LMFDB - Embedded newform 561.2.m.d.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(103,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("561.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.m (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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			256.1
Character	$\chi$	$=$	561.256
Dual form			561.2.m.d.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80508 + 1.31147i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.920329 - 2.83248i) q^{4} +(0.625886 + 0.454733i) q^{5} +(-1.80508 - 1.31147i) q^{6} +(-0.926218 + 2.85061i) q^{7} +(0.674481 + 2.07584i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.80508 + 1.31147i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.920329 - 2.83248i) q^{4} +(0.625886 + 0.454733i) q^{5} +(-1.80508 - 1.31147i) q^{6} +(-0.926218 + 2.85061i) q^{7} +(0.674481 + 2.07584i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.72614 q^{10} +(-3.25702 - 0.625976i) q^{11} +2.97825 q^{12} +(1.11980 - 0.813579i) q^{13} +(-2.06658 - 6.36027i) q^{14} +(-0.239067 + 0.735773i) q^{15} +(0.879025 + 0.638649i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.689478 - 2.12200i) q^{18} +(1.40514 + 4.32458i) q^{19} +(1.86404 - 1.35431i) q^{20} -2.99730 q^{21} +(6.70011 - 3.14153i) q^{22} -8.15616 q^{23} +(-1.76581 + 1.28294i) q^{24} +(-1.36013 - 4.18606i) q^{25} +(-0.954337 + 2.93715i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(7.22186 + 5.24699i) q^{28} +(-2.31559 + 7.12667i) q^{29} +(-0.533407 - 1.64166i) q^{30} +(-2.20308 + 1.60063i) q^{31} -6.78961 q^{32} +(-0.411134 - 3.29104i) q^{33} +2.23120 q^{34} +(-1.87597 + 1.36297i) q^{35} +(0.920329 + 2.83248i) q^{36} +(1.63432 - 5.02991i) q^{37} +(-8.20793 - 5.96341i) q^{38} +(1.11980 + 0.813579i) q^{39} +(-0.521804 + 1.60595i) q^{40} +(1.06083 + 3.26490i) q^{41} +(5.41037 - 3.93086i) q^{42} -8.13536 q^{43} +(-4.77059 + 8.64934i) q^{44} -0.773638 q^{45} +(14.7225 - 10.6965i) q^{46} +(-2.92230 - 8.99392i) q^{47} +(-0.335758 + 1.03336i) q^{48} +(-1.60495 - 1.16607i) q^{49} +(7.94502 + 5.77240i) q^{50} +(0.309017 - 0.951057i) q^{51} +(-1.27387 - 3.92056i) q^{52} +(5.67160 - 4.12066i) q^{53} +2.23120 q^{54} +(-1.75387 - 1.87286i) q^{55} -6.54211 q^{56} +(-3.67871 + 2.67274i) q^{57} +(-5.16655 - 15.9010i) q^{58} +(1.62381 - 4.99757i) q^{59} +(1.86404 + 1.35431i) q^{60} +(4.24357 + 3.08313i) q^{61} +(1.87755 - 5.77852i) q^{62} +(-0.926218 - 2.85061i) q^{63} +(10.4977 - 7.62704i) q^{64} +1.07083 q^{65} +(5.05822 + 5.40140i) q^{66} +2.54301 q^{67} +(-2.40945 + 1.75057i) q^{68} +(-2.52039 - 7.75697i) q^{69} +(1.59878 - 4.92054i) q^{70} +(10.2237 + 7.42796i) q^{71} +(-1.76581 - 1.28294i) q^{72} +(3.17535 - 9.77274i) q^{73} +(3.64649 + 11.2227i) q^{74} +(3.56088 - 2.58713i) q^{75} +13.5425 q^{76} +(4.80112 - 8.70468i) q^{77} -3.08830 q^{78} +(-12.4204 + 9.02392i) q^{79} +(0.259755 + 0.799443i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.19669 - 4.50216i) q^{82} +(-6.07142 - 4.41114i) q^{83} +(-2.75851 + 8.48981i) q^{84} +(-0.239067 - 0.735773i) q^{85} +(14.6850 - 10.6692i) q^{86} -7.49342 q^{87} +(-0.897369 - 7.18325i) q^{88} -16.9530 q^{89} +(1.39648 - 1.01460i) q^{90} +(1.28202 + 3.94565i) q^{91} +(-7.50636 + 23.1022i) q^{92} +(-2.20308 - 1.60063i) q^{93} +(17.0702 + 12.4022i) q^{94} +(-1.08707 + 3.34566i) q^{95} +(-2.09810 - 6.45730i) q^{96} +(-3.43730 + 2.49734i) q^{97} +4.42632 q^{98} +(3.00292 - 1.40800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.80508	+	1.31147i	−1.27638	+	0.927346i	−0.999437	−	0.0335394i	$-0.989322\pi$
$2$	−1.80508	+	1.31147i	−1.27638	+	0.927346i	−0.276945	+	0.960886i	$0.589322\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.920329	−	2.83248i	0.460165	−	1.41624i
$5$	0.625886	+	0.454733i	0.279905	+	0.203363i	0.718876	−	0.695138i	$-0.244657\pi$
$5$	0.625886	+	0.454733i	0.279905	+	0.203363i	−0.438971	+	0.898501i	$0.644657\pi$
$6$	−1.80508	−	1.31147i	−0.736920	−	0.535404i
$7$	−0.926218	+	2.85061i	−0.350077	+	1.07743i	0.608732	+	0.793376i	$0.291679\pi$
$7$	−0.926218	+	2.85061i	−0.350077	+	1.07743i	−0.958809	+	0.284051i	$0.908321\pi$
$8$	0.674481	+	2.07584i	0.238465	+	0.733920i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.72614			−0.545853
$11$	−3.25702	−	0.625976i	−0.982027	−	0.188739i
$11$	−3.25702	−	0.625976i	−0.982027	−	0.188739i
$12$	2.97825			0.859746
$13$	1.11980	−	0.813579i	0.310575	−	0.225646i	−0.421568	−	0.906797i	$-0.638520\pi$
$13$	1.11980	−	0.813579i	0.310575	−	0.225646i	0.732143	+	0.681151i	$0.238520\pi$
$14$	−2.06658	−	6.36027i	−0.552316	−	1.69985i
$15$	−0.239067	+	0.735773i	−0.0617269	+	0.189976i
$16$	0.879025	+	0.638649i	0.219756	+	0.159662i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	0.689478	−	2.12200i	0.162512	−	0.500159i
$19$	1.40514	+	4.32458i	0.322362	+	0.992127i	0.972618	+	0.232412i	$0.0746617\pi$
$19$	1.40514	+	4.32458i	0.322362	+	0.992127i	−0.650256	+	0.759715i	$0.725338\pi$
$20$	1.86404	−	1.35431i	0.416813	−	0.302832i
$21$	−2.99730			−0.654065
$22$	6.70011	−	3.14153i	1.42847	−	0.669776i
$23$	−8.15616			−1.70068			−0.850339	−	0.526236i	$-0.823603\pi$
$23$	−8.15616			−1.70068			−0.850339	+	0.526236i	$0.823603\pi$
$24$	−1.76581	+	1.28294i	−0.360445	+	0.261879i
$25$	−1.36013	−	4.18606i	−0.272027	−	0.837212i
$26$	−0.954337	+	2.93715i	−0.187161	+	0.576022i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	7.22186	+	5.24699i	1.36480	+	0.991588i
$29$	−2.31559	+	7.12667i	−0.429995	+	1.32339i	0.468134	+	0.883657i	$0.344926\pi$
$29$	−2.31559	+	7.12667i	−0.429995	+	1.32339i	−0.898129	+	0.439732i	$0.855074\pi$
$30$	−0.533407	−	1.64166i	−0.0973863	−	0.299724i
$31$	−2.20308	+	1.60063i	−0.395684	+	0.287481i	−0.767781	−	0.640713i	$-0.778639\pi$
$31$	−2.20308	+	1.60063i	−0.395684	+	0.287481i	0.372097	+	0.928194i	$0.378639\pi$
$32$	−6.78961			−1.20024
$33$	−0.411134	−	3.29104i	−0.0715693	−	0.572897i
$34$	2.23120			0.382647
$35$	−1.87597	+	1.36297i	−0.317097	+	0.230385i
$36$	0.920329	+	2.83248i	0.153388	+	0.472080i
$37$	1.63432	−	5.02991i	0.268680	−	0.826912i	−0.722143	−	0.691744i	$-0.756843\pi$
$37$	1.63432	−	5.02991i	0.268680	−	0.826912i	0.990823	−	0.135168i	$-0.0431574\pi$
$38$	−8.20793	−	5.96341i	−1.33150	−	0.967393i
$39$	1.11980	+	0.813579i	0.179311	+	0.130277i
$40$	−0.521804	+	1.60595i	−0.0825045	+	0.253923i
$41$	1.06083	+	3.26490i	0.165674	+	0.509892i	0.999085	−	0.0427612i	$-0.0136155\pi$
$41$	1.06083	+	3.26490i	0.165674	+	0.509892i	−0.833411	+	0.552653i	$0.813615\pi$
$42$	5.41037	−	3.93086i	0.834838	−	0.606545i
$43$	−8.13536			−1.24063			−0.620315	−	0.784353i	$-0.712995\pi$
$43$	−8.13536			−1.24063			−0.620315	+	0.784353i	$0.712995\pi$
$44$	−4.77059	+	8.64934i	−0.719194	+	1.30394i
$45$	−0.773638			−0.115327
$46$	14.7225	−	10.6965i	2.17072	−	1.57712i
$47$	−2.92230	−	8.99392i	−0.426261	−	1.31190i	−0.901781	−	0.432193i	$-0.857740\pi$
$47$	−2.92230	−	8.99392i	−0.426261	−	1.31190i	0.475520	−	0.879705i	$-0.342260\pi$
$48$	−0.335758	+	1.03336i	−0.0484624	+	0.149152i
$49$	−1.60495	−	1.16607i	−0.229279	−	0.166581i
$50$	7.94502	+	5.77240i	1.12360	+	0.816340i
$51$	0.309017	−	0.951057i	0.0432710	−	0.133175i
$52$	−1.27387	−	3.92056i	−0.176654	−	0.543684i
$53$	5.67160	−	4.12066i	0.779054	−	0.566015i	−0.125641	−	0.992076i	$-0.540099\pi$
$53$	5.67160	−	4.12066i	0.779054	−	0.566015i	0.904695	+	0.426060i	$0.140099\pi$
$54$	2.23120			0.303628
$55$	−1.75387	−	1.87286i	−0.236492	−	0.252537i
$56$	−6.54211			−0.874227
$57$	−3.67871	+	2.67274i	−0.487257	+	0.354013i
$58$	−5.16655	−	15.9010i	−0.678402	−	2.08791i
$59$	1.62381	−	4.99757i	0.211402	−	0.650628i	−0.787988	−	0.615691i	$-0.788877\pi$
$59$	1.62381	−	4.99757i	0.211402	−	0.650628i	0.999390	−	0.0349371i	$-0.0111231\pi$
$60$	1.86404	+	1.35431i	0.240647	+	0.174840i
$61$	4.24357	+	3.08313i	0.543333	+	0.394755i	0.825321	−	0.564663i	$-0.190994\pi$
$61$	4.24357	+	3.08313i	0.543333	+	0.394755i	−0.281988	+	0.959418i	$0.590994\pi$
$62$	1.87755	−	5.77852i	0.238450	−	0.733872i
$63$	−0.926218	−	2.85061i	−0.116692	−	0.359143i
$64$	10.4977	−	7.62704i	1.31221	−	0.953380i
$65$	1.07083			0.132820
$66$	5.05822	+	5.40140i	0.622624	+	0.664866i
$67$	2.54301			0.310679			0.155339	−	0.987861i	$-0.450353\pi$
$67$	2.54301			0.310679			0.155339	+	0.987861i	$0.450353\pi$
$68$	−2.40945	+	1.75057i	−0.292189	+	0.212288i
$69$	−2.52039	−	7.75697i	−0.303420	−	0.933830i
$70$	1.59878	−	4.92054i	0.191091	−	0.588118i
$71$	10.2237	+	7.42796i	1.21333	+	0.881537i	0.995529	−	0.0944556i	$-0.0301111\pi$
$71$	10.2237	+	7.42796i	1.21333	+	0.881537i	0.217803	+	0.975993i	$0.430111\pi$
$72$	−1.76581	−	1.28294i	−0.208103	−	0.151196i
$73$	3.17535	−	9.77274i	0.371647	−	1.14381i	−0.574066	−	0.818809i	$-0.694635\pi$
$73$	3.17535	−	9.77274i	0.371647	−	1.14381i	0.945713	−	0.325003i	$-0.105365\pi$
$74$	3.64649	+	11.2227i	0.423895	+	1.30462i
$75$	3.56088	−	2.58713i	0.411174	−	0.298736i
$76$	13.5425			1.55343
$77$	4.80112	−	8.70468i	0.547138	−	0.991990i
$78$	−3.08830			−0.349681
$79$	−12.4204	+	9.02392i	−1.39740	+	1.01527i	−0.402392	+	0.915467i	$0.631821\pi$
$79$	−12.4204	+	9.02392i	−1.39740	+	1.01527i	−0.995007	+	0.0998029i	$0.968179\pi$
