LMFDB - Embedded newform 825.2.n.k.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.2
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.k.526.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.359123 - 1.10527i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.525387 - 0.381716i) q^{4} +(0.359123 - 1.10527i) q^{6} +(-3.46813 + 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.359123 - 1.10527i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.525387 - 0.381716i) q^{4} +(0.359123 - 1.10527i) q^{6} +(-3.46813 + 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.15911 + 1.00996i) q^{11} +0.649414 q^{12} +(-1.59676 - 4.91433i) q^{13} +(4.03048 + 2.92831i) q^{14} +(-0.704384 + 2.16787i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(0.940197 - 0.683093i) q^{18} +(-4.53048 - 3.29158i) q^{19} -4.28684 q^{21} +(2.25079 + 3.12896i) q^{22} +0.219819 q^{23} +(-0.951466 - 2.92831i) q^{24} +(-4.85822 + 3.52970i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.860283 + 2.64768i) q^{28} +(-5.19262 + 3.77266i) q^{29} +(-0.874813 - 2.69240i) q^{31} -3.50898 q^{32} +(-3.14941 - 1.03980i) q^{33} +5.81074 q^{34} +(0.525387 + 0.381716i) q^{36} +(3.17784 - 2.30883i) q^{37} +(-2.01108 + 6.18947i) q^{38} +(1.59676 - 4.91433i) q^{39} +(-4.74165 - 3.44501i) q^{41} +(1.53950 + 4.73811i) q^{42} +8.90173 q^{43} +(-1.27424 + 1.73650i) q^{44} +(-0.0789420 - 0.242959i) q^{46} +(-0.192447 - 0.139821i) q^{47} +(-1.84410 + 1.33982i) q^{48} +(3.51569 - 10.8202i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(-2.71480 - 1.97242i) q^{52} +(-0.783885 - 2.41255i) q^{53} +1.16215 q^{54} +13.1992 q^{56} +(-1.73049 - 5.32589i) q^{57} +(6.03459 + 4.38439i) q^{58} +(6.36725 - 4.62608i) q^{59} +(-1.50123 + 4.62030i) q^{61} +(-2.66165 + 1.93381i) q^{62} +(-3.46813 - 2.51974i) q^{63} +(2.66892 + 8.21410i) q^{64} +(-0.0182340 + 3.85436i) q^{66} -12.1280 q^{67} +(1.00340 + 3.08815i) q^{68} +(0.177837 + 0.129206i) q^{69} +(-3.08459 + 9.49339i) q^{71} +(0.951466 - 2.92831i) q^{72} +(11.7813 - 8.55964i) q^{73} +(-3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(8.41136 - 11.4628i) q^{77} -6.00509 q^{78} +(2.47274 + 7.61030i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.10482 + 6.47797i) q^{82} +(-3.87908 + 11.9386i) q^{83} +(-2.25225 + 1.63636i) q^{84} +(-3.19682 - 9.83880i) q^{86} -6.41843 q^{87} +(9.69707 + 3.20157i) q^{88} -2.56545 q^{89} +(17.9206 + 13.0201i) q^{91} +(0.115490 - 0.0839083i) q^{92} +(0.874813 - 2.69240i) q^{93} +(-0.0854274 + 0.262919i) q^{94} +(-2.83882 - 2.06253i) q^{96} +(-0.621738 - 1.91351i) q^{97} -13.2218 q^{98} +(-1.93675 - 2.69240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.359123	−	1.10527i	−0.253938	−	0.781542i	−0.994037	−	0.109044i	$-0.965221\pi$
$2$	−0.359123	−	1.10527i	−0.253938	−	0.781542i	0.740098	−	0.672499i	$-0.234779\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.525387	−	0.381716i	0.262693	−	0.190858i
$5$		0			0
$5$		0			0
$6$	0.359123	−	1.10527i	0.146611	−	0.451224i
$7$	−3.46813	+	2.51974i	−1.31083	+	0.952373i	−0.310831	+	0.950465i	$0.600607\pi$
$7$	−3.46813	+	2.51974i	−1.31083	+	0.952373i	−0.999998	+	0.00190785i	$0.999393\pi$
$8$	−2.49097	−	1.80980i	−0.880691	−	0.639860i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−3.15911	+	1.00996i	−0.952508	+	0.304514i
$11$	−3.15911	+	1.00996i	−0.952508	+	0.304514i
$12$	0.649414			0.187470
$13$	−1.59676	−	4.91433i	−0.442863	−	1.36299i	−0.884811	−	0.465950i	$-0.845713\pi$
$13$	−1.59676	−	4.91433i	−0.442863	−	1.36299i	0.441948	−	0.897040i	$-0.354287\pi$
$14$	4.03048	+	2.92831i	1.07719	+	0.782624i
$15$		0			0
$16$	−0.704384	+	2.16787i	−0.176096	+	0.541968i
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	0.568917	+	0.822395i	$0.307363\pi$
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	−0.943655	+	0.330930i	$0.892637\pi$
$18$	0.940197	−	0.683093i	0.221607	−	0.161007i
$19$	−4.53048	−	3.29158i	−1.03936	−	0.755141i	−0.0692013	−	0.997603i	$-0.522045\pi$
$19$	−4.53048	−	3.29158i	−1.03936	−	0.755141i	−0.970161	+	0.242462i	$0.922045\pi$
$20$		0			0
$21$	−4.28684			−0.935466
$22$	2.25079	+	3.12896i	0.479869	+	0.667097i
$23$	0.219819			0.0458354			0.0229177	−	0.999737i	$-0.492704\pi$
$23$	0.219819			0.0458354			0.0229177	+	0.999737i	$0.492704\pi$
$24$	−0.951466	−	2.92831i	−0.194217	−	0.597739i
$25$		0			0
$26$	−4.85822	+	3.52970i	−0.952775	+	0.692232i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.860283	+	2.64768i	−0.162578	+	0.500364i
$29$	−5.19262	+	3.77266i	−0.964246	+	0.700566i	−0.954133	−	0.299383i	$-0.903219\pi$
$29$	−5.19262	+	3.77266i	−0.964246	+	0.700566i	−0.0101128	+	0.999949i	$0.503219\pi$
$30$		0			0
$31$	−0.874813	−	2.69240i	−0.157121	−	0.483569i	0.841249	−	0.540649i	$-0.181821\pi$
$31$	−0.874813	−	2.69240i	−0.157121	−	0.483569i	−0.998370	+	0.0570796i	$0.981821\pi$
$32$	−3.50898			−0.620306
$33$	−3.14941	−	1.03980i	−0.548243	−	0.181007i
$34$	5.81074			0.996533
$35$		0			0
$36$	0.525387	+	0.381716i	0.0875645	+	0.0636193i
$37$	3.17784	−	2.30883i	0.522433	−	0.379570i	−0.295087	−	0.955471i	$-0.595348\pi$
$37$	3.17784	−	2.30883i	0.522433	−	0.379570i	0.817520	+	0.575901i	$0.195348\pi$
$38$	−2.01108	+	6.18947i	−0.326240	+	1.00406i
$39$	1.59676	−	4.91433i	0.255687	−	0.786923i
$40$		0			0
$41$	−4.74165	−	3.44501i	−0.740521	−	0.538020i	0.152353	−	0.988326i	$-0.451315\pi$
$41$	−4.74165	−	3.44501i	−0.740521	−	0.538020i	−0.892874	+	0.450306i	$0.851315\pi$
$42$	1.53950	+	4.73811i	0.237551	+	0.731106i
$43$	8.90173			1.35750			0.678751	−	0.734369i	$-0.262522\pi$
$43$	8.90173			1.35750			0.678751	+	0.734369i	$0.262522\pi$
$44$	−1.27424	+	1.73650i	−0.192099	+	0.261788i
$45$		0			0
$46$	−0.0789420	−	0.242959i	−0.0116394	−	0.0358223i
$47$	−0.192447	−	0.139821i	−0.0280713	−	0.0203950i	0.573661	−	0.819093i	$-0.305523\pi$
$47$	−0.192447	−	0.139821i	−0.0280713	−	0.0203950i	−0.601732	+	0.798698i	$0.705523\pi$
$48$	−1.84410	+	1.33982i	−0.266173	+	0.193386i
$49$	3.51569	−	10.8202i	0.502241	−	1.54574i
$50$		0			0
$51$	−4.04508	+	2.93893i	−0.566425	+	0.411532i
$52$	−2.71480	−	1.97242i	−0.376475	−	0.273525i
$53$	−0.783885	−	2.41255i	−0.107675	−	0.331389i	0.882674	−	0.469986i	$-0.155741\pi$
$53$	−0.783885	−	2.41255i	−0.107675	−	0.331389i	−0.990349	+	0.138596i	$0.955741\pi$
$54$	1.16215			0.158148
$55$		0			0
$56$	13.1992			1.76382
$57$	−1.73049	−	5.32589i	−0.229209	−	0.705432i
$58$	6.03459	+	4.38439i	0.792381	+	0.575698i
$59$	6.36725	−	4.62608i	0.828945	−	0.602264i	−0.0903156	−	0.995913i	$-0.528788\pi$
$59$	6.36725	−	4.62608i	0.828945	−	0.602264i	0.919261	+	0.393649i	$0.128788\pi$
$60$		0			0
$61$	−1.50123	+	4.62030i	−0.192212	+	0.591569i	0.807785	+	0.589477i	$0.200666\pi$
$61$	−1.50123	+	4.62030i	−0.192212	+	0.591569i	−0.999998	+	0.00209225i	$0.999334\pi$
$62$	−2.66165	+	1.93381i	−0.338031	+	0.245594i
$63$	−3.46813	−	2.51974i	−0.436943	−	0.317458i
$64$	2.66892	+	8.21410i	0.333615	+	1.02676i
$65$		0			0
$66$	−0.0182340	+	3.85436i	−0.00224445	+	0.474439i
$67$	−12.1280			−1.48167			−0.740834	−	0.671688i	$-0.765569\pi$
$67$	−12.1280			−1.48167			−0.740834	+	0.671688i	$0.765569\pi$
$68$	1.00340	+	3.08815i	0.121680	+	0.374493i
$69$	0.177837	+	0.129206i	0.0214091	+	0.0155546i
$70$		0			0
$71$	−3.08459	+	9.49339i	−0.366073	+	1.12666i	0.583233	+	0.812305i	$0.301788\pi$
$71$	−3.08459	+	9.49339i	−0.366073	+	1.12666i	−0.949306	+	0.314353i	$0.898212\pi$
$72$	0.951466	−	2.92831i	0.112131	−	0.345105i
$73$	11.7813	−	8.55964i	1.37890	−	1.00183i	0.381918	−	0.924196i	$-0.375264\pi$
$73$	11.7813	−	8.55964i	1.37890	−	1.00183i	0.996982	−	0.0776335i	$-0.0247364\pi$
$74$	−3.69311	−	2.68320i	−0.429316	−	0.311916i
$75$		0			0
$76$	−3.63670			−0.417158
$77$	8.41136	−	11.4628i	0.958564	−	1.30631i
$78$	−6.00509			−0.679942
$79$	2.47274	+	7.61030i	0.278205	+	0.856226i	0.988354	+	0.152174i	$0.0486275\pi$
$79$	2.47274	+	7.61030i	0.278205	+	0.856226i	−0.710149	+	0.704051i	$0.751372\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.10482	+	6.47797i	−0.232439	+	0.715373i
