LMFDB - Embedded newform 552.2.bb.a.133.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			133.35
Character	$\chi$	$=$	552.133
Dual form			552.2.bb.a.469.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09890 - 0.890185i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.415141 - 1.95644i) q^{4} +(-3.04584 - 0.437926i) q^{5} +(1.41344 + 0.0468661i) q^{6} +(-0.849690 - 1.86056i) q^{7} +(-1.28540 - 2.51947i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-3.73690 + 2.23013i) q^{10} +(-0.297354 - 1.01270i) q^{11} +(1.59494 - 1.20672i) q^{12} +(-5.65121 - 2.58082i) q^{13} +(-2.58996 - 1.28818i) q^{14} +(-2.01511 - 2.32557i) q^{15} +(-3.65532 - 1.62440i) q^{16} +(4.33292 - 2.78460i) q^{17} +(1.03751 + 0.961023i) q^{18} +(3.28427 - 5.11043i) q^{19} +(-2.12123 + 5.77721i) q^{20} +(0.576256 - 1.96255i) q^{21} +(-1.22825 - 0.848145i) q^{22} +(3.49487 + 3.28419i) q^{23} +(0.678466 - 2.74585i) q^{24} +(4.28792 + 1.25905i) q^{25} +(-8.50749 + 2.19457i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(-3.99282 + 0.889973i) q^{28} +(3.04098 + 4.73186i) q^{29} +(-4.28458 - 0.761728i) q^{30} +(1.17184 + 1.35237i) q^{31} +(-5.46282 + 1.46887i) q^{32} +(0.438449 - 0.960069i) q^{33} +(2.28261 - 6.91708i) q^{34} +(1.77323 + 6.03908i) q^{35} +(1.99561 + 0.132485i) q^{36} +(-2.54098 + 0.365337i) q^{37} +(-0.940156 - 8.53943i) q^{38} +(-2.58082 - 5.65121i) q^{39} +(2.81178 + 8.23683i) q^{40} +(-0.885877 + 6.16141i) q^{41} +(-1.11379 - 2.66961i) q^{42} +(-3.44066 - 2.98135i) q^{43} +(-2.10472 + 0.161345i) q^{44} -3.07716i q^{45} +(6.76403 + 0.497897i) q^{46} -1.40487 q^{47} +(-1.69875 - 3.62136i) q^{48} +(1.84431 - 2.12845i) q^{49} +(5.83276 - 2.43348i) q^{50} +(5.09812 + 0.733000i) q^{51} +(-7.39527 + 9.98485i) q^{52} +(12.3809 - 5.65417i) q^{53} +(0.154764 + 1.40572i) q^{54} +(0.462208 + 3.21473i) q^{55} +(-3.59545 + 4.53233i) q^{56} +(5.82870 - 1.71146i) q^{57} +(7.55395 + 2.49278i) q^{58} +(-1.90366 - 0.869372i) q^{59} +(-5.38639 + 2.97701i) q^{60} +(2.75831 - 2.39009i) q^{61} +(2.49159 + 0.442964i) q^{62} +(1.72070 - 1.10583i) q^{63} +(-4.69550 + 6.47706i) q^{64} +(16.0825 + 10.3356i) q^{65} +(-0.372830 - 1.44532i) q^{66} +(-3.51269 + 11.9631i) q^{67} +(-3.64913 - 9.63309i) q^{68} +(0.490560 + 4.77068i) q^{69} +(7.32449 + 5.05781i) q^{70} +(-6.40918 - 1.88191i) q^{71} +(2.31090 - 1.63087i) q^{72} +(-6.61472 - 4.25102i) q^{73} +(-2.46705 + 2.66341i) q^{74} +(2.41609 + 3.75951i) q^{75} +(-8.63481 - 8.54702i) q^{76} +(-1.63152 + 1.41372i) q^{77} +(-7.86667 - 3.91268i) q^{78} +(5.18193 - 11.3468i) q^{79} +(10.4222 + 6.54841i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.51131 + 7.55934i) q^{82} +(4.16725 - 0.599160i) q^{83} +(-3.60038 - 1.94214i) q^{84} +(-14.4168 + 6.58395i) q^{85} +(-6.43487 - 0.213365i) q^{86} +(-0.800488 + 5.56752i) q^{87} +(-2.16924 + 2.05089i) q^{88} +(8.33519 - 9.61932i) q^{89} +(-2.73925 - 3.38148i) q^{90} +12.7073i q^{91} +(7.87618 - 5.47410i) q^{92} +1.78945i q^{93} +(-1.54380 + 1.25059i) q^{94} +(-12.2414 + 14.1273i) q^{95} +(-5.09043 - 2.46729i) q^{96} +(0.988550 - 6.87552i) q^{97} +(0.131991 - 3.98072i) q^{98} +(0.960069 - 0.438449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.09890	−	0.890185i	0.777036	−	0.629456i
$2$	1.09890	−	0.890185i	0.777036	−	0.629456i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$4$	0.415141	−	1.95644i	0.207570	−	0.978220i
$5$	−3.04584	−	0.437926i	−1.36214	−	0.195847i	−0.577802	−	0.816177i	$-0.696089\pi$
$5$	−3.04584	−	0.437926i	−1.36214	−	0.195847i	−0.784341	+	0.620330i	$0.786999\pi$
$6$	1.41344	+	0.0468661i	0.577033	+	0.0191330i
$7$	−0.849690	−	1.86056i	−0.321152	−	0.703226i	0.678351	−	0.734738i	$-0.262695\pi$
$7$	−0.849690	−	1.86056i	−0.321152	−	0.703226i	−0.999503	+	0.0315123i	$0.989968\pi$
$8$	−1.28540	−	2.51947i	−0.454457	−	0.890769i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	−3.73690	+	2.23013i	−1.18171	+	0.705229i
$11$	−0.297354	−	1.01270i	−0.0896556	−	0.305339i	0.902441	−	0.430813i	$-0.141773\pi$
$11$	−0.297354	−	1.01270i	−0.0896556	−	0.305339i	−0.992097	+	0.125474i	$0.959955\pi$
$12$	1.59494	−	1.20672i	0.460419	−	0.348350i
$13$	−5.65121	−	2.58082i	−1.56736	−	0.715791i	−0.572778	−	0.819711i	$-0.694134\pi$
$13$	−5.65121	−	2.58082i	−1.56736	−	0.715791i	−0.994586	+	0.103920i	$0.966862\pi$
$14$	−2.58996	−	1.28818i	−0.692197	−	0.344280i
$15$	−2.01511	−	2.32557i	−0.520300	−	0.600459i
$16$	−3.65532	−	1.62440i	−0.913829	−	0.406099i
$17$	4.33292	−	2.78460i	1.05089	−	0.675364i	0.103231	−	0.994657i	$-0.467082\pi$
$17$	4.33292	−	2.78460i	1.05089	−	0.675364i	0.947656	+	0.319293i	$0.103446\pi$
$18$	1.03751	+	0.961023i	0.244544	+	0.226515i
$19$	3.28427	−	5.11043i	0.753463	−	1.17241i	−0.226651	−	0.973976i	$-0.572778\pi$
$19$	3.28427	−	5.11043i	0.753463	−	1.17241i	0.980114	−	0.198436i	$-0.0635861\pi$
$20$	−2.12123	+	5.77721i	−0.474321	+	1.29182i
$21$	0.576256	−	1.96255i	0.125749	−	0.428263i
$22$	−1.22825	−	0.848145i	−0.261863	−	0.180825i
$23$	3.49487	+	3.28419i	0.728731	+	0.684800i
$23$	3.49487	+	3.28419i	0.728731	+	0.684800i
$24$	0.678466	−	2.74585i	0.138491	−	0.560494i
$25$	4.28792	+	1.25905i	0.857584	+	0.251809i
$26$	−8.50749	+	2.19457i	−1.66846	+	0.430391i
$27$	−0.540641	+	0.841254i	−0.104046	+	0.161899i
$28$	−3.99282	+	0.889973i	−0.754571	+	0.168189i
$29$	3.04098	+	4.73186i	0.564696	+	0.878684i	0.999764	−	0.0217137i	$-0.00691223\pi$
$29$	3.04098	+	4.73186i	0.564696	+	0.878684i	−0.435069	+	0.900397i	$0.643276\pi$
$30$	−4.28458	−	0.761728i	−0.782254	−	0.139072i
$31$	1.17184	+	1.35237i	0.210469	+	0.242894i	0.851162	−	0.524903i	$-0.175898\pi$
$31$	1.17184	+	1.35237i	0.210469	+	0.242894i	−0.640693	+	0.767797i	$0.721353\pi$
$32$	−5.46282	+	1.46887i	−0.965700	+	0.259662i
$33$	0.438449	−	0.960069i	0.0763242	−	0.167127i
$34$	2.28261	−	6.91708i	0.391465	−	1.18627i
$35$	1.77323	+	6.03908i	0.299731	+	1.02079i
$36$	1.99561	+	0.132485i	0.332601	+	0.0220808i
$37$	−2.54098	+	0.365337i	−0.417734	+	0.0600610i	−0.347977	−	0.937503i	$-0.613131\pi$
$37$	−2.54098	+	0.365337i	−0.417734	+	0.0600610i	−0.0697566	+	0.997564i	$0.522222\pi$
$38$	−0.940156	−	8.53943i	−0.152513	−	1.38528i
$39$	−2.58082	−	5.65121i	−0.413262	−	0.904918i
$40$	2.81178	+	8.23683i	0.444581	+	1.30236i
$41$	−0.885877	+	6.16141i	−0.138351	+	0.962251i	0.795848	+	0.605497i	$0.207026\pi$
$41$	−0.885877	+	6.16141i	−0.138351	+	0.962251i	−0.934198	+	0.356754i	$0.883883\pi$
$42$	−1.11379	−	2.66961i	−0.171861	−	0.411929i
$43$	−3.44066	−	2.98135i	−0.524696	−	0.454651i	0.351790	−	0.936079i	$-0.385573\pi$
$43$	−3.44066	−	2.98135i	−0.524696	−	0.454651i	−0.876486	+	0.481428i	$0.840118\pi$
$44$	−2.10472	+	0.161345i	−0.317299	+	0.0243236i
$45$		−	3.07716i		−	0.458717i
$46$	6.76403	+	0.497897i	0.997302	+	0.0734108i
$47$	−1.40487			−0.204921			−0.102461	−	0.994737i	$-0.532672\pi$
$47$	−1.40487			−0.204921			−0.102461	+	0.994737i	$0.532672\pi$
$48$	−1.69875	−	3.62136i	−0.245194	−	0.522698i
$49$	1.84431	−	2.12845i	0.263473	−	0.304064i
$50$	5.83276	−	2.43348i	0.824876	−	0.344146i
$51$	5.09812	+	0.733000i	0.713880	+	0.102640i
$52$	−7.39527	+	9.98485i	−1.02554	+	1.38465i
$53$	12.3809	−	5.65417i	1.70065	−	0.776660i	0.702779	−	0.711408i	$-0.251942\pi$
$53$	12.3809	−	5.65417i	1.70065	−	0.776660i	0.997869	−	0.0652519i	$-0.0207851\pi$
$54$	0.154764	+	1.40572i	0.0210607	+	0.191294i
$55$	0.462208	+	3.21473i	0.0623242	+	0.433474i
$56$	−3.59545	+	4.53233i	−0.480462	+	0.605658i
$57$	5.82870	−	1.71146i	0.772031	−	0.226689i
$58$	7.55395	+	2.49278i	0.991882	+	0.327318i
$59$	−1.90366	−	0.869372i	−0.247835	−	0.113183i	0.287625	−	0.957743i	$-0.407134\pi$
$59$	−1.90366	−	0.869372i	−0.247835	−	0.113183i	−0.535460	+	0.844561i	$0.679862\pi$
$60$	−5.38639	+	2.97701i	−0.695379	+	0.384331i
$61$	2.75831	−	2.39009i	0.353165	−	0.306019i	−0.460152	−	0.887840i	$-0.652205\pi$
$61$	2.75831	−	2.39009i	0.353165	−	0.306019i	0.813317	+	0.581821i	$0.197660\pi$
$62$	2.49159	+	0.442964i	0.316433	+	0.0562565i
$63$	1.72070	−	1.10583i	0.216788	−	0.139321i
$64$	−4.69550	+	6.47706i	−0.586938	+	0.809632i
$65$	16.0825	+	10.3356i	1.99479	+	1.28197i
$66$	−0.372830	−	1.44532i	−0.0458922	−	0.177906i
$67$	−3.51269	+	11.9631i	−0.429143	+	1.46153i	0.407210	+	0.913335i	$0.366502\pi$
$67$	−3.51269	+	11.9631i	−0.429143	+	1.46153i	−0.836353	+	0.548192i	$0.815316\pi$
$68$	−3.64913	−	9.63309i	−0.442522	−	1.16818i
$69$	0.490560	+	4.77068i	0.0590565	+	0.574322i
$70$	7.32449	+	5.05781i	0.875445	+	0.604523i
$71$	−6.40918	−	1.88191i	−0.760630	−	0.223341i	−0.121659	−	0.992572i	$-0.538821\pi$
$71$	−6.40918	−	1.88191i	−0.760630	−	0.223341i	−0.638971	+	0.769231i	$0.720640\pi$
$72$	2.31090	−	1.63087i	0.272342	−	0.192200i
$73$	−6.61472	−	4.25102i	−0.774194	−	0.497544i	0.0929081	−	0.995675i	$-0.470384\pi$
$73$	−6.61472	−	4.25102i	−0.774194	−	0.497544i	−0.867102	+	0.498130i	$0.834020\pi$
$74$	−2.46705	+	2.66341i	−0.286788	+	0.309615i
$75$	2.41609	+	3.75951i	0.278986	+	0.434111i
$76$	−8.63481	−	8.54702i	−0.990480	−	0.980411i
$77$	−1.63152	+	1.41372i	−0.185929	+	0.161109i
$78$	−7.86667	−	3.91268i	−0.890726	−	0.443023i
$79$	5.18193	−	11.3468i	0.583013	−	1.27662i	−0.356561	−	0.934272i	$-0.616051\pi$
$79$	5.18193	−	11.3468i	0.583013	−	1.27662i	0.939573	−	0.342348i	$-0.111222\pi$
