LMFDB - Embedded newform 280.2.bj.f.171.9

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			171.9
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.f.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959261 - 1.03914i) q^{2} +(2.75363 + 1.58981i) q^{3} +(-0.159637 - 1.99362i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.29350 - 1.33638i) q^{6} +(-1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 + 6.15745i) q^{9} +O(q^{10})$	\(q+(0.959261 - 1.03914i) q^{2} +(2.75363 + 1.58981i) q^{3} +(-0.159637 - 1.99362i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.29350 - 1.33638i) q^{6} +(-1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 + 6.15745i) q^{9} +(-1.37955 - 0.311173i) q^{10} +(1.21003 - 2.09584i) q^{11} +(2.72990 - 5.74349i) q^{12} -1.53832 q^{13} +(1.52685 + 3.41595i) q^{14} -3.17962i q^{15} +(-3.94903 + 0.636512i) q^{16} +(-6.58087 - 3.79947i) q^{17} +(9.80864 + 2.21244i) q^{18} +(-1.52991 + 0.883293i) q^{19} +(-1.64671 + 1.13506i) q^{20} +(-6.73663 + 5.03864i) q^{21} +(-1.01714 - 3.26785i) q^{22} +(5.66247 - 3.26923i) q^{23} +(-3.34963 - 8.34626i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.47565 + 1.59854i) q^{26} +13.0683i q^{27} +(5.01431 + 1.69017i) q^{28} +2.34486i q^{29} +(-3.30408 - 3.05009i) q^{30} +(-1.04132 + 1.80363i) q^{31} +(-3.12672 + 4.71419i) q^{32} +(6.66397 - 3.84745i) q^{33} +(-10.2610 + 3.19379i) q^{34} +(2.62717 - 0.313017i) q^{35} +(11.7081 - 8.07028i) q^{36} +(2.47037 - 1.42627i) q^{37} +(-0.549713 + 2.43710i) q^{38} +(-4.23598 - 2.44564i) q^{39} +(-0.400131 + 2.79998i) q^{40} +6.90356i q^{41} +(-1.22632 + 11.8337i) q^{42} -1.39343 q^{43} +(-4.37147 - 2.07777i) q^{44} +(3.55500 - 6.15745i) q^{45} +(2.03459 - 9.02015i) q^{46} +(-5.65799 - 9.79993i) q^{47} +(-11.8861 - 4.52550i) q^{48} +(-4.82637 - 5.07012i) q^{49} +(0.420294 + 1.35032i) q^{50} +(-12.0809 - 20.9247i) q^{51} +(0.245574 + 3.06683i) q^{52} +(6.82251 + 3.93898i) q^{53} +(13.5798 + 12.5359i) q^{54} -2.42006 q^{55} +(6.56636 - 3.58928i) q^{56} -5.61708 q^{57} +(2.43665 + 2.24934i) q^{58} +(4.90087 + 2.82952i) q^{59} +(-6.33896 + 0.507586i) q^{60} +(4.93580 + 8.54905i) q^{61} +(0.875325 + 2.81223i) q^{62} +(-18.6792 + 2.22555i) q^{63} +(1.89937 + 7.77125i) q^{64} +(0.769162 + 1.33223i) q^{65} +(2.39444 - 10.6155i) q^{66} +(3.13260 - 5.42583i) q^{67} +(-6.52414 + 13.7263i) q^{68} +20.7898 q^{69} +(2.19487 - 3.03027i) q^{70} +3.98199i q^{71} +(2.84494 - 19.9079i) q^{72} +(-2.73292 - 1.57785i) q^{73} +(0.887631 - 3.93523i) q^{74} +(-2.75363 + 1.58981i) q^{75} +(2.00518 + 2.90905i) q^{76} +(3.83499 + 5.12736i) q^{77} +(-6.60478 + 2.05578i) q^{78} +(-1.75753 + 1.01471i) q^{79} +(2.52575 + 3.10171i) q^{80} +(-10.1111 + 17.5129i) q^{81} +(7.17379 + 6.62231i) q^{82} -0.288923i q^{83} +(11.1205 + 12.6259i) q^{84} +7.59894i q^{85} +(-1.33666 + 1.44797i) q^{86} +(-3.72789 + 6.45690i) q^{87} +(-6.35248 + 2.54946i) q^{88} +(12.0399 - 6.95124i) q^{89} +(-2.98829 - 9.60076i) q^{90} +(1.60371 - 3.74075i) q^{91} +(-7.42153 - 10.7669i) q^{92} +(-5.73485 + 3.31102i) q^{93} +(-15.6110 - 3.52122i) q^{94} +(1.52991 + 0.883293i) q^{95} +(-16.1045 + 8.01026i) q^{96} +0.249149i q^{97} +(-9.89833 + 0.151716i) q^{98} +17.2067 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 $

$2$	0.959261	−	1.03914i	0.678300	−	0.734785i
$2$	0.959261	−	1.03914i	0.678300	−	0.734785i
$3$	2.75363	+	1.58981i	1.58981	+	0.917878i	0.993337	+	0.115247i	$0.0367658\pi$
$3$	2.75363	+	1.58981i	1.58981	+	0.917878i	0.596475	+	0.802632i	$0.296568\pi$
$4$	−0.159637	−	1.99362i	−0.0798186	−	0.996809i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	4.29350	−	1.33638i	1.75281	−	0.545574i
$7$	−1.04250	+	2.43170i	−0.394030	+	0.919098i
$7$	−1.04250	+	2.43170i	−0.394030	+	0.919098i
$8$	−2.22479	−	1.74651i	−0.786582	−	0.617486i
$9$	3.55500	+	6.15745i	1.18500	+	2.05248i
$10$	−1.37955	−	0.311173i	−0.436254	−	0.0984014i
$11$	1.21003	−	2.09584i	0.364838	−	0.631919i	−0.623912	−	0.781495i	$-0.714458\pi$
$11$	1.21003	−	2.09584i	0.364838	−	0.631919i	0.988750	+	0.149576i	$0.0477909\pi$
$12$	2.72990	−	5.74349i	0.788053	−	1.65800i
$13$	−1.53832			−0.426654			−0.213327	−	0.976981i	$-0.568430\pi$
$13$	−1.53832			−0.426654			−0.213327	+	0.976981i	$0.568430\pi$
$14$	1.52685	+	3.41595i	0.408069	+	0.912951i
$15$		−	3.17962i		−	0.820975i
$16$	−3.94903	+	0.636512i	−0.987258	+	0.159128i
$17$	−6.58087	−	3.79947i	−1.59610	−	0.921506i	−0.992230	−	0.124421i	$-0.960293\pi$
$17$	−6.58087	−	3.79947i	−1.59610	−	0.921506i	−0.603866	−	0.797086i	$-0.706374\pi$
$18$	9.80864	+	2.21244i	2.31192	+	0.521477i
$19$	−1.52991	+	0.883293i	−0.350985	+	0.202641i	−0.665119	−	0.746737i	$-0.731619\pi$
$19$	−1.52991	+	0.883293i	−0.350985	+	0.202641i	0.314134	+	0.949379i	$0.398286\pi$
$20$	−1.64671	+	1.13506i	−0.368215	+	0.253807i
$21$	−6.73663	+	5.03864i	−1.47005	+	1.09952i
$22$	−1.01714	−	3.26785i	−0.216855	−	0.696708i
$23$	5.66247	−	3.26923i	1.18071	−	0.681681i	0.224528	−	0.974468i	$-0.427916\pi$
$23$	5.66247	−	3.26923i	1.18071	−	0.681681i	0.956178	+	0.292787i	$0.0945826\pi$
$24$	−3.34963	−	8.34626i	−0.683740	−	1.70367i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.47565	+	1.59854i	−0.289399	+	0.313499i
$27$			13.0683i			2.51499i
$28$	5.01431	+	1.69017i	0.947616	+	0.319411i
$29$			2.34486i			0.435430i	0.976012	+	0.217715i	$0.0698604\pi$
$29$			2.34486i			0.435430i	−0.976012	+	0.217715i	$0.930140\pi$
$30$	−3.30408	−	3.05009i	−0.603241	−	0.556867i
$31$	−1.04132	+	1.80363i	−0.187027	+	0.323941i	−0.944258	−	0.329207i	$-0.893219\pi$
$31$	−1.04132	+	1.80363i	−0.187027	+	0.323941i	0.757230	+	0.653148i	$0.226552\pi$
$32$	−3.12672	+	4.71419i	−0.552732	+	0.833359i
$33$	6.66397	−	3.84745i	1.16005	−	0.669754i
$34$	−10.2610	+	3.19379i	−1.75974	+	0.547730i
$35$	2.62717	−	0.313017i	0.444073	−	0.0529095i
$36$	11.7081	−	8.07028i	1.95135	−	1.34505i
$37$	2.47037	−	1.42627i	0.406126	−	0.234477i	−0.282998	−	0.959121i	$-0.591329\pi$
$37$	2.47037	−	1.42627i	0.406126	−	0.234477i	0.689124	+	0.724644i	$0.257996\pi$
$38$	−0.549713	+	2.43710i	−0.0891753	+	0.395350i
$39$	−4.23598	−	2.44564i	−0.678300	−	0.391617i
$40$	−0.400131	+	2.79998i	−0.0632663	+	0.442716i
$41$			6.90356i			1.07815i	0.842256	+	0.539077i	$0.181227\pi$
$41$			6.90356i			1.07815i	−0.842256	+	0.539077i	$0.818773\pi$
$42$	−1.22632	+	11.8337i	−0.189225	+	1.82598i
$43$	−1.39343			−0.212496			−0.106248	−	0.994340i	$-0.533884\pi$
$43$	−1.39343			−0.212496			−0.106248	+	0.994340i	$0.533884\pi$
$44$	−4.37147	−	2.07777i	−0.659023	−	0.313235i
$45$	3.55500	−	6.15745i	0.529949	−	0.917898i
$46$	2.03459	−	9.02015i	0.299984	−	1.32995i
$47$	−5.65799	−	9.79993i	−0.825303	−	1.42947i	−0.901688	−	0.432388i	$-0.857671\pi$
$47$	−5.65799	−	9.79993i	−0.825303	−	1.42947i	0.0763851	−	0.997078i	$-0.475662\pi$
$48$	−11.8861	−	4.52550i	−1.71561	−	0.653199i
$49$	−4.82637	−	5.07012i	−0.689481	−	0.724304i
$50$	0.420294	+	1.35032i	0.0594385	+	0.190964i
$51$	−12.0809	−	20.9247i	−1.69166	−	2.93004i
$52$	0.245574	+	3.06683i	0.0340549	+	0.425293i
$53$	6.82251	+	3.93898i	0.937144	+	0.541060i	0.889064	−	0.457783i	$-0.151356\pi$
$53$	6.82251	+	3.93898i	0.937144	+	0.541060i	0.0480800	+	0.998843i	$0.484690\pi$
$54$	13.5798	+	12.5359i	1.84798	+	1.70592i
$55$	−2.42006			−0.326321
$56$	6.56636	−	3.58928i	0.877467	−	0.479638i
$57$	−5.61708			−0.744000
$58$	2.43665	+	2.24934i	0.319948	+	0.295352i
$59$	4.90087	+	2.82952i	0.638038	+	0.368372i	0.783859	−	0.620939i	$-0.213249\pi$
$59$	4.90087	+	2.82952i	0.638038	+	0.368372i	−0.145820	+	0.989311i	$0.546582\pi$
$60$	−6.33896	+	0.507586i	−0.818356	+	0.0655291i
$61$	4.93580	+	8.54905i	0.631964	+	1.09459i	0.987150	+	0.159798i	$0.0510844\pi$
$61$	4.93580	+	8.54905i	0.631964	+	1.09459i	−0.355186	+	0.934796i	$0.615582\pi$
$62$	0.875325	+	2.81223i	0.111166	+	0.357154i
$63$	−18.6792	+	2.22555i	−2.35336	+	0.280393i
$64$	1.89937	+	7.77125i	0.237422	+	0.971407i
$65$	0.769162	+	1.33223i	0.0954027	+	0.165242i
$66$	2.39444	−	10.6155i	0.294735	−	1.30668i
$67$	3.13260	−	5.42583i	0.382708	−	0.662870i	−0.608740	−	0.793370i	$-0.708325\pi$
$67$	3.13260	−	5.42583i	0.382708	−	0.662870i	0.991448	+	0.130499i	$0.0416581\pi$
$68$	−6.52414	+	13.7263i	−0.791168	+	1.66456i
$69$	20.7898			2.50280
$70$	2.19487	−	3.03027i	0.262337	−	0.362187i
$71$			3.98199i			0.472575i	0.971683	+	0.236287i	$0.0759307\pi$
$71$			3.98199i			0.472575i	−0.971683	+	0.236287i	$0.924069\pi$
$72$	2.84494	−	19.9079i	0.335279	−	2.34617i
$73$	−2.73292	−	1.57785i	−0.319865	−	0.184674i	0.331468	−	0.943467i	$-0.392456\pi$
$73$	−2.73292	−	1.57785i	−0.319865	−	0.184674i	−0.651332	+	0.758793i	$0.725790\pi$
$74$	0.887631	−	3.93523i	0.103185	−	0.457461i
$75$	−2.75363	+	1.58981i	−0.317962	+	0.183576i
$76$	2.00518	+	2.90905i	0.230010	+	0.333691i
$77$	3.83499	+	5.12736i	0.437038	+	0.584317i
$78$	−6.60478	+	2.05578i	−0.747845	+	0.232771i
$79$	−1.75753	+	1.01471i	−0.197738	+	0.114164i	−0.595600	−	0.803281i	$-0.703086\pi$
