LMFDB - Embedded newform 627.2.j.c.400.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [627,2,Mod(58,627)] 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("627.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			400.3
Character	$\chi$	$=$	627.400
Dual form			627.2.j.c.58.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33357 - 0.968898i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.221621 + 0.682079i) q^{4} +(-0.761553 + 0.553300i) q^{5} +(1.33357 - 0.968898i) q^{6} +(0.786208 + 2.41970i) q^{7} +(-0.653442 + 2.01109i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.55168 q^{10} +(1.43950 - 2.98795i) q^{11} -0.717181 q^{12} +(0.101753 + 0.0739276i) q^{13} +(1.29598 - 3.98860i) q^{14} +(-0.290887 - 0.895259i) q^{15} +(3.98037 - 2.89191i) q^{16} +(-2.57732 + 1.87253i) q^{17} +(0.509380 + 1.56771i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(-0.546171 - 0.396816i) q^{20} -2.54422 q^{21} +(-4.81470 + 2.58992i) q^{22} -6.09645 q^{23} +(-1.71073 - 1.24292i) q^{24} +(-1.27126 + 3.91255i) q^{25} +(-0.0640663 - 0.197176i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.47619 + 1.07251i) q^{28} +(-3.17169 - 9.76146i) q^{29} +(-0.479495 + 1.47573i) q^{30} +(-2.39972 - 1.74350i) q^{31} -3.88092 q^{32} +(2.39688 + 2.29238i) q^{33} +5.25134 q^{34} +(-1.93756 - 1.40772i) q^{35} +(0.221621 - 0.682079i) q^{36} +(1.37031 + 4.21739i) q^{37} +(1.33357 - 0.968898i) q^{38} +(-0.101753 + 0.0739276i) q^{39} +(-0.615105 - 1.89310i) q^{40} +(-3.38115 + 10.4061i) q^{41} +(3.39291 + 2.46509i) q^{42} -2.13525 q^{43} +(2.35704 + 0.319663i) q^{44} +0.941331 q^{45} +(8.13006 + 5.90683i) q^{46} +(-2.56028 + 7.87972i) q^{47} +(1.52037 + 4.67921i) q^{48} +(0.426290 - 0.309718i) q^{49} +(5.48618 - 3.98595i) q^{50} +(-0.984449 - 3.02982i) q^{51} +(-0.0278740 + 0.0857873i) q^{52} +(-9.60348 - 6.97734i) q^{53} -1.64839 q^{54} +(0.556975 + 3.07196i) q^{55} -5.37997 q^{56} +(-0.809017 - 0.587785i) q^{57} +(-5.22817 + 16.0907i) q^{58} +(-0.347738 - 1.07023i) q^{59} +(0.546171 - 0.396816i) q^{60} +(-1.69698 + 1.23293i) q^{61} +(1.51093 + 4.65017i) q^{62} +(0.786208 - 2.41970i) q^{63} +(-2.78526 - 2.02361i) q^{64} -0.118394 q^{65} +(-0.975333 - 5.37938i) q^{66} -13.4724 q^{67} +(-1.84840 - 1.34294i) q^{68} +(1.88391 - 5.79807i) q^{69} +(1.21994 + 3.75460i) q^{70} +(0.882840 - 0.641421i) q^{71} +(1.71073 - 1.24292i) q^{72} +(4.30138 + 13.2383i) q^{73} +(2.25880 - 6.95189i) q^{74} +(-3.32821 - 2.41809i) q^{75} -0.717181 q^{76} +(8.36169 + 1.13402i) q^{77} +0.207323 q^{78} +(1.79076 + 1.30106i) q^{79} +(-1.43117 + 4.40468i) q^{80} +(0.309017 + 0.951057i) q^{81} +(14.5915 - 10.6013i) q^{82} +(-8.36082 + 6.07449i) q^{83} +(-0.563854 - 1.73536i) q^{84} +(0.926692 - 2.85206i) q^{85} +(2.84751 + 2.06883i) q^{86} +10.2638 q^{87} +(5.06839 + 4.84742i) q^{88} -10.9034 q^{89} +(-1.25533 - 0.912053i) q^{90} +(-0.0988840 + 0.304334i) q^{91} +(-1.35110 - 4.15826i) q^{92} +(2.39972 - 1.74350i) q^{93} +(11.0490 - 8.02754i) q^{94} +(-0.290887 - 0.895259i) q^{95} +(1.19927 - 3.69098i) q^{96} +(-9.61769 - 6.98766i) q^{97} -0.868574 q^{98} +(-2.92085 + 1.57118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{2} + 10 q^{3} - 3 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 13 q^{8} - 10 q^{9} + 10 q^{10} + 7 q^{11} - 42 q^{12} - 12 q^{13} - 2 q^{14} - 7 q^{15} - 27 q^{16} + 11 q^{17} - 4 q^{18} + 10 q^{19}+ \cdots - 13 q^{99}+O(q^{100}) $ 40 * q + q^2 + 10 * q^3 - 3 * q^4 + 2 * q^5 - q^6 + 4 * q^7 - 13 * q^8 - 10 * q^9 + 10 * q^10 + 7 * q^11 - 42 * q^12 - 12 * q^13 - 2 * q^14 - 7 * q^15 - 27 * q^16 + 11 * q^17 - 4 * q^18 + 10 * q^19 - 11 * q^20 + 6 * q^21 - 2 * q^22 - 60 * q^23 - 7 * q^24 - 18 * q^25 - 35 * q^26 + 10 * q^27 + 20 * q^28 + 25 * q^29 - 5 * q^30 - 12 * q^31 + 40 * q^32 + 3 * q^33 - 10 * q^34 + 24 * q^35 - 3 * q^36 - 23 * q^37 - q^38 + 12 * q^39 + 80 * q^40 + 18 * q^41 - 28 * q^42 - 6 * q^43 + 14 * q^44 - 18 * q^45 - 15 * q^46 - 9 * q^47 - 8 * q^48 - 4 * q^49 + 90 * q^50 + 4 * q^51 + 15 * q^52 - 26 * q^53 - 6 * q^54 + 38 * q^55 - 124 * q^56 - 10 * q^57 + 10 * q^58 + 7 * q^59 + 11 * q^60 + 18 * q^61 + 105 * q^62 + 4 * q^63 - 85 * q^64 + 36 * q^65 - 8 * q^66 - 88 * q^67 + 40 * q^68 - 103 * q^70 + 30 * q^71 + 7 * q^72 - 2 * q^73 - 4 * q^74 + 13 * q^75 - 42 * q^76 + 57 * q^77 + 20 * q^78 + 59 * q^79 + 11 * q^80 - 10 * q^81 + 40 * q^82 - 54 * q^83 - 15 * q^84 + 21 * q^85 - 108 * q^86 - 30 * q^87 + 83 * q^88 - 74 * q^89 - 10 * q^90 + q^91 - 125 * q^92 + 12 * q^93 - 10 * q^94 - 7 * q^95 + 55 * q^96 - 17 * q^97 + 78 * q^98 - 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	−1.33357	−	0.968898i	−0.942979	−	0.685114i	0.00615708	−	0.999981i	$-0.498040\pi$
$2$	−1.33357	−	0.968898i	−0.942979	−	0.685114i	−0.949136	+	0.314867i	$0.898040\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	0.221621	+	0.682079i	0.110811	+	0.341040i
$5$	−0.761553	+	0.553300i	−0.340577	+	0.247443i	−0.744905	−	0.667170i	$-0.767505\pi$
$5$	−0.761553	+	0.553300i	−0.340577	+	0.247443i	0.404328	+	0.914614i	$0.367505\pi$
$6$	1.33357	−	0.968898i	0.544429	−	0.395551i
$7$	0.786208	+	2.41970i	0.297159	+	0.914561i	0.982488	+	0.186327i	$0.0596585\pi$
$7$	0.786208	+	2.41970i	0.297159	+	0.914561i	−0.685329	+	0.728234i	$0.740342\pi$
$8$	−0.653442	+	2.01109i	−0.231027	+	0.711027i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	1.55168			0.490684
$11$	1.43950	−	2.98795i	0.434027	−	0.900900i
$11$	1.43950	−	2.98795i	0.434027	−	0.900900i
$12$	−0.717181			−0.207032
$13$	0.101753	+	0.0739276i	0.0282211	+	0.0205038i	0.601806	−	0.798642i	$-0.294448\pi$
$13$	0.101753	+	0.0739276i	0.0282211	+	0.0205038i	−0.573585	+	0.819146i	$0.694448\pi$
$14$	1.29598	−	3.98860i	0.346364	−	1.06600i
$15$	−0.290887	−	0.895259i	−0.0751068	−	0.231155i
$16$	3.98037	−	2.89191i	0.995094	−	0.722978i
$17$	−2.57732	+	1.87253i	−0.625092	+	0.454156i	−0.854696	−	0.519128i	$-0.826257\pi$
$17$	−2.57732	+	1.87253i	−0.625092	+	0.454156i	0.229605	+	0.973284i	$0.426257\pi$
$18$	0.509380	+	1.56771i	0.120062	+	0.369513i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	−0.546171	−	0.396816i	−0.122128	−	0.0887308i
$21$	−2.54422			−0.555195
$22$	−4.81470	+	2.58992i	−1.02650	+	0.552172i
$23$	−6.09645			−1.27120			−0.635598	−	0.772020i	$-0.719247\pi$
$23$	−6.09645			−1.27120			−0.635598	+	0.772020i	$0.719247\pi$
$24$	−1.71073	−	1.24292i	−0.349202	−	0.253710i
$25$	−1.27126	+	3.91255i	−0.254253	+	0.782510i
$26$	−0.0640663	−	0.197176i	−0.0125644	−	0.0386694i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−1.47619	+	1.07251i	−0.278973	+	0.202686i
$29$	−3.17169	−	9.76146i	−0.588968	−	1.81266i	−0.582715	−	0.812677i	$-0.698010\pi$
$29$	−3.17169	−	9.76146i	−0.588968	−	1.81266i	−0.00625324	−	0.999980i	$-0.501990\pi$
$30$	−0.479495	+	1.47573i	−0.0875434	+	0.269431i
$31$	−2.39972	−	1.74350i	−0.431002	−	0.313142i	0.351047	−	0.936358i	$-0.385826\pi$
$31$	−2.39972	−	1.74350i	−0.431002	−	0.313142i	−0.782050	+	0.623216i	$0.785826\pi$
$32$	−3.88092			−0.686056
$33$	2.39688	+	2.29238i	0.417243	+	0.399051i
$34$	5.25134			0.900597
$35$	−1.93756	−	1.40772i	−0.327507	−	0.237948i
$36$	0.221621	−	0.682079i	0.0369368	−	0.113680i
$37$	1.37031	+	4.21739i	0.225278	+	0.693334i	0.998263	+	0.0589103i	$0.0187626\pi$
$37$	1.37031	+	4.21739i	0.225278	+	0.693334i	−0.772985	+	0.634424i	$0.781237\pi$
$38$	1.33357	−	0.968898i	0.216334	−	0.157176i
$39$	−0.101753	+	0.0739276i	−0.0162935	+	0.0118379i
$40$	−0.615105	−	1.89310i	−0.0972567	−	0.299325i
$41$	−3.38115	+	10.4061i	−0.528047	+	1.62516i	0.230163	+	0.973152i	$0.426074\pi$
$41$	−3.38115	+	10.4061i	−0.528047	+	1.62516i	−0.758210	+	0.652010i	$0.773926\pi$
$42$	3.39291	+	2.46509i	0.523537	+	0.380372i
$43$	−2.13525			−0.325622			−0.162811	−	0.986657i	$-0.552056\pi$
$43$	−2.13525			−0.325622			−0.162811	+	0.986657i	$0.552056\pi$
$44$	2.35704	+	0.319663i	0.355337	+	0.0481911i
$45$	0.941331			0.140325
$46$	8.13006	+	5.90683i	1.19871	+	0.870915i
$47$	−2.56028	+	7.87972i	−0.373455	+	1.14937i	0.571061	+	0.820908i	$0.306532\pi$
$47$	−2.56028	+	7.87972i	−0.373455	+	1.14937i	−0.944515	+	0.328467i	$0.893468\pi$
$48$	1.52037	+	4.67921i	0.219446	+	0.675386i
$49$	0.426290	−	0.309718i	0.0608986	−	0.0442454i
$50$	5.48618	−	3.98595i	0.775863	−	0.563698i
$51$	−0.984449	−	3.02982i	−0.137850	−	0.424260i
$52$	−0.0278740	+	0.0857873i	−0.00386543	+	0.0118966i
$53$	−9.60348	−	6.97734i	−1.31914	−	0.958411i	−0.999943	−	0.0107232i	$-0.996587\pi$
$53$	−9.60348	−	6.97734i	−1.31914	−	0.958411i	−0.319198	−	0.947688i	$-0.603413\pi$
$54$	−1.64839			−0.224317
$55$	0.556975	+	3.07196i	0.0751025	+	0.414223i
$56$	−5.37997			−0.718929
$57$	−0.809017	−	0.587785i	−0.107157	−	0.0778541i
$58$	−5.22817	+	16.0907i	−0.686493	+	2.11281i
$59$	−0.347738	−	1.07023i	−0.0452717	−	0.139332i	0.925866	−	0.377853i	$-0.123337\pi$
$59$	−0.347738	−	1.07023i	−0.0452717	−	0.139332i	−0.971137	+	0.238521i	$0.923337\pi$
$60$	0.546171	−	0.396816i	0.0705104	−	0.0512288i
$61$	−1.69698	+	1.23293i	−0.217276	+	0.157861i	−0.691100	−	0.722759i	$-0.742874\pi$
$61$	−1.69698	+	1.23293i	−0.217276	+	0.157861i	0.473823	+	0.880620i	$0.342874\pi$
$62$	1.51093	+	4.65017i	0.191888	+	0.590572i
