LMFDB - Embedded newform 570.2.u.j.481.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.2
Root			$0.500000 - 1.80139i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.j.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(2.05756 - 3.56380i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(2.05756 - 3.56380i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(-1.17263 - 2.03106i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.04419 - 1.10799i) q^{13} +(-0.714584 - 4.05261i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-5.89612 + 4.94743i) q^{17} +1.00000 q^{18} +(1.33604 + 4.14910i) q^{19} +1.00000 q^{20} +(3.15237 - 2.64515i) q^{21} +(-2.20383 - 0.802128i) q^{22} +(1.45879 - 8.27322i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.61978 - 2.80554i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-3.15237 - 2.64515i) q^{28} +(6.52412 + 5.47439i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.07818 - 1.86746i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.407251 - 2.30964i) q^{33} +(-1.33654 + 7.57991i) q^{34} +(3.86695 + 1.40746i) q^{35} +(0.766044 - 0.642788i) q^{36} +3.17549 q^{37} +(3.69045 + 2.31960i) q^{38} +3.23956 q^{39} +(0.766044 - 0.642788i) q^{40} +(-4.88907 - 1.77948i) q^{41} +(0.714584 - 4.05261i) q^{42} +(0.378008 + 2.14379i) q^{43} +(-2.20383 + 0.802128i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.20042 - 7.27535i) q^{46} +(-0.984214 - 0.825853i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-4.96713 - 8.60332i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-7.23266 + 2.63247i) q^{51} +(-0.562543 - 3.19034i) q^{52} +(-1.18753 + 6.73480i) q^{53} +(0.939693 + 0.342020i) q^{54} +(1.79658 - 1.50751i) q^{55} -4.11513 q^{56} +(-0.163608 + 4.35583i) q^{57} +8.51664 q^{58} +(-6.56069 + 5.50507i) q^{59} +(0.939693 + 0.342020i) q^{60} +(-1.40900 + 7.99083i) q^{61} +(-0.374448 - 2.12360i) q^{62} +(3.86695 - 1.40746i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.61978 + 2.80554i) q^{65} +(-1.79658 - 1.50751i) q^{66} +(-3.25507 - 2.73133i) q^{67} +(3.84842 + 6.66566i) q^{68} +(4.20042 - 7.27535i) q^{69} +(3.86695 - 1.40746i) q^{70} +(1.22392 + 6.94117i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-0.897874 - 0.326799i) q^{73} +(2.43257 - 2.04116i) q^{74} -1.00000 q^{75} +(4.31806 - 0.595259i) q^{76} -9.65107 q^{77} +(2.48164 - 2.08235i) q^{78} +(-7.50324 - 2.73096i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-4.88907 + 1.77948i) q^{82} +(-5.59071 + 9.68340i) q^{83} +(-2.05756 - 3.56380i) q^{84} +(-5.89612 - 4.94743i) q^{85} +(1.66757 + 1.39926i) q^{86} +(4.25832 + 7.37563i) q^{87} +(-1.17263 + 2.03106i) q^{88} +(3.28340 - 1.19506i) q^{89} +(0.173648 + 0.984808i) q^{90} +(2.31493 - 13.1286i) q^{91} +(-7.89421 - 2.87326i) q^{92} +(1.65187 - 1.38608i) q^{93} -1.28480 q^{94} +(-3.85406 + 2.03622i) q^{95} -1.00000 q^{96} +(-11.4047 + 9.56971i) q^{97} +(-9.33515 - 3.39772i) q^{98} +(0.407251 - 2.30964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^7 - 6 * q^8	$ 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	2.05756	−	3.56380i	0.777686	−	1.34699i	−0.155587	−	0.987822i	$-0.549727\pi$
$7$	2.05756	−	3.56380i	0.777686	−	1.34699i	0.933273	−	0.359169i	$-0.116940\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	0.766044	+	0.642788i	0.242245	+	0.203267i
$11$	−1.17263	−	2.03106i	−0.353562	−	0.612388i	0.633309	−	0.773899i	$-0.281696\pi$
$11$	−1.17263	−	2.03106i	−0.353562	−	0.612388i	−0.986871	+	0.161512i	$0.948363\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.04419	−	1.10799i	0.844305	−	0.307302i	0.116589	−	0.993180i	$-0.462804\pi$
$13$	3.04419	−	1.10799i	0.844305	−	0.307302i	0.727716	+	0.685878i	$0.240582\pi$
$14$	−0.714584	−	4.05261i	−0.190981	−	1.08310i
$15$	−0.173648	+	0.984808i	−0.0448358	+	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−5.89612	+	4.94743i	−1.43002	+	1.19993i	−0.484317	+	0.874892i	$0.660932\pi$
$17$	−5.89612	+	4.94743i	−1.43002	+	1.19993i	−0.945702	+	0.325036i	$0.894624\pi$
$18$	1.00000			0.235702
$19$	1.33604	+	4.14910i	0.306508	+	0.951868i
$19$	1.33604	+	4.14910i	0.306508	+	0.951868i
$20$	1.00000			0.223607
$21$	3.15237	−	2.64515i	0.687903	−	0.577219i
$22$	−2.20383	−	0.802128i	−0.469858	−	0.171014i
$23$	1.45879	−	8.27322i	0.304179	−	1.72509i	−0.323165	−	0.946343i	$-0.604747\pi$
$23$	1.45879	−	8.27322i	0.304179	−	1.72509i	0.627344	−	0.778742i	$-0.284142\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	1.61978	−	2.80554i	0.317665	−	0.550211i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−3.15237	−	2.64515i	−0.595742	−	0.499887i
$29$	6.52412	+	5.47439i	1.21150	+	1.01657i	0.999225	+	0.0393587i	$0.0125315\pi$
$29$	6.52412	+	5.47439i	1.21150	+	1.01657i	0.212274	+	0.977210i	$0.431913\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	1.07818	−	1.86746i	0.193647	−	0.335406i	−0.752809	−	0.658239i	$-0.771302\pi$
$31$	1.07818	−	1.86746i	0.193647	−	0.335406i	0.946456	+	0.322833i	$0.104635\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.407251	−	2.30964i	−0.0708933	−	0.402056i
$34$	−1.33654	+	7.57991i	−0.229215	+	1.29994i
$35$	3.86695	+	1.40746i	0.653634	+	0.237903i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	3.17549			0.522047			0.261024	−	0.965332i	$-0.415940\pi$
$37$	3.17549			0.522047			0.261024	+	0.965332i	$0.415940\pi$
$38$	3.69045	+	2.31960i	0.598671	+	0.376289i
$39$	3.23956			0.518744
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	−4.88907	−	1.77948i	−0.763545	−	0.277908i	−0.0692511	−	0.997599i	$-0.522061\pi$
$41$	−4.88907	−	1.77948i	−0.763545	−	0.277908i	−0.694294	+	0.719692i	$0.744283\pi$
$42$	0.714584	−	4.05261i	0.110263	−	0.625331i
$43$	0.378008	+	2.14379i	0.0576457	+	0.326925i	0.999970	−	0.00777688i	$-0.00247548\pi$
$43$	0.378008	+	2.14379i	0.0576457	+	0.326925i	−0.942324	+	0.334702i	$0.891364\pi$
$44$	−2.20383	+	0.802128i	−0.332240	+	0.120925i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−4.20042	−	7.27535i	−0.619318	−	1.07269i
$47$	−0.984214	−	0.825853i	−0.143562	−	0.120463i	0.568178	−	0.822905i	$-0.307648\pi$
$47$	−0.984214	−	0.825853i	−0.143562	−	0.120463i	−0.711741	+	0.702442i	$0.752093\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−4.96713	−	8.60332i	−0.709590	−	1.22905i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−7.23266	+	2.63247i	−1.01278	+	0.368620i
$52$	−0.562543	−	3.19034i	−0.0780107	−	0.442420i
$53$	−1.18753	+	6.73480i	−0.163119	+	0.925096i	0.787863	+	0.615851i	$0.211188\pi$
$53$	−1.18753	+	6.73480i	−0.163119	+	0.925096i	−0.950982	+	0.309245i	$0.899924\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	1.79658	−	1.50751i	0.242251	−	0.203272i
$56$	−4.11513			−0.549907
$57$	−0.163608	+	4.35583i	−0.0216704	+	0.576943i
$58$	8.51664			1.11829
$59$	−6.56069	+	5.50507i	−0.854129	+	0.716700i	−0.960695	−	0.277606i	$-0.910459\pi$
$59$	−6.56069	+	5.50507i	−0.854129	+	0.716700i	0.106566	+	0.994306i	$0.466015\pi$
$60$	0.939693	+	0.342020i	0.121314	+	0.0441546i
$61$	−1.40900	+	7.99083i	−0.180404	+	1.02312i	0.751316	+	0.659943i	$0.229419\pi$
$61$	−1.40900	+	7.99083i	−0.180404	+	1.02312i	−0.931720	+	0.363178i	$0.881692\pi$
$62$	−0.374448	−	2.12360i	−0.0475549	−	0.269697i
$63$	3.86695	−	1.40746i	0.487190	−	0.177323i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.61978	+	2.80554i	0.200909	+	0.347984i
$66$	−1.79658	−	1.50751i	−0.221143	−	0.185561i
$67$	−3.25507	−	2.73133i	−0.397670	−	0.333685i	0.421922	−	0.906632i	$-0.361356\pi$
$67$	−3.25507	−	2.73133i	−0.397670	−	0.333685i	−0.819592	+	0.572947i	$0.805800\pi$
$68$	3.84842	+	6.66566i	0.466689	+	0.808330i
$69$	4.20042	−	7.27535i	0.505671	−	0.875849i
$70$	3.86695	−	1.40746i	0.462189	−	0.168223i
$71$	1.22392	+	6.94117i	0.145252	+	0.823765i	0.967164	+	0.254151i	$0.0817962\pi$
$71$	1.22392	+	6.94117i	0.145252	+	0.823765i	−0.821912	+	0.569614i	$0.807093\pi$
$72$	0.173648	−	0.984808i	0.0204646	−	0.116061i
$73$	−0.897874	−	0.326799i	−0.105088	−	0.0382490i	0.288941	−	0.957347i	$-0.406697\pi$
$73$	−0.897874	−	0.326799i	−0.105088	−	0.0382490i	−0.394029	+	0.919098i	$0.628919\pi$
$74$	2.43257	−	2.04116i	0.282780	−	0.237281i
$75$	−1.00000			−0.115470
$76$	4.31806	−	0.595259i	0.495316	−	0.0682809i
$77$	−9.65107			−1.09984
$78$	2.48164	−	2.08235i	0.280991	−	0.235779i
$79$	−7.50324	−	2.73096i	−0.844181	−	0.307257i	−0.116515	−	0.993189i	$-0.537172\pi$
$79$	−7.50324	−	2.73096i	−0.844181	−	0.307257i	−0.727665	+	0.685932i	$0.759395\pi$
$80$	0.173648	−	0.984808i	0.0194145	−	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−4.88907	+	1.77948i	−0.539908	+	0.196510i
$83$	−5.59071	+	9.68340i	−0.613660	+	1.06289i	0.376958	+	0.926231i	$0.376970\pi$
$83$	−5.59071	+	9.68340i	−0.613660	+	1.06289i	−0.990618	+	0.136660i	$0.956363\pi$
$84$	−2.05756	−	3.56380i	−0.224499	−	0.388843i
$85$	−5.89612	−	4.94743i	−0.639524	−	0.536624i
$86$	1.66757	+	1.39926i	0.179819	+	0.150886i
$87$	4.25832	+	7.37563i	0.456540	+	0.790750i
