LMFDB - Embedded newform 429.2.bb.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.b.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28832 - 1.77322i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.866514 + 2.66686i) q^{4} +(-1.37901 + 1.89804i) q^{5} +(-1.28832 + 1.77322i) q^{6} +(-1.10854 - 0.360186i) q^{7} +(1.67618 - 0.544625i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.28832 - 1.77322i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.866514 + 2.66686i) q^{4} +(-1.37901 + 1.89804i) q^{5} +(-1.28832 + 1.77322i) q^{6} +(-1.10854 - 0.360186i) q^{7} +(1.67618 - 0.544625i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.14227 q^{10} +(0.200908 + 3.31053i) q^{11} +2.80410 q^{12} +(0.338096 - 3.58966i) q^{13} +(0.789464 + 2.42972i) q^{14} +(2.23128 + 0.724988i) q^{15} +(1.41192 + 1.02582i) q^{16} +(0.0125477 + 0.00911645i) q^{17} +(2.08455 + 0.677311i) q^{18} +(6.57415 - 2.13607i) q^{19} +(-3.86688 - 5.32230i) q^{20} +1.16558i q^{21} +(5.61148 - 4.62129i) q^{22} +5.12124 q^{23} +(-1.03594 - 1.42585i) q^{24} +(-0.155819 - 0.479561i) q^{25} +(-6.80086 + 4.02513i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.92113 - 2.64420i) q^{28} +(-2.24080 + 6.89648i) q^{29} +(-1.58905 - 4.89059i) q^{30} +(3.89904 + 5.36657i) q^{31} -7.35012i q^{32} +(3.08642 - 1.21409i) q^{33} -0.0339948i q^{34} +(2.21233 - 1.60735i) q^{35} +(-0.866514 - 2.66686i) q^{36} +(2.60154 + 0.845291i) q^{37} +(-12.2574 - 8.90549i) q^{38} +(-3.51845 + 0.787719i) q^{39} +(-1.27775 + 3.93251i) q^{40} +(6.25647 - 2.03285i) q^{41} +(2.06684 - 1.50165i) q^{42} -4.75391 q^{43} +(-9.00281 - 2.33283i) q^{44} -2.34611i q^{45} +(-6.59781 - 9.08111i) q^{46} +(-10.7895 + 3.50571i) q^{47} +(0.539306 - 1.65981i) q^{48} +(-4.56400 - 3.31594i) q^{49} +(-0.649625 + 0.894132i) q^{50} +(0.00479280 - 0.0147507i) q^{51} +(9.28015 + 4.01215i) q^{52} +(-0.489008 + 0.355285i) q^{53} -2.19183i q^{54} +(-6.56059 - 4.18393i) q^{55} -2.05428 q^{56} +(-4.06305 - 5.59231i) q^{57} +(15.1159 - 4.91144i) q^{58} +(6.47719 + 2.10457i) q^{59} +(-3.86688 + 5.32230i) q^{60} +(8.95114 + 6.50339i) q^{61} +(4.49291 - 13.8278i) q^{62} +(1.10854 - 0.360186i) q^{63} +(-10.2096 + 7.41769i) q^{64} +(6.34710 + 5.59190i) q^{65} +(-6.12915 - 3.90878i) q^{66} +7.11879i q^{67} +(-0.0351850 + 0.0255634i) q^{68} +(-1.58255 - 4.87059i) q^{69} +(-5.70039 - 1.85217i) q^{70} +(0.767621 - 1.05654i) q^{71} +(-1.03594 + 1.42585i) q^{72} +(13.3786 + 4.34696i) q^{73} +(-1.85273 - 5.70212i) q^{74} +(-0.407939 + 0.296385i) q^{75} +19.3832i q^{76} +(0.969693 - 3.74221i) q^{77} +(5.92970 + 5.22417i) q^{78} +(-9.88779 + 7.18390i) q^{79} +(-3.89411 + 1.26527i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-11.6651 - 8.47516i) q^{82} +(-0.907276 + 1.24876i) q^{83} +(-3.10845 - 1.01000i) q^{84} +(-0.0346069 + 0.0112444i) q^{85} +(6.12457 + 8.42974i) q^{86} +7.25139 q^{87} +(2.13976 + 5.43964i) q^{88} +4.38093i q^{89} +(-4.16018 + 3.02255i) q^{90} +(-1.66774 + 3.85750i) q^{91} +(-4.43763 + 13.6576i) q^{92} +(3.89904 - 5.36657i) q^{93} +(20.1167 + 14.6157i) q^{94} +(-5.01146 + 15.4237i) q^{95} +(-6.99038 + 2.27131i) q^{96} +(-2.83756 - 3.90556i) q^{97} +12.3650i q^{98} +(-2.10842 - 2.56019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.28832	−	1.77322i	−0.910982	−	1.25386i	−0.966830	−	0.255419i	$-0.917786\pi$
$2$	−1.28832	−	1.77322i	−0.910982	−	1.25386i	0.0558487	−	0.998439i	$-0.482214\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.866514	+	2.66686i	−0.433257	+	1.33343i
$5$	−1.37901	+	1.89804i	−0.616712	+	0.848831i	−0.997108	−	0.0759923i	$-0.975788\pi$
$5$	−1.37901	+	1.89804i	−0.616712	+	0.848831i	0.380396	+	0.924824i	$0.375788\pi$
$6$	−1.28832	+	1.77322i	−0.525955	+	0.723916i
$7$	−1.10854	−	0.360186i	−0.418988	−	0.136137i	0.0919331	−	0.995765i	$-0.470695\pi$
$7$	−1.10854	−	0.360186i	−0.418988	−	0.136137i	−0.510921	+	0.859628i	$0.670695\pi$
$8$	1.67618	−	0.544625i	0.592620	−	0.192554i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	5.14227			1.62613
$11$	0.200908	+	3.31053i	0.0605760	+	0.998164i
$11$	0.200908	+	3.31053i	0.0605760	+	0.998164i
$12$	2.80410			0.809473
$13$	0.338096	−	3.58966i	0.0937711	−	0.995594i
$13$	0.338096	−	3.58966i	0.0937711	−	0.995594i
$14$	0.789464	+	2.42972i	0.210993	+	0.649370i
$15$	2.23128	+	0.724988i	0.576115	+	0.187191i
$16$	1.41192	+	1.02582i	0.352980	+	0.256455i
$17$	0.0125477	+	0.00911645i	0.00304327	+	0.00221106i	0.589306	−	0.807910i	$-0.299401\pi$
$17$	0.0125477	+	0.00911645i	0.00304327	+	0.00221106i	−0.586263	+	0.810121i	$0.699401\pi$
$18$	2.08455	+	0.677311i	0.491333	+	0.159644i
$19$	6.57415	−	2.13607i	1.50821	−	0.490048i	0.565813	−	0.824534i	$-0.308563\pi$
$19$	6.57415	−	2.13607i	1.50821	−	0.490048i	0.942401	+	0.334485i	$0.108563\pi$
$20$	−3.86688	−	5.32230i	−0.864660	−	1.19010i
$21$			1.16558i			0.254351i
$22$	5.61148	−	4.62129i	1.19637	−	0.985262i
$23$	5.12124			1.06785			0.533926	−	0.845531i	$-0.320716\pi$
$23$	5.12124			1.06785			0.533926	+	0.845531i	$0.320716\pi$
$24$	−1.03594	−	1.42585i	−0.211460	−	0.291050i
$25$	−0.155819	−	0.479561i	−0.0311638	−	0.0959123i
$26$	−6.80086	+	4.02513i	−1.33376	+	0.789392i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	1.92113	−	2.64420i	0.363059	−	0.499707i
$29$	−2.24080	+	6.89648i	−0.416106	+	1.28064i	0.495151	+	0.868807i	$0.335113\pi$
$29$	−2.24080	+	6.89648i	−0.416106	+	1.28064i	−0.911258	+	0.411837i	$0.864887\pi$
$30$	−1.58905	−	4.89059i	−0.290119	−	0.892895i
$31$	3.89904	+	5.36657i	0.700289	+	0.963865i	0.999952	+	0.00981960i	$0.00312573\pi$
$31$	3.89904	+	5.36657i	0.700289	+	0.963865i	−0.299663	+	0.954045i	$0.596874\pi$
$32$		−	7.35012i		−	1.29933i
$33$	3.08642	−	1.21409i	0.537277	−	0.211345i
$34$		−	0.0339948i		−	0.00583007i
$35$	2.21233	−	1.60735i	0.373952	−	0.271692i
$36$	−0.866514	−	2.66686i	−0.144419	−	0.444476i
$37$	2.60154	+	0.845291i	0.427690	+	0.138965i	0.514949	−	0.857221i	$-0.327811\pi$
$37$	2.60154	+	0.845291i	0.427690	+	0.138965i	−0.0872590	+	0.996186i	$0.527811\pi$
$38$	−12.2574	−	8.90549i	−1.98841	−	1.44466i
$39$	−3.51845	+	0.787719i	−0.563403	+	0.126136i
$40$	−1.27775	+	3.93251i	−0.202030	+	0.621785i
$41$	6.25647	−	2.03285i	0.977097	−	0.317478i	0.223419	−	0.974722i	$-0.428278\pi$
$41$	6.25647	−	2.03285i	0.977097	−	0.317478i	0.753677	+	0.657245i	$0.228278\pi$
$42$	2.06684	−	1.50165i	0.318921	−	0.231710i
$43$	−4.75391			−0.724964			−0.362482	−	0.931991i	$-0.618071\pi$
$43$	−4.75391			−0.724964			−0.362482	+	0.931991i	$0.618071\pi$
$44$	−9.00281	−	2.33283i	−1.35722	−	0.351688i
$45$		−	2.34611i		−	0.349738i
$46$	−6.59781	−	9.08111i	−0.972794	−	1.33894i
$47$	−10.7895	+	3.50571i	−1.57381	+	0.511361i	−0.960452	−	0.278447i	$-0.910180\pi$
$47$	−10.7895	+	3.50571i	−1.57381	+	0.511361i	−0.613355	+	0.789808i	$0.710180\pi$
$48$	0.539306	−	1.65981i	0.0778421	−	0.239573i
$49$	−4.56400	−	3.31594i	−0.652000	−	0.473706i
$50$	−0.649625	+	0.894132i	−0.0918708	+	0.126449i
$51$	0.00479280	−	0.0147507i	0.000671126	−	0.00206551i
$52$	9.28015	+	4.01215i	1.28693	+	0.556385i
$53$	−0.489008	+	0.355285i	−0.0671705	+	0.0488022i	−0.620864	−	0.783918i	$-0.713218\pi$
$53$	−0.489008	+	0.355285i	−0.0671705	+	0.0488022i	0.553693	+	0.832721i	$0.313218\pi$
$54$		−	2.19183i		−	0.298270i
$55$	−6.56059	−	4.18393i	−0.884630	−	0.564161i
$56$	−2.05428			−0.274514
$57$	−4.06305	−	5.59231i	−0.538164	−	0.740719i
$58$	15.1159	−	4.91144i	1.98481	−	0.644904i
$59$	6.47719	+	2.10457i	0.843258	+	0.273991i	0.698620	−	0.715493i	$-0.253798\pi$
$59$	6.47719	+	2.10457i	0.843258	+	0.273991i	0.144639	+	0.989485i	$0.453798\pi$
$60$	−3.86688	+	5.32230i	−0.499212	+	0.687106i
$61$	8.95114	+	6.50339i	1.14608	+	0.832673i	0.987954	−	0.154746i	$-0.0494560\pi$
$61$	8.95114	+	6.50339i	1.14608	+	0.832673i	0.158122	+	0.987420i	$0.449456\pi$
$62$	4.49291	−	13.8278i	0.570600	−	1.75613i
$63$	1.10854	−	0.360186i	0.139663	−	0.0453791i
$64$	−10.2096	+	7.41769i	−1.27620	+	0.927211i
$65$	6.34710	+	5.59190i	0.787261	+	0.693590i
$66$	−6.12915	−	3.90878i	−0.754447	−	0.481138i
$67$			7.11879i			0.869698i	0.900503	+	0.434849i	$0.143198\pi$
$67$			7.11879i			0.869698i	−0.900503	+	0.434849i	$0.856802\pi$
$68$	−0.0351850	+	0.0255634i	−0.00426681	+	0.00310002i
$69$	−1.58255	−	4.87059i	−0.190517	−	0.586350i
$70$	−5.70039	−	1.85217i	−0.681327	−	0.221377i
$71$	0.767621	−	1.05654i	0.0910998	−	0.125388i	−0.761034	−	0.648712i	$-0.775308\pi$
$71$	0.767621	−	1.05654i	0.0910998	−	0.125388i	0.852134	+	0.523324i	$0.175308\pi$
$72$	−1.03594	+	1.42585i	−0.122086	+	0.168038i
$73$	13.3786	+	4.34696i	1.56584	+	0.508773i	0.958361	−	0.285561i	$-0.0921798\pi$
$73$	13.3786	+	4.34696i	1.56584	+	0.508773i	0.607482	+	0.794334i	$0.292180\pi$
$74$	−1.85273	−	5.70212i	−0.215375	−	0.662858i
$75$	−0.407939	+	0.296385i	−0.0471048	+	0.0342236i
$76$			19.3832i			2.22341i
$77$	0.969693	−	3.74221i	0.110507	−	0.426465i
$78$	5.92970	+	5.22417i	0.671406	+	0.591520i
