LMFDB - Embedded newform 930.2.n.a.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.1
Root			$1.69513 - 1.23158i$ of defining polynomial
Character	$\chi$	$=$	930.481
Dual form			930.2.n.a.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.518200 + 1.59485i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.518200 + 1.59485i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.809017 + 0.587785i) q^{10} +(-1.18976 + 3.66171i) q^{11} +(0.809017 - 0.587785i) q^{12} +(-2.15163 - 1.56325i) q^{13} +(-0.518200 - 1.59485i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.938299 + 2.88779i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-3.05850 + 2.22213i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-1.35666 + 0.985674i) q^{21} +(-1.18976 - 3.66171i) q^{22} +(-0.770884 - 2.37254i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +2.65956 q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.35666 + 0.985674i) q^{28} +(-5.53991 + 4.02498i) q^{29} -1.00000 q^{30} +(5.52783 + 0.665657i) q^{31} +1.00000 q^{32} +(-3.11483 + 2.26306i) q^{33} +(-2.45650 - 1.78475i) q^{34} +(-0.518200 + 1.59485i) q^{35} +1.00000 q^{36} -5.39855 q^{37} +(1.16824 - 3.59548i) q^{38} +(-0.821848 - 2.52939i) q^{39} +(0.309017 + 0.951057i) q^{40} +(8.86495 - 6.44077i) q^{41} +(0.518200 - 1.59485i) q^{42} +(-9.64452 + 7.00716i) q^{43} +(3.11483 + 2.26306i) q^{44} +(0.309017 + 0.951057i) q^{45} +(2.01820 + 1.46631i) q^{46} +(6.53518 + 4.74808i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(3.38809 + 2.46159i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.938299 + 2.88779i) q^{51} +(-2.15163 + 1.56325i) q^{52} +(0.156995 + 0.483181i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.18976 + 3.66171i) q^{55} -1.67693 q^{56} -3.78051 q^{57} +(2.11606 - 6.51255i) q^{58} +(11.4148 + 8.29332i) q^{59} +(0.809017 - 0.587785i) q^{60} -4.85410 q^{61} +(-4.86337 + 2.71065i) q^{62} -1.67693 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.15163 - 1.56325i) q^{65} +(1.18976 - 3.66171i) q^{66} -13.9109 q^{67} +3.03640 q^{68} +(0.770884 - 2.37254i) q^{69} +(-0.518200 - 1.59485i) q^{70} +(2.38082 + 7.32740i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(5.01990 - 15.4497i) q^{73} +(4.36752 - 3.17319i) q^{74} +(0.809017 + 0.587785i) q^{75} +(1.16824 + 3.59548i) q^{76} +(-5.22335 - 3.79499i) q^{77} +(2.15163 + 1.56325i) q^{78} +(-0.834903 - 2.56957i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.38611 + 10.4214i) q^{82} +(1.81439 - 1.31823i) q^{83} +(0.518200 + 1.59485i) q^{84} +(0.938299 + 2.88779i) q^{85} +(3.68388 - 11.3378i) q^{86} -6.84770 q^{87} -3.85015 q^{88} +(-2.33749 + 7.19404i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(3.60813 - 2.62146i) q^{91} -2.49463 q^{92} +(4.08084 + 3.78770i) q^{93} -8.07792 q^{94} +(-3.05850 + 2.22213i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-4.26883 + 13.1381i) q^{97} -4.18791 q^{98} -3.85015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	−0.518200	+	1.59485i	−0.195861	+	0.602798i	0.804104	+	0.594488i	$0.202645\pi$
$7$	−0.518200	+	1.59485i	−0.195861	+	0.602798i	−0.999965	+	0.00831018i	$0.997355\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.809017	+	0.587785i	−0.255834	+	0.185874i
$11$	−1.18976	+	3.66171i	−0.358726	+	1.10405i	0.595091	+	0.803658i	$0.297116\pi$
$11$	−1.18976	+	3.66171i	−0.358726	+	1.10405i	−0.953817	+	0.300387i	$0.902884\pi$
$12$	0.809017	−	0.587785i	0.233543	−	0.169679i
$13$	−2.15163	−	1.56325i	−0.596754	−	0.433567i	0.247971	−	0.968767i	$-0.420236\pi$
$13$	−2.15163	−	1.56325i	−0.596754	−	0.433567i	−0.844725	+	0.535200i	$0.820236\pi$
$14$	−0.518200	−	1.59485i	−0.138495	−	0.426243i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.938299	+	2.88779i	0.227571	+	0.700391i	0.998020	+	0.0628903i	$0.0200318\pi$
$17$	0.938299	+	2.88779i	0.227571	+	0.700391i	−0.770450	+	0.637501i	$0.779968\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−3.05850	+	2.22213i	−0.701668	+	0.509792i	−0.880475	−	0.474093i	$-0.842776\pi$
$19$	−3.05850	+	2.22213i	−0.701668	+	0.509792i	0.178807	+	0.983884i	$0.442776\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	−1.35666	+	0.985674i	−0.296048	+	0.215092i
$22$	−1.18976	−	3.66171i	−0.253658	−	0.780678i
$23$	−0.770884	−	2.37254i	−0.160740	−	0.494708i	0.837957	−	0.545736i	$-0.183750\pi$
$23$	−0.770884	−	2.37254i	−0.160740	−	0.494708i	−0.998697	+	0.0510286i	$0.983750\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	2.65956			0.521582
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.35666	+	0.985674i	0.256385	+	0.186275i
$29$	−5.53991	+	4.02498i	−1.02873	+	0.747419i	−0.968055	−	0.250738i	$-0.919327\pi$
$29$	−5.53991	+	4.02498i	−1.02873	+	0.747419i	−0.0606796	+	0.998157i	$0.519327\pi$
$30$	−1.00000			−0.182574
$31$	5.52783	+	0.665657i	0.992828	+	0.119556i
$31$	5.52783	+	0.665657i	0.992828	+	0.119556i
$32$	1.00000			0.176777
$33$	−3.11483	+	2.26306i	−0.542223	+	0.393948i
$34$	−2.45650	−	1.78475i	−0.421286	−	0.306082i
$35$	−0.518200	+	1.59485i	−0.0875917	+	0.269580i
$36$	1.00000			0.166667
$37$	−5.39855			−0.887516			−0.443758	−	0.896147i	$-0.646355\pi$
$37$	−5.39855			−0.887516			−0.443758	+	0.896147i	$0.646355\pi$
$38$	1.16824	−	3.59548i	0.189514	−	0.583264i
$39$	−0.821848	−	2.52939i	−0.131601	−	0.405026i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	8.86495	−	6.44077i	1.38447	−	1.00588i	0.388027	−	0.921648i	$-0.373157\pi$
$41$	8.86495	−	6.44077i	1.38447	−	1.00588i	0.996446	−	0.0842308i	$-0.0268433\pi$
$42$	0.518200	−	1.59485i	0.0799599	−	0.246091i
$43$	−9.64452	+	7.00716i	−1.47078	+	1.06858i	−0.490388	+	0.871504i	$0.663145\pi$
$43$	−9.64452	+	7.00716i	−1.47078	+	1.06858i	−0.980388	+	0.197077i	$0.936855\pi$
$44$	3.11483	+	2.26306i	0.469579	+	0.341169i
$45$	0.309017	+	0.951057i	0.0460655	+	0.141775i
$46$	2.01820	+	1.46631i	0.297567	+	0.216195i
$47$	6.53518	+	4.74808i	0.953253	+	0.692579i	0.951574	−	0.307419i	$-0.0994655\pi$
$47$	6.53518	+	4.74808i	0.953253	+	0.692579i	0.00167932	+	0.999999i	$0.499465\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	3.38809	+	2.46159i	0.484013	+	0.351656i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	−0.938299	+	2.88779i	−0.131388	+	0.404371i
$52$	−2.15163	+	1.56325i	−0.298377	+	0.216784i
$53$	0.156995	+	0.483181i	0.0215649	+	0.0663700i	0.961260	−	0.275644i	$-0.0888910\pi$
$53$	0.156995	+	0.483181i	0.0215649	+	0.0663700i	−0.939695	+	0.342014i	$0.888891\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−1.18976	+	3.66171i	−0.160427	+	0.493744i
$56$	−1.67693			−0.224089
$57$	−3.78051			−0.500741
$58$	2.11606	−	6.51255i	0.277852	−	0.855140i
$59$	11.4148	+	8.29332i	1.48608	+	1.07970i	0.975535	+	0.219844i	$0.0705550\pi$
$59$	11.4148	+	8.29332i	1.48608	+	1.07970i	0.510541	+	0.859853i	$0.329445\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	−4.85410			−0.621504			−0.310752	−	0.950491i	$-0.600581\pi$
$61$	−4.85410			−0.621504			−0.310752	+	0.950491i	$0.600581\pi$
$62$	−4.86337	+	2.71065i	−0.617649	+	0.344253i
$63$	−1.67693			−0.211273
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.15163	−	1.56325i	−0.266876	−	0.193897i
$66$	1.18976	−	3.66171i	0.146449	−	0.450725i
$67$	−13.9109			−1.69949			−0.849745	−	0.527194i	$-0.823244\pi$
$67$	−13.9109			−1.69949			−0.849745	+	0.527194i	$0.823244\pi$
$68$	3.03640			0.368217
$69$	0.770884	−	2.37254i	0.0928035	−	0.285620i
$70$	−0.518200	−	1.59485i	−0.0619367	−	0.190622i
$71$	2.38082	+	7.32740i	0.282551	+	0.869602i	0.987122	+	0.159969i	$0.0511393\pi$
$71$	2.38082	+	7.32740i	0.282551	+	0.869602i	−0.704571	+	0.709633i	$0.748861\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	5.01990	−	15.4497i	0.587535	−	1.80825i	−0.00130879	−	0.999999i	$-0.500417\pi$
$73$	5.01990	−	15.4497i	0.587535	−	1.80825i	0.588844	−	0.808247i	$-0.299583\pi$
$74$	4.36752	−	3.17319i	0.507714	−	0.368875i
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$	1.16824	+	3.59548i	0.134007	+	0.412430i
$77$	−5.22335	−	3.79499i	−0.595256	−	0.432479i
$78$	2.15163	+	1.56325i	0.243624	+	0.177003i
$79$	−0.834903	−	2.56957i	−0.0939339	−	0.289099i	0.893040	−	0.449976i	$-0.148568\pi$
$79$	−0.834903	−	2.56957i	−0.0939339	−	0.289099i	−0.986974	+	0.160878i	$0.948568\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.38611	+	10.4214i	−0.373933	+	1.15085i
$83$	1.81439	−	1.31823i	0.199155	−	0.144694i	−0.483739	−	0.875213i	$-0.660721\pi$
$83$	1.81439	−	1.31823i	0.199155	−	0.144694i	0.682893	+	0.730518i	$0.260721\pi$
$84$	0.518200	+	1.59485i	0.0565402	+	0.174013i
$85$	0.938299	+	2.88779i	0.101773	+	0.313224i
$86$	3.68388	−	11.3378i	0.397243	−	1.22259i
