LMFDB - Embedded newform 825.2.n.a.751.1

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			751.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.751
Dual form			825.2.n.a.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.30902 - 0.951057i) q^{6} +(0.927051 - 2.85317i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.30902 - 0.951057i) q^{6} +(0.927051 - 2.85317i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 + 3.30220i) q^{11} +0.618034 q^{12} +(1.50000 - 1.08981i) q^{13} +(1.50000 + 4.61653i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-6.04508 - 4.39201i) q^{17} +(0.500000 - 1.53884i) q^{18} +(-0.854102 - 2.62866i) q^{19} +3.00000 q^{21} +(-3.54508 - 4.02874i) q^{22} +7.61803 q^{23} +(1.80902 - 1.31433i) q^{24} +(-0.927051 + 2.85317i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.50000 - 1.08981i) q^{28} +(1.11803 - 3.44095i) q^{29} +(7.16312 - 5.20431i) q^{31} -3.38197 q^{32} +(-3.04508 + 1.31433i) q^{33} +12.0902 q^{34} +(0.190983 + 0.587785i) q^{36} +(2.73607 - 8.42075i) q^{37} +(3.61803 + 2.62866i) q^{38} +(1.50000 + 1.08981i) q^{39} +(-0.0729490 - 0.224514i) q^{41} +(-3.92705 + 2.85317i) q^{42} +1.76393 q^{43} +(2.00000 + 0.449028i) q^{44} +(-9.97214 + 7.24518i) q^{46} +(2.89919 + 8.92278i) q^{47} +(-1.50000 + 4.61653i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(2.30902 - 7.10642i) q^{51} +(-0.354102 - 1.08981i) q^{52} +(0.381966 - 0.277515i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(2.23607 - 1.62460i) q^{57} +(1.80902 + 5.56758i) q^{58} +(-1.28115 + 3.94298i) q^{59} +(4.66312 + 3.38795i) q^{61} +(-4.42705 + 13.6251i) q^{62} +(0.927051 + 2.85317i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(2.73607 - 4.61653i) q^{66} -8.70820 q^{67} +(-3.73607 + 2.71441i) q^{68} +(2.35410 + 7.24518i) q^{69} +(-1.19098 - 0.865300i) q^{71} +(1.80902 + 1.31433i) q^{72} +(-2.11803 + 6.51864i) q^{73} +(4.42705 + 13.6251i) q^{74} -1.70820 q^{76} +(9.70820 + 2.17963i) q^{77} -3.00000 q^{78} +(6.11803 - 4.44501i) q^{79} +(0.309017 - 0.951057i) q^{81} +(0.309017 + 0.224514i) q^{82} +(-8.39919 - 6.10237i) q^{83} +(0.572949 - 1.76336i) q^{84} +(-2.30902 + 1.67760i) q^{86} +3.61803 q^{87} +(6.80902 - 2.93893i) q^{88} +2.56231 q^{89} +(-1.71885 - 5.29007i) q^{91} +(1.45492 - 4.47777i) q^{92} +(7.16312 + 5.20431i) q^{93} +(-12.2812 - 8.92278i) q^{94} +(-1.04508 - 3.21644i) q^{96} +(8.42705 - 6.12261i) q^{97} +3.23607 q^{98} +(-2.19098 - 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9	$ 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} - q^{11} - 2 q^{12} + 6 q^{13} + 6 q^{14} + 9 q^{16} - 13 q^{17} + 2 q^{18} + 10 q^{19} + 12 q^{21} - 3 q^{22} + 26 q^{23} + 5 q^{24} + 3 q^{26} - q^{27} - 6 q^{28} + 13 q^{31} - 18 q^{32} - q^{33} + 26 q^{34} + 3 q^{36} + 2 q^{37} + 10 q^{38} + 6 q^{39} - 7 q^{41} - 9 q^{42} + 16 q^{43} + 8 q^{44} - 22 q^{46} - 13 q^{47} - 6 q^{48} - 2 q^{49} + 7 q^{51} + 12 q^{52} + 6 q^{53} + 2 q^{54} + 5 q^{58} + 15 q^{59} + 3 q^{61} - 11 q^{62} - 3 q^{63} - 7 q^{64} + 2 q^{66} - 8 q^{67} - 6 q^{68} - 4 q^{69} - 7 q^{71} + 5 q^{72} - 4 q^{73} + 11 q^{74} + 20 q^{76} + 12 q^{77} - 12 q^{78} + 20 q^{79} - q^{81} - q^{82} - 9 q^{83} + 9 q^{84} - 7 q^{86} + 10 q^{87} + 25 q^{88} - 30 q^{89} - 27 q^{91} + 17 q^{92} + 13 q^{93} - 29 q^{94} + 7 q^{96} + 27 q^{97} + 4 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 - q^11 - 2 * q^12 + 6 * q^13 + 6 * q^14 + 9 * q^16 - 13 * q^17 + 2 * q^18 + 10 * q^19 + 12 * q^21 - 3 * q^22 + 26 * q^23 + 5 * q^24 + 3 * q^26 - q^27 - 6 * q^28 + 13 * q^31 - 18 * q^32 - q^33 + 26 * q^34 + 3 * q^36 + 2 * q^37 + 10 * q^38 + 6 * q^39 - 7 * q^41 - 9 * q^42 + 16 * q^43 + 8 * q^44 - 22 * q^46 - 13 * q^47 - 6 * q^48 - 2 * q^49 + 7 * q^51 + 12 * q^52 + 6 * q^53 + 2 * q^54 + 5 * q^58 + 15 * q^59 + 3 * q^61 - 11 * q^62 - 3 * q^63 - 7 * q^64 + 2 * q^66 - 8 * q^67 - 6 * q^68 - 4 * q^69 - 7 * q^71 + 5 * q^72 - 4 * q^73 + 11 * q^74 + 20 * q^76 + 12 * q^77 - 12 * q^78 + 20 * q^79 - q^81 - q^82 - 9 * q^83 + 9 * q^84 - 7 * q^86 + 10 * q^87 + 25 * q^88 - 30 * q^89 - 27 * q^91 + 17 * q^92 + 13 * q^93 - 29 * q^94 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	−0.944915	−	0.327315i	$-0.893856\pi$
$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	0.0193004	+	0.999814i	$0.493856\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−1.30902	−	0.951057i	−0.534404	−	0.388267i
$7$	0.927051	−	2.85317i	0.350392	−	1.07840i	−0.608241	−	0.793752i	$-0.708125\pi$
$7$	0.927051	−	2.85317i	0.350392	−	1.07840i	0.958633	−	0.284644i	$-0.0918755\pi$
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$	0.618034			0.178411
$13$	1.50000	−	1.08981i	0.416025	−	0.302260i	−0.360011	−	0.932948i	$-0.617227\pi$
$13$	1.50000	−	1.08981i	0.416025	−	0.302260i	0.776037	+	0.630688i	$0.217227\pi$
$14$	1.50000	+	4.61653i	0.400892	+	1.23382i
$15$		0			0
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−6.04508	−	4.39201i	−1.46615	−	1.06522i	−0.981708	−	0.190395i	$-0.939023\pi$
$17$	−6.04508	−	4.39201i	−1.46615	−	1.06522i	−0.484441	−	0.874824i	$-0.660977\pi$
$18$	0.500000	−	1.53884i	0.117851	−	0.362708i
$19$	−0.854102	−	2.62866i	−0.195944	−	0.603055i	−0.999964	−	0.00845249i	$-0.997309\pi$
$19$	−0.854102	−	2.62866i	−0.195944	−	0.603055i	0.804020	−	0.594602i	$-0.202691\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	−3.54508	−	4.02874i	−0.755815	−	0.858930i
$23$	7.61803			1.58847			0.794235	−	0.607611i	$-0.207872\pi$
$23$	7.61803			1.58847			0.794235	+	0.607611i	$0.207872\pi$
$24$	1.80902	−	1.31433i	0.369264	−	0.268286i
$25$		0			0
$26$	−0.927051	+	2.85317i	−0.181810	+	0.559553i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.50000	−	1.08981i	−0.283473	−	0.205955i
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	−0.791982	−	0.610544i	$-0.790951\pi$
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	0.999596	−	0.0284251i	$-0.00904922\pi$
$30$		0			0
$31$	7.16312	−	5.20431i	1.28653	−	0.934722i	0.286805	−	0.957989i	$-0.407407\pi$
$31$	7.16312	−	5.20431i	1.28653	−	0.934722i	0.999729	+	0.0232673i	$0.00740687\pi$
$32$	−3.38197			−0.597853
$33$	−3.04508	+	1.31433i	−0.530081	+	0.228795i
$34$	12.0902			2.07345
$35$		0			0
$36$	0.190983	+	0.587785i	0.0318305	+	0.0979642i
$37$	2.73607	−	8.42075i	0.449807	−	1.38436i	−0.427318	−	0.904101i	$-0.640542\pi$
$37$	2.73607	−	8.42075i	0.449807	−	1.38436i	0.877125	−	0.480262i	$-0.159458\pi$
$38$	3.61803	+	2.62866i	0.586923	+	0.426424i
$39$	1.50000	+	1.08981i	0.240192	+	0.174510i
$40$		0			0
$41$	−0.0729490	−	0.224514i	−0.0113927	−	0.0350632i	0.945199	−	0.326496i	$-0.105868\pi$
$41$	−0.0729490	−	0.224514i	−0.0113927	−	0.0350632i	−0.956591	+	0.291433i	$0.905868\pi$
$42$	−3.92705	+	2.85317i	−0.605957	+	0.440254i
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$	2.00000	+	0.449028i	0.301511	+	0.0676935i
$45$		0			0
$46$	−9.97214	+	7.24518i	−1.47031	+	1.06824i
$47$	2.89919	+	8.92278i	0.422890	+	1.30152i	0.905000	+	0.425411i	$0.139870\pi$
$47$	2.89919	+	8.92278i	0.422890	+	1.30152i	−0.482110	+	0.876110i	$0.660130\pi$
$48$	−1.50000	+	4.61653i	−0.216506	+	0.666338i
$49$	−1.61803	−	1.17557i	−0.231148	−	0.167939i
$50$		0			0
$51$	2.30902	−	7.10642i	0.323327	−	0.995098i
$52$	−0.354102	−	1.08981i	−0.0491051	−	0.151130i
$53$	0.381966	−	0.277515i	0.0524671	−	0.0381196i	−0.561243	−	0.827651i	$-0.689677\pi$
$53$	0.381966	−	0.277515i	0.0524671	−	0.0381196i	0.613710	+	0.789532i	$0.289677\pi$
$54$	1.61803			0.220187
$55$		0			0
$56$	−6.70820			−0.896421
$57$	2.23607	−	1.62460i	0.296174	−	0.215183i
$58$	1.80902	+	5.56758i	0.237536	+	0.731059i
$59$	−1.28115	+	3.94298i	−0.166792	+	0.513333i	−0.999164	−	0.0408847i	$-0.986982\pi$
$59$	−1.28115	+	3.94298i	−0.166792	+	0.513333i	0.832372	+	0.554217i	$0.186982\pi$
$60$		0			0
$61$	4.66312	+	3.38795i	0.597051	+	0.433783i	0.844831	−	0.535033i	$-0.179701\pi$
$61$	4.66312	+	3.38795i	0.597051	+	0.433783i	−0.247780	+	0.968816i	$0.579701\pi$
$62$	−4.42705	+	13.6251i	−0.562236	+	1.73038i
$63$	0.927051	+	2.85317i	0.116797	+	0.359466i
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$		0			0
$66$	2.73607	−	4.61653i	0.336787	−	0.568255i
$67$	−8.70820			−1.06388			−0.531938	−	0.846783i	$-0.678536\pi$
$67$	−8.70820			−1.06388			−0.531938	+	0.846783i	$0.678536\pi$
