LMFDB - Embedded newform 315.2.k.c.16.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(16,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.349525 - 0.605394i) q^{2} +(1.42094 - 0.990413i) q^{3} +(0.755665 - 1.30885i) q^{4} +1.00000 q^{5} +(-1.09625 - 0.514057i) q^{6} +(-1.62523 - 2.08773i) q^{7} -2.45459 q^{8} +(1.03816 - 2.81464i) q^{9} +(-0.349525 - 0.605394i) q^{10} -3.83823 q^{11} +(-0.222545 - 2.60822i) q^{12} +(2.28027 + 3.94954i) q^{13} +(-0.695843 + 1.71362i) q^{14} +(1.42094 - 0.990413i) q^{15} +(-0.653390 - 1.13171i) q^{16} +(2.93173 + 5.07790i) q^{17} +(-2.06683 + 0.355289i) q^{18} +(0.386961 - 0.670236i) q^{19} +(0.755665 - 1.30885i) q^{20} +(-4.37708 - 1.35690i) q^{21} +(1.34156 + 2.32364i) q^{22} +6.90532 q^{23} +(-3.48784 + 2.43106i) q^{24} +1.00000 q^{25} +(1.59402 - 2.76092i) q^{26} +(-1.31249 - 5.02766i) q^{27} +(-3.96066 + 0.549558i) q^{28} +(-3.95301 + 6.84682i) q^{29} +(-1.09625 - 0.514057i) q^{30} +(2.01894 - 3.49691i) q^{31} +(-2.91134 + 5.04260i) q^{32} +(-5.45391 + 3.80144i) q^{33} +(2.04942 - 3.54970i) q^{34} +(-1.62523 - 2.08773i) q^{35} +(-2.89944 - 3.48573i) q^{36} +(4.23407 - 7.33362i) q^{37} -0.541010 q^{38} +(7.15181 + 3.35367i) q^{39} -2.45459 q^{40} +(-1.60838 - 2.78579i) q^{41} +(0.708437 + 3.12413i) q^{42} +(4.19469 - 7.26541i) q^{43} +(-2.90042 + 5.02367i) q^{44} +(1.03816 - 2.81464i) q^{45} +(-2.41358 - 4.18044i) q^{46} +(1.66963 + 2.89189i) q^{47} +(-2.04929 - 0.960963i) q^{48} +(-1.71725 + 6.78609i) q^{49} +(-0.349525 - 0.605394i) q^{50} +(9.19504 + 4.31179i) q^{51} +6.89248 q^{52} +(1.32630 + 2.29721i) q^{53} +(-2.58497 + 2.55186i) q^{54} -3.83823 q^{55} +(3.98928 + 5.12453i) q^{56} +(-0.113961 - 1.33562i) q^{57} +5.52670 q^{58} +(3.36978 - 5.83663i) q^{59} +(-0.222545 - 2.60822i) q^{60} +(-3.50639 - 6.07324i) q^{61} -2.82268 q^{62} +(-7.56348 + 2.40704i) q^{63} +1.45678 q^{64} +(2.28027 + 3.94954i) q^{65} +(4.20764 + 1.97307i) q^{66} +(-7.28514 + 12.6182i) q^{67} +8.86162 q^{68} +(9.81207 - 6.83912i) q^{69} +(-0.695843 + 1.71362i) q^{70} -9.67100 q^{71} +(-2.54827 + 6.90880i) q^{72} +(7.00941 + 12.1407i) q^{73} -5.91964 q^{74} +(1.42094 - 0.990413i) q^{75} +(-0.584826 - 1.01295i) q^{76} +(6.23801 + 8.01320i) q^{77} +(-0.469442 - 5.50185i) q^{78} +(6.69289 + 11.5924i) q^{79} +(-0.653390 - 1.13171i) q^{80} +(-6.84443 - 5.84412i) q^{81} +(-1.12433 + 1.94740i) q^{82} +(0.442527 - 0.766479i) q^{83} +(-5.08359 + 4.70358i) q^{84} +(2.93173 + 5.07790i) q^{85} -5.86458 q^{86} +(1.16417 + 13.6441i) q^{87} +9.42130 q^{88} +(0.950003 - 1.64545i) q^{89} +(-2.06683 + 0.355289i) q^{90} +(4.53962 - 11.1795i) q^{91} +(5.21811 - 9.03803i) q^{92} +(-0.594584 - 6.96851i) q^{93} +(1.16716 - 2.02157i) q^{94} +(0.386961 - 0.670236i) q^{95} +(0.857397 + 10.0487i) q^{96} +(-3.07725 + 5.32996i) q^{97} +(4.70848 - 1.33229i) q^{98} +(-3.98471 + 10.8033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.349525	−	0.605394i	−0.247151	−	0.428078i	0.715583	−	0.698528i	$-0.246161\pi$
$2$	−0.349525	−	0.605394i	−0.247151	−	0.428078i	−0.962734	+	0.270449i	$0.912828\pi$
$3$	1.42094	−	0.990413i	0.820382	−	0.571815i
$3$	1.42094	−	0.990413i	0.820382	−	0.571815i
$4$	0.755665	−	1.30885i	0.377833	−	0.654425i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.09625	−	0.514057i	−0.447540	−	0.209863i
$7$	−1.62523	−	2.08773i	−0.614279	−	0.789089i
$7$	−1.62523	−	2.08773i	−0.614279	−	0.789089i
$8$	−2.45459			−0.867829
$9$	1.03816	−	2.81464i	0.346054	−	0.938214i
$10$	−0.349525	−	0.605394i	−0.110529	−	0.191442i
$11$	−3.83823			−1.15727			−0.578635	−	0.815586i	$-0.696415\pi$
$11$	−3.83823			−1.15727			−0.578635	+	0.815586i	$0.696415\pi$
$12$	−0.222545	−	2.60822i	−0.0642432	−	0.752929i
$13$	2.28027	+	3.94954i	0.632432	+	1.09541i	0.987053	+	0.160395i	$0.0512767\pi$
$13$	2.28027	+	3.94954i	0.632432	+	1.09541i	−0.354621	+	0.935010i	$0.615390\pi$
$14$	−0.695843	+	1.71362i	−0.185972	+	0.457984i
$15$	1.42094	−	0.990413i	0.366886	−	0.255724i
$16$	−0.653390	−	1.13171i	−0.163348	−	0.282926i
$17$	2.93173	+	5.07790i	0.711048	+	1.23157i	0.964464	+	0.264214i	$0.0851126\pi$
$17$	2.93173	+	5.07790i	0.711048	+	1.23157i	−0.253416	+	0.967357i	$0.581554\pi$
$18$	−2.06683	+	0.355289i	−0.487157	+	0.0837424i
$19$	0.386961	−	0.670236i	0.0887750	−	0.153763i	−0.818219	−	0.574907i	$-0.805038\pi$
$19$	0.386961	−	0.670236i	0.0887750	−	0.153763i	0.906994	+	0.421144i	$0.138371\pi$
$20$	0.755665	−	1.30885i	0.168972	−	0.292668i
$21$	−4.37708	−	1.35690i	−0.955157	−	0.296100i
$22$	1.34156	+	2.32364i	0.286021	+	0.495403i
$23$	6.90532			1.43986			0.719929	−	0.694048i	$-0.244174\pi$
$23$	6.90532			1.43986			0.719929	+	0.694048i	$0.244174\pi$
$24$	−3.48784	+	2.43106i	−0.711952	+	0.496238i
$25$	1.00000			0.200000
$26$	1.59402	−	2.76092i	0.312613	−	0.541461i
$27$	−1.31249	−	5.02766i	−0.252589	−	0.967574i
$28$	−3.96066	+	0.549558i	−0.748494	+	0.103857i
$29$	−3.95301	+	6.84682i	−0.734056	+	1.27142i	0.221080	+	0.975256i	$0.429042\pi$
$29$	−3.95301	+	6.84682i	−0.734056	+	1.27142i	−0.955136	+	0.296167i	$0.904292\pi$
$30$	−1.09625	−	0.514057i	−0.200146	−	0.0938536i
$31$	2.01894	−	3.49691i	0.362613	−	0.628064i	−0.625777	−	0.780002i	$-0.715218\pi$
$31$	2.01894	−	3.49691i	0.362613	−	0.628064i	0.988390	+	0.151938i	$0.0485513\pi$
$32$	−2.91134	+	5.04260i	−0.514658	+	0.891413i
$33$	−5.45391	+	3.80144i	−0.949404	+	0.661745i
$34$	2.04942	−	3.54970i	0.351473	−	0.608769i
$35$	−1.62523	−	2.08773i	−0.274714	−	0.352891i
$36$	−2.89944	−	3.48573i	−0.483241	−	0.580955i
$37$	4.23407	−	7.33362i	0.696076	−	1.20564i	−0.273740	−	0.961804i	$-0.588261\pi$
$37$	4.23407	−	7.33362i	0.696076	−	1.20564i	0.969816	−	0.243836i	$-0.0784059\pi$
$38$	−0.541010			−0.0877634
$39$	7.15181	+	3.35367i	1.14521	+	0.537016i
$40$	−2.45459			−0.388105
$41$	−1.60838	−	2.78579i	−0.251186	−	0.435067i	0.712667	−	0.701503i	$-0.247487\pi$
$41$	−1.60838	−	2.78579i	−0.251186	−	0.435067i	−0.963853	+	0.266436i	$0.914154\pi$
$42$	0.708437	+	3.12413i	0.109314	+	0.482063i
$43$	4.19469	−	7.26541i	0.639683	−	1.10796i	−0.345819	−	0.938301i	$-0.612399\pi$
$43$	4.19469	−	7.26541i	0.639683	−	1.10796i	0.985502	−	0.169663i	$-0.0542679\pi$
$44$	−2.90042	+	5.02367i	−0.437255	+	0.757347i
$45$	1.03816	−	2.81464i	0.154760	−	0.419582i
$46$	−2.41358	−	4.18044i	−0.355863	−	0.616372i
$47$	1.66963	+	2.89189i	0.243541	+	0.421826i	0.961720	−	0.274032i	$-0.0883576\pi$
$47$	1.66963	+	2.89189i	0.243541	+	0.421826i	−0.718179	+	0.695858i	$0.755024\pi$
$48$	−2.04929	−	0.960963i	−0.295789	−	0.138703i
$49$	−1.71725	+	6.78609i	−0.245321	+	0.969442i
$50$	−0.349525	−	0.605394i	−0.0494302	−	0.0856157i
$51$	9.19504	+	4.31179i	1.28756	+	0.603771i
$52$	6.89248			0.955814
$53$	1.32630	+	2.29721i	0.182181	+	0.315546i	0.942623	−	0.333859i	$-0.108351\pi$
$53$	1.32630	+	2.29721i	0.182181	+	0.315546i	−0.760442	+	0.649406i	$0.775018\pi$
$54$	−2.58497	+	2.55186i	−0.351770	+	0.347265i
$55$	−3.83823			−0.517547
$56$	3.98928	+	5.12453i	0.533090	+	0.684794i
$57$	−0.113961	−	1.33562i	−0.0150945	−	0.176907i
$58$	5.52670			0.725691
$59$	3.36978	−	5.83663i	0.438708	−	0.759864i	−0.558882	−	0.829247i	$-0.688770\pi$
$59$	3.36978	−	5.83663i	0.438708	−	0.759864i	0.997590	+	0.0693827i	$0.0221030\pi$
$60$	−0.222545	−	2.60822i	−0.0287304	−	0.336720i
$61$	−3.50639	−	6.07324i	−0.448947	−	0.777599i	0.549371	−	0.835579i	$-0.314868\pi$
$61$	−3.50639	−	6.07324i	−0.448947	−	0.777599i	−0.998318	+	0.0579795i	$0.981534\pi$
$62$	−2.82268			−0.358481
$63$	−7.56348	+	2.40704i	−0.952908	+	0.303258i
$64$	1.45678			0.182098
$65$	2.28027	+	3.94954i	0.282832	+	0.489880i
$66$	4.20764	+	1.97307i	0.517925	+	0.242868i
$67$	−7.28514	+	12.6182i	−0.890022	+	1.54156i	−0.0501748	+	0.998740i	$0.515978\pi$
$67$	−7.28514	+	12.6182i	−0.890022	+	1.54156i	−0.839847	+	0.542823i	$0.817356\pi$
$68$	8.86162			1.07463
$69$	9.81207	−	6.83912i	1.18123	−	0.823333i
$70$	−0.695843	+	1.71362i	−0.0831691	+	0.204817i
$71$	−9.67100			−1.14774			−0.573868	−	0.818948i	$-0.694558\pi$
$71$	−9.67100			−1.14774			−0.573868	+	0.818948i	$0.694558\pi$
$72$	−2.54827	+	6.90880i	−0.300316	+	0.814210i
$73$	7.00941	+	12.1407i	0.820389	+	1.42096i	0.905393	+	0.424575i	$0.139577\pi$
$73$	7.00941	+	12.1407i	0.820389	+	1.42096i	−0.0850031	+	0.996381i	$0.527090\pi$
$74$	−5.91964			−0.688144
$75$	1.42094	−	0.990413i	0.164076	−	0.114363i
$76$	−0.584826	−	1.01295i	−0.0670842	−	0.116193i
$77$	6.23801	+	8.01320i	0.710888	+	0.913189i
$78$	−0.469442	−	5.50185i	−0.0531538	−	0.622962i
$79$	6.69289	+	11.5924i	0.753009	+	1.30425i	0.946358	+	0.323120i	$0.104732\pi$
$79$	6.69289	+	11.5924i	0.753009	+	1.30425i	−0.193349	+	0.981130i	$0.561935\pi$
$80$	−0.653390	−	1.13171i	−0.0730513	−	0.126529i
$81$	−6.84443	−	5.84412i	−0.760493	−	0.649346i
