LMFDB - Embedded newform 429.2.n.b.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.3
Root			$-0.297979 - 0.216494i$ of defining polynomial
Character	$\chi$	$=$	429.157
Dual form			429.2.n.b.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.297979 + 0.216494i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.576112 + 1.77309i) q^{4} +(-0.859409 - 0.624397i) q^{5} +(0.297979 + 0.216494i) q^{6} +(1.08879 - 3.35095i) q^{7} +(-0.439831 - 1.35366i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.297979 + 0.216494i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.576112 + 1.77309i) q^{4} +(-0.859409 - 0.624397i) q^{5} +(0.297979 + 0.216494i) q^{6} +(1.08879 - 3.35095i) q^{7} +(-0.439831 - 1.35366i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.391264 q^{10} +(-0.965357 + 3.17302i) q^{11} +1.86434 q^{12} +(0.809017 - 0.587785i) q^{13} +(0.401025 + 1.23423i) q^{14} +(-0.328265 + 1.01030i) q^{15} +(-2.59244 - 1.88352i) q^{16} +(-3.20490 - 2.32850i) q^{17} +(0.113818 - 0.350295i) q^{18} +(-2.45762 - 7.56377i) q^{19} +(1.60223 - 1.16409i) q^{20} -3.52340 q^{21} +(-0.399286 - 1.15449i) q^{22} -1.09078 q^{23} +(-1.15149 + 0.836608i) q^{24} +(-1.19637 - 3.68206i) q^{25} +(-0.113818 + 0.350295i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.31427 + 3.86105i) q^{28} +(0.949350 - 2.92180i) q^{29} +(-0.120907 - 0.372115i) q^{30} +(5.78970 - 4.20646i) q^{31} +4.02691 q^{32} +(3.31604 - 0.0624091i) q^{33} +1.45910 q^{34} +(-3.02804 + 2.20000i) q^{35} +(-0.576112 - 1.77309i) q^{36} +(-0.875659 + 2.69500i) q^{37} +(2.36983 + 1.72178i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-0.467227 + 1.43798i) q^{40} +(-2.82868 - 8.70579i) q^{41} +(1.04990 - 0.762795i) q^{42} -3.48063 q^{43} +(-5.06991 - 3.53969i) q^{44} +1.06229 q^{45} +(0.325031 - 0.236149i) q^{46} +(1.79093 + 5.51192i) q^{47} +(-0.990225 + 3.04760i) q^{48} +(-4.38027 - 3.18245i) q^{49} +(1.15364 + 0.838168i) q^{50} +(-1.22416 + 3.76759i) q^{51} +(0.576112 + 1.77309i) q^{52} +(-6.40915 + 4.65652i) q^{53} -0.368322 q^{54} +(2.81086 - 2.12416i) q^{55} -5.01493 q^{56} +(-6.43413 + 4.67467i) q^{57} +(0.349667 + 1.07616i) q^{58} +(-2.15092 + 6.61986i) q^{59} +(-1.60223 - 1.16409i) q^{60} +(3.52614 + 2.56189i) q^{61} +(-0.814533 + 2.50687i) q^{62} +(1.08879 + 3.35095i) q^{63} +(3.98495 - 2.89524i) q^{64} -1.06229 q^{65} +(-0.974598 + 0.736500i) q^{66} +14.3737 q^{67} +(5.97503 - 4.34111i) q^{68} +(0.337071 + 1.03740i) q^{69} +(0.426004 - 1.31111i) q^{70} +(-10.0557 - 7.30586i) q^{71} +(1.15149 + 0.836608i) q^{72} +(-2.03720 + 6.26985i) q^{73} +(-0.322525 - 0.992629i) q^{74} +(-3.13214 + 2.27564i) q^{75} +14.8271 q^{76} +(9.58157 + 6.68962i) q^{77} +0.368322 q^{78} +(-6.94655 + 5.04697i) q^{79} +(1.05190 + 3.23743i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.72764 + 1.98175i) q^{82} +(9.82357 + 7.13724i) q^{83} +(2.02987 - 6.24730i) q^{84} +(1.30042 + 4.00227i) q^{85} +(1.03715 - 0.753536i) q^{86} -3.07216 q^{87} +(4.71979 - 0.0888283i) q^{88} -5.44615 q^{89} +(-0.316540 + 0.229979i) q^{90} +(-1.08879 - 3.35095i) q^{91} +(0.628414 - 1.93406i) q^{92} +(-5.78970 - 4.20646i) q^{93} +(-1.72696 - 1.25471i) q^{94} +(-2.61070 + 8.03490i) q^{95} +(-1.24438 - 3.82982i) q^{96} +(3.26300 - 2.37071i) q^{97} +1.99421 q^{98} +(-1.08407 - 3.13445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.297979	+	0.216494i	−0.210703	+	0.153085i	−0.688132	−	0.725586i	$-0.741569\pi$
$2$	−0.297979	+	0.216494i	−0.210703	+	0.153085i	0.477429	+	0.878670i	$0.341569\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.576112	+	1.77309i	−0.288056	+	0.886546i
$5$	−0.859409	−	0.624397i	−0.384339	−	0.279239i	0.378793	−	0.925482i	$-0.376339\pi$
$5$	−0.859409	−	0.624397i	−0.384339	−	0.279239i	−0.763132	+	0.646243i	$0.776339\pi$
$6$	0.297979	+	0.216494i	0.121649	+	0.0883835i
$7$	1.08879	−	3.35095i	0.411524	−	1.26654i	−0.503800	−	0.863820i	$-0.668065\pi$
$7$	1.08879	−	3.35095i	0.411524	−	1.26654i	0.915324	−	0.402719i	$-0.131935\pi$
$8$	−0.439831	−	1.35366i	−0.155504	−	0.478591i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.391264			0.123729
$11$	−0.965357	+	3.17302i	−0.291066	+	0.956703i
$11$	−0.965357	+	3.17302i	−0.291066	+	0.956703i
$12$	1.86434			0.538188
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	0.401025	+	1.23423i	0.107179	+	0.329862i
$15$	−0.328265	+	1.01030i	−0.0847577	+	0.260857i
$16$	−2.59244	−	1.88352i	−0.648111	−	0.470880i
$17$	−3.20490	−	2.32850i	−0.777304	−	0.564744i	0.126865	−	0.991920i	$-0.459509\pi$
$17$	−3.20490	−	2.32850i	−0.777304	−	0.564744i	−0.904169	+	0.427176i	$0.859509\pi$
$18$	0.113818	−	0.350295i	0.0268271	−	0.0825654i
$19$	−2.45762	−	7.56377i	−0.563816	−	1.73525i	−0.671443	−	0.741056i	$-0.734325\pi$
$19$	−2.45762	−	7.56377i	−0.563816	−	1.73525i	0.107627	−	0.994191i	$-0.465675\pi$
$20$	1.60223	−	1.16409i	0.358269	−	0.260298i
$21$	−3.52340			−0.768868
$22$	−0.399286	−	1.15449i	−0.0851280	−	0.246138i
$23$	−1.09078			−0.227444			−0.113722	−	0.993513i	$-0.536277\pi$
$23$	−1.09078			−0.227444			−0.113722	+	0.993513i	$0.536277\pi$
$24$	−1.15149	+	0.836608i	−0.235047	+	0.170772i
$25$	−1.19637	−	3.68206i	−0.239275	−	0.736411i
$26$	−0.113818	+	0.350295i	−0.0223215	+	0.0686986i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	5.31427	+	3.86105i	1.00430	+	0.729669i
$29$	0.949350	−	2.92180i	0.176290	−	0.542565i	−0.823400	−	0.567461i	$-0.807926\pi$
$29$	0.949350	−	2.92180i	0.176290	−	0.542565i	0.999690	+	0.0248967i	$0.00792568\pi$
$30$	−0.120907	−	0.372115i	−0.0220746	−	0.0679385i
$31$	5.78970	−	4.20646i	1.03986	−	0.755503i	0.0696021	−	0.997575i	$-0.477827\pi$
$31$	5.78970	−	4.20646i	1.03986	−	0.755503i	0.970258	+	0.242072i	$0.0778270\pi$
$32$	4.02691			0.711864
$33$	3.31604	−	0.0624091i	0.577248	−	0.0108640i
$34$	1.45910			0.250234
$35$	−3.02804	+	2.20000i	−0.511832	+	0.371868i
$36$	−0.576112	−	1.77309i	−0.0960187	−	0.295515i
$37$	−0.875659	+	2.69500i	−0.143957	+	0.443055i	−0.996875	−	0.0789895i	$-0.974831\pi$
$37$	−0.875659	+	2.69500i	−0.143957	+	0.443055i	0.852918	+	0.522045i	$0.174831\pi$
$38$	2.36983	+	1.72178i	0.384438	+	0.279310i
$39$	−0.809017	−	0.587785i	−0.129546	−	0.0941210i
$40$	−0.467227	+	1.43798i	−0.0738751	+	0.227364i
$41$	−2.82868	−	8.70579i	−0.441766	−	1.35962i	−0.885992	−	0.463701i	$-0.846521\pi$
$41$	−2.82868	−	8.70579i	−0.441766	−	1.35962i	0.444226	−	0.895915i	$-0.353479\pi$
$42$	1.04990	−	0.762795i	0.162003	−	0.117702i
$43$	−3.48063			−0.530790			−0.265395	−	0.964140i	$-0.585502\pi$
$43$	−3.48063			−0.530790			−0.265395	+	0.964140i	$0.585502\pi$
$44$	−5.06991	−	3.53969i	−0.764317	−	0.533628i
$45$	1.06229			0.158357
$46$	0.325031	−	0.236149i	0.0479232	−	0.0348182i
$47$	1.79093	+	5.51192i	0.261234	+	0.803997i	0.992537	+	0.121944i	$0.0389127\pi$
$47$	1.79093	+	5.51192i	0.261234	+	0.803997i	−0.731303	+	0.682053i	$0.761087\pi$
$48$	−0.990225	+	3.04760i	−0.142927	+	0.439883i
$49$	−4.38027	−	3.18245i	−0.625753	−	0.454636i
$50$	1.15364	+	0.838168i	0.163149	+	0.118535i
$51$	−1.22416	+	3.76759i	−0.171417	+	0.527568i
$52$	0.576112	+	1.77309i	0.0798924	+	0.245884i
$53$	−6.40915	+	4.65652i	−0.880365	+	0.639622i	−0.933348	−	0.358973i	$-0.883127\pi$
$53$	−6.40915	+	4.65652i	−0.880365	+	0.639622i	0.0529833	+	0.998595i	$0.483127\pi$
$54$	−0.368322			−0.0501223
$55$	2.81086	−	2.12416i	0.379017	−	0.286422i
$56$	−5.01493			−0.670148
$57$	−6.43413	+	4.67467i	−0.852221	+	0.619175i
$58$	0.349667	+	1.07616i	0.0459135	+	0.141307i
$59$	−2.15092	+	6.61986i	−0.280026	+	0.861832i	0.707819	+	0.706394i	$0.249679\pi$
$59$	−2.15092	+	6.61986i	−0.280026	+	0.861832i	−0.987846	+	0.155439i	$0.950321\pi$
$60$	−1.60223	−	1.16409i	−0.206847	−	0.150283i
$61$	3.52614	+	2.56189i	0.451476	+	0.328016i	0.790178	−	0.612877i	$-0.209988\pi$
$61$	3.52614	+	2.56189i	0.451476	+	0.328016i	−0.338703	+	0.940894i	$0.609988\pi$
$62$	−0.814533	+	2.50687i	−0.103446	+	0.318373i
$63$	1.08879	+	3.35095i	0.137175	+	0.422180i
$64$	3.98495	−	2.89524i	0.498119	−	0.361905i
$65$	−1.06229			−0.131761
$66$	−0.974598	+	0.736500i	−0.119965	+	0.0906569i
$67$	14.3737			1.75603			0.878014	−	0.478636i	$-0.158869\pi$
$67$	14.3737			1.75603			0.878014	+	0.478636i	$0.158869\pi$
$68$	5.97503	−	4.34111i	0.724579	−	0.526437i
$69$	0.337071	+	1.03740i	0.0405786	+	0.124888i
$70$	0.426004	−	1.31111i	0.0509173	−	0.156707i
$71$	−10.0557	−	7.30586i	−1.19339	−	0.867047i	−0.199769	−	0.979843i	$-0.564019\pi$
$71$	−10.0557	−	7.30586i	−1.19339	−	0.867047i	−0.993618	+	0.112796i	$0.964019\pi$
$72$	1.15149	+	0.836608i	0.135705	+	0.0985952i
$73$	−2.03720	+	6.26985i	−0.238436	+	0.733830i	0.758211	+	0.652009i	$0.226074\pi$
$73$	−2.03720	+	6.26985i	−0.238436	+	0.733830i	−0.996647	+	0.0818211i	$0.973926\pi$
$74$	−0.322525	−	0.992629i	−0.0374927	−	0.115391i
$75$	−3.13214	+	2.27564i	−0.361669	+	0.262768i
$76$	14.8271			1.70079