$68$	−3.73607	+	2.71441i	−0.453065	+	0.329171i
$69$	2.35410	+	7.24518i	0.283401	+	0.872217i
$70$		0			0
$71$	−1.19098	−	0.865300i	−0.141344	−	0.102692i	0.514866	−	0.857270i	$-0.327842\pi$
$71$	−1.19098	−	0.865300i	−0.141344	−	0.102692i	−0.656210	+	0.754578i	$0.727842\pi$
$72$	1.80902	+	1.31433i	0.213195	+	0.154895i
$73$	−2.11803	+	6.51864i	−0.247897	+	0.762949i	0.747249	+	0.664544i	$0.231374\pi$
$73$	−2.11803	+	6.51864i	−0.247897	+	0.762949i	−0.995146	+	0.0984051i	$0.968626\pi$
$74$	4.42705	+	13.6251i	0.514634	+	1.58388i
$75$		0			0
$76$	−1.70820			−0.195944
$77$	9.70820	+	2.17963i	1.10635	+	0.248392i
$78$	−3.00000			−0.339683
$79$	6.11803	−	4.44501i	0.688333	−	0.500103i	−0.187779	−	0.982211i	$-0.560129\pi$
$79$	6.11803	−	4.44501i	0.688333	−	0.500103i	0.876112	+	0.482108i	$0.160129\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.309017	+	0.224514i	0.0341252	+	0.0247934i
$83$	−8.39919	−	6.10237i	−0.921931	−	0.669822i	0.0220732	−	0.999756i	$-0.492973\pi$
$83$	−8.39919	−	6.10237i	−0.921931	−	0.669822i	−0.944004	+	0.329935i	$0.892973\pi$
$84$	0.572949	−	1.76336i	0.0625139	−	0.192398i
$85$		0			0
$86$	−2.30902	+	1.67760i	−0.248988	+	0.180900i
$87$	3.61803			0.387894
$88$	6.80902	−	2.93893i	0.725844	−	0.313291i
$89$	2.56231			0.271604			0.135802	−	0.990736i	$-0.456639\pi$
$89$	2.56231			0.271604			0.135802	+	0.990736i	$0.456639\pi$
$90$		0			0
$91$	−1.71885	−	5.29007i	−0.180184	−	0.554550i
$92$	1.45492	−	4.47777i	0.151685	−	0.466840i
$93$	7.16312	+	5.20431i	0.742781	+	0.539662i
$94$	−12.2812	−	8.92278i	−1.26670	−	0.920314i
$95$		0			0
$96$	−1.04508	−	3.21644i	−0.106664	−	0.328277i
$97$	8.42705	−	6.12261i	0.855637	−	0.621657i	−0.0710572	−	0.997472i	$-0.522637\pi$
$97$	8.42705	−	6.12261i	0.855637	−	0.621657i	0.926695	+	0.375815i	$0.122637\pi$
$98$	3.23607			0.326892
$99$	−2.19098	−	2.48990i	−0.220202	−	0.250244i
$100$		0			0
$101$	0.881966	−	0.640786i	0.0877589	−	0.0637606i	−0.543041	−	0.839706i	$-0.682727\pi$
$101$	0.881966	−	0.640786i	0.0877589	−	0.0637606i	0.630800	+	0.775946i	$0.282727\pi$
$102$	3.73607	+	11.4984i	0.369926	+	1.13851i
$103$	4.69098	−	14.4374i	0.462216	−	1.42256i	−0.400234	−	0.916413i	$-0.631071\pi$
$103$	4.69098	−	14.4374i	0.462216	−	1.42256i	0.862450	−	0.506142i	$-0.168929\pi$
$104$	−3.35410	−	2.43690i	−0.328897	−	0.238957i
$105$		0			0
$106$	−0.236068	+	0.726543i	−0.0229289	+	0.0705680i
$107$	5.07295	+	15.6129i	0.490420	+	1.50936i	0.823974	+	0.566628i	$0.191752\pi$
$107$	5.07295	+	15.6129i	0.490420	+	1.50936i	−0.333553	+	0.942731i	$0.608248\pi$
$108$	−0.500000	+	0.363271i	−0.0481125	+	0.0349558i
$109$	15.0000			1.43674			0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000			1.43674			0.718370	+	0.695662i	$0.244889\pi$
$110$		0			0
$111$	8.85410			0.840394
$112$	11.7812	−	8.55951i	1.11321	−	0.808798i
$113$	2.61803	+	8.05748i	0.246284	+	0.757984i	0.995423	+	0.0955708i	$0.0304676\pi$
$113$	2.61803	+	8.05748i	0.246284	+	0.757984i	−0.749139	+	0.662413i	$0.769532\pi$
$114$	−1.38197	+	4.25325i	−0.129433	+	0.398354i
$115$		0			0
$116$	−1.80902	−	1.31433i	−0.167963	−	0.122032i
$117$	−0.572949	+	1.76336i	−0.0529692	+	0.163022i
$118$	−2.07295	−	6.37988i	−0.190830	−	0.587316i
$119$	−18.1353	+	13.1760i	−1.66246	+	1.20785i
$120$		0			0
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$	−9.32624			−0.844358
$123$	0.190983	−	0.138757i	0.0172204	−	0.0125113i
$124$	−1.69098	−	5.20431i	−0.151855	−	0.467361i
$125$		0			0
$126$	−3.92705	−	2.85317i	−0.349850	−	0.254181i
$127$	−5.35410	−	3.88998i	−0.475100	−	0.345180i	0.324326	−	0.945945i	$-0.394863\pi$
$127$	−5.35410	−	3.88998i	−0.475100	−	0.345180i	−0.799425	+	0.600765i	$0.794863\pi$
$128$	4.20820	−	12.9515i	0.371956	−	1.14476i
$129$	0.545085	+	1.67760i	0.0479921	+	0.147704i
$130$		0			0
$131$	7.32624			0.640096			0.320048	−	0.947401i	$-0.396301\pi$
$131$	7.32624			0.640096			0.320048	+	0.947401i	$0.396301\pi$
$132$	0.190983	+	2.04087i	0.0166229	+	0.177635i
$133$	−8.29180			−0.718990
$134$	11.3992	−	8.28199i	0.984740	−	0.715455i
$135$		0			0
$136$	−5.16312	+	15.8904i	−0.442734	+	1.36259i
$137$	−10.3541	−	7.52270i	−0.884611	−	0.642707i	0.0498566	−	0.998756i	$-0.484124\pi$
$137$	−10.3541	−	7.52270i	−0.884611	−	0.642707i	−0.934467	+	0.356049i	$0.884124\pi$
$138$	−9.97214	−	7.24518i	−0.848885	−	0.616751i
$139$	1.80902	−	5.56758i	0.153439	−	0.472236i	−0.844561	−	0.535460i	$-0.820138\pi$
$139$	1.80902	−	5.56758i	0.153439	−	0.472236i	0.997999	+	0.0632239i	$0.0201382\pi$
$140$		0			0
$141$	−7.59017	+	5.51458i	−0.639208	+	0.464412i
$142$	2.38197			0.199890
$143$	4.06231	+	4.61653i	0.339707	+	0.386053i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	−3.42705	−	10.5474i	−0.283625	−	0.872907i
$147$	0.618034	−	1.90211i	0.0509746	−	0.156884i
$148$	−4.42705	−	3.21644i	−0.363901	−	0.264390i
$149$	−13.0902	−	9.51057i	−1.07239	−	0.779136i	−0.0960484	−	0.995377i	$-0.530620\pi$
$149$	−13.0902	−	9.51057i	−1.07239	−	0.779136i	−0.976340	+	0.216241i	$0.930620\pi$
$150$		0			0
$151$	−2.83688	−	8.73102i	−0.230862	−	0.710520i	−0.997643	−	0.0686121i	$-0.978143\pi$
$151$	−2.83688	−	8.73102i	−0.230862	−	0.710520i	0.766781	−	0.641908i	$-0.221857\pi$
$152$	−5.00000	+	3.63271i	−0.405554	+	0.294652i
$153$	7.47214			0.604086
$154$	−14.7812	+	6.37988i	−1.19110	+	0.514105i
$155$		0			0
$156$	0.927051	−	0.673542i	0.0742235	−	0.0539265i
$157$	5.50000	+	16.9273i	0.438948	+	1.35094i	0.888987	+	0.457933i	$0.151410\pi$
$157$	5.50000	+	16.9273i	0.438948	+	1.35094i	−0.450039	+	0.893009i	$0.648590\pi$
$158$	−3.78115	+	11.6372i	−0.300812	+	0.925805i
$159$	0.381966	+	0.277515i	0.0302919	+	0.0220083i
$160$		0			0
$161$	7.06231	−	21.7355i	0.556588	−	1.71300i
$162$	0.500000	+	1.53884i	0.0392837	+	0.120903i
$163$	−13.8262	+	10.0453i	−1.08295	+	0.786813i	−0.978196	−	0.207685i	$-0.933407\pi$
$163$	−13.8262	+	10.0453i	−1.08295	+	0.786813i	−0.104759	+	0.994498i	$0.533407\pi$
$164$	−0.145898			−0.0113927
$165$		0			0
$166$	16.7984			1.30381
$167$	16.9443	−	12.3107i	1.31119	−	0.952633i	0.311190	−	0.950348i	$-0.399273\pi$
$167$	16.9443	−	12.3107i	1.31119	−	0.952633i	0.999997	−	0.00228541i	$-0.000727468\pi$
$168$	−2.07295	−	6.37988i	−0.159931	−	0.492219i
$169$	−2.95492	+	9.09429i	−0.227301	+	0.699561i
$170$		0			0
$171$	2.23607	+	1.62460i	0.170996	+	0.124236i
$172$	0.336881	−	1.03681i	0.0256869	−	0.0790563i
$173$	−1.69098	−	5.20431i	−0.128563	−	0.395676i	0.865970	−	0.500095i	$-0.166702\pi$
$173$	−1.69098	−	5.20431i	−0.128563	−	0.395676i	−0.994533	+	0.104419i	$0.966702\pi$
$174$	−4.73607	+	3.44095i	−0.359040	+	0.260858i
$175$		0			0
$176$	−8.20820	+	13.8496i	−0.618717	+	1.04395i
$177$	−4.14590			−0.311625
$178$	−3.35410	+	2.43690i	−0.251401	+	0.182653i
$179$	−6.21885	−	19.1396i	−0.464818	−	1.43056i	−0.859211	−	0.511622i	$-0.829045\pi$
$179$	−6.21885	−	19.1396i	−0.464818	−	1.43056i	0.394392	−	0.918942i	$-0.370955\pi$
$180$		0			0
$181$	10.3541	+	7.52270i	0.769614	+	0.559158i	0.901844	−	0.432062i	$-0.142214\pi$
$181$	10.3541	+	7.52270i	0.769614	+	0.559158i	−0.132230	+	0.991219i	$0.542214\pi$
$182$	7.28115	+	5.29007i	0.539715	+	0.392126i
$183$	−1.78115	+	5.48183i	−0.131667	+	0.405228i
$184$	−5.26393	−	16.2007i	−0.388062	−	1.19433i
$185$		0			0
$186$	−14.3262			−1.05045
$187$	12.6353	−	21.3193i	0.923981	−	1.55902i
$188$	5.79837			0.422890
$189$	−2.42705	+	1.76336i	−0.176542	+	0.128265i
$190$		0			0
$191$	4.86475	−	14.9721i	0.352001	−	1.08335i	−0.605728	−	0.795672i	$-0.707118\pi$
$191$	4.86475	−	14.9721i	0.352001	−	1.08335i	0.957728	−	0.287674i	$-0.0928821\pi$
$192$	−3.42705	−	2.48990i	−0.247326	−	0.179693i
$193$	−14.9443	−	10.8576i	−1.07571	−	0.781551i	−0.0987819	−	0.995109i	$-0.531495\pi$
$193$	−14.9443	−	10.8576i	−1.07571	−	0.781551i	−0.976930	+	0.213558i	$0.931495\pi$
$194$	−5.20820	+	16.0292i	−0.373927	+	1.15083i
$195$		0			0
$196$	−1.00000	+	0.726543i	−0.0714286	+	0.0518959i
$197$	9.70820			0.691681			0.345840	−	0.938293i	$-0.387594\pi$
$197$	9.70820			0.691681			0.345840	+	0.938293i	$0.387594\pi$
$198$	5.23607	+	1.17557i	0.372111	+	0.0835442i
$199$	−8.29180			−0.587790			−0.293895	−	0.955838i	$-0.594952\pi$
$199$	−8.29180			−0.587790			−0.293895	+	0.955838i	$0.594952\pi$
$200$		0			0
$201$	−2.69098	−	8.28199i	−0.189807	−	0.584167i
$202$	−0.545085	+	1.67760i	−0.0383520	+	0.118035i