$80$	0.259755	+	0.799443i	0.0290415	+	0.0893805i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−6.19669	−	4.50216i	−0.684310	−	0.497180i
$83$	−6.07142	−	4.41114i	−0.666425	−	0.484186i	0.202402	−	0.979303i	$-0.435125\pi$
$83$	−6.07142	−	4.41114i	−0.666425	−	0.484186i	−0.868826	+	0.495117i	$0.835125\pi$
$84$	−2.75851	+	8.48981i	−0.300978	+	0.926314i
$85$	−0.239067	−	0.735773i	−0.0259305	−	0.0798058i
$86$	14.6850	−	10.6692i	1.58352	−	1.15049i
$87$	−7.49342			−0.803379
$88$	−0.897369	−	7.18325i	−0.0956599	−	0.765737i
$89$	−16.9530			−1.79702			−0.898510	−	0.438954i	$-0.855349\pi$
$89$	−16.9530			−1.79702			−0.898510	+	0.438954i	$0.855349\pi$
$90$	1.39648	−	1.01460i	0.147202	−	0.106948i
$91$	1.28202	+	3.94565i	0.134392	+	0.413616i
$92$	−7.50636	+	23.1022i	−0.782592	+	2.40857i
$93$	−2.20308	−	1.60063i	−0.228448	−	0.165977i
$94$	17.0702	+	12.4022i	1.76066	+	1.27919i
$95$	−1.08707	+	3.34566i	−0.111531	+	0.343257i
$96$	−2.09810	−	6.45730i	−0.214137	−	0.659045i
$97$	−3.43730	+	2.49734i	−0.349005	+	0.253567i	−0.748451	−	0.663190i	$-0.769202\pi$
$97$	−3.43730	+	2.49734i	−0.349005	+	0.253567i	0.399447	+	0.916756i	$0.369202\pi$
$98$	4.42632			0.447126
$99$	3.00292	−	1.40800i	0.301805	−	0.141509i
$100$	−13.1087			−1.31087
$101$	−9.50556	+	6.90620i	−0.945839	+	0.687192i	−0.949819	−	0.312800i	$-0.898733\pi$
$101$	−9.50556	+	6.90620i	−0.945839	+	0.687192i	0.00398024	+	0.999992i	$0.498733\pi$
$102$	0.689478	+	2.12200i	0.0682685	+	0.210109i
$103$	−2.80822	+	8.64283i	−0.276703	+	0.851603i	0.712061	+	0.702117i	$0.247762\pi$
$103$	−2.80822	+	8.64283i	−0.276703	+	0.851603i	−0.988764	+	0.149486i	$0.952238\pi$
$104$	2.44414	+	1.77577i	0.239668	+	0.174129i
$105$	−1.87597	−	1.36297i	−0.183076	−	0.133013i
$106$	−4.83357	+	14.8762i	−0.469478	+	1.44490i
$107$	0.118073	+	0.363391i	0.0114145	+	0.0351304i	0.956602	−	0.291399i	$-0.0941208\pi$
$107$	0.118073	+	0.363391i	0.0114145	+	0.0351304i	−0.945187	+	0.326529i	$0.894121\pi$
$108$	−2.40945	+	1.75057i	−0.231850	+	0.168449i
$109$	−5.43227			−0.520317			−0.260158	−	0.965566i	$-0.583775\pi$
$109$	−5.43227			−0.520317			−0.260158	+	0.965566i	$0.583775\pi$
$110$	5.62207	+	1.08052i	0.536043	+	0.103024i
$111$	5.28876			0.501987
$112$	−2.63471	+	1.91423i	−0.248956	+	0.180877i
$113$	1.15637	+	3.55894i	0.108782	+	0.334797i	0.990600	−	0.136794i	$-0.0436798\pi$
$113$	1.15637	+	3.55894i	0.108782	+	0.334797i	−0.881817	+	0.471591i	$0.843680\pi$
$114$	3.13515	−	9.64900i	0.293634	−	0.903712i
$115$	−5.10483	−	3.70888i	−0.476028	−	0.345855i
$116$	18.0551	+	13.1178i	1.67637	+	1.21795i
$117$	−0.427724	+	1.31640i	−0.0395431	+	0.121701i
$118$	3.62304	+	11.1506i	0.333528	+	1.02649i
$119$	2.42487	−	1.76177i	0.222287	−	0.161501i
$120$	−1.68859			−0.154147
$121$	10.2163	+	4.07763i	0.928755	+	0.370694i
$122$	−11.7034			−1.05958
$123$	−2.77729	+	2.01782i	−0.250420	+	0.181941i
$124$	2.50620	+	7.71328i	0.225063	+	0.692673i
$125$	2.24759	−	6.91736i	0.201030	−	0.618708i
$126$	5.41037	+	3.93086i	0.481994	+	0.350189i
$127$	12.3800	+	8.99461i	1.09855	+	0.798143i	0.980822	−	0.194904i	$-0.0624394\pi$
$127$	12.3800	+	8.99461i	1.09855	+	0.798143i	0.117727	+	0.993046i	$0.462439\pi$
$128$	−4.75039	+	14.6202i	−0.419879	+	1.29225i
$129$	−2.51396	−	7.73719i	−0.221342	−	0.681221i
$130$	−1.93292	+	1.40435i	−0.169529	+	0.123170i
$131$	2.34085			0.204521			0.102261	−	0.994758i	$-0.467392\pi$
$131$	2.34085			0.204521			0.102261	+	0.994758i	$0.467392\pi$
$132$	−9.70020	−	1.86431i	−0.844294	−	0.162268i
$133$	−13.6291			−1.18180
$134$	−4.59034	+	3.33508i	−0.396545	+	0.288107i
$135$	−0.239067	−	0.735773i	−0.0205756	−	0.0633253i
$136$	0.674481	−	2.07584i	0.0578363	−	0.178002i
$137$	17.2501	+	12.5329i	1.47378	+	1.07076i	0.979497	+	0.201459i	$0.0645683\pi$
$137$	17.2501	+	12.5329i	1.47378	+	1.07076i	0.494280	+	0.869303i	$0.335432\pi$
$138$	14.7225	+	10.6965i	1.25326	+	0.910549i
$139$	−0.203632	+	0.626715i	−0.0172719	+	0.0531573i	−0.959321	−	0.282318i	$-0.908897\pi$
$139$	−0.203632	+	0.626715i	−0.0172719	+	0.0531573i	0.942049	+	0.335475i	$0.108897\pi$
$140$	2.13409	+	6.56804i	0.180363	+	0.555101i
$141$	7.65068	−	5.55855i	0.644304	−	0.468114i
$142$	−28.1961			−2.36617
$143$	−4.15647	+	1.94888i	−0.347582	+	0.162973i
$144$	−1.08653			−0.0905446
$145$	−4.69003	+	3.40751i	−0.389486	+	0.282978i
$146$	7.08485	+	21.8049i	0.586346	+	1.80459i
$147$	0.613038	−	1.88674i	0.0505625	−	0.155615i
$148$	−12.7430	−	9.25835i	−1.04747	−	0.761032i
$149$	9.52457	+	6.92000i	0.780283	+	0.566909i	0.905064	−	0.425275i	$-0.139823\pi$
$149$	9.52457	+	6.92000i	0.780283	+	0.566909i	−0.124781	+	0.992184i	$0.539823\pi$
$150$	−3.03473	+	9.33993i	−0.247785	+	0.762602i
$151$	−2.45171	−	7.54558i	−0.199517	−	0.614051i	−0.999894	−	0.0145535i	$-0.995367\pi$
$151$	−2.45171	−	7.54558i	−0.199517	−	0.614051i	0.800377	−	0.599497i	$-0.204633\pi$
$152$	−8.02939	+	5.83369i	−0.651270	+	0.473175i
$153$	1.00000			0.0808452
$154$	2.74950	+	22.0091i	0.221561	+	1.77355i
$155$	−2.10673			−0.169217
$156$	3.33503	−	2.42304i	0.267016	−	0.193999i
$157$	2.02584	+	6.23489i	0.161680	+	0.497598i	0.998776	−	0.0494565i	$-0.0157489\pi$
$157$	2.02584	+	6.23489i	0.161680	+	0.497598i	−0.837097	+	0.547055i	$0.815749\pi$
$158$	10.5852	−	32.5778i	0.842110	−	2.59175i
$159$	5.67160	+	4.12066i	0.449787	+	0.326789i
$160$	−4.24952	−	3.08746i	−0.335954	−	0.244085i
$161$	7.55438	−	23.2500i	0.595369	−	1.83236i
$162$	0.689478	+	2.12200i	0.0541705	+	0.166720i
$163$	−16.3357	+	11.8686i	−1.27951	+	0.929621i	−0.999538	−	0.0303857i	$-0.990326\pi$
$163$	−16.3357	+	11.8686i	−1.27951	+	0.929621i	−0.279976	+	0.960007i	$0.590326\pi$
$164$	10.2241			0.798367
$165$	1.23922	−	2.24678i	0.0964734	−	0.174911i
$166$	16.7444			1.29962
$167$	−6.23235	+	4.52807i	−0.482273	+	0.350392i	−0.802205	−	0.597048i	$-0.796340\pi$
$167$	−6.23235	+	4.52807i	−0.482273	+	0.350392i	0.319932	+	0.947441i	$0.396340\pi$
$168$	−2.02162	−	6.22192i	−0.155972	−	0.480032i
$169$	−3.42519	+	10.5416i	−0.263476	+	0.810896i
$170$	1.39648	+	1.01460i	0.107105	+	0.0778162i
$171$	−3.67871	−	2.67274i	−0.281318	−	0.204389i
$172$	−7.48721	+	23.0433i	−0.570894	+	1.75703i
$173$	6.89071	+	21.2074i	0.523891	+	1.61237i	0.766499	+	0.642246i	$0.221997\pi$
$173$	6.89071	+	21.2074i	0.523891	+	1.61237i	−0.242608	+	0.970124i	$0.578003\pi$
$174$	13.5262	−	9.82737i	1.02542	−	0.745011i
$175$	13.1926			0.997266
$176$	−2.46322	−	2.63034i	−0.185672	−	0.198269i
$177$	5.25476			0.394972
$178$	30.6016	−	22.2333i	2.29368	−	1.66646i
$179$	7.86023	+	24.1913i	0.587501	+	1.80814i	0.588985	+	0.808144i	$0.299528\pi$
$179$	7.86023	+	24.1913i	0.587501	+	1.80814i	−0.00148364	+	0.999999i	$0.500472\pi$
$180$	−0.712002	+	2.19132i	−0.0530695	+	0.163331i
$181$	6.38443	+	4.63856i	0.474551	+	0.344781i	0.799212	−	0.601049i	$-0.205250\pi$
$181$	6.38443	+	4.63856i	0.474551	+	0.344781i	−0.324661	+	0.945830i	$0.605250\pi$
$182$	−7.48873	−	5.44088i	−0.555101	−	0.403305i
$183$	−1.62090	+	4.98861i	−0.119820	+	0.368769i
$184$	−5.50118	−	16.9309i	−0.405552	−	1.24816i
$185$	3.31016	−	2.40497i	0.243368	−	0.176817i
$186$	6.07589			0.445506
$187$	2.26704	+	2.42085i	0.165783	+	0.177030i
$188$	−28.1646			−2.05411
$189$	2.42487	−	1.76177i	0.176383	−	0.128150i
$190$	−2.42547	−	7.46483i	−0.175962	−	0.541556i
$191$	2.00128	−	6.15930i	0.144807	−	0.445671i	−0.852179	−	0.523251i	$-0.824719\pi$
$191$	2.00128	−	6.15930i	0.144807	−	0.445671i	0.996986	+	0.0775794i	$0.0247191\pi$
$192$	10.4977	+	7.62704i	0.757608	+	0.550434i
$193$	−9.50532	−	6.90602i	−0.684208	−	0.497106i	0.190543	−	0.981679i	$-0.438975\pi$
$193$	−9.50532	−	6.90602i	−0.684208	−	0.497106i	−0.874751	+	0.484573i	$0.838975\pi$
$194$	2.92941	−	9.01579i	0.210319	−	0.647296i
$195$	0.330903	+	1.01842i	0.0236965	+	0.0729303i
$196$	−4.77995	+	3.47284i	−0.341425	+	0.248060i
$197$	−6.47335			−0.461207			−0.230604	−	0.973048i	$-0.574070\pi$
$197$	−6.47335			−0.461207			−0.230604	+	0.973048i	$0.574070\pi$
$198$	−3.57396	+	6.47978i	−0.253990	+	0.460498i
$199$	−15.6905			−1.11227			−0.556136	−	0.831091i	$-0.687717\pi$
$199$	−15.6905			−1.11227			−0.556136	+	0.831091i	$0.687717\pi$
$200$	7.77220	−	5.64683i	0.549578	−	0.399292i
$201$	0.785834	+	2.41855i	0.0554285	+	0.170591i
$202$	8.10104	−	24.9324i	0.569987	−	1.75424i
$203$	−18.1706	−	13.2017i	−1.27532	−	0.926577i
$204$	−2.40945	−	1.75057i	−0.168695	−	0.122564i
$205$	−0.820699	+	2.52585i	−0.0573201	+	0.176413i
$206$	−6.26571	−	19.2839i	−0.436553	−	1.34357i
$207$	6.59847	−	4.79407i	0.458626	−	0.333211i
$208$	1.50392			0.104278
$209$	−1.86948	−	14.9648i	−0.129315	−	1.03514i
$210$	5.17377			0.357024
$211$	7.83123	−	5.68972i	0.539124	−	0.391696i	−0.284636	−	0.958636i	$-0.591873\pi$
$211$	7.83123	−	5.68972i	0.539124	−	0.391696i	0.823760	+	0.566939i	$0.191873\pi$
$212$	−6.45195	−	19.8571i	−0.443122	−	1.36379i
$213$	−3.90511	+	12.0187i	−0.267574	+	0.823508i
$214$	−0.689706	−	0.501101i	−0.0471474	−	0.0342546i
$215$	−5.09181	−	3.69942i	−0.347259	−	0.252298i
$216$	0.674481	−	2.07584i	0.0458926	−	0.141243i
$217$	−2.52223	−	7.76263i	−0.171220	−	0.526962i
$218$	9.80566	−	7.12423i	0.664123	−	0.482514i
