LMFDB - Embedded newform 570.2.u.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

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("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.b.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-2.11334 + 3.66041i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-2.11334 + 3.66041i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(1.06031 + 1.83651i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.868241 - 4.92404i) q^{13} +(-3.23783 + 2.71686i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-3.10607 - 1.13052i) q^{17} -1.00000 q^{18} +(-3.93969 + 1.86516i) q^{19} -1.00000 q^{20} +(-3.97178 - 1.44561i) q^{21} +(0.368241 + 2.08840i) q^{22} +(3.08125 + 2.58548i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-3.97178 + 1.44561i) q^{28} +(2.53209 - 0.921605i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-5.29086 + 9.16404i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.62449 + 1.36310i) q^{33} +(-2.53209 - 2.12467i) q^{34} +(-0.733956 - 4.16247i) q^{35} +(-0.939693 - 0.342020i) q^{36} +10.4757 q^{37} +(-4.34002 + 0.405223i) q^{38} +5.00000 q^{39} +(-0.939693 - 0.342020i) q^{40} +(1.69594 + 9.61814i) q^{41} +(-3.23783 - 2.71686i) q^{42} +(4.94356 - 4.14814i) q^{43} +(-0.368241 + 2.08840i) q^{44} +(0.500000 - 0.866025i) q^{45} +(2.01114 + 3.48340i) q^{46} +(8.35117 - 3.03958i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-5.43242 - 9.40923i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.573978 - 3.25519i) q^{51} +(3.83022 - 3.21394i) q^{52} +(6.05303 + 5.07910i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-1.99273 - 0.725293i) q^{55} -4.22668 q^{56} +(-2.52094 - 3.55596i) q^{57} +2.69459 q^{58} +(8.92514 + 3.24849i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-9.88713 - 8.29628i) q^{61} +(-8.10607 + 6.80180i) q^{62} +(0.733956 - 4.16247i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(-1.99273 + 0.725293i) q^{66} +(2.57398 - 0.936851i) q^{67} +(-1.65270 - 2.86257i) q^{68} +(-2.01114 + 3.48340i) q^{69} +(0.733956 - 4.16247i) q^{70} +(-7.04189 + 5.90885i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(0.0983261 + 0.557635i) q^{73} +(9.84389 + 3.58288i) q^{74} +1.00000 q^{75} +(-4.21688 - 1.10359i) q^{76} -8.96316 q^{77} +(4.69846 + 1.71010i) q^{78} +(-2.24123 - 12.7106i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.69594 + 9.61814i) q^{82} +(3.41147 - 5.90885i) q^{83} +(-2.11334 - 3.66041i) q^{84} +(3.10607 - 1.13052i) q^{85} +(6.06418 - 2.20718i) q^{86} +(1.34730 + 2.33359i) q^{87} +(-1.06031 + 1.83651i) q^{88} +(1.42215 - 8.06542i) q^{89} +(0.766044 - 0.642788i) q^{90} +(16.1891 + 13.5843i) q^{91} +(0.698463 + 3.96118i) q^{92} +(-9.94356 - 3.61916i) q^{93} +8.88713 q^{94} +(1.81908 - 3.96118i) q^{95} -1.00000 q^{96} +(7.83750 + 2.85262i) q^{97} +(-1.88666 - 10.6998i) q^{98} +(-1.62449 - 1.36310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	−2.11334	+	3.66041i	−0.798768	+	1.38351i	0.121651	+	0.992573i	$0.461181\pi$
$7$	−2.11334	+	3.66041i	−0.798768	+	1.38351i	−0.920419	+	0.390933i	$0.872152\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.939693	+	0.342020i	−0.297157	+	0.108156i
$11$	1.06031	+	1.83651i	0.319695	+	0.553727i	0.980424	−	0.196897i	$-0.0630863\pi$
$11$	1.06031	+	1.83651i	0.319695	+	0.553727i	−0.660730	+	0.750624i	$0.729753\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.868241	−	4.92404i	0.240807	−	1.36568i	−0.589226	−	0.807968i	$-0.700567\pi$
$13$	0.868241	−	4.92404i	0.240807	−	1.36568i	0.830033	−	0.557714i	$-0.188322\pi$
$14$	−3.23783	+	2.71686i	−0.865345	+	0.726111i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−3.10607	−	1.13052i	−0.753332	−	0.274190i	−0.0633248	−	0.997993i	$-0.520170\pi$
$17$	−3.10607	−	1.13052i	−0.753332	−	0.274190i	−0.690007	+	0.723803i	$0.742393\pi$
$18$	−1.00000			−0.235702
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$20$	−1.00000			−0.223607
$21$	−3.97178	−	1.44561i	−0.866714	−	0.315458i
$22$	0.368241	+	2.08840i	0.0785092	+	0.445248i
$23$	3.08125	+	2.58548i	0.642485	+	0.539109i	0.904780	−	0.425878i	$-0.140035\pi$
$23$	3.08125	+	2.58548i	0.642485	+	0.539109i	−0.262295	+	0.964988i	$0.584479\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−3.97178	+	1.44561i	−0.750596	+	0.273195i
$29$	2.53209	−	0.921605i	0.470197	−	0.171138i	−0.0960445	−	0.995377i	$-0.530619\pi$
$29$	2.53209	−	0.921605i	0.470197	−	0.171138i	0.566242	+	0.824239i	$0.308397\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−5.29086	+	9.16404i	−0.950266	+	1.64591i	−0.205420	+	0.978674i	$0.565856\pi$
$31$	−5.29086	+	9.16404i	−0.950266	+	1.64591i	−0.744847	+	0.667236i	$0.767477\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−1.62449	+	1.36310i	−0.282787	+	0.237286i
$34$	−2.53209	−	2.12467i	−0.434250	−	0.364379i
$35$	−0.733956	−	4.16247i	−0.124061	−	0.703586i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	10.4757			1.72219			0.861093	−	0.508447i	$-0.169780\pi$
$37$	10.4757			1.72219			0.861093	+	0.508447i	$0.169780\pi$
$38$	−4.34002	+	0.405223i	−0.704045	+	0.0657358i
$39$	5.00000			0.800641
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	1.69594	+	9.61814i	0.264861	+	1.50210i	0.769431	+	0.638730i	$0.220540\pi$
$41$	1.69594	+	9.61814i	0.264861	+	1.50210i	−0.504570	+	0.863371i	$0.668349\pi$
$42$	−3.23783	−	2.71686i	−0.499607	−	0.419220i
$43$	4.94356	−	4.14814i	0.753886	−	0.632586i	−0.182641	−	0.983180i	$-0.558465\pi$
$43$	4.94356	−	4.14814i	0.753886	−	0.632586i	0.936528	+	0.350594i	$0.114020\pi$
$44$	−0.368241	+	2.08840i	−0.0555144	+	0.314838i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	2.01114	+	3.48340i	0.296527	+	0.513600i
$47$	8.35117	−	3.03958i	1.21814	−	0.443368i	0.348622	−	0.937264i	$-0.386650\pi$
$47$	8.35117	−	3.03958i	1.21814	−	0.443368i	0.869521	+	0.493896i	$0.164428\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	−5.43242	−	9.40923i	−0.776060	−	1.34418i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.573978	−	3.25519i	0.0803730	−	0.455818i
$52$	3.83022	−	3.21394i	0.531156	−	0.445693i
$53$	6.05303	+	5.07910i	0.831448	+	0.697668i	0.955623	−	0.294593i	$-0.0951839\pi$
$53$	6.05303	+	5.07910i	0.831448	+	0.697668i	−0.124175	+	0.992260i	$0.539628\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	−1.99273	−	0.725293i	−0.268699	−	0.0977985i
$56$	−4.22668			−0.564814
$57$	−2.52094	−	3.55596i	−0.333907	−	0.470998i
$58$	2.69459			0.353817
$59$	8.92514	+	3.24849i	1.16195	+	0.422917i	0.849795	−	0.527113i	$-0.176725\pi$
$59$	8.92514	+	3.24849i	1.16195	+	0.422917i	0.312159	+	0.950030i	$0.398948\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	−9.88713	−	8.29628i	−1.26592	−	1.06223i	−0.995026	−	0.0996203i	$-0.968237\pi$
$61$	−9.88713	−	8.29628i	−1.26592	−	1.06223i	−0.270891	−	0.962610i	$-0.587318\pi$
$62$	−8.10607	+	6.80180i	−1.02947	+	0.863829i
$63$	0.733956	−	4.16247i	0.0924697	−	0.524422i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$	−1.99273	+	0.725293i	−0.245288	+	0.0892774i
$67$	2.57398	−	0.936851i	0.314461	−	0.114455i	−0.179968	−	0.983673i	$-0.557599\pi$
$67$	2.57398	−	0.936851i	0.314461	−	0.114455i	0.494429	+	0.869218i	$0.335377\pi$
$68$	−1.65270	−	2.86257i	−0.200420	−	0.347137i
$69$	−2.01114	+	3.48340i	−0.242113	+	0.419353i
$70$	0.733956	−	4.16247i	0.0877245	−	0.497510i
$71$	−7.04189	+	5.90885i	−0.835718	+	0.701251i	−0.956596	−	0.291416i	$-0.905874\pi$
$71$	−7.04189	+	5.90885i	−0.835718	+	0.701251i	0.120878	+	0.992667i	$0.461429\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	0.0983261	+	0.557635i	0.0115082	+	0.0652662i	0.990021	−	0.140920i	$-0.0450059\pi$
$73$	0.0983261	+	0.557635i	0.0115082	+	0.0652662i	−0.978513	+	0.206186i	$0.933895\pi$
$74$	9.84389	+	3.58288i	1.14433	+	0.416502i
$75$	1.00000			0.115470
$76$	−4.21688	−	1.10359i	−0.483709	−	0.126590i
$77$	−8.96316			−1.02145
$78$	4.69846	+	1.71010i	0.531996	+	0.193631i
$79$	−2.24123	−	12.7106i	−0.252158	−	1.43006i	−0.803264	−	0.595624i	$-0.796905\pi$
$79$	−2.24123	−	12.7106i	−0.252158	−	1.43006i	0.551106	−	0.834436i	$-0.314206\pi$
$80$	−0.766044	−	0.642788i	−0.0856464	−	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.69594	+	9.61814i	−0.187285	+	1.06215i
$83$	3.41147	−	5.90885i	0.374458	−	0.648580i	−0.615788	−	0.787912i	$-0.711162\pi$
$83$	3.41147	−	5.90885i	0.374458	−	0.648580i	0.990246	+	0.139332i	$0.0444955\pi$
$84$	−2.11334	−	3.66041i	−0.230584	−	0.399384i
$85$	3.10607	−	1.13052i	0.336900	−	0.122622i
$86$	6.06418	−	2.20718i	0.653917	−	0.238006i
$87$	1.34730	+	2.33359i	0.144445	+	0.250187i
$88$	−1.06031	+	1.83651i	−0.113029	+	0.195772i
$89$	1.42215	−	8.06542i	0.150748	−	0.854933i	−0.811823	−	0.583903i	$-0.801525\pi$
$89$	1.42215	−	8.06542i	0.150748	−	0.854933i	0.962571	−	0.271030i	$-0.0873642\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	16.1891	+	13.5843i	1.69708	+	1.42402i