$83$	−3.87908	+	11.9386i	−0.425784	+	1.31043i	0.476458	+	0.879197i	$0.341921\pi$
$83$	−3.87908	+	11.9386i	−0.425784	+	1.31043i	−0.902242	+	0.431231i	$0.858079\pi$
$84$	−2.25225	+	1.63636i	−0.245741	+	0.178541i
$85$		0			0
$86$	−3.19682	−	9.83880i	−0.344722	−	1.06094i
$87$	−6.41843			−0.688128
$88$	9.69707	+	3.20157i	1.03371	+	0.341288i
$89$	−2.56545			−0.271937			−0.135969	−	0.990713i	$-0.543415\pi$
$89$	−2.56545			−0.271937			−0.135969	+	0.990713i	$0.543415\pi$
$90$		0			0
$91$	17.9206	+	13.0201i	1.87859	+	1.36488i
$92$	0.115490	−	0.0839083i	0.0120407	−	0.00874805i
$93$	0.874813	−	2.69240i	0.0907139	−	0.279189i
$94$	−0.0854274	+	0.262919i	−0.00881116	+	0.0271180i
$95$		0			0
$96$	−2.83882	−	2.06253i	−0.289736	−	0.210506i
$97$	−0.621738	−	1.91351i	−0.0631279	−	0.194288i	0.914518	−	0.404545i	$-0.132570\pi$
$97$	−0.621738	−	1.91351i	−0.0631279	−	0.194288i	−0.977646	+	0.210257i	$0.932570\pi$
$98$	−13.2218			−1.33560
$99$	−1.93675	−	2.69240i	−0.194650	−	0.270596i
$100$		0			0
$101$	−2.34385	−	7.21362i	−0.233221	−	0.717782i	−0.997352	−	0.0727205i	$-0.976832\pi$
$101$	−2.34385	−	7.21362i	−0.233221	−	0.717782i	0.764131	−	0.645061i	$-0.223168\pi$
$102$	4.70098	+	3.41546i	0.465467	+	0.338181i
$103$	−13.6469	+	9.91508i	−1.34467	+	0.976962i	−0.345414	+	0.938450i	$0.612262\pi$
$103$	−13.6469	+	9.91508i	−1.34467	+	0.976962i	−0.999258	+	0.0385116i	$0.987738\pi$
$104$	−4.91645	+	15.1313i	−0.482098	+	1.48374i
$105$		0			0
$106$	−2.38500	+	1.73281i	−0.231652	+	0.168305i
$107$	6.27928	+	4.56216i	0.607041	+	0.441041i	0.848371	−	0.529402i	$-0.177584\pi$
$107$	6.27928	+	4.56216i	0.607041	+	0.441041i	−0.241330	+	0.970443i	$0.577584\pi$
$108$	0.200680	+	0.617629i	0.0193104	+	0.0594314i
$109$	4.45671			0.426876			0.213438	−	0.976957i	$-0.431534\pi$
$109$	4.45671			0.426876			0.213438	+	0.976957i	$0.431534\pi$
$110$		0			0
$111$	3.92802			0.372831
$112$	−3.01958	−	9.29332i	−0.285324	−	0.878136i
$113$	−6.23952	−	4.53327i	−0.586964	−	0.426455i	0.254264	−	0.967135i	$-0.418167\pi$
$113$	−6.23952	−	4.53327i	−0.586964	−	0.426455i	−0.841228	+	0.540680i	$0.818167\pi$
$114$	−5.26508	+	3.82530i	−0.493120	+	0.358273i
$115$		0			0
$116$	−1.28805	+	3.96421i	−0.119593	+	0.368068i
$117$	4.18038	−	3.03722i	0.386476	−	0.280792i
$118$	−7.39968	−	5.37618i	−0.681196	−	0.494918i
$119$	−6.62353	−	20.3851i	−0.607178	−	1.86870i
$120$		0			0
$121$	8.95996	−	6.38115i	0.814542	−	0.580105i
$122$	5.64579			0.511146
$123$	−1.81115	−	5.57414i	−0.163306	−	0.502603i
$124$	−1.48735	−	1.08062i	−0.133568	−	0.0970426i
$125$		0			0
$126$	−1.53950	+	4.73811i	−0.137150	+	0.422104i
$127$	−0.473149	+	1.45620i	−0.0419852	+	0.129217i	−0.969852	−	0.243695i	$-0.921641\pi$
$127$	−0.473149	+	1.45620i	−0.0419852	+	0.129217i	0.927867	+	0.372912i	$0.121641\pi$
$128$	2.44266	−	1.77470i	0.215903	−	0.156863i
$129$	7.20165	+	5.23231i	0.634070	+	0.460679i
$130$		0			0
$131$	2.66108			0.232500			0.116250	−	0.993220i	$-0.462913\pi$
$131$	2.66108			0.232500			0.116250	+	0.993220i	$0.462913\pi$
$132$	−2.05157	+	0.655882i	−0.178566	+	0.0570872i
$133$	24.0062			2.08160
$134$	4.35544	+	13.4047i	0.376252	+	1.15799i
$135$		0			0
$136$	12.4549	−	9.04898i	1.06799	−	0.775944i
$137$	−3.16911	+	9.75352i	−0.270756	+	0.833300i	0.719556	+	0.694435i	$0.244345\pi$
$137$	−3.16911	+	9.75352i	−0.270756	+	0.833300i	−0.990311	+	0.138865i	$0.955655\pi$
$138$	0.0789420	−	0.242959i	0.00671999	−	0.0206820i
$139$	4.28381	−	3.11237i	0.363348	−	0.263987i	−0.391099	−	0.920348i	$-0.627905\pi$
$139$	4.28381	−	3.11237i	0.363348	−	0.263987i	0.754447	+	0.656361i	$0.227905\pi$
$140$		0			0
$141$	−0.0735083	−	0.226235i	−0.00619051	−	0.0190524i
$142$	11.6005			0.973491
$143$	10.0076	+	13.9123i	0.836880	+	1.16340i
$144$	−2.27943			−0.189953
$145$		0			0
$146$	−13.6916	−	9.94756i	−1.13313	−	0.823266i
$147$	9.20420	−	6.68724i	0.759149	−	0.551554i
$148$	0.788275	−	2.42606i	0.0647958	−	0.199421i
$149$	1.17068	−	3.60300i	0.0959062	−	0.295169i	−0.891583	−	0.452858i	$-0.850404\pi$
$149$	1.17068	−	3.60300i	0.0959062	−	0.295169i	0.987489	+	0.157689i	$0.0504044\pi$
$150$		0			0
$151$	4.78939	+	3.47969i	0.389755	+	0.283173i	0.765355	−	0.643608i	$-0.222563\pi$
$151$	4.78939	+	3.47969i	0.389755	+	0.283173i	−0.375600	+	0.926782i	$0.622563\pi$
$152$	5.32819	+	16.3985i	0.432173	+	1.33009i
$153$	−5.00000			−0.404226
$154$	−15.6902	−	5.18024i	−1.26435	−	0.417436i
$155$		0			0
$156$	−1.03696	−	3.19144i	−0.0830233	−	0.255519i
$157$	−6.01026	−	4.36671i	−0.479671	−	0.348501i	0.321528	−	0.946900i	$-0.395804\pi$
$157$	−6.01026	−	4.36671i	−0.479671	−	0.348501i	−0.801198	+	0.598399i	$0.795804\pi$
$158$	7.52340	−	5.46607i	0.598530	−	0.434857i
$159$	0.783885	−	2.41255i	0.0621661	−	0.191328i
$160$		0			0
$161$	−0.762360	+	0.553887i	−0.0600824	+	0.0436524i
$162$	0.940197	+	0.683093i	0.0738688	+	0.0536689i
$163$	−1.64424	−	5.06044i	−0.128786	−	0.396364i	0.865785	−	0.500415i	$-0.166819\pi$
$163$	−1.64424	−	5.06044i	−0.128786	−	0.396364i	−0.994572	+	0.104051i	$0.966819\pi$
$164$	−3.80621			−0.297215
$165$		0			0
$166$	14.5884			1.13228
$167$	0.609193	+	1.87490i	0.0471407	+	0.145084i	0.971856	−	0.235575i	$-0.0756972\pi$
$167$	0.609193	+	1.87490i	0.0471407	+	0.145084i	−0.924716	+	0.380659i	$0.875697\pi$
$168$	10.6784	+	7.75831i	0.823856	+	0.598567i
$169$	−11.0838	+	8.05285i	−0.852599	+	0.619450i
$170$		0			0
$171$	1.73049	−	5.32589i	0.132334	−	0.407281i
$172$	4.67685	−	3.39793i	0.356607	−	0.259090i
$173$	−1.59784	−	1.16090i	−0.121482	−	0.0882617i	0.525385	−	0.850864i	$-0.323921\pi$
$173$	−1.59784	−	1.16090i	−0.121482	−	0.0882617i	−0.646867	+	0.762603i	$0.723921\pi$
$174$	2.30501	+	7.09409i	0.174742	+	0.537801i
$175$		0			0
$176$	0.0357642	−	7.55994i	0.00269583	−	0.569852i
$177$	7.87035			0.591572
$178$	0.921313	+	2.83551i	0.0690553	+	0.212530i
$179$	1.63676	+	1.18918i	0.122337	+	0.0888832i	0.647271	−	0.762260i	$-0.275910\pi$
$179$	1.63676	+	1.18918i	0.122337	+	0.0888832i	−0.524934	+	0.851143i	$0.675910\pi$
$180$		0			0
$181$	6.22299	−	19.1524i	0.462551	−	1.42359i	−0.399485	−	0.916740i	$-0.630811\pi$
$181$	6.22299	−	19.1524i	0.462551	−	1.42359i	0.862036	−	0.506846i	$-0.169189\pi$
$182$	7.95498	−	24.4829i	0.589662	−	1.81479i
$183$	−3.93026	+	2.85550i	−0.290533	+	0.211085i
$184$	−0.547562	−	0.397827i	−0.0403668	−	0.0293282i
$185$		0			0
$186$	−3.28999			−0.241234
$187$	0.0784497	−	16.5829i	0.00573681	−	1.21266i
$188$	−0.154481			−0.0112667
$189$	−1.32471	−	4.07703i	−0.0963583	−	0.296560i
$190$		0			0
$191$	−10.2463	+	7.44439i	−0.741398	+	0.538657i	−0.893149	−	0.449762i	$-0.851509\pi$
$191$	−10.2463	+	7.44439i	−0.741398	+	0.538657i	0.151751	+	0.988419i	$0.451509\pi$
$192$	−2.66892	+	8.21410i	−0.192613	+	0.592802i
$193$	4.30526	−	13.2502i	0.309900	−	0.953773i	−0.667904	−	0.744248i	$-0.732808\pi$
$193$	4.30526	−	13.2502i	0.309900	−	0.953773i	0.977803	−	0.209525i	$-0.0671919\pi$
$194$	−1.89166	+	1.37437i	−0.135813	+	0.0986743i
$195$		0			0
$196$	−2.28314	−	7.02678i	−0.163081	−	0.501913i
$197$	−14.6060			−1.04064			−0.520319	−	0.853972i	$-0.674187\pi$
$197$	−14.6060			−1.04064			−0.520319	+	0.853972i	$0.674187\pi$
$198$	−2.28029	+	3.10753i	−0.162053	+	0.220842i
$199$	−11.8748			−0.841784			−0.420892	−	0.907111i	$-0.638283\pi$
$199$	−11.8748			−0.841784			−0.420892	+	0.907111i	$0.638283\pi$
$200$		0			0
$201$	−9.81174	−	7.12864i	−0.692067	−	0.502816i
$202$	−7.13125	+	5.18115i	−0.501753	+	0.364545i
$203$	8.50254	−	26.1681i	0.596762	−	1.83664i
$204$	−1.00340	+	3.08815i	−0.0702520	+	0.216213i
$205$		0			0
$206$	15.8597	+	11.5228i	1.10500	+	0.802830i
$207$	0.0679277	+	0.209060i	0.00472130	+	0.0145307i
$208$	11.7784			0.816683
$209$	17.6366	+	5.82288i	1.21995	+	0.402777i
$210$		0			0
$211$	−6.90710	−	21.2579i	−0.475504	−	1.46345i	−0.845277	−	0.534329i	$-0.820564\pi$
$211$	−6.90710	−	21.2579i	−0.475504	−	1.46345i	0.369772	−	0.929122i	$-0.379436\pi$
$212$	−1.33275	−	0.968301i	−0.0915338	−	0.0665032i
$213$	−8.07556	+	5.86724i	−0.553328	+	0.402017i
