LMFDB - Embedded newform 825.2.n.b.301.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.301
Dual form			825.2.n.b.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.363271i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.236068 - 0.726543i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.363271i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.236068 - 0.726543i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} +1.61803 q^{12} +(1.00000 + 0.726543i) q^{13} +(-0.145898 + 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(-1.61803 + 1.17557i) q^{17} +(0.190983 + 0.587785i) q^{18} +(1.54508 - 4.75528i) q^{19} +0.763932 q^{21} +(-1.88197 - 0.812299i) q^{22} +2.38197 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.00000 + 0.726543i) q^{28} +(-1.80902 - 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} +5.61803 q^{32} +(-0.309017 + 3.30220i) q^{33} +1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(-2.30902 - 7.10642i) q^{37} +(-2.50000 + 1.81636i) q^{38} +(-1.00000 + 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(-0.381966 - 0.277515i) q^{42} -2.09017 q^{43} +(-2.73607 - 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(1.57295 - 4.84104i) q^{47} +(-0.572949 - 1.76336i) q^{48} +(5.19098 - 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(0.618034 - 1.90211i) q^{52} +(6.16312 + 4.47777i) q^{53} -0.618034 q^{54} +1.70820 q^{56} +(4.04508 + 2.93893i) q^{57} +(-1.11803 + 3.44095i) q^{58} +(-2.07295 - 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(1.33688 + 4.11450i) q^{62} +(-0.236068 + 0.726543i) q^{63} +(0.190983 + 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} -9.38197 q^{67} +(2.61803 + 1.90211i) q^{68} +(-0.736068 + 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(1.80902 - 1.31433i) q^{72} +(-4.16312 - 12.8128i) q^{73} +(-1.42705 + 4.39201i) q^{74} -8.09017 q^{76} +(-1.29180 - 2.17963i) q^{77} +0.763932 q^{78} +(6.54508 + 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.26393 + 0.918300i) q^{82} +(4.61803 - 3.35520i) q^{83} +(-0.381966 - 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} +5.85410 q^{87} +(-0.690983 + 7.38394i) q^{88} +10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(-1.19098 - 3.66547i) q^{92} +(5.66312 - 4.11450i) q^{93} +(-2.54508 + 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(-9.28115 - 6.74315i) q^{97} -3.96556 q^{98} +(-3.04508 - 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9 + 4 * q^11 + 2 * q^12 + 4 * q^13 - 14 * q^14 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 5 * q^19 + 12 * q^21 - 12 * q^22 + 14 * q^23 - 5 * q^24 + 8 * q^26 + q^27 - 4 * q^28 - 5 * q^29 - 7 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 2 * q^36 - 7 * q^37 - 10 * q^38 - 4 * q^39 - 17 * q^41 - 6 * q^42 + 14 * q^43 - 2 * q^44 - 7 * q^46 + 13 * q^47 - 9 * q^48 + 23 * q^49 + 2 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 - 20 * q^56 + 5 * q^57 - 15 * q^59 - 7 * q^61 + 21 * q^62 + 8 * q^63 + 3 * q^64 - 8 * q^66 - 42 * q^67 + 6 * q^68 + 6 * q^69 + 8 * q^71 + 5 * q^72 - q^73 + q^74 - 10 * q^76 - 32 * q^77 + 12 * q^78 + 15 * q^79 - q^81 - 14 * q^82 + 14 * q^83 - 6 * q^84 - 7 * q^86 + 10 * q^87 - 5 * q^88 + 30 * q^89 + 28 * q^91 - 7 * q^92 + 7 * q^93 + q^94 + 2 * q^96 - 17 * q^97 - 74 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	0.396805	−	0.917903i	$-0.370119\pi$
$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	−0.750358	+	0.661031i	$0.770119\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.363271i	0.204124	−	0.148305i
$7$	−0.236068	−	0.726543i	−0.0892253	−	0.274607i	0.896480	−	0.443083i	$-0.146115\pi$
$7$	−0.236068	−	0.726543i	−0.0892253	−	0.274607i	−0.985706	+	0.168476i	$0.946115\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$12$	1.61803			0.467086
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	0.717761	−	0.696290i	$-0.245167\pi$
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	−0.440411	+	0.897796i	$0.645167\pi$
$14$	−0.145898	+	0.449028i	−0.0389929	+	0.120008i
$15$		0			0
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	−0.766451	−	0.642303i	$-0.777979\pi$
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	0.374020	+	0.927421i	$0.377979\pi$
$18$	0.190983	+	0.587785i	0.0450151	+	0.138542i
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	−0.601851	−	0.798608i	$-0.705570\pi$
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	0.956318	−	0.292328i	$-0.0944300\pi$
$20$		0			0
$21$	0.763932			0.166704
$22$	−1.88197	−	0.812299i	−0.401237	−	0.173183i
$23$	2.38197			0.496674			0.248337	−	0.968674i	$-0.420116\pi$
$23$	2.38197			0.496674			0.248337	+	0.968674i	$0.420116\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$		0			0
$26$	−0.236068	−	0.726543i	−0.0462967	−	0.142487i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−1.00000	+	0.726543i	−0.188982	+	0.137304i
$29$	−1.80902	−	5.56758i	−0.335926	−	1.03387i	−0.966264	−	0.257553i	$-0.917084\pi$
$29$	−1.80902	−	5.56758i	−0.335926	−	1.03387i	0.630338	−	0.776321i	$-0.282916\pi$
$30$		0			0
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.0514344	−	0.998676i	$-0.516379\pi$
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.965692	+	0.259691i	$0.916379\pi$
$32$	5.61803			0.993137
$33$	−0.309017	+	3.30220i	−0.0537930	+	0.574839i
$34$	1.23607			0.211984
$35$		0			0
$36$	−0.500000	+	1.53884i	−0.0833333	+	0.256474i
$37$	−2.30902	−	7.10642i	−0.379600	−	1.16829i	−0.940322	−	0.340285i	$-0.889476\pi$
$37$	−2.30902	−	7.10642i	−0.379600	−	1.16829i	0.560722	−	0.828004i	$-0.310524\pi$
$38$	−2.50000	+	1.81636i	−0.405554	+	0.294652i
$39$	−1.00000	+	0.726543i	−0.160128	+	0.116340i
$40$		0			0
$41$	0.781153	−	2.40414i	0.121996	−	0.375464i	−0.871346	−	0.490669i	$-0.836752\pi$
$41$	0.781153	−	2.40414i	0.121996	−	0.375464i	0.993342	+	0.115205i	$0.0367525\pi$
$42$	−0.381966	−	0.277515i	−0.0589386	−	0.0428214i
$43$	−2.09017			−0.318748			−0.159374	−	0.987218i	$-0.550948\pi$
$43$	−2.09017			−0.318748			−0.159374	+	0.987218i	$0.550948\pi$
$44$	−2.73607	−	4.61653i	−0.412478	−	0.695967i
$45$		0			0
$46$	−1.19098	−	0.865300i	−0.175601	−	0.127581i
$47$	1.57295	−	4.84104i	0.229438	−	0.706138i	−0.768372	−	0.640003i	$-0.778933\pi$
$47$	1.57295	−	4.84104i	0.229438	−	0.706138i	0.997811	−	0.0661352i	$-0.0210669\pi$
$48$	−0.572949	−	1.76336i	−0.0826981	−	0.254518i
$49$	5.19098	−	3.77147i	0.741569	−	0.538781i
$50$		0			0
$51$	−0.618034	−	1.90211i	−0.0865421	−	0.266349i
$52$	0.618034	−	1.90211i	0.0857059	−	0.263776i
$53$	6.16312	+	4.47777i	0.846569	+	0.615069i	0.924198	−	0.381914i	$-0.124735\pi$
$53$	6.16312	+	4.47777i	0.846569	+	0.615069i	−0.0776285	+	0.996982i	$0.524735\pi$
$54$	−0.618034			−0.0841038
$55$		0			0
$56$	1.70820			0.228268
$57$	4.04508	+	2.93893i	0.535785	+	0.389270i
$58$	−1.11803	+	3.44095i	−0.146805	+	0.451820i
$59$	−2.07295	−	6.37988i	−0.269875	−	0.830590i	−0.990530	−	0.137296i	$-0.956159\pi$
$59$	−2.07295	−	6.37988i	−0.269875	−	0.830590i	0.720655	−	0.693294i	$-0.243841\pi$
$60$		0			0
$61$	−5.66312	+	4.11450i	−0.725088	+	0.526807i	−0.888006	−	0.459832i	$-0.847910\pi$
$61$	−5.66312	+	4.11450i	−0.725088	+	0.526807i	0.162918	+	0.986640i	$0.447910\pi$
$62$	1.33688	+	4.11450i	0.169784	+	0.522542i
$63$	−0.236068	+	0.726543i	−0.0297418	+	0.0915358i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$		0			0
$66$	1.35410	−	1.53884i	0.166678	−	0.189418i
$67$	−9.38197			−1.14619			−0.573095	−	0.819489i	$-0.694257\pi$
$67$	−9.38197			−1.14619			−0.573095	+	0.819489i	$0.694257\pi$
$68$	2.61803	+	1.90211i	0.317483	+	0.230665i
$69$	−0.736068	+	2.26538i	−0.0886122	+	0.272720i
$70$		0			0
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	−0.133283	−	0.991078i	$-0.542552\pi$
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	0.901384	+	0.433020i	$0.142552\pi$
$72$	1.80902	−	1.31433i	0.213195	−	0.154895i
$73$	−4.16312	−	12.8128i	−0.487256	−	1.49962i	−0.828686	−	0.559713i	$-0.810911\pi$
$73$	−4.16312	−	12.8128i	−0.487256	−	1.49962i	0.341430	−	0.939907i	$-0.389089\pi$
$74$	−1.42705	+	4.39201i	−0.165891	+	0.510561i
$75$		0			0