$63$	0.786208	−	2.41970i	0.0990530	−	0.304854i
$64$	−2.78526	−	2.02361i	−0.348157	−	0.252951i
$65$	−0.118394			−0.0146850
$66$	−0.975333	−	5.37938i	−0.120055	−	0.662156i
$67$	−13.4724			−1.64592			−0.822958	−	0.568102i	$-0.807678\pi$
$67$	−13.4724			−1.64592			−0.822958	+	0.568102i	$0.807678\pi$
$68$	−1.84840	−	1.34294i	−0.224152	−	0.162856i
$69$	1.88391	−	5.79807i	0.226796	−	0.698005i
$70$	1.21994	+	3.75460i	0.145811	+	0.448760i
$71$	0.882840	−	0.641421i	0.104774	−	0.0761226i	−0.534165	−	0.845380i	$-0.679374\pi$
$71$	0.882840	−	0.641421i	0.104774	−	0.0761226i	0.638939	+	0.769258i	$0.279374\pi$
$72$	1.71073	−	1.24292i	0.201612	−	0.146480i
$73$	4.30138	+	13.2383i	0.503439	+	1.54943i	0.803379	+	0.595468i	$0.203033\pi$
$73$	4.30138	+	13.2383i	0.503439	+	1.54943i	−0.299940	+	0.953958i	$0.596967\pi$
$74$	2.25880	−	6.95189i	0.262581	−	0.808140i
$75$	−3.32821	−	2.41809i	−0.384309	−	0.279217i
$76$	−0.717181			−0.0822663
$77$	8.36169	+	1.13402i	0.952903	+	0.129233i
$78$	0.207323			0.0234747
$79$	1.79076	+	1.30106i	0.201476	+	0.146381i	0.683949	−	0.729530i	$-0.260261\pi$
$79$	1.79076	+	1.30106i	0.201476	+	0.146381i	−0.482473	+	0.875911i	$0.660261\pi$
$80$	−1.43117	+	4.40468i	−0.160010	+	0.492459i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	14.5915	−	10.6013i	1.61136	−	1.17072i
$83$	−8.36082	+	6.07449i	−0.917719	+	0.666762i	−0.942955	−	0.332919i	$-0.891966\pi$
$83$	−8.36082	+	6.07449i	−0.917719	+	0.666762i	0.0252360	+	0.999682i	$0.491966\pi$
$84$	−0.563854	−	1.73536i	−0.0615215	−	0.189344i
$85$	0.926692	−	2.85206i	0.100514	−	0.309350i
$86$	2.84751	+	2.06883i	0.307055	+	0.223088i
$87$	10.2638			1.10040
$88$	5.06839	+	4.84742i	0.540293	+	0.516736i
$89$	−10.9034			−1.15576			−0.577878	−	0.816123i	$-0.696119\pi$
$89$	−10.9034			−1.15576			−0.577878	+	0.816123i	$0.696119\pi$
$90$	−1.25533	−	0.912053i	−0.132324	−	0.0961389i
$91$	−0.0988840	+	0.304334i	−0.0103659	+	0.0319028i
$92$	−1.35110	−	4.15826i	−0.140862	−	0.433529i
$93$	2.39972	−	1.74350i	0.248839	−	0.180792i
$94$	11.0490	−	8.02754i	1.13961	−	0.827977i
$95$	−0.290887	−	0.895259i	−0.0298444	−	0.0918516i
$96$	1.19927	−	3.69098i	0.122400	−	0.376709i
$97$	−9.61769	−	6.98766i	−0.976529	−	0.709490i	−0.0195986	−	0.999808i	$-0.506239\pi$
$97$	−9.61769	−	6.98766i	−0.976529	−	0.709490i	−0.956930	+	0.290318i	$0.906239\pi$
$98$	−0.868574			−0.0877392
$99$	−2.92085	+	1.57118i	−0.293557	+	0.157910i
$100$	−2.95041			−0.295041
$101$	13.0304	+	9.46714i	1.29657	+	0.942016i	0.999916	−	0.0129683i	$-0.00412807\pi$
$101$	13.0304	+	9.46714i	1.29657	+	0.942016i	0.296657	+	0.954984i	$0.404128\pi$
$102$	−1.62275	+	4.99432i	−0.160676	+	0.494511i
$103$	0.247558	+	0.761906i	0.0243926	+	0.0750728i	0.962512	−	0.271240i	$-0.0874336\pi$
$103$	0.247558	+	0.761906i	0.0243926	+	0.0750728i	−0.938119	+	0.346313i	$0.887434\pi$
$104$	−0.215164	+	0.156326i	−0.0210986	+	0.0153290i
$105$	1.93756	−	1.40772i	0.189087	−	0.137379i
$106$	6.04662	+	18.6096i	0.587300	+	1.80752i
$107$	−0.338474	+	1.04172i	−0.0327215	+	0.100706i	−0.966083	−	0.258230i	$-0.916861\pi$
$107$	−0.338474	+	1.04172i	−0.0327215	+	0.100706i	0.933362	+	0.358937i	$0.116861\pi$
$108$	0.580211	+	0.421548i	0.0558309	+	0.0405635i
$109$	4.72183			0.452269			0.226135	−	0.974096i	$-0.427391\pi$
$109$	4.72183			0.452269			0.226135	+	0.974096i	$0.427391\pi$
$110$	2.23364	−	4.63633i	0.212970	−	0.442057i
$111$	−4.43442			−0.420897
$112$	10.1270	+	7.35767i	0.956908	+	0.695234i
$113$	4.10209	−	12.6249i	0.385892	−	1.18765i	−0.549940	−	0.835204i	$-0.685349\pi$
$113$	4.10209	−	12.6249i	0.385892	−	1.18765i	0.935831	−	0.352448i	$-0.114651\pi$
$114$	0.509380	+	1.56771i	0.0477078	+	0.146829i
$115$	4.64276	−	3.37317i	0.432940	−	0.314549i
$116$	5.95518	−	4.32669i	0.552924	−	0.401723i
$117$	−0.0388661	−	0.119617i	−0.00359317	−	0.0110586i
$118$	−0.573208	+	1.76415i	−0.0527680	+	0.162403i
$119$	−6.55728	−	4.76414i	−0.601105	−	0.436728i
$120$	1.99052			0.181709
$121$	−6.85566	−	8.60232i	−0.623242	−	0.782029i
$122$	3.45763			0.313040
$123$	−8.85197	−	6.43133i	−0.798155	−	0.579894i
$124$	0.657376	−	2.02320i	0.0590341	−	0.181688i
$125$	−2.65112	−	8.15930i	−0.237123	−	0.729790i
$126$	−3.39291	+	2.46509i	−0.302264	+	0.219608i
$127$	11.6291	−	8.44903i	1.03192	−	0.749730i	0.0632240	−	0.997999i	$-0.479862\pi$
$127$	11.6291	−	8.44903i	1.03192	−	0.749730i	0.968691	+	0.248269i	$0.0798617\pi$
$128$	4.15222	+	12.7792i	0.367007	+	1.12953i
$129$	0.659827	−	2.03074i	0.0580946	−	0.178797i
$130$	0.157887	+	0.114712i	0.0138476	+	0.0100609i
$131$	2.76308			0.241411			0.120706	−	0.992688i	$-0.461484\pi$
$131$	2.76308			0.241411			0.120706	+	0.992688i	$0.461484\pi$
$132$	−1.03238	+	2.14290i	−0.0898575	+	0.186515i
$133$	−2.54422			−0.220612
$134$	17.9664	+	13.0534i	1.55206	+	1.12764i
$135$	−0.290887	+	0.895259i	−0.0250356	+	0.0770516i
$136$	−2.08170	−	6.40681i	−0.178504	−	0.549379i
$137$	11.8846	−	8.63465i	1.01537	−	0.737708i	0.0500396	−	0.998747i	$-0.484065\pi$
$137$	11.8846	−	8.63465i	1.01537	−	0.737708i	0.965328	+	0.261039i	$0.0840653\pi$
$138$	−8.13006	+	5.90683i	−0.692077	+	0.502823i
$139$	−4.34818	−	13.3823i	−0.368808	−	1.13507i	−0.947562	−	0.319573i	$-0.896461\pi$
$139$	−4.34818	−	13.3823i	−0.368808	−	1.13507i	0.578754	−	0.815502i	$-0.303539\pi$
$140$	0.530773	−	1.63355i	0.0448585	−	0.138060i
$141$	−6.70289	−	4.86993i	−0.564485	−	0.410122i
$142$	−1.79880			−0.150952
$143$	0.367365	−	0.197613i	0.0307206	−	0.0165252i
$144$	−4.92001			−0.410001
$145$	7.81643	+	5.67897i	0.649119	+	0.471612i
$146$	7.09035	−	21.8218i	0.586801	−	1.80599i
$147$	0.162828	+	0.501134i	0.0134299	+	0.0413328i
$148$	−2.57290	+	1.86932i	−0.211491	+	0.153657i
$149$	16.7778	−	12.1898i	1.37449	−	0.998627i	0.377120	−	0.926164i	$-0.376914\pi$
$149$	16.7778	−	12.1898i	1.37449	−	0.998627i	0.997371	−	0.0724624i	$-0.0230857\pi$
$150$	2.09554	+	6.44939i	0.171100	+	0.526591i
$151$	−4.06576	+	12.5131i	−0.330867	+	1.01830i	0.637856	+	0.770156i	$0.279822\pi$
$151$	−4.06576	+	12.5131i	−0.330867	+	1.01830i	−0.968722	+	0.248147i	$0.920178\pi$
$152$	−1.71073	−	1.24292i	−0.138759	−	0.100814i
$153$	3.18574			0.257552
$154$	−10.0522	−	9.61392i	−0.810028	−	0.774712i
$155$	2.79219			0.224274
$156$	−0.0729751	−	0.0530195i	−0.00584268	−	0.00424496i
$157$	−1.45732	+	4.48516i	−0.116307	+	0.357955i	−0.992217	−	0.124518i	$-0.960261\pi$
$157$	−1.45732	+	4.48516i	−0.116307	+	0.357955i	0.875911	+	0.482473i	$0.160261\pi$
$158$	−1.12751	−	3.47013i	−0.0897001	−	0.276068i
$159$	9.60348	−	6.97734i	0.761606	−	0.553339i
$160$	2.95553	−	2.14732i	0.233655	−	0.169760i
$161$	−4.79308	−	14.7516i	−0.377747	−	1.16259i
$162$	0.509380	−	1.56771i	0.0400206	−	0.123171i
$163$	−3.37669	−	2.45331i	−0.264483	−	0.192158i	0.447638	−	0.894215i	$-0.352265\pi$
$163$	−3.37669	−	2.45331i	−0.264483	−	0.192158i	−0.712121	+	0.702057i	$0.752265\pi$
$164$	−7.84713			−0.612758
$165$	−3.09372	−	0.419572i	−0.240846	−	0.0326636i
$166$	17.0353			1.32220
$167$	−9.20458	−	6.68752i	−0.712272	−	0.517496i	0.171634	−	0.985161i	$-0.445095\pi$
$167$	−9.20458	−	6.68752i	−0.712272	−	0.517496i	−0.883906	+	0.467665i	$0.845095\pi$
$168$	1.66250	−	5.11666i	0.128265	−	0.394759i
$169$	−4.01233	−	12.3487i	−0.308641	−	0.949899i
$170$	−3.99917	+	2.90557i	−0.306722	+	0.222847i
$171$	0.809017	−	0.587785i	0.0618671	−	0.0449491i
$172$	−0.473215	−	1.45641i	−0.0360823	−	0.111050i
$173$	0.200722	−	0.617759i	0.0152606	−	0.0469673i	−0.943136	−	0.332406i	$-0.892139\pi$
$173$	0.200722	−	0.617759i	0.0152606	−	0.0469673i	0.958397	+	0.285439i	$0.0921394\pi$
$174$	−13.6875	−	9.94458i	−1.03765	−	0.753896i
$175$	−10.4667			−0.791206
$176$	−2.91112	−	16.0561i	−0.219434	−	1.21027i
$177$	1.12531			0.0845831
$178$	14.5405	+	10.5643i	1.08985	+	0.791825i
$179$	−6.59984	+	20.3122i	−0.493295	+	1.51821i	0.326302	+	0.945265i	$0.394197\pi$
$179$	−6.59984	+	20.3122i	−0.493295	+	1.51821i	−0.819597	+	0.572940i	$0.805803\pi$
$180$	0.208619	+	0.642062i	0.0155495	+	0.0478565i
$181$	−14.3798	+	10.4476i	−1.06884	+	0.776561i	−0.975704	−	0.219092i	$-0.929690\pi$
$181$	−14.3798	+	10.4476i	−1.06884	+	0.776561i	−0.0931399	+	0.995653i	$0.529690\pi$
$182$	0.426737	−	0.310043i	0.0316319	−	0.0229819i
$183$	−0.648190	−	1.99492i	−0.0479156	−	0.147469i
$184$	3.98367	−	12.2605i	0.293680	−	0.903855i
$185$	−3.37705	−	2.45357i	−0.248285	−	0.180390i
$186$	−4.88947			−0.358514
$187$	1.88497	+	10.3964i	0.137843	+	0.760261i
$188$	−5.94200			−0.433365
$189$	2.05832	+	1.49546i	0.149721	+	0.108779i
$190$	−0.479495	+	1.47573i	−0.0347862	+	0.107061i
$191$	6.32484	+	19.4659i	0.457649	+	1.40850i	0.867997	+	0.496570i	$0.165408\pi$
$191$	6.32484	+	19.4659i	0.457649	+	1.40850i	−0.410347	+	0.911929i	$0.634592\pi$
$192$	2.78526	−	2.02361i	0.201008	−	0.146041i
$193$	8.97836	−	6.52316i	0.646276	−	0.469547i	−0.215724	−	0.976454i	$-0.569211\pi$
$193$	8.97836	−	6.52316i	0.646276	−	0.469547i	0.862001	+	0.506907i	$0.169211\pi$
$194$	6.05557	+	18.6371i	0.434764	+	1.33807i
$195$	0.0365858	−	0.112600i	0.00261996	−	0.00806342i
$196$	0.305727	+	0.222124i	0.0218377	+	0.0158660i
$197$	9.53633			0.679435			0.339718	−	0.940527i	$-0.389668\pi$
$197$	9.53633			0.679435			0.339718	+	0.940527i	$0.389668\pi$
$198$	5.41749	+	0.734723i	0.385004	+	0.0522145i