$87$	−6.84770			−0.734150
$88$	−3.85015			−0.410427
$89$	−2.33749	+	7.19404i	−0.247773	+	0.762567i	0.747395	+	0.664380i	$0.231304\pi$
$89$	−2.33749	+	7.19404i	−0.247773	+	0.762567i	−0.995168	+	0.0981869i	$0.968696\pi$
$90$	−0.809017	−	0.587785i	−0.0852779	−	0.0619580i
$91$	3.60813	−	2.62146i	0.378234	−	0.274803i
$92$	−2.49463			−0.260083
$93$	4.08084	+	3.78770i	0.423164	+	0.392767i
$94$	−8.07792			−0.833174
$95$	−3.05850	+	2.22213i	−0.313795	+	0.227986i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−4.26883	+	13.1381i	−0.433434	+	1.33397i	0.461248	+	0.887271i	$0.347402\pi$
$97$	−4.26883	+	13.1381i	−0.433434	+	1.33397i	−0.894683	+	0.446703i	$0.852598\pi$
$98$	−4.18791			−0.423043
$99$	−3.85015			−0.386954
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	−3.16651	−	9.74551i	−0.315079	−	0.969715i	−0.975722	−	0.219014i	$-0.929716\pi$
$101$	−3.16651	−	9.74551i	−0.315079	−	0.969715i	0.660642	−	0.750701i	$-0.270284\pi$
$102$	−0.938299	−	2.88779i	−0.0929054	−	0.285934i
$103$	9.11764	−	6.62435i	0.898388	−	0.652717i	−0.0396637	−	0.999213i	$-0.512629\pi$
$103$	9.11764	−	6.62435i	0.898388	−	0.652717i	0.938051	+	0.346496i	$0.112629\pi$
$104$	0.821848	−	2.52939i	0.0805889	−	0.248027i
$105$	−1.35666	+	0.985674i	−0.132397	+	0.0961919i
$106$	−0.411018	−	0.298622i	−0.0399216	−	0.0290048i
$107$	0.810823	+	2.49546i	0.0783852	+	0.241245i	0.982569	−	0.185899i	$-0.0595197\pi$
$107$	0.810823	+	2.49546i	0.0783852	+	0.241245i	−0.904184	+	0.427144i	$0.859520\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−8.79003	−	6.38633i	−0.841932	−	0.611699i	0.0809777	−	0.996716i	$-0.474196\pi$
$109$	−8.79003	−	6.38633i	−0.841932	−	0.611699i	−0.922910	+	0.385017i	$0.874196\pi$
$110$	−1.18976	−	3.66171i	−0.113439	−	0.349130i
$111$	−4.36752	−	3.17319i	−0.414546	−	0.301186i
$112$	1.35666	−	0.985674i	0.128193	−	0.0931374i
$113$	−2.48997	+	7.66335i	−0.234237	+	0.720908i	0.762985	+	0.646417i	$0.223733\pi$
$113$	−2.48997	+	7.66335i	−0.234237	+	0.720908i	−0.997222	+	0.0744910i	$0.976267\pi$
$114$	3.05850	−	2.22213i	0.286455	−	0.208122i
$115$	−0.770884	−	2.37254i	−0.0718853	−	0.221240i
$116$	2.11606	+	6.51255i	0.196471	+	0.604675i
$117$	0.821848	−	2.52939i	0.0759799	−	0.233842i
$118$	−14.1094			−1.29888
$119$	−5.09183			−0.466767
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	−3.09337	−	2.24747i	−0.281216	−	0.204315i
$122$	3.92705	−	2.85317i	0.355538	−	0.258314i
$123$	10.9577			0.988021
$124$	2.34127	−	5.05158i	0.210252	−	0.453645i
$125$	1.00000			0.0894427
$126$	1.35666	−	0.985674i	0.120861	−	0.0878108i
$127$	−16.2381	−	11.7977i	−1.44090	−	1.04688i	−0.987853	−	0.155391i	$-0.950336\pi$
$127$	−16.2381	−	11.7977i	−1.44090	−	1.04688i	−0.453049	−	0.891485i	$-0.649664\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−11.9213			−1.04961
$130$	2.65956			0.233259
$131$	1.29057	−	3.97198i	0.112758	−	0.347033i	−0.878715	−	0.477347i	$-0.841598\pi$
$131$	1.29057	−	3.97198i	0.112758	−	0.347033i	0.991473	+	0.130314i	$0.0415985\pi$
$132$	1.18976	+	3.66171i	0.103555	+	0.318711i
$133$	−1.95906	−	6.02937i	−0.169872	−	0.522813i
$134$	11.2542	−	8.17664i	0.972213	−	0.706354i
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$	−2.45650	+	1.78475i	−0.210643	+	0.153041i
$137$	9.13623	+	6.63786i	0.780561	+	0.567111i	0.905147	−	0.425098i	$-0.139760\pi$
$137$	9.13623	+	6.63786i	0.780561	+	0.567111i	−0.124586	+	0.992209i	$0.539760\pi$
$138$	0.770884	+	2.37254i	0.0656220	+	0.201964i
$139$	14.7530	+	10.7186i	1.25133	+	0.909144i	0.998298	−	0.0583142i	$-0.0185725\pi$
$139$	14.7530	+	10.7186i	1.25133	+	0.909144i	0.253031	+	0.967458i	$0.418573\pi$
$140$	1.35666	+	0.985674i	0.114659	+	0.0833047i
$141$	2.49622	+	7.68256i	0.210219	+	0.646988i
$142$	−6.23306	−	4.52858i	−0.523066	−	0.380030i
$143$	8.28408	−	6.01873i	0.692749	−	0.503312i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−5.53991	+	4.02498i	−0.460064	+	0.334256i
$146$	5.01990	+	15.4497i	0.415450	+	1.27862i
$147$	1.29414	+	3.98294i	0.106738	+	0.328507i
$148$	−1.66824	+	5.13432i	−0.137129	+	0.422039i
$149$	18.1675			1.48834			0.744171	−	0.667989i	$-0.232845\pi$
$149$	18.1675			1.48834			0.744171	+	0.667989i	$0.232845\pi$
$150$	−1.00000			−0.0816497
$151$	1.95440	−	6.01504i	0.159047	−	0.489497i	−0.839501	−	0.543358i	$-0.817153\pi$
$151$	1.95440	−	6.01504i	0.159047	−	0.489497i	0.998548	+	0.0538610i	$0.0171528\pi$
$152$	−3.05850	−	2.22213i	−0.248077	−	0.180239i
$153$	−2.45650	+	1.78475i	−0.198596	+	0.144289i
$154$	6.45642			0.520273
$155$	5.52783	+	0.665657i	0.444006	+	0.0534668i
$156$	−2.65956			−0.212935
$157$	−4.27222	+	3.10395i	−0.340961	+	0.247722i	−0.745067	−	0.666990i	$-0.767583\pi$
$157$	−4.27222	+	3.10395i	−0.340961	+	0.247722i	0.404106	+	0.914712i	$0.367583\pi$
$158$	2.18580	+	1.58808i	0.173893	+	0.126341i
$159$	−0.156995	+	0.483181i	−0.0124505	+	0.0383188i
$160$	1.00000			0.0790569
$161$	4.18332			0.329692
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	4.61898	+	14.2158i	0.361786	+	1.11346i	0.951969	+	0.306194i	$0.0990557\pi$
$163$	4.61898	+	14.2158i	0.361786	+	1.11346i	−0.590183	+	0.807270i	$0.700944\pi$
$164$	−3.38611	−	10.4214i	−0.264411	−	0.813773i
$165$	−3.11483	+	2.26306i	−0.242489	+	0.176179i
$166$	−0.693033	+	2.13294i	−0.0537898	+	0.165548i
$167$	−1.98402	+	1.44148i	−0.153528	+	0.111545i	−0.661897	−	0.749594i	$-0.730249\pi$
$167$	−1.98402	+	1.44148i	−0.153528	+	0.111545i	0.508369	+	0.861139i	$0.330249\pi$
$168$	−1.35666	−	0.985674i	−0.104669	−	0.0760464i
$169$	−1.83147	−	5.63668i	−0.140882	−	0.433591i
$170$	−2.45650	−	1.78475i	−0.188405	−	0.136884i
$171$	−3.05850	−	2.22213i	−0.233889	−	0.169931i
$172$	3.68388	+	11.3378i	0.280893	+	0.864501i
$173$	−0.00972012	−	0.00706208i	−0.000739007	−	0.000536920i	0.587416	−	0.809285i	$-0.300145\pi$
$173$	−0.00972012	−	0.00706208i	−0.000739007	−	0.000536920i	−0.588155	+	0.808748i	$0.700145\pi$
$174$	5.53991	−	4.02498i	0.419979	−	0.305133i
$175$	−0.518200	+	1.59485i	−0.0391722	+	0.120560i
$176$	3.11483	−	2.26306i	0.234789	−	0.170584i
$177$	4.36005	+	13.4189i	0.327722	+	1.00862i
$178$	−2.33749	−	7.19404i	−0.175202	−	0.539216i
$179$	4.36069	−	13.4208i	0.325933	−	1.00312i	−0.645084	−	0.764112i	$-0.723178\pi$
$179$	4.36069	−	13.4208i	0.325933	−	1.00312i	0.971017	−	0.239008i	$-0.0768224\pi$
$180$	1.00000			0.0745356
$181$	14.9596			1.11194			0.555968	−	0.831204i	$-0.312348\pi$
$181$	14.9596			1.11194			0.555968	+	0.831204i	$0.312348\pi$
$182$	−1.37818	+	4.24161i	−0.102158	+	0.314409i
$183$	−3.92705	−	2.85317i	−0.290296	−	0.210912i
$184$	2.01820	−	1.46631i	0.148784	−	0.108098i
$185$	−5.39855			−0.396909
$186$	−5.52783	−	0.665657i	−0.405320	−	0.0488083i
$187$	−11.6906			−0.854900
$188$	6.53518	−	4.74808i	0.476627	−	0.346290i
$189$	−1.35666	−	0.985674i	−0.0986828	−	0.0716972i
$190$	1.16824	−	3.59548i	0.0847533	−	0.260844i
$191$	4.48476			0.324506			0.162253	−	0.986749i	$-0.448124\pi$
$191$	4.48476			0.324506			0.162253	+	0.986749i	$0.448124\pi$
$192$	−1.00000			−0.0721688
$193$	5.55057	−	17.0829i	0.399539	−	1.22965i	−0.525831	−	0.850589i	$-0.676246\pi$
$193$	5.55057	−	17.0829i	0.399539	−	1.22965i	0.925370	−	0.379065i	$-0.123754\pi$
$194$	−4.26883	−	13.1381i	−0.306484	−	0.943262i
$195$	−0.821848	−	2.52939i	−0.0588538	−	0.181133i
$196$	3.38809	−	2.46159i	0.242006	−	0.175828i
$197$	1.20550	−	3.71016i	0.0858886	−	0.264338i	−0.898884	−	0.438187i	$-0.855621\pi$
$197$	1.20550	−	3.71016i	0.0858886	−	0.264338i	0.984772	+	0.173849i	$0.0556206\pi$
$198$	3.11483	−	2.26306i	0.221362	−	0.160829i
$199$	19.9327	+	14.4819i	1.41299	+	1.02660i	0.992879	+	0.119126i	$0.0380091\pi$
$199$	19.9327	+	14.4819i	1.41299	+	1.02660i	0.420112	+	0.907472i	$0.361991\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	−11.2542	−	8.17664i	−0.793808	−	0.576736i
$202$	8.29003	+	6.02306i	0.583284	+	0.423781i
$203$	−3.54847	−	10.9211i	−0.249054	−	0.766510i
$204$	2.45650	+	1.78475i	0.171989	+	0.124958i
$205$	8.86495	−	6.44077i	0.619155	−	0.449843i
$206$	−3.48263	+	10.7184i	−0.242646	+	0.746788i
$207$	2.01820	−	1.46631i	0.140275	−	0.101915i
$208$	0.821848	+	2.52939i	0.0569849	+	0.175382i
$209$	−4.49791	−	13.8431i	−0.311127	−	0.957549i
$210$	0.518200	−	1.59485i	0.0357592	−	0.110055i
$211$	19.8006			1.36313			0.681566	−	0.731757i	$-0.261299\pi$
$211$	19.8006			1.36313			0.681566	+	0.731757i	$0.261299\pi$
$212$	0.508047			0.0348928
$213$	−2.38082	+	7.32740i	−0.163131	+	0.502065i
$214$	−2.12276	−	1.54228i	−0.145109	−	0.105428i
$215$	−9.64452	+	7.00716i	−0.657751	+	0.477884i
$216$	−1.00000			−0.0680414
$217$	−3.92614	+	8.47114i	−0.266524	+	0.575058i
$218$	10.8651			0.735875
$219$	13.1423	−	9.54842i	0.888072	−	0.645222i
