LMFDB - Embedded newform 531.2.e.c.178.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(178,531)] 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("531.178"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [70] 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			178.20
Character	$\chi$	$=$	531.178
Dual form			531.2.e.c.355.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.208865 - 0.361765i) q^{2} +(1.01409 + 1.40415i) q^{3} +(0.912751 + 1.58093i) q^{4} +(0.573905 + 0.994032i) q^{5} +(0.719778 - 0.0735848i) q^{6} +(-1.97064 + 3.41324i) q^{7} +1.59803 q^{8} +(-0.943248 + 2.84786i) q^{9} +0.479474 q^{10} +(2.89543 - 5.01504i) q^{11} +(-1.29425 + 2.88484i) q^{12} +(-1.98545 - 3.43890i) q^{13} +(0.823194 + 1.42581i) q^{14} +(-0.813775 + 1.81388i) q^{15} +(-1.49173 + 2.58375i) q^{16} -1.31337 q^{17} +(0.833242 + 0.936051i) q^{18} +0.413128 q^{19} +(-1.04766 + 1.81461i) q^{20} +(-6.79109 + 0.694271i) q^{21} +(-1.20951 - 2.09493i) q^{22} +(1.59560 + 2.76365i) q^{23} +(1.62054 + 2.24386i) q^{24} +(1.84127 - 3.18917i) q^{25} -1.65877 q^{26} +(-4.95534 + 1.56352i) q^{27} -7.19480 q^{28} +(0.434197 - 0.752050i) q^{29} +(0.486230 + 0.673252i) q^{30} +(-3.19419 - 5.53250i) q^{31} +(2.22117 + 3.84717i) q^{32} +(9.97807 - 1.02008i) q^{33} +(-0.274316 + 0.475129i) q^{34} -4.52383 q^{35} +(-5.36321 + 1.10817i) q^{36} +7.30365 q^{37} +(0.0862879 - 0.149455i) q^{38} +(2.81530 - 6.27522i) q^{39} +(0.917115 + 1.58849i) q^{40} +(1.69185 + 2.93038i) q^{41} +(-1.16726 + 2.60179i) q^{42} +(1.47621 - 2.55686i) q^{43} +10.5712 q^{44} +(-3.37220 + 0.696779i) q^{45} +1.33306 q^{46} +(-4.44655 + 7.70164i) q^{47} +(-5.14071 + 0.525548i) q^{48} +(-4.26682 - 7.39036i) q^{49} +(-0.769152 - 1.33221i) q^{50} +(-1.33187 - 1.84416i) q^{51} +(3.62445 - 6.27773i) q^{52} +13.3767 q^{53} +(-0.469370 + 2.11923i) q^{54} +6.64682 q^{55} +(-3.14913 + 5.45445i) q^{56} +(0.418948 + 0.580091i) q^{57} +(-0.181377 - 0.314154i) q^{58} +(-0.500000 - 0.866025i) q^{59} +(-3.61040 + 0.369100i) q^{60} +(-1.62117 + 2.80795i) q^{61} -2.66862 q^{62} +(-7.86163 - 8.83163i) q^{63} -4.11122 q^{64} +(2.27892 - 3.94721i) q^{65} +(1.71504 - 3.82277i) q^{66} +(6.16422 + 10.6767i) q^{67} +(-1.19878 - 2.07634i) q^{68} +(-2.26249 + 5.04304i) q^{69} +(-0.944870 + 1.63656i) q^{70} +2.48962 q^{71} +(-1.50734 + 4.55095i) q^{72} -6.01500 q^{73} +(1.52548 - 2.64220i) q^{74} +(6.34526 - 0.648693i) q^{75} +(0.377083 + 0.653126i) q^{76} +(11.4117 + 19.7657i) q^{77} +(-1.68214 - 2.32915i) q^{78} +(-1.50663 + 2.60956i) q^{79} -3.42444 q^{80} +(-7.22057 - 5.37247i) q^{81} +1.41348 q^{82} +(6.49680 - 11.2528i) q^{83} +(-7.29617 - 10.1026i) q^{84} +(-0.753747 - 1.30553i) q^{85} +(-0.616655 - 1.06808i) q^{86} +(1.49630 - 0.152971i) q^{87} +(4.62698 - 8.01417i) q^{88} -2.89185 q^{89} +(-0.452263 + 1.36547i) q^{90} +15.6504 q^{91} +(-2.91276 + 5.04505i) q^{92} +(4.52924 - 10.0956i) q^{93} +(1.85746 + 3.21721i) q^{94} +(0.237096 + 0.410662i) q^{95} +(-3.14953 + 7.02022i) q^{96} +(3.93483 - 6.81532i) q^{97} -3.56476 q^{98} +(11.5510 + 12.9762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 44 q^{4} - 2 q^{5} + 4 q^{6} - 11 q^{7} + 2 q^{9} + 20 q^{10} + 2 q^{11} - 23 q^{13} + 2 q^{14} - 5 q^{15} - 62 q^{16} - 4 q^{17} - q^{18} + 46 q^{19} + q^{20} + 16 q^{21} - 16 q^{22} - 42 q^{24}+ \cdots - 37 q^{99}+O(q^{100}) $ 70 * q - 44 * q^4 - 2 * q^5 + 4 * q^6 - 11 * q^7 + 2 * q^9 + 20 * q^10 + 2 * q^11 - 23 * q^13 + 2 * q^14 - 5 * q^15 - 62 * q^16 - 4 * q^17 - q^18 + 46 * q^19 + q^20 + 16 * q^21 - 16 * q^22 - 42 * q^24 - 59 * q^25 - 12 * q^26 - 12 * q^27 + 68 * q^28 - q^29 + 69 * q^30 - 24 * q^31 + 10 * q^32 - 22 * q^33 - 30 * q^34 + 64 * q^35 - 38 * q^36 + 86 * q^37 + 2 * q^38 + 25 * q^39 - 36 * q^40 - 6 * q^41 - 52 * q^42 - 34 * q^43 - 72 * q^44 - 5 * q^45 + 80 * q^46 - 6 * q^47 + 61 * q^48 - 66 * q^49 - 12 * q^50 - 36 * q^51 - 48 * q^52 - 4 * q^53 - 46 * q^54 + 48 * q^55 - 14 * q^56 + 57 * q^57 - 26 * q^58 - 35 * q^59 - 32 * q^60 - 67 * q^61 + 102 * q^62 - 35 * q^63 + 208 * q^64 + 15 * q^65 + 157 * q^66 - 37 * q^67 + 25 * q^68 + 10 * q^69 - 22 * q^70 - 36 * q^71 - 136 * q^72 + 86 * q^73 + 11 * q^74 + 28 * q^75 - 76 * q^76 + 28 * q^77 - 67 * q^78 - 41 * q^79 + 6 * q^80 - 50 * q^81 + 64 * q^82 + 3 * q^83 + 164 * q^84 - 94 * q^85 - 36 * q^86 + 43 * q^87 - 48 * q^88 - 16 * q^89 - 84 * q^90 + 98 * q^91 + q^92 - 19 * q^93 - 34 * q^94 + 37 * q^95 - 7 * q^96 - 41 * q^97 - 106 * q^98 - 37 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.208865	−	0.361765i	0.147690	−	0.255806i	−0.782683	−	0.622420i	$-0.786150\pi$
$2$	0.208865	−	0.361765i	0.147690	−	0.255806i	0.930373	+	0.366614i	$0.119483\pi$
$3$	1.01409	+	1.40415i	0.585484	+	0.810684i
$3$	1.01409	+	1.40415i	0.585484	+	0.810684i
$4$	0.912751	+	1.58093i	0.456375	+	0.790465i
$5$	0.573905	+	0.994032i	0.256658	+	0.444545i	0.965345	−	0.260979i	$-0.0840453\pi$
$5$	0.573905	+	0.994032i	0.256658	+	0.444545i	−0.708687	+	0.705524i	$0.750712\pi$
$6$	0.719778	−	0.0735848i	0.293848	−	0.0300409i
$7$	−1.97064	+	3.41324i	−0.744831	+	1.29009i	0.205443	+	0.978669i	$0.434137\pi$
$7$	−1.97064	+	3.41324i	−0.744831	+	1.29009i	−0.950274	+	0.311416i	$0.899197\pi$
$8$	1.59803			0.564988
$9$	−0.943248	+	2.84786i	−0.314416	+	0.949285i
$10$	0.479474			0.151623
$11$	2.89543	−	5.01504i	0.873006	−	1.51209i	0.0141349	−	0.999900i	$-0.495501\pi$
$11$	2.89543	−	5.01504i	0.873006	−	1.51209i	0.858871	−	0.512191i	$-0.171166\pi$
$12$	−1.29425	+	2.88484i	−0.373617	+	0.832781i
$13$	−1.98545	−	3.43890i	−0.550665	−	0.953780i	−0.998227	−	0.0595272i	$-0.981041\pi$
$13$	−1.98545	−	3.43890i	−0.550665	−	0.953780i	0.447561	−	0.894253i	$-0.352293\pi$
$14$	0.823194	+	1.42581i	0.220008	+	0.381065i
$15$	−0.813775	+	1.81388i	−0.210116	+	0.468343i
$16$	−1.49173	+	2.58375i	−0.372933	+	0.645938i
$17$	−1.31337			−0.318538			−0.159269	−	0.987235i	$-0.550914\pi$
$17$	−1.31337			−0.318538			−0.159269	+	0.987235i	$0.550914\pi$
$18$	0.833242	+	0.936051i	0.196397	+	0.220629i
$19$	0.413128			0.0947780			0.0473890	−	0.998877i	$-0.484910\pi$
$19$	0.413128			0.0947780			0.0473890	+	0.998877i	$0.484910\pi$
$20$	−1.04766	+	1.81461i	−0.234265	+	0.405759i
$21$	−6.79109	+	0.694271i	−1.48194	+	0.151502i
$22$	−1.20951	−	2.09493i	−0.257868	−	0.446641i
$23$	1.59560	+	2.76365i	0.332705	+	0.576261i	0.983041	−	0.183385i	$-0.0587055\pi$
$23$	1.59560	+	2.76365i	0.332705	+	0.576261i	−0.650337	+	0.759646i	$0.725372\pi$
$24$	1.62054	+	2.24386i	0.330791	+	0.458026i
$25$	1.84127	−	3.18917i	0.368253	−	0.637833i
$26$	−1.65877			−0.325311
$27$	−4.95534	+	1.56352i	−0.953656	+	0.300900i
$28$	−7.19480			−1.35969
$29$	0.434197	−	0.752050i	0.0806283	−	0.139652i	−0.822892	−	0.568198i	$-0.807641\pi$
$29$	0.434197	−	0.752050i	0.0806283	−	0.139652i	0.903520	+	0.428546i	$0.140974\pi$
$30$	0.486230	+	0.673252i	0.0887730	+	0.122918i
$31$	−3.19419	−	5.53250i	−0.573694	−	0.993667i	−0.996182	−	0.0872987i	$-0.972177\pi$
$31$	−3.19419	−	5.53250i	−0.573694	−	0.993667i	0.422488	−	0.906368i	$-0.361157\pi$
$32$	2.22117	+	3.84717i	0.392651	+	0.680091i
$33$	9.97807	−	1.02008i	1.73696	−	0.177574i
$34$	−0.274316	+	0.475129i	−0.0470448	+	0.0814840i
$35$	−4.52383			−0.764667
$36$	−5.36321	+	1.10817i	−0.893869	+	0.184695i
$37$	7.30365			1.20071			0.600356	−	0.799733i	$-0.295025\pi$
$37$	7.30365			1.20071			0.600356	+	0.799733i	$0.295025\pi$
$38$	0.0862879	−	0.149455i	0.0139977	−	0.0242448i
$39$	2.81530	−	6.27522i	0.450808	−	1.00484i
$40$	0.917115	+	1.58849i	0.145009	+	0.251162i
$41$	1.69185	+	2.93038i	0.264223	+	0.457648i	0.967360	−	0.253407i	$-0.0815512\pi$
$41$	1.69185	+	2.93038i	0.264223	+	0.457648i	−0.703137	+	0.711055i	$0.748218\pi$
$42$	−1.16726	+	2.60179i	−0.180112	+	0.401464i
$43$	1.47621	−	2.55686i	0.225119	−	0.389918i	−0.731236	−	0.682125i	$-0.761056\pi$
$43$	1.47621	−	2.55686i	0.225119	−	0.389918i	0.956355	+	0.292207i	$0.0943895\pi$
$44$	10.5712			1.59367
$45$	−3.37220	+	0.696779i	−0.502697	+	0.103870i
$46$	1.33306			0.196548
$47$	−4.44655	+	7.70164i	−0.648595	+	1.12340i	0.334863	+	0.942267i	$0.391310\pi$
$47$	−4.44655	+	7.70164i	−0.648595	+	1.12340i	−0.983459	+	0.181133i	$0.942023\pi$
$48$	−5.14071	+	0.525548i	−0.741998	+	0.0758564i
$49$	−4.26682	−	7.39036i	−0.609546	−	1.05577i
$50$	−0.769152	−	1.33221i	−0.108775	−	0.188403i
$51$	−1.33187	−	1.84416i	−0.186499	−	0.258234i
$52$	3.62445	−	6.27773i	0.502620	−	0.870564i
$53$	13.3767			1.83743			0.918713	−	0.394927i	$-0.129230\pi$
$53$	13.3767			1.83743			0.918713	+	0.394927i	$0.129230\pi$
$54$	−0.469370	+	2.11923i	−0.0638732	+	0.288391i
$55$	6.64682			0.896256
$56$	−3.14913	+	5.45445i	−0.420820	+	0.728882i
$57$	0.418948	+	0.580091i	0.0554910	+	0.0768350i
$58$	−0.181377	−	0.314154i	−0.0238160	−	0.0412504i
$59$	−0.500000	−	0.866025i	−0.0650945	−	0.112747i
$59$	−0.500000	−	0.866025i	−0.0650945	−	0.112747i
$60$	−3.61040	+	0.369100i	−0.466100	+	0.0476507i
$61$	−1.62117	+	2.80795i	−0.207569	+	0.359521i	−0.950948	−	0.309350i	$-0.899889\pi$
