LMFDB - Embedded newform 231.2.y.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	231.16
Dual form			231.2.y.b.130.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21132 - 0.257474i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.426088 - 0.189706i) q^{4} +(0.0859924 + 0.0955042i) q^{5} +(0.382681 - 1.17777i) q^{6} +(-1.04835 - 2.42919i) q^{7} +(2.47103 + 1.79531i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-1.21132 - 0.257474i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.426088 - 0.189706i) q^{4} +(0.0859924 + 0.0955042i) q^{5} +(0.382681 - 1.17777i) q^{6} +(-1.04835 - 2.42919i) q^{7} +(2.47103 + 1.79531i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.0795744 - 0.137827i) q^{10} +(2.89856 - 1.61194i) q^{11} +(0.233206 - 0.403924i) q^{12} +(-0.694735 - 2.13817i) q^{13} +(0.644429 + 3.21245i) q^{14} +(-0.103970 + 0.0755384i) q^{15} +(-1.90678 - 2.11769i) q^{16} +(6.67323 - 1.41844i) q^{17} +(1.13132 + 0.503695i) q^{18} +(1.89512 - 0.843760i) q^{19} +(-0.0185225 - 0.0570065i) q^{20} +(2.52547 - 0.788684i) q^{21} +(-3.92611 + 1.20628i) q^{22} +(0.417771 - 0.723600i) q^{23} +(-2.04376 + 2.26983i) q^{24} +(0.520916 - 4.95618i) q^{25} +(0.291022 + 2.76889i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0141459 + 1.23393i) q^{28} +(-0.837155 + 0.608228i) q^{29} +(0.145390 - 0.0647317i) q^{30} +(0.374374 - 0.415785i) q^{31} +(-1.28989 - 2.23415i) q^{32} +(1.30013 + 3.05117i) q^{33} -8.44863 q^{34} +(0.141848 - 0.309013i) q^{35} +(0.377334 + 0.274150i) q^{36} +(-0.480555 - 4.57217i) q^{37} +(-2.51284 + 0.534120i) q^{38} +(2.19908 - 0.467429i) q^{39} +(0.0410302 + 0.390376i) q^{40} +(2.93095 + 2.12946i) q^{41} +(-3.26221 + 0.305106i) q^{42} -0.314251 q^{43} +(-1.54084 + 0.136954i) q^{44} +(-0.0642568 - 0.111296i) q^{45} +(-0.692362 + 0.768946i) q^{46} +(-10.0066 + 4.45521i) q^{47} +(2.30541 - 1.67498i) q^{48} +(-4.80194 + 5.09327i) q^{49} +(-1.90708 + 5.86940i) q^{50} +(0.713126 + 6.78494i) q^{51} +(-0.109607 + 1.04285i) q^{52} +(-2.31197 + 2.56770i) q^{53} +(-0.619191 + 1.07247i) q^{54} +(0.403201 + 0.138210i) q^{55} +(1.77065 - 7.88470i) q^{56} +(0.641044 + 1.97293i) q^{57} +(1.17067 - 0.521214i) q^{58} +(1.86011 + 0.828173i) q^{59} +(0.0586303 - 0.0124623i) q^{60} +(7.90746 + 8.78212i) q^{61} +(-0.560541 + 0.407257i) q^{62} +(0.520380 + 2.59407i) q^{63} +(2.74840 + 8.45872i) q^{64} +(0.144463 - 0.250217i) q^{65} +(-0.789278 - 4.03070i) q^{66} +(-7.21817 - 12.5022i) q^{67} +(-3.11247 - 0.661576i) q^{68} +(0.675967 + 0.491119i) q^{69} +(-0.251386 + 0.337792i) q^{70} +(-3.35771 + 10.3340i) q^{71} +(-2.04376 - 2.26983i) q^{72} +(10.3927 + 4.62711i) q^{73} +(-0.595110 + 5.66209i) q^{74} +(4.87458 + 1.03612i) q^{75} -0.967552 q^{76} +(-6.95441 - 5.35128i) q^{77} -2.78414 q^{78} +(-12.7774 - 2.71591i) q^{79} +(0.0382801 - 0.364211i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-3.00204 - 3.33410i) q^{82} +(3.48792 - 10.7347i) q^{83} +(-1.22569 - 0.143049i) q^{84} +(0.709314 + 0.515347i) q^{85} +(0.380658 + 0.0809114i) q^{86} +(-0.517390 - 0.896146i) q^{87} +(10.0563 + 1.22064i) q^{88} +(3.74598 - 6.48822i) q^{89} +(0.0491797 + 0.151360i) q^{90} +(-4.46571 + 3.92919i) q^{91} +(-0.315278 + 0.229063i) q^{92} +(0.374374 + 0.415785i) q^{93} +(13.2683 - 2.82026i) q^{94} +(0.243548 + 0.108435i) q^{95} +(2.35674 - 1.04929i) q^{96} +(2.42659 + 7.46829i) q^{97} +(7.12807 - 4.93320i) q^{98} +(-3.17036 + 0.974075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.21132	−	0.257474i	−0.856533	−	0.182062i	−0.241342	−	0.970440i	$-0.577588\pi$
$2$	−1.21132	−	0.257474i	−0.856533	−	0.182062i	−0.615191	+	0.788378i	$0.710921\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	−0.426088	−	0.189706i	−0.213044	−	0.0948532i
$5$	0.0859924	+	0.0955042i	0.0384570	+	0.0427108i	0.762066	−	0.647499i	$-0.224185\pi$
$5$	0.0859924	+	0.0955042i	0.0384570	+	0.0427108i	−0.723609	+	0.690210i	$0.757518\pi$
$6$	0.382681	−	1.17777i	0.156229	−	0.480823i
$7$	−1.04835	−	2.42919i	−0.396238	−	0.918148i
$7$	−1.04835	−	2.42919i	−0.396238	−	0.918148i
$8$	2.47103	+	1.79531i	0.873640	+	0.634737i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−0.0795744	−	0.137827i	−0.0251636	−	0.0435847i
$11$	2.89856	−	1.61194i	0.873948	−	0.486019i
$11$	2.89856	−	1.61194i	0.873948	−	0.486019i
$12$	0.233206	−	0.403924i	0.0673206	−	0.116603i
$13$	−0.694735	−	2.13817i	−0.192685	−	0.593023i	−0.999996	−	0.00289665i	$-0.999078\pi$
$13$	−0.694735	−	2.13817i	−0.192685	−	0.593023i	0.807311	−	0.590126i	$-0.200922\pi$
$14$	0.644429	+	3.21245i	0.172231	+	0.858563i
$15$	−0.103970	+	0.0755384i	−0.0268449	+	0.0195039i
$16$	−1.90678	−	2.11769i	−0.476695	−	0.529424i
$17$	6.67323	−	1.41844i	1.61850	−	0.344022i	0.692460	−	0.721456i	$-0.256527\pi$
$17$	6.67323	−	1.41844i	1.61850	−	0.344022i	0.926036	+	0.377434i	$0.123194\pi$
$18$	1.13132	+	0.503695i	0.266654	+	0.118722i
$19$	1.89512	−	0.843760i	0.434769	−	0.193572i	−0.177669	−	0.984090i	$-0.556856\pi$
$19$	1.89512	−	0.843760i	0.434769	−	0.193572i	0.612438	+	0.790519i	$0.290189\pi$
$20$	−0.0185225	−	0.0570065i	−0.00414176	−	0.0127470i
$21$	2.52547	−	0.788684i	0.551102	−	0.172105i
$22$	−3.92611	+	1.20628i	−0.837050	+	0.257179i
$23$	0.417771	−	0.723600i	0.0871112	−	0.150881i	−0.819178	−	0.573540i	$-0.805570\pi$
$23$	0.417771	−	0.723600i	0.0871112	−	0.150881i	0.906289	+	0.422659i	$0.138903\pi$
$24$	−2.04376	+	2.26983i	−0.417182	+	0.463327i
$25$	0.520916	−	4.95618i	0.104183	−	0.991237i
$26$	0.291022	+	2.76889i	0.0570741	+	0.543024i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.0141459	+	1.23393i	−0.00267332	+	0.233190i
$29$	−0.837155	+	0.608228i	−0.155456	+	0.112945i	−0.662794	−	0.748802i	$-0.730629\pi$
$29$	−0.837155	+	0.608228i	−0.155456	+	0.112945i	0.507338	+	0.861747i	$0.330629\pi$
$30$	0.145390	−	0.0647317i	0.0265444	−	0.0118183i
$31$	0.374374	−	0.415785i	0.0672396	−	0.0746771i	−0.708586	−	0.705624i	$-0.750667\pi$
$31$	0.374374	−	0.415785i	0.0672396	−	0.0746771i	0.775826	+	0.630947i	$0.217333\pi$
$32$	−1.28989	−	2.23415i	−0.228022	−	0.394946i
$33$	1.30013	+	3.05117i	0.226324	+	0.531141i
$34$	−8.44863			−1.44893
$35$	0.141848	−	0.309013i	0.0239767	−	0.0522328i
$36$	0.377334	+	0.274150i	0.0628891	+	0.0456916i
$37$	−0.480555	−	4.57217i	−0.0790027	−	0.751661i	−0.960276	−	0.279053i	$-0.909979\pi$
$37$	−0.480555	−	4.57217i	−0.0790027	−	0.751661i	0.881273	−	0.472608i	$-0.156687\pi$
$38$	−2.51284	+	0.534120i	−0.407636	+	0.0866458i
$39$	2.19908	−	0.467429i	0.352135	−	0.0748486i
$40$	0.0410302	+	0.390376i	0.00648744	+	0.0617239i
$41$	2.93095	+	2.12946i	0.457737	+	0.332566i	0.792643	−	0.609686i	$-0.208704\pi$
$41$	2.93095	+	2.12946i	0.457737	+	0.332566i	−0.334906	+	0.942252i	$0.608704\pi$
$42$	−3.26221	+	0.305106i	−0.503370	+	0.0470789i