$79$	−9.88779	+	7.18390i	−1.11246	+	0.808252i	−0.983050	−	0.183339i	$-0.941309\pi$
$79$	−9.88779	+	7.18390i	−1.11246	+	0.808252i	−0.129413	+	0.991591i	$0.541309\pi$
$80$	−3.89411	+	1.26527i	−0.435374	+	0.141462i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−11.6651	−	8.47516i	−1.28819	−	0.935924i
$83$	−0.907276	+	1.24876i	−0.0995865	+	0.137069i	−0.855902	−	0.517138i	$-0.826997\pi$
$83$	−0.907276	+	1.24876i	−0.0995865	+	0.137069i	0.756316	+	0.654207i	$0.226997\pi$
$84$	−3.10845	−	1.01000i	−0.339159	−	0.110200i
$85$	−0.0346069	+	0.0112444i	−0.00375364	+	0.00121963i
$86$	6.12457	+	8.42974i	0.660429	+	0.909003i
$87$	7.25139			0.777430
$88$	2.13976	+	5.43964i	0.228099	+	0.579867i
$89$			4.38093i			0.464378i	0.972671	+	0.232189i	$0.0745887\pi$
$89$			4.38093i			0.464378i	−0.972671	+	0.232189i	$0.925411\pi$
$90$	−4.16018	+	3.02255i	−0.438522	+	0.318605i
$91$	−1.66774	+	3.85750i	−0.174826	+	0.404376i
$92$	−4.43763	+	13.6576i	−0.462655	+	1.42390i
$93$	3.89904	−	5.36657i	0.404312	−	0.556488i
$94$	20.1167	+	14.6157i	2.07488	+	1.50749i
$95$	−5.01146	+	15.4237i	−0.514165	+	1.58244i
$96$	−6.99038	+	2.27131i	−0.713453	+	0.231815i
$97$	−2.83756	−	3.90556i	−0.288110	−	0.396550i	0.640289	−	0.768134i	$-0.278815\pi$
$97$	−2.83756	−	3.90556i	−0.288110	−	0.396550i	−0.928399	+	0.371584i	$0.878815\pi$
$98$			12.3650i			1.24905i
$99$	−2.10842	−	2.56019i	−0.211904	−	0.257309i
$100$	1.41394			0.141394
$101$	12.9900	−	9.43780i	1.29256	−	0.939096i	0.292701	−	0.956204i	$-0.405446\pi$
$101$	12.9900	−	9.43780i	1.29256	−	0.939096i	0.999854	+	0.0171077i	$0.00544583\pi$
$102$	−0.0323310	+	0.0105050i	−0.00320125	+	0.00104015i
$103$	−1.63878	+	5.04365i	−0.161474	+	0.496966i	−0.998759	−	0.0498007i	$-0.984141\pi$
$103$	−1.63878	+	5.04365i	−0.161474	+	0.496966i	0.837285	+	0.546766i	$0.184141\pi$
$104$	−1.38831	−	6.20107i	−0.136135	−	0.608065i
$105$	−2.21233	−	1.60735i	−0.215901	−	0.156862i
$106$	1.26000	+	0.409399i	0.122382	+	0.0397644i
$107$	−1.95952	−	6.03078i	−0.189434	−	0.583017i	0.810563	−	0.585652i	$-0.199161\pi$
$107$	−1.95952	−	6.03078i	−0.189434	−	0.583017i	−0.999997	+	0.00263448i	$0.999161\pi$
$108$	−2.26856	+	1.64821i	−0.218293	+	0.158599i
$109$		−	2.84376i		−	0.272383i	−0.990683	−	0.136192i	$-0.956514\pi$
$109$		−	2.84376i		−	0.272383i	0.990683	−	0.136192i	$-0.0434863\pi$
$110$	1.03312	+	17.0237i	0.0985044	+	1.62314i
$111$		−	2.73542i		−	0.259634i
$112$	−1.19568	−	1.64571i	−0.112981	−	0.155505i
$113$	6.14815	+	18.9221i	0.578370	+	1.78004i	0.624407	+	0.781099i	$0.285341\pi$
$113$	6.14815	+	18.9221i	0.578370	+	1.78004i	−0.0460373	+	0.998940i	$0.514659\pi$
$114$	−4.68189	+	14.4094i	−0.438500	+	1.34956i
$115$	−7.06224	+	9.72034i	−0.658557	+	0.906427i
$116$	−16.4502	−	11.9518i	−1.52736	−	1.10970i
$117$	1.83643	+	3.10283i	0.169778	+	0.286857i
$118$	−4.61284	−	14.1969i	−0.424647	−	1.30693i
$119$	−0.0106260	−	0.0146254i	−0.000974084	−	0.00134071i
$120$	4.13489			0.377462
$121$	−10.9193	+	1.33023i	−0.992661	+	0.120930i
$122$		−	24.2508i		−	2.19557i
$123$	−3.86671	−	5.32207i	−0.348650	−	0.479875i
$124$	−17.6904	+	5.74797i	−1.58865	+	0.516183i
$125$	−10.0313	−	3.25937i	−0.897229	−	0.291527i
$126$	−2.06684	−	1.50165i	−0.184129	−	0.133778i
$127$	11.1267	+	8.08401i	0.987333	+	0.717340i	0.959335	−	0.282268i	$-0.0910869\pi$
$127$	11.1267	+	8.08401i	0.987333	+	0.717340i	0.0279978	+	0.999608i	$0.491087\pi$
$128$	12.3257	+	4.00486i	1.08945	+	0.353983i
$129$	1.46904	+	4.52124i	0.129342	+	0.398073i
$130$	1.73858	−	18.4590i	0.152484	−	1.61896i
$131$	1.01106			0.0883367			0.0441683	−	0.999024i	$-0.485936\pi$
$131$	1.01106			0.0883367			0.0441683	+	0.999024i	$0.485936\pi$
$132$	0.563366	+	9.28306i	0.0490347	+	0.807987i
$133$	−8.05707			−0.698637
$134$	12.6232	−	9.17130i	1.09048	−	0.792279i
$135$	−2.23128	+	0.724988i	−0.192038	+	0.0623971i
$136$	0.0259973	+	0.00844704i	0.00222925	+	0.000724327i
$137$	8.74333	−	12.0342i	0.746993	−	1.02815i	−0.251193	−	0.967937i	$-0.580823\pi$
$137$	8.74333	−	12.0342i	0.746993	−	1.02815i	0.998186	−	0.0602107i	$-0.0191772\pi$
$138$	−6.59781	+	9.08111i	−0.561643	+	0.773035i
$139$	−1.07641	+	3.31285i	−0.0913000	+	0.280993i	−0.986272	−	0.165130i	$-0.947196\pi$
$139$	−1.07641	+	3.31285i	−0.0913000	+	0.280993i	0.894972	+	0.446123i	$0.147196\pi$
$140$	2.36956	+	7.29276i	0.200265	+	0.616351i
$141$	6.66826	+	9.17807i	0.561569	+	0.772933i
$142$	−2.86242			−0.240209
$143$	11.9516	+	0.398087i	0.999446	+	0.0332897i
$144$	−1.74523			−0.145436
$145$	−9.99973	−	13.7635i	−0.830433	−	1.14299i
$146$	−9.52777	−	29.3235i	−0.788524	−	2.42683i
$147$	−1.74329	+	5.36530i	−0.143784	+	0.442523i
$148$	−4.50854	+	6.20547i	−0.370600	+	0.510086i
$149$	1.59068	−	2.18938i	0.130313	−	0.179361i	−0.738874	−	0.673843i	$-0.764642\pi$
$149$	1.59068	−	2.18938i	0.130313	−	0.179361i	0.869188	+	0.494482i	$0.164642\pi$
$150$	1.05111	+	0.341528i	0.0858232	+	0.0278856i
$151$	−1.60060	+	0.520065i	−0.130255	+	0.0423223i	−0.373419	−	0.927663i	$-0.621815\pi$
$151$	−1.60060	+	0.520065i	−0.130255	+	0.0423223i	0.243164	+	0.969985i	$0.421815\pi$
$152$	9.85612	−	7.16089i	0.799437	−	0.580825i
$153$	−0.0155098			−0.00125390
$154$	−7.88506	+	3.10170i	−0.635396	+	0.249942i
$155$	−15.5628			−1.25003
$156$	0.948055	−	10.0658i	0.0759052	−	0.805907i
$157$	−5.07160	−	15.6088i	−0.404758	−	1.24572i	−0.921097	−	0.389332i	$-0.872706\pi$
$157$	−5.07160	−	15.6088i	−0.404758	−	1.24572i	0.516340	−	0.856384i	$-0.327294\pi$
$158$	25.4773	+	8.27808i	2.02687	+	0.658569i
$159$	0.489008	+	0.355285i	0.0387809	+	0.0281760i
$160$	13.9509	+	10.1359i	1.10291	+	0.801313i
$161$	−5.67709	−	1.84460i	−0.447417	−	0.145375i
$162$	−2.08455	+	0.677311i	−0.163778	+	0.0532146i
$163$	6.58988	+	9.07018i	0.516159	+	0.710432i	0.984943	−	0.172881i	$-0.0553077\pi$
$163$	6.58988	+	9.07018i	0.516159	+	0.710432i	−0.468784	+	0.883313i	$0.655308\pi$
$164$			18.4466i			1.44044i
$165$	−1.95182	+	7.53240i	−0.151949	+	0.586397i
$166$	3.38319			0.262587
$167$	4.16757	+	5.73617i	0.322497	+	0.443878i	0.939227	−	0.343296i	$-0.111543\pi$
$167$	4.16757	+	5.73617i	0.322497	+	0.443878i	−0.616731	+	0.787174i	$0.711543\pi$
$168$	0.634806	+	1.95373i	0.0489764	+	0.150734i
$169$	−12.7714	−	2.42731i	−0.982414	−	0.186716i
$170$	0.0645237	+	0.0468792i	0.00494874	+	0.00359547i
$171$	−4.06305	+	5.59231i	−0.310709	+	0.427654i
$172$	4.11933	−	12.6780i	0.314096	−	0.966687i
$173$	0.0822829	+	0.253241i	0.00625585	+	0.0192535i	0.954136	−	0.299374i	$-0.0967780\pi$
$173$	0.0822829	+	0.253241i	0.00625585	+	0.0192535i	−0.947880	+	0.318628i	$0.896778\pi$
$174$	−9.34212	−	12.8583i	−0.708225	−	0.974787i
$175$			0.587735i			0.0444286i
$176$	−3.11235	+	4.88031i	−0.234602	+	0.367867i
$177$		−	6.81052i		−	0.511910i
$178$	7.76837	−	5.64405i	0.582264	−	0.423040i
$179$	−5.88046	−	18.0982i	−0.439526	−	1.35272i	−0.888377	−	0.459115i	$-0.848166\pi$
$179$	−5.88046	−	18.0982i	−0.439526	−	1.35272i	0.448850	−	0.893607i	$-0.351834\pi$
$180$	6.25674	+	2.03294i	0.466350	+	0.151526i
$181$	2.28061	+	1.65696i	0.169517	+	0.123161i	0.669309	−	0.742984i	$-0.266590\pi$
$181$	2.28061	+	1.65696i	0.169517	+	0.123161i	−0.499792	+	0.866145i	$0.666590\pi$
$182$	8.98879	−	2.01243i	0.666294	−	0.149171i
$183$	3.41903	−	10.5227i	0.252742	−	0.777860i
$184$	8.58413	−	2.78915i	0.632831	−	0.205619i
$185$	−5.19195	+	3.77217i	−0.381720	+	0.277335i
$186$	−14.5394			−1.06608
$187$	−0.0276594	+	0.0433712i	−0.00202265	+	0.00317162i
$188$		−	31.8117i		−	2.32011i
$189$	−0.685114	−	0.942978i	−0.0498347	−	0.0685916i
$190$	33.8060	−	10.9842i	2.45255	−	0.796881i
$191$	−1.41420	+	4.35247i	−0.102328	+	0.314934i	−0.989094	−	0.147285i	$-0.952947\pi$
$191$	−1.41420	+	4.35247i	−0.102328	+	0.314934i	0.886766	+	0.462219i	$0.152947\pi$
$192$	10.2096	+	7.41769i	0.736813	+	0.535326i
$193$	14.6572	−	20.1739i	1.05505	−	1.45215i	0.170704	−	0.985322i	$-0.445396\pi$
$193$	14.6572	−	20.1739i	1.05505	−	1.45215i	0.884347	−	0.466830i	$-0.154604\pi$
$194$	−3.26975	+	10.0633i	−0.234754	+	0.722499i
$195$	3.35685	−	7.76445i	0.240389	−	0.556024i
$196$	12.7979	−	9.29822i	0.914136	−	0.664158i
$197$		−	2.37094i		−	0.168922i	−0.996427	−	0.0844612i	$-0.973083\pi$
$197$		−	2.37094i		−	0.168922i	0.996427	−	0.0844612i	$-0.0269169\pi$
$198$	−1.82346	+	7.03705i	−0.129588	+	0.500101i
$199$	−19.4842			−1.38120			−0.690599	−	0.723238i	$-0.742653\pi$
$199$	−19.4842			−1.38120			−0.690599	+	0.723238i	$0.742653\pi$
$200$	−0.522362	−	0.718969i	−0.0369366	−	0.0508388i
$201$	6.77037	−	2.19983i	0.477545	−	0.155164i
$202$	−33.4707	−	10.8753i	−2.35499	−	0.765182i
$203$	4.96802	−	6.83790i	0.348687	−	0.479926i
$204$	0.0351850	+	0.0255634i	0.00246344	+	0.00178980i
$205$	−4.76929	+	14.6784i	−0.333102	+	1.02518i
$206$	11.0548	−	3.59192i	0.770224	−	0.250261i
$207$	−4.14317	+	3.01019i	−0.287970	+	0.209223i
$208$	4.15972	−	4.72150i	0.288425	−	0.327377i
$209$	8.39234	+	21.3348i	0.580510	+	1.47576i
$210$			5.99375i			0.413608i
$211$	2.32193	−	1.68698i	0.159849	−	0.116137i	−0.504986	−	0.863128i	$-0.668502\pi$
