LMFDB - Embedded newform 945.2.k.c.856.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [945,2,Mod(361,945)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("945.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(945, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.k (of order $3$, degree $2$, not 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.11
Character	$\chi$	$=$	945.856
Dual form			945.2.k.c.361.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.349525 + 0.605394i) q^{2} +(0.755665 - 1.30885i) q^{4} -1.00000 q^{5} +(-1.62523 - 2.08773i) q^{7} +2.45459 q^{8} +(-0.349525 - 0.605394i) q^{10} +3.83823 q^{11} +(2.28027 + 3.94954i) q^{13} +(0.695843 - 1.71362i) q^{14} +(-0.653390 - 1.13171i) q^{16} +(-2.93173 - 5.07790i) q^{17} +(0.386961 - 0.670236i) q^{19} +(-0.755665 + 1.30885i) q^{20} +(1.34156 + 2.32364i) q^{22} -6.90532 q^{23} +1.00000 q^{25} +(-1.59402 + 2.76092i) q^{26} +(-3.96066 + 0.549558i) q^{28} +(3.95301 - 6.84682i) q^{29} +(2.01894 - 3.49691i) q^{31} +(2.91134 - 5.04260i) q^{32} +(2.04942 - 3.54970i) q^{34} +(1.62523 + 2.08773i) q^{35} +(4.23407 - 7.33362i) q^{37} +0.541010 q^{38} -2.45459 q^{40} +(1.60838 + 2.78579i) q^{41} +(4.19469 - 7.26541i) q^{43} +(2.90042 - 5.02367i) q^{44} +(-2.41358 - 4.18044i) q^{46} +(-1.66963 - 2.89189i) q^{47} +(-1.71725 + 6.78609i) q^{49} +(0.349525 + 0.605394i) q^{50} +6.89248 q^{52} +(-1.32630 - 2.29721i) q^{53} -3.83823 q^{55} +(-3.98928 - 5.12453i) q^{56} +5.52670 q^{58} +(-3.36978 + 5.83663i) q^{59} +(-3.50639 - 6.07324i) q^{61} +2.82268 q^{62} +1.45678 q^{64} +(-2.28027 - 3.94954i) q^{65} +(-7.28514 + 12.6182i) q^{67} -8.86162 q^{68} +(-0.695843 + 1.71362i) q^{70} +9.67100 q^{71} +(7.00941 + 12.1407i) q^{73} +5.91964 q^{74} +(-0.584826 - 1.01295i) q^{76} +(-6.23801 - 8.01320i) q^{77} +(6.69289 + 11.5924i) q^{79} +(0.653390 + 1.13171i) q^{80} +(-1.12433 + 1.94740i) q^{82} +(-0.442527 + 0.766479i) q^{83} +(2.93173 + 5.07790i) q^{85} +5.86458 q^{86} +9.42130 q^{88} +(-0.950003 + 1.64545i) q^{89} +(4.53962 - 11.1795i) q^{91} +(-5.21811 + 9.03803i) q^{92} +(1.16716 - 2.02157i) q^{94} +(-0.386961 + 0.670236i) q^{95} +(-3.07725 + 5.32996i) q^{97} +(-4.70848 + 1.33229i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) $ 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.349525	+	0.605394i	0.247151	+	0.428078i	0.962734	−	0.270449i	$-0.0871722\pi$
$2$	0.349525	+	0.605394i	0.247151	+	0.428078i	−0.715583	+	0.698528i	$0.753839\pi$
$3$		0			0
$3$		0			0
$4$	0.755665	−	1.30885i	0.377833	−	0.654425i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.62523	−	2.08773i	−0.614279	−	0.789089i
$7$	−1.62523	−	2.08773i	−0.614279	−	0.789089i
$8$	2.45459			0.867829
$9$		0			0
$10$	−0.349525	−	0.605394i	−0.110529	−	0.191442i
$11$	3.83823			1.15727			0.578635	−	0.815586i	$-0.303585\pi$
$11$	3.83823			1.15727			0.578635	+	0.815586i	$0.303585\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−0.653390	−	1.13171i	−0.163348	−	0.282926i
$17$	−2.93173	−	5.07790i	−0.711048	−	1.23157i	−0.964464	−	0.264214i	$-0.914887\pi$
$17$	−2.93173	−	5.07790i	−0.711048	−	1.23157i	0.253416	−	0.967357i	$-0.418446\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	1.34156	+	2.32364i	0.286021	+	0.495403i
$23$	−6.90532			−1.43986			−0.719929	−	0.694048i	$-0.755826\pi$
$23$	−6.90532			−1.43986			−0.719929	+	0.694048i	$0.755826\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.59402	+	2.76092i	−0.312613	+	0.541461i
$27$		0			0
$28$	−3.96066	+	0.549558i	−0.748494	+	0.103857i
$29$	3.95301	−	6.84682i	0.734056	−	1.27142i	−0.221080	−	0.975256i	$-0.570958\pi$
$29$	3.95301	−	6.84682i	0.734056	−	1.27142i	0.955136	−	0.296167i	$-0.0957084\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	2.04942	−	3.54970i	0.351473	−	0.608769i
$35$	1.62523	+	2.08773i	0.274714	+	0.352891i
$36$		0			0
$37$	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
$39$		0			0
$40$	−2.45459			−0.388105
$41$	1.60838	+	2.78579i	0.251186	+	0.435067i	0.963853	−	0.266436i	$-0.0858460\pi$
$41$	1.60838	+	2.78579i	0.251186	+	0.435067i	−0.712667	+	0.701503i	$0.752513\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	−2.41358	−	4.18044i	−0.355863	−	0.616372i
$47$	−1.66963	−	2.89189i	−0.243541	−	0.421826i	0.718179	−	0.695858i	$-0.244976\pi$
$47$	−1.66963	−	2.89189i	−0.243541	−	0.421826i	−0.961720	+	0.274032i	$0.911642\pi$
$48$		0			0
$49$	−1.71725	+	6.78609i	−0.245321	+	0.969442i
$50$	0.349525	+	0.605394i	0.0494302	+	0.0856157i
$51$		0			0
$52$	6.89248			0.955814
$53$	−1.32630	−	2.29721i	−0.182181	−	0.315546i	0.760442	−	0.649406i	$-0.224982\pi$
$53$	−1.32630	−	2.29721i	−0.182181	−	0.315546i	−0.942623	+	0.333859i	$0.891649\pi$
$54$		0			0
$55$	−3.83823			−0.517547
$56$	−3.98928	−	5.12453i	−0.533090	−	0.684794i
$57$		0			0
$58$	5.52670			0.725691
$59$	−3.36978	+	5.83663i	−0.438708	+	0.759864i	−0.997590	−	0.0693827i	$-0.977897\pi$
$59$	−3.36978	+	5.83663i	−0.438708	+	0.759864i	0.558882	+	0.829247i	$0.311230\pi$
$60$		0			0
$61$	−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
$63$		0			0
$64$	1.45678			0.182098
$65$	−2.28027	−	3.94954i	−0.282832	−	0.489880i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−0.695843	+	1.71362i	−0.0831691	+	0.204817i
$71$	9.67100			1.14774			0.573868	−	0.818948i	$-0.305442\pi$
$71$	9.67100			1.14774			0.573868	+	0.818948i	$0.305442\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	−0.584826	−	1.01295i	−0.0670842	−	0.116193i
$77$	−6.23801	−	8.01320i	−0.710888	−	0.913189i
$78$		0			0