$77$	9.58157	+	6.68962i	1.09192	+	0.762353i
$78$	0.368322			0.0417043
$79$	−6.94655	+	5.04697i	−0.781548	+	0.567828i	−0.905443	−	0.424467i	$-0.860461\pi$
$79$	−6.94655	+	5.04697i	−0.781548	+	0.567828i	0.123895	+	0.992295i	$0.460461\pi$
$80$	1.05190	+	3.23743i	0.117606	+	0.361956i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.72764	+	1.98175i	0.301218	+	0.218847i
$83$	9.82357	+	7.13724i	1.07828	+	0.783414i	0.977382	−	0.211483i	$-0.0678294\pi$
$83$	9.82357	+	7.13724i	1.07828	+	0.783414i	0.100895	+	0.994897i	$0.467829\pi$
$84$	2.02987	−	6.24730i	0.221477	−	0.681637i
$85$	1.30042	+	4.00227i	0.141050	+	0.434107i
$86$	1.03715	−	0.753536i	0.111839	−	0.0812559i
$87$	−3.07216			−0.329370
$88$	4.71979	−	0.0888283i	0.503131	−	0.00946913i
$89$	−5.44615			−0.577290			−0.288645	−	0.957436i	$-0.593205\pi$
$89$	−5.44615			−0.577290			−0.288645	+	0.957436i	$0.593205\pi$
$90$	−0.316540	+	0.229979i	−0.0333662	+	0.0242420i
$91$	−1.08879	−	3.35095i	−0.114136	−	0.351275i
$92$	0.628414	−	1.93406i	0.0655167	−	0.201640i
$93$	−5.78970	−	4.20646i	−0.600364	−	0.436190i
$94$	−1.72696	−	1.25471i	−0.178122	−	0.129414i
$95$	−2.61070	+	8.03490i	−0.267852	+	0.824364i
$96$	−1.24438	−	3.82982i	−0.127004	−	0.390879i
$97$	3.26300	−	2.37071i	0.331307	−	0.240709i	−0.409678	−	0.912230i	$-0.634359\pi$
$97$	3.26300	−	2.37071i	0.331307	−	0.240709i	0.740985	+	0.671521i	$0.234359\pi$
$98$	1.99421			0.201446
$99$	−1.08407	−	3.13445i	−0.108953	−	0.315024i
$100$	7.21787			0.721787
$101$	8.79386	−	6.38911i	0.875022	−	0.635740i	−0.0569082	−	0.998379i	$-0.518124\pi$
$101$	8.79386	−	6.38911i	0.875022	−	0.635740i	0.931930	+	0.362639i	$0.118124\pi$
$102$	−0.450887	−	1.38769i	−0.0446445	−	0.137402i
$103$	−2.34023	+	7.20247i	−0.230589	+	0.709681i	0.767087	+	0.641543i	$0.221706\pi$
$103$	−2.34023	+	7.20247i	−0.230589	+	0.709681i	−0.997676	+	0.0681374i	$0.978294\pi$
$104$	−1.15149	−	0.836608i	−0.112913	−	0.0820361i
$105$	3.02804	+	2.20000i	0.295506	+	0.214698i
$106$	0.901682	−	2.77509i	0.0875791	−	0.269541i
$107$	2.08098	+	6.40460i	0.201176	+	0.619156i	0.999849	+	0.0173903i	$0.00553580\pi$
$107$	2.08098	+	6.40460i	0.201176	+	0.619156i	−0.798673	+	0.601765i	$0.794464\pi$
$108$	−1.50828	+	1.09583i	−0.145134	+	0.105446i
$109$	10.1222			0.969529			0.484764	−	0.874645i	$-0.338905\pi$
$109$	10.1222			0.969529			0.484764	+	0.874645i	$0.338905\pi$
$110$	−0.377710	+	1.24149i	−0.0360132	+	0.118372i
$111$	2.83369			0.268962
$112$	−9.13420	+	6.63639i	−0.863101	+	0.627080i
$113$	−4.63268	−	14.2579i	−0.435806	−	1.34127i	−0.892259	−	0.451525i	$-0.850880\pi$
$113$	−4.63268	−	14.2579i	−0.435806	−	1.34127i	0.456453	−	0.889748i	$-0.349120\pi$
$114$	0.905195	−	2.78590i	0.0847793	−	0.260924i
$115$	0.937430	+	0.681083i	0.0874158	+	0.0635113i
$116$	4.63369	+	3.36657i	0.430227	+	0.312578i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	−0.792233	−	2.43824i	−0.0729309	−	0.224458i
$119$	−11.2921	+	8.20423i	−1.03515	+	0.752080i
$120$	1.51198			0.138024
$121$	−9.13617	−	6.12621i	−0.830561	−	0.556928i
$122$	−1.60535			−0.145341
$123$	−7.40558	+	5.38047i	−0.667739	+	0.485141i
$124$	4.12292	+	12.6891i	0.370250	+	1.13951i
$125$	−2.91222	+	8.96289i	−0.260477	+	0.801665i
$126$	−1.04990	−	0.762795i	−0.0935323	−	0.0679552i
$127$	6.95365	+	5.05212i	0.617037	+	0.448304i	0.851885	−	0.523728i	$-0.175459\pi$
$127$	6.95365	+	5.05212i	0.617037	+	0.448304i	−0.234848	+	0.972032i	$0.575459\pi$
$128$	−3.04940	+	9.38508i	−0.269531	+	0.829531i
$129$	1.07557	+	3.31027i	0.0946989	+	0.291453i
$130$	0.316540	−	0.229979i	0.0277624	−	0.0201705i
$131$	11.6022			1.01369			0.506845	−	0.862037i	$-0.330812\pi$
$131$	11.6022			1.01369			0.506845	+	0.862037i	$0.330812\pi$
$132$	−1.79975	+	5.91559i	−0.156648	+	0.514886i
$133$	−28.0216			−2.42978
$134$	−4.28306	+	3.11183i	−0.370000	+	0.268821i
$135$	−0.328265	−	1.01030i	−0.0282526	−	0.0869524i
$136$	−1.74238	+	5.36250i	−0.149408	+	0.459830i
$137$	13.3906	+	9.72885i	1.14404	+	0.831192i	0.987677	−	0.156508i	$-0.0500238\pi$
$137$	13.3906	+	9.72885i	1.14404	+	0.831192i	0.156361	+	0.987700i	$0.450024\pi$
$138$	−0.325031	−	0.236149i	−0.0276685	−	0.0201023i
$139$	4.20412	−	12.9389i	0.356589	−	1.09747i	−0.598494	−	0.801127i	$-0.704234\pi$
$139$	4.20412	−	12.9389i	0.356589	−	1.09747i	0.955083	−	0.296340i	$-0.0957661\pi$
$140$	−2.15631	−	6.63643i	−0.182241	−	0.560881i
$141$	4.68872	−	3.40656i	0.394862	−	0.286884i
$142$	4.57805			0.384182
$143$	1.08407	+	3.13445i	0.0906542	+	0.262116i
$144$	3.20444			0.267036
$145$	−2.64024	+	1.91825i	−0.219260	+	0.159302i
$146$	−0.750345	−	2.30933i	−0.0620990	−	0.191121i
$147$	−1.67312	+	5.14932i	−0.137996	+	0.424709i
$148$	−4.27400	−	3.10525i	−0.351321	−	0.255250i
$149$	−8.64057	−	6.27774i	−0.707863	−	0.514293i	0.174620	−	0.984636i	$-0.444130\pi$
$149$	−8.64057	−	6.27774i	−0.707863	−	0.514293i	−0.882484	+	0.470343i	$0.844130\pi$
$150$	0.440651	−	1.35618i	0.0359790	−	0.110732i
$151$	−0.593972	−	1.82806i	−0.0483368	−	0.148765i	0.923975	−	0.382453i	$-0.124921\pi$
$151$	−0.593972	−	1.82806i	−0.0483368	−	0.148765i	−0.972312	+	0.233688i	$0.924921\pi$
$152$	−9.15783	+	6.65356i	−0.742798	+	0.539675i
$153$	3.96148			0.320267
$154$	−4.30337	+	0.0809911i	−0.346776	+	0.00652645i
$155$	−7.60222			−0.610625
$156$	1.50828	−	1.09583i	0.120759	−	0.0877367i
$157$	−6.26963	−	19.2959i	−0.500371	−	1.53998i	−0.808417	−	0.588611i	$-0.799675\pi$
$157$	−6.26963	−	19.2959i	−0.500371	−	1.53998i	0.308046	−	0.951371i	$-0.400325\pi$
$158$	0.977287	−	3.00778i	0.0777488	−	0.239286i
$159$	6.40915	+	4.65652i	0.508279	+	0.369286i
$160$	−3.46076	−	2.51439i	−0.273597	−	0.198780i
$161$	−1.18763	+	3.65516i	−0.0935986	+	0.288067i
$162$	0.113818	+	0.350295i	0.00894237	+	0.0275218i
$163$	−10.0597	+	7.30881i	−0.787938	+	0.572470i	−0.907351	−	0.420374i	$-0.861899\pi$
$163$	−10.0597	+	7.30881i	−0.787938	+	0.572470i	0.119413	+	0.992845i	$0.461899\pi$
$164$	17.0658			1.33261
$165$	−2.88880	−	2.01689i	−0.224893	−	0.157015i
$166$	−4.47239			−0.347125
$167$	15.1260	−	10.9897i	1.17049	−	0.850408i	0.179419	−	0.983773i	$-0.442578\pi$
$167$	15.1260	−	10.9897i	1.17049	−	0.850408i	0.991067	+	0.133365i	$0.0425783\pi$
$168$	1.54970	+	4.76948i	0.119562	+	0.367973i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−1.25397	−	0.911059i	−0.0961747	−	0.0698750i
$171$	6.43413	+	4.67467i	0.492030	+	0.357481i
$172$	2.00523	−	6.17147i	0.152897	−	0.470570i
$173$	−4.86820	−	14.9828i	−0.370122	−	1.13912i	−0.946711	−	0.322084i	$-0.895617\pi$
$173$	−4.86820	−	14.9828i	−0.370122	−	1.13912i	0.576589	−	0.817034i	$-0.304383\pi$
$174$	0.915440	−	0.665106i	0.0693993	−	0.0504215i
$175$	−13.6410			−1.03116
$176$	8.47909	−	6.40762i	0.639135	−	0.482992i
$177$	6.96053			0.523186
$178$	1.62284	−	1.17906i	0.121637	−	0.0883743i
$179$	−4.33816	−	13.3515i	−0.324249	−	0.997937i	−0.971778	−	0.235896i	$-0.924197\pi$
$179$	−4.33816	−	13.3515i	−0.324249	−	0.997937i	0.647529	−	0.762041i	$-0.275803\pi$
$180$	−0.611997	+	1.88353i	−0.0456156	+	0.140390i
$181$	5.41057	+	3.93101i	0.402165	+	0.292190i	0.770422	−	0.637534i	$-0.220045\pi$
$181$	5.41057	+	3.93101i	0.402165	+	0.292190i	−0.368257	+	0.929724i	$0.620045\pi$
$182$	1.04990	+	0.762795i	0.0778236	+	0.0565422i
$183$	1.34686	−	4.14522i	0.0995631	−	0.306424i
$184$	0.479760	+	1.47655i	0.0353684	+	0.108853i
$185$	2.43530	−	1.76935i	0.179047	−	0.130085i
$186$	2.63588			0.193272
$187$	10.4823	−	7.92141i	0.766539	−	0.579271i
$188$	−10.8049			−0.788030
$189$	2.85049	−	2.07100i	0.207342	−	0.150643i
$190$	−0.961578	−	2.95943i	−0.0697602	−	0.214700i
$191$	−1.41536	+	4.35602i	−0.102412	+	0.315191i	−0.989114	−	0.147150i	$-0.952990\pi$
$191$	−1.41536	+	4.35602i	−0.102412	+	0.315191i	0.886703	+	0.462340i	$0.152990\pi$
$192$	−3.98495	−	2.89524i	−0.287589	−	0.208946i
$193$	−0.0939859	−	0.0682848i	−0.00676525	−	0.00491524i	0.584397	−	0.811468i	$-0.301331\pi$
$193$	−0.0939859	−	0.0682848i	−0.00676525	−	0.00491524i	−0.591163	+	0.806552i	$0.701331\pi$
$194$	−0.459060	+	1.41284i	−0.0329586	+	0.101436i
$195$	0.328265	+	1.01030i	0.0235076	+	0.0723488i
$196$	8.16631	−	5.93317i	0.583308	−	0.423798i
$197$	12.6011			0.897791			0.448895	−	0.893584i	$-0.351818\pi$
$197$	12.6011			0.897791			0.448895	+	0.893584i	$0.351818\pi$
$198$	1.00162	+	0.699307i	0.0711821	+	0.0496976i
$199$	−20.1515			−1.42850			−0.714251	−	0.699890i	$-0.753232\pi$
$199$	−20.1515			−1.42850			−0.714251	+	0.699890i	$0.753232\pi$
$200$	−4.45805	+	3.23896i	−0.315232	+	0.229029i
$201$	−4.44172	−	13.6702i	−0.313295	−	0.964222i
$202$	−1.23718	+	3.80764i	−0.0870475	+	0.267905i
$203$	−8.75716	−	6.36245i	−0.614632	−	0.446556i
$204$	−5.97503	−	4.34111i	−0.418336	−	0.303939i
$205$	−3.00487	+	9.24805i	−0.209870	+	0.645912i
$206$	−0.861957	−	2.65283i	−0.0600554	−	0.184832i
$207$	0.882463	−	0.641147i	0.0613354	−	0.0445628i
$208$	−3.20444			−0.222188
$209$	26.3725	−	0.496341i	1.82422	−	0.0343326i