$61$	−1.62117	+	2.80795i	−0.207569	+	0.359521i	0.743379	+	0.668871i	$0.233222\pi$
$62$	−2.66862			−0.338915
$63$	−7.86163	−	8.83163i	−0.990472	−	1.11268i
$64$	−4.11122			−0.513903
$65$	2.27892	−	3.94721i	0.282665	−	0.489591i
$66$	1.71504	−	3.82277i	0.211107	−	0.470551i
$67$	6.16422	+	10.6767i	0.753079	+	1.30437i	0.946324	+	0.323220i	$0.104766\pi$
$67$	6.16422	+	10.6767i	0.753079	+	1.30437i	−0.193245	+	0.981151i	$0.561901\pi$
$68$	−1.19878	−	2.07634i	−0.145373	−	0.251793i
$69$	−2.26249	+	5.04304i	−0.272372	+	0.607110i
$70$	−0.944870	+	1.63656i	−0.112934	+	0.195607i
$71$	2.48962			0.295464			0.147732	−	0.989027i	$-0.452803\pi$
$71$	2.48962			0.295464			0.147732	+	0.989027i	$0.452803\pi$
$72$	−1.50734	+	4.55095i	−0.177641	+	0.536334i
$73$	−6.01500			−0.704002			−0.352001	−	0.936000i	$-0.614499\pi$
$73$	−6.01500			−0.704002			−0.352001	+	0.936000i	$0.614499\pi$
$74$	1.52548	−	2.64220i	0.177333	−	0.307150i
$75$	6.34526	−	0.648693i	0.732688	−	0.0749046i
$76$	0.377083	+	0.653126i	0.0432544	+	0.0749187i
$77$	11.4117	+	19.7657i	1.30048	+	2.25250i
$78$	−1.68214	−	2.32915i	−0.190464	−	0.263724i
$79$	−1.50663	+	2.60956i	−0.169509	+	0.293599i	−0.938247	−	0.345965i	$-0.887552\pi$
$79$	−1.50663	+	2.60956i	−0.169509	+	0.293599i	0.768738	+	0.639564i	$0.220885\pi$
$80$	−3.42444			−0.382865
$81$	−7.22057	−	5.37247i	−0.802285	−	0.596941i
$82$	1.41348			0.156092
$83$	6.49680	−	11.2528i	0.713116	−	1.23515i	−0.250565	−	0.968100i	$-0.580616\pi$
$83$	6.49680	−	11.2528i	0.713116	−	1.23515i	0.963682	−	0.267054i	$-0.0860502\pi$
$84$	−7.29617	−	10.1026i	−0.796077	−	1.10228i
$85$	−0.753747	−	1.30553i	−0.0817553	−	0.141604i
$86$	−0.616655	−	1.06808i	−0.0664956	−	0.115174i
$87$	1.49630	−	0.152971i	0.160420	−	0.0164002i
$88$	4.62698	−	8.01417i	0.493238	−	0.854313i
$89$	−2.89185			−0.306535			−0.153268	−	0.988185i	$-0.548980\pi$
$89$	−2.89185			−0.306535			−0.153268	+	0.988185i	$0.548980\pi$
$90$	−0.452263	+	1.36547i	−0.0476727	+	0.143934i
$91$	15.6504			1.64061
$92$	−2.91276	+	5.04505i	−0.303676	+	0.525983i
$93$	4.52924	−	10.0956i	0.469661	−	1.04686i
$94$	1.85746	+	3.21721i	0.191582	+	0.331830i
$95$	0.237096	+	0.410662i	0.0243255	+	0.0421331i
$96$	−3.14953	+	7.02022i	−0.321448	+	0.716498i
$97$	3.93483	−	6.81532i	0.399521	−	0.691991i	−0.594146	−	0.804357i	$-0.702510\pi$
$97$	3.93483	−	6.81532i	0.399521	−	0.691991i	0.993667	+	0.112367i	$0.0358431\pi$
$98$	−3.56476			−0.360095
$99$	11.5510	+	12.9762i	1.16092	+	1.30416i
$100$	6.72247			0.672247
$101$	5.22926	−	9.05734i	0.520331	−	0.901239i	−0.479390	−	0.877602i	$-0.659142\pi$
$101$	5.22926	−	9.05734i	0.520331	−	0.901239i	0.999721	−	0.0236371i	$-0.00752461\pi$
$102$	−0.945332	+	0.0966437i	−0.0936018	+	0.00956916i
$103$	4.74229	+	8.21389i	0.467272	+	0.809339i	0.999301	−	0.0373875i	$-0.0119036\pi$
$103$	4.74229	+	8.21389i	0.467272	+	0.809339i	−0.532029	+	0.846726i	$0.678570\pi$
$104$	−3.17281	−	5.49546i	−0.311119	−	0.538874i
$105$	−4.58757	−	6.35212i	−0.447701	−	0.619903i
$106$	2.79392	−	4.83920i	0.271369	−	0.470025i
$107$	7.53932			0.728854			0.364427	−	0.931232i	$-0.381265\pi$
$107$	7.53932			0.728854			0.364427	+	0.931232i	$0.381265\pi$
$108$	−6.99481	−	6.40695i	−0.673076	−	0.616509i
$109$	−19.6480			−1.88194			−0.940971	−	0.338488i	$-0.890085\pi$
$109$	−19.6480			−1.88194			−0.940971	+	0.338488i	$0.890085\pi$
$110$	1.38829	−	2.40458i	0.132368	−	0.229268i
$111$	7.40655	+	10.2554i	0.702998	+	0.973398i
$112$	−5.87932	−	10.1833i	−0.555543	−	0.962229i
$113$	−5.50366	−	9.53261i	−0.517740	−	0.896753i	−0.999788	−	0.0206075i	$-0.993440\pi$
$113$	−5.50366	−	9.53261i	−0.517740	−	0.896753i	0.482047	−	0.876145i	$-0.339893\pi$
$114$	0.297360	−	0.0303999i	0.0278503	−	0.00284721i
$115$	−1.83144	+	3.17215i	−0.170783	+	0.295804i
$116$	1.58525			0.147187
$117$	11.6663	−	2.41054i	1.07855	−	0.222855i
$118$	−0.417730			−0.0384552
$119$	2.58817	−	4.48284i	0.237257	−	0.410941i
$120$	−1.30043	+	2.89863i	−0.118713	+	0.264608i
$121$	−11.2671	−	19.5152i	−1.02428	−	1.77411i
$122$	0.677211	+	1.17296i	0.0613118	+	0.106195i
$123$	−2.39898	+	5.34727i	−0.216309	+	0.482147i
$124$	5.83100	−	10.0996i	0.523640	−	0.906970i
$125$	9.96590			0.891377
$126$	−4.83699	+	0.999442i	−0.430913	+	0.0890374i
$127$	−15.6303			−1.38697			−0.693484	−	0.720472i	$-0.743925\pi$
$127$	−15.6303			−1.38697			−0.693484	+	0.720472i	$0.743925\pi$
$128$	−5.30102	+	9.18164i	−0.468549	+	0.811550i
$129$	5.08721	−	0.520079i	0.447904	−	0.0457904i
$130$	−0.951974	−	1.64887i	−0.0834936	−	0.144615i
$131$	−5.06899	−	8.77975i	−0.442880	−	0.767090i	0.555022	−	0.831836i	$-0.312710\pi$
$131$	−5.06899	−	8.77975i	−0.442880	−	0.767090i	−0.997902	+	0.0647453i	$0.979376\pi$
$132$	10.7202	+	14.8436i	0.933072	+	1.29197i
$133$	−0.814125	+	1.41011i	−0.0705936	+	0.122272i
$134$	5.14996			0.444888
$135$	−4.39808	−	4.02846i	−0.378527	−	0.346714i
$136$	−2.09879			−0.179970
$137$	−6.35108	+	11.0004i	−0.542609	+	0.939827i	0.456144	+	0.889906i	$0.349230\pi$
$137$	−6.35108	+	11.0004i	−0.542609	+	0.939827i	−0.998753	+	0.0499206i	$0.984103\pi$
$138$	1.35184	+	1.87180i	0.115076	+	0.159339i
$139$	−10.2667	−	17.7825i	−0.870812	−	1.50829i	−0.861158	−	0.508338i	$-0.830260\pi$
$139$	−10.2667	−	17.7825i	−0.870812	−	1.50829i	−0.00965440	−	0.999953i	$-0.503073\pi$
$140$	−4.12913	−	7.15187i	−0.348975	−	0.604443i
$141$	−15.3234	+	1.56655i	−1.29046	+	0.131928i
$142$	0.519995	−	0.900658i	0.0436370	−	0.0755816i
$143$	−22.9950			−1.92294
$144$	−5.95108	−	6.68535i	−0.495924	−	0.557113i
$145$	0.996750			0.0827756
$146$	−1.25632	+	2.17601i	−0.103974	+	0.180088i
$147$	6.05020	−	13.4857i	0.499012	−	1.11228i
$148$	6.66641	+	11.5466i	0.547976	+	0.949122i
$149$	−4.96612	−	8.60157i	−0.406840	−	0.704668i	0.587693	−	0.809084i	$-0.300036\pi$
$149$	−4.96612	−	8.60157i	−0.406840	−	0.704668i	−0.994534	+	0.104415i	$0.966703\pi$
$150$	1.09063	−	2.43098i	0.0890495	−	0.198489i
$151$	−9.45588	+	16.3781i	−0.769509	+	1.33283i	0.168321	+	0.985732i	$0.446166\pi$
$151$	−9.45588	+	16.3781i	−0.769509	+	1.33283i	−0.937830	+	0.347096i	$0.887168\pi$
$152$	0.660189			0.0535484
$153$	1.23883	−	3.74028i	0.100153	−	0.302383i
$154$	9.53402			0.768273
$155$	3.66633	−	6.35026i	0.294486	−	0.510065i
$156$	12.4904	−	1.27692i	1.00003	−	0.102236i
$157$	−9.54680	−	16.5355i	−0.761918	−	1.31968i	−0.941861	−	0.336003i	$-0.890925\pi$
$157$	−9.54680	−	16.5355i	−0.761918	−	1.31968i	0.179943	−	0.983677i	$-0.442409\pi$
$158$	0.629365	+	1.09009i	0.0500696	+	0.0867231i
$159$	13.5651	+	18.7828i	1.07578	+	1.48957i
$160$	−2.54948	+	4.41582i	−0.201554	+	0.349101i
$161$	−12.5774			−0.991235
$162$	−3.45169	+	1.49003i	−0.271191	+	0.117067i
$163$	17.3490			1.35888			0.679441	−	0.733730i	$-0.262223\pi$
$163$	17.3490			1.35888			0.679441	+	0.733730i	$0.262223\pi$
$164$	−3.08848	+	5.34941i	−0.241170	+	0.417718i
$165$	6.74046	+	9.33309i	0.524744	+	0.726580i
$166$	−2.71391	−	4.70062i	−0.210640	−	0.364839i
$167$	−1.08714	−	1.88298i	−0.0841254	−	0.145709i	0.820893	−	0.571082i	$-0.193476\pi$
$167$	−1.08714	−	1.88298i	−0.0841254	−	0.145709i	−0.905018	+	0.425373i	$0.860143\pi$
$168$	−10.8523	+	1.10946i	−0.837277	+	0.0855970i
$169$	−1.38404	+	2.39723i	−0.106465	+	0.184402i
$170$	−0.629725			−0.0482977
$171$	−0.389682	+	1.17653i	−0.0297997	+	0.0899714i
$172$	5.38963			0.410955
$173$	−3.92541	+	6.79901i	−0.298443	+	0.516919i	−0.975780	−	0.218754i	$-0.929801\pi$
$173$	−3.92541	+	6.79901i	−0.298443	+	0.516919i	0.677337	+	0.735673i	$0.263134\pi$
$174$	0.257186	−	0.573260i	0.0194972	−	0.0434587i
$175$	7.25694	+	12.5694i	0.548573	+	0.950156i
$176$	8.63841	+	14.9622i	0.651145	+	1.12782i
$177$	0.708981	−	1.58030i	0.0532903	−	0.118783i
$178$	−0.604006	+	1.04617i	−0.0452722	+	0.0784137i
$179$	6.74891			0.504437			0.252219	−	0.967670i	$-0.418840\pi$
$179$	6.74891			0.504437			0.252219	+	0.967670i	$0.418840\pi$
$180$	−4.17953	−	4.69522i	−0.311524	−	0.349961i
$181$	2.39503			0.178021			0.0890105	−	0.996031i	$-0.471630\pi$
$181$	2.39503			0.178021			0.0890105	+	0.996031i	$0.471630\pi$
$182$	3.26883	−	5.66177i	0.242301	−	0.419679i
$183$	−5.58678	+	0.571151i	−0.412986	+	0.0422207i
$184$	2.54980	+	4.41639i	0.187974	+	0.325581i
$185$	4.19160	+	7.26006i	0.308173	+	0.533770i
$186$	−2.70622	−	3.74713i	−0.198429	−	0.274753i
$187$	−3.80277	+	6.58658i	−0.278086	+	0.481659i
$188$	−16.2344			−1.18401
$189$	4.42850	−	19.9949i	0.322126	−	1.45442i
$190$	0.198084			0.0143705
$191$	12.2371	−	21.1953i	0.885446	−	1.53364i	0.0402450	−	0.999190i	$-0.487186\pi$
$191$	12.2371	−	21.1953i	0.885446	−	1.53364i	0.845201	−	0.534448i	$-0.179481\pi$
$192$	−4.16915	−	5.77276i	−0.300882	−	0.416613i
$193$	−11.4541	−	19.8390i	−0.824481	−	1.42804i	−0.902315	−	0.431077i	$-0.858134\pi$
$193$	−11.4541	−	19.8390i	−0.824481	−	1.42804i	0.0778340	−	0.996966i	$-0.475200\pi$
$194$	−1.64369	−	2.84696i	−0.118010	−	0.204400i
$195$	7.85348	−	0.802882i	0.562400	−	0.0574956i
$196$	7.78910	−	13.4911i	0.556364	−	0.963651i