$79$	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
$81$		0			0
$82$	−1.12433	+	1.94740i	−0.124162	+	0.215055i
$83$	−0.442527	+	0.766479i	−0.0485736	+	0.0841320i	−0.889290	−	0.457344i	$-0.848801\pi$
$83$	−0.442527	+	0.766479i	−0.0485736	+	0.0841320i	0.840716	+	0.541476i	$0.182134\pi$
$84$		0			0
$85$	2.93173	+	5.07790i	0.317990	+	0.550776i
$86$	5.86458			0.632394
$87$		0			0
$88$	9.42130			1.00431
$89$	−0.950003	+	1.64545i	−0.100700	+	0.174418i	−0.911973	−	0.410250i	$-0.865442\pi$
$89$	−0.950003	+	1.64545i	−0.100700	+	0.174418i	0.811273	+	0.584667i	$0.198775\pi$
$90$		0			0
$91$	4.53962	−	11.1795i	0.475881	−	1.17193i
$92$	−5.21811	+	9.03803i	−0.544025	+	0.942279i
$93$		0			0
$94$	1.16716	−	2.02157i	0.120383	−	0.208509i
$95$	−0.386961	+	0.670236i	−0.0397014	+	0.0687648i
$96$		0			0
$97$	−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
$99$		0			0
$100$	0.755665	−	1.30885i	0.0755665	−	0.130885i
$101$	1.54494			0.153727			0.0768635	−	0.997042i	$-0.475509\pi$
$101$	1.54494			0.153727			0.0768635	+	0.997042i	$0.475509\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	0.927146	−	1.60586i	0.0900524	−	0.155975i
$107$	1.00776	−	1.74549i	0.0974239	−	0.168743i	−0.813194	−	0.581993i	$-0.802273\pi$
$107$	1.00776	−	1.74549i	0.0974239	−	0.168743i	0.910618	+	0.413250i	$0.135606\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	−1.30079	+	3.20339i	−0.122913	+	0.302692i
$113$	−3.98925	−	6.90958i	−0.375277	−	0.649998i	0.615092	−	0.788456i	$-0.289119\pi$
$113$	−3.98925	−	6.90958i	−0.375277	−	0.649998i	−0.990368	+	0.138457i	$0.955786\pi$
$114$		0			0
$115$	6.90532			0.643924
$116$	−5.97431	−	10.3478i	−0.554701	−	0.960770i
$117$		0			0
$118$	−4.71128			−0.433709
$119$	−5.83656	+	14.3734i	−0.535037	+	1.31761i
$120$		0			0
$121$	3.73203			0.339275
$122$	2.45114	−	4.24550i	0.221916	−	0.384369i
$123$		0			0
$124$	−3.05129	−	5.28499i	−0.274014	−	0.474606i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−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
$129$		0			0
$130$	1.59402	−	2.76092i	0.139805	−	0.242149i
$131$	7.33888			0.641201			0.320600	−	0.947215i	$-0.396115\pi$
$131$	7.33888			0.641201			0.320600	+	0.947215i	$0.396115\pi$
$132$		0			0
$133$	−2.02818	+	0.281418i	−0.175865	+	0.0244020i
$134$	−10.1853			−0.879880
$135$		0			0
$136$	−7.19620	−	12.4642i	−0.617069	−	1.06879i
$137$	9.45201			0.807540			0.403770	−	0.914861i	$-0.367700\pi$
$137$	9.45201			0.807540			0.403770	+	0.914861i	$0.367700\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	3.38025	+	5.85477i	0.283664	+	0.491321i
$143$	8.75220	+	15.1593i	0.731896	+	1.26768i
$144$		0			0
$145$	−3.95301	+	6.84682i	−0.328280	+	0.568597i
$146$	−4.89992	+	8.48691i	−0.405520	+	0.702382i
$147$		0			0
$148$	−6.39908	−	11.0835i	−0.526001	−	0.911060i
$149$	12.8568			1.05327			0.526634	−	0.850092i	$-0.323454\pi$
$149$	12.8568			1.05327			0.526634	+	0.850092i	$0.323454\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	2.67081	−	6.57727i	0.215220	−	0.530011i
$155$	−2.01894	+	3.49691i	−0.162166	+	0.280879i
$156$		0			0
$157$	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
$159$		0			0
$160$	−2.91134	+	5.04260i	−0.230162	+	0.398652i
$161$	11.2227	+	14.4164i	0.884475	+	1.13618i
$162$		0			0
$163$	−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
$165$		0			0
$166$	−0.618696			−0.0480201
$167$	8.60497	+	14.9042i	0.665872	+	1.15332i	0.979048	+	0.203630i	$0.0652738\pi$
$167$	8.60497	+	14.9042i	0.665872	+	1.15332i	−0.313176	+	0.949695i	$0.601393\pi$
$168$		0			0
$169$	−3.89924	+	6.75368i	−0.299942	+	0.519514i
$170$	−2.04942	+	3.54970i	−0.157183	+	0.272250i
$171$		0			0
$172$	−6.33956	−	10.9804i	−0.483387	−	0.837250i
$173$	8.01528	+	13.8829i	0.609390	+	1.05550i	0.991341	+	0.131312i	$0.0419191\pi$
$173$	8.01528	+	13.8829i	0.609390	+	1.05550i	−0.381951	+	0.924183i	$0.624748\pi$
$174$		0			0
$175$	−1.62523	−	2.08773i	−0.122856	−	0.157818i
$176$	−2.50786	−	4.34375i	−0.189037	−	0.327422i
$177$		0			0
$178$	−1.32820			−0.0995526
$179$	−4.60018	−	7.96775i	−0.343834	−	0.595538i	0.641307	−	0.767284i	$-0.278392\pi$
$179$	−4.60018	−	7.96775i	−0.343834	−	0.595538i	−0.985141	+	0.171746i	$0.945059\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−16.9497			−1.24955
$185$	−4.23407	+	7.33362i	−0.311295	+	0.539178i
$186$		0			0
$187$	−11.2527	−	19.4902i	−0.822875	−	1.42526i
$188$	−5.04674			−0.368071
$189$		0			0
$190$	−0.541010			−0.0392490
$191$	1.15149	+	1.99444i	0.0833190	+	0.144313i	0.904674	−	0.426105i	$-0.140115\pi$
$191$	1.15149	+	1.99444i	0.0833190	+	0.144313i	−0.821355	+	0.570418i	$0.806781\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	7.58432	+	7.37564i	0.541737	+	0.526831i
$197$	−0.261164			−0.0186071			−0.00930357	−	0.999957i	$-0.502961\pi$
$197$	−0.261164			−0.0186071			−0.00930357	+	0.999957i	$0.502961\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	0.539993	+	0.935296i	0.0379938	+	0.0658072i
$203$	−20.7189	+	2.87483i	−1.45418	+	0.201773i
$204$		0			0
$205$	−1.60838	−	2.78579i	−0.112334	−	0.194568i
$206$	−4.12561	−	7.14577i	−0.287445	−	0.497869i
$207$		0			0
$208$	2.97981	−	5.16118i	0.206613	−	0.357864i
$209$	1.48525	−	2.57252i	0.102737	−	0.177945i
$210$		0			0
$211$	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
$213$		0			0
$214$	1.40895			0.0963137
$215$	−4.19469	+	7.26541i	−0.286075	+	0.495497i
$216$		0			0
$217$	−10.5819	+	1.46828i	−0.718344	+	0.0996732i
$218$	0.135088	−	0.233979i	0.00914929	−	0.0158470i
$219$		0			0
$220$	−2.90042	+	5.02367i	−0.195546	+	0.338696i
$221$	13.3702	−	23.1579i	0.899380	−	1.55777i
