LMFDB - Embedded newform 930.2.n.h.721.3

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 60 x^{13} + 480 x^{12} - 1202 x^{11} - 147 x^{10} - 2185 x^{9} + \cdots + 12851 $ x^16 - 4x^15 + 5x^14 - 60x^13 + 480x^12 - 1202x^11 - 147x^10 - 2185x^9 + 62400x^8 - 289745x^7 + 699483x^6 - 1042897x^5 + 1014415x^4 - 652345x^3 + 274580x^2 - 73519*x + 12851
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.3
Root			$-2.52433 - 4.00017i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.h.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.170108 + 0.123590i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.170108 + 0.123590i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(3.26921 + 2.37522i) q^{11} +(0.309017 - 0.951057i) q^{12} +(1.56012 + 4.80156i) q^{13} +(-0.170108 + 0.123590i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.78750 - 3.47832i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(1.30416 - 4.01380i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.0649753 + 0.199974i) q^{21} +(-3.26921 + 2.37522i) q^{22} +(-5.69368 + 4.13670i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -5.04866 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.0649753 - 0.199974i) q^{28} +(-2.77791 + 8.54953i) q^{29} +1.00000 q^{30} +(-2.91039 - 4.74654i) q^{31} -1.00000 q^{32} +(-1.24873 + 3.84318i) q^{33} +(1.82866 + 5.62804i) q^{34} +(-0.170108 - 0.123590i) q^{35} +1.00000 q^{36} -3.63049 q^{37} +(3.41434 + 2.48067i) q^{38} +(-4.08445 + 2.96753i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-1.63744 + 5.03951i) q^{41} +(-0.170108 - 0.123590i) q^{42} +(-2.89685 + 8.91559i) q^{43} +(-1.24873 - 3.84318i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-2.17479 - 6.69332i) q^{46} +(3.40422 + 10.4771i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-2.14946 - 6.61535i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(4.78750 + 3.47832i) q^{51} +(1.56012 - 4.80156i) q^{52} +(0.184355 - 0.133942i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-3.26921 - 2.37522i) q^{55} +0.210265 q^{56} +4.22036 q^{57} +(-7.27266 - 5.28390i) q^{58} +(2.47815 + 7.62696i) q^{59} +(-0.309017 + 0.951057i) q^{60} -9.93402 q^{61} +(5.41359 - 1.30119i) q^{62} -0.210265 q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.56012 - 4.80156i) q^{65} +(-3.26921 - 2.37522i) q^{66} +11.5594 q^{67} -5.91767 q^{68} +(-5.69368 - 4.13670i) q^{69} +(0.170108 - 0.123590i) q^{70} +(-1.67293 + 1.21546i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-3.95475 - 2.87329i) q^{73} +(1.12188 - 3.45280i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-3.41434 + 2.48067i) q^{76} +(0.262563 + 0.808086i) q^{77} +(-1.56012 - 4.80156i) q^{78} +(8.41721 - 6.11546i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.28686 - 3.11459i) q^{82} +(-0.946849 + 2.91410i) q^{83} +(0.170108 - 0.123590i) q^{84} +(-4.78750 + 3.47832i) q^{85} +(-7.58406 - 5.51014i) q^{86} -8.98950 q^{87} +4.04096 q^{88} +(-6.89602 - 5.01025i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-0.328038 + 1.00960i) q^{91} +7.03778 q^{92} +(3.61486 - 4.23471i) q^{93} -11.0163 q^{94} +(-1.30416 + 4.01380i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(7.71397 + 5.60453i) q^{97} +6.95579 q^{98} -4.04096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	0.170108	+	0.123590i	0.0642946	+	0.0467128i	0.619468	−	0.785022i	$-0.287348\pi$
$7$	0.170108	+	0.123590i	0.0642946	+	0.0467128i	−0.555174	+	0.831734i	$0.687348\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	3.26921	+	2.37522i	0.985703	+	0.716155i	0.958976	−	0.283487i	$-0.0914914\pi$
$11$	3.26921	+	2.37522i	0.985703	+	0.716155i	0.0267272	+	0.999643i	$0.491491\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	1.56012	+	4.80156i	0.432700	+	1.33171i	0.895425	+	0.445212i	$0.146872\pi$
$13$	1.56012	+	4.80156i	0.432700	+	1.33171i	−0.462726	+	0.886502i	$0.653128\pi$
$14$	−0.170108	+	0.123590i	−0.0454632	+	0.0330309i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.78750	−	3.47832i	1.16114	−	0.843617i	0.171218	−	0.985233i	$-0.445230\pi$
$17$	4.78750	−	3.47832i	1.16114	−	0.843617i	0.989922	+	0.141616i	$0.0452299\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	1.30416	−	4.01380i	0.299196	−	0.920829i	−0.682584	−	0.730807i	$-0.739144\pi$
$19$	1.30416	−	4.01380i	0.299196	−	0.920829i	0.981780	−	0.190022i	$-0.0608560\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−0.0649753	+	0.199974i	−0.0141788	+	0.0436378i
$22$	−3.26921	+	2.37522i	−0.696997	+	0.506398i
$23$	−5.69368	+	4.13670i	−1.18721	+	0.862562i	−0.992967	−	0.118391i	$-0.962226\pi$
$23$	−5.69368	+	4.13670i	−1.18721	+	0.862562i	−0.194247	+	0.980953i	$0.562226\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	−5.04866			−0.990124
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.0649753	−	0.199974i	−0.0122792	−	0.0377914i
$29$	−2.77791	+	8.54953i	−0.515845	+	1.58761i	0.265895	+	0.964002i	$0.414333\pi$
$29$	−2.77791	+	8.54953i	−0.515845	+	1.58761i	−0.781739	+	0.623605i	$0.785667\pi$
$30$	1.00000			0.182574
$31$	−2.91039	−	4.74654i	−0.522722	−	0.852503i
$31$	−2.91039	−	4.74654i	−0.522722	−	0.852503i
$32$	−1.00000			−0.176777
$33$	−1.24873	+	3.84318i	−0.217375	+	0.669012i
$34$	1.82866	+	5.62804i	0.313613	+	0.965201i
$35$	−0.170108	−	0.123590i	−0.0287534	−	0.0208906i
$36$	1.00000			0.166667
$37$	−3.63049			−0.596848			−0.298424	−	0.954433i	$-0.596461\pi$
$37$	−3.63049			−0.596848			−0.298424	+	0.954433i	$0.596461\pi$
$38$	3.41434	+	2.48067i	0.553880	+	0.402417i
$39$	−4.08445	+	2.96753i	−0.654036	+	0.475185i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−1.63744	+	5.03951i	−0.255724	+	0.787039i	0.737962	+	0.674843i	$0.235789\pi$
$41$	−1.63744	+	5.03951i	−0.255724	+	0.787039i	−0.993686	+	0.112196i	$0.964211\pi$
$42$	−0.170108	−	0.123590i	−0.0262482	−	0.0190704i
$43$	−2.89685	+	8.91559i	−0.441766	+	1.35962i	0.444226	+	0.895915i	$0.353479\pi$
$43$	−2.89685	+	8.91559i	−0.441766	+	1.35962i	−0.885992	+	0.463701i	$0.846521\pi$
$44$	−1.24873	−	3.84318i	−0.188253	−	0.579382i
$45$	0.809017	−	0.587785i	0.120601	−	0.0876219i
$46$	−2.17479	−	6.69332i	−0.320656	−	0.986876i
$47$	3.40422	+	10.4771i	0.496556	+	1.52824i	0.814518	+	0.580139i	$0.197002\pi$
$47$	3.40422	+	10.4771i	0.496556	+	1.52824i	−0.317962	+	0.948104i	$0.602998\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−2.14946	−	6.61535i	−0.307065	−	0.945050i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	4.78750	+	3.47832i	0.670384	+	0.487063i
$52$	1.56012	−	4.80156i	0.216350	−	0.665857i
$53$	0.184355	−	0.133942i	0.0253231	−	0.0183983i	−0.575052	−	0.818117i	$-0.695018\pi$
$53$	0.184355	−	0.133942i	0.0253231	−	0.0183983i	0.600375	+	0.799719i	$0.295018\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−3.26921	−	2.37522i	−0.440820	−	0.320274i
$56$	0.210265			0.0280978
$57$	4.22036			0.559000
$58$	−7.27266	−	5.28390i	−0.954947	−	0.693810i
$59$	2.47815	+	7.62696i	0.322628	+	0.992946i	0.972500	+	0.232903i	$0.0748224\pi$
$59$	2.47815	+	7.62696i	0.322628	+	0.992946i	−0.649872	+	0.760043i	$0.725178\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−9.93402			−1.27192			−0.635960	−	0.771722i	$-0.719396\pi$
$61$	−9.93402			−1.27192			−0.635960	+	0.771722i	$0.719396\pi$
$62$	5.41359	−	1.30119i	0.687526	−	0.165251i
$63$	−0.210265			−0.0264909
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.56012	−	4.80156i	−0.193509	−	0.595560i
$66$	−3.26921	−	2.37522i	−0.402412	−	0.292369i
$67$	11.5594			1.41221			0.706106	−	0.708106i	$-0.250450\pi$
$67$	11.5594			1.41221			0.706106	+	0.708106i	$0.250450\pi$
$68$	−5.91767			−0.717623
$69$	−5.69368	−	4.13670i	−0.685439	−	0.498000i
$70$	0.170108	−	0.123590i	0.0203318	−	0.0147719i
$71$	−1.67293	+	1.21546i	−0.198541	+	0.144248i	−0.682614	−	0.730779i	$-0.739157\pi$
$71$	−1.67293	+	1.21546i	−0.198541	+	0.144248i	0.484073	+	0.875028i	$0.339157\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−3.95475	−	2.87329i	−0.462868	−	0.336294i	0.331787	−	0.943354i	$-0.392348\pi$
$73$	−3.95475	−	2.87329i	−0.462868	−	0.336294i	−0.794655	+	0.607061i	$0.792348\pi$
$74$	1.12188	−	3.45280i	0.130416	−	0.401380i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	−3.41434	+	2.48067i	−0.391652	+	0.284552i
$77$	0.262563	+	0.808086i	0.0299218	+	0.0920899i
$78$	−1.56012	−	4.80156i	−0.176649	−	0.543670i
$79$	8.41721	−	6.11546i	0.947010	−	0.688043i	−0.00308775	−	0.999995i	$-0.500983\pi$
$79$	8.41721	−	6.11546i	0.947010	−	0.688043i	0.950098	+	0.311952i	$0.100983\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.28686	−	3.11459i	−0.473405	−	0.343949i
$83$	−0.946849	+	2.91410i	−0.103930	+	0.319864i	−0.989478	−	0.144684i	$-0.953783\pi$