$203$	−8.78115	−	6.37988i	−0.616316	−	0.447780i
$204$	−3.73607	−	2.71441i	−0.261577	−	0.190047i
$205$		0			0
$206$	7.59017	+	23.3601i	0.528832	+	1.62758i
$207$	−6.16312	+	4.47777i	−0.428366	+	0.311226i
$208$	9.00000			0.624038
$209$	8.41641	−	3.63271i	0.582175	−	0.251280i
$210$		0			0
$211$	−10.6631	+	7.74721i	−0.734079	+	0.533340i	−0.890851	−	0.454295i	$-0.849891\pi$
$211$	−10.6631	+	7.74721i	−0.734079	+	0.533340i	0.156772	+	0.987635i	$0.449891\pi$
$212$	−0.0901699	−	0.277515i	−0.00619290	−	0.0190598i
$213$	0.454915	−	1.40008i	0.0311703	−	0.0959322i
$214$	−21.4894	−	15.6129i	−1.46898	−	1.06728i
$215$		0			0
$216$	−0.690983	+	2.12663i	−0.0470154	+	0.144699i
$217$	−8.20820	−	25.2623i	−0.557209	−	1.71491i
$218$	−19.6353	+	14.2658i	−1.32987	+	0.966205i
$219$	−6.85410			−0.463157
$220$		0			0
$221$	−13.8541			−0.931928
$222$	−11.5902	+	8.42075i	−0.777881	+	0.565164i
$223$	−3.92705	−	12.0862i	−0.262975	−	0.809353i	−0.992153	−	0.125029i	$-0.960097\pi$
$223$	−3.92705	−	12.0862i	−0.262975	−	0.809353i	0.729178	−	0.684324i	$-0.239903\pi$
$224$	−3.13525	+	9.64932i	−0.209483	+	0.644722i
$225$		0			0
$226$	−11.0902	−	8.05748i	−0.737707	−	0.535976i
$227$	−4.50000	+	13.8496i	−0.298675	+	0.919229i	0.683287	+	0.730150i	$0.260550\pi$
$227$	−4.50000	+	13.8496i	−0.298675	+	0.919229i	−0.981962	+	0.189078i	$0.939450\pi$
$228$	−0.527864	−	1.62460i	−0.0349587	−	0.107592i
$229$	8.09017	−	5.87785i	0.534613	−	0.388419i	−0.287467	−	0.957790i	$-0.592813\pi$
$229$	8.09017	−	5.87785i	0.534613	−	0.388419i	0.822081	+	0.569371i	$0.192813\pi$
$230$		0			0
$231$	0.927051	+	9.90659i	0.0609955	+	0.651806i
$232$	−8.09017			−0.531146
$233$	5.11803	−	3.71847i	0.335294	−	0.243605i	−0.407380	−	0.913259i	$-0.633557\pi$
$233$	5.11803	−	3.71847i	0.335294	−	0.243605i	0.742673	+	0.669654i	$0.233557\pi$
$234$	−0.927051	−	2.85317i	−0.0606032	−	0.186518i
$235$		0			0
$236$	2.07295	+	1.50609i	0.134937	+	0.0980378i
$237$	6.11803	+	4.44501i	0.397409	+	0.288735i
$238$	11.2082	−	34.4953i	0.726520	−	2.23600i
$239$	−6.38197	−	19.6417i	−0.412815	−	1.27051i	−0.914191	−	0.405284i	$-0.867173\pi$
$239$	−6.38197	−	19.6417i	−0.412815	−	1.27051i	0.501376	−	0.865230i	$-0.332827\pi$
$240$		0			0
$241$	7.85410			0.505927			0.252964	−	0.967476i	$-0.418595\pi$
$241$	7.85410			0.505927			0.252964	+	0.967476i	$0.418595\pi$
$242$	12.2082	−	12.9515i	0.784773	−	0.832555i
$243$	1.00000			0.0641500
$244$	2.88197	−	2.09387i	0.184499	−	0.134046i
$245$		0			0
$246$	−0.118034	+	0.363271i	−0.00752557	+	0.0231613i
$247$	−4.14590	−	3.01217i	−0.263797	−	0.191660i
$248$	−16.0172	−	11.6372i	−1.01709	−	0.738962i
$249$	3.20820	−	9.87384i	0.203312	−	0.625729i
$250$		0			0
$251$	16.6353	−	12.0862i	1.05001	−	0.762875i	0.0777940	−	0.996969i	$-0.475212\pi$
$251$	16.6353	−	12.0862i	1.05001	−	0.762875i	0.972214	+	0.234094i	$0.0752124\pi$
$252$	1.85410			0.116797
$253$	2.35410	+	25.1563i	0.148001	+	1.58156i
$254$	10.7082			0.671892
$255$		0			0
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	3.10081	−	9.54332i	0.193423	−	0.595296i	−0.806568	−	0.591141i	$-0.798678\pi$
$257$	3.10081	−	9.54332i	0.193423	−	0.595296i	0.999991	−	0.00415466i	$-0.00132247\pi$
$258$	−2.30902	−	1.67760i	−0.143753	−	0.104443i
$259$	−21.4894	−	15.6129i	−1.33528	−	0.970140i
$260$		0			0
$261$	1.11803	+	3.44095i	0.0692046	+	0.212990i
$262$	−9.59017	+	6.96767i	−0.592483	+	0.430464i
$263$	−11.1246			−0.685973			−0.342986	−	0.939340i	$-0.611439\pi$
$263$	−11.1246			−0.685973			−0.342986	+	0.939340i	$0.611439\pi$
$264$	4.89919	+	5.56758i	0.301524	+	0.342661i
$265$		0			0
$266$	10.8541	−	7.88597i	0.665508	−	0.483520i
$267$	0.791796	+	2.43690i	0.0484571	+	0.149136i
$268$	−1.66312	+	5.11855i	−0.101591	+	0.312665i
$269$	0.427051	+	0.310271i	0.0260378	+	0.0189175i	0.600728	−	0.799453i	$-0.294877\pi$
$269$	0.427051	+	0.310271i	0.0260378	+	0.0189175i	−0.574690	+	0.818371i	$0.694877\pi$
$270$		0			0
$271$	−6.88197	+	21.1805i	−0.418050	+	1.28662i	0.491445	+	0.870909i	$0.336469\pi$
$271$	−6.88197	+	21.1805i	−0.418050	+	1.28662i	−0.909495	+	0.415716i	$0.863531\pi$
$272$	−11.2082	−	34.4953i	−0.679597	−	2.09159i
$273$	4.50000	−	3.26944i	0.272352	−	0.197876i
$274$	20.7082			1.25103
$275$		0			0
$276$	4.70820			0.283401
$277$	−19.3992	+	14.0943i	−1.16558	+	0.846846i	−0.990474	−	0.137702i	$-0.956028\pi$
$277$	−19.3992	+	14.0943i	−1.16558	+	0.846846i	−0.175111	+	0.984549i	$0.556028\pi$
$278$	2.92705	+	9.00854i	0.175553	+	0.540296i
$279$	−2.73607	+	8.42075i	−0.163804	+	0.504137i
$280$		0			0
$281$	2.69098	+	1.95511i	0.160531	+	0.116632i	0.665151	−	0.746709i	$-0.268367\pi$
$281$	2.69098	+	1.95511i	0.160531	+	0.116632i	−0.504620	+	0.863342i	$0.668367\pi$
$282$	4.69098	−	14.4374i	0.279344	−	0.859732i
$283$	8.37132	+	25.7643i	0.497623	+	1.53153i	0.812828	+	0.582504i	$0.197927\pi$
$283$	8.37132	+	25.7643i	0.497623	+	1.53153i	−0.315204	+	0.949024i	$0.602073\pi$
$284$	−0.736068	+	0.534785i	−0.0436776	+	0.0317336i
$285$		0			0
$286$	−9.70820	−	2.17963i	−0.574058	−	0.128884i
$287$	−0.708204			−0.0418040
$288$	2.73607	−	1.98787i	0.161224	−	0.117136i
$289$	12.0000	+	36.9322i	0.705882	+	2.17248i
$290$		0			0
$291$	8.42705	+	6.12261i	0.494002	+	0.358914i
$292$	3.42705	+	2.48990i	0.200553	+	0.145710i
$293$	−6.00000	+	18.4661i	−0.350524	+	1.07880i	0.608036	+	0.793909i	$0.291958\pi$
$293$	−6.00000	+	18.4661i	−0.350524	+	1.07880i	−0.958560	+	0.284892i	$0.908042\pi$
$294$	1.00000	+	3.07768i	0.0583212	+	0.179494i
$295$		0			0
$296$	−19.7984			−1.15076
$297$	1.69098	−	2.85317i	0.0981208	−	0.165558i
$298$	26.1803			1.51659
$299$	11.4271	−	8.30224i	0.660843	−	0.480131i
$300$		0			0
$301$	1.63525	−	5.03280i	0.0942545	−	0.290086i
$302$	12.0172	+	8.73102i	0.691513	+	0.502414i
$303$	0.881966	+	0.640786i	0.0506676	+	0.0368122i
$304$	4.14590	−	12.7598i	0.237784	−	0.731823i
$305$		0			0
$306$	−9.78115	+	7.10642i	−0.559151	+	0.406247i
$307$	15.8885			0.906807			0.453404	−	0.891305i	$-0.350210\pi$
$307$	15.8885			0.906807			0.453404	+	0.891305i	$0.350210\pi$
$308$	3.13525	−	5.29007i	0.178648	−	0.301430i
$309$	15.1803			0.863579
$310$		0			0
$311$	−5.72542	−	17.6210i	−0.324659	−	0.999198i	−0.971594	−	0.236653i	$-0.923950\pi$
$311$	−5.72542	−	17.6210i	−0.324659	−	0.999198i	0.646935	−	0.762545i	$-0.276050\pi$
$312$	1.28115	−	3.94298i	0.0725310	−	0.223227i
$313$	−24.8435	−	18.0498i	−1.40424	−	1.02024i	−0.994129	−	0.108199i	$-0.965492\pi$
$313$	−24.8435	−	18.0498i	−1.40424	−	1.02024i	−0.410106	−	0.912038i	$-0.634508\pi$
$314$	−23.2984	−	16.9273i	−1.31480	−	0.955261i
$315$		0			0
$316$	−1.44427	−	4.44501i	−0.0812466	−	0.250051i
$317$	−7.42705	+	5.39607i	−0.417145	+	0.303073i	−0.776488	−	0.630132i	$-0.783001\pi$
$317$	−7.42705	+	5.39607i	−0.417145	+	0.303073i	0.359343	+	0.933205i	$0.383001\pi$
$318$	−0.763932			−0.0428392
$319$	11.7082	+	2.62866i	0.655534	+	0.147176i
$320$		0			0
$321$	−13.2812	+	9.64932i	−0.741282	+	0.538573i
$322$	11.4271	+	35.1688i	0.636805	+	1.95988i
$323$	−6.38197	+	19.6417i	−0.355102	+	1.09289i
$324$	−0.500000	−	0.363271i	−0.0277778	−	0.0201817i
$325$		0			0
$326$	8.54508	−	26.2991i	0.473268	−	1.45657i
$327$	4.63525	+	14.2658i	0.256330	+	0.788903i
$328$	−0.427051	+	0.310271i	−0.0235799	+	0.0171318i
$329$	28.1459			1.55173
$330$		0			0
$331$	−16.4164			−0.902327			−0.451164	−	0.892441i	$-0.648991\pi$
$331$	−16.4164			−0.902327			−0.451164	+	0.892441i	$0.648991\pi$
$332$	−5.19098	+	3.77147i	−0.284892	+	0.206986i
$333$	2.73607	+	8.42075i	0.149936	+	0.461454i
$334$	−10.4721	+	32.2299i	−0.573010	+	1.76354i
$335$		0			0
$336$	11.7812	+	8.55951i	0.642715	+	0.466959i
$337$	−7.32624	+	22.5478i	−0.399086	+	1.22826i	0.526648	+	0.850083i	$0.323449\pi$
$337$	−7.32624	+	22.5478i	−0.399086	+	1.22826i	−0.925734	+	0.378176i	$0.876551\pi$
$338$	−4.78115	−	14.7149i	−0.260060	−	0.800384i
$339$	−6.85410	+	4.97980i	−0.372264	+	0.270465i
$340$		0			0
$341$	19.3992	+	22.0458i	1.05052	+	1.19385i
$342$	−4.47214			−0.241825
$343$	12.1353	−	8.81678i	0.655242	−	0.476061i
$344$	−1.21885	−	3.75123i	−0.0657158	−	0.202253i
$345$		0			0
$346$	7.16312	+	5.20431i	0.385092	+	0.279785i
$347$	9.97214	+	7.24518i	0.535332	+	0.388942i	0.822349	−	0.568984i	$-0.192663\pi$
$347$	9.97214	+	7.24518i	0.535332	+	0.388942i	−0.287016	+	0.957926i	$0.592663\pi$
$348$	0.690983	−	2.12663i	0.0370406	−	0.113999i
