LMFDB - Embedded newform 525.2.n.a.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
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			421.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	525.421
Dual form			525.2.n.a.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.23607 q^{5} +(0.500000 - 0.363271i) q^{6} -1.00000 q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.23607 q^{5} +(0.500000 - 0.363271i) q^{6} -1.00000 q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.427051 + 1.31433i) q^{10} +(-1.61803 + 4.97980i) q^{11} +(0.500000 + 1.53884i) q^{12} +(1.69098 + 5.20431i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(0.572949 + 1.76336i) q^{16} +(6.04508 - 4.39201i) q^{17} +0.618034 q^{18} +(1.11803 - 0.812299i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(2.61803 + 1.90211i) q^{22} +(-0.809017 + 2.48990i) q^{23} +2.23607 q^{24} +5.00000 q^{25} +3.38197 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.30902 - 0.951057i) q^{28} +(-5.42705 - 3.94298i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(-2.30902 + 1.67760i) q^{31} +5.61803 q^{32} +(-4.23607 + 3.07768i) q^{33} +(-1.42705 - 4.39201i) q^{34} +2.23607 q^{35} +(-0.500000 + 1.53884i) q^{36} +(2.42705 + 7.46969i) q^{37} +(-0.263932 - 0.812299i) q^{38} +(-1.69098 + 5.20431i) q^{39} +(-4.04508 + 2.93893i) q^{40} +(-1.88197 - 5.79210i) q^{41} +(-0.500000 + 0.363271i) q^{42} +1.00000 q^{43} +(-6.85410 + 4.97980i) q^{44} +(-0.690983 - 2.12663i) q^{45} +(1.30902 + 0.951057i) q^{46} +(-9.70820 - 7.05342i) q^{47} +(-0.572949 + 1.76336i) q^{48} +1.00000 q^{49} +(0.954915 - 2.93893i) q^{50} +7.47214 q^{51} +(-2.73607 + 8.42075i) q^{52} +(5.73607 + 4.16750i) q^{53} +(0.500000 + 0.363271i) q^{54} +(3.61803 - 11.1352i) q^{55} +(-1.80902 + 1.31433i) q^{56} +1.38197 q^{57} +(-3.35410 + 2.43690i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-1.11803 - 3.44095i) q^{60} +(4.23607 - 13.0373i) q^{61} +(0.545085 + 1.67760i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-3.78115 - 11.6372i) q^{65} +(1.00000 + 3.07768i) q^{66} +(8.28115 - 6.01661i) q^{67} +12.0902 q^{68} +(-2.11803 + 1.53884i) q^{69} +(0.427051 - 1.31433i) q^{70} +(6.04508 + 4.39201i) q^{71} +(1.80902 + 1.31433i) q^{72} +(0.899187 - 2.76741i) q^{73} +4.85410 q^{74} +(4.04508 + 2.93893i) q^{75} +2.23607 q^{76} +(1.61803 - 4.97980i) q^{77} +(2.73607 + 1.98787i) q^{78} +(-10.1631 - 7.38394i) q^{79} +(-1.28115 - 3.94298i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.76393 q^{82} +(-4.00000 + 2.90617i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(-13.5172 + 9.82084i) q^{85} +(0.190983 - 0.587785i) q^{86} +(-2.07295 - 6.37988i) q^{87} +(3.61803 + 11.1352i) q^{88} +(-1.38197 + 4.25325i) q^{89} -1.38197 q^{90} +(-1.69098 - 5.20431i) q^{91} +(-3.42705 + 2.48990i) q^{92} -2.85410 q^{93} +(-6.00000 + 4.35926i) q^{94} +(-2.50000 + 1.81636i) q^{95} +(4.54508 + 3.30220i) q^{96} +(-2.04508 - 1.48584i) q^{97} +(0.190983 - 0.587785i) q^{98} -5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + 2 q^{12} + 9 q^{13} - 3 q^{14} - 5 q^{15} + 9 q^{16} + 13 q^{17} - 2 q^{18} - 5 q^{20} - q^{21} + 6 q^{22} - q^{23} + 20 q^{25} + 18 q^{26} + q^{27} - 3 q^{28} - 15 q^{29} - 7 q^{31} + 18 q^{32} - 8 q^{33} + q^{34} - 2 q^{36} + 3 q^{37} - 10 q^{38} - 9 q^{39} - 5 q^{40} - 12 q^{41} - 2 q^{42} + 4 q^{43} - 14 q^{44} - 5 q^{45} + 3 q^{46} - 12 q^{47} - 9 q^{48} + 4 q^{49} + 15 q^{50} + 12 q^{51} - 2 q^{52} + 14 q^{53} + 2 q^{54} + 10 q^{55} - 5 q^{56} + 10 q^{57} - 20 q^{59} + 8 q^{61} - 9 q^{62} + q^{63} - 7 q^{64} + 5 q^{65} + 4 q^{66} + 13 q^{67} + 26 q^{68} - 4 q^{69} - 5 q^{70} + 13 q^{71} + 5 q^{72} - 21 q^{73} + 6 q^{74} + 5 q^{75} + 2 q^{77} + 2 q^{78} - 25 q^{79} + 15 q^{80} - q^{81} - 24 q^{82} - 16 q^{83} - 2 q^{84} - 25 q^{85} + 3 q^{86} - 15 q^{87} + 10 q^{88} - 10 q^{89} - 10 q^{90} - 9 q^{91} - 7 q^{92} + 2 q^{93} - 24 q^{94} - 10 q^{95} + 7 q^{96} + 3 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9 + 5 * q^10 - 2 * q^11 + 2 * q^12 + 9 * q^13 - 3 * q^14 - 5 * q^15 + 9 * q^16 + 13 * q^17 - 2 * q^18 - 5 * q^20 - q^21 + 6 * q^22 - q^23 + 20 * q^25 + 18 * q^26 + q^27 - 3 * q^28 - 15 * q^29 - 7 * q^31 + 18 * q^32 - 8 * q^33 + q^34 - 2 * q^36 + 3 * q^37 - 10 * q^38 - 9 * q^39 - 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 - 14 * q^44 - 5 * q^45 + 3 * q^46 - 12 * q^47 - 9 * q^48 + 4 * q^49 + 15 * q^50 + 12 * q^51 - 2 * q^52 + 14 * q^53 + 2 * q^54 + 10 * q^55 - 5 * q^56 + 10 * q^57 - 20 * q^59 + 8 * q^61 - 9 * q^62 + q^63 - 7 * q^64 + 5 * q^65 + 4 * q^66 + 13 * q^67 + 26 * q^68 - 4 * q^69 - 5 * q^70 + 13 * q^71 + 5 * q^72 - 21 * q^73 + 6 * q^74 + 5 * q^75 + 2 * q^77 + 2 * q^78 - 25 * q^79 + 15 * q^80 - q^81 - 24 * q^82 - 16 * q^83 - 2 * q^84 - 25 * q^85 + 3 * q^86 - 15 * q^87 + 10 * q^88 - 10 * q^89 - 10 * q^90 - 9 * q^91 - 7 * q^92 + 2 * q^93 - 24 * q^94 - 10 * q^95 + 7 * q^96 + 3 * q^97 + 3 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$	0.500000	−	0.363271i	0.204124	−	0.148305i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.427051	+	1.31433i	−0.135045	+	0.415627i
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	0.339946	+	0.940445i	$0.389591\pi$
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	−0.827802	+	0.561020i	$0.810409\pi$
$12$	0.500000	+	1.53884i	0.144338	+	0.444225i
$13$	1.69098	+	5.20431i	0.468994	+	1.44342i	0.853889	+	0.520455i	$0.174238\pi$
$13$	1.69098	+	5.20431i	0.468994	+	1.44342i	−0.384895	+	0.922961i	$0.625762\pi$
$14$	−0.190983	+	0.587785i	−0.0510424	+	0.157092i
$15$	−1.80902	−	1.31433i	−0.467086	−	0.339358i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	6.04508	−	4.39201i	1.46615	−	1.06522i	0.484441	−	0.874824i	$-0.339023\pi$
$17$	6.04508	−	4.39201i	1.46615	−	1.06522i	0.981708	−	0.190395i	$-0.0609770\pi$
$18$	0.618034			0.145672
$19$	1.11803	−	0.812299i	0.256495	−	0.186354i	−0.452106	−	0.891964i	$-0.649327\pi$
$19$	1.11803	−	0.812299i	0.256495	−	0.186354i	0.708600	+	0.705610i	$0.249327\pi$
$20$	−2.92705	−	2.12663i	−0.654508	−	0.475528i
$21$	−0.809017	−	0.587785i	−0.176542	−	0.128265i
$22$	2.61803	+	1.90211i	0.558167	+	0.405532i
$23$	−0.809017	+	2.48990i	−0.168692	+	0.519180i	−0.999289	−	0.0376933i	$-0.987999\pi$
$23$	−0.809017	+	2.48990i	−0.168692	+	0.519180i	0.830598	+	0.556873i	$0.187999\pi$
$24$	2.23607			0.456435
$25$	5.00000			1.00000
$26$	3.38197			0.663258
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.30902	−	0.951057i	−0.247381	−	0.179733i
$29$	−5.42705	−	3.94298i	−1.00778	−	0.732194i	−0.0440362	−	0.999030i	$-0.514022\pi$
$29$	−5.42705	−	3.94298i	−1.00778	−	0.732194i	−0.963742	+	0.266836i	$0.914022\pi$
$30$	−1.11803	+	0.812299i	−0.204124	+	0.148305i
$31$	−2.30902	+	1.67760i	−0.414712	+	0.301306i	−0.775507	−	0.631340i	$-0.782505\pi$
$31$	−2.30902	+	1.67760i	−0.414712	+	0.301306i	0.360795	+	0.932645i	$0.382505\pi$
$32$	5.61803			0.993137
$33$	−4.23607	+	3.07768i	−0.737405	+	0.535756i
$34$	−1.42705	−	4.39201i	−0.244737	−	0.753224i
$35$	2.23607			0.377964
$36$	−0.500000	+	1.53884i	−0.0833333	+	0.256474i
$37$	2.42705	+	7.46969i	0.399005	+	1.22801i	0.925799	+	0.378017i	$0.123394\pi$
$37$	2.42705	+	7.46969i	0.399005	+	1.22801i	−0.526794	+	0.849993i	$0.676606\pi$
$38$	−0.263932	−	0.812299i	−0.0428154	−	0.131772i
$39$	−1.69098	+	5.20431i	−0.270774	+	0.833357i
$40$	−4.04508	+	2.93893i	−0.639584	+	0.464685i
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	−0.983584	−	0.180450i	$-0.942245\pi$
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	0.689670	−	0.724123i	$-0.257755\pi$
$42$	−0.500000	+	0.363271i	−0.0771517	+	0.0560540i
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−6.85410	+	4.97980i	−1.03329	+	0.750733i
$45$	−0.690983	−	2.12663i	−0.103006	−	0.317019i
$46$	1.30902	+	0.951057i	0.193004	+	0.140226i
$47$	−9.70820	−	7.05342i	−1.41609	−	1.02885i	−0.992402	−	0.123038i	$-0.960736\pi$
$47$	−9.70820	−	7.05342i	−1.41609	−	1.02885i	−0.423685	−	0.905810i	$-0.639264\pi$
$48$	−0.572949	+	1.76336i	−0.0826981	+	0.254518i
$49$	1.00000			0.142857
$50$	0.954915	−	2.93893i	0.135045	−	0.415627i
$51$	7.47214			1.04631
$52$	−2.73607	+	8.42075i	−0.379424	+	1.16775i
$53$	5.73607	+	4.16750i	0.787910	+	0.572450i	0.907342	−	0.420393i	$-0.138108\pi$
$53$	5.73607	+	4.16750i	0.787910	+	0.572450i	−0.119433	+	0.992842i	$0.538108\pi$
$54$	0.500000	+	0.363271i	0.0680414	+	0.0494350i
$55$	3.61803	−	11.1352i	0.487856	−	1.50147i
$56$	−1.80902	+	1.31433i	−0.241740	+	0.175634i
$57$	1.38197			0.183046
$58$	−3.35410	+	2.43690i	−0.440415	+	0.319980i
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	−0.999204	−	0.0398899i	$-0.987299\pi$
$59$	−1.64590	−	5.06555i	−0.214278	−	0.659479i	0.784926	−	0.619589i	$-0.212701\pi$
$60$	−1.11803	−	3.44095i	−0.144338	−	0.444225i
$61$	4.23607	−	13.0373i	0.542373	−	1.66925i	−0.184783	−	0.982779i	$-0.559158\pi$
$61$	4.23607	−	13.0373i	0.542373	−	1.66925i	0.727155	−	0.686473i	$-0.240842\pi$
$62$	0.545085	+	1.67760i	0.0692259	+	0.213055i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	−3.78115	−	11.6372i	−0.468994	−	1.44342i