$83$	−0.946849	+	2.91410i	−0.103930	+	0.319864i	0.885548	+	0.464549i	$0.153783\pi$
$84$	0.170108	−	0.123590i	0.0185603	−	0.0134848i
$85$	−4.78750	+	3.47832i	−0.519277	+	0.377277i
$86$	−7.58406	−	5.51014i	−0.817810	−	0.594174i
$87$	−8.98950			−0.963776
$88$	4.04096			0.430768
$89$	−6.89602	−	5.01025i	−0.730977	−	0.531086i	0.158896	−	0.987295i	$-0.449207\pi$
$89$	−6.89602	−	5.01025i	−0.730977	−	0.531086i	−0.889872	+	0.456210i	$0.849207\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	−0.328038	+	1.00960i	−0.0343878	+	0.105835i
$92$	7.03778			0.733739
$93$	3.61486	−	4.23471i	0.374844	−	0.439119i
$94$	−11.0163			−1.13624
$95$	−1.30416	+	4.01380i	−0.133804	+	0.411807i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	7.71397	+	5.60453i	0.783235	+	0.569053i	0.905948	−	0.423389i	$-0.139160\pi$
$97$	7.71397	+	5.60453i	0.783235	+	0.569053i	−0.122713	+	0.992442i	$0.539160\pi$
$98$	6.95579			0.702641
$99$	−4.04096			−0.406132
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	5.51464	−	4.00662i	0.548728	−	0.398674i	−0.278589	−	0.960411i	$-0.589867\pi$
$101$	5.51464	−	4.00662i	0.548728	−	0.398674i	0.827316	+	0.561737i	$0.189867\pi$
$102$	−4.78750	+	3.47832i	−0.474033	+	0.344405i
$103$	5.23538	−	16.1128i	0.515857	−	1.58765i	−0.265859	−	0.964012i	$-0.585656\pi$
$103$	5.23538	−	16.1128i	0.515857	−	1.58765i	0.781716	−	0.623634i	$-0.214344\pi$
$104$	4.08445	+	2.96753i	0.400513	+	0.290990i
$105$	0.0649753	−	0.199974i	0.00634094	−	0.0195154i
$106$	0.0704173	+	0.216722i	0.00683953	+	0.0210499i
$107$	7.71662	−	5.60646i	0.745994	−	0.541997i	−0.148588	−	0.988899i	$-0.547473\pi$
$107$	7.71662	−	5.60646i	0.745994	−	0.541997i	0.894583	+	0.446903i	$0.147473\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	5.07253	+	15.6117i	0.485861	+	1.49533i	0.830730	+	0.556675i	$0.187923\pi$
$109$	5.07253	+	15.6117i	0.485861	+	1.49533i	−0.344870	+	0.938651i	$0.612077\pi$
$110$	3.26921	−	2.37522i	0.311707	−	0.226468i
$111$	−1.12188	−	3.45280i	−0.106484	−	0.327725i
$112$	−0.0649753	+	0.199974i	−0.00613959	+	0.0188957i
$113$	14.6968	+	10.6778i	1.38256	+	1.00449i	0.996636	+	0.0819532i	$0.0261158\pi$
$113$	14.6968	+	10.6778i	1.38256	+	1.00449i	0.385920	+	0.922532i	$0.373884\pi$
$114$	−1.30416	+	4.01380i	−0.122146	+	0.375927i
$115$	5.69368	−	4.13670i	0.530938	−	0.385749i
$116$	7.27266	−	5.28390i	0.675250	−	0.490598i
$117$	−4.08445	−	2.96753i	−0.377608	−	0.274348i
$118$	−8.01947			−0.738252
$119$	1.24428			0.114063
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	1.64687	+	5.06854i	0.149715	+	0.460777i
$122$	3.06978	−	9.44781i	0.277925	−	0.855365i
$123$	−5.29885			−0.477781
$124$	−0.435388	+	5.55072i	−0.0390990	+	0.498469i
$125$	−1.00000			−0.0894427
$126$	0.0649753	−	0.199974i	0.00578846	−	0.0178151i
$127$	3.44121	+	10.5909i	0.305358	+	0.939795i	0.979543	+	0.201233i	$0.0644947\pi$
$127$	3.44121	+	10.5909i	0.305358	+	0.939795i	−0.674186	+	0.738562i	$0.735505\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−9.37441			−0.825371
$130$	5.04866			0.442797
$131$	−5.15740	−	3.74707i	−0.450604	−	0.327383i	0.339230	−	0.940703i	$-0.389833\pi$
$131$	−5.15740	−	3.74707i	−0.450604	−	0.327383i	−0.789834	+	0.613321i	$0.789833\pi$
$132$	3.26921	−	2.37522i	0.284548	−	0.206736i
$133$	0.717916	−	0.521596i	0.0622512	−	0.0452281i
$134$	−3.57207	+	10.9937i	−0.308580	+	0.949710i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	1.82866	−	5.62804i	0.156806	−	0.482601i
$137$	−0.942236	−	2.89990i	−0.0805007	−	0.247756i	0.902704	−	0.430262i	$-0.141579\pi$
$137$	−0.942236	−	2.89990i	−0.0805007	−	0.247756i	−0.983205	+	0.182507i	$0.941579\pi$
$138$	5.69368	−	4.13670i	0.484678	−	0.352139i
$139$	−6.24293	−	19.2138i	−0.529519	−	1.62969i	−0.755203	−	0.655491i	$-0.772462\pi$
$139$	−6.24293	−	19.2138i	−0.529519	−	1.62969i	0.225685	−	0.974200i	$-0.427538\pi$
$140$	0.0649753	+	0.199974i	0.00549142	+	0.0169008i
$141$	−8.91236	+	6.47521i	−0.750556	+	0.545311i
$142$	−0.639004	−	1.96665i	−0.0536240	−	0.165038i
$143$	−6.30439	+	19.4029i	−0.527200	+	1.62255i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	2.77791	−	8.54953i	0.230693	−	0.710000i
$146$	3.95475	−	2.87329i	0.327297	−	0.237795i
$147$	5.62735	−	4.08851i	0.464136	−	0.337215i
$148$	2.93713	+	2.13395i	0.241430	+	0.175409i
$149$	−6.32256			−0.517965			−0.258982	−	0.965882i	$-0.583387\pi$
$149$	−6.32256			−0.517965			−0.258982	+	0.965882i	$0.583387\pi$
$150$	−1.00000			−0.0816497
$151$	−16.0593	−	11.6677i	−1.30689	−	0.949508i	−0.306888	−	0.951746i	$-0.599288\pi$
$151$	−16.0593	−	11.6677i	−1.30689	−	0.949508i	−0.999997	+	0.00223787i	$0.999288\pi$
$152$	−1.30416	−	4.01380i	−0.105782	−	0.325562i
$153$	−1.82866	+	5.62804i	−0.147839	+	0.455000i
$154$	−0.849671			−0.0684685
$155$	2.91039	+	4.74654i	0.233768	+	0.381251i
$156$	5.04866			0.404216
$157$	3.43610	−	10.5752i	0.274230	−	0.843995i	−0.715192	−	0.698929i	$-0.753661\pi$
$157$	3.43610	−	10.5752i	0.274230	−	0.843995i	0.989422	−	0.145066i	$-0.0463395\pi$
$158$	3.21509	+	9.89502i	0.255779	+	0.787206i
$159$	0.184355	+	0.133942i	0.0146203	+	0.0106223i
$160$	1.00000			0.0790569
$161$	−1.47980			−0.116624
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	−4.53409	+	3.29421i	−0.355137	+	0.258022i	−0.751021	−	0.660278i	$-0.770438\pi$
$163$	−4.53409	+	3.29421i	−0.355137	+	0.258022i	0.395884	+	0.918301i	$0.370438\pi$
$164$	4.28686	−	3.11459i	0.334748	−	0.243208i
$165$	1.24873	−	3.84318i	0.0972132	−	0.299191i
$166$	−2.47888	−	1.80101i	−0.192399	−	0.139786i
$167$	6.72424	−	20.6951i	0.520337	−	1.60143i	−0.253019	−	0.967461i	$-0.581423\pi$
$167$	6.72424	−	20.6951i	0.520337	−	1.60143i	0.773356	−	0.633972i	$-0.218577\pi$
$168$	0.0649753	+	0.199974i	0.00501296	+	0.0154283i
$169$	−10.1038	+	7.34083i	−0.777214	+	0.564679i
$170$	−1.82866	−	5.62804i	−0.140252	−	0.431651i
$171$	1.30416	+	4.01380i	0.0997318	+	0.306943i
$172$	7.58406	−	5.51014i	0.578279	−	0.420144i
$173$	7.94051	+	24.4384i	0.603706	+	1.85802i	0.505453	+	0.862854i	$0.331325\pi$
$173$	7.94051	+	24.4384i	0.603706	+	1.85802i	0.0982530	+	0.995161i	$0.468675\pi$
$174$	2.77791	−	8.54953i	0.210593	−	0.648138i
$175$	0.170108	+	0.123590i	0.0128589	+	0.00934256i
$176$	−1.24873	+	3.84318i	−0.0941263	+	0.289691i
$177$	−6.48788	+	4.71372i	−0.487659	+	0.354305i
$178$	6.89602	−	5.01025i	0.516879	−	0.375534i
$179$	5.71603	+	4.15294i	0.427236	+	0.310405i	0.780543	−	0.625102i	$-0.214943\pi$
$179$	5.71603	+	4.15294i	0.427236	+	0.310405i	−0.353307	+	0.935508i	$0.614943\pi$
$180$	−1.00000			−0.0745356
$181$	2.81778			0.209444			0.104722	−	0.994502i	$-0.466605\pi$
$181$	2.81778			0.209444			0.104722	+	0.994502i	$0.466605\pi$
$182$	−0.858816	−	0.623966i	−0.0636596	−	0.0462514i
$183$	−3.06978	−	9.44781i	−0.226925	−	0.698402i
$184$	−2.17479	+	6.69332i	−0.160328	+	0.493438i
$185$	3.63049			0.266919
$186$	2.91039	+	4.74654i	0.213400	+	0.348033i
$187$	23.9131			1.74870
$188$	3.40422	−	10.4771i	0.248278	−	0.764121i
$189$	−0.0649753	−	0.199974i	−0.00472626	−	0.0145459i
$190$	−3.41434	−	2.48067i	−0.247703	−	0.179966i
$191$	8.34418			0.603764			0.301882	−	0.953345i	$-0.402385\pi$
$191$	8.34418			0.603764			0.301882	+	0.953345i	$0.402385\pi$
$192$	1.00000			0.0721688
$193$	−11.0841	−	8.05306i	−0.797850	−	0.579672i	0.112432	−	0.993659i	$-0.464136\pi$
$193$	−11.0841	−	8.05306i	−0.797850	−	0.579672i	−0.910283	+	0.413987i	$0.864136\pi$
$194$	−7.71397	+	5.60453i	−0.553831	+	0.402381i
$195$	4.08445	−	2.96753i	0.292494	−	0.212509i
$196$	−2.14946	+	6.61535i	−0.153533	+	0.472525i
$197$	8.91634	+	6.47810i	0.635263	+	0.461546i	0.858220	−	0.513283i	$-0.171571\pi$
$197$	8.91634	+	6.47810i	0.635263	+	0.461546i	−0.222957	+	0.974828i	$0.571571\pi$
$198$	1.24873	−	3.84318i	0.0887431	−	0.273123i
$199$	3.38692	+	10.4239i	0.240093	+	0.738929i	0.996405	+	0.0847182i	$0.0269990\pi$
$199$	3.38692	+	10.4239i	0.240093	+	0.738929i	−0.756312	+	0.654211i	$0.773001\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	3.57207	+	10.9937i	0.251954	+	0.775435i
$202$	2.10641	+	6.48285i	0.148206	+	0.456132i
$203$	−1.52918	+	1.11102i	−0.107328	+	0.0779781i
$204$	−1.82866	−	5.62804i	−0.128032	−	0.394042i
$205$	1.63744	−	5.03951i	0.114363	−	0.351975i
$206$	13.7064	+	9.95829i	0.954971	+	0.693827i
$207$	2.17479	−	6.69332i	0.151159	−	0.465218i
$208$	−4.08445	+	2.96753i	−0.283206	+	0.205761i
$209$	13.7972	−	10.0243i	0.954375	−	0.693394i
$210$	0.170108	+	0.123590i	0.0117385	+	0.00852855i
$211$	13.3471			0.918849			0.459425	−	0.888217i	$-0.348056\pi$
$211$	13.3471			0.918849			0.459425	+	0.888217i	$0.348056\pi$
$212$	−0.227875			−0.0156505
$213$	−1.67293	−	1.21546i	−0.114628	−	0.0832818i
$214$	2.94749	+	9.07144i	0.201486	+	0.620111i
