LMFDB - Embedded newform 656.2.u.h.385.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			385.5
Root			$-0.620331 + 1.90918i$ of defining polynomial
Character	$\chi$	$=$	656.385
Dual form			656.2.u.h.305.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00743 q^{3} +(1.06040 + 0.770427i) q^{5} +(0.823910 + 2.53573i) q^{7} +1.02979 q^{9} +O(q^{10})$	\(q+2.00743 q^{3} +(1.06040 + 0.770427i) q^{5} +(0.823910 + 2.53573i) q^{7} +1.02979 q^{9} +(-0.383571 + 0.278681i) q^{11} +(0.477346 - 1.46912i) q^{13} +(2.12868 + 1.54658i) q^{15} +(4.19738 - 3.04957i) q^{17} +(1.37986 + 4.24678i) q^{19} +(1.65394 + 5.09032i) q^{21} +(-2.17737 + 6.70125i) q^{23} +(-1.01419 - 3.12136i) q^{25} -3.95507 q^{27} +(-0.481385 - 0.349747i) q^{29} +(2.56569 - 1.86408i) q^{31} +(-0.769994 + 0.559433i) q^{33} +(-1.07992 + 3.32366i) q^{35} +(1.06366 + 0.772792i) q^{37} +(0.958239 - 2.94916i) q^{39} +(-5.33634 - 3.53886i) q^{41} +(2.10794 - 6.48758i) q^{43} +(1.09199 + 0.793375i) q^{45} +(0.404687 - 1.24550i) q^{47} +(-0.0880017 + 0.0639370i) q^{49} +(8.42595 - 6.12181i) q^{51} +(1.60977 + 1.16957i) q^{53} -0.621443 q^{55} +(2.76998 + 8.52512i) q^{57} +(2.42795 - 7.47245i) q^{59} +(2.08205 + 6.40791i) q^{61} +(0.848451 + 2.61126i) q^{63} +(1.63803 - 1.19010i) q^{65} +(-9.25228 - 6.72218i) q^{67} +(-4.37092 + 13.4523i) q^{69} +(-3.24125 + 2.35490i) q^{71} -3.85396 q^{73} +(-2.03592 - 6.26592i) q^{75} +(-1.02269 - 0.743027i) q^{77} +8.19848 q^{79} -11.0289 q^{81} -4.85041 q^{83} +6.80038 q^{85} +(-0.966348 - 0.702093i) q^{87} +(-3.69571 - 11.3742i) q^{89} +4.11859 q^{91} +(5.15044 - 3.74201i) q^{93} +(-1.80862 + 5.56637i) q^{95} +(8.72456 + 6.33876i) q^{97} +(-0.394996 + 0.286982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.00743			1.15899			0.579496	−	0.814975i	$-0.303249\pi$
$3$	2.00743			1.15899			0.579496	+	0.814975i	$0.303249\pi$
$4$		0			0
$5$	1.06040	+	0.770427i	0.474226	+	0.344545i	0.799086	−	0.601217i	$-0.205317\pi$
$5$	1.06040	+	0.770427i	0.474226	+	0.344545i	−0.324860	+	0.945762i	$0.605317\pi$
$6$		0			0
$7$	0.823910	+	2.53573i	0.311409	+	0.958417i	0.977208	+	0.212286i	$0.0680909\pi$
$7$	0.823910	+	2.53573i	0.311409	+	0.958417i	−0.665799	+	0.746131i	$0.731909\pi$
$8$		0			0
$9$	1.02979			0.343262
$10$		0			0
$11$	−0.383571	+	0.278681i	−0.115651	+	0.0840254i	−0.644107	−	0.764935i	$-0.722771\pi$
$11$	−0.383571	+	0.278681i	−0.115651	+	0.0840254i	0.528456	+	0.848960i	$0.322771\pi$
$12$		0			0
$13$	0.477346	−	1.46912i	0.132392	−	0.407460i	−0.862783	−	0.505574i	$-0.831281\pi$
$13$	0.477346	−	1.46912i	0.132392	−	0.407460i	0.995175	+	0.0981135i	$0.0312808\pi$
$14$		0			0
$15$	2.12868	+	1.54658i	0.549624	+	0.399325i
$16$		0			0
$17$	4.19738	−	3.04957i	1.01801	−	0.739630i	0.0521390	−	0.998640i	$-0.483396\pi$
$17$	4.19738	−	3.04957i	1.01801	−	0.739630i	0.965875	+	0.259010i	$0.0833961\pi$
$18$		0			0
$19$	1.37986	+	4.24678i	0.316562	+	0.974278i	0.975107	+	0.221736i	$0.0711724\pi$
$19$	1.37986	+	4.24678i	0.316562	+	0.974278i	−0.658545	+	0.752542i	$0.728828\pi$
$20$		0			0
$21$	1.65394	+	5.09032i	0.360920	+	1.11080i
$22$		0			0
$23$	−2.17737	+	6.70125i	−0.454012	+	1.39731i	0.418278	+	0.908319i	$0.362634\pi$
$23$	−2.17737	+	6.70125i	−0.454012	+	1.39731i	−0.872291	+	0.488987i	$0.837366\pi$
$24$		0			0
$25$	−1.01419	−	3.12136i	−0.202838	−	0.624272i
$26$		0			0
$27$	−3.95507			−0.761154
$28$		0			0
$29$	−0.481385	−	0.349747i	−0.0893910	−	0.0649463i	0.542192	−	0.840255i	$-0.317595\pi$
$29$	−0.481385	−	0.349747i	−0.0893910	−	0.0649463i	−0.631583	+	0.775308i	$0.717595\pi$
$30$		0			0
$31$	2.56569	−	1.86408i	0.460811	−	0.334799i	−0.333039	−	0.942913i	$-0.608074\pi$
$31$	2.56569	−	1.86408i	0.460811	−	0.334799i	0.793849	+	0.608115i	$0.208074\pi$
$32$		0			0
$33$	−0.769994	+	0.559433i	−0.134039	+	0.0973848i
$34$		0			0
$35$	−1.07992	+	3.32366i	−0.182540	+	0.561801i
$36$		0			0
$37$	1.06366	+	0.772792i	0.174864	+	0.127046i	0.671775	−	0.740756i	$-0.265532\pi$
$37$	1.06366	+	0.772792i	0.174864	+	0.127046i	−0.496911	+	0.867802i	$0.665532\pi$
$38$		0			0
$39$	0.958239	−	2.94916i	0.153441	−	0.472243i
$40$		0			0
$41$	−5.33634	−	3.53886i	−0.833396	−	0.552677i
$41$	−5.33634	−	3.53886i	−0.833396	−	0.552677i
$42$		0			0
$43$	2.10794	−	6.48758i	0.321458	−	0.989346i	−0.651556	−	0.758601i	$-0.725883\pi$
$43$	2.10794	−	6.48758i	0.321458	−	0.989346i	0.973014	−	0.230746i	$-0.0741166\pi$
$44$		0			0
$45$	1.09199	+	0.793375i	0.162784	+	0.118269i
$46$		0			0
$47$	0.404687	−	1.24550i	0.0590297	−	0.181675i	−0.917194	−	0.398442i	$-0.869551\pi$
$47$	0.404687	−	1.24550i	0.0590297	−	0.181675i	0.976223	+	0.216767i	$0.0695512\pi$
$48$		0			0
$49$	−0.0880017	+	0.0639370i	−0.0125717	+	0.00913385i
$50$		0			0
$51$	8.42595	−	6.12181i	1.17987	−	0.857225i
$52$		0			0
$53$	1.60977	+	1.16957i	0.221119	+	0.160652i	0.692830	−	0.721101i	$-0.256364\pi$
$53$	1.60977	+	1.16957i	0.221119	+	0.160652i	−0.471711	+	0.881753i	$0.656364\pi$
$54$		0			0
$55$	−0.621443			−0.0837953
$56$		0			0
$57$	2.76998	+	8.52512i	0.366893	+	1.12918i
$58$		0			0
$59$	2.42795	−	7.47245i	0.316092	−	0.972831i	−0.659211	−	0.751958i	$-0.729110\pi$
$59$	2.42795	−	7.47245i	0.316092	−	0.972831i	0.975303	−	0.220873i	$-0.0708905\pi$
$60$		0			0
$61$	2.08205	+	6.40791i	0.266580	+	0.820448i	0.991325	+	0.131432i	$0.0419574\pi$
$61$	2.08205	+	6.40791i	0.266580	+	0.820448i	−0.724745	+	0.689017i	$0.758043\pi$
$62$		0			0
$63$	0.848451	+	2.61126i	0.106895	+	0.328988i
$64$		0			0
$65$	1.63803	−	1.19010i	0.203172	−	0.147613i
$66$		0			0
$67$	−9.25228	−	6.72218i	−1.13035	−	0.821245i	−0.144601	−	0.989490i	$-0.546190\pi$
$67$	−9.25228	−	6.72218i	−1.13035	−	0.821245i	−0.985745	+	0.168245i	$0.946190\pi$
$68$		0			0
$69$	−4.37092	+	13.4523i	−0.526197	+	1.61947i
$70$		0			0
$71$	−3.24125	+	2.35490i	−0.384665	+	0.279476i	−0.763266	−	0.646084i	$-0.776405\pi$
$71$	−3.24125	+	2.35490i	−0.384665	+	0.279476i	0.378601	+	0.925560i	$0.376405\pi$
$72$		0			0
$73$	−3.85396			−0.451072			−0.225536	−	0.974235i	$-0.572413\pi$
$73$	−3.85396			−0.451072			−0.225536	+	0.974235i	$0.572413\pi$
$74$		0			0
$75$	−2.03592	−	6.26592i	−0.235088	−	0.723526i
$76$		0			0
$77$	−1.02269	−	0.743027i	−0.116546	−	0.0846758i
$78$		0			0
$79$	8.19848			0.922402			0.461201	−	0.887296i	$-0.347419\pi$
$79$	8.19848			0.922402			0.461201	+	0.887296i	$0.347419\pi$
$80$		0			0
$81$	−11.0289			−1.22543
$82$		0			0
$83$	−4.85041			−0.532402			−0.266201	−	0.963918i	$-0.585768\pi$
