LMFDB - Embedded newform 930.2.y.b.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.60770 - 0.644430i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.22659 - 1.86962i) q^{5} +(-0.921873 - 1.46634i) q^{6} +(3.97153 - 1.29043i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.16942 + 2.07210i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60770 - 0.644430i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.22659 - 1.86962i) q^{5} +(-0.921873 - 1.46634i) q^{6} +(3.97153 - 1.29043i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.16942 + 2.07210i) q^{9} +(2.09127 - 0.791586i) q^{10} +(-0.533628 - 1.64234i) q^{11} +(0.116082 - 1.72816i) q^{12} +(1.61250 - 1.17155i) q^{13} +(3.97153 + 1.29043i) q^{14} +(-3.17683 + 2.21535i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-6.59273 - 2.14211i) q^{17} +(0.537145 + 2.95152i) q^{18} +(2.54582 + 1.84965i) q^{19} +(2.15715 + 0.588809i) q^{20} +(-7.21664 - 0.484747i) q^{21} +(0.533628 - 1.64234i) q^{22} +(-5.09370 - 1.65504i) q^{23} +(1.10970 - 1.32988i) q^{24} +(-1.99097 - 4.58651i) q^{25} +1.99315 q^{26} +(-2.15246 - 4.72937i) q^{27} +(2.45454 + 3.37839i) q^{28} +(6.72629 + 4.88694i) q^{29} +(-3.87226 - 0.0750387i) q^{30} +(5.29700 + 1.71517i) q^{31} -1.00000 q^{32} +(-0.200456 + 2.98428i) q^{33} +(-4.07453 - 5.60811i) q^{34} +(2.45881 - 9.00808i) q^{35} +(-1.30030 + 2.70356i) q^{36} -1.82468 q^{37} +(0.972416 + 2.99279i) q^{38} +(-3.34739 + 0.844359i) q^{39} +(1.39908 + 1.74430i) q^{40} +(4.31621 - 5.94076i) q^{41} +(-5.55345 - 4.63400i) q^{42} +(-2.23730 - 1.62549i) q^{43} +(1.39706 - 1.01502i) q^{44} +(6.53503 - 1.51438i) q^{45} +(-3.14808 - 4.33296i) q^{46} +(7.50569 - 5.45320i) q^{47} +(1.67945 - 0.423630i) q^{48} +(8.44474 - 6.13546i) q^{49} +(1.08515 - 4.88082i) q^{50} +(9.21871 + 7.69243i) q^{51} +(1.61250 + 1.17155i) q^{52} +(7.31127 + 2.37558i) q^{53} +(1.03848 - 5.09132i) q^{54} +(-3.72509 - 1.01679i) q^{55} +4.17592i q^{56} +(-2.90095 - 4.61428i) q^{57} +(2.56921 + 7.90723i) q^{58} +(-6.67417 - 9.18620i) q^{59} +(-3.08861 - 2.33676i) q^{60} +13.0269i q^{61} +(3.27721 + 4.50110i) q^{62} +(11.2898 + 5.42995i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.212483 - 4.45176i) q^{65} +(-1.91629 + 2.29651i) q^{66} -7.86369i q^{67} -6.93201i q^{68} +(7.12260 + 5.94335i) q^{69} +(7.28404 - 5.84244i) q^{70} +(-7.73546 - 2.51340i) q^{71} +(-2.64108 + 1.42293i) q^{72} +(1.99959 + 6.15410i) q^{73} +(-1.47620 - 1.07252i) q^{74} +(0.245206 + 8.65678i) q^{75} +(-0.972416 + 2.99279i) q^{76} +(-4.23864 - 5.83399i) q^{77} +(-3.20440 - 1.28445i) q^{78} +(-9.74641 - 3.16680i) q^{79} +(0.106606 + 2.23353i) q^{80} +(0.412767 + 8.99053i) q^{81} +(6.98378 - 2.26917i) q^{82} +(0.428315 - 0.589524i) q^{83} +(-1.76904 - 7.01322i) q^{84} +(-12.0915 + 9.69843i) q^{85} +(-0.854571 - 2.63010i) q^{86} +(-7.66459 - 12.1914i) q^{87} +1.72686 q^{88} +(4.02056 + 12.3740i) q^{89} +(6.17708 + 2.61604i) q^{90} +(4.89228 - 6.73365i) q^{91} -5.35583i q^{92} +(-7.41070 - 6.17102i) q^{93} +9.27755 q^{94} +(6.58081 - 2.49097i) q^{95} +(1.60770 + 0.644430i) q^{96} +(4.17102 - 1.35525i) q^{97} +10.4383 q^{98} +(2.24543 - 4.66865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.60770	−	0.644430i	−0.928208	−	0.372062i
$3$	−1.60770	−	0.644430i	−0.928208	−	0.372062i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.22659	−	1.86962i	0.548546	−	0.836120i
$5$	1.22659	−	1.86962i	0.548546	−	0.836120i
$6$	−0.921873	−	1.46634i	−0.376353	−	0.598630i
$7$	3.97153	−	1.29043i	1.50110	−	0.487736i	0.560760	−	0.827978i	$-0.310509\pi$
$7$	3.97153	−	1.29043i	1.50110	−	0.487736i	0.940338	+	0.340242i	$0.110509\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.16942	+	2.07210i	0.723140	+	0.690701i
$10$	2.09127	−	0.791586i	0.661316	−	0.250321i
$11$	−0.533628	−	1.64234i	−0.160895	−	0.495183i	0.837816	−	0.545953i	$-0.183832\pi$
$11$	−0.533628	−	1.64234i	−0.160895	−	0.495183i	−0.998710	+	0.0507700i	$0.983832\pi$
$12$	0.116082	−	1.72816i	0.0335099	−	0.498876i
$13$	1.61250	−	1.17155i	0.447226	−	0.324929i	−0.341274	−	0.939964i	$-0.610858\pi$
$13$	1.61250	−	1.17155i	0.447226	−	0.324929i	0.788500	+	0.615035i	$0.210858\pi$
$14$	3.97153	+	1.29043i	1.06144	+	0.344882i
$15$	−3.17683	+	2.21535i	−0.820253	+	0.572000i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−6.59273	−	2.14211i	−1.59897	−	0.519537i	−0.632119	−	0.774871i	$-0.717815\pi$
$17$	−6.59273	−	2.14211i	−1.59897	−	0.519537i	−0.966853	+	0.255334i	$0.917815\pi$
$18$	0.537145	+	2.95152i	0.126606	+	0.695680i
$19$	2.54582	+	1.84965i	0.584051	+	0.424338i	0.840182	−	0.542304i	$-0.182448\pi$
$19$	2.54582	+	1.84965i	0.584051	+	0.424338i	−0.256131	+	0.966642i	$0.582448\pi$
$20$	2.15715	+	0.588809i	0.482354	+	0.131662i
$21$	−7.21664	−	0.484747i	−1.57480	−	0.105780i
$22$	0.533628	−	1.64234i	0.113770	−	0.350148i
$23$	−5.09370	−	1.65504i	−1.06211	−	0.345100i	−0.274700	−	0.961530i	$-0.588578\pi$
$23$	−5.09370	−	1.65504i	−1.06211	−	0.345100i	−0.787410	+	0.616430i	$0.788578\pi$
$24$	1.10970	−	1.32988i	0.226516	−	0.271460i
$25$	−1.99097	−	4.58651i	−0.398194	−	0.917301i
$26$	1.99315			0.390890
$27$	−2.15246	−	4.72937i	−0.414241	−	0.910167i
$28$	2.45454	+	3.37839i	0.463865	+	0.638455i
$29$	6.72629	+	4.88694i	1.24904	+	0.907481i	0.998166	−	0.0605385i	$-0.0192818\pi$
$29$	6.72629	+	4.88694i	1.24904	+	0.907481i	0.250875	+	0.968020i	$0.419282\pi$
$30$	−3.87226	−	0.0750387i	−0.706974	−	0.0137001i
$31$	5.29700	+	1.71517i	0.951369	+	0.308053i
$31$	5.29700	+	1.71517i	0.951369	+	0.308053i
$32$	−1.00000			−0.176777
$33$	−0.200456	+	2.98428i	−0.0348950	+	0.519496i
$34$	−4.07453	−	5.60811i	−0.698776	−	0.961783i
$35$	2.45881	−	9.00808i	0.415616	−	1.52264i
$36$	−1.30030	+	2.70356i	−0.216717	+	0.450593i
$37$	−1.82468			−0.299976			−0.149988	−	0.988688i	$-0.547923\pi$
$37$	−1.82468			−0.299976			−0.149988	+	0.988688i	$0.547923\pi$
$38$	0.972416	+	2.99279i	0.157747	+	0.485495i
$39$	−3.34739	+	0.844359i	−0.536012	+	0.135206i
$40$	1.39908	+	1.74430i	0.221214	+	0.275798i
$41$	4.31621	−	5.94076i	0.674079	−	0.927791i	−0.325765	−	0.945451i	$-0.605622\pi$
$41$	4.31621	−	5.94076i	0.674079	−	0.927791i	0.999844	+	0.0176603i	$0.00562175\pi$
$42$	−5.55345	−	4.63400i	−0.856917	−	0.715042i
$43$	−2.23730	−	1.62549i	−0.341185	−	0.247885i	0.403977	−	0.914769i	$-0.367628\pi$
$43$	−2.23730	−	1.62549i	−0.341185	−	0.247885i	−0.745161	+	0.666884i	$0.767628\pi$
$44$	1.39706	−	1.01502i	0.210614	−	0.153020i
$45$	6.53503	−	1.51438i	0.974185	−	0.225750i
$46$	−3.14808	−	4.33296i	−0.464159	−	0.638860i
$47$	7.50569	−	5.45320i	1.09482	−	0.795432i	0.114611	−	0.993410i	$-0.463438\pi$
$47$	7.50569	−	5.45320i	1.09482	−	0.795432i	0.980206	+	0.197979i	$0.0634377\pi$
$48$	1.67945	−	0.423630i	0.242407	−	0.0611457i
$49$	8.44474	−	6.13546i	1.20639	−	0.876494i
$50$	1.08515	−	4.88082i	0.153464	−	0.690253i
$51$	9.21871	+	7.69243i	1.29088	+	1.07716i
$52$	1.61250	+	1.17155i	0.223613	+	0.162464i
$53$	7.31127	+	2.37558i	1.00428	+	0.326311i	0.764575	−	0.644535i	$-0.222949\pi$
$53$	7.31127	+	2.37558i	1.00428	+	0.326311i	0.239706	+	0.970846i	$0.422949\pi$
$54$	1.03848	−	5.09132i	0.141319	−	0.692841i
$55$	−3.72509	−	1.01679i	−0.502291	−	0.137104i
$56$			4.17592i			0.558030i
$57$	−2.90095	−	4.61428i	−0.384241	−	0.611177i
$58$	2.56921	+	7.90723i	0.337354	+	1.03827i
$59$	−6.67417	−	9.18620i	−0.868902	−	1.19594i	−0.979373	−	0.202062i	$-0.935236\pi$
$59$	−6.67417	−	9.18620i	−0.868902	−	1.19594i	0.110470	−	0.993879i	$-0.464764\pi$
$60$	−3.08861	−	2.33676i	−0.398738	−	0.301675i
$61$			13.0269i			1.66792i	0.551822	+	0.833962i	$0.313933\pi$
$61$			13.0269i			1.66792i	−0.551822	+	0.833962i	$0.686067\pi$
$62$	3.27721	+	4.50110i	0.416207	+	0.571640i
$63$	11.2898	+	5.42995i	1.42238	+	0.684109i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.212483	−	4.45176i	−0.0263553	−	0.552173i
$66$	−1.91629	+	2.29651i	−0.235879	+	0.282680i
$67$		−	7.86369i		−	0.960702i	−0.877076	−	0.480351i	$-0.840509\pi$
$67$		−	7.86369i		−	0.960702i	0.877076	−	0.480351i	$-0.159491\pi$
$68$		−	6.93201i		−	0.840629i
$69$	7.12260	+	5.94335i	0.857460	+	0.715495i
$70$	7.28404	−	5.84244i	0.870610	−	0.698305i
$71$	−7.73546	−	2.51340i	−0.918030	−	0.298286i	−0.188372	−	0.982098i	$-0.560321\pi$
$71$	−7.73546	−	2.51340i	−0.918030	−	0.298286i	−0.729658	+	0.683812i	$0.760321\pi$
$72$	−2.64108	+	1.42293i	−0.311254	+	0.167693i
$73$	1.99959	+	6.15410i	0.234034	+	0.720283i	0.997248	+	0.0741370i	$0.0236202\pi$
$73$	1.99959	+	6.15410i	0.234034	+	0.720283i	−0.763214	+	0.646146i	$0.776380\pi$
$74$	−1.47620	−	1.07252i	−0.171605	−	0.124678i
$75$	0.245206	+	8.65678i	0.0283140	+	0.999599i
$76$	−0.972416	+	2.99279i	−0.111544	+	0.343297i
$77$	−4.23864	−	5.83399i	−0.483038	−	0.664844i
$78$	−3.20440	−	1.28445i	−0.362827	−	0.145435i
$79$	−9.74641	−	3.16680i	−1.09656	−	0.356293i	−0.295780	−	0.955256i	$-0.595580\pi$
$79$	−9.74641	−	3.16680i	−1.09656	−	0.356293i	−0.800777	+	0.598963i	$0.795580\pi$
$80$	0.106606	+	2.23353i	0.0119190	+	0.249716i
$81$	0.412767	+	8.99053i	0.0458630	+	0.998948i