$76$	−8.09017			−0.928006
$77$	−1.29180	−	2.17963i	−0.147214	−	0.248392i
$78$	0.763932			0.0864983
$79$	6.54508	+	4.75528i	0.736380	+	0.535011i	0.891575	−	0.452873i	$-0.149601\pi$
$79$	6.54508	+	4.75528i	0.736380	+	0.535011i	−0.155196	+	0.987884i	$0.549601\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.26393	+	0.918300i	−0.139578	+	0.101409i
$83$	4.61803	−	3.35520i	0.506895	−	0.368281i	−0.304749	−	0.952433i	$-0.598573\pi$
$83$	4.61803	−	3.35520i	0.506895	−	0.368281i	0.811644	+	0.584152i	$0.198573\pi$
$84$	−0.381966	−	1.17557i	−0.0416759	−	0.128265i
$85$		0			0
$86$	1.04508	+	0.759299i	0.112694	+	0.0818773i
$87$	5.85410			0.627626
$88$	−0.690983	+	7.38394i	−0.0736590	+	0.787130i
$89$	10.8541			1.15053			0.575266	−	0.817966i	$-0.304898\pi$
$89$	10.8541			1.15053			0.575266	+	0.817966i	$0.304898\pi$
$90$		0			0
$91$	0.291796	−	0.898056i	0.0305885	−	0.0941418i
$92$	−1.19098	−	3.66547i	−0.124169	−	0.382152i
$93$	5.66312	−	4.11450i	0.587238	−	0.426653i
$94$	−2.54508	+	1.84911i	−0.262505	+	0.190721i
$95$		0			0
$96$	−1.73607	+	5.34307i	−0.177187	+	0.545325i
$97$	−9.28115	−	6.74315i	−0.942358	−	0.684663i	0.00662888	−	0.999978i	$-0.497890\pi$
$97$	−9.28115	−	6.74315i	−0.942358	−	0.684663i	−0.948987	+	0.315315i	$0.897890\pi$
$98$	−3.96556			−0.400582
$99$	−3.04508	−	1.31433i	−0.306043	−	0.132095i
$100$		0			0
$101$	0.454915	+	0.330515i	0.0452657	+	0.0328875i	0.610188	−	0.792257i	$-0.291094\pi$
$101$	0.454915	+	0.330515i	0.0452657	+	0.0328875i	−0.564922	+	0.825144i	$0.691094\pi$
$102$	−0.381966	+	1.17557i	−0.0378203	+	0.116399i
$103$	0.736068	+	2.26538i	0.0725269	+	0.223215i	0.980749	−	0.195274i	$-0.0625597\pi$
$103$	0.736068	+	2.26538i	0.0725269	+	0.223215i	−0.908222	+	0.418489i	$0.862560\pi$
$104$	−2.23607	+	1.62460i	−0.219265	+	0.159305i
$105$		0			0
$106$	−1.45492	−	4.47777i	−0.141314	−	0.434919i
$107$	0.881966	−	2.71441i	0.0852629	−	0.262412i	−0.899331	−	0.437268i	$-0.855946\pi$
$107$	0.881966	−	2.71441i	0.0852629	−	0.262412i	0.984594	+	0.174856i	$0.0559460\pi$
$108$	−1.30902	−	0.951057i	−0.125960	−	0.0915155i
$109$	4.14590			0.397105			0.198553	−	0.980090i	$-0.436376\pi$
$109$	4.14590			0.397105			0.198553	+	0.980090i	$0.436376\pi$
$110$		0			0
$111$	7.47214			0.709224
$112$	1.14590	+	0.832544i	0.108277	+	0.0786680i
$113$	1.69098	−	5.20431i	0.159074	−	0.489580i	−0.839477	−	0.543396i	$-0.817138\pi$
$113$	1.69098	−	5.20431i	0.159074	−	0.489580i	0.998551	+	0.0538155i	$0.0171383\pi$
$114$	−0.954915	−	2.93893i	−0.0894360	−	0.275256i
$115$		0			0
$116$	−7.66312	+	5.56758i	−0.711503	+	0.516937i
$117$	−0.381966	−	1.17557i	−0.0353128	−	0.108682i
$118$	−1.28115	+	3.94298i	−0.117940	+	0.362981i
$119$	1.23607	+	0.898056i	0.113310	+	0.0823247i
$120$		0			0
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$	4.32624			0.391679
$123$	2.04508	+	1.48584i	0.184399	+	0.133974i
$124$	−3.50000	+	10.7719i	−0.314309	+	0.967344i
$125$		0			0
$126$	0.381966	−	0.277515i	0.0340282	−	0.0247230i
$127$	−12.8992	+	9.37181i	−1.14462	+	0.831613i	−0.987756	−	0.156007i	$-0.950138\pi$
$127$	−12.8992	+	9.37181i	−1.14462	+	0.831613i	−0.156862	+	0.987621i	$0.550138\pi$
$128$	−3.51722	−	10.8249i	−0.310881	−	0.956794i
$129$	0.645898	−	1.98787i	0.0568682	−	0.175022i
$130$		0			0
$131$	13.1803			1.15157			0.575786	−	0.817601i	$-0.304696\pi$
$131$	13.1803			1.15157			0.575786	+	0.817601i	$0.304696\pi$
$132$	5.23607	−	1.17557i	0.455741	−	0.102320i
$133$	−3.81966			−0.331207
$134$	4.69098	+	3.40820i	0.405239	+	0.294424i
$135$		0			0
$136$	−1.38197	−	4.25325i	−0.118503	−	0.364714i
$137$	−15.1353	+	10.9964i	−1.29309	+	0.939486i	−0.999863	−	0.0165558i	$-0.994730\pi$
$137$	−15.1353	+	10.9964i	−1.29309	+	0.939486i	−0.293229	+	0.956042i	$0.594730\pi$
$138$	1.19098	−	0.865300i	0.101383	−	0.0736592i
$139$	6.54508	+	20.1437i	0.555147	+	1.70857i	0.695555	+	0.718473i	$0.255158\pi$
$139$	6.54508	+	20.1437i	0.555147	+	1.70857i	−0.140408	+	0.990094i	$0.544842\pi$
$140$		0			0
$141$	4.11803	+	2.99193i	0.346801	+	0.251966i
$142$	−4.94427			−0.414914
$143$	3.76393	+	1.62460i	0.314756	+	0.135856i
$144$	1.85410			0.154508
$145$		0			0
$146$	−2.57295	+	7.91872i	−0.212939	+	0.655358i
$147$	1.98278	+	6.10237i	0.163537	+	0.503315i
$148$	−9.78115	+	7.10642i	−0.804006	+	0.584144i
$149$	−16.2812	+	11.8290i	−1.33380	+	0.969065i	−0.334156	+	0.942518i	$0.608451\pi$
$149$	−16.2812	+	11.8290i	−1.33380	+	0.969065i	−0.999648	+	0.0265477i	$0.991549\pi$
$150$		0			0
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	0.719643	+	0.694344i	$0.244305\pi$
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	−0.990329	+	0.138740i	$0.955695\pi$
$152$	9.04508	+	6.57164i	0.733653	+	0.533030i
$153$	2.00000			0.161690
$154$	−0.145898	+	1.55909i	−0.0117568	+	0.125635i
$155$		0			0
$156$	1.61803	+	1.17557i	0.129546	+	0.0941210i
$157$	−1.02786	+	3.16344i	−0.0820325	+	0.252470i	−0.983658	−	0.180048i	$-0.942375\pi$
$157$	−1.02786	+	3.16344i	−0.0820325	+	0.252470i	0.901625	+	0.432518i	$0.142375\pi$
$158$	−1.54508	−	4.75528i	−0.122920	−	0.378310i
$159$	−6.16312	+	4.47777i	−0.488767	+	0.355110i
$160$		0			0
$161$	−0.562306	−	1.73060i	−0.0443159	−	0.136390i
$162$	0.190983	−	0.587785i	0.0150050	−	0.0461808i
$163$	−10.9721	−	7.97172i	−0.859404	−	0.624394i	0.0683187	−	0.997664i	$-0.478237\pi$
$163$	−10.9721	−	7.97172i	−0.859404	−	0.624394i	−0.927723	+	0.373270i	$0.878237\pi$
$164$	−4.09017			−0.319389
$165$		0			0
$166$	−3.52786			−0.273815
$167$	16.2082	+	11.7759i	1.25423	+	0.911250i	0.998459	−	0.0554876i	$-0.0176713\pi$
$167$	16.2082	+	11.7759i	1.25423	+	0.911250i	0.255769	+	0.966738i	$0.417671\pi$
$168$	−0.527864	+	1.62460i	−0.0407256	+	0.125340i
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$		0			0
$171$	−4.04508	+	2.93893i	−0.309335	+	0.224745i
$172$	1.04508	+	3.21644i	0.0796870	+	0.245251i
$173$	1.10081	−	3.38795i	0.0836933	−	0.257581i	−0.900449	−	0.434961i	$-0.856762\pi$
$173$	1.10081	−	3.38795i	0.0836933	−	0.257581i	0.984142	+	0.177380i	$0.0567621\pi$
$174$	−2.92705	−	2.12663i	−0.221899	−	0.161219i
$175$		0			0
$176$	−4.06231	+	4.61653i	−0.306208	+	0.347984i
$177$	6.70820			0.504219
$178$	−5.42705	−	3.94298i	−0.406775	−	0.295539i
$179$	−6.01722	+	18.5191i	−0.449748	+	1.38418i	0.427443	+	0.904042i	$0.359414\pi$
$179$	−6.01722	+	18.5191i	−0.449748	+	1.38418i	−0.877192	+	0.480141i	$0.840586\pi$
$180$		0			0
$181$	4.23607	−	3.07768i	0.314864	−	0.228762i	−0.419117	−	0.907932i	$-0.637660\pi$
$181$	4.23607	−	3.07768i	0.314864	−	0.228762i	0.733981	+	0.679170i	$0.237660\pi$
$182$	−0.472136	+	0.343027i	−0.0349970	+	0.0254268i
$183$	−2.16312	−	6.65740i	−0.159902	−	0.492129i
$184$	−1.64590	+	5.06555i	−0.121337	+	0.373438i
$185$		0			0
$186$	−4.32624			−0.317215
$187$	−4.38197	+	4.97980i	−0.320441	+	0.364159i
$188$	−8.23607			−0.600677
$189$	−0.618034	−	0.449028i	−0.0449554	−	0.0326620i
$190$		0			0
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	0.997392	+	0.0721737i	$0.0229936\pi$
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	−0.764484	+	0.644642i	$0.777006\pi$
$192$	−0.190983	+	0.138757i	−0.0137830	+	0.0100139i
$193$	17.0172	−	12.3637i	1.22493	−	0.889961i	0.228427	−	0.973561i	$-0.426642\pi$
$193$	17.0172	−	12.3637i	1.22493	−	0.889961i	0.996499	+	0.0836000i	$0.0266418\pi$
$194$	2.19098	+	6.74315i	0.157303	+	0.484130i
$195$		0			0
$196$	−8.39919	−	6.10237i	−0.599942	−	0.435883i
$197$	14.2361			1.01428			0.507139	−	0.861864i	$-0.330703\pi$
$197$	14.2361			1.01428			0.507139	+	0.861864i	$0.330703\pi$
$198$	1.04508	+	1.76336i	0.0742710	+	0.125316i
$199$	19.7984			1.40347			0.701735	−	0.712438i	$-0.252409\pi$
$199$	19.7984			1.40347			0.701735	+	0.712438i	$0.252409\pi$
$200$		0			0
$201$	2.89919	−	8.92278i	0.204493	−	0.629364i
$202$	−0.107391	−	0.330515i	−0.00755600	−	0.0232550i
$203$	−3.61803	+	2.62866i	−0.253936	+	0.184495i
$204$	−2.61803	+	1.90211i	−0.183299	+	0.133175i
$205$		0			0
$206$	0.454915	−	1.40008i	0.0316954	−	0.0975485i
$207$	−1.92705	−	1.40008i	−0.133939	−	0.0973126i
$208$	−2.29180			−0.158907
$209$	1.54508	−	16.5110i	0.106876	−	1.14209i
$210$		0			0
