LMFDB - Embedded newform 627.2.j.b.58.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(58,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, 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("627.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$627 = 3 \cdot 11 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	627.j (of order $5$ , degree $4$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.1
Character	$\chi$	$=$	627.58
Dual form			627.2.j.b.400.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95491 + 1.42032i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.18631 - 3.65109i) q^{4} +(2.19357 + 1.59372i) q^{5} +(1.95491 + 1.42032i) q^{6} +(0.612153 - 1.88401i) q^{7} +(1.37318 + 4.22622i) q^{8} +(-0.809017 + 0.587785i) q^{9} -6.55182 q^{10} +(2.49696 + 2.18293i) q^{11} -3.83898 q^{12} +(-3.29346 + 2.39284i) q^{13} +(1.47921 + 4.55253i) q^{14} +(0.837869 - 2.57869i) q^{15} +(-2.47543 - 1.79851i) q^{16} +(0.307924 + 0.223720i) q^{17} +(0.746708 - 2.29813i) q^{18} +(0.309017 + 0.951057i) q^{19} +(8.42107 - 6.11826i) q^{20} -1.98097 q^{21} +(-7.98179 - 0.720942i) q^{22} +3.81700 q^{23} +(3.59503 - 2.61194i) q^{24} +(0.726713 + 2.23659i) q^{25} +(3.03980 - 9.35554i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-6.15249 - 4.47005i) q^{28} +(1.50420 - 4.62945i) q^{29} +(2.02462 + 6.23115i) q^{30} +(5.07934 - 3.69035i) q^{31} -1.49371 q^{32} +(1.30449 - 3.04931i) q^{33} -0.919718 q^{34} +(4.34539 - 3.15711i) q^{35} +(1.18631 + 3.65109i) q^{36} +(-0.422107 + 1.29911i) q^{37} +(-1.95491 - 1.42032i) q^{38} +(3.29346 + 2.39284i) q^{39} +(-3.72324 + 11.4590i) q^{40} +(1.15653 + 3.55944i) q^{41} +(3.87261 - 2.81362i) q^{42} +3.45694 q^{43} +(10.9322 - 6.52698i) q^{44} -2.71140 q^{45} +(-7.46188 + 5.42137i) q^{46} +(3.96846 + 12.2137i) q^{47} +(-0.945531 + 2.91005i) q^{48} +(2.48834 + 1.80789i) q^{49} +(-4.59734 - 3.34016i) q^{50} +(0.117617 - 0.361987i) q^{51} +(4.82939 + 14.8633i) q^{52} +(1.13499 - 0.824619i) q^{53} -2.41640 q^{54} +(1.99827 + 8.76787i) q^{55} +8.80284 q^{56} +(0.809017 - 0.587785i) q^{57} +(3.63475 + 11.1866i) q^{58} +(-0.395132 + 1.21609i) q^{59} +(-8.42107 - 6.11826i) q^{60} +(-1.39489 - 1.01345i) q^{61} +(-4.68813 + 14.4286i) q^{62} +(0.612153 + 1.88401i) q^{63} +(7.87093 - 5.71856i) q^{64} -11.0379 q^{65} +(1.78085 + 7.81392i) q^{66} -7.59547 q^{67} +(1.18211 - 0.858856i) q^{68} +(-1.17952 - 3.63018i) q^{69} +(-4.01072 + 12.3437i) q^{70} +(8.02012 + 5.82696i) q^{71} +(-3.59503 - 2.61194i) q^{72} +(1.24682 - 3.83731i) q^{73} +(-1.01998 - 3.13917i) q^{74} +(1.90256 - 1.38229i) q^{75} +3.83898 q^{76} +(5.64120 - 3.36801i) q^{77} -9.83700 q^{78} +(-4.77622 + 3.47012i) q^{79} +(-2.56371 - 7.89030i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-7.31647 - 5.31573i) q^{82} +(-4.07923 - 2.96373i) q^{83} +(-2.35004 + 7.23269i) q^{84} +(0.318906 + 0.981490i) q^{85} +(-6.75799 + 4.90997i) q^{86} -4.86770 q^{87} +(-5.79677 + 13.5502i) q^{88} +15.9000 q^{89} +(5.30054 - 3.85106i) q^{90} +(2.49204 + 7.66970i) q^{91} +(4.52814 - 13.9362i) q^{92} +(-5.07934 - 3.69035i) q^{93} +(-25.1053 - 18.2401i) q^{94} +(-0.837869 + 2.57869i) q^{95} +(0.461582 + 1.42060i) q^{96} +(1.49893 - 1.08904i) q^{97} -7.43227 q^{98} +(-3.30318 - 0.298354i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + q^{2} + 8 q^{3} + q^{4} - 4 q^{5} - q^{6} + q^{7} - 13 q^{8} - 8 q^{9} + 10 q^{10} + 12 q^{11} - 26 q^{12} - 10 q^{13} + 18 q^{14} + 4 q^{15} - 19 q^{16} - 12 q^{17} - 4 q^{18} - 8 q^{19} + 15 q^{20}+ \cdots - 8 q^{99}+O(q^{100})$ 32 * q + q^2 + 8 * q^3 + q^4 - 4 * q^5 - q^6 + q^7 - 13 * q^8 - 8 * q^9 + 10 * q^10 + 12 * q^11 - 26 * q^12 - 10 * q^13 + 18 * q^14 + 4 * q^15 - 19 * q^16 - 12 * q^17 - 4 * q^18 - 8 * q^19 + 15 * q^20 + 4 * q^21 - 12 * q^22 + 72 * q^23 - 7 * q^24 - 10 * q^25 + 31 * q^26 + 8 * q^27 - 40 * q^28 - 9 * q^29 - 5 * q^30 + 8 * q^31 - 2 * q^33 + 6 * q^34 - 20 * q^35 + q^36 + 9 * q^37 + q^38 + 10 * q^39 - 70 * q^40 + 26 * q^41 + 22 * q^42 - 28 * q^43 - 74 * q^44 + 16 * q^45 - q^46 - 31 * q^47 - 16 * q^48 + 7 * q^49 - 12 * q^50 - 8 * q^51 - 19 * q^52 + 14 * q^53 - 6 * q^54 - 3 * q^55 + 28 * q^56 + 8 * q^57 + 42 * q^58 - q^59 - 15 * q^60 + 17 * q^61 - 47 * q^62 + q^63 + 39 * q^64 + 4 * q^65 - 8 * q^66 - 12 * q^68 + 8 * q^69 + 77 * q^70 - 2 * q^71 + 7 * q^72 + 14 * q^73 + 12 * q^74 + 10 * q^75 + 26 * q^76 - 36 * q^77 + 24 * q^78 - 19 * q^79 - 19 * q^80 - 8 * q^81 - 4 * q^82 + 36 * q^83 - 15 * q^84 - 4 * q^85 + 60 * q^86 - 26 * q^87 - 51 * q^88 + 70 * q^89 - 10 * q^90 - 39 * q^91 + q^92 - 8 * q^93 - 42 * q^94 - 4 * q^95 - 5 * q^96 + 23 * q^97 - 82 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$ .

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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

)

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

$2$	−1.95491	+	1.42032i	−1.38233	+	1.00432i	−0.385670	+	0.922637i	$0.626030\pi$
$2$	−1.95491	+	1.42032i	−1.38233	+	1.00432i	−0.996658	+	0.0816832i	$0.973970\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.18631	−	3.65109i	0.593155	−	1.82554i
$5$	2.19357	+	1.59372i	0.980994	+	0.712734i	0.957930	−	0.287000i	$-0.0926581\pi$
$5$	2.19357	+	1.59372i	0.980994	+	0.712734i	0.0230633	+	0.999734i	$0.492658\pi$
$6$	1.95491	+	1.42032i	0.798087	+	0.579844i
$7$	0.612153	−	1.88401i	0.231372	−	0.712090i	−0.766210	−	0.642590i	$-0.777860\pi$
$7$	0.612153	−	1.88401i	0.231372	−	0.712090i	0.997582	−	0.0694997i	$-0.0221403\pi$
$8$	1.37318	+	4.22622i	0.485493	+	1.49419i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−6.55182			−2.07187
$11$	2.49696	+	2.18293i	0.752861	+	0.658179i
$11$	2.49696	+	2.18293i	0.752861	+	0.658179i
$12$	−3.83898			−1.10822
$13$	−3.29346	+	2.39284i	−0.913441	+	0.663653i	−0.941883	−	0.335942i	$-0.890945\pi$
$13$	−3.29346	+	2.39284i	−0.913441	+	0.663653i	0.0284421	+	0.999595i	$0.490945\pi$
$14$	1.47921	+	4.55253i	0.395334	+	1.21671i
$15$	0.837869	−	2.57869i	0.216337	−	0.665816i
$16$	−2.47543	−	1.79851i	−0.618858	−	0.449627i
$17$	0.307924	+	0.223720i	0.0746826	+	0.0542601i	0.624500	−	0.781025i	$-0.285303\pi$
$17$	0.307924	+	0.223720i	0.0746826	+	0.0542601i	−0.549818	+	0.835285i	$0.685303\pi$
$18$	0.746708	−	2.29813i	0.176001	−	0.541675i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	8.42107	−	6.11826i	1.88301	−	1.36809i
$21$	−1.98097			−0.432283
$22$	−7.98179	−	0.720942i	−1.70172	−	0.153705i
$23$	3.81700			0.795899			0.397950	−	0.917407i	$-0.369722\pi$
$23$	3.81700			0.795899			0.397950	+	0.917407i	$0.369722\pi$
$24$	3.59503	−	2.61194i	0.733833	−	0.533161i
$25$	0.726713	+	2.23659i	0.145343	+	0.447318i
$26$	3.03980	−	9.35554i	0.596154	−	1.83477i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−6.15249	−	4.47005i	−1.16271	−	0.844759i
$29$	1.50420	−	4.62945i	0.279323	−	0.859668i	−0.708720	−	0.705490i	$-0.750727\pi$
$29$	1.50420	−	4.62945i	0.279323	−	0.859668i	0.988043	−	0.154178i	$-0.0492730\pi$
$30$	2.02462	+	6.23115i	0.369644	+	1.13765i
$31$	5.07934	−	3.69035i	0.912276	−	0.662807i	−0.0293138	−	0.999570i	$-0.509332\pi$
$31$	5.07934	−	3.69035i	0.912276	−	0.662807i	0.941589	+	0.336763i	$0.109332\pi$
$32$	−1.49371			−0.264053
$33$	1.30449	−	3.04931i	0.227083	−	0.530817i
$34$	−0.919718			−0.157730
$35$	4.34539	−	3.15711i	0.734505	−	0.533649i
$36$	1.18631	+	3.65109i	0.197718	+	0.608514i
$37$	−0.422107	+	1.29911i	−0.0693940	+	0.213573i	−0.979739	−	0.200277i	$-0.935816\pi$
$37$	−0.422107	+	1.29911i	−0.0693940	+	0.213573i	0.910345	+	0.413849i	$0.135816\pi$
$38$	−1.95491	−	1.42032i	−0.317128	−	0.230407i
$39$	3.29346	+	2.39284i	0.527375	+	0.383160i
$40$	−3.72324	+	11.4590i	−0.588696	+	1.81182i
$41$	1.15653	+	3.55944i	0.180620	+	0.555891i	0.999845	−	0.0175804i	$-0.00559630\pi$
$41$	1.15653	+	3.55944i	0.180620	+	0.555891i	−0.819225	+	0.573472i	$0.805596\pi$
$42$	3.87261	−	2.81362i	0.597557	−	0.434150i
$43$	3.45694			0.527178			0.263589	−	0.964635i	$-0.415094\pi$
$43$	3.45694			0.527178			0.263589	+	0.964635i	$0.415094\pi$
$44$	10.9322	−	6.52698i	1.64810	−	0.983979i
$45$	−2.71140			−0.404192
$46$	−7.46188	+	5.42137i	−1.10019	+	0.799338i
$47$	3.96846	+	12.2137i	0.578860	+	1.78155i	0.622643	+	0.782506i	$0.286059\pi$
$47$	3.96846	+	12.2137i	0.578860	+	1.78155i	−0.0437828	+	0.999041i	$0.513941\pi$
$48$	−0.945531	+	2.91005i	−0.136476	+	0.420029i
$49$	2.48834	+	1.80789i	0.355478	+	0.258270i
$50$	−4.59734	−	3.34016i	−0.650162	−	0.472370i
$51$	0.117617	−	0.361987i	0.0164696	−	0.0506883i
$52$	4.82939	+	14.8633i	0.669716	+	2.06117i
$53$	1.13499	−	0.824619i	0.155903	−	0.113270i	−0.507099	−	0.861888i	$-0.669282\pi$
