LMFDB - Embedded newform 228.2.w.b.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	228.67
Dual form			228.2.w.b.211.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05000 - 0.947369i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.204983 + 1.98947i) q^{4} +(1.27204 + 0.462984i) q^{5} +(-1.41330 - 0.0508027i) q^{6} +(-3.79268 - 2.18970i) q^{7} +(1.66953 - 2.28313i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.897018 - 1.69122i) q^{10} +(5.13267 - 2.96335i) q^{11} +(1.43583 + 1.39226i) q^{12} +(1.69665 - 2.02199i) q^{13} +(1.90784 + 5.89224i) q^{14} +(1.27204 - 0.462984i) q^{15} +(-3.91596 + 0.815613i) q^{16} +(0.539127 + 3.05754i) q^{17} +(-1.11531 + 0.869535i) q^{18} +(2.06520 - 3.83861i) q^{19} +(-0.660346 + 2.62558i) q^{20} +(-4.31287 + 0.760476i) q^{21} +(-8.19666 - 1.75103i) q^{22} +(-0.866649 - 2.38110i) q^{23} +(-0.188632 - 2.82213i) q^{24} +(-2.42650 - 2.03607i) q^{25} +(-3.69704 + 0.515725i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.57891 - 7.99426i) q^{28} +(2.70494 + 0.476954i) q^{29} +(-1.77425 - 0.718959i) q^{30} +(-5.45375 + 9.44617i) q^{31} +(4.88443 + 2.85347i) q^{32} +(2.02705 - 5.56927i) q^{33} +(2.33054 - 3.72115i) q^{34} +(-3.81063 - 4.54133i) q^{35} +(1.99484 + 0.143599i) q^{36} +6.57365i q^{37} +(-5.80504 + 2.07401i) q^{38} -2.63952i q^{39} +(3.18076 - 2.13126i) q^{40} +(3.24392 + 3.86595i) q^{41} +(5.24895 + 3.28739i) q^{42} +(-0.790384 + 2.17156i) q^{43} +(6.94759 + 9.60384i) q^{44} +(0.676837 - 1.17232i) q^{45} +(-1.34580 + 3.32118i) q^{46} +(-2.17246 - 0.383063i) q^{47} +(-2.47554 + 3.14193i) q^{48} +(6.08959 + 10.5475i) q^{49} +(0.618899 + 4.43665i) q^{50} +(2.37834 + 1.99567i) q^{51} +(4.37046 + 2.96095i) q^{52} +(-2.95468 - 8.11792i) q^{53} +(-0.295448 + 1.38301i) q^{54} +(7.90093 - 1.39315i) q^{55} +(-11.3314 + 5.00339i) q^{56} +(-0.885372 - 4.26803i) q^{57} +(-2.38832 - 3.06338i) q^{58} +(2.11216 + 11.9786i) q^{59} +(1.18184 + 2.43578i) q^{60} +(5.27335 - 1.91934i) q^{61} +(14.6754 - 4.75173i) q^{62} +(-2.81503 + 3.35482i) q^{63} +(-2.42534 - 7.62350i) q^{64} +(3.09435 - 1.78652i) q^{65} +(-7.40455 + 3.92735i) q^{66} +(-0.626632 + 3.55381i) q^{67} +(-5.97236 + 1.69932i) q^{68} +(-2.19443 - 1.26696i) q^{69} +(-0.301173 + 8.37846i) q^{70} +(2.55019 + 0.928194i) q^{71} +(-1.95853 - 2.04063i) q^{72} +(4.12575 - 3.46192i) q^{73} +(6.22767 - 6.90230i) q^{74} -3.16756 q^{75} +(8.06012 + 3.32181i) q^{76} -25.9554 q^{77} +(-2.50060 + 2.77148i) q^{78} +(-3.29918 + 2.76834i) q^{79} +(-5.35887 - 0.775538i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.256383 - 7.13242i) q^{82} +(5.76326 + 3.32742i) q^{83} +(-2.39701 - 8.42443i) q^{84} +(-0.729802 + 4.13891i) q^{85} +(2.88717 - 1.53134i) q^{86} +(2.37868 - 1.37333i) q^{87} +(1.80344 - 16.6659i) q^{88} +(3.11333 - 3.71033i) q^{89} +(-1.82129 + 0.589713i) q^{90} +(-10.8624 + 3.95358i) q^{91} +(4.55947 - 2.21225i) q^{92} +(1.89407 + 10.7418i) q^{93} +(1.91817 + 2.46034i) q^{94} +(4.40423 - 3.92670i) q^{95} +(5.57587 - 0.953765i) q^{96} +(-11.9550 + 2.10798i) q^{97} +(3.59831 - 16.8439i) q^{98} +(-2.02705 - 5.56927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.05000	−	0.947369i	−0.742459	−	0.669891i
$2$	−1.05000	−	0.947369i	−0.742459	−	0.669891i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	0.204983	+	1.98947i	0.102491	+	0.994734i
$5$	1.27204	+	0.462984i	0.568873	+	0.207053i	0.610412	−	0.792084i	$-0.291004\pi$
$5$	1.27204	+	0.462984i	0.568873	+	0.207053i	−0.0415392	+	0.999137i	$0.513226\pi$
$6$	−1.41330	−	0.0508027i	−0.576978	−	0.0207401i
$7$	−3.79268	−	2.18970i	−1.43350	−	0.827630i	−0.436111	−	0.899893i	$-0.643645\pi$
$7$	−3.79268	−	2.18970i	−1.43350	−	0.827630i	−0.997386	+	0.0722632i	$0.976978\pi$
$8$	1.66953	−	2.28313i	0.590268	−	0.807207i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−0.897018	−	1.69122i	−0.283662	−	0.534811i
$11$	5.13267	−	2.96335i	1.54756	−	0.893483i	0.549230	−	0.835671i	$-0.314921\pi$
$11$	5.13267	−	2.96335i	1.54756	−	0.893483i	0.998328	−	0.0578110i	$-0.0184121\pi$
$12$	1.43583	+	1.39226i	0.414489	+	0.401911i
$13$	1.69665	−	2.02199i	0.470565	−	0.560798i	−0.477599	−	0.878578i	$-0.658493\pi$
$13$	1.69665	−	2.02199i	0.470565	−	0.560798i	0.948165	+	0.317780i	$0.102937\pi$
$14$	1.90784	+	5.89224i	0.509891	+	1.57477i
$15$	1.27204	−	0.462984i	0.328439	−	0.119542i
$16$	−3.91596	+	0.815613i	−0.978991	+	0.203903i
$17$	0.539127	+	3.05754i	0.130757	+	0.741562i	0.977721	+	0.209911i	$0.0673173\pi$
$17$	0.539127	+	3.05754i	0.130757	+	0.741562i	−0.846963	+	0.531651i	$0.821572\pi$
$18$	−1.11531	+	0.869535i	−0.262880	+	0.204951i
$19$	2.06520	−	3.83861i	0.473790	−	0.880638i
$19$	2.06520	−	3.83861i	0.473790	−	0.880638i
$20$	−0.660346	+	2.62558i	−0.147658	+	0.587098i
$21$	−4.31287	+	0.760476i	−0.941146	+	0.165949i
$22$	−8.19666	−	1.75103i	−1.74753	−	0.373321i
$23$	−0.866649	−	2.38110i	−0.180709	−	0.496493i	0.815955	−	0.578116i	$-0.196212\pi$
$23$	−0.866649	−	2.38110i	−0.180709	−	0.496493i	−0.996663	+	0.0816229i	$0.973990\pi$
$24$	−0.188632	−	2.82213i	−0.0385044	−	0.576065i
$25$	−2.42650	−	2.03607i	−0.485299	−	0.407214i
$26$	−3.69704	+	0.515725i	−0.725049	+	0.101142i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	3.57891	−	7.99426i	0.676350	−	1.51077i
$29$	2.70494	+	0.476954i	0.502295	+	0.0885681i	0.419054	−	0.907961i	$-0.362362\pi$
$29$	2.70494	+	0.476954i	0.502295	+	0.0885681i	0.0832408	+	0.996529i	$0.473473\pi$
$30$	−1.77425	−	0.718959i	−0.323933	−	0.131263i
$31$	−5.45375	+	9.44617i	−0.979523	+	1.69658i	−0.315401	+	0.948959i	$0.602139\pi$
$31$	−5.45375	+	9.44617i	−0.979523	+	1.69658i	−0.664122	+	0.747624i	$0.731194\pi$
$32$	4.88443	+	2.85347i	0.863454	+	0.504428i
$33$	2.02705	−	5.56927i	0.352864	−	0.969485i
$34$	2.33054	−	3.72115i	0.399684	−	0.638173i
$35$	−3.81063	−	4.54133i	−0.644114	−	0.767625i
$36$	1.99484	+	0.143599i	0.332473	+	0.0239331i
$37$			6.57365i			1.08070i	0.841440	+	0.540350i	$0.181708\pi$
$37$			6.57365i			1.08070i	−0.841440	+	0.540350i	$0.818292\pi$
$38$	−5.80504	+	2.07401i	−0.941702	+	0.336449i
$39$		−	2.63952i		−	0.422661i
$40$	3.18076	−	2.13126i	0.502922	−	0.336982i
$41$	3.24392	+	3.86595i	0.506615	+	0.603760i	0.957362	−	0.288892i	$-0.0932868\pi$
$41$	3.24392	+	3.86595i	0.506615	+	0.603760i	−0.450747	+	0.892652i	$0.648842\pi$
$42$	5.24895	+	3.28739i	0.809930	+	0.507255i
$43$	−0.790384	+	2.17156i	−0.120532	+	0.331160i	−0.985256	−	0.171089i	$-0.945272\pi$
$43$	−0.790384	+	2.17156i	−0.120532	+	0.331160i	0.864723	+	0.502249i	$0.167494\pi$
$44$	6.94759	+	9.60384i	1.04739	+	1.44783i
$45$	0.676837	−	1.17232i	0.100897	−	0.174759i
$46$	−1.34580	+	3.32118i	−0.198428	+	0.489681i
$47$	−2.17246	−	0.383063i	−0.316886	−	0.0558756i	0.0129430	−	0.999916i	$-0.495880\pi$
$47$	−2.17246	−	0.383063i	−0.316886	−	0.0558756i	−0.329829	+	0.944041i	$0.606991\pi$
$48$	−2.47554	+	3.14193i	−0.357313	+	0.453498i
$49$	6.08959	+	10.5475i	0.869942	+	1.50678i
$50$	0.618899	+	4.43665i	0.0875255	+	0.627438i
$51$	2.37834	+	1.99567i	0.333035	+	0.279449i
$52$	4.37046	+	2.96095i	0.606074	+	0.410610i
$53$	−2.95468	−	8.11792i	−0.405857	−	1.11508i	−0.959348	−	0.282227i	$-0.908927\pi$
$53$	−2.95468	−	8.11792i	−0.405857	−	1.11508i	0.553491	−	0.832855i	$-0.313295\pi$
$54$	−0.295448	+	1.38301i	−0.0402054	+	0.188204i
$55$	7.90093	−	1.39315i	1.06536	−	0.187852i
$56$	−11.3314	+	5.00339i	−1.51422	+	0.668606i
$57$	−0.885372	−	4.26803i	−0.117270	−	0.565315i
$58$	−2.38832	−	3.06338i	−0.313602	−	0.402241i
$59$	2.11216	+	11.9786i	0.274980	+	1.55949i	0.739027	+	0.673676i	$0.235286\pi$
$59$	2.11216	+	11.9786i	0.274980	+	1.55949i	−0.464047	+	0.885810i	$0.653603\pi$
$60$	1.18184	+	2.43578i	0.152575	+	0.314457i
$61$	5.27335	−	1.91934i	0.675183	−	0.245747i	0.0184052	−	0.999831i	$-0.494141\pi$
$61$	5.27335	−	1.91934i	0.675183	−	0.245747i	0.656778	+	0.754084i	$0.271919\pi$
$62$	14.6754	−	4.75173i	1.86378	−	0.603470i
$63$	−2.81503	+	3.35482i	−0.354660	+	0.422667i
$64$	−2.42534	−	7.62350i	−0.303168	−	0.952937i
$65$	3.09435	−	1.78652i	0.383807	−	0.221591i
$66$	−7.40455	+	3.92735i	−0.911437	+	0.483423i
$67$	−0.626632	+	3.55381i	−0.0765553	+	0.434167i	0.922306	+	0.386460i	$0.126302\pi$
$67$	−0.626632	+	3.55381i	−0.0765553	+	0.434167i	−0.998861	+	0.0477066i	$0.984809\pi$
$68$	−5.97236	+	1.69932i	−0.724255	+	0.206073i
$69$	−2.19443	−	1.26696i	−0.264179	−	0.152524i
$70$	−0.301173	+	8.37846i	−0.0359970	+	1.00142i
$71$	2.55019	+	0.928194i	0.302652	+	0.110156i	0.488882	−	0.872350i	$-0.337405\pi$
$71$	2.55019	+	0.928194i	0.302652	+	0.110156i	−0.186230	+	0.982506i	$0.559627\pi$
$72$	−1.95853	−	2.04063i	−0.230815	−	0.240490i
$73$	4.12575	−	3.46192i	0.482883	−	0.405187i	−0.368585	−	0.929594i	$-0.620158\pi$
$73$	4.12575	−	3.46192i	0.482883	−	0.405187i	0.851467	+	0.524407i	$0.175713\pi$
$74$	6.22767	−	6.90230i	0.723952	−	0.802376i
$75$	−3.16756			−0.365759
$76$	8.06012	+	3.32181i	0.924560	+	0.381038i
$77$	−25.9554			−2.95789
$78$	−2.50060	+	2.77148i	−0.283137	+	0.313808i
$79$	−3.29918	+	2.76834i	−0.371186	+	0.311462i	−0.809231	−	0.587491i	$-0.800116\pi$
$79$	−3.29918	+	2.76834i	−0.371186	+	0.311462i	0.438044	+	0.898953i	$0.355671\pi$
$80$	−5.35887	−	0.775538i	−0.599140	−	0.0867078i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	0.256383	−	7.13242i	0.0283127	−	0.787644i