$82$	−1.12433	+	1.94740i	−0.124162	+	0.215055i
$83$	0.442527	−	0.766479i	0.0485736	−	0.0841320i	−0.840716	−	0.541476i	$-0.817866\pi$
$83$	0.442527	−	0.766479i	0.0485736	−	0.0841320i	0.889290	+	0.457344i	$0.151199\pi$
$84$	−5.08359	+	4.70358i	−0.554665	+	0.513203i
$85$	2.93173	+	5.07790i	0.317990	+	0.550776i
$86$	−5.86458			−0.632394
$87$	1.16417	+	13.6441i	0.124812	+	1.46280i
$88$	9.42130			1.00431
$89$	0.950003	−	1.64545i	0.100700	−	0.174418i	−0.811273	−	0.584667i	$-0.801225\pi$
$89$	0.950003	−	1.64545i	0.100700	−	0.174418i	0.911973	+	0.410250i	$0.134558\pi$
$90$	−2.06683	+	0.355289i	−0.217863	+	0.0374507i
$91$	4.53962	−	11.1795i	0.475881	−	1.17193i
$92$	5.21811	−	9.03803i	0.544025	−	0.942279i
$93$	−0.594584	−	6.96851i	−0.0616554	−	0.722601i
$94$	1.16716	−	2.02157i	0.120383	−	0.208509i
$95$	0.386961	−	0.670236i	0.0397014	−	0.0687648i
$96$	0.857397	+	10.0487i	0.0875077	+	1.02559i
$97$	−3.07725	+	5.32996i	−0.312448	+	0.541176i	−0.978892	−	0.204380i	$-0.934482\pi$
$97$	−3.07725	+	5.32996i	−0.312448	+	0.541176i	0.666444	+	0.745555i	$0.267816\pi$
$98$	4.70848	−	1.33229i	0.475629	−	0.134582i
$99$	−3.98471	+	10.8033i	−0.400479	+	1.08577i
$100$	0.755665	−	1.30885i	0.0755665	−	0.130885i
$101$	−1.54494			−0.153727			−0.0768635	−	0.997042i	$-0.524491\pi$
$101$	−1.54494			−0.153727			−0.0768635	+	0.997042i	$0.524491\pi$
$102$	−0.603559	−	7.07370i	−0.0597613	−	0.700401i
$103$	−11.8035			−1.16303			−0.581516	−	0.813535i	$-0.697540\pi$
$103$	−11.8035			−1.16303			−0.581516	+	0.813535i	$0.697540\pi$
$104$	−5.59713	−	9.69451i	−0.548843	−	0.950625i
$105$	−4.37708	−	1.35690i	−0.427159	−	0.132420i
$106$	0.927146	−	1.60586i	0.0900524	−	0.155975i
$107$	−1.00776	+	1.74549i	−0.0974239	+	0.168743i	−0.910618	−	0.413250i	$-0.864394\pi$
$107$	−1.00776	+	1.74549i	−0.0974239	+	0.168743i	0.813194	+	0.581993i	$0.197727\pi$
$108$	−7.57226	−	2.08138i	−0.728641	−	0.200281i
$109$	−0.193245	−	0.334710i	−0.0185095	−	0.0320594i	0.856622	−	0.515944i	$-0.172559\pi$
$109$	−0.193245	−	0.334710i	−0.0185095	−	0.0320594i	−0.875132	+	0.483885i	$0.839225\pi$
$110$	1.34156	+	2.32364i	0.127912	+	0.221551i
$111$	−1.24694	−	14.6141i	−0.118355	−	1.38711i
$112$	−1.30079	+	3.20339i	−0.122913	+	0.302692i
$113$	3.98925	+	6.90958i	0.375277	+	0.649998i	0.990368	−	0.138457i	$-0.0442144\pi$
$113$	3.98925	+	6.90958i	0.375277	+	0.649998i	−0.615092	+	0.788456i	$0.710881\pi$
$114$	−0.768744	+	0.535823i	−0.0719995	+	0.0501844i
$115$	6.90532			0.643924
$116$	5.97431	+	10.3478i	0.554701	+	0.960770i
$117$	13.4838	−	2.31787i	1.24658	−	0.214288i
$118$	−4.71128			−0.433709
$119$	5.83656	−	14.3734i	0.535037	−	1.31761i
$120$	−3.48784	+	2.43106i	−0.318395	+	0.221924i
$121$	3.73203			0.339275
$122$	−2.45114	+	4.24550i	−0.221916	+	0.384369i
$123$	−5.04450	−	2.36549i	−0.454847	−	0.213289i
$124$	−3.05129	−	5.28499i	−0.274014	−	0.474606i
$125$	1.00000			0.0894427
$126$	4.10083	+	3.73757i	0.365331	+	0.332969i
$127$	−1.89590			−0.168234			−0.0841170	−	0.996456i	$-0.526807\pi$
$127$	−1.89590			−0.168234			−0.0841170	+	0.996456i	$0.526807\pi$
$128$	5.31351	+	9.20326i	0.469652	+	0.813461i
$129$	−1.23534	−	14.4782i	−0.108766	−	1.27474i
$130$	1.59402	−	2.76092i	0.139805	−	0.242149i
$131$	−7.33888			−0.641201			−0.320600	−	0.947215i	$-0.603885\pi$
$131$	−7.33888			−0.641201			−0.320600	+	0.947215i	$0.603885\pi$
$132$	0.854180	+	10.0110i	0.0743468	+	0.871343i
$133$	−2.02818	+	0.281418i	−0.175865	+	0.0244020i
$134$	10.1853			0.879880
$135$	−1.31249	−	5.02766i	−0.112961	−	0.432712i
$136$	−7.19620	−	12.4642i	−0.617069	−	1.06879i
$137$	−9.45201			−0.807540			−0.403770	−	0.914861i	$-0.632300\pi$
$137$	−9.45201			−0.807540			−0.403770	+	0.914861i	$0.632300\pi$
$138$	−7.56992	−	3.54973i	−0.644394	−	0.302173i
$139$	3.28976	+	5.69803i	0.279034	+	0.483301i	0.971145	−	0.238490i	$-0.0766525\pi$
$139$	3.28976	+	5.69803i	0.279034	+	0.483301i	−0.692111	+	0.721791i	$0.743319\pi$
$140$	−3.96066	+	0.549558i	−0.334737	+	0.0464461i
$141$	5.23662	+	2.45559i	0.441003	+	0.206798i
$142$	3.38025	+	5.85477i	0.283664	+	0.491321i
$143$	−8.75220	−	15.1593i	−0.731896	−	1.26768i
$144$	−3.86367	+	0.664166i	−0.321973	+	0.0553472i
$145$	−3.95301	+	6.84682i	−0.328280	+	0.568597i
$146$	4.89992	−	8.48691i	0.405520	−	0.702382i
$147$	4.28092	+	11.3434i	0.353084	+	0.935591i
$148$	−6.39908	−	11.0835i	−0.526001	−	0.911060i
$149$	−12.8568			−1.05327			−0.526634	−	0.850092i	$-0.676546\pi$
$149$	−12.8568			−1.05327			−0.526634	+	0.850092i	$0.676546\pi$
$150$	−1.09625	−	0.514057i	−0.0895080	−	0.0419726i
$151$	6.72795			0.547513			0.273756	−	0.961799i	$-0.411734\pi$
$151$	6.72795			0.547513			0.273756	+	0.961799i	$0.411734\pi$
$152$	−0.949832	+	1.64516i	−0.0770415	+	0.133440i
$153$	17.3361	−	2.98008i	1.40154	−	0.240925i
$154$	2.67081	−	6.57727i	0.215220	−	0.530011i
$155$	2.01894	−	3.49691i	0.162166	−	0.280879i
$156$	9.79382	−	6.82640i	0.784133	−	0.546549i
$157$	6.05582	−	10.4890i	0.483307	−	0.837112i	−0.516509	−	0.856281i	$-0.672769\pi$
$157$	6.05582	−	10.4890i	0.483307	−	0.837112i	0.999816	+	0.0191696i	$0.00610224\pi$
$158$	4.67866	−	8.10368i	0.372214	−	0.644694i
$159$	4.15978	+	1.95063i	0.329892	+	0.154695i
$160$	−2.91134	+	5.04260i	−0.230162	+	0.398652i
$161$	−11.2227	−	14.4164i	−0.884475	−	1.13618i
$162$	−1.14570	+	6.18624i	−0.0900145	+	0.486037i
$163$	−8.11477	+	14.0552i	−0.635598	+	1.10089i	0.350790	+	0.936454i	$0.385913\pi$
$163$	−8.11477	+	14.0552i	−0.635598	+	1.10089i	−0.986388	+	0.164434i	$0.947420\pi$
$164$	−4.86158			−0.379625
$165$	−5.45391	+	3.80144i	−0.424587	+	0.295941i
$166$	−0.618696			−0.0480201
$167$	−8.60497	−	14.9042i	−0.665872	−	1.15332i	−0.979048	−	0.203630i	$-0.934726\pi$
$167$	−8.60497	−	14.9042i	−0.665872	−	1.15332i	0.313176	−	0.949695i	$-0.398607\pi$
$168$	10.7439	+	3.33064i	0.828913	+	0.256964i
$169$	−3.89924	+	6.75368i	−0.299942	+	0.519514i
$170$	2.04942	−	3.54970i	0.157183	−	0.272250i
$171$	−1.48475	−	1.78497i	−0.113541	−	0.136500i
$172$	−6.33956	−	10.9804i	−0.483387	−	0.837250i
$173$	−8.01528	−	13.8829i	−0.609390	−	1.05550i	−0.991341	−	0.131312i	$-0.958081\pi$
$173$	−8.01528	−	13.8829i	−0.609390	−	1.05550i	0.381951	−	0.924183i	$-0.375252\pi$
$174$	7.85313	−	5.47372i	0.595344	−	0.414961i
$175$	−1.62523	−	2.08773i	−0.122856	−	0.157818i
$176$	2.50786	+	4.34375i	0.189037	+	0.327422i
$177$	−0.992407	−	11.6310i	−0.0745939	−	0.874239i
$178$	−1.32820			−0.0995526
$179$	4.60018	+	7.96775i	0.343834	+	0.595538i	0.985141	−	0.171746i	$-0.0549410\pi$
$179$	4.60018	+	7.96775i	0.343834	+	0.595538i	−0.641307	+	0.767284i	$0.721608\pi$
$180$	−2.89944	−	3.48573i	−0.216112	−	0.259811i
$181$	−5.76356			−0.428402			−0.214201	−	0.976790i	$-0.568715\pi$
$181$	−5.76356			−0.428402			−0.214201	+	0.976790i	$0.568715\pi$
$182$	−8.35471	+	1.15925i	−0.619293	+	0.0859294i
$183$	−10.9974	−	5.15697i	−0.812952	−	0.381214i
$184$	−16.9497			−1.24955
$185$	4.23407	−	7.33362i	0.311295	−	0.539178i
$186$	−4.01087	+	2.79562i	−0.294091	+	0.204985i
$187$	−11.2527	−	19.4902i	−0.822875	−	1.42526i
$188$	5.04674			0.368071
$189$	−8.36331	+	10.9112i	−0.608341	+	0.793675i
$190$	−0.541010			−0.0392490
$191$	−1.15149	−	1.99444i	−0.0833190	−	0.144313i	0.821355	−	0.570418i	$-0.193219\pi$
$191$	−1.15149	−	1.99444i	−0.0833190	−	0.144313i	−0.904674	+	0.426105i	$0.859885\pi$
$192$	2.07001	−	1.44282i	0.149390	−	0.104126i
$193$	−9.97640	+	17.2796i	−0.718117	+	1.24382i	0.243628	+	0.969869i	$0.421662\pi$
$193$	−9.97640	+	17.2796i	−0.718117	+	1.24382i	−0.961745	+	0.273946i	$0.911671\pi$
$194$	4.30230			0.308887
$195$	7.15181	+	3.35367i	0.512152	+	0.240161i
$196$	7.58432	+	7.37564i	0.541737	+	0.526831i
$197$	0.261164			0.0186071			0.00930357	−	0.999957i	$-0.497039\pi$
$197$	0.261164			0.0186071			0.00930357	+	0.999957i	$0.497039\pi$
$198$	7.93298	−	1.36368i	0.563773	−	0.0969126i
$199$	−1.81496	−	3.14360i	−0.128659	−	0.222844i	0.794498	−	0.607266i	$-0.207734\pi$
$199$	−1.81496	−	3.14360i	−0.128659	−	0.222844i	−0.923157	+	0.384423i	$0.874401\pi$
$200$	−2.45459			−0.173566
$201$	2.14549	+	25.1451i	0.151331	+	1.77360i
$202$	0.539993	+	0.935296i	0.0379938	+	0.0658072i
$203$	20.7189	−	2.87483i	1.45418	−	0.201773i
$204$	12.5919	−	8.77666i	0.881607	−	0.614489i
$205$	−1.60838	−	2.78579i	−0.112334	−	0.194568i
$206$	4.12561	+	7.14577i	0.287445	+	0.497869i
$207$	7.16884	−	19.4360i	0.498269	−	1.35090i
$208$	2.97981	−	5.16118i	0.206613	−	0.357864i
$209$	−1.48525	+	2.57252i	−0.102737	+	0.177945i
$210$	0.708437	+	3.12413i	0.0488868	+	0.215585i
$211$	2.25267	+	3.90174i	0.155080	+	0.268607i	0.933088	−	0.359648i	$-0.117103\pi$
$211$	2.25267	+	3.90174i	0.155080	+	0.268607i	−0.778008	+	0.628254i	$0.783770\pi$
$212$	4.00894			0.275335
$213$	−13.7419	+	9.57829i	−0.941583	+	0.656293i