$53$	1.13499	−	0.824619i	0.155903	−	0.113270i	0.663002	+	0.748618i	$0.269282\pi$
$54$	−2.41640			−0.328830
$55$	1.99827	+	8.76787i	0.269446	+	1.18226i
$56$	8.80284			1.17633
$57$	0.809017	−	0.587785i	0.107157	−	0.0778541i
$58$	3.63475	+	11.1866i	0.477266	+	1.46887i
$59$	−0.395132	+	1.21609i	−0.0514418	+	0.158322i	−0.973477	−	0.228784i	$-0.926525\pi$
$59$	−0.395132	+	1.21609i	−0.0514418	+	0.158322i	0.922035	+	0.387106i	$0.126525\pi$
$60$	−8.42107	−	6.11826i	−1.08715	−	0.789864i
$61$	−1.39489	−	1.01345i	−0.178598	−	0.129759i	0.494895	−	0.868953i	$-0.335207\pi$
$61$	−1.39489	−	1.01345i	−0.178598	−	0.129759i	−0.673492	+	0.739194i	$0.735207\pi$
$62$	−4.68813	+	14.4286i	−0.595394	+	1.83243i
$63$	0.612153	+	1.88401i	0.0771240	+	0.237363i
$64$	7.87093	−	5.71856i	0.983866	−	0.714821i
$65$	−11.0379			−1.36909
$66$	1.78085	+	7.81392i	0.219208	+	0.961827i
$67$	−7.59547			−0.927935			−0.463967	−	0.885852i	$-0.653575\pi$
$67$	−7.59547			−0.927935			−0.463967	+	0.885852i	$0.653575\pi$
$68$	1.18211	−	0.858856i	0.143352	−	0.104152i
$69$	−1.17952	−	3.63018i	−0.141997	−	0.437023i
$70$	−4.01072	+	12.3437i	−0.479372	+	1.47536i
$71$	8.02012	+	5.82696i	0.951813	+	0.691532i	0.951235	−	0.308467i	$-0.0998161\pi$
$71$	8.02012	+	5.82696i	0.951813	+	0.691532i	0.000577876		1.00000i	$0.499816\pi$
$72$	−3.59503	−	2.61194i	−0.423679	−	0.307821i
$73$	1.24682	−	3.83731i	0.145929	−	0.449124i	−0.851200	−	0.524841i	$-0.824125\pi$
$73$	1.24682	−	3.83731i	0.145929	−	0.449124i	0.997129	+	0.0757175i	$0.0241247\pi$
$74$	−1.01998	−	3.13917i	−0.118570	−	0.364921i
$75$	1.90256	−	1.38229i	0.219688	−	0.159613i
$76$	3.83898			0.440361
$77$	5.64120	−	3.36801i	0.642874	−	0.383821i
$78$	−9.83700			−1.11382
$79$	−4.77622	+	3.47012i	−0.537366	+	0.390420i	−0.823106	−	0.567888i	$-0.807761\pi$
$79$	−4.77622	+	3.47012i	−0.537366	+	0.390420i	0.285740	+	0.958307i	$0.407761\pi$
$80$	−2.56371	−	7.89030i	−0.286632	−	0.882162i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−7.31647	−	5.31573i	−0.807969	−	0.587024i
$83$	−4.07923	−	2.96373i	−0.447753	−	0.325312i	0.340955	−	0.940080i	$-0.389250\pi$
$83$	−4.07923	−	2.96373i	−0.447753	−	0.325312i	−0.788708	+	0.614768i	$0.789250\pi$
$84$	−2.35004	+	7.23269i	−0.256411	+	0.789151i
$85$	0.318906	+	0.981490i	0.0345902	+	0.106458i
$86$	−6.75799	+	4.90997i	−0.728733	+	0.529456i
$87$	−4.86770			−0.521872
$88$	−5.79677	+	13.5502i	−0.617938	+	1.44446i
$89$	15.9000			1.68540			0.842700	−	0.538384i	$-0.180965\pi$
$89$	15.9000			1.68540			0.842700	+	0.538384i	$0.180965\pi$
$90$	5.30054	−	3.85106i	0.558725	−	0.405938i
$91$	2.49204	+	7.66970i	0.261236	+	0.804003i
$92$	4.52814	−	13.9362i	0.472092	−	1.45295i
$93$	−5.07934	−	3.69035i	−0.526703	−	0.382672i
$94$	−25.1053	−	18.2401i	−2.58942	−	1.88132i
$95$	−0.837869	+	2.57869i	−0.0859635	+	0.264569i
$96$	0.461582	+	1.42060i	0.0471100	+	0.144990i
$97$	1.49893	−	1.08904i	0.152193	−	0.110575i	−0.509083	−	0.860718i	$-0.670015\pi$
$97$	1.49893	−	1.08904i	0.152193	−	0.110575i	0.661276	+	0.750143i	$0.270015\pi$
$98$	−7.43227			−0.750772
$99$	−3.30318	−	0.298354i	−0.331982	−	0.0299857i
$100$	9.02809			0.902809
$101$	−12.1062	+	8.79566i	−1.20461	+	0.875200i	−0.994730	−	0.102527i	$-0.967307\pi$
$101$	−12.1062	+	8.79566i	−1.20461	+	0.875200i	−0.209880	+	0.977727i	$0.567307\pi$
$102$	0.284208	+	0.874704i	0.0281408	+	0.0866086i
$103$	2.93956	−	9.04704i	0.289644	−	0.891431i	−0.695325	−	0.718696i	$-0.744739\pi$
$103$	2.93956	−	9.04704i	0.289644	−	0.891431i	0.984968	−	0.172735i	$-0.0552606\pi$
$104$	−14.6352	−	10.6331i	−1.43509	−	1.04266i
$105$	−4.34539	−	3.15711i	−0.424067	−	0.308103i
$106$	−1.04758	+	3.22411i	−0.101750	+	0.313153i
$107$	5.01564	+	15.4366i	0.484880	+	1.49231i	0.832154	+	0.554544i	$0.187107\pi$
$107$	5.01564	+	15.4366i	0.484880	+	1.49231i	−0.347274	+	0.937764i	$0.612893\pi$
$108$	3.10580	−	2.25650i	0.298856	−	0.217131i
$109$	12.0781			1.15687			0.578436	−	0.815728i	$-0.303663\pi$
$109$	12.0781			1.15687			0.578436	+	0.815728i	$0.303663\pi$
$110$	−16.3596	−	14.3022i	−1.55983	−	1.36366i
$111$	1.36597			0.129652
$112$	−4.90375	+	3.56279i	−0.463361	+	0.336652i
$113$	−1.22401	−	3.76711i	−0.115145	−	0.354380i	0.876832	−	0.480796i	$-0.159652\pi$
$113$	−1.22401	−	3.76711i	−0.115145	−	0.354380i	−0.991977	+	0.126417i	$0.959652\pi$
$114$	−0.746708	+	2.29813i	−0.0699356	+	0.215240i
$115$	8.37285	+	6.08323i	0.780772	+	0.567264i
$116$	−15.1181	−	10.9839i	−1.40368	−	1.01983i
$117$	1.25799	−	3.87169i	0.116301	−	0.357938i
$118$	−0.954797	−	2.93856i	−0.0878962	−	0.270517i
$119$	0.609988	−	0.443182i	0.0559175	−	0.0406265i
$120$	12.0487			1.09989
$121$	1.46961	+	10.9014i	0.133601	+	0.991035i
$122$	4.16631			0.377200
$123$	3.02784	−	2.19986i	0.273011	−	0.198354i
$124$	−7.44813	−	22.9230i	−0.668862	−	2.05855i
$125$	2.21894	−	6.82918i	0.198468	−	0.610820i
$126$	−3.87261	−	2.81362i	−0.344999	−	0.250657i
$127$	0.747831	+	0.543331i	0.0663593	+	0.0482128i	0.620470	−	0.784230i	$-0.286942\pi$
$127$	0.747831	+	0.543331i	0.0663593	+	0.0482128i	−0.554111	+	0.832443i	$0.686942\pi$
$128$	−6.34156	+	19.5173i	−0.560520	+	1.72510i
$129$	−1.06825	−	3.28774i	−0.0940544	−	0.289470i
$130$	21.5781	−	15.6774i	1.89253	−	1.37500i
$131$	17.2255			1.50500			0.752499	−	0.658594i	$-0.228848\pi$
$131$	17.2255			1.50500			0.752499	+	0.658594i	$0.228848\pi$
$132$	−9.58577	−	8.38023i	−0.834335	−	0.729406i
$133$	1.98097			0.171772
$134$	14.8484	−	10.7880i	1.28271	−	0.931944i
$135$	0.837869	+	2.57869i	0.0721123	+	0.221939i
$136$	−0.522653	+	1.60856i	−0.0448172	+	0.137933i
$137$	−13.6862	−	9.94360i	−1.16929	−	0.849539i	−0.178367	−	0.983964i	$-0.557081\pi$
$137$	−13.6862	−	9.94360i	−1.16929	−	0.849539i	−0.990924	+	0.134425i	$0.957081\pi$
$138$	7.46188	+	5.42137i	0.635197	+	0.461498i
$139$	4.76648	−	14.6697i	0.404288	−	1.24427i	−0.517201	−	0.855864i	$-0.673026\pi$
$139$	4.76648	−	14.6697i	0.404288	−	1.24427i	0.921489	−	0.388405i	$-0.126974\pi$
$140$	−6.37191	−	19.6107i	−0.538524	−	1.65741i
$141$	10.3896	−	7.54847i	0.874960	−	0.635695i
$142$	−23.9547			−2.01024
$143$	−13.4470	−	1.21458i	−1.12450	−	0.101568i
$144$	3.05980			0.254984
$145$	10.6776	−	7.75775i	0.886729	−	0.644246i
$146$	3.01281	+	9.27248i	0.249342	+	0.767396i
$147$	0.950463	−	2.92522i	0.0783929	−	0.241268i
$148$	4.24242	+	3.08230i	0.348725	+	0.253363i
$149$	10.8478	+	7.88141i	0.888689	+	0.645670i	0.935536	−	0.353232i	$-0.114917\pi$
$149$	10.8478	+	7.88141i	0.888689	+	0.645670i	−0.0468471	+	0.998902i	$0.514917\pi$
$150$	−1.75603	+	5.40449i	−0.143379	+	0.441275i
$151$	3.07225	+	9.45541i	0.250016	+	0.769470i	0.994771	+	0.102132i	$0.0325665\pi$
$151$	3.07225	+	9.45541i	0.250016	+	0.769470i	−0.744755	+	0.667338i	$0.767434\pi$
$152$	−3.59503	+	2.61194i	−0.291596	+	0.211857i
$153$	−0.380615			−0.0307709
$154$	−6.24434	+	14.5965i	−0.503183	+	1.17622i
$155$	17.0233			1.36734
$156$	12.6435	−	9.18605i	1.01229	−	0.735473i
$157$	−7.57036	−	23.2992i	−0.604181	−	1.85948i	−0.502327	−	0.864678i	$-0.667522\pi$
$157$	−7.57036	−	23.2992i	−0.604181	−	1.85948i	−0.101854	−	0.994799i	$-0.532478\pi$
$158$	4.40836	−	13.5675i	0.350710	−	1.07938i
$159$	−1.13499	−	0.824619i	−0.0900106	−	0.0653965i
$160$	−3.27655	−	2.38056i	−0.259034	−	0.188199i
$161$	2.33659	−	7.19128i	0.184149	−	0.566752i
$162$	0.746708	+	2.29813i	0.0586669	+	0.180558i
$163$	4.21993	−	3.06596i	0.330530	−	0.240144i	−0.410125	−	0.912029i	$-0.634515\pi$
$163$	4.21993	−	3.06596i	0.330530	−	0.240144i	0.740656	+	0.671885i	$0.234515\pi$
$164$	14.3678			1.12194
$165$	7.72124	−	4.60988i	0.601098	−	0.358879i
$166$	12.1840			0.945659
$167$	−18.5069	+	13.4460i	−1.43211	+	1.04049i	−0.442485	+	0.896776i	$0.645903\pi$
$167$	−18.5069	+	13.4460i	−1.43211	+	1.04049i	−0.989620	+	0.143710i	$0.954097\pi$
$168$	−2.72023	−	8.37200i	−0.209870	−	0.645914i
$169$	1.10397	−	3.39767i	0.0849208	−	0.261359i
$170$	−2.01746	−	1.46577i	−0.154732	−	0.112420i
$171$	−0.809017	−	0.587785i	−0.0618671	−	0.0449491i
$172$	4.10100	−	12.6216i	0.312698	−	0.962387i
$173$	−5.03060	−	15.4826i	−0.382470	−	1.17712i	−0.938299	−	0.345825i	$-0.887599\pi$
$173$	−5.03060	−	15.4826i	−0.382470	−	1.17712i	0.555829	−	0.831296i	$-0.312401\pi$
$174$	9.51589	−	6.91370i	0.721398	−	0.524126i
$175$	4.65863			0.352159
$176$	−2.25503	−	9.89450i	−0.169980	−	0.745826i
$177$	1.27867			0.0961111
$178$	−31.0831	+	22.5832i	−2.32977	+	1.69268i
$179$	−6.47489	−	19.9277i	−0.483956	−	1.48946i	−0.833487	−	0.552539i	$-0.813659\pi$
$179$	−6.47489	−	19.9277i	−0.483956	−	1.48946i	0.349531	−	0.936925i	$-0.386341\pi$
$180$	−3.21656	+	9.89956i	−0.239748	+	0.737869i
