LMFDB - Embedded newform 930.2.n.c.481.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 205x^{8} + 675x^{6} + 795x^{4} + 230x^{2} + 5 $ x^12 + 25x^10 + 205x^8 + 675x^6 + 795x^4 + 230*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.3
Root			$1.27291i$ of defining polynomial
Character	$\chi$	$=$	930.481
Dual form			930.2.n.c.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.367362 - 1.13062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(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} +(0.367362 - 1.13062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(-0.867362 + 2.66946i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-2.01962 - 1.46734i) q^{13} +(0.367362 + 1.13062i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.51962 + 4.67692i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(3.29041 - 2.39062i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-0.961766 + 0.698764i) q^{21} +(-0.867362 - 2.66946i) q^{22} +(0.331303 + 1.01964i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +2.49639 q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.961766 - 0.698764i) q^{28} +(5.49805 - 3.99457i) q^{29} -1.00000 q^{30} +(-4.20700 + 3.64707i) q^{31} +1.00000 q^{32} +(2.27078 - 1.64982i) q^{33} +(-3.97843 - 2.89050i) q^{34} +(-0.367362 + 1.13062i) q^{35} +1.00000 q^{36} -4.80092 q^{37} +(-1.25682 + 3.86811i) q^{38} +(0.771428 + 2.37421i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(10.0759 - 7.32060i) q^{41} +(0.367362 - 1.13062i) q^{42} +(8.77363 - 6.37441i) q^{43} +(2.27078 + 1.64982i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(-0.867362 - 0.630175i) q^{46} +(-7.84065 - 5.69657i) q^{47} +(0.309017 + 0.951057i) q^{48} +(4.51976 + 3.28380i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(1.51962 - 4.67692i) q^{51} +(-2.01962 + 1.46734i) q^{52} +(1.28722 + 3.96165i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.867362 - 2.66946i) q^{55} +1.18881 q^{56} -4.06717 q^{57} +(-2.10007 + 6.46335i) q^{58} +(10.3703 + 7.53450i) q^{59} +(0.809017 - 0.587785i) q^{60} +10.3535 q^{61} +(1.25984 - 5.42336i) q^{62} +1.18881 q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.01962 + 1.46734i) q^{65} +(-0.867362 + 2.66946i) q^{66} +4.07721 q^{67} +4.91761 q^{68} +(0.331303 - 1.01964i) q^{69} +(-0.367362 - 1.13062i) q^{70} +(4.35072 + 13.3902i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(1.98624 - 6.11301i) q^{73} +(3.88403 - 2.82191i) q^{74} +(-0.809017 - 0.587785i) q^{75} +(-1.25682 - 3.86811i) q^{76} +(2.69952 + 1.96132i) q^{77} +(-2.01962 - 1.46734i) q^{78} +(-4.85956 - 14.9562i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.84867 + 11.8450i) q^{82} +(11.5149 - 8.36603i) q^{83} +(0.367362 + 1.13062i) q^{84} +(-1.51962 - 4.67692i) q^{85} +(-3.35123 + 10.3140i) q^{86} -6.79597 q^{87} -2.80684 q^{88} +(-2.27078 + 6.98875i) q^{89} +(0.809017 + 0.587785i) q^{90} +(-2.40095 + 1.74439i) q^{91} +1.07212 q^{92} +(5.54723 - 0.477730i) q^{93} +9.69158 q^{94} +(-3.29041 + 2.39062i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.377714 + 1.16248i) q^{97} -5.58674 q^{98} -2.80684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

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
$7$	0.367362	−	1.13062i	0.138850	−	0.427335i	−0.857319	−	0.514785i	$-0.827872\pi$
$7$	0.367362	−	1.13062i	0.138850	−	0.427335i	0.996169	+	0.0874497i	$0.0278717\pi$
$8$	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
$11$	−0.867362	+	2.66946i	−0.261519	+	0.804874i	0.730955	+	0.682425i	$0.239075\pi$
$11$	−0.867362	+	2.66946i	−0.261519	+	0.804874i	−0.992475	+	0.122449i	$0.960925\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	−2.01962	−	1.46734i	−0.560143	−	0.406968i	0.271368	−	0.962476i	$-0.412524\pi$
$13$	−2.01962	−	1.46734i	−0.560143	−	0.406968i	−0.831511	+	0.555508i	$0.812524\pi$
$14$	0.367362	+	1.13062i	0.0981816	+	0.302172i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.51962	+	4.67692i	0.368563	+	1.13432i	0.947720	+	0.319104i	$0.103382\pi$
$17$	1.51962	+	4.67692i	0.368563	+	1.13432i	−0.579156	+	0.815216i	$0.696618\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	3.29041	−	2.39062i	0.754871	−	0.548446i	−0.142462	−	0.989800i	$-0.545502\pi$
$19$	3.29041	−	2.39062i	0.754871	−	0.548446i	0.897333	+	0.441354i	$0.145502\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	−0.961766	+	0.698764i	−0.209874	+	0.152483i
$22$	−0.867362	−	2.66946i	−0.184922	−	0.569132i
$23$	0.331303	+	1.01964i	0.0690814	+	0.212611i	0.979637	−	0.200775i	$-0.0643461\pi$
$23$	0.331303	+	1.01964i	0.0690814	+	0.212611i	−0.910556	+	0.413386i	$0.864346\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	2.49639			0.489583
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.961766	−	0.698764i	−0.181757	−	0.132054i
$29$	5.49805	−	3.99457i	1.02096	−	0.741773i	0.0544830	−	0.998515i	$-0.482649\pi$
$29$	5.49805	−	3.99457i	1.02096	−	0.741773i	0.966480	+	0.256742i	$0.0826489\pi$
$30$	−1.00000			−0.182574
$31$	−4.20700	+	3.64707i	−0.755600	+	0.655034i
$31$	−4.20700	+	3.64707i	−0.755600	+	0.655034i
$32$	1.00000			0.176777
$33$	2.27078	−	1.64982i	0.395293	−	0.287197i
$34$	−3.97843	−	2.89050i	−0.682295	−	0.495716i
$35$	−0.367362	+	1.13062i	−0.0620955	+	0.191110i
$36$	1.00000			0.166667
$37$	−4.80092			−0.789266			−0.394633	−	0.918839i	$-0.629128\pi$
$37$	−4.80092			−0.789266			−0.394633	+	0.918839i	$0.629128\pi$
$38$	−1.25682	+	3.86811i	−0.203884	+	0.627490i
$39$	0.771428	+	2.37421i	0.123527	+	0.380178i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	10.0759	−	7.32060i	1.57360	−	1.14329i	0.649991	−	0.759942i	$-0.274773\pi$
$41$	10.0759	−	7.32060i	1.57360	−	1.14329i	0.923606	−	0.383343i	$-0.125227\pi$
$42$	0.367362	−	1.13062i	0.0566851	−	0.174459i
$43$	8.77363	−	6.37441i	1.33797	−	0.972089i	0.338450	−	0.940985i	$-0.390098\pi$
$43$	8.77363	−	6.37441i	1.33797	−	0.972089i	0.999516	−	0.0311044i	$-0.00990244\pi$
$44$	2.27078	+	1.64982i	0.342333	+	0.248720i
$45$	−0.309017	−	0.951057i	−0.0460655	−	0.141775i
$46$	−0.867362	−	0.630175i	−0.127886	−	0.0929143i
$47$	−7.84065	−	5.69657i	−1.14368	−	0.830930i	−0.156050	−	0.987749i	$-0.549876\pi$
$47$	−7.84065	−	5.69657i	−1.14368	−	0.830930i	−0.987627	+	0.156819i	$0.949876\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	4.51976	+	3.28380i	0.645681	+	0.469114i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	1.51962	−	4.67692i	0.212790	−	0.654900i
$52$	−2.01962	+	1.46734i	−0.280072	+	0.203484i
$53$	1.28722	+	3.96165i	0.176813	+	0.544174i	0.999712	−	0.0240141i	$-0.00764465\pi$
$53$	1.28722	+	3.96165i	0.176813	+	0.544174i	−0.822899	+	0.568188i	$0.807645\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	0.867362	−	2.66946i	0.116955	−	0.359951i
$56$	1.18881			0.158861
$57$	−4.06717			−0.538709
$58$	−2.10007	+	6.46335i	−0.275753	+	0.848680i
$59$	10.3703	+	7.53450i	1.35010	+	0.980908i	0.999006	+	0.0445693i	$0.0141916\pi$
$59$	10.3703	+	7.53450i	1.35010	+	0.980908i	0.351098	+	0.936339i	$0.385808\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	10.3535			1.32563			0.662815	−	0.748783i	$-0.269362\pi$
$61$	10.3535			1.32563			0.662815	+	0.748783i	$0.269362\pi$
$62$	1.25984	−	5.42336i	0.160000	−	0.688767i
$63$	1.18881			0.149776
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.01962	+	1.46734i	0.250504	+	0.182002i
$66$	−0.867362	+	2.66946i	−0.106765	+	0.328588i
$67$	4.07721			0.498110			0.249055	−	0.968489i	$-0.419880\pi$
$67$	4.07721			0.498110			0.249055	+	0.968489i	$0.419880\pi$
$68$	4.91761			0.596348
$69$	0.331303	−	1.01964i	0.0398842	−	0.122751i
$70$	−0.367362	−	1.13062i	−0.0439081	−	0.135135i
$71$	4.35072	+	13.3902i	0.516336	+	1.58912i	0.780838	+	0.624734i	$0.214792\pi$
$71$	4.35072	+	13.3902i	0.516336	+	1.58912i	−0.264502	+	0.964385i	$0.585208\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	1.98624	−	6.11301i	0.232471	−	0.715473i	−0.764975	−	0.644060i	$-0.777249\pi$
$73$	1.98624	−	6.11301i	0.232471	−	0.715473i	0.997447	−	0.0714139i	$-0.0227511\pi$
$74$	3.88403	−	2.82191i	0.451509	−	0.328040i
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$	−1.25682	−	3.86811i	−0.144168	−	0.443702i
$77$	2.69952	+	1.96132i	0.307639	+	0.223513i
$78$	−2.01962	−	1.46734i	−0.228677	−	0.166144i
$79$	−4.85956	−	14.9562i	−0.546744	−	1.68270i	−0.716807	−	0.697271i	$-0.754397\pi$
$79$	−4.85956	−	14.9562i	−0.546744	−	1.68270i	0.170064	−	0.985433i	$-0.445603\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.84867	+	11.8450i	−0.425014	+	1.30806i
$83$	11.5149	−	8.36603i	1.26392	−	0.918292i	0.264977	−	0.964255i	$-0.414636\pi$
$83$	11.5149	−	8.36603i	1.26392	−	0.918292i	0.998943	+	0.0459632i	$0.0146357\pi$