$43$	−0.314251			−0.0479228			−0.0239614	−	0.999713i	$-0.507628\pi$
$43$	−0.314251			−0.0479228			−0.0239614	+	0.999713i	$0.507628\pi$
$44$	−1.54084	+	0.136954i	−0.232290	+	0.0206467i
$45$	−0.0642568	−	0.111296i	−0.00957884	−	0.0165910i
$46$	−0.692362	+	0.768946i	−0.102083	+	0.113375i
$47$	−10.0066	+	4.45521i	−1.45961	+	0.649860i	−0.974458	−	0.224571i	$-0.927902\pi$
$47$	−10.0066	+	4.45521i	−1.45961	+	0.649860i	−0.485151	+	0.874431i	$0.661235\pi$
$48$	2.30541	−	1.67498i	0.332757	−	0.241762i
$49$	−4.80194	+	5.09327i	−0.685991	+	0.727610i
$50$	−1.90708	+	5.86940i	−0.269702	+	0.830059i
$51$	0.713126	+	6.78494i	0.0998576	+	0.950082i
$52$	−0.109607	+	1.04285i	−0.0151998	+	0.144617i
$53$	−2.31197	+	2.56770i	−0.317574	+	0.352701i	−0.880704	−	0.473667i	$-0.842930\pi$
$53$	−2.31197	+	2.56770i	−0.317574	+	0.352701i	0.563130	+	0.826368i	$0.309597\pi$
$54$	−0.619191	+	1.07247i	−0.0842612	+	0.145945i
$55$	0.403201	+	0.138210i	0.0543677	+	0.0186362i
$56$	1.77065	−	7.88470i	0.236613	−	1.05364i
$57$	0.641044	+	1.97293i	0.0849084	+	0.261321i
$58$	1.17067	−	0.521214i	0.153716	−	0.0684387i
$59$	1.86011	+	0.828173i	0.242165	+	0.107819i	0.524231	−	0.851576i	$-0.324353\pi$
$59$	1.86011	+	0.828173i	0.242165	+	0.107819i	−0.282066	+	0.959395i	$0.591020\pi$
$60$	0.0586303	−	0.0124623i	0.00756914	−	0.00160887i
$61$	7.90746	+	8.78212i	1.01245	+	1.12444i	0.992202	+	0.124640i	$0.0397776\pi$
$61$	7.90746	+	8.78212i	1.01245	+	1.12444i	0.0202439	+	0.999795i	$0.493556\pi$
$62$	−0.560541	+	0.407257i	−0.0711887	+	0.0517216i
$63$	0.520380	+	2.59407i	0.0655617	+	0.326822i
$64$	2.74840	+	8.45872i	0.343551	+	1.05734i
$65$	0.144463	−	0.250217i	0.0179184	−	0.0310356i
$66$	−0.789278	−	4.03070i	−0.0971534	−	0.496145i
$67$	−7.21817	−	12.5022i	−0.881840	−	1.52739i	−0.849293	−	0.527921i	$-0.822972\pi$
$67$	−7.21817	−	12.5022i	−0.881840	−	1.52739i	−0.0325467	−	0.999470i	$-0.510362\pi$
$68$	−3.11247	−	0.661576i	−0.377442	−	0.0802278i
$69$	0.675967	+	0.491119i	0.0813769	+	0.0591237i
$70$	−0.251386	+	0.337792i	−0.0300464	+	0.0403739i
$71$	−3.35771	+	10.3340i	−0.398486	+	1.22642i	0.527726	+	0.849414i	$0.323045\pi$
$71$	−3.35771	+	10.3340i	−0.398486	+	1.22642i	−0.926213	+	0.377001i	$0.876955\pi$
$72$	−2.04376	−	2.26983i	−0.240860	−	0.267502i
$73$	10.3927	+	4.62711i	1.21637	+	0.541562i	0.911684	−	0.410892i	$-0.134783\pi$
$73$	10.3927	+	4.62711i	1.21637	+	0.541562i	0.304684	+	0.952454i	$0.401449\pi$
$74$	−0.595110	+	5.66209i	−0.0691801	+	0.658205i
$75$	4.87458	+	1.03612i	0.562868	+	0.119641i
$76$	−0.967552			−0.110986
$77$	−6.95441	−	5.35128i	−0.792529	−	0.609834i
$78$	−2.78414			−0.315242
$79$	−12.7774	−	2.71591i	−1.43757	−	0.305564i	−0.577769	−	0.816201i	$-0.696076\pi$
$79$	−12.7774	−	2.71591i	−1.43757	−	0.305564i	−0.859797	+	0.510637i	$0.829410\pi$
$80$	0.0382801	−	0.364211i	0.00427985	−	0.0407200i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−3.00204	−	3.33410i	−0.331520	−	0.368190i
$83$	3.48792	−	10.7347i	0.382849	−	1.17829i	−0.555179	−	0.831731i	$-0.687350\pi$
$83$	3.48792	−	10.7347i	0.382849	−	1.17829i	0.938028	−	0.346558i	$-0.112650\pi$
$84$	−1.22569	−	0.143049i	−0.133734	−	0.0156079i
$85$	0.709314	+	0.515347i	0.0769359	+	0.0558972i
$86$	0.380658	+	0.0809114i	0.0410474	+	0.00872490i
$87$	−0.517390	−	0.896146i	−0.0554700	−	0.0960769i
$88$	10.0563	+	1.22064i	1.07201	+	0.130121i
$89$	3.74598	−	6.48822i	0.397073	−	0.687750i	−0.596291	−	0.802769i	$-0.703359\pi$
$89$	3.74598	−	6.48822i	0.397073	−	0.687750i	0.993363	+	0.115019i	$0.0366927\pi$
$90$	0.0491797	+	0.151360i	0.00518400	+	0.0159547i
$91$	−4.46571	+	3.92919i	−0.468134	+	0.411891i
$92$	−0.315278	+	0.229063i	−0.0328700	+	0.0238815i
$93$	0.374374	+	0.415785i	0.0388208	+	0.0431149i
$94$	13.2683	−	2.82026i	1.36852	−	0.290887i
$95$	0.243548	+	0.108435i	0.0249875	+	0.0111252i
$96$	2.35674	−	1.04929i	0.240534	−	0.107093i
$97$	2.42659	+	7.46829i	0.246383	+	0.758290i	0.995406	+	0.0957453i	$0.0305234\pi$
$97$	2.42659	+	7.46829i	0.246383	+	0.758290i	−0.749023	+	0.662544i	$0.769477\pi$
$98$	7.12807	−	4.93320i	0.720044	−	0.498329i
$99$	−3.17036	+	0.974075i	−0.318633	+	0.0978982i
$100$	−1.16218	+	2.01295i	−0.116218	+	0.201295i
$101$	6.44951	−	7.16290i	0.641750	−	0.712735i	−0.331250	−	0.943543i	$-0.607470\pi$
$101$	6.44951	−	7.16290i	0.641750	−	0.712735i	0.972999	+	0.230808i	$0.0741369\pi$
$102$	0.883122	−	8.40235i	0.0874421	−	0.831956i
$103$	−0.996707	−	9.48304i	−0.0982085	−	0.934391i	−0.927058	−	0.374919i	$-0.877670\pi$
$103$	−0.996707	−	9.48304i	−0.0982085	−	0.934391i	0.828849	−	0.559472i	$-0.188996\pi$
$104$	2.12197	−	6.53075i	0.208076	−	0.640393i
$105$	0.292493	+	0.173372i	0.0285444	+	0.0169194i
$106$	3.46166	−	2.51504i	0.336226	−	0.244282i
$107$	−1.48050	+	0.659163i	−0.143126	+	0.0637237i	−0.477050	−	0.878876i	$-0.658294\pi$
$107$	−1.48050	+	0.659163i	−0.143126	+	0.0637237i	0.333924	+	0.942600i	$0.391627\pi$
$108$	−0.312090	+	0.346611i	−0.0300309	+	0.0333527i
$109$	4.70168	+	8.14354i	0.450339	+	0.780010i	0.998407	−	0.0564239i	$-0.0179698\pi$
$109$	4.70168	+	8.14354i	0.450339	+	0.780010i	−0.548068	+	0.836434i	$0.684636\pi$
$110$	−0.452820	−	0.271230i	−0.0431747	−	0.0258608i
$111$	4.59736			0.436362
$112$	−3.14532	+	6.85201i	−0.297205	+	0.647454i
$113$	5.45197	+	3.96109i	0.512878	+	0.372628i	0.813914	−	0.580985i	$-0.197332\pi$
$113$	5.45197	+	3.96109i	0.512878	+	0.372628i	−0.301036	+	0.953613i	$0.597332\pi$
$114$	−0.268531	−	2.55490i	−0.0251502	−	0.239289i
$115$	0.105032	−	0.0223252i	0.00979428	−	0.00208184i
$116$	0.472086	−	0.100345i	0.0438321	−	0.00931680i
$117$	0.235002	+	2.23589i	0.0217259	+	0.206708i
$118$	−2.03995	−	1.48211i	−0.187793	−	0.136439i
$119$	−10.4415	−	14.7235i	−0.957172	−	1.34970i
$120$	−0.392527			−0.0358326
$121$	5.80327	−	9.34463i	0.527570	−	0.849511i
$122$	−7.31729	−	12.6739i	−0.662476	−	1.14744i
$123$	−2.42416	+	2.69230i	−0.218579	+	0.242757i
$124$	−0.238393	+	0.106139i	−0.0214083	+	0.00953161i
$125$	1.03798	−	0.754136i	0.0928397	−	0.0674520i
$126$	0.0375591	−	3.27623i	0.00334603	−	0.291870i
$127$	3.06248	−	9.42535i	0.271751	−	0.836365i	−0.718309	−	0.695724i	$-0.755084\pi$
$127$	3.06248	−	9.42535i	0.271751	−	0.836365i	0.990061	−	0.140641i	$-0.0449163\pi$
$128$	−0.611977	−	5.82257i	−0.0540916	−	0.514648i
$129$	0.0328481	−	0.312529i	0.00289212	−	0.0275167i
$130$	−0.239415	+	0.265897i	−0.0209981	+	0.0233207i
$131$	−1.75970	+	3.04790i	−0.153746	+	0.266296i	−0.932602	−	0.360907i	$-0.882467\pi$
$131$	−1.75970	+	3.04790i	−0.153746	+	0.266296i	0.778856	+	0.627203i	$0.215800\pi$
$132$	0.0248570	−	1.54671i	0.00216353	−	0.134624i
$133$	−4.03639	−	3.71905i	−0.350000	−	0.322482i
$134$	5.52451	+	17.0027i	0.477245	+	1.46881i
$135$	0.117403	−	0.0522712i	0.0101044	−	0.00449879i
$136$	19.0363	+	8.47550i	1.63235	+	0.726768i