$214$	1.40895			0.0963137
$215$	4.19469	−	7.26541i	0.286075	−	0.495497i
$216$	3.22162	+	12.3409i	0.219204	+	0.839689i
$217$	−10.5819	+	1.46828i	−0.718344	+	0.0996732i
$218$	−0.135088	+	0.233979i	−0.00914929	+	0.0158470i
$219$	21.9842	+	10.3090i	1.48556	+	0.696616i
$220$	−2.90042	+	5.02367i	−0.195546	+	0.338696i
$221$	−13.3702	+	23.1579i	−0.899380	+	1.55777i
$222$	−8.41148	+	5.86289i	−0.564541	+	0.393492i
$223$	−5.85329	+	10.1382i	−0.391966	+	0.678904i	−0.992709	−	0.120538i	$-0.961538\pi$
$223$	−5.85329	+	10.1382i	−0.391966	+	0.678904i	0.600743	+	0.799442i	$0.294871\pi$
$224$	15.2592	−	2.11728i	1.01955	−	0.141466i
$225$	1.03816	−	2.81464i	0.0692109	−	0.187643i
$226$	2.78868	−	4.83013i	0.185500	−	0.321296i
$227$	9.27518			0.615615			0.307808	−	0.951449i	$-0.400405\pi$
$227$	9.27518			0.615615			0.307808	+	0.951449i	$0.400405\pi$
$228$	−1.83424	−	0.860124i	−0.121476	−	0.0569631i
$229$	16.9065			1.11721			0.558606	−	0.829433i	$-0.311336\pi$
$229$	16.9065			1.11721			0.558606	+	0.829433i	$0.311336\pi$
$230$	−2.41358	−	4.18044i	−0.159147	−	0.275650i
$231$	16.8002	+	5.20810i	1.10538	+	0.342668i
$232$	9.70303	−	16.8061i	0.637035	−	1.10338i
$233$	−3.50083	+	6.06362i	−0.229347	+	0.397241i	−0.957615	−	0.288052i	$-0.906992\pi$
$233$	−3.50083	+	6.06362i	−0.229347	+	0.397241i	0.728268	+	0.685293i	$0.240326\pi$
$234$	−6.11616	−	7.35288i	−0.399826	−	0.480673i
$235$	1.66963	+	2.89189i	0.108915	+	0.188646i
$236$	−5.09285	−	8.82107i	−0.331516	−	0.574203i
$237$	20.9915	+	9.84346i	1.36355	+	0.639402i
$238$	−10.7416	+	1.49044i	−0.696275	+	0.0966110i
$239$	−8.00452	−	13.8642i	−0.517769	−	0.896803i	−0.999787	−	0.0206414i	$-0.993429\pi$
$239$	−8.00452	−	13.8642i	−0.517769	−	0.896803i	0.482017	−	0.876162i	$-0.339904\pi$
$240$	−2.04929	−	0.960963i	−0.132281	−	0.0620299i
$241$	−7.35462			−0.473752			−0.236876	−	0.971540i	$-0.576124\pi$
$241$	−7.35462			−0.473752			−0.236876	+	0.971540i	$0.576124\pi$
$242$	−1.30444	−	2.25935i	−0.0838523	−	0.145236i
$243$	−15.5136	−	1.52534i	−0.995201	−	0.0978509i
$244$	−10.5986			−0.678508
$245$	−1.71725	+	6.78609i	−0.109711	+	0.433548i
$246$	0.331119	+	3.88071i	0.0211114	+	0.247425i
$247$	3.52950			0.224577
$248$	−4.95568	+	8.58350i	−0.314686	+	0.545053i
$249$	−0.130325	−	1.52741i	−0.00825902	−	0.0967956i
$250$	−0.349525	−	0.605394i	−0.0221059	−	0.0382885i
$251$	15.4784			0.976991			0.488495	−	0.872566i	$-0.337546\pi$
$251$	15.4784			0.976991			0.488495	+	0.872566i	$0.337546\pi$
$252$	−2.56500	+	11.7184i	−0.161580	+	0.738188i
$253$	−26.5042			−1.66631
$254$	0.662664	+	1.14777i	0.0415792	+	0.0720173i
$255$	9.19504	+	4.31179i	0.575816	+	0.270015i
$256$	5.17118	−	8.95675i	0.323199	−	0.559797i
$257$	−0.355901			−0.0222005			−0.0111003	−	0.999938i	$-0.503533\pi$
$257$	−0.355901			−0.0222005			−0.0111003	+	0.999938i	$0.503533\pi$
$258$	−8.33324	+	5.80836i	−0.518805	+	0.361613i
$259$	−22.1920	+	3.07923i	−1.37894	+	0.191334i
$260$	6.89248			0.427453
$261$	15.1675	+	18.2344i	0.938844	+	1.12868i
$262$	2.56512	+	4.44291i	0.158473	+	0.274484i
$263$	19.1656			1.18180			0.590900	−	0.806745i	$-0.298773\pi$
$263$	19.1656			1.18180			0.590900	+	0.806745i	$0.298773\pi$
$264$	13.3871	−	9.33098i	0.823921	−	0.574282i
$265$	1.32630	+	2.29721i	0.0814737	+	0.141117i
$266$	0.879266	+	1.12948i	0.0539112	+	0.0692531i
$267$	−0.279778	−	3.27899i	−0.0171221	−	0.200671i
$268$	11.0103	+	19.0703i	0.672559	+	1.16491i
$269$	−4.18841	−	7.25453i	−0.255372	−	0.442317i	0.709625	−	0.704580i	$-0.248865\pi$
$269$	−4.18841	−	7.25453i	−0.255372	−	0.442317i	−0.964996	+	0.262263i	$0.915531\pi$
$270$	−2.58497	+	2.55186i	−0.157316	+	0.155301i
$271$	−0.0397516	+	0.0688517i	−0.00241474	+	0.00418244i	−0.867230	−	0.497907i	$-0.834102\pi$
$271$	−0.0397516	+	0.0688517i	−0.00241474	+	0.00418244i	0.864816	+	0.502090i	$0.167435\pi$
$272$	3.83113	−	6.63570i	0.232296	−	0.402349i
$273$	−4.62178	−	20.3815i	−0.279723	−	1.23355i
$274$	3.30371	+	5.72219i	0.199584	+	0.345690i
$275$	−3.83823			−0.231454
$276$	−1.53674	−	18.0106i	−0.0925011	−	1.08411i
$277$	21.3875			1.28505			0.642524	−	0.766265i	$-0.277887\pi$
$277$	21.3875			1.28505			0.642524	+	0.766265i	$0.277887\pi$
$278$	2.29970	−	3.98320i	0.137927	−	0.238897i
$279$	−7.74657	−	9.31297i	−0.463775	−	0.557553i
$280$	3.98928	+	5.12453i	0.238405	+	0.306249i
$281$	2.12078	−	3.67329i	0.126515	−	0.219130i	−0.795809	−	0.605547i	$-0.792954\pi$
$281$	2.12078	−	3.67329i	0.126515	−	0.219130i	0.922324	+	0.386417i	$0.126288\pi$
$282$	−0.343730	−	4.02851i	−0.0204688	−	0.239894i
$283$	2.99392	−	5.18562i	0.177970	−	0.308253i	−0.763215	−	0.646144i	$-0.776380\pi$
$283$	2.99392	−	5.18562i	0.177970	−	0.308253i	0.941185	+	0.337892i	$0.109714\pi$
$284$	−7.30804	+	12.6579i	−0.433652	+	0.751108i
$285$	−0.113961	−	1.33562i	−0.00675046	−	0.0791153i
$286$	−6.11822	+	10.5971i	−0.361778	+	0.626617i
$287$	−3.20200	+	7.88541i	−0.189008	+	0.465461i
$288$	11.1707	+	13.4294i	0.658237	+	0.791337i
$289$	−8.69005	+	15.0516i	−0.511180	+	0.885389i
$290$	5.52670			0.324539
$291$	0.906258	+	10.6213i	0.0531258	+	0.622633i
$292$	21.1871			1.23988
$293$	−6.26949	−	10.8591i	−0.366267	−	0.634393i	0.622711	−	0.782452i	$-0.286031\pi$
$293$	−6.26949	−	10.8591i	−0.366267	−	0.634393i	−0.988979	+	0.148058i	$0.952698\pi$
$294$	5.37097	−	6.55646i	0.313241	−	0.382380i
$295$	3.36978	−	5.83663i	0.196196	−	0.339822i
$296$	−10.3929	+	18.0010i	−0.604076	+	1.04629i
$297$	5.03764	+	19.2973i	0.292313	+	1.11974i
$298$	4.49376	+	7.78342i	0.260317	+	0.450882i
$299$	15.7460	+	27.2728i	0.910613	+	1.57723i
$300$	−0.222545	−	2.60822i	−0.0128486	−	0.150586i
$301$	−21.9856	+	3.05059i	−1.26723	+	0.175833i
$302$	−2.35158	−	4.07306i	−0.135318	−	0.234378i
$303$	−2.19527	+	1.53013i	−0.126115	+	0.0879035i
$304$	−1.01135			−0.0580047
$305$	−3.50639	−	6.07324i	−0.200775	−	0.347753i
$306$	−7.86351	−	9.45356i	−0.449527	−	0.540424i
$307$	−21.0767			−1.20291			−0.601455	−	0.798906i	$-0.705412\pi$
$307$	−21.0767			−1.20291			−0.601455	+	0.798906i	$0.705412\pi$
$308$	15.2019	−	2.10933i	0.866211	−	0.120190i
$309$	−16.7721	+	11.6903i	−0.954131	+	0.665040i
$310$	−2.82268			−0.160318
$311$	−6.41734	+	11.1152i	−0.363894	+	0.630283i	−0.988598	−	0.150579i	$-0.951886\pi$
$311$	−6.41734	+	11.1152i	−0.363894	+	0.630283i	0.624704	+	0.780862i	$0.285220\pi$
$312$	−17.5548	−	8.23188i	−0.993843	−	0.466039i
$313$	7.44794	+	12.9002i	0.420982	+	0.729163i	0.996036	−	0.0889532i	$-0.0283521\pi$
$313$	7.44794	+	12.9002i	0.420982	+	0.729163i	−0.575054	+	0.818116i	$0.695019\pi$
$314$	−8.46663			−0.477799
$315$	−7.56348	+	2.40704i	−0.426154	+	0.135621i
$316$	20.2303			1.13805
$317$	−17.1198	−	29.6524i	−0.961545	−	1.66545i	−0.718624	−	0.695399i	$-0.755228\pi$
$317$	−17.1198	−	29.6524i	−0.961545	−	1.66545i	−0.242922	−	0.970046i	$-0.578106\pi$
$318$	−0.273047	−	3.20010i	−0.0153117	−	0.179453i
$319$	15.1726	−	26.2797i	0.849502	−	1.47138i
$320$	1.45678			0.0814366
$321$	0.296788	+	3.47835i	0.0165651	+	0.194142i
$322$	−4.80502	+	11.8331i	−0.267773	+	0.659432i
$323$	4.53786			0.252493
$324$	−12.8212	+	4.54215i	−0.712288	+	0.252341i
$325$	2.28027	+	3.94954i	0.126486	+	0.219081i
$326$	11.3452			0.628355
$327$	−0.606091	−	0.284212i	−0.0335169	−	0.0157170i
$328$	3.94791	+	6.83798i	0.217987	+	0.377564i
$329$	3.32395	−	8.18574i	0.183255	−	0.451294i
$330$	4.20764	+	1.97307i	0.231623	+	0.108614i
$331$	−16.5881	−	28.7314i	−0.911764	−	1.57922i	−0.811572	−	0.584253i	$-0.801388\pi$
$331$	−16.5881	−	28.7314i	−0.911764	−	1.57922i	−0.100192	−	0.994968i	$-0.531946\pi$
$332$	−0.668804	−	1.15840i	−0.0367054	−	0.0635756i
$333$	−16.2459	−	19.5309i	−0.890268	−	1.07029i
$334$	−6.01529	+	10.4188i	−0.329142	+	0.570091i
$335$	−7.28514	+	12.6182i	−0.398030	+	0.689408i
$336$	1.32433	+	5.84015i	0.0722482	+	0.318606i
$337$	−10.8821	−	18.8484i	−0.592786	−	1.02674i	−0.993855	−	0.110688i	$-0.964695\pi$
$337$	−10.8821	−	18.8484i	−0.592786	−	1.02674i	0.401069	−	0.916048i	$-0.368639\pi$
$338$	5.45152			0.296524
$339$	12.5118	+	5.86712i	0.679549	+	0.318658i
$340$	8.86162			0.480589
$341$	−7.74918	+	13.4220i	−0.419641	+	0.726840i
$342$	−0.561656	+	1.52275i	−0.0303709	+	0.0823408i
$343$	16.9585	−	7.44381i	0.915671	−	0.401928i
$344$	−10.2962	+	17.8336i	−0.555136	+	0.961524i
$345$	9.81207	−	6.83912i	0.528264	−	0.368206i
$346$	−5.60307	+	9.70481i	−0.301223	+	0.521734i
$347$	−2.40973	+	4.17378i	−0.129361	+	0.224060i	−0.923429	−	0.383769i	$-0.874626\pi$
$347$	−2.40973	+	4.17378i	−0.129361	+	0.224060i	0.794068	+	0.607829i	$0.207959\pi$
$348$	18.7378	+	8.78662i	1.00445	+	0.471012i
$349$	3.26983	−	5.66352i	0.175030	−	0.303161i	−0.765142	−	0.643862i	$-0.777331\pi$
$349$	3.26983	−	5.66352i	0.175030	−	0.303161i	0.940172	+	0.340701i	$0.110664\pi$