$210$	−1.37858			−0.0951310
$211$	−10.9066	+	7.92413i	−0.750843	+	0.545520i	−0.896088	−	0.443876i	$-0.853603\pi$
$211$	−10.9066	+	7.92413i	−0.750843	+	0.545520i	0.145245	+	0.989396i	$0.453603\pi$
$212$	−4.56405	−	14.0467i	−0.313460	−	0.964731i
$213$	−3.84092	+	11.8211i	−0.263176	+	0.809971i
$214$	−2.00665	−	1.45791i	−0.137172	−	0.0996610i
$215$	2.99128	+	2.17329i	0.204004	+	0.148217i
$216$	0.439831	−	1.35366i	0.0299267	−	0.0921049i
$217$	−7.79187	−	23.9809i	−0.528947	−	1.62793i
$218$	−3.01620	+	2.19140i	−0.204283	+	0.148420i
$219$	6.59251			0.445480
$220$	2.14696	+	6.20768i	0.144748	+	0.418521i
$221$	−3.96148			−0.266478
$222$	−0.844380	+	0.613478i	−0.0566711	+	0.0411740i
$223$	0.911631	+	2.80571i	0.0610473	+	0.187884i	0.976929	−	0.213564i	$-0.0685071\pi$
$223$	0.911631	+	2.80571i	0.0610473	+	0.187884i	−0.915882	+	0.401448i	$0.868507\pi$
$224$	4.38445	−	13.4940i	0.292949	−	0.901603i
$225$	3.13214	+	2.27564i	0.208810	+	0.151709i
$226$	4.46720	+	3.24561i	0.297154	+	0.215895i
$227$	−4.61639	+	14.2078i	−0.306401	+	0.943005i	0.672750	+	0.739870i	$0.265113\pi$
$227$	−4.61639	+	14.2078i	−0.306401	+	0.943005i	−0.979151	+	0.203135i	$0.934887\pi$
$228$	−4.58183	−	14.1014i	−0.303439	−	0.933890i
$229$	8.09472	−	5.88116i	0.534914	−	0.388638i	−0.287279	−	0.957847i	$-0.592751\pi$
$229$	8.09472	−	5.88116i	0.534914	−	0.388638i	0.822193	+	0.569209i	$0.192751\pi$
$230$	−0.426785			−0.0281414
$231$	3.40134	−	11.1798i	0.223791	−	0.735578i
$232$	−4.37268			−0.287080
$233$	16.6661	−	12.1087i	1.09184	−	0.793265i	0.112127	−	0.993694i	$-0.464234\pi$
$233$	16.6661	−	12.1087i	1.09184	−	0.793265i	0.979708	+	0.200429i	$0.0642336\pi$
$234$	−0.113818	−	0.350295i	−0.00744051	−	0.0228995i
$235$	1.90249	−	5.85525i	0.124105	−	0.381954i
$236$	−10.4984	−	7.62757i	−0.683391	−	0.496512i
$237$	6.94655	+	5.04697i	0.451227	+	0.327836i
$238$	1.58865	−	4.88937i	0.102977	−	0.316931i
$239$	7.90765	+	24.3372i	0.511503	+	1.57425i	0.789555	+	0.613680i	$0.210311\pi$
$239$	7.90765	+	24.3372i	0.511503	+	1.57425i	−0.278052	+	0.960566i	$0.589689\pi$
$240$	2.75392	−	2.00084i	0.177765	−	0.129154i
$241$	4.71356			0.303627			0.151814	−	0.988409i	$-0.451489\pi$
$241$	4.71356			0.303627			0.151814	+	0.988409i	$0.451489\pi$
$242$	4.04868	−	0.152449i	0.260259	−	0.00979982i
$243$	−1.00000			−0.0641500
$244$	−6.57391	+	4.77623i	−0.420852	+	0.305767i
$245$	1.77733	+	5.47006i	0.113549	+	0.349469i
$246$	1.04187	−	3.20654i	0.0664270	−	0.204441i
$247$	−6.43413	−	4.67467i	−0.409394	−	0.297442i
$248$	−8.24060	−	5.98715i	−0.523279	−	0.380184i
$249$	3.75227	−	11.5483i	0.237790	−	0.731844i
$250$	−1.07263	−	3.30123i	−0.0678394	−	0.208788i
$251$	17.4324	−	12.6654i	1.10033	−	0.799434i	0.119213	−	0.992869i	$-0.461963\pi$
$251$	17.4324	−	12.6654i	1.10033	−	0.799434i	0.981113	+	0.193435i	$0.0619629\pi$
$252$	−6.56880			−0.413796
$253$	1.05300	−	3.46108i	0.0662013	−	0.217597i
$254$	−3.16580			−0.198640
$255$	3.40453	−	2.47354i	0.213200	−	0.154899i
$256$	1.92107	+	5.91245i	0.120067	+	0.369528i
$257$	2.12602	−	6.54323i	0.132618	−	0.408155i	−0.862594	−	0.505897i	$-0.831162\pi$
$257$	2.12602	−	6.54323i	0.132618	−	0.408155i	0.995212	+	0.0977412i	$0.0311618\pi$
$258$	−1.03715	−	0.753536i	−0.0645704	−	0.0469131i
$259$	8.07740	+	5.86857i	0.501905	+	0.364655i
$260$	0.611997	−	1.88353i	0.0379545	−	0.116812i
$261$	0.949350	+	2.92180i	0.0587633	+	0.180855i
$262$	−3.45721	+	2.51181i	−0.213587	+	0.155180i
$263$	−23.0579			−1.42181			−0.710904	−	0.703289i	$-0.751714\pi$
$263$	−23.0579			−1.42181			−0.710904	+	0.703289i	$0.751714\pi$
$264$	−1.54298	−	4.46134i	−0.0949636	−	0.274576i
$265$	8.41560			0.516966
$266$	8.34985	−	6.06652i	0.511962	−	0.371962i
$267$	1.68295	+	5.17959i	0.102995	+	0.316986i
$268$	−8.28087	+	25.4859i	−0.505834	+	1.55680i
$269$	−4.67793	−	3.39872i	−0.285218	−	0.207223i	0.435972	−	0.899960i	$-0.356405\pi$
$269$	−4.67793	−	3.39872i	−0.285218	−	0.207223i	−0.721190	+	0.692737i	$0.756405\pi$
$270$	0.316540	+	0.229979i	0.0192640	+	0.0139961i
$271$	−6.20898	+	19.1093i	−0.377169	+	1.16081i	0.564835	+	0.825204i	$0.308940\pi$
$271$	−6.20898	+	19.1093i	−0.377169	+	1.16081i	−0.942004	+	0.335602i	$0.891060\pi$
$272$	3.92276	+	12.0730i	0.237852	+	0.732034i
$273$	−2.85049	+	2.07100i	−0.172519	+	0.125343i
$274$	−6.09636			−0.368295
$275$	12.8382	−	0.241620i	0.774172	−	0.0145702i
$276$	−2.03359			−0.122408
$277$	7.88617	−	5.72964i	0.473834	−	0.344261i	−0.325099	−	0.945680i	$-0.605398\pi$
$277$	7.88617	−	5.72964i	0.473834	−	0.344261i	0.798934	+	0.601419i	$0.205398\pi$
$278$	1.54847	+	4.76570i	0.0928711	+	0.285828i
$279$	−2.21147	+	6.80620i	−0.132397	+	0.407476i
$280$	4.30987	+	3.13131i	0.257564	+	0.187131i
$281$	−22.6171	−	16.4323i	−1.34922	−	0.980269i	−0.999050	−	0.0435849i	$-0.986122\pi$
$281$	−22.6171	−	16.4323i	−1.34922	−	0.980269i	−0.350175	−	0.936684i	$-0.613878\pi$
$282$	−0.659640	+	2.03016i	−0.0392810	+	0.120895i
$283$	4.53885	+	13.9691i	0.269807	+	0.830380i	0.990547	+	0.137174i	$0.0438021\pi$
$283$	4.53885	+	13.9691i	0.269807	+	0.830380i	−0.720740	+	0.693205i	$0.756198\pi$
$284$	18.7472	−	13.6206i	1.11244	−	0.808234i
$285$	8.44840			0.500440
$286$	−1.00162	−	0.699307i	−0.0592271	−	0.0413509i
$287$	−32.2525			−1.90380
$288$	−3.25784	+	2.36696i	−0.191970	+	0.139474i
$289$	−0.403784	−	1.24272i	−0.0237520	−	0.0731012i
$290$	0.371447	−	1.14320i	0.0218121	−	0.0671308i
$291$	−3.26300	−	2.37071i	−0.191280	−	0.138973i
$292$	−9.94336	−	7.22427i	−0.581891	−	0.422769i
$293$	6.68256	−	20.5668i	0.390400	−	1.20153i	−0.542087	−	0.840322i	$-0.682366\pi$
$293$	6.68256	−	20.5668i	0.390400	−	1.20153i	0.932487	−	0.361204i	$-0.117634\pi$
$294$	−0.616246	−	1.89661i	−0.0359402	−	0.110612i
$295$	5.98195	−	4.34614i	0.348282	−	0.253042i
$296$	4.03325			0.234428
$297$	−2.64605	+	1.99961i	−0.153539	+	0.116029i
$298$	3.93381			0.227879
$299$	−0.882463	+	0.641147i	−0.0510341	+	0.0370785i
$300$	−2.23044	−	6.86460i	−0.128775	−	0.396328i
$301$	−3.78967	+	11.6634i	−0.218433	+	0.672267i
$302$	0.572756	+	0.416131i	0.0329584	+	0.0239457i
$303$	−8.79386	−	6.38911i	−0.505194	−	0.367045i
$304$	−7.87528	+	24.2376i	−0.451678	+	1.39012i
$305$	−1.43076	−	4.40342i	−0.0819250	−	0.252139i
$306$	−1.18044	+	0.857638i	−0.0674811	+	0.0490279i
$307$	4.28458			0.244534			0.122267	−	0.992497i	$-0.460984\pi$
$307$	4.28458			0.244534			0.122267	+	0.992497i	$0.460984\pi$
$308$	−17.3814	+	13.1350i	−0.990395	+	0.748438i
$309$	7.57313			0.430820
$310$	2.26530	−	1.64584i	0.128661	−	0.0934774i
$311$	−1.66314	−	5.11861i	−0.0943079	−	0.290250i	0.892765	−	0.450523i	$-0.148762\pi$
$311$	−1.66314	−	5.11861i	−0.0943079	−	0.290250i	−0.987073	+	0.160273i	$0.948762\pi$
$312$	−0.439831	+	1.35366i	−0.0249005	+	0.0766359i
$313$	10.0323	+	7.28887i	0.567058	+	0.411992i	0.834035	−	0.551711i	$-0.186025\pi$
$313$	10.0323	+	7.28887i	0.567058	+	0.411992i	−0.266978	+	0.963703i	$0.586025\pi$
$314$	6.04568	+	4.39244i	0.341177	+	0.247880i
$315$	1.15661	−	3.55967i	0.0651675	−	0.200565i
$316$	−4.94674	−	15.2245i	−0.278276	−	0.856445i
$317$	4.54172	−	3.29975i	0.255089	−	0.185333i	−0.452890	−	0.891566i	$-0.649607\pi$
$317$	4.54172	−	3.29975i	0.255089	−	0.185333i	0.707979	+	0.706233i	$0.249607\pi$
$318$	−2.91790			−0.163628
$319$	8.35448	+	5.83289i	0.467761	+	0.326579i
$320$	−5.23248			−0.292505
$321$	5.44808	−	3.95826i	0.304082	−	0.220928i
$322$	−0.437432	−	1.34628i	−0.0243771	−	0.0750251i
$323$	−9.73580	+	29.9637i	−0.541715	+	1.66723i
$324$	1.50828	+	1.09583i	0.0837934	+	0.0608795i
$325$	−3.13214	−	2.27564i	−0.173740	−	0.126230i
$326$	1.41527	−	4.35574i	0.0783844	−	0.241242i
$327$	−3.12793	−	9.62676i	−0.172975	−	0.532361i
$328$	−10.5405	+	7.65814i	−0.582004	+	0.422850i
$329$	20.4201			1.12580
$330$	1.29745	−	0.0244185i	0.0714221	−	0.00134419i
$331$	−6.69231			−0.367843			−0.183921	−	0.982941i	$-0.558879\pi$
$331$	−6.69231			−0.367843			−0.183921	+	0.982941i	$0.558879\pi$
$332$	−18.3145	+	13.3062i	−1.00514	+	0.730274i
$333$	−0.875659	−	2.69500i	−0.0479858	−	0.147685i
$334$	−2.12803	+	6.54939i	−0.116440	+	0.358367i
$335$	−12.3529	−	8.97490i	−0.674911	−	0.490351i
$336$	9.13420	+	6.63639i	0.498312	+	0.362045i
$337$	4.99932	−	15.3863i	0.272330	−	0.838147i	−0.717583	−	0.696473i	$-0.754752\pi$
$337$	4.99932	−	15.3863i	0.272330	−	0.838147i	0.989913	−	0.141674i	$-0.0452485\pi$
$338$	0.113818	+	0.350295i	0.00619087	+	0.0190536i
$339$	−12.1285	+	8.81188i	−0.658730	+	0.478596i
$340$	−7.84557			−0.425486
$341$	7.75808	+	22.4316i	0.420124	+	1.21474i
$342$	−2.92927			−0.158397
$343$	4.51998	−	3.28395i	0.244056	−	0.177317i
$344$	1.53089	+	4.71158i	0.0825399	+	0.254032i
$345$	0.358066	−	1.10201i	0.0192776	−	0.0593305i
$346$	4.69431	+	3.41061i	0.252367	+	0.183356i
$347$	−4.89187	−	3.55415i	−0.262609	−	0.190797i	0.448687	−	0.893689i	$-0.351892\pi$
$347$	−4.89187	−	3.55415i	−0.262609	−	0.190797i	−0.711297	+	0.702892i	$0.751892\pi$
