LMFDB - Embedded newform 280.2.bj.f.171.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			171.12
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.f.131.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39149 + 0.252502i) q^{2} +(-1.84104 - 1.06293i) q^{3} +(1.87249 + 0.702708i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.29340 - 1.94392i) q^{6} +(2.17552 - 1.50569i) q^{7} +(2.42811 + 1.45062i) q^{8} +(0.759621 + 1.31570i) q^{9} +O(q^{10})$	\(q+(1.39149 + 0.252502i) q^{2} +(-1.84104 - 1.06293i) q^{3} +(1.87249 + 0.702708i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.29340 - 1.94392i) q^{6} +(2.17552 - 1.50569i) q^{7} +(2.42811 + 1.45062i) q^{8} +(0.759621 + 1.31570i) q^{9} +(-0.477071 - 1.33132i) q^{10} +(2.04422 - 3.54069i) q^{11} +(-2.70039 - 3.28403i) q^{12} -4.95585 q^{13} +(3.40741 - 1.54583i) q^{14} +2.12585i q^{15} +(3.01240 + 2.63162i) q^{16} +(2.09103 + 1.20726i) q^{17} +(0.724787 + 2.02259i) q^{18} +(5.22809 - 3.01844i) q^{19} +(-0.327679 - 1.97297i) q^{20} +(-5.60566 + 0.459619i) q^{21} +(3.73854 - 4.41066i) q^{22} +(0.443005 - 0.255769i) q^{23} +(-2.92835 - 5.25154i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.89601 - 1.25136i) q^{26} +3.14787i q^{27} +(5.13169 - 1.29062i) q^{28} +3.08127i q^{29} +(-0.536782 + 2.95810i) q^{30} +(-2.30669 + 3.99530i) q^{31} +(3.52723 + 4.42251i) q^{32} +(-7.52697 + 4.34570i) q^{33} +(2.60481 + 2.20788i) q^{34} +(-2.39173 - 1.13121i) q^{35} +(0.497824 + 2.99742i) q^{36} +(-8.64910 + 4.99356i) q^{37} +(8.03700 - 2.88002i) q^{38} +(9.12392 + 5.26770i) q^{39} +(0.0422184 - 2.82811i) q^{40} +5.81092i q^{41} +(-7.91627 - 0.775887i) q^{42} -10.7069 q^{43} +(6.31584 - 5.19340i) q^{44} +(0.759621 - 1.31570i) q^{45} +(0.681020 - 0.244040i) q^{46} +(-0.698912 - 1.21055i) q^{47} +(-2.74874 - 8.04688i) q^{48} +(2.46579 - 6.55133i) q^{49} +(-0.914418 + 1.07881i) q^{50} +(-2.56645 - 4.44522i) q^{51} +(-9.27975 - 3.48252i) q^{52} +(6.79325 + 3.92208i) q^{53} +(-0.794845 + 4.38023i) q^{54} -4.08843 q^{55} +(7.46658 - 0.500126i) q^{56} -12.8335 q^{57} +(-0.778027 + 4.28755i) q^{58} +(8.82516 + 5.09521i) q^{59} +(-1.49385 + 3.98062i) q^{60} +(1.33141 + 2.30607i) q^{61} +(-4.21856 + 4.97698i) q^{62} +(3.63361 + 1.71859i) q^{63} +(3.79141 + 7.04451i) q^{64} +(2.47792 + 4.29189i) q^{65} +(-11.5710 + 4.14642i) q^{66} +(3.46437 - 6.00046i) q^{67} +(3.06708 + 3.72996i) q^{68} -1.08745 q^{69} +(-3.04243 - 2.17799i) q^{70} +1.54183i q^{71} +(-0.0641399 + 4.29659i) q^{72} +(6.99634 + 4.03934i) q^{73} +(-13.2960 + 4.76457i) q^{74} +(1.84104 - 1.06293i) q^{75} +(11.9106 - 1.97816i) q^{76} +(-0.883939 - 10.7808i) q^{77} +(11.3657 + 9.63375i) q^{78} +(-3.21095 + 1.85384i) q^{79} +(0.772851 - 3.92463i) q^{80} +(5.62481 - 9.74247i) q^{81} +(-1.46727 + 8.08584i) q^{82} -9.94035i q^{83} +(-10.8195 - 3.07852i) q^{84} -2.41452i q^{85} +(-14.8985 - 2.70351i) q^{86} +(3.27516 - 5.67274i) q^{87} +(10.0998 - 5.63179i) q^{88} +(-3.81064 + 2.20007i) q^{89} +(1.38922 - 1.63898i) q^{90} +(-10.7816 + 7.46197i) q^{91} +(1.00925 - 0.167621i) q^{92} +(8.49342 - 4.90368i) q^{93} +(-0.666861 - 1.86095i) q^{94} +(-5.22809 - 3.01844i) q^{95} +(-1.79298 - 11.8912i) q^{96} -5.67803i q^{97} +(5.08535 - 8.49348i) q^{98} +6.21132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.39149	+	0.252502i	0.983932	+	0.178546i
$2$	1.39149	+	0.252502i	0.983932	+	0.178546i
$3$	−1.84104	−	1.06293i	−1.06293	−	0.613680i	−0.136685	−	0.990615i	$-0.543645\pi$
$3$	−1.84104	−	1.06293i	−1.06293	−	0.613680i	−0.926240	+	0.376934i	$0.876978\pi$
$4$	1.87249	+	0.702708i	0.936243	+	0.351354i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−2.29340	−	1.94392i	−0.936276	−	0.793601i
$7$	2.17552	−	1.50569i	0.822270	−	0.569097i
$7$	2.17552	−	1.50569i	0.822270	−	0.569097i
$8$	2.42811	+	1.45062i	0.858466	+	0.512871i
$9$	0.759621	+	1.31570i	0.253207	+	0.438567i
$10$	−0.477071	−	1.33132i	−0.150863	−	0.420999i
$11$	2.04422	−	3.54069i	0.616354	−	1.06756i	−0.373791	−	0.927513i	$-0.621942\pi$
$11$	2.04422	−	3.54069i	0.616354	−	1.06756i	0.990145	−	0.140044i	$-0.0447245\pi$
$12$	−2.70039	−	3.28403i	−0.779537	−	0.948017i
$13$	−4.95585			−1.37450			−0.687252	−	0.726419i	$-0.741183\pi$
$13$	−4.95585			−1.37450			−0.687252	+	0.726419i	$0.741183\pi$
$14$	3.40741	−	1.54583i	0.910668	−	0.413140i
$15$			2.12585i			0.548892i
$16$	3.01240	+	2.63162i	0.753100	+	0.657906i
$17$	2.09103	+	1.20726i	0.507150	+	0.292803i	0.731661	−	0.681668i	$-0.238745\pi$
$17$	2.09103	+	1.20726i	0.507150	+	0.292803i	−0.224511	+	0.974471i	$0.572079\pi$
$18$	0.724787	+	2.02259i	0.170834	+	0.476729i
$19$	5.22809	−	3.01844i	1.19941	−	0.692478i	0.238984	−	0.971024i	$-0.423186\pi$
$19$	5.22809	−	3.01844i	1.19941	−	0.692478i	0.960423	+	0.278546i	$0.0898525\pi$
$20$	−0.327679	−	1.97297i	−0.0732713	−	0.441170i
$21$	−5.60566	+	0.459619i	−1.22326	+	0.100297i
$22$	3.73854	−	4.41066i	0.797059	−	0.940356i
$23$	0.443005	−	0.255769i	0.0923730	−	0.0533316i	−0.453102	−	0.891459i	$-0.649683\pi$
$23$	0.443005	−	0.255769i	0.0923730	−	0.0533316i	0.545475	+	0.838127i	$0.316349\pi$
$24$	−2.92835	−	5.25154i	−0.597746	−	1.07197i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.89601	−	1.25136i	−1.35242	−	0.245412i
$27$			3.14787i			0.605808i
$28$	5.13169	−	1.29062i	0.969799	−	0.243905i
$29$			3.08127i			0.572177i	0.958203	+	0.286088i	$0.0923551\pi$
$29$			3.08127i			0.572177i	−0.958203	+	0.286088i	$0.907645\pi$
$30$	−0.536782	+	2.95810i	−0.0980026	+	0.540072i
$31$	−2.30669	+	3.99530i	−0.414294	+	0.717578i	−0.995354	−	0.0962826i	$-0.969305\pi$
$31$	−2.30669	+	3.99530i	−0.414294	+	0.717578i	0.581060	+	0.813861i	$0.302638\pi$
$32$	3.52723	+	4.42251i	0.623533	+	0.781797i
$33$	−7.52697	+	4.34570i	−1.31028	+	0.756489i
$34$	2.60481	+	2.20788i	0.446722	+	0.378648i
$35$	−2.39173	−	1.13121i	−0.404276	−	0.191210i
$36$	0.497824	+	2.99742i	0.0829706	+	0.499571i
$37$	−8.64910	+	4.99356i	−1.42190	+	0.820937i	−0.996462	−	0.0840489i	$-0.973215\pi$
$37$	−8.64910	+	4.99356i	−1.42190	+	0.820937i	−0.425442	+	0.904986i	$0.639881\pi$
$38$	8.03700	−	2.88002i	1.30377	−	0.467201i
$39$	9.12392	+	5.26770i	1.46100	+	0.843507i
$40$	0.0422184	−	2.82811i	0.00667531	−	0.447164i
$41$			5.81092i			0.907514i	0.891126	+	0.453757i	$0.149917\pi$
$41$			5.81092i			0.907514i	−0.891126	+	0.453757i	$0.850083\pi$
$42$	−7.91627	−	0.775887i	−1.22151	−	0.119722i
$43$	−10.7069			−1.63278			−0.816390	−	0.577501i	$-0.804028\pi$
$43$	−10.7069			−1.63278			−0.816390	+	0.577501i	$0.804028\pi$
$44$	6.31584	−	5.19340i	0.952148	−	0.782934i
$45$	0.759621	−	1.31570i	0.113238	−	0.196133i
$46$	0.681020	−	0.244040i	0.100411	−	0.0359818i
$47$	−0.698912	−	1.21055i	−0.101947	−	0.176577i	0.810540	−	0.585683i	$-0.199174\pi$
$47$	−0.698912	−	1.21055i	−0.101947	−	0.176577i	−0.912487	+	0.409106i	$0.865840\pi$
$48$	−2.74874	−	8.04688i	−0.396746	−	1.16147i
$49$	2.46579	−	6.55133i	0.352256	−	0.935904i
$50$	−0.914418	+	1.07881i	−0.129318	+	0.152567i
$51$	−2.56645	−	4.44522i	−0.359375	−	0.622456i
$52$	−9.27975	−	3.48252i	−1.28687	−	0.482938i
$53$	6.79325	+	3.92208i	0.933124	+	0.538739i	0.887798	−	0.460233i	$-0.152234\pi$
$53$	6.79325	+	3.92208i	0.933124	+	0.538739i	0.0453258	+	0.998972i	$0.485567\pi$
$54$	−0.794845	+	4.38023i	−0.108165	+	0.596074i
$55$	−4.08843			−0.551284
$56$	7.46658	−	0.500126i	0.997764	−	0.0668321i
$57$	−12.8335			−1.69984
$58$	−0.778027	+	4.28755i	−0.102160	+	0.562983i
$59$	8.82516	+	5.09521i	1.14894	+	0.663339i	0.948628	−	0.316393i	$-0.102472\pi$
$59$	8.82516	+	5.09521i	1.14894	+	0.663339i	0.200310	+	0.979733i	$0.435805\pi$
$60$	−1.49385	+	3.98062i	−0.192856	+	0.513896i
$61$	1.33141	+	2.30607i	0.170469	+	0.295262i	0.938584	−	0.345051i	$-0.112138\pi$
$61$	1.33141	+	2.30607i	0.170469	+	0.295262i	−0.768115	+	0.640312i	$0.778805\pi$
$62$	−4.21856	+	4.97698i	−0.535757	+	0.632077i
$63$	3.63361	+	1.71859i	0.457792	+	0.216521i
$64$	3.79141	+	7.04451i	0.473927	+	0.880564i
$65$	2.47792	+	4.29189i	0.307349	+	0.532343i
$66$	−11.5710	+	4.14642i	−1.42429	+	0.510389i
$67$	3.46437	−	6.00046i	0.423240	−	0.733073i	−0.573014	−	0.819545i	$-0.694226\pi$
$67$	3.46437	−	6.00046i	0.423240	−	0.733073i	0.996254	+	0.0864725i	$0.0275595\pi$
$68$	3.06708	+	3.72996i	0.371938	+	0.452324i
$69$	−1.08745			−0.130914
$70$	−3.04243	−	2.17799i	−0.363640	−	0.260319i
$71$			1.54183i			0.182981i	0.995806	+	0.0914906i	$0.0291631\pi$
$71$			1.54183i			0.182981i	−0.995806	+	0.0914906i	$0.970837\pi$
$72$	−0.0641399	+	4.29659i	−0.00755896	+	0.506357i
$73$	6.99634	+	4.03934i	0.818859	+	0.472769i	0.850023	−	0.526746i	$-0.176588\pi$
$73$	6.99634	+	4.03934i	0.818859	+	0.472769i	−0.0311636	+	0.999514i	$0.509921\pi$
$74$	−13.2960	+	4.76457i	−1.54563	+	0.553870i
$75$	1.84104	−	1.06293i	0.212585	−	0.122736i
$76$	11.9106	−	1.97816i	1.36624	−	0.226911i
$77$	−0.883939	−	10.7808i	−0.100734	−	1.22859i
$78$	11.3657	+	9.63375i	1.28692	+	1.09081i