$83$	5.76326	+	3.32742i	0.632600	+	0.365232i	0.781758	−	0.623581i	$-0.214323\pi$
$83$	5.76326	+	3.32742i	0.632600	+	0.365232i	−0.149158	+	0.988813i	$0.547656\pi$
$84$	−2.39701	−	8.42443i	−0.261535	−	0.919181i
$85$	−0.729802	+	4.13891i	−0.0791581	+	0.448928i
$86$	2.88717	−	1.53134i	0.311331	−	0.165129i
$87$	2.37868	−	1.37333i	0.255022	−	0.147237i
$88$	1.80344	−	16.6659i	0.192248	−	1.77659i
$89$	3.11333	−	3.71033i	0.330013	−	0.393294i	−0.575368	−	0.817895i	$-0.695141\pi$
$89$	3.11333	−	3.71033i	0.330013	−	0.393294i	0.905381	+	0.424601i	$0.139586\pi$
$90$	−1.82129	+	0.589713i	−0.191981	+	0.0621612i
$91$	−10.8624	+	3.95358i	−1.13869	+	0.414448i
$92$	4.55947	−	2.21225i	0.475358	−	0.230643i
$93$	1.89407	+	10.7418i	0.196406	+	1.11387i
$94$	1.91817	+	2.46034i	0.197844	+	0.253764i
$95$	4.40423	−	3.92670i	0.451865	−	0.402871i
$96$	5.57587	−	0.953765i	0.569085	−	0.0973433i
$97$	−11.9550	+	2.10798i	−1.21384	+	0.214033i	−0.743673	−	0.668543i	$-0.766918\pi$
$97$	−11.9550	+	2.10798i	−1.21384	+	0.214033i	−0.470169	+	0.882576i	$0.655807\pi$
$98$	3.59831	−	16.8439i	0.363485	−	1.70149i
$99$	−2.02705	−	5.56927i	−0.203726	−	0.559733i
$100$	3.55331	−	5.24479i	0.355331	−	0.524479i
$101$	5.27310	+	4.42466i	0.524693	+	0.440270i	0.866264	−	0.499586i	$-0.166515\pi$
$101$	5.27310	+	4.42466i	0.524693	+	0.440270i	−0.341571	+	0.939856i	$0.610959\pi$
$102$	−0.606617	−	4.34861i	−0.0600640	−	0.430577i
$103$	2.46826	+	4.27515i	0.243205	+	0.421243i	0.961625	−	0.274366i	$-0.0884680\pi$
$103$	2.46826	+	4.27515i	0.243205	+	0.421243i	−0.718421	+	0.695609i	$0.755135\pi$
$104$	−1.78385	−	7.24943i	−0.174921	−	0.710865i
$105$	−5.83822	−	1.02944i	−0.569752	−	0.100463i
$106$	−4.58826	+	11.3230i	−0.445652	+	1.09978i
$107$	−4.62047	+	8.00290i	−0.446678	+	0.773669i	−0.998167	−	0.0605128i	$-0.980726\pi$
$107$	−4.62047	+	8.00290i	−0.446678	+	0.773669i	0.551489	+	0.834182i	$0.314060\pi$
$108$	1.62044	−	1.17225i	0.155927	−	0.112800i
$109$	−3.27066	+	8.98605i	−0.313272	+	0.860708i	0.678719	+	0.734398i	$0.262535\pi$
$109$	−3.27066	+	8.98605i	−0.313272	+	0.860708i	−0.991991	+	0.126310i	$0.959687\pi$
$110$	−9.61577	−	6.02230i	−0.916828	−	0.574204i
$111$	4.22546	+	5.03571i	0.401063	+	0.477968i
$112$	16.6379	+	5.48144i	1.57214	+	0.517947i
$113$		−	11.0103i		−	1.03576i	−0.855452	−	0.517882i	$-0.826721\pi$
$113$		−	11.0103i		−	1.03576i	0.855452	−	0.517882i	$-0.173279\pi$
$114$	−3.11377	+	5.32019i	−0.291631	+	0.498282i
$115$		−	3.43009i		−	0.319858i
$116$	−0.394418	+	5.47916i	−0.0366208	+	0.508727i
$117$	−1.69665	−	2.02199i	−0.156855	−	0.186933i
$118$	9.13044	−	14.5785i	0.840525	−	1.34206i
$119$	4.65037	−	12.7768i	0.426298	−	1.17125i
$120$	1.06665	−	3.67719i	0.0973717	−	0.335680i
$121$	12.0628	−	20.8935i	1.09662	−	1.89941i
$122$	−7.35532	−	2.98051i	−0.665919	−	0.269842i
$123$	4.96997	+	0.876339i	0.448127	+	0.0790169i
$124$	−19.9108	−	8.91376i	−1.78804	−	0.800479i
$125$	−5.52811	−	9.57497i	−0.494449	−	0.856412i
$126$	6.13402	−	0.855675i	0.546462	−	0.0762296i
$127$	−4.70719	−	3.94980i	−0.417695	−	0.350488i	0.409590	−	0.912270i	$-0.365672\pi$
$127$	−4.70719	−	3.94980i	−0.417695	−	0.350488i	−0.827286	+	0.561782i	$0.810116\pi$
$128$	−4.67567	+	10.3023i	−0.413275	+	0.910606i
$129$	0.790384	+	2.17156i	0.0695894	+	0.191195i
$130$	−4.94155	−	1.05565i	−0.433403	−	0.0925865i
$131$	−7.78789	+	1.37321i	−0.680431	+	0.119978i	−0.503172	−	0.864186i	$-0.667834\pi$
$131$	−7.78789	+	1.37321i	−0.680431	+	0.119978i	−0.177258	+	0.984164i	$0.556723\pi$
$132$	11.4954	+	2.89114i	1.00055	+	0.251642i
$133$	−16.2381	+	10.0364i	−1.40802	+	0.870268i
$134$	4.02473	−	3.13783i	0.347684	−	0.271067i
$135$	−0.235063	−	1.33311i	−0.0202310	−	0.114736i
$136$	7.88084	+	3.87376i	0.675776	+	0.332172i
$137$	5.98771	−	2.17935i	0.511564	−	0.186194i	−0.0733238	−	0.997308i	$-0.523361\pi$
$137$	5.98771	−	2.17935i	0.511564	−	0.186194i	0.584888	+	0.811114i	$0.301138\pi$
$138$	1.10387	+	3.40924i	0.0939676	+	0.290213i
$139$	12.4653	−	14.8556i	1.05729	−	1.26003i	0.0928684	−	0.995678i	$-0.470396\pi$
$139$	12.4653	−	14.8556i	1.05729	−	1.26003i	0.964425	−	0.264355i	$-0.0851592\pi$
$140$	8.25372	−	8.51202i	0.697567	−	0.719397i
$141$	−1.91043	+	1.10299i	−0.160887	+	0.0928883i
$142$	−1.79835	−	3.39057i	−0.150914	−	0.284531i
$143$	2.71648	−	15.4059i	0.227164	−	1.28831i
$144$	0.123222	+	3.99810i	0.0102685	+	0.333175i
$145$	3.21996	+	1.85905i	0.267403	+	0.154385i
$146$	−7.61174	−	0.273612i	−0.629952	−	0.0226443i
$147$	11.4447	+	4.16553i	0.943942	+	0.343567i
$148$	−13.0781	+	1.34748i	−1.07501	+	0.110763i
$149$	−9.73888	+	8.17189i	−0.797840	+	0.669467i	−0.947672	−	0.319244i	$-0.896571\pi$
$149$	−9.73888	+	8.17189i	−0.797840	+	0.669467i	0.149833	+	0.988711i	$0.452127\pi$
$150$	3.32593	+	3.00085i	0.271561	+	0.245019i
$151$	−3.01854			−0.245645			−0.122823	−	0.992429i	$-0.539195\pi$
$151$	−3.01854			−0.245645			−0.122823	+	0.992429i	$0.539195\pi$
$152$	−5.31612	−	11.1238i	−0.431194	−	0.902259i
$153$	3.10471			0.251001
$154$	27.2530	+	24.5893i	2.19611	+	1.98147i
$155$	−11.3108	+	9.49089i	−0.908506	+	0.762327i
$156$	5.25123	−	0.541055i	0.420435	−	0.0433191i
$157$	0.344255	+	0.125299i	0.0274745	+	0.00999992i	0.355721	−	0.934592i	$-0.384235\pi$
$157$	0.344255	+	0.125299i	0.0274745	+	0.00999992i	−0.328246	+	0.944592i	$0.606458\pi$
$158$	6.08676	+	0.218795i	0.484236	+	0.0174064i
$159$	−7.48151	−	4.31945i	−0.593323	−	0.342555i
$160$	4.89207	+	5.89114i	0.386752	+	0.465736i
$161$	−1.92698	+	10.9284i	−0.151867	+	0.861281i
$162$	0.662654	+	1.24936i	0.0520630	+	0.0981587i
$163$	−5.14331	+	2.96949i	−0.402855	+	0.232588i	−0.687715	−	0.725981i	$-0.741386\pi$
$163$	−5.14331	+	2.96949i	−0.402855	+	0.232588i	0.284860	+	0.958569i	$0.408053\pi$
$164$	−7.02623	+	7.24612i	−0.548657	+	0.565827i
$165$	5.15697	−	6.14583i	0.401469	−	0.478452i
$166$	−2.89911	−	8.95372i	−0.225014	−	0.694943i
$167$	−9.48707	+	3.45301i	−0.734131	+	0.267202i	−0.681913	−	0.731434i	$-0.738852\pi$
$167$	−9.48707	+	3.45301i	−0.734131	+	0.267202i	−0.0522188	+	0.998636i	$0.516629\pi$
$168$	−5.46420	+	11.1165i	−0.421573	+	0.857654i
$169$	1.04761	+	5.94130i	0.0805856	+	0.457023i
$170$	4.68737	−	3.65445i	0.359505	−	0.280283i
$171$	−3.42167	−	2.70040i	−0.261662	−	0.206505i
$172$	−4.48227	−	1.12731i	−0.341770	−	0.0859566i
$173$	8.14613	−	1.43638i	0.619339	−	0.109206i	0.144830	−	0.989457i	$-0.453737\pi$
$173$	8.14613	−	1.43638i	0.619339	−	0.109206i	0.474509	+	0.880250i	$0.342625\pi$
$174$	−3.79866	−	0.811497i	−0.287976	−	0.0615194i
$175$	4.74452	+	13.0355i	0.358652	+	0.985388i
$176$	−17.6824	+	15.7906i	−1.33286	+	1.19026i
$177$	9.31773	+	7.81850i	0.700364	+	0.587675i
$178$	−6.78404	+	0.946351i	−0.508485	+	0.0709320i
$179$	5.14874	+	8.91787i	0.384835	+	0.666553i	0.991746	−	0.128216i	$-0.0409251\pi$
$179$	5.14874	+	8.91787i	0.384835	+	0.666553i	−0.606912	+	0.794769i	$0.707592\pi$
$180$	2.47103	+	1.10624i	0.184179	+	0.0824544i
$181$	0.540312	+	0.0952716i	0.0401611	+	0.00708148i	0.193693	−	0.981062i	$-0.437954\pi$
$181$	0.540312	+	0.0952716i	0.0401611	+	0.00708148i	−0.153532	+	0.988144i	$0.549065\pi$
$182$	15.1510	+	6.13944i	1.12306	+	0.455086i
$183$	2.80589	−	4.85994i	0.207417	−	0.359257i
$184$	−6.88325	−	1.99664i	−0.507440	−	0.147195i
$185$	−3.04349	+	8.36193i	−0.223762	+	0.614781i
$186$	8.18768	−	13.0732i	0.600350	−	0.958575i
$187$	11.8277	+	14.0957i	0.864927	+	1.03078i
$188$	0.316775	−	4.40056i	0.0231032	−	0.320944i
$189$			4.37940i			0.318555i
$190$	−8.34446	−	0.0494158i	−0.605371	−	0.00358500i
$191$			16.5166i			1.19510i	0.801832	+	0.597550i	$0.203859\pi$
$191$			16.5166i			1.19510i	−0.801832	+	0.597550i	$0.796141\pi$
$192$	−6.75821	−	4.28096i	−0.487732	−	0.308952i
$193$	0.647862	+	0.772092i	0.0466341	+	0.0555764i	0.788857	−	0.614576i	$-0.210673\pi$
$193$	0.647862	+	0.772092i	0.0466341	+	0.0555764i	−0.742223	+	0.670153i	$0.766229\pi$
$194$	14.5497	+	9.11239i	1.04461	+	0.654232i
$195$	1.22205	−	3.35756i	0.0875131	−	0.240440i
$196$	−19.7356	+	14.2771i	−1.40969	+	1.01979i
$197$	5.88433	−	10.1920i	0.419241	−	0.726147i	−0.576622	−	0.817011i	$-0.695629\pi$
$197$	5.88433	−	10.1920i	0.419241	−	0.726147i	0.995863	+	0.0908637i	$0.0289628\pi$
$198$	−3.14776	+	7.76807i	−0.223702	+	0.552053i
$199$	−11.1781	−	1.97100i	−0.792395	−	0.139721i	−0.237222	−	0.971456i	$-0.576237\pi$
$199$	−11.1781	−	1.97100i	−0.792395	−	0.139721i	−0.555173	+	0.831735i	$0.687348\pi$
$200$	−8.69972	+	2.14072i	−0.615163	+	0.151372i
$201$	1.80432	+	3.12517i	0.127267	+	0.220432i
$202$	−1.34495	−	9.64145i	−0.0946304	−	0.678370i
$203$	−9.21457	−	7.73194i	−0.646736	−	0.542676i
$204$	−3.48279	+	5.14071i	−0.243844	+	0.359922i
$205$	2.33651	+	6.41952i	0.163189	+	0.448358i
$206$	1.45848	−	6.82724i	0.101617	−	0.475676i
$207$	−2.49542	+	0.440009i	−0.173443	+	0.0305827i
$208$	−4.99485	+	9.30183i	−0.346331	+	0.644966i
$209$	−0.775124	−	25.8222i	−0.0536165	−	1.78616i
$210$	5.15486	+	6.61186i	0.355719	+	0.456262i
$211$	−3.96624	−	22.4937i	−0.273047	−	1.54853i	−0.745097	−	0.666957i	$-0.767597\pi$
$211$	−3.96624	−	22.4937i	−0.273047	−	1.54853i	0.472049	−	0.881572i	$-0.343514\pi$
$212$	15.5447	−	7.54227i	1.06761	−	0.518006i