$80$	10.4222	+	6.54841i	1.16523	+	0.732135i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	4.51131	+	7.55934i	0.498191	+	0.834789i
$83$	4.16725	−	0.599160i	0.457415	−	0.0657664i	0.0902439	−	0.995920i	$-0.471235\pi$
$83$	4.16725	−	0.599160i	0.457415	−	0.0657664i	0.367171	+	0.930153i	$0.380326\pi$
$84$	−3.60038	−	1.94214i	−0.392833	−	0.211905i
$85$	−14.4168	+	6.58395i	−1.56373	+	0.714130i
$86$	−6.43487	−	0.213365i	−0.693890	−	0.0230077i
$87$	−0.800488	+	5.56752i	−0.0858213	+	0.596900i
$88$	−2.16924	+	2.05089i	−0.231242	+	0.218626i
$89$	8.33519	−	9.61932i	0.883529	−	1.01965i	−0.116123	−	0.993235i	$-0.537047\pi$
$89$	8.33519	−	9.61932i	0.883529	−	1.01965i	0.999651	−	0.0264114i	$-0.00840800\pi$
$90$	−2.73925	−	3.38148i	−0.288742	−	0.356439i
$91$			12.7073i			1.33209i
$92$	7.87618	−	5.47410i	0.821148	−	0.570715i
$93$			1.78945i			0.185557i
$94$	−1.54380	+	1.25059i	−0.159231	+	0.128989i
$95$	−12.2414	+	14.1273i	−1.25594	+	1.44943i
$96$	−5.09043	−	2.46729i	−0.519540	−	0.251817i
$97$	0.988550	−	6.87552i	0.100372	−	0.698103i	−0.876048	−	0.482224i	$-0.839829\pi$
$97$	0.988550	−	6.87552i	0.100372	−	0.698103i	0.976420	−	0.215879i	$-0.0692618\pi$
$98$	0.131991	−	3.98072i	0.0133331	−	0.402114i
$99$	0.960069	−	0.438449i	0.0964906	−	0.0440658i
$100$	4.24334	−	7.86637i	0.424334	−	0.786637i
$101$	17.6635	−	2.53963i	1.75759	−	0.252703i	0.813303	−	0.581840i	$-0.197667\pi$
$101$	17.6635	−	2.53963i	1.75759	−	0.252703i	0.944282	+	0.329137i	$0.106758\pi$
$102$	6.25481	−	3.73279i	0.619318	−	0.369601i
$103$	−0.00940064	+	0.00276028i	−0.000926272	+	0.000271978i	−0.282196	−	0.959357i	$-0.591063\pi$
$103$	−0.00940064	+	0.00276028i	−0.000926272	+	0.000271978i	0.281269	+	0.959629i	$0.409245\pi$
$104$	0.761743	+	17.5555i	0.0746951	+	1.72145i
$105$	−2.61463	+	5.72525i	−0.255162	+	0.558727i
$106$	8.57206	−	17.2346i	0.832592	−	1.67398i
$107$	−9.63489	+	8.34868i	−0.931440	+	0.807098i	−0.981463	−	0.191650i	$-0.938616\pi$
$107$	−9.63489	+	8.34868i	−0.931440	+	0.807098i	0.0500229	+	0.998748i	$0.484071\pi$
$108$	1.42142	+	1.40697i	0.136776	+	0.135386i
$109$	1.09193	+	1.69908i	0.104588	+	0.162742i	0.889603	−	0.456735i	$-0.150981\pi$
$109$	1.09193	+	1.69908i	0.104588	+	0.162742i	−0.785015	+	0.619477i	$0.787345\pi$
$110$	3.36962	+	3.12120i	0.321281	+	0.297595i
$111$	−2.15959	−	1.38788i	−0.204979	−	0.131732i
$112$	0.0835987	+	8.18117i	0.00789934	+	0.773048i
$113$	−5.29269	−	1.55407i	−0.497895	−	0.146195i	0.0231372	−	0.999732i	$-0.492635\pi$
$113$	−5.29269	−	1.55407i	−0.497895	−	0.146195i	−0.521032	+	0.853537i	$0.674453\pi$
$114$	4.88161	−	7.06934i	0.457205	−	0.662105i
$115$	−9.20659	−	11.5336i	−0.858519	−	1.07552i
$116$	10.5200	−	3.98511i	0.976760	−	0.370008i
$117$	1.75030	−	5.96098i	0.161815	−	0.551093i
$118$	−2.86582	+	0.739261i	−0.263820	+	0.0680545i
$119$	−8.86255	−	5.69561i	−0.812428	−	0.522116i
$120$	−3.26898	+	8.06631i	−0.298416	+	0.736350i
$121$	8.31666	−	5.34479i	0.756060	−	0.485890i
$122$	0.903471	−	5.08186i	0.0817964	−	0.460090i
$123$	−4.70437	+	4.07636i	−0.424179	+	0.367553i
$124$	3.13232	−	1.73121i	0.281291	−	0.155467i
$125$	1.48648	+	0.678852i	0.132955	+	0.0607184i
$126$	0.906478	−	2.74693i	0.0807554	−	0.244716i
$127$	10.2280	−	3.00322i	0.907592	−	0.266493i	0.205565	−	0.978643i	$-0.434097\pi$
$127$	10.2280	−	3.00322i	0.907592	−	0.266493i	0.702027	+	0.712150i	$0.252279\pi$
$128$	0.605916	+	11.2975i	0.0535559	+	0.998565i
$129$	−0.647909	−	4.50630i	−0.0570452	−	0.396758i
$130$	26.8736	−	2.95867i	2.35697	−	0.259492i
$131$	−6.87878	+	3.14143i	−0.601002	+	0.274468i	−0.692593	−	0.721328i	$-0.743532\pi$
$131$	−6.87878	+	3.14143i	−0.601002	+	0.274468i	0.0915913	+	0.995797i	$0.470805\pi$
$132$	−1.69630	−	1.25636i	−0.147644	−	0.109352i
$133$	−12.2989	−	1.76831i	−1.06645	−	0.153332i
$134$	6.78931	+	16.2731i	0.586507	+	1.40579i
$135$	2.01511	−	2.32557i	0.173433	−	0.200153i
$136$	−12.5852	−	7.33736i	−1.07918	−	0.629173i
$137$	−7.79721			−0.666161			−0.333080	−	0.942898i	$-0.608088\pi$
$137$	−7.79721			−0.666161			−0.333080	+	0.942898i	$0.608088\pi$
$138$	4.78586	+	4.80578i	0.407399	+	0.409095i
$139$			15.3636i			1.30312i	0.758595	+	0.651562i	$0.225886\pi$
$139$			15.3636i			1.30312i	−0.758595	+	0.651562i	$0.774114\pi$
$140$	12.5512	−	0.962159i	1.06077	−	0.0813173i
$141$	−1.06173	−	0.919993i	−0.0894137	−	0.0774774i
$142$	−8.71826	+	3.63734i	−0.731620	+	0.305239i
$143$	−0.933174	+	6.49037i	−0.0780360	+	0.542752i
$144$	1.08766	−	3.84929i	0.0906379	−	0.320774i
$145$	−7.19014	−	15.7442i	−0.597109	−	1.30749i
$146$	−11.0531	+	1.21690i	−0.914759	+	0.100711i
$147$	2.78768	−	0.400807i	0.229924	−	0.0330580i
$148$	−0.340102	+	5.12293i	−0.0279562	+	0.421102i
$149$	2.20121	+	7.49665i	0.180330	+	0.614149i	0.999193	+	0.0401599i	$0.0127867\pi$
$149$	2.20121	+	7.49665i	0.180330	+	0.614149i	−0.818863	+	0.573989i	$0.805395\pi$
$150$	6.00169	+	1.98054i	0.490036	+	0.161710i
$151$	−4.18487	+	9.16359i	−0.340560	+	0.745722i	−0.999982	−	0.00605099i	$-0.998074\pi$
$151$	−4.18487	+	9.16359i	−0.340560	+	0.745722i	0.659422	+	0.751773i	$0.270801\pi$
$152$	−17.0972	−	1.70570i	−1.38676	−	0.138351i
$153$	3.37289	+	3.89253i	0.272682	+	0.314692i
$154$	−0.534397	+	3.00589i	−0.0430629	+	0.242221i
$155$	−2.97700	−	4.63230i	−0.239118	−	0.372075i
$156$	−12.1277	+	2.70318i	−0.970990	+	0.216427i
$157$	13.0607	−	20.3229i	1.04236	−	1.62194i	0.297498	−	0.954722i	$-0.403848\pi$
$157$	13.0607	−	20.3229i	1.04236	−	1.62194i	0.744861	−	0.667220i	$-0.232516\pi$
$158$	−4.40640	−	17.0819i	−0.350554	−	1.35896i
$159$	13.0596	+	3.83463i	1.03569	+	0.304106i
$160$	17.2822	−	2.08163i	1.36627	−	0.164568i
$161$	3.14088	−	9.29296i	0.247536	−	0.732388i
$162$	−0.803588	+	1.16372i	−0.0631358	+	0.0914306i
$163$	2.73969	−	9.33052i	0.214589	−	0.730823i	−0.779893	−	0.625913i	$-0.784726\pi$
$163$	2.73969	−	9.33052i	0.214589	−	0.730823i	0.994482	−	0.104910i	$-0.0334554\pi$
$164$	11.6867	+	4.29102i	0.912576	+	0.335072i
$165$	−1.75589	+	2.73221i	−0.136696	+	0.212702i
$166$	4.04601	−	4.36804i	0.314031	−	0.339026i
$167$	−16.2622	+	10.4511i	−1.25841	+	0.808730i	−0.988065	−	0.154035i	$-0.950773\pi$
$167$	−16.2622	+	10.4511i	−1.25841	+	0.808730i	−0.270342	+	0.962764i	$0.587137\pi$
$168$	−5.68530	+	1.07079i	−0.438631	+	0.0826134i
$169$	16.7623	+	19.3448i	1.28941	+	1.48806i
$170$	−9.98166	+	20.0687i	−0.765558	+	1.53920i
$171$	5.52581	+	2.52355i	0.422569	+	0.192981i
$172$	−7.26119	+	5.49376i	−0.553660	+	0.418896i
$173$	−3.74308	−	12.7478i	−0.284581	−	0.969194i	−0.970416	−	0.241437i	$-0.922381\pi$
$173$	−3.74308	−	12.7478i	−0.284581	−	0.969194i	0.685835	−	0.727757i	$-0.259437\pi$
$174$	4.07647	+	6.83070i	0.309036	+	0.517834i
$175$	−1.30087	−	9.04773i	−0.0983363	−	0.683944i
$176$	−0.558094	+	4.18474i	−0.0420679	+	0.315437i
$177$	−0.869372	−	1.90366i	−0.0653460	−	0.143088i
$178$	0.596520	−	17.9905i	0.0447111	−	1.34844i
$179$	20.1382	+	2.89543i	1.50520	+	0.216415i	0.845036	−	0.534709i	$-0.179579\pi$
$179$	20.1382	+	2.89543i	1.50520	+	0.216415i	0.660161	+	0.751124i	$0.270488\pi$
$180$	−6.02029	−	1.27746i	−0.448726	−	0.0952159i
$181$	−6.64116	−	5.75460i	−0.493634	−	0.427736i	0.372136	−	0.928178i	$-0.378625\pi$
$181$	−6.64116	−	5.75460i	−0.493634	−	0.427736i	−0.865770	+	0.500442i	$0.833171\pi$
$182$	11.3119	+	13.9640i	0.838491	+	1.03508i
$183$	3.64977			0.269798
$184$	3.78213	−	13.0267i	0.278822	−	0.960343i
$185$	7.89940			0.580776
$186$	1.59294	+	1.96642i	0.116800	+	0.144185i
$187$	−4.10836	−	3.55991i	−0.300433	−	0.260327i
$188$	−0.583218	+	2.74854i	−0.0425355	+	0.200458i
$189$	2.02458	+	0.291091i	0.147267	+	0.0211737i
$190$	−0.876071	+	26.4215i	−0.0635569	+	1.91682i
$191$	0.00570268	+	0.0124871i	0.000412631	+	0.000903537i	0.909838	−	0.414963i	$-0.136206\pi$
$191$	0.00570268	+	0.0124871i	0.000412631	+	0.000903537i	−0.909426	+	0.415867i	$0.863478\pi$
$192$	−7.79019	+	1.82013i	−0.562209	+	0.131357i
$193$	1.98763	+	13.8243i	0.143073	+	0.995095i	0.927219	+	0.374519i	$0.122192\pi$
$193$	1.98763	+	13.8243i	0.143073	+	0.995095i	−0.784146	+	0.620576i	$0.786899\pi$
$194$	−5.03417	−	8.43547i	−0.361433	−	0.605631i
$195$	5.38596	+	18.3429i	0.385697	+	1.31356i
$196$	−3.39854	−	4.49189i	−0.242753	−	0.320849i
$197$	21.9116	+	10.0067i	1.56114	+	0.712949i	0.993867	−	0.110581i	$-0.0352711\pi$
$197$	21.9116	+	10.0067i	1.56114	+	0.712949i	0.567273	+	0.823530i	$0.307998\pi$
$198$	0.664715	−	1.33645i	0.0472392	−	0.0949773i
$199$	−5.42293	−	6.25839i	−0.384421	−	0.443646i	0.530252	−	0.847840i	$-0.322097\pi$
$199$	−5.42293	−	6.25839i	−0.384421	−	0.443646i	−0.914673	+	0.404194i	$0.867552\pi$
$200$	−2.33955	−	12.4217i	−0.165431	−	0.878345i
$201$	−10.4889	+	6.74080i	−0.739829	+	0.475459i
$202$	17.1496	−	18.5146i	1.20664	−	1.30268i
$203$	6.22002	−	9.67853i	0.436560	−	0.679300i
$204$	3.55051	−	9.66988i	0.248585	−	0.677027i
$205$	5.39649	−	18.3787i	0.376907	−	1.28363i
$206$	−0.00787316	+	0.0114016i	−0.000548549	+	0.000794385i
$207$	−2.75339	+	3.92669i	−0.191374	+	0.272923i
$208$	16.4647	+	18.6135i	1.14162	+	1.29062i
$209$	−6.15189	−	1.80636i	−0.425535	−	0.124948i
$210$	2.22333	+	8.61896i	0.153424	+	0.594765i
$211$	10.5627	−	16.4358i	0.727163	−	1.13149i	−0.259027	−	0.965870i	$-0.583402\pi$
$211$	10.5627	−	16.4358i	0.727163	−	1.13149i	0.986190	−	0.165618i	$-0.0529618\pi$