$215$	2.89685	−	8.91559i	0.197564	−	0.608038i
$216$	−1.00000			−0.0680414
$217$	0.0915467	−	1.16712i	0.00621460	−	0.0792292i
$218$	−16.4151			−1.11177
$219$	1.51058	−	4.64909i	0.102076	−	0.314156i
$220$	1.24873	+	3.84318i	0.0841891	+	0.259107i
$221$	24.1705	+	17.5609i	1.62588	+	1.18127i
$222$	3.63049			0.243662
$223$	16.9690			1.13633			0.568165	−	0.822915i	$-0.307653\pi$
$223$	16.9690			1.13633			0.568165	+	0.822915i	$0.307653\pi$
$224$	−0.170108	−	0.123590i	−0.0113658	−	0.00825773i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−14.6968	+	10.6778i	−0.977615	+	0.710279i
$227$	5.32530	−	16.3896i	0.353453	−	1.08782i	−0.603449	−	0.797402i	$-0.706207\pi$
$227$	5.32530	−	16.3896i	0.353453	−	1.08782i	0.956901	−	0.290413i	$-0.0937928\pi$
$228$	−3.41434	−	2.48067i	−0.226120	−	0.164286i
$229$	−7.12281	+	21.9217i	−0.470688	+	1.44863i	0.380997	+	0.924576i	$0.375581\pi$
$229$	−7.12281	+	21.9217i	−0.470688	+	1.44863i	−0.851685	+	0.524053i	$0.824419\pi$
$230$	2.17479	+	6.69332i	0.143402	+	0.441345i
$231$	−0.687399	+	0.499424i	−0.0452275	+	0.0328597i
$232$	2.77791	+	8.54953i	0.182379	+	0.561304i
$233$	−6.19733	−	19.0734i	−0.406001	−	1.24954i	−0.920057	−	0.391785i	$-0.871858\pi$
$233$	−6.19733	−	19.0734i	−0.406001	−	1.24954i	0.514056	−	0.857756i	$-0.328142\pi$
$234$	4.08445	−	2.96753i	0.267009	−	0.193993i
$235$	−3.40422	−	10.4771i	−0.222067	−	0.683451i
$236$	2.47815	−	7.62696i	0.161314	−	0.496473i
$237$	8.41721	+	6.11546i	0.546757	+	0.397242i
$238$	−0.384503	+	1.18338i	−0.0249236	+	0.0767070i
$239$	7.91614	−	5.75141i	0.512052	−	0.372028i	−0.301549	−	0.953451i	$-0.597504\pi$
$239$	7.91614	−	5.75141i	0.512052	−	0.372028i	0.813602	+	0.581423i	$0.197504\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−3.89661	−	2.83105i	−0.251002	−	0.182364i	0.455169	−	0.890405i	$-0.349579\pi$
$241$	−3.89661	−	2.83105i	−0.251002	−	0.182364i	−0.706171	+	0.708041i	$0.749579\pi$
$242$	−5.32938			−0.342586
$243$	1.00000			0.0641500
$244$	8.03679	+	5.83907i	0.514503	+	0.373808i
$245$	2.14946	+	6.61535i	0.137324	+	0.422639i
$246$	1.63744	−	5.03951i	0.104399	−	0.321307i
$247$	21.3072			1.35574
$248$	−5.14450	−	2.12934i	−0.326676	−	0.135213i
$249$	−3.06407			−0.194177
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−5.37933	−	16.5559i	−0.339540	−	1.04500i	−0.964442	−	0.264294i	$-0.914861\pi$
$251$	−5.37933	−	16.5559i	−0.339540	−	1.04500i	0.624902	−	0.780703i	$-0.285139\pi$
$252$	0.170108	+	0.123590i	0.0107158	+	0.00778547i
$253$	−28.4394			−1.78797
$254$	−11.1360			−0.698734
$255$	−4.78750	−	3.47832i	−0.299805	−	0.217821i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−13.1447	+	9.55019i	−0.819944	+	0.595724i	−0.916696	−	0.399584i	$-0.869154\pi$
$257$	−13.1447	+	9.55019i	−0.819944	+	0.595724i	0.0967525	+	0.995308i	$0.469154\pi$
$258$	2.89685	−	8.91559i	0.180350	−	0.555061i
$259$	−0.617574	−	0.448694i	−0.0383742	−	0.0278805i
$260$	−1.56012	+	4.80156i	−0.0967546	+	0.297780i
$261$	−2.77791	−	8.54953i	−0.171948	−	0.529202i
$262$	5.15740	−	3.74707i	0.318625	−	0.231495i
$263$	−1.57364	−	4.84318i	−0.0970351	−	0.298643i	0.890744	−	0.454506i	$-0.150184\pi$
$263$	−1.57364	−	4.84318i	−0.0970351	−	0.298643i	−0.987779	+	0.155863i	$0.950184\pi$
$264$	1.24873	+	3.84318i	0.0768538	+	0.236532i
$265$	−0.184355	+	0.133942i	−0.0113248	+	0.00822797i
$266$	0.274219	+	0.843960i	0.0168135	+	0.0517465i
$267$	2.63405	−	8.10676i	0.161201	−	0.496126i
$268$	−9.35179	−	6.79447i	−0.571252	−	0.415039i
$269$	−6.68835	+	20.5846i	−0.407796	+	1.25507i	0.510742	+	0.859734i	$0.329371\pi$
$269$	−6.68835	+	20.5846i	−0.407796	+	1.25507i	−0.918538	+	0.395333i	$0.870629\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	−11.9331	+	8.66994i	−0.724887	+	0.526661i	−0.887942	−	0.459956i	$-0.847865\pi$
$271$	−11.9331	+	8.66994i	−0.724887	+	0.526661i	0.163055	+	0.986617i	$0.447865\pi$
$272$	4.78750	+	3.47832i	0.290285	+	0.210904i
$273$	−1.06155			−0.0642482
$274$	3.04914			0.184205
$275$	3.26921	+	2.37522i	0.197141	+	0.143231i
$276$	2.17479	+	6.69332i	0.130907	+	0.402891i
$277$	7.21742	−	22.2129i	0.433653	−	1.33465i	−0.460808	−	0.887500i	$-0.652440\pi$
$277$	7.21742	−	22.2129i	0.433653	−	1.33465i	0.894461	−	0.447146i	$-0.147560\pi$
$278$	20.2026			1.21167
$279$	5.14450	+	2.12934i	0.307993	+	0.127480i
$280$	−0.210265			−0.0125657
$281$	2.85071	−	8.77359i	0.170059	−	0.523388i	−0.829314	−	0.558783i	$-0.811269\pi$
$281$	2.85071	−	8.77359i	0.170059	−	0.523388i	0.999373	+	0.0353941i	$0.0112686\pi$
$282$	−3.40422	−	10.4771i	−0.202718	−	0.623902i
$283$	21.3830	+	15.5357i	1.27109	+	0.923500i	0.999245	−	0.0388414i	$-0.0123667\pi$
$283$	21.3830	+	15.5357i	1.27109	+	0.923500i	0.271843	+	0.962341i	$0.412367\pi$
$284$	2.06786			0.122705
$285$	−4.22036			−0.249993
$286$	−16.5051	−	11.9917i	−0.975968	−	0.709082i
$287$	−0.901375	+	0.654888i	−0.0532065	+	0.0386568i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	5.56814	−	17.1370i	0.327538	−	1.00806i
$290$	7.27266	+	5.28390i	0.427065	+	0.310281i
$291$	−2.94647	+	9.06831i	−0.172725	+	0.531594i
$292$	1.51058	+	4.64909i	0.0884000	+	0.272067i
$293$	16.0983	−	11.6961i	0.940471	−	0.683292i	−0.00806272	−	0.999967i	$-0.502566\pi$
$293$	16.0983	−	11.6961i	0.940471	−	0.683292i	0.948534	+	0.316675i	$0.102566\pi$
$294$	2.14946	+	6.61535i	0.125359	+	0.385815i
$295$	−2.47815	−	7.62696i	−0.144284	−	0.444059i
$296$	−2.93713	+	2.13395i	−0.170717	+	0.124033i
$297$	−1.24873	−	3.84318i	−0.0724584	−	0.223004i
$298$	1.95378	−	6.01312i	0.113179	−	0.348330i
$299$	−28.7454	−	20.8848i	−1.66239	−	1.20780i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	−1.59466	+	1.15859i	−0.0919146	+	0.0667799i
$302$	16.0593	−	11.6677i	0.924108	−	0.671403i
$303$	5.51464	+	4.00662i	0.316808	+	0.230174i
$304$	4.22036			0.242054
$305$	9.93402			0.568820
$306$	−4.78750	−	3.47832i	−0.273683	−	0.198842i
$307$	−4.06330	−	12.5056i	−0.231905	−	0.713730i	−0.997517	−	0.0704273i	$-0.977564\pi$
$307$	−4.06330	−	12.5056i	−0.231905	−	0.713730i	0.765612	−	0.643303i	$-0.222436\pi$
$308$	0.262563	−	0.808086i	0.0149609	−	0.0460450i
$309$	16.9421			0.963800
$310$	−5.41359	+	1.30119i	−0.307471	+	0.0739024i
$311$	14.9154			0.845774			0.422887	−	0.906182i	$-0.361017\pi$
$311$	14.9154			0.845774			0.422887	+	0.906182i	$0.361017\pi$
$312$	−1.56012	+	4.80156i	−0.0883245	+	0.271835i
$313$	4.53841	+	13.9678i	0.256526	+	0.789505i	0.993525	+	0.113612i	$0.0362421\pi$
$313$	4.53841	+	13.9678i	0.256526	+	0.789505i	−0.736999	+	0.675893i	$0.763758\pi$
$314$	8.99582	+	6.53585i	0.507664	+	0.368839i
$315$	0.210265			0.0118471
$316$	−10.4042			−0.585284
$317$	13.1358	+	9.54369i	0.737778	+	0.536027i	0.892014	−	0.452007i	$-0.149292\pi$
$317$	13.1358	+	9.54369i	0.737778	+	0.536027i	−0.154236	+	0.988034i	$0.549292\pi$
$318$	−0.184355	+	0.133942i	−0.0103381	+	0.00751108i
$319$	−29.3886	+	21.3520i	−1.64544	+	1.19548i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	7.71662	+	5.60646i	0.430700	+	0.312922i
$322$	0.457282	−	1.40737i	0.0254833	−	0.0784296i
$323$	−7.71761	−	23.7524i	−0.429420	−	1.32162i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	1.56012	+	4.80156i	0.0865400	+	0.266343i
$326$	−1.73187	−	5.33014i	−0.0959193	−	0.295209i
$327$	−13.2801	+	9.64853i	−0.734389	+	0.533565i
$328$	1.63744	+	5.03951i	0.0904123	+	0.278260i
$329$	−0.715786	+	2.20296i	−0.0394626	+	0.121453i
$330$	3.26921	+	2.37522i	0.179964	+	0.130751i
$331$	9.47284	−	29.1544i	0.520675	−	1.60247i	−0.252039	−	0.967717i	$-0.581101\pi$
$331$	9.47284	−	29.1544i	0.520675	−	1.60247i	0.772714	−	0.634755i	$-0.218899\pi$
$332$	2.47888	−	1.80101i	0.136046	−	0.0988435i
$333$	2.93713	−	2.13395i	0.160954	−	0.116940i
$334$	17.6043	+	12.7903i	0.963264	+	0.699852i
$335$	−11.5594			−0.631560
$336$	−0.210265			−0.0114709
$337$	5.83412	+	4.23874i	0.317805	+	0.230899i	0.735238	−	0.677809i	$-0.237070\pi$
$337$	5.83412	+	4.23874i	0.317805	+	0.230899i	−0.417433	+	0.908708i	$0.637070\pi$
$338$	−3.85930	−	11.8777i	−0.209918	−	0.646062i
$339$	−5.61367	+	17.2771i	−0.304893	+	0.938363i
$340$	5.91767			0.320931
$341$	1.75939	−	22.4302i	0.0952762	−	1.21467i
$342$	−4.22036			−0.228211
$343$	0.906782	−	2.79079i	0.0489616	−	0.150688i
$344$	2.89685	+	8.91559i	0.156188	+	0.480697i
$345$	5.69368	+	4.13670i	0.306537	+	0.222712i
$346$	−25.6960			−1.38143
$347$	−24.8506			−1.33405			−0.667025	−	0.745035i	$-0.732433\pi$
$347$	−24.8506			−1.33405			−0.667025	+	0.745035i	$0.732433\pi$
$348$	7.27266	+	5.28390i	0.389856	+	0.283247i
$349$	18.4914	−	13.4348i	0.989825	−	0.719150i	0.0299419	−	0.999552i	$-0.490468\pi$
$349$	18.4914	−	13.4348i	0.989825	−	0.719150i	0.959883	+	0.280402i	$0.0904678\pi$
$350$	−0.170108	+	0.123590i	−0.00909264	+	0.00660619i