$211$	3.11803	+	2.26538i	0.214654	+	0.155955i	0.689917	−	0.723888i	$-0.257647\pi$
$211$	3.11803	+	2.26538i	0.214654	+	0.155955i	−0.475263	+	0.879844i	$0.657647\pi$
$212$	3.80902	−	11.7229i	0.261604	−	0.805135i
$213$	2.47214	+	7.60845i	0.169388	+	0.521323i
$214$	−1.42705	+	1.03681i	−0.0975512	+	0.0708751i
$215$		0			0
$216$	0.690983	+	2.12663i	0.0470154	+	0.144699i
$217$	−1.65248	+	5.08580i	−0.112177	+	0.345246i
$218$	−2.07295	−	1.50609i	−0.140398	−	0.102005i
$219$	13.4721			0.910363
$220$		0			0
$221$	−2.47214			−0.166294
$222$	−3.73607	−	2.71441i	−0.250748	−	0.182179i
$223$	2.48278	−	7.64121i	0.166259	−	0.511693i	−0.832868	−	0.553472i	$-0.813303\pi$
$223$	2.48278	−	7.64121i	0.166259	−	0.511693i	0.999127	+	0.0417790i	$0.0133025\pi$
$224$	−1.32624	−	4.08174i	−0.0886130	−	0.272723i
$225$		0			0
$226$	−2.73607	+	1.98787i	−0.182001	+	0.132231i
$227$	8.01722	+	24.6745i	0.532122	+	1.63770i	0.749788	+	0.661679i	$0.230156\pi$
$227$	8.01722	+	24.6745i	0.532122	+	1.63770i	−0.217666	+	0.976023i	$0.569844\pi$
$228$	2.50000	−	7.69421i	0.165567	−	0.509561i
$229$	−14.6353	−	10.6331i	−0.967125	−	0.702657i	−0.0123304	−	0.999924i	$-0.503925\pi$
$229$	−14.6353	−	10.6331i	−0.967125	−	0.702657i	−0.954795	+	0.297267i	$0.903925\pi$
$230$		0			0
$231$	2.47214	−	0.555029i	0.162655	−	0.0365182i
$232$	13.0902			0.859412
$233$	18.8262	+	13.6781i	1.23335	+	0.896080i	0.997137	−	0.0756220i	$-0.0240942\pi$
$233$	18.8262	+	13.6781i	1.23335	+	0.896080i	0.236211	+	0.971702i	$0.424094\pi$
$234$	−0.236068	+	0.726543i	−0.0154322	+	0.0474956i
$235$		0			0
$236$	−8.78115	+	6.37988i	−0.571604	+	0.415295i
$237$	−6.54508	+	4.75528i	−0.425149	+	0.308889i
$238$	−0.291796	−	0.898056i	−0.0189143	−	0.0582123i
$239$	−2.17376	+	6.69015i	−0.140609	+	0.432750i	−0.996420	−	0.0845383i	$-0.973058\pi$
$239$	−2.17376	+	6.69015i	−0.140609	+	0.432750i	0.855811	+	0.517288i	$0.173058\pi$
$240$		0			0
$241$	−1.61803			−0.104227			−0.0521134	−	0.998641i	$-0.516596\pi$
$241$	−1.61803			−0.104227			−0.0521134	+	0.998641i	$0.516596\pi$
$242$	−6.68034	−	1.26133i	−0.429429	−	0.0810812i
$243$	−1.00000			−0.0641500
$244$	9.16312	+	6.65740i	0.586609	+	0.426196i
$245$		0			0
$246$	−0.482779	−	1.48584i	−0.0307809	−	0.0947338i
$247$	5.00000	−	3.63271i	0.318142	−	0.231144i
$248$	12.6631	−	9.20029i	0.804109	−	0.584219i
$249$	1.76393	+	5.42882i	0.111785	+	0.344038i
$250$		0			0
$251$	−6.09017	−	4.42477i	−0.384408	−	0.279289i	0.378752	−	0.925498i	$-0.376353\pi$
$251$	−6.09017	−	4.42477i	−0.384408	−	0.279289i	−0.763160	+	0.646209i	$0.776353\pi$
$252$	1.23607			0.0778650
$253$	7.70820	−	1.73060i	0.484611	−	0.108802i
$254$	9.85410			0.618301
$255$		0			0
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−3.26393	−	10.0453i	−0.203598	−	0.626612i	−0.999768	−	0.0215381i	$-0.993144\pi$
$257$	−3.26393	−	10.0453i	−0.203598	−	0.626612i	0.796170	−	0.605074i	$-0.206856\pi$
$258$	−1.04508	+	0.759299i	−0.0650641	+	0.0472719i
$259$	−4.61803	+	3.35520i	−0.286951	+	0.208482i
$260$		0			0
$261$	−1.80902	+	5.56758i	−0.111975	+	0.344625i
$262$	−6.59017	−	4.78804i	−0.407142	−	0.295806i
$263$	−27.2148			−1.67814			−0.839068	−	0.544027i	$-0.816899\pi$
$263$	−27.2148			−1.67814			−0.839068	+	0.544027i	$0.816899\pi$
$264$	−6.80902	−	2.93893i	−0.419066	−	0.180878i
$265$		0			0
$266$	1.90983	+	1.38757i	0.117099	+	0.0850775i
$267$	−3.35410	+	10.3229i	−0.205268	+	0.631749i
$268$	4.69098	+	14.4374i	0.286547	+	0.881902i
$269$	4.73607	−	3.44095i	0.288763	−	0.209799i	−0.433967	−	0.900929i	$-0.642887\pi$
$269$	4.73607	−	3.44095i	0.288763	−	0.209799i	0.722731	+	0.691130i	$0.242887\pi$
$270$		0			0
$271$	6.37132	+	19.6089i	0.387030	+	1.19116i	0.934997	+	0.354656i	$0.115402\pi$
$271$	6.37132	+	19.6089i	0.387030	+	1.19116i	−0.547966	+	0.836500i	$0.684598\pi$
$272$	1.14590	−	3.52671i	0.0694803	−	0.213838i
$273$	0.763932	+	0.555029i	0.0462353	+	0.0335919i
$274$	11.5623			0.698504
$275$		0			0
$276$	3.85410			0.231990
$277$	7.00000	+	5.08580i	0.420589	+	0.305576i	0.777875	−	0.628419i	$-0.216298\pi$
$277$	7.00000	+	5.08580i	0.420589	+	0.305576i	−0.357286	+	0.933995i	$0.616298\pi$
$278$	4.04508	−	12.4495i	0.242608	−	0.746671i
$279$	2.16312	+	6.65740i	0.129503	+	0.398568i
$280$		0			0
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	−0.804018	−	0.594605i	$-0.797309\pi$
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	0.317047	+	0.948410i	$0.397309\pi$
$282$	−0.972136	−	2.99193i	−0.0578899	−	0.178167i
$283$	4.02786	−	12.3965i	0.239432	−	0.736895i	−0.757071	−	0.653333i	$-0.773370\pi$
$283$	4.02786	−	12.3965i	0.239432	−	0.736895i	0.996503	−	0.0835622i	$-0.0266297\pi$
$284$	−10.4721	−	7.60845i	−0.621407	−	0.451479i
$285$		0			0
$286$	−1.29180	−	2.17963i	−0.0763855	−	0.128884i
$287$	−1.93112			−0.113990
$288$	−4.54508	−	3.30220i	−0.267822	−	0.194584i
$289$	−4.01722	+	12.3637i	−0.236307	+	0.727279i
$290$		0			0
$291$	9.28115	−	6.74315i	0.544071	−	0.395291i
$292$	−17.6353	+	12.8128i	−1.03203	+	0.749810i
$293$	5.10739	+	15.7189i	0.298377	+	0.918310i	0.982066	+	0.188537i	$0.0603744\pi$
$293$	5.10739	+	15.7189i	0.298377	+	0.918310i	−0.683689	+	0.729773i	$0.739626\pi$
$294$	1.22542	−	3.77147i	0.0714682	−	0.219957i
$295$		0			0
$296$	16.7082			0.971145
$297$	2.19098	−	2.48990i	0.127134	−	0.144479i
$298$	12.4377			0.720496
$299$	2.38197	+	1.73060i	0.137753	+	0.100083i
$300$		0			0
$301$	0.493422	+	1.51860i	0.0284404	+	0.0875305i
$302$	5.38197	−	3.91023i	0.309697	−	0.225008i
$303$	−0.454915	+	0.330515i	−0.0261342	+	0.0189876i
$304$	2.86475	+	8.81678i	0.164304	+	0.505677i
$305$		0			0
$306$	−1.00000	−	0.726543i	−0.0571662	−	0.0415337i
$307$	12.1246			0.691988			0.345994	−	0.938237i	$-0.387542\pi$
$307$	12.1246			0.691988			0.345994	+	0.938237i	$0.387542\pi$
$308$	−2.70820	+	3.07768i	−0.154314	+	0.175367i
$309$	−2.38197			−0.135505
$310$		0			0
$311$	6.63525	−	20.4212i	0.376251	−	1.15798i	−0.566380	−	0.824144i	$-0.691657\pi$
$311$	6.63525	−	20.4212i	0.376251	−	1.15798i	0.942631	−	0.333837i	$-0.108343\pi$
$312$	−0.854102	−	2.62866i	−0.0483540	−	0.148818i
$313$	−0.381966	+	0.277515i	−0.0215900	+	0.0156860i	−0.598528	−	0.801102i	$-0.704247\pi$
$313$	−0.381966	+	0.277515i	−0.0215900	+	0.0156860i	0.576938	+	0.816788i	$0.304247\pi$
$314$	1.66312	−	1.20833i	0.0938552	−	0.0681898i
$315$		0			0
$316$	4.04508	−	12.4495i	0.227554	−	0.700339i
$317$	−24.6074	−	17.8783i	−1.38209	−	1.00415i	−0.996682	−	0.0813997i	$-0.974061\pi$
$317$	−24.6074	−	17.8783i	−1.38209	−	1.00415i	−0.385407	−	0.922747i	$-0.625939\pi$
$318$	4.70820			0.264023
$319$	−9.89919	−	16.7027i	−0.554248	−	0.935174i
$320$		0			0
$321$	2.30902	+	1.67760i	0.128877	+	0.0936344i
$322$	−0.347524	+	1.06957i	−0.0193668	+	0.0596048i
$323$	3.09017	+	9.51057i	0.171942	+	0.529182i
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$		0			0
$326$	2.59017	+	7.97172i	0.143456	+	0.441513i
$327$	−1.28115	+	3.94298i	−0.0708479	+	0.218047i
$328$	4.57295	+	3.32244i	0.252499	+	0.183451i
$329$	−3.88854			−0.214382
$330$		0			0
$331$	21.5967			1.18706			0.593532	−	0.804810i	$-0.297733\pi$
$331$	21.5967			1.18706			0.593532	+	0.804810i	$0.297733\pi$
$332$	−7.47214	−	5.42882i	−0.410087	−	0.297945i
$333$	−2.30902	+	7.10642i	−0.126533	+	0.389430i
$334$	−3.82624	−	11.7759i	−0.209362	−	0.644351i
$335$		0			0
$336$	−1.14590	+	0.832544i	−0.0625139	+	0.0454190i
$337$	−6.84346	−	21.0620i	−0.372787	−	1.14732i	−0.944960	−	0.327187i	$-0.893899\pi$
$337$	−6.84346	−	21.0620i	−0.372787	−	1.14732i	0.572173	−	0.820133i	$-0.306101\pi$
$338$	−2.19098	+	6.74315i	−0.119174	+	0.366779i
$339$	4.42705	+	3.21644i	0.240444	+	0.174693i
$340$		0			0
$341$	−21.3156	−	9.20029i	−1.15430	−	0.498224i
$342$	3.09017			0.167097
$343$	−8.29180	−	6.02434i	−0.447715	−	0.325284i
$344$	1.44427	−	4.44501i	0.0778699	−	0.239659i
$345$		0			0
$346$	−1.78115	+	1.29408i	−0.0957554	+	0.0695704i
$347$	−4.70820	+	3.42071i	−0.252750	+	0.183633i	−0.706945	−	0.707269i	$-0.749927\pi$
$347$	−4.70820	+	3.42071i	−0.252750	+	0.183633i	0.454195	+	0.890902i	$0.349927\pi$
$348$	−2.92705	−	9.00854i	−0.156906	−	0.482908i
$349$	8.57953	−	26.4051i	0.459252	−	1.41343i	−0.406819	−	0.913509i	$-0.633362\pi$