$92$	0.698463	+	3.96118i	0.0728198	+	0.412982i
$93$	−9.94356	−	3.61916i	−1.03110	−	0.375290i
$94$	8.88713			0.916637
$95$	1.81908	−	3.96118i	0.186633	−	0.406409i
$96$	−1.00000			−0.102062
$97$	7.83750	+	2.85262i	0.795777	+	0.289639i	0.707735	−	0.706478i	$-0.249717\pi$
$97$	7.83750	+	2.85262i	0.795777	+	0.289639i	0.0880417	+	0.996117i	$0.471939\pi$
$98$	−1.88666	−	10.6998i	−0.190581	−	1.08084i
$99$	−1.62449	−	1.36310i	−0.163267	−	0.136997i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	0.0368366	−	0.208911i	0.00366538	−	0.0207874i	−0.982920	−	0.184032i	$-0.941085\pi$
$101$	0.0368366	−	0.208911i	0.00366538	−	0.0207874i	0.986586	+	0.163245i	$0.0521960\pi$
$102$	1.65270	−	2.86257i	0.163642	−	0.283436i
$103$	−4.80793	−	8.32759i	−0.473740	−	0.820541i	0.525808	−	0.850603i	$-0.323763\pi$
$103$	−4.80793	−	8.32759i	−0.473740	−	0.820541i	−0.999548	+	0.0300618i	$0.990430\pi$
$104$	4.69846	−	1.71010i	0.460722	−	0.167689i
$105$	3.97178	−	1.44561i	0.387606	−	0.141077i
$106$	3.95084	+	6.84305i	0.383739	+	0.664656i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−5.04189	+	4.23065i	−0.482925	+	0.405223i	−0.851483	−	0.524382i	$-0.824296\pi$
$109$	−5.04189	+	4.23065i	−0.482925	+	0.405223i	0.368557	+	0.929605i	$0.379852\pi$
$110$	−1.62449	−	1.36310i	−0.154889	−	0.129967i
$111$	1.81908	+	10.3165i	0.172659	+	0.979199i
$112$	−3.97178	−	1.44561i	−0.375298	−	0.136597i
$113$	2.08378			0.196025			0.0980127	−	0.995185i	$-0.468751\pi$
$113$	2.08378			0.196025			0.0980127	+	0.995185i	$0.468751\pi$
$114$	−1.15270	−	4.20372i	−0.107961	−	0.393715i
$115$	−4.02229			−0.375080
$116$	2.53209	+	0.921605i	0.235099	+	0.0855689i
$117$	0.868241	+	4.92404i	0.0802689	+	0.455228i
$118$	7.27584	+	6.10516i	0.669796	+	0.562025i
$119$	10.7023	−	8.98032i	0.981081	−	0.823225i
$120$	0.173648	−	0.984808i	0.0158518	−	0.0899002i
$121$	3.25150	−	5.63176i	0.295591	−	0.511978i
$122$	−6.45336	−	11.1776i	−0.584260	−	1.01197i
$123$	−9.17752	+	3.34034i	−0.827509	+	0.301189i
$124$	−9.94356	+	3.61916i	−0.892958	+	0.325010i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	2.11334	−	3.66041i	0.188271	−	0.326096i
$127$	2.39306	−	13.5717i	0.212349	−	1.20429i	−0.673098	−	0.739553i	$-0.735037\pi$
$127$	2.39306	−	13.5717i	0.212349	−	1.20429i	0.885447	−	0.464740i	$-0.153852\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	4.94356	+	4.14814i	0.435256	+	0.365224i
$130$	0.868241	+	4.92404i	0.0761498	+	0.431867i
$131$	18.3614	+	6.68302i	1.60425	+	0.583898i	0.980290	−	0.197562i	$-0.0633024\pi$
$131$	18.3614	+	6.68302i	1.60425	+	0.583898i	0.623956	+	0.781460i	$0.285525\pi$
$132$	−2.12061			−0.184576
$133$	1.49866	−	18.3626i	0.129950	−	1.59224i
$134$	2.73917			0.236628
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	−0.573978	−	3.25519i	−0.0492182	−	0.279130i
$137$	16.5594	+	13.8950i	1.41477	+	1.18713i	0.954074	+	0.299572i	$0.0968438\pi$
$137$	16.5594	+	13.8950i	1.41477	+	1.18713i	0.460694	+	0.887559i	$0.347601\pi$
$138$	−3.08125	+	2.58548i	−0.262294	+	0.220090i
$139$	−1.57738	+	8.94578i	−0.133792	+	0.758771i	0.841902	+	0.539631i	$0.181436\pi$
$139$	−1.57738	+	8.94578i	−0.133792	+	0.758771i	−0.975693	+	0.219140i	$0.929675\pi$
$140$	2.11334	−	3.66041i	0.178610	−	0.309361i
$141$	4.44356	+	7.69648i	0.374216	+	0.648160i
$142$	−8.63816	+	3.14403i	−0.724898	+	0.263841i
$143$	9.96363	−	3.62646i	0.833201	−	0.303260i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.34730	+	2.33359i	−0.111887	+	0.193794i
$146$	−0.0983261	+	0.557635i	−0.00813752	+	0.0461502i
$147$	8.32295	−	6.98378i	0.686465	−	0.576013i
$148$	8.02481	+	6.73362i	0.659636	+	0.553500i
$149$	−2.80066	−	15.8833i	−0.229439	−	1.30121i	−0.854015	−	0.520249i	$-0.825839\pi$
$149$	−2.80066	−	15.8833i	−0.229439	−	1.30121i	0.624576	−	0.780964i	$-0.285272\pi$
$150$	0.939693	+	0.342020i	0.0767256	+	0.0279258i
$151$	−19.7297			−1.60558			−0.802789	−	0.596263i	$-0.796652\pi$
$151$	−19.7297			−1.60558			−0.802789	+	0.596263i	$0.796652\pi$
$152$	−3.58512	−	2.47929i	−0.290792	−	0.201097i
$153$	3.30541			0.267226
$154$	−8.42262	−	3.06558i	−0.678714	−	0.247032i
$155$	−1.83750	−	10.4210i	−0.147591	−	0.837032i
$156$	3.83022	+	3.21394i	0.306663	+	0.257321i
$157$	−3.52687	+	2.95940i	−0.281475	+	0.236186i	−0.772584	−	0.634912i	$-0.781036\pi$
$157$	−3.52687	+	2.95940i	−0.281475	+	0.236186i	0.491109	+	0.871098i	$0.336592\pi$
$158$	2.24123	−	12.7106i	0.178303	−	1.01120i
$159$	−3.95084	+	6.84305i	−0.313322	+	0.542689i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−15.9757	+	5.81466i	−1.25906	+	0.458260i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	−3.06418	−	5.30731i	−0.240005	−	0.415701i	0.720710	−	0.693236i	$-0.243816\pi$
$163$	−3.06418	−	5.30731i	−0.240005	−	0.415701i	−0.960715	+	0.277535i	$0.910482\pi$
$164$	−4.88326	+	8.45805i	−0.381318	+	0.660462i
$165$	0.368241	−	2.08840i	0.0286675	−	0.162582i
$166$	5.22668	−	4.38571i	0.405669	−	0.340397i
$167$	4.87346	+	4.08931i	0.377119	+	0.316441i	0.811570	−	0.584255i	$-0.198613\pi$
$167$	4.87346	+	4.08931i	0.377119	+	0.316441i	−0.434451	+	0.900695i	$0.643058\pi$
$168$	−0.733956	−	4.16247i	−0.0566259	−	0.321141i
$169$	−11.2763	−	4.10424i	−0.867409	−	0.315711i
$170$	3.30541			0.253513
$171$	3.06418	−	3.10013i	0.234324	−	0.237073i
$172$	6.45336			0.492064
$173$	−14.2417	−	5.18355i	−1.08278	−	0.394098i	−0.261836	−	0.965112i	$-0.584328\pi$
$173$	−14.2417	−	5.18355i	−1.08278	−	0.394098i	−0.820940	+	0.571014i	$0.806550\pi$
$174$	0.467911	+	2.65366i	0.0354722	+	0.201173i
$175$	3.23783	+	2.71686i	0.244757	+	0.205375i
$176$	−1.62449	+	1.36310i	−0.122450	+	0.102748i
$177$	−1.64930	+	9.35365i	−0.123969	+	0.703063i
$178$	4.09492	−	7.09261i	0.306927	−	0.531614i
$179$	0.969255	+	1.67880i	0.0724455	+	0.125479i	0.899973	−	0.435947i	$-0.143586\pi$
$179$	0.969255	+	1.67880i	0.0724455	+	0.125479i	−0.827527	+	0.561426i	$0.810253\pi$
$180$	0.939693	−	0.342020i	0.0700406	−	0.0254927i
$181$	−11.3969	+	4.14814i	−0.847127	+	0.308329i	−0.728868	−	0.684654i	$-0.759953\pi$
$181$	−11.3969	+	4.14814i	−0.847127	+	0.308329i	−0.118259	+	0.992983i	$0.537731\pi$
$182$	10.5667	+	18.3021i	0.783256	+	1.35664i
$183$	6.45336	−	11.1776i	0.477046	−	0.826268i
$184$	−0.698463	+	3.96118i	−0.0514914	+	0.292022i
$185$	−8.02481	+	6.73362i	−0.589996	+	0.495066i
$186$	−8.10607	−	6.80180i	−0.594366	−	0.498732i
$187$	−1.21719	−	6.90301i	−0.0890095	−	0.504798i
$188$	8.35117	+	3.03958i	0.609071	+	0.221684i
$189$	4.22668			0.307446
$190$	3.06418	−	3.10013i	0.222299	−	0.224907i
$191$	6.53714			0.473011			0.236505	−	0.971630i	$-0.423998\pi$
$191$	6.53714			0.473011			0.236505	+	0.971630i	$0.423998\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	0.453363	+	2.57115i	0.0326338	+	0.185075i	0.996767	−	0.0803421i	$-0.0256013\pi$
$193$	0.453363	+	2.57115i	0.0326338	+	0.185075i	−0.964134	+	0.265418i	$0.914490\pi$
$194$	6.38919	+	5.36116i	0.458717	+	0.384909i
$195$	−3.83022	+	3.21394i	−0.274288	+	0.230155i
$196$	1.88666	−	10.6998i	0.134761	−	0.764270i
$197$	0.144086	−	0.249563i	0.0102657	−	0.0177807i	−0.860847	−	0.508864i	$-0.830066\pi$
$197$	0.144086	−	0.249563i	0.0102657	−	0.0177807i	0.871113	+	0.491083i	$0.163399\pi$
$198$	−1.06031	−	1.83651i	−0.0753528	−	0.130515i
$199$	−8.79561	+	3.20134i	−0.623504	+	0.226937i	−0.634402	−	0.773004i	$-0.718753\pi$
$199$	−8.79561	+	3.20134i	−0.623504	+	0.226937i	0.0108975	+	0.999941i	$0.496531\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	1.36959	+	2.37219i	0.0966031	+	0.167321i
$202$	0.106067	−	0.183713i	0.00746284	−	0.0129260i
$203$	−1.97771	+	11.2162i	−0.138808	+	0.787220i
$204$	2.53209	−	2.12467i	0.177282	−	0.148757i
$205$	−7.48158	−	6.27779i	−0.522536	−	0.438460i
$206$	−1.66978	−	9.46978i	−0.116339	−	0.659791i
$207$	−3.77972	−	1.37570i	−0.262708	−	0.0956180i
$208$	5.00000			0.346688
$209$	−7.60266	−	5.25763i	−0.525887	−	0.363678i
$210$	4.22668			0.291669
$211$	23.0646	+	8.39484i	1.58784	+	0.577925i	0.976889	−	0.213747i	$-0.0685668\pi$
$211$	23.0646	+	8.39484i	1.58784	+	0.577925i	0.610947	+	0.791672i	$0.290789\pi$
$212$	1.37211	+	7.78163i	0.0942370	+	0.534445i
$213$	−7.04189	−	5.90885i	−0.482502	−	0.404867i
$214$	−9.19253	+	7.71345i	−0.628389	+	0.527281i
$215$	−1.12061	+	6.35532i	−0.0764253	+	0.433429i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−22.3628	−	38.7335i	−1.51808	−	2.62940i
$218$	−6.18479	+	2.25108i	−0.418887	+	0.152462i
$219$	−0.532089	+	0.193665i	−0.0359552	+	0.0130866i
$220$	−1.06031	−	1.83651i	−0.0714859	−	0.123817i
$221$	−8.26352	+	14.3128i	−0.555864	+	0.962785i
$222$	−1.81908	+	10.3165i	−0.122089	+	0.692398i
$223$	6.78699	−	5.69496i	0.454490	−	0.381363i	−0.386609	−	0.922244i	$-0.626354\pi$
$223$	6.78699	−	5.69496i	0.454490	−	0.381363i	0.841099	+	0.540881i	$0.181909\pi$
