LMFDB - Embedded newform 525.2.n.c.106.1

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			106.1
Character	$\chi$	$=$	525.106
Dual form			525.2.n.c.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758114 - 2.33323i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.25121 + 2.36214i) q^{4} +(0.447435 - 2.19084i) q^{5} +(1.98477 + 1.44202i) q^{6} +1.00000 q^{7} +(4.00669 + 2.91103i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.758114 - 2.33323i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.25121 + 2.36214i) q^{4} +(0.447435 - 2.19084i) q^{5} +(1.98477 + 1.44202i) q^{6} +1.00000 q^{7} +(4.00669 + 2.91103i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-5.45096 + 0.616938i) q^{10} +(-1.26290 - 3.88681i) q^{11} +(1.24185 - 3.82203i) q^{12} +(-0.686443 + 2.11265i) q^{13} +(-0.758114 - 2.33323i) q^{14} +(0.925763 + 2.03543i) q^{15} +(1.27088 - 3.91138i) q^{16} +(-3.33308 - 2.42162i) q^{17} -2.45331 q^{18} +(-5.18791 - 3.76923i) q^{19} +(3.72038 + 8.17981i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-8.11141 + 5.89329i) q^{22} +(0.955983 + 2.94221i) q^{23} -4.95254 q^{24} +(-4.59960 - 1.96052i) q^{25} +5.44972 q^{26} +(0.309017 + 0.951057i) q^{27} +(-3.25121 + 2.36214i) q^{28} +(-0.990627 + 0.719733i) q^{29} +(4.04729 - 3.70311i) q^{30} +(5.36645 + 3.89895i) q^{31} -0.184561 q^{32} +(3.30632 + 2.40218i) q^{33} +(-3.12336 + 9.61272i) q^{34} +(0.447435 - 2.19084i) q^{35} +(1.24185 + 3.82203i) q^{36} +(-2.12781 + 6.54871i) q^{37} +(-4.86148 + 14.9621i) q^{38} +(-0.686443 - 2.11265i) q^{39} +(8.17035 - 7.47554i) q^{40} +(2.14117 - 6.58983i) q^{41} +(1.98477 + 1.44202i) q^{42} -5.93592 q^{43} +(13.2872 + 9.65369i) q^{44} +(-1.94535 - 1.10254i) q^{45} +(6.14013 - 4.46106i) q^{46} +(-7.12926 + 5.17971i) q^{47} +(1.27088 + 3.91138i) q^{48} +1.00000 q^{49} +(-1.08734 + 12.2183i) q^{50} +4.11991 q^{51} +(-2.75862 - 8.49017i) q^{52} +(-6.26565 + 4.55226i) q^{53} +(1.98477 - 1.44202i) q^{54} +(-9.08046 + 1.02772i) q^{55} +(4.00669 + 2.91103i) q^{56} +6.41260 q^{57} +(2.43031 + 1.76573i) q^{58} +(-2.21767 + 6.82529i) q^{59} +(-7.81783 - 4.43082i) q^{60} +(-2.93182 - 9.02321i) q^{61} +(5.02879 - 15.4770i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-2.40185 - 7.39214i) q^{64} +(4.32136 + 2.44917i) q^{65} +(3.09828 - 9.53554i) q^{66} +(4.01287 + 2.91552i) q^{67} +16.5568 q^{68} +(-2.50279 - 1.81839i) q^{69} +(-5.45096 + 0.616938i) q^{70} +(4.91190 - 3.56871i) q^{71} +(4.00669 - 2.91103i) q^{72} +(-4.90718 - 15.1027i) q^{73} +16.8928 q^{74} +(4.87352 - 1.11748i) q^{75} +25.7705 q^{76} +(-1.26290 - 3.88681i) q^{77} +(-4.40892 + 3.20327i) q^{78} +(7.51223 - 5.45796i) q^{79} +(-8.00059 - 4.53440i) q^{80} +(-0.809017 - 0.587785i) q^{81} -16.9989 q^{82} +(4.92340 + 3.57706i) q^{83} +(1.24185 - 3.82203i) q^{84} +(-6.79674 + 6.21874i) q^{85} +(4.50011 + 13.8499i) q^{86} +(0.378386 - 1.16455i) q^{87} +(6.25457 - 19.2496i) q^{88} +(-5.22083 - 16.0681i) q^{89} +(-1.09770 + 5.37482i) q^{90} +(-0.686443 + 2.11265i) q^{91} +(-10.0580 - 7.30759i) q^{92} -6.63330 q^{93} +(17.4903 + 12.7074i) q^{94} +(-10.5791 + 9.67941i) q^{95} +(0.149313 - 0.108482i) q^{96} +(2.95926 - 2.15003i) q^{97} +(-0.758114 - 2.33323i) q^{98} -4.08683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.758114	−	2.33323i	−0.536067	−	1.64985i	−0.741331	−	0.671139i	$-0.765805\pi$
$2$	−0.758114	−	2.33323i	−0.536067	−	1.64985i	0.205264	−	0.978707i	$-0.434195\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−3.25121	+	2.36214i	−1.62561	+	1.18107i
$5$	0.447435	−	2.19084i	0.200099	−	0.979776i
$5$	0.447435	−	2.19084i	0.200099	−	0.979776i
$6$	1.98477	+	1.44202i	0.810278	+	0.588701i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	4.00669	+	2.91103i	1.41658	+	1.02920i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−5.45096	+	0.616938i	−1.72375	+	0.195093i
$11$	−1.26290	−	3.88681i	−0.380779	−	1.17192i	−0.939496	−	0.342559i	$-0.888706\pi$
$11$	−1.26290	−	3.88681i	−0.380779	−	1.17192i	0.558717	−	0.829358i	$-0.311294\pi$
$12$	1.24185	−	3.82203i	0.358492	−	1.10332i
$13$	−0.686443	+	2.11265i	−0.190385	+	0.585945i	−0.999999	−	0.00101713i	$-0.999676\pi$
$13$	−0.686443	+	2.11265i	−0.190385	+	0.585945i	0.809614	+	0.586962i	$0.199676\pi$
$14$	−0.758114	−	2.33323i	−0.202614	−	0.623583i
$15$	0.925763	+	2.03543i	0.239031	+	0.525545i
$16$	1.27088	−	3.91138i	0.317721	−	0.977845i
$17$	−3.33308	−	2.42162i	−0.808390	−	0.587330i	0.104973	−	0.994475i	$-0.466524\pi$
$17$	−3.33308	−	2.42162i	−0.808390	−	0.587330i	−0.913364	+	0.407145i	$0.866524\pi$
$18$	−2.45331			−0.578250
$19$	−5.18791	−	3.76923i	−1.19019	−	0.864722i	−0.196903	−	0.980423i	$-0.563088\pi$
$19$	−5.18791	−	3.76923i	−1.19019	−	0.864722i	−0.993284	+	0.115701i	$0.963088\pi$
$20$	3.72038	+	8.17981i	0.831903	+	1.82906i
$21$	−0.809017	+	0.587785i	−0.176542	+	0.128265i
$22$	−8.11141	+	5.89329i	−1.72936	+	1.25645i
$23$	0.955983	+	2.94221i	0.199336	+	0.613494i	0.999899	+	0.0142442i	$0.00453421\pi$
$23$	0.955983	+	2.94221i	0.199336	+	0.613494i	−0.800562	+	0.599249i	$0.795466\pi$
$24$	−4.95254			−1.01093
$25$	−4.59960	−	1.96052i	−0.919921	−	0.392105i
$26$	5.44972			1.06878
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−3.25121	+	2.36214i	−0.614421	+	0.446403i
$29$	−0.990627	+	0.719733i	−0.183955	+	0.133651i	−0.675952	−	0.736946i	$-0.736267\pi$
$29$	−0.990627	+	0.719733i	−0.183955	+	0.133651i	0.491997	+	0.870597i	$0.336267\pi$
$30$	4.04729	−	3.70311i	0.738931	−	0.676092i
$31$	5.36645	+	3.89895i	0.963843	+	0.700273i	0.954040	−	0.299679i	$-0.0968796\pi$
$31$	5.36645	+	3.89895i	0.963843	+	0.700273i	0.00980292	+	0.999952i	$0.496880\pi$
$32$	−0.184561			−0.0326261
$33$	3.30632	+	2.40218i	0.575556	+	0.418166i
$34$	−3.12336	+	9.61272i	−0.535652	+	1.64857i
$35$	0.447435	−	2.19084i	0.0756304	−	0.370320i
$36$	1.24185	+	3.82203i	0.206975	+	0.637005i
$37$	−2.12781	+	6.54871i	−0.349809	+	1.07660i	0.609149	+	0.793055i	$0.291511\pi$
$37$	−2.12781	+	6.54871i	−0.349809	+	1.07660i	−0.958959	+	0.283546i	$0.908489\pi$
$38$	−4.86148	+	14.9621i	−0.788637	+	2.42717i
$39$	−0.686443	−	2.11265i	−0.109919	−	0.338295i
$40$	8.17035	−	7.47554i	1.29185	−	1.18199i
$41$	2.14117	−	6.58983i	0.334394	−	1.02916i	−0.632626	−	0.774457i	$-0.718023\pi$
$41$	2.14117	−	6.58983i	0.334394	−	1.02916i	0.967020	−	0.254701i	$-0.0819771\pi$
$42$	1.98477	+	1.44202i	0.306256	+	0.222508i
$43$	−5.93592			−0.905220			−0.452610	−	0.891709i	$-0.649507\pi$
$43$	−5.93592			−0.905220			−0.452610	+	0.891709i	$0.649507\pi$
$44$	13.2872	+	9.65369i	2.00312	+	1.45535i
$45$	−1.94535	−	1.10254i	−0.289996	−	0.164358i
$46$	6.14013	−	4.46106i	0.905312	−	0.657748i
$47$	−7.12926	+	5.17971i	−1.03991	+	0.755539i	−0.970268	−	0.242033i	$-0.922186\pi$
$47$	−7.12926	+	5.17971i	−1.03991	+	0.755539i	−0.0696419	+	0.997572i	$0.522186\pi$
$48$	1.27088	+	3.91138i	0.183436	+	0.564559i
$49$	1.00000			0.142857
$50$	−1.08734	+	12.2183i	−0.153773	+	1.72792i
$51$	4.11991			0.576903
$52$	−2.75862	−	8.49017i	−0.382552	−	1.17737i
$53$	−6.26565	+	4.55226i	−0.860653	+	0.625301i	−0.928062	−	0.372425i	$-0.878527\pi$
$53$	−6.26565	+	4.55226i	−0.860653	+	0.625301i	0.0674098	+	0.997725i	$0.478527\pi$
$54$	1.98477	−	1.44202i	0.270093	−	0.196234i
$55$	−9.08046	+	1.02772i	−1.22441	+	0.138578i
$56$	4.00669	+	2.91103i	0.535416	+	0.389003i
$57$	6.41260			0.849370
$58$	2.43031	+	1.76573i	0.319116	+	0.231851i
$59$	−2.21767	+	6.82529i	−0.288716	+	0.888576i	0.696544	+	0.717514i	$0.254720\pi$
$59$	−2.21767	+	6.82529i	−0.288716	+	0.888576i	−0.985260	+	0.171063i	$0.945280\pi$
$60$	−7.81783	−	4.43082i	−1.00928	−	0.572016i
$61$	−2.93182	−	9.02321i	−0.375381	−	1.15530i	−0.943221	−	0.332165i	$-0.892221\pi$
$61$	−2.93182	−	9.02321i	−0.375381	−	1.15530i	0.567841	−	0.823139i	$-0.307779\pi$
$62$	5.02879	−	15.4770i	0.638658	−	1.96559i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	−2.40185	−	7.39214i	−0.300231	−	0.924017i
$65$	4.32136	+	2.44917i	0.535999	+	0.303782i
$66$	3.09828	−	9.53554i	0.381372	−	1.17374i
$67$	4.01287	+	2.91552i	0.490250	+	0.356188i	0.805281	−	0.592894i	$-0.202015\pi$
$67$	4.01287	+	2.91552i	0.490250	+	0.356188i	−0.315030	+	0.949082i	$0.602015\pi$
$68$	16.5568			2.00780
$69$	−2.50279	−	1.81839i	−0.301301	−	0.218908i
$70$	−5.45096	+	0.616938i	−0.651515	+	0.0737382i
$71$	4.91190	−	3.56871i	0.582935	−	0.423527i	−0.256846	−	0.966452i	$-0.582683\pi$
$71$	4.91190	−	3.56871i	0.582935	−	0.423527i	0.839781	+	0.542925i	$0.182683\pi$
$72$	4.00669	−	2.91103i	0.472193	−	0.343068i
$73$	−4.90718	−	15.1027i	−0.574341	−	1.76764i	−0.638411	−	0.769696i	$-0.720408\pi$
$73$	−4.90718	−	15.1027i	−0.574341	−	1.76764i	0.0640694	−	0.997945i	$-0.479592\pi$
$74$	16.8928			1.96375
$75$	4.87352	−	1.11748i	0.562746	−	0.129036i
$76$	25.7705			2.95607
$77$	−1.26290	−	3.88681i	−0.143921	−	0.442943i