$199$	−9.10785			−0.645639			−0.322819	−	0.946461i	$-0.604631\pi$
$199$	−9.10785			−0.645639			−0.322819	+	0.946461i	$0.604631\pi$
$200$	−7.03778	−	5.11325i	−0.497646	−	0.361561i
$201$	4.16320	−	12.8130i	0.293650	−	0.903761i
$202$	−8.20430	−	25.2503i	−0.577253	−	1.77660i
$203$	21.1262	−	15.3491i	1.48277	−	1.07729i
$204$	1.84840	−	1.34294i	0.129414	−	0.0940249i
$205$	−3.18278	−	9.79560i	−0.222295	−	0.684154i
$206$	0.408072	−	1.25592i	0.0284317	−	0.0875038i
$207$	4.93213	+	3.58340i	0.342807	+	0.249064i
$208$	0.618806			0.0429065
$209$	2.39688	+	2.29238i	0.165795	+	0.158567i
$210$	−3.94782			−0.272425
$211$	−8.26242	−	6.00300i	−0.568809	−	0.413264i	0.265864	−	0.964011i	$-0.414343\pi$
$211$	−8.26242	−	6.00300i	−0.568809	−	0.413264i	−0.834672	+	0.550747i	$0.814343\pi$
$212$	2.63077	−	8.09666i	0.180682	−	0.556081i
$213$	0.337215	+	1.03784i	0.0231056	+	0.0711117i
$214$	1.46070	−	1.06126i	0.0998511	−	0.0725461i
$215$	1.62610	−	1.18143i	0.110899	−	0.0805730i
$216$	0.653442	+	2.01109i	0.0444611	+	0.136837i
$217$	2.33206	−	7.17736i	0.158311	−	0.487231i
$218$	−6.29691	−	4.57497i	−0.426480	−	0.309856i
$219$	−13.9196			−0.940598
$220$	−1.97188	+	1.06071i	−0.132944	+	0.0715132i
$221$	−0.400681			−0.0269527
$222$	5.91363	+	4.29650i	0.396897	+	0.288362i
$223$	4.74890	−	14.6156i	0.318010	−	0.978733i	−0.656488	−	0.754336i	$-0.727959\pi$
$223$	4.74890	−	14.6156i	0.318010	−	0.978733i	0.974498	−	0.224397i	$-0.0720411\pi$
$224$	−3.05121	−	9.39067i	−0.203868	−	0.627440i
$225$	3.32821	−	2.41809i	0.221881	−	0.161206i
$226$	−17.7027	+	12.8618i	−1.17757	+	0.855551i
$227$	8.72377	+	26.8490i	0.579017	+	1.78203i	0.622074	+	0.782959i	$0.286290\pi$
$227$	8.72377	+	26.8490i	0.579017	+	1.78203i	−0.0430564	+	0.999073i	$0.513710\pi$
$228$	0.221621	−	0.682079i	0.0146772	−	0.0451718i
$229$	4.19197	+	3.04565i	0.277013	+	0.201262i	0.717614	−	0.696441i	$-0.245234\pi$
$229$	4.19197	+	3.04565i	0.277013	+	0.201262i	−0.440600	+	0.897703i	$0.645234\pi$
$230$	−9.45972			−0.623755
$231$	−3.66242	+	7.60201i	−0.240969	+	0.500175i
$232$	21.7037			1.42492
$233$	10.9268	+	7.93875i	0.715835	+	0.520085i	0.885051	−	0.465494i	$-0.154123\pi$
$233$	10.9268	+	7.93875i	0.715835	+	0.520085i	−0.169215	+	0.985579i	$0.554123\pi$
$234$	−0.0640663	+	0.197176i	−0.00418815	+	0.0128898i
$235$	−2.41007	−	7.41742i	−0.157215	−	0.483859i
$236$	0.652915	−	0.474371i	0.0425011	−	0.0308789i
$237$	−1.79076	+	1.30106i	−0.116322	+	0.0845131i
$238$	4.12865	+	12.7067i	0.267620	+	0.823651i
$239$	−9.53032	+	29.3313i	−0.616465	+	1.89729i	−0.240515	+	0.970645i	$0.577316\pi$
$239$	−9.53032	+	29.3313i	−0.616465	+	1.89729i	−0.375951	+	0.926640i	$0.622684\pi$
$240$	−3.74685	−	2.72224i	−0.241858	−	0.175720i
$241$	3.01568			0.194257			0.0971285	−	0.995272i	$-0.469034\pi$
$241$	3.01568			0.194257			0.0971285	+	0.995272i	$0.469034\pi$
$242$	0.807759	+	18.1143i	0.0519247	+	1.16443i
$243$	−1.00000			−0.0641500
$244$	−1.21704	−	0.884234i	−0.0779132	−	0.0566073i
$245$	−0.153275	+	0.471733i	−0.00979240	+	0.0301379i
$246$	5.57345	+	17.1533i	0.355350	+	1.09366i
$247$	−0.101753	+	0.0739276i	−0.00647437	+	0.00470390i
$248$	5.07441	−	3.68677i	0.322225	−	0.234110i
$249$	−3.19355	−	9.82873i	−0.202383	−	0.622871i
$250$	−4.37007	+	13.4497i	−0.276387	+	0.850632i
$251$	24.4537	+	17.7666i	1.54350	+	1.12142i	0.948091	+	0.318000i	$0.103011\pi$
$251$	24.4537	+	17.7666i	1.54350	+	1.12142i	0.595412	+	0.803421i	$0.296989\pi$
$252$	1.82467			0.114943
$253$	−8.77585	+	18.2159i	−0.551733	+	1.14522i
$254$	−23.6945			−1.48672
$255$	2.42611	+	1.76267i	0.151929	+	0.110383i
$256$	4.71671	−	14.5166i	0.294795	−	0.907285i
$257$	−0.910587	−	2.80250i	−0.0568009	−	0.174815i	0.918631	−	0.395117i	$-0.129296\pi$
$257$	−0.910587	−	2.80250i	−0.0568009	−	0.174815i	−0.975432	+	0.220302i	$0.929296\pi$
$258$	−2.84751	+	2.06883i	−0.177278	+	0.128800i
$259$	−9.12746	+	6.63149i	−0.567153	+	0.412061i
$260$	−0.0262386	−	0.0807542i	−0.00162725	−	0.00500817i
$261$	−3.17169	+	9.76146i	−0.196323	+	0.604219i
$262$	−3.68477	−	2.67714i	−0.227646	−	0.165394i
$263$	0.378241			0.0233234			0.0116617	−	0.999932i	$-0.496288\pi$
$263$	0.378241			0.0233234			0.0116617	+	0.999932i	$0.496288\pi$
$264$	−6.17639	+	3.32239i	−0.380130	+	0.204479i
$265$	11.1741			0.686421
$266$	3.39291	+	2.46509i	0.208033	+	0.151145i
$267$	3.36933	−	10.3697i	0.206200	−	0.634617i
$268$	−2.98577	−	9.18925i	−0.182385	−	0.561323i
$269$	9.44389	−	6.86139i	0.575804	−	0.418346i	−0.261405	−	0.965229i	$-0.584186\pi$
$269$	9.44389	−	6.86139i	0.575804	−	0.418346i	0.837209	+	0.546883i	$0.184186\pi$
$270$	1.25533	−	0.912053i	0.0763972	−	0.0555058i
$271$	0.190732	+	0.587013i	0.0115861	+	0.0356585i	0.956682	−	0.291133i	$-0.0940324\pi$
$271$	0.190732	+	0.587013i	0.0115861	+	0.0356585i	−0.945096	+	0.326792i	$0.894032\pi$
$272$	−4.84350	+	14.9068i	−0.293680	+	0.903855i
$273$	−0.258882	−	0.188088i	−0.0156682	−	0.0113836i
$274$	−24.2150			−1.46288
$275$	9.86050	+	9.43060i	0.594611	+	0.568686i
$276$	4.37225			0.263179
$277$	16.0507	+	11.6615i	0.964390	+	0.700671i	0.954166	−	0.299277i	$-0.0967455\pi$
$277$	16.0507	+	11.6615i	0.964390	+	0.700671i	0.0102241	+	0.999948i	$0.496746\pi$
$278$	−7.16749	+	22.0593i	−0.429878	+	1.32303i
$279$	0.916611	+	2.82104i	0.0548761	+	0.168891i
$280$	4.09713	−	2.97674i	0.244850	−	0.177894i
$281$	−14.8248	+	10.7708i	−0.884372	+	0.642534i	−0.934405	−	0.356213i	$-0.884068\pi$
$281$	−14.8248	+	10.7708i	−0.884372	+	0.642534i	0.0500322	+	0.998748i	$0.484068\pi$
$282$	4.22033	+	12.9888i	0.251317	+	0.773473i
$283$	−1.84847	+	5.68900i	−0.109880	+	0.338176i	−0.990845	−	0.135006i	$-0.956895\pi$
$283$	−1.84847	+	5.68900i	−0.109880	+	0.338176i	0.880965	+	0.473182i	$0.156895\pi$
$284$	0.633156	+	0.460015i	0.0375709	+	0.0272968i
$285$	0.941331			0.0557596
$286$	−0.681375	−	0.0924085i	−0.0402905	−	0.00546423i
$287$	−27.8380			−1.64322
$288$	3.13973	+	2.28115i	0.185010	+	0.134418i
$289$	−2.11709	+	6.51573i	−0.124535	+	0.383278i
$290$	−4.92144	−	15.1466i	−0.288997	−	0.889441i
$291$	9.61769	−	6.98766i	0.563799	−	0.409624i
$292$	−8.07630	+	5.86777i	−0.472629	+	0.343385i
$293$	1.37971	+	4.24632i	0.0806037	+	0.248073i	0.983235	−	0.182341i	$-0.0583676\pi$
$293$	1.37971	+	4.24632i	0.0806037	+	0.248073i	−0.902632	+	0.430414i	$0.858368\pi$
$294$	0.268404	−	0.826063i	0.0156537	−	0.0481770i
$295$	0.856979	+	0.622632i	0.0498953	+	0.0362510i
$296$	−9.37695			−0.545024
$297$	−0.591689	−	3.26342i	−0.0343333	−	0.189363i
$298$	−34.1851			−1.98029
$299$	−0.620330	−	0.450696i	−0.0358746	−	0.0260644i
$300$	0.911726	−	2.80600i	0.0526385	−	0.162005i
$301$	−1.67875	−	5.16666i	−0.0967615	−	0.297801i
$302$	17.5459	−	12.7478i	1.00965	−	0.733556i
$303$	−13.0304	+	9.46714i	−0.748577	+	0.543873i
$304$	1.52037	+	4.67921i	0.0871991	+	0.268371i
$305$	0.610161	−	1.87788i	0.0349377	−	0.107527i
$306$	−4.24842	−	3.08666i	−0.242866	−	0.176453i
$307$	2.31765			0.132275			0.0661377	−	0.997811i	$-0.478932\pi$
$307$	2.31765			0.132275			0.0661377	+	0.997811i	$0.478932\pi$
$308$	1.07964	+	5.95466i	0.0615180	+	0.339298i
$309$	−0.801115			−0.0455739
$310$	−3.72359	−	2.70535i	−0.211486	−	0.153653i
$311$	1.05175	−	3.23695i	0.0596392	−	0.183551i	−0.916798	−	0.399350i	$-0.869236\pi$
$311$	1.05175	−	3.23695i	0.0596392	−	0.183551i	0.976438	+	0.215800i	$0.0692358\pi$
$312$	−0.0821855	−	0.252941i	−0.00465284	−	0.0143200i
$313$	−14.0518	+	10.2092i	−0.794256	+	0.577061i	−0.909223	−	0.416309i	$-0.863324\pi$
$313$	−14.0518	+	10.2092i	−0.794256	+	0.577061i	0.114967	+	0.993369i	$0.463324\pi$
$314$	6.28911	−	4.56930i	0.354915	−	0.257861i
$315$	0.740082	+	2.27774i	0.0416989	+	0.128336i
$316$	−0.490558	+	1.50978i	−0.0275961	+	0.0849319i
$317$	11.1106	+	8.07235i	0.624036	+	0.453389i	0.854329	−	0.519733i	$-0.173968\pi$
$317$	11.1106	+	8.07235i	0.624036	+	0.453389i	−0.230293	+	0.973121i	$0.573968\pi$
$318$	−19.5673			−1.09728
$319$	−33.7324	−	4.57481i	−1.88865	−	0.256140i
$320$	3.24078			0.181165
$321$	−0.886137	−	0.643816i	−0.0494593	−	0.0359343i
$322$	−7.90085	+	24.3163i	−0.440297	+	1.35510i
$323$	−0.984449	−	3.02982i	−0.0547762	−	0.168584i
$324$	−0.580211	+	0.421548i	−0.0322340	+	0.0234193i
$325$	−0.418600	+	0.304131i	−0.0232197	+	0.0168701i
$326$	2.12606	+	6.54333i	0.117751	+	0.362402i
$327$	−1.45913	+	4.49073i	−0.0806899	+	0.248338i
$328$	−18.7182	−	13.5996i	−1.03354	−	0.750912i
$329$	−21.0795			−1.16215
$330$	3.71918	+	3.55703i	0.204734	+	0.195808i
$331$	10.8390			0.595766			0.297883	−	0.954602i	$-0.403720\pi$
$331$	10.8390			0.595766			0.297883	+	0.954602i	$0.403720\pi$
$332$	−5.99622	−	4.35651i	−0.329085	−	0.239094i
$333$	1.37031	−	4.21739i	0.0750926	−	0.231111i
$334$	5.79546	+	17.8366i	0.317114	+	0.975975i
$335$	10.2599	−	7.45429i	0.560561	−	0.407271i
$336$	−10.1270	+	7.35767i	−0.552471	+	0.401394i
$337$	−7.66055	−	23.5767i	−0.417297	−	1.28431i	−0.910180	−	0.414212i	$-0.864057\pi$
$337$	−7.66055	−	23.5767i	−0.417297	−	1.28431i	0.492884	−	0.870095i	$-0.335943\pi$
$338$	−6.61388	+	20.3554i	−0.359748	+	1.10719i
$339$	10.7394	+	7.80263i	0.583284	+	0.423781i
$340$	2.15071			0.116639
$341$	−8.66389	+	4.66047i	−0.469176	+	0.252378i
$342$	−1.64839			−0.0891346
$343$	15.4928	+	11.2562i	0.836534	+	0.607777i