$348$	1.76991	−	5.44722i	0.0948771	−	0.292002i
$349$	−1.07410	−	3.30575i	−0.0574955	−	0.176953i	0.918184	−	0.396153i	$-0.129655\pi$
$349$	−1.07410	−	3.30575i	−0.0574955	−	0.176953i	−0.975680	+	0.219200i	$0.929655\pi$
$350$	4.06473	−	2.95320i	0.217269	−	0.157855i
$351$	1.00000			0.0533761
$352$	−3.88741	+	12.7775i	−0.207199	+	0.681042i
$353$	−25.1212			−1.33706			−0.668532	−	0.743683i	$-0.733077\pi$
$353$	−25.1212			−1.33706			−0.668532	+	0.743683i	$0.733077\pi$
$354$	−2.07409	+	1.50692i	−0.110237	+	0.0800917i
$355$	4.08016	+	12.5575i	0.216553	+	0.666480i
$356$	3.13759	−	9.65652i	0.166292	−	0.511794i
$357$	11.2921	+	8.20423i	0.597644	+	0.434214i
$358$	4.18320	+	3.03928i	0.221089	+	0.160631i
$359$	8.46009	−	26.0375i	0.446507	−	1.37421i	−0.434316	−	0.900760i	$-0.643010\pi$
$359$	8.46009	−	26.0375i	0.446507	−	1.37421i	0.880823	−	0.473446i	$-0.156990\pi$
$360$	−0.467227	−	1.43798i	−0.0246250	−	0.0757880i
$361$	−35.7994	+	26.0098i	−1.88418	+	1.36894i
$362$	−2.46328			−0.129467
$363$	−3.00314	+	10.5821i	−0.157624	+	0.555417i
$364$	6.56880			0.344299
$365$	5.66566	−	4.11634i	0.296554	−	0.215459i
$366$	0.496080	+	1.52678i	0.0259305	+	0.0798060i
$367$	−1.66657	+	5.12917i	−0.0869941	+	0.267740i	−0.985085	−	0.172070i	$-0.944954\pi$
$367$	−1.66657	+	5.12917i	−0.0869941	+	0.267740i	0.898091	+	0.439811i	$0.144954\pi$
$368$	2.82780	+	2.05451i	0.147409	+	0.107099i
$369$	7.40558	+	5.38047i	0.385519	+	0.280096i
$370$	−0.342614	+	1.05446i	−0.0178117	+	0.0548186i
$371$	8.62555	+	26.5467i	0.447816	+	1.37824i
$372$	10.7940	−	7.84227i	0.559641	−	0.406603i
$373$	−7.81933			−0.404869			−0.202435	−	0.979296i	$-0.564885\pi$
$373$	−7.81933			−0.404869			−0.202435	+	0.979296i	$0.564885\pi$
$374$	−1.40855	+	4.62977i	−0.0728346	+	0.239399i
$375$	9.42414			0.486660
$376$	6.67356	−	4.84863i	0.344163	−	0.250049i
$377$	−0.949350	−	2.92180i	−0.0488940	−	0.150480i
$378$	−0.401025	+	1.23423i	−0.0206265	+	0.0634819i
$379$	1.72428	+	1.25276i	0.0885703	+	0.0643501i	0.631189	−	0.775629i	$-0.282567\pi$
$379$	1.72428	+	1.25276i	0.0885703	+	0.0643501i	−0.542619	+	0.839979i	$0.682567\pi$
$380$	−12.7426	−	9.25801i	−0.653680	−	0.474926i
$381$	2.65606	−	8.17451i	0.136074	−	0.418793i
$382$	−0.521308	−	1.60442i	−0.0266724	−	0.0820893i
$383$	5.48781	−	3.98712i	0.280414	−	0.203733i	−0.438684	−	0.898641i	$-0.644555\pi$
$383$	5.48781	−	3.98712i	0.280414	−	0.203733i	0.719098	+	0.694909i	$0.244555\pi$
$384$	9.86805			0.503577
$385$	−4.05751	−	11.7318i	−0.206790	−	0.597909i
$386$	0.0427891			0.00217791
$387$	2.81589	−	2.04586i	0.143140	−	0.103997i
$388$	2.32363	+	7.15139i	0.117964	+	0.363057i
$389$	−10.0744	+	31.0058i	−0.510793	+	1.57206i	0.280016	+	0.959995i	$0.409660\pi$
$389$	−10.0744	+	31.0058i	−0.510793	+	1.57206i	−0.790809	+	0.612063i	$0.790340\pi$
$390$	−0.316540	−	0.229979i	−0.0160286	−	0.0116455i
$391$	3.49586	+	2.53989i	0.176793	+	0.128448i
$392$	−2.38138	+	7.32914i	−0.120278	+	0.370177i
$393$	−3.58528	−	11.0344i	−0.180853	−	0.556610i
$394$	−3.75486	+	2.72807i	−0.189167	+	0.137438i
$395$	9.12124			0.458940
$396$	6.18222	−	0.116352i	0.310668	−	0.00584690i
$397$	34.0969			1.71128			0.855638	−	0.517575i	$-0.173165\pi$
$397$	34.0969			1.71128			0.855638	+	0.517575i	$0.173165\pi$
$398$	6.00472	−	4.36269i	0.300989	−	0.218682i
$399$	8.65916	+	26.6501i	0.433500	+	1.33418i
$400$	−3.83370	+	11.7989i	−0.191685	+	0.589946i
$401$	24.7314	+	17.9684i	1.23503	+	0.897298i	0.997257	−	0.0740234i	$-0.0235840\pi$
$401$	24.7314	+	17.9684i	1.23503	+	0.897298i	0.237769	+	0.971322i	$0.423584\pi$
$402$	4.28306	+	3.11183i	0.213620	+	0.155204i
$403$	2.21147	−	6.80620i	0.110161	−	0.339041i
$404$	6.26223	+	19.2732i	0.311558	+	0.958875i
$405$	−0.859409	+	0.624397i	−0.0427044	+	0.0310266i
$406$	3.98688			0.197866
$407$	−7.70598	−	5.38012i	−0.381971	−	0.266683i
$408$	5.63846			0.279145
$409$	−3.39702	+	2.46808i	−0.167972	+	0.122039i	−0.668595	−	0.743626i	$-0.733104\pi$
$409$	−3.39702	+	2.46808i	−0.167972	+	0.122039i	0.500623	+	0.865665i	$0.333104\pi$
$410$	−1.10676	−	3.40626i	−0.0546591	−	0.168223i
$411$	5.11476	−	15.7416i	0.252292	−	0.776476i
$412$	−11.4224	−	8.29887i	−0.562742	−	0.408856i
$413$	19.8409	+	14.4153i	0.976307	+	0.709329i
$414$	−0.124151	+	0.382097i	−0.00610167	+	0.0187790i
$415$	−3.98599	−	12.2676i	−0.195665	−	0.602194i
$416$	3.25784	−	2.36696i	0.159729	−	0.116050i
$417$	−13.6048			−0.666231
$418$	−7.75100	+	5.85740i	−0.379114	+	0.286495i
$419$	−6.59017			−0.321951			−0.160975	−	0.986958i	$-0.551464\pi$
$419$	−6.59017			−0.321951			−0.160975	+	0.986958i	$0.551464\pi$
$420$	−5.64529	+	4.10154i	−0.275462	+	0.200135i
$421$	−9.39446	−	28.9132i	−0.457858	−	1.40914i	−0.867747	−	0.497007i	$-0.834432\pi$
$421$	−9.39446	−	28.9132i	−0.457858	−	1.40914i	0.409889	−	0.912136i	$-0.365568\pi$
$422$	1.53442	−	4.72245i	0.0746942	−	0.229885i
$423$	−4.68872	−	3.40656i	−0.227973	−	0.165632i
$424$	9.12229	+	6.62773i	0.443017	+	0.321871i
$425$	−4.73941	+	14.5864i	−0.229895	+	0.707544i
$426$	−1.41470	−	4.35399i	−0.0685423	−	0.210951i
$427$	12.4240	−	9.02655i	0.601238	−	0.436825i
$428$	−12.5548			−0.606860
$429$	2.64605	−	1.99961i	0.127752	−	0.0965420i
$430$	−1.36185			−0.0656740
$431$	29.1798	−	21.2004i	1.40554	−	1.02119i	0.411591	−	0.911369i	$-0.364973\pi$
$431$	29.1798	−	21.2004i	1.40554	−	1.02119i	0.993952	−	0.109818i	$-0.0350268\pi$
$432$	−0.990225	−	3.04760i	−0.0476422	−	0.146628i
$433$	5.21993	−	16.0653i	0.250854	−	0.772049i	−0.743765	−	0.668442i	$-0.766962\pi$
$433$	5.21993	−	16.0653i	0.250854	−	0.772049i	0.994618	−	0.103607i	$-0.0330384\pi$
$434$	7.51355	+	5.45891i	0.360662	+	0.262036i
$435$	2.64024	+	1.91825i	0.126590	+	0.0919730i
$436$	−5.83151	+	17.9475i	−0.279279	+	0.859532i
$437$	2.68073	+	8.25044i	0.128237	+	0.394672i
$438$	−1.96443	+	1.42724i	−0.0938641	+	0.0681962i
$439$	−28.5683			−1.36349			−0.681746	−	0.731589i	$-0.738779\pi$
$439$	−28.5683			−1.36349			−0.681746	+	0.731589i	$0.738779\pi$
$440$	−4.11169	−	2.87068i	−0.196017	−	0.136854i
$441$	5.41431			0.257824
$442$	1.18044	−	0.857638i	0.0561477	−	0.0407937i
$443$	6.47295	+	19.9217i	0.307539	+	0.946509i	0.978717	+	0.205213i	$0.0657886\pi$
$443$	6.47295	+	19.9217i	0.307539	+	0.946509i	−0.671178	+	0.741296i	$0.734211\pi$
$444$	−1.63252	+	5.02439i	−0.0774762	+	0.238447i
$445$	4.68047	+	3.40056i	0.221876	+	0.161202i
$446$	−0.879068	−	0.638680i	−0.0416251	−	0.0302424i
$447$	−3.30041	+	10.1576i	−0.156104	+	0.480438i
$448$	−5.36302	−	16.5057i	−0.253379	−	0.779820i
$449$	31.5960	−	22.9559i	1.49111	−	1.08335i	0.517350	−	0.855774i	$-0.326919\pi$
$449$	31.5960	−	22.9559i	1.49111	−	1.08335i	0.973759	−	0.227580i	$-0.0730814\pi$
$450$	−1.42598			−0.0672212
$451$	30.3544	−	0.571281i	1.42933	−	0.0269006i
$452$	27.9495			1.31464
$453$	−1.55504	+	1.12980i	−0.0730621	+	0.0530827i
$454$	−1.70032	−	5.23305i	−0.0798000	−	0.245599i
$455$	−1.15661	+	3.55967i	−0.0542226	+	0.166880i
$456$	9.15783	+	6.65356i	0.428855	+	0.311581i
$457$	22.7598	+	16.5359i	1.06466	+	0.773519i	0.974944	−	0.222449i	$-0.0714051\pi$
$457$	22.7598	+	16.5359i	1.06466	+	0.773519i	0.0897126	+	0.995968i	$0.471405\pi$
$458$	−1.13882	+	3.50492i	−0.0532135	+	0.163774i
$459$	−1.22416	−	3.76759i	−0.0571391	−	0.175856i
$460$	−1.74769	+	1.26977i	−0.0814863	+	0.0592033i
$461$	−8.49269			−0.395544			−0.197772	−	0.980248i	$-0.563371\pi$
$461$	−8.49269			−0.395544			−0.197772	+	0.980248i	$0.563371\pi$
$462$	1.40684	+	4.06772i	0.0654522	+	0.189248i
$463$	5.51870			0.256476			0.128238	−	0.991743i	$-0.459068\pi$
$463$	5.51870			0.256476			0.128238	+	0.991743i	$0.459068\pi$
$464$	−7.96440	+	5.78648i	−0.369738	+	0.268631i
$465$	2.34922	+	7.23014i	0.108942	+	0.335290i
$466$	−2.34470	+	7.21625i	−0.108616	+	0.334287i
$467$	25.7350	+	18.6975i	1.19087	+	0.865219i	0.993356	−	0.115080i	$-0.0367126\pi$
$467$	25.7350	+	18.6975i	1.19087	+	0.865219i	0.197516	+	0.980300i	$0.436713\pi$
$468$	−1.50828	−	1.09583i	−0.0697203	−	0.0506548i
$469$	15.6499	−	48.1655i	0.722647	−	2.22408i
$470$	0.700728	+	2.15662i	0.0323222	+	0.0994774i
$471$	−16.4141	+	11.9255i	−0.756321	+	0.549500i
$472$	9.90708			0.456010
$473$	3.36005	−	11.0441i	0.154495	−	0.507809i
$474$	−3.16257			−0.145261
$475$	−24.9100	+	18.0982i	−1.14295	+	0.830401i
$476$	−8.04130	−	24.7486i	−0.368572	−	1.13435i
$477$	2.44808	−	7.53441i	0.112090	−	0.344977i
$478$	−7.62519	−	5.54003i	−0.348768	−	0.253395i
$479$	7.41754	+	5.38916i	0.338916	+	0.246237i	0.744204	−	0.667952i	$-0.232829\pi$
$479$	7.41754	+	5.38916i	0.338916	+	0.246237i	−0.405288	+	0.914189i	$0.632829\pi$
$480$	−1.32189	+	4.06837i	−0.0603359	+	0.185695i
$481$	0.875659	+	2.69500i	0.0399266	+	0.122881i
$482$	−1.40454	+	1.02046i	−0.0639752	+	0.0464807i
$483$	3.84326			0.174875
$484$	16.1258	−	12.6699i	0.732990	−	0.575904i
$485$	−4.28451			−0.194550
$486$	0.297979	−	0.216494i	0.0135166	−	0.00982039i