$78$	−4.40892	+	3.20327i	−0.499211	+	0.362698i
$79$	7.51223	−	5.45796i	0.845192	−	0.614068i	−0.0786242	−	0.996904i	$-0.525053\pi$
$79$	7.51223	−	5.45796i	0.845192	−	0.614068i	0.923816	+	0.382836i	$0.125053\pi$
$80$	−8.00059	−	4.53440i	−0.894493	−	0.506961i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−16.9989			−1.87721
$83$	4.92340	+	3.57706i	0.540413	+	0.392633i	0.824239	−	0.566243i	$-0.191604\pi$
$83$	4.92340	+	3.57706i	0.540413	+	0.392633i	−0.283825	+	0.958876i	$0.591604\pi$
$84$	1.24185	−	3.82203i	0.135497	−	0.417018i
$85$	−6.79674	+	6.21874i	−0.737210	+	0.674517i
$86$	4.50011	+	13.8499i	0.485259	+	1.49347i
$87$	0.378386	−	1.16455i	0.0405672	−	0.124853i
$88$	6.25457	−	19.2496i	0.666739	−	2.05201i
$89$	−5.22083	−	16.0681i	−0.553407	−	1.70321i	−0.700113	−	0.714032i	$-0.746867\pi$
$89$	−5.22083	−	16.0681i	−0.553407	−	1.70321i	0.146705	−	0.989180i	$-0.453133\pi$
$90$	−1.09770	+	5.37482i	−0.115707	+	0.566555i
$91$	−0.686443	+	2.11265i	−0.0719588	+	0.221466i
$92$	−10.0580	−	7.30759i	−1.04862	−	0.761869i
$93$	−6.63330			−0.687841
$94$	17.4903	+	12.7074i	1.80398	+	1.31067i
$95$	−10.5791	+	9.67941i	−1.08539	+	0.993086i
$96$	0.149313	−	0.108482i	0.0152392	−	0.0110719i
$97$	2.95926	−	2.15003i	0.300468	−	0.218302i	−0.427328	−	0.904097i	$-0.640545\pi$
$97$	2.95926	−	2.15003i	0.300468	−	0.218302i	0.727795	+	0.685794i	$0.240545\pi$
$98$	−0.758114	−	2.33323i	−0.0765811	−	0.235692i
$99$	−4.08683			−0.410742
$100$	19.5853	−	4.49085i	1.95853	−	0.449085i
$101$	−14.8193			−1.47457			−0.737286	−	0.675581i	$-0.763893\pi$
$101$	−14.8193			−1.47457			−0.737286	+	0.675581i	$0.763893\pi$
$102$	−3.12336	−	9.61272i	−0.309259	−	0.951801i
$103$	−5.12602	+	3.72427i	−0.505082	+	0.366964i	−0.810955	−	0.585109i	$-0.801052\pi$
$103$	−5.12602	+	3.72427i	−0.505082	+	0.366964i	0.305873	+	0.952072i	$0.401052\pi$
$104$	−8.90037	+	6.46649i	−0.872753	+	0.634092i
$105$	0.925763	+	2.03543i	0.0903453	+	0.198637i
$106$	15.3716	+	11.1681i	1.49302	+	1.08474i
$107$	2.81527			0.272162			0.136081	−	0.990698i	$-0.456549\pi$
$107$	2.81527			0.272162			0.136081	+	0.990698i	$0.456549\pi$
$108$	−3.25121	−	2.36214i	−0.312848	−	0.227297i
$109$	−1.73125	+	5.32823i	−0.165823	+	0.510352i	−0.999096	−	0.0425104i	$-0.986464\pi$
$109$	−1.73125	+	5.32823i	−0.165823	+	0.510352i	0.833273	+	0.552862i	$0.186464\pi$
$110$	9.28194	+	20.4077i	0.884999	+	1.94580i
$111$	−2.12781	−	6.54871i	−0.201962	−	0.621576i
$112$	1.27088	−	3.91138i	0.120087	−	0.369591i
$113$	4.82298	−	14.8436i	0.453708	−	1.39637i	−0.418937	−	0.908015i	$-0.637597\pi$
$113$	4.82298	−	14.8436i	0.453708	−	1.39637i	0.872645	−	0.488354i	$-0.162403\pi$
$114$	−4.86148	−	14.9621i	−0.455320	−	1.40133i
$115$	6.87367	−	0.777960i	0.640973	−	0.0725451i
$116$	1.52063	−	4.68001i	0.141187	−	0.434528i
$117$	1.79713	+	1.30569i	0.166145	+	0.120711i
$118$	17.6062			1.62079
$119$	−3.33308	−	2.42162i	−0.305543	−	0.221990i
$120$	−2.21594	+	10.8502i	−0.202287	+	0.990488i
$121$	−4.61318	+	3.35167i	−0.419380	+	0.304697i
$122$	−18.8306	+	13.6812i	−1.70484	+	1.23864i
$123$	2.14117	+	6.58983i	0.193062	+	0.594185i
$124$	−26.6574			−2.39390
$125$	−6.35323	+	9.19981i	−0.568250	+	0.822856i
$126$	−2.45331			−0.218558
$127$	2.52636	+	7.77532i	0.224178	+	0.689949i	0.998374	+	0.0570028i	$0.0181544\pi$
$127$	2.52636	+	7.77532i	0.224178	+	0.689949i	−0.774196	+	0.632946i	$0.781846\pi$
$128$	−15.7253	+	11.4251i	−1.38994	+	1.00985i
$129$	4.80226	−	3.48905i	0.422816	−	0.307194i
$130$	2.43840	−	11.9395i	0.213862	−	1.04716i
$131$	−7.45481	−	5.41624i	−0.651330	−	0.473219i	0.212394	−	0.977184i	$-0.431874\pi$
$131$	−7.45481	−	5.41624i	−0.651330	−	0.473219i	−0.863724	+	0.503965i	$0.831874\pi$
$132$	−16.4238			−1.42951
$133$	−5.18791	−	3.76923i	−0.449848	−	0.326834i
$134$	3.76038	−	11.5733i	0.324848	−	0.999778i
$135$	2.22188	−	0.251472i	0.191229	−	0.0216433i
$136$	−6.30519	−	19.4054i	−0.540666	−	1.66400i
$137$	5.91081	−	18.1916i	0.504995	−	1.55421i	−0.295785	−	0.955255i	$-0.595581\pi$
$137$	5.91081	−	18.1916i	0.504995	−	1.55421i	0.800779	−	0.598959i	$-0.204419\pi$
$138$	−2.34532	+	7.21815i	−0.199647	+	0.614450i
$139$	−1.58592	−	4.88097i	−0.134516	−	0.413999i	0.860998	−	0.508608i	$-0.169840\pi$
$139$	−1.58592	−	4.88097i	−0.134516	−	0.413999i	−0.995514	+	0.0946094i	$0.969840\pi$
$140$	3.72038	+	8.17981i	0.314430	+	0.691320i
$141$	2.72314	−	8.38095i	0.229329	−	0.705803i
$142$	−12.0504	−	8.75513i	−1.01125	−	0.734714i
$143$	9.07839			0.759173
$144$	−3.32722	−	2.41737i	−0.277268	−	0.201447i
$145$	1.13358	+	2.49234i	0.0941388	+	0.206978i
$146$	−31.5180	+	22.8992i	−2.60845	+	1.89515i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	−8.55105	−	26.3174i	−0.702892	−	2.16328i
$149$	15.2267			1.24742			0.623709	−	0.781657i	$-0.285625\pi$
$149$	15.2267			1.24742			0.623709	+	0.781657i	$0.285625\pi$
$150$	−6.30203	−	10.5239i	−0.514559	−	0.859272i
$151$	−9.19810			−0.748531			−0.374265	−	0.927322i	$-0.622105\pi$
$151$	−9.19810			−0.748531			−0.374265	+	0.927322i	$0.622105\pi$
$152$	−9.81397	−	30.2043i	−0.796018	−	2.44989i
$153$	−3.33308	+	2.42162i	−0.269463	+	0.195777i
$154$	−8.11141	+	5.89329i	−0.653636	+	0.474895i
$155$	10.9431	−	10.0125i	0.878975	−	0.804226i
$156$	7.22217	+	5.24721i	0.578236	+	0.420113i
$157$	5.06595			0.404307			0.202153	−	0.979354i	$-0.435206\pi$
$157$	5.06595			0.404307			0.202153	+	0.979354i	$0.435206\pi$
$158$	−18.4298	−	13.3900i	−1.46620	−	1.06525i
$159$	2.39326	−	7.36571i	0.189798	−	0.584139i
$160$	−0.0825791	+	0.404344i	−0.00652845	+	0.0319662i
$161$	0.955983	+	2.94221i	0.0753420	+	0.231879i
$162$	−0.758114	+	2.33323i	−0.0595630	+	0.183316i
$163$	−1.68422	+	5.18349i	−0.131918	+	0.406002i	−0.995098	−	0.0988943i	$-0.968469\pi$
$163$	−1.68422	+	5.18349i	−0.131918	+	0.406002i	0.863180	+	0.504897i	$0.168469\pi$
$164$	8.60474	+	26.4827i	0.671918	+	2.06795i
$165$	6.74217	−	6.16881i	0.524877	−	0.480241i
$166$	4.61362	−	14.1993i	0.358086	−	1.10208i
$167$	−1.44944	−	1.05308i	−0.112161	−	0.0814895i	0.530291	−	0.847816i	$-0.322083\pi$
$167$	−1.44944	−	1.05308i	−0.112161	−	0.0814895i	−0.642452	+	0.766326i	$0.722083\pi$
$168$	−4.95254			−0.382097
$169$	6.52512	+	4.74077i	0.501932	+	0.364675i
$170$	19.6625	+	11.1439i	1.50804	+	0.854696i
$171$	−5.18791	+	3.76923i	−0.396729	+	0.288241i
$172$	19.2990	−	14.0215i	1.47153	−	1.06913i
$173$	−3.44736	−	10.6099i	−0.262098	−	0.806655i	−0.992348	−	0.123475i	$-0.960596\pi$
$173$	−3.44736	−	10.6099i	−0.262098	−	0.806655i	0.730250	−	0.683180i	$-0.239404\pi$
$174$	−3.00403			−0.227735
$175$	−4.59960	−	1.96052i	−0.347697	−	0.148202i
$176$	−16.8078			−1.26693
$177$	−2.21767	−	6.82529i	−0.166690	−	0.513020i
$178$	−33.5326	+	24.3629i	−2.51337	+	1.82607i
$179$	13.8940	−	10.0946i	1.03849	−	0.754504i	0.0684962	−	0.997651i	$-0.478180\pi$
$179$	13.8940	−	10.0946i	1.03849	−	0.754504i	0.969989	+	0.243148i	$0.0781799\pi$
$180$	8.92912	−	1.01060i	0.665538	−	0.0753253i
$181$	−5.13715	−	3.73236i	−0.381842	−	0.277424i	0.380263	−	0.924879i	$-0.375834\pi$
$181$	−5.13715	−	3.73236i	−0.381842	−	0.277424i	−0.762104	+	0.647454i	$0.775834\pi$
$182$	5.44972			0.403960
$183$	7.67560	+	5.57665i	0.567397	+	0.412238i
$184$	−4.73454	+	14.5714i	−0.349035	+	1.07422i
$185$	13.3952	+	7.59182i	0.984832	+	0.558162i
$186$	5.02879	+	15.4770i	0.368729	+	1.13483i
$187$	−5.20304	+	16.0133i	−0.380484	+	1.17101i
$188$	10.9435	−	33.6807i	0.798138	−	2.45642i
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	30.6045	+	17.3453i	2.22028	+	1.25836i
$191$	−1.47822	+	4.54949i	−0.106960	+	0.329189i	−0.990186	−	0.139759i	$-0.955367\pi$
$191$	−1.47822	+	4.54949i	−0.106960	+	0.329189i	0.883225	+	0.468949i	$0.155367\pi$
$192$	6.28813	+	4.56859i	0.453807	+	0.329710i
$193$	16.8140			1.21030			0.605149	−	0.796112i	$-0.293114\pi$
$193$	16.8140			1.21030			0.605149	+	0.796112i	$0.293114\pi$
$194$	−7.25998	−	5.27468i	−0.521236	−	0.378700i
$195$	−4.93564	+	0.558614i	−0.353448	+	0.0400032i
$196$	−3.25121	+	2.36214i	−0.232229	+	0.168725i
$197$	18.1033	−	13.1528i	1.28980	−	0.937098i	0.290003	−	0.957026i	$-0.406344\pi$
$197$	18.1033	−	13.1528i	1.28980	−	0.937098i	0.999801	+	0.0199279i	$0.00634368\pi$
$198$	3.09828	+	9.53554i	0.220185	+	0.677661i
$199$	24.4637			1.73419			0.867093	−	0.498147i	$-0.165986\pi$
$199$	24.4637			1.73419			0.867093	+	0.498147i	$0.165986\pi$
$200$	−12.7220	−	21.2448i	−0.899584	−	1.50223i
$201$	−4.96018			−0.349864
$202$	11.2347	+	34.5768i	0.790470	+	2.43282i
$203$	−0.990627	+	0.719733i	−0.0695284	+	0.0505153i
$204$	−13.3947	+	9.73183i	−0.937817	+	0.681364i
$205$	−13.4793	−	7.63948i	−0.941432	−	0.533565i
$206$	12.5757	+	9.13679i	0.876192	+	0.636591i
$207$	3.09362			0.215022
$208$	7.39101	+	5.36988i	0.512474	+	0.372334i
$209$	−8.09848	+	24.9246i	−0.560184	+	1.72407i
$210$	4.04729	−	3.70311i	0.279290	−	0.255539i