$344$	1.39526	−	4.29417i	0.0752274	−	0.231526i
$345$	1.77338	+	5.45790i	0.0954755	+	0.293843i
$346$	−0.866222	+	0.629347i	−0.0465684	+	0.0338339i
$347$	−0.134266	+	0.0975498i	−0.00720777	+	0.00523675i	−0.591383	−	0.806391i	$-0.701418\pi$
$347$	−0.134266	+	0.0975498i	−0.00720777	+	0.00523675i	0.584176	+	0.811627i	$0.301418\pi$
$348$	2.27467	+	7.00073i	0.121935	+	0.375279i
$349$	9.18738	−	28.2758i	0.491789	−	1.51357i	−0.330113	−	0.943941i	$-0.607087\pi$
$349$	9.18738	−	28.2758i	0.491789	−	1.51357i	0.821902	−	0.569629i	$-0.192913\pi$
$350$	13.9581	+	10.1411i	0.746091	+	0.542067i
$351$	0.125773			0.00671328
$352$	−5.58660	+	11.5960i	−0.297767	+	0.618068i
$353$	−15.8172			−0.841862			−0.420931	−	0.907093i	$-0.638297\pi$
$353$	−15.8172			−0.841862			−0.420931	+	0.907093i	$0.638297\pi$
$354$	−1.50068	−	1.09031i	−0.0797601	−	0.0579491i
$355$	−0.317431	+	0.976951i	−0.0168475	+	0.0518512i
$356$	−2.41642	−	7.43697i	−0.128070	−	0.394159i
$357$	6.55728	−	4.76414i	0.347048	−	0.252145i
$358$	28.4818	−	20.6933i	1.50531	−	1.09367i
$359$	9.04353	+	27.8331i	0.477299	+	1.46898i	0.842832	+	0.538177i	$0.180887\pi$
$359$	9.04353	+	27.8331i	0.477299	+	1.46898i	−0.365532	+	0.930799i	$0.619113\pi$
$360$	−0.615105	+	1.89310i	−0.0324189	+	0.0997751i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	29.2992			1.53993
$363$	10.2998	−	3.86186i	0.540600	−	0.202695i
$364$	−0.229494			−0.0120288
$365$	−10.6005	−	7.70170i	−0.554855	−	0.403126i
$366$	−1.06847	+	3.28841i	−0.0558497	+	0.171888i
$367$	10.3393	+	31.8212i	0.539709	+	1.66105i	0.733248	+	0.679962i	$0.238004\pi$
$367$	10.3393	+	31.8212i	0.539709	+	1.66105i	−0.193538	+	0.981093i	$0.561996\pi$
$368$	−24.2661	+	17.6304i	−1.26496	+	0.919047i
$369$	8.85197	−	6.43133i	0.460815	−	0.334802i
$370$	2.12628	+	6.54402i	0.110540	+	0.340208i
$371$	9.33274	−	28.7232i	0.484531	−	1.49123i
$372$	1.72103	+	1.25040i	0.0892314	+	0.0648304i
$373$	17.7830			0.920769			0.460385	−	0.887720i	$-0.347711\pi$
$373$	17.7830			0.920769			0.460385	+	0.887720i	$0.347711\pi$
$374$	7.55932	−	15.6907i	0.390883	−	0.811348i
$375$	8.57919			0.443028
$376$	−14.1738	−	10.2979i	−0.730959	−	0.531072i
$377$	0.398914	−	1.22773i	0.0205451	−	0.0632313i
$378$	−1.29598	−	3.98860i	−0.0666578	−	0.205152i
$379$	2.90244	−	2.10875i	0.149088	−	0.108319i	−0.510741	−	0.859735i	$-0.670629\pi$
$379$	2.90244	−	2.10875i	0.149088	−	0.108319i	0.659829	+	0.751416i	$0.270629\pi$
$380$	0.546171	−	0.396816i	0.0280180	−	0.0203562i
$381$	4.44192	+	13.6708i	0.227566	+	0.700377i
$382$	10.4258	−	32.0873i	0.533430	−	1.64173i
$383$	−1.45893	−	1.05997i	−0.0745476	−	0.0541620i	0.549887	−	0.835239i	$-0.314671\pi$
$383$	−1.45893	−	1.05997i	−0.0745476	−	0.0541620i	−0.624435	+	0.781077i	$0.714671\pi$
$384$	−13.4369			−0.685697
$385$	−6.99532	+	3.76291i	−0.356514	+	0.191776i
$386$	−18.2936			−0.931118
$387$	1.72745	+	1.25507i	0.0878112	+	0.0637986i
$388$	2.63466	−	8.10864i	0.133755	−	0.411654i
$389$	−9.48932	−	29.2051i	−0.481128	−	1.48076i	−0.837512	−	0.546419i	$-0.815990\pi$
$389$	−9.48932	−	29.2051i	−0.481128	−	1.48076i	0.356384	−	0.934340i	$-0.384010\pi$
$390$	−0.157887	+	0.114712i	−0.00799494	+	0.00580866i
$391$	15.7125	−	11.4158i	0.794615	−	0.577322i
$392$	0.344314	+	1.05969i	0.0173905	+	0.0535224i
$393$	−0.853839	+	2.62785i	−0.0430705	+	0.132557i
$394$	−12.7174	−	9.23973i	−0.640693	−	0.465491i
$395$	−2.08364			−0.104839
$396$	−1.71899	−	1.64405i	−0.0863827	−	0.0826165i
$397$	10.9434			0.549232			0.274616	−	0.961554i	$-0.411449\pi$
$397$	10.9434			0.549232			0.274616	+	0.961554i	$0.411449\pi$
$398$	12.1460	+	8.82458i	0.608823	+	0.442336i
$399$	0.786208	−	2.41970i	0.0393597	−	0.121137i
$400$	6.25464	+	19.2498i	0.312732	+	0.962489i
$401$	12.6746	−	9.20866i	0.632941	−	0.459859i	−0.224477	−	0.974479i	$-0.572067\pi$
$401$	12.6746	−	9.20866i	0.632941	−	0.459859i	0.857418	+	0.514621i	$0.172067\pi$
$402$	−17.9664	+	13.0534i	−0.896085	+	0.651044i
$403$	−0.115285	−	0.354811i	−0.00574276	−	0.0176744i
$404$	−3.56953	+	10.9859i	−0.177591	+	0.546568i
$405$	−0.761553	−	0.553300i	−0.0378419	−	0.0274937i
$406$	−43.0450			−2.13629
$407$	14.5739	+	1.97652i	0.722401	+	0.0979725i
$408$	6.73652			0.333507
$409$	0.0619133	+	0.0449827i	0.00306142	+	0.00222425i	0.589315	−	0.807903i	$-0.299398\pi$
$409$	0.0619133	+	0.0449827i	0.00306142	+	0.00222425i	−0.586253	+	0.810128i	$0.699398\pi$
$410$	−5.24646	+	16.1469i	−0.259104	+	0.797441i
$411$	4.53950	+	13.9712i	0.223917	+	0.689146i
$412$	−0.464816	+	0.337709i	−0.0228999	+	0.0166377i
$413$	2.31624	−	1.68285i	0.113975	−	0.0828074i
$414$	−3.10541	−	9.55746i	−0.152622	−	0.469723i
$415$	3.00619	−	9.25209i	0.147568	−	0.454167i
$416$	−0.394894	−	0.286907i	−0.0193613	−	0.0140668i
$417$	14.0710			0.689061
$418$	−0.975333	−	5.37938i	−0.0477051	−	0.263114i
$419$	−5.41913			−0.264742			−0.132371	−	0.991200i	$-0.542259\pi$
$419$	−5.41913			−0.264742			−0.132371	+	0.991200i	$0.542259\pi$
$420$	1.38958	+	1.00959i	0.0678046	+	0.0492629i
$421$	−5.18013	+	15.9428i	−0.252464	+	0.777005i	0.741854	+	0.670561i	$0.233947\pi$
$421$	−5.18013	+	15.9428i	−0.252464	+	0.777005i	−0.994319	+	0.106444i	$0.966053\pi$
$422$	5.20225	+	16.0109i	0.253242	+	0.779398i
$423$	6.70289	−	4.86993i	0.325906	−	0.236784i
$424$	20.3074	−	14.7542i	0.986213	−	0.716526i
$425$	−4.04992	−	12.4644i	−0.196450	−	0.604611i
$426$	0.555861	−	1.71076i	0.0269315	−	0.0828867i
$427$	−4.31751	−	3.13685i	−0.208939	−	0.151803i
$428$	−0.785546			−0.0379708
$429$	0.0744186	+	0.410451i	0.00359297	+	0.0198167i
$430$	−3.31321			−0.159777
$431$	3.90618	+	2.83801i	0.188154	+	0.136702i	0.677875	−	0.735177i	$-0.262901\pi$
$431$	3.90618	+	2.83801i	0.188154	+	0.136702i	−0.489721	+	0.871879i	$0.662901\pi$
$432$	1.52037	−	4.67921i	0.0731487	−	0.225129i
$433$	−8.21719	−	25.2899i	−0.394893	−	1.21536i	−0.929045	−	0.369967i	$-0.879369\pi$
$433$	−8.21719	−	25.2899i	−0.394893	−	1.21536i	0.534152	−	0.845389i	$-0.320631\pi$
$434$	−10.0641	+	7.31200i	−0.483092	+	0.350987i
$435$	−7.81643	+	5.67897i	−0.374769	+	0.272286i
$436$	1.04646	+	3.22066i	0.0501162	+	0.154242i
$437$	1.88391	−	5.79807i	0.0901194	−	0.277359i
$438$	18.5628	+	13.4866i	0.886964	+	0.644417i
$439$	−15.7871			−0.753479			−0.376740	−	0.926319i	$-0.622955\pi$
$439$	−15.7871			−0.753479			−0.376740	+	0.926319i	$0.622955\pi$
$440$	−6.54193	−	0.887220i	−0.311874	−	0.0422965i
$441$	−0.526924			−0.0250916
$442$	0.534338	+	0.388219i	0.0254158	+	0.0184657i
$443$	−7.40514	+	22.7907i	−0.351829	+	1.08282i	0.605997	+	0.795467i	$0.292774\pi$
$443$	−7.40514	+	22.7907i	−0.351829	+	1.08282i	−0.957826	+	0.287350i	$0.907226\pi$
$444$	−0.982761	−	3.02463i	−0.0466398	−	0.143543i
$445$	8.30349	−	6.03284i	0.393623	−	0.285984i
$446$	−20.4940	+	14.8898i	−0.970420	+	0.705052i
$447$	6.40855	+	19.7235i	0.303114	+	0.932889i
$448$	2.70673	−	8.33046i	0.127881	−	0.393577i
$449$	−32.8605	−	23.8746i	−1.55078	−	1.12671i	−0.943090	−	0.332538i	$-0.892095\pi$
$449$	−32.8605	−	23.8746i	−1.55078	−	1.12671i	−0.607693	−	0.794172i	$-0.707905\pi$
$450$	−6.78129			−0.319673
$451$	26.2258	+	25.0823i	1.23492	+	1.18108i
$452$	9.52031			0.447798
$453$	−10.6443	−	7.73353i	−0.500112	−	0.363353i
$454$	14.3802	−	44.2576i	0.674894	−	2.07711i
$455$	−0.0930825	−	0.286479i	−0.00436378	−	0.0134303i
$456$	1.71073	−	1.24292i	0.0801124	−	0.0582051i
$457$	−29.0851	+	21.1315i	−1.36054	+	0.988491i	−0.362131	+	0.932127i	$0.617951\pi$
$457$	−29.0851	+	21.1315i	−1.36054	+	0.988491i	−0.998410	+	0.0563639i	$0.982049\pi$
$458$	−2.63938	−	8.12318i	−0.123330	−	0.379571i
$459$	−0.984449	+	3.02982i	−0.0459501	+	0.141420i
$460$	3.32970	+	2.41917i	0.155248	+	0.112794i
$461$	23.8422			1.11044			0.555222	−	0.831702i	$-0.312633\pi$
$461$	23.8422			1.11044			0.555222	+	0.831702i	$0.312633\pi$
$462$	12.2497	−	6.58933i	0.569906	−	0.306563i
$463$	−4.50998			−0.209597			−0.104798	−	0.994493i	$-0.533420\pi$
$463$	−4.50998			−0.209597			−0.104798	+	0.994493i	$0.533420\pi$
$464$	−40.8538	−	29.6820i	−1.89659	−	1.37795i
$465$	−0.862834	+	2.65553i	−0.0400130	+	0.123147i
$466$	−6.87979	−	21.1738i	−0.318700	−	0.980858i
$467$	−3.96568	+	2.88124i	−0.183510	+	0.133328i	−0.675748	−	0.737133i	$-0.736179\pi$
$467$	−3.96568	+	2.88124i	−0.183510	+	0.133328i	0.492238	+	0.870461i	$0.336179\pi$
$468$	0.0729751	−	0.0530195i	0.00337327	−	0.00245083i
$469$	−10.5921	−	32.5992i	−0.489099	−	1.50529i
$470$	−3.97272	+	12.2268i	−0.183248	+	0.563979i
$471$	−3.81531	−	2.77198i	−0.175800	−	0.127726i
$472$	2.37955			0.109528
$473$	−3.07369	+	6.38000i	−0.141329	+	0.293353i
$474$	3.64871			0.167591
$475$	−3.32821	−	2.41809i	−0.152709	−	0.110949i
$476$	1.79629	−	5.52842i	0.0823329	−	0.253395i
$477$	3.66820	+	11.2896i	0.167956	+	0.516914i
$478$	41.1284	−	29.8816i	1.88117	−	1.36675i
$479$	−15.5398	+	11.2903i	−0.710030	+	0.515867i	−0.883183	−	0.469028i	$-0.844604\pi$
$479$	−15.5398	+	11.2903i	−0.710030	+	0.515867i	0.173153	+	0.984895i	$0.444604\pi$
$480$	1.12891	+	3.47443i	0.0515275	+	0.158585i
$481$	−0.172349	+	0.530434i	−0.00785842	+	0.0241857i
$482$	−4.02163	−	2.92189i	−0.183180	−	0.133088i
$483$	15.5107			0.705762
$484$	4.34811	−	6.58256i	0.197641	−	0.299207i
$485$	11.1907			0.508141
$486$	1.33357	+	0.968898i	0.0604921	+	0.0439501i