$84$	0.367362	+	1.13062i	0.0400825	+	0.123361i
$85$	−1.51962	−	4.67692i	−0.164826	−	0.507284i
$86$	−3.35123	+	10.3140i	−0.361372	+	1.11219i
$87$	−6.79597			−0.728604
$88$	−2.80684			−0.299210
$89$	−2.27078	+	6.98875i	−0.240702	+	0.740806i	0.755611	+	0.655020i	$0.227340\pi$
$89$	−2.27078	+	6.98875i	−0.240702	+	0.740806i	−0.996314	+	0.0857856i	$0.972660\pi$
$90$	0.809017	+	0.587785i	0.0852779	+	0.0619580i
$91$	−2.40095	+	1.74439i	−0.251687	+	0.182862i
$92$	1.07212			0.111776
$93$	5.54723	−	0.477730i	0.575221	−	0.0495383i
$94$	9.69158			0.999610
$95$	−3.29041	+	2.39062i	−0.337589	+	0.245273i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−0.377714	+	1.16248i	−0.0383511	+	0.118032i	−0.968399	−	0.249405i	$-0.919765\pi$
$97$	−0.377714	+	1.16248i	−0.0383511	+	0.118032i	0.930048	+	0.367438i	$0.119765\pi$
$98$	−5.58674			−0.564346
$99$	−2.80684			−0.282098
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	4.69034	+	14.4354i	0.466706	+	1.43637i	0.856824	+	0.515609i	$0.172434\pi$
$101$	4.69034	+	14.4354i	0.466706	+	1.43637i	−0.390118	+	0.920765i	$0.627566\pi$
$102$	1.51962	+	4.67692i	0.150465	+	0.463085i
$103$	1.24551	−	0.904916i	0.122724	−	0.0891640i	−0.524730	−	0.851269i	$-0.675834\pi$
$103$	1.24551	−	0.904916i	0.122724	−	0.0891640i	0.647454	+	0.762105i	$0.275834\pi$
$104$	0.771428	−	2.37421i	0.0756447	−	0.232811i
$105$	0.961766	−	0.698764i	0.0938587	−	0.0681923i
$106$	−3.36998	−	2.44843i	−0.327321	−	0.237813i
$107$	−5.03663	−	15.5012i	−0.486910	−	1.49855i	−0.829196	−	0.558958i	$-0.811201\pi$
$107$	−5.03663	−	15.5012i	−0.486910	−	1.49855i	0.342286	−	0.939596i	$-0.388799\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	11.3486	+	8.24527i	1.08700	+	0.789753i	0.978890	−	0.204385i	$-0.0655196\pi$
$109$	11.3486	+	8.24527i	1.08700	+	0.789753i	0.108112	+	0.994139i	$0.465520\pi$
$110$	0.867362	+	2.66946i	0.0826997	+	0.254523i
$111$	3.88403	+	2.82191i	0.368655	+	0.267844i
$112$	−0.961766	+	0.698764i	−0.0908783	+	0.0660270i
$113$	−4.03294	+	12.4121i	−0.379387	+	1.16763i	0.561084	+	0.827759i	$0.310384\pi$
$113$	−4.03294	+	12.4121i	−0.379387	+	1.16763i	−0.940471	+	0.339874i	$0.889616\pi$
$114$	3.29041	−	2.39062i	0.308175	−	0.223902i
$115$	−0.331303	−	1.01964i	−0.0308941	−	0.0950824i
$116$	−2.10007	−	6.46335i	−0.194987	−	0.600107i
$117$	0.771428	−	2.37421i	0.0713185	−	0.219496i
$118$	−12.8185			−1.18003
$119$	5.84609			0.535910
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	2.52546	+	1.83485i	0.229587	+	0.166805i
$122$	−8.37615	+	6.08563i	−0.758341	+	0.550967i
$123$	−12.4545			−1.12299
$124$	2.16854	+	5.12810i	0.194740	+	0.460517i
$125$	−1.00000			−0.0894427
$126$	−0.961766	+	0.698764i	−0.0856809	+	0.0622508i
$127$	−0.333918	−	0.242606i	−0.0296304	−	0.0215278i	0.572871	−	0.819645i	$-0.305829\pi$
$127$	−0.333918	−	0.242606i	−0.0296304	−	0.0215278i	−0.602502	+	0.798117i	$0.705829\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−10.8448			−0.954831
$130$	−2.49639			−0.218948
$131$	4.51449	−	13.8942i	0.394433	−	1.21394i	−0.534970	−	0.844871i	$-0.679677\pi$
$131$	4.51449	−	13.8942i	0.394433	−	1.21394i	0.929402	−	0.369068i	$-0.120323\pi$
$132$	−0.867362	−	2.66946i	−0.0754941	−	0.232347i
$133$	−1.49412	−	4.59843i	−0.129557	−	0.398735i
$134$	−3.29853	+	2.39652i	−0.284950	+	0.207028i
$135$	−0.309017	+	0.951057i	−0.0265959	+	0.0818539i
$136$	−3.97843	+	2.89050i	−0.341148	+	0.247858i
$137$	−11.3095	−	8.21685i	−0.966238	−	0.702013i	−0.0116470	−	0.999932i	$-0.503707\pi$
$137$	−11.3095	−	8.21685i	−0.966238	−	0.702013i	−0.954591	+	0.297919i	$0.903707\pi$
$138$	0.331303	+	1.01964i	0.0282024	+	0.0867979i
$139$	1.72887	+	1.25610i	0.146641	+	0.106541i	0.658687	−	0.752417i	$-0.271112\pi$
$139$	1.72887	+	1.25610i	0.146641	+	0.106541i	−0.512046	+	0.858958i	$0.671112\pi$
$140$	0.961766	+	0.698764i	0.0812840	+	0.0590563i
$141$	2.99486	+	9.21724i	0.252213	+	0.776232i
$142$	−11.3903	−	8.27557i	−0.955856	−	0.694470i
$143$	5.66877	−	4.11860i	0.474046	−	0.344415i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−5.49805	+	3.99457i	−0.456589	+	0.331731i
$146$	1.98624	+	6.11301i	0.164382	+	0.505916i
$147$	−1.72640	−	5.31330i	−0.142391	−	0.438234i
$148$	−1.48357	+	4.56595i	−0.121948	+	0.375318i
$149$	0.287272			0.0235343			0.0117671	−	0.999931i	$-0.496254\pi$
$149$	0.287272			0.0235343			0.0117671	+	0.999931i	$0.496254\pi$
$150$	1.00000			0.0816497
$151$	0.0940048	−	0.289317i	0.00765001	−	0.0235443i	−0.947159	−	0.320765i	$-0.896060\pi$
$151$	0.0940048	−	0.289317i	0.00765001	−	0.0235443i	0.954809	+	0.297221i	$0.0960599\pi$
$152$	3.29041	+	2.39062i	0.266887	+	0.193905i
$153$	−3.97843	+	2.89050i	−0.321637	+	0.233683i
$154$	−3.33679			−0.268887
$155$	4.20700	−	3.64707i	0.337914	−	0.292940i
$156$	2.49639			0.199871
$157$	8.40960	−	6.10993i	0.671159	−	0.487626i	−0.199254	−	0.979948i	$-0.563852\pi$
$157$	8.40960	−	6.10993i	0.671159	−	0.487626i	0.870413	+	0.492322i	$0.163852\pi$
$158$	12.7225	+	9.24344i	1.01215	+	0.735369i
$159$	1.28722	−	3.96165i	0.102083	−	0.314179i
$160$	−1.00000			−0.0790569
$161$	1.27454			0.100448
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	4.59685	+	14.1477i	0.360053	+	1.10813i	0.953021	+	0.302904i	$0.0979561\pi$
$163$	4.59685	+	14.1477i	0.360053	+	1.10813i	−0.592968	+	0.805226i	$0.702044\pi$
$164$	−3.84867	−	11.8450i	−0.300530	−	0.924937i
$165$	−2.27078	+	1.64982i	−0.176780	+	0.128438i
$166$	−4.39828	+	13.5365i	−0.341373	+	1.05064i
$167$	−13.3083	+	9.66908i	−1.02983	+	0.748216i	−0.968275	−	0.249888i	$-0.919606\pi$
$167$	−13.3083	+	9.66908i	−1.02983	+	0.748216i	−0.0615559	+	0.998104i	$0.519606\pi$
$168$	−0.961766	−	0.698764i	−0.0742018	−	0.0539108i
$169$	−2.09143	−	6.43677i	−0.160879	−	0.495136i
$170$	3.97843	+	2.89050i	0.305132	+	0.221691i
$171$	3.29041	+	2.39062i	0.251624	+	0.182815i
$172$	−3.35123	−	10.3140i	−0.255529	−	0.786436i
$173$	11.0587	+	8.03461i	0.840776	+	0.610860i	0.922587	−	0.385788i	$-0.126070\pi$
$173$	11.0587	+	8.03461i	0.840776	+	0.610860i	−0.0818111	+	0.996648i	$0.526070\pi$
$174$	5.49805	−	3.99457i	0.416806	−	0.302828i
$175$	0.367362	−	1.13062i	0.0277699	−	0.0854671i
$176$	2.27078	−	1.64982i	0.171167	−	0.124360i
$177$	−3.96112	−	12.1911i	−0.297736	−	0.916337i
$178$	−2.27078	−	6.98875i	−0.170202	−	0.523829i
$179$	2.16845	−	6.67381i	0.162078	−	0.498824i	−0.836731	−	0.547613i	$-0.815536\pi$
$179$	2.16845	−	6.67381i	0.162078	−	0.498824i	0.998809	+	0.0487898i	$0.0155365\pi$
$180$	−1.00000			−0.0745356
$181$	−6.24158			−0.463933			−0.231967	−	0.972724i	$-0.574516\pi$
$181$	−6.24158			−0.463933			−0.231967	+	0.972724i	$0.574516\pi$
$182$	0.917080	−	2.82248i	0.0679785	−	0.209216i
$183$	−8.37615	−	6.08563i	−0.619183	−	0.449863i
$184$	−0.867362	+	0.630175i	−0.0639428	+	0.0464571i
$185$	4.80092			0.352971
$186$	−4.20700	+	3.64707i	−0.308472	+	0.267416i
$187$	−13.8030			−1.00937
$188$	−7.84065	+	5.69657i	−0.571839	+	0.415465i
$189$	−0.961766	−	0.698764i	−0.0699581	−	0.0508276i
$190$	1.25682	−	3.86811i	0.0911796	−	0.280622i
$191$	−17.2388			−1.24736			−0.623678	−	0.781682i	$-0.714362\pi$
$191$	−17.2388			−1.24736			−0.623678	+	0.781682i	$0.714362\pi$
$192$	1.00000			0.0721688
$193$	1.49747	−	4.60874i	0.107790	−	0.331745i	−0.882585	−	0.470153i	$-0.844199\pi$
$193$	1.49747	−	4.60874i	0.107790	−	0.331745i	0.990375	+	0.138409i	$0.0441987\pi$
$194$	−0.377714	−	1.16248i	−0.0271183	−	0.0834615i
$195$	−0.771428	−	2.37421i	−0.0552431	−	0.170021i
$196$	4.51976	−	3.28380i	0.322840	−	0.234557i
$197$	−7.15267	+	22.0137i	−0.509607	+	1.56841i	0.283279	+	0.959038i	$0.408578\pi$
$197$	−7.15267	+	22.0137i	−0.509607	+	1.56841i	−0.792885	+	0.609371i	$0.791422\pi$
$198$	2.27078	−	1.64982i	0.161377	−	0.117248i
$199$	−6.61983	−	4.80959i	−0.469268	−	0.340943i	0.327888	−	0.944717i	$-0.393663\pi$
$199$	−6.61983	−	4.80959i	−0.469268	−	0.340943i	−0.797156	+	0.603774i	$0.793663\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	−3.29853	−	2.39652i	−0.232660	−	0.169038i
$202$	−12.2795	−	8.92155i	−0.863980	−	0.627718i
$203$	−2.49658	−	7.68368i	−0.175225	−	0.539289i
$204$	−3.97843	−	2.89050i	−0.278546	−	0.202375i
$205$	−10.0759	+	7.32060i	−0.703734	+	0.511293i
$206$	−0.475742	+	1.46418i	−0.0331465	+	0.102015i
$207$	−0.867362	+	0.630175i	−0.0602858	+	0.0438002i
$208$	0.771428	+	2.37421i	0.0534889	+	0.164622i
$209$	3.52771	+	10.8572i	0.244016	+	0.751005i
$210$	−0.367362	+	1.13062i	−0.0253504	+	0.0780204i
$211$	−15.5812			−1.07266			−0.536328	−	0.844009i	$-0.680189\pi$
$211$	−15.5812			−1.07266			−0.536328	+	0.844009i	$0.680189\pi$
$212$	4.16552			0.286089
$213$	4.35072	−	13.3902i	0.298107	−	0.917478i
$214$	13.1861	+	9.58024i	0.901381	+	0.654892i
$215$	−8.77363	+	6.37441i	−0.598356	+	0.434731i