$224$	−3.23783	−	2.71686i	−0.216336	−	0.181528i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	1.95811	+	0.712694i	0.130252	+	0.0474077i
$227$	−14.7939			−0.981902			−0.490951	−	0.871187i	$-0.663351\pi$
$227$	−14.7939			−0.981902			−0.490951	+	0.871187i	$0.663351\pi$
$228$	0.354570	−	4.34445i	0.0234820	−	0.287718i
$229$	−0.0837781			−0.00553621			−0.00276811	−	0.999996i	$-0.500881\pi$
$229$	−0.0837781			−0.00553621			−0.00276811	+	0.999996i	$0.500881\pi$
$230$	−3.77972	−	1.37570i	−0.249227	−	0.0907112i
$231$	−1.55644	−	8.82699i	−0.102406	−	0.580773i
$232$	2.06418	+	1.73205i	0.135520	+	0.113715i
$233$	1.43376	−	1.20307i	0.0939289	−	0.0788157i	−0.594614	−	0.804011i	$-0.702695\pi$
$233$	1.43376	−	1.20307i	0.0939289	−	0.0788157i	0.688543	+	0.725196i	$0.258251\pi$
$234$	−0.868241	+	4.92404i	−0.0567587	+	0.321894i
$235$	−4.44356	+	7.69648i	−0.289866	+	0.502063i
$236$	4.74897	+	8.22546i	0.309132	+	0.535432i
$237$	12.1284	−	4.41436i	0.787821	−	0.286744i
$238$	13.1284	−	4.77833i	0.850985	−	0.309733i
$239$	12.7665	+	22.1122i	0.825797	+	1.43032i	0.901309	+	0.433177i	$0.142608\pi$
$239$	12.7665	+	22.1122i	0.825797	+	1.43032i	−0.0755117	+	0.997145i	$0.524059\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.72028	+	9.75622i	−0.110813	+	0.628453i	0.877925	+	0.478798i	$0.158927\pi$
$241$	−1.72028	+	9.75622i	−0.110813	+	0.628453i	−0.988738	+	0.149655i	$0.952184\pi$
$242$	4.98158	−	4.18004i	0.320228	−	0.268703i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	−2.24123	−	12.7106i	−0.143480	−	0.813716i
$245$	10.2096	+	3.71599i	0.652268	+	0.237406i
$246$	−9.76651			−0.622690
$247$	5.76352	+	21.0186i	0.366724	+	1.33738i
$248$	−10.5817			−0.671940
$249$	6.41147	+	2.33359i	0.406311	+	0.147885i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−4.14337	−	3.47670i	−0.261527	−	0.219447i	0.502590	−	0.864525i	$-0.332381\pi$
$251$	−4.14337	−	3.47670i	−0.261527	−	0.219447i	−0.764117	+	0.645078i	$0.776825\pi$
$252$	3.23783	−	2.71686i	0.203964	−	0.171146i
$253$	−1.48117	+	8.40014i	−0.0931204	+	0.528112i
$254$	6.89053	−	11.9347i	0.432350	−	0.748853i
$255$	1.65270	+	2.86257i	0.103496	+	0.179261i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	0.972659	−	0.354019i	0.0606728	−	0.0220831i	−0.311505	−	0.950244i	$-0.600833\pi$
$257$	0.972659	−	0.354019i	0.0606728	−	0.0220831i	0.372178	+	0.928161i	$0.378611\pi$
$258$	3.22668	+	5.58878i	0.200884	+	0.347942i
$259$	−22.1386	+	38.3452i	−1.37563	+	2.38266i
$260$	−0.868241	+	4.92404i	−0.0538460	+	0.305376i
$261$	−2.06418	+	1.73205i	−0.127769	+	0.107211i
$262$	14.9684	+	12.5600i	0.924749	+	0.775957i
$263$	−2.94996	−	16.7301i	−0.181902	−	1.03162i	−0.929871	−	0.367885i	$-0.880082\pi$
$263$	−2.94996	−	16.7301i	−0.181902	−	1.03162i	0.747969	−	0.663734i	$-0.231029\pi$
$264$	−1.99273	−	0.725293i	−0.122644	−	0.0446387i
$265$	−7.90167			−0.485396
$266$	7.68866	−	16.7427i	0.471422	−	1.02656i
$267$	8.18984			0.501210
$268$	2.57398	+	0.936851i	0.157231	+	0.0572273i
$269$	−0.179740	−	1.01936i	−0.0109589	−	0.0621513i	0.978838	−	0.204637i	$-0.0656015\pi$
$269$	−0.179740	−	1.01936i	−0.0109589	−	0.0621513i	−0.989797	+	0.142486i	$0.954490\pi$
$270$	0.766044	+	0.642788i	0.0466200	+	0.0391188i
$271$	13.1702	−	11.0511i	0.800035	−	0.671309i	−0.148172	−	0.988962i	$-0.547339\pi$
$271$	13.1702	−	11.0511i	0.800035	−	0.671309i	0.948207	+	0.317652i	$0.102894\pi$
$272$	0.573978	−	3.25519i	0.0348025	−	0.197375i
$273$	−10.5667	+	18.3021i	−0.639526	+	1.10769i
$274$	10.8084	+	18.7207i	0.652959	+	1.13096i
$275$	1.99273	−	0.725293i	0.120166	−	0.0437368i
$276$	−3.77972	+	1.37570i	−0.227512	+	0.0828076i
$277$	−0.110815	−	0.191936i	−0.00665820	−	0.0115323i	0.862677	−	0.505755i	$-0.168786\pi$
$277$	−0.110815	−	0.191936i	−0.00665820	−	0.0115323i	−0.869335	+	0.494223i	$0.835453\pi$
$278$	−4.54189	+	7.86678i	−0.272404	+	0.471818i
$279$	1.83750	−	10.4210i	0.110008	−	0.623886i
$280$	3.23783	−	2.71686i	0.193497	−	0.162363i
$281$	−1.92468	−	1.61500i	−0.114817	−	0.0963426i	0.583572	−	0.812062i	$-0.301655\pi$
$281$	−1.92468	−	1.61500i	−0.114817	−	0.0963426i	−0.698388	+	0.715719i	$0.746099\pi$
$282$	1.54323	+	8.75211i	0.0918982	+	0.521181i
$283$	−0.532089	−	0.193665i	−0.0316294	−	0.0115122i	0.326157	−	0.945316i	$-0.394246\pi$
$283$	−0.532089	−	0.193665i	−0.0316294	−	0.0115122i	−0.357786	+	0.933803i	$0.616468\pi$
$284$	−9.19253			−0.545476
$285$	4.21688	+	1.10359i	0.249786	+	0.0653710i
$286$	10.6031			0.626973
$287$	−38.7904	−	14.1186i	−2.28973	−	0.833393i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	−4.65317	−	3.90447i	−0.273716	−	0.229675i
$290$	−2.06418	+	1.73205i	−0.121213	+	0.101710i
$291$	−1.44831	+	8.21378i	−0.0849015	+	0.481500i
$292$	−0.283119	+	0.490376i	−0.0165683	+	0.0286971i
$293$	−15.6951	−	27.1846i	−0.916915	−	1.58814i	−0.804073	−	0.594531i	$-0.797338\pi$
$293$	−15.6951	−	27.1846i	−0.916915	−	1.58814i	−0.112842	−	0.993613i	$-0.535995\pi$
$294$	10.2096	−	3.71599i	0.595436	−	0.216721i
$295$	−8.92514	+	3.24849i	−0.519642	+	0.189134i
$296$	5.23783	+	9.07218i	0.304442	+	0.527310i
$297$	1.06031	−	1.83651i	0.0615253	−	0.106565i
$298$	2.80066	−	15.8833i	0.162238	−	0.920097i
$299$	15.4063	−	12.9274i	0.890967	−	0.747610i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	4.73648	+	26.8619i	0.273006	+	1.54830i
$302$	−18.5398	−	6.74795i	−1.06685	−	0.388301i
$303$	0.212134			0.0121868
$304$	−2.52094	−	3.55596i	−0.144586	−	0.203948i
$305$	12.9067			0.739037
$306$	3.10607	+	1.13052i	0.177562	+	0.0646273i
$307$	−2.30810	−	13.0899i	−0.131730	−	0.747078i	−0.977081	−	0.212867i	$-0.931720\pi$
$307$	−2.30810	−	13.0899i	−0.131730	−	0.747078i	0.845351	−	0.534211i	$-0.179391\pi$
$308$	−6.86618	−	5.76141i	−0.391237	−	0.328287i
$309$	7.36618	−	6.18096i	0.419047	−	0.351623i
$310$	1.83750	−	10.4210i	0.104363	−	0.591871i
$311$	2.83750	−	4.91469i	0.160900	−	0.278686i	−0.774292	−	0.632829i	$-0.781894\pi$
$311$	2.83750	−	4.91469i	0.160900	−	0.278686i	0.935192	+	0.354142i	$0.115227\pi$
$312$	2.50000	+	4.33013i	0.141535	+	0.245145i
$313$	−12.0770	+	4.39566i	−0.682631	+	0.248457i	−0.659977	−	0.751286i	$-0.729434\pi$
$313$	−12.0770	+	4.39566i	−0.682631	+	0.248457i	−0.0226541	+	0.999743i	$0.507212\pi$
$314$	−4.32635	+	1.57466i	−0.244150	+	0.0888634i
$315$	2.11334	+	3.66041i	0.119073	+	0.206241i
$316$	6.45336	−	11.1776i	0.363030	−	0.628786i
$317$	1.19800	−	6.79417i	0.0672862	−	0.381599i	−0.932505	−	0.361157i	$-0.882382\pi$
$317$	1.19800	−	6.79417i	0.0672862	−	0.381599i	0.999791	−	0.0204415i	$-0.00650718\pi$
$318$	−6.05303	+	5.07910i	−0.339437	+	0.284822i
$319$	4.37733	+	3.67301i	0.245083	+	0.205649i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	−11.2763	−	4.10424i	−0.629382	−	0.229076i
$322$	−17.0009			−0.947425
$323$	14.3455	−	1.33943i	0.798207	−	0.0745277i
$324$	1.00000			0.0555556
$325$	−4.69846	−	1.71010i	−0.260624	−	0.0948593i
$326$	−1.06418	−	6.03525i	−0.0589394	−	0.334262i
$327$	−5.04189	−	4.23065i	−0.278817	−	0.233955i
$328$	−7.48158	+	6.27779i	−0.413101	+	0.346633i
$329$	−6.52276	+	36.9924i	−0.359611	+	2.03946i
$330$	1.06031	−	1.83651i	0.0583680	−	0.101096i
$331$	10.7096	+	18.5496i	0.588653	+	1.01958i	0.994409	+	0.105596i	$0.0336750\pi$
$331$	10.7096	+	18.5496i	0.588653	+	1.01958i	−0.405756	+	0.913981i	$0.632992\pi$
$332$	6.41147	−	2.33359i	0.351875	−	0.128072i
$333$	−9.84389	+	3.58288i	−0.539442	+	0.196341i
$334$	3.18092	+	5.50952i	0.174052	+	0.301467i
$335$	−1.36959	+	2.37219i	−0.0748284	+	0.129607i
$336$	0.733956	−	4.16247i	0.0400406	−	0.227081i
$337$	−13.7365	+	11.5263i	−0.748274	+	0.627876i	−0.935046	−	0.354527i	$-0.884642\pi$
$337$	−13.7365	+	11.5263i	−0.748274	+	0.627876i	0.186772	+	0.982403i	$0.440197\pi$
$338$	−9.19253	−	7.71345i	−0.500008	−	0.419556i
$339$	0.361844	+	2.05212i	0.0196527	+	0.111456i
$340$	3.10607	+	1.13052i	0.168450	+	0.0613108i
$341$	−22.4397			−1.21518
$342$	3.93969	−	1.86516i	0.213034	−	0.100856i
$343$	16.3354			0.882031
$344$	6.06418	+	2.20718i	0.326959	+	0.119003i
$345$	−0.698463	−	3.96118i	−0.0376040	−	0.213263i
$346$	−11.6099	−	9.74189i	−0.624154	−	0.523727i
$347$	−9.03003	+	7.57709i	−0.484757	+	0.406760i	−0.852143	−	0.523309i	$-0.824697\pi$
$347$	−9.03003	+	7.57709i	−0.484757	+	0.406760i	0.367386	+	0.930069i	$0.380253\pi$
$348$	−0.467911	+	2.65366i	−0.0250827	+	0.142251i
$349$	−0.120615	+	0.208911i	−0.00645636	+	0.0111827i	−0.869236	−	0.494398i	$-0.835388\pi$
$349$	−0.120615	+	0.208911i	−0.00645636	+	0.0111827i	0.862779	+	0.505581i	$0.168722\pi$
$350$	2.11334	+	3.66041i	0.112963	+	0.195657i
$351$	−4.69846	+	1.71010i	−0.250785	+	0.0912784i
$352$	−1.99273	+	0.725293i	−0.106213	+	0.0386582i
$353$	8.58172	+	14.8640i	0.456759	+	0.791129i	0.998787	−	0.0492306i	$-0.0156769\pi$
$353$	8.58172	+	14.8640i	0.456759	+	0.791129i	−0.542029	+	0.840360i	$0.682344\pi$
$354$	−4.74897	+	8.22546i	−0.252405	+	0.437178i
$355$	1.59627	−	9.05288i	0.0847210	−	0.480477i