$79$	−3.21095	+	1.85384i	−0.361260	+	0.208574i	−0.669633	−	0.742692i	$-0.733549\pi$
$79$	−3.21095	+	1.85384i	−0.361260	+	0.208574i	0.308373	+	0.951265i	$0.400215\pi$
$80$	0.772851	−	3.92463i	0.0864074	−	0.438787i
$81$	5.62481	−	9.74247i	0.624979	−	1.08250i
$82$	−1.46727	+	8.08584i	−0.162033	+	0.892931i
$83$		−	9.94035i		−	1.09109i	−0.838080	−	0.545547i	$-0.816322\pi$
$83$		−	9.94035i		−	1.09109i	0.838080	−	0.545547i	$-0.183678\pi$
$84$	−10.8195	−	3.07852i	−1.18050	−	0.335894i
$85$		−	2.41452i		−	0.261891i
$86$	−14.8985	−	2.70351i	−1.60654	−	0.291527i
$87$	3.27516	−	5.67274i	0.351134	−	0.608181i
$88$	10.0998	−	5.63179i	1.07664	−	0.600351i
$89$	−3.81064	+	2.20007i	−0.403927	+	0.233207i	−0.688177	−	0.725543i	$-0.741589\pi$
$89$	−3.81064	+	2.20007i	−0.403927	+	0.233207i	0.284250	+	0.958750i	$0.408255\pi$
$90$	1.38922	−	1.63898i	0.146437	−	0.172764i
$91$	−10.7816	+	7.46197i	−1.13021	+	0.782227i
$92$	1.00925	−	0.167621i	0.105222	−	0.0174756i
$93$	8.49342	−	4.90368i	0.880727	−	0.508488i
$94$	−0.666861	−	1.86095i	−0.0687815	−	0.191942i
$95$	−5.22809	−	3.01844i	−0.536391	−	0.309685i
$96$	−1.79298	−	11.8912i	−0.182995	−	1.21364i
$97$		−	5.67803i		−	0.576517i	−0.957553	−	0.288258i	$-0.906924\pi$
$97$		−	5.67803i		−	0.576517i	0.957553	−	0.288258i	$-0.0930762\pi$
$98$	5.08535	−	8.49348i	0.513698	−	0.857971i
$99$	6.21132			0.624261
$100$	−1.54481	+	1.27027i	−0.154481	+	0.127027i
$101$	7.38908	−	12.7983i	0.735241	−	1.27348i	−0.219376	−	0.975640i	$-0.570402\pi$
$101$	7.38908	−	12.7983i	0.735241	−	1.27348i	0.954617	−	0.297835i	$-0.0962645\pi$
$102$	−2.44876	−	6.83352i	−0.242463	−	0.676619i
$103$	−4.73633	−	8.20356i	−0.466684	−	0.808321i	0.532591	−	0.846373i	$-0.321218\pi$
$103$	−4.73633	−	8.20356i	−0.466684	−	0.808321i	−0.999276	+	0.0380514i	$0.987885\pi$
$104$	−12.0333	−	7.18904i	−1.17997	−	0.704944i
$105$	3.20087	+	4.62484i	0.312373	+	0.451338i
$106$	8.46239	+	7.17285i	0.821940	+	0.696688i
$107$	9.53855	+	16.5212i	0.922126	+	1.59717i	0.796119	+	0.605140i	$0.206883\pi$
$107$	9.53855	+	16.5212i	0.922126	+	1.59717i	0.126007	+	0.992029i	$0.459784\pi$
$108$	−2.21204	+	5.89434i	−0.212853	+	0.567183i
$109$	0.554540	+	0.320164i	0.0531153	+	0.0306662i	0.526323	−	0.850285i	$-0.323570\pi$
$109$	0.554540	+	0.320164i	0.0531153	+	0.0306662i	−0.473207	+	0.880951i	$0.656904\pi$
$110$	−5.68901	−	1.03234i	−0.542426	−	0.0984296i
$111$	21.2311			2.01517
$112$	10.5160	+	1.18941i	0.993664	+	0.112389i
$113$	−14.8422			−1.39623			−0.698117	−	0.715984i	$-0.745978\pi$
$113$	−14.8422			−1.39623			−0.698117	+	0.715984i	$0.745978\pi$
$114$	−17.8577	−	3.24049i	−1.67253	−	0.303500i
$115$	−0.443005	−	0.255769i	−0.0413105	−	0.0238506i
$116$	−2.16523	+	5.76963i	−0.201037	+	0.535696i
$117$	−3.76457	−	6.52042i	−0.348034	−	0.602813i
$118$	10.9936	+	9.31830i	1.01204	+	0.857819i
$119$	6.36685	−	0.522030i	0.583648	−	0.0478544i
$120$	−3.08380	+	5.16179i	−0.281511	+	0.471205i
$121$	−2.85764	−	4.94958i	−0.259786	−	0.449962i
$122$	1.27035	+	3.54505i	0.115012	+	0.320954i
$123$	6.17658	−	10.6981i	0.556923	−	0.964619i
$124$	−7.12678	+	5.86022i	−0.640004	+	0.526263i
$125$	1.00000			0.0894427
$126$	4.62219	+	3.30889i	0.411777	+	0.294779i
$127$		−	7.19222i		−	0.638207i	−0.947720	−	0.319103i	$-0.896618\pi$
$127$		−	7.19222i		−	0.638207i	0.947720	−	0.319103i	$-0.103382\pi$
$128$	3.49696	+	10.7597i	0.309090	+	0.951033i
$129$	19.7118	+	11.3806i	1.73552	+	1.00201i
$130$	2.36429	+	6.59780i	0.207362	+	0.578665i
$131$	−6.50864	+	3.75777i	−0.568663	+	0.328318i	−0.756615	−	0.653860i	$-0.773148\pi$
$131$	−6.50864	+	3.75777i	−0.568663	+	0.328318i	0.187952	+	0.982178i	$0.439815\pi$
$132$	−17.1479	+	2.84799i	−1.49253	+	0.247886i
$133$	6.82899	−	14.4386i	0.592149	−	1.25198i
$134$	6.33576	−	7.47481i	0.547326	−	0.645726i
$135$	2.72614	−	1.57394i	0.234628	−	0.135463i
$136$	3.32598	+	5.96464i	0.285201	+	0.511464i
$137$	1.70968	−	2.96124i	0.146067	−	0.252996i	−0.783703	−	0.621135i	$-0.786672\pi$
$137$	1.70968	−	2.96124i	0.146067	−	0.252996i	0.929771	+	0.368139i	$0.120005\pi$
$138$	−1.51318	−	0.274585i	−0.128811	−	0.0233742i
$139$			11.0468i			0.936981i	0.883468	+	0.468491i	$0.155202\pi$
$139$			11.0468i			0.936981i	−0.883468	+	0.468491i	$0.844798\pi$
$140$	−3.68356	−	3.79887i	−0.311318	−	0.321063i
$141$			2.97156i			0.250251i
$142$	−0.389315	+	2.14544i	−0.0326706	+	0.180041i
$143$	−10.1308	+	17.5471i	−0.847182	+	1.46736i
$144$	−1.17415	+	5.96246i	−0.0978456	+	0.496871i
$145$	2.66845	−	1.54063i	0.221603	−	0.127943i
$146$	8.71539	+	7.38729i	0.721291	+	0.611376i
$147$	−11.5032	+	9.44030i	−0.948768	+	0.778623i
$148$	−19.7043	+	3.27257i	−1.61969	+	0.269004i
$149$	−8.88620	+	5.13045i	−0.727986	+	0.420303i	−0.817685	−	0.575666i	$-0.804743\pi$
$149$	−8.88620	+	5.13045i	−0.727986	+	0.420303i	0.0896992	+	0.995969i	$0.471409\pi$
$150$	2.83018	−	1.01418i	0.231083	−	0.0828076i
$151$	−14.2514	−	8.22804i	−1.15976	−	0.669588i	−0.208514	−	0.978019i	$-0.566863\pi$
$151$	−14.2514	−	8.22804i	−1.15976	−	0.669588i	−0.951247	+	0.308431i	$0.900196\pi$
$152$	17.0730	+	0.254867i	1.38480	+	0.0206725i
$153$			3.66824i			0.296559i
$154$	1.49218	−	15.2246i	0.120244	−	1.22683i
$155$	4.61338			0.370556
$156$	13.3827	+	16.2751i	1.07148	+	1.30305i
$157$	−11.1196	+	19.2597i	−0.887441	+	1.53709i	−0.0445519	+	0.999007i	$0.514186\pi$
$157$	−11.1196	+	19.2597i	−0.887441	+	1.53709i	−0.842890	+	0.538087i	$0.819147\pi$
$158$	−4.93610	+	1.76883i	−0.392695	+	0.140721i
$159$	−8.33776	−	14.4414i	−0.661227	−	1.14528i
$160$	2.06639	−	5.26593i	0.163363	−	0.416308i
$161$	0.578659	−	1.22346i	0.0456047	−	0.0964222i
$162$	10.2869	−	12.1363i	0.808212	−	0.953514i
$163$	−6.48712	−	11.2360i	−0.508111	−	0.880073i	−0.999956	−	0.00939084i	$-0.997011\pi$
$163$	−6.48712	−	11.2360i	−0.508111	−	0.880073i	0.491845	−	0.870683i	$-0.336323\pi$
$164$	−4.08338	+	10.8809i	−0.318859	+	0.849653i
$165$	7.52697	+	4.34570i	0.585974	+	0.338312i
$166$	2.50996	−	13.8319i	0.194811	−	1.07356i
$167$	11.9246			0.922755			0.461377	−	0.887204i	$-0.347355\pi$
$167$	11.9246			0.922755			0.461377	+	0.887204i	$0.347355\pi$
$168$	−14.2779	−	7.01567i	−1.10156	−	0.541271i
$169$	11.5604			0.889264
$170$	0.609671	−	3.35978i	0.0467596	−	0.257683i
$171$	7.94273	+	4.58574i	0.607396	+	0.350680i
$172$	−20.0484	−	7.52380i	−1.52868	−	0.573684i
$173$	5.55929	+	9.62897i	0.422665	+	0.732077i	0.996199	−	0.0871047i	$-0.0277615\pi$
$173$	5.55929	+	9.62897i	0.422665	+	0.732077i	−0.573534	+	0.819181i	$0.694428\pi$
$174$	5.98972	−	7.06657i	0.454080	−	0.535715i
$175$	0.216205	+	2.63690i	0.0163436	+	0.199331i
$176$	15.4758	−	5.28636i	1.16653	−	0.398475i
$177$	−10.8317	−	18.7610i	−0.814157	−	1.41016i
$178$	−5.85798	+	2.09918i	−0.439074	+	0.157340i
$179$	4.27641	−	7.40695i	0.319634	−	0.553622i	−0.660778	−	0.750581i	$-0.729773\pi$
$179$	4.27641	−	7.40695i	0.319634	−	0.553622i	0.980412	+	0.196960i	$0.0631068\pi$
$180$	2.34693	−	1.92984i	0.174930	−	0.143842i
$181$	−0.821960			−0.0610958			−0.0305479	−	0.999533i	$-0.509725\pi$
$181$	−0.821960			−0.0610958			−0.0305479	+	0.999533i	$0.509725\pi$
$182$	−16.8866	+	7.66089i	−1.25172	+	0.567863i
$183$		−	5.66075i		−	0.418455i
$184$	1.44669	+	0.0215963i	0.106651	+	0.00159210i
$185$	8.64910	+	4.99356i	0.635895	+	0.367134i
$186$	13.0567	−	4.67881i	0.957363	−	0.343067i
$187$	8.54905	−	4.93580i	0.625168	−	0.360941i
$188$	−0.458038	−	2.75787i	−0.0334058	−	0.201138i
$189$	4.73972	+	6.84826i	0.344764	+	0.498138i
$190$	−6.51267	−	5.52023i	−0.472479	−	0.400480i
$191$	19.4375	−	11.2222i	1.40645	−	0.812012i	0.411402	−	0.911454i	$-0.365039\pi$
$191$	19.4375	−	11.2222i	1.40645	−	0.812012i	0.995043	+	0.0994420i	$0.0317058\pi$
$192$	0.507646	−	16.9992i	0.0366362	−	1.22681i
$193$	2.15591	−	3.73414i	0.155186	−	0.268789i	−0.777941	−	0.628337i	$-0.783736\pi$
$193$	2.15591	−	3.73414i	0.155186	−	0.268789i	0.933127	+	0.359548i	$0.117069\pi$
$194$	1.43372	−	7.90092i	0.102935	−	0.567253i
$195$		−	10.5354i		−	0.754455i
$196$	9.22083	−	10.5345i	0.658631	−	0.752466i
$197$			6.67148i			0.475323i	0.971348	+	0.237662i	$0.0763809\pi$
$197$			6.67148i			0.475323i	−0.971348	+	0.237662i	$0.923619\pi$
$198$	8.64298	+	1.56837i	0.614230	+	0.111459i
$199$	−4.68875	+	8.12116i	−0.332377	+	0.575693i	−0.982977	−	0.183727i	$-0.941184\pi$
$199$	−4.68875	+	8.12116i	−0.332377	+	0.575693i	0.650601	+	0.759420i	$0.274517\pi$
$200$	−2.47033	+	1.37749i	−0.174678	+	0.0974035i
$201$	−12.7561	+	7.36473i	−0.899745	+	0.519468i
$202$	13.5134	−	15.9429i	0.950801	−	1.12174i
$203$	4.63943	+	6.70336i	0.325624	+	0.470484i
$204$	−1.68195	−	10.1271i	−0.117760	−	0.709038i
$205$	5.03241	−	2.90546i	0.351479	−	0.202926i
$206$	−4.51913	−	12.6111i	−0.314863	−	0.878657i
$207$	0.673032	+	0.388575i	0.0467790	+	0.0270079i
$208$	−14.9290	−	13.0419i	−1.03514	−	0.904295i
$209$		−	24.6814i		−	1.70725i
$210$	3.28620	+	7.24364i	0.226769	+	0.499858i
$211$	6.08038			0.418590			0.209295	−	0.977852i	$-0.432883\pi$
$211$	6.08038			0.418590			0.209295	+	0.977852i	$0.432883\pi$