$216$	1.00000			0.0680414
$217$	2.57797	+	6.09633i	0.175004	+	0.413846i
$218$	−14.0277			−0.950075
$219$	−5.20004	+	3.77805i	−0.351386	+	0.255297i
$220$	−2.27078	−	1.64982i	−0.153096	−	0.111231i
$221$	3.79358	−	11.6754i	0.255184	−	0.785375i
$222$	−4.80092			−0.322217
$223$	−0.570601			−0.0382102			−0.0191051	−	0.999817i	$-0.506082\pi$
$223$	−0.570601			−0.0382102			−0.0191051	+	0.999817i	$0.506082\pi$
$224$	0.367362	−	1.13062i	0.0245454	−	0.0755429i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−4.03294	−	12.4121i	−0.268267	−	0.825641i
$227$	−3.07568	+	2.23461i	−0.204140	+	0.148316i	−0.685158	−	0.728394i	$-0.740267\pi$
$227$	−3.07568	+	2.23461i	−0.204140	+	0.148316i	0.481018	+	0.876711i	$0.340267\pi$
$228$	−1.25682	+	3.86811i	−0.0832352	+	0.256172i
$229$	3.67990	−	2.67360i	0.243175	−	0.176677i	−0.459522	−	0.888166i	$-0.651979\pi$
$229$	3.67990	−	2.67360i	0.243175	−	0.176677i	0.702696	+	0.711490i	$0.251979\pi$
$230$	0.867362	+	0.630175i	0.0571921	+	0.0415525i
$231$	−1.03113	−	3.17348i	−0.0678431	−	0.208800i
$232$	5.49805	+	3.99457i	0.360965	+	0.262256i
$233$	10.2225	+	7.42708i	0.669699	+	0.486565i	0.869924	−	0.493185i	$-0.164168\pi$
$233$	10.2225	+	7.42708i	0.669699	+	0.486565i	−0.200226	+	0.979750i	$0.564168\pi$
$234$	0.771428	+	2.37421i	0.0504298	+	0.155207i
$235$	7.84065	+	5.69657i	0.511468	+	0.371603i
$236$	10.3703	−	7.53450i	0.675052	−	0.490454i
$237$	−4.85956	+	14.9562i	−0.315663	+	0.971510i
$238$	−4.72959	+	3.43625i	−0.306574	+	0.222739i
$239$	−4.87926	−	15.0168i	−0.315613	−	0.971357i	−0.975501	−	0.219993i	$-0.929396\pi$
$239$	−4.87926	−	15.0168i	−0.315613	−	0.971357i	0.659888	−	0.751364i	$-0.270604\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	2.45826	−	7.56576i	0.158351	−	0.487353i	−0.840134	−	0.542378i	$-0.817524\pi$
$241$	2.45826	−	7.56576i	0.158351	−	0.487353i	0.998485	+	0.0550252i	$0.0175239\pi$
$242$	−3.12164			−0.200667
$243$	1.00000			0.0641500
$244$	3.19941	−	9.84676i	0.204821	−	0.630374i
$245$	−4.51976	−	3.28380i	−0.288757	−	0.209794i
$246$	10.0759	−	7.32060i	0.642418	−	0.466744i
$247$	−10.1533			−0.646036
$248$	−4.76861	−	2.87409i	−0.302807	−	0.182505i
$249$	−14.2331			−0.901989
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−13.7456	−	9.98675i	−0.867613	−	0.630358i	0.0623321	−	0.998055i	$-0.480146\pi$
$251$	−13.7456	−	9.98675i	−0.867613	−	0.630358i	−0.929945	+	0.367697i	$0.880146\pi$
$252$	0.367362	−	1.13062i	0.0231416	−	0.0712226i
$253$	−3.00927			−0.189191
$254$	0.412745			0.0258980
$255$	−1.51962	+	4.67692i	−0.0951626	+	0.292880i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−8.87031	−	27.3000i	−0.553314	−	1.70293i	−0.700354	−	0.713796i	$-0.746974\pi$
$257$	−8.87031	−	27.3000i	−0.553314	−	1.70293i	0.147039	−	0.989131i	$-0.453026\pi$
$258$	8.77363	−	6.37441i	0.546222	−	0.396854i
$259$	−1.76367	+	5.42803i	−0.109589	+	0.337281i
$260$	2.01962	−	1.46734i	0.125252	−	0.0910008i
$261$	5.49805	+	3.99457i	0.340321	+	0.247258i
$262$	4.51449	+	13.8942i	0.278906	+	0.858385i
$263$	−0.787589	−	0.572217i	−0.0485648	−	0.0352844i	0.563238	−	0.826295i	$-0.309555\pi$
$263$	−0.787589	−	0.572217i	−0.0485648	−	0.0352844i	−0.611803	+	0.791010i	$0.709555\pi$
$264$	2.27078	+	1.64982i	0.139757	+	0.101539i
$265$	−1.28722	−	3.96165i	−0.0790731	−	0.243362i
$266$	3.91166	+	2.84199i	0.239839	+	0.174253i
$267$	5.94499	−	4.31929i	0.363827	−	0.264336i
$268$	1.25993	−	3.87766i	0.0769623	−	0.236866i
$269$	−18.0449	+	13.1104i	−1.10021	+	0.799352i	−0.981095	−	0.193528i	$-0.938007\pi$
$269$	−18.0449	+	13.1104i	−1.10021	+	0.799352i	−0.119119	+	0.992880i	$0.538007\pi$
$270$	−0.309017	−	0.951057i	−0.0188062	−	0.0578795i
$271$	−2.34410	−	7.21439i	−0.142394	−	0.438243i	0.854273	−	0.519825i	$-0.174003\pi$
$271$	−2.34410	−	7.21439i	−0.142394	−	0.438243i	−0.996667	+	0.0815820i	$0.974003\pi$
$272$	1.51962	−	4.67692i	0.0921408	−	0.283580i
$273$	2.96773			0.179615
$274$	13.9793			0.844523
$275$	−0.867362	+	2.66946i	−0.0523039	+	0.160975i
$276$	−0.867362	−	0.630175i	−0.0522090	−	0.0379321i
$277$	−11.0580	+	8.03412i	−0.664412	+	0.482723i	−0.868150	−	0.496302i	$-0.834691\pi$
$277$	−11.0580	+	8.03412i	−0.664412	+	0.482723i	0.203738	+	0.979025i	$0.434691\pi$
$278$	−2.13700			−0.128169
$279$	−4.76861	−	2.87409i	−0.285489	−	0.172067i
$280$	−1.18881			−0.0710448
$281$	7.95668	−	5.78086i	0.474656	−	0.344857i	−0.324597	−	0.945852i	$-0.605229\pi$
$281$	7.95668	−	5.78086i	0.474656	−	0.344857i	0.799253	+	0.600995i	$0.205229\pi$
$282$	−7.84065	−	5.69657i	−0.466904	−	0.339226i
$283$	2.50552	−	7.71119i	0.148938	−	0.458383i	−0.848559	−	0.529101i	$-0.822529\pi$
$283$	2.50552	−	7.71119i	0.148938	−	0.458383i	0.997496	+	0.0707184i	$0.0225292\pi$
$284$	14.0792			0.835449
$285$	4.06717			0.240918
$286$	−2.16528	+	6.66404i	−0.128035	+	0.394053i
$287$	−4.57532	−	14.0814i	−0.270073	−	0.831199i
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−5.81107	+	4.22199i	−0.341828	+	0.248352i
$290$	2.10007	−	6.46335i	0.123320	−	0.379541i
$291$	0.988868	−	0.718455i	0.0579685	−	0.0421166i
$292$	−5.20004	−	3.77805i	−0.304309	−	0.221093i
$293$	1.72746	+	5.31658i	0.100919	+	0.310598i	0.988751	−	0.149570i	$-0.0477890\pi$
$293$	1.72746	+	5.31658i	0.100919	+	0.310598i	−0.887832	+	0.460168i	$0.847789\pi$
$294$	4.51976	+	3.28380i	0.263598	+	0.191515i
$295$	−10.3703	−	7.53450i	−0.603785	−	0.438675i
$296$	−1.48357	−	4.56595i	−0.0862305	−	0.265390i
$297$	2.27078	+	1.64982i	0.131764	+	0.0957323i
$298$	−0.232408	+	0.168854i	−0.0134630	+	0.00978147i
$299$	0.827062	−	2.54543i	0.0478302	−	0.147206i
$300$	−0.809017	+	0.587785i	−0.0467086	+	0.0339358i
$301$	−3.98396	−	12.2614i	−0.229632	−	0.706734i
$302$	0.0940048	+	0.289317i	0.00540937	+	0.0166483i
$303$	4.69034	−	14.4354i	0.269453	−	0.829291i
$304$	−4.06717			−0.233268
$305$	−10.3535			−0.592840
$306$	1.51962	−	4.67692i	0.0868712	−	0.267362i
$307$	22.7703	+	16.5436i	1.29957	+	0.944194i	0.999951	−	0.00986518i	$-0.00314023\pi$
$307$	22.7703	+	16.5436i	1.29957	+	0.944194i	0.299620	+	0.954059i	$0.403140\pi$
$308$	2.69952	−	1.96132i	0.153820	−	0.111757i
$309$	−1.53953			−0.0875811
$310$	−1.25984	+	5.42336i	−0.0715541	+	0.308026i
$311$	32.7379			1.85640			0.928199	−	0.372085i	$-0.121357\pi$
$311$	32.7379			1.85640			0.928199	+	0.372085i	$0.121357\pi$
$312$	−2.01962	+	1.46734i	−0.114339	+	0.0830720i
$313$	6.46653	+	4.69821i	0.365510	+	0.265558i	0.755347	−	0.655326i	$-0.227469\pi$
$313$	6.46653	+	4.69821i	0.365510	+	0.265558i	−0.389837	+	0.920884i	$0.627469\pi$
$314$	−3.21218	+	9.88608i	−0.181274	+	0.557904i
$315$	−1.18881			−0.0669817
$316$	−15.7259			−0.884650
$317$	−5.20684	+	16.0250i	−0.292445	+	0.900055i	0.691622	+	0.722260i	$0.256896\pi$
$317$	−5.20684	+	16.0250i	−0.292445	+	0.900055i	−0.984068	+	0.177795i	$0.943104\pi$
$318$	1.28722	+	3.96165i	0.0721835	+	0.222158i
$319$	5.89456	+	18.1416i	0.330032	+	1.01573i
$320$	0.809017	−	0.587785i	0.0452254	−	0.0328582i
$321$	−5.03663	+	15.5012i	−0.281117	+	0.865190i
$322$	−1.03113	+	0.749157i	−0.0574624	+	0.0417489i
$323$	16.1809	+	11.7561i	0.900331	+	0.654129i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−2.01962	−	1.46734i	−0.112029	−	0.0813936i
$326$	−12.0347	−	8.74373i	−0.666541	−	0.484271i
$327$	−4.33479	−	13.3411i	−0.239715	−	0.737766i
$328$	10.0759	+	7.32060i	0.556351	+	0.404212i
$329$	−9.32103	+	6.77212i	−0.513885	+	0.373359i
$330$	0.867362	−	2.66946i	0.0477467	−	0.146949i
$331$	14.6292	−	10.6287i	0.804091	−	0.584207i	−0.108020	−	0.994149i	$-0.534451\pi$
$331$	14.6292	−	10.6287i	0.804091	−	0.584207i	0.912112	+	0.409942i	$0.134451\pi$
$332$	−4.39828	−	13.5365i	−0.241387	−	0.742913i
$333$	−1.48357	−	4.56595i	−0.0812989	−	0.250212i
$334$	5.08334	−	15.6449i	0.278148	−	0.856051i
$335$	−4.07721			−0.222762
$336$	1.18881			0.0648548
$337$	−9.76621	+	30.0573i	−0.532000	+	1.63733i	0.218045	+	0.975939i	$0.430032\pi$
$337$	−9.76621	+	30.0573i	−0.532000	+	1.63733i	−0.750044	+	0.661387i	$0.769968\pi$
$338$	5.47544	+	3.97814i	0.297825	+	0.216382i
$339$	10.5584	−	7.67110i	0.573452	−	0.416637i
$340$	−4.91761			−0.266695
$341$	−6.08674	−	14.3938i	−0.329615	−	0.779467i
$342$	−4.06717			−0.219927
$343$	12.1055	−	8.79515i	0.653635	−	0.474894i
$344$	8.77363	+	6.37441i	0.473042	+	0.343685i
$345$	−0.331303	+	1.01964i	−0.0178367	+	0.0548958i
$346$	−13.6693			−0.734865
$347$	−3.79283			−0.203610			−0.101805	−	0.994804i	$-0.532462\pi$
$347$	−3.79283			−0.203610			−0.101805	+	0.994804i	$0.532462\pi$
$348$	−2.10007	+	6.46335i	−0.112576	+	0.346472i
$349$	7.62607	+	23.4706i	0.408214	+	1.25635i	0.918181	+	0.396160i	$0.129658\pi$
$349$	7.62607	+	23.4706i	0.408214	+	1.25635i	−0.509967	+	0.860194i	$0.670342\pi$
