LMFDB - Embedded newform 345.2.t.a.4.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.18
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19202 - 0.544376i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.185160 + 0.213686i) q^{4} +(1.80362 + 1.32173i) q^{5} +(0.858156 + 0.990364i) q^{6} +(0.0307032 - 0.00441445i) q^{7} +(-0.842776 + 2.87023i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(2.86946 + 0.593679i) q^{10} +(-0.773045 + 1.69273i) q^{11} +(-0.257196 - 0.117457i) q^{12} +(-3.64081 - 0.523469i) q^{13} +(0.0341956 - 0.0219762i) q^{14} +(-0.760052 + 2.10293i) q^{15} +(0.477404 + 3.32042i) q^{16} +(3.69929 - 3.20545i) q^{17} +(-0.708477 + 1.10241i) q^{18} +(4.16208 - 4.80329i) q^{19} +(-0.616392 + 0.140676i) q^{20} +(0.0128857 + 0.0282158i) q^{21} +2.43860i q^{22} +(-0.304986 - 4.78612i) q^{23} -2.99140 q^{24} +(1.50606 + 4.76778i) q^{25} +(-4.62487 + 1.35799i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.00474169 + 0.00737821i) q^{28} +(3.14945 + 3.63465i) q^{29} +(0.238790 + 2.92049i) q^{30} +(8.92439 + 2.62044i) q^{31} +(-0.857919 - 1.33495i) q^{32} +(-1.84196 - 0.264834i) q^{33} +(2.66465 - 5.83476i) q^{34} +(0.0612114 + 0.0326193i) q^{35} +(0.0402391 - 0.279869i) q^{36} +(-3.98029 - 6.19345i) q^{37} +(2.34647 - 7.99135i) q^{38} +(-0.523469 - 3.64081i) q^{39} +(-5.31371 + 4.06287i) q^{40} +(-2.14944 - 1.38136i) q^{41} +(0.0307200 + 0.0266190i) q^{42} +(1.96465 + 6.69098i) q^{43} +(-0.218576 - 0.478615i) q^{44} +(-2.23188 - 0.136801i) q^{45} +(-2.96900 - 5.53912i) q^{46} -8.76007i q^{47} +(-3.05142 + 1.39353i) q^{48} +(-6.71553 + 1.97186i) q^{49} +(4.39073 + 4.86342i) q^{50} +(4.11782 + 2.64636i) q^{51} +(0.785990 - 0.681064i) q^{52} +(-0.438626 + 0.0630649i) q^{53} +(-1.25736 - 0.369194i) q^{54} +(-3.63161 + 2.03128i) q^{55} +(-0.0132054 + 0.0918455i) q^{56} +(5.78132 + 2.64024i) q^{57} +(5.73282 + 2.61809i) q^{58} +(1.82915 - 12.7220i) q^{59} +(-0.308636 - 0.551791i) q^{60} +(-6.68313 - 1.96234i) q^{61} +(12.0645 - 1.73462i) q^{62} +(-0.0234425 + 0.0203131i) q^{63} +(-7.39344 - 4.75148i) q^{64} +(-5.87474 - 5.75630i) q^{65} +(-2.33982 + 0.687032i) q^{66} +(-7.01995 + 3.20590i) q^{67} +1.38401i q^{68} +(4.50633 - 1.64104i) q^{69} +(0.0907223 + 0.00556073i) q^{70} +(-3.37753 - 7.39577i) q^{71} +(-0.842776 - 2.87023i) q^{72} +(1.33789 + 1.15929i) q^{73} +(-8.11615 - 5.21593i) q^{74} +(-4.15035 + 2.78830i) q^{75} +(0.255746 + 1.77875i) q^{76} +(-0.0162625 + 0.0553848i) q^{77} +(-2.60596 - 4.05495i) q^{78} +(-0.400564 + 2.78598i) q^{79} +(-3.52764 + 6.61975i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-3.31415 - 0.476503i) q^{82} +(4.73969 + 7.37510i) q^{83} +(-0.00841523 - 0.00247093i) q^{84} +(10.9088 - 0.891948i) q^{85} +(5.98430 + 6.90626i) q^{86} +(-2.60012 + 4.04587i) q^{87} +(-4.20703 - 3.64541i) q^{88} +(5.24980 - 1.54148i) q^{89} +(-2.73491 + 1.05191i) q^{90} -0.114095 q^{91} +(1.07920 + 0.821027i) q^{92} +9.30116i q^{93} +(-4.76877 - 10.4422i) q^{94} +(13.8554 - 3.16216i) q^{95} +(1.03917 - 1.19927i) q^{96} +(-9.44472 + 14.6963i) q^{97} +(-6.93160 + 6.00626i) q^{98} +(-0.264834 - 1.84196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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 $

$2$	1.19202	−	0.544376i	0.842884	−	0.384932i	0.0533029	−	0.998578i	$-0.483025\pi$
$2$	1.19202	−	0.544376i	0.842884	−	0.384932i	0.789581	+	0.613646i	$0.210298\pi$
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$3$	0.281733	+	0.959493i	0.162658	+	0.553964i
$4$	−0.185160	+	0.213686i	−0.0925799	+	0.106843i
$5$	1.80362	+	1.32173i	0.806602	+	0.591095i
$5$	1.80362	+	1.32173i	0.806602	+	0.591095i
$6$	0.858156	+	0.990364i	0.350341	+	0.404315i
$7$	0.0307032	−	0.00441445i	0.0116047	−	0.00166850i	−0.136510	−	0.990639i	$-0.543589\pi$
$7$	0.0307032	−	0.00441445i	0.0116047	−	0.00166850i	0.148115	+	0.988970i	$0.452680\pi$
$8$	−0.842776	+	2.87023i	−0.297966	+	1.01478i
$9$	−0.841254	+	0.540641i	−0.280418	+	0.180214i
$10$	2.86946	+	0.593679i	0.907403	+	0.187738i
$11$	−0.773045	+	1.69273i	−0.233082	+	0.510378i	−0.989644	−	0.143544i	$-0.954150\pi$
$11$	−0.773045	+	1.69273i	−0.233082	+	0.510378i	0.756562	+	0.653922i	$0.226878\pi$
$12$	−0.257196	−	0.117457i	−0.0742460	−	0.0339070i
$13$	−3.64081	−	0.523469i	−1.00978	−	0.145184i	−0.382481	−	0.923964i	$-0.624930\pi$
$13$	−3.64081	−	0.523469i	−1.00978	−	0.145184i	−0.627298	+	0.778779i	$0.715839\pi$
$14$	0.0341956	−	0.0219762i	0.00913916	−	0.00587338i
$15$	−0.760052	+	2.10293i	−0.196245	+	0.542975i
$16$	0.477404	+	3.32042i	0.119351	+	0.830104i
$17$	3.69929	−	3.20545i	0.897209	−	0.777436i	−0.0784069	−	0.996921i	$-0.524983\pi$
$17$	3.69929	−	3.20545i	0.897209	−	0.777436i	0.975616	+	0.219486i	$0.0704379\pi$
$18$	−0.708477	+	1.10241i	−0.166990	+	0.259841i
$19$	4.16208	−	4.80329i	0.954846	−	1.10195i	−0.0398619	−	0.999205i	$-0.512692\pi$
$19$	4.16208	−	4.80329i	0.954846	−	1.10195i	0.994708	−	0.102746i	$-0.0327628\pi$
$20$	−0.616392	+	0.140676i	−0.137830	+	0.0314562i
$21$	0.0128857	+	0.0282158i	0.00281189	+	0.00615719i
$22$			2.43860i			0.519910i
$23$	−0.304986	−	4.78612i	−0.0635941	−	0.997976i
$23$	−0.304986	−	4.78612i	−0.0635941	−	0.997976i
$24$	−2.99140			−0.610618
$25$	1.50606	+	4.76778i	0.301213	+	0.953557i
$26$	−4.62487	+	1.35799i	−0.907013	+	0.266323i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−0.00474169	+	0.00737821i	−0.000896095	+	0.00139435i
$29$	3.14945	+	3.63465i	0.584837	+	0.674938i	0.968638	−	0.248478i	$-0.0799303\pi$
$29$	3.14945	+	3.63465i	0.584837	+	0.674938i	−0.383800	+	0.923416i	$0.625385\pi$
$30$	0.238790	+	2.92049i	0.0435969	+	0.533206i
$31$	8.92439	+	2.62044i	1.60287	+	0.470645i	0.956343	−	0.292247i	$-0.0944031\pi$
$31$	8.92439	+	2.62044i	1.60287	+	0.470645i	0.646526	+	0.762892i	$0.276221\pi$
$32$	−0.857919	−	1.33495i	−0.151660	−	0.235988i
$33$	−1.84196	−	0.264834i	−0.320644	−	0.0461016i
$34$	2.66465	−	5.83476i	0.456983	−	1.00065i
$35$	0.0612114	+	0.0326193i	0.0103466	+	0.00551367i
$36$	0.0402391	−	0.279869i	0.00670652	−	0.0466448i
$37$	−3.98029	−	6.19345i	−0.654356	−	1.01820i	−0.996899	−	0.0786953i	$-0.974925\pi$
$37$	−3.98029	−	6.19345i	−0.654356	−	1.01820i	0.342543	−	0.939502i	$-0.388712\pi$
$38$	2.34647	−	7.99135i	0.380648	−	1.29637i
$39$	−0.523469	−	3.64081i	−0.0838222	−	0.582996i
$40$	−5.31371	+	4.06287i	−0.840171	+	0.642397i
$41$	−2.14944	−	1.38136i	−0.335686	−	0.215732i	0.361928	−	0.932206i	$-0.382119\pi$
$41$	−2.14944	−	1.38136i	−0.335686	−	0.215732i	−0.697614	+	0.716474i	$0.745755\pi$
$42$	0.0307200	+	0.0266190i	0.00474020	+	0.00410741i
$43$	1.96465	+	6.69098i	0.299606	+	1.02036i	0.962417	+	0.271577i	$0.0875452\pi$
$43$	1.96465	+	6.69098i	0.299606	+	1.02036i	−0.662811	+	0.748787i	$0.730637\pi$
$44$	−0.218576	−	0.478615i	−0.0329516	−	0.0721539i
$45$	−2.23188	−	0.136801i	−0.332709	−	0.0203930i
$46$	−2.96900	−	5.53912i	−0.437756	−	0.816699i
$47$		−	8.76007i		−	1.27779i	−0.769295	−	0.638894i	$-0.779392\pi$
$47$		−	8.76007i		−	1.27779i	0.769295	−	0.638894i	$-0.220608\pi$
$48$	−3.05142	+	1.39353i	−0.440434	+	0.201139i
$49$	−6.71553	+	1.97186i	−0.959361	+	0.281694i
$50$	4.39073	+	4.86342i	0.620942	+	0.687791i
$51$	4.11782	+	2.64636i	0.576610	+	0.370565i
$52$	0.785990	−	0.681064i	0.108997	−	0.0944466i
$53$	−0.438626	+	0.0630649i	−0.0602499	+	0.00866263i	−0.172374	−	0.985032i	$-0.555144\pi$
$53$	−0.438626	+	0.0630649i	−0.0602499	+	0.00866263i	0.112124	+	0.993694i	$0.464235\pi$
$54$	−1.25736	−	0.369194i	−0.171105	−	0.0502409i
$55$	−3.63161	+	2.03128i	−0.489686	+	0.273898i
$56$	−0.0132054	+	0.0918455i	−0.00176464	+	0.0122734i
$57$	5.78132	+	2.64024i	0.765754	+	0.349708i
$58$	5.73282	+	2.61809i	0.752756	+	0.343772i
$59$	1.82915	−	12.7220i	0.238135	−	1.65626i	−0.423099	−	0.906084i	$-0.639058\pi$
$59$	1.82915	−	12.7220i	0.238135	−	1.65626i	0.661234	−	0.750180i	$-0.270033\pi$
$60$	−0.308636	−	0.551791i	−0.0398447	−	0.0712359i
$61$	−6.68313	−	1.96234i	−0.855687	−	0.251252i	−0.175670	−	0.984449i	$-0.556209\pi$
$61$	−6.68313	−	1.96234i	−0.855687	−	0.251252i	−0.680017	+	0.733197i	$0.738027\pi$
$62$	12.0645	−	1.73462i	1.53220	−	0.220297i
$63$	−0.0234425	+	0.0203131i	−0.00295348	+	0.00255920i
$64$	−7.39344	−	4.75148i	−0.924180	−	0.593934i
$65$	−5.87474	−	5.75630i	−0.728672	−	0.713981i
$66$	−2.33982	+	0.687032i	−0.288011	+	0.0845678i
$67$	−7.01995	+	3.20590i	−0.857623	+	0.391663i	−0.795172	−	0.606385i	$-0.792619\pi$
$67$	−7.01995	+	3.20590i	−0.857623	+	0.391663i	−0.0624517	+	0.998048i	$0.519892\pi$
$68$			1.38401i			0.167835i
$69$	4.50633	−	1.64104i	0.542498	−	0.197558i
$70$	0.0907223	+	0.00556073i	0.0108434	+	0.000664634i
$71$	−3.37753	−	7.39577i	−0.400839	−	0.877716i	−0.997184	−	0.0749877i	$-0.976108\pi$
$71$	−3.37753	−	7.39577i	−0.400839	−	0.877716i	0.596345	−	0.802728i	$-0.296619\pi$
$72$	−0.842776	−	2.87023i	−0.0993221	−	0.338260i
$73$	1.33789	+	1.15929i	0.156588	+	0.135685i	0.729631	−	0.683841i	$-0.239692\pi$
$73$	1.33789	+	1.15929i	0.156588	+	0.135685i	−0.573043	+	0.819525i	$0.694237\pi$
$74$	−8.11615	−	5.21593i	−0.943483	−	0.606340i
$75$	−4.15035	+	2.78830i	−0.479241	+	0.321965i
$76$	0.255746	+	1.77875i	0.0293361	+	0.204037i
$77$	−0.0162625	+	0.0553848i	−0.00185328	+	0.00631169i
$78$	−2.60596	−	4.05495i	−0.295066	−	0.459132i
$79$	−0.400564	+	2.78598i	−0.0450670	+	0.313448i	0.954802	+	0.297243i	$0.0960673\pi$