$137$	−8.50359	+	1.80749i	−0.726511	+	0.154425i	−0.556298	−	0.830983i	$-0.687779\pi$
$137$	−8.50359	+	1.80749i	−0.726511	+	0.154425i	−0.170213	+	0.985407i	$0.554445\pi$
$138$	−0.692362	−	0.768946i	−0.0589378	−	0.0654570i
$139$	11.3914	−	8.27636i	0.966209	−	0.701992i	0.0116243	−	0.999932i	$-0.496300\pi$
$139$	11.3914	−	8.27636i	0.966209	−	0.701992i	0.954584	+	0.297941i	$0.0962998\pi$
$140$	−0.119062	+	0.104757i	−0.0100625	+	0.00885361i
$141$	−3.38483	−	10.4175i	−0.285055	−	0.877308i
$142$	6.72798	−	11.6532i	0.564600	−	0.977916i
$143$	−5.46035	−	5.07775i	−0.456617	−	0.424623i
$144$	1.42482	+	2.46786i	0.118735	+	0.205655i
$145$	−0.130077	−	0.0276488i	−0.0108023	−	0.00229611i
$146$	−11.3975	−	8.28075i	−0.943261	−	0.685319i
$147$	−4.56343	−	5.30803i	−0.376385	−	0.437799i
$148$	−0.662612	+	2.03931i	−0.0544664	+	0.167630i
$149$	10.8703	+	12.0727i	0.890529	+	0.989033i	0.999988	−	0.00495830i	$-0.00157828\pi$
$149$	10.8703	+	12.0727i	0.890529	+	0.989033i	−0.109458	+	0.993991i	$0.534912\pi$
$150$	−5.63790	−	2.51016i	−0.460333	−	0.204953i
$151$	−2.37224	+	22.5703i	−0.193050	+	1.83675i	0.285134	+	0.958488i	$0.407962\pi$
$151$	−2.37224	+	22.5703i	−0.193050	+	1.83675i	−0.478184	+	0.878260i	$0.658705\pi$
$152$	6.19769	+	1.31736i	0.502699	+	0.106852i
$153$	−6.82232			−0.551552
$154$	7.04620	+	8.27269i	0.567799	+	0.666632i
$155$	0.0719025			0.00577535
$156$	−1.02568	−	0.218014i	−0.0821198	−	0.0174551i
$157$	0.253402	−	2.41096i	0.0202237	−	0.192415i	−0.979746	−	0.200246i	$-0.935826\pi$
$157$	0.253402	−	2.41096i	0.0202237	−	0.192415i	0.999969	+	0.00783061i	$0.00249259\pi$
$158$	14.7782	+	6.57968i	1.17569	+	0.523451i
$159$	−2.31197	−	2.56770i	−0.183351	−	0.203632i
$160$	0.102450	−	0.315310i	0.00809941	−	0.0249274i
$161$	−2.19573	−	0.256261i	−0.173048	−	0.0201962i
$162$	−1.00187	−	0.727902i	−0.0787145	−	0.0571894i
$163$	−11.9710	−	2.54451i	−0.937641	−	0.199302i	−0.286346	−	0.958126i	$-0.592441\pi$
$163$	−11.9710	−	2.54451i	−0.937641	−	0.199302i	−0.651295	+	0.758825i	$0.725774\pi$
$164$	−0.844869	−	1.46336i	−0.0659732	−	0.114269i
$165$	−0.179598	+	0.386546i	−0.0139817	+	0.0300925i
$166$	−6.98890	+	12.1051i	−0.542444	+	0.939541i
$167$	7.39720	+	22.7662i	0.572412	+	1.76170i	0.644826	+	0.764329i	$0.276930\pi$
$167$	7.39720	+	22.7662i	0.572412	+	1.76170i	−0.0724136	+	0.997375i	$0.523070\pi$
$168$	7.65642	+	2.58513i	0.590706	+	0.199447i
$169$	6.42809	−	4.67028i	0.494468	−	0.359252i
$170$	−0.726518	−	0.806880i	−0.0557214	−	0.0618849i
$171$	−2.02913	+	0.431305i	−0.155172	+	0.0329827i
$172$	0.133898	+	0.0596154i	0.0102097	+	0.00454563i
$173$	0.516904	−	0.230140i	0.0392995	−	0.0174972i	−0.386993	−	0.922083i	$-0.626486\pi$
$173$	0.516904	−	0.230140i	0.0392995	−	0.0174972i	0.426292	+	0.904585i	$0.359820\pi$
$174$	0.395991	+	1.21873i	0.0300200	+	0.0923920i
$175$	−12.5856	+	3.93039i	−0.951383	+	0.297110i
$176$	−8.94052	−	3.06464i	−0.673917	−	0.231006i
$177$	−1.01807	+	1.76335i	−0.0765228	+	0.132541i
$178$	−6.20812	+	6.89482i	−0.465319	+	0.516789i
$179$	−0.934532	+	8.89147i	−0.0698502	+	0.664580i	0.902442	+	0.430811i	$0.141773\pi$
$179$	−0.934532	+	8.89147i	−0.0698502	+	0.664580i	−0.972292	+	0.233769i	$0.924894\pi$
$180$	0.00626545	+	0.0596118i	0.000466999	+	0.00444320i
$181$	−7.09813	+	21.8458i	−0.527600	+	1.62379i	0.231516	+	0.972831i	$0.425631\pi$
$181$	−7.09813	+	21.8458i	−0.527600	+	1.62379i	−0.759116	+	0.650955i	$0.774369\pi$
$182$	6.42107	−	3.60970i	0.475961	−	0.267569i
$183$	−9.56056	+	6.94616i	−0.706737	+	0.513475i
$184$	2.33141	−	1.03801i	0.171874	−	0.0765230i
$185$	0.395338	−	0.439067i	0.0290658	−	0.0322808i
$186$	−0.346433	−	0.600040i	−0.0254017	−	0.0439970i
$187$	17.0563	−	14.8683i	1.24728	−	1.08728i
$188$	5.10886			0.372602
$189$	−2.63425	+	0.246375i	−0.191614	+	0.0179212i
$190$	−0.267096	−	0.194056i	−0.0193772	−	0.0140783i
$191$	1.83514	+	17.4602i	0.132786	+	1.26338i	0.834536	+	0.550953i	$0.185736\pi$
$191$	1.83514	+	17.4602i	0.132786	+	1.26338i	−0.701750	+	0.712423i	$0.747598\pi$
$192$	−8.69967	+	1.84917i	−0.627845	+	0.133452i
$193$	−23.6269	+	5.02206i	−1.70070	+	0.361496i	−0.953101	−	0.302651i	$-0.902128\pi$
$193$	−23.6269	+	5.02206i	−1.70070	+	0.361496i	−0.747602	+	0.664147i	$0.768795\pi$
$194$	−1.01649	−	9.67127i	−0.0729798	−	0.694357i
$195$	0.233746	+	0.169826i	0.0167389	+	0.0121615i
$196$	3.01227	−	1.25922i	0.215162	−	0.0899442i
$197$	−15.6437			−1.11457			−0.557283	−	0.830323i	$-0.688156\pi$
$197$	−15.6437			−1.11457			−0.557283	+	0.830323i	$0.688156\pi$
$198$	4.09112	−	0.363632i	0.290743	−	0.0258422i
$199$	8.28755	+	14.3545i	0.587489	+	1.01756i	0.994560	+	0.104164i	$0.0332167\pi$
$199$	8.28755	+	14.3545i	0.587489	+	1.01756i	−0.407071	+	0.913396i	$0.633450\pi$
$200$	10.1851	−	11.3117i	0.720193	−	0.799855i
$201$	13.1883	−	5.87179i	0.930228	−	0.414164i
$202$	−9.65668	+	7.01599i	−0.679441	+	0.493643i
$203$	2.35513	+	1.39597i	0.165298	+	0.0979782i
$204$	0.983293	−	3.02627i	0.0688443	−	0.211881i
$205$	0.0486670	+	0.463035i	0.00339905	+	0.0323398i
$206$	−1.23430	+	11.7436i	−0.0859980	+	0.818217i
$207$	−0.559086	+	0.620928i	−0.0388592	+	0.0431575i
$208$	−3.20329	+	5.54827i	−0.222108	+	0.384703i
$209$	4.13301	−	5.50051i	0.285886	−	0.380478i
$210$	−0.309664	−	0.285318i	−0.0213689	−	0.0196888i
$211$	−6.51479	−	20.0505i	−0.448497	−	1.38033i	−0.878603	−	0.477553i	$-0.841524\pi$
$211$	−6.51479	−	20.0505i	−0.448497	−	1.38033i	0.430106	−	0.902778i	$-0.358476\pi$
$212$	1.47221	−	0.655471i	0.101112	−	0.0450180i
$213$	−9.92637	−	4.41951i	−0.680144	−	0.302820i
$214$	1.96308	−	0.417266i	0.134193	−	0.0285237i
$215$	−0.0270232	−	0.0300123i	−0.00184296	−	0.00204682i
$216$	2.47103	−	1.79531i	0.168132	−	0.122155i
$217$	−1.40249	−	0.473540i	−0.0952075	−	0.0321460i
$218$	−3.59848	−	11.0750i	−0.243720	−	0.750093i
$219$	−5.68809	+	9.85206i	−0.384365	+	0.665740i
$220$	−0.145580	−	0.135379i	−0.00981499	−	0.00912727i
$221$	−7.66900	−	13.2831i	−0.515873	−	0.893518i
$222$	−5.56887	−	1.18370i	−0.373758	−	0.0794447i
$223$	−3.33425	−	2.42248i	−0.223278	−	0.162221i	0.470523	−	0.882388i	$-0.344065\pi$
$223$	−3.33425	−	2.42248i	−0.223278	−	0.162221i	−0.693801	+	0.720167i	$0.744065\pi$
$224$	−4.07493	+	5.47555i	−0.272268	+	0.365850i
$225$	−1.53998	+	4.73958i	−0.102665	+	0.315972i
$226$	−5.58420	−	6.20188i	−0.371456	−	0.412543i
$227$	−20.5350	−	9.14279i	−1.36296	−	0.606828i	−0.410602	−	0.911815i	$-0.634682\pi$
$227$	−20.5350	−	9.14279i	−1.36296	−	0.606828i	−0.952357	+	0.304986i	$0.901348\pi$
$228$	0.101137	−	0.962252i	0.00669795	−	0.0637267i
$229$	9.15568	+	1.94610i	0.605024	+	0.128602i	0.500231	−	0.865892i	$-0.333249\pi$
$229$	9.15568	+	1.94610i	0.605024	+	0.128602i	0.104793	+	0.994494i	$0.466582\pi$
$230$	−0.132975			−0.00876814
$231$	6.04889	−	6.35695i	0.397988	−	0.418257i
$232$	−3.16059			−0.207503