$79$	−1.75753	+	1.01471i	−0.197738	+	0.114164i	0.397862	+	0.917445i	$0.369752\pi$
$80$	2.52575	+	3.10171i	0.282388	+	0.346781i
$81$	−10.1111	+	17.5129i	−1.12345	+	1.94588i
$82$	7.17379	+	6.62231i	0.792212	+	0.731312i
$83$		−	0.288923i		−	0.0317134i	−0.999874	−	0.0158567i	$-0.994952\pi$
$83$		−	0.288923i		−	0.0317134i	0.999874	−	0.0158567i	$-0.00504756\pi$
$84$	11.1205	+	12.6259i	1.21335	+	1.37760i
$85$			7.59894i			0.824220i
$86$	−1.33666	+	1.44797i	−0.144136	+	0.156139i
$87$	−3.72789	+	6.45690i	−0.399672	+	0.692252i
$88$	−6.35248	+	2.54946i	−0.677176	+	0.271773i
$89$	12.0399	−	6.95124i	1.27623	−	0.736830i	0.300074	−	0.953916i	$-0.402989\pi$
$89$	12.0399	−	6.95124i	1.27623	−	0.736830i	0.976152	+	0.217086i	$0.0696553\pi$
$90$	−2.98829	−	9.60076i	−0.314994	−	1.01201i
$91$	1.60371	−	3.74075i	0.168114	−	0.392137i
$92$	−7.42153	−	10.7669i	−0.773748	−	1.12253i
$93$	−5.73485	+	3.31102i	−0.594677	+	0.343337i
$94$	−15.6110	−	3.52122i	−1.61015	−	0.363186i
$95$	1.52991	+	0.883293i	0.156965	+	0.0906240i
$96$	−16.1045	+	8.01026i	−1.64366	+	0.817543i
$97$			0.249149i			0.0252972i	0.999920	+	0.0126486i	$0.00402629\pi$
$97$			0.249149i			0.0252972i	−0.999920	+	0.0126486i	$0.995974\pi$
$98$	−9.89833	+	0.151716i	−0.999883	+	0.0153256i
$99$	17.2067			1.72934
$100$	1.80634	+	0.858559i	0.180634	+	0.0858559i
$101$	−4.87755	+	8.44817i	−0.485335	+	0.840624i	−0.999858	−	0.0168520i	$-0.994636\pi$
$101$	−4.87755	+	8.44817i	−0.485335	+	0.840624i	0.514523	+	0.857476i	$0.327969\pi$
$102$	−33.3325	−	7.51848i	−3.30041	−	0.744440i
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511902i	0.679565	−	0.733615i	$-0.262168\pi$
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511902i	−0.975112	+	0.221713i	$0.928835\pi$
$104$	3.42244	+	2.68670i	0.335598	+	0.263453i
$105$	7.73190	+	3.31477i	0.754557	+	0.323489i
$106$	10.6377	−	3.31106i	1.03323	−	0.321598i
$107$	−0.0626308	−	0.108480i	−0.00605475	−	0.0104871i	0.862982	−	0.505234i	$-0.168594\pi$
$107$	−0.0626308	−	0.108480i	−0.00605475	−	0.0104871i	−0.869037	+	0.494747i	$0.835261\pi$
$108$	26.0532	−	2.08618i	2.50697	−	0.200743i
$109$	−0.399788	−	0.230818i	−0.0382928	−	0.0221083i	0.480731	−	0.876868i	$-0.340371\pi$
$109$	−0.399788	−	0.230818i	−0.0382928	−	0.0221083i	−0.519024	+	0.854760i	$0.673705\pi$
$110$	−2.32147	+	2.51479i	−0.221344	+	0.239776i
$111$	9.06999			0.860885
$112$	2.56908	−	10.2664i	0.242755	−	0.970088i
$113$	−9.65049			−0.907842			−0.453921	−	0.891042i	$-0.649975\pi$
$113$	−9.65049			−0.907842			−0.453921	+	0.891042i	$0.649975\pi$
$114$	−5.38824	+	5.83695i	−0.504655	+	0.546680i
$115$	−5.66247	−	3.26923i	−0.528028	−	0.304857i
$116$	4.67477	−	0.374328i	0.434041	−	0.0347555i
$117$	−5.46874	−	9.47214i	−0.505586	−	0.875700i
$118$	7.64148	−	2.37846i	0.703455	−	0.218955i
$119$	16.0998	−	12.0418i	1.47586	−	1.10387i
$120$	−5.55326	+	7.07399i	−0.506941	+	0.645764i
$121$	2.57165	+	4.45422i	0.233786	+	0.404929i
$122$	13.6184	+	3.07177i	1.23295	+	0.278105i
$123$	−10.9754	+	19.0099i	−0.989615	+	1.71406i
$124$	3.76198	+	1.78808i	0.337836	+	0.160574i
$125$	1.00000			0.0894427
$126$	−15.6056	+	21.5452i	−1.39025	+	1.91940i
$127$		−	9.40385i		−	0.834457i	−0.908802	−	0.417229i	$-0.863001\pi$
$127$		−	9.40385i		−	0.834457i	0.908802	−	0.417229i	$-0.136999\pi$
$128$	9.89744	+	5.48094i	0.874818	+	0.484451i
$129$	−3.83699	−	2.21529i	−0.337828	−	0.195045i
$130$	2.12220	+	0.478684i	0.186129	+	0.0419834i
$131$	16.2949	−	9.40788i	1.42369	−	0.821970i	0.427082	−	0.904213i	$-0.359541\pi$
$131$	16.2949	−	9.40788i	1.42369	−	0.821970i	0.996612	+	0.0822423i	$0.0262081\pi$
$132$	−8.73416	−	12.6712i	−0.760211	−	1.10289i
$133$	−0.552971	−	4.64112i	−0.0479486	−	0.402436i
$134$	−2.63323	−	8.46001i	−0.227476	−	0.730833i
$135$	11.3175	−	6.53414i	0.974052	−	0.562369i
$136$	8.00523	+	19.9466i	0.686443	+	1.71041i
$137$	7.55473	−	13.0852i	0.645444	−	1.11794i	−0.338755	−	0.940875i	$-0.610006\pi$
$137$	7.55473	−	13.0852i	0.645444	−	1.11794i	0.984199	−	0.177067i	$-0.0566609\pi$
$138$	19.9429	−	21.6036i	1.69765	−	1.83902i
$139$			11.1193i			0.943129i	0.881831	+	0.471565i	$0.156311\pi$
$139$			11.1193i			0.943129i	−0.881831	+	0.471565i	$0.843689\pi$
$140$	−1.04343	−	5.18761i	−0.0881859	−	0.438433i
$141$		−	35.9806i		−	3.03011i
$142$	4.13786	+	3.81976i	0.347241	+	0.320548i
$143$	−1.86142	+	3.22407i	−0.155660	+	0.269611i
$144$	−17.9581	−	22.0532i	−1.49651	−	1.83776i
$145$	2.03071	−	1.17243i	0.168641	−	0.0973652i
$146$	−4.26120	+	1.32633i	−0.352660	+	0.109767i
$147$	−5.22951	−	21.6343i	−0.431323	−	1.78437i
$148$	−3.23780	−	4.69729i	−0.266145	−	0.386115i
$149$	9.67998	−	5.58874i	0.793014	−	0.457847i	−0.0480082	−	0.998847i	$-0.515287\pi$
$149$	9.67998	−	5.58874i	0.793014	−	0.457847i	0.841023	+	0.541000i	$0.181954\pi$
$150$	−0.989412	+	4.38647i	−0.0807851	+	0.358153i
$151$	−13.1832	−	7.61131i	−1.07283	−	0.619399i	−0.143878	−	0.989595i	$-0.545957\pi$
$151$	−13.1832	−	7.61131i	−1.07283	−	0.619399i	−0.928954	+	0.370196i	$0.879290\pi$
$152$	4.94641	+	0.706866i	0.401207	+	0.0573344i
$153$		−	54.0285i		−	4.36794i
$154$	9.00682	+	0.933370i	0.725790	+	0.0752131i
$155$	2.08265			0.167282
$156$	−4.19946	+	8.83535i	−0.336226	+	0.707394i
$157$	−0.357836	+	0.619791i	−0.0285584	+	0.0494647i	−0.879951	−	0.475064i	$-0.842425\pi$
$157$	−0.357836	+	0.619791i	−0.0285584	+	0.0494647i	0.851393	+	0.524528i	$0.175758\pi$
$158$	−0.631502	+	2.79970i	−0.0502396	+	0.222733i
$159$	12.5245	+	21.6930i	0.993255	+	1.72037i
$160$	5.64597	+	0.350728i	0.446353	+	0.0277275i
$161$	2.04664	+	17.1776i	0.161298	+	1.35379i
$162$	8.49926	+	27.3063i	0.667765	+	2.14539i
$163$	0.890005	+	1.54153i	0.0697105	+	0.120742i	0.898774	−	0.438413i	$-0.144459\pi$
$163$	0.890005	+	1.54153i	0.0697105	+	0.120742i	−0.829063	+	0.559155i	$0.811126\pi$
$164$	13.7631	−	1.10207i	1.07471	−	0.0860568i
$165$	−6.66397	−	3.84745i	−0.518790	−	0.299523i
$166$	−0.300233	−	0.277153i	−0.0233026	−	0.0215112i
$167$	−5.69155			−0.440426			−0.220213	−	0.975452i	$-0.570675\pi$
$167$	−5.69155			−0.440426			−0.220213	+	0.975452i	$0.570675\pi$
$168$	23.7876	+	0.555710i	1.83526	+	0.0428739i
$169$	−10.6336			−0.817966
$170$	7.89638	+	7.28936i	0.605625	+	0.559069i
$171$	−10.8777	−	6.28022i	−0.831835	−	0.480260i
$172$	0.222443	+	2.77796i	0.0169611	+	0.211818i
$173$	9.46941	+	16.4015i	0.719946	+	1.24698i	0.961021	+	0.276476i	$0.0891666\pi$
$173$	9.46941	+	16.4015i	0.719946	+	1.24698i	−0.241075	+	0.970506i	$0.577500\pi$
$174$	3.13362	+	10.0677i	0.237559	+	0.763228i
$175$	−1.58467	−	2.11869i	−0.119789	−	0.160158i
$176$	−3.44443	+	9.04673i	−0.259634	+	0.681923i
$177$	8.99680	+	15.5829i	0.676241	+	1.17128i
$178$	4.32607	−	19.1792i	0.324253	−	1.43754i
$179$	−1.49172	+	2.58374i	−0.111497	+	0.193118i	−0.916374	−	0.400323i	$-0.868898\pi$
$179$	−1.49172	+	2.58374i	−0.111497	+	0.193118i	0.804877	+	0.593441i	$0.202231\pi$
$180$	−12.8431	−	6.10436i	−0.957269	−	0.454992i
$181$	−14.9790			−1.11338			−0.556691	−	0.830720i	$-0.687929\pi$
$181$	−14.9790			−1.11338			−0.556691	+	0.830720i	$0.687929\pi$
$182$	−2.34880	−	5.25483i	−0.174104	−	0.389514i
$183$			31.3880i			2.32026i
$184$	−18.3075	−	2.61624i	−1.34965	−	0.192872i
$185$	−2.47037	−	1.42627i	−0.181625	−	0.104861i
$186$	−2.06060	+	9.13547i	−0.151090	+	0.669845i
$187$	−15.9261	+	9.19496i	−1.16463	+	0.672402i
$188$	−18.6341	+	12.8443i	−1.35903	+	0.936767i
$189$	−31.7782	−	13.6237i	−2.31152	−	0.990981i
$190$	2.38545	−	0.742486i	0.173059	−	0.0538656i
$191$	22.4510	−	12.9621i	1.62450	−	0.937904i	0.638801	−	0.769372i	$-0.279431\pi$
$191$	22.4510	−	12.9621i	1.62450	−	0.937904i	0.985696	−	0.168532i	$-0.0539026\pi$
$192$	−7.12465	+	24.4188i	−0.514177	+	1.76228i
$193$	−3.55040	+	6.14947i	−0.255563	+	0.442648i	−0.965048	−	0.262072i	$-0.915594\pi$
$193$	−3.55040	+	6.14947i	−0.255563	+	0.442648i	0.709485	+	0.704720i	$0.248928\pi$
$194$	0.258901	+	0.238999i	0.0185880	+	0.0171591i
$195$			4.89129i			0.350272i
$196$	−9.33743	+	10.4313i	−0.666959	+	0.745094i
$197$			0.614082i			0.0437515i	0.999761	+	0.0218758i	$0.00696383\pi$
$197$			0.614082i			0.0437515i	−0.999761	+	0.0218758i	$0.993036\pi$
$198$	16.5057	−	17.8802i	1.17301	−	1.27069i
$199$	4.47143	−	7.74474i	0.316971	−	0.549010i	−0.662884	−	0.748723i	$-0.730668\pi$
$199$	4.47143	−	7.74474i	0.316971	−	0.549010i	0.979854	+	0.199713i	$0.0640009\pi$
$200$	2.62492	−	1.05347i	0.185610	−	0.0744913i
$201$	17.2521	−	9.96050i	1.21687	−	0.702559i
$202$	4.10001	+	13.1725i	0.288476	+	0.926812i
$203$	−5.70202	−	2.44453i	−0.400203	−	0.171572i
$204$	−39.7873	+	27.4250i	−2.78567	+	1.92014i
$205$	5.97866	−	3.45178i	0.417568	−	0.241083i
$206$	−8.27586	−	1.86671i	−0.576607	−	0.130060i
$207$	40.2602	+	23.2442i	2.79828	+	1.61559i
$208$	6.07489	−	0.979161i	0.421218	−	0.0678926i
$209$			4.27525i			0.295725i
$210$	10.8614	−	4.85482i	0.749510	−	0.335015i
$211$	10.6756			0.734942			0.367471	−	0.930035i	$-0.380224\pi$