$214$	2.78738	−	8.57866i	0.190541	−	0.586425i
$215$		0			0
$216$	2.49097	−	1.80980i	0.169489	−	0.123141i
$217$	9.81811	+	7.13328i	0.666497	+	0.484238i
$218$	−1.60051	−	4.92586i	−0.108400	−	0.333621i
$219$	14.5625			0.984044
$220$		0			0
$221$	25.8362			1.73793
$222$	−1.41064	−	4.34152i	−0.0946762	−	0.291384i
$223$	−15.4994	−	11.2610i	−1.03792	−	0.754091i	−0.0680388	−	0.997683i	$-0.521674\pi$
$223$	−15.4994	−	11.2610i	−1.03792	−	0.754091i	−0.969878	+	0.243592i	$0.921674\pi$
$224$	12.1696	−	8.84173i	0.813115	−	0.590763i
$225$		0			0
$226$	−2.76973	+	8.52434i	−0.184239	+	0.567031i
$227$	12.4394	−	9.03772i	0.825629	−	0.599855i	−0.0926901	−	0.995695i	$-0.529547\pi$
$227$	12.4394	−	9.03772i	0.825629	−	0.599855i	0.918319	+	0.395840i	$0.129547\pi$
$228$	−2.94215	−	2.13760i	−0.194849	−	0.141566i
$229$	2.75064	+	8.46560i	0.181767	+	0.559422i	0.999878	−	0.0156388i	$-0.00497820\pi$
$229$	2.75064	+	8.46560i	0.181767	+	0.559422i	−0.818110	+	0.575061i	$0.804978\pi$
$230$		0			0
$231$	13.5426	−	4.32954i	0.891038	−	0.284863i
$232$	19.7624			1.29747
$233$	−7.05677	−	21.7185i	−0.462304	−	1.42283i	−0.862342	−	0.506327i	$-0.831003\pi$
$233$	−7.05677	−	21.7185i	−0.462304	−	1.42283i	0.400037	−	0.916499i	$-0.368997\pi$
$234$	−4.85822	−	3.52970i	−0.317592	−	0.230744i
$235$		0			0
$236$	1.57942	−	4.86096i	0.102812	−	0.316422i
$237$	−2.47274	+	7.61030i	−0.160621	+	0.494342i
$238$	−20.1524	+	14.6416i	−1.30628	+	0.949071i
$239$	−13.6405	−	9.91037i	−0.882327	−	0.641048i	0.0515388	−	0.998671i	$-0.483587\pi$
$239$	−13.6405	−	9.91037i	−0.882327	−	0.641048i	−0.933866	+	0.357623i	$0.883587\pi$
$240$		0			0
$241$	−11.9607			−0.770459			−0.385229	−	0.922821i	$-0.625878\pi$
$241$	−11.9607			−0.770459			−0.385229	+	0.922821i	$0.625878\pi$
$242$	−10.2706	−	7.61154i	−0.660220	−	0.489288i
$243$	−1.00000			−0.0641500
$244$	0.974917	+	3.00049i	0.0624127	+	0.192087i
$245$		0			0
$246$	−5.51049	+	4.00361i	−0.351336	+	0.255261i
$247$	−8.94184	+	27.5201i	−0.568955	+	1.75106i
$248$	−2.69356	+	8.28992i	−0.171041	+	0.526410i
$249$	−10.1556	+	7.37844i	−0.643582	+	0.467590i
$250$		0			0
$251$	4.94533	+	15.2201i	0.312146	+	0.960687i	0.976913	+	0.213637i	$0.0685308\pi$
$251$	4.94533	+	15.2201i	0.312146	+	0.960687i	−0.664767	+	0.747051i	$0.731469\pi$
$252$	−2.78393			−0.175371
$253$	−0.694432	+	0.222008i	−0.0436586	+	0.0139575i
$254$	1.77941			0.111650
$255$		0			0
$256$	11.1359	+	8.09073i	0.695996	+	0.505671i
$257$	4.42893	−	3.21780i	0.276269	−	0.200721i	−0.441019	−	0.897498i	$-0.645383\pi$
$257$	4.42893	−	3.21780i	0.276269	−	0.200721i	0.717288	+	0.696776i	$0.245383\pi$
$258$	3.19682	−	9.83880i	0.199025	−	0.612537i
$259$	−5.20348	+	16.0147i	−0.323328	+	0.995103i
$260$		0			0
$261$	−5.19262	−	3.77266i	−0.321415	−	0.233522i
$262$	−0.955657	−	2.94121i	−0.0590407	−	0.181709i
$263$	−11.9841			−0.738971			−0.369486	−	0.929236i	$-0.620466\pi$
$263$	−11.9841			−0.738971			−0.369486	+	0.929236i	$0.620466\pi$
$264$	5.96326	+	8.28992i	0.367014	+	0.510209i
$265$		0			0
$266$	−8.62119	−	26.5333i	−0.528599	−	1.62686i
$267$	−2.07549	−	1.50793i	−0.127018	−	0.0922841i
$268$	−6.37188	+	4.62944i	−0.389224	+	0.282788i
$269$	4.21700	−	12.9786i	0.257115	−	0.791318i	−0.736291	−	0.676665i	$-0.763424\pi$
$269$	4.21700	−	12.9786i	0.257115	−	0.791318i	0.993406	−	0.114653i	$-0.0365755\pi$
$270$		0			0
$271$	−9.57702	+	6.95812i	−0.581763	+	0.422675i	−0.839359	−	0.543577i	$-0.817070\pi$
$271$	−9.57702	+	6.95812i	−0.581763	+	0.422675i	0.257596	+	0.966253i	$0.417070\pi$
$272$	−9.22050	−	6.69909i	−0.559075	−	0.406192i
$273$	6.84507	+	21.0670i	0.414283	+	1.27503i
$274$	11.9184			0.720014
$275$		0			0
$276$	0.142753			0.00859274
$277$	−3.17170	−	9.76148i	−0.190569	−	0.586511i	0.809431	−	0.587215i	$-0.199776\pi$
$277$	−3.17170	−	9.76148i	−0.190569	−	0.586511i	−1.00000		0.000704561i	$0.999776\pi$
$278$	−4.97841	−	3.61703i	−0.298585	−	0.216935i
$279$	2.29029	−	1.66399i	0.137116	−	0.0996207i
$280$		0			0
$281$	−0.908167	+	2.79505i	−0.0541767	+	0.166739i	−0.974484	−	0.224458i	$-0.927939\pi$
$281$	−0.908167	+	2.79505i	−0.0541767	+	0.166739i	0.920307	+	0.391197i	$0.127939\pi$
$282$	−0.223652	+	0.162493i	−0.0133183	+	0.00967629i
$283$	17.6592	+	12.8301i	1.04973	+	0.762673i	0.972161	−	0.234314i	$-0.0752844\pi$
$283$	17.6592	+	12.8301i	1.04973	+	0.762673i	0.0775682	+	0.996987i	$0.475284\pi$
$284$	2.00318	+	6.16514i	0.118867	+	0.365834i
$285$		0			0
$286$	11.7828	−	16.0573i	0.696731	−	0.949490i
$287$	25.1252			1.48309
$288$	−1.08433	−	3.33724i	−0.0638950	−	0.196649i
$289$	−6.47214	−	4.70228i	−0.380714	−	0.276605i
$290$		0			0
$291$	0.621738	−	1.91351i	0.0364469	−	0.112172i
$292$	2.92241	−	8.99424i	0.171021	−	0.526348i
$293$	−20.0365	+	14.5574i	−1.17055	+	0.850452i	−0.991074	−	0.133311i	$-0.957439\pi$
$293$	−20.0365	+	14.5574i	−1.17055	+	0.850452i	−0.179473	+	0.983763i	$0.557439\pi$
$294$	−10.6966	−	7.77156i	−0.623840	−	0.453246i
$295$		0			0
$296$	−12.0944			−0.702974
$297$	0.0156899	−	3.31659i	0.000910423	−	0.192448i
$298$	−4.40269			−0.255041
$299$	−0.350999	−	1.08026i	−0.0202988	−	0.0624732i
$300$		0			0
$301$	−30.8723	+	22.4301i	−1.77945	+	1.29285i
$302$	2.12601	−	6.54319i	0.122338	−	0.376518i
$303$	2.34385	−	7.21362i	0.134650	−	0.414411i
$304$	10.3269	−	7.50295i	0.592289	−	0.430323i
$305$		0			0
$306$	1.79562	+	5.52634i	0.102649	+	0.315920i
$307$	4.94023			0.281954			0.140977	−	0.990013i	$-0.454976\pi$
$307$	4.94023			0.281954			0.140977	+	0.990013i	$0.454976\pi$
$308$	0.0436798	−	9.23316i	0.00248889	−	0.526108i
$309$	−16.8685			−0.959618
$310$		0			0
$311$	11.1722	+	8.11707i	0.633517	+	0.460277i	0.857617	−	0.514289i	$-0.171944\pi$
$311$	11.1722	+	8.11707i	0.633517	+	0.460277i	−0.224100	+	0.974566i	$0.571944\pi$
$312$	−12.8714	+	9.35164i	−0.728701	+	0.529432i
$313$	1.25750	−	3.87017i	0.0710779	−	0.218755i	−0.909207	−	0.416344i	$-0.863311\pi$
$313$	1.25750	−	3.87017i	0.0710779	−	0.218755i	0.980285	+	0.197589i	$0.0633111\pi$
$314$	−2.66796	+	8.21113i	−0.150562	+	0.463381i
$315$		0			0
$316$	4.20412	+	3.05447i	0.236500	+	0.171827i
$317$	−7.97880	−	24.5562i	−0.448134	−	1.37921i	−0.879010	−	0.476803i	$-0.841795\pi$
$317$	−7.97880	−	24.5562i	−0.448134	−	1.37921i	0.430876	−	0.902411i	$-0.358205\pi$
$318$	−2.94803			−0.165317
$319$	12.5938	−	17.1626i	0.705119	−	0.960921i
$320$		0			0
$321$	2.39847	+	7.38173i	0.133870	+	0.412008i
$322$	0.885974	+	0.643698i	0.0493734	+	0.0358719i
$323$	22.6524	−	16.4579i	1.26041	−	0.915743i
$324$	−0.200680	+	0.617629i	−0.0111489	+	0.0343127i
$325$		0			0
$326$	−5.00265	+	3.63464i	−0.277071	+	0.201304i
$327$	3.60556	+	2.61959i	0.199388	+	0.144864i
$328$	5.57654	+	17.1628i	0.307913	+	0.947659i
$329$	1.01974			0.0562203
$330$		0			0
$331$	−3.35008			−0.184137			−0.0920684	−	0.995753i	$-0.529348\pi$
$331$	−3.35008			−0.184137			−0.0920684	+	0.995753i	$0.529348\pi$
$332$	2.51913	+	7.75307i	0.138255	+	0.425505i
$333$	3.17784	+	2.30883i	0.174144	+	0.126523i
$334$	1.85349	−	1.34664i	0.101419	−	0.0736850i
$335$		0			0
$336$	3.01958	−	9.29332i	0.164732	−	0.506992i
$337$	−22.1669	+	16.1052i	−1.20751	+	0.877307i	−0.995002	−	0.0998530i	$-0.968163\pi$
$337$	−22.1669	+	16.1052i	−1.20751	+	0.877307i	−0.212507	+	0.977160i	$0.568163\pi$
$338$	12.8810	+	9.35859i	0.700634	+	0.509040i
$339$	−2.38328	−	7.33499i	−0.129442	−	0.398382i
$340$		0			0
$341$	5.48285	+	7.62206i	0.296913	+	0.412758i
$342$	−6.50800			−0.351912
$343$	5.79826	+	17.8452i	0.313076	+	0.963550i
$344$	−22.1739	−	16.1103i	−1.19554	−	0.868610i
$345$		0			0
$346$	−0.709284	+	2.18295i	−0.0381313	+	0.117356i
$347$	−4.89065	+	15.0519i	−0.262544	+	0.808027i	0.729705	+	0.683762i	$0.239657\pi$
$347$	−4.89065	+	15.0519i	−0.262544	+	0.808027i	−0.992249	+	0.124265i	$0.960343\pi$
$348$	−3.37216	+	2.45002i	−0.180767	+	0.131335i
$349$	2.96043	+	2.15088i	0.158468	+	0.115134i	0.664194	−	0.747561i	$-0.268775\pi$
$349$	2.96043	+	2.15088i	0.158468	+	0.115134i	−0.505725	+	0.862695i	$0.668775\pi$
$350$		0			0