$356$	6.27379	−	5.26433i	0.332510	−	0.279009i
$357$	10.7023	+	8.98032i	0.566428	+	0.475289i
$358$	0.336619	+	1.90906i	0.0177909	+	0.100897i
$359$	−25.6459	−	9.33434i	−1.35354	−	0.492648i	−0.439488	−	0.898248i	$-0.644840\pi$
$359$	−25.6459	−	9.33434i	−1.35354	−	0.492648i	−0.914050	+	0.405601i	$0.867062\pi$
$360$	1.00000			0.0527046
$361$	12.0424	−	14.6963i	0.633808	−	0.773490i
$362$	−12.1284			−0.637452
$363$	6.11081	+	2.22415i	0.320735	+	0.116738i
$364$	3.66978	+	20.8123i	0.192349	+	1.09086i
$365$	−0.433763	−	0.363970i	−0.0227042	−	0.0190511i
$366$	9.88713	−	8.29628i	0.516808	−	0.433654i
$367$	−0.143619	+	0.814502i	−0.00749683	+	0.0425167i	−0.988327	−	0.152349i	$-0.951316\pi$
$367$	−0.143619	+	0.814502i	−0.00749683	+	0.0425167i	0.980830	+	0.194866i	$0.0624272\pi$
$368$	−2.01114	+	3.48340i	−0.104838	+	0.181585i
$369$	−4.88326	−	8.45805i	−0.254212	−	0.440308i
$370$	−9.84389	+	3.58288i	−0.511760	+	0.186265i
$371$	−31.3837	+	11.4227i	−1.62936	+	0.593039i
$372$	−5.29086	−	9.16404i	−0.274318	−	0.475133i
$373$	−7.73190	+	13.3920i	−0.400342	+	0.693413i	−0.993767	−	0.111476i	$-0.964442\pi$
$373$	−7.73190	+	13.3920i	−0.400342	+	0.693413i	0.593425	+	0.804890i	$0.297775\pi$
$374$	1.21719	−	6.90301i	0.0629392	−	0.356946i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	6.80793	+	5.71253i	0.351092	+	0.294601i
$377$	−2.33956	−	13.2683i	−0.120493	−	0.683351i
$378$	3.97178	+	1.44561i	0.204286	+	0.0743542i
$379$	15.3013			0.785974			0.392987	−	0.919544i	$-0.371442\pi$
$379$	15.3013			0.785974			0.392987	+	0.919544i	$0.371442\pi$
$380$	3.93969	−	1.86516i	0.202102	−	0.0956807i
$381$	13.7811			0.706025
$382$	6.14290	+	2.23583i	0.314298	+	0.114395i
$383$	−2.15405	−	12.2162i	−0.110067	−	0.624219i	−0.989075	−	0.147413i	$-0.952905\pi$
$383$	−2.15405	−	12.2162i	−0.110067	−	0.624219i	0.879008	−	0.476806i	$-0.158206\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	6.86618	−	5.76141i	0.349933	−	0.293629i
$386$	−0.453363	+	2.57115i	−0.0230756	+	0.130868i
$387$	−3.22668	+	5.58878i	−0.164021	+	0.284093i
$388$	4.17024	+	7.22308i	0.211712	+	0.366696i
$389$	16.2344	−	5.90885i	0.823118	−	0.299590i	0.104087	−	0.994568i	$-0.466808\pi$
$389$	16.2344	−	5.90885i	0.823118	−	0.299590i	0.719031	+	0.694978i	$0.244586\pi$
$390$	−4.69846	+	1.71010i	−0.237916	+	0.0865943i
$391$	−6.64765	−	11.5141i	−0.336186	−	0.582292i
$392$	5.43242	−	9.40923i	0.274379	−	0.475238i
$393$	−3.39306	+	19.2430i	−0.171157	+	0.970680i
$394$	0.220752	−	0.185233i	0.0111213	−	0.00933189i
$395$	9.88713	+	8.29628i	0.497475	+	0.417431i
$396$	−0.368241	−	2.08840i	−0.0185048	−	0.104946i
$397$	1.76604	+	0.642788i	0.0886352	+	0.0322606i	0.385957	−	0.922517i	$-0.373871\pi$
$397$	1.76604	+	0.642788i	0.0886352	+	0.0322606i	−0.297322	+	0.954777i	$0.596093\pi$
$398$	−9.36009			−0.469179
$399$	18.3439	−	1.71275i	0.918343	−	0.0857447i
$400$	1.00000			0.0500000
$401$	−27.0428	−	9.84278i	−1.35045	−	0.491525i	−0.437365	−	0.899284i	$-0.644088\pi$
$401$	−27.0428	−	9.84278i	−1.35045	−	0.491525i	−0.913090	+	0.407759i	$0.866310\pi$
$402$	0.475652	+	2.69756i	0.0237234	+	0.134542i
$403$	40.5303	+	34.0090i	2.01896	+	1.69411i
$404$	0.162504	−	0.136357i	0.00808487	−	0.00678401i
$405$	−0.173648	+	0.984808i	−0.00862865	+	0.0489355i
$406$	−5.69459	+	9.86332i	−0.282618	+	0.489509i
$407$	11.1074	+	19.2386i	0.550574	+	0.953622i
$408$	3.10607	−	1.13052i	0.153773	−	0.0559689i
$409$	29.7511	−	10.8285i	1.47110	−	0.535435i	0.522698	−	0.852518i	$-0.324925\pi$
$409$	29.7511	−	10.8285i	1.47110	−	0.535435i	0.948398	+	0.317082i	$0.102703\pi$
$410$	−4.88326	−	8.45805i	−0.241167	−	0.417713i
$411$	−10.8084	+	18.7207i	−0.533139	+	0.923424i
$412$	1.66978	−	9.46978i	0.0822640	−	0.466543i
$413$	−30.7527	+	25.8046i	−1.51324	+	1.26976i
$414$	−3.08125	−	2.58548i	−0.151435	−	0.127069i
$415$	1.18479	+	6.71929i	0.0581592	+	0.329837i
$416$	4.69846	+	1.71010i	0.230361	+	0.0838446i
$417$	−9.08378			−0.444835
$418$	−5.34595	−	7.54082i	−0.261479	−	0.368833i
$419$	3.04963			0.148984			0.0744921	−	0.997222i	$-0.476266\pi$
$419$	3.04963			0.148984			0.0744921	+	0.997222i	$0.476266\pi$
$420$	3.97178	+	1.44561i	0.193803	+	0.0705386i
$421$	−0.837496	−	4.74968i	−0.0408171	−	0.231485i	0.957574	−	0.288187i	$-0.0930526\pi$
$421$	−0.837496	−	4.74968i	−0.0408171	−	0.231485i	−0.998391	+	0.0567022i	$0.981941\pi$
$422$	18.8025	+	15.7771i	0.915290	+	0.768019i
$423$	−6.80793	+	5.71253i	−0.331013	+	0.277753i
$424$	−1.37211	+	7.78163i	−0.0666356	+	0.377909i
$425$	−1.65270	+	2.86257i	−0.0801679	+	0.138855i
$426$	−4.59627	−	7.96097i	−0.222690	−	0.385710i
$427$	51.2627	−	18.6581i	2.48078	−	0.902929i
$428$	−11.2763	+	4.10424i	−0.545061	+	0.198386i
$429$	5.30154	+	9.18253i	0.255961	+	0.443337i
$430$	−3.22668	+	5.58878i	−0.155604	+	0.269515i
$431$	6.35504	−	36.0412i	0.306111	−	1.73604i	−0.312116	−	0.950044i	$-0.601038\pi$
$431$	6.35504	−	36.0412i	0.306111	−	1.73604i	0.618227	−	0.786000i	$-0.287851\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	−12.4757	−	10.4683i	−0.599542	−	0.503075i	0.291757	−	0.956493i	$-0.405760\pi$
$433$	−12.4757	−	10.4683i	−0.599542	−	0.503075i	−0.891298	+	0.453417i	$0.850205\pi$
$434$	−7.76651	−	44.0461i	−0.372804	−	2.11428i
$435$	−2.53209	−	0.921605i	−0.121404	−	0.0441876i
$436$	−6.58172			−0.315207
$437$	−16.9615	−	4.43896i	−0.811379	−	0.212344i
$438$	−0.566237			−0.0270559
$439$	−11.9709	−	4.35705i	−0.571340	−	0.207951i	0.0401626	−	0.999193i	$-0.487212\pi$
$439$	−11.9709	−	4.35705i	−0.571340	−	0.207951i	−0.611503	+	0.791242i	$0.709435\pi$
$440$	−0.368241	−	2.08840i	−0.0175552	−	0.0995605i
$441$	8.32295	+	6.98378i	0.396331	+	0.332561i
$442$	−12.6604	+	10.6234i	−0.602196	+	0.505302i
$443$	−2.51249	+	14.2490i	−0.119372	+	0.676992i	0.865120	+	0.501564i	$0.167242\pi$
$443$	−2.51249	+	14.2490i	−0.119372	+	0.676992i	−0.984492	+	0.175428i	$0.943869\pi$
$444$	−5.23783	+	9.07218i	−0.248576	+	0.430547i
$445$	4.09492	+	7.09261i	0.194118	+	0.336222i
$446$	8.32547	−	3.03022i	0.394223	−	0.143485i
$447$	15.1557	−	5.51622i	0.716840	−	0.260908i
$448$	−2.11334	−	3.66041i	−0.0998460	−	0.172938i
$449$	7.57785	−	13.1252i	0.357621	−	0.619417i	−0.629942	−	0.776642i	$-0.716921\pi$
$449$	7.57785	−	13.1252i	0.357621	−	0.619417i	0.987563	+	0.157225i	$0.0502547\pi$
$450$	−0.173648	+	0.984808i	−0.00818585	+	0.0464243i
$451$	−15.8656	+	13.3128i	−0.747080	+	0.626874i
$452$	1.59627	+	1.33943i	0.0750821	+	0.0630013i
$453$	−3.42602	−	19.4299i	−0.160969	−	0.912898i
$454$	−13.9017	−	5.05980i	−0.652438	−	0.237468i
$455$	−21.1334			−0.990749
$456$	1.81908	−	3.96118i	0.0851861	−	0.185499i
$457$	11.6304			0.544048			0.272024	−	0.962290i	$-0.412307\pi$
$457$	11.6304			0.544048			0.272024	+	0.962290i	$0.412307\pi$
$458$	−0.0787257	−	0.0286538i	−0.00367861	−	0.00133890i
$459$	0.573978	+	3.25519i	0.0267910	+	0.151939i
$460$	−3.08125	−	2.58548i	−0.143664	−	0.120549i
$461$	−16.2645	+	13.6475i	−0.757511	+	0.635627i	−0.937478	−	0.348045i	$-0.886845\pi$
$461$	−16.2645	+	13.6475i	−0.757511	+	0.635627i	0.179967	+	0.983673i	$0.442401\pi$
$462$	1.55644	−	8.82699i	0.0724120	−	0.410669i
$463$	15.8268	−	27.4129i	0.735535	−	1.27398i	−0.218954	−	0.975735i	$-0.570264\pi$
$463$	15.8268	−	27.4129i	0.735535	−	1.27398i	0.954488	−	0.298248i	$-0.0964023\pi$
$464$	1.34730	+	2.33359i	0.0625467	+	0.108334i
$465$	9.94356	−	3.61916i	0.461122	−	0.167835i
$466$	1.75877	−	0.640140i	0.0814735	−	0.0296539i
$467$	−8.33275	−	14.4327i	−0.385594	−	0.667868i	0.606258	−	0.795268i	$-0.292670\pi$
$467$	−8.33275	−	14.4327i	−0.385594	−	0.667868i	−0.991851	+	0.127400i	$0.959337\pi$
$468$	−2.50000	+	4.33013i	−0.115563	+	0.200160i
$469$	−2.01043	+	11.4017i	−0.0928330	+	0.526482i
$470$	−6.80793	+	5.71253i	−0.314027	+	0.263500i
$471$	−3.52687	−	2.95940i	−0.162510	−	0.136362i
$472$	1.64930	+	9.35365i	0.0759152	+	0.430536i
$473$	12.8598	+	4.68058i	0.591294	+	0.215213i
$474$	12.9067			0.592826
$475$	1.15270	+	4.20372i	0.0528897	+	0.192880i
$476$	13.9709			0.640355
$477$	−7.42514	−	2.70253i	−0.339974	−	0.123740i
$478$	4.43376	+	25.1451i	0.202796	+	1.15011i
$479$	−3.66044	−	3.07148i	−0.167250	−	0.140339i	0.555321	−	0.831636i	$-0.312595\pi$
$479$	−3.66044	−	3.07148i	−0.167250	−	0.140339i	−0.722571	+	0.691297i	$0.757040\pi$
$480$	0.766044	−	0.642788i	0.0349650	−	0.0293391i
$481$	9.09539	−	51.5825i	0.414714	−	2.35196i
$482$	−4.95336	+	8.57948i	−0.225620	+	0.390784i
$483$	−8.50047	−	14.7232i	−0.386785	−	0.669931i
$484$	6.11081	−	2.22415i	0.277764	−	0.101098i
$485$	−7.83750	+	2.85262i	−0.355882	+	0.129531i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−3.04916	+	5.28131i	−0.138171	+	0.239319i	−0.926804	−	0.375545i	$-0.877456\pi$
$487$	−3.04916	+	5.28131i	−0.138171	+	0.239319i	0.788633	+	0.614864i	$0.210789\pi$
$488$	2.24123	−	12.7106i	0.101456	−	0.575384i
$489$	4.69459	−	3.93923i	0.212297	−	0.178138i
