LMFDB - Embedded newform 552.2.bb.a.469.35

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			469.35
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.35

$q$-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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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	−0.784341	−	0.620330i	$-0.786999\pi$
$5$	−3.04584	+	0.437926i	−1.36214	+	0.195847i	−0.577802	+	0.816177i	$0.696089\pi$
$6$	1.41344	−	0.0468661i	0.577033	−	0.0191330i
$7$	−0.849690	+	1.86056i	−0.321152	+	0.703226i	−0.999503	−	0.0315123i	$-0.989968\pi$
$7$	−0.849690	+	1.86056i	−0.321152	+	0.703226i	0.678351	+	0.734738i	$0.262695\pi$
$8$	−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	−0.992097	−	0.125474i	$-0.959955\pi$
$11$	−0.297354	+	1.01270i	−0.0896556	+	0.305339i	0.902441	+	0.430813i	$0.141773\pi$
$12$	1.59494	+	1.20672i	0.460419	+	0.348350i
$13$	−5.65121	+	2.58082i	−1.56736	+	0.715791i	−0.994586	−	0.103920i	$-0.966862\pi$
$13$	−5.65121	+	2.58082i	−1.56736	+	0.715791i	−0.572778	+	0.819711i	$0.694134\pi$
$14$	−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	0.947656	−	0.319293i	$-0.103446\pi$
$17$	4.33292	+	2.78460i	1.05089	+	0.675364i	0.103231	+	0.994657i	$0.467082\pi$
$18$	1.03751	−	0.961023i	0.244544	−	0.226515i
$19$	3.28427	+	5.11043i	0.753463	+	1.17241i	0.980114	+	0.198436i	$0.0635861\pi$
$19$	3.28427	+	5.11043i	0.753463	+	1.17241i	−0.226651	+	0.973976i	$0.572778\pi$
$20$	−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	−0.435069	−	0.900397i	$-0.643276\pi$
$29$	3.04098	−	4.73186i	0.564696	−	0.878684i	0.999764	+	0.0217137i	$0.00691223\pi$
$30$	−4.28458	+	0.761728i	−0.782254	+	0.139072i
$31$	1.17184	−	1.35237i	0.210469	−	0.242894i	−0.640693	−	0.767797i	$-0.721353\pi$
$31$	1.17184	−	1.35237i	0.210469	−	0.242894i	0.851162	+	0.524903i	$0.175898\pi$
$32$	−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	−0.0697566	−	0.997564i	$-0.522222\pi$
$37$	−2.54098	−	0.365337i	−0.417734	−	0.0600610i	−0.347977	+	0.937503i	$0.613131\pi$
$38$	−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	−0.934198	−	0.356754i	$-0.883883\pi$
$41$	−0.885877	−	6.16141i	−0.138351	−	0.962251i	0.795848	−	0.605497i	$-0.207026\pi$
$42$	−1.11379	+	2.66961i	−0.171861	+	0.411929i
$43$	−3.44066	+	2.98135i	−0.524696	+	0.454651i	−0.876486	−	0.481428i	$-0.840118\pi$
$43$	−3.44066	+	2.98135i	−0.524696	+	0.454651i	0.351790	+	0.936079i	$0.385573\pi$
$44$	−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	0.997869	+	0.0652519i	$0.0207851\pi$
$53$	12.3809	+	5.65417i	1.70065	+	0.776660i	0.702779	+	0.711408i	$0.251942\pi$
$54$	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	−0.535460	−	0.844561i	$-0.679862\pi$
$59$	−1.90366	+	0.869372i	−0.247835	+	0.113183i	0.287625	+	0.957743i	$0.407134\pi$
$60$	−5.38639	−	2.97701i	−0.695379	−	0.384331i
$61$	2.75831	+	2.39009i	0.353165	+	0.306019i	0.813317	−	0.581821i	$-0.197660\pi$
$61$	2.75831	+	2.39009i	0.353165	+	0.306019i	−0.460152	+	0.887840i	$0.652205\pi$
$62$	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	−0.836353	−	0.548192i	$-0.815316\pi$
$67$	−3.51269	−	11.9631i	−0.429143	−	1.46153i	0.407210	−	0.913335i	$-0.366502\pi$
$68$	−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	−0.638971	−	0.769231i	$-0.720640\pi$
$71$	−6.40918	+	1.88191i	−0.760630	+	0.223341i	−0.121659	+	0.992572i	$0.538821\pi$
$72$	2.31090	+	1.63087i	0.272342	+	0.192200i
$73$	−6.61472	+	4.25102i	−0.774194	+	0.497544i	−0.867102	−	0.498130i	$-0.834020\pi$
$73$	−6.61472	+	4.25102i	−0.774194	+	0.497544i	0.0929081	+	0.995675i	$0.470384\pi$
$74$	−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	0.939573	+	0.342348i	$0.111222\pi$
$79$	5.18193	+	11.3468i	0.583013	+	1.27662i	−0.356561	+	0.934272i	$0.616051\pi$
$80$	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	0.367171	−	0.930153i	$-0.380326\pi$