$349$	8.94427	+	27.5276i	0.478776	+	1.47352i	0.840797	+	0.541351i	$0.182087\pi$
$349$	8.94427	+	27.5276i	0.478776	+	1.47352i	−0.362021	+	0.932170i	$0.617913\pi$
$350$		0			0
$351$	−1.85410			−0.0989646
$352$	−1.04508	−	11.1679i	−0.0557032	−	0.595252i
$353$	−8.88854			−0.473089			−0.236545	−	0.971621i	$-0.576015\pi$
$353$	−8.88854			−0.473089			−0.236545	+	0.971621i	$0.576015\pi$
$354$	5.42705	−	3.94298i	0.288445	−	0.209567i
$355$		0			0
$356$	0.489357	−	1.50609i	0.0259359	−	0.0798224i
$357$	−18.1353	−	13.1760i	−0.959819	−	0.697350i
$358$	26.3435	+	19.1396i	1.39230	+	1.01156i
$359$	5.62868	−	17.3233i	0.297070	−	0.914288i	−0.685448	−	0.728122i	$-0.740394\pi$
$359$	5.62868	−	17.3233i	0.297070	−	0.914288i	0.982518	−	0.186167i	$-0.0596064\pi$
$360$		0			0
$361$	9.19098	−	6.67764i	0.483736	−	0.351455i
$362$	−20.7082			−1.08840
$363$	−5.28115	−	9.64932i	−0.277189	−	0.506458i
$364$	−3.43769			−0.180184
$365$		0			0
$366$	−2.88197	−	8.86978i	−0.150643	−	0.463631i
$367$	−5.81966	+	17.9111i	−0.303784	+	0.934950i	0.676344	+	0.736585i	$0.263563\pi$
$367$	−5.81966	+	17.9111i	−0.303784	+	0.934950i	−0.980128	+	0.198365i	$0.936437\pi$
$368$	29.9164	+	21.7355i	1.55950	+	1.13304i
$369$	0.190983	+	0.138757i	0.00994218	+	0.00722342i
$370$		0			0
$371$	−0.437694	−	1.34708i	−0.0227239	−	0.0699371i
$372$	4.42705	−	3.21644i	0.229532	−	0.166765i
$373$	17.4164			0.901787			0.450894	−	0.892578i	$-0.351105\pi$
$373$	17.4164			0.901787			0.450894	+	0.892578i	$0.351105\pi$
$374$	3.73607	+	39.9241i	0.193187	+	2.06443i
$375$		0			0
$376$	16.9721	−	12.3310i	0.875271	−	0.635922i
$377$	−2.07295	−	6.37988i	−0.106762	−	0.328581i
$378$	1.50000	−	4.61653i	0.0771517	−	0.237448i
$379$	18.7812	+	13.6453i	0.964723	+	0.700912i	0.954243	−	0.299033i	$-0.0966640\pi$
$379$	18.7812	+	13.6453i	0.964723	+	0.700912i	0.0104802	+	0.999945i	$0.496664\pi$
$380$		0			0
$381$	2.04508	−	6.29412i	0.104773	−	0.322458i
$382$	7.87132	+	24.2254i	0.402732	+	1.23948i
$383$	17.4164	−	12.6538i	0.889937	−	0.646577i	−0.0459247	−	0.998945i	$-0.514623\pi$
$383$	17.4164	−	12.6538i	0.889937	−	0.646577i	0.935862	+	0.352368i	$0.114623\pi$
$384$	13.6180			0.694942
$385$		0			0
$386$	29.8885			1.52129
$387$	−1.42705	+	1.03681i	−0.0725411	+	0.0527042i
$388$	−1.98936	−	6.12261i	−0.100994	−	0.310828i
$389$	−5.59017	+	17.2048i	−0.283433	+	0.872317i	0.703431	+	0.710763i	$0.251650\pi$
$389$	−5.59017	+	17.2048i	−0.283433	+	0.872317i	−0.986864	+	0.161553i	$0.948350\pi$
$390$		0			0
$391$	−46.0517	−	33.4585i	−2.32893	−	1.69207i
$392$	−1.38197	+	4.25325i	−0.0697998	+	0.214822i
$393$	2.26393	+	6.96767i	0.114200	+	0.351472i
$394$	−12.7082	+	9.23305i	−0.640230	+	0.465154i
$395$		0			0
$396$	−1.88197	+	0.812299i	−0.0945724	+	0.0408196i
$397$	−19.5623			−0.981804			−0.490902	−	0.871215i	$-0.663333\pi$
$397$	−19.5623			−0.981804			−0.490902	+	0.871215i	$0.663333\pi$
$398$	10.8541	−	7.88597i	0.544067	−	0.395288i
$399$	−2.56231	−	7.88597i	−0.128276	−	0.394792i
$400$		0			0
$401$	−0.663119	−	0.481784i	−0.0331146	−	0.0240592i	0.571105	−	0.820877i	$-0.306515\pi$
$401$	−0.663119	−	0.481784i	−0.0331146	−	0.0240592i	−0.604219	+	0.796818i	$0.706515\pi$
$402$	11.3992	+	8.28199i	0.568540	+	0.413068i
$403$	5.07295	−	15.6129i	0.252702	−	0.777736i
$404$	−0.208204	−	0.640786i	−0.0103585	−	0.0318803i
$405$		0			0
$406$	17.5623			0.871603
$407$	28.6525	+	6.43288i	1.42025	+	0.318866i
$408$	−16.7082			−0.827179
$409$	8.19098	−	5.95110i	0.405018	−	0.294263i	−0.366564	−	0.930393i	$-0.619466\pi$
$409$	8.19098	−	5.95110i	0.405018	−	0.294263i	0.771582	+	0.636130i	$0.219466\pi$
$410$		0			0
$411$	3.95492	−	12.1720i	0.195082	−	0.600399i
$412$	−7.59017	−	5.51458i	−0.373941	−	0.271684i
$413$	10.0623	+	7.31069i	0.495134	+	0.359736i
$414$	3.80902	−	11.7229i	0.187203	−	0.576152i
$415$		0			0
$416$	−5.07295	+	3.68571i	−0.248722	+	0.180707i
$417$	5.85410			0.286677
$418$	−7.56231	+	12.7598i	−0.369884	+	0.624100i
$419$	18.9443			0.925488			0.462744	−	0.886492i	$-0.346865\pi$
$419$	18.9443			0.925488			0.462744	+	0.886492i	$0.346865\pi$
$420$		0			0
$421$	−2.24671	−	6.91467i	−0.109498	−	0.337000i	0.881262	−	0.472628i	$-0.156695\pi$
$421$	−2.24671	−	6.91467i	−0.109498	−	0.337000i	−0.990760	+	0.135628i	$0.956695\pi$
$422$	6.59017	−	20.2825i	0.320804	−	0.987335i
$423$	−7.59017	−	5.51458i	−0.369047	−	0.268128i
$424$	−0.854102	−	0.620541i	−0.0414789	−	0.0301362i
$425$		0			0
$426$	0.736068	+	2.26538i	0.0356626	+	0.109758i
$427$	13.9894	−	10.1639i	0.676992	−	0.491864i
$428$	10.1459			0.490420
$429$	−3.13525	+	5.29007i	−0.151372	+	0.255407i
$430$		0			0
$431$	−13.0623	+	9.49032i	−0.629189	+	0.457133i	−0.856119	−	0.516778i	$-0.827131\pi$
$431$	−13.0623	+	9.49032i	−0.629189	+	0.457133i	0.226930	+	0.973911i	$0.427131\pi$
$432$	−1.50000	−	4.61653i	−0.0721688	−	0.222113i
$433$	−8.39919	+	25.8500i	−0.403639	+	1.24227i	0.518387	+	0.855146i	$0.326533\pi$
$433$	−8.39919	+	25.8500i	−0.403639	+	1.24227i	−0.922026	+	0.387127i	$0.873467\pi$
$434$	34.7705	+	25.2623i	1.66904	+	1.21263i
$435$		0			0
$436$	2.86475	−	8.81678i	0.137196	−	0.422247i
$437$	−6.50658	−	20.0252i	−0.311252	−	0.957935i
$438$	8.97214	−	6.51864i	0.428705	−	0.311473i
$439$	7.43769			0.354982			0.177491	−	0.984122i	$-0.443202\pi$
$439$	7.43769			0.354982			0.177491	+	0.984122i	$0.443202\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	18.1353	−	13.1760i	0.862606	−	0.626720i
$443$	−8.50000	−	26.1603i	−0.403847	−	1.24291i	−0.921854	−	0.387537i	$-0.873326\pi$
$443$	−8.50000	−	26.1603i	−0.403847	−	1.24291i	0.518007	−	0.855376i	$-0.326674\pi$
$444$	1.69098	−	5.20431i	0.0802505	−	0.246986i
$445$		0			0
$446$	16.6353	+	12.0862i	0.787702	+	0.572299i
$447$	5.00000	−	15.3884i	0.236492	−	0.727847i
$448$	3.92705	+	12.0862i	0.185536	+	0.571020i
$449$	−11.7082	+	8.50651i	−0.552544	+	0.401447i	−0.828723	−	0.559659i	$-0.810932\pi$
$449$	−11.7082	+	8.50651i	−0.552544	+	0.401447i	0.276178	+	0.961106i	$0.410932\pi$
$450$		0			0
$451$	0.718847	−	0.310271i	0.0338492	−	0.0146101i
$452$	5.23607			0.246284
$453$	7.42705	−	5.39607i	0.348953	−	0.253529i
$454$	−7.28115	−	22.4091i	−0.341721	−	1.05171i
$455$		0			0
$456$	−5.00000	−	3.63271i	−0.234146	−	0.170117i
$457$	−19.0344	−	13.8293i	−0.890394	−	0.646909i	0.0455870	−	0.998960i	$-0.485484\pi$
$457$	−19.0344	−	13.8293i	−0.890394	−	0.646909i	−0.935981	+	0.352052i	$0.885484\pi$
$458$	−5.00000	+	15.3884i	−0.233635	+	0.719054i
$459$	2.30902	+	7.10642i	0.107776	+	0.331699i
$460$		0			0
$461$	−9.18034			−0.427571			−0.213786	−	0.976881i	$-0.568579\pi$
$461$	−9.18034			−0.427571			−0.213786	+	0.976881i	$0.568579\pi$
$462$	−10.6353	−	12.0862i	−0.494797	−	0.562302i
$463$	−9.29180			−0.431826			−0.215913	−	0.976413i	$-0.569273\pi$
$463$	−9.29180			−0.431826			−0.215913	+	0.976413i	$0.569273\pi$
$464$	14.2082	−	10.3229i	0.659599	−	0.479227i
$465$		0			0
$466$	−3.16312	+	9.73508i	−0.146529	+	0.450969i
$467$	4.01722	+	2.91868i	0.185895	+	0.135060i	0.676841	−	0.736130i	$-0.263349\pi$
$467$	4.01722	+	2.91868i	0.185895	+	0.135060i	−0.490946	+	0.871190i	$0.663349\pi$
$468$	0.927051	+	0.673542i	0.0428529	+	0.0311345i
$469$	−8.07295	+	24.8460i	−0.372774	+	1.14728i
$470$		0			0
$471$	−14.3992	+	10.4616i	−0.663480	+	0.482046i
$472$	9.27051			0.426710
$473$	0.545085	+	5.82485i	0.0250630	+	0.267827i
$474$	−12.2361			−0.562021
$475$		0			0
$476$	4.28115	+	13.1760i	0.196226	+	0.603923i
$477$	−0.145898	+	0.449028i	−0.00668021	+	0.0205596i
$478$	27.0344	+	19.6417i	1.23653	+	0.898389i
$479$	−5.95492	−	4.32650i	−0.272087	−	0.197683i	0.443372	−	0.896338i	$-0.353782\pi$
$479$	−5.95492	−	4.32650i	−0.272087	−	0.197683i	−0.715459	+	0.698655i	$0.753782\pi$
$480$		0			0
$481$	−5.07295	−	15.6129i	−0.231307	−	0.711888i
$482$	−10.2812	+	7.46969i	−0.468294	+	0.340235i
$483$	22.8541			1.03990
$484$	−0.864745	+	6.74315i	−0.0393066	+	0.306507i
$485$		0			0
$486$	−1.30902	+	0.951057i	−0.0593782	+	0.0431408i
$487$	−0.392609	−	1.20833i	−0.0177908	−	0.0547545i	0.941767	−	0.336266i	$-0.109164\pi$
$487$	−0.392609	−	1.20833i	−0.0177908	−	0.0547545i	−0.959558	+	0.281512i	$0.909164\pi$
$488$	3.98278	−	12.2577i	0.180292	−	0.554882i
$489$	−13.8262	−	10.0453i	−0.625244	−	0.454266i
$490$		0			0
$491$	−4.28115	+	13.1760i	−0.193206	+	0.594626i	0.806787	+	0.590842i	$0.201204\pi$
