LMFDB - Embedded newform 429.2.n.d.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	429.235
Dual form			429.2.n.d.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09213 - 1.52002i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.44850 + 4.45804i) q^{4} +(0.296923 - 0.215727i) q^{5} +(-2.09213 + 1.52002i) q^{6} +(0.607096 + 1.86845i) q^{7} +(2.14760 - 6.60965i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.09213 - 1.52002i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.44850 + 4.45804i) q^{4} +(0.296923 - 0.215727i) q^{5} +(-2.09213 + 1.52002i) q^{6} +(0.607096 + 1.86845i) q^{7} +(2.14760 - 6.60965i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.949111 q^{10} +(-2.93321 + 1.54800i) q^{11} +4.68746 q^{12} +(0.809017 + 0.587785i) q^{13} +(1.56996 - 4.83183i) q^{14} +(-0.113415 - 0.349054i) q^{15} +(-6.95539 + 5.05339i) q^{16} +(-5.32452 + 3.86849i) q^{17} +(0.799122 + 2.45944i) q^{18} +(-2.43695 + 7.50017i) q^{19} +(1.39181 + 1.01121i) q^{20} +1.96460 q^{21} +(8.48963 + 1.21992i) q^{22} +5.41688 q^{23} +(-5.62250 - 4.08499i) q^{24} +(-1.50346 + 4.62717i) q^{25} +(-0.799122 - 2.45944i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-7.45024 + 5.41291i) q^{28} +(0.628581 + 1.93457i) q^{29} +(-0.293291 + 0.902658i) q^{30} +(-7.68038 - 5.58012i) q^{31} +8.33323 q^{32} +(0.565822 + 3.26800i) q^{33} +17.0198 q^{34} +(0.583336 + 0.423819i) q^{35} +(1.44850 - 4.45804i) q^{36} +(-0.0969332 - 0.298330i) q^{37} +(16.4988 - 11.9871i) q^{38} +(0.809017 - 0.587785i) q^{39} +(-0.788208 - 2.42585i) q^{40} +(-1.23233 + 3.79272i) q^{41} +(-4.11020 - 2.98624i) q^{42} +4.61254 q^{43} +(-11.1498 - 10.8341i) q^{44} -0.367017 q^{45} +(-11.3328 - 8.23376i) q^{46} +(1.28446 - 3.95317i) q^{47} +(2.65672 + 8.17655i) q^{48} +(2.54058 - 1.84584i) q^{49} +(10.1788 - 7.39535i) q^{50} +(2.03379 + 6.25935i) q^{51} +(-1.44850 + 4.45804i) q^{52} +(8.75168 + 6.35846i) q^{53} +2.58601 q^{54} +(-0.536992 + 1.09241i) q^{55} +13.6536 q^{56} +(6.38002 + 4.63536i) q^{57} +(1.62552 - 5.00283i) q^{58} +(-0.576886 - 1.77547i) q^{59} +(1.39181 - 1.01121i) q^{60} +(8.17945 - 5.94272i) q^{61} +(7.58644 + 23.3486i) q^{62} +(0.607096 - 1.86845i) q^{63} +(-3.52339 - 2.55989i) q^{64} +0.367017 q^{65} +(3.78366 - 7.69714i) q^{66} -1.34743 q^{67} +(-24.9585 - 18.1334i) q^{68} +(1.67391 - 5.15176i) q^{69} +(-0.576201 - 1.77337i) q^{70} +(-3.80561 + 2.76494i) q^{71} +(-5.62250 + 4.08499i) q^{72} +(-0.692320 - 2.13074i) q^{73} +(-0.250670 + 0.771484i) q^{74} +(3.93611 + 2.85975i) q^{75} -36.9659 q^{76} +(-4.67309 - 4.54077i) q^{77} -2.58601 q^{78} +(-3.09550 - 2.24901i) q^{79} +(-0.975063 + 3.00094i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.34320 - 6.06169i) q^{82} +(-10.7171 + 7.78641i) q^{83} +(2.84574 + 8.75828i) q^{84} +(-0.746435 + 2.29729i) q^{85} +(-9.65001 - 7.01114i) q^{86} +2.03413 q^{87} +(3.93235 + 22.7120i) q^{88} -2.86133 q^{89} +(0.767847 + 0.557873i) q^{90} +(-0.607096 + 1.86845i) q^{91} +(7.84637 + 24.1486i) q^{92} +(-7.68038 + 5.58012i) q^{93} +(-8.69616 + 6.31813i) q^{94} +(0.894403 + 2.75269i) q^{95} +(2.57511 - 7.92537i) q^{96} +(9.81555 + 7.13142i) q^{97} -8.12093 q^{98} +(3.28290 + 0.471740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.09213	−	1.52002i	−1.47936	−	1.07482i	−0.977763	−	0.209713i	$-0.932747\pi$
$2$	−2.09213	−	1.52002i	−1.47936	−	1.07482i	−0.501595	−	0.865103i	$-0.667253\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.44850	+	4.45804i	0.724252	+	2.22902i
$5$	0.296923	−	0.215727i	0.132788	−	0.0964762i	−0.519408	−	0.854526i	$-0.673848\pi$
$5$	0.296923	−	0.215727i	0.132788	−	0.0964762i	0.652197	+	0.758050i	$0.273848\pi$
$6$	−2.09213	+	1.52002i	−0.854107	+	0.620545i
$7$	0.607096	+	1.86845i	0.229461	+	0.706208i	0.997808	+	0.0661745i	$0.0210794\pi$
$7$	0.607096	+	1.86845i	0.229461	+	0.706208i	−0.768347	+	0.640033i	$0.778921\pi$
$8$	2.14760	−	6.60965i	0.759293	−	2.33686i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.949111			−0.300135
$11$	−2.93321	+	1.54800i	−0.884395	+	0.466739i
$11$	−2.93321	+	1.54800i	−0.884395	+	0.466739i
$12$	4.68746			1.35315
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$14$	1.56996	−	4.83183i	0.419589	−	1.29136i
$15$	−0.113415	−	0.349054i	−0.0292835	−	0.0901254i
$16$	−6.95539	+	5.05339i	−1.73885	+	1.26335i
$17$	−5.32452	+	3.86849i	−1.29139	+	0.938248i	−0.999832	−	0.0183066i	$-0.994172\pi$
$17$	−5.32452	+	3.86849i	−1.29139	+	0.938248i	−0.291555	+	0.956554i	$0.594172\pi$
$18$	0.799122	+	2.45944i	0.188355	+	0.579696i
$19$	−2.43695	+	7.50017i	−0.559075	+	1.72066i	0.125856	+	0.992048i	$0.459832\pi$
$19$	−2.43695	+	7.50017i	−0.559075	+	1.72066i	−0.684931	+	0.728608i	$0.740168\pi$
$20$	1.39181	+	1.01121i	0.311219	+	0.226114i
$21$	1.96460			0.428712
$22$	8.48963	+	1.21992i	1.81000	+	0.260089i
$23$	5.41688			1.12950			0.564749	−	0.825263i	$-0.308973\pi$
$23$	5.41688			1.12950			0.564749	+	0.825263i	$0.308973\pi$
$24$	−5.62250	−	4.08499i	−1.14769	−	0.833845i
$25$	−1.50346	+	4.62717i	−0.300692	+	0.925435i
$26$	−0.799122	−	2.45944i	−0.156721	−	0.482337i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−7.45024	+	5.41291i	−1.40796	+	1.02294i
$29$	0.628581	+	1.93457i	0.116725	+	0.359241i	0.992303	−	0.123835i	$-0.0395193\pi$
$29$	0.628581	+	1.93457i	0.116725	+	0.359241i	−0.875578	+	0.483076i	$0.839519\pi$
$30$	−0.293291	+	0.902658i	−0.0535474	+	0.164802i
$31$	−7.68038	−	5.58012i	−1.37944	−	1.00222i	−0.996933	−	0.0782654i	$-0.975062\pi$
$31$	−7.68038	−	5.58012i	−1.37944	−	1.00222i	−0.382504	−	0.923954i	$-0.624938\pi$
$32$	8.33323			1.47312
$33$	0.565822	+	3.26800i	0.0984970	+	0.568886i
$34$	17.0198			2.91887
$35$	0.583336	+	0.423819i	0.0986019	+	0.0716384i
$36$	1.44850	−	4.45804i	0.241417	−	0.743006i
$37$	−0.0969332	−	0.298330i	−0.0159357	−	0.0490451i	0.942772	−	0.333437i	$-0.108208\pi$
$37$	−0.0969332	−	0.298330i	−0.0159357	−	0.0490451i	−0.958708	+	0.284392i	$0.908208\pi$
$38$	16.4988	−	11.9871i	2.67646	−	1.94456i
$39$	0.809017	−	0.587785i	0.129546	−	0.0941210i
$40$	−0.788208	−	2.42585i	−0.124627	−	0.383561i
$41$	−1.23233	+	3.79272i	−0.192458	+	0.592323i	0.807539	+	0.589814i	$0.200799\pi$
$41$	−1.23233	+	3.79272i	−0.192458	+	0.592323i	−0.999997	+	0.00250961i	$0.999201\pi$
$42$	−4.11020	−	2.98624i	−0.634218	−	0.460786i
$43$	4.61254			0.703405			0.351702	−	0.936112i	$-0.385603\pi$
$43$	4.61254			0.703405			0.351702	+	0.936112i	$0.385603\pi$
$44$	−11.1498	−	10.8341i	−1.68089	−	1.63330i
$45$	−0.367017			−0.0547117
$46$	−11.3328	−	8.23376i	−1.67093	−	1.21400i
$47$	1.28446	−	3.95317i	0.187358	−	0.576629i	−0.812623	−	0.582790i	$-0.801961\pi$
$47$	1.28446	−	3.95317i	0.187358	−	0.576629i	0.999981	+	0.00616070i	$0.00196102\pi$
$48$	2.65672	+	8.17655i	0.383465	+	1.18018i
$49$	2.54058	−	1.84584i	0.362940	−	0.263691i
$50$	10.1788	−	7.39535i	1.43950	−	1.04586i
$51$	2.03379	+	6.25935i	0.284787	+	0.876485i
$52$	−1.44850	+	4.45804i	−0.200871	+	0.618218i
$53$	8.75168	+	6.35846i	1.20214	+	0.873402i	0.994493	−	0.104803i	$-0.0334211\pi$
$53$	8.75168	+	6.35846i	1.20214	+	0.873402i	0.207642	+	0.978205i	$0.433421\pi$
$54$	2.58601			0.351912
$55$	−0.536992	+	1.09241i	−0.0724080	+	0.147300i
$56$	13.6536			1.82454
$57$	6.38002	+	4.63536i	0.845055	+	0.613968i
$58$	1.62552	−	5.00283i	0.213441	−	0.656904i
$59$	−0.576886	−	1.77547i	−0.0751042	−	0.231147i	0.906456	−	0.422300i	$-0.138777\pi$
$59$	−0.576886	−	1.77547i	−0.0751042	−	0.231147i	−0.981560	+	0.191153i	$0.938777\pi$
$60$	1.39181	−	1.01121i	0.179682	−	0.130547i
$61$	8.17945	−	5.94272i	1.04727	−	0.760887i	0.0755796	−	0.997140i	$-0.475919\pi$
$61$	8.17945	−	5.94272i	1.04727	−	0.760887i	0.971692	+	0.236253i	$0.0759193\pi$
$62$	7.58644	+	23.3486i	0.963478	+	2.96528i
$63$	0.607096	−	1.86845i	0.0764869	−	0.235403i
$64$	−3.52339	−	2.55989i	−0.440424	−	0.319987i
$65$	0.367017			0.0455229
$66$	3.78366	−	7.69714i	0.465736	−	0.947452i
$67$	−1.34743			−0.164615			−0.0823074	−	0.996607i	$-0.526229\pi$
$67$	−1.34743			−0.164615			−0.0823074	+	0.996607i	$0.526229\pi$
$68$	−24.9585	−	18.1334i	−3.02666	−	2.19900i
$69$	1.67391	−	5.15176i	0.201515	−	0.620199i
$70$	−0.576201	−	1.77337i	−0.0688692	−	0.211958i
$71$	−3.80561	+	2.76494i	−0.451642	+	0.328137i	−0.790244	−	0.612792i	$-0.790046\pi$
$71$	−3.80561	+	2.76494i	−0.451642	+	0.328137i	0.338601	+	0.940930i	$0.390046\pi$
$72$	−5.62250	+	4.08499i	−0.662618	+	0.481420i
$73$	−0.692320	−	2.13074i	−0.0810299	−	0.249384i	0.902332	−	0.431042i	$-0.141854\pi$
$73$	−0.692320	−	2.13074i	−0.0810299	−	0.249384i	−0.983362	+	0.181657i	$0.941854\pi$
$74$	−0.250670	+	0.771484i	−0.0291399	+	0.0896832i
$75$	3.93611	+	2.85975i	0.454503	+	0.330216i
$76$	−36.9659			−4.24029
$77$	−4.67309	−	4.54077i	−0.532548	−	0.517468i
$78$	−2.58601			−0.292808