$83$	4.16725	+	0.599160i	0.457415	+	0.0657664i	0.0902439	+	0.995920i	$0.471235\pi$
$84$	−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	0.999651	+	0.0264114i	$0.00840800\pi$
$89$	8.33519	+	9.61932i	0.883529	+	1.01965i	−0.116123	+	0.993235i	$0.537047\pi$
$90$	−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	0.976420	+	0.215879i	$0.0692618\pi$
$97$	0.988550	+	6.87552i	0.100372	+	0.698103i	−0.876048	+	0.482224i	$0.839829\pi$
$98$	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	0.944282	−	0.329137i	$-0.106758\pi$
$101$	17.6635	+	2.53963i	1.75759	+	0.252703i	0.813303	+	0.581840i	$0.197667\pi$
$102$	6.25481	+	3.73279i	0.619318	+	0.369601i
$103$	−0.00940064	−	0.00276028i	−0.000926272	−	0.000271978i	0.281269	−	0.959629i	$-0.409245\pi$
$103$	−0.00940064	−	0.00276028i	−0.000926272	−	0.000271978i	−0.282196	+	0.959357i	$0.591063\pi$
$104$	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	0.0500229	−	0.998748i	$-0.484071\pi$
$107$	−9.63489	−	8.34868i	−0.931440	−	0.807098i	−0.981463	+	0.191650i	$0.938616\pi$
$108$	1.42142	−	1.40697i	0.136776	−	0.135386i
$109$	1.09193	−	1.69908i	0.104588	−	0.162742i	−0.785015	−	0.619477i	$-0.787345\pi$
$109$	1.09193	−	1.69908i	0.104588	−	0.162742i	0.889603	+	0.456735i	$0.150981\pi$
$110$	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	−0.521032	−	0.853537i	$-0.674453\pi$
$113$	−5.29269	+	1.55407i	−0.497895	+	0.146195i	0.0231372	+	0.999732i	$0.492635\pi$
$114$	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	0.702027	−	0.712150i	$-0.252279\pi$
$127$	10.2280	+	3.00322i	0.907592	+	0.266493i	0.205565	+	0.978643i	$0.434097\pi$
$128$	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	0.0915913	−	0.995797i	$-0.470805\pi$
$131$	−6.87878	−	3.14143i	−0.601002	−	0.274468i	−0.692593	+	0.721328i	$0.743532\pi$
$132$	−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	$-0.774114\pi$
$139$		−	15.3636i		−	1.30312i	0.758595	−	0.651562i	$-0.225886\pi$
$140$	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	−0.818863	−	0.573989i	$-0.805395\pi$
$149$	2.20121	−	7.49665i	0.180330	−	0.614149i	0.999193	−	0.0401599i	$-0.0127867\pi$
$150$	6.00169	−	1.98054i	0.490036	−	0.161710i
$151$	−4.18487	−	9.16359i	−0.340560	−	0.745722i	0.659422	−	0.751773i	$-0.270801\pi$
$151$	−4.18487	−	9.16359i	−0.340560	−	0.745722i	−0.999982	+	0.00605099i	$0.998074\pi$
$152$	−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	0.744861	+	0.667220i	$0.232516\pi$
$157$	13.0607	+	20.3229i	1.04236	+	1.62194i	0.297498	+	0.954722i	$0.403848\pi$
$158$	−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	0.994482	+	0.104910i	$0.0334554\pi$
$163$	2.73969	+	9.33052i	0.214589	+	0.730823i	−0.779893	+	0.625913i	$0.784726\pi$
$164$	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	−0.270342	−	0.962764i	$-0.587137\pi$
$167$	−16.2622	−	10.4511i	−1.25841	−	0.808730i	−0.988065	+	0.154035i	$0.950773\pi$
$168$	−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	0.685835	+	0.727757i	$0.259437\pi$
$173$	−3.74308	+	12.7478i	−0.284581	+	0.969194i	−0.970416	+	0.241437i	$0.922381\pi$
$174$	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	0.660161	−	0.751124i	$-0.270488\pi$
$179$	20.1382	−	2.89543i	1.50520	−	0.216415i	0.845036	+	0.534709i	$0.179579\pi$
$180$	−6.02029	+	1.27746i	−0.448726	+	0.0952159i
$181$	−6.64116	+	5.75460i	−0.493634	+	0.427736i	−0.865770	−	0.500442i	$-0.833171\pi$
$181$	−6.64116	+	5.75460i	−0.493634	+	0.427736i	0.372136	+	0.928178i	$0.378625\pi$
$182$	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	−0.909426	−	0.415867i	$-0.863478\pi$
$191$	0.00570268	−	0.0124871i	0.000412631	−	0.000903537i	0.909838	+	0.414963i	$0.136206\pi$
$192$	−7.79019	−	1.82013i	−0.562209	−	0.131357i
$193$	1.98763	−	13.8243i	0.143073	−	0.995095i	−0.784146	−	0.620576i	$-0.786899\pi$