$219$	10.2757			0.694365
$220$	−6.91899	+	3.24415i	−0.466478	+	0.218721i
$221$	−1.38414			−0.0931076
$222$	−9.54663	+	6.93603i	−0.640728	+	0.465516i
$223$	−4.73706	−	14.5792i	−0.317217	−	0.976293i	−0.974832	−	0.222939i	$-0.928435\pi$
$223$	−4.73706	−	14.5792i	−0.317217	−	0.976293i	0.657615	−	0.753354i	$-0.271565\pi$
$224$	6.28866	−	19.3545i	0.420178	−	1.29318i
$225$	3.56088	+	2.58713i	0.237392	+	0.172475i
$226$	−6.75477	−	4.90763i	−0.449321	−	0.326451i
$227$	−6.91162	+	21.2718i	−0.458741	+	1.41186i	0.407946	+	0.913006i	$0.366245\pi$
$227$	−6.91162	+	21.2718i	−0.458741	+	1.41186i	−0.866687	+	0.498852i	$0.833755\pi$
$228$	4.18486	+	12.8797i	0.277149	+	0.852977i
$229$	−8.29381	+	6.02580i	−0.548070	+	0.398196i	−0.827073	−	0.562094i	$-0.809996\pi$
$229$	−8.29381	+	6.02580i	−0.548070	+	0.398196i	0.279003	+	0.960290i	$0.409996\pi$
$230$	14.0787			0.928321
$231$	9.76227	+	1.87624i	0.642310	+	0.123448i
$232$	−16.3556			−1.07380
$233$	10.0457	−	7.29863i	0.658116	−	0.478149i	−0.207910	−	0.978148i	$-0.566666\pi$
$233$	10.0457	−	7.29863i	0.658116	−	0.478149i	0.866026	+	0.499999i	$0.166666\pi$
$234$	−0.954337	−	2.93715i	−0.0623870	−	0.192007i
$235$	2.26080	−	6.95804i	0.147479	−	0.453892i
$236$	−12.6611	−	9.19882i	−0.824167	−	0.598792i
$237$	−12.4204	−	9.02392i	−0.806789	−	0.586167i
$238$	−2.06658	+	6.36027i	−0.133956	+	0.412275i
$239$	−0.324102	−	0.997482i	−0.0209644	−	0.0645218i	0.940027	−	0.341100i	$-0.110799\pi$
$239$	−0.324102	−	0.997482i	−0.0209644	−	0.0645218i	−0.960991	+	0.276578i	$0.910799\pi$
$240$	−0.680047	+	0.494083i	−0.0438969	+	0.0318929i
$241$	−6.06097			−0.390421			−0.195211	−	0.980761i	$-0.562539\pi$
$241$	−6.06097			−0.390421			−0.195211	+	0.980761i	$0.562539\pi$
$242$	−23.7889	+	6.03790i	−1.52921	+	0.388131i
$243$	1.00000			0.0641500
$244$	12.6384	−	9.18233i	0.809091	−	0.587839i
$245$	−0.474269	−	1.45965i	−0.0303000	−	0.0932537i
$246$	2.36692	−	7.28464i	0.150910	−	0.464452i
$247$	5.09186	+	3.69945i	0.323987	+	0.235391i
$248$	−4.80858	−	3.49364i	−0.305345	−	0.221846i
$249$	2.31907	−	7.13738i	0.146965	−	0.452313i
$250$	5.01481	+	15.4340i	0.317165	+	0.976133i
$251$	20.1411	−	14.6334i	1.27130	−	0.923651i	0.272043	−	0.962285i	$-0.412301\pi$
$251$	20.1411	−	14.6334i	1.27130	−	0.923651i	0.999253	+	0.0386338i	$0.0123006\pi$
$252$	−8.92672			−0.562330
$253$	26.5648	+	5.10557i	1.67011	+	0.320984i
$254$	−34.1430			−2.14232
$255$	0.625886	−	0.454733i	0.0391945	−	0.0284765i
$256$	−2.57952	−	7.93895i	−0.161220	−	0.496184i
$257$	−3.05436	+	9.40034i	−0.190526	+	0.586377i	−1.00000		0.000778229i	$-0.999752\pi$
$257$	−3.05436	+	9.40034i	−0.190526	+	0.586377i	0.809474	+	0.587155i	$0.199752\pi$
$258$	14.6850	+	10.6692i	0.914245	+	0.664238i
$259$	12.8246	+	9.31759i	0.796879	+	0.578967i
$260$	0.985513	−	3.03310i	0.0611189	−	0.188105i
$261$	−2.31559	−	7.12667i	−0.143332	−	0.441130i
$262$	−4.22542	+	3.06995i	−0.261048	+	0.189662i
$263$	8.99231			0.554490			0.277245	−	0.960799i	$-0.410579\pi$
$263$	8.99231			0.554490			0.277245	+	0.960799i	$0.410579\pi$
$264$	6.55437	−	3.07319i	0.403394	−	0.189142i
$265$	5.42357			0.333167
$266$	24.6017	−	17.8742i	1.50842	−	1.09593i
$267$	−5.23878	−	16.1233i	−0.320608	−	0.986730i
$268$	2.34041	−	7.20304i	0.142963	−	0.439996i
$269$	−0.663862	−	0.482324i	−0.0404764	−	0.0294078i	0.567363	−	0.823468i	$-0.307964\pi$
$269$	−0.663862	−	0.482324i	−0.0404764	−	0.0294078i	−0.607840	+	0.794060i	$0.707964\pi$
$270$	1.39648	+	1.01460i	0.0849869	+	0.0617466i
$271$	−2.86504	+	8.81768i	−0.174039	+	0.535636i	−0.999588	−	0.0286938i	$-0.990865\pi$
$271$	−2.86504	+	8.81768i	−0.174039	+	0.535636i	0.825550	+	0.564329i	$0.190865\pi$
$272$	−0.335758	−	1.03336i	−0.0203583	−	0.0626564i
$273$	−3.35637	+	2.43854i	−0.203137	+	0.147587i
$274$	−47.5743			−2.87407
$275$	1.80960	+	14.4855i	0.109123	+	0.873507i
$276$	−24.2911			−1.46215
$277$	3.47768	−	2.52668i	0.208953	−	0.151814i	−0.478387	−	0.878149i	$-0.658778\pi$
$277$	3.47768	−	2.52668i	0.208953	−	0.151814i	0.687340	+	0.726336i	$0.258778\pi$
$278$	−0.454344	−	1.39833i	−0.0272497	−	0.0838660i
$279$	0.841500	−	2.58987i	0.0503793	−	0.155052i
$280$	−4.09462	−	2.97491i	−0.244700	−	0.177785i
$281$	−4.54932	−	3.30527i	−0.271390	−	0.197176i	0.443763	−	0.896144i	$-0.353643\pi$
$281$	−4.54932	−	3.30527i	−0.271390	−	0.197176i	−0.715153	+	0.698968i	$0.753643\pi$
$282$	−6.52023	+	20.0672i	−0.388274	+	1.19499i
$283$	5.56048	+	17.1134i	0.330536	+	1.01729i	0.968879	+	0.247534i	$0.0796203\pi$
$283$	5.56048	+	17.1134i	0.330536	+	1.01729i	−0.638343	+	0.769752i	$0.720380\pi$
$284$	30.4488	−	22.1223i	1.80680	−	1.31272i
$285$	−3.51784			−0.208379
$286$	4.94688	−	8.96895i	0.292515	−	0.530345i
$287$	−10.2895			−0.607370
$288$	5.49291	−	3.99083i	0.323673	−	0.235162i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	3.99704	−	12.3016i	0.234714	−	0.722377i
$291$	−3.43730	−	2.49734i	−0.201498	−	0.146397i
$292$	−24.7587	−	17.9883i	−1.44890	−	1.05268i
$293$	6.01957	−	18.5263i	0.351667	−	1.08232i	−0.606249	−	0.795275i	$-0.707327\pi$
$293$	6.01957	−	18.5263i	0.351667	−	1.08232i	0.957917	−	0.287046i	$-0.0926733\pi$
$294$	1.36781	+	4.20968i	0.0797723	+	0.245514i
$295$	3.28888	−	2.38951i	0.191486	−	0.139123i
$296$	11.5436			0.670958
$297$	2.26704	+	2.42085i	0.131547	+	0.140472i
$298$	−26.2679			−1.52166
$299$	−9.13324	+	6.63569i	−0.528189	+	0.383752i
$300$	−4.05081	−	12.4671i	−0.233874	−	0.719790i
$301$	7.53512	−	23.1907i	0.434317	−	1.33669i
$302$	14.3213	+	10.4050i	0.824098	+	0.598742i
$303$	−9.50556	−	6.90620i	−0.546080	−	0.396751i
$304$	−1.52673	+	4.69881i	−0.0875643	+	0.269495i
$305$	1.25399	+	3.85938i	0.0718032	+	0.220988i
$306$	−1.80508	+	1.31147i	−0.103189	+	0.0749715i
$307$	26.2133			1.49607			0.748035	−	0.663659i	$-0.230998\pi$
$307$	26.2133			1.49607			0.748035	+	0.663659i	$0.230998\pi$
$308$	−20.2372	−	21.6103i	−1.15312	−	1.23136i
$309$	−9.08761			−0.516976
$310$	3.80282	−	2.76291i	0.215986	−	0.156923i
$311$	7.99905	+	24.6185i	0.453585	+	1.39599i	0.872789	+	0.488098i	$0.162309\pi$
$311$	7.99905	+	24.6185i	0.453585	+	1.39599i	−0.419204	+	0.907892i	$0.637691\pi$
$312$	−0.933578	+	2.87326i	−0.0528535	+	0.162666i
$313$	−9.35345	−	6.79568i	−0.528688	−	0.384114i	0.291179	−	0.956669i	$-0.405953\pi$
$313$	−9.35345	−	6.79568i	−0.528688	−	0.384114i	−0.819867	+	0.572554i	$0.805953\pi$
$314$	−11.8336	−	8.59764i	−0.667811	−	0.485193i
$315$	0.716557	−	2.20534i	0.0403734	−	0.124257i
$316$	14.1293	+	43.4854i	0.794834	+	2.44625i
$317$	−12.1686	+	8.84101i	−0.683457	+	0.496561i	−0.874503	−	0.485020i	$-0.838812\pi$
$317$	−12.1686	+	8.84101i	−0.683457	+	0.496561i	0.191046	+	0.981581i	$0.438812\pi$
$318$	−15.6418			−0.877147
$319$	12.0031	−	21.7622i	0.672042	−	1.21845i
$320$	10.0386			0.561177
$321$	−0.309119	+	0.224588i	−0.0172533	+	0.0125353i
$322$	16.8553	+	51.8754i	0.939311	+	2.89090i
$323$	1.40514	−	4.32458i	0.0781842	−	0.240626i
$324$	−2.40945	−	1.75057i	−0.133859	−	0.0972539i
$325$	−4.92876	−	3.58096i	−0.273399	−	0.198636i
$326$	13.9220	−	42.8475i	0.771069	−	2.37311i
$327$	−1.67866	−	5.16639i	−0.0928302	−	0.285702i
$328$	−6.06190	+	4.40423i	−0.334712	+	0.243183i
$329$	28.3448			1.56270
$330$	0.709676	+	5.68080i	0.0390664	+	0.312718i
$331$	−29.4093			−1.61648			−0.808241	−	0.588852i	$-0.799580\pi$
$331$	−29.4093			−1.61648			−0.808241	+	0.588852i	$0.799580\pi$
$332$	−18.0822	+	13.1375i	−0.992389	+	0.721013i
$333$	1.63432	+	5.02991i	0.0895600	+	0.275637i
$334$	5.31147	−	16.3470i	0.290631	−	0.894469i
$335$	1.59164	+	1.15639i	0.0869604	+	0.0631805i
$336$	−2.63471	−	1.91423i	−0.143735	−	0.104430i
$337$	5.04619	−	15.5306i	0.274884	−	0.846005i	−0.714367	−	0.699772i	$-0.753285\pi$
$337$	5.04619	−	15.5306i	0.274884	−	0.846005i	0.989250	−	0.146233i	$-0.0467150\pi$
$338$	−7.64228	−	23.5205i	−0.415685	−	1.27935i
$339$	−3.02742	+	2.19955i	−0.164427	+	0.119463i
$340$	−2.30409			−0.124957
$341$	8.17741	−	3.83420i	0.442832	−	0.207634i
$342$	10.1456			0.548609
$343$	−12.1636	+	8.83734i	−0.656770	+	0.477172i
$344$	−5.48714	−	16.8877i	−0.295847	−	0.910523i
$345$	1.94987	−	6.00109i	0.104978	−	0.323088i
$346$	−40.2511	−	29.2441i	−2.16391	−	1.57217i
$347$	−11.8356	−	8.59908i	−0.635369	−	0.461623i	0.222887	−	0.974844i	$-0.428452\pi$
$347$	−11.8356	−	8.59908i	−0.635369	−	0.461623i	−0.858256	+	0.513222i	$0.828452\pi$
$348$	−6.89642	+	21.2250i	−0.369687	+	1.13778i
$349$	−6.16344	−	18.9691i	−0.329921	−	1.01539i	−0.969170	−	0.246393i	$-0.920754\pi$
$349$	−6.16344	−	18.9691i	−0.329921	−	1.01539i	0.639248	−	0.769000i	$-0.279246\pi$
$350$	−23.8136	+	17.3016i	−1.27289	+	0.924811i
$351$	−1.38414			−0.0738801
$352$	22.1139	+	4.25013i	1.17867	+	0.226533i
$353$	19.3070			1.02761			0.513805	−	0.857907i	$-0.328236\pi$
$353$	19.3070			1.02761			0.513805	+	0.857907i	$0.328236\pi$
$354$	−9.48524	+	6.89143i	−0.504135	+	0.366276i
$355$	3.02114	+	9.29812i	0.160346	+	0.493493i
$356$	−15.6024	+	48.0192i	−0.826925	+	2.54501i
$357$	2.42487	+	1.76177i	0.128338	+	0.0932428i
$358$	−45.9144	−	33.3588i	−2.42665	−	1.76307i
$359$	−5.12538	+	15.7743i	−0.270507	+	0.832536i	0.719866	+	0.694113i	$0.244203\pi$
$359$	−5.12538	+	15.7743i	−0.270507	+	0.832536i	−0.990373	+	0.138423i	$0.955797\pi$