$222$		0			0
$223$	−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
$225$		0			0
$226$	2.78868	−	4.83013i	0.185500	−	0.321296i
$227$	−9.27518			−0.615615			−0.307808	−	0.951449i	$-0.599595\pi$
$227$	−9.27518			−0.615615			−0.307808	+	0.951449i	$0.599595\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	9.70303	−	16.8061i	0.637035	−	1.10338i
$233$	3.50083	−	6.06362i	0.229347	−	0.397241i	−0.728268	−	0.685293i	$-0.759674\pi$
$233$	3.50083	−	6.06362i	0.229347	−	0.397241i	0.957615	+	0.288052i	$0.0930076\pi$
$234$		0			0
$235$	1.66963	+	2.89189i	0.108915	+	0.188646i
$236$	5.09285	+	8.82107i	0.331516	+	0.574203i
$237$		0			0
$238$	−10.7416	+	1.49044i	−0.696275	+	0.0966110i
$239$	8.00452	+	13.8642i	0.517769	+	0.896803i	0.999787	+	0.0206414i	$0.00657084\pi$
$239$	8.00452	+	13.8642i	0.517769	+	0.896803i	−0.482017	+	0.876162i	$0.660096\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−10.5986			−0.678508
$245$	1.71725	−	6.78609i	0.109711	−	0.433548i
$246$		0			0
$247$	3.52950			0.224577
$248$	4.95568	−	8.58350i	0.314686	−	0.545053i
$249$		0			0
$250$	−0.349525	−	0.605394i	−0.0221059	−	0.0382885i
$251$	−15.4784			−0.976991			−0.488495	−	0.872566i	$-0.662454\pi$
$251$	−15.4784			−0.976991			−0.488495	+	0.872566i	$0.662454\pi$
$252$		0			0
$253$	−26.5042			−1.66631
$254$	−0.662664	−	1.14777i	−0.0415792	−	0.0720173i
$255$		0			0
$256$	5.17118	−	8.95675i	0.323199	−	0.559797i
$257$	0.355901			0.0222005			0.0111003	−	0.999938i	$-0.496467\pi$
$257$	0.355901			0.0222005			0.0111003	+	0.999938i	$0.496467\pi$
$258$		0			0
$259$	−22.1920	+	3.07923i	−1.37894	+	0.191334i
$260$	−6.89248			−0.427453
$261$		0			0
$262$	2.56512	+	4.44291i	0.158473	+	0.274484i
$263$	−19.1656			−1.18180			−0.590900	−	0.806745i	$-0.701227\pi$
$263$	−19.1656			−1.18180			−0.590900	+	0.806745i	$0.701227\pi$
$264$		0			0
$265$	1.32630	+	2.29721i	0.0814737	+	0.141117i
$266$	−0.879266	−	1.12948i	−0.0539112	−	0.0692531i
$267$		0			0
$268$	11.0103	+	19.0703i	0.672559	+	1.16491i
$269$	4.18841	+	7.25453i	0.255372	+	0.442317i	0.964996	−	0.262263i	$-0.0844688\pi$
$269$	4.18841	+	7.25453i	0.255372	+	0.442317i	−0.709625	+	0.704580i	$0.751135\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	3.30371	+	5.72219i	0.199584	+	0.345690i
$275$	3.83823			0.231454
$276$		0			0
$277$	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
$279$		0			0
$280$	3.98928	+	5.12453i	0.238405	+	0.306249i
$281$	−2.12078	+	3.67329i	−0.126515	+	0.219130i	−0.922324	−	0.386417i	$-0.873712\pi$
$281$	−2.12078	+	3.67329i	−0.126515	+	0.219130i	0.795809	+	0.605547i	$0.207046\pi$
$282$		0			0
$283$	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			0
$286$	−6.11822	+	10.5971i	−0.361778	+	0.626617i
$287$	3.20200	−	7.88541i	0.189008	−	0.465461i
$288$		0			0
$289$	−8.69005	+	15.0516i	−0.511180	+	0.885389i
$290$	−5.52670			−0.324539
$291$		0			0
$292$	21.1871			1.23988
$293$	6.26949	+	10.8591i	0.366267	+	0.634393i	0.988979	−	0.148058i	$-0.0473023\pi$
$293$	6.26949	+	10.8591i	0.366267	+	0.634393i	−0.622711	+	0.782452i	$0.713969\pi$
$294$		0			0
$295$	3.36978	−	5.83663i	0.196196	−	0.339822i
$296$	10.3929	−	18.0010i	0.604076	−	1.04629i
$297$		0			0
$298$	4.49376	+	7.78342i	0.260317	+	0.450882i
$299$	−15.7460	−	27.2728i	−0.910613	−	1.57723i
$300$		0			0
$301$	−21.9856	+	3.05059i	−1.26723	+	0.175833i
$302$	2.35158	+	4.07306i	0.135318	+	0.234378i
$303$		0			0
$304$	−1.01135			−0.0580047
$305$	3.50639	+	6.07324i	0.200775	+	0.347753i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−2.82268			−0.160318
$311$	6.41734	−	11.1152i	0.363894	−	0.630283i	−0.624704	−	0.780862i	$-0.714780\pi$
$311$	6.41734	−	11.1152i	0.363894	−	0.630283i	0.988598	+	0.150579i	$0.0481137\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	20.2303			1.13805
$317$	17.1198	+	29.6524i	0.961545	+	1.66545i	0.718624	+	0.695399i	$0.244772\pi$
$317$	17.1198	+	29.6524i	0.961545	+	1.66545i	0.242922	+	0.970046i	$0.421894\pi$
$318$		0			0
$319$	15.1726	−	26.2797i	0.849502	−	1.47138i
$320$	−1.45678			−0.0814366
$321$		0			0
$322$	−4.80502	+	11.8331i	−0.267773	+	0.659432i
$323$	−4.53786			−0.252493
$324$		0			0
$325$	2.28027	+	3.94954i	0.126486	+	0.219081i
$326$	−11.3452			−0.628355
$327$		0			0
$328$	3.94791	+	6.83798i	0.217987	+	0.377564i
$329$	−3.32395	+	8.18574i	−0.183255	+	0.451294i
$330$		0			0
$331$	−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
$333$		0			0
$334$	−6.01529	+	10.4188i	−0.329142	+	0.570091i
$335$	7.28514	−	12.6182i	0.398030	−	0.689408i
$336$		0			0
$337$	−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
$339$		0			0
$340$	8.86162			0.480589
$341$	7.74918	−	13.4220i	0.419641	−	0.726840i
$342$		0			0
$343$	16.9585	−	7.44381i	0.915671	−	0.401928i
$344$	10.2962	−	17.8336i	0.555136	−	0.961524i
$345$		0			0
$346$	−5.60307	+	9.70481i	−0.301223	+	0.521734i
$347$	2.40973	−	4.17378i	0.129361	−	0.224060i	−0.794068	−	0.607829i	$-0.792041\pi$
$347$	2.40973	−	4.17378i	0.129361	−	0.224060i	0.923429	+	0.383769i	$0.125374\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	11.1744	−	19.3547i	0.595598	−	1.03161i
$353$	0.354435			0.0188647			0.00943233	−	0.999956i	$-0.496998\pi$
$353$	0.354435			0.0188647			0.00943233	+	0.999956i	$0.496998\pi$
$354$		0			0
$355$	−9.67100			−0.513283
$356$	1.43577	+	2.48683i	0.0760956	+	0.131801i
$357$		0			0
$358$	3.21575	−	5.56985i	0.169958	−	0.294376i
$359$	−6.26344	+	10.8486i	−0.330572	+	0.572567i	−0.982624	−	0.185607i	$-0.940575\pi$
$359$	−6.26344	+	10.8486i	−0.330572	+	0.572567i	0.652052	+	0.758174i	$0.273908\pi$