$82$	6.98378	−	2.26917i	0.771229	−	0.250588i
$83$	0.428315	−	0.589524i	0.0470136	−	0.0647087i	−0.784863	−	0.619669i	$-0.787267\pi$
$83$	0.428315	−	0.589524i	0.0470136	−	0.0647087i	0.831877	+	0.554961i	$0.187267\pi$
$84$	−1.76904	−	7.01322i	−0.193018	−	0.765205i
$85$	−12.0915	+	9.69843i	−1.31151	+	1.05194i
$86$	−0.854571	−	2.63010i	−0.0921508	−	0.283611i
$87$	−7.66459	−	12.1914i	−0.821730	−	1.30705i
$88$	1.72686			0.184083
$89$	4.02056	+	12.3740i	0.426178	+	1.31164i	0.901861	+	0.432025i	$0.142201\pi$
$89$	4.02056	+	12.3740i	0.426178	+	1.31164i	−0.475683	+	0.879617i	$0.657799\pi$
$90$	6.17708	+	2.61604i	0.651122	+	0.275755i
$91$	4.89228	−	6.73365i	0.512850	−	0.705878i
$92$		−	5.35583i		−	0.558384i
$93$	−7.41070	−	6.17102i	−0.768454	−	0.639905i
$94$	9.27755			0.956906
$95$	6.58081	−	2.49097i	0.675176	−	0.255568i
$96$	1.60770	+	0.644430i	0.164086	+	0.0657719i
$97$	4.17102	−	1.35525i	0.423503	−	0.137604i	−0.0895088	−	0.995986i	$-0.528530\pi$
$97$	4.17102	−	1.35525i	0.423503	−	0.137604i	0.513012	+	0.858382i	$0.328530\pi$
$98$	10.4383			1.05442
$99$	2.24543	−	4.66865i	0.225674	−	0.469217i
$100$	3.74678	−	3.31083i	0.374678	−	0.331083i
$101$	5.58138	+	1.81350i	0.555368	+	0.180450i	0.573236	−	0.819390i	$-0.305688\pi$
$101$	5.58138	+	1.81350i	0.555368	+	0.180450i	−0.0178678	+	0.999840i	$0.505688\pi$
$102$	2.93660	+	11.6419i	0.290767	+	1.15272i
$103$	−3.19353	+	4.39552i	−0.314668	+	0.433103i	−0.936830	−	0.349785i	$-0.886255\pi$
$103$	−3.19353	+	4.39552i	−0.314668	+	0.433103i	0.622162	+	0.782889i	$0.286255\pi$
$104$	0.615919	+	1.89560i	0.0603958	+	0.185879i
$105$	−9.75812	+	12.8978i	−0.952295	+	1.25870i
$106$	4.51862	+	6.21934i	0.438887	+	0.604076i
$107$	−4.36642	+	13.4385i	−0.422118	+	1.29914i	0.483610	+	0.875284i	$0.339325\pi$
$107$	−4.36642	+	13.4385i	−0.422118	+	1.29914i	−0.905727	+	0.423861i	$0.860675\pi$
$108$	3.83275	−	3.50856i	0.368807	−	0.337612i
$109$	−2.61334	+	1.89870i	−0.250313	+	0.181863i	−0.705865	−	0.708346i	$-0.749442\pi$
$109$	−2.61334	+	1.89870i	−0.250313	+	0.181863i	0.455553	+	0.890209i	$0.349442\pi$
$110$	−2.41601	−	3.01215i	−0.230357	−	0.287197i
$111$	2.93355	+	1.17588i	0.278440	+	0.111610i
$112$	−2.45454	+	3.37839i	−0.231932	+	0.319228i
$113$	2.54158	+	7.82218i	0.239092	+	0.735849i	0.996552	+	0.0829676i	$0.0264398\pi$
$113$	2.54158	+	7.82218i	0.239092	+	0.735849i	−0.757461	+	0.652881i	$0.773560\pi$
$114$	0.365286	−	5.43817i	0.0342122	−	0.509332i
$115$	−9.34217	+	7.49324i	−0.871162	+	0.698748i
$116$	−2.56921	+	7.90723i	−0.238546	+	0.734168i
$117$	5.92575	+	0.799682i	0.547836	+	0.0739307i
$118$		−	11.3548i		−	1.04529i
$119$	−28.9475			−2.65361
$120$	−1.12523	−	3.70592i	−0.102719	−	0.338303i
$121$	6.48667	−	4.71284i	0.589698	−	0.428440i
$122$	−7.65702	+	10.5390i	−0.693234	+	0.954155i
$123$	−10.7676	+	6.76948i	−0.970881	+	0.610383i
$124$	0.00564386	+	5.56776i	0.000506833	+	0.500000i
$125$	−11.0171	−	1.90339i	−0.985402	−	0.170244i
$126$	5.94202	+	11.0289i	0.529357	+	0.982533i
$127$	1.60163	−	1.16365i	0.142122	−	0.103257i	−0.514453	−	0.857519i	$-0.672005\pi$
$127$	1.60163	−	1.16365i	0.142122	−	0.103257i	0.656574	+	0.754261i	$0.272005\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.54939	+	4.05509i	0.224462	+	0.357031i
$130$	2.44478	−	3.72644i	0.214421	−	0.326831i
$131$	5.95623	−	1.93530i	0.520398	−	0.169088i	−0.0370280	−	0.999314i	$-0.511789\pi$
$131$	5.95623	−	1.93530i	0.520398	−	0.169088i	0.557426	+	0.830227i	$0.311789\pi$
$132$	−2.90016	+	0.731547i	−0.252427	+	0.0636730i
$133$	12.4976	+	4.06073i	1.08368	+	0.352110i
$134$	4.62216	−	6.36186i	0.399294	−	0.549581i
$135$	−11.4823	−	1.77670i	−0.988240	−	0.152914i
$136$	4.07453	−	5.60811i	0.349388	−	0.480892i
$137$	−8.08945	−	11.1342i	−0.691128	−	0.951256i	−1.00000		0.000152541i	$-0.999951\pi$
$137$	−8.08945	−	11.1342i	−0.691128	−	0.951256i	0.308872	−	0.951104i	$-0.400049\pi$
$138$	2.26889	+	8.99483i	0.193141	+	0.765691i
$139$	6.45504	+	8.88459i	0.547509	+	0.753581i	0.989672	−	0.143353i	$-0.0457886\pi$
$139$	6.45504	+	8.88459i	0.547509	+	0.753581i	−0.442163	+	0.896935i	$0.645789\pi$
$140$	9.32701	−	0.445179i	0.788276	−	0.0376245i
$141$	−15.5811	+	3.93024i	−1.31217	+	0.330986i
$142$	−4.78078	−	6.58017i	−0.401194	−	0.552196i
$143$	−2.78455	−	2.02309i	−0.232856	−	0.169179i
$144$	−2.97305	−	0.401214i	−0.247754	−	0.0334345i
$145$	17.3871	−	6.58136i	1.44392	−	0.546553i
$146$	−1.99959	+	6.15410i	−0.165487	+	0.509317i
$147$	−17.5305	+	4.42196i	−1.44589	+	0.364717i
$148$	−0.563858	−	1.73538i	−0.0463488	−	0.142647i
$149$			3.01684i			0.247149i	0.992335	+	0.123575i	$0.0394358\pi$
$149$			3.01684i			0.247149i	−0.992335	+	0.123575i	$0.960564\pi$
$150$	−4.88995	+	7.14761i	−0.399263	+	0.583600i
$151$	6.36361	−	2.06766i	0.517863	−	0.168264i	−0.0384123	−	0.999262i	$-0.512230\pi$
$151$	6.36361	−	2.06766i	0.517863	−	0.168264i	0.556275	+	0.830998i	$0.312230\pi$
$152$	−2.54582	+	1.84965i	−0.206493	+	0.150026i
$153$	−9.86373	−	18.3080i	−0.797435	−	1.48011i
$154$		−	7.21120i		−	0.581095i
$155$	9.70394	−	7.79959i	0.779439	−	0.626478i
$156$	−1.83743	−	2.92264i	−0.147113	−	0.233998i
$157$	−6.78647	+	9.34078i	−0.541619	+	0.745475i	−0.988845	−	0.148946i	$-0.952412\pi$
$157$	−6.78647	+	9.34078i	−0.541619	+	0.745475i	0.447226	+	0.894421i	$0.352412\pi$
$158$	−6.02361	−	8.29079i	−0.479213	−	0.659580i
$159$	−10.2235	−	8.53083i	−0.810774	−	0.676539i
$160$	−1.22659	+	1.86962i	−0.0969702	+	0.147807i
$161$	−22.3655			−1.76265
$162$	−4.95057	+	7.51611i	−0.388953	+	0.590521i
$163$	−14.9280	−	4.85040i	−1.16925	−	0.379913i	−0.340888	−	0.940104i	$-0.610728\pi$
$163$	−14.9280	−	4.85040i	−1.16925	−	0.379913i	−0.828364	+	0.560191i	$0.810728\pi$
$164$	6.98378	+	2.26917i	0.545342	+	0.177192i
$165$	5.33359	+	4.03525i	0.415220	+	0.314144i
$166$	0.693027	−	0.225178i	0.0537894	−	0.0174772i
$167$	7.28550	−	10.0276i	0.563769	−	0.775961i	−0.428031	−	0.903764i	$-0.640792\pi$
$167$	7.28550	−	10.0276i	0.563769	−	0.775961i	0.991800	+	0.127803i	$0.0407925\pi$
$168$	2.69108	−	6.71363i	0.207622	−	0.517968i
$169$	−2.78960	+	8.58551i	−0.214585	+	0.660424i
$170$	−15.4828	+	0.738996i	−1.18748	+	0.0566784i
$171$	1.69029	+	9.28786i	0.129260	+	0.710261i
$172$	0.854571	−	2.63010i	0.0651605	−	0.200543i
$173$	−19.3499	+	14.0585i	−1.47114	+	1.06885i	−0.490863	+	0.871237i	$0.663318\pi$
$173$	−19.3499	+	14.0585i	−1.47114	+	1.06885i	−0.980281	+	0.197611i	$0.936682\pi$
$174$	0.965120	−	14.3682i	0.0731656	−	1.08925i
$175$	−13.8258	−	15.6463i	−1.04513	−	1.18275i
$176$	1.39706	+	1.01502i	0.105307	+	0.0765100i
$177$	4.81022	+	19.0697i	0.361558	+	1.43337i
$178$	−4.02056	+	12.3740i	−0.301354	+	0.927471i
$179$	2.17167	+	6.68372i	0.162318	+	0.499565i	0.998829	−	0.0483866i	$-0.0154079\pi$
$179$	2.17167	+	6.68372i	0.162318	+	0.499565i	−0.836510	+	0.547951i	$0.815408\pi$
$180$	3.45970	+	5.74722i	0.257871	+	0.428372i
$181$			9.64775i			0.717111i	0.933508	+	0.358556i	$0.116731\pi$
$181$			9.64775i			0.717111i	−0.933508	+	0.358556i	$0.883269\pi$
$182$	7.91588	−	2.57202i	0.586764	−	0.190651i
$183$	8.39493	−	20.9434i	0.620571	−	1.54818i
$184$	3.14808	−	4.33296i	0.232080	−	0.319430i
$185$	−2.23813	+	3.41147i	−0.164551	+	0.250816i
$186$	−2.36815	−	9.34836i	−0.173641	−	0.685455i
$187$			11.9706i			0.875375i
$188$	7.50569	+	5.45320i	0.547409	+	0.397716i
$189$	−14.6515	−	16.0052i	−1.06574	−	1.16421i
$190$	6.78814	+	1.85287i	0.492463	+	0.134421i
$191$			15.5272i			1.12351i	0.827303	+	0.561756i	$0.189874\pi$
$191$			15.5272i			1.12351i	−0.827303	+	0.561756i	$0.810126\pi$
$192$	0.921873	+	1.46634i	0.0665304	+	0.105824i
$193$	3.88837	−	1.26341i	0.279891	−	0.0909421i	−0.165708	−	0.986175i	$-0.552991\pi$
$193$	3.88837	−	1.26341i	0.279891	−	0.0909421i	0.445599	+	0.895233i	$0.352991\pi$
$194$	4.17102	+	1.35525i	0.299462	+	0.0973011i
$195$	−2.52724	+	7.29404i	−0.180979	+	0.522337i
$196$	8.44474	+	6.13546i	0.603196	+	0.438247i
$197$	−4.98867	+	1.62092i	−0.355428	+	0.115486i	−0.481288	−	0.876562i	$-0.659831\pi$
$197$	−4.98867	+	1.62092i	−0.355428	+	0.115486i	0.125860	+	0.992048i	$0.459831\pi$
$198$	4.56076	−	2.45719i	0.324119	−	0.174625i
$199$	−9.62744	−	13.2510i	−0.682471	−	0.939341i	0.317489	−	0.948262i	$-0.397160\pi$
$199$	−9.62744	−	13.2510i	−0.682471	−	0.939341i	−0.999960	+	0.00892064i	$0.997160\pi$
$200$	4.97727	−	0.476216i	0.351946	−	0.0336736i
$201$	−5.06759	+	12.6425i	−0.357441	+	0.891731i
$202$	3.44948	+	4.74781i	0.242705	+	0.334055i
$203$	33.0199	+	10.7288i	2.31754	+	0.753016i
$204$	−4.46719	+	11.1446i	−0.312766	+	0.780279i
$205$	−5.81276	−	15.3565i	−0.405981	−	1.07255i
$206$	−5.16724	+	1.67894i	−0.360019	+	0.116977i
$207$	−7.62095	−	14.1452i	−0.529693	−	0.983157i
$208$	−0.615919	+	1.89560i	−0.0427063	+	0.131436i
$209$	1.67922	−	5.16812i	0.116154	−	0.357486i
$210$	−15.4756	+	4.69885i	−1.06792	+	0.324252i
$211$	−5.36344			−0.369234			−0.184617	−	0.982811i	$-0.559105\pi$
$211$	−5.36344			−0.369234			−0.184617	+	0.982811i	$0.559105\pi$
$212$			7.68753i			0.527982i
$213$	10.8166	+	9.02577i	0.741142	+	0.618435i
$214$	−11.4314	+	8.30542i	−0.781437	+	0.567747i