$79$	−3.09550	−	2.24901i	−0.348271	−	0.253034i	0.399872	−	0.916571i	$-0.369054\pi$
$79$	−3.09550	−	2.24901i	−0.348271	−	0.253034i	−0.748143	+	0.663537i	$0.769054\pi$
$80$	−0.975063	+	3.00094i	−0.109015	+	0.335515i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	8.34320	−	6.06169i	0.921352	−	0.669402i
$83$	−10.7171	+	7.78641i	−1.17635	+	0.854670i	−0.991755	−	0.128145i	$-0.959098\pi$
$83$	−10.7171	+	7.78641i	−1.17635	+	0.854670i	−0.184596	+	0.982814i	$0.559098\pi$
$84$	2.84574	+	8.75828i	0.310495	+	0.955606i
$85$	−0.746435	+	2.29729i	−0.0809622	+	0.249176i
$86$	−9.65001	−	7.01114i	−1.04059	−	0.756031i
$87$	2.03413			0.218082
$88$	3.93235	+	22.7120i	0.419190	+	2.42110i
$89$	−2.86133			−0.303300			−0.151650	−	0.988434i	$-0.548459\pi$
$89$	−2.86133			−0.303300			−0.151650	+	0.988434i	$0.548459\pi$
$90$	0.767847	+	0.557873i	0.0809382	+	0.0588050i
$91$	−0.607096	+	1.86845i	−0.0636410	+	0.195867i
$92$	7.84637	+	24.1486i	0.818041	+	2.51767i
$93$	−7.68038	+	5.58012i	−0.796418	+	0.578632i
$94$	−8.69616	+	6.31813i	−0.896940	+	0.651665i
$95$	0.894403	+	2.75269i	0.0917638	+	0.282420i
$96$	2.57511	−	7.92537i	0.262821	−	0.808880i
$97$	9.81555	+	7.13142i	0.996618	+	0.724086i	0.961360	−	0.275293i	$-0.0887747\pi$
$97$	9.81555	+	7.13142i	0.996618	+	0.724086i	0.0352579	+	0.999378i	$0.488775\pi$
$98$	−8.12093			−0.820338
$99$	3.28290	+	0.471740i	0.329944	+	0.0474116i
$100$	−22.8059			−2.28059
$101$	−12.2713	−	8.91561i	−1.22104	−	0.887136i	−0.224853	−	0.974393i	$-0.572190\pi$
$101$	−12.2713	−	8.91561i	−1.22104	−	0.887136i	−0.996186	+	0.0872564i	$0.972190\pi$
$102$	5.25940	−	16.1868i	0.520758	−	1.60273i
$103$	4.76659	+	14.6700i	0.469666	+	1.44548i	0.853018	+	0.521881i	$0.174769\pi$
$103$	4.76659	+	14.6700i	0.469666	+	1.44548i	−0.383353	+	0.923602i	$0.625231\pi$
$104$	5.62250	−	4.08499i	0.551332	−	0.400566i
$105$	0.583336	−	0.423819i	0.0569278	−	0.0413605i
$106$	−8.64463	−	26.6054i	−0.839641	−	2.58415i
$107$	−2.63846	+	8.12036i	−0.255070	+	0.785025i	0.738746	+	0.673984i	$0.235418\pi$
$107$	−2.63846	+	8.12036i	−0.255070	+	0.785025i	−0.993816	+	0.111041i	$0.964582\pi$
$108$	−3.79223	−	2.75522i	−0.364908	−	0.265121i
$109$	1.11441			0.106741			0.0533707	−	0.998575i	$-0.483003\pi$
$109$	1.11441			0.106741			0.0533707	+	0.998575i	$0.483003\pi$
$110$	2.78394	−	1.46922i	0.265438	−	0.140085i
$111$	−0.313683			−0.0297734
$112$	−13.6646	−	9.92791i	−1.29118	−	0.938099i
$113$	−0.792208	+	2.43816i	−0.0745246	+	0.229363i	−0.981379	−	0.192081i	$-0.938477\pi$
$113$	−0.792208	+	2.43816i	−0.0745246	+	0.229363i	0.906855	+	0.421444i	$0.138477\pi$
$114$	−6.30199	−	19.3955i	−0.590235	−	1.81656i
$115$	1.60840	−	1.16857i	0.149984	−	0.108970i
$116$	−7.71390	+	5.60448i	−0.716218	+	0.520363i
$117$	−0.309017	−	0.951057i	−0.0285686	−	0.0879252i
$118$	−1.49184	+	4.59140i	−0.137335	+	0.422672i
$119$	−10.4606	−	7.60006i	−0.958920	−	0.696696i
$120$	−2.55069			−0.232845
$121$	6.20741	−	9.08119i	0.564310	−	0.825563i
$122$	−26.1455			−2.36710
$123$	3.22628	+	2.34403i	0.290904	+	0.211354i
$124$	13.7513	−	42.3222i	1.23491	−	3.80065i
$125$	1.11887	+	3.44352i	0.100075	+	0.307998i
$126$	−4.11020	+	2.98624i	−0.366166	+	0.266035i
$127$	2.47410	−	1.79754i	0.219541	−	0.159506i	−0.472579	−	0.881288i	$-0.656677\pi$
$127$	2.47410	−	1.79754i	0.219541	−	0.159506i	0.692120	+	0.721783i	$0.256677\pi$
$128$	−1.66992	−	5.13950i	−0.147602	−	0.454272i
$129$	1.42535	−	4.38678i	0.125495	−	0.386235i
$130$	−0.767847	−	0.557873i	−0.0673446	−	0.0489287i
$131$	−3.96956			−0.346822			−0.173411	−	0.984850i	$-0.555479\pi$
$131$	−3.96956			−0.346822			−0.173411	+	0.984850i	$0.555479\pi$
$132$	−13.7493	+	7.25617i	−1.19672	+	0.631569i
$133$	−15.4931			−1.34343
$134$	2.81900	+	2.04812i	0.243524	+	0.176931i
$135$	−0.113415	+	0.349054i	−0.00976117	+	0.0300418i
$136$	14.1344	+	43.5012i	1.21202	+	3.73020i
$137$	4.06980	−	2.95688i	0.347707	−	0.252624i	−0.400200	−	0.916428i	$-0.631059\pi$
$137$	4.06980	−	2.95688i	0.347707	−	0.252624i	0.747906	+	0.663804i	$0.231059\pi$
$138$	−11.3328	+	8.23376i	−0.964712	+	0.700905i
$139$	−4.94546	−	15.2206i	−0.419469	−	1.29099i	−0.908192	−	0.418553i	$-0.862537\pi$
$139$	−4.94546	−	15.2206i	−0.419469	−	1.29099i	0.488723	−	0.872439i	$-0.337463\pi$
$140$	−1.04443	+	3.21444i	−0.0882708	+	0.271670i
$141$	−3.36277	−	2.44319i	−0.283196	−	0.205754i
$142$	12.1646			1.02083
$143$	−3.28290	−	0.471740i	−0.274530	−	0.0394489i
$144$	8.59734			0.716445
$145$	0.603981	+	0.438818i	0.0501579	+	0.0364418i
$146$	−1.79035	+	5.51012i	−0.148170	+	0.456021i
$147$	−0.970415	−	2.98663i	−0.0800385	−	0.246333i
$148$	1.18956	−	0.864264i	0.0977810	−	0.0710420i
$149$	18.0021	−	13.0793i	1.47479	−	1.07150i	0.495596	−	0.868553i	$-0.334950\pi$
$149$	18.0021	−	13.0793i	1.47479	−	1.07150i	0.979191	−	0.202943i	$-0.0650505\pi$
$150$	−3.88796	−	11.9659i	−0.317451	−	0.977014i
$151$	−7.26958	+	22.3735i	−0.591590	+	1.82073i	−0.0205756	+	0.999788i	$0.506550\pi$
$151$	−7.26958	+	22.3735i	−0.591590	+	1.82073i	−0.571015	+	0.820940i	$0.693450\pi$
$152$	44.3399	+	32.2148i	3.59644	+	2.61296i
$153$	6.58147			0.532081
$154$	2.87465	+	16.6031i	0.231646	+	1.33791i
$155$	−3.48427			−0.279863
$156$	3.79223	+	2.75522i	0.303622	+	0.220594i
$157$	4.30473	−	13.2486i	0.343555	−	1.05735i	−0.618798	−	0.785550i	$-0.712380\pi$
$157$	4.30473	−	13.2486i	0.343555	−	1.05735i	0.962353	−	0.271803i	$-0.0876200\pi$
$158$	3.05764	+	9.41045i	0.243253	+	0.748655i
$159$	8.75168	−	6.35846i	0.694053	−	0.504259i
$160$	2.47433	−	1.79770i	0.195613	−	0.142121i
$161$	3.28857	+	10.1212i	0.259175	+	0.797660i
$162$	0.799122	−	2.45944i	0.0627849	−	0.193232i
$163$	−8.12675	−	5.90443i	−0.636536	−	0.462471i	0.222122	−	0.975019i	$-0.428702\pi$
$163$	−8.12675	−	5.90443i	−0.636536	−	0.462471i	−0.858658	+	0.512548i	$0.828702\pi$
$164$	−18.6931			−1.45969
$165$	0.873003	+	0.848283i	0.0679632	+	0.0660387i
$166$	34.2570			2.65886
$167$	10.2111	+	7.41878i	0.790157	+	0.574083i	0.908010	−	0.418948i	$-0.137601\pi$
$167$	10.2111	+	7.41878i	0.790157	+	0.574083i	−0.117853	+	0.993031i	$0.537601\pi$
$168$	4.21919	−	12.9853i	0.325518	−	1.00184i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	5.05356	−	3.67163i	0.387591	−	0.281601i
$171$	6.38002	−	4.63536i	0.487893	−	0.354475i
$172$	6.68127	+	20.5628i	0.509442	+	1.56790i
$173$	−2.13889	+	6.58284i	−0.162617	+	0.500484i	−0.998853	−	0.0478864i	$-0.984751\pi$
$173$	−2.13889	+	6.58284i	−0.162617	+	0.500484i	0.836236	+	0.548370i	$0.184751\pi$
$174$	−4.25566	−	3.09192i	−0.322621	−	0.234398i
$175$	−9.55839			−0.722546
$176$	12.5790	−	25.5896i	0.948176	−	1.92889i
$177$	−1.86684			−0.140321
$178$	5.98627	+	4.34928i	0.448690	+	0.325992i
$179$	−3.66261	+	11.2724i	−0.273757	+	0.842536i	0.715789	+	0.698316i	$0.246067\pi$
$179$	−3.66261	+	11.2724i	−0.273757	+	0.842536i	−0.989546	+	0.144220i	$0.953933\pi$
$180$	−0.531626	−	1.63618i	−0.0396250	−	0.121953i
$181$	−1.59037	+	1.15547i	−0.118211	+	0.0858856i	−0.645320	−	0.763912i	$-0.723276\pi$
$181$	−1.59037	+	1.15547i	−0.118211	+	0.0858856i	0.527109	+	0.849798i	$0.323276\pi$
$182$	4.11020	−	2.98624i	0.304669	−	0.221355i
$183$	−3.12427	−	9.61552i	−0.230953	−	0.710800i
$184$	11.6333	−	35.8037i	0.857620	−	2.63948i
$185$	−0.0931396	−	0.0676699i	−0.00684776	−	0.00497519i
$186$	24.5502			1.80011
$187$	9.62952	−	19.5894i	0.704180	−	1.43252i
$188$	19.4839			1.42101
$189$	−1.58940	−	1.15477i	−0.115612	−	0.0839968i
$190$	2.31294	−	7.11849i	0.167798	−	0.516429i
$191$	4.53285	+	13.9507i	0.327985	+	1.00943i	0.970075	+	0.242805i	$0.0780676\pi$
$191$	4.53285	+	13.9507i	0.327985	+	1.00943i	−0.642090	+	0.766629i	$0.721932\pi$
$192$	−3.52339	+	2.55989i	−0.254279	+	0.184744i
$193$	0.206159	−	0.149784i	0.0148397	−	0.0107817i	−0.580341	−	0.814374i	$-0.697081\pi$
$193$	0.206159	−	0.149784i	0.0148397	−	0.0107817i	0.595180	+	0.803592i	$0.297081\pi$
$194$	−9.69550	−	29.8397i	−0.696096	−	2.14236i
$195$	0.113415	−	0.349054i	0.00812178	−	0.0249963i
$196$	11.9089	+	8.65229i	0.850633	+	0.618021i
$197$	−8.02426			−0.571705			−0.285852	−	0.958274i	$-0.592277\pi$
$197$	−8.02426			−0.571705			−0.285852	+	0.958274i	$0.592277\pi$
$198$	−6.15120	−	5.97702i	−0.437147	−	0.424768i
$199$	−18.1025			−1.28325			−0.641627	−	0.767017i	$-0.721740\pi$
$199$	−18.1025			−1.28325			−0.641627	+	0.767017i	$0.721740\pi$
$200$	27.3552	+	19.8747i	1.93430	+	1.40535i
$201$	−0.416379	+	1.28148i	−0.0293691	+	0.0903888i
$202$	12.1212	+	37.3052i	0.852844	+	2.62478i
$203$	−3.23305	+	2.34895i	−0.226915	+	0.164864i
$204$	−24.9585	+	18.1334i	−1.74744	+	1.26959i
$205$	0.452286	+	1.39199i	0.0315890	+	0.0972210i
$206$	12.3265	−	37.9369i	0.858825	−	2.64319i
$207$	−4.38235	−	3.18396i	−0.304594	−	0.221301i
$208$	−8.59734			−0.596118
$209$	−4.46215	−	25.7719i	−0.308654	−	1.78268i
$210$	−1.86463			−0.128671
$211$	2.58591	+	1.87878i	0.178022	+	0.129340i	0.673228	−	0.739435i	$-0.264907\pi$
