LMFDB - Embedded newform 462.2.j.g.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, 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("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$-0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.g.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.26728 + 1.64728i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.26728 + 1.64728i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.80252 q^{10} +(0.921216 - 3.18612i) q^{11} +1.00000 q^{12} +(-0.706258 + 0.513127i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.866025 + 2.66535i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.92055 + 2.84845i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.10570 + 3.40299i) q^{19} +(2.26728 - 1.64728i) q^{20} +1.00000 q^{21} +(-1.12747 - 3.11910i) q^{22} -2.89765 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.881966 + 2.71441i) q^{25} +(-0.269767 + 0.830257i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.687377 + 2.11553i) q^{29} +(0.866025 + 2.66535i) q^{30} +(-4.70378 + 3.41749i) q^{31} -1.00000 q^{32} +(3.31485 - 0.108436i) q^{33} +4.84607 q^{34} +(2.26728 - 1.64728i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.83414 - 5.64492i) q^{37} +(2.89476 + 2.10317i) q^{38} +(-0.706258 - 0.513127i) q^{39} +(0.866025 - 2.66535i) q^{40} +(-2.18850 - 6.73551i) q^{41} +(0.809017 - 0.587785i) q^{42} +3.74009 q^{43} +(-2.74551 - 1.86069i) q^{44} -2.80252 q^{45} +(-2.34425 + 1.70320i) q^{46} +(-3.53344 - 10.8748i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.30902 + 1.67760i) q^{50} +(-1.49752 + 4.60888i) q^{51} +(0.269767 + 0.830257i) q^{52} +(-10.1109 + 7.34598i) q^{53} -1.00000 q^{54} +(7.33708 - 5.70634i) q^{55} -1.00000 q^{56} +(-2.89476 + 2.10317i) q^{57} +(0.687377 + 2.11553i) q^{58} +(2.04467 - 6.29286i) q^{59} +(2.26728 + 1.64728i) q^{60} +(8.35994 + 6.07385i) q^{61} +(-1.79668 + 5.52962i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.44655 q^{65} +(2.61803 - 2.03615i) q^{66} -7.98782 q^{67} +(3.92055 - 2.84845i) q^{68} +(-0.895424 - 2.75583i) q^{69} +(0.866025 - 2.66535i) q^{70} +(-8.26662 - 6.00605i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.85523 + 14.9428i) q^{73} +(-1.83414 - 5.64492i) q^{74} +(-2.30902 + 1.67760i) q^{75} +3.57812 q^{76} +(-2.74551 - 1.86069i) q^{77} -0.872983 q^{78} +(4.97106 - 3.61169i) q^{79} +(-0.866025 - 2.66535i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.72957 - 4.16277i) q^{82} +(-8.08032 - 5.87069i) q^{83} +(0.309017 - 0.951057i) q^{84} +(4.19682 + 12.9165i) q^{85} +(3.02579 - 2.19837i) q^{86} -2.22440 q^{87} +(-3.31485 + 0.108436i) q^{88} -12.6952 q^{89} +(-2.26728 + 1.64728i) q^{90} +(0.269767 + 0.830257i) q^{91} +(-0.895424 + 2.75583i) q^{92} +(-4.70378 - 3.41749i) q^{93} +(-9.25068 - 6.72101i) q^{94} +(-3.09874 + 9.53695i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(2.34827 - 1.70612i) q^{97} -1.00000 q^{98} +(1.12747 + 3.11910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.26728	+	1.64728i	1.01396	+	0.736685i	0.965036	−	0.262117i	$-0.0844207\pi$
$5$	2.26728	+	1.64728i	1.01396	+	0.736685i	0.0489242	+	0.998802i	$0.484421\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	2.80252			0.886234
$11$	0.921216	−	3.18612i	0.277757	−	0.960651i
$11$	0.921216	−	3.18612i	0.277757	−	0.960651i
$12$	1.00000			0.288675
$13$	−0.706258	+	0.513127i	−0.195881	+	0.142316i	−0.681403	−	0.731909i	$-0.738630\pi$
$13$	−0.706258	+	0.513127i	−0.195881	+	0.142316i	0.485522	+	0.874225i	$0.338630\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.866025	+	2.66535i	−0.223607	+	0.688191i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.92055	+	2.84845i	0.950873	+	0.690850i	0.951013	−	0.309150i	$-0.100045\pi$
$17$	3.92055	+	2.84845i	0.950873	+	0.690850i	−0.000139955		1.00000i	$0.500045\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	1.10570	+	3.40299i	0.253665	+	0.780700i	0.994090	+	0.108561i	$0.0346243\pi$
$19$	1.10570	+	3.40299i	0.253665	+	0.780700i	−0.740425	+	0.672139i	$0.765376\pi$
$20$	2.26728	−	1.64728i	0.506980	−	0.368343i
$21$	1.00000			0.218218
$22$	−1.12747	−	3.11910i	−0.240378	−	0.664995i
$23$	−2.89765			−0.604202			−0.302101	−	0.953276i	$-0.597688\pi$
$23$	−2.89765			−0.604202			−0.302101	+	0.953276i	$0.597688\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	0.881966	+	2.71441i	0.176393	+	0.542882i
$26$	−0.269767	+	0.830257i	−0.0529056	+	0.162827i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	−0.687377	+	2.11553i	−0.127643	+	0.392844i	−0.994373	−	0.105933i	$-0.966217\pi$
$29$	−0.687377	+	2.11553i	−0.127643	+	0.392844i	0.866731	+	0.498777i	$0.166217\pi$
$30$	0.866025	+	2.66535i	0.158114	+	0.486624i
$31$	−4.70378	+	3.41749i	−0.844823	+	0.613800i	−0.923714	−	0.383083i	$-0.874862\pi$
$31$	−4.70378	+	3.41749i	−0.844823	+	0.613800i	0.0788907	+	0.996883i	$0.474862\pi$
$32$	−1.00000			−0.176777
$33$	3.31485	−	0.108436i	0.577042	−	0.0188764i
$34$	4.84607			0.831094
$35$	2.26728	−	1.64728i	0.383241	−	0.278441i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	1.83414	−	5.64492i	0.301531	−	0.928018i	−0.679417	−	0.733752i	$-0.737767\pi$
$37$	1.83414	−	5.64492i	0.301531	−	0.928018i	0.980949	−	0.194266i	$-0.0622326\pi$
$38$	2.89476	+	2.10317i	0.469592	+	0.341178i
$39$	−0.706258	−	0.513127i	−0.113092	−	0.0821660i
$40$	0.866025	−	2.66535i	0.136931	−	0.421429i
$41$	−2.18850	−	6.73551i	−0.341786	−	1.05191i	−0.963282	−	0.268492i	$-0.913475\pi$
$41$	−2.18850	−	6.73551i	−0.341786	−	1.05191i	0.621495	−	0.783418i	$-0.286525\pi$
$42$	0.809017	−	0.587785i	0.124834	−	0.0906972i
$43$	3.74009			0.570358			0.285179	−	0.958474i	$-0.407947\pi$
$43$	3.74009			0.570358			0.285179	+	0.958474i	$0.407947\pi$
$44$	−2.74551	−	1.86069i	−0.413901	−	0.280510i
$45$	−2.80252			−0.417775
$46$	−2.34425	+	1.70320i	−0.345641	+	0.251123i
$47$	−3.53344	−	10.8748i	−0.515406	−	1.58626i	−0.782542	−	0.622597i	$-0.786077\pi$
$47$	−3.53344	−	10.8748i	−0.515406	−	1.58626i	0.267136	−	0.963659i	$-0.413923\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	2.30902	+	1.67760i	0.326544	+	0.237248i
$51$	−1.49752	+	4.60888i	−0.209694	+	0.645373i
$52$	0.269767	+	0.830257i	0.0374099	+	0.115136i
$53$	−10.1109	+	7.34598i	−1.38883	+	1.00905i	−0.392843	+	0.919606i	$0.628508\pi$
$53$	−10.1109	+	7.34598i	−1.38883	+	1.00905i	−0.995992	+	0.0894417i	$0.971492\pi$
$54$	−1.00000			−0.136083
$55$	7.33708	−	5.70634i	0.989332	−	0.769443i
$56$	−1.00000			−0.133631
$57$	−2.89476	+	2.10317i	−0.383420	+	0.278571i
$58$	0.687377	+	2.11553i	0.0902570	+	0.277783i
$59$	2.04467	−	6.29286i	0.266194	−	0.819260i	−0.725222	−	0.688515i	$-0.758263\pi$
$59$	2.04467	−	6.29286i	0.266194	−	0.819260i	0.991416	−	0.130745i	$-0.0417371\pi$
$60$	2.26728	+	1.64728i	0.292705	+	0.212663i
$61$	8.35994	+	6.07385i	1.07038	+	0.777677i	0.975981	−	0.217858i	$-0.0699069\pi$
$61$	8.35994	+	6.07385i	1.07038	+	0.777677i	0.0943996	+	0.995534i	$0.469907\pi$
$62$	−1.79668	+	5.52962i	−0.228179	+	0.702262i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.44655			−0.303457
$66$	2.61803	−	2.03615i	0.322258	−	0.250632i
$67$	−7.98782			−0.975868			−0.487934	−	0.872881i	$-0.662249\pi$
$67$	−7.98782			−0.975868			−0.487934	+	0.872881i	$0.662249\pi$
$68$	3.92055	−	2.84845i	0.475437	−	0.345425i
$69$	−0.895424	−	2.75583i	−0.107796	−	0.331763i
$70$	0.866025	−	2.66535i	0.103510	−	0.318571i
$71$	−8.26662	−	6.00605i	−0.981067	−	0.712787i	−0.0231203	−	0.999733i	$-0.507360\pi$
$71$	−8.26662	−	6.00605i	−0.981067	−	0.712787i	−0.957947	+	0.286946i	$0.907360\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−4.85523	+	14.9428i	−0.568261	+	1.74893i	0.0897963	+	0.995960i	$0.471378\pi$
$73$	−4.85523	+	14.9428i	−0.568261	+	1.74893i	−0.658057	+	0.752968i	$0.728622\pi$
$74$	−1.83414	−	5.64492i	−0.213215	−	0.656208i
$75$	−2.30902	+	1.67760i	−0.266622	+	0.193712i
$76$	3.57812			0.410438
$77$	−2.74551	−	1.86069i	−0.312880	−	0.212046i
$78$	−0.872983			−0.0988459
$79$	4.97106	−	3.61169i	0.559288	−	0.406346i	−0.271910	−	0.962323i	$-0.587655\pi$
$79$	4.97106	−	3.61169i	0.559288	−	0.406346i	0.831198	+	0.555976i	$0.187655\pi$
$80$	−0.866025	−	2.66535i	−0.0968246	−	0.297995i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.72957	−	4.16277i	−0.632725	−	0.459702i
$83$	−8.08032	−	5.87069i	−0.886930	−	0.644392i	0.0481456	−	0.998840i	$-0.484669\pi$
$83$	−8.08032	−	5.87069i	−0.886930	−	0.644392i	−0.935076	+	0.354448i	$0.884669\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	4.19682	+	12.9165i	0.455209	+	1.40099i
$86$	3.02579	−	2.19837i	0.326280	−	0.237056i
$87$	−2.22440			−0.238481
$88$	−3.31485	+	0.108436i	−0.353364	+	0.0115594i
$89$	−12.6952			−1.34569			−0.672844	−	0.739784i	$-0.734928\pi$
$89$	−12.6952			−1.34569			−0.672844	+	0.739784i	$0.734928\pi$
$90$	−2.26728	+	1.64728i	−0.238993	+	0.173638i