$351$	1.56012	−	4.80156i	0.0832731	−	0.256288i
$352$	−3.26921	−	2.37522i	−0.174249	−	0.126600i
$353$	−7.39574	+	22.7618i	−0.393636	+	1.21149i	0.536383	+	0.843974i	$0.319790\pi$
$353$	−7.39574	+	22.7618i	−0.393636	+	1.21149i	−0.930019	+	0.367511i	$0.880210\pi$
$354$	−2.47815	−	7.62696i	−0.131712	−	0.405369i
$355$	1.67293	−	1.21546i	0.0887901	−	0.0645098i
$356$	2.63405	+	8.10676i	0.139604	+	0.429657i
$357$	0.384503	+	1.18338i	0.0203501	+	0.0626310i
$358$	−5.71603	+	4.15294i	−0.302102	+	0.219490i
$359$	−7.37080	−	22.6850i	−0.389016	−	1.19727i	−0.933525	−	0.358512i	$-0.883284\pi$
$359$	−7.37080	−	22.6850i	−0.389016	−	1.19727i	0.544509	−	0.838755i	$-0.316716\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	0.961562	+	0.698616i	0.0506085	+	0.0367692i
$362$	−0.870743	+	2.67987i	−0.0457652	+	0.140851i
$363$	−4.31156	+	3.13253i	−0.226298	+	0.164415i
$364$	0.858816	−	0.623966i	0.0450142	−	0.0327047i
$365$	3.95475	+	2.87329i	0.207001	+	0.150395i
$366$	9.93402			0.519259
$367$	0.939030			0.0490170			0.0245085	−	0.999700i	$-0.492198\pi$
$367$	0.939030			0.0490170			0.0245085	+	0.999700i	$0.492198\pi$
$368$	−5.69368	−	4.13670i	−0.296804	−	0.215640i
$369$	−1.63744	−	5.03951i	−0.0852415	−	0.262346i
$370$	−1.12188	+	3.45280i	−0.0583239	+	0.179502i
$371$	0.0479141			0.00248758
$372$	−5.41359	+	1.30119i	−0.280681	+	0.0674634i
$373$	−35.9686			−1.86238			−0.931192	−	0.364529i	$-0.881230\pi$
$373$	−35.9686			−1.86238			−0.931192	+	0.364529i	$0.881230\pi$
$374$	−7.38956	+	22.7427i	−0.382105	+	1.17600i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	8.91236	+	6.47521i	0.459620	+	0.333933i
$377$	−45.3849			−2.33744
$378$	0.210265			0.0108148
$379$	3.31625	+	2.40940i	0.170344	+	0.123762i	0.669691	−	0.742640i	$-0.266427\pi$
$379$	3.31625	+	2.40940i	0.170344	+	0.123762i	−0.499347	+	0.866402i	$0.666427\pi$
$380$	3.41434	−	2.48067i	0.175152	−	0.127255i
$381$	−9.00920	+	6.54557i	−0.461555	+	0.335339i
$382$	−2.57849	+	7.93579i	−0.131927	+	0.406030i
$383$	−13.7261	−	9.97262i	−0.701373	−	0.509577i	0.179006	−	0.983848i	$-0.442712\pi$
$383$	−13.7261	−	9.97262i	−0.701373	−	0.509577i	−0.880379	+	0.474271i	$0.842712\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−0.262563	−	0.808086i	−0.0133814	−	0.0411839i
$386$	11.0841	−	8.05306i	0.564165	−	0.409890i
$387$	−2.89685	−	8.91559i	−0.147255	−	0.453205i
$388$	−2.94647	−	9.06831i	−0.149585	−	0.460374i
$389$	−9.79460	+	7.11619i	−0.496606	+	0.360805i	−0.807719	−	0.589568i	$-0.799298\pi$
$389$	−9.79460	+	7.11619i	−0.496606	+	0.360805i	0.311113	+	0.950373i	$0.399298\pi$
$390$	1.56012	+	4.80156i	0.0789998	+	0.243136i
$391$	−12.8697	+	39.6089i	−0.650849	+	2.00311i
$392$	−5.62735	−	4.08851i	−0.284224	−	0.206501i
$393$	1.96995	−	6.06288i	0.0993708	−	0.305832i
$394$	−8.91634	+	6.47810i	−0.449199	+	0.326362i
$395$	−8.41721	+	6.11546i	−0.423516	+	0.307702i
$396$	3.26921	+	2.37522i	0.164284	+	0.119359i
$397$	27.0353			1.35686			0.678431	−	0.734665i	$-0.262660\pi$
$397$	27.0353			1.35686			0.678431	+	0.734665i	$0.262660\pi$
$398$	−10.9603			−0.549391
$399$	0.717916	+	0.521596i	0.0359407	+	0.0261125i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−5.70926	+	17.5713i	−0.285107	+	0.877468i	0.701260	+	0.712906i	$0.252621\pi$
$401$	−5.70926	+	17.5713i	−0.285107	+	0.877468i	−0.986367	+	0.164563i	$0.947379\pi$
$402$	−11.5594			−0.576533
$403$	18.2502	−	21.3796i	0.909108	−	1.06499i
$404$	−6.81647			−0.339132
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−0.584096	−	1.79766i	−0.0289882	−	0.0892165i
$407$	−11.8688	−	8.62320i	−0.588315	−	0.427436i
$408$	5.91767			0.292969
$409$	−17.8853			−0.884371			−0.442185	−	0.896924i	$-0.645797\pi$
$409$	−17.8853			−0.884371			−0.442185	+	0.896924i	$0.645797\pi$
$410$	4.28686	+	3.11459i	0.211713	+	0.153819i
$411$	2.46681	−	1.79224i	0.121679	−	0.0884047i
$412$	−13.7064	+	9.95829i	−0.675266	+	0.490610i
$413$	−0.521067	+	1.60368i	−0.0256401	+	0.0789120i
$414$	5.69368	+	4.13670i	0.279829	+	0.203308i
$415$	0.946849	−	2.91410i	0.0464790	−	0.143048i
$416$	−1.56012	−	4.80156i	−0.0764913	−	0.235416i
$417$	16.3442	−	11.8748i	0.800380	−	0.581510i
$418$	5.27007	+	16.2196i	0.257768	+	0.793328i
$419$	−5.54317	−	17.0601i	−0.270802	−	0.833442i	−0.990300	−	0.138947i	$-0.955628\pi$
$419$	−5.54317	−	17.0601i	−0.270802	−	0.833442i	0.719498	−	0.694494i	$-0.244372\pi$
$420$	−0.170108	+	0.123590i	−0.00830040	+	0.00603060i
$421$	−3.03573	−	9.34303i	−0.147953	−	0.455351i	0.849426	−	0.527707i	$-0.176948\pi$
$421$	−3.03573	−	9.34303i	−0.147953	−	0.455351i	−0.997379	+	0.0723561i	$0.976948\pi$
$422$	−4.12447	+	12.6938i	−0.200776	+	0.617925i
$423$	−8.91236	−	6.47521i	−0.433334	−	0.314835i
$424$	0.0704173	−	0.216722i	0.00341977	−	0.0105250i
$425$	4.78750	−	3.47832i	0.232228	−	0.168723i
$426$	1.67293	−	1.21546i	0.0810539	−	0.0588891i
$427$	−1.68985	−	1.22775i	−0.0817777	−	0.0594150i
$428$	−9.53827			−0.461050
$429$	−20.4014			−0.984991
$430$	7.58406	+	5.51014i	0.365736	+	0.265723i
$431$	12.5582	+	38.6501i	0.604906	+	1.86171i	0.497434	+	0.867502i	$0.334276\pi$
$431$	12.5582	+	38.6501i	0.604906	+	1.86171i	0.107472	+	0.994208i	$0.465724\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	12.2245			0.587471			0.293735	−	0.955887i	$-0.405102\pi$
$433$	12.2245			0.587471			0.293735	+	0.955887i	$0.405102\pi$
$434$	1.08171	+	0.447726i	0.0519236	+	0.0214915i
$435$	8.98950			0.431014
$436$	5.07253	−	15.6117i	0.242930	−	0.747663i
$437$	9.17841	+	28.2482i	0.439063	+	1.35130i
$438$	3.95475	+	2.87329i	0.188965	+	0.137291i
$439$	39.9929			1.90876			0.954379	−	0.298597i	$-0.0965187\pi$
$439$	39.9929			1.90876			0.954379	+	0.298597i	$0.0965187\pi$
$440$	−4.04096			−0.192645
$441$	5.62735	+	4.08851i	0.267969	+	0.194691i
$442$	−24.1705	+	17.5609i	−1.14967	+	0.835285i
$443$	−20.4820	+	14.8810i	−0.973129	+	0.707019i	−0.956162	−	0.292837i	$-0.905401\pi$
$443$	−20.4820	+	14.8810i	−0.973129	+	0.707019i	−0.0169662	+	0.999856i	$0.505401\pi$
$444$	−1.12188	+	3.45280i	−0.0532422	+	0.163863i
$445$	6.89602	+	5.01025i	0.326903	+	0.237509i
$446$	−5.24372	+	16.1385i	−0.248297	+	0.764180i
$447$	−1.95378	−	6.01312i	−0.0924106	−	0.284411i
$448$	0.170108	−	0.123590i	0.00803683	−	0.00583910i
$449$	−5.34944	−	16.4639i	−0.252456	−	0.776979i	−0.994320	−	0.106429i	$-0.966058\pi$
$449$	−5.34944	−	16.4639i	−0.252456	−	0.776979i	0.741864	−	0.670550i	$-0.233942\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−17.3231	+	12.5859i	−0.815711	+	0.592648i
$452$	−5.61367	−	17.2771i	−0.264045	−	0.812646i
$453$	6.13410	−	18.8788i	0.288205	−	0.887004i
$454$	13.9418	+	10.1293i	0.654322	+	0.475393i
$455$	0.328038	−	1.00960i	0.0153787	−	0.0473307i
$456$	3.41434	−	2.48067i	0.159891	−	0.116168i
$457$	−20.3935	+	14.8167i	−0.953968	+	0.693098i	−0.951742	−	0.306900i	$-0.900708\pi$
$457$	−20.3935	+	14.8167i	−0.953968	+	0.693098i	−0.00222561	+	0.999998i	$0.500708\pi$
$458$	−18.6477	−	13.5484i	−0.871352	−	0.633074i
$459$	−5.91767			−0.276213
$460$	−7.03778			−0.328138
$461$	−21.4269	−	15.5675i	−0.997949	−	0.725052i	−0.0363014	−	0.999341i	$-0.511558\pi$
$461$	−21.4269	−	15.5675i	−0.997949	−	0.725052i	−0.961647	+	0.274289i	$0.911558\pi$
$462$	−0.262563	−	0.808086i	−0.0122155	−	0.0375955i
$463$	6.98455	−	21.4962i	0.324599	−	0.999014i	−0.647022	−	0.762472i	$-0.723986\pi$
$463$	6.98455	−	21.4962i	0.324599	−	0.999014i	0.971621	−	0.236543i	$-0.0760143\pi$
$464$	−8.98950			−0.417327
$465$	−3.61486	+	4.23471i	−0.167635	+	0.196380i
$466$	20.0550			0.929029
$467$	5.99076	−	18.4377i	0.277219	−	0.853193i	−0.711404	−	0.702783i	$-0.751940\pi$
$467$	5.99076	−	18.4377i	0.277219	−	0.853193i	0.988624	−	0.150410i	$-0.0480595\pi$
$468$	1.56012	+	4.80156i	0.0721166	+	0.221952i
$469$	1.96635	+	1.42864i	0.0907976	+	0.0659683i
$470$	11.0163			0.508143
$471$	11.1194			0.512357
$472$	6.48788	+	4.71372i	0.298629	+	0.216967i
$473$	−30.6469	+	22.2663i	−1.40915	+	1.02380i
$474$	−8.41721	+	6.11546i	−0.386615	+	0.280892i
$475$	1.30416	−	4.01380i	0.0598391	−	0.184166i
$476$	−1.00664	−	0.731368i	−0.0461393	−	0.0335222i
$477$	−0.0704173	+	0.216722i	−0.00322419	+	0.00992303i
$478$	3.02370	+	9.30598i	0.138301	+	0.425646i
$479$	−0.381606	+	0.277253i	−0.0174360	+	0.0126680i	−0.596469	−	0.802636i	$-0.703430\pi$
$479$	−0.381606	+	0.277253i	−0.0174360	+	0.0126680i	0.579033	+	0.815304i	$0.303430\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−5.66400	−	17.4320i	−0.258256	−	0.794831i
$482$	3.89661	−	2.83105i	0.177486	−	0.128951i
$483$	−0.457282	−	1.40737i	−0.0208070	−	0.0640375i
$484$	1.64687	−	5.06854i	0.0748577	−	0.230388i
$485$	−7.71397	−	5.60453i	−0.350273	−	0.254488i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−14.5084	+	10.5410i	−0.657439	+	0.477658i	−0.865797	−	0.500395i	$-0.833188\pi$