$83$	−4.85041			−0.532402			−0.266201	+	0.963918i	$0.585768\pi$
$84$		0			0
$85$	6.80038			0.737605
$86$		0			0
$87$	−0.966348	−	0.702093i	−0.103603	−	0.0752723i
$88$		0			0
$89$	−3.69571	−	11.3742i	−0.391744	−	1.20566i	−0.931468	−	0.363822i	$-0.881471\pi$
$89$	−3.69571	−	11.3742i	−0.391744	−	1.20566i	0.539724	−	0.841842i	$-0.318529\pi$
$90$		0			0
$91$	4.11859			0.431745
$92$		0			0
$93$	5.15044	−	3.74201i	0.534076	−	0.388029i
$94$		0			0
$95$	−1.80862	+	5.56637i	−0.185561	+	0.571098i
$96$		0			0
$97$	8.72456	+	6.33876i	0.885845	+	0.643604i	0.934791	−	0.355198i	$-0.115586\pi$
$97$	8.72456	+	6.33876i	0.885845	+	0.643604i	−0.0489467	+	0.998801i	$0.515586\pi$
$98$		0			0
$99$	−0.394996	+	0.286982i	−0.0396986	+	0.0288427i
$100$		0			0
$101$	−5.41748	−	16.6733i	−0.539059	−	1.65905i	−0.734711	−	0.678380i	$-0.762682\pi$
$101$	−5.41748	−	16.6733i	−0.539059	−	1.65905i	0.195652	−	0.980673i	$-0.437318\pi$
$102$		0			0
$103$	3.54416	+	10.9078i	0.349216	+	1.07478i	0.959288	+	0.282431i	$0.0911408\pi$
$103$	3.54416	+	10.9078i	0.349216	+	1.07478i	−0.610071	+	0.792347i	$0.708859\pi$
$104$		0			0
$105$	−2.16787	+	6.67202i	−0.211562	+	0.651122i
$106$		0			0
$107$	−0.636436	−	1.95875i	−0.0615266	−	0.189359i	0.915569	−	0.402162i	$-0.131741\pi$
$107$	−0.636436	−	1.95875i	−0.0615266	−	0.189359i	−0.977095	+	0.212802i	$0.931741\pi$
$108$		0			0
$109$	−2.57069			−0.246228			−0.123114	−	0.992393i	$-0.539288\pi$
$109$	−2.57069			−0.246228			−0.123114	+	0.992393i	$0.539288\pi$
$110$		0			0
$111$	2.13522	+	1.55133i	0.202666	+	0.147246i
$112$		0			0
$113$	−5.62903	+	4.08973i	−0.529535	+	0.384730i	−0.820184	−	0.572100i	$-0.806129\pi$
$113$	−5.62903	+	4.08973i	−0.529535	+	0.384730i	0.290649	+	0.956830i	$0.406129\pi$
$114$		0			0
$115$	−7.47170	+	5.42851i	−0.696740	+	0.506211i
$116$		0			0
$117$	0.491564	−	1.51288i	0.0454451	−	0.139866i
$118$		0			0
$119$	11.1912	+	8.13086i	1.02589	+	0.745355i
$120$		0			0
$121$	−3.32972	+	10.2478i	−0.302702	+	0.931621i
$122$		0			0
$123$	−10.7123	−	7.10402i	−0.965899	−	0.640548i
$124$		0			0
$125$	3.35452	−	10.3241i	0.300037	−	0.923419i
$126$		0			0
$127$	0.188758	+	0.137141i	0.0167496	+	0.0121693i	0.596129	−	0.802889i	$-0.296705\pi$
$127$	0.188758	+	0.137141i	0.0167496	+	0.0121693i	−0.579379	+	0.815058i	$0.696705\pi$
$128$		0			0
$129$	4.23155	−	13.0234i	0.372567	−	1.14664i
$130$		0			0
$131$	−7.65842	+	5.56417i	−0.669119	+	0.486143i	−0.869730	−	0.493528i	$-0.835707\pi$
$131$	−7.65842	+	5.56417i	−0.669119	+	0.486143i	0.200611	+	0.979671i	$0.435707\pi$
$132$		0			0
$133$	−9.63182	+	6.99793i	−0.835185	+	0.606797i
$134$		0			0
$135$	−4.19396	−	3.04709i	−0.360959	−	0.262252i
$136$		0			0
$137$	16.0549			1.37166			0.685831	−	0.727761i	$-0.259439\pi$
$137$	16.0549			1.37166			0.685831	+	0.727761i	$0.259439\pi$
$138$		0			0
$139$	−7.05825	−	21.7231i	−0.598673	−	1.84253i	−0.535521	−	0.844522i	$-0.679885\pi$
$139$	−7.05825	−	21.7231i	−0.598673	−	1.84253i	−0.0631516	−	0.998004i	$-0.520115\pi$
$140$		0			0
$141$	0.812382	−	2.50026i	0.0684149	−	0.210559i
$142$		0			0
$143$	0.226319	+	0.696539i	0.0189258	+	0.0582475i
$144$		0			0
$145$	−0.241007	−	0.741744i	−0.0200146	−	0.0615985i
$146$		0			0
$147$	−0.176657	+	0.128349i	−0.0145705	+	0.0105861i
$148$		0			0
$149$	0.670397	+	0.487072i	0.0549211	+	0.0399025i	0.614907	−	0.788600i	$-0.289194\pi$
$149$	0.670397	+	0.487072i	0.0549211	+	0.0399025i	−0.559986	+	0.828502i	$0.689194\pi$
$150$		0			0
$151$	1.77286	−	5.45631i	0.144273	−	0.444028i	−0.852643	−	0.522493i	$-0.825002\pi$
$151$	1.77286	−	5.45631i	0.144273	−	0.444028i	0.996917	+	0.0784653i	$0.0250020\pi$
$152$		0			0
$153$	4.32240	−	3.14041i	0.349445	−	0.253887i
$154$		0			0
$155$	4.15679			0.333882
$156$		0			0
$157$	−5.36561	−	16.5136i	−0.428222	−	1.31793i	−0.899875	−	0.436148i	$-0.856343\pi$
$157$	−5.36561	−	16.5136i	−0.428222	−	1.31793i	0.471653	−	0.881784i	$-0.343657\pi$
$158$		0			0
$159$	3.23150	+	2.34783i	0.256275	+	0.186195i
$160$		0			0
$161$	−18.7865			−1.48059
$162$		0			0
$163$	3.83892			0.300688			0.150344	−	0.988634i	$-0.451962\pi$
$163$	3.83892			0.300688			0.150344	+	0.988634i	$0.451962\pi$
$164$		0			0
$165$	−1.24750			−0.0971181
$166$		0			0
$167$	−22.7727			−1.76220			−0.881101	−	0.472928i	$-0.843197\pi$
$167$	−22.7727			−1.76220			−0.881101	+	0.472928i	$0.843197\pi$
$168$		0			0
$169$	8.58677	+	6.23865i	0.660521	+	0.479896i
$170$		0			0
$171$	1.42096	+	4.37327i	0.108664	+	0.334433i
$172$		0			0
$173$	−18.1088			−1.37679			−0.688394	−	0.725337i	$-0.741684\pi$
$173$	−18.1088			−1.37679			−0.688394	+	0.725337i	$0.741684\pi$
$174$		0			0
$175$	7.07934	−	5.14344i	0.535148	−	0.388807i
$176$		0			0
$177$	4.87394	−	15.0004i	0.366348	−	1.12750i
$178$		0			0
$179$	−5.70763	−	4.14683i	−0.426608	−	0.309949i	0.353683	−	0.935365i	$-0.384929\pi$
$179$	−5.70763	−	4.14683i	−0.426608	−	0.309949i	−0.780291	+	0.625416i	$0.784929\pi$
$180$		0			0
$181$	−13.5231	+	9.82509i	−1.00516	+	0.730293i	−0.963189	−	0.268826i	$-0.913364\pi$
$181$	−13.5231	+	9.82509i	−1.00516	+	0.730293i	−0.0419734	+	0.999119i	$0.513364\pi$
$182$		0			0
$183$	4.17958	+	12.8634i	0.308964	+	0.950893i
$184$		0			0
$185$	0.532524	+	1.63894i	0.0391519	+	0.120497i
$186$		0			0
$187$	−0.760136	+	2.33946i	−0.0555866	+	0.171078i
$188$		0			0
$189$	−3.25862	−	10.0290i	−0.237030	−	0.729503i
$190$		0			0
$191$	−16.6185			−1.20247			−0.601237	−	0.799071i	$-0.705325\pi$
$191$	−16.6185			−1.20247			−0.601237	+	0.799071i	$0.705325\pi$
$192$		0			0
$193$	11.0818	+	8.05142i	0.797687	+	0.579554i	0.910235	−	0.414093i	$-0.135901\pi$
$193$	11.0818	+	8.05142i	0.797687	+	0.579554i	−0.112547	+	0.993646i	$0.535901\pi$
$194$		0			0
$195$	3.28823	−	2.38904i	0.235475	−	0.171083i
$196$		0			0
$197$	16.8158	−	12.2174i	1.19808	−	0.870454i	0.203983	−	0.978974i	$-0.434611\pi$
$197$	16.8158	−	12.2174i	1.19808	−	0.870454i	0.994094	+	0.108520i	$0.0346112\pi$
$198$		0			0
$199$	−8.22368	+	25.3099i	−0.582961	+	1.79417i	0.0243463	+	0.999704i	$0.492250\pi$
$199$	−8.22368	+	25.3099i	−0.582961	+	1.79417i	−0.607308	+	0.794467i	$0.707750\pi$
$200$		0			0
$201$	−18.5733	−	13.4943i	−1.31006	−	0.951816i
$202$		0			0
$203$	0.490247	−	1.50882i	0.0344086	−	0.105899i
$204$		0			0
$205$	−2.93223	−	7.86386i	−0.204796	−	0.549236i
$206$		0			0
$207$	−2.24222	+	6.90085i	−0.155845	+	0.479642i
$208$		0			0
$209$	−1.71277	−	1.24440i	−0.118475	−	0.0860770i
$210$		0			0
$211$	3.75162	−	11.5463i	0.258272	−	0.794880i	−0.734895	−	0.678181i	$-0.762769\pi$