$211$	−2.80854	−	8.64380i	−0.193348	−	0.595063i	−0.999992	−	0.00402594i	$-0.998718\pi$
$211$	−2.80854	−	8.64380i	−0.193348	−	0.595063i	0.806644	−	0.591038i	$-0.201282\pi$
$212$	9.61786	−	29.6007i	0.660557	−	2.03299i
$213$	−1.87618	+	5.77429i	−0.128554	+	0.395648i
$214$	−2.13429	−	6.56868i	−0.145897	−	0.449025i
$215$	−2.65594	+	13.0047i	−0.181134	+	0.886912i
$216$	−1.53042	+	4.71015i	−0.104132	+	0.320485i
$217$	5.36645	+	3.89895i	0.364298	+	0.264678i
$218$	13.7445			0.930895
$219$	12.8472	+	9.33400i	0.868130	+	0.630733i
$220$	27.0949	−	24.7907i	1.82674	−	1.67139i
$221$	7.40402	−	5.37934i	0.498048	−	0.361853i
$222$	−13.6666	+	9.92934i	−0.917240	+	0.666414i
$223$	4.78728	+	14.7337i	0.320580	+	0.986643i	0.973396	+	0.229127i	$0.0735872\pi$
$223$	4.78728	+	14.7337i	0.320580	+	0.986643i	−0.652817	+	0.757516i	$0.726413\pi$
$224$	−0.184561			−0.0123315
$225$	−3.28592	+	3.76865i	−0.219062	+	0.251243i
$226$	−38.2900			−2.54701
$227$	−0.180892	−	0.556728i	−0.0120062	−	0.0369513i	0.944874	−	0.327434i	$-0.106184\pi$
$227$	−0.180892	−	0.556728i	−0.0120062	−	0.0369513i	−0.956880	+	0.290483i	$0.906184\pi$
$228$	−20.8487	+	15.1475i	−1.38074	+	1.00317i
$229$	−15.4039	+	11.1916i	−1.01792	+	0.739561i	−0.965855	−	0.259083i	$-0.916580\pi$
$229$	−15.4039	+	11.1916i	−1.01792	+	0.739561i	−0.0520632	+	0.998644i	$0.516580\pi$
$230$	−7.02619	−	15.4481i	−0.463293	−	1.01862i
$231$	3.30632	+	2.40218i	0.217540	+	0.158052i
$232$	−6.06430			−0.398141
$233$	−24.4405	−	17.7571i	−1.60115	−	1.16331i	−0.885261	−	0.465094i	$-0.846020\pi$
$233$	−24.4405	−	17.7571i	−1.60115	−	1.16331i	−0.715892	−	0.698211i	$-0.753980\pi$
$234$	1.68406	−	5.18299i	0.110090	−	0.338823i
$235$	8.15806	+	17.9367i	0.532173	+	1.17006i
$236$	−8.91219	−	27.4289i	−0.580134	−	1.78547i
$237$	−2.86942	+	8.83116i	−0.186389	+	0.573645i
$238$	−3.12336	+	9.61272i	−0.202458	+	0.623100i
$239$	1.85400	+	5.70603i	0.119925	+	0.369093i	0.992942	−	0.118597i	$-0.0378397\pi$
$239$	1.85400	+	5.70603i	0.119925	+	0.369093i	−0.873017	+	0.487690i	$0.837840\pi$
$240$	9.13787	−	1.03422i	0.589847	−	0.0667587i
$241$	7.51610	−	23.1322i	0.484155	−	1.49007i	−0.349047	−	0.937105i	$-0.613495\pi$
$241$	7.51610	−	23.1322i	0.484155	−	1.49007i	0.833201	−	0.552969i	$-0.186505\pi$
$242$	11.3175	+	8.22268i	0.727520	+	0.528574i
$243$	1.00000			0.0641500
$244$	30.8461	+	22.4110i	1.97472	+	1.43472i
$245$	0.447435	−	2.19084i	0.0285856	−	0.139968i
$246$	13.7524	−	9.99168i	0.876819	−	0.637046i
$247$	11.5243	−	8.37289i	0.733273	−	0.532754i
$248$	10.1517	+	31.2438i	0.644635	+	1.98398i
$249$	−6.08566			−0.385663
$250$	26.2818	+	7.84907i	1.66221	+	0.496419i
$251$	0.614266			0.0387721			0.0193861	−	0.999812i	$-0.493829\pi$
$251$	0.614266			0.0387721			0.0193861	+	0.999812i	$0.493829\pi$
$252$	1.24185	+	3.82203i	0.0782294	+	0.240765i
$253$	10.2285	−	7.43144i	0.643061	−	0.467211i
$254$	16.2264	−	11.7892i	1.01813	−	0.739718i
$255$	1.84339	−	9.02609i	0.115438	−	0.565236i
$256$	26.0028	+	18.8922i	1.62518	+	1.18076i
$257$	−6.88064			−0.429202			−0.214601	−	0.976702i	$-0.568845\pi$
$257$	−6.88064			−0.429202			−0.214601	+	0.976702i	$0.568845\pi$
$258$	−11.7814	−	8.55971i	−0.733480	−	0.532904i
$259$	−2.12781	+	6.54871i	−0.132215	+	0.406917i
$260$	−19.8349	+	2.24491i	−1.23011	+	0.139224i
$261$	0.378386	+	1.16455i	0.0234215	+	0.0720840i
$262$	−6.98576	+	21.4999i	−0.431581	+	1.32827i
$263$	7.50019	−	23.0832i	0.462481	−	1.42337i	−0.399641	−	0.916672i	$-0.630865\pi$
$263$	7.50019	−	23.0832i	0.462481	−	1.42337i	0.862123	−	0.506700i	$-0.169135\pi$
$264$	6.25457	+	19.2496i	0.384942	+	1.18473i
$265$	7.16982	+	15.7639i	0.440438	+	0.968369i
$266$	−4.86148	+	14.9621i	−0.298077	+	0.917386i
$267$	13.6683	+	9.93062i	0.836488	+	0.607744i
$268$	−19.9336			−1.21764
$269$	0.247275	+	0.179656i	0.0150766	+	0.0109538i	0.595298	−	0.803505i	$-0.297034\pi$
$269$	0.247275	+	0.179656i	0.0150766	+	0.0109538i	−0.580221	+	0.814459i	$0.697034\pi$
$270$	−2.27118	−	4.99353i	−0.138220	−	0.303896i
$271$	12.4586	−	9.05168i	0.756804	−	0.549850i	−0.141124	−	0.989992i	$-0.545072\pi$
$271$	12.4586	−	9.05168i	0.756804	−	0.549850i	0.897928	+	0.440142i	$0.145072\pi$
$272$	−13.7078	+	9.95934i	−0.831160	+	0.603873i
$273$	−0.686443	−	2.11265i	−0.0415454	−	0.127864i
$274$	−46.9264			−2.83492
$275$	−1.81134	+	20.3537i	−0.109228	+	1.22738i
$276$	12.4324			0.748343
$277$	−0.114217	−	0.351525i	−0.00686265	−	0.0211211i	0.947567	−	0.319558i	$-0.103535\pi$
$277$	−0.114217	−	0.351525i	−0.00686265	−	0.0211211i	−0.954429	+	0.298437i	$0.903535\pi$
$278$	−10.1861	+	7.40067i	−0.610924	+	0.443862i
$279$	5.36645	−	3.89895i	0.321281	−	0.233424i
$280$	8.17035	−	7.47554i	0.488272	−	0.446749i
$281$	10.6675	+	7.75042i	0.636372	+	0.462351i	0.858602	−	0.512643i	$-0.171334\pi$
$281$	10.6675	+	7.75042i	0.636372	+	0.462351i	−0.222230	+	0.974994i	$0.571334\pi$
$282$	−21.6192			−1.28740
$283$	0.270488	+	0.196521i	0.0160789	+	0.0116820i	0.595796	−	0.803136i	$-0.296837\pi$
$283$	0.270488	+	0.196521i	0.0160789	+	0.0116820i	−0.579717	+	0.814818i	$0.696837\pi$
$284$	−7.53984	+	23.2052i	−0.447407	+	1.37698i
$285$	2.86923	−	14.0490i	0.169958	−	0.832192i
$286$	−6.88246	−	21.1820i	−0.406968	−	1.25252i
$287$	2.14117	−	6.58983i	0.126389	−	0.388985i
$288$	−0.0570324	+	0.175528i	−0.00336067	+	0.0103431i
$289$	−0.00813464	−	0.0250359i	−0.000478508	−	0.00147270i
$290$	4.95584	−	4.53439i	0.291017	−	0.266269i
$291$	−1.13034	+	3.47882i	−0.0662616	+	0.203932i
$292$	51.6291	+	37.5107i	3.02136	+	2.19515i
$293$	−17.4079			−1.01698			−0.508489	−	0.861068i	$-0.669796\pi$
$293$	−17.4079			−1.01698			−0.508489	+	0.861068i	$0.669796\pi$
$294$	1.98477	+	1.44202i	0.115754	+	0.0841002i
$295$	13.9609	+	7.91244i	0.812834	+	0.460680i
$296$	−27.5890	+	20.0446i	−1.60358	+	1.16507i
$297$	3.30632	−	2.40218i	0.191852	−	0.139389i
$298$	−11.5435	−	35.5274i	−0.668700	−	2.05805i
$299$	−6.87210			−0.397424
$300$	−13.2052	+	15.1451i	−0.762403	+	0.874405i
$301$	−5.93592			−0.342141
$302$	6.97321	+	21.4613i	0.401263	+	1.23496i
$303$	11.9890	−	8.71055i	0.688752	−	0.500408i
$304$	−21.3361	+	15.5016i	−1.22371	+	0.889078i
$305$	−21.0802	+	2.38586i	−1.20705	+	0.136614i
$306$	8.17707	+	5.94099i	0.467452	+	0.339624i
$307$	0.0842740			0.00480977			0.00240488	−	0.999997i	$-0.499235\pi$
$307$	0.0842740			0.00480977			0.00240488	+	0.999997i	$0.499235\pi$
$308$	13.2872	+	9.65369i	0.757106	+	0.550070i
$309$	1.95797	−	6.02600i	0.111385	−	0.342807i
$310$	−31.6577	−	17.9423i	−1.79804	−	1.01905i
$311$	−10.3281	−	31.7866i	−0.585652	−	1.80245i	−0.596637	−	0.802512i	$-0.703497\pi$
$311$	−10.3281	−	31.7866i	−0.585652	−	1.80245i	0.0109846	−	0.999940i	$-0.496503\pi$
$312$	3.39964	−	10.4630i	0.192467	−	0.592351i
$313$	−7.19251	+	22.1363i	−0.406544	+	1.25122i	0.513054	+	0.858356i	$0.328514\pi$
$313$	−7.19251	+	22.1363i	−0.406544	+	1.25122i	−0.919599	+	0.392859i	$0.871486\pi$
$314$	−3.84057	−	11.8201i	−0.216736	−	0.667044i
$315$	−1.94535	−	1.10254i	−0.109608	−	0.0621214i
$316$	−11.5314	+	35.4899i	−0.648691	+	1.99647i
$317$	14.8273	+	10.7727i	0.832786	+	0.605055i	0.920346	−	0.391105i	$-0.127907\pi$
$317$	14.8273	+	10.7727i	0.832786	+	0.605055i	−0.0875600	+	0.996159i	$0.527907\pi$
$318$	−19.0003			−1.06548
$319$	4.04853	+	2.94143i	0.226674	+	0.164688i
$320$	−17.2697	+	1.95458i	−0.965406	+	0.109264i
$321$	−2.27760	+	1.65477i	−0.127123	+	0.0923604i
$322$	6.14013	−	4.46106i	0.342176	−	0.248605i
$323$	8.16403	+	25.1263i	0.454259	+	1.39807i
$324$	4.01872			0.223262
$325$	7.29927	−	8.37158i	0.404891	−	0.464372i
$326$	13.3711			0.740559
$327$	−1.73125	−	5.32823i	−0.0957382	−	0.294652i
$328$	27.7622	−	20.1704i	1.53291	−	1.11372i
$329$	−7.12926	+	5.17971i	−0.393049	+	0.285567i
$330$	−19.5046	−	11.0544i	−1.07369	−	0.608525i
$331$	−18.4261	−	13.3874i	−1.01279	−	0.735835i	−0.0479980	−	0.998847i	$-0.515284\pi$
$331$	−18.4261	−	13.3874i	−1.01279	−	0.735835i	−0.964793	+	0.263012i	$0.915284\pi$
$332$	−24.4565			−1.34223
$333$	5.57067	+	4.04733i	0.305271	+	0.221792i
$334$	−1.35824	+	4.18023i	−0.0743195	+	0.228732i
$335$	8.18296	−	7.48707i	0.447083	−	0.409062i
$336$	1.27088	+	3.91138i	0.0693324	+	0.213383i
$337$	−8.66988	+	26.6831i	−0.472278	+	1.45352i	0.377315	+	0.926085i	$0.376847\pi$
$337$	−8.66988	+	26.6831i	−0.472278	+	1.45352i	−0.849593	+	0.527438i	$0.823153\pi$
$338$	6.11456	−	18.8187i	0.332588	−	1.02360i
$339$	4.82298	+	14.8436i	0.261948	+	0.806194i
$340$	7.40809	−	36.2733i	0.401760	−	1.96720i
$341$	8.37720	−	25.7824i	0.453651	−	1.39619i
$342$	12.7275	+	9.24709i	0.688226	+	0.500025i
$343$	1.00000			0.0539949
$344$	−23.7834	−	17.2797i	−1.28232	−	0.931657i
$345$	−5.10364	+	4.66962i	−0.274771	+	0.251404i
$346$	−22.1419	+	16.0870i	−1.19035	+	0.864843i
$347$	4.88664	−	3.55035i	0.262329	−	0.190593i	−0.448844	−	0.893610i	$-0.648164\pi$
$347$	4.88664	−	3.55035i	0.262329	−	0.190593i	0.711173	+	0.703017i	$0.248164\pi$