$193$	1.98763	−	13.8243i	0.143073	−	0.995095i	0.927219	−	0.374519i	$-0.122192\pi$
$194$	−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	0.567273	−	0.823530i	$-0.307998\pi$
$197$	21.9116	−	10.0067i	1.56114	−	0.712949i	0.993867	+	0.110581i	$0.0352711\pi$
$198$	0.664715	+	1.33645i	0.0472392	+	0.0949773i
$199$	−5.42293	+	6.25839i	−0.384421	+	0.443646i	−0.914673	−	0.404194i	$-0.867552\pi$
$199$	−5.42293	+	6.25839i	−0.384421	+	0.443646i	0.530252	+	0.847840i	$0.322097\pi$
$200$	−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	0.986190	+	0.165618i	$0.0529618\pi$
$211$	10.5627	+	16.4358i	0.727163	+	1.13149i	−0.259027	+	0.965870i	$0.583402\pi$
$212$	−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	0.270474	+	0.962727i	$0.412820\pi$
$223$	−9.47107	+	20.7387i	−0.634229	+	1.38877i	−0.904704	+	0.426042i	$0.859908\pi$
$224$	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	−0.980814	−	0.194944i	$-0.937548\pi$
$227$	−13.9733	+	12.1079i	−0.927440	+	0.803631i	0.0533749	+	0.998575i	$0.483002\pi$
$228$	−0.928642	+	12.1140i	−0.0615008	+	0.802270i
$229$			6.90517i			0.456306i	0.973625	+	0.228153i	$0.0732687\pi$
$229$			6.90517i			0.456306i	−0.973625	+	0.228153i	$0.926731\pi$
$230$	−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	0.633534	−	0.773715i	$-0.281604\pi$
$233$	−3.39580	−	3.91896i	−0.222466	−	0.256740i	−0.856001	+	0.516975i	$0.827058\pi$
$234$	−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	0.817814	+	0.575482i	$0.195186\pi$
$239$	−1.99437	+	13.8711i	−0.129005	+	0.897249i	−0.946819	+	0.321766i	$0.895723\pi$
$240$	3.58824	−	11.7740i	0.231620	−	0.760010i
$241$	−4.89209	−	1.43645i	−0.315127	−	0.0925297i	0.120344	−	0.992732i	$-0.461600\pi$
$241$	−4.89209	−	1.43645i	−0.315127	−	0.0925297i	−0.435472	+	0.900202i	$0.643418\pi$
$242$	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	0.935037	−	0.354549i	$-0.115366\pi$
$251$	−0.685205	−	2.33360i	−0.0432498	−	0.147295i	−0.978287	+	0.207254i	$0.933547\pi$
$252$	−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	−0.802339	−	0.596869i	$-0.796411\pi$
$257$	−9.50189	+	6.10649i	−0.592711	+	0.380913i	0.209627	+	0.977781i	$0.432775\pi$
$258$	−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	0.766681	−	0.642028i	$-0.221907\pi$
$263$	−3.57755	−	7.83374i	−0.220601	−	0.483049i	−0.987282	+	0.158979i	$0.949180\pi$
$264$	−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	−0.426435	−	0.904518i	$-0.640231\pi$
$269$	−22.7859	−	10.4060i	−1.38928	−	0.634463i	−0.962845	+	0.270056i	$0.912958\pi$
$270$	0.144215	+	4.34938i	0.00877662	+	0.264695i
$271$	0.351470	+	2.44453i	0.0213503	+	0.148495i	0.997708	−	0.0676666i	$-0.0215554\pi$
$271$	0.351470	+	2.44453i	0.0213503	+	0.148495i	−0.976358	+	0.216161i	$0.930646\pi$
$272$	−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	$-0.827404\pi$
$277$		−	17.1773i		−	1.03209i	0.856563	−	0.516043i	$-0.172596\pi$
$278$	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	−0.943299	−	0.331945i	$-0.892295\pi$
$281$	−2.20820	−	15.3584i	−0.131730	−	0.916203i	0.811569	−	0.584257i	$-0.198614\pi$
$282$	−1.98569	+	0.0658407i	−0.118246	+	0.00392076i
$283$	−2.63215	−	1.20206i	−0.156465	−	0.0714552i	0.335643	−	0.941989i	$-0.391046\pi$
$283$	−2.63215	−	1.20206i	−0.156465	−	0.0714552i	−0.492108	+	0.870534i	$0.663774\pi$
$284$	−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	−0.549722	−	0.835347i	$-0.685267\pi$
$293$	7.50590	−	11.6794i	0.438499	−	0.682318i	0.988222	+	0.153029i	$0.0489029\pi$
$294$	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	0.188969	−	0.981983i	$-0.439485\pi$
$307$	−13.2484	−	11.4798i	−0.756126	−	0.655187i	−0.945095	+	0.326796i	$0.894031\pi$
$308$	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	0.278307	−	0.960492i	$-0.410227\pi$
$311$	−0.120743	−	0.0354534i	−0.00684672	−	0.00201038i	−0.285154	+	0.958482i	$0.592045\pi$