$211$	3.75162	−	11.5463i	0.258272	−	0.794880i	0.993167	−	0.116700i	$-0.0372314\pi$
$212$		0			0
$213$	−6.50658	+	4.72731i	−0.445824	+	0.323910i
$214$		0			0
$215$	7.23347	−	5.25542i	0.493318	−	0.358417i
$216$		0			0
$217$	6.84070	+	4.97006i	0.464377	+	0.337390i
$218$		0			0
$219$	−7.73656			−0.522789
$220$		0			0
$221$	−2.47659	−	7.62215i	−0.166593	−	0.512721i
$222$		0			0
$223$	1.75853	−	5.41221i	0.117760	−	0.362428i	−0.874753	−	0.484570i	$-0.838976\pi$
$223$	1.75853	−	5.41221i	0.117760	−	0.362428i	0.992513	+	0.122142i	$0.0389762\pi$
$224$		0			0
$225$	−1.04440	−	3.21433i	−0.0696267	−	0.214289i
$226$		0			0
$227$	5.75052	+	17.6983i	0.381675	+	1.17468i	0.938863	+	0.344290i	$0.111880\pi$
$227$	5.75052	+	17.6983i	0.381675	+	1.17468i	−0.557188	+	0.830386i	$0.688120\pi$
$228$		0			0
$229$	4.85678	−	3.52866i	0.320945	−	0.233180i	−0.415633	−	0.909532i	$-0.636440\pi$
$229$	4.85678	−	3.52866i	0.320945	−	0.233180i	0.736579	+	0.676352i	$0.236440\pi$
$230$		0			0
$231$	−2.05298	−	1.49158i	−0.135076	−	0.0981385i
$232$		0			0
$233$	−6.46349	+	19.8926i	−0.423438	+	1.30321i	0.481045	+	0.876696i	$0.340257\pi$
$233$	−6.46349	+	19.8926i	−0.423438	+	1.30321i	−0.904482	+	0.426511i	$0.859743\pi$
$234$		0			0
$235$	1.38870	−	1.00895i	0.0905886	−	0.0658164i
$236$		0			0
$237$	16.4579			1.06906
$238$		0			0
$239$	−7.01409	−	21.5872i	−0.453704	−	1.39636i	−0.872650	−	0.488346i	$-0.837600\pi$
$239$	−7.01409	−	21.5872i	−0.453704	−	1.39636i	0.418946	−	0.908011i	$-0.362400\pi$
$240$		0			0
$241$	11.8826	+	8.63320i	0.765424	+	0.556113i	0.900569	−	0.434713i	$-0.143150\pi$
$241$	11.8826	+	8.63320i	0.765424	+	0.556113i	−0.135145	+	0.990826i	$0.543150\pi$
$242$		0			0
$243$	−10.2746			−0.659113
$244$		0			0
$245$	−0.142576			−0.00910883
$246$		0			0
$247$	6.89769			0.438890
$248$		0			0
$249$	−9.73687			−0.617049
$250$		0			0
$251$	−5.17396	−	3.75910i	−0.326577	−	0.237272i	0.412400	−	0.911003i	$-0.364691\pi$
$251$	−5.17396	−	3.75910i	−0.326577	−	0.237272i	−0.738977	+	0.673731i	$0.764691\pi$
$252$		0			0
$253$	−1.03233	−	3.17720i	−0.0649023	−	0.199749i
$254$		0			0
$255$	13.6513			0.854878
$256$		0			0
$257$	14.2256	−	10.3355i	0.887371	−	0.644713i	−0.0478199	−	0.998856i	$-0.515227\pi$
$257$	14.2256	−	10.3355i	0.887371	−	0.644713i	0.935191	+	0.354143i	$0.115227\pi$
$258$		0			0
$259$	−1.08324	+	3.33386i	−0.0673091	+	0.207156i
$260$		0			0
$261$	−0.495724	−	0.360164i	−0.0306845	−	0.0222936i
$262$		0			0
$263$	−9.51094	+	6.91011i	−0.586470	+	0.426095i	−0.841051	−	0.540956i	$-0.818062\pi$
$263$	−9.51094	+	6.91011i	−0.586470	+	0.426095i	0.254581	+	0.967051i	$0.418062\pi$
$264$		0			0
$265$	0.805937	+	2.48042i	0.0495083	+	0.152371i
$266$		0			0
$267$	−7.41888	−	22.8330i	−0.454028	−	1.39736i
$268$		0			0
$269$	4.35309	−	13.3974i	0.265412	−	0.816855i	−0.726186	−	0.687498i	$-0.758709\pi$
$269$	4.35309	−	13.3974i	0.265412	−	0.816855i	0.991598	−	0.129357i	$-0.0412912\pi$
$270$		0			0
$271$	9.09008	+	27.9764i	0.552183	+	1.69945i	0.703268	+	0.710925i	$0.251723\pi$
$271$	9.09008	+	27.9764i	0.552183	+	1.69945i	−0.151085	+	0.988521i	$0.548277\pi$
$272$		0			0
$273$	8.26778			0.500389
$274$		0			0
$275$	1.25888	+	0.914628i	0.0759132	+	0.0551542i
$276$		0			0
$277$	−23.5442	+	17.1058i	−1.41463	+	1.02779i	−0.422004	+	0.906594i	$0.638673\pi$
$277$	−23.5442	+	17.1058i	−1.41463	+	1.02779i	−0.992629	+	0.121196i	$0.961327\pi$
$278$		0			0
$279$	2.64211	−	1.91960i	0.158179	−	0.114924i
$280$		0			0
$281$	−9.97062	+	30.6864i	−0.594797	+	1.83060i	−0.0390648	+	0.999237i	$0.512438\pi$
$281$	−9.97062	+	30.6864i	−0.594797	+	1.83060i	−0.555732	+	0.831361i	$0.687562\pi$
$282$		0			0
$283$	26.2461	+	19.0689i	1.56017	+	1.13353i	0.935872	+	0.352340i	$0.114614\pi$
$283$	26.2461	+	19.0689i	1.56017	+	1.13353i	0.624295	+	0.781188i	$0.285386\pi$
$284$		0			0
$285$	−3.63069	+	11.1741i	−0.215064	+	0.661897i
$286$		0			0
$287$	4.57694	−	16.4472i	0.270168	−	0.970849i
$288$		0			0
$289$	3.06480	−	9.43247i	0.180282	−	0.554851i
$290$		0			0
$291$	17.5140	+	12.7246i	1.02669	+	0.745931i
$292$		0			0
$293$	−3.86875	+	11.9068i	−0.226015	+	0.695603i	0.772172	+	0.635414i	$0.219170\pi$
$293$	−3.86875	+	11.9068i	−0.226015	+	0.695603i	−0.998187	+	0.0601891i	$0.980830\pi$
$294$		0			0
$295$	8.33158	−	6.05324i	0.485083	−	0.352434i
$296$		0			0
$297$	1.51705	−	1.10220i	0.0880283	−	0.0639563i
$298$		0			0
$299$	8.80557	+	6.39762i	0.509239	+	0.369984i
$300$		0			0
$301$	18.1875			1.04831
$302$		0			0
$303$	−10.8752	−	33.4705i	−0.624765	−	1.92283i
$304$		0			0
$305$	−2.72901	+	8.39902i	−0.156263	+	0.480927i
$306$		0			0
$307$	−8.03234	−	24.7210i	−0.458430	−	1.41090i	−0.867060	−	0.498203i	$-0.833993\pi$
$307$	−8.03234	−	24.7210i	−0.458430	−	1.41090i	0.408630	−	0.912700i	$-0.366007\pi$
$308$		0			0
$309$	7.11466	+	21.8967i	0.404739	+	1.24566i
$310$		0			0
$311$	12.4776	−	9.06550i	0.707539	−	0.514057i	−0.174840	−	0.984597i	$-0.555941\pi$
$311$	12.4776	−	9.06550i	0.707539	−	0.514057i	0.882379	+	0.470540i	$0.155941\pi$
$312$		0			0
$313$	23.7809	+	17.2778i	1.34417	+	0.976599i	0.999279	+	0.0379579i	$0.0120853\pi$
$313$	23.7809	+	17.2778i	1.34417	+	0.976599i	0.344894	+	0.938642i	$0.387915\pi$
$314$		0			0
$315$	−1.11209	+	3.42266i	−0.0626591	+	0.192845i
$316$		0			0
$317$	7.63106	−	5.54429i	0.428603	−	0.311399i	−0.352487	−	0.935817i	$-0.614664\pi$
$317$	7.63106	−	5.54429i	0.428603	−	0.311399i	0.781090	+	0.624418i	$0.214664\pi$
$318$		0			0
$319$	0.282113			0.0157953
$320$		0			0
$321$	−1.27760	−	3.93205i	−0.0713088	−	0.219466i
$322$		0			0
$323$	18.7427	+	13.6173i	1.04287	+	0.757689i
$324$		0			0
$325$	−5.06977			−0.281220
$326$		0			0
$327$	−5.16049			−0.285376
$328$		0			0
$329$	3.49168			0.192503
$330$		0			0
$331$	29.6956			1.63222			0.816110	−	0.577896i	$-0.196126\pi$
$331$	29.6956			1.63222			0.816110	+	0.577896i	$0.196126\pi$
$332$		0			0
$333$	1.09534	+	0.795810i	0.0600242	+	0.0436101i
$334$		0			0
$335$	−4.63219	−	14.2564i	−0.253083	−	0.778911i
$336$		0			0
$337$	3.01331			0.164145			0.0820727	−	0.996626i	$-0.473846\pi$
$337$	3.01331			0.164145			0.0820727	+	0.996626i	$0.473846\pi$
$338$		0			0
$339$	−11.2999	+	8.20986i	−0.613727	+	0.445899i
$340$		0			0
$341$	−0.464640	+	1.43001i	−0.0251617	+	0.0774396i
$342$		0			0
$343$	14.8645	+	10.7997i	0.802610	+	0.583130i
$344$		0			0
$345$	−14.9989	+	10.8974i	−0.807516	+	0.586694i
$346$		0			0
$347$	0.0794324	+	0.244468i	0.00426416	+	0.0131237i	0.953166	−	0.302448i	$-0.0978038\pi$