$360$		0			0
$361$	9.20052	+	15.9358i	0.484238	+	0.838725i
$362$	−2.01451	−	3.48923i	−0.105880	−	0.183390i
$363$		0			0
$364$	−11.2019	−	14.3896i	−0.587137	−	0.754222i
$365$	−7.00941	−	12.1407i	−0.366889	−	0.635471i
$366$		0			0
$367$	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
$369$		0			0
$370$	−5.91964			−0.307747
$371$	−2.64043	+	6.50245i	−0.137084	+	0.337590i
$372$		0			0
$373$	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
$375$		0			0
$376$	−4.09827	−	7.09841i	−0.211352	−	0.366073i
$377$	36.0557			1.85696
$378$		0			0
$379$	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
$381$		0			0
$382$	−0.804949	+	1.39421i	−0.0411848	+	0.0713341i
$383$	−26.0999			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$383$	−26.0999			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$384$		0			0
$385$	6.23801	+	8.01320i	0.317919	+	0.408391i
$386$	−13.9480			−0.709934
$387$		0			0
$388$	4.65075	+	8.05533i	0.236106	+	0.408948i
$389$	−0.160490			−0.00813716			−0.00406858	−	0.999992i	$-0.501295\pi$
$389$	−0.160490			−0.00813716			−0.00406858	+	0.999992i	$0.501295\pi$
$390$		0			0
$391$	20.2445	+	35.0645i	1.02381	+	1.77329i
$392$	−4.21515	+	16.6571i	−0.212897	+	0.841310i
$393$		0			0
$394$	−0.0912831	−	0.158107i	−0.00459878	−	0.00796531i
$395$	−6.69289	−	11.5924i	−0.336756	−	0.583278i
$396$		0			0
$397$	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
$399$		0			0
$400$	−0.653390	−	1.13171i	−0.0326695	−	0.0565853i
$401$	18.8416			0.940906			0.470453	−	0.882425i	$-0.344091\pi$
$401$	18.8416			0.940906			0.470453	+	0.882425i	$0.344091\pi$
$402$		0			0
$403$	18.4149			0.917313
$404$	1.16746	−	2.02209i	0.0580831	−	0.100603i
$405$		0			0
$406$	−8.98216	−	11.5383i	−0.445777	−	0.572635i
$407$	16.2513	−	28.1481i	0.805549	−	1.39525i
$408$		0			0
$409$	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
$411$		0			0
$412$	−8.91949	+	15.4490i	−0.439432	+	0.761118i
$413$	17.6620	−	2.45067i	0.869089	−	0.120590i
$414$		0			0
$415$	0.442527	−	0.766479i	0.0217228	−	0.0376250i
$416$	26.5546			1.30195
$417$		0			0
$418$	2.07652			0.101566
$419$	2.29886	+	3.98174i	0.112307	+	0.194521i	0.916700	−	0.399576i	$-0.130843\pi$
$419$	2.29886	+	3.98174i	0.112307	+	0.194521i	−0.804393	+	0.594097i	$0.797509\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−3.25552	−	5.63872i	−0.158102	−	0.273840i
$425$	−2.93173	−	5.07790i	−0.142210	−	0.246314i
$426$		0			0
$427$	−6.98062	+	17.1908i	−0.337816	+	0.831922i
$428$	−1.52306	−	2.63802i	−0.0736199	−	0.127513i
$429$		0			0
$430$	−5.86458			−0.282815
$431$	8.75901	+	15.1710i	0.421907	+	0.730764i	0.996126	−	0.0879379i	$-0.0280277\pi$
$431$	8.75901	+	15.1710i	0.421907	+	0.730764i	−0.574219	+	0.818701i	$0.694694\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−0.584114			−0.0279740
$437$	−2.67209	+	4.62819i	−0.127823	+	0.221397i
$438$		0			0
$439$	−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
$441$		0			0
$442$	18.6929			0.889131
$443$	18.0671	+	31.2931i	0.858394	+	1.48678i	0.873460	+	0.486896i	$0.161871\pi$
$443$	18.0671	+	31.2931i	0.858394	+	1.48678i	−0.0150658	+	0.999887i	$0.504796\pi$
$444$		0			0
$445$	0.950003	−	1.64545i	0.0450345	−	0.0780020i
$446$	−8.18348			−0.387499
$447$		0			0
$448$	−2.36761	−	3.04137i	−0.111859	−	0.143691i
$449$	−17.2314			−0.813202			−0.406601	−	0.913606i	$-0.633286\pi$
$449$	−17.2314			−0.813202			−0.406601	+	0.913606i	$0.633286\pi$
$450$		0			0
$451$	6.17332	+	10.6925i	0.290690	+	0.503491i
$452$	−12.0581			−0.567167
$453$		0			0
$454$	−3.24190	−	5.61514i	−0.152150	−	0.263532i
$455$	−4.53962	+	11.1795i	−0.212821	+	0.524103i
$456$		0			0
$457$	−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
$459$		0			0
$460$	5.21811	−	9.03803i	0.243296	−	0.421400i
$461$	−7.95525	+	13.7789i	−0.370513	+	0.641747i	−0.989645	−	0.143540i	$-0.954151\pi$
$461$	−7.95525	+	13.7789i	−0.370513	+	0.641747i	0.619132	+	0.785287i	$0.287485\pi$
$462$		0			0
$463$	−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			0
$466$	4.89451			0.226734
$467$	−13.1371	+	22.7541i	−0.607912	+	1.05294i	0.383671	+	0.923470i	$0.374660\pi$
$467$	−13.1371	+	22.7541i	−0.607912	+	1.05294i	−0.991584	+	0.129466i	$0.958674\pi$
$468$		0			0
$469$	38.1835	−	5.29812i	1.76315	−	0.244645i
$470$	−1.16716	+	2.02157i	−0.0538369	+	0.0932482i
$471$		0			0
$472$	−8.27143	+	14.3265i	−0.380724	+	0.659433i
$473$	16.1002	−	27.8863i	0.740287	−	1.28221i
$474$		0			0
$475$	0.386961	−	0.670236i	0.0177550	−	0.0307526i
$476$	14.4022	+	18.5007i	0.660123	+	0.847977i
$477$		0			0
$478$	−5.59555	+	9.69178i	−0.255935	+	0.443292i
$479$	7.33270			0.335040			0.167520	−	0.985869i	$-0.446424\pi$
$479$	7.33270			0.335040			0.167520	+	0.985869i	$0.446424\pi$
$480$		0			0
$481$	38.6192			1.76089
$482$	−2.57062	−	4.45244i	−0.117088	−	0.202803i
$483$		0			0
$484$	2.82017	−	4.88467i	0.128189	−	0.222030i
$485$	3.07725	−	5.32996i	0.139731	−	0.242021i
$486$		0			0
$487$	−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
$489$		0			0
$490$	4.70848	−	1.33229i	0.212708	−	0.0601868i
$491$	−10.2358	−	17.7289i	−0.461934	−	0.800093i	0.537123	−	0.843504i	$-0.319511\pi$
$491$	−10.2358	−	17.7289i	−0.461934	−	0.800093i	−0.999057	+	0.0434107i	$0.986178\pi$
$492$		0			0
$493$	−46.3566			−2.08780
$494$	1.23365	+	2.13674i	0.0555044	+	0.0961364i
$495$		0			0
$496$	−5.27663			−0.236928
$497$	−15.7176	−	20.1905i	−0.705031	−	0.905666i
$498$		0			0
$499$	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
$501$		0			0
$502$	−5.41010	−	9.37056i	−0.241464	−	0.418229i