$211$	2.58591	+	1.87878i	0.178022	+	0.129340i	−0.495206	+	0.868776i	$0.664907\pi$
$212$	−15.6694	+	48.2255i	−1.07618	+	3.31214i
$213$	1.45361	+	4.47376i	0.0995999	+	0.306537i
$214$	17.8631	−	12.9783i	1.22110	−	0.887179i
$215$	1.36957	−	0.995050i	0.0934038	−	0.0678618i
$216$	2.14760	+	6.60965i	0.146126	+	0.449730i
$217$	5.76345	−	17.7381i	0.391248	−	1.20414i
$218$	−2.33150	−	1.69393i	−0.157909	−	0.114727i
$219$	−2.24039			−0.151392
$220$	−5.64783	−	0.811571i	−0.380777	−	0.0547161i
$221$	−6.58147			−0.442718
$222$	0.656264	+	0.476804i	0.0440455	+	0.0320010i
$223$	7.96425	−	24.5114i	0.533326	−	1.64141i	−0.213913	−	0.976853i	$-0.568621\pi$
$223$	7.96425	−	24.5114i	0.533326	−	1.64141i	0.747239	−	0.664555i	$-0.231379\pi$
$224$	5.05907	+	15.5702i	0.338023	+	1.04033i
$225$	3.93611	−	2.85975i	0.262407	−	0.190650i
$226$	5.36346	−	3.89678i	0.356772	−	0.259210i
$227$	2.45985	+	7.57063i	0.163266	+	0.502480i	0.998904	−	0.0467994i	$-0.0149022\pi$
$227$	2.45985	+	7.57063i	0.163266	+	0.502480i	−0.835639	+	0.549280i	$0.814902\pi$
$228$	−11.4231	+	35.1567i	−0.756514	+	2.32831i
$229$	1.48670	+	1.08015i	0.0982440	+	0.0713785i	0.635823	−	0.771835i	$-0.280661\pi$
$229$	1.48670	+	1.08015i	0.0982440	+	0.0713785i	−0.537579	+	0.843214i	$0.680661\pi$
$230$	−5.14122			−0.339002
$231$	−5.76259	+	3.04120i	−0.379151	+	0.200096i
$232$	14.1368			0.928126
$233$	7.20534	+	5.23499i	0.472037	+	0.342955i	0.798235	−	0.602346i	$-0.205767\pi$
$233$	7.20534	+	5.23499i	0.472037	+	0.342955i	−0.326197	+	0.945302i	$0.605767\pi$
$234$	−0.799122	+	2.45944i	−0.0522402	+	0.160779i
$235$	−0.471420	−	1.45088i	−0.0307521	−	0.0946451i
$236$	7.07951	−	5.14356i	0.460837	−	0.334817i
$237$	−3.09550	+	2.24901i	−0.201074	+	0.146089i
$238$	10.3326	+	31.8006i	0.669765	+	2.06133i
$239$	1.67658	−	5.15998i	0.108449	−	0.333771i	−0.882076	−	0.471108i	$-0.843854\pi$
$239$	1.67658	−	5.15998i	0.108449	−	0.333771i	0.990524	+	0.137337i	$0.0438542\pi$
$240$	2.55275	+	1.85468i	0.164779	+	0.119719i
$241$	10.7084			0.689786			0.344893	−	0.938642i	$-0.387915\pi$
$241$	10.7084			0.689786			0.344893	+	0.938642i	$0.387915\pi$
$242$	−26.7903	+	9.56363i	−1.72214	+	0.614773i
$243$	1.00000			0.0641500
$244$	38.3408	+	27.8562i	2.45452	+	1.78331i
$245$	0.356159	−	1.09614i	0.0227542	−	0.0700301i
$246$	−3.18682	−	9.80802i	−0.203184	−	0.625336i
$247$	−6.38002	+	4.63536i	−0.405951	+	0.294941i
$248$	−53.3770	+	38.7807i	−3.38945	+	2.46258i
$249$	4.09356	+	12.5987i	0.259419	+	0.798409i
$250$	2.89341	−	8.90499i	0.182995	−	0.563201i
$251$	−19.3319	−	14.0455i	−1.22022	−	0.886543i	−0.224103	−	0.974565i	$-0.571945\pi$
$251$	−19.3319	−	14.0455i	−1.22022	−	0.886543i	−0.996118	+	0.0880225i	$0.971945\pi$
$252$	9.20900			0.580112
$253$	−15.8888	+	8.38532i	−0.998922	+	0.527180i
$254$	−7.90841			−0.496218
$255$	1.95419	+	1.41980i	0.122376	+	0.0889116i
$256$	−7.01007	+	21.5748i	−0.438130	+	1.34842i
$257$	−6.07097	−	18.6845i	−0.378697	−	1.16551i	−0.940951	−	0.338544i	$-0.890066\pi$
$257$	−6.07097	−	18.6845i	−0.378697	−	1.16551i	0.562254	−	0.826965i	$-0.309934\pi$
$258$	−9.65001	+	7.01114i	−0.600783	+	0.436495i
$259$	0.498566	−	0.362230i	0.0309794	−	0.0225079i
$260$	0.531626	+	1.63618i	0.0329700	+	0.101471i
$261$	0.628581	−	1.93457i	0.0389082	−	0.119747i
$262$	8.30483	+	6.03381i	0.513074	+	0.372770i
$263$	2.80762			0.173125			0.0865626	−	0.996246i	$-0.472412\pi$
$263$	2.80762			0.173125			0.0865626	+	0.996246i	$0.472412\pi$
$264$	22.8155	+	3.27850i	1.40420	+	0.201777i
$265$	3.97027			0.243892
$266$	32.4136	+	23.5499i	1.98741	+	1.44394i
$267$	−0.884200	+	2.72129i	−0.0541122	+	0.166540i
$268$	−1.95176	−	6.00689i	−0.119223	−	0.366929i
$269$	1.69348	−	1.23038i	0.103253	−	0.0750178i	−0.534961	−	0.844877i	$-0.679674\pi$
$269$	1.69348	−	1.23038i	0.103253	−	0.0750178i	0.638214	+	0.769859i	$0.279674\pi$
$270$	0.767847	−	0.557873i	0.0467297	−	0.0339511i
$271$	−1.82690	−	5.62263i	−0.110976	−	0.341550i	0.880110	−	0.474770i	$-0.157469\pi$
$271$	−1.82690	−	5.62263i	−0.110976	−	0.341550i	−0.991087	+	0.133219i	$0.957469\pi$
$272$	17.4852	−	53.8138i	1.06019	−	3.26294i
$273$	1.58940	+	1.15477i	0.0961948	+	0.0698896i
$274$	−13.0091			−0.785907
$275$	−2.75289	−	15.8998i	−0.166006	−	0.958795i
$276$	25.3914			1.52838
$277$	−22.7717	−	16.5446i	−1.36822	−	0.994070i	−0.997874	−	0.0651762i	$-0.979239\pi$
$277$	−22.7717	−	16.5446i	−1.36822	−	0.994070i	−0.370346	−	0.928894i	$-0.620761\pi$
$278$	−12.7890	+	39.3606i	−0.767035	+	2.36069i
$279$	2.93364	+	9.02882i	0.175633	+	0.540542i
$280$	4.05407	−	2.94545i	0.242277	−	0.176025i
$281$	11.9111	−	8.65391i	0.710556	−	0.516249i	−0.172797	−	0.984957i	$-0.555280\pi$
$281$	11.9111	−	8.65391i	0.710556	−	0.516249i	0.883353	+	0.468708i	$0.155280\pi$
$282$	3.32164	+	10.2229i	0.197801	+	0.608768i
$283$	−6.48586	+	19.9614i	−0.385545	+	1.18658i	0.550540	+	0.834809i	$0.314422\pi$
$283$	−6.48586	+	19.9614i	−0.385545	+	1.18658i	−0.936084	+	0.351775i	$0.885578\pi$
$284$	−17.8386	−	12.9605i	−1.05853	−	0.769065i
$285$	2.89435			0.171446
$286$	6.15120	+	5.97702i	0.363728	+	0.353429i
$287$	−7.83465			−0.462465
$288$	−6.74172	−	4.89815i	−0.397260	−	0.288626i
$289$	8.13203	−	25.0278i	0.478355	−	1.47222i
$290$	−0.596593	−	1.83613i	−0.0350332	−	0.107821i
$291$	9.81555	−	7.13142i	0.575398	−	0.418051i
$292$	8.49610	−	6.17278i	0.497197	−	0.361234i
$293$	4.55963	+	14.0331i	0.266377	+	0.819823i	0.991373	+	0.131071i	$0.0418414\pi$
$293$	4.55963	+	14.0331i	0.266377	+	0.819823i	−0.724996	+	0.688753i	$0.758159\pi$
$294$	−2.50951	+	7.72346i	−0.146357	+	0.450441i
$295$	−0.554309	−	0.402729i	−0.0322731	−	0.0234478i
$296$	−2.18003			−0.126712
$297$	1.46312	−	2.97645i	0.0848991	−	0.172711i
$298$	−57.5434			−3.33340
$299$	4.38235	+	3.18396i	0.253438	+	0.184133i
$300$	−7.04740	+	21.6897i	−0.406882	+	1.25225i
$301$	2.80025	+	8.61829i	0.161404	+	0.496750i
$302$	49.2170	−	35.7583i	2.83212	−	2.05766i
$303$	−12.2713	+	8.91561i	−0.704967	+	0.512188i
$304$	−20.9513	−	64.4815i	−1.20164	−	3.69827i
$305$	1.14666	−	3.52906i	0.0656576	−	0.202073i
$306$	−13.7693	−	10.0040i	−0.787138	−	0.571889i
$307$	−13.1537			−0.750723			−0.375362	−	0.926878i	$-0.622482\pi$
$307$	−13.1537			−0.750723			−0.375362	+	0.926878i	$0.622482\pi$
$308$	13.4739	−	27.4101i	0.767747	−	1.56184i
$309$	15.4250			0.877498
$310$	7.28953	+	5.29615i	0.414017	+	0.300801i
$311$	−9.29184	+	28.5973i	−0.526892	+	1.62161i	0.233652	+	0.972320i	$0.424932\pi$
$311$	−9.29184	+	28.5973i	−0.526892	+	1.62161i	−0.760544	+	0.649286i	$0.775068\pi$
$312$	−2.14760	−	6.60965i	−0.121584	−	0.374198i
$313$	5.93303	−	4.31060i	0.335355	−	0.243649i	−0.407345	−	0.913274i	$-0.633545\pi$
$313$	5.93303	−	4.31060i	0.335355	−	0.243649i	0.742699	+	0.669625i	$0.233545\pi$
$314$	−29.1442	+	21.1745i	−1.64470	+	1.19495i
$315$	−0.222815	−	0.685753i	−0.0125542	−	0.0386378i
$316$	5.54234	−	17.0576i	0.311781	−	0.959563i
$317$	15.4275	+	11.2087i	0.866494	+	0.629545i	0.929644	−	0.368459i	$-0.120115\pi$
$317$	15.4275	+	11.2087i	0.866494	+	0.629545i	−0.0631497	+	0.998004i	$0.520115\pi$
$318$	−27.9746			−1.56874
$319$	−4.83847	−	4.70147i	−0.270903	−	0.263232i
$320$	−1.59841			−0.0893541
$321$	6.90759	+	5.01866i	0.385544	+	0.280114i
$322$	8.50427	−	26.1735i	0.473925	−	1.45859i
$323$	−16.0387	−	49.3622i	−0.892419	−	2.74658i
$324$	−3.79223	+	2.75522i	−0.210680	+	0.153068i
$325$	−3.93611	+	2.85975i	−0.218336	+	0.158630i
$326$	8.02735	+	24.7056i	0.444594	+	1.36832i
$327$	0.344373	−	1.05987i	0.0190439	−	0.0586110i
$328$	22.4220	+	16.2905i	1.23805	+	0.899494i
$329$	8.16609			0.450211
$330$	−0.537028	−	3.10170i	−0.0295624	−	0.170743i
$331$	−17.7497			−0.975609			−0.487805	−	0.872953i	$-0.662202\pi$
$331$	−17.7497			−0.975609			−0.487805	+	0.872953i	$0.662202\pi$
$332$	−50.2358	−	36.4985i	−2.75705	−	2.00311i
$333$	−0.0969332	+	0.298330i	−0.00531191	+	0.0163484i
$334$	−10.0862	−	31.0421i	−0.551891	−	1.69855i
$335$	−0.400083	+	0.290678i	−0.0218589	+	0.0158814i
$336$	−13.6646	+	9.92791i	−0.745465	+	0.541612i
$337$	1.41979	+	4.36967i	0.0773409	+	0.238031i	0.982251	−	0.187572i	$-0.0600619\pi$
$337$	1.41979	+	4.36967i	0.0773409	+	0.238031i	−0.904910	+	0.425603i	$0.860062\pi$
$338$	0.799122	−	2.45944i	0.0434665	−	0.133776i
$339$	2.07403	+	1.50687i	0.112646	+	0.0818419i
$340$	−11.3226			−0.614055
$341$	31.1661	+	4.47845i	1.68774	+	0.242522i
$342$	−20.3937			−1.10276
$343$	16.1170	+	11.7097i	0.870237	+	0.632265i
$344$	9.90590	−	30.4872i	0.534090	−	1.64376i
$345$	−0.614353	−	1.89078i	−0.0330757	−	0.101796i
$346$	14.4809	−	10.5210i	0.778497	−	0.565611i
$347$	26.3286	−	19.1289i	1.41339	−	1.02689i	0.420576	−	0.907257i	$-0.361828\pi$
$347$	26.3286	−	19.1289i	1.41339	−	1.02689i	0.992818	−	0.119634i	$-0.0381720\pi$
$348$	2.94645	+	9.06823i	0.157946	+	0.486108i