$212$	9.96417	+	12.1177i	0.684342	+	0.832248i
$213$	1.63885	−	2.83857i	0.112292	−	0.194495i
$214$	9.10113	+	25.3976i	0.622141	+	1.73615i
$215$	5.35343	+	9.27241i	0.365101	+	0.632373i
$216$	−4.56636	+	7.64337i	−0.310701	+	0.520065i
$217$	0.997435	+	12.1650i	0.0677103	+	0.825816i
$218$	0.690795	+	0.585528i	0.0467865	+	0.0396569i
$219$	−8.58703	−	14.8732i	−0.580258	−	1.00504i
$220$	−7.65553	−	2.87298i	−0.516136	−	0.193696i
$221$	−10.3628	−	5.98299i	−0.697080	−	0.402459i
$222$	29.5429	+	5.36091i	1.98279	+	0.359801i
$223$	−15.1265			−1.01295			−0.506474	−	0.862255i	$-0.669051\pi$
$223$	−15.1265			−1.01295			−0.506474	+	0.862255i	$0.669051\pi$
$224$	14.3325	+	4.31035i	0.957631	+	0.287998i
$225$	−1.51924			−0.101283
$226$	−20.6527	−	3.74768i	−1.37380	−	0.249292i
$227$	−19.6959	−	11.3714i	−1.30726	−	0.754747i	−0.325622	−	0.945500i	$-0.605574\pi$
$227$	−19.6959	−	11.3714i	−1.30726	−	0.754747i	−0.981638	+	0.190753i	$0.938907\pi$
$228$	−24.0306	−	9.01821i	−1.59146	−	0.597246i
$229$	−1.35800	−	2.35213i	−0.0897393	−	0.155433i	0.817662	−	0.575699i	$-0.195270\pi$
$229$	−1.35800	−	2.35213i	−0.0897393	−	0.155433i	−0.907401	+	0.420266i	$0.861937\pi$
$230$	−0.551855	−	0.467760i	−0.0363882	−	0.0308432i
$231$	−9.83182	+	20.7875i	−0.646886	+	1.36771i
$232$	−4.46974	+	7.48165i	−0.293453	+	0.491194i
$233$	8.54513	+	14.8006i	0.559810	+	0.969620i	0.997512	+	0.0704994i	$0.0224593\pi$
$233$	8.54513	+	14.8006i	0.559810	+	0.969620i	−0.437702	+	0.899120i	$0.644207\pi$
$234$	−3.59193	−	10.0237i	−0.234812	−	0.655267i
$235$	−0.698912	+	1.21055i	−0.0455920	+	0.0789676i
$236$	12.9445	+	15.7422i	0.842617	+	1.02473i
$237$	7.88199			0.511990
$238$	8.99121	+	0.881244i	0.582814	+	0.0571225i
$239$		−	14.8013i		−	0.957416i	−0.877974	−	0.478708i	$-0.841105\pi$
$239$		−	14.8013i		−	0.957416i	0.877974	−	0.478708i	$-0.158895\pi$
$240$	−5.59444	+	6.40392i	−0.361119	+	0.413371i
$241$	−15.4371	−	8.91260i	−0.994389	−	0.574111i	−0.0878059	−	0.996138i	$-0.527986\pi$
$241$	−15.4371	−	8.91260i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$242$	−2.72660	−	7.60885i	−0.175272	−	0.489115i
$243$	−12.5326	+	7.23571i	−0.803968	+	0.464171i
$244$	0.872550	+	5.25367i	0.0558593	+	0.336332i
$245$	−6.90651	+	1.14022i	−0.441241	+	0.0728461i
$246$	11.2959	−	13.3268i	0.720203	−	0.849683i
$247$	−25.9096	+	14.9589i	−1.64859	+	0.951814i
$248$	−11.3966	+	6.35490i	−0.723682	+	0.403537i
$249$	−10.5658	+	18.3006i	−0.669583	+	1.15975i
$250$	1.39149	+	0.252502i	0.0880055	+	0.0159696i
$251$			25.9720i			1.63934i	0.572837	+	0.819669i	$0.305843\pi$
$251$			25.9720i			1.63934i	−0.572837	+	0.819669i	$0.694157\pi$
$252$	5.59622	+	5.77139i	0.352529	+	0.363564i
$253$		−	2.09139i		−	0.131485i
$254$	1.81605	−	10.0079i	0.113949	−	0.627952i
$255$	−2.56645	+	4.44522i	−0.160717	+	0.278371i
$256$	2.14913	+	15.8550i	0.134320	+	0.990938i
$257$	8.43972	−	4.87268i	0.526455	−	0.303949i	−0.213116	−	0.977027i	$-0.568361\pi$
$257$	8.43972	−	4.87268i	0.526455	−	0.303949i	0.739572	+	0.673078i	$0.235028\pi$
$258$	24.5551	+	20.8132i	1.52873	+	1.29578i
$259$	−11.2976	+	23.8865i	−0.701996	+	1.48423i
$260$	1.62393	+	9.77776i	0.100712	+	0.606391i
$261$	−4.05403	+	2.34059i	−0.250938	+	0.144879i
$262$	−10.0056	+	3.58545i	−0.618145	+	0.221510i
$263$	−5.12532	−	2.95910i	−0.316041	−	0.182466i	0.333586	−	0.942720i	$-0.391741\pi$
$263$	−5.12532	−	2.95910i	−0.316041	−	0.182466i	−0.649626	+	0.760254i	$0.725075\pi$
$264$	−24.5802	−	0.366937i	−1.51281	−	0.0225834i
$265$		−	7.84416i		−	0.481863i
$266$	13.1482	−	18.3668i	0.806171	−	1.12614i
$267$	9.35405			0.572459
$268$	10.7035	−	8.80133i	0.653823	−	0.537627i
$269$	10.3914	−	17.9984i	0.633572	−	1.09738i	−0.353244	−	0.935531i	$-0.614921\pi$
$269$	10.3914	−	17.9984i	0.633572	−	1.09738i	0.986816	−	0.161848i	$-0.0517453\pi$
$270$	4.19081	−	1.50176i	0.255045	−	0.0913941i
$271$	−5.73115	−	9.92664i	−0.348143	−	0.603001i	0.637777	−	0.770221i	$-0.279854\pi$
$271$	−5.73115	−	9.92664i	−0.348143	−	0.603001i	−0.985920	+	0.167221i	$0.946521\pi$
$272$	3.12198	+	9.13956i	0.189298	+	0.554167i
$273$	27.7808	−	2.27780i	1.68137	−	0.137859i
$274$	3.12672	−	3.68884i	0.188892	−	0.222851i
$275$	2.04422	+	3.54069i	0.123271	+	0.213511i
$276$	−2.03624	−	0.764164i	−0.122567	−	0.0459972i
$277$	28.4995	+	16.4542i	1.71237	+	0.988638i	0.931343	+	0.364143i	$0.118638\pi$
$277$	28.4995	+	16.4542i	1.71237	+	0.988638i	0.781029	+	0.624495i	$0.214695\pi$
$278$	−2.78935	+	15.3716i	−0.167294	+	0.921925i
$279$	−7.00884			−0.419608
$280$	−4.16641	−	6.21619i	−0.248991	−	0.371488i
$281$	−23.6717			−1.41214			−0.706068	−	0.708144i	$-0.749533\pi$
$281$	−23.6717			−1.41214			−0.706068	+	0.708144i	$0.749533\pi$
$282$	−0.750327	+	4.13490i	−0.0446813	+	0.246230i
$283$	−17.3451	−	10.0142i	−1.03106	−	0.595283i	−0.113772	−	0.993507i	$-0.536293\pi$
$283$	−17.3451	−	10.0142i	−1.03106	−	0.595283i	−0.917288	+	0.398224i	$0.869627\pi$
$284$	−1.08346	+	2.88705i	−0.0642912	+	0.171315i
$285$	6.41675	+	11.1141i	0.380096	+	0.658345i
$286$	−18.5276	+	21.8586i	−1.09556	+	1.29252i
$287$	8.74945	+	12.6418i	0.516464	+	0.746221i
$288$	−3.13935	+	8.00022i	−0.184988	+	0.471418i
$289$	−5.58505	−	9.67360i	−0.328533	−	0.569035i
$290$	4.10214	−	1.46998i	0.240886	−	0.0863204i
$291$	−6.03532	+	10.4535i	−0.353797	+	0.612794i
$292$	10.2621	+	12.4800i	0.600542	+	0.730336i
$293$	4.76771			0.278533			0.139266	−	0.990255i	$-0.455526\pi$
$293$	4.76771			0.278533			0.139266	+	0.990255i	$0.455526\pi$
$294$	−18.3903	+	10.2315i	−1.07254	+	0.596713i
$295$		−	10.1904i		−	0.593309i
$296$	−28.2447	−	0.421640i	−1.64169	−	0.0245073i
$297$	11.1456	+	6.43493i	0.646735	+	0.373393i
$298$	−13.6605	+	4.89518i	−0.791331	+	0.283570i
$299$	−2.19547	+	1.26755i	−0.126967	+	0.0733045i
$300$	4.19425	−	0.696597i	0.242155	−	0.0402181i
$301$	−23.2930	+	16.1212i	−1.34259	+	0.929211i
$302$	−17.7530	−	15.0477i	−1.02157	−	0.865900i
$303$	−27.2072	+	15.7081i	−1.56301	+	0.902406i
$304$	23.6925	+	4.66561i	1.35886	+	0.267591i
$305$	1.33141	−	2.30607i	0.0762362	−	0.132045i
$306$	−0.926238	+	5.10431i	−0.0529495	+	0.291794i
$307$			14.4066i			0.822231i	0.911583	+	0.411115i	$0.134861\pi$
$307$			14.4066i			0.822231i	−0.911583	+	0.411115i	$0.865139\pi$
$308$	5.92060	−	20.8080i	0.337357	−	1.18565i
$309$			20.1375i			1.14558i
$310$	6.41947	+	1.16489i	0.364601	+	0.0661613i
$311$	0.00739749	−	0.0128128i	0.000419473	−	0.000726549i	−0.865816	−	0.500363i	$-0.833200\pi$
$311$	0.00739749	−	0.0128128i	0.000419473	−	0.000726549i	0.866235	+	0.499637i	$0.166533\pi$
$312$	14.5124	+	26.0259i	0.821605	+	1.47342i
$313$	−12.0601	+	6.96291i	−0.681678	+	0.393567i	−0.800487	−	0.599350i	$-0.795426\pi$
$313$	−12.0601	+	6.96291i	−0.681678	+	0.393567i	0.118809	+	0.992917i	$0.462092\pi$
$314$	−20.3359	+	23.9920i	−1.14762	+	1.35395i
$315$	−0.328467	−	4.00609i	−0.0185070	−	0.225718i
$316$	−7.31517	+	1.21493i	−0.411511	+	0.0683453i
$317$	20.7904	−	12.0034i	1.16771	−	0.674176i	0.214568	−	0.976709i	$-0.431166\pi$
$317$	20.7904	−	12.0034i	1.16771	−	0.674176i	0.953139	+	0.302533i	$0.0978323\pi$
$318$	−7.95541	−	22.2004i	−0.446117	−	1.24494i
$319$	10.9098	+	6.29878i	0.610831	+	0.352664i
$320$	4.20502	−	6.80572i	0.235068	−	0.380451i
$321$		−	40.5550i		−	2.26356i
$322$	1.11412	−	1.55632i	0.0620877	−	0.0867303i
$323$	14.5762			0.811039
$324$	17.3785	−	14.2900i	0.965472	−	0.793890i
$325$	2.47792	−	4.29189i	0.137450	−	0.238071i
$326$	−6.18964	−	17.2728i	−0.342812	−	0.956653i
$327$	−0.680621	−	1.17887i	−0.0376384	−	0.0651917i
$328$	−8.42943	+	14.1095i	−0.465437	+	0.779069i
$329$	−3.34321	−	1.58124i	−0.184317	−	0.0871763i
$330$	9.37640	+	7.94757i	0.516154	+	0.437499i
$331$	−0.783208	−	1.35656i	−0.0430490	−	0.0745630i	0.843698	−	0.536818i	$-0.180374\pi$
$331$	−0.783208	−	1.35656i	−0.0430490	−	0.0745630i	−0.886747	+	0.462255i	$0.847040\pi$
$332$	6.98517	−	18.6132i	0.383361	−	1.02153i
$333$	−13.1401	−	7.58643i	−0.720072	−	0.415734i
$334$	16.5930	+	3.01099i	0.907928	+	0.164754i
$335$	−6.92873			−0.378557
$336$	−18.0960	−	13.3674i	−0.987220	−	0.729253i
$337$	0.0592518			0.00322765			0.00161383	−	0.999999i	$-0.499486\pi$
$337$	0.0592518			0.00322765			0.00161383	+	0.999999i	$0.499486\pi$
$338$	16.0862	+	2.91904i	0.874975	+	0.158775i
$339$	27.3250	+	15.7761i	1.48409	+	0.856841i
$340$	1.69670	−	4.52115i	0.0920166	−	0.245194i
$341$	9.43075	+	16.3345i	0.510704	+	0.884565i
$342$	9.89432	+	8.38657i	0.535024	+	0.453494i
$343$	−4.49988	−	17.9653i	−0.242970	−	0.970034i
$344$	−25.9974	−	15.5316i	−1.40169	−	0.837406i
$345$	0.543727	+	0.941763i	0.0292733	+	0.0507028i
$346$	5.30435	+	14.8023i	0.285164	+	0.795779i
$347$	−0.0461825	+	0.0799904i	−0.00247921	+	0.00429411i	−0.867262	−	0.497851i	$-0.834122\pi$
$347$	−0.0461825	+	0.0799904i	−0.00247921	+	0.00429411i	0.864783	+	0.502146i	$0.167456\pi$
$348$	10.1190	−	8.32064i	0.542433	−	0.446033i
$349$	−15.4400			−0.826483			−0.413241	−	0.910622i	$-0.635603\pi$
$349$	−15.4400			−0.826483			−0.413241	+	0.910622i	$0.635603\pi$