$312$	−10.9207	−	13.7664i	−0.618263	−	0.779367i
$313$	1.97845	−	13.7604i	0.111828	−	0.777784i	−0.854311	−	0.519763i	$-0.826020\pi$
$313$	1.97845	−	13.7604i	0.111828	−	0.777784i	0.966139	−	0.258021i	$-0.0830705\pi$
$314$	−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	0.678503	−	0.734598i	$-0.262629\pi$
$317$	27.3563	−	3.93324i	1.53648	−	0.220913i	0.857979	+	0.513685i	$0.171720\pi$
$318$	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	−0.588279	−	0.808658i	$-0.700194\pi$
$331$	−25.1170	−	3.61128i	−1.38055	−	0.198494i	−0.792275	+	0.610164i	$0.791103\pi$
$332$	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	0.188949	−	0.981987i	$-0.439492\pi$
$337$	20.8184	−	24.0257i	1.13405	−	1.30876i	0.945101	−	0.326777i	$-0.105963\pi$
$338$	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	−0.991332	−	0.131379i	$-0.958059\pi$
$347$	−4.25461	−	14.4899i	−0.228399	−	0.777857i	0.762933	−	0.646478i	$-0.223759\pi$
$348$	10.5602	−	3.87741i	0.566086	−	0.207851i
$349$	5.00036	+	7.78071i	0.267663	+	0.416492i	0.948903	−	0.315568i	$-0.102195\pi$
$349$	5.00036	+	7.78071i	0.267663	+	0.416492i	−0.681240	+	0.732060i	$0.738559\pi$
$350$	−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	0.118496	+	0.992954i	$0.462193\pi$
$353$	−16.5565	+	19.1073i	−0.881215	+	1.01698i	−0.999711	+	0.0240218i	$0.992353\pi$
$354$	−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	−0.714762	−	0.699368i	$-0.753465\pi$
$359$	3.18470	−	22.1500i	0.168082	−	1.16903i	0.882844	−	0.469667i	$-0.155626\pi$
$360$	−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	−0.366393	−	0.930460i	$-0.619407\pi$
$373$	−8.80304	+	1.26569i	−0.455804	+	0.0655347i	−0.0894108	+	0.995995i	$0.528498\pi$
$374$	−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	−0.629667	−	0.776865i	$-0.716809\pi$
$379$	6.23067	−	21.2197i	0.320048	−	1.08998i	0.949714	−	0.313117i	$-0.101373\pi$
$380$	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	−0.580937	−	0.813949i	$-0.697314\pi$
$383$	6.01600	−	6.94283i	0.307403	−	0.354762i	0.888340	+	0.459187i	$0.151859\pi$
$384$	−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	0.992390	−	0.123137i	$-0.0392955\pi$
$389$	1.79412	+	6.11020i	0.0909653	+	0.309799i	−0.901424	+	0.432937i	$0.857477\pi$
$390$	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	−0.822020	−	0.569458i	$-0.807153\pi$
$397$	0.746317	−	1.16129i	0.0374566	−	0.0582835i	0.859477	+	0.511175i	$0.170789\pi$
$398$	−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	0.915128	+	0.403164i	$0.132090\pi$
$401$	12.4263	+	27.2097i	0.620537	+	1.35879i	−0.294590	+	0.955624i	$0.595183\pi$
$402$	−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	−0.991289	−	0.131706i	$-0.957955\pi$
$409$	−1.56249	−	10.8673i	−0.0772600	−	0.537355i	0.914029	−	0.405649i	$-0.132955\pi$
$410$	−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	−0.293103	−	0.956081i	$-0.594688\pi$
$419$	−6.24265	+	0.897558i	−0.304973	+	0.0438486i	−0.0118708	+	0.999930i	$0.503779\pi$
$420$	10.1157	−	7.49216i	0.493594	−	0.365580i
$421$	−13.5899	−	6.20628i	−0.662329	−	0.302476i	0.0557421	−	0.998445i	$-0.482248\pi$
$421$	−13.5899	−	6.20628i	−0.662329	−	0.302476i	−0.718071	+	0.695970i	$0.754975\pi$
$422$	−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	−0.390146	−	0.920753i	$-0.627575\pi$
$431$	−28.8523	−	18.5422i	−1.38976	−	0.893148i	−0.999619	+	0.0276053i	$0.991212\pi$
$432$	3.34274	+	2.19683i	0.160828	+	0.105695i
$433$	−6.56046	+	4.21615i	−0.315275	+	0.202615i	−0.688702	−	0.725045i	$-0.741819\pi$
$433$	−6.56046	+	4.21615i	−0.315275	+	0.202615i	0.373427	+	0.927660i	$0.378183\pi$
$434$	−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	0.631240	−	0.775587i	$-0.282546\pi$
$439$	33.1379	−	9.73018i	1.58159	−	0.464396i	0.950347	+	0.311191i	$0.100728\pi$
