$	−0.00246343	+	0.00758167i	−8.22516e−5	+	0.000253144i
$898$	7.16798	−	22.0608i	0.239199	−	0.736178i
$899$	1.16133			0.0387326
$900$	33.8900	−	24.6225i	1.12967	−	0.820750i
$901$	0.155039			0.00516509
$902$	−1.02822	−	12.6137i	−0.0342359	−	0.419990i
$903$	2.18964			0.0728666
$904$	9.08552	−	6.60102i	0.302180	−	0.219547i
$905$	−86.1951			−2.86522
$906$	−0.0168197	+	0.0517657i	−0.000558797	+	0.00171980i
$907$	−11.3237	+	34.8507i	−0.375997	+	1.15720i	0.566807	+	0.823851i	$0.308179\pi$
$907$	−11.3237	+	34.8507i	−0.375997	+	1.15720i	−0.942804	+	0.333348i	$0.891821\pi$
$908$	22.8611	−	16.6096i	0.758673	−	0.551208i
$909$	14.3051	+	10.3933i	0.474470	+	0.344723i
$910$	−0.142652	−	0.439038i	−0.00472887	−	0.0145540i
$911$	−14.9190			−0.494288			−0.247144	−	0.968979i	$-0.579492\pi$
$911$	−14.9190			−0.494288			−0.247144	+	0.968979i	$0.579492\pi$
$912$	−1.59168	−	4.89868i	−0.0527057	−	0.162212i
$913$	−3.47328	−	10.6896i	−0.114949	−	0.353776i
$914$	−11.5280	+	35.4796i	−0.381313	+	1.17356i
$915$	5.49518	−	3.99248i	0.181665	−	0.131987i
$916$	−23.0698			−0.762249
$917$	3.12529	−	9.61867i	0.103206	−	0.317636i
$918$	−0.0664832	−	0.0483029i	−0.00219427	−	0.00159423i
$919$	−0.318812	−	0.981202i	−0.0105166	−	0.0323669i	0.945660	−	0.325156i	$-0.105417\pi$
$919$	−0.318812	−	0.981202i	−0.0105166	−	0.0323669i	−0.956177	+	0.292789i	$0.905417\pi$
$920$	2.37877	−	1.72828i	0.0784258	−	0.0569797i
$921$	−6.19949	−	4.50419i	−0.204280	−	0.148418i
$922$	−44.5516	−	32.3687i	−1.46723	−	1.06600i
$923$	0.249567	+	0.181321i	0.00821459	+	0.00596825i
$924$	0.264604	+	0.192246i	0.00870483	+	0.00632443i
$925$	87.5406	−	63.6020i	2.87832	−	2.09122i
$926$	11.2117	+	34.5061i	0.368440	+	1.13394i
$927$	1.00575	+	0.730723i	0.0330333	+	0.0240001i
$928$	0.754895	−	2.32333i	0.0247806	−	0.0762669i
$929$	14.9325			0.489918			0.244959	−	0.969533i	$-0.421225\pi$
$929$	14.9325			0.489918			0.244959	+	0.969533i	$0.421225\pi$
$930$	−4.16560	+	3.02648i	−0.136595	+	0.0992423i
$931$	−1.33225	+	4.10025i	−0.0436628	+	0.134380i
$932$	4.26359	+	13.1220i	0.139658	+	0.429825i
$933$	0.753567	+	2.31924i	0.0246707	+	0.0759285i
$934$	69.3342			2.26868
$935$	0.0440426	+	0.135549i	0.00144035	+	0.00443293i
$936$	−0.207425	−	0.150703i	−0.00677990	−	0.00492589i
$937$	10.1572	−	7.37964i	0.331821	−	0.241082i	−0.409382	−	0.912363i	$-0.634256\pi$
$937$	10.1572	−	7.37964i	0.331821	−	0.241082i	0.741203	+	0.671281i	$0.234256\pi$
$938$	4.32600	−	13.3141i	0.141249	−	0.434720i
$939$	0.706588	−	2.17465i	0.0230586	−	0.0709671i
$940$	−56.4744			−1.84199
$941$	−38.5624	+	28.0172i	−1.25710	+	0.913336i	−0.998612	−	0.0526789i	$-0.983224\pi$
$941$	−38.5624	+	28.0172i	−1.25710	+	0.913336i	−0.258487	+	0.966015i	$0.583224\pi$
$942$	−5.26503			−0.171544
$943$	3.25884	+	0.772745i	0.106122	+	0.0251640i
$944$	−17.7285			−0.577012
$945$	4.72508	−	3.43297i	0.153707	−	0.111675i
$946$	17.9175			0.582547
$947$	−7.38001	+	22.7133i	−0.239818	+	0.738084i	0.756628	+	0.653846i	$0.226846\pi$
$947$	−7.38001	+	22.7133i	−0.239818	+	0.738084i	−0.996446	+	0.0842379i	$0.973154\pi$
$948$	0.336335	−	1.03513i	0.0109237	−	0.0336196i
$949$	−0.427655	+	0.310710i	−0.0138823	+	0.0100861i
$950$	−72.4964	−	52.6717i	−2.35209	−	1.70890i