$66$	1.00000	+	3.07768i	0.123091	+	0.378837i
$67$	8.28115	−	6.01661i	1.01170	−	0.735046i	0.0471381	−	0.998888i	$-0.484990\pi$
$67$	8.28115	−	6.01661i	1.01170	−	0.735046i	0.964566	+	0.263843i	$0.0849899\pi$
$68$	12.0902			1.46615
$69$	−2.11803	+	1.53884i	−0.254981	+	0.185255i
$70$	0.427051	−	1.31433i	0.0510424	−	0.157092i
$71$	6.04508	+	4.39201i	0.717420	+	0.521236i	0.885559	−	0.464527i	$-0.153776\pi$
$71$	6.04508	+	4.39201i	0.717420	+	0.521236i	−0.168139	+	0.985763i	$0.553776\pi$
$72$	1.80902	+	1.31433i	0.213195	+	0.154895i
$73$	0.899187	−	2.76741i	0.105242	−	0.323901i	−0.884545	−	0.466454i	$-0.845531\pi$
$73$	0.899187	−	2.76741i	0.105242	−	0.323901i	0.989787	+	0.142553i	$0.0455312\pi$
$74$	4.85410			0.564278
$75$	4.04508	+	2.93893i	0.467086	+	0.339358i
$76$	2.23607			0.256495
$77$	1.61803	−	4.97980i	0.184392	−	0.567500i
$78$	2.73607	+	1.98787i	0.309799	+	0.225082i
$79$	−10.1631	−	7.38394i	−1.14344	−	0.830758i	−0.155845	−	0.987781i	$-0.549810\pi$
$79$	−10.1631	−	7.38394i	−1.14344	−	0.830758i	−0.987595	+	0.157024i	$0.949810\pi$
$80$	−1.28115	−	3.94298i	−0.143237	−	0.440839i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.76393			−0.415657
$83$	−4.00000	+	2.90617i	−0.439057	+	0.318994i	−0.785260	−	0.619166i	$-0.787471\pi$
$83$	−4.00000	+	2.90617i	−0.439057	+	0.318994i	0.346203	+	0.938160i	$0.387471\pi$
$84$	−0.500000	−	1.53884i	−0.0545545	−	0.167901i
$85$	−13.5172	+	9.82084i	−1.46615	+	1.06522i
$86$	0.190983	−	0.587785i	0.0205942	−	0.0633825i
$87$	−2.07295	−	6.37988i	−0.222243	−	0.683995i
$88$	3.61803	+	11.1352i	0.385684	+	1.18701i
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	−0.997199	−	0.0747893i	$-0.976172\pi$
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	0.850711	+	0.525633i	$0.176172\pi$
$90$	−1.38197			−0.145672
$91$	−1.69098	−	5.20431i	−0.177263	−	0.545560i
$92$	−3.42705	+	2.48990i	−0.357295	+	0.259590i
$93$	−2.85410			−0.295957
$94$	−6.00000	+	4.35926i	−0.618853	+	0.449623i
$95$	−2.50000	+	1.81636i	−0.256495	+	0.186354i
$96$	4.54508	+	3.30220i	0.463881	+	0.337029i
$97$	−2.04508	−	1.48584i	−0.207647	−	0.150864i	0.479101	−	0.877760i	$-0.340963\pi$
$97$	−2.04508	−	1.48584i	−0.207647	−	0.150864i	−0.686748	+	0.726895i	$0.740963\pi$
$98$	0.190983	−	0.587785i	0.0192922	−	0.0593753i
$99$	−5.23607			−0.526245
$100$	6.54508	+	4.75528i	0.654508	+	0.475528i
$101$	3.18034			0.316456			0.158228	−	0.987403i	$-0.449422\pi$
$101$	3.18034			0.316456			0.158228	+	0.987403i	$0.449422\pi$
$102$	1.42705	−	4.39201i	0.141299	−	0.434874i
$103$	2.54508	+	1.84911i	0.250775	+	0.182198i	0.706070	−	0.708142i	$-0.250466\pi$
$103$	2.54508	+	1.84911i	0.250775	+	0.182198i	−0.455295	+	0.890340i	$0.650466\pi$
$104$	9.89919	+	7.19218i	0.970695	+	0.705251i
$105$	1.80902	+	1.31433i	0.176542	+	0.128265i
$106$	3.54508	−	2.57565i	0.344329	−	0.250170i
$107$	5.29180			0.511577			0.255789	−	0.966733i	$-0.417665\pi$
$107$	5.29180			0.511577			0.255789	+	0.966733i	$0.417665\pi$
$108$	−1.30902	+	0.951057i	−0.125960	+	0.0915155i
$109$	3.88197	+	11.9475i	0.371825	+	1.14436i	0.945596	+	0.325344i	$0.105480\pi$
$109$	3.88197	+	11.9475i	0.371825	+	1.14436i	−0.573771	+	0.819016i	$0.694520\pi$
$110$	−5.85410	−	4.25325i	−0.558167	−	0.405532i
$111$	−2.42705	+	7.46969i	−0.230365	+	0.708992i
$112$	−0.572949	−	1.76336i	−0.0541386	−	0.166621i
$113$	−4.26393	−	13.1230i	−0.401117	−	1.23451i	−0.924094	−	0.382165i	$-0.875179\pi$
$113$	−4.26393	−	13.1230i	−0.401117	−	1.23451i	0.522977	−	0.852347i	$-0.324821\pi$
$114$	0.263932	−	0.812299i	0.0247195	−	0.0760788i
$115$	1.80902	−	5.56758i	0.168692	−	0.519180i
$116$	−3.35410	−	10.3229i	−0.311421	−	0.958454i
$117$	−4.42705	+	3.21644i	−0.409281	+	0.297360i
$118$	−3.29180			−0.303034
$119$	−6.04508	+	4.39201i	−0.554152	+	0.402615i
$120$	−5.00000			−0.456435
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	−6.85410	−	4.97980i	−0.620541	−	0.450850i
$123$	1.88197	−	5.79210i	0.169691	−	0.522256i
$124$	−4.61803			−0.414712
$125$	−11.1803			−1.00000
$126$	−0.618034			−0.0550588
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	−0.640529	−	0.767934i	$-0.721285\pi$
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	0.969579	−	0.244778i	$-0.0787150\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	0.809017	+	0.587785i	0.0712300	+	0.0517516i
$130$	−7.56231			−0.663258
$131$	11.2082	−	8.14324i	0.979265	−	0.711478i	0.0217210	−	0.999764i	$-0.493085\pi$
$131$	11.2082	−	8.14324i	0.979265	−	0.711478i	0.957544	+	0.288286i	$0.0930854\pi$
$132$	−8.47214			−0.737405
$133$	−1.11803	+	0.812299i	−0.0969458	+	0.0704353i
$134$	−1.95492	−	6.01661i	−0.168879	−	0.519756i
$135$	0.690983	−	2.12663i	0.0594703	−	0.183031i
$136$	5.16312	−	15.8904i	0.442734	−	1.36259i
$137$	4.50000	+	13.8496i	0.384461	+	1.18325i	0.936871	+	0.349676i	$0.113708\pi$
$137$	4.50000	+	13.8496i	0.384461	+	1.18325i	−0.552410	+	0.833573i	$0.686292\pi$
$138$	0.500000	+	1.53884i	0.0425628	+	0.130995i
$139$	1.64590	−	5.06555i	0.139603	−	0.429655i	−0.856674	−	0.515858i	$-0.827473\pi$
$139$	1.64590	−	5.06555i	0.139603	−	0.429655i	0.996278	+	0.0862030i	$0.0274734\pi$
$140$	2.92705	+	2.12663i	0.247381	+	0.179733i
$141$	−3.70820	−	11.4127i	−0.312287	−	0.961121i
$142$	3.73607	−	2.71441i	0.313524	−	0.227788i
$143$	−28.6525			−2.39604
$144$	−1.50000	+	1.08981i	−0.125000	+	0.0908178i
$145$	12.1353	+	8.81678i	1.00778	+	0.732194i
$146$	−1.45492	−	1.05706i	−0.120410	−	0.0874827i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	−3.92705	+	12.0862i	−0.322802	+	0.993481i
$149$	−5.32624			−0.436342			−0.218171	−	0.975911i	$-0.570009\pi$
$149$	−5.32624			−0.436342			−0.218171	+	0.975911i	$0.570009\pi$
$150$	2.50000	−	1.81636i	0.204124	−	0.148305i
$151$	−15.5623			−1.26644			−0.633221	−	0.773971i	$-0.718268\pi$
$151$	−15.5623			−1.26644			−0.633221	+	0.773971i	$0.718268\pi$
$152$	0.954915	−	2.93893i	0.0774538	−	0.238378i
$153$	6.04508	+	4.39201i	0.488716	+	0.355073i
$154$	−2.61803	−	1.90211i	−0.210967	−	0.153277i
$155$	5.16312	−	3.75123i	0.414712	−	0.301306i
$156$	−7.16312	+	5.20431i	−0.573509	+	0.416678i
$157$	17.8541			1.42491			0.712456	−	0.701717i	$-0.247583\pi$
$157$	17.8541			1.42491			0.712456	+	0.701717i	$0.247583\pi$
$158$	−6.28115	+	4.56352i	−0.499702	+	0.363055i
$159$	2.19098	+	6.74315i	0.173756	+	0.534767i
$160$	−12.5623			−0.993137
$161$	0.809017	−	2.48990i	0.0637595	−	0.196231i
$162$	0.190983	+	0.587785i	0.0150050	+	0.0461808i
$163$	−0.545085	−	1.67760i	−0.0426944	−	0.131400i	0.927437	−	0.373979i	$-0.122007\pi$
$163$	−0.545085	−	1.67760i	−0.0426944	−	0.131400i	−0.970132	+	0.242579i	$0.922007\pi$
$164$	3.04508	−	9.37181i	0.237781	−	0.731815i
$165$	9.47214	−	6.88191i	0.737405	−	0.535756i
$166$	0.944272	+	2.90617i	0.0732897	+	0.225563i
$167$	9.66312	−	7.02067i	0.747755	−	0.543276i	−0.147375	−	0.989081i	$-0.547083\pi$
$167$	9.66312	−	7.02067i	0.747755	−	0.543276i	0.895130	+	0.445805i	$0.147083\pi$
$168$	−2.23607			−0.172516
$169$	−13.7082	+	9.95959i	−1.05448	+	0.766123i
$170$	3.19098	+	9.82084i	0.244737	+	0.753224i
$171$	1.11803	+	0.812299i	0.0854982	+	0.0621181i
$172$	1.30902	+	0.951057i	0.0998116	+	0.0725174i
$173$	0.673762	−	2.07363i	0.0512252	−	0.157655i	−0.922172	−	0.386781i	$-0.873587\pi$
$173$	0.673762	−	2.07363i	0.0512252	−	0.157655i	0.973397	+	0.229126i	$0.0735869\pi$
$174$	−4.14590			−0.314300
$175$	−5.00000			−0.377964
$176$	−9.70820			−0.731783
$177$	1.64590	−	5.06555i	0.123713	−	0.380750i
$178$	2.23607	+	1.62460i	0.167600	+	0.121769i
$179$	−7.23607	−	5.25731i	−0.540849	−	0.392950i	0.283551	−	0.958957i	$-0.408487\pi$
$179$	−7.23607	−	5.25731i	−0.540849	−	0.392950i	−0.824400	+	0.566007i	$0.808487\pi$
$180$	1.11803	−	3.44095i	0.0833333	−	0.256474i
$181$	1.57295	−	1.14281i	0.116916	−	0.0849447i	−0.527791	−	0.849375i	$-0.676979\pi$
$181$	1.57295	−	1.14281i	0.116916	−	0.0849447i	0.644707	+	0.764430i	$0.276979\pi$
$182$	−3.38197			−0.250688
$183$	11.0902	−	8.05748i	0.819809	−	0.595626i
$184$	1.80902	+	5.56758i	0.133363	+	0.410448i
$185$	−5.42705	−	16.7027i	−0.399005	−	1.22801i
$186$	−0.545085	+	1.67760i	−0.0399676	+	0.123008i
$187$	12.0902	+	37.2097i	0.884121	+	2.72104i
$188$	−6.00000	−	18.4661i	−0.437595	−	1.34678i
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	0.590170	+	1.81636i	0.0428154	+	0.131772i
$191$	2.06231	+	6.34712i	0.149223	+	0.459262i	0.997530	−	0.0702434i	$-0.0223776\pi$
$191$	2.06231	+	6.34712i	0.149223	+	0.459262i	−0.848307	+	0.529505i	$0.822378\pi$
$192$	−0.190983	+	0.138757i	−0.0137830	+	0.0100139i
$193$	−12.4164			−0.893753			−0.446876	−	0.894596i	$-0.647464\pi$
$193$	−12.4164			−0.893753			−0.446876	+	0.894596i	$0.647464\pi$
$194$	−1.26393	+	0.918300i	−0.0907450	+	0.0659301i
$195$	3.78115	−	11.6372i	0.270774	−	0.833357i
$196$	1.30902	+	0.951057i	0.0935012	+	0.0679326i
$197$	6.73607	+	4.89404i	0.479925	+	0.348686i	0.801297	−	0.598267i	$-0.204144\pi$
$197$	6.73607	+	4.89404i	0.479925	+	0.348686i	−0.321372	+	0.946953i	$0.604144\pi$
$198$	−1.00000	+	3.07768i	−0.0710669	+	0.218721i
$199$	−11.7082			−0.829973			−0.414986	−	0.909828i	$-0.636214\pi$
$199$	−11.7082			−0.829973			−0.414986	+	0.909828i	$0.636214\pi$