$349$	3.87164	−	11.9157i	0.207244	−	0.637833i	−0.792369	−	0.610042i	$-0.791153\pi$
$349$	3.87164	−	11.9157i	0.207244	−	0.637833i	0.999614	−	0.0277910i	$-0.00884728\pi$
$350$	19.9974	+	14.5289i	1.06890	+	0.776604i
$351$	−1.00000			−0.0533761
$352$	−24.4431	+	12.8998i	−1.30282	+	0.687562i
$353$	32.9306			1.75272			0.876358	−	0.481659i	$-0.159966\pi$
$353$	32.9306			1.75272			0.876358	+	0.481659i	$0.159966\pi$
$354$	3.90568	+	2.83764i	0.207584	+	0.150819i
$355$	−0.533501	+	1.64195i	−0.0283153	+	0.0871455i
$356$	−4.14465	−	12.7559i	−0.219666	−	0.676062i
$357$	−10.4606	+	7.60006i	−0.553633	+	0.402238i
$358$	24.7969	−	18.0160i	1.31056	−	0.952174i
$359$	−2.51717	−	7.74706i	−0.132851	−	0.408874i	0.862398	−	0.506230i	$-0.168961\pi$
$359$	−2.51717	−	7.74706i	−0.132851	−	0.408874i	−0.995250	+	0.0973562i	$0.968961\pi$
$360$	−0.788208	+	2.42585i	−0.0415422	+	0.127854i
$361$	−34.9424	−	25.3872i	−1.83908	−	1.33617i
$362$	5.08360			0.267188
$363$	−6.71853	−	8.70984i	−0.352632	−	0.457148i
$364$	−9.20900			−0.482683
$365$	−0.665225	−	0.483314i	−0.0348195	−	0.0252978i
$366$	−8.07940	+	24.8658i	−0.422317	+	1.29976i
$367$	9.02983	+	27.7910i	0.471353	+	1.45068i	0.850813	+	0.525468i	$0.176110\pi$
$367$	9.02983	+	27.7910i	0.471353	+	1.45068i	−0.379460	+	0.925208i	$0.623890\pi$
$368$	−37.6765	+	27.3736i	−1.96402	+	1.42695i
$369$	3.22628	−	2.34403i	0.167953	−	0.122025i
$370$	0.0920004	+	0.283148i	0.00478287	+	0.0147202i
$371$	−6.56736	+	20.2123i	−0.340960	+	1.04937i
$372$	−36.0014	−	26.1566i	−1.86659	−	1.35616i
$373$	24.7193			1.27992			0.639958	−	0.768410i	$-0.278952\pi$
$373$	24.7193			1.27992			0.639958	+	0.768410i	$0.278952\pi$
$374$	−49.9225	+	26.3466i	−2.58143	+	1.36235i
$375$	3.62073			0.186974
$376$	−23.3706	−	16.9797i	−1.20524	−	0.875661i
$377$	−0.628581	+	1.93457i	−0.0323736	+	0.0996356i
$378$	1.56996	+	4.83183i	0.0807499	+	0.248523i
$379$	−17.1425	+	12.4547i	−0.880550	+	0.639757i	−0.933397	−	0.358845i	$-0.883171\pi$
$379$	−17.1425	+	12.4547i	−0.880550	+	0.639757i	0.0528466	+	0.998603i	$0.483171\pi$
$380$	−10.9760	+	7.97456i	−0.563059	+	0.409087i
$381$	−0.945021	−	2.90847i	−0.0484149	−	0.149006i
$382$	11.7220	−	36.0766i	0.599749	−	1.84584i
$383$	−8.86548	−	6.44114i	−0.453005	−	0.329127i	0.337776	−	0.941226i	$-0.390325\pi$
$383$	−8.86548	−	6.44114i	−0.453005	−	0.329127i	−0.790781	+	0.612099i	$0.790325\pi$
$384$	−5.40399			−0.275771
$385$	−2.36712	−	0.340145i	−0.120639	−	0.0173354i
$386$	−0.658986			−0.0335415
$387$	−3.73162	−	2.71118i	−0.189689	−	0.137817i
$388$	−17.5742	+	54.0880i	−0.892197	+	2.74590i
$389$	6.03932	+	18.5871i	0.306206	+	0.942404i	0.979225	+	0.202779i	$0.0649973\pi$
$389$	6.03932	+	18.5871i	0.306206	+	0.942404i	−0.673019	+	0.739625i	$0.735003\pi$
$390$	−0.767847	+	0.557873i	−0.0388814	+	0.0282490i
$391$	−28.8423	+	20.9552i	−1.45862	+	1.05975i
$392$	−6.74419	−	20.7565i	−0.340633	−	1.04836i
$393$	−1.22666	+	3.77528i	−0.0618769	+	0.190438i
$394$	16.7878	+	12.1970i	0.845756	+	0.614478i
$395$	−1.40430			−0.0706580
$396$	2.65227	+	15.3186i	0.133281	+	0.769790i
$397$	−14.8051			−0.743047			−0.371523	−	0.928424i	$-0.621164\pi$
$397$	−14.8051			−0.743047			−0.371523	+	0.928424i	$0.621164\pi$
$398$	37.8728	+	27.5162i	1.89839	+	1.37926i
$399$	−4.78765	+	14.7349i	−0.239682	+	0.737666i
$400$	−12.9258	−	39.7814i	−0.646288	−	1.98907i
$401$	−5.91492	+	4.29744i	−0.295377	+	0.214604i	−0.725597	−	0.688120i	$-0.758436\pi$
$401$	−5.91492	+	4.29744i	−0.295377	+	0.214604i	0.430220	+	0.902724i	$0.358436\pi$
$402$	2.81900	−	2.04812i	0.140599	−	0.102151i
$403$	−2.93364	−	9.02882i	−0.146135	−	0.449758i
$404$	21.9711	−	67.6201i	1.09310	−	3.36423i
$405$	0.296923	+	0.215727i	0.0147542	+	0.0107196i
$406$	10.3344			0.512887
$407$	0.746139	+	0.725011i	0.0369847	+	0.0359374i
$408$	45.7399			2.26446
$409$	21.6924	+	15.7605i	1.07262	+	0.779305i	0.976382	−	0.216053i	$-0.0693186\pi$
$409$	21.6924	+	15.7605i	1.07262	+	0.779305i	0.0962394	+	0.995358i	$0.469319\pi$
$410$	1.16962	−	3.59971i	0.0577633	−	0.177777i
$411$	−1.55453	−	4.78434i	−0.0766791	−	0.235994i
$412$	−58.4952	+	42.4992i	−2.88185	+	2.09379i
$413$	2.96716	−	2.15577i	0.146004	−	0.106078i
$414$	4.32875	+	13.3225i	0.212746	+	0.654766i
$415$	−1.50241	+	4.62393i	−0.0737502	+	0.226980i
$416$	6.74172	+	4.89815i	0.330540	+	0.240151i
$417$	−16.0039			−0.783712
$418$	−29.8385	+	60.7007i	−1.45945	+	2.96897i
$419$	4.00202			0.195511			0.0977556	−	0.995210i	$-0.468834\pi$
$419$	4.00202			0.195511			0.0977556	+	0.995210i	$0.468834\pi$
$420$	2.73436	+	1.98663i	0.133423	+	0.0969377i
$421$	−6.55167	+	20.1640i	−0.319309	+	0.982732i	0.654635	+	0.755945i	$0.272822\pi$
$421$	−6.55167	+	20.1640i	−0.319309	+	0.982732i	−0.973944	+	0.226787i	$0.927178\pi$
$422$	−2.55428	−	7.86128i	−0.124341	−	0.382681i
$423$	−3.36277	+	2.44319i	−0.163503	+	0.118792i
$424$	60.8223	−	44.1900i	2.95379	−	2.14606i
$425$	−9.89498	−	30.4536i	−0.479977	−	1.47722i
$426$	3.75906	−	11.5692i	0.182127	−	0.560529i
$427$	16.0694	+	11.6751i	0.777652	+	0.564997i
$428$	−40.0227			−1.93457
$429$	−1.46312	+	2.97645i	−0.0706403	+	0.143704i
$430$	−4.37781			−0.211117
$431$	20.2632	+	14.7221i	0.976045	+	0.709138i	0.956821	−	0.290677i	$-0.0938806\pi$
$431$	20.2632	+	14.7221i	0.976045	+	0.709138i	0.0192236	+	0.999815i	$0.493881\pi$
$432$	2.65672	−	8.17655i	0.127822	−	0.393395i
$433$	11.0765	+	34.0898i	0.532301	+	1.63825i	0.749410	+	0.662106i	$0.230337\pi$
$433$	11.0765	+	34.0898i	0.532301	+	1.63825i	−0.217110	+	0.976147i	$0.569663\pi$
$434$	−39.0201	+	28.3497i	−1.87302	+	1.36083i
$435$	0.603981	−	0.438818i	0.0289587	−	0.0210397i
$436$	1.61423	+	4.96810i	0.0773077	+	0.237929i
$437$	−13.2007	+	40.6275i	−0.631474	+	1.94348i
$438$	4.68719	+	3.40544i	0.223963	+	0.162718i
$439$	34.6225			1.65244			0.826220	−	0.563347i	$-0.190487\pi$
$439$	34.6225			1.65244			0.826220	+	0.563347i	$0.190487\pi$
$440$	6.06719	+	5.89539i	0.289242	+	0.281052i
$441$	−3.14033			−0.149540
$442$	13.7693	+	10.0040i	0.654938	+	0.475840i
$443$	10.7807	−	33.1797i	0.512208	−	1.57642i	−0.276096	−	0.961130i	$-0.589041\pi$
$443$	10.7807	−	33.1797i	0.512208	−	1.57642i	0.788304	−	0.615285i	$-0.210959\pi$
$444$	−0.454370	−	1.39841i	−0.0215635	−	0.0663655i
$445$	−0.849595	+	0.617267i	−0.0402747	+	0.0292613i
$446$	−53.9201	+	39.1753i	−2.55319	+	1.85500i
$447$	−6.87618	−	21.1627i	−0.325232	−	1.00096i
$448$	2.64399	−	8.13738i	0.124917	−	0.384455i
$449$	19.2145	+	13.9601i	0.906788	+	0.658820i	0.940200	−	0.340622i	$-0.110638\pi$
$449$	19.2145	+	13.9601i	0.906788	+	0.658820i	−0.0334126	+	0.999442i	$0.510638\pi$
$450$	−12.5817			−0.593108
$451$	−2.25644	−	13.0325i	−0.106252	−	0.613675i
$452$	−12.0169			−0.565229
$453$	19.0320	+	13.8276i	0.894202	+	0.649676i
$454$	6.36119	−	19.5777i	0.298546	−	0.918829i
$455$	0.222815	+	0.685753i	0.0104457	+	0.0321486i
$456$	44.3399	−	32.2148i	2.07640	−	1.50860i
$457$	31.5966	−	22.9563i	1.47803	−	1.07385i	0.499843	−	0.866116i	$-0.333391\pi$
$457$	31.5966	−	22.9563i	1.47803	−	1.07385i	0.978185	−	0.207735i	$-0.0666091\pi$
$458$	−1.46852	−	4.51963i	−0.0686193	−	0.211189i
$459$	2.03379	−	6.25935i	0.0949291	−	0.292162i
$460$	7.53929	+	5.47762i	0.351521	+	0.255395i
$461$	1.66600			0.0775935			0.0387967	−	0.999247i	$-0.487648\pi$
$461$	1.66600			0.0775935			0.0387967	+	0.999247i	$0.487648\pi$
$462$	16.6788	+	2.39667i	0.775966	+	0.111503i
$463$	23.6462			1.09893			0.549466	−	0.835516i	$-0.314831\pi$
$463$	23.6462			1.09893			0.549466	+	0.835516i	$0.314831\pi$
$464$	−14.1482	−	10.2793i	−0.656813	−	0.477203i
$465$	−1.07670	+	3.31373i	−0.0499306	+	0.153671i
$466$	−7.11721	−	21.9045i	−0.329698	−	1.01471i
$467$	−2.47170	+	1.79580i	−0.114377	+	0.0830996i	−0.643503	−	0.765443i	$-0.722520\pi$
$467$	−2.47170	+	1.79580i	−0.114377	+	0.0830996i	0.529126	+	0.848543i	$0.322520\pi$
$468$	3.79223	−	2.75522i	0.175296	−	0.127360i
$469$	−0.818020	−	2.51761i	−0.0377726	−	0.116252i
$470$	−1.21910	+	3.75200i	−0.0562328	+	0.173067i
$471$	−11.2699	−	8.18809i	−0.519291	−	0.377287i
$472$	−12.9742			−0.597185
$473$	−13.5295	+	7.14019i	−0.622088	+	0.328306i
$474$	9.89473			0.454480
$475$	−31.0407	−	22.5524i	−1.42425	−	1.03478i
$476$	18.7291	−	57.6424i	0.858449	−	2.64203i
$477$	−3.34284	−	10.2882i	−0.153058	−	0.471065i
$478$	−11.3509	+	8.24690i	−0.519177	+	0.377204i
$479$	10.8398	−	7.87560i	0.495285	−	0.359845i	−0.311928	−	0.950106i	$-0.600975\pi$
$479$	10.8398	−	7.87560i	0.495285	−	0.359845i	0.807213	+	0.590260i	$0.200975\pi$
$480$	−0.945109	−	2.90875i	−0.0431381	−	0.132766i
$481$	0.0969332	−	0.298330i	0.00441977	−	0.0136027i
$482$	−22.4033	−	16.2769i	−1.02044	−	0.741393i
$483$	10.6420			0.484229
$484$	49.4757	+	14.5187i	2.24890	+	0.659941i
$485$	4.45291			0.202196
$486$	−2.09213	−	1.52002i	−0.0949008	−	0.0689495i
$487$	1.29781	−	3.99425i	0.0588095	−	0.180997i	−0.917336	−	0.398113i	$-0.869665\pi$