$79$	−0.400564	+	2.78598i	−0.0450670	+	0.313448i	−0.999869	+	0.0162043i	$0.994842\pi$
$80$	−3.52764	+	6.61975i	−0.394402	+	0.740111i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−3.31415	−	0.476503i	−0.365987	−	0.0526209i
$83$	4.73969	+	7.37510i	0.520248	+	0.809522i	0.997604	−	0.0691882i	$-0.0220409\pi$
$83$	4.73969	+	7.37510i	0.520248	+	0.809522i	−0.477355	+	0.878710i	$0.658405\pi$
$84$	−0.00841523	−	0.00247093i	−0.000918177	−	0.000269601i
$85$	10.9088	−	0.891948i	1.18323	−	0.0967453i
$86$	5.98430	+	6.90626i	0.645304	+	0.744721i
$87$	−2.60012	+	4.04587i	−0.278763	+	0.433763i
$88$	−4.20703	−	3.64541i	−0.448471	−	0.388602i
$89$	5.24980	−	1.54148i	0.556477	−	0.163397i	0.00861187	−	0.999963i	$-0.497259\pi$
$89$	5.24980	−	1.54148i	0.556477	−	0.163397i	0.547866	+	0.836566i	$0.315441\pi$
$90$	−2.73491	+	1.05191i	−0.288285	+	0.110881i
$91$	−0.114095			−0.0119604
$92$	1.07920	+	0.821027i	0.112514	+	0.0855980i
$93$			9.30116i			0.964485i
$94$	−4.76877	−	10.4422i	−0.491861	−	1.07703i
$95$	13.8554	−	3.16216i	1.42154	−	0.324431i
$96$	1.03917	−	1.19927i	0.106060	−	0.122400i
$97$	−9.44472	+	14.6963i	−0.958966	+	1.49218i	−0.0908220	+	0.995867i	$0.528949\pi$
$97$	−9.44472	+	14.6963i	−0.958966	+	1.49218i	−0.868144	+	0.496313i	$0.834687\pi$
$98$	−6.93160	+	6.00626i	−0.700197	+	0.606724i
$99$	−0.264834	−	1.84196i	−0.0266168	−	0.185124i
$100$	−1.29767	−	0.560978i	−0.129767	−	0.0560978i
$101$	−13.9574	+	8.96986i	−1.38881	+	0.892535i	−0.999591	−	0.0286098i	$-0.990892\pi$
$101$	−13.9574	+	8.96986i	−1.38881	+	0.892535i	−0.389221	+	0.921145i	$0.627256\pi$
$102$	6.34913	+	0.912867i	0.628657	+	0.0903873i
$103$	9.10912	+	4.16000i	0.897548	+	0.409897i	0.810113	−	0.586274i	$-0.199406\pi$
$103$	9.10912	+	4.16000i	0.897548	+	0.409897i	0.0874352	+	0.996170i	$0.472133\pi$
$104$	4.57086	−	10.0088i	0.448210	−	0.981443i
$105$	−0.0140527	+	0.0679219i	−0.00137141	+	0.00662849i
$106$	−0.488519	+	0.313952i	−0.0474492	+	0.0304937i
$107$	−0.653313	+	2.22498i	−0.0631582	+	0.215097i	−0.985026	−	0.172409i	$-0.944845\pi$
$107$	−0.653313	+	2.22498i	−0.0631582	+	0.215097i	0.921867	+	0.387506i	$0.126663\pi$
$108$	0.279869	−	0.0402391i	0.0269304	−	0.00387201i
$109$	4.73329	+	5.46251i	0.453367	+	0.523214i	0.935711	−	0.352769i	$-0.114760\pi$
$109$	4.73329	+	5.46251i	0.453367	+	0.523214i	−0.482343	+	0.875982i	$0.660214\pi$
$110$	−3.22316	+	4.39829i	−0.307317	+	0.419361i
$111$	4.82120	−	5.56396i	0.457608	−	0.528108i
$112$	0.0293156	+	0.0998398i	0.00277006	+	0.00943397i
$113$	4.61825	−	2.10908i	0.434448	−	0.198406i	−0.186172	−	0.982517i	$-0.559608\pi$
$113$	4.61825	−	2.10908i	0.434448	−	0.198406i	0.620620	+	0.784111i	$0.286881\pi$
$114$	8.32872			0.780056
$115$	5.77588	−	9.03544i	0.538604	−	0.842559i
$116$	−1.35983			−0.126257
$117$	3.34585	−	1.52800i	0.309324	−	0.141264i
$118$	−4.74518	−	16.1606i	−0.436829	−	1.48770i
$119$	0.0994295	−	0.114748i	0.00911469	−	0.0105189i
$120$	−5.39534	−	3.95382i	−0.492525	−	0.360933i
$121$	4.93572	+	5.69613i	0.448702	+	0.517830i
$122$	−9.03466	+	1.29899i	−0.817960	+	0.117605i
$123$	0.719839	−	2.45155i	0.0649057	−	0.221048i
$124$	−2.21239	+	1.42182i	−0.198679	+	0.127683i
$125$	−3.58536	+	10.5899i	−0.320684	+	0.947186i
$126$	−0.0168860	+	0.0369751i	−0.00150432	+	0.00329400i
$127$	1.68504	+	0.769530i	0.149523	+	0.0682847i	0.488771	−	0.872412i	$-0.337445\pi$
$127$	1.68504	+	0.769530i	0.149523	+	0.0682847i	−0.339248	+	0.940697i	$0.610173\pi$
$128$	−8.25830	−	1.18736i	−0.729937	−	0.104949i
$129$	−5.86644	+	3.77013i	−0.516511	+	0.331942i
$130$	−10.1364	−	3.66355i	−0.889020	−	0.321314i
$131$	−1.33024	−	9.25199i	−0.116223	−	0.808350i	−0.961654	−	0.274265i	$-0.911565\pi$
$131$	−1.33024	−	9.25199i	−0.116223	−	0.808350i	0.845431	−	0.534085i	$-0.179344\pi$
$132$	0.397648	−	0.344564i	0.0346108	−	0.0299904i
$133$	0.106585	−	0.165850i	0.00924209	−	0.0143810i
$134$	−6.62269	+	7.64299i	−0.572113	+	0.660254i
$135$	−0.497534	−	2.18001i	−0.0428209	−	0.187626i
$136$	6.08271	+	13.3193i	0.521588	+	1.14212i
$137$		−	6.67355i		−	0.570160i	−0.958504	−	0.285080i	$-0.907980\pi$
$137$		−	6.67355i		−	0.570160i	0.958504	−	0.285080i	$-0.0920201\pi$
$138$	4.47828	−	4.40929i	0.381217	−	0.375343i
$139$	−11.2490			−0.954131			−0.477066	−	0.878868i	$-0.658300\pi$
$139$	−11.2490			−0.954131			−0.477066	+	0.878868i	$0.658300\pi$
$140$	−0.0183042	+	0.00704024i	−0.00154699	+	0.000595008i
$141$	8.40522	−	2.46800i	0.707847	−	0.207843i
$142$	−8.05216	−	6.97724i	−0.675722	−	0.585517i
$143$	3.70060	−	5.75825i	0.309460	−	0.481529i
$144$	−2.19677	−	2.53521i	−0.183064	−	0.211267i
$145$	0.876364	+	10.7182i	0.0727781	+	0.890101i
$146$	2.22588	+	0.653578i	0.184215	+	0.0540905i
$147$	−3.78397	−	5.88797i	−0.312096	−	0.485631i
$148$	2.06044	+	0.296247i	0.169367	+	0.0243514i
$149$	8.74636	−	19.1519i	0.716530	−	1.56898i	−0.102174	−	0.994767i	$-0.532580\pi$
$149$	8.74636	−	19.1519i	0.716530	−	1.56898i	0.818704	−	0.574215i	$-0.194693\pi$
$150$	−3.42941	+	5.58305i	−0.280010	+	0.455854i
$151$	1.23131	−	8.56393i	0.100202	−	0.696922i	−0.876355	−	0.481666i	$-0.840032\pi$
$151$	1.23131	−	8.56393i	0.100202	−	0.696922i	0.976557	−	0.215257i	$-0.0690589\pi$
$152$	10.2789	+	15.9942i	0.833725	+	1.29730i
$153$	−1.37904	+	4.69658i	−0.111489	+	0.379696i
$154$	0.0107651	+	0.0748726i	0.000867473	+	0.00603341i
$155$	12.6327	+	16.5219i	1.01468	+	1.32707i
$156$	0.874915	+	0.562274i	0.0700493	+	0.0450179i
$157$	1.84978	+	1.60285i	0.147629	+	0.127921i	0.725544	−	0.688176i	$-0.241588\pi$
$157$	1.84978	+	1.60285i	0.147629	+	0.127921i	−0.577915	+	0.816097i	$0.696134\pi$
$158$	1.03914	+	3.53900i	0.0826699	+	0.281548i
$159$	−0.184086	−	0.403091i	−0.0145989	−	0.0319672i
$160$	0.217083	−	3.54167i	0.0171619	−	0.279994i
$161$	−0.0304921	−	0.145603i	−0.00240312	−	0.0114751i
$162$		−	1.31044i		−	0.102958i
$163$	2.30667	−	1.05342i	0.180673	−	0.0825104i	−0.323025	−	0.946390i	$-0.604700\pi$
$163$	2.30667	−	1.05342i	0.180673	−	0.0825104i	0.503698	+	0.863880i	$0.331973\pi$
$164$	0.693167	−	0.203532i	0.0541273	−	0.0158932i
$165$	−2.97215	−	2.91223i	−0.231381	−	0.226717i
$166$	9.66462	+	6.21108i	0.750120	+	0.482073i
$167$	0.0245686	−	0.0212888i	0.00190117	−	0.00164738i	−0.653910	−	0.756573i	$-0.726872\pi$
$167$	0.0245686	−	0.0212888i	0.00190117	−	0.00164738i	0.655811	+	0.754925i	$0.272327\pi$
$168$	−0.0918455	+	0.0132054i	−0.00708604	+	0.00101882i
$169$	0.508060	+	0.149180i	0.0390815	+	0.0114754i
$170$	12.5180	−	7.00173i	0.960084	−	0.537008i
$171$	−0.904506	+	6.29097i	−0.0691693	+	0.481083i
$172$	−1.79354	−	0.819083i	−0.136756	−	0.0624545i
$173$	−2.35803	−	1.07688i	−0.179278	−	0.0818735i	0.323754	−	0.946141i	$-0.395055\pi$
$173$	−2.35803	−	1.07688i	−0.179278	−	0.0818735i	−0.503032	+	0.864268i	$0.667782\pi$
$174$	−0.896918	+	6.23820i	−0.0679951	+	0.472917i
$175$	0.0672881	+	0.139738i	0.00508650	+	0.0105632i
$176$	−5.98963	−	1.75871i	−0.451485	−	0.132568i
$177$	12.7220	−	1.82915i	0.956244	−	0.137487i
$178$	5.41871	−	4.69534i	0.406149	−	0.351930i
$179$	−0.0584505	−	0.0375639i	−0.00436880	−	0.00280766i	0.538455	−	0.842655i	$-0.319008\pi$
$179$	−0.0584505	−	0.0375639i	−0.00436880	−	0.00280766i	−0.542823	+	0.839847i	$0.682645\pi$
$180$	0.442487	−	0.451591i	0.0329810	−	0.0336596i
$181$	−16.8946	+	4.96070i	−1.25577	+	0.368726i	−0.840917	−	0.541165i	$-0.817984\pi$
$181$	−16.8946	+	4.96070i	−1.25577	+	0.368726i	−0.414848	+	0.909891i	$0.636165\pi$
$182$	−0.136004	+	0.0621107i	−0.0100813	+	0.00460395i
$183$		−	6.96527i		−	0.514888i
$184$	13.9943	+	3.15825i	1.03167	+	0.232829i
$185$	1.00715	−	16.4315i	0.0740471	−	1.20807i
$186$	5.06333	+	11.0871i	0.371261	+	0.812949i
$187$	2.56626	+	8.73986i	0.187663	+	0.639122i
$188$	1.87190	+	1.62201i	0.136523	+	0.118297i
$189$	−0.0260947	−	0.0167701i	−0.00189811	−	0.00121984i
$190$	14.7945	−	11.3119i	1.07331	−	0.820653i
$191$	1.84803	+	12.8533i	0.133719	+	0.930036i	0.940647	+	0.339386i	$0.110219\pi$
$191$	1.84803	+	12.8533i	0.133719	+	0.930036i	−0.806928	+	0.590649i	$0.798872\pi$
$192$	2.47603	−	8.43260i	0.178692	−	0.608570i
$193$	3.32642	+	5.17601i	0.239441	+	0.372578i	0.940089	−	0.340930i	$-0.110742\pi$
$193$	3.32642	+	5.17601i	0.239441	+	0.372578i	−0.700648	+	0.713507i	$0.747105\pi$
$194$	−3.25797	+	22.6597i	−0.233909	+	1.62687i
$195$	3.86803	−	7.25851i	0.276995	−	0.519792i
$196$	0.822088	−	1.80012i	0.0587206	−	0.128580i
$197$	−27.5302	−	3.95825i	−1.96145	−	0.282014i	−0.999975	−	0.00711316i	$-0.997736\pi$
$197$	−27.5302	−	3.95825i	−1.96145	−	0.282014i	−0.961473	−	0.274900i	$-0.911355\pi$
$198$	−1.31840	−	2.05148i	−0.0936949	−	0.145792i
$199$	14.2728	+	4.19088i	1.01177	+	0.297084i	0.745279	−	0.666753i	$-0.232316\pi$
$199$	14.2728	+	4.19088i	1.01177	+	0.297084i	0.266495	+	0.963836i	$0.414134\pi$
$200$	−14.9539	+	0.304579i	−1.05740	+	0.0215370i
$201$	−5.05379	−	5.83238i	−0.356467	−	0.411385i
$202$	−11.7545	+	18.2903i	−0.827041	+	1.28690i
$203$	0.112743	+	0.0976923i	0.00791300	+	0.00685666i
$204$	−1.32794	+	0.389920i	−0.0929747	+	0.0272998i
$205$	−2.05098	−	5.33242i	−0.143247	−	0.372432i
$206$	13.1228			0.914312
$207$	2.84414	+	3.86146i	0.197682	+	0.268390i
$208$		−	12.3389i		−	0.855549i
$209$	4.91322	+	10.7584i	0.339854	+	0.744177i
$210$	0.0202240	+	0.0886141i	0.00139559	+	0.00611495i
$211$	9.04607	−	10.4397i	0.622757	−	0.718700i	−0.353471	−	0.935446i	$-0.614999\pi$