$351$	5.16724			0.275807
$352$	11.0853	−	3.54393i	0.590846	−	0.188892i
$353$	27.4937			1.46334			0.731671	−	0.681658i	$-0.238741\pi$
$353$	27.4937			1.46334			0.731671	+	0.681658i	$0.238741\pi$
$354$	−2.82643	−	8.69884i	−0.150223	−	0.462338i
$355$		0			0
$356$	−1.34785	+	0.979273i	−0.0714361	+	0.0519014i
$357$	6.62353	−	20.3851i	0.350555	−	1.07890i
$358$	0.726559	−	2.23612i	0.0383998	−	0.118183i
$359$	−0.387309	+	0.281397i	−0.0204414	+	0.0148515i	−0.597959	−	0.801527i	$-0.704021\pi$
$359$	−0.387309	+	0.281397i	−0.0204414	+	0.0148515i	0.577518	+	0.816378i	$0.304021\pi$
$360$		0			0
$361$	3.81936	+	11.7548i	0.201019	+	0.618673i
$362$	−23.4033			−1.23005
$363$	10.9995	+	0.104074i	0.577324	+	0.00546247i
$364$	14.3852			0.753992
$365$		0			0
$366$	4.56754	+	3.31851i	0.238749	+	0.173462i
$367$	−20.5961	+	14.9639i	−1.07511	+	0.781111i	−0.976823	−	0.214047i	$-0.931335\pi$
$367$	−20.5961	+	14.9639i	−1.07511	+	0.781111i	−0.0982843	+	0.995158i	$0.531335\pi$
$368$	−0.154837	+	0.476539i	−0.00807143	+	0.0248413i
$369$	1.81115	−	5.57414i	0.0942846	−	0.290178i
$370$		0			0
$371$	8.79762	+	6.39184i	0.456750	+	0.331848i
$372$	−0.568116	−	1.74848i	−0.0294554	−	0.0906545i
$373$	2.75967			0.142890			0.0714451	−	0.997445i	$-0.477239\pi$
$373$	2.75967			0.142890			0.0714451	+	0.997445i	$0.477239\pi$
$374$	−18.3568	+	5.86861i	−0.949205	+	0.303459i
$375$		0			0
$376$	0.226333	+	0.696580i	0.0116722	+	0.0359234i
$377$	26.8315	+	19.4942i	1.38189	+	1.00400i
$378$	−4.03048	+	2.92831i	−0.207305	+	0.150616i
$379$	−6.69130	+	20.5937i	−0.343709	+	1.05783i	0.618562	+	0.785736i	$0.287716\pi$
$379$	−6.69130	+	20.5937i	−0.343709	+	1.05783i	−0.962271	+	0.272092i	$0.912284\pi$
$380$		0			0
$381$	−1.23872	+	0.899983i	−0.0634616	+	0.0461075i
$382$	11.9077	+	8.65148i	0.609253	+	0.442648i
$383$	−5.01518	−	15.4351i	−0.256264	−	0.788699i	−0.993578	−	0.113149i	$-0.963906\pi$
$383$	−5.01518	−	15.4351i	−0.256264	−	0.788699i	0.737314	−	0.675550i	$-0.236094\pi$
$384$	3.01930			0.154078
$385$		0			0
$386$	−16.1912			−0.824109
$387$	2.75079	+	8.46605i	0.139830	+	0.430353i
$388$	−1.05707	−	0.768007i	−0.0536647	−	0.0389897i
$389$	13.1802	−	9.57598i	0.668263	−	0.485522i	−0.201180	−	0.979554i	$-0.564478\pi$
$389$	13.1802	−	9.57598i	0.668263	−	0.485522i	0.869443	+	0.494033i	$0.164478\pi$
$390$		0			0
$391$	−0.339639	+	1.04530i	−0.0171763	+	0.0528631i
$392$	−28.3398	+	20.5901i	−1.43138	+	1.03996i
$393$	2.15286	+	1.56415i	0.108598	+	0.0789007i
$394$	5.24537	+	16.1436i	0.264258	+	0.813302i
$395$		0			0
$396$	−2.04527	−	0.675263i	−0.102779	−	0.0339332i
$397$	19.9673			1.00213			0.501064	−	0.865410i	$-0.332942\pi$
$397$	19.9673			1.00213			0.501064	+	0.865410i	$0.332942\pi$
$398$	4.26453	+	13.1249i	0.213761	+	0.657890i
$399$	19.4214	+	14.1105i	0.972288	+	0.706408i
$400$		0			0
$401$	−8.44448	+	25.9894i	−0.421697	+	1.29785i	0.484425	+	0.874833i	$0.339029\pi$
$401$	−8.44448	+	25.9894i	−0.421697	+	1.29785i	−0.906122	+	0.423017i	$0.860971\pi$
$402$	−4.35544	+	13.4047i	−0.217229	+	0.668563i
$403$	−11.8345	+	8.59825i	−0.589517	+	0.428309i
$404$	−3.98498	−	2.89526i	−0.198260	−	0.144044i
$405$		0			0
$406$	−31.9763			−1.58696
$407$	−7.70731	+	10.5034i	−0.382037	+	0.520632i
$408$	15.3950			0.762168
$409$	7.70626	+	23.7174i	0.381050	+	1.17275i	0.939305	+	0.343082i	$0.111471\pi$
$409$	7.70626	+	23.7174i	0.381050	+	1.17275i	−0.558255	+	0.829669i	$0.688529\pi$
$410$		0			0
$411$	−8.29684	+	6.02801i	−0.409253	+	0.297340i
$412$	−3.38518	+	10.4185i	−0.166776	+	0.513283i
$413$	−10.4259	+	32.0876i	−0.513025	+	1.57893i
$414$	0.206673	−	0.150157i	0.0101574	−	0.00737980i
$415$		0			0
$416$	5.60301	+	17.2443i	0.274710	+	0.845471i
$417$	5.29507			0.259301
$418$	0.102110	−	21.5843i	0.00499437	−	1.05572i
$419$	16.8256			0.821986			0.410993	−	0.911639i	$-0.365182\pi$
$419$	16.8256			0.821986			0.410993	+	0.911639i	$0.365182\pi$
$420$		0			0
$421$	−19.0933	−	13.8721i	−0.930551	−	0.676085i	0.0155763	−	0.999879i	$-0.495042\pi$
$421$	−19.0933	−	13.8721i	−0.930551	−	0.676085i	−0.946128	+	0.323793i	$0.895042\pi$
$422$	−21.0151	+	15.2684i	−1.02300	+	0.743253i
$423$	0.0735083	−	0.226235i	0.00357409	−	0.0109999i
$424$	−2.41359	+	7.42826i	−0.117214	+	0.360748i
$425$		0			0
$426$	9.38499	+	6.81859i	0.454704	+	0.330362i
$427$	−6.43552	−	19.8065i	−0.311437	−	0.958504i
$428$	5.04050			0.243642
$429$	−0.0810736	+	17.1376i	−0.00391427	+	0.827411i
$430$		0			0
$431$	−11.6362	−	35.8126i	−0.560497	−	1.72503i	−0.680966	−	0.732315i	$-0.738440\pi$
$431$	−11.6362	−	35.8126i	−0.560497	−	1.72503i	0.120469	−	0.992717i	$-0.461560\pi$
$432$	−1.84410	−	1.33982i	−0.0887243	−	0.0644620i
$433$	−25.0594	+	18.2068i	−1.20428	+	0.874961i	−0.994699	−	0.102831i	$-0.967210\pi$
$433$	−25.0594	+	18.2068i	−1.20428	+	0.874961i	−0.209581	+	0.977791i	$0.567210\pi$
$434$	4.35827	−	13.4134i	0.209204	−	0.643862i
$435$		0			0
$436$	2.34150	−	1.70120i	0.112137	−	0.0814726i
$437$	−0.995884	−	0.723552i	−0.0476396	−	0.0346122i
$438$	−5.22974	−	16.0955i	−0.249887	−	0.769072i
$439$	−28.2131			−1.34654			−0.673268	−	0.739399i	$-0.735110\pi$
$439$	−28.2131			−1.34654			−0.673268	+	0.739399i	$0.735110\pi$
$440$		0			0
$441$	11.3770			0.541762
$442$	−9.27837	−	28.5559i	−0.441327	−	1.35827i
$443$	11.8456	+	8.60636i	0.562803	+	0.408900i	0.832484	−	0.554050i	$-0.186918\pi$
$443$	11.8456	+	8.60636i	0.562803	+	0.408900i	−0.269681	+	0.962950i	$0.586918\pi$
$444$	2.06373	−	1.49939i	0.0979404	−	0.0711578i
$445$		0			0
$446$	−6.88019	+	21.1751i	−0.325787	+	1.00267i
$447$	3.06489	−	2.22677i	0.144964	−	0.105323i
$448$	−29.9536	−	21.7626i	−1.41517	−	1.02818i
$449$	3.70749	+	11.4105i	0.174967	+	0.538493i	0.999632	−	0.0271282i	$-0.00863625\pi$
$449$	3.70749	+	11.4105i	0.174967	+	0.538493i	−0.824665	+	0.565622i	$0.808636\pi$
$450$		0			0
$451$	18.4587	+	6.09429i	0.869187	+	0.286969i
$452$	−5.00858			−0.235584
$453$	1.82938	+	5.63026i	0.0859519	+	0.264533i
$454$	−14.4564	−	10.5032i	−0.678471	−	0.492938i
$455$		0			0
$456$	−5.32819	+	16.3985i	−0.249515	+	0.767929i
$457$	−3.10367	+	9.55211i	−0.145183	+	0.446829i	−0.997035	−	0.0769553i	$-0.975480\pi$
$457$	−3.10367	+	9.55211i	−0.145183	+	0.446829i	0.851851	+	0.523784i	$0.175480\pi$
$458$	8.36893	−	6.08039i	0.391055	−	0.284118i
$459$	−4.04508	−	2.93893i	−0.188808	−	0.137177i
$460$		0			0
$461$	−13.4491			−0.626386			−0.313193	−	0.949689i	$-0.601399\pi$
$461$	−13.4491			−0.626386			−0.313193	+	0.949689i	$0.601399\pi$
$462$	−9.64876	−	13.4134i	−0.448901	−	0.624046i
$463$	−18.7836			−0.872946			−0.436473	−	0.899717i	$-0.643773\pi$
$463$	−18.7836			−0.872946			−0.436473	+	0.899717i	$0.643773\pi$
$464$	−4.52104	−	13.9143i	−0.209884	−	0.645957i
$465$		0			0
$466$	−21.4705	+	15.5992i	−0.994602	+	0.722620i
$467$	−8.20470	+	25.2515i	−0.379668	+	1.16850i	0.560607	+	0.828082i	$0.310568\pi$
$467$	−8.20470	+	25.2515i	−0.379668	+	1.16850i	−0.940275	+	0.340416i	$0.889432\pi$
$468$	1.03696	−	3.19144i	0.0479335	−	0.147524i
$469$	42.0614	−	30.5594i	1.94221	−	1.41110i
$470$		0			0
$471$	−2.29571	−	7.06548i	−0.105781	−	0.325560i
$472$	−24.2329			−1.11541
$473$	−28.1216	+	8.99039i	−1.29303	+	0.413379i
$474$	9.29944			0.427137
$475$		0			0
$476$	−11.2613	−	8.18178i	−0.516159	−	0.375011i
$477$	2.05224	−	1.49104i	0.0939655	−	0.0682699i
$478$	−6.05501	+	18.6354i	−0.276950	+	0.852363i
$479$	3.33214	−	10.2553i	0.152249	−	0.468575i	−0.845623	−	0.533781i	$-0.820771\pi$
$479$	3.33214	−	10.2553i	0.152249	−	0.468575i	0.997872	+	0.0652062i	$0.0207705\pi$
$480$		0			0
$481$	−16.4206	−	11.9303i	−0.748716	−	0.543974i
$482$	4.29538	+	13.2198i	0.195649	+	0.602146i
$483$	−0.942328			−0.0428774
$484$	2.27166	−	6.77273i	0.103257	−	0.307851i
$485$		0			0
$486$	0.359123	+	1.10527i	0.0162902	+	0.0501360i
$487$	5.51018	+	4.00338i	0.249690	+	0.181410i	0.705589	−	0.708621i	$-0.250682\pi$
$487$	5.51018	+	4.00338i	0.249690	+	0.181410i	−0.455899	+	0.890031i	$0.650682\pi$
$488$	12.1013	−	8.79212i	0.547801	−	0.398001i
$489$	1.64424	−	5.06044i	0.0743549	−	0.228841i