$350$	−0.695843	+	1.71362i	−0.0371944	+	0.0915968i
$351$	16.8641	−	16.6481i	0.900140	−	0.888612i
$352$	11.1744	−	19.3547i	0.595598	−	1.03161i
$353$	−0.354435			−0.0188647			−0.00943233	−	0.999956i	$-0.503002\pi$
$353$	−0.354435			−0.0188647			−0.00943233	+	0.999956i	$0.503002\pi$
$354$	−6.69447	+	4.66612i	−0.355807	+	0.248001i
$355$	−9.67100			−0.513283
$356$	−1.43577	−	2.48683i	−0.0760956	−	0.131801i
$357$	−5.94220	−	26.2044i	−0.314495	−	1.38689i
$358$	3.21575	−	5.56985i	0.169958	−	0.294376i
$359$	6.26344	−	10.8486i	0.330572	−	0.572567i	−0.652052	−	0.758174i	$-0.726092\pi$
$359$	6.26344	−	10.8486i	0.330572	−	0.572567i	0.982624	+	0.185607i	$0.0594251\pi$
$360$	−2.54827	+	6.90880i	−0.134305	+	0.364126i
$361$	9.20052	+	15.9358i	0.484238	+	0.838725i
$362$	2.01451	+	3.48923i	0.105880	+	0.183390i
$363$	5.30301	−	3.69625i	0.278336	−	0.194003i
$364$	−11.2019	−	14.3896i	−0.587137	−	0.754222i
$365$	7.00941	+	12.1407i	0.366889	+	0.635471i
$366$	0.721866	+	8.46025i	0.0377325	+	0.442224i
$367$	12.9540			0.676192			0.338096	−	0.941112i	$-0.390217\pi$
$367$	12.9540			0.676192			0.338096	+	0.941112i	$0.390217\pi$
$368$	−4.51187	−	7.81478i	−0.235197	−	0.407374i
$369$	−9.51076	+	1.63490i	−0.495110	+	0.0851096i
$370$	−5.91964			−0.307747
$371$	2.64043	−	6.50245i	0.137084	−	0.337590i
$372$	−9.57004	−	4.48764i	−0.496184	−	0.232673i
$373$	10.3804			0.537475			0.268738	−	0.963213i	$-0.413394\pi$
$373$	10.3804			0.537475			0.268738	+	0.963213i	$0.413394\pi$
$374$	−7.86616	+	13.6246i	−0.406749	+	0.704510i
$375$	1.42094	−	0.990413i	0.0733772	−	0.0511447i
$376$	−4.09827	−	7.09841i	−0.211352	−	0.366073i
$377$	−36.0557			−1.85696
$378$	9.52878	+	1.24936i	0.490108	+	0.0642600i
$379$	5.82342			0.299129			0.149564	−	0.988752i	$-0.452213\pi$
$379$	5.82342			0.299129			0.149564	+	0.988752i	$0.452213\pi$
$380$	−0.584826	−	1.01295i	−0.0300010	−	0.0519632i
$381$	−2.69397	+	1.87773i	−0.138016	+	0.0961988i
$382$	−0.804949	+	1.39421i	−0.0411848	+	0.0713341i
$383$	26.0999			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$383$	26.0999			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$384$	16.6652	+	7.81475i	0.850444	+	0.398795i
$385$	6.23801	+	8.01320i	0.317919	+	0.408391i
$386$	13.9480			0.709934
$387$	−16.0948	−	19.3492i	−0.818143	−	0.983576i
$388$	4.65075	+	8.05533i	0.236106	+	0.408948i
$389$	0.160490			0.00813716			0.00406858	−	0.999992i	$-0.498705\pi$
$389$	0.160490			0.00813716			0.00406858	+	0.999992i	$0.498705\pi$
$390$	−0.469442	−	5.50185i	−0.0237711	−	0.278597i
$391$	20.2445	+	35.0645i	1.02381	+	1.77329i
$392$	4.21515	−	16.6571i	0.212897	−	0.841310i
$393$	−10.4281	+	7.26852i	−0.526030	+	0.366648i
$394$	−0.0912831	−	0.158107i	−0.00459878	−	0.00796531i
$395$	6.69289	+	11.5924i	0.336756	+	0.583278i
$396$	11.1287	+	13.3790i	0.559240	+	0.672322i
$397$	6.09165	−	10.5510i	0.305731	−	0.529542i	−0.671693	−	0.740830i	$-0.734433\pi$
$397$	6.09165	−	10.5510i	0.305731	−	0.529542i	0.977424	+	0.211288i	$0.0677659\pi$
$398$	−1.26874	+	2.19753i	−0.0635964	+	0.110152i
$399$	−2.60320	+	2.40861i	−0.130323	+	0.120581i
$400$	−0.653390	−	1.13171i	−0.0326695	−	0.0565853i
$401$	−18.8416			−0.940906			−0.470453	−	0.882425i	$-0.655909\pi$
$401$	−18.8416			−0.940906			−0.470453	+	0.882425i	$0.655909\pi$
$402$	14.4728	−	10.0877i	0.721838	−	0.503129i
$403$	18.4149			0.917313
$404$	−1.16746	+	2.02209i	−0.0580831	+	0.100603i
$405$	−6.84443	−	5.84412i	−0.340103	−	0.290397i
$406$	−8.98216	−	11.5383i	−0.445777	−	0.572635i
$407$	−16.2513	+	28.1481i	−0.805549	+	1.39525i
$408$	−22.5701	−	10.5837i	−1.11739	−	0.523971i
$409$	0.737626	−	1.27761i	0.0364733	−	0.0631736i	−0.847213	−	0.531254i	$-0.821721\pi$
$409$	0.737626	−	1.27761i	0.0364733	−	0.0631736i	0.883686	+	0.468081i	$0.155054\pi$
$410$	−1.12433	+	1.94740i	−0.0555269	+	0.0961754i
$411$	−13.4308	+	9.36140i	−0.662492	+	0.461764i
$412$	−8.91949	+	15.4490i	−0.439432	+	0.761118i
$413$	−17.6620	+	2.45067i	−0.869089	+	0.120590i
$414$	−14.2721	+	2.45338i	−0.701437	+	0.120577i
$415$	0.442527	−	0.766479i	0.0217228	−	0.0376250i
$416$	−26.5546			−1.30195
$417$	10.3180	+	4.83836i	0.505273	+	0.236936i
$418$	2.07652			0.101566
$419$	−2.29886	−	3.98174i	−0.112307	−	0.194521i	0.804393	−	0.594097i	$-0.202491\pi$
$419$	−2.29886	−	3.98174i	−0.112307	−	0.194521i	−0.916700	+	0.399576i	$0.869157\pi$
$420$	−5.08359	+	4.70358i	−0.248054	+	0.229511i
$421$	−8.56269	+	14.8310i	−0.417320	+	0.722819i	−0.995669	−	0.0929702i	$-0.970364\pi$
$421$	−8.56269	+	14.8310i	−0.417320	+	0.722819i	0.578349	+	0.815789i	$0.303697\pi$
$422$	1.57473	−	2.72750i	0.0766564	−	0.132773i
$423$	9.87299	−	1.69717i	0.480041	−	0.0825192i
$424$	−3.25552	−	5.63872i	−0.158102	−	0.273840i
$425$	2.93173	+	5.07790i	0.142210	+	0.246314i
$426$	10.6018	+	4.97145i	0.513658	+	0.240868i
$427$	−6.98062	+	17.1908i	−0.337816	+	0.831922i
$428$	1.52306	+	2.63802i	0.0736199	+	0.127513i
$429$	−27.4503	−	12.8722i	−1.32531	−	0.621473i
$430$	−5.86458			−0.282815
$431$	−8.75901	−	15.1710i	−0.421907	−	0.730764i	0.574219	−	0.818701i	$-0.305306\pi$
$431$	−8.75901	−	15.1710i	−0.421907	−	0.730764i	−0.996126	+	0.0879379i	$0.971972\pi$
$432$	−4.83226	+	4.77038i	−0.232492	+	0.229515i
$433$	31.4428			1.51104			0.755522	−	0.655124i	$-0.227383\pi$
$433$	31.4428			1.51104			0.755522	+	0.655124i	$0.227383\pi$
$434$	4.58751	+	5.89300i	0.220208	+	0.282873i
$435$	1.16417	+	13.6441i	0.0558177	+	0.654183i
$436$	−0.584114			−0.0279740
$437$	2.67209	−	4.62819i	0.127823	−	0.221397i
$438$	−1.44304	−	16.9124i	−0.0689510	−	0.808104i
$439$	−20.1678	−	34.9316i	−0.962555	−	1.66719i	−0.716045	−	0.698054i	$-0.754049\pi$
$439$	−20.1678	−	34.9316i	−0.962555	−	1.66719i	−0.246510	−	0.969140i	$-0.579284\pi$
$440$	9.42130			0.449143
$441$	17.3176	+	11.8785i	0.824650	+	0.565644i
$442$	18.6929			0.889131
$443$	−18.0671	−	31.2931i	−0.858394	−	1.48678i	−0.873460	−	0.486896i	$-0.838129\pi$
$443$	−18.0671	−	31.2931i	−0.858394	−	1.48678i	0.0150658	−	0.999887i	$-0.495204\pi$
$444$	−20.0700	−	9.41134i	−0.952480	−	0.446642i
$445$	0.950003	−	1.64545i	0.0450345	−	0.0780020i
$446$	8.18348			0.387499
$447$	−18.2688	+	12.7335i	−0.864083	+	0.602275i
$448$	−2.36761	−	3.04137i	−0.111859	−	0.143691i
$449$	17.2314			0.813202			0.406601	−	0.913606i	$-0.366714\pi$
$449$	17.2314			0.813202			0.406601	+	0.913606i	$0.366714\pi$
$450$	−2.06683	+	0.355289i	−0.0974314	+	0.0167485i
$451$	6.17332	+	10.6925i	0.290690	+	0.503491i
$452$	12.0581			0.567167
$453$	9.56004	−	6.66345i	0.449170	−	0.313076i
$454$	−3.24190	−	5.61514i	−0.152150	−	0.263532i
$455$	4.53962	−	11.1795i	0.212821	−	0.524103i
$456$	0.279728	+	3.27840i	0.0130994	+	0.153525i
$457$	−4.58643	−	7.94394i	−0.214544	−	0.371602i	0.738587	−	0.674158i	$-0.235493\pi$
$457$	−4.58643	−	7.94394i	−0.214544	−	0.371602i	−0.953132	+	0.302556i	$0.902160\pi$
$458$	−5.90923	−	10.2351i	−0.276120	−	0.478254i
$459$	21.6821	−	21.4044i	1.01203	−	0.999073i
$460$	5.21811	−	9.03803i	0.243296	−	0.421400i
$461$	7.95525	−	13.7789i	0.370513	−	0.641747i	−0.619132	−	0.785287i	$-0.712515\pi$
$461$	7.95525	−	13.7789i	0.370513	−	0.641747i	0.989645	+	0.143540i	$0.0458486\pi$
$462$	−2.71915	−	11.9911i	−0.126506	−	0.557878i
$463$	−4.80144	−	8.31634i	−0.223142	−	0.386493i	0.732618	−	0.680640i	$-0.238298\pi$
$463$	−4.80144	−	8.31634i	−0.223142	−	0.386493i	−0.955760	+	0.294146i	$0.904965\pi$
$464$	10.3314			0.479625
$465$	−0.594584	−	6.96851i	−0.0275732	−	0.323157i
$466$	4.89451			0.226734
$467$	13.1371	−	22.7541i	0.607912	−	1.05294i	−0.383671	−	0.923470i	$-0.625340\pi$
$467$	13.1371	−	22.7541i	0.607912	−	1.05294i	0.991584	−	0.129466i	$-0.0413262\pi$
$468$	7.15551	−	19.3999i	0.330764	−	0.896759i
$469$	38.1835	−	5.29812i	1.76315	−	0.244645i
$470$	1.16716	−	2.02157i	0.0538369	−	0.0932482i
$471$	−1.78345	−	20.9020i	−0.0821771	−	0.963114i
$472$	−8.27143	+	14.3265i	−0.380724	+	0.659433i
$473$	−16.1002	+	27.8863i	−0.740287	+	1.28221i
$474$	−1.37788	−	16.1487i	−0.0632879	−	0.741733i
$475$	0.386961	−	0.670236i	0.0177550	−	0.0307526i
$476$	−14.4022	−	18.5007i	−0.660123	−	0.847977i
$477$	7.84274	−	1.34817i	0.359095	−	0.0617284i
$478$	−5.59555	+	9.69178i	−0.255935	+	0.443292i
$479$	−7.33270			−0.335040			−0.167520	−	0.985869i	$-0.553576\pi$
$479$	−7.33270			−0.335040			−0.167520	+	0.985869i	$0.553576\pi$
$480$	0.857397	+	10.0487i	0.0391347	+	0.458657i
$481$	38.6192			1.76089
$482$	2.57062	+	4.45244i	0.117088	+	0.202803i
$483$	−30.2251	−	9.36982i	−1.37529	−	0.426342i
$484$	2.82017	−	4.88467i	0.128189	−	0.222030i
$485$	−3.07725	+	5.32996i	−0.139731	+	0.242021i
$486$	4.49897	+	9.92502i	0.204077	+	0.450208i
$487$	−16.8879	−	29.2507i	−0.765262	−	1.32547i	−0.940108	−	0.340878i	$-0.889276\pi$
$487$	−16.8879	−	29.2507i	−0.765262	−	1.32547i	0.174845	−	0.984596i	$-0.444057\pi$