$487$	0.188530	+	0.580234i	0.00854309	+	0.0262929i	0.955237	−	0.295841i	$-0.0955999\pi$
$487$	0.188530	+	0.580234i	0.00854309	+	0.0262929i	−0.946694	+	0.322134i	$0.895600\pi$
$488$	1.91702	−	5.89999i	0.0867795	−	0.267080i
$489$	10.0597	+	7.30881i	0.454916	+	0.330516i
$490$	−1.71384	−	1.24518i	−0.0774236	−	0.0562515i
$491$	6.07511	−	18.6973i	0.274166	−	0.843796i	−0.715273	−	0.698845i	$-0.753698\pi$
$491$	6.07511	−	18.6973i	0.274166	−	0.843796i	0.989439	−	0.144951i	$-0.0463024\pi$
$492$	−5.27362	−	16.2305i	−0.237753	−	0.731729i
$493$	−9.84599	+	7.15353i	−0.443441	+	0.322179i
$494$	2.92927			0.131794
$495$	−1.02549	+	3.37067i	−0.0460922	+	0.151500i
$496$	−22.9324			−1.02970
$497$	−35.4301	+	25.7414i	−1.58926	+	1.15466i
$498$	1.38204	+	4.25350i	0.0619309	+	0.190604i
$499$	3.55581	−	10.9436i	0.159180	−	0.489905i	−0.839381	−	0.543544i	$-0.817082\pi$
$499$	3.55581	−	10.9436i	0.159180	−	0.489905i	0.998560	+	0.0536392i	$0.0170821\pi$
$500$	−14.2143	−	10.3273i	−0.635681	−	0.461849i
$501$	−15.1260	−	10.9897i	−0.675780	−	0.490983i
$502$	−2.45251	+	7.54805i	−0.109461	+	0.336886i
$503$	4.35124	+	13.3917i	0.194012	+	0.597108i	0.999987	+	0.00515771i	$0.00164176\pi$
$503$	4.35124	+	13.3917i	0.194012	+	0.597108i	−0.805975	+	0.591950i	$0.798358\pi$
$504$	4.05716	−	2.94770i	0.180720	−	0.131301i
$505$	−11.5469			−0.513829
$506$	0.435535	+	1.25930i	0.0193619	+	0.0559826i
$507$	−1.00000			−0.0444116
$508$	−12.9640	+	9.41887i	−0.575183	+	0.417895i
$509$	−3.99153	−	12.2847i	−0.176921	−	0.544508i	0.822795	−	0.568339i	$-0.192414\pi$
$509$	−3.99153	−	12.2847i	−0.176921	−	0.544508i	−0.999716	+	0.0238309i	$0.992414\pi$
$510$	−0.478972	+	1.47412i	−0.0212092	+	0.0652753i
$511$	18.7919	+	13.6531i	0.831303	+	0.603977i
$512$	−17.8193	−	12.9465i	−0.787509	−	0.572159i
$513$	2.45762	−	7.56377i	0.108506	−	0.333949i
$514$	0.783062	+	2.41002i	0.0345394	+	0.106301i
$515$	6.50842	−	4.72864i	0.286795	−	0.208369i
$516$	−6.48907			−0.285665
$517$	−19.2184	+	0.361697i	−0.845222	+	0.0159074i
$518$	−3.67741			−0.161576
$519$	−12.7451	+	9.25986i	−0.559448	+	0.406463i
$520$	0.467227	+	1.43798i	0.0204893	+	0.0630594i
$521$	−8.05623	+	24.7945i	−0.352950	+	1.08627i	0.604239	+	0.796803i	$0.293477\pi$
$521$	−8.05623	+	24.7945i	−0.352950	+	1.08627i	−0.957189	+	0.289465i	$0.906523\pi$
$522$	−0.915440	−	0.665106i	−0.0400677	−	0.0291109i
$523$	27.6291	+	20.0737i	1.20814	+	0.877763i	0.995060	−	0.0992719i	$-0.0316513\pi$
$523$	27.6291	+	20.0737i	1.20814	+	0.877763i	0.213077	+	0.977035i	$0.431651\pi$
$524$	−6.68418	+	20.5718i	−0.292000	+	0.898682i
$525$	4.21529	+	12.9733i	0.183971	+	0.566203i
$526$	6.87076	−	4.99190i	0.299579	−	0.217657i
$527$	−28.3502			−1.23495
$528$	−8.71419	−	6.08403i	−0.379236	−	0.264774i
$529$	−21.8102			−0.948269
$530$	−2.50767	+	1.82193i	−0.108926	+	0.0791396i
$531$	−2.15092	−	6.61986i	−0.0933421	−	0.287277i
$532$	16.1436	−	49.6849i	0.699914	−	2.15411i
$533$	−7.40558	−	5.38047i	−0.320771	−	0.233054i
$534$	−1.62284	−	1.17906i	−0.0702271	−	0.0510229i
$535$	2.21060	−	6.80353i	0.0955726	−	0.294142i
$536$	−6.32200	−	19.4571i	−0.273069	−	0.840419i
$537$	−11.3575	+	8.25168i	−0.490110	+	0.356086i
$538$	2.12973			0.0918191
$539$	14.3265	−	10.8265i	0.617087	−	0.466331i
$540$	1.98046			0.0852256
$541$	−19.6865	+	14.3030i	−0.846387	+	0.614936i	−0.924147	−	0.382036i	$-0.875223\pi$
$541$	−19.6865	+	14.3030i	−0.846387	+	0.614936i	0.0777606	+	0.996972i	$0.475223\pi$
$542$	−2.28691	−	7.03837i	−0.0982310	−	0.302324i
$543$	2.06666	−	6.36051i	0.0886887	−	0.272956i
$544$	−12.9059	−	9.37666i	−0.553334	−	0.402021i
$545$	−8.69909	−	6.32026i	−0.372628	−	0.270730i
$546$	0.401025	−	1.23423i	0.0171623	−	0.0528201i
$547$	2.30149	+	7.08326i	0.0984047	+	0.302858i	0.988126	−	0.153646i	$-0.0491014\pi$
$547$	2.30149	+	7.08326i	0.0984047	+	0.302858i	−0.889721	+	0.456504i	$0.849101\pi$
$548$	−24.9646	+	18.1379i	−1.06644	+	0.774811i
$549$	−4.35854			−0.186018
$550$	−3.77320	+	2.85139i	−0.160890	+	0.121584i
$551$	−24.4330			−1.04088
$552$	1.25603	−	0.912558i	0.0534601	−	0.0388411i
$553$	9.34879	+	28.7726i	0.397551	+	1.22354i
$554$	−1.10948	+	3.41463i	−0.0471372	+	0.145074i
$555$	−2.43530	−	1.76935i	−0.103373	−	0.0751047i
$556$	20.5199	+	14.9086i	0.870237	+	0.632264i
$557$	1.34288	−	4.13295i	0.0568995	−	0.175119i	−0.918568	−	0.395264i	$-0.870653\pi$
$557$	1.34288	−	4.13295i	0.0568995	−	0.175119i	0.975467	+	0.220145i	$0.0706531\pi$
$558$	−0.814533	−	2.50687i	−0.0344819	−	0.106124i
$559$	−2.81589	+	2.04586i	−0.119099	+	0.0865307i
$560$	11.9938			0.506829
$561$	−10.7729	−	7.52138i	−0.454832	−	0.317553i
$562$	10.2969			0.434350
$563$	−26.7931	+	19.4663i	−1.12919	+	0.820407i	−0.985577	−	0.169226i	$-0.945873\pi$
$563$	−26.7931	+	19.4663i	−1.12919	+	0.820407i	−0.143616	+	0.989633i	$0.545873\pi$
$564$	3.33890	+	10.2761i	0.140593	+	0.432702i
$565$	−4.92124	+	15.1460i	−0.207038	+	0.637198i
$566$	−4.37672	−	3.17988i	−0.183967	−	0.133660i
$567$	−2.85049	−	2.07100i	−0.119709	−	0.0869738i
$568$	−5.46687	+	16.8253i	−0.229385	+	0.705973i
$569$	7.15647	+	22.0253i	0.300015	+	0.923350i	0.981491	+	0.191510i	$0.0613384\pi$
$569$	7.15647	+	22.0253i	0.300015	+	0.923350i	−0.681476	+	0.731840i	$0.738662\pi$
$570$	−2.51744	+	1.82903i	−0.105444	+	0.0766097i
$571$	37.7891			1.58142			0.790712	−	0.612188i	$-0.209711\pi$
$571$	37.7891			1.58142			0.790712	+	0.612188i	$0.209711\pi$
$572$	−6.18222	+	0.116352i	−0.258491	+	0.00486491i
$573$	4.58019			0.191340
$574$	9.61056	−	6.98248i	0.401137	−	0.291443i
$575$	1.30498	+	4.01633i	0.0544216	+	0.167492i
$576$	−1.52212	+	4.68459i	−0.0634215	+	0.195191i
$577$	−23.7109	−	17.2270i	−0.987097	−	0.717168i	−0.0278132	−	0.999613i	$-0.508854\pi$
$577$	−23.7109	−	17.2270i	−0.987097	−	0.717168i	−0.959283	+	0.282445i	$0.908854\pi$
$578$	0.389361	+	0.282887i	0.0161953	+	0.0117666i
$579$	−0.0358994	+	0.110487i	−0.00149193	+	0.00459169i
$580$	−1.88015	−	5.78652i	−0.0780692	−	0.240272i
$581$	34.6123	−	25.1473i	1.43596	−	1.04329i
$582$	1.48555			0.0615780
$583$	−8.58813	−	24.8316i	−0.355684	−	1.02842i
$584$	9.38326			0.388282
$585$	0.859409	−	0.624397i	0.0355322	−	0.0258157i
$586$	2.46134	+	7.57522i	0.101677	+	0.312929i
$587$	7.83069	−	24.1004i	0.323207	−	0.994729i	−0.649036	−	0.760757i	$-0.724828\pi$
$587$	7.83069	−	24.1004i	0.323207	−	0.994729i	0.972243	−	0.233972i	$-0.0751723\pi$
$588$	−8.16631	−	5.93317i	−0.336773	−	0.244680i
$589$	−46.0456	−	33.4541i	−1.89727	−	1.37845i
$590$	−0.841580	+	2.59012i	−0.0346473	+	0.106633i
$591$	−3.89395	−	11.9844i	−0.160176	−	0.492970i
$592$	7.34618	−	5.33731i	0.301926	−	0.219362i
$593$	3.80759			0.156359			0.0781795	−	0.996939i	$-0.475089\pi$
$593$	3.80759			0.156359			0.0781795	+	0.996939i	$0.475089\pi$
$594$	0.355563	−	1.16870i	0.0145889	−	0.0479522i
$595$	14.8273			0.607859
$596$	16.1090	−	11.7038i	0.659849	−	0.479408i
$597$	6.22715	+	19.1652i	0.254860	+	0.784380i
$598$	0.124151	−	0.382097i	0.00507690	−	0.0156251i
$599$	−36.9542	−	26.8488i	−1.50991	−	1.09701i	−0.966219	−	0.257724i	$-0.917027\pi$
$599$	−36.9542	−	26.8488i	−1.50991	−	1.09701i	−0.543688	−	0.839287i	$-0.682973\pi$
$600$	4.45805	+	3.23896i	0.181999	+	0.132230i
$601$	8.41586	−	25.9014i	0.343290	−	1.05654i	−0.619203	−	0.785231i	$-0.712544\pi$
$601$	8.41586	−	25.9014i	0.343290	−	1.05654i	0.962493	−	0.271307i	$-0.0874560\pi$
$602$	−1.39582	−	4.29589i	−0.0568893	−	0.175087i
$603$	−11.6286	+	8.44865i	−0.473552	+	0.344056i
$604$	3.58351			0.145811
$605$	4.02652	+	10.9695i	0.163701	+	0.445974i
$606$	4.00359			0.162635
$607$	30.9912	−	22.5164i	1.25789	−	0.913912i	0.259240	−	0.965813i	$-0.416528\pi$
$607$	30.9912	−	22.5164i	1.25789	−	0.913912i	0.998652	+	0.0519006i	$0.0165279\pi$
$608$	−9.89660	−	30.4586i	−0.401360	−	1.23526i
$609$	−3.34494	+	10.2947i	−0.135544	+	0.417160i
$610$	1.37965	+	1.00238i	0.0558605	+	0.0405850i
$611$	4.68872	+	3.40656i	0.189685	+	0.137814i
$612$	−2.28226	+	7.02407i	−0.0922548	+	0.283931i
$613$	−0.800338	−	2.46319i	−0.0323254	−	0.0994872i	0.933592	−	0.358338i	$-0.116656\pi$
$613$	−0.800338	−	2.46319i	−0.0323254	−	0.0994872i	−0.965917	+	0.258850i	$0.916656\pi$
$614$	−1.27672	+	0.927588i	−0.0515240	+	0.0374344i
$615$	9.72398			0.392109
$616$	4.84120	−	15.9125i	0.195057	−	0.641132i
$617$	9.07593			0.365383			0.182692	−	0.983170i	$-0.441519\pi$
$617$	9.07593			0.365383			0.182692	+	0.983170i	$0.441519\pi$
$618$	−2.25663	+	1.63954i	−0.0907751	+	0.0659520i
$619$	10.9211	+	33.6116i	0.438955	+	1.35097i	0.888978	+	0.457949i	$0.151416\pi$
$619$	10.9211	+	33.6116i	0.438955	+	1.35097i	−0.450023	+	0.893017i	$0.648584\pi$
$620$	4.37973	−	13.4794i	0.175894	−	0.541347i
$621$	−0.882463	−	0.641147i	−0.0354120	−	0.0257283i
$622$	1.60373	+	1.16518i	0.0643037	+	0.0467194i
$623$	−5.92971	+	18.2498i	−0.237569	+	0.731161i
$624$	0.990225	+	3.04760i	0.0396407	+	0.122002i
$625$	−7.56154	+	5.49378i	−0.302461	+	0.219751i
$626$	−4.56741			−0.182550