$348$	1.52063	+	4.68001i	0.0815142	+	0.250875i
$349$	−26.2091			−1.40294			−0.701470	−	0.712699i	$-0.747472\pi$
$349$	−26.2091			−1.40294			−0.701470	+	0.712699i	$0.747472\pi$
$350$	−1.08734	+	12.2183i	−0.0581207	+	0.653093i
$351$	−2.22138			−0.118568
$352$	0.233082	+	0.717353i	0.0124233	+	0.0382350i
$353$	−0.00924696	+	0.00671831i	−0.000492166	+	0.000357579i	−0.588031	−	0.808838i	$-0.700097\pi$
$353$	−0.00924696	+	0.00671831i	−0.000492166	+	0.000357579i	0.587539	+	0.809196i	$0.300097\pi$
$354$	−14.2437	+	10.3487i	−0.757046	+	0.550026i
$355$	−5.62072	−	12.3580i	−0.298317	−	0.655893i
$356$	54.9292	+	39.9084i	2.91124	+	2.11514i
$357$	4.11991			0.218049
$358$	−34.0862	−	24.7651i	−1.80151	−	1.30888i
$359$	−9.28618	+	28.5799i	−0.490106	+	1.50839i	0.334342	+	0.942452i	$0.391486\pi$
$359$	−9.28618	+	28.5799i	−0.490106	+	1.50839i	−0.824447	+	0.565939i	$0.808514\pi$
$360$	−4.58488	−	10.0805i	−0.241644	−	0.531291i
$361$	6.83592	+	21.0388i	0.359785	+	1.10730i
$362$	−4.81393	+	14.8157i	−0.253014	+	0.778698i
$363$	1.76208	−	5.42312i	0.0924851	−	0.284640i
$364$	−2.75862	−	8.49017i	−0.144591	−	0.445006i
$365$	−35.2834	+	3.99336i	−1.84682	+	0.209022i
$366$	7.19265	−	22.1367i	0.375966	−	1.15710i
$367$	0.862752	+	0.626826i	0.0450353	+	0.0327201i	0.610075	−	0.792344i	$-0.291139\pi$
$367$	0.862752	+	0.626826i	0.0450353	+	0.0327201i	−0.565040	+	0.825064i	$0.691139\pi$
$368$	12.7231			0.663235
$369$	−5.60564	−	4.07274i	−0.291818	−	0.212018i
$370$	7.55844	−	37.0095i	0.392945	−	1.92403i
$371$	−6.26565	+	4.55226i	−0.325296	+	0.236341i
$372$	21.5663	−	15.6688i	1.11816	−	0.812390i
$373$	9.47576	+	29.1634i	0.490636	+	1.51002i	0.823648	+	0.567101i	$0.191935\pi$
$373$	9.47576	+	29.1634i	0.490636	+	1.51002i	−0.333012	+	0.942923i	$0.608065\pi$
$374$	41.3073			2.13595
$375$	−0.267642	−	11.1771i	−0.0138210	−	0.577185i
$376$	−43.6430			−2.25072
$377$	−0.840538	−	2.58691i	−0.0432899	−	0.133233i
$378$	1.98477	−	1.44202i	0.102085	−	0.0741694i
$379$	22.4763	−	16.3300i	1.15453	−	0.838814i	0.165452	−	0.986218i	$-0.447092\pi$
$379$	22.4763	−	16.3300i	1.15453	−	0.838814i	0.989076	+	0.147404i	$0.0470917\pi$
$380$	11.5306	−	56.4591i	0.591508	−	2.89629i
$381$	−6.61409	−	4.80541i	−0.338850	−	0.246189i
$382$	11.7357			0.600450
$383$	2.27631	+	1.65383i	0.116314	+	0.0845070i	0.644421	−	0.764670i	$-0.277098\pi$
$383$	2.27631	+	1.65383i	0.116314	+	0.0845070i	−0.528108	+	0.849177i	$0.677098\pi$
$384$	6.00654	−	18.4862i	0.306520	−	0.943372i
$385$	−9.08046	+	1.02772i	−0.462783	+	0.0523776i
$386$	−12.7469	−	39.2310i	−0.648801	−	1.99680i
$387$	−1.83430	+	5.64540i	−0.0932428	+	0.286972i
$388$	−4.54251	+	13.9804i	−0.230611	+	0.709748i
$389$	3.32786	+	10.2421i	0.168729	+	0.519295i	0.999292	−	0.0376302i	$-0.0119809\pi$
$389$	3.32786	+	10.2421i	0.168729	+	0.519295i	−0.830562	+	0.556925i	$0.811981\pi$
$390$	5.04515	+	11.0925i	0.255471	+	0.561691i
$391$	3.93856	−	12.1217i	0.199182	−	0.613018i
$392$	4.00669	+	2.91103i	0.202368	+	0.147029i
$393$	9.21465			0.464818
$394$	−44.4129	−	32.2679i	−2.23749	−	1.62563i
$395$	−8.59629	−	18.9002i	−0.432527	−	0.950973i
$396$	13.2872	−	9.65369i	0.667705	−	0.485116i
$397$	31.0197	−	22.5372i	1.55684	−	1.13111i	0.618292	−	0.785948i	$-0.287825\pi$
$397$	31.0197	−	22.5372i	1.55684	−	1.13111i	0.938544	−	0.345160i	$-0.112175\pi$
$398$	−18.5463	−	57.0795i	−0.929640	−	2.86114i
$399$	6.41260			0.321032
$400$	−13.5139	+	15.4992i	−0.675696	+	0.774960i
$401$	−17.7054			−0.884167			−0.442084	−	0.896974i	$-0.645761\pi$
$401$	−17.7054			−0.884167			−0.442084	+	0.896974i	$0.645761\pi$
$402$	3.76038	+	11.5733i	0.187551	+	0.577222i
$403$	−11.9209	+	8.66105i	−0.593823	+	0.431437i
$404$	48.1806	−	35.0052i	2.39707	−	1.74158i
$405$	−1.64973	+	1.50943i	−0.0819757	+	0.0750044i
$406$	2.43031	+	1.76573i	0.120614	+	0.0876315i
$407$	28.1408			1.39489
$408$	16.5072	+	11.9932i	0.817229	+	0.593751i
$409$	6.00070	−	18.4683i	0.296716	−	0.913197i	−0.685924	−	0.727673i	$-0.740602\pi$
$409$	6.00070	−	18.4683i	0.296716	−	0.913197i	0.982640	−	0.185524i	$-0.0593982\pi$
$410$	−7.60590	+	37.2419i	−0.375628	+	1.83925i
$411$	5.91081	+	18.1916i	0.291559	+	0.897326i
$412$	7.86852	−	24.2168i	0.387654	−	1.19308i
$413$	−2.21767	+	6.82529i	−0.109124	+	0.335850i
$414$	−2.34532	−	7.21815i	−0.115266	−	0.354753i
$415$	10.0397	−	9.18590i	0.492829	−	0.450918i
$416$	0.126691	−	0.389913i	0.00621151	−	0.0191171i
$417$	4.15200	+	3.01661i	0.203324	+	0.147724i
$418$	64.2944			3.14474
$419$	−16.8649	−	12.2531i	−0.823905	−	0.598602i	0.0939235	−	0.995579i	$-0.470059\pi$
$419$	−16.8649	−	12.2531i	−0.823905	−	0.598602i	−0.917828	+	0.396978i	$0.870059\pi$
$420$	−7.81783	−	4.43082i	−0.381471	−	0.216202i
$421$	−24.9428	+	18.1220i	−1.21564	+	0.883214i	−0.995731	−	0.0923069i	$-0.970576\pi$
$421$	−24.9428	+	18.1220i	−1.21564	+	0.883214i	−0.219909	+	0.975520i	$0.570576\pi$
$422$	−18.0388	+	13.1060i	−0.878116	+	0.637988i
$423$	2.72314	+	8.38095i	0.132403	+	0.407496i
$424$	−38.3563			−1.86274
$425$	10.5832	+	17.6731i	0.513360	+	0.857271i
$426$	14.8951			0.721671
$427$	−2.93182	−	9.02321i	−0.141881	−	0.436664i
$428$	−9.15303	+	6.65007i	−0.442428	+	0.321443i
$429$	−7.34458	+	5.33615i	−0.354599	+	0.257632i
$430$	32.3565	−	3.66210i	1.56037	−	0.176602i
$431$	13.3837	+	9.72383i	0.644670	+	0.468380i	0.861451	−	0.507840i	$-0.169556\pi$
$431$	13.3837	+	9.72383i	0.644670	+	0.468380i	−0.216781	+	0.976220i	$0.569556\pi$
$432$	4.11267			0.197871
$433$	−26.9892	−	19.6088i	−1.29702	−	0.942340i	−0.297098	−	0.954847i	$-0.596019\pi$
$433$	−26.9892	−	19.6088i	−1.29702	−	0.942340i	−0.999922	+	0.0125067i	$0.996019\pi$
$434$	5.02879	−	15.4770i	0.241390	−	0.742922i
$435$	−2.38205	−	1.35005i	−0.114211	−	0.0647298i
$436$	−6.95740	−	21.4127i	−0.333199	−	1.02548i
$437$	6.13034	−	18.8672i	0.293254	−	0.902542i
$438$	12.0388	−	37.0517i	0.575237	−	1.77040i
$439$	5.15206	+	15.8564i	0.245894	+	0.756785i	0.995488	+	0.0948868i	$0.0302489\pi$
$439$	5.15206	+	15.8564i	0.245894	+	0.756785i	−0.749594	+	0.661898i	$0.769751\pi$
$440$	−39.3743	−	22.3157i	−1.87710	−	1.06386i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	−18.1643	−	13.1972i	−0.863990	−	0.627725i
$443$	−25.4448			−1.20892			−0.604459	−	0.796636i	$-0.706611\pi$
$443$	−25.4448			−1.20892			−0.604459	+	0.796636i	$0.706611\pi$
$444$	22.3870	+	16.2651i	1.06244	+	0.771906i
$445$	−37.5387	+	4.24861i	−1.77950	+	0.201403i
$446$	30.7479	−	22.3397i	1.45596	−	1.05781i
$447$	−12.3186	+	8.95001i	−0.582651	+	0.423321i
$448$	−2.40185	−	7.39214i	−0.113477	−	0.349246i
$449$	−18.8977			−0.891838			−0.445919	−	0.895073i	$-0.647123\pi$
$449$	−18.8977			−0.891838			−0.445919	+	0.895073i	$0.647123\pi$
$450$	11.2842	+	4.80977i	0.531944	+	0.226735i
$451$	−28.3175			−1.33342
$452$	19.3822	+	59.6523i	0.911663	+	2.80581i
$453$	7.44142	−	5.40651i	0.349628	−	0.254020i
$454$	−1.16184	+	0.844127i	−0.0545279	+	0.0396168i
$455$	4.32136	+	2.44917i	0.202588	+	0.114819i
$456$	25.6933	+	18.6673i	1.20320	+	0.874176i
$457$	−5.28146			−0.247056			−0.123528	−	0.992341i	$-0.539421\pi$
$457$	−5.28146			−0.247056			−0.123528	+	0.992341i	$0.539421\pi$
$458$	37.7905	+	27.4564i	1.76583	+	1.28295i
$459$	1.27312	−	3.91827i	0.0594243	−	0.182889i
$460$	−20.5101	+	18.7659i	−0.956289	+	0.874965i
$461$	2.83839	+	8.73567i	0.132197	+	0.406861i	0.995144	−	0.0984346i	$-0.0313835\pi$
$461$	2.83839	+	8.73567i	0.132197	+	0.406861i	−0.862946	+	0.505295i	$0.831384\pi$
$462$	3.09828	−	9.53554i	0.144145	−	0.443633i
$463$	−3.19066	+	9.81984i	−0.148283	+	0.456367i	−0.997419	−	0.0718076i	$-0.977123\pi$
$463$	−3.19066	+	9.81984i	−0.148283	+	0.456367i	0.849136	+	0.528174i	$0.177123\pi$
$464$	1.55618	+	4.78942i	0.0722437	+	0.222343i
$465$	−2.96797	+	14.5325i	−0.137636	+	0.673930i
$466$	−22.9027	+	70.4874i	−1.06095	+	3.26527i
$467$	−2.87994	−	2.09240i	−0.133268	−	0.0968248i	0.519154	−	0.854681i	$-0.326247\pi$
$467$	−2.87994	−	2.09240i	−0.133268	−	0.0968248i	−0.652422	+	0.757856i	$0.726247\pi$
$468$	−8.92709			−0.412655
$469$	4.01287	+	2.91552i	0.185297	+	0.134626i
$470$	35.6658	−	32.6327i	1.64514	−	1.50524i
$471$	−4.09844	+	2.97769i	−0.188846	+	0.137205i
$472$	−28.7541	+	20.8911i	−1.32352	+	0.961591i
$473$	7.49648	+	23.0718i	0.344689	+	1.06084i
$474$	22.7805			1.04634
$475$	16.4726	+	27.5080i	0.755816	+	1.26215i
$476$	16.5568			0.758878
$477$	2.39326	+	7.36571i	0.109580	+	0.337253i
$478$	11.9080	−	8.65165i	0.544658	−	0.395717i
$479$	−26.2236	+	19.0525i	−1.19819	+	0.870533i	−0.994105	−	0.108422i	$-0.965420\pi$
$479$	−26.2236	+	19.0525i	−1.19819	+	0.870533i	−0.204080	+	0.978954i	$0.565420\pi$
$480$	−0.170860	−	0.375660i	−0.00779864	−	0.0171465i
$481$	−12.3745	−	8.99064i	−0.564231	−	0.409938i
$482$	−59.6709			−2.71793
$483$	−2.50279	−	1.81839i	−0.113881	−	0.0827395i
$484$	7.08130	−	21.7940i	0.321877	−	0.990636i
$485$	−3.38630	−	7.44528i	−0.153764	−	0.338073i