$88$	−1.17263	+	2.03106i	−0.125003	+	0.216512i
$89$	3.28340	−	1.19506i	0.348039	−	0.126676i	−0.162085	−	0.986777i	$-0.551822\pi$
$89$	3.28340	−	1.19506i	0.348039	−	0.126676i	0.510124	+	0.860101i	$0.329600\pi$
$90$	0.173648	+	0.984808i	0.0183041	+	0.103808i
$91$	2.31493	−	13.1286i	0.242671	−	1.37626i
$92$	−7.89421	−	2.87326i	−0.823028	−	0.299558i
$93$	1.65187	−	1.38608i	0.171291	−	0.143730i
$94$	−1.28480			−0.132517
$95$	−3.85406	+	2.03622i	−0.395418	+	0.208912i
$96$	−1.00000			−0.102062
$97$	−11.4047	+	9.56971i	−1.15798	+	0.971657i	−0.999876	−	0.0157660i	$-0.994981\pi$
$97$	−11.4047	+	9.56971i	−1.15798	+	0.971657i	−0.158100	+	0.987423i	$0.550537\pi$
$98$	−9.33515	−	3.39772i	−0.942993	−	0.343221i
$99$	0.407251	−	2.30964i	0.0409303	−	0.232127i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	−13.0604	+	4.75359i	−1.29956	+	0.473000i	−0.896852	−	0.442330i	$-0.854152\pi$
$101$	−13.0604	+	4.75359i	−1.29956	+	0.473000i	−0.402704	+	0.915330i	$0.631930\pi$
$102$	−3.84842	+	6.66566i	−0.381050	+	0.659998i
$103$	5.47822	+	9.48855i	0.539785	+	0.934935i	0.998915	+	0.0465660i	$0.0148278\pi$
$103$	5.47822	+	9.48855i	0.539785	+	0.934935i	−0.459130	+	0.888369i	$0.651839\pi$
$104$	−2.48164	−	2.08235i	−0.243345	−	0.204191i
$105$	3.15237	+	2.64515i	0.307640	+	0.258140i
$106$	3.41935	+	5.92249i	0.332117	+	0.575243i
$107$	8.03890	−	13.9238i	0.777150	−	1.34606i	−0.156429	−	0.987689i	$-0.549998\pi$
$107$	8.03890	−	13.9238i	0.777150	−	1.34606i	0.933578	−	0.358374i	$-0.116669\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	−1.78634	−	10.1308i	−0.171100	−	0.970356i	−0.942550	−	0.334066i	$-0.891579\pi$
$109$	−1.78634	−	10.1308i	−0.171100	−	0.970356i	0.771450	−	0.636290i	$-0.219532\pi$
$110$	0.407251	−	2.30964i	0.0388299	−	0.220215i
$111$	2.98398	+	1.08608i	0.283227	+	0.103086i
$112$	−3.15237	+	2.64515i	−0.297871	+	0.249943i
$113$	10.8216			1.01801			0.509006	−	0.860763i	$-0.330013\pi$
$113$	10.8216			1.01801			0.509006	+	0.860763i	$0.330013\pi$
$114$	2.67454	+	3.44192i	0.250494	+	0.322366i
$115$	8.40084			0.783383
$116$	6.52412	−	5.47439i	0.605750	−	0.508284i
$117$	3.04419	+	1.10799i	0.281435	+	0.102434i
$118$	−1.48719	+	8.43426i	−0.136907	+	0.776437i
$119$	5.50004	+	31.1923i	0.504188	+	2.85939i
$120$	0.939693	−	0.342020i	0.0857818	−	0.0312220i
$121$	2.74986	−	4.76290i	0.249988	−	0.432991i
$122$	4.05705	+	7.02702i	0.367308	+	0.636196i
$123$	−3.98561	−	3.34432i	−0.359370	−	0.301547i
$124$	−1.65187	−	1.38608i	−0.148342	−	0.124474i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	2.05756	−	3.56380i	0.183302	−	0.317489i
$127$	8.23161	−	2.99606i	0.730437	−	0.265858i	0.0500875	−	0.998745i	$-0.484050\pi$
$127$	8.23161	−	2.99606i	0.730437	−	0.265858i	0.680350	+	0.732887i	$0.261828\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.378008	+	2.14379i	−0.0332818	+	0.188750i
$130$	3.04419	+	1.10799i	0.266993	+	0.0971774i
$131$	−14.9734	+	12.5642i	−1.30823	+	1.09774i	−0.319575	+	0.947561i	$0.603540\pi$
$131$	−14.9734	+	12.5642i	−1.30823	+	1.09774i	−0.988659	+	0.150178i	$0.952015\pi$
$132$	−2.34527			−0.204129
$133$	17.5355	+	3.77564i	1.52052	+	0.327390i
$134$	−4.24920			−0.367075
$135$	−0.766044	+	0.642788i	−0.0659306	+	0.0553223i
$136$	7.23266	+	2.63247i	0.620196	+	0.225733i
$137$	1.64287	−	9.31720i	0.140360	−	0.796023i	−0.830616	−	0.556846i	$-0.812011\pi$
$137$	1.64287	−	9.31720i	0.140360	−	0.796023i	0.970976	−	0.239177i	$-0.0768775\pi$
$138$	−1.45879	−	8.27322i	−0.124181	−	0.704263i
$139$	17.3028	−	6.29772i	1.46761	−	0.534166i	0.520158	−	0.854070i	$-0.325873\pi$
$139$	17.3028	−	6.29772i	1.46761	−	0.534166i	0.947450	+	0.319904i	$0.103651\pi$
$140$	2.05756	−	3.56380i	0.173896	−	0.301196i
$141$	−0.642400	−	1.11267i	−0.0540998	−	0.0937036i
$142$	5.39927	+	4.53053i	0.453097	+	0.380193i
$143$	−5.82012	−	4.88366i	−0.486702	−	0.408392i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.25832	+	7.37563i	−0.353634	+	0.612512i
$146$	−0.897874	+	0.326799i	−0.0743085	+	0.0270461i
$147$	−1.72507	−	9.78333i	−0.142281	−	0.806916i
$148$	0.551418	−	3.12725i	0.0453263	−	0.257058i
$149$	−3.80670	−	1.38552i	−0.311857	−	0.113507i	0.181350	−	0.983419i	$-0.441953\pi$
$149$	−3.80670	−	1.38552i	−0.311857	−	0.113507i	−0.493207	+	0.869912i	$0.664175\pi$
$150$	−0.766044	+	0.642788i	−0.0625473	+	0.0524834i
$151$	−16.7558			−1.36357			−0.681783	−	0.731555i	$-0.738795\pi$
$151$	−16.7558			−1.36357			−0.681783	+	0.731555i	$0.738795\pi$
$152$	2.92520	−	3.23159i	0.237265	−	0.262117i
$153$	−7.69684			−0.622252
$154$	−7.39315	+	6.20359i	−0.595757	+	0.499899i
$155$	2.02631	+	0.737518i	0.162757	+	0.0592389i
$156$	0.562543	−	3.19034i	0.0450395	−	0.255432i
$157$	−0.718319	−	4.07379i	−0.0573281	−	0.325124i	0.942634	−	0.333828i	$-0.108340\pi$
$157$	−0.718319	−	4.07379i	−0.0573281	−	0.325124i	−0.999962	+	0.00870417i	$0.997229\pi$
$158$	−7.50324	+	2.73096i	−0.596926	+	0.217263i
$159$	−3.41935	+	5.92249i	−0.271172	+	0.469684i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−26.4826	−	22.2215i	−2.08712	−	1.75130i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	9.34690	+	16.1893i	0.732106	+	1.26804i	0.955981	+	0.293427i	$0.0947958\pi$
$163$	9.34690	+	16.1893i	0.732106	+	1.26804i	−0.223875	+	0.974618i	$0.571871\pi$
$164$	−2.60142	+	4.50579i	−0.203137	+	0.351843i
$165$	2.20383	−	0.802128i	0.171568	−	0.0624456i
$166$	1.94163	+	11.0116i	0.150700	+	0.854662i
$167$	−0.621749	+	3.52611i	−0.0481124	+	0.272859i	−0.999368	−	0.0355443i	$-0.988684\pi$
$167$	−0.621749	+	3.52611i	−0.0481124	+	0.272859i	0.951256	+	0.308403i	$0.0997946\pi$
$168$	−3.86695	−	1.40746i	−0.298342	−	0.108588i
$169$	−1.91916	+	1.61036i	−0.147627	+	0.123874i
$170$	−7.69684			−0.590320
$171$	−1.64352	+	4.03718i	−0.125683	+	0.308731i
$172$	2.17686			0.165984
$173$	2.19180	−	1.83914i	0.166640	−	0.139827i	−0.555654	−	0.831413i	$-0.687532\pi$
$173$	2.19180	−	1.83914i	0.166640	−	0.139827i	0.722294	+	0.691586i	$0.243088\pi$
$174$	8.00302	+	2.91286i	0.606708	+	0.220824i
$175$	−0.714584	+	4.05261i	−0.0540175	+	0.306348i
$176$	0.407251	+	2.30964i	0.0306977	+	0.174095i
$177$	−8.04788	+	2.92919i	−0.604916	+	0.220171i
$178$	1.74706	−	3.02600i	0.130948	−	0.226808i
$179$	0.841089	+	1.45681i	0.0628660	+	0.108887i	0.895745	−	0.444567i	$-0.146643\pi$
$179$	0.841089	+	1.45681i	0.0628660	+	0.108887i	−0.832879	+	0.553455i	$0.813309\pi$
$180$	0.766044	+	0.642788i	0.0570976	+	0.0479106i
$181$	−15.0701	−	12.6453i	−1.12015	−	0.939920i	−0.121541	−	0.992586i	$-0.538784\pi$
$181$	−15.0701	−	12.6453i	−1.12015	−	0.939920i	−0.998612	+	0.0526661i	$0.983228\pi$
$182$	−6.66559	−	11.5451i	−0.494086	−	0.855783i
$183$	−4.05705	+	7.02702i	−0.299906	+	0.519452i
$184$	−7.89421	+	2.87326i	−0.581969	+	0.211819i
$185$	0.551418	+	3.12725i	0.0405410	+	0.229920i
$186$	0.374448	−	2.12360i	0.0274558	−	0.155710i
$187$	16.9625	+	6.17385i	1.24042	+	0.451477i
$188$	−0.984214	+	0.825853i	−0.0717812	+	0.0602315i
$189$	4.11513			0.299331
$190$	−1.64352	+	4.03718i	−0.119234	+	0.292888i
$191$	−1.29643			−0.0938067			−0.0469033	−	0.998899i	$-0.514935\pi$
$191$	−1.29643			−0.0938067			−0.0469033	+	0.998899i	$0.514935\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	14.4633	+	5.26420i	1.04109	+	0.378926i	0.805293	−	0.592877i	$-0.202008\pi$
$193$	14.4633	+	5.26420i	1.04109	+	0.378926i	0.235797	+	0.971802i	$0.424230\pi$
$194$	−2.58524	+	14.6617i	−0.185610	+	1.05265i
$195$	0.562543	+	3.19034i	0.0402845	+	0.228465i
$196$	−9.33515	+	3.39772i	−0.666796	+	0.242694i
$197$	5.96067	−	10.3242i	0.424680	−	0.735568i	−0.571710	−	0.820456i	$-0.693720\pi$
$197$	5.96067	−	10.3242i	0.424680	−	0.735568i	0.996391	+	0.0848876i	$0.0270531\pi$
$198$	−1.17263	−	2.03106i	−0.0833354	−	0.144341i
$199$	−2.61438	−	2.19373i	−0.185329	−	0.155509i	0.545403	−	0.838174i	$-0.316377\pi$
$199$	−2.61438	−	2.19373i	−0.185329	−	0.155509i	−0.730732	+	0.682665i	$0.760821\pi$
$200$	0.766044	+	0.642788i	0.0541675	+	0.0454519i
$201$	−2.12460	−	3.67991i	−0.149858	−	0.259561i
$202$	−6.94929	+	12.0365i	−0.488950	+	0.846886i
$203$	32.9334	−	11.9868i	2.31147	−	0.841308i
$204$	1.33654	+	7.57991i	0.0935766	+	0.530700i
$205$	0.903464	−	5.12380i	0.0631007	−	0.357862i
$206$	10.2957	+	3.74732i	0.717334	+	0.261088i
$207$	6.43542	−	5.39996i	0.447293	−	0.375323i
$208$	−3.23956			−0.224623
$209$	6.86038	−	7.57894i	0.474542	−	0.524247i
$210$	4.11513			0.283971
$211$	14.1254	−	11.8526i	0.972435	−	0.815970i	−0.0104958	−	0.999945i	$-0.503341\pi$
$211$	14.1254	−	11.8526i	0.972435	−	0.815970i	0.982931	+	0.183975i	$0.0588965\pi$
$212$	6.42627	+	2.33897i	0.441358	+	0.160641i
$213$	−1.22392	+	6.94117i	−0.0838613	+	0.475601i
$214$	−2.79188	−	15.8335i	−0.190849	−	1.08236i
$215$	−2.04558	+	0.744531i	−0.139507	+	0.0507766i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−4.43684	−	7.68484i	−0.301193	−	0.521681i
$218$	−7.88038	−	6.61242i	−0.533726	−	0.447850i
$219$	−0.731953	−	0.614182i	−0.0494608	−	0.0415026i