$503$	23.7168			1.05748			0.528739	−	0.848784i	$-0.322665\pi$
$503$	23.7168			1.05748			0.528739	+	0.848784i	$0.322665\pi$
$504$		0			0
$505$	−1.54494			−0.0687488
$506$	−9.26387	−	16.0455i	−0.411829	−	0.713309i
$507$		0			0
$508$	−1.43267	+	2.48145i	−0.0635643	+	0.110097i
$509$	1.16561			0.0516649			0.0258324	−	0.999666i	$-0.491776\pi$
$509$	1.16561			0.0516649			0.0258324	+	0.999666i	$0.491776\pi$
$510$		0			0
$511$	13.9545	−	34.3651i	0.617312	−	1.52022i
$512$	−14.0242			−0.619788
$513$		0			0
$514$	0.124396	+	0.215461i	0.00548688	+	0.00950356i
$515$	11.8035			0.520124
$516$		0			0
$517$	−6.40844	−	11.0997i	−0.281843	−	0.488166i
$518$	−9.62078	−	12.3586i	−0.422713	−	0.543007i
$519$		0			0
$520$	−5.59713	−	9.69451i	−0.245450	−	0.425132i
$521$	−15.6184	−	27.0519i	−0.684254	−	1.18516i	−0.973670	−	0.227960i	$-0.926794\pi$
$521$	−15.6184	−	27.0519i	−0.684254	−	1.18516i	0.289416	−	0.957203i	$-0.406539\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	−6.69883	−	11.6027i	−0.292083	−	0.505903i
$527$	−23.6760			−1.03134
$528$		0			0
$529$	24.6834			1.07319
$530$	−0.927146	+	1.60586i	−0.0402726	+	0.0697543i
$531$		0			0
$532$	−1.16429	+	2.86724i	−0.0504783	+	0.124310i
$533$	−7.33506	+	12.7047i	−0.317717	+	0.550301i
$534$		0			0
$535$	−1.00776	+	1.74549i	−0.0435693	+	0.0754642i
$536$	−17.8821	+	30.9726i	−0.772387	+	1.33781i
$537$		0			0
$538$	−2.92790	+	5.07127i	−0.126231	+	0.218638i
$539$	−6.59120	+	26.0466i	−0.283903	+	1.12191i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−34.1411			−1.46379
$545$	0.193245	+	0.334710i	0.00827770	+	0.0143374i
$546$		0			0
$547$	−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
$549$		0			0
$550$	1.34156	+	2.32364i	0.0572042	+	0.0990805i
$551$	−3.05932	−	5.29891i	−0.130332	−	0.225741i
$552$		0			0
$553$	13.3244	−	32.8133i	0.566611	−	1.39537i
$554$	7.47545	+	12.9479i	0.317601	+	0.550101i
$555$		0			0
$556$	9.94383			0.421712
$557$	−12.1738	−	21.0857i	−0.515822	−	0.893430i	−0.999831	−	0.0183672i	$-0.994153\pi$
$557$	−12.1738	−	21.0857i	−0.515822	−	0.893430i	0.484009	−	0.875063i	$-0.339180\pi$
$558$		0			0
$559$	38.2600			1.61823
$560$	1.30079	−	3.20339i	0.0549683	−	0.135368i
$561$		0			0
$562$	−2.96505			−0.125073
$563$	−13.1260	+	22.7349i	−0.553194	+	0.958160i	0.444848	+	0.895606i	$0.353258\pi$
$563$	−13.1260	+	22.7349i	−0.553194	+	0.958160i	−0.998042	+	0.0625535i	$0.980076\pi$
$564$		0			0
$565$	3.98925	+	6.90958i	0.167829	+	0.290688i
$566$	4.18579			0.175942
$567$		0			0
$568$	23.7384			0.996039
$569$	−3.65815	−	6.33610i	−0.153358	−	0.265623i	0.779102	−	0.626897i	$-0.215675\pi$
$569$	−3.65815	−	6.33610i	−0.153358	−	0.265623i	−0.932460	+	0.361274i	$0.882342\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	5.89296	−	0.817672i	0.245967	−	0.0341290i
$575$	−6.90532			−0.287972
$576$		0			0
$577$	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
$579$		0			0
$580$	5.97431	+	10.3478i	0.248070	+	0.429669i
$581$	2.31941	−	0.321828i	0.0962254	−	0.0133517i
$582$		0			0
$583$	−5.09063	−	8.81723i	−0.210832	−	0.365173i
$584$	17.2052	+	29.8004i	0.711958	+	1.23315i
$585$		0			0
$586$	−4.38268	+	7.59102i	−0.181047	+	0.313582i
$587$	16.4446	−	28.4830i	0.678743	−	1.17562i	−0.296616	−	0.954997i	$-0.595858\pi$
$587$	16.4446	−	28.4830i	0.678743	−	1.17562i	0.975360	−	0.220621i	$-0.0708084\pi$
$588$		0			0
$589$	−1.56251	−	2.70634i	−0.0643819	−	0.111513i
$590$	4.71128			0.193960
$591$		0			0
$592$	−11.0660			−0.454810
$593$	11.6851	−	20.2392i	0.479851	−	0.831125i	−0.519882	−	0.854238i	$-0.674024\pi$
$593$	11.6851	−	20.2392i	0.479851	−	0.831125i	0.999733	+	0.0231124i	$0.00735756\pi$
$594$		0			0
$595$	5.83656	−	14.3734i	0.239276	−	0.589253i
$596$	9.71543	−	16.8276i	0.397959	−	0.689286i
$597$		0			0
$598$	11.0072	−	19.0650i	0.450118	−	0.779627i
$599$	−3.67779	+	6.37012i	−0.150270	+	0.260276i	−0.931327	−	0.364185i	$-0.881348\pi$
$599$	−3.67779	+	6.37012i	−0.150270	+	0.260276i	0.781056	+	0.624460i	$0.214681\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	5.08408	−	8.80588i	0.206868	−	0.358306i
$605$	−3.73203			−0.151729
$606$		0			0
$607$	−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
$609$		0			0
$610$	−2.45114	+	4.24550i	−0.0992437	+	0.171895i
$611$	7.61442	−	13.1886i	0.308047	−	0.533552i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−15.3118	−	19.6691i	−0.616929	−	0.792492i
$617$	3.65695	+	6.33402i	0.147223	+	0.254998i	0.930200	−	0.367053i	$-0.119633\pi$
$617$	3.65695	+	6.33402i	0.147223	+	0.254998i	−0.782977	+	0.622051i	$0.786300\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	8.97207			0.359747
$623$	4.97924	−	0.690890i	0.199489	−	0.0276799i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.20647	+	9.01787i	−0.208092	+	0.360427i
$627$		0			0
$628$	−9.15234	−	15.8523i	−0.365218	−	0.632576i
$629$	−49.6525			−1.97978
$630$		0			0
$631$	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
$633$		0			0
$634$	−11.9676	+	20.7285i	−0.475294	+	0.823233i
$635$	1.89590			0.0752365
$636$		0			0
$637$	−30.7177	+	8.69176i	−1.21708	+	0.344380i
$638$	21.2128			0.839821
$639$		0			0
$640$	5.31351	+	9.20326i	0.210035	+	0.363791i
$641$	27.5418			1.08784			0.543918	−	0.839139i	$-0.316940\pi$
$641$	27.5418			1.08784			0.543918	+	0.839139i	$0.316940\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	−1.58609	−	2.74719i	−0.0624040	−	0.108087i
$647$	−24.2181	−	41.9469i	−0.952110	−	1.64910i	−0.740847	−	0.671673i	$-0.765576\pi$
$647$	−24.2181	−	41.9469i	−0.952110	−	1.64910i	−0.211263	−	0.977429i	$-0.567757\pi$
$648$		0			0