$200$	9.04508	−	6.57164i	0.639584	−	0.464685i
$201$	10.2361			0.721997
$202$	0.607391	−	1.86936i	0.0427359	−	0.131527i
$203$	5.42705	+	3.94298i	0.380904	+	0.276743i
$204$	9.78115	+	7.10642i	0.684818	+	0.497549i
$205$	4.20820	+	12.9515i	0.293914	+	0.904573i
$206$	1.57295	−	1.14281i	0.109593	−	0.0796236i
$207$	−2.61803			−0.181966
$208$	−8.20820	+	5.96361i	−0.569137	+	0.413502i
$209$	2.23607	+	6.88191i	0.154672	+	0.476032i
$210$	1.11803	−	0.812299i	0.0771517	−	0.0560540i
$211$	2.16312	−	6.65740i	0.148915	−	0.458314i	−0.848578	−	0.529070i	$-0.822541\pi$
$211$	2.16312	−	6.65740i	0.148915	−	0.458314i	0.997494	+	0.0707556i	$0.0225410\pi$
$212$	3.54508	+	10.9106i	0.243477	+	0.749346i
$213$	2.30902	+	7.10642i	0.158211	+	0.486924i
$214$	1.01064	−	3.11044i	0.0690861	−	0.212625i
$215$	−2.23607			−0.152499
$216$	0.690983	+	2.12663i	0.0470154	+	0.144699i
$217$	2.30902	−	1.67760i	0.156746	−	0.113883i
$218$	7.76393			0.525840
$219$	2.35410	−	1.71036i	0.159075	−	0.115575i
$220$	15.3262	−	11.1352i	1.03329	−	0.750733i
$221$	33.0795	+	24.0337i	2.22517	+	1.61668i
$222$	3.92705	+	2.85317i	0.263566	+	0.191492i
$223$	−1.56231	+	4.80828i	−0.104620	+	0.321986i	−0.989641	−	0.143564i	$-0.954144\pi$
$223$	−1.56231	+	4.80828i	−0.104620	+	0.321986i	0.885021	+	0.465551i	$0.154144\pi$
$224$	−5.61803			−0.375371
$225$	1.54508	+	4.75528i	0.103006	+	0.317019i
$226$	−8.52786			−0.567265
$227$	−5.13525	+	15.8047i	−0.340839	+	1.04899i	0.622935	+	0.782274i	$0.285940\pi$
$227$	−5.13525	+	15.8047i	−0.340839	+	1.04899i	−0.963774	+	0.266721i	$0.914060\pi$
$228$	1.80902	+	1.31433i	0.119805	+	0.0870435i
$229$	11.0172	+	8.00448i	0.728038	+	0.528951i	0.888942	−	0.458019i	$-0.151441\pi$
$229$	11.0172	+	8.00448i	0.728038	+	0.528951i	−0.160904	+	0.986970i	$0.551441\pi$
$230$	−2.92705	−	2.12663i	−0.193004	−	0.140226i
$231$	4.23607	−	3.07768i	0.278713	−	0.202497i
$232$	−15.0000			−0.984798
$233$	21.7533	−	15.8047i	1.42511	−	1.03540i	0.434203	−	0.900815i	$-0.357030\pi$
$233$	21.7533	−	15.8047i	1.42511	−	1.03540i	0.990902	−	0.134585i	$-0.0429700\pi$
$234$	1.04508	+	3.21644i	0.0683193	+	0.210265i
$235$	21.7082	+	15.7719i	1.41609	+	1.02885i
$236$	2.66312	−	8.19624i	0.173354	−	0.533530i
$237$	−3.88197	−	11.9475i	−0.252161	−	0.776071i
$238$	1.42705	+	4.39201i	0.0925020	+	0.284692i
$239$	−1.38197	+	4.25325i	−0.0893920	+	0.275120i	−0.985752	−	0.168207i	$-0.946202\pi$
$239$	−1.38197	+	4.25325i	−0.0893920	+	0.275120i	0.896360	+	0.443328i	$0.146202\pi$
$240$	1.28115	−	3.94298i	0.0826981	−	0.254518i
$241$	−6.98278	−	21.4908i	−0.449800	−	1.38434i	−0.877133	−	0.480248i	$-0.840547\pi$
$241$	−6.98278	−	21.4908i	−0.449800	−	1.38434i	0.427332	−	0.904095i	$-0.359453\pi$
$242$	−8.20820	+	5.96361i	−0.527643	+	0.383355i
$243$	−1.00000			−0.0641500
$244$	17.9443	−	13.0373i	1.14876	−	0.834626i
$245$	−2.23607			−0.142857
$246$	−3.04508	−	2.21238i	−0.194148	−	0.141056i
$247$	6.11803	+	4.44501i	0.389281	+	0.282829i
$248$	−1.97214	+	6.06961i	−0.125231	+	0.385421i
$249$	−4.94427			−0.313331
$250$	−2.13525	+	6.57164i	−0.135045	+	0.415627i
$251$	−13.8541			−0.874463			−0.437232	−	0.899349i	$-0.644041\pi$
$251$	−13.8541			−0.874463			−0.437232	+	0.899349i	$0.644041\pi$
$252$	0.500000	−	1.53884i	0.0314970	−	0.0969379i
$253$	−11.0902	−	8.05748i	−0.697233	−	0.506569i
$254$	−6.00000	−	4.35926i	−0.376473	−	0.273524i
$255$	−16.7082			−1.04631
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	14.7639			0.920949			0.460474	−	0.887673i	$-0.347679\pi$
$257$	14.7639			0.920949			0.460474	+	0.887673i	$0.347679\pi$
$258$	0.500000	−	0.363271i	0.0311286	−	0.0226163i
$259$	−2.42705	−	7.46969i	−0.150810	−	0.464144i
$260$	6.11803	−	18.8294i	0.379424	−	1.16775i
$261$	2.07295	−	6.37988i	0.128312	−	0.394905i
$262$	−2.64590	−	8.14324i	−0.163464	−	0.503091i
$263$	9.25329	+	28.4787i	0.570582	+	1.75607i	0.650752	+	0.759290i	$0.274454\pi$
$263$	9.25329	+	28.4787i	0.570582	+	1.75607i	−0.0801698	+	0.996781i	$0.525546\pi$
$264$	−3.61803	+	11.1352i	−0.222675	+	0.685322i
$265$	−12.8262	−	9.31881i	−0.787910	−	0.572450i
$266$	0.263932	+	0.812299i	0.0161827	+	0.0498053i
$267$	−3.61803	+	2.62866i	−0.221420	+	0.160871i
$268$	16.5623			1.01170
$269$	−19.2082	+	13.9556i	−1.17114	+	0.850887i	−0.991146	−	0.132780i	$-0.957610\pi$
$269$	−19.2082	+	13.9556i	−1.17114	+	0.850887i	−0.179999	+	0.983667i	$0.557610\pi$
$270$	−1.11803	−	0.812299i	−0.0680414	−	0.0494350i
$271$	11.2082	+	8.14324i	0.680850	+	0.494666i	0.873640	−	0.486574i	$-0.161753\pi$
$271$	11.2082	+	8.14324i	0.680850	+	0.494666i	−0.192790	+	0.981240i	$0.561753\pi$
$272$	11.2082	+	8.14324i	0.679597	+	0.493756i
$273$	1.69098	−	5.20431i	0.102343	−	0.314979i
$274$	9.00000			0.543710
$275$	−8.09017	+	24.8990i	−0.487856	+	1.50147i
$276$	−4.23607			−0.254981
$277$	9.98936	−	30.7441i	0.600202	−	1.84723i	0.0732943	−	0.997310i	$-0.476649\pi$
$277$	9.98936	−	30.7441i	0.600202	−	1.84723i	0.526908	−	0.849922i	$-0.323351\pi$
$278$	−2.66312	−	1.93487i	−0.159723	−	0.116046i
$279$	−2.30902	−	1.67760i	−0.138237	−	0.100435i
$280$	4.04508	−	2.93893i	0.241740	−	0.175634i
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	−0.431044	−	0.902331i	$-0.641855\pi$
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	0.724968	+	0.688783i	$0.241855\pi$
$282$	−7.41641			−0.441641
$283$	−20.3435	+	14.7804i	−1.20929	+	0.878603i	−0.995166	−	0.0982030i	$-0.968691\pi$
$283$	−20.3435	+	14.7804i	−1.20929	+	0.878603i	−0.214127	+	0.976806i	$0.568691\pi$
$284$	3.73607	+	11.4984i	0.221695	+	0.682307i
$285$	−3.09017			−0.183046
$286$	−5.47214	+	16.8415i	−0.323574	+	0.995859i
$287$	1.88197	+	5.79210i	0.111089	+	0.341897i
$288$	1.73607	+	5.34307i	0.102299	+	0.314843i
$289$	12.0000	−	36.9322i	0.705882	−	2.17248i
$290$	7.50000	−	5.44907i	0.440415	−	0.319980i
$291$	−0.781153	−	2.40414i	−0.0457920	−	0.140933i
$292$	3.80902	−	2.76741i	0.222906	−	0.161951i
$293$	4.41641			0.258009			0.129005	−	0.991644i	$-0.458822\pi$
$293$	4.41641			0.258009			0.129005	+	0.991644i	$0.458822\pi$
$294$	0.500000	−	0.363271i	0.0291606	−	0.0211864i
$295$	3.68034	+	11.3269i	0.214278	+	0.659479i
$296$	14.2082	+	10.3229i	0.825835	+	0.600004i
$297$	−4.23607	−	3.07768i	−0.245802	−	0.178585i
$298$	−1.01722	+	3.13068i	−0.0589260	+	0.181356i
$299$	−14.3262			−0.828508
$300$	2.50000	+	7.69421i	0.144338	+	0.444225i
$301$	−1.00000			−0.0576390
$302$	−2.97214	+	9.14729i	−0.171027	+	0.526368i
$303$	2.57295	+	1.86936i	0.147812	+	0.107392i
$304$	2.07295	+	1.50609i	0.118892	+	0.0863799i
$305$	−9.47214	+	29.1522i	−0.542373	+	1.66925i
$306$	3.73607	−	2.71441i	0.213577	−	0.155173i
$307$	10.6180			0.606003			0.303002	−	0.952990i	$-0.402011\pi$
$307$	10.6180			0.606003			0.303002	+	0.952990i	$0.402011\pi$
$308$	6.85410	−	4.97980i	0.390549	−	0.283750i
$309$	0.972136	+	2.99193i	0.0553029	+	0.170205i
$310$	−1.21885	−	3.75123i	−0.0692259	−	0.213055i
$311$	−8.52786	+	26.2461i	−0.483571	+	1.48828i	0.350469	+	0.936574i	$0.386022\pi$
$311$	−8.52786	+	26.2461i	−0.483571	+	1.48828i	−0.834040	+	0.551704i	$0.813978\pi$
$312$	3.78115	+	11.6372i	0.214066	+	0.658826i
$313$	−7.68034	−	23.6377i	−0.434118	−	1.33608i	−0.893987	−	0.448092i	$-0.852104\pi$
$313$	−7.68034	−	23.6377i	−0.434118	−	1.33608i	0.459869	−	0.887987i	$-0.347896\pi$
$314$	3.40983	−	10.4944i	0.192428	−	0.592232i
$315$	0.690983	+	2.12663i	0.0389325	+	0.119822i
$316$	−6.28115	−	19.3314i	−0.353342	−	1.08748i
$317$	−4.80902	+	3.49396i	−0.270101	+	0.196240i	−0.714588	−	0.699545i	$-0.753386\pi$
$317$	−4.80902	+	3.49396i	−0.270101	+	0.196240i	0.444487	+	0.895785i	$0.353386\pi$
$318$	4.38197			0.245728
$319$	28.4164	−	20.6457i	1.59101	−	1.15594i
$320$	0.163119	−	0.502029i	0.00911863	−	0.0280642i
$321$	4.28115	+	3.11044i	0.238951	+	0.173608i
$322$	−1.30902	−	0.951057i	−0.0729487	−	0.0530003i
$323$	3.19098	−	9.82084i	0.177551	−	0.546446i
$324$	−1.61803			−0.0898908
$325$	8.45492	+	26.0216i	0.468994	+	1.44342i
$326$	−1.09017			−0.0603789
$327$	−3.88197	+	11.9475i	−0.214673	+	0.660696i
$328$	−11.0172	−	8.00448i	−0.608324	−	0.441973i
$329$	9.70820	+	7.05342i	0.535231	+	0.388868i
$330$	−2.23607	−	6.88191i	−0.123091	−	0.378837i
$331$	10.5172	−	7.64121i	0.578079	−	0.419999i	−0.259952	−	0.965621i	$-0.583707\pi$
$331$	10.5172	−	7.64121i	0.578079	−	0.419999i	0.838031	+	0.545623i	$0.183707\pi$
$332$	−8.00000			−0.439057
$333$	−6.35410	+	4.61653i	−0.348203	+	0.252984i
$334$	−2.28115	−	7.02067i	−0.124819	−	0.384154i
$335$	−18.5172	+	13.4535i	−1.01170	+	0.735046i
$336$	0.572949	−	1.76336i	0.0312569	−	0.0961989i
$337$	3.21885	+	9.90659i	0.175342	+	0.539646i	0.999649	−	0.0264964i	$-0.00843505\pi$
$337$	3.21885	+	9.90659i	0.175342	+	0.539646i	−0.824307	+	0.566143i	$0.808435\pi$
$338$	3.23607	+	9.95959i	0.176019	+	0.541730i
$339$	4.26393	−	13.1230i	0.231585	−	0.712745i
$340$	−27.0344			−1.46615
$341$	−4.61803	−	14.2128i	−0.250081	−	0.769669i
$342$	0.690983	−	0.502029i	0.0373641	−	0.0271466i
$343$	−1.00000			−0.0539949
$344$	1.80902	−	1.31433i	0.0975357	−	0.0708638i
$345$	4.73607	−	3.44095i	0.254981	−	0.185255i
$346$	−1.09017	−	0.792055i	−0.0586079	−	0.0425811i
$347$	−13.4271	−	9.75532i	−0.720802	−	0.523693i	0.165838	−	0.986153i	$-0.446967\pi$