$220$	−1.17263	−	2.03106i	−0.0790589	−	0.136934i
$221$	−12.4672	+	21.5938i	−0.838632	+	1.45255i
$222$	2.98398	−	1.08608i	0.200272	−	0.0728930i
$223$	−3.76090	−	21.3291i	−0.251848	−	1.42830i	−0.804035	−	0.594582i	$-0.797317\pi$
$223$	−3.76090	−	21.3291i	−0.251848	−	1.42830i	0.552186	−	0.833721i	$-0.313794\pi$
$224$	−0.714584	+	4.05261i	−0.0477452	+	0.270776i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	8.28983	−	6.95600i	0.551432	−	0.462706i
$227$	6.54252			0.434242			0.217121	−	0.976145i	$-0.430333\pi$
$227$	6.54252			0.434242			0.217121	+	0.976145i	$0.430333\pi$
$228$	4.26124	+	0.917504i	0.282208	+	0.0607632i
$229$	−17.0276			−1.12522			−0.562609	−	0.826723i	$-0.690202\pi$
$229$	−17.0276			−1.12522			−0.562609	+	0.826723i	$0.690202\pi$
$230$	6.43542	−	5.39996i	0.424339	−	0.356063i
$231$	−9.06904	−	3.30086i	−0.596699	−	0.217181i
$232$	1.47890	−	8.38725i	0.0970945	−	0.550650i
$233$	5.01637	+	28.4492i	0.328633	+	1.86377i	0.482805	+	0.875728i	$0.339618\pi$
$233$	5.01637	+	28.4492i	0.328633	+	1.86377i	−0.154172	+	0.988044i	$0.549271\pi$
$234$	3.04419	−	1.10799i	0.199005	−	0.0724318i
$235$	0.642400	−	1.11267i	0.0419055	−	0.0725825i
$236$	4.28219	+	7.41697i	0.278747	+	0.482803i
$237$	−6.11670	−	5.13252i	−0.397322	−	0.333393i
$238$	24.2633	+	20.3593i	1.57275	+	1.31970i
$239$	4.80406	+	8.32088i	0.310749	+	0.538233i	0.978525	−	0.206130i	$-0.0660868\pi$
$239$	4.80406	+	8.32088i	0.310749	+	0.538233i	−0.667776	+	0.744362i	$0.732754\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−12.3255	+	4.48610i	−0.793953	+	0.288975i	−0.706978	−	0.707235i	$-0.749942\pi$
$241$	−12.3255	+	4.48610i	−0.793953	+	0.288975i	−0.0869747	+	0.996211i	$0.527720\pi$
$242$	−0.955017	−	5.41617i	−0.0613908	−	0.348165i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	7.62476	+	2.77519i	0.488125	+	0.177663i
$245$	7.61008	−	6.38562i	0.486190	−	0.407962i
$246$	−5.20284			−0.331721
$247$	8.66432	+	11.1503i	0.551298	+	0.709477i
$248$	−2.15636			−0.136929
$249$	−8.56547	+	7.18728i	−0.542814	+	0.455475i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	4.39414	−	24.9204i	0.277356	−	1.57296i	−0.454022	−	0.890990i	$-0.650011\pi$
$251$	4.39414	−	24.9204i	0.277356	−	1.57296i	0.731378	−	0.681972i	$-0.238878\pi$
$252$	−0.714584	−	4.05261i	−0.0450146	−	0.255290i
$253$	−18.5140	+	6.73856i	−1.16397	+	0.423649i
$254$	4.37995	−	7.58630i	0.274822	−	0.476006i
$255$	−3.84842	−	6.66566i	−0.240997	−	0.417420i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−10.1650	−	8.52948i	−0.634077	−	0.532054i	0.268116	−	0.963387i	$-0.413599\pi$
$257$	−10.1650	−	8.52948i	−0.634077	−	0.532054i	−0.902193	+	0.431333i	$0.858044\pi$
$258$	1.08843	+	1.88522i	0.0677628	+	0.117369i
$259$	6.53377	−	11.3168i	0.405988	−	0.703193i
$260$	3.04419	−	1.10799i	0.188792	−	0.0687148i
$261$	1.47890	+	8.38725i	0.0915415	+	0.519158i
$262$	−3.39420	+	19.2495i	−0.209694	+	1.18924i
$263$	9.80953	+	3.57038i	0.604881	+	0.220159i	0.626262	−	0.779613i	$-0.284584\pi$
$263$	9.80953	+	3.57038i	0.604881	+	0.220159i	−0.0213808	+	0.999771i	$0.506806\pi$
$264$	−1.79658	+	1.50751i	−0.110572	+	0.0927807i
$265$	−6.83870			−0.420098
$266$	15.8599	−	8.37932i	0.972436	−	0.513769i
$267$	3.49412			0.213837
$268$	−3.25507	+	2.73133i	−0.198835	+	0.166843i
$269$	−3.38745	−	1.23293i	−0.206536	−	0.0751731i	0.236680	−	0.971588i	$-0.423941\pi$
$269$	−3.38745	−	1.23293i	−0.206536	−	0.0751731i	−0.443217	+	0.896414i	$0.646163\pi$
$270$	−0.173648	+	0.984808i	−0.0105679	+	0.0599335i
$271$	2.98932	+	16.9533i	0.181588	+	1.02984i	0.930261	+	0.366898i	$0.119580\pi$
$271$	2.98932	+	16.9533i	0.181588	+	1.02984i	−0.748673	+	0.662940i	$0.769309\pi$
$272$	7.23266	−	2.63247i	0.438545	−	0.159617i
$273$	6.66559	−	11.5451i	0.403420	−	0.698744i
$274$	−4.73047	−	8.19341i	−0.285778	−	0.494982i
$275$	1.79658	+	1.50751i	0.108338	+	0.0909062i
$276$	−6.43542	−	5.39996i	−0.387367	−	0.325039i
$277$	3.28003	+	5.68119i	0.197078	+	0.341349i	0.947580	−	0.319519i	$-0.103521\pi$
$277$	3.28003	+	5.68119i	0.197078	+	0.341349i	−0.750502	+	0.660869i	$0.770188\pi$
$278$	9.20665	−	15.9464i	0.552178	−	0.956401i
$279$	2.02631	−	0.737518i	0.121312	−	0.0441541i
$280$	−0.714584	−	4.05261i	−0.0427046	−	0.242190i
$281$	2.60486	−	14.7729i	0.155393	−	0.881276i	−0.803033	−	0.595934i	$-0.796782\pi$
$281$	2.60486	−	14.7729i	0.155393	−	0.881276i	0.958426	−	0.285341i	$-0.0921070\pi$
$282$	−1.20732	−	0.439427i	−0.0718947	−	0.0261675i
$283$	20.4002	−	17.1178i	1.21267	−	1.01755i	0.213491	−	0.976945i	$-0.431517\pi$
$283$	20.4002	−	17.1178i	1.21267	−	1.01755i	0.999175	−	0.0406028i	$-0.0129278\pi$
$284$	7.04825			0.418237
$285$	−4.31806	+	0.595259i	−0.255780	+	0.0352601i
$286$	−7.59762			−0.449257
$287$	−16.4013	+	13.7623i	−0.968137	+	0.812363i
$288$	−0.939693	−	0.342020i	−0.0553719	−	0.0201537i
$289$	7.33513	−	41.5996i	0.431478	−	2.44703i
$290$	1.47890	+	8.38725i	0.0868439	+	0.492516i
$291$	−13.9900	+	5.09194i	−0.820107	+	0.298495i
$292$	−0.477749	+	0.827485i	−0.0279581	+	0.0484249i
$293$	−6.34419	−	10.9885i	−0.370632	−	0.641953i	0.619031	−	0.785366i	$-0.287525\pi$
$293$	−6.34419	−	10.9885i	−0.370632	−	0.641953i	−0.989663	+	0.143414i	$0.954192\pi$
$294$	−7.61008	−	6.38562i	−0.443829	−	0.372417i
$295$	−6.56069	−	5.50507i	−0.381978	−	0.320518i
$296$	−1.58774	−	2.75005i	−0.0922858	−	0.159844i
$297$	1.17263	−	2.03106i	0.0680431	−	0.117854i
$298$	−3.80670	+	1.38552i	−0.220516	+	0.0802613i
$299$	−4.72584	−	26.8015i	−0.273302	−	1.54997i
$300$	−0.173648	+	0.984808i	−0.0100256	+	0.0568579i
$301$	8.41782	+	3.06384i	0.485195	+	0.176597i
$302$	−12.8357	+	10.7704i	−0.738610	+	0.619767i
$303$	−13.8986			−0.798452
$304$	0.163608	−	4.35583i	0.00938357	−	0.249824i
$305$	−8.11410			−0.464612
$306$	−5.89612	+	4.94743i	−0.337059	+	0.282826i
$307$	14.5059	+	5.27973i	0.827898	+	0.301330i	0.720996	−	0.692939i	$-0.243685\pi$
$307$	14.5059	+	5.27973i	0.827898	+	0.301330i	0.106902	+	0.994270i	$0.465907\pi$
$308$	−1.67589	+	9.50444i	−0.0954927	+	0.541566i
$309$	1.90257	+	10.7900i	0.108233	+	0.613821i
$310$	2.02631	−	0.737518i	0.115087	−	0.0418882i
$311$	16.6221	−	28.7903i	0.942553	−	1.63255i	0.181974	−	0.983303i	$-0.441751\pi$
$311$	16.6221	−	28.7903i	0.942553	−	1.63255i	0.760579	−	0.649246i	$-0.224915\pi$
$312$	−1.61978	−	2.80554i	−0.0917019	−	0.158832i
$313$	4.05897	+	3.40588i	0.229426	+	0.192512i	0.750253	−	0.661151i	$-0.229932\pi$
$313$	4.05897	+	3.40588i	0.229426	+	0.192512i	−0.520827	+	0.853663i	$0.674376\pi$
$314$	−3.16885	−	2.65898i	−0.178828	−	0.150055i
$315$	2.05756	+	3.56380i	0.115931	+	0.200798i
$316$	−3.99239	+	6.91502i	−0.224590	+	0.389001i
$317$	18.4535	−	6.71651i	1.03645	−	0.377237i	0.232917	−	0.972497i	$-0.425173\pi$
$317$	18.4535	−	6.71651i	1.03645	−	0.377237i	0.803533	+	0.595260i	$0.202951\pi$
$318$	1.18753	+	6.73480i	0.0665932	+	0.377669i
$319$	3.46841	−	19.6703i	0.194194	−	1.10133i
$320$	−0.939693	−	0.342020i	−0.0525304	−	0.0191195i
$321$	12.3163	−	10.3346i	0.687429	−	0.576822i
$322$	−34.5705			−1.92654
$323$	−28.4048	−	17.8536i	−1.58049	−	0.993401i
$324$	1.00000			0.0555556
$325$	−2.48164	+	2.08235i	−0.137657	+	0.115508i
$326$	17.5664	+	6.39366i	0.972915	+	0.354112i
$327$	1.78634	−	10.1308i	0.0987846	−	0.560235i
$328$	0.903464	+	5.12380i	0.0498855	+	0.282915i
$329$	−4.96826	+	1.80830i	−0.273909	+	0.0996947i
$330$	1.17263	−	2.03106i	0.0645513	−	0.111806i
$331$	2.42635	+	4.20256i	0.133364	+	0.230993i	0.924971	−	0.380037i	$-0.124089\pi$
$331$	2.42635	+	4.20256i	0.133364	+	0.230993i	−0.791607	+	0.611030i	$0.790755\pi$
$332$	8.56547	+	7.18728i	0.470091	+	0.394453i
$333$	2.43257	+	2.04116i	0.133304	+	0.111855i
$334$	1.79026	+	3.10081i	0.0979584	+	0.169669i
$335$	2.12460	−	3.67991i	0.116079	−	0.201055i
$336$	−3.86695	+	1.40746i	−0.210960	+	0.0767830i
$337$	−3.24481	−	18.4022i	−0.176756	−	1.00243i	−0.936098	−	0.351740i	$-0.885590\pi$
$337$	−3.24481	−	18.4022i	−0.176756	−	1.00243i	0.759342	−	0.650692i	$-0.225521\pi$
$338$	−0.435037	+	2.46722i	−0.0236629	+	0.134199i
$339$	10.1690	+	3.70121i	0.552304	+	0.201022i
$340$	−5.89612	+	4.94743i	−0.319762	+	0.268312i
$341$	−5.05724			−0.273865
$342$	1.33604	+	4.14910i	0.0722447	+	0.224357i
$343$	−12.0748			−0.651980
$344$	1.66757	−	1.39926i	0.0899095	−	0.0754430i
$345$	7.89421	+	2.87326i	0.425010	+	0.154691i
$346$	0.496841	−	2.81773i	0.0267103	−	0.151482i
$347$	−4.23527	−	24.0194i	−0.227361	−	1.28943i	−0.858119	−	0.513451i	$-0.828367\pi$
$347$	−4.23527	−	24.0194i	−0.227361	−	1.28943i	0.630758	−	0.775980i	$-0.282744\pi$
$348$	8.00302	−	2.91286i	0.429007	−	0.156146i
$349$	3.73795	−	6.47432i	0.200088	−	0.346563i	−0.748469	−	0.663170i	$-0.769211\pi$
$349$	3.73795	−	6.47432i	0.200088	−	0.346563i	0.948557	+	0.316608i	$0.102544\pi$
$350$	2.05756	+	3.56380i	0.109981	+	0.190493i
$351$	2.48164	+	2.08235i	0.132460	+	0.111147i
$352$	1.79658	+	1.50751i	0.0957579	+	0.0803505i
$353$	1.87492	+	3.24746i	0.0997920	+	0.172845i	0.911598	−	0.411082i	$-0.134849\pi$