$211$	10.6756			0.734942			0.367471	+	0.930035i	$0.380224\pi$
$212$	6.76369	−	14.2303i	0.464532	−	0.977341i
$213$	−6.33061	+	10.9649i	−0.433766	+	0.751305i
$214$	−0.172805	−	0.0389780i	−0.0118127	−	0.00266448i
$215$	0.696713	+	1.20674i	0.0475154	+	0.0822992i
$216$	22.8239	−	29.0742i	1.55297	−	1.97825i
$217$	−3.30030	−	4.41248i	−0.224039	−	0.299539i
$218$	−0.623354	+	0.194023i	−0.0422189	+	0.0131409i
$219$	−5.01698	−	8.68967i	−0.339016	−	0.587194i
$220$	0.386332	+	4.82469i	0.0260465	+	0.325280i
$221$	10.1235	+	5.84481i	0.680981	+	0.393164i
$222$	8.70048	−	9.42502i	0.583938	−	0.632566i
$223$	−1.40260			−0.0939252			−0.0469626	−	0.998897i	$-0.514954\pi$
$223$	−1.40260			−0.0939252			−0.0469626	+	0.998897i	$0.514954\pi$
$224$	−8.20389	−	12.5178i	−0.548146	−	0.836383i
$225$	−7.11001			−0.474000
$226$	−9.25734	+	10.0282i	−0.615789	+	0.667069i
$227$	3.48428	+	2.01165i	0.231260	+	0.133518i	0.611153	−	0.791512i	$-0.290706\pi$
$227$	3.48428	+	2.01165i	0.231260	+	0.133518i	−0.379893	+	0.925030i	$0.624039\pi$
$228$	0.896695	+	11.1983i	0.0593851	+	0.741626i
$229$	−10.8680	−	18.8239i	−0.718178	−	1.24392i	−0.961721	−	0.274031i	$-0.911643\pi$
$229$	−10.8680	−	18.8239i	−0.718178	−	1.24392i	0.243542	−	0.969890i	$-0.421690\pi$
$230$	−8.82898	+	2.74807i	−0.582165	+	0.181203i
$231$	2.40863	+	20.2158i	0.158476	+	1.33010i
$232$	4.09534	−	5.21683i	0.268872	−	0.342502i
$233$	5.69230	+	9.85935i	0.372915	+	0.645907i	0.990013	−	0.140979i	$-0.0450251\pi$
$233$	5.69230	+	9.85935i	0.372915	+	0.645907i	−0.617098	+	0.786886i	$0.711692\pi$
$234$	−15.0889	−	3.40345i	−0.986390	−	0.222490i
$235$	−5.65799	+	9.79993i	−0.369087	+	0.639277i
$236$	4.85862	−	10.2222i	0.316269	−	0.665406i
$237$	−6.45281			−0.419155
$238$	2.93076	−	28.2812i	0.189973	−	1.83320i
$239$		−	25.7524i		−	1.66578i	−0.553435	−	0.832892i	$-0.686683\pi$
$239$		−	25.7524i		−	1.66578i	0.553435	−	0.832892i	$-0.313317\pi$
$240$	2.02387	+	12.5564i	0.130640	+	0.810514i
$241$	−1.67062	−	0.964530i	−0.107614	−	0.0621309i	0.445227	−	0.895418i	$-0.353123\pi$
$241$	−1.67062	−	0.964530i	−0.107614	−	0.0621309i	−0.552841	+	0.833287i	$0.686456\pi$
$242$	7.09545	+	1.60045i	0.456113	+	0.102881i
$243$	−21.7321	+	12.5470i	−1.39412	+	0.804893i
$244$	16.2556	−	11.2048i	1.04066	−	0.717317i
$245$	−1.97767	+	6.71482i	−0.126349	+	0.428994i
$246$	9.22576	+	29.6404i	0.588213	+	1.88980i
$247$	2.35349	−	1.35879i	0.149749	−	0.0864577i
$248$	5.46679	−	2.19400i	0.347141	−	0.139319i
$249$	0.459334	−	0.795589i	0.0291091	−	0.0504184i
$250$	0.959261	−	1.03914i	0.0606690	−	0.0657212i
$251$			12.9948i			0.820222i	0.912036	+	0.410111i	$0.134510\pi$
$251$			12.9948i			0.820222i	−0.912036	+	0.410111i	$0.865490\pi$
$252$	7.41879	+	36.8839i	0.467340	+	2.32347i
$253$		−	15.8235i		−	0.994813i
$254$	−9.77195	−	9.02075i	−0.613147	−	0.566012i
$255$	−12.0809	+	20.9247i	−0.756534	+	1.31036i
$256$	15.1897	−	5.02721i	0.949357	−	0.314201i
$257$	−14.4110	+	8.32019i	−0.898933	+	0.518999i	−0.876854	−	0.480757i	$-0.840362\pi$
$257$	−14.4110	+	8.32019i	−0.898933	+	0.518999i	−0.0220792	+	0.999756i	$0.507029\pi$
$258$	−5.98267	+	1.86214i	−0.372465	+	0.115932i
$259$	0.892891	+	7.49409i	0.0554815	+	0.465660i
$260$	2.53317	−	1.74609i	0.157100	−	0.108288i
$261$	−14.4384	+	8.33600i	−0.893713	+	0.515985i
$262$	5.85495	−	25.9574i	0.361720	−	1.60365i
$263$	5.95477	+	3.43799i	0.367187	+	0.211995i	0.672229	−	0.740343i	$-0.265337\pi$
$263$	5.95477	+	3.43799i	0.367187	+	0.211995i	−0.305042	+	0.952339i	$0.598670\pi$
$264$	−21.5456	−	3.07897i	−1.32604	−	0.189497i
$265$		−	7.87796i		−	0.483939i
$266$	−5.35323	−	3.87743i	−0.328228	−	0.237740i
$267$	44.2046			2.70528
$268$	−11.3171	−	5.37905i	−0.691303	−	0.328578i
$269$	−11.0639	+	19.1633i	−0.674580	+	1.16841i	0.302012	+	0.953304i	$0.402342\pi$
$269$	−11.0639	+	19.1633i	−0.674580	+	1.16841i	−0.976591	+	0.215102i	$0.930991\pi$
$270$	4.06649	−	18.0284i	0.247479	−	1.09717i
$271$	5.29547	+	9.17203i	0.321677	+	0.557161i	0.980834	−	0.194844i	$-0.0624201\pi$
$271$	5.29547	+	9.17203i	0.321677	+	0.557161i	−0.659157	+	0.752005i	$0.729087\pi$
$272$	28.4065	+	10.8154i	1.72240	+	0.655781i
$273$	10.3631	−	7.75105i	0.627204	−	0.469115i
$274$	−6.35041	−	20.4025i	−0.383642	−	1.23256i
$275$	1.21003	+	2.09584i	0.0729677	+	0.126384i
$276$	−3.31883	−	41.4470i	−0.199770	−	2.49481i
$277$	−16.5032	−	9.52815i	−0.991583	−	0.572491i	−0.0858360	−	0.996309i	$-0.527356\pi$
$277$	−16.5032	−	9.52815i	−0.991583	−	0.572491i	−0.905747	+	0.423818i	$0.860689\pi$
$278$	11.5546	+	10.6663i	0.692997	+	0.639724i
$279$	−14.8076			−0.886511
$280$	−6.39159	−	3.89199i	−0.381970	−	0.232591i
$281$	−17.6280			−1.05160			−0.525799	−	0.850609i	$-0.676234\pi$
$281$	−17.6280			−1.05160			−0.525799	+	0.850609i	$0.676234\pi$
$282$	−37.3890	−	34.5147i	−2.22648	−	2.05532i
$283$	0.485654	+	0.280393i	0.0288691	+	0.0166676i	0.514365	−	0.857571i	$-0.328028\pi$
$283$	0.485654	+	0.280393i	0.0288691	+	0.0166676i	−0.485496	+	0.874239i	$0.661361\pi$
$284$	7.93857	−	0.635674i	0.471067	−	0.0377203i
$285$	2.80854	+	4.86453i	0.166364	+	0.288150i
$286$	1.56469	+	5.02701i	0.0925219	+	0.297253i
$287$	−16.7874	−	7.19699i	−0.990930	−	0.424825i
$288$	−40.1429	−	2.49368i	−2.36544	−	0.146941i
$289$	20.3719	+	35.2852i	1.19835	+	2.07560i
$290$	0.729658	−	3.23487i	0.0428470	−	0.189958i
$291$	−0.396100	+	0.686065i	−0.0232198	+	0.0402179i
$292$	−2.70936	+	5.70029i	−0.158554	+	0.333584i
$293$	−23.8016			−1.39051			−0.695253	−	0.718765i	$-0.744708\pi$
$293$	−23.8016			−1.39051			−0.695253	+	0.718765i	$0.744708\pi$
$294$	−27.4976	−	15.3187i	−1.60369	−	0.893406i
$295$		−	5.65903i		−	0.329482i
$296$	−7.98704	−	1.14139i	−0.464238	−	0.0663419i
$297$	27.3890	+	15.8130i	1.58927	+	0.917565i
$298$	3.47812	−	15.4199i	0.201482	−	0.893253i
$299$	−8.71070	+	5.02913i	−0.503753	+	0.290842i
$300$	3.60906	+	5.23591i	0.208369	+	0.302295i
$301$	1.45265	−	3.38840i	0.0837295	−	0.195304i
$302$	−20.5553	+	6.39797i	−1.18283	+	0.368162i
$303$	−26.8620	+	15.5088i	−1.54318	+	0.890956i
$304$	5.47943	−	4.46196i	0.314267	−	0.255911i
$305$	4.93580	−	8.54905i	0.282623	−	0.489517i
$306$	−56.1433	−	51.8274i	−3.20950	−	2.96278i
$307$		−	9.32160i		−	0.532012i	−0.963971	−	0.266006i	$-0.914296\pi$
$307$		−	9.32160i		−	0.532012i	0.963971	−	0.266006i	$-0.0857041\pi$
$308$	9.60979	−	8.46403i	0.547569	−	0.482283i
$309$		−	19.0744i		−	1.08510i
$310$	1.99780	−	2.16417i	0.113468	−	0.122917i
$311$	−2.73260	+	4.73300i	−0.154951	+	0.268384i	−0.933041	−	0.359769i	$-0.882855\pi$
$311$	−2.73260	+	4.73300i	−0.154951	+	0.268384i	0.778090	+	0.628153i	$0.216189\pi$
$312$	5.15281	+	12.8392i	0.291720	+	0.726879i
$313$	−19.9919	+	11.5423i	−1.13001	+	0.652412i	−0.943937	−	0.330124i	$-0.892909\pi$
$313$	−19.9919	+	11.5423i	−1.13001	+	0.652412i	−0.186073	+	0.982536i	$0.559576\pi$
$314$	0.300793	+	0.966384i	0.0169747	+	0.0545362i
$315$	11.2670	+	15.0639i	0.634822	+	0.848754i
$316$	2.30352	+	3.34187i	0.129583	+	0.187995i
$317$	−26.2154	+	15.1355i	−1.47241	+	0.850094i	−0.999518	−	0.0310291i	$-0.990122\pi$
$317$	−26.2154	+	15.1355i	−1.47241	+	0.850094i	−0.472887	+	0.881123i	$0.656788\pi$
$318$	34.5564	+	7.79454i	1.93783	+	0.437096i
$319$	4.91445	+	2.83736i	0.275157	+	0.158862i
$320$	5.78042	−	5.53053i	0.323135	−	0.309166i
$321$		−	0.398285i		−	0.0222301i
$322$	19.8133	+	14.3511i	1.10415	+	0.799754i
$323$	13.4242			0.746941
$324$	36.5282	+	17.3619i	2.02934	+	0.964552i
$325$	0.769162	−	1.33223i	0.0426654	−	0.0738987i
$326$	2.45562	+	0.553890i	0.136004	+	0.0306771i
$327$	−0.733914	−	1.27118i	−0.0405855	−	0.0702962i
$328$	12.0572	−	15.3590i	0.665746	−	0.848057i
$329$	29.7290	−	3.54209i	1.63901	−	0.195282i
$330$	−10.3905	+	3.23412i	−0.571980	+	0.178032i
$331$	0.262181	+	0.454110i	0.0144108	+	0.0249602i	0.873141	−	0.487468i	$-0.162079\pi$
$331$	0.262181	+	0.454110i	0.0144108	+	0.0249602i	−0.858730	+	0.512428i	$0.828746\pi$
$332$	−0.576003	+	0.0461229i	−0.0316123	+	0.00253132i
$333$	17.5643	+	10.1408i	0.962519	+	0.555711i
$334$	−5.45969	+	5.91434i	−0.298741	+	0.323618i
$335$	−6.26521			−0.342305
$336$	23.3960	−	24.1857i	1.27636	−	1.31944i
$337$	−3.41643			−0.186105			−0.0930524	−	0.995661i	$-0.529662\pi$
$337$	−3.41643			−0.186105			−0.0930524	+	0.995661i	$0.529662\pi$
$338$	−10.2004	+	11.0498i	−0.554826	+	0.601030i
$339$	−26.5739	−	15.3425i	−1.44330	−	0.833288i
$340$	15.1494	−	1.21307i	0.821591	−	0.0657881i
$341$	2.52007	+	4.36489i	0.136470	+	0.236372i
$342$	−16.9606	+	5.27908i	−0.917122	+	0.285460i
$343$	17.3606	−	6.45067i	0.937382	−	0.348304i
$344$	3.10008	+	2.43364i	0.167145	+	0.131213i
$345$	−10.3949	−	18.0045i	−0.559643	−	0.969330i
$346$	26.1271	+	5.89324i	1.40460	+	0.316823i
$347$	4.64349	−	8.04275i	0.249275	−	0.431758i	−0.714050	−	0.700095i	$-0.753141\pi$
$347$	4.64349	−	8.04275i	0.249275	−	0.431758i	0.963325	+	0.268337i	$0.0864742\pi$
$348$	13.4677	+	6.40124i	0.721945	+	0.343142i
$349$	18.6699			0.999374			0.499687	−	0.866206i	$-0.333448\pi$