$215$	−5.78329	+	2.18909i	−0.394417	+	0.149295i
$216$	5.16304	−	0.585654i	0.351301	−	0.0398487i
$217$	23.2505	−	0.0235683i	1.57835	−	0.00159992i
$218$	−3.23027			−0.218781
$219$	0.751141	−	11.1826i	0.0507574	−	0.755647i
$220$	−0.184094	−	3.85698i	−0.0124116	−	0.260037i
$221$	−13.1403	+	4.26955i	−0.883914	+	0.287201i
$222$	1.68213	+	2.67560i	0.112897	+	0.179575i
$223$	23.4310			1.56906			0.784528	−	0.620093i	$-0.212905\pi$
$223$	23.4310			1.56906			0.784528	+	0.620093i	$0.212905\pi$
$224$	−3.97153	+	1.29043i	−0.265359	+	0.0862204i
$225$	5.18447	−	14.0756i	0.345631	−	0.938370i
$226$	−2.54158	+	7.82218i	−0.169063	+	0.520323i
$227$	17.4816	+	12.7011i	1.16029	+	0.843002i	0.989815	−	0.142360i	$-0.0454690\pi$
$227$	17.4816	+	12.7011i	1.16029	+	0.843002i	0.170477	+	0.985362i	$0.445469\pi$
$228$	3.49200	−	4.18486i	0.231263	−	0.277149i
$229$	−6.40738	+	8.81900i	−0.423412	+	0.582776i	−0.966425	−	0.256948i	$-0.917283\pi$
$229$	−6.40738	+	8.81900i	−0.423412	+	0.582776i	0.543014	+	0.839724i	$0.317283\pi$
$230$	−11.9624	+	0.570966i	−0.788777	+	0.0376484i
$231$	3.05488	+	12.1108i	0.200996	+	0.796834i
$232$	−6.72629	+	4.88694i	−0.441603	+	0.320843i
$233$	−13.9107	+	10.1067i	−0.911318	+	0.662111i	−0.941348	−	0.337438i	$-0.890440\pi$
$233$	−13.9107	+	10.1067i	−0.911318	+	0.662111i	0.0300301	+	0.999549i	$0.490440\pi$
$234$	4.32399	+	4.13002i	0.282668	+	0.269988i
$235$	−0.989046	−	20.7216i	−0.0645182	−	1.35173i
$236$	6.67417	−	9.18620i	0.434451	−	0.597971i
$237$	13.6286	+	11.3722i	0.885270	+	0.738701i
$238$	−23.4190	−	17.0149i	−1.51803	−	1.10291i
$239$	0.568428	−	1.74944i	0.0367685	−	0.113162i	−0.930988	−	0.365051i	$-0.881052\pi$
$239$	0.568428	−	1.74944i	0.0367685	−	0.113162i	0.967756	+	0.251889i	$0.0810517\pi$
$240$	1.26796	−	3.65955i	0.0818464	−	0.236223i
$241$	23.8006	−	7.73328i	1.53313	−	0.498144i	0.583660	−	0.811998i	$-0.301620\pi$
$241$	23.8006	−	7.73328i	1.53313	−	0.498144i	0.949471	+	0.313854i	$0.101620\pi$
$242$	8.01797			0.515415
$243$	5.13016	−	14.7201i	0.329100	−	0.944295i
$244$	−12.3893	+	4.02553i	−0.793145	+	0.257708i
$245$	−1.11279	−	23.3141i	−0.0710933	−	1.48949i
$246$	−12.6902	−	0.852408i	−0.809095	−	0.0543476i
$247$	6.27207			0.399082
$248$	−3.26808	+	4.50773i	−0.207523	+	0.286241i
$249$	−1.06851	+	0.671762i	−0.0677141	+	0.0425712i
$250$	−7.79426	−	8.01558i	−0.492952	−	0.506950i
$251$	−7.75501	+	5.63434i	−0.489492	+	0.355636i	−0.804989	−	0.593290i	$-0.797829\pi$
$251$	−7.75501	+	5.63434i	−0.489492	+	0.355636i	0.315497	+	0.948927i	$0.397829\pi$
$252$	−1.67544	+	12.4152i	−0.105543	+	0.782084i
$253$			9.24875i			0.581464i
$254$	1.97972			0.124219
$255$	25.6895	−	7.80008i	1.60874	−	0.488460i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	2.39028	−	7.35652i	0.149102	−	0.458887i	−0.848414	−	0.529333i	$-0.822442\pi$
$257$	2.39028	−	7.35652i	0.149102	−	0.458887i	0.997516	+	0.0704458i	$0.0224422\pi$
$258$	−0.321018	+	4.77913i	−0.0199857	+	0.297536i
$259$	−7.24678	+	2.35462i	−0.450293	+	0.146309i
$260$	4.16821	−	1.57775i	0.258502	−	0.0978481i
$261$	4.46591	+	24.5394i	0.276433	+	1.51895i
$262$	5.95623	+	1.93530i	0.367977	+	0.119563i
$263$	15.2910	+	21.0463i	0.942886	+	1.29777i	0.954616	+	0.297840i	$0.0962661\pi$
$263$	15.2910	+	21.0463i	0.942886	+	1.29777i	−0.0117301	+	0.999931i	$0.503734\pi$
$264$	−2.77627	−	1.11284i	−0.170868	−	0.0684904i
$265$	13.4093	−	10.7555i	0.823729	−	0.660703i
$266$	7.72397	+	10.6311i	0.473587	+	0.651836i
$267$	1.51031	−	22.4847i	0.0924298	−	1.37604i
$268$	7.47881	−	2.43001i	0.456841	−	0.148437i
$269$	−0.0647591	−	0.0470503i	−0.00394843	−	0.00286870i	0.585809	−	0.810449i	$-0.300777\pi$
$269$	−0.0647591	−	0.0470503i	−0.00394843	−	0.00286870i	−0.589758	+	0.807580i	$0.700777\pi$
$270$	−8.24506	−	8.18651i	−0.501779	−	0.498215i
$271$	−14.2057	−	4.61572i	−0.862937	−	0.280385i	−0.156082	−	0.987744i	$-0.549886\pi$
$271$	−14.2057	−	4.61572i	−0.862937	−	0.280385i	−0.706855	+	0.707359i	$0.749886\pi$
$272$	6.59273	−	2.14211i	0.399743	−	0.129884i
$273$	−12.2047	+	7.67297i	−0.738662	+	0.464389i
$274$		−	13.7626i		−	0.831428i
$275$	−6.47015	+	5.71733i	−0.390165	+	0.344768i
$276$	−3.45146	+	8.61059i	−0.207753	+	0.518297i
$277$	−2.48688	−	1.80682i	−0.149422	−	0.108561i	0.510563	−	0.859841i	$-0.329437\pi$
$277$	−2.48688	−	1.80682i	−0.149422	−	0.108561i	−0.659985	+	0.751279i	$0.729437\pi$
$278$			10.9820i			0.658654i
$279$	7.93742	+	14.6969i	0.475201	+	0.879877i
$280$	7.80738	+	5.12212i	0.466580	+	0.306105i
$281$	−7.58772	+	10.4436i	−0.452646	+	0.623013i	−0.972963	−	0.230960i	$-0.925814\pi$
$281$	−7.58772	+	10.4436i	−0.452646	+	0.623013i	0.520318	+	0.853973i	$0.325814\pi$
$282$	−14.9155	−	5.97873i	−0.888208	−	0.356028i
$283$	−9.71441	+	3.15640i	−0.577462	+	0.187629i	−0.583163	−	0.812355i	$-0.698185\pi$
$283$	−9.71441	+	3.15640i	−0.577462	+	0.187629i	0.00570153	+	0.999984i	$0.498185\pi$
$284$		−	8.13354i		−	0.482637i
$285$	−12.1852	−	0.236132i	−0.721791	−	0.0139873i
$286$	−1.06360	−	3.27343i	−0.0628921	−	0.193562i
$287$	9.47585	−	29.1637i	0.559342	−	1.72148i
$288$	−2.16942	−	2.07210i	−0.127834	−	0.122100i
$289$	25.1222	+	18.2523i	1.47777	+	1.07367i
$290$	17.9349	+	4.89544i	1.05317	+	0.287470i
$291$	−7.57913	−	0.509096i	−0.444296	−	0.0298437i
$292$	−5.23499	+	3.80344i	−0.306355	+	0.222580i
$293$	−8.27855	+	25.4788i	−0.483638	+	1.48849i	0.350306	+	0.936635i	$0.386078\pi$
$293$	−8.27855	+	25.4788i	−0.483638	+	1.48849i	−0.833944	+	0.551850i	$0.813922\pi$
$294$	−16.7816	−	6.72673i	−0.978725	−	0.392311i
$295$	−25.3612	+	1.21049i	−1.47658	+	0.0704775i
$296$	0.563858	−	1.73538i	0.0327736	−	0.100867i
$297$	−6.61861	+	6.05878i	−0.384051	+	0.351566i
$298$	−1.77325	+	2.44068i	−0.102722	+	0.141385i
$299$	−10.1525	+	3.29876i	−0.587136	+	0.190772i
$300$	−8.15732	+	2.90830i	−0.470963	+	0.167911i
$301$	−10.9831	−	3.56862i	−0.633054	−	0.205692i
$302$	6.36361	+	2.06766i	0.366184	+	0.118981i
$303$	−7.80453	−	6.51238i	−0.448359	−	0.374127i
$304$	−3.14681			−0.180482
$305$	24.3554	+	15.9786i	1.39459	+	0.914934i
$306$	2.78122	−	20.6092i	0.158992	−	1.17815i
$307$	−4.32366	−	5.95101i	−0.246764	−	0.339642i	0.667610	−	0.744511i	$-0.267317\pi$
$307$	−4.32366	−	5.95101i	−0.246764	−	0.339642i	−0.914375	+	0.404869i	$0.867317\pi$
$308$	4.23864	−	5.83399i	0.241519	−	0.332422i
$309$	7.96686	−	5.00868i	0.453219	−	0.284934i
$310$	12.4351	−	0.606165i	0.706268	−	0.0344278i
$311$			4.82262i			0.273466i	0.990608	+	0.136733i	$0.0436602\pi$
$311$			4.82262i			0.273466i	−0.990608	+	0.136733i	$0.956340\pi$
$312$	0.231369	−	3.44448i	0.0130987	−	0.195005i
$313$	15.5678	−	11.3107i	0.879946	−	0.639318i	−0.0532910	−	0.998579i	$-0.516971\pi$
$313$	15.5678	−	11.3107i	0.879946	−	0.639318i	0.933237	+	0.359261i	$0.116971\pi$
$314$	−10.9807	+	3.56786i	−0.619679	+	0.201346i
$315$	23.9999	−	14.4474i	1.35224	−	0.814019i
$316$		−	10.2480i		−	0.576494i
$317$	4.85578	+	14.9446i	0.272728	+	0.839370i	0.989812	+	0.142383i	$0.0454765\pi$
$317$	4.85578	+	14.9446i	0.272728	+	0.839370i	−0.717084	+	0.696987i	$0.754523\pi$
$318$	−3.25666	−	12.9108i	−0.182625	−	0.724001i
$319$	4.43666	−	13.6546i	0.248405	−	0.764513i
$320$	−2.09127	+	0.791586i	−0.116905	+	0.0442510i
$321$	15.6800	−	18.7912i	0.875175	−	1.04882i
$322$	−18.0941	−	13.1461i	−1.00834	−	0.732604i
$323$	−12.8218	−	17.6476i	−0.713422	−	0.981941i
$324$	−8.42295	+	3.17079i	−0.467942	+	0.176155i
$325$	−8.58374	−	5.06321i	−0.476140	−	0.280856i
$326$	−9.22602	−	12.6985i	−0.510982	−	0.703306i
$327$	5.42506	−	1.36844i	0.300006	−	0.0756747i
$328$	4.31621	+	5.94076i	0.238323	+	0.328023i
$329$	22.7721	−	31.3431i	1.25547	−	1.72800i
$330$	1.94310	+	6.39959i	0.106964	+	0.352286i
$331$	−4.43863	+	6.10925i	−0.243969	+	0.335795i	−0.913388	−	0.407091i	$-0.866543\pi$
$331$	−4.43863	+	6.10925i	−0.243969	+	0.335795i	0.669419	+	0.742885i	$0.266543\pi$
$332$	0.693027	+	0.225178i	0.0380348	+	0.0123583i
$333$	−3.95850	−	3.78093i	−0.216925	−	0.207194i
$334$	11.7882	−	3.83021i	0.645021	−	0.209580i
$335$	−14.7021	−	9.64549i	−0.803262	−	0.526990i
$336$	6.12331	−	3.84966i	0.334054	−	0.210016i
$337$	−9.02482	−	27.7755i	−0.491613	−	1.51303i	−0.822169	−	0.569243i	$-0.807236\pi$
$337$	−9.02482	−	27.7755i	−0.491613	−	1.51303i	0.330556	−	0.943786i	$-0.392764\pi$
$338$	−7.30327	+	5.30613i	−0.397245	+	0.288616i
$339$	0.954739	−	14.2136i	0.0518543	−	0.771977i
$340$	−12.9602	−	8.50271i	−0.702867	−	0.461124i
$341$	−0.00974613	−	9.61472i	−0.000527783	−	0.520666i
$342$	−4.09179	+	8.50757i	−0.221259	+	0.460037i
$343$	8.43938	−	11.6158i	0.455684	−	0.627195i
$344$	2.23730	−	1.62549i	0.120627	−	0.0876406i
$345$	19.8483	−	6.02653i	1.06860	−	0.324457i
$346$	−23.9178			−1.28583
$347$		−	0.277740i		−	0.0149099i	−0.999972	−	0.00745494i	$-0.997627\pi$
$347$		−	0.277740i		−	0.0149099i	0.999972	−	0.00745494i	$-0.00237300\pi$
$348$	9.22619	−	11.0568i	0.494576	−	0.592707i
$349$	0.265812	−	0.818085i	0.0142286	−	0.0437911i	−0.943690	−	0.330831i	$-0.892671\pi$
$349$	0.265812	−	0.818085i	0.0142286	−	0.0437911i	0.957919	+	0.287040i	$0.0926711\pi$
$350$	−1.98864	−	20.7847i	−0.106297	−	1.11099i
$351$	−9.01151	−	5.10438i	−0.480999	−	0.272452i