$353$	1.87492	+	3.24746i	0.0997920	+	0.172845i	−0.811806	+	0.583927i	$0.801516\pi$
$354$	−4.28219	+	7.41697i	−0.227596	+	0.394207i
$355$	−6.62319	+	2.41064i	−0.351522	+	0.127944i
$356$	−0.606747	−	3.44103i	−0.0321575	−	0.182374i
$357$	−5.50004	+	31.1923i	−0.291093	+	1.65087i
$358$	1.58073	+	0.575339i	0.0835442	+	0.0304076i
$359$	15.6415	−	13.1248i	0.825527	−	0.692699i	−0.128732	−	0.991679i	$-0.541091\pi$
$359$	15.6415	−	13.1248i	0.825527	−	0.692699i	0.954259	+	0.298980i	$0.0966464\pi$
$360$	1.00000			0.0527046
$361$	−15.4300	+	11.0867i	−0.812105	+	0.583511i
$362$	−19.6726			−1.03397
$363$	4.21303	−	3.53516i	0.221127	−	0.185548i
$364$	−12.5272	−	4.55953i	−0.656604	−	0.238984i
$365$	0.165920	−	0.940981i	0.00868467	−	0.0492532i
$366$	1.40900	+	7.99083i	0.0736495	+	0.417687i
$367$	−21.5808	+	7.85476i	−1.12651	+	0.410015i	−0.837023	−	0.547167i	$-0.815706\pi$
$367$	−21.5808	+	7.85476i	−1.12651	+	0.410015i	−0.289485	+	0.957183i	$0.593484\pi$
$368$	−4.20042	+	7.27535i	−0.218962	+	0.379254i
$369$	−2.60142	−	4.50579i	−0.135425	−	0.234562i
$370$	2.43257	+	2.04116i	0.126463	+	0.106115i
$371$	21.5581	+	18.0894i	1.11924	+	0.939154i
$372$	−1.07818	−	1.86746i	−0.0559010	−	0.0968234i
$373$	8.34398	−	14.4522i	0.432035	−	0.748306i	−0.565014	−	0.825081i	$-0.691129\pi$
$373$	8.34398	−	14.4522i	0.432035	−	0.748306i	0.997048	+	0.0767755i	$0.0244625\pi$
$374$	16.9625	−	6.17385i	0.877111	−	0.319242i
$375$	−0.173648	−	0.984808i	−0.00896715	−	0.0508553i
$376$	−0.223103	+	1.26528i	−0.0115057	+	0.0652519i
$377$	25.9262	+	9.43638i	1.33527	+	0.485998i
$378$	3.15237	−	2.64515i	0.162140	−	0.136052i
$379$	−33.0992			−1.70019			−0.850096	−	0.526627i	$-0.823456\pi$
$379$	−33.0992			−1.70019			−0.850096	+	0.526627i	$0.823456\pi$
$380$	1.33604	+	4.14910i	0.0685374	+	0.212844i
$381$	8.75990			0.448783
$382$	−0.993126	+	0.833332i	−0.0508127	+	0.0426370i
$383$	−5.09187	−	1.85329i	−0.260182	−	0.0946986i	0.208636	−	0.977993i	$-0.433098\pi$
$383$	−5.09187	−	1.85329i	−0.260182	−	0.0946986i	−0.468818	+	0.883295i	$0.655320\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−1.67589	−	9.50444i	−0.0854113	−	0.484391i
$386$	14.4633	−	5.26420i	0.736162	−	0.267941i
$387$	−1.08843	+	1.88522i	−0.0553281	+	0.0958310i
$388$	7.44391	+	12.8932i	0.377908	+	0.654555i
$389$	24.2644	+	20.3602i	1.23025	+	1.03230i	0.998223	+	0.0595949i	$0.0189809\pi$
$389$	24.2644	+	20.3602i	1.23025	+	1.03230i	0.232029	+	0.972709i	$0.425464\pi$
$390$	2.48164	+	2.08235i	0.125663	+	0.105444i
$391$	32.3300	+	55.9971i	1.63500	+	2.83190i
$392$	−4.96713	+	8.60332i	−0.250878	+	0.434533i
$393$	−18.3676	+	6.68527i	−0.926524	+	0.337227i
$394$	−2.07012	−	11.7402i	−0.104291	−	0.591465i
$395$	1.38654	−	7.86348i	0.0697646	−	0.395654i
$396$	−2.20383	−	0.802128i	−0.110747	−	0.0403085i
$397$	13.7930	−	11.5737i	0.692250	−	0.580867i	−0.227307	−	0.973823i	$-0.572992\pi$
$397$	13.7930	−	11.5737i	0.692250	−	0.580867i	0.919557	+	0.392956i	$0.128548\pi$
$398$	−3.41284			−0.171070
$399$	15.1867	+	9.54546i	0.760285	+	0.477870i
$400$	1.00000			0.0500000
$401$	−5.20051	+	4.36375i	−0.259701	+	0.217915i	−0.763336	−	0.646001i	$-0.776440\pi$
$401$	−5.20051	+	4.36375i	−0.259701	+	0.217915i	0.503635	+	0.863916i	$0.331996\pi$
$402$	−3.99294	−	1.45331i	−0.199150	−	0.0724845i
$403$	1.21304	−	6.87952i	0.0604260	−	0.342693i
$404$	2.41346	+	13.6874i	0.120074	+	0.680975i
$405$	−0.939693	+	0.342020i	−0.0466937	+	0.0169951i
$406$	17.5235	−	30.3516i	0.869678	−	1.50633i
$407$	−3.72368	−	6.44961i	−0.184576	−	0.319695i
$408$	5.89612	+	4.94743i	0.291901	+	0.244934i
$409$	−11.9183	−	10.0006i	−0.589321	−	0.494499i	0.298672	−	0.954356i	$-0.403456\pi$
$409$	−11.9183	−	10.0006i	−0.589321	−	0.494499i	−0.887993	+	0.459857i	$0.847901\pi$
$410$	−2.60142	−	4.50579i	−0.128475	−	0.222525i
$411$	4.73047	−	8.19341i	0.233337	−	0.404151i
$412$	10.2957	−	3.74732i	0.507232	−	0.184617i
$413$	6.11996	+	34.7080i	0.301144	+	1.70787i
$414$	1.45879	−	8.27322i	0.0716957	−	0.406606i
$415$	−10.5071	−	3.82427i	−0.515773	−	0.187726i
$416$	−2.48164	+	2.08235i	−0.121673	+	0.102095i
$417$	18.4133			0.901703
$418$	0.383705	−	10.2156i	0.0187676	−	0.499660i
$419$	3.56234			0.174032			0.0870159	−	0.996207i	$-0.472267\pi$
$419$	3.56234			0.174032			0.0870159	+	0.996207i	$0.472267\pi$
$420$	3.15237	−	2.64515i	0.153820	−	0.129070i
$421$	−8.03673	−	2.92513i	−0.391686	−	0.142562i	0.138667	−	0.990339i	$-0.455718\pi$
$421$	−8.03673	−	2.92513i	−0.391686	−	0.142562i	−0.530353	+	0.847777i	$0.677941\pi$
$422$	3.20198	−	18.1593i	0.155870	−	0.883981i
$423$	−0.223103	−	1.26528i	−0.0108476	−	0.0615200i
$424$	6.42627	−	2.33897i	0.312087	−	0.113591i
$425$	3.84842	−	6.66566i	0.186676	−	0.323332i
$426$	3.52412	+	6.10396i	0.170744	+	0.295738i
$427$	25.5786	+	21.4630i	1.23784	+	1.03867i
$428$	−12.3163	−	10.3346i	−0.595331	−	0.499542i
$429$	−3.79881	−	6.57973i	−0.183408	−	0.317672i
$430$	−1.08843	+	1.88522i	−0.0524888	+	0.0909133i
$431$	8.27572	−	3.01212i	0.398628	−	0.145089i	−0.134924	−	0.990856i	$-0.543079\pi$
$431$	8.27572	−	3.01212i	0.398628	−	0.145089i	0.533552	+	0.845767i	$0.320857\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	−5.87613	+	33.3252i	−0.282389	+	1.60151i	0.432078	+	0.901836i	$0.357781\pi$
$433$	−5.87613	+	33.3252i	−0.282389	+	1.60151i	−0.714467	+	0.699670i	$0.753331\pi$
$434$	−8.33854	−	3.03498i	−0.400263	−	0.145684i
$435$	−6.52412	+	5.47439i	−0.312808	+	0.262477i
$436$	−10.2871			−0.492663
$437$	36.2754	−	5.00068i	1.73529	−	0.239215i
$438$	−0.955497			−0.0456554
$439$	−13.8743	+	11.6419i	−0.662184	+	0.555639i	−0.910741	−	0.412979i	$-0.864488\pi$
$439$	−13.8743	+	11.6419i	−0.662184	+	0.555639i	0.248556	+	0.968617i	$0.420044\pi$
$440$	−2.20383	−	0.802128i	−0.105063	−	0.0382400i
$441$	1.72507	−	9.78333i	0.0821460	−	0.465873i
$442$	4.32980	+	24.5555i	0.205948	+	1.16799i
$443$	13.0711	−	4.75749i	0.621027	−	0.226035i	−0.0122944	−	0.999924i	$-0.503914\pi$
$443$	13.0711	−	4.75749i	0.621027	−	0.226035i	0.633321	+	0.773889i	$0.281691\pi$
$444$	1.58774	−	2.75005i	0.0753510	−	0.130512i
$445$	1.74706	+	3.02600i	0.0828185	+	0.143446i
$446$	−16.5911	−	13.9216i	−0.785612	−	0.659206i
$447$	−3.10325	−	2.60393i	−0.146779	−	0.123162i
$448$	2.05756	+	3.56380i	0.0972107	+	0.168374i
$449$	−3.24891	+	5.62729i	−0.153326	+	0.265568i	−0.932448	−	0.361304i	$-0.882332\pi$
$449$	−3.24891	+	5.62729i	−0.153326	+	0.265568i	0.779122	+	0.626872i	$0.215665\pi$
$450$	−0.939693	+	0.342020i	−0.0442975	+	0.0161230i
$451$	2.11886	+	12.0167i	0.0997734	+	0.565843i
$452$	1.87915	−	10.6572i	0.0883879	−	0.501273i
$453$	−15.7453	−	5.73081i	−0.739778	−	0.269257i
$454$	5.01186	−	4.20545i	0.235218	−	0.197371i
$455$	13.3312			0.624975
$456$	3.85406	−	2.03622i	0.180483	−	0.0953550i
$457$	−24.1544			−1.12989			−0.564947	−	0.825127i	$-0.691104\pi$
$457$	−24.1544			−1.12989			−0.564947	+	0.825127i	$0.691104\pi$
$458$	−13.0439	+	10.9451i	−0.609502	+	0.511433i
$459$	−7.23266	−	2.63247i	−0.337592	−	0.122873i
$460$	1.45879	−	8.27322i	0.0680165	−	0.385741i
$461$	4.57005	+	25.9180i	0.212848	+	1.20712i	0.884601	+	0.466348i	$0.154431\pi$
$461$	4.57005	+	25.9180i	0.212848	+	1.20712i	−0.671753	+	0.740775i	$0.734458\pi$
$462$	−9.06904	+	3.30086i	−0.421930	+	0.153570i
$463$	−4.65918	+	8.06994i	−0.216531	+	0.375042i	−0.953745	−	0.300617i	$-0.902807\pi$
$463$	−4.65918	+	8.06994i	−0.216531	+	0.375042i	0.737214	+	0.675659i	$0.236141\pi$
$464$	−4.25832	−	7.37563i	−0.197688	−	0.342405i
$465$	1.65187	+	1.38608i	0.0766035	+	0.0642780i
$466$	22.1296	+	18.5689i	1.02513	+	0.860189i
$467$	−2.46905	−	4.27652i	−0.114254	−	0.197894i	0.803227	−	0.595673i	$-0.203114\pi$
$467$	−2.46905	−	4.27652i	−0.114254	−	0.197894i	−0.917481	+	0.397779i	$0.869781\pi$
$468$	1.61978	−	2.80554i	0.0748743	−	0.129686i
$469$	−16.4314	+	5.98056i	−0.758733	+	0.276156i
$470$	−0.223103	−	1.26528i	−0.0102910	−	0.0583630i
$471$	0.718319	−	4.07379i	0.0330984	−	0.187710i
$472$	8.04788	+	2.92919i	0.370434	+	0.134827i
$473$	3.91090	−	3.28164i	0.179824	−	0.150890i
$474$	−7.98478			−0.366753
$475$	−2.67454	−	3.44192i	−0.122716	−	0.157926i
$476$	31.6735			1.45175
$477$	−5.23875	+	4.39583i	−0.239866	+	0.201271i
$478$	9.02868	+	3.28617i	0.412962	+	0.150306i
$479$	−3.70550	+	21.0149i	−0.169309	+	0.960196i	0.775202	+	0.631714i	$0.217648\pi$
$479$	−3.70550	+	21.0149i	−0.169309	+	0.960196i	−0.944510	+	0.328482i	$0.893463\pi$
$480$	−0.173648	−	0.984808i	−0.00792592	−	0.0449501i
$481$	9.66678	−	3.51842i	0.440767	−	0.160426i
$482$	−6.55824	+	11.3592i	−0.298720	+	0.517398i
$483$	−17.2853	−	29.9390i	−0.786507	−	1.36227i
$484$	−4.21303	−	3.53516i	−0.191502	−	0.160689i
$485$	−11.4047	−	9.56971i	−0.517863	−	0.434538i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−1.72438	+	2.98671i	−0.0781391	+	0.135341i	−0.902447	−	0.430801i	$-0.858231\pi$
$487$	−1.72438	+	2.98671i	−0.0781391	+	0.135341i	0.824308	+	0.566142i	$0.191564\pi$
$488$	7.62476	−	2.77519i	0.345157	−	0.125627i