$220$	3.11483	+	2.26306i	0.210002	+	0.152575i
$221$	2.49546	−	7.68023i	0.167863	−	0.516628i
$222$	5.39855			0.362327
$223$	18.5384			1.24142			0.620712	−	0.784038i	$-0.286844\pi$
$223$	18.5384			1.24142			0.620712	+	0.784038i	$0.286844\pi$
$224$	−0.518200	+	1.59485i	−0.0346237	+	0.106561i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−2.48997	−	7.66335i	−0.165631	−	0.509759i
$227$	0.436960	−	0.317470i	0.0290020	−	0.0210712i	−0.573190	−	0.819423i	$-0.694294\pi$
$227$	0.436960	−	0.317470i	0.0290020	−	0.0210712i	0.602192	+	0.798351i	$0.294294\pi$
$228$	−1.16824	+	3.59548i	−0.0773688	+	0.238117i
$229$	−6.22719	+	4.52432i	−0.411505	+	0.298976i	−0.774211	−	0.632928i	$-0.781853\pi$
$229$	−6.22719	+	4.52432i	−0.411505	+	0.298976i	0.362706	+	0.931904i	$0.381853\pi$
$230$	2.01820	+	1.46631i	0.133076	+	0.0966855i
$231$	−1.99514	−	6.14042i	−0.131271	−	0.404010i
$232$	−5.53991	−	4.02498i	−0.363713	−	0.264253i
$233$	−3.48101	−	2.52910i	−0.228049	−	0.165687i	0.467894	−	0.883785i	$-0.345013\pi$
$233$	−3.48101	−	2.52910i	−0.228049	−	0.165687i	−0.695942	+	0.718098i	$0.745013\pi$
$234$	0.821848	+	2.52939i	0.0537259	+	0.165351i
$235$	6.53518	+	4.74808i	0.426308	+	0.309731i
$236$	11.4148	−	8.29332i	0.743038	−	0.539849i
$237$	0.834903	−	2.56957i	0.0542328	−	0.166911i
$238$	4.11937	−	2.99290i	0.267019	−	0.194001i
$239$	−5.96688	−	18.3642i	−0.385966	−	1.18788i	−0.935777	−	0.352592i	$-0.885301\pi$
$239$	−5.96688	−	18.3642i	−0.385966	−	1.18788i	0.549812	−	0.835289i	$-0.314699\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	4.26049	−	13.1124i	0.274442	−	0.844646i	−0.714924	−	0.699202i	$-0.753539\pi$
$241$	4.26049	−	13.1124i	0.274442	−	0.844646i	0.989366	−	0.145444i	$-0.0464611\pi$
$242$	3.82362			0.245791
$243$	−1.00000			−0.0641500
$244$	−1.50000	+	4.61653i	−0.0960277	+	0.295543i
$245$	3.38809	+	2.46159i	0.216457	+	0.157265i
$246$	−8.86495	+	6.44077i	−0.565209	+	0.410648i
$247$	10.0545			0.639752
$248$	1.07512	+	5.46298i	0.0682699	+	0.346899i
$249$	2.24270			0.142126
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	2.08725	+	1.51647i	0.131746	+	0.0957190i	0.651707	−	0.758471i	$-0.274053\pi$
$251$	2.08725	+	1.51647i	0.131746	+	0.0957190i	−0.519961	+	0.854190i	$0.674053\pi$
$252$	−0.518200	+	1.59485i	−0.0326435	+	0.100466i
$253$	9.60469			0.603842
$254$	20.0715			1.25939
$255$	−0.938299	+	2.88779i	−0.0587586	+	0.180840i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.22655	−	3.77495i	−0.0765104	−	0.235475i	0.905485	−	0.424377i	$-0.139507\pi$
$257$	−1.22655	−	3.77495i	−0.0765104	−	0.235475i	−0.981996	+	0.188903i	$0.939507\pi$
$258$	9.64452	−	7.00716i	0.600442	−	0.436247i
$259$	2.79752	−	8.60990i	0.173830	−	0.534993i
$260$	−2.15163	+	1.56325i	−0.133438	+	0.0969486i
$261$	−5.53991	−	4.02498i	−0.342912	−	0.249140i
$262$	1.29057	+	3.97198i	0.0797319	+	0.245390i
$263$	24.5731	+	17.8534i	1.51524	+	1.10089i	0.963784	+	0.266682i	$0.0859275\pi$
$263$	24.5731	+	17.8534i	1.51524	+	1.10089i	0.551456	+	0.834204i	$0.314072\pi$
$264$	−3.11483	−	2.26306i	−0.191705	−	0.139282i
$265$	0.156995	+	0.483181i	0.00964413	+	0.0296816i
$266$	5.12889	+	3.72635i	0.314472	+	0.228477i
$267$	−6.11962	+	4.44616i	−0.374515	+	0.272101i
$268$	−4.29871	+	13.2301i	−0.262586	+	0.808156i
$269$	6.74787	−	4.90261i	0.411425	−	0.298917i	−0.362754	−	0.931885i	$-0.618163\pi$
$269$	6.74787	−	4.90261i	0.411425	−	0.298917i	0.774178	+	0.632968i	$0.218163\pi$
$270$	−0.309017	−	0.951057i	−0.0188062	−	0.0578795i
$271$	−0.491953	−	1.51408i	−0.0298840	−	0.0919736i	0.935002	−	0.354642i	$-0.115397\pi$
$271$	−0.491953	−	1.51408i	−0.0298840	−	0.0919736i	−0.964886	+	0.262669i	$0.915397\pi$
$272$	0.938299	−	2.88779i	0.0568927	−	0.175098i
$273$	4.45989			0.269925
$274$	−11.2930			−0.682235
$275$	−1.18976	+	3.66171i	−0.0717452	+	0.220809i
$276$	−2.01820	−	1.46631i	−0.121481	−	0.0882614i
$277$	2.59899	−	1.88828i	0.156158	−	0.113456i	−0.506962	−	0.861968i	$-0.669232\pi$
$277$	2.59899	−	1.88828i	0.156158	−	0.113456i	0.663120	+	0.748513i	$0.269232\pi$
$278$	−18.2357			−1.09370
$279$	1.07512	+	5.46298i	0.0643655	+	0.327060i
$280$	−1.67693			−0.100216
$281$	−6.07670	+	4.41498i	−0.362505	+	0.263376i	−0.754096	−	0.656764i	$-0.771925\pi$
$281$	−6.07670	+	4.41498i	−0.362505	+	0.263376i	0.391591	+	0.920139i	$0.371925\pi$
$282$	−6.53518	−	4.74808i	−0.389164	−	0.282744i
$283$	1.94344	−	5.98131i	0.115526	−	0.355552i	−0.876531	−	0.481346i	$-0.840148\pi$
$283$	1.94344	−	5.98131i	0.115526	−	0.355552i	0.992056	+	0.125794i	$0.0401480\pi$
$284$	7.70448			0.457177
$285$	−3.78051			−0.223938
$286$	−3.16424	+	9.73851i	−0.187105	+	0.575850i
$287$	5.67827	+	17.4759i	0.335178	+	1.03157i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	6.29438	−	4.57313i	0.370258	−	0.269008i
$290$	2.11606	−	6.51255i	0.124259	−	0.382430i
$291$	−11.1760	+	8.11980i	−0.655146	+	0.475991i
$292$	−13.1423	−	9.54842i	−0.769093	−	0.558779i
$293$	−8.12230	−	24.9979i	−0.474510	−	1.46039i	−0.846618	−	0.532201i	$-0.821365\pi$
$293$	−8.12230	−	24.9979i	−0.474510	−	1.46039i	0.372108	−	0.928189i	$-0.378635\pi$
$294$	−3.38809	−	2.46159i	−0.197597	−	0.143563i
$295$	11.4148	+	8.29332i	0.664594	+	0.482855i
$296$	−1.66824	−	5.13432i	−0.0969647	−	0.298427i
$297$	−3.11483	−	2.26306i	−0.180741	−	0.131316i
$298$	−14.6978	+	10.6786i	−0.851423	+	0.618595i
$299$	−2.05021	+	6.30989i	−0.118567	+	0.364911i
$300$	0.809017	−	0.587785i	0.0467086	−	0.0339358i
$301$	−6.17761	−	19.0127i	−0.356071	−	1.09587i
$302$	1.95440	+	6.01504i	0.112463	+	0.346126i
$303$	3.16651	−	9.74551i	0.181911	−	0.559865i
$304$	3.78051			0.216827
$305$	−4.85410			−0.277945
$306$	0.938299	−	2.88779i	0.0536390	−	0.165084i
$307$	9.55441	+	6.94169i	0.545299	+	0.396183i	0.826049	−	0.563598i	$-0.190583\pi$
$307$	9.55441	+	6.94169i	0.545299	+	0.396183i	−0.280750	+	0.959781i	$0.590583\pi$
$308$	−5.22335	+	3.79499i	−0.297628	+	0.216240i
$309$	11.2700			0.641129
$310$	−4.86337	+	2.71065i	−0.276221	+	0.153955i
$311$	−5.82094			−0.330075			−0.165038	−	0.986287i	$-0.552775\pi$
$311$	−5.82094			−0.330075			−0.165038	+	0.986287i	$0.552775\pi$
$312$	2.15163	−	1.56325i	0.121812	−	0.0885015i
$313$	8.82969	+	6.41514i	0.499084	+	0.362605i	0.808667	−	0.588267i	$-0.200190\pi$
$313$	8.82969	+	6.41514i	0.499084	+	0.362605i	−0.309583	+	0.950872i	$0.600190\pi$
$314$	1.63184	−	5.02230i	0.0920903	−	0.283425i
$315$	−1.67693			−0.0944842
$316$	−2.70180			−0.151988
$317$	0.410981	−	1.26487i	0.0230830	−	0.0710421i	−0.938851	−	0.344322i	$-0.888109\pi$
$317$	0.410981	−	1.26487i	0.0230830	−	0.0710421i	0.961934	+	0.273280i	$0.0881087\pi$
$318$	−0.156995	−	0.483181i	−0.00880385	−	0.0270955i
$319$	−8.14712	−	25.0743i	−0.456151	−	1.40389i
$320$	−0.809017	+	0.587785i	−0.0452254	+	0.0328582i
$321$	−0.810823	+	2.49546i	−0.0452557	+	0.139283i
$322$	−3.38438	+	2.45889i	−0.188604	+	0.137029i
$323$	−9.28683	−	6.74727i	−0.516733	−	0.375428i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−2.15163	−	1.56325i	−0.119351	−	0.0867134i
$326$	−12.0926	−	8.78582i	−0.669749	−	0.486601i
$327$	−3.35749	−	10.3333i	−0.185670	−	0.571433i
$328$	8.86495	+	6.44077i	0.489485	+	0.355632i
$329$	−10.9590	+	7.96220i	−0.604191	+	0.438970i
$330$	1.18976	−	3.66171i	0.0654941	−	0.201570i
$331$	22.3438	−	16.2337i	1.22813	−	0.892286i	0.231378	−	0.972864i	$-0.425677\pi$
$331$	22.3438	−	16.2337i	1.22813	−	0.892286i	0.996748	+	0.0805780i	$0.0256766\pi$
$332$	−0.693033	−	2.13294i	−0.0380352	−	0.117060i
$333$	−1.66824	−	5.13432i	−0.0914192	−	0.281359i
$334$	0.757829	−	2.33236i	0.0414666	−	0.127621i
$335$	−13.9109			−0.760035
$336$	1.67693			0.0914840
$337$	3.09944	−	9.53909i	0.168837	−	0.519628i	−0.830461	−	0.557076i	$-0.811923\pi$
$337$	3.09944	−	9.53909i	0.168837	−	0.519628i	0.999299	+	0.0374487i	$0.0119231\pi$
$338$	4.79485	+	3.48366i	0.260805	+	0.189486i
$339$	−6.51884	+	4.73621i	−0.354055	+	0.257236i
$340$	3.03640			0.164672
$341$	−9.01423	+	19.4493i	−0.488148	+	1.05324i
$342$	3.78051			0.204427
$343$	−15.1782	+	11.0276i	−0.819548	+	0.595436i
$344$	−9.64452	−	7.00716i	−0.519998	−	0.377801i
$345$	0.770884	−	2.37254i	0.0415030	−	0.127733i
$346$	0.0120147			0.000645916
$347$	−35.1983			−1.88954			−0.944772	−	0.327727i	$-0.893717\pi$
$347$	−35.1983			−1.88954			−0.944772	+	0.327727i	$0.893717\pi$
$348$	−2.11606	+	6.51255i	−0.113432	+	0.349109i
$349$	2.39739	+	7.37842i	0.128330	+	0.394958i	0.994493	−	0.104803i	$-0.0334212\pi$
$349$	2.39739	+	7.37842i	0.128330	+	0.394958i	−0.866163	+	0.499761i	$0.833421\pi$
$350$	−0.518200	−	1.59485i	−0.0276989	−	0.0852485i
$351$	2.15163	−	1.56325i	0.114845	−	0.0834400i
$352$	−1.18976	+	3.66171i	−0.0634144	+	0.195170i