$360$	−0.521804	−	1.60595i	−0.0275015	−	0.0846409i
$361$	−1.35625	+	0.985376i	−0.0713818	+	0.0518619i
$362$	−17.6077			−0.925440
$363$	−0.721044	+	10.9763i	−0.0378450	+	0.576109i
$364$	12.3559			0.647623
$365$	6.43140	−	4.67268i	0.336635	−	0.244579i
$366$	−3.61655	−	11.1306i	−0.189040	−	0.581805i
$367$	1.87154	−	5.76000i	0.0976934	−	0.300669i	−0.890253	−	0.455467i	$-0.849472\pi$
$367$	1.87154	−	5.76000i	0.0976934	−	0.300669i	0.987946	+	0.154797i	$0.0494724\pi$
$368$	−7.16947	−	5.20893i	−0.373735	−	0.271534i
$369$	−2.77729	−	2.01782i	−0.144580	−	0.105044i
$370$	−2.82106	+	8.68233i	−0.146660	+	0.451373i
$371$	6.49323	+	19.9841i	0.337112	+	1.03752i
$372$	−6.56131	+	4.76707i	−0.340188	+	0.247161i
$373$	1.05138			0.0544384			0.0272192	−	0.999629i	$-0.491335\pi$
$373$	1.05138			0.0544384			0.0272192	+	0.999629i	$0.491335\pi$
$374$	−7.26705	−	1.39668i	−0.375770	−	0.0722205i
$375$	7.27335			0.375594
$376$	16.6989	−	12.1324i	0.861179	−	0.625683i
$377$	3.20512	+	9.86433i	0.165072	+	0.508039i
$378$	−2.06658	+	6.36027i	−0.106293	+	0.327137i
$379$	7.20654	+	5.23585i	0.370175	+	0.268948i	0.757283	−	0.653086i	$-0.226526\pi$
$379$	7.20654	+	5.23585i	0.370175	+	0.268948i	−0.387109	+	0.922034i	$0.626526\pi$
$380$	8.47606	+	6.15822i	0.434813	+	0.315910i
$381$	−4.72875	+	14.5536i	−0.242261	+	0.745603i
$382$	4.46525	+	13.7426i	0.228462	+	0.703134i
$383$	17.7408	−	12.8894i	0.906512	−	0.658619i	−0.0336186	−	0.999435i	$-0.510703\pi$
$383$	17.7408	−	12.8894i	0.906512	−	0.658619i	0.940130	+	0.340816i	$0.110703\pi$
$384$	−15.3726			−0.784479
$385$	6.96326	−	3.26491i	0.354881	−	0.166395i
$386$	26.2148			1.33430
$387$	6.58164	−	4.78184i	0.334564	−	0.243075i
$388$	3.91023	+	12.0345i	0.198512	+	0.610957i
$389$	−0.891189	+	2.74280i	−0.0451851	+	0.139065i	−0.971104	−	0.238657i	$-0.923293\pi$
$389$	−0.891189	+	2.74280i	−0.0451851	+	0.139065i	0.925919	+	0.377723i	$0.123293\pi$
$390$	−1.93292	−	1.40435i	−0.0978774	−	0.0711121i
$391$	6.59847	+	4.79407i	0.333699	+	0.242447i
$392$	1.33806	−	4.11812i	0.0675821	−	0.207996i
$393$	0.723364	+	2.22629i	0.0364889	+	0.112301i
$394$	11.6849	−	8.48958i	0.588677	−	0.427699i
$395$	−11.8772			−0.597607
$396$	−1.22446	−	9.80154i	−0.0615315	−	0.492546i
$397$	−6.04844			−0.303562			−0.151781	−	0.988414i	$-0.548501\pi$
$397$	−6.04844			−0.303562			−0.151781	+	0.988414i	$0.548501\pi$
$398$	28.3226	−	20.5776i	1.41968	−	1.03146i
$399$	−4.21164	−	12.9621i	−0.210846	−	0.648916i
$400$	1.47783	−	4.54830i	0.0738916	−	0.227415i
$401$	16.2406	+	11.7995i	0.811015	+	0.589237i	0.914125	−	0.405433i	$-0.132879\pi$
$401$	16.2406	+	11.7995i	0.811015	+	0.589237i	−0.103110	+	0.994670i	$0.532879\pi$
$402$	−4.59034	−	3.33508i	−0.228945	−	0.166338i
$403$	−1.16476	+	3.58475i	−0.0580207	+	0.178569i
$404$	10.8134	+	33.2803i	0.537988	+	1.65576i
$405$	0.625886	−	0.454733i	0.0311005	−	0.0225959i
$406$	50.1129			2.48706
$407$	−8.47160	+	15.3595i	−0.419922	+	0.761340i
$408$	2.18267			0.108058
$409$	−19.6765	+	14.2958i	−0.972940	+	0.706882i	−0.956120	−	0.292976i	$-0.905354\pi$
$409$	−19.6765	+	14.2958i	−0.972940	+	0.706882i	−0.0168203	+	0.999859i	$0.505354\pi$
$410$	−1.83114	−	5.63568i	−0.0904337	−	0.278326i
$411$	−6.58896	+	20.2787i	−0.325009	+	1.00028i
$412$	21.8962	+	15.9085i	1.07875	+	0.783755i
$413$	12.7421	+	9.25768i	0.626998	+	0.455541i
$414$	−5.62350	+	17.3073i	−0.276380	+	0.850610i
$415$	−1.79412	−	5.52175i	−0.0880701	−	0.271052i
$416$	−7.60297	+	5.52388i	−0.372766	+	0.270831i
$417$	−0.658967			−0.0322698
$418$	23.0004	+	24.5609i	1.12499	+	1.20131i
$419$	16.9180			0.826500			0.413250	−	0.910618i	$-0.364394\pi$
$419$	16.9180			0.826500			0.413250	+	0.910618i	$0.364394\pi$
$420$	−5.58711	+	4.05927i	−0.272623	+	0.198072i
$421$	−4.40896	−	13.5694i	−0.214879	−	0.661331i	−0.999162	−	0.0409274i	$-0.986969\pi$
$421$	−4.40896	−	13.5694i	−0.214879	−	0.661331i	0.784283	−	0.620404i	$-0.213031\pi$
$422$	−6.67410	+	20.5408i	−0.324890	+	0.999909i
$423$	7.65068	+	5.55855i	0.371989	+	0.270266i
$424$	12.3792	+	8.99401i	0.601187	+	0.436788i
$425$	−1.36013	+	4.18606i	−0.0659762	+	0.203054i
$426$	−8.71308	−	26.8161i	−0.422150	−	1.29924i
$427$	−12.7193	+	9.24109i	−0.615528	+	0.447208i
$428$	1.13797			0.0550056
$429$	−3.13791	−	3.35081i	−0.151500	−	0.161778i
$430$	14.0428			0.677203
$431$	26.6102	−	19.3334i	1.28177	−	0.931257i	0.282161	−	0.959367i	$-0.408949\pi$
$431$	26.6102	−	19.3334i	1.28177	−	0.931257i	0.999605	+	0.0281096i	$0.00894874\pi$
$432$	−0.335758	−	1.03336i	−0.0161541	−	0.0497174i
$433$	−3.22037	+	9.91128i	−0.154761	+	0.476306i	−0.998137	−	0.0610190i	$-0.980565\pi$
$433$	−3.22037	+	9.91128i	−0.154761	+	0.476306i	0.843376	+	0.537325i	$0.180565\pi$
$434$	14.7332	+	10.7043i	0.707219	+	0.513824i
$435$	−4.69003	−	3.40751i	−0.224870	−	0.163377i
$436$	−4.99947	+	15.3868i	−0.239431	+	0.736894i
$437$	−11.4606	−	35.2720i	−0.548233	−	1.68729i
$438$	−18.5484	+	13.4762i	−0.886275	+	0.643917i
$439$	23.6745			1.12992			0.564962	−	0.825117i	$-0.308891\pi$
$439$	23.6745			1.12992			0.564962	+	0.825117i	$0.308891\pi$
$440$	2.70481	−	4.90396i	0.128947	−	0.233787i
$441$	1.98383			0.0944682
$442$	2.49849	−	1.81526i	0.118841	−	0.0863430i
$443$	5.40866	+	16.6462i	0.256973	+	0.790883i	0.993434	+	0.114403i	$0.0364954\pi$
$443$	5.40866	+	16.6462i	0.256973	+	0.790883i	−0.736461	+	0.676480i	$0.763505\pi$
$444$	4.86740	−	14.9803i	0.230997	−	0.710935i
$445$	−10.6107	−	7.70911i	−0.502994	−	0.365447i
$446$	27.6708	+	20.1040i	1.31025	+	0.951954i
$447$	−3.63806	+	11.1968i	−0.172074	+	0.529591i
$448$	12.0185	+	36.9892i	0.567821	+	1.74757i
$449$	5.75161	−	4.17879i	0.271435	−	0.197209i	−0.443738	−	0.896157i	$-0.646348\pi$
$449$	5.75161	−	4.17879i	0.271435	−	0.197209i	0.715173	+	0.698947i	$0.246348\pi$
$450$	−9.82059			−0.462947
$451$	−1.41139	−	11.2979i	−0.0664599	−	0.531997i
$452$	11.1449			0.524211
$453$	6.41865	−	4.66342i	0.301575	−	0.219107i
$454$	−15.4212	−	47.4616i	−0.723753	−	2.22748i
$455$	−0.991818	+	3.05250i	−0.0464972	+	0.143104i
$456$	−8.02939	−	5.83369i	−0.376011	−	0.273188i
$457$	−23.7350	−	17.2445i	−1.11028	−	0.806663i	−0.127569	−	0.991830i	$-0.540717\pi$
$457$	−23.7350	−	17.2445i	−1.11028	−	0.806663i	−0.982707	+	0.185167i	$0.940717\pi$
$458$	7.06833	−	21.7541i	0.330282	−	1.01650i
$459$	0.309017	+	0.951057i	0.0144237	+	0.0443915i
$460$	−15.2035	+	11.0460i	−0.708865	+	0.515020i
$461$	2.58547			0.120417			0.0602087	−	0.998186i	$-0.480823\pi$
$461$	2.58547			0.120417			0.0602087	+	0.998186i	$0.480823\pi$
$462$	−20.0823	+	9.41612i	−0.934312	+	0.438077i
$463$	17.3700			0.807253			0.403627	−	0.914924i	$-0.367749\pi$
$463$	17.3700			0.807253			0.403627	+	0.914924i	$0.367749\pi$
$464$	−6.58691	+	4.78567i	−0.305789	+	0.222169i
$465$	−0.651016	−	2.00362i	−0.0301902	−	0.0929158i
$466$	−8.56138	+	26.3492i	−0.396598	+	1.22060i
$467$	−29.6308	−	21.5280i	−1.37115	−	0.996198i	−0.997646	−	0.0685681i	$-0.978157\pi$
$467$	−29.6308	−	21.5280i	−1.37115	−	0.996198i	−0.373502	−	0.927629i	$-0.621843\pi$
$468$	3.33503	+	2.42304i	0.154162	+	0.112005i
$469$	−2.35538	+	7.24913i	−0.108762	+	0.334734i
$470$	5.04430	+	15.5248i	0.232676	+	0.716104i
$471$	−5.30371	+	3.85337i	−0.244382	+	0.177554i
$472$	11.4694			0.527921
$473$	26.4970	+	5.09254i	1.21833	+	0.234155i
$474$	34.2543			1.57335
$475$	16.1918	−	11.7640i	0.742930	−	0.539770i
$476$	−2.75851	−	8.48981i	−0.126436	−	0.389130i
$477$	−2.16636	+	6.66736i	−0.0991907	+	0.305277i
$478$	1.89319	+	1.37548i	0.0865926	+	0.0629132i
$479$	11.1267	+	8.08401i	0.508391	+	0.369368i	0.812213	−	0.583361i	$-0.198263\pi$
$479$	11.1267	+	8.08401i	0.508391	+	0.369368i	−0.303822	+	0.952729i	$0.598263\pi$
$480$	1.62317	−	4.99561i	0.0740874	−	0.228017i
$481$	−2.26213	−	6.96212i	−0.103144	−	0.317445i
$482$	10.9405	−	7.94875i	0.498327	−	0.362056i
$483$	24.4465			1.11235
$484$	20.9522	−	25.1847i	0.952372	−	1.14476i
$485$	−3.28698			−0.149254
$486$	−1.80508	+	1.31147i	−0.0818800	+	0.0594893i
$487$	12.4805	+	38.4110i	0.565546	+	1.74057i	0.666324	+	0.745662i	$0.267867\pi$
$487$	12.4805	+	38.4110i	0.565546	+	1.74057i	−0.100779	+	0.994909i	$0.532133\pi$
$488$	−3.53788	+	10.8885i	−0.160152	+	0.492898i
$489$	−16.3357	−	11.8686i	−0.738728	−	0.536717i
$490$	2.77038	+	2.01280i	0.125153	+	0.0909288i
$491$	−0.198459	+	0.610794i	−0.00895633	+	0.0275648i	−0.955435	−	0.295202i	$-0.904613\pi$
$491$	−0.198459	+	0.610794i	−0.00895633	+	0.0275648i	0.946478	+	0.322767i	$0.104613\pi$
$492$	3.15942	+	9.72369i	0.142438	+	0.438378i
$493$	6.06231	−	4.40452i	0.273033	−	0.198370i
$494$	−14.0429			−0.631820
$495$	2.51975	+	0.484279i	0.113254	+	0.0217667i
$496$	−2.95880			−0.132854
$497$	−30.6436	+	22.2639i	−1.37455	+	0.998671i
$498$	5.17432	+	15.9249i	0.231867	+	0.713612i
$499$	2.45618	−	7.55935i	0.109954	−	0.338403i	−0.880907	−	0.473289i	$-0.843067\pi$
$499$	2.45618	−	7.55935i	0.109954	−	0.338403i	0.990861	+	0.134886i	$0.0430667\pi$
$500$	−17.5248	−	12.7325i	−0.783732	−	0.569415i
$501$	−6.23235	−	4.52807i	−0.278441	−	0.202299i
$502$	−17.1651	+	52.8288i	−0.766117	+	2.35786i
$503$	3.03600	+	9.34384i	0.135369	+	0.416621i	0.995647	−	0.0932027i	$-0.0297105\pi$