$490$	8.32295	+	6.98378i	0.375992	+	0.315495i
$491$	−1.99613	−	11.3206i	−0.0900841	−	0.510892i	−0.996143	−	0.0877413i	$-0.972035\pi$
$491$	−1.99613	−	11.3206i	−0.0900841	−	0.510892i	0.906059	−	0.423151i	$-0.139076\pi$
$492$	−9.17752	−	3.34034i	−0.413754	−	0.150594i
$493$	−8.90673			−0.401139
$494$	−1.77285	+	21.7223i	−0.0797644	+	0.977331i
$495$	2.12061			0.0953145
$496$	−9.94356	−	3.61916i	−0.446479	−	0.162505i
$497$	−6.74691	−	38.2636i	−0.302640	−	1.71636i
$498$	5.22668	+	4.38571i	0.234213	+	0.196528i
$499$	−30.7108	+	25.7694i	−1.37480	+	1.15360i	−0.403713	+	0.914886i	$0.632281\pi$
$499$	−30.7108	+	25.7694i	−1.37480	+	1.15360i	−0.971090	+	0.238712i	$0.923275\pi$
$500$	−0.173648	+	0.984808i	−0.00776578	+	0.0440419i
$501$	−3.18092	+	5.50952i	−0.142113	+	0.246147i
$502$	−2.70439	−	4.68415i	−0.120703	−	0.209064i
$503$	−6.91400	+	2.51649i	−0.308280	+	0.112205i	−0.491527	−	0.870862i	$-0.663561\pi$
$503$	−6.91400	+	2.51649i	−0.308280	+	0.112205i	0.183247	+	0.983067i	$0.441339\pi$
$504$	3.97178	−	1.44561i	0.176917	−	0.0643926i
$505$	0.106067	+	0.183713i	0.00471991	+	0.00817513i
$506$	−4.26486	+	7.38696i	−0.189596	+	0.328390i
$507$	2.08378	−	11.8177i	0.0925438	−	0.524842i
$508$	10.5569	−	8.85829i	0.468387	−	0.393023i
$509$	32.0874	+	26.9245i	1.42225	+	1.19341i	0.950122	+	0.311878i	$0.100958\pi$
$509$	32.0874	+	26.9245i	1.42225	+	1.19341i	0.472127	+	0.881531i	$0.343486\pi$
$510$	0.573978	+	3.25519i	0.0254162	+	0.144142i
$511$	−2.24897	−	0.818558i	−0.0994886	−	0.0362109i
$512$	−1.00000			−0.0441942
$513$	3.58512	+	2.47929i	0.158287	+	0.109463i
$514$	1.03508			0.0456555
$515$	9.03596	+	3.28882i	0.398172	+	0.144923i
$516$	1.12061	+	6.35532i	0.0493323	+	0.279777i
$517$	14.4370	+	12.1141i	0.634939	+	0.532777i
$518$	−33.9183	+	28.4609i	−1.49029	+	1.25050i
$519$	2.63176	−	14.9254i	0.115521	−	0.655154i
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	−16.4338	−	28.4641i	−0.719976	−	1.24704i	−0.961009	−	0.276518i	$-0.910819\pi$
$521$	−16.4338	−	28.4641i	−0.719976	−	1.24704i	0.241032	−	0.970517i	$-0.422514\pi$
$522$	−2.53209	+	0.921605i	−0.110827	+	0.0403376i
$523$	8.44831	−	3.07493i	0.369419	−	0.134457i	−0.150638	−	0.988589i	$-0.548133\pi$
$523$	8.44831	−	3.07493i	0.369419	−	0.134457i	0.520057	+	0.854131i	$0.325911\pi$
$524$	9.76991	+	16.9220i	0.426801	+	0.739241i
$525$	−2.11334	+	3.66041i	−0.0922338	+	0.159754i
$526$	2.94996	−	16.7301i	0.128624	−	0.729465i
$527$	26.7939	−	22.4827i	1.16716	−	0.979362i
$528$	−1.62449	−	1.36310i	−0.0706966	−	0.0593215i
$529$	−1.18449	−	6.71756i	−0.0514995	−	0.292068i
$530$	−7.42514	−	2.70253i	−0.322528	−	0.117390i
$531$	−9.49794			−0.412176
$532$	12.9513	−	13.1033i	0.561510	−	0.568099i
$533$	48.8326			2.11517
$534$	7.69594	+	2.80109i	0.333036	+	0.121215i
$535$	−2.08378	−	11.8177i	−0.0900896	−	0.510923i
$536$	2.09833	+	1.76070i	0.0906339	+	0.0760509i
$537$	−1.48499	+	1.24605i	−0.0640818	+	0.0537711i
$538$	0.179740	−	1.01936i	0.00774915	−	0.0439476i
$539$	11.5201	−	19.9533i	0.496204	−	0.859451i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	6.49020	−	2.36224i	0.279035	−	0.101561i	−0.198712	−	0.980058i	$-0.563676\pi$
$541$	6.49020	−	2.36224i	0.279035	−	0.101561i	0.477747	+	0.878497i	$0.341454\pi$
$542$	16.1557	−	5.88019i	0.693947	−	0.252576i
$543$	−6.06418	−	10.5035i	−0.260239	−	0.450747i
$544$	1.65270	−	2.86257i	0.0708591	−	0.122732i
$545$	1.14290	−	6.48173i	0.0489566	−	0.277647i
$546$	−16.1891	+	13.5843i	−0.692831	+	0.581354i
$547$	16.1898	+	13.5849i	0.692228	+	0.580848i	0.919551	−	0.392971i	$-0.128553\pi$
$547$	16.1898	+	13.5849i	0.692228	+	0.580848i	−0.227323	+	0.973819i	$0.572997\pi$
$548$	3.75372	+	21.2884i	0.160351	+	0.909395i
$549$	12.1284	+	4.41436i	0.517626	+	0.188400i
$550$	2.12061			0.0904233
$551$	−8.25671	+	8.35359i	−0.351748	+	0.355875i
$552$	−4.02229			−0.171200
$553$	51.2627	+	18.6581i	2.17991	+	0.793423i
$554$	−0.0384855	−	0.218262i	−0.00163509	−	0.00927307i
$555$	−8.02481	−	6.73362i	−0.340634	−	0.285826i
$556$	−6.95858	+	5.83894i	−0.295109	+	0.247626i
$557$	−1.12078	+	6.35624i	−0.0474888	+	0.269323i	−0.999302	−	0.0373558i	$-0.988107\pi$
$557$	−1.12078	+	6.35624i	−0.0474888	+	0.269323i	0.951813	+	0.306678i	$0.0992176\pi$
$558$	5.29086	−	9.16404i	0.223980	−	0.387945i
$559$	−16.1334	−	27.9439i	−0.682370	−	1.18190i
$560$	3.97178	−	1.44561i	0.167838	−	0.0610882i
$561$	6.58677	−	2.39739i	0.278094	−	0.101218i
$562$	−1.25624	−	2.17588i	−0.0529915	−	0.0917839i
$563$	8.61856	−	14.9278i	0.363229	−	0.629131i	−0.625261	−	0.780415i	$-0.715008\pi$
$563$	8.61856	−	14.9278i	0.363229	−	0.629131i	0.988490	+	0.151285i	$0.0483410\pi$
$564$	−1.54323	+	8.75211i	−0.0649818	+	0.368530i
$565$	−1.59627	+	1.33943i	−0.0671554	+	0.0563501i
$566$	−0.433763	−	0.363970i	−0.0182324	−	0.0152988i
$567$	0.733956	+	4.16247i	0.0308232	+	0.174807i
$568$	−8.63816	−	3.14403i	−0.362449	−	0.131921i
$569$	27.2226			1.14123			0.570615	−	0.821218i	$-0.306705\pi$
$569$	27.2226			1.14123			0.570615	+	0.821218i	$0.306705\pi$
$570$	3.58512	+	2.47929i	0.150164	+	0.103846i
$571$	42.8972			1.79519			0.897597	−	0.440818i	$-0.145311\pi$
$571$	42.8972			1.79519			0.897597	+	0.440818i	$0.145311\pi$
$572$	9.96363	+	3.62646i	0.416600	+	0.151630i
$573$	1.13516	+	6.43783i	0.0474221	+	0.268944i
$574$	−31.6223	−	26.5342i	−1.31989	−	1.10752i
$575$	3.08125	−	2.58548i	0.128497	−	0.107822i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	−3.03714	−	5.26048i	−0.126328	−	0.218807i
$579$	−2.45336	+	0.892951i	−0.101958	+	0.0371098i
$580$	−2.53209	+	0.921605i	−0.105139	+	0.0382676i
$581$	14.4192	+	24.9748i	0.598210	+	1.03613i
$582$	−4.17024	+	7.22308i	−0.172862	+	0.299406i
$583$	−2.90972	+	16.5018i	−0.120508	+	0.683436i
$584$	−0.433763	+	0.363970i	−0.0179492	+	0.0150612i
$585$	−3.83022	−	3.21394i	−0.158360	−	0.132880i
$586$	−5.45084	−	30.9132i	−0.225172	−	1.27701i
$587$	−13.1652	−	4.79174i	−0.543386	−	0.197776i	0.0557196	−	0.998446i	$-0.482255\pi$
$587$	−13.1652	−	4.79174i	−0.543386	−	0.197776i	−0.599105	+	0.800670i	$0.704477\pi$
$588$	10.8648			0.448058
$589$	3.75196	−	45.9718i	0.154597	−	1.89423i
$590$	−9.49794			−0.391024
$591$	0.270792	+	0.0985603i	0.0111389	+	0.00405423i
$592$	1.81908	+	10.3165i	0.0747636	+	0.424006i
$593$	4.29086	+	3.60046i	0.176204	+	0.147853i	0.726625	−	0.687035i	$-0.241088\pi$
$593$	4.29086	+	3.60046i	0.176204	+	0.147853i	−0.550420	+	0.834888i	$0.685532\pi$
$594$	1.62449	−	1.36310i	0.0666534	−	0.0559289i
$595$	−2.42602	+	13.7587i	−0.0994572	+	0.564050i
$596$	8.06418	−	13.9676i	0.330322	−	0.572134i
$597$	−4.68004	−	8.10608i	−0.191541	−	0.331760i
$598$	18.8986	−	6.87852i	0.772820	−	0.281284i
$599$	−8.54488	+	3.11008i	−0.349134	+	0.127075i	−0.510634	−	0.859798i	$-0.670589\pi$
$599$	−8.54488	+	3.11008i	−0.349134	+	0.127075i	0.161499	+	0.986873i	$0.448367\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	9.27244	−	16.0603i	0.378231	−	0.655115i	−0.612574	−	0.790413i	$-0.709866\pi$
$601$	9.27244	−	16.0603i	0.378231	−	0.655115i	0.990805	+	0.135298i	$0.0431993\pi$
$602$	−4.73648	+	26.8619i	−0.193045	+	1.09481i
$603$	−2.09833	+	1.76070i	−0.0854504	+	0.0717014i
$604$	−15.1138	−	12.6820i	−0.614972	−	0.516023i
$605$	1.12923	+	6.40420i	0.0459098	+	0.260368i
$606$	0.199340	+	0.0725540i	0.00809765	+	0.00294730i
$607$	17.8726			0.725426			0.362713	−	0.931901i	$-0.381851\pi$
$607$	17.8726			0.725426			0.362713	+	0.931901i	$0.381851\pi$
$608$	−1.15270	−	4.20372i	−0.0467483	−	0.170483i
$609$	−11.3892			−0.461513
$610$	12.1284	+	4.41436i	0.491063	+	0.178732i
$611$	−7.71617	−	43.7606i	−0.312163	−	1.77036i
$612$	2.53209	+	2.12467i	0.102354	+	0.0858849i
$613$	16.0096	−	13.4336i	0.646620	−	0.542578i	−0.259423	−	0.965764i	$-0.583533\pi$
$613$	16.0096	−	13.4336i	0.646620	−	0.542578i	0.906043	+	0.423185i	$0.139088\pi$
$614$	2.30810	−	13.0899i	0.0931472	−	0.528264i
$615$	4.88326	−	8.45805i	0.196912	−	0.341061i
$616$	−4.48158	−	7.76233i	−0.180568	−	0.312753i
$617$	26.5621	−	9.66782i	1.06935	−	0.389212i	0.253417	−	0.967357i	$-0.418446\pi$
$617$	26.5621	−	9.66782i	1.06935	−	0.389212i	0.815934	+	0.578145i	$0.196223\pi$
$618$	9.03596	−	3.28882i	0.363480	−	0.132296i
$619$	−23.4051	−	40.5389i	−0.940732	−	1.62940i	−0.764080	−	0.645122i	$-0.776807\pi$
$619$	−23.4051	−	40.5389i	−0.940732	−	1.62940i	−0.176652	−	0.984273i	$-0.556527\pi$
$620$	5.29086	−	9.16404i	0.212486	−	0.368037i
$621$	0.698463	−	3.96118i	0.0280284	−	0.158957i
$622$	4.34730	−	3.64781i	0.174311	−	0.146264i
$623$	26.5173	+	22.2507i	1.06239	+	0.891453i
$624$	0.868241	+	4.92404i	0.0347575	+	0.197119i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−12.8520			−0.513671
$627$	3.85756	−	8.40014i	0.154056	−	0.335469i
$628$	−4.60401			−0.183720
$629$	−32.5381	−	11.8429i	−1.29738	−	0.472207i
$630$	0.733956	+	4.16247i	0.0292415	+	0.165837i
$631$	−7.57398	−	6.35532i	−0.301515	−	0.253001i	0.479459	−	0.877564i	$-0.340833\pi$