$350$	0.367362	+	1.13062i	0.0196363	+	0.0604344i
$351$	−2.01962	+	1.46734i	−0.107800	+	0.0783210i
$352$	−0.867362	+	2.66946i	−0.0462305	+	0.142283i
$353$	−5.97149	+	4.33854i	−0.317830	+	0.230917i	−0.735249	−	0.677797i	$-0.762935\pi$
$353$	−5.97149	+	4.33854i	−0.317830	+	0.230917i	0.417419	+	0.908714i	$0.362935\pi$
$354$	10.3703	+	7.53450i	0.551178	+	0.400454i
$355$	−4.35072	−	13.3902i	−0.230912	−	0.710675i
$356$	5.94499	+	4.31929i	0.315084	+	0.228922i
$357$	−4.72959	−	3.43625i	−0.250316	−	0.181865i
$358$	2.16845	+	6.67381i	0.114606	+	0.352722i
$359$	−22.8995	−	16.6375i	−1.20859	−	0.878093i	−0.213489	−	0.976946i	$-0.568483\pi$
$359$	−22.8995	−	16.6375i	−1.20859	−	0.878093i	−0.995102	+	0.0988529i	$0.968483\pi$
$360$	0.809017	−	0.587785i	0.0426389	−	0.0309790i
$361$	−0.759610	+	2.33784i	−0.0399795	+	0.123044i
$362$	5.04955	−	3.66871i	0.265398	−	0.192823i
$363$	−0.964640	−	2.96886i	−0.0506305	−	0.155825i
$364$	0.917080	+	2.82248i	0.0480680	+	0.147938i
$365$	−1.98624	+	6.11301i	−0.103964	+	0.319969i
$366$	10.3535			0.541186
$367$	12.2315			0.638480			0.319240	−	0.947674i	$-0.396572\pi$
$367$	12.2315			0.638480			0.319240	+	0.947674i	$0.396572\pi$
$368$	0.331303	−	1.01964i	0.0172703	−	0.0531527i
$369$	10.0759	+	7.32060i	0.524532	+	0.381095i
$370$	−3.88403	+	2.82191i	−0.201921	+	0.146704i
$371$	4.95200			0.257095
$372$	1.25984	−	5.42336i	0.0653197	−	0.281188i
$373$	21.4206			1.10912			0.554558	−	0.832145i	$-0.312887\pi$
$373$	21.4206			1.10912			0.554558	+	0.832145i	$0.312887\pi$
$374$	11.1668	−	8.11317i	0.577423	−	0.419522i
$375$	0.809017	+	0.587785i	0.0417775	+	0.0303531i
$376$	2.99486	−	9.21724i	0.154448	−	0.475343i
$377$	−16.9654			−0.873763
$378$	1.18881			0.0611457
$379$	−7.79400	+	23.9875i	−0.400351	+	1.23215i	0.524364	+	0.851494i	$0.324303\pi$
$379$	−7.79400	+	23.9875i	−0.400351	+	1.23215i	−0.924715	+	0.380660i	$0.875697\pi$
$380$	1.25682	+	3.86811i	0.0644737	+	0.198430i
$381$	0.127545	+	0.392544i	0.00653435	+	0.0201107i
$382$	13.9465	−	10.1327i	0.713564	−	0.518434i
$383$	−1.24102	+	3.81946i	−0.0634131	+	0.195165i	−0.977744	−	0.209803i	$-0.932718\pi$
$383$	−1.24102	+	3.81946i	−0.0634131	+	0.195165i	0.914331	+	0.404969i	$0.132718\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	−2.69952	−	1.96132i	−0.137580	−	0.0999581i
$386$	1.49747	+	4.60874i	0.0762193	+	0.234579i
$387$	8.77363	+	6.37441i	0.445989	+	0.324030i
$388$	0.988868	+	0.718455i	0.0502022	+	0.0364740i
$389$	11.3035	+	34.7885i	0.573108	+	1.76385i	0.642532	+	0.766259i	$0.277884\pi$
$389$	11.3035	+	34.7885i	0.573108	+	1.76385i	−0.0694236	+	0.997587i	$0.522116\pi$
$390$	2.01962	+	1.46734i	0.102268	+	0.0743018i
$391$	−4.26535	+	3.09896i	−0.215708	+	0.156721i
$392$	−1.72640	+	5.31330i	−0.0871962	+	0.268362i
$393$	−11.8191	+	8.58707i	−0.596194	+	0.433160i
$394$	−7.15267	−	22.0137i	−0.360346	−	1.10903i
$395$	4.85956	+	14.9562i	0.244511	+	0.752528i
$396$	−0.867362	+	2.66946i	−0.0435866	+	0.134146i
$397$	20.9678			1.05234			0.526171	−	0.850378i	$-0.323627\pi$
$397$	20.9678			1.05234			0.526171	+	0.850378i	$0.323627\pi$
$398$	8.18257			0.410155
$399$	−1.49412	+	4.59843i	−0.0747996	+	0.230210i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−17.5074	+	12.7198i	−0.874276	+	0.635199i	−0.931731	−	0.363149i	$-0.881701\pi$
$401$	−17.5074	+	12.7198i	−0.874276	+	0.635199i	0.0574548	+	0.998348i	$0.481701\pi$
$402$	4.07721			0.203353
$403$	13.8481	−	1.19260i	0.689822	−	0.0594078i
$404$	15.1783			0.755146
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	6.53613	+	4.74878i	0.324383	+	0.235678i
$407$	4.16413	−	12.8159i	0.206408	−	0.635260i
$408$	4.91761			0.243458
$409$	30.4884			1.50755			0.753777	−	0.657130i	$-0.228230\pi$
$409$	30.4884			1.50755			0.753777	+	0.657130i	$0.228230\pi$
$410$	3.84867	−	11.8450i	0.190072	−	0.584982i
$411$	4.31985	+	13.2951i	0.213083	+	0.655801i
$412$	−0.475742	−	1.46418i	−0.0234381	−	0.0721352i
$413$	12.3283	−	8.95707i	0.606638	−	0.440749i
$414$	0.331303	−	1.01964i	0.0162826	−	0.0501128i
$415$	−11.5149	+	8.36603i	−0.565242	+	0.410672i
$416$	−2.01962	−	1.46734i	−0.0990203	−	0.0719424i
$417$	−0.660370	−	2.03241i	−0.0323385	−	0.0995276i
$418$	−9.23565	−	6.71009i	−0.451731	−	0.328201i
$419$	−4.24178	−	3.08183i	−0.207224	−	0.150557i	0.479333	−	0.877633i	$-0.340879\pi$
$419$	−4.24178	−	3.08183i	−0.207224	−	0.150557i	−0.686557	+	0.727076i	$0.740879\pi$
$420$	−0.367362	−	1.13062i	−0.0179254	−	0.0551688i
$421$	−15.8030	−	11.4815i	−0.770190	−	0.559576i	0.131829	−	0.991272i	$-0.457915\pi$
$421$	−15.8030	−	11.4815i	−0.770190	−	0.559576i	−0.902019	+	0.431697i	$0.857915\pi$
$422$	12.6055	−	9.15842i	0.613626	−	0.445825i
$423$	2.99486	−	9.21724i	0.145615	−	0.448158i
$424$	−3.36998	+	2.44843i	−0.163661	+	0.118906i
$425$	1.51962	+	4.67692i	0.0737126	+	0.226864i
$426$	4.35072	+	13.3902i	0.210793	+	0.648755i
$427$	3.80348	−	11.7059i	0.184063	−	0.566488i
$428$	−16.2989			−0.787836
$429$	−7.00698			−0.338300
$430$	3.35123	−	10.3140i	0.161611	−	0.497386i
$431$	4.68057	+	3.40063i	0.225455	+	0.163803i	0.694779	−	0.719223i	$-0.255502\pi$
$431$	4.68057	+	3.40063i	0.225455	+	0.163803i	−0.469324	+	0.883026i	$0.655502\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	5.87415			0.282294			0.141147	−	0.989989i	$-0.454921\pi$
$433$	5.87415			0.282294			0.141147	+	0.989989i	$0.454921\pi$
$434$	−5.66896	−	3.41674i	−0.272119	−	0.164009i
$435$	6.79597			0.325842
$436$	11.3486	−	8.24527i	0.543501	−	0.394877i
$437$	3.52771	+	2.56303i	0.168753	+	0.122606i
$438$	1.98624	−	6.11301i	0.0949061	−	0.292091i
$439$	−14.1985			−0.677658			−0.338829	−	0.940848i	$-0.610031\pi$
$439$	−14.1985			−0.677658			−0.338829	+	0.940848i	$0.610031\pi$
$440$	2.80684			0.133811
$441$	−1.72640	+	5.31330i	−0.0822094	+	0.253014i
$442$	3.79358	+	11.6754i	0.180442	+	0.555344i
$443$	−10.6287	−	32.7119i	−0.504986	−	1.55419i	−0.800794	−	0.598940i	$-0.795589\pi$
$443$	−10.6287	−	32.7119i	−0.504986	−	1.55419i	0.295807	−	0.955248i	$-0.404411\pi$
$444$	3.88403	−	2.82191i	0.184328	−	0.133922i
$445$	2.27078	−	6.98875i	0.107645	−	0.331299i
$446$	0.461626	−	0.335391i	0.0218586	−	0.0158812i
$447$	−0.232408	−	0.168854i	−0.0109925	−	0.00798654i
$448$	0.367362	+	1.13062i	0.0173562	+	0.0534169i
$449$	18.3560	+	13.3364i	0.866275	+	0.629385i	0.929585	−	0.368609i	$-0.120166\pi$
$449$	18.3560	+	13.3364i	0.866275	+	0.629385i	−0.0633100	+	0.997994i	$0.520166\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	10.8026	+	33.2470i	0.508674	+	1.56554i
$452$	10.5584	+	7.67110i	0.496624	+	0.360818i
$453$	−0.246108	+	0.178808i	−0.0115632	+	0.00840112i
$454$	1.17481	−	3.61568i	0.0551364	−	0.169692i
$455$	2.40095	−	1.74439i	0.112558	−	0.0817782i
$456$	−1.25682	−	3.86811i	−0.0588562	−	0.181141i
$457$	6.58188	+	20.2569i	0.307887	+	0.947580i	0.978584	+	0.205848i	$0.0659952\pi$
$457$	6.58188	+	20.2569i	0.307887	+	0.947580i	−0.670697	+	0.741732i	$0.734005\pi$
$458$	−1.40560	+	4.32598i	−0.0656792	+	0.202140i
$459$	4.91761			0.229534
$460$	−1.07212			−0.0499878
$461$	3.07702	−	9.47011i	0.143311	−	0.441067i	−0.853479	−	0.521128i	$-0.825511\pi$
$461$	3.07702	−	9.47011i	0.143311	−	0.441067i	0.996790	+	0.0800609i	$0.0255115\pi$
$462$	2.69952	+	1.96132i	0.125593	+	0.0912488i
$463$	−18.1757	+	13.2054i	−0.844696	+	0.613708i	−0.923678	−	0.383168i	$-0.874833\pi$
$463$	−18.1757	+	13.2054i	−0.844696	+	0.613708i	0.0789825	+	0.996876i	$0.474833\pi$
$464$	−6.79597			−0.315495
$465$	−5.54723	+	0.477730i	−0.257247	+	0.0221542i
$466$	−12.6357			−0.585338
$467$	9.63588	−	7.00088i	0.445895	−	0.323962i	−0.342078	−	0.939672i	$-0.611131\pi$
$467$	9.63588	−	7.00088i	0.445895	−	0.323962i	0.787973	+	0.615710i	$0.211131\pi$
$468$	−2.01962	−	1.46734i	−0.0933572	−	0.0678280i
$469$	1.49781	−	4.60979i	0.0691625	−	0.212860i
$470$	−9.69158			−0.447039
$471$	−10.3948			−0.478969
$472$	−3.96112	+	12.1911i	−0.182325	+	0.561140i
$473$	9.40636	+	28.9498i	0.432505	+	1.33111i
$474$	−4.85956	−	14.9562i	−0.223207	−	0.686961i
$475$	3.29041	−	2.39062i	0.150974	−	0.109689i
$476$	1.80654	−	5.55996i	0.0828027	−	0.254840i
$477$	−3.36998	+	2.44843i	−0.154301	+	0.112106i
$478$	12.7741	+	9.28090i	0.584272	+	0.424499i
$479$	0.781877	+	2.40637i	0.0357249	+	0.109950i	0.967329	−	0.253525i	$-0.0815901\pi$
$479$	0.781877	+	2.40637i	0.0357249	+	0.109950i	−0.931604	+	0.363475i	$0.881590\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	9.69606	+	7.04460i	0.442102	+	0.321206i
$482$	2.45826	+	7.56576i	0.111971	+	0.344611i
$483$	−1.03113	−	0.749157i	−0.0469179	−	0.0340878i
$484$	2.52546	−	1.83485i	0.114794	−	0.0834025i
$485$	0.377714	−	1.16248i	0.0171511	−	0.0527857i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	4.86867	+	14.9842i	0.220621	+	0.679000i	0.998707	+	0.0508425i	$0.0161907\pi$