$349$	8.57953	−	26.4051i	0.459252	−	1.41343i	0.866070	−	0.499922i	$-0.166638\pi$
$350$		0			0
$351$	1.23607			0.0659764
$352$	18.1803	−	4.08174i	0.969015	−	0.217558i
$353$	−35.8328			−1.90719			−0.953594	−	0.301095i	$-0.902648\pi$
$353$	−35.8328			−1.90719			−0.953594	+	0.301095i	$0.902648\pi$
$354$	−3.35410	−	2.43690i	−0.178269	−	0.129520i
$355$		0			0
$356$	−5.42705	−	16.7027i	−0.287633	−	0.885244i
$357$	−1.23607	+	0.898056i	−0.0654197	+	0.0475302i
$358$	9.73607	−	7.07367i	0.514567	−	0.373855i
$359$	5.16312	+	15.8904i	0.272499	+	0.838666i	0.989870	+	0.141975i	$0.0453451\pi$
$359$	5.16312	+	15.8904i	0.272499	+	0.838666i	−0.717371	+	0.696691i	$0.754655\pi$
$360$		0			0
$361$	−4.85410	−	3.52671i	−0.255479	−	0.185616i
$362$	−3.23607			−0.170084
$363$	1.39919	+	10.9106i	0.0734383	+	0.572661i
$364$	−1.52786			−0.0800818
$365$		0			0
$366$	−1.33688	+	4.11450i	−0.0698799	+	0.215068i
$367$	−5.60081	−	17.2375i	−0.292360	−	0.899792i	−0.984095	−	0.177641i	$-0.943154\pi$
$367$	−5.60081	−	17.2375i	−0.292360	−	0.899792i	0.691735	−	0.722151i	$-0.256846\pi$
$368$	−3.57295	+	2.59590i	−0.186253	+	0.135321i
$369$	−2.04508	+	1.48584i	−0.106463	+	0.0773498i
$370$		0			0
$371$	1.79837	−	5.53483i	0.0933669	−	0.287354i
$372$	−9.16312	−	6.65740i	−0.475086	−	0.345170i
$373$	9.74265			0.504455			0.252228	−	0.967668i	$-0.418837\pi$
$373$	9.74265			0.504455			0.252228	+	0.967668i	$0.418837\pi$
$374$	4.00000	−	0.898056i	0.206835	−	0.0464374i
$375$		0			0
$376$	9.20820	+	6.69015i	0.474877	+	0.345018i
$377$	2.23607	−	6.88191i	0.115163	−	0.354436i
$378$	0.145898	+	0.449028i	0.00750419	+	0.0230955i
$379$	4.04508	−	2.93893i	0.207782	−	0.150963i	−0.479028	−	0.877800i	$-0.659011\pi$
$379$	4.04508	−	2.93893i	0.207782	−	0.150963i	0.686810	+	0.726837i	$0.259011\pi$
$380$		0			0
$381$	−4.92705	−	15.1639i	−0.252420	−	0.776870i
$382$	1.98936	−	6.12261i	0.101784	−	0.313260i
$383$	25.3713	+	18.4333i	1.29641	+	0.941900i	0.999914	−	0.0131328i	$-0.00418043\pi$
$383$	25.3713	+	18.4333i	1.29641	+	0.941900i	0.296500	+	0.955033i	$0.404180\pi$
$384$	11.3820			0.580834
$385$		0			0
$386$	−13.0000			−0.661683
$387$	1.69098	+	1.22857i	0.0859575	+	0.0624518i
$388$	−5.73607	+	17.6538i	−0.291205	+	0.896236i
$389$	−12.0344	−	37.0382i	−0.610170	−	1.87791i	−0.456316	−	0.889818i	$-0.650831\pi$
$389$	−12.0344	−	37.0382i	−0.610170	−	1.87791i	−0.153855	−	0.988093i	$-0.549169\pi$
$390$		0			0
$391$	−3.85410	+	2.80017i	−0.194910	+	0.141611i
$392$	4.43363	+	13.6453i	0.223932	+	0.689192i
$393$	−4.07295	+	12.5352i	−0.205453	+	0.632320i
$394$	−7.11803	−	5.17155i	−0.358601	−	0.260539i
$395$		0			0
$396$	−0.500000	+	5.34307i	−0.0251259	+	0.268499i
$397$	36.2705			1.82036			0.910182	−	0.414208i	$-0.135941\pi$
$397$	36.2705			1.82036			0.910182	+	0.414208i	$0.135941\pi$
$398$	−9.89919	−	7.19218i	−0.496201	−	0.360511i
$399$	1.18034	−	3.63271i	0.0590909	−	0.181863i
$400$		0			0
$401$	−3.95492	+	2.87341i	−0.197499	+	0.143491i	−0.682140	−	0.731222i	$-0.738950\pi$
$401$	−3.95492	+	2.87341i	−0.197499	+	0.143491i	0.484641	+	0.874713i	$0.338950\pi$
$402$	−4.69098	+	3.40820i	−0.233965	+	0.169985i
$403$	−2.67376	−	8.22899i	−0.133190	−	0.409915i
$404$	0.281153	−	0.865300i	0.0139879	−	0.0430503i
$405$		0			0
$406$	2.76393			0.137172
$407$	−12.6353	−	21.3193i	−0.626306	−	1.05676i
$408$	4.47214			0.221404
$409$	−29.3713	−	21.3395i	−1.45232	−	1.05517i	−0.985283	−	0.170933i	$-0.945322\pi$
$409$	−29.3713	−	21.3395i	−1.45232	−	1.05517i	−0.467036	−	0.884238i	$-0.654678\pi$
$410$		0			0
$411$	−5.78115	−	17.7926i	−0.285163	−	0.877642i
$412$	3.11803	−	2.26538i	0.153615	−	0.111607i
$413$	−4.14590	+	3.01217i	−0.204006	+	0.148219i
$414$	0.454915	+	1.40008i	0.0223579	+	0.0688104i
$415$		0			0
$416$	5.61803	+	4.08174i	0.275447	+	0.200124i
$417$	−21.1803			−1.03721
$418$	−6.77051	+	7.69421i	−0.331156	+	0.376336i
$419$	24.5967			1.20163			0.600815	−	0.799388i	$-0.294843\pi$
$419$	24.5967			1.20163			0.600815	+	0.799388i	$0.294843\pi$
$420$		0			0
$421$	0.881966	−	2.71441i	0.0429844	−	0.132292i	−0.927261	−	0.374415i	$-0.877844\pi$
$421$	0.881966	−	2.71441i	0.0429844	−	0.132292i	0.970246	+	0.242123i	$0.0778436\pi$
$422$	−0.736068	−	2.26538i	−0.0358312	−	0.110277i
$423$	−4.11803	+	2.99193i	−0.200226	+	0.145472i
$424$	−13.7812	+	10.0126i	−0.669272	+	0.486255i
$425$		0			0
$426$	1.52786	−	4.70228i	0.0740253	−	0.227826i
$427$	4.32624	+	3.14320i	0.209361	+	0.152110i
$428$	−4.61803			−0.223221
$429$	−2.70820	+	3.07768i	−0.130753	+	0.148592i
$430$		0			0
$431$	−16.0902	−	11.6902i	−0.775036	−	0.563097i	0.128449	−	0.991716i	$-0.459000\pi$
$431$	−16.0902	−	11.6902i	−0.775036	−	0.563097i	−0.903485	+	0.428619i	$0.859000\pi$
$432$	−0.572949	+	1.76336i	−0.0275660	+	0.0848395i
$433$	8.66312	+	26.6623i	0.416323	+	1.28131i	0.911062	+	0.412269i	$0.135264\pi$
$433$	8.66312	+	26.6623i	0.416323	+	1.28131i	−0.494739	+	0.869041i	$0.664736\pi$
$434$	2.67376	−	1.94260i	0.128345	−	0.0932479i
$435$		0			0
$436$	−2.07295	−	6.37988i	−0.0992763	−	0.305541i
$437$	3.68034	−	11.3269i	0.176055	−	0.541840i
$438$	−6.73607	−	4.89404i	−0.321862	−	0.233846i
$439$	9.67376			0.461703			0.230852	−	0.972989i	$-0.425849\pi$
$439$	9.67376			0.461703			0.230852	+	0.972989i	$0.425849\pi$
$440$		0			0
$441$	−6.41641			−0.305543
$442$	1.23607	+	0.898056i	0.0587938	+	0.0427162i
$443$	7.80902	−	24.0337i	0.371018	−	1.14187i	−0.575109	−	0.818077i	$-0.695040\pi$
$443$	7.80902	−	24.0337i	0.371018	−	1.14187i	0.946126	−	0.323798i	$-0.104960\pi$
$444$	−3.73607	−	11.4984i	−0.177306	−	0.545692i
$445$		0			0
$446$	−4.01722	+	2.91868i	−0.190221	+	0.138204i
$447$	−6.21885	−	19.1396i	−0.294141	−	0.905274i
$448$	0.0557281	−	0.171513i	0.00263290	−	0.00810325i
$449$	0.590170	+	0.428784i	0.0278518	+	0.0202355i	0.601624	−	0.798779i	$-0.294521\pi$
$449$	0.590170	+	0.428784i	0.0278518	+	0.0202355i	−0.573772	+	0.819015i	$0.694521\pi$
$450$		0			0
$451$	0.781153	−	8.34751i	0.0367831	−	0.393069i
$452$	−8.85410			−0.416462
$453$	−8.70820	−	6.32688i	−0.409147	−	0.297263i
$454$	4.95492	−	15.2497i	0.232546	−	0.715702i
$455$		0			0
$456$	−9.04508	+	6.57164i	−0.423575	+	0.307745i
$457$	−1.19098	+	0.865300i	−0.0557118	+	0.0404770i	−0.615293	−	0.788299i	$-0.710962\pi$
$457$	−1.19098	+	0.865300i	−0.0557118	+	0.0404770i	0.559581	+	0.828776i	$0.310962\pi$
$458$	3.45492	+	10.6331i	0.161438	+	0.496854i
$459$	−0.618034	+	1.90211i	−0.0288474	+	0.0887830i
$460$		0			0
$461$	25.9443			1.20835			0.604173	−	0.796853i	$-0.293504\pi$
$461$	25.9443			1.20835			0.604173	+	0.796853i	$0.293504\pi$
$462$	−1.43769	−	0.620541i	−0.0668876	−	0.0288702i
$463$	−33.2705			−1.54621			−0.773106	−	0.634277i	$-0.781298\pi$
$463$	−33.2705			−1.54621			−0.773106	+	0.634277i	$0.781298\pi$
$464$	8.78115	+	6.37988i	0.407655	+	0.296179i
$465$		0			0
$466$	−4.44427	−	13.6781i	−0.205877	−	0.633624i
$467$	−3.95492	+	2.87341i	−0.183012	+	0.132966i	−0.675519	−	0.737342i	$-0.736080\pi$
$467$	−3.95492	+	2.87341i	−0.183012	+	0.132966i	0.492507	+	0.870308i	$0.336080\pi$
$468$	−1.61803	+	1.17557i	−0.0747936	+	0.0543408i
$469$	2.21478	+	6.81640i	0.102269	+	0.314752i
$470$		0			0
$471$	−2.69098	−	1.95511i	−0.123994	−	0.0900869i
$472$	15.0000			0.690431
$473$	−6.76393	+	1.51860i	−0.311006	+	0.0698252i
$474$	5.00000			0.229658
$475$		0			0
$476$	0.763932	−	2.35114i	0.0350148	−	0.107764i
$477$	−2.35410	−	7.24518i	−0.107787	−	0.331734i
$478$	3.51722	−	2.55541i	0.160874	−	0.116882i
$479$	−27.0344	+	19.6417i	−1.23524	+	0.897451i	−0.997271	−	0.0738231i	$-0.976480\pi$
$479$	−27.0344	+	19.6417i	−1.23524	+	0.897451i	−0.237964	+	0.971274i	$0.576480\pi$
$480$		0			0
$481$	2.85410	−	8.78402i	0.130136	−	0.400517i
$482$	0.809017	+	0.587785i	0.0368497	+	0.0267729i
$483$	1.81966			0.0827974
$484$	−12.2082	−	12.9515i	−0.554918	−	0.588705i
$485$		0			0
$486$	0.500000	+	0.363271i	0.0226805	+	0.0164783i
$487$	−4.38197	+	13.4863i	−0.198566	+	0.611123i	0.801351	+	0.598195i	$0.204115\pi$
$487$	−4.38197	+	13.4863i	−0.198566	+	0.611123i	−0.999916	+	0.0129278i	$0.995885\pi$
$488$	−4.83688	−	14.8864i	−0.218955	−	0.673875i
$489$	10.9721	−	7.97172i	0.496177	−	0.360494i
$490$		0			0