$213$	2.55019	−	0.928194i	0.174736	−	0.0635988i
$214$	12.4332	−	4.02571i	0.849914	−	0.275192i
$215$	−2.01080	+	2.39637i	−0.137135	+	0.163431i
$216$	−2.81201	−	0.304291i	−0.191333	−	0.0207044i
$217$	41.3686	−	23.8842i	2.80828	−	1.62136i
$218$	11.9473	−	6.33680i	0.809172	−	0.429182i
$219$	0.935232	−	5.30396i	0.0631971	−	0.358409i
$220$	4.39118	+	15.4331i	0.296053	+	1.04050i
$221$	7.09701	+	4.09746i	0.477396	+	0.275625i
$222$	0.333959	−	9.29054i	0.0224138	−	0.623540i
$223$	15.3403	+	5.58343i	1.02727	+	0.373894i	0.800039	−	0.599948i	$-0.204812\pi$
$223$	15.3403	+	5.58343i	1.02727	+	0.373894i	0.227226	+	0.973842i	$0.427034\pi$
$224$	−12.2768	−	21.5178i	−0.820279	−	1.43772i
$225$	−2.42650	+	2.03607i	−0.161766	+	0.135738i
$226$	−10.4308	+	11.5608i	−0.693849	+	0.769012i
$227$	13.6748			0.907626			0.453813	−	0.891097i	$-0.350063\pi$
$227$	13.6748			0.907626			0.453813	+	0.891097i	$0.350063\pi$
$228$	8.30963	−	2.63629i	0.550319	−	0.174593i
$229$	−24.9453			−1.64843			−0.824214	−	0.566278i	$-0.808383\pi$
$229$	−24.9453			−1.64843			−0.824214	+	0.566278i	$0.808383\pi$
$230$	−3.24956	+	3.60158i	−0.214270	+	0.237481i
$231$	−19.8830	+	16.6838i	−1.30820	+	1.09771i
$232$	5.60492	−	5.37943i	0.367981	−	0.353177i
$233$	14.6686	+	5.33892i	0.960969	+	0.349764i	0.774413	−	0.632680i	$-0.218045\pi$
$233$	14.6686	+	5.33892i	0.960969	+	0.349764i	0.186556	+	0.982444i	$0.440268\pi$
$234$	−0.134094	+	3.73043i	−0.00876602	+	0.243866i
$235$	−2.58610	−	1.49309i	−0.168699	−	0.0973982i
$236$	−23.3982	+	6.65749i	−1.52309	+	0.433365i
$237$	−0.747862	+	4.24134i	−0.0485789	+	0.275505i
$238$	−16.9872	+	9.00995i	−1.10112	+	0.584028i
$239$	25.6006	−	14.7805i	1.65596	−	0.956071i	0.681414	−	0.731899i	$-0.261366\pi$
$239$	25.6006	−	14.7805i	1.65596	−	0.956071i	0.974550	−	0.224172i	$-0.0719678\pi$
$240$	−4.60364	+	2.85052i	−0.297164	+	0.184000i
$241$	−7.78225	+	9.27452i	−0.501299	+	0.597425i	−0.956054	−	0.293192i	$-0.905282\pi$
$241$	−7.78225	+	9.27452i	−0.501299	+	0.597425i	0.454755	+	0.890617i	$0.349727\pi$
$242$	−32.4598	+	10.5101i	−2.08659	+	0.675613i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	4.89941	+	10.0977i	0.313653	+	0.646441i
$245$	2.86288	+	16.2362i	0.182903	+	1.03729i
$246$	−4.38823	−	5.62855i	−0.279783	−	0.358863i
$247$	−4.25769	−	10.6886i	−0.270910	−	0.680098i
$248$	12.4616	+	28.2223i	0.791314	+	1.79212i
$249$	6.55374	−	1.15560i	0.415326	−	0.0732333i
$250$	−3.26654	+	15.2908i	−0.206594	+	0.967078i
$251$	−3.65321	−	10.0371i	−0.230589	−	0.633537i	0.769398	−	0.638770i	$-0.220556\pi$
$251$	−3.65321	−	10.0371i	−0.230589	−	0.633537i	−0.999986	+	0.00523308i	$0.998334\pi$
$252$	−7.25134	−	4.91273i	−0.456791	−	0.309473i
$253$	−11.5042	−	9.65320i	−0.723265	−	0.606892i
$254$	1.20061	+	8.60672i	0.0753329	+	0.540034i
$255$	2.10138	+	3.63970i	0.131594	+	0.227927i
$256$	14.6696	−	6.38782i	0.916847	−	0.399239i
$257$	−2.34060	−	0.412712i	−0.146003	−	0.0257443i	0.100169	−	0.994970i	$-0.468062\pi$
$257$	−2.34060	−	0.412712i	−0.146003	−	0.0257443i	−0.246172	+	0.969226i	$0.579173\pi$
$258$	1.22737	−	3.02892i	0.0764128	−	0.188572i
$259$	14.3943	−	24.9317i	0.894420	−	1.54918i
$260$	4.18852	+	5.78990i	0.259761	+	0.359074i
$261$	0.939416	−	2.58102i	0.0581484	−	0.159761i
$262$	9.47819	+	5.93614i	0.585565	+	0.366736i
$263$	3.95847	+	4.71753i	0.244090	+	0.290895i	0.874155	−	0.485647i	$-0.161416\pi$
$263$	3.95847	+	4.71753i	0.244090	+	0.290895i	−0.630065	+	0.776543i	$0.716972\pi$
$264$	−9.33113	−	13.9261i	−0.574292	−	0.857090i
$265$		−	11.6943i		−	0.718373i
$266$	26.5581	+	4.84525i	1.62838	+	0.297081i
$267$		−	4.84349i		−	0.296417i
$268$	−7.19864	−	0.518195i	−0.439727	−	0.0316538i
$269$	3.77906	+	4.50371i	0.230414	+	0.274596i	0.868847	−	0.495081i	$-0.164862\pi$
$269$	3.77906	+	4.50371i	0.230414	+	0.274596i	−0.638433	+	0.769677i	$0.720417\pi$
$270$	−1.01613	+	1.62245i	−0.0618398	+	0.0987392i
$271$	−0.884307	+	2.42961i	−0.0537178	+	0.147588i	−0.963650	−	0.267170i	$-0.913912\pi$
$271$	−0.884307	+	2.42961i	−0.0537178	+	0.147588i	0.909932	+	0.414758i	$0.136134\pi$
$272$	−4.60497	−	11.5335i	−0.279217	−	0.699321i
$273$	−5.77975	+	10.0108i	−0.349807	+	0.605883i
$274$	−8.35171	−	3.38426i	−0.504545	−	0.204451i
$275$	−18.4880	−	3.25993i	−1.11487	−	0.196581i
$276$	2.07075	−	4.62546i	0.124644	−	0.278420i
$277$	−11.9503	−	20.6985i	−0.718022	−	1.24365i	−0.961782	−	0.273816i	$-0.911714\pi$
$277$	−11.9503	−	20.6985i	−0.718022	−	1.24365i	0.243760	−	0.969836i	$-0.421619\pi$
$278$	−27.1622	+	3.78904i	−1.62908	+	0.227252i
$279$	8.35563	+	7.01121i	0.500239	+	0.419750i
$280$	−16.7304	+	1.11827i	−0.999833	+	0.0668291i
$281$	−1.57605	−	4.33017i	−0.0940195	−	0.258317i	0.883764	−	0.467932i	$-0.155001\pi$
$281$	−1.57605	−	4.33017i	−0.0940195	−	0.258317i	−0.977784	+	0.209616i	$0.932779\pi$
$282$	3.05088	+	0.651751i	0.181677	+	0.0388112i
$283$	−6.75769	+	1.19156i	−0.401703	+	0.0708310i	−0.370850	−	0.928693i	$-0.620933\pi$
$283$	−6.75769	+	1.19156i	−0.401703	+	0.0708310i	−0.0308530	+	0.999524i	$0.509822\pi$
$284$	−1.32387	+	5.26379i	−0.0785570	+	0.312348i
$285$	0.849804	−	5.83902i	0.0503380	−	0.345873i
$286$	−17.4474	+	13.6027i	−1.03169	+	0.804342i
$287$	−3.83784	−	21.7655i	−0.226541	−	1.28478i
$288$	3.65830	−	4.31473i	0.215567	−	0.254248i
$289$	6.91689	−	2.51754i	0.406876	−	0.148091i
$290$	−1.61974	−	5.00249i	−0.0951147	−	0.293756i
$291$	−7.80305	+	9.29931i	−0.457423	+	0.545135i
$292$	7.73308	+	7.49842i	0.452544	+	0.438812i
$293$	−3.81436	+	2.20222i	−0.222837	+	0.128655i	−0.607263	−	0.794501i	$-0.707733\pi$
$293$	−3.81436	+	2.20222i	−0.222837	+	0.128655i	0.384426	+	0.923156i	$0.374399\pi$
$294$	−8.07058	−	15.2161i	−0.470686	−	0.887423i
$295$	−2.85917	+	16.2152i	−0.166468	+	0.944085i
$296$	15.0085	+	10.9749i	0.872350	+	0.637903i
$297$	−5.13267	−	2.96335i	−0.297828	−	0.171951i
$298$	17.9676	+	0.645864i	1.04083	+	0.0374139i
$299$	−6.28494	−	2.28753i	−0.363468	−	0.132291i
$300$	−0.649296	−	6.30177i	−0.0374871	−	0.363833i
$301$	7.75274	−	6.50532i	0.446860	−	0.374960i
$302$	3.16945	+	2.85967i	0.182381	+	0.164556i
$303$	6.88355			0.395449
$304$	−4.95645	+	16.7163i	−0.284272	+	0.958744i
$305$	7.59653			0.434976
$306$	−3.25993	−	2.94130i	−0.186358	−	0.168143i
$307$	4.95497	−	4.15772i	0.282795	−	0.237293i	−0.490345	−	0.871528i	$-0.663129\pi$
$307$	4.95497	−	4.15772i	0.282795	−	0.237293i	0.773140	+	0.634235i	$0.218685\pi$
$308$	−5.32041	−	51.6374i	−0.303158	−	2.94231i
$309$	4.63880	+	1.68839i	0.263892	+	0.0960490i
$310$	20.8677	+	0.750112i	1.18520	+	0.0426035i
$311$	−6.07381	−	3.50671i	−0.344414	−	0.198848i	0.317808	−	0.948155i	$-0.397053\pi$
$311$	−6.07381	−	3.50671i	−0.344414	−	0.198848i	−0.662222	+	0.749307i	$0.730387\pi$
$312$	−6.02635	−	4.40675i	−0.341175	−	0.249483i
$313$	−2.81995	+	15.9928i	−0.159393	+	0.903964i	0.795265	+	0.606261i	$0.207331\pi$
$313$	−2.81995	+	15.9928i	−0.159393	+	0.903964i	−0.954659	+	0.297703i	$0.903780\pi$
$314$	−0.242762	−	0.457700i	−0.0136999	−	0.0258295i
$315$	−5.13405	+	2.96414i	−0.289271	+	0.167011i
$316$	−6.18379	−	5.99614i	−0.347865	−	0.337309i
$317$	−2.84369	+	3.38897i	−0.159717	+	0.190344i	−0.839968	−	0.542636i	$-0.817426\pi$
$317$	−2.84369	+	3.38897i	−0.159717	+	0.190344i	0.680251	+	0.732979i	$0.261871\pi$
$318$	3.76344	+	11.6232i	0.211043	+	0.651795i
$319$	15.2969	−	5.56763i	0.856464	−	0.311727i
$320$	0.444431	−	10.8203i	0.0248445	−	0.604872i
$321$	1.60467	+	9.10056i	0.0895642	+	0.507944i
$322$	12.3766	−	9.64925i	0.689720	−	0.537732i
$323$	12.8501	+	4.24495i	0.714999	+	0.236195i
$324$	0.487817	−	1.93960i	0.0271010	−	0.107755i
$325$	−8.23382	+	1.45184i	−0.456730	+	0.0805338i
$326$	8.21365	+	1.75466i	0.454912	+	0.0971816i
$327$	3.27066	+	8.98605i	0.180868	+	0.496930i
$328$	14.2423	−	0.951957i	0.786398	−	0.0525631i
$329$	7.40064	+	6.20988i	0.408011	+	0.342362i
$330$	−11.2372	+	1.56755i	−0.618586	+	0.0862907i
$331$	−5.68637	−	9.84909i	−0.312551	−	0.541355i	0.666363	−	0.745628i	$-0.267850\pi$
$331$	−5.68637	−	9.84909i	−0.312551	−	0.541355i	−0.978914	+	0.204273i	$0.934517\pi$
$332$	−5.43843	+	12.1479i	−0.298473	+	0.666702i
$333$	6.47378	+	1.14150i	0.354761	+	0.0625539i
$334$	13.2327	+	5.36211i	0.724059	+	0.293402i
$335$	−2.44246	+	4.23046i	−0.133446	+	0.231135i
$336$	16.2688	−	6.49563i	0.887536	−	0.354366i
$337$	−4.03960	+	11.0987i	−0.220051	+	0.604585i	−0.999768	−	0.0215471i	$-0.993141\pi$
$337$	−4.03960	+	11.0987i	−0.220051	+	0.604585i	0.779717	+	0.626132i	$0.215363\pi$
$338$	4.52862	−	7.23082i	0.246324	−	0.393305i
$339$	−7.07729	−	8.43439i	−0.384386	−	0.458093i
$340$	−8.38383	−	0.603512i	−0.454677	−	0.0327300i
$341$			64.6454i			3.50075i
$342$	1.03447	+	6.07700i	0.0559377	+	0.328606i
$343$		−	22.6817i		−	1.22470i
$344$	3.63838	+	5.43003i	0.196168	+	0.292768i
$345$	−2.20482	−	2.62760i	−0.118704	−	0.141465i
$346$	−9.91419	−	6.20920i	−0.532990	−	0.333809i
$347$	−4.91637	+	13.5076i	−0.263924	+	0.725127i	0.734969	+	0.678101i	$0.237197\pi$
$347$	−4.91637	+	13.5076i	−0.263924	+	0.725127i	−0.998894	+	0.0470261i	$0.985026\pi$
$348$	3.21979	+	4.45080i	0.172599	+	0.238588i
$349$	9.67492	−	16.7575i	0.517887	−	0.897006i	−0.481897	−	0.876228i	$-0.660052\pi$
$349$	9.67492	−	16.7575i	0.517887	−	0.897006i	0.999784	−	0.0207785i	$-0.00661447\pi$