$631$	−7.57398	−	6.35532i	−0.301515	−	0.253001i	−0.780975	+	0.624563i	$0.785277\pi$
$632$	9.88713	−	8.29628i	0.393289	−	0.330008i
$633$	−4.26217	+	24.1720i	−0.169406	+	0.960750i
$634$	3.44949	−	5.97470i	0.136997	−	0.237286i
$635$	6.89053	+	11.9347i	0.273442	+	0.473616i
$636$	−7.42514	+	2.70253i	−0.294426	+	0.107162i
$637$	−51.0480	+	18.5800i	−2.02260	+	0.736165i
$638$	2.85710	+	4.94864i	0.113114	+	0.195918i
$639$	4.59627	−	7.96097i	0.181825	−	0.314931i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	27.2572	−	22.8715i	1.07659	−	0.903369i	0.0809602	−	0.996717i	$-0.474201\pi$
$641$	27.2572	−	22.8715i	1.07659	−	0.903369i	0.995634	+	0.0933479i	$0.0297569\pi$
$642$	−9.19253	−	7.71345i	−0.362800	−	0.304426i
$643$	3.34049	+	18.9449i	0.131736	+	0.747112i	0.977077	+	0.212885i	$0.0682861\pi$
$643$	3.34049	+	18.9449i	0.131736	+	0.747112i	−0.845341	+	0.534227i	$0.820603\pi$
$644$	−15.9757	−	5.81466i	−0.629529	−	0.229130i
$645$	−6.45336			−0.254101
$646$	13.9385	+	3.64781i	0.548403	+	0.143521i
$647$	4.02229			0.158132			0.0790662	−	0.996869i	$-0.474806\pi$
$647$	4.02229			0.158132			0.0790662	+	0.996869i	$0.474806\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	3.49753	+	19.8355i	0.137290	+	0.778611i
$650$	−3.83022	−	3.21394i	−0.150234	−	0.126061i
$651$	34.2618	−	28.7490i	1.34282	−	1.12676i
$652$	1.06418	−	6.03525i	0.0416764	−	0.236359i
$653$	0.645430	−	1.11792i	0.0252576	−	0.0437475i	−0.853120	−	0.521714i	$-0.825293\pi$
$653$	0.645430	−	1.11792i	0.0252576	−	0.0437475i	0.878378	+	0.477967i	$0.158626\pi$
$654$	−3.29086	−	5.69994i	−0.128683	−	0.222885i
$655$	−18.3614	+	6.68302i	−0.717441	+	0.261127i
$656$	−9.17752	+	3.34034i	−0.358322	+	0.130419i
$657$	−0.283119	−	0.490376i	−0.0110455	−	0.0191314i
$658$	−18.7815	+	32.5306i	−0.732180	+	1.26817i
$659$	−8.81150	+	49.9725i	−0.343247	+	1.94665i	−0.0216811	+	0.999765i	$0.506902\pi$
$659$	−8.81150	+	49.9725i	−0.343247	+	1.94665i	−0.321566	+	0.946887i	$0.604209\pi$
$660$	1.62449	−	1.36310i	0.0632330	−	0.0530588i
$661$	31.5149	+	26.4441i	1.22579	+	1.02856i	0.998501	+	0.0547279i	$0.0174291\pi$
$661$	31.5149	+	26.4441i	1.22579	+	1.02856i	0.227284	+	0.973828i	$0.427015\pi$
$662$	3.71941	+	21.0938i	0.144559	+	0.819834i
$663$	−15.5303	−	5.65258i	−0.603148	−	0.219528i
$664$	6.82295			0.264782
$665$	10.6552	+	15.0299i	0.413192	+	0.582835i
$666$	−10.4757			−0.405923
$667$	10.1848	+	3.70696i	0.394357	+	0.143534i
$668$	1.10472	+	6.26519i	0.0427430	+	0.242408i
$669$	6.78699	+	5.69496i	0.262400	+	0.220180i
$670$	−2.09833	+	1.76070i	−0.0810654	+	0.0680220i
$671$	4.75278	−	26.9544i	0.183479	−	1.04056i
$672$	2.11334	−	3.66041i	0.0815239	−	0.141204i
$673$	4.20708	+	7.28688i	0.162171	+	0.280889i	0.935647	−	0.352937i	$-0.114817\pi$
$673$	4.20708	+	7.28688i	0.162171	+	0.280889i	−0.773476	+	0.633826i	$0.781484\pi$
$674$	−16.8503	+	6.13300i	−0.649049	+	0.236234i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	5.70843	−	9.88728i	0.219393	−	0.379999i	−0.735230	−	0.677818i	$-0.762926\pi$
$677$	5.70843	−	9.88728i	0.219393	−	0.379999i	0.954622	+	0.297819i	$0.0962591\pi$
$678$	−0.361844	+	2.05212i	−0.0138965	+	0.0788112i
$679$	−27.0051	+	22.6599i	−1.03636	+	0.869608i
$680$	2.53209	+	2.12467i	0.0971012	+	0.0814776i
$681$	−2.56893	−	14.5691i	−0.0984414	−	0.558289i
$682$	−21.0865	−	7.67485i	−0.807443	−	0.293885i
$683$	2.44326			0.0934887			0.0467443	−	0.998907i	$-0.485115\pi$
$683$	2.44326			0.0934887			0.0467443	+	0.998907i	$0.485115\pi$
$684$	4.34002	−	0.405223i	0.165945	−	0.0154941i
$685$	−21.6168			−0.825935
$686$	15.3503	+	5.58705i	0.586077	+	0.213315i
$687$	−0.0145479	−	0.0825054i	−0.000555038	−	0.00314778i
$688$	4.94356	+	4.14814i	0.188472	+	0.158146i
$689$	30.2652	−	25.3955i	1.15301	−	0.967491i
$690$	0.698463	−	3.96118i	0.0265900	−	0.150800i
$691$	12.5364	−	21.7137i	0.476908	−	0.826029i	−0.522742	−	0.852491i	$-0.675091\pi$
$691$	12.5364	−	21.7137i	0.476908	−	0.826029i	0.999650	+	0.0264620i	$0.00842411\pi$
$692$	−7.57785	−	13.1252i	−0.288067	−	0.498946i
$693$	8.42262	−	3.06558i	0.319949	−	0.116452i
$694$	−11.0770	+	4.03169i	−0.420476	+	0.153041i
$695$	−4.54189	−	7.86678i	−0.172284	−	0.298404i
$696$	−1.34730	+	2.33359i	−0.0510691	+	0.0884543i
$697$	5.60576	−	31.7919i	0.212333	−	1.20420i
$698$	−0.184793	+	0.155059i	−0.00699450	+	0.00586908i
$699$	1.43376	+	1.20307i	0.0542299	+	0.0455043i
$700$	0.733956	+	4.16247i	0.0277409	+	0.157327i
$701$	44.3063	+	16.1262i	1.67343	+	0.609078i	0.992386	−	0.123167i	$-0.0393051\pi$
$701$	44.3063	+	16.1262i	1.67343	+	0.609078i	0.681041	+	0.732245i	$0.261527\pi$
$702$	−5.00000			−0.188713
$703$	−41.2708	+	19.5388i	−1.55656	+	0.736919i
$704$	−2.12061			−0.0799237
$705$	−8.35117	−	3.03958i	−0.314523	−	0.114477i
$706$	2.98040	+	16.9027i	0.112169	+	0.636141i
$707$	0.686852	+	0.576337i	0.0258317	+	0.0216754i
$708$	−7.27584	+	6.10516i	−0.273443	+	0.229446i
$709$	2.36865	−	13.4333i	0.0889566	−	0.504498i	−0.907476	−	0.420104i	$-0.861994\pi$
$709$	2.36865	−	13.4333i	0.0889566	−	0.504498i	0.996432	−	0.0843937i	$-0.0268953\pi$
$710$	4.59627	−	7.96097i	0.172495	−	0.298770i
$711$	6.45336	+	11.1776i	0.242020	+	0.419191i
$712$	7.69594	−	2.80109i	0.288417	−	0.104975i
$713$	−39.9959	+	14.5573i	−1.49786	+	0.545176i
$714$	6.98545	+	12.0992i	0.261424	+	0.452800i
$715$	−5.30154	+	9.18253i	−0.198266	+	0.343407i
$716$	−0.336619	+	1.90906i	−0.0125800	+	0.0713449i
$717$	−19.5594	+	16.4123i	−0.730460	+	0.612929i
$718$	−20.9067	−	17.5428i	−0.780232	−	0.654692i
$719$	6.47472	+	36.7200i	0.241466	+	1.36942i	0.828558	+	0.559903i	$0.189162\pi$
$719$	6.47472	+	36.7200i	0.241466	+	1.36942i	−0.587092	+	0.809520i	$0.699727\pi$
$720$	0.939693	+	0.342020i	0.0350203	+	0.0127463i
$721$	40.6432			1.51363
$722$	16.3425	−	9.69129i	0.608207	−	0.360672i
$723$	−9.90673			−0.368435
$724$	−11.3969	−	4.14814i	−0.423563	−	0.154164i
$725$	−0.467911	−	2.65366i	−0.0173778	−	0.0985543i
$726$	4.98158	+	4.18004i	0.184884	+	0.155136i
$727$	−29.2080	+	24.5084i	−1.08327	+	0.908968i	−0.996188	−	0.0872340i	$-0.972197\pi$
$727$	−29.2080	+	24.5084i	−1.08327	+	0.908968i	−0.0870775	+	0.996202i	$0.527753\pi$
$728$	−3.66978	+	20.8123i	−0.136011	+	0.771357i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.283119	−	0.490376i	−0.0104787	−	0.0181496i
$731$	−20.0446	+	7.29563i	−0.741375	+	0.269839i
$732$	12.1284	−	4.41436i	0.448277	−	0.163159i
$733$	15.5744	+	26.9757i	0.575255	+	0.996371i	0.996014	+	0.0891987i	$0.0284306\pi$
$733$	15.5744	+	26.9757i	0.575255	+	0.996371i	−0.420759	+	0.907173i	$0.638236\pi$
$734$	−0.413534	+	0.716261i	−0.0152638	+	0.0264377i
$735$	−1.88666	+	10.6998i	−0.0695905	+	0.394667i
$736$	−3.08125	+	2.58548i	−0.113576	+	0.0953020i
$737$	4.44974	+	3.73378i	0.163908	+	0.137535i
$738$	−1.69594	−	9.61814i	−0.0624283	−	0.354048i
$739$	0.284463	+	0.103536i	0.0104641	+	0.00380863i	0.347247	−	0.937774i	$-0.387117\pi$
$739$	0.284463	+	0.103536i	0.0104641	+	0.00380863i	−0.336783	+	0.941582i	$0.609339\pi$
$740$	−10.4757			−0.385093
$741$	−19.6985	+	9.32580i	−0.723641	+	0.342592i
$742$	−33.3979			−1.22607
$743$	−40.4552	−	14.7245i	−1.48416	−	0.540189i	−0.532253	−	0.846586i	$-0.678654\pi$
$743$	−40.4552	−	14.7245i	−1.48416	−	0.540189i	−0.951904	+	0.306397i	$0.900877\pi$
$744$	−1.83750	−	10.4210i	−0.0673659	−	0.382051i
$745$	12.3550	+	10.3671i	0.452654	+	0.379821i
$746$	−11.8460	+	9.93993i	−0.433711	+	0.363927i
$747$	−1.18479	+	6.71929i	−0.0433493	+	0.245846i
$748$	3.50475	−	6.07040i	0.128146	−	0.221956i
$749$	−25.3601	−	43.9250i	−0.926638	−	1.60498i
$750$	−0.939693	+	0.342020i	−0.0343127	+	0.0124888i
$751$	−40.2918	+	14.6650i	−1.47027	+	0.535134i	−0.948173	−	0.317753i	$-0.897072\pi$
$751$	−40.2918	+	14.6650i	−1.47027	+	0.535134i	−0.522095	+	0.852887i	$0.674849\pi$
$752$	4.44356	+	7.69648i	0.162040	+	0.280662i
$753$	2.70439	−	4.68415i	0.0985536	−	0.170700i
$754$	2.33956	−	13.2683i	0.0852016	−	0.483202i
$755$	15.1138	−	12.6820i	0.550048	−	0.461545i
$756$	3.23783	+	2.71686i	0.117759	+	0.0988112i
$757$	−0.00134417	−	0.00762319i	−4.88548e−5	−	0.000277069i	0.984783	−	0.173787i	$-0.0556003\pi$
$757$	−0.00134417	−	0.00762319i	−4.88548e−5	−	0.000277069i	−0.984832	+	0.173510i	$0.944489\pi$
$758$	14.3785	+	5.23335i	0.522251	+	0.190084i
$759$	−8.52972			−0.309609
$760$	4.34002	−	0.405223i	0.157429	−	0.0146990i
$761$	−31.3233			−1.13547			−0.567734	−	0.823212i	$-0.692180\pi$
$761$	−31.3233			−1.13547			−0.567734	+	0.823212i	$0.692180\pi$
$762$	12.9500	+	4.71340i	0.469128	+	0.170748i
$763$	−4.83069	−	27.3962i	−0.174883	−	0.991809i
$764$	5.00774	+	4.20199i	0.181174	+	0.152023i
$765$	−2.53209	+	2.12467i	−0.0915479	+	0.0768178i
$766$	2.15405	−	12.2162i	0.0778289	−	0.441390i
$767$	23.7449	−	41.1273i	0.857377	−	1.48502i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	10.6694	−	3.88333i	0.384747	−	0.140037i	−0.142403	−	0.989809i	$-0.545483\pi$