$491$	9.82624	+	30.2421i	0.443452	+	1.36480i	0.884173	+	0.467160i	$0.154723\pi$
$491$	9.82624	+	30.2421i	0.443452	+	1.36480i	−0.440721	+	0.897644i	$0.645277\pi$
$492$	1.26393	−	3.88998i	0.0569825	−	0.175374i
$493$	9.47214	+	6.88191i	0.426604	+	0.309946i
$494$	−3.81966			−0.171855
$495$		0			0
$496$	12.9787			0.582761
$497$	−4.94427	−	3.59222i	−0.221781	−	0.161133i
$498$	1.09017	−	3.35520i	0.0488517	−	0.150350i
$499$	−3.45492	−	10.6331i	−0.154663	−	0.476005i	0.843463	−	0.537187i	$-0.180513\pi$
$499$	−3.45492	−	10.6331i	−0.154663	−	0.476005i	−0.998127	+	0.0611822i	$0.980513\pi$
$500$		0			0
$501$	−16.2082	+	11.7759i	−0.724129	+	0.526111i
$502$	1.43769	+	4.42477i	0.0641674	+	0.197487i
$503$	−6.76393	+	20.8172i	−0.301589	+	0.928195i	0.679339	+	0.733824i	$0.262266\pi$
$503$	−6.76393	+	20.8172i	−0.301589	+	0.928195i	−0.980928	+	0.194371i	$0.937734\pi$
$504$	−1.38197	−	1.00406i	−0.0615577	−	0.0447243i
$505$		0			0
$506$	−4.48278	−	1.93487i	−0.199284	−	0.0860154i
$507$	11.4721			0.509495
$508$	20.8713	+	15.1639i	0.926015	+	0.672789i
$509$	0.163119	−	0.502029i	0.00723012	−	0.0222520i	−0.947376	−	0.320122i	$-0.896276\pi$
$509$	0.163119	−	0.502029i	0.00723012	−	0.0222520i	0.954606	+	0.297870i	$0.0962761\pi$
$510$		0			0
$511$	−8.32624	+	6.04937i	−0.368331	+	0.267608i
$512$	−15.1353	+	10.9964i	−0.668890	+	0.485977i
$513$	−1.54508	−	4.75528i	−0.0682172	−	0.209951i
$514$	−2.01722	+	6.20837i	−0.0889758	+	0.273839i
$515$		0			0
$516$	−3.38197			−0.148883
$517$	1.57295	−	16.8087i	0.0691782	−	0.739248i
$518$	3.52786			0.155005
$519$	2.88197	+	2.09387i	0.126504	+	0.0919107i
$520$		0			0
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	−0.999579	−	0.0290150i	$-0.990763\pi$
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	0.791622	−	0.611011i	$-0.209237\pi$
$522$	2.92705	−	2.12663i	0.128114	−	0.0930799i
$523$	−6.66312	+	4.84104i	−0.291358	+	0.211684i	−0.723856	−	0.689951i	$-0.757632\pi$
$523$	−6.66312	+	4.84104i	−0.291358	+	0.211684i	0.432498	+	0.901635i	$0.357632\pi$
$524$	−6.59017	−	20.2825i	−0.287893	−	0.886043i
$525$		0			0
$526$	13.6074	+	9.88635i	0.593310	+	0.431065i
$527$	14.0000			0.609850
$528$	−3.13525	−	5.29007i	−0.136444	−	0.230221i
$529$	−17.3262			−0.753315
$530$		0			0
$531$	−2.07295	+	6.37988i	−0.0899583	+	0.276863i
$532$	1.90983	+	5.87785i	0.0828016	+	0.254837i
$533$	2.52786	−	1.83660i	0.109494	−	0.0795520i
$534$	5.42705	−	3.94298i	0.234851	−	0.170630i
$535$		0			0
$536$	6.48278	−	19.9519i	0.280013	−	0.861793i
$537$	−15.7533	−	11.4454i	−0.679805	−	0.493907i
$538$	−3.61803			−0.155985
$539$	14.0582	−	15.9762i	0.605531	−	0.688144i
$540$		0			0
$541$	−0.500000	−	0.363271i	−0.0214967	−	0.0156183i	0.576985	−	0.816755i	$-0.304229\pi$
$541$	−0.500000	−	0.363271i	−0.0214967	−	0.0156183i	−0.598482	+	0.801136i	$0.704229\pi$
$542$	3.93769	−	12.1190i	0.169138	−	0.520555i
$543$	1.61803	+	4.97980i	0.0694365	+	0.213704i
$544$	−9.09017	+	6.60440i	−0.389738	+	0.283161i
$545$		0			0
$546$	−0.180340	−	0.555029i	−0.00771783	−	0.0237531i
$547$	−7.83688	+	24.1194i	−0.335081	+	1.03127i	0.631601	+	0.775293i	$0.282398\pi$
$547$	−7.83688	+	24.1194i	−0.335081	+	1.03127i	−0.966682	+	0.255979i	$0.917602\pi$
$548$	24.4894	+	17.7926i	1.04613	+	0.760060i
$549$	7.00000			0.298753
$550$		0			0
$551$	−29.2705			−1.24697
$552$	−4.30902	−	3.13068i	−0.183404	−	0.133251i
$553$	1.90983	−	5.87785i	0.0812142	−	0.249952i
$554$	−1.65248	−	5.08580i	−0.0702070	−	0.216075i
$555$		0			0
$556$	27.7254	−	20.1437i	1.17582	−	0.854283i
$557$	9.70163	+	29.8585i	0.411071	+	1.26515i	0.915718	+	0.401821i	$0.131623\pi$
$557$	9.70163	+	29.8585i	0.411071	+	1.26515i	−0.504647	+	0.863326i	$0.668377\pi$
$558$	1.33688	−	4.11450i	0.0565947	−	0.174181i
$559$	−2.09017	−	1.51860i	−0.0884048	−	0.0642298i
$560$		0			0
$561$	−3.38197	−	5.70634i	−0.142787	−	0.240922i
$562$	6.23607			0.263053
$563$	−29.3885	−	21.3520i	−1.23858	−	0.899881i	−0.241077	−	0.970506i	$-0.577500\pi$
$563$	−29.3885	−	21.3520i	−1.23858	−	0.899881i	−0.997503	+	0.0706255i	$0.977500\pi$
$564$	2.54508	−	7.83297i	0.107167	−	0.329827i
$565$		0			0
$566$	−6.51722	+	4.73504i	−0.273939	+	0.199028i
$567$	0.618034	−	0.449028i	0.0259550	−	0.0188574i
$568$	5.52786	+	17.0130i	0.231944	+	0.713850i
$569$	−0.753289	+	2.31838i	−0.0315795	+	0.0971917i	−0.965604	−	0.260017i	$-0.916272\pi$
$569$	−0.753289	+	2.31838i	−0.0315795	+	0.0971917i	0.934024	+	0.357209i	$0.116272\pi$
$570$		0			0
$571$	0.0901699			0.00377349			0.00188675	−	0.999998i	$-0.499399\pi$
$571$	0.0901699			0.00377349			0.00188675	+	0.999998i	$0.499399\pi$
$572$	0.618034	−	6.60440i	0.0258413	−	0.276144i
$573$	−10.4164			−0.435152
$574$	0.965558	+	0.701519i	0.0403016	+	0.0292808i
$575$		0			0
$576$	−0.0729490	−	0.224514i	−0.00303954	−	0.00935475i
$577$	37.2254	−	27.0459i	1.54971	−	1.12593i	0.605861	−	0.795571i	$-0.292829\pi$
$577$	37.2254	−	27.0459i	1.54971	−	1.12593i	0.943854	−	0.330363i	$-0.107171\pi$
$578$	6.50000	−	4.72253i	0.270364	−	0.196431i
$579$	6.50000	+	20.0049i	0.270131	+	0.831377i
$580$		0			0
$581$	−3.52786	−	2.56314i	−0.146360	−	0.106337i
$582$	−7.09017			−0.293897
$583$	23.1976	+	10.0126i	0.960745	+	0.414679i
$584$	30.1246			1.24657
$585$		0			0
$586$	3.15654	−	9.71483i	0.130396	−	0.401316i
$587$	−5.98936	−	18.4333i	−0.247207	−	0.760826i	−0.995266	−	0.0971926i	$-0.969014\pi$
$587$	−5.98936	−	18.4333i	−0.247207	−	0.760826i	0.748058	−	0.663633i	$-0.230986\pi$
$588$	8.39919	−	6.10237i	0.346377	−	0.251657i
$589$	−28.3156	+	20.5725i	−1.16672	+	0.847674i
$590$		0			0
$591$	−4.39919	+	13.5393i	−0.180958	+	0.556933i
$592$	11.2082	+	8.14324i	0.460654	+	0.334685i
$593$	38.8885			1.59696			0.798481	−	0.602021i	$-0.205638\pi$
$593$	38.8885			1.59696			0.798481	+	0.602021i	$0.205638\pi$
$594$	−2.00000	+	0.449028i	−0.0820610	+	0.0184238i
$595$		0			0
$596$	26.3435	+	19.1396i	1.07907	+	0.783990i
$597$	−6.11803	+	18.8294i	−0.250394	+	0.770635i
$598$	−0.562306	−	1.73060i	−0.0229944	−	0.0707695i
$599$	17.9894	−	13.0700i	0.735025	−	0.534027i	−0.156124	−	0.987737i	$-0.549900\pi$
$599$	17.9894	−	13.0700i	0.735025	−	0.534027i	0.891149	+	0.453710i	$0.149900\pi$
$600$		0			0
$601$	10.6180	+	32.6789i	0.433119	+	1.33300i	0.895002	+	0.446062i	$0.147174\pi$
$601$	10.6180	+	32.6789i	0.433119	+	1.33300i	−0.461884	+	0.886941i	$0.652826\pi$
$602$	0.304952	−	0.938545i	0.0124289	−	0.0382522i
$603$	7.59017	+	5.51458i	0.309096	+	0.224571i
$604$	17.4164			0.708664
$605$		0			0
$606$	0.347524			0.0141172
$607$	26.6976	+	19.3969i	1.08362	+	0.787296i	0.978311	−	0.207143i	$-0.0664165\pi$
$607$	26.6976	+	19.3969i	1.08362	+	0.787296i	0.105310	+	0.994439i	$0.466417\pi$
$608$	8.68034	−	26.7153i	0.352034	−	1.08345i
$609$	−1.38197	−	4.25325i	−0.0560001	−	0.172351i
$610$		0			0
$611$	5.09017	−	3.69822i	0.205926	−	0.149614i
$612$	−1.00000	−	3.07768i	−0.0404226	−	0.124408i
$613$	2.54508	−	7.83297i	0.102795	−	0.316371i	−0.886412	−	0.462898i	$-0.846810\pi$
$613$	2.54508	−	7.83297i	0.102795	−	0.316371i	0.989207	+	0.146527i	$0.0468096\pi$
$614$	−6.06231	−	4.40452i	−0.244655	−	0.177752i
$615$		0			0
$616$	5.52786	−	1.24108i	0.222724	−	0.0500047i
$617$	−38.2492			−1.53986			−0.769928	−	0.638131i	$-0.779708\pi$
$617$	−38.2492			−1.53986			−0.769928	+	0.638131i	$0.779708\pi$
$618$	1.19098	+	0.865300i	0.0479084	+	0.0348075i
$619$	2.19756	−	6.76340i	0.0883274	−	0.271844i	−0.897130	−	0.441767i	$-0.854352\pi$
$619$	2.19756	−	6.76340i	0.0883274	−	0.271844i	0.985457	+	0.169923i	$0.0543519\pi$
$620$		0			0
$621$	1.92705	−	1.40008i	0.0773299	−	0.0561835i
$622$	−10.7361	+	7.80021i	−0.430477	+	0.312760i
$623$	−2.56231	−	7.88597i	−0.102657	−	0.315945i
$624$	0.708204	−	2.17963i	0.0283508	−	0.0872549i
$625$		0			0
$626$	0.291796			0.0116625
$627$	15.2254	+	6.57164i	0.608045	+	0.262446i
$628$	5.38197			0.214764
$629$	12.0902	+	8.78402i	0.482067	+	0.350242i
$630$		0			0
$631$	11.9377	+	36.7404i	0.475232	+	1.46261i	0.845644	+	0.533747i	$0.179216\pi$
$631$	11.9377	+	36.7404i	0.475232	+	1.46261i	−0.370412	+	0.928867i	$0.620784\pi$
$632$	−14.6353	+	10.6331i	−0.582159	+	0.422963i
$633$	−3.11803	+	2.26538i	−0.123931	+	0.0900409i