$91$	0.269767	+	0.830257i	0.0282792	+	0.0870345i
$92$	−0.895424	+	2.75583i	−0.0933544	+	0.287315i
$93$	−4.70378	−	3.41749i	−0.487759	−	0.354378i
$94$	−9.25068	−	6.72101i	−0.954135	−	0.693219i
$95$	−3.09874	+	9.53695i	−0.317924	+	0.978470i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	2.34827	−	1.70612i	0.238430	−	0.173230i	−0.462153	−	0.886800i	$-0.652923\pi$
$97$	2.34827	−	1.70612i	0.238430	−	0.173230i	0.700584	+	0.713570i	$0.252923\pi$
$98$	−1.00000			−0.101015
$99$	1.12747	+	3.11910i	0.113315	+	0.313482i
$100$	2.85410			0.285410
$101$	4.82289	−	3.50403i	0.479895	−	0.348664i	−0.321390	−	0.946947i	$-0.604150\pi$
$101$	4.82289	−	3.50403i	0.479895	−	0.348664i	0.801285	+	0.598283i	$0.204150\pi$
$102$	1.49752	+	4.60888i	0.148276	+	0.456348i
$103$	−0.800288	+	2.46303i	−0.0788548	+	0.242690i	−0.982711	−	0.185146i	$-0.940724\pi$
$103$	−0.800288	+	2.46303i	−0.0788548	+	0.242690i	0.903856	+	0.427836i	$0.140724\pi$
$104$	0.706258	+	0.513127i	0.0692543	+	0.0503162i
$105$	2.26728	+	1.64728i	0.221264	+	0.160758i
$106$	−3.86201	+	11.8860i	−0.375111	+	1.15447i
$107$	−2.40999	−	7.41718i	−0.232982	−	0.717046i	−0.997383	−	0.0723038i	$-0.976965\pi$
$107$	−2.40999	−	7.41718i	−0.232982	−	0.717046i	0.764400	−	0.644742i	$-0.223035\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−11.6276			−1.11372			−0.556859	−	0.830607i	$-0.687994\pi$
$109$	−11.6276			−1.11372			−0.556859	+	0.830607i	$0.687994\pi$
$110$	2.58172	−	8.92916i	0.246158	−	0.851362i
$111$	5.93542			0.563365
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	4.40958	+	13.5713i	0.414818	+	1.27668i	0.912414	+	0.409269i	$0.134216\pi$
$113$	4.40958	+	13.5713i	0.414818	+	1.27668i	−0.497596	+	0.867409i	$0.665784\pi$
$114$	−1.10570	+	3.40299i	−0.103558	+	0.318719i
$115$	−6.56980	−	4.77324i	−0.612637	−	0.445107i
$116$	1.79958	+	1.30747i	0.167086	+	0.121395i
$117$	0.269767	−	0.830257i	0.0249399	−	0.0767572i
$118$	−2.04467	−	6.29286i	−0.188227	−	0.579305i
$119$	3.92055	−	2.84845i	0.359396	−	0.261117i
$120$	2.80252			0.255834
$121$	−9.30272	−	5.87021i	−0.845702	−	0.533656i
$122$	10.3334			0.935547
$123$	5.72957	−	4.16277i	0.516618	−	0.375345i
$124$	1.79668	+	5.52962i	0.161347	+	0.496575i
$125$	1.85840	−	5.71957i	0.166221	−	0.511574i
$126$	0.809017	+	0.587785i	0.0720730	+	0.0523641i
$127$	11.4463	+	8.31626i	1.01570	+	0.737948i	0.965397	−	0.260786i	$-0.0839816\pi$
$127$	11.4463	+	8.31626i	1.01570	+	0.737948i	0.0503020	+	0.998734i	$0.483982\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	1.15575	+	3.55703i	0.101758	+	0.313179i
$130$	−1.97930	+	1.43805i	−0.173596	+	0.126125i
$131$	12.5014			1.09225			0.546124	−	0.837704i	$-0.316103\pi$
$131$	12.5014			1.09225			0.546124	+	0.837704i	$0.316103\pi$
$132$	0.921216	−	3.18612i	0.0801816	−	0.277316i
$133$	3.57812			0.310262
$134$	−6.46228	+	4.69512i	−0.558256	+	0.405597i
$135$	−0.866025	−	2.66535i	−0.0745356	−	0.229397i
$136$	1.49752	−	4.60888i	0.128411	−	0.395209i
$137$	3.28256	+	2.38492i	0.280448	+	0.203757i	0.719113	−	0.694893i	$-0.244548\pi$
$137$	3.28256	+	2.38492i	0.280448	+	0.203757i	−0.438665	+	0.898651i	$0.644548\pi$
$138$	−2.34425	−	1.70320i	−0.199556	−	0.144986i
$139$	3.48270	−	10.7186i	0.295399	−	0.909144i	−0.687688	−	0.726006i	$-0.741374\pi$
$139$	3.48270	−	10.7186i	0.295399	−	0.909144i	0.983087	−	0.183138i	$-0.0586255\pi$
$140$	−0.866025	−	2.66535i	−0.0731925	−	0.225263i
$141$	9.25068	−	6.72101i	0.779048	−	0.566011i
$142$	−10.2181			−0.857484
$143$	0.984267	+	2.72292i	0.0823085	+	0.227702i
$144$	1.00000			0.0833333
$145$	−5.04334	+	3.66420i	−0.418827	+	0.304296i
$146$	4.85523	+	14.9428i	0.401821	+	1.23668i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−4.80185	−	3.48875i	−0.394710	−	0.286773i
$149$	1.23607	+	0.898056i	0.101263	+	0.0735716i	0.637264	−	0.770645i	$-0.280066\pi$
$149$	1.23607	+	0.898056i	0.101263	+	0.0735716i	−0.536002	+	0.844217i	$0.680066\pi$
$150$	−0.881966	+	2.71441i	−0.0720122	+	0.221631i
$151$	3.97797	+	12.2429i	0.323723	+	0.996316i	0.972014	+	0.234923i	$0.0754839\pi$
$151$	3.97797	+	12.2429i	0.323723	+	0.996316i	−0.648291	+	0.761392i	$0.724516\pi$
$152$	2.89476	−	2.10317i	0.234796	−	0.170589i
$153$	−4.84607			−0.391781
$154$	−3.31485	+	0.108436i	−0.267118	+	0.00873806i
$155$	−16.2944			−1.30879
$156$	−0.706258	+	0.513127i	−0.0565459	+	0.0410830i
$157$	0.859067	+	2.64394i	0.0685610	+	0.211009i	0.979467	−	0.201605i	$-0.0646157\pi$
$157$	0.859067	+	2.64394i	0.0685610	+	0.211009i	−0.910906	+	0.412614i	$0.864616\pi$
$158$	1.89878	−	5.84383i	0.151058	−	0.464910i
$159$	−10.1109	−	7.34598i	−0.801844	−	0.582574i
$160$	−2.26728	−	1.64728i	−0.179245	−	0.130229i
$161$	−0.895424	+	2.75583i	−0.0705693	+	0.217190i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	6.85410	−	4.97980i	0.536855	−	0.390048i	−0.286061	−	0.958211i	$-0.592346\pi$
$163$	6.85410	−	4.97980i	0.536855	−	0.390048i	0.822916	+	0.568164i	$0.192346\pi$
$164$	−7.08214			−0.553022
$165$	7.69433	+	5.21463i	0.599003	+	0.405958i
$166$	−9.98782			−0.775205
$167$	4.02264	−	2.92262i	0.311282	−	0.226159i	−0.421165	−	0.906984i	$-0.638379\pi$
$167$	4.02264	−	2.92262i	0.311282	−	0.226159i	0.732446	+	0.680825i	$0.238379\pi$
$168$	−0.309017	−	0.951057i	−0.0238412	−	0.0733756i
$169$	−3.78172	+	11.6389i	−0.290901	+	0.895303i
$170$	10.9874	+	7.98282i	0.842696	+	0.612254i
$171$	−2.89476	−	2.10317i	−0.221368	−	0.160833i
$172$	1.15575	−	3.55703i	0.0881251	−	0.271221i
$173$	−2.95107	−	9.08247i	−0.224366	−	0.690527i	−0.998355	−	0.0573288i	$-0.981742\pi$
$173$	−2.95107	−	9.08247i	−0.224366	−	0.690527i	0.773989	−	0.633199i	$-0.218258\pi$
$174$	−1.79958	+	1.30747i	−0.136426	+	0.0991189i
$175$	2.85410			0.215750
$176$	−2.61803	+	2.03615i	−0.197342	+	0.153480i
$177$	6.61670			0.497342
$178$	−10.2706	+	7.46205i	−0.769817	+	0.559305i
$179$	3.41541	+	10.5116i	0.255280	+	0.785670i	0.993774	+	0.111411i	$0.0355370\pi$
$179$	3.41541	+	10.5116i	0.255280	+	0.785670i	−0.738495	+	0.674259i	$0.764463\pi$
$180$	−0.866025	+	2.66535i	−0.0645497	+	0.198664i
$181$	3.24083	+	2.35460i	0.240889	+	0.175016i	0.701679	−	0.712493i	$-0.252434\pi$
$181$	3.24083	+	2.35460i	0.240889	+	0.175016i	−0.460790	+	0.887509i	$0.652434\pi$
$182$	0.706258	+	0.513127i	0.0523514	+	0.0380355i
$183$	−3.19321	+	9.82769i	−0.236049	+	0.726484i
$184$	0.895424	+	2.75583i	0.0660115	+	0.203163i
$185$	13.4573	−	9.77728i	0.989398	−	0.718840i
$186$	−5.81419			−0.426317
$187$	12.6872	−	9.86731i	0.927778	−	0.721569i
$188$	−11.4345			−0.833944
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	3.09874	+	9.53695i	0.224806	+	0.691883i
$191$	2.40305	−	7.39582i	0.173878	−	0.535143i	−0.825702	−	0.564106i	$-0.809221\pi$
$191$	2.40305	−	7.39582i	0.173878	−	0.535143i	0.999580	+	0.0289638i	$0.00922076\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	13.6541	+	9.92031i	0.982846	+	0.714080i	0.958343	−	0.285620i	$-0.0921996\pi$
$193$	13.6541	+	9.92031i	0.982846	+	0.714080i	0.0245033	+	0.999700i	$0.492200\pi$
$194$	0.896958	−	2.76055i	0.0643979	−	0.198196i
$195$	−0.756026	−	2.32681i	−0.0541401	−	0.166626i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−10.6863			−0.761371			−0.380685	−	0.924705i	$-0.624312\pi$
$197$	−10.6863			−0.761371			−0.380685	+	0.924705i	$0.624312\pi$
$198$	2.74551	+	1.86069i	0.195115	+	0.132234i
$199$	−19.4630			−1.37970			−0.689849	−	0.723954i	$-0.742323\pi$
$199$	−19.4630			−1.37970			−0.689849	+	0.723954i	$0.742323\pi$
$200$	2.30902	−	1.67760i	0.163272	−	0.118624i
$201$	−2.46837	−	7.59687i	−0.174106	−	0.535842i
$202$	1.84218	−	5.66964i	0.129615	−	0.398915i
$203$	1.79958	+	1.30747i	0.126305	+	0.0917663i
$204$	3.92055	+	2.84845i	0.274493	+	0.199431i
$205$	6.13331	−	18.8764i	0.428369	−	1.31838i
$206$	0.800288	+	2.46303i	0.0557587	+	0.171608i
$207$	2.34425	−	1.70320i	0.162937	−	0.118380i
$208$	0.872983			0.0605305
$209$	11.8609	−	0.387998i	0.820438	−	0.0268384i
$210$	2.80252			0.193392
$211$	2.48480	−	1.80531i	0.171061	−	0.124283i	−0.498961	−	0.866625i	$-0.666285\pi$
$211$	2.48480	−	1.80531i	0.171061	−	0.124283i	0.670022	+	0.742342i	$0.266285\pi$
$212$	3.86201	+	11.8860i	0.265244	+	0.816337i
$213$	3.15757	−	9.71799i	0.216353	−	0.665866i
$214$	−6.30943	−	4.58407i	−0.431304	−	0.313360i
$215$	8.47983	+	6.16096i	0.578320	+	0.420174i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	1.79668	+	5.52962i	0.121967	+	0.375375i
$218$	−9.40689	+	6.83450i	−0.637115	+	0.462891i
$219$	−15.7118			−1.06171
$220$	−3.15977	−	8.74134i	−0.213031	−	0.589341i
$221$	−4.23054			−0.284577
$222$	4.80185	−	3.48875i	0.322279	−	0.234150i
$223$	4.49375	+	13.8304i	0.300924	+	0.926149i	0.981167	+	0.193162i	$0.0618743\pi$
$223$	4.49375	+	13.8304i	0.300924	+	0.926149i	−0.680243	+	0.732987i	$0.738126\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	−2.30902	−	1.67760i	−0.153934	−	0.111840i
$226$	11.5444	+	8.38751i	0.767923	+	0.557929i
$227$	−7.93135	+	24.4102i	−0.526422	+	1.62016i	0.235064	+	0.971980i	$0.424470\pi$