$347$	−13.4271	−	9.75532i	−0.720802	−	0.523693i	−0.886640	+	0.462460i	$0.846967\pi$
$348$	3.35410	−	10.3229i	0.179799	−	0.553364i
$349$	9.67376			0.517825			0.258912	−	0.965901i	$-0.416636\pi$
$349$	9.67376			0.517825			0.258912	+	0.965901i	$0.416636\pi$
$350$	−0.954915	+	2.93893i	−0.0510424	+	0.157092i
$351$	−5.47214			−0.292081
$352$	−9.09017	+	27.9767i	−0.484508	+	1.49116i
$353$	18.9894	+	13.7966i	1.01070	+	0.734318i	0.964356	−	0.264608i	$-0.0852425\pi$
$353$	18.9894	+	13.7966i	1.01070	+	0.734318i	0.0463454	+	0.998925i	$0.485243\pi$
$354$	−2.66312	−	1.93487i	−0.141543	−	0.102837i
$355$	−13.5172	−	9.82084i	−0.717420	−	0.521236i
$356$	−5.85410	+	4.25325i	−0.310267	+	0.225422i
$357$	−7.47214			−0.395467
$358$	−4.47214	+	3.24920i	−0.236360	+	0.171725i
$359$	0.791796	+	2.43690i	0.0417894	+	0.128615i	0.969775	−	0.244002i	$-0.0784605\pi$
$359$	0.791796	+	2.43690i	0.0417894	+	0.128615i	−0.927985	+	0.372617i	$0.878461\pi$
$360$	−4.04508	−	2.93893i	−0.213195	−	0.154895i
$361$	−5.28115	+	16.2537i	−0.277955	+	0.855459i
$362$	−0.371323	−	1.14281i	−0.0195163	−	0.0600650i
$363$	−5.07295	−	15.6129i	−0.266261	−	0.819466i
$364$	2.73607	−	8.42075i	0.143409	−	0.441367i
$365$	−2.01064	+	6.18812i	−0.105242	+	0.323901i
$366$	−2.61803	−	8.05748i	−0.136847	−	0.421171i
$367$	5.45492	−	3.96323i	0.284744	−	0.206879i	−0.436240	−	0.899830i	$-0.643690\pi$
$367$	5.45492	−	3.96323i	0.284744	−	0.206879i	0.720984	+	0.692952i	$0.243690\pi$
$368$	−4.85410			−0.253038
$369$	4.92705	−	3.57971i	0.256492	−	0.186352i
$370$	−10.8541			−0.564278
$371$	−5.73607	−	4.16750i	−0.297802	−	0.216366i
$372$	−3.73607	−	2.71441i	−0.193706	−	0.140736i
$373$	7.28115	−	22.4091i	0.377004	−	1.16030i	−0.565113	−	0.825014i	$-0.691167\pi$
$373$	7.28115	−	22.4091i	0.377004	−	1.16030i	0.942117	−	0.335285i	$-0.108833\pi$
$374$	24.1803			1.25034
$375$	−9.04508	−	6.57164i	−0.467086	−	0.339358i
$376$	−26.8328			−1.38380
$377$	11.3435	−	34.9116i	0.584218	−	1.79804i
$378$	−0.500000	−	0.363271i	−0.0257172	−	0.0186847i
$379$	18.8435	+	13.6906i	0.967923	+	0.703238i	0.954977	−	0.296679i	$-0.0958790\pi$
$379$	18.8435	+	13.6906i	0.967923	+	0.703238i	0.0129461	+	0.999916i	$0.495879\pi$
$380$	−5.00000			−0.256495
$381$	9.70820	−	7.05342i	0.497366	−	0.361358i
$382$	4.12461			0.211033
$383$	5.73607	−	4.16750i	0.293099	−	0.212949i	−0.431511	−	0.902107i	$-0.642020\pi$
$383$	5.73607	−	4.16750i	0.293099	−	0.212949i	0.724611	+	0.689158i	$0.242020\pi$
$384$	3.51722	+	10.8249i	0.179487	+	0.552406i
$385$	−3.61803	+	11.1352i	−0.184392	+	0.567500i
$386$	−2.37132	+	7.29818i	−0.120697	+	0.371468i
$387$	0.309017	+	0.951057i	0.0157082	+	0.0483449i
$388$	−1.26393	−	3.88998i	−0.0641664	−	0.197484i
$389$	−3.55573	+	10.9434i	−0.180283	+	0.554853i	−0.999835	−	0.0181511i	$-0.994222\pi$
$389$	−3.55573	+	10.9434i	−0.180283	+	0.554853i	0.819553	+	0.573004i	$0.194222\pi$
$390$	−6.11803	−	4.44501i	−0.309799	−	0.225082i
$391$	6.04508	+	18.6049i	0.305713	+	0.940888i
$392$	1.80902	−	1.31433i	0.0913692	−	0.0663836i
$393$	13.8541			0.698847
$394$	4.16312	−	3.02468i	0.209735	−	0.152381i
$395$	22.7254	+	16.5110i	1.14344	+	0.830758i
$396$	−6.85410	−	4.97980i	−0.344432	−	0.250244i
$397$	−4.28115	−	3.11044i	−0.214865	−	0.156108i	0.475147	−	0.879906i	$-0.342395\pi$
$397$	−4.28115	−	3.11044i	−0.214865	−	0.156108i	−0.690012	+	0.723798i	$0.742395\pi$
$398$	−2.23607	+	6.88191i	−0.112084	+	0.344959i
$399$	−1.38197			−0.0691848
$400$	2.86475	+	8.81678i	0.143237	+	0.440839i
$401$	−8.20163			−0.409570			−0.204785	−	0.978807i	$-0.565649\pi$
$401$	−8.20163			−0.409570			−0.204785	+	0.978807i	$0.565649\pi$
$402$	1.95492	−	6.01661i	0.0975023	−	0.300081i
$403$	−12.6353	−	9.18005i	−0.629407	−	0.457291i
$404$	4.16312	+	3.02468i	0.207123	+	0.150484i
$405$	1.80902	−	1.31433i	0.0898908	−	0.0653095i
$406$	3.35410	−	2.43690i	0.166461	−	0.120941i
$407$	−41.1246			−2.03847
$408$	13.5172	−	9.82084i	0.669202	−	0.486204i
$409$	−5.16312	−	15.8904i	−0.255300	−	0.785732i	−0.993770	−	0.111446i	$-0.964452\pi$
$409$	−5.16312	−	15.8904i	−0.255300	−	0.785732i	0.738471	−	0.674286i	$-0.235548\pi$
$410$	8.41641			0.415657
$411$	−4.50000	+	13.8496i	−0.221969	+	0.683149i
$412$	1.57295	+	4.84104i	0.0774936	+	0.238501i
$413$	1.64590	+	5.06555i	0.0809893	+	0.249260i
$414$	−0.500000	+	1.53884i	−0.0245737	+	0.0756299i
$415$	8.94427	−	6.49839i	0.439057	−	0.318994i
$416$	9.50000	+	29.2380i	0.465776	+	1.43351i
$417$	4.30902	−	3.13068i	0.211013	−	0.153310i
$418$	4.47214			0.218739
$419$	−18.5172	+	13.4535i	−0.904625	+	0.657249i	−0.939650	−	0.342138i	$-0.888849\pi$
$419$	−18.5172	+	13.4535i	−0.904625	+	0.657249i	0.0350244	+	0.999386i	$0.488849\pi$
$420$	1.11803	+	3.44095i	0.0545545	+	0.167901i
$421$	−13.7533	−	9.99235i	−0.670294	−	0.486997i	0.199829	−	0.979831i	$-0.435961\pi$
$421$	−13.7533	−	9.99235i	−0.670294	−	0.486997i	−0.870124	+	0.492833i	$0.835961\pi$
$422$	−3.50000	−	2.54290i	−0.170377	−	0.123786i
$423$	3.70820	−	11.4127i	0.180299	−	0.554903i
$424$	15.8541			0.769943
$425$	30.2254	−	21.9601i	1.46615	−	1.06522i
$426$	4.61803			0.223744
$427$	−4.23607	+	13.0373i	−0.204998	+	0.630918i
$428$	6.92705	+	5.03280i	0.334832	+	0.243269i
$429$	−23.1803	−	16.8415i	−1.11916	−	0.813115i
$430$	−0.427051	+	1.31433i	−0.0205942	+	0.0633825i
$431$	−19.6074	+	14.2456i	−0.944455	+	0.686187i	−0.949489	−	0.313801i	$-0.898398\pi$
$431$	−19.6074	+	14.2456i	−0.944455	+	0.686187i	0.00503407	+	0.999987i	$0.498398\pi$
$432$	−1.85410			−0.0892055
$433$	−12.5172	+	9.09429i	−0.601539	+	0.437044i	−0.846425	−	0.532508i	$-0.821250\pi$
$433$	−12.5172	+	9.09429i	−0.601539	+	0.437044i	0.244886	+	0.969552i	$0.421250\pi$
$434$	−0.545085	−	1.67760i	−0.0261649	−	0.0805273i
$435$	4.63525	+	14.2658i	0.222243	+	0.683995i
$436$	−6.28115	+	19.3314i	−0.300813	+	0.925806i
$437$	1.11803	+	3.44095i	0.0534828	+	0.164603i
$438$	−0.555728	−	1.71036i	−0.0265537	−	0.0817239i
$439$	−9.20820	+	28.3399i	−0.439484	+	1.35259i	0.448938	+	0.893563i	$0.351802\pi$
$439$	−9.20820	+	28.3399i	−0.439484	+	1.35259i	−0.888422	+	0.459028i	$0.848198\pi$
$440$	−8.09017	−	24.8990i	−0.385684	−	1.18701i
$441$	0.309017	+	0.951057i	0.0147151	+	0.0452884i
$442$	20.4443	−	14.8536i	0.972435	−	0.706515i
$443$	−4.20163			−0.199625			−0.0998126	−	0.995006i	$-0.531824\pi$
$443$	−4.20163			−0.199625			−0.0998126	+	0.995006i	$0.531824\pi$
$444$	−10.2812	+	7.46969i	−0.487922	+	0.354496i
$445$	3.09017	−	9.51057i	0.146488	−	0.450844i
$446$	2.52786	+	1.83660i	0.119698	+	0.0869656i
$447$	−4.30902	−	3.13068i	−0.203810	−	0.148076i
$448$	0.0729490	−	0.224514i	0.00344652	−	0.0106073i
$449$	16.9098			0.798024			0.399012	−	0.916946i	$-0.369353\pi$
$449$	16.9098			0.798024			0.399012	+	0.916946i	$0.369353\pi$
$450$	3.09017			0.145672
$451$	31.8885			1.50157
$452$	6.89919	−	21.2335i	0.324510	−	0.998740i
$453$	−12.5902	−	9.14729i	−0.591538	−	0.429777i
$454$	8.30902	+	6.03685i	0.389961	+	0.283324i
$455$	3.78115	+	11.6372i	0.177263	+	0.545560i
$456$	2.50000	−	1.81636i	0.117073	−	0.0850587i
$457$	−9.50658			−0.444699			−0.222349	−	0.974967i	$-0.571373\pi$
$457$	−9.50658			−0.444699			−0.222349	+	0.974967i	$0.571373\pi$
$458$	6.80902	−	4.94704i	0.318164	−	0.231160i
$459$	2.30902	+	7.10642i	0.107776	+	0.331699i
$460$	7.66312	−	5.56758i	0.357295	−	0.259590i
$461$	−5.56231	+	17.1190i	−0.259062	+	0.797312i	0.733940	+	0.679215i	$0.237680\pi$
$461$	−5.56231	+	17.1190i	−0.259062	+	0.797312i	−0.993002	+	0.118097i	$0.962320\pi$
$462$	−1.00000	−	3.07768i	−0.0465242	−	0.143187i
$463$	−3.57295	−	10.9964i	−0.166049	−	0.511046i	0.833063	−	0.553178i	$-0.186585\pi$
$463$	−3.57295	−	10.9964i	−0.166049	−	0.511046i	−0.999112	+	0.0421317i	$0.986585\pi$
$464$	3.84346	−	11.8290i	0.178428	−	0.549145i
$465$	6.38197			0.295957
$466$	−5.13525	−	15.8047i	−0.237886	−	0.732138i
$467$	−7.47214	+	5.42882i	−0.345769	+	0.251216i	−0.747092	−	0.664721i	$-0.768551\pi$
$467$	−7.47214	+	5.42882i	−0.345769	+	0.251216i	0.401323	+	0.915937i	$0.368551\pi$
$468$	−8.85410			−0.409281
$469$	−8.28115	+	6.01661i	−0.382388	+	0.277821i
$470$	13.4164	−	9.74759i	0.618853	−	0.449623i
$471$	14.4443	+	10.4944i	0.665557	+	0.483555i
$472$	−9.63525	−	7.00042i	−0.443499	−	0.322221i
$473$	−1.61803	+	4.97980i	−0.0743973	+	0.228971i
$474$	−7.76393			−0.356609
$475$	5.59017	−	4.06150i	0.256495	−	0.186354i
$476$	−12.0902			−0.554152
$477$	−2.19098	+	6.74315i	−0.100318	+	0.308748i
$478$	2.23607	+	1.62460i	0.102275	+	0.0743074i
$479$	6.54508	+	4.75528i	0.299053	+	0.217274i	0.727185	−	0.686442i	$-0.240828\pi$
$479$	6.54508	+	4.75528i	0.299053	+	0.217274i	−0.428132	+	0.903716i	$0.640828\pi$
$480$	−10.1631	−	7.38394i	−0.463881	−	0.337029i
$481$	−34.7705	+	25.2623i	−1.58540	+	1.15186i
$482$	−13.9656			−0.636114
$483$	2.11803	−	1.53884i	0.0963739	−	0.0700197i
$484$	−8.20820	−	25.2623i	−0.373100	−	1.14828i
$485$	4.57295	+	3.32244i	0.207647	+	0.150864i
$486$	−0.190983	+	0.587785i	−0.00866317	+	0.0266625i
$487$	−5.07295	−	15.6129i	−0.229877	−	0.707489i	−0.997760	−	0.0668988i	$-0.978690\pi$
$487$	−5.07295	−	15.6129i	−0.229877	−	0.707489i	0.767883	−	0.640591i	$-0.221310\pi$