$769$	10.6694	−	3.88333i	0.384747	−	0.140037i	0.527150	+	0.849772i	$0.323261\pi$
$770$	8.42262	−	3.06558i	0.303530	−	0.110476i
$771$	0.517541	+	0.896407i	0.0186388	+	0.0322833i
$772$	−1.30541	+	2.26103i	−0.0469826	+	0.0813763i
$773$	−4.44175	+	25.1904i	−0.159759	+	0.906037i	0.794547	+	0.607203i	$0.207709\pi$
$773$	−4.44175	+	25.1904i	−0.159759	+	0.906037i	−0.954305	+	0.298833i	$0.903402\pi$
$774$	−4.94356	+	4.14814i	−0.177693	+	0.149102i
$775$	8.10607	+	6.80180i	0.291179	+	0.244328i
$776$	1.44831	+	8.21378i	0.0519913	+	0.294857i
$777$	−41.6070	−	15.1437i	−1.49264	−	0.543278i
$778$	17.2763			0.619386
$779$	−24.6208	−	34.7293i	−0.882133	−	1.24431i
$780$	−5.00000			−0.179029
$781$	−18.3182	−	6.66728i	−0.655477	−	0.238574i
$782$	−2.30871	−	13.0933i	−0.0825591	−	0.468216i
$783$	−2.06418	−	1.73205i	−0.0737677	−	0.0618984i
$784$	8.32295	−	6.98378i	0.297248	−	0.249421i
$785$	0.799478	−	4.53406i	0.0285346	−	0.161828i
$786$	−9.76991	+	16.9220i	−0.348481	+	0.603587i
$787$	18.3105	+	31.7146i	0.652697	+	1.13051i	0.982466	+	0.186443i	$0.0596960\pi$
$787$	18.3105	+	31.7146i	0.652697	+	1.13051i	−0.329768	+	0.944062i	$0.606971\pi$
$788$	0.270792	−	0.0985603i	0.00964657	−	0.00351107i
$789$	15.9636	−	5.81029i	0.568320	−	0.206852i
$790$	6.45336	+	11.1776i	0.229600	+	0.397679i
$791$	−4.40373	+	7.62749i	−0.156579	+	0.271202i
$792$	0.368241	−	2.08840i	0.0130849	−	0.0742080i
$793$	−49.4356	+	41.4814i	−1.75551	+	1.47305i
$794$	1.43969	+	1.20805i	0.0510928	+	0.0428719i
$795$	−1.37211	−	7.78163i	−0.0486638	−	0.275986i
$796$	−8.79561	−	3.20134i	−0.311752	−	0.113468i
$797$	35.9840			1.27462			0.637310	−	0.770608i	$-0.280047\pi$
$797$	35.9840			1.27462			0.637310	+	0.770608i	$0.280047\pi$
$798$	17.8234	+	4.66452i	0.630942	+	0.165122i
$799$	−29.3756			−1.03923
$800$	0.939693	+	0.342020i	0.0332232	+	0.0120922i
$801$	1.42215	+	8.06542i	0.0502493	+	0.284978i
$802$	−22.0455	−	18.4984i	−0.778454	−	0.653201i
$803$	−0.919844	+	0.771841i	−0.0324606	+	0.0272377i
$804$	−0.475652	+	2.69756i	−0.0167749	+	0.0951355i
$805$	8.50047	−	14.7232i	0.299602	−	0.518926i
$806$	26.4543	+	45.8202i	0.931813	+	1.61395i
$807$	0.972659	−	0.354019i	0.0342392	−	0.0124621i
$808$	0.199340	−	0.0725540i	0.00701277	−	0.00255244i
$809$	−1.05169	−	1.82158i	−0.0369754	−	0.0640433i	0.846945	−	0.531680i	$-0.178439\pi$
$809$	−1.05169	−	1.82158i	−0.0369754	−	0.0640433i	−0.883921	+	0.467636i	$0.845106\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−0.985614	+	5.58970i	−0.0346096	+	0.196281i	−0.997210	−	0.0746434i	$-0.976218\pi$
$811$	−0.985614	+	5.58970i	−0.0346096	+	0.196281i	0.962601	+	0.270924i	$0.0873293\pi$
$812$	−8.72462	+	7.32083i	−0.306174	+	0.256911i
$813$	13.1702	+	11.0511i	0.461901	+	0.387581i
$814$	3.85756	+	21.8773i	0.135208	+	0.766800i
$815$	5.75877	+	2.09602i	0.201721	+	0.0734204i
$816$	3.30541			0.115712
$817$	−11.7392	+	25.5629i	−0.410702	+	0.894334i
$818$	31.6604			1.10698
$819$	−19.8589	−	7.22805i	−0.693926	−	0.252569i
$820$	−1.69594	−	9.61814i	−0.0592247	−	0.335880i
$821$	14.4388	+	12.1156i	0.503918	+	0.422838i	0.858983	−	0.512004i	$-0.171097\pi$
$821$	14.4388	+	12.1156i	0.503918	+	0.422838i	−0.355065	+	0.934842i	$0.615541\pi$
$822$	−16.5594	+	13.8950i	−0.577576	+	0.484644i
$823$	0.558248	−	3.16598i	0.0194593	−	0.110359i	−0.973531	−	0.228555i	$-0.926600\pi$
$823$	0.558248	−	3.16598i	0.0194593	−	0.110359i	0.992990	+	0.118196i	$0.0377110\pi$
$824$	4.80793	−	8.32759i	0.167492	−	0.290105i
$825$	1.06031	+	1.83651i	0.0369152	+	0.0639389i
$826$	−37.7237	+	13.7303i	−1.31258	+	0.477739i
$827$	−14.4064	+	5.24351i	−0.500960	+	0.182335i	−0.580126	−	0.814527i	$-0.696997\pi$
$827$	−14.4064	+	5.24351i	−0.500960	+	0.182335i	0.0791655	+	0.996861i	$0.474774\pi$
$828$	−2.01114	−	3.48340i	−0.0698921	−	0.121057i
$829$	−7.98545	+	13.8312i	−0.277346	+	0.480378i	−0.970724	−	0.240196i	$-0.922788\pi$
$829$	−7.98545	+	13.8312i	−0.277346	+	0.480378i	0.693378	+	0.720574i	$0.256122\pi$
$830$	−1.18479	+	6.71929i	−0.0411247	+	0.233230i
$831$	0.169778	−	0.142460i	0.00588953	−	0.00494190i
$832$	3.83022	+	3.21394i	0.132789	+	0.111423i
$833$	6.23618	+	35.3671i	0.216071	+	1.22540i
$834$	−8.53596	−	3.10684i	−0.295576	−	0.107581i
$835$	−6.36184			−0.220161
$836$	−2.44444	−	8.91447i	−0.0845427	−	0.308314i
$837$	10.5817			0.365758
$838$	2.86571	+	1.04303i	0.0989945	+	0.0360310i
$839$	−0.294978	−	1.67290i	−0.0101838	−	0.0577551i	0.979292	−	0.202451i	$-0.0648907\pi$
$839$	−0.294978	−	1.67290i	−0.0101838	−	0.0577551i	−0.989476	+	0.144696i	$0.953780\pi$
$840$	3.23783	+	2.71686i	0.111716	+	0.0937405i
$841$	−16.6532	+	13.9737i	−0.574247	+	0.481851i
$842$	0.837496	−	4.74968i	0.0288620	−	0.163685i
$843$	1.25624	−	2.17588i	0.0432674	−	0.0749412i
$844$	12.2724	+	21.2565i	0.422435	+	0.731679i
$845$	11.2763	−	4.10424i	0.387917	−	0.141190i
$846$	−8.35117	+	3.03958i	−0.287119	+	0.104503i
$847$	13.7430	+	23.8036i	0.472216	+	0.817903i
$848$	−3.95084	+	6.84305i	−0.135672	+	0.234991i
$849$	0.0983261	−	0.557635i	0.00337454	−	0.0191380i
$850$	−2.53209	+	2.12467i	−0.0868499	+	0.0728757i
$851$	32.2781	+	27.0846i	1.10648	+	0.928447i
$852$	−1.59627	−	9.05288i	−0.0546872	−	0.310146i
$853$	−33.8987	−	12.3381i	−1.16067	−	0.422450i	−0.311334	−	0.950301i	$-0.600776\pi$
$853$	−33.8987	−	12.3381i	−1.16067	−	0.422450i	−0.849337	+	0.527851i	$0.822998\pi$
$854$	54.5526			1.86675
$855$	−0.354570	+	4.34445i	−0.0121260	+	0.148577i
$856$	−12.0000			−0.410152
$857$	18.8033	+	6.84386i	0.642310	+	0.233782i	0.642580	−	0.766218i	$-0.277864\pi$
$857$	18.8033	+	6.84386i	0.642310	+	0.233782i	−0.000270354		1.00000i	$0.500086\pi$
$858$	1.84120	+	10.4420i	0.0628577	+	0.356484i
$859$	4.82366	+	4.04753i	0.164581	+	0.138100i	0.721359	−	0.692562i	$-0.243518\pi$
$859$	4.82366	+	4.04753i	0.164581	+	0.138100i	−0.556777	+	0.830662i	$0.687962\pi$
$860$	−4.94356	+	4.14814i	−0.168574	+	0.141450i
$861$	7.16819	−	40.6528i	0.244291	−	1.38544i
$862$	18.2986	−	31.6941i	0.623253	−	1.07951i
$863$	0.0876485	+	0.151812i	0.00298359	+	0.00516773i	0.867513	−	0.497414i	$-0.165717\pi$
$863$	0.0876485	+	0.151812i	0.00298359	+	0.00516773i	−0.864530	+	0.502582i	$0.832384\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	14.2417	−	5.18355i	0.484232	−	0.176246i
$866$	−8.14290	−	14.1039i	−0.276707	−	0.479271i
$867$	3.03714	−	5.26048i	0.103147	−	0.178655i
$868$	7.76651	−	44.0461i	0.263613	−	1.49502i
$869$	20.9668	−	17.5932i	0.711249	−	0.596809i
$870$	−2.06418	−	1.73205i	−0.0699822	−	0.0587220i
$871$	−2.37826	−	13.4878i	−0.0805842	−	0.457016i
$872$	−6.18479	−	2.25108i	−0.209444	−	0.0762312i
$873$	−8.34049			−0.282283
$874$	−14.4204	−	9.97244i	−0.487777	−	0.337323i
$875$	−4.22668			−0.142888
$876$	−0.532089	−	0.193665i	−0.0179776	−	0.00654332i
$877$	−7.82816	−	44.3957i	−0.264338	−	1.49914i	−0.770913	−	0.636941i	$-0.780200\pi$
$877$	−7.82816	−	44.3957i	−0.264338	−	1.49914i	0.506575	−	0.862196i	$-0.330912\pi$
$878$	−9.75877	−	8.18858i	−0.329343	−	0.276351i
$879$	24.0462	−	20.1772i	0.811059	−	0.680559i
$880$	0.368241	−	2.08840i	0.0124134	−	0.0703999i
$881$	−21.5822	+	37.3814i	−0.727122	+	1.25941i	0.230972	+	0.972960i	$0.425809\pi$
$881$	−21.5822	+	37.3814i	−0.727122	+	1.25941i	−0.958094	+	0.286452i	$0.907524\pi$
$882$	5.43242	+	9.40923i	0.182919	+	0.316825i
$883$	−5.70233	+	2.07548i	−0.191899	+	0.0698455i	−0.436182	−	0.899858i	$-0.643670\pi$
$883$	−5.70233	+	2.07548i	−0.191899	+	0.0698455i	0.244283	+	0.969704i	$0.421447\pi$
$884$	−15.5303	+	5.65258i	−0.522342	+	0.190117i
$885$	−4.74897	−	8.22546i	−0.159635	−	0.276496i
$886$	−7.23442	+	12.5304i	−0.243045	+	0.420967i
$887$	−3.87362	+	21.9684i	−0.130063	+	0.737626i	0.848108	+	0.529824i	$0.177742\pi$
$887$	−3.87362	+	21.9684i	−0.130063	+	0.737626i	−0.978171	+	0.207802i	$0.933369\pi$
$888$	−8.02481	+	6.73362i	−0.269295	+	0.225965i
$889$	44.6207	+	37.4412i	1.49653	+	1.25574i
$890$	1.42215	+	8.06542i	0.0476706	+	0.270354i
$891$	1.99273	+	0.725293i	0.0667588	+	0.0242982i
$892$	8.85978			0.296648
$893$	−27.2317	+	27.5513i	−0.911275	+	0.921968i
$894$	16.1284			0.539413
$895$	−1.82160	−	0.663010i	−0.0608895	−	0.0221620i
$896$	−0.733956	−	4.16247i	−0.0245197	−	0.139058i
$897$	15.4063	+	12.9274i	0.514400	+	0.431633i
$898$	11.6099	−	9.74189i	0.387429	−	0.325091i
$899$	−4.95130	+	28.0802i	−0.165135	+	0.936528i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−13.0591	−	22.6191i	−0.435063	−	0.753550i
$902$	−19.4620	+	7.08358i	−0.648013	+	0.235857i
$903$	−25.6313	+	9.32905i	−0.852958	+	0.310451i
$904$	1.04189	+	1.80460i	0.0346527	+	0.0600203i
$905$	6.06418	−	10.5035i	0.201580	−	0.349147i
$906$	3.42602	−	19.4299i	0.113822	−	0.645516i
$907$	−10.6340	+	8.92302i	−0.353097	+	0.296284i	−0.802032	−	0.597281i	$-0.796248\pi$
$907$	−10.6340	+	8.92302i	−0.353097	+	0.296284i	0.448935	+	0.893564i	$0.351803\pi$