$627$	−8.62160	−	24.9284i	−0.344314	−	0.995543i
$628$	37.8254			1.50940
$629$	9.08171	−	6.59825i	0.362111	−	0.263089i
$630$	0.426004	+	1.31111i	0.0169724	+	0.0522357i
$631$	12.8792	−	39.6380i	0.512711	−	1.57796i	−0.274698	−	0.961531i	$-0.588578\pi$
$631$	12.8792	−	39.6380i	0.512711	−	1.57796i	0.787409	−	0.616431i	$-0.211422\pi$
$632$	9.88718	+	7.18346i	0.393291	+	0.285743i
$633$	10.9066	+	7.92413i	0.433500	+	0.314956i
$634$	−0.638960	+	1.96652i	−0.0253763	+	0.0781003i
$635$	−2.82150	−	8.68368i	−0.111968	−	0.344601i
$636$	−11.9488	+	8.68133i	−0.473802	+	0.344237i
$637$	−5.41431			−0.214523
$638$	−3.75225	+	0.0706188i	−0.148553	+	0.00279582i
$639$	12.4295			0.491703
$640$	8.48070	−	6.16159i	0.335229	−	0.243558i
$641$	−6.68161	−	20.5639i	−0.263908	−	0.812225i	−0.991943	−	0.126685i	$-0.959566\pi$
$641$	−6.68161	−	20.5639i	−0.263908	−	0.812225i	0.728035	−	0.685540i	$-0.240434\pi$
$642$	−0.766471	+	2.35896i	−0.0302502	+	0.0931006i
$643$	34.1126	+	24.7843i	1.34527	+	0.977396i	0.999232	+	0.0391750i	$0.0124730\pi$
$643$	34.1126	+	24.7843i	1.34527	+	0.977396i	0.346037	+	0.938221i	$0.387527\pi$
$644$	−5.79672	−	4.21157i	−0.228423	−	0.165959i
$645$	1.14257	−	3.51646i	0.0449886	−	0.138461i
$646$	−3.58591	−	11.0363i	−0.141086	−	0.434218i
$647$	0.290820	−	0.211293i	0.0114333	−	0.00830679i	−0.582054	−	0.813150i	$-0.697751\pi$
$647$	0.290820	−	0.211293i	0.0114333	−	0.00830679i	0.593487	+	0.804843i	$0.297751\pi$
$648$	−1.42332			−0.0559134
$649$	−18.9286	−	13.2155i	−0.743011	−	0.518752i
$650$	1.42598			0.0559314
$651$	−20.3994	+	14.8210i	−0.799515	+	0.580882i
$652$	−7.16366	−	22.0475i	−0.280551	−	0.863446i
$653$	14.1925	−	43.6800i	0.555395	−	1.70933i	−0.139503	−	0.990222i	$-0.544550\pi$
$653$	14.1925	−	43.6800i	0.555395	−	1.70933i	0.694898	−	0.719108i	$-0.255450\pi$
$654$	3.01620	+	2.19140i	0.117943	+	0.0856903i
$655$	−9.97104	−	7.24439i	−0.389601	−	0.283062i
$656$	−9.06433	+	27.8971i	−0.353903	+	1.08920i
$657$	−2.03720	−	6.26985i	−0.0794786	−	0.244610i
$658$	−6.08477	+	4.42084i	−0.237209	+	0.172342i
$659$	5.87720			0.228943			0.114472	−	0.993427i	$-0.463483\pi$
$659$	5.87720			0.228943			0.114472	+	0.993427i	$0.463483\pi$
$660$	5.24040	−	3.96015i	0.203982	−	0.154149i
$661$	27.8313			1.08251			0.541256	−	0.840858i	$-0.317949\pi$
$661$	27.8313			1.08251			0.541256	+	0.840858i	$0.317949\pi$
$662$	1.99417	−	1.44885i	0.0775055	−	0.0563111i
$663$	1.22416	+	3.76759i	0.0475426	+	0.146321i
$664$	5.34069	−	16.4369i	0.207259	−	0.637877i
$665$	24.0820	+	17.4966i	0.933861	+	0.678490i
$666$	0.844380	+	0.613478i	0.0327191	+	0.0237718i
$667$	−1.03554	+	3.18705i	−0.0400961	+	0.123403i
$668$	10.7714	+	33.1511i	0.416760	+	1.28265i
$669$	2.38668	−	1.73402i	0.0922744	−	0.0670413i
$670$	5.62392			0.217271
$671$	−11.5329	+	8.71538i	−0.445223	+	0.336454i
$672$	−14.1884			−0.547329
$673$	−17.3250	+	12.5873i	−0.667828	+	0.485206i	−0.869298	−	0.494289i	$-0.835428\pi$
$673$	−17.3250	+	12.5873i	−0.667828	+	0.485206i	0.201469	+	0.979495i	$0.435428\pi$
$674$	1.84136	+	5.66713i	0.0709266	+	0.218290i
$675$	1.19637	−	3.68206i	0.0460484	−	0.141722i
$676$	1.50828	+	1.09583i	0.0580108	+	0.0421473i
$677$	−21.8790	−	15.8960i	−0.840879	−	0.610934i	0.0817373	−	0.996654i	$-0.473953\pi$
$677$	−21.8790	−	15.8960i	−0.840879	−	0.610934i	−0.922616	+	0.385720i	$0.873953\pi$
$678$	1.70632	−	5.25151i	0.0655308	−	0.201683i
$679$	−4.39140	−	13.5153i	−0.168526	−	0.518671i
$680$	4.84575	−	3.52064i	0.185826	−	0.135010i
$681$	14.9390			0.572462
$682$	−7.16806	−	5.00456i	−0.274479	−	0.191635i
$683$	−34.2998			−1.31245			−0.656223	−	0.754567i	$-0.727847\pi$
$683$	−34.2998			−1.31245			−0.656223	+	0.754567i	$0.727847\pi$
$684$	−11.9954	+	8.71516i	−0.458655	+	0.333233i
$685$	−5.43335	−	16.7221i	−0.207598	−	0.638919i
$686$	−0.635900	+	1.95710i	−0.0242788	+	0.0747224i
$687$	−8.09472	−	5.88116i	−0.308833	−	0.224380i
$688$	9.02333	+	6.55583i	0.344011	+	0.249939i
$689$	−2.44808	+	7.53441i	−0.0932643	+	0.287038i
$690$	0.131884	+	0.405897i	0.00502073	+	0.0154522i
$691$	−18.9787	+	13.7888i	−0.721984	+	0.524552i	−0.887018	−	0.461736i	$-0.847227\pi$
$691$	−18.9787	+	13.7888i	−0.721984	+	0.524552i	0.165033	+	0.986288i	$0.447227\pi$
$692$	29.3704			1.11650
$693$	−11.6837	+	0.219892i	−0.443827	+	0.00835301i
$694$	2.22713			0.0845407
$695$	−11.6921	+	8.49481i	−0.443507	+	0.322227i
$696$	1.35123	+	4.15866i	0.0512183	+	0.157634i
$697$	−11.2058	+	34.4878i	−0.424449	+	1.30632i
$698$	1.03574	+	0.752508i	0.0392033	+	0.0284828i
$699$	−16.6661	−	12.1087i	−0.630371	−	0.457992i
$700$	7.85874	−	24.1867i	0.297032	−	0.914171i
$701$	−4.39664	−	13.5315i	−0.166059	−	0.511076i	0.833054	−	0.553192i	$-0.186590\pi$
$701$	−4.39664	−	13.5315i	−0.166059	−	0.511076i	−0.999113	+	0.0421156i	$0.986590\pi$
$702$	−0.297979	+	0.216494i	−0.0112465	+	0.00817106i
$703$	22.5364			0.849976
$704$	5.33976	+	15.4393i	0.201250	+	0.581890i
$705$	−6.15657			−0.231870
$706$	7.48558	−	5.43859i	0.281724	−	0.204684i
$707$	−11.8349	−	36.4242i	−0.445098	−	1.36987i
$708$	−4.01005	+	12.3417i	−0.150707	+	0.463828i
$709$	−3.11167	−	2.26076i	−0.116861	−	0.0849046i	0.527820	−	0.849356i	$-0.323010\pi$
$709$	−3.11167	−	2.26076i	−0.116861	−	0.0849046i	−0.644681	+	0.764452i	$0.723010\pi$
$710$	−3.93442	−	2.85852i	−0.147656	−	0.107279i
$711$	2.65335	−	8.16616i	0.0995083	−	0.306255i
$712$	2.39538	+	7.37223i	0.0897708	+	0.276286i
$713$	−6.31531	+	4.58834i	−0.236510	+	0.171835i
$714$	−5.14099			−0.192397
$715$	1.02549	−	3.37067i	0.0383511	−	0.126056i
$716$	26.1727			0.978119
$717$	20.7025	−	15.0412i	0.773149	−	0.561726i
$718$	3.11604	+	9.59019i	0.116290	+	0.357903i
$719$	6.11737	−	18.8273i	0.228140	−	0.702141i	−0.769818	−	0.638263i	$-0.779653\pi$
$719$	6.11737	−	18.8273i	0.228140	−	0.702141i	0.997958	−	0.0638781i	$-0.0203469\pi$
$720$	−2.75392	−	2.00084i	−0.102633	−	0.0745670i
$721$	21.5871	+	15.6839i	0.803946	+	0.584101i
$722$	5.03649	−	15.5007i	0.187439	−	0.576878i
$723$	−1.45657	−	4.48286i	−0.0541704	−	0.166720i
$724$	−10.0871	+	7.32874i	−0.374886	+	0.272370i
$725$	−11.8940			−0.441732
$726$	−1.39610	−	3.80341i	−0.0518140	−	0.141158i
$727$	−15.5435			−0.576476			−0.288238	−	0.957559i	$-0.593069\pi$
$727$	−15.5435			−0.576476			−0.288238	+	0.957559i	$0.593069\pi$
$728$	−4.05716	+	2.94770i	−0.150368	+	0.109249i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.797083	+	2.45317i	−0.0295014	+	0.0907958i
$731$	11.1551	+	8.10464i	0.412585	+	0.299761i
$732$	6.57391	+	4.77623i	0.242979	+	0.176534i
$733$	7.55447	−	23.2503i	0.279031	−	0.858769i	−0.709094	−	0.705114i	$-0.750896\pi$
$733$	7.55447	−	23.2503i	0.279031	−	0.858769i	0.988125	−	0.153654i	$-0.0491042\pi$
$734$	−0.613834	−	1.88919i	−0.0226570	−	0.0697312i
$735$	4.65311	−	3.38068i	0.171633	−	0.124698i
$736$	−4.39249			−0.161909
$737$	−13.8758	+	45.6081i	−0.511120	+	1.68000i
$738$	−3.37155			−0.124108
$739$	10.7111	−	7.78204i	0.394013	−	0.286267i	−0.373085	−	0.927797i	$-0.621700\pi$
$739$	10.7111	−	7.78204i	0.394013	−	0.286267i	0.767098	+	0.641530i	$0.221700\pi$
$740$	1.73421	+	5.33735i	0.0637509	+	0.196205i
$741$	−2.45762	+	7.56377i	−0.0902828	+	0.277862i
$742$	−8.31744	−	6.04298i	−0.305343	−	0.221845i
$743$	5.71937	+	4.15536i	0.209823	+	0.152445i	0.687734	−	0.725963i	$-0.258606\pi$
$743$	5.71937	+	4.15536i	0.209823	+	0.152445i	−0.477910	+	0.878409i	$0.658606\pi$
$744$	−3.14763	+	9.68741i	−0.115398	+	0.355158i
$745$	3.50598	+	10.7903i	0.128449	+	0.395326i
$746$	2.33000	−	1.69284i	0.0853072	−	0.0619793i
$747$	−12.1426			−0.444274
$748$	8.00642	+	23.1496i	0.292744	+	0.846435i
$749$	23.7272			0.866974
$750$	−2.80819	+	2.04027i	−0.102541	+	0.0745002i
$751$	5.54145	+	17.0548i	0.202210	+	0.622339i	0.999816	+	0.0191607i	$0.00609940\pi$
$751$	5.54145	+	17.0548i	0.202210	+	0.622339i	−0.797606	+	0.603179i	$0.793901\pi$
$752$	5.73893	−	17.6626i	0.209277	−	0.644089i
$753$	−17.4324	−	12.6654i	−0.635274	−	0.461553i
$754$	0.915440	+	0.665106i	0.0333383	+	0.0242217i
$755$	−0.630970	+	1.94193i	−0.0229633	+	0.0706739i
$756$	2.02987	+	6.24730i	0.0738257	+	0.227212i
$757$	23.9636	−	17.4106i	0.870972	−	0.632798i	−0.0598755	−	0.998206i	$-0.519070\pi$
$757$	23.9636	−	17.4106i	0.870972	−	0.632798i	0.930848	+	0.365408i	$0.119070\pi$
$758$	−0.785015			−0.0285130
$759$	−3.61708	+	0.0680749i	−0.131292	+	0.00247096i
$760$	12.0248			0.436185
$761$	5.21354	−	3.78786i	0.188991	−	0.137310i	−0.489267	−	0.872134i	$-0.662735\pi$
$761$	5.21354	−	3.78786i	0.188991	−	0.137310i	0.678257	+	0.734824i	$0.262735\pi$
$762$	0.978286	+	3.01085i	0.0354396	+	0.109072i
$763$	11.0209	−	33.9189i	0.398984	−	1.22795i
$764$	−6.90822	−	5.01912i	−0.249931	−	0.181585i
$765$	−3.40453	−	2.47354i	−0.123091	−	0.0894309i
$766$	−0.772061	+	2.37616i	−0.0278957	+	0.0858541i
$767$	2.15092	+	6.61986i	0.0776653	+	0.239029i
$768$	5.02943	−	3.65410i	0.181484	−	0.131856i
$769$	−22.1539			−0.798890			−0.399445	−	0.916757i	$-0.630797\pi$