$488$	−9.47214	−	29.1522i	−0.428783	−	1.31966i
$489$	0.545085	−	1.67760i	0.0246496	−	0.0758637i
$490$	−0.427051	+	1.31433i	−0.0192922	+	0.0593753i
$491$	−6.35410	−	19.5559i	−0.286757	−	0.882546i	−0.985867	−	0.167532i	$-0.946420\pi$
$491$	−6.35410	−	19.5559i	−0.286757	−	0.882546i	0.699110	−	0.715014i	$-0.253580\pi$
$492$	7.97214	−	5.79210i	0.359412	−	0.261128i
$493$	−50.1246			−2.25750
$494$	3.78115	−	2.74717i	0.170122	−	0.123601i
$495$	11.7082			0.526245
$496$	−4.28115	−	3.11044i	−0.192229	−	0.139663i
$497$	−6.04508	−	4.39201i	−0.271159	−	0.197009i
$498$	−0.944272	+	2.90617i	−0.0423138	+	0.130229i
$499$	−24.6738			−1.10455			−0.552275	−	0.833662i	$-0.686240\pi$
$499$	−24.6738			−1.10455			−0.552275	+	0.833662i	$0.686240\pi$
$500$	−14.6353	−	10.6331i	−0.654508	−	0.475528i
$501$	11.9443			0.533631
$502$	−2.64590	+	8.14324i	−0.118092	+	0.363450i
$503$	−22.4164	−	16.2865i	−0.999498	−	0.726178i	−0.0375177	−	0.999296i	$-0.511945\pi$
$503$	−22.4164	−	16.2865i	−0.999498	−	0.726178i	−0.961981	+	0.273118i	$0.911945\pi$
$504$	−1.80902	−	1.31433i	−0.0805800	−	0.0585448i
$505$	−7.11146			−0.316456
$506$	−6.85410	+	4.97980i	−0.304702	+	0.221379i
$507$	−16.9443			−0.752522
$508$	15.7082	−	11.4127i	0.696939	−	0.506356i
$509$	−8.35410	−	25.7113i	−0.370289	−	1.13963i	−0.946602	−	0.322404i	$-0.895509\pi$
$509$	−8.35410	−	25.7113i	−0.370289	−	1.13963i	0.576313	−	0.817229i	$-0.304491\pi$
$510$	−3.19098	+	9.82084i	−0.141299	+	0.434874i
$511$	−0.899187	+	2.76741i	−0.0397777	+	0.122423i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	0.427051	+	1.31433i	0.0188548	+	0.0580290i
$514$	2.81966	−	8.67802i	0.124370	−	0.382771i
$515$	−5.69098	−	4.13474i	−0.250775	−	0.182198i
$516$	0.500000	+	1.53884i	0.0220113	+	0.0677437i
$517$	50.8328	−	36.9322i	2.23562	−	1.62428i
$518$	−4.85410			−0.213277
$519$	1.76393	−	1.28157i	0.0774280	−	0.0562548i
$520$	−22.1353	−	16.0822i	−0.970695	−	0.705251i
$521$	1.47214	+	1.06957i	0.0644954	+	0.0468587i	0.619566	−	0.784945i	$-0.287309\pi$
$521$	1.47214	+	1.06957i	0.0644954	+	0.0468587i	−0.555070	+	0.831803i	$0.687309\pi$
$522$	−3.35410	−	2.43690i	−0.146805	−	0.106660i
$523$	−4.52786	+	13.9353i	−0.197990	+	0.609350i	0.801939	+	0.597406i	$0.203802\pi$
$523$	−4.52786	+	13.9353i	−0.197990	+	0.609350i	−0.999929	+	0.0119436i	$0.996198\pi$
$524$	22.4164			0.979265
$525$	−4.04508	−	2.93893i	−0.176542	−	0.128265i
$526$	18.5066			0.806925
$527$	−6.59017	+	20.2825i	−0.287072	+	0.883518i
$528$	−7.85410	−	5.70634i	−0.341806	−	0.248337i
$529$	13.0623	+	9.49032i	0.567926	+	0.412623i
$530$	−7.92705	+	5.75934i	−0.344329	+	0.250170i
$531$	4.30902	−	3.13068i	0.186995	−	0.135860i
$532$	−2.23607			−0.0969458
$533$	26.9615	−	19.5887i	1.16783	−	0.848480i
$534$	0.854102	+	2.62866i	0.0369606	+	0.113753i
$535$	−11.8328			−0.511577
$536$	7.07295	−	21.7683i	0.305505	−	0.940247i
$537$	−2.76393	−	8.50651i	−0.119272	−	0.367083i
$538$	4.53444	+	13.9556i	0.195494	+	0.601668i
$539$	−1.61803	+	4.97980i	−0.0696937	+	0.214495i
$540$	2.92705	−	2.12663i	0.125960	−	0.0915155i
$541$	−4.74671	−	14.6089i	−0.204077	−	0.628085i	−0.999750	−	0.0223581i	$-0.992883\pi$
$541$	−4.74671	−	14.6089i	−0.204077	−	0.628085i	0.795673	−	0.605726i	$-0.207117\pi$
$542$	6.92705	−	5.03280i	0.297542	−	0.216177i
$543$	1.94427			0.0834367
$544$	33.9615	−	24.6745i	1.45609	−	1.05791i
$545$	−8.68034	−	26.7153i	−0.371825	−	1.14436i
$546$	−2.73607	−	1.98787i	−0.117093	−	0.0850730i
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	0.717489	−	0.696570i	$-0.245291\pi$
$547$	6.47214	+	4.70228i	0.276729	+	0.201055i	−0.440761	+	0.897625i	$0.645291\pi$
$548$	−7.28115	+	22.4091i	−0.311035	+	0.957269i
$549$	13.7082			0.585052
$550$	13.0902	+	9.51057i	0.558167	+	0.405532i
$551$	−9.27051			−0.394937
$552$	−1.80902	+	5.56758i	−0.0769969	+	0.236972i
$553$	10.1631	+	7.38394i	0.432180	+	0.313997i
$554$	−16.1631	−	11.7432i	−0.686705	−	0.498920i
$555$	5.42705	−	16.7027i	0.230365	−	0.708992i
$556$	6.97214	−	5.06555i	0.295684	−	0.214827i
$557$	−23.1246			−0.979821			−0.489911	−	0.871773i	$-0.662971\pi$
$557$	−23.1246			−0.979821			−0.489911	+	0.871773i	$0.662971\pi$
$558$	−1.42705	+	1.03681i	−0.0604119	+	0.0438918i
$559$	1.69098	+	5.20431i	0.0715210	+	0.220119i
$560$	1.28115	+	3.94298i	0.0541386	+	0.166621i
$561$	−12.0902	+	37.2097i	−0.510447	+	1.57100i
$562$	−1.16312	−	3.57971i	−0.0490632	−	0.151001i
$563$	0.961493	+	2.95917i	0.0405221	+	0.124714i	0.969271	−	0.245995i	$-0.0791147\pi$
$563$	0.961493	+	2.95917i	0.0405221	+	0.124714i	−0.928749	+	0.370709i	$0.879115\pi$
$564$	6.00000	−	18.4661i	0.252646	−	0.777563i
$565$	9.53444	+	29.3440i	0.401117	+	1.23451i
$566$	4.80244	+	14.7804i	0.201862	+	0.621266i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	16.7082			0.701061
$569$	8.35410	−	6.06961i	0.350222	−	0.254451i	−0.398740	−	0.917064i	$-0.630552\pi$
$569$	8.35410	−	6.06961i	0.350222	−	0.254451i	0.748962	+	0.662613i	$0.230552\pi$
$570$	−0.590170	+	1.81636i	−0.0247195	+	0.0760788i
$571$	12.5902	+	9.14729i	0.526882	+	0.382802i	0.819190	−	0.573522i	$-0.194423\pi$
$571$	12.5902	+	9.14729i	0.526882	+	0.382802i	−0.292308	+	0.956324i	$0.594423\pi$
$572$	−37.5066	−	27.2501i	−1.56823	−	1.13938i
$573$	−2.06231	+	6.34712i	−0.0861541	+	0.265155i
$574$	3.76393			0.157103
$575$	−4.04508	+	12.4495i	−0.168692	+	0.519180i
$576$	−0.236068			−0.00983617
$577$	6.53444	−	20.1109i	0.272032	−	0.837230i	−0.717957	−	0.696087i	$-0.754923\pi$
$577$	6.53444	−	20.1109i	0.272032	−	0.837230i	0.989989	−	0.141142i	$-0.0450774\pi$
$578$	−19.4164	−	14.1068i	−0.807616	−	0.586767i
$579$	−10.0451	−	7.29818i	−0.417459	−	0.303302i
$580$	7.50000	+	23.0826i	0.311421	+	0.958454i
$581$	4.00000	−	2.90617i	0.165948	−	0.120568i
$582$	−1.56231			−0.0647597
$583$	−30.0344	+	21.8213i	−1.24390	+	0.903746i
$584$	−2.01064	−	6.18812i	−0.0832010	−	0.256066i
$585$	9.89919	−	7.19218i	0.409281	−	0.297360i
$586$	0.843459	−	2.59590i	0.0348430	−	0.107236i
$587$	−6.29180	−	19.3642i	−0.259690	−	0.799244i	−0.992869	−	0.119209i	$-0.961964\pi$
$587$	−6.29180	−	19.3642i	−0.259690	−	0.799244i	0.733179	−	0.680036i	$-0.238036\pi$
$588$	0.500000	+	1.53884i	0.0206197	+	0.0634608i
$589$	−1.21885	+	3.75123i	−0.0502217	+	0.154567i
$590$	7.36068			0.303034
$591$	2.57295	+	7.91872i	0.105837	+	0.325733i
$592$	−11.7812	+	8.55951i	−0.484202	+	0.351794i
$593$	−6.11146			−0.250967			−0.125484	−	0.992096i	$-0.540048\pi$
$593$	−6.11146			−0.250967			−0.125484	+	0.992096i	$0.540048\pi$
$594$	−2.61803	+	1.90211i	−0.107419	+	0.0780446i
$595$	13.5172	−	9.82084i	0.554152	−	0.402615i
$596$	−6.97214	−	5.06555i	−0.285590	−	0.207493i
$597$	−9.47214	−	6.88191i	−0.387669	−	0.281658i
$598$	−2.73607	+	8.42075i	−0.111886	+	0.344350i
$599$	−11.1803			−0.456816			−0.228408	−	0.973565i	$-0.573352\pi$
$599$	−11.1803			−0.456816			−0.228408	+	0.973565i	$0.573352\pi$
$600$	11.1803			0.456435
$601$	−2.27051			−0.0926160			−0.0463080	−	0.998927i	$-0.514746\pi$
$601$	−2.27051			−0.0926160			−0.0463080	+	0.998927i	$0.514746\pi$
$602$	−0.190983	+	0.587785i	−0.00778389	+	0.0239563i
$603$	8.28115	+	6.01661i	0.337235	+	0.245015i
$604$	−20.3713	−	14.8006i	−0.828897	−	0.602229i
$605$	29.6976	+	21.5765i	1.20738	+	0.877211i
$606$	1.59017	−	1.15533i	0.0645962	−	0.0469319i
$607$	−44.7082			−1.81465			−0.907325	−	0.420430i	$-0.861879\pi$
$607$	−44.7082			−1.81465			−0.907325	+	0.420430i	$0.861879\pi$
$608$	6.28115	−	4.56352i	0.254734	−	0.185075i
$609$	2.07295	+	6.37988i	0.0840001	+	0.258526i
$610$	15.3262	+	11.1352i	0.620541	+	0.450850i
$611$	20.2918	−	62.4517i	0.820918	−	2.52653i
$612$	3.73607	+	11.4984i	0.151022	+	0.464797i
$613$	−13.4098	−	41.2712i	−0.541618	−	1.66693i	−0.728898	−	0.684622i	$-0.759967\pi$
$613$	−13.4098	−	41.2712i	−0.541618	−	1.66693i	0.187280	−	0.982307i	$-0.440033\pi$
$614$	2.02786	−	6.24112i	0.0818379	−	0.251871i
$615$	−4.20820	+	12.9515i	−0.169691	+	0.522256i
$616$	−3.61803	−	11.1352i	−0.145775	−	0.448649i
$617$	1.47214	−	1.06957i	0.0592660	−	0.0430592i	−0.557758	−	0.830004i	$-0.688338\pi$
$617$	1.47214	−	1.06957i	0.0592660	−	0.0430592i	0.617024	+	0.786944i	$0.288338\pi$
$618$	1.94427			0.0782101
$619$	17.6631	−	12.8330i	0.709941	−	0.515802i	−0.173214	−	0.984884i	$-0.555415\pi$
$619$	17.6631	−	12.8330i	0.709941	−	0.515802i	0.883155	+	0.469082i	$0.155415\pi$
$620$	10.3262			0.414712
$621$	−2.11803	−	1.53884i	−0.0849938	−	0.0617516i
$622$	13.7984	+	10.0251i	0.553264	+	0.401970i
$623$	1.38197	−	4.25325i	0.0553673	−	0.170403i
$624$	−10.1459			−0.406161
$625$	25.0000			1.00000
$626$	−15.3607			−0.613936
$627$	−2.23607	+	6.88191i	−0.0893000	+	0.274837i
$628$	23.3713	+	16.9803i	0.932617	+	0.677586i
$629$	47.4787	+	34.4953i	1.89310	+	1.37542i
$630$	1.38197			0.0550588
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	−0.276390	−	0.961045i	$-0.589138\pi$
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	0.828599	+	0.559842i	$0.189138\pi$
$632$	−28.0902			−1.11737
$633$	5.66312	−	4.11450i	0.225089	−	0.163537i
$634$	1.13525	+	3.49396i	0.0450867	+	0.138763i
$635$	−8.29180	+	25.5195i	−0.329050	+	1.01271i
$636$	−3.54508	+	10.9106i	−0.140572	+	0.432635i