$181$	−14.1677	−	10.2934i	−1.05307	−	0.765103i	−0.0802793	−	0.996772i	$-0.525581\pi$
$181$	−14.1677	−	10.2934i	−1.05307	−	0.765103i	−0.972795	+	0.231669i	$0.925581\pi$
$182$	−15.7651	−	11.4540i	−1.16859	−	0.849031i
$183$	−0.532801	+	1.63979i	−0.0393858	+	0.121217i
$184$	5.24143	+	16.1315i	0.386403	+	1.18923i
$185$	−2.99634	+	2.17697i	−0.220295	+	0.160054i
$186$	15.1711			1.11240
$187$	0.280508	+	1.23080i	0.0205128	+	0.0900048i
$188$	49.3010			3.59565
$189$	1.60264	−	1.16438i	0.116575	−	0.0846965i
$190$	−2.02462	−	6.23115i	−0.146882	−	0.452055i
$191$	−7.68903	+	23.6644i	−0.556358	+	1.71230i	0.135970	+	0.990713i	$0.456585\pi$
$191$	−7.68903	+	23.6644i	−0.556358	+	1.71230i	−0.692329	+	0.721582i	$0.743415\pi$
$192$	−7.87093	−	5.71856i	−0.568035	−	0.412702i
$193$	−1.12816	−	0.819655i	−0.0812066	−	0.0590001i	0.546441	−	0.837497i	$-0.315982\pi$
$193$	−1.12816	−	0.819655i	−0.0812066	−	0.0590001i	−0.627648	+	0.778497i	$0.715982\pi$
$194$	−1.38349	+	4.25794i	−0.0993286	+	0.305702i
$195$	3.41091	+	10.4977i	0.244260	+	0.751756i
$196$	9.55270	−	6.94045i	0.682336	−	0.495746i
$197$	−3.64041			−0.259368			−0.129684	−	0.991555i	$-0.541396\pi$
$197$	−3.64041			−0.259368			−0.129684	+	0.991555i	$0.541396\pi$
$198$	6.88117	−	4.10833i	0.489023	−	0.291966i
$199$	−10.2786			−0.728629			−0.364315	−	0.931276i	$-0.618697\pi$
$199$	−10.2786			−0.728629			−0.364315	+	0.931276i	$0.618697\pi$
$200$	−8.45441	+	6.14249i	−0.597817	+	0.434339i
$201$	2.34713	+	7.22373i	0.165554	+	0.509522i
$202$	11.1738	−	34.3894i	0.786185	−	2.41963i
$203$	−7.80115	−	5.66787i	−0.547533	−	0.397806i
$204$	−1.18211	−	0.858856i	−0.0827646	−	0.0601320i
$205$	−3.13582	+	9.65107i	−0.219015	+	0.674060i
$206$	7.10315	+	21.8612i	0.494900	+	1.52315i
$207$	−3.08802	+	2.24358i	−0.214632	+	0.155939i
$208$	12.4563			0.863687
$209$	−1.30449	+	3.04931i	−0.0902334	+	0.210925i
$210$	12.9790			0.895633
$211$	0.496683	−	0.360861i	0.0341931	−	0.0248427i	−0.570557	−	0.821258i	$-0.693273\pi$
$211$	0.496683	−	0.360861i	0.0341931	−	0.0248427i	0.604751	+	0.796415i	$0.293273\pi$
$212$	−1.66430	−	5.12220i	−0.114305	−	0.351794i
$213$	3.06341	−	9.42821i	0.209902	−	0.646011i
$214$	−31.7300	−	23.0532i	−2.16902	−	1.57588i
$215$	7.58303	+	5.50940i	0.517159	+	0.375738i
$216$	−1.37318	+	4.22622i	−0.0934331	+	0.287558i
$217$	−3.84334	−	11.8286i	−0.260903	−	0.802977i
$218$	−23.6116	+	17.1548i	−1.59918	+	1.16187i
$219$	−4.03479			−0.272646
$220$	34.3828	+	3.10557i	2.31809	+	0.209377i
$221$	−1.54946			−0.104228
$222$	−2.67034	+	1.94011i	−0.179221	+	0.130212i
$223$	5.93641	+	18.2704i	0.397531	+	1.22348i	0.926973	+	0.375129i	$0.122402\pi$
$223$	5.93641	+	18.2704i	0.397531	+	1.22348i	−0.529442	+	0.848346i	$0.677598\pi$
$224$	−0.914379	+	2.81417i	−0.0610945	+	0.188029i
$225$	−1.90256	−	1.38229i	−0.126837	−	0.0921526i
$226$	7.74333	+	5.62586i	0.515078	+	0.374226i
$227$	4.43565	−	13.6515i	0.294404	−	0.906083i	−0.689017	−	0.724746i	$-0.741957\pi$
$227$	4.43565	−	13.6515i	0.294404	−	0.906083i	0.983421	−	0.181338i	$-0.0580427\pi$
$228$	−1.18631	−	3.65109i	−0.0785653	−	0.241799i
$229$	14.3679	−	10.4389i	0.949457	−	0.689821i	−0.00122126	−	0.999999i	$-0.500389\pi$
$229$	14.3679	−	10.4389i	0.949457	−	0.689821i	0.950678	+	0.310178i	$0.100389\pi$
$230$	−25.0083			−1.64900
$231$	−4.94640	−	4.32432i	−0.325449	−	0.284519i
$232$	21.6306			1.42012
$233$	−10.1291	+	7.35925i	−0.663582	+	0.482121i	−0.867871	−	0.496790i	$-0.834512\pi$
$233$	−10.1291	+	7.35925i	−0.663582	+	0.482121i	0.204289	+	0.978911i	$0.434512\pi$
$234$	3.03980	+	9.35554i	0.198718	+	0.611591i
$235$	−10.7601	+	33.1162i	−0.701911	+	2.16026i
$236$	3.97131	+	2.88532i	0.258510	+	0.187819i
$237$	4.77622	+	3.47012i	0.310249	+	0.225409i
$238$	−0.563008	+	1.73276i	−0.0364944	+	0.112318i
$239$	−1.30863	−	4.02753i	−0.0846479	−	0.260520i	0.899770	−	0.436365i	$-0.143734\pi$
$239$	−1.30863	−	4.02753i	−0.0846479	−	0.260520i	−0.984418	+	0.175845i	$0.943734\pi$
$240$	−6.71189	+	4.87647i	−0.433251	+	0.314775i
$241$	−6.89447			−0.444112			−0.222056	−	0.975034i	$-0.571277\pi$
$241$	−6.89447			−0.444112			−0.222056	+	0.975034i	$0.571277\pi$
$242$	−18.3564	−	19.2239i	−1.18000	−	1.23576i
$243$	−1.00000			−0.0641500
$244$	−5.35496	+	3.89061i	−0.342816	+	0.249071i
$245$	2.57709	+	7.93145i	0.164644	+	0.506722i
$246$	−2.79464	+	8.60102i	−0.178180	+	0.548381i
$247$	−3.29346	−	2.39284i	−0.209558	−	0.152253i
$248$	22.5711	+	16.3988i	1.43326	+	1.04133i
$249$	−1.55813	+	4.79542i	−0.0987422	+	0.303897i
$250$	5.36183	+	16.5020i	0.339112	+	1.04368i
$251$	−8.32832	+	6.05088i	−0.525679	+	0.381928i	−0.818739	−	0.574166i	$-0.805326\pi$
$251$	−8.32832	+	6.05088i	−0.525679	+	0.381928i	0.293060	+	0.956094i	$0.405326\pi$
$252$	7.60490			0.479064
$253$	9.53089	+	8.33225i	0.599202	+	0.523844i
$254$	−2.23365			−0.140151
$255$	0.834906	−	0.606594i	0.0522838	−	0.0379864i
$256$	−9.31088	−	28.6559i	−0.581930	−	1.79100i
$257$	−9.51457	+	29.2828i	−0.593503	+	1.82661i	−0.0314603	+	0.999505i	$0.510016\pi$
$257$	−9.51457	+	29.2828i	−0.593503	+	1.82661i	−0.562042	+	0.827108i	$0.689984\pi$
$258$	6.75799	+	4.90997i	0.420734	+	0.305681i
$259$	2.18915	+	1.59051i	0.136027	+	0.0988295i
$260$	−13.0944	+	40.3005i	−0.812081	+	2.49933i
$261$	1.50420	+	4.62945i	0.0931077	+	0.286556i
$262$	−33.6742	+	24.4658i	−2.08040	+	1.51150i
$263$	−27.9296			−1.72221			−0.861105	−	0.508427i	$-0.830227\pi$
$263$	−27.9296			−1.72221			−0.861105	+	0.508427i	$0.830227\pi$
$264$	14.6784	+	1.32580i	0.903390	+	0.0815972i
$265$	3.80389			0.233671
$266$	−3.87261	+	2.81362i	−0.237445	+	0.172514i
$267$	−4.91338	−	15.1218i	−0.300694	−	0.925440i
$268$	−9.01059	+	27.7317i	−0.550409	+	1.69399i
$269$	−15.3597	−	11.1595i	−0.936498	−	0.680406i	0.0110770	−	0.999939i	$-0.496474\pi$
$269$	−15.3597	−	11.1595i	−0.936498	−	0.680406i	−0.947575	+	0.319533i	$0.896474\pi$
$270$	−5.30054	−	3.85106i	−0.322580	−	0.234368i
$271$	4.61037	−	14.1892i	0.280060	−	0.861935i	−0.707776	−	0.706437i	$-0.750302\pi$
$271$	4.61037	−	14.1892i	0.280060	−	0.861935i	0.987836	−	0.155499i	$-0.0496985\pi$
$272$	−0.359884	−	1.10761i	−0.0218211	−	0.0671586i
$273$	6.52423	−	4.74013i	0.394865	−	0.286886i
$274$	40.8784			2.46955
$275$	−3.06776	+	7.17104i	−0.184993	+	0.432430i
$276$	−14.6534			−0.882030
$277$	−7.31815	+	5.31695i	−0.439705	+	0.319464i	−0.785518	−	0.618839i	$-0.787603\pi$
$277$	−7.31815	+	5.31695i	−0.439705	+	0.319464i	0.345813	+	0.938304i	$0.387603\pi$
$278$	11.5177	+	35.4479i	0.690787	+	2.12602i
$279$	−1.94013	+	5.97112i	−0.116153	+	0.357481i
$280$	19.3096	+	14.0293i	1.15397	+	0.838410i
$281$	−21.1224	−	15.3463i	−1.26006	−	0.915485i	−0.261296	−	0.965259i	$-0.584150\pi$
$281$	−21.1224	−	15.3463i	−1.26006	−	0.915485i	−0.998761	+	0.0497738i	$0.984150\pi$
$282$	−9.58939	+	29.5131i	−0.571040	+	1.75748i
$283$	−7.63707	−	23.5045i	−0.453977	−	1.39720i	−0.872332	−	0.488914i	$-0.837393\pi$
$283$	−7.63707	−	23.5045i	−0.453977	−	1.39720i	0.418355	−	0.908283i	$-0.362607\pi$
$284$	30.7891	−	22.3696i	1.82699	−	1.32739i
$285$	2.71140			0.160609
$286$	28.0128	−	16.7247i	1.65643	−	0.988954i
$287$	7.41401			0.437635
$288$	1.20844	−	0.877980i	0.0712078	−	0.0517355i
$289$	−5.20852	−	16.0302i	−0.306384	−	0.942952i
$290$	−9.85526	+	30.3314i	−0.578721	+	1.78112i
$291$	−1.49893	−	1.08904i	−0.0878689	−	0.0638405i
$292$	−12.5313	−	9.10449i	−0.733336	−	0.532800i
$293$	6.69398	−	20.6020i	0.391067	−	1.20358i	−0.540916	−	0.841077i	$-0.681922\pi$
$293$	6.69398	−	20.6020i	0.391067	−	1.20358i	0.931983	−	0.362503i	$-0.118078\pi$
$294$	2.29670	+	7.06851i	0.133946	+	0.412244i
$295$	−2.80486	+	2.03785i	−0.163305	+	0.118648i
$296$	−6.06996			−0.352809
$297$	0.736987	+	3.23371i	0.0427643	+	0.187639i
$298$	−32.4006			−1.87692
$299$	−12.5711	+	9.13346i	−0.727007	+	0.528201i
$300$	−2.78983	−	8.58623i	−0.161071	−	0.495726i
$301$	2.11618	−	6.51292i	0.121974	−	0.375398i
$302$	−19.4357	−	14.1209i	−1.11840	−	0.812564i
$303$	12.1062	+	8.79566i	0.695482	+	0.505297i
$304$	0.945531	−	2.91005i	0.0542299	−	0.166903i
$305$	−1.44464	−	4.44614i	−0.0827197	−	0.254585i
$306$	0.744067	−	0.540597i	0.0425355	−	0.0309038i
$307$	−8.39607			−0.479189			−0.239595	−	0.970873i	$-0.577015\pi$
$307$	−8.39607			−0.479189			−0.239595	+	0.970873i	$0.577015\pi$
$308$	−5.60471	−	24.5920i	−0.319358	−	1.40126i
$309$	−9.51262			−0.541154
$310$	−33.2789	+	24.1785i	−1.89011	+	1.37325i
$311$	6.17490	+	19.0044i	0.350147	+	1.07764i	0.958770	+	0.284182i	$0.0917219\pi$
$311$	6.17490	+	19.0044i	0.350147	+	1.07764i	−0.608624	+	0.793459i	$0.708278\pi$
$312$	−5.59013	+	17.2047i	−0.316479	+	0.974022i
$313$	5.95044	+	4.32325i	0.336339	+	0.244364i	0.743115	−	0.669163i	$-0.233347\pi$