$487$	1.29781	−	3.99425i	0.0588095	−	0.180997i	0.976146	+	0.217116i	$0.0696651\pi$
$488$	−21.7130	−	66.8259i	−0.982904	−	3.02507i
$489$	−8.12675	+	5.90443i	−0.367504	+	0.267007i
$490$	−2.41129	+	1.75191i	−0.108931	+	0.0791430i
$491$	−12.2817	−	37.7992i	−0.554266	−	1.70586i	−0.697874	−	0.716221i	$-0.745870\pi$
$491$	−12.2817	−	37.7992i	−0.554266	−	1.70586i	0.143608	−	0.989635i	$-0.454130\pi$
$492$	−5.77649	+	17.7782i	−0.260424	+	0.801504i
$493$	−10.8308	−	7.86903i	−0.487794	−	0.354403i
$494$	20.3937			0.917554
$495$	1.07654	−	0.568142i	0.0483868	−	0.0255361i
$496$	81.6186			3.66478
$497$	−7.47651	−	5.43200i	−0.335367	−	0.243659i
$498$	10.5860	−	32.5803i	0.474370	−	1.45996i
$499$	8.25177	+	25.3963i	0.369400	+	1.13690i	0.947180	+	0.320703i	$0.103919\pi$
$499$	8.25177	+	25.3963i	0.369400	+	1.13690i	−0.577780	+	0.816193i	$0.696081\pi$
$500$	−13.7307	+	9.97591i	−0.614054	+	0.446136i
$501$	10.2111	−	7.41878i	0.456197	−	0.331447i
$502$	19.0955	+	58.7699i	0.852273	+	2.62303i
$503$	8.74352	−	26.9098i	0.389854	−	1.19985i	−0.543043	−	0.839705i	$-0.682728\pi$
$503$	8.74352	−	26.9098i	0.389854	−	1.19985i	0.932897	−	0.360143i	$-0.117272\pi$
$504$	−11.0460	−	8.02538i	−0.492028	−	0.357479i
$505$	−5.56697			−0.247727
$506$	45.9873	+	6.60819i	2.04439	+	0.293770i
$507$	1.00000			0.0444116
$508$	11.5972	+	8.42587i	0.514543	+	0.373838i
$509$	−4.92062	+	15.1441i	−0.218103	+	0.671251i	0.780816	+	0.624761i	$0.214804\pi$
$509$	−4.92062	+	15.1441i	−0.218103	+	0.671251i	−0.998919	+	0.0464900i	$0.985196\pi$
$510$	−1.93029	−	5.94082i	−0.0854747	−	0.263064i
$511$	3.56088	−	2.58713i	0.157524	−	0.114448i
$512$	38.7162	−	28.1290i	1.71103	−	1.24314i
$513$	−2.43695	−	7.50017i	−0.107594	−	0.331140i
$514$	−15.6996	+	48.3184i	−0.692480	+	2.13123i
$515$	4.58004	+	3.32759i	0.201821	+	0.146631i
$516$	21.6211			0.951814
$517$	2.35190	+	13.5838i	0.103437	+	0.597416i
$518$	−1.59366			−0.0700214
$519$	5.59969	+	4.06842i	0.245799	+	0.178584i
$520$	0.788208	−	2.42585i	0.0345652	−	0.106381i
$521$	9.18890	+	28.2805i	0.402573	+	1.23899i	0.922905	+	0.385028i	$0.125808\pi$
$521$	9.18890	+	28.2805i	0.402573	+	1.23899i	−0.520332	+	0.853964i	$0.674192\pi$
$522$	−4.25566	+	3.09192i	−0.186265	+	0.135330i
$523$	−16.2489	+	11.8055i	−0.710515	+	0.516219i	−0.883340	−	0.468733i	$-0.844711\pi$
$523$	−16.2489	+	11.8055i	−0.710515	+	0.516219i	0.172825	+	0.984953i	$0.444711\pi$
$524$	−5.74993	−	17.6965i	−0.251187	−	0.773073i
$525$	−2.95370	+	9.09057i	−0.128910	+	0.396745i
$526$	−5.87390	−	4.26764i	−0.256114	−	0.186078i
$527$	62.4810			2.72172
$528$	−20.4500	−	19.8709i	−0.889972	−	0.864771i
$529$	6.34259			0.275765
$530$	−8.30631	−	6.03489i	−0.360803	−	0.262139i
$531$	−0.576886	+	1.77547i	−0.0250347	+	0.0770490i
$532$	−22.4419	−	69.0690i	−0.972979	−	2.99452i
$533$	−3.22628	+	2.34403i	−0.139746	+	0.101531i
$534$	5.98627	−	4.34928i	0.259051	−	0.188212i
$535$	0.968362	+	2.98031i	0.0418659	+	0.128850i
$536$	−2.89375	+	8.90604i	−0.124991	+	0.384682i
$537$	9.58885	+	6.96670i	0.413789	+	0.300635i
$538$	−5.41318			−0.233379
$539$	−4.59469	+	9.34704i	−0.197907	+	0.402606i
$540$	−1.72038			−0.0740332
$541$	−17.8939	−	13.0007i	−0.769320	−	0.558943i	0.132435	−	0.991192i	$-0.457720\pi$
$541$	−17.8939	−	13.0007i	−0.769320	−	0.558943i	−0.901755	+	0.432248i	$0.857720\pi$
$542$	−4.72439	+	14.5402i	−0.202930	+	0.624555i
$543$	0.607468	+	1.86959i	0.0260689	+	0.0802319i
$544$	−44.3705	+	32.2370i	−1.90237	+	1.38215i
$545$	0.330895	−	0.240409i	0.0141740	−	0.0102980i
$546$	−1.56996	−	4.83183i	−0.0671880	−	0.206783i
$547$	5.07882	−	15.6310i	0.217155	−	0.668334i	−0.781839	−	0.623481i	$-0.785718\pi$
$547$	5.07882	−	15.6310i	0.217155	−	0.668334i	0.998994	−	0.0448530i	$-0.0142820\pi$
$548$	19.0770	+	13.8603i	0.814930	+	0.592081i
$549$	−10.1104			−0.431499
$550$	−18.4086	+	37.4489i	−0.784946	+	1.59683i
$551$	−16.0415			−0.683389
$552$	−30.4564	−	22.1279i	−1.29631	−	0.941825i
$553$	2.32290	−	7.14916i	0.0987798	−	0.304013i
$554$	22.4932	+	69.2269i	0.955644	+	2.94117i
$555$	−0.0931396	+	0.0676699i	−0.00395356	+	0.00287243i
$556$	60.6903	−	44.0941i	2.57384	−	1.87001i
$557$	−1.26147	−	3.88239i	−0.0534501	−	0.164502i	0.920768	−	0.390110i	$-0.127563\pi$
$557$	−1.26147	−	3.88239i	−0.0534501	−	0.164502i	−0.974218	+	0.225608i	$0.927563\pi$
$558$	7.58644	−	23.3486i	0.321159	−	0.988427i
$559$	3.73162	+	2.71118i	0.157831	+	0.114671i
$560$	−6.19906			−0.261958
$561$	−15.6550	−	15.2117i	−0.660954	−	0.642238i
$562$	−38.0736			−1.60604
$563$	16.5913	+	12.0543i	0.699241	+	0.508028i	0.879685	−	0.475557i	$-0.157753\pi$
$563$	16.5913	+	12.0543i	0.699241	+	0.508028i	−0.180444	+	0.983585i	$0.557753\pi$
$564$	6.02087	−	18.5303i	0.253524	−	0.780267i
$565$	0.290754	+	0.894848i	0.0122321	+	0.0376465i
$566$	43.9110	−	31.9032i	1.84572	−	1.34099i
$567$	−1.58940	+	1.15477i	−0.0667485	+	0.0484956i
$568$	10.1023	+	31.0917i	0.423883	+	1.30458i
$569$	−11.6737	+	35.9279i	−0.489386	+	1.50617i	0.336141	+	0.941812i	$0.390878\pi$
$569$	−11.6737	+	35.9279i	−0.489386	+	1.50617i	−0.825527	+	0.564363i	$0.809122\pi$
$570$	−6.05535	−	4.39947i	−0.253631	−	0.184273i
$571$	−33.7260			−1.41139			−0.705695	−	0.708515i	$-0.749365\pi$
$571$	−33.7260			−1.41139			−0.705695	+	0.708515i	$0.749365\pi$
$572$	−2.65227	−	15.3186i	−0.110897	−	0.640504i
$573$	14.6686			0.612789
$574$	16.3911	+	11.9088i	0.684151	+	0.497065i
$575$	−8.14406	+	25.0648i	−0.339631	+	1.04528i
$576$	1.34581	+	4.14199i	0.0560756	+	0.172583i
$577$	8.55810	−	6.21782i	0.356278	−	0.258851i	−0.395220	−	0.918587i	$-0.629332\pi$
$577$	8.55810	−	6.21782i	0.356278	−	0.258851i	0.751498	+	0.659735i	$0.229332\pi$
$578$	−55.0560	+	40.0005i	−2.29003	+	1.66380i
$579$	−0.0787459	−	0.242355i	−0.00327257	−	0.0100719i
$580$	−1.08140	+	3.32820i	−0.0449026	+	0.138196i
$581$	−21.0548	−	15.2972i	−0.873501	−	0.634636i
$582$	−31.3753			−1.30055
$583$	−35.5134	−	5.10312i	−1.47081	−	0.211350i
$584$	−15.5703			−0.644303
$585$	−0.296923	−	0.215727i	−0.0122763	−	0.00891923i
$586$	11.7913	−	36.2898i	0.487093	−	1.49912i
$587$	−5.58366	−	17.1847i	−0.230462	−	0.709290i	−0.997691	−	0.0679161i	$-0.978365\pi$
$587$	−5.58366	−	17.1847i	−0.230462	−	0.709290i	0.767229	−	0.641373i	$-0.221635\pi$
$588$	11.9089	−	8.65229i	0.491113	−	0.356815i
$589$	60.5685	−	44.0056i	2.49568	−	1.81322i
$590$	0.547529	+	1.68512i	0.0225414	+	0.0693754i
$591$	−2.47963	+	7.63153i	−0.101998	+	0.313919i
$592$	2.18179	+	1.58516i	0.0896708	+	0.0651497i
$593$	2.83700			0.116502			0.0582509	−	0.998302i	$-0.481448\pi$
$593$	2.83700			0.116502			0.0582509	+	0.998302i	$0.481448\pi$
$594$	−7.58531	+	4.00314i	−0.311229	+	0.164251i
$595$	−4.74553			−0.194548
$596$	84.3839	+	61.3085i	3.45650	+	2.51129i
$597$	−5.59399	+	17.2165i	−0.228947	+	0.704625i
$598$	−4.32875	−	13.3225i	−0.177016	−	0.544798i
$599$	12.1302	−	8.81312i	0.495627	−	0.360094i	−0.311717	−	0.950175i	$-0.600904\pi$
$599$	12.1302	−	8.81312i	0.495627	−	0.360094i	0.807344	+	0.590081i	$0.200904\pi$
$600$	27.3552	−	19.8747i	1.11677	−	0.811380i
$601$	−1.52953	−	4.70741i	−0.0623909	−	0.192019i	0.915003	−	0.403448i	$-0.132188\pi$
$601$	−1.52953	−	4.70741i	−0.0623909	−	0.192019i	−0.977393	+	0.211429i	$0.932188\pi$
$602$	7.24149	−	22.2870i	0.295141	−	0.908350i
$603$	1.09009	+	0.792000i	0.0443921	+	0.0322527i
$604$	−110.272			−4.48690
$605$	−0.115938	−	4.03552i	−0.00471354	−	0.164067i
$606$	39.2250			1.59341
$607$	−27.5478	−	20.0146i	−1.11813	−	0.812368i	−0.134205	−	0.990954i	$-0.542848\pi$
$607$	−27.5478	−	20.0146i	−1.11813	−	0.812368i	−0.983924	+	0.178585i	$0.942848\pi$
$608$	−20.3077	+	62.5006i	−0.823585	+	2.53473i
$609$	1.23491	+	3.80067i	0.0500412	+	0.154011i
$610$	−7.76320	+	5.64030i	−0.314323	+	0.228369i
$611$	3.36277	−	2.44319i	0.136043	−	0.0988411i
$612$	9.53329	+	29.3405i	0.385360	+	1.18602i
$613$	−3.54631	+	10.9144i	−0.143234	+	0.440829i	−0.996780	−	0.0801891i	$-0.974448\pi$
$613$	−3.54631	+	10.9144i	−0.143234	+	0.440829i	0.853546	+	0.521018i	$0.174448\pi$
$614$	27.5193	+	19.9939i	1.11059	+	0.806890i
$615$	1.46363			0.0590192
$616$	−40.0488	+	21.1357i	−1.61361	+	0.851583i
$617$	20.4546			0.823470			0.411735	−	0.911304i	$-0.364923\pi$
$617$	20.4546			0.823470			0.411735	+	0.911304i	$0.364923\pi$
$618$	−32.2711	−	23.4463i	−1.29813	−	0.943149i
$619$	−13.7386	+	42.2830i	−0.552200	+	1.69950i	0.151027	+	0.988530i	$0.451742\pi$
$619$	−13.7386	+	42.2830i	−0.552200	+	1.69950i	−0.703226	+	0.710966i	$0.748258\pi$
$620$	−5.04697	−	15.5330i	−0.202691	−	0.623820i
$621$	−4.38235	+	3.18396i	−0.175858	+	0.127768i
$622$	62.9082	−	45.7055i	2.52239	−	1.83262i
$623$	−1.73710	−	5.34625i	−0.0695956	−	0.214193i
$624$	−2.65672	+	8.17655i	−0.106354	+	0.327324i
$625$	−18.6055	−	13.5177i	−0.744219	−	0.540706i
$626$	−18.9648			−0.757987