$350$	−0.364977	+	3.72381i	−0.0195089	+	0.199046i
$351$		−	15.6004i		−	0.832686i
$352$	22.8692	−	3.44826i	1.21893	−	0.183793i
$353$	−8.58726	−	4.95786i	−0.457054	−	0.263880i	0.253751	−	0.967270i	$-0.418336\pi$
$353$	−8.58726	−	4.95786i	−0.457054	−	0.263880i	−0.710805	+	0.703389i	$0.751669\pi$
$354$	−10.3349	−	28.8407i	−0.549296	−	1.53287i
$355$	1.33526	−	0.770914i	0.0708683	−	0.0409158i
$356$	−8.68137	+	1.44184i	−0.460112	+	0.0764171i
$357$	−12.2765	−	5.80640i	−0.649742	−	0.307307i
$358$	7.82085	−	9.22690i	0.413345	−	0.487657i
$359$	−9.04478	+	5.22201i	−0.477365	+	0.275607i	−0.719318	−	0.694681i	$-0.755545\pi$
$359$	−9.04478	+	5.22201i	−0.477365	+	0.275607i	0.241953	+	0.970288i	$0.422212\pi$
$360$	3.75302	−	2.09275i	0.197802	−	0.110297i
$361$	8.72196	−	15.1069i	0.459051	−	0.795099i
$362$	−1.14375	−	0.207547i	−0.0601141	−	0.0109084i
$363$			12.1498i			0.637701i
$364$	−25.4319	+	6.39614i	−1.33299	+	0.335249i
$365$		−	8.07867i		−	0.422857i
$366$	1.42935	−	7.87688i	0.0747135	−	0.411731i
$367$	14.3708	−	24.8910i	0.750152	−	1.29930i	−0.197596	−	0.980283i	$-0.563314\pi$
$367$	14.3708	−	24.8910i	0.750152	−	1.29930i	0.947749	−	0.319018i	$-0.103353\pi$
$368$	2.00760	+	0.395343i	0.104653	+	0.0206087i
$369$	−7.64544	+	4.41410i	−0.398006	+	0.229789i
$370$	10.7743	+	9.13241i	0.560127	+	0.474771i
$371$	20.6843	−	1.69595i	1.07388	−	0.0880491i
$372$	19.3497	−	3.21367i	1.00323	−	0.166621i
$373$	8.93722	−	5.15991i	0.462752	−	0.267170i	−0.250449	−	0.968130i	$-0.580578\pi$
$373$	8.93722	−	5.15991i	0.462752	−	0.267170i	0.713201	+	0.700960i	$0.247245\pi$
$374$	13.1422	−	4.70945i	0.679568	−	0.243520i
$375$	−1.84104	−	1.06293i	−0.0950709	−	0.0548892i
$376$	0.0590138	−	3.95320i	0.00304341	−	0.203871i
$377$		−	15.2703i		−	0.786460i
$378$	4.86607	+	10.7261i	0.250283	+	0.551690i
$379$	−20.1192			−1.03346			−0.516728	−	0.856150i	$-0.672850\pi$
$379$	−20.1192			−1.03346			−0.516728	+	0.856150i	$0.672850\pi$
$380$	−7.66844	−	9.32581i	−0.393383	−	0.478404i
$381$	−7.64480	+	13.2412i	−0.391655	+	0.678366i
$382$	29.8807	−	10.7076i	1.52883	−	0.547849i
$383$	15.9182	+	27.5710i	0.813380	+	1.40881i	0.910486	+	0.413541i	$0.135708\pi$
$383$	15.9182	+	27.5710i	0.813380	+	1.40881i	−0.0971062	+	0.995274i	$0.530959\pi$
$384$	4.99873	−	23.5261i	0.255090	−	1.20056i
$385$	−8.89448	+	6.15591i	−0.453304	+	0.313734i
$386$	3.94280	−	4.65164i	0.200683	−	0.236762i
$387$	−8.13315	−	14.0870i	−0.413431	−	0.716084i
$388$	3.99000	−	10.6320i	0.202562	−	0.539760i
$389$	−11.9293	−	6.88741i	−0.604842	−	0.349205i	0.166102	−	0.986109i	$-0.446882\pi$
$389$	−11.9293	−	6.88741i	−0.604842	−	0.349205i	−0.770944	+	0.636903i	$0.780215\pi$
$390$	2.66021	−	14.6599i	0.134705	−	0.742332i
$391$	1.23512			0.0624626
$392$	15.4907	−	12.3304i	0.782398	−	0.622779i
$393$	15.9769			0.805928
$394$	−1.68456	+	9.28329i	−0.0848671	+	0.467685i
$395$	3.21095	+	1.85384i	0.161561	+	0.0932770i
$396$	11.6306	+	4.36475i	0.584460	+	0.219337i
$397$	−15.3003	−	26.5009i	−0.767900	−	1.33004i	−0.938700	−	0.344736i	$-0.887969\pi$
$397$	−15.3003	−	26.5009i	−0.767900	−	1.33004i	0.170800	−	0.985306i	$-0.445365\pi$
$398$	−8.57496	+	10.1166i	−0.429824	+	0.507098i
$399$	−27.9196	+	19.3233i	−1.39773	+	0.967374i
$400$	−3.78525	+	1.29301i	−0.189263	+	0.0646503i
$401$	9.62164	+	16.6652i	0.480482	+	0.832219i	0.999749	−	0.0223928i	$-0.00712846\pi$
$401$	9.62164	+	16.6652i	0.480482	+	0.832219i	−0.519267	+	0.854612i	$0.673795\pi$
$402$	−19.6096	+	7.02700i	−0.978036	+	0.350475i
$403$	11.4316	−	19.8001i	0.569449	−	0.986314i
$404$	22.8294	−	18.7722i	1.13581	−	0.933952i
$405$	−11.2496			−0.558999
$406$	4.76311	+	10.4991i	0.236389	+	0.521063i
$407$			40.8317i			2.02395i
$408$	0.216703	−	14.5164i	0.0107284	−	0.718670i
$409$	−4.36225	−	2.51854i	−0.215699	−	0.124534i	0.388258	−	0.921551i	$-0.373077\pi$
$409$	−4.36225	−	2.51854i	−0.215699	−	0.124534i	−0.603957	+	0.797017i	$0.706410\pi$
$410$	7.73618	−	2.77222i	0.382062	−	0.136910i
$411$	−6.29516	+	3.63451i	−0.310518	+	0.179277i
$412$	−3.10399	−	18.6893i	−0.152923	−	0.920756i
$413$	26.8711	−	2.20322i	1.32224	−	0.108413i
$414$	0.838401	+	0.710641i	0.0412052	+	0.0349261i
$415$	−8.60859	+	4.97017i	−0.422579	+	0.243976i
$416$	−17.4804	−	21.9173i	−0.857049	−	1.07458i
$417$	11.7420	−	20.3377i	0.575007	−	0.995941i
$418$	6.23210	−	34.3439i	0.304822	−	1.67981i
$419$		−	15.6895i		−	0.766483i	−0.923648	−	0.383242i	$-0.874808\pi$
$419$		−	15.6895i		−	0.766483i	0.923648	−	0.383242i	$-0.125192\pi$
$420$	2.74368	+	10.9092i	0.133878	+	0.532315i
$421$			17.3487i			0.845525i	0.906240	+	0.422763i	$0.138940\pi$
$421$			17.3487i			0.845525i	−0.906240	+	0.422763i	$0.861060\pi$
$422$	8.46078	+	1.53531i	0.411864	+	0.0747377i
$423$	1.06182	−	1.83912i	0.0516273	−	0.0894210i
$424$	10.8053	+	19.3776i	0.524751	+	0.941061i
$425$	−2.09103	+	1.20726i	−0.101430	+	0.0585606i
$426$	2.99718	−	3.53602i	0.145214	−	0.171321i
$427$	6.36873	+	3.01221i	0.308205	+	0.145771i
$428$	6.25117	+	37.6386i	0.302161	+	1.81933i
$429$	37.3025	−	21.5366i	1.80098	−	1.03980i
$430$	5.10793	+	14.2542i	0.246326	+	0.687399i
$431$	−6.75727	−	3.90131i	−0.325486	−	0.187920i	0.328349	−	0.944556i	$-0.393508\pi$
$431$	−6.75727	−	3.90131i	−0.325486	−	0.187920i	−0.653835	+	0.756637i	$0.726841\pi$
$432$	−8.28401	+	9.48265i	−0.398565	+	0.456234i
$433$			8.76403i			0.421172i	0.977575	+	0.210586i	$0.0675372\pi$
$433$			8.76403i			0.421172i	−0.977575	+	0.210586i	$0.932463\pi$
$434$	−1.68378	+	17.1794i	−0.0808240	+	0.824636i
$435$	−6.55031			−0.314063
$436$	0.813387	+	0.989183i	0.0389542	+	0.0473733i
$437$	1.54405	−	2.67437i	0.0738619	−	0.127932i
$438$	−8.19325	−	22.8641i	−0.391489	−	1.09249i
$439$	1.26642	+	2.19350i	0.0604428	+	0.104690i	0.894663	−	0.446741i	$-0.147415\pi$
$439$	1.26642	+	2.19350i	0.0604428	+	0.104690i	−0.834221	+	0.551431i	$0.814082\pi$
$440$	−9.92716	−	5.93076i	−0.473259	−	0.282738i
$441$	10.4927	−	1.73227i	0.499650	−	0.0824892i
$442$	−12.9091	−	10.9419i	−0.614022	−	0.520454i
$443$	−14.7957	−	25.6269i	−0.702964	−	1.21757i	−0.967421	−	0.253172i	$-0.918526\pi$
$443$	−14.7957	−	25.6269i	−0.702964	−	1.21757i	0.264458	−	0.964397i	$-0.414807\pi$
$444$	39.7550	+	14.9193i	1.88669	+	0.708039i
$445$	3.81064	+	2.20007i	0.180642	+	0.104293i
$446$	−21.0484	−	3.81948i	−0.996671	−	0.180858i
$447$	21.8131			1.03173
$448$	18.8552	+	9.61680i	0.890823	+	0.454351i
$449$	−12.4051			−0.585434			−0.292717	−	0.956199i	$-0.594559\pi$
$449$	−12.4051			−0.585434			−0.292717	+	0.956199i	$0.594559\pi$
$450$	−2.11401	−	0.383612i	−0.0996553	−	0.0180836i
$451$	20.5747	+	11.8788i	0.968823	+	0.559350i
$452$	−27.7917	−	10.4297i	−1.30721	−	0.490573i
$453$	17.4916	+	30.2963i	0.821826	+	1.42344i
$454$	−24.5353	−	20.7964i	−1.15150	−	0.976026i
$455$	11.8530	+	5.60612i	0.555679	+	0.262819i
$456$	−31.1611	−	18.6165i	−1.45925	−	0.871798i
$457$	19.1981	+	33.2521i	0.898049	+	1.55547i	0.829985	+	0.557785i	$0.188349\pi$
$457$	19.1981	+	33.2521i	0.898049	+	1.55547i	0.0680633	+	0.997681i	$0.478318\pi$
$458$	−1.29573	−	3.61586i	−0.0605454	−	0.168958i
$459$	−3.80029	+	6.58230i	−0.177383	+	0.307236i
$460$	−0.649790	−	0.790228i	−0.0302966	−	0.0368446i
$461$	−19.3759			−0.902426			−0.451213	−	0.892416i	$-0.649008\pi$
$461$	−19.3759			−0.902426			−0.451213	+	0.892416i	$0.649008\pi$
$462$	−18.9297	+	26.4430i	−0.880692	+	1.23024i
$463$		−	34.4968i		−	1.60320i	−0.597860	−	0.801600i	$-0.703982\pi$
$463$		−	34.4968i		−	1.60320i	0.597860	−	0.801600i	$-0.296018\pi$
$464$	−8.10873	+	9.28201i	−0.376438	+	0.430907i
$465$	−8.49342	−	4.90368i	−0.393873	−	0.227403i
$466$	8.15327	+	22.7525i	0.377693	+	1.05399i
$467$	18.4058	−	10.6266i	0.851720	−	0.491741i	−0.00951086	−	0.999955i	$-0.503027\pi$
$467$	18.4058	−	10.6266i	0.851720	−	0.491741i	0.861231	+	0.508214i	$0.169694\pi$
$468$	−2.46714	−	14.8548i	−0.114044	−	0.686662i
$469$	−1.49803	−	18.2704i	−0.0691724	−	0.843649i
$470$	−1.27820	+	1.50799i	−0.0589587	+	0.0695585i
$471$	40.9433	−	23.6386i	1.88657	−	1.08921i
$472$	14.0372	+	25.1736i	0.646116	+	1.15871i
$473$	−21.8871	+	37.9096i	−1.00637	+	1.74309i
$474$	10.9677	+	1.99022i	0.503763	+	0.0914139i
$475$			6.03688i			0.276991i
$476$	12.2887	+	3.49654i	0.563250	+	0.160264i
$477$			11.9172i			0.545650i
$478$	3.73736	−	20.5958i	0.170943	−	0.942032i
$479$	2.99806	−	5.19279i	0.136985	−	0.237265i	−0.789369	−	0.613919i	$-0.789592\pi$
$479$	2.99806	−	5.19279i	0.136985	−	0.237265i	0.926354	+	0.376654i	$0.122925\pi$
$480$	−9.40160	+	7.49837i	−0.429122	+	0.342252i
$481$	42.8636	−	24.7473i	1.95441	−	1.12838i
$482$	−19.2301	−	16.2997i	−0.875906	−	0.742430i
$483$	−2.36578	+	1.63737i	−0.107647	+	0.0745029i
$484$	−1.87278	−	11.2761i	−0.0851263	−	0.512550i
$485$	−4.91732	+	2.83902i	−0.223284	+	0.128913i
$486$	−19.2660	+	6.90390i	−0.873925	+	0.313167i
$487$	−8.18300	−	4.72445i	−0.370807	−	0.214085i	0.303004	−	0.952989i	$-0.402010\pi$
$487$	−8.18300	−	4.72445i	−0.370807	−	0.214085i	−0.673811	+	0.738904i	$0.735344\pi$