$486$	−0.758114	−	2.33323i	−0.0343887	−	0.105838i
$487$	3.55855	−	10.9521i	0.161253	−	0.496287i	−0.837487	−	0.546457i	$-0.815976\pi$
$487$	3.55855	−	10.9521i	0.161253	−	0.496287i	0.998741	+	0.0501697i	$0.0159762\pi$
$488$	14.5199	−	44.6878i	0.657287	−	2.02292i
$489$	−1.68422	−	5.18349i	−0.0761630	−	0.234406i
$490$	−5.45096	+	0.616938i	−0.246249	+	0.0278704i
$491$	−5.36045	+	16.4978i	−0.241914	+	0.744533i	0.754215	+	0.656627i	$0.228018\pi$
$491$	−5.36045	+	16.4978i	−0.241914	+	0.744533i	−0.996129	+	0.0879060i	$0.971982\pi$
$492$	−22.5275	−	16.3672i	−1.01562	−	0.737890i
$493$	5.04476			0.227205
$494$	−28.2726	−	20.5413i	−1.27205	−	0.924195i
$495$	−1.82859	+	8.95362i	−0.0821892	+	0.402435i
$496$	22.0704	−	16.0351i	0.990992	−	0.719998i
$497$	4.91190	−	3.56871i	0.220329	−	0.160078i
$498$	4.61362	+	14.1993i	0.206741	+	0.636284i
$499$	−11.4275			−0.511565			−0.255783	−	0.966734i	$-0.582333\pi$
$499$	−11.4275			−0.511565			−0.255783	+	0.966734i	$0.582333\pi$
$500$	−1.07558	−	44.9178i	−0.0481014	−	2.00878i
$501$	1.79160			0.0800429
$502$	−0.465683	−	1.43323i	−0.0207845	−	0.0639680i
$503$	12.7196	−	9.24135i	0.567140	−	0.412052i	−0.266925	−	0.963717i	$-0.586008\pi$
$503$	12.7196	−	9.24135i	0.567140	−	0.412052i	0.834065	+	0.551666i	$0.186008\pi$
$504$	4.00669	−	2.91103i	0.178472	−	0.129668i
$505$	−6.63067	+	32.4667i	−0.295061	+	1.44475i
$506$	−25.0937	−	18.2316i	−1.11555	−	0.810494i
$507$	−8.06549			−0.358201
$508$	−26.5802	−	19.3116i	−1.17930	−	0.856814i
$509$	1.11607	−	3.43492i	0.0494691	−	0.152250i	−0.923270	−	0.384151i	$-0.874494\pi$
$509$	1.11607	−	3.43492i	0.0494691	−	0.152250i	0.972740	+	0.231900i	$0.0744944\pi$
$510$	−22.4575	+	2.54173i	−0.994434	+	0.112550i
$511$	−4.90718	−	15.1027i	−0.217081	−	0.668106i
$512$	12.3537	−	38.0207i	0.545960	−	1.68029i
$513$	1.98160	−	6.09875i	0.0874899	−	0.269266i
$514$	5.21631	+	16.0541i	0.230081	+	0.708118i
$515$	5.86574	+	12.8967i	0.258476	+	0.568296i
$516$	−7.37154	+	22.6873i	−0.324514	+	0.998752i
$517$	29.1361	+	21.1686i	1.28140	+	0.930995i
$518$	16.8928			0.742227
$519$	9.02531	+	6.55727i	0.396167	+	0.287832i
$520$	10.1847	+	22.3927i	0.446631	+	0.981983i
$521$	9.67700	−	7.03075i	0.423957	−	0.308023i	−0.355271	−	0.934763i	$-0.615611\pi$
$521$	9.67700	−	7.03075i	0.423957	−	0.308023i	0.779228	+	0.626741i	$0.215611\pi$
$522$	2.43031	−	1.76573i	0.106372	−	0.0772837i
$523$	6.40173	+	19.7025i	0.279928	+	0.861531i	0.987873	+	0.155263i	$0.0496225\pi$
$523$	6.40173	+	19.7025i	0.279928	+	0.861531i	−0.707945	+	0.706268i	$0.750378\pi$
$524$	37.0311			1.61771
$525$	4.87352	−	1.11748i	0.212698	−	0.0487709i
$526$	−59.5445			−2.59626
$527$	−8.44500	−	25.9910i	−0.367870	−	1.13219i
$528$	13.5978	−	9.87937i	0.591768	−	0.429944i
$529$	10.8647	−	7.89365i	0.472378	−	0.343202i
$530$	31.3453	−	28.6797i	1.36155	−	1.24577i
$531$	5.80593	+	4.21826i	0.251956	+	0.183057i
$532$	25.7705			1.11729
$533$	12.4522	+	9.04709i	0.539367	+	0.391873i
$534$	12.8083	−	39.4199i	0.554270	−	1.70587i
$535$	1.25965	−	6.16781i	0.0544594	−	0.266658i
$536$	7.59116	+	23.3632i	0.327888	+	1.00914i
$537$	−5.30703	+	16.3334i	−0.229015	+	0.704837i
$538$	0.231717	−	0.713150i	0.00999001	−	0.0307461i
$539$	−1.26290	−	3.88681i	−0.0543970	−	0.167417i
$540$	−6.62980	+	6.06600i	−0.285301	+	0.261039i
$541$	0.902889	−	2.77881i	0.0388182	−	0.119470i	−0.929770	−	0.368142i	$-0.879994\pi$
$541$	0.902889	−	2.77881i	0.0388182	−	0.119470i	0.968588	+	0.248672i	$0.0799940\pi$
$542$	−30.5647	−	22.2066i	−1.31287	−	0.953853i
$543$	6.34987			0.272499
$544$	0.615156	+	0.446937i	0.0263746	+	0.0191623i
$545$	10.8987	+	6.17693i	0.466849	+	0.264591i
$546$	−4.40892	+	3.20327i	−0.188684	+	0.137087i
$547$	29.2918	−	21.2817i	1.25243	−	0.909941i	0.254067	−	0.967187i	$-0.418232\pi$
$547$	29.2918	−	21.2817i	1.25243	−	0.909941i	0.998360	+	0.0572453i	$0.0182317\pi$
$548$	23.7539	+	73.1070i	1.01472	+	3.12298i
$549$	−9.48756			−0.404919
$550$	48.8632	−	11.2042i	2.08353	−	0.477747i
$551$	7.85212			0.334512
$552$	−4.73454	−	14.5714i	−0.201516	−	0.620201i
$553$	7.51223	−	5.45796i	0.319453	−	0.232096i
$554$	−0.733600	+	0.532991i	−0.0311677	+	0.0226446i
$555$	−15.2993	+	1.73157i	−0.649418	+	0.0735009i
$556$	16.6857	+	12.1229i	0.707633	+	0.514125i
$557$	−32.2733			−1.36746			−0.683732	−	0.729733i	$-0.739644\pi$
$557$	−32.2733			−1.36746			−0.683732	+	0.729733i	$0.739644\pi$
$558$	−13.1656	−	9.56534i	−0.557342	−	0.404933i
$559$	4.07467	−	12.5406i	0.172340	−	0.530409i
$560$	−8.00059	−	4.53440i	−0.338087	−	0.191613i
$561$	−5.20304	−	16.0133i	−0.219673	−	0.676083i
$562$	9.99634	−	30.7656i	0.421670	−	1.29777i
$563$	−4.65226	+	14.3182i	−0.196069	+	0.603439i	0.803893	+	0.594774i	$0.202758\pi$
$563$	−4.65226	+	14.3182i	−0.196069	+	0.603439i	−0.999962	+	0.00866540i	$0.997242\pi$
$564$	10.9435	+	33.6807i	0.460805	+	1.41821i
$565$	−30.3621	−	17.2080i	−1.27734	−	0.723944i
$566$	0.253469	−	0.780099i	0.0106541	−	0.0327900i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	30.0691			1.26167
$569$	22.8614	+	16.6098i	0.958398	+	0.696317i	0.952778	−	0.303667i	$-0.0982111\pi$
$569$	22.8614	+	16.6098i	0.958398	+	0.696317i	0.00562011	+	0.999984i	$0.498211\pi$
$570$	−34.9549	+	3.95618i	−1.46410	+	0.165706i
$571$	7.12181	−	5.17429i	0.298038	−	0.216538i	−0.428709	−	0.903443i	$-0.641031\pi$
$571$	7.12181	−	5.17429i	0.298038	−	0.216538i	0.726747	+	0.686905i	$0.241031\pi$
$572$	−29.5158	+	21.4445i	−1.23412	+	0.896639i
$573$	−1.47822	−	4.54949i	−0.0617535	−	0.190058i
$574$	−16.9989			−0.709519
$575$	1.37114	−	15.4072i	0.0571803	−	0.642526i
$576$	−7.77255			−0.323856
$577$	4.79587	+	14.7602i	0.199655	+	0.614474i	0.999891	+	0.0147885i	$0.00470749\pi$
$577$	4.79587	+	14.7602i	0.199655	+	0.614474i	−0.800236	+	0.599685i	$0.795293\pi$
$578$	−0.0522475	+	0.0379601i	−0.00217321	+	0.00157893i
$579$	−13.6028	+	9.88302i	−0.565313	+	0.410724i
$580$	−9.57279	−	5.42546i	−0.397489	−	0.225280i
$581$	4.92340	+	3.57706i	0.204257	+	0.148401i
$582$	8.97383			0.371977
$583$	25.6066	+	18.6043i	1.06052	+	0.770512i
$584$	24.3030	−	74.7969i	1.00566	−	3.09512i
$585$	3.66467	−	3.35302i	0.151515	−	0.138630i
$586$	13.1971	+	40.6166i	0.545169	+	1.67786i
$587$	0.100841	−	0.310358i	0.00416217	−	0.0128098i	−0.948954	−	0.315415i	$-0.897856\pi$
$587$	0.100841	−	0.310358i	0.00416217	−	0.0128098i	0.953116	+	0.302605i	$0.0978563\pi$
$588$	1.24185	−	3.82203i	0.0512131	−	0.157618i
$589$	−13.1446	−	40.4548i	−0.541612	−	1.66691i
$590$	7.87765	−	38.5725i	0.324318	−	1.58801i
$591$	−6.91483	+	21.2817i	−0.284438	+	0.875411i
$592$	22.9103	+	16.6453i	0.941608	+	0.684118i
$593$	−25.5930			−1.05098			−0.525489	−	0.850800i	$-0.676118\pi$
$593$	−25.5930			−1.05098			−0.525489	+	0.850800i	$0.676118\pi$
$594$	−8.11141	−	5.89329i	−0.332815	−	0.241805i
$595$	−6.79674	+	6.21874i	−0.278639	+	0.254943i
$596$	−49.5051	+	35.9676i	−2.02781	+	1.47329i
$597$	−19.7915	+	14.3794i	−0.810014	+	0.588510i
$598$	5.20984	+	16.0342i	0.213046	+	0.655688i
$599$	22.4898			0.918908			0.459454	−	0.888202i	$-0.348045\pi$
$599$	22.4898			0.918908			0.459454	+	0.888202i	$0.348045\pi$
$600$	22.7797	+	9.70957i	0.929978	+	0.396392i
$601$	40.2891			1.64343			0.821714	−	0.569900i	$-0.193018\pi$
$601$	40.2891			1.64343			0.821714	+	0.569900i	$0.193018\pi$
$602$	4.50011	+	13.8499i	0.183411	+	0.564480i
$603$	4.01287	−	2.91552i	0.163417	−	0.118729i
$604$	29.9050	−	21.7272i	1.21682	−	0.884069i
$605$	5.27889	+	11.6064i	0.214617	+	0.471868i
$606$	−29.4128	−	21.3697i	−1.19481	−	0.868083i
$607$	−14.7379			−0.598193			−0.299096	−	0.954223i	$-0.596685\pi$
$607$	−14.7379			−0.598193			−0.299096	+	0.954223i	$0.596685\pi$
$608$	0.957484	+	0.695653i	0.0388311	+	0.0282125i
$609$	0.378386	−	1.16455i	0.0153330	−	0.0471900i
$610$	21.5480	+	47.3764i	0.872452	+	1.91821i
$611$	−6.04911	−	18.6172i	−0.244721	−	0.753173i
$612$	5.11632	−	15.7464i	0.206815	−	0.636512i
$613$	9.32078	−	28.6864i	0.376463	−	1.15863i	−0.566024	−	0.824389i	$-0.691519\pi$
$613$	9.32078	−	28.6864i	0.376463	−	1.15863i	0.942487	−	0.334244i	$-0.108481\pi$
$614$	−0.0638893	−	0.196631i	−0.00257836	−	0.00793538i
$615$	15.3953	−	1.74244i	0.620800	−	0.0702619i
$616$	6.25457	−	19.2496i	0.252004	−	0.775588i
$617$	−8.87145	−	6.44548i	−0.357151	−	0.259485i	0.394712	−	0.918805i	$-0.370844\pi$
$617$	−8.87145	−	6.44548i	−0.357151	−	0.259485i	−0.751863	+	0.659320i	$0.770844\pi$
$618$	−15.5444			−0.625289
$619$	39.9054	+	28.9929i	1.60393	+	1.16532i	0.879401	+	0.476082i	$0.157943\pi$
$619$	39.9054	+	28.9929i	1.60393	+	1.16532i	0.724530	+	0.689243i	$0.242057\pi$
$620$	−11.9275	+	58.4022i	−0.479018	+	2.34549i
$621$	−2.50279	+	1.81839i	−0.100434	+	0.0729694i
$622$	−66.3357	+	48.1957i	−2.65982	+	1.93247i
$623$	−5.22083	−	16.0681i	−0.209168	−	0.643754i
$624$	−9.13579			−0.365724
$625$	17.3127	+	18.0353i	0.692508	+	0.721410i
$626$	57.1018			2.28225