$627$	−25.8894	−	3.72021i	−1.03393	−	0.148571i
$628$	65.2982			2.60568
$629$	1.67021	+	1.21348i	0.0665956	+	0.0483846i
$630$	−0.576201	+	1.77337i	−0.0229564	+	0.0706526i
$631$	−4.01037	−	12.3426i	−0.159650	−	0.491353i	0.838952	−	0.544205i	$-0.183169\pi$
$631$	−4.01037	−	12.3426i	−0.159650	−	0.491353i	−0.998602	+	0.0528525i	$0.983169\pi$
$632$	−21.5131	+	15.6302i	−0.855745	+	0.621735i
$633$	2.58591	−	1.87878i	0.102781	−	0.0746746i
$634$	−15.2388	−	46.9002i	−0.605210	−	1.86264i
$635$	0.346839	−	1.06746i	0.0137639	−	0.0423609i
$636$	41.0231	+	29.8050i	1.62667	+	1.18185i
$637$	3.14033			0.124424
$638$	2.97639	+	17.1906i	0.117836	+	0.680584i
$639$	4.70399			0.186087
$640$	−1.60457	−	1.16579i	−0.0634262	−	0.0460818i
$641$	0.955919	−	2.94202i	0.0377565	−	0.116203i	−0.930402	−	0.366541i	$-0.880542\pi$
$641$	0.955919	−	2.94202i	0.0377565	−	0.116203i	0.968158	+	0.250338i	$0.0805419\pi$
$642$	−6.82310	−	20.9993i	−0.269286	−	0.828778i
$643$	22.0125	−	15.9930i	0.868089	−	0.630704i	−0.0619844	−	0.998077i	$-0.519743\pi$
$643$	22.0125	−	15.9930i	0.868089	−	0.630704i	0.930074	+	0.367373i	$0.119743\pi$
$644$	−40.3570	+	29.3211i	−1.59029	+	1.15541i
$645$	−0.523129	−	1.61002i	−0.0205982	−	0.0633946i
$646$	−41.4764	+	127.651i	−1.63187	+	5.02237i
$647$	7.15270	+	5.19674i	0.281201	+	0.204305i	0.719441	−	0.694553i	$-0.244398\pi$
$647$	7.15270	+	5.19674i	0.281201	+	0.204305i	−0.438240	+	0.898858i	$0.644398\pi$
$648$	6.94980			0.273014
$649$	4.44056	+	4.31481i	0.174307	+	0.169371i
$650$	12.5817			0.493496
$651$	−15.0889	−	10.9627i	−0.591381	−	0.429663i
$652$	14.5505	−	44.7819i	0.569843	−	1.75380i
$653$	10.7132	+	32.9717i	0.419238	+	1.29028i	0.908405	+	0.418092i	$0.137301\pi$
$653$	10.7132	+	32.9717i	0.419238	+	1.29028i	−0.489167	+	0.872190i	$0.662699\pi$
$654$	−2.33150	+	1.69393i	−0.0911687	+	0.0662379i
$655$	−1.17865	+	0.856343i	−0.0460539	+	0.0334601i
$656$	−10.5948	−	32.6073i	−0.413656	−	1.27310i
$657$	−0.692320	+	2.13074i	−0.0270100	+	0.0831282i
$658$	−17.0845	−	12.4126i	−0.666024	−	0.483894i
$659$	9.14287			0.356156			0.178078	−	0.984016i	$-0.443012\pi$
$659$	9.14287			0.356156			0.178078	+	0.984016i	$0.443012\pi$
$660$	−2.51713	+	5.12062i	−0.0979790	+	0.199320i
$661$	14.4774			0.563107			0.281553	−	0.959546i	$-0.409150\pi$
$661$	14.4774			0.563107			0.281553	+	0.959546i	$0.409150\pi$
$662$	37.1345	+	26.9798i	1.44328	+	1.04860i
$663$	−2.03379	+	6.25935i	−0.0789858	+	0.243093i
$664$	28.4494	+	87.5582i	1.10405	+	3.39792i
$665$	−4.60027	+	3.34229i	−0.178391	+	0.129609i
$666$	0.656264	−	0.476804i	0.0254297	−	0.0184758i
$667$	3.40495	+	10.4794i	0.131840	+	0.405762i
$668$	−18.2824	+	56.2675i	−0.707368	+	2.17705i
$669$	−20.8507	−	15.1489i	−0.806134	−	0.585691i
$670$	1.27886			0.0494067
$671$	−14.7927	+	30.0930i	−0.571066	+	1.16173i
$672$	16.3715			0.631544
$673$	−2.35296	−	1.70953i	−0.0906999	−	0.0658974i	0.541511	−	0.840694i	$-0.317852\pi$
$673$	−2.35296	−	1.70953i	−0.0906999	−	0.0658974i	−0.632211	+	0.774796i	$0.717852\pi$
$674$	3.67160	−	11.3000i	0.141425	−	0.435260i
$675$	−1.50346	−	4.62717i	−0.0578682	−	0.178100i
$676$	−3.79223	+	2.75522i	−0.145855	+	0.105970i
$677$	26.9340	−	19.5687i	1.03516	−	0.752086i	0.0658229	−	0.997831i	$-0.479033\pi$
$677$	26.9340	−	19.5687i	1.03516	−	0.752086i	0.969334	+	0.245746i	$0.0790328\pi$
$678$	−2.04866	−	6.30512i	−0.0786782	−	0.242147i
$679$	−7.36571	+	22.6693i	−0.282670	+	0.869969i
$680$	13.5812	+	9.86734i	0.520817	+	0.378395i
$681$	7.96023			0.305037
$682$	−58.3962	−	56.7426i	−2.23611	−	2.17279i
$683$	12.7596			0.488232			0.244116	−	0.969746i	$-0.421502\pi$
$683$	12.7596			0.488232			0.244116	+	0.969746i	$0.421502\pi$
$684$	29.9061	+	21.7280i	1.14349	+	0.830792i
$685$	0.570538	−	1.75594i	0.0217991	−	0.0670908i
$686$	−15.9199	−	48.9964i	−0.607824	−	1.87069i
$687$	1.48670	−	1.08015i	0.0567212	−	0.0412104i
$688$	−32.0820	+	23.3089i	−1.22311	+	0.888645i
$689$	3.34284	+	10.2882i	0.127352	+	0.391950i
$690$	−1.58872	+	4.88959i	−0.0604817	+	0.186144i
$691$	19.8959	+	14.4552i	0.756876	+	0.549903i	0.897951	−	0.440096i	$-0.145056\pi$
$691$	19.8959	+	14.4552i	0.756876	+	0.549903i	−0.141075	+	0.989999i	$0.545056\pi$
$692$	−32.4447			−1.23336
$693$	1.11162	+	6.42033i	0.0422268	+	0.243888i
$694$	−84.1591			−3.19463
$695$	−4.75192	−	3.45247i	−0.180250	−	0.130960i
$696$	4.36851	−	13.4449i	0.165588	−	0.509627i
$697$	−8.11054	−	24.9617i	−0.307209	−	0.945491i
$698$	−26.2121	+	19.0442i	−0.992141	+	0.720833i
$699$	7.20534	−	5.23499i	0.272531	−	0.198005i
$700$	−13.8454	−	42.6116i	−0.523305	−	1.61057i
$701$	−6.13775	+	18.8900i	−0.231820	+	0.713467i	0.765708	+	0.643189i	$0.222389\pi$
$701$	−6.13775	+	18.8900i	−0.231820	+	0.713467i	−0.997527	+	0.0702786i	$0.977611\pi$
$702$	2.09213	+	1.52002i	0.0789623	+	0.0573694i
$703$	2.47374			0.0932991
$704$	14.2975	+	2.05450i	0.538859	+	0.0774318i
$705$	−1.52555			−0.0574554
$706$	−68.8949	−	50.0551i	−2.59289	−	1.88385i
$707$	9.20852	−	28.3409i	0.346322	−	1.06587i
$708$	−2.70413	−	8.32246i	−0.101627	−	0.312777i
$709$	7.10138	−	5.15945i	0.266698	−	0.193767i	−0.446397	−	0.894835i	$-0.647293\pi$
$709$	7.10138	−	5.15945i	0.266698	−	0.193767i	0.713095	+	0.701068i	$0.247293\pi$
$710$	3.61194	−	2.62423i	0.135554	−	0.0984856i
$711$	1.18238	+	3.63898i	0.0443426	+	0.136472i
$712$	−6.14501	+	18.9124i	−0.230294	+	0.708772i
$713$	−41.6037	−	30.2268i	−1.55807	−	1.13200i
$714$	33.4371			1.25135
$715$	−1.07654	+	0.568142i	−0.0402602	+	0.0212473i
$716$	−55.5579			−2.07630
$717$	−4.38934	−	3.18904i	−0.163923	−	0.119097i
$718$	−6.50944	+	20.0340i	−0.242930	+	0.747662i
$719$	−0.918250	−	2.82608i	−0.0342450	−	0.105395i	0.932473	−	0.361240i	$-0.117646\pi$
$719$	−0.918250	−	2.82608i	−0.0342450	−	0.105395i	−0.966718	+	0.255845i	$0.917646\pi$
$720$	2.55275	−	1.85468i	0.0951353	−	0.0691199i
$721$	−24.5165	+	17.8123i	−0.913041	+	0.663363i
$722$	34.5150	+	106.226i	1.28452	+	3.95334i
$723$	3.30907	−	10.1843i	0.123065	−	0.378757i
$724$	−7.45480	−	5.41623i	−0.277055	−	0.201292i
$725$	−9.89666			−0.367553
$726$	0.816901	+	28.4344i	0.0303180	+	1.05530i
$727$	11.4794			0.425747			0.212874	−	0.977080i	$-0.431718\pi$
$727$	11.4794			0.425747			0.212874	+	0.977080i	$0.431718\pi$
$728$	11.0460	+	8.02538i	0.409392	+	0.297441i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.657088	+	2.02231i	0.0243199	+	0.0748491i
$731$	−24.5596	+	17.8436i	−0.908368	+	0.659968i
$732$	38.3408	−	27.8562i	1.41712	−	1.02960i
$733$	−4.03200	−	12.4092i	−0.148925	−	0.458345i	0.848570	−	0.529084i	$-0.177464\pi$
$733$	−4.03200	−	12.4092i	−0.148925	−	0.458345i	−0.997495	+	0.0707389i	$0.977464\pi$
$734$	23.3513	−	71.8678i	0.861910	−	2.65269i
$735$	−0.932437	−	0.677455i	−0.0343934	−	0.0249883i
$736$	45.1401			1.66389
$737$	3.95229	−	2.08582i	0.145585	−	0.0768321i
$738$	−10.3128			−0.379618
$739$	1.46491	+	1.06432i	0.0538874	+	0.0391515i	0.614403	−	0.788992i	$-0.289397\pi$
$739$	1.46491	+	1.06432i	0.0538874	+	0.0391515i	−0.560515	+	0.828144i	$0.689397\pi$
$740$	0.166762	−	0.513240i	0.00613028	−	0.0188671i
$741$	2.43695	+	7.50017i	0.0895237	+	0.275525i
$742$	44.4628	−	32.3041i	1.63228	−	1.18592i
$743$	−3.14019	+	2.28148i	−0.115202	+	0.0836994i	−0.643895	−	0.765114i	$-0.722683\pi$
$743$	−3.14019	+	2.28148i	−0.115202	+	0.0836994i	0.528692	+	0.848814i	$0.322683\pi$
$744$	20.3882	+	62.7485i	0.747468	+	2.30047i
$745$	2.52368	−	7.76708i	0.0924603	−	0.284564i
$746$	−51.7159	−	37.5738i	−1.89345	−	1.37567i
$747$	13.2470			0.484684
$748$	101.279	+	14.5534i	3.70312	+	0.532123i
$749$	−16.7743			−0.612919
$750$	−7.57504	−	5.50359i	−0.276601	−	0.200963i
$751$	6.86981	−	21.1431i	0.250683	−	0.771522i	−0.743967	−	0.668217i	$-0.767058\pi$
$751$	6.86981	−	21.1431i	0.250683	−	0.771522i	0.994650	−	0.103306i	$-0.0329420\pi$
$752$	11.0430	+	33.9868i	0.402695	+	1.23937i
$753$	−19.3319	+	14.0455i	−0.704495	+	0.511846i
$754$	4.25566	−	3.09192i	0.154982	−	0.112601i
$755$	2.66806	+	8.21145i	0.0971007	+	0.298845i
$756$	2.84574	−	8.75828i	0.103498	−	0.318535i
$757$	−14.7200	−	10.6947i	−0.535007	−	0.388706i	0.287220	−	0.957865i	$-0.407269\pi$
$757$	−14.7200	−	10.6947i	−0.535007	−	0.388706i	−0.822227	+	0.569159i	$0.807269\pi$
$758$	54.7957			1.99027
$759$	3.06499	+	17.7024i	0.111252	+	0.642556i
$760$	20.1151			0.729653
$761$	−1.36962	−	0.995084i	−0.0496485	−	0.0360718i	0.562684	−	0.826672i	$-0.309769\pi$
$761$	−1.36962	−	0.995084i	−0.0496485	−	0.0360718i	−0.612333	+	0.790600i	$0.709769\pi$
$762$	−2.44383	+	7.52135i	−0.0885308	+	0.272470i
$763$	0.676556	+	2.08223i	0.0244930	+	0.0753817i
$764$	−55.6267	+	40.4152i	−2.01250	+	1.46217i
$765$	1.95419	−	1.41980i	0.0706540	−	0.0513331i
$766$	8.75704	+	26.9514i	0.316405	+	0.973793i
$767$	0.576886	−	1.77547i	0.0208302	−	0.0641086i
$768$	18.3526	+	13.3340i	0.662243	+	0.481148i
$769$	17.0462			0.614702			0.307351	−	0.951596i	$-0.400557\pi$