$487$	−14.5084	+	10.5410i	−0.657439	+	0.477658i	0.208358	+	0.978053i	$0.433188\pi$
$488$	−8.03679	+	5.83907i	−0.363808	+	0.264322i
$489$	−4.53409	−	3.29421i	−0.205039	−	0.148969i
$490$	−6.95579			−0.314231
$491$	14.5980			0.658800			0.329400	−	0.944191i	$-0.393154\pi$
$491$	14.5980			0.658800			0.329400	+	0.944191i	$0.393154\pi$
$492$	4.28686	+	3.11459i	0.193267	+	0.140416i
$493$	16.4388	+	50.5933i	0.740365	+	2.27861i
$494$	−6.58428	+	20.2643i	−0.296241	+	0.911735i
$495$	4.04096			0.181628
$496$	3.61486	−	4.23471i	0.162312	−	0.190144i
$497$	−0.434798			−0.0195034
$498$	0.946849	−	2.91410i	0.0424293	−	0.130584i
$499$	−3.51482	−	10.8175i	−0.157345	−	0.484258i	0.841046	−	0.540963i	$-0.181940\pi$
$499$	−3.51482	−	10.8175i	−0.157345	−	0.484258i	−0.998391	+	0.0567058i	$0.981940\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	21.7601			0.972169
$502$	17.4079			0.776951
$503$	21.5921	+	15.6876i	0.962744	+	0.699474i	0.953786	−	0.300486i	$-0.0971487\pi$
$503$	21.5921	+	15.6876i	0.962744	+	0.699474i	0.00895748	+	0.999960i	$0.497149\pi$
$504$	−0.170108	+	0.123590i	−0.00757720	+	0.00550516i
$505$	−5.51464	+	4.00662i	−0.245398	+	0.178292i
$506$	8.78825	−	27.0475i	0.390686	−	1.20241i
$507$	−10.1038	−	7.34083i	−0.448725	−	0.326018i
$508$	3.44121	−	10.5909i	0.152679	−	0.469897i
$509$	−7.00080	−	21.5463i	−0.310305	−	0.955021i	−0.977644	−	0.210267i	$-0.932567\pi$
$509$	−7.00080	−	21.5463i	−0.310305	−	0.955021i	0.667339	−	0.744754i	$-0.267433\pi$
$510$	4.78750	−	3.47832i	0.211994	−	0.154023i
$511$	−0.317621	−	0.977538i	−0.0140507	−	0.0432437i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−3.41434	+	2.48067i	−0.150747	+	0.109524i
$514$	−5.02083	−	15.4525i	−0.221459	−	0.681582i
$515$	−5.23538	+	16.1128i	−0.230698	+	0.710017i
$516$	7.58406	+	5.51014i	0.333870	+	0.242570i
$517$	−13.7563	+	42.3376i	−0.605002	+	1.86200i
$518$	0.617574	−	0.448694i	0.0271346	−	0.0197145i
$519$	−20.7885	+	15.1037i	−0.912515	+	0.662981i
$520$	−4.08445	−	2.96753i	−0.179115	−	0.130135i
$521$	−19.5140			−0.854924			−0.427462	−	0.904033i	$-0.640592\pi$
$521$	−19.5140			−0.854924			−0.427462	+	0.904033i	$0.640592\pi$
$522$	8.98950			0.393460
$523$	17.5659	+	12.7624i	0.768104	+	0.558060i	0.901385	−	0.433018i	$-0.142551\pi$
$523$	17.5659	+	12.7624i	0.768104	+	0.558060i	−0.133281	+	0.991078i	$0.542551\pi$
$524$	1.96995	+	6.06288i	0.0860577	+	0.264858i
$525$	−0.0649753	+	0.199974i	−0.00283576	+	0.00872756i
$526$	5.09242			0.222040
$527$	−30.4435	−	12.6008i	−1.32614	−	0.548898i
$528$	−4.04096			−0.175860
$529$	8.19831	−	25.2318i	0.356448	−	1.09703i
$530$	−0.0704173	−	0.216722i	−0.00305873	−	0.00941381i
$531$	−6.48788	−	4.71372i	−0.281550	−	0.204558i
$532$	−0.887393			−0.0384733
$533$	−26.7521			−1.15876
$534$	6.89602	+	5.01025i	0.298420	+	0.216815i
$535$	−7.71662	+	5.60646i	−0.333619	+	0.242388i
$536$	9.35179	−	6.79447i	0.403936	−	0.293477i
$537$	−2.18333	+	6.71959i	−0.0942176	+	0.289972i
$538$	−17.5103	−	12.7220i	−0.754924	−	0.548484i
$539$	8.68588	−	26.7324i	0.374127	−	1.15144i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	−1.05185	+	0.764216i	−0.0452227	+	0.0328562i	−0.610167	−	0.792273i	$-0.708898\pi$
$541$	−1.05185	+	0.764216i	−0.0452227	+	0.0328562i	0.564944	+	0.825129i	$0.308898\pi$
$542$	−4.55805	−	14.0283i	−0.195785	−	0.602565i
$543$	0.870743	+	2.67987i	0.0373672	+	0.115004i
$544$	−4.78750	+	3.47832i	−0.205262	+	0.149132i
$545$	−5.07253	−	15.6117i	−0.217284	−	0.668730i
$546$	0.328038	−	1.00960i	0.0140387	−	0.0432068i
$547$	9.81611	+	7.13182i	0.419707	+	0.304935i	0.777520	−	0.628858i	$-0.216478\pi$
$547$	9.81611	+	7.13182i	0.419707	+	0.304935i	−0.357813	+	0.933793i	$0.616478\pi$
$548$	−0.942236	+	2.89990i	−0.0402503	+	0.123878i
$549$	8.03679	−	5.83907i	0.343002	−	0.249205i
$550$	−3.26921	+	2.37522i	−0.139399	+	0.101280i
$551$	30.6933	+	22.3000i	1.30758	+	0.950010i
$552$	−7.03778			−0.299548
$553$	2.18764			0.0930281
$554$	18.8954	+	13.7283i	0.802791	+	0.583262i
$555$	1.12188	+	3.45280i	0.0476212	+	0.146563i
$556$	−6.24293	+	19.2138i	−0.264759	+	0.814845i
$557$	−6.88374			−0.291673			−0.145837	−	0.989309i	$-0.546587\pi$
$557$	−6.88374			−0.291673			−0.145837	+	0.989309i	$0.546587\pi$
$558$	−3.61486	+	4.23471i	−0.153029	+	0.179269i
$559$	−47.3282			−2.00177
$560$	0.0649753	−	0.199974i	0.00274571	−	0.00845042i
$561$	7.38956	+	22.7427i	0.311987	+	0.960198i
$562$	7.46326	+	5.42238i	0.314819	+	0.228729i
$563$	28.8376			1.21536			0.607680	−	0.794182i	$-0.292100\pi$
$563$	28.8376			1.21536			0.607680	+	0.794182i	$0.292100\pi$
$564$	11.0163			0.463869
$565$	−14.6968	−	10.6778i	−0.618298	−	0.449220i
$566$	−21.3830	+	15.5357i	−0.898796	+	0.653013i
$567$	0.170108	−	0.123590i	0.00714385	−	0.00519031i
$568$	−0.639004	+	1.96665i	−0.0268120	+	0.0825189i
$569$	−4.17731	−	3.03499i	−0.175122	−	0.127233i	0.496772	−	0.867881i	$-0.334519\pi$
$569$	−4.17731	−	3.03499i	−0.175122	−	0.127233i	−0.671893	+	0.740648i	$0.734519\pi$
$570$	1.30416	−	4.01380i	0.0546254	−	0.168120i
$571$	−2.07438	−	6.38428i	−0.0868100	−	0.267174i	0.898223	−	0.439540i	$-0.144859\pi$
$571$	−2.07438	−	6.38428i	−0.0868100	−	0.267174i	−0.985033	+	0.172367i	$0.944859\pi$
$572$	16.5051	−	11.9917i	0.690114	−	0.501397i
$573$	2.57849	+	7.93579i	0.107718	+	0.331522i
$574$	−0.344295	−	1.05963i	−0.0143706	−	0.0442281i
$575$	−5.69368	+	4.13670i	−0.237443	+	0.172512i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−0.708053	+	2.17916i	−0.0294766	+	0.0907197i	−0.964713	−	0.263305i	$-0.915187\pi$
$577$	−0.708053	+	2.17916i	−0.0294766	+	0.0907197i	0.935236	+	0.354025i	$0.115187\pi$
$578$	14.5776	+	10.5912i	0.606347	+	0.440537i
$579$	4.23375	−	13.0301i	0.175948	−	0.541514i
$580$	−7.27266	+	5.28390i	−0.301981	+	0.219402i
$581$	−0.521222	+	0.378690i	−0.0216239	+	0.0157107i
$582$	−7.71397	−	5.60453i	−0.319754	−	0.232315i
$583$	0.920835			0.0381371
$584$	−4.88834			−0.202281
$585$	4.08445	+	2.96753i	0.168871	+	0.122692i
$586$	6.14899	+	18.9247i	0.254013	+	0.781770i
$587$	7.35579	−	22.6388i	0.303606	−	0.934403i	−0.676588	−	0.736362i	$-0.736542\pi$
$587$	7.35579	−	22.6388i	0.303606	−	0.934403i	0.980194	−	0.198041i	$-0.0634579\pi$
$588$	−6.95579			−0.286852
$589$	−22.8473	+	5.49148i	−0.941406	+	0.226272i
$590$	8.01947			0.330156
$591$	−3.40574	+	10.4818i	−0.140093	+	0.431163i
$592$	−1.12188	−	3.45280i	−0.0461091	−	0.141909i
$593$	32.4042	+	23.5431i	1.33068	+	0.966798i	0.999732	+	0.0231497i	$0.00736942\pi$
$593$	32.4042	+	23.5431i	1.33068	+	0.966798i	0.330951	+	0.943648i	$0.392631\pi$
$594$	4.04096			0.165803
$595$	−1.24428			−0.0510104
$596$	5.11506	+	3.71631i	0.209521	+	0.152226i
$597$	−8.86708	+	6.44231i	−0.362905	+	0.263666i
$598$	28.7454	−	20.8848i	1.17549	−	0.854043i
$599$	6.60542	−	20.3294i	0.269890	−	0.830637i	−0.720636	−	0.693314i	$-0.756150\pi$
$599$	6.60542	−	20.3294i	0.269890	−	0.830637i	0.990526	−	0.137323i	$-0.0438499\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−0.748341	+	2.30316i	−0.0305255	+	0.0939477i	−0.965158	−	0.261666i	$-0.915728\pi$
$601$	−0.748341	+	2.30316i	−0.0305255	+	0.0939477i	0.934633	+	0.355614i	$0.115728\pi$
$602$	−0.609105	−	1.87463i	−0.0248253	−	0.0764044i
$603$	−9.35179	+	6.79447i	−0.380834	+	0.276692i
$604$	6.13410	+	18.8788i	0.249593	+	0.768168i
$605$	−1.64687	−	5.06854i	−0.0669547	−	0.206066i
$606$	−5.51464	+	4.00662i	−0.224017	+	0.162758i
$607$	−8.16825	−	25.1393i	−0.331539	−	1.02037i	−0.968402	−	0.249395i	$-0.919768\pi$
$607$	−8.16825	−	25.1393i	−0.331539	−	1.02037i	0.636863	−	0.770977i	$-0.280232\pi$
$608$	−1.30416	+	4.01380i	−0.0528908	+	0.162781i
$609$	−1.52918	−	1.11102i	−0.0619656	−	0.0450207i
$610$	−3.06978	+	9.44781i	−0.124292	+	0.382531i
$611$	−44.9954	+	32.6911i	−1.82032	+	1.32254i
$612$	4.78750	−	3.47832i	0.193523	−	0.140603i
$613$	−13.0148	−	9.45578i	−0.525661	−	0.381915i	0.293071	−	0.956091i	$-0.405323\pi$
$613$	−13.0148	−	9.45578i	−0.525661	−	0.381915i	−0.818732	+	0.574175i	$0.805323\pi$
$614$	13.1491			0.530655
$615$	5.29885			0.213670
$616$	0.687399	+	0.499424i	0.0276961	+	0.0201224i
$617$	−0.826089	−	2.54244i	−0.0332571	−	0.102355i	0.933050	−	0.359747i	$-0.117137\pi$
$617$	−0.826089	−	2.54244i	−0.0332571	−	0.102355i	−0.966307	+	0.257392i	$0.917137\pi$
$618$	−5.23538	+	16.1128i	−0.210598	+	0.648154i
$619$	31.3547			1.26025			0.630126	−	0.776493i	$-0.283003\pi$
$619$	31.3547			1.26025			0.630126	+	0.776493i	$0.283003\pi$
$620$	0.435388	−	5.55072i	0.0174856	−	0.222922i
$621$	7.03778			0.282416
$622$	−4.60911	+	14.1854i	−0.184808	+	0.568782i
$623$	−0.553847	−	1.70456i	−0.0221894	−	0.0682919i
$624$	−4.08445	−	2.96753i	−0.163509	−	0.118796i