$347$	0.0794324	+	0.244468i	0.00426416	+	0.0131237i	−0.948902	+	0.315572i	$0.897804\pi$
$348$		0			0
$349$	11.1862	+	34.4277i	0.598786	+	1.84287i	0.534897	+	0.844917i	$0.320350\pi$
$349$	11.1862	+	34.4277i	0.598786	+	1.84287i	0.0638890	+	0.997957i	$0.479650\pi$
$350$		0			0
$351$	−1.88794	+	5.81047i	−0.100771	+	0.310140i
$352$		0			0
$353$	−5.59065	−	17.2063i	−0.297560	−	0.915797i	−0.982349	−	0.187055i	$-0.940106\pi$
$353$	−5.59065	−	17.2063i	−0.297560	−	0.915797i	0.684789	−	0.728742i	$-0.259894\pi$
$354$		0			0
$355$	−5.25130			−0.278710
$356$		0			0
$357$	22.4655	+	16.3222i	1.18900	+	0.863860i
$358$		0			0
$359$	10.5095	−	7.63561i	0.554671	−	0.402992i	−0.274834	−	0.961492i	$-0.588623\pi$
$359$	10.5095	−	7.63561i	0.554671	−	0.402992i	0.829505	+	0.558500i	$0.188623\pi$
$360$		0			0
$361$	−0.759786	+	0.552017i	−0.0399887	+	0.0290535i
$362$		0			0
$363$	−6.68419	+	20.5718i	−0.350829	+	1.07974i
$364$		0			0
$365$	−4.08674	−	2.96919i	−0.213910	−	0.155415i
$366$		0			0
$367$	0.0265740	−	0.0817862i	0.00138715	−	0.00426921i	−0.950361	−	0.311151i	$-0.899286\pi$
$367$	0.0265740	−	0.0817862i	0.00138715	−	0.00426921i	0.951748	+	0.306882i	$0.0992856\pi$
$368$		0			0
$369$	−5.49528	−	3.64427i	−0.286073	−	0.189713i
$370$		0			0
$371$	−1.63940	+	5.04557i	−0.0851136	+	0.261953i
$372$		0			0
$373$	20.5874	+	14.9576i	1.06597	+	0.774474i	0.975184	−	0.221396i	$-0.0710612\pi$
$373$	20.5874	+	14.9576i	1.06597	+	0.774474i	0.0907886	+	0.995870i	$0.471061\pi$
$374$		0			0
$375$	6.73396	−	20.7250i	0.347740	−	1.07023i
$376$		0			0
$377$	−0.743607	+	0.540262i	−0.0382977	+	0.0278249i
$378$		0			0
$379$	−2.88877	+	2.09881i	−0.148386	+	0.107809i	−0.659501	−	0.751703i	$-0.729233\pi$
$379$	−2.88877	+	2.09881i	−0.148386	+	0.107809i	0.511115	+	0.859512i	$0.329233\pi$
$380$		0			0
$381$	0.378919	+	0.275301i	0.0194126	+	0.0141041i
$382$		0			0
$383$	−12.4128			−0.634266			−0.317133	−	0.948381i	$-0.602720\pi$
$383$	−12.4128			−0.634266			−0.317133	+	0.948381i	$0.602720\pi$
$384$		0			0
$385$	−0.512013	−	1.57581i	−0.0260946	−	0.0803109i
$386$		0			0
$387$	2.17073	−	6.68082i	0.110344	−	0.339605i
$388$		0			0
$389$	7.10704	+	21.8732i	0.360341	+	1.10902i	0.952847	+	0.303450i	$0.0981387\pi$
$389$	7.10704	+	21.8732i	0.360341	+	1.10902i	−0.592506	+	0.805566i	$0.701861\pi$
$390$		0			0
$391$	11.2967	+	34.7677i	0.571299	+	1.75828i
$392$		0			0
$393$	−15.3738	+	11.1697i	−0.775503	+	0.563436i
$394$		0			0
$395$	8.69368	+	6.31633i	0.437427	+	0.317809i
$396$		0			0
$397$	8.47231	−	26.0751i	0.425213	−	1.30867i	−0.477577	−	0.878590i	$-0.658485\pi$
$397$	8.47231	−	26.0751i	0.425213	−	1.30867i	0.902790	−	0.430082i	$-0.141515\pi$
$398$		0			0
$399$	−19.3352	+	14.0479i	−0.967972	+	0.703273i
$400$		0			0
$401$	12.6800			0.633208			0.316604	−	0.948558i	$-0.397457\pi$
$401$	12.6800			0.633208			0.316604	+	0.948558i	$0.397457\pi$
$402$		0			0
$403$	−1.51384	−	4.65911i	−0.0754095	−	0.232087i
$404$		0			0
$405$	−11.6951	−	8.49696i	−0.581132	−	0.422217i
$406$		0			0
$407$	−0.623351			−0.0308983
$408$		0			0
$409$	−4.87425			−0.241016			−0.120508	−	0.992712i	$-0.538452\pi$
$409$	−4.87425			−0.241016			−0.120508	+	0.992712i	$0.538452\pi$
$410$		0			0
$411$	32.2291			1.58975
$412$		0			0
$413$	20.9486			1.03081
$414$		0			0
$415$	−5.14338	−	3.73688i	−0.252479	−	0.183436i
$416$		0			0
$417$	−14.1690	−	43.6076i	−0.693857	−	2.13547i
$418$		0			0
$419$	7.52661			0.367699			0.183849	−	0.982954i	$-0.441144\pi$
$419$	7.52661			0.367699			0.183849	+	0.982954i	$0.441144\pi$
$420$		0			0
$421$	18.7190	−	13.6002i	0.912308	−	0.662831i	−0.0292893	−	0.999571i	$-0.509324\pi$
$421$	18.7190	−	13.6002i	0.912308	−	0.662831i	0.941598	+	0.336740i	$0.109324\pi$
$422$		0			0
$423$	0.416741	−	1.28260i	0.0202627	−	0.0623620i
$424$		0			0
$425$	−13.7758	−	10.0087i	−0.668223	−	0.485492i
$426$		0			0
$427$	−14.5333	+	10.5591i	−0.703317	+	0.510989i
$428$		0			0
$429$	0.454321	+	1.39826i	0.0219348	+	0.0675084i
$430$		0			0
$431$	2.98008	+	9.17174i	0.143545	+	0.441787i	0.996821	−	0.0796728i	$-0.0253875\pi$
$431$	2.98008	+	9.17174i	0.143545	+	0.441787i	−0.853276	+	0.521460i	$0.825388\pi$
$432$		0			0
$433$	0.245690	−	0.756157i	0.0118071	−	0.0363386i	−0.944979	−	0.327130i	$-0.893919\pi$
$433$	0.245690	−	0.756157i	0.0118071	−	0.0363386i	0.956787	+	0.290791i	$0.0939185\pi$
$434$		0			0
$435$	−0.483806	−	1.48900i	−0.0231967	−	0.0713921i
$436$		0			0
$437$	−31.4632			−1.50509
$438$		0			0
$439$	−9.52798	−	6.92248i	−0.454746	−	0.330392i	0.336721	−	0.941605i	$-0.390682\pi$
$439$	−9.52798	−	6.92248i	−0.454746	−	0.330392i	−0.791467	+	0.611212i	$0.790682\pi$
$440$		0			0
$441$	−0.0906229	+	0.0658414i	−0.00431538	+	0.00313530i
$442$		0			0
$443$	−23.3641	+	16.9750i	−1.11006	+	0.806508i	−0.982674	−	0.185344i	$-0.940660\pi$
$443$	−23.3641	+	16.9750i	−1.11006	+	0.806508i	−0.127390	+	0.991853i	$0.540660\pi$
$444$		0			0
$445$	4.84407	−	14.9085i	0.229631	−	0.706731i
$446$		0			0
$447$	1.34578	+	0.977764i	0.0636531	+	0.0462467i
$448$		0			0
$449$	5.35014	−	16.4660i	0.252489	−	0.777081i	−0.741825	−	0.670593i	$-0.766040\pi$
$449$	5.35014	−	16.4660i	0.252489	−	0.777081i	0.994314	−	0.106488i	$-0.0339604\pi$
$450$		0			0
$451$	3.03308	−	0.129730i	0.142822	−	0.00610876i
$452$		0			0
$453$	3.55890	−	10.9532i	0.167212	−	0.514625i
$454$		0			0
$455$	4.36735	+	3.17307i	0.204745	+	0.148756i
$456$		0			0
$457$	3.38479	−	10.4173i	0.158334	−	0.487301i	−0.840150	−	0.542355i	$-0.817533\pi$
$457$	3.38479	−	10.4173i	0.158334	−	0.487301i	0.998483	+	0.0550534i	$0.0175329\pi$
$458$		0			0
$459$	−16.6009	+	12.0613i	−0.774865	+	0.562973i
$460$		0			0
$461$	−5.07692	+	3.68860i	−0.236456	+	0.171795i	−0.699703	−	0.714434i	$-0.746684\pi$
$461$	−5.07692	+	3.68860i	−0.236456	+	0.171795i	0.463247	+	0.886229i	$0.346684\pi$
$462$		0			0
$463$	5.80950	+	4.22085i	0.269990	+	0.196160i	0.714540	−	0.699595i	$-0.246636\pi$
$463$	5.80950	+	4.22085i	0.269990	+	0.196160i	−0.444549	+	0.895754i	$0.646636\pi$
$464$		0			0
$465$	8.34448			0.386966
$466$		0			0
$467$	−6.24984	−	19.2350i	−0.289208	−	0.890092i	−0.985106	−	0.171950i	$-0.944993\pi$
$467$	−6.24984	−	19.2350i	−0.289208	−	0.890092i	0.695897	−	0.718141i	$-0.255007\pi$
$468$		0			0
$469$	9.42261	−	28.9998i	0.435095	−	1.33909i
$470$		0			0
$471$	−10.7711	−	33.1500i	−0.496306	−	1.52747i
$472$		0			0
$473$	0.999418	+	3.07589i	0.0459533	+	0.141430i
$474$		0			0
$475$	11.8563	−	8.61409i	0.544003	−	0.395242i
$476$		0			0
$477$	1.65772	+	1.20440i	0.0759017	+	0.0551458i