$350$	7.36767	−	18.1820i	0.393818	−	0.971868i
$351$	−2.59942	−	0.458347i	−0.138747	−	0.0244648i
$352$	33.5260	+	0.171662i	1.78694	+	0.00914964i
$353$	−1.09781	−	1.90147i	−0.0584306	−	0.101205i	0.835330	−	0.549748i	$-0.185276\pi$
$353$	−1.09781	−	1.90147i	−0.0584306	−	0.101205i	−0.893761	+	0.448543i	$0.851943\pi$
$354$	−2.37657	−	17.0367i	−0.126313	−	0.905492i
$355$	2.81420	+	2.36140i	0.149362	+	0.125330i
$356$	8.01975	+	5.43332i	0.425046	+	0.287966i
$357$	−4.65037	−	12.7768i	−0.246124	−	0.676219i
$358$	3.04237	−	14.2415i	0.160794	−	0.752686i
$359$	−23.4335	+	4.13195i	−1.23677	+	0.218076i	−0.753531	−	0.657412i	$-0.771651\pi$
$359$	−23.4335	+	4.13195i	−1.23677	+	0.218076i	−0.483240	+	0.875488i	$0.660540\pi$
$360$	−1.54655	−	3.50252i	−0.0815102	−	0.184599i
$361$	−10.4699	−	15.8550i	−0.551045	−	0.834475i
$362$	−0.477068	−	0.611910i	−0.0250741	−	0.0321613i
$363$	−4.18938	−	23.7592i	−0.219885	−	1.24703i
$364$	−10.0921	−	20.7999i	−0.528971	−	1.09021i
$365$	6.85093	−	2.49353i	0.358594	−	0.130517i
$366$	−7.55034	+	2.44471i	−0.394662	+	0.127787i
$367$	6.06857	−	7.23225i	0.316777	−	0.377520i	−0.584036	−	0.811728i	$-0.698527\pi$
$367$	6.06857	−	7.23225i	0.316777	−	0.377520i	0.900813	+	0.434208i	$0.142972\pi$
$368$	5.33582	+	8.61744i	0.278149	+	0.449215i
$369$	4.37052	−	2.52332i	0.227520	−	0.131359i
$370$	11.1175	−	5.89668i	0.577971	−	0.306554i
$371$	−6.56968	+	37.2585i	−0.341081	+	1.93436i
$372$	−20.9822	+	5.97007i	−1.08788	+	0.309534i
$373$	7.06955	+	4.08160i	0.366047	+	0.211337i	0.671730	−	0.740796i	$-0.265551\pi$
$373$	7.06955	+	4.08160i	0.366047	+	0.211337i	−0.305683	+	0.952133i	$0.598885\pi$
$374$	0.934801	−	26.0056i	0.0483374	−	1.34472i
$375$	−10.3895	−	3.78145i	−0.536509	−	0.195273i
$376$	−4.50157	+	4.32047i	−0.232151	+	0.222811i
$377$	5.55372	−	4.66013i	0.286031	−	0.240009i
$378$	4.14891	−	4.59836i	0.213397	−	0.236514i
$379$	17.1183			0.879306			0.439653	−	0.898168i	$-0.355101\pi$
$379$	17.1183			0.879306			0.439653	+	0.898168i	$0.355101\pi$
$380$	8.71484	+	7.95718i	0.447062	+	0.408195i
$381$	−6.14480			−0.314808
$382$	15.6473	−	17.3424i	0.800587	−	0.887312i
$383$	26.7201	−	22.4208i	1.36533	−	1.14565i	0.391039	−	0.920374i	$-0.372116\pi$
$383$	26.7201	−	22.4208i	1.36533	−	1.14565i	0.974295	−	0.225277i	$-0.0723288\pi$
$384$	3.04044	+	10.8975i	0.155157	+	0.556111i
$385$	−33.0162	−	12.0169i	−1.68266	−	0.612439i
$386$	0.0512037	−	1.42446i	0.00260620	−	0.0725030i
$387$	2.00132	+	1.15546i	0.101733	+	0.0587355i
$388$	−6.64432	−	23.3519i	−0.337314	−	1.18551i
$389$	−1.83506	+	10.4071i	−0.0930410	+	0.527662i	0.902289	+	0.431132i	$0.141886\pi$
$389$	−1.83506	+	10.4071i	−0.0930410	+	0.527662i	−0.995330	+	0.0965302i	$0.969226\pi$
$390$	−4.46400	+	2.36769i	−0.226044	+	0.119893i
$391$	6.81306	−	3.93352i	0.344552	−	0.198927i
$392$	34.2480	+	3.70602i	1.72979	+	0.187182i
$393$	−5.08318	+	6.05790i	−0.256413	+	0.305581i
$394$	−15.8341	+	5.12688i	−0.797709	+	0.258289i
$395$	−5.47837	+	1.99396i	−0.275647	+	0.100327i
$396$	10.6644	−	5.17435i	0.535905	−	0.260021i
$397$	−2.72505	−	15.4545i	−0.136766	−	0.775641i	−0.973613	−	0.228204i	$-0.926715\pi$
$397$	−2.72505	−	15.4545i	−0.136766	−	0.775641i	0.836847	−	0.547437i	$-0.184396\pi$
$398$	9.86970	+	12.6593i	0.494723	+	0.634555i
$399$	−5.98779	+	18.1260i	−0.299765	+	0.907434i
$400$	11.1627	+	5.99410i	0.558136	+	0.299705i
$401$	−37.7248	+	6.65189i	−1.88388	+	0.332180i	−0.992616	−	0.121297i	$-0.961295\pi$
$401$	−37.7248	+	6.65189i	−1.88388	+	0.332180i	−0.891268	+	0.453476i	$0.850184\pi$
$402$	1.06616	−	4.99077i	0.0531754	−	0.248917i
$403$	9.84694	+	27.0542i	0.490511	+	1.34767i
$404$	−7.72182	+	11.3976i	−0.384175	+	0.567054i
$405$	−1.03697	−	0.870125i	−0.0515277	−	0.0432369i
$406$	2.35026	+	16.8481i	0.116641	+	0.836158i
$407$	19.4800	+	33.7403i	0.965587	+	1.67245i
$408$	8.52707	−	2.09823i	0.422153	−	0.103878i
$409$	−30.1537	−	5.31692i	−1.49101	−	0.262905i	−0.632040	−	0.774936i	$-0.717782\pi$
$409$	−30.1537	−	5.31692i	−1.49101	−	0.262905i	−0.858967	+	0.512031i	$0.828893\pi$
$410$	3.62832	−	8.95400i	0.179190	−	0.442207i
$411$	3.18599	−	5.51830i	0.157153	−	0.272198i
$412$	−7.99931	+	5.78685i	−0.394098	+	0.285098i
$413$	18.2189	−	50.0561i	0.896495	−	2.46310i
$414$	3.03703	+	1.90207i	0.149262	+	0.0934818i
$415$	5.79055	+	6.90091i	0.284247	+	0.338752i
$416$	14.0568	−	5.03492i	0.689194	−	0.246857i
$417$		−	19.3926i		−	0.949659i
$418$	−23.6493	+	27.8476i	−1.15673	+	1.36207i
$419$		−	21.0004i		−	1.02594i	−0.858407	−	0.512968i	$-0.828546\pi$
$419$		−	21.0004i		−	1.02594i	0.858407	−	0.512968i	$-0.171454\pi$
$420$	0.851296	−	11.8260i	0.0415390	−	0.577049i
$421$	12.1705	+	14.5042i	0.593153	+	0.706892i	0.976209	−	0.216833i	$-0.0695728\pi$
$421$	12.1705	+	14.5042i	0.593153	+	0.706892i	−0.383056	+	0.923725i	$0.625128\pi$
$422$	−17.1453	+	27.3758i	−0.834619	+	1.33263i
$423$	−0.754488	+	2.07294i	−0.0366845	+	0.100790i
$424$	−23.4672	−	6.80719i	−1.13967	−	0.330587i
$425$	4.91718	−	8.51680i	0.238518	−	0.413126i
$426$	−3.55703	−	1.44137i	−0.172339	−	0.0698348i
$427$	−24.2029	−	4.26762i	−1.17126	−	0.206525i
$428$	−16.8686	−	7.55183i	−0.815376	−	0.365031i
$429$	−7.82180	−	13.5478i	−0.377640	−	0.654092i
$430$	4.38158	−	0.611216i	0.211298	−	0.0294754i
$431$	3.90574	+	3.27730i	0.188133	+	0.157862i	0.731989	−	0.681316i	$-0.238592\pi$
$431$	3.90574	+	3.27730i	0.188133	+	0.157862i	−0.543857	+	0.839178i	$0.683036\pi$
$432$	2.66432	+	2.98352i	0.128187	+	0.143545i
$433$	8.65856	+	23.7892i	0.416104	+	1.14324i	0.953890	+	0.300155i	$0.0970385\pi$
$433$	8.65856	+	23.7892i	0.416104	+	1.14324i	−0.537786	+	0.843081i	$0.680739\pi$
$434$	−66.0640	−	14.1131i	−3.17117	−	0.677449i
$435$	3.66161	−	0.645640i	0.175561	−	0.0309561i
$436$	−18.5479	−	4.66488i	−0.888283	−	0.223407i
$437$	−10.9299	−	1.59073i	−0.522849	−	0.0760948i
$438$	−6.00680	+	4.68313i	−0.287016	+	0.223769i
$439$	3.15650	+	17.9014i	0.150652	+	0.854388i	0.962654	+	0.270734i	$0.0872663\pi$
$439$	3.15650	+	17.9014i	0.150652	+	0.854388i	−0.812003	+	0.583654i	$0.801623\pi$
$440$	10.0101	−	20.3647i	0.477213	−	0.970850i
$441$	11.4447	−	4.16553i	0.544985	−	0.198358i
$442$	−3.57002	−	11.0258i	−0.169809	−	0.524444i
$443$	−23.0742	+	27.4988i	−1.09629	+	1.30651i	−0.148040	+	0.988981i	$0.547297\pi$
$443$	−23.0742	+	27.4988i	−1.09629	+	1.30651i	−0.948250	+	0.317526i	$0.897148\pi$
$444$	−9.15223	+	9.43865i	−0.434346	+	0.447938i
$445$	5.67810	−	3.27825i	0.269168	−	0.155404i
$446$	−10.8177	−	20.3955i	−0.512234	−	0.965757i
$447$	−2.20762	+	12.5201i	−0.104417	+	0.592178i
$448$	−7.49466	+	34.2242i	−0.354089	+	1.61694i
$449$	14.7330	+	8.50612i	0.695295	+	0.401429i	0.805593	−	0.592470i	$-0.201847\pi$
$449$	14.7330	+	8.50612i	0.695295	+	0.401429i	−0.110298	+	0.993899i	$0.535180\pi$
$450$	4.47672	+	0.160921i	0.211035	+	0.00758587i
$451$	28.1061	+	10.2298i	1.32346	+	0.481701i
$452$	21.9047	−	2.25692i	1.03031	−	0.106157i
$453$	−2.31233	+	1.94028i	−0.108643	+	0.0911622i
$454$	−14.3584	−	12.9551i	−0.673875	−	0.608011i
$455$	−15.6478			−0.733581
$456$	−11.2226	−	5.10419i	−0.525547	−	0.239026i
$457$	−30.2390			−1.41452			−0.707261	−	0.706952i	$-0.750069\pi$
$457$	−30.2390			−1.41452			−0.707261	+	0.706952i	$0.750069\pi$
$458$	26.1924	+	23.6324i	1.22389	+	1.10427i
$459$	2.37834	−	1.99567i	0.111012	−	0.0931497i
$460$	6.82406	−	0.703110i	0.318173	−	0.0327827i
$461$	3.72180	+	1.35462i	0.173342	+	0.0630912i	0.427233	−	0.904142i	$-0.359488\pi$
$461$	3.72180	+	1.35462i	0.173342	+	0.0630912i	−0.253891	+	0.967233i	$0.581711\pi$
$462$	36.6828	+	1.31860i	1.70664	+	0.0613469i
$463$	−5.81173	−	3.35540i	−0.270094	−	0.155939i	0.358836	−	0.933400i	$-0.383174\pi$
$463$	−5.81173	−	3.35540i	−0.270094	−	0.155939i	−0.628930	+	0.777462i	$0.716507\pi$
$464$	−10.9815	+	0.338450i	−0.509801	+	0.0157122i
$465$	−2.56395	+	14.5409i	−0.118900	+	0.674318i
$466$	−10.3440	−	19.5024i	−0.479176	−	0.903430i
$467$	4.67829	−	2.70101i	0.216486	−	0.124988i	−0.387836	−	0.921728i	$-0.626777\pi$
$467$	4.67829	−	2.70101i	0.216486	−	0.124988i	0.604322	+	0.796740i	$0.293444\pi$
$468$	3.67489	−	3.78990i	0.169872	−	0.175188i
$469$	10.1584	−	12.1063i	0.469071	−	0.559017i
$470$	1.30089	+	4.01773i	0.0600056	+	0.185324i
$471$	0.344255	−	0.125299i	0.0158624	−	0.00577346i
$472$	30.8751	+	15.1764i	1.42114	+	0.698549i
$473$	2.37831	+	13.4881i	0.109355	+	0.620182i
$474$	4.80337	−	3.74489i	0.220626	−	0.172008i
$475$	−12.8269	+	5.10947i	−0.588538	+	0.234438i
$476$	26.3722	+	6.63274i	1.20877	+	0.304011i
$477$	−8.50766	+	1.50013i	−0.389539	+	0.0686863i
$478$	−40.8831	−	8.73373i	−1.86995	−	0.399472i
$479$	−14.1702	−	38.9323i	−0.647453	−	1.77886i	−0.626932	−	0.779074i	$-0.715689\pi$
$479$	−14.1702	−	38.9323i	−0.647453	−	1.77886i	−0.0205218	−	0.999789i	$-0.506533\pi$
$480$	7.53430	+	1.36831i	0.343892	+	0.0624547i
$481$	13.2918	+	11.1532i	0.606055	+	0.508541i
$482$	16.9577	−	2.36555i	0.772403	−	0.107748i
$483$	5.54851	+	9.61030i	0.252466	+	0.437284i
$484$	44.0395	+	19.7158i	2.00180	+	0.896175i
$485$	−16.1831	−	2.85352i	−0.734838	−	0.129572i
$486$	1.31069	+	0.531116i	0.0594542	+	0.0240919i
$487$	−11.6050	+	20.1005i	−0.525874	+	0.910840i	0.473672	+	0.880701i	$0.342928\pi$
$487$	−11.6050	+	20.1005i	−0.525874	+	0.910840i	−0.999546	+	0.0301388i	$0.990405\pi$