$197$	7.95534			0.566794			0.283397	−	0.959003i	$-0.408539\pi$
$197$	7.95534			0.566794			0.283397	+	0.959003i	$0.408539\pi$
$198$	7.10693	−	1.46847i	0.505068	−	0.104359i
$199$	−1.26999			−0.0900275			−0.0450137	−	0.998986i	$-0.514333\pi$
$199$	−1.26999			−0.0900275			−0.0450137	+	0.998986i	$0.514333\pi$
$200$	2.94239	−	5.09637i	0.208059	−	0.360368i
$201$	−8.74063	+	19.4826i	−0.616516	+	1.37420i
$202$	−2.18442	−	3.78352i	−0.153695	−	0.266208i
$203$	1.71129	+	2.96404i	0.120109	+	0.208035i
$204$	1.69982	−	3.78885i	0.119011	−	0.265273i
$205$	−1.94193	+	3.36351i	−0.135630	+	0.234918i
$206$	3.96199			0.276045
$207$	−9.37553	+	1.93722i	−0.651644	+	0.134646i
$208$	11.8470			0.821444
$209$	1.19618	−	2.07185i	0.0827418	−	0.143313i
$210$	−3.25616	+	0.332885i	−0.224696	+	0.0229713i
$211$	0.687364	+	1.19055i	0.0473201	+	0.0819608i	0.888715	−	0.458459i	$-0.151599\pi$
$211$	0.687364	+	1.19055i	0.0473201	+	0.0819608i	−0.841395	+	0.540420i	$0.818265\pi$
$212$	12.2096	+	21.1476i	0.838556	+	1.45242i
$213$	2.52470	+	3.49579i	0.172990	+	0.239528i
$214$	1.57470	−	2.72746i	0.107644	−	0.186445i
$215$	3.38881			0.231115
$216$	−7.91877	+	2.49855i	−0.538804	+	0.170005i
$217$	25.1784			1.70922
$218$	−4.10379	+	7.10797i	−0.277944	+	0.481413i
$219$	−6.09974	−	8.44593i	−0.412182	−	0.570723i
$220$	6.06689	+	10.5082i	0.409029	+	0.708460i
$221$	2.60763	+	4.51654i	0.175408	+	0.303815i
$222$	5.25700	−	0.537437i	0.352827	−	0.0360704i
$223$	−10.8981	+	18.8760i	−0.729790	+	1.26403i	0.227182	+	0.973852i	$0.427049\pi$
$223$	−10.8981	+	18.8760i	−0.729790	+	1.26403i	−0.956972	+	0.290181i	$0.906284\pi$
$224$	−17.5085			−1.16983
$225$	7.34552	+	8.25184i	0.489701	+	0.550122i
$226$	−4.59808			−0.305860
$227$	−6.55672	+	11.3566i	−0.435185	+	0.753762i	−0.997311	−	0.0732894i	$-0.976650\pi$
$227$	−6.55672	+	11.3566i	−0.435185	+	0.753762i	0.562126	+	0.827052i	$0.309984\pi$
$228$	−0.534689	+	1.19181i	−0.0354107	+	0.0789294i
$229$	−0.166258	−	0.287968i	−0.0109867	−	0.0190294i	0.860480	−	0.509485i	$-0.170164\pi$
$229$	−0.166258	−	0.287968i	−0.0109867	−	0.0190294i	−0.871466	+	0.490455i	$0.836831\pi$
$230$	0.765047	+	1.32510i	0.0504457	+	0.0873745i
$231$	−16.1814	+	36.0678i	−1.06466	+	2.37309i
$232$	0.693858	−	1.20180i	0.0455540	−	0.0789018i
$233$	18.8820			1.23700			0.618500	−	0.785784i	$-0.287741\pi$
$233$	18.8820			1.23700			0.618500	+	0.785784i	$0.287741\pi$
$234$	1.56463	−	4.72393i	0.102283	−	0.308813i
$235$	−10.2076			−0.665869
$236$	0.912751	−	1.58093i	0.0594150	−	0.102910i
$237$	−5.19206	+	0.530798i	−0.337261	+	0.0344791i
$238$	−1.08116	−	1.87262i	−0.0700809	−	0.121384i
$239$	9.59834	+	16.6248i	0.620865	+	1.07537i	0.989325	+	0.145726i	$0.0465517\pi$
$239$	9.59834	+	16.6248i	0.620865	+	1.07537i	−0.368460	+	0.929643i	$0.620115\pi$
$240$	−3.47269	−	4.80842i	−0.224161	−	0.310382i
$241$	−3.84466	+	6.65914i	−0.247656	+	0.428953i	−0.962875	−	0.269948i	$-0.912994\pi$
$241$	−3.84466	+	6.65914i	−0.247656	+	0.428953i	0.715219	+	0.698900i	$0.246327\pi$
$242$	−9.41319			−0.605103
$243$	0.221433	−	15.5869i	0.0142049	−	0.999899i
$244$	−5.91889			−0.378918
$245$	4.89750	−	8.48272i	0.312890	−	0.541941i
$246$	1.43339	+	1.98472i	0.0913896	+	0.126541i
$247$	−0.820246	−	1.42071i	−0.0521910	−	0.0903974i
$248$	−5.10440	−	8.84109i	−0.324130	−	0.561410i
$249$	22.3889	−	2.28887i	1.41884	−	0.145051i
$250$	2.08153	−	3.60531i	0.131647	−	0.228020i
$251$	0.0467303			0.00294959			0.00147480	−	0.999999i	$-0.499531\pi$
$251$	0.0467303			0.00294959			0.00147480	+	0.999999i	$0.499531\pi$
$252$	6.78649	−	20.4898i	0.427508	−	1.29073i
$253$	18.4798			1.16181
$254$	−3.26463	+	5.65450i	−0.204841	+	0.354795i
$255$	1.06878	−	2.38229i	0.0669299	−	0.149185i
$256$	−1.89683	−	3.28540i	−0.118552	−	0.205338i
$257$	−9.88160	−	17.1154i	−0.616397	−	1.06763i	−0.990138	−	0.140098i	$-0.955258\pi$
$257$	−9.88160	−	17.1154i	−0.616397	−	1.06763i	0.373741	−	0.927533i	$-0.378075\pi$
$258$	0.874394	−	1.94900i	0.0544374	−	0.121339i
$259$	−14.3928	+	24.9291i	−0.894328	+	1.54902i
$260$	8.32035			0.516006
$261$	1.73218	+	1.94590i	0.107219	+	0.120448i
$262$	−4.23494			−0.261635
$263$	−4.19333	+	7.26305i	−0.258572	+	0.447859i	−0.965859	−	0.259067i	$-0.916585\pi$
$263$	−4.19333	+	7.26305i	−0.258572	+	0.447859i	0.707288	+	0.706926i	$0.249918\pi$
$264$	15.9452	−	1.63012i	0.981361	−	0.100327i
$265$	7.67693	+	13.2968i	0.471590	+	0.816818i
$266$	0.340084	+	0.589043i	0.0208519	+	0.0361166i
$267$	−2.93259	−	4.06058i	−0.179472	−	0.248503i
$268$	−11.2528	+	19.4904i	−0.687374	+	1.19057i
$269$	10.8133			0.659300			0.329650	−	0.944103i	$-0.393069\pi$
$269$	10.8133			0.659300			0.329650	+	0.944103i	$0.393069\pi$
$270$	−2.37596	+	0.749668i	−0.144596	+	0.0456234i
$271$	7.73828			0.470067			0.235034	−	0.971987i	$-0.424480\pi$
$271$	7.73828			0.470067			0.235034	+	0.971987i	$0.424480\pi$
$272$	1.95919	−	3.39341i	0.118793	−	0.205756i
$273$	15.8709	+	21.9755i	0.960552	+	1.33002i
$274$	2.65303	+	4.59519i	0.160276	+	0.277606i
$275$	−10.6625	−	18.4680i	−0.642975	−	1.11367i
$276$	−10.0378	+	1.02619i	−0.604204	+	0.0617693i
$277$	0.948077	−	1.64212i	0.0569644	−	0.0986653i	−0.836137	−	0.548521i	$-0.815191\pi$
$277$	0.948077	−	1.64212i	0.0569644	−	0.0986653i	0.893101	+	0.449855i	$0.148525\pi$
$278$	−8.57744			−0.514440
$279$	18.7687	−	3.87808i	1.12365	−	0.232174i
$280$	−7.22921			−0.432028
$281$	−1.42276	+	2.46430i	−0.0848749	+	0.147008i	−0.905338	−	0.424692i	$-0.860382\pi$
$281$	−1.42276	+	2.46430i	−0.0848749	+	0.147008i	0.820463	+	0.571700i	$0.193716\pi$
$282$	−2.63380	+	5.87067i	−0.156841	+	0.349593i
$283$	2.94507	+	5.10102i	0.175066	+	0.303224i	0.940184	−	0.340666i	$-0.110653\pi$
$283$	2.94507	+	5.10102i	0.175066	+	0.303224i	−0.765118	+	0.643890i	$0.777319\pi$
$284$	2.27241	+	3.93592i	0.134843	+	0.233554i
$285$	−0.336193	+	0.749365i	−0.0199144	+	0.0443886i
$286$	−4.80285	+	8.31878i	−0.283998	+	0.491900i
$287$	−13.3361			−0.787206
$288$	−13.0513	+	2.69672i	−0.769056	+	0.158906i
$289$	−15.2751			−0.898534
$290$	0.208186	−	0.360589i	0.0122251	−	0.0211745i
$291$	13.5600	−	1.38627i	0.794899	−	0.0812646i
$292$	−5.49019	−	9.50930i	−0.321289	−	0.556489i
$293$	−11.9672	−	20.7278i	−0.699133	−	1.21093i	−0.968768	−	0.247971i	$-0.920236\pi$
$293$	−11.9672	−	20.7278i	−0.699133	−	1.21093i	0.269635	−	0.962963i	$-0.413097\pi$
$294$	−3.61498	−	5.00544i	−0.210830	−	0.291923i
$295$	0.573905	−	0.994032i	0.0334140	−	0.0578748i
$296$	11.6714			0.678388
$297$	−6.50674	+	29.3783i	−0.377560	+	1.70470i
$298$	−4.14899			−0.240345
$299$	6.33596	−	10.9742i	0.366418	−	0.634654i
$300$	6.81718	+	9.43933i	0.393590	+	0.544980i
$301$	5.81813	+	10.0773i	0.335352	+	0.580846i
$302$	3.95000	+	6.84161i	0.227297	+	0.393690i
$303$	18.0208	−	1.84231i	1.03527	−	0.105838i
$304$	−0.616275	+	1.06742i	−0.0353458	+	0.0612207i
$305$	−3.72159			−0.213097
$306$	−1.09435	−	1.22938i	−0.0625599	−	0.0702788i
$307$	32.1495			1.83487			0.917435	−	0.397886i	$-0.130256\pi$
$307$	32.1495			1.83487			0.917435	+	0.397886i	$0.130256\pi$
$308$	−20.8321	+	36.0822i	−1.18702	+	2.05598i
$309$	−6.72439	+	14.9885i	−0.382537	+	0.852665i
$310$	−1.53153	−	2.65269i	−0.0869853	−	0.150663i
$311$	11.4488	+	19.8299i	0.649202	+	1.12445i	0.983314	+	0.181917i	$0.0582302\pi$
$311$	11.4488	+	19.8299i	0.649202	+	1.12445i	−0.334112	+	0.942533i	$0.608436\pi$
$312$	4.49892	−	10.0280i	0.254701	−	0.567722i
$313$	−13.3972	+	23.2046i	−0.757253	+	1.31160i	0.186993	+	0.982361i	$0.440126\pi$
$313$	−13.3972	+	23.2046i	−0.757253	+	1.31160i	−0.944246	+	0.329240i	$0.893208\pi$
$314$	−7.97597			−0.450110
$315$	4.26710	−	12.8832i	0.240424	−	0.725888i
$316$	−5.50072			−0.309440
$317$	−1.61115	+	2.79059i	−0.0904911	+	0.156735i	−0.907718	−	0.419581i	$-0.862177\pi$
$317$	−1.61115	+	2.79059i	−0.0904911	+	0.156735i	0.817227	+	0.576316i	$0.195510\pi$
$318$	9.62822	−	0.984318i	0.539924	−	0.0551978i
$319$	−2.51438	−	4.35503i	−0.140778	−	0.243835i
$320$	−2.35945	−	4.08669i	−0.131897	−	0.228453i
$321$	7.64554	+	10.5863i	0.426733	+	0.590870i
$322$	−2.62697	+	4.55005i	−0.146395	+	0.253564i
$323$	−0.542588			−0.0301904
$324$	1.90292	−	16.3189i	0.105718	−	0.906608i
$325$	−14.6230			−0.811137
$326$	3.62361	−	6.27627i	0.200693	−	0.347610i
$327$	−19.9249	−	27.5887i	−1.10185	−	1.52566i
$328$	2.70363	+	4.68282i	0.149283	+	0.258565i
$329$	−17.5251	−	30.3543i	−0.966188	−	1.67349i
$330$	4.78423	−	0.489104i	0.263363	−	0.0269243i
$331$	−5.18902	+	8.98765i	−0.285214	+	0.494006i	−0.972661	−	0.232229i	$-0.925398\pi$
$331$	−5.18902	+	8.98765i	−0.285214	+	0.494006i	0.687447	+	0.726235i	$0.258731\pi$
$332$	23.7198			1.30179
$333$	−6.88915	+	20.7997i	−0.377523	+	1.13982i
$334$	−0.908261			−0.0496978
$335$	−7.07535	+	12.2549i	−0.386568	+	0.669555i
$336$	8.33665	−	18.5822i	0.454802	−	1.01374i
$337$	−1.10169	−	1.90818i	−0.0600129	−	0.103945i	0.834458	−	0.551071i	$-0.185781\pi$
$337$	−1.10169	−	1.90818i	−0.0600129	−	0.103945i	−0.894471	+	0.447126i	$0.852448\pi$
$338$	0.578156	+	1.00140i	0.0314475	+	0.0544687i