$352$	0.533628	+	1.64234i	0.0284425	+	0.0875369i
$353$	0.513796	−	0.707179i	0.0273466	−	0.0376393i	−0.795125	−	0.606446i	$-0.792595\pi$
$353$	0.513796	−	0.707179i	0.0273466	−	0.0376393i	0.822471	+	0.568807i	$0.192595\pi$
$354$	−7.31735	+	18.2551i	−0.388913	+	0.970248i
$355$	−14.1873	+	11.3795i	−0.752985	+	0.603960i
$356$	−10.5260	+	7.64756i	−0.557875	+	0.405320i
$357$	46.5389	+	18.6546i	2.46310	+	0.987307i
$358$	−2.17167	+	6.68372i	−0.114776	+	0.353246i
$359$	6.25725	+	8.61236i	0.330245	+	0.454543i	0.941561	−	0.336844i	$-0.109359\pi$
$359$	6.25725	+	8.61236i	0.330245	+	0.454543i	−0.611316	+	0.791387i	$0.709359\pi$
$360$	−0.579177	+	6.68315i	−0.0305253	+	0.352233i
$361$	−2.81132	−	8.65235i	−0.147964	−	0.455387i
$362$	−5.67080	+	7.80519i	−0.298051	+	0.410232i
$363$	−13.4657	+	3.39665i	−0.706768	+	0.178278i
$364$	7.91588	+	2.57202i	0.414905	+	0.134811i
$365$	13.9585	+	3.81006i	0.730622	+	0.199428i
$366$	19.1019	−	12.0092i	0.998470	−	0.627728i
$367$	7.84083			0.409288			0.204644	−	0.978836i	$-0.434396\pi$
$367$	7.84083			0.409288			0.204644	+	0.978836i	$0.434396\pi$
$368$	5.09370	−	1.65504i	0.265527	−	0.0862751i
$369$	21.6736	−	3.94436i	1.12828	−	0.205335i
$370$	−3.81590	+	1.44439i	−0.198379	+	0.0750904i
$371$	32.1025			1.66668
$372$	3.57896	−	8.95495i	0.185560	−	0.464292i
$373$			32.3821i			1.67668i	0.545146	+	0.838341i	$0.316474\pi$
$373$			32.3821i			1.67668i	−0.545146	+	0.838341i	$0.683526\pi$
$374$	−7.03613	+	9.68440i	−0.363829	+	0.500768i
$375$	16.4857	+	10.1599i	0.851316	+	0.524652i
$376$	2.86692	+	8.82347i	0.147850	+	0.455036i
$377$	16.5714			0.853470
$378$	−2.44564	−	21.5604i	−0.125790	−	1.10895i
$379$	−2.23614	−	6.88212i	−0.114863	−	0.353511i	0.877056	−	0.480389i	$-0.159504\pi$
$379$	−2.23614	−	6.88212i	−0.114863	−	0.353511i	−0.991918	+	0.126878i	$0.959504\pi$
$380$	4.40263	+	5.48897i	0.225850	+	0.281578i
$381$	−3.32483	+	0.838668i	−0.170336	+	0.0429663i
$382$	−9.12668	+	12.5618i	−0.466962	+	0.642718i
$383$	−32.6623	+	10.6126i	−1.66897	+	0.542280i	−0.982722	−	0.185090i	$-0.940742\pi$
$383$	−32.6623	+	10.6126i	−1.66897	+	0.542280i	−0.686246	+	0.727370i	$0.740742\pi$
$384$	−0.116082	+	1.72816i	−0.00592377	+	0.0881896i
$385$	−16.1064	+	0.768760i	−0.820858	+	0.0391797i
$386$	3.88837	+	1.26341i	0.197913	+	0.0643058i
$387$	−1.48545	−	8.16229i	−0.0755096	−	0.414912i
$388$	2.57783	+	3.54808i	0.130870	+	0.180127i
$389$	6.74164	−	20.7486i	0.341815	−	1.05200i	−0.621452	−	0.783452i	$-0.713457\pi$
$389$	6.74164	−	20.7486i	0.341815	−	1.05200i	0.963267	−	0.268546i	$-0.0865431\pi$
$390$	−6.33191	+	4.41553i	−0.320629	+	0.223589i
$391$	30.0361	+	21.8225i	1.51899	+	1.10361i
$392$	3.22560	+	9.92738i	0.162918	+	0.501409i
$393$	−10.8230	−	0.726990i	−0.545948	−	0.0366718i
$394$	−4.98867	−	1.62092i	−0.251326	−	0.0816607i
$395$	−17.8755	+	14.3377i	−0.899416	+	0.721410i
$396$	5.13403	+	0.692840i	0.257995	+	0.0348165i
$397$			30.7452i			1.54306i	0.636193	+	0.771530i	$0.280508\pi$
$397$			30.7452i			1.54306i	−0.636193	+	0.771530i	$0.719492\pi$
$398$		−	16.3792i		−	0.821014i
$399$	−17.4756	−	14.5823i	−0.874876	−	0.730028i
$400$	4.30661	+	2.54030i	0.215330	+	0.127015i
$401$	−16.4986	−	11.9870i	−0.823903	−	0.598601i	0.0939248	−	0.995579i	$-0.470059\pi$
$401$	−16.4986	−	11.9870i	−0.823903	−	0.598601i	−0.917828	+	0.396979i	$0.870059\pi$
$402$	−11.5308	+	7.24932i	−0.575105	+	0.361563i
$403$	10.5508	−	3.43999i	0.525572	−	0.171358i
$404$			5.86861i			0.291974i
$405$	17.3152	+	10.2559i	0.860398	+	0.509622i
$406$	20.4074	+	28.0884i	1.01280	+	1.39400i
$407$	0.973701	+	2.99674i	0.0482646	+	0.148543i
$408$	−10.1647	+	6.39043i	−0.503226	+	0.316373i
$409$			11.3458i			0.561016i	0.959852	+	0.280508i	$0.0905029\pi$
$409$			11.3458i			0.561016i	−0.959852	+	0.280508i	$0.909497\pi$
$410$	4.32373	−	15.8404i	0.213534	−	0.782299i
$411$	5.83024	+	23.1135i	0.287584	+	1.14011i
$412$	−5.16724	−	1.67894i	−0.254572	−	0.0827154i
$413$	−38.3608	−	27.8708i	−1.88761	−	1.37143i
$414$	2.14884	−	15.9232i	0.105610	−	0.782581i
$415$	−0.576823	−	1.52389i	−0.0283151	−	0.0748048i
$416$	−1.61250	+	1.17155i	−0.0790591	+	0.0574398i
$417$	−4.65228	−	18.4436i	−0.227823	−	0.903187i
$418$	4.39626	−	3.19407i	0.215028	−	0.156227i
$419$	−14.7134	−	20.2512i	−0.718795	−	0.989336i	−0.999563	−	0.0295606i	$-0.990589\pi$
$419$	−14.7134	−	20.2512i	−0.718795	−	0.989336i	0.280768	−	0.959776i	$-0.409411\pi$
$420$	−15.2820	−	5.29489i	−0.745683	−	0.258364i
$421$	4.86512	−	3.53472i	0.237111	−	0.172272i	−0.462884	−	0.886419i	$-0.653185\pi$
$421$	4.86512	−	3.53472i	0.237111	−	0.172272i	0.699995	+	0.714147i	$0.253185\pi$
$422$	−4.33911	−	3.15255i	−0.211225	−	0.153464i
$423$	27.5826	+	3.72229i	1.34111	+	0.180984i
$424$	−4.51862	+	6.21934i	−0.219443	+	0.302038i
$425$	3.30113	+	34.5025i	0.160128	+	1.67362i
$426$	3.44561	+	13.6598i	0.166940	+	0.661822i
$427$	16.8103	+	51.7368i	0.813507	+	2.50372i
$428$	−14.1300			−0.683001
$429$	3.17299	+	5.04698i	0.153193	+	0.243670i
$430$	−5.96550	−	1.62832i	−0.287682	−	0.0785246i
$431$	−17.8709	−	24.5972i	−0.860811	−	1.18480i	−0.981376	−	0.192099i	$-0.938471\pi$
$431$	−17.8709	−	24.5972i	−0.860811	−	1.18480i	0.120565	−	0.992705i	$-0.461529\pi$
$432$	4.52123	+	2.56096i	0.217528	+	0.123214i
$433$	27.4846			1.32082			0.660412	−	0.750904i	$-0.270382\pi$
$433$	27.4846			1.32082			0.660412	+	0.750904i	$0.270382\pi$
$434$	18.8239	+	13.6472i	0.903576	+	0.655088i
$435$	−32.1945	−	0.623883i	−1.54361	−	0.0299129i
$436$	−2.61334	−	1.89870i	−0.125156	−	0.0909314i
$437$	−9.90640	−	13.6350i	−0.473887	−	0.652250i
$438$	7.18063	−	8.60537i	0.343104	−	0.411181i
$439$	−27.3101			−1.30344			−0.651719	−	0.758460i	$-0.725952\pi$
$439$	−27.3101			−1.30344			−0.651719	+	0.758460i	$0.725952\pi$
$440$	2.11814	−	3.22857i	0.100978	−	0.153916i
$441$	31.0335	+	4.18799i	1.47779	+	0.199428i
$442$	−13.1403	−	4.26955i	−0.625022	−	0.203082i
$443$	−3.28408	+	10.1073i	−0.156031	+	0.480215i	−0.998264	−	0.0588995i	$-0.981241\pi$
$443$	−3.28408	+	10.1073i	−0.156031	+	0.480215i	0.842233	+	0.539114i	$0.181241\pi$
$444$	−0.211812	+	3.15334i	−0.0100522	+	0.149651i
$445$	28.0663	+	7.66087i	1.33047	+	0.363160i
$446$	18.9561	+	13.7724i	0.897597	+	0.652142i
$447$	1.94414	−	4.85018i	0.0919548	−	0.229406i
$448$	−3.97153	−	1.29043i	−0.187637	−	0.0609670i
$449$	5.66463	−	4.11559i	0.267330	−	0.194227i	−0.446042	−	0.895012i	$-0.647167\pi$
$449$	5.66463	−	4.11559i	0.267330	−	0.194227i	0.713372	+	0.700785i	$0.247167\pi$
$450$	12.4677	−	8.34001i	0.587734	−	0.393152i
$451$	−12.0600	−	3.91853i	−0.567882	−	0.184516i
$452$	−6.65394	+	4.83437i	−0.312975	+	0.227390i
$453$	−11.5633	−	0.776713i	−0.543289	−	0.0364932i
$454$	6.67736	+	20.5508i	0.313384	+	0.964497i
$455$	−6.58856	−	17.4061i	−0.308877	−	0.816011i
$456$	5.28489	−	1.33308i	0.247488	−	0.0624272i
$457$	−6.47063	+	19.9145i	−0.302683	+	0.931563i	0.677848	+	0.735202i	$0.262913\pi$
$457$	−6.47063	+	19.9145i	−0.302683	+	0.931563i	−0.980532	+	0.196361i	$0.937087\pi$
$458$	−10.3674	+	3.36856i	−0.484435	+	0.157402i
$459$	4.05976	+	35.7902i	0.189493	+	1.67055i
$460$	−10.0134	−	6.56939i	−0.466876	−	0.306300i
$461$	12.4457	+	38.3038i	0.579653	+	1.78399i	0.619759	+	0.784793i	$0.287231\pi$
$461$	12.4457	+	38.3038i	0.579653	+	1.78399i	−0.0401058	+	0.999195i	$0.512769\pi$
$462$	−4.64712	+	11.5935i	−0.216203	+	0.539377i
$463$	−33.3793	−	24.2515i	−1.55127	−	1.12706i	−0.942741	−	0.333526i	$-0.891762\pi$
$463$	−33.3793	−	24.2515i	−1.55127	−	1.12706i	−0.608525	−	0.793535i	$-0.708238\pi$
$464$	−8.31415			−0.385975
$465$	−20.6273	+	6.28591i	−0.956570	+	0.291502i
$466$	−17.1945			−0.796521
$467$	6.20450	+	4.50783i	0.287110	+	0.208598i	0.722013	−	0.691880i	$-0.243217\pi$
$467$	6.20450	+	4.50783i	0.287110	+	0.208598i	−0.434903	+	0.900477i	$0.643217\pi$
$468$	1.07061	+	5.88284i	0.0494891	+	0.271934i
$469$	−10.1475	−	31.2309i	−0.468569	−	1.44211i
$470$	11.3797	−	17.3455i	0.524907	−	0.800088i
$471$	16.9301	−	10.6438i	0.780098	−	0.490440i
$472$	10.7990	−	3.50882i	0.497065	−	0.161506i
$473$	−1.47572	+	4.54180i	−0.0678537	+	0.208832i
$474$	4.34135	+	17.2109i	0.199405	+	0.790524i
$475$	3.41476	−	15.3590i	0.156680	−	0.704719i
$476$	−8.94526	−	27.5307i	−0.410005	−	1.26187i
$477$	10.9388	+	20.3033i	0.500852	+	0.929626i
$478$	1.48816	−	1.08121i	0.0680670	−	0.0494536i
$479$	38.2267	+	12.4206i	1.74662	+	0.567511i	0.995679	−	0.0928580i	$-0.0296003\pi$
$479$	38.2267	+	12.4206i	1.74662	+	0.567511i	0.750941	+	0.660369i	$0.229600\pi$
$480$	3.17683	−	2.21535i	0.145002	−	0.101116i
$481$	−2.94229	+	2.13770i	−0.134157	+	0.0974708i
$482$	23.8006	+	7.73328i	1.08409	+	0.352241i
$483$	35.9571	+	14.4130i	1.63610	+	0.655814i
$484$	6.48667	+	4.71284i	0.294849	+	0.214220i
$485$	2.58232	−	9.46056i	0.117257	−	0.429582i
$486$	12.8026	−	8.89338i	0.580740	−	0.403412i
$487$	12.3332	−	37.9576i	0.558869	−	1.72002i	−0.126632	−	0.991950i	$-0.540417\pi$
$487$	12.3332	−	37.9576i	0.558869	−	1.72002i	0.685501	−	0.728072i	$-0.259583\pi$
$488$	−12.3893	−	4.02553i	−0.560838	−	0.182227i
$489$	20.8741	+	17.4181i	0.943958	+	0.787672i