$490$		0			0
$491$	−21.1116	+	15.3385i	−0.952754	+	0.692216i	−0.951457	−	0.307783i	$-0.900413\pi$
$491$	−21.1116	+	15.3385i	−0.952754	+	0.692216i	−0.00129727	+	0.999999i	$0.500413\pi$
$492$	−3.07929	−	2.23724i	−0.138825	−	0.100862i
$493$	−9.91703	−	30.5215i	−0.446640	−	1.37462i
$494$	33.6283			1.51301
$495$		0			0
$496$	6.45297			0.289747
$497$	−13.2231	−	40.6967i	−0.593139	−	1.82549i
$498$	11.8022	+	8.57484i	0.528871	+	0.384248i
$499$	−15.6815	+	11.3933i	−0.702000	+	0.510033i	−0.880583	−	0.473892i	$-0.842849\pi$
$499$	−15.6815	+	11.3933i	−0.702000	+	0.510033i	0.178583	+	0.983925i	$0.442849\pi$
$500$		0			0
$501$	−0.609193	+	1.87490i	−0.0272167	+	0.0837644i
$502$	15.0464	−	10.9318i	0.671552	−	0.487911i
$503$	15.2437	+	11.0752i	0.679683	+	0.493819i	0.873253	−	0.487268i	$-0.162007\pi$
$503$	15.2437	+	11.0752i	0.679683	+	0.493819i	−0.193570	+	0.981087i	$0.562007\pi$
$504$	4.07878	+	12.5532i	0.181684	+	0.559164i
$505$		0			0
$506$	0.494765	+	0.687805i	0.0219950	+	0.0305767i
$507$	−13.7003			−0.608453
$508$	0.307270	+	0.945678i	0.0136329	+	0.0419577i
$509$	4.16741	+	3.02780i	0.184717	+	0.134205i	0.676301	−	0.736625i	$-0.263582\pi$
$509$	4.16741	+	3.02780i	0.184717	+	0.134205i	−0.491584	+	0.870830i	$0.663582\pi$
$510$		0			0
$511$	−19.2911	+	59.3718i	−0.853387	+	2.62645i
$512$	6.80928	−	20.9568i	0.300930	−	0.926168i
$513$	4.53048	−	3.29158i	0.200025	−	0.145327i
$514$	−5.14707	−	3.73956i	−0.227027	−	0.164945i
$515$		0			0
$516$	5.78091			0.254490
$517$	0.749175	+	0.247346i	0.0329487	+	0.0108783i
$518$	19.5692			0.859820
$519$	−0.610322	−	1.87838i	−0.0267902	−	0.0824516i
$520$		0			0
$521$	33.5759	−	24.3944i	1.47099	−	1.06874i	0.490663	−	0.871349i	$-0.336754\pi$
$521$	33.5759	−	24.3944i	1.47099	−	1.06874i	0.980326	−	0.197387i	$-0.0632455\pi$
$522$	−2.30501	+	7.09409i	−0.100887	+	0.310500i
$523$	2.13926	−	6.58397i	0.0935434	−	0.287897i	−0.893328	−	0.449405i	$-0.851636\pi$
$523$	2.13926	−	6.58397i	0.0935434	−	0.287897i	0.986871	+	0.161508i	$0.0516359\pi$
$524$	1.39810	−	1.01578i	0.0610762	−	0.0443745i
$525$		0			0
$526$	4.30377	+	13.2456i	0.187653	+	0.577537i
$527$	14.1548			0.616592
$528$	4.47256	−	6.09510i	0.194643	−	0.265255i
$529$	−22.9517			−0.997899
$530$		0			0
$531$	6.36725	+	4.62608i	0.276315	+	0.200755i
$532$	12.6125	−	9.16355i	0.546823	−	0.397290i
$533$	−9.35863	+	28.8029i	−0.405367	+	1.24759i
$534$	−0.921313	+	2.83551i	−0.0398691	+	0.122704i
$535$		0			0
$536$	30.2104	+	21.9492i	1.30489	+	0.948059i
$537$	0.625187	+	1.92413i	0.0269788	+	0.0830322i
$538$	−15.8592			−0.683740
$539$	−0.178505	+	37.7329i	−0.00768874	+	1.62527i
$540$		0			0
$541$	−8.78173	−	27.0274i	−0.377556	−	1.16200i	−0.941738	−	0.336348i	$-0.890808\pi$
$541$	−8.78173	−	27.0274i	−0.377556	−	1.16200i	0.564182	−	0.825651i	$-0.309192\pi$
$542$	11.1299	+	8.08635i	0.478071	+	0.347339i
$543$	16.2920	−	11.8368i	0.699156	−	0.507967i
$544$	5.42167	−	16.6862i	0.232452	−	0.715415i
$545$		0			0
$546$	20.8264	−	15.1313i	0.891288	−	0.647559i
$547$	20.9205	+	15.1996i	0.894496	+	0.649889i	0.937046	−	0.349205i	$-0.113548\pi$
$547$	20.9205	+	15.1996i	0.894496	+	0.649889i	−0.0425503	+	0.999094i	$0.513548\pi$
$548$	2.05807	+	6.33407i	0.0879162	+	0.270578i
$549$	−4.85807			−0.207337
$550$		0			0
$551$	35.9431			1.53123
$552$	−0.209150	−	0.643698i	−0.00890202	−	0.0273976i
$553$	−27.7518	−	20.1628i	−1.18012	−	0.857411i
$554$	−9.65002	+	7.01115i	−0.409990	+	0.297875i
$555$		0			0
$556$	1.06262	−	3.27039i	0.0450649	−	0.138696i
$557$	−6.52399	+	4.73996i	−0.276430	+	0.200838i	−0.717359	−	0.696704i	$-0.754649\pi$
$557$	−6.52399	+	4.73996i	−0.276430	+	0.200838i	0.440929	+	0.897542i	$0.354649\pi$
$558$	−2.66165	−	1.93381i	−0.112677	−	0.0818645i
$559$	−14.2140	−	43.7461i	−0.601186	−	1.85026i
$560$		0			0
$561$	9.81067	−	13.3698i	0.414207	−	0.564472i
$562$	3.41542			0.144071
$563$	−9.16284	−	28.2003i	−0.386168	−	1.18850i	−0.935630	−	0.352983i	$-0.885167\pi$
$563$	−9.16284	−	28.2003i	−0.386168	−	1.18850i	0.549462	−	0.835519i	$-0.314833\pi$
$564$	−0.124978	−	0.0908017i	−0.00526252	−	0.00382344i
$565$		0			0
$566$	7.83892	−	24.1257i	0.329494	−	1.01408i
$567$	1.32471	−	4.07703i	0.0556325	−	0.171219i
$568$	24.8647	−	18.0653i	1.04330	−	0.758002i
$569$	34.0618	+	24.7473i	1.42794	+	1.03746i	0.990395	+	0.138266i	$0.0441529\pi$
$569$	34.0618	+	24.7473i	1.42794	+	1.03746i	0.437548	+	0.899195i	$0.355847\pi$
$570$		0			0
$571$	−26.6823			−1.11662			−0.558311	−	0.829632i	$-0.688550\pi$
$571$	−26.6823			−1.11662			−0.558311	+	0.829632i	$0.688550\pi$
$572$	10.5684	+	3.48924i	0.441887	+	0.145893i
$573$	−12.6652			−0.529094
$574$	−9.02304	−	27.7700i	−0.376614	−	1.15910i
$575$		0			0
$576$	−6.98733	+	5.07659i	−0.291139	+	0.211525i
$577$	1.02228	−	3.14627i	0.0425582	−	0.130981i	−0.927520	−	0.373774i	$-0.878064\pi$
$577$	1.02228	−	3.14627i	0.0425582	−	0.130981i	0.970078	+	0.242793i	$0.0780636\pi$
$578$	−2.87299	+	8.84214i	−0.119500	+	0.367785i
$579$	11.2713	−	8.18910i	0.468420	−	0.340327i
$580$		0			0
$581$	−16.6290	−	51.1788i	−0.689887	−	2.12325i
$582$	−2.33822			−0.0969225
$583$	4.91296	+	6.82982i	0.203474	+	0.282862i
$584$	−44.8381			−1.85542
$585$		0			0
$586$	23.2854	+	16.9178i	0.961911	+	0.698869i
$587$	−6.89906	+	5.01246i	−0.284755	+	0.206886i	−0.720989	−	0.692947i	$-0.756312\pi$
$587$	−6.89906	+	5.01246i	−0.284755	+	0.206886i	0.436234	+	0.899833i	$0.356312\pi$
$588$	2.28314	−	7.02678i	0.0941550	−	0.289779i
$589$	−4.89893	+	15.0774i	−0.201857	+	0.621252i
$590$		0			0
$591$	−11.8165	−	8.58522i	−0.486068	−	0.353149i
$592$	2.76684	+	8.51544i	0.113716	+	0.349983i
$593$	23.4343			0.962333			0.481167	−	0.876629i	$-0.340213\pi$
$593$	23.4343			0.962333			0.481167	+	0.876629i	$0.340213\pi$
$594$	−3.67135	+	1.17372i	−0.150637	+	0.0481584i
$595$		0			0
$596$	−0.760259	−	2.33984i	−0.0311414	−	0.0958434i
$597$	−9.60694	−	6.97985i	−0.393186	−	0.285666i
$598$	−1.06793	+	0.775895i	−0.0436708	+	0.0317287i
$599$	5.82017	−	17.9126i	0.237805	−	0.731890i	−0.758931	−	0.651171i	$-0.774278\pi$
$599$	5.82017	−	17.9126i	0.237805	−	0.731890i	0.996737	−	0.0807194i	$-0.0257218\pi$
$600$		0			0
$601$	30.4664	−	22.1351i	1.24275	−	0.902911i	0.244971	−	0.969530i	$-0.421221\pi$
$601$	30.4664	−	22.1351i	1.24275	−	0.902911i	0.997778	+	0.0666198i	$0.0212214\pi$
$602$	35.8782	+	26.0670i	1.46229	+	1.06241i
$603$	−3.74775	−	11.5344i	−0.152620	−	0.469717i
$604$	3.84453			0.156432
$605$		0			0
$606$	−8.81471			−0.358073
$607$	9.07520	+	27.9306i	0.368351	+	1.13367i	0.947856	+	0.318699i	$0.103246\pi$
$607$	9.07520	+	27.9306i	0.368351	+	1.13367i	−0.579505	+	0.814969i	$0.696754\pi$
$608$	15.8973	+	11.5501i	0.644723	+	0.468418i
$609$	22.2599	−	16.1728i	0.902019	−	0.655355i
$610$		0			0
$611$	−0.379834	+	1.16901i	−0.0153665	+	0.0472931i
$612$	−2.62693	+	1.90858i	−0.106188	+	0.0771498i
$613$	−10.4453	−	7.58894i	−0.421881	−	0.306515i	0.356513	−	0.934290i	$-0.383965\pi$
$613$	−10.4453	−	7.58894i	−0.421881	−	0.306515i	−0.778394	+	0.627776i	$0.783965\pi$
$614$	−1.77415	−	5.46027i	−0.0715989	−	0.220359i
$615$		0			0
$616$	−41.6978	+	13.3307i	−1.68005	+	0.537109i
$617$	−41.6041			−1.67492			−0.837459	−	0.546500i	$-0.815960\pi$
$617$	−41.6041			−1.67492			−0.837459	+	0.546500i	$0.815960\pi$
$618$	6.05789	+	18.6443i	0.243684	+	0.749982i
$619$	−3.45545	−	2.51053i	−0.138886	−	0.100907i	0.516173	−	0.856484i	$-0.327356\pi$
$619$	−3.45545	−	2.51053i	−0.138886	−	0.100907i	−0.655059	+	0.755578i	$0.727356\pi$
$620$		0			0
$621$	−0.0679277	+	0.209060i	−0.00272585	+	0.00838929i
$622$	4.95935	−	15.2633i	0.198852	−	0.612002i
$623$	8.89731	−	6.46427i	0.356463	−	0.258986i
$624$	9.52890	+	6.92315i	0.381461	+	0.277148i
$625$		0			0
$626$	−4.72918			−0.189016
$627$	10.8457	+	15.0774i	0.433137	+	0.602132i
$628$	−4.82455			−0.192521
$629$	6.06913	+	18.6789i	0.241992	+	0.744775i
$630$		0			0
$631$	22.2892	−	16.1941i	0.887319	−	0.644675i	−0.0478586	−	0.998854i	$-0.515240\pi$
$631$	22.2892	−	16.1941i	0.887319	−	0.644675i	0.935178	+	0.354179i	$0.115240\pi$