$212$	−5.92223	−	26.5698i	−0.406740	−	1.82482i
$213$	−3.61135	−	5.61937i	−0.247446	−	0.385033i
$214$	−3.15586	+	17.7512i	−0.215730	+	1.21344i
$215$	9.17410	+	10.5875i	0.625668	+	0.722060i
$216$	2.81446	+	0.280785i	0.191499	+	0.0191050i
$217$	1.52048	−	3.32938i	0.103217	−	0.226013i
$218$	2.71241	+	0.895088i	0.183708	+	0.0606230i
$219$	−2.21524	−	7.54443i	−0.149692	−	0.509805i
$220$	6.48131	+	0.430282i	0.436970	+	0.0290096i
$221$	−31.6728	+	4.55386i	−2.13054	+	0.306326i
$222$	−3.60863	+	0.397295i	−0.242195	+	0.0266647i
$223$	−9.47107	−	20.7387i	−0.634229	−	1.38877i	−0.904704	−	0.426042i	$-0.859908\pi$
$223$	−9.47107	−	20.7387i	−0.634229	−	1.38877i	0.270474	−	0.962727i	$-0.412820\pi$
$224$	7.37462	+	8.91583i	0.492738	+	0.595714i
$225$	−0.635997	+	4.42345i	−0.0423998	+	0.294897i
$226$	−7.19953	+	3.00371i	−0.478905	+	0.199804i
$227$	−13.9733	−	12.1079i	−0.927440	−	0.803631i	0.0533749	−	0.998575i	$-0.483002\pi$
$227$	−13.9733	−	12.1079i	−0.927440	−	0.803631i	−0.980814	+	0.194944i	$0.937548\pi$
$228$	−0.928642	−	12.1140i	−0.0615008	−	0.802270i
$229$		−	6.90517i		−	0.456306i	−0.973625	−	0.228153i	$-0.926731\pi$
$229$		−	6.90517i		−	0.456306i	0.973625	−	0.228153i	$-0.0732687\pi$
$230$	−20.3841	−	4.47866i	−1.34409	−	0.295314i
$231$	−2.15881			−0.142039
$232$	8.01292	−	13.7440i	0.526074	−	0.902337i
$233$	−3.39580	+	3.91896i	−0.222466	+	0.256740i	−0.856001	−	0.516975i	$-0.827058\pi$
$233$	−3.39580	+	3.91896i	−0.222466	+	0.256740i	0.633534	+	0.773715i	$0.281604\pi$
$234$	−3.38298	−	8.10858i	−0.221152	−	0.530075i
$235$	4.27901	+	0.615229i	0.279132	+	0.0401331i
$236$	−2.49116	+	3.36348i	−0.162161	+	0.218944i
$237$	11.3468	−	5.18193i	0.737057	−	0.336603i
$238$	−14.8092	+	1.63043i	−0.959935	+	0.105685i
$239$	−1.99437	−	13.8711i	−0.129005	−	0.897249i	−0.946819	−	0.321766i	$-0.895723\pi$
$239$	−1.99437	−	13.8711i	−0.129005	−	0.897249i	0.817814	−	0.575482i	$-0.195186\pi$
$240$	3.58824	+	11.7740i	0.231620	+	0.760010i
$241$	−4.89209	+	1.43645i	−0.315127	+	0.0925297i	−0.435472	−	0.900202i	$-0.643418\pi$
$241$	−4.89209	+	1.43645i	−0.315127	+	0.0925297i	0.120344	+	0.992732i	$0.461600\pi$
$242$	4.38128	−	13.2767i	0.281639	−	0.853460i
$243$	−0.909632	−	0.415415i	−0.0583529	−	0.0266489i
$244$	−3.53098	−	6.38869i	−0.226048	−	0.408994i
$245$	−6.54959	+	5.67525i	−0.418438	+	0.362579i
$246$	−1.54089	+	8.66725i	−0.0982437	+	0.552604i
$247$	−31.7492	+	20.4040i	−2.02015	+	1.29827i
$248$	1.90099	−	4.69076i	0.120713	−	0.297864i
$249$	3.54176	+	2.27615i	0.224450	+	0.144245i
$250$	2.23779	−	0.577254i	0.141530	−	0.0365087i
$251$	−0.685205	+	2.33360i	−0.0432498	+	0.147295i	−0.978287	−	0.207254i	$-0.933547\pi$
$251$	−0.685205	+	2.33360i	−0.0432498	+	0.147295i	0.935037	+	0.354549i	$0.115366\pi$
$252$	−1.44915	−	3.82552i	−0.0912879	−	0.240985i
$253$	2.28667	−	4.51580i	0.143762	−	0.283906i
$254$	8.56612	−	12.4051i	0.537486	−	0.778364i
$255$	−15.2071	−	4.46520i	−0.952305	−	0.279622i
$256$	10.7227	+	11.8754i	0.670168	+	0.742210i
$257$	−9.50189	−	6.10649i	−0.592711	−	0.380913i	0.209627	−	0.977781i	$-0.432775\pi$
$257$	−9.50189	−	6.10649i	−0.592711	−	0.380913i	−0.802339	+	0.596869i	$0.796411\pi$
$258$	−4.72343	−	4.37520i	−0.294068	−	0.272388i
$259$	2.83877	+	4.41722i	0.176393	+	0.274472i
$260$	26.8975	−	27.1737i	1.66811	−	1.68524i
$261$	−4.25092	+	3.68344i	−0.263125	+	0.227999i
$262$	−4.76260	+	9.57550i	−0.294234	+	0.591576i
$263$	−3.57755	+	7.83374i	−0.220601	+	0.483049i	−0.987282	−	0.158979i	$-0.949180\pi$
$263$	−3.57755	+	7.83374i	−0.220601	+	0.483049i	0.766681	+	0.642028i	$0.221907\pi$
$264$	−2.98245	+	0.129411i	−0.183557	+	0.00796467i
$265$	−40.1864	+	11.7998i	−2.46863	+	0.724856i
$266$	−15.0893	+	9.00508i	−0.925183	+	0.552137i
$267$	12.5986	−	1.81141i	0.771024	−	0.110857i
$268$	21.9469	+	11.8387i	1.34062	+	0.723166i
$269$	−22.7859	+	10.4060i	−1.38928	+	0.634463i	−0.962845	−	0.270056i	$-0.912958\pi$
$269$	−22.7859	+	10.4060i	−1.38928	+	0.634463i	−0.426435	+	0.904518i	$0.640231\pi$
$270$	0.144215	−	4.34938i	0.00877662	−	0.264695i
$271$	0.351470	−	2.44453i	0.0213503	−	0.148495i	−0.976358	−	0.216161i	$-0.930646\pi$
$271$	0.351470	−	2.44453i	0.0213503	−	0.148495i	0.997708	+	0.0676666i	$0.0215554\pi$
$272$	−20.3615	+	3.14021i	−1.23460	+	0.190403i
$273$	−8.32152	+	9.60355i	−0.503641	+	0.581233i
$274$	−8.56832	+	6.94096i	−0.517631	+	0.419319i
$275$		−	4.71674i		−	0.284430i
$276$	9.53719	+	1.02075i	0.574072	+	0.0614419i
$277$			17.1773i			1.03209i	0.856563	+	0.516043i	$0.172596\pi$
$277$			17.1773i			1.03209i	−0.856563	+	0.516043i	$0.827404\pi$
$278$	13.6765	+	16.8830i	0.820260	+	1.01258i
$279$	−1.17184	+	1.35237i	−0.0701562	+	0.0809646i
$280$	12.9360	−	12.2302i	0.773073	−	0.730896i
$281$	−2.20820	+	15.3584i	−0.131730	+	0.916203i	0.811569	+	0.584257i	$0.198614\pi$
$281$	−2.20820	+	15.3584i	−0.131730	+	0.916203i	−0.943299	+	0.331945i	$0.892295\pi$
$282$	−1.98569	−	0.0658407i	−0.118246	−	0.00392076i
$283$	−2.63215	+	1.20206i	−0.156465	+	0.0714552i	−0.492108	−	0.870534i	$-0.663774\pi$
$283$	−2.63215	+	1.20206i	−0.156465	+	0.0714552i	0.335643	+	0.941989i	$0.391046\pi$
$284$	−6.34255	+	11.7579i	−0.376361	+	0.697705i
$285$	−18.5028	+	2.66030i	−1.09601	+	0.157583i
$286$	4.75217	+	7.96293i	0.281002	+	0.470858i
$287$	12.2164	−	3.58706i	0.721111	−	0.211737i
$288$	−2.23136	−	5.19818i	−0.131484	−	0.306305i
$289$	3.95814	−	8.66712i	0.232832	−	0.509831i
$290$	−21.9165	−	10.9007i	−1.28698	−	0.640110i
$291$	5.24960	−	4.54881i	0.307737	−	0.266656i
$292$	−11.0629	+	11.1765i	−0.647408	+	0.654057i
$293$	7.50590	+	11.6794i	0.438499	+	0.682318i	0.988222	−	0.153029i	$-0.0489029\pi$
$293$	7.50590	+	11.6794i	0.438499	+	0.682318i	−0.549722	+	0.835347i	$0.685267\pi$
$294$	2.70657	−	2.92199i	0.157850	−	0.170414i
$295$	5.41753	+	3.48163i	0.315421	+	0.202709i
$296$	4.18662	+	5.93232i	0.243343	+	0.344809i
$297$	1.01270	+	0.297354i	0.0587625	+	0.0172542i
$298$	9.09231	+	6.27854i	0.526703	+	0.363706i
$299$	−11.2743	−	27.5793i	−0.652012	−	1.59495i
$300$	8.35828	−	3.16621i	0.482566	−	0.182801i
$301$	−2.62349	+	8.93477i	−0.151215	+	0.514992i
$302$	3.55856	+	13.7951i	0.204772	+	0.793821i
$303$	15.0123	+	9.64782i	0.862434	+	0.554253i
$304$	−20.3064	+	13.3453i	−1.16465	+	0.765404i
$305$	−9.44806	+	6.07190i	−0.540994	+	0.347676i
$306$	7.17152	+	1.27498i	0.409969	+	0.0728856i
$307$	−13.2484	+	11.4798i	−0.756126	+	0.655187i	−0.945095	−	0.326796i	$-0.894031\pi$
$307$	−13.2484	+	11.4798i	−0.756126	+	0.655187i	0.188969	+	0.981983i	$0.439485\pi$
$308$	2.08855	+	3.77887i	0.119006	+	0.215321i
$309$	−0.00891213	−	0.00407003i	−0.000506993	−	0.000231536i
$310$	−7.39502	−	2.44033i	−0.420009	−	0.138602i
$311$	−0.120743	+	0.0354534i	−0.00684672	+	0.00201038i	−0.285154	−	0.958482i	$-0.592045\pi$
$311$	−0.120743	+	0.0354534i	−0.00684672	+	0.00201038i	0.278307	+	0.960492i	$0.410227\pi$
$312$	−10.9207	+	13.7664i	−0.618263	+	0.779367i
$313$	1.97845	+	13.7604i	0.111828	+	0.777784i	0.966139	+	0.258021i	$0.0830705\pi$
$313$	1.97845	+	13.7604i	0.111828	+	0.777784i	−0.854311	+	0.519763i	$0.826020\pi$
$314$	−3.73877	−	33.9592i	−0.210991	−	1.91643i
$315$	−5.72525	+	2.61463i	−0.322581	+	0.147318i
$316$	−20.0482	−	14.8487i	−1.12780	−	0.835303i
$317$	27.3563	+	3.93324i	1.53648	+	0.220913i	0.857979	−	0.513685i	$-0.171720\pi$
$317$	27.3563	+	3.93324i	1.53648	+	0.220913i	0.678503	+	0.734598i	$0.262629\pi$
$318$	17.7646	−	7.41157i	0.996190	−	0.415620i
$319$	3.88768	−	4.48662i	0.217668	−	0.251203i
$320$	17.1382	−	17.6718i	0.958057	−	0.987885i
$321$	−12.7488			−0.711568
$322$	−4.82096	−	13.0079i	−0.268662	−	0.724904i
$323$		−	31.2884i		−	1.74093i
$324$	0.152869	+	1.99415i	0.00849269	+	0.110786i
$325$	−20.9826	−	18.1815i	−1.16390	−	1.00853i
$326$	−5.29526	−	12.6921i	−0.293277	−	0.702950i
$327$	−0.287433	+	1.99914i	−0.0158951	+	0.110553i
$328$	16.6622	−	5.68792i	0.920017	−	0.314063i
$329$	1.19370	+	2.61384i	0.0658109	+	0.144106i
$330$	0.502641	+	4.56548i	0.0276695	+	0.251321i
$331$	−25.1170	+	3.61128i	−1.38055	+	0.198494i	−0.792275	−	0.610164i	$-0.791103\pi$
$331$	−25.1170	+	3.61128i	−1.38055	+	0.198494i	−0.588279	+	0.808658i	$0.700194\pi$
$332$	0.557774	−	8.40171i	0.0306118	−	0.461104i
$333$	−0.723237	−	2.46312i	−0.0396331	−	0.134978i
$334$	−8.56706	+	25.9610i	−0.468769	+	1.42052i
$335$	15.9381	−	34.8995i	0.870789	−	1.90676i
$336$	−5.29435	+	6.23766i	−0.288830	+	0.340292i
$337$	20.8184	+	24.0257i	1.13405	+	1.30876i	0.945101	+	0.326777i	$0.105963\pi$
$337$	20.8184	+	24.0257i	1.13405	+	1.30876i	0.188949	+	0.981987i	$0.439492\pi$
$338$	35.6405	+	6.33629i	1.93859	+	0.344649i
$339$	−2.98225	−	4.64047i	−0.161973	−	0.252036i
$340$	6.89609	+	30.9389i	0.373993	+	1.67790i
$341$	1.02109	−	1.58885i	0.0552952	−	0.0860411i
$342$	8.31871	−	2.14587i	0.449824	−	0.116036i
$343$	−19.2650	−	5.65672i	−1.04021	−	0.305434i
$344$	−3.08881	+	12.5009i	−0.166538	+	0.674002i
$345$	0.595034	−	14.7456i	0.0320356	−	0.793874i
$346$	−15.4611	−	10.6764i	−0.831195	−	0.573968i
$347$	−4.25461	+	14.4899i	−0.228399	+	0.777857i	0.762933	+	0.646478i	$0.223759\pi$
$347$	−4.25461	+	14.4899i	−0.228399	+	0.777857i	−0.991332	+	0.131379i	$0.958059\pi$
$348$	10.5602	+	3.87741i	0.566086	+	0.207851i
$349$	5.00036	−	7.78071i	0.267663	−	0.416492i	−0.681240	−	0.732060i	$-0.738559\pi$