$489$	3.24615	+	18.4098i	0.146796	+	0.832520i
$490$	1.72507	−	9.78333i	0.0779305	−	0.441966i
$491$	−34.9650	−	12.7262i	−1.57795	−	0.574326i	−0.603190	−	0.797597i	$-0.706104\pi$
$491$	−34.9650	−	12.7262i	−1.57795	−	0.574326i	−0.974756	+	0.223272i	$0.928326\pi$
$492$	−3.98561	+	3.34432i	−0.179685	+	0.150774i
$493$	−65.5512			−2.95228
$494$	13.8045	+	2.97231i	0.621095	+	0.133730i
$495$	2.34527			0.105412
$496$	−1.65187	+	1.38608i	−0.0741710	+	0.0622369i
$497$	27.2552	+	9.92010i	1.22256	+	0.444977i
$498$	−1.94163	+	11.0116i	−0.0870067	+	0.493440i
$499$	3.71590	+	21.0739i	0.166347	+	0.943398i	0.947665	+	0.319266i	$0.103436\pi$
$499$	3.71590	+	21.0739i	0.166347	+	0.943398i	−0.781319	+	0.624132i	$0.785453\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	−1.79026	+	3.10081i	−0.0799827	+	0.138534i
$502$	−12.6524	−	21.9146i	−0.564705	−	0.978099i
$503$	−0.833010	−	0.698978i	−0.0371421	−	0.0311659i	0.624028	−	0.781402i	$-0.285495\pi$
$503$	−0.833010	−	0.698978i	−0.0371421	−	0.0311659i	−0.661170	+	0.750236i	$0.729940\pi$
$504$	−3.15237	−	2.64515i	−0.140418	−	0.117824i
$505$	−6.94929	−	12.0365i	−0.309239	−	0.535618i
$506$	−9.85111	+	17.0626i	−0.437935	+	0.758526i
$507$	−2.35419	+	0.856856i	−0.104553	+	0.0380543i
$508$	−1.52114	−	8.62682i	−0.0674897	−	0.382753i
$509$	7.11225	−	40.3356i	0.315245	−	1.78784i	−0.255597	−	0.966783i	$-0.582272\pi$
$509$	7.11225	−	40.3356i	0.315245	−	1.78784i	0.570842	−	0.821060i	$-0.306617\pi$
$510$	−7.23266	−	2.63247i	−0.320268	−	0.116568i
$511$	−3.01208	+	2.52743i	−0.133247	+	0.111807i
$512$	1.00000			0.0441942
$513$	−2.92520	+	3.23159i	−0.129151	+	0.142678i
$514$	−13.2695			−0.585293
$515$	−8.39312	+	7.04266i	−0.369845	+	0.310337i
$516$	2.04558	+	0.744531i	0.0900517	+	0.0327761i
$517$	−0.523236	+	2.96742i	−0.0230119	+	0.130507i
$518$	−2.26915	−	12.8690i	−0.0997009	−	0.565432i
$519$	2.68864	−	0.978586i	0.118018	−	0.0429552i
$520$	1.61978	−	2.80554i	0.0710320	−	0.123031i
$521$	2.71331	+	4.69960i	0.118872	+	0.205893i	0.919321	−	0.393508i	$-0.128739\pi$
$521$	2.71331	+	4.69960i	0.118872	+	0.205893i	−0.800449	+	0.599401i	$0.795405\pi$
$522$	6.52412	+	5.47439i	0.285553	+	0.239608i
$523$	14.9466	+	12.5417i	0.653571	+	0.548411i	0.908152	−	0.418640i	$-0.137493\pi$
$523$	14.9466	+	12.5417i	0.653571	+	0.548411i	−0.254581	+	0.967051i	$0.581938\pi$
$524$	9.77321	+	16.9277i	0.426945	+	0.739490i
$525$	−2.05756	+	3.56380i	−0.0897994	+	0.155537i
$526$	9.80953	−	3.57038i	0.427716	−	0.155676i
$527$	2.88206	+	16.3450i	0.125545	+	0.711999i
$528$	−0.407251	+	2.30964i	−0.0177233	+	0.100514i
$529$	−44.7051	−	16.2713i	−1.94370	−	0.707449i
$530$	−5.23875	+	4.39583i	−0.227557	+	0.190943i
$531$	−8.56437			−0.371662
$532$	6.76330	−	16.6135i	0.293226	−	0.720287i
$533$	−16.8549			−0.730067
$534$	2.67665	−	2.24598i	0.115830	−	0.0971929i
$535$	15.1082	+	5.49893i	0.653184	+	0.237740i
$536$	−0.737865	+	4.18464i	−0.0318709	+	0.180749i
$537$	0.292107	+	1.65662i	0.0126054	+	0.0714885i
$538$	−3.38745	+	1.23293i	−0.146043	+	0.0531554i
$539$	−11.6492	+	20.1771i	−0.501768	+	0.869088i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	14.8739	+	12.4807i	0.639477	+	0.536585i	0.903858	−	0.427833i	$-0.140723\pi$
$541$	14.8739	+	12.4807i	0.639477	+	0.536585i	−0.264380	+	0.964419i	$0.585167\pi$
$542$	13.1873	+	11.0655i	0.566443	+	0.475302i
$543$	−9.83632	−	17.0370i	−0.422117	−	0.731128i
$544$	3.84842	−	6.66566i	0.165000	−	0.285788i
$545$	9.66671	−	3.51840i	0.414076	−	0.150712i
$546$	−2.31493	−	13.1286i	−0.0990701	−	0.561854i
$547$	−0.890015	+	5.04753i	−0.0380543	+	0.215817i	−0.997905	−	0.0646943i	$-0.979393\pi$
$547$	−0.890015	+	5.04753i	−0.0380543	+	0.215817i	0.959851	+	0.280511i	$0.0905039\pi$
$548$	−8.89037	−	3.23583i	−0.379778	−	0.138228i
$549$	−6.21576	+	5.21564i	−0.265282	+	0.222598i
$550$	2.34527			0.100002
$551$	−13.9973	+	34.3832i	−0.596304	+	1.46477i
$552$	−8.40084			−0.357564
$553$	−25.1710	+	21.1210i	−1.07038	+	0.898155i
$554$	6.16445	+	2.24368i	0.261902	+	0.0953246i
$555$	−0.551418	+	3.12725i	−0.0234064	+	0.132744i
$556$	−3.19744	−	18.1336i	−0.135602	−	0.769034i
$557$	−29.0409	+	10.5700i	−1.23050	+	0.447866i	−0.873769	−	0.486340i	$-0.838332\pi$
$557$	−29.0409	+	10.5700i	−1.23050	+	0.447866i	−0.356733	+	0.934207i	$0.616109\pi$
$558$	1.07818	−	1.86746i	0.0456430	−	0.0790559i
$559$	3.52603	+	6.10727i	0.149135	+	0.258310i
$560$	−3.15237	−	2.64515i	−0.133212	−	0.111778i
$561$	13.8280	+	11.6030i	0.583817	+	0.489881i
$562$	−7.50038	−	12.9910i	−0.316385	−	0.547994i
$563$	22.3471	−	38.7063i	0.941818	−	1.63128i	0.179818	−	0.983700i	$-0.442449\pi$
$563$	22.3471	−	38.7063i	0.941818	−	1.63128i	0.762000	−	0.647577i	$-0.224218\pi$
$564$	−1.20732	+	0.439427i	−0.0508372	+	0.0185032i
$565$	1.87915	+	10.6572i	0.0790566	+	0.448352i
$566$	4.62435	−	26.2260i	0.194376	−	1.10236i
$567$	3.86695	+	1.40746i	0.162397	+	0.0591076i
$568$	5.39927	−	4.53053i	0.226548	−	0.190097i
$569$	23.7352			0.995033			0.497516	−	0.867455i	$-0.334245\pi$
$569$	23.7352			0.995033			0.497516	+	0.867455i	$0.334245\pi$
$570$	−2.92520	+	3.23159i	−0.122523	+	0.135356i
$571$	−13.8106			−0.577956			−0.288978	−	0.957336i	$-0.593315\pi$
$571$	−13.8106			−0.577956			−0.288978	+	0.957336i	$0.593315\pi$
$572$	−5.82012	+	4.88366i	−0.243351	+	0.204196i
$573$	−1.21825	−	0.443406i	−0.0508931	−	0.0185236i
$574$	−3.71787	+	21.0851i	−0.155181	+	0.880074i
$575$	1.45879	+	8.27322i	0.0608358	+	0.345017i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−17.4203	+	30.1728i	−0.725217	+	1.25611i	0.233668	+	0.972316i	$0.424927\pi$
$577$	−17.4203	+	30.1728i	−0.725217	+	1.25611i	−0.958885	+	0.283796i	$0.908406\pi$
$578$	−21.1207	−	36.5820i	−0.878503	−	1.52161i
$579$	11.7906	+	9.89347i	0.490000	+	0.411159i
$580$	6.52412	+	5.47439i	0.270900	+	0.227312i
$581$	23.0065	+	39.8484i	0.954470	+	1.65319i
$582$	−7.44391	+	12.8932i	−0.308560	+	0.534442i
$583$	15.0713	−	5.48551i	0.624190	−	0.227187i
$584$	0.165920	+	0.940981i	0.00686583	+	0.0389381i
$585$	−0.562543	+	3.19034i	−0.0232583	+	0.131904i
$586$	−11.9232	−	4.33968i	−0.492542	−	0.179271i
$587$	−21.7014	+	18.2097i	−0.895714	+	0.751593i	−0.969348	−	0.245692i	$-0.920985\pi$
$587$	−21.7014	+	18.2097i	−0.895714	+	0.751593i	0.0736341	+	0.997285i	$0.476540\pi$
$588$	−9.93426			−0.409682
$589$	9.18877	+	1.97847i	0.378617	+	0.0815214i
$590$	−8.56437			−0.352590
$591$	9.13228	−	7.66290i	0.375652	−	0.315209i
$592$	−2.98398	−	1.08608i	−0.122641	−	0.0446377i
$593$	2.33030	−	13.2158i	0.0956939	−	0.542707i	−0.898839	−	0.438280i	$-0.855588\pi$
$593$	2.33030	−	13.2158i	0.0956939	−	0.542707i	0.994533	−	0.104427i	$-0.0333010\pi$
$594$	−0.407251	−	2.30964i	−0.0167097	−	0.0947655i
$595$	−29.7633	+	10.8330i	−1.22018	+	0.444108i
$596$	−2.02550	+	3.50827i	−0.0829678	+	0.143704i
$597$	−1.70642	−	2.95560i	−0.0698390	−	0.120965i
$598$	−20.8479	−	17.4935i	−0.852534	−	0.715361i
$599$	−1.40681	−	1.18046i	−0.0574808	−	0.0482321i	0.613595	−	0.789621i	$-0.289723\pi$
$599$	−1.40681	−	1.18046i	−0.0574808	−	0.0482321i	−0.671075	+	0.741389i	$0.734167\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	20.7950	−	36.0180i	0.848247	−	1.46921i	−0.0345244	−	0.999404i	$-0.510992\pi$
$601$	20.7950	−	36.0180i	0.848247	−	1.46921i	0.882771	−	0.469803i	$-0.155675\pi$
$602$	8.41782	−	3.06384i	0.343085	−	0.124873i
$603$	−0.737865	−	4.18464i	−0.0300482	−	0.170412i
$604$	−2.90961	+	16.5012i	−0.118390	+	0.671425i
$605$	5.16805	+	1.88102i	0.210111	+	0.0764742i
$606$	−10.6469	+	8.93383i	−0.432502	+	0.362912i
$607$	18.4116			0.747305			0.373652	−	0.927569i	$-0.378105\pi$
$607$	18.4116			0.747305			0.373652	+	0.927569i	$0.378105\pi$
$608$	−2.67454	−	3.44192i	−0.108467	−	0.139588i
$609$	35.0470			1.42018
$610$	−6.21576	+	5.21564i	−0.251669	+	0.211175i
$611$	−3.91117	−	1.42355i	−0.158229	−	0.0575906i
$612$	−1.33654	+	7.57991i	−0.0540265	+	0.306400i
$613$	−1.92435	−	10.9135i	−0.0777237	−	0.440793i	−0.998691	−	0.0511527i	$-0.983710\pi$
$613$	−1.92435	−	10.9135i	−0.0777237	−	0.440793i	0.920967	−	0.389640i	$-0.127401\pi$
$614$	14.5059	−	5.27973i	0.585412	−	0.213073i
$615$	2.60142	−	4.50579i	0.104899	−	0.181691i
$616$	4.82553	+	8.35807i	0.194426	+	0.336756i
$617$	−36.3173	−	30.4738i	−1.46208	−	1.22683i	−0.923129	−	0.384491i	$-0.874377\pi$
$617$	−36.3173	−	30.4738i	−1.46208	−	1.22683i	−0.538949	−	0.842338i	$-0.681179\pi$
$618$	8.39312	+	7.04266i	0.337621	+	0.283297i
$619$	17.8450	+	30.9084i	0.717251	+	1.24231i	0.962085	+	0.272750i	$0.0879332\pi$
$619$	17.8450	+	30.9084i	0.717251	+	1.24231i	−0.244834	+	0.969565i	$0.578734\pi$
$620$	1.07818	−	1.86746i	0.0433007	−	0.0749991i
$621$	7.89421	−	2.87326i	0.316784	−	0.115300i
$622$	−5.77279	−	32.7391i	−0.231468	−	1.31272i
$623$	2.49684	−	14.1603i	0.100034	−	0.567320i
$624$	−3.04419	−	1.10799i	−0.121865	−	0.0443552i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	5.29861			0.211775
$627$	9.03880	−	4.77549i	0.360975	−	0.190715i
$628$	−4.13663			−0.165070