$490$	12.8034	−	19.5156i	0.578401	−	0.881626i
$491$	−22.4770			−1.01437			−0.507185	−	0.861837i	$-0.669314\pi$
$491$	−22.4770			−1.01437			−0.507185	+	0.861837i	$0.669314\pi$
$492$	−9.76553	−	8.14871i	−0.440264	−	0.367372i
$493$	−33.8763	−	46.6267i	−1.52571	−	2.09996i
$494$	5.07421	+	3.68663i	0.228300	+	0.165869i
$495$	−5.97440	−	9.92462i	−0.268529	−	0.446078i
$496$	−5.29351	+	1.72590i	−0.237686	+	0.0774952i
$497$	−33.9650			−1.52354
$498$	−1.25929	−	0.0845878i	−0.0564303	−	0.00379047i
$499$	20.7786	+	28.5993i	0.930178	+	1.28028i	0.959790	+	0.280718i	$0.0905727\pi$
$499$	20.7786	+	28.5993i	0.930178	+	1.28028i	−0.0296124	+	0.999561i	$0.509427\pi$
$500$	−1.59425	−	11.0661i	−0.0712970	−	0.494891i
$501$	−18.1750	+	11.4265i	−0.812000	+	0.510497i
$502$	−9.58571			−0.427831
$503$	0.875376	+	2.69413i	0.0390311	+	0.120125i	0.968674	−	0.248337i	$-0.0798842\pi$
$503$	0.875376	+	2.69413i	0.0390311	+	0.120125i	−0.929642	+	0.368463i	$0.879884\pi$
$504$	−8.65293	+	9.05932i	−0.385432	+	0.403534i
$505$	10.2366	−	8.21066i	0.455523	−	0.365369i
$506$	−5.43628	+	7.48240i	−0.241672	+	0.332633i
$507$	10.0176	−	12.0052i	0.444898	−	0.533172i
$508$	1.60163	+	1.16365i	0.0710608	+	0.0516287i
$509$	13.3832	−	9.72346i	0.593199	−	0.430985i	−0.250259	−	0.968179i	$-0.580516\pi$
$509$	13.3832	−	9.72346i	0.593199	−	0.430985i	0.843459	+	0.537194i	$0.180516\pi$
$510$	25.3680	+	8.78950i	1.12331	+	0.389206i
$511$	15.8829	+	21.8609i	0.702616	+	0.967068i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	3.26789	−	16.0214i	0.144281	−	0.707362i
$514$	6.25783	−	4.54658i	0.276021	−	0.200541i
$515$	4.30081	+	11.3622i	0.189516	+	0.500678i
$516$	−3.06881	+	3.67771i	−0.135097	+	0.161902i
$517$	−12.9612	−	9.41690i	−0.570035	−	0.414155i
$518$	−7.24678	−	2.35462i	−0.318405	−	0.103456i
$519$	40.1686	−	10.1323i	1.76320	−	0.444757i
$520$	4.29954	+	1.17359i	0.188547	+	0.0514652i
$521$		−	24.1572i		−	1.05835i	−0.848514	−	0.529173i	$-0.822502\pi$
$521$		−	24.1572i		−	1.05835i	0.848514	−	0.529173i	$-0.177498\pi$
$522$	−10.8109	+	22.4778i	−0.473180	+	0.983826i
$523$	5.33305	+	16.4134i	0.233198	+	0.717709i	0.997355	+	0.0726795i	$0.0231550\pi$
$523$	5.33305	+	16.4134i	0.233198	+	0.717709i	−0.764158	+	0.645030i	$0.776845\pi$
$524$	3.68115	+	5.06667i	0.160812	+	0.221338i
$525$	12.1448	+	34.0643i	0.530043	+	1.48669i
$526$			26.0147i			1.13429i
$527$	−31.2476	−	22.6544i	−1.36117	−	0.986840i
$528$	−1.59194	−	2.53216i	−0.0692804	−	0.110198i
$529$	4.59922	+	3.34153i	0.199966	+	0.145284i
$530$	17.1703	−	0.819540i	0.745830	−	0.0355985i
$531$	4.55570	−	33.7583i	0.197700	−	1.46499i
$532$			13.1408i			0.569726i
$533$		−	14.6361i		−	0.633960i
$534$	14.4380	−	17.3028i	0.624795	−	0.748764i
$535$	19.7690	+	24.6470i	0.854690	+	1.06558i
$536$	7.47881	+	2.43001i	0.323035	+	0.104961i
$537$	0.815784	−	12.1449i	0.0352037	−	0.524092i
$538$	−0.0247358	−	0.0761289i	−0.00106644	−	0.00328215i
$539$	−14.5828	−	10.5951i	−0.628128	−	0.456361i
$540$	−1.85849	−	11.4694i	−0.0799765	−	0.493562i
$541$	4.61194	−	14.1941i	0.198283	−	0.610252i	−0.801640	−	0.597807i	$-0.796039\pi$
$541$	4.61194	−	14.1941i	0.198283	−	0.610252i	0.999923	−	0.0124444i	$-0.00396126\pi$
$542$	−8.77962	−	12.0841i	−0.377117	−	0.519057i
$543$	6.21730	−	15.5107i	0.266810	−	0.665629i
$544$	6.59273	+	2.14211i	0.282661	+	0.0918421i
$545$	0.344367	+	7.21488i	0.0147511	+	0.309052i
$546$	−14.3839	−	0.966176i	−0.615573	−	0.0413485i
$547$	−9.34367	+	3.03594i	−0.399506	+	0.129807i	−0.501877	−	0.864939i	$-0.667357\pi$
$547$	−9.34367	+	3.03594i	−0.399506	+	0.129807i	0.102371	+	0.994746i	$0.467357\pi$
$548$	8.08945	−	11.1342i	0.345564	−	0.475628i
$549$	−26.9931	+	28.2608i	−1.15204	+	1.20614i
$550$	−8.59503	+	0.822357i	−0.366493	+	0.0350654i
$551$	8.08482	+	24.8825i	0.344425	+	1.06003i
$552$	−7.85347	+	4.93740i	−0.334266	+	0.210150i
$553$	−42.7947			−1.81982
$554$	−0.949903	−	2.92350i	−0.0403575	−	0.124208i
$555$	5.79670	−	4.04231i	0.246056	−	0.171586i
$556$	−6.45504	+	8.88459i	−0.273754	+	0.376791i
$557$		−	11.9543i		−	0.506521i	−0.967398	−	0.253260i	$-0.918497\pi$
$557$		−	11.9543i		−	0.506521i	0.967398	−	0.253260i	$-0.0815029\pi$
$558$	−2.21709	+	16.5555i	−0.0938568	+	0.700850i
$559$	−5.51197			−0.233132
$560$	3.30560	+	8.73295i	0.139687	+	0.369034i
$561$	7.71420	−	19.2451i	0.325694	−	0.812530i
$562$	−12.2772	+	3.98910i	−0.517882	+	0.168270i
$563$	12.4146			0.523214			0.261607	−	0.965175i	$-0.415748\pi$
$563$	12.4146			0.523214			0.261607	+	0.965175i	$0.415748\pi$
$564$	−8.55272	−	13.6040i	−0.360134	−	0.572833i
$565$	17.7420	+	4.84279i	0.746411	+	0.203738i
$566$	−9.71441	−	3.15640i	−0.408327	−	0.132673i
$567$	13.2410	+	35.1735i	0.556068	+	1.47715i
$568$	4.78078	−	6.58017i	0.200597	−	0.276098i
$569$	−10.3329	−	31.8015i	−0.433179	−	1.33319i	−0.894941	−	0.446184i	$-0.852783\pi$
$569$	−10.3329	−	31.8015i	−0.433179	−	1.33319i	0.461763	−	0.887003i	$-0.347217\pi$
$570$	−9.71927	−	7.35334i	−0.407095	−	0.307997i
$571$	3.08594	+	4.24743i	0.129142	+	0.177749i	0.868692	−	0.495353i	$-0.164961\pi$
$571$	3.08594	+	4.24743i	0.129142	+	0.177749i	−0.739549	+	0.673102i	$0.764961\pi$
$572$	1.06360	−	3.27343i	0.0444715	−	0.136869i
$573$	10.0062	−	24.9632i	0.418016	−	1.04285i
$574$	24.8081	−	18.0241i	1.03547	−	0.752313i
$575$	2.55053	+	26.6574i	0.106365	+	1.11169i
$576$	−0.537145	−	2.95152i	−0.0223811	−	0.122980i
$577$	14.1941	−	19.5365i	0.590909	−	0.813317i	−0.403929	−	0.914790i	$-0.632356\pi$
$577$	14.1941	−	19.5365i	0.590909	−	0.813317i	0.994838	+	0.101474i	$0.0323558\pi$
$578$	9.59581	+	29.5329i	0.399133	+	1.22841i
$579$	−7.06552	−	0.474597i	−0.293633	−	0.0197236i
$580$	11.6322	+	14.5024i	0.482999	+	0.602178i
$581$	0.940325	−	2.89402i	0.0390113	−	0.120064i
$582$	−5.83240	−	4.86677i	−0.241761	−	0.201734i
$583$		−	13.2753i		−	0.549805i
$584$	−6.47080			−0.267764
$585$	8.76355	−	10.0980i	0.362328	−	0.417502i
$586$	−21.6735	+	15.7467i	−0.895325	+	0.650492i
$587$	12.9414	−	17.8123i	0.534148	−	0.735192i	−0.453607	−	0.891202i	$-0.649863\pi$
$587$	12.9414	−	17.8123i	0.534148	−	0.735192i	0.987756	+	0.156009i	$0.0498630\pi$
$588$	−9.62276	−	15.3060i	−0.396836	−	0.631211i
$589$	10.3128	+	14.1641i	0.424930	+	0.583621i
$590$	−21.2291	−	13.9276i	−0.873989	−	0.573391i
$591$	9.06488	+	0.608895i	0.372879	+	0.0250466i
$592$	1.47620	−	1.07252i	0.0606714	−	0.0440804i
$593$	8.20117	+	25.2406i	0.336782	+	1.03651i	0.965838	+	0.259148i	$0.0834416\pi$
$593$	8.20117	+	25.2406i	0.336782	+	1.03651i	−0.629056	+	0.777360i	$0.716558\pi$
$594$	−8.91583	+	1.01134i	−0.365821	+	0.0414958i
$595$	−35.5066	+	54.1208i	−1.45563	+	2.21874i
$596$	−2.86919	+	0.932255i	−0.117526	+	0.0381867i
$597$	6.93871	+	27.5080i	0.283982	+	1.12583i
$598$	−10.1525	−	3.29876i	−0.415168	−	0.134896i
$599$	−12.4148	+	17.0875i	−0.507254	+	0.698175i	−0.983453	−	0.181163i	$-0.942014\pi$
$599$	−12.4148	+	17.0875i	−0.507254	+	0.698175i	0.476200	+	0.879337i	$0.342014\pi$
$600$	−8.30886	−	2.44189i	−0.339208	−	0.0996896i
$601$	19.8793	−	27.3615i	0.810894	−	1.11610i	−0.180291	−	0.983613i	$-0.557704\pi$
$601$	19.8793	−	27.3615i	0.810894	−	1.11610i	0.991185	−	0.132486i	$-0.0422961\pi$
$602$	−6.78791	−	9.34276i	−0.276655	−	0.380783i
$603$	16.2944	−	17.0596i	0.663558	−	0.694722i
$604$	3.93293	+	5.41321i	0.160028	+	0.220260i
$605$	−0.854767	−	17.9083i	−0.0347512	−	0.728077i
$606$	−2.48612	−	9.85602i	−0.100992	−	0.400373i
$607$	17.6107	+	24.2391i	0.714797	+	0.983833i	0.999681	+	0.0252712i	$0.00804494\pi$
$607$	17.6107	+	24.2391i	0.714797	+	0.983833i	−0.284884	+	0.958562i	$0.591955\pi$
$608$	−2.54582	−	1.84965i	−0.103247	−	0.0750130i
$609$	−46.1723	−	38.5278i	−1.87099	−	1.56122i
$610$	10.3119	+	27.2427i	0.417517	+	1.10303i
$611$	5.71421	−	17.5865i	0.231172	−	0.711475i
$612$	14.3638	−	15.0384i	0.580624	−	0.607893i
$613$	−7.62889	−	23.4793i	−0.308128	−	0.948320i	−0.978491	−	0.206287i	$-0.933862\pi$
$613$	−7.62889	−	23.4793i	−0.308128	−	0.948320i	0.670364	−	0.742033i	$-0.266138\pi$
$614$		−	7.35585i		−	0.296858i
$615$	−0.551023	+	28.4347i	−0.0222194	+	1.14660i
$616$	6.85826	−	2.22838i	0.276327	−	0.0897842i
$617$	9.74528	−	7.08036i	0.392330	−	0.285044i	−0.374080	−	0.927397i	$-0.622041\pi$
$617$	9.74528	−	7.08036i	0.392330	−	0.285044i	0.766410	+	0.642352i	$0.222041\pi$
$618$	9.38935	+	0.630690i	0.377695	+	0.0253701i
$619$			24.6624i			0.991264i	0.868533	+	0.495632i	$0.165064\pi$
$619$			24.6624i			0.991264i	−0.868533	+	0.495632i	$0.834936\pi$
$620$	10.4165	+	6.81879i	0.418338	+	0.273849i
$621$	3.13666	+	27.6524i	0.125870	+	1.10965i
$622$	−2.83466	+	3.90158i	−0.113660	+	0.156439i
$623$	31.9355	+	43.9555i	1.27947	+	1.76104i
$624$	2.21180	−	2.65065i	0.0885428	−	0.106111i
$625$	−17.0721	+	18.2632i	−0.682883	+	0.730528i
$626$	19.2429			0.769101
$627$	−6.03018	+	7.22666i	−0.240822	+	0.288605i
$628$	−10.9807	−	3.56786i	−0.438179	−	0.142373i
$629$	12.0296	+	3.90867i	0.479653	+	0.155849i
$630$	27.9083	+	2.41859i	1.11189	+	0.0963590i
$631$	−13.7239	+	4.45918i	−0.546342	+	0.177517i	−0.569167	−	0.822222i	$-0.692734\pi$
$631$	−13.7239	+	4.45918i	−0.546342	+	0.177517i	0.0228247	+	0.999739i	$0.492734\pi$