$769$	−22.1539			−0.798890			−0.399445	+	0.916757i	$0.630797\pi$
$770$	3.74893	+	2.61741i	0.135102	+	0.0943249i
$771$	−6.87996			−0.247776
$772$	0.175222	−	0.127306i	0.00630636	−	0.00458184i
$773$	5.21149	+	16.0393i	0.187444	+	0.576894i	0.999982	−	0.00601480i	$-0.00191458\pi$
$773$	5.21149	+	16.0393i	0.187444	+	0.576894i	−0.812538	+	0.582909i	$0.801915\pi$
$774$	−0.396157	+	1.21925i	−0.0142396	+	0.0438249i
$775$	−22.4151	−	16.2855i	−0.805173	−	0.584992i
$776$	−4.64430	−	3.37428i	−0.166721	−	0.121130i
$777$	3.08529	−	9.49555i	0.110684	−	0.340651i
$778$	−3.71063	−	11.4201i	−0.133032	−	0.409432i
$779$	−58.8967	+	42.7910i	−2.11019	+	1.53315i
$780$	−1.98046			−0.0709120
$781$	32.8890	−	24.8541i	1.17686	−	0.889349i
$782$	−1.59156			−0.0569142
$783$	2.48543	−	1.80577i	0.0888221	−	0.0645330i
$784$	5.36139	+	16.5007i	0.191478	+	0.589309i
$785$	−6.66015	+	20.4978i	−0.237711	+	0.731599i
$786$	3.45721	+	2.51181i	0.123315	+	0.0895934i
$787$	−37.6385	−	27.3460i	−1.34167	−	0.974779i	−0.999381	−	0.0351834i	$-0.988798\pi$
$787$	−37.6385	−	27.3460i	−1.34167	−	0.974779i	−0.342287	−	0.939595i	$-0.611202\pi$
$788$	−7.25964	+	22.3429i	−0.258614	+	0.795932i
$789$	7.12527	+	21.9293i	0.253666	+	0.780705i
$790$	−2.71794	+	1.97470i	−0.0966999	+	0.0702566i
$791$	−52.8216			−1.87812
$792$	−3.76618	+	2.84609i	−0.133825	+	0.101131i
$793$	4.35854			0.154776
$794$	−10.1602	+	7.38180i	−0.360571	+	0.261970i
$795$	−2.60056	−	8.00371i	−0.0922325	−	0.283862i
$796$	11.6095	−	35.7304i	0.411489	−	1.26643i
$797$	20.7923	+	15.1065i	0.736501	+	0.535099i	0.891613	−	0.452798i	$-0.149574\pi$
$797$	20.7923	+	15.1065i	0.736501	+	0.535099i	−0.155112	+	0.987897i	$0.549574\pi$
$798$	−8.34985	−	6.06652i	−0.295582	−	0.214753i
$799$	7.09474	−	21.8354i	0.250994	−	0.772480i
$800$	−4.81769	−	14.8273i	−0.170331	−	0.524225i
$801$	4.40603	−	3.20117i	0.155679	−	0.113108i
$802$	−11.2595			−0.397586
$803$	−17.9278	−	12.5167i	−0.632657	−	0.441706i
$804$	26.7974			0.945073
$805$	3.30294	−	2.39972i	0.116413	−	0.0845791i
$806$	0.814533	+	2.50687i	0.0286907	+	0.0883009i
$807$	−1.78681	+	5.49924i	−0.0628987	+	0.193582i
$808$	−12.5165	−	9.09376i	−0.440329	−	0.319917i
$809$	−10.9786	−	7.97645i	−0.385989	−	0.280437i	0.377821	−	0.925879i	$-0.376673\pi$
$809$	−10.9786	−	7.97645i	−0.385989	−	0.280437i	−0.763810	+	0.645441i	$0.776673\pi$
$810$	0.120907	−	0.372115i	0.00424825	−	0.0130748i
$811$	9.13379	+	28.1109i	0.320731	+	0.987108i	0.973331	+	0.229406i	$0.0736782\pi$
$811$	9.13379	+	28.1109i	0.320731	+	0.987108i	−0.652600	+	0.757703i	$0.726322\pi$
$812$	16.3263	−	11.8618i	0.572941	−	0.416266i
$813$	20.0927			0.704681
$814$	3.46099	−	0.0651371i	0.121308	−	0.00228306i
$815$	13.2090			0.462692
$816$	10.2699	−	7.46153i	0.359519	−	0.261206i
$817$	8.55405	+	26.3266i	0.299268	+	0.921053i
$818$	0.477915	−	1.47087i	0.0167099	−	0.0514279i
$819$	2.85049	+	2.07100i	0.0996041	+	0.0723666i
$820$	−14.6665	−	10.6558i	−0.512176	−	0.372118i
$821$	−4.66301	+	14.3513i	−0.162740	+	0.500863i	−0.998863	−	0.0476800i	$-0.984817\pi$
$821$	−4.66301	+	14.3513i	−0.162740	+	0.500863i	0.836122	+	0.548543i	$0.184817\pi$
$822$	1.88388	+	5.79799i	0.0657078	+	0.202228i
$823$	−29.8583	+	21.6933i	−1.04080	+	0.756182i	−0.970441	−	0.241340i	$-0.922413\pi$
$823$	−29.8583	+	21.6933i	−1.04080	+	0.756182i	−0.0703549	+	0.997522i	$0.522413\pi$
$824$	10.7790			0.375504
$825$	−4.19701	−	12.1352i	−0.146121	−	0.422493i
$826$	−9.03300			−0.314298
$827$	15.2779	−	11.1000i	0.531265	−	0.385986i	−0.289566	−	0.957158i	$-0.593511\pi$
$827$	15.2779	−	11.1000i	0.531265	−	0.385986i	0.820831	+	0.571172i	$0.193511\pi$
$828$	0.628414	+	1.93406i	0.0218389	+	0.0672132i
$829$	−5.77691	+	17.7795i	−0.200640	+	0.617507i	0.799224	+	0.601033i	$0.205244\pi$
$829$	−5.77691	+	17.7795i	−0.200640	+	0.617507i	−0.999864	+	0.0164740i	$0.994756\pi$
$830$	3.84361	+	2.79255i	0.133414	+	0.0969308i
$831$	−7.88617	−	5.72964i	−0.273568	−	0.198759i
$832$	1.52212	−	4.68459i	0.0527699	−	0.162409i
$833$	6.62801	+	20.3989i	0.229647	+	0.706781i
$834$	4.05395	−	2.94537i	0.140377	−	0.101990i
$835$	−19.8614			−0.687331
$836$	−14.3135	+	47.0468i	−0.495042	+	1.62715i
$837$	7.15646			0.247363
$838$	1.96373	−	1.42673i	0.0678360	−	0.0492857i
$839$	−0.981217	−	3.01988i	−0.0338754	−	0.104258i	0.932689	−	0.360681i	$-0.117456\pi$
$839$	−0.981217	−	3.01988i	−0.0338754	−	0.104258i	−0.966565	+	0.256424i	$0.917456\pi$
$840$	1.64623	−	5.06656i	0.0568002	−	0.174813i
$841$	15.8258	+	11.4982i	0.545719	+	0.396488i
$842$	9.05889	+	6.58167i	0.312190	+	0.226819i
$843$	−8.63897	+	26.5880i	−0.297542	+	0.915740i
$844$	−7.76676	−	23.9036i	−0.267343	−	0.822797i
$845$	−0.859409	+	0.624397i	−0.0295646	+	0.0214799i
$846$	2.13464			0.0733905
$847$	−30.4760	+	23.9447i	−1.04717	+	0.822749i
$848$	25.3860			0.871759
$849$	11.8829	−	8.63341i	0.407819	−	0.296298i
$850$	−1.74563	−	5.37250i	−0.0598746	−	0.184275i
$851$	0.955154	−	2.93966i	0.0327423	−	0.100770i
$852$	−18.7472	−	13.6206i	−0.642267	−	0.466634i
$853$	−7.94679	−	5.77368i	−0.272093	−	0.197687i	0.443368	−	0.896339i	$-0.353783\pi$
$853$	−7.94679	−	5.77368i	−0.272093	−	0.197687i	−0.715461	+	0.698653i	$0.753783\pi$
$854$	−1.74789	+	5.37944i	−0.0598114	+	0.184081i
$855$	−2.61070	−	8.03490i	−0.0892840	−	0.274788i
$856$	7.75437	−	5.63388i	0.265039	−	0.192562i
$857$	−28.6512			−0.978705			−0.489352	−	0.872086i	$-0.662767\pi$
$857$	−28.6512			−0.978705			−0.489352	+	0.872086i	$0.662767\pi$
$858$	−0.355563	+	1.16870i	−0.0121387	+	0.0398986i
$859$	54.2057			1.84947			0.924737	−	0.380606i	$-0.124285\pi$
$859$	54.2057			1.84947			0.924737	+	0.380606i	$0.124285\pi$
$860$	−5.57676	+	4.05176i	−0.190166	+	0.138164i
$861$	9.96656	+	30.6739i	0.339660	+	1.04536i
$862$	−4.10521	+	12.6345i	−0.139824	+	0.430334i
$863$	5.77087	+	4.19278i	0.196443	+	0.142724i	0.681659	−	0.731670i	$-0.261259\pi$
$863$	5.77087	+	4.19278i	0.196443	+	0.142724i	−0.485216	+	0.874394i	$0.661259\pi$
$864$	3.25784	+	2.36696i	0.110834	+	0.0805255i
$865$	−5.17143	+	15.9160i	−0.175834	+	0.541161i
$866$	1.92262	+	5.91720i	0.0653332	+	0.201075i
$867$	−1.05712	+	0.768043i	−0.0359017	+	0.0260841i
$868$	47.0094			1.59560
$869$	−9.30824	−	26.9137i	−0.315760	−	0.912985i
$870$	−1.20203			−0.0407525
$871$	11.6286	−	8.44865i	0.394019	−	0.286272i
$872$	−4.45205	−	13.7020i	−0.150765	−	0.464008i
$873$	−1.24635	+	3.83589i	−0.0421827	+	0.129825i
$874$	−2.58497	−	1.87809i	−0.0874381	−	0.0635275i
$875$	26.8634	+	19.5174i	0.908148	+	0.659808i
$876$	−3.79803	+	11.6891i	−0.128323	+	0.394939i
$877$	8.86845	+	27.2943i	0.299466	+	0.921663i	0.981684	+	0.190514i	$0.0610155\pi$
$877$	8.86845	+	27.2943i	0.299466	+	0.921663i	−0.682218	+	0.731149i	$0.738985\pi$
$878$	8.51276	−	6.18488i	0.287292	−	0.208730i
$879$	−21.6252			−0.729401
$880$	−11.2879	+	0.212443i	−0.380515	+	0.00716145i
$881$	−10.0032			−0.337015			−0.168508	−	0.985700i	$-0.553895\pi$
$881$	−10.0032			−0.337015			−0.168508	+	0.985700i	$0.553895\pi$
$882$	−1.61335	+	1.17217i	−0.0543244	+	0.0394690i
$883$	9.11012	+	28.0381i	0.306580	+	0.943557i	0.979083	+	0.203462i	$0.0652193\pi$
$883$	9.11012	+	28.0381i	0.306580	+	0.943557i	−0.672503	+	0.740095i	$0.734781\pi$
$884$	2.28226	−	7.02407i	0.0767606	−	0.236245i
$885$	−5.98195	−	4.34614i	−0.201081	−	0.146094i
$886$	−6.24174	−	4.53489i	−0.209695	−	0.152353i
$887$	3.15124	−	9.69852i	0.105808	−	0.325644i	−0.884111	−	0.467277i	$-0.845235\pi$
$887$	3.15124	−	9.69852i	0.105808	−	0.325644i	0.989919	+	0.141632i	$0.0452351\pi$
$888$	−1.24634	−	3.83585i	−0.0418246	−	0.128723i
$889$	24.5005	−	17.8006i	0.821719	−	0.597014i
$890$	−2.13088			−0.0714274
$891$	2.71941	+	1.89863i	0.0911038	+	0.0636064i
$892$	−5.49998			−0.184153
$893$	37.2895	−	27.0924i	1.24785	−	0.906612i
$894$	−1.21561	−	3.74127i	−0.0406562	−	0.125127i
$895$	−4.60838	+	14.1831i	−0.154041	+	0.474090i
$896$	28.1288	+	20.4367i	0.939716	+	0.682743i
$897$	0.882463	+	0.641147i	0.0294646	+	0.0214073i
$898$	−4.44514	+	13.6807i	−0.148336	+	0.456532i
$899$	−6.79399	−	20.9097i	−0.226592	−	0.697379i
$900$	−5.83938	+	4.24256i	−0.194646	+	0.141419i
$901$	31.3834			1.04553
$902$	−8.92128	+	6.74178i	−0.297046	+	0.224477i
$903$	12.2636			0.408108
$904$	−17.2628	+	12.5421i	−0.574151	+	0.417145i
$905$	−2.19538	−	6.75670i	−0.0729770	−	0.224600i
$906$	0.218773	−	0.673315i	0.00726825	−	0.0223694i
$907$	46.6051	+	33.8606i	1.54750	+	1.12432i	0.945406	+	0.325896i	$0.105666\pi$
$907$	46.6051	+	33.8606i	1.54750	+	1.12432i	0.602092	+	0.798427i	$0.294334\pi$
$908$	−22.5322	−	16.3706i	−0.747756	−	0.543277i
$909$	−3.35895	+	10.3378i	−0.111409	+	0.342883i
$910$	−0.426004	−	1.31111i	−0.0141219	−	0.0434628i
$911$	18.9790	−	13.7890i	0.628802	−	0.456851i	−0.227183	−	0.973852i	$-0.572952\pi$
$911$	18.9790	−	13.7890i	0.628802	−	0.456851i	0.855985	+	0.517001i	$0.172952\pi$
$912$	25.4849			0.843891
$913$	−32.1299	+	24.2804i	−1.06334	+	0.803565i