$313$	5.95044	+	4.32325i	0.336339	+	0.244364i	−0.406777	+	0.913528i	$0.633347\pi$
$314$	47.8917	+	34.7954i	2.70269	+	1.96362i
$315$	−1.65979	+	5.10831i	−0.0935187	+	0.287821i
$316$	7.00365	+	21.5550i	0.393986	+	1.21256i
$317$	−3.30938	+	2.40441i	−0.185873	+	0.135045i	−0.676831	−	0.736139i	$-0.736647\pi$
$317$	−3.30938	+	2.40441i	−0.185873	+	0.135045i	0.490957	+	0.871184i	$0.336647\pi$
$318$	3.39003			0.190103
$319$	13.8617	−	8.27599i	0.776107	−	0.463366i
$320$	26.3792			1.47464
$321$	13.1311	−	9.54031i	0.732907	−	0.532488i
$322$	5.64613	+	17.3770i	0.314646	+	0.968382i
$323$	−0.117617	+	0.361987i	−0.00654436	+	0.0201415i
$324$	−3.10580	−	2.25650i	−0.172544	−	0.125361i
$325$	−7.74519	−	5.62721i	−0.429626	−	0.312142i
$326$	−3.89492	+	11.9873i	−0.215719	+	0.663916i
$327$	−3.73234	−	11.4870i	−0.206399	−	0.635230i
$328$	−13.4548	+	9.77551i	−0.742919	+	0.539762i
$329$	25.4400			1.40255
$330$	−8.54678	+	19.9786i	−0.470485	+	1.09978i
$331$	−17.3165			−0.951803			−0.475901	−	0.879499i	$-0.657878\pi$
$331$	−17.3165			−0.951803			−0.475901	+	0.879499i	$0.657878\pi$
$332$	−15.6601	+	11.3777i	−0.859458	+	0.624433i
$333$	−0.422107	−	1.29911i	−0.0231313	−	0.0711909i
$334$	17.0815	−	52.5715i	0.934659	−	2.87658i
$335$	−16.6612	−	12.1051i	−0.910298	−	0.661370i
$336$	4.90375	+	3.56279i	0.267522	+	0.194366i
$337$	−0.948618	+	2.91954i	−0.0516745	+	0.159038i	−0.973564	−	0.228416i	$-0.926645\pi$
$337$	−0.948618	+	2.91954i	−0.0516745	+	0.159038i	0.921889	+	0.387454i	$0.126645\pi$
$338$	2.66763	+	8.21012i	0.145100	+	0.446572i
$339$	−3.20449	+	2.32820i	−0.174044	+	0.126450i
$340$	3.96183			0.214860
$341$	20.7387	+	1.87319i	1.12306	+	0.101439i
$342$	2.41640			0.130664
$343$	16.1478	−	11.7321i	0.871899	−	0.633472i
$344$	4.74700	+	14.6098i	0.255941	+	0.787706i
$345$	3.19814	−	9.84288i	0.172182	−	0.529923i
$346$	31.8247	+	23.1220i	1.71090	+	1.24305i
$347$	3.81288	+	2.77022i	0.204686	+	0.148713i	0.685406	−	0.728161i	$-0.259625\pi$
$347$	3.81288	+	2.77022i	0.204686	+	0.148713i	−0.480720	+	0.876874i	$0.659625\pi$
$348$	−5.77460	+	17.7724i	−0.309551	+	0.952699i
$349$	0.572014	+	1.76048i	0.0306192	+	0.0942362i	0.965198	−	0.261519i	$-0.0842235\pi$
$349$	0.572014	+	1.76048i	0.0306192	+	0.0942362i	−0.934579	+	0.355756i	$0.884224\pi$
$350$	−9.10718	+	6.61676i	−0.486799	+	0.353680i
$351$	−4.07094			−0.217290
$352$	−3.72973	−	3.26067i	−0.198795	−	0.173794i
$353$	−7.20110			−0.383276			−0.191638	−	0.981466i	$-0.561380\pi$
$353$	−7.20110			−0.383276			−0.191638	+	0.981466i	$0.561380\pi$
$354$	−2.49969	+	1.81613i	−0.132857	+	0.0965263i
$355$	8.30614	+	25.5637i	0.440844	+	1.35678i
$356$	18.8624	−	58.0524i	0.999703	−	3.07677i
$357$	−0.609988	−	0.443182i	−0.0322840	−	0.0234557i
$358$	40.9615	+	29.7603i	2.16488	+	1.57288i
$359$	7.30987	−	22.4975i	0.385800	−	1.18737i	−0.550098	−	0.835100i	$-0.685410\pi$
$359$	7.30987	−	22.4975i	0.385800	−	1.18737i	0.935898	−	0.352271i	$-0.114590\pi$
$360$	−3.72324	−	11.4590i	−0.196232	−	0.603940i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	42.3164			2.22410
$363$	9.91370	−	4.76640i	0.520334	−	0.250171i
$364$	30.9591			1.62270
$365$	8.85059	−	6.43033i	0.463261	−	0.336579i
$366$	−1.28746	−	3.96239i	−0.0672966	−	0.207118i
$367$	5.79801	−	17.8444i	0.302653	−	0.931472i	−0.677889	−	0.735164i	$-0.737105\pi$
$367$	5.79801	−	17.8444i	0.302653	−	0.931472i	0.980542	−	0.196307i	$-0.0628950\pi$
$368$	−9.44873	−	6.86490i	−0.492549	−	0.357858i
$369$	−3.02784	−	2.19986i	−0.157623	−	0.114520i
$370$	2.76557	−	8.51155i	0.143775	−	0.442494i
$371$	−0.858805	−	2.64313i	−0.0445869	−	0.137224i
$372$	−19.4995	+	14.1672i	−1.01100	+	0.734535i
$373$	17.7552			0.919332			0.459666	−	0.888092i	$-0.347969\pi$
$373$	17.7552			0.919332			0.459666	+	0.888092i	$0.347969\pi$
$374$	−2.29650	−	2.00768i	−0.118749	−	0.103815i
$375$	−7.18062			−0.370806
$376$	−46.1682	+	33.5432i	−2.38094	+	1.72986i
$377$	6.12351	+	18.8462i	0.315377	+	0.970629i
$378$	−1.47921	+	4.55253i	−0.0760821	+	0.234157i
$379$	28.3680	+	20.6106i	1.45717	+	1.05869i	0.984090	+	0.177672i	$0.0568567\pi$
$379$	28.3680	+	20.6106i	1.45717	+	1.05869i	0.473077	+	0.881021i	$0.343143\pi$
$380$	8.42107	+	6.11826i	0.431992	+	0.313860i
$381$	0.285646	−	0.879128i	0.0146341	−	0.0450391i
$382$	−18.5797	−	57.1826i	−0.950623	−	2.92572i
$383$	25.6687	−	18.6494i	1.31161	−	0.952938i	0.311611	−	0.950210i	$-0.399132\pi$
$383$	25.6687	−	18.6494i	1.31161	−	0.952938i	0.999996	−	0.00272837i	$-0.000868468\pi$
$384$	20.5217			1.04724
$385$	17.7420	+	1.60252i	0.904217	+	0.0816719i
$386$	3.36962			0.171509
$387$	−2.79672	+	2.03194i	−0.142165	+	0.103289i
$388$	−2.19797	−	6.76467i	−0.111585	−	0.343424i
$389$	0.641382	−	1.97397i	0.0325194	−	0.100084i	−0.933479	−	0.358631i	$-0.883244\pi$
$389$	0.641382	−	1.97397i	0.0325194	−	0.100084i	0.965999	+	0.258547i	$0.0832436\pi$
$390$	−21.5781	−	15.6774i	−1.09265	−	0.793858i
$391$	1.17535	+	0.853939i	0.0594398	+	0.0431856i
$392$	−4.22358	+	12.9988i	−0.213323	+	0.656540i
$393$	−5.32297	−	16.3824i	−0.268508	−	0.826383i
$394$	7.11666	−	5.17056i	0.358532	−	0.260489i
$395$	−16.0074			−0.805418
$396$	−5.00791	+	11.7062i	−0.251657	+	0.588261i
$397$	−35.6381			−1.78863			−0.894313	−	0.447443i	$-0.852335\pi$
$397$	−35.6381			−1.78863			−0.894313	+	0.447443i	$0.852335\pi$
$398$	20.0937	−	14.5989i	1.00720	−	0.731777i
$399$	−0.612153	−	1.88401i	−0.0306460	−	0.0943186i
$400$	2.22360	−	6.84353i	0.111180	−	0.342176i
$401$	−18.8963	−	13.7290i	−0.943637	−	0.685593i	0.00565610	−	0.999984i	$-0.498200\pi$
$401$	−18.8963	−	13.7290i	−0.943637	−	0.685593i	−0.949293	+	0.314391i	$0.898200\pi$
$402$	−14.8484	−	10.7880i	−0.740573	−	0.538058i
$403$	−7.89816	+	24.3080i	−0.393435	+	1.21087i
$404$	17.7520	+	54.6351i	0.883196	+	2.71820i
$405$	2.19357	−	1.59372i	0.108999	−	0.0791926i
$406$	23.3007			1.15640
$407$	−3.88986	+	2.32240i	−0.192813	+	0.115117i
$408$	1.69134			0.0837339
$409$	−16.2832	+	11.8305i	−0.805154	+	0.584979i	−0.912422	−	0.409252i	$-0.865790\pi$
$409$	−16.2832	+	11.8305i	−0.805154	+	0.584979i	0.107268	+	0.994230i	$0.465790\pi$
$410$	−7.57739	−	23.3208i	−0.374221	−	1.15173i
$411$	−5.22766	+	16.0891i	−0.257862	+	0.793616i
$412$	−29.5443	−	21.4652i	−1.45554	−	1.05751i
$413$	2.04925	+	1.48887i	0.100837	+	0.0732624i
$414$	2.85018	−	8.77197i	0.140079	−	0.431119i
$415$	−4.22470	−	13.0023i	−0.207383	−	0.638258i
$416$	4.91947	−	3.57420i	0.241197	−	0.175240i
$417$	−15.4247			−0.755349
$418$	−1.78085	−	7.81392i	−0.0871044	−	0.382191i
$419$	−12.7433			−0.622552			−0.311276	−	0.950320i	$-0.600756\pi$
$419$	−12.7433			−0.622552			−0.311276	+	0.950320i	$0.600756\pi$
$420$	−16.6819	+	12.1201i	−0.813992	+	0.591400i
$421$	1.55680	+	4.79135i	0.0758739	+	0.233516i	0.981799	−	0.189921i	$-0.0608233\pi$
$421$	1.55680	+	4.79135i	0.0758739	+	0.233516i	−0.905925	+	0.423437i	$0.860823\pi$
$422$	−0.458429	+	1.41090i	−0.0223160	+	0.0686816i
$423$	−10.3896	−	7.54847i	−0.505158	−	0.367019i
$424$	5.04356	+	3.66436i	0.244937	+	0.177957i
$425$	−0.276598	+	0.851281i	−0.0134170	+	0.0412932i
$426$	7.40242	+	22.7823i	0.358649	+	1.10381i
$427$	−2.76324	+	2.00761i	−0.133722	+	0.0971550i
$428$	62.3103			3.01188
$429$	3.00023	+	13.1642i	0.144852	+	0.635574i
$430$	−22.6492			−1.09224
$431$	22.2781	−	16.1860i	1.07310	−	0.779652i	0.0966322	−	0.995320i	$-0.469193\pi$
$431$	22.2781	−	16.1860i	1.07310	−	0.779652i	0.976467	+	0.215668i	$0.0691929\pi$
$432$	−0.945531	−	2.91005i	−0.0454919	−	0.140010i
$433$	−4.99904	+	15.3854i	−0.240238	+	0.739377i	0.756145	+	0.654404i	$0.227080\pi$
$433$	−4.99904	+	15.3854i	−0.240238	+	0.739377i	−0.996383	+	0.0849733i	$0.972920\pi$
$434$	24.3138	+	17.6650i	1.16710	+	0.847948i
$435$	−10.6776	−	7.75775i	−0.511953	−	0.371956i
$436$	14.3284	−	44.0982i	0.686204	−	2.11192i
$437$	1.17952	+	3.63018i	0.0564240	+	0.173655i
$438$	7.88764	−	5.73071i	0.376886	−	0.273824i
$439$	−15.2525			−0.727963			−0.363981	−	0.931406i	$-0.618583\pi$
$439$	−15.2525			−0.727963			−0.363981	+	0.931406i	$0.618583\pi$
$440$	−34.3109	+	20.4850i	−1.63571	+	0.976583i
$441$	−3.07576			−0.146465
$442$	3.02905	−	2.20073i	0.144077	−	0.104678i
$443$	−2.16153	−	6.65250i	−0.102697	−	0.316070i	0.886486	−	0.462756i	$-0.153139\pi$
$443$	−2.16153	−	6.65250i	−0.102697	−	0.316070i	−0.989183	+	0.146686i	$0.953139\pi$
$444$	1.62046	−	4.98726i	0.0769036	−	0.236685i
$445$	34.8778	+	25.3402i	1.65337	+	1.20124i
$446$	−37.5550	−	27.2853i	−1.77828	−	1.29200i
$447$	4.14350	−	12.7524i	0.195981	−	0.603167i
$448$	−5.95564	−	18.3296i	−0.281377	−	0.865991i
$449$	−20.0691	+	14.5811i	−0.947120	+	0.688123i	−0.950124	−	0.311872i	$-0.899044\pi$