$632$	6.02361	−	8.29079i	0.239606	−	0.329790i
$633$	8.62282	+	3.45636i	0.342726	+	0.137378i
$634$	−4.85578	+	14.9446i	−0.192848	+	0.593524i
$635$	−0.211051	−	4.42176i	−0.00837530	−	0.175472i
$636$	4.95407	−	12.3593i	0.196442	−	0.490077i
$637$	6.42912	−	19.7868i	0.254731	−	0.783982i
$638$	11.6153	−	8.43903i	0.459855	−	0.334104i
$639$	−11.5734	−	21.4813i	−0.457838	−	0.849787i
$640$	−2.15715	−	0.588809i	−0.0852689	−	0.0232747i
$641$	−15.9935	−	11.6200i	−0.631707	−	0.458962i	0.225284	−	0.974293i	$-0.427669\pi$
$641$	−15.9935	−	11.6200i	−0.631707	−	0.458962i	−0.856991	+	0.515331i	$0.827669\pi$
$642$	23.7306	−	5.98590i	0.936573	−	0.236245i
$643$	9.54590	−	29.3792i	0.376453	−	1.15860i	−0.566040	−	0.824378i	$-0.691525\pi$
$643$	9.54590	−	29.3792i	0.376453	−	1.15860i	0.942493	−	0.334226i	$-0.108475\pi$
$644$	−6.91132	−	21.2709i	−0.272344	−	0.838189i
$645$	10.7085	+	0.207516i	0.421648	+	0.00817093i
$646$		−	21.8137i		−	0.858248i
$647$	1.22010	−	0.396435i	0.0479671	−	0.0155855i	−0.284935	−	0.958547i	$-0.591972\pi$
$647$	1.22010	−	0.396435i	0.0479671	−	0.0155855i	0.332902	+	0.942961i	$0.391972\pi$
$648$	−8.67805	−	2.38566i	−0.340906	−	0.0937176i
$649$	−11.5253	+	15.8632i	−0.452408	+	0.622687i
$650$	−3.96831	−	9.14161i	−0.155650	−	0.358564i
$651$	−37.3951	−	14.9454i	−1.46563	−	0.585758i
$652$		−	15.6962i		−	0.614712i
$653$	18.2650	+	13.2703i	0.714765	+	0.519307i	0.884707	−	0.466147i	$-0.154358\pi$
$653$	18.2650	+	13.2703i	0.714765	+	0.519307i	−0.169942	+	0.985454i	$0.554358\pi$
$654$	5.19331	+	2.08168i	0.203075	+	0.0814002i
$655$	3.68756	−	13.5097i	0.144085	−	0.527867i
$656$			7.34318i			0.286703i
$657$	−8.41399	+	17.4942i	−0.328261	+	0.682513i
$658$	36.8461	−	11.9720i	1.43641	−	0.466718i
$659$	−9.67175	−	3.14254i	−0.376758	−	0.122416i	0.114516	−	0.993421i	$-0.463468\pi$
$659$	−9.67175	−	3.14254i	−0.376758	−	0.122416i	−0.491273	+	0.871005i	$0.663468\pi$
$660$	−2.18958	+	6.31951i	−0.0852294	+	0.245987i
$661$	−9.48455	−	6.89093i	−0.368906	−	0.268026i	0.387851	−	0.921722i	$-0.373218\pi$
$661$	−9.48455	−	6.89093i	−0.368906	−	0.268026i	−0.756757	+	0.653696i	$0.773218\pi$
$662$	−7.18185	+	2.33352i	−0.279131	+	0.0906950i
$663$	23.8772	+	1.60385i	0.927313	+	0.0622883i
$664$	0.428315	+	0.589524i	0.0166218	+	0.0228780i
$665$	22.9215	−	18.3850i	0.888856	−	0.712940i
$666$	−0.980120	−	5.38559i	−0.0379789	−	0.208687i
$667$	−26.1736	−	36.0249i	−1.01345	−	1.39489i
$668$	11.7882	+	3.83021i	0.456099	+	0.148195i
$669$	−37.6701	−	15.0996i	−1.45641	−	0.583786i
$670$	−6.22478	−	16.4451i	−0.240484	−	0.635328i
$671$	21.3946	−	6.95152i	0.825928	−	0.268360i
$672$	7.21664	+	0.484747i	0.278388	+	0.0186995i
$673$	−0.649428	+	1.99874i	−0.0250336	+	0.0770456i	−0.962793	−	0.270241i	$-0.912897\pi$
$673$	−0.649428	+	1.99874i	−0.0250336	+	0.0770456i	0.937759	+	0.347286i	$0.112897\pi$
$674$	9.02482	−	27.7755i	0.347623	−	1.06987i
$675$	−17.4058	+	19.2883i	−0.669950	+	0.742407i
$676$	−9.02734			−0.347205
$677$		−	23.2013i		−	0.891699i	−0.895108	−	0.445850i	$-0.852902\pi$
$677$		−	23.2013i		−	0.891699i	0.895108	−	0.445850i	$-0.147098\pi$
$678$	9.12695	−	10.9379i	0.350518	−	0.420066i
$679$	14.8165	−	10.7648i	0.568605	−	0.413116i
$680$	−5.48728	−	14.4967i	−0.210428	−	0.555922i
$681$	−19.9202	−	31.6852i	−0.763344	−	1.21418i
$682$	5.64351	−	7.78420i	0.216101	−	0.298072i
$683$	7.19691			0.275382			0.137691	−	0.990475i	$-0.456032\pi$
$683$	7.19691			0.275382			0.137691	+	0.990475i	$0.456032\pi$
$684$	−8.31095	+	4.47767i	−0.317777	+	0.171208i
$685$	−30.7391	+	1.46718i	−1.17448	+	0.0560581i
$686$	13.6552	−	4.43684i	0.521358	−	0.169399i
$687$	15.9844	−	10.0492i	0.609843	−	0.383402i
$688$	2.76545			0.105432
$689$	14.5725	−	4.73489i	0.555168	−	0.180385i
$690$	19.5999	+	6.79098i	0.746156	+	0.258528i
$691$	12.0532	−	37.0958i	0.458524	−	1.41119i	−0.408423	−	0.912793i	$-0.633921\pi$
$691$	12.0532	−	37.0958i	0.458524	−	1.41119i	0.866947	−	0.498400i	$-0.166079\pi$
$692$	−19.3499	−	14.0585i	−0.735572	−	0.534424i
$693$	2.89324	−	21.4393i	0.109905	−	0.814411i
$694$	0.163252	−	0.224697i	0.00619695	−	0.00852937i
$695$	24.5285	−	1.17075i	0.930419	−	0.0444090i
$696$	13.9632	−	3.52212i	0.529272	−	0.133506i
$697$	−41.1814	+	29.9200i	−1.55986	+	1.13330i
$698$	0.695905	−	0.505604i	0.0263404	−	0.0191374i
$699$	28.8773	−	7.28411i	1.09224	−	0.275510i
$700$	10.6081	−	17.9840i	0.400948	−	0.679733i
$701$	25.2168	−	34.7080i	0.952426	−	1.31090i	0.00198465	−	0.999998i	$-0.499368\pi$
$701$	25.2168	−	34.7080i	0.952426	−	1.31090i	0.950441	−	0.310904i	$-0.100632\pi$
$702$	−4.29018	−	9.42636i	−0.161922	−	0.355775i
$703$	−4.64531	−	3.37502i	−0.175201	−	0.127291i
$704$	−0.533628	+	1.64234i	−0.0201119	+	0.0618979i
$705$	−11.7635	+	33.9516i	−0.443041	+	1.27869i
$706$	0.831339	−	0.270118i	0.0312878	−	0.0101660i
$707$	24.5068			0.921674
$708$	−16.6499	+	10.4677i	−0.625743	+	0.393398i
$709$	44.9028	−	14.5898i	1.68636	−	0.547932i	0.700233	−	0.713914i	$-0.253079\pi$
$709$	44.9028	−	14.5898i	1.68636	−	0.547932i	0.986129	+	0.165982i	$0.0530794\pi$
$710$	−18.1665	+	0.867088i	−0.681776	+	0.0325412i
$711$	−14.5821	−	27.0657i	−0.546872	−	1.01504i
$712$	−13.0108			−0.487600
$713$	−24.1427	−	17.5033i	−0.904150	−	0.655504i
$714$	26.6859	+	42.4468i	0.998694	+	1.58853i
$715$	−7.19791	+	2.72455i	−0.269186	+	0.101892i
$716$	−5.68551	+	4.13077i	−0.212478	+	0.154374i
$717$	−2.04125	+	2.44627i	−0.0762321	+	0.0913576i
$718$			10.6455i			0.397285i
$719$	17.2964			0.645049			0.322524	−	0.946561i	$-0.395469\pi$
$719$	17.2964			0.645049			0.322524	+	0.946561i	$0.395469\pi$
$720$	−4.39682	+	5.06635i	−0.163860	+	0.188812i
$721$	−7.01111	+	21.5780i	−0.261107	+	0.803606i
$722$	2.81132	−	8.65235i	0.104626	−	0.322007i
$723$	−43.2479	−	2.90499i	−1.60840	−	0.108038i
$724$	−9.17555	+	2.98132i	−0.341007	+	0.110800i
$725$	9.02212	−	40.5799i	0.335073	−	1.50710i
$726$	−12.8905	−	5.16702i	−0.478412	−	0.191766i
$727$	6.36991	+	2.06971i	0.236247	+	0.0767612i	0.424748	−	0.905312i	$-0.360363\pi$
$727$	6.36991	+	2.06971i	0.236247	+	0.0767612i	−0.188501	+	0.982073i	$0.560363\pi$
$728$	4.89228	+	6.73365i	0.181320	+	0.249566i
$729$	−17.7338	+	20.3595i	−0.656809	+	0.754057i
$730$	9.05317	+	11.2870i	0.335073	+	0.417751i
$731$	11.2679	+	15.5090i	0.416759	+	0.573619i
$732$	22.5125	+	1.51218i	0.832087	+	0.0558919i
$733$	−41.1573	+	13.3728i	−1.52018	+	0.493936i	−0.945827	−	0.324672i	$-0.894746\pi$
$733$	−41.1573	+	13.3728i	−1.52018	+	0.493936i	−0.574353	+	0.818608i	$0.694746\pi$
$734$	6.34337	+	4.60873i	0.234138	+	0.170111i
$735$	−13.2353	+	38.1993i	−0.488191	+	1.40900i
$736$	5.09370	+	1.65504i	0.187756	+	0.0610057i
$737$	−12.9148	+	4.19628i	−0.475724	+	0.154572i
$738$	19.8527	+	9.54834i	0.730788	+	0.351479i
$739$		−	5.84347i		−	0.214956i	−0.994207	−	0.107478i	$-0.965723\pi$
$739$		−	5.84347i		−	0.214956i	0.994207	−	0.107478i	$-0.0342775\pi$
$740$	−3.93612	−	1.07439i	−0.144695	−	0.0394953i
$741$	−10.0836	−	4.04191i	−0.370431	−	0.148483i
$742$	25.9714	+	18.8694i	0.953442	+	0.692716i
$743$			8.92562i			0.327449i	0.986506	+	0.163725i	$0.0523509\pi$
$743$			8.92562i			0.327449i	−0.986506	+	0.163725i	$0.947649\pi$
$744$	8.15902	−	5.14104i	0.299124	−	0.188480i
$745$	5.64035	+	3.70042i	0.206646	+	0.135573i
$746$	−19.0337	+	26.1977i	−0.696874	+	0.959165i
$747$	2.15075	−	0.391414i	0.0786918	−	0.0143211i
$748$	−11.3847	+	3.69911i	−0.416266	+	0.135253i
$749$			59.0058i			2.15603i
$750$	7.36538	+	17.9095i	0.268946	+	0.653964i
$751$	−11.7227	−	36.0786i	−0.427766	−	1.31653i	−0.900321	−	0.435227i	$-0.856668\pi$
$751$	−11.7227	−	36.0786i	−0.427766	−	1.31653i	0.472555	−	0.881301i	$-0.343332\pi$
$752$	−2.86692	+	8.82347i	−0.104546	+	0.321759i
$753$	16.0987	−	4.06079i	0.586669	−	0.147983i
$754$	13.4065	+	9.74042i	0.488237	+	0.354725i
$755$	3.93977	−	14.4337i	0.143383	−	0.525296i
$756$	10.6943	−	18.8803i	0.388949	−	0.686669i
$757$	12.0471	−	8.75272i	0.437859	−	0.318123i	−0.346925	−	0.937893i	$-0.612774\pi$
$757$	12.0471	−	8.75272i	0.437859	−	0.318123i	0.784784	+	0.619770i	$0.212774\pi$
$758$	2.23614	−	6.88212i	0.0812201	−	0.249970i
$759$	5.96017	−	14.8692i	0.216341	−	0.539720i
$760$	0.335470	+	7.02847i	0.0121688	+	0.254949i
$761$	4.07099	−	12.5292i	0.147573	−	0.454184i	−0.849760	−	0.527170i	$-0.823253\pi$
$761$	4.07099	−	12.5292i	0.147573	−	0.454184i	0.997333	+	0.0729865i	$0.0232530\pi$
$762$	−3.18280	−	1.27579i	−0.115301	−	0.0462171i
$763$	−7.92882	+	10.9131i	−0.287043	+	0.395080i
$764$	−14.7673	+	4.79818i	−0.534262	+	0.173592i
$765$	−46.3277	−	4.01486i	−1.67498	−	0.145157i
$766$	−32.6623	−	10.6126i	−1.18014	−	0.383450i
$767$	−21.5241	−	6.99361i	−0.777191	−	0.252525i
$768$	−1.10970	+	1.32988i	−0.0400427	+	0.0479878i
$769$	−48.9356			−1.76466			−0.882331	−	0.470629i	$-0.844027\pi$
$769$	−48.9356			−1.76466			−0.882331	+	0.470629i	$0.844027\pi$
$770$	−13.4822	−	8.84517i	−0.485866	−	0.318758i
$771$	−8.58362	+	10.2867i	−0.309132	+	0.370468i
$772$	2.40314	+	3.30765i	0.0864911	+	0.119045i
$773$	−22.9961	+	31.6515i	−0.827114	+	1.13842i	0.161340	+	0.986899i	$0.448419\pi$