$503$	3.03600	+	9.34384i	0.135369	+	0.416621i	−0.860279	+	0.509824i	$0.829710\pi$
$504$	5.29268	−	3.84536i	0.235755	−	0.171286i
$505$	−9.08988			−0.404494
$506$	−54.6472	+	25.6228i	−2.42937	+	1.13907i
$507$	−11.0841			−0.492264
$508$	36.8708	−	26.7882i	1.63588	−	1.18853i
$509$	−6.45648	−	19.8710i	−0.286179	−	0.880767i	−0.986043	−	0.166491i	$-0.946756\pi$
$509$	−6.45648	−	19.8710i	−0.286179	−	0.880767i	0.699864	−	0.714276i	$-0.253244\pi$
$510$	−0.533407	+	1.64166i	−0.0236196	+	0.0726938i
$511$	24.9171	+	18.1034i	1.10227	+	0.800846i
$512$	−9.80547	−	7.12409i	−0.433345	−	0.314843i
$513$	1.40514	−	4.32458i	0.0620385	−	0.190935i
$514$	−6.81488	−	20.9740i	−0.300591	−	0.925125i
$515$	−5.68781	+	4.13243i	−0.250635	+	0.182097i
$516$	−24.2291			−1.06663
$517$	3.88800	+	31.1226i	0.170994	+	1.36877i
$518$	−35.3690			−1.55403
$519$	−18.0401	+	13.1069i	−0.791873	+	0.575329i
$520$	0.722252	+	2.22286i	0.0316728	+	0.0974790i
$521$	5.45030	−	16.7743i	0.238782	−	0.734896i	−0.757815	−	0.652469i	$-0.773733\pi$
$521$	5.45030	−	16.7743i	0.238782	−	0.734896i	0.996597	−	0.0824262i	$-0.0262669\pi$
$522$	13.5262	+	9.82737i	0.592026	+	0.430132i
$523$	−20.4790	−	14.8788i	−0.895482	−	0.650606i	0.0418193	−	0.999125i	$-0.486685\pi$
$523$	−20.4790	−	14.8788i	−0.895482	−	0.650606i	−0.937302	+	0.348519i	$0.886685\pi$
$524$	2.15436	−	6.63043i	0.0941135	−	0.289652i
$525$	4.07673	+	12.5469i	0.177923	+	0.547591i
$526$	−16.2318	+	11.7931i	−0.707741	+	0.514204i
$527$	2.72315			0.118622
$528$	1.74042	−	3.15548i	0.0757423	−	0.137325i
$529$	43.5230			1.89230
$530$	−9.78997	+	7.11283i	−0.425249	+	0.308962i
$531$	1.62381	+	4.99757i	0.0704673	+	0.216876i
$532$	−12.5433	+	38.6043i	−0.543821	+	1.67371i
$533$	3.84417	+	2.79295i	0.166509	+	0.120976i
$534$	30.6016	+	22.2333i	1.32426	+	0.962131i
$535$	−0.0913458	+	0.281133i	−0.00394922	+	0.0121545i
$536$	1.71521	+	5.27889i	0.0740860	+	0.228013i
$537$	−20.5784	+	14.9510i	−0.888021	+	0.645185i
$538$	1.83087			0.0789346
$539$	4.49743	+	4.80256i	0.193718	+	0.206861i
$540$	−2.30409			−0.0991521
$541$	−2.92068	+	2.12200i	−0.125570	+	0.0912320i	−0.648798	−	0.760961i	$-0.724728\pi$
$541$	−2.92068	+	2.12200i	−0.125570	+	0.0912320i	0.523228	+	0.852193i	$0.324728\pi$
$542$	−6.39247	−	19.6740i	−0.274580	−	0.845070i
$543$	−2.43863	+	7.50535i	−0.104652	+	0.322085i
$544$	5.49291	+	3.99083i	0.235506	+	0.171105i
$545$	−3.39998	−	2.47023i	−0.145639	−	0.105813i
$546$	2.86044	−	8.80353i	0.122415	−	0.376756i
$547$	−1.49653	−	4.60584i	−0.0639870	−	0.196932i	0.913952	−	0.405822i	$-0.133015\pi$
$547$	−1.49653	−	4.60584i	−0.0639870	−	0.196932i	−0.977939	+	0.208891i	$0.933015\pi$
$548$	51.3751	−	37.3262i	2.19464	−	1.59450i
$549$	−5.24534			−0.223866
$550$	−22.2637	−	23.7742i	−0.949326	−	1.01373i
$551$	−34.0736			−1.45158
$552$	14.4023	−	10.4639i	0.613001	−	0.445371i
$553$	−14.2197	−	43.7637i	−0.604682	−	1.86102i
$554$	−2.96382	+	9.12171i	−0.125921	+	0.387544i
$555$	3.31016	+	2.40497i	0.140509	+	0.102085i
$556$	1.58775	+	1.15357i	0.0673356	+	0.0489222i
$557$	9.08776	−	27.9693i	0.385061	−	1.18510i	−0.551375	−	0.834257i	$-0.685897\pi$
$557$	9.08776	−	27.9693i	0.385061	−	1.18510i	0.936436	−	0.350838i	$-0.114103\pi$
$558$	1.87755	+	5.77852i	0.0794832	+	0.244624i
$559$	−9.10994	+	6.61876i	−0.385309	+	0.279944i
$560$	−2.51949			−0.106468
$561$	−1.60181	+	2.90417i	−0.0676286	+	0.122614i
$562$	12.5466			0.529248
$563$	−13.6345	+	9.90607i	−0.574627	+	0.417491i	−0.836783	−	0.547534i	$-0.815567\pi$
$563$	−13.6345	+	9.90607i	−0.574627	+	0.417491i	0.262156	+	0.965026i	$0.415567\pi$
$564$	−8.70334	−	26.7861i	−0.366477	−	1.12790i
$565$	−0.894613	+	2.75333i	−0.0376366	+	0.115834i
$566$	−32.4808	−	23.5987i	−1.36527	−	0.991925i
$567$	2.42487	+	1.76177i	0.101835	+	0.0739874i
$568$	−8.52355	+	26.2328i	−0.357640	+	1.10070i
$569$	3.53774	+	10.8880i	0.148310	+	0.456450i	0.997422	−	0.0717624i	$-0.0228623\pi$
$569$	3.53774	+	10.8880i	0.148310	+	0.456450i	−0.849112	+	0.528213i	$0.822862\pi$
$570$	6.34997	−	4.61352i	0.265971	−	0.193239i
$571$	1.44666			0.0605407			0.0302704	−	0.999542i	$-0.490363\pi$
$571$	1.44666			0.0605407			0.0302704	+	0.999542i	$0.490363\pi$
$572$	1.69483	+	13.5667i	0.0708644	+	0.567254i
$573$	6.47627			0.270550
$574$	18.5734	−	13.4943i	0.775237	−	0.563243i
$575$	11.0935	+	34.1422i	0.462630	+	1.42383i
$576$	−4.00977	+	12.3408i	−0.167074	+	0.514200i
$577$	21.4873	+	15.6114i	0.894527	+	0.649912i	0.937054	−	0.349183i	$-0.113541\pi$
$577$	21.4873	+	15.6114i	0.894527	+	0.649912i	−0.0425274	+	0.999095i	$0.513541\pi$
$578$	−1.80508	−	1.31147i	−0.0750813	−	0.0545498i
$579$	3.63071	−	11.1742i	0.150887	−	0.464383i
$580$	5.33533	+	16.4205i	0.221538	+	0.681822i
$581$	18.1979	−	13.2215i	0.754975	−	0.548522i
$582$	9.47976			0.392949
$583$	−21.0519	+	9.87076i	−0.871881	+	0.408805i
$584$	22.4283			0.928091
$585$	−0.866317	+	0.629416i	−0.0358178	+	0.0260231i
$586$	13.4309	+	41.3360i	0.554824	+	1.70757i
$587$	−5.33418	+	16.4169i	−0.220165	+	0.677598i	0.778581	+	0.627544i	$0.215940\pi$
$587$	−5.33418	+	16.4169i	−0.220165	+	0.677598i	−0.998746	+	0.0500546i	$0.984060\pi$
$588$	−4.77995	−	3.47284i	−0.197122	−	0.143217i
$589$	−10.0177	−	7.27827i	−0.412771	−	0.299896i
$590$	−2.80292	+	8.62651i	−0.115394	+	0.355148i
$591$	−2.00038	−	6.15652i	−0.0822844	−	0.253245i
$592$	4.64895	−	3.37766i	0.191071	−	0.138821i
$593$	−27.2387			−1.11856			−0.559280	−	0.828979i	$-0.688922\pi$
$593$	−27.2387			−1.11856			−0.559280	+	0.828979i	$0.688922\pi$
$594$	−7.26705	−	1.39668i	−0.298171	−	0.0573064i
$595$	2.31883			0.0950627
$596$	28.3665	−	20.6095i	1.16194	−	0.844198i
$597$	−4.84864	−	14.9226i	−0.198442	−	0.610740i
$598$	7.78373	−	23.9559i	0.318300	−	0.979628i
$599$	−2.15824	−	1.56805i	−0.0881833	−	0.0640689i	0.542820	−	0.839849i	$-0.317357\pi$
$599$	−2.15824	−	1.56805i	−0.0881833	−	0.0640689i	−0.631003	+	0.775780i	$0.717357\pi$
$600$	7.77220	+	5.64683i	0.317299	+	0.230531i
$601$	9.93981	−	30.5916i	0.405453	−	1.24786i	−0.515063	−	0.857152i	$-0.672231\pi$
$601$	9.93981	−	30.5916i	0.405453	−	1.24786i	0.920516	−	0.390704i	$-0.127769\pi$
$602$	16.8123	+	51.7431i	0.685220	+	2.10889i
$603$	−2.05734	+	1.49475i	−0.0837814	+	0.0608708i
$604$	−23.6291			−0.961454
$605$	4.54001	+	7.19782i	0.184578	+	0.292633i
$606$	26.2155			1.06493
$607$	−13.3551	+	9.70302i	−0.542065	+	0.393833i	−0.824851	−	0.565349i	$-0.808741\pi$
$607$	−13.3551	+	9.70302i	−0.542065	+	0.393833i	0.282786	+	0.959183i	$0.408741\pi$
$608$	−9.54036	−	29.3622i	−0.386913	−	1.19079i
$609$	6.94054	−	21.3608i	0.281245	−	0.865583i
$610$	−7.32499	−	5.32192i	−0.296580	−	0.215478i
$611$	−10.5896	−	7.69383i	−0.428411	−	0.311259i
$612$	0.920329	−	2.83248i	0.0372021	−	0.114496i
$613$	−6.99492	−	21.5282i	−0.282522	−	0.869514i	−0.987130	−	0.159918i	$-0.948877\pi$
$613$	−6.99492	−	21.5282i	−0.282522	−	0.869514i	0.704608	−	0.709597i	$-0.251123\pi$
$614$	−47.3170	+	34.3778i	−1.90956	+	1.38737i
$615$	−2.65584			−0.107094
$616$	21.3078	+	4.09521i	0.858514	+	0.165001i
$617$	−45.6734			−1.83874			−0.919371	−	0.393393i	$-0.871301\pi$
$617$	−45.6734			−1.83874			−0.919371	+	0.393393i	$0.871301\pi$
$618$	16.4038	−	11.9181i	0.659859	−	0.479416i
$619$	−10.9642	−	33.7443i	−0.440688	−	1.35630i	−0.887144	−	0.461493i	$-0.847314\pi$
$619$	−10.9642	−	33.7443i	−0.440688	−	1.35630i	0.446456	−	0.894806i	$-0.352686\pi$
$620$	−1.93889	+	5.96729i	−0.0778676	+	0.239652i
$621$	6.59847	+	4.79407i	0.264788	+	0.192380i
$622$	−46.7253	−	33.9479i	−1.87351	−	1.36119i
$623$	15.7022	−	48.3265i	0.629096	−	1.93616i
$624$	0.464737	+	1.43031i	0.0186044	+	0.0572584i
$625$	−13.2521	+	9.62821i	−0.530084	+	0.385128i
$626$	25.7960			1.03102
$627$	13.6547	−	6.40237i	0.545315	−	0.255686i
$628$	19.5247			0.779118
$629$	−4.27870	+	3.10866i	−0.170603	+	0.123950i
$630$	1.59878	+	4.92054i	0.0636970	+	0.196039i
$631$	−2.68113	+	8.25168i	−0.106734	+	0.328494i	−0.990134	−	0.140127i	$-0.955249\pi$
$631$	−2.68113	+	8.25168i	−0.106734	+	0.328494i	0.883399	+	0.468621i	$0.155249\pi$
$632$	−27.1095	−	19.6962i	−1.07836	−	0.783473i
$633$	7.83123	+	5.68972i	0.311263	+	0.226146i
$634$	10.3706	−	31.9174i	0.411869	−	1.26760i
$635$	3.65834	+	11.2592i	0.145177	+	0.446808i
$636$	16.8914	−	12.2723i	0.669788	−	0.486630i
$637$	−2.74591			−0.108797
$638$	6.87389	+	55.0240i	0.272140	+	2.17842i
$639$	−12.6372			−0.499920
$640$	−9.62149	+	6.99042i	−0.380323	+	0.276321i
$641$	−6.86363	−	21.1241i	−0.271097	−	0.834351i	−0.990226	−	0.139474i	$-0.955459\pi$
$641$	−6.86363	−	21.1241i	−0.271097	−	0.834351i	0.719129	−	0.694877i	$-0.244541\pi$
$642$	0.263444	−	0.810798i	0.0103973	−	0.0319997i
$643$	−13.6324	−	9.90452i	−0.537609	−	0.390596i	0.285587	−	0.958353i	$-0.407811\pi$
$643$	−13.6324	−	9.90452i	−0.537609	−	0.390596i	−0.823196	+	0.567757i	$0.807811\pi$
$644$	−58.9027	−	42.7953i	−2.32109	−	1.68637i
$645$	1.94490	−	5.98578i	0.0765803	−	0.235690i
$646$	3.13515	+	9.64900i	0.123351	+	0.379635i
$647$	18.0255	−	13.0963i	0.708656	−	0.514869i	−0.174084	−	0.984731i	$-0.555696\pi$
$647$	18.0255	−	13.0963i	0.708656	−	0.514869i	0.882740	+	0.469862i	$0.155696\pi$
$648$	2.18267			0.0857432