$627$	−8.09848	−	24.9246i	−0.323422	−	0.995391i
$628$	−16.4705	+	11.9665i	−0.657244	+	0.477516i
$629$	22.9507	−	16.6746i	0.915103	−	0.664861i
$630$	−1.09770	+	5.37482i	−0.0437333	+	0.214138i
$631$	24.4141	+	17.7379i	0.971911	+	0.706134i	0.955886	−	0.293737i	$-0.0948991\pi$
$631$	24.4141	+	17.7379i	0.971911	+	0.706134i	0.0160244	+	0.999872i	$0.494899\pi$
$632$	45.9875			1.82928
$633$	7.35285	+	5.34216i	0.292250	+	0.212332i
$634$	13.8944	−	42.7626i	0.551817	−	1.69832i
$635$	18.1649	−	2.05590i	0.720853	−	0.0815858i
$636$	9.61786	+	29.6007i	0.381373	+	1.17374i
$637$	−0.686443	+	2.11265i	−0.0271979	+	0.0837064i
$638$	3.79380	−	11.6761i	0.150198	−	0.462261i
$639$	−1.87618	−	5.77429i	−0.0742205	−	0.228427i
$640$	17.9946	+	39.5638i	0.711299	+	1.56390i
$641$	3.96177	−	12.1931i	0.156480	−	0.481597i	−0.841827	−	0.539747i	$-0.818520\pi$
$641$	3.96177	−	12.1931i	0.156480	−	0.481597i	0.998308	+	0.0581495i	$0.0185200\pi$
$642$	5.58765	+	4.05967i	0.220527	+	0.160222i
$643$	3.18822			0.125731			0.0628655	−	0.998022i	$-0.479976\pi$
$643$	3.18822			0.125731			0.0628655	+	0.998022i	$0.479976\pi$
$644$	−10.0580	−	7.30759i	−0.396342	−	0.287959i
$645$	−5.49526	−	12.0821i	−0.216376	−	0.475734i
$646$	52.4363	−	38.0972i	2.06308	−	1.49891i
$647$	−22.7672	+	16.5413i	−0.895070	+	0.650306i	−0.937195	−	0.348806i	$-0.886587\pi$
$647$	−22.7672	+	16.5413i	−0.895070	+	0.650306i	0.0421253	+	0.999112i	$0.486587\pi$
$648$	−1.53042	−	4.71015i	−0.0601206	−	0.185032i
$649$	29.3293			1.15127
$650$	−25.0665	−	10.6843i	−0.983191	−	0.419073i
$651$	−6.63330			−0.259979
$652$	−6.76840	−	20.8310i	−0.265071	−	0.815805i
$653$	34.4247	−	25.0110i	1.34714	−	0.978756i	0.347993	−	0.937497i	$-0.386863\pi$
$653$	34.4247	−	25.0110i	1.34714	−	0.978756i	0.999148	−	0.0412588i	$-0.0131368\pi$
$654$	−11.1195	+	8.07881i	−0.434808	+	0.315906i
$655$	−15.2017	+	13.9089i	−0.593979	+	0.543466i
$656$	−23.0542	−	16.7498i	−0.900114	−	0.653971i
$657$	−15.8800			−0.619536
$658$	17.4903	+	12.7074i	0.681842	+	0.495387i
$659$	−12.9494	+	39.8543i	−0.504439	+	1.55250i	0.297274	+	0.954792i	$0.403923\pi$
$659$	−12.9494	+	39.8543i	−0.504439	+	1.55250i	−0.801712	+	0.597710i	$0.796077\pi$
$660$	−7.34861	+	35.9821i	−0.286044	+	1.40060i
$661$	−4.77514	−	14.6964i	−0.185732	−	0.571623i	0.814229	−	0.580544i	$-0.197160\pi$
$661$	−4.77514	−	14.6964i	−0.185732	−	0.571623i	−0.999960	+	0.00892133i	$0.997160\pi$
$662$	−17.2667	+	53.1416i	−0.671091	+	2.06541i
$663$	−2.82809	+	8.70395i	−0.109834	+	0.338033i
$664$	9.31361	+	28.6643i	0.361438	+	1.11239i
$665$	−10.5791	+	9.67941i	−0.410238	+	0.375351i
$666$	5.22016	−	16.0660i	0.202277	−	0.622545i
$667$	−3.06463	−	2.22658i	−0.118663	−	0.0862136i
$668$	7.19994			0.278574
$669$	−12.5333	−	9.10594i	−0.484564	−	0.352056i
$670$	−23.6727	−	13.4167i	−0.914557	−	0.518333i
$671$	−31.3689	+	22.7908i	−1.21098	+	0.879830i
$672$	0.149313	−	0.108482i	0.00575987	−	0.00418479i
$673$	−8.80528	−	27.0999i	−0.339419	−	1.04462i	−0.964504	−	0.264067i	$-0.914936\pi$
$673$	−8.80528	−	27.0999i	−0.339419	−	1.04462i	0.625086	−	0.780556i	$-0.285064\pi$
$674$	68.8308			2.65126
$675$	0.443213	−	4.98032i	0.0170593	−	0.191693i
$676$	−32.4129			−1.24665
$677$	4.45463	+	13.7099i	0.171205	+	0.526916i	0.999440	−	0.0334659i	$-0.0106545\pi$
$677$	4.45463	+	13.7099i	0.171205	+	0.526916i	−0.828235	+	0.560382i	$0.810655\pi$
$678$	30.9773	−	22.5063i	1.18967	−	0.864349i
$679$	2.95926	−	2.15003i	0.113566	−	0.0825106i
$680$	−45.3354	+	5.13104i	−1.73853	+	0.196766i
$681$	0.473581	+	0.344077i	0.0181477	+	0.0131851i
$682$	−66.5072			−2.54669
$683$	−12.8420	−	9.33024i	−0.491385	−	0.357012i	0.314332	−	0.949313i	$-0.398220\pi$
$683$	−12.8420	−	9.33024i	−0.491385	−	0.357012i	−0.805717	+	0.592301i	$0.798220\pi$
$684$	7.96351	−	24.5092i	0.304492	−	0.937131i
$685$	−37.2103	−	21.0892i	−1.42173	−	0.805779i
$686$	−0.758114	−	2.33323i	−0.0289449	−	0.0890833i
$687$	5.88377	−	18.1084i	0.224480	−	0.690877i
$688$	−7.54387	+	23.2177i	−0.287608	+	0.885165i
$689$	−5.31634	−	16.3620i	−0.202536	−	0.623343i
$690$	14.7645	+	8.36789i	0.562074	+	0.318560i
$691$	10.9056	−	33.5641i	0.414870	−	1.27684i	−0.497498	−	0.867465i	$-0.665748\pi$
$691$	10.9056	−	33.5641i	0.414870	−	1.27684i	0.912367	−	0.409372i	$-0.134252\pi$
$692$	36.2702	+	26.3518i	1.37879	+	1.00175i
$693$	−4.08683			−0.155246
$694$	−11.9884	−	8.71011i	−0.455075	−	0.330631i
$695$	−11.4031	+	1.29059i	−0.432542	+	0.0489550i
$696$	4.90612	−	3.56451i	0.185966	−	0.135112i
$697$	−23.0948	+	16.7793i	−0.874776	+	0.635562i
$698$	19.8695	+	61.1519i	0.752070	+	2.31463i
$699$	30.2102			1.14265
$700$	19.5853	−	4.49085i	0.740256	−	0.169738i
$701$	39.2486			1.48240			0.741199	−	0.671285i	$-0.234257\pi$
$701$	39.2486			1.48240			0.741199	+	0.671285i	$0.234257\pi$
$702$	1.68406	+	5.18299i	0.0635606	+	0.195619i
$703$	35.7225	−	25.9539i	1.34730	−	0.978870i
$704$	−25.6985	+	18.6711i	−0.968550	+	0.703693i
$705$	−17.1429	−	9.71590i	−0.645640	−	0.365922i
$706$	0.0226856	+	0.0164821i	0.000853785	+	0.000620311i
$707$	−14.8193			−0.557336
$708$	23.3324	+	16.9520i	0.876886	+	0.637095i
$709$	−13.1578	+	40.4956i	−0.494153	+	1.52085i	0.324120	+	0.946016i	$0.394932\pi$
$709$	−13.1578	+	40.4956i	−0.494153	+	1.52085i	−0.818273	+	0.574830i	$0.805068\pi$
$710$	−24.5729	+	22.4832i	−0.922205	+	0.843780i
$711$	−2.86942	−	8.83116i	−0.107612	−	0.331194i
$712$	25.8564	−	79.5778i	0.969009	−	2.98230i
$713$	−6.34132	+	19.5166i	−0.237484	+	0.730901i
$714$	−3.12336	−	9.61272i	−0.116889	−	0.359747i
$715$	4.06200	−	19.8894i	0.151910	−	0.743820i
$716$	−21.3275	+	65.6392i	−0.797045	+	2.45305i
$717$	−4.85384	−	3.52652i	−0.181270	−	0.131700i
$718$	73.7236			2.75134
$719$	−31.2158	−	22.6796i	−1.16415	−	0.845807i	−0.173856	−	0.984771i	$-0.555623\pi$
$719$	−31.2158	−	22.6796i	−1.16415	−	0.845807i	−0.990297	+	0.138965i	$0.955623\pi$
$720$	−6.78479	+	6.20781i	−0.252854	+	0.231351i
$721$	−5.12602	+	3.72427i	−0.190903	+	0.138699i
$722$	43.9060	−	31.8996i	1.63401	−	1.18718i
$723$	7.51610	+	23.1322i	0.279527	+	0.860295i
$724$	25.5184			0.948382
$725$	5.96755	−	1.36834i	0.221629	−	0.0508188i
$726$	−13.9893			−0.519190
$727$	−5.07885	−	15.6311i	−0.188364	−	0.579725i	0.811626	−	0.584177i	$-0.198583\pi$
$727$	−5.07885	−	15.6311i	−0.188364	−	0.579725i	−0.999990	+	0.00445243i	$0.998583\pi$
$728$	−8.90037	+	6.46649i	−0.329870	+	0.239664i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	36.0663	+	79.2970i	1.33487	+	2.93491i
$731$	19.7849	+	14.3746i	0.731771	+	0.531663i
$732$	−38.1279			−1.40925
$733$	−27.4170	−	19.9196i	−1.01267	−	0.735747i	−0.0479018	−	0.998852i	$-0.515253\pi$
$733$	−27.4170	−	19.9196i	−1.01267	−	0.735747i	−0.964767	+	0.263105i	$0.915253\pi$
$734$	0.808468	−	2.48821i	0.0298411	−	0.0918415i
$735$	0.925763	+	2.03543i	0.0341473	+	0.0750778i
$736$	−0.176437	−	0.543017i	−0.00650355	−	0.0200159i
$737$	6.26422	−	19.2793i	0.230745	−	0.710161i
$738$	−5.25294	+	16.1669i	−0.193363	+	0.595111i
$739$	−15.5388	−	47.8236i	−0.571605	−	1.75922i	−0.647459	−	0.762100i	$-0.724168\pi$
$739$	−15.5388	−	47.8236i	−0.571605	−	1.75922i	0.0758537	−	0.997119i	$-0.475832\pi$
$740$	−61.4835	+	6.95868i	−2.26018	+	0.255806i
$741$	−4.40189	+	13.5476i	−0.161707	+	0.497684i
$742$	15.3716	+	11.1681i	0.564308	+	0.409993i
$743$	−40.6206			−1.49023			−0.745113	−	0.666938i	$-0.767605\pi$
$743$	−40.6206			−1.49023			−0.745113	+	0.666938i	$0.767605\pi$
$744$	−26.5776	−	19.3097i	−0.974381	−	0.707929i
$745$	6.81295	−	33.3593i	0.249607	−	1.22219i
$746$	60.8613	−	44.2184i	2.22829	−	1.61895i
$747$	4.92340	−	3.57706i	0.180138	−	0.130878i
$748$	−20.9096	−	64.3530i	−0.764529	−	2.35298i
$749$	2.81527			0.102868
$750$	−25.8760	+	9.09801i	−0.944857	+	0.332212i
$751$	14.6409			0.534255			0.267127	−	0.963661i	$-0.413926\pi$
$751$	14.6409			0.534255			0.267127	+	0.963661i	$0.413926\pi$
$752$	11.1994	+	34.4681i	0.408399	+	1.25692i
$753$	−0.496951	+	0.361056i	−0.0181099	+	0.0131576i
$754$	−5.39864	+	3.92234i	−0.196607	+	0.142843i
$755$	−4.11556	+	20.1516i	−0.149780	+	0.733392i
$756$	−3.25121	−	2.36214i	−0.118245	−	0.0859104i
$757$	−41.8009			−1.51928			−0.759639	−	0.650345i	$-0.774624\pi$
$757$	−41.8009			−1.51928			−0.759639	+	0.650345i	$0.774624\pi$
$758$	−55.1412	−	40.0624i	−2.00282	−	1.45513i
$759$	−3.90694	+	12.0243i	−0.141813	+	0.436455i
$760$	−70.5641	+	7.98642i	−2.55963	+	0.289698i
$761$	7.23501	+	22.2671i	0.262269	+	0.807181i	0.992310	+	0.123777i	$0.0395009\pi$
$761$	7.23501	+	22.2671i	0.262269	+	0.807181i	−0.730041	+	0.683403i	$0.760499\pi$
$762$	−6.19793	+	19.0753i	−0.224527	+	0.691024i
$763$	−1.73125	+	5.32823i	−0.0626753	+	0.192895i
$764$	−5.94055	−	18.2831i	−0.214921	−	0.661460i
$765$	3.81406	+	8.38578i	0.137898	+	0.303188i
$766$	2.13308	−	6.56495i	0.0770714	−	0.237201i
$767$	−12.8972	−	9.37034i	−0.465690	−	0.338343i
$768$	−32.1413			−1.15980