$773$	−22.9961	+	31.6515i	−0.827114	+	1.13842i	−0.988453	+	0.151525i	$0.951581\pi$
$774$	3.59592	−	7.47655i	0.129253	−	0.268739i
$775$	−2.67955	−	27.7096i	−0.0962522	−	0.995357i
$776$			4.38567i			0.157436i
$777$	13.1681	+	0.884510i	0.472402	+	0.0317316i
$778$	17.6499	−	12.8234i	0.632778	−	0.459740i
$779$	21.9766	−	7.14063i	0.787393	−	0.255840i
$780$	−7.71800	−	0.149564i	−0.276349	−	0.00535524i
$781$			14.0455i			0.502586i
$782$	11.4728	+	35.3096i	0.410265	+	1.26267i
$783$	8.63406	−	42.3300i	0.308556	−	1.51275i
$784$	−3.22560	+	9.92738i	−0.115200	+	0.354549i
$785$	9.13952	+	24.1454i	0.326204	+	0.861787i
$786$	−8.32868	−	6.94975i	−0.297074	−	0.247889i
$787$	−19.8449	−	14.4182i	−0.707395	−	0.513953i	0.174937	−	0.984580i	$-0.444028\pi$
$787$	−19.8449	−	14.4182i	−0.707395	−	0.513953i	−0.882332	+	0.470627i	$0.844028\pi$
$788$	−3.08317	−	4.24362i	−0.109833	−	0.151173i
$789$	−11.0206	−	43.6902i	−0.392343	−	1.55541i
$790$	−22.8891	+	1.09250i	−0.814359	+	0.0388694i
$791$	20.1879	+	27.7863i	0.717800	+	0.987967i
$792$	3.74628	+	3.57823i	0.133118	+	0.127147i
$793$	15.2616	+	21.0058i	0.541956	+	0.745939i
$794$	−18.0716	+	24.8734i	−0.641337	+	0.882725i
$795$	−28.4894	+	8.65021i	−1.01041	+	0.306791i
$796$	9.62744	−	13.2510i	0.341236	−	0.469671i
$797$	15.5895	+	5.06533i	0.552207	+	0.179423i	0.571812	−	0.820385i	$-0.306241\pi$
$797$	15.5895	+	5.06533i	0.552207	+	0.179423i	−0.0196046	+	0.999808i	$0.506241\pi$
$798$	−5.56683	−	22.0693i	−0.197064	−	0.781243i
$799$	−61.1643	+	19.8735i	−2.16384	+	0.703074i
$800$	1.99097	+	4.58651i	0.0703914	+	0.162157i
$801$	−16.9180	+	35.1754i	−0.597766	+	1.24286i
$802$	−6.30192	−	19.3953i	−0.222529	−	0.684873i
$803$	9.04007	−	6.56800i	0.319017	−	0.231780i
$804$	−13.5897	−	0.912829i	−0.479271	−	0.0321930i
$805$	−27.4332	+	41.8150i	−0.966895	+	1.47379i
$806$	10.5577	+	3.41859i	0.371880	+	0.120415i
$807$	0.0737929	+	0.117376i	0.00259763	+	0.00413182i
$808$	−3.44948	+	4.74781i	−0.121352	+	0.167027i
$809$	9.47969	−	6.88740i	0.333288	−	0.242148i	−0.408536	−	0.912742i	$-0.633961\pi$
$809$	9.47969	−	6.88740i	0.333288	−	0.242148i	0.741825	+	0.670594i	$0.233961\pi$
$810$	7.97998	+	18.4748i	0.280388	+	0.649140i
$811$	−11.6494			−0.409067			−0.204533	−	0.978860i	$-0.565568\pi$
$811$	−11.6494			−0.409067			−0.204533	+	0.978860i	$0.565568\pi$
$812$			34.7192i			1.21840i
$813$	19.8641	+	16.5753i	0.696664	+	0.581321i
$814$	−0.973701	+	2.99674i	−0.0341282	+	0.105036i
$815$	−27.3789	+	21.9603i	−0.959042	+	0.769235i
$816$	−11.9796	−	0.804679i	−0.419370	−	0.0281694i
$817$	−2.68917	−	8.27641i	−0.0940821	−	0.289555i
$818$	−6.66892	+	9.17898i	−0.233173	+	0.320935i
$819$	24.5662	−	4.47079i	0.858413	−	0.156222i
$820$	12.8087	−	10.2737i	0.447299	−	0.358773i
$821$	−12.7650	+	9.27431i	−0.445501	+	0.323676i	−0.787817	−	0.615909i	$-0.788789\pi$
$821$	−12.7650	+	9.27431i	−0.445501	+	0.323676i	0.342316	+	0.939585i	$0.388789\pi$
$822$	−8.86902	+	22.1262i	−0.309343	+	0.771738i
$823$	−12.3384	+	37.9736i	−0.430088	+	1.32368i	0.467949	+	0.883756i	$0.344993\pi$
$823$	−12.3384	+	37.9736i	−0.430088	+	1.32368i	−0.898037	+	0.439920i	$0.855007\pi$
$824$	−3.19353	−	4.39552i	−0.111252	−	0.153125i
$825$	14.0865	−	5.02221i	0.490429	−	0.174851i
$826$	−14.6525	−	45.0958i	−0.509826	−	1.56908i
$827$	−16.1174	+	22.1838i	−0.560458	+	0.771405i	−0.991385	−	0.130982i	$-0.958187\pi$
$827$	−16.1174	+	22.1838i	−0.560458	+	0.771405i	0.430926	+	0.902387i	$0.358187\pi$
$828$	11.0978	−	11.6191i	0.385677	−	0.403790i
$829$	9.49836	+	3.08621i	0.329892	+	0.107188i	0.469280	−	0.883049i	$-0.344514\pi$
$829$	9.49836	+	3.08621i	0.329892	+	0.107188i	−0.139388	+	0.990238i	$0.544514\pi$
$830$	0.429060	−	1.57190i	0.0148929	−	0.0545614i
$831$	2.83379	+	4.50745i	0.0983031	+	0.156362i
$832$	−1.99315			−0.0691002
$833$	−68.8167	+	22.3599i	−2.38436	+	0.774725i
$834$	7.07711	−	17.6557i	0.245060	−	0.611368i
$835$	−9.81158	−	25.9209i	−0.339544	−	0.897029i
$836$	5.43408			0.187942
$837$	−3.28992	−	28.7433i	−0.113716	−	0.993513i
$838$		−	25.0319i		−	0.864712i
$839$	−25.5154	+	35.1189i	−0.880889	+	1.21244i	0.0952849	+	0.995450i	$0.469624\pi$
$839$	−25.5154	+	35.1189i	−0.880889	+	1.21244i	−0.976174	+	0.216990i	$0.930376\pi$
$840$	−9.25110	−	13.2662i	−0.319193	−	0.457726i
$841$	12.3993	+	38.1612i	0.427563	+	1.31590i
$842$	6.01362			0.207243
$843$	18.9290	−	11.9005i	0.651949	−	0.409874i
$844$	−1.65739	−	5.10093i	−0.0570499	−	0.175581i
$845$	12.6300	+	15.7464i	0.434484	+	0.541691i
$846$	20.1269	+	19.2240i	0.691977	+	0.660936i
$847$	19.6804	−	27.0878i	0.676228	−	0.930748i
$848$	−7.31127	+	2.37558i	−0.251070	+	0.0815776i
$849$	17.6520	+	1.18570i	0.605814	+	0.0406930i
$850$	−17.6094	+	29.8534i	−0.603996	+	1.02396i
$851$	9.29439	+	3.01993i	0.318607	+	0.103522i
$852$	−5.24150	+	13.0763i	−0.179571	+	0.447987i
$853$	−6.38749	−	8.79163i	−0.218704	−	0.301020i	0.685541	−	0.728034i	$-0.259566\pi$
$853$	−6.38749	−	8.79163i	−0.218704	−	0.301020i	−0.904245	+	0.427014i	$0.859566\pi$
$854$	−16.8103	+	51.7368i	−0.575236	+	1.77040i
$855$	19.4381	+	8.23216i	0.664768	+	0.281534i
$856$	−11.4314	−	8.30542i	−0.390718	−	0.283873i
$857$	−4.68798	−	14.4281i	−0.160138	−	0.492855i	0.838507	−	0.544891i	$-0.183429\pi$
$857$	−4.68798	−	14.4281i	−0.160138	−	0.492855i	−0.998645	+	0.0520357i	$0.983429\pi$
$858$	−0.399540	+	5.94813i	−0.0136401	+	0.203066i
$859$	−7.99332	−	2.59719i	−0.272728	−	0.0886149i	0.169460	−	0.985537i	$-0.445798\pi$
$859$	−7.99332	−	2.59719i	−0.272728	−	0.0886149i	−0.442188	+	0.896922i	$0.645798\pi$
$860$	−3.86909	−	4.82377i	−0.131935	−	0.164489i
$861$	−34.0283	+	40.7800i	−1.15968	+	1.38978i
$862$		−	30.4038i		−	1.03556i
$863$		−	19.5300i		−	0.664810i	−0.943137	−	0.332405i	$-0.892140\pi$
$863$		−	19.5300i		−	0.664810i	0.943137	−	0.332405i	$-0.107860\pi$
$864$	2.15246	+	4.72937i	0.0732281	+	0.160896i
$865$	2.54979	+	53.4209i	0.0866953	+	1.81637i
$866$	22.2355	+	16.1550i	0.755592	+	0.548970i
$867$	−28.6266	−	45.5338i	−0.972212	−	1.54641i
$868$	7.20721	+	22.1053i	0.244629	+	0.750301i
$869$			17.6968i			0.600323i
$870$	−25.6792	−	19.4282i	−0.870607	−	0.658678i
$871$	−9.21267	−	12.6802i	−0.312160	−	0.429651i
$872$	−0.998207	−	3.07217i	−0.0338036	−	0.104037i
$873$	11.8569	+	5.70269i	0.401296	+	0.193007i
$874$		−	16.8538i		−	0.570087i
$875$	−46.2111	+	6.65745i	−1.56222	+	0.225063i
$876$	10.8674	−	2.74122i	0.367174	−	0.0926174i
$877$	−3.31982	−	1.07867i	−0.112102	−	0.0364242i	0.252429	−	0.967615i	$-0.418771\pi$
$877$	−3.31982	−	1.07867i	−0.112102	−	0.0364242i	−0.364531	+	0.931191i	$0.618771\pi$
$878$	−22.0943	−	16.0525i	−0.745647	−	0.541744i
$879$	29.7287	−	35.6273i	1.00273	−	1.20168i
$880$	3.61131	−	1.36695i	0.121737	−	0.0460800i
$881$	2.00991	−	1.46028i	0.0677155	−	0.0491982i	−0.553413	−	0.832907i	$-0.686675\pi$
$881$	2.00991	−	1.46028i	0.0677155	−	0.0491982i	0.621128	+	0.783709i	$0.286675\pi$
$882$	22.6450	+	21.6292i	0.762497	+	0.728293i
$883$	0.0408265	−	0.0296622i	0.00137392	−	0.000998213i	−0.587098	−	0.809516i	$-0.699730\pi$
$883$	0.0408265	−	0.0296622i	0.00137392	−	0.000998213i	0.588472	+	0.808518i	$0.299730\pi$
$884$	−8.12117	−	11.1778i	−0.273144	−	0.375951i
$885$	41.5533	+	14.3974i	1.39680	+	0.483963i
$886$	−8.59782	+	6.24669i	−0.288850	+	0.209861i
$887$	13.1029	+	9.51980i	0.439952	+	0.319644i	0.785616	−	0.618715i	$-0.212346\pi$
$887$	13.1029	+	9.51980i	0.439952	+	0.319644i	−0.345664	+	0.938358i	$0.612346\pi$
$888$	−2.02484	+	2.42660i	−0.0679493	+	0.0814315i
$889$	4.85931	−	6.68826i	0.162976	−	0.224317i
$890$	18.2031	+	22.6947i	0.610171	+	0.760729i
$891$	14.5452	−	5.47550i	0.487283	−	0.183436i
$892$	7.24058	+	22.2842i	0.242433	+	0.746131i
$893$	29.1946			0.976961
$894$	4.42371	−	2.78114i	0.147951	−	0.0930154i
$895$	15.1598	+	4.13796i	0.506735	+	0.138317i
$896$	−2.45454	−	3.37839i	−0.0820005	−	0.112864i
$897$	18.4481	+	1.23917i	0.615963	+	0.0413747i
$898$	7.00186			0.233655
$899$	27.2473	+	37.4228i	0.908747	+	1.24812i
$900$	14.9887	+	0.581138i	0.499625	+	0.0193713i
$901$	−43.1125	−	31.3231i	−1.43629	−	1.04352i
$902$	−7.45348	−	10.2588i	−0.248174	−	0.341582i
$903$	15.3578	+	12.8151i	0.511076	+	0.426460i
$904$	−8.22472			−0.273550
$905$	18.0376	+	11.8338i	0.599591	+	0.393369i
$906$	−8.89833	−	7.42508i	−0.295627	−	0.246682i
$907$	4.10378	+	1.33340i	0.136264	+	0.0442748i	0.376355	−	0.926476i	$-0.377177\pi$
$907$	4.10378	+	1.33340i	0.136264	+	0.0442748i	−0.240091	+	0.970750i	$0.577177\pi$
$908$	−6.67736	+	20.5508i	−0.221596	+	0.682003i
$909$	8.35060	+	15.4995i	0.276972	+	0.514084i
$910$	4.90080	−	17.9545i	0.162460	−	0.595186i
$911$	−1.11764	−	0.812016i	−0.0370292	−	0.0269033i	0.569117	−	0.822257i	$-0.307285\pi$
$911$	−1.11764	−	0.812016i	−0.0370292	−	0.0269033i	−0.606146	+	0.795353i	$0.707285\pi$
$912$	5.05913	+	2.02790i	0.167525	+	0.0671503i
$913$	−1.19676	−	0.388850i	−0.0396069	−	0.0128691i
$914$	−16.9403	+	12.3079i	−0.560336	+	0.407108i
$915$	−28.8591	−	41.3842i	−0.954053	−	1.36812i
$916$	−10.3674	−	3.36856i	−0.342547	−	0.111300i
$917$	21.1580	−	15.3722i	0.698698	−	0.507634i
$918$	−17.7526	+	31.3412i	−0.585922	+	1.03441i