$951$	0.719586	+	2.21466i	0.0233342	+	0.0718152i
$952$	0.0439986			0.00142600
$953$	2.35497	+	7.24784i	0.0762848	+	0.234781i	0.981926	−	0.189264i	$-0.0606101\pi$
$953$	2.35497	+	7.24784i	0.0762848	+	0.234781i	−0.905641	+	0.424044i	$0.860610\pi$
$954$	−7.95376	−	24.4792i	−0.257513	−	0.792542i
$955$	15.4933	−	47.6834i	0.501350	−	1.54300i
$956$	17.7292	−	12.8810i	0.573404	−	0.416602i
$957$	0.105841			0.00342135
$958$	4.32544	−	13.3124i	0.139749	−	0.430103i
$959$	18.1421	+	13.1810i	0.585838	+	0.425637i
$960$	0.341972	+	1.05248i	0.0110371	+	0.0339687i
$961$	18.2106	−	13.2308i	0.587439	−	0.426799i
$962$	0.858818	+	0.623968i	0.0276894	+	0.0201175i
$963$	42.7057	+	31.0275i	1.37617	+	0.999847i
$964$	2.77554	+	2.01655i	0.0893942	+	0.0649487i
$965$	64.1579	+	46.6134i	2.06532	+	1.50054i
$966$	−0.183739	+	0.133494i	−0.00591170	+	0.00429510i
$967$	13.5123	+	41.5865i	0.434525	+	1.33733i	0.893573	+	0.448919i	$0.148191\pi$
$967$	13.5123	+	41.5865i	0.434525	+	1.33733i	−0.459048	+	0.888412i	$0.651809\pi$
$968$	10.9416	+	7.94951i	0.351675	+	0.255507i
$969$	−0.0102500	+	0.0315462i	−0.000329277	+	0.00101341i
$970$	−71.7308			−2.30314
$971$	16.7219	−	12.1491i	0.536630	−	0.389885i	−0.286202	−	0.958169i	$-0.592393\pi$
$971$	16.7219	−	12.1491i	0.536630	−	0.389885i	0.822832	+	0.568285i	$0.192393\pi$
$972$	−2.41799	+	7.44180i	−0.0775569	+	0.238696i
$973$	1.29961	+	3.99978i	0.0416635	+	0.128227i
$974$	9.19640	+	28.3036i	0.294672	+	0.906906i
$975$	0.176219			0.00564353
$976$	−10.5620	−	32.5066i	−0.338082	−	1.04051i
$977$	32.9395	+	23.9320i	1.05383	+	0.765652i	0.972937	−	0.231071i	$-0.0742231\pi$
$977$	32.9395	+	23.9320i	1.05383	+	0.765652i	0.0808922	+	0.996723i	$0.474223\pi$
$978$	3.86026	−	2.80464i	0.123437	−	0.0896826i
$979$	−4.52535	+	13.9276i	−0.144631	+	0.445127i
$980$	1.54889	−	4.76698i	0.0494774	−	0.152276i
$981$	28.3183			0.904135
$982$	−50.7804	+	36.8941i	−1.62047	+	1.17734i
$983$	−19.6728			−0.627466			−0.313733	−	0.949511i	$-0.601580\pi$
$983$	−19.6728			−0.627466			−0.313733	+	0.949511i	$0.601580\pi$
$984$	1.11111	−	1.82461i	0.0354210	−	0.0581663i
$985$	42.6668			1.35948
$986$	−0.0184634	+	0.0134144i	−0.000587995	+	0.000427203i
$987$	−2.72144			−0.0866243
$988$	0.103535	−	0.318649i	0.00329390	−	0.0101376i
$989$	−1.46528	+	4.50966i	−0.0465931	+	0.143399i
$990$	19.1425	−	13.9078i	0.608388	−	0.442020i
$991$	14.9865	+	10.8883i	0.476061	+	0.345879i	0.799799	−	0.600268i	$-0.204939\pi$
$991$	14.9865	+	10.8883i	0.476061	+	0.345879i	−0.323737	+	0.946147i	$0.604939\pi$
$992$	5.51900	+	16.9857i	0.175228	+	0.539298i
$993$	4.53797			0.144008
$994$	2.71579	+	8.35834i	0.0861396	+	0.265111i
$995$	−23.0738	−	71.0138i	−0.731488	−	2.25129i
$996$	−0.939772	+	2.89232i	−0.0297778	+	0.0916467i
$997$	27.1897	−	19.7545i	0.861108	−	0.625631i	−0.0670784	−	0.997748i	$-0.521368\pi$
$997$	27.1897	−	19.7545i	0.861108	−	0.625631i	0.928186	+	0.372116i	$0.121368\pi$
$998$	32.4604			1.02752
$999$	−4.15032	+	12.7734i	−0.131310	+	0.404132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.d.78.8	✓	40
41.10	even	5	inner	287.2.h.d.92.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.d.78.8	✓	40	1.1	even	1	trivial