$488$	8.60676	+	14.9073i	0.389610	+	0.674823i
$489$	2.38982	+	28.0086i	0.108071	+	1.26659i
$490$	4.70848	−	1.33229i	0.212708	−	0.0601868i
$491$	10.2358	+	17.7289i	0.461934	+	0.800093i	0.999057	−	0.0434107i	$-0.0138224\pi$
$491$	10.2358	+	17.7289i	0.461934	+	0.800093i	−0.537123	+	0.843504i	$0.680489\pi$
$492$	−6.90803	+	4.81497i	−0.311438	+	0.217076i
$493$	−46.3566			−2.08780
$494$	−1.23365	−	2.13674i	−0.0555044	−	0.0961364i
$495$	−3.98471	+	10.8033i	−0.179099	+	0.485570i
$496$	−5.27663			−0.236928
$497$	15.7176	+	20.1905i	0.705031	+	0.905666i
$498$	−0.879132	+	0.612765i	−0.0393949	+	0.0274586i
$499$	24.3396			1.08959			0.544796	−	0.838569i	$-0.316607\pi$
$499$	24.3396			1.08959			0.544796	+	0.838569i	$0.316607\pi$
$500$	0.755665	−	1.30885i	0.0337944	−	0.0585336i
$501$	−26.9885	−	12.6556i	−1.20576	−	0.565411i
$502$	−5.41010	−	9.37056i	−0.241464	−	0.418229i
$503$	−23.7168			−1.05748			−0.528739	−	0.848784i	$-0.677335\pi$
$503$	−23.7168			−1.05748			−0.528739	+	0.848784i	$0.677335\pi$
$504$	18.5652	−	5.90830i	0.826962	−	0.263177i
$505$	−1.54494			−0.0687488
$506$	9.26387	+	16.0455i	0.411829	+	0.713309i
$507$	1.14833	+	13.4585i	0.0509993	+	0.597711i
$508$	−1.43267	+	2.48145i	−0.0635643	+	0.110097i
$509$	−1.16561			−0.0516649			−0.0258324	−	0.999666i	$-0.508224\pi$
$509$	−1.16561			−0.0516649			−0.0258324	+	0.999666i	$0.508224\pi$
$510$	−0.603559	−	7.07370i	−0.0267260	−	0.313229i
$511$	13.9545	−	34.3651i	0.617312	−	1.52022i
$512$	14.0242			0.619788
$513$	−3.87760	−	1.06583i	−0.171200	−	0.0470576i
$514$	0.124396	+	0.215461i	0.00548688	+	0.00950356i
$515$	−11.8035			−0.520124
$516$	−19.8833	−	9.32380i	−0.875314	−	0.410457i
$517$	−6.40844	−	11.0997i	−0.281843	−	0.488166i
$518$	9.62078	+	12.3586i	0.422713	+	0.543007i
$519$	−25.1390	−	11.7883i	−1.10348	−	0.517451i
$520$	−5.59713	−	9.69451i	−0.245450	−	0.425132i
$521$	15.6184	+	27.0519i	0.684254	+	1.18516i	0.973670	+	0.227960i	$0.0732055\pi$
$521$	15.6184	+	27.0519i	0.684254	+	1.18516i	−0.289416	+	0.957203i	$0.593461\pi$
$522$	5.73762	−	15.5557i	0.251129	−	0.680854i
$523$	−7.10144	+	12.3000i	−0.310524	+	0.537844i	−0.978476	−	0.206361i	$-0.933838\pi$
$523$	−7.10144	+	12.3000i	−0.310524	+	0.537844i	0.667952	+	0.744205i	$0.267171\pi$
$524$	−5.54573	+	9.60549i	−0.242267	+	0.419618i
$525$	−4.37708	−	1.35690i	−0.191031	−	0.0592200i
$526$	−6.69883	−	11.6027i	−0.292083	−	0.505903i
$527$	23.6760			1.03134
$528$	7.86564	+	3.68840i	0.342308	+	0.160517i
$529$	24.6834			1.07319
$530$	0.927146	−	1.60586i	0.0402726	−	0.0697543i
$531$	−12.9296	−	15.5441i	−0.561099	−	0.674556i
$532$	−1.16429	+	2.86724i	−0.0504783	+	0.124310i
$533$	7.33506	−	12.7047i	0.317717	−	0.550301i
$534$	−1.88729	+	1.31546i	−0.0816712	+	0.0569257i
$535$	−1.00776	+	1.74549i	−0.0435693	+	0.0754642i
$536$	17.8821	−	30.9726i	0.772387	−	1.33781i
$537$	14.4280	+	6.76565i	0.622613	+	0.291959i
$538$	−2.92790	+	5.07127i	−0.126231	+	0.218638i
$539$	6.59120	−	26.0466i	0.283903	−	1.12191i
$540$	−7.57226	−	2.08138i	−0.325858	−	0.0895682i
$541$	−1.38923	+	2.40621i	−0.0597275	+	0.103451i	−0.894343	−	0.447382i	$-0.852356\pi$
$541$	−1.38923	+	2.40621i	−0.0597275	+	0.103451i	0.834616	+	0.550833i	$0.185690\pi$
$542$	0.0555766			0.00238722
$543$	−8.18970	+	5.70831i	−0.351453	+	0.244967i
$544$	−34.1411			−1.46379
$545$	−0.193245	−	0.334710i	−0.00827770	−	0.0143374i
$546$	−10.7234	+	9.92185i	−0.458921	+	0.424616i
$547$	−8.59132	+	14.8806i	−0.367338	+	0.636248i	−0.989148	−	0.146919i	$-0.953064\pi$
$547$	−8.59132	+	14.8806i	−0.367338	+	0.636248i	0.621810	+	0.783168i	$0.286398\pi$
$548$	−7.14256	+	12.3713i	−0.305115	+	0.528475i
$549$	−20.7342	+	3.56422i	−0.884915	+	0.152117i
$550$	1.34156	+	2.32364i	0.0572042	+	0.0990805i
$551$	3.05932	+	5.29891i	0.130332	+	0.225741i
$552$	−24.0846	+	16.7872i	−1.02511	+	0.714512i
$553$	13.3244	−	32.8133i	0.566611	−	1.39537i
$554$	−7.47545	−	12.9479i	−0.317601	−	0.550101i
$555$	−1.24694	−	14.6141i	−0.0529297	−	0.620336i
$556$	9.94383			0.421712
$557$	12.1738	+	21.0857i	0.515822	+	0.893430i	0.999831	+	0.0183672i	$0.00584679\pi$
$557$	12.1738	+	21.0857i	0.515822	+	0.893430i	−0.484009	+	0.875063i	$0.660820\pi$
$558$	−2.93040	+	7.94484i	−0.124054	+	0.336332i
$559$	38.2600			1.61823
$560$	−1.30079	+	3.20339i	−0.0549683	+	0.135368i
$561$	−35.2927	−	16.5497i	−1.49006	−	0.698727i
$562$	−2.96505			−0.125073
$563$	13.1260	−	22.7349i	0.553194	−	0.958160i	−0.444848	−	0.895606i	$-0.646742\pi$
$563$	13.1260	−	22.7349i	0.553194	−	0.958160i	0.998042	−	0.0625535i	$-0.0199244\pi$
$564$	7.17113	−	4.99836i	0.301959	−	0.210469i
$565$	3.98925	+	6.90958i	0.167829	+	0.290688i
$566$	−4.18579			−0.175942
$567$	−1.07717	+	23.7874i	−0.0452367	+	0.998976i
$568$	23.7384			0.996039
$569$	3.65815	+	6.33610i	0.153358	+	0.265623i	0.932460	−	0.361274i	$-0.117658\pi$
$569$	3.65815	+	6.33610i	0.153358	+	0.265623i	−0.779102	+	0.626897i	$0.784325\pi$
$570$	−0.768744	+	0.535823i	−0.0321992	+	0.0224432i
$571$	5.72058	−	9.90834i	0.239399	−	0.414651i	−0.721143	−	0.692786i	$-0.756383\pi$
$571$	5.72058	−	9.90834i	0.239399	−	0.414651i	0.960542	+	0.278135i	$0.0897163\pi$
$572$	−26.4549			−1.10614
$573$	−3.61153	−	1.69354i	−0.150874	−	0.0707485i
$574$	5.89296	−	0.817672i	0.245967	−	0.0341290i
$575$	6.90532			0.287972
$576$	1.51238	−	4.10032i	0.0630158	−	0.170847i
$577$	17.3881	+	30.1170i	0.723875	+	1.25379i	0.959436	+	0.281928i	$0.0909739\pi$
$577$	17.3881	+	30.1170i	0.723875	+	1.25379i	−0.235561	+	0.971860i	$0.575693\pi$
$578$	12.1495			0.505354
$579$	2.93807	+	34.4341i	0.122102	+	1.43103i
$580$	5.97431	+	10.3478i	0.248070	+	0.429669i
$581$	−2.31941	+	0.321828i	−0.0962254	+	0.0133517i
$582$	6.11333	−	4.26106i	0.253406	−	0.176627i
$583$	−5.09063	−	8.81723i	−0.210832	−	0.365173i
$584$	−17.2052	−	29.8004i	−0.711958	−	1.23315i
$585$	13.4838	−	2.31787i	0.557488	−	0.0958323i
$586$	−4.38268	+	7.59102i	−0.181047	+	0.313582i
$587$	−16.4446	+	28.4830i	−0.678743	+	1.17562i	0.296616	+	0.954997i	$0.404142\pi$
$587$	−16.4446	+	28.4830i	−0.678743	+	1.17562i	−0.975360	+	0.220621i	$0.929192\pi$
$588$	18.0818	+	2.96876i	0.745682	+	0.122430i
$589$	−1.56251	−	2.70634i	−0.0643819	−	0.111513i
$590$	−4.71128			−0.193960
$591$	0.371099	−	0.258660i	0.0152650	−	0.0106398i
$592$	−11.0660			−0.454810
$593$	−11.6851	+	20.2392i	−0.479851	+	0.831125i	−0.999733	−	0.0231124i	$-0.992642\pi$
$593$	−11.6851	+	20.2392i	−0.479851	+	0.831125i	0.519882	+	0.854238i	$0.325976\pi$
$594$	9.92172	−	9.79465i	0.407093	−	0.401879i
$595$	5.83656	−	14.3734i	0.239276	−	0.589253i
$596$	−9.71543	+	16.8276i	−0.397959	+	0.689286i
$597$	−5.69241	−	2.66932i	−0.232975	−	0.109248i
$598$	11.0072	−	19.0650i	0.450118	−	0.779627i
$599$	3.67779	−	6.37012i	0.150270	−	0.260276i	−0.781056	−	0.624460i	$-0.785319\pi$
$599$	3.67779	−	6.37012i	0.150270	−	0.260276i	0.931327	+	0.364185i	$0.118652\pi$
$600$	−3.48784	+	2.43106i	−0.142390	+	0.0992476i
$601$	−15.8014	+	27.3689i	−0.644553	+	1.11640i	0.339851	+	0.940479i	$0.389623\pi$
$601$	−15.8014	+	27.3689i	−0.644553	+	1.11640i	−0.984405	+	0.175920i	$0.943710\pi$
$602$	9.53130	+	12.2437i	0.388467	+	0.499015i
$603$	27.9527	+	33.6049i	1.13832	+	1.36850i
$604$	5.08408	−	8.80588i	0.206868	−	0.358306i
$605$	3.73203			0.151729
$606$	1.69363	+	0.794187i	0.0687990	+	0.0322616i
$607$	−1.99685			−0.0810498			−0.0405249	−	0.999179i	$-0.512903\pi$
$607$	−1.99685			−0.0810498			−0.0405249	+	0.999179i	$0.512903\pi$
$608$	2.25315	+	3.90258i	0.0913775	+	0.158270i
$609$	26.5931	−	24.6052i	1.07761	−	0.997054i
$610$	−2.45114	+	4.24550i	−0.0992437	+	0.171895i
$611$	−7.61442	+	13.1886i	−0.308047	+	0.533552i
$612$	9.19980	−	24.9423i	0.371880	−	1.00823i
$613$	−3.00257	−	5.20061i	−0.121273	−	0.210051i	0.798997	−	0.601335i	$-0.205364\pi$
$613$	−3.00257	−	5.20061i	−0.121273	−	0.210051i	−0.920270	+	0.391284i	$0.872031\pi$
$614$	7.36682	+	12.7597i	0.297301	+	0.514940i
$615$	−5.04450	−	2.36549i	−0.203414	−	0.0953859i
$616$	−15.3118	−	19.6691i	−0.616929	−	0.792492i
$617$	−3.65695	−	6.33402i	−0.147223	−	0.254998i	0.782977	−	0.622051i	$-0.213700\pi$
$617$	−3.65695	−	6.33402i	−0.147223	−	0.254998i	−0.930200	+	0.367053i	$0.880367\pi$
$618$	12.9395	+	6.06767i	0.520504	+	0.244078i
$619$	−18.6023			−0.747690			−0.373845	−	0.927491i	$-0.621961\pi$
$619$	−18.6023			−0.747690			−0.373845	+	0.927491i	$0.621961\pi$
$620$	−3.05129	−	5.28499i	−0.122543	−	0.212250i
$621$	−9.06315	−	34.7176i	−0.363692	−	1.39317i
$622$	8.97207			0.359747
$623$	−4.97924	+	0.690890i	−0.199489	+	0.0276799i
$624$	−0.877561	−	10.2850i	−0.0351305	−	0.411729i
$625$	1.00000			0.0400000
$626$	5.20647	−	9.01787i	0.208092	−	0.360427i
$627$	0.437409	+	5.12642i	0.0174684	+	0.204729i
$628$	−9.15234	−	15.8523i	−0.365218	−	0.632576i