$478$		0			0
$479$	−4.54454	+	13.9866i	−0.207645	+	0.639066i	0.791949	+	0.610587i	$0.209066\pi$
$479$	−4.54454	+	13.9866i	−0.207645	+	0.639066i	−0.999594	+	0.0284791i	$0.990934\pi$
$480$		0			0
$481$	1.64306	−	1.19375i	0.0749169	−	0.0544303i
$482$		0			0
$483$	−37.7127			−1.71599
$484$		0			0
$485$	4.36798	+	13.4433i	0.198340	+	0.610427i
$486$		0			0
$487$	5.43861	+	3.95139i	0.246447	+	0.179054i	0.704151	−	0.710050i	$-0.251328\pi$
$487$	5.43861	+	3.95139i	0.246447	+	0.179054i	−0.457704	+	0.889105i	$0.651328\pi$
$488$		0			0
$489$	7.70638			0.348494
$490$		0			0
$491$	2.70171			0.121926			0.0609632	−	0.998140i	$-0.480583\pi$
$491$	2.70171			0.121926			0.0609632	+	0.998140i	$0.480583\pi$
$492$		0			0
$493$	−3.08713			−0.139038
$494$		0			0
$495$	−0.639953			−0.0287637
$496$		0			0
$497$	−8.64190	−	6.27871i	−0.387642	−	0.281639i
$498$		0			0
$499$	1.78317	+	5.48804i	0.0798258	+	0.245678i	0.983003	−	0.183589i	$-0.0587717\pi$
$499$	1.78317	+	5.48804i	0.0798258	+	0.245678i	−0.903177	+	0.429268i	$0.858772\pi$
$500$		0			0
$501$	−45.7146			−2.04238
$502$		0			0
$503$	3.01863	−	2.19317i	0.134594	−	0.0977884i	−0.518451	−	0.855107i	$-0.673491\pi$
$503$	3.01863	−	2.19317i	0.134594	−	0.0977884i	0.653045	+	0.757319i	$0.273491\pi$
$504$		0			0
$505$	7.10084	−	21.8541i	0.315983	−	0.972496i
$506$		0			0
$507$	17.2374	+	12.5237i	0.765538	+	0.556196i
$508$		0			0
$509$	−24.7905	+	18.0114i	−1.09882	+	0.798339i	−0.980867	−	0.194680i	$-0.937633\pi$
$509$	−24.7905	+	18.0114i	−1.09882	+	0.798339i	−0.117953	+	0.993019i	$0.537633\pi$
$510$		0			0
$511$	−3.17532	−	9.77262i	−0.140468	−	0.432315i
$512$		0			0
$513$	−5.45745	−	16.7963i	−0.240952	−	0.741575i
$514$		0			0
$515$	−4.64543	+	14.2972i	−0.204702	+	0.630008i
$516$		0			0
$517$	0.191870	+	0.590516i	0.00843845	+	0.0259709i
$518$		0			0
$519$	−36.3523			−1.59569
$520$		0			0
$521$	11.6484	+	8.46303i	0.510324	+	0.370772i	0.812947	−	0.582338i	$-0.197862\pi$
$521$	11.6484	+	8.46303i	0.510324	+	0.370772i	−0.302622	+	0.953111i	$0.597862\pi$
$522$		0			0
$523$	−6.76561	+	4.91551i	−0.295840	+	0.214940i	−0.725797	−	0.687909i	$-0.758529\pi$
$523$	−6.76561	+	4.91551i	−0.295840	+	0.214940i	0.429957	+	0.902849i	$0.358529\pi$
$524$		0			0
$525$	14.2113	−	10.3251i	0.620232	−	0.450625i
$526$		0			0
$527$	5.08450	−	15.6485i	0.221484	−	0.681659i
$528$		0			0
$529$	−21.5584	−	15.6631i	−0.937321	−	0.681003i
$530$		0			0
$531$	2.50027	−	7.69503i	0.108502	−	0.333936i
$532$		0			0
$533$	−7.74628	+	6.15045i	−0.335529	+	0.266406i
$534$		0			0
$535$	0.834194	−	2.56739i	0.0360654	−	0.110998i
$536$		0			0
$537$	−11.4577	−	8.32449i	−0.494435	−	0.359228i
$538$		0			0
$539$	0.0159369	−	0.0490488i	0.000686451	−	0.00211268i
$540$		0			0
$541$	−4.67221	+	3.39456i	−0.200874	+	0.145944i	−0.683675	−	0.729787i	$-0.739619\pi$
$541$	−4.67221	+	3.39456i	−0.200874	+	0.145944i	0.482801	+	0.875730i	$0.339619\pi$
$542$		0			0
$543$	−27.1467	+	19.7232i	−1.16497	+	0.846404i
$544$		0			0
$545$	−2.72597	−	1.98053i	−0.116768	−	0.0848366i
$546$		0			0
$547$	0.651982			0.0278767			0.0139384	−	0.999903i	$-0.495563\pi$
$547$	0.651982			0.0278767			0.0139384	+	0.999903i	$0.495563\pi$
$548$		0			0
$549$	2.14407	+	6.59877i	0.0915067	+	0.281629i
$550$		0			0
$551$	0.821052	−	2.52694i	0.0349780	−	0.107651i
$552$		0			0
$553$	6.75481	+	20.7892i	0.287244	+	0.884046i
$554$		0			0
$555$	1.06901	+	3.29006i	0.0453767	+	0.139655i
$556$		0			0
$557$	−8.07615	+	5.86766i	−0.342197	+	0.248621i	−0.745588	−	0.666407i	$-0.767831\pi$
$557$	−8.07615	+	5.86766i	−0.342197	+	0.248621i	0.403391	+	0.915028i	$0.367831\pi$
$558$		0			0
$559$	−8.52481	−	6.19364i	−0.360561	−	0.261963i
$560$		0			0
$561$	−1.52592	+	4.69630i	−0.0644245	+	0.198278i
$562$		0			0
$563$	−6.14933	+	4.46775i	−0.259164	+	0.188293i	−0.709778	−	0.704425i	$-0.751205\pi$
$563$	−6.14933	+	4.46775i	−0.259164	+	0.188293i	0.450615	+	0.892719i	$0.351205\pi$
$564$		0			0
$565$	−9.11987			−0.383676
$566$		0			0
$567$	−9.08682	−	27.9664i	−0.381611	−	1.17448i
$568$		0			0
$569$	37.8324	+	27.4869i	1.58602	+	1.15231i	0.909360	+	0.416011i	$0.136572\pi$
$569$	37.8324	+	27.4869i	1.58602	+	1.15231i	0.676658	+	0.736298i	$0.263428\pi$
$570$		0			0
$571$	−14.3218			−0.599349			−0.299674	−	0.954042i	$-0.596878\pi$
$571$	−14.3218			−0.599349			−0.299674	+	0.954042i	$0.596878\pi$
$572$		0			0
$573$	−33.3606			−1.39366
$574$		0			0
$575$	23.1253			0.964390
$576$		0			0
$577$	9.66508			0.402362			0.201181	−	0.979554i	$-0.435522\pi$
$577$	9.66508			0.402362			0.201181	+	0.979554i	$0.435522\pi$
$578$		0			0
$579$	22.2460	+	16.1627i	0.924513	+	0.671698i
$580$		0			0
$581$	−3.99630	−	12.2993i	−0.165794	−	0.510263i
$582$		0			0
$583$	−0.943397			−0.0390715
$584$		0			0
$585$	1.68682	−	1.22554i	0.0697413	−	0.0506700i
$586$		0			0
$587$	−5.03381	+	15.4925i	−0.207768	+	0.639443i	0.791821	+	0.610754i	$0.209133\pi$
$587$	−5.03381	+	15.4925i	−0.207768	+	0.639443i	−0.999588	+	0.0286894i	$0.990867\pi$
$588$		0			0
$589$	11.4566	+	8.32373i	0.472062	+	0.342973i
$590$		0			0
$591$	33.7566	−	24.5256i	1.38856	−	1.00885i
$592$		0			0
$593$	0.406627	+	1.25147i	0.0166982	+	0.0513917i	0.959058	−	0.283208i	$-0.0913988\pi$
$593$	0.406627	+	1.25147i	0.0166982	+	0.0513917i	−0.942360	+	0.334600i	$0.891399\pi$
$594$		0			0
$595$	5.60290	+	17.2440i	0.229696	+	0.706933i
$596$		0			0
$597$	−16.5085	+	50.8079i	−0.675647	+	2.07943i
$598$		0			0
$599$	−10.7896	−	33.2070i	−0.440851	−	1.35680i	−0.886970	−	0.461827i	$-0.847194\pi$
$599$	−10.7896	−	33.2070i	−0.440851	−	1.35680i	0.446118	−	0.894974i	$-0.352806\pi$
$600$		0			0
$601$	−39.5375			−1.61277			−0.806383	−	0.591393i	$-0.798578\pi$
$601$	−39.5375			−1.61277			−0.806383	+	0.591393i	$0.798578\pi$
$602$		0			0
$603$	−9.52787	−	6.92240i	−0.388005	−	0.281902i
$604$		0			0
$605$	−11.4260	+	8.30151i	−0.464535	+	0.337504i
$606$		0			0
$607$	−12.4006	+	9.00953i	−0.503323	+	0.365686i	−0.810285	−	0.586036i	$-0.800688\pi$
$607$	−12.4006	+	9.00953i	−0.503323	+	0.365686i	0.306962	+	0.951722i	$0.400688\pi$
$608$		0			0
$609$	0.984137	−	3.02886i	0.0398793	−	0.122736i
$610$		0			0
$611$	−1.63661	−	1.18907i	−0.0662102	−	0.0481045i
$612$		0			0
$613$	12.7711	−	39.3055i	0.515821	−	1.58753i	−0.265963	−	0.963983i	$-0.585690\pi$
$613$	12.7711	−	39.3055i	0.515821	−	1.58753i	0.781784	−	0.623550i	$-0.214310\pi$
$614$		0			0
$615$	−5.88625	−	15.7862i	−0.237356	−	0.636560i
$616$		0			0