$233$	21.7440	+	4.62183i	1.42450	+	0.302786i	0.854753	−	0.519035i	$-0.173709\pi$
$233$	21.7440	+	4.62183i	1.42450	+	0.302786i	0.569745	+	0.821822i	$0.307042\pi$
$234$	0.291022	−	2.76889i	0.0190247	−	0.181008i
$235$	−1.28598	−	0.572555i	−0.0838881	−	0.0373494i
$236$	−0.635459	−	0.705748i	−0.0413648	−	0.0459403i
$237$	4.03663	−	12.4235i	0.262207	−	0.806991i
$238$	8.85709	+	20.5233i	0.574120	+	1.33033i
$239$	−2.66828	−	1.93862i	−0.172597	−	0.125399i	0.498133	−	0.867100i	$-0.334019\pi$
$239$	−2.66828	−	1.93862i	−0.172597	−	0.125399i	−0.670730	+	0.741702i	$0.734019\pi$
$240$	0.358215	+	0.0761409i	0.0231227	+	0.00491487i
$241$	−3.27489	−	5.67228i	−0.210954	−	0.365384i	0.741059	−	0.671440i	$-0.234324\pi$
$241$	−3.27489	−	5.67228i	−0.210954	−	0.365384i	−0.952013	+	0.306056i	$0.900990\pi$
$242$	−9.43562	+	9.82514i	−0.606545	+	0.631584i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.70324	−	5.24205i	−0.109039	−	0.335588i
$245$	−0.899359	−	0.0206234i	−0.0574579	−	0.00131758i
$246$	3.62963	−	2.63708i	0.231417	−	0.168134i
$247$	−3.12071	−	3.46590i	−0.198566	−	0.220530i
$248$	1.67155	−	0.355299i	0.106143	−	0.0225615i
$249$	10.3113	+	4.59090i	0.653454	+	0.290936i
$250$	−1.45150	+	0.646248i	−0.0918007	+	0.0408723i
$251$	8.76613	+	26.9794i	0.553313	+	1.70292i	0.700357	+	0.713793i	$0.253024\pi$
$251$	8.76613	+	26.9794i	0.553313	+	1.70292i	−0.147043	+	0.989130i	$0.546976\pi$
$252$	0.270384	−	1.20402i	0.0170326	−	0.0758462i
$253$	0.0445295	−	2.77082i	0.00279955	−	0.174200i
$254$	−6.13643	+	10.6286i	−0.385034	+	0.666898i
$255$	−0.586667	+	0.651560i	−0.0367385	+	0.0408023i
$256$	1.10150	−	10.4800i	0.0688435	−	0.655002i
$257$	1.10012	+	10.4669i	0.0686236	+	0.652910i	0.973727	+	0.227718i	$0.0731266\pi$
$257$	1.10012	+	10.4669i	0.0686236	+	0.652910i	−0.905103	+	0.425192i	$0.860207\pi$
$258$	−0.120258	+	0.370115i	−0.00748692	+	0.0230424i
$259$	−10.6029	+	5.96058i	−0.658832	+	0.370372i
$260$	−0.109022	+	0.0792088i	−0.00676123	+	0.00491232i
$261$	0.945319	−	0.420883i	0.0585137	−	0.0260520i
$262$	2.91632	−	3.23890i	0.180171	−	0.200100i
$263$	2.33731	+	4.04835i	0.144125	+	0.249632i	0.929046	−	0.369964i	$-0.120630\pi$
$263$	2.33731	+	4.04835i	0.144125	+	0.249632i	−0.784921	+	0.619596i	$0.787297\pi$
$264$	−2.26513	+	9.87367i	−0.139409	+	0.607682i
$265$	−0.444039			−0.0272771
$266$	3.93181	+	5.54422i	0.241074	+	0.339938i
$267$	6.06112	+	4.40366i	0.370934	+	0.269500i
$268$	0.703818	+	6.69638i	0.0429925	+	0.409047i
$269$	−1.29346	+	0.274933i	−0.0788634	+	0.0167629i	−0.247174	−	0.968971i	$-0.579502\pi$
$269$	−1.29346	+	0.274933i	−0.0788634	+	0.0167629i	0.168311	+	0.985734i	$0.446169\pi$
$270$	−0.155671	+	0.0330889i	−0.00947384	+	0.00201373i
$271$	−0.602511	−	5.73251i	−0.0365999	−	0.348225i	−0.997462	−	0.0711985i	$-0.977318\pi$
$271$	−0.602511	−	5.73251i	−0.0365999	−	0.348225i	0.960862	−	0.277027i	$-0.0893490\pi$
$272$	−15.7282	−	11.4272i	−0.953663	−	0.692877i
$273$	−3.44087	−	4.85196i	−0.208251	−	0.293654i
$274$	10.7660			0.650395
$275$	−6.47919	−	15.2055i	−0.390710	−	0.916925i
$276$	−0.194853	−	0.337495i	−0.0117288	−	0.0203148i
$277$	14.4026	−	15.9957i	0.865365	−	0.961086i	−0.134188	−	0.990956i	$-0.542843\pi$
$277$	14.4026	−	15.9957i	0.865365	−	0.961086i	0.999554	+	0.0298701i	$0.00950937\pi$
$278$	−15.9296	+	7.09232i	−0.955395	+	0.425369i
$279$	−0.452640	+	0.328862i	−0.0270988	+	0.0196884i
$280$	0.905285	−	0.508920i	0.0541011	−	0.0304138i
$281$	3.16683	−	9.74651i	0.188917	−	0.581428i	−0.811076	−	0.584940i	$-0.801118\pi$
$281$	3.16683	−	9.74651i	0.188917	−	0.581428i	0.999994	+	0.00351229i	$0.00111800\pi$
$282$	1.41790	+	13.4904i	0.0844344	+	0.803340i
$283$	−0.125052	+	1.18979i	−0.00743357	+	0.0707257i	−0.997610	−	0.0690995i	$-0.977987\pi$
$283$	−0.125052	+	1.18979i	−0.00743357	+	0.0707257i	0.990176	+	0.139825i	$0.0446541\pi$
$284$	3.39110	−	3.76619i	0.201225	−	0.223482i
$285$	−0.133298	+	0.230879i	−0.00789591	+	0.0136761i
$286$	5.30684	+	7.55667i	0.313800	+	0.446836i
$287$	2.10021	−	9.35225i	0.123972	−	0.552046i
$288$	0.797195	+	2.45351i	0.0469751	+	0.144575i
$289$	26.9898	−	12.0166i	1.58763	−	0.706860i
$290$	0.150446	+	0.0669830i	0.00883452	+	0.00393338i
$291$	−7.68102	+	1.63265i	−0.450270	+	0.0957078i
$292$	−3.55039	−	3.94311i	−0.207771	−	0.230753i
$293$	14.7139	−	10.6903i	0.859595	−	0.624532i	−0.0681796	−	0.997673i	$-0.521719\pi$
$293$	14.7139	−	10.6903i	0.859595	−	0.624532i	0.927775	+	0.373141i	$0.121719\pi$
$294$	4.16109	+	7.60468i	0.242680	+	0.443514i
$295$	0.0808610	+	0.248865i	0.00470791	+	0.0144895i
$296$	7.02099	−	12.1607i	0.408087	−	0.706827i
$297$	−0.637346	−	3.25481i	−0.0369826	−	0.188863i
$298$	−10.0590	−	17.4227i	−0.582702	−	1.00927i
$299$	−1.83742	−	0.390556i	−0.106261	−	0.0225864i
$300$	−1.88044	−	1.36622i	−0.108567	−	0.0788787i
$301$	0.329444	+	0.763375i	0.0189888	+	0.0440002i
$302$	8.68481	−	26.7291i	0.499755	−	1.53809i
$303$	6.44951	+	7.16290i	0.370514	+	0.411498i
$304$	−5.40040	−	2.40441i	−0.309734	−	0.137902i
$305$	−0.158748	+	1.51039i	−0.00908991	+	0.0864847i
$306$	8.26401	+	1.75657i	0.472422	+	0.100416i
$307$	−6.87121			−0.392160			−0.196080	−	0.980588i	$-0.562821\pi$
$307$	−6.87121			−0.392160			−0.196080	+	0.980588i	$0.562821\pi$
$308$	1.94802	+	3.59941i	0.110999	+	0.205095i
$309$	9.53527			0.542443
$310$	−0.0870969	−	0.0185130i	−0.00494677	−	0.00105147i
$311$	−0.610663	+	5.81007i	−0.0346275	+	0.329459i	0.963471	+	0.267814i	$0.0863013\pi$
$311$	−0.610663	+	5.81007i	−0.0346275	+	0.329459i	−0.998098	+	0.0616449i	$0.980365\pi$
$312$	6.27317	+	2.79299i	0.355148	+	0.158122i
$313$	7.21317	+	8.01104i	0.407712	+	0.452811i	0.911673	−	0.410916i	$-0.134791\pi$
$313$	7.21317	+	8.01104i	0.407712	+	0.452811i	−0.503961	+	0.863727i	$0.668124\pi$
$314$	−0.927709	+	2.85519i	−0.0523536	+	0.161128i
$315$	−0.202996	+	0.272769i	−0.0114375	+	0.0153688i
$316$	4.92905	+	3.58116i	0.277281	+	0.201456i
$317$	−24.6276	−	5.23476i	−1.38322	−	0.294013i	−0.544587	−	0.838704i	$-0.683314\pi$
$317$	−24.6276	−	5.23476i	−1.38322	−	0.294013i	−0.838637	+	0.544691i	$0.816647\pi$
$318$	2.13942	+	3.70558i	0.119973	+	0.207799i
$319$	−1.44611	+	3.11243i	−0.0809666	+	0.174263i
$320$	−0.571502	+	0.989870i	−0.0319479	+	0.0553354i
$321$	−0.500797	−	1.54129i	−0.0279518	−	0.0860267i
$322$	2.59375	+	0.875758i	0.144544	+	0.0488041i
$323$	11.4497	−	8.31871i	0.637080	−	0.462866i
$324$	−0.312090	−	0.346611i	−0.0173383	−	0.0192562i
$325$	−10.9591	+	2.32943i	−0.607901	+	0.129213i
$326$	13.8456	+	6.16444i	0.766835	+	0.341417i
$327$	−8.59039	+	3.82469i	−0.475050	+	0.211506i
$328$	3.41942	+	10.5239i	0.188806	+	0.581086i
$329$	21.3129	+	19.6373i	1.17502	+	1.08264i
$330$	0.317077	−	0.421989i	0.0174545	−	0.0232297i
$331$	−11.6893	+	20.2464i	−0.642501	+	1.11284i	0.342372	+	0.939564i	$0.388770\pi$