$449$	−20.0691	+	14.5811i	−0.947120	+	0.688123i	0.00300379	+	0.999995i	$0.499044\pi$
$450$	5.68262			0.267881
$451$	−4.88221	+	11.4124i	−0.229894	+	0.537389i
$452$	−15.2061			−0.715234
$453$	8.04325	−	5.84377i	0.377905	−	0.274564i
$454$	10.7183	+	32.9875i	0.503034	+	1.54818i
$455$	−6.75691	+	20.7956i	−0.316769	+	0.974914i
$456$	3.59503	+	2.61194i	0.168353	+	0.122316i
$457$	18.0942	+	13.1462i	0.846410	+	0.614953i	0.924154	−	0.382020i	$-0.124772\pi$
$457$	18.0942	+	13.1462i	0.846410	+	0.614953i	−0.0777438	+	0.996973i	$0.524772\pi$
$458$	−13.2613	+	40.8141i	−0.619660	+	1.90712i
$459$	0.117617	+	0.361987i	0.00548987	+	0.0168961i
$460$	32.1432	−	23.3534i	1.49868	−	1.08886i
$461$	−18.8329			−0.877137			−0.438568	−	0.898698i	$-0.644514\pi$
$461$	−18.8329			−0.877137			−0.438568	+	0.898698i	$0.644514\pi$
$462$	15.8117	+	1.42816i	0.735626	+	0.0664442i
$463$	−9.61412			−0.446806			−0.223403	−	0.974726i	$-0.571717\pi$
$463$	−9.61412			−0.446806			−0.223403	+	0.974726i	$0.571717\pi$
$464$	−12.0497	+	8.75459i	−0.559391	+	0.406421i
$465$	−5.26048	−	16.1901i	−0.243949	−	0.750797i
$466$	9.34902	−	28.7733i	0.433085	−	1.33290i
$467$	−28.4898	−	20.6990i	−1.31835	−	0.957836i	−0.999951	−	0.00987923i	$-0.996855\pi$
$467$	−28.4898	−	20.6990i	−1.31835	−	0.957836i	−0.318398	−	0.947957i	$-0.603145\pi$
$468$	−12.6435	−	9.18605i	−0.584447	−	0.424625i
$469$	−4.64959	+	14.3100i	−0.214698	+	0.660773i
$470$	−26.0007	−	80.0218i	−1.19932	−	3.69113i
$471$	−19.8195	+	14.3997i	−0.913233	+	0.663503i
$472$	−5.68205			−0.261538
$473$	8.63183	+	7.54626i	0.396892	+	0.346978i
$474$	−14.2658			−0.655248
$475$	−1.90256	+	1.38229i	−0.0872954	+	0.0634238i
$476$	−0.894462	−	2.75287i	−0.0409976	−	0.126178i
$477$	−0.433528	+	1.33426i	−0.0198499	+	0.0610916i
$478$	8.27864	+	6.01479i	0.378656	+	0.275110i
$479$	9.65705	+	7.01626i	0.441242	+	0.320581i	0.786128	−	0.618063i	$-0.212083\pi$
$479$	9.65705	+	7.01626i	0.441242	+	0.320581i	−0.344886	+	0.938644i	$0.612083\pi$
$480$	−1.25153	+	3.85182i	−0.0571244	+	0.175811i
$481$	−1.71837	−	5.28860i	−0.0783510	−	0.241139i
$482$	13.4781	−	9.79238i	0.613909	−	0.446031i
$483$	−7.56136			−0.344054
$484$	41.5453	+	7.56675i	1.88842	+	0.343943i
$485$	5.02363			0.228111
$486$	1.95491	−	1.42032i	0.0886764	−	0.0644272i
$487$	−0.499890	−	1.53850i	−0.0226522	−	0.0697162i	0.939091	−	0.343667i	$-0.111669\pi$
$487$	−0.499890	−	1.53850i	−0.0226522	−	0.0697162i	−0.961744	+	0.273951i	$0.911669\pi$
$488$	2.36761	−	7.28676i	0.107177	−	0.329856i
$489$	−4.21993	−	3.06596i	−0.190832	−	0.138647i
$490$	−16.3032	−	11.8450i	−0.736503	−	0.535101i
$491$	7.22478	−	22.2356i	0.326050	−	1.00348i	−0.644915	−	0.764255i	$-0.723107\pi$
$491$	7.22478	−	22.2356i	0.326050	−	1.00348i	0.970964	−	0.239224i	$-0.0768930\pi$
$492$	−4.43990	−	13.6646i	−0.200166	−	0.616049i
$493$	1.49888	−	1.08900i	0.0675062	−	0.0490461i
$494$	9.83700			0.442588
$495$	−6.77026	−	5.91880i	−0.304300	−	0.266030i
$496$	−19.2107			−0.862585
$497$	15.8876	−	11.5430i	0.712656	−	0.517775i
$498$	−3.76505	−	11.5876i	−0.168716	−	0.519255i
$499$	−3.33533	+	10.2651i	−0.149310	+	0.459529i	−0.997540	−	0.0700990i	$-0.977668\pi$
$499$	−3.33533	+	10.2651i	−0.149310	+	0.459529i	0.848230	+	0.529628i	$0.177668\pi$
$500$	−22.3016	−	16.2030i	−0.997357	−	0.724622i
$501$	18.5069	+	13.4460i	0.826826	+	0.600724i
$502$	7.68689	−	23.6578i	0.343083	−	1.05590i
$503$	−2.46710	−	7.59296i	−0.110003	−	0.338553i	0.880869	−	0.473359i	$-0.156959\pi$
$503$	−2.46710	−	7.59296i	−0.110003	−	0.338553i	−0.990872	+	0.134806i	$0.956959\pi$
$504$	−7.12165	+	5.17418i	−0.317223	+	0.230476i
$505$	−40.5736			−1.80550
$506$	−30.4665	−	2.75184i	−1.35440	−	0.122334i
$507$	−3.57252			−0.158661
$508$	2.87091	−	2.08584i	0.127376	−	0.0925441i
$509$	−12.4968	−	38.4611i	−0.553909	−	1.70476i	−0.698807	−	0.715310i	$-0.746285\pi$
$509$	−12.4968	−	38.4611i	−0.553909	−	1.70476i	0.144898	−	0.989447i	$-0.453715\pi$
$510$	−0.770603	+	2.37167i	−0.0341229	+	0.105019i
$511$	−6.46631	−	4.69805i	−0.286053	−	0.207829i
$512$	25.6978	+	18.6705i	1.13569	+	0.825128i
$513$	−0.309017	+	0.951057i	−0.0136434	+	0.0419902i
$514$	−22.9910	−	70.7590i	−1.01409	−	3.12105i
$515$	20.8666	−	15.1605i	0.919492	−	0.668050i
$516$	−13.2711			−0.584228
$517$	−16.7525	+	39.1599i	−0.736776	+	1.72225i
$518$	−6.53862			−0.287291
$519$	−13.1703	+	9.56878i	−0.578112	+	0.420023i
$520$	−15.1571	−	46.6487i	−0.664682	−	2.04568i
$521$	3.32563	−	10.2352i	0.145699	−	0.448414i	−0.851402	−	0.524514i	$-0.824247\pi$
$521$	3.32563	−	10.2352i	0.145699	−	0.448414i	0.997100	+	0.0761002i	$0.0242469\pi$
$522$	−9.51589	−	6.91370i	−0.416499	−	0.302604i
$523$	16.6692	+	12.1109i	0.728894	+	0.529572i	0.889213	−	0.457493i	$-0.151252\pi$
$523$	16.6692	+	12.1109i	0.728894	+	0.529572i	−0.160320	+	0.987065i	$0.551252\pi$
$524$	20.4348	−	62.8917i	0.892697	−	2.74744i
$525$	−1.43959	−	4.43062i	−0.0628291	−	0.193368i
$526$	54.5997	−	39.6690i	2.38066	−	1.72965i
$527$	2.38966			0.104095
$528$	−8.71339	+	5.20223i	−0.379202	+	0.226398i
$529$	−8.43051			−0.366544
$530$	−7.43625	+	5.40276i	−0.323010	+	0.234681i
$531$	−0.395132	−	1.21609i	−0.0171473	−	0.0527739i
$532$	2.35004	−	7.23269i	0.101887	−	0.313577i
$533$	−12.3261	−	8.95547i	−0.533905	−	0.387904i
$534$	31.0831	+	22.5832i	1.34510	+	0.977269i
$535$	−13.5994	+	41.8547i	−0.587954	+	1.80954i
$536$	−10.4300	−	32.1001i	−0.450506	−	1.38651i
$537$	−16.9515	+	12.3160i	−0.731511	+	0.531474i
$538$	45.8769			1.97789
$539$	2.26680	+	9.94611i	0.0976378	+	0.428409i
$540$	10.4090			0.447932
$541$	8.97671	−	6.52196i	0.385939	−	0.280401i	−0.377851	−	0.925867i	$-0.623337\pi$
$541$	8.97671	−	6.52196i	0.385939	−	0.280401i	0.763789	+	0.645466i	$0.223337\pi$
$542$	11.1405	+	34.2869i	0.478525	+	1.47275i
$543$	−5.41156	+	16.6551i	−0.232232	+	0.714738i
$544$	−0.459949	−	0.334173i	−0.0197202	−	0.0143275i
$545$	26.4941	+	19.2491i	1.13488	+	0.824542i
$546$	−6.02175	+	18.5330i	−0.257707	+	0.793141i
$547$	4.37178	+	13.4549i	0.186924	+	0.575292i	0.999976	−	0.00689842i	$-0.00219585\pi$
$547$	4.37178	+	13.4549i	0.186924	+	0.575292i	−0.813053	+	0.582190i	$0.802196\pi$
$548$	−52.5410	+	38.1733i	−2.24444	+	1.63068i
$549$	1.72418			0.0735863
$550$	−4.18802	−	18.3759i	−0.178578	−	0.783552i
$551$	4.86770			0.207371
$552$	13.7222	−	9.96979i	0.584057	−	0.424343i
$553$	3.61399	+	11.1227i	0.153682	+	0.472985i
$554$	6.75452	−	20.7883i	0.286972	−	0.883209i
$555$	2.99634	+	2.17697i	0.127188	+	0.0924072i
$556$	−47.9059	−	34.8057i	−2.03166	−	1.47609i
$557$	2.42343	−	7.45854i	0.102684	−	0.316028i	−0.886496	−	0.462736i	$-0.846868\pi$
$557$	2.42343	−	7.45854i	0.102684	−	0.316028i	0.989180	+	0.146708i	$0.0468677\pi$
$558$	−4.68813	−	14.4286i	−0.198465	−	0.610811i
$559$	−11.3853	+	8.27189i	−0.481546	+	0.349864i
$560$	−16.4348			−0.694498
$561$	1.08388	−	0.647117i	0.0457613	−	0.0273213i
$562$	63.0891			2.66125
$563$	3.52737	−	2.56279i	0.148661	−	0.108009i	−0.510969	−	0.859599i	$-0.670713\pi$
$563$	3.52737	−	2.56279i	0.148661	−	0.108009i	0.659630	+	0.751591i	$0.270713\pi$
$564$	−15.2348	−	46.8880i	−0.641503	−	1.97434i
$565$	3.31877	−	10.2141i	0.139622	−	0.429712i
$566$	48.3137	+	35.1020i	2.03078	+	1.47545i
$567$	−1.60264	−	1.16438i	−0.0673044	−	0.0488995i
$568$	−13.6129	+	41.8962i	−0.571185	+	1.75793i
$569$	7.91458	+	24.3586i	0.331796	+	1.02116i	0.968279	+	0.249873i	$0.0803889\pi$
$569$	7.91458	+	24.3586i	0.331796	+	1.02116i	−0.636482	+	0.771291i	$0.719611\pi$
$570$	−5.30054	+	3.85106i	−0.222015	+	0.161303i
$571$	−12.3483			−0.516759			−0.258380	−	0.966043i	$-0.583189\pi$
$571$	−12.3483			−0.516759			−0.258380	+	0.966043i	$0.583189\pi$
$572$	−20.3869	+	47.6554i	−0.852418	+	1.99257i
$573$	24.8822			1.03947
$574$	−14.4937	+	10.5303i	−0.604955	+	0.439526i
$575$	2.77386	+	8.53707i	0.115678	+	0.356020i
$576$	−3.00643	+	9.25283i	−0.125268	+	0.385535i
$577$	12.8677	+	9.34891i	0.535688	+	0.389200i	0.822481	−	0.568792i	$-0.192589\pi$
$577$	12.8677	+	9.34891i	0.535688	+	0.389200i	−0.286793	+	0.957993i	$0.592589\pi$
$578$	32.9502	+	23.9397i	1.37055	+	0.995762i
$579$	−0.430918	+	1.32623i	−0.0179084	+	0.0551162i
$580$	−15.6572	−	48.1880i	−0.650132	−	2.00090i
$581$	−8.08082	+	5.87106i	−0.335249	+	0.243573i
$582$	4.47706			0.185580
$583$	4.63411	+	0.418568i	0.191925	+	0.0173353i
$584$	17.9294			0.741925
$585$	8.92988	−	6.48794i	0.369205	−	0.268243i
$586$	16.1753	+	49.7825i	0.668197	+	2.05650i
$587$	−11.9057	+	36.6418i	−0.491399	+	1.51237i	0.331096	+	0.943597i	$0.392582\pi$
$587$	−11.9057	+	36.6418i	−0.491399	+	1.51237i	−0.822495	+	0.568773i	$0.807418\pi$
$588$	−9.55270	−	6.94045i	−0.393947	−	0.286219i