$227$	−7.93135	+	24.4102i	−0.526422	+	1.62016i	−0.761486	+	0.648181i	$0.775530\pi$
$228$	1.10570	+	3.40299i	0.0732267	+	0.225369i
$229$	4.40937	−	3.20359i	0.291379	−	0.211699i	−0.432486	−	0.901641i	$-0.642364\pi$
$229$	4.40937	−	3.20359i	0.291379	−	0.211699i	0.723866	+	0.689941i	$0.242364\pi$
$230$	−8.12072			−0.535464
$231$	0.921216	−	3.18612i	0.0606116	−	0.209631i
$232$	2.22440			0.146039
$233$	23.4499	−	17.0373i	1.53625	−	1.11615i	0.583623	−	0.812025i	$-0.301635\pi$
$233$	23.4499	−	17.0373i	1.53625	−	1.11615i	0.952631	−	0.304129i	$-0.0983655\pi$
$234$	−0.269767	−	0.830257i	−0.0176352	−	0.0542756i
$235$	9.90254	−	30.4769i	0.645970	−	1.98809i
$236$	−5.35303	−	3.88920i	−0.348452	−	0.253165i
$237$	4.97106	+	3.61169i	0.322905	+	0.234604i
$238$	1.49752	−	4.60888i	0.0970696	−	0.298750i
$239$	−8.42196	−	25.9201i	−0.544771	−	1.67663i	−0.721533	−	0.692380i	$-0.756562\pi$
$239$	−8.42196	−	25.9201i	−0.544771	−	1.67663i	0.176762	−	0.984254i	$-0.443438\pi$
$240$	2.26728	−	1.64728i	0.146353	−	0.106331i
$241$	13.6089			0.876628			0.438314	−	0.898822i	$-0.355576\pi$
$241$	13.6089			0.876628			0.438314	+	0.898822i	$0.355576\pi$
$242$	−10.9765	+	0.718901i	−0.705595	+	0.0462127i
$243$	1.00000			0.0641500
$244$	8.35994	−	6.07385i	0.535190	−	0.388838i
$245$	−0.866025	−	2.66535i	−0.0553283	−	0.170283i
$246$	2.18850	−	6.73551i	0.139534	−	0.429441i
$247$	−2.52708	−	1.83603i	−0.160794	−	0.116824i
$248$	4.70378	+	3.41749i	0.298690	+	0.217011i
$249$	3.08641	−	9.49898i	0.195593	−	0.601974i
$250$	−1.85840	−	5.71957i	−0.117536	−	0.361738i
$251$	18.2010	−	13.2238i	1.14884	−	0.834681i	0.160513	−	0.987034i	$-0.448685\pi$
$251$	18.2010	−	13.2238i	1.14884	−	0.834681i	0.988326	+	0.152353i	$0.0486851\pi$
$252$	1.00000			0.0629941
$253$	−2.66936	+	9.23227i	−0.167822	+	0.580428i
$254$	14.1485			0.887753
$255$	−10.9874	+	7.98282i	−0.688058	+	0.499904i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.19769	+	3.68610i	−0.0747097	+	0.229933i	−0.981437	−	0.191785i	$-0.938573\pi$
$257$	−1.19769	+	3.68610i	−0.0747097	+	0.229933i	0.906727	+	0.421717i	$0.138573\pi$
$258$	3.02579	+	2.19837i	0.188378	+	0.136864i
$259$	−4.80185	−	3.48875i	−0.298373	−	0.216780i
$260$	−0.756026	+	2.32681i	−0.0468867	+	0.144303i
$261$	−0.687377	−	2.11553i	−0.0425476	−	0.130948i
$262$	10.1138	−	7.34811i	0.624833	−	0.453968i
$263$	3.53672			0.218084			0.109042	−	0.994037i	$-0.465222\pi$
$263$	3.53672			0.218084			0.109042	+	0.994037i	$0.465222\pi$
$264$	−1.12747	−	3.11910i	−0.0693913	−	0.191967i
$265$	−35.0251			−2.15157
$266$	2.89476	−	2.10317i	0.177489	−	0.128953i
$267$	−3.92303	−	12.0739i	−0.240086	−	0.738908i
$268$	−2.46837	+	7.59687i	−0.150780	+	0.464053i
$269$	21.1862	+	15.3927i	1.29175	+	0.938509i	0.999839	−	0.0179376i	$-0.00571002\pi$
$269$	21.1862	+	15.3927i	1.29175	+	0.938509i	0.291908	+	0.956447i	$0.405710\pi$
$270$	−2.26728	−	1.64728i	−0.137983	−	0.100250i
$271$	2.58528	−	7.95668i	0.157045	−	0.483334i	−0.841318	−	0.540541i	$-0.818220\pi$
$271$	2.58528	−	7.95668i	0.157045	−	0.483334i	0.998362	+	0.0572070i	$0.0182195\pi$
$272$	−1.49752	−	4.60888i	−0.0908003	−	0.279455i
$273$	−0.706258	+	0.513127i	−0.0427447	+	0.0310558i
$274$	4.05747			0.245121
$275$	9.46092	−	0.309489i	0.570515	−	0.0186629i
$276$	−2.89765			−0.174418
$277$	4.24799	−	3.08635i	0.255237	−	0.185441i	−0.452808	−	0.891608i	$-0.649578\pi$
$277$	4.24799	−	3.08635i	0.255237	−	0.185441i	0.708045	+	0.706168i	$0.249578\pi$
$278$	−3.48270	−	10.7186i	−0.208878	−	0.642862i
$279$	1.79668	−	5.52962i	0.107565	−	0.331050i
$280$	−2.26728	−	1.64728i	−0.135496	−	0.0984437i
$281$	5.53275	+	4.01978i	0.330056	+	0.239800i	0.740454	−	0.672107i	$-0.234610\pi$
$281$	5.53275	+	4.01978i	0.330056	+	0.239800i	−0.410398	+	0.911906i	$0.634610\pi$
$282$	3.53344	−	10.8748i	0.210414	−	0.647586i
$283$	1.34801	+	4.14876i	0.0801311	+	0.246618i	0.983094	−	0.183100i	$-0.0586131\pi$
$283$	1.34801	+	4.14876i	0.0801311	+	0.246618i	−0.902963	+	0.429718i	$0.858613\pi$
$284$	−8.26662	+	6.00605i	−0.490534	+	0.356394i
$285$	−10.0277			−0.593992
$286$	2.39678	+	1.62435i	0.141725	+	0.0960501i
$287$	−7.08214			−0.418045
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	2.00378	+	6.16700i	0.117869	+	0.362765i
$290$	−1.92639	+	5.92881i	−0.113121	+	0.348151i
$291$	2.34827	+	1.70612i	0.137658	+	0.100014i
$292$	12.7111	+	9.23519i	0.743863	+	0.540448i
$293$	−6.02717	+	18.5497i	−0.352111	+	1.08369i	0.605555	+	0.795804i	$0.292951\pi$
$293$	−6.02717	+	18.5497i	−0.352111	+	1.08369i	−0.957666	+	0.287883i	$0.907049\pi$
$294$	−0.309017	−	0.951057i	−0.0180222	−	0.0554667i
$295$	15.0019	−	10.8996i	0.873447	−	0.634596i
$296$	−5.93542			−0.344989
$297$	−2.61803	+	2.03615i	−0.151914	+	0.118149i
$298$	1.52786			0.0885068
$299$	2.04649	−	1.48686i	0.118352	−	0.0859875i
$300$	0.881966	+	2.71441i	0.0509203	+	0.156717i
$301$	1.15575	−	3.55703i	0.0666163	−	0.205024i
$302$	10.4145	+	7.56655i	0.599285	+	0.435406i
$303$	4.82289	+	3.50403i	0.277068	+	0.201301i
$304$	1.10570	−	3.40299i	0.0634162	−	0.195175i
$305$	8.94903	+	27.5423i	0.512420	+	1.57707i
$306$	−3.92055	+	2.84845i	−0.224123	+	0.162835i
$307$	12.2886			0.701346			0.350673	−	0.936498i	$-0.385953\pi$
$307$	12.2886			0.701346			0.350673	+	0.936498i	$0.385953\pi$
$308$	−2.61803	+	2.03615i	−0.149176	+	0.116020i
$309$	−2.58979			−0.147328
$310$	−13.1824	+	9.57758i	−0.748711	+	0.543970i
$311$	9.98994	+	30.7459i	0.566478	+	1.74344i	0.663520	+	0.748158i	$0.269062\pi$
$311$	9.98994	+	30.7459i	0.566478	+	1.74344i	−0.0970425	+	0.995280i	$0.530938\pi$
$312$	−0.269767	+	0.830257i	−0.0152725	+	0.0470040i
$313$	18.2239	+	13.2404i	1.03008	+	0.748393i	0.968324	−	0.249698i	$-0.0803314\pi$
$313$	18.2239	+	13.2404i	1.03008	+	0.748393i	0.0617515	+	0.998092i	$0.480331\pi$
$314$	2.24907	+	1.63404i	0.126922	+	0.0922144i
$315$	−0.866025	+	2.66535i	−0.0487950	+	0.150176i
$316$	−1.89878	−	5.84383i	−0.106814	−	0.328741i
$317$	2.22622	−	1.61744i	0.125037	−	0.0908445i	−0.523509	−	0.852020i	$-0.675377\pi$
$317$	2.22622	−	1.61744i	0.125037	−	0.0908445i	0.648546	+	0.761176i	$0.275377\pi$
$318$	−12.4977			−0.700837
$319$	6.10711	+	4.13893i	0.341932	+	0.231735i
$320$	−2.80252			−0.156665
$321$	6.30943	−	4.58407i	0.352158	−	0.255858i
$322$	0.895424	+	2.75583i	0.0499000	+	0.153576i
$323$	−5.35829	+	16.4911i	−0.298143	+	0.917591i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−2.01573	−	1.46452i	−0.111813	−	0.0812367i
$326$	2.61803	−	8.05748i	0.144999	−	0.446263i
$327$	−3.59311	−	11.0585i	−0.198699	−	0.611534i
$328$	−5.72957	+	4.16277i	−0.316362	+	0.229851i
$329$	−11.4345			−0.630403
$330$	9.28993	−	0.303895i	0.511394	−	0.0167289i
$331$	−14.4366			−0.793508			−0.396754	−	0.917925i	$-0.629863\pi$
$331$	−14.4366			−0.793508			−0.396754	+	0.917925i	$0.629863\pi$
$332$	−8.08032	+	5.87069i	−0.443465	+	0.322196i
$333$	1.83414	+	5.64492i	0.100510	+	0.309339i
$334$	1.53651	−	4.72890i	0.0840743	−	0.258754i
$335$	−18.1107	−	13.1582i	−0.989491	−	0.718907i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	6.69252	−	20.5975i	0.364565	−	1.12201i	−0.585689	−	0.810536i	$-0.699176\pi$
$337$	6.69252	−	20.5975i	0.364565	−	1.12201i	0.950253	−	0.311478i	$-0.100824\pi$
$338$	3.78172	+	11.6389i	0.205698	+	0.633075i
$339$	−11.5444	+	8.38751i	−0.627007	+	0.455547i
$340$	13.5812			0.736543
$341$	6.55535	+	18.1350i	0.354992	+	0.982068i
$342$	−3.57812			−0.193482
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−1.15575	−	3.55703i	−0.0623139	−	0.191782i
$345$	2.50944	−	7.72326i	0.135104	−	0.415807i
$346$	−7.72601	−	5.61327i	−0.415353	−	0.301771i
$347$	−13.3245	−	9.68085i	−0.715299	−	0.519695i	0.169580	−	0.985516i	$-0.445759\pi$
$347$	−13.3245	−	9.68085i	−0.715299	−	0.519695i	−0.884879	+	0.465821i	$0.845759\pi$
$348$	−0.687377	+	2.11553i	−0.0368473	+	0.113404i
$349$	3.65411	+	11.2462i	0.195600	+	0.601995i	0.999969	+	0.00786475i	$0.00250345\pi$
$349$	3.65411	+	11.2462i	0.195600	+	0.601995i	−0.804369	+	0.594130i	$0.797497\pi$
$350$	2.30902	−	1.67760i	0.123422	−	0.0896714i
$351$	0.872983			0.0465964
$352$	−0.921216	+	3.18612i	−0.0491010	+	0.169821i
$353$	23.8231			1.26798			0.633989	−	0.773342i	$-0.281417\pi$
$353$	23.8231			1.26798			0.633989	+	0.773342i	$0.281417\pi$
$354$	5.35303	−	3.88920i	0.284510	−	0.206709i
$355$	−8.84914	−	27.2348i	−0.469663	−	1.44548i
$356$	−3.92303	+	12.0739i	−0.207920	+	0.639913i
$357$	3.92055	+	2.84845i	0.207498	+	0.150756i
$358$	8.94166	+	6.49650i	0.472581	+	0.343351i
$359$	−6.24861	+	19.2312i	−0.329789	+	1.01499i	0.639444	+	0.768838i	$0.279165\pi$
$359$	−6.24861	+	19.2312i	−0.329789	+	1.01499i	−0.969232	+	0.246148i	$0.920835\pi$
$360$	0.866025	+	2.66535i	0.0456435	+	0.140476i
$361$	5.01353	−	3.64255i	0.263870	−	0.191713i
$362$	4.00588			0.210544
$363$	2.70820	−	10.6614i	0.142144	−	0.559579i
$364$	0.872983			0.0457568
$365$	−35.6232	+	25.8818i	−1.86460	+	1.35471i