$487$	4.86867	+	14.9842i	0.220621	+	0.679000i	−0.778086	+	0.628158i	$0.783809\pi$
$488$	3.19941	+	9.84676i	0.144830	+	0.445742i
$489$	4.59685	−	14.1477i	0.207877	−	0.639779i
$490$	5.58674			0.252383
$491$	−6.96945			−0.314527			−0.157263	−	0.987557i	$-0.550267\pi$
$491$	−6.96945			−0.314527			−0.157263	+	0.987557i	$0.550267\pi$
$492$	−3.84867	+	11.8450i	−0.173511	+	0.534013i
$493$	27.0373	+	19.6437i	1.21770	+	0.884709i
$494$	8.21415	−	5.96793i	0.369572	−	0.268510i
$495$	2.80684			0.126158
$496$	5.54723	−	0.477730i	0.249078	−	0.0214507i
$497$	16.7375			0.750780
$498$	11.5149	−	8.36603i	0.515993	−	0.374891i
$499$	19.2253	+	13.9680i	0.860641	+	0.625292i	0.928059	−	0.372432i	$-0.121476\pi$
$499$	19.2253	+	13.9680i	0.860641	+	0.625292i	−0.0674181	+	0.997725i	$0.521476\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	16.4500			0.734933
$502$	16.9905			0.758322
$503$	6.85010	−	21.0824i	0.305431	−	0.940019i	−0.674086	−	0.738653i	$-0.735462\pi$
$503$	6.85010	−	21.0824i	0.305431	−	0.940019i	0.979516	−	0.201366i	$-0.0645379\pi$
$504$	0.367362	+	1.13062i	0.0163636	+	0.0503620i
$505$	−4.69034	−	14.4354i	−0.208717	−	0.642366i
$506$	2.43455	−	1.76880i	0.108229	−	0.0786328i
$507$	−2.09143	+	6.43677i	−0.0928838	+	0.285867i
$508$	−0.333918	+	0.242606i	−0.0148152	+	0.0107639i
$509$	−10.0094	−	7.27228i	−0.443661	−	0.322338i	0.343427	−	0.939179i	$-0.388412\pi$
$509$	−10.0094	−	7.27228i	−0.443661	−	0.322338i	−0.787088	+	0.616841i	$0.788412\pi$
$510$	−1.51962	−	4.67692i	−0.0672901	−	0.207098i
$511$	−6.18184	−	4.49137i	−0.273469	−	0.198687i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.25682	−	3.86811i	−0.0554901	−	0.170781i
$514$	23.2228	+	16.8723i	1.02431	+	0.744206i
$515$	−1.24551	+	0.904916i	−0.0548837	+	0.0398754i
$516$	−3.35123	+	10.3140i	−0.147530	+	0.454049i
$517$	22.0075	−	15.9894i	0.967888	−	0.703212i
$518$	−1.76367	−	5.42803i	−0.0774914	−	0.238494i
$519$	−4.22404	−	13.0003i	−0.185415	−	0.570648i
$520$	−0.771428	+	2.37421i	−0.0338294	+	0.104116i
$521$	−7.54306			−0.330467			−0.165234	−	0.986254i	$-0.552838\pi$
$521$	−7.54306			−0.330467			−0.165234	+	0.986254i	$0.552838\pi$
$522$	−6.79597			−0.297451
$523$	−6.81141	+	20.9634i	−0.297842	+	0.916664i	0.684410	+	0.729098i	$0.260060\pi$
$523$	−6.81141	+	20.9634i	−0.297842	+	0.916664i	−0.982252	+	0.187566i	$0.939940\pi$
$524$	−11.8191	−	8.58707i	−0.516319	−	0.375128i
$525$	−0.961766	+	0.698764i	−0.0419749	+	0.0304965i
$526$	0.973513			0.0424472
$527$	−23.4501	−	14.1336i	−1.02150	−	0.615671i
$528$	−2.80684			−0.122152
$529$	17.6775	−	12.8434i	0.768586	−	0.558410i
$530$	3.36998	+	2.44843i	0.146382	+	0.106353i
$531$	−3.96112	+	12.1911i	−0.171898	+	0.529048i
$532$	−4.83508			−0.209627
$533$	−31.0914			−1.34672
$534$	−2.27078	+	6.98875i	−0.0982664	+	0.302433i
$535$	5.03663	+	15.5012i	0.217753	+	0.670174i
$536$	1.25993	+	3.87766i	0.0544205	+	0.167489i
$537$	−5.67708	+	4.12464i	−0.244984	+	0.177991i
$538$	6.89252	−	21.2130i	0.297158	−	0.914557i
$539$	−12.6863	+	9.21711i	−0.546436	+	0.397009i
$540$	0.809017	+	0.587785i	0.0348145	+	0.0252942i
$541$	−13.9616	−	42.9692i	−0.600254	−	1.84739i	−0.526609	−	0.850108i	$-0.676537\pi$
$541$	−13.9616	−	42.9692i	−0.600254	−	1.84739i	−0.0736449	−	0.997285i	$-0.523463\pi$
$542$	6.13692	+	4.45874i	0.263603	+	0.191519i
$543$	5.04955	+	3.66871i	0.216697	+	0.157439i
$544$	1.51962	+	4.67692i	0.0651534	+	0.200521i
$545$	−11.3486	−	8.24527i	−0.486122	−	0.353188i
$546$	−2.40095	+	1.74439i	−0.102751	+	0.0746530i
$547$	7.45668	−	22.9493i	0.318825	−	0.981242i	−0.655327	−	0.755346i	$-0.727469\pi$
$547$	7.45668	−	22.9493i	0.318825	−	0.981242i	0.974151	−	0.225896i	$-0.0725310\pi$
$548$	−11.3095	+	8.21685i	−0.483119	+	0.351007i
$549$	3.19941	+	9.84676i	0.136547	+	0.420250i
$550$	−0.867362	−	2.66946i	−0.0369844	−	0.113826i
$551$	8.54134	−	26.2875i	0.363873	−	1.11989i
$552$	1.07212			0.0456324
$553$	−18.6950			−0.794994
$554$	4.22379	−	12.9995i	0.179452	−	0.552295i
$555$	−3.88403	−	2.82191i	−0.164868	−	0.119783i
$556$	1.72887	−	1.25610i	0.0733205	−	0.0532705i
$557$	−33.4285			−1.41641			−0.708205	−	0.706006i	$-0.750495\pi$
$557$	−33.4285			−1.41641			−0.708205	+	0.706006i	$0.750495\pi$
$558$	5.54723	−	0.477730i	0.234833	−	0.0202239i
$559$	−27.0729			−1.14506
$560$	0.961766	−	0.698764i	0.0406420	−	0.0295282i
$561$	11.1668	+	8.11317i	0.471464	+	0.342538i
$562$	−3.03918	+	9.35363i	−0.128200	+	0.394559i
$563$	8.01273			0.337696			0.168848	−	0.985642i	$-0.445995\pi$
$563$	8.01273			0.337696			0.168848	+	0.985642i	$0.445995\pi$
$564$	9.69158			0.408089
$565$	4.03294	−	12.4121i	0.169667	−	0.522181i
$566$	2.50552	+	7.71119i	0.105315	+	0.324126i
$567$	0.367362	+	1.13062i	0.0154277	+	0.0474817i
$568$	−11.3903	+	8.27557i	−0.477928	+	0.347235i
$569$	7.48154	−	23.0258i	0.313642	−	0.965292i	−0.662667	−	0.748914i	$-0.730576\pi$
$569$	7.48154	−	23.0258i	0.313642	−	0.965292i	0.976310	−	0.216378i	$-0.0694244\pi$
$570$	−3.29041	+	2.39062i	−0.137820	+	0.100132i
$571$	−20.8619	−	15.1571i	−0.873044	−	0.634303i	0.0583584	−	0.998296i	$-0.481413\pi$
$571$	−20.8619	−	15.1571i	−0.873044	−	0.634303i	−0.931402	+	0.363992i	$0.881413\pi$
$572$	−2.16528	−	6.66404i	−0.0905348	−	0.278637i
$573$	13.9465	+	10.1327i	0.582622	+	0.423300i
$574$	11.9784	+	8.70278i	0.499967	+	0.363247i
$575$	0.331303	+	1.01964i	0.0138163	+	0.0425221i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	1.61464	−	1.17310i	0.0672182	−	0.0488369i	−0.553669	−	0.832737i	$-0.686773\pi$
$577$	1.61464	−	1.17310i	0.0672182	−	0.0488369i	0.620887	+	0.783900i	$0.286773\pi$
$578$	2.21963	−	6.83133i	0.0923245	−	0.284146i
$579$	−3.92043	+	2.84836i	−0.162928	+	0.118374i
$580$	2.10007	+	6.46335i	0.0872007	+	0.268376i
$581$	−5.22871	−	16.0923i	−0.216924	−	0.667622i
$582$	−0.377714	+	1.16248i	−0.0156568	+	0.0481865i
$583$	−11.6920			−0.484231
$584$	6.42760			0.265976
$585$	−0.771428	+	2.37421i	−0.0318946	+	0.0981616i
$586$	−4.52256	−	3.28583i	−0.186825	−	0.135736i
$587$	−7.54163	+	5.47931i	−0.311276	+	0.226155i	−0.732444	−	0.680827i	$-0.761620\pi$
$587$	−7.54163	+	5.47931i	−0.311276	+	0.226155i	0.421168	+	0.906983i	$0.361620\pi$
$588$	−5.58674			−0.230393
$589$	−5.12398	+	22.0577i	−0.211130	+	0.908872i
$590$	12.8185			0.527727
$591$	18.7259	−	13.6052i	0.770282	−	0.559643i
$592$	3.88403	+	2.82191i	0.159632	+	0.115980i
$593$	−0.521616	+	1.60537i	−0.0214202	+	0.0659246i	−0.961195	−	0.275869i	$-0.911034\pi$
$593$	−0.521616	+	1.60537i	−0.0214202	+	0.0659246i	0.939775	+	0.341794i	$0.111034\pi$
$594$	−2.80684			−0.115166
$595$	−5.84609			−0.239666
$596$	0.0887720	−	0.273212i	0.00363624	−	0.0111912i
$597$	2.52855	+	7.78208i	0.103487	+	0.318499i
$598$	0.827062	+	2.54543i	0.0338211	+	0.104091i
$599$	15.7101	−	11.4140i	0.641895	−	0.466364i	−0.218605	−	0.975813i	$-0.570151\pi$
$599$	15.7101	−	11.4140i	0.641895	−	0.466364i	0.860501	+	0.509449i	$0.170151\pi$
$600$	0.309017	−	0.951057i	0.0126156	−	0.0388267i
$601$	18.5575	−	13.4828i	0.756975	−	0.549974i	−0.141006	−	0.990009i	$-0.545034\pi$
$601$	18.5575	−	13.4828i	0.756975	−	0.549974i	0.897981	+	0.440034i	$0.145034\pi$
$602$	10.4302	+	7.57795i	0.425101	+	0.308854i
$603$	1.25993	+	3.87766i	0.0513082	+	0.157910i
$604$	−0.246108	−	0.178808i	−0.0100140	−	0.00727559i
$605$	−2.52546	−	1.83485i	−0.102675	−	0.0745974i
$606$	4.69034	+	14.4354i	0.190532	+	0.586397i
$607$	35.3444	+	25.6792i	1.43459	+	1.04229i	0.989140	+	0.146979i	$0.0469549\pi$
$607$	35.3444	+	25.6792i	1.43459	+	1.04229i	0.445446	+	0.895309i	$0.353045\pi$
$608$	3.29041	−	2.39062i	0.133444	−	0.0969525i
$609$	−2.49658	+	7.68368i	−0.101166	+	0.311358i
$610$	8.37615	−	6.08563i	0.339141	−	0.246400i
$611$	7.47636	+	23.0099i	0.302461	+	0.930880i
$612$	1.51962	+	4.67692i	0.0614272	+	0.189053i
$613$	7.89329	−	24.2930i	0.318807	−	0.981187i	−0.655352	−	0.755324i	$-0.727480\pi$
$613$	7.89329	−	24.2930i	0.318807	−	0.981187i	0.974159	−	0.225863i	$-0.0725203\pi$
$614$	−28.1457			−1.13587
$615$	12.4545			0.502216
$616$	−1.03113	+	3.17348i	−0.0415453	+	0.127863i
$617$	−28.6242	−	20.7967i	−1.15237	−	0.837245i	−0.163574	−	0.986531i	$-0.552302\pi$
$617$	−28.6242	−	20.7967i	−1.15237	−	0.837245i	−0.988794	+	0.149286i	$0.952302\pi$
$618$	1.24551	−	0.904916i	0.0501017	−	0.0364010i
$619$	11.7185			0.471007			0.235504	−	0.971873i	$-0.424326\pi$
$619$	11.7185			0.471007			0.235504	+	0.971873i	$0.424326\pi$
$620$	−2.16854	−	5.12810i	−0.0870906	−	0.205950i
$621$	1.07212			0.0430226
$622$	−26.4855	+	19.2429i	−1.06197	+	0.771569i
$623$	7.06744	+	5.13480i	0.283151	+	0.205721i
$624$	0.771428	−	2.37421i	0.0308818	−	0.0950445i
$625$	1.00000			0.0400000
$626$	−7.99307			−0.319467