$349$	5.00036	−	7.78071i	0.267663	−	0.416492i	0.948903	+	0.315568i	$0.102195\pi$
$350$	−9.48367	−	8.78449i	−0.506924	−	0.469551i
$351$	5.22640	−	3.35880i	0.278965	−	0.179280i
$352$	3.11191	+	5.09540i	0.165865	+	0.271586i
$353$	−16.5565	−	19.1073i	−0.881215	−	1.01698i	−0.999711	−	0.0240218i	$-0.992353\pi$
$353$	−16.5565	−	19.1073i	−0.881215	−	1.01698i	0.118496	−	0.992954i	$-0.462193\pi$
$354$	−2.64996	−	1.31802i	−0.140844	−	0.0700519i
$355$	18.6972	+	8.53874i	0.992346	+	0.453189i
$356$	−15.3594	−	20.3007i	−0.814044	−	1.07593i
$357$	−2.96803	−	10.1082i	−0.157085	−	0.534982i
$358$	24.7072	−	14.7449i	1.30582	−	0.779294i
$359$	3.18470	+	22.1500i	0.168082	+	1.16903i	0.882844	+	0.469667i	$0.155626\pi$
$359$	3.18470	+	22.1500i	0.168082	+	1.16903i	−0.714762	+	0.699368i	$0.753465\pi$
$360$	−7.75284	+	3.95538i	−0.408610	+	0.208467i
$361$	−7.43712	−	16.2850i	−0.391428	−	0.857107i
$362$	−12.4206	−	0.411837i	−0.652812	−	0.0216457i
$363$	9.78540	+	1.40693i	0.513600	+	0.0738446i
$364$	24.8611	+	5.27532i	1.30308	+	0.276502i
$365$	18.2858	+	15.8447i	0.957120	+	0.829350i
$366$	4.01071	−	3.24897i	0.209643	−	0.169826i
$367$	22.8095			1.19065			0.595324	−	0.803486i	$-0.297024\pi$
$367$	22.8095			1.19065			0.595324	+	0.803486i	$0.297024\pi$
$368$	−7.44004	−	17.6818i	−0.387839	−	0.921727i
$369$	−6.22477			−0.324049
$370$	8.68062	−	7.03193i	0.451284	−	0.365573i
$371$	−21.0398	−	18.2311i	−1.09233	−	0.946513i
$372$	3.50095	+	0.742872i	0.181516	+	0.0385161i
$373$	−8.80304	−	1.26569i	−0.455804	−	0.0655347i	−0.0894108	−	0.995995i	$-0.528498\pi$
$373$	−8.80304	−	1.26569i	−0.455804	−	0.0655347i	−0.366393	+	0.930460i	$0.619407\pi$
$374$	−7.68364	−	0.254771i	−0.397311	−	0.0131739i
$375$	0.678852	+	1.48648i	0.0350558	+	0.0767614i
$376$	1.80582	+	3.53953i	0.0931278	+	0.182537i
$377$	−4.97314	−	34.5889i	−0.256130	−	1.78142i
$378$	2.48393	−	1.48237i	0.127759	−	0.0762450i
$379$	6.23067	+	21.2197i	0.320048	+	1.08998i	0.949714	+	0.313117i	$0.101373\pi$
$379$	6.23067	+	21.2197i	0.320048	+	1.08998i	−0.629667	+	0.776865i	$0.716809\pi$
$380$	22.5573	+	29.8143i	1.15717	+	1.52944i
$381$	9.69653	+	4.42826i	0.496768	+	0.226867i
$382$	0.0173825	+	0.00864560i	0.000889366	+	0.000442347i
$383$	6.01600	+	6.94283i	0.307403	+	0.354762i	0.888340	−	0.459187i	$-0.151859\pi$
$383$	6.01600	+	6.94283i	0.307403	+	0.354762i	−0.580937	+	0.813949i	$0.697314\pi$
$384$	−6.94035	+	8.93485i	−0.354173	+	0.455955i
$385$	5.58847	−	3.59149i	0.284815	−	0.183039i
$386$	14.4904	+	13.4221i	0.737541	+	0.683167i
$387$	2.46135	−	3.82993i	0.125117	−	0.194686i
$388$	−13.0412	−	4.78835i	−0.662064	−	0.243091i
$389$	1.79412	−	6.11020i	0.0909653	−	0.309799i	−0.901424	−	0.432937i	$-0.857477\pi$
$389$	1.79412	−	6.11020i	0.0909653	−	0.309799i	0.992390	+	0.123137i	$0.0392955\pi$
$390$	22.2472	+	15.3624i	1.12653	+	0.777907i
$391$	24.2881	+	4.49831i	1.22830	+	0.227489i
$392$	−7.73325	−	1.91079i	−0.390588	−	0.0965095i
$393$	−7.25584	−	2.13051i	−0.366009	−	0.107470i
$394$	32.9864	−	8.50910i	1.66183	−	0.428682i
$395$	−20.7524	+	32.2914i	−1.04417	+	1.62476i
$396$	−0.459236	−	2.06034i	−0.0230775	−	0.103536i
$397$	0.746317	+	1.16129i	0.0374566	+	0.0582835i	0.859477	−	0.511175i	$-0.170789\pi$
$397$	0.746317	+	1.16129i	0.0374566	+	0.0582835i	−0.822020	+	0.569458i	$0.807153\pi$
$398$	−11.5304	−	2.04991i	−0.577965	−	0.102753i
$399$	−8.13687	−	9.39044i	−0.407353	−	0.470110i
$400$	−13.6285	−	11.5675i	−0.681426	−	0.578374i
$401$	12.4263	−	27.2097i	0.620537	−	1.35879i	−0.294590	−	0.955624i	$-0.595183\pi$
$401$	12.4263	−	27.2097i	0.620537	−	1.35879i	0.915128	−	0.403164i	$-0.132090\pi$
$402$	−5.52562	+	16.7445i	−0.275593	+	0.835138i
$403$	−3.13207	−	10.6669i	−0.156020	−	0.531354i
$404$	2.36421	−	35.6119i	0.117624	−	1.77176i
$405$	3.04584	−	0.437926i	0.151349	−	0.0217607i
$406$	−1.78054	−	16.1727i	−0.0883669	−	0.802636i
$407$	1.12554	+	2.46460i	0.0557912	+	0.122166i
$408$	−4.70635	−	13.7868i	−0.232999	−	0.682548i
$409$	−1.56249	+	10.8673i	−0.0772600	+	0.537355i	0.914029	+	0.405649i	$0.132955\pi$
$409$	−1.56249	+	10.8673i	−0.0772600	+	0.537355i	−0.991289	+	0.131706i	$0.957955\pi$
$410$	−10.4303	−	25.0002i	−0.515117	−	1.23467i
$411$	−5.89274	−	5.10609i	−0.290667	−	0.251865i
$412$	0.00149773	+	0.0195377i	7.37879e−5	+	0.000962553i
$413$			4.28057i			0.210633i
$414$	0.469793	+	6.76604i	0.0230891	+	0.332533i
$415$	−12.9552			−0.635945
$416$	34.6624	+	5.79768i	1.69947	+	0.284255i
$417$	−10.0610	+	11.6110i	−0.492691	+	0.568595i
$418$	−8.36828	+	3.49133i	−0.409306	+	0.170766i
$419$	−6.24265	−	0.897558i	−0.304973	−	0.0438486i	−0.0118708	−	0.999930i	$-0.503779\pi$
$419$	−6.24265	−	0.897558i	−0.304973	−	0.0438486i	−0.293103	+	0.956081i	$0.594688\pi$
$420$	10.1157	+	7.49216i	0.493594	+	0.365580i
$421$	−13.5899	+	6.20628i	−0.662329	+	0.302476i	−0.718071	−	0.695970i	$-0.754975\pi$
$421$	−13.5899	+	6.20628i	−0.662329	+	0.302476i	0.0557421	+	0.998445i	$0.482248\pi$
$422$	−3.02367	−	27.4639i	−0.147190	−	1.33692i
$423$	−0.199934	−	1.39057i	−0.00972111	−	0.0676118i
$424$	−30.1599	−	23.9255i	−1.46470	−	1.16193i
$425$	22.0851	−	6.48478i	1.07129	−	0.314558i
$426$	−8.97078	−	2.96033i	−0.434636	−	0.143428i
$427$	−6.79061	−	3.10117i	−0.328621	−	0.150076i
$428$	12.3339	+	22.3160i	0.596180	+	1.07868i
$429$	−4.95553	+	4.29400i	−0.239255	+	0.207316i
$430$	19.5062	+	3.46788i	0.940672	+	0.167236i
$431$	−28.8523	+	18.5422i	−1.38976	+	0.893148i	−0.999619	−	0.0276053i	$-0.991212\pi$
$431$	−28.8523	+	18.5422i	−1.38976	+	0.893148i	−0.390146	+	0.920753i	$0.627575\pi$
$432$	3.34274	−	2.19683i	0.160828	−	0.105695i
$433$	−6.56046	−	4.21615i	−0.315275	−	0.202615i	0.373427	−	0.927660i	$-0.378183\pi$
$433$	−6.56046	−	4.21615i	−0.315275	−	0.202615i	−0.688702	+	0.725045i	$0.741819\pi$
$434$	−1.29292	−	5.01214i	−0.0620621	−	0.240590i
$435$	4.87632	−	16.6072i	0.233802	−	0.796256i
$436$	3.77745	−	1.43094i	0.180907	−	0.0685297i
$437$	28.2617	−	7.07411i	1.35194	−	0.338400i
$438$	−9.15026	−	6.31855i	−0.437216	−	0.301912i
$439$	33.1379	+	9.73018i	1.58159	+	0.464396i	0.950347	−	0.311191i	$-0.100728\pi$
$439$	33.1379	+	9.73018i	1.58159	+	0.464396i	0.631240	+	0.775587i	$0.282546\pi$
$440$	7.50531	−	5.29673i	0.357802	−	0.252512i
$441$	2.36926	+	1.52263i	0.112822	+	0.0725062i
$442$	−30.7513	+	33.1988i	−1.46269	+	1.57911i
$443$	−2.66143	−	4.14127i	−0.126448	−	0.196758i	0.772257	−	0.635310i	$-0.219128\pi$
$443$	−2.66143	−	4.14127i	−0.126448	−	0.196758i	−0.898706	+	0.438552i	$0.855491\pi$
$444$	−3.61184	+	3.64893i	−0.171410	+	0.173171i
$445$	−29.6002	+	25.6488i	−1.40319	+	1.21587i
$446$	−28.8690	−	14.3587i	−1.36699	−	0.679904i
$447$	−3.24569	+	7.10708i	−0.153516	+	0.336153i
$448$	16.0407	+	3.23278i	0.757851	+	0.152734i
$449$	33.3986	−	9.80670i	1.57618	−	0.462807i	0.627384	−	0.778710i	$-0.284126\pi$
$449$	33.3986	−	9.80670i	1.57618	−	0.462807i	0.948791	+	0.315903i	$0.102307\pi$
$450$	3.23880	+	5.42707i	0.152679	+	0.255834i
$451$	6.50305	−	0.934997i	0.306217	−	0.0440273i
$452$	−5.23767	+	9.70968i	−0.246359	+	0.456705i
$453$	−9.16359	+	4.18487i	−0.430543	+	0.196622i
$454$	−26.1335	−	0.866521i	−1.22650	−	0.0406679i
$455$	5.56487	−	38.7045i	0.260885	−	1.81449i
$456$	−11.8042	−	12.4854i	−0.552782	−	0.584680i
$457$	−3.07542	+	3.54923i	−0.143862	+	0.166026i	−0.823108	−	0.567885i	$-0.807762\pi$
$457$	−3.07542	+	3.54923i	−0.143862	+	0.166026i	0.679245	+	0.733911i	$0.262307\pi$
$458$	−6.14688	−	7.58805i	−0.287225	−	0.354566i
$459$			5.15055i			0.240407i
$460$	−26.3869	+	13.2241i	−1.23029	+	0.616576i
$461$			17.2294i			0.802452i	0.915979	+	0.401226i	$0.131416\pi$
$461$			17.2294i			0.802452i	−0.915979	+	0.401226i	$0.868584\pi$
$462$	−2.37231	+	1.92174i	−0.110370	+	0.0894076i
$463$	−5.42827	+	6.26455i	−0.252273	+	0.291139i	−0.867734	−	0.497029i	$-0.834424\pi$
$463$	−5.42827	+	6.26455i	−0.252273	+	0.291139i	0.615461	+	0.788167i	$0.288970\pi$
$464$	−3.42934	−	22.2362i	−0.159203	−	1.03229i
$465$	0.783646	−	5.45038i	0.0363407	−	0.252755i
$466$	−0.243025	+	7.32942i	−0.0112579	+	0.339529i
$467$	33.5603	−	15.3265i	1.55299	−	0.709225i	0.560114	−	0.828415i	$-0.310757\pi$
$467$	33.5603	−	15.3265i	1.55299	−	0.709225i	0.992871	+	0.119190i	$0.0380299\pi$
$468$	−10.9357	−	5.89900i	−0.505502	−	0.272681i
$469$	25.2428	−	3.62936i	1.16560	−	0.167588i
$470$	5.24985	−	3.13304i	0.242158	−	0.144516i
$471$	23.1793	−	6.80605i	1.06805	−	0.313606i
$472$	0.256600	+	5.91371i	0.0118110	+	0.272201i
$473$	−1.99610	+	4.37085i	−0.0917809	+	0.200972i
$474$	7.85611	−	15.7952i	0.360843	−	0.725497i
$475$	20.5169	−	17.7780i	0.941382	−	0.815712i
$476$	−14.8223	+	14.9746i	−0.679380	+	0.686358i
$477$	7.35860	+	11.4502i	0.336927	+	0.524269i
$478$	−14.5395	−	13.4676i	−0.665020	−	0.615992i
$479$	20.3730	+	13.0929i	0.930864	+	0.598230i	0.915791	−	0.401656i	$-0.131565\pi$
$479$	20.3730	+	13.0929i	0.930864	+	0.598230i	0.0150737	+	0.999886i	$0.495202\pi$
$480$	14.4242	+	9.74421i	0.658370	+	0.444760i
$481$	15.3025	+	4.49321i	0.697732	+	0.204873i
$482$	−4.09719	+	5.93337i	−0.186622	+	0.270258i
$483$	8.45931	−	4.96631i	0.384912	−	0.225975i
$484$	−7.00418	−	18.4899i	−0.318372	−	0.840449i
$485$	−6.02194	+	20.5088i	−0.273442	+	0.931259i
$486$	−1.36939	+	0.353243i	−0.0621166	+	0.0160234i