$331$	−11.6893	+	20.2464i	−0.642501	+	1.11284i	−0.984873	+	0.173279i	$0.944564\pi$
$332$	−3.52261	+	3.91225i	−0.193328	+	0.214713i
$333$	−0.480555	+	4.57217i	−0.0263342	+	0.250554i
$334$	−3.09866	−	29.4818i	−0.169551	−	1.61317i
$335$	0.573309	−	1.76446i	0.0313232	−	0.0964029i
$336$	−6.48570	−	3.84432i	−0.353824	−	0.209725i
$337$	−4.58037	+	3.32784i	−0.249509	+	0.181279i	−0.705509	−	0.708701i	$-0.749282\pi$
$337$	−4.58037	+	3.32784i	−0.249509	+	0.181279i	0.456000	+	0.889980i	$0.349282\pi$
$338$	−8.98895	+	4.00214i	−0.488934	+	0.217688i
$339$	−4.50927	+	5.00806i	−0.244910	+	0.272000i
$340$	−0.204465	−	0.354144i	−0.0110887	−	0.0192062i
$341$	0.414923	−	1.80865i	0.0224694	−	0.0979437i
$342$	2.56898			0.138914
$343$	17.4066	+	6.32532i	0.939869	+	0.341535i
$344$	−0.776522	−	0.564176i	−0.0418673	−	0.0304184i
$345$	0.0112241	+	0.106790i	0.000604285	+	0.00574939i
$346$	−0.685391	+	0.145684i	−0.0368468	+	0.00783204i
$347$	−21.8541	+	4.64523i	−1.17319	+	0.249369i	−0.752971	−	0.658054i	$-0.771380\pi$
$347$	−21.8541	+	4.64523i	−1.17319	+	0.249369i	−0.420218	+	0.907423i	$0.638047\pi$
$348$	0.0504489	+	0.479989i	0.00270434	+	0.0257301i
$349$	−23.1874	−	16.8466i	−1.24119	−	0.901780i	−0.243516	−	0.969897i	$-0.578301\pi$
$349$	−23.1874	−	16.8466i	−1.24119	−	0.901780i	−0.997677	+	0.0681170i	$0.978301\pi$
$350$	16.2572	−	1.52049i	0.868983	−	0.0812738i
$351$	−2.24821			−0.120001
$352$	−7.34014	−	4.39659i	−0.391231	−	0.234339i
$353$	9.58391	+	16.5998i	0.510100	+	0.883519i	0.999932	+	0.0117023i	$0.00372503\pi$
$353$	9.58391	+	16.5998i	0.510100	+	0.883519i	−0.489831	+	0.871817i	$0.662942\pi$
$354$	1.68722	−	1.87385i	0.0896750	−	0.0995942i
$355$	−1.27567	+	0.567967i	−0.0677057	+	0.0301445i
$356$	−2.82697	+	2.05392i	−0.149829	+	0.108857i
$357$	15.7343	−	8.84529i	0.832749	−	0.468142i
$358$	3.42134	−	10.5298i	0.180823	−	0.556517i
$359$	0.0211397	+	0.201130i	0.00111571	+	0.0106153i	0.995066	−	0.0992193i	$-0.0316345\pi$
$359$	0.0211397	+	0.201130i	0.00111571	+	0.0106153i	−0.993950	+	0.109835i	$0.964968\pi$
$360$	0.0410302	−	0.390376i	0.00216248	−	0.0205746i
$361$	−9.83395	+	10.9217i	−0.517576	+	0.574827i
$362$	14.2228	−	24.6347i	0.747536	−	1.29477i
$363$	8.68683	+	6.74826i	0.455940	+	0.354192i
$364$	2.64818	−	0.827006i	0.138802	−	0.0433469i
$365$	0.451781	+	1.39044i	0.0236473	+	0.0727789i
$366$	13.3694	−	5.95242i	0.698827	−	0.311138i
$367$	−6.75609	−	3.00800i	−0.352665	−	0.157017i	0.222755	−	0.974874i	$-0.428495\pi$
$367$	−6.75609	−	3.00800i	−0.352665	−	0.157017i	−0.575420	+	0.817858i	$0.695162\pi$
$368$	−2.32896	+	0.495036i	−0.121405	+	0.0258055i
$369$	−2.42416	−	2.69230i	−0.126197	−	0.140156i
$370$	−0.591929	+	0.430061i	−0.0307729	+	0.0223578i
$371$	8.66119	+	2.92438i	0.449667	+	0.151826i
$372$	−0.0806392	−	0.248182i	−0.00418095	−	0.0128676i
$373$	7.18059	−	12.4371i	0.371797	−	0.643971i	−0.618045	−	0.786143i	$-0.712075\pi$
$373$	7.18059	−	12.4371i	0.371797	−	0.643971i	0.989842	+	0.142172i	$0.0454085\pi$
$374$	−24.4888	+	13.6187i	−1.26629	+	0.704207i
$375$	0.641507	+	1.11112i	0.0331273	+	0.0573781i
$376$	−32.7250	−	6.95591i	−1.68766	−	0.358724i
$377$	1.88210	+	1.36742i	0.0969330	+	0.0704260i
$378$	3.25436	+	0.379813i	0.167386	+	0.0195355i
$379$	10.0556	−	30.9481i	0.516523	−	1.58969i	−0.263970	−	0.964531i	$-0.585032\pi$
$379$	10.0556	−	30.9481i	0.516523	−	1.58969i	0.780493	−	0.625164i	$-0.214968\pi$
$380$	−0.0832021	−	0.0924053i	−0.00426818	−	0.00474029i
$381$	9.05360	+	4.03092i	0.463830	+	0.206510i
$382$	2.27260	−	21.6224i	0.116277	−	1.10630i
$383$	3.92095	+	0.833424i	0.200351	+	0.0425860i	0.306994	−	0.951711i	$-0.400677\pi$
$383$	3.92095	+	0.833424i	0.200351	+	0.0425860i	−0.106643	+	0.994297i	$0.534010\pi$
$384$	5.85464			0.298769
$385$	−0.0869571	−	1.12434i	−0.00443175	−	0.0573019i
$386$	29.9128			1.52252
$387$	0.307384	+	0.0653364i	0.0156252	+	0.00332124i
$388$	0.382841	−	3.64249i	0.0194358	−	0.184919i
$389$	3.17588	+	1.41399i	0.161024	+	0.0716923i	0.485666	−	0.874145i	$-0.338577\pi$
$389$	3.17588	+	1.41399i	0.161024	+	0.0716923i	−0.324642	+	0.945837i	$0.605244\pi$
$390$	−0.239415	−	0.265897i	−0.0121232	−	0.0134642i
$391$	1.76150	−	5.42133i	0.0890828	−	0.274169i
$392$	−21.0097	+	3.96465i	−1.06115	+	0.200245i
$393$	−2.84726	−	2.06866i	−0.143625	−	0.104350i
$394$	18.9495	+	4.02784i	0.954661	+	0.202920i
$395$	−0.839375	−	1.45384i	−0.0422335	−	0.0731506i
$396$	1.53564	+	0.186396i	0.0771688	+	0.00936676i
$397$	−1.05200	+	1.82212i	−0.0527984	+	0.0914495i	−0.891217	−	0.453578i	$-0.850147\pi$
$397$	−1.05200	+	1.82212i	−0.0527984	+	0.0914495i	0.838418	+	0.545027i	$0.183481\pi$
$398$	−6.34297	−	19.5217i	−0.317945	−	0.978533i
$399$	4.12059	−	3.62553i	0.206288	−	0.181504i
$400$	−11.4890	+	8.34721i	−0.574448	+	0.417361i
$401$	15.6531	+	17.3845i	0.781676	+	0.868139i	0.994036	−	0.109052i	$-0.0347816\pi$
$401$	15.6531	+	17.3845i	0.781676	+	0.868139i	−0.212360	+	0.977192i	$0.568115\pi$
$402$	−17.4870	+	3.71698i	−0.872174	+	0.185386i
$403$	−1.14911	−	0.511617i	−0.0572413	−	0.0254855i
$404$	−4.10690	+	1.82851i	−0.204326	+	0.0909718i
$405$	0.0397129	+	0.122224i	0.00197335	+	0.00607334i
$406$	−2.49339	−	2.29736i	−0.123745	−	0.114016i
$407$	−8.76300	−	12.4781i	−0.434366	−	0.618515i
$408$	−10.4189	+	18.0461i	−0.515812	+	0.893413i
$409$	−3.64450	+	4.04762i	−0.180209	+	0.200142i	−0.826481	−	0.562965i	$-0.809661\pi$
$409$	−3.64450	+	4.04762i	−0.180209	+	0.200142i	0.646272	+	0.763107i	$0.276327\pi$
$410$	0.0602683	−	0.573414i	0.00297644	−	0.0283189i
$411$	−0.908725	−	8.64594i	−0.0448241	−	0.426473i
$412$	−1.37431	+	4.22969i	−0.0677073	+	0.208382i
$413$	0.0617544	−	5.38677i	0.00303874	−	0.265065i
$414$	0.837105	−	0.608192i	0.0411415	−	0.0298910i
$415$	1.32515	−	0.589993i	0.0650489	−	0.0289616i
$416$	−3.88088	+	4.31015i	−0.190276	+	0.211322i
$417$	7.04029	+	12.1941i	0.344765	+	0.597150i
$418$	−6.42263	+	5.59873i	−0.314141	+	0.273843i
$419$	1.26831			0.0619612			0.0309806	−	0.999520i	$-0.490137\pi$
$419$	1.26831			0.0619612			0.0309806	+	0.999520i	$0.490137\pi$
$420$	−0.0917381	−	0.129359i	−0.00447636	−	0.00631210i
$421$	−6.50939	−	4.72935i	−0.317248	−	0.230495i	0.417752	−	0.908561i	$-0.362818\pi$
$421$	−6.50939	−	4.72935i	−0.317248	−	0.230495i	−0.735000	+	0.678067i	$0.762818\pi$
$422$	2.72902	+	25.9649i	0.132847	+	1.26395i
$423$	10.7142	−	2.27737i	0.520942	−	0.110730i
$424$	−10.3228	+	2.19417i	−0.501318	+	0.106558i
$425$	−3.55385	−	33.8127i	−0.172387	−	1.64015i
$426$	10.8861	+	7.90922i	0.527434	+	0.383203i
$427$	13.0437	−	28.4154i	0.631229	−	1.37512i
$428$	0.755872			0.0365364
$429$	5.62069	−	4.89967i	0.271370	−	0.236558i
$430$	0.0250063	+	0.0433122i	0.00120591	+	0.00208870i
$431$	17.7842	−	19.7514i	0.856637	−	0.951392i	−0.142626	−	0.989777i	$-0.545555\pi$
$431$	17.7842	−	19.7514i	0.856637	−	0.951392i	0.999263	+	0.0383848i	$0.0122213\pi$