$637$	1.69098	+	5.20431i	0.0669992	+	0.206202i
$638$	−6.70820	−	20.6457i	−0.265580	−	0.817372i
$639$	−2.30902	+	7.10642i	−0.0913433	+	0.281126i
$640$	−20.5902	−	14.9596i	−0.813898	−	0.591331i
$641$	12.1631	+	37.4342i	0.480414	+	1.47856i	0.838514	+	0.544880i	$0.183425\pi$
$641$	12.1631	+	37.4342i	0.480414	+	1.47856i	−0.358100	+	0.933683i	$0.616575\pi$
$642$	2.64590	−	1.92236i	0.104425	−	0.0758694i
$643$	−11.1115			−0.438193			−0.219097	−	0.975703i	$-0.570311\pi$
$643$	−11.1115			−0.438193			−0.219097	+	0.975703i	$0.570311\pi$
$644$	3.42705	−	2.48990i	0.135045	−	0.0981157i
$645$	−1.80902	−	1.31433i	−0.0712300	−	0.0517516i
$646$	−5.16312	−	3.75123i	−0.203140	−	0.147590i
$647$	7.59017	+	5.51458i	0.298400	+	0.216801i	0.726903	−	0.686740i	$-0.240959\pi$
$647$	7.59017	+	5.51458i	0.298400	+	0.216801i	−0.428503	+	0.903540i	$0.640959\pi$
$648$	−0.690983	+	2.12663i	−0.0271444	+	0.0835418i
$649$	27.8885			1.09472
$650$	16.9098			0.663258
$651$	2.85410			0.111861
$652$	0.881966	−	2.71441i	0.0345405	−	0.106305i
$653$	−18.0451	−	13.1105i	−0.706159	−	0.513054i	0.175773	−	0.984431i	$-0.443757\pi$
$653$	−18.0451	−	13.1105i	−0.706159	−	0.513054i	−0.881932	+	0.471376i	$0.843757\pi$
$654$	6.28115	+	4.56352i	0.245613	+	0.178448i
$655$	−25.0623	+	18.2088i	−0.979265	+	0.711478i
$656$	9.13525	−	6.63715i	0.356672	−	0.259137i
$657$	2.90983			0.113523
$658$	6.00000	−	4.35926i	0.233904	−	0.169941i
$659$	−2.46149	−	7.57570i	−0.0958861	−	0.295107i	0.891597	−	0.452829i	$-0.149585\pi$
$659$	−2.46149	−	7.57570i	−0.0958861	−	0.295107i	−0.987484	+	0.157722i	$0.949585\pi$
$660$	18.9443			0.737405
$661$	−14.6459	+	45.0754i	−0.569659	+	1.75323i	0.0840245	+	0.996464i	$0.473223\pi$
$661$	−14.6459	+	45.0754i	−0.569659	+	1.75323i	−0.653684	+	0.756768i	$0.726777\pi$
$662$	−2.48278	−	7.64121i	−0.0964959	−	0.296984i
$663$	12.6353	+	38.8873i	0.490713	+	1.51026i
$664$	−3.41641	+	10.5146i	−0.132582	+	0.408046i
$665$	2.50000	−	1.81636i	0.0969458	−	0.0704353i
$666$	1.50000	+	4.61653i	0.0581238	+	0.178887i
$667$	14.2082	−	10.3229i	0.550144	−	0.399703i
$668$	19.3262			0.747755
$669$	−4.09017	+	2.97168i	−0.158135	+	0.114892i
$670$	4.37132	+	13.4535i	0.168879	+	0.519756i
$671$	58.0689	+	42.1895i	2.24172	+	1.62871i
$672$	−4.54508	−	3.30220i	−0.175330	−	0.127385i
$673$	−3.27051	+	10.0656i	−0.126069	+	0.388000i	−0.994094	−	0.108520i	$-0.965389\pi$
$673$	−3.27051	+	10.0656i	−0.126069	+	0.388000i	0.868025	+	0.496520i	$0.165389\pi$
$674$	6.43769			0.247971
$675$	−1.54508	+	4.75528i	−0.0594703	+	0.183031i
$676$	−27.4164			−1.05448
$677$	6.77458	−	20.8500i	0.260368	−	0.801331i	−0.732356	−	0.680922i	$-0.761579\pi$
$677$	6.77458	−	20.8500i	0.260368	−	0.801331i	0.992724	−	0.120409i	$-0.0384206\pi$
$678$	−6.89919	−	5.01255i	−0.264962	−	0.192506i
$679$	2.04508	+	1.48584i	0.0784832	+	0.0570214i
$680$	−11.5451	+	35.5321i	−0.442734	+	1.36259i
$681$	−13.4443	+	9.76784i	−0.515186	+	0.374304i
$682$	−9.23607			−0.353667
$683$	12.1803	−	8.84953i	0.466068	−	0.338618i	−0.329839	−	0.944037i	$-0.606994\pi$
$683$	12.1803	−	8.84953i	0.466068	−	0.338618i	0.795907	+	0.605419i	$0.206994\pi$
$684$	0.690983	+	2.12663i	0.0264204	+	0.0813136i
$685$	−10.0623	−	30.9686i	−0.384461	−	1.18325i
$686$	−0.190983	+	0.587785i	−0.00729177	+	0.0224417i
$687$	4.20820	+	12.9515i	0.160553	+	0.494131i
$688$	0.572949	+	1.76336i	0.0218435	+	0.0672273i
$689$	−11.9894	+	36.8994i	−0.456758	+	1.40576i
$690$	−1.11803	−	3.44095i	−0.0425628	−	0.130995i
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	−0.986621	−	0.163028i	$-0.947874\pi$
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	0.702368	−	0.711814i	$-0.252126\pi$
$692$	2.85410	−	2.07363i	0.108497	−	0.0788275i
$693$	5.23607			0.198902
$694$	−8.29837	+	6.02912i	−0.315002	+	0.228862i
$695$	−3.68034	+	11.3269i	−0.139603	+	0.429655i
$696$	−12.1353	−	8.81678i	−0.459986	−	0.334199i
$697$	−36.8156	−	26.7481i	−1.39449	−	1.01316i
$698$	1.84752	−	5.68609i	0.0699298	−	0.215222i
$699$	26.8885			1.01702
$700$	−6.54508	−	4.75528i	−0.247381	−	0.179733i
$701$	−19.1803			−0.724431			−0.362216	−	0.932094i	$-0.617980\pi$
$701$	−19.1803			−0.724431			−0.362216	+	0.932094i	$0.617980\pi$
$702$	−1.04508	+	3.21644i	−0.0394442	+	0.121397i
$703$	8.78115	+	6.37988i	0.331187	+	0.240622i
$704$	−1.00000	−	0.726543i	−0.0376889	−	0.0273826i
$705$	8.29180	+	25.5195i	0.312287	+	0.961121i
$706$	11.7361	−	8.52675i	0.441693	−	0.320909i
$707$	−3.18034			−0.119609
$708$	6.97214	−	5.06555i	0.262029	−	0.190375i
$709$	3.65654	+	11.2537i	0.137324	+	0.422641i	0.995944	−	0.0899719i	$-0.0286777\pi$
$709$	3.65654	+	11.2537i	0.137324	+	0.422641i	−0.858620	+	0.512613i	$0.828678\pi$
$710$	−8.35410	+	6.06961i	−0.313524	+	0.227788i
$711$	3.88197	−	11.9475i	0.145585	−	0.448065i
$712$	3.09017	+	9.51057i	0.115809	+	0.356423i
$713$	−2.30902	−	7.10642i	−0.0864734	−	0.266138i
$714$	−1.42705	+	4.39201i	−0.0534060	+	0.164367i
$715$	64.0689			2.39604
$716$	−4.47214	−	13.7638i	−0.167132	−	0.514378i
$717$	−3.61803	+	2.62866i	−0.135118	+	0.0981689i
$718$	1.58359			0.0590991
$719$	−21.9721	+	15.9637i	−0.819422	+	0.595345i	−0.916547	−	0.399927i	$-0.869035\pi$
$719$	−21.9721	+	15.9637i	−0.819422	+	0.595345i	0.0971246	+	0.995272i	$0.469035\pi$
$720$	3.35410	−	2.43690i	0.125000	−	0.0908178i
$721$	−2.54508	−	1.84911i	−0.0947839	−	0.0688645i
$722$	8.54508	+	6.20837i	0.318015	+	0.231052i
$723$	6.98278	−	21.4908i	0.259692	−	0.799251i
$724$	3.14590			0.116916
$725$	−27.1353	−	19.7149i	−1.00778	−	0.732194i
$726$	−10.1459			−0.376550
$727$	−9.21885	+	28.3727i	−0.341908	+	1.05228i	0.621310	+	0.783565i	$0.286601\pi$
$727$	−9.21885	+	28.3727i	−0.341908	+	1.05228i	−0.963218	+	0.268720i	$0.913399\pi$
$728$	−9.89919	−	7.19218i	−0.366888	−	0.266560i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	3.25329	+	2.36365i	0.120410	+	0.0874827i
$731$	6.04508	−	4.39201i	0.223586	−	0.162444i
$732$	22.1803			0.819809
$733$	19.3541	−	14.0616i	0.714860	−	0.519376i	−0.169878	−	0.985465i	$-0.554337\pi$
$733$	19.3541	−	14.0616i	0.714860	−	0.519376i	0.884738	+	0.466089i	$0.154337\pi$
$734$	−1.28773	−	3.96323i	−0.0475310	−	0.146285i
$735$	−1.80902	−	1.31433i	−0.0667266	−	0.0484797i
$736$	−4.54508	+	13.9883i	−0.167534	+	0.515617i
$737$	16.5623	+	50.9735i	0.610080	+	1.87763i
$738$	−1.16312	−	3.57971i	−0.0428150	−	0.131771i
$739$	−11.1565	+	34.3363i	−0.410400	+	1.26308i	0.505901	+	0.862591i	$0.331160\pi$
$739$	−11.1565	+	34.3363i	−0.410400	+	1.26308i	−0.916301	+	0.400490i	$0.868840\pi$
$740$	8.78115	−	27.0256i	0.322802	−	0.993481i
$741$	2.33688	+	7.19218i	0.0858475	+	0.264211i
$742$	−3.54508	+	2.57565i	−0.130144	+	0.0945553i
$743$	5.34752			0.196182			0.0980908	−	0.995177i	$-0.468726\pi$
$743$	5.34752			0.196182			0.0980908	+	0.995177i	$0.468726\pi$
$744$	−5.16312	+	3.75123i	−0.189289	+	0.137527i
$745$	11.9098			0.436342
$746$	−11.7812	−	8.55951i	−0.431339	−	0.313386i
$747$	−4.00000	−	2.90617i	−0.146352	−	0.106331i
$748$	−19.5623	+	60.2066i	−0.715269	+	2.20137i
$749$	−5.29180			−0.193358
$750$	−5.59017	+	4.06150i	−0.204124	+	0.148305i
$751$	−30.3607			−1.10788			−0.553938	−	0.832558i	$-0.686876\pi$
$751$	−30.3607			−1.10788			−0.553938	+	0.832558i	$0.686876\pi$
$752$	6.87539	−	21.1603i	0.250720	−	0.771636i
$753$	−11.2082	−	8.14324i	−0.408450	−	0.296756i
$754$	−18.3541	−	13.3350i	−0.668417	−	0.485633i
$755$	34.7984			1.26644
$756$	1.30902	−	0.951057i	0.0476085	−	0.0345896i
$757$	−26.2148			−0.952792			−0.476396	−	0.879231i	$-0.658057\pi$
$757$	−26.2148			−0.952792			−0.476396	+	0.879231i	$0.658057\pi$
$758$	11.6459	−	8.46124i	0.422998	−	0.307326i
$759$	−4.23607	−	13.0373i	−0.153760	−	0.473223i
$760$	−2.13525	+	6.57164i	−0.0774538	+	0.238378i
$761$	11.8992	−	36.6219i	0.431345	−	1.32754i	−0.465441	−	0.885079i	$-0.654104\pi$
$761$	11.8992	−	36.6219i	0.431345	−	1.32754i	0.896786	−	0.442465i	$-0.145896\pi$
$762$	−2.29180	−	7.05342i	−0.0830230	−	0.255519i
$763$	−3.88197	−	11.9475i	−0.140537	−	0.432527i
$764$	−3.33688	+	10.2699i	−0.120724	+	0.371551i
$765$	−13.5172	−	9.82084i	−0.488716	−	0.355073i
$766$	−1.35410	−	4.16750i	−0.0489257	−	0.150578i
$767$	23.5795	−	17.1315i	0.851407	−	0.618584i
$768$	6.56231			0.236797
$769$	26.5066	−	19.2582i	0.955852	−	0.694467i	0.00366804	−	0.999993i	$-0.498832\pi$
$769$	26.5066	−	19.2582i	0.955852	−	0.694467i	0.952184	+	0.305526i	$0.0988324\pi$
$770$	5.85410	+	4.25325i	0.210967	+	0.153277i
$771$	11.9443	+	8.67802i	0.430162	+	0.312531i
$772$	−16.2533	−	11.8087i	−0.584969	−	0.425005i
$773$	8.07295	−	24.8460i	0.290364	−	0.893648i	−0.694376	−	0.719613i	$-0.744319\pi$
$773$	8.07295	−	24.8460i	0.290364	−	0.893648i	0.984739	−	0.174035i	$-0.0556806\pi$
$774$	0.618034			0.0222148
$775$	−11.5451	+	8.38800i	−0.414712	+	0.301306i
$776$	−5.65248			−0.202912
$777$	2.42705	−	7.46969i	0.0870700	−	0.267974i
$778$	5.75329	+	4.18001i	0.206265	+	0.149861i
$779$	−6.80902	−	4.94704i	−0.243958	−	0.177246i
$780$	16.0172	−	11.6372i	0.573509	−	0.416678i
$781$	−31.6525	+	22.9969i	−1.13261	+	0.822893i
$782$	12.0902			0.432344
$783$	5.42705	−	3.94298i	0.193947	−	0.140911i
$784$	0.572949	+	1.76336i	0.0204625	+	0.0629770i