$634$	5.80902	+	17.8783i	0.230706	+	0.710039i
$635$		0			0
$636$	9.97214	+	7.24518i	0.395421	+	0.287290i
$637$	7.93112			0.314242
$638$	−1.11803	+	11.9475i	−0.0442634	+	0.473005i
$639$	−8.00000			−0.316475
$640$		0			0
$641$	−0.0729490	+	0.224514i	−0.00288131	+	0.00886777i	−0.952487	−	0.304580i	$-0.901484\pi$
$641$	−0.0729490	+	0.224514i	−0.00288131	+	0.00886777i	0.949606	+	0.313448i	$0.101484\pi$
$642$	−0.545085	−	1.67760i	−0.0215128	−	0.0662096i
$643$	23.7254	−	17.2375i	0.935639	−	0.679782i	−0.0117276	−	0.999931i	$-0.503733\pi$
$643$	23.7254	−	17.2375i	0.935639	−	0.679782i	0.947367	+	0.320149i	$0.103733\pi$
$644$	−2.38197	+	1.73060i	−0.0938626	+	0.0681952i
$645$		0			0
$646$	1.90983	−	5.87785i	0.0751413	−	0.231261i
$647$	14.2361	+	10.3431i	0.559678	+	0.406630i	0.831341	−	0.555763i	$-0.187574\pi$
$647$	14.2361	+	10.3431i	0.559678	+	0.406630i	−0.271663	+	0.962392i	$0.587574\pi$
$648$	−2.23607			−0.0878410
$649$	−11.3435	−	19.1396i	−0.445270	−	0.751297i
$650$		0			0
$651$	−4.32624	−	3.14320i	−0.169559	−	0.123192i
$652$	−6.78115	+	20.8702i	−0.265570	+	0.817342i
$653$	7.24265	+	22.2906i	0.283427	+	0.872297i	0.986866	+	0.161542i	$0.0516467\pi$
$653$	7.24265	+	22.2906i	0.283427	+	0.872297i	−0.703439	+	0.710755i	$0.748353\pi$
$654$	2.07295	−	1.50609i	0.0810587	−	0.0588926i
$655$		0			0
$656$	1.44834	+	4.45752i	0.0565481	+	0.174037i
$657$	−4.16312	+	12.8128i	−0.162419	+	0.499873i
$658$	1.94427	+	1.41260i	0.0757956	+	0.0550687i
$659$	12.9656			0.505066			0.252533	−	0.967588i	$-0.418736\pi$
$659$	12.9656			0.505066			0.252533	+	0.967588i	$0.418736\pi$
$660$		0			0
$661$	3.90983			0.152075			0.0760374	−	0.997105i	$-0.475773\pi$
$661$	3.90983			0.152075			0.0760374	+	0.997105i	$0.475773\pi$
$662$	−10.7984	−	7.84548i	−0.419691	−	0.304923i
$663$	0.763932	−	2.35114i	0.0296687	−	0.0913108i
$664$	3.94427	+	12.1392i	0.153067	+	0.471093i
$665$		0			0
$666$	3.73607	−	2.71441i	0.144770	−	0.105181i
$667$	−4.30902	−	13.2618i	−0.166846	−	0.513499i
$668$	10.0172	−	30.8298i	0.387578	−	1.19284i
$669$	6.50000	+	4.72253i	0.251305	+	0.182583i
$670$		0			0
$671$	−15.3369	+	17.4293i	−0.592074	+	0.672850i
$672$	4.29180			0.165560
$673$	−22.0902	−	16.0494i	−0.851513	−	0.618661i	0.0740494	−	0.997255i	$-0.476408\pi$
$673$	−22.0902	−	16.0494i	−0.851513	−	0.618661i	−0.925563	+	0.378594i	$0.876408\pi$
$674$	−4.22949	+	13.0170i	−0.162914	+	0.501397i
$675$		0			0
$676$	−15.0172	+	10.9106i	−0.577585	+	0.419640i
$677$	9.66312	−	7.02067i	0.371384	−	0.269826i	−0.386401	−	0.922331i	$-0.626282\pi$
$677$	9.66312	−	7.02067i	0.371384	−	0.269826i	0.757785	+	0.652505i	$0.226282\pi$
$678$	−1.04508	−	3.21644i	−0.0401362	−	0.123527i
$679$	−2.70820	+	8.33499i	−0.103931	+	0.319868i
$680$		0			0
$681$	−25.9443			−0.994187
$682$	7.31559	+	12.3435i	0.280129	+	0.472657i
$683$	−2.29180			−0.0876931			−0.0438466	−	0.999038i	$-0.513961\pi$
$683$	−2.29180			−0.0876931			−0.0438466	+	0.999038i	$0.513961\pi$
$684$	6.54508	+	4.75528i	0.250258	+	0.181823i
$685$		0			0
$686$	1.95743	+	6.02434i	0.0747349	+	0.230010i
$687$	14.6353	−	10.6331i	0.558370	−	0.405679i
$688$	3.13525	−	2.27790i	0.119530	−	0.0868440i
$689$	2.90983	+	8.95554i	0.110856	+	0.341179i
$690$		0			0
$691$	−26.9443	−	19.5762i	−1.02501	−	0.744712i	−0.0577049	−	0.998334i	$-0.518378\pi$
$691$	−26.9443	−	19.5762i	−1.02501	−	0.744712i	−0.967304	+	0.253621i	$0.918378\pi$
$692$	−5.76393			−0.219112
$693$	−0.236068	+	2.52265i	−0.00896748	+	0.0958277i
$694$	3.59675			0.136531
$695$		0			0
$696$	−4.04508	+	12.4495i	−0.153329	+	0.471897i
$697$	1.56231	+	4.80828i	0.0591766	+	0.182127i
$698$	−13.8820	+	10.0858i	−0.525440	+	0.381755i
$699$	−18.8262	+	13.6781i	−0.712074	+	0.517352i
$700$		0			0
$701$	4.19756	−	12.9188i	0.158540	−	0.487935i	−0.839963	−	0.542644i	$-0.817423\pi$
$701$	4.19756	−	12.9188i	0.158540	−	0.487935i	0.998502	+	0.0547093i	$0.0174232\pi$
$702$	−0.618034	−	0.449028i	−0.0233262	−	0.0169475i
$703$	−37.3607			−1.40908
$704$	0.718847	+	0.310271i	0.0270926	+	0.0116938i
$705$		0			0
$706$	17.9164	+	13.0170i	0.674293	+	0.489902i
$707$	0.132742	−	0.408539i	0.00499229	−	0.0153647i
$708$	−3.35410	−	10.3229i	−0.126055	−	0.387957i
$709$	−33.3156	+	24.2052i	−1.25119	+	0.909045i	−0.998291	−	0.0584464i	$-0.981385\pi$
$709$	−33.3156	+	24.2052i	−1.25119	+	0.909045i	−0.252903	+	0.967492i	$0.581385\pi$
$710$		0			0
$711$	−2.50000	−	7.69421i	−0.0937573	−	0.288555i
$712$	−7.50000	+	23.0826i	−0.281074	+	0.865058i
$713$	−13.4894	−	9.80059i	−0.505180	−	0.367035i
$714$	0.944272			0.0353385
$715$		0			0
$716$	31.5066			1.17746
$717$	−5.69098	−	4.13474i	−0.212534	−	0.154415i
$718$	3.19098	−	9.82084i	0.119086	−	0.366510i
$719$	11.7705	+	36.2259i	0.438966	+	1.35100i	0.888967	+	0.457970i	$0.151423\pi$
$719$	11.7705	+	36.2259i	0.438966	+	1.35100i	−0.450001	+	0.893028i	$0.648577\pi$
$720$		0			0
$721$	1.47214	−	1.06957i	0.0548252	−	0.0398328i
$722$	1.14590	+	3.52671i	0.0426459	+	0.131251i
$723$	0.500000	−	1.53884i	0.0185952	−	0.0572301i
$724$	−6.85410	−	4.97980i	−0.254731	−	0.185073i
$725$		0			0
$726$	3.26393	−	5.96361i	0.121136	−	0.221330i
$727$	37.3262			1.38435			0.692177	−	0.721728i	$-0.256652\pi$
$727$	37.3262			1.38435			0.692177	+	0.721728i	$0.256652\pi$
$728$	1.70820	+	1.24108i	0.0633102	+	0.0459976i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	3.38197	−	2.45714i	0.125087	−	0.0908807i
$732$	−9.16312	+	6.65740i	−0.338679	+	0.246064i
$733$	0.572949	+	1.76336i	0.0211624	+	0.0651310i	0.961080	−	0.276270i	$-0.0890985\pi$
$733$	0.572949	+	1.76336i	0.0211624	+	0.0651310i	−0.939918	+	0.341401i	$0.889098\pi$
$734$	−3.46149	+	10.6534i	−0.127766	+	0.393223i
$735$		0			0
$736$	13.3820			0.493266
$737$	−30.3607	+	6.81640i	−1.11835	+	0.251085i
$738$	1.56231			0.0575093
$739$	16.1803	+	11.7557i	0.595203	+	0.432441i	0.844173	−	0.536071i	$-0.180092\pi$
$739$	16.1803	+	11.7557i	0.595203	+	0.432441i	−0.248970	+	0.968511i	$0.580092\pi$
$740$		0			0
$741$	1.90983	+	5.87785i	0.0701594	+	0.215928i
$742$	−2.90983	+	2.11412i	−0.106823	+	0.0776116i
$743$	−0.281153	+	0.204270i	−0.0103145	+	0.00749392i	−0.592931	−	0.805254i	$-0.702029\pi$
$743$	−0.281153	+	0.204270i	−0.0103145	+	0.00749392i	0.582616	+	0.812748i	$0.302029\pi$
$744$	4.83688	+	14.8864i	0.177329	+	0.545762i
$745$		0			0
$746$	−4.87132	−	3.53922i	−0.178352	−	0.129580i
$747$	−5.70820			−0.208852
$748$	9.85410	+	4.25325i	0.360302	+	0.155514i
$749$	−2.18034			−0.0796679
$750$		0			0
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	0.261335	+	0.965248i	$0.415837\pi$
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	−0.778783	+	0.627293i	$0.784163\pi$
$752$	2.91641	+	8.97578i	0.106350	+	0.327313i
$753$	6.09017	−	4.42477i	0.221938	−	0.161247i
$754$	−3.61803	+	2.62866i	−0.131761	+	0.0957300i
$755$		0			0
$756$	−0.381966	+	1.17557i	−0.0138920	+	0.0427551i
$757$	19.5623	+	14.2128i	0.711004	+	0.516575i	0.883497	−	0.468436i	$-0.155182\pi$
$757$	19.5623	+	14.2128i	0.711004	+	0.516575i	−0.172493	+	0.985011i	$0.555182\pi$
$758$	−3.09017			−0.112240
$759$	−0.736068	+	7.86572i	−0.0267176	+	0.285508i
$760$		0			0
$761$	−31.5795	−	22.9439i	−1.14476	−	0.831715i	−0.156982	−	0.987601i	$-0.550176\pi$
$761$	−31.5795	−	22.9439i	−1.14476	−	0.831715i	−0.987775	+	0.155887i	$0.950176\pi$
$762$	−3.04508	+	9.37181i	−0.110312	+	0.339505i
$763$	−0.978714	−	3.01217i	−0.0354318	−	0.109048i
$764$	13.6353	−	9.90659i	0.493306	−	0.358408i
$765$		0			0
$766$	−5.98936	−	18.4333i	−0.216404	−	0.666024i
$767$	2.56231	−	7.88597i	0.0925195	−	0.284746i
$768$	−5.30902	−	3.85723i	−0.191573	−	0.139186i
$769$	12.7639			0.460279			0.230140	−	0.973158i	$-0.426082\pi$
$769$	12.7639			0.460279			0.230140	+	0.973158i	$0.426082\pi$
$770$		0			0
$771$	10.5623			0.380392
$772$	−27.5344	−	20.0049i	−0.990986	−	0.719994i
$773$	−3.24671	+	9.99235i	−0.116776	+	0.359400i	−0.992313	−	0.123751i	$-0.960508\pi$
$773$	−3.24671	+	9.99235i	−0.116776	+	0.359400i	0.875537	+	0.483151i	$0.160508\pi$
$774$	−0.399187	−	1.22857i	−0.0143485	−	0.0441601i
$775$		0			0
$776$	20.7533	−	15.0781i	0.745000	−	0.541274i
$777$	−1.76393	−	5.42882i	−0.0632807	−	0.194758i