$629$	49.6525			1.97978
$630$	4.10083	+	3.73757i	0.163381	+	0.148908i
$631$	4.53109			0.180380			0.0901899	−	0.995925i	$-0.471253\pi$
$631$	4.53109			0.180380			0.0901899	+	0.995925i	$0.471253\pi$
$632$	−16.4283	−	28.4547i	−0.653484	−	1.13187i
$633$	7.06525	+	3.31308i	0.280818	+	0.131683i
$634$	−11.9676	+	20.7285i	−0.475294	+	0.823233i
$635$	−1.89590			−0.0752365
$636$	5.69648	−	3.97051i	0.225880	−	0.157441i
$637$	−30.7177	+	8.69176i	−1.21708	+	0.344380i
$638$	−21.2128			−0.839821
$639$	−10.0401	+	27.2204i	−0.397179	+	1.07682i
$640$	5.31351	+	9.20326i	0.210035	+	0.363791i
$641$	−27.5418			−1.08784			−0.543918	−	0.839139i	$-0.683060\pi$
$641$	−27.5418			−1.08784			−0.543918	+	0.839139i	$0.683060\pi$
$642$	2.00204	−	1.39544i	0.0790141	−	0.0550737i
$643$	1.10409	+	1.91233i	0.0435409	+	0.0754150i	0.886975	−	0.461818i	$-0.152803\pi$
$643$	1.10409	+	1.91233i	0.0435409	+	0.0754150i	−0.843434	+	0.537233i	$0.819469\pi$
$644$	−27.3496	+	3.79487i	−1.07773	+	0.149539i
$645$	−1.23534	−	14.4782i	−0.0486416	−	0.570079i
$646$	−1.58609	−	2.74719i	−0.0624040	−	0.108087i
$647$	24.2181	+	41.9469i	0.952110	+	1.64910i	0.740847	+	0.671673i	$0.234424\pi$
$647$	24.2181	+	41.9469i	0.952110	+	1.64910i	0.211263	+	0.977429i	$0.432243\pi$
$648$	16.8003	+	14.3449i	0.659978	+	0.563522i
$649$	−12.9340	+	22.4023i	−0.507704	+	0.879369i
$650$	1.59402	−	2.76092i	0.0625226	−	0.108292i
$651$	−13.5820	+	12.5668i	−0.532322	+	0.492530i
$652$	12.2641	+	21.2420i	0.480299	+	0.831902i
$653$	−19.4509			−0.761173			−0.380587	−	0.924745i	$-0.624278\pi$
$653$	−19.4509			−0.761173			−0.380587	+	0.924745i	$0.624278\pi$
$654$	0.0397836	+	0.466263i	0.00155566	+	0.0182323i
$655$	−7.33888			−0.286754
$656$	−2.10180	+	3.64042i	−0.0820613	+	0.142134i
$657$	41.4485	−	7.12501i	1.61706	−	0.277973i
$658$	−6.11740	+	0.848814i	−0.238481	+	0.0330902i
$659$	1.04114	−	1.80330i	0.0405569	−	0.0702467i	−0.845034	−	0.534712i	$-0.820420\pi$
$659$	1.04114	−	1.80330i	0.0405569	−	0.0702467i	0.885591	+	0.464465i	$0.153753\pi$
$660$	0.854180	+	10.0110i	0.0332489	+	0.389677i
$661$	22.7432	−	39.3923i	0.884606	−	1.53218i	0.0384419	−	0.999261i	$-0.487761\pi$
$661$	22.7432	−	39.3923i	0.884606	−	1.53218i	0.846164	−	0.532922i	$-0.178906\pi$
$662$	−11.5959	+	20.0847i	−0.450687	+	0.780612i
$663$	3.93757	+	46.1482i	0.152922	+	1.79225i
$664$	−1.08622	+	1.88139i	−0.0421536	+	0.0730122i
$665$	−2.02818	+	0.281418i	−0.0786493	+	0.0109129i
$666$	−6.14555	+	16.6617i	−0.238135	+	0.645627i
$667$	−27.2968	+	47.2794i	−1.05694	+	1.83067i
$668$	−26.0099			−1.00635
$669$	1.72381	+	20.2030i	0.0666463	+	0.781093i
$670$	10.1853			0.393494
$671$	13.4583	+	23.3105i	0.519553	+	0.899893i
$672$	19.5855	−	18.1214i	0.755526	−	0.699050i
$673$	−17.4910	+	30.2953i	−0.674229	+	1.16780i	0.302464	+	0.953161i	$0.402191\pi$
$673$	−17.4910	+	30.2953i	−0.674229	+	1.16780i	−0.976694	+	0.214639i	$0.931143\pi$
$674$	−7.60712	+	13.1759i	−0.293015	+	0.507518i
$675$	−1.31249	−	5.02766i	−0.0505177	−	0.193515i
$676$	5.89304	+	10.2070i	0.226655	+	0.392579i
$677$	5.91975	+	10.2533i	0.227514	+	0.394066i	0.957071	−	0.289854i	$-0.0936068\pi$
$677$	5.91975	+	10.2533i	0.227514	+	0.394066i	−0.729557	+	0.683921i	$0.760273\pi$
$678$	−0.821272	−	9.62529i	−0.0315408	−	0.369657i
$679$	16.1288	−	2.23793i	0.618966	−	0.0858840i
$680$	−7.19620	−	12.4642i	−0.275961	−	0.477979i
$681$	13.1795	−	9.18626i	0.505040	−	0.352018i
$682$	10.8341			0.414860
$683$	0.504725	+	0.874210i	0.0193128	+	0.0334507i	0.875520	−	0.483181i	$-0.160519\pi$
$683$	0.504725	+	0.874210i	0.0193128	+	0.0334507i	−0.856207	+	0.516632i	$0.827186\pi$
$684$	−3.45823	+	0.594471i	−0.132229	+	0.0227302i
$685$	−9.45201			−0.361143
$686$	−10.4338	−	7.66477i	−0.398366	−	0.292642i
$687$	24.0232	−	16.7444i	0.916541	−	0.638839i
$688$	−10.9631			−0.417963
$689$	−6.04862	+	10.4765i	−0.230434	+	0.399123i
$690$	−7.56992	−	3.54973i	−0.288182	−	0.135136i
$691$	10.1696	+	17.6143i	0.386870	+	0.670078i	0.992027	−	0.126028i	$-0.0402230\pi$
$691$	10.1696	+	17.6143i	0.386870	+	0.670078i	−0.605157	+	0.796106i	$0.706890\pi$
$692$	−24.2275			−0.920990
$693$	29.0304	−	9.23877i	1.10277	−	0.350952i
$694$	3.36904			0.127887
$695$	3.28976	+	5.69803i	0.124788	+	0.216139i
$696$	−2.85756	−	33.4906i	−0.108316	−	1.26946i
$697$	9.43064	−	16.3344i	0.357211	−	0.618708i
$698$	−4.57155			−0.173036
$699$	1.03100	+	12.0833i	0.0389961	+	0.457034i
$700$	−3.96066	+	0.549558i	−0.149699	+	0.0207713i
$701$	−33.4009			−1.26154			−0.630768	−	0.775972i	$-0.717260\pi$
$701$	−33.4009			−1.26154			−0.630768	+	0.775972i	$0.717260\pi$
$702$	−15.9731	−	4.39051i	−0.602866	−	0.165709i
$703$	−3.27684	−	5.67565i	−0.123588	−	0.214061i
$704$	−5.59147			−0.210737
$705$	5.23662	+	2.45559i	0.197223	+	0.0924828i
$706$	0.123884	+	0.214573i	0.00466242	+	0.00807555i
$707$	2.51088	+	3.22541i	0.0944313	+	0.121304i
$708$	−15.9732	−	7.49023i	−0.600308	−	0.281500i
$709$	19.5316	+	33.8296i	0.733523	+	1.27050i	0.955368	+	0.295417i	$0.0954587\pi$
$709$	19.5316	+	33.8296i	0.733523	+	1.27050i	−0.221845	+	0.975082i	$0.571208\pi$
$710$	3.38025	+	5.85477i	0.126859	+	0.219725i
$711$	39.5769	−	6.80327i	1.48425	−	0.255143i
$712$	−2.33187	+	4.03892i	−0.0873906	+	0.151365i
$713$	13.9414	−	24.1473i	0.522111	−	0.904323i
$714$	−13.7871	+	12.7565i	−0.515968	+	0.477399i
$715$	−8.75220	−	15.1593i	−0.327314	−	0.566924i
$716$	13.9048			0.519647
$717$	−25.1053	−	11.7725i	−0.937575	−	0.439653i
$718$	−8.75691			−0.326805
$719$	1.55174	−	2.68769i	0.0578702	−	0.100234i	−0.835639	−	0.549279i	$-0.814902\pi$
$719$	1.55174	−	2.68769i	0.0578702	−	0.100234i	0.893509	+	0.449045i	$0.148236\pi$
$720$	−3.86367	+	0.664166i	−0.143991	+	0.0247520i
$721$	19.1834	+	24.6425i	0.714427	+	0.917736i
$722$	6.43162	−	11.1399i	0.239360	−	0.414584i
$723$	−10.4505	+	7.28411i	−0.388658	+	0.270899i
$724$	−4.35532	+	7.54364i	−0.161864	+	0.280357i
$725$	−3.95301	+	6.84682i	−0.146811	+	0.254284i
$726$	−4.09122	−	1.91848i	−0.151839	−	0.0712014i
$727$	21.5168	−	37.2683i	0.798015	−	1.38220i	−0.122892	−	0.992420i	$-0.539217\pi$
$727$	21.5168	−	37.2683i	0.798015	−	1.38220i	0.920907	−	0.389783i	$-0.127450\pi$
$728$	−11.1429	+	27.4411i	−0.412984	+	1.01704i
$729$	−23.5547	+	13.1975i	−0.872398	+	0.488796i
$730$	4.89992	−	8.48691i	0.181354	−	0.314115i
$731$	49.1907			1.81938
$732$	−15.0601	+	10.4970i	−0.556636	+	0.387981i
$733$	23.8253			0.880009			0.440004	−	0.897996i	$-0.354977\pi$
$733$	23.8253			0.880009			0.440004	+	0.897996i	$0.354977\pi$
$734$	−4.52773	−	7.84226i	−0.167122	−	0.289463i
$735$	4.28092	+	11.3434i	0.157904	+	0.418409i
$736$	−20.1038	+	34.8207i	−0.741034	+	1.28351i
$737$	27.9621	−	48.4317i	1.03000	−	1.78401i
$738$	4.31400	+	5.18632i	0.158801	+	0.190911i
$739$	−0.522437	−	0.904887i	−0.0192181	−	0.0332868i	0.856256	−	0.516551i	$-0.172784\pi$
$739$	−0.522437	−	0.904887i	−0.0192181	−	0.0332868i	−0.875475	+	0.483264i	$0.839451\pi$
$740$	−6.39908	−	11.0835i	−0.235235	−	0.407438i
$741$	5.01522	−	3.49566i	0.184239	−	0.128416i
$742$	−4.85944	+	0.674267i	−0.178396	+	0.0247531i
$743$	23.6637	+	40.9867i	0.868137	+	1.50366i	0.863899	+	0.503666i	$0.168016\pi$
$743$	23.6637	+	40.9867i	0.868137	+	1.50366i	0.00423816	+	0.999991i	$0.498651\pi$
$744$	1.45946	+	17.1048i	0.0535064	+	0.627094i
$745$	−12.8568			−0.471036
$746$	−3.62820	−	6.28422i	−0.132838	−	0.230082i
$747$	−1.69795	−	2.04129i	−0.0621248	−	0.0746867i
$748$	−34.0130			−1.24364
$749$	5.28196	−	0.732894i	0.192999	−	0.0267794i
$750$	−1.09625	−	0.514057i	−0.0400292	−	0.0187707i
$751$	−44.4958			−1.62368			−0.811838	−	0.583883i	$-0.801533\pi$
$751$	−44.4958			−1.62368			−0.811838	+	0.583883i	$0.801533\pi$
$752$	2.18185	−	3.77907i	0.0795637	−	0.137808i
$753$	21.9940	−	15.3301i	0.801506	−	0.558658i
$754$	12.6024	+	21.8279i	0.458951	+	0.794926i
$755$	6.72795			0.244855
$756$	7.96131	+	19.1916i	0.289550	+	0.697990i
$757$	15.8107			0.574650			0.287325	−	0.957833i	$-0.407234\pi$
$757$	15.8107			0.574650			0.287325	+	0.957833i	$0.407234\pi$
$758$	−2.03543	−	3.52546i	−0.0739301	−	0.128051i
$759$	−37.6610	+	26.2501i	−1.36701	+	0.952819i
$760$	−0.949832	+	1.64516i	−0.0344540	+	0.0596761i
$761$	28.8757			1.04674			0.523372	−	0.852104i	$-0.324674\pi$
$761$	28.8757			1.04674			0.523372	+	0.852104i	$0.324674\pi$
$762$	2.07837	+	0.974602i	0.0752915	+	0.0353061i
$763$	−0.384717	+	0.947425i	−0.0139277	+	0.0342991i
$764$	−3.48057			−0.125923
$765$	17.3361	−	2.98008i	0.626788	−	0.107745i
$766$	−9.12257	−	15.8008i	−0.329612	−	0.570905i
$767$	30.7360			1.10981
$768$	−1.52293	−	17.8487i	−0.0549538	−	0.644058i
$769$	−20.2272	−	35.0345i	−0.729411	−	1.26338i	−0.957133	−	0.289650i	$-0.906461\pi$
$769$	−20.2272	−	35.0345i	−0.729411	−	1.26338i	0.227722	−	0.973726i	$-0.426872\pi$