$339$	7.80398	−	17.3948i	0.423854	−	0.944758i
$340$	1.37597	−	2.38324i	0.0746223	−	0.129250i
$341$	−36.9943			−2.00335
$342$	0.344236	+	0.386709i	0.0186141	+	0.0209108i
$343$	6.04453			0.326374
$344$	2.35902	−	4.08593i	0.127190	−	0.220299i
$345$	−6.31140	+	0.645231i	−0.339794	+	0.0347381i
$346$	1.63976	+	2.84015i	0.0881541	+	0.152687i
$347$	−6.14672	−	10.6464i	−0.329973	−	0.571531i	0.652533	−	0.757760i	$-0.273706\pi$
$347$	−6.14672	−	10.6464i	−0.329973	−	0.571531i	−0.982506	+	0.186230i	$0.940373\pi$
$348$	1.60759	+	2.22593i	0.0861757	+	0.119322i
$349$	3.68683	−	6.38578i	0.197352	−	0.341823i	−0.750317	−	0.661078i	$-0.770099\pi$
$349$	3.68683	−	6.38578i	0.197352	−	0.341823i	0.947669	+	0.319255i	$0.103433\pi$
$350$	6.06288			0.324075
$351$	15.2154	+	13.9366i	0.812138	+	0.743883i
$352$	25.7250			1.37115
$353$	10.8848	−	18.8530i	0.579338	−	1.00344i	−0.416217	−	0.909265i	$-0.636644\pi$
$353$	10.8848	−	18.8530i	0.579338	−	1.00344i	0.995555	−	0.0941781i	$-0.0300223\pi$
$354$	−0.423615	−	0.586553i	−0.0225149	−	0.0311750i
$355$	1.42881	+	2.47477i	0.0758332	+	0.131347i
$356$	−2.63954	−	4.57181i	−0.139895	−	0.242306i
$357$	8.91919	−	0.911832i	0.472054	−	0.0482593i
$358$	1.40961	−	2.44152i	0.0745002	−	0.129038i
$359$	−22.9901			−1.21337			−0.606684	−	0.794943i	$-0.707501\pi$
$359$	−22.9901			−1.21337			−0.606684	+	0.794943i	$0.707501\pi$
$360$	−5.38886	+	1.11347i	−0.284018	+	0.0586851i
$361$	−18.8293			−0.991017
$362$	0.500237	−	0.866436i	0.0262919	−	0.0455389i
$363$	15.9763	−	35.6107i	0.838538	−	1.86908i
$364$	14.2849	+	24.7422i	0.748734	+	1.29685i
$365$	−3.45204	−	5.97910i	−0.180688	−	0.312961i
$366$	−0.960259	+	2.14039i	−0.0501936	+	0.111880i
$367$	4.25297	−	7.36636i	0.222003	−	0.384521i	−0.733413	−	0.679783i	$-0.762074\pi$
$367$	4.25297	−	7.36636i	0.222003	−	0.384521i	0.955416	+	0.295263i	$0.0954071\pi$
$368$	−9.52079			−0.496305
$369$	−9.94112	+	2.05408i	−0.517514	+	0.106931i
$370$	3.50191			0.182056
$371$	−26.3605	+	45.6578i	−1.36857	+	2.37044i
$372$	20.0945	−	2.05431i	1.04185	−	0.106511i
$373$	5.11184	+	8.85396i	0.264681	+	0.458441i	0.967480	−	0.252948i	$-0.0814000\pi$
$373$	5.11184	+	8.85396i	0.264681	+	0.458441i	−0.702799	+	0.711388i	$0.748067\pi$
$374$	1.58853	+	2.75141i	0.0821409	+	0.142272i
$375$	10.1063	+	13.9936i	0.521887	+	0.722625i
$376$	−7.10570	+	12.3074i	−0.366448	+	0.634707i
$377$	−3.44831			−0.177597
$378$	−6.30850	−	5.77831i	−0.324474	−	0.297204i
$379$	14.1382			0.726232			0.363116	−	0.931744i	$-0.381713\pi$
$379$	14.1382			0.726232			0.363116	+	0.931744i	$0.381713\pi$
$380$	−0.432819	+	0.749665i	−0.0222032	+	0.0384570i
$381$	−15.8505	−	21.9473i	−0.812048	−	1.12439i
$382$	−5.11181	−	8.85391i	−0.261543	−	0.453005i
$383$	−9.27392	−	16.0629i	−0.473875	−	0.820776i	0.525677	−	0.850684i	$-0.323812\pi$
$383$	−9.27392	−	16.0629i	−0.473875	−	0.820776i	−0.999553	+	0.0299079i	$0.990479\pi$
$384$	−18.2681	+	1.86759i	−0.932239	+	0.0953052i
$385$	−13.0985	+	22.6872i	−0.667560	+	1.15625i
$386$	−9.56941			−0.487070
$387$	5.88915	+	6.61578i	0.299362	+	0.336299i
$388$	14.3661			0.729326
$389$	−7.14666	+	12.3784i	−0.362350	+	0.627608i	−0.988347	−	0.152217i	$-0.951359\pi$
$389$	−7.14666	+	12.3784i	−0.362350	+	0.627608i	0.625997	+	0.779825i	$0.284692\pi$
$390$	1.34986	−	3.00881i	0.0683530	−	0.152357i
$391$	−2.09560	−	3.62969i	−0.105979	−	0.183561i
$392$	−6.81850	−	11.8100i	−0.344386	−	0.596494i
$393$	7.18764	−	16.0210i	0.362568	−	0.808155i
$394$	1.66159	−	2.87796i	0.0837097	−	0.144990i
$395$	−3.45865			−0.174024
$396$	−9.97130	+	30.1054i	−0.501077	+	1.51285i
$397$	21.8151			1.09487			0.547433	−	0.836849i	$-0.315605\pi$
$397$	21.8151			1.09487			0.547433	+	0.836849i	$0.315605\pi$
$398$	−0.265257	+	0.459439i	−0.0132961	+	0.0230296i
$399$	−2.80559	+	0.286823i	−0.140455	+	0.0143591i
$400$	5.49334	+	9.51475i	0.274667	+	0.475738i
$401$	−4.39954	−	7.62023i	−0.219703	−	0.380536i	0.735014	−	0.678052i	$-0.237175\pi$
$401$	−4.39954	−	7.62023i	−0.219703	−	0.380536i	−0.954717	+	0.297515i	$0.903842\pi$
$402$	5.22251	+	7.23129i	0.260475	+	0.360664i
$403$	−12.6838	+	21.9690i	−0.631827	+	1.09436i
$404$	19.0920			0.949864
$405$	1.19649	−	10.2608i	0.0594541	−	0.509861i
$406$	1.42971			0.0709554
$407$	21.1472	−	36.6281i	1.04823	−	1.81559i
$408$	−2.12836	−	2.94701i	−0.105370	−	0.145899i
$409$	−4.63974	−	8.03626i	−0.229420	−	0.397368i	0.728216	−	0.685348i	$-0.240350\pi$
$409$	−4.63974	−	8.03626i	−0.229420	−	0.397368i	−0.957636	+	0.287980i	$0.907016\pi$
$410$	0.811200	+	1.40504i	0.0400623	+	0.0693900i
$411$	−21.8867	+	2.23753i	−1.07959	+	0.110369i
$412$	−8.65706	+	14.9945i	−0.426503	+	0.738725i
$413$	3.94128			0.193937
$414$	−1.25740	+	3.79635i	−0.0617980	+	0.186580i
$415$	14.9142			0.732108
$416$	8.82004	−	15.2768i	0.432438	−	0.749005i
$417$	14.5578	−	32.4490i	0.712900	−	1.58903i
$418$	−0.499682	−	0.865475i	−0.0244402	−	0.0423317i
$419$	−3.46768	−	6.00620i	−0.169407	−	0.293422i	0.768804	−	0.639484i	$-0.220852\pi$
$419$	−3.46768	−	6.00620i	−0.169407	−	0.293422i	−0.938212	+	0.346062i	$0.887519\pi$
$420$	5.85495	−	13.0505i	0.285693	−	0.636801i
$421$	−7.36232	+	12.7519i	−0.358818	+	0.621490i	−0.987764	−	0.155959i	$-0.950153\pi$
$421$	−7.36232	+	12.7519i	−0.358818	+	0.621490i	0.628946	+	0.777449i	$0.283487\pi$
$422$	0.574265			0.0279548
$423$	−17.7390	−	19.9277i	−0.862498	−	0.968917i
$424$	21.3763			1.03812
$425$	−2.41826	+	4.18854i	−0.117303	+	0.203174i
$426$	1.79198	−	0.183198i	0.0868215	−	0.00887599i
$427$	−6.38947	−	11.0669i	−0.309208	−	0.535564i
$428$	6.88152	+	11.9191i	0.332631	+	0.576134i
$429$	−23.3190	−	32.2883i	−1.12585	−	1.55889i
$430$	0.707803	−	1.22595i	0.0341333	−	0.0591206i
$431$	27.4582			1.32262			0.661308	−	0.750114i	$-0.270001\pi$
$431$	27.4582			1.32262			0.661308	+	0.750114i	$0.270001\pi$
$432$	3.35228	−	15.1357i	0.161287	−	0.728218i
$433$	−39.6358			−1.90477			−0.952386	−	0.304894i	$-0.901379\pi$
$433$	−39.6358			−1.90477			−0.952386	+	0.304894i	$0.901379\pi$
$434$	5.25888	−	9.10865i	0.252434	−	0.437229i
$435$	1.01079	+	1.39958i	0.0484638	+	0.0671048i
$436$	−17.9338	−	31.0622i	−0.858872	−	1.48761i
$437$	0.659185	+	1.14174i	0.0315331	+	0.0546169i
$438$	−4.32946	+	0.442612i	−0.206870	+	0.0211488i
$439$	3.29676	−	5.71016i	0.157346	−	0.272531i	−0.776565	−	0.630037i	$-0.783040\pi$
$439$	3.29676	−	5.71016i	0.157346	−	0.272531i	0.933911	+	0.357506i	$0.116373\pi$
$440$	10.6218			0.506374
$441$	25.0713	−	5.18036i	1.19387	−	0.246684i
$442$	2.17857			0.103624
$443$	−6.87632	+	11.9101i	−0.326704	+	0.565868i	−0.981856	−	0.189629i	$-0.939271\pi$
$443$	−6.87632	+	11.9101i	−0.326704	+	0.565868i	0.655152	+	0.755497i	$0.272605\pi$
$444$	−9.45272	+	21.0699i	−0.448606	+	0.999931i
$445$	−1.65965	−	2.87459i	−0.0786748	−	0.136269i
$446$	4.55246	+	7.88509i	0.215565	+	0.373370i
$447$	7.04177	−	15.6959i	0.333064	−	0.742391i
$448$	8.10173	−	14.0326i	0.382771	−	0.662979i
$449$	−25.5598			−1.20624			−0.603120	−	0.797651i	$-0.706076\pi$
$449$	−25.5598			−1.20624			−0.603120	+	0.797651i	$0.706076\pi$
$450$	4.51944	−	0.933829i	0.213049	−	0.0440211i
$451$	19.5946			0.922674
$452$	10.0469	−	17.4018i	0.472568	−	0.818512i
$453$	−32.5863	+	3.33138i	−1.53104	+	0.156522i
$454$	2.73894	+	4.74398i	0.128545	+	0.222646i
$455$	8.98186	+	15.5570i	0.421076	+	0.729325i
$456$	0.669490	+	0.927001i	0.0313518	+	0.0434108i
$457$	−5.74059	+	9.94299i	−0.268533	+	0.465113i	−0.968483	−	0.249079i	$-0.919872\pi$
$457$	−5.74059	+	9.94299i	−0.268533	+	0.465113i	0.699950	+	0.714192i	$0.253206\pi$
$458$	−0.138902			−0.00649047
$459$	6.50818	−	2.05348i	0.303776	−	0.0958480i
$460$	−6.68659			−0.311764
$461$	6.01737	−	10.4224i	0.280257	−	0.485419i	−0.691191	−	0.722672i	$-0.742914\pi$
$461$	6.01737	−	10.4224i	0.280257	−	0.485419i	0.971448	+	0.237253i	$0.0762470\pi$
$462$	9.66834	+	13.3871i	0.449812	+	0.622827i
$463$	17.3073	+	29.9771i	0.804337	+	1.39315i	0.916738	+	0.399489i	$0.130813\pi$
$463$	17.3073	+	29.9771i	0.804337	+	1.39315i	−0.112401	+	0.993663i	$0.535854\pi$
$464$	1.29541	+	2.24371i	0.0601378	+	0.104162i
$465$	12.6347	−	1.29168i	0.585919	−	0.0599000i
$466$	3.94379	−	6.83084i	0.182692	−	0.316433i
$467$	−21.5480			−0.997124			−0.498562	−	0.866854i	$-0.666138\pi$
$467$	−21.5480			−0.997124			−0.498562	+	0.866854i	$0.666138\pi$
$468$	14.4593	+	16.2434i	0.668382	+	0.750849i
$469$	−48.5898			−2.24367
$470$	−2.13201	+	3.69274i	−0.0983421	+	0.170333i
$471$	13.5370	−	30.1736i	0.623752	−	1.39033i
$472$	−0.799013	−	1.38393i	−0.0367776	−	0.0637006i
$473$	−8.54851	−	14.8065i	−0.393061	−	0.680802i
$474$	−0.892416	+	1.98917i	−0.0409900	+	0.0913656i
$475$	0.760678	−	1.31753i	0.0349023	−	0.0604526i
$476$	9.44941			0.433113
$477$	−12.6175	+	38.0948i	−0.577716	+	1.74424i
$478$	8.01902			0.366782
$479$	−15.2669	+	26.4430i	−0.697562	+	1.20821i	0.271748	+	0.962368i	$0.412398\pi$
$479$	−15.2669	+	26.4430i	−0.697562	+	1.20821i	−0.969309	+	0.245844i	$0.920935\pi$
$480$	−8.78585	+	0.898201i	−0.401017	+	0.0409971i