$211$	2.32193	−	1.68698i	0.159849	−	0.116137i	0.664834	+	0.746991i	$0.268502\pi$
$212$	−0.523762	−	1.61197i	−0.0359721	−	0.110711i
$213$	−1.24204	−	0.403562i	−0.0851029	−	0.0276516i
$214$	−8.16943	+	11.2443i	−0.558451	+	0.768641i
$215$	6.55569	−	9.02313i	0.447094	−	0.615372i
$216$	1.67618	+	0.544625i	0.114050	+	0.0370570i
$217$	−2.38927	−	7.35342i	−0.162194	−	0.499183i
$218$	−5.04263	+	3.66369i	−0.341530	+	0.248136i
$219$		−	14.0671i		−	0.950563i
$220$	16.8428	−	13.8707i	1.13554	−	0.935164i
$221$	0.0369673	−	0.0419599i	0.00248669	−	0.00282253i
$222$	−4.85051	+	3.52410i	−0.325545	+	0.236522i
$223$	−12.5701	+	4.08427i	−0.841755	+	0.273503i	−0.697989	−	0.716109i	$-0.745921\pi$
$223$	−12.5701	+	4.08427i	−0.841755	+	0.273503i	−0.143767	+	0.989612i	$0.545921\pi$
$224$	−2.64741	+	8.14789i	−0.176887	+	0.544404i
$225$	0.407939	+	0.296385i	0.0271960	+	0.0197590i
$226$	25.6323	−	35.2798i	1.70503	−	2.34678i
$227$	−14.6069	−	4.74608i	−0.969496	−	0.315008i	−0.218883	−	0.975751i	$-0.570241\pi$
$227$	−14.6069	−	4.74608i	−0.969496	−	0.315008i	−0.750612	+	0.660743i	$0.770241\pi$
$228$	18.4346	−	5.98975i	1.22086	−	0.396681i
$229$	3.35503	+	4.61780i	0.221706	+	0.305153i	0.905352	−	0.424661i	$-0.139607\pi$
$229$	3.35503	+	4.61780i	0.221706	+	0.305153i	−0.683646	+	0.729814i	$0.739607\pi$
$230$	26.3348			1.73646
$231$	−3.85871	+	0.234175i	−0.253884	+	0.0154076i
$232$			12.7801i			0.839058i
$233$	1.43180	−	1.04026i	0.0938003	−	0.0681499i	−0.539897	−	0.841731i	$-0.681537\pi$
$233$	1.43180	−	1.04026i	0.0938003	−	0.0681499i	0.633697	+	0.773581i	$0.281537\pi$
$234$	3.13610	−	7.25384i	0.205013	−	0.474198i
$235$	8.22479	−	25.3133i	0.536526	−	1.65126i
$236$	−11.2252	+	15.4501i	−0.730695	+	1.00572i
$237$	9.88779	+	7.18390i	0.642281	+	0.466644i
$238$	−0.0122445	+	0.0376845i	−0.000793690	+	0.00244273i
$239$	−17.1334	+	5.56698i	−1.10827	+	0.360098i	−0.805279	−	0.592896i	$-0.797984\pi$
$239$	−17.1334	+	5.56698i	−1.10827	+	0.360098i	−0.302989	+	0.952994i	$0.597984\pi$
$240$	2.40669	+	3.31253i	0.155351	+	0.213823i
$241$			0.218212i			0.0140563i	0.999975	+	0.00702814i	$0.00223714\pi$
$241$			0.218212i			0.0140563i	−0.999975	+	0.00702814i	$0.997763\pi$
$242$	16.4263	+	17.6486i	1.05592	+	1.13449i
$243$	−1.00000			−0.0641500
$244$	−25.0999	+	18.2361i	−1.60686	+	1.16745i
$245$	12.5876	−	4.08996i	0.804192	−	0.261298i
$246$	−4.45565	+	13.7131i	−0.284082	+	0.874315i
$247$	−5.44508	−	24.3212i	−0.346462	−	1.54752i
$248$	9.45827	+	6.87184i	0.600601	+	0.436362i
$249$	1.46800	+	0.476983i	0.0930310	+	0.0302276i
$250$	7.14398	+	21.9869i	0.451825	+	1.39057i
$251$	−1.64153	+	1.19264i	−0.103613	+	0.0752791i	−0.638385	−	0.769717i	$-0.720397\pi$
$251$	−1.64153	+	1.19264i	−0.103613	+	0.0752791i	0.534772	+	0.844996i	$0.320397\pi$
$252$			3.26841i			0.205891i
$253$	1.02890	+	16.9540i	0.0646863	+	1.06589i
$254$		−	30.1449i		−	1.89146i
$255$	0.0213882	+	0.0294383i	0.00133938	+	0.00184350i
$256$	−0.978525	−	3.01159i	−0.0611578	−	0.188224i
$257$	2.65862	−	8.18238i	0.165840	−	0.510403i	−0.833257	−	0.552886i	$-0.813527\pi$
$257$	2.65862	−	8.18238i	0.165840	−	0.510403i	0.999097	+	0.0424825i	$0.0135267\pi$
$258$	6.12457	−	8.42974i	0.381299	−	0.524813i
$259$	−2.57944	−	1.87407i	−0.160279	−	0.116449i
$260$	−20.4127	+	12.0813i	−1.26594	+	0.749253i
$261$	−2.24080	−	6.89648i	−0.138702	−	0.426881i
$262$	−1.30257	−	1.79284i	−0.0804731	−	0.110762i
$263$	11.1970			0.690440			0.345220	−	0.938522i	$-0.387804\pi$
$263$	11.1970			0.690440			0.345220	+	0.938522i	$0.387804\pi$
$264$	4.51218	−	3.71597i	0.277706	−	0.228702i
$265$		−	1.41810i		−	0.0871133i
$266$	10.3801	+	14.2870i	0.636445	+	0.875992i
$267$	4.16651	−	1.35378i	0.254986	−	0.0828501i
$268$	−18.9848	−	6.16853i	−1.15968	−	0.376803i
$269$	24.1198	+	17.5240i	1.47061	+	1.06846i	0.980437	+	0.196833i	$0.0630656\pi$
$269$	24.1198	+	17.5240i	1.47061	+	1.06846i	0.490171	+	0.871626i	$0.336934\pi$
$270$	4.16018	+	3.02255i	0.253181	+	0.183946i
$271$	−3.13885	−	1.01987i	−0.190672	−	0.0619530i	0.212125	−	0.977243i	$-0.431962\pi$
$271$	−3.13885	−	1.01987i	−0.190672	−	0.0619530i	−0.402796	+	0.915290i	$0.631962\pi$
$272$	0.00836454	+	0.0257434i	0.000507175	+	0.00156092i
$273$	4.18406	+	0.394080i	0.253231	+	0.0238508i
$274$	−32.6035			−1.96965
$275$	1.55630	−	0.612192i	0.0938484	−	0.0369165i
$276$	14.3605			0.864398
$277$	17.1930	−	12.4914i	1.03303	−	0.750537i	0.0641133	−	0.997943i	$-0.479578\pi$
$277$	17.1930	−	12.4914i	1.03303	−	0.750537i	0.968912	+	0.247406i	$0.0795781\pi$
$278$	7.26120	−	2.35931i	0.435498	−	0.141502i
$279$	−6.30878	−	2.04985i	−0.377697	−	0.122721i
$280$	2.83287	−	3.89911i	0.169296	−	0.233016i
$281$	−3.20064	+	4.40530i	−0.190934	+	0.262798i	−0.893742	−	0.448582i	$-0.851929\pi$
$281$	−3.20064	+	4.40530i	−0.190934	+	0.262798i	0.702808	+	0.711380i	$0.251929\pi$
$282$	7.68391	−	23.6486i	0.457570	−	1.40826i
$283$	−1.99120	−	6.12827i	−0.118364	−	0.364288i	0.874270	−	0.485441i	$-0.161341\pi$
$283$	−1.99120	−	6.12827i	−0.118364	−	0.364288i	−0.992634	+	0.121153i	$0.961341\pi$
$284$	2.15248	+	2.96264i	0.127726	+	0.175800i
$285$	16.2174			0.960638
$286$	−14.6917	−	21.7058i	−0.868736	−	1.28349i
$287$	−7.66773			−0.452612
$288$	4.32030	+	5.94638i	0.254576	+	0.350394i
$289$	−5.25321	−	16.1677i	−0.309013	−	0.951043i
$290$	−11.5228	+	35.4635i	−0.676642	+	2.08249i
$291$	−2.83756	+	3.90556i	−0.166341	+	0.228948i
$292$	−23.1854	+	31.9120i	−1.35682	+	1.86751i
$293$	−26.6368	−	8.65482i	−1.55614	−	0.505620i	−0.600365	−	0.799726i	$-0.704978\pi$
$293$	−26.6368	−	8.65482i	−1.55614	−	0.505620i	−0.955773	+	0.294106i	$0.904978\pi$
$294$	11.7598	−	3.82099i	0.685846	−	0.222845i
$295$	−12.9267	+	9.39178i	−0.752620	+	0.546810i
$296$	4.82102			0.280216
$297$	−1.78335	+	2.79637i	−0.103480	+	0.162262i
$298$	−5.93156			−0.343606
$299$	1.73147	−	18.3835i	0.100134	−	1.06315i
$300$	−0.436932	−	1.34474i	−0.0252263	−	0.0776384i
$301$	5.26988	+	1.71229i	0.303751	+	0.0986947i
$302$	2.98428	+	2.16820i	0.171726	+	0.124766i
$303$	−12.9900	−	9.43780i	−0.746257	−	0.542187i
$304$	11.4734	+	3.72794i	0.658045	+	0.213812i
$305$	−24.6874	+	8.02143i	−1.41360	+	0.459306i
$306$	0.0199817	+	0.0275024i	0.00114228	+	0.00157221i
$307$			34.4373i			1.96544i	0.185099	+	0.982720i	$0.440739\pi$
$307$			34.4373i			1.96544i	−0.185099	+	0.982720i	$0.559261\pi$
$308$	9.13969	+	5.82871i	0.520782	+	0.332122i
$309$	5.30321			0.301689
$310$	20.0499	+	27.5963i	1.13876	+	1.56737i
$311$	−3.95362	−	12.1680i	−0.224189	−	0.689984i	−0.998373	−	0.0570226i	$-0.981839\pi$
$311$	−3.95362	−	12.1680i	−0.224189	−	0.689984i	0.774184	−	0.632961i	$-0.218161\pi$
$312$	−5.46855	+	3.23659i	−0.309596	+	0.183236i
$313$	26.2723	+	19.0880i	1.48500	+	1.07891i	0.975903	+	0.218205i	$0.0700203\pi$
$313$	26.2723	+	19.0880i	1.48500	+	1.07891i	0.509096	+	0.860710i	$0.329980\pi$
$314$	−21.1440	+	29.1022i	−1.19322	+	1.64233i
$315$	−0.845036	+	2.60075i	−0.0476124	+	0.146536i
$316$	−10.5905	−	32.5942i	−0.595763	−	1.83357i
$317$	−2.48827	−	3.42480i	−0.139755	−	0.192356i	0.733402	−	0.679795i	$-0.237931\pi$
$317$	−2.48827	−	3.42480i	−0.139755	−	0.192356i	−0.873157	+	0.487439i	$0.837931\pi$
$318$		−	1.32484i		−	0.0742936i
$319$	−23.2812	−	6.03269i	−1.30350	−	0.337766i
$320$		−	29.6073i		−	1.65510i
$321$	−5.13009	+	3.72723i	−0.286334	+	0.208033i
$322$	4.04303	+	12.4432i	0.225309	+	0.693431i
$323$	0.101964	+	0.0331301i	0.00567343	+	0.00184341i
$324$	2.26856	+	1.64821i	0.126031	+	0.0915671i
$325$	−1.77415	+	0.397200i	−0.0984119	+	0.0220327i
$326$	7.59358	−	23.3706i	0.420570	−	1.29438i
$327$	−2.70458	+	0.878771i	−0.149564	+	0.0485962i
$328$	9.37984	−	6.81486i	0.517915	−	0.376287i
$329$	13.2232			0.729021
$330$	15.8712	−	6.24316i	0.873681	−	0.343674i
$331$			1.16634i			0.0641080i	0.999486	+	0.0320540i	$0.0102049\pi$
$331$			1.16634i			0.0641080i	−0.999486	+	0.0320540i	$0.989795\pi$
$332$	−2.54409	−	3.50164i	−0.139625	−	0.192178i
$333$	−2.60154	+	0.845291i	−0.142563	+	0.0463217i
$334$	4.80234	−	14.7801i	0.262772	−	0.808730i
$335$	−13.5118	−	9.81688i	−0.738227	−	0.536353i
$336$	−1.19568	+	1.64571i	−0.0652298	+	0.0897811i
$337$	−4.14809	+	12.7665i	−0.225961	+	0.695436i	0.772232	+	0.635341i	$0.219140\pi$
$337$	−4.14809	+	12.7665i	−0.225961	+	0.695436i	−0.998193	+	0.0600951i	$0.980860\pi$
$338$	12.1495	+	25.7737i	0.660846	+	1.40190i
$339$	16.0961	−	11.6945i	0.874219	−	0.635157i
$340$		−	0.102035i		−	0.00553362i
$341$	−16.9829	+	13.9861i	−0.919674	+	0.757390i
$342$	15.1509			0.819268
$343$	8.66080	+	11.9206i	0.467639	+	0.643650i
$344$	−7.96842	+	2.58910i	−0.429628	+	0.139595i
$345$	11.4269	+	3.71284i	0.615206	+	0.199893i
$346$	0.343045	−	0.472162i	0.0184422	−	0.0253836i
$347$	−26.3620	−	19.1531i	−1.41519	−	1.02819i	−0.992543	−	0.121897i	$-0.961102\pi$
$347$	−26.3620	−	19.1531i	−1.41519	−	1.02819i	−0.422644	−	0.906296i	$-0.638898\pi$
$348$	−6.28343	+	19.3384i	−0.336827	+	1.03665i
$349$	−23.5784	+	7.66107i	−1.26212	+	0.410088i	−0.862250	−	0.506484i	$-0.830945\pi$