$487$	7.47429	+	4.80344i	0.338693	+	0.217664i	0.698920	−	0.715200i	$-0.253664\pi$
$487$	7.47429	+	4.80344i	0.338693	+	0.217664i	−0.360227	+	0.932865i	$0.617301\pi$
$488$	−9.56729	−	3.87727i	−0.433091	−	0.175516i
$489$	8.18071	−	5.25742i	0.369944	−	0.237749i
$490$	−2.14529	+	12.0669i	−0.0969141	+	0.545125i
$491$	−1.89272	+	1.64005i	−0.0854171	+	0.0740143i	−0.696523	−	0.717535i	$-0.745270\pi$
$491$	−1.89272	+	1.64005i	−0.0854171	+	0.0740143i	0.611106	+	0.791549i	$0.290725\pi$
$492$	6.02218	+	10.8961i	0.271501	+	0.491233i
$493$	26.3526	+	12.0348i	1.18686	+	0.542022i
$494$	−16.7257	+	50.6845i	−0.752526	+	2.28040i
$495$	−3.11623	+	0.915008i	−0.140064	+	0.0411265i
$496$	−2.08665	−	6.84689i	−0.0936935	−	0.307434i
$497$	1.94442	+	13.5237i	0.0872190	+	0.606621i
$498$	5.91823	−	0.651572i	0.265202	−	0.0291977i
$499$	19.6863	−	8.99044i	0.881281	−	0.402468i	0.0772198	−	0.997014i	$-0.475396\pi$
$499$	19.6863	−	8.99044i	0.881281	−	0.402468i	0.804061	+	0.594547i	$0.202668\pi$
$500$	1.94523	−	2.62639i	0.0869933	−	0.117456i
$501$	−19.1342	−	2.75108i	−0.854852	−	0.122909i
$502$	1.32436	+	3.17434i	0.0591092	+	0.141678i
$503$	1.19141	−	1.37496i	0.0531223	−	0.0613064i	−0.728567	−	0.684975i	$-0.759813\pi$
$503$	1.19141	−	1.37496i	0.0531223	−	0.0613064i	0.781689	+	0.623669i	$0.214359\pi$
$504$	−4.99788	−	2.91383i	−0.222623	−	0.129792i
$505$	−54.9125			−2.44357
$506$	−1.50709	−	6.99795i	−0.0669985	−	0.311097i
$507$			25.5968i			1.13679i
$508$	−1.62955	−	21.2573i	−0.0722998	−	0.943141i
$509$	−1.56719	−	1.35798i	−0.0694646	−	0.0601914i	0.619437	−	0.785047i	$-0.287361\pi$
$509$	−1.56719	−	1.35798i	−0.0694646	−	0.0601914i	−0.688901	+	0.724855i	$0.741907\pi$
$510$	−20.6859	+	8.63034i	−0.915985	+	0.382158i
$511$	−2.28883	+	15.9191i	−0.101252	+	0.704221i
$512$	22.3544	+	3.50460i	0.987933	+	0.154883i
$513$	2.52355	+	5.52581i	0.111418	+	0.243970i
$514$	−15.8775	+	1.74805i	−0.700326	+	0.0771030i
$515$	0.0298417	−	0.00429058i	0.00131498	−	0.000189066i
$516$	−9.08529	−	0.603155i	−0.399958	−	0.0265524i
$517$	0.417743	+	1.42270i	0.0183723	+	0.0625704i
$518$	7.05165	+	2.32702i	0.309832	+	0.102244i
$519$	5.51918	−	12.0853i	0.242265	−	0.530486i
$520$	5.36785	−	53.8048i	0.235396	−	2.35950i
$521$	−0.608146	−	0.701838i	−0.0266434	−	0.0307481i	0.742271	−	0.670099i	$-0.233748\pi$
$521$	−0.608146	−	0.701838i	−0.0266434	−	0.0307481i	−0.768915	+	0.639351i	$0.779203\pi$
$522$	−1.39237	+	7.83182i	−0.0609422	+	0.342789i
$523$	−20.7683	−	32.3161i	−0.908135	−	1.41309i	−0.910691	−	0.413088i	$-0.864450\pi$
$523$	−20.7683	−	32.3161i	−0.908135	−	1.41309i	0.00255637	−	0.999997i	$-0.499186\pi$
$524$	3.29037	+	14.7621i	0.143740	+	0.644884i
$525$	4.94187	−	7.68970i	0.215681	−	0.335606i
$526$	3.04213	+	11.7931i	0.132643	+	0.514205i
$527$	8.84330	+	2.59663i	0.385220	+	0.113111i
$528$	−3.16220	+	2.79714i	−0.137617	+	0.121730i
$529$	1.42822	+	22.9556i	0.0620966	+	0.998070i
$530$	−33.6566	+	48.7401i	−1.46195	+	2.11713i
$531$	0.589604	−	2.00801i	0.0255866	−	0.0871401i
$532$	−8.56535	+	23.3279i	−0.371355	+	1.01139i
$533$	20.9078	−	32.5331i	0.905616	−	1.40917i
$534$	12.2321	−	13.2057i	0.529334	−	0.571465i
$535$	33.0025	−	21.2094i	1.42682	−	0.916963i
$536$	34.6559	−	6.52724i	1.49691	−	0.281934i
$537$	13.3233	+	15.3759i	0.574943	+	0.663520i
$538$	−15.7761	+	31.7187i	−0.680154	+	1.36749i
$539$	−2.70388	−	1.23482i	−0.116465	−	0.0531876i
$540$	−3.71327	−	4.90789i	−0.159794	−	0.211202i
$541$	12.6045	+	42.9270i	0.541910	+	1.84557i	0.533805	+	0.845607i	$0.320761\pi$
$541$	12.6045	+	42.9270i	0.541910	+	1.84557i	0.00810409	+	0.999967i	$0.497420\pi$
$542$	−1.78986	−	2.99916i	−0.0768809	−	0.128825i
$543$	−1.25059	−	8.69808i	−0.0536681	−	0.373270i
$544$	−19.5798	+	21.5762i	−0.839475	+	0.925074i
$545$	−2.58178	−	5.65331i	−0.110591	−	0.242161i
$546$	−0.595542	+	17.9610i	−0.0254868	+	0.768659i
$547$	38.1647	+	5.48726i	1.63180	+	0.234618i	0.896476	−	0.443092i	$-0.146119\pi$
$547$	38.1647	+	5.48726i	1.63180	+	0.234618i	0.735329	+	0.677710i	$0.237028\pi$
$548$	−3.23694	+	15.2548i	−0.138275	+	0.651652i
$549$	2.75831	+	2.39009i	0.117722	+	0.102006i
$550$	−4.19877	−	5.18320i	−0.179036	−	0.221012i
$551$	34.1692			1.45566
$552$	11.3890	−	7.36817i	0.484749	−	0.313610i
$553$	−25.5145			−1.08499
$554$	15.2910	+	18.8761i	0.649653	+	0.801968i
$555$	5.96997	+	5.17301i	0.253411	+	0.219582i
$556$	30.0580	+	6.37806i	1.27474	+	0.270490i
$557$	−7.64714	−	1.09949i	−0.324020	−	0.0465870i	−0.0216143	−	0.999766i	$-0.506881\pi$
$557$	−7.64714	−	1.09949i	−0.324020	−	0.0465870i	−0.302406	+	0.953179i	$0.597790\pi$
$558$	−0.0838644	+	2.52927i	−0.00355026	+	0.107073i
$559$	11.7496	+	25.7279i	0.496953	+	1.08818i
$560$	3.32812	−	24.9552i	0.140639	−	1.05455i
$561$	−0.773643	−	5.38081i	−0.0326632	−	0.227178i
$562$	11.2452	+	18.8429i	0.474350	+	0.794841i
$563$	5.36677	+	18.2776i	0.226183	+	0.770307i	0.991888	+	0.127116i	$0.0405719\pi$
$563$	5.36677	+	18.2776i	0.226183	+	0.770307i	−0.765705	+	0.643191i	$0.777610\pi$
$564$	−2.24068	+	1.69528i	−0.0943496	+	0.0713843i
$565$	15.4401	+	7.05128i	0.649572	+	0.296649i
$566$	−1.82240	+	3.66404i	−0.0766011	+	0.154011i
$567$	1.33945	+	1.54581i	0.0562517	+	0.0649179i
$568$	3.49694	+	18.5668i	0.146728	+	0.779044i
$569$	−1.95217	+	1.25458i	−0.0818392	+	0.0525949i	−0.580920	−	0.813960i	$-0.697307\pi$
$569$	−1.95217	+	1.25458i	−0.0818392	+	0.0525949i	0.499081	+	0.866555i	$0.333671\pi$
$570$	−17.9645	+	19.3943i	−0.752449	+	0.812339i
$571$	3.46138	−	5.38601i	0.144854	−	0.225398i	−0.761243	−	0.648466i	$-0.775411\pi$
$571$	3.46138	−	5.38601i	0.144854	−	0.225398i	0.906098	+	0.423069i	$0.139047\pi$
$572$	12.3106	+	4.52012i	0.514733	+	0.188996i
$573$	−0.00386753	+	0.0131716i	−0.000161568	+	0.000550251i
$574$	10.2314	−	14.8167i	0.427050	−	0.618435i
$575$	10.8508	+	18.4825i	0.452508	+	0.770775i
$576$	−7.07937	−	3.72593i	−0.294974	−	0.155247i
$577$	13.2180	+	3.88117i	0.550274	+	0.161575i	0.545038	−	0.838411i	$-0.316515\pi$
$577$	13.2180	+	3.88117i	0.550274	+	0.161575i	0.00523612	+	0.999986i	$0.498333\pi$
$578$	−3.36576	−	13.0477i	−0.139997	−	0.542714i
$579$	−7.55084	+	11.7493i	−0.313802	+	0.488286i
$580$	−33.7875	+	7.53102i	−1.40295	+	0.312709i
$581$	−4.65564	−	7.24432i	−0.193149	−	0.300545i
$582$	1.71948	−	9.67178i	0.0712748	−	0.400908i
$583$	−9.40746	−	10.8568i	−0.389617	−	0.449642i
$584$	−2.20779	+	22.1299i	−0.0913590	+	0.915740i
$585$	−7.94161	+	17.3897i	−0.328345	+	0.718976i
$586$	18.6450	+	6.15280i	0.770219	+	0.254170i
$587$	4.42507	+	15.0704i	0.182642	+	0.622022i	0.999010	+	0.0444898i	$0.0141662\pi$
$587$	4.42507	+	15.0704i	0.182642	+	0.622022i	−0.816368	+	0.577533i	$0.804016\pi$
$588$	0.373122	−	5.62031i	0.0153873	−	0.231778i
$589$	10.7598	−	1.54703i	0.443352	−	0.0637444i
$590$	9.05259	−	0.996653i	0.372689	−	0.0410316i
$591$	10.0067	+	21.9116i	0.411621	+	0.901325i
$592$	9.88152	+	2.79213i	0.406128	+	0.114756i
$593$	−1.16641	+	8.11255i	−0.0478986	+	0.333142i	0.951756	+	0.306856i	$0.0992771\pi$
$593$	−1.16641	+	8.11255i	−0.0478986	+	0.333142i	−0.999654	+	0.0262860i	$0.991632\pi$
$594$	1.37755	−	0.574725i	0.0565214	−	0.0235813i
$595$	24.4997	+	21.2291i	1.00439	+	0.870308i
$596$	15.5806	−	1.19438i	0.638204	−	0.0489238i
$597$		−	8.28104i		−	0.338920i
$598$	−36.9400	−	20.2705i	−1.51059	−	0.828921i
$599$	−33.7810			−1.38025			−0.690127	−	0.723688i	$-0.742446\pi$
$599$	−33.7810			−1.38025			−0.690127	+	0.723688i	$0.742446\pi$
$600$	6.36636	−	10.9198i	0.259905	−	0.445797i
$601$	15.5532	−	17.9494i	0.634430	−	0.732172i	−0.343949	−	0.938988i	$-0.611765\pi$
$601$	15.5532	−	17.9494i	0.634430	−	0.732172i	0.978380	+	0.206817i	$0.0663103\pi$
$602$	5.07067	+	12.1538i	0.206665	+	0.495351i
$603$	−12.3413	−	1.77440i	−0.502575	−	0.0722593i
$604$	16.1907	+	11.9916i	0.658790	+	0.487932i
$605$	−27.6719	+	12.6373i	−1.12502	+	0.513780i
$606$	25.0853	−	2.76179i	1.01902	−	0.112190i
$607$	−1.45309	−	10.1065i	−0.0589793	−	0.410210i	−0.997828	−	0.0658789i	$-0.979015\pi$
$607$	−1.45309	−	10.1065i	−0.0589793	−	0.410210i	0.938848	−	0.344331i	$-0.111894\pi$
$608$	−10.4348	+	32.7415i	−0.423189	+	1.32784i
$609$	11.0389	−	3.24130i	0.447317	−	0.131344i
$610$	−4.97731	+	15.0829i	−0.201525	+	0.610689i
$611$	7.93921	+	3.62571i	0.321186	+	0.146681i
$612$	9.01572	−	4.98292i	0.364439	−	0.201423i
$613$	0.833996	−	0.722662i	0.0336848	−	0.0291880i	−0.637856	−	0.770156i	$-0.720178\pi$
$613$	0.833996	−	0.722662i	0.0336848	−	0.0291880i	0.671540	+	0.740968i	$0.265633\pi$
$614$	−4.33945	+	24.4086i	−0.175126	+	0.985052i
$615$	16.1139	−	10.3558i	0.649776	−	0.417585i
$616$	5.65899	+	2.29338i	0.228007	+	0.0924030i
$617$	−22.8810	−	14.7047i	−0.921154	−	0.591989i	−0.00816151	−	0.999967i	$-0.502598\pi$
$617$	−22.8810	−	14.7047i	−0.921154	−	0.591989i	−0.912992	+	0.407977i	$0.866234\pi$
$618$	−0.0134166	+	0.00346091i	−0.000539694	+	0.000139218i
$619$	−13.5048	+	45.9930i	−0.542802	+	1.84861i	−0.0139471	+	0.999903i	$0.504440\pi$
$619$	−13.5048	+	45.9930i	−0.542802	+	1.84861i	−0.528855	+	0.848712i	$0.677379\pi$
$620$	−10.2987	+	3.90127i	−0.413605	+	0.156679i
$621$	−4.65230	+	1.16451i	−0.186691	+	0.0467300i
$622$	−0.101124	+	0.146443i	−0.00405470	+	0.00587184i
$623$	−24.9797	−	7.33469i	−1.00079	−	0.293858i
$624$	0.253920	+	24.8492i	0.0101649	+	0.994766i
$625$	−23.0279	−	14.7991i	−0.921114	−	0.591964i