$778$	−7.43769	+	22.8909i	−0.266654	+	0.820677i
$779$	−10.2254	−	7.42921i	−0.366364	−	0.266179i
$780$		0			0
$781$	17.5279	−	19.9192i	0.627196	−	0.712765i
$782$	2.94427			0.105287
$783$	−4.73607	−	3.44095i	−0.169253	−	0.122970i
$784$	−3.67627	+	11.3144i	−0.131296	+	0.404086i
$785$		0			0
$786$	6.59017	−	4.78804i	0.235064	−	0.170784i
$787$	6.63525	−	4.82079i	0.236521	−	0.171843i	−0.463211	−	0.886248i	$-0.653303\pi$
$787$	6.63525	−	4.82079i	0.236521	−	0.171843i	0.699732	+	0.714405i	$0.253303\pi$
$788$	−7.11803	−	21.9071i	−0.253569	−	0.780407i
$789$	8.40983	−	25.8828i	0.299398	−	0.921452i
$790$		0			0
$791$	−4.18034			−0.148636
$792$	4.89919	−	5.56758i	0.174085	−	0.197835i
$793$	−8.65248			−0.307258
$794$	−18.1353	−	13.1760i	−0.643596	−	0.467600i
$795$		0			0
$796$	−9.89919	−	30.4666i	−0.350867	−	1.07986i
$797$	−23.2254	+	16.8743i	−0.822687	+	0.597717i	−0.917481	−	0.397780i	$-0.869781\pi$
$797$	−23.2254	+	16.8743i	−0.822687	+	0.597717i	0.0947941	+	0.995497i	$0.469781\pi$
$798$	−1.90983	+	1.38757i	−0.0676073	+	0.0491195i
$799$	3.14590	+	9.68208i	0.111294	+	0.342527i
$800$		0			0
$801$	−8.78115	−	6.37988i	−0.310267	−	0.225422i
$802$	3.02129			0.106685
$803$	−22.7812	−	38.4383i	−0.803929	−	1.35646i
$804$	−15.1803			−0.535369
$805$		0			0
$806$	−1.65248	+	5.08580i	−0.0582060	+	0.179140i
$807$	1.80902	+	5.56758i	0.0636804	+	0.195988i
$808$	−1.01722	+	0.739054i	−0.0357857	+	0.0259998i
$809$	−36.6697	+	26.6421i	−1.28924	+	0.936686i	−0.999790	−	0.0205075i	$-0.993472\pi$
$809$	−36.6697	+	26.6421i	−1.28924	+	0.936686i	−0.289448	+	0.957194i	$0.593472\pi$
$810$		0			0
$811$	−10.7016	+	32.9362i	−0.375785	+	1.15655i	0.567163	+	0.823606i	$0.308041\pi$
$811$	−10.7016	+	32.9362i	−0.375785	+	1.15655i	−0.942948	+	0.332941i	$0.891959\pi$
$812$	5.85410	+	4.25325i	0.205439	+	0.149260i
$813$	−20.6180			−0.723106
$814$	−1.42705	+	15.2497i	−0.0500181	+	0.534500i
$815$		0			0
$816$	3.00000	+	2.17963i	0.105021	+	0.0763022i
$817$	−3.22949	+	9.93935i	−0.112986	+	0.347734i
$818$	6.93363	+	21.3395i	0.242429	+	0.746119i
$819$	−0.763932	+	0.555029i	−0.0266939	+	0.0193943i
$820$		0			0
$821$	13.3435	+	41.0669i	0.465690	+	1.43325i	0.858113	+	0.513461i	$0.171637\pi$
$821$	13.3435	+	41.0669i	0.465690	+	1.43325i	−0.392423	+	0.919785i	$0.628363\pi$
$822$	−3.57295	+	10.9964i	−0.124621	+	0.383544i
$823$	−20.6074	−	14.9721i	−0.718328	−	0.521896i	0.167521	−	0.985868i	$-0.446424\pi$
$823$	−20.6074	−	14.9721i	−0.718328	−	0.521896i	−0.885850	+	0.463972i	$0.846424\pi$
$824$	−5.32624			−0.185548
$825$		0			0
$826$	3.16718			0.110200
$827$	19.8885	+	14.4499i	0.691592	+	0.502471i	0.877183	−	0.480156i	$-0.159420\pi$
$827$	19.8885	+	14.4499i	0.691592	+	0.502471i	−0.185591	+	0.982627i	$0.559420\pi$
$828$	−1.19098	+	3.66547i	−0.0413895	+	0.127384i
$829$	0.892609	+	2.74717i	0.0310016	+	0.0954131i	0.965360	−	0.260921i	$-0.0840264\pi$
$829$	0.892609	+	2.74717i	0.0310016	+	0.0954131i	−0.934358	+	0.356335i	$0.884026\pi$
$830$		0			0
$831$	−7.00000	+	5.08580i	−0.242827	+	0.176424i
$832$	0.0901699	+	0.277515i	0.00312608	+	0.00962109i
$833$	−3.96556	+	12.2047i	−0.137398	+	0.422869i
$834$	10.5902	+	7.69421i	0.366708	+	0.266429i
$835$		0			0
$836$	−26.1803	+	5.87785i	−0.905466	+	0.203290i
$837$	−7.00000			−0.241955
$838$	−12.2984	−	8.93529i	−0.424840	−	0.308665i
$839$	−8.12868	+	25.0175i	−0.280633	+	0.863700i	0.707041	+	0.707173i	$0.250030\pi$
$839$	−8.12868	+	25.0175i	−0.280633	+	0.863700i	−0.987674	+	0.156527i	$0.949970\pi$
$840$		0			0
$841$	−4.26393	+	3.09793i	−0.147032	+	0.106825i
$842$	−1.42705	+	1.03681i	−0.0491794	+	0.0357309i
$843$	−3.11803	−	9.59632i	−0.107391	−	0.330515i
$844$	1.92705	−	5.93085i	0.0663318	−	0.204148i
$845$		0			0
$846$	3.14590			0.108158
$847$	−5.76393	−	6.11488i	−0.198051	−	0.210110i
$848$	−14.1246			−0.485041
$849$	10.5451	+	7.66145i	0.361906	+	0.262940i
$850$		0			0
$851$	−5.50000	−	16.9273i	−0.188538	−	0.580259i
$852$	10.4721	−	7.60845i	0.358769	−	0.260661i
$853$	17.2812	−	12.5555i	0.591695	−	0.429892i	−0.251226	−	0.967928i	$-0.580834\pi$
$853$	17.2812	−	12.5555i	0.591695	−	0.429892i	0.842922	+	0.538037i	$0.180834\pi$
$854$	−1.02129	−	3.14320i	−0.0349477	−	0.107558i
$855$		0			0
$856$	5.16312	+	3.75123i	0.176472	+	0.128214i
$857$	35.0132			1.19603			0.598013	−	0.801486i	$-0.295957\pi$
$857$	35.0132			1.19603			0.598013	+	0.801486i	$0.295957\pi$
$858$	2.47214	−	0.555029i	0.0843973	−	0.0189484i
$859$	−5.72949			−0.195488			−0.0977438	−	0.995212i	$-0.531163\pi$
$859$	−5.72949			−0.195488			−0.0977438	+	0.995212i	$0.531163\pi$
$860$		0			0
$861$	0.596748	−	1.83660i	0.0203371	−	0.0625912i
$862$	3.79837	+	11.6902i	0.129373	+	0.398170i
$863$	4.88197	−	3.54696i	0.166184	−	0.120740i	−0.501585	−	0.865108i	$-0.667249\pi$
$863$	4.88197	−	3.54696i	0.166184	−	0.120740i	0.667769	+	0.744369i	$0.267249\pi$
$864$	4.54508	−	3.30220i	0.154627	−	0.112343i
$865$		0			0
$866$	5.35410	−	16.4782i	0.181940	−	0.559953i
$867$	−10.5172	−	7.64121i	−0.357184	−	0.259509i
$868$	8.65248			0.293684
$869$	24.6353	+	10.6331i	0.835694	+	0.360704i
$870$		0			0
$871$	−9.38197	−	6.81640i	−0.317896	−	0.230965i
$872$	−2.86475	+	8.81678i	−0.0970125	+	0.298574i
$873$	3.54508	+	10.9106i	0.119983	+	0.369270i
$874$	−5.95492	+	4.32650i	−0.201428	+	0.146346i
$875$		0			0
$876$	−6.73607	−	20.7315i	−0.227591	−	0.700452i
$877$	5.09017	−	15.6659i	0.171883	−	0.529001i	−0.827595	−	0.561326i	$-0.810291\pi$
$877$	5.09017	−	15.6659i	0.171883	−	0.529001i	0.999477	+	0.0323254i	$0.0102913\pi$
$878$	−4.83688	−	3.51420i	−0.163237	−	0.118598i
$879$	−16.5279			−0.557471
$880$		0			0
$881$	−23.8541			−0.803665			−0.401833	−	0.915713i	$-0.631627\pi$
$881$	−23.8541			−0.803665			−0.401833	+	0.915713i	$0.631627\pi$
$882$	3.20820	+	2.33090i	0.108026	+	0.0784854i
$883$	5.79837	−	17.8456i	0.195131	−	0.600551i	−0.804844	−	0.593486i	$-0.797751\pi$
$883$	5.79837	−	17.8456i	0.195131	−	0.600551i	0.999975	−	0.00706479i	$-0.00224881\pi$
$884$	1.23607	+	3.80423i	0.0415735	+	0.127950i
$885$		0			0
$886$	−12.6353	+	9.18005i	−0.424490	+	0.308410i
$887$	16.6353	+	51.1981i	0.558557	+	1.71906i	0.686359	+	0.727263i	$0.259208\pi$
$887$	16.6353	+	51.1981i	0.558557	+	1.71906i	−0.127802	+	0.991800i	$0.540792\pi$
$888$	−5.16312	+	15.8904i	−0.173263	+	0.533248i
$889$	9.85410	+	7.15942i	0.330496	+	0.240119i
$890$		0			0
$891$	1.69098	+	2.85317i	0.0566501	+	0.0955848i
$892$	−13.0000			−0.435272
$893$	−20.5902	−	14.9596i	−0.689024	−	0.500605i
$894$	−3.84346	+	11.8290i	−0.128544	+	0.395619i
$895$		0			0
$896$	−7.03444	+	5.11082i	−0.235004	+	0.170741i
$897$	−2.38197	+	1.73060i	−0.0795315	+	0.0577830i
$898$	−0.139320	−	0.428784i	−0.00464918	−	0.0143087i
$899$	−12.6631	+	38.9731i	−0.422339	+	1.29982i
$900$		0			0
$901$	−15.2361			−0.507587
$902$	−3.42299	+	3.88998i	−0.113973	+	0.129522i
$903$	−1.59675			−0.0531364
$904$	9.89919	+	7.19218i	0.329242	+	0.239208i
$905$		0			0
$906$	2.05573	+	6.32688i	0.0682970	+	0.210197i
$907$	−7.37132	+	5.35558i	−0.244761	+	0.177829i	−0.703402	−	0.710793i	$-0.748336\pi$
$907$	−7.37132	+	5.35558i	−0.244761	+	0.177829i	0.458641	+	0.888622i	$0.348336\pi$
$908$	33.9615	−	24.6745i	1.12705	−	0.818851i
$909$	−0.173762	−	0.534785i	−0.00576332	−	0.0177377i
$910$		0			0
$911$	47.6525	+	34.6216i	1.57880	+	1.14706i	0.918057	+	0.396448i	$0.129757\pi$
$911$	47.6525	+	34.6216i	1.57880	+	1.14706i	0.660740	+	0.750615i	$0.270243\pi$
$912$	−9.27051			−0.306977
$913$	12.5066	−	14.2128i	0.413907	−	0.470377i
$914$	0.909830			0.0300945
$915$		0			0
$916$	−9.04508	+	27.8379i	−0.298858	+	0.919790i
$917$	−3.11146	−	9.57608i	−0.102749	−	0.316230i
$918$	1.00000	−	0.726543i	0.0330049	−	0.0239795i
$919$	14.3713	−	10.4414i	0.474066	−	0.344429i	−0.324958	−	0.945729i	$-0.605350\pi$
$919$	14.3713	−	10.4414i	0.474066	−	0.344429i	0.799024	+	0.601299i	$0.205350\pi$
$920$		0			0
$921$	−3.74671	+	11.5312i	−0.123458	+	0.379966i
$922$	−12.9721	−	9.42481i	−0.427215	−	0.310390i
$923$	9.88854			0.325485
$924$	−2.09017	−	3.52671i	−0.0687615	−	0.116020i
$925$		0			0
$926$	16.6353	+	12.0862i	0.546668	+	0.397178i
$927$	0.736068	−	2.26538i	0.0241756	−	0.0744050i