$627$	3.52771	−	10.8572i	0.140883	−	0.433593i
$628$	−3.21218	−	9.88608i	−0.128180	−	0.394497i
$629$	−7.29560	−	22.4535i	−0.290895	−	0.895281i
$630$	0.961766	−	0.698764i	0.0383177	−	0.0278394i
$631$	−3.94724	+	12.1484i	−0.157137	+	0.483619i	−0.998371	−	0.0570527i	$-0.981830\pi$
$631$	−3.94724	+	12.1484i	−0.157137	+	0.483619i	0.841234	+	0.540671i	$0.181830\pi$
$632$	12.7225	−	9.24344i	0.506074	−	0.367684i
$633$	12.6055	+	9.15842i	0.501023	+	0.364015i
$634$	−5.20684	−	16.0250i	−0.206790	−	0.636435i
$635$	0.333918	+	0.242606i	0.0132511	+	0.00962751i
$636$	−3.36998	−	2.44843i	−0.133628	−	0.0970866i
$637$	−4.30977	−	13.2641i	−0.170759	−	0.525543i
$638$	−15.4322	−	11.2121i	−0.610965	−	0.443892i
$639$	−11.3903	+	8.27557i	−0.450595	+	0.327376i
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−16.4179	+	11.9283i	−0.648469	+	0.471140i	−0.862749	−	0.505632i	$-0.831259\pi$
$641$	−16.4179	+	11.9283i	−0.648469	+	0.471140i	0.214281	+	0.976772i	$0.431259\pi$
$642$	−5.03663	−	15.5012i	−0.198780	−	0.611782i
$643$	−13.3170	−	40.9854i	−0.525170	−	1.61631i	−0.763980	−	0.645240i	$-0.776757\pi$
$643$	−13.3170	−	40.9854i	−0.525170	−	1.61631i	0.238810	−	0.971066i	$-0.423243\pi$
$644$	0.393855	−	1.21216i	0.0155201	−	0.0477659i
$645$	10.8448			0.427014
$646$	−20.0007			−0.786919
$647$	−2.72153	+	8.37602i	−0.106995	+	0.329295i	−0.990193	−	0.139703i	$-0.955385\pi$
$647$	−2.72153	+	8.37602i	−0.106995	+	0.329295i	0.883199	+	0.468999i	$0.155385\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−29.1079	+	21.1481i	−1.14259	+	0.830137i
$650$	2.49639			0.0979166
$651$	1.49771	−	6.44733i	0.0586998	−	0.252691i
$652$	14.8757			0.582578
$653$	21.0747	−	15.3117i	0.824716	−	0.599191i	−0.0933434	−	0.995634i	$-0.529755\pi$
$653$	21.0747	−	15.3117i	0.824716	−	0.599191i	0.918059	+	0.396443i	$0.129755\pi$
$654$	11.3486	+	8.24527i	0.443767	+	0.322415i
$655$	−4.51449	+	13.8942i	−0.176396	+	0.542890i
$656$	−12.4545			−0.486268
$657$	6.42760			0.250764
$658$	3.56032	−	10.9575i	0.138796	−	0.427169i
$659$	0.810154	+	2.49340i	0.0315591	+	0.0971289i	0.965595	−	0.260049i	$-0.0837388\pi$
$659$	0.810154	+	2.49340i	0.0315591	+	0.0971289i	−0.934036	+	0.357178i	$0.883739\pi$
$660$	0.867362	+	2.66946i	0.0337620	+	0.103909i
$661$	−0.776992	+	0.564518i	−0.0302215	+	0.0219572i	−0.602793	−	0.797897i	$-0.705946\pi$
$661$	−0.776992	+	0.564518i	−0.0302215	+	0.0219572i	0.572572	+	0.819854i	$0.305946\pi$
$662$	−5.58784	+	17.1976i	−0.217178	+	0.668404i
$663$	−9.93173	+	7.21582i	−0.385716	+	0.280239i
$664$	11.5149	+	8.36603i	0.446863	+	0.324665i
$665$	1.49412	+	4.59843i	0.0579396	+	0.178320i
$666$	3.88403	+	2.82191i	0.150503	+	0.109347i
$667$	5.89456	+	4.28265i	0.228238	+	0.165825i
$668$	5.08334	+	15.6449i	0.196680	+	0.605319i
$669$	0.461626	+	0.335391i	0.0178475	+	0.0129670i
$670$	3.29853	−	2.39652i	0.127433	−	0.0925858i
$671$	−8.98023	+	27.6383i	−0.346678	+	1.06696i
$672$	−0.961766	+	0.698764i	−0.0371009	+	0.0269554i
$673$	−3.36269	−	10.3493i	−0.129622	−	0.398936i	0.865093	−	0.501612i	$-0.167259\pi$
$673$	−3.36269	−	10.3493i	−0.129622	−	0.398936i	−0.994715	+	0.102676i	$0.967259\pi$
$674$	−9.76621	−	30.0573i	−0.376180	−	1.15776i
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$	−6.76802			−0.260308
$677$	45.4855			1.74815			0.874074	−	0.485793i	$-0.161469\pi$
$677$	45.4855			1.74815			0.874074	+	0.485793i	$0.161469\pi$
$678$	−4.03294	+	12.4121i	−0.154884	+	0.476684i
$679$	1.17557	+	0.854105i	0.0451144	+	0.0327775i
$680$	3.97843	−	2.89050i	0.152566	−	0.110846i
$681$	3.80175			0.145683
$682$	13.3847	+	8.06711i	0.512528	+	0.308906i
$683$	−20.9623			−0.802099			−0.401049	−	0.916056i	$-0.631354\pi$
$683$	−20.9623			−0.802099			−0.401049	+	0.916056i	$0.631354\pi$
$684$	3.29041	−	2.39062i	0.125812	−	0.0914077i
$685$	11.3095	+	8.21685i	0.432115	+	0.313950i
$686$	−4.62389	+	14.2309i	−0.176541	+	0.543337i
$687$	−4.54860			−0.173540
$688$	−10.8448			−0.413454
$689$	3.21340	−	9.88983i	0.122421	−	0.376772i
$690$	−0.331303	−	1.01964i	−0.0126125	−	0.0388172i
$691$	−8.72817	−	26.8625i	−0.332035	−	1.02190i	−0.968164	−	0.250316i	$-0.919465\pi$
$691$	−8.72817	−	26.8625i	−0.332035	−	1.02190i	0.636129	−	0.771583i	$-0.280535\pi$
$692$	11.0587	−	8.03461i	0.420388	−	0.305430i
$693$	−1.03113	+	3.17348i	−0.0391692	+	0.120551i
$694$	3.06846	−	2.22937i	0.116477	−	0.0846256i
$695$	−1.72887	−	1.25610i	−0.0655799	−	0.0476466i
$696$	−2.10007	−	6.46335i	−0.0796029	−	0.244993i
$697$	49.5495	+	35.9998i	1.87682	+	1.36359i
$698$	−19.9653	−	14.5056i	−0.755698	−	0.549047i
$699$	−3.90465	−	12.0173i	−0.147687	−	0.454535i
$700$	−0.961766	−	0.698764i	−0.0363513	−	0.0264108i
$701$	4.04967	−	2.94226i	0.152954	−	0.111128i	−0.508676	−	0.860958i	$-0.669865\pi$
$701$	4.04967	−	2.94226i	0.152954	−	0.111128i	0.661630	+	0.749830i	$0.269865\pi$
$702$	0.771428	−	2.37421i	0.0291157	−	0.0896088i
$703$	−15.7970	+	11.4772i	−0.595794	+	0.432870i
$704$	−0.867362	−	2.66946i	−0.0326899	−	0.100609i
$705$	−2.99486	−	9.21724i	−0.112793	−	0.347141i
$706$	2.28091	−	7.01990i	0.0858430	−	0.264198i
$707$	18.0440			0.678615
$708$	−12.8185			−0.481747
$709$	6.27828	−	19.3226i	0.235786	−	0.725674i	−0.761230	−	0.648482i	$-0.775404\pi$
$709$	6.27828	−	19.3226i	0.235786	−	0.725674i	0.997016	−	0.0771928i	$-0.0245957\pi$
$710$	11.3903	+	8.27557i	0.427472	+	0.310577i
$711$	12.7225	−	9.24344i	0.477131	−	0.346656i
$712$	−7.34841			−0.275393
$713$	−5.11251	−	3.08136i	−0.191465	−	0.115398i
$714$	5.84609			0.218784
$715$	−5.66877	+	4.11860i	−0.212000	+	0.154027i
$716$	−5.67708	−	4.12464i	−0.212162	−	0.154145i
$717$	−4.87926	+	15.0168i	−0.182219	+	0.560813i
$718$	28.3054			1.05635
$719$	−42.9510			−1.60180			−0.800902	−	0.598796i	$-0.795646\pi$
$719$	−42.9510			−1.60180			−0.800902	+	0.598796i	$0.795646\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	−0.565566	−	1.74063i	−0.0210628	−	0.0648246i
$722$	−0.759610	−	2.33784i	−0.0282698	−	0.0870054i
$723$	−6.43582	+	4.67590i	−0.239351	+	0.173898i
$724$	−1.92876	+	5.93610i	−0.0716816	+	0.220613i
$725$	5.49805	−	3.99457i	0.204193	−	0.148355i
$726$	2.52546	+	1.83485i	0.0937286	+	0.0680978i
$727$	6.89645	+	21.2251i	0.255775	+	0.787195i	0.993676	+	0.112286i	$0.0358172\pi$
$727$	6.89645	+	21.2251i	0.255775	+	0.787195i	−0.737901	+	0.674909i	$0.764183\pi$
$728$	−2.40095	−	1.74439i	−0.0889850	−	0.0646514i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−1.98624	−	6.11301i	−0.0735139	−	0.226253i
$731$	43.1453	+	31.3469i	1.59579	+	1.15941i
$732$	−8.37615	+	6.08563i	−0.309592	+	0.224931i
$733$	−5.31275	+	16.3510i	−0.196231	+	0.603937i	0.803729	+	0.594996i	$0.202846\pi$
$733$	−5.31275	+	16.3510i	−0.196231	+	0.603937i	−0.999960	+	0.00894154i	$0.997154\pi$
$734$	−9.89550	+	7.18950i	−0.365249	+	0.265369i
$735$	1.72640	+	5.31330i	0.0636791	+	0.195984i
$736$	0.331303	+	1.01964i	0.0122120	+	0.0375846i
$737$	−3.53641	+	10.8840i	−0.130266	+	0.400916i
$738$	−12.4545			−0.458458
$739$	−33.6424			−1.23755			−0.618777	−	0.785567i	$-0.712372\pi$
$739$	−33.6424			−1.23755			−0.618777	+	0.785567i	$0.712372\pi$
$740$	1.48357	−	4.56595i	0.0545370	−	0.167848i
$741$	8.21415	+	5.96793i	0.301754	+	0.219237i
$742$	−4.00625	+	2.91071i	−0.147074	+	0.106856i
$743$	−4.22378			−0.154956			−0.0774778	−	0.996994i	$-0.524687\pi$
$743$	−4.22378			−0.154956			−0.0774778	+	0.996994i	$0.524687\pi$
$744$	2.16854	+	5.12810i	0.0795024	+	0.188005i
$745$	−0.287272			−0.0105248
$746$	−17.3296	+	12.5907i	−0.634483	+	0.460979i
$747$	11.5149	+	8.36603i	0.421307	+	0.306097i
$748$	−4.26535	+	13.1274i	−0.155957	+	0.479985i
$749$	−19.3762			−0.707992
$750$	−1.00000			−0.0365148
$751$	9.55232	−	29.3990i	0.348569	−	1.07279i	−0.611076	−	0.791572i	$-0.709263\pi$
$751$	9.55232	−	29.3990i	0.348569	−	1.07279i	0.959645	−	0.281214i	$-0.0907370\pi$
$752$	2.99486	+	9.21724i	0.109211	+	0.336118i
$753$	5.25034	+	16.1589i	0.191333	+	0.588863i
$754$	13.7253	−	9.97202i	0.499846	−	0.363160i
$755$	−0.0940048	+	0.289317i	−0.00342119	+	0.0105293i
$756$	−0.961766	+	0.698764i	−0.0349791	+	0.0254138i
$757$	17.7196	+	12.8740i	0.644030	+	0.467915i	0.861232	−	0.508211i	$-0.169693\pi$
$757$	17.7196	+	12.8740i	0.644030	+	0.467915i	−0.217202	+	0.976127i	$0.569693\pi$
$758$	−7.79400	−	23.9875i	−0.283091	−	0.871264i
$759$	2.43455	+	1.76880i	0.0883685	+	0.0642034i
$760$	−3.29041	−	2.39062i	−0.119356	−	0.0867169i
$761$	1.35207	+	4.16124i	0.0490124	+	0.150845i	0.972567	−	0.232621i	$-0.0747303\pi$
$761$	1.35207	+	4.16124i	0.0490124	+	0.150845i	−0.923555	+	0.383466i	$0.874730\pi$
$762$	−0.333918	−	0.242606i	−0.0120966	−	0.00878868i
$763$	13.4913	−	9.80204i	0.488419	−	0.354858i
$764$	−5.32708	+	16.3951i	−0.192727	+	0.593153i
$765$	3.97843	−	2.89050i	0.143840	−	0.104506i