$487$	−1.64342	+	5.05793i	−0.0744705	+	0.229197i	−0.981362	−	0.192167i	$-0.938448\pi$
$487$	−1.64342	+	5.05793i	−0.0744705	+	0.229197i	0.906892	+	0.421364i	$0.138448\pi$
$488$	−1.37065	−	4.21843i	−0.0620465	−	0.190959i
$489$	3.37669	−	2.45331i	0.152699	−	0.110942i
$490$	0.661465	−	0.480582i	0.0298819	−	0.0217105i
$491$	−9.75317	−	30.0172i	−0.440155	−	1.35466i	−0.887711	−	0.460401i	$-0.847706\pi$
$491$	−9.75317	−	30.0172i	−0.440155	−	1.35466i	0.447557	−	0.894256i	$-0.352294\pi$
$492$	2.42490	−	7.46307i	0.109323	−	0.336461i
$493$	26.4531	+	19.2193i	1.19139	+	0.865594i
$494$	0.207323			0.00932790
$495$	1.35505	−	2.81265i	0.0609049	−	0.126419i
$496$	−14.5938			−0.655282
$497$	2.24614	+	1.63192i	0.100753	+	0.0732015i
$498$	−5.26421	+	16.2016i	−0.235895	+	0.726009i
$499$	−2.24123	−	6.89781i	−0.100331	−	0.308788i	0.888275	−	0.459312i	$-0.151904\pi$
$499$	−2.24123	−	6.89781i	−0.100331	−	0.308788i	−0.988606	+	0.150524i	$0.951904\pi$
$500$	4.97774	−	3.61654i	0.222612	−	0.161737i
$501$	9.20458	−	6.68752i	0.411230	−	0.298776i
$502$	−15.3967	−	47.3862i	−0.687189	−	2.11495i
$503$	2.26664	−	6.97599i	0.101064	−	0.311044i	−0.887722	−	0.460379i	$-0.847713\pi$
$503$	2.26664	−	6.97599i	0.101064	−	0.311044i	0.988787	+	0.149335i	$0.0477134\pi$
$504$	4.35249	+	3.16227i	0.193875	+	0.140859i
$505$	−15.1615			−0.674678
$506$	29.3526	−	15.7893i	1.30488	−	0.701919i
$507$	12.9842			0.576648
$508$	8.34016	+	6.05948i	0.370035	+	0.268846i
$509$	−3.14609	+	9.68267i	−0.139448	+	0.429177i	−0.996255	−	0.0864600i	$-0.972445\pi$
$509$	−3.14609	+	9.68267i	−0.139448	+	0.429177i	0.856807	+	0.515637i	$0.172445\pi$
$510$	−1.52755	−	4.70131i	−0.0676409	−	0.208177i
$511$	−28.6509	+	20.8161i	−1.26744	+	0.920851i
$512$	1.38614	−	1.00709i	0.0612594	−	0.0445076i
$513$	0.309017	+	0.951057i	0.0136434	+	0.0419902i
$514$	−1.50100	+	4.61960i	−0.0662063	+	0.203762i
$515$	−0.610092	−	0.443257i	−0.0268838	−	0.0195323i
$516$	1.53136			0.0674142
$517$	19.8587	+	18.9928i	0.873383	+	0.835304i
$518$	18.5974			0.817122
$519$	0.525497	+	0.381796i	0.0230667	+	0.0167590i
$520$	0.0773637	−	0.238101i	0.00339262	−	0.0104414i
$521$	6.43228	+	19.7965i	0.281803	+	0.867301i	0.987339	+	0.158627i	$0.0507066\pi$
$521$	6.43228	+	19.7965i	0.281803	+	0.867301i	−0.705535	+	0.708675i	$0.749293\pi$
$522$	13.6875	−	9.94458i	0.599087	−	0.435262i
$523$	−15.0413	+	10.9281i	−0.657710	+	0.477855i	−0.865889	−	0.500236i	$-0.833246\pi$
$523$	−15.0413	+	10.9281i	−0.657710	+	0.477855i	0.208179	+	0.978091i	$0.433246\pi$
$524$	0.612357	+	1.88464i	0.0267509	+	0.0823309i
$525$	3.23438	−	9.95440i	0.141160	−	0.434446i
$526$	−0.504412	−	0.366477i	−0.0219934	−	0.0159792i
$527$	9.44960			0.411631
$528$	16.1698	+	2.19296i	0.703701	+	0.0954363i
$529$	14.1667			0.615942
$530$	−14.9015	−	10.8266i	−0.647280	−	0.470277i
$531$	−0.347738	+	1.07023i	−0.0150906	+	0.0464440i
$532$	−0.563854	−	1.73536i	−0.0244462	−	0.0752375i
$533$	−1.11334	+	0.808890i	−0.0482241	+	0.0350369i
$534$	−14.5405	+	10.5643i	−0.629227	+	0.457160i
$535$	−0.318616	−	0.980599i	−0.0137750	−	0.0423950i
$536$	8.80344	−	27.0942i	0.380251	−	1.17029i
$537$	−17.2786	−	12.5536i	−0.745626	−	0.541729i
$538$	−19.2421			−0.829586
$539$	−0.311775	−	1.71957i	−0.0134291	−	0.0740672i
$540$	−0.675104			−0.0290519
$541$	3.93740	+	2.86069i	0.169282	+	0.122991i	0.669201	−	0.743082i	$-0.266637\pi$
$541$	3.93740	+	2.86069i	0.169282	+	0.122991i	−0.499918	+	0.866073i	$0.666637\pi$
$542$	0.314400	−	0.967624i	0.0135046	−	0.0415630i
$543$	−5.49260	−	16.9045i	−0.235710	−	0.725441i
$544$	10.0024	−	7.26715i	0.428848	−	0.311577i
$545$	−3.59592	+	2.61259i	−0.154032	+	0.111911i
$546$	0.162999	+	0.501660i	0.00697572	+	0.0214690i
$547$	2.21620	−	6.82076i	0.0947578	−	0.291635i	−0.892433	−	0.451181i	$-0.851003\pi$
$547$	2.21620	−	6.82076i	0.0947578	−	0.291635i	0.987190	+	0.159546i	$0.0510030\pi$
$548$	8.52339	+	6.19260i	0.364101	+	0.264535i
$549$	2.09759			0.0895228
$550$	−4.01242	−	22.1302i	−0.171090	−	0.943635i
$551$	10.2638			0.437253
$552$	10.4294	+	7.57740i	0.443905	+	0.322516i
$553$	−1.74027	+	5.35601i	−0.0740039	+	0.227761i
$554$	−10.1059	−	31.1029i	−0.429360	−	1.32143i
$555$	3.37705	−	2.45357i	0.143348	−	0.104148i
$556$	8.16417	−	5.93161i	0.346238	−	0.251556i
$557$	8.72944	+	26.8664i	0.369878	+	1.13837i	0.946870	+	0.321618i	$0.104227\pi$
$557$	8.72944	+	26.8664i	0.369878	+	1.13837i	−0.576992	+	0.816750i	$0.695773\pi$
$558$	1.51093	−	4.65017i	0.0639628	−	0.196857i
$559$	−0.217267	−	0.157854i	−0.00918941	−	0.00667650i
$560$	−11.7832			−0.497932
$561$	−10.4701	−	1.41996i	−0.442046	−	0.0599506i
$562$	30.2058			1.27415
$563$	−23.9406	−	17.3939i	−1.00898	−	0.733064i	−0.0449819	−	0.998988i	$-0.514323\pi$
$563$	−23.9406	−	17.3939i	−1.00898	−	0.733064i	−0.963994	+	0.265924i	$0.914323\pi$
$564$	1.83618	−	5.65118i	0.0773171	−	0.237958i
$565$	3.86142	+	11.8842i	0.162451	+	0.499973i
$566$	7.97713	−	5.79573i	0.335304	−	0.243613i
$567$	−2.05832	+	1.49546i	−0.0864413	+	0.0628033i
$568$	0.713069	+	2.19460i	0.0299197	+	0.0920834i
$569$	−1.11924	+	3.44466i	−0.0469210	+	0.144408i	−0.971772	−	0.235921i	$-0.924189\pi$
$569$	−1.11924	+	3.44466i	−0.0469210	+	0.144408i	0.924851	+	0.380329i	$0.124189\pi$
$570$	−1.25533	−	0.912053i	−0.0525801	−	0.0382017i
$571$	−14.2793			−0.597571			−0.298785	−	0.954320i	$-0.596582\pi$
$571$	−14.2793			−0.597571			−0.298785	+	0.954320i	$0.596582\pi$
$572$	0.216203	+	0.206777i	0.00903991	+	0.00864579i
$573$	−20.4676			−0.855047
$574$	37.1240	+	26.9722i	1.54953	+	1.12580i
$575$	7.75019	−	23.8526i	0.323205	−	0.994724i
$576$	1.06387	+	3.27426i	0.0443280	+	0.136428i
$577$	33.6994	−	24.4840i	1.40292	−	1.01928i	0.408619	−	0.912705i	$-0.366011\pi$
$577$	33.6994	−	24.4840i	1.40292	−	1.01928i	0.994304	−	0.106578i	$-0.0339894\pi$
$578$	9.13637	−	6.63796i	0.380023	−	0.276103i
$579$	3.42943	+	10.5547i	0.142522	+	0.438638i
$580$	−2.14122	+	6.59000i	−0.0889094	+	0.273635i
$581$	−21.2718	−	15.4549i	−0.882503	−	0.641176i
$582$	−19.5962			−0.812290
$583$	−34.6722	+	18.6508i	−1.43597	+	0.772437i
$584$	−29.4341			−1.21799
$585$	0.0957829	+	0.0695904i	0.00396014	+	0.00287721i
$586$	2.27430	−	6.99958i	0.0939506	−	0.289150i
$587$	−7.08334	−	21.8003i	−0.292361	−	0.899794i	−0.984095	−	0.177642i	$-0.943153\pi$
$587$	−7.08334	−	21.8003i	−0.292361	−	0.899794i	0.691734	−	0.722152i	$-0.256847\pi$
$588$	−0.305727	+	0.222124i	−0.0126080	+	0.00916023i
$589$	2.39972	−	1.74350i	0.0988787	−	0.0718396i
$590$	−0.539578	−	1.66065i	−0.0222141	−	0.0683679i
$591$	−2.94689	+	9.06959i	−0.121219	+	0.373073i
$592$	17.6507	+	12.8240i	0.725438	+	0.527061i
$593$	37.3157			1.53237			0.766186	−	0.642618i	$-0.222152\pi$
$593$	37.3157			1.53237			0.766186	+	0.642618i	$0.222152\pi$
$594$	−2.37286	+	4.92529i	−0.0973596	+	0.202087i
$595$	7.62971			0.312788
$596$	12.0327	+	8.74228i	0.492879	+	0.358098i
$597$	2.81448	−	8.66208i	0.115189	−	0.354515i
$598$	0.390577	+	1.20207i	0.0159719	+	0.0491564i
$599$	29.0504	−	21.1064i	1.18697	−	0.862383i	0.194028	−	0.980996i	$-0.437845\pi$
$599$	29.0504	−	21.1064i	1.18697	−	0.862383i	0.992941	+	0.118613i	$0.0378449\pi$
$600$	7.03778	−	5.11325i	0.287316	−	0.208747i
$601$	5.62699	+	17.3181i	0.229530	+	0.706420i	0.997800	+	0.0662943i	$0.0211176\pi$
$601$	5.62699	+	17.3181i	0.229530	+	0.706420i	−0.768270	+	0.640125i	$0.778882\pi$
$602$	−2.76723	+	8.51665i	−0.112784	+	0.347113i
$603$	10.8994	+	7.91888i	0.443858	+	0.322482i
$604$	−9.43599			−0.383945
$605$	9.98061	+	2.75788i	0.405770	+	0.112124i
$606$	26.5497			1.07851
$607$	−3.01448	−	2.19015i	−0.122354	−	0.0888953i	0.524925	−	0.851148i	$-0.324093\pi$
$607$	−3.01448	−	2.19015i	−0.122354	−	0.0888953i	−0.647279	+	0.762253i	$0.724093\pi$
$608$	1.19927	−	3.69098i	0.0486369	−	0.149689i
$609$	8.06949	+	24.8353i	0.326992	+	1.00638i
$610$	−2.63317	+	1.91311i	−0.106614	+	0.0774596i
$611$	−0.843044	+	0.612507i	−0.0341059	+	0.0247794i
$612$	0.706028	+	2.17293i	0.0285395	+	0.0878355i
$613$	3.94549	−	12.1430i	0.159357	−	0.490451i	−0.839219	−	0.543793i	$-0.816988\pi$
$613$	3.94549	−	12.1430i	0.159357	−	0.490451i	0.998576	+	0.0533427i	$0.0169876\pi$
$614$	−3.09076	−	2.24557i	−0.124733	−	0.0906238i
$615$	10.2997			0.415324
$616$	−7.74449	+	16.0751i	−0.312034	+	0.647683i
$617$	−0.724060			−0.0291496			−0.0145748	−	0.999894i	$-0.504639\pi$
$617$	−0.724060			−0.0291496			−0.0145748	+	0.999894i	$0.504639\pi$
$618$	1.06835	+	0.776199i	0.0429752	+	0.0312233i
$619$	−6.69829	+	20.6152i	−0.269227	+	0.828596i	0.721462	+	0.692454i	$0.243470\pi$
$619$	−6.69829	+	20.6152i	−0.269227	+	0.828596i	−0.990689	+	0.136142i	$0.956530\pi$
$620$	0.618808	+	1.90450i	0.0248519	+	0.0764864i
$621$	−4.93213	+	3.58340i	−0.197920	+	0.143797i
$622$	−4.53886	+	3.29767i	−0.181992	+	0.132225i
$623$	−8.57233	−	26.3829i	−0.343443	−	1.05701i
$624$	−0.191222	+	0.588519i	−0.00765499	+	0.0235596i
$625$	−10.1076	−	7.34357i	−0.404302	−	0.293743i
$626$	28.6309			1.14432
$627$	−2.92085	+	1.57118i	−0.116648	+	0.0627470i
$628$	−3.38221			−0.134965
$629$	−11.4289	−	8.30360i	−0.455701	−	0.331086i
$630$	1.21994	−	3.75460i	0.0486037	−	0.149587i
$631$	−6.19938	−	19.0797i	−0.246793	−	0.759552i	−0.995336	−	0.0964657i	$-0.969246\pi$