$491$	−4.28115	+	13.1760i	−0.193206	+	0.594626i	−0.999993	+	0.00378385i	$0.998796\pi$
$492$	−0.0450850	−	0.138757i	−0.00203259	−	0.00625566i
$493$	−21.8713	+	15.8904i	−0.985035	+	0.715670i
$494$	8.29180			0.373066
$495$		0			0
$496$	42.9787			1.92980
$497$	−3.57295	+	2.59590i	−0.160269	+	0.116442i
$498$	5.19098	+	15.9762i	0.232614	+	0.715911i
$499$	3.65654	−	11.2537i	0.163689	−	0.503784i	−0.835248	−	0.549873i	$-0.814676\pi$
$499$	3.65654	−	11.2537i	0.163689	−	0.503784i	0.998937	+	0.0460896i	$0.0146760\pi$
$500$		0			0
$501$	16.9443	+	12.3107i	0.757014	+	0.550003i
$502$	−10.2812	+	31.6421i	−0.458870	+	1.41226i
$503$	−1.06231	−	3.26944i	−0.0473659	−	0.145777i	0.924576	−	0.380997i	$-0.124419\pi$
$503$	−1.06231	−	3.26944i	−0.0473659	−	0.145777i	−0.971942	+	0.235220i	$0.924419\pi$
$504$	5.42705	−	3.94298i	0.241740	−	0.175634i
$505$		0			0
$506$	−27.0066	−	30.6911i	−1.20059	−	1.36438i
$507$	−9.56231			−0.424677
$508$	−3.30902	+	2.40414i	−0.146814	+	0.106667i
$509$	−4.57295	−	14.0741i	−0.202692	−	0.623823i	−0.999800	−	0.0199861i	$-0.993638\pi$
$509$	−4.57295	−	14.0741i	−0.202692	−	0.623823i	0.797108	−	0.603837i	$-0.206362\pi$
$510$		0			0
$511$	16.6353	+	12.0862i	0.735900	+	0.534663i
$512$	4.28115	+	3.11044i	0.189202	+	0.137463i
$513$	−0.854102	+	2.62866i	−0.0377095	+	0.116058i
$514$	5.01722	+	15.4414i	0.221300	+	0.681092i
$515$		0			0
$516$	1.09017			0.0479921
$517$	−28.5689	+	12.3310i	−1.25646	+	0.542316i
$518$	42.9787			1.88838
$519$	4.42705	−	3.21644i	0.194326	−	0.141186i
$520$		0			0
$521$	−13.3647	+	41.1325i	−0.585520	+	1.80205i	0.0116515	+	0.999932i	$0.496291\pi$
$521$	−13.3647	+	41.1325i	−0.585520	+	1.80205i	−0.597172	+	0.802113i	$0.703709\pi$
$522$	−4.73607	−	3.44095i	−0.207292	−	0.150607i
$523$	−31.3885	−	22.8051i	−1.37253	−	0.997198i	−0.997535	−	0.0701691i	$-0.977646\pi$
$523$	−31.3885	−	22.8051i	−1.37253	−	0.997198i	−0.374990	−	0.927029i	$-0.622354\pi$
$524$	1.39919	−	4.30625i	0.0611238	−	0.188120i
$525$		0			0
$526$	14.5623	−	10.5801i	0.634947	−	0.461316i
$527$	−66.1591			−2.88193
$528$	−15.7082	−	3.52671i	−0.683612	−	0.153480i
$529$	35.0344			1.52324
$530$		0			0
$531$	−1.28115	−	3.94298i	−0.0555973	−	0.171111i
$532$	−1.58359	+	4.87380i	−0.0686574	+	0.211306i
$533$	−0.354102	−	0.257270i	−0.0153379	−	0.0111436i
$534$	−3.35410	−	2.43690i	−0.145146	−	0.105455i
$535$		0			0
$536$	6.01722	+	18.5191i	0.259904	+	0.799903i
$537$	16.2812	−	11.8290i	0.702584	−	0.510457i
$538$	−0.854102			−0.0368230
$539$	3.38197	−	5.70634i	0.145672	−	0.245789i
$540$		0			0
$541$	20.0902	−	14.5964i	0.863744	−	0.627547i	−0.0651570	−	0.997875i	$-0.520755\pi$
$541$	20.0902	−	14.5964i	0.863744	−	0.627547i	0.928901	+	0.370328i	$0.120755\pi$
$542$	−11.1353	−	34.2708i	−0.478300	−	1.47206i
$543$	−3.95492	+	12.1720i	−0.169722	+	0.522350i
$544$	20.4443	+	14.8536i	0.876541	+	0.636844i
$545$		0			0
$546$	−2.78115	+	8.55951i	−0.119022	+	0.366313i
$547$	6.57953	+	20.2497i	0.281320	+	0.865815i	0.987478	+	0.157760i	$0.0504271\pi$
$547$	6.57953	+	20.2497i	0.281320	+	0.865815i	−0.706157	+	0.708055i	$0.749573\pi$
$548$	−6.39919	+	4.64928i	−0.273360	+	0.198607i
$549$	−5.76393			−0.245999
$550$		0			0
$551$	−10.0000			−0.426014
$552$	13.7812	−	10.0126i	0.586565	−	0.426164i
$553$	−7.01064	−	21.5765i	−0.298123	−	0.917528i
$554$	11.9894	−	36.8994i	0.509379	−	1.56771i
$555$		0			0
$556$	−2.92705	−	2.12663i	−0.124135	−	0.0901891i
$557$	−9.43769	+	29.0462i	−0.399888	+	1.23073i	0.525201	+	0.850978i	$0.323990\pi$
$557$	−9.43769	+	29.0462i	−0.399888	+	1.23073i	−0.925089	+	0.379750i	$0.876010\pi$
$558$	−4.42705	−	13.6251i	−0.187412	−	0.576795i
$559$	2.64590	−	1.92236i	0.111910	−	0.0813071i
$560$		0			0
$561$	24.1803	+	5.42882i	1.02089	+	0.229205i
$562$	−5.38197			−0.227025
$563$	14.4271	−	10.4819i	0.608028	−	0.441758i	−0.240692	−	0.970602i	$-0.577374\pi$
$563$	14.4271	−	10.4819i	0.608028	−	0.441758i	0.848719	+	0.528844i	$0.177374\pi$
$564$	1.79180	+	5.51458i	0.0754482	+	0.232206i
$565$		0			0
$566$	−35.4615	−	25.7643i	−1.49056	−	1.08295i
$567$	−2.42705	−	1.76336i	−0.101927	−	0.0740540i
$568$	−1.01722	+	3.13068i	−0.0426816	+	0.131361i
$569$	4.79837	+	14.7679i	0.201158	+	0.619102i	0.999849	+	0.0173602i	$0.00552620\pi$
$569$	4.79837	+	14.7679i	0.201158	+	0.619102i	−0.798691	+	0.601741i	$0.794474\pi$
$570$		0			0
$571$	13.5836			0.568456			0.284228	−	0.958757i	$-0.408263\pi$
$571$	13.5836			0.568456			0.284228	+	0.958757i	$0.408263\pi$
$572$	3.48936	−	1.50609i	0.145897	−	0.0629726i
$573$	15.7426			0.657658
$574$	0.927051	−	0.673542i	0.0386944	−	0.0281131i
$575$		0			0
$576$	1.30902	−	4.02874i	0.0545424	−	0.167864i
$577$	16.3541	+	11.8820i	0.680830	+	0.494652i	0.873633	−	0.486585i	$-0.161758\pi$
$577$	16.3541	+	11.8820i	0.680830	+	0.494652i	−0.192803	+	0.981238i	$0.561758\pi$
$578$	−50.8328	−	36.9322i	−2.11437	−	1.53618i
$579$	5.70820	−	17.5680i	0.237225	−	0.730103i
$580$		0			0
$581$	−25.1976	+	18.3071i	−1.04537	+	0.759506i
$582$	−16.8541			−0.698625
$583$	1.03444	+	1.17557i	0.0428422	+	0.0486872i
$584$	15.3262			0.634204
$585$		0			0
$586$	−9.70820	−	29.8788i	−0.401042	−	1.23428i
$587$	10.6008	−	32.6259i	0.437542	−	1.34662i	−0.452916	−	0.891553i	$-0.649616\pi$
$587$	10.6008	−	32.6259i	0.437542	−	1.34662i	0.890459	−	0.455064i	$-0.150384\pi$
$588$	−1.00000	−	0.726543i	−0.0412393	−	0.0299621i
$589$	−19.7984	−	14.3844i	−0.815778	−	0.592697i
$590$		0			0
$591$	3.00000	+	9.23305i	0.123404	+	0.379797i
$592$	34.7705	−	25.2623i	1.42906	−	1.03827i
$593$	25.5066			1.04743			0.523715	−	0.851894i	$-0.324546\pi$
$593$	25.5066			1.04743			0.523715	+	0.851894i	$0.324546\pi$
$594$	0.500000	+	5.34307i	0.0205152	+	0.219229i
$595$		0			0
$596$	−8.09017	+	5.87785i	−0.331386	+	0.240766i
$597$	−2.56231	−	7.88597i	−0.104868	−	0.322751i
$598$	−7.06231	+	21.7355i	−0.288799	+	0.888832i
$599$	−27.8885	−	20.2622i	−1.13950	−	0.827892i	−0.152446	−	0.988312i	$-0.548715\pi$
$599$	−27.8885	−	20.2622i	−1.13950	−	0.827892i	−0.987049	+	0.160420i	$0.948715\pi$
$600$		0			0
$601$	−9.07953	+	27.9439i	−0.370362	+	1.13986i	0.576193	+	0.817313i	$0.304538\pi$
$601$	−9.07953	+	27.9439i	−0.370362	+	1.13986i	−0.946555	+	0.322542i	$0.895462\pi$
$602$	2.64590	+	8.14324i	0.107839	+	0.331894i
$603$	7.04508	−	5.11855i	0.286898	−	0.208444i
$604$	−5.67376			−0.230862
$605$		0			0
$606$	−1.76393			−0.0716548
$607$	−23.3435	+	16.9600i	−0.947482	+	0.688386i	−0.950210	−	0.311610i	$-0.899132\pi$
$607$	−23.3435	+	16.9600i	−0.947482	+	0.688386i	0.00272816	+	0.999996i	$0.499132\pi$
$608$	2.88854	+	8.89002i	0.117146	+	0.360538i
$609$	3.35410	−	10.3229i	0.135915	−	0.418304i
$610$		0			0
$611$	14.0729	+	10.2246i	0.569331	+	0.413643i
$612$	1.42705	−	4.39201i	0.0576851	−	0.177537i
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	0.977067	+	0.212932i	$0.0683012\pi$
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	−0.665306	+	0.746571i	$0.731699\pi$
$614$	−20.7984	+	15.1109i	−0.839354	+	0.609826i
$615$		0			0
$616$	−2.07295	−	22.1518i	−0.0835215	−	0.892522i
$617$	9.05573			0.364570			0.182285	−	0.983246i	$-0.441651\pi$
$617$	9.05573			0.364570			0.182285	+	0.983246i	$0.441651\pi$
$618$	−19.8713	+	14.4374i	−0.799342	+	0.580756i
$619$	0.815595	+	2.51014i	0.0327815	+	0.100891i	0.966108	−	0.258136i	$-0.0831084\pi$
$619$	0.815595	+	2.51014i	0.0327815	+	0.100891i	−0.933327	+	0.359028i	$0.883108\pi$
$620$		0			0
$621$	−6.16312	−	4.47777i	−0.247317	−	0.179687i
$622$	24.2533	+	17.6210i	0.972468	+	0.706540i
$623$	2.37539	−	7.31069i	0.0951679	−	0.292897i
$624$	2.78115	+	8.55951i	0.111335	+	0.342655i
$625$		0			0
$626$	49.6869			1.98589
$627$	6.05573	+	6.88191i	0.241842	+	0.274837i
$628$	11.0000			0.438948
$629$	−53.5238	+	38.8873i	−2.13413	+	1.55054i
$630$		0			0
$631$	−15.1976	+	46.7733i	−0.605005	+	1.86201i	−0.108251	+	0.994124i	$0.534525\pi$
$631$	−15.1976	+	46.7733i	−0.605005	+	1.86201i	−0.496754	+	0.867891i	$0.665475\pi$
$632$	−13.6803	−	9.93935i	−0.544175	−	0.395366i
$633$	−10.6631	−	7.74721i	−0.423821	−	0.307924i
$634$	4.59017	−	14.1271i	0.182299	−	0.561058i
$635$		0			0
$636$	0.236068	−	0.171513i	0.00936070	−	0.00680095i
$637$	−3.70820			−0.146924
$638$	−17.8262	+	7.69421i	−0.705748	+	0.304617i
$639$	1.47214			0.0582368
$640$		0			0
$641$	12.1008	+	37.2425i	0.477953	+	1.47099i	0.841933	+	0.539582i	$0.181418\pi$