$488$	4.42191	−	15.2441i	0.200170	−	0.690069i
$489$	−2.03125	+	5.58081i	−0.0918563	+	0.252373i
$490$	12.3757	−	19.7601i	0.559075	−	0.892672i
$491$	−8.63394	−	10.2895i	−0.389644	−	0.464360i	0.535189	−	0.844732i	$-0.320240\pi$
$491$	−8.63394	−	10.2895i	−0.389644	−	0.464360i	−0.924833	+	0.380372i	$0.875796\pi$
$492$	−0.724691	+	10.0672i	−0.0326716	+	0.453866i
$493$			8.52759i			0.384064i
$494$	−5.65548	+	15.2566i	−0.254452	+	0.686426i
$495$		−	8.02281i		−	0.360599i
$496$	13.6523	−	41.4390i	0.613005	−	1.86067i
$497$	−7.63958	−	9.10450i	−0.342682	−	0.408392i
$498$	−7.97618	−	4.99544i	−0.357421	−	0.223851i
$499$	−14.3271	+	39.3635i	−0.641371	+	1.76215i	0.00600684	+	0.999982i	$0.498088\pi$
$499$	−14.3271	+	39.3635i	−0.641371	+	1.76215i	−0.647378	+	0.762169i	$0.724134\pi$
$500$	17.9159	−	12.9607i	0.801225	−	0.579620i
$501$	−5.04796	+	8.74333i	−0.225526	+	0.390623i
$502$	−5.67300	+	13.9999i	−0.253198	+	0.624845i
$503$	37.8278	+	6.67006i	1.68666	+	0.297403i	0.933004	−	0.359867i	$-0.117178\pi$
$503$	37.8278	+	6.67006i	1.68666	+	0.297403i	0.753655	+	0.657270i	$0.228289\pi$
$504$	2.95971	+	12.0280i	0.131836	+	0.535771i
$505$	4.65904	+	8.06970i	0.207325	+	0.359097i
$506$	2.93425	+	21.0346i	0.130444	+	0.935101i
$507$	4.62151	+	3.87791i	0.205249	+	0.172224i
$508$	6.89311	−	10.1744i	0.305832	−	0.451418i
$509$	11.0874	+	30.4624i	0.491441	+	1.35022i	0.899362	+	0.437205i	$0.144032\pi$
$509$	11.0874	+	30.4624i	0.491441	+	1.35022i	−0.407921	+	0.913017i	$0.633746\pi$
$510$	1.24170	−	5.81245i	0.0549833	−	0.257380i
$511$	−23.2282	+	4.09576i	−1.02756	+	0.181186i
$512$	−21.4546	−	7.19029i	−0.948168	−	0.317769i
$513$	−4.35694	+	0.130785i	−0.192363	+	0.00577431i
$514$	2.06663	+	2.65076i	0.0911554	+	0.116920i
$515$	1.16039	+	6.58091i	0.0511330	+	0.289990i
$516$	−4.15824	+	2.01758i	−0.183056	+	0.0888188i
$517$	−12.2857	+	4.47162i	−0.540323	+	0.196661i
$518$	−38.7335	+	12.5414i	−1.70185	+	0.551040i
$519$	5.31701	−	6.33657i	0.233391	−	0.278144i
$520$	1.08725	−	10.0474i	0.0476789	−	0.440610i
$521$	9.81770	−	5.66825i	0.430121	−	0.248331i	−0.269277	−	0.963063i	$-0.586785\pi$
$521$	9.81770	−	5.66825i	0.430121	−	0.248331i	0.699398	+	0.714732i	$0.253451\pi$
$522$	−3.43156	+	1.82009i	−0.150195	+	0.0796632i
$523$	1.82714	−	10.3622i	0.0798952	−	0.453108i	−0.918447	−	0.395545i	$-0.870556\pi$
$523$	1.82714	−	10.3622i	0.0798952	−	0.453108i	0.998342	−	0.0575633i	$-0.0183331\pi$
$524$	−4.32835	−	15.2123i	−0.189085	−	0.664551i
$525$	12.0135	+	6.93602i	0.524314	+	0.302713i
$526$	0.312858	−	8.70352i	0.0136412	−	0.379491i
$527$	−31.8223	−	11.5824i	−1.38620	−	0.504536i
$528$	−3.39548	+	23.4623i	−0.147769	+	1.02107i
$529$	12.7005	−	10.6570i	0.552195	−	0.463346i
$530$	−11.0788	+	12.2789i	−0.481232	+	0.533363i
$531$	12.1634			0.527848
$532$	−23.2957	−	30.2478i	−1.00999	−	1.31141i
$533$	13.3207			0.576983
$534$	−4.58857	+	5.08564i	−0.198567	+	0.220077i
$535$	−9.58263	+	8.04078i	−0.414293	+	0.347633i
$536$	7.06762	+	7.36387i	0.305275	+	0.318071i
$537$	9.67646	+	3.52194i	0.417570	+	0.151983i
$538$	0.298678	−	8.30905i	0.0128769	−	0.358228i
$539$	62.5117	+	36.0911i	2.69257	+	1.55456i
$540$	2.60399	−	0.740915i	0.112058	−	0.0318839i
$541$	5.14553	−	29.1817i	0.221223	−	1.25462i	−0.648551	−	0.761171i	$-0.724625\pi$
$541$	5.14553	−	29.1817i	0.221223	−	1.25462i	0.869775	−	0.493449i	$-0.164264\pi$
$542$	3.23026	−	1.71332i	0.138751	−	0.0735933i
$543$	0.475143	−	0.274324i	0.0203903	−	0.0117724i
$544$	−6.09128	+	16.4727i	−0.261161	+	0.706262i
$545$	−8.32080	+	9.91634i	−0.356424	+	0.424769i
$546$	15.5527	−	5.03577i	0.665593	−	0.215511i
$547$	−25.6392	+	9.33190i	−1.09625	+	0.399003i	−0.825933	−	0.563768i	$-0.809351\pi$
$547$	−25.6392	+	9.33190i	−1.09625	+	0.399003i	−0.270319	+	0.962771i	$0.587129\pi$
$548$	5.56312	+	11.4656i	0.237645	+	0.489787i
$549$	−0.974475	−	5.52652i	−0.0415896	−	0.235866i
$550$	16.3239	+	20.9379i	0.696055	+	0.892793i
$551$	7.41709	−	9.39820i	0.315979	−	0.400377i
$552$	−6.55629	+	2.89495i	−0.279054	+	0.123217i
$553$	18.5745	−	3.27519i	0.789870	−	0.139275i
$554$	−7.06137	+	33.0546i	−0.300009	+	1.40436i
$555$	3.04349	+	8.36193i	0.129189	+	0.354944i
$556$	32.1099	+	21.7542i	1.36176	+	0.922583i
$557$	−23.0246	−	19.3199i	−0.975584	−	0.818612i	0.00783334	−	0.999969i	$-0.497507\pi$
$557$	−23.0246	−	19.3199i	−0.975584	−	0.818612i	−0.983417	+	0.181357i	$0.941951\pi$
$558$	−2.13118	−	15.2776i	−0.0902199	−	0.646753i
$559$	3.04986	+	5.28252i	0.128995	+	0.223427i
$560$	18.6263	+	14.6757i	0.787103	+	0.620161i
$561$	18.1211	+	3.19524i	0.765073	+	0.134903i
$562$	−2.44742	+	6.03977i	−0.103238	+	0.254772i
$563$	−11.8637	+	20.5485i	−0.499996	+	0.866018i	−1.00000		4.90221e-6i	$-0.999998\pi$
$563$	−11.8637	+	20.5485i	−0.499996	+	0.866018i	0.500004	+	0.866023i	$0.333332\pi$
$564$	−2.58596	−	3.57465i	−0.108889	−	0.150520i
$565$	5.09760	−	14.0055i	0.214458	−	0.589217i
$566$	8.22439	+	5.15089i	0.345697	+	0.216508i
$567$	2.81503	+	3.35482i	0.118220	+	0.140889i
$568$	6.37680	−	4.27276i	0.267565	−	0.179281i
$569$		−	35.9928i		−	1.50890i	−0.656360	−	0.754448i	$-0.727905\pi$
$569$		−	35.9928i		−	1.50890i	0.656360	−	0.754448i	$-0.272095\pi$
$570$	−6.42399	+	5.32586i	−0.269072	+	0.223076i
$571$		−	20.5478i		−	0.859898i	−0.902853	−	0.429949i	$-0.858531\pi$
$571$		−	20.5478i		−	0.859898i	0.902853	−	0.429949i	$-0.141469\pi$
$572$	31.2064	+	2.24640i	1.30481	+	0.0939268i
$573$	10.6167	+	12.6524i	0.443518	+	0.528564i
$574$	−16.5902	+	26.4895i	−0.692463	+	1.10565i
$575$	−2.74517	+	7.54228i	−0.114481	+	0.314535i
$576$	−7.92884	+	1.06469i	−0.330368	+	0.0443620i
$577$	−15.8443	+	27.4432i	−0.659609	+	1.14248i	0.321108	+	0.947043i	$0.395945\pi$
$577$	−15.8443	+	27.4432i	−0.659609	+	1.14248i	−0.980717	+	0.195433i	$0.937389\pi$
$578$	−9.64775	−	3.90944i	−0.401293	−	0.162611i
$579$	0.992583	+	0.175019i	0.0412503	+	0.00727354i
$580$	−3.03848	+	6.78709i	−0.126166	+	0.281818i
$581$	−14.5721	−	25.2397i	−0.604554	−	1.04712i
$582$	17.0031	−	2.37187i	0.704799	−	0.0983172i
$583$	−39.2216	−	32.9108i	−1.62439	−	1.36303i
$584$	−1.01593	−	15.1994i	−0.0420396	−	0.628955i
$585$	−1.22205	−	3.35756i	−0.0505257	−	0.138818i
$586$	6.09138	+	1.30128i	0.251633	+	0.0537555i
$587$	41.1920	−	7.26326i	1.70017	−	0.299787i	0.762419	−	0.647083i	$-0.224011\pi$
$587$	41.1920	−	7.26326i	1.70017	−	0.299787i	0.937755	+	0.347297i	$0.112900\pi$
$588$	−5.94122	+	23.6227i	−0.245012	+	0.974184i
$589$	24.9971	+	40.4431i	1.02999	+	1.66643i
$590$	18.3639	−	14.3172i	0.756029	−	0.589429i
$591$	−2.04361	−	11.5899i	−0.0840628	−	0.476744i
$592$	−5.36155	−	25.7422i	−0.220358	−	1.05800i
$593$	−18.5602	+	6.75536i	−0.762176	+	0.277410i	−0.693720	−	0.720245i	$-0.744030\pi$
$593$	−18.5602	+	6.75536i	−0.762176	+	0.277410i	−0.0684562	+	0.997654i	$0.521807\pi$
$594$	2.58190	+	7.97403i	0.105936	+	0.327179i
$595$	11.8309	−	14.0995i	0.485019	−	0.578023i
$596$	−18.2540	−	17.7001i	−0.747713	−	0.725024i
$597$	−9.82986	+	5.67527i	−0.402309	+	0.232273i
$598$	4.43203	+	8.35606i	0.181239	+	0.341705i
$599$	4.35008	−	24.6705i	0.177740	−	1.00801i	−0.757194	−	0.653189i	$-0.773431\pi$
$599$	4.35008	−	24.6705i	0.177740	−	1.00801i	0.934934	−	0.354822i	$-0.115458\pi$
$600$	−5.28834	+	7.23195i	−0.215896	+	0.295243i
$601$	−15.8922	−	9.17535i	−0.648255	−	0.374270i	0.139532	−	0.990218i	$-0.455440\pi$
$601$	−15.8922	−	9.17535i	−0.648255	−	0.374270i	−0.787787	+	0.615947i	$0.788773\pi$
$602$	−14.3033	−	0.514147i	−0.582958	−	0.0209551i
$603$	3.39100	+	1.23422i	0.138092	+	0.0502615i
$604$	−0.618748	−	6.00528i	−0.0251765	−	0.244351i
$605$	25.0177	−	20.9924i	1.01712	−	0.853461i
$606$	−7.22769	−	6.52126i	−0.293605	−	0.264908i
$607$	−0.761410			−0.0309047			−0.0154523	−	0.999881i	$-0.504919\pi$
$607$	−0.761410			−0.0309047			−0.0154523	+	0.999881i	$0.504919\pi$
$608$	21.0407	−	12.8564i	0.853314	−	0.521397i
$609$	−12.0288			−0.487430
$610$	−7.97632	−	7.19671i	−0.322952	−	0.291386i
$611$	−4.46045	+	3.74276i	−0.180451	+	0.151416i
$612$	0.636411	+	6.17671i	0.0257254	+	0.249679i
$613$	16.5923	+	6.03909i	0.670156	+	0.243917i	0.654615	−	0.755963i	$-0.272831\pi$
$613$	16.5923	+	6.03909i	0.670156	+	0.243917i	0.0155407	+	0.999879i	$0.495053\pi$
$614$	−9.14160	−	0.328605i	−0.368925	−	0.0132614i
$615$	5.91626	+	3.41575i	0.238567	+	0.137736i
$616$	−43.3333	+	59.2594i	−1.74595	+	2.38763i
$617$	−0.229138	+	1.29951i	−0.00922474	+	0.0523161i	−0.989073	−	0.147429i	$-0.952900\pi$
$617$	−0.229138	+	1.29951i	−0.00922474	+	0.0523161i	0.979848	+	0.199745i	$0.0640114\pi$
$618$	−3.27120	−	6.16746i	−0.131587	−	0.248092i
$619$	15.5131	−	8.95649i	0.623524	−	0.359992i	−0.154716	−	0.987959i	$-0.549446\pi$
$619$	15.5131	−	8.95649i	0.623524	−	0.359992i	0.778240	+	0.627967i	$0.216113\pi$
$620$	−21.2003	−	20.5570i	−0.851426	−	0.825590i
$621$	−1.62877	+	1.94109i	−0.0653602	+	0.0778932i
$622$	3.05532	+	9.43617i	0.122507	+	0.378356i
$623$	−19.9324	+	7.25479i	−0.798574	+	0.290657i
$624$	2.15282	+	10.3362i	0.0861819	+	0.413781i
$625$	0.151298	+	0.858054i	0.00605192	+	0.0343222i
$626$	18.1120	−	14.1208i	0.723900	−	0.564380i
$627$	−17.1920	−	19.2827i	−0.686582	−	0.770078i
$628$	−0.178711	+	0.710568i	−0.00713135	+	0.0283548i
$629$	−20.0992	+	3.54403i	−0.801407	+	0.141310i
$630$	8.19887	+	1.75150i	0.326651	+	0.0697815i