$440$	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	−0.898706	−	0.438552i	$-0.855491\pi$
$443$	−2.66143	+	4.14127i	−0.126448	+	0.196758i	0.772257	+	0.635310i	$0.219128\pi$
$444$	−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	0.948791	−	0.315903i	$-0.102307\pi$
$449$	33.3986	+	9.80670i	1.57618	+	0.462807i	0.627384	+	0.778710i	$0.284126\pi$
$450$	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	0.679245	−	0.733911i	$-0.262307\pi$
$457$	−3.07542	−	3.54923i	−0.143862	−	0.166026i	−0.823108	+	0.567885i	$0.807762\pi$
$458$	−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	$-0.868584\pi$
$461$		−	17.2294i		−	0.802452i	0.915979	−	0.401226i	$-0.131416\pi$
$462$	−2.37231	−	1.92174i	−0.110370	−	0.0894076i
$463$	−5.42827	−	6.26455i	−0.252273	−	0.291139i	0.615461	−	0.788167i	$-0.288970\pi$
$463$	−5.42827	−	6.26455i	−0.252273	−	0.291139i	−0.867734	+	0.497029i	$0.834424\pi$
$464$	−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	0.992871	−	0.119190i	$-0.0380299\pi$
$467$	33.5603	+	15.3265i	1.55299	+	0.709225i	0.560114	+	0.828415i	$0.310757\pi$
$468$	−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	0.0150737	−	0.999886i	$-0.495202\pi$
$479$	20.3730	−	13.0929i	0.930864	−	0.598230i	0.915791	+	0.401656i	$0.131565\pi$
$480$	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	−0.360227	−	0.932865i	$-0.617301\pi$
$487$	7.47429	−	4.80344i	0.338693	−	0.217664i	0.698920	+	0.715200i	$0.253664\pi$
$488$	−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	0.611106	−	0.791549i	$-0.290725\pi$
$491$	−1.89272	−	1.64005i	−0.0854171	−	0.0740143i	−0.696523	+	0.717535i	$0.745270\pi$
$492$	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	0.804061	−	0.594547i	$-0.202668\pi$
$499$	19.6863	+	8.99044i	0.881281	+	0.402468i	0.0772198	+	0.997014i	$0.475396\pi$
$500$	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	0.781689	−	0.623669i	$-0.214359\pi$
$503$	1.19141	+	1.37496i	0.0531223	+	0.0613064i	−0.728567	+	0.684975i	$0.759813\pi$
$504$	−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	−0.688901	−	0.724855i	$-0.741907\pi$
$509$	−1.56719	+	1.35798i	−0.0694646	+	0.0601914i	0.619437	+	0.785047i	$0.287361\pi$
$510$	−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	−0.768915	−	0.639351i	$-0.779203\pi$
$521$	−0.608146	+	0.701838i	−0.0266434	+	0.0307481i	0.742271	+	0.670099i	$0.233748\pi$
$522$	−1.39237	−	7.83182i	−0.0609422	−	0.342789i
$523$	−20.7683	+	32.3161i	−0.908135	+	1.41309i	0.00255637	+	0.999997i	$0.499186\pi$
$523$	−20.7683	+	32.3161i	−0.908135	+	1.41309i	−0.910691	+	0.413088i	$0.864450\pi$
$524$	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	0.00810409	−	0.999967i	$-0.497420\pi$
$541$	12.6045	−	42.9270i	0.541910	−	1.84557i	0.533805	−	0.845607i	$-0.320761\pi$
$542$	−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	0.735329	−	0.677710i	$-0.237028\pi$
$547$	38.1647	−	5.48726i	1.63180	−	0.234618i	0.896476	+	0.443092i	$0.146119\pi$
$548$	−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	−0.302406	−	0.953179i	$-0.597790\pi$
$557$	−7.64714	+	1.09949i	−0.324020	+	0.0465870i	−0.0216143	+	0.999766i	$0.506881\pi$
$558$	−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	−0.765705	−	0.643191i	$-0.777610\pi$
$563$	5.36677	−	18.2776i	0.226183	−	0.770307i	0.991888	−	0.127116i	$-0.0405719\pi$
$564$	−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	0.499081	−	0.866555i	$-0.333671\pi$
$569$	−1.95217	−	1.25458i	−0.0818392	−	0.0525949i	−0.580920	+	0.813960i	$0.697307\pi$
$570$	−17.9645	−	19.3943i	−0.752449	−	0.812339i
$571$	3.46138	+	5.38601i	0.144854	+	0.225398i	0.906098	−	0.423069i	$-0.139047\pi$
$571$	3.46138	+	5.38601i	0.144854	+	0.225398i	−0.761243	+	0.648466i	$0.775411\pi$
$572$	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	0.00523612	−	0.999986i	$-0.498333\pi$