$353$	−1.86663	+	1.35618i	−0.0993506	+	0.0721824i	−0.636351	−	0.771399i	$-0.719557\pi$
$353$	−1.86663	+	1.35618i	−0.0993506	+	0.0721824i	0.537001	+	0.843582i	$0.319557\pi$
$354$	−11.4148	−	8.29332i	−0.606688	−	0.440785i
$355$	2.38082	+	7.32740i	0.126361	+	0.388898i
$356$	6.11962	+	4.44616i	0.324339	+	0.235646i
$357$	−4.11937	−	2.99290i	−0.218020	−	0.158401i
$358$	4.36069	+	13.4208i	0.230470	+	0.709313i
$359$	18.0116	+	13.0862i	0.950618	+	0.690665i	0.950953	−	0.309335i	$-0.100107\pi$
$359$	18.0116	+	13.0862i	0.950618	+	0.690665i	−0.000334704		1.00000i	$0.500107\pi$
$360$	−0.809017	+	0.587785i	−0.0426389	+	0.0309790i
$361$	−1.45476	+	4.47730i	−0.0765665	+	0.235648i
$362$	−12.1026	+	8.79302i	−0.636096	+	0.462151i
$363$	−1.18156	−	3.63648i	−0.0620160	−	0.190865i
$364$	−1.37818	−	4.24161i	−0.0722363	−	0.222321i
$365$	5.01990	−	15.4497i	0.262754	−	0.808672i
$366$	4.85410			0.253728
$367$	−23.3763			−1.22023			−0.610116	−	0.792312i	$-0.708877\pi$
$367$	−23.3763			−1.22023			−0.610116	+	0.792312i	$0.708877\pi$
$368$	−0.770884	+	2.37254i	−0.0401851	+	0.123677i
$369$	8.86495	+	6.44077i	0.461491	+	0.335293i
$370$	4.36752	−	3.17319i	0.227056	−	0.164966i
$371$	−0.851958			−0.0442315
$372$	4.86337	−	2.71065i	0.252154	−	0.140541i
$373$	19.6859			1.01930			0.509650	−	0.860382i	$-0.329775\pi$
$373$	19.6859			1.01930			0.509650	+	0.860382i	$0.329775\pi$
$374$	9.45788	−	6.87155i	0.489055	−	0.355319i
$375$	0.809017	+	0.587785i	0.0417775	+	0.0303531i
$376$	−2.49622	+	7.68256i	−0.128732	+	0.396198i
$377$	18.2118			0.937958
$378$	1.67693			0.0862519
$379$	−2.65648	+	8.17582i	−0.136454	+	0.419963i	−0.995813	−	0.0914093i	$-0.970863\pi$
$379$	−2.65648	+	8.17582i	−0.136454	+	0.419963i	0.859359	+	0.511373i	$0.170863\pi$
$380$	1.16824	+	3.59548i	0.0599296	+	0.184444i
$381$	−6.20242	−	19.0891i	−0.317760	−	0.977963i
$382$	−3.62825	+	2.63608i	−0.185637	+	0.134873i
$383$	4.54596	−	13.9910i	0.232288	−	0.714908i	−0.765182	−	0.643814i	$-0.777351\pi$
$383$	4.54596	−	13.9910i	0.232288	−	0.714908i	0.997470	−	0.0710937i	$-0.0226489\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	−5.22335	−	3.79499i	−0.266207	−	0.193411i
$386$	5.55057	+	17.0829i	0.282517	+	0.869497i
$387$	−9.64452	−	7.00716i	−0.490259	−	0.356194i
$388$	11.1760	+	8.11980i	0.567373	+	0.412221i
$389$	11.5687	+	35.6049i	0.586558	+	1.80524i	0.592923	+	0.805259i	$0.297974\pi$
$389$	11.5687	+	35.6049i	0.586558	+	1.80524i	−0.00636558	+	0.999980i	$0.502026\pi$
$390$	2.15163	+	1.56325i	0.108952	+	0.0791582i
$391$	6.12806	−	4.45230i	0.309909	−	0.225162i
$392$	−1.29414	+	3.98294i	−0.0653637	+	0.201169i
$393$	3.37876	−	2.45482i	0.170436	−	0.123829i
$394$	1.20550	+	3.71016i	0.0607324	+	0.186915i
$395$	−0.834903	−	2.56957i	−0.0420085	−	0.129289i
$396$	−1.18976	+	3.66171i	−0.0597877	+	0.184008i
$397$	−15.1170			−0.758700			−0.379350	−	0.925253i	$-0.623852\pi$
$397$	−15.1170			−0.758700			−0.379350	+	0.925253i	$0.623852\pi$
$398$	−24.6382			−1.23500
$399$	1.95906	−	6.02937i	0.0980757	−	0.301846i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−28.4912	+	20.7001i	−1.42278	+	1.03371i	−0.431481	+	0.902122i	$0.642009\pi$
$401$	−28.4912	+	20.7001i	−1.42278	+	1.03371i	−0.991304	+	0.131592i	$0.957991\pi$
$402$	13.9109			0.693814
$403$	−10.8532	−	10.0736i	−0.540638	−	0.501803i
$404$	−10.2470			−0.509809
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	9.29003	+	6.74960i	0.461056	+	0.334977i
$407$	6.42298	−	19.7679i	0.318375	−	0.979858i
$408$	−3.03640			−0.150324
$409$	−24.0640			−1.18989			−0.594943	−	0.803768i	$-0.702825\pi$
$409$	−24.0640			−1.18989			−0.594943	+	0.803768i	$0.702825\pi$
$410$	−3.38611	+	10.4214i	−0.167228	+	0.514675i
$411$	3.48973	+	10.7403i	0.172136	+	0.529779i
$412$	−3.48263	−	10.7184i	−0.171577	−	0.528059i
$413$	−19.1418	+	13.9073i	−0.941904	+	0.684333i
$414$	−0.770884	+	2.37254i	−0.0378869	+	0.116604i
$415$	1.81439	−	1.31823i	0.0890647	−	0.0647093i
$416$	−2.15163	−	1.56325i	−0.105492	−	0.0766446i
$417$	5.63513	+	17.3431i	0.275953	+	0.849297i
$418$	11.7757	+	8.55552i	0.575967	+	0.418464i
$419$	4.70854	+	3.42096i	0.230027	+	0.167125i	0.696829	−	0.717237i	$-0.254594\pi$
$419$	4.70854	+	3.42096i	0.230027	+	0.167125i	−0.466801	+	0.884362i	$0.654594\pi$
$420$	0.518200	+	1.59485i	0.0252855	+	0.0778209i
$421$	−25.3582	−	18.4238i	−1.23588	−	0.897922i	−0.238567	−	0.971126i	$-0.576678\pi$
$421$	−25.3582	−	18.4238i	−1.23588	−	0.897922i	−0.997317	+	0.0732041i	$0.976678\pi$
$422$	−16.0191	+	11.6385i	−0.779795	+	0.566554i
$423$	−2.49622	+	7.68256i	−0.121370	+	0.373539i
$424$	−0.411018	+	0.298622i	−0.0199608	+	0.0145024i
$425$	0.938299	+	2.88779i	0.0455142	+	0.140078i
$426$	−2.38082	−	7.32740i	−0.115351	−	0.355013i
$427$	2.51539	−	7.74158i	0.121728	−	0.374642i
$428$	2.62388			0.126830
$429$	10.2397			0.494376
$430$	3.68388	−	11.3378i	0.177652	−	0.546758i
$431$	18.7422	+	13.6170i	0.902778	+	0.655907i	0.939178	−	0.343431i	$-0.111589\pi$
$431$	18.7422	+	13.6170i	0.902778	+	0.655907i	−0.0364001	+	0.999337i	$0.511589\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	1.83752			0.0883056			0.0441528	−	0.999025i	$-0.485941\pi$
$433$	1.83752			0.0883056			0.0441528	+	0.999025i	$0.485941\pi$
$434$	−1.80289	−	9.16103i	−0.0865416	−	0.439743i
$435$	−6.84770			−0.328322
$436$	−8.79003	+	6.38633i	−0.420966	+	0.305850i
$437$	7.62983	+	5.54340i	0.364984	+	0.265177i
$438$	−5.01990	+	15.4497i	−0.239860	+	0.738213i
$439$	1.91593			0.0914424			0.0457212	−	0.998954i	$-0.485441\pi$
$439$	1.91593			0.0914424			0.0457212	+	0.998954i	$0.485441\pi$
$440$	−3.85015			−0.183548
$441$	−1.29414	+	3.98294i	−0.0616255	+	0.189664i
$442$	2.49546	+	7.68023i	0.118697	+	0.365312i
$443$	−0.106391	−	0.327438i	−0.00505479	−	0.0155570i	0.948497	−	0.316785i	$-0.102603\pi$
$443$	−0.106391	−	0.327438i	−0.00505479	−	0.0155570i	−0.953552	+	0.301228i	$0.902603\pi$
$444$	−4.36752	+	3.17319i	−0.207273	+	0.150593i
$445$	−2.33749	+	7.19404i	−0.110807	+	0.341030i
$446$	−14.9979	+	10.8966i	−0.710171	+	0.515969i
$447$	14.6978	+	10.6786i	0.695184	+	0.505081i
$448$	−0.518200	−	1.59485i	−0.0244826	−	0.0753498i
$449$	−22.5681	−	16.3967i	−1.06505	−	0.773807i	−0.0900368	−	0.995938i	$-0.528698\pi$
$449$	−22.5681	−	16.3967i	−1.06505	−	0.773807i	−0.975017	+	0.222132i	$0.928698\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	13.0370	+	40.1238i	0.613889	+	1.88936i
$452$	6.51884	+	4.73621i	0.306620	+	0.222773i
$453$	5.11669	−	3.71750i	0.240403	−	0.174663i
$454$	−0.166904	+	0.513677i	−0.00783318	+	0.0241080i
$455$	3.60813	−	2.62146i	0.169152	−	0.122896i
$456$	−1.16824	−	3.59548i	−0.0547080	−	0.168374i
$457$	−9.40918	−	28.9585i	−0.440143	−	1.35462i	−0.887724	−	0.460377i	$-0.847714\pi$
$457$	−9.40918	−	28.9585i	−0.440143	−	1.35462i	0.447581	−	0.894243i	$-0.352286\pi$
$458$	2.37858	−	7.32051i	0.111144	−	0.342065i
$459$	−3.03640			−0.141727
$460$	−2.49463			−0.116313
$461$	−2.13875	+	6.58240i	−0.0996116	+	0.306573i	−0.988428	−	0.151690i	$-0.951528\pi$
$461$	−2.13875	+	6.58240i	−0.0996116	+	0.306573i	0.888816	+	0.458263i	$0.151528\pi$
$462$	5.22335	+	3.79499i	0.243012	+	0.176559i
$463$	−3.39270	+	2.46494i	−0.157672	+	0.114556i	−0.663824	−	0.747889i	$-0.731068\pi$
$463$	−3.39270	+	2.46494i	−0.157672	+	0.114556i	0.506152	+	0.862444i	$0.331068\pi$
$464$	6.84770			0.317896
$465$	4.08084	+	3.78770i	0.189245	+	0.175651i
$466$	4.30277			0.199322
$467$	16.8293	−	12.2272i	0.778769	−	0.565809i	−0.125840	−	0.992051i	$-0.540163\pi$
$467$	16.8293	−	12.2272i	0.778769	−	0.565809i	0.904609	+	0.426241i	$0.140163\pi$
$468$	−2.15163	−	1.56325i	−0.0994590	−	0.0722612i
$469$	7.20864	−	22.1859i	0.332864	−	1.02445i
$470$	−8.07792			−0.372607
$471$	−5.28076			−0.243324
$472$	−4.36005	+	13.4189i	−0.200688	+	0.617653i
$473$	−14.1835	−	43.6522i	−0.652157	−	2.00713i
$474$	0.834903	+	2.56957i	0.0383483	+	0.118024i
$475$	−3.05850	+	2.22213i	−0.140334	+	0.101958i
$476$	−1.57346	+	4.84261i	−0.0721194	+	0.221961i
$477$	−0.411018	+	0.298622i	−0.0188192	+	0.0136730i
$478$	15.6215	+	11.3497i	0.714511	+	0.519123i
$479$	0.0796188	+	0.245042i	0.00363788	+	0.0111962i	0.952859	−	0.303414i	$-0.0981264\pi$
$479$	0.0796188	+	0.245042i	0.00363788	+	0.0111962i	−0.949221	+	0.314610i	$0.898126\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	11.6157	+	8.43927i	0.529629	+	0.384798i
$482$	4.26049	+	13.1124i	0.194060	+	0.597255i
$483$	3.38438	+	2.45889i	0.153994	+	0.111884i
$484$	−3.09337	+	2.24747i	−0.140608	+	0.102158i
$485$	−4.26883	+	13.1381i	−0.193838	+	0.596571i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−0.0931990	−	0.286837i	−0.00422325	−	0.0129978i	0.948923	−	0.315509i	$-0.102175\pi$