$349$	18.6699			0.999374			0.499687	+	0.866206i	$0.333448\pi$
$350$	−3.72173	−	0.385680i	−0.198935	−	0.0206155i
$351$		−	20.1032i		−	1.07303i
$352$	6.09674	+	12.2574i	0.324957	+	0.653323i
$353$	−11.7057	−	6.75828i	−0.623030	−	0.359707i	0.155018	−	0.987912i	$-0.450457\pi$
$353$	−11.7057	−	6.75828i	−0.623030	−	0.359707i	−0.778048	+	0.628205i	$0.783790\pi$
$354$	24.8232	+	5.59911i	1.31934	+	0.297590i
$355$	3.44850	−	1.99099i	0.183027	−	0.105671i
$356$	−15.7801	−	22.8933i	−0.836345	−	1.21334i
$357$	63.4770	−	7.56303i	3.35956	−	0.400278i
$358$	1.25392	+	4.02860i	0.0662720	+	0.212918i
$359$	−22.8266	+	13.1789i	−1.20474	+	0.695558i	−0.961606	−	0.274435i	$-0.911509\pi$
$359$	−22.8266	+	13.1789i	−1.20474	+	0.695558i	−0.243135	+	0.969992i	$0.578176\pi$
$360$	−18.6632	+	7.49016i	−0.983637	+	0.394766i
$361$	−7.93959	+	13.7518i	−0.417873	+	0.723777i
$362$	−14.3688	+	15.5653i	−0.755207	+	0.818096i
$363$			16.3537i			0.858348i
$364$	−7.71363	−	2.60002i	−0.404304	−	0.136278i
$365$			3.15571i			0.165177i
$366$	32.6166	+	30.1092i	1.70490	+	1.57384i
$367$	−17.7819	+	30.7992i	−0.928208	+	1.60770i	−0.141889	+	0.989883i	$0.545318\pi$
$367$	−17.7819	+	30.7992i	−0.928208	+	1.60770i	−0.786319	+	0.617821i	$0.788016\pi$
$368$	−20.2804	+	16.5145i	−1.05719	+	0.860878i
$369$	−42.5083	+	24.5422i	−2.21289	+	1.27761i
$370$	−3.85182	+	1.19890i	−0.200247	+	0.0623280i
$371$	−16.6909	+	12.4839i	−0.866550	+	0.648133i
$372$	7.51641	+	10.9046i	0.389708	+	0.565375i
$373$	20.6623	−	11.9294i	1.06985	−	0.617680i	0.141712	−	0.989908i	$-0.454739\pi$
$373$	20.6623	−	11.9294i	1.06985	−	0.617680i	0.928141	+	0.372228i	$0.121406\pi$
$374$	−5.72244	+	25.3699i	−0.295900	+	1.31185i
$375$	2.75363	+	1.58981i	0.142197	+	0.0820975i
$376$	−4.52788	+	31.6845i	−0.233507	+	1.63400i
$377$		−	3.60716i		−	0.185778i
$378$	−44.6406	+	19.9534i	−2.29606	+	1.02629i
$379$	−25.9215			−1.33150			−0.665748	−	0.746177i	$-0.731887\pi$
$379$	−25.9215			−1.33150			−0.665748	+	0.746177i	$0.731887\pi$
$380$	1.51672	−	3.19106i	0.0778061	−	0.163698i
$381$	14.9504	−	25.8948i	0.765930	−	1.32663i
$382$	8.06690	−	35.7638i	0.412738	−	1.82984i
$383$	−16.8541	−	29.1922i	−0.861205	−	1.49165i	−0.870766	−	0.491697i	$-0.836377\pi$
$383$	−16.8541	−	29.1922i	−0.861205	−	1.49165i	0.00956071	−	0.999954i	$-0.496957\pi$
$384$	18.5403	+	30.8276i	0.946130	+	1.57316i
$385$	2.52293	−	5.88488i	0.128580	−	0.299921i
$386$	2.98442	+	9.58832i	0.151903	+	0.488032i
$387$	−4.95364	−	8.57995i	−0.251807	−	0.436143i
$388$	0.496708	−	0.0397735i	0.0252165	−	0.00201919i
$389$	29.0131	+	16.7507i	1.47102	+	0.849294i	0.999470	−	0.0325451i	$-0.0103612\pi$
$389$	29.0131	+	16.7507i	1.47102	+	0.849294i	0.471550	+	0.881839i	$0.343695\pi$
$390$	5.08275	+	4.69202i	0.257375	+	0.237590i
$391$	−49.6853			−2.51269
$392$	1.88261	+	19.7093i	0.0950860	+	0.995469i
$393$	59.8271			3.01788
$394$	0.638119	+	0.589065i	0.0321480	+	0.0296766i
$395$	1.75753	+	1.01471i	0.0884311	+	0.0510557i
$396$	−2.74683	−	34.3035i	−0.138033	−	1.72382i
$397$	−2.24042	−	3.88052i	−0.112443	−	0.194757i	0.804312	−	0.594208i	$-0.202534\pi$
$397$	−2.24042	−	3.88052i	−0.112443	−	0.194757i	−0.916755	+	0.399450i	$0.869201\pi$
$398$	−3.75863	−	12.0757i	−0.188403	−	0.605299i
$399$	5.85583	−	13.6591i	0.293158	−	0.683809i
$400$	1.42328	−	3.73822i	0.0711640	−	0.186911i
$401$	−15.5291	−	26.8973i	−0.775488	−	1.34318i	−0.934520	−	0.355911i	$-0.884171\pi$
$401$	−15.5291	−	26.8973i	−0.775488	−	1.34318i	0.159032	−	0.987273i	$-0.449163\pi$
$402$	6.19887	−	27.4821i	0.309172	−	1.37068i
$403$	1.60189	−	2.77456i	0.0797960	−	0.138211i
$404$	17.6211	+	8.37534i	0.876681	+	0.416689i
$405$	20.2222			1.00485
$406$	−8.00994	+	3.58027i	−0.397527	+	0.177686i
$407$		−	6.90332i		−	0.342185i
$408$	−9.66788	+	67.6525i	−0.478631	+	3.34930i
$409$	−22.6647	−	13.0855i	−1.12070	−	0.647034i	−0.179117	−	0.983828i	$-0.557324\pi$
$409$	−22.6647	−	13.0855i	−1.12070	−	0.647034i	−0.941579	+	0.336794i	$0.890658\pi$
$410$	2.14820	−	9.52384i	0.106092	−	0.470349i
$411$	41.6059	−	24.0212i	2.05227	−	1.18488i
$412$	−9.87849	+	6.80915i	−0.486678	+	0.335463i
$413$	−11.9897	+	8.96767i	−0.589976	+	0.441270i
$414$	62.7741	−	19.5388i	3.08518	−	0.960280i
$415$	−0.250215	+	0.144462i	−0.0122826	+	0.00709134i
$416$	4.80991	−	7.25195i	0.235825	−	0.355556i
$417$	−17.6776	+	30.6186i	−0.865678	+	1.49940i
$418$	4.44260	+	4.10108i	0.217295	+	0.200590i
$419$		−	3.71538i		−	0.181508i	−0.995873	−	0.0907540i	$-0.971072\pi$
$419$		−	3.71538i		−	0.181508i	0.995873	−	0.0907540i	$-0.0289277\pi$
$420$	5.37409	−	15.9436i	0.262229	−	0.777969i
$421$			9.89335i			0.482172i	0.970504	+	0.241086i	$0.0775037\pi$
$421$			9.89335i			0.482172i	−0.970504	+	0.241086i	$0.922496\pi$
$422$	10.2407	−	11.0935i	0.498511	−	0.540024i
$423$	40.2283	−	69.6775i	1.95597	−	3.38784i
$424$	−8.29917	−	20.6790i	−0.403043	−	1.00426i
$425$	6.58087	−	3.79947i	0.319219	−	0.184301i
$426$	5.32144	+	17.0966i	0.257824	+	0.828335i
$427$	−25.9344	+	3.08997i	−1.25505	+	0.149534i
$428$	−0.206269	+	0.142179i	−0.00997039	+	0.00687250i
$429$	−10.2513	+	5.91862i	−0.494940	+	0.285753i
$430$	1.92231	+	0.433596i	0.0927019	+	0.0209099i
$431$	21.9155	+	12.6529i	1.05563	+	0.609471i	0.924222	−	0.381857i	$-0.124715\pi$
$431$	21.9155	+	12.6529i	1.05563	+	0.609471i	0.131413	+	0.991328i	$0.458049\pi$
$432$	−8.31811	−	51.6070i	−0.400205	−	2.48294i
$433$			3.51643i			0.168989i	0.996424	+	0.0844944i	$0.0269275\pi$
$433$			3.51643i			0.168989i	−0.996424	+	0.0844944i	$0.973073\pi$
$434$	−7.75105	−	0.803235i	−0.372062	−	0.0385565i
$435$	7.45579			0.357478
$436$	−0.396342	+	0.833872i	−0.0189813	+	0.0399352i
$437$	−5.77537	+	10.0032i	−0.276273	+	0.478520i
$438$	−13.8424	−	3.12230i	−0.661416	−	0.149189i
$439$	4.56047	+	7.89896i	0.217659	+	0.376997i	0.954092	−	0.299514i	$-0.0968245\pi$
$439$	4.56047	+	7.89896i	0.217659	+	0.376997i	−0.736433	+	0.676511i	$0.763491\pi$
$440$	5.38413	+	4.22668i	0.256678	+	0.201499i
$441$	14.0613	−	47.7424i	0.669584	−	2.27345i
$442$	15.7847	−	4.91308i	0.750801	−	0.233691i
$443$	−1.72708	−	2.99140i	−0.0820563	−	0.142126i	0.822077	−	0.569377i	$-0.192815\pi$
$443$	−1.72708	−	2.99140i	−0.0820563	−	0.142126i	−0.904133	+	0.427251i	$0.859482\pi$
$444$	−1.44791	−	18.0821i	−0.0687147	−	0.858138i
$445$	−12.0399	−	6.95124i	−0.570746	−	0.329520i
$446$	−1.34546	+	1.45750i	−0.0637094	+	0.0690148i
$447$	35.5402			1.68099
$448$	−20.8775	−	3.48285i	−0.986369	−	0.164549i
$449$	10.3646			0.489133			0.244567	−	0.969632i	$-0.421354\pi$
$449$	10.3646			0.489133			0.244567	+	0.969632i	$0.421354\pi$
$450$	−6.82035	+	7.38832i	−0.321514	+	0.348289i
$451$	14.4687	+	8.35353i	0.681306	+	0.393352i
$452$	1.54058	+	19.2394i	0.0724627	+	0.904945i
$453$	−24.2011	−	41.9175i	−1.13707	−	1.96946i
$454$	5.43272	−	1.69097i	0.254970	−	0.0793610i
$455$	−4.04144	+	0.481521i	−0.189465	+	0.0225740i
$456$	12.4968	+	9.81031i	0.585217	+	0.459410i
$457$	13.4566	+	23.3076i	0.629475	+	1.09028i	0.987657	+	0.156630i	$0.0500632\pi$
$457$	13.4566	+	23.3076i	0.629475	+	1.09028i	−0.358183	+	0.933652i	$0.616603\pi$
$458$	−29.9860	−	6.76366i	−1.40116	−	0.316045i
$459$	49.6525	−	86.0006i	2.31758	−	4.01417i
$460$	−5.61365	+	11.8107i	−0.261738	+	0.550676i
$461$	9.19023			0.428032			0.214016	−	0.976830i	$-0.431346\pi$
$461$	9.19023			0.428032			0.214016	+	0.976830i	$0.431346\pi$
$462$	23.3176	+	16.8893i	1.08483	+	0.785762i
$463$			10.8548i			0.504464i	0.967667	+	0.252232i	$0.0811645\pi$
$463$			10.8548i			0.504464i	−0.967667	+	0.252232i	$0.918835\pi$
$464$	−1.49253	−	9.25994i	−0.0692891	−	0.429882i
$465$	5.73485	+	3.31102i	0.265947	+	0.153545i
$466$	15.7057	+	3.54257i	0.727551	+	0.164107i
$467$	25.9792	−	14.9991i	1.20218	−	0.694077i	0.241137	−	0.970491i	$-0.422480\pi$
$467$	25.9792	−	14.9991i	1.20218	−	0.694077i	0.961039	+	0.276414i	$0.0891463\pi$
$468$	−18.0108	+	12.4147i	−0.832551	+	0.573870i
$469$	9.92825	+	13.2740i	0.458444	+	0.612937i
$470$	4.75604	+	15.2801i	0.219380	+	0.704821i
$471$	−1.97070	+	1.13778i	−0.0908051	+	0.0524263i
$472$	−5.96160	−	14.8545i	−0.274405	−	0.683734i
$473$	−1.68609	+	2.92039i	−0.0775265	+	0.134280i
$474$	−6.18993	+	6.70539i	−0.284313	+	0.307989i
$475$		−	1.76659i		−	0.0810565i
$476$	−26.5768	−	30.1745i	−1.21815	−	1.38305i
$477$			56.0123i			2.56463i
$478$	−26.7604	−	24.7033i	−1.22399	−	1.12990i
$479$	4.67977	−	8.10560i	0.213824	−	0.370355i	−0.739084	−	0.673613i	$-0.764741\pi$
$479$	4.67977	−	8.10560i	0.213824	−	0.370355i	0.952908	+	0.303259i	$0.0980747\pi$
$480$	14.9894	+	9.94181i	0.684167	+	0.453779i
$481$	−3.80022	+	2.19406i	−0.173275	+	0.100041i
$482$	−2.60484	+	0.810773i	−0.118647	+	0.0369297i
$483$	−21.6735	+	50.5547i	−0.986177	+	2.30032i
$484$	8.46949	−	5.83794i	0.384977	−	0.265361i
$485$	0.215769	−	0.124575i	0.00979758	−	0.00565664i
$486$	−7.80859	+	34.6187i	−0.354205	+	1.57033i
$487$	14.9682	+	8.64189i	0.678273	+	0.391601i	0.799204	−	0.601060i	$-0.205255\pi$