$626$	14.4234	+	13.3601i	0.576476	+	0.533975i
$627$	−3.46638	−	5.39379i	−0.138434	−	0.215407i
$628$	−34.3385	−	33.9894i	−1.37025	−	1.35632i
$629$	−9.99252	+	8.65857i	−0.398428	+	0.345240i
$630$	−3.96394	+	7.96974i	−0.157927	+	0.317522i
$631$	19.7498	−	43.2460i	0.786226	−	1.72159i	0.0990744	−	0.995080i	$-0.468412\pi$
$631$	19.7498	−	43.2460i	0.786226	−	1.72159i	0.687151	−	0.726514i	$-0.258861\pi$
$632$	−35.2489	+	1.52947i	−1.40213	+	0.0608392i
$633$	18.7459	−	5.50429i	0.745082	−	0.218776i
$634$	33.5630	−	20.0299i	1.33296	−	0.795491i
$635$	−32.4682	+	4.66822i	−1.28846	+	0.185253i
$636$	12.9238	−	23.9583i	0.512461	−	0.950010i
$637$	−15.9157	+	7.26848i	−0.630605	+	0.287987i
$638$	0.278228	−	8.39108i	0.0110151	−	0.332206i
$639$	0.950629	−	6.61177i	0.0376063	−	0.261558i
$640$	3.10193	−	34.6757i	0.122615	−	1.37068i
$641$	−2.77947	+	3.20768i	−0.109783	+	0.126696i	−0.807981	−	0.589208i	$-0.799440\pi$
$641$	−2.77947	+	3.20768i	−0.109783	+	0.126696i	0.698199	+	0.715904i	$0.253985\pi$
$642$	−14.0096	+	11.3488i	−0.552914	+	0.447901i
$643$		−	33.1259i		−	1.30636i	−0.757204	−	0.653179i	$-0.773435\pi$
$643$		−	33.1259i		−	1.30636i	0.757204	−	0.653179i	$-0.226565\pi$
$644$	−16.8772	−	10.0028i	−0.665055	−	0.394166i
$645$			14.0092i			0.551613i
$646$	−27.8525	−	34.3827i	−1.09584	−	1.35277i
$647$	18.4266	−	21.2654i	0.724423	−	0.836028i	−0.267409	−	0.963583i	$-0.586167\pi$
$647$	18.4266	−	21.2654i	0.724423	−	0.836028i	0.991832	+	0.127555i	$0.0407129\pi$
$648$	1.94315	+	2.05528i	0.0763341	+	0.0807390i
$649$	−0.314348	+	2.18634i	−0.0123392	+	0.0858213i
$650$	−39.2425	−	1.30119i	−1.53922	−	0.0510367i
$651$	3.32938	−	1.52048i	0.130489	−	0.0595921i
$652$	−17.1173	−	9.23351i	−0.670363	−	0.361612i
$653$	9.53930	−	1.37154i	0.373302	−	0.0536727i	0.0468891	−	0.998900i	$-0.485069\pi$
$653$	9.53930	−	1.37154i	0.373302	−	0.0536727i	0.326412	+	0.945227i	$0.394160\pi$
$654$	1.46375	+	2.45272i	0.0572371	+	0.0959088i
$655$	22.3274	−	6.55592i	0.872404	−	0.256161i
$656$	13.2467	−	21.0829i	0.517198	−	0.823149i
$657$	3.26638	−	7.15237i	0.127434	−	0.279041i
$658$	3.63856	+	1.80972i	0.141846	+	0.0705504i
$659$	14.1816	−	12.2884i	0.552435	−	0.478688i	−0.333337	−	0.942808i	$-0.608175\pi$
$659$	14.1816	−	12.2884i	0.552435	−	0.478688i	0.885772	+	0.464120i	$0.153629\pi$
$660$	4.61647	+	4.56954i	0.179696	+	0.177869i
$661$	13.6545	+	21.2468i	0.531099	+	0.826407i	0.998332	−	0.0577276i	$-0.0183855\pi$
$661$	13.6545	+	21.2468i	0.531099	+	0.826407i	−0.467233	+	0.884134i	$0.654749\pi$
$662$	−24.3862	+	26.3272i	−0.947797	+	1.02323i
$663$	−26.9188	−	17.2997i	−1.04544	−	0.671864i
$664$	−6.86615	−	9.72912i	−0.266458	−	0.377563i
$665$	36.6860	+	10.7720i	1.42262	+	0.417720i
$666$	−2.98739	−	2.06289i	−0.115759	−	0.0799355i
$667$	−4.91248	+	26.5244i	−0.190212	+	1.02703i
$668$	13.6958	+	36.1547i	0.529907	+	1.39887i
$669$	6.42323	−	21.8755i	0.248337	−	0.845757i
$670$	−13.5527	−	52.5387i	−0.523588	−	2.02975i
$671$	−3.24063	−	2.08262i	−0.125103	−	0.0803988i
$672$	−0.265258	+	11.5675i	−0.0102325	+	0.446225i
$673$	39.2720	−	25.2386i	1.51383	−	0.972876i	0.520967	−	0.853577i	$-0.325572\pi$
$673$	39.2720	−	25.2386i	1.51383	−	0.972876i	0.992858	−	0.119299i	$-0.0380649\pi$
$674$	44.2646	+	7.86950i	1.70501	+	0.303122i
$675$	−3.37740	+	2.92653i	−0.129996	+	0.112642i
$676$	44.8056	−	24.7637i	1.72329	−	0.952451i
$677$	−23.8908	−	10.9106i	−0.918199	−	0.419328i	−0.100476	−	0.994939i	$-0.532037\pi$
$677$	−23.8908	−	10.9106i	−0.918199	−	0.419328i	−0.817723	+	0.575612i	$0.804764\pi$
$678$	−7.40805	−	2.44463i	−0.284505	−	0.0938856i
$679$	−13.6323	+	4.00280i	−0.523159	+	0.153613i
$680$	35.1195	+	27.8599i	1.34677	+	1.06838i
$681$	−2.63130	−	18.3011i	−0.100832	−	0.701300i
$682$	−0.292298	−	2.65494i	−0.0111927	−	0.101663i
$683$	−34.7421	+	15.8662i	−1.32937	+	0.607102i	−0.948280	−	0.317436i	$-0.897178\pi$
$683$	−34.7421	+	15.8662i	−1.32937	+	0.607102i	−0.381089	+	0.924538i	$0.624451\pi$
$684$	7.23117	−	9.76329i	0.276491	−	0.373309i
$685$	23.7491	+	3.41460i	0.907406	+	0.130465i
$686$	−26.2058	+	10.9333i	−1.00054	+	0.417435i
$687$	4.52192	−	5.21858i	0.172522	−	0.199101i
$688$	7.73381	+	16.4868i	0.294849	+	0.628552i
$689$	−84.5595			−3.22146
$690$	−12.4724	−	16.7335i	−0.474816	−	0.637034i
$691$		−	10.3627i		−	0.394215i	−0.980382	−	0.197108i	$-0.936845\pi$
$691$		−	10.3627i		−	0.394215i	0.980382	−	0.197108i	$-0.0631549\pi$
$692$	−26.4941	+	2.03100i	−1.00716	+	0.0772071i
$693$	−1.63152	−	1.41372i	−0.0619764	−	0.0537028i
$694$	8.22330	+	19.7102i	0.312152	+	0.748190i
$695$	6.72813	−	46.7952i	0.255212	−	1.77504i
$696$	15.0562	−	5.13967i	0.570702	−	0.194819i
$697$	13.3186	+	29.1637i	0.504479	+	1.10465i
$698$	−1.43140	−	13.0014i	−0.0541795	−	0.492112i
$699$	−5.13275	+	0.737978i	−0.194138	+	0.0279129i
$700$	−18.2414	−	1.21101i	−0.689460	−	0.0457719i
$701$	−3.16603	−	10.7825i	−0.119579	−	0.407250i	0.877848	−	0.478940i	$-0.158979\pi$
$701$	−3.16603	−	10.7825i	−0.119579	−	0.407250i	−0.997427	+	0.0716904i	$0.977161\pi$
$702$	2.75331	−	8.34344i	0.103917	−	0.314903i
$703$	−6.47822	+	14.1853i	−0.244331	+	0.535010i
$704$	7.95551	+	2.82913i	0.299835	+	0.106627i
$705$	2.83097	+	3.26711i	0.106621	+	0.123047i
$706$	−35.2029	−	6.25849i	−1.32488	−	0.235541i
$707$	−19.7336	−	30.7061i	−0.742160	−	1.15482i
$708$	−4.08531	+	0.910588i	−0.153535	+	0.0342220i
$709$	−1.74920	+	2.72181i	−0.0656927	+	0.102220i	−0.872546	−	0.488532i	$-0.837532\pi$
$709$	−1.74920	+	2.72181i	−0.0656927	+	0.102220i	0.806853	+	0.590752i	$0.201169\pi$
$710$	28.1474	−	7.26082i	1.05635	−	0.272494i
$711$	11.9688	+	3.51436i	0.448866	+	0.131799i
$712$	−34.9497	−	8.63564i	−1.30979	−	0.323634i
$713$	−0.346027	+	8.57491i	−0.0129588	+	0.321133i
$714$	−12.2597	−	8.46574i	−0.458808	−	0.316822i
$715$	5.68461	−	19.3600i	0.212592	−	0.724023i
$716$	14.0249	−	38.1971i	0.524136	−	1.42749i
$717$	7.57642	−	11.7891i	0.282946	−	0.440273i
$718$	23.2173	+	21.5056i	0.866461	+	0.802582i
$719$	−13.1972	+	8.48134i	−0.492173	+	0.316300i	−0.763079	−	0.646305i	$-0.776313\pi$
$719$	−13.1972	+	8.48134i	−0.492173	+	0.316300i	0.270906	+	0.962606i	$0.412677\pi$
$720$	−4.99853	+	11.2480i	−0.186284	+	0.419189i
$721$	0.0131233	+	0.0151451i	0.000488737	+	0.000564032i
$722$	−22.6693	−	11.2751i	−0.843664	−	0.419617i
$723$	−4.63787	−	2.11804i	−0.172484	−	0.0787709i
$724$	−14.0156	+	10.6041i	−0.520884	+	0.394097i
$725$	7.08184	+	24.1185i	0.263013	+	0.895740i
$726$	12.0056	−	7.16475i	0.445568	−	0.265909i
$727$	7.04440	+	48.9949i	0.261262	+	1.81712i	0.523397	+	0.852089i	$0.324664\pi$
$727$	7.04440	+	48.9949i	0.261262	+	1.81712i	−0.262135	+	0.965031i	$0.584427\pi$
$728$	32.0158	−	16.3340i	1.18658	−	0.605377i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	34.1988	+	1.13395i	1.26576	+	0.0419694i
$731$	−23.2099	−	3.33709i	−0.858451	−	0.123427i
$732$	1.51517	−	7.14055i	0.0560021	−	0.263922i
$733$	−12.6326	−	10.9462i	−0.466594	−	0.404306i	0.389581	−	0.920992i	$-0.372620\pi$
$733$	−12.6326	−	10.9462i	−0.466594	−	0.404306i	−0.856175	+	0.516686i	$0.827165\pi$
$734$	25.0653	−	20.3047i	0.925177	−	0.749461i
$735$	−8.66635			−0.319663
$736$	−23.9159	−	12.8074i	−0.881551	−	0.472088i
$737$	13.1595			0.484736
$738$	−6.84037	+	5.54120i	−0.251797	+	0.203974i
$739$	12.1882	+	10.5611i	0.448349	+	0.388497i	0.849563	−	0.527488i	$-0.176866\pi$
$739$	12.1882	+	10.5611i	0.448349	+	0.388497i	−0.401213	+	0.915985i	$0.631411\pi$
$740$	3.27936	−	15.4547i	0.120552	−	0.568126i
$741$	−37.3562	−	5.37101i	−1.37231	−	0.197309i
$742$	−39.3497	−	1.30474i	−1.44457	−	0.0478985i
$743$	3.36691	+	7.37250i	0.123520	+	0.270471i	0.961283	−	0.275563i	$-0.0888643\pi$
$743$	3.36691	+	7.37250i	0.123520	+	0.270471i	−0.837763	+	0.546034i	$0.816137\pi$
$744$	4.50847	−	2.30015i	0.165289	−	0.0843277i
$745$	−3.42158	−	23.7976i	−0.125357	−	0.871876i
$746$	−10.8003	+	6.44548i	−0.395427	+	0.235986i
$747$	1.18612	+	4.03957i	0.0433980	+	0.147800i
$748$	−8.67030	+	6.55990i	−0.317018	+	0.239854i
$749$	23.7199	+	10.8325i	0.866706	+	0.395811i
$750$	2.06923	+	1.02918i	0.0755575	+	0.0375803i
$751$	28.1839	+	32.5260i	1.02845	+	1.18689i	0.982177	+	0.187961i	$0.0601878\pi$
$751$	28.1839	+	32.5260i	1.02845	+	1.18689i	0.0462695	+	0.998929i	$0.485267\pi$
$752$	5.13524	+	2.28206i	0.187263	+	0.0832182i
$753$	−2.04602	+	1.31490i	−0.0745612	+	0.0479176i
$754$	−36.2555	−	33.5826i	−1.32035	−	1.22301i
$755$	16.7594	−	26.0782i	0.609938	−	0.949082i
$756$	1.40999	−	3.84013i	0.0512807	−	0.139664i
$757$	8.95872	−	30.5106i	0.325610	−	1.10893i	−0.620264	−	0.784393i	$-0.712975\pi$
$757$	8.95872	−	30.5106i	0.325610	−	1.10893i	0.945874	−	0.324533i	$-0.105207\pi$
$758$	25.7363	+	17.7718i	0.934785	+	0.645500i
$759$	4.68537	−	1.91537i	0.170068	−	0.0695235i
$760$	51.3284	+	12.6826i	1.86188	+	0.460047i
$761$	31.1497	+	9.14638i	1.12918	+	0.331556i	0.792384	−	0.610023i	$-0.208840\pi$
$761$	31.1497	+	9.14638i	1.12918	+	0.331556i	0.336792	+	0.941579i	$0.390658\pi$
$762$	14.5974	−	3.76552i	0.528809	−	0.136410i
$763$	2.23344	−	3.47529i	0.0808558	−	0.125814i
$764$	0.0267977	−	0.00597304i	0.000969508	−	0.000216097i
$765$	−8.56866	−	13.3331i	−0.309801	−	0.482059i
$766$	12.7914	+	2.27409i	0.462171	+	0.0821663i
$767$	8.51428	+	9.82601i	0.307433	+	0.354797i