$919$	8.71424	+	26.8197i	0.287456	+	0.884699i	0.985652	+	0.168792i	$0.0539866\pi$
$919$	8.71424	+	26.8197i	0.287456	+	0.884699i	−0.698196	+	0.715907i	$0.746013\pi$
$920$	−4.23960	−	11.2005i	−0.139776	−	0.369269i
$921$	3.11616	+	12.3538i	0.102681	+	0.407070i
$922$	−12.4457	+	38.3038i	−0.409876	+	1.26147i
$923$	−15.4180	+	5.00960i	−0.507488	+	0.164893i
$924$	−10.5741	+	6.64781i	−0.347861	+	0.218697i
$925$	3.63289	+	8.36892i	0.119449	+	0.275168i
$926$	−12.7497	−	39.2397i	−0.418983	−	1.28950i
$927$	−16.0361	+	2.91840i	−0.526694	+	0.0958527i
$928$	−6.72629	−	4.88694i	−0.220801	−	0.160422i
$929$	−49.1526			−1.61265			−0.806323	−	0.591476i	$-0.798545\pi$
$929$	−49.1526			−1.61265			−0.806323	+	0.591476i	$0.798545\pi$
$930$	−20.3826	−	7.03904i	−0.668373	−	0.230819i
$931$	32.8472			1.07652
$932$	−13.9107	−	10.1067i	−0.455659	−	0.331056i
$933$	3.10784	−	7.75334i	0.101746	−	0.253833i
$934$	2.36991	+	7.29382i	0.0775457	+	0.238661i
$935$	22.3804	+	14.6829i	0.731919	+	0.480184i
$936$	−2.59170	+	5.38861i	−0.0847124	+	0.176132i
$937$	2.35042	−	0.763697i	0.0767848	−	0.0249489i	−0.270373	−	0.962756i	$-0.587147\pi$
$937$	2.35042	−	0.763697i	0.0767848	−	0.0249489i	0.347157	+	0.937807i	$0.387147\pi$
$938$	10.1475	−	31.2309i	0.331328	−	1.01972i
$939$	−32.3174	+	8.15186i	−1.05464	+	0.266026i
$940$	19.4018	−	7.34397i	0.632817	−	0.239534i
$941$	1.82156	+	5.60618i	0.0593811	+	0.182756i	0.976347	−	0.216209i	$-0.0693693\pi$
$941$	1.82156	+	5.60618i	0.0593811	+	0.182756i	−0.916966	+	0.398966i	$0.869369\pi$
$942$	19.9530	+	1.34026i	0.650104	+	0.0436680i
$943$	−31.8177	+	23.1169i	−1.03613	+	0.752790i
$944$	10.7990	+	3.50882i	0.351478	+	0.114202i
$945$	−47.8950	+	7.76088i	−1.55803	+	0.252461i
$946$	−3.86349	+	2.80699i	−0.125613	+	0.0912631i
$947$	−33.4313	−	10.8625i	−1.08637	−	0.352983i	−0.289528	−	0.957170i	$-0.593498\pi$
$947$	−33.4313	−	10.8625i	−1.08637	−	0.352983i	−0.796843	+	0.604186i	$0.793498\pi$
$948$	−6.60411	+	16.4757i	−0.214491	+	0.535106i
$949$	10.4341	+	7.58085i	0.338707	+	0.246085i
$950$	11.7904	−	10.4185i	0.382531	−	0.338022i
$951$	1.82407	−	27.1556i	0.0591494	−	0.880582i
$952$	8.94526	−	27.5307i	0.289918	−	0.892274i
$953$	36.8161	+	11.9623i	1.19259	+	0.387496i	0.837030	−	0.547158i	$-0.184290\pi$
$953$	36.8161	+	11.9623i	1.19259	+	0.387496i	0.355560	+	0.934653i	$0.384290\pi$
$954$	−3.08435	+	22.8554i	−0.0998594	+	0.739971i
$955$	29.0301	+	19.0455i	0.939391	+	0.616298i
$956$	1.83947			0.0594927
$957$	−15.9323	+	19.0935i	−0.515018	+	0.617205i
$958$	23.6254	+	32.5175i	0.763301	+	1.05059i
$959$	−46.4953	−	33.7808i	−1.50141	−	1.09084i
$960$	3.87226	+	0.0750387i	0.124977	+	0.00242186i
$961$	25.1164	+	18.1705i	0.810207	+	0.586144i
$962$	−3.63687			−0.117258
$963$	−37.3185	+	20.1060i	−1.20257	+	0.647906i
$964$	14.7096	+	20.2460i	0.473764	+	0.652080i
$965$	2.40733	−	8.81946i	0.0774947	−	0.283908i
$966$	20.6182	+	32.7954i	0.663378	+	1.05518i
$967$	−17.3213			−0.557014			−0.278507	−	0.960434i	$-0.589840\pi$
$967$	−17.3213			−0.557014			−0.278507	+	0.960434i	$0.589840\pi$
$968$	2.47769	+	7.62554i	0.0796359	+	0.245094i
$969$	9.24092	+	36.6349i	0.296861	+	1.17688i
$970$	7.64992	−	6.13590i	0.245624	−	0.197012i
$971$	19.0653	−	26.2411i	0.611834	−	0.842118i	−0.384893	−	0.922961i	$-0.625762\pi$
$971$	19.0653	−	26.2411i	0.611834	−	0.842118i	0.996727	+	0.0808438i	$0.0257615\pi$
$972$	15.5850	+	0.330309i	0.499888	+	0.0105947i
$973$	37.1013	+	26.9557i	1.18941	+	0.864159i
$974$	32.2886	−	23.4591i	1.03459	−	0.751677i
$975$	10.5372	+	13.6718i	0.337461	+	0.437847i
$976$	−7.65702	−	10.5390i	−0.245095	−	0.337345i
$977$	4.55906	−	3.31235i	0.145857	−	0.105971i	−0.512464	−	0.858709i	$-0.671267\pi$
$977$	4.55906	−	3.31235i	0.145857	−	0.105971i	0.658321	+	0.752738i	$0.271267\pi$
$978$	6.64939	+	26.3610i	0.212624	+	0.842931i
$979$	18.1768	−	13.2062i	0.580933	−	0.422073i
$980$	21.8292	−	8.26279i	0.697308	−	0.263945i
$981$	−9.60375	−	1.29603i	−0.306624	−	0.0413791i
$982$	−18.1842	−	13.2116i	−0.580282	−	0.421600i
$983$	44.1505	+	14.3454i	1.40818	+	0.457546i	0.911827	−	0.410574i	$-0.134672\pi$
$983$	44.1505	+	14.3454i	1.40818	+	0.457546i	0.496355	+	0.868120i	$0.334672\pi$
$984$	−3.11079	−	12.3325i	−0.0991683	−	0.393145i
$985$	−3.08854	+	11.3151i	−0.0984090	+	0.360530i
$986$		−	57.6337i		−	1.83543i
$987$	−56.8093	+	35.7154i	−1.80826	+	1.13683i
$988$	1.93818	+	5.96509i	0.0616616	+	0.189775i
$989$	8.70586	+	11.9826i	0.276830	+	0.381024i
$990$	1.00015	−	11.5408i	0.0317870	−	0.366792i
$991$		−	40.6014i		−	1.28975i	−0.764290	−	0.644873i	$-0.776910\pi$
$991$		−	40.6014i		−	1.28975i	0.764290	−	0.644873i	$-0.223090\pi$
$992$	−5.29700	−	1.71517i	−0.168180	−	0.0544566i
$993$	11.0730	−	6.96147i	0.351390	−	0.220916i
$994$	−27.4783	−	19.9641i	−0.871557	−	0.633223i
$995$	−36.5833	+	1.74613i	−1.15977	+	0.0553559i
$996$	−0.969071	−	0.808628i	−0.0307062	−	0.0256223i
$997$		−	20.4330i		−	0.647119i	−0.946208	−	0.323559i	$-0.895120\pi$
$997$		−	20.4330i		−	0.647119i	0.946208	−	0.323559i	$-0.104880\pi$
$998$			35.3507i			1.11901i
$999$	3.92755	+	8.62960i	0.124262	+	0.273028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.3	yes	128
3.2	odd	2		930.2.y.a.29.18	✓	128
5.4	even	2		930.2.y.a.29.30	yes	128
15.14	odd	2	inner	930.2.y.b.29.15	yes	128
31.15	odd	10	inner	930.2.y.b.449.15	yes	128
93.77	even	10		930.2.y.a.449.30	yes	128
155.139	odd	10		930.2.y.a.449.18	yes	128
465.449	even	10	inner	930.2.y.b.449.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.18	✓	128	3.2	odd	2
930.2.y.a.29.30	yes	128	5.4	even	2
930.2.y.a.449.18	yes	128	155.139	odd	10
930.2.y.a.449.30	yes	128	93.77	even	10
930.2.y.b.29.3	yes	128	1.1	even	1	trivial
930.2.y.b.29.15	yes	128	15.14	odd	2	inner
930.2.y.b.449.3	yes	128	465.449	even	10	inner
930.2.y.b.449.15	yes	128	31.15	odd	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60770 - 0.644430i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.22659 - 1.86962i) q^{5} +(-0.921873 - 1.46634i) q^{6} +(3.97153 - 1.29043i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.16942 + 2.07210i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60770 - 0.644430i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.22659 - 1.86962i) q^{5} +(-0.921873 - 1.46634i) q^{6} +(3.97153 - 1.29043i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.16942 + 2.07210i) q^{9} +(2.09127 - 0.791586i) q^{10} +(-0.533628 - 1.64234i) q^{11} +(0.116082 - 1.72816i) q^{12} +(1.61250 - 1.17155i) q^{13} +(3.97153 + 1.29043i) q^{14} +(-3.17683 + 2.21535i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-6.59273 - 2.14211i) q^{17} +(0.537145 + 2.95152i) q^{18} +(2.54582 + 1.84965i) q^{19} +(2.15715 + 0.588809i) q^{20} +(-7.21664 - 0.484747i) q^{21} +(0.533628 - 1.64234i) q^{22} +(-5.09370 - 1.65504i) q^{23} +(1.10970 - 1.32988i) q^{24} +(-1.99097 - 4.58651i) q^{25} +1.99315 q^{26} +(-2.15246 - 4.72937i) q^{27} +(2.45454 + 3.37839i) q^{28} +(6.72629 + 4.88694i) q^{29} +(-3.87226 - 0.0750387i) q^{30} +(5.29700 + 1.71517i) q^{31} -1.00000 q^{32} +(-0.200456 + 2.98428i) q^{33} +(-4.07453 - 5.60811i) q^{34} +(2.45881 - 9.00808i) q^{35} +(-1.30030 + 2.70356i) q^{36} -1.82468 q^{37} +(0.972416 + 2.99279i) q^{38} +(-3.34739 + 0.844359i) q^{39} +(1.39908 + 1.74430i) q^{40} +(4.31621 - 5.94076i) q^{41} +(-5.55345 - 4.63400i) q^{42} +(-2.23730 - 1.62549i) q^{43} +(1.39706 - 1.01502i) q^{44} +(6.53503 - 1.51438i) q^{45} +(-3.14808 - 4.33296i) q^{46} +(7.50569 - 5.45320i) q^{47} +(1.67945 - 0.423630i) q^{48} +(8.44474 - 6.13546i) q^{49} +(1.08515 - 4.88082i) q^{50} +(9.21871 + 7.69243i) q^{51} +(1.61250 + 1.17155i) q^{52} +(7.31127 + 2.37558i) q^{53} +(1.03848 - 5.09132i) q^{54} +(-3.72509 - 1.01679i) q^{55} +4.17592i q^{56} +(-2.90095 - 4.61428i) q^{57} +(2.56921 + 7.90723i) q^{58} +(-6.67417 - 9.18620i) q^{59} +(-3.08861 - 2.33676i) q^{60} +13.0269i q^{61} +(3.27721 + 4.50110i) q^{62} +(11.2898 + 5.42995i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.212483 - 4.45176i) q^{65} +(-1.91629 + 2.29651i) q^{66} -7.86369i q^{67} -6.93201i q^{68} +(7.12260 + 5.94335i) q^{69} +(7.28404 - 5.84244i) q^{70} +(-7.73546 - 2.51340i) q^{71} +(-2.64108 + 1.42293i) q^{72} +(1.99959 + 6.15410i) q^{73} +(-1.47620 - 1.07252i) q^{74} +(0.245206 + 8.65678i) q^{75} +(-0.972416 + 2.99279i) q^{76} +(-4.23864 - 5.83399i) q^{77} +(-3.20440 - 1.28445i) q^{78} +(-9.74641 - 3.16680i) q^{79} +(0.106606 + 2.23353i) q^{80} +(0.412767 + 8.99053i) q^{81} +(6.98378 - 2.26917i) q^{82} +(0.428315 - 0.589524i) q^{83} +(-1.76904 - 7.01322i) q^{84} +(-12.0915 + 9.69843i) q^{85} +(-0.854571 - 2.63010i) q^{86} +(-7.66459 - 12.1914i) q^{87} +1.72686 q^{88} +(4.02056 + 12.3740i) q^{89} +(6.17708 + 2.61604i) q^{90} +(4.89228 - 6.73365i) q^{91} -5.35583i q^{92} +(-7.41070 - 6.17102i) q^{93} +9.27755 q^{94} +(6.58081 - 2.49097i) q^{95} +(1.60770 + 0.644430i) q^{96} +(4.17102 - 1.35525i) q^{97} +10.4383 q^{98} +(2.24543 - 4.66865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

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