$432$	−2.60327	+	1.15905i	−0.125250	+	0.0557649i
$433$	−11.3558	+	8.25048i	−0.545725	+	0.396493i	−0.826207	−	0.563367i	$-0.809506\pi$
$433$	−11.3558	+	8.25048i	−0.545725	+	0.396493i	0.280482	+	0.959859i	$0.409506\pi$
$434$	1.57694	+	0.934714i	0.0756958	+	0.0448677i
$435$	0.0410941	−	0.126475i	0.00197031	−	0.00606399i
$436$	−0.458444	−	4.36180i	−0.0219555	−	0.208892i
$437$	0.181179	−	1.72380i	0.00866697	−	0.0824607i
$438$	9.42674	−	10.4695i	0.450427	−	0.500250i
$439$	−17.0705	+	29.5670i	−0.814730	+	1.41115i	0.0947914	+	0.995497i	$0.469782\pi$
$439$	−17.0705	+	29.5670i	−0.814730	+	1.41115i	−0.909522	+	0.415657i	$0.863552\pi$
$440$	0.748193	+	1.06539i	0.0356687	+	0.0507905i
$441$	5.75596	−	3.98359i	0.274093	−	0.189695i
$442$	5.86956	+	18.0646i	0.279186	+	0.859248i
$443$	−17.5726	+	7.82383i	−0.834900	+	0.371722i	−0.779238	−	0.626728i	$-0.784394\pi$
$443$	−17.5726	+	7.82383i	−0.834900	+	0.371722i	−0.0556623	+	0.998450i	$0.517727\pi$
$444$	−1.95888	−	0.872148i	−0.0929642	−	0.0413903i
$445$	0.941778	−	0.200181i	0.0446446	−	0.00948949i
$446$	3.41512	+	3.79288i	0.161711	+	0.179598i
$447$	−13.1428	+	9.54881i	−0.621633	+	0.451643i
$448$	17.6666	−	15.5441i	0.834667	−	0.734388i
$449$	−2.90277	−	8.93379i	−0.136990	−	0.421612i	0.858904	−	0.512136i	$-0.171146\pi$
$449$	−2.90277	−	8.93379i	−0.136990	−	0.421612i	−0.995894	+	0.0905244i	$0.971146\pi$
$450$	3.08573	−	5.34464i	0.145463	−	0.251949i
$451$	11.9281	+	1.44783i	0.561672	+	0.0681758i
$452$	−1.57157	−	2.72204i	−0.0739206	−	0.128034i
$453$	−22.1987	−	4.71848i	−1.04299	−	0.221694i
$454$	22.5205	+	16.3621i	1.05694	+	0.767911i
$455$	−0.759271	−	0.0886138i	−0.0355952	−	0.00415428i
$456$	−1.95798	+	6.02604i	−0.0916908	+	0.282195i
$457$	14.3414	+	15.9277i	0.670862	+	0.745068i	0.978457	−	0.206449i	$-0.0661909\pi$
$457$	14.3414	+	15.9277i	0.670862	+	0.745068i	−0.307595	+	0.951517i	$0.599524\pi$
$458$	−10.5894	−	4.71470i	−0.494809	−	0.220303i
$459$	0.713126	−	6.78494i	0.0332859	−	0.316694i
$460$	−0.0489880	−	0.0104127i	−0.00228408	−	0.000485496i
$461$	−29.6922			−1.38291			−0.691453	−	0.722422i	$-0.743029\pi$
$461$	−29.6922			−1.38291			−0.691453	+	0.722422i	$0.743029\pi$
$462$	−8.96390	+	6.14287i	−0.417038	+	0.285792i
$463$	25.7191			1.19527			0.597634	−	0.801769i	$-0.296108\pi$
$463$	25.7191			1.19527			0.597634	+	0.801769i	$0.296108\pi$
$464$	2.88431	+	0.613079i	0.133901	+	0.0284615i
$465$	−0.00751586	+	0.0715086i	−0.000348540	+	0.00331613i
$466$	−25.1490	−	11.1970i	−1.16500	−	0.518693i
$467$	26.9433	+	29.9236i	1.24679	+	1.38470i	0.893425	+	0.449212i	$0.148295\pi$
$467$	26.9433	+	29.9236i	1.24679	+	1.38470i	0.353362	+	0.935487i	$0.385038\pi$
$468$	0.324032	−	0.997268i	0.0149784	−	0.0460987i
$469$	−22.8032	+	30.6410i	−1.05295	+	1.41487i
$470$	1.41032	+	1.02465i	0.0650530	+	0.0472638i
$471$	2.37126	+	0.504027i	0.109262	+	0.0232243i
$472$	3.10955	+	5.38590i	0.143129	+	0.247906i
$473$	−0.910874	+	0.506555i	−0.0418820	+	0.0232914i
$474$	−8.08837	+	14.0095i	−0.371511	+	0.643477i
$475$	−3.19463	−	9.83207i	−0.146580	−	0.451126i
$476$	1.65585	+	8.25434i	0.0758958	+	0.378337i
$477$	2.79531	−	2.03091i	0.127988	−	0.0929889i
$478$	2.73300	+	3.03530i	0.125004	+	0.138831i
$479$	15.7595	−	3.34978i	0.720070	−	0.153056i	0.166720	−	0.986004i	$-0.446683\pi$
$479$	15.7595	−	3.34978i	0.720070	−	0.153056i	0.553350	+	0.832949i	$0.313349\pi$
$480$	0.302873	+	0.134848i	0.0138242	+	0.00615494i
$481$	−9.44224	+	4.20396i	−0.430529	+	0.191684i
$482$	2.50648	+	7.71414i	0.114167	+	0.351370i
$483$	0.484374	−	2.15692i	0.0220398	−	0.0981430i
$484$	−4.24544	+	2.88071i	−0.192974	+	0.130941i
$485$	−0.504584	+	0.873966i	−0.0229120	+	0.0396847i
$486$	0.828639	−	0.920297i	0.0375878	−	0.0417455i
$487$	2.43049	−	23.1246i	0.110136	−	1.04788i	−0.790250	−	0.612784i	$-0.790050\pi$
$487$	2.43049	−	23.1246i	0.110136	−	1.04788i	0.900386	−	0.435091i	$-0.143284\pi$
$488$	3.77294	+	35.8972i	0.170793	+	1.62499i
$489$	3.78188	−	11.6394i	0.171023	−	0.526354i
$490$	1.08410	+	0.256543i	0.0489747	+	0.0115894i
$491$	−3.85452	+	2.80047i	−0.173952	+	0.126384i	−0.671355	−	0.741136i	$-0.734287\pi$
$491$	−3.85452	+	2.80047i	−0.173952	+	0.126384i	0.497402	+	0.867520i	$0.334287\pi$
$492$	1.54365	−	0.687279i	0.0695932	−	0.0309849i
$493$	−4.72379	+	5.24630i	−0.212749	+	0.236282i
$494$	2.88780	+	5.00181i	0.129928	+	0.225042i
$495$	−0.365655	−	0.219020i	−0.0164350	−	0.00984420i
$496$	−1.59435			−0.0715886
$497$	28.6232	−	2.67705i	1.28393	−	0.120082i
$498$	−11.3083	−	8.21595i	−0.506736	−	0.368165i
$499$	−1.71138	−	16.2827i	−0.0766119	−	0.728914i	−0.963641	−	0.267200i	$-0.913902\pi$
$499$	−1.71138	−	16.2827i	−0.0766119	−	0.728914i	0.887029	−	0.461713i	$-0.152765\pi$
$500$	−0.585335	+	0.124417i	−0.0261770	+	0.00556409i
$501$	−23.4147	+	4.97696i	−1.04609	+	0.222354i
$502$	−3.67210	−	34.9377i	−0.163894	−	1.55935i
$503$	4.89148	+	3.55387i	0.218100	+	0.158459i	0.691471	−	0.722404i	$-0.256963\pi$
$503$	4.89148	+	3.55387i	0.218100	+	0.158459i	−0.473371	+	0.880863i	$0.656963\pi$
$504$	−3.37128	+	7.34426i	−0.150169	+	0.327139i
$505$	1.23870			0.0551212
$506$	−0.767353	+	3.34488i	−0.0341130	+	0.148698i
$507$	3.97278	+	6.88105i	0.176437	+	0.305598i
$508$	−3.09294	+	3.43505i	−0.137227	+	0.152406i
$509$	−19.4262	+	8.64910i	−0.861051	+	0.383365i	−0.789263	−	0.614055i	$-0.789537\pi$
$509$	−19.4262	+	8.64910i	−0.861051	+	0.383365i	−0.0717881	+	0.997420i	$0.522871\pi$
$510$	0.878401	−	0.638196i	0.0388963	−	0.0282598i
$511$	0.345030	−	30.0966i	0.0152632	−	1.33139i
$512$	−7.65097	+	23.5473i	−0.338128	+	1.04065i
$513$	−0.216840	−	2.06310i	−0.00957374	−	0.0910880i
$514$	1.36237	−	12.9621i	0.0600915	−	0.571732i
$515$	0.819961	−	0.910659i	0.0361318	−	0.0401284i
$516$	−0.0732850	+	0.126933i	−0.00322619	+	0.00558793i
$517$	−21.8231	+	29.0437i	−0.959777	+	1.27734i
$518$	14.3782	−	4.49020i	0.631741	−	0.197288i
$519$	0.174848	+	0.538128i	0.00767500	+	0.0236212i
$520$	0.806187	−	0.358938i	0.0353537	−	0.0157405i
$521$	−33.4292	−	14.8836i	−1.46456	−	0.652063i	−0.489096	−	0.872230i	$-0.662673\pi$
$521$	−33.4292	−	14.8836i	−1.46456	−	0.652063i	−0.975462	+	0.220167i	$0.929340\pi$
$522$	−1.25345	+	0.266429i	−0.0548620	+	0.0116613i
$523$	8.03641	+	8.92534i	0.351408	+	0.390278i	0.892771	−	0.450511i	$-0.148758\pi$
$523$	8.03641	+	8.92534i	0.351408	+	0.390278i	−0.541363	+	0.840789i	$0.682092\pi$
$524$	1.32799	−	0.964844i	0.0580137	−	0.0421494i
$525$	−2.59331	−	12.9275i	−0.113181	−	0.564203i
$526$	−1.78889	−	5.50564i	−0.0779994	−	0.240057i
$527$	1.90852	−	3.30565i	0.0831364	−	0.143997i
$528$	3.98239	−	8.57120i	0.173311	−	0.373014i
$529$	11.1509	+	19.3140i	0.484823	+	0.839739i
$530$	0.537873	+	0.114328i	0.0233637	+	0.00496611i
$531$	−1.64727	−	1.19681i	−0.0714855	−	0.0519373i
$532$	1.01433	+	2.35037i	0.0439768	+	0.101901i