$649$	−12.9340	+	22.4023i	−0.507704	+	0.879369i
$650$	−1.59402	+	2.76092i	−0.0625226	+	0.108292i
$651$		0			0
$652$	12.2641	+	21.2420i	0.480299	+	0.831902i
$653$	19.4509			0.761173			0.380587	−	0.924745i	$-0.375722\pi$
$653$	19.4509			0.761173			0.380587	+	0.924745i	$0.375722\pi$
$654$		0			0
$655$	−7.33888			−0.286754
$656$	2.10180	−	3.64042i	0.0820613	−	0.142134i
$657$		0			0
$658$	−6.11740	+	0.848814i	−0.238481	+	0.0330902i
$659$	−1.04114	+	1.80330i	−0.0405569	+	0.0702467i	−0.885591	−	0.464465i	$-0.846247\pi$
$659$	−1.04114	+	1.80330i	−0.0405569	+	0.0702467i	0.845034	+	0.534712i	$0.179580\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−1.08622	+	1.88139i	−0.0421536	+	0.0730122i
$665$	2.02818	−	0.281418i	0.0786493	−	0.0109129i
$666$		0			0
$667$	−27.2968	+	47.2794i	−1.05694	+	1.83067i
$668$	26.0099			1.00635
$669$		0			0
$670$	10.1853			0.393494
$671$	−13.4583	−	23.3105i	−0.519553	−	0.899893i
$672$		0			0
$673$	−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
$675$		0			0
$676$	5.89304	+	10.2070i	0.226655	+	0.392579i
$677$	−5.91975	−	10.2533i	−0.227514	−	0.394066i	0.729557	−	0.683921i	$-0.239727\pi$
$677$	−5.91975	−	10.2533i	−0.227514	−	0.394066i	−0.957071	+	0.289854i	$0.906393\pi$
$678$		0			0
$679$	16.1288	−	2.23793i	0.618966	−	0.0858840i
$680$	7.19620	+	12.4642i	0.275961	+	0.477979i
$681$		0			0
$682$	10.8341			0.414860
$683$	−0.504725	−	0.874210i	−0.0193128	−	0.0334507i	0.856207	−	0.516632i	$-0.172814\pi$
$683$	−0.504725	−	0.874210i	−0.0193128	−	0.0334507i	−0.875520	+	0.483181i	$0.839481\pi$
$684$		0			0
$685$	−9.45201			−0.361143
$686$	10.4338	+	7.66477i	0.398366	+	0.292642i
$687$		0			0
$688$	−10.9631			−0.417963
$689$	6.04862	−	10.4765i	0.230434	−	0.399123i
$690$		0			0
$691$	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
$693$		0			0
$694$	3.36904			0.127887
$695$	−3.28976	−	5.69803i	−0.124788	−	0.216139i
$696$		0			0
$697$	9.43064	−	16.3344i	0.357211	−	0.618708i
$698$	4.57155			0.173036
$699$		0			0
$700$	−3.96066	+	0.549558i	−0.149699	+	0.0207713i
$701$	33.4009			1.26154			0.630768	−	0.775972i	$-0.282740\pi$
$701$	33.4009			1.26154			0.630768	+	0.775972i	$0.282740\pi$
$702$		0			0
$703$	−3.27684	−	5.67565i	−0.123588	−	0.214061i
$704$	5.59147			0.210737
$705$		0			0
$706$	0.123884	+	0.214573i	0.00466242	+	0.00807555i
$707$	−2.51088	−	3.22541i	−0.0944313	−	0.121304i
$708$		0			0
$709$	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
$711$		0			0
$712$	−2.33187	+	4.03892i	−0.0873906	+	0.151365i
$713$	−13.9414	+	24.1473i	−0.522111	+	0.904323i
$714$		0			0
$715$	−8.75220	−	15.1593i	−0.327314	−	0.566924i
$716$	−13.9048			−0.519647
$717$		0			0
$718$	−8.75691			−0.326805
$719$	−1.55174	+	2.68769i	−0.0578702	+	0.100234i	−0.893509	−	0.449045i	$-0.851764\pi$
$719$	−1.55174	+	2.68769i	−0.0578702	+	0.100234i	0.835639	+	0.549279i	$0.185098\pi$
$720$		0			0
$721$	19.1834	+	24.6425i	0.714427	+	0.917736i
$722$	−6.43162	+	11.1399i	−0.239360	+	0.414584i
$723$		0			0
$724$	−4.35532	+	7.54364i	−0.161864	+	0.280357i
$725$	3.95301	−	6.84682i	0.146811	−	0.254284i
$726$		0			0
$727$	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
$729$		0			0
$730$	4.89992	−	8.48691i	0.181354	−	0.314115i
$731$	−49.1907			−1.81938
$732$		0			0
$733$	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
$735$		0			0
$736$	−20.1038	+	34.8207i	−0.741034	+	1.28351i
$737$	−27.9621	+	48.4317i	−1.03000	+	1.78401i
$738$		0			0
$739$	−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
$741$		0			0
$742$	−4.85944	+	0.674267i	−0.178396	+	0.0247531i
$743$	−23.6637	−	40.9867i	−0.868137	−	1.50366i	−0.863899	−	0.503666i	$-0.831984\pi$
$743$	−23.6637	−	40.9867i	−0.868137	−	1.50366i	−0.00423816	−	0.999991i	$-0.501349\pi$
$744$		0			0
$745$	−12.8568			−0.471036
$746$	3.62820	+	6.28422i	0.132838	+	0.230082i
$747$		0			0
$748$	−34.0130			−1.24364
$749$	−5.28196	+	0.732894i	−0.192999	+	0.0267794i
$750$		0			0
$751$	−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
$753$		0			0
$754$	12.6024	+	21.8279i	0.458951	+	0.794926i
$755$	−6.72795			−0.244855
$756$		0			0
$757$	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
$759$		0			0
$760$	−0.949832	+	1.64516i	−0.0344540	+	0.0596761i
$761$	−28.8757			−1.04674			−0.523372	−	0.852104i	$-0.675326\pi$
$761$	−28.8757			−1.04674			−0.523372	+	0.852104i	$0.675326\pi$
$762$		0			0
$763$	−0.384717	+	0.947425i	−0.0139277	+	0.0342991i
$764$	3.48057			0.125923
$765$		0			0
$766$	−9.12257	−	15.8008i	−0.329612	−	0.570905i
$767$	−30.7360			−1.10981
$768$		0			0
$769$	−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			0
$772$	15.0776	+	26.1152i	0.542656	+	0.939908i
$773$	−0.958668	−	1.66046i	−0.0344809	−	0.0597226i	0.848270	−	0.529564i	$-0.177644\pi$
$773$	−0.958668	−	1.66046i	−0.0344809	−	0.0597226i	−0.882751	+	0.469841i	$0.844311\pi$
$774$		0			0
$775$	2.01894	−	3.49691i	0.0725226	−	0.125613i
$776$	−7.55340	+	13.0829i	−0.271151	+	0.469648i
$777$		0			0
$778$	−0.0560951	−	0.0971596i	−0.00201111	−	0.00348334i
$779$	2.48952			0.0891962
$780$		0			0
$781$	37.1195			1.32824
$782$	−14.1519	+	24.5118i	−0.506071	+	0.876541i
$783$		0			0
$784$	8.80189	−	2.49055i	0.314353	−	0.0889481i
$785$	−6.05582	+	10.4890i	−0.216141	+	0.374368i
$786$		0			0
$787$	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
$789$		0			0
$790$	4.67866	−	8.10368i	0.166459	−	0.288316i
$791$	−7.94190	+	19.5581i	−0.282381	+	0.695407i
$792$		0			0
$793$	15.9910	−	27.6972i	0.567857	−	0.983558i
$794$	8.51672			0.302247
$795$		0			0
$796$	−5.48600			−0.194446