$487$	−0.0931990	−	0.286837i	−0.00422325	−	0.0129978i	−0.953146	+	0.302511i	$0.902175\pi$
$488$	−1.50000	−	4.61653i	−0.0679018	−	0.208980i
$489$	−4.61898	+	14.2158i	−0.208877	+	0.642859i
$490$	−4.18791			−0.189190
$491$	−19.6973			−0.888926			−0.444463	−	0.895797i	$-0.646606\pi$
$491$	−19.6973			−0.888926			−0.444463	+	0.895797i	$0.646606\pi$
$492$	3.38611	−	10.4214i	0.152658	−	0.469832i
$493$	−16.8214	−	12.2214i	−0.757596	−	0.550426i
$494$	−8.13426	+	5.90988i	−0.365977	+	0.265898i
$495$	−3.85015			−0.173051
$496$	−4.08084	−	3.78770i	−0.183235	−	0.170073i
$497$	−12.9199			−0.579535
$498$	−1.81439	+	1.31823i	−0.0813045	+	0.0590712i
$499$	9.65864	+	7.01741i	0.432380	+	0.314143i	0.782600	−	0.622525i	$-0.213893\pi$
$499$	9.65864	+	7.01741i	0.432380	+	0.314143i	−0.350220	+	0.936668i	$0.613893\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−2.45239			−0.109565
$502$	−2.57998			−0.115150
$503$	−3.70335	+	11.3977i	−0.165124	+	0.508200i	−0.999045	−	0.0436836i	$-0.986091\pi$
$503$	−3.70335	+	11.3977i	−0.165124	+	0.508200i	0.833921	+	0.551883i	$0.186091\pi$
$504$	−0.518200	−	1.59485i	−0.0230824	−	0.0710405i
$505$	−3.16651	−	9.74551i	−0.140908	−	0.433670i
$506$	−7.77036	+	5.64550i	−0.345435	+	0.250973i
$507$	1.83147	−	5.63668i	0.0813384	−	0.250334i
$508$	−16.2381	+	11.7977i	−0.720451	+	0.523438i
$509$	4.33251	+	3.14775i	0.192035	+	0.139522i	0.679648	−	0.733538i	$-0.262132\pi$
$509$	4.33251	+	3.14775i	0.192035	+	0.139522i	−0.487613	+	0.873060i	$0.662132\pi$
$510$	−0.938299	−	2.88779i	−0.0415486	−	0.127873i
$511$	22.0386	+	16.0120i	0.974932	+	0.708330i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.16824	−	3.59548i	−0.0515792	−	0.158744i
$514$	3.21116	+	2.33305i	0.141638	+	0.102906i
$515$	9.11764	−	6.62435i	0.401771	−	0.291904i
$516$	−3.68388	+	11.3378i	−0.162174	+	0.499120i
$517$	−25.1614	+	18.2808i	−1.10660	+	0.803989i
$518$	2.79752	+	8.60990i	0.122916	+	0.378297i
$519$	−0.00371276	−	0.0114267i	−0.000162972	−	0.000501576i
$520$	0.821848	−	2.52939i	0.0360404	−	0.110921i
$521$	−37.8297			−1.65735			−0.828674	−	0.559732i	$-0.810904\pi$
$521$	−37.8297			−1.65735			−0.828674	+	0.559732i	$0.810904\pi$
$522$	6.84770			0.299716
$523$	−5.85544	+	18.0212i	−0.256041	+	0.788012i	0.737582	+	0.675257i	$0.235967\pi$
$523$	−5.85544	+	18.0212i	−0.256041	+	0.788012i	−0.993623	+	0.112755i	$0.964033\pi$
$524$	−3.37876	−	2.45482i	−0.147602	−	0.107239i
$525$	−1.35666	+	0.985674i	−0.0592097	+	0.0430183i
$526$	−30.3740			−1.32437
$527$	3.26448	+	16.5878i	0.142203	+	0.722575i
$528$	3.85015			0.167556
$529$	13.5727	−	9.86116i	0.590119	−	0.428746i
$530$	−0.411018	−	0.298622i	−0.0178535	−	0.0129713i
$531$	−4.36005	+	13.4189i	−0.189210	+	0.582329i
$532$	−6.33965			−0.274859
$533$	−29.1426			−1.26231
$534$	2.33749	−	7.19404i	0.101153	−	0.311317i
$535$	0.810823	+	2.49546i	0.0350549	+	0.107888i
$536$	−4.29871	−	13.2301i	−0.185676	−	0.571452i
$537$	11.4164	−	8.29453i	0.492656	−	0.357935i
$538$	−2.57746	+	7.93259i	−0.111122	+	0.341998i
$539$	−13.0446	+	9.47748i	−0.561872	+	0.408224i
$540$	0.809017	+	0.587785i	0.0348145	+	0.0252942i
$541$	−12.8537	−	39.5595i	−0.552622	−	1.70079i	−0.702143	−	0.712036i	$-0.747773\pi$
$541$	−12.8537	−	39.5595i	−0.552622	−	1.70079i	0.149521	−	0.988759i	$-0.452227\pi$
$542$	1.28795	+	0.935751i	0.0553222	+	0.0401939i
$543$	12.1026	+	8.79302i	0.519370	+	0.377345i
$544$	0.938299	+	2.88779i	0.0402292	+	0.123813i
$545$	−8.79003	−	6.38633i	−0.376523	−	0.273560i
$546$	−3.60813	+	2.62146i	−0.154414	+	0.112188i
$547$	−9.05243	+	27.8605i	−0.387054	+	1.19123i	0.547925	+	0.836527i	$0.315418\pi$
$547$	−9.05243	+	27.8605i	−0.387054	+	1.19123i	−0.934979	+	0.354702i	$0.884582\pi$
$548$	9.13623	−	6.63786i	0.390281	−	0.283555i
$549$	−1.50000	−	4.61653i	−0.0640184	−	0.197028i
$550$	−1.18976	−	3.66171i	−0.0507315	−	0.156136i
$551$	7.99978	−	24.6208i	0.340802	−	1.04888i
$552$	2.49463			0.106179
$553$	4.53073			0.192666
$554$	−0.992725	+	3.05529i	−0.0421769	+	0.129807i
$555$	−4.36752	−	3.17319i	−0.185391	−	0.134694i
$556$	14.7530	−	10.7186i	0.625665	−	0.454572i
$557$	10.3856			0.440052			0.220026	−	0.975494i	$-0.429386\pi$
$557$	10.3856			0.440052			0.220026	+	0.975494i	$0.429386\pi$
$558$	−4.08084	−	3.78770i	−0.172756	−	0.160346i
$559$	31.7053			1.34099
$560$	1.35666	−	0.985674i	0.0573295	−	0.0416523i
$561$	−9.45788	−	6.87155i	−0.399312	−	0.290117i
$562$	2.32109	−	7.14359i	0.0979094	−	0.301334i
$563$	−20.7504			−0.874527			−0.437264	−	0.899333i	$-0.644052\pi$
$563$	−20.7504			−0.874527			−0.437264	+	0.899333i	$0.644052\pi$
$564$	8.07792			0.340142
$565$	−2.48997	+	7.66335i	−0.104754	+	0.322400i
$566$	1.94344	+	5.98131i	0.0816891	+	0.251413i
$567$	−0.518200	−	1.59485i	−0.0217623	−	0.0669776i
$568$	−6.23306	+	4.52858i	−0.261533	+	0.190015i
$569$	−11.0575	+	34.0315i	−0.463555	+	1.42668i	0.397236	+	0.917717i	$0.369969\pi$
$569$	−11.0575	+	34.0315i	−0.463555	+	1.42668i	−0.860791	+	0.508959i	$0.830031\pi$
$570$	3.05850	−	2.22213i	0.128106	−	0.0930748i
$571$	23.3830	+	16.9887i	0.978548	+	0.710957i	0.957384	−	0.288819i	$-0.0932626\pi$
$571$	23.3830	+	16.9887i	0.978548	+	0.710957i	0.0211646	+	0.999776i	$0.493263\pi$
$572$	−3.16424	−	9.73851i	−0.132303	−	0.407188i
$573$	3.62825	+	2.63608i	0.151572	+	0.110124i
$574$	−14.8659	−	10.8007i	−0.620491	−	0.450813i
$575$	−0.770884	−	2.37254i	−0.0321481	−	0.0989416i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	2.10462	−	1.52910i	0.0876164	−	0.0636571i	−0.543115	−	0.839659i	$-0.682755\pi$
$577$	2.10462	−	1.52910i	0.0876164	−	0.0636571i	0.630731	+	0.776001i	$0.282755\pi$
$578$	−2.40424	+	7.39949i	−0.100003	+	0.307778i
$579$	14.5316	−	10.5578i	0.603912	−	0.438768i
$580$	2.11606	+	6.51255i	0.0878644	+	0.270419i
$581$	1.16217	+	3.57678i	0.0482148	+	0.148390i
$582$	4.26883	−	13.1381i	0.176949	−	0.544592i
$583$	−1.95605			−0.0810115
$584$	16.2447			0.672212
$585$	0.821848	−	2.52939i	0.0339792	−	0.104577i
$586$	21.2644	+	15.4495i	0.878426	+	0.638214i
$587$	25.5508	−	18.5638i	1.05460	−	0.766208i	0.0815144	−	0.996672i	$-0.474024\pi$
$587$	25.5508	−	18.5638i	1.05460	−	0.766208i	0.973081	+	0.230464i	$0.0740243\pi$
$588$	4.18791			0.172706
$589$	−18.3860	+	10.2476i	−0.757584	+	0.422247i
$590$	−14.1094			−0.580876
$591$	3.15605	−	2.29301i	0.129823	−	0.0943216i
$592$	4.36752	+	3.17319i	0.179504	+	0.130417i
$593$	−8.66800	+	26.6774i	−0.355952	+	1.09551i	0.599503	+	0.800372i	$0.295365\pi$
$593$	−8.66800	+	26.6774i	−0.355952	+	1.09551i	−0.955455	+	0.295136i	$0.904635\pi$
$594$	3.85015			0.157973
$595$	−5.09183			−0.208744
$596$	5.61408	−	17.2784i	0.229962	−	0.707749i
$597$	7.61361	+	23.4323i	0.311604	+	0.959019i
$598$	−2.05021	−	6.30989i	−0.0838393	−	0.258031i
$599$	−13.7497	+	9.98976i	−0.561799	+	0.408171i	−0.832117	−	0.554600i	$-0.812871\pi$
$599$	−13.7497	+	9.98976i	−0.561799	+	0.408171i	0.270318	+	0.962771i	$0.412871\pi$
$600$	−0.309017	+	0.951057i	−0.0126156	+	0.0388267i
$601$	−17.3201	+	12.5838i	−0.706500	+	0.513302i	−0.882043	−	0.471170i	$-0.843832\pi$
$601$	−17.3201	+	12.5838i	−0.706500	+	0.513302i	0.175543	+	0.984472i	$0.443832\pi$
$602$	16.1732	+	11.7505i	0.659170	+	0.478915i
$603$	−4.29871	−	13.2301i	−0.175057	−	0.538770i
$604$	−5.11669	−	3.71750i	−0.208195	−	0.151263i
$605$	−3.09337	−	2.24747i	−0.125763	−	0.0913725i
$606$	3.16651	+	9.74551i	0.128631	+	0.395884i
$607$	37.5690	+	27.2955i	1.52488	+	1.10789i	0.959002	+	0.283398i	$0.0914617\pi$
$607$	37.5690	+	27.2955i	1.52488	+	1.10789i	0.565875	+	0.824491i	$0.308538\pi$
$608$	−3.05850	+	2.22213i	−0.124039	+	0.0901193i
$609$	3.54847	−	10.9211i	0.143791	−	0.442545i
$610$	3.92705	−	2.85317i	0.159002	−	0.115521i
$611$	−6.63883	−	20.4322i	−0.268578	−	0.826599i
$612$	0.938299	+	2.88779i	0.0379285	+	0.116732i
$613$	2.30955	−	7.10806i	0.0932818	−	0.287092i	−0.893520	−	0.449023i	$-0.851772\pi$
$613$	2.30955	−	7.10806i	0.0932818	−	0.287092i	0.986802	+	0.161931i	$0.0517722\pi$
$614$	−11.8099			−0.476609
$615$	10.9577			0.441857
$616$	1.99514	−	6.14042i	0.0803866	−	0.247405i
$617$	18.3053	+	13.2996i	0.736942	+	0.535420i	0.891752	−	0.452524i	$-0.149476\pi$
$617$	18.3053	+	13.2996i	0.736942	+	0.535420i	−0.154810	+	0.987944i	$0.549476\pi$
$618$	−9.11764	+	6.62435i	−0.366765	+	0.266471i
$619$	−33.2346			−1.33581			−0.667906	−	0.744246i	$-0.732809\pi$
$619$	−33.2346			−1.33581			−0.667906	+	0.744246i	$0.732809\pi$
$620$	2.34127	−	5.05158i	0.0940277	−	0.202876i
$621$	2.49463			0.100106
$622$	4.70924	−	3.42146i	0.188823	−	0.137188i
$623$	−10.2622	−	7.45590i	−0.411145	−	0.298714i
$624$	−0.821848	+	2.52939i	−0.0329003	+	0.101257i
$625$	1.00000			0.0400000
$626$	−10.9141			−0.436215