$349$	−23.5784	+	7.66107i	−1.26212	+	0.410088i	−0.399871	+	0.916571i	$0.630945\pi$
$350$	1.04219	−	0.757193i	0.0557072	−	0.0404737i
$351$	2.38348	−	2.70537i	0.127221	−	0.144402i
$352$	24.3328	−	1.47670i	1.29694	−	0.0787083i
$353$			16.0650i			0.855055i	0.904002	+	0.427528i	$0.140615\pi$
$353$			16.0650i			0.855055i	−0.904002	+	0.427528i	$0.859385\pi$
$354$	−12.0766	+	8.77415i	−0.641863	+	0.466341i
$355$	0.946802	+	2.91396i	0.0502510	+	0.154657i
$356$	−11.6833	−	3.79614i	−0.619214	−	0.201195i
$357$	−0.0106260	+	0.0146254i	−0.000562387	+	0.000774060i
$358$	−24.5162	+	33.7437i	−1.29572	+	1.78341i
$359$	−3.38698	−	1.10050i	−0.178758	−	0.0580820i	0.218270	−	0.975888i	$-0.429959\pi$
$359$	−3.38698	−	1.10050i	−0.178758	−	0.0580820i	−0.397028	+	0.917806i	$0.629959\pi$
$360$	−1.27775	−	3.93251i	−0.0673433	−	0.207262i
$361$	23.2853	−	16.9178i	1.22554	−	0.890410i
$362$		−	6.17874i		−	0.324747i
$363$	4.63936	+	9.97378i	0.243503	+	0.523488i
$364$	−8.84227	−	7.79019i	−0.463461	−	0.408317i
$365$	−26.6999	+	19.3986i	−1.39754	+	1.01537i
$366$	−23.0639	+	7.49392i	−1.20557	+	0.391714i
$367$	−9.29911	+	28.6197i	−0.485410	+	1.49394i	0.345977	+	0.938243i	$0.387548\pi$
$367$	−9.29911	+	28.6197i	−0.485410	+	1.49394i	−0.831387	+	0.555695i	$0.812452\pi$
$368$	7.23079	+	5.25348i	0.376931	+	0.273856i
$369$	−3.86671	+	5.32207i	−0.201293	+	0.277056i
$370$	13.3778	+	4.34671i	0.695479	+	0.225975i
$371$	0.670053	−	0.217713i	0.0347874	−	0.0113031i
$372$	10.9333	+	15.0484i	0.566865	+	0.780223i
$373$	−6.41165			−0.331982			−0.165991	−	0.986127i	$-0.553082\pi$
$373$	−6.41165			−0.331982			−0.165991	+	0.986127i	$0.553082\pi$
$374$	0.112541	−	0.00682984i	0.00581936	−	0.000353162i
$375$			10.5476i			0.544673i
$376$	−16.1758	+	11.7524i	−0.834204	+	0.606085i
$377$	23.9984	+	10.3754i	1.23598	+	0.534360i
$378$	−0.789464	+	2.42972i	−0.0406056	+	0.124971i
$379$	11.3042	−	15.5589i	0.580656	−	0.799205i	−0.413111	−	0.910681i	$-0.635558\pi$
$379$	11.3042	−	15.5589i	0.580656	−	0.799205i	0.993767	+	0.111476i	$0.0355578\pi$
$380$	−36.7903	−	26.7297i	−1.88730	−	1.37120i
$381$	4.25001	−	13.0802i	0.217735	−	0.670119i
$382$	9.53986	−	3.09969i	0.488102	−	0.158594i
$383$	8.43432	+	11.6089i	0.430974	+	0.593185i	0.968176	−	0.250269i	$-0.0805189\pi$
$383$	8.43432	+	11.6089i	0.430974	+	0.593185i	−0.537203	+	0.843453i	$0.680519\pi$
$384$		−	12.9600i		−	0.661362i
$385$	5.76567	+	7.00107i	0.293846	+	0.356808i
$386$	−54.6562			−2.78193
$387$	3.84599	−	2.79428i	0.195503	−	0.142041i
$388$	12.8744	−	4.18313i	0.653596	−	0.212366i
$389$	10.1437	−	31.2190i	0.514305	−	1.58287i	−0.270238	−	0.962794i	$-0.587102\pi$
$389$	10.1437	−	31.2190i	0.514305	−	1.58287i	0.784543	−	0.620075i	$-0.212898\pi$
$390$	−18.0928	+	4.05066i	−0.916165	+	0.205113i
$391$	0.0642599	+	0.0466875i	0.00324976	+	0.00236109i
$392$	−9.45603	−	3.07245i	−0.477602	−	0.155182i
$393$	−0.312435	−	0.961575i	−0.0157602	−	0.0485050i
$394$	−4.20421	+	3.05453i	−0.211805	+	0.153885i
$395$		−	28.6741i		−	1.44275i
$396$	8.65463	−	3.40442i	0.434911	−	0.171078i
$397$			12.1982i			0.612208i	0.951998	+	0.306104i	$0.0990255\pi$
$397$			12.1982i			0.612208i	−0.951998	+	0.306104i	$0.900974\pi$
$398$	25.1019	+	34.5498i	1.25825	+	1.73183i
$399$	2.48977	+	7.66273i	0.124645	+	0.383616i
$400$	0.271940	−	0.836945i	0.0135970	−	0.0418473i
$401$	−1.77229	+	2.43935i	−0.0885039	+	0.121815i	−0.850973	−	0.525210i	$-0.823987\pi$
$401$	−1.77229	+	2.43935i	−0.0885039	+	0.121815i	0.762469	+	0.647025i	$0.223987\pi$
$402$	−12.6232	−	9.17130i	−0.629588	−	0.457423i
$403$	20.5824	−	12.1818i	1.02528	−	0.606820i
$404$	13.9132	+	42.8205i	0.692209	+	2.13040i
$405$	1.37901	+	1.89804i	0.0685236	+	0.0943146i
$406$	−18.5255			−0.919407
$407$	−2.27569	+	8.78231i	−0.112802	+	0.435323i
$408$		−	0.0273352i		−	0.00135329i
$409$	0.563324	+	0.775349i	0.0278546	+	0.0383385i	0.822717	−	0.568451i	$-0.192457\pi$
$409$	0.563324	+	0.775349i	0.0278546	+	0.0383385i	−0.794863	+	0.606789i	$0.792457\pi$
$410$	32.1724	−	10.4535i	1.58888	−	0.516260i
$411$	−14.1470	−	4.59664i	−0.697820	−	0.226736i
$412$	−12.0307	−	8.74078i	−0.592708	−	0.430628i
$413$	−6.42217	−	4.66598i	−0.316014	−	0.229598i
$414$	10.6755	+	3.46867i	0.524671	+	0.170476i
$415$	−1.11906	−	3.44410i	−0.0549323	−	0.169064i
$416$	−26.3845	−	2.48505i	−1.29361	−	0.121840i
$417$	3.48334			0.170580
$418$	27.0193	−	42.3676i	1.32156	−	2.07227i
$419$	28.9303			1.41334			0.706669	−	0.707544i	$-0.250197\pi$
$419$	28.9303			1.41334			0.706669	+	0.707544i	$0.250197\pi$
$420$	6.20359	−	4.50718i	0.302704	−	0.219928i
$421$	−4.53897	+	1.47480i	−0.221216	+	0.0718774i	−0.417528	−	0.908664i	$-0.637103\pi$
$421$	−4.53897	+	1.47480i	−0.221216	+	0.0718774i	0.196312	+	0.980541i	$0.437103\pi$
$422$	−5.98280	−	1.94393i	−0.291238	−	0.0946290i
$423$	6.66826	−	9.17807i	0.324222	−	0.446253i
$424$	−0.626170	+	0.861849i	−0.0304095	+	0.0418551i
$425$	0.00241673	−	0.00743792i	0.000117228	−	0.000360792i
$426$	0.884537	+	2.72233i	0.0428560	+	0.131897i
$427$	−7.58025	−	10.4333i	−0.366834	−	0.504904i
$428$	17.7812			0.859485
$429$	−3.31465	−	11.4897i	−0.160033	−	0.554728i
$430$	−24.4459			−1.17888
$431$	0.364499	+	0.501690i	0.0175573	+	0.0241655i	0.817705	−	0.575637i	$-0.195246\pi$
$431$	0.364499	+	0.501690i	0.0175573	+	0.0241655i	−0.800148	+	0.599802i	$0.795246\pi$
$432$	0.539306	+	1.65981i	0.0259474	+	0.0798578i
$433$	5.35063	−	16.4675i	0.257135	−	0.791379i	−0.736267	−	0.676691i	$-0.763413\pi$
$433$	5.35063	−	16.4675i	0.257135	−	0.791379i	0.993402	−	0.114688i	$-0.0365868\pi$
$434$	−9.96111	+	13.7103i	−0.478149	+	0.658115i
$435$	−9.99973	+	13.7635i	−0.479450	+	0.659907i
$436$	7.58391	+	2.46416i	0.363203	+	0.118012i
$437$	33.6678	−	10.9393i	1.61055	−	0.523299i
$438$	−24.9440	+	18.1229i	−1.19187	+	0.865946i
$439$	0.0710851			0.00339271			0.00169635	−	0.999999i	$-0.499460\pi$
$439$	0.0710851			0.00339271			0.00169635	+	0.999999i	$0.499460\pi$
$440$	−13.2754	−	3.43996i	−0.632881	−	0.163994i
$441$	5.64141			0.268639
$442$	−0.122030	−	0.0114935i	−0.00580438	−	0.000546692i
$443$	1.86346	+	5.73513i	0.0885356	+	0.272484i	0.985515	−	0.169588i	$-0.0542436\pi$
$443$	1.86346	+	5.73513i	0.0885356	+	0.272484i	−0.896980	+	0.442072i	$0.854244\pi$
$444$	7.29497	+	2.37028i	0.346204	+	0.112488i
$445$	−8.31520	−	6.04135i	−0.394178	−	0.286387i
$446$	23.4367	+	17.0277i	1.10976	+	0.806286i
$447$	−2.57377	−	0.836268i	−0.121735	−	0.0395541i
$448$	13.9894	−	4.54544i	0.660939	−	0.214752i
$449$	16.1371	+	22.2109i	0.761558	+	1.04819i	0.997083	+	0.0763265i	$0.0243191\pi$
$449$	16.1371	+	22.2109i	0.761558	+	1.04819i	−0.235525	+	0.971868i	$0.575681\pi$
$450$		−	1.10521i		−	0.0521000i
$451$	7.98680	+	20.3038i	0.376084	+	0.956071i
$452$	−55.7899			−2.62414
$453$	0.989223	+	1.36155i	0.0464778	+	0.0639711i
$454$	10.4026	+	32.0158i	0.488217	+	1.50258i
$455$	−5.02188	−	8.48497i	−0.235429	−	0.397781i
$456$	−9.85612	−	7.16089i	−0.461555	−	0.335339i
$457$	13.8218	−	19.0241i	0.646556	−	0.889908i	−0.352388	−	0.935854i	$-0.614630\pi$
$457$	13.8218	−	19.0241i	0.646556	−	0.889908i	0.998944	+	0.0459458i	$0.0146301\pi$
$458$	3.86603	−	11.8984i	0.180648	−	0.555977i
$459$	0.00479280	+	0.0147507i	0.000223709	+	0.000688505i
$460$	−19.8032	−	27.2568i	−0.923330	−	1.27085i
$461$			7.91502i			0.368639i	0.982866	+	0.184320i	$0.0590082\pi$
$461$			7.91502i			0.368639i	−0.982866	+	0.184320i	$0.940992\pi$
$462$	5.38651	+	6.54066i	0.250603	+	0.304299i
$463$			14.7781i			0.686795i	0.939190	+	0.343397i	$0.111578\pi$
$463$			14.7781i			0.686795i	−0.939190	+	0.343397i	$0.888422\pi$
$464$	−10.2384	+	7.43862i	−0.475305	+	0.345329i
$465$	4.80917	+	14.8011i	0.223020	+	0.686385i
$466$	−3.68924	−	1.19871i	−0.170901	−	0.0555290i
$467$	1.58112	+	1.14875i	0.0731654	+	0.0531577i	0.623767	−	0.781611i	$-0.285602\pi$
$467$	1.58112	+	1.14875i	0.0731654	+	0.0531577i	−0.550601	+	0.834768i	$0.685602\pi$
$468$	−9.86608	+	2.20884i	−0.456060	+	0.102104i
$469$	2.56408	−	7.89144i	0.118398	−	0.364393i
$470$	−55.4823	+	18.0273i	−2.55921	+	0.831538i
$471$	−13.2776	+	9.64675i	−0.611800	+	0.444499i
$472$	12.0031			0.552490
$473$	−0.955098	−	15.7380i	−0.0439155	−	0.723633i
$474$		−	26.7884i		−	1.23043i
$475$	−2.04875	−	2.81987i	−0.0940033	−	0.129384i
$476$	0.0482115	−	0.0156649i	0.00220977	−	0.000717998i
$477$	0.186785	−	0.574864i	0.00855228	−	0.0263212i
$478$	31.9448	+	23.2093i	1.46112	+	1.06157i
$479$	6.40231	−	8.81202i	0.292529	−	0.402631i	−0.637305	−	0.770612i	$-0.719951\pi$
$479$	6.40231	−	8.81202i	0.292529	−	0.402631i	0.929833	+	0.367981i	$0.119951\pi$
$480$	5.32876	−	16.4002i	0.243223	−	0.748564i
$481$	3.91388	−	9.05286i	0.178458	−	0.412775i
$482$	0.386939	−	0.281128i	0.0176246	−	0.0128050i
$483$			5.96924i			0.271610i
$484$	5.91418	−	30.2728i	0.268826	−	1.37604i
$485$	11.3260			0.514285
$486$	1.28832	+	1.77322i	0.0584395	+	0.0804351i
$487$	−31.7377	+	10.3122i	−1.43817	+	0.467291i	−0.921328	−	0.388787i	$-0.872894\pi$