$488$	−0.112420	+	7.53075i	−0.00508900	+	0.340901i
$489$			27.5813i			1.24727i
$490$	−9.89825	−	0.157303i	−0.447157	−	0.00710621i
$491$	24.6604			1.11291			0.556454	−	0.830879i	$-0.312162\pi$
$491$	24.6604			1.11291			0.556454	+	0.830879i	$0.312162\pi$
$492$	19.0832	−	15.6918i	0.860338	−	0.707440i
$493$	−3.71989	+	6.44303i	−0.167535	+	0.290179i
$494$	−39.8301	+	14.2730i	−1.79204	+	0.642170i
$495$	−3.10566	−	5.37916i	−0.139589	−	0.241775i
$496$	−17.4628	+	5.96512i	−0.784103	+	0.267842i
$497$	2.32151	+	3.35428i	0.104134	+	0.150460i
$498$	−19.3232	+	22.7972i	−0.865894	+	1.02157i
$499$	−11.1699	−	19.3469i	−0.500035	−	0.866086i	−1.00000		4.07161e-5i	$-0.999987\pi$
$499$	−11.1699	−	19.3469i	−0.500035	−	0.866086i	0.499965	−	0.866046i	$-0.333346\pi$
$500$	1.87249	+	0.702708i	0.0837401	+	0.0314261i
$501$	−21.9537	−	12.6750i	−0.980820	−	0.566276i
$502$	−6.55799	+	36.1398i	−0.292697	+	1.61300i
$503$	7.59124			0.338477			0.169238	−	0.985575i	$-0.445869\pi$
$503$	7.59124			0.338477			0.169238	+	0.985575i	$0.445869\pi$
$504$	6.32979	+	9.44389i	0.281951	+	0.420664i
$505$	−14.7782			−0.657620
$506$	0.528081	−	2.91015i	0.0234761	−	0.129372i
$507$	−21.2832	−	12.2879i	−0.945221	−	0.545724i
$508$	5.05404	−	13.4673i	0.224237	−	0.597516i
$509$	−16.7288	−	28.9751i	−0.741490	−	1.28430i	−0.951817	−	0.306668i	$-0.900786\pi$
$509$	−16.7288	−	28.9751i	−0.741490	−	1.28430i	0.210326	−	0.977631i	$-0.432547\pi$
$510$	−4.69362	+	5.53745i	−0.207837	+	0.245202i
$511$	21.3027	−	1.74665i	0.942375	−	0.0772672i
$512$	−1.01294	+	22.6047i	−0.0447660	+	0.998997i
$513$	9.50166	+	16.4574i	0.419509	+	0.726610i
$514$	12.9741	−	4.64923i	0.572265	−	0.205069i
$515$	−4.73633	+	8.20356i	−0.208708	+	0.361492i
$516$	28.9127	+	35.1616i	1.27281	+	1.54790i
$517$	−5.71491			−0.251341
$518$	−21.7518	+	30.3851i	−0.955720	+	1.33505i
$519$		−	23.6364i		−	1.03752i
$520$	−0.209228	+	14.0157i	−0.00917524	+	0.614629i
$521$	−4.24541	−	2.45109i	−0.185995	−	0.107384i	0.404111	−	0.914710i	$-0.367581\pi$
$521$	−4.24541	−	2.45109i	−0.185995	−	0.107384i	−0.590106	+	0.807326i	$0.700914\pi$
$522$	−6.23214	+	2.23326i	−0.272773	+	0.0977472i
$523$	2.15135	−	1.24208i	0.0940721	−	0.0543125i	−0.452226	−	0.891903i	$-0.649370\pi$
$523$	2.15135	−	1.24208i	0.0940721	−	0.0543125i	0.546298	+	0.837591i	$0.316037\pi$
$524$	−14.8280	+	2.46268i	−0.647762	+	0.107583i
$525$	2.40479	−	5.08445i	0.104954	−	0.221904i
$526$	−6.38465	−	5.41172i	−0.278384	−	0.235962i
$527$	−9.64673	+	5.56954i	−0.420218	+	0.242613i
$528$	−34.1105	−	6.71716i	−1.48447	−	0.292327i
$529$	−11.3692	+	19.6920i	−0.494311	+	0.856173i
$530$	1.98067	−	10.9151i	0.0860348	−	0.474120i
$531$			15.4817i			0.671849i
$532$	22.9333	−	22.2372i	0.994284	−	0.964106i
$533$		−	28.7981i		−	1.24738i
$534$	13.0161	+	2.36192i	0.563260	+	0.102210i
$535$	9.53855	−	16.5212i	0.412387	−	0.714276i
$536$	17.1162	−	9.54429i	0.739309	−	0.412250i
$537$	−15.7461	+	9.09100i	−0.679493	+	0.392306i
$538$	19.0041	−	22.4207i	0.819324	−	0.966624i
$539$	−18.1556	−	22.1229i	−0.782016	−	0.952902i
$540$	6.21067	−	1.03149i	0.267265	−	0.0443883i
$541$	23.1290	−	13.3535i	0.994392	−	0.574113i	0.0878078	−	0.996137i	$-0.472014\pi$
$541$	23.1290	−	13.3535i	0.994392	−	0.574113i	0.906584	+	0.422025i	$0.138681\pi$
$542$	−5.46833	−	15.2599i	−0.234885	−	0.655471i
$543$	1.51326	+	0.873682i	0.0649403	+	0.0374933i
$544$	2.03645	+	13.5059i	0.0873119	+	0.579061i
$545$		−	0.640328i		−	0.0274286i
$546$	39.2318	+	3.84518i	1.67897	+	0.164558i
$547$	21.5603			0.921851			0.460926	−	0.887439i	$-0.347517\pi$
$547$	21.5603			0.921851			0.460926	+	0.887439i	$0.347517\pi$
$548$	5.28223	−	4.34348i	0.225646	−	0.185544i
$549$	−2.02273	+	3.50347i	−0.0863281	+	0.149525i
$550$	1.95047	+	5.44300i	0.0831685	+	0.232090i
$551$	9.30062	+	16.1091i	0.396220	+	0.686273i
$552$	−2.64046	−	1.57748i	−0.112385	−	0.0671421i
$553$	−4.19418	+	8.86778i	−0.178355	+	0.377096i
$554$	35.5021	+	30.0921i	1.50834	+	1.27849i
$555$	−10.6156	−	18.3867i	−0.450606	−	0.780472i
$556$	−7.76271	+	20.6851i	−0.329212	+	0.877242i
$557$	−11.7177	−	6.76520i	−0.496493	−	0.286651i	0.230771	−	0.973008i	$-0.425875\pi$
$557$	−11.7177	−	6.76520i	−0.496493	−	0.286651i	−0.727264	+	0.686358i	$0.759209\pi$
$558$	−9.75273	−	1.76975i	−0.412866	−	0.0749194i
$559$	53.0616			2.24426
$560$	−4.22792	−	9.70179i	−0.178662	−	0.409975i
$561$	−20.9855			−0.886010
$562$	−32.9389	−	5.97716i	−1.38945	−	0.252131i
$563$	0.290557	+	0.167753i	0.0122455	+	0.00706994i	0.506110	−	0.862469i	$-0.331083\pi$
$563$	0.290557	+	0.167753i	0.0122455	+	0.00706994i	−0.493865	+	0.869539i	$0.664416\pi$
$564$	−2.08814	+	5.56421i	−0.0879267	+	0.234296i
$565$	7.42108	+	12.8537i	0.312207	+	0.540759i
$566$	−21.6069	−	18.3144i	−0.908208	−	0.769810i
$567$	−2.43222	−	29.6642i	−0.102144	−	1.24578i
$568$	−2.23660	+	3.74372i	−0.0938458	+	0.157083i
$569$	−6.01354	−	10.4158i	−0.252101	−	0.436651i	0.712003	−	0.702176i	$-0.247788\pi$
$569$	−6.01354	−	10.4158i	−0.252101	−	0.436651i	−0.964104	+	0.265525i	$0.914455\pi$
$570$	6.12250	+	17.0855i	0.256443	+	0.715631i
$571$	17.2292	−	29.8419i	0.721020	−	1.24884i	−0.239571	−	0.970879i	$-0.577007\pi$
$571$	17.2292	−	29.8419i	0.721020	−	1.24884i	0.960591	−	0.277965i	$-0.0896599\pi$
$572$	−31.3003	+	25.7377i	−1.30873	+	1.07615i
$573$	−47.7136			−1.99326
$574$	8.98268	+	19.8002i	0.374930	+	0.826443i
$575$			0.511539i			0.0213326i
$576$	−6.38844	+	10.3395i	−0.266185	+	0.430814i
$577$	26.7684	+	15.4547i	1.11438	+	0.643389i	0.939961	−	0.341282i	$-0.110861\pi$
$577$	26.7684	+	15.4547i	1.11438	+	0.643389i	0.174422	+	0.984671i	$0.444194\pi$
$578$	−5.32894	−	14.8709i	−0.221655	−	0.618550i
$579$	−7.93823	+	4.58314i	−0.329901	+	0.190469i
$580$	6.07926	−	1.00967i	0.252427	−	0.0419241i
$581$	−14.9671	−	21.6254i	−0.620939	−	0.897175i
$582$	−11.0376	+	13.0220i	−0.457524	+	0.539779i
$583$	27.7737	−	16.0352i	1.15027	−	0.664109i
$584$	11.1283	+	19.9570i	0.460493	+	0.825825i
$585$	−3.76457	+	6.52042i	−0.155646	+	0.269586i
$586$	6.63422	+	1.20386i	0.274057	+	0.0497309i
$587$		−	11.3376i		−	0.467955i	−0.972242	−	0.233977i	$-0.924826\pi$
$587$		−	11.3376i		−	0.467955i	0.972242	−	0.233977i	$-0.0751742\pi$
$588$	−28.1733	+	9.59343i	−1.16185	+	0.395626i
$589$			27.8504i			1.14756i
$590$	2.57310	−	14.1799i	0.105933	−	0.583775i
$591$	7.09128	−	12.2825i	0.291696	−	0.505233i
$592$	−39.1957	−	7.71856i	−1.61094	−	0.317231i
$593$	26.3586	−	15.2182i	1.08242	−	0.624935i	0.150872	−	0.988553i	$-0.451792\pi$
$593$	26.3586	−	15.2182i	1.08242	−	0.624935i	0.931548	+	0.363618i	$0.118459\pi$
$594$	13.8842	+	11.7684i	0.569675	+	0.482865i
$595$	−3.63551	−	5.25284i	−0.149042	−	0.215345i
$596$	−20.2445	+	3.36228i	−0.829246	+	0.137724i
$597$	17.2644	−	9.96759i	0.706583	−	0.407946i
$598$	−3.37503	+	1.20943i	−0.138015	+	0.0494571i
$599$	11.1298	+	6.42577i	0.454750	+	0.262550i	0.709834	−	0.704369i	$-0.248770\pi$
$599$	11.1298	+	6.42577i	0.454750	+	0.262550i	−0.255084	+	0.966919i	$0.582103\pi$
$600$	6.01214	+	0.0897499i	0.245445	+	0.00366403i
$601$			17.2953i			0.705489i	0.935720	+	0.352745i	$0.114752\pi$
$601$			17.2953i			0.705489i	−0.935720	+	0.352745i	$0.885248\pi$
$602$	−36.4826	+	16.5510i	−1.48692	+	0.674567i
$603$	10.5264			0.428669
$604$	−20.9036	−	25.4214i	−0.850555	−	1.03438i
$605$	−2.85764	+	4.94958i	−0.116180	+	0.201229i
$606$	−41.8249	+	14.9878i	−1.69902	+	0.608836i
$607$	7.03358	+	12.1825i	0.285484	+	0.494473i	0.972726	−	0.231955i	$-0.0745123\pi$
$607$	7.03358	+	12.1825i	0.285484	+	0.494473i	−0.687242	+	0.726428i	$0.741179\pi$
$608$	31.7898	+	12.4746i	1.28925	+	0.505910i
$609$	−1.41621	−	17.2725i	−0.0573877	−	0.699918i
$610$	2.43493	−	2.87268i	0.0985874	−	0.116312i
$611$	3.46370	+	5.99931i	0.140126	+	0.242706i
$612$	−2.57770	+	6.86872i	−0.104197	+	0.277651i
$613$	8.38938	+	4.84361i	0.338844	+	0.195632i	0.659761	−	0.751476i	$-0.270658\pi$
$613$	8.38938	+	4.84361i	0.338844	+	0.195632i	−0.320917	+	0.947107i	$0.603991\pi$
$614$	−3.63771	+	20.0467i	−0.146806	+	0.809019i
$615$	−12.3532			−0.498127
$616$	13.4925	−	27.4592i	0.543629	−	1.10636i
$617$	−36.8175			−1.48222			−0.741108	−	0.671386i	$-0.765699\pi$
$617$	−36.8175			−1.48222			−0.741108	+	0.671386i	$0.765699\pi$
$618$	−5.08476	+	28.0211i	−0.204539	+	1.12717i
$619$	−14.5742	−	8.41442i	−0.585787	−	0.338204i	0.177643	−	0.984095i	$-0.443153\pi$
$619$	−14.5742	−	8.41442i	−0.585787	−	0.338204i	−0.763430	+	0.645891i	$0.776486\pi$
$620$	8.63849	+	3.24186i	0.346930	+	0.130196i
$621$	0.805129	+	1.39452i	0.0323087	+	0.0559603i
$622$	0.0135288	−	0.0159610i	0.000542455	−	0.000639979i
$623$	−4.97750	+	10.5239i	−0.199419	+	0.421633i
$624$	13.6223	+	39.8791i	0.545329	+	1.59644i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−18.5397	+	6.64361i	−0.740994	+	0.265532i
$627$	−26.2345	+	45.4394i	−1.04770	+	1.81468i
$628$	−34.3553	+	28.2497i	−1.37092	+	1.12729i
$629$	−24.1141			−0.961492
$630$	0.554489	−	5.65737i	0.0220914	−	0.225395i