$625$	1.00000			0.0400000
$626$	−14.6866			−0.586994
$627$	13.7972	+	10.0243i	0.551008	+	0.400331i
$628$	−8.99582	+	6.53585i	−0.358972	+	0.260809i
$629$	−17.3810	+	12.6280i	−0.693024	+	0.503511i
$630$	−0.0649753	+	0.199974i	−0.00258868	+	0.00796714i
$631$	−17.1613	−	12.4684i	−0.683180	−	0.496359i	0.191231	−	0.981545i	$-0.438752\pi$
$631$	−17.1613	−	12.4684i	−0.683180	−	0.496359i	−0.874411	+	0.485186i	$0.838752\pi$
$632$	3.21509	−	9.89502i	0.127889	−	0.393603i
$633$	4.12447	+	12.6938i	0.163933	+	0.504533i
$634$	−13.1358	+	9.54369i	−0.521688	+	0.379028i
$635$	−3.44121	−	10.5909i	−0.136560	−	0.420289i
$636$	−0.0704173	−	0.216722i	−0.00279223	−	0.00859360i
$637$	28.4106	−	20.6415i	1.12567	−	0.817846i
$638$	−11.2254	−	34.5483i	−0.444419	−	1.36778i
$639$	0.639004	−	1.96665i	0.0252786	−	0.0777996i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	6.88155	−	21.1792i	0.271805	−	0.836529i	−0.718242	−	0.695793i	$-0.755053\pi$
$641$	6.88155	−	21.1792i	0.271805	−	0.836529i	0.990047	−	0.140736i	$-0.0449469\pi$
$642$	−7.71662	+	5.60646i	−0.304551	+	0.221269i
$643$	22.3352	−	16.2275i	0.880815	−	0.639949i	−0.0526521	−	0.998613i	$-0.516767\pi$
$643$	22.3352	−	16.2275i	0.880815	−	0.639949i	0.933467	+	0.358664i	$0.116767\pi$
$644$	1.19718	+	0.869802i	0.0471755	+	0.0342750i
$645$	9.37441			0.369117
$646$	24.9747			0.982617
$647$	−26.2766	−	19.0911i	−1.03304	−	0.750548i	−0.0641253	−	0.997942i	$-0.520426\pi$
$647$	−26.2766	−	19.0911i	−1.03304	−	0.750548i	−0.968915	+	0.247394i	$0.920426\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	−10.0141	+	30.8203i	−0.393088	+	1.20980i
$650$	−5.04866			−0.198025
$651$	1.13829	−	0.273593i	0.0446129	−	0.0107230i
$652$	5.60444			0.219487
$653$	6.62461	−	20.3885i	0.259241	−	0.797862i	−0.733723	−	0.679448i	$-0.762219\pi$
$653$	6.62461	−	20.3885i	0.259241	−	0.797862i	0.992964	−	0.118414i	$-0.0377809\pi$
$654$	−5.07253	−	15.6117i	−0.198352	−	0.610464i
$655$	5.15740	+	3.74707i	0.201516	+	0.146410i
$656$	−5.29885			−0.206885
$657$	4.88834			0.190712
$658$	−1.87395	−	1.36151i	−0.0730543	−	0.0530771i
$659$	0.267633	−	0.194447i	0.0104255	−	0.00757458i	−0.582560	−	0.812787i	$-0.697949\pi$
$659$	0.267633	−	0.194447i	0.0104255	−	0.00757458i	0.592986	+	0.805213i	$0.297949\pi$
$660$	−3.26921	+	2.37522i	−0.127254	+	0.0924552i
$661$	7.50582	−	23.1005i	0.291943	−	0.898507i	−0.692289	−	0.721621i	$-0.743397\pi$
$661$	7.50582	−	23.1005i	0.291943	−	0.898507i	0.984231	−	0.176886i	$-0.0566025\pi$
$662$	24.8002	+	18.0184i	0.963888	+	0.700306i
$663$	−9.23229	+	28.4141i	−0.358553	+	1.10351i
$664$	0.946849	+	2.91410i	0.0367449	+	0.113089i
$665$	−0.717916	+	0.521596i	−0.0278396	+	0.0202266i
$666$	1.12188	+	3.45280i	0.0434721	+	0.133793i
$667$	−19.5503	−	60.1696i	−0.756991	−	2.32978i
$668$	−17.6043	+	12.7903i	−0.681130	+	0.494870i
$669$	5.24372	+	16.1385i	0.202734	+	0.623951i
$670$	3.57207	−	10.9937i	0.138001	−	0.424723i
$671$	−32.4764	−	23.5955i	−1.25374	−	0.910893i
$672$	0.0649753	−	0.199974i	0.00250648	−	0.00771415i
$673$	−0.292416	+	0.212452i	−0.0112718	+	0.00818944i	−0.593407	−	0.804903i	$-0.702217\pi$
$673$	−0.292416	+	0.212452i	−0.0112718	+	0.00818944i	0.582135	+	0.813092i	$0.302217\pi$
$674$	−5.83412	+	4.23874i	−0.224722	+	0.163270i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	12.4890			0.480345
$677$	−7.60236			−0.292182			−0.146091	−	0.989271i	$-0.546669\pi$
$677$	−7.60236			−0.292182			−0.146091	+	0.989271i	$0.546669\pi$
$678$	−14.6968	−	10.6778i	−0.564426	−	0.410080i
$679$	0.619539	+	1.90675i	0.0237757	+	0.0731742i
$680$	−1.82866	+	5.62804i	−0.0701260	+	0.215826i
$681$	17.2330			0.660371
$682$	20.7887	+	8.60460i	0.796042	+	0.329487i
$683$	2.20436			0.0843476			0.0421738	−	0.999110i	$-0.486572\pi$
$683$	2.20436			0.0843476			0.0421738	+	0.999110i	$0.486572\pi$
$684$	1.30416	−	4.01380i	0.0498659	−	0.153472i
$685$	0.942236	+	2.89990i	0.0360010	+	0.110800i
$686$	2.37399	+	1.72480i	0.0906392	+	0.0658532i
$687$	−23.0499			−0.879408
$688$	−9.37441			−0.357396
$689$	0.930745	+	0.676226i	0.0354586	+	0.0257622i
$690$	−5.69368	+	4.13670i	−0.216755	+	0.157481i
$691$	15.4103	−	11.1962i	0.586235	−	0.425925i	−0.254731	−	0.967012i	$-0.581987\pi$
$691$	15.4103	−	11.1962i	0.586235	−	0.425925i	0.840967	+	0.541087i	$0.181987\pi$
$692$	7.94051	−	24.4384i	0.301853	−	0.929008i
$693$	−0.687399	−	0.499424i	−0.0261121	−	0.0189716i
$694$	7.67926	−	23.6343i	0.291501	−	0.897147i
$695$	6.24293	+	19.2138i	0.236808	+	0.728820i
$696$	−7.27266	+	5.28390i	−0.275670	+	0.200286i
$697$	9.68981	+	29.8222i	0.367028	+	1.12960i
$698$	7.06311	+	21.7380i	0.267342	+	0.822796i
$699$	16.2248	−	11.7880i	0.613679	−	0.445864i
$700$	−0.0649753	−	0.199974i	−0.00245584	−	0.00755829i
$701$	15.0337	−	46.2691i	0.567816	−	1.74756i	−0.0916156	−	0.995794i	$-0.529203\pi$
$701$	15.0337	−	46.2691i	0.567816	−	1.74756i	0.659432	−	0.751764i	$-0.270797\pi$
$702$	4.08445	+	2.96753i	0.154158	+	0.112002i
$703$	−4.73475	+	14.5721i	−0.178574	+	0.549595i
$704$	3.26921	−	2.37522i	0.123213	−	0.0895194i
$705$	8.91236	−	6.47521i	0.335659	−	0.243870i
$706$	−19.3623	−	14.0675i	−0.728710	−	0.529439i
$707$	1.43326			0.0539034
$708$	8.01947			0.301390
$709$	−19.1035	−	13.8795i	−0.717446	−	0.521255i	0.168121	−	0.985766i	$-0.446230\pi$
$709$	−19.1035	−	13.8795i	−0.717446	−	0.521255i	−0.885567	+	0.464512i	$0.846230\pi$
$710$	0.639004	+	1.96665i	0.0239814	+	0.0738072i
$711$	−3.21509	+	9.89502i	−0.120575	+	0.371092i
$712$	−8.52395			−0.319449
$713$	36.2058	+	14.9858i	1.35592	+	0.561224i
$714$	−1.24428			−0.0465659
$715$	6.30439	−	19.4029i	0.235771	−	0.725628i
$716$	−2.18333	−	6.71959i	−0.0815948	−	0.251123i
$717$	7.91614	+	5.75141i	0.295634	+	0.214790i
$718$	23.8524			0.890164
$719$	−6.26234			−0.233546			−0.116773	−	0.993159i	$-0.537255\pi$
$719$	−6.26234			−0.233546			−0.116773	+	0.993159i	$0.537255\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	2.88197	−	2.09388i	0.107330	−	0.0779800i
$722$	−0.961562	+	0.698616i	−0.0357856	+	0.0259998i
$723$	1.48837	−	4.58073i	0.0553531	−	0.170359i
$724$	−2.27963	−	1.65625i	−0.0847220	−	0.0615541i
$725$	−2.77791	+	8.54953i	−0.103169	+	0.317521i
$726$	−1.64687	−	5.06854i	−0.0611210	−	0.188111i
$727$	8.07745	−	5.86861i	0.299576	−	0.217655i	−0.427835	−	0.903857i	$-0.640723\pi$
$727$	8.07745	−	5.86861i	0.299576	−	0.217655i	0.727411	+	0.686202i	$0.240723\pi$
$728$	0.328038	+	1.00960i	0.0121579	+	0.0374182i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.95475	+	2.87329i	−0.146372	+	0.106345i
$731$	17.1426	+	52.7596i	0.634043	+	1.95138i
$732$	−3.06978	+	9.44781i	−0.113462	+	0.349201i
$733$	20.8128	+	15.1214i	0.768740	+	0.558522i	0.901579	−	0.432615i	$-0.142409\pi$
$733$	20.8128	+	15.1214i	0.768740	+	0.558522i	−0.132839	+	0.991138i	$0.542409\pi$
$734$	−0.290176	+	0.893071i	−0.0107106	+	0.0329638i
$735$	−5.62735	+	4.08851i	−0.207568	+	0.150807i
$736$	5.69368	−	4.13670i	0.209872	−	0.152481i
$737$	37.7902	+	27.4562i	1.39202	+	1.01136i
$738$	5.29885			0.195053
$739$	37.2611			1.37067			0.685336	−	0.728227i	$-0.259655\pi$
$739$	37.2611			1.37067			0.685336	+	0.728227i	$0.259655\pi$
$740$	−2.93713	−	2.13395i	−0.107971	−	0.0784454i
$741$	6.58428	+	20.2643i	0.241879	+	0.744428i
$742$	−0.0148063	+	0.0455690i	−0.000543555	+	0.00167289i
$743$	−15.6410			−0.573812			−0.286906	−	0.957959i	$-0.592627\pi$
$743$	−15.6410			−0.573812			−0.286906	+	0.957959i	$0.592627\pi$
$744$	0.435388	−	5.55072i	0.0159621	−	0.203499i
$745$	6.32256			0.231641
$746$	11.1149	−	34.2082i	0.406946	−	1.25245i
$747$	−0.946849	−	2.91410i	−0.0346434	−	0.106621i
$748$	−19.3461	−	14.0558i	−0.707364	−	0.513930i
$749$	2.00556			0.0732816
$750$	1.00000			0.0365148
$751$	10.9843	+	7.98057i	0.400823	+	0.291215i	0.769876	−	0.638193i	$-0.220318\pi$
$751$	10.9843	+	7.98057i	0.400823	+	0.291215i	−0.369053	+	0.929408i	$0.620318\pi$
$752$	−8.91236	+	6.47521i	−0.325000	+	0.236126i
$753$	14.0833	−	10.2321i	0.513223	−	0.372878i
$754$	14.0247	−	43.1636i	0.510750	−	1.57193i
$755$	16.0593	+	11.6677i	0.584457	+	0.424633i
$756$	−0.0649753	+	0.199974i	−0.00236313	+	0.00727297i
$757$	12.0265	+	37.0137i	0.437109	+	1.34528i	0.890910	+	0.454181i	$0.150068\pi$
$757$	12.0265	+	37.0137i	0.437109	+	1.34528i	−0.453800	+	0.891103i	$0.649932\pi$
$758$	−3.31625	+	2.40940i	−0.120452	+	0.0875132i
$759$	−8.78825	−	27.0475i	−0.318993	−	0.981761i
$760$	1.30416	+	4.01380i	0.0473070	+	0.145596i
$761$	22.1872	−	16.1199i	0.804284	−	0.584347i	−0.107884	−	0.994164i	$-0.534407\pi$
$761$	22.1872	−	16.1199i	0.804284	−	0.584347i	0.912168	+	0.409817i	$0.134407\pi$
$762$	−3.44121	−	10.5909i	−0.124662	−	0.383670i
$763$	−1.06657	+	3.28258i	−0.0386126	+	0.118837i
$764$	−6.75059	−	4.90459i	−0.244228	−	0.177442i