$785$	−39.9230			−1.42491
$786$	2.64590	−	8.14324i	0.0943761	−	0.290460i
$787$	13.2812	+	40.8752i	0.473422	+	1.45704i	0.848074	+	0.529878i	$0.177762\pi$
$787$	13.2812	+	40.8752i	0.473422	+	1.45704i	−0.374652	+	0.927165i	$0.622238\pi$
$788$	4.16312	+	12.8128i	0.148305	+	0.456436i
$789$	−9.25329	+	28.4787i	−0.329426	+	1.01387i
$790$	14.0451	−	10.2044i	0.499702	−	0.363055i
$791$	4.26393	+	13.1230i	0.151608	+	0.466601i
$792$	−9.47214	+	6.88191i	−0.336578	+	0.244538i
$793$	75.0132			2.66380
$794$	−2.64590	+	1.92236i	−0.0938994	+	0.0682219i
$795$	−4.89919	−	15.0781i	−0.173756	−	0.534767i
$796$	−15.3262	−	11.1352i	−0.543224	−	0.394675i
$797$	−43.5517	−	31.6421i	−1.54268	−	1.12082i	−0.948628	−	0.316395i	$-0.897528\pi$
$797$	−43.5517	−	31.6421i	−1.54268	−	1.12082i	−0.594051	−	0.804427i	$-0.702472\pi$
$798$	−0.263932	+	0.812299i	−0.00934309	+	0.0287551i
$799$	−89.6656			−3.17214
$800$	28.0902			0.993137
$801$	−4.47214			−0.158015
$802$	−1.56637	+	4.82079i	−0.0553105	+	0.170228i
$803$	12.3262	+	8.95554i	0.434983	+	0.316034i
$804$	13.3992	+	9.73508i	0.472553	+	0.343330i
$805$	−1.80902	+	5.56758i	−0.0637595	+	0.196231i
$806$	−7.80902	+	5.67358i	−0.275061	+	0.199843i
$807$	−23.7426			−0.835781
$808$	5.75329	−	4.18001i	0.202400	−	0.147052i
$809$	−7.03444	−	21.6498i	−0.247318	−	0.761166i	−0.995247	−	0.0973870i	$-0.968952\pi$
$809$	−7.03444	−	21.6498i	−0.247318	−	0.761166i	0.747929	−	0.663779i	$-0.231048\pi$
$810$	−0.427051	−	1.31433i	−0.0150050	−	0.0461808i
$811$	−10.7639	+	33.1280i	−0.377973	+	1.16328i	0.563478	+	0.826131i	$0.309463\pi$
$811$	−10.7639	+	33.1280i	−0.377973	+	1.16328i	−0.941451	+	0.337150i	$0.890537\pi$
$812$	3.35410	+	10.3229i	0.117706	+	0.362262i
$813$	4.28115	+	13.1760i	0.150147	+	0.462104i
$814$	−7.85410	+	24.1724i	−0.275286	+	0.847244i
$815$	1.21885	+	3.75123i	0.0426944	+	0.131400i
$816$	4.28115	+	13.1760i	0.149870	+	0.461253i
$817$	1.11803	−	0.812299i	0.0391151	−	0.0284188i
$818$	−10.3262			−0.361048
$819$	4.42705	−	3.21644i	0.154694	−	0.112392i
$820$	−6.80902	+	20.9560i	−0.237781	+	0.731815i
$821$	10.8820	+	7.90621i	0.379783	+	0.275929i	0.761256	−	0.648451i	$-0.224583\pi$
$821$	10.8820	+	7.90621i	0.379783	+	0.275929i	−0.381473	+	0.924380i	$0.624583\pi$
$822$	7.28115	+	5.29007i	0.253959	+	0.184512i
$823$	17.0172	−	52.3736i	0.593183	−	1.82563i	0.0296129	−	0.999561i	$-0.490573\pi$
$823$	17.0172	−	52.3736i	0.593183	−	1.82563i	0.563570	−	0.826068i	$-0.309427\pi$
$824$	7.03444			0.245056
$825$	−21.1803	+	15.3884i	−0.737405	+	0.535756i
$826$	3.29180			0.114536
$827$	−2.83688	+	8.73102i	−0.0986480	+	0.303607i	−0.988187	−	0.153251i	$-0.951026\pi$
$827$	−2.83688	+	8.73102i	−0.0986480	+	0.303607i	0.889539	+	0.456859i	$0.151026\pi$
$828$	−3.42705	−	2.48990i	−0.119098	−	0.0865299i
$829$	15.3262	+	11.1352i	0.532302	+	0.386740i	0.821218	−	0.570614i	$-0.193295\pi$
$829$	15.3262	+	11.1352i	0.532302	+	0.386740i	−0.288916	+	0.957354i	$0.593295\pi$
$830$	−2.11146	−	6.49839i	−0.0732897	−	0.225563i
$831$	26.1525	−	19.0009i	0.907219	−	0.659133i
$832$	−1.29180			−0.0447850
$833$	6.04508	−	4.39201i	0.209450	−	0.152174i
$834$	−1.01722	−	3.13068i	−0.0352235	−	0.108407i
$835$	−21.6074	+	15.6987i	−0.747755	+	0.543276i
$836$	−3.61803	+	11.1352i	−0.125132	+	0.385118i
$837$	−0.881966	−	2.71441i	−0.0304852	−	0.0938238i
$838$	4.37132	+	13.4535i	0.151005	+	0.464745i
$839$	2.70163	−	8.31475i	0.0932705	−	0.287057i	−0.893529	−	0.449006i	$-0.851778\pi$
$839$	2.70163	−	8.31475i	0.0932705	−	0.287057i	0.986799	+	0.161949i	$0.0517781\pi$
$840$	5.00000			0.172516
$841$	4.94427	+	15.2169i	0.170492	+	0.524721i
$842$	−8.50000	+	6.17561i	−0.292929	+	0.212826i
$843$	6.09017			0.209757
$844$	9.16312	−	6.65740i	0.315408	−	0.229157i
$845$	30.6525	−	22.2703i	1.05448	−	0.766123i
$846$	−6.00000	−	4.35926i	−0.206284	−	0.149874i
$847$	13.2812	+	9.64932i	0.456346	+	0.331555i
$848$	−4.06231	+	12.5025i	−0.139500	+	0.429337i
$849$	−25.1459			−0.863005
$850$	−7.13525	−	21.9601i	−0.244737	−	0.753224i
$851$	−20.5623			−0.704867
$852$	−3.73607	+	11.4984i	−0.127996	+	0.393930i
$853$	−19.7533	−	14.3516i	−0.676340	−	0.491390i	0.195802	−	0.980644i	$-0.437269\pi$
$853$	−19.7533	−	14.3516i	−0.676340	−	0.491390i	−0.872141	+	0.489254i	$0.837269\pi$
$854$	6.85410	+	4.97980i	0.234543	+	0.170405i
$855$	−2.50000	−	1.81636i	−0.0854982	−	0.0621181i
$856$	9.57295	−	6.95515i	0.327197	−	0.237722i
$857$	−18.6525			−0.637156			−0.318578	−	0.947897i	$-0.603205\pi$
$857$	−18.6525			−0.637156			−0.318578	+	0.947897i	$0.603205\pi$
$858$	−14.3262	+	10.4086i	−0.489090	+	0.355344i
$859$	−5.48936	−	16.8945i	−0.187294	−	0.576433i	0.812686	−	0.582702i	$-0.198005\pi$
$859$	−5.48936	−	16.8945i	−0.187294	−	0.576433i	−0.999980	+	0.00626898i	$0.998005\pi$
$860$	−2.92705	−	2.12663i	−0.0998116	−	0.0725174i
$861$	−1.88197	+	5.79210i	−0.0641372	+	0.197394i
$862$	4.62868	+	14.2456i	0.157653	+	0.485207i
$863$	−9.65248	−	29.7073i	−0.328574	−	1.01125i	−0.969801	−	0.243896i	$-0.921574\pi$
$863$	−9.65248	−	29.7073i	−0.328574	−	1.01125i	0.641227	−	0.767351i	$-0.278426\pi$
$864$	−1.73607	+	5.34307i	−0.0590622	+	0.181775i
$865$	−1.50658	+	4.63677i	−0.0512252	+	0.157655i
$866$	2.95492	+	9.09429i	0.100412	+	0.309037i
$867$	31.4164	−	22.8254i	1.06696	−	0.775190i
$868$	4.61803			0.156746
$869$	53.2148	−	38.6628i	1.80519	−	1.31155i
$870$	9.27051			0.314300
$871$	45.3156	+	32.9237i	1.53546	+	1.11558i
$872$	22.7254	+	16.5110i	0.769580	+	0.559133i
$873$	0.781153	−	2.40414i	0.0264380	−	0.0813679i
$874$	2.23607			0.0756361
$875$	11.1803			0.377964
$876$	4.70820			0.159075
$877$	0.920473	−	2.83293i	0.0310822	−	0.0956611i	−0.934312	−	0.356456i	$-0.883985\pi$
$877$	0.920473	−	2.83293i	0.0310822	−	0.0956611i	0.965394	+	0.260795i	$0.0839848\pi$
$878$	14.8992	+	10.8249i	0.502823	+	0.365322i
$879$	3.57295	+	2.59590i	0.120513	+	0.0875575i
$880$	21.7082			0.731783
$881$	−10.6631	+	7.74721i	−0.359250	+	0.261010i	−0.752739	−	0.658319i	$-0.771268\pi$
$881$	−10.6631	+	7.74721i	−0.359250	+	0.261010i	0.393489	+	0.919329i	$0.371268\pi$
$882$	0.618034			0.0208103
$883$	20.6976	−	15.0377i	0.696528	−	0.506057i	−0.182271	−	0.983248i	$-0.558345\pi$
$883$	20.6976	−	15.0377i	0.696528	−	0.506057i	0.878800	+	0.477191i	$0.158345\pi$
$884$	20.4443	+	62.9210i	0.687615	+	2.11626i
$885$	−3.68034	+	11.3269i	−0.123713	+	0.380750i
$886$	−0.802439	+	2.46965i	−0.0269585	+	0.0829696i
$887$	6.96149	+	21.4253i	0.233744	+	0.719390i	0.997286	+	0.0736314i	$0.0234588\pi$
$887$	6.96149	+	21.4253i	0.233744	+	0.719390i	−0.763541	+	0.645759i	$0.776541\pi$
$888$	5.42705	+	16.7027i	0.182120	+	0.560507i
$889$	−3.70820	+	11.4127i	−0.124369	+	0.382769i
$890$	−5.00000	−	3.63271i	−0.167600	−	0.121769i
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	−6.61803	+	4.80828i	−0.221588	+	0.160993i
$893$	−16.5836			−0.554949
$894$	−2.66312	+	1.93487i	−0.0890680	+	0.0647117i
$895$	16.1803	+	11.7557i	0.540849	+	0.392950i
$896$	−9.20820	−	6.69015i	−0.307625	−	0.223502i
$897$	−11.5902	−	8.42075i	−0.386985	−	0.281161i
$898$	3.22949	−	9.93935i	0.107769	−	0.331680i
$899$	19.1459			0.638551
$900$	−2.50000	+	7.69421i	−0.0833333	+	0.256474i
$901$	52.9787			1.76498
$902$	6.09017	−	18.7436i	0.202780	−	0.624094i
$903$	−0.809017	−	0.587785i	−0.0269224	−	0.0195603i
$904$	−24.9615	−	18.1356i	−0.830207	−	0.603181i
$905$	−3.51722	+	2.55541i	−0.116916	+	0.0849447i
$906$	−7.78115	+	5.65334i	−0.258511	+	0.187820i
$907$	37.2492			1.23684			0.618420	−	0.785848i	$-0.287773\pi$
$907$	37.2492			1.23684			0.618420	+	0.785848i	$0.287773\pi$
$908$	−21.7533	+	15.8047i	−0.721908	+	0.524497i
$909$	0.982779	+	3.02468i	0.0325967	+	0.100322i
$910$	7.56231			0.250688
$911$	13.5836	−	41.8060i	0.450044	−	1.38509i	−0.426811	−	0.904341i	$-0.640363\pi$
$911$	13.5836	−	41.8060i	0.450044	−	1.38509i	0.876856	−	0.480754i	$-0.159637\pi$
$912$	0.791796	+	2.43690i	0.0262190	+	0.0806937i
$913$	−8.00000	−	24.6215i	−0.264761	−	0.814852i
$914$	−1.81559	+	5.58783i	−0.0600545	+	0.184829i
$915$	−24.7984	+	18.0171i	−0.819809	+	0.595626i
$916$	6.80902	+	20.9560i	0.224976	+	0.692406i
$917$	−11.2082	+	8.14324i	−0.370128	+	0.268913i
$918$	4.61803			0.152418
$919$	9.47214	−	6.88191i	0.312457	−	0.227013i	−0.420493	−	0.907296i	$-0.638143\pi$
$919$	9.47214	−	6.88191i	0.312457	−	0.227013i	0.732950	+	0.680282i	$0.238143\pi$
$920$	−4.04508	−	12.4495i	−0.133363	−	0.410448i
$921$	8.59017	+	6.24112i	0.283056	+	0.205652i
$922$	9.00000	+	6.53888i	0.296399	+	0.215347i
$923$	−12.6353	+	38.8873i	−0.415894	+	1.27999i
$924$	8.47214			0.278713
$925$	12.1353	+	37.3485i	0.399005	+	1.22801i
$926$	−7.14590			−0.234829
$927$	−0.972136	+	2.99193i	−0.0319291	+	0.0982678i
$928$	−30.4894	−	22.1518i	−1.00086	−	0.727169i
$929$	−43.6418	−	31.7076i	−1.43184	−	1.04029i	−0.989670	−	0.143364i	$-0.954208\pi$
$929$	−43.6418	−	31.7076i	−1.43184	−	1.04029i	−0.442172	−	0.896930i	$-0.645792\pi$
$930$	1.21885	−	3.75123i	0.0399676	−	0.123008i
$931$	1.11803	−	0.812299i	0.0366421	−	0.0266220i
$932$	43.5066			1.42511
$933$	−22.3262	+	16.2210i	−0.730928	+	0.531050i
$934$	1.76393	+	5.42882i	0.0577176	+	0.177637i
$935$	−27.0344	−	83.2035i	−0.884121	−	2.72104i