$577$	13.2180	−	3.88117i	0.550274	−	0.161575i	0.545038	+	0.838411i	$0.316515\pi$
$578$	−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	−0.816368	−	0.577533i	$-0.804016\pi$
$587$	4.42507	−	15.0704i	0.182642	−	0.622022i	0.999010	−	0.0444898i	$-0.0141662\pi$
$588$	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	−0.999654	−	0.0262860i	$-0.991632\pi$
$593$	−1.16641	−	8.11255i	−0.0478986	−	0.333142i	0.951756	−	0.306856i	$-0.0992771\pi$
$594$	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	0.978380	−	0.206817i	$-0.0663103\pi$
$601$	15.5532	+	17.9494i	0.634430	+	0.732172i	−0.343949	+	0.938988i	$0.611765\pi$
$602$	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	0.938848	+	0.344331i	$0.111894\pi$
$607$	−1.45309	+	10.1065i	−0.0589793	+	0.410210i	−0.997828	+	0.0658789i	$0.979015\pi$
$608$	−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	0.671540	−	0.740968i	$-0.265633\pi$
$613$	0.833996	+	0.722662i	0.0336848	+	0.0291880i	−0.637856	+	0.770156i	$0.720178\pi$
$614$	−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	−0.912992	−	0.407977i	$-0.866234\pi$
$617$	−22.8810	+	14.7047i	−0.921154	+	0.591989i	−0.00816151	+	0.999967i	$0.502598\pi$
$618$	−0.0134166	−	0.00346091i	−0.000539694	−	0.000139218i
$619$	−13.5048	−	45.9930i	−0.542802	−	1.84861i	−0.528855	−	0.848712i	$-0.677379\pi$
$619$	−13.5048	−	45.9930i	−0.542802	−	1.84861i	−0.0139471	−	0.999903i	$-0.504440\pi$
$620$	−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	0.687151	+	0.726514i	$0.258861\pi$
$631$	19.7498	+	43.2460i	0.786226	+	1.72159i	0.0990744	+	0.995080i	$0.468412\pi$
$632$	−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	0.698199	−	0.715904i	$-0.253985\pi$
$641$	−2.77947	−	3.20768i	−0.109783	−	0.126696i	−0.807981	+	0.589208i	$0.799440\pi$
$642$	−14.0096	−	11.3488i	−0.552914	−	0.447901i
$643$			33.1259i			1.30636i	0.757204	+	0.653179i	$0.226565\pi$
$643$			33.1259i			1.30636i	−0.757204	+	0.653179i	$0.773435\pi$
$644$	−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	0.991832	−	0.127555i	$-0.0407129\pi$
$647$	18.4266	+	21.2654i	0.724423	+	0.836028i	−0.267409	+	0.963583i	$0.586167\pi$
$648$	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	0.326412	−	0.945227i	$-0.394160\pi$
$653$	9.53930	+	1.37154i	0.373302	+	0.0536727i	0.0468891	+	0.998900i	$0.485069\pi$
$654$	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	0.885772	−	0.464120i	$-0.153629\pi$
$659$	14.1816	+	12.2884i	0.552435	+	0.478688i	−0.333337	+	0.942808i	$0.608175\pi$
$660$	4.61647	−	4.56954i	0.179696	−	0.177869i
$661$	13.6545	−	21.2468i	0.531099	−	0.826407i	−0.467233	−	0.884134i	$-0.654749\pi$
$661$	13.6545	−	21.2468i	0.531099	−	0.826407i	0.998332	+	0.0577276i	$0.0183855\pi$
$662$	−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	0.992858	+	0.119299i	$0.0380649\pi$
$673$	39.2720	+	25.2386i	1.51383	+	0.972876i	0.520967	+	0.853577i	$0.325572\pi$
$674$	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	−0.817723	−	0.575612i	$-0.804764\pi$
$677$	−23.8908	+	10.9106i	−0.918199	+	0.419328i	−0.100476	+	0.994939i	$0.532037\pi$
$678$	−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	−0.381089	−	0.924538i	$-0.624451\pi$
$683$	−34.7421	−	15.8662i	−1.32937	−	0.607102i	−0.948280	+	0.317436i	$0.897178\pi$
$684$	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	$0.0631549\pi$
$691$			10.3627i			0.394215i	−0.980382	+	0.197108i	$0.936845\pi$
$692$	−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	−0.997427	−	0.0716904i	$-0.977161\pi$
$701$	−3.16603	+	10.7825i	−0.119579	+	0.407250i	0.877848	+	0.478940i	$0.158979\pi$
$702$	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	0.806853	−	0.590752i	$-0.201169\pi$
$709$	−1.74920	−	2.72181i	−0.0656927	−	0.102220i	−0.872546	+	0.488532i	$0.837532\pi$
$710$	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	0.270906	−	0.962606i	$-0.412677\pi$