$765$	1.82866	−	5.62804i	0.0661154	−	0.203482i
$766$	13.7261	−	9.97262i	0.495945	−	0.360325i
$767$	−32.7551	+	23.7980i	−1.18272	+	0.859295i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	17.4238			0.628318			0.314159	−	0.949370i	$-0.398278\pi$
$769$	17.4238			0.628318			0.314159	+	0.949370i	$0.398278\pi$
$770$	0.849671			0.0306200
$771$	−13.1447	−	9.55019i	−0.473395	−	0.343942i
$772$	4.23375	+	13.0301i	0.152376	+	0.468965i
$773$	0.702790	−	2.16296i	0.0252776	−	0.0777964i	−0.937622	−	0.347657i	$-0.886977\pi$
$773$	0.702790	−	2.16296i	0.0252776	−	0.0777964i	0.962900	+	0.269860i	$0.0869775\pi$
$774$	9.37441			0.336956
$775$	−2.91039	−	4.74654i	−0.104544	−	0.170501i
$776$	9.53499			0.342286
$777$	0.235892	−	0.726001i	0.00846258	−	0.0260452i
$778$	−3.74120	−	11.5142i	−0.134129	−	0.412806i
$779$	18.0921	+	13.1447i	0.648217	+	0.470957i
$780$	−5.04866			−0.180771
$781$	−8.35615			−0.299007
$782$	−33.6933	−	24.4796i	−1.20487	−	0.875390i
$783$	7.27266	−	5.28390i	0.259904	−	0.188831i
$784$	5.62735	−	4.08851i	0.200977	−	0.146018i
$785$	−3.43610	+	10.5752i	−0.122640	+	0.377446i
$786$	5.15740	+	3.74707i	0.183958	+	0.133653i
$787$	0.519609	−	1.59919i	0.0185220	−	0.0570050i	−0.941368	−	0.337381i	$-0.890459\pi$
$787$	0.519609	−	1.59919i	0.0185220	−	0.0570050i	0.959890	+	0.280376i	$0.0904590\pi$
$788$	−3.40574	−	10.4818i	−0.121324	−	0.373398i
$789$	4.11986	−	2.99325i	0.146671	−	0.106563i
$790$	−3.21509	−	9.89502i	−0.114388	−	0.352049i
$791$	1.18036	+	3.63276i	0.0419686	+	0.129166i
$792$	−3.26921	+	2.37522i	−0.116166	+	0.0843997i
$793$	−15.4983	−	47.6988i	−0.550360	−	1.69383i
$794$	−8.35436	+	25.7121i	−0.296485	+	0.912487i
$795$	−0.184355	−	0.133942i	−0.00653840	−	0.00475042i
$796$	3.38692	−	10.4239i	0.120046	−	0.369464i
$797$	−30.3362	+	22.0406i	−1.07456	+	0.780717i	−0.976727	−	0.214485i	$-0.931193\pi$
$797$	−30.3362	+	22.0406i	−1.07456	+	0.780717i	−0.0978377	+	0.995202i	$0.531193\pi$
$798$	−0.717916	+	0.521596i	−0.0254139	+	0.0184643i
$799$	52.7404	+	38.3182i	1.86582	+	1.35560i
$800$	−1.00000			−0.0353553
$801$	8.52395			0.301179
$802$	−14.9470	−	10.8597i	−0.527798	−	0.383468i
$803$	−6.10420	−	18.7868i	−0.215412	−	0.662971i
$804$	3.57207	−	10.9937i	0.125977	−	0.387718i
$805$	1.47980			0.0521559
$806$	14.6936	+	23.9637i	0.517559	+	0.844084i
$807$	−21.6440			−0.761904
$808$	2.10641	−	6.48285i	0.0741031	−	0.228066i
$809$	−3.93463	−	12.1095i	−0.138334	−	0.425749i	0.857760	−	0.514051i	$-0.171856\pi$
$809$	−3.93463	−	12.1095i	−0.138334	−	0.425749i	−0.996094	+	0.0883023i	$0.971856\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	5.00846			0.175871			0.0879355	−	0.996126i	$-0.471973\pi$
$811$	5.00846			0.175871			0.0879355	+	0.996126i	$0.471973\pi$
$812$	1.89017			0.0663321
$813$	−11.9331	−	8.66994i	−0.418514	−	0.304068i
$814$	11.8688	−	8.62320i	0.416002	−	0.302243i
$815$	4.53409	−	3.29421i	0.158822	−	0.115391i
$816$	−1.82866	+	5.62804i	−0.0640160	+	0.197021i
$817$	32.0075	+	23.2548i	1.11980	+	0.813582i
$818$	5.52686	−	17.0099i	0.193242	−	0.594738i
$819$	−0.328038	−	1.00960i	−0.0114626	−	0.0352782i
$820$	−4.28686	+	3.11459i	−0.149704	+	0.108766i
$821$	−5.39061	−	16.5906i	−0.188134	−	0.579016i	0.811855	−	0.583860i	$-0.198458\pi$
$821$	−5.39061	−	16.5906i	−0.188134	−	0.579016i	−0.999988	+	0.00484384i	$0.998458\pi$
$822$	0.942236	+	2.89990i	0.0328643	+	0.101146i
$823$	5.18965	−	3.77050i	0.180900	−	0.131431i	−0.493650	−	0.869661i	$-0.664338\pi$
$823$	5.18965	−	3.77050i	0.180900	−	0.131431i	0.674550	+	0.738229i	$0.264338\pi$
$824$	−5.23538	−	16.1128i	−0.182383	−	0.561318i
$825$	−1.24873	+	3.84318i	−0.0434751	+	0.133802i
$826$	−1.36417	−	0.991129i	−0.0474656	−	0.0344858i
$827$	−1.07338	+	3.30353i	−0.0373251	+	0.114875i	−0.967983	−	0.251015i	$-0.919235\pi$
$827$	−1.07338	+	3.30353i	−0.0373251	+	0.114875i	0.930658	+	0.365890i	$0.119235\pi$
$828$	−5.69368	+	4.13670i	−0.197869	+	0.143760i
$829$	−1.75608	+	1.27587i	−0.0609911	+	0.0443126i	−0.617863	−	0.786286i	$-0.712001\pi$
$829$	−1.75608	+	1.27587i	−0.0609911	+	0.0443126i	0.556872	+	0.830598i	$0.312001\pi$
$830$	2.47888	+	1.80101i	0.0860433	+	0.0625141i
$831$	23.3561			0.810213
$832$	5.04866			0.175031
$833$	−33.3008	−	24.1945i	−1.15381	−	0.838289i
$834$	6.24293	+	19.2138i	0.216175	+	0.665319i
$835$	−6.72424	+	20.6951i	−0.232702	+	0.716183i
$836$	−17.0543			−0.589836
$837$	−0.435388	+	5.55072i	−0.0150492	+	0.191861i
$838$	17.9381			0.619661
$839$	7.13053	−	21.9455i	0.246173	−	0.757644i	−0.749268	−	0.662267i	$-0.769594\pi$
$839$	7.13053	−	21.9455i	0.246173	−	0.757644i	0.995441	−	0.0953766i	$-0.0304055\pi$
$840$	−0.0649753	−	0.199974i	−0.00224186	−	0.00689974i
$841$	−41.9161	−	30.4539i	−1.44538	−	1.05013i
$842$	9.82384			0.338552
$843$	9.22510			0.317729
$844$	−10.7980	−	7.84520i	−0.371682	−	0.270043i
$845$	10.1038	−	7.34083i	0.347581	−	0.252532i
$846$	8.91236	−	6.47521i	0.306413	−	0.222622i
$847$	−0.346278	+	1.06573i	−0.0118983	+	0.0366191i
$848$	0.184355	+	0.133942i	0.00633077	+	0.00459958i
$849$	−8.16759	+	25.1373i	−0.280311	+	0.862708i
$850$	1.82866	+	5.62804i	0.0627226	+	0.193040i
$851$	20.6708	−	15.0182i	0.708587	−	0.514819i
$852$	0.639004	+	1.96665i	0.0218919	+	0.0673764i
$853$	9.50912	+	29.2661i	0.325586	+	1.00205i	0.971175	+	0.238366i	$0.0766118\pi$
$853$	9.50912	+	29.2661i	0.325586	+	1.00205i	−0.645589	+	0.763685i	$0.723388\pi$
$854$	1.68985	−	1.22775i	0.0578256	−	0.0420127i
$855$	−1.30416	−	4.01380i	−0.0446014	−	0.137269i
$856$	2.94749	−	9.07144i	0.100743	−	0.310055i
$857$	−33.6848	−	24.4734i	−1.15065	−	0.835996i	−0.162083	−	0.986777i	$-0.551821\pi$
$857$	−33.6848	−	24.4734i	−1.15065	−	0.835996i	−0.988567	+	0.150781i	$0.951821\pi$
$858$	6.30439	−	19.4029i	0.215228	−	0.662405i
$859$	12.3847	−	8.99798i	0.422559	−	0.307007i	−0.356108	−	0.934445i	$-0.615896\pi$
$859$	12.3847	−	8.99798i	0.422559	−	0.307007i	0.778667	+	0.627438i	$0.215896\pi$
$860$	−7.58406	+	5.51014i	−0.258614	+	0.187894i
$861$	−0.901375	−	0.654888i	−0.0307188	−	0.0223185i
$862$	−40.6391			−1.38417
$863$	−3.68188			−0.125333			−0.0626663	−	0.998035i	$-0.519960\pi$
$863$	−3.68188			−0.125333			−0.0626663	+	0.998035i	$0.519960\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−7.94051	−	24.4384i	−0.269985	−	0.830930i
$866$	−3.77757	+	11.6262i	−0.128367	+	0.395073i
$867$	18.0189			0.611953
$868$	−0.760078	+	0.890409i	−0.0257987	+	0.0302225i
$869$	42.0432			1.42622
$870$	−2.77791	+	8.54953i	−0.0941800	+	0.289856i
$871$	18.0341	+	55.5034i	0.611064	+	1.88066i
$872$	13.2801	+	9.64853i	0.449720	+	0.326741i
$873$	−9.53499			−0.322710
$874$	−29.7019			−1.00468
$875$	−0.170108	−	0.123590i	−0.00575069	−	0.00417812i
$876$	−3.95475	+	2.87329i	−0.133619	+	0.0970796i
$877$	−15.5255	+	11.2799i	−0.524258	+	0.380896i	−0.818206	−	0.574926i	$-0.805031\pi$
$877$	−15.5255	+	11.2799i	−0.524258	+	0.380896i	0.293948	+	0.955822i	$0.405031\pi$
$878$	−12.3585	+	38.0355i	−0.417079	+	1.28364i
$879$	16.0983	+	11.6961i	0.542981	+	0.394499i
$880$	1.24873	−	3.84318i	0.0420946	−	0.129554i
$881$	13.5688	+	41.7606i	0.457146	+	1.40695i	0.868597	+	0.495519i	$0.165022\pi$
$881$	13.5688	+	41.7606i	0.457146	+	1.40695i	−0.411451	+	0.911432i	$0.634978\pi$
$882$	−5.62735	+	4.08851i	−0.189483	+	0.137667i
$883$	10.8098	+	33.2691i	0.363778	+	1.11959i	0.950743	+	0.309981i	$0.100323\pi$
$883$	10.8098	+	33.2691i	0.363778	+	1.11959i	−0.586965	+	0.809612i	$0.699677\pi$
$884$	−9.23229	−	28.4141i	−0.310516	−	0.955669i
$885$	6.48788	−	4.71372i	0.218088	−	0.158450i
$886$	−7.82342	−	24.0780i	−0.262833	−	0.808917i
$887$	−5.95294	+	18.3213i	−0.199880	+	0.615168i	0.800005	+	0.599994i	$0.204830\pi$
$887$	−5.95294	+	18.3213i	−0.199880	+	0.615168i	−0.999885	+	0.0151743i	$0.995170\pi$
$888$	−2.93713	−	2.13395i	−0.0985635	−	0.0716106i
$889$	−0.723564	+	2.22690i	−0.0242676	+	0.0746879i
$890$	−6.89602	+	5.01025i	−0.231155	+	0.167944i
$891$	3.26921	−	2.37522i	0.109523	−	0.0795728i
$892$	−13.7282	−	9.97414i	−0.459655	−	0.333959i
$893$	46.4927			1.55582
$894$	6.32256			0.211458
$895$	−5.71603	−	4.15294i	−0.191066	−	0.138817i
$896$	0.0649753	+	0.199974i	0.00217067	+	0.00668065i
$897$	10.9798	−	33.7923i	0.366604	−	1.12829i
$898$	17.3112			0.577681
$899$	48.6655	−	11.6970i	1.62308	−	0.390118i
$900$	1.00000			0.0333333
$901$	0.416707	−	1.28249i	0.0138825	−	0.0427260i
$902$	−6.61682	−	20.3645i	−0.220316	−	0.678063i
$903$	−1.59466	−	1.15859i	−0.0530669	−	0.0385554i
$904$	18.1662			0.604199
$905$	−2.81778			−0.0936663
$906$	16.0593	+	11.6677i	0.533534	+	0.387635i
$907$	−18.6171	+	13.5261i	−0.618172	+	0.449128i	−0.852282	−	0.523082i	$-0.824782\pi$
$907$	−18.6171	+	13.5261i	−0.618172	+	0.449128i	0.234111	+	0.972210i	$0.424782\pi$