287.2.h.d.92.8	yes	40	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45435 - 1.05664i) q^{2} -0.241537 q^{3} +(0.380592 - 1.17134i) q^{4} +(1.25760 - 3.87050i) q^{5} +(-0.351279 + 0.255219i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.426843 + 1.31369i) q^{8} -2.94166 q^{9} +O(q^{10})\)	\(q+(1.45435 - 1.05664i) q^{2} -0.241537 q^{3} +(0.380592 - 1.17134i) q^{4} +(1.25760 - 3.87050i) q^{5} +(-0.351279 + 0.255219i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.426843 + 1.31369i) q^{8} -2.94166 q^{9} +(-2.26075 - 6.95788i) q^{10} +(-0.339751 - 1.04564i) q^{11} +(-0.0919270 + 0.282922i) q^{12} +(0.0510485 - 0.0370889i) q^{13} +1.79767 q^{14} +(-0.303757 + 0.934868i) q^{15} +(4.00168 + 2.90739i) q^{16} +(-0.00984317 - 0.0302942i) q^{17} +(-4.27819 + 3.10829i) q^{18} +(3.48788 + 2.53410i) q^{19} +(-4.05504 - 2.94616i) q^{20} +(-0.195408 - 0.141972i) q^{21} +(-1.59899 - 1.16173i) q^{22} +(0.423162 - 0.307445i) q^{23} +(-0.103098 - 0.317304i) q^{24} +(-9.35409 - 6.79615i) q^{25} +(0.0350524 - 0.107880i) q^{26} +1.43513 q^{27} +(0.996402 - 0.723929i) q^{28} +(0.123161 - 0.379051i) q^{29} +(0.546055 + 1.68059i) q^{30} +(0.900425 + 2.77122i) q^{31} +6.12933 q^{32} +(0.0820624 + 0.252562i) q^{33} +(-0.0463255 - 0.0336575i) q^{34} +(3.29244 - 2.39210i) q^{35} +(-1.11957 + 3.44569i) q^{36} +(-2.89195 + 8.90049i) q^{37} +7.75023 q^{38} +(-0.0123301 + 0.00895835i) q^{39} +5.62142 q^{40} +(4.17210 + 4.85733i) q^{41} -0.434204 q^{42} +(-7.33409 + 5.32852i) q^{43} -1.35411 q^{44} +(-3.69943 + 11.3857i) q^{45} +(0.290564 - 0.894264i) q^{46} +(9.11532 - 6.62267i) q^{47} +(-0.966555 - 0.702243i) q^{48} +(0.309017 + 0.951057i) q^{49} -20.7852 q^{50} +(0.00237749 + 0.00731717i) q^{51} +(-0.0240151 - 0.0739109i) q^{52} +(-1.50408 + 4.62907i) q^{53} +(2.08718 - 1.51642i) q^{54} -4.47443 q^{55} +(-0.426843 + 1.31369i) q^{56} +(-0.842453 - 0.612078i) q^{57} +(-0.221403 - 0.681409i) q^{58} +(-2.89964 + 2.10671i) q^{59} +(0.979442 + 0.711606i) q^{60} +(-5.59033 - 4.06161i) q^{61} +(4.23773 + 3.07889i) q^{62} +(-2.37985 - 1.72906i) q^{63} +(0.910798 - 0.661734i) q^{64} +(-0.0793539 - 0.244226i) q^{65} +(0.386215 + 0.280602i) q^{66} +(2.40645 - 7.40629i) q^{67} -0.0392310 q^{68} +(-0.102209 + 0.0742594i) q^{69} +(2.26075 - 6.95788i) q^{70} +(1.51073 + 4.64954i) q^{71} +(-1.25563 - 3.86442i) q^{72} -8.37743 q^{73} +(5.19877 + 16.0002i) q^{74} +(2.25936 + 1.64152i) q^{75} +(4.29575 - 3.12104i) q^{76} +(0.339751 - 1.04564i) q^{77} +(-0.00846646 + 0.0260571i) q^{78} -3.65872 q^{79} +(16.2856 - 11.8322i) q^{80} +8.47834 q^{81} +(11.2001 + 2.65581i) q^{82} +10.2230 q^{83} +(-0.240668 + 0.174856i) q^{84} -0.129632 q^{85} +(-5.03594 + 15.4990i) q^{86} +(-0.0297480 + 0.0915549i) q^{87} +(1.22863 - 0.892652i) q^{88} +(-10.7758 - 7.82907i) q^{89} +(6.65036 + 20.4677i) q^{90} +0.0630994 q^{91} +(-0.199071 - 0.612678i) q^{92} +(-0.217486 - 0.669353i) q^{93} +(6.25903 - 19.2633i) q^{94} +(14.1946 - 10.3130i) q^{95} -1.48046 q^{96} +(3.02983 - 9.32485i) q^{97} +(1.45435 + 1.05664i) q^{98} +(0.999431 + 3.07593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

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