$719$	−13.1972	−	8.48134i	−0.492173	−	0.316300i	−0.763079	+	0.646305i	$0.776313\pi$
$720$	−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	−0.262135	−	0.965031i	$-0.584427\pi$
$727$	7.04440	−	48.9949i	0.261262	−	1.81712i	0.523397	−	0.852089i	$-0.324664\pi$
$728$	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	−0.856175	−	0.516686i	$-0.827165\pi$
$733$	−12.6326	+	10.9462i	−0.466594	+	0.404306i	0.389581	+	0.920992i	$0.372620\pi$
$734$	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	−0.401213	−	0.915985i	$-0.631411\pi$
$739$	12.1882	−	10.5611i	0.448349	−	0.388497i	0.849563	+	0.527488i	$0.176866\pi$
$740$	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	−0.837763	−	0.546034i	$-0.816137\pi$
$743$	3.36691	−	7.37250i	0.123520	−	0.270471i	0.961283	+	0.275563i	$0.0888643\pi$
$744$	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	0.0462695	−	0.998929i	$-0.485267\pi$
$751$	28.1839	−	32.5260i	1.02845	−	1.18689i	0.982177	−	0.187961i	$-0.0601878\pi$
$752$	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	0.945874	+	0.324533i	$0.105207\pi$
$757$	8.95872	+	30.5106i	0.325610	+	1.10893i	−0.620264	+	0.784393i	$0.712975\pi$
$758$	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	0.336792	−	0.941579i	$-0.390658\pi$
$761$	31.1497	−	9.14638i	1.12918	−	0.331556i	0.792384	+	0.610023i	$0.208840\pi$
$762$	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	0.881576	+	0.472042i	$0.156483\pi$
$769$	18.3304	+	40.1380i	0.661012	+	1.44741i	−0.220564	+	0.975373i	$0.570790\pi$
$770$	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	−0.289775	−	0.957095i	$-0.593581\pi$
$773$	−23.2837	−	3.34769i	−0.837457	−	0.120408i	−0.547682	+	0.836687i	$0.684490\pi$
$774$	−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	0.0220433	−	0.999757i	$-0.492983\pi$
$787$	9.11341	−	1.31031i	0.324858	−	0.0467075i	0.302815	+	0.953050i	$0.402074\pi$
$788$	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	0.573490	−	0.819212i	$-0.305589\pi$
$797$	−4.39750	−	3.81045i	−0.155767	−	0.134973i	−0.729258	+	0.684239i	$0.760134\pi$
$798$	−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	0.0674131	−	0.997725i	$-0.478525\pi$
$809$	28.5277	−	18.3336i	1.00298	−	0.644576i	0.935567	+	0.353149i	$0.114889\pi$
$810$	2.95723	+	3.19260i	0.103906	+	0.112177i
$811$	22.2872	−	34.6796i	0.782611	−	1.21777i	−0.189185	−	0.981941i	$-0.560585\pi$
$811$	22.2872	−	34.6796i	0.782611	−	1.21777i	0.971796	−	0.235824i	$-0.0757790\pi$
$812$	−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	0.810147	−	0.586227i	$-0.199387\pi$
$821$	25.7202	+	11.7460i	0.897640	+	0.409938i	0.0874927	+	0.996165i	$0.472115\pi$
$822$	−11.0209	+	0.365425i	−0.384397	+	0.0127457i
$823$	2.92716	+	20.3589i	0.102035	+	0.709666i	0.975052	+	0.221977i	$0.0712509\pi$
$823$	2.92716	+	20.3589i	0.102035	+	0.709666i	−0.873017	+	0.487689i	$0.837840\pi$
$824$	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	$0.335748\pi$
$827$			50.0264i			1.73959i	−0.493415	+	0.869794i	$0.664252\pi$
$828$	6.53928	−	7.01696i	0.227256	−	0.243856i
$829$			4.16726i			0.144735i	0.997378	+	0.0723674i	$0.0230554\pi$
$829$			4.16726i			0.144735i	−0.997378	+	0.0723674i	$0.976945\pi$
$830$	−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	0.667987	−	0.744173i	$-0.267156\pi$
$839$	23.9719	+	7.03879i	0.827603	+	0.243006i	0.159616	+	0.987179i	$0.448974\pi$
$840$	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	0.999050	+	0.0435771i	$0.0138754\pi$
$853$	5.32006	+	18.1184i	0.182155	+	0.620364i	−0.816895	+	0.576787i	$0.804306\pi$
$854$	−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	0.775339	−	0.631545i	$-0.217579\pi$
$857$	15.3092	+	9.83863i	0.522953	+	0.336081i	−0.252386	+	0.967627i	$0.581215\pi$
$858$	−1.62316	−	9.12999i	−0.0554138	−	0.311693i