$769$	17.0462			0.614702			0.307351	+	0.951596i	$0.400557\pi$
$770$	4.43528	+	4.30969i	0.159837	+	0.155310i
$771$	−19.6461			−0.707536
$772$	0.966364	+	0.702104i	0.0347802	+	0.0252693i
$773$	10.7921	−	33.2147i	0.388165	−	1.19465i	−0.545993	−	0.837790i	$-0.683847\pi$
$773$	10.7921	−	33.2147i	0.388165	−	1.19465i	0.934158	−	0.356860i	$-0.116153\pi$
$774$	3.68598	+	11.3443i	0.132490	+	0.407761i
$775$	37.3673	−	27.1490i	1.34227	−	0.975219i
$776$	68.2161	−	49.5619i	2.44881	−	1.77917i
$777$	−0.190435	−	0.586100i	−0.00683183	−	0.0210262i
$778$	15.6178	−	48.0665i	0.559924	−	1.72327i
$779$	−25.4429	−	18.4854i	−0.911587	−	0.662306i
$780$	1.72038			0.0615994
$781$	6.88252	−	14.0012i	0.246276	−	0.501002i
$782$	92.1941			3.29685
$783$	−1.64565	−	1.19563i	−0.0588106	−	0.0427284i
$784$	−8.34299	+	25.6771i	−0.297964	+	0.917038i
$785$	−1.57991	−	4.86247i	−0.0563894	−	0.173549i
$786$	8.30483	−	6.03381i	0.296223	−	0.215219i
$787$	−31.1628	+	22.6411i	−1.11084	+	0.807069i	−0.982795	−	0.184700i	$-0.940869\pi$
$787$	−31.1628	+	22.6411i	−1.11084	+	0.807069i	−0.128040	+	0.991769i	$0.540869\pi$
$788$	−11.6232	−	35.7725i	−0.414058	−	1.27434i
$789$	0.867602	−	2.67021i	0.0308875	−	0.0950618i
$790$	2.93797	+	2.13456i	0.104528	+	0.0759443i
$791$	−5.03653			−0.179079
$792$	10.1684	−	20.6857i	0.361319	−	0.735035i
$793$	10.1104			0.359029
$794$	30.9742	+	22.5040i	1.09923	+	0.798639i
$795$	1.22688	−	3.77595i	0.0435130	−	0.133919i
$796$	−26.2216	−	80.7017i	−0.929399	−	2.86040i
$797$	23.3458	−	16.9617i	0.826952	−	0.600816i	−0.0917435	−	0.995783i	$-0.529244\pi$
$797$	23.3458	−	16.9617i	0.826952	−	0.600816i	0.918695	+	0.394967i	$0.129244\pi$
$798$	32.4136	−	23.5499i	1.14743	−	0.833657i
$799$	8.45366	+	26.0177i	0.299069	+	0.920440i
$800$	−12.5287	+	38.5593i	−0.442956	+	1.36328i
$801$	2.31487	+	1.68185i	0.0817917	+	0.0594252i
$802$	18.9070			0.667628
$803$	5.32910	+	5.17820i	0.188060	+	0.182735i
$804$	−6.31602			−0.222749
$805$	3.15986	+	2.29578i	0.111371	+	0.0809155i
$806$	−7.58644	+	23.3486i	−0.267221	+	0.822421i
$807$	−0.646851	−	1.99080i	−0.0227702	−	0.0700796i
$808$	−85.2829	+	61.9617i	−3.00024	+	2.17980i
$809$	−1.28031	+	0.930201i	−0.0450134	+	0.0327041i	−0.610064	−	0.792352i	$-0.708856\pi$
$809$	−1.28031	+	0.930201i	−0.0450134	+	0.0327041i	0.565051	+	0.825056i	$0.308856\pi$
$810$	−0.293291	−	0.902658i	−0.0103052	−	0.0317162i
$811$	−7.28405	+	22.4180i	−0.255778	+	0.787203i	0.737898	+	0.674912i	$0.235819\pi$
$811$	−7.28405	+	22.4180i	−0.255778	+	0.787203i	−0.993675	+	0.112290i	$0.964181\pi$
$812$	−15.1548	−	11.0106i	−0.531828	−	0.386396i
$813$	−5.91198			−0.207342
$814$	−0.458987	−	2.65096i	−0.0160875	−	0.0929161i
$815$	−3.68677			−0.129142
$816$	−45.7767	−	33.2587i	−1.60251	−	1.16429i
$817$	−11.2405	+	34.5948i	−0.393256	+	1.21032i
$818$	−21.4271	−	65.9458i	−0.749181	−	2.30574i
$819$	1.58940	−	1.15477i	0.0555381	−	0.0403508i
$820$	−5.55042	+	4.03262i	−0.193829	+	0.140825i
$821$	−15.7889	−	48.5933i	−0.551037	−	1.69592i	−0.706187	−	0.708025i	$-0.749586\pi$
$821$	−15.7889	−	48.5933i	−0.551037	−	1.69592i	0.155150	−	0.987891i	$-0.450414\pi$
$822$	−4.02002	+	12.3724i	−0.140214	+	0.431536i
$823$	13.3666	+	9.71141i	0.465931	+	0.338518i	0.795853	−	0.605490i	$-0.207023\pi$
$823$	13.3666	+	9.71141i	0.465931	+	0.338518i	−0.329923	+	0.944008i	$0.607023\pi$
$824$	107.201			3.73451
$825$	−15.9723	−	2.29516i	−0.556084	−	0.0799070i
$826$	−9.48448			−0.330007
$827$	3.54776	+	2.57760i	0.123368	+	0.0896319i	0.647758	−	0.761846i	$-0.275707\pi$
$827$	3.54776	+	2.57760i	0.123368	+	0.0896319i	−0.524390	+	0.851478i	$0.675707\pi$
$828$	7.84637	−	24.1486i	0.272680	−	0.839224i
$829$	−6.08621	−	18.7314i	−0.211383	−	0.650569i	−0.999391	−	0.0349039i	$-0.988887\pi$
$829$	−6.08621	−	18.7314i	−0.211383	−	0.650569i	0.788008	−	0.615665i	$-0.211113\pi$
$830$	10.1717	−	7.39017i	0.353065	−	0.256516i
$831$	−22.7717	+	16.5446i	−0.789942	+	0.573927i
$832$	−1.34581	−	4.14199i	−0.0466577	−	0.143598i
$833$	−6.38676	+	19.6564i	−0.221288	+	0.681055i
$834$	33.4821	+	24.3262i	1.15939	+	0.842347i
$835$	4.63234			0.160309
$836$	108.429	−	57.2232i	3.75009	−	1.97911i
$837$	9.49347			0.328142
$838$	−8.37273	−	6.08314i	−0.289231	−	0.210139i
$839$	8.85264	−	27.2456i	0.305627	−	0.940623i	−0.673815	−	0.738900i	$-0.735346\pi$
$839$	8.85264	−	27.2456i	0.305627	−	0.940623i	0.979442	−	0.201724i	$-0.0646543\pi$
$840$	−1.54852	−	4.76584i	−0.0534289	−	0.164437i
$841$	20.1140	−	14.6137i	0.693587	−	0.503921i
$842$	44.3566	−	32.2269i	1.52863	−	1.11061i
$843$	−4.54963	−	14.0023i	−0.156698	−	0.482266i
$844$	−4.62994	+	14.2495i	−0.159369	+	0.490488i
$845$	0.296923	+	0.215727i	0.0102145	+	0.00742124i
$846$	10.7490			0.369560
$847$	20.7362	+	6.08507i	0.712506	+	0.209086i
$848$	−93.0031			−3.19374
$849$	16.9802	+	12.3368i	0.582759	+	0.423399i
$850$	−25.5885	+	78.7534i	−0.877680	+	2.70122i
$851$	−0.525076	−	1.61602i	−0.0179994	−	0.0553963i
$852$	−17.8386	+	12.9605i	−0.611141	+	0.444020i
$853$	−41.3015	+	30.0073i	−1.41414	+	1.02743i	−0.421431	+	0.906861i	$0.638472\pi$
$853$	−41.3015	+	30.0073i	−1.41414	+	1.02743i	−0.992705	+	0.120569i	$0.961528\pi$
$854$	−15.8728	−	48.8516i	−0.543157	−	1.67167i
$855$	0.894403	−	2.75269i	0.0305879	−	0.0941400i
$856$	48.0063	+	34.8786i	1.64082	+	1.19213i
$857$	18.3951			0.628365			0.314183	−	0.949363i	$-0.398270\pi$
$857$	18.3951			0.628365			0.314183	+	0.949363i	$0.398270\pi$
$858$	7.58531	−	4.00314i	0.258958	−	0.136665i
$859$	19.9253			0.679843			0.339922	−	0.940454i	$-0.389599\pi$
$859$	19.9253			0.679843			0.339922	+	0.940454i	$0.389599\pi$
$860$	6.41979	+	4.66425i	0.218913	+	0.159050i
$861$	−2.42104	+	7.45119i	−0.0825088	+	0.253936i
$862$	−20.0154	−	61.6010i	−0.681726	−	2.09814i
$863$	−32.8451	+	23.8633i	−1.11806	+	0.812318i	−0.983914	−	0.178644i	$-0.942829\pi$
$863$	−32.8451	+	23.8633i	−1.11806	+	0.812318i	−0.134146	+	0.990962i	$0.542829\pi$
$864$	−6.74172	+	4.89815i	−0.229358	+	0.166638i
$865$	0.785010	+	2.41601i	0.0266912	+	0.0821469i
$866$	28.6439	−	88.1567i	0.973358	−	2.99569i
$867$	−21.2899	−	15.4680i	−0.723044	−	0.525322i
$868$	87.4253			2.96741
$869$	12.5612	+	1.80500i	0.426110	+	0.0612303i
$870$	−1.93062			−0.0654540
$871$	−1.09009	−	0.792000i	−0.0369364	−	0.0268359i
$872$	2.39332	−	7.36588i	0.0810481	−	0.249440i
$873$	−3.74921	−	11.5389i	−0.126891	−	0.390532i
$874$	89.3721	−	64.9326i	3.02306	−	2.19638i
$875$	−5.75479	+	4.18110i	−0.194547	+	0.141347i
$876$	−3.24522	−	9.98776i	−0.109646	−	0.337455i
$877$	−0.380096	+	1.16982i	−0.0128349	+	0.0395019i	−0.957269	−	0.289199i	$-0.906611\pi$
$877$	−0.380096	+	1.16982i	−0.0128349	+	0.0395019i	0.944434	+	0.328701i	$0.106611\pi$
$878$	−72.4346	−	52.6269i	−2.44455	−	1.77607i
$879$	14.7553			0.497684
$880$	−1.78538	−	10.3118i	−0.0601851	−	0.347609i
$881$	−26.1169			−0.879902			−0.439951	−	0.898022i	$-0.645004\pi$
$881$	−26.1169			−0.879902			−0.439951	+	0.898022i	$0.645004\pi$
$882$	6.56997	+	4.77336i	0.221222	+	0.160727i
$883$	5.10544	−	15.7129i	0.171812	−	0.528782i	−0.827662	−	0.561227i	$-0.810329\pi$
$883$	5.10544	−	15.7129i	0.171812	−	0.528782i	0.999474	+	0.0324453i	$0.0103295\pi$
$884$	−9.53329	−	29.3405i	−0.320639	−	0.986826i
$885$	−0.554309	+	0.402729i	−0.0186329	+	0.0135376i
$886$	−72.9885	+	53.0292i	−2.45210	+	1.78155i
$887$	1.02813	+	3.16425i	0.0345212	+	0.106245i	0.966832	−	0.255412i	$-0.0822111\pi$
$887$	1.02813	+	3.16425i	0.0345212	+	0.106245i	−0.932311	+	0.361657i	$0.882211\pi$
$888$	−0.673666	+	2.07333i	−0.0226068	+	0.0695764i
$889$	4.86062	+	3.53145i	0.163020	+	0.118441i
$890$	2.71572			0.0910311
$891$	−2.37864	−	2.31129i	−0.0796876	−	0.0774311i
$892$	120.809			4.04499
$893$	26.5193	+	19.2674i	0.887433	+	0.644758i
$894$	−17.7819	+	54.7270i	−0.594715	+	1.83034i
$895$	1.34424	+	4.13715i	0.0449331	+	0.138290i
$896$	8.58909	−	6.24034i	0.286941	−	0.208475i
$897$	4.38235	−	3.18396i	0.146322	−	0.106309i
$898$	−18.9795	−	58.4128i	−0.633353	−	1.94926i
$899$	5.96742	−	18.3658i	0.199024	−	0.612534i
$900$	18.4503	+	13.4050i	0.615011	+	0.446832i
$901$	−71.1962			−2.37189
$902$	−15.0889	+	30.6954i	−0.502404	+	1.02205i
$903$	9.06181			0.301558
$904$	14.4141	+	10.4724i	0.479404	+	0.348308i
$905$	−0.222951	+	0.686173i	−0.00741115	+	0.0228092i
$906$	−18.7992	−	57.8581i	−0.624563	−	1.92221i
$907$	−28.9559	+	21.0377i	−0.961463	+	0.698544i	−0.953490	−	0.301424i	$-0.902538\pi$
$907$	−28.9559	+	21.0377i	−0.961463	+	0.698544i	−0.00797332	+	0.999968i	$0.502538\pi$
$908$	−30.1870	+	21.9322i	−1.00179	+	0.727845i
$909$	4.68721	+	14.4258i	0.155465	+	0.478472i
$910$	0.576201	−	1.77337i	0.0191009	−	0.0587865i
$911$	15.6616	+	11.3788i	0.518892	+	0.376997i	0.816186	−	0.577789i	$-0.196084\pi$
$911$	15.6616	+	11.3788i	0.518892	+	0.376997i	−0.297294	+	0.954786i	$0.596084\pi$
$912$	−67.7998			−2.24508