$631$	−6.19938	−	19.0797i	−0.246793	−	0.759552i	0.748543	−	0.663086i	$-0.230754\pi$
$632$	−3.78671	+	2.75121i	−0.150627	+	0.109437i
$633$	8.26242	−	6.00300i	0.328402	−	0.238598i
$634$	−6.99557	−	21.5302i	−0.277830	−	0.855072i
$635$	−4.18131	+	12.8688i	−0.165930	+	0.510681i
$636$	6.88743	+	5.00401i	0.273105	+	0.198422i
$637$	0.0662729			0.00262583
$638$	40.5521	+	38.7841i	1.60547	+	1.53548i
$639$	−1.09125			−0.0431692
$640$	−10.2329	−	7.43461i	−0.404490	−	0.293879i
$641$	1.18819	−	3.65687i	0.0469306	−	0.144438i	−0.924845	−	0.380344i	$-0.875806\pi$
$641$	1.18819	−	3.65687i	0.0469306	−	0.144438i	0.971776	+	0.235906i	$0.0758057\pi$
$642$	0.557936	+	1.71715i	0.0220200	+	0.0677706i
$643$	−26.2043	+	19.0385i	−1.03339	+	0.750805i	−0.968985	−	0.247118i	$-0.920516\pi$
$643$	−26.2043	+	19.0385i	−1.03339	+	0.750805i	−0.0644096	+	0.997924i	$0.520516\pi$
$644$	8.99950	−	6.53852i	0.354630	−	0.257654i
$645$	0.621116	+	1.91160i	0.0244564	+	0.0752691i
$646$	−1.62275	+	4.99432i	−0.0638463	+	0.196499i
$647$	27.8284	+	20.2185i	1.09405	+	0.794873i	0.980078	−	0.198612i	$-0.0636432\pi$
$647$	27.8284	+	20.2185i	1.09405	+	0.794873i	0.113970	+	0.993484i	$0.463643\pi$
$648$	−2.11458			−0.0830687
$649$	−3.69836	−	0.501574i	−0.145173	−	0.0196885i
$650$	0.852905			0.0334537
$651$	6.10542	+	4.43585i	0.239290	+	0.173855i
$652$	0.925006	−	2.84688i	0.0362260	−	0.111492i
$653$	−6.81780	−	20.9830i	−0.266801	−	0.821130i	−0.991273	−	0.131825i	$-0.957916\pi$
$653$	−6.81780	−	20.9830i	−0.266801	−	0.821130i	0.724472	−	0.689305i	$-0.242084\pi$
$654$	6.29691	−	4.57497i	0.246229	−	0.178896i
$655$	−2.10423	+	1.52881i	−0.0822191	+	0.0597357i
$656$	16.6353	+	51.1982i	0.649500	+	1.99896i
$657$	4.30138	−	13.2383i	0.167813	−	0.516475i
$658$	28.1110	+	20.4238i	1.09588	+	0.796205i
$659$	4.38630			0.170866			0.0854330	−	0.996344i	$-0.472773\pi$
$659$	4.38630			0.170866			0.0854330	+	0.996344i	$0.472773\pi$
$660$	−0.399452	−	2.20315i	−0.0155486	−	0.0857574i
$661$	41.4634			1.61274			0.806369	−	0.591412i	$-0.201429\pi$
$661$	41.4634			1.61274			0.806369	+	0.591412i	$0.201429\pi$
$662$	−14.4546	−	10.5019i	−0.561794	−	0.408168i
$663$	0.123817	−	0.381070i	0.00480866	−	0.0147995i
$664$	−6.75303	−	20.7837i	−0.262068	−	0.806563i
$665$	1.93756	−	1.40772i	0.0751354	−	0.0545890i
$666$	−5.91363	+	4.29650i	−0.229148	+	0.166486i
$667$	19.3360	+	59.5102i	0.748694	+	2.30424i
$668$	2.52149	−	7.76035i	0.0975594	−	0.300257i
$669$	12.4328	+	9.03294i	0.480679	+	0.349234i
$670$	−20.9048			−0.807624
$671$	1.24112	+	6.84530i	0.0479129	+	0.264260i
$672$	9.87393			0.380895
$673$	9.73226	+	7.07090i	0.375151	+	0.272563i	0.759344	−	0.650690i	$-0.225520\pi$
$673$	9.73226	+	7.07090i	0.375151	+	0.272563i	−0.384193	+	0.923253i	$0.625520\pi$
$674$	−12.6276	+	38.8636i	−0.486395	+	1.49697i
$675$	1.27126	+	3.91255i	0.0489310	+	0.150594i
$676$	7.53357	−	5.47346i	0.289753	−	0.210518i
$677$	−31.2234	+	22.6852i	−1.20001	+	0.871861i	−0.994286	−	0.106748i	$-0.965956\pi$
$677$	−31.2234	+	22.6852i	−1.20001	+	0.871861i	−0.205728	+	0.978609i	$0.565956\pi$
$678$	−6.76183	−	20.8108i	−0.259686	−	0.799232i
$679$	9.34654	−	28.7657i	0.358687	−	1.10393i
$680$	5.13021	+	3.72732i	0.196735	+	0.142936i
$681$	−28.2307			−1.08180
$682$	16.0694	+	2.17935i	0.615331	+	0.0834515i
$683$	14.2530			0.545377			0.272688	−	0.962102i	$-0.412087\pi$
$683$	14.2530			0.545377			0.272688	+	0.962102i	$0.412087\pi$
$684$	0.580211	+	0.421548i	0.0221849	+	0.0161183i
$685$	−4.27317	+	13.1515i	−0.163270	+	0.502492i
$686$	−9.75471	−	30.0219i	−0.372437	−	1.14624i
$687$	−4.19197	+	3.04565i	−0.159934	+	0.116199i
$688$	−8.49908	+	6.17494i	−0.324024	+	0.235417i
$689$	−0.461362	−	1.41993i	−0.0175765	−	0.0540949i
$690$	2.92321	−	8.99673i	0.111285	−	0.342500i
$691$	24.6553	+	17.9131i	0.937933	+	0.681448i	0.947922	−	0.318502i	$-0.103180\pi$
$691$	24.6553	+	17.9131i	0.937933	+	0.681448i	−0.00998927	+	0.999950i	$0.503180\pi$
$692$	0.465845			0.0177088
$693$	−6.09819	−	5.83232i	−0.231651	−	0.221551i
$694$	0.273569			0.0103845
$695$	10.7158	+	7.78550i	0.406474	+	0.295321i
$696$	−6.70680	+	20.6414i	−0.254221	+	0.782411i
$697$	−10.7715	−	33.1512i	−0.407999	−	1.25569i
$698$	−39.6484	+	28.8063i	−1.50072	+	1.09033i
$699$	−10.9268	+	7.93875i	−0.413288	+	0.300271i
$700$	−2.31964	−	7.13910i	−0.0876740	−	0.269833i
$701$	4.53749	−	13.9649i	0.171378	−	0.527449i	−0.828071	−	0.560623i	$-0.810562\pi$
$701$	4.53749	−	13.9649i	0.171378	−	0.527449i	0.999450	+	0.0331744i	$0.0105617\pi$
$702$	−0.167728	−	0.121861i	−0.00633048	−	0.00459936i
$703$	−4.43442			−0.167247
$704$	−10.0558	+	5.40921i	−0.378993	+	0.203867i
$705$	7.79914			0.293732
$706$	21.0933	+	15.3252i	0.793858	+	0.576772i
$707$	−12.6630	+	38.9728i	−0.476242	+	1.46572i
$708$	0.249391	+	0.767548i	0.00937270	+	0.0288462i
$709$	2.67744	−	1.94527i	0.100553	−	0.0730563i	−0.536372	−	0.843981i	$-0.680206\pi$
$709$	2.67744	−	1.94527i	0.100553	−	0.0730563i	0.636926	+	0.770925i	$0.280206\pi$
$710$	1.36988	−	0.995278i	0.0514108	−	0.0373521i
$711$	−0.684009	−	2.10516i	−0.0256524	−	0.0789498i
$712$	7.12473	−	21.9276i	0.267010	−	0.821773i
$713$	14.6298	+	10.6291i	0.547889	+	0.398065i
$714$	−13.3606			−0.500007
$715$	−0.170429	+	0.353756i	−0.00637368	+	0.0132297i
$716$	−15.3172			−0.572431
$717$	−24.9507	−	18.1278i	−0.931801	−	0.676993i
$718$	14.9072	−	45.8798i	0.556333	−	1.71222i
$719$	−1.03699	−	3.19152i	−0.0386732	−	0.119024i	0.929856	−	0.367923i	$-0.119931\pi$
$719$	−1.03699	−	3.19152i	−0.0386732	−	0.119024i	−0.968529	+	0.248900i	$0.919931\pi$
$720$	3.74685	−	2.72224i	0.139637	−	0.101452i
$721$	−1.64895	+	1.19803i	−0.0614102	+	0.0446171i
$722$	0.509380	+	1.56771i	0.0189571	+	0.0583441i
$723$	−0.931896	+	2.86808i	−0.0346576	+	0.106665i
$724$	−10.3129	−	7.49278i	−0.383277	−	0.278467i
$725$	42.2242			1.56817
$726$	−17.4773	−	4.82939i	−0.648643	−	0.179235i
$727$	−23.1461			−0.858440			−0.429220	−	0.903200i	$-0.641212\pi$
$727$	−23.1461			−0.858440			−0.429220	+	0.903200i	$0.641212\pi$
$728$	−0.547427	−	0.397729i	−0.0202890	−	0.0147408i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	6.67436	+	20.5416i	0.247029	+	0.760278i
$731$	5.50321	−	3.99832i	0.203544	−	0.147883i
$732$	1.21704	−	0.884234i	0.0449832	−	0.0326822i
$733$	−9.77164	−	30.0740i	−0.360924	−	1.11081i	−0.952494	−	0.304556i	$-0.901492\pi$
$733$	−9.77164	−	30.0740i	−0.360924	−	1.11081i	0.591570	−	0.806253i	$-0.298508\pi$
$734$	17.0432	−	52.4537i	0.629078	−	1.93610i
$735$	−0.401280	−	0.291547i	−0.0148014	−	0.0107539i
$736$	23.6598			0.872113
$737$	−19.3936	+	40.2548i	−0.714371	+	1.48281i
$738$	−18.0361			−0.663917
$739$	4.12444	+	2.99658i	0.151720	+	0.110231i	0.661056	−	0.750337i	$-0.270109\pi$
$739$	4.12444	+	2.99658i	0.151720	+	0.110231i	−0.509336	+	0.860568i	$0.670109\pi$
$740$	0.925104	−	2.84718i	0.0340075	−	0.104664i
$741$	−0.0388661	−	0.119617i	−0.00142778	−	0.00439426i
$742$	−40.2757	+	29.2620i	−1.47857	+	1.07424i
$743$	−14.0943	+	10.2401i	−0.517069	+	0.375672i	−0.815499	−	0.578759i	$-0.803537\pi$
$743$	−14.0943	+	10.2401i	−0.517069	+	0.375672i	0.298430	+	0.954432i	$0.403537\pi$
$744$	1.93825	+	5.96532i	0.0710597	+	0.218699i
$745$	−6.03257	+	18.5663i	−0.221016	+	0.680218i
$746$	−23.7149	−	17.2299i	−0.868266	−	0.630832i
$747$	10.3345			0.378121
$748$	−6.67343	+	3.58976i	−0.244005	+	0.131255i
$749$	−2.78675			−0.101826
$750$	−11.4410	−	8.31236i	−0.417766	−	0.303524i
$751$	−4.12996	+	12.7107i	−0.150704	+	0.463820i	−0.997700	−	0.0677792i	$-0.978409\pi$
$751$	−4.12996	+	12.7107i	−0.150704	+	0.463820i	0.846996	+	0.531599i	$0.178409\pi$
$752$	12.5966	+	38.7683i	0.459350	+	1.41373i
$753$	−24.4537	+	17.7666i	−0.891142	+	0.647452i
$754$	−1.72153	+	1.25076i	−0.0626943	+	0.0455500i
$755$	−3.82722	−	11.7790i	−0.139287	−	0.428681i
$756$	−0.563854	+	1.73536i	−0.0205072	+	0.0631145i
$757$	6.36462	+	4.62417i	0.231326	+	0.168068i	0.697410	−	0.716672i	$-0.254336\pi$
$757$	6.36462	+	4.62417i	0.231326	+	0.168068i	−0.466084	+	0.884740i	$0.654336\pi$
$758$	−5.91378			−0.214798
$759$	−14.6124	−	13.9753i	−0.530397	−	0.507273i
$760$	1.99052			0.0722038
$761$	−18.6765	−	13.5693i	−0.677023	−	0.491886i	0.195346	−	0.980734i	$-0.437417\pi$
$761$	−18.6765	−	13.5693i	−0.677023	−	0.491886i	−0.872369	+	0.488849i	$0.837417\pi$
$762$	7.32200	−	22.5348i	0.265248	−	0.816350i
$763$	3.71234	+	11.4254i	0.134396	+	0.413628i
$764$	−11.8755	+	8.62809i	−0.429642	+	0.312153i
$765$	−2.42611	+	1.76267i	−0.0877162	+	0.0637296i
$766$	0.918580	+	2.82710i	0.0331896	+	0.102147i
$767$	0.0437362	−	0.134606i	0.00157922	−	0.00486035i
$768$	12.3485	+	8.97172i	0.445589	+	0.323739i
$769$	19.8978			0.717535			0.358767	−	0.933427i	$-0.383197\pi$
$769$	19.8978			0.717535			0.358767	+	0.933427i	$0.383197\pi$
$770$	12.9746	+	1.75963i	0.467574	+	0.0634126i
$771$	2.94672			0.106124
$772$	6.43911	+	4.67828i	0.231748	+	0.168375i
$773$	15.4136	−	47.4382i	0.554389	−	1.70623i	−0.143161	−	0.989699i	$-0.545727\pi$
$773$	15.4136	−	47.4382i	0.554389	−	1.70623i	0.697551	−	0.716535i	$-0.254273\pi$
$774$	−1.08765	−	3.34745i	−0.0390948	−	0.120321i
$775$	9.87220	−	7.17257i	0.354620	−	0.257646i
$776$	20.3374	−	14.7760i	0.730070	−	0.530427i
$777$	−3.48638	−	10.7300i	−0.125073	−	0.384936i
$778$	−15.6421	+	48.1414i	−0.560796	+	1.72595i