$631$	−6.95951	−	19.1211i	−0.277054	−	0.761198i	−0.997693	−	0.0678883i	$-0.978374\pi$
$631$	−6.95951	−	19.1211i	−0.277054	−	0.761198i	0.720639	−	0.693310i	$-0.243848\pi$
$632$	0.812394	+	12.1543i	0.0323153	+	0.483470i
$633$	−17.4970	−	14.6817i	−0.695442	−	0.583545i
$634$	6.19647	−	0.864387i	0.246093	−	0.0343292i
$635$	−4.15903	−	7.20365i	−0.165046	−	0.285868i
$636$	7.05983	−	15.7696i	0.279941	−	0.625307i
$637$	31.6588	+	5.58229i	1.25437	+	0.221178i
$638$	−21.3363	−	8.64586i	−0.844713	−	0.342293i
$639$	1.35693	−	2.35027i	0.0536793	−	0.0929752i
$640$	−10.7174	+	10.9402i	−0.423644	+	0.432449i
$641$	2.55576	−	7.02188i	0.100946	−	0.277348i	−0.878931	−	0.476949i	$-0.841743\pi$
$641$	2.55576	−	7.02188i	0.100946	−	0.277348i	0.979877	+	0.199602i	$0.0639648\pi$
$642$	6.93669	−	11.0758i	0.273769	−	0.437126i
$643$	−17.0762	−	20.3507i	−0.673421	−	0.802552i	0.315824	−	0.948818i	$-0.397719\pi$
$643$	−17.0762	−	20.3507i	−0.673421	−	0.802552i	−0.989245	+	0.146265i	$0.953275\pi$
$644$	−22.1368	−	1.59352i	−0.872311	−	0.0627935i
$645$			3.12824i			0.123174i
$646$	−9.47103	−	16.6310i	−0.372633	−	0.654337i
$647$		−	12.0426i		−	0.473443i	−0.971578	−	0.236721i	$-0.923927\pi$
$647$		−	12.0426i		−	0.473443i	0.971578	−	0.236721i	$-0.0760728\pi$
$648$	−2.34972	+	1.57443i	−0.0923057	+	0.0618493i
$649$	46.3379	+	55.2233i	1.81892	+	2.16771i
$650$	10.0209	+	6.27603i	0.393052	+	0.246166i
$651$	16.3377	−	44.8876i	0.640327	−	1.75928i
$652$	−6.96199	−	9.62375i	−0.272653	−	0.376895i
$653$	−8.34739	+	14.4581i	−0.326659	+	0.565789i	−0.981847	−	0.189677i	$-0.939256\pi$
$653$	−8.34739	+	14.4581i	−0.326659	+	0.565789i	0.655188	+	0.755466i	$0.272589\pi$
$654$	5.07894	−	12.5338i	0.198602	−	0.490112i
$655$	−10.5423	−	1.85889i	−0.411920	−	0.0726327i
$656$	−15.8562	−	12.4931i	−0.619080	−	0.487775i
$657$	−2.69289	−	4.66423i	−0.105060	−	0.181969i
$658$	−1.88760	−	13.5315i	−0.0735862	−	0.527512i
$659$	−23.0730	−	19.3605i	−0.898795	−	0.754179i	0.0711594	−	0.997465i	$-0.477330\pi$
$659$	−23.0730	−	19.3605i	−0.898795	−	0.754179i	−0.969955	+	0.243286i	$0.921775\pi$
$660$	13.2840	+	8.99983i	0.517080	+	0.350318i
$661$	−6.66707	−	18.3176i	−0.259319	−	0.712473i	−0.999210	−	0.0397463i	$-0.987345\pi$
$661$	−6.66707	−	18.3176i	−0.259319	−	0.712473i	0.739891	−	0.672727i	$-0.234877\pi$
$662$	−3.36005	+	15.7286i	−0.130592	+	0.611309i
$663$	8.07042	−	1.42303i	0.313429	−	0.0552660i
$664$	17.2189	−	7.60303i	0.668222	−	0.295055i
$665$	−25.3021	+	5.24874i	−0.981175	+	0.203538i
$666$	−5.71602	−	7.33163i	−0.221491	−	0.284095i
$667$	−1.20856	−	6.85408i	−0.0467956	−	0.265391i
$668$	−8.81434	−	18.1664i	−0.341037	−	0.702879i
$669$	15.3403	−	5.58343i	0.593092	−	0.215868i
$670$	6.57238	−	2.12806i	0.253913	−	0.0822140i
$671$	21.3787	−	25.4781i	0.825314	−	0.983571i
$672$	−23.2359	−	8.59217i	−0.896345	−	0.331450i
$673$	−8.19541	+	4.73162i	−0.315910	+	0.182391i	−0.649568	−	0.760303i	$-0.725050\pi$
$673$	−8.19541	+	4.73162i	−0.315910	+	0.182391i	0.333658	+	0.942694i	$0.391717\pi$
$674$	14.7561	−	7.82661i	0.568385	−	0.301470i
$675$	−0.550042	+	3.11944i	−0.0211711	+	0.120067i
$676$	−11.6053	+	3.30206i	−0.446357	+	0.127002i
$677$	5.60219	+	3.23442i	0.215310	+	0.124309i	0.603777	−	0.797154i	$-0.293662\pi$
$677$	5.60219	+	3.23442i	0.215310	+	0.124309i	−0.388467	+	0.921463i	$0.626995\pi$
$678$	−0.559353	+	15.5609i	−0.0214818	+	0.597612i
$679$	49.9572	+	18.1829i	1.91718	+	0.697796i
$680$	8.23124	+	8.57627i	0.315654	+	0.328885i
$681$	10.4755	−	8.78997i	0.401421	−	0.336832i
$682$	61.2431	−	67.8774i	2.34512	−	2.59916i
$683$	−49.8043			−1.90571			−0.952855	−	0.303426i	$-0.901869\pi$
$683$	−49.8043			−1.90571			−0.952855	+	0.303426i	$0.901869\pi$
$684$	4.67097	−	7.36085i	0.178599	−	0.281449i
$685$	8.62559			0.329567
$686$	−21.4880	+	23.8157i	−0.820415	+	0.909289i
$687$	−19.1092	+	16.0345i	−0.729060	+	0.611754i
$688$	1.32396	−	9.14840i	0.0504755	−	0.348780i
$689$	−21.4274	−	7.79893i	−0.816318	−	0.297115i
$690$	−0.174258	+	4.84775i	−0.00663388	+	0.184551i
$691$	15.3832	+	8.88147i	0.585203	+	0.337867i	0.763198	−	0.646164i	$-0.223628\pi$
$691$	15.3832	+	8.88147i	0.585203	+	0.337867i	−0.177995	+	0.984031i	$0.556961\pi$
$692$	4.52745	+	15.9120i	0.172108	+	0.604885i
$693$	−4.50711	+	25.5611i	−0.171211	+	0.970985i
$694$	17.9589	−	9.52532i	0.681709	−	0.361576i
$695$	22.7342	−	13.1256i	0.862359	−	0.497883i
$696$	0.835787	−	7.72366i	0.0316804	−	0.292765i
$697$	−10.0714	+	12.0026i	−0.381482	+	0.454632i
$698$	−26.0341	+	8.42954i	−0.985406	+	0.319063i
$699$	14.6686	−	5.33892i	0.554816	−	0.201936i
$700$	−24.9611	+	12.1111i	−0.943440	+	0.457757i
$701$	−6.54715	−	37.1307i	−0.247282	−	1.40241i	−0.815132	−	0.579276i	$-0.803335\pi$
$701$	−6.54715	−	37.1307i	−0.247282	−	1.40241i	0.567849	−	0.823133i	$-0.307776\pi$
$702$	2.29515	+	2.94387i	0.0866249	+	0.111109i
$703$	25.2337	+	13.5759i	0.951706	+	0.512026i
$704$	−35.0395	−	31.9417i	−1.32060	−	1.20385i
$705$	−2.94081	+	0.518543i	−0.110757	+	0.0195295i
$706$	−0.648692	+	3.03656i	−0.0244139	+	0.114283i
$707$	−10.3105	−	28.3278i	−0.387766	−	1.06538i
$708$	−13.6447	+	20.1400i	−0.512799	+	0.756907i
$709$	36.6926	+	30.7888i	1.37802	+	1.15630i	0.969938	+	0.243351i	$0.0782467\pi$
$709$	36.6926	+	30.7888i	1.37802	+	1.15630i	0.408082	+	0.912945i	$0.366198\pi$
$710$	−0.717786	−	5.14554i	−0.0269380	−	0.193109i
$711$	2.15338	+	3.72977i	0.0807582	+	0.139877i
$712$	−3.27334	−	13.3026i	−0.122674	−	0.498537i
$713$	27.2188	+	4.79940i	1.01935	+	0.179739i
$714$	−7.22146	+	17.8212i	−0.270256	+	0.666941i
$715$	10.5882	−	18.3392i	0.395975	−	0.685849i
$716$	−16.6864	+	12.0713i	−0.623601	+	0.451124i
$717$	10.1105	−	27.7782i	0.377582	−	1.03740i
$718$	28.5195	+	17.8616i	1.06434	+	0.666589i
$719$	−16.7640	−	19.9786i	−0.625193	−	0.745076i	0.356761	−	0.934196i	$-0.383881\pi$
$719$	−16.7640	−	19.9786i	−0.625193	−	0.745076i	−0.981954	+	0.189120i	$0.939437\pi$
$720$	−1.69431	+	5.14279i	−0.0631434	+	0.191660i
$721$		−	21.6190i		−	0.805133i
$722$	−4.02726	+	26.5665i	−0.149879	+	0.988704i
$723$			12.1070i			0.450265i
$724$	−0.0787851	+	1.09446i	−0.00292803	+	0.0406754i
$725$	−5.59241	−	6.66478i	−0.207697	−	0.247524i
$726$	−18.1099	+	28.9159i	−0.672120	+	1.07317i
$727$	0.802042	−	2.20359i	0.0297461	−	0.0817267i	−0.923931	−	0.382560i	$-0.875043\pi$
$727$	0.802042	−	2.20359i	0.0297461	−	0.0817267i	0.953677	+	0.300833i	$0.0972648\pi$
$728$	−9.10853	+	31.4008i	−0.337585	+	1.16379i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−9.55574	−	3.87216i	−0.353674	−	0.143315i
$731$	−7.06575	−	1.24588i	−0.261336	−	0.0460806i
$732$	10.2439	+	4.58602i	0.378624	+	0.169504i
$733$	1.21384	+	2.10243i	0.0448342	+	0.0776551i	0.887572	−	0.460670i	$-0.152391\pi$
$733$	1.21384	+	2.10243i	0.0448342	+	0.0776551i	−0.842737	+	0.538325i	$0.819057\pi$
$734$	−13.2236	+	1.84465i	−0.488091	+	0.0680872i
$735$	12.6295	+	10.5974i	0.465846	+	0.390892i
$736$	2.56131	−	14.1033i	0.0944112	−	0.519854i
$737$	7.31487	+	20.0974i	0.269447	+	0.740299i
$738$	−6.97954	−	1.49102i	−0.256920	−	0.0548852i
$739$	−38.8772	+	6.85510i	−1.43012	+	0.252169i	−0.834460	−	0.551068i	$-0.814221\pi$
$739$	−38.8772	+	6.85510i	−1.43012	+	0.252169i	−0.595660	+	0.803237i	$0.703109\pi$
$740$	−17.2597	−	4.34088i	−0.634477	−	0.159574i
$741$	−10.1321	−	5.45114i	−0.372211	−	0.200253i
$742$	42.1957	−	32.8974i	1.54905	−	1.20770i
$743$	−1.56711	−	8.88754i	−0.0574918	−	0.326052i	0.942474	−	0.334278i	$-0.108493\pi$
$743$	−1.56711	−	8.88754i	−0.0574918	−	0.326052i	−0.999966	+	0.00822620i	$0.997381\pi$
$744$	27.6871	+	13.6093i	1.01506	+	0.498943i
$745$	−16.1717	+	5.88601i	−0.592484	+	0.215647i
$746$	−3.55621	−	10.9831i	−0.130202	−	0.402121i
$747$	4.27765	−	5.09791i	0.156511	−	0.186523i
$748$	−25.6185	+	26.4202i	−0.936704	+	0.966018i
$749$	35.0479	−	20.2349i	1.28062	−	0.739368i
$750$	7.32645	+	13.8132i	0.267524	+	0.504385i
$751$	−2.89775	+	16.4340i	−0.105740	+	0.599684i	0.885182	+	0.465246i	$0.154034\pi$
$751$	−2.89775	+	16.4340i	−0.105740	+	0.599684i	−0.990922	+	0.134438i	$0.957077\pi$
$752$	8.81971	−	0.271825i	0.321622	−	0.00991243i
$753$	−9.25025	−	5.34064i	−0.337098	−	0.194624i
$754$	−10.2462	−	0.368313i	−0.373146	−	0.0134132i
$755$	−3.83969	−	1.39753i	−0.139741	−	0.0508615i
$756$	−8.71268	+	0.897702i	−0.316877	+	0.0326491i
$757$	−34.9629	+	29.3373i	−1.27075	+	1.06628i	−0.276297	+	0.961072i	$0.589108\pi$
$757$	−34.9629	+	29.3373i	−1.27075	+	1.06628i	−0.994450	+	0.105211i	$0.966448\pi$
$758$	−17.9741	−	16.2173i	−0.652849	−	0.589039i
$759$	−15.0177			−0.545108
$760$	−1.61216	−	16.6112i	−0.0584792	−	0.602551i
$761$	0.484522			0.0175639			0.00878196	−	0.999961i	$-0.497205\pi$
$761$	0.484522			0.0175639			0.00878196	+	0.999961i	$0.497205\pi$
$762$	6.45201	+	5.82139i	0.233732	+	0.210887i
$763$	32.0813	−	26.9194i	1.16142	−	0.974548i
$764$	−32.8592	+	3.38562i	−1.18881	+	0.122487i
$765$	3.94930	+	1.43743i	0.142787	+	0.0519704i
$766$	−49.2968	−	1.77203i	−1.78117	−	0.0640260i
$767$	27.8042	+	16.0528i	1.00395	+	0.579632i
$768$	7.13151	−	14.3228i	0.257336	−	0.516828i
$769$	2.01395	−	11.4217i	0.0726250	−	0.411877i	−0.926722	−	0.375747i	$-0.877386\pi$
$769$	2.01395	−	11.4217i	0.0726250	−	0.411877i	0.999347	−	0.0361294i	$-0.0115029\pi$