$481$	−14.5010	−	25.1166i	−0.661191	−	1.14522i
$482$	1.60603	+	2.78172i	0.0731525	+	0.126704i
$483$	−12.7546	−	17.6604i	−0.580353	−	0.803578i
$484$	20.5681	−	35.6250i	0.934913	−	1.61932i
$485$	9.03286			0.410161
$486$	−5.59254	−	3.33566i	−0.253683	−	0.151309i
$487$	−20.6857			−0.937358			−0.468679	−	0.883369i	$-0.655270\pi$
$487$	−20.6857			−0.937358			−0.468679	+	0.883369i	$0.655270\pi$
$488$	−2.59067	+	4.48717i	−0.117274	+	0.203125i
$489$	17.5935	+	24.3606i	0.795604	+	1.10162i
$490$	−2.04583	−	3.54349i	−0.0924213	−	0.160078i
$491$	−6.38394	−	11.0573i	−0.288103	−	0.499010i	0.685254	−	0.728304i	$-0.259691\pi$
$491$	−6.38394	−	11.0573i	−0.288103	−	0.499010i	−0.973357	+	0.229295i	$0.926358\pi$
$492$	−10.6433	+	1.08810i	−0.479839	+	0.0490552i
$493$	−0.570259	+	0.987718i	−0.0256832	+	0.0444846i
$494$	−0.685282			−0.0308323
$495$	−6.26960	+	18.9292i	−0.281797	+	0.850803i
$496$	19.0595			0.855796
$497$	−4.90615	+	8.49770i	−0.220071	+	0.381174i
$498$	3.84822	−	8.57757i	0.172443	−	0.384370i
$499$	12.6435	+	21.8992i	0.566001	+	0.980342i	0.996956	+	0.0779689i	$0.0248435\pi$
$499$	12.6435	+	21.8992i	0.566001	+	0.980342i	−0.430955	+	0.902374i	$0.641823\pi$
$500$	9.09638	+	15.7554i	0.406802	+	0.704603i
$501$	1.54152	−	3.43601i	0.0688702	−	0.153510i
$502$	0.00976032	−	0.0169054i	0.000435625	−	0.000754524i
$503$	42.3360			1.88767			0.943834	−	0.330421i	$-0.107191\pi$
$503$	42.3360			1.88767			0.943834	+	0.330421i	$0.107191\pi$
$504$	−12.5631	−	14.1132i	−0.559604	−	0.628651i
$505$	12.0044			0.534188
$506$	3.85978	−	6.68533i	0.171588	−	0.297199i
$507$	−4.76960	+	0.487609i	−0.211826	+	0.0216555i
$508$	−14.2666	−	24.7105i	−0.632978	−	1.09635i
$509$	−16.8995	−	29.2708i	−0.749058	−	1.29741i	−0.948275	−	0.317451i	$-0.897173\pi$
$509$	−16.8995	−	29.2708i	−0.749058	−	1.29741i	0.199216	−	0.979956i	$-0.436160\pi$
$510$	−0.638597	−	0.884226i	−0.0282776	−	0.0391542i
$511$	11.8534	−	20.5307i	0.524363	−	0.908223i
$512$	−22.7888			−1.00713
$513$	−2.04719	+	0.645934i	−0.0903856	+	0.0285187i
$514$	−8.25568			−0.364142
$515$	−5.44325	+	9.42798i	−0.239858	+	0.415447i
$516$	5.46556	+	7.56782i	0.240608	+	0.333155i
$517$	25.7494	+	44.5992i	1.13246	+	1.96147i
$518$	6.01232	+	10.4136i	0.264166	+	0.457549i
$519$	−13.5275	+	1.38295i	−0.593791	+	0.0607049i
$520$	3.64178	−	6.30774i	0.159702	−	0.276613i
$521$	13.6099			0.596261			0.298130	−	0.954525i	$-0.403637\pi$
$521$	13.6099			0.596261			0.298130	+	0.954525i	$0.403637\pi$
$522$	1.06575	−	0.220210i	0.0466466	−	0.00963833i
$523$	7.68729			0.336142			0.168071	−	0.985775i	$-0.446246\pi$
$523$	7.68729			0.336142			0.168071	+	0.985775i	$0.446246\pi$
$524$	9.25345	−	16.0274i	0.404239	−	0.700162i
$525$	−10.2901	+	22.9363i	−0.449095	+	1.00102i
$526$	1.75168	+	3.03399i	0.0763768	+	0.132288i
$527$	4.19514	+	7.26620i	0.182743	+	0.316521i
$528$	−12.2489	+	27.3026i	−0.533067	+	1.18819i
$529$	6.40815	−	11.0992i	0.278615	−	0.482576i
$530$	6.41377			0.278596
$531$	2.93794	−	0.607051i	0.127496	−	0.0263438i
$532$	−2.97237			−0.128869
$533$	6.71819	−	11.6362i	0.290997	−	0.504022i
$534$	−2.08149	+	0.212796i	−0.0900748	+	0.00920859i
$535$	4.32685	+	7.49433i	0.187066	+	0.324008i
$536$	9.85058	+	17.0617i	0.425480	+	0.736954i
$537$	6.84399	+	9.47645i	0.295340	+	0.408939i
$538$	2.25853	−	3.91188i	0.0973720	−	0.168653i
$539$	−49.4172			−2.12855
$540$	2.35436	−	10.6300i	0.101315	−	0.457444i
$541$	−8.22875			−0.353781			−0.176891	−	0.984231i	$-0.556604\pi$
$541$	−8.22875			−0.353781			−0.176891	+	0.984231i	$0.556604\pi$
$542$	1.61626	−	2.79944i	0.0694242	−	0.120246i
$543$	2.42877	+	3.36297i	0.104229	+	0.144319i
$544$	−2.91720	−	5.05275i	−0.125074	−	0.216635i
$545$	−11.2761	−	19.5308i	−0.483015	−	0.836607i
$546$	11.2648	−	1.15163i	0.482090	−	0.0492854i
$547$	0.562448	−	0.974189i	0.0240486	−	0.0416533i	−0.853751	−	0.520682i	$-0.825678\pi$
$547$	0.562448	−	0.974189i	0.0240486	−	0.0416533i	0.877799	+	0.479029i	$0.159011\pi$
$548$	−23.1878			−0.990534
$549$	−6.46746	−	7.26545i	−0.276025	−	0.310082i
$550$	−8.90812			−0.379843
$551$	0.179379	−	0.310693i	0.00764179	−	0.0132360i
$552$	−3.61553	+	8.05891i	−0.153887	+	0.343010i
$553$	−5.93805	−	10.2850i	−0.252512	−	0.437363i
$554$	−0.396040	−	0.685962i	−0.0168261	−	0.0291437i
$555$	−5.94353	+	13.2480i	−0.252289	+	0.562345i
$556$	18.7419	−	32.4620i	0.794835	−	1.37669i
$557$	9.03641			0.382885			0.191442	−	0.981504i	$-0.438683\pi$
$557$	9.03641			0.382885			0.191442	+	0.981504i	$0.438683\pi$
$558$	2.51717	−	7.59984i	0.106560	−	0.321727i
$559$	−11.7237			−0.495861
$560$	6.74834	−	11.6885i	0.285169	−	0.493928i
$561$	−13.1049	+	1.33974i	−0.553288	+	0.0565640i
$562$	0.594330	+	1.02941i	0.0250703	+	0.0434231i
$563$	−10.8739	−	18.8341i	−0.458280	−	0.793764i	0.540590	−	0.841286i	$-0.318201\pi$
$563$	−10.8739	−	18.8341i	−0.458280	−	0.793764i	−0.998870	+	0.0475217i	$0.984868\pi$
$564$	−16.4631	−	22.7954i	−0.693221	−	0.959859i
$565$	6.31715	−	10.9416i	0.265764	−	0.460318i
$566$	2.46049			0.103422
$567$	32.5667	−	14.0584i	1.36767	−	0.590396i
$568$	3.97849			0.166934
$569$	19.6253	−	33.9921i	0.822736	−	1.42502i	−0.0809005	−	0.996722i	$-0.525780\pi$
$569$	19.6253	−	33.9921i	0.822736	−	1.42502i	0.903637	−	0.428299i	$-0.140887\pi$
$570$	0.200875	+	0.278139i	0.00841373	+	0.0116500i
$571$	−6.92081	−	11.9872i	−0.289627	−	0.501648i	0.684094	−	0.729394i	$-0.260198\pi$
$571$	−6.92081	−	11.9872i	−0.289627	−	0.501648i	−0.973721	+	0.227746i	$0.926864\pi$
$572$	−20.9887	−	36.3535i	−0.877582	−	1.52002i
$573$	42.1708	−	4.31123i	1.76171	−	0.180104i
$574$	−2.78545	+	4.82454i	−0.116262	+	0.201372i
$575$	11.7517			0.490078
$576$	3.87790	−	11.7082i	0.161579	−	0.487841i
$577$	36.0177			1.49944			0.749719	−	0.661756i	$-0.230189\pi$
$577$	36.0177			1.49944			0.749719	+	0.661756i	$0.230189\pi$
$578$	−3.19043	+	5.52598i	−0.132704	+	0.229851i
$579$	16.2414	−	36.2017i	0.674971	−	1.50449i
$580$	0.909784	+	1.57579i	0.0377767	+	0.0654312i
$581$	25.6057	+	44.3503i	1.06230	+	1.83996i
$582$	2.33070	−	5.19506i	0.0966105	−	0.215342i
$583$	38.7312	−	67.0845i	1.60408	−	2.77835i
$584$	−9.61213			−0.397753
$585$	9.09149	+	10.2132i	0.375887	+	0.422265i
$586$	−9.99813			−0.413019
$587$	−18.3221	+	31.7347i	−0.756232	+	1.30983i	0.188527	+	0.982068i	$0.439629\pi$
$587$	−18.3221	+	31.7347i	−0.756232	+	1.30983i	−0.944759	+	0.327764i	$0.893705\pi$
$588$	26.8423	−	2.74416i	1.10696	−	0.113167i
$589$	−1.31961	−	2.28563i	−0.0543736	−	0.0941778i
$590$	−0.239737	−	0.415237i	−0.00986982	−	0.0170950i
$591$	8.06742	+	11.1704i	0.331849	+	0.459491i
$592$	−10.8951	+	18.8708i	−0.447785	+	0.775586i
$593$	−23.6771			−0.972302			−0.486151	−	0.873875i	$-0.661600\pi$
$593$	−23.6771			−0.972302			−0.486151	+	0.873875i	$0.661600\pi$
$594$	9.26900	+	8.49001i	0.380312	+	0.348349i
$595$	5.94145			0.243576
$596$	9.06566	−	15.7022i	0.371344	−	0.643187i
$597$	−1.28789	−	1.78326i	−0.0527097	−	0.0729838i
$598$	−2.64672	−	4.58425i	−0.108232	−	0.187464i
$599$	22.6632	+	39.2539i	0.925995	+	1.60387i	0.789954	+	0.613166i	$0.210104\pi$
$599$	22.6632	+	39.2539i	0.925995	+	1.60387i	0.136041	+	0.990703i	$0.456562\pi$
$600$	10.1399	−	1.03663i	0.413960	−	0.0423202i
$601$	5.24485	−	9.08434i	0.213942	−	0.370558i	−0.739003	−	0.673702i	$-0.764703\pi$
$601$	5.24485	−	9.08434i	0.213942	−	0.370558i	0.952945	+	0.303144i	$0.0980364\pi$
$602$	4.86081			0.198112
$603$	−36.2202	+	7.48399i	−1.47500	+	0.304772i
$604$	−34.5235			−1.40474
$605$	12.9325	−	22.3997i	0.525780	−	0.910677i
$606$	3.09742	−	6.90407i	0.125824	−	0.280459i
$607$	0.0662138	+	0.114686i	0.00268753	+	0.00465495i	0.867366	−	0.497671i	$-0.165811\pi$
$607$	0.0662138	+	0.114686i	0.00268753	+	0.00465495i	−0.864679	+	0.502326i	$0.832478\pi$
$608$	0.917626	+	1.58937i	0.0372146	+	0.0644576i
$609$	−2.42654	+	5.40869i	−0.0983284	+	0.219171i
$610$	−0.777309	+	1.34634i	−0.0314723	+	0.0545117i
$611$	35.3136			1.42864
$612$	7.04386	−	1.45544i	0.284731	−	0.0588325i
$613$	−12.9324			−0.522336			−0.261168	−	0.965293i	$-0.584108\pi$
$613$	−12.9324			−0.522336			−0.261168	+	0.965293i	$0.584108\pi$
$614$	6.71491	−	11.6306i	0.270992	−	0.469371i
$615$	−6.69215	+	0.684156i	−0.269853	+	0.0275878i
$616$	18.2362	+	31.5860i	0.734758	+	1.27264i
$617$	18.9941	+	32.8987i	0.764672	+	1.32445i	0.940420	+	0.340016i	$0.110432\pi$
$617$	18.9941	+	32.8987i	0.764672	+	1.32445i	−0.175748	+	0.984435i	$0.556234\pi$
$618$	4.01781	+	5.56322i	0.161620	+	0.223785i
$619$	−17.9359	+	31.0659i	−0.720906	+	1.24865i	0.239731	+	0.970839i	$0.422941\pi$
$619$	−17.9359	+	31.0659i	−0.720906	+	1.24865i	−0.960637	+	0.277806i	$0.910393\pi$
$620$	13.3858			0.537585
$621$	−12.2277	−	11.2001i	−0.490683	−	0.449444i
$622$	9.56501			0.383522
$623$	5.69879	−	9.87059i	0.228317	−	0.395457i
$624$	12.0139	+	16.6350i	0.480943	+	0.665931i
$625$	−3.48686	−	6.03941i	−0.139474	−	0.241577i
$626$	5.59640	+	9.69325i	0.223677	+	0.387420i
$627$	4.12222	−	0.421425i	0.164626	−	0.0168301i
$628$	17.4277	−	30.1857i	0.695441	−	1.20454i
$629$	−9.59236			−0.382473