$770$	2.67081	−	6.57727i	0.0962492	−	0.237028i
$771$	−0.505716	+	0.352489i	−0.0182129	+	0.0126946i
$772$	15.0776	+	26.1152i	0.542656	+	0.939908i
$773$	0.958668	+	1.66046i	0.0344809	+	0.0597226i	0.882751	−	0.469841i	$-0.155689\pi$
$773$	0.958668	+	1.66046i	0.0344809	+	0.0597226i	−0.848270	+	0.529564i	$0.822356\pi$
$774$	−6.08839	+	16.5067i	−0.218843	+	0.593321i
$775$	2.01894	−	3.49691i	0.0725226	−	0.125613i
$776$	7.55340	−	13.0829i	0.271151	−	0.469648i
$777$	−28.4838	+	26.3546i	−1.02185	+	0.945467i
$778$	−0.0560951	−	0.0971596i	−0.00201111	−	0.00348334i
$779$	−2.48952			−0.0891962
$780$	9.79382	−	6.82640i	0.350675	−	0.244424i
$781$	37.1195			1.32824
$782$	14.1519	−	24.5118i	0.506071	−	0.876541i
$783$	39.6118	+	10.8880i	1.41561	+	0.389107i
$784$	8.80189	−	2.49055i	0.314353	−	0.0889481i
$785$	6.05582	−	10.4890i	0.216141	−	0.374368i
$786$	8.04521	+	3.77260i	0.286963	+	0.134564i
$787$	9.54909	−	16.5395i	0.340388	−	0.589570i	−0.644117	−	0.764927i	$-0.722775\pi$
$787$	9.54909	−	16.5395i	0.340388	−	0.589570i	0.984505	+	0.175358i	$0.0561082\pi$
$788$	0.197352	−	0.341824i	0.00703038	−	0.0121770i
$789$	27.2332	−	18.9818i	0.969527	−	0.675771i
$790$	4.67866	−	8.10368i	0.166459	−	0.288316i
$791$	7.94190	−	19.5581i	0.282381	−	0.695407i
$792$	9.78084	−	26.5176i	0.347547	−	0.942261i
$793$	15.9910	−	27.6972i	0.567857	−	0.983558i
$794$	−8.51672			−0.302247
$795$	4.15978	+	1.95063i	0.147532	+	0.0691817i
$796$	−5.48600			−0.194446
$797$	20.4912	+	35.4919i	0.725837	+	1.25719i	0.958628	+	0.284660i	$0.0918808\pi$
$797$	20.4912	+	35.4919i	0.725837	+	1.25719i	−0.232791	+	0.972527i	$0.574786\pi$
$798$	2.36804	+	0.734096i	0.0838278	+	0.0259867i
$799$	−9.78982	+	16.9565i	−0.346339	+	0.599877i
$800$	−2.91134	+	5.04260i	−0.102932	+	0.178283i
$801$	−3.64511	−	4.38217i	−0.128794	−	0.154836i
$802$	6.58561	+	11.4066i	0.232546	+	0.402781i
$803$	−26.9037	−	46.5987i	−0.949413	−	1.64443i
$804$	34.5325	+	16.1932i	1.21787	+	0.571089i
$805$	−11.2227	−	14.4164i	−0.395549	−	0.508113i
$806$	−6.43647	−	11.1483i	−0.226715	−	0.392682i
$807$	−13.1365	−	6.16003i	−0.462426	−	0.216843i
$808$	3.79219			0.133409
$809$	19.3458	+	33.5079i	0.680163	+	1.17808i	0.974931	+	0.222508i	$0.0714242\pi$
$809$	19.3458	+	33.5079i	0.680163	+	1.17808i	−0.294768	+	0.955569i	$0.595242\pi$
$810$	−1.14570	+	6.18624i	−0.0402557	+	0.217362i
$811$	−48.0986			−1.68897			−0.844485	−	0.535580i	$-0.820093\pi$
$811$	−48.0986			−1.68897			−0.844485	+	0.535580i	$0.820093\pi$
$812$	11.8938	−	29.2903i	0.417391	−	1.02789i
$813$	0.0117069	+	0.137205i	0.000410580	+	0.00481199i
$814$	22.7210			0.796369
$815$	−8.11477	+	14.0552i	−0.284248	+	0.492332i
$816$	−1.12827	−	13.2234i	−0.0394975	−	0.462910i
$817$	−3.24636	−	5.62286i	−0.113576	−	0.196719i
$818$	−1.03127			−0.0360576
$819$	−26.7534	−	24.3836i	−0.934841	−	0.852030i
$820$	−4.86158			−0.169774
$821$	−10.8094	−	18.7224i	−0.377251	−	0.653418i	0.613410	−	0.789764i	$-0.289797\pi$
$821$	−10.8094	−	18.7224i	−0.377251	−	0.653418i	−0.990661	+	0.136347i	$0.956464\pi$
$822$	10.3617	+	4.85888i	0.361407	+	0.169473i
$823$	−12.9732	+	22.4702i	−0.452217	+	0.783263i	−0.998523	−	0.0543227i	$-0.982700\pi$
$823$	−12.9732	+	22.4702i	−0.452217	+	0.783263i	0.546307	+	0.837585i	$0.316033\pi$
$824$	28.9728			1.00931
$825$	−5.45391	+	3.80144i	−0.189881	+	0.132349i
$826$	7.65692	+	9.83589i	0.266418	+	0.342234i
$827$	−45.3663			−1.57754			−0.788770	−	0.614689i	$-0.789282\pi$
$827$	−45.3663			−1.57754			−0.788770	+	0.614689i	$0.789282\pi$
$828$	−20.0216	−	24.0701i	−0.695798	−	0.836492i
$829$	−20.8415	−	36.0986i	−0.723857	−	1.25376i	−0.959443	−	0.281903i	$-0.909034\pi$
$829$	−20.8415	−	36.0986i	−0.723857	−	1.25376i	0.235586	−	0.971853i	$-0.424299\pi$
$830$	−0.618696			−0.0214753
$831$	30.3904	−	21.1824i	1.05423	−	0.734811i
$832$	3.32185	+	5.75362i	0.115165	+	0.199471i
$833$	−39.4936	+	11.1749i	−1.36837	+	0.387189i
$834$	−0.677268	−	7.93757i	−0.0234519	−	0.274855i
$835$	−8.60497	−	14.9042i	−0.297787	−	0.515783i
$836$	2.24470	+	3.88793i	0.0776345	+	0.134467i
$837$	−20.2311	−	5.56091i	−0.699290	−	0.192213i
$838$	−1.60702	+	2.78343i	−0.0555135	+	0.0961521i
$839$	−16.8414	+	29.1701i	−0.581429	+	1.00706i	0.413881	+	0.910331i	$0.364173\pi$
$839$	−16.8414	+	29.1701i	−0.581429	+	1.00706i	−0.995310	+	0.0967337i	$0.969160\pi$
$840$	10.7439	+	3.33064i	0.370701	+	0.114918i
$841$	−16.7526	−	29.0164i	−0.577677	−	1.00057i
$842$	11.9715			0.412564
$843$	−0.624573	−	7.31999i	−0.0215114	−	0.252114i
$844$	6.80905			0.234377
$845$	−3.89924	+	6.75368i	−0.134138	+	0.232334i
$846$	−4.47831	−	5.38385i	−0.153967	−	0.185101i
$847$	−6.06541	−	7.79148i	−0.208410	−	0.267718i
$848$	1.73318	−	3.00195i	0.0595176	−	0.103087i
$849$	−0.881715	−	10.3337i	−0.0302604	−	0.354651i
$850$	2.04942	−	3.54970i	0.0702946	−	0.121754i
$851$	29.2376	−	50.6410i	1.00225	−	1.73595i
$852$	2.15223	+	25.2241i	0.0737343	+	0.864165i
$853$	25.3194	−	43.8545i	0.866920	−	1.50155i	0.00179188	−	0.999998i	$-0.499430\pi$
$853$	25.3194	−	43.8545i	0.866920	−	1.50155i	0.865128	−	0.501551i	$-0.167237\pi$
$854$	12.8471	−	1.78259i	0.439619	−	0.0609990i
$855$	−1.48475	−	1.78497i	−0.0507773	−	0.0610448i
$856$	2.47364	−	4.28447i	0.0845473	−	0.146440i
$857$	13.6216			0.465306			0.232653	−	0.972560i	$-0.425259\pi$
$857$	13.6216			0.465306			0.232653	+	0.972560i	$0.425259\pi$
$858$	1.80183	+	21.1174i	0.0615134	+	0.720936i
$859$	4.14348			0.141374			0.0706869	−	0.997499i	$-0.477481\pi$
$859$	4.14348			0.141374			0.0706869	+	0.997499i	$0.477481\pi$
$860$	−6.33956	−	10.9804i	−0.216177	−	0.374430i
$861$	3.25995	+	14.3760i	0.111099	+	0.489934i
$862$	−6.12298	+	10.6053i	−0.208549	+	0.361218i
$863$	−12.8153	+	22.1968i	−0.436238	+	0.755587i	−0.997396	−	0.0721222i	$-0.977023\pi$
$863$	−12.8153	+	22.1968i	−0.436238	+	0.755587i	0.561158	+	0.827709i	$0.310356\pi$
$864$	29.1736	+	8.01890i	0.992505	+	0.272809i
$865$	−8.01528	−	13.8829i	−0.272528	−	0.472032i
$866$	−10.9900	−	19.0353i	−0.373456	−	0.646845i
$867$	2.55924	+	29.9942i	0.0869163	+	1.01866i
$868$	−6.07459	+	14.9596i	−0.206185	+	0.507762i
$869$	−25.6889	−	44.4944i	−0.871436	−	1.50937i
$870$	7.85313	−	5.47372i	0.266246	−	0.185576i
$871$	−66.4483			−2.25152
$872$	0.474337	+	0.821577i	0.0160631	+	0.0278221i
$873$	11.8072	+	14.1947i	0.399615	+	0.480419i
$874$	−3.73584			−0.126367
$875$	−1.62523	−	2.08773i	−0.0549428	−	0.0705782i
$876$	30.1056	−	20.9840i	1.01718	−	0.708982i
$877$	9.89011			0.333965			0.166983	−	0.985960i	$-0.446598\pi$
$877$	9.89011			0.333965			0.166983	+	0.985960i	$0.446598\pi$
$878$	−14.0983	+	24.4189i	−0.475793	+	0.824098i
$879$	−19.6636	−	9.22074i	−0.663235	−	0.311008i
$880$	2.50786	+	4.34375i	0.0845401	+	0.146428i
$881$	−14.6040			−0.492022			−0.246011	−	0.969267i	$-0.579120\pi$
$881$	−14.6040			−0.492022			−0.246011	+	0.969267i	$0.579120\pi$
$882$	1.13824	−	14.6358i	0.0383267	−	0.492814i
$883$	15.8128			0.532142			0.266071	−	0.963953i	$-0.414274\pi$
$883$	15.8128			0.532142			0.266071	+	0.963953i	$0.414274\pi$
$884$	20.2069	+	34.9993i	0.679630	+	1.17715i
$885$	−0.992407	−	11.6310i	−0.0333594	−	0.390972i
$886$	−12.6298	+	21.8754i	−0.424306	+	0.734920i
$887$	−21.8316			−0.733033			−0.366517	−	0.930412i	$-0.619450\pi$
$887$	−21.8316			−0.733033			−0.366517	+	0.930412i	$0.619450\pi$
$888$	3.06073	+	35.8718i	0.102712	+	1.20378i
$889$	3.08128	+	3.95813i	0.103343	+	0.132752i
$890$	−1.32820			−0.0445213
$891$	26.2705	+	22.4311i	0.880096	+	0.751470i
$892$	8.84626	+	15.3222i	0.296195	+	0.513024i
$893$	2.58433			0.0864814
$894$	14.0942	+	6.60913i	0.471380	+	0.221042i
$895$	4.60018	+	7.96775i	0.153767	+	0.266333i
$896$	10.5783	−	26.0506i	0.353395	−	0.870290i
$897$	49.3855	+	23.1581i	1.64893	+	0.773227i
$898$	−6.02281	−	10.4318i	−0.200984	−	0.348114i
$899$	15.9618	+	27.6467i	0.532357	+	0.922069i
$900$	−2.89944	−	3.48573i	−0.0966481	−	0.116191i
$901$	−7.77668	+	13.4696i	−0.259079	+	0.448737i
$902$	4.31545	−	7.47459i	0.143689	−	0.248877i
$903$	−28.2189	+	26.1095i	−0.939066	+	0.868870i
$904$	−9.79197	−	16.9602i	−0.325676	−	0.564088i
$905$	−5.76356			−0.191587
$906$	−7.37548	−	3.45855i	−0.245034	−	0.114903i
$907$	−45.5220			−1.51153			−0.755767	−	0.654841i	$-0.772736\pi$
$907$	−45.5220			−1.51153			−0.755767	+	0.654841i	$0.772736\pi$
$908$	7.00893	−	12.1398i	0.232600	−	0.402874i
$909$	−1.60390	+	4.34845i	−0.0531979	+	0.144229i
$910$	−8.35471	+	1.15925i	−0.276956	+	0.0384288i
$911$	23.4277	−	40.5779i	0.776193	−	1.34441i	−0.157928	−	0.987451i	$-0.550481\pi$
$911$	23.4277	−	40.5779i	0.776193	−	1.34441i	0.934121	−	0.356956i	$-0.116185\pi$
$912$	−1.43707	+	1.00165i	−0.0475860	+	0.0331680i
$913$	−1.69852	+	2.94193i	−0.0562129	+	0.0973635i
$914$	−3.20614	+	5.55320i	−0.106050	+	0.183684i