$487$	−31.7377	+	10.3122i	−1.43817	+	0.467291i	−0.516846	+	0.856078i	$0.672894\pi$
$488$	18.5457	+	6.02585i	0.839522	+	0.272777i
$489$	6.58988	−	9.07018i	0.298004	−	0.410168i
$490$	−23.4693	−	17.0514i	−1.06023	−	0.770306i
$491$	10.6091	−	32.6513i	0.478780	−	1.47353i	−0.362010	−	0.932174i	$-0.617909\pi$
$491$	10.6091	−	32.6513i	0.478780	−	1.47353i	0.840791	−	0.541361i	$-0.182091\pi$
$492$	17.5438	−	5.70031i	0.790934	−	0.256990i
$493$	−0.0909883	+	0.0661069i	−0.00409791	+	0.00297730i
$494$	−36.1119	+	40.9889i	−1.62475	+	1.84418i
$495$	7.76688	−	0.471353i	0.349095	−	0.0211857i
$496$			11.5769i			0.519818i
$497$	−1.23149	+	0.894727i	−0.0552397	+	0.0401340i
$498$	−1.04546	−	3.21761i	−0.0468484	−	0.144184i
$499$	−15.3171	−	4.97683i	−0.685688	−	0.222794i	−0.0546041	−	0.998508i	$-0.517390\pi$
$499$	−15.3171	−	4.97683i	−0.685688	−	0.222794i	−0.631084	+	0.775715i	$0.717390\pi$
$500$	17.3846	−	23.9278i	0.777461	−	1.07008i
$501$	4.16757	−	5.73617i	0.186193	−	0.256273i
$502$	4.22965	+	1.37430i	0.188779	+	0.0613379i
$503$	−8.82691	−	27.1664i	−0.393573	−	1.21129i	−0.930068	−	0.367388i	$-0.880252\pi$
$503$	−8.82691	−	27.1664i	−0.393573	−	1.21129i	0.536495	−	0.843904i	$-0.319748\pi$
$504$	1.66194	−	1.20747i	0.0740289	−	0.0537851i
$505$			37.6704i			1.67631i
$506$	28.7378	−	23.6667i	1.27755	−	1.05211i
$507$	1.63807	+	12.8964i	0.0727492	+	0.572749i
$508$	−31.2003	+	22.6683i	−1.38429	+	1.00575i
$509$	18.4349	−	5.98985i	0.817111	−	0.265496i	0.129504	−	0.991579i	$-0.458661\pi$
$509$	18.4349	−	5.98985i	0.817111	−	0.265496i	0.687607	+	0.726083i	$0.258661\pi$
$510$	0.0246459	−	0.0758522i	0.00109134	−	0.00335879i
$511$	−13.2649	−	9.63753i	−0.586806	−	0.426339i
$512$	11.1558	−	15.3547i	0.493022	−	0.678586i
$513$	6.57415	+	2.13607i	0.290256	+	0.0943098i
$514$	−17.9344	+	5.82723i	−0.791051	+	0.257028i
$515$	−7.31317	−	10.0657i	−0.322257	−	0.443549i
$516$	−13.3304			−0.586839
$517$	−13.7735	−	35.0146i	−0.605756	−	1.53994i
$518$			6.98833i			0.307050i
$519$	0.215419	−	0.156511i	0.00945586	−	0.00687008i
$520$	13.6844	+	5.91626i	0.600100	+	0.259445i
$521$	5.08064	−	15.6366i	0.222587	−	0.685052i	−0.775941	−	0.630806i	$-0.782724\pi$
$521$	5.08064	−	15.6366i	0.222587	−	0.685052i	0.998528	−	0.0542462i	$-0.0172756\pi$
$522$	−9.34212	+	12.8583i	−0.408894	+	0.562794i
$523$	18.1664	+	13.1986i	0.794360	+	0.577136i	0.909254	−	0.416242i	$-0.136653\pi$
$523$	18.1664	+	13.1986i	0.794360	+	0.577136i	−0.114894	+	0.993378i	$0.536653\pi$
$524$	−0.876097	+	2.69635i	−0.0382725	+	0.117791i
$525$	0.558970	−	0.181620i	0.0243954	−	0.00792656i
$526$	−14.4254	−	19.8549i	−0.628978	−	0.865714i
$527$			0.102884i			0.00448168i
$528$	5.60322	+	1.45192i	0.243849	+	0.0631868i
$529$	3.22710			0.140309
$530$	−2.51461	+	1.82697i	−0.109228	+	0.0793586i
$531$	−6.47719	+	2.10457i	−0.281086	+	0.0913304i
$532$	6.98156	−	21.4870i	0.302689	−	0.931582i
$533$	−5.18196	−	23.1459i	−0.224456	−	1.00256i
$534$	−7.76837	−	5.64405i	−0.336170	−	0.244242i
$535$	14.1489	+	4.59725i	0.611709	+	0.198756i
$536$	3.87707	+	11.9324i	0.167464	+	0.515401i
$537$	−15.3952	+	11.1853i	−0.664354	+	0.482681i
$538$		−	65.3463i		−	2.81728i
$539$	10.0606	−	15.7755i	0.433340	−	0.679498i
$540$		−	6.57873i		−	0.283103i
$541$	−24.3888	−	33.5683i	−1.04855	−	1.44321i	−0.890055	−	0.455853i	$-0.849334\pi$
$541$	−24.3888	−	33.5683i	−1.04855	−	1.44321i	−0.158500	−	0.987359i	$-0.550666\pi$
$542$	2.23539	+	6.87981i	0.0960181	+	0.295513i
$543$	0.871117	−	2.68102i	0.0373832	−	0.115054i
$544$	0.0670071	−	0.0922273i	0.00287290	−	0.00395421i
$545$	5.39759	+	3.92158i	0.231207	+	0.167982i
$546$	−4.69162	−	7.92697i	−0.200783	−	0.339243i
$547$	−10.0413	−	30.9039i	−0.429334	−	1.32136i	−0.898782	−	0.438395i	$-0.855547\pi$
$547$	−10.0413	−	30.9039i	−0.429334	−	1.32136i	0.469448	−	0.882960i	$-0.344453\pi$
$548$	24.5172	+	33.7450i	1.04732	+	1.44151i
$549$	−11.0642			−0.472209
$550$	−3.09057	−	1.97097i	−0.131782	−	0.0840423i
$551$			50.1250i			2.13540i
$552$	−5.30529	−	7.30210i	−0.225808	−	0.310798i
$553$	13.5485	−	4.40218i	0.576141	−	0.187200i
$554$	−44.3002	−	14.3940i	−1.88213	−	0.611542i
$555$	5.19195	+	3.77217i	0.220386	+	0.160120i
$556$	−7.90218	−	5.74127i	−0.335127	−	0.243484i
$557$	9.77754	+	3.17691i	0.414287	+	0.134610i	0.508742	−	0.860919i	$-0.330111\pi$
$557$	9.77754	+	3.17691i	0.414287	+	0.134610i	−0.0944546	+	0.995529i	$0.530111\pi$
$558$	4.49291	+	13.8278i	0.190200	+	0.585375i
$559$	−1.60728	+	17.0649i	−0.0679807	+	0.721770i
$560$	4.77249			0.201675
$561$	0.0497957	+	0.0129032i	0.00210238	+	0.000544773i
$562$	11.9350			0.503449
$563$	28.8921	−	20.9913i	1.21766	−	0.884678i	0.221752	−	0.975103i	$-0.428823\pi$
$563$	28.8921	−	20.9913i	1.21766	−	0.884678i	0.995903	+	0.0904249i	$0.0288225\pi$
$564$	−30.2547	+	9.83036i	−1.27395	+	0.413933i
$565$	−44.3933	−	14.4243i	−1.86764	−	0.606833i
$566$	−8.30150	+	11.4260i	−0.348938	+	0.480272i
$567$	−0.685114	+	0.942978i	−0.0287721	+	0.0396014i
$568$	0.711255	−	2.18902i	0.0298436	−	0.0918491i
$569$	−9.26001	−	28.4994i	−0.388200	−	1.19476i	−0.934132	−	0.356927i	$-0.883824\pi$
$569$	−9.26001	−	28.4994i	−0.388200	−	1.19476i	0.545932	−	0.837829i	$-0.316176\pi$
$570$	−20.8933	−	28.7571i	−0.875123	−	1.20450i
$571$	43.1376			1.80525			0.902626	−	0.430426i	$-0.141637\pi$
$571$	43.1376			1.80525			0.902626	+	0.430426i	$0.141637\pi$
$572$	−11.4179	+	31.5283i	−0.477406	+	1.31827i
$573$	4.57646			0.191184
$574$	9.87851	+	13.5966i	0.412321	+	0.567511i
$575$	−0.797986	−	2.45595i	−0.0332783	−	0.102420i
$576$	3.89971	−	12.0021i	0.162488	−	0.500086i
$577$	−8.75288	+	12.0473i	−0.364387	+	0.501536i	−0.951364	−	0.308068i	$-0.900318\pi$
$577$	−8.75288	+	12.0473i	−0.364387	+	0.501536i	0.586977	+	0.809603i	$0.300318\pi$
$578$	−21.9012	+	30.1444i	−0.910969	+	1.25384i
$579$	−23.7159	−	7.70576i	−0.985599	−	0.320241i
$580$	45.3700	−	14.7416i	1.88389	−	0.612112i
$581$	1.45553	−	1.05751i	0.0603857	−	0.0438728i
$582$	10.5811			0.438602
$583$	−1.27443	−	1.54750i	−0.0527815	−	0.0640909i
$584$	24.7924			1.02592
$585$	−8.42175	−	0.793212i	−0.348197	−	0.0327953i
$586$	18.9699	+	58.3832i	0.783637	+	2.41179i
$587$	27.0705	+	8.79573i	1.11732	+	0.363039i	0.808744	−	0.588161i	$-0.200148\pi$
$587$	27.0705	+	8.79573i	1.11732	+	0.363039i	0.308575	+	0.951200i	$0.400148\pi$
$588$	−12.7979	−	9.29822i	−0.527776	−	0.383452i
$589$	37.0963	+	26.9520i	1.52853	+	1.11054i
$590$	33.3074	+	10.8222i	1.37125	+	0.445545i
$591$	−2.25490	+	0.732661i	−0.0927541	+	0.0301376i
$592$	2.80605	+	3.86220i	0.115328	+	0.158735i
$593$			0.0576954i			0.00236926i	0.999999	+	0.00118463i	$0.000377080\pi$
$593$			0.0576954i			0.00236926i	−0.999999	+	0.00118463i	$0.999623\pi$
$594$	7.25611	−	0.440355i	0.297722	−	0.0180680i
$595$	0.0424131			0.00173877
$596$	4.46041	+	6.13923i	0.182706	+	0.251473i
$597$	6.02095	+	18.5306i	0.246421	+	0.758406i
$598$	−34.8288	+	20.6136i	−1.42426	+	0.842954i
$599$	19.0473	+	13.8387i	0.778251	+	0.565432i	0.904453	−	0.426572i	$-0.140279\pi$
$599$	19.0473	+	13.8387i	0.778251	+	0.565432i	−0.126203	+	0.992004i	$0.540279\pi$
$600$	−0.522362	+	0.718969i	−0.0213253	+	0.0293518i
$601$	−10.1685	+	31.2953i	−0.414780	+	1.27656i	0.497668	+	0.867368i	$0.334190\pi$
$601$	−10.1685	+	31.2953i	−0.414780	+	1.27656i	−0.912448	+	0.409193i	$0.865810\pi$
$602$	−3.75304	−	11.5507i	−0.152962	−	0.470770i
$603$	−4.18432	−	5.75922i	−0.170399	−	0.234534i
$604$		−	4.71920i		−	0.192022i
$605$	12.5330	−	22.5597i	0.509537	−	0.917180i
$606$			35.1931i			1.42962i
$607$	−35.3723	+	25.6995i	−1.43572	+	1.04311i	−0.446802	+	0.894633i	$0.647437\pi$
$607$	−35.3723	+	25.6995i	−1.43572	+	1.04311i	−0.988916	+	0.148477i	$0.952563\pi$
$608$	−15.7004	−	48.3208i	−0.636735	−	1.95967i
$609$	−8.03843	−	2.61184i	−0.325734	−	0.105837i
$610$	46.0292	+	33.4422i	1.86367	+	1.35403i
$611$	8.93645	+	39.9159i	0.361530	+	1.61482i
$612$	0.0134395	−	0.0413625i	0.000543259	−	0.00167198i
$613$	18.7469	−	6.09124i	0.757181	−	0.246023i	0.0951127	−	0.995467i	$-0.469679\pi$
$613$	18.7469	−	6.09124i	0.757181	−	0.246023i	0.662068	+	0.749443i	$0.269679\pi$
$614$	61.0650	−	44.3663i	2.46438	−	1.79048i
$615$	15.4338			0.622349
$616$	−0.412720	−	6.80075i	−0.0166290	−	0.274010i
$617$		−	40.0866i		−	1.61382i	−0.590671	−	0.806912i	$-0.701137\pi$
$617$		−	40.0866i		−	1.61382i	0.590671	−	0.806912i	$-0.298863\pi$
$618$	−6.83224	−	9.40377i	−0.274833	−	0.378275i
$619$	38.8229	−	12.6143i	1.56043	−	0.507013i	0.603504	−	0.797360i	$-0.293771\pi$
$619$	38.8229	−	12.6143i	1.56043	−	0.507013i	0.956921	+	0.290347i	$0.0937707\pi$
$620$	13.4854	−	41.5038i	0.541586	−	1.66683i
$621$	4.14317	+	3.01019i	0.166260	+	0.120795i
$622$	−16.4830	+	22.6870i	−0.660910	+	0.909664i
$623$	1.57795	−	4.85642i	0.0632191	−	0.194569i
$624$	−5.77583	−	2.49710i	−0.231218	−	0.0999642i
$625$	22.0594	−	16.0271i	0.882377	−	0.641084i
$626$		−	71.1781i		−	2.84485i
$627$	17.6972	−	14.5744i	0.706759	−	0.582045i
$628$	46.0210			1.83644
$629$	0.0249373	+	0.0343233i	0.000994316	+	0.00136856i