$627$	4.49791	−	13.8431i	0.179629	−	0.552841i
$628$	1.63184	+	5.02230i	0.0651177	+	0.200412i
$629$	−5.06545	−	15.5899i	−0.201973	−	0.621608i
$630$	1.35666	−	0.985674i	0.0540508	−	0.0392702i
$631$	1.31727	−	4.05414i	0.0524397	−	0.161393i	−0.921407	−	0.388599i	$-0.872959\pi$
$631$	1.31727	−	4.05414i	0.0524397	−	0.161393i	0.973847	+	0.227206i	$0.0729591\pi$
$632$	2.18580	−	1.58808i	0.0869466	−	0.0631704i
$633$	16.0191	+	11.6385i	0.636700	+	0.462590i
$634$	0.410981	+	1.26487i	0.0163221	+	0.0502344i
$635$	−16.2381	−	11.7977i	−0.644391	−	0.468178i
$636$	0.411018	+	0.298622i	0.0162979	+	0.0118411i
$637$	−3.44183	−	10.5929i	−0.136370	−	0.419704i
$638$	21.3294	+	15.4967i	0.844441	+	0.613522i
$639$	−6.23306	+	4.52858i	−0.246576	+	0.179148i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	−17.8198	+	12.9469i	−0.703841	+	0.511371i	−0.881181	−	0.472779i	$-0.843251\pi$
$641$	−17.8198	+	12.9469i	−0.703841	+	0.511371i	0.177340	+	0.984150i	$0.443251\pi$
$642$	−0.810823	−	2.49546i	−0.0320006	−	0.0984879i
$643$	−4.87472	−	15.0028i	−0.192240	−	0.591654i	−0.999998	−	0.00213956i	$-0.999319\pi$
$643$	−4.87472	−	15.0028i	−0.192240	−	0.591654i	0.807758	−	0.589515i	$-0.200681\pi$
$644$	1.29272	−	3.97857i	0.0509402	−	0.156778i
$645$	−11.9213			−0.469400
$646$	11.4791			0.451641
$647$	0.0213451	−	0.0656935i	0.000839163	−	0.00258268i	−0.950636	−	0.310308i	$-0.899568\pi$
$647$	0.0213451	−	0.0656935i	0.000839163	−	0.00258268i	0.951475	+	0.307725i	$0.0995678\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−43.9485	+	31.9305i	−1.72513	+	1.25338i
$650$	2.65956			0.104316
$651$	−8.15553	+	4.54557i	−0.319640	+	0.178155i
$652$	14.9473			0.585383
$653$	16.7612	−	12.1777i	0.655916	−	0.476551i	−0.209365	−	0.977838i	$-0.567140\pi$
$653$	16.7612	−	12.1777i	0.655916	−	0.476551i	0.865281	+	0.501287i	$0.167140\pi$
$654$	8.79003	+	6.38633i	0.343717	+	0.249725i
$655$	1.29057	−	3.97198i	0.0504269	−	0.155198i
$656$	−10.9577			−0.427826
$657$	16.2447			0.633768
$658$	4.18598	−	12.8831i	0.163186	−	0.502236i
$659$	−0.359759	−	1.10722i	−0.0140142	−	0.0431313i	0.943805	−	0.330503i	$-0.107218\pi$
$659$	−0.359759	−	1.10722i	−0.0140142	−	0.0431313i	−0.957819	+	0.287372i	$0.907218\pi$
$660$	1.18976	+	3.66171i	0.0463114	+	0.142532i
$661$	24.3789	−	17.7123i	0.948229	−	0.688928i	−0.00215856	−	0.999998i	$-0.500687\pi$
$661$	24.3789	−	17.7123i	0.948229	−	0.688928i	0.950387	+	0.311069i	$0.100687\pi$
$662$	−8.53457	+	26.2667i	−0.331706	+	1.02088i
$663$	6.53320	−	4.74665i	0.253728	−	0.184344i
$664$	1.81439	+	1.31823i	0.0704118	+	0.0511572i
$665$	−1.95906	−	6.02937i	−0.0759691	−	0.233809i
$666$	4.36752	+	3.17319i	0.169238	+	0.122958i
$667$	13.8200	+	10.0408i	0.535113	+	0.388783i
$668$	0.757829	+	2.33236i	0.0293213	+	0.0902417i
$669$	14.9979	+	10.8966i	0.579852	+	0.421287i
$670$	11.2542	−	8.17664i	0.434787	−	0.315891i
$671$	5.77522	−	17.7743i	0.222950	−	0.686169i
$672$	−1.35666	+	0.985674i	−0.0523344	+	0.0380232i
$673$	−7.90452	−	24.3276i	−0.304697	−	0.937761i	−0.979790	−	0.200028i	$-0.935897\pi$
$673$	−7.90452	−	24.3276i	−0.304697	−	0.937761i	0.675093	−	0.737732i	$-0.264103\pi$
$674$	3.09944	+	9.53909i	0.119386	+	0.367432i
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$	−5.92676			−0.227952
$677$	41.2455			1.58519			0.792597	−	0.609746i	$-0.208729\pi$
$677$	41.2455			1.58519			0.792597	+	0.609746i	$0.208729\pi$
$678$	2.48997	−	7.66335i	0.0956269	−	0.294309i
$679$	−18.7413	−	13.6163i	−0.719224	−	0.522547i
$680$	−2.45650	+	1.78475i	−0.0942024	+	0.0684421i
$681$	0.540112			0.0206971
$682$	−4.13935	−	21.0333i	−0.158504	−	0.805405i
$683$	−7.77607			−0.297543			−0.148771	−	0.988872i	$-0.547532\pi$
$683$	−7.77607			−0.297543			−0.148771	+	0.988872i	$0.547532\pi$
$684$	−3.05850	+	2.22213i	−0.116945	+	0.0849653i
$685$	9.13623	+	6.63786i	0.349078	+	0.253620i
$686$	5.79757	−	17.8431i	0.221352	−	0.681252i
$687$	−7.69723			−0.293668
$688$	11.9213			0.454495
$689$	0.417537	−	1.28505i	0.0159069	−	0.0489564i
$690$	0.770884	+	2.37254i	0.0293470	+	0.0903209i
$691$	−1.16438	−	3.58358i	−0.0442950	−	0.136326i	0.926463	−	0.376385i	$-0.122833\pi$
$691$	−1.16438	−	3.58358i	−0.0442950	−	0.136326i	−0.970758	+	0.240059i	$0.922833\pi$
$692$	−0.00972012	+	0.00706208i	−0.000369504	+	0.000268460i
$693$	1.99514	−	6.14042i	0.0757892	−	0.233255i
$694$	28.4760	−	20.6891i	1.08094	−	0.785346i
$695$	14.7530	+	10.7186i	0.559611	+	0.406582i
$696$	−2.11606	−	6.51255i	−0.0802089	−	0.246858i
$697$	26.9175	+	19.5567i	1.01957	+	0.740764i
$698$	−6.27646	−	4.56011i	−0.237567	−	0.172603i
$699$	−1.32963	−	4.09217i	−0.0502911	−	0.154780i
$700$	1.35666	+	0.985674i	0.0512771	+	0.0372550i
$701$	5.89836	−	4.28541i	0.222778	−	0.161858i	−0.470798	−	0.882241i	$-0.656034\pi$
$701$	5.89836	−	4.28541i	0.222778	−	0.161858i	0.693576	+	0.720383i	$0.256034\pi$
$702$	−0.821848	+	2.52939i	−0.0310187	+	0.0954656i
$703$	16.5115	−	11.9963i	0.622741	−	0.452448i
$704$	−1.18976	−	3.66171i	−0.0448408	−	0.138006i
$705$	2.49622	+	7.68256i	0.0940129	+	0.289342i
$706$	0.712989	−	2.19435i	0.0268337	−	0.0825856i
$707$	17.1836			0.646254
$708$	14.1094			0.530265
$709$	2.35152	−	7.23723i	0.0883131	−	0.271800i	−0.897140	−	0.441746i	$-0.854359\pi$
$709$	2.35152	−	7.23723i	0.0883131	−	0.271800i	0.985453	+	0.169946i	$0.0543593\pi$
$710$	−6.23306	−	4.52858i	−0.233922	−	0.169955i
$711$	2.18580	−	1.58808i	0.0819740	−	0.0595576i
$712$	−7.56426			−0.283483
$713$	−2.68202	−	13.6281i	−0.100442	−	0.510377i
$714$	5.09183			0.190557
$715$	8.28408	−	6.01873i	0.309807	−	0.225088i
$716$	−11.4164	−	8.29453i	−0.426652	−	0.309981i
$717$	5.96688	−	18.3642i	0.222837	−	0.685823i
$718$	−22.2636			−0.830871
$719$	9.19960			0.343087			0.171544	−	0.985177i	$-0.445125\pi$
$719$	9.19960			0.343087			0.171544	+	0.985177i	$0.445125\pi$
$720$	0.309017	−	0.951057i	0.0115164	−	0.0354438i
$721$	5.84012	+	17.9740i	0.217497	+	0.669388i
$722$	−1.45476	−	4.47730i	−0.0541407	−	0.166628i
$723$	11.1541	−	8.10393i	0.414825	−	0.301388i
$724$	4.62276	−	14.2274i	0.171804	−	0.528757i
$725$	−5.53991	+	4.02498i	−0.205747	+	0.149484i
$726$	3.09337	+	2.24747i	0.114806	+	0.0834113i
$727$	−14.9230	−	45.9284i	−0.553465	−	1.70339i	−0.699963	−	0.714179i	$-0.746800\pi$
$727$	−14.9230	−	45.9284i	−0.553465	−	1.70339i	0.146498	−	0.989211i	$-0.453200\pi$
$728$	3.60813	+	2.62146i	0.133726	+	0.0971576i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	5.01990	+	15.4497i	0.185795	+	0.571818i
$731$	−29.2846	−	21.2765i	−1.08313	−	0.786941i
$732$	−3.92705	+	2.85317i	−0.145148	+	0.105456i
$733$	3.37368	−	10.3831i	0.124610	−	0.383509i	−0.869220	−	0.494425i	$-0.835379\pi$
$733$	3.37368	−	10.3831i	0.124610	−	0.383509i	0.993830	+	0.110916i	$0.0353785\pi$
$734$	18.9118	−	13.7402i	0.698048	−	0.507161i
$735$	1.29414	+	3.98294i	0.0477349	+	0.146913i
$736$	−0.770884	−	2.37254i	−0.0284151	−	0.0874528i
$737$	16.5507	−	50.9377i	0.609652	−	1.87632i
$738$	−10.9577			−0.403358
$739$	13.3199			0.489979			0.244990	−	0.969526i	$-0.421215\pi$
$739$	13.3199			0.489979			0.244990	+	0.969526i	$0.421215\pi$
$740$	−1.66824	+	5.13432i	−0.0613258	+	0.188742i
$741$	8.13426	+	5.90988i	0.298819	+	0.217105i
$742$	0.689249	−	0.500768i	0.0253031	−	0.0183838i
$743$	4.08463			0.149851			0.0749253	−	0.997189i	$-0.476128\pi$
$743$	4.08463			0.149851			0.0749253	+	0.997189i	$0.476128\pi$
$744$	−2.34127	+	5.05158i	−0.0858351	+	0.185200i
$745$	18.1675			0.665607
$746$	−15.9263	+	11.5711i	−0.583102	+	0.423648i
$747$	1.81439	+	1.31823i	0.0663849	+	0.0482314i
$748$	−3.61259	+	11.1184i	−0.132089	+	0.406529i
$749$	−4.40006			−0.160775
$750$	−1.00000			−0.0365148
$751$	4.70543	−	14.4818i	0.171704	−	0.528450i	−0.827764	−	0.561077i	$-0.810387\pi$
$751$	4.70543	−	14.4818i	0.171704	−	0.528450i	0.999468	+	0.0326270i	$0.0103873\pi$
$752$	−2.49622	−	7.68256i	−0.0910276	−	0.280154i
$753$	0.797258	+	2.45371i	0.0290537	+	0.0894180i
$754$	−14.7337	+	10.7047i	−0.536570	+	0.389841i
$755$	1.95440	−	6.01504i	0.0711280	−	0.218910i
$756$	−1.35666	+	0.985674i	−0.0493414	+	0.0358486i
$757$	−9.45844	−	6.87196i	−0.343773	−	0.249766i	0.402479	−	0.915429i	$-0.368149\pi$
$757$	−9.45844	−	6.87196i	−0.343773	−	0.249766i	−0.746252	+	0.665664i	$0.768149\pi$
$758$	−2.65648	−	8.17582i	−0.0964878	−	0.296959i
$759$	7.77036	+	5.64550i	0.282046	+	0.204919i
$760$	−3.05850	−	2.22213i	−0.110943	−	0.0806051i
$761$	−2.64940	−	8.15403i	−0.0960408	−	0.295583i	0.891483	−	0.453055i	$-0.149666\pi$
$761$	−2.64940	−	8.15403i	−0.0960408	−	0.295583i	−0.987524	+	0.157471i	$0.949666\pi$
$762$	16.2381	+	11.7977i	0.588246	+	0.427386i
$763$	14.7403	−	10.7094i	0.533633	−	0.387707i
$764$	1.38587	−	4.26526i	0.0501389	−	0.154312i