$632$	7.61358	−	23.4322i	0.302852	−	0.932082i
$633$	6.90710	−	21.2579i	0.274532	−	0.844924i
$634$	−24.2758	+	17.6374i	−0.964116	+	0.700471i
$635$		0			0
$636$	−0.509066	−	1.56674i	−0.0201858	−	0.0621254i
$637$	−58.7877			−2.32925
$638$	−23.4920	−	7.75607i	−0.930057	−	0.307066i
$639$	−9.98194			−0.394879
$640$		0			0
$641$	−7.41712	−	5.38885i	−0.292958	−	0.212847i	0.431591	−	0.902069i	$-0.357952\pi$
$641$	−7.41712	−	5.38885i	−0.292958	−	0.212847i	−0.724550	+	0.689222i	$0.757952\pi$
$642$	7.29744	−	5.30190i	0.288007	−	0.209249i
$643$	1.05346	−	3.24223i	0.0415446	−	0.127861i	−0.928133	−	0.372249i	$-0.878587\pi$
$643$	1.05346	−	3.24223i	0.0415446	−	0.127861i	0.969678	+	0.244387i	$0.0785869\pi$
$644$	−0.189106	+	0.582010i	−0.00745184	+	0.0229344i
$645$		0			0
$646$	−26.3254	−	19.1265i	−1.03576	−	0.752523i
$647$	−6.90986	−	21.2663i	−0.271654	−	0.836066i	−0.990085	−	0.140468i	$-0.955139\pi$
$647$	−6.90986	−	21.2663i	−0.271654	−	0.836066i	0.718431	−	0.695598i	$-0.244861\pi$
$648$	3.07901			0.120955
$649$	−15.4427	+	21.0450i	−0.606179	+	0.826087i
$650$		0			0
$651$	3.75019	+	11.5419i	0.146981	+	0.452362i
$652$	−2.79551	−	2.03106i	−0.109481	−	0.0795423i
$653$	−11.9699	+	8.69667i	−0.468420	+	0.340327i	−0.796825	−	0.604210i	$-0.793489\pi$
$653$	−11.9699	+	8.69667i	−0.468420	+	0.340327i	0.328405	+	0.944537i	$0.393489\pi$
$654$	1.60051	−	4.92586i	0.0625848	−	0.192616i
$655$		0			0
$656$	10.8083	−	7.85267i	0.421992	−	0.306595i
$657$	11.7813	+	8.55964i	0.459633	+	0.333943i
$658$	−0.366214	−	1.12709i	−0.0142765	−	0.0439385i
$659$	−47.4724			−1.84926			−0.924631	−	0.380864i	$-0.875627\pi$
$659$	−47.4724			−1.84926			−0.924631	+	0.380864i	$0.875627\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	1.20309	+	3.70273i	0.0467594	+	0.143911i
$663$	20.9019	+	15.1861i	0.811763	+	0.589780i
$664$	31.2690	−	22.7183i	1.21347	−	0.881641i
$665$		0			0
$666$	1.41064	−	4.34152i	0.0546614	−	0.168230i
$667$	−1.14144	+	0.829302i	−0.0441966	+	0.0321107i
$668$	1.03574	+	0.752510i	0.0400740	+	0.0291155i
$669$	−5.92024	−	18.2206i	−0.228890	−	0.704451i
$670$		0			0
$671$	0.0762228	−	16.1122i	0.00294255	−	0.622005i
$672$	15.0424			0.580275
$673$	11.8639	+	36.5133i	0.457319	+	1.40748i	0.868391	+	0.495880i	$0.165154\pi$
$673$	11.8639	+	36.5133i	0.457319	+	1.40748i	−0.411072	+	0.911603i	$0.634846\pi$
$674$	25.7612	+	18.7166i	0.992285	+	0.720937i
$675$		0			0
$676$	−2.74938	+	8.46172i	−0.105745	+	0.325451i
$677$	7.08677	−	21.8108i	0.272367	−	0.838259i	−0.717537	−	0.696520i	$-0.754731\pi$
$677$	7.08677	−	21.8108i	0.272367	−	0.838259i	0.989904	−	0.141739i	$-0.0452693\pi$
$678$	−7.25124	+	5.26833i	−0.278482	+	0.202329i
$679$	6.97782	+	5.06969i	0.267784	+	0.194557i
$680$		0			0
$681$	15.3759			0.589206
$682$	6.45540	−	8.79727i	0.247190	−	0.336865i
$683$	−25.9084			−0.991359			−0.495680	−	0.868505i	$-0.665081\pi$
$683$	−25.9084			−0.991359			−0.495680	+	0.868505i	$0.665081\pi$
$684$	−1.12380	−	3.45871i	−0.0429697	−	0.132247i
$685$		0			0
$686$	17.6414	−	12.8173i	0.673553	−	0.489365i
$687$	−2.75064	+	8.46560i	−0.104943	+	0.322983i
$688$	−6.27024	+	19.2978i	−0.239050	+	0.735722i
$689$	−10.6044	+	7.70454i	−0.403995	+	0.293520i
$690$		0			0
$691$	4.57824	+	14.0904i	0.174165	+	0.536023i	0.999594	−	0.0284814i	$-0.00906715\pi$
$691$	4.57824	+	14.0904i	0.174165	+	0.536023i	−0.825430	+	0.564505i	$0.809067\pi$
$692$	−1.28262			−0.0487579
$693$	13.5010	+	4.45748i	0.512862	+	0.169325i
$694$	18.3927			0.698177
$695$		0			0
$696$	15.9881	+	11.6161i	0.606029	+	0.440305i
$697$	23.7082	−	17.2250i	0.898014	−	0.652445i
$698$	1.31414	−	4.04450i	0.0497409	−	0.153087i
$699$	7.05677	−	21.7185i	0.266911	−	0.821469i
$700$		0			0
$701$	−4.45471	−	3.23653i	−0.168252	−	0.122242i	0.500473	−	0.865752i	$-0.333160\pi$
$701$	−4.45471	−	3.23653i	−0.168252	−	0.122242i	−0.668725	+	0.743510i	$0.733160\pi$
$702$	−1.85567	−	5.71118i	−0.0700379	−	0.215555i
$703$	−21.9968			−0.829626
$704$	−16.7273	−	23.2538i	−0.630435	−	0.876409i
$705$		0			0
$706$	−9.87362	−	30.3879i	−0.371599	−	1.14366i
$707$	26.3052	+	19.1119i	0.989309	+	0.718775i
$708$	4.13498	−	3.00424i	0.155402	−	0.112906i
$709$	−5.53161	+	17.0245i	−0.207744	+	0.639370i	0.791846	+	0.610721i	$0.209120\pi$
$709$	−5.53161	+	17.0245i	−0.207744	+	0.639370i	−0.999590	+	0.0286488i	$0.990880\pi$
$710$		0			0
$711$	−6.47371	+	4.70342i	−0.242783	+	0.176392i
$712$	6.39046	+	4.64294i	0.239493	+	0.174002i
$713$	−0.192300	−	0.591840i	−0.00720171	−	0.0221646i
$714$	−24.9097			−0.932222
$715$		0			0
$716$	1.31386			0.0491012
$717$	−5.21019	−	16.0353i	−0.194578	−	0.598850i
$718$	0.450110	+	0.327024i	0.0167980	+	0.0122044i
$719$	−26.3673	+	19.1570i	−0.983334	+	0.714434i	−0.958451	−	0.285256i	$-0.907921\pi$
$719$	−26.3673	+	19.1570i	−0.983334	+	0.714434i	−0.0248831	+	0.999690i	$0.507921\pi$
$720$		0			0
$721$	22.3459	−	68.7735i	0.832204	−	2.56126i
$722$	11.6206	−	8.44284i	0.432473	−	0.314210i
$723$	−9.67644	−	7.03035i	−0.359871	−	0.261461i
$724$	−4.04130	−	12.4378i	−0.150194	−	0.462248i
$725$		0			0
$726$	−3.83515	−	12.1948i	−0.142336	−	0.452591i
$727$	43.0199			1.59552			0.797759	−	0.602976i	$-0.206018\pi$
$727$	43.0199			1.59552			0.797759	+	0.602976i	$0.206018\pi$
$728$	−21.0760	−	64.8654i	−0.781130	−	2.40407i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−13.7539	+	42.3302i	−0.508708	+	1.56564i
$732$	−0.974917	+	3.00049i	−0.0360340	+	0.110901i
$733$	32.9323	−	23.9267i	1.21638	−	0.883755i	0.220589	−	0.975367i	$-0.429202\pi$
$733$	32.9323	−	23.9267i	1.21638	−	0.883755i	0.995795	+	0.0916123i	$0.0292021\pi$
$734$	23.9357	+	17.3903i	0.883483	+	0.641888i
$735$		0			0
$736$	−0.771340			−0.0284320
$737$	38.3136	−	12.2488i	1.41130	−	0.451189i
$738$	−6.81134			−0.250729
$739$	11.7810	+	36.2581i	0.433370	+	1.33377i	0.894748	+	0.446571i	$0.147355\pi$
$739$	11.7810	+	36.2581i	0.433370	+	1.33377i	−0.461379	+	0.887203i	$0.652645\pi$
$740$		0			0
$741$	−23.4100	+	17.0084i	−0.859989	+	0.624819i
$742$	3.90527	−	12.0192i	0.143367	−	0.441238i
$743$	5.57409	−	17.1553i	0.204493	−	0.629366i	−0.795240	−	0.606294i	$-0.792655\pi$
$743$	5.57409	−	17.1553i	0.204493	−	0.629366i	0.999734	−	0.0230717i	$-0.00734459\pi$
$744$	−7.05183	+	5.12345i	−0.258532	+	0.187835i
$745$		0			0
$746$	−0.991061	−	3.05017i	−0.0362853	−	0.111675i
$747$	−12.5530			−0.459289
$748$	−6.28875	−	8.74240i	−0.229940	−	0.319654i
$749$	−33.2728			−1.21576
$750$		0			0
$751$	14.1861	+	10.3068i	0.517657	+	0.376100i	0.815720	−	0.578446i	$-0.196341\pi$
$751$	14.1861	+	10.3068i	0.517657	+	0.376100i	−0.298064	+	0.954546i	$0.596341\pi$
$752$	0.438670	−	0.318713i	0.0159967	−	0.0116223i
$753$	−4.94533	+	15.2201i	−0.180218	+	0.554653i
$754$	11.9105	−	36.6568i	0.433756	−	1.33496i
$755$		0			0
$756$	−2.25225	−	1.63636i	−0.0819136	−	0.0595137i
$757$	8.02236	+	24.6903i	0.291578	+	0.897383i	0.984350	+	0.176227i	$0.0563892\pi$
$757$	8.02236	+	24.6903i	0.291578	+	0.897383i	−0.692772	+	0.721157i	$0.743611\pi$
$758$	25.1646			0.914019
$759$	−0.692300	−	0.228568i	−0.0251289	−	0.00829651i
$760$		0			0
$761$	8.65430	+	26.6352i	0.313718	+	0.965525i	0.976279	+	0.216517i	$0.0694697\pi$
$761$	8.65430	+	26.6352i	0.313718	+	0.965525i	−0.662561	+	0.749008i	$0.730530\pi$
$762$	1.43958	+	1.04591i	0.0521503	+	0.0378894i
$763$	−15.4564	+	11.2298i	−0.559561	+	0.406545i
$764$	−2.54164	+	7.82237i	−0.0919534	+	0.283003i
$765$		0			0
$766$	−15.2589	+	11.0862i	−0.551326	+	0.400562i
$767$	−32.9011	−	23.9040i	−1.18799	−	0.863124i
$768$	4.25355	+	13.0911i	0.153487	+	0.472384i
$769$	22.9537			0.827732			0.413866	−	0.910338i	$-0.364178\pi$
$769$	22.9537			0.827732			0.413866	+	0.910338i	$0.364178\pi$
$770$		0			0
$771$	5.47446			0.197158
$772$	−2.79590	−	8.60489i	−0.100627	−	0.309697i
$773$	−19.0347	−	13.8295i	−0.684631	−	0.497414i	0.190259	−	0.981734i	$-0.439067\pi$
$773$	−19.0347	−	13.8295i	−0.684631	−	0.497414i	−0.874891	+	0.484320i	$0.839067\pi$
$774$	8.36938	−	6.08071i	0.300831	−	0.218567i
$775$		0			0