$630$	5.70039	−	1.85217i	0.227109	−	0.0737922i
$631$	37.4780	+	12.1773i	1.49198	+	0.484772i	0.937666	−	0.347539i	$-0.112982\pi$
$631$	37.4780	+	12.1773i	1.49198	+	0.484772i	0.554309	+	0.832311i	$0.312982\pi$
$632$	−12.6612	+	17.4267i	−0.503636	+	0.693195i
$633$	−2.32193	−	1.68698i	−0.0922886	−	0.0670516i
$634$	−2.86726	+	8.82450i	−0.113873	+	0.350466i
$635$	−30.6876	+	9.97101i	−1.21780	+	0.395687i
$636$	−1.37123	+	0.996255i	−0.0543727	+	0.0395041i
$637$	−13.4462	+	15.2621i	−0.532757	+	0.604707i
$638$	19.2964	+	49.0549i	0.763952	+	1.94210i
$639$			1.30595i			0.0516627i
$640$	−24.5986	+	17.8720i	−0.972346	+	0.706451i
$641$	5.12506	+	15.7733i	0.202428	+	0.623008i	0.999809	+	0.0195326i	$0.00621782\pi$
$641$	5.12506	+	15.7733i	0.202428	+	0.623008i	−0.797382	+	0.603475i	$0.793782\pi$
$642$	13.2184	+	4.29492i	0.521689	+	0.169507i
$643$	15.6944	−	21.6016i	0.618929	−	0.851882i	−0.378346	−	0.925664i	$-0.623507\pi$
$643$	15.6944	−	21.6016i	0.618929	−	0.851882i	0.997274	+	0.0737823i	$0.0235070\pi$
$644$	9.83855	−	13.5416i	0.387693	−	0.533614i
$645$	−10.6073	−	3.44653i	−0.417663	−	0.135707i
$646$	−0.0726154	−	0.223487i	−0.00285701	−	0.00879299i
$647$	−33.1268	+	24.0680i	−1.30235	+	0.946212i	−0.999976	−	0.00697744i	$-0.997779\pi$
$647$	−33.1268	+	24.0680i	−1.30235	+	0.946212i	−0.302374	+	0.953190i	$0.597779\pi$
$648$		−	1.76244i		−	0.0692353i
$649$	−5.66592	+	21.8658i	−0.222407	+	0.858307i
$650$	2.99000	+	2.63424i	0.117277	+	0.103323i
$651$	−6.25519	+	4.54466i	−0.245160	+	0.178119i
$652$	−29.8991	+	9.71480i	−1.17094	+	0.380461i
$653$	−9.03603	+	27.8100i	−0.353607	+	1.08829i	0.603206	+	0.797586i	$0.293890\pi$
$653$	−9.03603	+	27.8100i	−0.353607	+	1.08829i	−0.956813	+	0.290705i	$0.906110\pi$
$654$	5.04263	+	3.66369i	0.197182	+	0.143261i
$655$	−1.39426	+	1.91904i	−0.0544783	+	0.0749829i
$656$	10.9190	+	3.54779i	0.426315	+	0.138518i
$657$	−13.3786	+	4.34696i	−0.521947	+	0.169591i
$658$	−17.0358	−	23.4478i	−0.664124	−	0.914089i
$659$	−29.8448			−1.16259			−0.581293	−	0.813694i	$-0.697453\pi$
$659$	−29.8448			−1.16259			−0.581293	+	0.813694i	$0.697453\pi$
$660$	−18.3965	−	11.7321i	−0.716085	−	0.456673i
$661$			12.9766i			0.504732i	0.967632	+	0.252366i	$0.0812088\pi$
$661$			12.9766i			0.504732i	−0.967632	+	0.252366i	$0.918791\pi$
$662$	2.06819	−	1.50263i	0.0803824	−	0.0584012i
$663$	−0.0513297	−	0.0221917i	−0.00199348	−	0.000861855i
$664$	−0.840656	+	2.58727i	−0.0326238	+	0.100406i
$665$	11.1108	−	15.2927i	0.430858	−	0.593025i
$666$	4.85051	+	3.52410i	0.187953	+	0.136556i
$667$	−11.4757	+	35.3185i	−0.444340	+	1.36754i
$668$	−18.9088	+	6.14384i	−0.731604	+	0.237712i
$669$	7.76874	+	10.6928i	0.300357	+	0.413406i
$670$			36.6067i			1.41424i
$671$	−19.7313	+	30.9396i	−0.761719	+	1.19441i
$672$	8.56719			0.330487
$673$	−5.97697	+	4.34252i	−0.230395	+	0.167392i	−0.696994	−	0.717077i	$-0.745479\pi$
$673$	−5.97697	+	4.34252i	−0.230395	+	0.167392i	0.466598	+	0.884469i	$0.345479\pi$
$674$	27.9820	−	9.09189i	1.07782	−	0.350206i
$675$	0.155819	−	0.479561i	0.00599747	−	0.0184583i
$676$	17.5399	−	31.9561i	0.674610	−	1.22908i
$677$	−34.1333	−	24.7993i	−1.31185	−	0.953115i	−0.999996	−	0.00298452i	$-0.999050\pi$
$677$	−34.1333	−	24.7993i	−1.31185	−	0.953115i	−0.311854	−	0.950130i	$-0.600950\pi$
$678$	−41.4739	−	13.4757i	−1.59279	−	0.517530i
$679$	1.73881	+	5.35151i	0.0667294	+	0.205372i
$680$	−0.0518834	+	0.0376955i	−0.00198964	+	0.00144556i
$681$			15.3586i			0.588544i
$682$	46.6799	+	12.0958i	1.78747	+	0.463173i
$683$		−	0.318068i		−	0.0121705i	−0.999981	−	0.00608527i	$-0.998063\pi$
$683$		−	0.318068i		−	0.0121705i	0.999981	−	0.00608527i	$-0.00193701\pi$
$684$	−11.3932	−	15.6814i	−0.435629	−	0.599592i
$685$	10.7842	+	33.1905i	0.412044	+	1.26814i
$686$	9.97994	−	30.7151i	0.381036	−	1.17271i
$687$	3.35503	−	4.61780i	0.128002	−	0.176180i
$688$	−6.71214	−	4.87666i	−0.255898	−	0.185921i
$689$	1.11002	+	1.87550i	0.0422885	+	0.0714507i
$690$	−8.13790	−	25.0459i	−0.309804	−	0.953480i
$691$	−16.2470	−	22.3621i	−0.618067	−	0.850696i	0.379144	−	0.925338i	$-0.376219\pi$
$691$	−16.2470	−	22.3621i	−0.618067	−	0.850696i	−0.997210	+	0.0746418i	$0.976219\pi$
$692$	−0.746655			−0.0283836
$693$	1.41512	+	3.59749i	0.0537560	+	0.136657i
$694$			71.4211i			2.71111i
$695$	−4.80356	−	6.61153i	−0.182209	−	0.250790i
$696$	12.1546	−	3.94928i	0.460721	−	0.149697i
$697$	0.0970368	+	0.0315292i	0.00367553	+	0.00119425i
$698$	43.9613	+	31.9398i	1.66396	+	1.20894i
$699$	−1.43180	−	1.04026i	−0.0541557	−	0.0393464i
$700$	−1.56741	−	0.509281i	−0.0592424	−	0.0192490i
$701$	−0.0928548	−	0.285778i	−0.00350708	−	0.0107937i	0.949288	−	0.314409i	$-0.101806\pi$
$701$	−0.0928548	−	0.285778i	−0.00350708	−	0.0107937i	−0.952795	+	0.303615i	$0.901806\pi$
$702$	−7.86792	−	0.741048i	−0.296955	−	0.0279691i
$703$	18.9085			0.713148
$704$	−26.6077	−	32.3089i	−1.00282	−	1.21769i
$705$	−26.6160			−1.00242
$706$	28.4869	−	20.6969i	1.07212	−	0.778940i
$707$	−17.7993	+	5.78333i	−0.669411	+	0.217505i
$708$	18.1627	+	5.90141i	0.682595	+	0.221789i
$709$	0.0280238	−	0.0385714i	0.00105245	−	0.00144858i	−0.808490	−	0.588509i	$-0.799715\pi$
$709$	0.0280238	−	0.0385714i	0.00105245	−	0.00144858i	0.809543	+	0.587061i	$0.199715\pi$
$710$	3.94731	−	5.43301i	0.148140	−	0.203897i
$711$	3.77680	−	11.6238i	0.141641	−	0.435926i
$712$	2.38596	+	7.34324i	0.0894177	+	0.275199i
$713$	19.9679	+	27.4835i	0.747805	+	1.02927i
$714$	0.0396239			0.00148289
$715$	−17.2370	+	22.1358i	−0.644628	+	0.827831i
$716$	53.3608			1.99419
$717$	10.5890	+	14.5745i	0.395454	+	0.544296i
$718$	2.41209	+	7.42366i	0.0900186	+	0.277049i
$719$	0.453262	−	1.39500i	0.0169038	−	0.0520246i	−0.942249	−	0.334914i	$-0.891293\pi$
$719$	0.453262	−	1.39500i	0.0169038	−	0.0520246i	0.959153	+	0.282889i	$0.0912928\pi$
$720$	2.40669	−	3.31253i	0.0896921	−	0.123451i
$721$	3.63330	−	5.00081i	0.135311	−	0.186240i
$722$	−59.9980	−	19.4945i	−2.23290	−	0.725512i
$723$	0.207532	−	0.0674312i	0.00771820	−	0.00250780i
$724$	−6.39506	+	4.64628i	−0.237671	+	0.172678i
$725$	3.65644			0.135797
$726$	11.7088	−	21.0761i	0.434553	−	0.782206i
$727$	2.04791			0.0759527			0.0379763	−	0.999279i	$-0.487909\pi$
$727$	2.04791			0.0759527			0.0379763	+	0.999279i	$0.487909\pi$
$728$	−0.694543	+	7.37416i	−0.0257415	+	0.273305i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	68.7961	+	22.3532i	2.54626	+	0.827330i
$731$	−0.0596507	−	0.0433388i	−0.00220626	−	0.00160294i
$732$	25.0999	+	18.2361i	0.927718	+	0.674027i
$733$	−41.2261	−	13.3952i	−1.52272	−	0.494762i	−0.576174	−	0.817327i	$-0.695455\pi$
$733$	−41.2261	−	13.3952i	−1.52272	−	0.494762i	−0.946547	+	0.322565i	$0.895455\pi$
$734$	62.7294	−	20.3820i	2.31539	−	0.752315i
$735$	−7.77956	−	10.7076i	−0.286954	−	0.394958i
$736$		−	37.6418i		−	1.38749i
$737$	−23.5670	+	1.43022i	−0.868101	+	0.0526829i
$738$	14.4188			0.530763
$739$	−5.37843	−	7.40278i	−0.197849	−	0.272316i	0.698553	−	0.715559i	$-0.253828\pi$
$739$	−5.37843	−	7.40278i	−0.197849	−	0.272316i	−0.896401	+	0.443243i	$0.853828\pi$
$740$	−5.56094	−	17.1148i	−0.204424	−	0.629153i
$741$	−21.4482	+	12.6942i	−0.787920	+	0.466335i
$742$	−1.24930	−	0.907668i	−0.0458632	−	0.0333216i
$743$	10.8447	−	14.9265i	0.397855	−	0.547600i	−0.562349	−	0.826900i	$-0.690102\pi$
$743$	10.8447	−	14.9265i	0.397855	−	0.547600i	0.960204	+	0.279300i	$0.0901023\pi$
$744$	3.61274	−	11.1189i	0.132449	−	0.407637i
$745$	1.96198	+	6.03835i	0.0718813	+	0.221228i
$746$	8.26027	+	11.3693i	0.302430	+	0.416259i
$747$		−	1.54355i		−	0.0564756i
$748$	−0.0916975	−	0.111345i	−0.00335279	−	0.00407119i
$749$			7.39113i			0.270066i
$750$	18.7032	−	13.5887i	0.682943	−	0.496187i
$751$	2.53855	+	7.81285i	0.0926330	+	0.285095i	0.986630	−	0.162979i	$-0.0521102\pi$
$751$	2.53855	+	7.81285i	0.0926330	+	0.285095i	−0.893997	+	0.448074i	$0.852110\pi$
$752$	−18.8301	−	6.11828i	−0.686664	−	0.223111i
$753$	1.64153	+	1.19264i	0.0598208	+	0.0434624i
$754$	−12.5198	−	55.9215i	−0.455945	−	2.03654i
$755$	1.22013	−	3.75518i	0.0444051	−	0.136665i
$756$	3.10845	−	1.01000i	0.113053	−	0.0367332i
$757$	−3.48376	+	2.53110i	−0.126619	+	0.0919944i	−0.649292	−	0.760539i	$-0.724935\pi$
$757$	−3.48376	+	2.53110i	−0.126619	+	0.0919944i	0.522673	+	0.852533i	$0.324935\pi$
$758$	−42.1528			−1.53106
$759$	15.8063	−	6.21763i	0.573733	−	0.225686i
$760$			28.5823i			1.03679i
$761$	7.12413	+	9.80552i	0.258249	+	0.355450i	0.918379	−	0.395702i	$-0.129499\pi$
$761$	7.12413	+	9.80552i	0.258249	+	0.355450i	−0.660130	+	0.751152i	$0.729499\pi$
$762$	−28.6695	+	9.31529i	−1.03859	+	0.337457i
$763$	−1.02428	+	3.15242i	−0.0370815	+	0.114125i
$764$	−10.3820	−	7.54295i	−0.375607	−	0.272895i
$765$	0.0213882	−	0.0294383i	0.000773292	−	0.00106435i
$766$	9.71896	−	29.9119i	0.351160	−	1.08076i
$767$	9.74460	−	22.5394i	0.351857	−	0.813850i
$768$	−2.56181	+	1.86127i	−0.0924415	+	0.0671626i
$769$		−	33.8692i		−	1.22136i	−0.791879	−	0.610678i	$-0.790897\pi$
$769$		−	33.8692i		−	1.22136i	0.791879	−	0.610678i	$-0.209103\pi$