$617$	10.9796	−	33.7917i	0.442021	−	1.36040i	−0.443696	−	0.896177i	$-0.646333\pi$
$617$	10.9796	−	33.7917i	0.442021	−	1.36040i	0.885717	−	0.464225i	$-0.153667\pi$
$618$		0			0
$619$	−5.06983	−	3.68345i	−0.203774	−	0.148050i	0.481218	−	0.876601i	$-0.340194\pi$
$619$	−5.06983	−	3.68345i	−0.203774	−	0.148050i	−0.684992	+	0.728550i	$0.740194\pi$
$620$		0			0
$621$	8.61164	−	26.5039i	0.345573	−	1.06357i
$622$		0			0
$623$	25.7971	−	18.7427i	1.03354	−	0.750909i
$624$		0			0
$625$	−1.76482	+	1.28221i	−0.0705927	+	0.0512886i
$626$		0			0
$627$	−3.43827	−	2.49805i	−0.137311	−	0.0997626i
$628$		0			0
$629$	6.82126			0.271981
$630$		0			0
$631$	0.575389	+	1.77087i	0.0229059	+	0.0704970i	0.961856	−	0.273556i	$-0.0881999\pi$
$631$	0.575389	+	1.77087i	0.0229059	+	0.0704970i	−0.938950	+	0.344053i	$0.888200\pi$
$632$		0			0
$633$	7.53113	−	23.1784i	0.299336	−	0.921260i
$634$		0			0
$635$	0.0945023	+	0.290848i	0.00375021	+	0.0115420i
$636$		0			0
$637$	0.0519238	+	0.159805i	0.00205729	+	0.00633170i
$638$		0			0
$639$	−3.33779	+	2.42505i	−0.132041	+	0.0959334i
$640$		0			0
$641$	21.7060	+	15.7703i	0.857334	+	0.622889i	0.927158	−	0.374670i	$-0.122244\pi$
$641$	21.7060	+	15.7703i	0.857334	+	0.622889i	−0.0698246	+	0.997559i	$0.522244\pi$
$642$		0			0
$643$	−1.03695	+	3.19140i	−0.0408932	+	0.125856i	−0.969419	−	0.245412i	$-0.921077\pi$
$643$	−1.03695	+	3.19140i	−0.0408932	+	0.125856i	0.928526	+	0.371268i	$0.121077\pi$
$644$		0			0
$645$	14.5207	−	10.5499i	0.571752	−	0.415402i
$646$		0			0
$647$	−35.4980			−1.39557			−0.697786	−	0.716306i	$-0.745831\pi$
$647$	−35.4980			−1.39557			−0.697786	+	0.716306i	$0.745831\pi$
$648$		0			0
$649$	1.15114	+	3.54284i	0.0451862	+	0.139069i
$650$		0			0
$651$	13.7323	+	9.97707i	0.538209	+	0.391032i
$652$		0			0
$653$	5.94355			0.232589			0.116294	−	0.993215i	$-0.462898\pi$
$653$	5.94355			0.232589			0.116294	+	0.993215i	$0.462898\pi$
$654$		0			0
$655$	−12.4078			−0.484812
$656$		0			0
$657$	−3.96875			−0.154836
$658$		0			0
$659$	30.6945			1.19569			0.597844	−	0.801612i	$-0.296024\pi$
$659$	30.6945			1.19569			0.597844	+	0.801612i	$0.296024\pi$
$660$		0			0
$661$	13.1747	+	9.57198i	0.512436	+	0.372307i	0.813747	−	0.581219i	$-0.197424\pi$
$661$	13.1747	+	9.57198i	0.512436	+	0.372307i	−0.301311	+	0.953526i	$0.597424\pi$
$662$		0			0
$663$	−4.97158	−	15.3010i	−0.193080	−	0.594240i
$664$		0			0
$665$	−15.6050			−0.605135
$666$		0			0
$667$	3.39189	−	2.46435i	0.131335	−	0.0954201i
$668$		0			0
$669$	3.53014	−	10.8646i	0.136483	−	0.420051i
$670$		0			0
$671$	−2.58438	−	1.87766i	−0.0997688	−	0.0724863i
$672$		0			0
$673$	−21.0192	+	15.2714i	−0.810232	+	0.588668i	−0.913898	−	0.405944i	$-0.866943\pi$
$673$	−21.0192	+	15.2714i	−0.810232	+	0.588668i	0.103666	+	0.994612i	$0.466943\pi$
$674$		0			0
$675$	4.01120	+	12.3452i	0.154391	+	0.475167i
$676$		0			0
$677$	1.88190	+	5.79189i	0.0723273	+	0.222600i	0.980685	−	0.195593i	$-0.0626633\pi$
$677$	1.88190	+	5.79189i	0.0723273	+	0.222600i	−0.908358	+	0.418194i	$0.862663\pi$
$678$		0			0
$679$	−8.88517	+	27.3457i	−0.340981	+	1.04943i
$680$		0			0
$681$	11.5438	+	35.5281i	0.442359	+	1.36144i
$682$		0			0
$683$	−8.61594			−0.329680			−0.164840	−	0.986320i	$-0.552711\pi$
$683$	−8.61594			−0.329680			−0.164840	+	0.986320i	$0.552711\pi$
$684$		0			0
$685$	17.0246	+	12.3691i	0.650478	+	0.472600i
$686$		0			0
$687$	9.74967	−	7.08355i	0.371973	−	0.270254i
$688$		0			0
$689$	2.48665	−	1.80666i	0.0947338	−	0.0688281i
$690$		0			0
$691$	1.37342	−	4.22694i	0.0522472	−	0.160800i	−0.921528	−	0.388311i	$-0.873059\pi$
$691$	1.37342	−	4.22694i	0.0522472	−	0.160800i	0.973776	+	0.227511i	$0.0730587\pi$
$692$		0			0
$693$	−1.05315	−	0.765159i	−0.0400059	−	0.0290660i
$694$		0			0
$695$	9.25144	−	28.4730i	0.350927	−	1.08004i
$696$		0			0
$697$	−33.1906	+	1.41962i	−1.25718	+	0.0537721i
$698$		0			0
$699$	−12.9750	+	39.9330i	−0.490761	+	1.51041i
$700$		0			0
$701$	1.01482	+	0.737307i	0.0383291	+	0.0278477i	0.606785	−	0.794866i	$-0.292459\pi$
$701$	1.01482	+	0.737307i	0.0383291	+	0.0278477i	−0.568456	+	0.822714i	$0.692459\pi$
$702$		0			0
$703$	−1.81418	+	5.58346i	−0.0684230	+	0.210584i
$704$		0			0
$705$	2.78771	−	2.02539i	0.104991	−	0.0762807i
$706$		0			0
$707$	37.8155	−	27.4746i	1.42220	−	1.03329i
$708$		0			0
$709$	5.29098	+	3.84412i	0.198707	+	0.144369i	0.682689	−	0.730709i	$-0.260810\pi$
$709$	5.29098	+	3.84412i	0.198707	+	0.144369i	−0.483983	+	0.875078i	$0.660810\pi$
$710$		0			0
$711$	8.44268			0.316625
$712$		0			0
$713$	6.90522	+	21.2521i	0.258602	+	0.795896i
$714$		0			0
$715$	−0.296643	+	0.912973i	−0.0110938	+	0.0341433i
$716$		0			0
$717$	−14.0803	−	43.3348i	−0.525839	−	1.61837i
$718$		0			0
$719$	6.46072	+	19.8841i	0.240944	+	0.741550i	0.996277	+	0.0862089i	$0.0274753\pi$
$719$	6.46072	+	19.8841i	0.240944	+	0.741550i	−0.755333	+	0.655341i	$0.772525\pi$
$720$		0			0
$721$	−24.7392	+	17.9741i	−0.921337	+	0.669390i
$722$		0			0
$723$	23.8535	+	17.3306i	0.887120	+	0.644530i
$724$		0			0
$725$	−0.603469	+	1.85729i	−0.0224123	+	0.0689779i
$726$		0			0
$727$	36.8978	−	26.8078i	1.36846	−	0.994247i	0.370609	−	0.928789i	$-0.379149\pi$
$727$	36.8978	−	26.8078i	1.36846	−	0.994247i	0.997855	−	0.0654585i	$-0.0208510\pi$
$728$		0			0
$729$	12.4612			0.461527
$730$		0			0
$731$	−10.9365	−	33.6591i	−0.404502	−	1.24493i
$732$		0			0
$733$	−31.8900	−	23.1694i	−1.17788	−	0.855783i	−0.185952	−	0.982559i	$-0.559537\pi$
$733$	−31.8900	−	23.1694i	−1.17788	−	0.855783i	−0.991931	+	0.126776i	$0.959537\pi$
$734$		0			0
$735$	−0.286211			−0.0105571
$736$		0			0
$737$	5.42225			0.199731
$738$		0			0
$739$	−39.5452			−1.45469			−0.727346	−	0.686271i	$-0.759247\pi$
$739$	−39.5452			−1.45469			−0.727346	+	0.686271i	$0.759247\pi$
$740$		0			0
$741$	13.8467			0.508670
$742$		0			0
$743$	−32.0060	−	23.2537i	−1.17419	−	0.853095i	−0.182681	−	0.983172i	$-0.558478\pi$
$743$	−32.0060	−	23.2537i	−1.17419	−	0.853095i	−0.991504	+	0.130077i	$0.958478\pi$
$744$		0			0
$745$	0.335637	+	1.03298i	0.0122968	+	0.0378456i
$746$		0			0
$747$	−4.99488			−0.182753
$748$		0			0
$749$	4.44250	−	3.22766i	0.162325	−	0.117936i
$750$		0			0
$751$	−9.65071	+	29.7018i	−0.352160	+	1.08384i	0.605479	+	0.795862i	$0.292982\pi$
$751$	−9.65071	+	29.7018i	−0.352160	+	1.08384i	−0.957638	+	0.287974i	$0.907018\pi$
$752$		0			0
$753$	−10.3864	−	7.54614i	−0.378500	−	0.274997i
$754$		0			0
$755$	6.08363	−	4.42002i	0.221406	−	0.160861i
$756$		0			0
$757$	12.2023	+	37.5548i	0.443500	+	1.36495i	0.884120	+	0.467260i	$0.154759\pi$