$765$	−2.45650	+	1.78475i	−0.0888149	+	0.0645278i
$766$	4.54596	+	13.9910i	0.164252	+	0.505516i
$767$	−11.5958	−	35.6882i	−0.418700	−	1.28863i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	8.29383			0.299083			0.149542	−	0.988755i	$-0.452220\pi$
$769$	8.29383			0.299083			0.149542	+	0.988755i	$0.452220\pi$
$770$	6.45642			0.232673
$771$	1.22655	−	3.77495i	0.0441733	−	0.135951i
$772$	−14.5316	−	10.5578i	−0.523003	−	0.379984i
$773$	−6.06240	+	4.40459i	−0.218049	+	0.158422i	−0.691448	−	0.722426i	$-0.743027\pi$
$773$	−6.06240	+	4.40459i	−0.218049	+	0.158422i	0.473399	+	0.880848i	$0.343027\pi$
$774$	11.9213			0.428502
$775$	5.52783	+	0.665657i	0.198566	+	0.0239111i
$776$	−13.8142			−0.495902
$777$	7.32402	−	5.32121i	0.262748	−	0.190897i
$778$	−30.2873	−	22.0050i	−1.08585	−	0.788918i
$779$	−12.8012	+	39.3982i	−0.458652	+	1.41159i
$780$	−2.65956			−0.0952274
$781$	−29.6634			−1.06144
$782$	−2.34071	+	7.20397i	−0.0837036	+	0.257613i
$783$	−2.11606	−	6.51255i	−0.0756217	−	0.232740i
$784$	−1.29414	−	3.98294i	−0.0462191	−	0.142248i
$785$	−4.27222	+	3.10395i	−0.152482	+	0.110785i
$786$	−1.29057	+	3.97198i	−0.0460332	+	0.141676i
$787$	−43.8205	+	31.8375i	−1.56203	+	1.13488i	−0.627716	+	0.778443i	$0.716010\pi$
$787$	−43.8205	+	31.8375i	−1.56203	+	1.13488i	−0.934318	+	0.356441i	$0.883990\pi$
$788$	−3.15605	−	2.29301i	−0.112430	−	0.0816849i
$789$	9.38608	+	28.8874i	0.334153	+	1.02842i
$790$	2.18580	+	1.58808i	0.0777674	+	0.0565013i
$791$	−10.9316	−	7.94229i	−0.388684	−	0.282395i
$792$	−1.18976	−	3.66171i	−0.0422763	−	0.130113i
$793$	10.4442	+	7.58817i	0.370885	+	0.269464i
$794$	12.2299	−	8.88555i	0.434023	−	0.315336i
$795$	−0.156995	+	0.483181i	−0.00556804	+	0.0171367i
$796$	19.9327	−	14.4819i	0.706495	−	0.513299i
$797$	−8.99329	−	27.6785i	−0.318559	−	0.980423i	−0.974265	−	0.225407i	$-0.927629\pi$
$797$	−8.99329	−	27.6785i	−0.318559	−	0.980423i	0.655706	−	0.755016i	$-0.272371\pi$
$798$	1.95906	+	6.02937i	0.0693500	+	0.213437i
$799$	−7.57951	+	23.3273i	−0.268144	+	0.825261i
$800$	1.00000			0.0353553
$801$	−7.56426			−0.267270
$802$	10.8827	−	33.4935i	0.384281	−	1.18270i
$803$	50.5996	+	36.7628i	1.78562	+	1.29733i
$804$	−11.2542	+	8.17664i	−0.396904	+	0.288368i
$805$	4.18332			0.147443
$806$	14.7016	+	1.77035i	0.517841	+	0.0623580i
$807$	8.34082			0.293611
$808$	8.29003	−	6.02306i	0.291642	−	0.211890i
$809$	−1.61157	−	1.17087i	−0.0566598	−	0.0411658i	0.559095	−	0.829104i	$-0.311149\pi$
$809$	−1.61157	−	1.17087i	−0.0566598	−	0.0411658i	−0.615755	+	0.787938i	$0.711149\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	34.0879			1.19699			0.598494	−	0.801127i	$-0.295766\pi$
$811$	34.0879			1.19699			0.598494	+	0.801127i	$0.295766\pi$
$812$	−11.4831			−0.402978
$813$	0.491953	−	1.51408i	0.0172536	−	0.0531010i
$814$	6.42298	+	19.7679i	0.225125	+	0.692864i
$815$	4.61898	+	14.2158i	0.161796	+	0.497956i
$816$	2.45650	−	1.78475i	0.0859946	−	0.0624788i
$817$	13.9270	−	42.8628i	0.487243	−	1.49958i
$818$	19.4681	−	14.1444i	0.680688	−	0.494549i
$819$	3.60813	+	2.62146i	0.126078	+	0.0916011i
$820$	−3.38611	−	10.4214i	−0.118248	−	0.363930i
$821$	43.1311	+	31.3366i	1.50529	+	1.09365i	0.968216	+	0.250117i	$0.0804691\pi$
$821$	43.1311	+	31.3366i	1.50529	+	1.09365i	0.537071	+	0.843537i	$0.319531\pi$
$822$	−9.13623	−	6.63786i	−0.318663	−	0.231522i
$823$	0.915264	+	2.81689i	0.0319041	+	0.0981907i	0.965741	−	0.259510i	$-0.0835609\pi$
$823$	0.915264	+	2.81689i	0.0319041	+	0.0981907i	−0.933836	+	0.357700i	$0.883561\pi$
$824$	9.11764	+	6.62435i	0.317628	+	0.230770i
$825$	−3.11483	+	2.26306i	−0.108445	+	0.0787896i
$826$	7.31150	−	22.5025i	0.254400	−	0.782962i
$827$	−25.4036	+	18.4568i	−0.883371	+	0.641807i	−0.934141	−	0.356904i	$-0.883832\pi$
$827$	−25.4036	+	18.4568i	−0.883371	+	0.641807i	0.0507701	+	0.998710i	$0.483832\pi$
$828$	−0.770884	−	2.37254i	−0.0267901	−	0.0824513i
$829$	0.198051	+	0.609539i	0.00687860	+	0.0211702i	0.954437	−	0.298413i	$-0.0964572\pi$
$829$	0.198051	+	0.609539i	0.00687860	+	0.0211702i	−0.947558	+	0.319583i	$0.896457\pi$
$830$	−0.693033	+	2.13294i	−0.0240555	+	0.0740353i
$831$	3.21253			0.111441
$832$	2.65956			0.0922036
$833$	−3.92951	+	12.0938i	−0.136149	+	0.419025i
$834$	−14.7530	−	10.7186i	−0.510853	−	0.371156i
$835$	−1.98402	+	1.44148i	−0.0686599	+	0.0498844i
$836$	−14.5555			−0.503413
$837$	−2.34127	+	5.05158i	−0.0809262	+	0.174608i
$838$	−5.82008			−0.201051
$839$	−34.6574	+	25.1801i	−1.19651	+	0.869313i	−0.993937	−	0.109954i	$-0.964929\pi$
$839$	−34.6574	+	25.1801i	−1.19651	+	0.869313i	−0.202570	+	0.979268i	$0.564929\pi$
$840$	−1.35666	−	0.985674i	−0.0468094	−	0.0340090i
$841$	5.52862	−	17.0153i	0.190642	−	0.586736i
$842$	31.3445			1.08020
$843$	−7.51121			−0.258700
$844$	6.11873	−	18.8315i	0.210616	−	0.648208i
$845$	−1.83147	−	5.63668i	−0.0630044	−	0.193908i
$846$	−2.49622	−	7.68256i	−0.0858216	−	0.264132i
$847$	5.18736	−	3.76884i	0.178240	−	0.129499i
$848$	0.156995	−	0.483181i	0.00539123	−	0.0165925i
$849$	5.08800	−	3.69665i	0.174620	−	0.126869i
$850$	−2.45650	−	1.78475i	−0.0842572	−	0.0612164i
$851$	4.16165	+	12.8082i	0.142660	+	0.439061i
$852$	6.23306	+	4.52858i	0.213541	+	0.155147i
$853$	−19.6781	−	14.2969i	−0.673764	−	0.489518i	0.197519	−	0.980299i	$-0.436712\pi$
$853$	−19.6781	−	14.2969i	−0.673764	−	0.489518i	−0.871283	+	0.490781i	$0.836712\pi$
$854$	2.51539	+	7.74158i	0.0860750	+	0.264912i
$855$	−3.05850	−	2.22213i	−0.104598	−	0.0759953i
$856$	−2.12276	+	1.54228i	−0.0725545	+	0.0527140i
$857$	−15.3801	+	47.3350i	−0.525373	+	1.61693i	0.238205	+	0.971215i	$0.423441\pi$
$857$	−15.3801	+	47.3350i	−0.525373	+	1.61693i	−0.763577	+	0.645716i	$0.776559\pi$
$858$	−8.28408	+	6.01873i	−0.282814	+	0.205476i
$859$	4.83321	+	14.8751i	0.164907	+	0.507532i	0.999029	−	0.0440476i	$-0.0140253\pi$
$859$	4.83321	+	14.8751i	0.164907	+	0.507532i	−0.834122	+	0.551579i	$0.814025\pi$
$860$	3.68388	+	11.3378i	0.125619	+	0.386616i
$861$	−5.67827	+	17.4759i	−0.193515	+	0.595578i
$862$	−23.1666			−0.789057
$863$	15.4301			0.525248			0.262624	−	0.964898i	$-0.415412\pi$
$863$	15.4301			0.525248			0.262624	+	0.964898i	$0.415412\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−0.00972012	−	0.00706208i	−0.000330494	−	0.000240118i
$866$	−1.48659	+	1.08007i	−0.0505162	+	0.0367022i
$867$	7.78028			0.264232
$868$	6.84329	+	6.35171i	0.232276	+	0.215591i
$869$	10.4023			0.352875
$870$	5.53991	−	4.02498i	0.187820	−	0.136459i
$871$	29.9311	+	21.7462i	1.01418	+	0.736843i
$872$	3.35749	−	10.3333i	0.113699	−	0.349930i
$873$	−13.8142			−0.467541
$874$	−9.43099			−0.319008
$875$	−0.518200	+	1.59485i	−0.0175183	+	0.0539159i
$876$	−5.01990	−	15.4497i	−0.169607	−	0.521996i
$877$	2.43988	+	7.50919i	0.0823890	+	0.253567i	0.983762	−	0.179475i	$-0.0574400\pi$
$877$	2.43988	+	7.50919i	0.0823890	+	0.253567i	−0.901374	+	0.433042i	$0.857440\pi$
$878$	−1.55002	+	1.12616i	−0.0523107	+	0.0380059i
$879$	8.12230	−	24.9979i	0.273958	−	0.843157i
$880$	3.11483	−	2.26306i	0.105001	−	0.0762877i
$881$	20.8035	+	15.1146i	0.700888	+	0.509225i	0.880221	−	0.474564i	$-0.157394\pi$
$881$	20.8035	+	15.1146i	0.700888	+	0.509225i	−0.179334	+	0.983788i	$0.557394\pi$
$882$	−1.29414	−	3.98294i	−0.0435758	−	0.134113i
$883$	25.6154	+	18.6107i	0.862026	+	0.626299i	0.928435	−	0.371494i	$-0.121154\pi$
$883$	25.6154	+	18.6107i	0.862026	+	0.626299i	−0.0664093	+	0.997792i	$0.521154\pi$
$884$	−6.53320	−	4.74665i	−0.219735	−	0.159647i
$885$	4.36005	+	13.4189i	0.146562	+	0.451070i
$886$	0.278535	+	0.202368i	0.00935758	+	0.00679868i
$887$	41.7064	−	30.3014i	1.40036	−	1.01742i	0.405725	−	0.913995i	$-0.367019\pi$
$887$	41.7064	−	30.3014i	1.40036	−	1.01742i	0.994637	−	0.103428i	$-0.0329810\pi$
$888$	1.66824	−	5.13432i	0.0559826	−	0.172297i
$889$	27.2302	−	19.7839i	0.913272	−	0.663531i
$890$	−2.33749	−	7.19404i	−0.0783527	−	0.241145i
$891$	−1.18976	−	3.66171i	−0.0398585	−	0.122672i
$892$	5.72869	−	17.6311i	0.191811	−	0.590332i
$893$	−30.5387			−1.02194
$894$	−18.1675			−0.607613
$895$	4.36069	−	13.4208i	0.145762	−	0.448609i
$896$	1.35666	+	0.985674i	0.0453230	+	0.0329291i
$897$	−5.36752	+	3.89973i	−0.179216	+	0.130208i
$898$	27.8957			0.930891
$899$	−33.3029	+	18.5617i	−1.11071	+	0.619068i
$900$	1.00000			0.0333333
$901$	−1.24802	+	0.906737i	−0.0415774	+	0.0302078i
$902$	−34.1314	−	24.7979i	−1.13645	−	0.825679i
$903$	6.17761	−	19.0127i	0.205578	−	0.632704i
$904$	−8.05773			−0.267996
$905$	14.9596			0.497273
$906$	−1.95440	+	6.01504i	−0.0649307	+	0.199836i
$907$	5.44586	+	16.7606i	0.180827	+	0.556528i	0.999852	−	0.0172304i	$-0.00548487\pi$
$907$	5.44586	+	16.7606i	0.180827	+	0.556528i	−0.819025	+	0.573758i	$0.805485\pi$