$629$	−18.7231	+	15.7105i	−0.746537	+	0.626419i
$630$	3.86695	+	1.40746i	0.154063	+	0.0560744i
$631$	−4.74411	+	26.9052i	−0.188860	+	1.07108i	0.732035	+	0.681267i	$0.238571\pi$
$631$	−4.74411	+	26.9052i	−0.188860	+	1.07108i	−0.920895	+	0.389811i	$0.872540\pi$
$632$	1.38654	+	7.86348i	0.0551537	+	0.312792i
$633$	17.3274	−	6.30666i	0.688703	−	0.250667i
$634$	9.81889	−	17.0068i	0.389958	−	0.675427i
$635$	4.37995	+	7.58630i	0.173813	+	0.301053i
$636$	5.23875	+	4.39583i	0.207730	+	0.174306i
$637$	−24.6533	−	20.6866i	−0.976799	−	0.819632i
$638$	−9.98689	−	17.2978i	−0.395385	−	0.684827i
$639$	−3.52412	+	6.10396i	−0.139412	+	0.241469i
$640$	−0.939693	+	0.342020i	−0.0371446	+	0.0135195i
$641$	−4.97458	−	28.2123i	−0.196484	−	1.11432i	−0.910289	−	0.413973i	$-0.864141\pi$
$641$	−4.97458	−	28.2123i	−0.196484	−	1.11432i	0.713805	−	0.700344i	$-0.246970\pi$
$642$	2.79188	−	15.8335i	0.110187	−	0.624900i
$643$	−3.60684	−	1.31278i	−0.142240	−	0.0517710i	0.269919	−	0.962883i	$-0.413003\pi$
$643$	−3.60684	−	1.31278i	−0.142240	−	0.0517710i	−0.412159	+	0.911112i	$0.635225\pi$
$644$	−26.4826	+	22.2215i	−1.04356	+	0.875650i
$645$	−2.17686			−0.0857139
$646$	−33.2354	+	4.58161i	−1.30763	+	0.180261i
$647$	−27.3306			−1.07448			−0.537238	−	0.843431i	$-0.680532\pi$
$647$	−27.3306			−1.07448			−0.537238	+	0.843431i	$0.680532\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	18.8744	+	6.86973i	0.740886	+	0.269660i
$650$	−0.562543	+	3.19034i	−0.0220647	+	0.125135i
$651$	−1.54090	−	8.73888i	−0.0603926	−	0.342504i
$652$	17.5664	−	6.39366i	0.687955	−	0.250395i
$653$	4.57736	−	7.92823i	0.179126	−	0.310255i	−0.762455	−	0.647041i	$-0.776006\pi$
$653$	4.57736	−	7.92823i	0.179126	−	0.310255i	0.941581	+	0.336785i	$0.109340\pi$
$654$	−5.14355	−	8.90889i	−0.201129	−	0.348365i
$655$	−14.9734	−	12.5642i	−0.585060	−	0.490924i
$656$	3.98561	+	3.34432i	0.155612	+	0.130574i
$657$	−0.477749	−	0.827485i	−0.0186387	−	0.0322833i
$658$	−2.64356	+	4.57877i	−0.103057	+	0.178499i
$659$	−18.2474	+	6.64153i	−0.710819	+	0.258717i	−0.672023	−	0.740530i	$-0.734575\pi$
$659$	−18.2474	+	6.64153i	−0.710819	+	0.258717i	−0.0387961	+	0.999247i	$0.512352\pi$
$660$	−0.407251	−	2.30964i	−0.0158522	−	0.0899025i
$661$	−5.89471	+	33.4306i	−0.229278	+	1.30030i	0.625058	+	0.780578i	$0.285075\pi$
$661$	−5.89471	+	33.4306i	−0.229278	+	1.30030i	−0.854336	+	0.519721i	$0.826036\pi$
$662$	4.56004	+	1.65972i	0.177231	+	0.0645068i
$663$	−19.1008	+	16.0275i	−0.741814	+	0.622456i
$664$	11.1814			0.433923
$665$	−0.673268	+	17.9248i	−0.0261082	+	0.695093i
$666$	3.17549			0.123048
$667$	54.8082	−	45.9895i	2.12218	−	1.78072i
$668$	3.36458	+	1.22461i	0.130179	+	0.0473815i
$669$	3.76090	−	21.3291i	0.145405	−	0.824631i
$670$	−0.737865	−	4.18464i	−0.0285062	−	0.161667i
$671$	17.8821	−	6.50855i	0.690331	−	0.251260i
$672$	−2.05756	+	3.56380i	−0.0793722	+	0.137477i
$673$	16.2154	+	28.0859i	0.625057	+	1.08263i	0.988530	+	0.151026i	$0.0482578\pi$
$673$	16.2154	+	28.0859i	0.625057	+	1.08263i	−0.363472	+	0.931605i	$0.618409\pi$
$674$	−14.3144	−	12.0112i	−0.551369	−	0.462654i
$675$	−0.766044	−	0.642788i	−0.0294851	−	0.0247409i
$676$	1.25264	+	2.16964i	0.0481785	+	0.0834475i
$677$	7.10545	−	12.3070i	0.273085	−	0.472996i	−0.696565	−	0.717493i	$-0.745289\pi$
$677$	7.10545	−	12.3070i	0.273085	−	0.472996i	0.969650	+	0.244497i	$0.0786228\pi$
$678$	10.1690	−	3.70121i	0.390538	−	0.142144i
$679$	10.6386	+	60.3345i	0.408272	+	2.31543i
$680$	−1.33654	+	7.57991i	−0.0512540	+	0.290676i
$681$	6.14795	+	2.23767i	0.235590	+	0.0857478i
$682$	−3.87407	+	3.25073i	−0.148346	+	0.124477i
$683$	−38.5350			−1.47450			−0.737251	−	0.675619i	$-0.763876\pi$
$683$	−38.5350			−1.47450			−0.737251	+	0.675619i	$0.763876\pi$
$684$	3.69045	+	2.31960i	0.141108	+	0.0886922i
$685$	9.46094			0.361484
$686$	−9.24987	+	7.76156i	−0.353162	+	0.296338i
$687$	−16.0007	−	5.82379i	−0.610466	−	0.222192i
$688$	0.378008	−	2.14379i	0.0144114	−	0.0817313i
$689$	3.84706	+	21.8178i	0.146561	+	0.831191i
$690$	7.89421	−	2.87326i	0.300528	−	0.109383i
$691$	16.6088	−	28.7673i	0.631829	−	1.09436i	−0.355348	−	0.934734i	$-0.615638\pi$
$691$	16.6088	−	28.7673i	0.631829	−	1.09436i	0.987178	−	0.159626i	$-0.0510289\pi$
$692$	−1.43060	−	2.47787i	−0.0543831	−	0.0941944i
$693$	−7.39315	−	6.20359i	−0.280842	−	0.235655i
$694$	−18.6838	−	15.6776i	−0.709227	−	0.595112i
$695$	9.20665	+	15.9464i	0.349228	+	0.604881i
$696$	4.25832	−	7.37563i	0.161411	−	0.279572i
$697$	37.6304	−	13.6963i	1.42535	−	0.518786i
$698$	−1.29818	−	7.36233i	−0.0491367	−	0.278668i
$699$	−5.01637	+	28.4492i	−0.189737	+	1.07605i
$700$	3.86695	+	1.40746i	0.146157	+	0.0531968i
$701$	3.55007	−	2.97886i	0.134084	−	0.112510i	−0.573279	−	0.819360i	$-0.694329\pi$
$701$	3.55007	−	2.97886i	0.134084	−	0.112510i	0.707363	+	0.706850i	$0.249884\pi$
$702$	3.23956			0.122269
$703$	4.24258	+	13.1754i	0.160012	+	0.496920i
$704$	2.34527			0.0883906
$705$	0.984214	−	0.825853i	0.0370676	−	0.0311034i
$706$	3.52370	+	1.28252i	0.132616	+	0.0482683i
$707$	−9.93170	+	56.3255i	−0.373520	+	2.11834i
$708$	1.48719	+	8.43426i	0.0558919	+	0.316979i
$709$	−18.3307	+	6.67183i	−0.688424	+	0.250566i	−0.662460	−	0.749097i	$-0.730488\pi$
$709$	−18.3307	+	6.67183i	−0.688424	+	0.250566i	−0.0259638	+	0.999663i	$0.508265\pi$
$710$	−3.52412	+	6.10396i	−0.132258	+	0.229078i
$711$	−3.99239	−	6.91502i	−0.149726	−	0.259334i
$712$	−2.67665	−	2.24598i	−0.100312	−	0.0841715i
$713$	−13.8771	−	11.6442i	−0.519701	−	0.436081i
$714$	15.8367	+	27.4300i	0.592675	+	1.02654i
$715$	3.79881	−	6.57973i	0.142067	−	0.246068i
$716$	1.58073	−	0.575339i	0.0590747	−	0.0215014i
$717$	1.66843	+	9.46215i	0.0623088	+	0.353371i
$718$	3.54564	−	20.1083i	0.132322	−	0.750436i
$719$	30.8171	+	11.2165i	1.14928	+	0.418305i	0.845258	−	0.534358i	$-0.179447\pi$
$719$	30.8171	+	11.2165i	1.14928	+	0.418305i	0.304026	+	0.952664i	$0.401669\pi$
$720$	0.766044	−	0.642788i	0.0285488	−	0.0239553i
$721$	45.0871			1.67913
$722$	−4.69366	+	18.4111i	−0.174680	+	0.685191i
$723$	−13.1165			−0.487807
$724$	−15.0701	+	12.6453i	−0.560077	+	0.469960i
$725$	−8.00302	−	2.91286i	−0.297225	−	0.108181i
$726$	0.955017	−	5.41617i	0.0354440	−	0.201013i
$727$	−0.739500	−	4.19391i	−0.0274265	−	0.155544i	0.968019	−	0.250878i	$-0.0807192\pi$
$727$	−0.739500	−	4.19391i	−0.0274265	−	0.155544i	−0.995445	+	0.0953340i	$0.969608\pi$
$728$	−12.5272	+	4.55953i	−0.464289	+	0.168987i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.477749	−	0.827485i	−0.0176823	−	0.0306266i
$731$	−12.8350	−	10.7699i	−0.474721	−	0.398338i
$732$	6.21576	+	5.21564i	0.229741	+	0.192776i
$733$	−1.56681	−	2.71379i	−0.0578713	−	0.100236i	0.835638	−	0.549280i	$-0.185098\pi$
$733$	−1.56681	−	2.71379i	−0.0578713	−	0.100236i	−0.893510	+	0.449044i	$0.851765\pi$
$734$	−11.4829	+	19.8890i	−0.423841	+	0.734115i
$735$	9.33515	−	3.39772i	0.344332	−	0.125327i
$736$	1.45879	+	8.27322i	0.0537718	+	0.304955i
$737$	−1.73049	+	9.81410i	−0.0637434	+	0.361507i
$738$	−4.88907	−	1.77948i	−0.179969	−	0.0655035i
$739$	3.36399	−	2.82272i	0.123746	−	0.103836i	−0.578814	−	0.815459i	$-0.696484\pi$
$739$	3.36399	−	2.82272i	0.123746	−	0.103836i	0.702561	+	0.711624i	$0.252040\pi$
$740$	3.17549			0.116733
$741$	4.32817	+	13.4412i	0.158999	+	0.493776i
$742$	28.1421			1.03313
$743$	−2.19565	+	1.84237i	−0.0805505	+	0.0675899i	−0.682174	−	0.731190i	$-0.738965\pi$
$743$	−2.19565	+	1.84237i	−0.0805505	+	0.0675899i	0.601623	+	0.798780i	$0.294521\pi$
$744$	−2.02631	−	0.737518i	−0.0742883	−	0.0270387i
$745$	0.703449	−	3.98946i	0.0257724	−	0.146162i
$746$	−2.89783	−	16.4344i	−0.106097	−	0.601707i
$747$	−10.5071	+	3.82427i	−0.384435	+	0.139923i
$748$	9.02557	−	15.6327i	0.330007	−	0.571590i
$749$	−33.0811	−	57.2981i	−1.20876	−	2.09363i
$750$	−0.766044	−	0.642788i	−0.0279720	−	0.0234713i
$751$	−22.4855	−	18.8676i	−0.820509	−	0.688489i	0.132582	−	0.991172i	$-0.457673\pi$
$751$	−22.4855	−	18.8676i	−0.820509	−	0.688489i	−0.953091	+	0.302683i	$0.902118\pi$
$752$	0.642400	+	1.11267i	0.0234259	+	0.0405749i
$753$	12.6524	−	21.9146i	0.461080	−	0.798614i
$754$	25.9262	−	9.43638i	0.944178	−	0.343653i
$755$	−2.90961	−	16.5012i	−0.105892	−	0.600541i
$756$	0.714584	−	4.05261i	0.0259892	−	0.147392i
$757$	19.9577	+	7.26401i	0.725375	+	0.264015i	0.678206	−	0.734872i	$-0.262758\pi$
$757$	19.9577	+	7.26401i	0.725375	+	0.264015i	0.0471690	+	0.998887i	$0.484980\pi$
$758$	−25.3555	+	21.2758i	−0.920952	+	0.772771i
$759$	−19.7022			−0.715145
$760$	3.69045	+	2.31960i	0.133867	+	0.0841408i
$761$	−15.3364			−0.555946			−0.277973	−	0.960589i	$-0.589663\pi$
$761$	−15.3364			−0.555946			−0.277973	+	0.960589i	$0.589663\pi$
$762$	6.71047	−	5.63075i	0.243095	−	0.203981i
$763$	−39.7797	−	14.4786i	−1.44012	−	0.524162i
$764$	−0.225123	+	1.27674i	−0.00814468	+	0.0461908i
$765$	−1.33654	−	7.57991i	−0.0483228	−	0.274052i
$766$	−5.09187	+	1.85329i	−0.183977	+	0.0669620i