$766$	−1.24102	−	3.81946i	−0.0448398	−	0.138003i
$767$	−9.88851	−	30.4337i	−0.357054	−	1.09890i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	−52.7621			−1.90265			−0.951325	−	0.308188i	$-0.900277\pi$
$769$	−52.7621			−1.90265			−0.951325	+	0.308188i	$0.900277\pi$
$770$	3.33679			0.120250
$771$	−8.87031	+	27.3000i	−0.319456	+	0.983185i
$772$	−3.92043	−	2.84836i	−0.141099	−	0.102515i
$773$	5.33251	−	3.87430i	0.191797	−	0.139349i	−0.487743	−	0.872987i	$-0.662180\pi$
$773$	5.33251	−	3.87430i	0.191797	−	0.139349i	0.679540	+	0.733639i	$0.262180\pi$
$774$	−10.8448			−0.389808
$775$	−4.20700	+	3.64707i	−0.151120	+	0.131007i
$776$	−1.22231			−0.0438783
$777$	4.61736	−	3.35471i	0.165647	−	0.120349i
$778$	−29.5929	−	21.5005i	−1.06096	−	0.770829i
$779$	15.6532	−	48.1755i	0.560833	−	1.72607i
$780$	−2.49639			−0.0893852
$781$	−39.5182			−1.41407
$782$	1.62922	−	5.01422i	0.0582607	−	0.179308i
$783$	−2.10007	−	6.46335i	−0.0750504	−	0.230981i
$784$	−1.72640	−	5.31330i	−0.0616570	−	0.189761i
$785$	−8.40960	+	6.10993i	−0.300151	+	0.218073i
$786$	4.51449	−	13.8942i	0.161026	−	0.495589i
$787$	10.4672	−	7.60485i	0.373115	−	0.271084i	−0.385387	−	0.922755i	$-0.625932\pi$
$787$	10.4672	−	7.60485i	0.373115	−	0.271084i	0.758501	+	0.651672i	$0.225932\pi$
$788$	18.7259	+	13.6052i	0.667084	+	0.484665i
$789$	0.300832	+	0.925866i	0.0107099	+	0.0329617i
$790$	−12.7225	−	9.24344i	−0.452646	−	0.328867i
$791$	12.5519	+	9.11947i	0.446293	+	0.324251i
$792$	−0.867362	−	2.66946i	−0.0308204	−	0.0948553i
$793$	−20.9102	−	15.1921i	−0.742542	−	0.539489i
$794$	−16.9633	+	12.3246i	−0.602005	+	0.437382i
$795$	−1.28722	+	3.96165i	−0.0456529	+	0.140505i
$796$	−6.61983	+	4.80959i	−0.234634	+	0.170471i
$797$	−14.8070	−	45.5714i	−0.524493	−	1.61422i	−0.765317	−	0.643653i	$-0.777418\pi$
$797$	−14.8070	−	45.5714i	−0.524493	−	1.61422i	0.240825	−	0.970569i	$-0.422582\pi$
$798$	−1.49412	−	4.59843i	−0.0528913	−	0.162783i
$799$	14.7276	−	45.3268i	0.521024	−	1.60355i
$800$	1.00000			0.0353553
$801$	−7.34841			−0.259643
$802$	6.68722	−	20.5811i	0.236134	−	0.726745i
$803$	14.5957	+	10.6044i	0.515070	+	0.374220i
$804$	−3.29853	+	2.39652i	−0.116330	+	0.0845188i
$805$	−1.27454			−0.0449217
$806$	−10.5023	+	9.10453i	−0.369929	+	0.320693i
$807$	22.3047			0.785161
$808$	−12.2795	+	8.92155i	−0.431990	+	0.313859i
$809$	8.94013	+	6.49538i	0.314318	+	0.228366i	0.733747	−	0.679423i	$-0.237770\pi$
$809$	8.94013	+	6.49538i	0.314318	+	0.228366i	−0.419429	+	0.907788i	$0.637770\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−27.2730			−0.957683			−0.478842	−	0.877901i	$-0.658943\pi$
$811$	−27.2730			−0.957683			−0.478842	+	0.877901i	$0.658943\pi$
$812$	−8.07910			−0.283521
$813$	−2.34410	+	7.21439i	−0.0822110	+	0.253020i
$814$	4.16413	+	12.8159i	0.145953	+	0.449197i
$815$	−4.59685	−	14.1477i	−0.161021	−	0.495571i
$816$	−3.97843	+	2.89050i	−0.139273	+	0.101188i
$817$	13.6300	−	41.9488i	0.476853	−	1.46760i
$818$	−24.6656	+	17.9206i	−0.862414	+	0.626580i
$819$	−2.40095	−	1.74439i	−0.0838958	−	0.0609539i
$820$	3.84867	+	11.8450i	0.134401	+	0.413644i
$821$	−31.3976	−	22.8117i	−1.09578	−	0.796134i	−0.115418	−	0.993317i	$-0.536821\pi$
$821$	−31.3976	−	22.8117i	−1.09578	−	0.796134i	−0.980367	+	0.197183i	$0.936821\pi$
$822$	−11.3095	−	8.21685i	−0.394465	−	0.286596i
$823$	−6.06206	−	18.6571i	−0.211310	−	0.650346i	−0.999395	−	0.0347793i	$-0.988927\pi$
$823$	−6.06206	−	18.6571i	−0.211310	−	0.650346i	0.788085	−	0.615567i	$-0.211073\pi$
$824$	1.24551	+	0.904916i	0.0433894	+	0.0315242i
$825$	2.27078	−	1.64982i	0.0790585	−	0.0574394i
$826$	−4.70901	+	14.4928i	−0.163847	+	0.504270i
$827$	−6.07760	+	4.41564i	−0.211339	+	0.153547i	−0.688419	−	0.725313i	$-0.741695\pi$
$827$	−6.07760	+	4.41564i	−0.211339	+	0.153547i	0.477080	+	0.878860i	$0.341695\pi$
$828$	0.331303	+	1.01964i	0.0115136	+	0.0354351i
$829$	7.58217	+	23.3355i	0.263340	+	0.810476i	0.992071	+	0.125677i	$0.0401102\pi$
$829$	7.58217	+	23.3355i	0.263340	+	0.810476i	−0.728732	+	0.684799i	$0.759890\pi$
$830$	4.39828	−	13.5365i	0.152667	−	0.469860i
$831$	13.6685			0.474154
$832$	2.49639			0.0865469
$833$	−8.48974	+	26.1287i	−0.294152	+	0.905307i
$834$	1.72887	+	1.25610i	0.0598659	+	0.0434952i
$835$	13.3083	−	9.66908i	0.460554	−	0.334612i
$836$	11.4159			0.394827
$837$	2.16854	+	5.12810i	0.0749556	+	0.177253i
$838$	5.24312			0.181121
$839$	10.6776	−	7.75771i	0.368630	−	0.267826i	−0.388012	−	0.921654i	$-0.626838\pi$
$839$	10.6776	−	7.75771i	0.368630	−	0.267826i	0.756643	+	0.653828i	$0.226838\pi$
$840$	0.961766	+	0.698764i	0.0331841	+	0.0241096i
$841$	5.31052	−	16.3441i	0.183121	−	0.563589i
$842$	19.5335			0.673171
$843$	−9.83499			−0.338735
$844$	−4.81487	+	14.8186i	−0.165735	+	0.510079i
$845$	2.09143	+	6.43677i	0.0719475	+	0.221432i
$846$	2.99486	+	9.21724i	0.102966	+	0.316895i
$847$	3.00229	−	2.18129i	0.103160	−	0.0749500i
$848$	1.28722	−	3.96165i	0.0442032	−	0.136043i
$849$	−6.55953	+	4.76578i	−0.225123	+	0.163561i
$850$	−3.97843	−	2.89050i	−0.136459	−	0.0991433i
$851$	−1.59056	−	4.89523i	−0.0545236	−	0.167806i
$852$	−11.3903	−	8.27557i	−0.390227	−	0.283516i
$853$	−41.3809	−	30.0650i	−1.41686	−	1.02941i	−0.992280	−	0.124014i	$-0.960423\pi$
$853$	−41.3809	−	30.0650i	−1.41686	−	1.02941i	−0.424576	−	0.905392i	$-0.639577\pi$
$854$	3.80348	+	11.7059i	0.130152	+	0.400568i
$855$	−3.29041	−	2.39062i	−0.112530	−	0.0817575i
$856$	13.1861	−	9.58024i	0.450691	−	0.327446i
$857$	−2.56928	+	7.90743i	−0.0877650	+	0.270113i	−0.985301	−	0.170829i	$-0.945355\pi$
$857$	−2.56928	+	7.90743i	−0.0877650	+	0.270113i	0.897536	+	0.440942i	$0.145355\pi$
$858$	5.66877	−	4.11860i	0.193529	−	0.140607i
$859$	−1.90767	−	5.87121i	−0.0650889	−	0.200323i	0.913223	−	0.407460i	$-0.133585\pi$
$859$	−1.90767	−	5.87121i	−0.0650889	−	0.200323i	−0.978312	+	0.207137i	$0.933585\pi$
$860$	3.35123	+	10.3140i	0.114276	+	0.351705i
$861$	−4.57532	+	14.0814i	−0.155927	+	0.479893i
$862$	−5.78550			−0.197055
$863$	−25.6051			−0.871607			−0.435803	−	0.900042i	$-0.643536\pi$
$863$	−25.6051			−0.871607			−0.435803	+	0.900042i	$0.643536\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−11.0587	−	8.03461i	−0.376007	−	0.273185i
$866$	−4.75229	+	3.45274i	−0.161489	+	0.117329i
$867$	7.18288			0.243943
$868$	6.59459	−	0.567929i	0.223835	−	0.0192768i
$869$	44.1401			1.49735
$870$	−5.49805	+	3.99457i	−0.186402	+	0.135429i
$871$	−8.23443	−	5.98266i	−0.279013	−	0.202715i
$872$	−4.33479	+	13.3411i	−0.146795	+	0.451787i
$873$	−1.22231			−0.0413689
$874$	−4.36048			−0.147496
$875$	−0.367362	+	1.13062i	−0.0124191	+	0.0382220i
$876$	1.98624	+	6.11301i	0.0671087	+	0.206539i
$877$	−9.84658	−	30.3046i	−0.332495	−	1.02332i	−0.967943	−	0.251171i	$-0.919184\pi$
$877$	−9.84658	−	30.3046i	−0.332495	−	1.02332i	0.635447	−	0.772144i	$-0.280816\pi$
$878$	11.4868	−	8.34568i	0.387662	−	0.281653i
$879$	1.72746	−	5.31658i	0.0582659	−	0.179324i
$880$	−2.27078	+	1.64982i	−0.0765481	+	0.0556154i
$881$	−9.07364	−	6.59239i	−0.305699	−	0.222103i	0.424350	−	0.905498i	$-0.360503\pi$
$881$	−9.07364	−	6.59239i	−0.305699	−	0.222103i	−0.730049	+	0.683395i	$0.760503\pi$
$882$	−1.72640	−	5.31330i	−0.0581308	−	0.178908i
$883$	38.7248	+	28.1352i	1.30319	+	0.946825i	0.999981	−	0.00609796i	$-0.00194105\pi$
$883$	38.7248	+	28.1352i	1.30319	+	0.946825i	0.303212	+	0.952923i	$0.401941\pi$
$884$	−9.93173	−	7.21582i	−0.334040	−	0.242694i
$885$	3.96112	+	12.1911i	0.133152	+	0.409798i
$886$	27.8264	+	20.2170i	0.934845	+	0.679205i
$887$	−4.74715	+	3.44901i	−0.159394	+	0.115806i	−0.664623	−	0.747179i	$-0.731408\pi$
$887$	−4.74715	+	3.44901i	−0.159394	+	0.115806i	0.505229	+	0.862985i	$0.331408\pi$
$888$	−1.48357	+	4.56595i	−0.0497852	+	0.153223i
$889$	−0.396964	+	0.288411i	−0.0133138	+	0.00967301i
$890$	2.27078	+	6.98875i	0.0761168	+	0.234263i
$891$	−0.867362	−	2.66946i	−0.0290577	−	0.0894304i
$892$	−0.176325	+	0.542673i	−0.00590381	+	0.0181701i
$893$	−39.4173			−1.31905
$894$	0.287272			0.00960782
$895$	−2.16845	+	6.67381i	−0.0724833	+	0.223081i
$896$	−0.961766	−	0.698764i	−0.0321303	−	0.0233441i
$897$	−2.16528	+	1.57317i	−0.0722965	+	0.0525265i
$898$	−22.6893			−0.757152
$899$	−8.56183	+	36.8570i	−0.285553	+	1.22925i
$900$	1.00000			0.0333333
$901$	−16.5722	+	12.0404i	−0.552101	+	0.401125i
$902$	−28.2816	−	20.5478i	−0.941673	−	0.684165i
$903$	−3.98396	+	12.2614i	−0.132578	+	0.408033i
$904$	−13.0509			−0.434065
$905$	6.24158			0.207477
$906$	0.0940048	−	0.289317i	0.00312310	−	0.00961192i
$907$	−1.42601	−	4.38882i	−0.0473500	−	0.145728i	0.924586	−	0.380973i	$-0.124411\pi$
$907$	−1.42601	−	4.38882i	−0.0473500	−	0.145728i	−0.971936	+	0.235245i	$0.924411\pi$
$908$	1.17481	+	3.61568i	0.0389873	+	0.119991i