$915$	−10.9974	−	5.15697i	−0.363563	−	0.170484i
$916$	12.7756	−	22.1281i	0.422119	−	0.731132i
$917$	11.9274	+	15.3216i	0.393876	+	0.505964i
$918$	−20.5365	−	5.64485i	−0.677807	−	0.186308i
$919$	−24.5539	+	42.5286i	−0.809958	+	1.40289i	0.102935	+	0.994688i	$0.467177\pi$
$919$	−24.5539	+	42.5286i	−0.809958	+	1.40289i	−0.912892	+	0.408200i	$0.866157\pi$
$920$	−16.9497			−0.558816
$921$	−29.9488	+	20.8746i	−0.986847	+	0.687843i
$922$	−11.1222			−0.366291
$923$	−22.0525	−	38.1960i	−0.725866	−	1.25724i
$924$	19.5120	−	18.0534i	0.641897	−	0.593914i
$925$	4.23407	−	7.33362i	0.139215	−	0.241128i
$926$	−3.35644	+	5.81353i	−0.110300	+	0.191045i
$927$	−12.2539	+	33.2226i	−0.402472	+	1.09117i
$928$	−23.0172	−	39.8669i	−0.755575	−	1.30869i
$929$	−26.4882	−	45.8789i	−0.869050	−	1.50524i	−0.862969	−	0.505257i	$-0.831398\pi$
$929$	−26.4882	−	45.8789i	−0.869050	−	1.50524i	−0.00608051	−	0.999982i	$-0.501935\pi$
$930$	−4.01087	+	2.79562i	−0.131522	+	0.0916720i
$931$	3.88378	+	3.77692i	0.127286	+	0.123783i
$932$	5.29091	+	9.16413i	0.173310	+	0.300181i
$933$	1.88992	+	22.1498i	0.0618732	+	0.725153i
$934$	−18.3670			−0.600985
$935$	−11.2527	−	19.4902i	−0.368001	−	0.637397i
$936$	−33.0973	+	5.68944i	−1.08182	+	0.185965i
$937$	22.9340			0.749220			0.374610	−	0.927183i	$-0.377777\pi$
$937$	22.9340			0.749220			0.374610	+	0.927183i	$0.377777\pi$
$938$	−16.5535	−	21.2643i	−0.540492	−	0.694303i
$939$	23.3596	+	10.9539i	0.762313	+	0.357468i
$940$	5.04674			0.164606
$941$	15.4761	−	26.8054i	0.504507	−	0.873831i	−0.495480	−	0.868619i	$-0.665008\pi$
$941$	15.4761	−	26.8054i	0.504507	−	0.873831i	0.999986	−	0.00521168i	$-0.00165894\pi$
$942$	−12.0306	+	8.38546i	−0.391978	+	0.273213i
$943$	−11.1063	−	19.2368i	−0.361672	−	0.626435i
$944$	−8.80712			−0.286648
$945$	−8.36331	+	10.9112i	−0.272059	+	0.354942i
$946$	22.5096			0.731851
$947$	−6.42093	−	11.1214i	−0.208652	−	0.361396i	0.742638	−	0.669693i	$-0.233574\pi$
$947$	−6.42093	−	11.1214i	−0.208652	−	0.361396i	−0.951290	+	0.308297i	$0.900241\pi$
$948$	28.7462	−	20.0364i	0.933633	−	0.650752i
$949$	−31.9667	+	55.3679i	−1.03768	+	1.79732i
$950$	−0.541010			−0.0175527
$951$	−53.6944	−	25.1787i	−1.74116	−	0.816475i
$952$	−14.3264	+	35.2809i	−0.464321	+	1.14346i
$953$	47.3316			1.53322			0.766611	−	0.642112i	$-0.221942\pi$
$953$	47.3316			1.53322			0.766611	+	0.642112i	$0.221942\pi$
$954$	−3.55741	−	4.27673i	−0.115175	−	0.138464i
$955$	−1.15149	−	1.99444i	−0.0372614	−	0.0645386i
$956$	−24.1950			−0.782521
$957$	−4.46836	−	52.3691i	−0.144442	−	1.69285i
$958$	2.56296	+	4.43917i	0.0828054	+	0.143423i
$959$	15.3617	+	19.7333i	0.496055	+	0.637221i
$960$	2.07001	−	1.44282i	0.0668092	−	0.0465667i
$961$	7.34773	+	12.7266i	0.237024	+	0.410537i
$962$	−13.4984	−	23.3799i	−0.435205	−	0.753797i
$963$	3.86672	+	4.64859i	0.124603	+	0.149799i
$964$	−5.55763	+	9.62609i	−0.178999	+	0.310036i
$965$	−9.97640	+	17.2796i	−0.321152	+	0.556251i
$966$	4.89198	+	21.5731i	0.157397	+	0.694103i
$967$	−10.2481	−	17.7503i	−0.329557	−	0.570810i	0.652867	−	0.757473i	$-0.273566\pi$
$967$	−10.2481	−	17.7503i	−0.329557	−	0.570810i	−0.982424	+	0.186663i	$0.940233\pi$
$968$	−9.16061			−0.294433
$969$	6.44804	−	4.49436i	0.207141	−	0.144379i
$970$	4.30230			0.138139
$971$	28.6673	−	49.6533i	0.919979	−	1.59345i	0.120534	−	0.992709i	$-0.461539\pi$
$971$	28.6673	−	49.6533i	0.919979	−	1.59345i	0.799444	−	0.600740i	$-0.205127\pi$
$972$	−13.7196	+	19.1524i	−0.440056	+	0.614314i
$973$	6.54934	−	16.1288i	0.209962	−	0.517064i
$974$	−11.8054	+	20.4476i	−0.378271	+	0.655185i
$975$	7.15181	+	3.35367i	0.229041	+	0.107403i
$976$	−4.58208	+	7.93640i	−0.146669	+	0.254038i
$977$	4.45153	−	7.71028i	0.142417	−	0.246674i	−0.785989	−	0.618240i	$-0.787846\pi$
$977$	4.45153	−	7.71028i	0.142417	−	0.246674i	0.928406	+	0.371567i	$0.121179\pi$
$978$	16.1210	−	11.2365i	0.515491	−	0.359303i
$979$	−3.64633	+	6.31564i	−0.116537	+	0.201849i
$980$	7.58432	+	7.37564i	0.242272	+	0.235606i
$981$	−1.14271	+	0.196432i	−0.0364839	+	0.00627159i
$982$	7.15531	−	12.3934i	0.228335	−	0.395488i
$983$	1.90661			0.0608115			0.0304058	−	0.999538i	$-0.490320\pi$
$983$	1.90661			0.0608115			0.0304058	+	0.999538i	$0.490320\pi$
$984$	12.3822	+	5.80632i	0.394729	+	0.185099i
$985$	0.261164			0.00832136
$986$	16.2028	+	28.0640i	0.516002	+	0.893741i
$987$	−3.38411	−	14.9236i	−0.107718	−	0.475022i
$988$	2.66712	−	4.61959i	0.0848524	−	0.146969i
$989$	28.9656	−	50.1699i	0.921053	−	1.59531i
$990$	7.93298	−	1.36368i	0.252127	−	0.0433406i
$991$	−4.29788	−	7.44415i	−0.136527	−	0.236471i	0.789653	−	0.613554i	$-0.210261\pi$
$991$	−4.29788	−	7.44415i	−0.136527	−	0.236471i	−0.926180	+	0.377083i	$0.876927\pi$
$992$	11.7557	+	20.3614i	0.373243	+	0.646476i
$993$	−52.0267	−	24.3967i	−1.65102	−	0.774204i
$994$	6.72950	−	16.5724i	0.213447	−	0.525645i
$995$	−1.81496	−	3.14360i	−0.0575380	−	0.0996587i
$996$	−2.09763	−	0.983633i	−0.0664660	−	0.0311676i
$997$	43.4530			1.37617			0.688085	−	0.725630i	$-0.258451\pi$
$997$	43.4530			1.37617			0.688085	+	0.725630i	$0.258451\pi$
$998$	−8.50730	−	14.7351i	−0.269294	−	0.466431i
$999$	−42.4281	−	11.6622i	−1.34237	−	0.368974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.8	✓	36
3.2	odd	2		945.2.k.c.856.11		36
7.4	even	3		315.2.l.c.151.11	yes	36
9.4	even	3		315.2.l.c.121.11	yes	36
9.5	odd	6		945.2.l.c.226.8		36
21.11	odd	6		945.2.l.c.46.8		36
63.4	even	3	inner	315.2.k.c.256.8	yes	36
63.32	odd	6		945.2.k.c.361.11		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.8	✓	36	1.1	even	1	trivial
315.2.k.c.256.8	yes	36	63.4	even	3	inner
315.2.l.c.121.11	yes	36	9.4	even	3
315.2.l.c.151.11	yes	36	7.4	even	3
945.2.k.c.361.11		36	63.32	odd	6
945.2.k.c.856.11		36	3.2	odd	2
945.2.l.c.46.8		36	21.11	odd	6
945.2.l.c.226.8		36	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.349525 - 0.605394i) q^{2} +(1.42094 - 0.990413i) q^{3} +(0.755665 - 1.30885i) q^{4} +1.00000 q^{5} +(-1.09625 - 0.514057i) q^{6} +(-1.62523 - 2.08773i) q^{7} -2.45459 q^{8} +(1.03816 - 2.81464i) q^{9} +(-0.349525 - 0.605394i) q^{10} -3.83823 q^{11} +(-0.222545 - 2.60822i) q^{12} +(2.28027 + 3.94954i) q^{13} +(-0.695843 + 1.71362i) q^{14} +(1.42094 - 0.990413i) q^{15} +(-0.653390 - 1.13171i) q^{16} +(2.93173 + 5.07790i) q^{17} +(-2.06683 + 0.355289i) q^{18} +(0.386961 - 0.670236i) q^{19} +(0.755665 - 1.30885i) q^{20} +(-4.37708 - 1.35690i) q^{21} +(1.34156 + 2.32364i) q^{22} +6.90532 q^{23} +(-3.48784 + 2.43106i) q^{24} +1.00000 q^{25} +(1.59402 - 2.76092i) q^{26} +(-1.31249 - 5.02766i) q^{27} +(-3.96066 + 0.549558i) q^{28} +(-3.95301 + 6.84682i) q^{29} +(-1.09625 - 0.514057i) q^{30} +(2.01894 - 3.49691i) q^{31} +(-2.91134 + 5.04260i) q^{32} +(-5.45391 + 3.80144i) q^{33} +(2.04942 - 3.54970i) q^{34} +(-1.62523 - 2.08773i) q^{35} +(-2.89944 - 3.48573i) q^{36} +(4.23407 - 7.33362i) q^{37} -0.541010 q^{38} +(7.15181 + 3.35367i) q^{39} -2.45459 q^{40} +(-1.60838 - 2.78579i) q^{41} +(0.708437 + 3.12413i) q^{42} +(4.19469 - 7.26541i) q^{43} +(-2.90042 + 5.02367i) q^{44} +(1.03816 - 2.81464i) q^{45} +(-2.41358 - 4.18044i) q^{46} +(1.66963 + 2.89189i) q^{47} +(-2.04929 - 0.960963i) q^{48} +(-1.71725 + 6.78609i) q^{49} +(-0.349525 - 0.605394i) q^{50} +(9.19504 + 4.31179i) q^{51} +6.89248 q^{52} +(1.32630 + 2.29721i) q^{53} +(-2.58497 + 2.55186i) q^{54} -3.83823 q^{55} +(3.98928 + 5.12453i) q^{56} +(-0.113961 - 1.33562i) q^{57} +5.52670 q^{58} +(3.36978 - 5.83663i) q^{59} +(-0.222545 - 2.60822i) q^{60} +(-3.50639 - 6.07324i) q^{61} -2.82268 q^{62} +(-7.56348 + 2.40704i) q^{63} +1.45678 q^{64} +(2.28027 + 3.94954i) q^{65} +(4.20764 + 1.97307i) q^{66} +(-7.28514 + 12.6182i) q^{67} +8.86162 q^{68} +(9.81207 - 6.83912i) q^{69} +(-0.695843 + 1.71362i) q^{70} -9.67100 q^{71} +(-2.54827 + 6.90880i) q^{72} +(7.00941 + 12.1407i) q^{73} -5.91964 q^{74} +(1.42094 - 0.990413i) q^{75} +(-0.584826 - 1.01295i) q^{76} +(6.23801 + 8.01320i) q^{77} +(-0.469442 - 5.50185i) q^{78} +(6.69289 + 11.5924i) q^{79} +(-0.653390 - 1.13171i) q^{80} +(-6.84443 - 5.84412i) q^{81} +(-1.12433 + 1.94740i) q^{82} +(0.442527 - 0.766479i) q^{83} +(-5.08359 + 4.70358i) q^{84} +(2.93173 + 5.07790i) q^{85} -5.86458 q^{86} +(1.16417 + 13.6441i) q^{87} +9.42130 q^{88} +(0.950003 - 1.64545i) q^{89} +(-2.06683 + 0.355289i) q^{90} +(4.53962 - 11.1795i) q^{91} +(5.21811 - 9.03803i) q^{92} +(-0.594584 - 6.96851i) q^{93} +(1.16716 - 2.02157i) q^{94} +(0.386961 - 0.670236i) q^{95} +(0.857397 + 10.0487i) q^{96} +(-3.07725 + 5.32996i) q^{97} +(4.70848 - 1.33229i) q^{98} +(-3.98471 + 10.8033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23}+ \cdots - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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