$908$	−0.166904	−	0.513677i	−0.00553889	−	0.0170470i
$909$	8.29003	−	6.02306i	0.274963	−	0.199772i
$910$	−1.37818	+	4.24161i	−0.0456863	+	0.140608i
$911$	29.9655	−	21.7712i	0.992801	−	0.721312i	0.0322684	−	0.999479i	$-0.489727\pi$
$911$	29.9655	−	21.7712i	0.992801	−	0.721312i	0.960533	+	0.278167i	$0.0897269\pi$
$912$	3.05850	+	2.22213i	0.101277	+	0.0735821i
$913$	2.66828	+	8.21212i	0.0883072	+	0.271781i
$914$	24.6335	+	17.8973i	0.814805	+	0.591991i
$915$	−3.92705	−	2.85317i	−0.129824	−	0.0943229i
$916$	2.37858	+	7.32051i	0.0785904	+	0.241876i
$917$	5.66595	+	4.11655i	0.187106	+	0.135941i
$918$	2.45650	−	1.78475i	0.0810765	−	0.0589055i
$919$	−17.3587	+	53.4246i	−0.572611	+	1.76232i	0.0715615	+	0.997436i	$0.477202\pi$
$919$	−17.3587	+	53.4246i	−0.572611	+	1.76232i	−0.644173	+	0.764880i	$0.722798\pi$
$920$	2.01820	−	1.46631i	0.0665381	−	0.0483427i
$921$	3.64946	+	11.2319i	0.120254	+	0.370103i
$922$	−2.13875	−	6.58240i	−0.0704360	−	0.216780i
$923$	6.33191	−	19.4876i	0.208417	−	0.641443i
$924$	−6.45642			−0.212401
$925$	−5.39855			−0.177503
$926$	1.29590	−	3.98836i	0.0425858	−	0.131066i
$927$	9.11764	+	6.62435i	0.299463	+	0.217572i
$928$	−5.53991	+	4.02498i	−0.181856	+	0.132126i
$929$	−4.75181			−0.155902			−0.0779508	−	0.996957i	$-0.524838\pi$
$929$	−4.75181			−0.155902			−0.0779508	+	0.996957i	$0.524838\pi$
$930$	−5.52783	−	0.665657i	−0.181265	−	0.0218277i
$931$	−15.8324			−0.518888
$932$	−3.48101	+	2.52910i	−0.114024	+	0.0828435i
$933$	−4.70924	−	3.42146i	−0.154174	−	0.112014i
$934$	−6.42824	+	19.7841i	−0.210338	+	0.647355i
$935$	−11.6906			−0.382323
$936$	2.65956			0.0869303
$937$	−3.59463	+	11.0631i	−0.117432	+	0.361417i	−0.992446	−	0.122679i	$-0.960851\pi$
$937$	−3.59463	+	11.0631i	−0.117432	+	0.361417i	0.875015	+	0.484096i	$0.160851\pi$
$938$	7.20864	+	22.1859i	0.235370	+	0.724395i
$939$	3.37264	+	10.3799i	0.110062	+	0.338736i
$940$	6.53518	−	4.74808i	0.213154	−	0.154865i
$941$	17.4503	−	53.7066i	0.568865	−	1.75079i	−0.0873139	−	0.996181i	$-0.527828\pi$
$941$	17.4503	−	53.7066i	0.568865	−	1.75079i	0.656179	−	0.754605i	$-0.272172\pi$
$942$	4.27222	−	3.10395i	0.139197	−	0.101132i
$943$	−22.1148	−	16.0673i	−0.720157	−	0.523225i
$944$	−4.36005	−	13.4189i	−0.141908	−	0.436747i
$945$	−1.35666	−	0.985674i	−0.0441323	−	0.0320640i
$946$	37.1328	+	26.9786i	1.20729	+	0.877149i
$947$	−5.66830	−	17.4452i	−0.184195	−	0.566894i	0.815739	−	0.578421i	$-0.196331\pi$
$947$	−5.66830	−	17.4452i	−0.184195	−	0.566894i	−0.999934	+	0.0115269i	$0.996331\pi$
$948$	−2.18580	−	1.58808i	−0.0709916	−	0.0515784i
$949$	−34.9526	+	25.3946i	−1.13461	+	0.824342i
$950$	1.16824	−	3.59548i	0.0379028	−	0.116653i
$951$	1.07596	−	0.781732i	0.0348904	−	0.0253494i
$952$	−1.57346	−	4.84261i	−0.0509962	−	0.156950i
$953$	7.77814	+	23.9387i	0.251959	+	0.775449i	0.994414	+	0.105553i	$0.0336613\pi$
$953$	7.77814	+	23.9387i	0.251959	+	0.775449i	−0.742455	+	0.669896i	$0.766339\pi$
$954$	0.156995	−	0.483181i	0.00508290	−	0.0156436i
$955$	4.48476			0.145123
$956$	−19.3092			−0.624506
$957$	8.14712	−	25.0743i	0.263359	−	0.810536i
$958$	−0.208445	−	0.151444i	−0.00673455	−	0.00489293i
$959$	−15.3208	+	11.1312i	−0.494735	+	0.359446i
$960$	−1.00000			−0.0322749
$961$	30.1138	+	7.35928i	0.971413	+	0.237396i
$962$	−14.3577			−0.462912
$963$	−2.12276	+	1.54228i	−0.0684051	+	0.0496992i
$964$	−11.1541	−	8.10393i	−0.359249	−	0.261010i
$965$	5.55057	−	17.0829i	0.178679	−	0.549918i
$966$	−4.18332			−0.134596
$967$	−55.8047			−1.79456			−0.897280	−	0.441462i	$-0.854460\pi$
$967$	−55.8047			−1.79456			−0.897280	+	0.441462i	$0.854460\pi$
$968$	1.18156	−	3.63648i	0.0379769	−	0.116881i
$969$	−3.54725	−	10.9173i	−0.113954	−	0.350715i
$970$	−4.26883	−	13.1381i	−0.137064	−	0.421840i
$971$	−32.0844	+	23.3107i	−1.02964	+	0.748075i	−0.968236	−	0.250038i	$-0.919557\pi$
$971$	−32.0844	+	23.3107i	−1.02964	+	0.748075i	−0.0614008	+	0.998113i	$0.519557\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−24.7397	+	17.9744i	−0.793117	+	0.576233i
$974$	0.243998	+	0.177275i	0.00781821	+	0.00568026i
$975$	−0.821848	−	2.52939i	−0.0263202	−	0.0810053i
$976$	3.92705	+	2.85317i	0.125702	+	0.0913277i
$977$	25.5526	+	18.5650i	0.817500	+	0.593948i	0.915995	−	0.401189i	$-0.131403\pi$
$977$	25.5526	+	18.5650i	0.817500	+	0.593948i	−0.0984954	+	0.995138i	$0.531403\pi$
$978$	−4.61898	−	14.2158i	−0.147699	−	0.454570i
$979$	−23.5614	−	17.1184i	−0.753026	−	0.547105i
$980$	3.38809	−	2.46159i	0.108229	−	0.0786327i
$981$	3.35749	−	10.3333i	0.107196	−	0.329917i
$982$	15.9354	−	11.5778i	0.508520	−	0.369462i
$983$	−14.4709	−	44.5370i	−0.461551	−	1.42051i	−0.863269	−	0.504745i	$-0.831587\pi$
$983$	−14.4709	−	44.5370i	−0.461551	−	1.42051i	0.401718	−	0.915764i	$-0.368413\pi$
$984$	3.38611	+	10.4214i	0.107945	+	0.332221i
$985$	1.20550	−	3.71016i	0.0384106	−	0.118216i
$986$	20.7923			0.662163
$987$	−13.5461			−0.431177
$988$	3.10701	−	9.56239i	0.0988471	−	0.304220i
$989$	24.0595	+	17.4803i	0.765049	+	0.555840i
$990$	3.11483	−	2.26306i	0.0989959	−	0.0719247i
$991$	17.6127			0.559487			0.279743	−	0.960075i	$-0.409751\pi$
$991$	17.6127			0.559487			0.279743	+	0.960075i	$0.409751\pi$
$992$	5.52783	+	0.665657i	0.175509	+	0.0211346i
$993$	27.6185			0.876445
$994$	10.4524	−	7.59411i	0.331530	−	0.240870i
$995$	19.9327	+	14.4819i	0.631909	+	0.459109i
$996$	0.693033	−	2.13294i	0.0219596	−	0.0675847i
$997$	36.2796			1.14899			0.574494	−	0.818509i	$-0.305199\pi$
$997$	36.2796			1.14899			0.574494	+	0.818509i	$0.305199\pi$
$998$	−11.9387			−0.377914
$999$	1.66824	−	5.13432i	0.0527809	−	0.162443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.a.481.1	✓	8
31.2	even	5	inner	930.2.n.a.901.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.a.481.1	✓	8	1.1	even	1	trivial
930.2.n.a.901.1	yes	8	31.2	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.518200 + 1.59485i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.518200 + 1.59485i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.809017 + 0.587785i) q^{10} +(-1.18976 + 3.66171i) q^{11} +(0.809017 - 0.587785i) q^{12} +(-2.15163 - 1.56325i) q^{13} +(-0.518200 - 1.59485i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.938299 + 2.88779i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-3.05850 + 2.22213i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-1.35666 + 0.985674i) q^{21} +(-1.18976 - 3.66171i) q^{22} +(-0.770884 - 2.37254i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +2.65956 q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.35666 + 0.985674i) q^{28} +(-5.53991 + 4.02498i) q^{29} -1.00000 q^{30} +(5.52783 + 0.665657i) q^{31} +1.00000 q^{32} +(-3.11483 + 2.26306i) q^{33} +(-2.45650 - 1.78475i) q^{34} +(-0.518200 + 1.59485i) q^{35} +1.00000 q^{36} -5.39855 q^{37} +(1.16824 - 3.59548i) q^{38} +(-0.821848 - 2.52939i) q^{39} +(0.309017 + 0.951057i) q^{40} +(8.86495 - 6.44077i) q^{41} +(0.518200 - 1.59485i) q^{42} +(-9.64452 + 7.00716i) q^{43} +(3.11483 + 2.26306i) q^{44} +(0.309017 + 0.951057i) q^{45} +(2.01820 + 1.46631i) q^{46} +(6.53518 + 4.74808i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(3.38809 + 2.46159i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.938299 + 2.88779i) q^{51} +(-2.15163 + 1.56325i) q^{52} +(0.156995 + 0.483181i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-1.18976 + 3.66171i) q^{55} -1.67693 q^{56} -3.78051 q^{57} +(2.11606 - 6.51255i) q^{58} +(11.4148 + 8.29332i) q^{59} +(0.809017 - 0.587785i) q^{60} -4.85410 q^{61} +(-4.86337 + 2.71065i) q^{62} -1.67693 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.15163 - 1.56325i) q^{65} +(1.18976 - 3.66171i) q^{66} -13.9109 q^{67} +3.03640 q^{68} +(0.770884 - 2.37254i) q^{69} +(-0.518200 - 1.59485i) q^{70} +(2.38082 + 7.32740i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(5.01990 - 15.4497i) q^{73} +(4.36752 - 3.17319i) q^{74} +(0.809017 + 0.587785i) q^{75} +(1.16824 + 3.59548i) q^{76} +(-5.22335 - 3.79499i) q^{77} +(2.15163 + 1.56325i) q^{78} +(-0.834903 - 2.56957i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.38611 + 10.4214i) q^{82} +(1.81439 - 1.31823i) q^{83} +(0.518200 + 1.59485i) q^{84} +(0.938299 + 2.88779i) q^{85} +(3.68388 - 11.3378i) q^{86} -6.84770 q^{87} -3.85015 q^{88} +(-2.33749 + 7.19404i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(3.60813 - 2.62146i) q^{91} -2.49463 q^{92} +(4.08084 + 3.78770i) q^{93} -8.07792 q^{94} +(-3.05850 + 2.22213i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-4.26883 + 13.1381i) q^{97} -4.18791 q^{98} -3.85015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more