$770$	23.2824	+	43.8963i	0.839041	+	1.58191i
$771$	−2.05829	+	1.18836i	−0.0741276	+	0.0427976i
$772$	−1.40325	+	1.44717i	−0.0505041	+	0.0520847i
$773$	24.8043	−	29.5606i	0.892149	−	1.06322i	−0.105481	−	0.994421i	$-0.533638\pi$
$773$	24.8043	−	29.5606i	0.892149	−	1.06322i	0.997630	−	0.0688006i	$-0.0219172\pi$
$774$	−1.00673	−	3.10922i	−0.0361861	−	0.111759i
$775$	32.4666	−	11.8169i	1.16623	−	0.424475i
$776$	−15.1464	+	30.8140i	−0.543723	+	1.10616i
$777$	−4.99910	−	28.3513i	−0.179342	−	1.01710i
$778$	11.7862	−	9.18895i	0.422555	−	0.329440i
$779$	21.5392	−	4.46815i	0.771723	−	0.160088i
$780$	6.93027	+	1.74299i	0.248143	+	0.0624092i
$781$	15.8398	−	2.79299i	0.566794	−	0.0999411i
$782$	−10.8802	−	2.32430i	−0.389075	−	0.0831169i
$783$	−0.939416	−	2.58102i	−0.0335720	−	0.0922382i
$784$	−32.4493	−	36.3368i	−1.15890	−	1.29774i
$785$	0.379894	+	0.318769i	0.0135590	+	0.0113774i
$786$	11.0764	−	1.54512i	0.395082	−	0.0551126i
$787$	−5.95925	−	10.3217i	−0.212424	−	0.367930i	0.740048	−	0.672554i	$-0.234803\pi$
$787$	−5.95925	−	10.3217i	−0.212424	−	0.367930i	−0.952473	+	0.304624i	$0.901469\pi$
$788$	21.4828	+	9.61751i	0.765292	+	0.342610i
$789$	6.06473	+	1.06938i	0.215910	+	0.0380708i
$790$	7.64129	+	3.09639i	0.271865	+	0.110165i
$791$	−24.1093	+	41.7585i	−0.857228	+	1.48476i
$792$	−16.0996	−	4.67005i	−0.572073	−	0.165943i
$793$	5.06613	−	13.9191i	0.179904	−	0.494281i
$794$	−11.7799	+	18.8088i	−0.418052	+	0.667500i
$795$	−7.51693	−	8.95833i	−0.266598	−	0.317719i
$796$	1.62993	−	22.6425i	0.0577712	−	0.802542i
$797$		−	45.7141i		−	1.61928i	−0.586929	−	0.809639i	$-0.699663\pi$
$797$		−	45.7141i		−	1.61928i	0.586929	−	0.809639i	$-0.300337\pi$
$798$	23.4591	−	13.3595i	0.830445	−	0.472923i
$799$		−	6.84890i		−	0.242297i
$800$	−6.04218	−	16.8690i	−0.213623	−	0.596409i
$801$	−3.11333	−	3.71033i	−0.110004	−	0.131098i
$802$	45.9126	+	28.7548i	1.62123	+	1.01537i
$803$	10.9172	−	29.9949i	0.385261	−	1.05850i
$804$	−5.84756	+	4.23023i	−0.206228	+	0.149189i
$805$	−7.51088	+	13.0092i	−0.264724	+	0.458515i
$806$	15.2911	−	37.7355i	0.538606	−	1.32918i
$807$	5.78986	+	1.02091i	0.203813	+	0.0359377i
$808$	18.9057	−	4.65207i	0.665099	−	0.163659i
$809$	−0.00131388	−	0.00227570i	−4.61934e−5	−	8.00093e-5i	0.866002	−	0.500040i	$-0.166681\pi$
$809$	−0.00131388	−	0.00227570i	−4.61934e−5	−	8.00093e-5i	−0.866048	+	0.499960i	$0.833348\pi$
$810$	0.264489	+	1.89603i	0.00929321	+	0.0666196i
$811$	40.5235	+	34.0032i	1.42297	+	1.19402i	0.949725	+	0.313086i	$0.101363\pi$
$811$	40.5235	+	34.0032i	1.42297	+	1.19402i	0.473248	+	0.880929i	$0.343082\pi$
$812$	13.4936	−	19.9170i	0.473533	−	0.698950i
$813$	0.884307	+	2.42961i	0.0310140	+	0.0852102i
$814$	11.5106	−	53.8820i	0.403448	−	1.88856i
$815$	−7.91731	+	1.39604i	−0.277331	+	0.0489010i
$816$	−10.9412	−	5.87515i	−0.383018	−	0.205671i
$817$	6.70347	+	7.51869i	0.234525	+	0.263046i
$818$	26.6242	+	34.1495i	0.930894	+	1.19401i
$819$	2.00729	+	11.3839i	0.0701403	+	0.397785i
$820$	−12.2925	+	5.96431i	−0.429272	+	0.208283i
$821$	9.61642	−	3.50009i	0.335616	−	0.122154i	−0.168715	−	0.985665i	$-0.553962\pi$
$821$	9.61642	−	3.50009i	0.335616	−	0.122154i	0.504330	+	0.863511i	$0.331739\pi$
$822$	−8.57315	+	2.77588i	−0.299023	+	0.0968200i
$823$	−16.9654	+	20.2186i	−0.591377	+	0.704775i	−0.975870	−	0.218353i	$-0.929932\pi$
$823$	−16.9654	+	20.2186i	−0.591377	+	0.704775i	0.384493	+	0.923128i	$0.374376\pi$
$824$	13.8815	+	1.50214i	0.483586	+	0.0523295i
$825$	−16.2581	+	9.38659i	−0.566033	+	0.326799i
$826$	−66.5514	+	35.2986i	−2.31562	+	1.22820i
$827$	−5.70255	+	32.3407i	−0.198297	+	1.12460i	0.709348	+	0.704859i	$0.248990\pi$
$827$	−5.70255	+	32.3407i	−0.198297	+	1.12460i	−0.907645	+	0.419739i	$0.862122\pi$
$828$	−1.38690	−	4.87435i	−0.0481981	−	0.169396i
$829$	−12.6239	−	7.28838i	−0.438445	−	0.253136i	0.264493	−	0.964388i	$-0.414795\pi$
$829$	−12.6239	−	7.28838i	−0.438445	−	0.253136i	−0.702938	+	0.711252i	$0.748129\pi$
$830$	0.457655	−	12.7317i	0.0158854	−	0.441924i
$831$	−22.4592	−	8.17447i	−0.779100	−	0.283569i
$832$	−19.5296	−	8.03039i	−0.677066	−	0.278404i
$833$	−28.9663	+	24.3056i	−1.00362	+	0.842139i
$834$	−18.3719	+	20.3621i	−0.636168	+	0.705083i
$835$	−13.6666			−0.472952
$836$	51.2136	−	6.83520i	1.77126	−	0.236400i
$837$	10.9075			0.377018
$838$	−19.8951	+	22.0503i	−0.687266	+	0.761716i
$839$	6.55786	−	5.50270i	0.226403	−	0.189974i	−0.522529	−	0.852621i	$-0.675011\pi$
$839$	6.55786	−	5.50270i	0.226403	−	0.189974i	0.748932	+	0.662647i	$0.230567\pi$
$840$	−12.0974	+	11.6107i	−0.417401	+	0.400608i
$841$	−20.1619	−	7.33832i	−0.695237	−	0.253046i
$842$	0.961893	−	26.7593i	0.0331490	−	0.922186i
$843$	−3.99071	−	2.30404i	−0.137447	−	0.0793553i
$844$	43.9374	−	12.5015i	1.51239	−	0.430320i
$845$	−1.41813	+	8.04259i	−0.0487850	+	0.276674i
$846$	2.75605	−	1.46180i	0.0947548	−	0.0502576i
$847$	−91.5009	+	52.8281i	−3.14401	+	1.81519i
$848$	18.1915	+	29.3796i	0.624699	+	1.00890i
$849$	−4.41077	+	5.25655i	−0.151377	+	0.180404i
$850$	−13.2316	+	4.28422i	−0.453839	+	0.146948i
$851$	15.6525	−	5.69704i	0.536561	−	0.195292i
$852$	2.36936	+	4.88326i	0.0811728	+	0.167298i
$853$	6.66797	+	37.8159i	0.228307	+	1.29479i	0.856261	+	0.516543i	$0.172781\pi$
$853$	6.66797	+	37.8159i	0.228307	+	1.29479i	−0.627955	+	0.778250i	$0.716108\pi$
$854$	21.3699	+	27.4101i	0.731264	+	0.937953i
$855$	−3.10226	−	5.01919i	−0.106095	−	0.171653i
$856$	10.5576	+	23.9102i	0.360852	+	0.817234i
$857$	26.4405	−	4.66218i	0.903191	−	0.159257i	0.297281	−	0.954790i	$-0.403920\pi$
$857$	26.4405	−	4.66218i	0.903191	−	0.159257i	0.605910	+	0.795533i	$0.292809\pi$
$858$	−4.62187	+	21.6352i	−0.157788	+	0.738614i
$859$	6.84364	+	18.8027i	0.233502	+	0.641541i	1.00000		0.000705745i	$-0.000224646\pi$
$859$	6.84364	+	18.8027i	0.233502	+	0.641541i	−0.766498	+	0.642247i	$0.778002\pi$
$860$	−5.17969	−	3.50920i	−0.176626	−	0.119663i
$861$	−16.9306	−	14.2064i	−0.576992	−	0.484154i
$862$	−0.996193	−	7.14133i	−0.0339305	−	0.243235i
$863$	−0.178282	−	0.308794i	−0.00606880	−	0.0105115i	0.862975	−	0.505247i	$-0.168598\pi$
$863$	−0.178282	−	0.308794i	−0.00606880	−	0.0105115i	−0.869044	+	0.494735i	$0.835265\pi$
$864$	0.0289643	−	5.65678i	0.000985385	−	0.192448i
$865$	11.0272	+	1.94440i	0.374937	+	0.0661114i
$866$	13.4457	−	33.1814i	0.456904	−	1.12755i
$867$	3.68040	−	6.37464i	0.124993	−	0.216494i
$868$	55.9967	+	77.4057i	1.90065	+	2.62732i
$869$	−8.73003	+	23.9855i	−0.296146	+	0.813654i
$870$	−4.45633	−	2.79098i	−0.151084	−	0.0946229i
$871$	6.12258	+	7.29660i	0.207456	+	0.247236i
$872$	15.0558	+	22.4698i	0.509855	+	0.760924i
$873$			12.1394i			0.410856i
$874$	9.96936	+	12.0249i	0.337219	+	0.406749i
$875$			48.4197i			1.63688i
$876$	10.7438	+	0.773393i	0.362998	+	0.0261305i
$877$	2.98517	+	3.55759i	0.100802	+	0.120131i	0.814087	−	0.580743i	$-0.197238\pi$
$877$	2.98517	+	3.55759i	0.100802	+	0.120131i	−0.713285	+	0.700874i	$0.752793\pi$
$878$	13.6449	−	21.7868i	0.460494	−	0.735268i
$879$	−1.50641	+	4.13882i	−0.0508099	+	0.139599i
$880$	−29.8035	+	11.8996i	−1.00468	+	0.401136i
$881$	−23.6580	+	40.9769i	−0.797058	+	1.38055i	0.124466	+	0.992224i	$0.460278\pi$
$881$	−23.6580	+	40.9769i	−0.797058	+	1.38055i	−0.921524	+	0.388321i	$0.873055\pi$
$882$	−15.9632	−	6.46856i	−0.537508	−	0.217808i
$883$	−36.7417	−	6.47856i	−1.23646	−	0.218021i	−0.483061	−	0.875587i	$-0.660475\pi$
$883$	−36.7417	−	6.47856i	−1.23646	−	0.218021i	−0.753397	+	0.657566i	$0.771586\pi$
$884$	−6.69700	+	14.9592i	−0.225244	+	0.503132i
$885$	8.23267	+	14.2594i	0.276738	+	0.479324i
$886$	50.2794	−	7.01381i	1.68917	−	0.235633i
$887$	27.7168	+	23.2571i	0.930638	+	0.780898i	0.975932	−	0.218076i	$-0.0699779\pi$
$887$	27.7168	+	23.2571i	0.930638	+	0.780898i	−0.0452938	+	0.998974i	$0.514422\pi$
$888$	18.5517	−	1.24000i	0.622554	−	0.0416117i
$889$	9.20395	+	25.2877i	0.308691	+	0.848121i
$890$	−9.06770	−	1.93711i	−0.303950	−	0.0649319i
$891$	−5.83665	+	1.02916i	−0.195535	+	0.0344781i
$892$	−7.96354	+	31.6636i	−0.266639	+	1.06018i
$893$	−5.95701	+	7.54813i	−0.199344	+	0.252588i
$894$	14.1791	−	11.0546i	0.474221	−	0.369720i
$895$	2.42056	+	13.7277i	0.0809103	+	0.458865i
$896$	40.2923	−	28.8351i	1.34607	−	0.963313i
$897$	−6.28494	+	2.28753i	−0.209848	+	0.0763785i
$898$	−7.41119	−	22.8890i	−0.247315	−	0.763817i
$899$	−19.2575	+	22.9501i	−0.642272	+	0.765430i
$900$	−4.54809	−	4.41007i	−0.151603	−	0.147002i
$901$	23.2279	−	13.4106i	0.773834	−	0.446773i
$902$	−19.8199	−	37.3681i	−0.659930	−	1.24422i
$903$	1.75740	−	9.96673i	0.0584827	−	0.331672i
$904$	−25.1379	−	18.3820i	−0.836076	−	0.611378i
$905$	0.643189	+	0.371345i	0.0213803	+	0.0123439i
$906$	4.26610	+	0.153350i	0.141732	+	0.00509470i
$907$	−4.41916	−	1.60844i	−0.146736	−	0.0534075i	0.267608	−	0.963528i	$-0.413767\pi$
$907$	−4.41916	−	1.60844i	−0.146736	−	0.0534075i	−0.414344	+	0.910120i	$0.635989\pi$
$908$	2.80309	+	27.2055i	0.0930238	+	0.902846i
$909$	5.27310	−	4.42466i	0.174898	−	0.146757i
$910$	16.4301	+	14.8243i	0.544654	+	0.491419i
$911$	29.5004			0.977390			0.488695	−	0.872455i	$-0.337473\pi$
$911$	29.5004			0.977390			0.488695	+	0.872455i	$0.337473\pi$
$912$	6.94815	+	15.9913i	0.230076	+	0.529526i
$913$	39.4412			1.30531
$914$	31.7509	+	28.6475i	1.05022	+	0.947576i