$909$	−12.2795	+	8.92155i	−0.407284	+	0.295909i
$910$	−0.917080	+	2.82248i	−0.0304009	+	0.0935643i
$911$	−37.5394	+	27.2740i	−1.24374	+	0.903628i	−0.997841	−	0.0656688i	$-0.979082\pi$
$911$	−37.5394	+	27.2740i	−1.24374	+	0.903628i	−0.245895	+	0.969296i	$0.579082\pi$
$912$	3.29041	+	2.39062i	0.108956	+	0.0791614i
$913$	12.3453	+	37.9949i	0.408569	+	1.25745i
$914$	−17.2316	−	12.5195i	−0.569970	−	0.414107i
$915$	8.37615	+	6.08563i	0.276907	+	0.201185i
$916$	−1.40560	−	4.32598i	−0.0464422	−	0.142934i
$917$	−14.0506	−	10.2084i	−0.463992	−	0.337110i
$918$	−3.97843	+	2.89050i	−0.131308	+	0.0954007i
$919$	−15.6749	+	48.2423i	−0.517067	+	1.59137i	0.262423	+	0.964953i	$0.415478\pi$
$919$	−15.6749	+	48.2423i	−0.517067	+	1.59137i	−0.779490	+	0.626415i	$0.784522\pi$
$920$	0.867362	−	0.630175i	0.0285961	−	0.0207763i
$921$	−8.69749	−	26.7681i	−0.286592	−	0.882040i
$922$	3.07702	+	9.47011i	0.101336	+	0.311881i
$923$	10.8611	−	33.4271i	0.357498	−	1.10027i
$924$	−3.33679			−0.109772
$925$	−4.80092			−0.157853
$926$	6.94250	−	21.3668i	0.228145	−	0.702157i
$927$	1.24551	+	0.904916i	0.0409079	+	0.0297213i
$928$	5.49805	−	3.99457i	0.180482	−	0.131128i
$929$	−7.64140			−0.250706			−0.125353	−	0.992112i	$-0.540006\pi$
$929$	−7.64140			−0.250706			−0.125353	+	0.992112i	$0.540006\pi$
$930$	4.20700	−	3.64707i	0.137953	−	0.119592i
$931$	22.7222			0.744690
$932$	10.2225	−	7.42708i	0.334849	−	0.243282i
$933$	−26.4855	−	19.2429i	−0.867097	−	0.629983i
$934$	−3.68058	+	11.3277i	−0.120432	+	0.370652i
$935$	13.8030			0.451405
$936$	2.49639			0.0815972
$937$	−0.776439	+	2.38963i	−0.0253651	+	0.0780659i	−0.962938	−	0.269724i	$-0.913068\pi$
$937$	−0.776439	+	2.38963i	−0.0253651	+	0.0780659i	0.937573	+	0.347790i	$0.113068\pi$
$938$	1.49781	+	4.60979i	0.0489052	+	0.150515i
$939$	−2.46999	−	7.60186i	−0.0806052	−	0.248077i
$940$	7.84065	−	5.69657i	0.255734	−	0.185802i
$941$	5.76138	−	17.7317i	0.187816	−	0.578037i	−0.812170	−	0.583421i	$-0.801714\pi$
$941$	5.76138	−	17.7317i	0.187816	−	0.578037i	0.999986	+	0.00538403i	$0.00171380\pi$
$942$	8.40960	−	6.10993i	0.274000	−	0.199072i
$943$	10.8026	+	7.84854i	0.351781	+	0.255584i
$944$	−3.96112	−	12.1911i	−0.128923	−	0.396786i
$945$	0.961766	+	0.698764i	0.0312862	+	0.0227308i
$946$	−24.6262	−	17.8920i	−0.800666	−	0.581718i
$947$	6.24215	+	19.2114i	0.202843	+	0.624286i	0.999795	+	0.0202434i	$0.00644412\pi$
$947$	6.24215	+	19.2114i	0.202843	+	0.624286i	−0.796952	+	0.604042i	$0.793556\pi$
$948$	12.7225	+	9.24344i	0.413208	+	0.300213i
$949$	−12.9813	+	9.43149i	−0.421392	+	0.306159i
$950$	−1.25682	+	3.86811i	−0.0407767	+	0.125498i
$951$	13.6317	−	9.90400i	0.442038	−	0.321159i
$952$	1.80654	+	5.55996i	0.0585503	+	0.180199i
$953$	2.02078	+	6.21933i	0.0654596	+	0.201464i	0.978437	−	0.206547i	$-0.0662226\pi$
$953$	2.02078	+	6.21933i	0.0654596	+	0.201464i	−0.912977	+	0.408011i	$0.866223\pi$
$954$	1.28722	−	3.96165i	0.0416752	−	0.128263i
$955$	17.2388			0.557834
$956$	−15.7896			−0.510673
$957$	5.89456	−	18.1416i	0.190544	−	0.586435i
$958$	−2.04698	−	1.48722i	−0.0661349	−	0.0480498i
$959$	−13.4449	+	9.76826i	−0.434157	+	0.315433i
$960$	−1.00000			−0.0322749
$961$	4.39772	−	30.6865i	0.141862	−	0.989886i
$962$	−11.9850			−0.386411
$963$	13.1861	−	9.58024i	0.424915	−	0.308719i
$964$	−6.43582	−	4.67590i	−0.207284	−	0.150600i
$965$	−1.49747	+	4.60874i	−0.0482053	+	0.148361i
$966$	1.27454			0.0410077
$967$	−41.7673			−1.34315			−0.671573	−	0.740939i	$-0.734381\pi$
$967$	−41.7673			−1.34315			−0.671573	+	0.740939i	$0.734381\pi$
$968$	−0.964640	+	2.96886i	−0.0310047	+	0.0954227i
$969$	−6.18057	−	19.0218i	−0.198548	−	0.611069i
$970$	0.377714	+	1.16248i	0.0121277	+	0.0373251i
$971$	30.5314	−	22.1824i	0.979799	−	0.711866i	0.0221354	−	0.999755i	$-0.492954\pi$
$971$	30.5314	−	22.1824i	0.979799	−	0.711866i	0.957664	+	0.287889i	$0.0929535\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	2.05530	−	1.49326i	0.0658898	−	0.0478717i
$974$	−12.7463	−	9.26076i	−0.408419	−	0.296734i
$975$	0.771428	+	2.37421i	0.0247055	+	0.0760356i
$976$	−8.37615	−	6.08563i	−0.268114	−	0.194796i
$977$	23.0377	+	16.7379i	0.737043	+	0.535493i	0.891784	−	0.452462i	$-0.149454\pi$
$977$	23.0377	+	16.7379i	0.737043	+	0.535493i	−0.154741	+	0.987955i	$0.549454\pi$
$978$	4.59685	+	14.1477i	0.146991	+	0.452392i
$979$	−16.6866	−	12.1235i	−0.533307	−	0.387470i
$980$	−4.51976	+	3.28380i	−0.144379	+	0.104897i
$981$	−4.33479	+	13.3411i	−0.138399	+	0.425949i
$982$	5.63840	−	4.09654i	0.179929	−	0.130726i
$983$	7.94118	+	24.4404i	0.253284	+	0.779529i	0.994163	+	0.107890i	$0.0344094\pi$
$983$	7.94118	+	24.4404i	0.253284	+	0.779529i	−0.740878	+	0.671639i	$0.765591\pi$
$984$	−3.84867	−	11.8450i	−0.122691	−	0.377604i
$985$	7.15267	−	22.0137i	0.227903	−	0.701414i
$986$	−33.4199			−1.06431
$987$	11.5214			0.366731
$988$	−3.13753	+	9.65631i	−0.0998180	+	0.307208i
$989$	9.40636	+	6.83412i	0.299105	+	0.217313i
$990$	−2.27078	+	1.64982i	−0.0721702	+	0.0524347i
$991$	−48.1393			−1.52919			−0.764597	−	0.644508i	$-0.777062\pi$
$991$	−48.1393			−1.52919			−0.764597	+	0.644508i	$0.777062\pi$
$992$	−4.20700	+	3.64707i	−0.133572	+	0.115795i
$993$	−18.0826			−0.573835
$994$	−13.5409	+	9.83806i	−0.429492	+	0.312044i
$995$	6.61983	+	4.80959i	0.209863	+	0.152474i
$996$	−4.39828	+	13.5365i	−0.139365	+	0.428921i
$997$	−3.21362			−0.101776			−0.0508881	−	0.998704i	$-0.516205\pi$
$997$	−3.21362			−0.101776			−0.0508881	+	0.998704i	$0.516205\pi$
$998$	−23.7637			−0.752228
$999$	−1.48357	+	4.56595i	−0.0469379	+	0.144460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.c.481.3	✓	12
31.2	even	5	inner	930.2.n.c.901.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.c.481.3	✓	12	1.1	even	1	trivial
930.2.n.c.901.3	yes	12	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.367362 - 1.13062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(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} +(0.367362 - 1.13062i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(-0.867362 + 2.66946i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-2.01962 - 1.46734i) q^{13} +(0.367362 + 1.13062i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.51962 + 4.67692i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(3.29041 - 2.39062i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-0.961766 + 0.698764i) q^{21} +(-0.867362 - 2.66946i) q^{22} +(0.331303 + 1.01964i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +2.49639 q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.961766 - 0.698764i) q^{28} +(5.49805 - 3.99457i) q^{29} -1.00000 q^{30} +(-4.20700 + 3.64707i) q^{31} +1.00000 q^{32} +(2.27078 - 1.64982i) q^{33} +(-3.97843 - 2.89050i) q^{34} +(-0.367362 + 1.13062i) q^{35} +1.00000 q^{36} -4.80092 q^{37} +(-1.25682 + 3.86811i) q^{38} +(0.771428 + 2.37421i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(10.0759 - 7.32060i) q^{41} +(0.367362 - 1.13062i) q^{42} +(8.77363 - 6.37441i) q^{43} +(2.27078 + 1.64982i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(-0.867362 - 0.630175i) q^{46} +(-7.84065 - 5.69657i) q^{47} +(0.309017 + 0.951057i) q^{48} +(4.51976 + 3.28380i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(1.51962 - 4.67692i) q^{51} +(-2.01962 + 1.46734i) q^{52} +(1.28722 + 3.96165i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.867362 - 2.66946i) q^{55} +1.18881 q^{56} -4.06717 q^{57} +(-2.10007 + 6.46335i) q^{58} +(10.3703 + 7.53450i) q^{59} +(0.809017 - 0.587785i) q^{60} +10.3535 q^{61} +(1.25984 - 5.42336i) q^{62} +1.18881 q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.01962 + 1.46734i) q^{65} +(-0.867362 + 2.66946i) q^{66} +4.07721 q^{67} +4.91761 q^{68} +(0.331303 - 1.01964i) q^{69} +(-0.367362 - 1.13062i) q^{70} +(4.35072 + 13.3902i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(1.98624 - 6.11301i) q^{73} +(3.88403 - 2.82191i) q^{74} +(-0.809017 - 0.587785i) q^{75} +(-1.25682 - 3.86811i) q^{76} +(2.69952 + 1.96132i) q^{77} +(-2.01962 - 1.46734i) q^{78} +(-4.85956 - 14.9562i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.84867 + 11.8450i) q^{82} +(11.5149 - 8.36603i) q^{83} +(0.367362 + 1.13062i) q^{84} +(-1.51962 - 4.67692i) q^{85} +(-3.35123 + 10.3140i) q^{86} -6.79597 q^{87} -2.80684 q^{88} +(-2.27078 + 6.98875i) q^{89} +(0.809017 + 0.587785i) q^{90} +(-2.40095 + 1.74439i) q^{91} +1.07212 q^{92} +(5.54723 - 0.477730i) q^{93} +9.69158 q^{94} +(-3.29041 + 2.39062i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.377714 + 1.16248i) q^{97} -5.58674 q^{98} -2.80684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

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