$797$	−20.4912	−	35.4919i	−0.725837	−	1.25719i	−0.958628	−	0.284660i	$-0.908119\pi$
$797$	−20.4912	−	35.4919i	−0.725837	−	1.25719i	0.232791	−	0.972527i	$-0.425214\pi$
$798$		0			0
$799$	−9.78982	+	16.9565i	−0.346339	+	0.599877i
$800$	2.91134	−	5.04260i	0.102932	−	0.178283i
$801$		0			0
$802$	6.58561	+	11.4066i	0.232546	+	0.402781i
$803$	26.9037	+	46.5987i	0.949413	+	1.64443i
$804$		0			0
$805$	−11.2227	−	14.4164i	−0.395549	−	0.508113i
$806$	6.43647	+	11.1483i	0.226715	+	0.392682i
$807$		0			0
$808$	3.79219			0.133409
$809$	−19.3458	−	33.5079i	−0.680163	−	1.17808i	−0.974931	−	0.222508i	$-0.928576\pi$
$809$	−19.3458	−	33.5079i	−0.680163	−	1.17808i	0.294768	−	0.955569i	$-0.404758\pi$
$810$		0			0
$811$	−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			0
$814$	22.7210			0.796369
$815$	8.11477	−	14.0552i	0.284248	−	0.492332i
$816$		0			0
$817$	−3.24636	−	5.62286i	−0.113576	−	0.196719i
$818$	1.03127			0.0360576
$819$		0			0
$820$	−4.86158			−0.169774
$821$	10.8094	+	18.7224i	0.377251	+	0.653418i	0.990661	−	0.136347i	$-0.0435361\pi$
$821$	10.8094	+	18.7224i	0.377251	+	0.653418i	−0.613410	+	0.789764i	$0.710203\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	7.65692	+	9.83589i	0.266418	+	0.342234i
$827$	45.3663			1.57754			0.788770	−	0.614689i	$-0.210718\pi$
$827$	45.3663			1.57754			0.788770	+	0.614689i	$0.210718\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	3.32185	+	5.75362i	0.115165	+	0.199471i
$833$	39.4936	−	11.1749i	1.36837	−	0.387189i
$834$		0			0
$835$	−8.60497	−	14.9042i	−0.297787	−	0.515783i
$836$	−2.24470	−	3.88793i	−0.0776345	−	0.134467i
$837$		0			0
$838$	−1.60702	+	2.78343i	−0.0555135	+	0.0961521i
$839$	16.8414	−	29.1701i	0.581429	−	1.00706i	−0.413881	−	0.910331i	$-0.635827\pi$
$839$	16.8414	−	29.1701i	0.581429	−	1.00706i	0.995310	−	0.0967337i	$-0.0308395\pi$
$840$		0			0
$841$	−16.7526	−	29.0164i	−0.577677	−	1.00057i
$842$	−11.9715			−0.412564
$843$		0			0
$844$	6.80905			0.234377
$845$	3.89924	−	6.75368i	0.134138	−	0.232334i
$846$		0			0
$847$	−6.06541	−	7.79148i	−0.208410	−	0.267718i
$848$	−1.73318	+	3.00195i	−0.0595176	+	0.103087i
$849$		0			0
$850$	2.04942	−	3.54970i	0.0702946	−	0.121754i
$851$	−29.2376	+	50.6410i	−1.00225	+	1.73595i
$852$		0			0
$853$	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
$855$		0			0
$856$	2.47364	−	4.28447i	0.0845473	−	0.146440i
$857$	−13.6216			−0.465306			−0.232653	−	0.972560i	$-0.574741\pi$
$857$	−13.6216			−0.465306			−0.232653	+	0.972560i	$0.574741\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	−6.12298	+	10.6053i	−0.208549	+	0.361218i
$863$	12.8153	−	22.1968i	0.436238	−	0.755587i	−0.561158	−	0.827709i	$-0.689644\pi$
$863$	12.8153	−	22.1968i	0.436238	−	0.755587i	0.997396	+	0.0721222i	$0.0229772\pi$
$864$		0			0
$865$	−8.01528	−	13.8829i	−0.272528	−	0.472032i
$866$	10.9900	+	19.0353i	0.373456	+	0.646845i
$867$		0			0
$868$	−6.07459	+	14.9596i	−0.206185	+	0.507762i
$869$	25.6889	+	44.4944i	0.871436	+	1.50937i
$870$		0			0
$871$	−66.4483			−2.25152
$872$	−0.474337	−	0.821577i	−0.0160631	−	0.0278221i
$873$		0			0
$874$	−3.73584			−0.126367
$875$	1.62523	+	2.08773i	0.0549428	+	0.0705782i
$876$		0			0
$877$	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
$879$		0			0
$880$	2.50786	+	4.34375i	0.0845401	+	0.146428i
$881$	14.6040			0.492022			0.246011	−	0.969267i	$-0.420880\pi$
$881$	14.6040			0.492022			0.246011	+	0.969267i	$0.420880\pi$
$882$		0			0
$883$	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			0
$886$	−12.6298	+	21.8754i	−0.424306	+	0.734920i
$887$	21.8316			0.733033			0.366517	−	0.930412i	$-0.380550\pi$
$887$	21.8316			0.733033			0.366517	+	0.930412i	$0.380550\pi$
$888$		0			0
$889$	3.08128	+	3.95813i	0.103343	+	0.132752i
$890$	1.32820			0.0445213
$891$		0			0
$892$	8.84626	+	15.3222i	0.296195	+	0.513024i
$893$	−2.58433			−0.0864814
$894$		0			0
$895$	4.60018	+	7.96775i	0.153767	+	0.266333i
$896$	−10.5783	+	26.0506i	−0.353395	+	0.870290i
$897$		0			0
$898$	−6.02281	−	10.4318i	−0.200984	−	0.348114i
$899$	−15.9618	−	27.6467i	−0.532357	−	0.922069i
$900$		0			0
$901$	−7.77668	+	13.4696i	−0.259079	+	0.448737i
$902$	−4.31545	+	7.47459i	−0.143689	+	0.248877i
$903$		0			0
$904$	−9.79197	−	16.9602i	−0.325676	−	0.564088i
$905$	5.76356			0.191587
$906$		0			0
$907$	−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
$909$		0			0
$910$	−8.35471	+	1.15925i	−0.276956	+	0.0384288i
$911$	−23.4277	+	40.5779i	−0.776193	+	1.34441i	0.157928	+	0.987451i	$0.449519\pi$
$911$	−23.4277	+	40.5779i	−0.776193	+	1.34441i	−0.934121	+	0.356956i	$0.883815\pi$
$912$		0			0
$913$	−1.69852	+	2.94193i	−0.0562129	+	0.0973635i
$914$	3.20614	−	5.55320i	0.106050	−	0.183684i
$915$		0			0
$916$	12.7756	−	22.1281i	0.422119	−	0.731132i
$917$	−11.9274	−	15.3216i	−0.393876	−	0.505964i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−11.1222			−0.366291
$923$	22.0525	+	38.1960i	0.725866	+	1.25724i
$924$		0			0
$925$	4.23407	−	7.33362i	0.139215	−	0.241128i
$926$	3.35644	−	5.81353i	0.110300	−	0.191045i
$927$		0			0
$928$	−23.0172	−	39.8669i	−0.755575	−	1.30869i
$929$	26.4882	+	45.8789i	0.869050	+	1.50524i	0.862969	+	0.505257i	$0.168602\pi$
$929$	26.4882	+	45.8789i	0.869050	+	1.50524i	0.00608051	+	0.999982i	$0.498065\pi$
$930$		0			0
$931$	3.88378	+	3.77692i	0.127286	+	0.123783i
$932$	−5.29091	−	9.16413i	−0.173310	−	0.300181i
$933$		0			0
$934$	−18.3670			−0.600985
$935$	11.2527	+	19.4902i	0.368001	+	0.637397i
$936$		0			0
$937$	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
$939$		0			0