$915$	5.81928	−	4.88295i	0.192379	−	0.161425i
$916$	−5.11335	−	49.6278i	−0.168950	−	1.63975i
$917$	32.5439	+	11.8450i	1.07469	+	0.391156i
$918$	−4.38788	−	0.157727i	−0.144822	−	0.00520578i
$919$	−39.3140	−	22.6980i	−1.29685	−	0.748737i	−0.316991	−	0.948428i	$-0.602673\pi$
$919$	−39.3140	−	22.6980i	−1.29685	−	0.748737i	−0.979859	+	0.199692i	$0.936006\pi$
$920$	−7.83134	−	5.72664i	−0.258192	−	0.188802i
$921$	1.12320	−	6.36999i	0.0370107	−	0.209898i
$922$	−2.62455	−	4.94827i	−0.0864348	−	0.162963i
$923$	6.20357	−	3.58163i	0.204193	−	0.117891i
$924$	−37.2675	−	36.1367i	−1.22601	−	1.18881i
$925$	13.3844	−	15.9509i	0.440077	−	0.524463i
$926$	2.92348	+	9.02901i	0.0960717	+	0.296712i
$927$	4.63880	−	1.68839i	0.152358	−	0.0554539i
$928$	11.8511	+	10.0481i	0.389032	+	0.329846i
$929$	7.41786	+	42.0688i	0.243372	+	1.38023i	0.824243	+	0.566236i	$0.191601\pi$
$929$	7.41786	+	42.0688i	0.243372	+	1.38023i	−0.580871	+	0.813996i	$0.697288\pi$
$930$	16.4677	−	12.8389i	0.539998	−	0.421003i
$931$	53.0639	−	1.59286i	1.73910	−	0.0522038i
$932$	−7.61480	+	30.2770i	−0.249431	+	0.991756i
$933$	−6.90688	+	1.21787i	−0.226121	+	0.0398712i
$934$	−7.47105	−	1.59602i	−0.244460	−	0.0522233i
$935$	8.51920	+	23.4063i	0.278608	+	0.765468i
$936$	−7.44906	+	0.497897i	−0.243480	+	0.0162743i
$937$	−16.8596	−	14.1469i	−0.550780	−	0.462159i	0.324425	−	0.945911i	$-0.394829\pi$
$937$	−16.8596	−	14.1469i	−0.550780	−	0.462159i	−0.875205	+	0.483752i	$0.839274\pi$
$938$	−22.1354	+	3.08782i	−0.722747	+	0.100821i
$939$	8.11973	+	14.0638i	0.264978	+	0.458955i
$940$	2.44034	−	5.45102i	0.0795951	−	0.177793i
$941$	21.9305	+	3.86694i	0.714914	+	0.126059i	0.519262	−	0.854615i	$-0.326207\pi$
$941$	21.9305	+	3.86694i	0.714914	+	0.126059i	0.195652	+	0.980673i	$0.437318\pi$
$942$	−0.480170	−	0.194574i	−0.0156448	−	0.00633955i
$943$	6.39387	−	11.0745i	0.208213	−	0.360635i
$944$	−18.0411	−	45.1852i	−0.587187	−	1.47065i
$945$	−2.02759	+	5.57077i	−0.0659576	+	0.181217i
$946$	10.2810	−	16.4156i	0.334263	−	0.533716i
$947$	8.10951	+	9.66454i	0.263524	+	0.314055i	0.881539	−	0.472110i	$-0.156508\pi$
$947$	8.10951	+	9.66454i	0.263524	+	0.314055i	−0.618016	+	0.786166i	$0.712063\pi$
$948$	−8.59130	−	0.618447i	−0.279033	−	0.0200862i
$949$		−	14.2159i		−	0.461467i
$950$	18.3087	+	6.78689i	0.594014	+	0.220196i
$951$			4.42399i			0.143458i
$952$	−21.4071	−	31.9486i	−0.693808	−	1.03546i
$953$	−36.0482	−	42.9605i	−1.16771	−	1.39163i	−0.904274	−	0.426952i	$-0.859587\pi$
$953$	−36.0482	−	42.9605i	−1.16771	−	1.39163i	−0.263440	−	0.964676i	$-0.584857\pi$
$954$	10.3542	+	6.48477i	0.335229	+	0.209952i
$955$	−7.64692	+	21.0097i	−0.247449	+	0.679859i
$956$	34.6530	+	47.9018i	1.12076	+	1.54925i
$957$	8.13933	−	14.0977i	0.263107	−	0.455715i
$958$	−22.0046	+	54.3032i	−0.710937	+	1.75446i
$959$	−27.4815	−	4.84574i	−0.887425	−	0.156477i
$960$	−6.61468	−	8.57449i	−0.213488	−	0.276740i
$961$	−43.9868	−	76.1874i	−1.41893	−	2.45766i
$962$	−3.39019	−	24.3030i	−0.109304	−	0.783562i
$963$	7.07898	+	5.93997i	0.228117	+	0.191413i
$964$	−20.0466	−	13.5814i	−0.645657	−	0.437428i
$965$	0.466639	+	1.28208i	0.0150216	+	0.0412716i
$966$	3.27859	−	15.3473i	0.105487	−	0.493790i
$967$	−27.5167	+	4.85194i	−0.884878	+	0.156028i	−0.597576	−	0.801812i	$-0.703869\pi$
$967$	−27.5167	+	4.85194i	−0.884878	+	0.156028i	−0.287302	+	0.957840i	$0.592758\pi$
$968$	−27.5631	−	62.4233i	−0.885913	−	2.00636i
$969$	12.5724	−	5.00807i	0.403882	−	0.160882i
$970$	14.2889	+	18.3276i	0.458788	+	0.588463i
$971$	1.99816	+	11.3321i	0.0641240	+	0.363665i	0.999938	+	0.0111700i	$0.00355560\pi$
$971$	1.99816	+	11.3321i	0.0641240	+	0.363665i	−0.935814	+	0.352495i	$0.885333\pi$
$972$	−0.873059	−	1.79938i	−0.0280034	−	0.0577151i
$973$	−79.8062	+	29.0471i	−2.55847	+	0.931206i
$974$	31.2278	−	10.1112i	1.00060	−	0.323983i
$975$	−5.37424	+	6.40477i	−0.172113	+	0.205117i
$976$	−19.0848	+	11.8171i	−0.610890	+	0.378256i
$977$	−50.6945	+	29.2685i	−1.62186	+	0.936382i	−0.635439	+	0.772151i	$0.719181\pi$
$977$	−50.6945	+	29.2685i	−1.62186	+	0.936382i	−0.986422	+	0.164231i	$0.947486\pi$
$978$	7.41990	−	3.93549i	0.237262	−	0.125843i
$979$	4.98472	−	28.2697i	0.159312	−	0.903505i
$980$	−31.7145	+	9.02374i	−1.01308	+	0.288253i
$981$	8.28159	+	4.78138i	0.264411	+	0.152658i
$982$	−0.682383	+	18.9835i	−0.0217757	+	0.605788i
$983$	−9.12982	−	3.32298i	−0.291196	−	0.105987i	0.192292	−	0.981338i	$-0.438408\pi$
$983$	−9.12982	−	3.32298i	−0.291196	−	0.105987i	−0.483488	+	0.875351i	$0.660630\pi$
$984$	10.2983	−	9.88399i	0.328298	−	0.315090i
$985$	12.2038	−	10.2402i	0.388846	−	0.326280i
$986$	8.07878	−	8.95394i	0.257281	−	0.285152i
$987$	9.66086			0.307508
$988$	20.3918	−	10.6615i	0.648751	−	0.339188i
$989$	5.85568			0.186200
$990$	−7.60057	+	8.42392i	−0.241562	+	0.267730i
$991$	6.00336	−	5.03741i	0.190703	−	0.160019i	−0.542437	−	0.840096i	$-0.682498\pi$
$991$	6.00336	−	5.03741i	0.190703	−	0.160019i	0.733140	+	0.680078i	$0.238054\pi$
$992$	−53.5929	+	30.5771i	−1.70158	+	0.970823i
$993$	−10.6869	−	3.88971i	−0.339138	−	0.123436i
$994$	−0.603793	+	16.7972i	−0.0191512	+	0.532774i
$995$	−13.3064	−	7.68247i	−0.421842	−	0.243551i
$996$	3.64244	+	12.8016i	0.115415	+	0.405634i
$997$	1.78025	−	10.0963i	0.0563809	−	0.319752i	−0.943553	−	0.331221i	$-0.892540\pi$
$997$	1.78025	−	10.0963i	0.0563809	−	0.319752i	0.999934	+	0.0114686i	$0.00365064\pi$
$998$	52.3352	−	27.7584i	1.65664	−	0.878677i
$999$	5.69295	−	3.28682i	0.180117	−	0.103990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.b.67.3	yes	60
3.2	odd	2		684.2.cf.b.523.8		60
4.3	odd	2		228.2.w.a.67.4	✓	60
12.11	even	2		684.2.cf.c.523.7		60
19.2	odd	18		228.2.w.a.211.4	yes	60
57.2	even	18		684.2.cf.c.667.7		60
76.59	even	18	inner	228.2.w.b.211.3	yes	60
228.59	odd	18		684.2.cf.b.667.8		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.4	✓	60	4.3	odd	2
228.2.w.a.211.4	yes	60	19.2	odd	18
228.2.w.b.67.3	yes	60	1.1	even	1	trivial
228.2.w.b.211.3	yes	60	76.59	even	18	inner
684.2.cf.b.523.8		60	3.2	odd	2
684.2.cf.b.667.8		60	228.59	odd	18
684.2.cf.c.523.7		60	12.11	even	2
684.2.cf.c.667.7		60	57.2	even	18

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05000 - 0.947369i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.204983 + 1.98947i) q^{4} +(1.27204 + 0.462984i) q^{5} +(-1.41330 - 0.0508027i) q^{6} +(-3.79268 - 2.18970i) q^{7} +(1.66953 - 2.28313i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.897018 - 1.69122i) q^{10} +(5.13267 - 2.96335i) q^{11} +(1.43583 + 1.39226i) q^{12} +(1.69665 - 2.02199i) q^{13} +(1.90784 + 5.89224i) q^{14} +(1.27204 - 0.462984i) q^{15} +(-3.91596 + 0.815613i) q^{16} +(0.539127 + 3.05754i) q^{17} +(-1.11531 + 0.869535i) q^{18} +(2.06520 - 3.83861i) q^{19} +(-0.660346 + 2.62558i) q^{20} +(-4.31287 + 0.760476i) q^{21} +(-8.19666 - 1.75103i) q^{22} +(-0.866649 - 2.38110i) q^{23} +(-0.188632 - 2.82213i) q^{24} +(-2.42650 - 2.03607i) q^{25} +(-3.69704 + 0.515725i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(3.57891 - 7.99426i) q^{28} +(2.70494 + 0.476954i) q^{29} +(-1.77425 - 0.718959i) q^{30} +(-5.45375 + 9.44617i) q^{31} +(4.88443 + 2.85347i) q^{32} +(2.02705 - 5.56927i) q^{33} +(2.33054 - 3.72115i) q^{34} +(-3.81063 - 4.54133i) q^{35} +(1.99484 + 0.143599i) q^{36} +6.57365i q^{37} +(-5.80504 + 2.07401i) q^{38} -2.63952i q^{39} +(3.18076 - 2.13126i) q^{40} +(3.24392 + 3.86595i) q^{41} +(5.24895 + 3.28739i) q^{42} +(-0.790384 + 2.17156i) q^{43} +(6.94759 + 9.60384i) q^{44} +(0.676837 - 1.17232i) q^{45} +(-1.34580 + 3.32118i) q^{46} +(-2.17246 - 0.383063i) q^{47} +(-2.47554 + 3.14193i) q^{48} +(6.08959 + 10.5475i) q^{49} +(0.618899 + 4.43665i) q^{50} +(2.37834 + 1.99567i) q^{51} +(4.37046 + 2.96095i) q^{52} +(-2.95468 - 8.11792i) q^{53} +(-0.295448 + 1.38301i) q^{54} +(7.90093 - 1.39315i) q^{55} +(-11.3314 + 5.00339i) q^{56} +(-0.885372 - 4.26803i) q^{57} +(-2.38832 - 3.06338i) q^{58} +(2.11216 + 11.9786i) q^{59} +(1.18184 + 2.43578i) q^{60} +(5.27335 - 1.91934i) q^{61} +(14.6754 - 4.75173i) q^{62} +(-2.81503 + 3.35482i) q^{63} +(-2.42534 - 7.62350i) q^{64} +(3.09435 - 1.78652i) q^{65} +(-7.40455 + 3.92735i) q^{66} +(-0.626632 + 3.55381i) q^{67} +(-5.97236 + 1.69932i) q^{68} +(-2.19443 - 1.26696i) q^{69} +(-0.301173 + 8.37846i) q^{70} +(2.55019 + 0.928194i) q^{71} +(-1.95853 - 2.04063i) q^{72} +(4.12575 - 3.46192i) q^{73} +(6.22767 - 6.90230i) q^{74} -3.16756 q^{75} +(8.06012 + 3.32181i) q^{76} -25.9554 q^{77} +(-2.50060 + 2.77148i) q^{78} +(-3.29918 + 2.76834i) q^{79} +(-5.35887 - 0.775538i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.256383 - 7.13242i) q^{82} +(5.76326 + 3.32742i) q^{83} +(-2.39701 - 8.42443i) q^{84} +(-0.729802 + 4.13891i) q^{85} +(2.88717 - 1.53134i) q^{86} +(2.37868 - 1.37333i) q^{87} +(1.80344 - 16.6659i) q^{88} +(3.11333 - 3.71033i) q^{89} +(-1.82129 + 0.589713i) q^{90} +(-10.8624 + 3.95358i) q^{91} +(4.55947 - 2.21225i) q^{92} +(1.89407 + 10.7418i) q^{93} +(1.91817 + 2.46034i) q^{94} +(4.40423 - 3.92670i) q^{95} +(5.57587 - 0.953765i) q^{96} +(-11.9550 + 2.10798i) q^{97} +(3.59831 - 16.8439i) q^{98} +(-2.02705 - 5.56927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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