$641$	12.1008	+	37.2425i	0.477953	+	1.47099i	−0.363979	+	0.931407i	$0.618582\pi$
$642$	8.20820	−	25.2623i	0.323952	−	0.997022i
$643$	−16.4894	−	11.9802i	−0.650277	−	0.472454i	0.213089	−	0.977033i	$-0.431648\pi$
$643$	−16.4894	−	11.9802i	−0.650277	−	0.472454i	−0.863365	+	0.504579i	$0.831648\pi$
$644$	−11.4271	−	8.30224i	−0.450289	−	0.327154i
$645$		0			0
$646$	−10.3262	−	31.7809i	−0.406280	−	1.25040i
$647$	−10.6803	+	7.75972i	−0.419887	+	0.305066i	−0.777593	−	0.628768i	$-0.783559\pi$
$647$	−10.6803	+	7.75972i	−0.419887	+	0.305066i	0.357705	+	0.933835i	$0.383559\pi$
$648$	−2.23607			−0.0878410
$649$	−13.4164	−	3.01217i	−0.526640	−	0.118238i
$650$		0			0
$651$	21.4894	−	15.6129i	0.842234	−	0.611919i
$652$	3.26393	+	10.0453i	0.127825	+	0.393406i
$653$	−1.52786	+	4.70228i	−0.0597899	+	0.184015i	−0.976491	−	0.215560i	$-0.930842\pi$
$653$	−1.52786	+	4.70228i	−0.0597899	+	0.184015i	0.916701	+	0.399575i	$0.130842\pi$
$654$	−19.6353	−	14.2658i	−0.767799	−	0.557839i
$655$		0			0
$656$	0.354102	−	1.08981i	0.0138254	−	0.0425501i
$657$	−2.11803	−	6.51864i	−0.0826324	−	0.254316i
$658$	−36.8435	+	26.7683i	−1.43631	+	1.04354i
$659$	−44.0689			−1.71668			−0.858340	−	0.513081i	$-0.828504\pi$
$659$	−44.0689			−1.71668			−0.858340	+	0.513081i	$0.828504\pi$
$660$		0			0
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$	21.4894	−	15.6129i	0.835208	−	0.606814i
$663$	−4.28115	−	13.1760i	−0.166266	−	0.511715i
$664$	−7.17376	+	22.0786i	−0.278396	+	0.856815i
$665$		0			0
$666$	−11.5902	−	8.42075i	−0.449110	−	0.326297i
$667$	8.51722	−	26.2133i	0.329788	−	1.01498i
$668$	−4.00000	−	12.3107i	−0.154765	−	0.476317i
$669$	10.2812	−	7.46969i	0.397492	−	0.288795i
$670$		0			0
$671$	−9.74671	+	16.4455i	−0.376268	+	0.634871i
$672$	−10.1459			−0.391387
$673$	18.2082	−	13.2290i	0.701875	−	0.509942i	−0.178668	−	0.983910i	$-0.557179\pi$
$673$	18.2082	−	13.2290i	0.701875	−	0.509942i	0.880542	+	0.473968i	$0.157179\pi$
$674$	−11.8541	−	36.4832i	−0.456603	−	1.40528i
$675$		0			0
$676$	4.78115	+	3.47371i	0.183890	+	0.133604i
$677$	6.09017	+	4.42477i	0.234064	+	0.170058i	0.698635	−	0.715479i	$-0.253791\pi$
$677$	6.09017	+	4.42477i	0.234064	+	0.170058i	−0.464570	+	0.885536i	$0.653791\pi$
$678$	4.23607	−	13.0373i	0.162685	−	0.500694i
$679$	−9.65654	−	29.7198i	−0.370584	−	1.14054i
$680$		0			0
$681$	−14.5623			−0.558029
$682$	−46.3607	−	10.4086i	−1.77524	−	0.398567i
$683$	−12.7082			−0.486266			−0.243133	−	0.969993i	$-0.578175\pi$
$683$	−12.7082			−0.486266			−0.243133	+	0.969993i	$0.578175\pi$
$684$	1.38197	−	1.00406i	0.0528408	−	0.0383911i
$685$		0			0
$686$	−7.50000	+	23.0826i	−0.286351	+	0.881299i
$687$	8.09017	+	5.87785i	0.308659	+	0.224254i
$688$	6.92705	+	5.03280i	0.264091	+	0.191874i
$689$	0.270510	−	0.832544i	0.0103056	−	0.0317174i
$690$		0			0
$691$	19.9894	−	14.5231i	0.760431	−	0.552485i	−0.138612	−	0.990347i	$-0.544264\pi$
$691$	19.9894	−	14.5231i	0.760431	−	0.552485i	0.899042	+	0.437861i	$0.144264\pi$
$692$	−3.38197			−0.128563
$693$	−9.13525	+	3.94298i	−0.347020	+	0.149782i
$694$	−19.9443			−0.757074
$695$		0			0
$696$	−2.50000	−	7.69421i	−0.0947623	−	0.291648i
$697$	−0.545085	+	1.67760i	−0.0206466	+	0.0635436i
$698$	−37.8885	−	27.5276i	−1.43410	−	1.04194i
$699$	5.11803	+	3.71847i	0.193582	+	0.140645i
$700$		0			0
$701$	4.39919	+	13.5393i	0.166155	+	0.511373i	0.999120	−	0.0419539i	$-0.0133582\pi$
$701$	4.39919	+	13.5393i	0.166155	+	0.511373i	−0.832965	+	0.553326i	$0.813358\pi$
$702$	2.42705	−	1.76336i	0.0916031	−	0.0665536i
$703$	−24.4721			−0.922984
$704$	−9.28115	−	10.5474i	−0.349797	−	0.397519i
$705$		0			0
$706$	11.6353	−	8.45351i	0.437899	−	0.318152i
$707$	−1.01064	−	3.11044i	−0.0380091	−	0.116980i
$708$	−0.791796	+	2.43690i	−0.0297575	+	0.0915842i
$709$	7.66312	+	5.56758i	0.287794	+	0.209095i	0.722310	−	0.691569i	$-0.243080\pi$
$709$	7.66312	+	5.56758i	0.287794	+	0.209095i	−0.434516	+	0.900664i	$0.643080\pi$
$710$		0			0
$711$	−2.33688	+	7.19218i	−0.0876399	+	0.269728i
$712$	−1.77051	−	5.44907i	−0.0663527	−	0.204212i
$713$	54.5689	−	39.6466i	2.04362	−	1.48478i
$714$	36.2705			1.35739
$715$		0			0
$716$	−12.4377			−0.464818
$717$	16.7082	−	12.1392i	0.623979	−	0.453348i
$718$	9.10739	+	28.0297i	0.339885	+	1.04606i
$719$	−8.05166	+	24.7805i	−0.300276	+	0.924156i	0.681121	+	0.732170i	$0.261493\pi$
$719$	−8.05166	+	24.7805i	−0.300276	+	0.924156i	−0.981398	+	0.191985i	$0.938507\pi$
$720$		0			0
$721$	−36.8435	−	26.7683i	−1.37212	−	0.996905i
$722$	−5.68034	+	17.4823i	−0.211400	+	0.650623i
$723$	2.42705	+	7.46969i	0.0902630	+	0.277801i
$724$	6.39919	−	4.64928i	0.237824	−	0.172789i
$725$		0			0
$726$	16.0902	+	7.60845i	0.597162	+	0.282376i
$727$	0.236068			0.00875528			0.00437764	−	0.999990i	$-0.498607\pi$
$727$	0.236068			0.00875528			0.00437764	+	0.999990i	$0.498607\pi$
$728$	−10.0623	+	7.31069i	−0.372934	+	0.270952i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−10.6631	−	7.74721i	−0.394390	−	0.286541i
$732$	2.88197	+	2.09387i	0.106521	+	0.0773917i
$733$	1.98936	−	6.12261i	0.0734786	−	0.226144i	−0.907572	−	0.419897i	$-0.862066\pi$
$733$	1.98936	−	6.12261i	0.0734786	−	0.226144i	0.981050	+	0.193753i	$0.0620661\pi$
$734$	−9.41641	−	28.9807i	−0.347566	−	1.06970i
$735$		0			0
$736$	−25.7639			−0.949671
$737$	−2.69098	−	28.7562i	−0.0991236	−	1.05925i
$738$	−0.381966			−0.0140604
$739$	−35.8156	+	26.0216i	−1.31750	+	0.957218i	−0.317538	+	0.948245i	$0.602856\pi$
$739$	−35.8156	+	26.0216i	−1.31750	+	0.957218i	−0.999960	+	0.00897282i	$0.997144\pi$
$740$		0			0
$741$	1.58359	−	4.87380i	0.0581747	−	0.179043i
$742$	1.85410	+	1.34708i	0.0680662	+	0.0494530i
$743$	30.0795	+	21.8541i	1.10351	+	0.801748i	0.981629	−	0.190797i	$-0.0611073\pi$
$743$	30.0795	+	21.8541i	1.10351	+	0.801748i	0.121881	+	0.992545i	$0.461107\pi$
$744$	6.11803	−	18.8294i	0.224298	−	0.690318i
$745$		0			0
$746$	−22.7984	+	16.5640i	−0.834708	+	0.606451i
$747$	10.3820			0.379856
$748$	−10.1180	−	11.4984i	−0.369952	−	0.420424i
$749$	49.2492			1.79953
$750$		0			0
$751$	−5.39919	−	16.6170i	−0.197019	−	0.606363i	−0.999947	−	0.0102865i	$-0.996726\pi$
$751$	−5.39919	−	16.6170i	−0.197019	−	0.606363i	0.802928	−	0.596076i	$-0.203274\pi$
$752$	−14.0729	+	43.3121i	−0.513188	+	1.57943i
$753$	16.6353	+	12.0862i	0.606222	+	0.440446i
$754$	8.78115	+	6.37988i	0.319791	+	0.232342i
$755$		0			0
$756$	0.572949	+	1.76336i	0.0208380	+	0.0641326i
$757$	31.5795	−	22.9439i	1.14778	−	0.833909i	0.159594	−	0.987183i	$-0.448982\pi$
$757$	31.5795	−	22.9439i	1.14778	−	0.833909i	0.988184	+	0.153274i	$0.0489816\pi$
$758$	−37.5623			−1.36432
$759$	−23.1976	+	10.0126i	−0.842018	+	0.363434i
$760$		0			0
$761$	0.0901699	−	0.0655123i	0.00326866	−	0.00237482i	−0.586150	−	0.810203i	$-0.699357\pi$
$761$	0.0901699	−	0.0655123i	0.00326866	−	0.00237482i	0.589418	+	0.807828i	$0.299357\pi$
$762$	3.30902	+	10.1841i	0.119873	+	0.368931i
$763$	13.9058	−	42.7975i	0.503422	−	1.54938i
$764$	−7.87132	−	5.71885i	−0.284774	−	0.206901i
$765$		0			0
$766$	−10.7639	+	33.1280i	−0.388917	+	1.19696i
$767$	2.37539	+	7.31069i	0.0857703	+	0.263974i
$768$	−10.9721	+	7.97172i	−0.395923	+	0.287655i
$769$	−24.1459			−0.870723			−0.435362	−	0.900256i	$-0.643380\pi$
$769$	−24.1459			−0.870723			−0.435362	+	0.900256i	$0.643380\pi$
$770$		0			0
$771$	10.0344			0.361382
$772$	−9.23607	+	6.71040i	−0.332413	+	0.241512i
$773$	−6.69098	−	20.5927i	−0.240658	−	0.740669i	−0.996320	−	0.0857076i	$-0.972685\pi$
$773$	−6.69098	−	20.5927i	−0.240658	−	0.740669i	0.755662	−	0.654961i	$-0.227315\pi$
$774$	0.881966	−	2.71441i	0.0317016	−	0.0975675i
$775$		0			0
$776$	−18.8435	−	13.6906i	−0.676441	−	0.491463i
$777$	8.20820	−	25.2623i	0.294468	−	0.906278i
$778$	−9.04508	−	27.8379i	−0.324282	−	0.998037i
$779$	−0.527864	+	0.383516i	−0.0189127	+	0.0137409i
$780$		0			0
$781$	2.48936	−	4.20025i	0.0890762	−	0.150297i
$782$	92.1033			3.29361
$783$	−2.92705	+	2.12663i	−0.104604	+	0.0759994i
$784$	−3.00000	−	9.23305i	−0.107143	−	0.329752i
$785$		0			0
$786$	−9.59017	−	6.96767i	−0.342070	−	0.248528i
$787$	20.7254	+	15.0579i	0.738782	+	0.536756i	0.892329	−	0.451385i	$-0.149070\pi$
$787$	20.7254	+	15.0579i	0.738782	+	0.536756i	−0.153548	+	0.988141i	$0.549070\pi$
$788$	1.85410	−	5.70634i	0.0660496	−	0.203280i
$789$	−3.43769	−	10.5801i	−0.122385	−	0.376663i