$211$	9.04607	−	10.4397i	0.622757	−	0.718700i	0.976228	+	0.216745i	$0.0695441\pi$
$212$	0.0677399	−	0.105405i	0.00465239	−	0.00723927i
$213$	6.14462	−	5.32435i	0.421023	−	0.364818i
$214$	0.432466	+	3.00787i	0.0295628	+	0.205613i
$215$	−5.30019	+	14.6647i	−0.361470	+	1.00012i
$216$	2.51653	−	1.61727i	0.171228	−	0.110042i
$217$	0.285575	+	0.0410595i	0.0193861	+	0.00278730i
$218$	8.61583	+	3.93472i	0.583538	+	0.266493i
$219$	−0.735403	+	1.61031i	−0.0496939	+	0.108815i
$220$	0.238372	−	1.15214i	0.0160710	−	0.0776770i
$221$	−15.1463	+	9.73397i	−1.01885	+	0.654778i
$222$	2.71807	−	9.25689i	0.182425	−	0.621282i
$223$	18.9735	−	2.72798i	1.27056	−	0.182679i	0.526144	−	0.850396i	$-0.323637\pi$
$223$	18.9735	−	2.72798i	1.27056	−	0.182679i	0.744416	+	0.667717i	$0.232728\pi$
$224$	−0.0322339	−	0.0371999i	−0.00215372	−	0.00248552i
$225$	−3.84464	−	3.19668i	−0.256309	−	0.213112i
$226$	4.35690	−	5.02813i	0.289817	−	0.334466i
$227$	5.72940	+	19.5125i	0.380273	+	1.29509i	0.898170	+	0.439649i	$0.144897\pi$
$227$	5.72940	+	19.5125i	0.380273	+	1.29509i	−0.517896	+	0.855443i	$0.673285\pi$
$228$	−1.63465	+	0.746520i	−0.108257	+	0.0494395i
$229$	−0.310620			−0.0205264			−0.0102632	−	0.999947i	$-0.503267\pi$
$229$	−0.310620			−0.0205264			−0.0102632	+	0.999947i	$0.503267\pi$
$230$	1.96627	−	13.9147i	0.129652	−	0.917506i
$231$	−0.0577230			−0.00379790
$232$	−13.0866	+	5.97644i	−0.859175	+	0.392372i
$233$	−2.08085	−	7.08673i	−0.136321	−	0.464267i	0.862829	−	0.505497i	$-0.168691\pi$
$233$	−2.08085	−	7.08673i	−0.136321	−	0.464267i	−0.999150	+	0.0412297i	$0.986872\pi$
$234$	3.15651	−	3.64281i	0.206347	−	0.238138i
$235$	11.5784	−	15.7998i	0.755294	−	1.03067i
$236$	2.37983	+	2.74647i	0.154914	+	0.178780i
$237$	−2.78598	+	0.400564i	−0.180969	+	0.0260194i
$238$	0.0560558	−	0.190908i	0.00363356	−	0.0123748i
$239$	−7.53451	+	4.84214i	−0.487367	+	0.313212i	−0.761146	−	0.648581i	$-0.775363\pi$
$239$	−7.53451	+	4.84214i	−0.487367	+	0.313212i	0.273779	+	0.961793i	$0.411726\pi$
$240$	−7.34546	−	1.51974i	−0.474147	−	0.0980989i
$241$	1.02491	−	2.24423i	0.0660201	−	0.144564i	−0.873746	−	0.486383i	$-0.838316\pi$
$241$	1.02491	−	2.24423i	0.0660201	−	0.144564i	0.939766	+	0.341820i	$0.111043\pi$
$242$	8.98431	+	4.10300i	0.577533	+	0.263751i
$243$	0.989821	+	0.142315i	0.0634971	+	0.00912950i
$244$	1.65677	−	1.06474i	0.106064	−	0.0681632i
$245$	−14.7185	−	5.31963i	−0.940330	−	0.339859i
$246$	−0.476503	−	3.31415i	−0.0303807	−	0.211302i
$247$	−17.6677	+	15.3091i	−1.12417	+	0.974098i
$248$	−15.0425	+	23.4066i	−0.955201	+	1.48632i
$249$	−5.74103	+	6.62550i	−0.363823	+	0.419874i
$250$	1.49106	+	14.5751i	0.0943030	+	0.921810i
$251$	−2.40421	−	5.26449i	−0.151752	−	0.332292i	0.818454	−	0.574573i	$-0.194832\pi$
$251$	−2.40421	−	5.26449i	−0.151752	−	0.332292i	−0.970206	+	0.242281i	$0.922104\pi$
$252$		−	0.00877050i		−	0.000552489i
$253$	8.33740	+	3.18363i	0.524168	+	0.200153i
$254$	2.42751			0.152315
$255$	3.92919	+	10.2157i	0.246055	+	0.639729i
$256$	6.37478	−	1.87181i	0.398424	−	0.116988i
$257$	15.6383	+	13.5506i	0.975489	+	0.845266i	0.987968	−	0.154656i	$-0.0494270\pi$
$257$	15.6383	+	13.5506i	0.975489	+	0.845266i	−0.0124794	+	0.999922i	$0.503972\pi$
$258$	−4.94053	+	7.68762i	−0.307584	+	0.478610i
$259$	−0.149548	−	0.172588i	−0.00929247	−	0.0107241i
$260$	2.31781	−	0.189513i	0.143744	−	0.0117531i
$261$	−4.61452	−	1.35495i	−0.285632	−	0.0838691i
$262$	−6.62223	−	10.3044i	−0.409123	−	0.636608i
$263$	−11.2767	−	1.62135i	−0.695354	−	0.0999768i	−0.214430	−	0.976739i	$-0.568790\pi$
$263$	−11.2767	−	1.62135i	−0.695354	−	0.0999768i	−0.480924	+	0.876762i	$0.659699\pi$
$264$	2.31249	−	5.06365i	0.142324	−	0.311646i
$265$	−0.874468	−	0.466000i	−0.0537181	−	0.0286262i
$266$	0.0367667	−	0.255718i	0.00225431	−	0.0156791i
$267$	2.95808	+	4.60286i	0.181031	+	0.281690i
$268$	0.614757	−	2.09367i	0.0375522	−	0.127891i
$269$	0.603617	+	4.19825i	0.0368032	+	0.255972i	0.999914	−	0.0131343i	$-0.00418090\pi$
$269$	0.603617	+	4.19825i	0.0368032	+	0.255972i	−0.963111	+	0.269106i	$0.913272\pi$
$270$	−1.77982	−	2.32777i	−0.108316	−	0.141664i
$271$	−6.79273	−	4.36542i	−0.412629	−	0.265181i	0.317815	−	0.948153i	$-0.397051\pi$
$271$	−6.79273	−	4.36542i	−0.412629	−	0.265181i	−0.730445	+	0.682972i	$0.760687\pi$
$272$	12.4095	+	10.7529i	0.752435	+	0.651989i
$273$	−0.0321443	−	0.109474i	−0.00194546	−	0.00662564i
$274$	−3.63292	−	7.95499i	−0.219473	−	0.480578i
$275$	−9.23484	−	1.13635i	−0.556882	−	0.0685244i
$276$	−0.483724	+	1.26679i	−0.0291168	+	0.0762520i
$277$		−	4.83493i		−	0.290503i	−0.989395	−	0.145251i	$-0.953601\pi$
$277$		−	4.83493i		−	0.290503i	0.989395	−	0.145251i	$-0.0463991\pi$
$278$	−13.4091	+	6.12371i	−0.804222	+	0.367276i
$279$	−8.92439	+	2.62044i	−0.534290	+	0.156882i
$280$	−0.145212	+	0.148200i	−0.00867810	+	0.00885665i
$281$	−25.1330	−	16.1520i	−1.49931	−	0.963546i	−0.994984	−	0.100030i	$-0.968106\pi$
$281$	−25.1330	−	16.1520i	−1.49931	−	0.963546i	−0.504322	−	0.863516i	$-0.668258\pi$
$282$	8.67566	−	7.51750i	0.516628	−	0.447661i
$283$	−30.2913	+	4.35523i	−1.80063	+	0.258891i	−0.959453	−	0.281869i	$-0.909046\pi$
$283$	−30.2913	+	4.35523i	−1.80063	+	0.258891i	−0.841177	+	0.540760i	$0.818137\pi$
$284$	2.20575	+	0.647668i	0.130887	+	0.0384320i
$285$	6.93760	+	12.4033i	0.410948	+	0.734709i
$286$	1.27653	−	8.87846i	0.0754828	−	0.524994i
$287$	−0.0720925	−	0.0329235i	−0.00425549	−	0.00194342i
$288$	1.44346	+	0.659204i	0.0850564	+	0.0388440i
$289$	0.990459	−	6.88879i	0.0582623	−	0.405223i
$290$	6.87940	+	12.2993i	0.403972	+	0.722237i
$291$	−16.7618	−	4.92172i	−0.982597	−	0.288517i
$292$	−0.495448	+	0.0712346i	−0.0289939	+	0.00416869i
$293$	−17.6189	+	15.2668i	−1.02930	+	0.891897i	−0.994207	−	0.107487i	$-0.965720\pi$
$293$	−17.6189	+	15.2668i	−1.02930	+	0.891897i	−0.0350977	+	0.999384i	$0.511174\pi$
$294$	−7.71583	−	4.95866i	−0.449996	−	0.289195i
$295$	20.1141	−	20.5280i	1.17109	−	1.19518i
$296$	21.1311	−	6.20466i	1.22822	−	0.360638i
$297$	1.69273	−	0.773045i	0.0982223	−	0.0448566i
$298$		−	27.5907i		−	1.59829i
$299$	−1.39499	+	17.5850i	−0.0806745	+	1.01697i
$300$	0.172658	−	1.40315i	0.00996842	−	0.0810110i
$301$	0.0898579	+	0.196761i	0.00517932	+	0.0113411i
$302$	−3.19426	−	10.8787i	−0.183809	−	0.625996i
$303$	−12.5388	−	10.8649i	−0.720333	−	0.624173i
$304$	17.9359	+	11.5267i	1.02870	+	0.661102i
$305$	−9.46011	−	12.3726i	−0.541684	−	0.708453i
$306$	0.912867	+	6.34913i	0.0521851	+	0.362955i
$307$	7.85215	−	26.7420i	0.448146	−	1.52624i	−0.357538	−	0.933899i	$-0.616384\pi$
$307$	7.85215	−	26.7420i	0.448146	−	1.52624i	0.805684	−	0.592346i	$-0.201798\pi$
$308$	−0.00882380	−	0.0137301i	−0.000502783	−	0.000782345i
$309$	−1.42515	+	9.91214i	−0.0810740	+	0.563882i
$310$	24.0525	+	12.8175i	1.36609	+	0.727983i
$311$	12.0446	−	26.3741i	0.682989	−	1.49554i	−0.176455	−	0.984309i	$-0.556463\pi$
$311$	12.0446	−	26.3741i	0.682989	−	1.49554i	0.859444	−	0.511229i	$-0.170810\pi$
$312$	10.8911	+	1.56591i	0.616589	+	0.0886521i
$313$	14.7352	+	22.9284i	0.832883	+	1.29599i	0.952920	+	0.303222i	$0.0980623\pi$
$313$	14.7352	+	22.9284i	0.832883	+	1.29599i	−0.120037	+	0.992769i	$0.538301\pi$
$314$	3.07753	+	0.903643i	0.173675	+	0.0509955i
$315$	−0.0691296	+	0.00565230i	−0.00389501	+	0.000318471i
$316$	−0.521157	−	0.601448i	−0.0293174	−	0.0338341i
$317$	6.63263	−	10.3206i	0.372526	−	0.579661i	−0.603488	−	0.797372i	$-0.706223\pi$
$317$	6.63263	−	10.3206i	0.372526	−	0.579661i	0.976013	+	0.217711i	$0.0698591\pi$
$318$	−0.438867	−	0.380280i	−0.0246104	−	0.0213251i
$319$	−8.58716	+	2.52142i	−0.480789	+	0.141172i
$320$	−7.05477	−	18.3420i	−0.394373	−	1.02535i
$321$	−2.31891			−0.129429
$322$	−0.115610	−	0.156962i	−0.00644269	−	0.00874715i
$323$		−	31.1101i		−	1.73101i
$324$	0.117457	+	0.257196i	0.00652541	+	0.0142887i
$325$	−2.98750	−	18.1470i	−0.165717	−	1.00661i
$326$	2.17614	−	2.51140i	0.120525	−	0.139093i
$327$	−3.90772	+	6.08053i	−0.216097	+	0.336254i
$328$	5.77632	−	5.00521i	0.318944	−	0.276366i
$329$	−0.0386709	−	0.268962i	−0.00213199	−	0.0148283i
$330$	−5.12820	−	1.85346i	−0.282298	−	0.102030i
$331$	−21.5598	+	13.8556i	−1.18503	+	0.761574i	−0.976305	−	0.216400i	$-0.930568\pi$
$331$	−21.5598	+	13.8556i	−1.18503	+	0.761574i	−0.208727	+	0.977974i	$0.566932\pi$
$332$	−2.45355	−	0.352768i	−0.134656	−	0.0193607i
$333$	6.69687	+	3.05836i	0.366986	+	0.167597i
$334$	0.0176971	−	0.0387512i	0.000968340	−	0.00212037i
$335$	−16.8986	−	3.49625i	−0.923271	−	0.191021i
$336$	−0.0875364	+	0.0562562i	−0.00477550	+	0.00306903i
$337$	1.26594	−	4.31139i	0.0689600	−	0.234856i	−0.917800	−	0.397043i	$-0.870036\pi$
$337$	1.26594	−	4.31139i	0.0689600	−	0.234856i	0.986760	+	0.162187i	$0.0518546\pi$
$338$	0.686826	−	0.0987507i	0.0373584	−	0.00537133i
$339$	3.32476	+	3.83698i	0.180576	+	0.208396i
$340$	−1.82928	+	2.49622i	−0.0992067	+	0.135376i
$341$	−11.3347	+	13.0809i	−0.613806	+	0.708370i
$342$	2.34647	+	7.99135i	0.126883	+	0.432123i
$343$	−0.394994	+	0.180388i	−0.0213277	+	0.00974001i
$344$	−20.8604			−1.12472
$345$	10.2967	+	2.99634i	0.554355	+	0.161317i
$346$	−3.39704			−0.182626
$347$	18.2071	−	8.31491i	0.977409	−	0.446368i	0.138335	−	0.990385i	$-0.455825\pi$
$347$	18.2071	−	8.31491i	0.977409	−	0.446368i	0.839074	+	0.544018i	$0.183098\pi$
$348$	−0.383107	−	1.30474i	−0.0205367	−	0.0699416i