$770$	4.98642	−	19.2435i	0.179698	−	0.693486i
$771$	−8.60347			−0.309846
$772$	41.1003	+	56.5697i	1.47923	+	2.03599i
$773$	25.6919	−	8.34779i	0.924072	−	0.300249i	0.191936	−	0.981407i	$-0.438523\pi$
$773$	25.6919	−	8.34779i	0.924072	−	0.300249i	0.732136	+	0.681158i	$0.238523\pi$
$774$	−9.90976	−	3.21988i	−0.356199	−	0.115736i
$775$	1.96606	−	2.70604i	0.0706228	−	0.0972040i
$776$	−6.88333	−	5.00103i	−0.247097	−	0.179527i
$777$	−0.985258	+	3.03231i	−0.0353459	+	0.108784i
$778$	−68.4267	+	22.2332i	−2.45322	+	0.797098i
$779$	36.7887	−	26.7285i	1.31809	−	0.957649i
$780$	17.7979	+	15.6802i	0.637267	+	0.561443i
$781$	3.65193	+	2.32897i	0.130676	+	0.0833370i
$782$		−	0.174096i		−	0.00622565i
$783$	−5.86649	+	4.26226i	−0.209651	+	0.152321i
$784$	−3.04245	−	9.36369i	−0.108659	−	0.334417i
$785$	36.6199	+	11.8985i	1.30702	+	0.424677i
$786$	−1.30257	+	1.79284i	−0.0464612	+	0.0639483i
$787$	13.5649	−	18.6705i	0.483537	−	0.665531i	−0.495643	−	0.868526i	$-0.665068\pi$
$787$	13.5649	−	18.6705i	0.483537	−	0.665531i	0.979180	+	0.202995i	$0.0650676\pi$
$788$	6.32295	+	2.05445i	0.225246	+	0.0731868i
$789$	−3.46008	−	10.6490i	−0.123182	−	0.379115i
$790$	−50.8456	+	36.9415i	−1.80901	+	1.31432i
$791$		−	23.1903i		−	0.824552i
$792$	−4.92844	−	3.14304i	−0.175124	−	0.111683i
$793$	26.3713	−	29.9328i	0.936473	−	1.06295i
$794$	21.6301	−	15.7152i	0.767622	−	0.557710i
$795$	−1.34870	+	0.438218i	−0.0478333	+	0.0155420i
$796$	16.8833	−	51.9615i	0.598414	−	1.84173i
$797$	−3.15360	−	2.29122i	−0.111706	−	0.0811592i	0.530530	−	0.847666i	$-0.321993\pi$
$797$	−3.15360	−	2.29122i	−0.111706	−	0.0811592i	−0.642236	+	0.766507i	$0.721993\pi$
$798$	10.3801	−	14.2870i	0.367452	−	0.505754i
$799$	−0.167343	−	0.0543730i	−0.00592017	−	0.00192358i
$800$	−3.52484	+	1.14529i	−0.124622	+	0.0404921i
$801$	−2.57505	−	3.54425i	−0.0909848	−	0.125230i
$802$	6.60879			0.233364
$803$	−11.7029	+	45.1635i	−0.412986	+	1.59379i
$804$			19.9618i			0.703998i
$805$	11.3299	−	8.23164i	0.399326	−	0.290127i
$806$	−48.1179	−	20.8031i	−1.69488	−	0.732760i
$807$	9.21293	−	28.3545i	0.324310	−	0.998125i
$808$	16.6336	−	22.8942i	0.585167	−	0.805414i
$809$	−11.0308	−	8.01434i	−0.387822	−	0.281769i	0.376740	−	0.926319i	$-0.377045\pi$
$809$	−11.0308	−	8.01434i	−0.387822	−	0.281769i	−0.764562	+	0.644550i	$0.777045\pi$
$810$	1.58905	−	4.89059i	0.0558335	−	0.171838i
$811$	−40.0707	+	13.0198i	−1.40707	+	0.457186i	−0.911471	−	0.411363i	$-0.865053\pi$
$811$	−40.0707	+	13.0198i	−1.40707	+	0.457186i	−0.495603	+	0.868549i	$0.665053\pi$
$812$	13.9308	+	19.1741i	0.488876	+	0.672880i
$813$			3.30038i			0.115750i
$814$	18.5048	−	7.27913i	0.648594	−	0.255133i
$815$	−26.3031			−0.921358
$816$	0.0218987	−	0.0159103i	0.000766607	−	0.000556972i
$817$	−31.2529	+	10.1547i	−1.09340	+	0.355267i
$818$	0.649124	−	1.99780i	0.0226961	−	0.0698514i
$819$	−0.918153	−	4.10105i	−0.0320829	−	0.143302i
$820$	−35.0125	−	25.4380i	−1.22269	−	0.888335i
$821$	−37.0583	−	12.0410i	−1.29334	−	0.420232i	−0.420082	−	0.907486i	$-0.637999\pi$
$821$	−37.0583	−	12.0410i	−1.29334	−	0.420232i	−0.873260	+	0.487254i	$0.837999\pi$
$822$	10.0750	+	31.0078i	0.351407	+	1.08152i
$823$	−17.4675	+	12.6909i	−0.608880	+	0.442377i	−0.849020	−	0.528361i	$-0.822807\pi$
$823$	−17.4675	+	12.6909i	−0.608880	+	0.442377i	0.240140	+	0.970738i	$0.422807\pi$
$824$			9.34660i			0.325604i
$825$	−1.06315	−	1.29095i	−0.0370142	−	0.0449451i
$826$			17.3992i			0.605397i
$827$	−14.6324	−	20.1398i	−0.508820	−	0.700331i	0.474900	−	0.880040i	$-0.342484\pi$
$827$	−14.6324	−	20.1398i	−0.508820	−	0.700331i	−0.983720	+	0.179709i	$0.942484\pi$
$828$	−4.43763	−	13.6576i	−0.154218	−	0.474635i
$829$	4.08103	−	12.5601i	0.141740	−	0.436231i	−0.854837	−	0.518896i	$-0.826343\pi$
$829$	4.08103	−	12.5601i	0.141740	−	0.436231i	0.996577	+	0.0826649i	$0.0263431\pi$
$830$	−4.66546	+	6.42145i	−0.161940	+	0.222892i
$831$	−17.1930	−	12.4914i	−0.596417	−	0.433323i
$832$	23.1752	+	39.1568i	0.803455	+	1.35752i
$833$	−0.0270382	−	0.0832149i	−0.000936817	−	0.00288323i
$834$	−4.48767	−	6.17674i	−0.155395	−	0.213883i
$835$	−16.6346			−0.575665
$836$	−64.1689	+	3.89425i	−2.21933	+	0.134685i
$837$			6.63345i			0.229285i
$838$	−37.2716	−	51.2999i	−1.28753	−	1.77213i
$839$	−2.11841	+	0.688312i	−0.0731355	+	0.0237632i	−0.345356	−	0.938472i	$-0.612242\pi$
$839$	−2.11841	+	0.688312i	−0.0731355	+	0.0237632i	0.272221	+	0.962235i	$0.412242\pi$
$840$	−4.58367	−	1.48933i	−0.158152	−	0.0513866i
$841$	−19.0787	−	13.8615i	−0.657887	−	0.477983i
$842$	8.46281	+	6.14859i	0.291648	+	0.211894i
$843$	5.17874	+	1.68267i	0.178365	+	0.0579544i
$844$	2.48695	+	7.65406i	0.0856045	+	0.263463i
$845$	22.2190	−	20.8934i	0.764357	−	0.718754i
$846$	−24.8656			−0.854899
$847$	12.5835	+	2.45836i	0.432376	+	0.0844702i
$848$	−1.05490			−0.0362254
$849$	−5.21302	+	3.78748i	−0.178910	+	0.129986i
$850$	−0.0163026	+	0.00529704i	−0.000559175	+	0.000181687i
$851$	13.3231	+	4.32894i	0.456710	+	0.148394i
$852$	2.15248	−	2.96264i	0.0737429	−	0.101498i
$853$	−20.2619	+	27.8880i	−0.693753	+	0.954869i	0.306243	+	0.951953i	$0.400928\pi$
$853$	−20.2619	+	27.8880i	−0.693753	+	0.954869i	−0.999996	+	0.00291522i	$0.999072\pi$
$854$	−8.73480	+	26.8830i	−0.298899	+	0.919916i
$855$	−5.01146	−	15.4237i	−0.171388	−	0.527479i
$856$	−6.56902	−	9.04148i	−0.224525	−	0.309031i
$857$	−43.4500			−1.48422			−0.742111	−	0.670277i	$-0.766175\pi$
$857$	−43.4500			−1.48422			−0.742111	+	0.670277i	$0.766175\pi$
$858$	−16.1035	+	20.6801i	−0.549763	+	0.706005i
$859$	−4.75686			−0.162302			−0.0811511	−	0.996702i	$-0.525860\pi$
$859$	−4.75686			−0.162302			−0.0811511	+	0.996702i	$0.525860\pi$
$860$	18.3828	+	25.3017i	0.626848	+	0.862782i
$861$	2.36946	+	7.29245i	0.0807510	+	0.248526i
$862$	0.420016	−	1.29268i	0.0143058	−	0.0440287i
$863$	2.78849	−	3.83803i	0.0949214	−	0.130648i	−0.758915	−	0.651190i	$-0.774270\pi$
$863$	2.78849	−	3.83803i	0.0949214	−	0.130648i	0.853836	+	0.520542i	$0.174270\pi$
$864$	4.32030	−	5.94638i	0.146979	−	0.202300i
$865$	−0.594131	−	0.193045i	−0.0202011	−	0.00656372i
$866$	−36.0940	+	11.7276i	−1.22652	+	0.398521i
$867$	−13.7531	+	9.99221i	−0.467080	+	0.339353i
$868$	21.6809			0.735896
$869$	−25.7691	−	31.2906i	−0.874156	−	1.06146i
$870$	37.2886			1.26420
$871$	25.5541	+	2.40684i	0.865866	+	0.0815525i
$872$	−1.54878	−	4.76667i	−0.0524484	−	0.161420i
$873$	4.59126	+	1.49179i	0.155391	+	0.0504895i
$874$	−62.7729	−	45.6072i	−2.12332	−	1.54269i
$875$	9.94611	+	7.22627i	0.336240	+	0.244293i
$876$	37.5148	+	12.1893i	1.26751	+	0.411838i
$877$	19.3765	−	6.29582i	0.654300	−	0.212595i	0.0369906	−	0.999316i	$-0.488223\pi$
$877$	19.3765	−	6.29582i	0.654300	−	0.212595i	0.617309	+	0.786721i	$0.288223\pi$
$878$	−0.0915806	−	0.126050i	−0.00309069	−	0.00425398i
$879$			28.0076i			0.944672i
$880$	−4.97108	−	12.6374i	−0.167575	−	0.426006i
$881$	43.2360			1.45666			0.728328	−	0.685228i	$-0.240298\pi$
$881$	43.2360			1.45666			0.728328	+	0.685228i	$0.240298\pi$
$882$	−7.26796	−	10.0035i	−0.244725	−	0.336835i
$883$	−2.93130	−	9.02160i	−0.0986460	−	0.303601i	0.889541	−	0.456856i	$-0.151024\pi$
$883$	−2.93130	−	9.02160i	−0.0986460	−	0.303601i	−0.988187	+	0.153255i	$0.951024\pi$
$884$	0.0798682	+	0.134945i	0.00268626	+	0.00453870i
$885$	12.9267	+	9.39178i	0.434525	+	0.315701i
$886$	7.76894	−	10.6930i	0.261003	−	0.359239i
$887$	−3.38796	+	10.4271i	−0.113757	+	0.350107i	−0.991686	−	0.128684i	$-0.958925\pi$
$887$	−3.38796	+	10.4271i	−0.113757	+	0.350107i	0.877929	+	0.478791i	$0.158925\pi$
$888$	−1.48978	−	4.58506i	−0.0499936	−	0.153865i
$889$	−9.42260	−	12.9691i	−0.316024	−	0.434969i
$890$			22.5279i			0.755138i
$891$	3.21059	+	0.831936i	0.107559	+	0.0278709i
$892$		−	37.0617i		−	1.24092i
$893$	−63.4432	+	46.0942i	−2.12304	+	1.54248i
$894$	1.83295	+	5.64125i	0.0613031	+	0.188672i
$895$	42.4604	+	13.7962i	1.41929	+	0.461157i
$896$	−12.2210	−	8.87906i	−0.408274	−	0.296629i
$897$	−18.0188	+	4.03410i	−0.601631	+	0.134695i
$898$	18.5950	−	57.2295i	0.620523	−	1.90977i
$899$	−45.7474	+	14.8642i	−1.52576	+	0.495750i
$900$	−1.14390	+	0.831093i	−0.0381301	+	0.0277031i
$901$	−0.00937488			−0.000312323
$902$	25.7137	−	40.3203i	0.856172	−	1.34252i
$903$		−	5.54108i		−	0.184396i
$904$	20.6109	+	28.3684i	0.685507	+	0.943519i
$905$	−6.28998	+	2.04374i	−0.209086	+	0.0679361i
$906$	1.13989	−	3.50823i	0.0378704	−	0.116553i
$907$	7.56458	+	5.49599i	0.251178	+	0.182491i	0.706249	−	0.707964i	$-0.250386\pi$
$907$	7.56458	+	5.49599i	0.251178	+	0.182491i	−0.455071	+	0.890455i	$0.650386\pi$
$908$	25.3142	−	34.8420i	0.840082	−	1.15627i
$909$	−4.96174	+	15.2707i	−0.164571	+	0.506497i
$910$	−8.57595	+	19.8363i	−0.284290	+	0.657567i
$911$	−40.7944	+	29.6388i	−1.35158	+	0.981979i	−0.352647	+	0.935757i	$0.614718\pi$
$911$	−40.7944	+	29.6388i	−1.35158	+	0.981979i	−0.998931	+	0.0462223i	$0.985282\pi$
$912$		−	12.0639i		−	0.399474i
$913$	−4.31634	−	2.75268i	−0.142850	−	0.0911005i
$914$	−51.5409			−1.70482