$790$		0			0
$791$	25.4164			0.903703
$792$	−3.78115	+	6.37988i	−0.134357	+	0.226699i
$793$	10.6869			0.379504
$794$	25.6074	−	18.6049i	0.908772	−	0.660262i
$795$		0			0
$796$	−1.58359	+	4.87380i	−0.0561289	+	0.172747i
$797$	33.4894	+	24.3314i	1.18625	+	0.861864i	0.992863	−	0.119258i	$-0.0380516\pi$
$797$	33.4894	+	24.3314i	1.18625	+	0.861864i	0.193391	+	0.981122i	$0.438052\pi$
$798$	10.8541	+	7.88597i	0.384231	+	0.279160i
$799$	21.6631	−	66.6722i	0.766386	−	2.35869i
$800$		0			0
$801$	−2.07295	+	1.50609i	−0.0732441	+	0.0532149i
$802$	1.32624			0.0468311
$803$	−22.1803	−	4.97980i	−0.782727	−	0.175733i
$804$	−5.38197			−0.189807
$805$		0			0
$806$	8.20820	+	25.2623i	0.289122	+	0.889825i
$807$	−0.163119	+	0.502029i	−0.00574206	+	0.0176722i
$808$	−1.97214	−	1.43284i	−0.0693795	−	0.0504072i
$809$	−1.80902	−	1.31433i	−0.0636017	−	0.0462093i	0.555530	−	0.831496i	$-0.312515\pi$
$809$	−1.80902	−	1.31433i	−0.0636017	−	0.0462093i	−0.619132	+	0.785287i	$0.712515\pi$
$810$		0			0
$811$	−6.09017	−	18.7436i	−0.213855	−	0.658177i	−0.999233	−	0.0391610i	$-0.987531\pi$
$811$	−6.09017	−	18.7436i	−0.213855	−	0.658177i	0.785378	−	0.619016i	$-0.212469\pi$
$812$	−5.42705	+	3.94298i	−0.190452	+	0.138372i
$813$	−22.2705			−0.781061
$814$	−43.6246	+	18.8294i	−1.52904	+	0.659969i
$815$		0			0
$816$	29.3435	−	21.3193i	1.02723	−	0.746324i
$817$	−1.50658	−	4.63677i	−0.0527085	−	0.162220i
$818$	−5.06231	+	15.5802i	−0.176999	+	0.544748i
$819$	4.50000	+	3.26944i	0.157243	+	0.114244i
$820$		0			0
$821$	17.4271	−	53.6349i	0.608208	−	1.87187i	0.135191	−	0.990820i	$-0.456835\pi$
$821$	17.4271	−	53.6349i	0.608208	−	1.87187i	0.473018	−	0.881053i	$-0.343165\pi$
$822$	6.39919	+	19.6947i	0.223197	+	0.686931i
$823$	−2.80902	+	2.04087i	−0.0979162	+	0.0711403i	−0.635666	−	0.771964i	$-0.719274\pi$
$823$	−2.80902	+	2.04087i	−0.0979162	+	0.0711403i	0.537750	+	0.843104i	$0.319274\pi$
$824$	−33.9443			−1.18250
$825$		0			0
$826$	−20.1246			−0.700225
$827$	−37.9164	+	27.5479i	−1.31848	+	0.957934i	−0.318533	+	0.947912i	$0.603190\pi$
$827$	−37.9164	+	27.5479i	−1.31848	+	0.957934i	−0.999950	+	0.0100219i	$0.996810\pi$
$828$	1.45492	+	4.47777i	0.0505618	+	0.155613i
$829$	−7.82624	+	24.0867i	−0.271816	+	0.836565i	0.718228	+	0.695808i	$0.244954\pi$
$829$	−7.82624	+	24.0867i	−0.271816	+	0.836565i	−0.990044	+	0.140757i	$0.955046\pi$
$830$		0			0
$831$	−19.3992	−	14.0943i	−0.672950	−	0.488927i
$832$	−2.42705	+	7.46969i	−0.0841429	+	0.258965i
$833$	4.61803	+	14.2128i	0.160005	+	0.492446i
$834$	−7.66312	+	5.56758i	−0.265352	+	0.192790i
$835$		0			0
$836$	−0.527864	−	5.64083i	−0.0182566	−	0.195092i
$837$	−8.85410			−0.306043
$838$	−24.7984	+	18.0171i	−0.856646	+	0.622389i
$839$	7.66312	+	23.5847i	0.264560	+	0.814233i	0.991794	+	0.127843i	$0.0408054\pi$
$839$	7.66312	+	23.5847i	0.264560	+	0.814233i	−0.727234	+	0.686389i	$0.759195\pi$
$840$		0			0
$841$	12.8713	+	9.35156i	0.443839	+	0.322468i
$842$	9.51722	+	6.91467i	0.327985	+	0.238295i
$843$	−1.02786	+	3.16344i	−0.0354015	+	0.108955i
$844$	2.51722	+	7.74721i	0.0866463	+	0.266670i
$845$		0			0
$846$	15.1803			0.521911
$847$	−4.19756	+	32.7319i	−0.144230	+	1.12468i
$848$	2.29180			0.0787006
$849$	−21.9164	+	15.9232i	−0.752169	+	0.546483i
$850$		0			0
$851$	20.8435	−	64.1496i	0.714505	−	2.19902i
$852$	−0.736068	−	0.534785i	−0.0252173	−	0.0183214i
$853$	43.4336	+	31.5564i	1.48714	+	1.08047i	0.975168	+	0.221467i	$0.0710846\pi$
$853$	43.4336	+	31.5564i	1.48714	+	1.08047i	0.511971	+	0.859003i	$0.328915\pi$
$854$	−8.64590	+	26.6093i	−0.295857	+	0.910553i
$855$		0			0
$856$	29.6976	−	21.5765i	1.01504	−	0.737471i
$857$	−10.0902			−0.344674			−0.172337	−	0.985038i	$-0.555132\pi$
$857$	−10.0902			−0.344674			−0.172337	+	0.985038i	$0.555132\pi$
$858$	−0.927051	−	9.90659i	−0.0316490	−	0.338205i
$859$	−2.56231			−0.0874247			−0.0437124	−	0.999044i	$-0.513919\pi$
$859$	−2.56231			−0.0874247			−0.0437124	+	0.999044i	$0.513919\pi$
$860$		0			0
$861$	−0.218847	−	0.673542i	−0.00745829	−	0.0229542i
$862$	8.07295	−	24.8460i	0.274966	−	0.846258i
$863$	28.0066	+	20.3480i	0.953355	+	0.692653i	0.951598	−	0.307346i	$-0.0994407\pi$
$863$	28.0066	+	20.3480i	0.953355	+	0.692653i	0.00175700	+	0.999998i	$0.499441\pi$
$864$	2.73607	+	1.98787i	0.0930829	+	0.0676287i
$865$		0			0
$866$	−13.5902	−	41.8262i	−0.461813	−	1.42131i
$867$	−31.4164	+	22.8254i	−1.06696	+	0.775190i
$868$	−16.4164			−0.557209
$869$	16.5689	+	18.8294i	0.562061	+	0.638743i
$870$		0			0
$871$	−13.0623	+	9.49032i	−0.442599	+	0.321567i
$872$	−10.3647	−	31.8994i	−0.350995	−	1.08025i
$873$	−3.21885	+	9.90659i	−0.108941	+	0.335287i
$874$	27.5623	+	20.0252i	0.932309	+	0.677362i
$875$		0			0
$876$	−1.30902	+	4.02874i	−0.0442276	+	0.136119i
$877$	9.14183	+	28.1357i	0.308698	+	0.950074i	0.978271	+	0.207328i	$0.0664768\pi$
$877$	9.14183	+	28.1357i	0.308698	+	0.950074i	−0.669574	+	0.742746i	$0.733523\pi$
$878$	−9.73607	+	7.07367i	−0.328576	+	0.238725i
$879$	−19.4164			−0.654899
$880$		0			0
$881$	−34.1803			−1.15156			−0.575782	−	0.817603i	$-0.695302\pi$
$881$	−34.1803			−1.15156			−0.575782	+	0.817603i	$0.695302\pi$
$882$	−2.61803	+	1.90211i	−0.0881538	+	0.0640475i
$883$	5.15654	+	15.8702i	0.173531	+	0.534075i	0.999563	−	0.0295485i	$-0.00940696\pi$
$883$	5.15654	+	15.8702i	0.173531	+	0.534075i	−0.826032	+	0.563623i	$0.809407\pi$
$884$	−2.64590	+	8.14324i	−0.0889912	+	0.273887i
$885$		0			0
$886$	36.0066	+	26.1603i	1.20966	+	0.878873i
$887$	−5.61803	+	17.2905i	−0.188635	+	0.580559i	−0.999992	−	0.00399187i	$-0.998729\pi$
$887$	−5.61803	+	17.2905i	−0.188635	+	0.580559i	0.811357	+	0.584551i	$0.198729\pi$
$888$	−6.11803	−	18.8294i	−0.205308	−	0.631872i
$889$	−16.0623	+	11.6699i	−0.538712	+	0.391398i
$890$		0			0
$891$	3.23607	+	0.726543i	0.108412	+	0.0243401i
$892$	−7.85410			−0.262975
$893$	20.9787	−	15.2419i	0.702026	−	0.510052i
$894$	8.09017	+	24.8990i	0.270576	+	0.832747i
$895$		0			0
$896$	−33.0517	−	24.0134i	−1.10418	−	0.802233i
$897$	11.4271	+	8.30224i	0.381538	+	0.277204i
$898$	7.23607	−	22.2703i	0.241471	−	0.743170i
$899$	−9.89919	−	30.4666i	−0.330156	−	1.01612i
$900$		0			0
$901$	−3.52786			−0.117530
$902$	−0.645898	+	1.08981i	−0.0215061	+	0.0362868i
$903$	5.29180			0.176100
$904$	15.3262	−	11.1352i	0.509743	−	0.370350i
$905$		0			0
$906$	−4.59017	+	14.1271i	−0.152498	+	0.469341i
$907$	43.5517	+	31.6421i	1.44611	+	1.05066i	0.986721	+	0.162424i	$0.0519313\pi$
$907$	43.5517	+	31.6421i	1.44611	+	1.05066i	0.459388	+	0.888236i	$0.348069\pi$
$908$	7.28115	+	5.29007i	0.241634	+	0.175557i
$909$	−0.336881	+	1.03681i	−0.0111736	+	0.0343889i
$910$		0			0
$911$	−43.7148	+	31.7606i	−1.44834	+	1.05228i	−0.462119	+	0.886818i	$0.652911\pi$
$911$	−43.7148	+	31.7606i	−1.44834	+	1.05228i	−0.986217	+	0.165459i	$0.947089\pi$
$912$	13.4164			0.444262
$913$	17.5557	−	29.6215i	0.581010	−	0.980329i
$914$	38.0689			1.25921
$915$		0			0
$916$	−1.90983	−	5.87785i	−0.0631026	−	0.194210i
$917$	6.79180	−	20.9030i	0.224285	−	0.690278i
$918$	−9.78115	−	7.10642i	−0.322826	−	0.234547i
$919$	−12.8262	−	9.31881i	−0.423099	−	0.307399i	0.355785	−	0.934568i	$-0.384214\pi$
$919$	−12.8262	−	9.31881i	−0.423099	−	0.307399i	−0.778883	+	0.627169i	$0.784214\pi$
$920$		0			0
$921$	4.90983	+	15.1109i	0.161784	+	0.497921i
$922$	12.0172	−	8.73102i	0.395766	−	0.287541i
$923$	−2.72949			−0.0898423
$924$	6.00000	+	1.34708i	0.197386	+	0.0443158i
$925$		0			0
$926$	12.1631	−	8.83702i	0.399705	−	0.290403i
$927$	4.69098	+	14.4374i	0.154072	+	0.474185i
$928$	−3.78115	+	11.6372i	−0.124122	+	0.382010i
$929$	44.0689	+	32.0179i	1.44585	+	1.05047i	0.986778	+	0.162076i	$0.0518191\pi$
$929$	44.0689	+	32.0179i	1.44585	+	1.05047i	0.459075	+	0.888398i	$0.348181\pi$
$930$		0			0
$931$	−1.70820	+	5.25731i	−0.0559841	+	0.172301i
$932$	−1.20820	−	3.71847i	−0.0395760	−	0.121803i
$933$	14.9894	−	10.8904i	0.490730	−	0.356536i
$934$	−8.03444			−0.262895
$935$		0			0
$936$	4.14590			0.135513
$937$	−29.4615	+	21.4050i	−0.962465	+	0.699272i	−0.953722	−	0.300690i	$-0.902783\pi$
$937$	−29.4615	+	21.4050i	−0.962465	+	0.699272i	−0.00874309	+	0.999962i	$0.502783\pi$
$938$	−13.0623	−	40.2016i	−0.426499	−	1.31263i
$939$	9.48936	−	29.2052i	0.309673	−	0.953077i
$940$		0			0
$941$	2.42705	+	1.76336i	0.0791196	+	0.0574838i	0.626642	−	0.779307i	$-0.284429\pi$