$366$	3.19321	+	9.82769i	0.166912	+	0.513702i
$367$	−3.86715	+	11.9019i	−0.201864	+	0.621272i	0.797964	+	0.602705i	$0.205910\pi$
$367$	−3.86715	+	11.9019i	−0.201864	+	0.621272i	−0.999828	+	0.0185670i	$0.994090\pi$
$368$	2.34425	+	1.70320i	0.122202	+	0.0887853i
$369$	5.72957	+	4.16277i	0.298269	+	0.216705i
$370$	5.14022	−	15.8200i	0.267227	−	0.822441i
$371$	3.86201	+	11.8860i	0.200505	+	0.617092i
$372$	−4.70378	+	3.41749i	−0.243879	+	0.177189i
$373$	−35.4217			−1.83407			−0.917034	−	0.398810i	$-0.869423\pi$
$373$	−35.4217			−1.83407			−0.917034	+	0.398810i	$0.869423\pi$
$374$	4.46428	−	15.4402i	0.230842	−	0.798391i
$375$	6.01392			0.310557
$376$	−9.25068	+	6.72101i	−0.477067	+	0.346610i
$377$	−0.600069	−	1.84682i	−0.0309051	−	0.0951161i
$378$	−0.309017	+	0.951057i	−0.0158941	+	0.0489171i
$379$	−15.3611	−	11.1605i	−0.789045	−	0.573274i	0.118635	−	0.992938i	$-0.462148\pi$
$379$	−15.3611	−	11.1605i	−0.789045	−	0.573274i	−0.907680	+	0.419663i	$0.862148\pi$
$380$	8.11261	+	5.89416i	0.416168	+	0.302364i
$381$	−4.37211	+	13.4560i	−0.223990	+	0.689371i
$382$	−2.40305	−	7.39582i	−0.122951	−	0.378403i
$383$	−9.08802	+	6.60283i	−0.464376	+	0.337389i	−0.795245	−	0.606288i	$-0.792658\pi$
$383$	−9.08802	+	6.60283i	−0.464376	+	0.337389i	0.330869	+	0.943677i	$0.392658\pi$
$384$	−1.00000			−0.0510310
$385$	−3.15977	−	8.74134i	−0.161037	−	0.445500i
$386$	16.8774			0.859039
$387$	−3.02579	+	2.19837i	−0.153810	+	0.111749i
$388$	−0.896958	−	2.76055i	−0.0455362	−	0.140146i
$389$	8.22571	−	25.3161i	0.417060	−	1.28358i	−0.493335	−	0.869839i	$-0.664222\pi$
$389$	8.22571	−	25.3161i	0.417060	−	1.28358i	0.910395	−	0.413739i	$-0.135778\pi$
$390$	−1.97930	−	1.43805i	−0.100226	−	0.0728183i
$391$	−11.3604	−	8.25381i	−0.574520	−	0.417413i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	3.86313	+	11.8895i	0.194869	+	0.599746i
$394$	−8.64544	+	6.28128i	−0.435551	+	0.316446i
$395$	17.2203			0.866445
$396$	3.31485	−	0.108436i	0.166578	−	0.00544914i
$397$	−19.5534			−0.981359			−0.490680	−	0.871340i	$-0.663251\pi$
$397$	−19.5534			−0.981359			−0.490680	+	0.871340i	$0.663251\pi$
$398$	−15.7459	+	11.4401i	−0.789272	+	0.573439i
$399$	1.10570	+	3.40299i	0.0553542	+	0.170363i
$400$	0.881966	−	2.71441i	0.0440983	−	0.135721i
$401$	4.10135	+	2.97981i	0.204812	+	0.148804i	0.685463	−	0.728107i	$-0.259600\pi$
$401$	4.10135	+	2.97981i	0.204812	+	0.148804i	−0.480651	+	0.876912i	$0.659600\pi$
$402$	−6.46228	−	4.69512i	−0.322309	−	0.234172i
$403$	1.56847	−	4.82727i	0.0781312	−	0.240463i
$404$	−1.84218	−	5.66964i	−0.0916518	−	0.282075i
$405$	2.26728	−	1.64728i	0.112662	−	0.0818539i
$406$	2.22440			0.110395
$407$	−16.2957	−	11.0440i	−0.807750	−	0.547430i
$408$	4.84607			0.239916
$409$	1.84391	−	1.33968i	0.0911757	−	0.0662430i	−0.541263	−	0.840853i	$-0.682054\pi$
$409$	1.84391	−	1.33968i	0.0911757	−	0.0662430i	0.632439	+	0.774610i	$0.282054\pi$
$410$	−6.13331	−	18.8764i	−0.302903	−	0.932238i
$411$	−1.25383	+	3.85888i	−0.0618467	+	0.190345i
$412$	2.09518	+	1.52224i	0.103222	+	0.0749953i
$413$	−5.35303	−	3.88920i	−0.263405	−	0.191375i
$414$	0.895424	−	2.75583i	0.0440077	−	0.135442i
$415$	−8.64971	−	26.6211i	−0.424597	−	1.30678i
$416$	0.706258	−	0.513127i	0.0346272	−	0.0251581i
$417$	11.2703			0.551907
$418$	9.36764	−	7.28558i	0.458186	−	0.356349i
$419$	−20.6719			−1.00989			−0.504945	−	0.863152i	$-0.668487\pi$
$419$	−20.6719			−1.00989			−0.504945	+	0.863152i	$0.668487\pi$
$420$	2.26728	−	1.64728i	0.110632	−	0.0803789i
$421$	−6.18853	−	19.0463i	−0.301610	−	0.928262i	−0.980920	−	0.194410i	$-0.937721\pi$
$421$	−6.18853	−	19.0463i	−0.301610	−	0.928262i	0.679310	−	0.733852i	$-0.262279\pi$
$422$	0.949109	−	2.92106i	0.0462019	−	0.142195i
$423$	9.25068	+	6.72101i	0.449783	+	0.326787i
$424$	10.1109	+	7.34598i	0.491027	+	0.356752i
$425$	−4.27407	+	13.1542i	−0.207323	+	0.638074i
$426$	−3.15757	−	9.71799i	−0.152985	−	0.470838i
$427$	8.35994	−	6.07385i	0.404566	−	0.293934i
$428$	−7.79888			−0.376973
$429$	−2.28550	+	1.77752i	−0.110345	+	0.0858196i
$430$	10.4817			0.505470
$431$	−23.5646	+	17.1207i	−1.13507	+	0.824674i	−0.986424	−	0.164217i	$-0.947490\pi$
$431$	−23.5646	+	17.1207i	−1.13507	+	0.824674i	−0.148642	+	0.988891i	$0.547490\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−6.59600	+	20.3004i	−0.316984	+	0.975576i	0.657946	+	0.753065i	$0.271425\pi$
$433$	−6.59600	+	20.3004i	−0.316984	+	0.975576i	−0.974930	+	0.222511i	$0.928575\pi$
$434$	4.70378	+	3.41749i	0.225788	+	0.164045i
$435$	−5.04334	−	3.66420i	−0.241810	−	0.175685i
$436$	−3.59311	+	11.0585i	−0.172079	+	0.529604i
$437$	−3.20393	−	9.86069i	−0.153265	−	0.471701i
$438$	−12.7111	+	9.23519i	−0.607362	+	0.441274i
$439$	26.9372			1.28564			0.642820	−	0.766017i	$-0.277764\pi$
$439$	26.9372			1.28564			0.642820	+	0.766017i	$0.277764\pi$
$440$	−7.69433	−	5.21463i	−0.366813	−	0.248598i
$441$	1.00000			0.0476190
$442$	−3.42258	+	2.48665i	−0.162795	+	0.118278i
$443$	−3.25160	−	10.0074i	−0.154488	−	0.475465i	0.843621	−	0.536940i	$-0.180420\pi$
$443$	−3.25160	−	10.0074i	−0.154488	−	0.475465i	−0.998109	+	0.0614744i	$0.980420\pi$
$444$	1.83414	−	5.64492i	0.0870446	−	0.267896i
$445$	−28.7836	−	20.9125i	−1.36448	−	0.991349i
$446$	11.7648	+	8.54763i	0.557079	+	0.404742i
$447$	−0.472136	+	1.45309i	−0.0223313	+	0.0687286i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	27.2327	−	19.7857i	1.28519	−	0.933746i	0.285495	−	0.958380i	$-0.407842\pi$
$449$	27.2327	−	19.7857i	1.28519	−	0.933746i	0.999697	+	0.0246343i	$0.00784212\pi$
$450$	−2.85410			−0.134544
$451$	−23.4762	+	0.767962i	−1.10545	+	0.0361619i
$452$	14.2697			0.671190
$453$	−10.4145	+	7.56655i	−0.489314	+	0.355508i
$454$	7.93135	+	24.4102i	0.372237	+	1.14563i
$455$	−0.756026	+	2.32681i	−0.0354430	+	0.109082i
$456$	2.89476	+	2.10317i	0.135559	+	0.0984897i
$457$	0.579449	+	0.420994i	0.0271055	+	0.0196933i	0.601256	−	0.799057i	$-0.294667\pi$
$457$	0.579449	+	0.420994i	0.0271055	+	0.0196933i	−0.574150	+	0.818750i	$0.694667\pi$
$458$	1.68423	−	5.18352i	0.0786989	−	0.242210i
$459$	−1.49752	−	4.60888i	−0.0698981	−	0.215124i
$460$	−6.56980	+	4.77324i	−0.306319	+	0.222553i
$461$	−9.64710			−0.449310			−0.224655	−	0.974438i	$-0.572126\pi$
$461$	−9.64710			−0.449310			−0.224655	+	0.974438i	$0.572126\pi$
$462$	−1.12747	−	3.11910i	−0.0524549	−	0.145114i
$463$	−19.6747			−0.914360			−0.457180	−	0.889374i	$-0.651140\pi$
$463$	−19.6747			−0.914360			−0.457180	+	0.889374i	$0.651140\pi$
$464$	1.79958	−	1.30747i	0.0835432	−	0.0606977i
$465$	−5.03523	−	15.4969i	−0.233503	−	0.718649i
$466$	8.95706	−	27.5670i	0.414928	−	1.27702i
$467$	26.0857	+	18.9524i	1.20710	+	0.877011i	0.994964	−	0.100229i	$-0.0319575\pi$
$467$	26.0857	+	18.9524i	1.20710	+	0.877011i	0.212137	+	0.977240i	$0.431958\pi$
$468$	−0.706258	−	0.513127i	−0.0326468	−	0.0237193i
$469$	−2.46837	+	7.59687i	−0.113979	+	0.350791i
$470$	−9.90254	−	30.4769i	−0.456770	−	1.40579i
$471$	−2.24907	+	1.63404i	−0.103632	+	0.0752927i
$472$	−6.61670			−0.304558
$473$	3.44543	−	11.9164i	0.158421	−	0.547915i
$474$	6.14457			0.282229
$475$	−8.26194	+	6.00265i	−0.379084	+	0.275420i
$476$	−1.49752	−	4.60888i	−0.0686386	−	0.211248i
$477$	3.86201	−	11.8860i	0.176829	−	0.544224i
$478$	−22.0490	−	16.0195i	−1.00850	−	0.732716i
$479$	−1.00215	−	0.728107i	−0.0457895	−	0.0332680i	0.564655	−	0.825327i	$-0.309009\pi$
$479$	−1.00215	−	0.728107i	−0.0457895	−	0.0332680i	−0.610445	+	0.792059i	$0.709009\pi$
$480$	0.866025	−	2.66535i	0.0395285	−	0.121656i
$481$	1.60118	+	4.92792i	0.0730074	+	0.224694i
$482$	11.0099	−	7.99913i	0.501485	−	0.364350i
$483$	−2.89765			−0.131848
$484$	−8.45760	+	7.03342i	−0.384436	+	0.319701i
$485$	8.13464			0.369375
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	8.47953	+	26.0973i	0.384244	+	1.18258i	0.937027	+	0.349257i	$0.113566\pi$
$487$	8.47953	+	26.0973i	0.384244	+	1.18258i	−0.552783	+	0.833326i	$0.686434\pi$
$488$	3.19321	−	9.82769i	0.144550	−	0.444879i
$489$	6.85410	+	4.97980i	0.309953	+	0.225194i
$490$	−2.26728	−	1.64728i	−0.102425	−	0.0744164i
$491$	−6.79281	+	20.9061i	−0.306555	+	0.943480i	0.672537	+	0.740064i	$0.265205\pi$
$491$	−6.79281	+	20.9061i	−0.306555	+	0.943480i	−0.979092	+	0.203417i	$0.934795\pi$
$492$	−2.18850	−	6.73551i	−0.0986652	−	0.303660i
$493$	−8.72087	+	6.33608i	−0.392768	+	0.285363i
$494$	−3.12364			−0.140539
$495$	−2.58172	+	8.92916i	−0.116040	+	0.401336i
$496$	5.81419			0.261065
$497$	−8.26662	+	6.00605i	−0.370809	+	0.269408i
$498$	−3.08641	−	9.49898i	−0.138305	−	0.425660i
$499$	9.35415	−	28.7891i	0.418749	−	1.28878i	−0.490105	−	0.871663i	$-0.663042\pi$
$499$	9.35415	−	28.7891i	0.418749	−	1.28878i	0.908854	−	0.417114i	$-0.136958\pi$
$500$	−4.86536	−	3.53489i	−0.217586	−	0.158085i
$501$	4.02264	+	2.92262i	0.179718	+	0.130573i
$502$	6.95218	−	21.3966i	0.310291	−	0.954977i
$503$	−0.123254	−	0.379336i	−0.00549561	−	0.0169137i	0.948271	−	0.317462i	$-0.102830\pi$