$533$	2.51692	−	7.74629i	0.109020	−	0.335529i
$534$	−6.20812	−	6.89482i	−0.268652	−	0.298368i
$535$	−0.190265	−	0.0847114i	−0.00822587	−	0.00366239i
$536$	4.60905	−	43.8522i	0.199081	−	1.89413i
$537$	−8.74508	−	1.85882i	−0.377378	−	0.0802142i
$538$	1.63758			0.0706010
$539$	−5.70864	+	22.5036i	−0.245888	+	0.969298i
$540$	−0.0599402			−0.00257941
$541$	−16.2897	−	3.46248i	−0.700349	−	0.148864i	−0.156043	−	0.987750i	$-0.549874\pi$
$541$	−16.2897	−	3.46248i	−0.700349	−	0.148864i	−0.544306	+	0.838887i	$0.683207\pi$
$542$	−0.746139	+	7.09903i	−0.0320494	+	0.304930i
$543$	−20.9842	−	9.34276i	−0.900517	−	0.400936i
$544$	−11.7767	−	13.0794i	−0.504923	−	0.560774i
$545$	−0.373434	+	1.14931i	−0.0159962	+	0.0492311i
$546$	2.91874	+	6.76321i	0.124911	+	0.289439i
$547$	19.8490	+	14.4212i	0.848683	+	0.616605i	0.924783	−	0.380496i	$-0.124247\pi$
$547$	19.8490	+	14.4212i	0.848683	+	0.616605i	−0.0760993	+	0.997100i	$0.524247\pi$
$548$	3.96617	+	0.843035i	0.169426	+	0.0360127i
$549$	−5.90875	−	10.2343i	−0.252179	−	0.436788i
$550$	3.93335	+	20.0869i	0.167719	+	0.856509i
$551$	−1.07331	+	1.85902i	−0.0457244	+	0.0791970i
$552$	0.788624	+	2.42714i	0.0335661	+	0.103306i
$553$	6.79763	+	33.8859i	0.289065	+	1.44097i
$554$	−21.5646	+	15.6676i	−0.916191	+	0.665651i
$555$	0.395338	+	0.439067i	0.0167812	+	0.0186374i
$556$	−6.42383	+	1.36543i	−0.272431	+	0.0579070i
$557$	19.0032	+	8.46077i	0.805192	+	0.358494i	0.767706	−	0.640803i	$-0.221398\pi$
$557$	19.0032	+	8.46077i	0.805192	+	0.358494i	0.0374860	+	0.999297i	$0.488065\pi$
$558$	0.632965	−	0.281814i	0.0267955	−	0.0119301i
$559$	0.218321	+	0.671923i	0.00923399	+	0.0284193i
$560$	−0.924869	+	0.288830i	−0.0390829	+	0.0122053i
$561$	13.0040	+	18.5170i	0.549029	+	0.781790i
$562$	−6.34552	+	10.9908i	−0.267670	+	0.463617i
$563$	−7.86359	+	8.73340i	−0.331411	+	0.368069i	−0.885702	−	0.464254i	$-0.846323\pi$
$563$	−7.86359	+	8.73340i	−0.331411	+	0.368069i	0.554292	+	0.832323i	$0.312989\pi$
$564$	−0.534021	+	5.08087i	−0.0224863	+	0.213943i
$565$	0.0905273	+	0.861309i	0.00380851	+	0.0362356i
$566$	0.457818	−	1.40902i	0.0192435	−	0.0592255i
$567$	0.0303292	−	2.64558i	0.00127371	−	0.111104i
$568$	−26.8496	+	19.5074i	−1.12658	+	0.818512i
$569$	34.0518	−	15.1609i	1.42753	−	0.635576i	0.459903	−	0.887969i	$-0.347884\pi$
$569$	34.0518	−	15.1609i	1.42753	−	0.635576i	0.967625	+	0.252393i	$0.0812176\pi$
$570$	0.220912	−	0.245348i	0.00925300	−	0.0102765i
$571$	14.0323	+	24.3046i	0.587233	+	1.01712i	0.994593	+	0.103850i	$0.0331162\pi$
$571$	14.0323	+	24.3046i	0.587233	+	1.01712i	−0.407360	+	0.913268i	$0.633551\pi$
$572$	1.36330	+	3.19943i	0.0570026	+	0.133775i
$573$	−17.5564			−0.733428
$574$	−4.95199	+	10.7878i	−0.206692	+	0.450275i
$575$	−3.36867	−	2.44748i	−0.140483	−	0.102067i
$576$	−0.929679	−	8.84530i	−0.0387366	−	0.368554i
$577$	20.4596	−	4.34882i	0.851743	−	0.181044i	0.238700	−	0.971093i	$-0.423279\pi$
$577$	20.4596	−	4.34882i	0.851743	−	0.181044i	0.613043	+	0.790050i	$0.289945\pi$
$578$	−35.7872	+	7.60681i	−1.48855	+	0.316402i
$579$	−2.52486	−	24.0224i	−0.104930	−	0.998339i
$580$	0.0501792	+	0.0364573i	0.00208358	+	0.00151381i
$581$	−29.7332	+	2.78087i	−1.23354	+	0.115370i
$582$	9.72454			0.403095
$583$	−2.56239	+	11.1694i	−0.106123	+	0.462590i
$584$	17.3735	+	30.0917i	0.718919	+	1.24520i
$585$	−0.193329	+	0.214713i	−0.00799317	+	0.00887731i
$586$	−20.5757	+	9.16090i	−0.849975	+	0.378433i
$587$	0.295913	−	0.214993i	0.0122136	−	0.00887372i	−0.581662	−	0.813431i	$-0.697597\pi$
$587$	0.295913	−	0.214993i	0.0122136	−	0.00887372i	0.593875	+	0.804557i	$0.297597\pi$
$588$	0.937453	+	3.12740i	0.0386599	+	0.128972i
$589$	0.358660	−	1.10384i	0.0147783	−	0.0454830i
$590$	−0.0338724	−	0.322274i	−0.00139450	−	0.0132678i
$591$	1.63521	−	15.5580i	0.0672635	−	0.639969i
$592$	−8.76615	+	9.73580i	−0.360287	+	0.400139i
$593$	13.1852	−	22.8375i	0.541452	−	0.937823i	−0.457369	−	0.889277i	$-0.651208\pi$
$593$	13.1852	−	22.8375i	0.541452	−	0.937823i	0.998821	−	0.0485458i	$-0.0154587\pi$
$594$	−0.0659986	+	4.10672i	−0.00270796	+	0.168501i
$595$	0.508269	−	2.26332i	0.0208370	−	0.0927871i
$596$	−2.34143	−	7.20619i	−0.0959088	−	0.295177i
$597$	−15.1421	+	6.74170i	−0.619725	+	0.275919i
$598$	2.12515	+	0.946177i	0.0869038	+	0.0386921i
$599$	8.78330	−	1.86695i	0.358876	−	0.0762814i	−0.0249455	−	0.999689i	$-0.507941\pi$
$599$	8.78330	−	1.86695i	0.358876	−	0.0762814i	0.383821	+	0.923407i	$0.374608\pi$
$600$	10.1851	+	11.3117i	0.415804	+	0.461797i
$601$	20.2788	−	14.7334i	0.827191	−	0.600990i	−0.0915719	−	0.995798i	$-0.529189\pi$
$601$	20.2788	−	14.7334i	0.827191	−	0.600990i	0.918763	+	0.394809i	$0.129189\pi$
$602$	−0.202512	−	1.00951i	−0.00825379	−	0.0411447i
$603$	4.46108	+	13.7298i	0.181669	+	0.559120i
$604$	5.29252	−	9.16691i	0.215350	−	0.372996i
$605$	1.39149	−	0.249330i	0.0565720	−	0.0101367i
$606$	−5.96815	−	10.3371i	−0.242440	−	0.419918i
$607$	28.7148	+	6.10353i	1.16550	+	0.247735i	0.749735	−	0.661738i	$-0.230181\pi$
$607$	28.7148	+	6.10353i	1.16550	+	0.247735i	0.415764	+	0.909472i	$0.363514\pi$
$608$	−4.32958	−	3.14562i	−0.175587	−	0.127572i
$609$	−1.63451	+	2.19631i	−0.0662335	+	0.0889990i
$610$	0.581181	−	1.78869i	0.0235314	−	0.0724221i
$611$	16.4779	+	18.3006i	0.666626	+	0.740363i
$612$	2.90690	+	1.29424i	0.117505	+	0.0523164i
$613$	−0.843012	+	8.02073i	−0.0340489	+	0.323954i	0.964218	+	0.265110i	$0.0854082\pi$
$613$	−0.843012	+	8.02073i	−0.0340489	+	0.323954i	−0.998267	+	0.0588443i	$0.981258\pi$
$614$	8.32323	+	1.76916i	0.335898	+	0.0713974i
$615$	−0.465586			−0.0187742
$616$	−7.57737	−	25.7085i	−0.305301	−	1.03582i
$617$	1.51904			0.0611543			0.0305772	−	0.999532i	$-0.490265\pi$
$617$	1.51904			0.0611543			0.0305772	+	0.999532i	$0.490265\pi$
$618$	−11.5503	−	2.45508i	−0.464620	−	0.0987580i
$619$	2.51181	−	23.8982i	0.100958	−	0.960551i	−0.820388	−	0.571807i	$-0.806242\pi$
$619$	2.51181	−	23.8982i	0.100958	−	0.960551i	0.921346	−	0.388744i	$-0.127091\pi$
$620$	−0.0306368	−	0.0136404i	−0.00123040	−	0.000547810i
$621$	−0.559086	−	0.620928i	−0.0224354	−	0.0249170i
$622$	2.23565	−	6.88063i	0.0896415	−	0.275888i
$623$	−19.6882	−	2.29779i	−0.788792	−	0.0920590i
$624$	−5.18304	−	3.76570i	−0.207488	−	0.150748i
$625$	−24.2116	−	5.14634i	−0.968465	−	0.205854i
$626$	−6.67482	−	11.5611i	−0.266780	−	0.462076i
$627$	5.03836	+	4.68533i	0.201213	+	0.187114i
$628$	−0.565345	+	0.979207i	−0.0225597	+	0.0390746i
$629$	−9.69220	−	29.8295i	−0.386453	−	1.18938i
$630$	0.316124	−	0.278144i	0.0125947	−	0.0110815i
$631$	−2.70693	+	1.96670i	−0.107761	+	0.0782931i	−0.640361	−	0.768074i	$-0.721215\pi$
$631$	−2.70693	+	1.96670i	−0.107761	+	0.0782931i	0.532600	+	0.846367i	$0.321215\pi$
$632$	−26.6973	−	29.6504i	−1.06196	−	1.17943i
$633$	20.6216	−	4.38326i	0.819635	−	0.174219i