$757$	12.2023	+	37.5548i	0.443500	+	1.36495i	−0.440620	+	0.897694i	$0.645241\pi$
$758$		0			0
$759$	−2.07234	−	6.37801i	−0.0752212	−	0.231507i
$760$		0			0
$761$	−15.2358	+	46.8910i	−0.552298	+	1.69980i	0.150676	+	0.988583i	$0.451855\pi$
$761$	−15.2358	+	46.8910i	−0.552298	+	1.69980i	−0.702974	+	0.711215i	$0.748145\pi$
$762$		0			0
$763$	−2.11802	−	6.51860i	−0.0766775	−	0.235989i
$764$		0			0
$765$	7.00293			0.253192
$766$		0			0
$767$	−9.81895	−	7.13389i	−0.354542	−	0.257590i
$768$		0			0
$769$	−3.84772	+	2.79554i	−0.138752	+	0.100810i	−0.654996	−	0.755632i	$-0.727330\pi$
$769$	−3.84772	+	2.79554i	−0.138752	+	0.100810i	0.516244	+	0.856442i	$0.327330\pi$
$770$		0			0
$771$	28.5570	−	20.7479i	1.02846	−	0.747217i
$772$		0			0
$773$	4.18364	−	12.8759i	0.150475	−	0.463115i	−0.847199	−	0.531275i	$-0.821713\pi$
$773$	4.18364	−	12.8759i	0.150475	−	0.463115i	0.997674	+	0.0681604i	$0.0217130\pi$
$774$		0			0
$775$	−8.42056	−	6.11789i	−0.302475	−	0.219761i
$776$		0			0
$777$	−2.17453	+	6.69250i	−0.0780107	+	0.240092i
$778$		0			0
$779$	7.66534	−	27.5454i	0.274639	−	0.986915i
$780$		0			0
$781$	0.586983	−	1.80655i	0.0210039	−	0.0646433i
$782$		0			0
$783$	1.90391	+	1.38327i	0.0680403	+	0.0494342i
$784$		0			0
$785$	7.03285	−	21.6449i	0.251013	−	0.772539i
$786$		0			0
$787$	24.1922	−	17.5767i	0.862360	−	0.626541i	−0.0661662	−	0.997809i	$-0.521077\pi$
$787$	24.1922	−	17.5767i	0.862360	−	0.626541i	0.928526	+	0.371268i	$0.121077\pi$
$788$		0			0
$789$	−19.0926	+	13.8716i	−0.679714	+	0.493841i
$790$		0			0
$791$	−15.0083	−	10.9042i	−0.533633	−	0.387707i
$792$		0			0
$793$	10.4078			0.369593
$794$		0			0
$795$	1.61786	+	4.97927i	0.0573797	+	0.176597i
$796$		0			0
$797$	11.9802	−	36.8711i	0.424359	−	1.30604i	−0.479248	−	0.877680i	$-0.659090\pi$
$797$	11.9802	−	36.8711i	0.424359	−	1.30604i	0.903607	−	0.428363i	$-0.140910\pi$
$798$		0			0
$799$	−2.09962	−	6.46195i	−0.0742791	−	0.228608i
$800$		0			0
$801$	−3.80579	−	11.7130i	−0.134471	−	0.413859i
$802$		0			0
$803$	1.47827	−	1.07402i	0.0521670	−	0.0379015i
$804$		0			0
$805$	−19.9213	−	14.4736i	−0.702132	−	0.510129i
$806$		0			0
$807$	8.73853	−	26.8944i	0.307611	−	0.946728i
$808$		0			0
$809$	−45.2743	+	32.8937i	−1.59176	+	1.15648i	−0.690380	+	0.723447i	$0.742557\pi$
$809$	−45.2743	+	32.8937i	−1.59176	+	1.15648i	−0.901378	+	0.433033i	$0.857443\pi$
$810$		0			0
$811$	−37.8222			−1.32812			−0.664058	−	0.747681i	$-0.731167\pi$
$811$	−37.8222			−1.32812			−0.664058	+	0.747681i	$0.731167\pi$
$812$		0			0
$813$	18.2477	+	56.1607i	0.639976	+	1.96964i
$814$		0			0
$815$	4.07080	+	2.95761i	0.142594	+	0.103600i
$816$		0			0
$817$	30.4600			1.06566
$818$		0			0
$819$	4.24126			0.148202
$820$		0			0
$821$	−29.7665			−1.03886			−0.519428	−	0.854514i	$-0.673855\pi$
$821$	−29.7665			−1.03886			−0.519428	+	0.854514i	$0.673855\pi$
$822$		0			0
$823$	43.3133			1.50981			0.754904	−	0.655835i	$-0.227683\pi$
$823$	43.3133			1.50981			0.754904	+	0.655835i	$0.227683\pi$
$824$		0			0
$825$	2.52711	+	1.83605i	0.0879828	+	0.0639232i
$826$		0			0
$827$	−1.58963	−	4.89238i	−0.0552768	−	0.170125i	0.919606	−	0.392841i	$-0.128508\pi$
$827$	−1.58963	−	4.89238i	−0.0552768	−	0.170125i	−0.974883	+	0.222716i	$0.928508\pi$
$828$		0			0
$829$	−33.1325			−1.15074			−0.575371	−	0.817893i	$-0.695142\pi$
$829$	−33.1325			−1.15074			−0.575371	+	0.817893i	$0.695142\pi$
$830$		0			0
$831$	−47.2633	+	34.3388i	−1.63955	+	1.19120i
$832$		0			0
$833$	−0.174396	+	0.536735i	−0.00604246	+	0.0185968i
$834$		0			0
$835$	−24.1482	−	17.5447i	−0.835682	−	0.607158i
$836$		0			0
$837$	−10.1475	+	7.37257i	−0.350748	+	0.254833i
$838$		0			0
$839$	−4.52731	−	13.9336i	−0.156300	−	0.481042i	0.841990	−	0.539493i	$-0.181384\pi$
$839$	−4.52731	−	13.9336i	−0.156300	−	0.481042i	−0.998290	+	0.0584505i	$0.981384\pi$
$840$		0			0
$841$	−8.85208	−	27.2439i	−0.305244	−	0.939445i
$842$		0			0
$843$	−20.0153	+	61.6009i	−0.689365	+	2.12165i
$844$		0			0
$845$	4.29900	+	13.2310i	0.147890	+	0.455159i
$846$		0			0
$847$	−28.7292			−0.987146
$848$		0			0
$849$	52.6872	+	38.2795i	1.80822	+	1.31375i
$850$		0			0
$851$	−7.49464	+	5.44517i	−0.256913	+	0.186658i
$852$		0			0
$853$	−19.9682	+	14.5077i	−0.683698	+	0.496736i	−0.874582	−	0.484877i	$-0.838864\pi$
$853$	−19.9682	+	14.5077i	−0.683698	+	0.496736i	0.190885	+	0.981612i	$0.438864\pi$
$854$		0			0
$855$	−1.86250	+	5.73217i	−0.0636960	+	0.196036i
$856$		0			0
$857$	26.1461	+	18.9963i	0.893134	+	0.648900i	0.936693	−	0.350151i	$-0.113870\pi$
$857$	26.1461	+	18.9963i	0.893134	+	0.648900i	−0.0435592	+	0.999051i	$0.513870\pi$
$858$		0			0
$859$	−2.87526	+	8.84914i	−0.0981026	+	0.301929i	−0.988050	−	0.154135i	$-0.950741\pi$
$859$	−2.87526	+	8.84914i	−0.0981026	+	0.301929i	0.889947	+	0.456063i	$0.150741\pi$
$860$		0			0
$861$	9.18791	−	33.0167i	0.313123	−	1.12521i
$862$		0			0
$863$	4.06440	−	12.5089i	0.138354	−	0.425809i	−0.857743	−	0.514079i	$-0.828134\pi$
$863$	4.06440	−	12.5089i	0.138354	−	0.425809i	0.996097	+	0.0882699i	$0.0281338\pi$
$864$		0			0
$865$	−19.2026	−	13.9515i	−0.652909	−	0.474366i
$866$		0			0
$867$	6.15237	−	18.9350i	0.208945	−	0.643068i
$868$		0			0
$869$	−3.14470	+	2.28476i	−0.106677	+	0.0775052i
$870$		0			0
$871$	−14.2922	+	10.3839i	−0.484273	+	0.351845i
$872$		0			0
$873$	8.98443	+	6.52757i	0.304077	+	0.220925i
$874$		0			0
$875$	28.9431			0.978455
$876$		0			0
$877$	−5.66344	−	17.4303i	−0.191241	−	0.588579i	−1.00000		0.000438693i	$-0.999860\pi$
$877$	−5.66344	−	17.4303i	−0.191241	−	0.588579i	0.808759	−	0.588140i	$-0.200140\pi$
$878$		0			0
$879$	−7.76626	+	23.9021i	−0.261950	+	0.806198i
$880$		0			0
$881$	3.29897	+	10.1532i	0.111145	+	0.342069i	0.991123	−	0.132944i	$-0.0424432\pi$
$881$	3.29897	+	10.1532i	0.111145	+	0.342069i	−0.879979	+	0.475013i	$0.842443\pi$
$882$		0			0
$883$	5.66612	+	17.4385i	0.190680	+	0.586853i	1.00000		0.000515463i	$-0.000164077\pi$
$883$	5.66612	+	17.4385i	0.190680	+	0.586853i	−0.809320	+	0.587368i	$0.800164\pi$
$884$		0			0
$885$	16.7251	−	12.1515i	0.562207	−	0.408468i
$886$		0			0
$887$	27.2960	+	19.8317i	0.916511	+	0.665884i	0.942653	−	0.333774i	$-0.108322\pi$
$887$	27.2960	+	19.8317i	0.916511	+	0.665884i	−0.0261420	+	0.999658i	$0.508322\pi$
$888$		0			0
$889$	−0.192233	+	0.591631i	−0.00644728	+	0.0198427i
$890$		0			0
$891$	4.23037	−	3.07354i	0.141723	−	0.102968i
$892$		0			0
$893$	5.84777			0.195688
$894$		0			0
$895$	−2.85754	−	8.79461i	−0.0955171	−	0.293971i
$896$		0			0