$631$			40.9250i			1.62920i	0.580023	+	0.814600i	$0.303043\pi$
$631$			40.9250i			1.62920i	−0.580023	+	0.814600i	$0.696957\pi$
$632$	−10.4858	−	0.156532i	−0.417101	−	0.00622653i
$633$	−11.1942	−	6.46299i	−0.444930	−	0.256881i
$634$	31.9605	−	11.4529i	1.26932	−	0.454853i
$635$	−6.22865	+	3.59611i	−0.247176	+	0.142707i
$636$	−5.46422	−	32.9004i	−0.216670	−	1.30458i
$637$	−12.2201	+	32.4674i	−0.484178	+	1.28640i
$638$	13.5904	+	11.5194i	0.538050	+	0.456059i
$639$	−2.02858	+	1.17120i	−0.0802496	+	0.0463321i
$640$	7.56970	−	8.40831i	0.299219	−	0.332367i
$641$	−22.3915	+	38.7833i	−0.884413	+	1.53185i	−0.0380272	+	0.999277i	$0.512107\pi$
$641$	−22.3915	+	38.7833i	−0.884413	+	1.53185i	−0.846385	+	0.532571i	$0.821226\pi$
$642$	10.2402	−	56.4319i	0.404150	−	2.22719i
$643$			35.9649i			1.41832i	0.705049	+	0.709159i	$0.250925\pi$
$643$			35.9649i			1.41832i	−0.705049	+	0.709159i	$0.749075\pi$
$644$	1.94327	−	1.88428i	0.0765754	−	0.0742512i
$645$		−	22.7612i		−	0.896221i
$646$	20.2826	+	3.68051i	0.798007	+	0.144808i
$647$	10.7834	−	18.6773i	0.423937	−	0.734281i	−0.572383	−	0.819986i	$-0.693981\pi$
$647$	10.7834	−	18.6773i	0.423937	−	0.734281i	0.996321	+	0.0857054i	$0.0273144\pi$
$648$	27.7903	−	15.4963i	1.09170	−	0.608752i
$649$	36.0811	−	20.8314i	1.41631	−	0.817704i
$650$	4.53172	−	5.34644i	0.177749	−	0.209705i
$651$	11.0942	−	23.4565i	0.434816	−	0.919334i
$652$	−4.25139	−	25.5978i	−0.166497	−	1.00249i
$653$	−26.3715	+	15.2256i	−1.03200	+	0.595824i	−0.917556	−	0.397606i	$-0.869841\pi$
$653$	−26.3715	+	15.2256i	−1.03200	+	0.595824i	−0.114441	+	0.993430i	$0.536508\pi$
$654$	−0.649410	−	1.81224i	−0.0253939	−	0.0708643i
$655$	6.50864	+	3.75777i	0.254314	+	0.146828i
$656$	−15.2922	+	17.5048i	−0.597058	+	0.683449i
$657$			12.2735i			0.478833i
$658$	−4.25278	−	3.04444i	−0.165791	−	0.118685i
$659$	−4.95909			−0.193179			−0.0965894	−	0.995324i	$-0.530793\pi$
$659$	−4.95909			−0.193179			−0.0965894	+	0.995324i	$0.530793\pi$
$660$	11.0404	+	13.4265i	0.429746	+	0.522627i
$661$	8.90153	−	15.4179i	0.346230	−	0.599687i	−0.639347	−	0.768918i	$-0.720795\pi$
$661$	8.90153	−	15.4179i	0.346230	−	0.599687i	0.985576	+	0.169231i	$0.0541285\pi$
$662$	−0.747292	−	2.08539i	−0.0290443	−	0.0810511i
$663$	12.7189	+	22.0299i	0.493963	+	0.855569i
$664$	14.4196	−	24.1362i	0.559591	−	0.936668i
$665$	−15.9187	+	1.30520i	−0.617299	+	0.0506136i
$666$	−16.3687	−	13.8743i	−0.634274	−	0.537620i
$667$	0.788093	+	1.36502i	0.0305151	+	0.0528537i
$668$	22.3287	+	8.37953i	0.863922	+	0.324214i
$669$	27.8486	+	16.0784i	1.07669	+	0.621626i
$670$	−9.64126	−	1.74952i	−0.372474	−	0.0675899i
$671$	10.8867			0.420278
$672$	−21.8052	−	23.1699i	−0.841152	−	0.893799i
$673$	20.2860			0.781968			0.390984	−	0.920397i	$-0.372135\pi$
$673$	20.2860			0.781968			0.390984	+	0.920397i	$0.372135\pi$
$674$	0.0824483	+	0.0149612i	0.00317579	+	0.000576285i
$675$	−2.72614	−	1.57394i	−0.104929	−	0.0605808i
$676$	21.6467	+	8.12361i	0.832567	+	0.312447i
$677$	−12.8287	−	22.2199i	−0.493046	−	0.853980i	0.506922	−	0.861992i	$-0.330783\pi$
$677$	−12.8287	−	22.2199i	−0.493046	−	0.853980i	−0.999968	+	0.00801166i	$0.997450\pi$
$678$	34.0390	+	28.8519i	1.30726	+	1.10805i
$679$	−8.54936	−	12.3527i	−0.328094	−	0.474053i
$680$	3.50254	−	5.86271i	0.134316	−	0.224825i
$681$	24.1739	+	41.8705i	0.926347	+	1.60448i
$682$	8.99828	+	25.1106i	0.344562	+	0.961535i
$683$	11.8802	−	20.5772i	0.454585	−	0.787365i	−0.544079	−	0.839034i	$-0.683121\pi$
$683$	11.8802	−	20.5772i	0.454585	−	0.787365i	0.998664	+	0.0516694i	$0.0164542\pi$
$684$	11.6502	+	14.1682i	0.445457	+	0.541733i
$685$	−3.41935			−0.130647
$686$	−1.72526	−	26.1347i	−0.0658706	−	0.997828i
$687$			5.77382i			0.220285i
$688$	−32.2534	−	28.1764i	−1.22965	−	1.07422i
$689$	−33.6663	−	19.4372i	−1.28258	−	0.740500i
$690$	0.518793	+	1.44775i	0.0197501	+	0.0551148i
$691$	−8.25902	+	4.76835i	−0.314188	+	0.181396i	−0.648799	−	0.760960i	$-0.724728\pi$
$691$	−8.25902	+	4.76835i	−0.314188	+	0.181396i	0.334611	+	0.942356i	$0.391395\pi$
$692$	3.64332	+	21.9367i	0.138498	+	0.833906i
$693$	13.5129	−	9.35232i	0.513311	−	0.355265i
$694$	−0.0844602	+	0.0996446i	−0.00320606	+	0.00378246i
$695$	9.56685	−	5.52342i	0.362891	−	0.209515i
$696$	16.1814	−	9.02302i	0.613355	−	0.342017i
$697$	−7.01529	+	12.1508i	−0.265723	+	0.460246i
$698$	−21.4846	−	3.89863i	−0.813202	−	0.147565i
$699$		−	36.3313i		−	1.37418i
$700$	−1.44813	+	5.08949i	−0.0547343	+	0.192365i
$701$			19.1213i			0.722201i	0.932527	+	0.361101i	$0.117599\pi$
$701$			19.1213i			0.722201i	−0.932527	+	0.361101i	$0.882401\pi$
$702$	3.93913	−	21.7078i	0.148673	−	0.819306i
$703$	−30.1455	+	52.2136i	−1.13696	+	1.96927i
$704$	32.6929	+	0.976303i	1.23216	+	0.0367958i
$705$	2.57345	−	1.48578i	0.0969217	−	0.0559578i
$706$	−10.6972	−	9.06711i	−0.402595	−	0.341245i
$707$	−3.19511	−	38.9686i	−0.120165	−	1.46556i
$708$	−7.09861	−	42.7411i	−0.266782	−	1.60631i
$709$	−42.0444	+	24.2743i	−1.57901	+	0.911642i	−0.584012	+	0.811745i	$0.698518\pi$
$709$	−42.0444	+	24.2743i	−1.57901	+	0.911642i	−0.994998	+	0.0998972i	$0.968149\pi$
$710$	2.05266	−	0.735561i	0.0770349	−	0.0276051i
$711$	−4.87821	−	2.81644i	−0.182947	−	0.105625i
$712$	−12.4441	−	0.185767i	−0.466362	−	0.00696191i
$713$			2.35992i			0.0883798i
$714$	−15.6165	−	11.1794i	−0.584433	−	0.418378i
$715$	20.2617			0.757743
$716$	13.2124	−	10.8643i	0.493772	−	0.406020i
$717$	−15.7327	+	27.2498i	−0.587547	+	1.01766i
$718$	−13.9043	+	4.98254i	−0.518903	+	0.185947i
$719$	14.8570	+	25.7331i	0.554073	+	0.959682i	0.997975	+	0.0636067i	$0.0202603\pi$
$719$	14.8570	+	25.7331i	0.554073	+	0.959682i	−0.443903	+	0.896075i	$0.646406\pi$
$720$	5.75071	−	1.96439i	0.214316	−	0.0732084i
$721$	−22.6560	−	10.7156i	−0.843754	−	0.399069i
$722$	15.9510	−	18.8187i	0.593636	−	0.700361i
$723$	18.9469	+	32.8169i	0.704641	+	1.22047i
$724$	−1.53911	−	0.577598i	−0.0572005	−	0.0214663i
$725$	−2.66845	−	1.54063i	−0.0991039	−	0.0572177i
$726$	−3.06786	+	16.9064i	−0.113859	+	0.627454i
$727$	−3.32731			−0.123403			−0.0617015	−	0.998095i	$-0.519653\pi$
$727$	−3.32731			−0.123403			−0.0617015	+	0.998095i	$0.519653\pi$
$728$	−37.0033	+	2.47855i	−1.37143	+	0.0918611i
$729$	−2.98481			−0.110548
$730$	2.03988	−	11.2414i	0.0754995	−	0.416062i
$731$	−22.3884	−	12.9259i	−0.828065	−	0.478083i
$732$	3.97786	−	10.5997i	0.147026	−	0.391775i
$733$	−16.6332	−	28.8096i	−0.614362	−	1.06411i	−0.990496	−	0.137540i	$-0.956080\pi$
$733$	−16.6332	−	28.8096i	−0.614362	−	1.06411i	0.376135	−	0.926565i	$-0.377253\pi$
$734$	26.2819	−	31.0069i	0.970084	−	1.14449i
$735$	13.9271	+	5.24191i	0.513710	+	0.193351i
$736$	2.69373	+	1.05704i	0.0992921	+	0.0389630i
$737$	−14.1638	−	24.5325i	−0.521731	−	0.903665i
$738$	−11.7531	+	4.21168i	−0.432638	+	0.155034i
$739$	−8.20295	+	14.2079i	−0.301750	+	0.522647i	−0.976533	−	0.215370i	$-0.930904\pi$
$739$	−8.20295	+	14.2079i	−0.301750	+	0.522647i	0.674782	+	0.738017i	$0.264238\pi$
$740$	12.6863	+	15.4282i	0.466358	+	0.567151i
$741$	63.6009			2.33644
$742$	29.2102	+	2.86294i	1.07234	+	0.105102i
$743$		−	28.3857i		−	1.04137i	−0.853749	−	0.520685i	$-0.825677\pi$
$743$		−	28.3857i		−	1.04137i	0.853749	−	0.520685i	$-0.174323\pi$
$744$	27.7363	+	0.414051i	1.01686	+	0.0151798i
$745$	8.88620	+	5.13045i	0.325565	+	0.187965i
$746$	13.7389	−	4.92329i	0.503018	−	0.180254i
$747$	13.0785	−	7.55090i	0.478519	−	0.276273i
$748$	19.4764	−	3.23472i	0.712127	−	0.118273i
$749$	45.6272	+	21.5802i	1.66718	+	0.788525i
$750$	−2.29340	−	1.94392i	−0.0837430	−	0.0709818i
$751$	−27.1307	+	15.6639i	−0.990014	+	0.571585i	−0.905278	−	0.424819i	$-0.860338\pi$
$751$	−27.1307	+	15.6639i	−0.990014	+	0.571585i	−0.0847355	+	0.996403i	$0.527005\pi$
$752$	1.08031	−	5.48594i	0.0393948	−	0.200052i
$753$	27.6063	−	47.8155i	1.00603	−	1.74249i
$754$	3.85578	−	21.2484i	0.140419	−	0.773823i
$755$			16.4561i			0.598898i
$756$	4.06272	+	16.1539i	0.147760	+	0.587512i
$757$		−	12.5842i		−	0.457380i	−0.973499	−	0.228690i	$-0.926556\pi$
$757$		−	12.5842i		−	0.457380i	0.973499	−	0.228690i	$-0.0734442\pi$
$758$	−27.9957	−	5.08015i	−1.01685	−	0.184519i
$759$	−2.22299	+	3.85034i	−0.0806895	+	0.139758i
$760$	−8.31577	−	14.9131i	−0.301645	−	0.540954i
$761$	10.7941	−	6.23196i	0.391285	−	0.225908i	−0.291432	−	0.956592i	$-0.594132\pi$
$761$	10.7941	−	6.23196i	0.391285	−	0.225908i	0.682717	+	0.730683i	$0.260798\pi$
$762$	−13.9811	+	16.4946i	−0.506481	+	0.597537i
$763$	1.68848	−	0.138442i	0.0611272	−	0.00501194i
$764$	44.2823	−	7.35458i	1.60208	−	0.266079i
$765$	3.17678	−	1.83412i	0.114857	−	0.0663127i
$766$	15.1882	+	42.3842i	0.548771	+	1.53140i
$767$	−43.7361	−	25.2511i	−1.57922	−	0.911763i
$768$	12.8961	−	31.4741i	0.465347	−	1.13572i
$769$		−	31.8352i		−	1.14801i	−0.818853	−	0.574003i	$-0.805390\pi$
$769$		−	31.8352i		−	1.14801i	0.818853	−	0.574003i	$-0.194610\pi$
$770$	−13.9310	+	6.32001i	−0.502037	+	0.227757i
$771$	−20.7172			−0.746111
$772$	6.66092	−	5.47715i	0.239732	−	0.197127i