$779$	−8.85197	−	6.43133i	−0.317155	−	0.230426i
$780$	0.0849100			0.00304027
$781$	−0.645681	−	3.56121i	−0.0231043	−	0.127430i
$782$	−32.0145			−1.14484
$783$	−8.30359	−	6.03291i	−0.296746	−	0.215599i
$784$	0.801118	−	2.46559i	0.0286113	−	0.0880567i
$785$	−1.37182	−	4.22202i	−0.0489623	−	0.150690i
$786$	3.68477	−	2.67714i	0.131431	−	0.0954905i
$787$	2.34953	−	1.70703i	0.0837517	−	0.0608492i	−0.545121	−	0.838357i	$-0.683516\pi$
$787$	2.34953	−	1.70703i	0.0837517	−	0.0608492i	0.628873	+	0.777508i	$0.283516\pi$
$788$	2.11345	+	6.50453i	0.0752886	+	0.231714i
$789$	−0.116883	+	0.359729i	−0.00416114	+	0.0128067i
$790$	2.77868	+	2.01883i	0.0988611	+	0.0718268i
$791$	33.7736			1.20085
$792$	−1.25118	−	6.90077i	−0.0444586	−	0.245208i
$793$	−0.263820			−0.00936853
$794$	−14.5938	−	10.6030i	−0.517914	−	0.376287i
$795$	−3.45299	+	10.6272i	−0.122465	+	0.376909i
$796$	−2.01849	−	6.21228i	−0.0715435	−	0.220188i
$797$	3.11780	−	2.26521i	0.110438	−	0.0802380i	−0.531195	−	0.847249i	$-0.678257\pi$
$797$	3.11780	−	2.26521i	0.110438	−	0.0802380i	0.641634	+	0.767011i	$0.278257\pi$
$798$	−3.39291	+	2.46509i	−0.120108	+	0.0872633i
$799$	−8.15638	−	25.1027i	−0.288552	−	0.888071i
$800$	4.93368	−	15.1843i	0.174432	−	0.536846i
$801$	8.82102	+	6.40884i	0.311675	+	0.226445i
$802$	−25.8248			−0.911906
$803$	45.7472	+	6.20426i	1.61438	+	0.218944i
$804$	9.66215			0.340758
$805$	11.8122	+	8.58209i	0.416327	+	0.302479i
$806$	−0.190035	+	0.584866i	−0.00669368	+	0.0206010i
$807$	3.60724	+	11.1020i	0.126981	+	0.390807i
$808$	−27.5539	+	20.0191i	−0.969341	+	0.704268i
$809$	−41.2437	+	29.9653i	−1.45005	+	1.05352i	−0.464232	+	0.885714i	$0.653670\pi$
$809$	−41.2437	+	29.9653i	−1.45005	+	1.05352i	−0.985819	+	0.167810i	$0.946330\pi$
$810$	0.479495	+	1.47573i	0.0168477	+	0.0518520i
$811$	2.61612	−	8.05160i	0.0918645	−	0.282730i	−0.894559	−	0.446949i	$-0.852510\pi$
$811$	2.61612	−	8.05160i	0.0918645	−	0.282730i	0.986424	+	0.164219i	$0.0525105\pi$
$812$	15.1513	+	11.0081i	0.531707	+	0.386307i
$813$	−0.617222			−0.0216469
$814$	−17.5203	−	16.7565i	−0.614087	−	0.587313i
$815$	3.92894			0.137625
$816$	−12.6804	−	9.21288i	−0.443904	−	0.322515i
$817$	0.659827	−	2.03074i	0.0230844	−	0.0710466i
$818$	−0.0389823	−	0.119975i	−0.00136299	−	0.00419484i
$819$	0.258882	−	0.188088i	0.00904605	−	0.00657234i
$820$	5.97600	−	4.34182i	0.208691	−	0.151623i
$821$	0.447970	+	1.37871i	0.0156342	+	0.0481173i	0.958569	−	0.284859i	$-0.0919469\pi$
$821$	0.447970	+	1.37871i	0.0156342	+	0.0481173i	−0.942935	+	0.332977i	$0.891947\pi$
$822$	7.48286	−	23.0299i	0.260995	−	0.803259i
$823$	−17.2273	−	12.5164i	−0.600506	−	0.436293i	0.245552	−	0.969383i	$-0.421031\pi$
$823$	−17.2273	−	12.5164i	−0.600506	−	0.436293i	−0.846058	+	0.533090i	$0.821031\pi$
$824$	−1.69403			−0.0590142
$825$	−12.0161	+	6.46368i	−0.418347	+	0.225036i
$826$	−4.71938			−0.164208
$827$	−4.76791	−	3.46409i	−0.165796	−	0.120458i	0.501793	−	0.864988i	$-0.332674\pi$
$827$	−4.76791	−	3.46409i	−0.165796	−	0.120458i	−0.667590	+	0.744530i	$0.732674\pi$
$828$	−1.35110	+	4.15826i	−0.0469540	+	0.144510i
$829$	5.94192	+	18.2873i	0.206371	+	0.635146i	0.999654	+	0.0262926i	$0.00837017\pi$
$829$	5.94192	+	18.2873i	0.206371	+	0.635146i	−0.793283	+	0.608853i	$0.791630\pi$
$830$	−12.9733	+	9.42565i	−0.450310	+	0.327169i
$831$	−16.0507	+	11.6615i	−0.556791	+	0.404532i
$832$	−0.133807	−	0.411815i	−0.00463891	−	0.0142771i
$833$	−0.518729	+	1.59648i	−0.0179729	+	0.0553149i
$834$	−18.7647	−	13.6334i	−0.649770	−	0.472085i
$835$	10.7100			0.370634
$836$	−1.03238	+	2.14290i	−0.0357057	+	0.0741137i
$837$	−2.96622			−0.102527
$838$	7.22681	+	5.25058i	0.249646	+	0.181378i
$839$	1.10671	−	3.40610i	0.0382078	−	0.117592i	−0.930133	−	0.367222i	$-0.880309\pi$
$839$	1.10671	−	3.40610i	0.0382078	−	0.117592i	0.968341	+	0.249630i	$0.0803090\pi$
$840$	1.56497	+	4.81647i	0.0539964	+	0.166184i
$841$	−61.7649	+	44.8749i	−2.12983	+	1.54741i
$842$	22.3550	−	16.2419i	0.770406	−	0.559733i
$843$	−5.66256	−	17.4276i	−0.195029	−	0.600238i
$844$	2.26340	−	6.96602i	0.0779093	−	0.239780i
$845$	9.88814	+	7.18415i	0.340162	+	0.247142i
$846$	−13.6573			−0.469546
$847$	15.4251	−	23.3519i	0.530011	−	0.802380i
$848$	−58.4033			−2.00558
$849$	−4.83936	−	3.51600i	−0.166086	−	0.120669i
$850$	−6.67584	+	20.5461i	−0.228979	+	0.704726i
$851$	−8.35403	−	25.7111i	−0.286373	−	0.881364i
$852$	−0.633156	+	0.460015i	−0.0216916	+	0.0157598i
$853$	−10.3084	+	7.48947i	−0.352952	+	0.256435i	−0.750106	−	0.661317i	$-0.769998\pi$
$853$	−10.3084	+	7.48947i	−0.352952	+	0.256435i	0.397154	+	0.917752i	$0.369998\pi$
$854$	2.71842	+	8.36644i	0.0930225	+	0.286294i
$855$	−0.290887	+	0.895259i	−0.00994813	+	0.0306172i
$856$	−1.87381	−	1.36140i	−0.0640455	−	0.0465318i
$857$	−11.0419			−0.377186			−0.188593	−	0.982055i	$-0.560393\pi$
$857$	−11.0419			−0.377186			−0.188593	+	0.982055i	$0.560393\pi$
$858$	0.298442	−	0.619470i	0.0101886	−	0.0211484i
$859$	−15.6763			−0.534868			−0.267434	−	0.963576i	$-0.586176\pi$
$859$	−15.6763			−0.534868			−0.267434	+	0.963576i	$0.586176\pi$
$860$	1.16621	+	0.847300i	0.0397674	+	0.0288927i
$861$	8.60241	−	26.4755i	0.293169	−	0.902282i
$862$	−2.45944	−	7.56938i	−0.0837689	−	0.257814i
$863$	−9.00136	+	6.53987i	−0.306410	+	0.222620i	−0.730354	−	0.683068i	$-0.760645\pi$
$863$	−9.00136	+	6.53987i	−0.306410	+	0.222620i	0.423945	+	0.905688i	$0.360645\pi$
$864$	−3.13973	+	2.28115i	−0.106816	+	0.0776062i
$865$	0.188946	+	0.581515i	0.00642435	+	0.0197721i
$866$	−13.5451	+	41.6876i	−0.460282	+	1.41660i
$867$	−5.54261	−	4.02694i	−0.188237	−	0.136762i
$868$	5.41236			0.183708
$869$	6.46531	−	3.47781i	0.219321	−	0.117977i
$870$	15.9261			0.539946
$871$	−1.37085	−	0.995983i	−0.0464496	−	0.0337476i
$872$	−3.08544	+	9.49602i	−0.104486	+	0.321576i
$873$	3.67363	+	11.3063i	0.124334	+	0.382659i
$874$	−8.13006	+	5.90683i	−0.275003	+	0.199802i
$875$	17.6587	−	12.8298i	0.596974	−	0.433727i
$876$	−3.08487	−	9.49425i	−0.104228	−	0.320781i
$877$	8.26520	−	25.4377i	0.279096	−	0.858970i	−0.709010	−	0.705198i	$-0.750858\pi$
$877$	8.26520	−	25.4377i	0.279096	−	0.858970i	0.988106	−	0.153771i	$-0.0491420\pi$
$878$	21.0533	+	15.2961i	0.710515	+	0.516219i
$879$	−4.46485			−0.150596
$880$	11.1008	+	10.6168i	0.374208	+	0.357893i
$881$	31.8226			1.07213			0.536065	−	0.844176i	$-0.319910\pi$
$881$	31.8226			1.07213			0.536065	+	0.844176i	$0.319910\pi$
$882$	0.702691	+	0.510535i	0.0236608	+	0.0171906i
$883$	0.169160	−	0.520622i	0.00569270	−	0.0175203i	−0.948170	−	0.317764i	$-0.897068\pi$
$883$	0.169160	−	0.520622i	0.00569270	−	0.0175203i	0.953863	+	0.300244i	$0.0970680\pi$
$884$	−0.0887994	−	0.273296i	−0.00298665	−	0.00919195i
$885$	−0.856979	+	0.622632i	−0.0288070	+	0.0209295i
$886$	31.9571	−	23.2182i	1.07362	−	0.780031i
$887$	−11.5318	−	35.4913i	−0.387201	−	1.19168i	−0.934871	−	0.354988i	$-0.884485\pi$
$887$	−11.5318	−	35.4913i	−0.387201	−	1.19168i	0.547670	−	0.836694i	$-0.315515\pi$
$888$	2.89764	−	8.91801i	0.0972384	−	0.299269i
$889$	29.5870	+	21.4962i	0.992317	+	0.720960i
$890$	−16.9185			−0.567110
$891$	3.28654	+	0.445722i	0.110103	+	0.0149323i
$892$	11.0215			0.369026
$893$	−6.70289	−	4.86993i	−0.224304	−	0.162966i
$894$	10.5638	−	32.5120i	0.353306	−	1.08736i
$895$	−6.21263	−	19.1205i	−0.207665	−	0.639128i
$896$	−27.6574	+	20.0942i	−0.923967	+	0.671301i
$897$	0.620330	−	0.450696i	0.0207122	−	0.0150483i
$898$	20.6899	+	63.6769i	0.690431	+	2.12493i
$899$	−9.40792	+	28.9546i	−0.313772	+	0.965690i
$900$	2.38693	+	1.73421i	0.0795643	+	0.0578069i
$901$	37.8165			1.25985
$902$	−10.6717	−	58.8592i	−0.355330	−	1.95980i
$903$	5.43254			0.180784
$904$	22.7094	+	16.4993i	0.755302	+	0.548759i
$905$	5.17036	−	15.9127i	0.171868	−	0.528957i
$906$	6.70194	+	20.6265i	0.222657	+	0.685268i
$907$	−6.14388	+	4.46379i	−0.204004	+	0.148218i	−0.685097	−	0.728452i	$-0.740240\pi$
$907$	−6.14388	+	4.46379i	−0.204004	+	0.148218i	0.481093	+	0.876670i	$0.340240\pi$
$908$	−16.3798	+	11.9006i	−0.543582	+	0.394936i
$909$	−4.97717	−	15.3182i	−0.165082	−	0.508071i
$910$	−0.153436	+	0.472228i	−0.00508636	+	0.0156542i
$911$	14.7880	+	10.7441i	0.489949	+	0.355969i	0.805165	−	0.593051i	$-0.202077\pi$
$911$	14.7880	+	10.7441i	0.489949	+	0.355969i	−0.315216	+	0.949020i	$0.602077\pi$
$912$	−4.92001			−0.162918
$913$	6.11484	+	33.7259i	0.202372	+	1.11617i
$914$	59.2613			1.96019
$915$	1.59742	+	1.16060i	0.0528092	+	0.0383681i
$916$	−1.14834	+	3.53424i	−0.0379423	+	0.116774i
$917$	2.17236	+	6.68583i	0.0717376	+	0.220786i
$918$	4.24842	−	3.08666i	0.140219	−	0.101875i
$919$	−16.6921	+	12.1275i	−0.550622	+	0.400050i	−0.828015	−	0.560706i	$-0.810530\pi$
$919$	−16.6921	+	12.1275i	−0.550622	+	0.400050i	0.277393	+	0.960757i	$0.410530\pi$
$920$	3.74996	+	11.5412i	0.123632	+	0.380501i
$921$	−0.716194	+	2.20422i	−0.0235994	+	0.0726315i
$922$	−31.7954	−	23.1007i	−1.04712	−	0.760780i
$923$	0.137250			0.00451764
$924$	−5.99684	−	0.813295i	−0.197282	−	0.0267555i
$925$	−18.2428			−0.599818
$926$	6.01439	+	4.36971i	0.197645	+	0.143598i
$927$	0.247558	−	0.761906i	0.00813088	−	0.0250243i
$928$	12.3091	+	37.8835i	0.404065	+	1.24359i
$929$	−1.24410	+	0.903893i	−0.0408177	+	0.0296558i	−0.608007	−	0.793932i	$-0.708031\pi$