$859$	−11.7442	−	10.1764i	−0.400709	−	0.347216i	0.431075	−	0.902316i	$-0.358134\pi$
$859$	−11.7442	−	10.1764i	−0.400709	−	0.347216i	−0.831784	+	0.555100i	$0.812680\pi$
$860$	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	−0.334039	−	0.942559i	$-0.608412\pi$
$863$	−33.0383	−	9.70092i	−1.12464	−	0.330223i	−0.790598	+	0.612336i	$0.790230\pi$
$864$	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	−0.991951	−	0.126624i	$-0.959586\pi$
$877$	−29.8447	+	25.8606i	−1.00778	+	0.873250i	−0.0158338	+	0.999875i	$0.505040\pi$
$878$	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	0.543821	+	0.839201i	$0.316977\pi$
$881$	−13.2538	+	29.0218i	−0.446532	+	0.977769i	−0.990353	+	0.138568i	$0.955750\pi$
$882$	3.95899	+	0.435868i	0.133306	+	0.0146764i
$883$	−31.3715	−	4.51054i	−1.05573	−	0.151792i	−0.407479	−	0.913215i	$-0.633592\pi$
$883$	−31.3715	−	4.51054i	−1.05573	−	0.151792i	−0.648255	+	0.761423i	$0.724501\pi$
$884$	−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	0.703310	−	0.710883i	$-0.251705\pi$
$887$	−8.77126	−	19.2064i	−0.294510	−	0.644887i	−0.997820	+	0.0659965i	$0.978977\pi$
$888$	−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	−0.837695	−	0.546138i	$-0.816097\pi$
$907$	−29.3191	+	13.3896i	−0.973525	+	0.444594i	−0.135830	+	0.990732i	$0.543370\pi$
$908$	−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	−0.901435	−	0.432914i	$-0.857485\pi$
$911$	2.57917	−	17.9385i	0.0854516	−	0.594329i	0.986887	−	0.161415i	$-0.0516057\pi$
$912$	−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	−0.778070	−	0.628178i	$-0.783801\pi$
$929$	4.43358	−	30.8362i	0.145461	−	1.01170i	0.923531	−	0.383525i	$-0.125290\pi$
$930$	−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	0.831099	−	0.556125i	$-0.187712\pi$
$937$	20.5237	+	13.1898i	0.670481	+	0.430892i	−0.160618	+	0.987017i	$0.551349\pi$
$938$	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	−0.978972	−	0.203995i	$-0.934607\pi$
$941$	−8.15043	−	27.7578i	−0.265696	−	0.904879i	0.713275	−	0.700884i	$-0.247211\pi$
$942$	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	0.668696	−	0.743536i	$-0.266853\pi$
$947$	−8.78379	−	13.6678i	−0.285435	−	0.444145i	−0.954131	+	0.299391i	$0.903217\pi$
$948$	−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	0.706993	−	0.707221i	$-0.250051\pi$
$953$	−8.96704	−	19.6351i	−0.290471	−	0.636042i	−0.997464	+	0.0711784i	$0.977324\pi$
$954$	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	0.0868238	−	0.996224i	$-0.472328\pi$
$971$	14.0473	−	2.01970i	0.450799	−	0.0648152i	0.363976	+	0.931409i	$0.381419\pi$
$972$	−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	0.993701	−	0.112060i	$-0.0357448\pi$
$977$	55.2959	+	16.2363i	1.76907	+	0.519447i	0.775371	+	0.631506i	$0.217563\pi$
$978$	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	0.416521	−	0.909126i	$-0.363249\pi$
$983$	−7.44378	−	4.78383i	−0.237420	−	0.152580i	−0.653941	+	0.756546i	$0.726886\pi$
$984$	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	−0.342092	−	0.939666i	$-0.611135\pi$
$991$	−3.83605	+	1.12637i	−0.121856	+	0.0357802i	0.220236	+	0.975447i	$0.429317\pi$
$992$	−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	0.609579	−	0.792726i	$-0.291339\pi$
$997$	−2.78892	−	2.41662i	−0.0883261	−	0.0765350i	−0.697905	+	0.716191i	$0.745884\pi$
$998$	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.469.35	yes	480
8.5	even	2	inner	552.2.bb.a.469.27	yes	480
23.18	even	11	inner	552.2.bb.a.133.27	✓	480
184.133	even	22	inner	552.2.bb.a.133.35	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.27	✓	480	23.18	even	11	inner
552.2.bb.a.133.35	yes	480	184.133	even	22	inner
552.2.bb.a.469.27	yes	480	8.5	even	2	inner
552.2.bb.a.469.35	yes	480	1.1	even	1	trivial

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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