$630$	−3.76945	−	4.23454i	−0.150178	−	0.168708i
$631$	−46.1001			−1.83522			−0.917608	−	0.397487i	$-0.869882\pi$
$631$	−46.1001			−1.83522			−0.917608	+	0.397487i	$0.869882\pi$
$632$	−2.40764	+	4.17015i	−0.0957707	+	0.165880i
$633$	−0.974657	+	2.17248i	−0.0387391	+	0.0863484i
$634$	0.673025	+	1.16571i	0.0267292	+	0.0462964i
$635$	−8.97032	−	15.5371i	−0.355976	−	0.616569i
$636$	−17.3127	+	38.5895i	−0.686493	+	1.53017i
$637$	−16.9432	+	29.3464i	−0.671312	+	1.16275i
$638$	−2.10066			−0.0831659
$639$	−2.34833	+	7.09009i	−0.0928986	+	0.280480i
$640$	−12.1691			−0.481027
$641$	6.38208	−	11.0541i	0.252077	−	0.436610i	−0.712020	−	0.702159i	$-0.752220\pi$
$641$	6.38208	−	11.0541i	0.252077	−	0.436610i	0.964098	+	0.265548i	$0.0855530\pi$
$642$	5.42664	−	0.554779i	0.214172	−	0.0218954i
$643$	−16.4597	−	28.5090i	−0.649106	−	1.12429i	−0.983337	−	0.181794i	$-0.941810\pi$
$643$	−16.4597	−	28.5090i	−0.649106	−	1.12429i	0.334230	−	0.942491i	$-0.391524\pi$
$644$	−11.4800	−	19.8839i	−0.452375	−	0.783537i
$645$	3.43655	+	4.75838i	0.135314	+	0.187361i
$646$	−0.113328	+	0.196289i	−0.00445882	+	0.00772289i
$647$	31.3170			1.23120			0.615599	−	0.788060i	$-0.288914\pi$
$647$	31.3170			1.23120			0.615599	+	0.788060i	$0.288914\pi$
$648$	−11.5387	−	8.58535i	−0.453281	−	0.337264i
$649$	−5.79087			−0.227311
$650$	−3.05423	+	5.29008i	−0.119797	+	0.207494i
$651$	25.5331	+	35.3541i	1.00072	+	1.38564i
$652$	15.8353	+	27.4276i	0.620160	+	1.07415i
$653$	9.80142	+	16.9766i	0.383559	+	0.664344i	0.991568	−	0.129586i	$-0.0413649\pi$
$653$	9.80142	+	16.9766i	0.383559	+	0.664344i	−0.608009	+	0.793930i	$0.708032\pi$
$654$	−14.1422	+	1.44580i	−0.553005	+	0.0565351i
$655$	5.81824	−	10.0775i	0.227337	−	0.393760i
$656$	−10.0952			−0.394149
$657$	5.67364	−	17.1298i	0.221350	−	0.668299i
$658$	−14.6415			−0.570784
$659$	4.17640	−	7.23374i	0.162690	−	0.281787i	−0.773143	−	0.634232i	$-0.781316\pi$
$659$	4.17640	−	7.23374i	0.162690	−	0.281787i	0.935832	+	0.352445i	$0.114650\pi$
$660$	−8.60262	+	19.1750i	−0.334856	+	0.746386i
$661$	−13.6743	−	23.6845i	−0.531867	−	0.921221i	−0.999308	−	0.0371967i	$-0.988157\pi$
$661$	−13.6743	−	23.6845i	−0.531867	−	0.921221i	0.467441	−	0.884024i	$-0.345176\pi$
$662$	2.16761	+	3.75441i	0.0842465	+	0.145919i
$663$	−3.69751	+	8.24166i	−0.143600	+	0.320079i
$664$	10.3821	−	17.9822i	0.402902	−	0.697847i
$665$	−1.86892			−0.0724737
$666$	6.08571	+	6.83659i	0.235816	+	0.264912i
$667$	2.77121			0.107302
$668$	1.98457	−	3.43738i	0.0767855	−	0.132996i
$669$	−37.5563	+	3.83948i	−1.45201	+	0.148443i
$670$	2.95558	+	5.11922i	0.114184	+	0.197773i
$671$	9.38798	+	16.2605i	0.362419	+	0.627728i
$672$	−17.7551	−	24.5844i	−0.684919	−	0.948365i
$673$	−6.30981	+	10.9289i	−0.243225	+	0.421278i	−0.961631	−	0.274346i	$-0.911539\pi$
$673$	−6.30981	+	10.9289i	−0.243225	+	0.421278i	0.718406	+	0.695624i	$0.244872\pi$
$674$	−0.920418			−0.0354532
$675$	−4.13777	+	18.6823i	−0.159263	+	0.719081i
$676$	−5.05314			−0.194352
$677$	−17.6853	+	30.6318i	−0.679700	+	1.17727i	0.295372	+	0.955382i	$0.404557\pi$
$677$	−17.6853	+	30.6318i	−0.679700	+	1.17727i	−0.975071	+	0.221892i	$0.928777\pi$
$678$	−4.66286	−	6.45638i	−0.179076	−	0.247956i
$679$	15.5082	+	26.8610i	0.595151	+	1.03083i
$680$	−1.20451	−	2.08627i	−0.0461908	−	0.0800048i
$681$	−22.5954	+	2.30998i	−0.865857	+	0.0885188i
$682$	−7.72681	+	13.3832i	−0.295875	+	0.512470i
$683$	−10.6601			−0.407898			−0.203949	−	0.978981i	$-0.565378\pi$
$683$	−10.6601			−0.407898			−0.203949	+	0.978981i	$0.565378\pi$
$684$	−2.21569	+	0.457817i	−0.0847191	+	0.0175051i
$685$	−14.5797			−0.557060
$686$	1.26249	−	2.18670i	0.0482021	−	0.0834886i
$687$	0.235748	−	0.525476i	0.00899434	−	0.0200481i
$688$	4.40420	+	7.62830i	0.167909	+	0.290826i
$689$	−26.5587	−	46.0010i	−1.01181	−	1.75250i
$690$	−1.08481	+	2.41801i	−0.0412979	+	0.0920519i
$691$	4.30737	−	7.46059i	0.163860	−	0.283814i	−0.772390	−	0.635149i	$-0.780939\pi$
$691$	4.30737	−	7.46059i	0.163860	−	0.283814i	0.936250	+	0.351335i	$0.114272\pi$
$692$	−14.3317			−0.544809
$693$	−67.0538	+	13.8550i	−2.54716	+	0.526307i
$694$	−5.13534			−0.194935
$695$	11.7842	−	20.4109i	0.447002	−	0.774230i
$696$	2.39113	−	0.244452i	0.0906356	−	0.00926591i
$697$	−2.22202	−	3.84866i	−0.0841651	−	0.145778i
$698$	−1.54010	−	2.66753i	−0.0582937	−	0.100968i
$699$	19.1480	+	26.5131i	0.724245	+	1.00282i
$700$	−13.2476	+	22.9454i	−0.500710	+	0.867256i
$701$	−20.3495			−0.768590			−0.384295	−	0.923210i	$-0.625555\pi$
$701$	−20.3495			−0.768590			−0.384295	+	0.923210i	$0.625555\pi$
$702$	8.21975	−	2.59352i	0.310234	−	0.0978859i
$703$	3.01734			0.113801
$704$	−11.9038	+	20.6180i	−0.448641	+	0.777068i
$705$	−10.3514	−	14.3329i	−0.389856	−	0.539809i
$706$	−4.54690	−	7.87546i	−0.171125	−	0.296397i
$707$	20.6099	+	35.6975i	0.775117	+	1.34254i
$708$	3.14547	−	0.321569i	0.118214	−	0.0120853i
$709$	1.87425	−	3.24630i	0.0703891	−	0.121918i	−0.828683	−	0.559719i	$-0.810909\pi$
$709$	1.87425	−	3.24630i	0.0703891	−	0.121918i	0.899072	+	0.437801i	$0.144243\pi$
$710$	1.19371			0.0447992
$711$	−6.01053	−	6.75214i	−0.225413	−	0.253225i
$712$	−4.62125			−0.173189
$713$	10.1933	−	17.6553i	0.381741	−	0.661195i
$714$	1.53304	−	3.41710i	0.0573725	−	0.127882i
$715$	−13.1969	−	22.8578i	−0.493537	−	0.854832i
$716$	6.16007	+	10.6696i	0.230213	+	0.398740i
$717$	−13.6101	+	30.3365i	−0.508278	+	1.13294i
$718$	−4.80182	+	8.31699i	−0.179202	+	0.310387i
$719$	5.88942			0.219638			0.109819	−	0.993952i	$-0.464973\pi$
$719$	5.88942			0.219638			0.109819	+	0.993952i	$0.464973\pi$
$720$	3.23010	−	9.75232i	0.120379	−	0.363448i
$721$	−37.3814			−1.39215
$722$	−3.93279	+	6.81179i	−0.146363	+	0.253508i
$723$	−13.2492	+	1.35450i	−0.492744	+	0.0503745i
$724$	2.18606	+	3.78637i	0.0812444	+	0.140719i
$725$	−1.59894	−	2.76945i	−0.0593833	−	0.102855i
$726$	−9.54581	−	13.2175i	−0.354278	−	0.490547i
$727$	−23.8388	+	41.2899i	−0.884130	+	1.53136i	−0.0374231	+	0.999300i	$0.511915\pi$
$727$	−23.8388	+	41.2899i	−0.884130	+	1.53136i	−0.846707	+	0.532059i	$0.821418\pi$
$728$	25.0098			0.926925
$729$	22.1108	−	15.4956i	0.818919	−	0.573910i
$730$	−2.88404			−0.106743
$731$	−1.93880	+	3.35810i	−0.0717090	+	0.124204i
$732$	−6.00228	−	8.31099i	−0.221851	−	0.307183i
$733$	18.8635	+	32.6725i	0.696739	+	1.20679i	0.969591	+	0.244731i	$0.0786997\pi$
$733$	18.8635	+	32.6725i	0.696739	+	1.20679i	−0.272852	+	0.962056i	$0.587967\pi$
$734$	−1.77659	−	3.07715i	−0.0655752	−	0.113580i
$735$	16.8775	−	1.72543i	0.622535	−	0.0636434i
$736$	−7.08817	+	12.2771i	−0.261273	+	0.452539i
$737$	71.3923			2.62977
$738$	−1.33326	+	4.02537i	−0.0490779	+	0.148176i
$739$	−32.2093			−1.18484			−0.592419	−	0.805630i	$-0.701827\pi$
$739$	−32.2093			−1.18484			−0.592419	+	0.805630i	$0.701827\pi$
$740$	−7.65177	+	13.2533i	−0.281285	+	0.487199i
$741$	1.16308	−	2.59247i	0.0427267	−	0.0952367i
$742$	11.0116	+	19.0726i	0.404248	+	0.700178i
$743$	6.10650	+	10.5768i	0.224026	+	0.388024i	0.956027	−	0.293279i	$-0.0947466\pi$
$743$	6.10650	+	10.5768i	0.224026	+	0.388024i	−0.732001	+	0.681304i	$0.761413\pi$
$744$	7.23785	−	16.1330i	0.265353	−	0.591463i
$745$	5.70016	−	9.87297i	0.208838	−	0.361718i
$746$	4.27074			0.156363
$747$	25.9182	+	29.1161i	0.948298	+	1.06530i
$748$	−13.8839			−0.507646
$749$	−14.8573	+	25.7335i	−0.542873	+	0.940283i
$750$	7.17323	−	0.733338i	0.261929	−	0.0267777i
$751$	−12.4354	−	21.5388i	−0.453775	−	0.785962i	0.544842	−	0.838539i	$-0.316590\pi$
$751$	−12.4354	−	21.5388i	−0.453775	−	0.785962i	−0.998617	+	0.0525772i	$0.983256\pi$
$752$	−13.2661	−	22.9775i	−0.483765	−	0.837905i
$753$	0.0473887	+	0.0656162i	0.00172694	+	0.00239119i
$754$	−0.720230	+	1.24748i	−0.0262292	+	0.0454304i
$755$	−21.7071			−0.790002
$756$	35.6527	−	11.2492i	1.29668	−	0.409131i
$757$	27.8241			1.01128			0.505642	−	0.862744i	$-0.331256\pi$
$757$	27.8241			1.01128			0.505642	+	0.862744i	$0.331256\pi$
$758$	2.95298	−	5.11471i	0.107257	−	0.185775i
$759$	18.7401	+	25.9483i	0.680223	+	0.941863i
$760$	0.378886	+	0.656249i	0.0137436	+	0.0238047i
$761$	2.74022	+	4.74620i	0.0993329	+	0.172050i	0.911409	−	0.411502i	$-0.134996\pi$
$761$	2.74022	+	4.74620i	0.0993329	+	0.172050i	−0.812076	+	0.583552i	$0.801662\pi$
$762$	−11.2504	+	1.15015i	−0.407558	+	0.0416657i
$763$	38.7192	−	67.0636i	1.40173	−	2.42786i
$764$	44.6777			1.61638
$765$	4.42893	−	0.915126i	0.160128	−	0.0330865i
$766$	−7.74799			−0.279946
$767$	−1.98545	+	3.43890i	−0.0716905	+	0.124172i
$768$	2.68963	−	5.99511i	0.0970537	−	0.216330i
$769$	−10.8550	−	18.8015i	−0.391443	−	0.677998i	0.601197	−	0.799100i	$-0.294691\pi$
$769$	−10.8550	−	18.8015i	−0.391443	−	0.677998i	−0.992640	+	0.121102i	$0.961357\pi$
$770$	5.47162	+	9.47712i	0.197184	+	0.341532i
$771$	14.0117	−	31.2318i	0.504620	−	1.12478i
$772$	20.9094	−	36.2161i	0.752546	−	1.30345i
$773$	−33.3972			−1.20121			−0.600607	−	0.799544i	$-0.705074\pi$
$773$	−33.3972			−1.20121			−0.600607	+	0.799544i	$0.705074\pi$