$649$	−8.41713	+	15.2607i	−0.330401	+	0.599035i
$650$	13.5931			0.533165
$651$	6.60329	−	4.79757i	0.258803	−	0.188032i
$652$	18.5834	+	57.1937i	0.727781	+	2.23988i
$653$	5.46900	−	16.8319i	0.214019	−	0.658681i	−0.785203	−	0.619238i	$-0.787442\pi$
$653$	5.46900	−	16.8319i	0.214019	−	0.658681i	0.999222	−	0.0394433i	$-0.0125584\pi$
$654$	9.80566	+	7.12423i	0.383432	+	0.278579i
$655$	1.46511	+	1.06446i	0.0572465	+	0.0415920i
$656$	−1.15263	+	3.54743i	−0.0450026	+	0.138504i
$657$	3.17535	+	9.77274i	0.123882	+	0.381271i
$658$	−51.1646	+	37.1732i	−1.99460	+	1.44916i
$659$	−20.3929			−0.794393			−0.397196	−	0.917734i	$-0.630017\pi$
$659$	−20.3929			−0.794393			−0.397196	+	0.917734i	$0.630017\pi$
$660$	−5.22346	−	5.57785i	−0.203323	−	0.217118i
$661$	29.0966			1.13173			0.565864	−	0.824499i	$-0.308543\pi$
$661$	29.0966			1.13173			0.565864	+	0.824499i	$0.308543\pi$
$662$	53.0861	−	38.5693i	2.06325	−	1.49904i
$663$	−0.427724	−	1.31640i	−0.0166114	−	0.0511247i
$664$	5.06177	−	15.5785i	0.196435	−	0.604564i
$665$	−8.53029	−	6.19762i	−0.330791	−	0.240333i
$666$	−9.54663	−	6.93603i	−0.369924	−	0.268766i
$667$	18.8864	−	58.1263i	0.731283	−	2.25066i
$668$	7.08985	+	21.8203i	0.274315	+	0.844254i
$669$	12.4018	−	9.01042i	0.479481	−	0.348363i
$670$	−4.38960			−0.169585
$671$	−11.8914	−	12.6982i	−0.459062	−	0.490208i
$672$	20.3505			0.785038
$673$	27.7331	−	20.1493i	1.06903	−	0.776697i	0.0932935	−	0.995639i	$-0.470261\pi$
$673$	27.7331	−	20.1493i	1.06903	−	0.776697i	0.975738	+	0.218942i	$0.0702605\pi$
$674$	11.2591	+	34.6518i	0.433683	+	1.33474i
$675$	−1.36013	+	4.18606i	−0.0523516	+	0.161122i
$676$	26.7067	+	19.4036i	1.02718	+	0.746291i
$677$	27.8411	+	20.2277i	1.07002	+	0.777415i	0.975916	−	0.218148i	$-0.0700015\pi$
$677$	27.8411	+	20.2277i	1.07002	+	0.777415i	0.0941036	+	0.995562i	$0.470002\pi$
$678$	2.58009	−	7.94071i	0.0990879	−	0.304961i
$679$	−3.93525	−	12.1115i	−0.151021	−	0.464795i
$680$	1.36610	−	0.992530i	0.0523876	−	0.0380618i
$681$	−22.3665			−0.857085
$682$	−9.73244	+	17.6454i	−0.372674	+	0.675678i
$683$	−23.6143			−0.903576			−0.451788	−	0.892125i	$-0.649214\pi$
$683$	−23.6143			−0.903576			−0.451788	+	0.892125i	$0.649214\pi$
$684$	−10.9561	+	7.96008i	−0.418917	+	0.304361i
$685$	5.09747	+	15.6884i	0.194764	+	0.599423i
$686$	10.3663	−	31.9042i	0.395787	−	1.21811i
$687$	−8.29381	−	6.02580i	−0.316429	−	0.229899i
$688$	−7.15118	−	5.19564i	−0.272636	−	0.198082i
$689$	2.99855	−	9.22858i	0.114236	−	0.351581i
$690$	4.35055	+	13.3896i	0.165623	+	0.509734i
$691$	8.34746	−	6.06478i	0.317552	−	0.230715i	−0.417578	−	0.908641i	$-0.637121\pi$
$691$	8.34746	−	6.06478i	0.317552	−	0.230715i	0.735130	+	0.677926i	$0.237121\pi$
$692$	66.4114			2.52458
$693$	1.23230	+	9.86426i	0.0468110	+	0.374712i
$694$	32.6416			1.23906
$695$	−0.412439	+	0.299654i	−0.0156447	+	0.0113665i
$696$	−5.05417	−	15.5551i	−0.191578	−	0.589616i
$697$	1.06083	−	3.26490i	0.0401818	−	0.123667i
$698$	36.0028	+	26.1576i	1.36273	+	0.990080i
$699$	10.0457	+	7.29863i	0.379964	+	0.276060i
$700$	12.1415	−	37.3678i	0.458906	−	1.41237i
$701$	−6.95738	−	21.4126i	−0.262776	−	0.808743i	−0.992197	−	0.124678i	$-0.960210\pi$
$701$	−6.95738	−	21.4126i	−0.262776	−	0.808743i	0.729421	−	0.684065i	$-0.239790\pi$
$702$	2.49849	−	1.81526i	0.0942993	−	0.0685125i
$703$	24.0487			0.907014
$704$	−38.9656	+	18.2701i	−1.46857	+	0.688579i
$705$	7.31611			0.275541
$706$	−34.8507	+	25.3205i	−1.31162	+	0.952950i
$707$	−10.8826	−	33.4933i	−0.409283	−	1.25964i
$708$	4.83611	−	14.8840i	0.181752	−	0.559375i
$709$	30.6107	+	22.2400i	1.14961	+	0.835239i	0.988429	−	0.151686i	$-0.0484703\pi$
$709$	30.6107	+	22.2400i	1.14961	+	0.835239i	0.161179	+	0.986925i	$0.448470\pi$
$710$	−17.6476	−	12.8217i	−0.662301	−	0.481190i
$711$	4.74415	−	14.6010i	0.177920	−	0.547581i
$712$	−11.4345	−	35.1918i	−0.428526	−	1.31887i
$713$	17.9686	−	13.0550i	0.672931	−	0.488913i
$714$	−6.68758			−0.250276
$715$	−3.48770	−	0.670312i	−0.130433	−	0.0250682i
$716$	75.7554			2.83111
$717$	0.848509	−	0.616478i	0.0316882	−	0.0230228i
$718$	−11.4357	−	35.1956i	−0.426778	−	1.31349i
$719$	−9.42265	+	28.9999i	−0.351405	+	1.08151i	0.606659	+	0.794962i	$0.292509\pi$
$719$	−9.42265	+	28.9999i	−0.351405	+	1.08151i	−0.958065	+	0.286553i	$0.907491\pi$
$720$	−0.680047	−	0.494083i	−0.0253439	−	0.0184134i
$721$	−22.0363	−	16.0103i	−0.820673	−	0.596254i
$722$	1.15586	−	3.55736i	0.0430165	−	0.132391i
$723$	−1.87294	−	5.76433i	−0.0696555	−	0.214378i
$724$	19.0144	−	13.8148i	0.706665	−	0.513422i
$725$	32.9822			1.22493
$726$	−13.0936	−	20.7588i	−0.485947	−	0.770430i
$727$	−5.45468			−0.202303			−0.101151	−	0.994871i	$-0.532253\pi$
$727$	−5.45468			−0.202303			−0.101151	+	0.994871i	$0.532253\pi$
$728$	−7.32583	+	5.32253i	−0.271513	+	0.197266i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−5.48111	+	16.8691i	−0.202865	+	0.624354i
$731$	6.58164	+	4.78184i	0.243431	+	0.176863i
$732$	12.6384	+	9.18233i	0.467129	+	0.339389i
$733$	1.59373	−	4.90500i	0.0588658	−	0.181170i	−0.917300	−	0.398197i	$-0.869636\pi$
$733$	1.59373	−	4.90500i	0.0588658	−	0.181170i	0.976166	+	0.217027i	$0.0696359\pi$
$734$	4.17577	+	12.8517i	0.154130	+	0.474365i
$735$	1.24165	−	0.902114i	0.0457991	−	0.0332750i
$736$	55.3771			2.04123
$737$	−8.28264	−	1.59187i	−0.305095	−	0.0586371i
$738$	7.65953			0.281951
$739$	1.22890	−	0.892848i	0.0452058	−	0.0328439i	−0.564953	−	0.825123i	$-0.691106\pi$
$739$	1.22890	−	0.892848i	0.0452058	−	0.0328439i	0.610159	+	0.792279i	$0.291106\pi$
$740$	−3.76561	−	11.5893i	−0.138426	−	0.426033i
$741$	−1.94492	+	5.98584i	−0.0714483	+	0.219895i
$742$	−37.9293	−	27.5572i	−1.39243	−	1.01166i
$743$	25.6089	+	18.6060i	0.939500	+	0.682586i	0.948300	−	0.317375i	$-0.102801\pi$
$743$	25.6089	+	18.6060i	0.939500	+	0.682586i	−0.00880048	+	0.999961i	$0.502801\pi$
$744$	1.83671	−	5.65282i	0.0673372	−	0.207243i
$745$	2.81454	+	8.66227i	0.103117	+	0.317361i
$746$	−1.89782	+	1.37885i	−0.0694842	+	0.0504832i
$747$	7.50468			0.274582
$748$	8.94344	−	4.19337i	0.327005	−	0.153325i
$749$	−1.14525			−0.0418464
$750$	−13.1290	+	9.53874i	−0.479402	+	0.348306i
$751$	13.6976	+	42.1568i	0.499832	+	1.53832i	0.809289	+	0.587411i	$0.199853\pi$
$751$	13.6976	+	42.1568i	0.499832	+	1.53832i	−0.309457	+	0.950913i	$0.600147\pi$
$752$	3.17518	−	9.77220i	0.115787	−	0.356356i
$753$	20.1411	+	14.6334i	0.733984	+	0.533270i
$754$	−18.7222	−	13.6025i	−0.681823	−	0.495373i
$755$	1.89673	−	5.83755i	0.0690292	−	0.212450i
$756$	−2.75851	−	8.48981i	−0.100326	−	0.308771i
$757$	−20.4276	+	14.8415i	−0.742455	+	0.539425i	−0.893479	−	0.449105i	$-0.851743\pi$
$757$	−20.4276	+	14.8415i	−0.742455	+	0.539425i	0.151024	+	0.988530i	$0.451743\pi$
$758$	−19.8750			−0.721893
$759$	3.35328	+	26.8423i	0.121716	+	0.974313i
$760$	−7.67826			−0.278520
$761$	−27.5655	+	20.0275i	−0.999248	+	0.725996i	−0.961927	−	0.273307i	$-0.911882\pi$
$761$	−27.5655	+	20.0275i	−0.999248	+	0.725996i	−0.0373210	+	0.999303i	$0.511882\pi$
$762$	−10.5508	−	32.4719i	−0.382214	−	1.17633i
$763$	5.03146	−	15.4852i	0.182151	−	0.560604i
$764$	−15.6043	−	11.3372i	−0.564543	−	0.410164i
$765$	0.625886	+	0.454733i	0.0226290	+	0.0164409i
$766$	−15.1194	+	46.5329i	−0.546288	+	1.68130i
$767$	−2.24759	−	6.91736i	−0.0811556	−	0.249771i
$768$	6.75327	−	4.90654i	0.243688	−	0.177049i
$769$	−16.8913			−0.609114			−0.304557	−	0.952494i	$-0.598508\pi$
$769$	−16.8913			−0.609114			−0.304557	+	0.952494i	$0.598508\pi$
$770$	−8.28740	+	15.0255i	−0.298657	+	0.541481i
$771$	−9.88410			−0.355967
$772$	−28.3092	+	20.5678i	−1.01887	+	0.740253i
$773$	4.43474	+	13.6487i	0.159506	+	0.490910i	0.998590	−	0.0530929i	$-0.0169079\pi$
$773$	4.43474	+	13.6487i	0.159506	+	0.490910i	−0.839083	+	0.544003i	$0.816908\pi$
$774$	−5.60915	+	17.2632i	−0.201617	+	0.620513i
$775$	9.69680	+	7.04514i	0.348319	+	0.253069i
$776$	−7.50247	−	5.45086i	−0.269323	−	0.195675i
$777$	−4.89855	+	15.0762i	−0.175734	+	0.540855i
$778$	−1.98842	−	6.11973i	−0.0712883	−	0.219403i
$779$	−12.6287	+	9.17530i	−0.452471	+	0.328739i
$780$	3.18919			0.114191
$781$	−28.6491	−	30.5928i	−1.02514	−	1.09470i
$782$	−18.1980			−0.650760
$783$	6.06231	−	4.40452i	0.216649	−	0.157405i
$784$	−0.666087	−	2.05000i	−0.0237888	−	0.0732145i
$785$	−1.56727	+	4.82355i	−0.0559381	+	0.172160i
$786$	−4.22542	−	3.06995i	−0.150716	−	0.109502i
$787$	−16.2149	−	11.7808i	−0.577997	−	0.419939i	0.260004	−	0.965607i	$-0.416276\pi$
$787$	−16.2149	−	11.7808i	−0.577997	−	0.419939i	−0.838001	+	0.545668i	$0.816276\pi$
$788$	−5.95761	+	18.3357i	−0.212231	+	0.653181i
$789$	2.77878	+	8.55220i	0.0989271	+	0.304466i
$790$	21.4393	−	15.5765i	0.762775	−	0.554189i
$791$	−11.2162			−0.398802
$792$	4.94819	+	5.28391i	0.175826	+	0.187756i
$793$	7.26030			0.257821
$794$	10.9179	−	7.93232i	0.387462	−	0.281507i
$795$	1.67598	+	5.15812i	0.0594407	+	0.182940i
$796$	−14.4404	+	44.4431i	−0.511828	+	1.57524i
$797$	−13.5884	−	9.87252i	−0.481325	−	0.349703i	0.320514	−	0.947244i	$-0.396144\pi$
$797$	−13.5884	−	9.87252i	−0.481325	−	0.349703i	−0.801838	+	0.597541i	$0.796144\pi$
$798$	24.6017	+	17.8742i	0.870889	+	0.632738i
$799$	−2.92230	+	8.99392i	−0.103384	+	0.318182i