$908$	−11.3327	−	9.50931i	−0.376090	−	0.315577i
$909$	0.0368366	+	0.208911i	0.00122179	+	0.00692914i
$910$	−19.8589	−	7.22805i	−0.658316	−	0.239608i
$911$	−0.251334			−0.00832708			−0.00416354	−	0.999991i	$-0.501325\pi$
$911$	−0.251334			−0.00832708			−0.00416354	+	0.999991i	$0.501325\pi$
$912$	3.06418	−	3.10013i	0.101465	−	0.102656i
$913$	14.4688			0.478849
$914$	10.9290	+	3.97784i	0.361500	+	0.131575i
$915$	2.24123	+	12.7106i	0.0740928	+	0.420201i
$916$	−0.0641778	−	0.0538515i	−0.00212049	−	0.00177931i
$917$	−63.2666	+	53.0870i	−2.08925	+	1.75309i
$918$	−0.573978	+	3.25519i	−0.0189441	+	0.107437i
$919$	3.63547	−	6.29681i	0.119923	−	0.207713i	−0.799814	−	0.600248i	$-0.795069\pi$
$919$	3.63547	−	6.29681i	0.119923	−	0.207713i	0.919737	+	0.392535i	$0.128402\pi$
$920$	−2.01114	−	3.48340i	−0.0663055	−	0.114844i
$921$	12.4902	−	4.54606i	0.411566	−	0.149798i
$922$	−19.9513	+	7.26168i	−0.657061	+	0.239151i
$923$	22.9813	+	39.8048i	0.756440	+	1.31019i
$924$	4.48158	−	7.76233i	0.147433	−	0.255362i
$925$	1.81908	−	10.3165i	0.0598109	−	0.339205i
$926$	24.2481	−	20.3466i	0.796842	−	0.668630i
$927$	7.36618	+	6.18096i	0.241937	+	0.203009i
$928$	0.467911	+	2.65366i	0.0153599	+	0.0871105i
$929$	20.0360	+	7.29249i	0.657359	+	0.239259i	0.649095	−	0.760707i	$-0.275148\pi$
$929$	20.0360	+	7.29249i	0.657359	+	0.239259i	0.00826301	+	0.999966i	$0.497370\pi$
$930$	10.5817			0.346988
$931$	38.9518	+	26.9371i	1.27659	+	0.882829i
$932$	1.87164			0.0613078
$933$	5.33275	+	1.94096i	0.174586	+	0.0635442i
$934$	−2.89393	−	16.4123i	−0.0946924	−	0.537027i
$935$	5.36959	+	4.50562i	0.175604	+	0.147349i
$936$	−3.83022	+	3.21394i	−0.125195	+	0.105051i
$937$	−2.09234	+	11.8662i	−0.0683538	+	0.387653i	0.931368	+	0.364078i	$0.118616\pi$
$937$	−2.09234	+	11.8662i	−0.0683538	+	0.387653i	−0.999722	+	0.0235751i	$0.992495\pi$
$938$	−5.78880	+	10.0265i	−0.189011	+	0.327377i
$939$	−6.42602	−	11.1302i	−0.209705	−	0.363220i
$940$	−8.35117	+	3.03958i	−0.272385	+	0.0991400i
$941$	18.3310	−	6.67194i	0.597573	−	0.217499i	−0.0254838	−	0.999675i	$-0.508113\pi$
$941$	18.3310	−	6.67194i	0.597573	−	0.217499i	0.623057	+	0.782176i	$0.285890\pi$
$942$	−2.30200	−	3.98719i	−0.0750033	−	0.129910i
$943$	−19.6419	+	34.0207i	−0.639627	+	1.10787i
$944$	−1.64930	+	9.35365i	−0.0536801	+	0.304435i
$945$	−3.23783	+	2.71686i	−0.105326	+	0.0883794i
$946$	10.4834	+	8.79661i	0.340844	+	0.286002i
$947$	4.50744	+	25.5629i	0.146472	+	0.830684i	0.966173	+	0.257893i	$0.0830282\pi$
$947$	4.50744	+	25.5629i	0.146472	+	0.830684i	−0.819701	+	0.572791i	$0.805861\pi$
$948$	12.1284	+	4.41436i	0.393911	+	0.143372i
$949$	2.83119			0.0919042
$950$	−0.354570	+	4.34445i	−0.0115038	+	0.140953i
$951$	6.89899			0.223715
$952$	13.1284	+	4.77833i	0.425492	+	0.154867i
$953$	3.43107	+	19.4586i	0.111143	+	0.630326i	0.988588	+	0.150647i	$0.0481357\pi$
$953$	3.43107	+	19.4586i	0.111143	+	0.630326i	−0.877444	+	0.479679i	$0.840753\pi$
$954$	−6.05303	−	5.07910i	−0.195974	−	0.164442i
$955$	−5.00774	+	4.20199i	−0.162047	+	0.135973i
$956$	−4.43376	+	25.1451i	−0.143398	+	0.813251i
$957$	−2.85710	+	4.94864i	−0.0923568	+	0.159967i
$958$	−2.38919	−	4.13819i	−0.0771911	−	0.133699i
$959$	−85.8572	+	31.2495i	−2.77247	+	1.00910i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	−40.4864	−	70.1245i	−1.30601	−	2.26208i
$962$	26.1891	−	45.3609i	0.844371	−	1.46249i
$963$	2.08378	−	11.8177i	0.0671488	−	0.380820i
$964$	−7.58899	+	6.36792i	−0.244425	+	0.205097i
$965$	−2.00000	−	1.67820i	−0.0643823	−	0.0540231i
$966$	−2.95218	−	16.7427i	−0.0949849	−	0.538686i
$967$	−4.39868	−	1.60099i	−0.141452	−	0.0514843i	0.270324	−	0.962769i	$-0.412869\pi$
$967$	−4.39868	−	1.60099i	−0.141452	−	0.0514843i	−0.411776	+	0.911285i	$0.635091\pi$
$968$	6.50299			0.209014
$969$	3.81016	+	13.8950i	0.122400	+	0.446372i
$970$	−8.34049			−0.267797
$971$	−5.86871	−	2.13603i	−0.188336	−	0.0685486i	0.246131	−	0.969237i	$-0.420841\pi$
$971$	−5.86871	−	2.13603i	−0.188336	−	0.0685486i	−0.434466	+	0.900688i	$0.643063\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	−29.4117	−	24.6793i	−0.942896	−	0.791183i
$974$	−4.67159	+	3.91993i	−0.149687	+	0.125603i
$975$	0.868241	−	4.92404i	0.0278060	−	0.157695i
$976$	6.45336	−	11.1776i	0.206567	−	0.357785i
$977$	5.12061	+	8.86916i	0.163823	+	0.283750i	0.936237	−	0.351370i	$-0.114284\pi$
$977$	5.12061	+	8.86916i	0.163823	+	0.283750i	−0.772414	+	0.635120i	$0.780951\pi$
$978$	5.75877	−	2.09602i	0.184145	−	0.0670234i
$979$	16.3201	−	5.94004i	0.521593	−	0.189844i
$980$	5.43242	+	9.40923i	0.173532	+	0.300567i
$981$	3.29086	−	5.69994i	0.105069	−	0.181985i
$982$	1.99613	−	11.3206i	0.0636991	−	0.361255i
$983$	8.47044	−	7.10754i	0.270165	−	0.226695i	−0.497632	−	0.867388i	$-0.665797\pi$
$983$	8.47044	−	7.10754i	0.270165	−	0.226695i	0.767797	+	0.640693i	$0.221353\pi$
$984$	−7.48158	−	6.27779i	−0.238504	−	0.200129i
$985$	0.0500404	+	0.283793i	0.00159442	+	0.00904240i
$986$	−8.36959	−	3.04628i	−0.266542	−	0.0970133i
$987$	−37.5631			−1.19565
$988$	−9.09539	+	19.8059i	−0.289363	+	0.630110i
$989$	25.9573			0.825394
$990$	1.99273	+	0.725293i	0.0633330	+	0.0230513i
$991$	5.84255	+	33.1347i	0.185595	+	1.05256i	0.925189	+	0.379507i	$0.123906\pi$
$991$	5.84255	+	33.1347i	0.185595	+	1.05256i	−0.739594	+	0.673053i	$0.764983\pi$
$992$	−8.10607	−	6.80180i	−0.257368	−	0.215957i
$993$	−16.4081	+	13.7680i	−0.520694	+	0.436914i
$994$	6.74691	−	38.2636i	0.213999	−	1.21365i
$995$	4.68004	−	8.10608i	0.148367	−	0.256980i
$996$	3.41147	+	5.90885i	0.108097	+	0.187229i
$997$	24.1844	−	8.80240i	0.765927	−	0.278775i	0.0706353	−	0.997502i	$-0.477497\pi$
$997$	24.1844	−	8.80240i	0.765927	−	0.278775i	0.695292	+	0.718728i	$0.255275\pi$
$998$	−37.6724	+	13.7116i	−1.19250	+	0.434034i
$999$	−5.23783	−	9.07218i	−0.165717	−	0.287031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.b.61.1	✓	6
19.5	even	9	inner	570.2.u.b.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.b.61.1	✓	6	1.1	even	1	trivial
570.2.u.b.271.1	yes	6	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-2.11334 + 3.66041i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-2.11334 + 3.66041i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(1.06031 + 1.83651i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.868241 - 4.92404i) q^{13} +(-3.23783 + 2.71686i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-3.10607 - 1.13052i) q^{17} -1.00000 q^{18} +(-3.93969 + 1.86516i) q^{19} -1.00000 q^{20} +(-3.97178 - 1.44561i) q^{21} +(0.368241 + 2.08840i) q^{22} +(3.08125 + 2.58548i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-3.97178 + 1.44561i) q^{28} +(2.53209 - 0.921605i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-5.29086 + 9.16404i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.62449 + 1.36310i) q^{33} +(-2.53209 - 2.12467i) q^{34} +(-0.733956 - 4.16247i) q^{35} +(-0.939693 - 0.342020i) q^{36} +10.4757 q^{37} +(-4.34002 + 0.405223i) q^{38} +5.00000 q^{39} +(-0.939693 - 0.342020i) q^{40} +(1.69594 + 9.61814i) q^{41} +(-3.23783 - 2.71686i) q^{42} +(4.94356 - 4.14814i) q^{43} +(-0.368241 + 2.08840i) q^{44} +(0.500000 - 0.866025i) q^{45} +(2.01114 + 3.48340i) q^{46} +(8.35117 - 3.03958i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-5.43242 - 9.40923i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.573978 - 3.25519i) q^{51} +(3.83022 - 3.21394i) q^{52} +(6.05303 + 5.07910i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-1.99273 - 0.725293i) q^{55} -4.22668 q^{56} +(-2.52094 - 3.55596i) q^{57} +2.69459 q^{58} +(8.92514 + 3.24849i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-9.88713 - 8.29628i) q^{61} +(-8.10607 + 6.80180i) q^{62} +(0.733956 - 4.16247i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(-1.99273 + 0.725293i) q^{66} +(2.57398 - 0.936851i) q^{67} +(-1.65270 - 2.86257i) q^{68} +(-2.01114 + 3.48340i) q^{69} +(0.733956 - 4.16247i) q^{70} +(-7.04189 + 5.90885i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(0.0983261 + 0.557635i) q^{73} +(9.84389 + 3.58288i) q^{74} +1.00000 q^{75} +(-4.21688 - 1.10359i) q^{76} -8.96316 q^{77} +(4.69846 + 1.71010i) q^{78} +(-2.24123 - 12.7106i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.69594 + 9.61814i) q^{82} +(3.41147 - 5.90885i) q^{83} +(-2.11334 - 3.66041i) q^{84} +(3.10607 - 1.13052i) q^{85} +(6.06418 - 2.20718i) q^{86} +(1.34730 + 2.33359i) q^{87} +(-1.06031 + 1.83651i) q^{88} +(1.42215 - 8.06542i) q^{89} +(0.766044 - 0.642788i) q^{90} +(16.1891 + 13.5843i) q^{91} +(0.698463 + 3.96118i) q^{92} +(-9.94356 - 3.61916i) q^{93} +8.88713 q^{94} +(1.81908 - 3.96118i) q^{95} -1.00000 q^{96} +(7.83750 + 2.85262i) q^{97} +(-1.88666 - 10.6998i) q^{98} +(-1.62449 - 1.36310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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