$769$	22.7824	+	16.5524i	0.821556	+	0.596895i	0.917158	−	0.398524i	$-0.130478\pi$
$769$	22.7824	+	16.5524i	0.821556	+	0.596895i	−0.0956018	+	0.995420i	$0.530478\pi$
$770$	9.28194	+	20.4077i	0.334498	+	0.735443i
$771$	5.56655	−	4.04434i	0.200474	−	0.145653i
$772$	−54.6659	+	39.7171i	−1.96747	+	1.42945i
$773$	2.32439	+	7.15374i	0.0836026	+	0.257302i	0.984116	−	0.177526i	$-0.0568092\pi$
$773$	2.32439	+	7.15374i	0.0836026	+	0.257302i	−0.900514	+	0.434828i	$0.856809\pi$
$774$	14.5627			0.523444
$775$	−17.0396	−	28.4547i	−0.612079	−	1.02212i
$776$	18.1156			0.650314
$777$	−2.12781	−	6.54871i	−0.0763346	−	0.234934i
$778$	21.3743	−	15.5294i	0.766307	−	0.556755i
$779$	−35.9468	+	26.1169i	−1.28793	+	0.935734i
$780$	14.7273	−	13.4749i	0.527321	−	0.482477i
$781$	−20.0741	−	14.5847i	−0.718308	−	0.521882i
$782$	−31.2685			−1.11816
$783$	−0.990627	−	0.719733i	−0.0354021	−	0.0257212i
$784$	1.27088	−	3.91138i	0.0453887	−	0.139692i
$785$	2.26669	−	11.0987i	0.0809015	−	0.396130i
$786$	−6.98576	−	21.4999i	−0.249174	−	0.766878i
$787$	−3.59966	+	11.0786i	−0.128314	+	0.394910i	−0.994490	−	0.104829i	$-0.966571\pi$
$787$	−3.59966	+	11.0786i	−0.128314	+	0.394910i	0.866176	+	0.499739i	$0.166571\pi$
$788$	−27.7888	+	85.5251i	−0.989934	+	3.04670i
$789$	7.50019	+	23.0832i	0.267014	+	0.821784i
$790$	−37.5817	+	34.3857i	−1.33710	+	1.22339i
$791$	4.82298	−	14.8436i	0.171485	−	0.527778i
$792$	−16.3747	−	11.8969i	−0.581849	−	0.422738i
$793$	21.0754			0.748411
$794$	−76.1010	−	55.2906i	−2.70072	−	1.96219i
$795$	−15.0663	−	8.53895i	−0.534346	−	0.302845i
$796$	−79.5367	+	57.7868i	−2.81910	+	2.04820i
$797$	22.0667	−	16.0324i	0.781642	−	0.567896i	−0.123829	−	0.992304i	$-0.539517\pi$
$797$	22.0667	−	16.0324i	0.781642	−	0.567896i	0.905471	+	0.424407i	$0.139517\pi$
$798$	−4.86148	−	14.9621i	−0.172095	−	0.529653i
$799$	36.3057			1.28440
$800$	0.848907	+	0.361836i	0.0300134	+	0.0127928i
$801$	−16.8950			−0.596955
$802$	13.4227	+	41.3109i	0.473973	+	1.45874i
$803$	−52.5042	+	38.1465i	−1.85283	+	1.34616i
$804$	16.1266	−	11.7167i	0.568742	−	0.413215i
$805$	6.87367	−	0.777960i	0.242265	−	0.0274195i
$806$	29.2457	+	21.2482i	1.03013	+	0.748436i
$807$	−0.305649			−0.0107593
$808$	−59.3762	−	43.1393i	−2.08885	−	1.51764i
$809$	3.66496	−	11.2796i	0.128853	−	0.396569i	−0.865730	−	0.500511i	$-0.833146\pi$
$809$	3.66496	−	11.2796i	0.128853	−	0.396569i	0.994583	+	0.103942i	$0.0331455\pi$
$810$	4.77255	+	2.70488i	0.167690	+	0.0950399i
$811$	−3.26846	−	10.0593i	−0.114771	−	0.353229i	0.877128	−	0.480256i	$-0.159456\pi$
$811$	−3.26846	−	10.0593i	−0.114771	−	0.353229i	−0.991899	+	0.127027i	$0.959456\pi$
$812$	1.52063	−	4.68001i	0.0533636	−	0.164236i
$813$	−4.75875	+	14.6459i	−0.166897	+	0.513655i
$814$	−21.3339	−	65.6591i	−0.747754	−	2.30135i
$815$	10.6026	+	6.00914i	0.371395	+	0.210491i
$816$	5.23593	−	16.1145i	0.183294	−	0.564122i
$817$	30.7950	+	22.3739i	1.07738	+	0.782763i
$818$	−47.6400			−1.66569
$819$	1.79713	+	1.30569i	0.0627968	+	0.0456246i
$820$	61.8695	−	7.00237i	2.16058	−	0.244533i
$821$	−8.80753	+	6.39904i	−0.307385	+	0.223328i	−0.730774	−	0.682620i	$-0.760840\pi$
$821$	−8.80753	+	6.39904i	−0.307385	+	0.223328i	0.423389	+	0.905948i	$0.360840\pi$
$822$	37.9642	−	27.5826i	1.32415	−	0.962054i
$823$	4.94127	+	15.2077i	0.172242	+	0.530106i	0.999497	−	0.0317209i	$-0.0100988\pi$
$823$	4.94127	+	15.2077i	0.172242	+	0.530106i	−0.827255	+	0.561827i	$0.810099\pi$
$824$	−31.3799			−1.09317
$825$	−10.4982	−	17.5312i	−0.365501	−	0.610358i
$826$	17.6062			0.612599
$827$	−2.01460	−	6.20031i	−0.0700546	−	0.215606i	0.909900	−	0.414828i	$-0.136158\pi$
$827$	−2.01460	−	6.20031i	−0.0700546	−	0.215606i	−0.979954	+	0.199222i	$0.936158\pi$
$828$	−10.0580	+	7.30759i	−0.349541	+	0.253956i
$829$	5.41897	−	3.93711i	0.188209	−	0.136742i	−0.489691	−	0.871896i	$-0.662890\pi$
$829$	5.41897	−	3.93711i	0.188209	−	0.136742i	0.677900	+	0.735154i	$0.262890\pi$
$830$	−29.0441	−	16.4610i	−1.00813	−	0.571369i
$831$	0.299025	+	0.217254i	0.0103731	+	0.00753646i
$832$	17.2658			0.598583
$833$	−3.33308	−	2.42162i	−0.115484	−	0.0839043i
$834$	3.89076	−	11.9745i	0.134726	−	0.414644i
$835$	−2.95566	+	2.70431i	−0.102285	+	0.0935864i
$836$	−32.5455	−	100.165i	−1.12561	−	3.46427i
$837$	−2.04980	+	6.30864i	−0.0708515	+	0.218059i
$838$	−15.8038	+	48.6390i	−0.545932	+	1.68021i
$839$	6.19281	+	19.0595i	0.213800	+	0.658007i	0.999237	+	0.0390658i	$0.0124382\pi$
$839$	6.19281	+	19.0595i	0.213800	+	0.658007i	−0.785437	+	0.618941i	$0.787562\pi$
$840$	−2.21594	+	10.8502i	−0.0764573	+	0.374369i
$841$	−8.49817	+	26.1547i	−0.293040	+	0.901885i
$842$	61.1924	+	44.4589i	2.10883	+	1.53216i
$843$	−13.1858			−0.454143
$844$	29.5491	+	21.4686i	1.01712	+	0.738981i
$845$	13.3059	−	12.1743i	0.457736	−	0.418810i
$846$	17.4903	−	12.7074i	0.601328	−	0.436890i
$847$	−4.61318	+	3.35167i	−0.158511	+	0.115165i
$848$	9.84270	+	30.2927i	0.338000	+	1.04026i
$849$	−0.334342			−0.0114746
$850$	33.2122	−	38.0913i	1.13917	−	1.30652i
$851$	−21.3018			−0.730218
$852$	−7.53984	−	23.2052i	−0.258311	−	0.794998i
$853$	18.1434	−	13.1820i	0.621220	−	0.451343i	−0.232128	−	0.972685i	$-0.574569\pi$
$853$	18.1434	−	13.1820i	0.621220	−	0.451343i	0.853347	+	0.521343i	$0.174569\pi$
$854$	−18.8306	+	13.6812i	−0.644370	+	0.468162i
$855$	5.93655	+	13.0524i	0.203026	+	0.446382i
$856$	11.2799	+	8.19533i	0.385539	+	0.280110i
$857$	31.3275			1.07013			0.535063	−	0.844812i	$-0.320288\pi$
$857$	31.3275			1.07013			0.535063	+	0.844812i	$0.320288\pi$
$858$	18.0185	+	13.0912i	0.615142	+	0.446927i
$859$	−1.30702	+	4.02260i	−0.0445951	+	0.137249i	−0.970875	−	0.239587i	$-0.922988\pi$
$859$	−1.30702	+	4.02260i	−0.0445951	+	0.137249i	0.926280	+	0.376836i	$0.122988\pi$
$860$	−22.0839	−	48.5547i	−0.753055	−	1.65570i
$861$	2.14117	+	6.58983i	0.0729707	+	0.224581i
$862$	12.5416	−	38.5991i	0.427169	−	1.31469i
$863$	−9.31266	+	28.6614i	−0.317007	+	0.975646i	0.657914	+	0.753093i	$0.271439\pi$
$863$	−9.31266	+	28.6614i	−0.317007	+	0.975646i	−0.974921	+	0.222553i	$0.928561\pi$
$864$	−0.0570324	−	0.175528i	−0.00194028	−	0.00597158i
$865$	−24.7871	+	2.80540i	−0.842787	+	0.0953863i
$866$	−25.2911	+	77.8379i	−0.859426	+	2.64504i
$867$	0.0212968	+	0.0154730i	0.000723276	+	0.000525491i
$868$	−26.6574			−0.904810
$869$	−30.7012	−	22.3058i	−1.04147	−	0.756671i
$870$	−1.34411	+	6.58137i	−0.0455696	+	0.223129i
$871$	−8.91410	+	6.47647i	−0.302043	+	0.219447i
$872$	−22.4472	+	16.3089i	−0.760158	+	0.552287i
$873$	−1.13034	−	3.47882i	−0.0382561	−	0.117740i
$874$	−48.6692			−1.64626
$875$	−6.35323	+	9.19981i	−0.214778	+	0.311010i
$876$	−63.8171			−2.15618
$877$	3.02769	+	9.31827i	0.102238	+	0.314656i	0.989072	−	0.147432i	$-0.0471007\pi$
$877$	3.02769	+	9.31827i	0.102238	+	0.314656i	−0.886834	+	0.462087i	$0.847101\pi$
$878$	33.0909	−	24.0419i	1.11676	−	0.811376i
$879$	14.0833	−	10.2321i	0.475017	−	0.345120i
$880$	−7.52040	+	36.8233i	−0.253513	+	1.24131i
$881$	42.1893	+	30.6523i	1.42139	+	1.03270i	0.991540	+	0.129804i	$0.0414347\pi$
$881$	42.1893	+	30.6523i	1.42139	+	1.03270i	0.429853	+	0.902899i	$0.358565\pi$
$882$	−2.45331			−0.0826072
$883$	23.1894	+	16.8481i	0.780385	+	0.566983i	0.905094	−	0.425211i	$-0.139800\pi$
$883$	23.1894	+	16.8481i	0.780385	+	0.566983i	−0.124710	+	0.992193i	$0.539800\pi$
$884$	−11.3653	+	34.9787i	−0.382256	+	1.17646i
$885$	−15.9454	+	1.80470i	−0.535999	+	0.0606642i
$886$	19.2900	+	59.3687i	0.648062	+	1.99453i
$887$	13.2421	−	40.7551i	0.444628	−	1.36842i	−0.438264	−	0.898846i	$-0.644407\pi$
$887$	13.2421	−	40.7551i	0.444628	−	1.36842i	0.882892	−	0.469577i	$-0.155593\pi$
$888$	10.5380	−	32.4328i	0.353634	−	1.08837i
$889$	2.52636	+	7.77532i	0.0847313	+	0.260776i
$890$	38.3716	+	84.3655i	1.28622	+	2.82794i
$891$	−1.26290	+	3.88681i	−0.0423088	+	0.130213i
$892$	−50.3676	−	36.5942i	−1.68643	−	1.22527i
$893$	56.5095			1.89102
$894$	30.2214	+	21.9571i	1.01075	+	0.734356i
$895$	−15.8990	−	34.9562i	−0.531444	−	1.16846i
$896$	−15.7253	+	11.4251i	−0.525347	+	0.381687i
$897$	5.55965	−	4.03932i	0.185631	−	0.134869i
$898$	14.3266	+	44.0928i	0.478086	+	1.47140i
$899$	−8.12236			−0.270896
$900$	1.78115	−	20.0145i	0.0593717	−	0.667150i
$901$	31.9077			1.06300
$902$	21.4679	+	66.0713i	0.714802	+	2.19994i
$903$	4.80226	−	3.48905i	0.159809	−	0.116108i
$904$	62.5344	−	45.4339i	2.07986	−	1.51111i
$905$	−10.4756	+	9.58472i	−0.348220	+	0.318607i
$906$	−18.2561	−	13.2638i	−0.606518	−	0.440661i
$907$	−4.39393			−0.145898			−0.0729490	−	0.997336i	$-0.523241\pi$
$907$	−4.39393			−0.145898			−0.0729490	+	0.997336i	$0.523241\pi$
$908$	1.90319	+	1.38275i	0.0631596	+	0.0458881i
$909$	−4.57941	+	14.0940i	−0.151889	+	0.467467i
$910$	2.43840	−	11.9395i	0.0808321	−	0.395790i
$911$	6.86099	+	21.1160i	0.227315	+	0.699603i	0.998048	+	0.0624455i	$0.0198900\pi$
$911$	6.86099	+	21.1160i	0.227315	+	0.699603i	−0.770734	+	0.637158i	$0.780110\pi$