$800$	9.23477	+	28.4217i	0.326498	+	1.00486i
$801$	13.7153	−	9.96475i	0.484606	−	0.352087i
$802$	−44.7901			−1.58159
$803$	−16.4597	+	29.8423i	−0.580850	+	1.05311i
$804$	7.57373			0.267105
$805$	15.3007	−	11.1166i	0.539280	−	0.391810i
$806$	−2.59880	−	7.99830i	−0.0915390	−	0.281728i
$807$	0.253573	−	0.780417i	0.00892619	−	0.0274720i
$808$	−20.7475	−	15.0739i	−0.729893	−	0.530299i
$809$	26.4375	+	19.2080i	0.929493	+	0.675316i	0.945869	−	0.324550i	$-0.105213\pi$
$809$	26.4375	+	19.2080i	0.929493	+	0.675316i	−0.0163757	+	0.999866i	$0.505213\pi$
$810$	−0.533407	+	1.64166i	−0.0187420	+	0.0576819i
$811$	−15.8989	−	48.9319i	−0.558287	−	1.71823i	−0.687101	−	0.726562i	$-0.741117\pi$
$811$	−15.8989	−	48.9319i	−0.558287	−	1.71823i	0.128814	−	0.991669i	$-0.458883\pi$
$812$	−54.1165	+	39.3179i	−1.89912	+	1.37979i
$813$	−9.27145			−0.325164
$814$	−4.85150	−	38.8352i	−0.170045	−	1.36117i
$815$	−15.6214			−0.547193
$816$	0.879025	−	0.638649i	0.0307720	−	0.0223572i
$817$	−11.4313	−	35.1820i	−0.399932	−	1.23086i
$818$	16.7691	−	51.6101i	0.586319	−	1.80450i
$819$	−3.35637	−	2.43854i	−0.117281	−	0.0852096i
$820$	6.39912	+	4.64923i	0.223467	+	0.162358i
$821$	−8.41467	+	25.8977i	−0.293674	+	0.903836i	0.689990	+	0.723819i	$0.257615\pi$
$821$	−8.41467	+	25.8977i	−0.293674	+	0.903836i	−0.983664	+	0.180016i	$0.942385\pi$
$822$	−14.7013	−	45.2459i	−0.512766	−	1.57813i
$823$	26.5747	−	19.3076i	0.926335	−	0.673022i	−0.0187579	−	0.999824i	$-0.505971\pi$
$823$	26.5747	−	19.3076i	0.926335	−	0.673022i	0.945093	+	0.326802i	$0.105971\pi$
$824$	−19.8352			−0.690992
$825$	−13.2173	+	6.19729i	−0.460168	+	0.215762i
$826$	−35.1416			−1.22273
$827$	−40.2391	+	29.2354i	−1.39925	+	1.01661i	−0.404472	+	0.914550i	$0.632545\pi$
$827$	−40.2391	+	29.2354i	−1.39925	+	1.01661i	−0.994778	+	0.102064i	$0.967455\pi$
$828$	−7.50636	−	23.1022i	−0.260864	−	0.802857i
$829$	−5.76005	+	17.7276i	−0.200055	+	0.615706i	0.799825	+	0.600233i	$0.204925\pi$
$829$	−5.76005	+	17.7276i	−0.200055	+	0.615706i	−0.999880	+	0.0154728i	$0.995075\pi$
$830$	10.4801	+	7.61425i	0.363770	+	0.264294i
$831$	3.47768	+	2.52668i	0.120639	+	0.0876496i
$832$	5.55010	−	17.0815i	0.192415	−	0.592193i
$833$	0.613038	+	1.88674i	0.0212405	+	0.0653715i
$834$	1.18949	−	0.864213i	0.0411886	−	0.0299253i
$835$	−5.95980			−0.206247
$836$	−44.1081	−	8.47728i	−1.52551	−	0.293193i
$837$	2.72315			0.0941259
$838$	−30.5384	+	22.1874i	−1.05493	+	0.766451i
$839$	12.6372	+	38.8932i	0.436283	+	1.34274i	0.891766	+	0.452497i	$0.149467\pi$
$839$	12.6372	+	38.8932i	0.436283	+	1.34274i	−0.455483	+	0.890245i	$0.650533\pi$
$840$	1.56401	−	4.81351i	0.0539633	−	0.166082i
$841$	−21.9659	−	15.9592i	−0.757446	−	0.550317i
$842$	25.7543	+	18.7116i	0.887551	+	0.644844i
$843$	1.73769	−	5.34805i	0.0598491	−	0.184196i
$844$	−8.90872	−	27.4182i	−0.306651	−	0.943774i
$845$	−6.93741	+	5.04033i	−0.238654	+	0.173393i
$846$	−21.0999			−0.725430
$847$	−21.0862	+	25.3459i	−0.724532	+	0.870895i
$848$	7.61713			0.261573
$849$	−14.5575	+	10.5767i	−0.499613	+	0.362990i
$850$	−3.03473	−	9.33993i	−0.104090	−	0.320357i
$851$	−13.3298	+	41.0248i	−0.456938	+	1.40631i
$852$	30.4488	+	22.1223i	1.04316	+	0.757898i
$853$	42.3428	+	30.7638i	1.44979	+	1.05333i	0.985881	+	0.167449i	$0.0535531\pi$
$853$	42.3428	+	30.7638i	1.44979	+	1.05333i	0.463908	+	0.885883i	$0.346447\pi$
$854$	10.8399	−	33.3618i	0.370933	−	1.14162i
$855$	−1.08707	−	3.34566i	−0.0371770	−	0.114419i
$856$	−0.674704	+	0.490201i	−0.0230609	+	0.0167547i
$857$	−15.1131			−0.516254			−0.258127	−	0.966111i	$-0.583105\pi$
$857$	−15.1131			−0.516254			−0.258127	+	0.966111i	$0.583105\pi$
$858$	10.0586	+	1.93320i	0.343396	+	0.0659984i
$859$	−34.5931			−1.18030			−0.590150	−	0.807293i	$-0.700932\pi$
$859$	−34.5931			−1.18030			−0.590150	+	0.807293i	$0.700932\pi$
$860$	−15.1647	+	11.0178i	−0.517111	+	0.375703i
$861$	−3.17963	−	9.78590i	−0.108362	−	0.333503i
$862$	−22.6783	+	69.7966i	−0.772426	+	2.37728i
$863$	38.1621	+	27.7264i	1.29905	+	0.943817i	0.999946	−	0.0104020i	$-0.00331111\pi$
$863$	38.1621	+	27.7264i	1.29905	+	0.943817i	0.299107	+	0.954219i	$0.403311\pi$
$864$	5.49291	+	3.99083i	0.186872	+	0.135771i
$865$	−5.33091	+	16.4069i	−0.181257	+	0.557850i
$866$	−7.18528	−	22.1140i	−0.244166	−	0.751465i
$867$	−0.809017	+	0.587785i	−0.0274757	+	0.0199622i
$868$	−24.3088			−0.825094
$869$	46.1021	−	21.6162i	1.56391	−	0.733279i
$870$	12.9347			0.438527
$871$	2.84766	−	2.06894i	0.0964891	−	0.0701035i
$872$	−3.66396	−	11.2765i	−0.124077	−	0.381871i
$873$	1.31293	−	4.04078i	0.0444360	−	0.136760i
$874$	66.9452	+	48.6385i	2.26446	+	1.64522i
$875$	17.6369	+	12.8140i	0.596237	+	0.433191i
$876$	9.45699	−	29.1056i	0.319522	−	0.983388i
$877$	−4.76961	−	14.6793i	−0.161058	−	0.495686i	0.837666	−	0.546183i	$-0.183920\pi$
$877$	−4.76961	−	14.6793i	−0.161058	−	0.495686i	−0.998724	+	0.0504965i	$0.983920\pi$
$878$	−42.7344	+	31.0483i	−1.44222	+	1.04783i
$879$	19.4798			0.657036
$880$	−0.345593	−	2.76640i	−0.0116499	−	0.0932553i
$881$	−28.7442			−0.968416			−0.484208	−	0.874953i	$-0.660892\pi$
$881$	−28.7442			−0.968416			−0.484208	+	0.874953i	$0.660892\pi$
$882$	−3.58097	+	2.60173i	−0.120578	+	0.0876047i
$883$	0.533610	+	1.64228i	0.0179574	+	0.0552673i	0.959634	−	0.281253i	$-0.0907500\pi$
$883$	0.533610	+	1.64228i	0.0179574	+	0.0552673i	−0.941676	+	0.336520i	$0.890750\pi$
$884$	−1.27387	+	3.92056i	−0.0428448	+	0.131863i
$885$	3.28888	+	2.38951i	0.110555	+	0.0803225i
$886$	−31.5939	−	22.9543i	−1.06142	−	0.771166i
$887$	11.7147	−	36.0542i	0.393341	−	1.21058i	−0.536904	−	0.843643i	$-0.680406\pi$
$887$	11.7147	−	36.0542i	0.393341	−	1.21058i	0.930246	−	0.366937i	$-0.119594\pi$
$888$	3.56717	+	10.9786i	0.119706	+	0.368418i
$889$	−37.1067	+	26.9596i	−1.24452	+	0.904195i
$890$	29.2633			0.980909
$891$	−1.60181	+	2.90417i	−0.0536627	+	0.0972933i
$892$	−45.6549			−1.52864
$893$	34.7887	−	25.2755i	1.16416	−	0.845811i
$894$	−8.11724	−	24.9823i	−0.271481	−	0.835533i
$895$	−6.08097	+	18.7153i	−0.203265	+	0.625584i
$896$	−37.2765	−	27.0830i	−1.24532	−	0.904779i
$897$	−9.13324	−	6.63569i	−0.304950	−	0.221559i
$898$	−4.90177	+	15.0861i	−0.163574	+	0.503429i
$899$	−6.30572	−	19.4070i	−0.210307	−	0.647260i
$900$	10.6052	−	7.70511i	0.353506	−	0.256837i
$901$	−7.01048			−0.233553
$902$	17.3645	+	18.5426i	0.578174	+	0.617400i
$903$	24.3841			0.811454
$904$	−6.60784	+	4.80088i	−0.219774	+	0.159675i
$905$	1.88662	+	5.80642i	0.0627134	+	0.193012i
$906$	−5.47025	+	16.8357i	−0.181737	+	0.559328i
$907$	−6.90936	−	5.01995i	−0.229422	−	0.166685i	0.467136	−	0.884186i	$-0.345286\pi$
$907$	−6.90936	−	5.01995i	−0.229422	−	0.166685i	−0.696557	+	0.717501i	$0.745286\pi$
$908$	53.8910	+	39.1541i	1.78844	+	1.29937i
$909$	3.63080	−	11.1745i	0.120426	−	0.370633i
$910$	−2.21294	−	6.81074i	−0.0733584	−	0.225774i
$911$	25.9105	−	18.8251i	0.858452	−	0.623702i	−0.0690115	−	0.997616i	$-0.521985\pi$
$911$	25.9105	−	18.8251i	0.858452	−	0.623702i	0.927463	+	0.373914i	$0.121985\pi$
$912$	−4.94062			−0.163600
$913$	17.0134	+	18.1677i	0.563062	+	0.601264i
$914$	65.4591			2.16519
$915$	−3.28299	+	2.38523i	−0.108532	+	0.0788532i
$916$	9.43495	+	29.0378i	0.311740	+	0.959436i
$917$	−2.16814	+	6.67285i	−0.0715983	+	0.220357i
$918$	−1.80508	−	1.31147i	−0.0595764	−	0.0432848i
$919$	−19.1373	−	13.9041i	−0.631282	−	0.458653i	0.225562	−	0.974229i	$-0.427578\pi$
$919$	−19.1373	−	13.9041i	−0.631282	−	0.458653i	−0.856844	+	0.515575i	$0.827578\pi$
$920$	4.25592	−	13.0984i	0.140313	−	0.431841i
$921$	8.10034	+	24.9303i	0.266915	+	0.821481i
$922$	−4.66698	+	3.39076i	−0.153699	+	0.111669i
$923$	17.4917			0.575747
$924$	14.2989	−	25.9247i	0.470400	−	0.852860i
$925$	−23.2784			−0.765389
$926$	−31.3542	+	22.7802i	−1.03036	+	0.748604i
$927$	−2.80822	−	8.64283i	−0.0922342	−	0.283868i
$928$	15.7220	−	48.3873i	0.516099	−	1.58839i
$929$	44.8212	+	32.5645i	1.47054	+	1.06841i	0.980458	+	0.196728i	$0.0630316\pi$
$929$	44.8212	+	32.5645i	1.47054	+	1.06841i	0.490078	+	0.871679i	$0.336968\pi$
$930$	3.80282	+	2.76291i	0.124699	+	0.0905993i
$931$	2.78756	−	8.57924i	0.0913588	−	0.281173i
$932$	−11.4279	−	35.1714i	−0.374333	−	1.15208i
$933$	−20.9418	+	15.2151i	−0.685603	+	0.498120i
$934$	81.7191			2.67393
$935$	0.318069	+	2.54608i	0.0104020	+	0.0832656i
$936$	−3.02112			−0.0987485
$937$	6.94626	−	5.04675i	0.226924	−	0.164870i	−0.468514	−	0.883456i	$-0.655210\pi$
$937$	6.94626	−	5.04675i	0.226924	−	0.164870i	0.695438	+	0.718586i	$0.255210\pi$
$938$	−5.25533	−	16.1742i	−0.171593	−	0.528108i
$939$	3.57270	−	10.9956i	0.116591	−	0.358829i
$940$	−17.6278	−	12.8074i	−0.574956	−	0.417730i
$941$	−37.8298	−	27.4850i	−1.23322	−	0.895985i	−0.236090	−	0.971731i	$-0.575866\pi$
$941$	−37.8298	−	27.4850i	−1.23322	−	0.895985i	−0.997127	+	0.0757466i	$0.975866\pi$
$942$	4.52005	−	13.9113i	0.147271	−	0.453254i
$943$	−8.65231	−	26.6291i	−0.281758	−	0.867162i
$944$	4.61906	−	3.35595i	0.150338	−	0.109227i
$945$	2.31883			0.0754315
$946$	−54.5078	+	25.5575i	−1.77220	+	0.830945i
$947$	19.1783			0.623210			0.311605	−	0.950212i	$-0.399133\pi$
$947$	19.1783			0.623210			0.311605	+	0.950212i	$0.399133\pi$