$941$	2.42705	+	1.76336i	0.0791196	+	0.0574838i	−0.547522	+	0.836791i	$0.684429\pi$
$942$	8.89919	−	27.3889i	0.289951	−	0.892378i
$943$	−0.555728	−	1.71036i	−0.0180970	−	0.0556968i
$944$	−16.2812	+	11.8290i	−0.529906	+	0.385000i
$945$		0			0
$946$	−6.25329	−	7.10642i	−0.203312	−	0.231050i
$947$	21.4934			0.698442			0.349221	−	0.937040i	$-0.386446\pi$
$947$	21.4934			0.698442			0.349221	+	0.937040i	$0.386446\pi$
$948$	3.78115	−	2.74717i	0.122806	−	0.0892239i
$949$	3.92705	+	12.0862i	0.127477	+	0.392335i
$950$		0			0
$951$	−7.42705	−	5.39607i	−0.240839	−	0.174980i
$952$	40.5517	+	29.4625i	1.31429	+	0.954885i
$953$	−17.2188	+	52.9942i	−0.557773	+	1.71665i	0.130732	+	0.991418i	$0.458267\pi$
$953$	−17.2188	+	52.9942i	−0.557773	+	1.71665i	−0.688505	+	0.725232i	$0.741733\pi$
$954$	−0.236068	−	0.726543i	−0.00764298	−	0.0235227i
$955$		0			0
$956$	−12.7639			−0.412815
$957$	1.11803	+	11.9475i	0.0361409	+	0.386207i
$958$	11.9098			0.384789
$959$	−31.0623	+	22.5681i	−1.00305	+	0.728762i
$960$		0			0
$961$	14.6459	−	45.0754i	0.472448	−	1.45405i
$962$	21.4894	+	15.6129i	0.692845	+	0.503381i
$963$	−13.2812	−	9.64932i	−0.427979	−	0.310945i
$964$	1.50000	−	4.61653i	0.0483117	−	0.148688i
$965$		0			0
$966$	−29.9164	+	21.7355i	−0.962545	+	0.699330i
$967$	−5.21478			−0.167696			−0.0838480	−	0.996479i	$-0.526721\pi$
$967$	−5.21478			−0.167696			−0.0838480	+	0.996479i	$0.526721\pi$
$968$	11.8090	+	21.5765i	0.379556	+	0.693496i
$969$	−20.6525			−0.663453
$970$		0			0
$971$	18.3820	+	56.5739i	0.589905	+	1.81554i	0.578608	+	0.815606i	$0.303596\pi$
$971$	18.3820	+	56.5739i	0.589905	+	1.81554i	0.0112975	+	0.999936i	$0.496404\pi$
$972$	0.190983	−	0.587785i	0.00612578	−	0.0188532i
$973$	−14.2082	−	10.3229i	−0.455494	−	0.330936i
$974$	1.66312	+	1.20833i	0.0532898	+	0.0387173i
$975$		0			0
$976$	8.64590	+	26.6093i	0.276748	+	0.851744i
$977$	29.3435	−	21.3193i	0.938780	−	0.682064i	−0.00934637	−	0.999956i	$-0.502975\pi$
$977$	29.3435	−	21.3193i	0.938780	−	0.682064i	0.948127	+	0.317892i	$0.102975\pi$
$978$	27.6525			0.884229
$979$	0.791796	+	8.46124i	0.0253059	+	0.270422i
$980$		0			0
$981$	−12.1353	+	8.81678i	−0.387449	+	0.281498i
$982$	−6.92705	−	21.3193i	−0.221051	−	0.680325i
$983$	−0.270510	+	0.832544i	−0.00862792	+	0.0265540i	−0.955278	−	0.295710i	$-0.904444\pi$
$983$	−0.270510	+	0.832544i	−0.00862792	+	0.0265540i	0.946650	+	0.322264i	$0.104444\pi$
$984$	−0.427051	−	0.310271i	−0.0136139	−	0.00989107i
$985$		0			0
$986$	13.5172	−	41.6017i	0.430476	−	1.32487i
$987$	8.69756	+	26.7683i	0.276846	+	0.852046i
$988$	−2.56231	+	1.86162i	−0.0815178	+	0.0592262i
$989$	13.4377			0.427294
$990$		0			0
$991$	−48.4508			−1.53909			−0.769546	−	0.638591i	$-0.779517\pi$
$991$	−48.4508			−1.53909			−0.769546	+	0.638591i	$0.779517\pi$
$992$	−24.2254	+	17.6008i	−0.769158	+	0.558826i
$993$	−5.07295	−	15.6129i	−0.160985	−	0.495461i
$994$	2.20820	−	6.79615i	0.0700400	−	0.215561i
$995$		0			0
$996$	−5.19098	−	3.77147i	−0.164483	−	0.119504i
$997$	4.54508	−	13.9883i	0.143944	−	0.443015i	−0.852929	−	0.522026i	$-0.825176\pi$
$997$	4.54508	−	13.9883i	0.143944	−	0.443015i	0.996874	+	0.0790113i	$0.0251763\pi$
$998$	5.91641	+	18.2088i	0.187281	+	0.576390i
$999$	−7.16312	+	5.20431i	−0.226631	+	0.164657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.a.751.1	yes	4
5.2	odd	4		825.2.bx.a.124.1		8
5.3	odd	4		825.2.bx.a.124.2		8
5.4	even	2		825.2.n.e.751.1	yes	4
11.2	odd	10		9075.2.a.bb.1.1		2
11.4	even	5	inner	825.2.n.a.301.1	✓	4
11.9	even	5		9075.2.a.bz.1.2		2
55.4	even	10		825.2.n.e.301.1	yes	4
55.9	even	10		9075.2.a.y.1.1		2
55.24	odd	10		9075.2.a.bu.1.2		2
55.37	odd	20		825.2.bx.a.499.2		8
55.48	odd	20		825.2.bx.a.499.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.a.301.1	✓	4	11.4	even	5	inner
825.2.n.a.751.1	yes	4	1.1	even	1	trivial
825.2.n.e.301.1	yes	4	55.4	even	10
825.2.n.e.751.1	yes	4	5.4	even	2
825.2.bx.a.124.1		8	5.2	odd	4
825.2.bx.a.124.2		8	5.3	odd	4
825.2.bx.a.499.1		8	55.48	odd	20
825.2.bx.a.499.2		8	55.37	odd	20
9075.2.a.y.1.1		2	55.9	even	10
9075.2.a.bb.1.1		2	11.2	odd	10
9075.2.a.bu.1.2		2	55.24	odd	10
9075.2.a.bz.1.2		2	11.9	even	5

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)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.30902 - 0.951057i) q^{6} +(0.927051 - 2.85317i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.30902 - 0.951057i) q^{6} +(0.927051 - 2.85317i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 + 3.30220i) q^{11} +0.618034 q^{12} +(1.50000 - 1.08981i) q^{13} +(1.50000 + 4.61653i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-6.04508 - 4.39201i) q^{17} +(0.500000 - 1.53884i) q^{18} +(-0.854102 - 2.62866i) q^{19} +3.00000 q^{21} +(-3.54508 - 4.02874i) q^{22} +7.61803 q^{23} +(1.80902 - 1.31433i) q^{24} +(-0.927051 + 2.85317i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.50000 - 1.08981i) q^{28} +(1.11803 - 3.44095i) q^{29} +(7.16312 - 5.20431i) q^{31} -3.38197 q^{32} +(-3.04508 + 1.31433i) q^{33} +12.0902 q^{34} +(0.190983 + 0.587785i) q^{36} +(2.73607 - 8.42075i) q^{37} +(3.61803 + 2.62866i) q^{38} +(1.50000 + 1.08981i) q^{39} +(-0.0729490 - 0.224514i) q^{41} +(-3.92705 + 2.85317i) q^{42} +1.76393 q^{43} +(2.00000 + 0.449028i) q^{44} +(-9.97214 + 7.24518i) q^{46} +(2.89919 + 8.92278i) q^{47} +(-1.50000 + 4.61653i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(2.30902 - 7.10642i) q^{51} +(-0.354102 - 1.08981i) q^{52} +(0.381966 - 0.277515i) q^{53} +1.61803 q^{54} -6.70820 q^{56} +(2.23607 - 1.62460i) q^{57} +(1.80902 + 5.56758i) q^{58} +(-1.28115 + 3.94298i) q^{59} +(4.66312 + 3.38795i) q^{61} +(-4.42705 + 13.6251i) q^{62} +(0.927051 + 2.85317i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(2.73607 - 4.61653i) q^{66} -8.70820 q^{67} +(-3.73607 + 2.71441i) q^{68} +(2.35410 + 7.24518i) q^{69} +(-1.19098 - 0.865300i) q^{71} +(1.80902 + 1.31433i) q^{72} +(-2.11803 + 6.51864i) q^{73} +(4.42705 + 13.6251i) q^{74} -1.70820 q^{76} +(9.70820 + 2.17963i) q^{77} -3.00000 q^{78} +(6.11803 - 4.44501i) q^{79} +(0.309017 - 0.951057i) q^{81} +(0.309017 + 0.224514i) q^{82} +(-8.39919 - 6.10237i) q^{83} +(0.572949 - 1.76336i) q^{84} +(-2.30902 + 1.67760i) q^{86} +3.61803 q^{87} +(6.80902 - 2.93893i) q^{88} +2.56231 q^{89} +(-1.71885 - 5.29007i) q^{91} +(1.45492 - 4.47777i) q^{92} +(7.16312 + 5.20431i) q^{93} +(-12.2812 - 8.92278i) q^{94} +(-1.04508 - 3.21644i) q^{96} +(8.42705 - 6.12261i) q^{97} +3.23607 q^{98} +(-2.19098 - 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{6} - 3 q^{7} - 5 q^{8} - q^{9} - q^{11} - 2 q^{12} + 6 q^{13} + 6 q^{14} + 9 q^{16} - 13 q^{17} + 2 q^{18} + 10 q^{19} + 12 q^{21} - 3 q^{22} + 26 q^{23} + 5 q^{24} + 3 q^{26} - q^{27} - 6 q^{28} + 13 q^{31} - 18 q^{32} - q^{33} + 26 q^{34} + 3 q^{36} + 2 q^{37} + 10 q^{38} + 6 q^{39} - 7 q^{41} - 9 q^{42} + 16 q^{43} + 8 q^{44} - 22 q^{46} - 13 q^{47} - 6 q^{48} - 2 q^{49} + 7 q^{51} + 12 q^{52} + 6 q^{53} + 2 q^{54} + 5 q^{58} + 15 q^{59} + 3 q^{61} - 11 q^{62} - 3 q^{63} - 7 q^{64} + 2 q^{66} - 8 q^{67} - 6 q^{68} - 4 q^{69} - 7 q^{71} + 5 q^{72} - 4 q^{73} + 11 q^{74} + 20 q^{76} + 12 q^{77} - 12 q^{78} + 20 q^{79} - q^{81} - q^{82} - 9 q^{83} + 9 q^{84} - 7 q^{86} + 10 q^{87} + 25 q^{88} - 30 q^{89} - 27 q^{91} + 17 q^{92} + 13 q^{93} - 29 q^{94} + 7 q^{96} + 27 q^{97} + 4 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 3 * q^6 - 3 * q^7 - 5 * q^8 - q^9 - q^11 - 2 * q^12 + 6 * q^13 + 6 * q^14 + 9 * q^16 - 13 * q^17 + 2 * q^18 + 10 * q^19 + 12 * q^21 - 3 * q^22 + 26 * q^23 + 5 * q^24 + 3 * q^26 - q^27 - 6 * q^28 + 13 * q^31 - 18 * q^32 - q^33 + 26 * q^34 + 3 * q^36 + 2 * q^37 + 10 * q^38 + 6 * q^39 - 7 * q^41 - 9 * q^42 + 16 * q^43 + 8 * q^44 - 22 * q^46 - 13 * q^47 - 6 * q^48 - 2 * q^49 + 7 * q^51 + 12 * q^52 + 6 * q^53 + 2 * q^54 + 5 * q^58 + 15 * q^59 + 3 * q^61 - 11 * q^62 - 3 * q^63 - 7 * q^64 + 2 * q^66 - 8 * q^67 - 6 * q^68 - 4 * q^69 - 7 * q^71 + 5 * q^72 - 4 * q^73 + 11 * q^74 + 20 * q^76 + 12 * q^77 - 12 * q^78 + 20 * q^79 - q^81 - q^82 - 9 * q^83 + 9 * q^84 - 7 * q^86 + 10 * q^87 + 25 * q^88 - 30 * q^89 - 27 * q^91 + 17 * q^92 + 13 * q^93 - 29 * q^94 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 11 * q^99

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