$503$	−0.123254	−	0.379336i	−0.00549561	−	0.0169137i	−0.953767	+	0.300548i	$0.902830\pi$
$504$	0.809017	−	0.587785i	0.0360365	−	0.0261820i
$505$	16.7070			0.743450
$506$	3.26703	+	9.03808i	0.145237	+	0.401791i
$507$	−12.2379			−0.543504
$508$	11.4463	−	8.31626i	0.507849	−	0.368974i
$509$	−4.22829	−	13.0133i	−0.187416	−	0.576806i	0.812566	−	0.582869i	$-0.198070\pi$
$509$	−4.22829	−	13.0133i	−0.187416	−	0.576806i	−0.999982	+	0.00606333i	$0.998070\pi$
$510$	−4.19682	+	12.9165i	−0.185838	+	0.571951i
$511$	12.7111	+	9.23519i	0.562308	+	0.408541i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	1.10570	−	3.40299i	0.0488178	−	0.150246i
$514$	1.19769	+	3.68610i	0.0528277	+	0.162587i
$515$	−5.87178	+	4.26610i	−0.258742	+	0.187987i
$516$	3.74009			0.164648
$517$	−37.9036	+	1.23991i	−1.66700	+	0.0545313i
$518$	−5.93542			−0.260787
$519$	7.72601	−	5.61327i	0.339134	−	0.246395i
$520$	0.756026	+	2.32681i	0.0331539	+	0.102037i
$521$	9.69973	−	29.8527i	0.424953	−	1.30787i	−0.478087	−	0.878313i	$-0.658669\pi$
$521$	9.69973	−	29.8527i	0.424953	−	1.30787i	0.903039	−	0.429558i	$-0.141331\pi$
$522$	−1.79958	−	1.30747i	−0.0787653	−	0.0572264i
$523$	23.1950	+	16.8522i	1.01425	+	0.736893i	0.965095	−	0.261898i	$-0.0843485\pi$
$523$	23.1950	+	16.8522i	1.01425	+	0.736893i	0.0491509	+	0.998791i	$0.484348\pi$
$524$	3.86313	−	11.8895i	0.168762	−	0.519395i
$525$	0.881966	+	2.71441i	0.0384922	+	0.118467i
$526$	2.86127	−	2.07883i	0.124757	−	0.0906414i
$527$	−28.1759			−1.22736
$528$	−2.74551	−	1.86069i	−0.119483	−	0.0809763i
$529$	−14.6036			−0.634940
$530$	−28.3359	+	20.5872i	−1.23083	+	0.894252i
$531$	2.04467	+	6.29286i	0.0887313	+	0.273087i
$532$	1.10570	−	3.40299i	0.0479381	−	0.147538i
$533$	5.00182	+	3.63403i	0.216653	+	0.157407i
$534$	−10.2706	−	7.46205i	−0.444454	−	0.322915i
$535$	6.75403	−	20.7868i	0.292002	−	0.898690i
$536$	2.46837	+	7.59687i	0.106617	+	0.328135i
$537$	−8.94166	+	6.49650i	−0.385861	+	0.280345i
$538$	26.1876			1.12903
$539$	−2.61803	+	2.03615i	−0.112767	+	0.0877031i
$540$	−2.80252			−0.120601
$541$	−32.6577	+	23.7272i	−1.40406	+	1.02011i	−0.409912	+	0.912125i	$0.634440\pi$
$541$	−32.6577	+	23.7272i	−1.40406	+	1.02011i	−0.994152	+	0.107987i	$0.965560\pi$
$542$	−2.58528	−	7.95668i	−0.111047	−	0.341769i
$543$	−1.23789	+	3.80982i	−0.0531228	+	0.163495i
$544$	−3.92055	−	2.84845i	−0.168092	−	0.122126i
$545$	−26.3630	−	19.1538i	−1.12927	−	0.820459i
$546$	−0.269767	+	0.830257i	−0.0115449	+	0.0355317i
$547$	9.02019	+	27.7613i	0.385676	+	1.18699i	0.935989	+	0.352029i	$0.114508\pi$
$547$	9.02019	+	27.7613i	0.385676	+	1.18699i	−0.550314	+	0.834958i	$0.685492\pi$
$548$	3.28256	−	2.38492i	0.140224	−	0.101879i
$549$	−10.3334			−0.441021
$550$	7.47214	−	5.81137i	0.318613	−	0.247798i
$551$	−7.95916			−0.339072
$552$	−2.34425	+	1.70320i	−0.0997779	+	0.0724929i
$553$	−1.89878	−	5.84383i	−0.0807442	−	0.248505i
$554$	1.62259	−	4.99381i	0.0689372	−	0.212167i
$555$	13.4573	+	9.77728i	0.571229	+	0.415022i
$556$	−9.11783	−	6.62449i	−0.386682	−	0.280941i
$557$	3.43719	−	10.5786i	0.145638	−	0.448228i	−0.851454	−	0.524429i	$-0.824279\pi$
$557$	3.43719	−	10.5786i	0.145638	−	0.448228i	0.997093	+	0.0762004i	$0.0242789\pi$
$558$	−1.79668	−	5.52962i	−0.0760596	−	0.234087i
$559$	−2.64147	+	1.91914i	−0.111722	+	0.0811709i
$560$	−2.80252			−0.118428
$561$	13.3049	+	9.01705i	0.561734	+	0.380700i
$562$	6.83886			0.288480
$563$	12.0455	−	8.75157i	0.507657	−	0.368834i	−0.304277	−	0.952584i	$-0.598415\pi$
$563$	12.0455	−	8.75157i	0.507657	−	0.368834i	0.811934	+	0.583749i	$0.198415\pi$
$564$	−3.53344	−	10.8748i	−0.148785	−	0.457913i
$565$	−12.3579	+	38.0337i	−0.519901	+	1.60009i
$566$	3.52914	+	2.56407i	0.148341	+	0.107776i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	−3.15757	+	9.71799i	−0.132489	+	0.407758i
$569$	4.22539	+	13.0044i	0.177138	+	0.545174i	0.999725	−	0.0234655i	$-0.00747000\pi$
$569$	4.22539	+	13.0044i	0.177138	+	0.545174i	−0.822587	+	0.568639i	$0.807470\pi$
$570$	−8.11261	+	5.89416i	−0.339800	+	0.246879i
$571$	−14.9587			−0.626002			−0.313001	−	0.949753i	$-0.601334\pi$
$571$	−14.9587			−0.626002			−0.313001	+	0.949753i	$0.601334\pi$
$572$	2.89381	−	0.0946632i	0.120996	−	0.00395807i
$573$	7.77642			0.324865
$574$	−5.72957	+	4.16277i	−0.239148	+	0.173751i
$575$	−2.55563	−	7.86542i	−0.106577	−	0.328011i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	10.4493	+	7.59185i	0.435009	+	0.316053i	0.783649	−	0.621204i	$-0.213356\pi$
$577$	10.4493	+	7.59185i	0.435009	+	0.316053i	−0.348639	+	0.937257i	$0.613356\pi$
$578$	5.24597	+	3.81142i	0.218203	+	0.158534i
$579$	−5.21542	+	16.0514i	−0.216745	+	0.667073i
$580$	1.92639	+	5.92881i	0.0799888	+	0.246180i
$581$	−8.08032	+	5.87069i	−0.335228	+	0.243557i
$582$	2.90262			0.120317
$583$	14.0909	+	38.9817i	0.583584	+	1.61446i
$584$	15.7118			0.650161
$585$	1.97930	−	1.43805i	0.0818340	−	0.0594559i
$586$	6.02717	+	18.5497i	0.248980	+	0.766282i
$587$	−13.6727	+	42.0804i	−0.564335	+	1.73684i	0.105586	+	0.994410i	$0.466328\pi$
$587$	−13.6727	+	42.0804i	−0.564335	+	1.73684i	−0.669920	+	0.742433i	$0.733672\pi$
$588$	−0.809017	−	0.587785i	−0.0333633	−	0.0242399i
$589$	−16.8307	−	12.2282i	−0.693496	−	0.503854i
$590$	5.73023	−	17.6358i	0.235910	−	0.726056i
$591$	−3.30226	−	10.1633i	−0.135837	−	0.418063i
$592$	−4.80185	+	3.48875i	−0.197355	+	0.143387i
$593$	5.83880			0.239771			0.119885	−	0.992788i	$-0.461747\pi$
$593$	5.83880			0.239771			0.119885	+	0.992788i	$0.461747\pi$
$594$	−0.921216	+	3.18612i	−0.0377980	+	0.130728i
$595$	13.5812			0.556774
$596$	1.23607	−	0.898056i	0.0506313	−	0.0367858i
$597$	−6.01441	−	18.5104i	−0.246153	−	0.757582i
$598$	0.781690	−	2.40579i	0.0319657	−	0.0983803i
$599$	−33.9887	−	24.6942i	−1.38874	−	1.00898i	−0.996002	−	0.0893285i	$-0.971528\pi$
$599$	−33.9887	−	24.6942i	−1.38874	−	1.00898i	−0.392738	−	0.919650i	$-0.628472\pi$
$600$	2.30902	+	1.67760i	0.0942652	+	0.0684877i
$601$	−5.01663	+	15.4396i	−0.204633	+	0.629795i	0.795095	+	0.606484i	$0.207421\pi$
$601$	−5.01663	+	15.4396i	−0.204633	+	0.629795i	−0.999728	+	0.0233107i	$0.992579\pi$
$602$	−1.15575	−	3.55703i	−0.0471048	−	0.144974i
$603$	6.46228	−	4.69512i	0.263165	−	0.191200i
$604$	12.8730			0.523794
$605$	−11.4220	−	28.6336i	−0.464372	−	1.16412i
$606$	5.96141			0.242166
$607$	7.48294	−	5.43667i	0.303723	−	0.220668i	−0.425475	−	0.904970i	$-0.639893\pi$
$607$	7.48294	−	5.43667i	0.303723	−	0.220668i	0.729198	+	0.684302i	$0.239893\pi$
$608$	−1.10570	−	3.40299i	−0.0448420	−	0.138010i
$609$	−0.687377	+	2.11553i	−0.0278539	+	0.0857256i
$610$	23.4289	+	17.0221i	0.948607	+	0.689203i
$611$	8.07569	+	5.86733i	0.326707	+	0.237367i
$612$	−1.49752	+	4.60888i	−0.0605335	+	0.186303i
$613$	15.0435	+	46.2991i	0.607601	+	1.87000i	0.477814	+	0.878461i	$0.341429\pi$
$613$	15.0435	+	46.2991i	0.607601	+	1.87000i	0.129787	+	0.991542i	$0.458571\pi$
$614$	9.94166	−	7.22304i	0.401213	−	0.291498i
$615$	19.8478			0.800341
$616$	−0.921216	+	3.18612i	−0.0371169	+	0.128372i
$617$	36.6494			1.47545			0.737725	−	0.675102i	$-0.235900\pi$
$617$	36.6494			1.47545			0.737725	+	0.675102i	$0.235900\pi$
$618$	−2.09518	+	1.52224i	−0.0842806	+	0.0612334i
$619$	−12.4835	−	38.4202i	−0.501753	−	1.54424i	−0.806161	−	0.591696i	$-0.798459\pi$
$619$	−12.4835	−	38.4202i	−0.501753	−	1.54424i	0.304408	−	0.952542i	$-0.401541\pi$
$620$	−5.03523	+	15.4969i	−0.202220	+	0.622369i
$621$	2.34425	+	1.70320i	0.0940715	+	0.0683470i
$622$	26.1540	+	19.0020i	1.04868	+	0.761911i
$623$	−3.92303	+	12.0739i	−0.157173	+	0.483729i
$624$	0.269767	+	0.830257i	0.0107993	+	0.0332369i
$625$	25.1803	−	18.2946i	1.00721	−	0.731784i
$626$	22.5260			0.900319
$627$	4.03424	+	11.1605i	0.161112	+	0.445708i
$628$	2.78000			0.110934
$629$	23.2701	−	16.9067i	0.927840	−	0.674115i
$630$	0.866025	+	2.66535i	0.0345033	+	0.106190i
$631$	5.35441	−	16.4792i	0.213156	−	0.656026i	−0.786124	−	0.618069i	$-0.787915\pi$
$631$	5.35441	−	16.4792i	0.213156	−	0.656026i	0.999279	−	0.0379569i	$-0.0120849\pi$
$632$	−4.97106	−	3.61169i	−0.197738	−	0.143665i
$633$	2.48480	+	1.80531i	0.0987620	+	0.0717548i
$634$	0.850339	−	2.61707i	0.0337713	−	0.103937i
$635$	12.2529	+	37.7106i	0.486242	+	1.49650i
$636$	−10.1109	+	7.34598i	−0.400922	+	0.291287i
$637$	0.872983			0.0345889
$638$	7.37355	−	0.241206i	0.291922	−	0.00954943i
$639$	10.2181			0.404222
$640$	−2.26728	+	1.64728i	−0.0896223	+	0.0651144i
$641$	−14.7337	−	45.3458i	−0.581948	−	1.79105i	−0.611197	−	0.791479i	$-0.709312\pi$
$641$	−14.7337	−	45.3458i	−0.581948	−	1.79105i	0.0292488	−	0.999572i	$-0.490688\pi$
$642$	2.40999	−	7.41718i	0.0951146	−	0.292733i
$643$	22.7133	+	16.5022i	0.895727	+	0.650784i	0.937365	−	0.348349i	$-0.113258\pi$
$643$	22.7133	+	16.5022i	0.895727	+	0.650784i	−0.0416380	+	0.999133i	$0.513258\pi$
$644$	2.34425	+	1.70320i	0.0923764	+	0.0671154i