$774$	3.62339	−	0.748682i	0.130240	−	0.0269108i
$775$	−23.5254			−0.845059
$776$	6.28796	−	10.8911i	0.225724	−	0.390966i
$777$	−49.5998	+	5.07071i	−1.77938	+	0.181911i
$778$	2.98537	+	5.17082i	0.107031	+	0.185383i
$779$	0.698951	+	1.21062i	0.0250425	+	0.0433749i
$780$	8.43757	+	11.6830i	0.302114	+	0.418318i
$781$	7.20854	−	12.4856i	0.257942	−	0.446769i
$782$	−1.75079			−0.0626081
$783$	−0.975745	+	4.40554i	−0.0348703	+	0.157441i
$784$	25.4598			0.909279
$785$	10.9579	−	18.9797i	0.391105	−	0.677413i
$786$	−4.29460	−	5.94647i	−0.153183	−	0.212104i
$787$	19.4904	+	33.7584i	0.694758	+	1.20336i	0.970262	+	0.242056i	$0.0778218\pi$
$787$	19.4904	+	33.7584i	0.694758	+	1.20336i	−0.275504	+	0.961300i	$0.588845\pi$
$788$	7.26124	+	12.5768i	0.258671	+	0.448031i
$789$	−14.4508	+	1.47734i	−0.514462	+	0.0525948i
$790$	−0.722391	+	1.25122i	−0.0257015	+	0.0445164i
$791$	43.3828			1.54252
$792$	18.4588	+	20.7363i	0.655905	+	0.736833i
$793$	12.8750			0.457205
$794$	4.55640	−	7.89192i	0.161701	−	0.280074i
$795$	−10.8856	+	24.2637i	−0.386072	+	0.860544i
$796$	−1.15919	−	2.00777i	−0.0410863	−	0.0711636i
$797$	−16.3088	−	28.2478i	−0.577689	−	1.00059i	−0.995744	−	0.0921649i	$-0.970621\pi$
$797$	−16.3088	−	28.2478i	−0.577689	−	1.00059i	0.418055	−	0.908422i	$-0.362712\pi$
$798$	−0.482227	+	1.07487i	−0.0170706	+	0.0380500i
$799$	5.83994	−	10.1151i	0.206602	−	0.357846i
$800$	16.3590			0.578379
$801$	2.72773	−	8.23557i	0.0963797	−	0.290990i
$802$	−3.67564			−0.129791
$803$	−17.4160	+	30.1655i	−0.614598	+	1.06452i
$804$	−38.7787	+	3.96445i	−1.36762	+	0.139815i
$805$	−7.21821	−	12.5023i	−0.254408	−	0.440648i
$806$	5.29842	+	9.17713i	0.186629	+	0.323251i
$807$	10.9657	+	15.1835i	0.386010	+	0.534484i
$808$	8.35649	−	14.4739i	0.293980	−	0.509189i
$809$	28.5055			1.00220			0.501100	−	0.865390i	$-0.332929\pi$
$809$	28.5055			1.00220			0.501100	+	0.865390i	$0.332929\pi$
$810$	−3.46208	−	2.57596i	−0.121645	−	0.0905101i
$811$	−18.6973			−0.656550			−0.328275	−	0.944582i	$-0.606467\pi$
$811$	−18.6973			−0.656550			−0.328275	+	0.944582i	$0.606467\pi$
$812$	−3.12396	+	5.41086i	−0.109629	+	0.189884i
$813$	7.84731	+	10.8657i	0.275217	+	0.381076i
$814$	−8.83383	−	15.3006i	−0.309626	−	0.536287i
$815$	9.95669	+	17.2455i	0.348768	+	0.604084i
$816$	6.75163	−	0.690237i	0.236354	−	0.0241631i
$817$	0.609861	−	1.05631i	0.0213364	−	0.0369556i
$818$	−3.87632			−0.135532
$819$	−14.7622	+	44.5702i	−0.515834	+	1.55741i
$820$	−7.08998			−0.247593
$821$	−7.17723	+	12.4313i	−0.250487	+	0.433856i	−0.963660	−	0.267132i	$-0.913924\pi$
$821$	−7.17723	+	12.4313i	−0.250487	+	0.433856i	0.713173	+	0.700988i	$0.247257\pi$
$822$	−3.76190	+	8.38518i	−0.131211	+	0.292467i
$823$	−9.28070	−	16.0746i	−0.323505	−	0.560327i	0.657704	−	0.753277i	$-0.271528\pi$
$823$	−9.28070	−	16.0746i	−0.323505	−	0.560327i	−0.981209	+	0.192950i	$0.938195\pi$
$824$	7.57831	+	13.1260i	0.264003	+	0.457266i
$825$	15.1191	−	33.7000i	0.526378	−	1.17328i
$826$	0.823194	−	1.42581i	0.0286426	−	0.0496104i
$827$	−42.6739			−1.48392			−0.741958	−	0.670446i	$-0.766103\pi$
$827$	−42.6739			−1.48392			−0.741958	+	0.670446i	$0.766103\pi$
$828$	−11.6201	−	13.0539i	−0.403827	−	0.453653i
$829$	−16.0132			−0.556161			−0.278081	−	0.960558i	$-0.589698\pi$
$829$	−16.0132			−0.556161			−0.278081	+	0.960558i	$0.589698\pi$
$830$	3.11505	−	5.39542i	0.108125	−	0.187278i
$831$	3.26721	−	0.334015i	0.113338	−	0.0115869i
$832$	8.16264	+	14.1381i	0.282989	+	0.490151i
$833$	5.60390	+	9.70624i	0.194164	+	0.336301i
$834$	−8.69828	−	12.0440i	−0.301197	−	0.417048i
$835$	1.24783	−	2.16130i	0.0431829	−	0.0747950i
$836$	4.36727			0.151045
$837$	24.4785	+	22.4213i	0.846101	+	0.774992i
$838$	−2.89711			−0.100079
$839$	−4.99872	+	8.65804i	−0.172575	+	0.298909i	−0.939319	−	0.343044i	$-0.888542\pi$
$839$	−4.99872	+	8.65804i	−0.172575	+	0.298909i	0.766744	+	0.641953i	$0.221875\pi$
$840$	−7.33106	−	10.1509i	−0.252945	−	0.350238i
$841$	14.1229	+	24.4617i	0.486998	+	0.843506i
$842$	3.07546	+	5.32686i	0.105987	+	0.183576i
$843$	−4.90304	+	0.501250i	−0.168870	+	0.0172640i
$844$	−1.25478	+	2.17335i	−0.0431915	+	0.0748098i
$845$	−3.17724			−0.109300
$846$	−10.9142	+	2.25514i	−0.375237	+	0.0775333i
$847$	88.8133			3.05166
$848$	−19.9544	+	34.5620i	−0.685236	+	1.18686i
$849$	−4.17600	+	9.30820i	−0.143320	+	0.319457i
$850$	1.01018	+	1.74968i	0.0346488	+	0.0600135i
$851$	11.6537	+	20.1847i	0.399483	+	0.691924i
$852$	−3.22219	+	7.18217i	−0.110390	+	0.246057i
$853$	1.25284	−	2.16997i	0.0428963	−	0.0742985i	−0.843780	−	0.536689i	$-0.819675\pi$
$853$	1.25284	−	2.16997i	0.0428963	−	0.0742985i	0.886676	+	0.462391i	$0.153008\pi$
$854$	−5.33815			−0.182668
$855$	−1.39315	+	0.287859i	−0.0476446	+	0.00984456i
$856$	12.0480			0.411793
$857$	−22.0445	+	38.1822i	−0.753026	+	1.30428i	0.193324	+	0.981135i	$0.438073\pi$
$857$	−22.0445	+	38.1822i	−0.753026	+	1.30428i	−0.946350	+	0.323144i	$0.895260\pi$
$858$	−16.5513	+	1.69208i	−0.565051	+	0.0577667i
$859$	18.1221	+	31.3884i	0.618319	+	1.07096i	0.989792	+	0.142516i	$0.0455193\pi$
$859$	18.1221	+	31.3884i	0.618319	+	1.07096i	−0.371474	+	0.928444i	$0.621147\pi$
$860$	3.09314	+	5.35747i	0.105475	+	0.182688i
$861$	−13.5240	−	18.7258i	−0.460897	−	0.638175i
$862$	5.73506	−	9.93342i	0.195337	−	0.338334i
$863$	17.0056			0.578876			0.289438	−	0.957197i	$-0.406532\pi$
$863$	17.0056			0.578876			0.289438	+	0.957197i	$0.406532\pi$
$864$	−17.0218	−	15.5912i	−0.579093	−	0.530424i
$865$	−9.01124			−0.306391
$866$	−8.27852	+	14.3388i	−0.281316	+	0.487253i
$867$	−15.4903	−	21.4484i	−0.526077	−	0.728426i
$868$	22.9816	+	39.8053i	0.780046	+	1.35108i
$869$	8.72471	+	15.1116i	0.295965	+	0.512627i
$870$	0.717439	−	0.0733456i	0.0243234	−	0.00248665i
$871$	24.4775	−	42.3963i	0.829389	−	1.43654i
$872$	−31.3981			−1.06327
$873$	15.6975	+	17.6344i	0.531281	+	0.596832i
$874$	0.550722			0.0186285
$875$	−19.6392	+	34.0160i	−0.663925	+	1.14995i
$876$	7.78489	−	17.3523i	0.263027	−	0.586280i
$877$	−21.5482	−	37.3226i	−0.727631	−	1.26029i	−0.957882	−	0.287163i	$-0.907288\pi$
$877$	−21.5482	−	37.3226i	−0.727631	−	1.26029i	0.230251	−	0.973131i	$-0.426045\pi$
$878$	−1.37716	−	2.38530i	−0.0464768	−	0.0805001i
$879$	16.9691	−	37.8236i	0.572353	−	1.27576i
$880$	−9.91525	+	17.1737i	−0.334243	+	0.578926i
$881$	−44.0821			−1.48516			−0.742582	−	0.669755i	$-0.766399\pi$
$881$	−44.0821			−1.48516			−0.742582	+	0.669755i	$0.766399\pi$
$882$	3.36245	−	10.1519i	0.113220	−	0.341833i
$883$	10.2962			0.346496			0.173248	−	0.984878i	$-0.444574\pi$
$883$	10.2962			0.346496			0.173248	+	0.984878i	$0.444574\pi$
$884$	−4.76023	+	8.24495i	−0.160104	+	0.277308i
$885$	1.97776	−	0.202191i	0.0664815	−	0.00679658i
$886$	2.87245	+	4.97522i	0.0965017	+	0.167146i
$887$	21.3070	+	36.9047i	0.715418	+	1.23914i	0.962798	+	0.270221i	$0.0870969\pi$
$887$	21.3070	+	36.9047i	0.715418	+	1.23914i	−0.247381	+	0.968918i	$0.579570\pi$
$888$	11.8359	+	16.3884i	0.397185	+	0.549958i
$889$	30.8017	−	53.3501i	1.03306	−	1.78931i
$890$	−1.38657			−0.0464779
$891$	−47.8498	+	20.6558i	−1.60303	+	0.691995i
$892$	−39.7890			−1.33223
$893$	−1.83699	+	3.18176i	−0.0614726	+	0.106474i
$894$	−4.20745	−	5.82579i	−0.140718	−	0.194844i
$895$	3.87323	+	6.70863i	0.129468	+	0.224245i
$896$	−20.8928	−	36.1874i	−0.697979	−	1.20894i
$897$	21.8346	−	2.23221i	0.729036	−	0.0745312i
$898$	−5.33854	+	9.24662i	−0.178149	+	0.308564i
$899$	−5.54763			−0.185024
$900$	−6.34096	+	19.1446i	−0.211365	+	0.638154i
$901$	−17.5684			−0.585290
$902$	4.09262	−	7.08863i	0.136269	−	0.236026i
$903$	−8.24989	+	18.3888i	−0.274539	+	0.611940i
$904$	−8.79499	−	15.2334i	−0.292517	−	0.506654i
$905$	1.37452	+	2.38073i	0.0456905	+	0.0791383i
$906$	−5.60096	+	12.4844i	−0.186079	+	0.414766i
$907$	0.223570	−	0.387234i	0.00742351	−	0.0128579i	−0.862290	−	0.506415i	$-0.830970\pi$
$907$	0.223570	−	0.387234i	0.00742351	−	0.0128579i	0.869713	+	0.493557i	$0.164304\pi$
$908$	−23.9386			−0.794431
$909$	20.8615	+	23.4355i	0.691933	+	0.777306i
$910$	7.50398			0.248755
$911$	−9.25045	+	16.0222i	−0.306481	+	0.530841i	−0.977590	−	0.210518i	$-0.932485\pi$
$911$	−9.25045	+	16.0222i	−0.306481	+	0.530841i	0.671109	+	0.741359i	$0.265818\pi$
$912$	−2.12377	+	0.217119i	−0.0703251	+	0.00718952i
$913$	−37.6221	−	65.1634i	−1.24511	−	2.15659i
$914$	2.39801	+	4.15348i	0.0793193	+	0.137385i
$915$	−3.77402	−	5.22565i	−0.124765	−	0.172755i
$916$	0.303505	−	0.525686i	0.0100281	−	0.0173691i
$917$	39.9566			1.31948
$918$	0.616455	−	2.78333i	0.0203460	−	0.0918635i
$919$	22.1500			0.730661			0.365331	−	0.930878i	$-0.380956\pi$
$919$	22.1500			0.730661			0.365331	+	0.930878i	$0.380956\pi$
$920$	−2.92669	+	5.06917i	−0.0964901	+	0.167126i
$921$	32.6025	+	45.1426i	1.07429	+	1.48750i
$922$	−2.51364	−	4.35375i	−0.0827822	−	0.143383i
$923$	−4.94303	−	8.56158i	−0.162702	−	0.281808i
$924$	−71.7903	+	7.33931i	−2.36173	+	0.241446i
$925$	13.4480	−	23.2926i	0.442166	−	0.765855i
$926$	14.4595			0.475169
$927$	−27.8651	+	5.75763i	−0.915211	+	0.189105i