$776$	−1.91434	+	5.89172i	−0.0687207	+	0.211500i
$777$	−13.6229	+	9.89761i	−0.488718	+	0.355075i
$778$	−15.3173	−	11.1287i	−0.549153	−	0.398983i
$779$	10.1424	+	31.2151i	0.363389	+	1.11840i
$780$		0			0
$781$	0.156616	−	33.1060i	0.00560416	−	1.18463i
$782$	1.27731			0.0456765
$783$	−1.98341	−	6.10429i	−0.0708811	−	0.218150i
$784$	20.9804	+	15.2431i	0.749298	+	0.544397i
$785$		0			0
$786$	0.955657	−	2.94121i	0.0340872	−	0.104910i
$787$	7.80964	−	24.0356i	0.278384	−	0.856777i	−0.709921	−	0.704282i	$-0.751269\pi$
$787$	7.80964	−	24.0356i	0.278384	−	0.856777i	0.988304	−	0.152495i	$-0.0487308\pi$
$788$	−7.67383	+	5.57536i	−0.273369	+	0.198614i
$789$	−9.69534	−	7.04408i	−0.345163	−	0.250776i
$790$		0			0
$791$	33.0621			1.17555
$792$	−0.0483095	+	10.2118i	−0.00171660	+	0.362861i
$793$	25.1028			0.891427
$794$	−7.17071	−	22.0692i	−0.254479	−	0.783205i
$795$		0			0
$796$	−6.23888	+	4.53281i	−0.221131	+	0.160661i
$797$	−2.67499	+	8.23277i	−0.0947530	+	0.291620i	−0.987189	−	0.159554i	$-0.948994\pi$
$797$	−2.67499	+	8.23277i	−0.0947530	+	0.291620i	0.892436	+	0.451173i	$0.148994\pi$
$798$	8.62119	−	26.5333i	0.305187	−	0.939268i
$799$	0.962236	−	0.699105i	0.0340414	−	0.0247326i
$800$		0			0
$801$	−0.792768	−	2.43989i	−0.0280111	−	0.0862092i
$802$	31.7579			1.12141
$803$	−28.5736	+	38.9395i	−1.00834	+	1.37415i
$804$	−7.87607			−0.277768
$805$		0			0
$806$	13.7534	+	9.99243i	0.484443	+	0.351968i
$807$	11.0402	−	8.02120i	0.388635	−	0.282360i
$808$	−7.21672	+	22.2108i	−0.253883	+	0.781373i
$809$	−3.15582	+	9.71261i	−0.110953	+	0.341477i	−0.991081	−	0.133258i	$-0.957456\pi$
$809$	−3.15582	+	9.71261i	−0.110953	+	0.341477i	0.880129	+	0.474735i	$0.157456\pi$
$810$		0			0
$811$	38.5273	+	27.9917i	1.35288	+	0.982923i	0.998862	+	0.0476835i	$0.0151839\pi$
$811$	38.5273	+	27.9917i	1.35288	+	0.982923i	0.354015	+	0.935240i	$0.384816\pi$
$812$	−5.52167	−	16.9940i	−0.193773	−	0.596371i
$813$	−11.8379			−0.415172
$814$	14.3769	+	4.74664i	0.503910	+	0.166370i
$815$		0			0
$816$	−3.52192	−	10.8394i	−0.123292	−	0.379453i
$817$	−40.3291	−	29.3008i	−1.41094	−	1.02510i
$818$	23.4466	−	17.0350i	0.819792	−	0.595613i
$819$	−6.84507	+	21.0670i	−0.239186	+	0.736139i
$820$		0			0
$821$	38.4767	−	27.9550i	1.34285	−	0.975635i	0.343512	−	0.939148i	$-0.388383\pi$
$821$	38.4767	−	27.9550i	1.34285	−	0.975635i	0.999334	−	0.0364868i	$-0.0116167\pi$
$822$	9.64215	+	7.00543i	0.336309	+	0.244343i
$823$	7.64384	+	23.5253i	0.266448	+	0.820041i	0.991356	+	0.131196i	$0.0418818\pi$
$823$	7.64384	+	23.5253i	0.266448	+	0.820041i	−0.724909	+	0.688845i	$0.758118\pi$
$824$	51.9384			1.80936
$825$		0			0
$826$	39.2096			1.36428
$827$	0.482580	+	1.48523i	0.0167810	+	0.0516465i	0.959096	−	0.283080i	$-0.0913561\pi$
$827$	0.482580	+	1.48523i	0.0167810	+	0.0516465i	−0.942315	+	0.334726i	$0.891356\pi$
$828$	0.115490	+	0.0839083i	0.00401355	+	0.00291602i
$829$	−34.1365	+	24.8016i	−1.18561	+	0.861396i	−0.992793	−	0.119839i	$-0.961762\pi$
$829$	−34.1365	+	24.8016i	−1.18561	+	0.861396i	−0.192817	+	0.981235i	$0.561762\pi$
$830$		0			0
$831$	3.17170	−	9.76148i	0.110025	−	0.338622i
$832$	36.1052	−	26.2320i	1.25172	−	0.909430i
$833$	46.0210	+	33.4362i	1.59453	+	1.15850i
$834$	−1.90158	−	5.85247i	−0.0658465	−	0.202655i
$835$		0			0
$836$	11.4887	−	3.67292i	0.397346	−	0.127031i
$837$	2.83095			0.0978521
$838$	−6.04247	−	18.5968i	−0.208734	−	0.642416i
$839$	5.09236	+	3.69982i	0.175808	+	0.127732i	0.672209	−	0.740361i	$-0.265346\pi$
$839$	5.09236	+	3.69982i	0.175808	+	0.127732i	−0.496401	+	0.868093i	$0.665346\pi$
$840$		0			0
$841$	3.76886	−	11.5994i	0.129961	−	0.399978i
$842$	−8.47554	+	26.0850i	−0.292086	+	0.898949i
$843$	−2.37761	+	1.72744i	−0.0818893	+	0.0594961i
$844$	−11.7434	−	8.53205i	−0.404223	−	0.293685i
$845$		0			0
$846$	−0.276449			−0.00950451
$847$	−14.9954	+	44.7074i	−0.515249	+	1.53617i
$848$	5.78225			0.198563
$849$	6.74521	+	20.7596i	0.231495	+	0.712468i
$850$		0			0
$851$	0.698548	−	0.507525i	0.0239459	−	0.0173977i
$852$	−2.00318	+	6.16514i	−0.0686276	+	0.211214i
$853$	2.24692	−	6.91532i	0.0769332	−	0.236776i	−0.905193	−	0.425002i	$-0.860274\pi$
$853$	2.24692	−	6.91532i	0.0769332	−	0.236776i	0.982126	+	0.188225i	$0.0602735\pi$
$854$	−19.5803	+	14.2259i	−0.670025	+	0.486802i
$855$		0			0
$856$	−7.38491	−	22.7284i	−0.252411	−	0.776841i
$857$	−39.8590			−1.36156			−0.680779	−	0.732489i	$-0.738359\pi$
$857$	−39.8590			−1.36156			−0.680779	+	0.732489i	$0.738359\pi$
$858$	18.9707	−	6.06490i	0.647650	−	0.207052i
$859$	13.5278			0.461564			0.230782	−	0.973006i	$-0.425872\pi$
$859$	13.5278			0.461564			0.230782	+	0.973006i	$0.425872\pi$
$860$		0			0
$861$	20.3267	+	14.7682i	0.692732	+	0.503299i
$862$	−35.4037	+	25.7223i	−1.20585	+	0.876104i
$863$	−15.5472	+	47.8493i	−0.529232	+	1.62881i	0.226560	+	0.973997i	$0.427252\pi$
$863$	−15.5472	+	47.8493i	−0.529232	+	1.62881i	−0.755792	+	0.654812i	$0.772748\pi$
$864$	1.08433	−	3.33724i	0.0368898	−	0.113535i
$865$		0			0
$866$	29.1228	+	21.1589i	0.989632	+	0.719010i
$867$	−2.47214	−	7.60845i	−0.0839581	−	0.258397i
$868$	7.88119			0.267505
$869$	−15.4977	−	21.5444i	−0.525725	−	0.730844i
$870$		0			0
$871$	19.3655	+	59.6009i	0.656175	+	2.01950i
$872$	−11.1015	−	8.06574i	−0.375946	−	0.273140i
$873$	1.62773	−	1.18262i	0.0550903	−	0.0400255i
$874$	−0.442073	+	1.36056i	−0.0149534	+	0.0460217i
$875$		0			0
$876$	7.65096	−	5.55875i	0.258502	−	0.187813i
$877$	−0.976773	−	0.709667i	−0.0329833	−	0.0239638i	0.571171	−	0.820831i	$-0.306489\pi$
$877$	−0.976773	−	0.709667i	−0.0329833	−	0.0239638i	−0.604155	+	0.796867i	$0.706489\pi$
$878$	10.1320	+	31.1830i	0.341937	+	1.05237i
$879$	−24.7665			−0.835354
$880$		0			0
$881$	1.91816			0.0646245			0.0323123	−	0.999478i	$-0.489713\pi$
$881$	1.91816			0.0646245			0.0323123	+	0.999478i	$0.489713\pi$
$882$	−4.08575	−	12.5746i	−0.137574	−	0.423410i
$883$	46.9950	+	34.1439i	1.58151	+	1.14903i	0.914941	+	0.403587i	$0.132237\pi$
$883$	46.9950	+	34.1439i	1.58151	+	1.14903i	0.666566	+	0.745446i	$0.267763\pi$
$884$	13.5740	−	9.86208i	0.456543	−	0.331698i
$885$		0			0
$886$	5.25828	−	16.1833i	0.176656	−	0.543690i
$887$	24.4668	−	17.7762i	0.821516	−	0.596866i	−0.0956306	−	0.995417i	$-0.530487\pi$
$887$	24.4668	−	17.7762i	0.821516	−	0.596866i	0.917146	+	0.398551i	$0.130487\pi$
$888$	−9.78459	−	7.10892i	−0.328349	−	0.238560i
$889$	−2.02832	−	6.24251i	−0.0680275	−	0.209367i
$890$		0			0
$891$	1.96213	−	2.67395i	0.0657340	−	0.0895808i
$892$	−12.4417			−0.416578
$893$	0.411644	+	1.26691i	0.0137752	+	0.0423956i
$894$	−3.56185	−	2.58784i	−0.119126	−	0.0865503i
$895$		0			0
$896$	−3.99968	+	12.3098i	−0.133620	+	0.411240i
$897$	0.350999	−	1.08026i	0.0117195	−	0.0360689i
$898$	11.2802	−	8.19553i	0.376425	−	0.273488i
$899$	14.7001	+	10.6802i	0.490275	+	0.356206i
$900$		0			0
$901$	12.6835			0.422550
$902$	0.106870	−	22.5904i	0.00355837	−	0.752179i
$903$	−38.1603			−1.26990
$904$	7.33815	+	22.5845i	0.244063	+	0.751149i
$905$		0			0
$906$	5.56597	−	4.04391i	0.184917	−	0.134350i
$907$	9.87830	−	30.4023i	0.328004	−	1.00949i	−0.642063	−	0.766652i	$-0.721921\pi$
$907$	9.87830	−	30.4023i	0.328004	−	1.00949i	0.970066	−	0.242839i	$-0.0780788\pi$
$908$	3.08563	−	9.49660i	0.102400	−	0.315156i
$909$	6.13627	−	4.45826i	0.203527	−	0.147871i
$910$		0			0
$911$	−16.0211	−	49.3079i	−0.530803	−	1.63364i	−0.752547	−	0.658538i	$-0.771175\pi$
$911$	−16.0211	−	49.3079i	−0.530803	−	1.63364i	0.221745	−	0.975105i	$-0.428825\pi$
$912$	12.7648			0.422684
$913$	0.196955	−	41.6330i	0.00651826	−	1.37785i
$914$	11.6722			0.386083
$915$		0			0
$916$	4.67660	+	3.39775i	0.154519	+	0.112265i
$917$	−9.22898	+	6.70525i	−0.304768	+	0.221427i
$918$	−1.79562	+	5.52634i	−0.0592642	+	0.182396i
$919$	−10.5710	+	32.5341i	−0.348704	+	1.07320i	0.610866	+	0.791734i	$0.290821\pi$
$919$	−10.5710	+	32.5341i	−0.348704	+	1.07320i	−0.959571	+	0.281468i	$0.909179\pi$
$920$		0			0
$921$	3.99673	+	2.90379i	0.131697	+	0.0956832i
$922$	4.82988	+	14.8648i	0.159064	+	0.489547i
$923$	51.5790			1.69774