$908$	−13.9418	+	10.1293i	−0.462675	+	0.336153i
$909$	−2.10641	+	6.48285i	−0.0698651	+	0.215023i
$910$	0.858816	+	0.623966i	0.0284695	+	0.0206843i
$911$	4.21934	−	12.9858i	0.139793	−	0.430239i	−0.856512	−	0.516128i	$-0.827373\pi$
$911$	4.21934	−	12.9858i	0.139793	−	0.430239i	0.996305	+	0.0858888i	$0.0273730\pi$
$912$	1.30416	+	4.01380i	0.0431852	+	0.132910i
$913$	−10.0171	+	7.27783i	−0.331517	+	0.240861i
$914$	−7.78962	−	23.9740i	−0.257658	−	0.792989i
$915$	3.06978	+	9.44781i	0.101484	+	0.312335i
$916$	18.6477	−	13.5484i	0.616139	−	0.447651i
$917$	−0.414211	−	1.27481i	−0.0136784	−	0.0420979i
$918$	1.82866	−	5.62804i	0.0603548	−	0.185753i
$919$	−26.3701	−	19.1590i	−0.869870	−	0.631997i	0.0606823	−	0.998157i	$-0.480672\pi$
$919$	−26.3701	−	19.1590i	−0.869870	−	0.631997i	−0.930552	+	0.366160i	$0.880672\pi$
$920$	2.17479	−	6.69332i	0.0717008	−	0.220672i
$921$	10.6379	−	7.72886i	0.350529	−	0.254675i
$922$	21.4269	−	15.5675i	0.705656	−	0.512689i
$923$	−8.44608	−	6.13643i	−0.278006	−	0.201983i
$924$	0.849671			0.0279521
$925$	−3.63049			−0.119370
$926$	18.2858	+	13.2854i	0.600908	+	0.436585i
$927$	5.23538	+	16.1128i	0.171952	+	0.529215i
$928$	2.77791	−	8.54953i	0.0911894	−	0.280652i
$929$	24.5602			0.805794			0.402897	−	0.915245i	$-0.368003\pi$
$929$	24.5602			0.805794			0.402897	+	0.915245i	$0.368003\pi$
$930$	−2.91039	−	4.74654i	−0.0954355	−	0.155645i
$931$	−29.3559			−0.962102
$932$	−6.19733	+	19.0734i	−0.203000	+	0.624771i
$933$	4.60911	+	14.1854i	0.150895	+	0.464408i
$934$	15.6840	+	11.3951i	0.513197	+	0.372859i
$935$	−23.9131			−0.782042
$936$	−5.04866			−0.165021
$937$	24.3891	+	17.7197i	0.796757	+	0.578878i	0.909961	−	0.414694i	$-0.136111\pi$
$937$	24.3891	+	17.7197i	0.796757	+	0.578878i	−0.113204	+	0.993572i	$0.536111\pi$
$938$	−1.96635	+	1.42864i	−0.0642036	+	0.0466467i
$939$	−11.8817	+	8.63256i	−0.387745	+	0.281713i
$940$	−3.40422	+	10.4771i	−0.111033	+	0.341725i
$941$	14.7101	+	10.6875i	0.479535	+	0.348403i	0.801146	−	0.598469i	$-0.204224\pi$
$941$	14.7101	+	10.6875i	0.479535	+	0.348403i	−0.321611	+	0.946872i	$0.604224\pi$
$942$	−3.43610	+	10.5752i	−0.111954	+	0.344559i
$943$	−11.5239	−	35.4669i	−0.375270	−	1.15496i
$944$	−6.48788	+	4.71372i	−0.211163	+	0.153419i
$945$	0.0649753	+	0.199974i	0.00211365	+	0.00650514i
$946$	−11.7061	−	36.0276i	−0.380597	−	1.17136i
$947$	−14.4371	+	10.4892i	−0.469144	+	0.340853i	−0.797108	−	0.603837i	$-0.793638\pi$
$947$	−14.4371	+	10.4892i	−0.469144	+	0.340853i	0.327963	+	0.944690i	$0.393638\pi$
$948$	−3.21509	−	9.89502i	−0.104421	−	0.321375i
$949$	7.62640	−	23.4716i	0.247563	−	0.761922i
$950$	3.41434	+	2.48067i	0.110776	+	0.0804834i
$951$	−5.01742	+	15.4420i	−0.162701	+	0.500742i
$952$	1.00664	−	0.731368i	0.0326254	−	0.0237038i
$953$	−4.71087	+	3.42264i	−0.152600	+	0.110870i	−0.661465	−	0.749976i	$-0.730065\pi$
$953$	−4.71087	+	3.42264i	−0.152600	+	0.110870i	0.508865	+	0.860846i	$0.330065\pi$
$954$	−0.184355	−	0.133942i	−0.00596871	−	0.00433652i
$955$	−8.34418			−0.270011
$956$	−9.78489			−0.316466
$957$	−29.3886	−	21.3520i	−0.949997	−	0.690213i
$958$	−0.145761	−	0.448605i	−0.00470931	−	0.0144938i
$959$	0.198119	−	0.609747i	0.00639759	−	0.0196898i
$960$	−1.00000			−0.0322749
$961$	−14.0592	+	27.6286i	−0.453524	+	0.891244i
$962$	18.3291			0.590954
$963$	−2.94749	+	9.07144i	−0.0949815	+	0.292323i
$964$	1.48837	+	4.58073i	0.0479372	+	0.147536i
$965$	11.0841	+	8.05306i	0.356809	+	0.259237i
$966$	1.47980			0.0476116
$967$	26.3071			0.845980			0.422990	−	0.906134i	$-0.360981\pi$
$967$	26.3071			0.845980			0.422990	+	0.906134i	$0.360981\pi$
$968$	4.31156	+	3.13253i	0.138579	+	0.100683i
$969$	20.2050	−	14.6798i	0.649077	−	0.471582i
$970$	7.71397	−	5.60453i	0.247681	−	0.179950i
$971$	8.65849	−	26.6481i	0.277864	−	0.855178i	−0.710583	−	0.703613i	$-0.751569\pi$
$971$	8.65849	−	26.6481i	0.277864	−	0.855178i	0.988447	−	0.151565i	$-0.0484311\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	1.31267	−	4.03998i	0.0420822	−	0.129516i
$974$	−5.54172	−	17.0557i	−0.177568	−	0.546499i
$975$	−4.08445	+	2.96753i	−0.130807	+	0.0950369i
$976$	−3.06978	−	9.44781i	−0.0982613	−	0.302417i
$977$	12.5992	+	38.7762i	0.403083	+	1.24056i	0.922486	+	0.386032i	$0.126154\pi$
$977$	12.5992	+	38.7762i	0.403083	+	1.24056i	−0.519403	+	0.854530i	$0.673846\pi$
$978$	4.53409	−	3.29421i	0.144984	−	0.105337i
$979$	−10.6441	−	32.7591i	−0.340186	−	1.04699i
$980$	2.14946	−	6.61535i	0.0686619	−	0.211320i
$981$	−13.2801	−	9.64853i	−0.424000	−	0.308054i
$982$	−4.51104	+	13.8835i	−0.143953	+	0.443042i
$983$	7.50496	−	5.45267i	0.239371	−	0.173913i	−0.461632	−	0.887072i	$-0.652736\pi$
$983$	7.50496	−	5.45267i	0.239371	−	0.173913i	0.701003	+	0.713158i	$0.252736\pi$
$984$	−4.28686	+	3.11459i	−0.136660	+	0.0992894i
$985$	−8.91634	−	6.47810i	−0.284098	−	0.206409i
$986$	−53.1970			−1.69414
$987$	−2.31633			−0.0737297
$988$	−17.2379	−	12.5240i	−0.548409	−	0.398443i
$989$	−20.3874	−	62.7459i	−0.648281	−	1.99521i
$990$	−1.24873	+	3.84318i	−0.0396871	+	0.122144i
$991$	−16.4280			−0.521852			−0.260926	−	0.965359i	$-0.584028\pi$
$991$	−16.4280			−0.521852			−0.260926	+	0.965359i	$0.584028\pi$
$992$	2.91039	+	4.74654i	0.0924050	+	0.150703i
$993$	30.6548			0.972800
$994$	0.134360	−	0.413517i	0.00426164	−	0.0131160i
$995$	−3.38692	−	10.4239i	−0.107373	−	0.330459i
$996$	2.47888	+	1.80101i	0.0785464	+	0.0570673i
$997$	−15.2514			−0.483017			−0.241509	−	0.970399i	$-0.577642\pi$
$997$	−15.2514			−0.483017			−0.241509	+	0.970399i	$0.577642\pi$
$998$	11.3742			0.360044
$999$	2.93713	+	2.13395i	0.0929265	+	0.0675151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.h.721.3	✓	16
31.4	even	5	inner	930.2.n.h.841.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.h.721.3	✓	16	1.1	even	1	trivial
930.2.n.h.841.3	yes	16	31.4	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.170108 + 0.123590i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.170108 + 0.123590i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(3.26921 + 2.37522i) q^{11} +(0.309017 - 0.951057i) q^{12} +(1.56012 + 4.80156i) q^{13} +(-0.170108 + 0.123590i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.78750 - 3.47832i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(1.30416 - 4.01380i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.0649753 + 0.199974i) q^{21} +(-3.26921 + 2.37522i) q^{22} +(-5.69368 + 4.13670i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -5.04866 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.0649753 - 0.199974i) q^{28} +(-2.77791 + 8.54953i) q^{29} +1.00000 q^{30} +(-2.91039 - 4.74654i) q^{31} -1.00000 q^{32} +(-1.24873 + 3.84318i) q^{33} +(1.82866 + 5.62804i) q^{34} +(-0.170108 - 0.123590i) q^{35} +1.00000 q^{36} -3.63049 q^{37} +(3.41434 + 2.48067i) q^{38} +(-4.08445 + 2.96753i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-1.63744 + 5.03951i) q^{41} +(-0.170108 - 0.123590i) q^{42} +(-2.89685 + 8.91559i) q^{43} +(-1.24873 - 3.84318i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-2.17479 - 6.69332i) q^{46} +(3.40422 + 10.4771i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-2.14946 - 6.61535i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(4.78750 + 3.47832i) q^{51} +(1.56012 - 4.80156i) q^{52} +(0.184355 - 0.133942i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-3.26921 - 2.37522i) q^{55} +0.210265 q^{56} +4.22036 q^{57} +(-7.27266 - 5.28390i) q^{58} +(2.47815 + 7.62696i) q^{59} +(-0.309017 + 0.951057i) q^{60} -9.93402 q^{61} +(5.41359 - 1.30119i) q^{62} -0.210265 q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.56012 - 4.80156i) q^{65} +(-3.26921 - 2.37522i) q^{66} +11.5594 q^{67} -5.91767 q^{68} +(-5.69368 - 4.13670i) q^{69} +(0.170108 - 0.123590i) q^{70} +(-1.67293 + 1.21546i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-3.95475 - 2.87329i) q^{73} +(1.12188 - 3.45280i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-3.41434 + 2.48067i) q^{76} +(0.262563 + 0.808086i) q^{77} +(-1.56012 - 4.80156i) q^{78} +(8.41721 - 6.11546i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.28686 - 3.11459i) q^{82} +(-0.946849 + 2.91410i) q^{83} +(0.170108 - 0.123590i) q^{84} +(-4.78750 + 3.47832i) q^{85} +(-7.58406 - 5.51014i) q^{86} -8.98950 q^{87} +4.04096 q^{88} +(-6.89602 - 5.01025i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-0.328038 + 1.00960i) q^{91} +7.03778 q^{92} +(3.61486 - 4.23471i) q^{93} -11.0163 q^{94} +(-1.30416 + 4.01380i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(7.71397 + 5.60453i) q^{97} +6.95579 q^{98} -4.04096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

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