$913$	19.3821	−	39.4292i	0.641453	−	1.30491i
$914$	−100.998			−3.34072
$915$	−3.00200	−	2.18108i	−0.0992430	−	0.0721043i
$916$	−2.66186	+	8.19238i	−0.0879505	+	0.270684i
$917$	−2.40991	−	7.41693i	−0.0795821	−	0.244929i
$918$	−13.7693	+	10.0040i	−0.454454	+	0.330180i
$919$	−40.4317	+	29.3753i	−1.33372	+	0.969003i	−0.334068	+	0.942549i	$0.608421\pi$
$919$	−40.4317	+	29.3753i	−1.33372	+	0.969003i	−0.999650	+	0.0264536i	$0.991579\pi$
$920$	−4.26963	−	13.1406i	−0.140765	−	0.433232i
$921$	−4.06473	+	12.5099i	−0.133937	+	0.412217i
$922$	−3.48549	−	2.53236i	−0.114788	−	0.0833987i
$923$	−4.70399			−0.154834
$924$	−21.9049	−	21.2847i	−0.720619	−	0.700214i
$925$	1.52616			0.0501798
$926$	−49.4709	−	35.9427i	−1.62571	−	1.18115i
$927$	4.76659	−	14.6700i	0.156555	−	0.481828i
$928$	5.23811	+	16.1212i	0.171949	+	0.529206i
$929$	−40.9762	+	29.7709i	−1.34438	+	0.976753i	−0.345114	+	0.938561i	$0.612160\pi$
$929$	−40.9762	+	29.7709i	−1.34438	+	0.976753i	−0.999270	+	0.0381920i	$0.987840\pi$
$930$	7.28953	−	5.29615i	0.239033	−	0.173668i
$931$	7.65283	+	23.5530i	0.250811	+	0.771918i
$932$	−12.9008	+	39.7046i	−0.422580	+	1.30057i
$933$	24.3263	+	17.6741i	0.796409	+	0.578625i
$934$	7.90076			0.258521
$935$	−1.36675	−	7.89391i	−0.0446975	−	0.258158i
$936$	−6.94980			−0.227161
$937$	−19.9591	−	14.5011i	−0.652034	−	0.473730i	0.211929	−	0.977285i	$-0.432025\pi$
$937$	−19.9591	−	14.5011i	−0.652034	−	0.473730i	−0.863963	+	0.503555i	$0.832025\pi$
$938$	−2.11541	+	6.51056i	−0.0690706	+	0.212577i
$939$	−2.26621	−	6.97469i	−0.0739551	−	0.227610i
$940$	5.78523	−	4.20322i	0.188693	−	0.137094i
$941$	11.7505	−	8.53723i	0.383055	−	0.278306i	−0.379549	−	0.925172i	$-0.623921\pi$
$941$	11.7505	−	8.53723i	0.383055	−	0.278306i	0.762604	+	0.646866i	$0.223921\pi$
$942$	11.1321	+	34.2610i	0.362703	+	1.11629i
$943$	−6.67538	+	20.5447i	−0.217380	+	0.669028i
$944$	12.9846	+	9.43389i	0.422614	+	0.307047i
$945$	−0.721044			−0.0234555
$946$	39.1587	+	5.62695i	1.27316	+	0.182948i
$947$	−4.33880			−0.140992			−0.0704960	−	0.997512i	$-0.522458\pi$
$947$	−4.33880			−0.140992			−0.0704960	+	0.997512i	$0.522458\pi$
$948$	−14.5100	−	10.5422i	−0.471264	−	0.342393i
$949$	0.692320	−	2.13074i	0.0224737	−	0.0691668i
$950$	30.6610	+	94.3650i	0.994776	+	3.06160i
$951$	15.4275	−	11.2087i	0.500271	−	0.363468i
$952$	−72.6989	+	52.8189i	−2.35619	+	1.71187i
$953$	14.7581	+	45.4208i	0.478062	+	1.47132i	0.841783	+	0.539816i	$0.181506\pi$
$953$	14.7581	+	45.4208i	0.478062	+	1.47132i	−0.363720	+	0.931508i	$0.618494\pi$
$954$	−8.64463	+	26.6054i	−0.279880	+	0.861383i
$955$	4.35545	+	3.16442i	0.140939	+	0.102398i
$956$	25.4319			0.822527
$957$	−5.96653	+	3.14883i	−0.192871	+	0.101787i
$958$	−34.6494			−1.11947
$959$	7.99555	+	5.80911i	0.258190	+	0.187586i
$960$	−0.493937	+	1.52018i	−0.0159418	+	0.0490637i
$961$	18.2709	+	56.2321i	0.589385	+	1.81394i
$962$	−0.656264	+	0.476804i	−0.0211588	+	0.0153728i
$963$	6.90759	−	5.01866i	0.222594	−	0.161724i
$964$	15.5111	+	47.7383i	0.499579	+	1.53755i
$965$	0.0289011	−	0.0889484i	0.000930359	−	0.00286335i
$966$	−22.2645	−	16.1761i	−0.716348	−	0.520457i
$967$	2.53359			0.0814748			0.0407374	−	0.999170i	$-0.487029\pi$
$967$	2.53359			0.0814748			0.0407374	+	0.999170i	$0.487029\pi$
$968$	−46.6924	−	60.5316i	−1.50075	−	1.94556i
$969$	−51.9024			−1.66735
$970$	−9.31605	−	6.76850i	−0.299120	−	0.217324i
$971$	11.1371	−	34.2764i	0.357406	−	1.09998i	−0.597195	−	0.802096i	$-0.703718\pi$
$971$	11.1371	−	34.2764i	0.357406	−	1.09998i	0.954601	−	0.297887i	$-0.0962818\pi$
$972$	1.44850	+	4.45804i	0.0464608	+	0.142992i
$973$	25.4365	−	18.4807i	0.815457	−	0.592464i
$974$	−8.78653	+	6.38379i	−0.281539	+	0.204550i
$975$	1.50346	+	4.62717i	0.0481493	+	0.148188i
$976$	−26.8604	+	82.6679i	−0.859781	+	2.64613i
$977$	−5.25187	−	3.81571i	−0.168022	−	0.122075i	0.500596	−	0.865681i	$-0.333114\pi$
$977$	−5.25187	−	3.81571i	−0.168022	−	0.122075i	−0.668619	+	0.743606i	$0.733114\pi$
$978$	25.9770			0.830654
$979$	8.39288	−	4.42933i	0.268238	−	0.141562i
$980$	5.40255			0.172578
$981$	−0.901580	−	0.655036i	−0.0287852	−	0.0209137i
$982$	−31.7607	+	97.7493i	−1.01352	+	3.11930i
$983$	0.413437	+	1.27243i	0.0131866	+	0.0405842i	0.957433	−	0.288655i	$-0.0932079\pi$
$983$	0.413437	+	1.27243i	0.0131866	+	0.0405842i	−0.944247	+	0.329239i	$0.893208\pi$
$984$	22.4220	−	16.2905i	0.714787	−	0.519323i
$985$	−2.38259	+	1.73105i	−0.0759156	+	0.0551559i
$986$	10.6983	+	32.9260i	0.340704	+	1.04858i
$987$	2.52346	−	7.76642i	0.0803227	−	0.247208i
$988$	−29.9061	−	21.7280i	−0.951439	−	0.691261i
$989$	24.9855			0.794494
$990$	−3.11584	−	0.447733i	−0.0990279	−	0.0142299i
$991$	−12.0631			−0.383196			−0.191598	−	0.981473i	$-0.561367\pi$
$991$	−12.0631			−0.383196			−0.191598	+	0.981473i	$0.561367\pi$
$992$	−64.0023	−	46.5004i	−2.03208	−	1.47639i
$993$	−5.48495	+	16.8809i	−0.174059	+	0.535700i
$994$	7.38506	+	22.7289i	0.234240	+	0.720917i
$995$	−5.37506	+	3.90521i	−0.170401	+	0.123803i
$996$	−50.2358	+	36.4985i	−1.59178	+	1.15650i
$997$	−1.45434	−	4.47600i	−0.0460594	−	0.141756i	0.925382	−	0.379036i	$-0.123744\pi$
$997$	−1.45434	−	4.47600i	−0.0460594	−	0.141756i	−0.971441	+	0.237280i	$0.923744\pi$
$998$	21.3392	−	65.6752i	0.675479	−	2.07891i
$999$	0.253774	+	0.184378i	0.00802907	+	0.00583346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.235.1	yes	36
11.3	even	5	inner	429.2.n.d.157.1	✓	36
11.5	even	5		4719.2.a.bq.1.17		18
11.6	odd	10		4719.2.a.br.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.1	✓	36	11.3	even	5	inner
429.2.n.d.235.1	yes	36	1.1	even	1	trivial
4719.2.a.bq.1.17		18	11.5	even	5
4719.2.a.br.1.2		18	11.6	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.09213 - 1.52002i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.44850 + 4.45804i) q^{4} +(0.296923 - 0.215727i) q^{5} +(-2.09213 + 1.52002i) q^{6} +(0.607096 + 1.86845i) q^{7} +(2.14760 - 6.60965i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.09213 - 1.52002i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.44850 + 4.45804i) q^{4} +(0.296923 - 0.215727i) q^{5} +(-2.09213 + 1.52002i) q^{6} +(0.607096 + 1.86845i) q^{7} +(2.14760 - 6.60965i) q^{8} +(-0.809017 - 0.587785i) q^{9} -0.949111 q^{10} +(-2.93321 + 1.54800i) q^{11} +4.68746 q^{12} +(0.809017 + 0.587785i) q^{13} +(1.56996 - 4.83183i) q^{14} +(-0.113415 - 0.349054i) q^{15} +(-6.95539 + 5.05339i) q^{16} +(-5.32452 + 3.86849i) q^{17} +(0.799122 + 2.45944i) q^{18} +(-2.43695 + 7.50017i) q^{19} +(1.39181 + 1.01121i) q^{20} +1.96460 q^{21} +(8.48963 + 1.21992i) q^{22} +5.41688 q^{23} +(-5.62250 - 4.08499i) q^{24} +(-1.50346 + 4.62717i) q^{25} +(-0.799122 - 2.45944i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-7.45024 + 5.41291i) q^{28} +(0.628581 + 1.93457i) q^{29} +(-0.293291 + 0.902658i) q^{30} +(-7.68038 - 5.58012i) q^{31} +8.33323 q^{32} +(0.565822 + 3.26800i) q^{33} +17.0198 q^{34} +(0.583336 + 0.423819i) q^{35} +(1.44850 - 4.45804i) q^{36} +(-0.0969332 - 0.298330i) q^{37} +(16.4988 - 11.9871i) q^{38} +(0.809017 - 0.587785i) q^{39} +(-0.788208 - 2.42585i) q^{40} +(-1.23233 + 3.79272i) q^{41} +(-4.11020 - 2.98624i) q^{42} +4.61254 q^{43} +(-11.1498 - 10.8341i) q^{44} -0.367017 q^{45} +(-11.3328 - 8.23376i) q^{46} +(1.28446 - 3.95317i) q^{47} +(2.65672 + 8.17655i) q^{48} +(2.54058 - 1.84584i) q^{49} +(10.1788 - 7.39535i) q^{50} +(2.03379 + 6.25935i) q^{51} +(-1.44850 + 4.45804i) q^{52} +(8.75168 + 6.35846i) q^{53} +2.58601 q^{54} +(-0.536992 + 1.09241i) q^{55} +13.6536 q^{56} +(6.38002 + 4.63536i) q^{57} +(1.62552 - 5.00283i) q^{58} +(-0.576886 - 1.77547i) q^{59} +(1.39181 - 1.01121i) q^{60} +(8.17945 - 5.94272i) q^{61} +(7.58644 + 23.3486i) q^{62} +(0.607096 - 1.86845i) q^{63} +(-3.52339 - 2.55989i) q^{64} +0.367017 q^{65} +(3.78366 - 7.69714i) q^{66} -1.34743 q^{67} +(-24.9585 - 18.1334i) q^{68} +(1.67391 - 5.15176i) q^{69} +(-0.576201 - 1.77337i) q^{70} +(-3.80561 + 2.76494i) q^{71} +(-5.62250 + 4.08499i) q^{72} +(-0.692320 - 2.13074i) q^{73} +(-0.250670 + 0.771484i) q^{74} +(3.93611 + 2.85975i) q^{75} -36.9659 q^{76} +(-4.67309 - 4.54077i) q^{77} -2.58601 q^{78} +(-3.09550 - 2.24901i) q^{79} +(-0.975063 + 3.00094i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.34320 - 6.06169i) q^{82} +(-10.7171 + 7.78641i) q^{83} +(2.84574 + 8.75828i) q^{84} +(-0.746435 + 2.29729i) q^{85} +(-9.65001 - 7.01114i) q^{86} +2.03413 q^{87} +(3.93235 + 22.7120i) q^{88} -2.86133 q^{89} +(0.767847 + 0.557873i) q^{90} +(-0.607096 + 1.86845i) q^{91} +(7.84637 + 24.1486i) q^{92} +(-7.68038 + 5.58012i) q^{93} +(-8.69616 + 6.31813i) q^{94} +(0.894403 + 2.75269i) q^{95} +(2.57511 - 7.92537i) q^{96} +(9.81555 + 7.13142i) q^{97} -8.12093 q^{98} +(3.28290 + 0.471740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more