$915$	15.2577	+	21.0004i	0.504403	+	0.694251i
$916$	−15.2222	+	4.94599i	−0.502955	+	0.163420i
$917$	−1.12080	−	0.364169i	−0.0370120	−	0.0120259i
$918$	0.0199817	−	0.0275024i	0.000659493	−	0.000907715i
$919$	35.4606	+	25.7636i	1.16974	+	0.849864i	0.990977	−	0.134029i	$-0.0427916\pi$
$919$	35.4606	+	25.7636i	1.16974	+	0.849864i	0.178760	+	0.983893i	$0.442792\pi$
$920$	−6.54367	+	20.1393i	−0.215738	+	0.663974i
$921$	32.7518	−	10.6417i	1.07921	−	0.350656i
$922$	14.0351	−	10.1971i	0.462222	−	0.335824i
$923$	−3.53309	−	3.11271i	−0.116293	−	0.102456i
$924$	2.71911	−	10.4935i	0.0894522	−	0.345212i
$925$		−	1.37931i		−	0.0453514i
$926$	26.2048	−	19.0389i	0.861144	−	0.625658i
$927$	−1.63878	−	5.04365i	−0.0538246	−	0.165655i
$928$	50.6900	+	16.4702i	1.66398	+	0.540660i
$929$	−30.8581	+	42.4726i	−1.01242	+	1.39348i	−0.0950402	+	0.995473i	$0.530298\pi$
$929$	−30.8581	+	42.4726i	−1.01242	+	1.39348i	−0.917382	+	0.398007i	$0.869702\pi$
$930$	20.0499	−	27.5963i	0.657463	−	0.904920i
$931$	−37.0875	−	12.0505i	−1.21549	−	0.394938i
$932$	1.53356	+	4.71981i	0.0502334	+	0.154602i
$933$	−10.3507	+	7.52024i	−0.338867	+	0.246201i
$934$		−	4.28363i		−	0.140165i
$935$	−0.0441779	−	0.112308i	−0.00144477	−	0.00367287i
$936$	4.76806	+	4.20074i	0.155849	+	0.137306i
$937$	11.9599	−	8.68936i	0.390712	−	0.283869i	−0.375035	−	0.927011i	$-0.622369\pi$
$937$	11.9599	−	8.68936i	0.390712	−	0.283869i	0.765747	+	0.643142i	$0.222369\pi$
$938$	−17.2967	+	5.62002i	−0.564756	+	0.183500i
$939$	10.0351	−	30.8850i	0.327484	−	1.00789i
$940$	60.3800	+	43.8687i	1.96938	+	1.43084i
$941$	−11.1909	+	15.4030i	−0.364814	+	0.502124i	−0.951482	−	0.307704i	$-0.900439\pi$
$941$	−11.1909	+	15.4030i	−0.364814	+	0.502124i	0.586668	+	0.809828i	$0.300439\pi$
$942$	34.2117	+	11.1161i	1.11468	+	0.362181i
$943$	32.0409	−	10.4107i	1.04339	−	0.339020i
$944$	6.98637	+	9.61592i	0.227387	+	0.312972i
$945$	2.73459			0.0889563
$946$	−26.6765	+	21.9692i	−0.867327	+	0.714280i
$947$		−	27.0652i		−	0.879499i	−0.898120	−	0.439750i	$-0.855067\pi$
$947$		−	27.0652i		−	0.879499i	0.898120	−	0.439750i	$-0.144933\pi$
$948$	−27.7263	+	20.1444i	−0.900509	+	0.654258i
$949$	20.1274	−	46.5549i	0.653362	−	1.51123i
$950$	−2.36080	+	7.26580i	−0.0765945	+	0.235734i
$951$	−2.48827	+	3.42480i	−0.0806875	+	0.111057i
$952$	−0.0257765	−	0.0187277i	−0.000835420	−	0.000606968i
$953$	−6.36024	+	19.5748i	−0.206029	+	0.634091i	0.793641	+	0.608386i	$0.208183\pi$
$953$	−6.36024	+	19.5748i	−0.206029	+	0.634091i	−0.999670	+	0.0257043i	$0.991817\pi$
$954$	−1.26000	+	0.409399i	−0.0407940	+	0.0132548i
$955$	−6.31098	−	8.68632i	−0.204219	−	0.281083i
$956$		−	50.5162i		−	1.63381i
$957$	1.45686	+	24.0060i	0.0470936	+	0.776002i
$958$	−23.8739			−0.771331
$959$	−14.0268	+	10.1911i	−0.452950	+	0.329088i
$960$	−28.1582	+	9.14916i	−0.908802	+	0.295288i
$961$	−4.01803	+	12.3662i	−0.129614	+	0.398911i
$962$	−21.0951	+	4.72281i	−0.680133	+	0.152270i
$963$	5.13009	+	3.72723i	0.165315	+	0.120108i
$964$	−0.581940	−	0.189084i	−0.0187430	−	0.00608998i
$965$	18.0786	+	55.6401i	0.581970	+	1.79112i
$966$	10.5848	−	7.69031i	0.340560	−	0.247432i
$967$		−	2.33166i		−	0.0749811i	−0.999297	−	0.0374905i	$-0.988064\pi$
$967$		−	2.33166i		−	0.0749811i	0.999297	−	0.0374905i	$-0.0119364\pi$
$968$	−17.5782	+	8.17660i	−0.564985	+	0.262806i
$969$		−	0.107211i		−	0.00344412i
$970$	−14.5915	−	20.0834i	−0.468504	−	0.644841i
$971$	5.00085	+	15.3910i	0.160485	+	0.493922i	0.998675	−	0.0514558i	$-0.0163861\pi$
$971$	5.00085	+	15.3910i	0.160485	+	0.493922i	−0.838190	+	0.545378i	$0.816386\pi$
$972$	0.866514	−	2.66686i	0.0277934	−	0.0855394i
$973$	2.38648	−	3.28471i	0.0765071	−	0.105303i
$974$	59.1743	+	42.9927i	1.89607	+	1.37757i
$975$	0.926001	+	1.56457i	0.0296558	+	0.0501064i
$976$	5.96700	+	18.3645i	0.190999	+	0.587835i
$977$	15.6692	+	21.5668i	0.501301	+	0.689982i	0.982422	−	0.186672i	$-0.0597703\pi$
$977$	15.6692	+	21.5668i	0.501301	+	0.689982i	−0.481121	+	0.876654i	$0.659770\pi$
$978$	−24.5734			−0.785769
$979$	−14.5032	+	0.880164i	−0.463525	+	0.0281302i
$980$			37.1133i			1.18554i
$981$	1.67152	+	2.30065i	0.0533676	+	0.0734542i
$982$	−71.5661	+	23.2532i	−2.28376	+	0.742040i
$983$	0.299618	+	0.0973518i	0.00955633	+	0.00310504i	0.313791	−	0.949492i	$-0.398401\pi$
$983$	0.299618	+	0.0973518i	0.00955633	+	0.00310504i	−0.304235	+	0.952597i	$0.598401\pi$
$984$	−9.37984	−	6.81486i	−0.299018	−	0.217250i
$985$	4.50015	+	3.26955i	0.143387	+	0.104176i
$986$	0.234445	+	0.0761757i	0.00746624	+	0.00242593i
$987$	−4.08620	−	12.5760i	−0.130065	−	0.400300i
$988$	69.5793	+	6.55340i	2.21361	+	0.208492i
$989$	−24.3459			−0.774155
$990$	−10.8421	−	13.1652i	−0.344583	−	0.418417i
$991$	48.5810			1.54323			0.771613	−	0.636093i	$-0.219450\pi$
$991$	48.5810			1.54323			0.771613	+	0.636093i	$0.219450\pi$
$992$	39.4450	−	28.6584i	1.25238	−	0.909907i
$993$	1.10926	−	0.360420i	0.0352013	−	0.0114376i
$994$	3.17310	+	1.03100i	0.100645	+	0.0327014i
$995$	26.8689	−	36.9819i	0.851801	−	1.17240i
$996$	−2.54409	+	3.50164i	−0.0806126	+	0.110954i
$997$	16.2336	−	49.9619i	0.514123	−	1.58231i	−0.270748	−	0.962650i	$-0.587271\pi$
$997$	16.2336	−	49.9619i	0.514123	−	1.58231i	0.784872	−	0.619658i	$-0.212729\pi$
$998$	10.9083	+	33.5724i	0.345298	+	1.06272i
$999$	1.60784	+	2.21300i	0.0508698	+	0.0700162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.25.2	✓	56
11.4	even	5	inner	429.2.bb.b.103.13	yes	56
13.12	even	2	inner	429.2.bb.b.25.13	yes	56
143.103	even	10	inner	429.2.bb.b.103.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.2	✓	56	1.1	even	1	trivial
429.2.bb.b.25.13	yes	56	13.12	even	2	inner
429.2.bb.b.103.2	yes	56	143.103	even	10	inner
429.2.bb.b.103.13	yes	56	11.4	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28832 - 1.77322i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.866514 + 2.66686i) q^{4} +(-1.37901 + 1.89804i) q^{5} +(-1.28832 + 1.77322i) q^{6} +(-1.10854 - 0.360186i) q^{7} +(1.67618 - 0.544625i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.28832 - 1.77322i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.866514 + 2.66686i) q^{4} +(-1.37901 + 1.89804i) q^{5} +(-1.28832 + 1.77322i) q^{6} +(-1.10854 - 0.360186i) q^{7} +(1.67618 - 0.544625i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.14227 q^{10} +(0.200908 + 3.31053i) q^{11} +2.80410 q^{12} +(0.338096 - 3.58966i) q^{13} +(0.789464 + 2.42972i) q^{14} +(2.23128 + 0.724988i) q^{15} +(1.41192 + 1.02582i) q^{16} +(0.0125477 + 0.00911645i) q^{17} +(2.08455 + 0.677311i) q^{18} +(6.57415 - 2.13607i) q^{19} +(-3.86688 - 5.32230i) q^{20} +1.16558i q^{21} +(5.61148 - 4.62129i) q^{22} +5.12124 q^{23} +(-1.03594 - 1.42585i) q^{24} +(-0.155819 - 0.479561i) q^{25} +(-6.80086 + 4.02513i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.92113 - 2.64420i) q^{28} +(-2.24080 + 6.89648i) q^{29} +(-1.58905 - 4.89059i) q^{30} +(3.89904 + 5.36657i) q^{31} -7.35012i q^{32} +(3.08642 - 1.21409i) q^{33} -0.0339948i q^{34} +(2.21233 - 1.60735i) q^{35} +(-0.866514 - 2.66686i) q^{36} +(2.60154 + 0.845291i) q^{37} +(-12.2574 - 8.90549i) q^{38} +(-3.51845 + 0.787719i) q^{39} +(-1.27775 + 3.93251i) q^{40} +(6.25647 - 2.03285i) q^{41} +(2.06684 - 1.50165i) q^{42} -4.75391 q^{43} +(-9.00281 - 2.33283i) q^{44} -2.34611i q^{45} +(-6.59781 - 9.08111i) q^{46} +(-10.7895 + 3.50571i) q^{47} +(0.539306 - 1.65981i) q^{48} +(-4.56400 - 3.31594i) q^{49} +(-0.649625 + 0.894132i) q^{50} +(0.00479280 - 0.0147507i) q^{51} +(9.28015 + 4.01215i) q^{52} +(-0.489008 + 0.355285i) q^{53} -2.19183i q^{54} +(-6.56059 - 4.18393i) q^{55} -2.05428 q^{56} +(-4.06305 - 5.59231i) q^{57} +(15.1159 - 4.91144i) q^{58} +(6.47719 + 2.10457i) q^{59} +(-3.86688 + 5.32230i) q^{60} +(8.95114 + 6.50339i) q^{61} +(4.49291 - 13.8278i) q^{62} +(1.10854 - 0.360186i) q^{63} +(-10.2096 + 7.41769i) q^{64} +(6.34710 + 5.59190i) q^{65} +(-6.12915 - 3.90878i) q^{66} +7.11879i q^{67} +(-0.0351850 + 0.0255634i) q^{68} +(-1.58255 - 4.87059i) q^{69} +(-5.70039 - 1.85217i) q^{70} +(0.767621 - 1.05654i) q^{71} +(-1.03594 + 1.42585i) q^{72} +(13.3786 + 4.34696i) q^{73} +(-1.85273 - 5.70212i) q^{74} +(-0.407939 + 0.296385i) q^{75} +19.3832i q^{76} +(0.969693 - 3.74221i) q^{77} +(5.92970 + 5.22417i) q^{78} +(-9.88779 + 7.18390i) q^{79} +(-3.89411 + 1.26527i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-11.6651 - 8.47516i) q^{82} +(-0.907276 + 1.24876i) q^{83} +(-3.10845 - 1.01000i) q^{84} +(-0.0346069 + 0.0112444i) q^{85} +(6.12457 + 8.42974i) q^{86} +7.25139 q^{87} +(2.13976 + 5.43964i) q^{88} +4.38093i q^{89} +(-4.16018 + 3.02255i) q^{90} +(-1.66774 + 3.85750i) q^{91} +(-4.43763 + 13.6576i) q^{92} +(3.89904 - 5.36657i) q^{93} +(20.1167 + 14.6157i) q^{94} +(-5.01146 + 15.4237i) q^{95} +(-6.99038 + 2.27131i) q^{96} +(-2.83756 - 3.90556i) q^{97} +12.3650i q^{98} +(-2.10842 - 2.56019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

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