$487$	14.9682	+	8.64189i	0.678273	+	0.391601i	−0.120931	+	0.992661i	$0.538588\pi$
$488$	3.94993	−	27.6403i	0.178805	−	1.25122i
$489$			5.65976i			0.255943i
$490$	5.08056	+	8.49635i	0.229516	+	0.383826i
$491$	−28.4313			−1.28309			−0.641543	−	0.767087i	$-0.721705\pi$
$491$	−28.4313			−1.28309			−0.641543	+	0.767087i	$0.721705\pi$
$492$	39.6505	+	18.8460i	1.78758	+	0.849643i
$493$	8.90924	−	15.4313i	0.401252	−	0.694989i
$494$	0.845637	−	3.74905i	0.0380470	−	0.168678i
$495$	−8.60334	−	14.9014i	−0.386691	−	0.669769i
$496$	2.96419	−	7.78539i	0.133096	−	0.349575i
$497$	−9.68301	−	4.15124i	−0.434343	−	0.186209i
$498$	−0.386110	−	1.24049i	−0.0173020	−	0.0555877i
$499$	12.1835	+	21.1025i	0.545409	+	0.944676i	0.998581	+	0.0532527i	$0.0169589\pi$
$499$	12.1835	+	21.1025i	0.545409	+	0.944676i	−0.453172	+	0.891423i	$0.649708\pi$
$500$	−0.159637	−	1.99362i	−0.00713920	−	0.0891573i
$501$	−15.6725	−	9.04850i	−0.700194	−	0.404257i
$502$	13.5034	+	12.4654i	0.602687	+	0.556357i
$503$	22.0798			0.984489			0.492245	−	0.870457i	$-0.336177\pi$
$503$	22.0798			0.984489			0.492245	+	0.870457i	$0.336177\pi$
$504$	45.4442	+	27.6721i	2.02425	+	1.23261i
$505$	9.75511			0.434097
$506$	−16.4429	−	15.1788i	−0.730974	−	0.674782i
$507$	−29.2809	−	16.9054i	−1.30041	−	0.750794i
$508$	−18.7477	+	1.50121i	−0.831795	+	0.0666052i
$509$	−7.47946	−	12.9548i	−0.331521	−	0.574212i	0.651289	−	0.758830i	$-0.274229\pi$
$509$	−7.47946	−	12.9548i	−0.331521	−	0.574212i	−0.982810	+	0.184618i	$0.940895\pi$
$510$	10.1550	+	32.6260i	0.449673	+	1.44470i
$511$	6.68596	−	5.00074i	0.295770	−	0.221220i
$512$	9.34690	−	20.6067i	0.413078	−	0.910695i
$513$	−11.5431	−	19.9933i	−0.509641	−	0.882724i
$514$	−5.17803	+	22.9563i	−0.228393	+	1.01256i
$515$	−2.99947	+	5.19523i	−0.132172	+	0.228929i
$516$	−3.80391	+	8.00313i	−0.167458	+	0.352318i
$517$	−27.3854			−1.20441
$518$	8.64395	+	6.26095i	0.379793	+	0.275090i
$519$			60.2183i			2.64329i
$520$	0.615531	−	4.30728i	0.0269928	−	0.188887i
$521$	13.6812	+	7.89884i	0.599384	+	0.346055i	0.768799	−	0.639490i	$-0.220855\pi$
$521$	13.6812	+	7.89884i	0.599384	+	0.346055i	−0.169415	+	0.985545i	$0.554188\pi$
$522$	−5.18787	+	22.9999i	−0.227067	+	1.00668i
$523$	17.4282	−	10.0622i	0.762083	−	0.439989i	−0.0679602	−	0.997688i	$-0.521649\pi$
$523$	17.4282	−	10.0622i	0.762083	−	0.439989i	0.830043	+	0.557699i	$0.188316\pi$
$524$	−21.3570	−	30.9840i	−0.932985	−	1.35354i
$525$	−0.995275	−	8.35341i	−0.0434374	−	0.364573i
$526$	9.28474	−	2.88993i	0.404834	−	0.126007i
$527$	13.7056	−	7.91296i	0.597027	−	0.344694i
$528$	−23.8673	+	19.4354i	−1.03869	+	0.845817i
$529$	9.87568	−	17.1052i	0.429377	−	0.743703i
$530$	−8.18633	−	7.55702i	−0.355591	−	0.328256i
$531$			40.2358i			1.74608i
$532$	−9.16435	+	1.84331i	−0.397325	+	0.0799176i
$533$		−	10.6199i		−	0.459999i
$534$	42.4038	−	45.9349i	1.83499	−	1.98780i
$535$	−0.0626308	+	0.108480i	−0.00270776	+	0.00468999i
$536$	−16.4457	+	6.60019i	−0.710345	+	0.285085i
$537$	−8.21532	+	4.74312i	−0.354517	+	0.204681i
$538$	9.30021	+	29.8796i	0.400961	+	1.28820i
$539$	−16.4662	+	3.98027i	−0.709250	+	0.171442i
$540$	−14.8333	−	21.5196i	−0.638322	−	0.926056i
$541$	−14.0280	+	8.09904i	−0.603109	+	0.348205i	−0.770264	−	0.637726i	$-0.779875\pi$
$541$	−14.0280	+	8.09904i	−0.603109	+	0.348205i	0.167155	+	0.985931i	$0.446542\pi$
$542$	14.6108	+	3.29561i	0.627587	+	0.141559i
$543$	−41.2467	−	23.8138i	−1.77007	−	1.02195i
$544$	38.4880	−	19.1436i	1.65016	−	0.820775i
$545$			0.461636i			0.0197743i
$546$	1.88647	−	18.2040i	0.0807335	−	0.779061i
$547$	−29.9614			−1.28106			−0.640529	−	0.767934i	$-0.721285\pi$
$547$	−29.9614			−1.28106			−0.640529	+	0.767934i	$0.721285\pi$
$548$	−27.2929	−	12.9724i	−1.16589	−	0.554152i
$549$	−35.0936	+	60.7838i	−1.49776	+	2.59419i
$550$	3.33861	+	0.753058i	0.142359	+	0.0321105i
$551$	−2.07120	−	3.58743i	−0.0882362	−	0.152830i
$552$	−46.2530	−	36.3097i	−1.96866	−	1.54544i
$553$	−0.635244	−	5.33165i	−0.0270133	−	0.226725i
$554$	−25.7320	+	8.00924i	−1.09325	+	0.340280i
$555$	−4.53499	−	7.85484i	−0.192500	−	0.333419i
$556$	22.1677	−	1.77506i	0.940120	−	0.0752793i
$557$	−36.5898	−	21.1251i	−1.55036	−	0.895100i	−0.998112	−	0.0614182i	$-0.980438\pi$
$557$	−36.5898	−	21.1251i	−1.55036	−	0.895100i	−0.552246	−	0.833681i	$-0.686229\pi$
$558$	−14.2044	+	15.3873i	−0.601320	+	0.651395i
$559$	2.14354			0.0906621
$560$	−10.1755	+	2.90834i	−0.429995	+	0.122900i
$561$	−58.4730			−2.46873
$562$	−16.9099	+	18.3180i	−0.713299	+	0.772699i
$563$	19.4740	+	11.2433i	0.820731	+	0.473849i	0.850669	−	0.525702i	$-0.176197\pi$
$563$	19.4740	+	11.2433i	0.820731	+	0.473849i	−0.0299372	+	0.999552i	$0.509531\pi$
$564$	−71.7315	+	5.74384i	−3.02044	+	0.241859i
$565$	4.82525	+	8.35757i	0.203000	+	0.351606i
$566$	0.757237	−	0.235695i	0.0318291	−	0.00990698i
$567$	−32.0454	−	42.8445i	−1.34578	−	1.79930i
$568$	6.95460	−	8.85908i	0.291808	−	0.371719i
$569$	−15.7198	−	27.2275i	−0.659008	−	1.14144i	−0.980873	−	0.194650i	$-0.937643\pi$
$569$	−15.7198	−	27.2275i	−0.659008	−	1.14144i	0.321864	−	0.946786i	$-0.395690\pi$
$570$	7.74907	+	1.74788i	0.324573	+	0.0732107i
$571$	−4.27788	+	7.40950i	−0.179024	+	0.310078i	−0.941546	−	0.336883i	$-0.890627\pi$
$571$	−4.27788	+	7.40950i	−0.179024	+	0.310078i	0.762523	+	0.646961i	$0.223961\pi$
$572$	6.72473	+	3.19628i	0.281175	+	0.133643i
$573$	82.4291			3.44353
$574$	−23.5822	+	10.5407i	−0.984302	+	0.439962i
$575$			6.53845i			0.272672i
$576$	−41.0988	+	39.3221i	−1.71245	+	1.63842i
$577$	35.0221	+	20.2200i	1.45799	+	0.841771i	0.998912	−	0.0466251i	$-0.0148466\pi$
$577$	35.0221	+	20.2200i	1.45799	+	0.841771i	0.459078	+	0.888396i	$0.348180\pi$
$578$	56.2083	+	12.6784i	2.33796	+	0.527350i
$579$	−19.5530	+	11.2889i	−0.812595	+	0.469152i
$580$	−2.66156	−	3.86130i	−0.110515	−	0.160332i
$581$	0.702576	+	0.301204i	0.0291478	+	0.0124960i
$582$	0.332957	+	1.06972i	0.0138015	+	0.0443413i
$583$	16.5109	−	9.53258i	0.683812	−	0.394799i
$584$	3.32443	+	8.28349i	0.137566	+	0.342773i
$585$	−5.46874	+	9.47214i	−0.226105	+	0.391625i
$586$	−22.8320	+	24.7333i	−0.943180	+	1.02172i
$587$		−	46.5032i		−	1.91939i	−0.281038	−	0.959697i	$-0.590679\pi$
$587$		−	46.5032i		−	1.91939i	0.281038	−	0.959697i	$-0.409321\pi$
$588$	−42.2957	+	13.8793i	−1.74425	+	0.572372i
$589$		−	3.67918i		−	0.151598i
$590$	−5.88055	−	5.42849i	−0.242098	−	0.223487i
$591$	−0.976274	+	1.69096i	−0.0401586	+	0.0695567i
$592$	−8.84772	+	7.20479i	−0.363639	+	0.296115i
$593$	5.42655	−	3.13302i	0.222842	−	0.128658i	−0.384424	−	0.923157i	$-0.625600\pi$
$593$	5.42655	−	3.13302i	0.222842	−	0.128658i	0.607265	+	0.794499i	$0.292267\pi$
$594$	42.7052	−	13.2922i	1.75221	−	0.545387i
$595$	−18.4784	−	7.92193i	−0.757539	−	0.324767i
$596$	−12.6871	−	18.4060i	−0.519684	−	0.753940i
$597$	24.6253	−	14.2175i	1.00785	−	0.581882i
$598$	−3.12985	+	13.8759i	−0.127989	+	0.567428i
$599$	−35.7470	−	20.6385i	−1.46058	−	0.843268i	−0.461544	−	0.887117i	$-0.652705\pi$
$599$	−35.7470	−	20.6385i	−1.46058	−	0.843268i	−0.999038	+	0.0438493i	$0.986038\pi$
$600$	8.90289	+	1.27227i	0.363459	+	0.0519401i
$601$			18.4478i			0.752502i	0.926518	+	0.376251i	$0.122787\pi$
$601$			18.4478i			0.752502i	−0.926518	+	0.376251i	$0.877213\pi$
$602$	−2.12756	−	4.75987i	−0.0867129	−	0.193998i
$603$	44.5457			1.81404
$604$	−13.0695	+	27.4973i	−0.531791	+	1.11885i
$605$	2.57165	−	4.45422i	0.104552	−	0.181090i
$606$	−9.65182	+	42.7904i	−0.392078	+	1.73824i
$607$	3.76477	+	6.52077i	0.152807	+	0.264670i	0.932258	−	0.361793i	$-0.117835\pi$
$607$	3.76477	+	6.52077i	0.152807	+	0.264670i	−0.779451	+	0.626463i	$0.784502\pi$
$608$	0.619591	−	9.97409i	0.0251277	−	0.404503i
$609$	−11.8149	−	15.7965i	−0.478765	−	0.640106i
$610$	−4.14897	−	13.3298i	−0.167987	−	0.539707i
$611$	8.70382	+	15.0755i	0.352119	+	0.609888i
$612$	−107.712	+	8.62496i	−4.35401	+	0.348643i
$613$	15.3991	+	8.89067i	0.621963	+	0.359091i	0.777633	−	0.628719i	$-0.216420\pi$
$613$	15.3991	+	8.89067i	0.621963	+	0.359091i	−0.155670	+	0.987809i	$0.549754\pi$
$614$	−9.68648	−	8.94185i	−0.390914	−	0.360864i
$615$	21.9507			0.885138
$616$	0.422960	−	18.1052i	0.0170415	−	0.729478i
$617$	−25.4606			−1.02500			−0.512502	−	0.858686i	$-0.671281\pi$
$617$	−25.4606			−1.02500			−0.512502	+	0.858686i	$0.671281\pi$
$618$	−19.8210	−	18.2973i	−0.797317	−	0.736025i
$619$	1.54568	+	0.892398i	0.0621261	+	0.0358685i	0.530741	−	0.847534i	$-0.321914\pi$
$619$	1.54568	+	0.892398i	0.0621261	+	0.0358685i	−0.468615	+	0.883402i	$0.655247\pi$
$620$	−0.332468	−	4.15201i	−0.0133522	−	0.166749i
$621$	42.7231	+	73.9987i	1.71442	+	2.96946i
$622$	2.29699	+	7.37974i	0.0921009	+	0.295901i
$623$	4.35170	+	36.5242i	0.174347	+	1.46331i
$624$	18.2847	+	6.96168i	0.731974	+	0.278690i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.18332	+	31.8466i	−0.287103	+	1.27285i
$627$	−6.79685	+	11.7725i	−0.271440	+	0.470148i
$628$	1.29275	+	0.614447i	0.0515863	+	0.0245191i
$629$	−21.6762			−0.864288