$645$	−3.23901	+	9.96864i	−0.127536	+	0.392515i
$646$	5.35829	+	16.4911i	0.210819	+	0.648835i
$647$	14.3996	−	10.4620i	0.566108	−	0.411302i	−0.267581	−	0.963535i	$-0.586224\pi$
$647$	14.3996	−	10.4620i	0.566108	−	0.411302i	0.833689	+	0.552233i	$0.186224\pi$
$648$	−1.00000			−0.0392837
$649$	−18.1662	−	12.3117i	−0.713086	−	0.483275i
$650$	−2.49158			−0.0977279
$651$	−4.70378	+	3.41749i	−0.184356	+	0.133942i
$652$	−2.61803	−	8.05748i	−0.102530	−	0.315555i
$653$	−3.87562	+	11.9279i	−0.151665	+	0.466776i	−0.997808	−	0.0661797i	$-0.978919\pi$
$653$	−3.87562	+	11.9279i	−0.151665	+	0.466776i	0.846143	+	0.532956i	$0.178919\pi$
$654$	−9.40689	−	6.83450i	−0.367838	−	0.267250i
$655$	28.3441	+	20.5932i	1.10750	+	0.804643i
$656$	−2.18850	+	6.73551i	−0.0854466	+	0.262978i
$657$	−4.85523	−	14.9428i	−0.189420	−	0.582976i
$658$	−9.25068	+	6.72101i	−0.360629	+	0.262012i
$659$	31.1808			1.21463			0.607317	−	0.794460i	$-0.292246\pi$
$659$	31.1808			1.21463			0.607317	+	0.794460i	$0.292246\pi$
$660$	7.33708	−	5.70634i	0.285596	−	0.222119i
$661$	−29.7716			−1.15798			−0.578990	−	0.815335i	$-0.696553\pi$
$661$	−29.7716			−1.15798			−0.578990	+	0.815335i	$0.696553\pi$
$662$	−11.6795	+	8.48563i	−0.453936	+	0.329803i
$663$	−1.30731	−	4.02348i	−0.0507716	−	0.156259i
$664$	−3.08641	+	9.49898i	−0.119776	+	0.368632i
$665$	8.11261	+	5.89416i	0.314594	+	0.228566i
$666$	4.80185	+	3.48875i	0.186068	+	0.135186i
$667$	1.99178	−	6.13007i	0.0771220	−	0.237357i
$668$	−1.53651	−	4.72890i	−0.0594495	−	0.182967i
$669$	−11.7648	+	8.54763i	−0.454853	+	0.330470i
$670$	−22.3860			−0.864847
$671$	27.0533	−	21.0404i	1.04438	−	0.812257i
$672$	−1.00000			−0.0385758
$673$	36.0403	−	26.1848i	1.38925	−	1.00935i	0.393305	−	0.919408i	$-0.371331\pi$
$673$	36.0403	−	26.1848i	1.38925	−	1.00935i	0.995947	−	0.0899431i	$-0.0286685\pi$
$674$	−6.69252	−	20.5975i	−0.257786	−	0.793384i
$675$	0.881966	−	2.71441i	0.0339469	−	0.104478i
$676$	9.90067	+	7.19326i	0.380795	+	0.276664i
$677$	−30.0171	−	21.8087i	−1.15365	−	0.838177i	−0.164690	−	0.986345i	$-0.552662\pi$
$677$	−30.0171	−	21.8087i	−1.15365	−	0.838177i	−0.988962	+	0.148168i	$0.952662\pi$
$678$	−4.40958	+	13.5713i	−0.169349	+	0.521202i
$679$	−0.896958	−	2.76055i	−0.0344221	−	0.105940i
$680$	10.9874	−	7.98282i	0.421348	−	0.306127i
$681$	−25.6664			−0.983538
$682$	15.9629	+	10.8184i	0.611251	+	0.414259i
$683$	19.6972			0.753692			0.376846	−	0.926276i	$-0.377009\pi$
$683$	19.6972			0.753692			0.376846	+	0.926276i	$0.377009\pi$
$684$	−2.89476	+	2.10317i	−0.110684	+	0.0804165i
$685$	3.51387	+	10.8146i	0.134258	+	0.413204i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	4.40937	+	3.20359i	0.168228	+	0.122225i
$688$	−3.02579	−	2.19837i	−0.115357	−	0.0838120i
$689$	3.37147	−	10.3763i	0.128443	−	0.395306i
$690$	−2.50944	−	7.72326i	−0.0955328	−	0.294020i
$691$	−30.7345	+	22.3299i	−1.16920	+	0.849471i	−0.990913	−	0.134508i	$-0.957055\pi$
$691$	−30.7345	+	22.3299i	−1.16920	+	0.849471i	−0.178284	+	0.983979i	$0.557055\pi$
$692$	−9.54987			−0.363032
$693$	3.31485	−	0.108436i	0.125921	−	0.00411916i
$694$	−16.4700			−0.625194
$695$	25.5529	−	18.5652i	0.969275	−	0.704220i
$696$	0.687377	+	2.11553i	0.0260550	+	0.0801889i
$697$	10.6056	−	32.6407i	0.401717	−	1.23636i
$698$	9.56658	+	6.95053i	0.362100	+	0.263081i
$699$	23.4499	+	17.0373i	0.886957	+	0.644412i
$700$	0.881966	−	2.71441i	0.0333352	−	0.102595i
$701$	−12.0154	−	36.9797i	−0.453817	−	1.39670i	−0.872519	−	0.488580i	$-0.837515\pi$
$701$	−12.0154	−	36.9797i	−0.453817	−	1.39670i	0.418702	−	0.908124i	$-0.362485\pi$
$702$	0.706258	−	0.513127i	0.0266560	−	0.0193667i
$703$	21.2376			0.800992
$704$	1.12747	+	3.11910i	0.0424933	+	0.117556i
$705$	32.0453			1.20690
$706$	19.2733	−	14.0029i	0.725361	−	0.527006i
$707$	−1.84218	−	5.66964i	−0.0692823	−	0.213229i
$708$	2.04467	−	6.29286i	0.0768435	−	0.236500i
$709$	9.16949	+	6.66202i	0.344367	+	0.250198i	0.746502	−	0.665383i	$-0.231732\pi$
$709$	9.16949	+	6.66202i	0.344367	+	0.250198i	−0.402135	+	0.915580i	$0.631732\pi$
$710$	−23.1673	−	16.8321i	−0.869455	−	0.631696i
$711$	−1.89878	+	5.84383i	−0.0712097	+	0.219161i
$712$	3.92303	+	12.0739i	0.147022	+	0.452487i
$713$	13.6299	−	9.90271i	0.510444	−	0.370859i
$714$	4.84607			0.181360
$715$	−2.25380	+	7.79500i	−0.0842874	+	0.291517i
$716$	11.0525			0.413051
$717$	22.0490	−	16.0195i	0.823434	−	0.598260i
$718$	6.24861	+	19.2312i	0.233196	+	0.717703i
$719$	10.9500	−	33.7005i	0.408365	−	1.25682i	−0.509688	−	0.860359i	$-0.670239\pi$
$719$	10.9500	−	33.7005i	0.408365	−	1.25682i	0.918053	−	0.396458i	$-0.129761\pi$
$720$	2.26728	+	1.64728i	0.0844967	+	0.0613904i
$721$	2.09518	+	1.52224i	0.0780287	+	0.0566911i
$722$	1.91500	−	5.89376i	0.0712689	−	0.219343i
$723$	4.20539	+	12.9429i	0.156400	+	0.481350i
$724$	3.24083	−	2.35460i	0.120444	−	0.0875079i
$725$	−6.34866			−0.235783
$726$	−4.07564	−	10.2171i	−0.151261	−	0.379192i
$727$	34.8985			1.29431			0.647156	−	0.762357i	$-0.275958\pi$
$727$	34.8985			1.29431			0.647156	+	0.762357i	$0.275958\pi$
$728$	0.706258	−	0.513127i	0.0261757	−	0.0190177i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−13.6069	+	41.8776i	−0.503612	+	1.54996i
$731$	14.6632	+	10.6534i	0.542338	+	0.394032i
$732$	8.35994	+	6.07385i	0.308992	+	0.224496i
$733$	6.89018	−	21.2058i	0.254494	−	0.783253i	−0.739434	−	0.673229i	$-0.764907\pi$
$733$	6.89018	−	21.2058i	0.254494	−	0.783253i	0.993929	−	0.110025i	$-0.0350930\pi$
$734$	3.86715	+	11.9019i	0.142739	+	0.439306i
$735$	2.26728	−	1.64728i	0.0836300	−	0.0607608i
$736$	2.89765			0.106809
$737$	−7.35851	+	25.4502i	−0.271054	+	0.937469i
$738$	7.08214			0.260697
$739$	0.164779	−	0.119719i	0.00606151	−	0.00440394i	−0.584750	−	0.811213i	$-0.698808\pi$
$739$	0.164779	−	0.119719i	0.00606151	−	0.00440394i	0.590812	+	0.806809i	$0.298808\pi$
$740$	−5.14022	−	15.8200i	−0.188958	−	0.581554i
$741$	0.965257	−	2.97076i	0.0354596	−	0.109133i
$742$	10.1109	+	7.34598i	0.371182	+	0.269679i
$743$	−35.7216	−	25.9532i	−1.31050	−	0.952132i	−0.999999	−	0.00155865i	$-0.999504\pi$
$743$	−35.7216	−	25.9532i	−1.31050	−	0.952132i	−0.310499	−	0.950574i	$-0.600496\pi$
$744$	−1.79668	+	5.52962i	−0.0658696	+	0.202726i
$745$	1.32317	+	4.07230i	0.0484772	+	0.149197i
$746$	−28.6568	+	20.8204i	−1.04920	+	0.762288i
$747$	9.98782			0.365435
$748$	−5.46382	−	15.1154i	−0.199777	−	0.552673i
$749$	−7.79888			−0.284965
$750$	4.86536	−	3.53489i	0.177658	−	0.129076i
$751$	7.74999	+	23.8520i	0.282801	+	0.870373i	0.987049	+	0.160419i	$0.0512844\pi$
$751$	7.74999	+	23.8520i	0.282801	+	0.870373i	−0.704248	+	0.709954i	$0.748716\pi$
$752$	−3.53344	+	10.8748i	−0.128851	+	0.396564i
$753$	18.2010	+	13.2238i	0.663283	+	0.481903i
$754$	−1.57100	−	1.14140i	−0.0572125	−	0.0415673i
$755$	−11.1483	+	34.3110i	−0.405729	+	1.24871i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	41.5796	−	30.2093i	1.51124	−	1.09798i	0.545611	−	0.838038i	$-0.316297\pi$
$757$	41.5796	−	30.2093i	1.51124	−	1.09798i	0.965625	−	0.259939i	$-0.0837025\pi$
$758$	−18.9873			−0.689650
$759$	−9.60529	+	0.314211i	−0.348650	+	0.0114051i
$760$	10.0277			0.363744
$761$	9.20203	−	6.68567i	0.333573	−	0.242355i	−0.408372	−	0.912816i	$-0.633903\pi$
$761$	9.20203	−	6.68567i	0.333573	−	0.242355i	0.741945	+	0.670460i	$0.233903\pi$
$762$	4.37211	+	13.4560i	0.158385	+	0.487459i
$763$	−3.59311	+	11.0585i	−0.130079	+	0.400343i
$764$	−6.29126	−	4.57087i	−0.227610	−	0.165368i
$765$	−10.9874	−	7.98282i	−0.397251	−	0.288620i
$766$	−3.47131	+	10.6836i	−0.125424	+	0.386014i
$767$	1.78497	+	5.49356i	0.0644514	+	0.198361i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−46.3417			−1.67112			−0.835562	−	0.549396i	$-0.814858\pi$
$769$	−46.3417			−1.67112			−0.835562	+	0.549396i	$0.814858\pi$
$770$	−7.69433	−	5.21463i	−0.277285	−	0.187922i
$771$	−3.87580			−0.139583
$772$	13.6541	−	9.92031i	0.491423	−	0.357040i
$773$	2.58533	+	7.95683i	0.0929879	+	0.286187i	0.986724	−	0.162406i	$-0.0519253\pi$
$773$	2.58533	+	7.95683i	0.0929879	+	0.286187i	−0.893736	+	0.448593i	$0.851925\pi$
$774$	−1.15575	+	3.55703i	−0.0415426	+	0.127855i
$775$	−13.4251	−	9.75387i	−0.482242	−	0.350369i
$776$	−2.34827	−	1.70612i	−0.0842979	−	0.0612460i
$777$	1.83414	−	5.64492i	0.0657996	−	0.202510i
$778$	−8.22571	−	25.3161i	−0.294906	−	0.907627i
$779$	20.5011	−	14.8949i	0.734527	−	0.533665i
$780$	−2.44655			−0.0876006
$781$	−26.7513	+	20.8056i	−0.957238	+	0.744482i
$782$	−14.0422			−0.502149
$783$	1.79958	−	1.30747i	0.0643116	−	0.0467251i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−2.40755	+	7.40968i	−0.0859292	+	0.264463i
$786$	10.1138	+	7.34811i	0.360748	+	0.262099i
$787$	6.78691	+	4.93098i	0.241927	+	0.175770i	0.702141	−	0.712038i	$-0.252227\pi$
$787$	6.78691	+	4.93098i	0.241927	+	0.175770i	−0.460214	+	0.887808i	$0.652227\pi$
$788$	−3.30226	+	10.1633i	−0.117638	+	0.362053i
$789$	1.09291	+	3.36362i	0.0389085	+	0.119748i