$928$	3.85769			0.126635
$929$	−20.2843	+	35.1335i	−0.665507	+	1.15269i	0.313640	+	0.949542i	$0.398451\pi$
$929$	−20.2843	+	35.1335i	−0.665507	+	1.15269i	−0.979147	+	0.203151i	$0.934882\pi$
$930$	2.17166	−	4.84056i	0.0712114	−	0.158728i
$931$	−1.76274	−	3.05316i	−0.0577716	−	0.100063i
$932$	17.2346	+	29.8511i	0.564537	+	0.977806i
$933$	−16.2340	+	36.1851i	−0.531476	+	1.18465i
$934$	−4.50063	+	7.79532i	−0.147265	+	0.255071i
$935$	−8.72970			−0.285492
$936$	18.6430	−	3.85211i	0.609366	−	0.125910i
$937$	23.6715			0.773315			0.386657	−	0.922223i	$-0.373630\pi$
$937$	23.6715			0.773315			0.386657	+	0.922223i	$0.373630\pi$
$938$	−10.1487	+	17.5781i	−0.331367	+	0.573944i
$939$	−46.1685	+	4.71993i	−1.50665	+	0.154029i
$940$	−9.31697	−	16.1375i	−0.303886	−	0.526346i
$941$	9.20449	+	15.9426i	0.300058	+	0.519715i	0.976149	−	0.217103i	$-0.0696607\pi$
$941$	9.20449	+	15.9426i	0.300058	+	0.519715i	−0.676091	+	0.736818i	$0.736327\pi$
$942$	−8.08834	−	11.1994i	−0.263532	−	0.364897i
$943$	−5.39903	+	9.35139i	−0.175816	+	0.304523i
$944$	2.98346			0.0971034
$945$	22.4171	−	7.07311i	0.729230	−	0.230088i
$946$	−7.14194			−0.232204
$947$	−11.3771	+	19.7057i	−0.369705	+	0.640348i	−0.989519	−	0.144401i	$-0.953875\pi$
$947$	−11.3771	+	19.7057i	−0.369705	+	0.640348i	0.619814	+	0.784749i	$0.287208\pi$
$948$	−5.57822	−	7.72381i	−0.181172	−	0.250858i
$949$	11.9425	+	20.6850i	0.387670	+	0.671464i
$950$	−0.317758	−	0.550373i	−0.0103094	−	0.0178565i
$951$	−5.55224	+	0.567620i	−0.180044	+	0.0184063i
$952$	4.13596	−	7.16370i	0.134047	−	0.232177i
$953$	17.8027			0.576687			0.288343	−	0.957527i	$-0.406896\pi$
$953$	17.8027			0.576687			0.288343	+	0.957527i	$0.406896\pi$
$954$	11.1460	+	12.5212i	0.360865	+	0.405390i
$955$	28.0917			0.909028
$956$	−17.5218	+	30.3486i	−0.566695	+	0.981544i
$957$	3.56529	−	7.94693i	0.115249	−	0.256888i
$958$	6.37743	+	11.0460i	0.206046	+	0.356881i
$959$	−25.0313	−	43.3556i	−0.808304	−	1.40002i
$960$	3.34561	−	7.45728i	0.107979	−	0.240683i
$961$	−4.90573	+	8.49698i	−0.158249	+	0.274096i
$962$	−12.1150			−0.390605
$963$	−7.11145	+	21.4709i	−0.229163	+	0.691890i
$964$	−14.0368			−0.452096
$965$	13.1471	−	22.7714i	0.423219	−	0.733038i
$966$	−9.05290	+	0.925502i	−0.291272	+	0.0297775i
$967$	22.7665	+	39.4327i	0.732121	+	1.26807i	0.955975	+	0.293448i	$0.0948028\pi$
$967$	22.7665	+	39.4327i	0.732121	+	1.26807i	−0.223854	+	0.974623i	$0.571864\pi$
$968$	−18.0051	−	31.1857i	−0.578706	−	1.00235i
$969$	−0.550232	−	0.761872i	−0.0176760	−	0.0244749i
$970$	1.88665	−	3.26777i	0.0605766	−	0.104922i
$971$	46.6192			1.49608			0.748040	−	0.663653i	$-0.230995\pi$
$971$	46.6192			1.49608			0.748040	+	0.663653i	$0.230995\pi$
$972$	24.8439	−	13.8769i	0.796868	−	0.445101i
$973$	80.9280			2.59443
$974$	−4.32051	+	7.48335i	−0.138438	+	0.239782i
$975$	−14.8290	−	20.5328i	−0.474908	−	0.657576i
$976$	−4.83669	−	8.37740i	−0.154819	−	0.268154i
$977$	−15.7652	−	27.3061i	−0.504372	−	0.873599i	−0.999987	−	0.00505613i	$-0.998391\pi$
$977$	−15.7652	−	27.3061i	−0.504372	−	0.873599i	0.495615	−	0.868542i	$-0.334943\pi$
$978$	12.4874	−	1.27662i	0.399305	−	0.0408220i
$979$	−8.37316	+	14.5027i	−0.267607	+	0.463510i
$980$	17.8808			0.571181
$981$	18.5330	−	55.9548i	0.591713	−	1.78650i
$982$	−5.33353			−0.170200
$983$	14.4950	−	25.1061i	0.462320	−	0.800761i	−0.536756	−	0.843737i	$-0.680351\pi$
$983$	14.4950	−	25.1061i	0.462320	−	0.800761i	0.999076	+	0.0429760i	$0.0136839\pi$
$984$	−3.83364	+	8.54508i	−0.122212	+	0.272407i
$985$	4.56561	+	7.90786i	0.145472	+	0.251965i
$986$	0.238214	+	0.412599i	0.00758629	+	0.0131398i
$987$	24.8499	−	55.3897i	0.790980	−	1.76307i
$988$	1.49736	−	2.59350i	0.0476374	−	0.0825103i
$989$	9.42171			0.299593
$990$	5.53841	+	6.22176i	0.176022	+	0.197740i
$991$	6.78731			0.215606			0.107803	−	0.994172i	$-0.465618\pi$
$991$	6.78731			0.215606			0.107803	+	0.994172i	$0.465618\pi$
$992$	14.1897	−	24.5772i	0.450522	−	0.780328i
$993$	−17.8821	+	1.82813i	−0.567471	+	0.0580140i
$994$	2.04944	+	3.54974i	0.0650044	+	0.112591i
$995$	−0.728856	−	1.26241i	−0.0231063	−	0.0400212i
$996$	24.0540	+	33.3061i	0.762181	+	1.05534i
$997$	−6.63037	+	11.4841i	−0.209986	+	0.363707i	−0.951710	−	0.306999i	$-0.900675\pi$
$997$	−6.63037	+	11.4841i	−0.209986	+	0.363707i	0.741724	+	0.670705i	$0.234009\pi$
$998$	10.5631			0.334370
$999$	−36.1921	+	11.4194i	−1.14507	+	0.361294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.e.c.178.20	✓	70
9.2	odd	6		4779.2.a.m.1.20		35
9.4	even	3	inner	531.2.e.c.355.20	yes	70
9.7	even	3		4779.2.a.n.1.16		35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.e.c.178.20	✓	70	1.1	even	1	trivial
531.2.e.c.355.20	yes	70	9.4	even	3	inner
4779.2.a.m.1.20		35	9.2	odd	6
4779.2.a.n.1.16		35	9.7	even	3

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.208865 - 0.361765i) q^{2} +(1.01409 + 1.40415i) q^{3} +(0.912751 + 1.58093i) q^{4} +(0.573905 + 0.994032i) q^{5} +(0.719778 - 0.0735848i) q^{6} +(-1.97064 + 3.41324i) q^{7} +1.59803 q^{8} +(-0.943248 + 2.84786i) q^{9} +0.479474 q^{10} +(2.89543 - 5.01504i) q^{11} +(-1.29425 + 2.88484i) q^{12} +(-1.98545 - 3.43890i) q^{13} +(0.823194 + 1.42581i) q^{14} +(-0.813775 + 1.81388i) q^{15} +(-1.49173 + 2.58375i) q^{16} -1.31337 q^{17} +(0.833242 + 0.936051i) q^{18} +0.413128 q^{19} +(-1.04766 + 1.81461i) q^{20} +(-6.79109 + 0.694271i) q^{21} +(-1.20951 - 2.09493i) q^{22} +(1.59560 + 2.76365i) q^{23} +(1.62054 + 2.24386i) q^{24} +(1.84127 - 3.18917i) q^{25} -1.65877 q^{26} +(-4.95534 + 1.56352i) q^{27} -7.19480 q^{28} +(0.434197 - 0.752050i) q^{29} +(0.486230 + 0.673252i) q^{30} +(-3.19419 - 5.53250i) q^{31} +(2.22117 + 3.84717i) q^{32} +(9.97807 - 1.02008i) q^{33} +(-0.274316 + 0.475129i) q^{34} -4.52383 q^{35} +(-5.36321 + 1.10817i) q^{36} +7.30365 q^{37} +(0.0862879 - 0.149455i) q^{38} +(2.81530 - 6.27522i) q^{39} +(0.917115 + 1.58849i) q^{40} +(1.69185 + 2.93038i) q^{41} +(-1.16726 + 2.60179i) q^{42} +(1.47621 - 2.55686i) q^{43} +10.5712 q^{44} +(-3.37220 + 0.696779i) q^{45} +1.33306 q^{46} +(-4.44655 + 7.70164i) q^{47} +(-5.14071 + 0.525548i) q^{48} +(-4.26682 - 7.39036i) q^{49} +(-0.769152 - 1.33221i) q^{50} +(-1.33187 - 1.84416i) q^{51} +(3.62445 - 6.27773i) q^{52} +13.3767 q^{53} +(-0.469370 + 2.11923i) q^{54} +6.64682 q^{55} +(-3.14913 + 5.45445i) q^{56} +(0.418948 + 0.580091i) q^{57} +(-0.181377 - 0.314154i) q^{58} +(-0.500000 - 0.866025i) q^{59} +(-3.61040 + 0.369100i) q^{60} +(-1.62117 + 2.80795i) q^{61} -2.66862 q^{62} +(-7.86163 - 8.83163i) q^{63} -4.11122 q^{64} +(2.27892 - 3.94721i) q^{65} +(1.71504 - 3.82277i) q^{66} +(6.16422 + 10.6767i) q^{67} +(-1.19878 - 2.07634i) q^{68} +(-2.26249 + 5.04304i) q^{69} +(-0.944870 + 1.63656i) q^{70} +2.48962 q^{71} +(-1.50734 + 4.55095i) q^{72} -6.01500 q^{73} +(1.52548 - 2.64220i) q^{74} +(6.34526 - 0.648693i) q^{75} +(0.377083 + 0.653126i) q^{76} +(11.4117 + 19.7657i) q^{77} +(-1.68214 - 2.32915i) q^{78} +(-1.50663 + 2.60956i) q^{79} -3.42444 q^{80} +(-7.22057 - 5.37247i) q^{81} +1.41348 q^{82} +(6.49680 - 11.2528i) q^{83} +(-7.29617 - 10.1026i) q^{84} +(-0.753747 - 1.30553i) q^{85} +(-0.616655 - 1.06808i) q^{86} +(1.49630 - 0.152971i) q^{87} +(4.62698 - 8.01417i) q^{88} -2.89185 q^{89} +(-0.452263 + 1.36547i) q^{90} +15.6504 q^{91} +(-2.91276 + 5.04505i) q^{92} +(4.52924 - 10.0956i) q^{93} +(1.85746 + 3.21721i) q^{94} +(0.237096 + 0.410662i) q^{95} +(-3.14953 + 7.02022i) q^{96} +(3.93483 - 6.81532i) q^{97} -3.56476 q^{98} +(11.5510 + 12.9762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 44 q^{4} - 2 q^{5} + 4 q^{6} - 11 q^{7} + 2 q^{9} + 20 q^{10} + 2 q^{11} - 23 q^{13} + 2 q^{14} - 5 q^{15} - 62 q^{16} - 4 q^{17} - q^{18} + 46 q^{19} + q^{20} + 16 q^{21} - 16 q^{22} - 42 q^{24}+ \cdots - 37 q^{99}+O(q^{100}) \) 70 * q - 44 * q^4 - 2 * q^5 + 4 * q^6 - 11 * q^7 + 2 * q^9 + 20 * q^10 + 2 * q^11 - 23 * q^13 + 2 * q^14 - 5 * q^15 - 62 * q^16 - 4 * q^17 - q^18 + 46 * q^19 + q^20 + 16 * q^21 - 16 * q^22 - 42 * q^24 - 59 * q^25 - 12 * q^26 - 12 * q^27 + 68 * q^28 - q^29 + 69 * q^30 - 24 * q^31 + 10 * q^32 - 22 * q^33 - 30 * q^34 + 64 * q^35 - 38 * q^36 + 86 * q^37 + 2 * q^38 + 25 * q^39 - 36 * q^40 - 6 * q^41 - 52 * q^42 - 34 * q^43 - 72 * q^44 - 5 * q^45 + 80 * q^46 - 6 * q^47 + 61 * q^48 - 66 * q^49 - 12 * q^50 - 36 * q^51 - 48 * q^52 - 4 * q^53 - 46 * q^54 + 48 * q^55 - 14 * q^56 + 57 * q^57 - 26 * q^58 - 35 * q^59 - 32 * q^60 - 67 * q^61 + 102 * q^62 - 35 * q^63 + 208 * q^64 + 15 * q^65 + 157 * q^66 - 37 * q^67 + 25 * q^68 + 10 * q^69 - 22 * q^70 - 36 * q^71 - 136 * q^72 + 86 * q^73 + 11 * q^74 + 28 * q^75 - 76 * q^76 + 28 * q^77 - 67 * q^78 - 41 * q^79 + 6 * q^80 - 50 * q^81 + 64 * q^82 + 3 * q^83 + 164 * q^84 - 94 * q^85 - 36 * q^86 + 43 * q^87 - 48 * q^88 - 16 * q^89 - 84 * q^90 + 98 * q^91 + q^92 - 19 * q^93 - 34 * q^94 + 37 * q^95 - 7 * q^96 - 41 * q^97 - 106 * q^98 - 37 * q^99

Introduction

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