$928$	−10.1631	−	31.2789i	−0.333621	−	1.02678i
$929$	3.35410	−	2.43690i	0.110045	−	0.0799520i	−0.531402	−	0.847120i	$-0.678335\pi$
$929$	3.35410	−	2.43690i	0.110045	−	0.0799520i	0.641447	+	0.767168i	$0.278335\pi$
$930$		0			0
$931$	−9.91390	−	30.5118i	−0.324915	−	0.999985i
$932$	11.6353	−	35.8096i	0.381125	−	1.17298i
$933$	17.3713	+	12.6210i	0.568712	+	0.413193i
$934$	3.02129			0.0988595
$935$		0			0
$936$	2.76393			0.0903419
$937$	−33.8156	−	24.5685i	−1.10471	−	0.802617i	−0.122885	−	0.992421i	$-0.539215\pi$
$937$	−33.8156	−	24.5685i	−1.10471	−	0.802617i	−0.981822	+	0.189804i	$0.939215\pi$
$938$	1.36881	−	4.21277i	0.0446932	−	0.137552i
$939$	−0.145898	−	0.449028i	−0.00476120	−	0.0146535i
$940$		0			0
$941$	−3.00000	+	2.17963i	−0.0977972	+	0.0710538i	−0.635609	−	0.772011i	$-0.719251\pi$
$941$	−3.00000	+	2.17963i	−0.0977972	+	0.0710538i	0.537812	+	0.843065i	$0.319251\pi$
$942$	0.635255	+	1.95511i	0.0206977	+	0.0637010i
$943$	1.86068	−	5.72658i	0.0605921	−	0.186483i
$944$	10.0623	+	7.31069i	0.327500	+	0.237943i
$945$		0			0
$946$	3.93363	+	1.69784i	0.127893	+	0.0552017i
$947$	−15.5623			−0.505707			−0.252853	−	0.967505i	$-0.581369\pi$
$947$	−15.5623			−0.505707			−0.252853	+	0.967505i	$0.581369\pi$
$948$	10.5902	+	7.69421i	0.343953	+	0.249896i
$949$	5.14590	−	15.8374i	0.167043	−	0.514105i
$950$		0			0
$951$	24.6074	−	17.8783i	0.797949	−	0.579744i
$952$	−2.76393	+	2.00811i	−0.0895796	+	0.0650834i
$953$	11.7148	+	36.0544i	0.379479	+	1.16792i	0.940407	+	0.340052i	$0.110445\pi$
$953$	11.7148	+	36.0544i	0.379479	+	1.16792i	−0.560928	+	0.827865i	$0.689555\pi$
$954$	−1.45492	+	4.47777i	−0.0471046	+	0.144973i
$955$		0			0
$956$	11.3820			0.368119
$957$	18.9443	−	4.25325i	0.612381	−	0.137488i
$958$	20.6525			0.667251
$959$	11.5623	+	8.40051i	0.373366	+	0.271267i
$960$		0			0
$961$	5.56231	+	17.1190i	0.179429	+	0.552226i
$962$	−4.61803	+	3.35520i	−0.148891	+	0.108176i
$963$	−2.30902	+	1.67760i	−0.0744070	+	0.0540599i
$964$	0.809017	+	2.48990i	0.0260567	+	0.0801942i
$965$		0			0
$966$	−0.909830	−	0.661030i	−0.0292733	−	0.0212683i
$967$	−48.3262			−1.55407			−0.777034	−	0.629459i	$-0.783276\pi$
$967$	−48.3262			−1.55407			−0.777034	+	0.629459i	$0.783276\pi$
$968$	3.12868	+	24.3970i	0.100559	+	0.784148i
$969$	−10.0000			−0.321246
$970$		0			0
$971$	10.9828	−	33.8015i	0.352454	−	1.08474i	−0.605017	−	0.796213i	$-0.706834\pi$
$971$	10.9828	−	33.8015i	0.352454	−	1.08474i	0.957471	−	0.288530i	$-0.0931664\pi$
$972$	0.500000	+	1.53884i	0.0160375	+	0.0493584i
$973$	13.0902	−	9.51057i	0.419652	−	0.304895i
$974$	7.09017	−	5.15131i	0.227184	−	0.165059i
$975$		0			0
$976$	4.01064	−	12.3435i	0.128378	−	0.395105i
$977$	28.2426	+	20.5195i	0.903562	+	0.656476i	0.939378	−	0.342882i	$-0.111403\pi$
$977$	28.2426	+	20.5195i	0.903562	+	0.656476i	−0.0358162	+	0.999358i	$0.511403\pi$
$978$	−8.38197			−0.268026
$979$	35.1246	−	7.88597i	1.12259	−	0.252037i
$980$		0			0
$981$	−3.35410	−	2.43690i	−0.107088	−	0.0778042i
$982$	6.07295	−	18.6906i	0.193796	−	0.596441i
$983$	−5.87132	−	18.0701i	−0.187266	−	0.576346i	0.812714	−	0.582663i	$-0.197989\pi$
$983$	−5.87132	−	18.0701i	−0.187266	−	0.576346i	−0.999980	+	0.00631707i	$0.997989\pi$
$984$	−4.57295	+	3.32244i	−0.145780	+	0.105916i
$985$		0			0
$986$	−2.23607	−	6.88191i	−0.0712109	−	0.219165i
$987$	1.20163	−	3.69822i	0.0382482	−	0.117716i
$988$	−8.09017	−	5.87785i	−0.257383	−	0.186999i
$989$	−4.97871			−0.158314
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−31.8156	−	23.1154i	−1.01015	−	0.733914i
$993$	−6.67376	+	20.5397i	−0.211785	+	0.651809i
$994$	1.16718	+	3.59222i	0.0370208	+	0.113938i
$995$		0			0
$996$	7.47214	−	5.42882i	0.236764	−	0.172019i
$997$	−7.63525	−	23.4989i	−0.241811	−	0.744218i	−0.996145	−	0.0877264i	$-0.972040\pi$
$997$	−7.63525	−	23.4989i	−0.241811	−	0.744218i	0.754334	−	0.656491i	$-0.227960\pi$
$998$	−2.13525	+	6.57164i	−0.0675903	+	0.208022i
$999$	−6.04508	−	4.39201i	−0.191258	−	0.138957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.b.301.1	✓	4
5.2	odd	4		825.2.bx.c.499.2		8
5.3	odd	4		825.2.bx.c.499.1		8
5.4	even	2		825.2.n.d.301.1	yes	4
11.3	even	5	inner	825.2.n.b.751.1	yes	4
11.5	even	5		9075.2.a.z.1.2		2
11.6	odd	10		9075.2.a.bt.1.1		2
55.3	odd	20		825.2.bx.c.124.2		8
55.14	even	10		825.2.n.d.751.1	yes	4
55.39	odd	10		9075.2.a.bc.1.2		2
55.47	odd	20		825.2.bx.c.124.1		8
55.49	even	10		9075.2.a.by.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.b.301.1	✓	4	1.1	even	1	trivial
825.2.n.b.751.1	yes	4	11.3	even	5	inner
825.2.n.d.301.1	yes	4	5.4	even	2
825.2.n.d.751.1	yes	4	55.14	even	10
825.2.bx.c.124.1		8	55.47	odd	20
825.2.bx.c.124.2		8	55.3	odd	20
825.2.bx.c.499.1		8	5.3	odd	4
825.2.bx.c.499.2		8	5.2	odd	4
9075.2.a.z.1.2		2	11.5	even	5
9075.2.a.bc.1.2		2	55.39	odd	10
9075.2.a.bt.1.1		2	11.6	odd	10
9075.2.a.by.1.1		2	55.49	even	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.363271i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.236068 - 0.726543i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.363271i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.236068 - 0.726543i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} +1.61803 q^{12} +(1.00000 + 0.726543i) q^{13} +(-0.145898 + 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(-1.61803 + 1.17557i) q^{17} +(0.190983 + 0.587785i) q^{18} +(1.54508 - 4.75528i) q^{19} +0.763932 q^{21} +(-1.88197 - 0.812299i) q^{22} +2.38197 q^{23} +(-1.80902 - 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-1.00000 + 0.726543i) q^{28} +(-1.80902 - 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} +5.61803 q^{32} +(-0.309017 + 3.30220i) q^{33} +1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(-2.30902 - 7.10642i) q^{37} +(-2.50000 + 1.81636i) q^{38} +(-1.00000 + 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(-0.381966 - 0.277515i) q^{42} -2.09017 q^{43} +(-2.73607 - 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(1.57295 - 4.84104i) q^{47} +(-0.572949 - 1.76336i) q^{48} +(5.19098 - 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(0.618034 - 1.90211i) q^{52} +(6.16312 + 4.47777i) q^{53} -0.618034 q^{54} +1.70820 q^{56} +(4.04508 + 2.93893i) q^{57} +(-1.11803 + 3.44095i) q^{58} +(-2.07295 - 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(1.33688 + 4.11450i) q^{62} +(-0.236068 + 0.726543i) q^{63} +(0.190983 + 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} -9.38197 q^{67} +(2.61803 + 1.90211i) q^{68} +(-0.736068 + 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(1.80902 - 1.31433i) q^{72} +(-4.16312 - 12.8128i) q^{73} +(-1.42705 + 4.39201i) q^{74} -8.09017 q^{76} +(-1.29180 - 2.17963i) q^{77} +0.763932 q^{78} +(6.54508 + 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.26393 + 0.918300i) q^{82} +(4.61803 - 3.35520i) q^{83} +(-0.381966 - 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} +5.85410 q^{87} +(-0.690983 + 7.38394i) q^{88} +10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(-1.19098 - 3.66547i) q^{92} +(5.66312 - 4.11450i) q^{93} +(-2.54508 + 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(-9.28115 - 6.74315i) q^{97} -3.96556 q^{98} +(-3.04508 - 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 - 5 * q^8 - q^9 + 4 * q^11 + 2 * q^12 + 4 * q^13 - 14 * q^14 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 5 * q^19 + 12 * q^21 - 12 * q^22 + 14 * q^23 - 5 * q^24 + 8 * q^26 + q^27 - 4 * q^28 - 5 * q^29 - 7 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 2 * q^36 - 7 * q^37 - 10 * q^38 - 4 * q^39 - 17 * q^41 - 6 * q^42 + 14 * q^43 - 2 * q^44 - 7 * q^46 + 13 * q^47 - 9 * q^48 + 23 * q^49 + 2 * q^51 - 2 * q^52 + 9 * q^53 + 2 * q^54 - 20 * q^56 + 5 * q^57 - 15 * q^59 - 7 * q^61 + 21 * q^62 + 8 * q^63 + 3 * q^64 - 8 * q^66 - 42 * q^67 + 6 * q^68 + 6 * q^69 + 8 * q^71 + 5 * q^72 - q^73 + q^74 - 10 * q^76 - 32 * q^77 + 12 * q^78 + 15 * q^79 - q^81 - 14 * q^82 + 14 * q^83 - 6 * q^84 - 7 * q^86 + 10 * q^87 - 5 * q^88 + 30 * q^89 + 28 * q^91 - 7 * q^92 + 7 * q^93 + q^94 + 2 * q^96 - 17 * q^97 - 74 * q^98 - q^99

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