$349$	−14.5805	+	16.8268i	−0.780476	+	0.900718i	−0.997144	−	0.0755278i	$-0.975936\pi$
$349$	−14.5805	+	16.8268i	−0.780476	+	0.900718i	0.216667	+	0.976245i	$0.430481\pi$
$350$	0.156278	+	0.129940i	0.00835344	+	0.00694557i
$351$	2.40874	+	2.77983i	0.128569	+	0.148377i
$352$	2.92292	−	0.420253i	0.155792	−	0.0223995i
$353$	−2.38350	+	8.11745i	−0.126861	+	0.432049i	−0.998289	−	0.0584749i	$-0.981376\pi$
$353$	−2.38350	+	8.11745i	−0.126861	+	0.432049i	0.871428	+	0.490523i	$0.163194\pi$
$354$	14.1691	−	9.10594i	0.753080	−	0.483975i
$355$	3.68342	−	17.8033i	0.195496	−	0.944901i
$356$	−0.642659	+	1.40723i	−0.0340609	+	0.0745829i
$357$	0.138112	+	0.0630737i	0.00730967	+	0.00333822i
$358$	−0.0901230	−	0.0129577i	−0.00476315	−	0.000684837i
$359$	13.7764	−	8.85357i	0.727092	−	0.467273i	−0.124006	−	0.992282i	$-0.539574\pi$
$359$	13.7764	−	8.85357i	0.727092	−	0.467273i	0.851097	+	0.525008i	$0.175938\pi$
$360$	2.27362	−	6.29072i	0.119830	−	0.331550i
$361$	−3.04475	−	21.1767i	−0.160250	−	1.11456i
$362$	−17.4382	+	15.1103i	−0.916530	+	0.794178i
$363$	−4.07484	+	6.34057i	−0.213874	+	0.332794i
$364$	0.0211258	−	0.0243805i	0.00110730	−	0.00127789i
$365$	0.880777	+	3.85925i	0.0461020	+	0.202002i
$366$	−3.79173	−	8.30273i	−0.198197	−	0.433991i
$367$		−	27.9432i		−	1.45862i	−0.684181	−	0.729312i	$-0.739840\pi$
$367$		−	27.9432i		−	1.45862i	0.684181	−	0.729312i	$-0.260160\pi$
$368$	15.7463	−	3.29759i	0.820834	−	0.171899i
$369$	2.55504			0.133010
$370$	−7.74437	−	20.1349i	−0.402611	−	1.04676i
$371$	−0.0131888	+	0.00387258i	−0.000684729	+	0.000201055i
$372$	−1.98753	−	1.72220i	−0.103048	−	0.0892920i
$373$	−8.24390	+	12.8278i	−0.426853	+	0.664196i	−0.986355	−	0.164633i	$-0.947356\pi$
$373$	−8.24390	+	12.8278i	−0.426853	+	0.664196i	0.559502	+	0.828829i	$0.310992\pi$
$374$	7.81680	+	9.02107i	0.404197	+	0.466468i
$375$	−11.1710	−	0.456616i	−0.576869	−	0.0235795i
$376$	25.1434	+	7.38277i	1.29667	+	0.380737i
$377$	−9.56390	−	14.8817i	−0.492566	−	0.766448i
$378$	−0.0402346	−	0.00578487i	−0.00206945	−	0.000297542i
$379$	−0.348353	+	0.762787i	−0.0178937	+	0.0391817i	−0.918368	−	0.395728i	$-0.870492\pi$
$379$	−0.348353	+	0.762787i	−0.0178937	+	0.0391817i	0.900474	+	0.434910i	$0.143220\pi$
$380$	−1.88976	+	3.54622i	−0.0969428	+	0.181917i
$381$	−0.263629	+	1.83358i	−0.0135061	+	0.0939372i
$382$	9.19995	+	14.3154i	0.470710	+	0.732439i
$383$	−3.75487	+	12.7879i	−0.191865	+	0.653432i	0.806222	+	0.591613i	$0.201509\pi$
$383$	−3.75487	+	12.7879i	−0.191865	+	0.653432i	−0.998087	+	0.0618196i	$0.980310\pi$
$384$	−1.18736	−	8.25830i	−0.0605924	−	0.421430i
$385$	−0.102535	+	0.0783984i	−0.00522567	+	0.00399555i
$386$	6.78286	+	4.35908i	0.345238	+	0.221871i
$387$	−5.27018	−	4.56664i	−0.267898	−	0.232135i
$388$	−1.39160	−	4.73936i	−0.0706479	−	0.240605i
$389$	3.23065	+	7.07415i	0.163801	+	0.358673i	0.973679	−	0.227925i	$-0.0731940\pi$
$389$	3.23065	+	7.07415i	0.163801	+	0.358673i	−0.809878	+	0.586598i	$0.800467\pi$
$390$	0.659396	−	10.7579i	0.0333898	−	0.544749i
$391$	−16.4699	−	16.7276i	−0.832919	−	0.845952i
$392$		−	20.9369i		−	1.05748i
$393$	8.50245	−	3.88294i	0.428892	−	0.195868i
$394$	−34.9713	+	10.2685i	−1.76183	+	0.517320i
$395$	−4.40478	+	4.49541i	−0.221629	+	0.226189i
$396$	0.442637	+	0.284465i	0.0222433	+	0.0142949i
$397$	−13.9655	+	12.1012i	−0.700910	+	0.607342i	−0.930650	−	0.365910i	$-0.880758\pi$
$397$	−13.9655	+	12.1012i	−0.700910	+	0.607342i	0.229740	+	0.973252i	$0.426212\pi$
$398$	19.2949	−	2.77419i	0.967165	−	0.139057i
$399$	0.189160	+	0.0555424i	0.00946984	+	0.00278060i
$400$	−15.1120	+	7.27692i	−0.755601	+	0.363846i
$401$	−1.49699	+	10.4118i	−0.0747562	+	0.519940i	0.917694	+	0.397289i	$0.130049\pi$
$401$	−1.49699	+	10.4118i	−0.0747562	+	0.519940i	−0.992450	+	0.122652i	$0.960860\pi$
$402$	−9.19922	−	4.20114i	−0.458815	−	0.209534i
$403$	−31.1203	−	14.2122i	−1.55021	−	0.707958i
$404$	0.667614	−	4.64335i	0.0332150	−	0.231016i
$405$	1.95154	−	1.09156i	0.0969726	−	0.0542401i
$406$	0.187573	+	0.0550764i	0.00930909	+	0.00273340i
$407$	13.5608	−	1.94975i	0.672184	−	0.0966455i
$408$	−11.0661	+	9.58879i	−0.547851	+	0.474716i
$409$	3.31574	+	2.13090i	0.163953	+	0.105366i	0.620044	−	0.784567i	$-0.287115\pi$
$409$	3.31574	+	2.13090i	0.163953	+	0.105366i	−0.456091	+	0.889933i	$0.650751\pi$
$410$	−5.34765	−	5.23984i	−0.264102	−	0.258777i
$411$	6.40322	−	1.88016i	0.315848	−	0.0927412i
$412$	−2.57558	+	1.17623i	−0.126890	+	0.0579485i
$413$		−	0.398680i		−	0.0196178i
$414$	5.49236	+	3.05464i	0.269935	+	0.150127i
$415$	−1.19930	+	19.5664i	−0.0588715	+	0.960478i
$416$	2.42472	+	5.30939i	0.118881	+	0.260314i
$417$	−3.16922	−	10.7934i	−0.155197	−	0.528554i
$418$	11.7133	+	10.1496i	0.572916	+	0.496434i
$419$	3.42368	+	2.20027i	0.167258	+	0.107490i	0.621592	−	0.783341i	$-0.286486\pi$
$419$	3.42368	+	2.20027i	0.167258	+	0.107490i	−0.454334	+	0.890831i	$0.650123\pi$
$420$	−0.0119119	−	0.0155793i	−0.000581243	−	0.000760191i
$421$	−1.60504	−	11.1633i	−0.0782247	−	0.544065i	−0.990819	−	0.135198i	$-0.956833\pi$
$421$	−1.60504	−	11.1633i	−0.0782247	−	0.544065i	0.912594	−	0.408867i	$-0.134076\pi$
$422$	5.09994	−	17.3688i	0.248261	−	0.845500i
$423$	4.73605	+	7.36944i	0.230275	+	0.358314i
$424$	0.188653	−	1.31211i	0.00916178	−	0.0637216i
$425$	20.8543	+	12.8098i	1.01158	+	0.621366i
$426$	4.42605	−	9.69171i	0.214443	−	0.469565i
$427$	−0.213856	−	0.0307478i	−0.0103492	−	0.00148799i
$428$	−0.354480	−	0.551581i	−0.0171344	−	0.0266617i
$429$	6.56758	+	1.92842i	0.317086	+	0.0931048i
$430$	1.66519	+	20.3659i	0.0803026	+	0.982129i
$431$	−18.5686	−	21.4293i	−0.894416	−	1.03221i	−0.999288	−	0.0377255i	$-0.987989\pi$
$431$	−18.5686	−	21.4293i	−0.894416	−	1.03221i	0.104872	−	0.994486i	$-0.466557\pi$
$432$	1.81361	−	2.82204i	0.0872575	−	0.135775i
$433$	−8.72488	−	7.56015i	−0.419291	−	0.363318i	0.419515	−	0.907749i	$-0.362200\pi$
$433$	−8.72488	−	7.56015i	−0.419291	−	0.363318i	−0.838806	+	0.544431i	$0.816746\pi$
$434$	0.362762	−	0.106517i	0.0174131	−	0.00511296i
$435$	−10.0372	+	3.86054i	−0.481246	+	0.185099i
$436$	−2.04368			−0.0978744
$437$	−24.2585	−	18.4553i	−1.16044	−	0.882836i
$438$			2.31985i			0.110847i
$439$	−1.16882	−	2.55936i	−0.0557847	−	0.122151i	0.879687	−	0.475553i	$-0.157752\pi$
$439$	−1.16882	−	2.55936i	−0.0557847	−	0.122151i	−0.935472	+	0.353402i	$0.885025\pi$
$440$	−2.76962	−	12.1355i	−0.132036	−	0.578536i
$441$	4.58340	−	5.28952i	0.218257	−	0.251882i
$442$	−12.7558	+	19.8484i	−0.606731	+	0.944091i
$443$	21.2507	−	18.4139i	1.00965	−	0.874869i	0.0174932	−	0.999847i	$-0.494431\pi$
$443$	21.2507	−	18.4139i	1.00965	−	0.874869i	0.992160	+	0.124978i	$0.0398860\pi$
$444$	0.296247	+	2.06044i	0.0140593	+	0.0977843i
$445$	11.5060	+	4.15857i	0.545439	+	0.197135i
$446$	21.1317	−	13.5805i	1.00062	−	0.643056i
$447$	20.8402	+	2.99637i	0.985708	+	0.141723i
$448$	−0.247977	−	0.113247i	−0.0117158	−	0.00535044i
$449$	−7.84595	+	17.1802i	−0.370273	+	0.810786i	0.629165	+	0.777272i	$0.283397\pi$
$449$	−7.84595	+	17.1802i	−0.370273	+	0.810786i	−0.999438	+	0.0335138i	$0.989330\pi$
$450$	−6.32308	−	1.71756i	−0.298073	−	0.0809667i
$451$	3.99989	−	2.57057i	0.188347	−	0.121044i
$452$	−0.404433	+	1.37737i	−0.0190229	+	0.0647861i
$453$	8.56393	−	1.23131i	0.402368	−	0.0578518i
$454$	17.4517	+	20.1403i	0.819049	+	0.945233i
$455$	−0.205784	−	0.150803i	−0.00964730	−	0.00706975i
$456$	−12.4504	+	14.3686i	−0.583046	+	0.672871i
$457$	4.20077	+	14.3065i	0.196504	+	0.669230i	0.997507	+	0.0705701i	$0.0224818\pi$
$457$	4.20077	+	14.3065i	0.196504	+	0.669230i	−0.801003	+	0.598660i	$0.795700\pi$
$458$	−0.370265	+	0.169094i	−0.0173013	+	0.00790126i
$459$	−4.89486			−0.228472
$460$	0.861285	+	2.90723i	0.0401576	+	0.135550i
$461$	23.7520			1.10624			0.553120	−	0.833102i	$-0.313437\pi$
$461$	23.7520			1.10624			0.553120	+	0.833102i	$0.313437\pi$
$462$	−0.0688069	+	0.0314230i	−0.00320119	+	0.00146193i
$463$	6.40709	+	21.8205i	0.297763	+	1.01409i	0.963457	+	0.267862i	$0.0863172\pi$
$463$	6.40709	+	21.8205i	0.297763	+	1.01409i	−0.665695	+	0.746224i	$0.731865\pi$
$464$	−10.5650	+	12.1927i	−0.490468	+	0.566030i
$465$	−12.2936	+	16.7757i	−0.570102	+	0.777955i
$466$	−6.33826	−	7.31474i	−0.293614	−	0.338849i
$467$	3.32793	−	0.478484i	0.153998	−	0.0221416i	−0.0648844	−	0.997893i	$-0.520668\pi$
$467$	3.32793	−	0.478484i	0.153998	−	0.0221416i	0.218883	+	0.975751i	$0.429759\pi$
$468$	−0.293006	+	0.997886i	−0.0135442	+	0.0461273i
$469$	−0.201382	+	0.129421i	−0.00929897	+	0.00597609i
$470$	5.20067	−	25.1367i	0.239889	−	1.15947i
$471$	−1.01678	+	2.22643i	−0.0468505	+	0.102588i
$472$	34.9735	+	15.9719i	1.60979	+	0.735165i
$473$	−12.8448	−	1.84680i	−0.590604	−	0.0849161i
$474$	−3.10289	+	1.99410i	−0.142520	+	0.0915922i
$475$	29.1694	+	12.6098i	1.33838	+	0.578578i
$476$	0.00610962	+	0.0424934i	0.000280034	+	0.00194768i
$477$	0.334900	−	0.290193i	0.0153340	−	0.0132870i
$478$	−6.34533	+	9.87352i	−0.290229	+	0.451604i
$479$	1.89392	−	2.18570i	0.0865356	−	0.0998674i	−0.710830	−	0.703363i	$-0.751681\pi$
$479$	1.89392	−	2.18570i	0.0865356	−	0.0998674i	0.797366	+	0.603496i	$0.206226\pi$
$480$	3.45937	−	0.789515i	0.157898	−	0.0360362i
$481$	11.2494	+	24.6327i	0.512928	+	1.12316i
$482$		−	3.23310i		−	0.147264i
$483$	0.131114	−	0.0702780i	0.00596590	−	0.00319776i
$484$	−2.13108			−0.0968673
$485$	−36.4591	+	14.0231i	−1.65552	+	0.636755i