$773$	−3.58420	+	6.20801i	−0.128915	+	0.223287i	−0.923256	−	0.384184i	$-0.874483\pi$
$773$	−3.58420	+	6.20801i	−0.128915	+	0.223287i	0.794342	+	0.607471i	$0.207816\pi$
$774$	−7.76019	−	21.6556i	−0.278934	−	0.778394i
$775$	−2.30669	−	3.99530i	−0.0828588	−	0.143516i
$776$	8.23666	−	13.7869i	0.295679	−	0.494920i
$777$	46.1888	−	31.9675i	1.65701	−	1.14683i
$778$	−14.8605	−	12.5959i	−0.532774	−	0.451586i
$779$	17.5399	+	30.3800i	0.628433	+	1.08848i
$780$	7.40331	−	19.7274i	0.265081	−	0.706353i
$781$	5.45913	+	3.15183i	0.195343	+	0.112781i
$782$	1.71865	+	0.311870i	0.0614590	+	0.0111525i
$783$	−9.69943			−0.346629
$784$	24.6686	−	13.2462i	0.881021	−	0.473078i
$785$	22.2392			0.793752
$786$	22.2317	+	4.03421i	0.792978	+	0.143895i
$787$	5.41950	+	3.12895i	0.193184	+	0.111535i	0.593472	−	0.804854i	$-0.297757\pi$
$787$	5.41950	+	3.12895i	0.193184	+	0.111535i	−0.400288	+	0.916389i	$0.631090\pi$
$788$	−4.68810	+	12.4922i	−0.167007	+	0.445018i
$789$	6.29061	+	10.8957i	0.223952	+	0.387896i
$790$	3.99990	+	3.39038i	0.142310	+	0.120624i
$791$	−32.2895	+	22.3477i	−1.14808	+	0.794593i
$792$	15.0817	+	9.01025i	0.535907	+	0.320165i
$793$	−6.59826	−	11.4285i	−0.234311	−	0.405839i
$794$	−14.5987	−	40.7391i	−0.518087	−	1.44578i
$795$	−8.33776	+	14.4414i	−0.295710	+	0.512185i
$796$	−14.4864	+	11.9119i	−0.513458	+	0.422207i
$797$	−22.8115			−0.808024			−0.404012	−	0.914754i	$-0.632385\pi$
$797$	−22.8115			−0.808024			−0.404012	+	0.914754i	$0.632385\pi$
$798$	−43.7290	+	19.8384i	−1.54799	+	0.702271i
$799$		−	3.37507i		−	0.119401i
$800$	−5.59363	+	0.843418i	−0.197765	+	0.0298193i
$801$	−5.78928	−	3.34244i	−0.204554	−	0.118099i
$802$	9.18042	+	25.6189i	0.324172	+	0.904635i
$803$	28.6041	−	16.5146i	1.00942	−	0.582786i
$804$	−29.0608	+	4.82654i	−1.02490	+	0.170219i
$805$	−1.34888	+	0.110597i	−0.0475417	+	0.00389804i
$806$	20.9065	−	24.6652i	0.736401	−	0.868793i
$807$	−38.2618	+	22.0905i	−1.34688	+	0.777621i
$808$	36.5069	−	20.3568i	1.28431	−	0.716151i
$809$	−21.2796	+	36.8573i	−0.748150	+	1.29583i	0.200558	+	0.979682i	$0.435724\pi$
$809$	−21.2796	+	36.8573i	−0.748150	+	1.29583i	−0.948708	+	0.316152i	$0.897609\pi$
$810$	−15.6537	−	2.84056i	−0.550016	−	0.0998070i
$811$			18.7275i			0.657613i	0.944397	+	0.328806i	$0.106646\pi$
$811$			18.7275i			0.657613i	−0.944397	+	0.328806i	$0.893354\pi$
$812$	3.97676	+	15.8121i	0.139557	+	0.554897i
$813$			24.3671i			0.854593i
$814$	−10.3101	+	56.8169i	−0.361369	+	1.99143i
$815$	−6.48712	+	11.2360i	−0.227234	+	0.393581i
$816$	3.96697	−	20.1447i	0.138872	−	0.705207i
$817$	−55.9764	+	32.3180i	−1.95837	+	1.13066i
$818$	−5.43408	−	4.60600i	−0.189998	−	0.161045i
$819$	−18.0076	−	8.51705i	−0.629237	−	0.297610i
$820$	11.4648	−	1.90412i	0.400368	−	0.0664947i
$821$	−23.7690	+	13.7231i	−0.829545	+	0.478938i	−0.853697	−	0.520770i	$-0.825645\pi$
$821$	−23.7690	+	13.7231i	−0.829545	+	0.478938i	0.0241517	+	0.999708i	$0.492312\pi$
$822$	−9.67738	+	3.46785i	−0.337537	+	0.120955i
$823$	30.6664	+	17.7052i	1.06896	+	0.617166i	0.927898	−	0.372834i	$-0.121614\pi$
$823$	30.6664	+	17.7052i	1.06896	+	0.617166i	0.141065	+	0.990000i	$0.454947\pi$
$824$	0.399920	−	26.7897i	0.0139319	−	0.933265i
$825$		−	8.69140i		−	0.302596i
$826$	37.9472	+	3.71927i	1.32035	+	0.129410i
$827$	−11.1678			−0.388341			−0.194170	−	0.980968i	$-0.562202\pi$
$827$	−11.1678			−0.388341			−0.194170	+	0.980968i	$0.562202\pi$
$828$	0.987188	+	1.20055i	0.0343071	+	0.0417219i
$829$	14.7123	−	25.4824i	0.510979	−	0.885041i	−0.488940	−	0.872317i	$-0.662616\pi$
$829$	14.7123	−	25.4824i	0.510979	−	0.885041i	0.999919	−	0.0127241i	$-0.00405030\pi$
$830$	−13.2337	+	4.74225i	−0.459350	+	0.164606i
$831$	−34.9792	−	60.5858i	−1.21342	−	2.10170i
$832$	−18.7897	−	34.9115i	−0.651415	−	1.21034i
$833$	13.0652	−	10.7222i	0.452682	−	0.371502i
$834$	21.4741	−	25.3348i	0.743589	−	0.877273i
$835$	−5.96231	−	10.3270i	−0.206334	−	0.357381i
$836$	17.3438	−	46.2155i	0.599848	−	1.59840i
$837$	−12.5767	−	7.26116i	−0.434715	−	0.250983i
$838$	3.96164	−	21.8318i	0.136853	−	0.754167i
$839$	−17.3994			−0.600694			−0.300347	−	0.953830i	$-0.597103\pi$
$839$	−17.3994			−0.600694			−0.300347	+	0.953830i	$0.597103\pi$
$840$	1.06319	+	15.8728i	0.0366836	+	0.547665i
$841$	19.5058			0.672614
$842$	−4.38059	+	24.1406i	−0.150965	+	0.831939i
$843$	43.5806	+	25.1613i	1.50100	+	0.866600i
$844$	11.3854	+	4.27273i	0.391902	+	0.147074i
$845$	−5.78022	−	10.0116i	−0.198845	−	0.344410i
$846$	1.94189	−	2.29100i	0.0667635	−	0.0787663i
$847$	−13.6694	−	6.46520i	−0.469686	−	0.222147i
$848$	10.1425	+	29.6921i	0.348296	+	1.01963i
$849$	21.2887	+	36.8731i	0.730627	+	1.26548i
$850$	−3.21449	+	1.15190i	−0.110256	+	0.0395097i
$851$	−2.55440	+	4.42435i	−0.0875637	+	0.151665i
$852$	5.06340	−	4.16354i	0.173469	−	0.142641i
$853$	16.9463			0.580229			0.290115	−	0.956992i	$-0.406307\pi$
$853$	16.9463			0.580229			0.290115	+	0.956992i	$0.406307\pi$
$854$	8.10143	+	5.79958i	0.277225	+	0.198458i
$855$		−	9.17148i		−	0.313658i
$856$	−0.805403	+	53.9521i	−0.0275281	+	1.84405i
$857$	−15.3141	−	8.84161i	−0.523120	−	0.302024i	0.215090	−	0.976594i	$-0.430995\pi$
$857$	−15.3141	−	8.84161i	−0.523120	−	0.302024i	−0.738210	+	0.674571i	$0.764329\pi$
$858$	57.3441	−	20.5490i	1.95770	−	0.701532i
$859$	4.85975	−	2.80578i	0.165813	−	0.0957319i	−0.414797	−	0.909914i	$-0.636148\pi$
$859$	4.85975	−	2.80578i	0.165813	−	0.0957319i	0.580610	+	0.814182i	$0.302814\pi$
$860$	3.50841	+	21.1244i	0.119636	+	0.720334i
$861$	−2.67081	−	32.5741i	−0.0910210	−	1.11012i
$862$	−8.41758	−	7.13486i	−0.286704	−	0.243014i
$863$	−25.4111	+	14.6711i	−0.865003	+	0.499410i	−0.865685	−	0.500590i	$-0.833116\pi$
$863$	−25.4111	+	14.6711i	−0.865003	+	0.499410i	0.000681370		1.00000i	$0.499783\pi$
$864$	−13.9215	+	11.1033i	−0.473619	+	0.377741i
$865$	5.55929	−	9.62897i	0.189021	−	0.327395i
$866$	−2.21294	+	12.1950i	−0.0751987	+	0.414405i
$867$			23.7460i			0.806456i
$868$	−6.68079	+	23.4798i	−0.226761	+	0.796955i
$869$			15.1586i			0.514221i
$870$	−9.11469	−	1.65397i	−0.309017	−	0.0560748i
$871$	−17.1689	+	29.7374i	−0.581745	+	1.00761i
$872$	0.882048	+	1.58182i	0.0298699	+	0.0535672i
$873$	7.47060	−	4.31315i	0.252841	−	0.145978i
$874$	2.82381	−	3.33148i	0.0955169	−	0.112689i
$875$	2.17552	−	1.50569i	0.0735461	−	0.0509016i
$876$	−5.62758	−	33.8840i	−0.190138	−	1.14483i
$877$	37.6795	−	21.7543i	1.27235	−	0.734589i	0.296917	−	0.954903i	$-0.404042\pi$
$877$	37.6795	−	21.7543i	1.27235	−	0.734589i	0.975429	+	0.220314i	$0.0707082\pi$
$878$	1.20834	+	3.37201i	0.0407796	+	0.113800i
$879$	−8.77756	−	5.06772i	−0.296060	−	0.170930i
$880$	−12.3160	−	10.7592i	−0.415172	−	0.362693i
$881$			21.3654i			0.719817i	0.932988	+	0.359909i	$0.117192\pi$
$881$			21.3654i			0.719817i	−0.932988	+	0.359909i	$0.882808\pi$
$882$	15.0378	+	0.238981i	0.506350	+	0.00804690i
$883$	26.9203			0.905939			0.452970	−	0.891526i	$-0.350365\pi$
$883$	26.9203			0.905939			0.452970	+	0.891526i	$0.350365\pi$
$884$	−15.2000	−	18.4851i	−0.511230	−	0.621722i
$885$	−10.8317	+	18.7610i	−0.364102	+	0.630643i
$886$	−14.1172	−	39.3954i	−0.474276	−	1.32352i
$887$	−1.58078	−	2.73799i	−0.0530774	−	0.0919327i	0.838266	−	0.545262i	$-0.183570\pi$
$887$	−1.58078	−	2.73799i	−0.0530774	−	0.0919327i	−0.891343	+	0.453329i	$0.850236\pi$
$888$	51.5515	+	30.7983i	1.72995	+	1.03352i
$889$	−10.8293	−	15.6468i	−0.363202	−	0.524778i
$890$	4.74694	+	4.02357i	0.159118	+	0.134870i
$891$	−22.9967	−	39.8314i	−0.770418	−	1.33440i
$892$	−28.3242	−	10.6295i	−0.948365	−	0.355903i
$893$	−7.30795	−	4.21925i	−0.244551	−	0.141192i
$894$	30.3527	+	5.50787i	1.01515	+	0.184211i
$895$	−8.55281			−0.285889
$896$	23.8085	+	18.1427i	0.795386	+	0.606103i
$897$	5.38926			0.179942
$898$	−17.2616	−	3.13232i	−0.576027	−	0.104527i
$899$	−12.3106	−	7.10753i	−0.410581	−	0.237049i
$900$	−2.84476	−	1.06758i	−0.0948253	−	0.0355861i
$901$	9.46993	+	16.4024i	0.315489	+	0.546443i
$902$	25.6300	+	21.7243i	0.853385	+	0.723342i
$903$	60.0190	−	4.92108i	1.99731	−	0.163763i
$904$	−36.0384	−	21.5303i	−1.19862	−	0.716088i
$905$	0.410980	+	0.711839i	0.0136614	+	0.0236623i
$906$	16.6895	+	46.5737i	0.554470	+	1.54731i
$907$	−11.6003	+	20.0923i	−0.385182	+	0.667154i	−0.991794	−	0.127843i	$-0.959195\pi$
$907$	−11.6003	+	20.0923i	−0.385182	+	0.667154i	0.606613	+	0.794998i	$0.292528\pi$
$908$	−28.8894	−	35.1333i	−0.958729	−	1.16594i
$909$	22.4516			0.744673
$910$	15.0778	+	10.7938i	0.499825	+	0.357810i
$911$			16.0632i			0.532197i	0.963946	+	0.266098i	$0.0857346\pi$
$911$			16.0632i			0.532197i	−0.963946	+	0.266098i	$0.914265\pi$
$912$	−38.6597	−	33.7729i	−1.28015	−	1.11833i
$913$	−35.1957	−	20.3202i	−1.16481	−	0.672501i
$914$	18.3177	+	51.1175i	0.605896	+	1.69082i
$915$	−4.90236	+	2.83038i	−0.162067	+	0.0935693i
$916$	−0.889978	−	5.35861i	−0.0294057	−	0.177053i
$917$	−8.50167	+	17.9751i	−0.280750	+	0.593590i
$918$	−6.95012	+	8.19962i	−0.229388	+	0.270628i