$630$	26.4615	+	2.74219i	1.05425	+	0.109251i
$631$			25.2033i			1.00333i	0.865063	+	0.501663i	$0.167278\pi$
$631$			25.2033i			1.00333i	−0.865063	+	0.501663i	$0.832722\pi$
$632$	5.68235	+	0.812037i	0.226032	+	0.0323011i
$633$	29.3968	+	16.9723i	1.16842	+	0.674587i
$634$	−9.41950	+	41.7605i	−0.374096	+	1.65852i
$635$	−8.14398	+	4.70193i	−0.323184	+	0.186590i
$636$	41.2482	−	28.4320i	1.63560	−	1.12740i
$637$	7.42451	+	7.79949i	0.294170	+	0.309027i
$638$	7.66267	−	2.38505i	0.303368	−	0.0944251i
$639$	−24.5189	+	14.1560i	−0.969952	+	0.560002i
$640$	−0.202090	−	11.3119i	−0.00798829	−	0.447142i
$641$	1.24626	−	2.15858i	0.0492242	−	0.0852587i	−0.840363	−	0.542023i	$-0.817658\pi$
$641$	1.24626	−	2.15858i	0.0492242	−	0.0852587i	0.889588	+	0.456765i	$0.150992\pi$
$642$	−0.413875	−	0.382059i	−0.0163343	−	0.0150787i
$643$		−	39.1121i		−	1.54243i	−0.636575	−	0.771215i	$-0.719650\pi$
$643$		−	39.1121i		−	1.54243i	0.636575	−	0.771215i	$-0.280350\pi$
$644$	33.9189	−	6.82242i	1.33659	−	0.268841i
$645$			4.43057i			0.174454i
$646$	12.8773	−	13.9496i	0.506650	−	0.548841i
$647$	−7.69474	+	13.3277i	−0.302512	+	0.523965i	−0.976704	−	0.214590i	$-0.931158\pi$
$647$	−7.69474	+	13.3277i	−0.302512	+	0.523965i	0.674193	+	0.738556i	$0.264492\pi$
$648$	53.0816	−	21.3034i	2.08524	−	0.836876i
$649$	11.8604	−	6.84761i	0.465562	−	0.268792i
$650$	−0.646548	−	2.07722i	−0.0253597	−	0.0814754i
$651$	−2.07281	−	17.3972i	−0.0812398	−	0.681851i
$652$	2.93115	−	2.02042i	0.114793	−	0.0791256i
$653$	−1.33623	+	0.771475i	−0.0522909	+	0.0301902i	−0.525918	−	0.850536i	$-0.676278\pi$
$653$	−1.33623	+	0.771475i	−0.0522909	+	0.0301902i	0.473627	+	0.880726i	$0.342945\pi$
$654$	−2.02495	−	0.456748i	−0.0791818	−	0.0178603i
$655$	−16.2949	−	9.40788i	−0.636696	−	0.367596i
$656$	−4.39420	−	27.2624i	−0.171565	−	1.06442i
$657$		−	22.4371i		−	0.875355i
$658$	24.8371	−	34.2905i	0.968252	−	1.33678i
$659$	23.4292			0.912670			0.456335	−	0.889808i	$-0.349162\pi$
$659$	23.4292			0.912670			0.456335	+	0.889808i	$0.349162\pi$
$660$	−6.60652	+	13.8996i	−0.257159	+	0.541042i
$661$	10.1419	−	17.5663i	0.394474	−	0.683249i	−0.598560	−	0.801078i	$-0.704260\pi$
$661$	10.1419	−	17.5663i	0.394474	−	0.683249i	0.993034	+	0.117829i	$0.0375935\pi$
$662$	0.723385	+	0.163167i	0.0281152	+	0.00634166i
$663$	18.5843	+	32.1889i	0.721754	+	1.25011i
$664$	−0.504609	+	0.642793i	−0.0195826	+	0.0249452i
$665$	−3.74284	+	2.79945i	−0.145141	+	0.108558i
$666$	27.3865	−	8.52421i	1.06120	−	0.330306i
$667$	7.66589	+	13.2777i	0.296825	+	0.514115i
$668$	0.908584	+	11.3468i	0.0351542	+	0.439020i
$669$	−3.86225	−	2.22987i	−0.149323	−	0.0862119i
$670$	−6.00997	+	6.51045i	−0.232185	+	0.251520i
$671$	23.8899			0.922259
$672$	−2.68952	−	47.5122i	−0.103750	−	1.83282i
$673$	−14.3296			−0.552364			−0.276182	−	0.961105i	$-0.589069\pi$
$673$	−14.3296			−0.552364			−0.276182	+	0.961105i	$0.589069\pi$
$674$	−3.27725	+	3.55016i	−0.126235	+	0.136747i
$675$	−11.3175	−	6.53414i	−0.435609	−	0.251499i
$676$	1.69751	+	21.1993i	0.0652890	+	0.815357i
$677$	−9.11144	−	15.7815i	−0.350181	−	0.606531i	0.636100	−	0.771607i	$-0.280547\pi$
$677$	−9.11144	−	15.7815i	−0.350181	−	0.606531i	−0.986281	+	0.165075i	$0.947213\pi$
$678$	−41.4344	+	12.8967i	−1.59128	+	0.495295i
$679$	−0.605857	−	0.259739i	−0.0232506	−	0.00996787i
$680$	13.2717	−	16.9060i	0.508945	−	0.648317i
$681$	6.39628	+	11.0787i	0.245106	+	0.424536i
$682$	6.95315	+	1.56835i	0.266250	+	0.0600554i
$683$	11.4579	−	19.8456i	0.438422	−	0.759370i	−0.559146	−	0.829069i	$-0.688871\pi$
$683$	11.4579	−	19.8456i	0.438422	−	0.759370i	0.997568	+	0.0696995i	$0.0222041\pi$
$684$	−10.7839	+	22.6885i	−0.412332	+	0.867515i
$685$	−15.1095			−0.577302
$686$	9.95013	−	24.2280i	0.379898	−	0.925029i
$687$		−	69.1124i		−	2.63680i
$688$	5.50269	−	0.886932i	0.209788	−	0.0338140i
$689$	−10.4952	−	6.05942i	−0.399836	−	0.230846i
$690$	−28.6807	−	6.46922i	−1.09186	−	0.246279i
$691$	14.4278	−	8.32990i	0.548860	−	0.316884i	−0.199802	−	0.979836i	$-0.564030\pi$
$691$	14.4278	−	8.32990i	0.548860	−	0.316884i	0.748662	+	0.662952i	$0.230697\pi$
$692$	31.1867	−	21.4967i	1.18554	−	0.817181i
$693$	−17.9380	+	41.8415i	−0.681410	+	1.58943i
$694$	−3.90326	−	12.5403i	−0.148166	−	0.476025i
$695$	9.62962	−	5.55967i	0.365272	−	0.210890i
$696$	19.5708	−	7.85442i	0.741831	−	0.297721i
$697$	26.2299	−	45.4314i	0.993526	−	1.72084i
$698$	17.9093	−	19.4006i	0.677875	−	0.734325i
$699$			36.1987i			1.36916i
$700$	−3.97088	+	3.49744i	−0.150085	+	0.132191i
$701$		−	3.87396i		−	0.146317i	−0.997320	−	0.0731587i	$-0.976692\pi$
$701$		−	3.87396i		−	0.146317i	0.997320	−	0.0731587i	$-0.0233080\pi$
$702$	−20.8901	−	19.2842i	−0.788447	−	0.727837i
$703$	−2.51962	+	4.36412i	−0.0950294	+	0.164596i
$704$	18.5856	+	5.42269i	0.700471	+	0.204375i
$705$	−31.1601	+	17.9903i	−1.17356	+	0.677553i
$706$	−18.2516	+	5.68093i	−0.686909	+	0.213804i
$707$	−15.4586	−	20.6680i	−0.581380	−	0.777301i
$708$	29.6302	−	20.4238i	1.11357	−	0.767573i
$709$	24.1848	−	13.9631i	0.908281	−	0.524396i	0.0284031	−	0.999597i	$-0.490958\pi$
$709$	24.1848	−	13.9631i	0.908281	−	0.524396i	0.879878	+	0.475200i	$0.157624\pi$
$710$	1.23909	−	5.49337i	0.0465021	−	0.206163i
$711$	−12.4961	−	7.21462i	−0.468640	−	0.270569i
$712$	−38.9267	−	5.56281i	−1.45884	−	0.208475i
$713$			13.6173i			0.509972i
$714$	53.0320	−	73.2167i	1.98467	−	2.74006i
$715$	3.72284			0.139226
$716$	5.38913	+	2.56147i	0.201401	+	0.0957265i
$717$	40.9415	−	70.9127i	1.52899	−	2.64828i
$718$	−8.20185	+	36.3621i	−0.306090	+	1.35702i
$719$	−8.27114	−	14.3260i	−0.308461	−	0.534271i	0.669565	−	0.742754i	$-0.266481\pi$
$719$	−8.27114	−	14.3260i	−0.308461	−	0.534271i	−0.978026	+	0.208483i	$0.933147\pi$
$720$	−10.1195	+	26.5788i	−0.377133	+	0.990532i
$721$	15.7602	−	1.87777i	0.586942	−	0.0699317i
$722$	6.67392	+	21.4419i	0.248378	+	0.797985i
$723$	−3.06684	−	5.31193i	−0.114057	−	0.197553i
$724$	2.39121	+	29.8625i	0.0888686	+	1.10983i
$725$	−2.03071	−	1.17243i	−0.0754188	−	0.0435430i
$726$	16.9939	+	15.6875i	0.630701	+	0.582217i
$727$	−6.76375			−0.250854			−0.125427	−	0.992103i	$-0.540030\pi$
$727$	−6.76375			−0.250854			−0.125427	+	0.992103i	$0.540030\pi$
$728$	−10.1012	+	5.52147i	−0.374375	+	0.204639i
$729$	−19.1232			−0.708268
$730$	3.27923	+	3.02715i	0.121370	+	0.112040i
$731$	9.16996	+	5.29428i	0.339163	+	0.195816i
$732$	62.5756	−	5.01069i	2.31286	−	0.185200i
$733$	−17.1394	−	29.6863i	−0.633059	−	1.09649i	−0.986923	−	0.161193i	$-0.948466\pi$
$733$	−17.1394	−	29.6863i	−0.633059	−	1.09649i	0.353864	−	0.935297i	$-0.384867\pi$
$734$	14.9473	+	48.0224i	0.551713	+	1.77254i
$735$	−16.1211	+	15.3460i	−0.594635	+	0.566047i
$736$	−2.29322	+	36.9159i	−0.0845291	+	1.36074i
$737$	−7.58110	−	13.1309i	−0.279253	−	0.483681i
$738$	−15.2737	+	67.7146i	−0.562233	+	2.49261i
$739$	−19.2212	+	33.2921i	−0.707063	+	1.22467i	0.258879	+	0.965910i	$0.416647\pi$
$739$	−19.2212	+	33.2921i	−0.707063	+	1.22467i	−0.965942	+	0.258759i	$0.916687\pi$
$740$	−2.44907	+	5.15266i	−0.0900296	+	0.189415i
$741$	8.64088			0.317431
$742$	−3.03837	+	29.3196i	−0.111542	+	1.07636i
$743$		−	30.1845i		−	1.10736i	−0.832729	−	0.553681i	$-0.813223\pi$
$743$		−	30.1845i		−	1.10736i	0.832729	−	0.553681i	$-0.186777\pi$
$744$	18.5416	+	2.64968i	0.679767	+	0.0971422i
$745$	−9.67998	−	5.58874i	−0.354647	−	0.204755i
$746$	7.42420	−	32.9145i	0.271819	−	1.20509i
$747$	1.77903	−	1.02712i	0.0650913	−	0.0375805i
$748$	20.8736	+	30.2828i	0.763216	+	1.10725i
$749$	0.329083	−	0.0392089i	0.0120244	−	0.00143266i
$750$	4.29350	−	1.33638i	0.156776	−	0.0487976i
$751$	26.8007	−	15.4734i	0.977972	−	0.564632i	0.0763147	−	0.997084i	$-0.475685\pi$
$751$	26.8007	−	15.4734i	0.977972	−	0.564632i	0.901657	+	0.432451i	$0.142351\pi$
$752$	28.5814	+	35.0988i	1.04225	+	1.27992i
$753$	−20.6592	+	35.7828i	−0.752864	+	1.30400i
$754$	−3.74835	−	3.46021i	−0.136507	−	0.126013i
$755$			15.2226i			0.554008i
$756$	−22.0876	+	65.5284i	−0.803317	+	2.38325i
$757$			32.7932i			1.19189i	0.803025	+	0.595945i	$0.203223\pi$
$757$			32.7932i			1.19189i	−0.803025	+	0.595945i	$0.796777\pi$
$758$	−24.8654	+	26.9361i	−0.903153	+	0.978363i
$759$	25.1563	−	43.5721i	0.913117	−	1.58157i
$760$	−1.86104	−	4.63715i	−0.0675070	−	0.168207i
$761$	−11.1966	+	6.46436i	−0.405876	+	0.234333i	−0.689016	−	0.724746i	$-0.741957\pi$
$761$	−11.1966	+	6.46436i	−0.405876	+	0.234333i	0.283140	+	0.959079i	$0.408624\pi$
$762$	−12.5671	−	40.3754i	−0.455258	−	1.46265i
$763$	0.978062	−	0.731538i	0.0354082	−	0.0264835i
$764$	−29.4255	−	42.6895i	−1.06458	−	1.54445i
$765$	−46.7900	+	27.0142i	−1.69170	+	0.976702i
$766$	−46.5024	−	10.4891i	−1.68020	−	0.378986i
$767$	−7.53912	−	4.35271i	−0.272222	−	0.157167i
$768$	49.8192	+	10.3057i	1.79770	+	0.371874i
$769$		−	1.25520i		−	0.0452635i	−0.999744	−	0.0226318i	$-0.992795\pi$
$769$		−	1.25520i		−	0.0452635i	0.999744	−	0.0226318i	$-0.00720453\pi$
$770$	−3.69509	−	8.26682i	−0.133162	−	0.297915i
$771$	−52.9102			−1.90551