$486$	1.25736	−	0.369194i	0.0570349	−	0.0167470i
$487$	−24.8628	−	21.5437i	−1.12664	−	0.976239i	−0.126762	−	0.991933i	$-0.540459\pi$
$487$	−24.8628	−	21.5437i	−1.12664	−	0.976239i	−0.999877	+	0.0156946i	$0.995004\pi$
$488$	11.2648	−	17.5283i	0.509931	−	0.793469i
$489$	1.66062	+	1.91645i	0.0750957	+	0.0866651i
$490$	−20.4406	+	1.67130i	−0.923412	+	0.0755017i
$491$	8.48703	+	2.49202i	0.383014	+	0.112463i	0.467571	−	0.883956i	$-0.345129\pi$
$491$	8.48703	+	2.49202i	0.383014	+	0.112463i	−0.0845568	+	0.996419i	$0.526947\pi$
$492$	0.390575	+	0.607747i	0.0176085	+	0.0273994i
$493$	23.3014	+	3.35024i	1.04944	+	0.150887i
$494$	−12.7263	+	27.8667i	−0.572582	+	1.25378i
$495$	1.95691	−	3.67222i	0.0879566	−	0.165054i
$496$	−4.44041	+	30.8837i	−0.199380	+	1.38672i
$497$	−0.136349	−	0.212163i	−0.00611610	−	0.00951683i
$498$	−3.23665	+	11.0230i	−0.145038	+	0.493952i
$499$	5.87535	+	40.8639i	0.263017	+	1.82932i	0.509851	+	0.860263i	$0.329701\pi$
$499$	5.87535	+	40.8639i	0.263017	+	1.82932i	−0.246834	+	0.969058i	$0.579390\pi$
$500$	−1.59904	−	2.72696i	−0.0715113	−	0.121953i
$501$	0.0273482	+	0.0175756i	0.00122183	+	0.000785221i
$502$	−5.73173	−	4.96657i	−0.255820	−	0.221669i
$503$	6.80021	+	23.1594i	0.303206	+	1.03263i	0.960335	+	0.278848i	$0.0899525\pi$
$503$	6.80021	+	23.1594i	0.303206	+	1.03263i	−0.657129	+	0.753778i	$0.728229\pi$
$504$	−0.0385464	−	0.0844047i	−0.00171699	−	0.00375969i
$505$	−37.0295	−	2.26968i	−1.64779	−	0.101000i
$506$	11.6714	−	0.743739i	0.518858	−	0.0330632i
$507$			0.529508i			0.0235163i
$508$	−0.476439	+	0.217582i	−0.0211385	+	0.00965365i
$509$	27.5018	−	8.07525i	1.21899	−	0.357929i	0.391909	−	0.920004i	$-0.371815\pi$
$509$	27.5018	−	8.07525i	1.21899	−	0.357929i	0.827086	+	0.562075i	$0.189997\pi$
$510$	10.2448	+	10.0383i	0.453649	+	0.444503i
$511$	0.0461951	+	0.0296878i	0.00204355	+	0.00131331i
$512$	19.1907	−	16.6288i	0.848116	−	0.734896i
$513$	−6.29097	+	0.904506i	−0.277753	+	0.0399349i
$514$	26.0178	+	7.63950i	1.14759	+	0.336964i
$515$	10.9310	+	19.5428i	0.481676	+	0.861160i
$516$	0.280605	−	1.95165i	0.0123530	−	0.0859167i
$517$	14.8285	+	6.77193i	0.652155	+	0.297829i
$518$	−0.272217	−	0.124317i	−0.0119605	−	0.00546219i
$519$	0.368922	−	2.56591i	0.0161939	−	0.112631i
$520$	21.4730	−	12.0106i	0.941653	−	0.526699i
$521$	24.7233	+	7.25941i	1.08315	+	0.318040i	0.774137	−	0.633019i	$-0.218184\pi$
$521$	24.7233	+	7.25941i	1.08315	+	0.318040i	0.309009	+	0.951059i	$0.400003\pi$
$522$	−6.23820	+	0.896918i	−0.273039	+	0.0392570i
$523$	4.46195	−	3.86630i	0.195107	−	0.169061i	−0.551828	−	0.833958i	$-0.686070\pi$
$523$	4.46195	−	3.86630i	0.195107	−	0.169061i	0.746936	+	0.664896i	$0.231524\pi$
$524$	2.22333	+	1.42885i	0.0971265	+	0.0624194i
$525$	−0.115120	+	0.103931i	−0.00502425	+	0.00453592i
$526$	−14.3247	+	4.20612i	−0.624587	+	0.183395i
$527$	41.4136	−	18.9129i	1.80400	−	0.823861i
$528$		−	6.24250i		−	0.271670i
$529$	−22.8140	+	2.91941i	−0.991912	+	0.126931i
$530$	−1.29606	−	0.0794407i	−0.0562973	−	0.00345068i
$531$	5.33926	+	11.6913i	0.231704	+	0.507361i
$532$	0.0157044	+	0.0534844i	0.000680874	+	0.00231884i
$533$	7.10260	+	6.15443i	0.307648	+	0.266578i
$534$	6.03177	+	3.87638i	0.261020	+	0.167748i
$535$	−4.11915	+	3.14951i	−0.178086	+	0.136165i
$536$	−3.28544	−	22.8507i	−0.141909	−	0.987001i
$537$	0.0195749	−	0.0666658i	0.000844717	−	0.00287684i
$538$	3.00495	+	4.67579i	0.129553	+	0.201588i
$539$	1.85358	−	12.8919i	0.0798393	−	0.555295i
$540$	0.557962	+	0.297335i	0.0240108	+	0.0127953i
$541$	−2.88543	+	6.31821i	−0.124054	+	0.271641i	−0.961462	−	0.274938i	$-0.911343\pi$
$541$	−2.88543	+	6.31821i	−0.124054	+	0.271641i	0.837408	+	0.546579i	$0.184070\pi$
$542$	−10.4735	−	1.50586i	−0.449875	−	0.0646823i
$543$	−9.51951	−	14.8127i	−0.408521	−	0.635672i
$544$	−7.45280	−	2.18834i	−0.319536	−	0.0938243i
$545$	1.31708	+	16.1084i	0.0564177	+	0.690008i
$546$	−0.0979114	−	0.112996i	−0.00419022	−	0.00483577i
$547$	−24.9135	+	38.7662i	−1.06523	+	1.65752i	−0.388176	+	0.921585i	$0.626895\pi$
$547$	−24.9135	+	38.7662i	−1.06523	+	1.65752i	−0.677049	+	0.735938i	$0.736741\pi$
$548$	1.42604	+	1.23567i	0.0609175	+	0.0527853i
$549$	6.68313	−	1.96234i	0.285229	−	0.0837508i
$550$	−11.6267	+	3.67268i	−0.495764	+	0.156604i
$551$	30.5665			1.30218
$552$	0.912337	+	14.3172i	0.0388316	+	0.609382i
$553$			0.0873068i			0.00371266i
$554$	−2.63202	−	5.76333i	−0.111824	−	0.244860i
$555$	16.0496	−	3.66293i	0.681269	−	0.155483i
$556$	2.08287	−	2.40376i	0.0883334	−	0.101942i
$557$	1.55973	−	2.42699i	0.0660881	−	0.102835i	−0.806637	−	0.591048i	$-0.798715\pi$
$557$	1.55973	−	2.42699i	0.0660881	−	0.102835i	0.872725	+	0.488213i	$0.162351\pi$
$558$	−9.21153	+	7.98184i	−0.389955	+	0.337898i
$559$	−3.65039	−	25.3890i	−0.154395	−	1.07384i
$560$	−0.0790870	+	0.218820i	−0.00334204	+	0.00924683i
$561$	−7.66284	+	4.92461i	−0.323525	+	0.207917i
$562$	−38.7517	−	5.57165i	−1.63464	−	0.235026i
$563$	12.0623	+	5.50868i	0.508366	+	0.232163i	0.653050	−	0.757315i	$-0.273489\pi$
$563$	12.0623	+	5.50868i	0.508366	+	0.232163i	−0.144684	+	0.989478i	$0.546216\pi$
$564$	−1.02893	+	2.25305i	−0.0433259	+	0.0948706i
$565$	11.1172	+	2.30010i	0.467703	+	0.0967657i
$566$	−33.7369	+	21.6814i	−1.41807	+	0.911336i
$567$	0.00873903	−	0.0297624i	0.000367005	−	0.00124990i
$568$	24.0741	−	3.46133i	1.01012	−	0.145234i
$569$	6.92276	+	7.98929i	0.290217	+	0.334929i	0.882071	−	0.471117i	$-0.156149\pi$
$569$	6.92276	+	7.98929i	0.290217	+	0.334929i	−0.591853	+	0.806046i	$0.701604\pi$
$570$	15.0218	+	11.0083i	0.629195	+	0.461087i
$571$	−7.02705	+	8.10964i	−0.294073	+	0.339378i	−0.883489	−	0.468451i	$-0.844812\pi$
$571$	−7.02705	+	8.10964i	−0.294073	+	0.339378i	0.589417	+	0.807829i	$0.299358\pi$
$572$	0.545254	+	1.85696i	0.0227982	+	0.0776436i
$573$	−11.8120	+	5.39438i	−0.493455	+	0.225353i
$574$	−0.103858			−0.00433496
$575$	22.3599	−	8.66232i	0.932471	−	0.361244i
$576$	8.78860			0.366192
$577$	21.1006	−	9.63634i	0.878431	−	0.401166i	0.0754353	−	0.997151i	$-0.475965\pi$
$577$	21.1006	−	9.63634i	0.878431	−	0.401166i	0.802996	+	0.595985i	$0.203238\pi$
$578$	−2.56945	−	8.75075i	−0.106875	−	0.363983i
$579$	−4.02919	+	4.64993i	−0.167447	+	0.193244i
$580$	−2.45260	−	1.79732i	−0.101839	−	0.0746297i
$581$	0.178080	+	0.205516i	0.00738802	+	0.00852623i
$582$	−22.6597	+	3.25797i	−0.939275	+	0.135047i
$583$	0.232326	−	0.791229i	0.00962195	−	0.0327694i
$584$	−4.45497	+	2.86304i	−0.184348	+	0.118473i
$585$	8.05424	+	1.66639i	0.333002	+	0.0688965i
$586$	−12.6911	+	27.7896i	−0.524264	+	1.14798i
$587$	−12.5510	−	5.73185i	−0.518035	−	0.236579i	0.139200	−	0.990264i	$-0.455547\pi$
$587$	−12.5510	−	5.73185i	−0.518035	−	0.236579i	−0.657235	+	0.753686i	$0.728274\pi$
$588$	1.95881	+	0.281635i	0.0807801	+	0.0116144i
$589$	49.7307	−	31.9600i	2.04912	−	1.31689i
$590$	12.8015	−	35.4194i	0.527027	−	1.45819i
$591$	−3.95825	−	27.5302i	−0.162821	−	1.13244i
$592$	18.6646	−	16.1730i	0.767112	−	0.664706i
$593$	15.1585	−	23.5871i	0.622486	−	0.968608i	−0.376621	−	0.926367i	$-0.622914\pi$
$593$	15.1585	−	23.5871i	0.622486	−	0.968608i	0.999107	−	0.0422403i	$-0.0134495\pi$
$594$	1.59694	−	1.84297i	0.0655233	−	0.0756179i
$595$	0.330998	−	0.0755421i	0.0135696	−	0.00309692i
$596$	2.47301	+	5.41513i	0.101298	+	0.221812i
$597$			14.8754i			0.608809i
$598$	7.91001	+	21.7211i	0.323464	+	0.888240i
$599$	−17.9452			−0.733220			−0.366610	−	0.930375i	$-0.619482\pi$
$599$	−17.9452			−0.733220			−0.366610	+	0.930375i	$0.619482\pi$
$600$	−4.50525	−	14.2624i	−0.183926	−	0.582259i
$601$	−13.9517	+	4.09658i	−0.569101	+	0.167103i	−0.553609	−	0.832777i	$-0.686750\pi$
$601$	−13.9517	+	4.09658i	−0.569101	+	0.167103i	−0.0154922	+	0.999880i	$0.504932\pi$
$602$	0.214224	+	0.185626i	0.00873113	+	0.00756557i
$603$	4.17231	−	6.49225i	0.169910	−	0.264385i
$604$	1.60200	+	1.84881i	0.0651845	+	0.0752270i
$605$	1.37341	+	16.7973i	0.0558372	+	0.682908i
$606$	−20.8610	−	6.12535i	−0.847422	−	0.248825i
$607$	−11.5298	−	17.9407i	−0.467980	−	0.728191i	0.524391	−	0.851477i	$-0.324293\pi$
$607$	−11.5298	−	17.9407i	−0.467980	−	0.728191i	−0.992371	+	0.123287i	$0.960657\pi$
$608$	−9.98287	−	1.43532i	−0.404859	−	0.0582099i
$609$	−0.0619717	+	0.135699i	−0.00251122	+	0.00549881i
$610$	−18.0120	−	9.59850i	−0.729284	−	0.388632i
$611$	−4.58563	+	31.8937i	−0.185515	+	1.29028i
$612$	−0.748250	−	1.16430i	−0.0302462	−	0.0470640i
$613$	7.51761	−	25.6026i	0.303634	−	1.03408i	−0.656451	−	0.754369i	$-0.727943\pi$
$613$	7.51761	−	25.6026i	0.303634	−	1.03408i	0.960084	−	0.279712i	$-0.0902389\pi$
$614$	−5.19779	−	36.1514i	−0.209766	−	1.45895i
$615$	4.53859	−	3.47022i	0.183014	−	0.139933i
$616$	−0.145262	−	0.0933540i	−0.00585276	−	0.00376134i
$617$	24.6486	+	21.3582i	0.992317	+	0.859847i	0.990130	−	0.140150i	$-0.0447585\pi$
$617$	24.6486	+	21.3582i	0.992317	+	0.859847i	0.00218656	+	0.999998i	$0.499304\pi$
$618$	3.69713	+	12.5913i	0.148720	+	0.506495i
$619$	11.5193	+	25.2237i	0.462999	+	1.01383i	0.986794	+	0.161982i	$0.0517886\pi$
$619$	11.5193	+	25.2237i	0.462999	+	1.01383i	−0.523795	+	0.851844i	$0.675484\pi$
$620$	−5.86956	−	0.359768i	−0.235727	−	0.0144486i
$621$	−2.90375	+	3.81683i	−0.116524	+	0.153164i
$622$		−	37.9952i		−	1.52347i
$623$	0.154381	−	0.0705033i	0.00618513	−	0.00282465i
$624$	11.8391	−	3.47627i	0.473943	−	0.139162i
$625$	−20.4635	+	14.3612i	−0.818542	+	0.574447i