$914$	−10.3619			−0.342740
$915$	−3.74577	+	2.72146i	−0.123831	+	0.0899688i
$916$	5.76436	+	17.7409i	0.190460	+	0.586175i
$917$	12.6324	−	38.8784i	0.417157	−	1.28388i
$918$	1.18044	+	0.857638i	0.0389603	+	0.0283063i
$919$	−12.7873	−	9.29054i	−0.421815	−	0.306467i	0.356553	−	0.934275i	$-0.383952\pi$
$919$	−12.7873	−	9.29054i	−0.421815	−	0.306467i	−0.778368	+	0.627809i	$0.783952\pi$
$920$	0.509644	−	1.56852i	0.0168025	−	0.0517126i
$921$	−1.32401	−	4.07488i	−0.0436276	−	0.134272i
$922$	2.53064	−	1.83862i	0.0833423	−	0.0605517i
$923$	−12.4295			−0.409121
$924$	17.8633	+	12.4717i	0.587659	+	0.410289i
$925$	10.9708			0.360716
$926$	−1.64446	+	1.19477i	−0.0540402	+	0.0392625i
$927$	−2.34023	−	7.20247i	−0.0768631	−	0.236560i
$928$	3.82295	−	11.7658i	0.125494	−	0.386232i
$929$	−38.7389	−	28.1455i	−1.27098	−	0.923422i	−0.271741	−	0.962370i	$-0.587599\pi$
$929$	−38.7389	−	28.1455i	−1.27098	−	0.923422i	−0.999241	+	0.0389480i	$0.987599\pi$
$930$	−2.26530	−	1.64584i	−0.0742822	−	0.0539692i
$931$	−13.3063	+	40.9526i	−0.436097	+	1.34217i
$932$	11.8682	+	36.5265i	0.388756	+	1.19647i
$933$	−4.35415	+	3.16348i	−0.142548	+	0.103568i
$934$	−11.7164			−0.383372
$935$	−13.9547	+	0.262632i	−0.456366	+	0.00858899i
$936$	1.42332			0.0465227
$937$	−22.0508	+	16.0208i	−0.720367	+	0.523377i	−0.886501	−	0.462726i	$-0.846871\pi$
$937$	−22.0508	+	16.0208i	−0.720367	+	0.523377i	0.166134	+	0.986103i	$0.446871\pi$
$938$	5.76422	+	17.7404i	0.188208	+	0.579246i
$939$	3.83199	−	11.7936i	0.125052	−	0.384871i
$940$	9.28585	+	6.74656i	0.302871	+	0.220049i
$941$	4.55393	+	3.30863i	0.148454	+	0.107858i	0.659533	−	0.751676i	$-0.270754\pi$
$941$	4.55393	+	3.30863i	0.148454	+	0.107858i	−0.511079	+	0.859534i	$0.670754\pi$
$942$	2.30924	−	7.10712i	0.0752392	−	0.231562i
$943$	3.08548	+	9.49613i	0.100477	+	0.309237i
$944$	18.0448	−	13.1103i	0.587308	−	0.426704i
$945$	−3.74286			−0.121755
$946$	1.38976	+	4.01834i	0.0451852	+	0.130648i
$947$	−30.3760			−0.987086			−0.493543	−	0.869721i	$-0.664299\pi$
$947$	−30.3760			−0.987086			−0.493543	+	0.869721i	$0.664299\pi$
$948$	−12.9507	+	9.40925i	−0.420620	+	0.305598i
$949$	2.03720	+	6.26985i	0.0661302	+	0.203528i
$950$	3.50450	−	10.7858i	0.113701	−	0.349936i
$951$	−4.54172	−	3.29975i	−0.147275	−	0.107002i
$952$	16.0724	+	11.6773i	0.520908	+	0.378462i
$953$	−14.5370	+	44.7402i	−0.470899	+	1.44928i	0.380511	+	0.924777i	$0.375748\pi$
$953$	−14.5370	+	44.7402i	−0.470899	+	1.44928i	−0.851410	+	0.524501i	$0.824252\pi$
$954$	0.901682	+	2.77509i	0.0291930	+	0.0898469i
$955$	3.93626	−	2.85986i	0.127374	−	0.0925429i
$956$	−47.7079			−1.54298
$957$	2.96573	−	9.74804i	0.0958686	−	0.315110i
$958$	−3.37699			−0.109106
$959$	47.1804	−	34.2786i	1.52354	−	1.10691i
$960$	1.61693	+	4.97639i	0.0521861	+	0.160612i
$961$	6.24675	−	19.2255i	0.201508	−	0.620178i
$962$	−0.844380	−	0.613478i	−0.0272239	−	0.0197793i
$963$	−5.44808	−	3.95826i	−0.175562	−	0.127553i
$964$	−2.71554	+	8.35758i	−0.0874617	+	0.269179i
$965$	0.0381355	+	0.117369i	0.00122763	+	0.00377824i
$966$	−1.14521	+	0.832045i	−0.0368466	+	0.0267706i
$967$	−25.5851			−0.822760			−0.411380	−	0.911464i	$-0.634953\pi$
$967$	−25.5851			−0.822760			−0.411380	+	0.911464i	$0.634953\pi$
$968$	−4.27443	+	15.0618i	−0.137385	+	0.484103i
$969$	31.5057			1.01211
$970$	1.27670	−	0.927574i	0.0409922	−	0.0297826i
$971$	8.33292	+	25.6461i	0.267416	+	0.823023i	0.991127	+	0.132919i	$0.0424350\pi$
$971$	8.33292	+	25.6461i	0.267416	+	0.823023i	−0.723711	+	0.690104i	$0.757565\pi$
$972$	0.576112	−	1.77309i	0.0184788	−	0.0568719i
$973$	−38.7803	−	28.1756i	−1.24324	−	0.903267i
$974$	−0.181795	−	0.132082i	−0.00582510	−	0.00423218i
$975$	−1.19637	+	3.68206i	−0.0383146	+	0.117920i
$976$	−4.31594	−	13.2831i	−0.138150	−	0.425182i
$977$	32.4750	−	23.5945i	1.03897	−	0.754854i	0.0688833	−	0.997625i	$-0.478056\pi$
$977$	32.4750	−	23.5945i	1.03897	−	0.754854i	0.970084	+	0.242771i	$0.0780564\pi$
$978$	−4.57990			−0.146449
$979$	5.25748	−	17.2808i	0.168030	−	0.552296i
$980$	−10.7229			−0.342529
$981$	−8.18902	+	5.94967i	−0.261455	+	0.189958i
$982$	2.23760	+	6.88662i	0.0714046	+	0.219761i
$983$	2.17225	−	6.68550i	0.0692840	−	0.213234i	−0.910420	−	0.413686i	$-0.864241\pi$
$983$	2.17225	−	6.68550i	0.0692840	−	0.213234i	0.979704	+	0.200452i	$0.0642411\pi$
$984$	10.5405	+	7.65814i	0.336020	+	0.244133i
$985$	−10.8295	−	7.86809i	−0.345056	−	0.250698i
$986$	1.38520	−	4.26320i	0.0441137	−	0.135768i
$987$	−6.31016	−	19.4207i	−0.200855	−	0.618167i
$988$	11.9954	−	8.71516i	0.381624	−	0.277266i
$989$	3.79661			0.120725
$990$	−0.424157	−	1.22640i	−0.0134806	−	0.0389776i
$991$	−0.142470			−0.00452571			−0.00226286	−	0.999997i	$-0.500720\pi$
$991$	−0.142470			−0.00452571			−0.00226286	+	0.999997i	$0.500720\pi$
$992$	23.3146	−	16.9390i	0.740239	−	0.537815i
$993$	2.06804	+	6.36477i	0.0656272	+	0.201980i
$994$	4.98453	−	15.3408i	0.158100	−	0.486581i
$995$	17.3184	+	12.5825i	0.549029	+	0.398893i
$996$	18.3145	+	13.3062i	0.580316	+	0.421624i
$997$	−1.22402	+	3.76716i	−0.0387652	+	0.119307i	−0.968566	−	0.248755i	$-0.919979\pi$
$997$	−1.22402	+	3.76716i	−0.0387652	+	0.119307i	0.929801	+	0.368062i	$0.119979\pi$
$998$	1.30968	+	4.03079i	0.0414573	+	0.127592i
$999$	−2.29250	+	1.66560i	−0.0725316	+	0.0526973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.157.3	✓	20
11.2	odd	10		4719.2.a.bi.1.6		10
11.4	even	5	inner	429.2.n.b.235.3	yes	20
11.9	even	5		4719.2.a.bn.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.157.3	✓	20	1.1	even	1	trivial
429.2.n.b.235.3	yes	20	11.4	even	5	inner
4719.2.a.bi.1.6		10	11.2	odd	10
4719.2.a.bn.1.5		10	11.9	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.297979 + 0.216494i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.576112 + 1.77309i) q^{4} +(-0.859409 - 0.624397i) q^{5} +(0.297979 + 0.216494i) q^{6} +(1.08879 - 3.35095i) q^{7} +(-0.439831 - 1.35366i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.297979 + 0.216494i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.576112 + 1.77309i) q^{4} +(-0.859409 - 0.624397i) q^{5} +(0.297979 + 0.216494i) q^{6} +(1.08879 - 3.35095i) q^{7} +(-0.439831 - 1.35366i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.391264 q^{10} +(-0.965357 + 3.17302i) q^{11} +1.86434 q^{12} +(0.809017 - 0.587785i) q^{13} +(0.401025 + 1.23423i) q^{14} +(-0.328265 + 1.01030i) q^{15} +(-2.59244 - 1.88352i) q^{16} +(-3.20490 - 2.32850i) q^{17} +(0.113818 - 0.350295i) q^{18} +(-2.45762 - 7.56377i) q^{19} +(1.60223 - 1.16409i) q^{20} -3.52340 q^{21} +(-0.399286 - 1.15449i) q^{22} -1.09078 q^{23} +(-1.15149 + 0.836608i) q^{24} +(-1.19637 - 3.68206i) q^{25} +(-0.113818 + 0.350295i) q^{26} +(0.809017 + 0.587785i) q^{27} +(5.31427 + 3.86105i) q^{28} +(0.949350 - 2.92180i) q^{29} +(-0.120907 - 0.372115i) q^{30} +(5.78970 - 4.20646i) q^{31} +4.02691 q^{32} +(3.31604 - 0.0624091i) q^{33} +1.45910 q^{34} +(-3.02804 + 2.20000i) q^{35} +(-0.576112 - 1.77309i) q^{36} +(-0.875659 + 2.69500i) q^{37} +(2.36983 + 1.72178i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-0.467227 + 1.43798i) q^{40} +(-2.82868 - 8.70579i) q^{41} +(1.04990 - 0.762795i) q^{42} -3.48063 q^{43} +(-5.06991 - 3.53969i) q^{44} +1.06229 q^{45} +(0.325031 - 0.236149i) q^{46} +(1.79093 + 5.51192i) q^{47} +(-0.990225 + 3.04760i) q^{48} +(-4.38027 - 3.18245i) q^{49} +(1.15364 + 0.838168i) q^{50} +(-1.22416 + 3.76759i) q^{51} +(0.576112 + 1.77309i) q^{52} +(-6.40915 + 4.65652i) q^{53} -0.368322 q^{54} +(2.81086 - 2.12416i) q^{55} -5.01493 q^{56} +(-6.43413 + 4.67467i) q^{57} +(0.349667 + 1.07616i) q^{58} +(-2.15092 + 6.61986i) q^{59} +(-1.60223 - 1.16409i) q^{60} +(3.52614 + 2.56189i) q^{61} +(-0.814533 + 2.50687i) q^{62} +(1.08879 + 3.35095i) q^{63} +(3.98495 - 2.89524i) q^{64} -1.06229 q^{65} +(-0.974598 + 0.736500i) q^{66} +14.3737 q^{67} +(5.97503 - 4.34111i) q^{68} +(0.337071 + 1.03740i) q^{69} +(0.426004 - 1.31111i) q^{70} +(-10.0557 - 7.30586i) q^{71} +(1.15149 + 0.836608i) q^{72} +(-2.03720 + 6.26985i) q^{73} +(-0.322525 - 0.992629i) q^{74} +(-3.13214 + 2.27564i) q^{75} +14.8271 q^{76} +(9.58157 + 6.68962i) q^{77} +0.368322 q^{78} +(-6.94655 + 5.04697i) q^{79} +(1.05190 + 3.23743i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.72764 + 1.98175i) q^{82} +(9.82357 + 7.13724i) q^{83} +(2.02987 - 6.24730i) q^{84} +(1.30042 + 4.00227i) q^{85} +(1.03715 - 0.753536i) q^{86} -3.07216 q^{87} +(4.71979 - 0.0888283i) q^{88} -5.44615 q^{89} +(-0.316540 + 0.229979i) q^{90} +(-1.08879 - 3.35095i) q^{91} +(0.628414 - 1.93406i) q^{92} +(-5.78970 - 4.20646i) q^{93} +(-1.72696 - 1.25471i) q^{94} +(-2.61070 + 8.03490i) q^{95} +(-1.24438 - 3.82982i) q^{96} +(3.26300 - 2.37071i) q^{97} +1.99421 q^{98} +(-1.08407 - 3.13445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

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