$790$	13.9315	−	10.1218i	0.495660	−	0.360118i
$791$	14.2697			0.507372
$792$	2.61803	−	2.03615i	0.0930278	−	0.0723514i
$793$	−9.02093			−0.320343
$794$	−15.8191	+	11.4932i	−0.561398	+	0.407879i
$795$	−10.8233	−	33.3108i	−0.383864	−	1.18141i
$796$	−6.01441	+	18.5104i	−0.213175	+	0.656085i
$797$	−7.02492	−	5.10390i	−0.248835	−	0.180790i	0.456375	−	0.889787i	$-0.349148\pi$
$797$	−7.02492	−	5.10390i	−0.248835	−	0.180790i	−0.705211	+	0.708998i	$0.749148\pi$
$798$	2.89476	+	2.10317i	0.102473	+	0.0744512i
$799$	17.1233	−	52.7001i	0.605779	−	1.86440i
$800$	−0.881966	−	2.71441i	−0.0311822	−	0.0959690i
$801$	10.2706	−	7.46205i	0.362895	−	0.263659i
$802$	5.06955			0.179012
$803$	43.1370	+	29.2349i	1.52227	+	1.03168i
$804$	−7.98782			−0.281709
$805$	−6.56980	+	4.77324i	−0.231555	+	0.168235i
$806$	−1.56847	−	4.82727i	−0.0552471	−	0.170033i
$807$	−8.09242	+	24.9059i	−0.284867	+	0.876729i
$808$	−4.82289	−	3.50403i	−0.169669	−	0.123271i
$809$	3.70129	+	2.68915i	0.130131	+	0.0945454i	0.650946	−	0.759124i	$-0.274372\pi$
$809$	3.70129	+	2.68915i	0.130131	+	0.0945454i	−0.520816	+	0.853669i	$0.674372\pi$
$810$	0.866025	−	2.66535i	0.0304290	−	0.0936509i
$811$	−10.7257	−	33.0103i	−0.376630	−	1.15915i	−0.942372	−	0.334566i	$-0.891410\pi$
$811$	−10.7257	−	33.0103i	−0.376630	−	1.15915i	0.565742	−	0.824582i	$-0.308590\pi$
$812$	1.79958	−	1.30747i	0.0631527	−	0.0458832i
$813$	8.36615			0.293414
$814$	−19.6750	+	0.643615i	−0.689609	+	0.0225587i
$815$	23.7433			0.831692
$816$	3.92055	−	2.84845i	0.137247	−	0.0997156i
$817$	4.13541	+	12.7275i	0.144680	+	0.445278i
$818$	0.704313	−	2.16765i	0.0246257	−	0.0757902i
$819$	−0.706258	−	0.513127i	−0.0246787	−	0.0179301i
$820$	−16.0572	−	11.6662i	−0.560742	−	0.407403i
$821$	4.02861	−	12.3988i	0.140599	−	0.432720i	−0.855820	−	0.517274i	$-0.826947\pi$
$821$	4.02861	−	12.3988i	0.140599	−	0.432720i	0.996419	+	0.0845543i	$0.0269466\pi$
$822$	1.25383	+	3.85888i	0.0437322	+	0.134594i
$823$	−38.3444	+	27.8588i	−1.33660	+	0.971098i	−0.337040	+	0.941490i	$0.609426\pi$
$823$	−38.3444	+	27.8588i	−1.33660	+	0.971098i	−0.999562	+	0.0296079i	$0.990574\pi$
$824$	2.58979			0.0902195
$825$	3.21793	+	8.90224i	0.112034	+	0.309936i
$826$	−6.61670			−0.230225
$827$	−5.14034	+	3.73468i	−0.178747	+	0.129867i	−0.673561	−	0.739131i	$-0.735236\pi$
$827$	−5.14034	+	3.73468i	−0.178747	+	0.129867i	0.494814	+	0.868999i	$0.335236\pi$
$828$	−0.895424	−	2.75583i	−0.0311181	−	0.0957718i
$829$	2.80139	−	8.62180i	0.0972964	−	0.299448i	−0.890549	−	0.454887i	$-0.849679\pi$
$829$	2.80139	−	8.62180i	0.0972964	−	0.299448i	0.987845	+	0.155440i	$0.0496795\pi$
$830$	−22.6452	−	16.4527i	−0.786027	−	0.571082i
$831$	4.24799	+	3.08635i	0.147361	+	0.107064i
$832$	0.269767	−	0.830257i	0.00935248	−	0.0287840i
$833$	−1.49752	−	4.60888i	−0.0518859	−	0.159688i
$834$	9.11783	−	6.62449i	0.315725	−	0.229387i
$835$	13.9348			0.482235
$836$	3.29622	−	11.4003i	0.114002	−	0.394288i
$837$	5.81419			0.200968
$838$	−16.7239	+	12.1507i	−0.577719	+	0.419737i
$839$	−0.0183944	−	0.0566121i	−0.000635045	−	0.00195447i	0.950738	−	0.309994i	$-0.100327\pi$
$839$	−0.0183944	−	0.0566121i	−0.000635045	−	0.00195447i	−0.951374	+	0.308040i	$0.900327\pi$
$840$	0.866025	−	2.66535i	0.0298807	−	0.0919634i
$841$	19.4585	+	14.1374i	0.670983	+	0.487498i
$842$	−16.2018	−	11.7713i	−0.558350	−	0.405665i
$843$	−2.11332	+	6.50414i	−0.0727867	+	0.224014i
$844$	−0.949109	−	2.92106i	−0.0326697	−	0.100547i
$845$	−27.7468	+	20.1592i	−0.954519	+	0.693498i
$846$	11.4345			0.393125
$847$	−8.45760	+	7.03342i	−0.290607	+	0.241671i
$848$	12.4977			0.429174
$849$	−3.52914	+	2.56407i	−0.121120	+	0.0879988i
$850$	4.27407	+	13.1542i	0.146599	+	0.451186i
$851$	−5.31471	+	16.3570i	−0.182186	+	0.560711i
$852$	−8.26662	−	6.00605i	−0.283210	−	0.205764i
$853$	−43.0804	−	31.2997i	−1.47504	−	1.07168i	−0.979112	−	0.203321i	$-0.934826\pi$
$853$	−43.0804	−	31.2997i	−1.47504	−	1.07168i	−0.495932	−	0.868361i	$-0.665174\pi$
$854$	3.19321	−	9.82769i	0.109269	−	0.336297i
$855$	−3.09874	−	9.53695i	−0.105975	−	0.326157i
$856$	−6.30943	+	4.58407i	−0.215652	+	0.156680i
$857$	−2.70283			−0.0923269			−0.0461635	−	0.998934i	$-0.514700\pi$
$857$	−2.70283			−0.0923269			−0.0461635	+	0.998934i	$0.514700\pi$
$858$	−0.804207	+	2.78143i	−0.0274552	+	0.0949564i
$859$	−4.14359			−0.141378			−0.0706888	−	0.997498i	$-0.522520\pi$
$859$	−4.14359			−0.141378			−0.0706888	+	0.997498i	$0.522520\pi$
$860$	8.47983	−	6.16096i	0.289160	−	0.210087i
$861$	−2.18850	−	6.73551i	−0.0745839	−	0.229546i
$862$	−9.00087	+	27.7018i	−0.306571	+	0.943528i
$863$	16.9763	+	12.3340i	0.577879	+	0.419854i	0.837959	−	0.545733i	$-0.183749\pi$
$863$	16.9763	+	12.3340i	0.577879	+	0.419854i	−0.260080	+	0.965587i	$0.583749\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	8.27043	−	25.4538i	0.281203	−	0.865454i
$866$	6.59600	+	20.3004i	0.224141	+	0.689836i
$867$	−5.24597	+	3.81142i	−0.178162	+	0.129443i
$868$	5.81419			0.197346
$869$	−6.92784	−	19.1655i	−0.235011	−	0.650146i
$870$	−6.23392			−0.211350
$871$	5.64147	−	4.09877i	0.191154	−	0.138881i
$872$	3.59311	+	11.0585i	0.121678	+	0.374487i
$873$	−0.896958	+	2.76055i	−0.0303574	+	0.0934306i
$874$	−8.38800	−	6.09424i	−0.283728	−	0.206141i
$875$	−4.86536	−	3.53489i	−0.164479	−	0.119501i
$876$	−4.85523	+	14.9428i	−0.164043	+	0.504872i
$877$	−1.12348	−	3.45770i	−0.0379371	−	0.116758i	0.930295	−	0.366813i	$-0.119551\pi$
$877$	−1.12348	−	3.45770i	−0.0379371	−	0.116758i	−0.968232	+	0.250055i	$0.919551\pi$
$878$	21.7926	−	15.8333i	0.735465	−	0.534347i
$879$	−19.5043			−0.657865
$880$	−9.28993	+	0.303895i	−0.313163	+	0.0102443i
$881$	16.8954			0.569221			0.284610	−	0.958643i	$-0.408136\pi$
$881$	16.8954			0.569221			0.284610	+	0.958643i	$0.408136\pi$
$882$	0.809017	−	0.587785i	0.0272410	−	0.0197918i
$883$	1.80818	+	5.56500i	0.0608500	+	0.187277i	0.976861	−	0.213877i	$-0.0686092\pi$
$883$	1.80818	+	5.56500i	0.0608500	+	0.187277i	−0.916011	+	0.401154i	$0.868609\pi$
$884$	−1.30731	+	4.02348i	−0.0439695	+	0.135324i
$885$	15.0019	+	10.8996i	0.504285	+	0.366384i
$886$	−8.51279	−	6.18491i	−0.285993	−	0.207786i
$887$	−5.81746	+	17.9043i	−0.195331	+	0.601168i	0.804641	+	0.593761i	$0.202358\pi$
$887$	−5.81746	+	17.9043i	−0.195331	+	0.601168i	−0.999973	+	0.00740663i	$0.997642\pi$
$888$	−1.83414	−	5.64492i	−0.0615498	−	0.189431i
$889$	11.4463	−	8.31626i	0.383898	−	0.278918i
$890$	−35.5785			−1.19259
$891$	−2.74551	−	1.86069i	−0.0919780	−	0.0623356i
$892$	14.5421			0.486905
$893$	33.1000	−	24.0486i	1.10765	−	0.804755i
$894$	0.472136	+	1.45309i	0.0157906	+	0.0485984i
$895$	−9.57175	+	29.4588i	−0.319948	+	0.984699i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	2.04649	+	1.48686i	0.0683304	+	0.0496449i
$898$	10.4020	−	32.0140i	0.347118	−	1.06832i
$899$	−3.99654	−	12.3001i	−0.133292	−	0.410231i
$900$	−2.30902	+	1.67760i	−0.0769672	+	0.0559200i
$901$	−60.5648			−2.01771
$902$	−18.5413	+	14.4203i	−0.617357	+	0.480143i
$903$	3.74009			0.124462
$904$	11.5444	−	8.38751i	0.383962	−	0.278964i
$905$	3.46920	+	10.6771i	0.115320	+	0.354918i
$906$	−3.97797	+	12.2429i	−0.132159	+	0.406744i
$907$	−43.1095	−	31.3209i	−1.43143	−	1.03999i	−0.989749	−	0.142818i	$-0.954384\pi$
$907$	−43.1095	−	31.3209i	−1.43143	−	1.03999i	−0.441677	−	0.897174i	$-0.645616\pi$
$908$	20.7645	+	15.0863i	0.689096	+	0.500657i
$909$	−1.84218	+	5.66964i	−0.0611012	+	0.188050i
$910$	0.756026	+	2.32681i	0.0250620	+	0.0771329i
$911$	−40.8640	+	29.6895i	−1.35389	+	0.983655i	−0.355078	+	0.934837i	$0.615546\pi$
$911$	−40.8640	+	29.6895i	−1.35389	+	0.983655i	−0.998808	+	0.0488188i	$0.984454\pi$
$912$	3.57812			0.118483
$913$	−26.1485	+	20.3367i	−0.865388	+	0.673046i
$914$	0.716238			0.0236911
$915$	−23.4289	+	17.0221i	−0.774534	+	0.562732i
$916$	−1.68423	−	5.18352i	−0.0556485	−	0.171268i
$917$	3.86313	−	11.8895i	0.127572	−	0.392626i
$918$	−3.92055	−	2.84845i	−0.129397	−	0.0940128i
$919$	39.8294	+	28.9378i	1.31385	+	0.954569i	0.999987	+	0.00510074i	$0.00162362\pi$
$919$	39.8294	+	28.9378i	1.31385	+	0.954569i	0.313864	+	0.949468i	$0.398376\pi$
$920$	−2.50944	+	7.72326i	−0.0827338	+	0.254628i
$921$	3.79738	+	11.6871i	0.125128	+	0.385104i
$922$	−7.80467	+	5.67042i	−0.257033	+	0.186745i
$923$	8.92023			0.293613
$924$	−2.74551	−	1.86069i	−0.0903206	−	0.0612123i
$925$	16.9403			0.556993
$926$	−15.9171	+	11.5645i	−0.523070	+	0.380033i
$927$	−0.800288	−	2.46303i	−0.0262849	−	0.0808967i
$928$	0.687377	−	2.11553i	0.0225643	−	0.0694456i
$929$	−33.9712	−	24.6815i	−1.11456	−	0.809775i	−0.131184	−	0.991358i	$-0.541878\pi$
$929$	−33.9712	−	24.6815i	−1.11456	−	0.809775i	−0.983376	+	0.181583i	$0.941878\pi$
$930$	−13.1824	−	9.57758i	−0.432268	−	0.314061i
$931$	1.10570	−	3.40299i	0.0362378	−	0.111529i
$932$	−8.95706	−	27.5670i	−0.293398	−	0.902987i
$933$	−26.1540	+	19.0020i	−0.856244	+	0.622097i
$934$	32.2437			1.05505
$935$	45.0196	−	1.47270i	1.47230	−	0.0481623i