$929$	−1.24410	+	0.903893i	−0.0408177	+	0.0296558i	0.567189	+	0.823587i	$0.308031\pi$
$930$	3.72359	−	2.70535i	0.122101	−	0.0887118i
$931$	0.162828	+	0.501134i	0.00533648	+	0.0164240i
$932$	−2.99326	+	9.21231i	−0.0980475	+	0.301759i
$933$	2.75351	+	2.00055i	0.0901460	+	0.0654949i
$934$	8.08015			0.264391
$935$	−7.18784	−	6.87446i	−0.235068	−	0.224819i
$936$	0.265958			0.00869311
$937$	−35.6157	−	25.8763i	−1.16351	−	0.845342i	−0.173295	−	0.984870i	$-0.555441\pi$
$937$	−35.6157	−	25.8763i	−1.16351	−	0.845342i	−0.990218	+	0.139528i	$0.955441\pi$
$938$	−17.4599	+	53.7361i	−0.570087	+	1.75455i
$939$	−5.36732	−	16.5189i	−0.175156	−	0.539074i
$940$	4.52515	−	3.28771i	0.147594	−	0.107233i
$941$	41.0897	−	29.8534i	1.33949	−	0.973194i	0.340024	−	0.940417i	$-0.389565\pi$
$941$	41.0897	−	29.8534i	1.33949	−	0.973194i	0.999463	−	0.0327772i	$-0.0104352\pi$
$942$	2.40222	+	7.39329i	0.0782687	+	0.240886i
$943$	20.6130	−	63.4403i	0.671252	−	2.06590i
$944$	−4.47914	−	3.25428i	−0.145783	−	0.105918i
$945$	−2.39496			−0.0779079
$946$	10.2806	−	5.53011i	0.334250	−	0.179799i
$947$	−43.7790			−1.42263			−0.711313	−	0.702875i	$-0.751899\pi$
$947$	−43.7790			−1.42263			−0.711313	+	0.702875i	$0.751899\pi$
$948$	−1.28430	−	0.933097i	−0.0417121	−	0.0303056i
$949$	−0.540999	+	1.66502i	−0.0175616	+	0.0540490i
$950$	2.09554	+	6.44939i	0.0679881	+	0.209246i
$951$	−11.1106	+	8.07235i	−0.360287	+	0.261764i
$952$	13.8659	−	10.0742i	0.449397	−	0.326506i
$953$	−0.181325	−	0.558061i	−0.00587369	−	0.0180774i	0.948077	−	0.318042i	$-0.103025\pi$
$953$	−0.181325	−	0.558061i	−0.00587369	−	0.0180774i	−0.953950	+	0.299964i	$0.903025\pi$
$954$	6.04662	−	18.6096i	0.195767	−	0.602508i
$955$	−15.5872	−	11.3247i	−0.504389	−	0.366460i
$956$	−22.1184			−0.715360
$957$	14.7748	−	30.6677i	0.477601	−	0.991346i
$958$	31.6626			1.02297
$959$	30.2370	+	21.9685i	0.976404	+	0.709399i
$960$	−1.00146	+	3.08217i	−0.0323219	+	0.0994765i
$961$	−6.86066	−	21.1149i	−0.221312	−	0.681127i
$962$	0.743776	−	0.540385i	0.0239803	−	0.0174227i
$963$	0.886137	−	0.643816i	0.0285553	−	0.0207467i
$964$	0.668338	+	2.05693i	0.0215257	+	0.0662494i
$965$	−3.22823	+	9.93546i	−0.103920	+	0.319834i
$966$	−20.6847	−	15.0283i	−0.665519	−	0.483528i
$967$	−24.4395			−0.785923			−0.392961	−	0.919555i	$-0.628549\pi$
$967$	−24.4395			−0.785923			−0.392961	+	0.919555i	$0.628549\pi$
$968$	21.7798	−	8.16622i	0.700029	−	0.262472i
$969$	3.18574			0.102341
$970$	−14.9236	−	10.8426i	−0.479167	−	0.348135i
$971$	−12.1616	+	37.4296i	−0.390285	+	1.20117i	0.542288	+	0.840193i	$0.317558\pi$
$971$	−12.1616	+	37.4296i	−0.390285	+	1.20117i	−0.932573	+	0.360981i	$0.882442\pi$
$972$	−0.221621	−	0.682079i	−0.00710850	−	0.0218777i
$973$	28.9627	−	21.0426i	0.928501	−	0.674595i
$974$	7.09224	−	5.15281i	0.227250	−	0.165107i
$975$	−0.159891	−	0.492094i	−0.00512061	−	0.0157596i
$976$	−3.18910	+	9.81505i	−0.102081	+	0.314172i
$977$	−30.7848	−	22.3664i	−0.984891	−	0.715566i	−0.0260950	−	0.999659i	$-0.508307\pi$
$977$	−30.7848	−	22.3664i	−0.984891	−	0.715566i	−0.958796	+	0.284094i	$0.908307\pi$
$978$	−6.88007			−0.220000
$979$	−15.6954	+	32.5787i	−0.501629	+	1.04122i
$980$	−0.355728			−0.0113633
$981$	−3.82004	−	2.77542i	−0.121965	−	0.0886124i
$982$	−16.0770	+	49.4799i	−0.513038	+	1.57897i
$983$	−10.7402	−	33.0550i	−0.342560	−	1.05429i	−0.962877	−	0.269940i	$-0.912996\pi$
$983$	−10.7402	−	33.0550i	−0.342560	−	1.05429i	0.620317	−	0.784351i	$-0.287004\pi$
$984$	18.7182	−	13.5996i	0.596715	−	0.433539i
$985$	−7.26242	+	5.27645i	−0.231400	+	0.168122i
$986$	−16.6556	−	51.2607i	−0.530423	−	1.63247i
$987$	6.51391	−	20.0478i	0.207340	−	0.638127i
$988$	−0.0729751	−	0.0530195i	−0.00232165	−	0.00168677i
$989$	13.0174			0.413930
$990$	−4.53222	+	2.43797i	−0.144044	+	0.0774837i
$991$	−23.4653			−0.745399			−0.372700	−	0.927952i	$-0.621568\pi$
$991$	−23.4653			−0.745399			−0.372700	+	0.927952i	$0.621568\pi$
$992$	9.31312	+	6.76638i	0.295692	+	0.214833i
$993$	−3.34944	+	10.3085i	−0.106291	+	0.327131i
$994$	−1.41423	−	4.35256i	−0.0448568	−	0.138055i
$995$	6.93611	−	5.03938i	0.219889	−	0.159759i
$996$	5.99622	−	4.35651i	0.189997	−	0.138041i
$997$	−2.19596	−	6.75847i	−0.0695467	−	0.214043i	0.910242	−	0.414076i	$-0.135895\pi$
$997$	−2.19596	−	6.75847i	−0.0695467	−	0.214043i	−0.979789	+	0.200033i	$0.935895\pi$
$998$	−3.69442	+	11.3703i	−0.116945	+	0.359919i
$999$	3.58752	+	2.60649i	0.113504	+	0.0824656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.j.c.400.3	yes	40
11.3	even	5	inner	627.2.j.c.58.3	✓	40
11.5	even	5		6897.2.a.bo.1.15		20
11.6	odd	10		6897.2.a.bn.1.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.c.58.3	✓	40	11.3	even	5	inner
627.2.j.c.400.3	yes	40	1.1	even	1	trivial
6897.2.a.bn.1.6		20	11.6	odd	10
6897.2.a.bo.1.15		20	11.5	even	5

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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33357 - 0.968898i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.221621 + 0.682079i) q^{4} +(-0.761553 + 0.553300i) q^{5} +(1.33357 - 0.968898i) q^{6} +(0.786208 + 2.41970i) q^{7} +(-0.653442 + 2.01109i) q^{8} +(-0.809017 - 0.587785i) q^{9} +1.55168 q^{10} +(1.43950 - 2.98795i) q^{11} -0.717181 q^{12} +(0.101753 + 0.0739276i) q^{13} +(1.29598 - 3.98860i) q^{14} +(-0.290887 - 0.895259i) q^{15} +(3.98037 - 2.89191i) q^{16} +(-2.57732 + 1.87253i) q^{17} +(0.509380 + 1.56771i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(-0.546171 - 0.396816i) q^{20} -2.54422 q^{21} +(-4.81470 + 2.58992i) q^{22} -6.09645 q^{23} +(-1.71073 - 1.24292i) q^{24} +(-1.27126 + 3.91255i) q^{25} +(-0.0640663 - 0.197176i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.47619 + 1.07251i) q^{28} +(-3.17169 - 9.76146i) q^{29} +(-0.479495 + 1.47573i) q^{30} +(-2.39972 - 1.74350i) q^{31} -3.88092 q^{32} +(2.39688 + 2.29238i) q^{33} +5.25134 q^{34} +(-1.93756 - 1.40772i) q^{35} +(0.221621 - 0.682079i) q^{36} +(1.37031 + 4.21739i) q^{37} +(1.33357 - 0.968898i) q^{38} +(-0.101753 + 0.0739276i) q^{39} +(-0.615105 - 1.89310i) q^{40} +(-3.38115 + 10.4061i) q^{41} +(3.39291 + 2.46509i) q^{42} -2.13525 q^{43} +(2.35704 + 0.319663i) q^{44} +0.941331 q^{45} +(8.13006 + 5.90683i) q^{46} +(-2.56028 + 7.87972i) q^{47} +(1.52037 + 4.67921i) q^{48} +(0.426290 - 0.309718i) q^{49} +(5.48618 - 3.98595i) q^{50} +(-0.984449 - 3.02982i) q^{51} +(-0.0278740 + 0.0857873i) q^{52} +(-9.60348 - 6.97734i) q^{53} -1.64839 q^{54} +(0.556975 + 3.07196i) q^{55} -5.37997 q^{56} +(-0.809017 - 0.587785i) q^{57} +(-5.22817 + 16.0907i) q^{58} +(-0.347738 - 1.07023i) q^{59} +(0.546171 - 0.396816i) q^{60} +(-1.69698 + 1.23293i) q^{61} +(1.51093 + 4.65017i) q^{62} +(0.786208 - 2.41970i) q^{63} +(-2.78526 - 2.02361i) q^{64} -0.118394 q^{65} +(-0.975333 - 5.37938i) q^{66} -13.4724 q^{67} +(-1.84840 - 1.34294i) q^{68} +(1.88391 - 5.79807i) q^{69} +(1.21994 + 3.75460i) q^{70} +(0.882840 - 0.641421i) q^{71} +(1.71073 - 1.24292i) q^{72} +(4.30138 + 13.2383i) q^{73} +(2.25880 - 6.95189i) q^{74} +(-3.32821 - 2.41809i) q^{75} -0.717181 q^{76} +(8.36169 + 1.13402i) q^{77} +0.207323 q^{78} +(1.79076 + 1.30106i) q^{79} +(-1.43117 + 4.40468i) q^{80} +(0.309017 + 0.951057i) q^{81} +(14.5915 - 10.6013i) q^{82} +(-8.36082 + 6.07449i) q^{83} +(-0.563854 - 1.73536i) q^{84} +(0.926692 - 2.85206i) q^{85} +(2.84751 + 2.06883i) q^{86} +10.2638 q^{87} +(5.06839 + 4.84742i) q^{88} -10.9034 q^{89} +(-1.25533 - 0.912053i) q^{90} +(-0.0988840 + 0.304334i) q^{91} +(-1.35110 - 4.15826i) q^{92} +(2.39972 - 1.74350i) q^{93} +(11.0490 - 8.02754i) q^{94} +(-0.290887 - 0.895259i) q^{95} +(1.19927 - 3.69098i) q^{96} +(-9.61769 - 6.98766i) q^{97} -0.868574 q^{98} +(-2.92085 + 1.57118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{2} + 10 q^{3} - 3 q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 13 q^{8} - 10 q^{9} + 10 q^{10} + 7 q^{11} - 42 q^{12} - 12 q^{13} - 2 q^{14} - 7 q^{15} - 27 q^{16} + 11 q^{17} - 4 q^{18} + 10 q^{19}+ \cdots - 13 q^{99}+O(q^{100}) \) 40 * q + q^2 + 10 * q^3 - 3 * q^4 + 2 * q^5 - q^6 + 4 * q^7 - 13 * q^8 - 10 * q^9 + 10 * q^10 + 7 * q^11 - 42 * q^12 - 12 * q^13 - 2 * q^14 - 7 * q^15 - 27 * q^16 + 11 * q^17 - 4 * q^18 + 10 * q^19 - 11 * q^20 + 6 * q^21 - 2 * q^22 - 60 * q^23 - 7 * q^24 - 18 * q^25 - 35 * q^26 + 10 * q^27 + 20 * q^28 + 25 * q^29 - 5 * q^30 - 12 * q^31 + 40 * q^32 + 3 * q^33 - 10 * q^34 + 24 * q^35 - 3 * q^36 - 23 * q^37 - q^38 + 12 * q^39 + 80 * q^40 + 18 * q^41 - 28 * q^42 - 6 * q^43 + 14 * q^44 - 18 * q^45 - 15 * q^46 - 9 * q^47 - 8 * q^48 - 4 * q^49 + 90 * q^50 + 4 * q^51 + 15 * q^52 - 26 * q^53 - 6 * q^54 + 38 * q^55 - 124 * q^56 - 10 * q^57 + 10 * q^58 + 7 * q^59 + 11 * q^60 + 18 * q^61 + 105 * q^62 + 4 * q^63 - 85 * q^64 + 36 * q^65 - 8 * q^66 - 88 * q^67 + 40 * q^68 - 103 * q^70 + 30 * q^71 + 7 * q^72 - 2 * q^73 - 4 * q^74 + 13 * q^75 - 42 * q^76 + 57 * q^77 + 20 * q^78 + 59 * q^79 + 11 * q^80 - 10 * q^81 + 40 * q^82 - 54 * q^83 - 15 * q^84 + 21 * q^85 - 108 * q^86 - 30 * q^87 + 83 * q^88 - 74 * q^89 - 10 * q^90 + q^91 - 125 * q^92 + 12 * q^93 - 10 * q^94 - 7 * q^95 + 55 * q^96 - 17 * q^97 + 78 * q^98 - 13 * q^99

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