$936$	−3.78115	+	11.6372i	−0.123591	+	0.380374i
$937$	11.3475	+	34.9241i	0.370707	+	1.14092i	0.946329	+	0.323204i	$0.104760\pi$
$937$	11.3475	+	34.9241i	0.370707	+	1.14092i	−0.575622	+	0.817716i	$0.695240\pi$
$938$	1.95492	+	6.01661i	0.0638302	+	0.196449i
$939$	7.68034	−	23.6377i	0.250638	−	0.771386i
$940$	13.4164	+	41.2915i	0.437595	+	1.34678i
$941$	−4.74671	−	14.6089i	−0.154738	−	0.476236i	0.843396	−	0.537293i	$-0.180553\pi$
$941$	−4.74671	−	14.6089i	−0.154738	−	0.476236i	−0.998134	+	0.0610569i	$0.980553\pi$
$942$	8.92705	−	6.48588i	0.290859	−	0.211321i
$943$	15.9443			0.519217
$944$	7.98936	−	5.80461i	0.260031	−	0.188924i
$945$	−0.690983	+	2.12663i	−0.0224777	+	0.0691792i
$946$	2.61803	+	1.90211i	0.0851196	+	0.0618430i
$947$	11.3713	+	8.26175i	0.369518	+	0.268471i	0.757011	−	0.653402i	$-0.226659\pi$
$947$	11.3713	+	8.26175i	0.369518	+	0.268471i	−0.387493	+	0.921873i	$0.626659\pi$
$948$	6.28115	−	19.3314i	0.204002	−	0.627855i
$949$	15.9230			0.516882
$950$	−1.31966	−	4.06150i	−0.0428154	−	0.131772i
$951$	−5.94427			−0.192756
$952$	−5.16312	+	15.8904i	−0.167338	+	0.515012i
$953$	24.3156	+	17.6663i	0.787659	+	0.572268i	0.907268	−	0.420553i	$-0.138164\pi$
$953$	24.3156	+	17.6663i	0.787659	+	0.572268i	−0.119609	+	0.992821i	$0.538164\pi$
$954$	3.54508	+	2.57565i	0.114776	+	0.0833899i
$955$	−4.61146	−	14.1926i	−0.149223	−	0.459262i
$956$	−5.85410	+	4.25325i	−0.189335	+	0.137560i
$957$	35.1246			1.13542
$958$	4.04508	−	2.93893i	0.130691	−	0.0949524i
$959$	−4.50000	−	13.8496i	−0.145313	−	0.447226i
$960$	0.427051	−	0.310271i	0.0137830	−	0.0100139i
$961$	−7.06231	+	21.7355i	−0.227816	+	0.701147i
$962$	8.20820	+	25.2623i	0.264643	+	0.814488i
$963$	1.63525	+	5.03280i	0.0526954	+	0.162180i
$964$	11.2984	−	34.7728i	0.363896	−	1.11996i
$965$	27.7639			0.893753
$966$	−0.500000	−	1.53884i	−0.0160872	−	0.0495114i
$967$	−37.0066	+	26.8869i	−1.19005	+	0.864623i	−0.993270	−	0.115824i	$-0.963049\pi$
$967$	−37.0066	+	26.8869i	−1.19005	+	0.864623i	−0.196782	+	0.980447i	$0.563049\pi$
$968$	−36.7082			−1.17985
$969$	8.35410	−	6.06961i	0.268372	−	0.194984i
$970$	2.82624	−	2.05338i	0.0907450	−	0.0659301i
$971$	−5.33688	−	3.87747i	−0.171269	−	0.124434i	0.498849	−	0.866689i	$-0.333756\pi$
$971$	−5.33688	−	3.87747i	−0.171269	−	0.124434i	−0.670117	+	0.742255i	$0.733756\pi$
$972$	−1.30902	−	0.951057i	−0.0419867	−	0.0305052i
$973$	−1.64590	+	5.06555i	−0.0527651	+	0.162394i
$974$	−10.1459			−0.325096
$975$	−8.45492	+	26.0216i	−0.270774	+	0.833357i
$976$	25.4164			0.813559
$977$	4.50000	−	13.8496i	0.143968	−	0.443087i	−0.852909	−	0.522060i	$-0.825164\pi$
$977$	4.50000	−	13.8496i	0.143968	−	0.443087i	0.996877	+	0.0789723i	$0.0251639\pi$
$978$	−0.881966	−	0.640786i	−0.0282022	−	0.0204901i
$979$	−18.9443	−	13.7638i	−0.605462	−	0.439894i
$980$	−2.92705	−	2.12663i	−0.0935012	−	0.0679326i
$981$	−10.1631	+	7.38394i	−0.324483	+	0.235751i
$982$	−12.7082			−0.405535
$983$	−36.1976	+	26.2991i	−1.15452	+	0.838810i	−0.989076	−	0.147409i	$-0.952907\pi$
$983$	−36.1976	+	26.2991i	−1.15452	+	0.838810i	−0.165447	+	0.986219i	$0.552907\pi$
$984$	−4.20820	−	12.9515i	−0.134153	−	0.412879i
$985$	−15.0623	−	10.9434i	−0.479925	−	0.348686i
$986$	−9.57295	+	29.4625i	−0.304865	+	0.938277i
$987$	3.70820	+	11.4127i	0.118033	+	0.363270i
$988$	3.78115	+	11.6372i	0.120295	+	0.370228i
$989$	−0.809017	+	2.48990i	−0.0257252	+	0.0791742i
$990$	2.23607	−	6.88191i	0.0710669	−	0.218721i
$991$	−19.2426	−	59.2228i	−0.611263	−	1.88127i	−0.446028	−	0.895019i	$-0.647162\pi$
$991$	−19.2426	−	59.2228i	−0.611263	−	1.88127i	−0.165235	−	0.986254i	$-0.552838\pi$
$992$	−12.9721	+	9.42481i	−0.411866	+	0.299238i
$993$	13.0000			0.412543
$994$	−3.73607	+	2.71441i	−0.118501	+	0.0860959i
$995$	26.1803			0.829973
$996$	−6.47214	−	4.70228i	−0.205077	−	0.148998i
$997$	33.0795	+	24.0337i	1.04764	+	0.761154i	0.971762	−	0.235963i	$-0.0758244\pi$
$997$	33.0795	+	24.0337i	1.04764	+	0.761154i	0.0758770	+	0.997117i	$0.475824\pi$
$998$	−4.71227	+	14.5029i	−0.149164	+	0.459080i
$999$	−7.85410			−0.248493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.a.421.1	yes	4
25.6	even	5	inner	525.2.n.a.106.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.a.106.1	✓	4	25.6	even	5	inner
525.2.n.a.421.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.23607 q^{5} +(0.500000 - 0.363271i) q^{6} -1.00000 q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.23607 q^{5} +(0.500000 - 0.363271i) q^{6} -1.00000 q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.427051 + 1.31433i) q^{10} +(-1.61803 + 4.97980i) q^{11} +(0.500000 + 1.53884i) q^{12} +(1.69098 + 5.20431i) q^{13} +(-0.190983 + 0.587785i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(0.572949 + 1.76336i) q^{16} +(6.04508 - 4.39201i) q^{17} +0.618034 q^{18} +(1.11803 - 0.812299i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(2.61803 + 1.90211i) q^{22} +(-0.809017 + 2.48990i) q^{23} +2.23607 q^{24} +5.00000 q^{25} +3.38197 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.30902 - 0.951057i) q^{28} +(-5.42705 - 3.94298i) q^{29} +(-1.11803 + 0.812299i) q^{30} +(-2.30902 + 1.67760i) q^{31} +5.61803 q^{32} +(-4.23607 + 3.07768i) q^{33} +(-1.42705 - 4.39201i) q^{34} +2.23607 q^{35} +(-0.500000 + 1.53884i) q^{36} +(2.42705 + 7.46969i) q^{37} +(-0.263932 - 0.812299i) q^{38} +(-1.69098 + 5.20431i) q^{39} +(-4.04508 + 2.93893i) q^{40} +(-1.88197 - 5.79210i) q^{41} +(-0.500000 + 0.363271i) q^{42} +1.00000 q^{43} +(-6.85410 + 4.97980i) q^{44} +(-0.690983 - 2.12663i) q^{45} +(1.30902 + 0.951057i) q^{46} +(-9.70820 - 7.05342i) q^{47} +(-0.572949 + 1.76336i) q^{48} +1.00000 q^{49} +(0.954915 - 2.93893i) q^{50} +7.47214 q^{51} +(-2.73607 + 8.42075i) q^{52} +(5.73607 + 4.16750i) q^{53} +(0.500000 + 0.363271i) q^{54} +(3.61803 - 11.1352i) q^{55} +(-1.80902 + 1.31433i) q^{56} +1.38197 q^{57} +(-3.35410 + 2.43690i) q^{58} +(-1.64590 - 5.06555i) q^{59} +(-1.11803 - 3.44095i) q^{60} +(4.23607 - 13.0373i) q^{61} +(0.545085 + 1.67760i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-3.78115 - 11.6372i) q^{65} +(1.00000 + 3.07768i) q^{66} +(8.28115 - 6.01661i) q^{67} +12.0902 q^{68} +(-2.11803 + 1.53884i) q^{69} +(0.427051 - 1.31433i) q^{70} +(6.04508 + 4.39201i) q^{71} +(1.80902 + 1.31433i) q^{72} +(0.899187 - 2.76741i) q^{73} +4.85410 q^{74} +(4.04508 + 2.93893i) q^{75} +2.23607 q^{76} +(1.61803 - 4.97980i) q^{77} +(2.73607 + 1.98787i) q^{78} +(-10.1631 - 7.38394i) q^{79} +(-1.28115 - 3.94298i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.76393 q^{82} +(-4.00000 + 2.90617i) q^{83} +(-0.500000 - 1.53884i) q^{84} +(-13.5172 + 9.82084i) q^{85} +(0.190983 - 0.587785i) q^{86} +(-2.07295 - 6.37988i) q^{87} +(3.61803 + 11.1352i) q^{88} +(-1.38197 + 4.25325i) q^{89} -1.38197 q^{90} +(-1.69098 - 5.20431i) q^{91} +(-3.42705 + 2.48990i) q^{92} -2.85410 q^{93} +(-6.00000 + 4.35926i) q^{94} +(-2.50000 + 1.81636i) q^{95} +(4.54508 + 3.30220i) q^{96} +(-2.04508 - 1.48584i) q^{97} +(0.190983 - 0.587785i) q^{98} -5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{6} - 4 q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 2 q^{11} + 2 q^{12} + 9 q^{13} - 3 q^{14} - 5 q^{15} + 9 q^{16} + 13 q^{17} - 2 q^{18} - 5 q^{20} - q^{21} + 6 q^{22} - q^{23} + 20 q^{25} + 18 q^{26} + q^{27} - 3 q^{28} - 15 q^{29} - 7 q^{31} + 18 q^{32} - 8 q^{33} + q^{34} - 2 q^{36} + 3 q^{37} - 10 q^{38} - 9 q^{39} - 5 q^{40} - 12 q^{41} - 2 q^{42} + 4 q^{43} - 14 q^{44} - 5 q^{45} + 3 q^{46} - 12 q^{47} - 9 q^{48} + 4 q^{49} + 15 q^{50} + 12 q^{51} - 2 q^{52} + 14 q^{53} + 2 q^{54} + 10 q^{55} - 5 q^{56} + 10 q^{57} - 20 q^{59} + 8 q^{61} - 9 q^{62} + q^{63} - 7 q^{64} + 5 q^{65} + 4 q^{66} + 13 q^{67} + 26 q^{68} - 4 q^{69} - 5 q^{70} + 13 q^{71} + 5 q^{72} - 21 q^{73} + 6 q^{74} + 5 q^{75} + 2 q^{77} + 2 q^{78} - 25 q^{79} + 15 q^{80} - q^{81} - 24 q^{82} - 16 q^{83} - 2 q^{84} - 25 q^{85} + 3 q^{86} - 15 q^{87} + 10 q^{88} - 10 q^{89} - 10 q^{90} - 9 q^{91} - 7 q^{92} + 2 q^{93} - 24 q^{94} - 10 q^{95} + 7 q^{96} + 3 q^{97} + 3 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^6 - 4 * q^7 + 5 * q^8 - q^9 + 5 * q^10 - 2 * q^11 + 2 * q^12 + 9 * q^13 - 3 * q^14 - 5 * q^15 + 9 * q^16 + 13 * q^17 - 2 * q^18 - 5 * q^20 - q^21 + 6 * q^22 - q^23 + 20 * q^25 + 18 * q^26 + q^27 - 3 * q^28 - 15 * q^29 - 7 * q^31 + 18 * q^32 - 8 * q^33 + q^34 - 2 * q^36 + 3 * q^37 - 10 * q^38 - 9 * q^39 - 5 * q^40 - 12 * q^41 - 2 * q^42 + 4 * q^43 - 14 * q^44 - 5 * q^45 + 3 * q^46 - 12 * q^47 - 9 * q^48 + 4 * q^49 + 15 * q^50 + 12 * q^51 - 2 * q^52 + 14 * q^53 + 2 * q^54 + 10 * q^55 - 5 * q^56 + 10 * q^57 - 20 * q^59 + 8 * q^61 - 9 * q^62 + q^63 - 7 * q^64 + 5 * q^65 + 4 * q^66 + 13 * q^67 + 26 * q^68 - 4 * q^69 - 5 * q^70 + 13 * q^71 + 5 * q^72 - 21 * q^73 + 6 * q^74 + 5 * q^75 + 2 * q^77 + 2 * q^78 - 25 * q^79 + 15 * q^80 - q^81 - 24 * q^82 - 16 * q^83 - 2 * q^84 - 25 * q^85 + 3 * q^86 - 15 * q^87 + 10 * q^88 - 10 * q^89 - 10 * q^90 - 9 * q^91 - 7 * q^92 + 2 * q^93 - 24 * q^94 - 10 * q^95 + 7 * q^96 + 3 * q^97 + 3 * q^98 - 12 * q^99

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