$768$	0.326956	+	15.9967i	0.0117980	+	0.577230i
$769$	18.3304	−	40.1380i	0.661012	−	1.44741i	−0.220564	−	0.975373i	$-0.570790\pi$
$769$	18.3304	−	40.1380i	0.661012	−	1.44741i	0.881576	−	0.472042i	$-0.156483\pi$
$770$	2.94405	−	8.92144i	0.106096	−	0.321506i
$771$	−3.18215	−	10.8374i	−0.114602	−	0.390299i
$772$	27.8716	+	1.85034i	1.00312	+	0.0665952i
$773$	−23.2837	+	3.34769i	−0.837457	+	0.120408i	−0.547682	−	0.836687i	$-0.684490\pi$
$773$	−23.2837	+	3.34769i	−0.837457	+	0.120408i	−0.289775	+	0.957095i	$0.593581\pi$
$774$	−0.704585	−	6.39974i	−0.0253258	−	0.230034i
$775$	3.32205	+	7.27427i	0.119332	+	0.261300i
$776$	−18.5934	+	6.34715i	−0.667463	+	0.227850i
$777$	−0.747260	+	5.19731i	−0.0268078	+	0.186452i
$778$	−3.46766	−	8.31157i	−0.124322	−	0.297984i
$779$	28.5780	+	24.7630i	1.02391	+	0.887225i
$780$	38.1227	−	2.92243i	1.36501	−	0.104640i
$781$			7.05014i			0.252274i
$782$	30.6944	−	16.6778i	1.09763	−	0.596395i
$783$	−5.62477			−0.201013
$784$	−10.1990	+	4.78427i	−0.364250	+	0.170867i
$785$	−48.6808	+	56.1807i	−1.73749	+	2.00517i
$786$	−9.86995	+	4.11784i	−0.352050	+	0.146878i
$787$	9.11341	+	1.31031i	0.324858	+	0.0467075i	0.302815	−	0.953050i	$-0.402074\pi$
$787$	9.11341	+	1.31031i	0.324858	+	0.0467075i	0.0220433	+	0.999757i	$0.492983\pi$
$788$	28.6740	−	38.7146i	1.02147	−	1.37915i
$789$	−7.83374	+	3.57755i	−0.278888	+	0.127364i
$790$	5.94060	+	53.9584i	0.211357	+	1.91975i
$791$	1.60570	+	11.1679i	0.0570920	+	0.397083i
$792$	−2.33873	−	1.85529i	−0.0831032	−	0.0659248i
$793$	−21.7562	+	6.38819i	−0.772584	+	0.226851i
$794$	1.85389	+	0.611777i	0.0657920	+	0.0217112i
$795$	−38.0981	−	17.3988i	−1.35120	−	0.617072i
$796$	−14.4954	+	8.01152i	−0.513778	+	0.283961i
$797$	−4.39750	+	3.81045i	−0.155767	+	0.134973i	−0.729258	−	0.684239i	$-0.760134\pi$
$797$	−4.39750	+	3.81045i	−0.155767	+	0.134973i	0.573490	+	0.819212i	$0.305589\pi$
$798$	−17.3008	−	3.07579i	−0.612442	−	0.108882i
$799$	−6.08718	+	3.91199i	−0.215349	+	0.138396i
$800$	−25.2735	−	0.579555i	−0.893553	−	0.0204904i
$801$	10.7076	+	6.88138i	0.378336	+	0.243142i
$802$	−10.5665	−	40.9623i	−0.373117	−	1.44643i
$803$	−2.33807	+	7.96275i	−0.0825089	+	0.280999i
$804$	8.83360	+	23.3192i	0.311537	+	0.822406i
$805$	−13.6362	+	26.9294i	−0.480615	+	0.949137i
$806$	−12.9373	−	8.93364i	−0.455697	−	0.314674i
$807$	−24.0349	−	7.05727i	−0.846068	−	0.248428i
$808$	−29.1032	−	41.2383i	−1.02385	−	1.45076i
$809$	28.5277	+	18.3336i	1.00298	+	0.644576i	0.935567	−	0.353149i	$-0.114889\pi$
$809$	28.5277	+	18.3336i	1.00298	+	0.644576i	0.0674131	+	0.997725i	$0.478525\pi$
$810$	2.95723	−	3.19260i	0.103906	−	0.112177i
$811$	22.2872	+	34.6796i	0.782611	+	1.21777i	0.971796	+	0.235824i	$0.0757790\pi$
$811$	22.2872	+	34.6796i	0.782611	+	1.21777i	−0.189185	+	0.981941i	$0.560585\pi$
$812$	−16.3533	−	16.1870i	−0.573888	−	0.568054i
$813$	1.86645	−	1.61729i	0.0654593	−	0.0567208i
$814$	3.43080	+	1.70639i	0.120250	+	0.0598090i
$815$	−12.4307	+	27.2195i	−0.435430	+	0.953458i
$816$	−17.4446	−	10.9607i	−0.610682	−	0.383702i
$817$	−26.5360	+	7.79168i	−0.928377	+	0.272596i
$818$	7.95693	+	13.3330i	0.278207	+	0.466176i
$819$	−12.5780	+	1.80844i	−0.439510	+	0.0631920i
$820$	−33.7166	−	18.1877i	−1.17744	−	0.635141i
$821$	25.7202	−	11.7460i	0.897640	−	0.409938i	0.0874927	−	0.996165i	$-0.472115\pi$
$821$	25.7202	−	11.7460i	0.897640	−	0.409938i	0.810147	+	0.586227i	$0.199387\pi$
$822$	−11.0209	−	0.365425i	−0.384397	−	0.0127457i
$823$	2.92716	−	20.3589i	0.102035	−	0.709666i	−0.873017	−	0.487689i	$-0.837840\pi$
$823$	2.92716	−	20.3589i	0.102035	−	0.709666i	0.975052	−	0.221977i	$-0.0712509\pi$
$824$	0.0190380	+	0.0201366i	0.000663221	+	0.000701492i
$825$	3.08881	−	3.56467i	0.107538	−	0.124106i
$826$	3.81050	+	4.70390i	0.132584	+	0.163669i
$827$		−	50.0264i		−	1.73959i	−0.493415	−	0.869794i	$-0.664252\pi$
$827$		−	50.0264i		−	1.73959i	0.493415	−	0.869794i	$-0.335748\pi$
$828$	6.53928	+	7.01696i	0.227256	+	0.243856i
$829$		−	4.16726i		−	0.144735i	−0.997378	−	0.0723674i	$-0.976945\pi$
$829$		−	4.16726i		−	0.144735i	0.997378	−	0.0723674i	$-0.0230554\pi$
$830$	−14.2364	+	11.5325i	−0.494152	+	0.400299i
$831$	−11.2488	+	12.9818i	−0.390215	+	0.450332i
$832$	43.2514	−	24.4850i	1.49947	−	0.848863i
$833$	2.06438	−	14.3581i	0.0715265	−	0.497477i
$834$	−0.720033	+	21.7155i	−0.0249327	+	0.751946i
$835$	54.1090	−	24.7107i	1.87252	−	0.855150i
$836$	−6.08793	+	11.2859i	−0.210556	+	0.390332i
$837$	−1.77123	+	0.254665i	−0.0612228	+	0.00880251i
$838$	−7.65901	+	4.57079i	−0.264576	+	0.157895i
$839$	23.9719	−	7.03879i	0.827603	−	0.243006i	0.159616	−	0.987179i	$-0.448974\pi$
$839$	23.9719	−	7.03879i	0.827603	−	0.243006i	0.667987	+	0.744173i	$0.267156\pi$
$840$	17.7855	−	0.771724i	0.613657	−	0.0266270i
$841$	−1.09587	+	2.39962i	−0.0377887	+	0.0827457i
$842$	−9.40909	+	18.9175i	−0.324259	+	0.651942i
$843$	−11.7264	+	10.1610i	−0.403880	+	0.349964i
$844$	−27.7707	−	27.4884i	−0.955907	−	0.946189i
$845$	−42.5839	−	66.2618i	−1.46493	−	2.27948i
$846$	−1.45757	−	1.35011i	−0.0501123	−	0.0464178i
$847$	−17.0109	−	10.9322i	−0.584501	−	0.375636i
$848$	−54.4407	+	0.556299i	−1.86950	+	0.0191034i
$849$	−2.77643	−	0.815233i	−0.0952868	−	0.0279787i
$850$	18.4966	−	26.7860i	0.634428	−	0.918751i
$851$	−10.0802	−	7.06823i	−0.345545	−	0.242296i
$852$	−12.4932	+	4.73256i	−0.428009	+	0.162135i
$853$	5.32006	−	18.1184i	0.182155	−	0.620364i	−0.816895	−	0.576787i	$-0.804306\pi$
$853$	5.32006	−	18.1184i	0.182155	−	0.620364i	0.999050	−	0.0435771i	$-0.0138754\pi$
$854$	−10.2228	+	2.63704i	−0.349816	+	0.0902378i
$855$	−15.7256	−	10.1062i	−0.537805	−	0.345626i
$856$	33.4190	+	13.5435i	1.14224	+	0.462907i
$857$	15.3092	−	9.83863i	0.522953	−	0.336081i	−0.252386	−	0.967627i	$-0.581215\pi$
$857$	15.3092	−	9.83863i	0.522953	−	0.336081i	0.775339	+	0.631545i	$0.217579\pi$
$858$	−1.62316	+	9.12999i	−0.0554138	+	0.311693i
$859$	−11.7442	+	10.1764i	−0.400709	+	0.347216i	−0.831784	−	0.555100i	$-0.812680\pi$
$859$	−11.7442	+	10.1764i	−0.400709	+	0.347216i	0.431075	+	0.902316i	$0.358134\pi$
$860$	24.5223	−	13.5533i	0.836203	−	0.462163i
$861$	11.5816	+	5.28912i	0.394699	+	0.180253i
$862$	−15.1996	+	46.0598i	−0.517700	+	1.56880i
$863$	−33.0383	+	9.70092i	−1.12464	+	0.330223i	−0.790598	−	0.612336i	$-0.790230\pi$
$863$	−33.0383	+	9.70092i	−1.12464	+	0.330223i	−0.334039	+	0.942559i	$0.608412\pi$
$864$	1.71773	−	5.38975i	0.0584385	−	0.183363i
$865$	5.81826	+	40.4669i	0.197827	+	1.37591i
$866$	−10.9624	+	1.20692i	−0.372518	+	0.0410127i
$867$	8.66712	−	3.95814i	0.294351	−	0.134426i
$868$	−5.88252	−	4.35688i	−0.199666	−	0.147882i
$869$	−13.0318	−	1.87368i	−0.442072	−	0.0635604i
$870$	−9.42494	−	22.5904i	−0.319535	−	0.765887i
$871$	50.7256	−	58.5404i	1.71877	−	1.98357i
$872$	2.87722	−	4.93509i	0.0974349	−	0.167123i
$873$	6.94622			0.235094
$874$	24.7594	−	32.9318i	0.837498	−	1.11394i
$875$		−	3.34250i		−	0.112997i
$876$	−15.6799	+	1.20199i	−0.529773	+	0.0406116i
$877$	−29.8447	−	25.8606i	−1.00778	−	0.873250i	−0.0158338	−	0.999875i	$-0.505040\pi$
$877$	−29.8447	−	25.8606i	−1.00778	−	0.873250i	−0.991951	+	0.126624i	$0.959586\pi$
$878$	45.0768	−	18.8065i	1.52127	−	0.634687i
$879$	−1.97580	+	13.7420i	−0.0666422	+	0.463507i
$880$	3.53247	−	12.5017i	0.119080	−	0.421431i
$881$	−13.2538	−	29.0218i	−0.446532	−	0.977769i	−0.990353	−	0.138568i	$-0.955750\pi$
$881$	−13.2538	−	29.0218i	−0.446532	−	0.977769i	0.543821	−	0.839201i	$-0.316977\pi$
$882$	3.95899	−	0.435868i	0.133306	−	0.0146764i
$883$	−31.3715	+	4.51054i	−1.05573	+	0.151792i	−0.648255	−	0.761423i	$-0.724501\pi$
$883$	−31.3715	+	4.51054i	−1.05573	+	0.151792i	−0.407479	+	0.913215i	$0.633592\pi$
$884$	−4.23930	+	63.8564i	−0.142583	+	2.14772i
$885$	1.81431	+	6.17897i	0.0609873	+	0.207704i
$886$	−6.61113	−	2.18165i	−0.222105	−	0.0732940i
$887$	−8.77126	+	19.2064i	−0.294510	+	0.644887i	−0.997820	−	0.0659965i	$-0.978977\pi$
$887$	−8.77126	+	19.2064i	−0.294510	+	0.644887i	0.703310	+	0.710883i	$0.251705\pi$
$888$	−0.720804	+	7.22500i	−0.0241886	+	0.242455i
$889$	−14.2783	−	16.4781i	−0.478880	−	0.552657i
$890$	−9.69542	+	54.5350i	−0.324991	+	1.82802i
$891$	0.570618	+	0.887900i	0.0191164	+	0.0297458i
$892$	−44.5059	+	9.92008i	−1.49017	+	0.332149i
$893$	−4.61397	+	7.17948i	−0.154401	+	0.240252i
$894$	2.75994	+	10.6992i	0.0923061	+	0.357835i
$895$	−60.0697	−	17.6381i	−2.00791	−	0.589575i
$896$	20.5048	−	10.7267i	0.685017	−	0.358353i
$897$	9.54000	−	28.2261i	0.318531	−	0.942443i
$898$	27.9717	−	40.5074i	0.933429	−	1.35175i
$899$	−2.83570	+	9.65752i	−0.0945760	+	0.322096i
$900$	8.39020	+	3.08064i	0.279673	+	0.102688i
$901$	37.9009	−	58.9749i	1.26266	−	1.96474i
$902$	6.31385	−	6.81638i	0.210228	−	0.226961i
$903$	−7.83373	+	5.03443i	−0.260690	+	0.167535i
$904$	2.88777	+	15.3324i	0.0960457	+	0.509948i
$905$	17.7079	+	20.4360i	0.588629	+	0.679314i
$906$	−6.34451	+	12.7560i	−0.210782	+	0.423790i
$907$	−29.3191	−	13.3896i	−0.973525	−	0.444594i	−0.135830	−	0.990732i	$-0.543370\pi$
$907$	−29.3191	−	13.3896i	−0.973525	−	0.444594i	−0.837695	+	0.546138i	$0.816097\pi$
$908$	−29.4893	+	22.3114i	−0.978637	+	0.740430i
$909$	5.02756	+	17.1223i	0.166754	+	0.567911i
$910$	−28.3390	−	47.4859i	−0.939427	−	1.57414i
$911$	2.57917	+	17.9385i	0.0854516	+	0.594329i	0.986887	+	0.161415i	$0.0516057\pi$