$589$	5.07934	+	3.69035i	0.209290	+	0.152058i
$590$	2.58884	−	7.96762i	0.106581	−	0.328022i
$591$	1.12495	+	3.46223i	0.0462742	+	0.142417i
$592$	3.38136	−	2.45670i	0.138973	−	0.100970i
$593$	24.9717			1.02547			0.512733	−	0.858548i	$-0.328633\pi$
$593$	24.9717			1.02547			0.512733	+	0.858548i	$0.328633\pi$
$594$	−6.03365	−	5.27483i	−0.247564	−	0.216429i
$595$	2.04436			0.0838106
$596$	41.6446	−	30.2566i	1.70583	−	1.23936i
$597$	3.17626	+	9.77551i	0.129996	+	0.400085i
$598$	11.6029	−	35.7101i	0.474479	−	1.46030i
$599$	4.77109	+	3.46640i	0.194942	+	0.141633i	0.680974	−	0.732307i	$-0.261556\pi$
$599$	4.77109	+	3.46640i	0.194942	+	0.141633i	−0.486033	+	0.873941i	$0.661556\pi$
$600$	8.45441	+	6.14249i	0.345150	+	0.250766i
$601$	10.5271	−	32.3992i	0.429411	−	1.32159i	−0.469295	−	0.883041i	$-0.655492\pi$
$601$	10.5271	−	32.3992i	0.429411	−	1.32159i	0.898706	−	0.438551i	$-0.144508\pi$
$602$	5.11352	+	15.7378i	0.208412	+	0.641425i
$603$	6.14487	−	4.46451i	0.250238	−	0.181809i
$604$	38.1672			1.55300
$605$	−14.1501	+	26.2551i	−0.575283	+	1.06742i
$606$	−36.1591			−1.46886
$607$	25.2634	−	18.3549i	1.02541	−	0.745002i	0.0580234	−	0.998315i	$-0.481520\pi$
$607$	25.2634	−	18.3549i	1.02541	−	0.745002i	0.967384	+	0.253313i	$0.0815202\pi$
$608$	−0.461582	−	1.42060i	−0.0187196	−	0.0576130i
$609$	−2.97977	+	9.17080i	−0.120747	+	0.371620i
$610$	9.13908	+	6.63993i	0.370031	+	0.268843i
$611$	−42.2953	−	30.7293i	−1.71108	−	1.24318i
$612$	−0.451528	+	1.38966i	−0.0182519	+	0.0561736i
$613$	−11.3659	−	34.9805i	−0.459062	−	1.41285i	−0.866299	−	0.499526i	$-0.833507\pi$
$613$	−11.3659	−	34.9805i	−0.459062	−	1.41285i	0.407236	−	0.913323i	$-0.366493\pi$
$614$	16.4135	−	11.9251i	0.662397	−	0.481259i
$615$	10.1477			0.409196
$616$	21.9803	+	19.2160i	0.885613	+	0.774235i
$617$	34.0252			1.36980			0.684902	−	0.728636i	$-0.259845\pi$
$617$	34.0252			1.36980			0.684902	+	0.728636i	$0.259845\pi$
$618$	18.5963	−	13.5110i	0.748052	−	0.543492i
$619$	9.84117	+	30.2880i	0.395550	+	1.21738i	0.928532	+	0.371251i	$0.121071\pi$
$619$	9.84117	+	30.2880i	0.395550	+	1.21738i	−0.532982	+	0.846126i	$0.678929\pi$
$620$	20.1949	−	62.1534i	0.811045	−	2.49614i
$621$	3.08802	+	2.24358i	0.123918	+	0.0900316i
$622$	−39.0638	−	28.3815i	−1.56631	−	1.13799i
$623$	9.73325	−	29.9559i	0.389954	−	1.20016i
$624$	−3.84920	−	11.8466i	−0.154091	−	0.474244i
$625$	25.2640	−	18.3554i	1.01056	−	0.734214i
$626$	−17.7730			−0.710350
$627$	3.30318	+	0.298354i	0.131916	+	0.0119151i
$628$	−94.0481			−3.75293
$629$	−0.420614	+	0.305594i	−0.0167710	+	0.0121848i
$630$	−4.01072	−	12.3437i	−0.159791	−	0.491786i
$631$	4.54757	−	13.9960i	0.181036	−	0.557171i	−0.818822	−	0.574048i	$-0.805372\pi$
$631$	4.54757	−	13.9960i	0.181036	−	0.557171i	0.999858	+	0.0168770i	$0.00537236\pi$
$632$	−21.2241	−	15.4202i	−0.844250	−	0.613383i
$633$	−0.496683	−	0.360861i	−0.0197414	−	0.0143429i
$634$	3.05450	−	9.40079i	0.121310	−	0.373353i
$635$	0.774501	+	2.38367i	0.0307351	+	0.0945930i
$636$	−4.35720	+	3.16569i	−0.172774	+	0.125528i
$637$	−12.5212			−0.496109
$638$	−15.3438	+	35.8669i	−0.607466	+	1.41998i
$639$	−9.91341			−0.392168
$640$	−45.0158	+	32.7059i	−1.77941	+	1.29281i
$641$	6.50222	+	20.0118i	0.256822	+	0.790417i	0.993465	+	0.114136i	$0.0364098\pi$
$641$	6.50222	+	20.0118i	0.256822	+	0.790417i	−0.736643	+	0.676282i	$0.763590\pi$
$642$	−12.1198	+	37.3009i	−0.478330	+	1.47215i
$643$	−27.3878	−	19.8984i	−1.08007	−	0.784717i	−0.102375	−	0.994746i	$-0.532644\pi$
$643$	−27.3878	−	19.8984i	−1.08007	−	0.784717i	−0.977695	+	0.210029i	$0.932644\pi$
$644$	−23.4841	−	17.0622i	−0.925402	−	0.672344i
$645$	2.89646	−	8.91439i	0.114048	−	0.351004i
$646$	−0.284208	−	0.874704i	−0.0111820	−	0.0344148i
$647$	−38.1665	+	27.7296i	−1.50048	+	1.09016i	−0.530288	+	0.847817i	$0.677916\pi$
$647$	−38.1665	+	27.7296i	−1.50048	+	1.09016i	−0.970190	+	0.242344i	$0.922084\pi$
$648$	4.44371			0.174565
$649$	−3.64128	+	2.17398i	−0.142933	+	0.0853364i
$650$	23.1336			0.907374
$651$	−10.0620	+	7.31047i	−0.394361	+	0.286520i
$652$	−6.18793	−	19.0445i	−0.242338	−	0.745840i
$653$	0.599736	−	1.84580i	0.0234695	−	0.0722316i	−0.938636	−	0.344910i	$-0.887909\pi$
$653$	0.599736	−	1.84580i	0.0234695	−	0.0722316i	0.962105	+	0.272678i	$0.0879095\pi$
$654$	23.6116	+	17.1548i	0.923285	+	0.670806i
$655$	37.7853	+	27.4526i	1.47639	+	1.07266i
$656$	3.53876	−	10.8912i	0.138165	−	0.425229i
$657$	1.24682	+	3.83731i	0.0486430	+	0.149708i
$658$	−49.7329	+	36.1331i	−1.93879	+	1.40861i
$659$	−7.79796			−0.303766			−0.151883	−	0.988399i	$-0.548534\pi$
$659$	−7.79796			−0.303766			−0.151883	+	0.988399i	$0.548534\pi$
$660$	−7.67130	−	33.6597i	−0.298605	−	1.31020i
$661$	−41.6336			−1.61936			−0.809679	−	0.586872i	$-0.800359\pi$
$661$	−41.6336			−1.61936			−0.809679	+	0.586872i	$0.800359\pi$
$662$	33.8522	−	24.5951i	1.31570	−	0.955914i
$663$	0.478810	+	1.47362i	0.0185954	+	0.0572308i
$664$	6.92385	−	21.3094i	0.268698	−	0.826966i
$665$	4.34539	+	3.15711i	0.168507	+	0.122428i
$666$	2.67034	+	1.94011i	0.103474	+	0.0751779i
$667$	5.74153	−	17.6706i	0.222313	−	0.684209i
$668$	27.1377	+	83.5214i	1.04999	+	3.23154i
$669$	15.5417	−	11.2917i	0.600877	−	0.436563i
$670$	49.7642			1.92256
$671$	−1.27070	−	5.57549i	−0.0490548	−	0.215240i
$672$	2.95899			0.114146
$673$	−16.2992	+	11.8420i	−0.628287	+	0.456477i	−0.855806	−	0.517296i	$-0.826939\pi$
$673$	−16.2992	+	11.8420i	−0.628287	+	0.456477i	0.227519	+	0.973774i	$0.426939\pi$
$674$	−2.29224	−	7.05478i	−0.0882937	−	0.271740i
$675$	−0.726713	+	2.23659i	−0.0279712	+	0.0860864i
$676$	−11.0955	−	8.06138i	−0.426751	−	0.310053i
$677$	14.1337	+	10.2688i	0.543204	+	0.394661i	0.825273	−	0.564733i	$-0.191021\pi$
$677$	14.1337	+	10.2688i	0.543204	+	0.394661i	−0.282070	+	0.959394i	$0.591021\pi$
$678$	2.95769	−	9.10283i	0.113589	−	0.349592i
$679$	−1.13419	−	3.49067i	−0.0435261	−	0.133959i
$680$	−3.71007	+	2.69553i	−0.142275	+	0.103369i
$681$	−14.3541			−0.550049
$682$	−43.2027	+	25.7937i	−1.65432	+	0.987693i
$683$	−9.67208			−0.370092			−0.185046	−	0.982730i	$-0.559243\pi$
$683$	−9.67208			−0.370092			−0.185046	+	0.982730i	$0.559243\pi$
$684$	−3.10580	+	2.25650i	−0.118753	+	0.0862793i
$685$	−14.1743	−	43.6240i	−0.541572	−	1.66679i
$686$	−14.9041	+	45.8702i	−0.569042	+	1.75133i
$687$	−14.3679	−	10.4389i	−0.548169	−	0.398268i
$688$	−8.55742	−	6.21733i	−0.326249	−	0.237033i
$689$	−1.76486	+	5.43169i	−0.0672360	+	0.206931i
$690$	7.72799	+	23.7843i	0.294200	+	0.905453i
$691$	−18.5718	+	13.4932i	−0.706503	+	0.513305i	−0.882044	−	0.471167i	$-0.843833\pi$
$691$	−18.5718	+	13.4932i	−0.706503	+	0.513305i	0.175540	+	0.984472i	$0.443833\pi$
$692$	−62.4962			−2.37575
$693$	−2.58415	+	6.04059i	−0.0981639	+	0.229463i
$694$	−11.3884			−0.432299
$695$	33.8350	−	24.5826i	1.28344	−	0.932471i
$696$	−6.68423	−	20.5719i	−0.253365	−	0.779777i
$697$	−0.440194	+	1.35478i	−0.0166735	+	0.0513158i
$698$	−3.61868	−	2.62913i	−0.136969	−	0.0995139i
$699$	10.1291	+	7.35925i	0.383119	+	0.278353i
$700$	5.52657	−	17.0090i	0.208885	−	0.642882i
$701$	−9.05057	−	27.8548i	−0.341835	−	1.05206i	−0.963256	−	0.268584i	$-0.913444\pi$
$701$	−9.05057	−	27.8548i	−0.341835	−	1.05206i	0.621421	−	0.783477i	$-0.286556\pi$
$702$	7.95830	−	5.78204i	0.300367	−	0.218229i
$703$	−1.36597			−0.0515184
$704$	32.1366	+	2.90269i	1.21119	+	0.109399i
$705$	34.8204			1.31141
$706$	14.0775	−	10.2279i	0.529813	−	0.384931i
$707$	9.16030	+	28.1925i	0.344508	+	1.06029i
$708$	1.51690	−	4.66855i	0.0570088	−	0.175455i
$709$	−21.4749	−	15.6025i	−0.806508	−	0.585963i	0.106308	−	0.994333i	$-0.466097\pi$
$709$	−21.4749	−	15.6025i	−0.806508	−	0.585963i	−0.912816	+	0.408371i	$0.866097\pi$
$710$	−52.5464	−	38.1772i	−1.97203	−	1.43276i
$711$	1.82435	−	5.61478i	0.0684186	−	0.210571i
$712$	21.8336	+	67.1969i	0.818249	+	2.51831i
$713$	19.3878	−	14.0861i	0.726080	−	0.527528i
$714$	1.82193			0.0681841
$715$	−27.5613	−	24.0951i	−1.03073	−	0.901105i
$716$	−80.4389			−3.00614
$717$	−3.42603	+	2.48915i	−0.127947	+	0.0929591i
$718$	17.6636	+	54.3628i	0.659198	+	2.02880i
$719$	−5.05638	+	15.5619i	−0.188571	+	0.580363i	−0.999992	−	0.00410042i	$-0.998695\pi$
$719$	−5.05638	+	15.5619i	−0.188571	+	0.580363i	0.811420	+	0.584463i	$0.198695\pi$
$720$	6.71189	+	4.87647i	0.250137	+	0.181735i
$721$	−15.2453	−	11.0763i	−0.567764	−	0.412505i
$722$	0.746708	−	2.29813i	0.0277896	−	0.0855276i
$723$	2.13051	+	6.55703i	0.0792345	+	0.243859i
$724$	−54.3894	+	39.5162i	−2.02136	+	1.46861i
$725$	11.4473			0.425143
$726$	−12.6105	+	23.3985i	−0.468021	+	0.868400i
$727$	25.2731			0.937328			0.468664	−	0.883376i	$-0.344735\pi$