$897$	17.6766	+	12.8428i	0.590204	+	0.428808i
$898$		0			0
$899$	−1.88704			−0.0629363
$900$		0			0
$901$	10.3235			0.343925
$902$		0			0
$903$	36.5102			1.21498
$904$		0			0
$905$	−21.9094			−0.728293
$906$		0			0
$907$	−3.61250	−	2.62463i	−0.119951	−	0.0871495i	0.526192	−	0.850366i	$-0.323619\pi$
$907$	−3.61250	−	2.62463i	−0.119951	−	0.0871495i	−0.646143	+	0.763216i	$0.723619\pi$
$908$		0			0
$909$	−5.57884	−	17.1699i	−0.185038	−	0.569490i
$910$		0			0
$911$	6.70291			0.222077			0.111039	−	0.993816i	$-0.464582\pi$
$911$	6.70291			0.222077			0.111039	+	0.993816i	$0.464582\pi$
$912$		0			0
$913$	1.86048	−	1.35172i	0.0615728	−	0.0447353i
$914$		0			0
$915$	−5.47830	+	16.8605i	−0.181107	+	0.557390i
$916$		0			0
$917$	−20.4191	−	14.8353i	−0.674298	−	0.489906i
$918$		0			0
$919$	−48.6251	+	35.3282i	−1.60399	+	1.16537i	−0.724730	+	0.689033i	$0.758036\pi$
$919$	−48.6251	+	35.3282i	−1.60399	+	1.16537i	−0.879263	+	0.476337i	$0.841964\pi$
$920$		0			0
$921$	−16.1244	−	49.6258i	−0.531317	−	1.63522i
$922$		0			0
$923$	1.91244	+	5.88588i	0.0629487	+	0.193736i
$924$		0			0
$925$	1.33341	−	4.10381i	0.0438423	−	0.134933i
$926$		0			0
$927$	3.64973	+	11.2327i	0.119873	+	0.368930i
$928$		0			0
$929$	−25.1361			−0.824690			−0.412345	−	0.911028i	$-0.635290\pi$
$929$	−25.1361			−0.824690			−0.412345	+	0.911028i	$0.635290\pi$
$930$		0			0
$931$	−0.392956	−	0.285499i	−0.0128786	−	0.00935687i
$932$		0			0
$933$	25.0479	−	18.1984i	0.820032	−	0.595788i
$934$		0			0
$935$	−2.60843	+	1.89514i	−0.0853048	+	0.0619775i
$936$		0			0
$937$	16.4752	−	50.7054i	0.538221	−	1.65647i	−0.198364	−	0.980128i	$-0.563563\pi$
$937$	16.4752	−	50.7054i	0.538221	−	1.65647i	0.736585	−	0.676345i	$-0.236437\pi$
$938$		0			0
$939$	47.7385	+	34.6840i	1.55789	+	1.13187i
$940$		0			0
$941$	8.97616	−	27.6258i	0.292615	−	0.900575i	−0.691398	−	0.722474i	$-0.743005\pi$
$941$	8.97616	−	27.6258i	0.292615	−	0.900575i	0.984012	−	0.178101i	$-0.0569953\pi$
$942$		0			0
$943$	35.3339	−	28.0547i	1.15063	−	0.913587i
$944$		0			0
$945$	4.27117	−	13.1453i	0.138941	−	0.427617i
$946$		0			0
$947$	27.0357	+	19.6426i	0.878542	+	0.638298i	0.932865	−	0.360226i	$-0.117300\pi$
$947$	27.0357	+	19.6426i	0.878542	+	0.638298i	−0.0543236	+	0.998523i	$0.517300\pi$
$948$		0			0
$949$	−1.83967	+	5.66193i	−0.0597183	+	0.183794i
$950$		0			0
$951$	15.3188	−	11.1298i	0.496748	−	0.360908i
$952$		0			0
$953$	11.5825	−	8.41518i	0.375194	−	0.272594i	−0.384167	−	0.923263i	$-0.625511\pi$
$953$	11.5825	−	8.41518i	0.375194	−	0.272594i	0.759361	+	0.650669i	$0.225511\pi$
$954$		0			0
$955$	−17.6223	−	12.8033i	−0.570244	−	0.414307i
$956$		0			0
$957$	0.566323			0.0183066
$958$		0			0
$959$	13.2278	+	40.7109i	0.427148	+	1.31463i
$960$		0			0
$961$	−6.47158	+	19.9175i	−0.208761	+	0.642499i
$962$		0			0
$963$	−0.655393	−	2.01709i	−0.0211197	−	0.0649999i
$964$		0			0
$965$	5.54816	+	17.0755i	0.178601	+	0.549679i
$966$		0			0
$967$	9.98521	−	7.25468i	0.321103	−	0.233295i	−0.415543	−	0.909573i	$-0.636409\pi$
$967$	9.98521	−	7.25468i	0.321103	−	0.233295i	0.736646	+	0.676279i	$0.236409\pi$
$968$		0			0
$969$	37.6246	+	27.3359i	1.20868	+	0.878156i
$970$		0			0
$971$	−9.61472	+	29.5911i	−0.308551	+	0.949622i	0.669777	+	0.742562i	$0.266390\pi$
$971$	−9.61472	+	29.5911i	−0.308551	+	0.949622i	−0.978328	+	0.207060i	$0.933610\pi$
$972$		0			0
$973$	49.2685	−	35.7957i	1.57948	−	1.14756i
$974$		0			0
$975$	−10.1772			−0.325932
$976$		0			0
$977$	−8.46281	−	26.0458i	−0.270749	−	0.833280i	−0.990313	−	0.138854i	$-0.955658\pi$
$977$	−8.46281	−	26.0458i	−0.270749	−	0.833280i	0.719564	−	0.694427i	$-0.244342\pi$
$978$		0			0
$979$	4.58734	+	3.33290i	0.146612	+	0.106520i
$980$		0			0
$981$	−2.64726			−0.0845206
$982$		0			0
$983$	30.5278			0.973685			0.486843	−	0.873490i	$-0.338149\pi$
$983$	30.5278			0.973685			0.486843	+	0.873490i	$0.338149\pi$
$984$		0			0
$985$	27.2441			0.868070
$986$		0			0
$987$	7.00931			0.223109
$988$		0			0
$989$	38.8851	+	28.2517i	1.23647	+	0.898351i
$990$		0			0
$991$	10.6411	+	32.7499i	0.338026	+	1.04034i	0.965212	+	0.261467i	$0.0842063\pi$
$991$	10.6411	+	32.7499i	0.338026	+	1.04034i	−0.627187	+	0.778869i	$0.715794\pi$
$992$		0			0
$993$	59.6120			1.89173
$994$		0			0
$995$	−28.2198	+	20.5029i	−0.894628	+	0.649985i
$996$		0			0
$997$	10.3892	−	31.9747i	0.329030	−	1.01265i	−0.640559	−	0.767909i	$-0.721297\pi$
$997$	10.3892	−	31.9747i	0.329030	−	1.01265i	0.969589	−	0.244741i	$-0.0787028\pi$
$998$		0			0
$999$	−4.20684	−	3.05645i	−0.133098	−	0.0967017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.385.5		20
4.3	odd	2		328.2.m.c.57.1	✓	20
41.18	even	5	inner	656.2.u.h.305.5		20
164.59	odd	10		328.2.m.c.305.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.57.1	✓	20	4.3	odd	2
328.2.m.c.305.1	yes	20	164.59	odd	10
656.2.u.h.305.5		20	41.18	even	5	inner
656.2.u.h.385.5		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00743 q^{3} +(1.06040 + 0.770427i) q^{5} +(0.823910 + 2.53573i) q^{7} +1.02979 q^{9} +O(q^{10})\)	\(q+2.00743 q^{3} +(1.06040 + 0.770427i) q^{5} +(0.823910 + 2.53573i) q^{7} +1.02979 q^{9} +(-0.383571 + 0.278681i) q^{11} +(0.477346 - 1.46912i) q^{13} +(2.12868 + 1.54658i) q^{15} +(4.19738 - 3.04957i) q^{17} +(1.37986 + 4.24678i) q^{19} +(1.65394 + 5.09032i) q^{21} +(-2.17737 + 6.70125i) q^{23} +(-1.01419 - 3.12136i) q^{25} -3.95507 q^{27} +(-0.481385 - 0.349747i) q^{29} +(2.56569 - 1.86408i) q^{31} +(-0.769994 + 0.559433i) q^{33} +(-1.07992 + 3.32366i) q^{35} +(1.06366 + 0.772792i) q^{37} +(0.958239 - 2.94916i) q^{39} +(-5.33634 - 3.53886i) q^{41} +(2.10794 - 6.48758i) q^{43} +(1.09199 + 0.793375i) q^{45} +(0.404687 - 1.24550i) q^{47} +(-0.0880017 + 0.0639370i) q^{49} +(8.42595 - 6.12181i) q^{51} +(1.60977 + 1.16957i) q^{53} -0.621443 q^{55} +(2.76998 + 8.52512i) q^{57} +(2.42795 - 7.47245i) q^{59} +(2.08205 + 6.40791i) q^{61} +(0.848451 + 2.61126i) q^{63} +(1.63803 - 1.19010i) q^{65} +(-9.25228 - 6.72218i) q^{67} +(-4.37092 + 13.4523i) q^{69} +(-3.24125 + 2.35490i) q^{71} -3.85396 q^{73} +(-2.03592 - 6.26592i) q^{75} +(-1.02269 - 0.743027i) q^{77} +8.19848 q^{79} -11.0289 q^{81} -4.85041 q^{83} +6.80038 q^{85} +(-0.966348 - 0.702093i) q^{87} +(-3.69571 - 11.3742i) q^{89} +4.11859 q^{91} +(5.15044 - 3.74201i) q^{93} +(-1.80862 + 5.56637i) q^{95} +(8.72456 + 6.33876i) q^{97} +(-0.394996 + 0.286982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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