$772$	12.8265	+	6.09645i	0.461635	+	0.219416i
$773$	−11.0046	+	19.0605i	−0.395808	+	0.685559i	−0.993204	−	0.116387i	$-0.962869\pi$
$773$	−11.0046	+	19.0605i	−0.395808	+	0.685559i	0.597396	+	0.801946i	$0.296202\pi$
$774$	−13.6676	−	3.08287i	−0.491273	−	0.110812i
$775$	−1.04132	−	1.80363i	−0.0374055	−	0.0647882i
$776$	0.435142	−	0.554304i	0.0156207	−	0.0198984i
$777$	−9.45550	+	22.0555i	−0.339214	+	0.791238i
$778$	45.2375	−	14.0804i	1.62184	−	0.504808i
$779$	−6.09787	−	10.5618i	−0.218479	−	0.378416i
$780$	9.75137	−	0.780832i	0.349155	−	0.0279583i
$781$	8.34560	+	4.81833i	0.298629	+	0.172413i
$782$	−47.6611	+	51.6301i	−1.70436	+	1.84629i
$783$	−30.6433			−1.09510
$784$	22.2867	+	16.9500i	0.795953	+	0.605359i
$785$	0.715672			0.0255434
$786$	57.3897	−	62.1689i	2.04702	−	2.21749i
$787$	29.8525	+	17.2354i	1.06413	+	0.614375i	0.926571	−	0.376119i	$-0.122742\pi$
$787$	29.8525	+	17.2354i	1.06413	+	0.614375i	0.137557	+	0.990494i	$0.456075\pi$
$788$	1.22424	−	0.0980303i	0.0436119	−	0.00349219i
$789$	10.9315	+	18.9339i	0.389172	+	0.674066i
$790$	2.74037	−	0.852955i	0.0974978	−	0.0303468i
$791$	10.0607	−	23.4671i	0.357717	−	0.834395i
$792$	−38.2812	−	30.0517i	−1.36026	−	1.06784i
$793$	−7.59285	−	13.1512i	−0.269630	−	0.467013i
$794$	−6.18156	−	1.39431i	−0.219375	−	0.0494823i
$795$	12.5245	−	21.6930i	0.444197	−	0.769372i
$796$	−16.1539	−	7.67797i	−0.572558	−	0.272138i
$797$	21.2444			0.752515			0.376258	−	0.926515i	$-0.377211\pi$
$797$	21.2444			0.752515			0.376258	+	0.926515i	$0.377211\pi$
$798$	−8.57646	−	19.1877i	−0.303604	−	0.679236i
$799$			85.9894i			3.04209i
$800$	−2.51925	−	5.06492i	−0.0890688	−	0.179072i
$801$	85.6037	+	49.4233i	3.02466	+	1.74629i
$802$	−42.8466	−	9.66449i	−1.51297	−	0.341265i
$803$	−6.61385	+	3.81851i	−0.233398	+	0.134752i
$804$	−22.6115	−	32.8040i	−0.797447	−	1.15691i
$805$	13.8529	−	10.3613i	0.488252	−	0.365186i
$806$	−1.34653	−	4.32612i	−0.0474296	−	0.152381i
$807$	−60.9321	+	35.1791i	−2.14491	+	1.23836i
$808$	25.6064	−	10.2767i	0.900829	−	0.361532i
$809$	−1.39597	+	2.41789i	−0.0490796	+	0.0850084i	−0.889522	−	0.456893i	$-0.848962\pi$
$809$	−1.39597	+	2.41789i	−0.0490796	+	0.0850084i	0.840442	+	0.541902i	$0.182295\pi$
$810$	19.3983	−	21.0137i	0.681588	−	0.738348i
$811$		−	46.1196i		−	1.61948i	−0.586790	−	0.809739i	$-0.699609\pi$
$811$		−	46.1196i		−	1.61948i	0.586790	−	0.809739i	$-0.300391\pi$
$812$	−3.96321	+	11.7579i	−0.139081	+	0.412621i
$813$			33.6752i			1.18104i
$814$	−7.17354	−	6.62208i	−0.251432	−	0.232104i
$815$	0.890005	−	1.54153i	0.0311755	−	0.0539975i
$816$	61.0266	+	74.9427i	2.13636	+	2.62352i
$817$	2.13181	−	1.23080i	0.0745828	−	0.0430604i
$818$	−35.3390	+	10.9995i	−1.23560	+	0.384588i
$819$	28.7346	−	3.42362i	1.00407	−	0.119631i
$820$	−7.83595	−	11.3681i	−0.273643	−	0.396992i
$821$	47.1623	−	27.2292i	1.64598	−	0.950305i	0.667327	−	0.744765i	$-0.267438\pi$
$821$	47.1623	−	27.2292i	1.64598	−	0.950305i	0.978649	−	0.205540i	$-0.0658951\pi$
$822$	14.9495	−	66.2771i	0.521423	−	2.31168i
$823$	11.9130	+	6.87795i	0.415259	+	0.239750i	0.693047	−	0.720892i	$-0.256268\pi$
$823$	11.9130	+	6.87795i	0.415259	+	0.239750i	−0.277788	+	0.960643i	$0.589601\pi$
$824$	−2.40036	+	16.7969i	−0.0836206	+	0.585148i
$825$			7.69489i			0.267902i
$826$	−2.18257	+	21.0614i	−0.0759415	+	0.732819i
$827$	19.8375			0.689816			0.344908	−	0.938636i	$-0.387910\pi$
$827$	19.8375			0.689816			0.344908	+	0.938636i	$0.387910\pi$
$828$	39.9131	−	83.9741i	1.38708	−	2.91830i
$829$	1.25335	−	2.17087i	0.0435308	−	0.0753975i	−0.843439	−	0.537225i	$-0.819473\pi$
$829$	1.25335	−	2.17087i	0.0435308	−	0.0753975i	0.886970	+	0.461827i	$0.152806\pi$
$830$	−0.0899050	+	0.398585i	−0.00312065	+	0.0138351i
$831$	−30.2959	−	52.4741i	−1.05095	−	1.82031i
$832$	−2.92185	−	11.9547i	−0.101297	−	0.414455i
$833$	12.4979	+	51.7035i	0.433028	+	1.79142i
$834$	14.8596	+	47.7408i	0.514546	+	1.65313i
$835$	2.84578	+	4.92903i	0.0984822	+	0.170576i
$836$	8.52322	−	0.682489i	0.294782	−	0.0236044i
$837$	−23.5703	−	13.6083i	−0.814708	−	0.470372i
$838$	−3.86081	−	3.56401i	−0.133369	−	0.123117i
$839$	27.1009			0.935628			0.467814	−	0.883827i	$-0.345042\pi$
$839$	27.1009			0.935628			0.467814	+	0.883827i	$0.345042\pi$
$840$	−11.4126	−	20.8786i	−0.393771	−	0.720378i
$841$	23.5016			0.810400
$842$	10.2806	+	9.49031i	0.354293	+	0.327058i
$843$	−48.5411	−	28.0252i	−1.67184	−	0.965240i
$844$	−1.70423	−	21.2832i	−0.0586620	−	0.732597i
$845$	5.31678	+	9.20893i	0.182903	+	0.316797i
$846$	−33.8155	−	108.642i	−1.16260	−	3.73519i
$847$	−13.5123	+	1.60994i	−0.464288	+	0.0553180i
$848$	−29.4495	−	11.2125i	−1.01130	−	0.385040i
$849$	0.891543	+	1.54420i	0.0305977	+	0.0529967i
$850$	2.36458	−	10.4831i	0.0811045	−	0.359569i
$851$	9.32558	−	16.1524i	0.319677	−	0.553697i
$852$	22.8705	+	10.8704i	0.783531	+	0.372414i
$853$	8.16785			0.279662			0.139831	−	0.990175i	$-0.455344\pi$
$853$	8.16785			0.279662			0.139831	+	0.990175i	$0.455344\pi$
$854$	−21.6669	+	29.9136i	−0.741426	+	1.02362i
$855$			12.5604i			0.429558i
$856$	−0.0501211	+	0.350730i	−0.00171310	+	0.0119877i
$857$	−13.4380	−	7.75845i	−0.459035	−	0.265024i	0.252604	−	0.967570i	$-0.418713\pi$
$857$	−13.4380	−	7.75845i	−0.459035	−	0.265024i	−0.711638	+	0.702546i	$0.752046\pi$
$858$	−3.68342	+	16.3301i	−0.125750	+	0.557501i
$859$	46.6347	−	26.9246i	1.59116	−	0.918654i	0.598046	−	0.801462i	$-0.295944\pi$
$859$	46.6347	−	26.9246i	1.59116	−	0.918654i	0.993109	−	0.117192i	$-0.0373894\pi$
$860$	2.29456	−	1.58162i	0.0782440	−	0.0539328i
$861$	−34.7845	−	46.5067i	−1.18545	−	1.58494i
$862$	34.1710	−	10.6359i	1.16387	−	0.362261i
$863$	−33.2448	+	19.1939i	−1.13167	+	0.653368i	−0.944353	−	0.328932i	$-0.893311\pi$
$863$	−33.2448	+	19.1939i	−1.13167	+	0.653368i	−0.187313	+	0.982300i	$0.559978\pi$
$864$	−61.6063	−	40.8609i	−2.09589	−	1.39012i
$865$	9.46941	−	16.4015i	0.321969	−	0.557667i
$866$	3.65407	+	3.37317i	0.124170	+	0.114625i
$867$			129.550i			4.39975i
$868$	−8.26995	+	7.28394i	−0.280701	+	0.247233i
$869$			4.91134i			0.166606i
$870$	7.15204	−	7.74763i	0.242477	−	0.262669i
$871$	−4.81896	+	8.34668i	−0.163284	+	0.282816i
$872$	0.486318	+	1.21176i	0.0164688	+	0.0410353i
$873$	−1.53412	+	0.885726i	−0.0519222	+	0.0299773i
$874$	4.85471	+	15.5971i	0.164213	+	0.527581i
$875$	−1.04250	+	2.43170i	−0.0352431	+	0.0822066i
$876$	−16.5230	+	11.3891i	−0.558260	+	0.384804i
$877$	15.9417	−	9.20394i	0.538313	−	0.310795i	−0.206082	−	0.978535i	$-0.566071\pi$
$877$	15.9417	−	9.20394i	0.538313	−	0.310795i	0.744395	+	0.667740i	$0.232738\pi$
$878$	12.5828	+	2.83819i	0.424650	+	0.0957841i
$879$	−65.5410	−	37.8401i	−2.21064	−	1.27632i
$880$	9.55691	−	1.54040i	0.322163	−	0.0519268i
$881$			21.5756i			0.726902i	0.931613	+	0.363451i	$0.118402\pi$
$881$			21.5756i			0.726902i	−0.931613	+	0.363451i	$0.881598\pi$
$882$	−36.1228	−	60.4091i	−1.21632	−	2.03408i
$883$	23.5384			0.792131			0.396065	−	0.918222i	$-0.370375\pi$
$883$	23.5384			0.792131			0.396065	+	0.918222i	$0.370375\pi$
$884$	10.0362	−	21.1155i	0.337555	−	0.710190i
$885$	8.99680	−	15.5829i	0.302424	−	0.523814i
$886$	−4.76522	−	1.07484i	−0.160091	−	0.0361101i
$887$	16.6515	+	28.8413i	0.559104	+	0.968397i	0.997572	+	0.0696497i	$0.0221881\pi$
$887$	16.6515	+	28.8413i	0.559104	+	0.968397i	−0.438467	+	0.898747i	$0.644479\pi$
$888$	−20.1788	−	15.8409i	−0.677157	−	0.531585i
$889$	22.8674	+	9.80356i	0.766948	+	0.328801i
$890$	−18.7727	+	5.84313i	−0.629263	+	0.195862i
$891$	24.4695	+	42.3824i	0.819759	+	1.41986i
$892$	0.223908	+	2.79625i	0.00749698	+	0.0936255i
$893$	17.3124	+	9.99533i	0.579338	+	0.334481i
$894$	34.0923	−	36.9313i	1.14022	−	1.23517i
$895$	2.98345			0.0997256
$896$	−23.6461	+	18.3537i	−0.789962	+	0.613156i
$897$	−31.9815			−1.06783
$898$	9.94231	−	10.7703i	0.331779	−	0.359408i
$899$	−4.22926	−	2.44176i	−0.141054	−	0.0814374i
$900$	1.13502	+	14.1746i	0.0378341	+	0.472488i
$901$	−29.9320	−	51.8438i	−0.997181	−	1.72717i
$902$	22.5598	−	7.02187i	0.751159	−	0.233803i
$903$	9.38700	−	7.02097i	0.312380	−	0.233643i
$904$	21.4703	+	16.8547i	0.714092	+	0.560580i
$905$	7.48951	+	12.9722i	0.248960	+	0.431211i
$906$	−66.7735	−	15.0614i	−2.21840	−	0.500383i
$907$	−25.9103	+	44.8780i	−0.860338	+	1.49015i	0.0112647	+	0.999937i	$0.496414\pi$
$907$	−25.9103	+	44.8780i	−0.860338	+	1.49015i	−0.871603	+	0.490213i	$0.836919\pi$
$908$	3.45424	−	7.26745i	0.114633	−	0.241179i
$909$	−69.3589			−2.30049
$910$	−3.37642	+	4.66153i	−0.111927	+	0.154528i
$911$		−	3.37980i		−	0.111978i	−0.998431	−	0.0559889i	$-0.982169\pi$
$911$		−	3.37980i		−	0.111978i	0.998431	−	0.0559889i	$-0.0178312\pi$
$912$	22.1820	−	3.57534i	0.734520	−	0.118391i
$913$	−0.605536	−	0.349606i	−0.0200403	−	0.0115703i
$914$	37.1283	+	8.37467i	1.22810	+	0.277009i
$915$	27.1828	−	15.6940i	0.898635	−	0.518827i
$916$	−35.7928	+	24.6717i	−1.18263	+	0.815175i
$917$	5.88965	+	49.4322i	0.194493	+	1.63240i
$918$	−41.7373	−	134.093i	−1.37754	−	4.42573i