$919$	7.06952	−	4.08159i	0.233202	−	0.134639i	−0.378846	−	0.925460i	$-0.623679\pi$
$919$	7.06952	−	4.08159i	0.233202	−	0.134639i	0.612048	+	0.790820i	$0.290346\pi$
$920$	−0.704641	−	1.26367i	−0.0232313	−	0.0416619i
$921$	15.3132	−	26.5232i	0.504587	−	0.873970i
$922$	−26.9614	−	4.89246i	−0.887925	−	0.161125i
$923$		−	7.64106i		−	0.251509i
$924$	−33.0175	+	32.0153i	−1.08619	+	1.05323i
$925$		−	9.98713i		−	0.328375i
$926$	8.71051	−	48.0019i	0.286245	−	1.57744i
$927$	7.19563	−	12.4632i	0.236335	−	0.409345i
$928$	−13.6269	+	10.8683i	−0.447326	+	0.356771i
$929$	3.96274	−	2.28789i	0.130013	−	0.0750633i	−0.433583	−	0.901114i	$-0.642751\pi$
$929$	3.96274	−	2.28789i	0.130013	−	0.0750633i	0.563596	+	0.826051i	$0.309417\pi$
$930$	−10.5803	−	8.96803i	−0.346942	−	0.294073i
$931$	−6.88339	−	41.6938i	−0.225594	−	1.36646i
$932$	5.60012	+	33.7186i	0.183438	+	1.10449i
$933$	−0.0272382	+	0.0157260i	−0.000891737	+	0.000514845i
$934$	28.2948	−	10.1393i	0.925833	−	0.331768i
$935$	−8.54905	−	4.93580i	−0.279584	−	0.161418i
$936$	0.317868	−	21.2932i	0.0103898	−	0.695991i
$937$			15.7959i			0.516028i	0.966141	+	0.258014i	$0.0830681\pi$
$937$			15.7959i			0.516028i	−0.966141	+	0.258014i	$0.916932\pi$
$938$	2.52883	−	25.8013i	0.0825692	−	0.842443i
$939$	29.6042			0.966097
$940$	−2.15937	+	1.77561i	−0.0704308	+	0.0579139i
$941$	20.9789	−	36.3366i	0.683894	−	1.18454i	−0.289889	−	0.957060i	$-0.593619\pi$
$941$	20.9789	−	36.3366i	0.683894	−	1.18454i	0.973783	−	0.227479i	$-0.0730482\pi$
$942$	62.9410	−	22.5546i	2.05073	−	0.734869i
$943$	1.48626	+	2.57427i	0.0483991	+	0.0838298i
$944$	13.1763	+	38.5733i	0.428851	+	1.25545i
$945$	3.56091	−	7.52885i	0.115836	−	0.244913i
$946$	−40.0280	+	47.2243i	−1.30142	+	1.53539i
$947$	26.3811	+	45.6935i	0.857272	+	1.48484i	0.874521	+	0.484987i	$0.161176\pi$
$947$	26.3811	+	45.6935i	0.857272	+	1.48484i	−0.0172491	+	0.999851i	$0.505491\pi$
$948$	14.7589	+	5.53874i	0.479347	+	0.179890i
$949$	−34.6728	−	20.0183i	−1.12553	−	0.649823i
$950$	−1.52433	+	8.40025i	−0.0494557	+	0.272540i
$951$	−51.0347			−1.65491
$952$	16.2167	+	7.96832i	0.525585	+	0.258255i
$953$	13.4387			0.435323			0.217661	−	0.976024i	$-0.430157\pi$
$953$	13.4387			0.435323			0.217661	+	0.976024i	$0.430157\pi$
$954$	−3.00912	+	16.5826i	−0.0974237	+	0.536882i
$955$	−19.4375	−	11.2222i	−0.628982	−	0.363143i
$956$	10.4010	−	27.7152i	0.336392	−	0.896373i
$957$	−13.3903	−	23.1926i	−0.432846	−	0.749710i
$958$	5.48296	−	6.46870i	0.177146	−	0.208994i
$959$	−0.739280	−	9.01650i	−0.0238726	−	0.291158i
$960$	−14.9756	+	8.05998i	−0.483335	+	0.260135i
$961$	4.85836	+	8.41493i	0.156721	+	0.271449i
$962$	65.8931	−	23.6125i	2.12448	−	0.761297i
$963$	−14.4914	+	25.0998i	−0.466977	+	0.808829i
$964$	−22.6427	−	27.5365i	−0.729273	−	0.886890i
$965$	−4.31181			−0.138802
$966$	−3.70540	+	1.68102i	−0.119219	+	0.0540858i
$967$			0.422493i			0.0135865i	0.999977	+	0.00679323i	$0.00216237\pi$
$967$			0.422493i			0.0135865i	−0.999977	+	0.00679323i	$0.997838\pi$
$968$	0.241290	−	16.1635i	0.00775535	−	0.519513i
$969$	−26.8353	−	15.4934i	−0.862074	−	0.497718i
$970$	−7.55926	+	2.70883i	−0.242713	+	0.0869752i
$971$	−21.7350	+	12.5487i	−0.697511	+	0.402708i	−0.806420	−	0.591344i	$-0.798598\pi$
$971$	−21.7350	+	12.5487i	−0.697511	+	0.402708i	0.108909	+	0.994052i	$0.465264\pi$
$972$	−28.5517	+	4.74198i	−0.915797	+	0.152099i
$973$	16.6331	+	24.0327i	0.533234	+	0.770452i
$974$	−10.1936	−	8.64025i	−0.326625	−	0.276852i
$975$	−9.12392	+	5.26770i	−0.292199	+	0.168701i
$976$	−2.05796	+	10.4506i	−0.0658737	+	0.334514i
$977$	16.5269	−	28.6254i	0.528743	−	0.915809i	−0.470696	−	0.882296i	$-0.655997\pi$
$977$	16.5269	−	28.6254i	0.528743	−	0.915809i	0.999438	−	0.0335135i	$-0.0106697\pi$
$978$	−6.96434	+	38.3791i	−0.222695	+	1.22723i
$979$			17.9897i			0.574953i
$980$	−13.7336	−	2.71821i	−0.438703	−	0.0868302i
$981$			0.972813i			0.0310595i
$982$	34.3147	+	6.22680i	1.09502	+	0.198705i
$983$	16.6386	−	28.8188i	0.530688	−	0.919178i	−0.468671	−	0.883373i	$-0.655267\pi$
$983$	16.6386	−	28.8188i	0.530688	−	0.919178i	0.999359	−	0.0358054i	$-0.0113997\pi$
$984$	30.5163	−	17.0164i	0.972825	−	0.542463i
$985$	5.77767	−	3.33574i	0.184092	−	0.106285i
$986$	−6.80306	+	8.02613i	−0.216654	+	0.255604i
$987$	4.47426	+	6.46470i	0.142417	+	0.205774i
$988$	−59.0272	+	9.80346i	−1.87790	+	0.311890i
$989$	−4.74320	+	2.73849i	−0.150825	+	0.0870788i
$990$	−2.96324	−	8.26923i	−0.0941780	−	0.262813i
$991$	27.1291	+	15.6630i	0.861785	+	0.497552i	0.864610	−	0.502444i	$-0.167566\pi$
$991$	27.1291	+	15.6630i	0.861785	+	0.497552i	−0.00282457	+	0.999996i	$0.500899\pi$
$992$	−25.8055	+	3.89101i	−0.819326	+	0.123540i
$993$			3.32996i			0.105673i
$994$	2.38340	+	5.25363i	0.0755968	+	0.166635i
$995$	9.37750			0.297287
$996$	−32.6444	+	26.8429i	−1.03438	+	0.850549i
$997$	−0.280864	+	0.486471i	−0.00889505	+	0.0154067i	−0.870439	−	0.492277i	$-0.836165\pi$
$997$	−0.280864	+	0.486471i	−0.00889505	+	0.0154067i	0.861544	+	0.507684i	$0.169498\pi$
$998$	−10.6577	−	29.7414i	−0.337364	−	0.941449i
$999$	−15.7191	−	27.2263i	−0.497330	−	0.861401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.f.171.12	yes	24
4.3	odd	2		1120.2.bz.e.591.11		24
7.5	odd	6		280.2.bj.e.131.5	✓	24
8.3	odd	2		280.2.bj.e.171.5	yes	24
8.5	even	2		1120.2.bz.f.591.11		24
28.19	even	6		1120.2.bz.f.271.11		24
56.5	odd	6		1120.2.bz.e.271.11		24
56.19	even	6	inner	280.2.bj.f.131.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.5	✓	24	7.5	odd	6
280.2.bj.e.171.5	yes	24	8.3	odd	2
280.2.bj.f.131.12	yes	24	56.19	even	6	inner
280.2.bj.f.171.12	yes	24	1.1	even	1	trivial
1120.2.bz.e.271.11		24	56.5	odd	6
1120.2.bz.e.591.11		24	4.3	odd	2
1120.2.bz.f.271.11		24	28.19	even	6
1120.2.bz.f.591.11		24	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39149 + 0.252502i) q^{2} +(-1.84104 - 1.06293i) q^{3} +(1.87249 + 0.702708i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.29340 - 1.94392i) q^{6} +(2.17552 - 1.50569i) q^{7} +(2.42811 + 1.45062i) q^{8} +(0.759621 + 1.31570i) q^{9} +O(q^{10})\)	\(q+(1.39149 + 0.252502i) q^{2} +(-1.84104 - 1.06293i) q^{3} +(1.87249 + 0.702708i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.29340 - 1.94392i) q^{6} +(2.17552 - 1.50569i) q^{7} +(2.42811 + 1.45062i) q^{8} +(0.759621 + 1.31570i) q^{9} +(-0.477071 - 1.33132i) q^{10} +(2.04422 - 3.54069i) q^{11} +(-2.70039 - 3.28403i) q^{12} -4.95585 q^{13} +(3.40741 - 1.54583i) q^{14} +2.12585i q^{15} +(3.01240 + 2.63162i) q^{16} +(2.09103 + 1.20726i) q^{17} +(0.724787 + 2.02259i) q^{18} +(5.22809 - 3.01844i) q^{19} +(-0.327679 - 1.97297i) q^{20} +(-5.60566 + 0.459619i) q^{21} +(3.73854 - 4.41066i) q^{22} +(0.443005 - 0.255769i) q^{23} +(-2.92835 - 5.25154i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.89601 - 1.25136i) q^{26} +3.14787i q^{27} +(5.13169 - 1.29062i) q^{28} +3.08127i q^{29} +(-0.536782 + 2.95810i) q^{30} +(-2.30669 + 3.99530i) q^{31} +(3.52723 + 4.42251i) q^{32} +(-7.52697 + 4.34570i) q^{33} +(2.60481 + 2.20788i) q^{34} +(-2.39173 - 1.13121i) q^{35} +(0.497824 + 2.99742i) q^{36} +(-8.64910 + 4.99356i) q^{37} +(8.03700 - 2.88002i) q^{38} +(9.12392 + 5.26770i) q^{39} +(0.0422184 - 2.82811i) q^{40} +5.81092i q^{41} +(-7.91627 - 0.775887i) q^{42} -10.7069 q^{43} +(6.31584 - 5.19340i) q^{44} +(0.759621 - 1.31570i) q^{45} +(0.681020 - 0.244040i) q^{46} +(-0.698912 - 1.21055i) q^{47} +(-2.74874 - 8.04688i) q^{48} +(2.46579 - 6.55133i) q^{49} +(-0.914418 + 1.07881i) q^{50} +(-2.56645 - 4.44522i) q^{51} +(-9.27975 - 3.48252i) q^{52} +(6.79325 + 3.92208i) q^{53} +(-0.794845 + 4.38023i) q^{54} -4.08843 q^{55} +(7.46658 - 0.500126i) q^{56} -12.8335 q^{57} +(-0.778027 + 4.28755i) q^{58} +(8.82516 + 5.09521i) q^{59} +(-1.49385 + 3.98062i) q^{60} +(1.33141 + 2.30607i) q^{61} +(-4.21856 + 4.97698i) q^{62} +(3.63361 + 1.71859i) q^{63} +(3.79141 + 7.04451i) q^{64} +(2.47792 + 4.29189i) q^{65} +(-11.5710 + 4.14642i) q^{66} +(3.46437 - 6.00046i) q^{67} +(3.06708 + 3.72996i) q^{68} -1.08745 q^{69} +(-3.04243 - 2.17799i) q^{70} +1.54183i q^{71} +(-0.0641399 + 4.29659i) q^{72} +(6.99634 + 4.03934i) q^{73} +(-13.2960 + 4.76457i) q^{74} +(1.84104 - 1.06293i) q^{75} +(11.9106 - 1.97816i) q^{76} +(-0.883939 - 10.7808i) q^{77} +(11.3657 + 9.63375i) q^{78} +(-3.21095 + 1.85384i) q^{79} +(0.772851 - 3.92463i) q^{80} +(5.62481 - 9.74247i) q^{81} +(-1.46727 + 8.08584i) q^{82} -9.94035i q^{83} +(-10.8195 - 3.07852i) q^{84} -2.41452i q^{85} +(-14.8985 - 2.70351i) q^{86} +(3.27516 - 5.67274i) q^{87} +(10.0998 - 5.63179i) q^{88} +(-3.81064 + 2.20007i) q^{89} +(1.38922 - 1.63898i) q^{90} +(-10.7816 + 7.46197i) q^{91} +(1.00925 - 0.167621i) q^{92} +(8.49342 - 4.90368i) q^{93} +(-0.666861 - 1.86095i) q^{94} +(-5.22809 - 3.01844i) q^{95} +(-1.79298 - 11.8912i) q^{96} -5.67803i q^{97} +(5.08535 - 8.49348i) q^{98} +6.21132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

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