$912$	8.14968	−	25.0821i	0.269863	−	0.830552i
$913$	7.68558	−	23.6538i	0.254356	−	0.782826i
$914$	4.00395	+	12.3229i	0.132439	+	0.407605i
$915$	15.6519	−	14.3209i	0.517436	−	0.473433i
$916$	23.6452	−	72.7725i	0.781260	−	2.40447i
$917$	−7.45481	−	5.41624i	−0.246180	−	0.178860i
$918$	−10.1074			−0.333594
$919$	20.0841	+	14.5919i	0.662513	+	0.481344i	0.867511	−	0.497419i	$-0.165719\pi$
$919$	20.0841	+	14.5919i	0.662513	+	0.481344i	−0.204998	+	0.978762i	$0.565719\pi$
$920$	29.8053	+	16.8924i	0.982653	+	0.556927i
$921$	−0.0681791	+	0.0495350i	−0.00224658	+	0.00163223i
$922$	18.2305	−	13.2453i	0.600391	−	0.436210i
$923$	4.16770	+	12.8269i	0.137182	+	0.422201i
$924$	−16.4238			−0.540305
$925$	22.6260	−	25.9499i	0.743937	−	0.853226i
$926$	25.3309			0.832424
$927$	1.95797	+	6.02600i	0.0643081	+	0.197920i
$928$	0.182831	−	0.132835i	0.00600172	−	0.00436051i
$929$	−11.7571	+	8.54200i	−0.385736	+	0.280254i	−0.763706	−	0.645564i	$-0.776622\pi$
$929$	−11.7571	+	8.54200i	−0.385736	+	0.280254i	0.377970	+	0.925818i	$0.376622\pi$
$930$	36.1579	−	4.09233i	1.18566	−	0.134193i
$931$	−5.18791	−	3.76923i	−0.170027	−	0.123532i
$932$	121.406			3.97679
$933$	27.0393	+	19.6452i	0.885226	+	0.643154i
$934$	−2.69874	+	8.30587i	−0.0883055	+	0.271776i
$935$	32.7547	+	18.5640i	1.07119	+	0.607107i
$936$	3.39964	+	10.4630i	0.111121	+	0.341994i
$937$	9.96676	−	30.6745i	0.325600	−	1.00209i	−0.645569	−	0.763702i	$-0.723380\pi$
$937$	9.96676	−	30.6745i	0.325600	−	1.00209i	0.971169	−	0.238391i	$-0.0766201\pi$
$938$	3.76038	−	11.5733i	0.122781	−	0.377881i
$939$	−7.19251	−	22.1363i	−0.234719	−	0.722389i
$940$	−68.8927	−	39.0455i	−2.24703	−	1.27352i
$941$	5.14992	−	15.8498i	0.167883	−	0.516689i	−0.831355	−	0.555742i	$-0.812434\pi$
$941$	5.14992	−	15.8498i	0.167883	−	0.516689i	0.999237	+	0.0390529i	$0.0124341\pi$
$942$	10.0547	+	7.30519i	0.327601	+	0.238016i
$943$	21.4356			0.698039
$944$	23.8779	+	17.3483i	0.777159	+	0.564639i
$945$	2.22188	−	0.251472i	0.0722778	−	0.00818038i
$946$	48.1487	−	34.9821i	1.56545	−	1.13737i
$947$	−33.3654	+	24.2414i	−1.08423	+	0.787740i	−0.978416	−	0.206646i	$-0.933745\pi$
$947$	−33.3654	+	24.2414i	−1.08423	+	0.787740i	−0.105815	+	0.994386i	$0.533745\pi$
$948$	−11.5314	−	35.4899i	−0.374522	−	1.15266i
$949$	35.2754			1.14509
$950$	51.6945	−	59.2887i	1.67719	−	1.92358i
$951$	−18.3276			−0.594313
$952$	−6.30519	−	19.4054i	−0.204352	−	0.628932i
$953$	2.42391	−	1.76107i	0.0785182	−	0.0570468i	−0.547834	−	0.836587i	$-0.684547\pi$
$953$	2.42391	−	1.76107i	0.0785182	−	0.0570468i	0.626352	+	0.779540i	$0.284547\pi$
$954$	15.3716	−	11.1681i	0.497673	−	0.361580i
$955$	9.30582	+	5.27415i	0.301129	+	0.170668i
$956$	−19.5062	−	14.1721i	−0.630877	−	0.458359i
$957$	−5.00426			−0.161765
$958$	64.3345	+	46.7417i	2.07855	+	1.51016i
$959$	5.91081	−	18.1916i	0.190870	−	0.587438i
$960$	12.8226	−	11.7322i	0.413848	−	0.378654i
$961$	4.01742	+	12.3643i	0.129594	+	0.398850i
$962$	−11.5959	+	35.6887i	−0.373868	+	1.15065i
$963$	0.869965	−	2.67748i	0.0280342	−	0.0862805i
$964$	30.2051	+	92.9618i	0.972841	+	2.99410i
$965$	7.52318	−	36.8368i	0.242180	−	1.18582i
$966$	−2.34532	+	7.21815i	−0.0754594	+	0.232240i
$967$	7.56037	+	5.49293i	0.243125	+	0.176641i	0.702674	−	0.711512i	$-0.251989\pi$
$967$	7.56037	+	5.49293i	0.243125	+	0.176641i	−0.459549	+	0.888152i	$0.651989\pi$
$968$	−28.2404			−0.907681
$969$	−21.3737	−	15.5289i	−0.686623	−	0.498861i
$970$	−14.8044	+	13.5454i	−0.475340	+	0.434917i
$971$	19.6220	−	14.2562i	0.629700	−	0.457503i	−0.226597	−	0.973989i	$-0.572760\pi$
$971$	19.6220	−	14.2562i	0.629700	−	0.457503i	0.856296	+	0.516485i	$0.172760\pi$
$972$	−3.25121	+	2.36214i	−0.104283	+	0.0757658i
$973$	−1.58592	−	4.88097i	−0.0508424	−	0.156477i
$974$	−28.2516			−0.905240
$975$	−0.984543	+	11.0632i	−0.0315306	+	0.354305i
$976$	−39.0192			−1.24897
$977$	−15.3297	−	47.1801i	−0.490442	−	1.50943i	−0.823941	−	0.566675i	$-0.808229\pi$
$977$	−15.3297	−	47.1801i	−0.490442	−	1.50943i	0.333499	−	0.942750i	$-0.391771\pi$
$978$	−10.8175	+	7.85935i	−0.345905	+	0.251314i
$979$	−55.8601	+	40.5848i	−1.78530	+	1.29709i
$980$	3.72038	+	8.17981i	0.118843	+	0.261294i
$981$	4.53246	+	3.29303i	0.144710	+	0.105138i
$982$	42.5570			1.35805
$983$	4.04353	+	2.93779i	0.128968	+	0.0937011i	0.650399	−	0.759592i	$-0.274602\pi$
$983$	4.04353	+	2.93779i	0.128968	+	0.0937011i	−0.521431	+	0.853294i	$0.674602\pi$
$984$	−10.6042	+	32.6364i	−0.338050	+	1.04041i
$985$	−20.7157	−	45.5465i	−0.660057	−	1.45123i
$986$	−3.82450	−	11.7706i	−0.121797	−	0.374853i
$987$	2.72314	−	8.38095i	0.0866784	−	0.266769i
$988$	−17.6900	+	54.4441i	−0.562792	+	1.73210i
$989$	−5.67464	−	17.4647i	−0.180443	−	0.555347i
$990$	22.2772	−	2.52132i	0.708015	−	0.0801329i
$991$	3.92286	−	12.0733i	0.124614	−	0.383522i	−0.869217	−	0.494431i	$-0.835376\pi$
$991$	3.92286	−	12.0733i	0.124614	−	0.383522i	0.993831	+	0.110910i	$0.0353764\pi$
$992$	−0.990437	−	0.719594i	−0.0314464	−	0.0228471i
$993$	22.7759			0.722772
$994$	−12.0504	−	8.75513i	−0.382216	−	0.277696i
$995$	10.9459	−	53.5962i	0.347009	−	1.69911i
$996$	19.7858	−	14.3752i	0.626936	−	0.455496i
$997$	38.8823	−	28.2496i	1.23141	−	0.894675i	0.234419	−	0.972136i	$-0.424681\pi$
$997$	38.8823	−	28.2496i	1.23141	−	0.894675i	0.996995	+	0.0774602i	$0.0246811\pi$
$998$	8.66335	+	26.6630i	0.274233	+	0.844004i
$999$	−6.88572			−0.217855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.106.1	✓	24
25.21	even	5	inner	525.2.n.c.421.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.106.1	✓	24	1.1	even	1	trivial
525.2.n.c.421.1	yes	24	25.21	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.758114 - 2.33323i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.25121 + 2.36214i) q^{4} +(0.447435 - 2.19084i) q^{5} +(1.98477 + 1.44202i) q^{6} +1.00000 q^{7} +(4.00669 + 2.91103i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.758114 - 2.33323i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.25121 + 2.36214i) q^{4} +(0.447435 - 2.19084i) q^{5} +(1.98477 + 1.44202i) q^{6} +1.00000 q^{7} +(4.00669 + 2.91103i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-5.45096 + 0.616938i) q^{10} +(-1.26290 - 3.88681i) q^{11} +(1.24185 - 3.82203i) q^{12} +(-0.686443 + 2.11265i) q^{13} +(-0.758114 - 2.33323i) q^{14} +(0.925763 + 2.03543i) q^{15} +(1.27088 - 3.91138i) q^{16} +(-3.33308 - 2.42162i) q^{17} -2.45331 q^{18} +(-5.18791 - 3.76923i) q^{19} +(3.72038 + 8.17981i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-8.11141 + 5.89329i) q^{22} +(0.955983 + 2.94221i) q^{23} -4.95254 q^{24} +(-4.59960 - 1.96052i) q^{25} +5.44972 q^{26} +(0.309017 + 0.951057i) q^{27} +(-3.25121 + 2.36214i) q^{28} +(-0.990627 + 0.719733i) q^{29} +(4.04729 - 3.70311i) q^{30} +(5.36645 + 3.89895i) q^{31} -0.184561 q^{32} +(3.30632 + 2.40218i) q^{33} +(-3.12336 + 9.61272i) q^{34} +(0.447435 - 2.19084i) q^{35} +(1.24185 + 3.82203i) q^{36} +(-2.12781 + 6.54871i) q^{37} +(-4.86148 + 14.9621i) q^{38} +(-0.686443 - 2.11265i) q^{39} +(8.17035 - 7.47554i) q^{40} +(2.14117 - 6.58983i) q^{41} +(1.98477 + 1.44202i) q^{42} -5.93592 q^{43} +(13.2872 + 9.65369i) q^{44} +(-1.94535 - 1.10254i) q^{45} +(6.14013 - 4.46106i) q^{46} +(-7.12926 + 5.17971i) q^{47} +(1.27088 + 3.91138i) q^{48} +1.00000 q^{49} +(-1.08734 + 12.2183i) q^{50} +4.11991 q^{51} +(-2.75862 - 8.49017i) q^{52} +(-6.26565 + 4.55226i) q^{53} +(1.98477 - 1.44202i) q^{54} +(-9.08046 + 1.02772i) q^{55} +(4.00669 + 2.91103i) q^{56} +6.41260 q^{57} +(2.43031 + 1.76573i) q^{58} +(-2.21767 + 6.82529i) q^{59} +(-7.81783 - 4.43082i) q^{60} +(-2.93182 - 9.02321i) q^{61} +(5.02879 - 15.4770i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-2.40185 - 7.39214i) q^{64} +(4.32136 + 2.44917i) q^{65} +(3.09828 - 9.53554i) q^{66} +(4.01287 + 2.91552i) q^{67} +16.5568 q^{68} +(-2.50279 - 1.81839i) q^{69} +(-5.45096 + 0.616938i) q^{70} +(4.91190 - 3.56871i) q^{71} +(4.00669 - 2.91103i) q^{72} +(-4.90718 - 15.1027i) q^{73} +16.8928 q^{74} +(4.87352 - 1.11748i) q^{75} +25.7705 q^{76} +(-1.26290 - 3.88681i) q^{77} +(-4.40892 + 3.20327i) q^{78} +(7.51223 - 5.45796i) q^{79} +(-8.00059 - 4.53440i) q^{80} +(-0.809017 - 0.587785i) q^{81} -16.9989 q^{82} +(4.92340 + 3.57706i) q^{83} +(1.24185 - 3.82203i) q^{84} +(-6.79674 + 6.21874i) q^{85} +(4.50011 + 13.8499i) q^{86} +(0.378386 - 1.16455i) q^{87} +(6.25457 - 19.2496i) q^{88} +(-5.22083 - 16.0681i) q^{89} +(-1.09770 + 5.37482i) q^{90} +(-0.686443 + 2.11265i) q^{91} +(-10.0580 - 7.30759i) q^{92} -6.63330 q^{93} +(17.4903 + 12.7074i) q^{94} +(-10.5791 + 9.67941i) q^{95} +(0.149313 - 0.108482i) q^{96} +(2.95926 - 2.15003i) q^{97} +(-0.758114 - 2.33323i) q^{98} -4.08683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Introduction

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