$911$	2.57917	+	17.9385i	0.0854516	+	0.594329i	−0.901435	+	0.432914i	$0.857485\pi$
$912$	−24.0858	−	3.21218i	−0.797562	−	0.106366i
$913$	−1.84592	−	4.04199i	−0.0610909	−	0.133770i
$914$	−0.220097	+	6.63793i	−0.00728017	+	0.219563i
$915$	−11.1166	−	1.59833i	−0.367504	−	0.0528391i
$916$	−13.5095	−	2.86661i	−0.446368	−	0.0947156i
$917$	11.6897	+	10.1291i	0.386027	+	0.334494i
$918$	4.58494	+	5.65991i	0.151326	+	0.186805i
$919$	−52.1321			−1.71968			−0.859839	−	0.510565i	$-0.829436\pi$
$919$	−52.1321			−1.71968			−0.859839	+	0.510565i	$0.829436\pi$
$920$	−17.2245	+	38.0211i	−0.567875	+	1.25352i
$921$	−17.5301			−0.577638
$922$	15.3373	+	18.9333i	0.505108	+	0.623534i
$923$	31.3628	+	27.1760i	1.03232	+	0.894509i
$924$	−0.896211	+	4.22359i	−0.0294832	+	0.138946i
$925$	−11.3555	−	1.63267i	−0.373366	−	0.0536819i
$926$	−0.388482	+	11.7163i	−0.0127663	+	0.385020i
$927$	−0.00407003	−	0.00891213i	−0.000133677	−	0.000292713i
$928$	−23.5628	−	21.3825i	−0.773487	−	0.701915i
$929$	4.43358	+	30.8362i	0.145461	+	1.01170i	0.923531	+	0.383525i	$0.125290\pi$
$929$	4.43358	+	30.8362i	0.145461	+	1.01170i	−0.778070	+	0.628178i	$0.783801\pi$
$930$	−3.99070	−	6.68699i	−0.130860	−	0.219275i
$931$	−4.82006	−	16.4156i	−0.157971	−	0.538000i
$932$	6.25748	+	8.27060i	0.204971	+	0.270912i
$933$	−0.114469	−	0.0522761i	−0.00374754	−	0.00171144i
$934$	23.2358	−	46.7171i	0.760300	−	1.52863i
$935$	10.9544	+	12.6421i	0.358248	+	0.413441i
$936$	−17.2684	+	3.25239i	−0.564434	+	0.106308i
$937$	20.5237	−	13.1898i	0.670481	−	0.430892i	−0.160618	−	0.987017i	$-0.551349\pi$
$937$	20.5237	−	13.1898i	0.670481	−	0.430892i	0.831099	+	0.556125i	$0.187712\pi$
$938$	24.5084	−	26.4590i	0.800226	−	0.863918i
$939$	−7.51594	+	11.6950i	−0.245273	+	0.381653i
$940$	2.98005	−	8.11622i	0.0971985	−	0.264722i
$941$	−8.15043	+	27.7578i	−0.265696	+	0.904879i	0.713275	+	0.700884i	$0.247211\pi$
$941$	−8.15043	+	27.7578i	−0.265696	+	0.904879i	−0.978972	+	0.203995i	$0.934607\pi$
$942$	19.4130	−	28.1130i	0.632508	−	0.915971i
$943$	−23.3313	+	18.6239i	−0.759770	+	0.606479i
$944$	5.54627	+	6.27012i	0.180516	+	0.204075i
$945$	−6.03908	−	1.77323i	−0.196451	−	0.0576833i
$946$	1.69736	+	6.58001i	0.0551860	+	0.213935i
$947$	−8.78379	+	13.6678i	−0.285435	+	0.444145i	−0.954131	−	0.299391i	$-0.903217\pi$
$947$	−8.78379	+	13.6678i	−0.285435	+	0.444145i	0.668696	+	0.743536i	$0.266853\pi$
$948$	−5.42760	−	24.3507i	−0.176280	−	0.790872i
$949$	26.4100	+	41.0948i	0.857306	+	1.33399i
$950$	6.72023	−	37.8001i	0.218033	−	1.22640i
$951$	18.0988	+	20.8871i	0.586893	+	0.677311i
$952$	−2.95805	+	29.6501i	−0.0958709	+	0.960965i
$953$	−8.96704	+	19.6351i	−0.290471	+	0.636042i	−0.997464	−	0.0711784i	$-0.977324\pi$
$953$	−8.96704	+	19.6351i	−0.290471	+	0.636042i	0.706993	+	0.707221i	$0.250051\pi$
$954$	18.2791	+	6.03206i	0.591809	+	0.195295i
$955$	−0.0119010	−	0.0405312i	−0.000385108	−	0.00131156i
$956$	−27.9660	−	1.85661i	−0.904485	−	0.0600470i
$957$	5.87622	−	0.844874i	0.189951	−	0.0273109i
$958$	34.0429	−	3.74798i	1.09987	−	0.121092i
$959$	6.62521	+	14.5072i	0.213939	+	0.468461i
$960$	24.5248	−	2.13231i	0.791534	−	0.0688200i
$961$	3.95605	−	27.5149i	0.127615	−	0.887578i
$962$	20.8156	−	8.68446i	0.671121	−	0.279998i
$963$	−9.63489	−	8.34868i	−0.310480	−	0.269033i
$964$	0.779419	+	10.1674i	0.0251034	+	0.327470i
$965$		−	42.9771i		−	1.38348i
$966$	4.87495	−	12.9878i	0.156849	−	0.417876i
$967$	−40.8664			−1.31417			−0.657087	−	0.753815i	$-0.728212\pi$
$967$	−40.8664			−1.31417			−0.657087	+	0.753815i	$0.728212\pi$
$968$	−24.1563	−	14.0834i	−0.776412	−	0.452658i
$969$	20.4896	−	23.6462i	0.658220	−	0.759626i
$970$	11.6392	+	27.8977i	0.373712	+	0.895741i
$971$	14.0473	+	2.01970i	0.450799	+	0.0648152i	0.363976	−	0.931409i	$-0.381419\pi$
$971$	14.0473	+	2.01970i	0.450799	+	0.0648152i	0.0868238	+	0.996224i	$0.472328\pi$
$972$	−1.19036	+	1.60719i	−0.0381808	+	0.0515505i
$973$	28.5849	−	13.0543i	0.916391	−	0.418502i
$974$	12.4894	−	1.37503i	0.400187	−	0.0440589i
$975$	−3.95121	−	27.4813i	−0.126540	−	0.880106i
$976$	−13.9649	+	4.25595i	−0.447007	+	0.136230i
$977$	55.2959	−	16.2363i	1.76907	−	0.519447i	0.775371	−	0.631506i	$-0.217563\pi$
$977$	55.2959	−	16.2363i	1.76907	−	0.519447i	0.993701	+	0.112060i	$0.0357448\pi$
$978$	4.30966	−	13.0597i	0.137808	−	0.417603i
$979$	−12.2199	−	5.58066i	−0.390551	−	0.178359i
$980$	8.38429	+	15.1699i	0.267826	+	0.484585i
$981$	−1.52639	+	1.32262i	−0.0487338	+	0.0422281i
$982$	−0.619950	+	3.48711i	−0.0197834	+	0.111278i
$983$	−7.44378	+	4.78383i	−0.237420	+	0.152580i	−0.653941	−	0.756546i	$-0.726886\pi$
$983$	−7.44378	+	4.78383i	−0.237420	+	0.152580i	0.416521	+	0.909126i	$0.363249\pi$
$984$	16.3173	+	6.61279i	0.520175	+	0.210808i
$985$	−62.3573	−	40.0746i	−1.98687	−	1.27688i
$986$	39.6720	−	10.2337i	1.26341	−	0.325907i
$987$	−0.809563	+	2.75712i	−0.0257687	+	0.0877601i
$988$	26.7388	+	70.5859i	0.850674	+	2.24564i
$989$	−2.23335	−	21.7192i	−0.0710163	−	0.690630i
$990$	−2.60988	+	3.77952i	−0.0829475	+	0.120121i
$991$	−3.83605	−	1.12637i	−0.121856	−	0.0357802i	0.220236	−	0.975447i	$-0.429317\pi$
$991$	−3.83605	−	1.12637i	−0.121856	−	0.0357802i	−0.342092	+	0.939666i	$0.611135\pi$
$992$	−8.38801	−	5.66650i	−0.266320	−	0.179912i
$993$	−21.3470	−	13.7189i	−0.677427	−	0.435356i
$994$	14.1753	+	13.1302i	0.449614	+	0.416466i
$995$	13.7767	+	21.4369i	0.436750	+	0.679596i
$996$	5.92349	−	5.98433i	0.187693	−	0.189621i
$997$	−2.78892	+	2.41662i	−0.0883261	+	0.0765350i	−0.697905	−	0.716191i	$-0.745884\pi$
$997$	−2.78892	+	2.41662i	−0.0883261	+	0.0765350i	0.609579	+	0.792726i	$0.291339\pi$
$998$	13.6300	−	27.4040i	0.431452	−	0.867459i
$999$	1.06641	−	2.33512i	0.0337398	−	0.0738799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.133.35	yes	480
8.5	even	2	inner	552.2.bb.a.133.27	✓	480
23.9	even	11	inner	552.2.bb.a.469.27	yes	480
184.101	even	22	inner	552.2.bb.a.469.35	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.27	✓	480	8.5	even	2	inner
552.2.bb.a.133.35	yes	480	1.1	even	1	trivial
552.2.bb.a.469.27	yes	480	23.9	even	11	inner
552.2.bb.a.469.35	yes	480	184.101	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09890 - 0.890185i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.415141 - 1.95644i) q^{4} +(-3.04584 - 0.437926i) q^{5} +(1.41344 + 0.0468661i) q^{6} +(-0.849690 - 1.86056i) q^{7} +(-1.28540 - 2.51947i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-3.73690 + 2.23013i) q^{10} +(-0.297354 - 1.01270i) q^{11} +(1.59494 - 1.20672i) q^{12} +(-5.65121 - 2.58082i) q^{13} +(-2.58996 - 1.28818i) q^{14} +(-2.01511 - 2.32557i) q^{15} +(-3.65532 - 1.62440i) q^{16} +(4.33292 - 2.78460i) q^{17} +(1.03751 + 0.961023i) q^{18} +(3.28427 - 5.11043i) q^{19} +(-2.12123 + 5.77721i) q^{20} +(0.576256 - 1.96255i) q^{21} +(-1.22825 - 0.848145i) q^{22} +(3.49487 + 3.28419i) q^{23} +(0.678466 - 2.74585i) q^{24} +(4.28792 + 1.25905i) q^{25} +(-8.50749 + 2.19457i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(-3.99282 + 0.889973i) q^{28} +(3.04098 + 4.73186i) q^{29} +(-4.28458 - 0.761728i) q^{30} +(1.17184 + 1.35237i) q^{31} +(-5.46282 + 1.46887i) q^{32} +(0.438449 - 0.960069i) q^{33} +(2.28261 - 6.91708i) q^{34} +(1.77323 + 6.03908i) q^{35} +(1.99561 + 0.132485i) q^{36} +(-2.54098 + 0.365337i) q^{37} +(-0.940156 - 8.53943i) q^{38} +(-2.58082 - 5.65121i) q^{39} +(2.81178 + 8.23683i) q^{40} +(-0.885877 + 6.16141i) q^{41} +(-1.11379 - 2.66961i) q^{42} +(-3.44066 - 2.98135i) q^{43} +(-2.10472 + 0.161345i) q^{44} -3.07716i q^{45} +(6.76403 + 0.497897i) q^{46} -1.40487 q^{47} +(-1.69875 - 3.62136i) q^{48} +(1.84431 - 2.12845i) q^{49} +(5.83276 - 2.43348i) q^{50} +(5.09812 + 0.733000i) q^{51} +(-7.39527 + 9.98485i) q^{52} +(12.3809 - 5.65417i) q^{53} +(0.154764 + 1.40572i) q^{54} +(0.462208 + 3.21473i) q^{55} +(-3.59545 + 4.53233i) q^{56} +(5.82870 - 1.71146i) q^{57} +(7.55395 + 2.49278i) q^{58} +(-1.90366 - 0.869372i) q^{59} +(-5.38639 + 2.97701i) q^{60} +(2.75831 - 2.39009i) q^{61} +(2.49159 + 0.442964i) q^{62} +(1.72070 - 1.10583i) q^{63} +(-4.69550 + 6.47706i) q^{64} +(16.0825 + 10.3356i) q^{65} +(-0.372830 - 1.44532i) q^{66} +(-3.51269 + 11.9631i) q^{67} +(-3.64913 - 9.63309i) q^{68} +(0.490560 + 4.77068i) q^{69} +(7.32449 + 5.05781i) q^{70} +(-6.40918 - 1.88191i) q^{71} +(2.31090 - 1.63087i) q^{72} +(-6.61472 - 4.25102i) q^{73} +(-2.46705 + 2.66341i) q^{74} +(2.41609 + 3.75951i) q^{75} +(-8.63481 - 8.54702i) q^{76} +(-1.63152 + 1.41372i) q^{77} +(-7.86667 - 3.91268i) q^{78} +(5.18193 - 11.3468i) q^{79} +(10.4222 + 6.54841i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.51131 + 7.55934i) q^{82} +(4.16725 - 0.599160i) q^{83} +(-3.60038 - 1.94214i) q^{84} +(-14.4168 + 6.58395i) q^{85} +(-6.43487 - 0.213365i) q^{86} +(-0.800488 + 5.56752i) q^{87} +(-2.16924 + 2.05089i) q^{88} +(8.33519 - 9.61932i) q^{89} +(-2.73925 - 3.38148i) q^{90} +12.7073i q^{91} +(7.87618 - 5.47410i) q^{92} +1.78945i q^{93} +(-1.54380 + 1.25059i) q^{94} +(-12.2414 + 14.1273i) q^{95} +(-5.09043 - 2.46729i) q^{96} +(0.988550 - 6.87552i) q^{97} +(0.131991 - 3.98072i) q^{98} +(0.960069 - 0.438449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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