$626$	30.0463	+	19.3096i	1.20089	+	0.771767i
$627$	−8.93844	+	7.74520i	−0.356967	+	0.309314i
$628$	−0.685011	+	0.0984897i	−0.0273349	+	0.00393017i
$629$	−34.5770	−	10.1527i	−1.37868	−	0.404816i
$630$	−0.0793268	+	0.0443702i	−0.00316046	+	0.00176775i
$631$	5.65806	−	39.3527i	0.225244	−	1.56660i	−0.492509	−	0.870307i	$-0.663920\pi$
$631$	5.65806	−	39.3527i	0.225244	−	1.56660i	0.717753	−	0.696298i	$-0.245171\pi$
$632$	−7.65883	−	3.49767i	−0.304652	−	0.139130i
$633$	12.5654	+	5.73843i	0.499430	+	0.228082i
$634$	2.28794	−	15.9130i	0.0908656	−	0.631984i
$635$	2.02205	+	3.61510i	0.0802425	+	0.143461i
$636$	0.120220	+	0.0352998i	0.00476704	+	0.00139973i
$637$	25.4822	−	3.66378i	1.00964	−	0.145164i
$638$	−8.86345	+	7.68023i	−0.350907	+	0.304063i
$639$	6.83981	+	4.39568i	0.270579	+	0.173890i
$640$	−13.3254	−	13.0568i	−0.526734	−	0.516115i
$641$	−8.80729	+	2.58605i	−0.347867	+	0.102143i	−0.450998	−	0.892525i	$-0.648932\pi$
$641$	−8.80729	+	2.58605i	−0.347867	+	0.102143i	0.103131	+	0.994668i	$0.467114\pi$
$642$	−2.76419	+	1.26236i	−0.109094	+	0.0498214i
$643$			18.7996i			0.741385i	0.928756	+	0.370692i	$0.120880\pi$
$643$			18.7996i			0.741385i	−0.928756	+	0.370692i	$0.879120\pi$
$644$	0.0367592	+	0.0204441i	0.00144851	+	0.000805609i
$645$	−15.5639	−	0.953972i	−0.612828	−	0.0375626i
$646$	−16.9356	−	37.0838i	−0.666322	−	1.45904i
$647$	6.17805	+	21.0405i	0.242884	+	0.827188i	0.987217	+	0.159379i	$0.0509493\pi$
$647$	6.17805	+	21.0405i	0.242884	+	0.827188i	−0.744333	+	0.667808i	$0.767233\pi$
$648$	2.26075	+	1.95895i	0.0888107	+	0.0769549i
$649$	20.1209	+	12.9309i	0.789816	+	0.507584i
$650$	−13.4399	−	20.0052i	−0.527158	−	0.784668i
$651$	0.0410595	+	0.285575i	0.00160925	+	0.0111926i
$652$	−0.202002	+	0.687955i	−0.00791101	+	0.0269424i
$653$	−22.1268	−	34.4299i	−0.865888	−	1.34735i	−0.936800	−	0.349865i	$-0.886227\pi$
$653$	−22.1268	−	34.4299i	−0.865888	−	1.34735i	0.0709122	−	0.997483i	$-0.477409\pi$
$654$	−1.34797	+	9.37537i	−0.0527100	+	0.366606i
$655$	9.82939	−	18.4453i	0.384066	−	0.720716i
$656$	3.56054	−	7.79650i	0.139016	−	0.304402i
$657$	−1.75227	−	0.251938i	−0.0683624	−	0.00982903i
$658$	−0.192513	−	0.299556i	−0.00750493	−	0.0116779i
$659$	−1.79752	−	0.527798i	−0.0700213	−	0.0205601i	0.246534	−	0.969134i	$-0.420708\pi$
$659$	−1.79752	−	0.527798i	−0.0700213	−	0.0205601i	−0.316556	+	0.948574i	$0.602526\pi$
$660$	1.17262	−	0.0958782i	0.0456443	−	0.00373206i
$661$	−22.9040	−	26.4326i	−0.890861	−	1.02811i	−0.999421	−	0.0340183i	$-0.989170\pi$
$661$	−22.9040	−	26.4326i	−0.890861	−	1.02811i	0.108560	−	0.994090i	$-0.465376\pi$
$662$	−18.1570	+	28.2528i	−0.705690	+	1.09808i
$663$	−13.6069	−	11.7904i	−0.528448	−	0.457903i
$664$	−25.1627	+	7.38844i	−0.976503	+	0.286727i
$665$	0.411447	−	0.158252i	0.0159552	−	0.00613676i
$666$	9.64768			0.373840
$667$	16.4354	−	16.1822i	0.636380	−	0.626576i
$668$			0.00919178i			0.000355641i
$669$	7.96293	+	17.4364i	0.307865	+	0.674129i
$670$	−22.0468	+	5.03162i	−0.851740	+	0.194389i
$671$	8.48808	−	9.79577i	0.327679	−	0.378162i
$672$	0.0266117	−	0.0414086i	0.00102657	−	0.00159737i
$673$	−29.4259	+	25.4977i	−1.13428	+	0.982863i	−0.999967	−	0.00807529i	$-0.997430\pi$
$673$	−29.4259	+	25.4977i	−1.13428	+	0.982863i	−0.134317	+	0.990938i	$0.542884\pi$
$674$	−0.837997	−	5.82840i	−0.0322785	−	0.224502i
$675$	1.98403	−	4.58951i	0.0763653	−	0.176650i
$676$	−0.125950	+	0.0809431i	−0.00484423	+	0.00311319i
$677$	−14.5768	−	2.09583i	−0.560233	−	0.0805494i	−0.143619	−	0.989633i	$-0.545874\pi$
$677$	−14.5768	−	2.09583i	−0.560233	−	0.0805494i	−0.416614	+	0.909084i	$0.636783\pi$
$678$	6.05194	+	2.76383i	0.232423	+	0.106144i
$679$	−0.225107	+	0.492915i	−0.00863880	+	0.0189163i
$680$	−6.63360	+	32.0626i	−0.254387	+	1.22954i
$681$	−17.1080	+	10.9946i	−0.655579	+	0.421315i
$682$	−6.39019	+	21.7630i	−0.244693	+	0.833348i
$683$	−15.9874	+	2.29865i	−0.611743	+	0.0879553i	−0.441221	−	0.897399i	$-0.645454\pi$
$683$	−15.9874	+	2.29865i	−0.611743	+	0.0879553i	−0.170522	+	0.985354i	$0.554545\pi$
$684$	−1.17681	−	1.35812i	−0.0449966	−	0.0519289i
$685$	8.82062	−	12.0365i	0.337019	−	0.459892i
$686$	−0.372641	+	0.430051i	−0.0142275	+	0.0164194i
$687$	−0.0875118	−	0.298038i	−0.00333878	−	0.0113709i
$688$	−21.2789	+	9.71774i	−0.811250	+	0.370485i
$689$	1.62997			0.0620968
$690$	13.9050	−	2.03359i	0.529354	−	0.0774174i
$691$	17.9274			0.681992			0.340996	−	0.940065i	$-0.389236\pi$
$691$	17.9274			0.681992			0.340996	+	0.940065i	$0.389236\pi$
$692$	0.666727	−	0.304484i	0.0253451	−	0.0115747i
$693$	−0.0162625	−	0.0553848i	−0.000617759	−	0.00210390i
$694$	17.1768	−	19.8230i	0.652021	−	0.752473i
$695$	−20.2890	−	14.8682i	−0.769604	−	0.563983i
$696$	−9.42126	−	10.8727i	−0.357112	−	0.412129i
$697$	−12.3793	+	1.77987i	−0.468898	+	0.0674174i
$698$	−8.22011	+	27.9951i	−0.311136	+	1.05963i
$699$	6.21342	−	3.99312i	0.235013	−	0.151034i
$700$	−0.0423190	−	0.0114953i	−0.00159951	−	0.000434481i
$701$	16.0177	−	35.0739i	0.604981	−	1.32472i	−0.320974	−	0.947088i	$-0.604010\pi$
$701$	16.0177	−	35.0739i	0.604981	−	1.32472i	0.925955	−	0.377635i	$-0.123263\pi$
$702$	4.38454	+	2.00235i	0.165484	+	0.0755739i
$703$	−46.3152	−	6.65913i	−1.74681	−	0.251154i
$704$	13.7584	−	8.84202i	0.518541	−	0.333246i
$705$	18.4218	+	6.65811i	0.693806	+	0.250759i
$706$	1.57778	+	10.9737i	0.0593804	+	0.413000i
$707$	−0.388939	+	0.337017i	−0.0146275	+	0.0126748i
$708$	−1.96474	+	3.05720i	−0.0738395	+	0.114897i
$709$	−6.41040	+	7.39799i	−0.240748	+	0.277837i	−0.863246	−	0.504784i	$-0.831572\pi$
$709$	−6.41040	+	7.39799i	−0.240748	+	0.277837i	0.622498	+	0.782621i	$0.286118\pi$
$710$	−5.30099	−	23.2270i	−0.198943	−	0.871695i
$711$	−1.16924	−	2.56028i	−0.0438500	−	0.0960180i
$712$			16.3672i			0.613389i
$713$	9.81993	−	43.5125i	0.367759	−	1.62955i
$714$	0.198968			0.00744619
$715$	14.2853	−	5.49448i	0.534241	−	0.205482i
$716$	0.0188496	−	0.00553473i	0.000704441	−	0.000206843i
$717$	−6.76871	−	5.86512i	−0.252782	−	0.219037i
$718$	11.6021	−	18.0532i	0.432985	−	0.673738i
$719$	−26.7685	−	30.8925i	−0.998298	−	1.15210i	−0.988358	−	0.152146i	$-0.951382\pi$
$719$	−26.7685	−	30.8925i	−0.998298	−	1.15210i	−0.00993950	−	0.999951i	$-0.503164\pi$
$720$	−0.611273	−	7.47608i	−0.0227808	−	0.278617i
$721$	0.298043	+	0.0875133i	0.0110997	+	0.00325916i
$722$	−15.1575	−	23.5856i	−0.564104	−	0.877763i
$723$	2.44208	+	0.351117i	0.0908218	+	0.0130582i
$724$	2.06817	−	4.52866i	0.0768629	−	0.168306i
$725$	−12.5860	+	20.4899i	−0.467432	+	0.760976i
$726$	−1.40562	+	9.77633i	−0.0521676	+	0.362834i
$727$	−5.69978	−	8.86903i	−0.211393	−	0.328934i	0.719324	−	0.694675i	$-0.244452\pi$
$727$	−5.69978	−	8.86903i	−0.211393	−	0.328934i	−0.930717	+	0.365741i	$0.880816\pi$
$728$	0.0961566	−	0.327479i	0.00356380	−	0.0121372i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	3.15078	+	4.12082i	0.116616	+	0.152518i
$731$	28.7154	+	18.4543i	1.06208	+	0.682555i
$732$	1.48838	+	1.28969i	0.0550121	+	0.0476683i
$733$	−2.28296	−	7.77504i	−0.0843230	−	0.287178i	0.906527	−	0.422149i	$-0.138724\pi$
$733$	−2.28296	−	7.77504i	−0.0843230	−	0.287178i	−0.990850	+	0.134971i	$0.956906\pi$
$734$	−15.2116	−	33.3088i	−0.561471	−	1.22945i
$735$	0.957473	−	15.6210i	0.0353169	−	0.576190i
$736$	−6.12757	+	4.51325i	−0.225865	+	0.166361i
$737$		−	14.3612i		−	0.529002i
$738$	3.04566	−	1.39091i	0.112112	−	0.0511999i
$739$	−12.4741	+	3.66272i	−0.458866	+	0.134735i	−0.502993	−	0.864291i	$-0.667768\pi$
$739$	−12.4741	+	3.66272i	−0.458866	+	0.134735i	0.0441263	+	0.999026i	$0.485950\pi$
$740$	3.32469	+	3.25766i	0.122218	+	0.119754i
$741$	−19.6666	−	12.6389i	−0.722470	−	0.464303i
$742$	−0.0136132	+	0.0117959i	−0.000499755	+	0.000433040i
$743$	27.5882	−	3.96658i	1.01211	−	0.145520i	0.383746	−	0.923438i	$-0.374634\pi$
$743$	27.5882	−	3.96658i	1.01211	−	0.145520i	0.628365	+	0.777919i	$0.283725\pi$
$744$	−26.6965	−	7.83879i	−0.978740	−	0.287384i
$745$	41.0887	−	22.9823i	1.50537	−	0.842006i
$746$	−2.84375	+	19.7787i	−0.104117	+	0.724150i
$747$	−7.97456	−	3.64186i	−0.291774	−	0.133249i
$748$	−2.34275	−	1.06990i	−0.0856595	−	0.0391194i
$749$	−0.0102367	+	0.0711980i	−0.000374042	+	0.00260152i
$750$	−13.5646	+	5.53694i	−0.495310	+	0.202181i
$751$	13.7719	+	4.04379i	0.502543	+	0.147560i	0.523172	−	0.852227i	$-0.324749\pi$
$751$	13.7719	+	4.04379i	0.502543	+	0.147560i	−0.0206286	+	0.999787i	$0.506567\pi$
$752$	29.0871	−	4.18209i	1.06070	−	0.152505i
$753$	4.37390	−	3.79000i	0.159394	−	0.138115i
$754$	−19.5016	−	12.5329i	−0.710206	−	0.456422i
$755$	13.5400	−	13.8186i	0.492771	−	0.502910i
$756$	0.00841523	−	0.00247093i	0.000306059	−	8.98670e-5i
$757$	34.4078	−	15.7135i	1.25057	−	0.571118i	0.323582	−	0.946200i	$-0.395113\pi$
$757$	34.4078	−	15.7135i	1.25057	−	0.571118i	0.926991	+	0.375082i	$0.122386\pi$
$758$			1.09889i			0.0399135i
$759$	−0.705754	+	8.89661i	−0.0256173	+	0.322926i
$760$	−2.60090	+	42.4333i	−0.0943447	+	1.53922i
$761$	11.9314	+	26.1261i	0.432513	+	0.947071i	0.992912	+	0.118849i	$0.0379204\pi$
$761$	11.9314	+	26.1261i	0.432513	+	0.947071i	−0.560399	+	0.828223i	$0.689352\pi$
$762$	0.683908	+	2.32918i	0.0247754	+	0.0843771i
$763$	0.169441	+	0.146821i	0.00613418	+	0.00531529i
$764$	−3.08876	−	1.98503i	−0.111747	−	0.0718157i
$765$	−8.69487	+	6.64811i	−0.314364	+	0.240363i
$766$	2.48557	+	17.2875i	0.0898072	+	0.624623i