$940$	5.04674			0.164606
$941$	−15.4761	+	26.8054i	−0.504507	+	0.873831i	0.495480	+	0.868619i	$0.334992\pi$
$941$	−15.4761	+	26.8054i	−0.504507	+	0.873831i	−0.999986	+	0.00521168i	$0.998341\pi$
$942$		0			0
$943$	−11.1063	−	19.2368i	−0.361672	−	0.626435i
$944$	8.80712			0.286648
$945$		0			0
$946$	22.5096			0.731851
$947$	6.42093	+	11.1214i	0.208652	+	0.361396i	0.951290	−	0.308297i	$-0.0997591\pi$
$947$	6.42093	+	11.1214i	0.208652	+	0.361396i	−0.742638	+	0.669693i	$0.766426\pi$
$948$		0			0
$949$	−31.9667	+	55.3679i	−1.03768	+	1.79732i
$950$	0.541010			0.0175527
$951$		0			0
$952$	−14.3264	+	35.2809i	−0.464321	+	1.14346i
$953$	−47.3316			−1.53322			−0.766611	−	0.642112i	$-0.778058\pi$
$953$	−47.3316			−1.53322			−0.766611	+	0.642112i	$0.778058\pi$
$954$		0			0
$955$	−1.15149	−	1.99444i	−0.0372614	−	0.0645386i
$956$	24.1950			0.782521
$957$		0			0
$958$	2.56296	+	4.43917i	0.0828054	+	0.143423i
$959$	−15.3617	−	19.7333i	−0.496055	−	0.637221i
$960$		0			0
$961$	7.34773	+	12.7266i	0.237024	+	0.410537i
$962$	13.4984	+	23.3799i	0.435205	+	0.753797i
$963$		0			0
$964$	−5.55763	+	9.62609i	−0.178999	+	0.310036i
$965$	9.97640	−	17.2796i	0.321152	−	0.556251i
$966$		0			0
$967$	−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
$969$		0			0
$970$	4.30230			0.138139
$971$	−28.6673	+	49.6533i	−0.919979	+	1.59345i	−0.120534	+	0.992709i	$0.538461\pi$
$971$	−28.6673	+	49.6533i	−0.919979	+	1.59345i	−0.799444	+	0.600740i	$0.794873\pi$
$972$		0			0
$973$	6.54934	−	16.1288i	0.209962	−	0.517064i
$974$	11.8054	−	20.4476i	0.378271	−	0.655185i
$975$		0			0
$976$	−4.58208	+	7.93640i	−0.146669	+	0.254038i
$977$	−4.45153	+	7.71028i	−0.142417	+	0.246674i	−0.928406	−	0.371567i	$-0.878821\pi$
$977$	−4.45153	+	7.71028i	−0.142417	+	0.246674i	0.785989	+	0.618240i	$0.212154\pi$
$978$		0			0
$979$	−3.64633	+	6.31564i	−0.116537	+	0.201849i
$980$	−7.58432	−	7.37564i	−0.242272	−	0.235606i
$981$		0			0
$982$	7.15531	−	12.3934i	0.228335	−	0.395488i
$983$	−1.90661			−0.0608115			−0.0304058	−	0.999538i	$-0.509680\pi$
$983$	−1.90661			−0.0608115			−0.0304058	+	0.999538i	$0.509680\pi$
$984$		0			0
$985$	0.261164			0.00832136
$986$	−16.2028	−	28.0640i	−0.516002	−	0.893741i
$987$		0			0
$988$	2.66712	−	4.61959i	0.0848524	−	0.146969i
$989$	−28.9656	+	50.1699i	−0.921053	+	1.59531i
$990$		0			0
$991$	−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
$993$		0			0
$994$	6.72950	−	16.5724i	0.213447	−	0.525645i
$995$	1.81496	+	3.14360i	0.0575380	+	0.0996587i
$996$		0			0
$997$	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
$999$		0			0

Twists

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

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

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.349525 + 0.605394i) q^{2} +(0.755665 - 1.30885i) q^{4} -1.00000 q^{5} +(-1.62523 - 2.08773i) q^{7} +2.45459 q^{8} +(-0.349525 - 0.605394i) q^{10} +3.83823 q^{11} +(2.28027 + 3.94954i) q^{13} +(0.695843 - 1.71362i) q^{14} +(-0.653390 - 1.13171i) q^{16} +(-2.93173 - 5.07790i) q^{17} +(0.386961 - 0.670236i) q^{19} +(-0.755665 + 1.30885i) q^{20} +(1.34156 + 2.32364i) q^{22} -6.90532 q^{23} +1.00000 q^{25} +(-1.59402 + 2.76092i) q^{26} +(-3.96066 + 0.549558i) q^{28} +(3.95301 - 6.84682i) q^{29} +(2.01894 - 3.49691i) q^{31} +(2.91134 - 5.04260i) q^{32} +(2.04942 - 3.54970i) q^{34} +(1.62523 + 2.08773i) q^{35} +(4.23407 - 7.33362i) q^{37} +0.541010 q^{38} -2.45459 q^{40} +(1.60838 + 2.78579i) q^{41} +(4.19469 - 7.26541i) q^{43} +(2.90042 - 5.02367i) q^{44} +(-2.41358 - 4.18044i) q^{46} +(-1.66963 - 2.89189i) q^{47} +(-1.71725 + 6.78609i) q^{49} +(0.349525 + 0.605394i) q^{50} +6.89248 q^{52} +(-1.32630 - 2.29721i) q^{53} -3.83823 q^{55} +(-3.98928 - 5.12453i) q^{56} +5.52670 q^{58} +(-3.36978 + 5.83663i) q^{59} +(-3.50639 - 6.07324i) q^{61} +2.82268 q^{62} +1.45678 q^{64} +(-2.28027 - 3.94954i) q^{65} +(-7.28514 + 12.6182i) q^{67} -8.86162 q^{68} +(-0.695843 + 1.71362i) q^{70} +9.67100 q^{71} +(7.00941 + 12.1407i) q^{73} +5.91964 q^{74} +(-0.584826 - 1.01295i) q^{76} +(-6.23801 - 8.01320i) q^{77} +(6.69289 + 11.5924i) q^{79} +(0.653390 + 1.13171i) q^{80} +(-1.12433 + 1.94740i) q^{82} +(-0.442527 + 0.766479i) q^{83} +(2.93173 + 5.07790i) q^{85} +5.86458 q^{86} +9.42130 q^{88} +(-0.950003 + 1.64545i) q^{89} +(4.53962 - 11.1795i) q^{91} +(-5.21811 + 9.03803i) q^{92} +(1.16716 - 2.02157i) q^{94} +(-0.386961 + 0.670236i) q^{95} +(-3.07725 + 5.32996i) q^{97} +(-4.70848 + 1.33229i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 22 q^{4} - 36 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{14} - 30 q^{16} + 5 q^{17} - 2 q^{19} + 22 q^{20} - 19 q^{22} - 6 q^{23} + 36 q^{25} + 4 q^{26} + 5 q^{28} + 8 q^{29} - 10 q^{32} + 10 q^{34}+ \cdots - 16 q^{98}+O(q^{100}) \) 36 * q - 22 * q^4 - 36 * q^5 - q^7 + 2 * q^11 + 2 * q^13 + 6 * q^14 - 30 * q^16 + 5 * q^17 - 2 * q^19 + 22 * q^20 - 19 * q^22 - 6 * q^23 + 36 * q^25 + 4 * q^26 + 5 * q^28 + 8 * q^29 - 10 * q^32 + 10 * q^34 + q^35 - 15 * q^37 - 44 * q^38 + 4 * q^41 - 29 * q^43 + 7 * q^44 - 24 * q^46 + 23 * q^47 - 7 * q^49 + 14 * q^52 - 2 * q^55 - 33 * q^56 + 40 * q^58 + 5 * q^59 - 3 * q^61 + 12 * q^62 + 128 * q^64 - 2 * q^65 - 35 * q^67 - 34 * q^68 - 6 * q^70 - 24 * q^71 - 10 * q^73 + 44 * q^74 + 10 * q^76 - 5 * q^77 - 28 * q^79 + 30 * q^80 - 8 * q^82 + 22 * q^83 - 5 * q^85 + 38 * q^86 + 100 * q^88 + 4 * q^89 + 7 * q^91 + 50 * q^92 - 2 * q^94 + 2 * q^95 + 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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