$936$	−0.872983			−0.0285344
$937$	42.7479	−	31.0582i	1.39651	−	1.01463i	0.401398	−	0.915904i	$-0.368525\pi$
$937$	42.7479	−	31.0582i	1.39651	−	1.01463i	0.995115	−	0.0987220i	$-0.0314755\pi$
$938$	2.46837	+	7.59687i	0.0805952	+	0.248047i
$939$	−6.96091	+	21.4235i	−0.227161	+	0.699128i
$940$	−25.9252	−	18.8357i	−0.845586	−	0.614354i
$941$	−5.11725	−	3.71790i	−0.166817	−	0.121200i	0.501244	−	0.865306i	$-0.332876\pi$
$941$	−5.11725	−	3.71790i	−0.166817	−	0.121200i	−0.668062	+	0.744106i	$0.732876\pi$
$942$	−0.859067	+	2.64394i	−0.0279899	+	0.0861441i
$943$	6.34151	+	19.5172i	0.206508	+	0.635567i
$944$	−5.35303	+	3.88920i	−0.174226	+	0.126583i
$945$	−2.80252			−0.0911659
$946$	−4.21685	−	11.6657i	−0.137102	−	0.379285i
$947$	−55.0356			−1.78842			−0.894208	−	0.447651i	$-0.852261\pi$
$947$	−55.0356			−1.78842			−0.894208	+	0.447651i	$0.852261\pi$
$948$	4.97106	−	3.61169i	0.161453	−	0.117302i
$949$	−4.23853	−	13.0449i	−0.137589	−	0.423454i
$950$	−3.15578	+	9.71249i	−0.102387	+	0.315115i
$951$	2.22622	+	1.61744i	0.0721900	+	0.0524491i
$952$	−3.92055	−	2.84845i	−0.127066	−	0.0923187i
$953$	14.4068	−	44.3395i	0.466681	−	1.43630i	−0.390174	−	0.920741i	$-0.627585\pi$
$953$	14.4068	−	44.3395i	0.466681	−	1.43630i	0.856856	−	0.515556i	$-0.172415\pi$
$954$	−3.86201	−	11.8860i	−0.125037	−	0.384825i
$955$	17.6314	−	12.8099i	0.570537	−	0.414520i
$956$	−27.2540			−0.881458
$957$	−2.04915	+	7.08720i	−0.0662397	+	0.229097i
$958$	−1.23873			−0.0400215
$959$	3.28256	−	2.38492i	0.105999	−	0.0770130i
$960$	−0.866025	−	2.66535i	−0.0279508	−	0.0860239i
$961$	0.866720	−	2.66749i	0.0279587	−	0.0860480i
$962$	4.19194	+	3.04562i	0.135153	+	0.0981947i
$963$	6.30943	+	4.58407i	0.203318	+	0.147720i
$964$	4.20539	−	12.9429i	0.135446	−	0.416861i
$965$	14.6163	+	44.9843i	0.470515	+	1.44810i
$966$	−2.34425	+	1.70320i	−0.0754250	+	0.0547995i
$967$	−3.41562			−0.109839			−0.0549195	−	0.998491i	$-0.517490\pi$
$967$	−3.41562			−0.109839			−0.0549195	+	0.998491i	$0.517490\pi$
$968$	−2.70820	+	10.6614i	−0.0870450	+	0.342671i
$969$	−17.3398			−0.557035
$970$	6.58106	−	4.78142i	0.211305	−	0.153522i
$971$	−7.26600	−	22.3625i	−0.233177	−	0.717645i	−0.997358	−	0.0726434i	$-0.976856\pi$
$971$	−7.26600	−	22.3625i	−0.233177	−	0.717645i	0.764181	−	0.645002i	$-0.223144\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−9.11783	−	6.62449i	−0.292304	−	0.212371i
$974$	22.1997	+	16.1290i	0.711325	+	0.516808i
$975$	0.769942	−	2.36964i	0.0246579	−	0.0758891i
$976$	−3.19321	−	9.82769i	−0.102212	−	0.314577i
$977$	−49.3426	+	35.8495i	−1.57861	+	1.14693i	−0.660342	+	0.750965i	$0.729589\pi$
$977$	−49.3426	+	35.8495i	−1.57861	+	1.14693i	−0.918267	+	0.395962i	$0.870411\pi$
$978$	8.47214			0.270909
$979$	−11.6950	+	40.4484i	−0.373775	+	1.29274i
$980$	−2.80252			−0.0895231
$981$	9.40689	−	6.83450i	0.300339	−	0.218209i
$982$	6.79281	+	20.9061i	0.216767	+	0.667141i
$983$	−11.8011	+	36.3201i	−0.376398	+	1.15843i	0.566133	+	0.824314i	$0.308439\pi$
$983$	−11.8011	+	36.3201i	−0.376398	+	1.15843i	−0.942531	+	0.334119i	$0.891561\pi$
$984$	−5.72957	−	4.16277i	−0.182652	−	0.132704i
$985$	−24.2290	−	17.6034i	−0.772000	−	0.560891i
$986$	−3.33108	+	10.2520i	−0.106083	+	0.326490i
$987$	−3.53344	−	10.8748i	−0.112471	−	0.346149i
$988$	−2.52708	+	1.83603i	−0.0803970	+	0.0584118i
$989$	−10.8375			−0.344611
$990$	3.15977	+	8.74134i	0.100424	+	0.277818i
$991$	5.79183			0.183983			0.0919917	−	0.995760i	$-0.470677\pi$
$991$	5.79183			0.183983			0.0919917	+	0.995760i	$0.470677\pi$
$992$	4.70378	−	3.41749i	0.149345	−	0.108506i
$993$	−4.46116	−	13.7300i	−0.141571	−	0.435710i
$994$	−3.15757	+	9.71799i	−0.100152	+	0.308236i
$995$	−44.1282	−	32.0610i	−1.39896	−	1.01640i
$996$	−8.08032	−	5.87069i	−0.256035	−	0.186020i
$997$	−6.67662	+	20.5485i	−0.211451	+	0.650779i	0.787936	+	0.615757i	$0.211150\pi$
$997$	−6.67662	+	20.5485i	−0.211451	+	0.650779i	−0.999387	+	0.0350212i	$0.988850\pi$
$998$	−9.35415	−	28.7891i	−0.296100	−	0.911303i
$999$	−4.80185	+	3.48875i	−0.151924	+	0.110379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.g.421.2	yes	8
11.2	odd	10		5082.2.a.ce.1.1		4
11.4	even	5	inner	462.2.j.g.169.2	✓	8
11.9	even	5		5082.2.a.bz.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.g.169.2	✓	8	11.4	even	5	inner
462.2.j.g.421.2	yes	8	1.1	even	1	trivial
5082.2.a.bz.1.1		4	11.9	even	5
5082.2.a.ce.1.1		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.26728 + 1.64728i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.26728 + 1.64728i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +2.80252 q^{10} +(0.921216 - 3.18612i) q^{11} +1.00000 q^{12} +(-0.706258 + 0.513127i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.866025 + 2.66535i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.92055 + 2.84845i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.10570 + 3.40299i) q^{19} +(2.26728 - 1.64728i) q^{20} +1.00000 q^{21} +(-1.12747 - 3.11910i) q^{22} -2.89765 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.881966 + 2.71441i) q^{25} +(-0.269767 + 0.830257i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(-0.687377 + 2.11553i) q^{29} +(0.866025 + 2.66535i) q^{30} +(-4.70378 + 3.41749i) q^{31} -1.00000 q^{32} +(3.31485 - 0.108436i) q^{33} +4.84607 q^{34} +(2.26728 - 1.64728i) q^{35} +(0.309017 + 0.951057i) q^{36} +(1.83414 - 5.64492i) q^{37} +(2.89476 + 2.10317i) q^{38} +(-0.706258 - 0.513127i) q^{39} +(0.866025 - 2.66535i) q^{40} +(-2.18850 - 6.73551i) q^{41} +(0.809017 - 0.587785i) q^{42} +3.74009 q^{43} +(-2.74551 - 1.86069i) q^{44} -2.80252 q^{45} +(-2.34425 + 1.70320i) q^{46} +(-3.53344 - 10.8748i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.30902 + 1.67760i) q^{50} +(-1.49752 + 4.60888i) q^{51} +(0.269767 + 0.830257i) q^{52} +(-10.1109 + 7.34598i) q^{53} -1.00000 q^{54} +(7.33708 - 5.70634i) q^{55} -1.00000 q^{56} +(-2.89476 + 2.10317i) q^{57} +(0.687377 + 2.11553i) q^{58} +(2.04467 - 6.29286i) q^{59} +(2.26728 + 1.64728i) q^{60} +(8.35994 + 6.07385i) q^{61} +(-1.79668 + 5.52962i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} -2.44655 q^{65} +(2.61803 - 2.03615i) q^{66} -7.98782 q^{67} +(3.92055 - 2.84845i) q^{68} +(-0.895424 - 2.75583i) q^{69} +(0.866025 - 2.66535i) q^{70} +(-8.26662 - 6.00605i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-4.85523 + 14.9428i) q^{73} +(-1.83414 - 5.64492i) q^{74} +(-2.30902 + 1.67760i) q^{75} +3.57812 q^{76} +(-2.74551 - 1.86069i) q^{77} -0.872983 q^{78} +(4.97106 - 3.61169i) q^{79} +(-0.866025 - 2.66535i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.72957 - 4.16277i) q^{82} +(-8.08032 - 5.87069i) q^{83} +(0.309017 - 0.951057i) q^{84} +(4.19682 + 12.9165i) q^{85} +(3.02579 - 2.19837i) q^{86} -2.22440 q^{87} +(-3.31485 + 0.108436i) q^{88} -12.6952 q^{89} +(-2.26728 + 1.64728i) q^{90} +(0.269767 + 0.830257i) q^{91} +(-0.895424 + 2.75583i) q^{92} +(-4.70378 - 3.41749i) q^{93} +(-9.25068 - 6.72101i) q^{94} +(-3.09874 + 9.53695i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(2.34827 - 1.70612i) q^{97} -1.00000 q^{98} +(1.12747 + 3.11910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 2 q^{18} - 4 q^{19} + 8 q^{21} + 2 q^{22} + 2 q^{24} + 16 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{31} - 8 q^{32} + 8 q^{33} + 20 q^{34} - 2 q^{36} - 24 q^{37} - 6 q^{38} + 6 q^{39} + 2 q^{42} + 8 q^{43} - 2 q^{44} - 10 q^{46} - 2 q^{47} - 2 q^{48} - 2 q^{49} + 14 q^{50} + 10 q^{51} + 6 q^{52} - 22 q^{53} - 8 q^{54} - 8 q^{56} + 6 q^{57} - 2 q^{58} + 10 q^{59} + 26 q^{61} - 6 q^{62} - 2 q^{63} - 2 q^{64} - 60 q^{65} + 12 q^{66} + 4 q^{67} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 2 q^{73} + 24 q^{74} - 14 q^{75} - 4 q^{76} - 2 q^{77} + 24 q^{78} - 12 q^{79} - 2 q^{81} - 10 q^{82} - 38 q^{83} - 2 q^{84} + 24 q^{85} + 22 q^{86} - 28 q^{87} - 8 q^{88} - 12 q^{89} + 6 q^{91} - 10 q^{92} - 4 q^{93} - 8 q^{94} - 36 q^{95} + 2 q^{96} + 6 q^{97} - 8 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 2 * q^18 - 4 * q^19 + 8 * q^21 + 2 * q^22 + 2 * q^24 + 16 * q^25 - 6 * q^26 - 2 * q^27 - 2 * q^28 + 2 * q^29 - 4 * q^31 - 8 * q^32 + 8 * q^33 + 20 * q^34 - 2 * q^36 - 24 * q^37 - 6 * q^38 + 6 * q^39 + 2 * q^42 + 8 * q^43 - 2 * q^44 - 10 * q^46 - 2 * q^47 - 2 * q^48 - 2 * q^49 + 14 * q^50 + 10 * q^51 + 6 * q^52 - 22 * q^53 - 8 * q^54 - 8 * q^56 + 6 * q^57 - 2 * q^58 + 10 * q^59 + 26 * q^61 - 6 * q^62 - 2 * q^63 - 2 * q^64 - 60 * q^65 + 12 * q^66 + 4 * q^67 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 2 * q^73 + 24 * q^74 - 14 * q^75 - 4 * q^76 - 2 * q^77 + 24 * q^78 - 12 * q^79 - 2 * q^81 - 10 * q^82 - 38 * q^83 - 2 * q^84 + 24 * q^85 + 22 * q^86 - 28 * q^87 - 8 * q^88 - 12 * q^89 + 6 * q^91 - 10 * q^92 - 4 * q^93 - 8 * q^94 - 36 * q^95 + 2 * q^96 + 6 * q^97 - 8 * q^98 - 2 * q^99

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