$767$	−13.3192	+	45.3609i	−0.480927	+	1.63789i
$768$	3.59197	+	5.58921i	0.129614	+	0.201683i
$769$	7.39936	−	51.4637i	0.266828	−	1.85583i	−0.211147	−	0.977454i	$-0.567720\pi$
$769$	7.39936	−	51.4637i	0.266828	−	1.85583i	0.477975	−	0.878374i	$-0.341371\pi$
$770$	−0.0795453	+	0.149270i	−0.00286661	+	0.00537932i
$771$	−8.59594	+	18.8225i	−0.309575	+	0.677875i
$772$	−1.72196	−	0.247581i	−0.0619747	−	0.00891062i
$773$	17.3670	+	27.0236i	0.624648	+	0.971971i	0.999001	+	0.0446846i	$0.0142283\pi$
$773$	17.3670	+	27.0236i	0.624648	+	0.971971i	−0.374354	+	0.927286i	$0.622135\pi$
$774$	−8.76812	−	2.57455i	−0.315164	−	0.0925404i
$775$	0.947025	+	46.4961i	0.0340182	+	1.67019i
$776$	−34.2219	−	39.4942i	−1.22849	−	1.41776i
$777$	0.123464	−	0.192114i	0.00442925	−	0.00689205i
$778$	7.70200	+	6.67382i	0.276130	+	0.239268i
$779$	−15.5812	+	4.57505i	−0.558255	+	0.163918i
$780$	0.834838	+	2.17053i	0.0298920	+	0.0777173i
$781$	15.1300			0.541395
$782$	−28.7386	−	10.9738i	−1.02769	−	0.392422i
$783$		−	4.80934i		−	0.171872i
$784$	−9.75340	−	21.3570i	−0.348336	−	0.762749i
$785$	1.21777	+	5.33583i	0.0434641	+	0.190444i
$786$	8.02130	−	9.25707i	0.286110	−	0.330189i
$787$	−15.6369	+	24.3315i	−0.557395	+	0.867323i	−0.999562	−	0.0296098i	$-0.990574\pi$
$787$	−15.6369	+	24.3315i	−0.557395	+	0.867323i	0.442167	+	0.896933i	$0.354210\pi$
$788$	5.94332	−	5.14991i	0.211722	−	0.183458i
$789$	−1.62135	−	11.2767i	−0.0577217	−	0.401463i
$790$	−2.80338	+	7.75647i	−0.0997399	+	0.275963i
$791$	0.132484	−	0.0851425i	0.00471060	−	0.00302732i
$792$	5.51004	+	0.792224i	0.195791	+	0.0281504i
$793$	23.3048	+	10.6429i	0.827576	+	0.377941i
$794$	−10.0596	+	22.0274i	−0.357000	+	0.781722i
$795$	0.200758	−	0.970333i	0.00712014	−	0.0344142i
$796$	−3.53829	+	2.27392i	−0.125411	+	0.0805969i
$797$	−8.33073	+	28.3719i	−0.295090	+	1.00498i	0.669847	+	0.742499i	$0.266360\pi$
$797$	−8.33073	+	28.3719i	−0.295090	+	1.00498i	−0.964936	+	0.262484i	$0.915458\pi$
$798$	0.255718	−	0.0367667i	0.00905232	−	0.00130153i
$799$	−28.0800	−	32.4060i	−0.993397	−	1.14644i
$800$	5.07266	−	6.10089i	0.179346	−	0.215699i
$801$	−3.58302	+	4.13503i	−0.126600	+	0.146104i
$802$	3.88350	+	13.2260i	0.137131	+	0.467026i
$803$	−2.99662	+	1.36851i	−0.105748	+	0.0482937i
$804$	2.18206			0.0769552
$805$	0.137451	−	0.302914i	0.00484452	−	0.0106763i
$806$	−44.8327			−1.57917
$807$	−3.85813	+	1.76195i	−0.135813	+	0.0620236i
$808$	−13.9826	−	47.6205i	−0.491907	−	1.67528i
$809$	30.8741	−	35.6307i	1.08548	−	1.25271i	0.119845	−	0.992793i	$-0.461760\pi$
$809$	30.8741	−	35.6307i	1.08548	−	1.25271i	0.965632	−	0.259914i	$-0.0836944\pi$
$810$	1.73205	−	2.36353i	0.0608579	−	0.0830460i
$811$	18.6133	+	21.4809i	0.653602	+	0.754297i	0.981718	−	0.190340i	$-0.0609592\pi$
$811$	18.6133	+	21.4809i	0.653602	+	0.754297i	−0.328116	+	0.944637i	$0.606414\pi$
$812$	−0.0417509	+	0.00600288i	−0.00146517	+	0.000210660i
$813$	2.27486	−	7.74746i	0.0797828	−	0.271715i
$814$	15.1033	−	9.70632i	0.529371	−	0.340206i
$815$	5.55270	+	1.14883i	0.194502	+	0.0402417i
$816$	−6.82115	+	14.9362i	−0.238788	+	0.522873i
$817$	40.3157	+	18.4116i	1.41047	+	0.644139i
$818$	5.11244	+	0.735058i	0.178752	+	0.0257007i
$819$	0.0959830	−	0.0616845i	0.00335392	−	0.00215543i
$820$	1.51922	+	0.549085i	0.0530535	+	0.0191749i
$821$	−4.92720	−	34.2694i	−0.171960	−	1.19601i	−0.874736	−	0.484600i	$-0.838965\pi$
$821$	−4.92720	−	34.2694i	−0.171960	−	1.19601i	0.702776	−	0.711412i	$-0.251944\pi$
$822$	6.60924	−	5.72694i	0.230524	−	0.199750i
$823$	28.2843	−	44.0112i	0.985929	−	1.53414i	0.147545	−	0.989055i	$-0.452863\pi$
$823$	28.2843	−	44.0112i	0.985929	−	1.53414i	0.838384	−	0.545080i	$-0.183501\pi$
$824$	−19.6171	+	22.6393i	−0.683394	+	0.788678i
$825$	−1.51144	−	9.18091i	−0.0526215	−	0.319638i
$826$	−0.217032	−	0.475234i	−0.00755152	−	0.0165355i
$827$			56.1101i			1.95114i	0.219688	+	0.975570i	$0.429496\pi$
$827$			56.1101i			1.95114i	−0.219688	+	0.975570i	$0.570504\pi$
$828$	−1.35176	−	0.107233i	−0.0469769	−	0.00372661i
$829$	47.2880			1.64238			0.821189	−	0.570656i	$-0.193311\pi$
$829$	47.2880			1.64238			0.821189	+	0.570656i	$0.193311\pi$
$830$	9.22191	+	23.9764i	0.320097	+	0.832233i
$831$	4.63908	−	1.36216i	0.160928	−	0.0472527i
$832$	24.4309	+	21.1695i	0.846987	+	0.733919i
$833$	−18.5220	+	28.8208i	−0.641748	+	0.998580i
$834$	−9.65343	−	11.1407i	−0.334271	−	0.385769i
$835$	0.0724503	−	0.00592381i	0.00250724	−	0.000205002i
$836$	−3.20866	−	0.942147i	−0.110974	−	0.0325848i
$837$	−5.02858	−	7.82463i	−0.173813	−	0.270459i
$838$	5.27886	+	0.758986i	0.182355	+	0.0262187i
$839$	0.484268	−	1.06040i	0.0167188	−	0.0366091i	−0.901088	−	0.433635i	$-0.857231\pi$
$839$	0.484268	−	1.06040i	0.0167188	−	0.0366091i	0.917807	+	0.397026i	$0.129958\pi$
$840$	−0.183108	−	0.0975774i	−0.00631783	−	0.00336674i
$841$	0.835428	−	5.81053i	0.0288079	−	0.200363i
$842$	−7.99026	−	12.4331i	−0.275363	−	0.428472i
$843$	8.41693	−	28.6654i	0.289894	−	0.987290i
$844$	0.555852	+	3.86604i	0.0191332	+	0.133074i
$845$	0.719169	+	0.940580i	0.0247402	+	0.0323569i
$846$	9.65721	+	6.20631i	0.332022	+	0.213377i
$847$	0.176688	+	0.153101i	0.00607105	+	0.00526060i
$848$	−0.418803	−	1.42631i	−0.0143818	−	0.0489798i
$849$	−12.7128	−	27.8373i	−0.436304	−	0.955372i
$850$	31.8320	+	3.91693i	1.09183	+	0.134350i
$851$	−28.4287	+	20.9391i	−0.974523	+	0.717783i
$852$			2.29888i			0.0787582i
$853$	−32.0525	+	14.6379i	−1.09746	+	0.501192i	−0.880046	−	0.474888i	$-0.842489\pi$
$853$	−32.0525	+	14.6379i	−1.09746	+	0.501192i	−0.217411	+	0.976080i	$0.569761\pi$
$854$	−0.271658	+	0.0797661i	−0.00929596	+	0.00272954i
$855$	−9.94635	+	10.1510i	−0.340158	+	0.347157i
$856$	−5.83561	−	3.75032i	−0.199457	−	0.128183i
$857$	−28.2272	+	24.4591i	−0.964224	+	0.835505i	−0.986419	−	0.164248i	$-0.947480\pi$
$857$	−28.2272	+	24.4591i	−0.964224	+	0.835505i	0.0221945	+	0.999754i	$0.492935\pi$
$858$	8.87846	−	1.27653i	0.303106	−	0.0435800i
$859$	−13.8971	−	4.08055i	−0.474163	−	0.139227i	0.0359154	−	0.999355i	$-0.488565\pi$
$859$	−13.8971	−	4.08055i	−0.474163	−	0.139227i	−0.510078	+	0.860128i	$0.670383\pi$
$860$	−2.15225	−	3.84789i	−0.0733913	−	0.131212i
$861$	0.0112791	−	0.0784479i	0.000384391	−	0.00267350i
$862$	−33.7996	−	15.4358i	−1.15122	−	0.525745i
$863$	12.0223	+	5.49039i	0.409243	+	0.186895i	0.609390	−	0.792871i	$-0.291415\pi$
$863$	12.0223	+	5.49039i	0.409243	+	0.186895i	−0.200146	+	0.979766i	$0.564142\pi$
$864$	−0.225833	+	1.57070i	−0.00768300	+	0.0534364i
$865$	−2.82965	−	5.05895i	−0.0962109	−	0.172010i
$866$	−14.5158	−	4.26222i	−0.493267	−	0.144836i
$867$	6.88879	−	0.990459i	0.233956	−	0.0336377i
$868$	−0.0616508	+	0.0534208i	−0.00209257	+	0.00181322i
$869$	−4.40627	−	2.83174i	−0.149473	−	0.0960602i
$870$	−9.86290	+	10.0658i	−0.334384	+	0.341264i
$871$	27.2365	−	7.99735i	0.922873	−	0.270980i
$872$	−19.6678	+	8.98197i	−0.666035	+	0.304168i
$873$		−	17.4695i		−	0.591253i
$874$	−38.9632	−	8.79325i	−1.31795	−	0.297436i
$875$	−0.0633334	+	0.340970i	−0.00214106	+	0.0115269i
$876$	−0.207933	−	0.455310i	−0.00702540	−	0.0153835i
$877$	4.40107	+	14.9887i	0.148614	+	0.506131i	0.999825	−	0.0186911i	$-0.00594991\pi$
$877$	4.40107	+	14.9887i	0.148614	+	0.506131i	−0.851212	+	0.524822i	$0.824132\pi$
$878$	−2.78651	−	2.41452i	−0.0940400	−	0.0814862i
$879$	−19.6122	−	12.6040i	−0.661503	−	0.425122i
$880$	−8.47845	−	11.0887i	−0.285809	−	0.373801i
$881$	−1.34188	−	9.33297i	−0.0452091	−	0.314436i	−0.999860	−	0.0167098i	$-0.994681\pi$
$881$	−1.34188	−	9.33297i	−0.0452091	−	0.314436i	0.954651	−	0.297726i	$-0.0962282\pi$
$882$	2.58400	−	8.80030i	0.0870078	−	0.296321i
$883$	12.6019	+	19.6090i	0.424089	+	0.659895i	0.985893	−	0.167375i	$-0.0535291\pi$
$883$	12.6019	+	19.6090i	0.424089	+	0.659895i	−0.561805	+	0.827270i	$0.689893\pi$
$884$	0.724485	−	5.03890i	0.0243671	−	0.169477i
$885$	25.3632	+	13.5160i	0.852576	+	0.454334i
$886$	15.3072	−	33.5181i	0.514255	−	1.12606i
$887$	−1.25490	−	0.180428i	−0.0421354	−	0.00605816i	0.121215	−	0.992626i	$-0.461321\pi$
$887$	−1.25490	−	0.180428i	−0.0421354	−	0.00605816i	−0.163350	+	0.986568i	$0.552230\pi$
$888$	11.9067	+	18.5271i	0.399561	+	0.621729i
$889$	0.0551330	+	0.0161885i	0.00184910	+	0.000542945i
$890$	15.9792	−	1.30652i	0.535625	−	0.0437948i
$891$	1.21863	+	1.40637i	0.0408256	+	0.0471153i
$892$	−2.93020	+	4.55948i	−0.0981104	+	0.152663i
$893$	−42.0772	−	36.4601i	−1.40806	−	1.22009i
$894$	26.4731	−	7.77319i	0.885392	−	0.259975i
$895$	−0.0557731	−	0.145007i	−0.00186429	−	0.00484704i
$896$	−0.258797			−0.00864582
$897$	−17.2657	+	3.61579i	−0.576485	+	0.120728i
$898$			24.7503i			0.825929i
$899$	18.5825	+	40.6900i	0.619761	+	1.35709i
$900$	1.39496	−	0.229649i	0.0464986	−	0.00765498i
$901$	−1.42045	+	1.63929i	−0.0473221	+	0.0546126i
$902$	3.36858	−	5.24161i	0.112161	−	0.174527i
$903$	−0.163475	+	0.141652i	−0.00544011	+	0.00471388i
$904$	2.16141	+	15.0329i	0.0718873	+	0.499987i
$905$	−37.0281	−	13.3829i	−1.23085	−	0.444862i
$906$	9.53806	−	6.12974i	0.316881	−	0.203647i
$907$	43.3341	+	6.23050i	1.43888	+	0.206880i	0.817185	−	0.576376i	$-0.195534\pi$
$907$	43.3341	+	6.23050i	1.43888	+	0.206880i	0.621699	+	0.783256i	$0.286443\pi$
$908$	−5.23041	−	2.38865i	−0.173577	−	0.0792700i
$909$	6.89222	−	15.0919i	0.228601	−	0.500565i
$910$	−0.327392	−	0.0677359i	−0.0108529	−	0.00224542i