$919$	16.6978	−	9.64048i	0.550810	−	0.318010i	−0.198639	−	0.980073i	$-0.563652\pi$
$919$	16.6978	−	9.64048i	0.550810	−	0.318010i	0.749448	+	0.662063i	$0.230319\pi$
$920$	6.88804	+	17.1629i	0.227092	+	0.565845i
$921$	14.8196	−	25.6683i	0.488322	−	0.845799i
$922$	8.81583	−	9.54997i	0.290334	−	0.314511i
$923$		−	6.12558i		−	0.201626i
$924$	39.9181	−	8.02908i	1.31321	−	0.264137i
$925$			2.85253i			0.0937908i
$926$	11.2797	+	10.4125i	0.370672	+	0.342178i
$927$	21.3262	−	36.9381i	0.700446	−	1.21321i
$928$	−11.0541	−	7.33175i	−0.362870	−	0.240676i
$929$	29.0690	−	16.7830i	0.953724	−	0.550633i	0.0594882	−	0.998229i	$-0.481053\pi$
$929$	29.0690	−	16.7830i	0.953724	−	0.550633i	0.894236	+	0.447596i	$0.147720\pi$
$930$	8.94184	−	2.78320i	0.293215	−	0.0912648i
$931$	11.8623	+	3.49373i	0.388771	+	0.114502i
$932$	18.7471	−	12.9222i	0.614081	−	0.423280i
$933$	−15.0492	+	8.68863i	−0.492687	+	0.284453i
$934$	9.33463	−	41.3842i	0.305439	−	1.35413i
$935$	15.9261	+	9.19496i	0.520840	+	0.300707i
$936$	−4.37643	+	30.6248i	−0.143048	+	1.00100i
$937$		−	21.4342i		−	0.700224i	−0.936708	−	0.350112i	$-0.886144\pi$
$937$		−	21.4342i		−	0.700224i	0.936708	−	0.350112i	$-0.113856\pi$
$938$	23.3174	+	2.41636i	0.761340	+	0.0788971i
$939$	−73.4006			−2.39534
$940$	20.4405	+	9.71544i	0.666697	+	0.316883i
$941$	−7.43223	+	12.8730i	−0.242284	+	0.419648i	−0.961364	−	0.275279i	$-0.911230\pi$
$941$	−7.43223	+	12.8730i	−0.242284	+	0.419648i	0.719081	+	0.694927i	$0.244563\pi$
$942$	−0.708095	+	3.13927i	−0.0230710	+	0.102283i
$943$	22.5693	+	39.0912i	0.734957	+	1.27298i
$944$	−21.1547	−	8.05439i	−0.688527	−	0.262148i
$945$	4.09059	+	34.3326i	0.133067	+	1.11684i
$946$	1.41731	+	4.55351i	0.0460806	+	0.148047i
$947$	21.9761	+	38.0637i	0.714127	+	1.23690i	0.963295	+	0.268444i	$0.0865095\pi$
$947$	21.9761	+	38.0637i	0.714127	+	1.23690i	−0.249168	+	0.968460i	$0.580157\pi$
$948$	1.03011	+	12.8644i	0.0334564	+	0.417818i
$949$	4.20412	+	2.42725i	0.136472	+	0.0787919i
$950$	−1.83574	−	1.69462i	−0.0595591	−	0.0549806i
$951$	−96.2503			−3.12113
$952$	−56.8497	−	1.32808i	−1.84251	−	0.0430434i
$953$	−24.5807			−0.796246			−0.398123	−	0.917332i	$-0.630338\pi$
$953$	−24.5807			−0.796246			−0.398123	+	0.917332i	$0.630338\pi$
$954$	58.2048	+	53.7304i	1.88445	+	1.73959i
$955$	−22.4510	−	12.9621i	−0.726497	−	0.419443i
$956$	−51.3405	+	4.11104i	−1.66047	+	0.132961i
$957$	9.02174	+	15.6261i	0.291631	+	0.505120i
$958$	−3.93376	−	12.6383i	−0.127094	−	0.408326i
$959$	23.9434	+	32.0122i	0.773173	+	1.03373i
$960$	24.7097	−	6.03930i	0.797501	−	0.194917i
$961$	13.3313	+	23.0905i	0.430042	+	0.744854i
$962$	−1.36546	+	6.05365i	−0.0440243	+	0.195178i
$963$	0.445305	−	0.771291i	0.0143498	−	0.0248545i
$964$	−1.65621	+	3.48455i	−0.0533430	+	0.112230i
$965$	7.10080			0.228583
$966$	31.7430	+	71.0170i	1.02132	+	2.28493i
$967$			9.58755i			0.308315i	0.988046	+	0.154157i	$0.0492663\pi$
$967$			9.58755i			0.308315i	−0.988046	+	0.154157i	$0.950734\pi$
$968$	2.05799	−	14.4011i	0.0661463	−	0.462869i
$969$	36.9653	+	21.3419i	1.18750	+	0.685601i
$970$	0.0775284	−	0.343715i	0.00248929	−	0.0110360i
$971$	−19.5510	+	11.2878i	−0.627421	+	0.362242i	−0.779753	−	0.626088i	$-0.784655\pi$
$971$	−19.5510	+	11.2878i	−0.627421	+	0.362242i	0.152332	+	0.988329i	$0.451322\pi$
$972$	28.4833	+	41.3226i	0.913602	+	1.32542i
$973$	−27.0389	−	11.5920i	−0.866828	−	0.371621i
$974$	23.3386	−	7.26427i	0.747816	−	0.232762i
$975$	4.23598	−	2.44564i	0.135660	−	0.0783233i
$976$	−24.9332	−	30.6188i	−0.798092	−	0.980084i
$977$	9.57609	−	16.5863i	0.306366	−	0.530642i	−0.671198	−	0.741278i	$-0.734220\pi$
$977$	9.57609	−	16.5863i	0.306366	−	0.530642i	0.977565	+	0.210636i	$0.0675535\pi$
$978$	5.88130	+	5.42919i	0.188063	+	0.173606i
$979$		−	33.6449i		−	1.07529i
$980$	13.7025	+	2.87079i	0.437710	+	0.0917040i
$981$		−	3.28223i		−	0.104794i
$982$	−27.2730	+	29.5442i	−0.870317	+	0.942792i
$983$	−14.3326	+	24.8248i	−0.457139	+	0.791787i	−0.998808	−	0.0488042i	$-0.984459\pi$
$983$	−14.3326	+	24.8248i	−0.457139	+	0.791787i	0.541670	+	0.840591i	$0.317792\pi$
$984$	57.6189	−	23.1244i	1.83682	−	0.737177i
$985$	0.531810	−	0.307041i	0.0169449	−	0.00978314i
$986$	−7.48900	−	24.0606i	−0.238498	−	0.766245i
$987$	87.4941	+	37.5099i	2.78497	+	1.19395i
$988$	−3.08461	−	4.47506i	−0.0981347	−	0.142370i
$989$	−7.89023	+	4.55543i	−0.250895	+	0.144854i
$990$	−23.7375	−	5.35425i	−0.754429	−	0.170169i
$991$	17.8817	+	10.3240i	0.568030	+	0.327952i	0.756362	−	0.654153i	$-0.226975\pi$
$991$	17.8817	+	10.3240i	0.568030	+	0.327952i	−0.188332	+	0.982105i	$0.560308\pi$
$992$	−5.24670	−	10.5484i	−0.166583	−	0.334913i
$993$			1.66727i			0.0529093i
$994$	−13.6023	+	6.07992i	−0.431438	+	0.192843i
$995$	−8.94285			−0.283507
$996$	−1.65943	−	0.788730i	−0.0525810	−	0.0249919i
$997$	9.92952	−	17.1984i	0.314471	−	0.544680i	−0.664854	−	0.746973i	$-0.731506\pi$
$997$	9.92952	−	17.1984i	0.314471	−	0.544680i	0.979325	+	0.202294i	$0.0648395\pi$
$998$	33.6156	+	7.58235i	1.06408	+	0.240015i
$999$	18.6389	+	32.2834i	0.589707	+	1.02140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.f.171.9	yes	24
4.3	odd	2		1120.2.bz.e.591.1		24
7.5	odd	6		280.2.bj.e.131.2	✓	24
8.3	odd	2		280.2.bj.e.171.2	yes	24
8.5	even	2		1120.2.bz.f.591.1		24
28.19	even	6		1120.2.bz.f.271.1		24
56.5	odd	6		1120.2.bz.e.271.1		24
56.19	even	6	inner	280.2.bj.f.131.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.2	✓	24	7.5	odd	6
280.2.bj.e.171.2	yes	24	8.3	odd	2
280.2.bj.f.131.9	yes	24	56.19	even	6	inner
280.2.bj.f.171.9	yes	24	1.1	even	1	trivial
1120.2.bz.e.271.1		24	56.5	odd	6
1120.2.bz.e.591.1		24	4.3	odd	2
1120.2.bz.f.271.1		24	28.19	even	6
1120.2.bz.f.591.1		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)

\(f(q)\)	\(=\)	\(q+(0.959261 - 1.03914i) q^{2} +(2.75363 + 1.58981i) q^{3} +(-0.159637 - 1.99362i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.29350 - 1.33638i) q^{6} +(-1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 + 6.15745i) q^{9} +O(q^{10})\)	\(q+(0.959261 - 1.03914i) q^{2} +(2.75363 + 1.58981i) q^{3} +(-0.159637 - 1.99362i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.29350 - 1.33638i) q^{6} +(-1.04250 + 2.43170i) q^{7} +(-2.22479 - 1.74651i) q^{8} +(3.55500 + 6.15745i) q^{9} +(-1.37955 - 0.311173i) q^{10} +(1.21003 - 2.09584i) q^{11} +(2.72990 - 5.74349i) q^{12} -1.53832 q^{13} +(1.52685 + 3.41595i) q^{14} -3.17962i q^{15} +(-3.94903 + 0.636512i) q^{16} +(-6.58087 - 3.79947i) q^{17} +(9.80864 + 2.21244i) q^{18} +(-1.52991 + 0.883293i) q^{19} +(-1.64671 + 1.13506i) q^{20} +(-6.73663 + 5.03864i) q^{21} +(-1.01714 - 3.26785i) q^{22} +(5.66247 - 3.26923i) q^{23} +(-3.34963 - 8.34626i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.47565 + 1.59854i) q^{26} +13.0683i q^{27} +(5.01431 + 1.69017i) q^{28} +2.34486i q^{29} +(-3.30408 - 3.05009i) q^{30} +(-1.04132 + 1.80363i) q^{31} +(-3.12672 + 4.71419i) q^{32} +(6.66397 - 3.84745i) q^{33} +(-10.2610 + 3.19379i) q^{34} +(2.62717 - 0.313017i) q^{35} +(11.7081 - 8.07028i) q^{36} +(2.47037 - 1.42627i) q^{37} +(-0.549713 + 2.43710i) q^{38} +(-4.23598 - 2.44564i) q^{39} +(-0.400131 + 2.79998i) q^{40} +6.90356i q^{41} +(-1.22632 + 11.8337i) q^{42} -1.39343 q^{43} +(-4.37147 - 2.07777i) q^{44} +(3.55500 - 6.15745i) q^{45} +(2.03459 - 9.02015i) q^{46} +(-5.65799 - 9.79993i) q^{47} +(-11.8861 - 4.52550i) q^{48} +(-4.82637 - 5.07012i) q^{49} +(0.420294 + 1.35032i) q^{50} +(-12.0809 - 20.9247i) q^{51} +(0.245574 + 3.06683i) q^{52} +(6.82251 + 3.93898i) q^{53} +(13.5798 + 12.5359i) q^{54} -2.42006 q^{55} +(6.56636 - 3.58928i) q^{56} -5.61708 q^{57} +(2.43665 + 2.24934i) q^{58} +(4.90087 + 2.82952i) q^{59} +(-6.33896 + 0.507586i) q^{60} +(4.93580 + 8.54905i) q^{61} +(0.875325 + 2.81223i) q^{62} +(-18.6792 + 2.22555i) q^{63} +(1.89937 + 7.77125i) q^{64} +(0.769162 + 1.33223i) q^{65} +(2.39444 - 10.6155i) q^{66} +(3.13260 - 5.42583i) q^{67} +(-6.52414 + 13.7263i) q^{68} +20.7898 q^{69} +(2.19487 - 3.03027i) q^{70} +3.98199i q^{71} +(2.84494 - 19.9079i) q^{72} +(-2.73292 - 1.57785i) q^{73} +(0.887631 - 3.93523i) q^{74} +(-2.75363 + 1.58981i) q^{75} +(2.00518 + 2.90905i) q^{76} +(3.83499 + 5.12736i) q^{77} +(-6.60478 + 2.05578i) q^{78} +(-1.75753 + 1.01471i) q^{79} +(2.52575 + 3.10171i) q^{80} +(-10.1111 + 17.5129i) q^{81} +(7.17379 + 6.62231i) q^{82} -0.288923i q^{83} +(11.1205 + 12.6259i) q^{84} +7.59894i q^{85} +(-1.33666 + 1.44797i) q^{86} +(-3.72789 + 6.45690i) q^{87} +(-6.35248 + 2.54946i) q^{88} +(12.0399 - 6.95124i) q^{89} +(-2.98829 - 9.60076i) q^{90} +(1.60371 - 3.74075i) q^{91} +(-7.42153 - 10.7669i) q^{92} +(-5.73485 + 3.31102i) q^{93} +(-15.6110 - 3.52122i) q^{94} +(1.52991 + 0.883293i) q^{95} +(-16.1045 + 8.01026i) q^{96} +0.249149i q^{97} +(-9.89833 + 0.151716i) q^{98} +17.2067 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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