$948$	−36.9909	+	26.8755i	−1.20141	+	0.872875i
$949$	−4.39515	−	13.5269i	−0.142673	−	0.439101i
$950$	−13.7993	+	42.4699i	−0.447709	+	1.37791i
$951$	−12.1686	−	8.84101i	−0.394594	−	0.286689i
$952$	5.29268	+	3.84536i	0.171537	+	0.124629i
$953$	−4.31375	+	13.2763i	−0.139736	+	0.430063i	−0.996297	−	0.0859833i	$-0.972597\pi$
$953$	−4.31375	+	13.2763i	−0.139736	+	0.430063i	0.856561	+	0.516046i	$0.172597\pi$
$954$	−4.83357	−	14.8762i	−0.156493	−	0.481635i
$955$	4.05341	−	2.94497i	0.131165	−	0.0952971i
$956$	−3.12363			−0.101025
$957$	24.4062	+	4.69071i	0.788940	+	0.151629i
$958$	−30.6864			−0.991433
$959$	−51.7038	+	37.5650i	−1.66960	+	1.21304i
$960$	3.10211	+	9.54732i	0.100120	+	0.308138i
$961$	−7.28799	+	22.4301i	−0.235097	+	0.723553i
$962$	13.2139	+	9.60046i	0.426033	+	0.309531i
$963$	−0.309119	−	0.224588i	−0.00996123	−	0.00723725i
$964$	−5.57809	+	17.1676i	−0.179658	+	0.552931i
$965$	−2.80885	−	8.64476i	−0.0904202	−	0.278285i
$966$	−44.1278	+	32.0608i	−1.41979	+	1.03154i
$967$	41.7179			1.34156			0.670778	−	0.741658i	$-0.265960\pi$
$967$	41.7179			1.34156			0.670778	+	0.741658i	$0.265960\pi$
$968$	−1.57380	+	23.9577i	−0.0505838	+	0.770029i
$969$	4.54713			0.146075
$970$	5.93325	−	4.31076i	0.190505	−	0.138410i
$971$	−15.7060	−	48.3380i	−0.504028	−	1.55124i	−0.802398	−	0.596789i	$-0.796443\pi$
$971$	−15.7060	−	48.3380i	−0.504028	−	1.55124i	0.298370	−	0.954450i	$-0.403557\pi$
$972$	0.920329	−	2.83248i	0.0295196	−	0.0908519i
$973$	−1.59791	−	1.16095i	−0.0512267	−	0.0372183i
$974$	−72.9031	−	52.9672i	−2.33596	−	1.69718i
$975$	1.88262	−	5.79411i	0.0602921	−	0.185560i
$976$	1.76116	+	5.42030i	0.0563734	+	0.173500i
$977$	−29.5884	+	21.4972i	−0.946616	+	0.687757i	−0.950004	−	0.312237i	$-0.898922\pi$
$977$	−29.5884	+	21.4972i	−0.946616	+	0.687757i	0.00338790	+	0.999994i	$0.498922\pi$
$978$	45.0526			1.44062
$979$	55.2163	+	10.6122i	1.76472	+	0.339168i
$980$	−4.57092			−0.146013
$981$	4.39480	−	3.19301i	0.140315	−	0.101945i
$982$	−0.442802	−	1.36280i	−0.0141304	−	0.0434888i
$983$	0.301712	−	0.928574i	0.00962312	−	0.0296169i	−0.946130	−	0.323788i	$-0.895044\pi$
$983$	0.301712	−	0.928574i	0.00962312	−	0.0296169i	0.955753	+	0.294171i	$0.0950435\pi$
$984$	−6.06190	−	4.40423i	−0.193246	−	0.140402i
$985$	−4.05158	−	2.94365i	−0.129094	−	0.0937924i
$986$	−5.16655	+	15.9010i	−0.164537	+	0.506391i
$987$	8.75902	+	26.9575i	0.278803	+	0.858067i
$988$	15.1648	−	11.0179i	0.482457	−	0.350526i
$989$	66.3533			2.10991
$990$	−5.18346	+	2.43041i	−0.164741	+	0.0772434i
$991$	−7.53480			−0.239351			−0.119675	−	0.992813i	$-0.538185\pi$
$991$	−7.53480			−0.239351			−0.119675	+	0.992813i	$0.538185\pi$
$992$	14.9580	−	10.8676i	0.474918	−	0.345048i
$993$	−9.08798	−	27.9699i	−0.288398	−	0.887598i
$994$	26.1158	−	80.3760i	0.828341	−	2.54937i
$995$	−9.82048	−	7.13500i	−0.311330	−	0.226195i
$996$	−18.0822	−	13.1375i	−0.572956	−	0.416277i
$997$	−2.94842	+	9.07429i	−0.0933773	+	0.287386i	−0.986827	−	0.161777i	$-0.948278\pi$
$997$	−2.94842	+	9.07429i	−0.0933773	+	0.287386i	0.893450	+	0.449162i	$0.148278\pi$
$998$	5.48023	+	16.8664i	0.173474	+	0.533897i
$999$	−4.27870	+	3.10866i	−0.135372	+	0.0983535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.m.d.256.1	yes	24
11.2	odd	10		6171.2.a.bl.1.2		12
11.4	even	5	inner	561.2.m.d.103.1	✓	24
11.9	even	5		6171.2.a.bk.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.m.d.103.1	✓	24	11.4	even	5	inner
561.2.m.d.256.1	yes	24	1.1	even	1	trivial
6171.2.a.bk.1.11		12	11.9	even	5
6171.2.a.bl.1.2		12	11.2	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:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80508 + 1.31147i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.920329 - 2.83248i) q^{4} +(0.625886 + 0.454733i) q^{5} +(-1.80508 - 1.31147i) q^{6} +(-0.926218 + 2.85061i) q^{7} +(0.674481 + 2.07584i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.80508 + 1.31147i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.920329 - 2.83248i) q^{4} +(0.625886 + 0.454733i) q^{5} +(-1.80508 - 1.31147i) q^{6} +(-0.926218 + 2.85061i) q^{7} +(0.674481 + 2.07584i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.72614 q^{10} +(-3.25702 - 0.625976i) q^{11} +2.97825 q^{12} +(1.11980 - 0.813579i) q^{13} +(-2.06658 - 6.36027i) q^{14} +(-0.239067 + 0.735773i) q^{15} +(0.879025 + 0.638649i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.689478 - 2.12200i) q^{18} +(1.40514 + 4.32458i) q^{19} +(1.86404 - 1.35431i) q^{20} -2.99730 q^{21} +(6.70011 - 3.14153i) q^{22} -8.15616 q^{23} +(-1.76581 + 1.28294i) q^{24} +(-1.36013 - 4.18606i) q^{25} +(-0.954337 + 2.93715i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(7.22186 + 5.24699i) q^{28} +(-2.31559 + 7.12667i) q^{29} +(-0.533407 - 1.64166i) q^{30} +(-2.20308 + 1.60063i) q^{31} -6.78961 q^{32} +(-0.411134 - 3.29104i) q^{33} +2.23120 q^{34} +(-1.87597 + 1.36297i) q^{35} +(0.920329 + 2.83248i) q^{36} +(1.63432 - 5.02991i) q^{37} +(-8.20793 - 5.96341i) q^{38} +(1.11980 + 0.813579i) q^{39} +(-0.521804 + 1.60595i) q^{40} +(1.06083 + 3.26490i) q^{41} +(5.41037 - 3.93086i) q^{42} -8.13536 q^{43} +(-4.77059 + 8.64934i) q^{44} -0.773638 q^{45} +(14.7225 - 10.6965i) q^{46} +(-2.92230 - 8.99392i) q^{47} +(-0.335758 + 1.03336i) q^{48} +(-1.60495 - 1.16607i) q^{49} +(7.94502 + 5.77240i) q^{50} +(0.309017 - 0.951057i) q^{51} +(-1.27387 - 3.92056i) q^{52} +(5.67160 - 4.12066i) q^{53} +2.23120 q^{54} +(-1.75387 - 1.87286i) q^{55} -6.54211 q^{56} +(-3.67871 + 2.67274i) q^{57} +(-5.16655 - 15.9010i) q^{58} +(1.62381 - 4.99757i) q^{59} +(1.86404 + 1.35431i) q^{60} +(4.24357 + 3.08313i) q^{61} +(1.87755 - 5.77852i) q^{62} +(-0.926218 - 2.85061i) q^{63} +(10.4977 - 7.62704i) q^{64} +1.07083 q^{65} +(5.05822 + 5.40140i) q^{66} +2.54301 q^{67} +(-2.40945 + 1.75057i) q^{68} +(-2.52039 - 7.75697i) q^{69} +(1.59878 - 4.92054i) q^{70} +(10.2237 + 7.42796i) q^{71} +(-1.76581 - 1.28294i) q^{72} +(3.17535 - 9.77274i) q^{73} +(3.64649 + 11.2227i) q^{74} +(3.56088 - 2.58713i) q^{75} +13.5425 q^{76} +(4.80112 - 8.70468i) q^{77} -3.08830 q^{78} +(-12.4204 + 9.02392i) q^{79} +(0.259755 + 0.799443i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.19669 - 4.50216i) q^{82} +(-6.07142 - 4.41114i) q^{83} +(-2.75851 + 8.48981i) q^{84} +(-0.239067 - 0.735773i) q^{85} +(14.6850 - 10.6692i) q^{86} -7.49342 q^{87} +(-0.897369 - 7.18325i) q^{88} -16.9530 q^{89} +(1.39648 - 1.01460i) q^{90} +(1.28202 + 3.94565i) q^{91} +(-7.50636 + 23.1022i) q^{92} +(-2.20308 - 1.60063i) q^{93} +(17.0702 + 12.4022i) q^{94} +(-1.08707 + 3.34566i) q^{95} +(-2.09810 - 6.45730i) q^{96} +(-3.43730 + 2.49734i) q^{97} +4.42632 q^{98} +(3.00292 - 1.40800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9	\( 24 q + 3 q^{2} - 6 q^{3} - 7 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{7} - 10 q^{8} - 6 q^{9} + 16 q^{10} - 7 q^{11} + 18 q^{12} + 6 q^{13} - 6 q^{14} + 7 q^{15} - 23 q^{16} - 6 q^{17} - 2 q^{18} + 6 q^{19} + 3 q^{20} - 10 q^{21} + 23 q^{22} - 78 q^{23} + 10 q^{24} + q^{25} + 10 q^{26} - 6 q^{27} - 13 q^{28} + 20 q^{29} + 11 q^{30} + 5 q^{31} - 22 q^{32} - 2 q^{33} - 2 q^{34} + 29 q^{35} - 7 q^{36} - 10 q^{37} + 2 q^{38} + 6 q^{39} + 44 q^{40} - 16 q^{41} + 19 q^{42} - 36 q^{43} + 3 q^{44} - 28 q^{45} + 23 q^{46} + 19 q^{47} + 12 q^{48} - 15 q^{49} + 34 q^{50} - 6 q^{51} - 6 q^{52} - 5 q^{53} - 2 q^{54} + 24 q^{55} - 50 q^{56} - 9 q^{57} - 79 q^{58} + 34 q^{59} + 3 q^{60} - 14 q^{61} + 36 q^{62} + 5 q^{63} - 20 q^{64} + 6 q^{65} + 3 q^{66} - 18 q^{67} - 2 q^{68} + 7 q^{69} + 46 q^{70} - 8 q^{71} + 10 q^{72} + 7 q^{73} + 47 q^{74} - 9 q^{75} + 58 q^{76} + 43 q^{77} - 50 q^{78} + 14 q^{79} - 51 q^{80} - 6 q^{81} - 88 q^{82} - 47 q^{83} + 22 q^{84} + 7 q^{85} - 13 q^{86} + 20 q^{87} + 115 q^{88} - 124 q^{89} - 19 q^{90} + 10 q^{91} - 19 q^{92} + 5 q^{93} + 28 q^{94} - 13 q^{95} - 27 q^{96} - 30 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 6 * q^3 - 7 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^7 - 10 * q^8 - 6 * q^9 + 16 * q^10 - 7 * q^11 + 18 * q^12 + 6 * q^13 - 6 * q^14 + 7 * q^15 - 23 * q^16 - 6 * q^17 - 2 * q^18 + 6 * q^19 + 3 * q^20 - 10 * q^21 + 23 * q^22 - 78 * q^23 + 10 * q^24 + q^25 + 10 * q^26 - 6 * q^27 - 13 * q^28 + 20 * q^29 + 11 * q^30 + 5 * q^31 - 22 * q^32 - 2 * q^33 - 2 * q^34 + 29 * q^35 - 7 * q^36 - 10 * q^37 + 2 * q^38 + 6 * q^39 + 44 * q^40 - 16 * q^41 + 19 * q^42 - 36 * q^43 + 3 * q^44 - 28 * q^45 + 23 * q^46 + 19 * q^47 + 12 * q^48 - 15 * q^49 + 34 * q^50 - 6 * q^51 - 6 * q^52 - 5 * q^53 - 2 * q^54 + 24 * q^55 - 50 * q^56 - 9 * q^57 - 79 * q^58 + 34 * q^59 + 3 * q^60 - 14 * q^61 + 36 * q^62 + 5 * q^63 - 20 * q^64 + 6 * q^65 + 3 * q^66 - 18 * q^67 - 2 * q^68 + 7 * q^69 + 46 * q^70 - 8 * q^71 + 10 * q^72 + 7 * q^73 + 47 * q^74 - 9 * q^75 + 58 * q^76 + 43 * q^77 - 50 * q^78 + 14 * q^79 - 51 * q^80 - 6 * q^81 - 88 * q^82 - 47 * q^83 + 22 * q^84 + 7 * q^85 - 13 * q^86 + 20 * q^87 + 115 * q^88 - 124 * q^89 - 19 * q^90 + 10 * q^91 - 19 * q^92 + 5 * q^93 + 28 * q^94 - 13 * q^95 - 27 * q^96 - 30 * q^97 - 14 * q^98 - 7 * q^99

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