$911$	0.317637	−	0.204133i	0.0105238	−	0.00676323i	−0.535368	−	0.844619i	$-0.679827\pi$
$911$	0.317637	−	0.204133i	0.0105238	−	0.00676323i	0.545892	+	0.837855i	$0.316191\pi$
$912$	−6.00667	+	20.4568i	−0.198901	+	0.677394i
$913$	−16.1481	+	2.32174i	−0.534423	+	0.0768384i
$914$	12.7955	+	14.7668i	0.423238	+	0.488443i
$915$	9.20620	−	12.5627i	0.304348	−	0.415309i
$916$	0.0575144	−	0.0663752i	0.00190033	−	0.00219310i
$917$	−0.0816849	−	0.278193i	−0.00269747	−	0.00918675i
$918$	−5.83476	+	2.66465i	−0.192576	+	0.0879464i
$919$	−42.2369			−1.39327			−0.696633	−	0.717428i	$-0.745319\pi$
$919$	−42.2369			−1.39327			−0.696633	+	0.717428i	$0.745319\pi$
$920$	21.0660	+	24.1930i	0.694526	+	0.797618i
$921$	27.8709			0.918379
$922$	28.3128	−	12.9300i	0.932432	−	0.425827i
$923$	8.42550	+	28.6946i	0.277329	+	0.944494i
$924$	0.0106880	−	0.0123346i	0.000351609	−	0.000405778i
$925$	23.5345	−	28.3049i	0.773809	−	0.930660i
$926$	19.5160	+	22.5226i	0.641334	+	0.740139i
$927$	−9.91214	+	1.42515i	−0.325557	+	0.0468081i
$928$	2.15011	−	7.32259i	0.0705807	−	0.240376i
$929$	46.3517	−	29.7884i	1.52075	−	0.977327i	0.529073	−	0.848576i	$-0.322540\pi$
$929$	46.3517	−	29.7884i	1.52075	−	0.977327i	0.991677	−	0.128750i	$-0.0410966\pi$
$930$	−5.52190	+	26.6893i	−0.181070	+	0.875177i
$931$	−18.4791	+	40.4637i	−0.605629	+	1.32614i
$932$	1.89962	+	0.867529i	0.0622242	+	0.0284169i
$933$	28.6991	+	4.12631i	0.939567	+	0.135089i
$934$	3.70648	−	2.38201i	0.121280	−	0.0779418i
$935$	−6.92319	+	19.1553i	−0.226413	+	0.626444i
$936$	1.56591	+	10.8911i	0.0511833	+	0.355988i
$937$	−9.16039	+	7.93752i	−0.299257	+	0.259308i	−0.791526	−	0.611135i	$-0.790713\pi$
$937$	−9.16039	+	7.93752i	−0.299257	+	0.259308i	0.492269	+	0.870443i	$0.336168\pi$
$938$	−0.169598	+	0.263899i	−0.00553757	+	0.00861662i
$939$	−17.8483	+	20.5980i	−0.582456	+	0.672191i
$940$	1.23233	+	5.39964i	0.0401943	+	0.176117i
$941$	19.3511	+	42.3730i	0.630827	+	1.38132i	0.907376	+	0.420320i	$0.138082\pi$
$941$	19.3511	+	42.3730i	0.630827	+	1.38132i	−0.276549	+	0.961000i	$0.589191\pi$
$942$			3.20745i			0.104504i
$943$	−5.95581	+	10.7088i	−0.193948	+	0.348726i
$944$	43.1156			1.40329
$945$	−0.0248994	−	0.0647370i	−0.000809978	−	0.00210589i
$946$	−16.3166	+	4.79098i	−0.530498	+	0.155768i
$947$	14.9394	+	12.9451i	0.485467	+	0.420659i	0.862898	−	0.505378i	$-0.168647\pi$
$947$	14.9394	+	12.9451i	0.485467	+	0.420659i	−0.377431	+	0.926038i	$0.623193\pi$
$948$	0.430258	−	0.669494i	0.0139741	−	0.0217442i
$949$	−4.26416	−	4.92110i	−0.138420	−	0.159746i
$950$	41.6350	−	0.848014i	1.35082	−	0.0275132i
$951$	11.7711	+	3.45632i	0.381706	+	0.112079i
$952$	0.245556	+	0.382092i	0.00795851	+	0.0123837i
$953$	−16.6571	−	2.39492i	−0.539575	−	0.0775791i	−0.132861	−	0.991135i	$-0.542416\pi$
$953$	−16.6571	−	2.39492i	−0.539575	−	0.0775791i	−0.406714	+	0.913556i	$0.633325\pi$
$954$	0.241233	−	0.528227i	0.00781021	−	0.0171020i
$955$	−13.6555	+	25.6251i	−0.441882	+	0.829209i
$956$	0.360393	−	2.50659i	0.0116559	−	0.0810688i
$957$	−4.83857	−	7.52896i	−0.156409	−	0.243377i
$958$	1.06775	−	3.63641i	0.0344973	−	0.117487i
$959$	−0.0294600	−	0.204899i	−0.000951314	−	0.00661653i
$960$	15.6114	−	11.9365i	0.503857	−	0.385250i
$961$	46.6993	+	30.0118i	1.50643	+	0.968122i
$962$	26.8190	+	23.2388i	0.864678	+	0.749248i
$963$	−0.653313	−	2.22498i	−0.0210527	−	0.0716990i
$964$	0.289789	+	0.634550i	0.00933349	+	0.0204375i
$965$	−0.841699	+	13.7322i	−0.0270952	+	0.442054i
$966$	0.118033	−	0.155148i	0.00379764	−	0.00499181i
$967$		−	33.9590i		−	1.09205i	−0.837769	−	0.546025i	$-0.816140\pi$
$967$		−	33.9590i		−	1.09205i	0.837769	−	0.546025i	$-0.183860\pi$
$968$	−20.5089	+	9.36610i	−0.659181	+	0.301038i
$969$	29.8499	−	8.76472i	0.958917	−	0.281563i
$970$	−35.8261	+	36.5632i	−1.15031	+	1.17398i
$971$	4.30733	+	2.76815i	0.138229	+	0.0888342i	0.607927	−	0.793993i	$-0.292001\pi$
$971$	4.30733	+	2.76815i	0.138229	+	0.0888342i	−0.469699	+	0.882827i	$0.655637\pi$
$972$	−0.213686	+	0.185160i	−0.00685398	+	0.00593901i
$973$	−0.345381	+	0.0496583i	−0.0110724	+	0.00159197i
$974$	−41.3648	−	12.1458i	−1.32541	−	0.389176i
$975$	16.5702	−	7.97908i	0.530672	−	0.255535i
$976$	3.32525	−	23.1276i	0.106439	−	0.740296i
$977$	−45.2558	−	20.6676i	−1.44786	−	0.661216i	−0.472400	−	0.881384i	$-0.656612\pi$
$977$	−45.2558	−	20.6676i	−1.44786	−	0.661216i	−0.975462	+	0.220168i	$0.929340\pi$
$978$	3.02276	+	1.38045i	0.0966571	+	0.0441418i
$979$	−1.44902	+	10.0781i	−0.0463108	+	0.322099i
$980$	3.86201	−	2.16015i	0.123367	−	0.0690035i
$981$	−6.93515	−	2.03635i	−0.221422	−	0.0650155i
$982$	11.4733	−	1.64961i	0.366127	−	0.0526411i
$983$	28.0401	−	24.2969i	0.894339	−	0.774949i	−0.0807564	−	0.996734i	$-0.525734\pi$
$983$	28.0401	−	24.2969i	0.894339	−	0.774949i	0.975096	+	0.221784i	$0.0711881\pi$
$984$	6.42984	+	4.13221i	0.204976	+	0.131730i
$985$	−44.4222	−	43.5267i	−1.41541	−	1.38687i
$986$	29.5995	−	8.69119i	0.942640	−	0.276784i
$987$	0.247172	−	0.112880i	0.00786757	−	0.00359300i
$988$		−	6.60998i		−	0.210291i
$989$	31.4246	−	11.4437i	0.999246	−	0.363889i
$990$	0.333601	−	5.44265i	0.0106026	−	0.172979i
$991$	−12.2936	−	26.9192i	−0.390519	−	0.855116i	−0.998144	−	0.0608928i	$-0.980605\pi$
$991$	−12.2936	−	26.9192i	−0.390519	−	0.855116i	0.607626	−	0.794223i	$-0.292122\pi$
$992$	−4.15826	−	14.1617i	−0.132025	−	0.449635i
$993$	−19.3685	−	16.7829i	−0.614639	−	0.532588i
$994$	−0.278027	−	0.178677i	−0.00881850	−	0.00566730i
$995$	20.2035	+	26.4236i	0.640494	+	0.837683i
$996$	−0.352768	−	2.45355i	−0.0111779	−	0.0777439i
$997$	13.3812	−	45.5722i	0.423787	−	1.44329i	−0.420450	−	0.907316i	$-0.638128\pi$
$997$	13.3812	−	45.5722i	0.423787	−	1.44329i	0.844237	−	0.535970i	$-0.180054\pi$
$998$	29.2489	+	45.5121i	0.925857	+	1.44066i
$999$	−1.04775	+	7.28724i	−0.0331492	+	0.230558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.4.18	yes	240
5.4	even	2	inner	345.2.t.a.4.7	✓	240
23.6	even	11	inner	345.2.t.a.259.7	yes	240
115.29	even	22	inner	345.2.t.a.259.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.7	✓	240	5.4	even	2	inner
345.2.t.a.4.18	yes	240	1.1	even	1	trivial
345.2.t.a.259.7	yes	240	23.6	even	11	inner
345.2.t.a.259.18	yes	240	115.29	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19202 - 0.544376i) q^{2} +(0.281733 + 0.959493i) q^{3} +(-0.185160 + 0.213686i) q^{4} +(1.80362 + 1.32173i) q^{5} +(0.858156 + 0.990364i) q^{6} +(0.0307032 - 0.00441445i) q^{7} +(-0.842776 + 2.87023i) q^{8} +(-0.841254 + 0.540641i) q^{9} +(2.86946 + 0.593679i) q^{10} +(-0.773045 + 1.69273i) q^{11} +(-0.257196 - 0.117457i) q^{12} +(-3.64081 - 0.523469i) q^{13} +(0.0341956 - 0.0219762i) q^{14} +(-0.760052 + 2.10293i) q^{15} +(0.477404 + 3.32042i) q^{16} +(3.69929 - 3.20545i) q^{17} +(-0.708477 + 1.10241i) q^{18} +(4.16208 - 4.80329i) q^{19} +(-0.616392 + 0.140676i) q^{20} +(0.0128857 + 0.0282158i) q^{21} +2.43860i q^{22} +(-0.304986 - 4.78612i) q^{23} -2.99140 q^{24} +(1.50606 + 4.76778i) q^{25} +(-4.62487 + 1.35799i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.00474169 + 0.00737821i) q^{28} +(3.14945 + 3.63465i) q^{29} +(0.238790 + 2.92049i) q^{30} +(8.92439 + 2.62044i) q^{31} +(-0.857919 - 1.33495i) q^{32} +(-1.84196 - 0.264834i) q^{33} +(2.66465 - 5.83476i) q^{34} +(0.0612114 + 0.0326193i) q^{35} +(0.0402391 - 0.279869i) q^{36} +(-3.98029 - 6.19345i) q^{37} +(2.34647 - 7.99135i) q^{38} +(-0.523469 - 3.64081i) q^{39} +(-5.31371 + 4.06287i) q^{40} +(-2.14944 - 1.38136i) q^{41} +(0.0307200 + 0.0266190i) q^{42} +(1.96465 + 6.69098i) q^{43} +(-0.218576 - 0.478615i) q^{44} +(-2.23188 - 0.136801i) q^{45} +(-2.96900 - 5.53912i) q^{46} -8.76007i q^{47} +(-3.05142 + 1.39353i) q^{48} +(-6.71553 + 1.97186i) q^{49} +(4.39073 + 4.86342i) q^{50} +(4.11782 + 2.64636i) q^{51} +(0.785990 - 0.681064i) q^{52} +(-0.438626 + 0.0630649i) q^{53} +(-1.25736 - 0.369194i) q^{54} +(-3.63161 + 2.03128i) q^{55} +(-0.0132054 + 0.0918455i) q^{56} +(5.78132 + 2.64024i) q^{57} +(5.73282 + 2.61809i) q^{58} +(1.82915 - 12.7220i) q^{59} +(-0.308636 - 0.551791i) q^{60} +(-6.68313 - 1.96234i) q^{61} +(12.0645 - 1.73462i) q^{62} +(-0.0234425 + 0.0203131i) q^{63} +(-7.39344 - 4.75148i) q^{64} +(-5.87474 - 5.75630i) q^{65} +(-2.33982 + 0.687032i) q^{66} +(-7.01995 + 3.20590i) q^{67} +1.38401i q^{68} +(4.50633 - 1.64104i) q^{69} +(0.0907223 + 0.00556073i) q^{70} +(-3.37753 - 7.39577i) q^{71} +(-0.842776 - 2.87023i) q^{72} +(1.33789 + 1.15929i) q^{73} +(-8.11615 - 5.21593i) q^{74} +(-4.15035 + 2.78830i) q^{75} +(0.255746 + 1.77875i) q^{76} +(-0.0162625 + 0.0553848i) q^{77} +(-2.60596 - 4.05495i) q^{78} +(-0.400564 + 2.78598i) q^{79} +(-3.52764 + 6.61975i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-3.31415 - 0.476503i) q^{82} +(4.73969 + 7.37510i) q^{83} +(-0.00841523 - 0.00247093i) q^{84} +(10.9088 - 0.891948i) q^{85} +(5.98430 + 6.90626i) q^{86} +(-2.60012 + 4.04587i) q^{87} +(-4.20703 - 3.64541i) q^{88} +(5.24980 - 1.54148i) q^{89} +(-2.73491 + 1.05191i) q^{90} -0.114095 q^{91} +(1.07920 + 0.821027i) q^{92} +9.30116i q^{93} +(-4.76877 - 10.4422i) q^{94} +(13.8554 - 3.16216i) q^{95} +(1.03917 - 1.19927i) q^{96} +(-9.44472 + 14.6963i) q^{97} +(-6.93160 + 6.00626i) q^{98} +(-0.264834 - 1.84196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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