$924$	5.46245	−	7.44411i	0.179702	−	0.244893i
$925$		0			0
$926$	6.74561	+	20.7609i	0.221675	+	0.682244i
$927$	−13.6469	−	9.91508i	−0.448224	−	0.325654i
$928$	18.2208	−	13.2382i	0.598127	−	0.434565i
$929$	5.66990	−	17.4502i	0.186023	−	0.572521i	−0.813941	−	0.580947i	$-0.802682\pi$
$929$	5.66990	−	17.4502i	0.186023	−	0.572521i	0.999964	+	0.00842624i	$0.00268219\pi$
$930$		0			0
$931$	−51.5433	+	37.4484i	−1.68926	+	1.22732i
$932$	−11.9978	−	8.71693i	−0.393002	−	0.285533i
$933$	4.26740	+	13.1337i	0.139708	+	0.429978i
$934$	30.8561			1.00964
$935$		0			0
$936$	−15.9100			−0.520033
$937$	−1.04576	−	3.21852i	−0.0341635	−	0.105144i	0.932521	−	0.361117i	$-0.117604\pi$
$937$	−1.04576	−	3.21852i	−0.0341635	−	0.105144i	−0.966684	+	0.255972i	$0.917604\pi$
$938$	−48.8815	−	35.5145i	−1.59604	−	1.15959i
$939$	3.29217	−	2.39190i	0.107436	−	0.0780567i
$940$		0			0
$941$	−10.8465	+	33.3822i	−0.353587	+	1.08823i	0.603237	+	0.797562i	$0.293877\pi$
$941$	−10.8465	+	33.3822i	−0.353587	+	1.08823i	−0.956824	+	0.290668i	$0.906123\pi$
$942$	−6.98480	+	5.07476i	−0.227577	+	0.165344i
$943$	−1.04230	−	0.757278i	−0.0339421	−	0.0246604i
$944$	5.54375	+	17.0619i	0.180434	+	0.555318i
$945$		0			0
$946$	20.0359	+	27.8532i	0.651423	+	0.905585i
$947$	39.0512			1.26899			0.634497	−	0.772925i	$-0.281207\pi$
$947$	39.0512			1.26899			0.634497	+	0.772925i	$0.281207\pi$
$948$	1.60583	+	4.94223i	0.0521549	+	0.160516i
$949$	−60.8769	−	44.2297i	−1.97615	−	1.43576i
$950$		0			0
$951$	7.97880	−	24.5562i	0.258730	−	0.796290i
$952$	−20.3939	+	62.7660i	−0.660971	+	2.03426i
$953$	19.9652	−	14.5055i	0.646735	−	0.469881i	−0.215422	−	0.976521i	$-0.569113\pi$
$953$	19.9652	−	14.5055i	0.646735	−	0.469881i	0.862158	+	0.506640i	$0.169113\pi$
$954$	−2.38500	−	1.73281i	−0.0772173	−	0.0561017i
$955$		0			0
$956$	−10.9495			−0.354131
$957$	20.2765	−	6.48236i	0.655448	−	0.209545i
$958$	−12.5315			−0.404873
$959$	−13.5855	−	41.8118i	−0.438698	−	1.35017i
$960$		0			0
$961$	18.5958	−	13.5107i	0.599865	−	0.435827i
$962$	−7.28913	+	22.4336i	−0.235011	+	0.723290i
$963$	−2.39847	+	7.38173i	−0.0772896	+	0.237873i
$964$	−6.28401	+	4.56560i	−0.202394	+	0.147048i
$965$		0			0
$966$	0.338412	+	1.04153i	0.0108882	+	0.0335105i
$967$	−1.20724			−0.0388222			−0.0194111	−	0.999812i	$-0.506179\pi$
$967$	−1.20724			−0.0388222			−0.0194111	+	0.999812i	$0.506179\pi$
$968$	−33.8676	−	0.320445i	−1.08855	−	0.0102995i
$969$	27.9999			0.899486
$970$		0			0
$971$	−40.7599	−	29.6138i	−1.30805	−	0.950353i	−0.308049	−	0.951370i	$-0.599676\pi$
$971$	−40.7599	−	29.6138i	−1.30805	−	0.950353i	−0.999999	+	0.00101751i	$0.999676\pi$
$972$	−0.525387	+	0.381716i	−0.0168518	+	0.0122435i
$973$	−7.01442	+	21.5882i	−0.224872	+	0.692085i
$974$	2.44597	−	7.52793i	0.0783740	−	0.241210i
$975$		0			0
$976$	−8.95877	−	6.50893i	−0.286763	−	0.208346i
$977$	1.81804	+	5.59535i	0.0581642	+	0.179011i	0.975917	−	0.218140i	$-0.0699989\pi$
$977$	1.81804	+	5.59535i	0.0581642	+	0.179011i	−0.917753	+	0.397151i	$0.869999\pi$
$978$	−6.18362			−0.197730
$979$	8.10454	−	2.59100i	0.259022	−	0.0828088i
$980$		0			0
$981$	1.37720	+	4.23858i	0.0439706	+	0.135328i
$982$	24.5348	+	17.8256i	0.782937	+	0.568837i
$983$	29.5210	−	21.4482i	0.941573	−	0.684093i	−0.00722580	−	0.999974i	$-0.502300\pi$
$983$	29.5210	−	21.4482i	0.941573	−	0.684093i	0.948799	+	0.315881i	$0.102300\pi$
$984$	−5.57654	+	17.1628i	−0.177774	+	0.547131i
$985$		0			0
$986$	−30.1730	+	21.9219i	−0.960903	+	0.698137i
$987$	0.824990	+	0.599391i	0.0262597	+	0.0190788i
$988$	5.80695	+	17.8720i	0.184744	+	0.568583i
$989$	1.95677			0.0622216
$990$		0			0
$991$	−36.8404			−1.17027			−0.585137	−	0.810934i	$-0.698959\pi$
$991$	−36.8404			−1.17027			−0.585137	+	0.810934i	$0.698959\pi$
$992$	3.06970	+	9.44757i	0.0974631	+	0.299961i
$993$	−2.71027	−	1.96913i	−0.0860078	−	0.0624883i
$994$	−40.2320	+	29.2302i	−1.27608	+	0.927127i
$995$		0			0
$996$	−2.51913	+	7.75307i	−0.0798216	+	0.245666i
$997$	28.2099	−	20.4957i	0.893417	−	0.649105i	−0.0433498	−	0.999060i	$-0.513803\pi$
$997$	28.2099	−	20.4957i	0.893417	−	0.649105i	0.936767	+	0.349955i	$0.113803\pi$
$998$	18.2242	+	13.2406i	0.576877	+	0.419125i
$999$	1.21383	+	3.73577i	0.0384037	+	0.118195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.k.676.2		8
5.2	odd	4		825.2.bx.h.49.3		16
5.3	odd	4		825.2.bx.h.49.2		16
5.4	even	2		165.2.m.a.16.1	✓	8
11.3	even	5		9075.2.a.cl.1.3		4
11.8	odd	10		9075.2.a.dj.1.2		4
11.9	even	5	inner	825.2.n.k.526.2		8
15.14	odd	2		495.2.n.d.181.2		8
55.9	even	10		165.2.m.a.31.1	yes	8
55.14	even	10		1815.2.a.x.1.2		4
55.19	odd	10		1815.2.a.o.1.3		4
55.42	odd	20		825.2.bx.h.724.2		16
55.53	odd	20		825.2.bx.h.724.3		16
165.14	odd	10		5445.2.a.be.1.3		4
165.74	even	10		5445.2.a.bv.1.2		4
165.119	odd	10		495.2.n.d.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.1	✓	8	5.4	even	2
165.2.m.a.31.1	yes	8	55.9	even	10
495.2.n.d.181.2		8	15.14	odd	2
495.2.n.d.361.2		8	165.119	odd	10
825.2.n.k.526.2		8	11.9	even	5	inner
825.2.n.k.676.2		8	1.1	even	1	trivial
825.2.bx.h.49.2		16	5.3	odd	4
825.2.bx.h.49.3		16	5.2	odd	4
825.2.bx.h.724.2		16	55.42	odd	20
825.2.bx.h.724.3		16	55.53	odd	20
1815.2.a.o.1.3		4	55.19	odd	10
1815.2.a.x.1.2		4	55.14	even	10
5445.2.a.be.1.3		4	165.14	odd	10
5445.2.a.bv.1.2		4	165.74	even	10
9075.2.a.cl.1.3		4	11.3	even	5
9075.2.a.dj.1.2		4	11.8	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.359123 - 1.10527i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.525387 - 0.381716i) q^{4} +(0.359123 - 1.10527i) q^{6} +(-3.46813 + 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.359123 - 1.10527i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.525387 - 0.381716i) q^{4} +(0.359123 - 1.10527i) q^{6} +(-3.46813 + 2.51974i) q^{7} +(-2.49097 - 1.80980i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-3.15911 + 1.00996i) q^{11} +0.649414 q^{12} +(-1.59676 - 4.91433i) q^{13} +(4.03048 + 2.92831i) q^{14} +(-0.704384 + 2.16787i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(0.940197 - 0.683093i) q^{18} +(-4.53048 - 3.29158i) q^{19} -4.28684 q^{21} +(2.25079 + 3.12896i) q^{22} +0.219819 q^{23} +(-0.951466 - 2.92831i) q^{24} +(-4.85822 + 3.52970i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.860283 + 2.64768i) q^{28} +(-5.19262 + 3.77266i) q^{29} +(-0.874813 - 2.69240i) q^{31} -3.50898 q^{32} +(-3.14941 - 1.03980i) q^{33} +5.81074 q^{34} +(0.525387 + 0.381716i) q^{36} +(3.17784 - 2.30883i) q^{37} +(-2.01108 + 6.18947i) q^{38} +(1.59676 - 4.91433i) q^{39} +(-4.74165 - 3.44501i) q^{41} +(1.53950 + 4.73811i) q^{42} +8.90173 q^{43} +(-1.27424 + 1.73650i) q^{44} +(-0.0789420 - 0.242959i) q^{46} +(-0.192447 - 0.139821i) q^{47} +(-1.84410 + 1.33982i) q^{48} +(3.51569 - 10.8202i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(-2.71480 - 1.97242i) q^{52} +(-0.783885 - 2.41255i) q^{53} +1.16215 q^{54} +13.1992 q^{56} +(-1.73049 - 5.32589i) q^{57} +(6.03459 + 4.38439i) q^{58} +(6.36725 - 4.62608i) q^{59} +(-1.50123 + 4.62030i) q^{61} +(-2.66165 + 1.93381i) q^{62} +(-3.46813 - 2.51974i) q^{63} +(2.66892 + 8.21410i) q^{64} +(-0.0182340 + 3.85436i) q^{66} -12.1280 q^{67} +(1.00340 + 3.08815i) q^{68} +(0.177837 + 0.129206i) q^{69} +(-3.08459 + 9.49339i) q^{71} +(0.951466 - 2.92831i) q^{72} +(11.7813 - 8.55964i) q^{73} +(-3.69311 - 2.68320i) q^{74} -3.63670 q^{76} +(8.41136 - 11.4628i) q^{77} -6.00509 q^{78} +(2.47274 + 7.61030i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.10482 + 6.47797i) q^{82} +(-3.87908 + 11.9386i) q^{83} +(-2.25225 + 1.63636i) q^{84} +(-3.19682 - 9.83880i) q^{86} -6.41843 q^{87} +(9.69707 + 3.20157i) q^{88} -2.56545 q^{89} +(17.9206 + 13.0201i) q^{91} +(0.115490 - 0.0839083i) q^{92} +(0.874813 - 2.69240i) q^{93} +(-0.0854274 + 0.262919i) q^{94} +(-2.83882 - 2.06253i) q^{96} +(-0.621738 - 1.91351i) q^{97} -13.2218 q^{98} +(-1.93675 - 2.69240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

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