$727$	25.2731			0.937328			0.468664	+	0.883376i	$0.344735\pi$
$728$	−28.9918	+	21.0638i	−1.07451	+	0.780675i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−8.16894	+	25.1414i	−0.302346	+	0.930525i
$731$	1.06447	+	0.773386i	0.0393710	+	0.0286047i
$732$	5.35496	+	3.89061i	0.197925	+	0.143801i
$733$	−12.3583	+	38.0349i	−0.456463	+	1.40485i	0.412945	+	0.910756i	$0.364500\pi$
$733$	−12.3583	+	38.0349i	−0.456463	+	1.40485i	−0.869409	+	0.494094i	$0.835500\pi$
$734$	14.0103	+	43.1192i	0.517129	+	1.59156i
$735$	6.74690	−	4.90191i	0.248863	−	0.180810i
$736$	−5.70149			−0.210160
$737$	−18.9656	−	16.5804i	−0.698606	−	0.610747i
$738$	9.04365			0.332901
$739$	34.1257	−	24.7937i	1.25533	−	0.912052i	0.256814	−	0.966461i	$-0.417327\pi$
$739$	34.1257	−	24.7937i	1.25533	−	0.912052i	0.998519	+	0.0544084i	$0.0173273\pi$
$740$	4.39372	+	13.5225i	0.161516	+	0.497096i
$741$	−1.25799	+	3.87169i	−0.0462134	+	0.142230i
$742$	5.43298	+	3.94729i	0.199451	+	0.144910i
$743$	1.96040	+	1.42432i	0.0719202	+	0.0522531i	0.623164	−	0.782091i	$-0.285847\pi$
$743$	1.96040	+	1.42432i	0.0719202	+	0.0522531i	−0.551244	+	0.834344i	$0.685847\pi$
$744$	8.62138	−	26.5339i	0.316075	−	0.972780i
$745$	11.2347	+	34.5768i	0.411607	+	1.26680i
$746$	−34.7098	+	25.2182i	−1.27082	+	0.923303i
$747$	5.04220			0.184485
$748$	4.82652	+	0.435947i	0.176475	+	0.0159398i
$749$	32.1530			1.17485
$750$	14.0375	−	10.1988i	0.512575	−	0.372408i
$751$	−4.42306	−	13.6128i	−0.161400	−	0.496737i	0.837353	−	0.546662i	$-0.184102\pi$
$751$	−4.42306	−	13.6128i	−0.161400	−	0.496737i	−0.998753	+	0.0499251i	$0.984102\pi$
$752$	12.1427	−	37.3714i	0.442799	−	1.36280i
$753$	8.32832	+	6.05088i	0.303501	+	0.220506i
$754$	−38.7386	−	28.1452i	−1.41078	−	1.02499i
$755$	−8.33010	+	25.6374i	−0.303163	+	0.933041i
$756$	−2.35004	−	7.23269i	−0.0854702	−	0.263050i
$757$	−3.74261	+	2.71917i	−0.136028	+	0.0988298i	−0.653718	−	0.756738i	$-0.726792\pi$
$757$	−3.74261	+	2.71917i	−0.136028	+	0.0988298i	0.517691	+	0.855568i	$0.326792\pi$
$758$	−84.7305			−3.07755
$759$	4.97924	−	11.6392i	0.180735	−	0.422477i
$760$	−12.0487			−0.437051
$761$	26.0782	−	18.9469i	0.945334	−	0.686825i	−0.00436472	−	0.999990i	$-0.501389\pi$
$761$	26.0782	−	18.9469i	0.945334	−	0.686825i	0.949699	+	0.313165i	$0.101389\pi$
$762$	0.690235	+	2.12432i	0.0250046	+	0.0769561i
$763$	7.39364	−	22.7553i	0.267668	−	0.823797i
$764$	77.2792	+	56.1466i	2.79586	+	2.03131i
$765$	−0.834906	−	0.606594i	−0.0301861	−	0.0219315i
$766$	−23.6917	+	72.9156i	−0.856016	+	2.63455i
$767$	−1.60856	−	4.95063i	−0.0580817	−	0.178757i
$768$	−24.3762	+	17.7103i	−0.879601	+	0.639067i
$769$	−40.2599			−1.45181			−0.725905	−	0.687795i	$-0.758579\pi$
$769$	−40.2599			−1.45181			−0.725905	+	0.687795i	$0.758579\pi$
$770$	−36.9601	+	22.0666i	−1.33195	+	0.795226i
$771$	30.7898			1.10887
$772$	−4.33098	+	3.14664i	−0.155875	+	0.113250i
$773$	−3.06339	−	9.42815i	−0.110183	−	0.339107i	0.880729	−	0.473620i	$-0.157053\pi$
$773$	−3.06339	−	9.42815i	−0.110183	−	0.339107i	−0.990912	+	0.134513i	$0.957053\pi$
$774$	2.58132	−	7.94450i	0.0927838	−	0.285559i
$775$	11.9450	+	8.67857i	0.429078	+	0.311743i
$776$	6.66081	+	4.83936i	0.239109	+	0.173723i
$777$	0.836181	−	2.57350i	0.0299978	−	0.0923238i
$778$	1.54983	+	4.76990i	0.0555643	+	0.171009i
$779$	−3.02784	+	2.19986i	−0.108484	+	0.0788180i
$780$	42.3744			1.51725
$781$	7.30605	+	32.0570i	0.261431	+	1.14709i
$782$	−3.51056			−0.125537
$783$	3.93805	−	2.86116i	0.140734	−	0.102250i
$784$	−2.90823	−	8.95061i	−0.103865	−	0.319665i
$785$	20.5263	−	63.1734i	0.732615	−	2.25476i
$786$	33.6742	+	24.4658i	1.20112	+	0.872664i
$787$	36.0857	+	26.2178i	1.28632	+	0.934565i	0.999724	−	0.0234877i	$-0.00747705\pi$
$787$	36.0857	+	26.2178i	1.28632	+	0.934565i	0.286594	+	0.958052i	$0.407477\pi$
$788$	−4.31865	+	13.2914i	−0.153846	+	0.473488i
$789$	8.63071	+	26.5626i	0.307261	+	0.945653i
$790$	31.2929	−	22.7356i	1.11335	−	0.808898i
$791$	−7.84656			−0.278991
$792$	−3.27495	−	14.3696i	−0.116370	−	0.510603i
$793$	7.01903			0.249253
$794$	69.6692	−	50.6176i	2.47247	−	1.79635i
$795$	−1.17547	−	3.61772i	−0.0416895	−	0.128307i
$796$	−12.1936	+	37.5280i	−0.432190	+	1.33014i
$797$	15.8059	+	11.4837i	0.559874	+	0.406772i	0.831413	−	0.555655i	$-0.187533\pi$
$797$	15.8059	+	11.4837i	0.559874	+	0.406772i	−0.271539	+	0.962427i	$0.587533\pi$
$798$	3.87261	+	2.81362i	0.137089	+	0.0996009i
$799$	−1.51046	+	4.64871i	−0.0534361	+	0.164460i
$800$	−1.08550	−	3.34082i	−0.0383781	−	0.118116i
$801$	−12.8634	+	9.34580i	−0.454505	+	0.330218i
$802$	56.4401			1.99297
$803$	11.4899	−	6.85989i	0.405468	−	0.242080i
$804$	29.1589			1.02835
$805$	16.5864	−	12.0507i	0.584592	−	0.424731i
$806$	−19.0851	−	58.7379i	−0.672244	−	2.06895i
$807$	−5.86689	+	18.0564i	−0.206524	+	0.635616i
$808$	−53.7963	−	39.0853i	−1.89255	−	1.37502i
$809$	3.46975	+	2.52092i	0.121990	+	0.0886308i	0.647107	−	0.762399i	$-0.275979\pi$
$809$	3.46975	+	2.52092i	0.121990	+	0.0886308i	−0.525117	+	0.851030i	$0.675979\pi$
$810$	−2.02462	+	6.23115i	−0.0711380	+	0.218940i
$811$	12.4372	+	38.2778i	0.436729	+	1.34411i	0.891304	+	0.453406i	$0.149791\pi$
$811$	12.4372	+	38.2778i	0.436729	+	1.34411i	−0.454575	+	0.890709i	$0.650209\pi$
$812$	−29.9485	+	21.7588i	−1.05098	+	0.763585i
$813$	−14.9195			−0.523248
$814$	4.30575	−	10.0649i	0.150917	−	0.352775i
$815$	14.1430			0.495407
$816$	−0.942187	+	0.684539i	−0.0329832	+	0.0239637i
$817$	1.06825	+	3.28774i	0.0373734	+	0.115024i
$818$	15.0291	−	46.2549i	0.525481	−	1.61726i
$819$	−6.52423	−	4.74013i	−0.227975	−	0.165634i
$820$	31.5168	+	22.8983i	1.10062	+	0.799644i
$821$	−8.77268	+	26.9995i	−0.306169	+	0.942290i	0.673070	+	0.739579i	$0.264975\pi$
$821$	−8.77268	+	26.9995i	−0.306169	+	0.942290i	−0.979239	+	0.202711i	$0.935025\pi$
$822$	−12.6321	−	38.8776i	−0.440595	−	1.35601i
$823$	−15.7712	+	11.4584i	−0.549749	+	0.399416i	−0.827693	−	0.561181i	$-0.810347\pi$
$823$	−15.7712	+	11.4584i	−0.549749	+	0.399416i	0.277944	+	0.960597i	$0.410347\pi$
$824$	42.2713			1.47259
$825$	7.76805	+	0.701637i	0.270449	+	0.0244278i
$826$	−6.12077			−0.212969
$827$	30.4006	−	22.0873i	1.05713	−	0.768052i	0.0835768	−	0.996501i	$-0.473366\pi$
$827$	30.4006	−	22.0873i	1.05713	−	0.768052i	0.973556	+	0.228450i	$0.0733656\pi$
$828$	4.52814	+	13.9362i	0.157364	+	0.484316i
$829$	12.7509	−	39.2432i	0.442857	−	1.36297i	−0.441960	−	0.897035i	$-0.645717\pi$
$829$	12.7509	−	39.2432i	0.442857	−	1.36297i	0.884817	−	0.465938i	$-0.154283\pi$
$830$	26.7264	+	19.4178i	0.927686	+	0.674003i
$831$	7.31815	+	5.31695i	0.253864	+	0.184443i
$832$	−12.2390	+	37.6677i	−0.424310	+	1.30589i
$833$	0.361761	+	1.11338i	0.0125343	+	0.0385765i
$834$	30.1538	−	21.9080i	1.04414	−	0.758612i
$835$	−62.0253			−2.14648
$836$	9.58577	+	8.38023i	0.331531	+	0.289836i
$837$	6.27840			0.217013
$838$	24.9120	−	18.0996i	0.860571	−	0.625241i
$839$	8.22774	+	25.3224i	0.284053	+	0.874225i	0.986681	+	0.162668i	$0.0520099\pi$
$839$	8.22774	+	25.3224i	0.284053	+	0.874225i	−0.702628	+	0.711558i	$0.747990\pi$
$840$	7.37563	−	22.6998i	0.254483	−	0.783219i
$841$	4.29227	+	3.11852i	0.148009	+	0.107535i
$842$	−9.84867	−	7.15548i	−0.339407	−	0.246594i
$843$	−8.06804	+	24.8309i	−0.277878	+	0.855221i
$844$	−0.728316	−	2.24153i	−0.0250697	−	0.0771565i
$845$	7.83657	−	5.69360i	0.269586	−	0.195866i
$846$	31.0319			1.06690
$847$	21.4380	+	3.90455i	0.736618	+	0.134162i
$848$	−4.29268			−0.147411
$849$	−19.9941	+	14.5266i	−0.686196	+	0.498551i
$850$	−0.668370	−	2.05703i	−0.0229249	−	0.0705556i
$851$	−1.61118	+	4.95871i	−0.0552306	+	0.169982i
$852$	−30.7891	−	22.3696i	−1.05482	−	0.766369i
$853$	−5.97778	−	4.34311i	−0.204675	−	0.148705i	0.480726	−	0.876871i	$-0.340373\pi$
$853$	−5.97778	−	4.34311i	−0.204675	−	0.148705i	−0.685401	+	0.728166i	$0.740373\pi$
$854$	2.55042	−	7.84938i	0.0872735	−	0.268600i
$855$	−0.837869	−	2.57869i	−0.0286545	−	0.0881895i
$856$	−58.3508	+	42.3943i	−1.99439	+	1.44901i
$857$	−21.9094			−0.748410			−0.374205	−	0.927346i	$-0.622084\pi$
$857$	−21.9094			−0.748410			−0.374205	+	0.927346i	$0.622084\pi$
$858$	−24.5626	−	21.4735i	−0.838553	−	0.733094i
$859$	10.6865			0.364617			0.182309	−	0.983241i	$-0.441643\pi$
$859$	10.6865			0.364617			0.182309	+	0.983241i	$0.441643\pi$
$860$	29.1111	−	21.1505i	0.992681	−	0.721225i
$861$	−2.29105	−	7.05114i	−0.0780789	−	0.240302i
$862$	−20.5623	+	63.2842i	−0.700355	+	2.15547i
$863$	8.78111	+	6.37985i	0.298912	+	0.217173i	0.727124	−	0.686506i	$-0.240856\pi$
$863$	8.78111	+	6.37985i	0.298912	+	0.217173i	−0.428212	+	0.903678i	$0.640856\pi$
$864$	−1.20844	−	0.877980i	−0.0411118	−	0.0298695i