$767$	−13.8724	+	24.0277i	−0.500903	+	0.867589i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	38.8570	+	32.6049i	1.40122	+	1.17576i	0.960555	+	0.278090i	$0.0897012\pi$
$769$	38.8570	+	32.6049i	1.40122	+	1.17576i	0.440663	+	0.897672i	$0.354743\pi$
$770$	−7.39315	−	6.20359i	−0.266430	−	0.223562i
$771$	−6.63475	−	11.4917i	−0.238945	−	0.413865i
$772$	7.69575	−	13.3294i	0.276976	−	0.479737i
$773$	−27.8865	+	10.1498i	−1.00301	+	0.365065i	−0.790743	−	0.612148i	$-0.790306\pi$
$773$	−27.8865	+	10.1498i	−1.00301	+	0.365065i	−0.212264	+	0.977212i	$0.568084\pi$
$774$	0.378008	+	2.14379i	0.0135872	+	0.0770570i
$775$	−0.374448	+	2.12360i	−0.0134506	+	0.0762819i
$776$	13.9900	+	5.09194i	0.502211	+	0.182790i
$777$	10.0103	−	8.39965i	0.359118	−	0.301336i
$778$	31.6749			1.13560
$779$	0.851228	−	22.6627i	0.0304984	−	0.811975i
$780$	3.23956			0.115995
$781$	12.6627	−	10.6253i	0.453108	−	0.380203i
$782$	60.7605	+	22.1150i	2.17279	+	0.790831i
$783$	−1.47890	+	8.38725i	−0.0528515	+	0.299736i
$784$	1.72507	+	9.78333i	0.0616095	+	0.349405i
$785$	3.88716	−	1.41481i	0.138739	−	0.0504968i
$786$	−9.77321	+	16.9277i	−0.348599	+	0.603791i
$787$	−15.9449	−	27.6174i	−0.568375	−	0.984454i	−0.996727	−	0.0808424i	$-0.974239\pi$
$787$	−15.9449	−	27.6174i	−0.568375	−	0.984454i	0.428352	−	0.903612i	$-0.359094\pi$
$788$	−9.13228	−	7.66290i	−0.325324	−	0.272979i
$789$	7.99680	+	6.71011i	0.284694	+	0.238886i
$790$	−3.99239	−	6.91502i	−0.142043	−	0.246026i
$791$	22.2661	−	38.5661i	0.791693	−	1.37125i
$792$	−2.20383	+	0.802128i	−0.0783097	+	0.0285024i
$793$	4.56453	+	25.8867i	0.162091	+	0.919265i
$794$	3.12662	−	17.7319i	0.110959	−	0.629282i
$795$	−6.42627	−	2.33897i	−0.227916	−	0.0829548i
$796$	−2.61438	+	2.19373i	−0.0926644	+	0.0777546i
$797$	32.9497			1.16714			0.583569	−	0.812064i	$-0.301656\pi$
$797$	32.9497			1.16714			0.583569	+	0.812064i	$0.301656\pi$
$798$	17.7694	−	2.44957i	0.629029	−	0.0867137i
$799$	9.88889			0.349844
$800$	0.766044	−	0.642788i	0.0270838	−	0.0227260i
$801$	3.28340	+	1.19506i	0.116013	+	0.0422253i
$802$	−1.17886	+	6.68565i	−0.0416270	+	0.236079i
$803$	0.389127	+	2.20685i	0.0137320	+	0.0778781i
$804$	−3.99294	+	1.45331i	−0.140820	+	0.0512543i
$805$	17.2853	−	29.9390i	0.609226	−	1.05521i
$806$	−3.49282	−	6.04975i	−0.123029	−	0.213093i
$807$	−2.76147	−	2.31715i	−0.0972084	−	0.0815675i
$808$	10.6469	+	8.93383i	0.374557	+	0.314291i
$809$	−13.0255	−	22.5609i	−0.457953	−	0.793198i	0.540900	−	0.841087i	$-0.318084\pi$
$809$	−13.0255	−	22.5609i	−0.457953	−	0.793198i	−0.998853	+	0.0478892i	$0.984751\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	19.4758	−	7.08862i	0.683889	−	0.248915i	0.0233723	−	0.999727i	$-0.492560\pi$
$811$	19.4758	−	7.08862i	0.683889	−	0.248915i	0.660516	+	0.750812i	$0.270337\pi$
$812$	−6.08585	−	34.5146i	−0.213572	−	1.21122i
$813$	−2.98932	+	16.9533i	−0.104840	+	0.594577i
$814$	−6.99823	−	2.54715i	−0.245288	−	0.0892775i
$815$	−14.3203	+	12.0161i	−0.501618	+	0.420907i
$816$	7.69684			0.269443
$817$	−8.38976	+	4.43258i	−0.293521	+	0.155076i
$818$	−15.5582			−0.543980
$819$	10.2123	−	8.56912i	0.356846	−	0.299429i
$820$	−4.88907	−	1.77948i	−0.170734	−	0.0621420i
$821$	0.840443	−	4.76639i	0.0293317	−	0.166348i	−0.966623	−	0.256202i	$-0.917529\pi$
$821$	0.840443	−	4.76639i	0.0293317	−	0.166348i	0.995955	+	0.0898537i	$0.0286399\pi$
$822$	−1.64287	−	9.31720i	−0.0573018	−	0.324975i
$823$	−0.788147	+	0.286862i	−0.0274731	+	0.00999938i	−0.355720	−	0.934593i	$-0.615764\pi$
$823$	−0.788147	+	0.286862i	−0.0274731	+	0.00999938i	0.328247	+	0.944592i	$0.393542\pi$
$824$	5.47822	−	9.48855i	0.190843	−	0.330549i
$825$	1.17263	+	2.03106i	0.0408258	+	0.0707124i
$826$	26.9981	+	22.6541i	0.939383	+	0.788236i
$827$	−8.48089	−	7.11631i	−0.294909	−	0.247458i	0.483312	−	0.875448i	$-0.339434\pi$
$827$	−8.48089	−	7.11631i	−0.294909	−	0.247458i	−0.778222	+	0.627990i	$0.783878\pi$
$828$	−4.20042	−	7.27535i	−0.145975	−	0.252836i
$829$	15.0282	−	26.0296i	0.521951	−	0.904045i	−0.477723	−	0.878510i	$-0.658538\pi$
$829$	15.0282	−	26.0296i	0.521951	−	0.904045i	0.999674	−	0.0255346i	$-0.00812880\pi$
$830$	−10.5071	+	3.82427i	−0.364707	+	0.132742i
$831$	1.13914	+	6.46041i	0.0395165	+	0.224109i
$832$	−0.562543	+	3.19034i	−0.0195027	+	0.110605i
$833$	71.8511	+	26.1517i	2.48949	+	0.906102i
$834$	14.1054	−	11.8358i	0.488430	−	0.409842i
$835$	−3.58051			−0.123909
$836$	−6.27251	−	8.07223i	−0.216939	−	0.279184i
$837$	2.15636			0.0745347
$838$	2.72891	−	2.28983i	0.0942687	−	0.0791008i
$839$	−33.3583	−	12.1414i	−1.15166	−	0.419169i	−0.305548	−	0.952177i	$-0.598840\pi$
$839$	−33.3583	−	12.1414i	−1.15166	−	0.419169i	−0.846111	+	0.533008i	$0.821062\pi$
$840$	0.714584	−	4.05261i	0.0246555	−	0.139828i
$841$	7.55945	+	42.8718i	0.260671	+	1.47834i
$842$	−8.03673	+	2.92513i	−0.276964	+	0.100807i
$843$	7.50038	−	12.9910i	0.258327	−	0.447435i
$844$	−9.21972	−	15.9690i	−0.317356	−	0.549677i
$845$	−1.91916	−	1.61036i	−0.0660210	−	0.0553982i
$846$	−0.984214	−	0.825853i	−0.0338380	−	0.0283934i
$847$	−11.3160	−	19.5999i	−0.388823	−	0.673462i
$848$	3.41935	−	5.92249i	0.117421	−	0.203379i
$849$	25.0246	−	9.10819i	0.858841	−	0.312592i
$850$	−1.33654	−	7.57991i	−0.0458430	−	0.259989i
$851$	4.63237	−	26.2715i	0.158796	−	0.900576i
$852$	6.62319	+	2.41064i	0.226907	+	0.0825873i
$853$	18.5821	−	15.5922i	0.636239	−	0.533868i	−0.266622	−	0.963801i	$-0.585907\pi$
$853$	18.5821	−	15.5922i	0.636239	−	0.533868i	0.902861	+	0.429933i	$0.141463\pi$
$854$	33.3905			1.14260
$855$	−4.26124	−	0.917504i	−0.145731	−	0.0313780i
$856$	−16.0778			−0.549528
$857$	26.0755	−	21.8800i	0.890723	−	0.747405i	−0.0776323	−	0.996982i	$-0.524736\pi$
$857$	26.0755	−	21.8800i	0.890723	−	0.747405i	0.968355	+	0.249577i	$0.0802916\pi$
$858$	−7.13943	−	2.59854i	−0.243736	−	0.0887127i
$859$	−0.747670	+	4.24025i	−0.0255102	+	0.144675i	−0.994903	−	0.100841i	$-0.967847\pi$
$859$	−0.747670	+	4.24025i	−0.0255102	+	0.144675i	0.969392	+	0.245517i	$0.0789576\pi$
$860$	0.378008	+	2.14379i	0.0128900	+	0.0731027i
$861$	−20.1191	+	7.32277i	−0.685659	+	0.249559i
$862$	4.40342	−	7.62695i	0.149981	−	0.259775i
$863$	−4.38980	−	7.60336i	−0.149431	−	0.258821i	0.781587	−	0.623797i	$-0.214411\pi$
$863$	−4.38980	−	7.60336i	−0.149431	−	0.258821i	−0.931017	+	0.364975i	$0.881077\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	2.19180	+	1.83914i	0.0745235	+	0.0625326i
$866$	16.9196	+	29.3057i	0.574953	+	0.995847i
$867$	21.1207	−	36.5820i	0.717295	−	1.24239i
$868$	−8.33854	+	3.03498i	−0.283028	+	0.103014i
$869$	3.25181	+	18.4419i	0.110310	+	0.625600i
$870$	−1.47890	+	8.38725i	−0.0501394	+	0.284354i
$871$	−12.9353	−	4.70808i	−0.438297	−	0.159527i
$872$	−7.88038	+	6.61242i	−0.266863	+	0.223925i
$873$	−14.8878			−0.503877
$874$	24.5742	−	27.1481i	0.831234	−	0.918298i
$875$	−4.11513			−0.139117
$876$	−0.731953	+	0.614182i	−0.0247304	+	0.0207513i
$877$	2.79731	+	1.01814i	0.0944585	+	0.0343801i	0.388817	−	0.921315i	$-0.372884\pi$
$877$	2.79731	+	1.01814i	0.0944585	+	0.0343801i	−0.294359	+	0.955695i	$0.595106\pi$
$878$	−3.14505	+	17.8365i	−0.106140	+	0.601951i
$879$	−2.20331	−	12.4956i	−0.0743160	−	0.421467i
$880$	−2.20383	+	0.802128i	−0.0742911	+	0.0270397i
$881$	−4.28217	+	7.41694i	−0.144270	+	0.249883i	−0.929100	−	0.369828i	$-0.879417\pi$
$881$	−4.28217	+	7.41694i	−0.144270	+	0.249883i	0.784830	+	0.619711i	$0.212750\pi$
$882$	−4.96713	−	8.60332i	−0.167252	−	0.289689i
$883$	−27.1991	−	22.8227i	−0.915322	−	0.768046i	0.0578020	−	0.998328i	$-0.481591\pi$
$883$	−27.1991	−	22.8227i	−0.915322	−	0.768046i	−0.973124	+	0.230282i	$0.926035\pi$
$884$	19.1008	+	16.0275i	0.642430	+	0.539062i
$885$	−4.28219	−	7.41697i	−0.143944	−	0.249319i
$886$	6.95499	−	12.0464i	0.233657	−	0.404706i
$887$	−19.0603	+	6.93739i	−0.639983	+	0.232935i	−0.641571	−	0.767064i	$-0.721717\pi$
$887$	−19.0603	+	6.93739i	−0.639983	+	0.232935i	0.00158744	+	0.999999i	$0.499495\pi$
$888$	−0.551418	−	3.12725i	−0.0185044	−	0.104943i
$889$	6.25968	−	35.5004i	0.209943	−	1.19065i
$890$	3.28340	+	1.19506i	0.110060	+	0.0400585i
$891$	1.79658	−	1.50751i	0.0601876	−	0.0505034i
$892$	−21.6581			−0.725168
$893$	2.11160	−	5.18697i	0.0706619	−	0.173575i
$894$	−4.05100			−0.135486
$895$	−1.28862	+	1.08128i	−0.0430739	+	0.0361433i
$896$	3.86695	+	1.40746i	0.129186	+	0.0470198i
$897$	4.72584	−	26.8015i	0.157791	−	0.894878i
$898$	1.12834	+	6.39911i	0.0376531	+	0.213541i
$899$	17.2574	−	6.28118i	0.575566	−	0.209489i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−26.3182	−	45.5844i	−0.876785	−	1.51864i
$902$	9.34731	+	7.84333i	0.311232	+	0.261154i
$903$	6.86227	+	5.75813i	0.228362	+	0.191619i
$904$	−5.41081	−	9.37179i	−0.179961	−	0.311701i
$905$	9.83632	−	17.0370i	0.326970	−	0.566329i
$906$	−15.7453	+	5.73081i	−0.523102	+	0.190393i
$907$	5.03043	+	28.5290i	0.167033	+	0.947289i	0.946944	+	0.321399i	$0.104153\pi$
$907$	5.03043	+	28.5290i	0.167033	+	0.947289i	−0.779911	+	0.625890i	$0.784736\pi$
$908$	1.13610	−	6.44312i	0.0377027	−	0.213822i