$865$	13.6400	−	41.9795i	0.463773	−	1.42735i
$866$	−12.0797	−	37.1774i	−0.410484	−	1.26334i
$867$	−13.6361	+	9.90720i	−0.463106	+	0.336466i
$868$	−47.7466			−1.62063
$869$	−19.5011	−	1.76140i	−0.661528	−	0.0597514i
$870$	31.8923			1.08125
$871$	25.0154	−	18.1747i	0.847613	−	0.615827i
$872$	16.5854	+	51.0446i	0.561653	+	1.72859i
$873$	−0.572541	+	1.76210i	−0.0193776	+	0.0596381i
$874$	−7.46188	−	5.42137i	−0.252402	−	0.183381i
$875$	−11.5079	−	8.36101i	−0.389039	−	0.282654i
$876$	−4.78651	+	14.7314i	−0.161721	+	0.497727i
$877$	−14.2999	−	44.0105i	−0.482873	−	1.48613i	−0.835038	−	0.550193i	$-0.814554\pi$
$877$	−14.2999	−	44.0105i	−0.482873	−	1.48613i	0.352165	−	0.935938i	$-0.385446\pi$
$878$	29.8172	−	21.6635i	1.00628	−	0.731108i
$879$	−21.6622			−0.730647
$880$	10.8225	−	25.2982i	0.364827	−	0.852801i
$881$	−8.75040			−0.294808			−0.147404	−	0.989076i	$-0.547092\pi$
$881$	−8.75040			−0.294808			−0.147404	+	0.989076i	$0.547092\pi$
$882$	6.01283	−	4.36858i	0.202463	−	0.147098i
$883$	10.0723	+	30.9993i	0.338959	+	1.04321i	0.964739	+	0.263210i	$0.0847811\pi$
$883$	10.0723	+	30.9993i	0.338959	+	1.04321i	−0.625779	+	0.780000i	$0.715219\pi$
$884$	−1.83814	+	5.65721i	−0.0618233	+	0.190273i
$885$	2.80486	+	2.03785i	0.0942844	+	0.0685016i
$886$	13.6743	+	9.93495i	0.459397	+	0.333771i
$887$	−12.2899	+	37.8245i	−0.412655	+	1.27002i	0.501676	+	0.865056i	$0.332717\pi$
$887$	−12.2899	+	37.8245i	−0.412655	+	1.27002i	−0.914331	+	0.404967i	$0.867283\pi$
$888$	1.87572	+	5.77287i	0.0629450	+	0.193725i
$889$	1.48143	−	1.07632i	0.0496856	−	0.0360987i
$890$	−104.174			−3.49192
$891$	2.84770	−	1.70019i	0.0954014	−	0.0569584i
$892$	73.7492			2.46930
$893$	−10.3896	+	7.54847i	−0.347674	+	0.252600i
$894$	10.0123	+	30.8148i	0.334863	+	1.03060i
$895$	17.5560	−	54.0319i	0.586833	−	1.80609i
$896$	32.8889	+	23.8952i	1.09874	+	0.798282i
$897$	12.5711	+	9.13346i	0.419738	+	0.304957i
$898$	18.5234	−	57.0093i	0.618135	−	1.90242i
$899$	−9.44398	−	29.0656i	−0.314974	−	0.969391i
$900$	−7.30388	+	5.30658i	−0.243463	+	0.176886i
$901$	0.533975			0.0177893
$902$	−6.66505	−	29.2445i	−0.221922	−	0.973736i
$903$	−6.84809			−0.227890
$904$	14.2398	−	10.3458i	0.473609	−	0.344097i
$905$	−14.6729	−	45.1586i	−0.487744	−	1.50112i
$906$	−7.42378	+	22.8480i	−0.246638	+	0.759075i
$907$	14.9821	+	10.8852i	0.497474	+	0.361436i	0.808051	−	0.589112i	$-0.200522\pi$
$907$	14.9821	+	10.8852i	0.497474	+	0.361436i	−0.310577	+	0.950548i	$0.600522\pi$
$908$	−44.5808	−	32.3899i	−1.47947	−	1.07490i
$909$	4.62415	−	14.2317i	0.153373	−	0.472035i
$910$	−16.3274	−	50.2505i	−0.541247	−	1.66579i
$911$	14.0326	−	10.1952i	0.464919	−	0.337784i	−0.330539	−	0.943792i	$-0.607230\pi$
$911$	14.0326	−	10.1952i	0.464919	−	0.337784i	0.795458	+	0.606009i	$0.207230\pi$
$912$	−3.05980			−0.101320
$913$	−3.71604	−	16.3050i	−0.122983	−	0.539617i
$914$	−54.0443			−1.78763
$915$	−3.78211	+	2.74786i	−0.125033	+	0.0908416i
$916$	−21.0685	−	64.8422i	−0.696123	−	2.14245i
$917$	10.5446	−	32.4530i	0.348214	−	1.07169i
$918$	−0.744067	−	0.540597i	−0.0245579	−	0.0178423i
$919$	12.9183	+	9.38568i	0.426135	+	0.309605i	0.780101	−	0.625653i	$-0.215167\pi$
$919$	12.9183	+	9.38568i	0.426135	+	0.309605i	−0.353967	+	0.935258i	$0.615167\pi$
$920$	−14.2116	+	43.7389i	−0.468543	+	1.44203i
$921$	2.59453	+	7.98514i	0.0854926	+	0.263119i
$922$	36.8166	−	26.7488i	1.21249	−	0.880926i
$923$	−40.3569			−1.32836
$924$	−21.6564	+	12.9297i	−0.712444	+	0.425357i
$925$	−3.21233			−0.105621
$926$	18.7947	−	13.6552i	0.617632	−	0.448736i
$927$	2.93956	+	9.04704i	0.0965478	+	0.297144i
$928$	−2.24684	+	6.91506i	−0.0737561	+	0.226998i
$929$	−33.1819	−	24.1081i	−1.08866	−	0.790960i	−0.109490	−	0.993988i	$-0.534922\pi$
$929$	−33.1819	−	24.1081i	−1.08866	−	0.790960i	−0.979173	+	0.203028i	$0.934922\pi$
$930$	33.2789	+	24.1785i	1.09126	+	0.792846i
$931$	−0.950463	+	2.92522i	−0.0311502	+	0.0958704i
$932$	14.8530	+	45.7127i	0.486525	+	1.49737i
$933$	16.1661	−	11.7454i	0.529255	−	0.384526i
$934$	85.0941			2.78436
$935$	−1.34623	+	3.14689i	−0.0440265	+	0.102914i
$936$	18.0900			0.591292
$937$	11.5738	−	8.40885i	0.378099	−	0.274705i	−0.382462	−	0.923971i	$-0.624924\pi$
$937$	11.5738	−	8.40885i	0.378099	−	0.274705i	0.760561	+	0.649266i	$0.224924\pi$
$938$	−11.2353	−	34.5786i	−0.366844	−	1.12903i
$939$	2.27287	−	6.99516i	0.0741722	−	0.228278i
$940$	108.145	+	78.5720i	3.52731	+	2.56274i
$941$	11.2796	+	8.19513i	0.367705	+	0.267153i	0.756259	−	0.654273i	$-0.227025\pi$
$941$	11.2796	+	8.19513i	0.367705	+	0.267153i	−0.388554	+	0.921426i	$0.627025\pi$
$942$	18.2930	−	56.3001i	0.596019	−	1.83436i
$943$	4.41448	+	13.5864i	0.143755	+	0.442433i
$944$	3.16527	−	2.29971i	0.103021	−	0.0748491i
$945$	5.37120			0.174725
$946$	−27.5926	−	2.49225i	−0.897112	−	0.0810301i
$947$	−20.4080			−0.663172			−0.331586	−	0.943425i	$-0.607584\pi$
$947$	−20.4080			−0.663172			−0.331586	+	0.943425i	$0.607584\pi$
$948$	18.3358	−	13.3217i	0.595519	−	0.432670i
$949$	5.07572	+	15.6215i	0.164765	+	0.507094i
$950$	1.75603	−	5.40449i	0.0569730	−	0.175345i
$951$	3.30938	+	2.40441i	0.107314	+	0.0779682i
$952$	2.71061	+	1.96937i	0.0878513	+	0.0638277i
$953$	−10.4906	+	32.2867i	−0.339823	+	1.04587i	0.624474	+	0.781046i	$0.285313\pi$
$953$	−10.4906	+	32.2867i	−0.339823	+	1.04587i	−0.964297	+	0.264823i	$0.914687\pi$
$954$	−1.04758	−	3.22411i	−0.0339165	−	0.104384i
$955$	−54.5808	+	39.6553i	−1.76619	+	1.28322i
$956$	−16.2573			−0.525799
$957$	−12.1544	−	10.6259i	−0.392897	−	0.343485i
$958$	−28.8440			−0.931907
$959$	−27.1119	+	19.6980i	−0.875490	+	0.636081i
$960$	−8.15163	−	25.0881i	−0.263093	−	0.809716i
$961$	2.60142	−	8.00633i	0.0839166	−	0.258269i
$962$	10.8708	+	7.89808i	0.350488	+	0.254644i
$963$	−13.1311	−	9.54031i	−0.423144	−	0.307432i
$964$	−8.17898	+	25.1723i	−0.263427	+	0.810746i
$965$	−1.16839	−	3.59594i	−0.0376119	−	0.115757i
$966$	14.7817	−	10.7396i	0.475595	−	0.345540i
$967$	14.7792			0.475268			0.237634	−	0.971355i	$-0.423628\pi$
$967$	14.7792			0.475268			0.237634	+	0.971355i	$0.423628\pi$
$968$	−44.0536	+	21.1805i	−1.41594	+	0.680766i
$969$	0.380615			0.0122271
$970$	−9.82074	+	7.13518i	−0.315325	+	0.229097i
$971$	−14.3778	−	44.2502i	−0.461404	−	1.42006i	−0.863449	−	0.504436i	$-0.831700\pi$
$971$	−14.3778	−	44.2502i	−0.461404	−	1.42006i	0.402045	−	0.915620i	$-0.368300\pi$
$972$	−1.18631	+	3.65109i	−0.0380509	+	0.117109i
$973$	−24.7201	−	17.9602i	−0.792491	−	0.575778i
$974$	3.16241	+	2.29763i	0.101330	+	0.0736207i
$975$	−2.95840	+	9.10502i	−0.0947446	+	0.291594i
$976$	1.63027	+	5.01745i	0.0521836	+	0.160605i
$977$	29.7555	−	21.6186i	0.951962	−	0.691641i	0.000692044	−	1.00000i	$-0.499780\pi$
$977$	29.7555	−	21.6186i	0.951962	−	0.691641i	0.951270	+	0.308359i	$0.0997797\pi$
$978$	12.6042			0.403038
$979$	39.7017	+	34.7087i	1.26887	+	1.10929i
$980$	32.0156			1.02270
$981$	−9.77139	+	7.09933i	−0.311976	+	0.226664i
$982$	17.4580	+	53.7301i	0.557106	+	1.71459i
$983$	14.6740	−	45.1621i	0.468029	−	1.44045i	−0.387103	−	0.922036i	$-0.626524\pi$
$983$	14.6740	−	45.1621i	0.468029	−	1.44045i	0.855133	−	0.518409i	$-0.173476\pi$
$984$	13.4548	+	9.77551i	0.428924	+	0.311632i
$985$	−7.98549	−	5.80180i	−0.254439	−	0.184861i
$986$	−1.38344	+	4.25779i	−0.0440577	+	0.135596i
$987$	−7.86140	−	24.1949i	−0.250231	−	0.770132i
$988$	−12.6435	+	9.18605i	−0.402244	+	0.292247i
$989$	13.1951			0.419581
$990$	21.6418	+	1.95476i	0.687823	+	0.0621264i
$991$	−8.43710			−0.268013			−0.134007	−	0.990980i	$-0.542784\pi$
$991$	−8.43710			−0.268013			−0.134007	+	0.990980i	$0.542784\pi$
$992$	−7.58705	+	5.51231i	−0.240889	+	0.175016i
$993$	5.35110	+	16.4690i	0.169812	+	0.522628i
$994$	−14.6640	+	45.1311i	−0.465113	+	1.43147i
$995$	−22.5468	−	16.3812i	−0.714781	−	0.519319i
$996$	15.6601	+	11.3777i	0.496208	+	0.360516i
$997$	8.27949	−	25.4817i	0.262214	−	0.807012i	−0.730108	−	0.683332i	$-0.760530\pi$
$997$	8.27949	−	25.4817i	0.262214	−	0.807012i	0.992322	−	0.123680i	$-0.0394698\pi$
$998$	−8.05949	−	24.8046i	−0.255119	−	0.785175i
$999$	−1.10509	+	0.802895i	−0.0349635	+	0.0254025i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.j.b.58.1	✓	32
11.2	odd	10		6897.2.a.bl.1.2		16
11.4	even	5	inner	627.2.j.b.400.1	yes	32
11.9	even	5		6897.2.a.bm.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.b.58.1	✓	32	1.1	even	1	trivial
627.2.j.b.400.1	yes	32	11.4	even	5	inner
6897.2.a.bl.1.2		16	11.2	odd	10
6897.2.a.bm.1.15		16	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	627.2.j.b.58.1

Level	$627$
Weight	$2$
Character	627.58
Analytic conductor	$5.007$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$