$909$	−13.0604	−	4.75359i	−0.433186	−	0.157667i
$910$	10.2123	−	8.56912i	0.338534	−	0.284063i
$911$	−30.1027			−0.997348			−0.498674	−	0.866790i	$-0.666179\pi$
$911$	−30.1027			−0.997348			−0.498674	+	0.866790i	$0.666179\pi$
$912$	1.64352	−	4.03718i	0.0544225	−	0.133684i
$913$	26.2234			0.867868
$914$	−18.5033	+	15.5261i	−0.612036	+	0.513559i
$915$	−7.62476	−	2.77519i	−0.252067	−	0.0917448i
$916$	−2.95682	+	16.7689i	−0.0976960	+	0.554061i
$917$	13.9676	+	79.2139i	0.461249	+	2.61588i
$918$	−7.23266	+	2.63247i	−0.238713	+	0.0868846i
$919$	9.46881	−	16.4005i	0.312347	−	0.541001i	−0.666523	−	0.745485i	$-0.732218\pi$
$919$	9.46881	−	16.4005i	0.312347	−	0.541001i	0.978870	+	0.204483i	$0.0655514\pi$
$920$	−4.20042	−	7.27535i	−0.138484	−	0.239861i
$921$	11.8254	+	9.92265i	0.389659	+	0.326963i
$922$	20.1607	+	16.9168i	0.663956	+	0.557125i
$923$	11.4166	+	19.7741i	0.375782	+	0.650873i
$924$	−4.82553	+	8.35807i	−0.158748	+	0.274960i
$925$	−2.98398	+	1.08608i	−0.0981128	+	0.0357101i
$926$	1.61812	+	9.17680i	0.0531747	+	0.301568i
$927$	−1.90257	+	10.7900i	−0.0624884	+	0.354390i
$928$	−8.00302	−	2.91286i	−0.262712	−	0.0956194i
$929$	12.6541	−	10.6181i	0.415169	−	0.348368i	−0.411153	−	0.911566i	$-0.634874\pi$
$929$	12.6541	−	10.6181i	0.415169	−	0.348368i	0.826322	+	0.563198i	$0.190429\pi$
$930$	2.15636			0.0707098
$931$	29.0597	−	32.1035i	0.952394	−	1.05215i
$932$	28.8881			0.946262
$933$	25.4665	−	21.3690i	0.833737	−	0.699588i
$934$	−4.64029	−	1.68893i	−0.151835	−	0.0552634i
$935$	−3.13455	+	17.7769i	−0.102511	+	0.581367i
$936$	−0.562543	−	3.19034i	−0.0183873	−	0.104280i
$937$	−24.8119	+	9.03080i	−0.810570	+	0.295023i	−0.713859	−	0.700289i	$-0.753054\pi$
$937$	−24.8119	+	9.03080i	−0.810570	+	0.295023i	−0.0967106	+	0.995313i	$0.530832\pi$
$938$	−8.74299	+	15.1433i	−0.285469	+	0.494446i
$939$	2.64930	+	4.58873i	0.0864567	+	0.149747i
$940$	−0.984214	−	0.825853i	−0.0321015	−	0.0269364i
$941$	19.6695	+	16.5046i	0.641206	+	0.538036i	0.904388	−	0.426710i	$-0.140328\pi$
$941$	19.6695	+	16.5046i	0.641206	+	0.538036i	−0.263182	+	0.964746i	$0.584772\pi$
$942$	−2.06832	−	3.58243i	−0.0673894	−	0.116722i
$943$	−21.8541	+	37.8525i	−0.711669	+	1.23265i
$944$	8.04788	−	2.92919i	0.261936	−	0.0953370i
$945$	0.714584	+	4.05261i	0.0232454	+	0.131831i
$946$	0.886530	−	5.02776i	0.0288236	−	0.163467i
$947$	−1.72989	−	0.629628i	−0.0562138	−	0.0204602i	0.313760	−	0.949502i	$-0.398411\pi$
$947$	−1.72989	−	0.629628i	−0.0562138	−	0.0204602i	−0.369974	+	0.929042i	$0.620633\pi$
$948$	−6.11670	+	5.13252i	−0.198661	+	0.166696i
$949$	−3.09539			−0.100480
$950$	−4.26124	−	0.917504i	−0.138253	−	0.0297678i
$951$	19.6378			0.636798
$952$	24.2633	−	20.3593i	0.786377	−	0.659849i
$953$	−12.7199	−	4.62967i	−0.412038	−	0.149970i	0.127680	−	0.991815i	$-0.459247\pi$
$953$	−12.7199	−	4.62967i	−0.412038	−	0.149970i	−0.539718	+	0.841846i	$0.681469\pi$
$954$	−1.18753	+	6.73480i	−0.0384476	+	0.218047i
$955$	−0.225123	−	1.27674i	−0.00728482	−	0.0413143i
$956$	9.02868	−	3.28617i	0.292008	−	0.106282i
$957$	9.98689	−	17.2978i	0.322830	−	0.559159i
$958$	10.6696	+	18.4802i	0.344718	+	0.597069i
$959$	−29.8244	−	25.0256i	−0.963079	−	0.808119i
$960$	−0.766044	−	0.642788i	−0.0247240	−	0.0207459i
$961$	13.1751	+	22.8199i	0.425002	+	0.736125i
$962$	5.14359	−	8.90895i	0.165836	−	0.287236i
$963$	15.1082	−	5.49893i	0.486855	−	0.177201i
$964$	2.27765	+	12.9172i	0.0733583	+	0.416036i
$965$	−2.67271	+	15.1577i	−0.0860375	+	0.487943i
$966$	−32.4857	−	11.8238i	−1.04521	−	0.380425i
$967$	3.14414	−	2.63824i	0.101109	−	0.0848402i	−0.590832	−	0.806795i	$-0.701200\pi$
$967$	3.14414	−	2.63824i	0.101109	−	0.0848402i	0.691941	+	0.721954i	$0.256756\pi$
$968$	−5.49973			−0.176768
$969$	−20.5855	−	26.4919i	−0.661302	−	0.851043i
$970$	−14.8878			−0.478019
$971$	−13.0105	+	10.9171i	−0.417526	+	0.350346i	−0.827221	−	0.561876i	$-0.810080\pi$
$971$	−13.0105	+	10.9171i	−0.417526	+	0.350346i	0.409695	+	0.912223i	$0.365635\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	13.1579	−	74.6219i	0.421821	−	2.39227i
$974$	0.598871	+	3.39636i	0.0191891	+	0.108827i
$975$	−3.04419	+	1.10799i	−0.0974920	+	0.0354842i
$976$	4.05705	−	7.02702i	0.129863	−	0.224929i
$977$	−8.77155	−	15.1928i	−0.280627	−	0.486060i	0.690912	−	0.722938i	$-0.257209\pi$
$977$	−8.77155	−	15.1928i	−0.280627	−	0.486060i	−0.971539	+	0.236878i	$0.923876\pi$
$978$	14.3203	+	12.0161i	0.457912	+	0.384234i
$979$	−6.27746	−	5.26741i	−0.200628	−	0.168347i
$980$	−4.96713	−	8.60332i	−0.158669	−	0.274823i
$981$	5.14355	−	8.90889i	0.164221	−	0.284439i
$982$	−34.9650	+	12.7262i	−1.11578	+	0.406109i
$983$	−6.43358	−	36.4867i	−0.205199	−	1.16374i	−0.897126	−	0.441776i	$-0.854349\pi$
$983$	−6.43358	−	36.4867i	−0.205199	−	1.16374i	0.691926	−	0.721968i	$-0.256762\pi$
$984$	−0.903464	+	5.12380i	−0.0288014	+	0.163341i
$985$	11.2024	+	4.07734i	0.356938	+	0.129915i
$986$	−50.2151	+	42.1355i	−1.59918	+	1.34187i
$987$	−5.28711			−0.168291
$988$	12.4854	−	6.59646i	0.397215	−	0.209861i
$989$	18.2875			0.581508
$990$	1.79658	−	1.50751i	0.0570990	−	0.0479118i
$991$	10.2810	+	3.74197i	0.326586	+	0.118868i	0.500110	−	0.865962i	$-0.333293\pi$
$991$	10.2810	+	3.74197i	0.326586	+	0.118868i	−0.173524	+	0.984830i	$0.555515\pi$
$992$	−0.374448	+	2.12360i	−0.0118887	+	0.0674243i
$993$	0.842661	+	4.77897i	0.0267410	+	0.151656i
$994$	27.2552	−	9.92010i	0.864484	−	0.314646i
$995$	1.70642	−	2.95560i	0.0540971	−	0.0936989i
$996$	5.59071	+	9.68340i	0.177148	+	0.306830i
$997$	34.3465	+	28.8201i	1.08776	+	0.912743i	0.996542	−	0.0830880i	$-0.0264783\pi$
$997$	34.3465	+	28.8201i	1.08776	+	0.912743i	0.0912220	+	0.995831i	$0.470923\pi$
$998$	16.3926	+	13.7550i	0.518899	+	0.435408i
$999$	1.58774	+	2.75005i	0.0502340	+	0.0870078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.j.481.2	yes	12
19.16	even	9	inner	570.2.u.j.301.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.j.301.2	✓	12	19.16	even	9	inner
570.2.u.j.481.2	yes	12	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(2.05756 - 3.56380i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(2.05756 - 3.56380i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(-1.17263 - 2.03106i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.04419 - 1.10799i) q^{13} +(-0.714584 - 4.05261i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-5.89612 + 4.94743i) q^{17} +1.00000 q^{18} +(1.33604 + 4.14910i) q^{19} +1.00000 q^{20} +(3.15237 - 2.64515i) q^{21} +(-2.20383 - 0.802128i) q^{22} +(1.45879 - 8.27322i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.61978 - 2.80554i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-3.15237 - 2.64515i) q^{28} +(6.52412 + 5.47439i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.07818 - 1.86746i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.407251 - 2.30964i) q^{33} +(-1.33654 + 7.57991i) q^{34} +(3.86695 + 1.40746i) q^{35} +(0.766044 - 0.642788i) q^{36} +3.17549 q^{37} +(3.69045 + 2.31960i) q^{38} +3.23956 q^{39} +(0.766044 - 0.642788i) q^{40} +(-4.88907 - 1.77948i) q^{41} +(0.714584 - 4.05261i) q^{42} +(0.378008 + 2.14379i) q^{43} +(-2.20383 + 0.802128i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.20042 - 7.27535i) q^{46} +(-0.984214 - 0.825853i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-4.96713 - 8.60332i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-7.23266 + 2.63247i) q^{51} +(-0.562543 - 3.19034i) q^{52} +(-1.18753 + 6.73480i) q^{53} +(0.939693 + 0.342020i) q^{54} +(1.79658 - 1.50751i) q^{55} -4.11513 q^{56} +(-0.163608 + 4.35583i) q^{57} +8.51664 q^{58} +(-6.56069 + 5.50507i) q^{59} +(0.939693 + 0.342020i) q^{60} +(-1.40900 + 7.99083i) q^{61} +(-0.374448 - 2.12360i) q^{62} +(3.86695 - 1.40746i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.61978 + 2.80554i) q^{65} +(-1.79658 - 1.50751i) q^{66} +(-3.25507 - 2.73133i) q^{67} +(3.84842 + 6.66566i) q^{68} +(4.20042 - 7.27535i) q^{69} +(3.86695 - 1.40746i) q^{70} +(1.22392 + 6.94117i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-0.897874 - 0.326799i) q^{73} +(2.43257 - 2.04116i) q^{74} -1.00000 q^{75} +(4.31806 - 0.595259i) q^{76} -9.65107 q^{77} +(2.48164 - 2.08235i) q^{78} +(-7.50324 - 2.73096i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-4.88907 + 1.77948i) q^{82} +(-5.59071 + 9.68340i) q^{83} +(-2.05756 - 3.56380i) q^{84} +(-5.89612 - 4.94743i) q^{85} +(1.66757 + 1.39926i) q^{86} +(4.25832 + 7.37563i) q^{87} +(-1.17263 + 2.03106i) q^{88} +(3.28340 - 1.19506i) q^{89} +(0.173648 + 0.984808i) q^{90} +(2.31493 - 13.1286i) q^{91} +(-7.89421 - 2.87326i) q^{92} +(1.65187 - 1.38608i) q^{93} -1.28480 q^{94} +(-3.85406 + 2.03622i) q^{95} -1.00000 q^{96} +(-11.4047 + 9.56971i) q^{97} +(-9.33515 - 3.39772i) q^{98} +(0.407251 - 2.30964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^7 - 6 * q^8	\( 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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