$634$	28.4841	+	12.6819i	1.13125	+	0.503664i
$635$	1.16351	−	0.518028i	0.0461725	−	0.0205573i
$636$	0.497993	+	1.53266i	0.0197467	+	0.0607741i
$637$	14.2264	+	6.72892i	0.563669	+	0.266609i
$638$	2.55307	−	3.39781i	0.101077	−	0.134521i
$639$	5.43288	−	9.41003i	0.214922	−	0.372255i
$640$	0.503455	−	0.559143i	0.0199008	−	0.0221021i
$641$	−2.58317	+	24.5772i	−0.102029	+	0.970741i	0.817023	+	0.576605i	$0.195623\pi$
$641$	−2.58317	+	24.5772i	−0.102029	+	0.970741i	−0.919052	+	0.394136i	$0.871044\pi$
$642$	0.209782	+	1.99594i	0.00827944	+	0.0787736i
$643$	−0.0379946	+	0.116935i	−0.00149836	+	0.00461148i	−0.951803	−	0.306710i	$-0.900772\pi$
$643$	−0.0379946	+	0.116935i	−0.00149836	+	0.00461148i	0.950305	+	0.311322i	$0.100772\pi$
$644$	0.886959	+	0.525734i	0.0349511	+	0.0207168i
$645$	0.0326725	−	0.0237380i	0.00128648	−	0.000934683i
$646$	−16.0111	+	7.12862i	−0.629950	+	0.280472i
$647$	7.73021	−	8.58527i	0.303906	−	0.337522i	−0.571776	−	0.820410i	$-0.693745\pi$
$647$	7.73021	−	8.58527i	0.303906	−	0.337522i	0.875682	+	0.482888i	$0.160412\pi$
$648$	1.52718	+	2.64515i	0.0599933	+	0.103911i
$649$	6.72659	−	0.597881i	0.264042	−	0.0234689i
$650$	13.8747			0.544211
$651$	0.617547	−	1.34531i	0.0242036	−	0.0527270i
$652$	4.61798	+	3.35516i	0.180854	+	0.131398i
$653$	−4.60733	−	43.8359i	−0.180299	−	1.71543i	−0.593537	−	0.804807i	$-0.702269\pi$
$653$	−4.60733	−	43.8359i	−0.180299	−	1.71543i	0.413238	−	0.910623i	$-0.364398\pi$
$654$	11.3905	−	2.42112i	0.445403	−	0.0946732i
$655$	−0.442408	+	0.0940367i	−0.0172863	+	0.00367432i
$656$	−1.07913	−	10.2673i	−0.0421331	−	0.400869i
$657$	−9.20352	−	6.68675i	−0.359063	−	0.260875i
$658$	−20.7607	−	29.2745i	−0.809335	−	1.14124i
$659$	−28.8069			−1.12216			−0.561079	−	0.827762i	$-0.689613\pi$
$659$	−28.8069			−1.12216			−0.561079	+	0.827762i	$0.689613\pi$
$660$	0.149855	−	0.130631i	0.00583309	−	0.00508482i
$661$	13.3260	+	23.0813i	0.518321	+	0.897758i	0.999773	+	0.0212861i	$0.00677608\pi$
$661$	13.3260	+	23.0813i	0.518321	+	0.897758i	−0.481452	+	0.876472i	$0.659891\pi$
$662$	19.3724	−	21.5152i	0.752929	−	0.836212i
$663$	14.0120	−	6.23853i	0.544179	−	0.242284i
$664$	27.8909	−	20.2639i	1.08238	−	0.786392i
$665$	0.00808565	−	0.705302i	0.000313548	−	0.0273504i
$666$	1.75932	−	5.41463i	0.0681723	−	0.209813i
$667$	0.0903754	+	0.859865i	0.00349935	+	0.0332941i
$668$	1.16705	−	11.1037i	0.0451544	−	0.429615i
$669$	2.75773	−	3.06277i	0.106620	−	0.118414i
$670$	−1.14876	+	1.98972i	−0.0443806	+	0.0768695i
$671$	37.0765	+	12.7091i	1.43132	+	0.490629i
$672$	−5.01961	−	4.62496i	−0.193636	−	0.178412i
$673$	7.74486	+	23.8362i	0.298543	+	0.918820i	0.982008	+	0.188837i	$0.0604718\pi$
$673$	7.74486	+	23.8362i	0.298543	+	0.918820i	−0.683466	+	0.729982i	$0.739528\pi$
$674$	6.40513	−	2.85175i	0.246716	−	0.109845i
$675$	−4.55264	−	2.02697i	−0.175231	−	0.0780179i
$676$	−3.62491	+	0.770499i	−0.139420	+	0.0296346i
$677$	5.32965	+	5.91918i	0.204835	+	0.227493i	0.836806	−	0.547500i	$-0.184420\pi$
$677$	5.32965	+	5.91918i	0.204835	+	0.227493i	−0.631971	+	0.774992i	$0.717754\pi$
$678$	6.75162	−	4.90534i	0.259294	−	0.188388i
$679$	15.5980	−	13.7240i	0.598596	−	0.526679i
$680$	0.827529	+	2.54687i	0.0317343	+	0.0976681i
$681$	11.2392	−	19.4669i	0.430687	−	0.745972i
$682$	−0.968284	+	2.08402i	−0.0370775	+	0.0798011i
$683$	−19.9562	−	34.5652i	−0.763603	−	1.32260i	−0.940982	−	0.338456i	$-0.890095\pi$
$683$	−19.9562	−	34.5652i	−0.763603	−	1.32260i	0.177379	−	0.984143i	$-0.443238\pi$
$684$	0.946409	+	0.201165i	0.0361869	+	0.00769175i
$685$	−0.903868	−	0.656698i	−0.0345350	−	0.0250912i
$686$	−19.4564	−	12.1437i	−0.742848	−	0.463650i
$687$	−2.89247	+	8.90210i	−0.110355	+	0.339636i
$688$	0.599207	+	0.665487i	0.0228446	+	0.0253715i
$689$	7.09641	+	3.15952i	0.270352	+	0.120368i
$690$	0.0138997	−	0.132247i	0.000529153	−	0.00503456i
$691$	34.6678	+	7.36887i	1.31882	+	0.280325i	0.812976	−	0.582297i	$-0.197846\pi$
$691$	34.6678	+	7.36887i	1.31882	+	0.280325i	0.505849	+	0.862622i	$0.331179\pi$
$692$	−0.263905			−0.0100322
$693$	5.68985	+	6.68024i	0.216139	+	0.253761i
$694$	27.6683			1.05028
$695$	1.77000	+	0.376226i	0.0671401	+	0.0142711i
$696$	0.330371	−	3.14327i	0.0125227	−	0.119146i
$697$	22.5794	+	10.0530i	0.855256	+	0.380785i
$698$	23.7498	+	26.3768i	0.898943	+	0.998378i
$699$	−6.86938	+	21.1418i	−0.259824	+	0.799656i
$700$	6.10820	+	0.712881i	0.230868	+	0.0269444i
$701$	−18.0663	−	13.1260i	−0.682356	−	0.495760i	0.191783	−	0.981437i	$-0.438573\pi$
$701$	−18.0663	−	13.1260i	−0.682356	−	0.495760i	−0.874138	+	0.485677i	$0.838573\pi$
$702$	2.72330	+	0.578856i	0.102784	+	0.0218475i
$703$	−4.76852	−	8.25933i	−0.179848	−	0.311506i
$704$	21.6014	+	20.0878i	0.814133	+	0.757088i
$705$	0.703840	−	1.21909i	0.0265082	−	0.0459135i
$706$	−7.33516	−	22.5753i	−0.276062	−	0.849633i
$707$	−24.1614	−	8.15788i	−0.908682	−	0.306809i
$708$	0.768306	−	0.558207i	0.0288747	−	0.0209787i
$709$	27.9055	+	30.9922i	1.04801	+	1.16394i	0.986150	+	0.165854i	$0.0530380\pi$
$709$	27.9055	+	30.9922i	1.04801	+	1.16394i	0.0618644	+	0.998085i	$0.480295\pi$
$710$	1.69149	−	0.359536i	0.0634803	−	0.0134932i
$711$	11.9335	+	5.31313i	0.447540	+	0.199258i
$712$	20.9048	−	9.30740i	0.783439	−	0.348809i
$713$	−0.144459	−	0.444600i	−0.00541004	−	0.0166504i
$714$	−21.3367	+	6.66330i	−0.798507	+	0.249368i
$715$	0.0153981	−	0.958134i	0.000575855	−	0.0358322i
$716$	2.08496	−	3.61126i	0.0779187	−	0.134959i
$717$	2.20691	−	2.45102i	0.0824186	−	0.0915351i
$718$	0.0261790	−	0.249076i	0.000976990	−	0.00929544i
$719$	−3.94909	−	37.5730i	−0.147276	−	1.40124i	−0.779476	−	0.626433i	$-0.784514\pi$
$719$	−3.94909	−	37.5730i	−0.147276	−	1.40124i	0.632200	−	0.774806i	$-0.282152\pi$
$720$	−0.113167	+	0.348293i	−0.00421750	+	0.0129801i
$721$	−21.9912	+	12.3627i	−0.818996	+	0.460411i
$722$	14.7241	−	10.6977i	0.547975	−	0.398127i
$723$	5.98352	−	2.66404i	0.222530	−	0.0990766i
$724$	7.16872	−	7.96167i	0.266423	−	0.295893i
$725$	2.57840	+	4.46593i	0.0957595	+	0.165860i
$726$	−8.78503	−	10.4109i	−0.326043	−	0.386386i
$727$	45.0926			1.67239			0.836195	−	0.548432i	$-0.184775\pi$
$727$	45.0926			1.67239			0.836195	+	0.548432i	$0.184775\pi$
$728$	−18.0890	+	1.69182i	−0.670423	+	0.0627029i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.189249	−	1.80059i	−0.00700443	−	0.0666427i
$731$	−2.09707	+	0.445746i	−0.0775629	+	0.0164865i
$732$	5.39137	−	1.14597i	0.199271	−	0.0423563i
$733$	2.53473	+	24.1163i	0.0936222	+	0.890756i	0.936031	+	0.351917i	$0.114470\pi$
$733$	2.53473	+	24.1163i	0.0936222	+	0.890756i	−0.842409	+	0.538839i	$0.818863\pi$
$734$	7.40930	+	5.38317i	0.273482	+	0.198697i
$735$	0.114519	−	0.892276i	0.00422410	−	0.0329121i
$736$	−2.15551			−0.0794531
$737$	−41.0752	−	24.6032i	−1.51302	−	0.906269i
$738$	2.24324	+	3.88540i	0.0825747	+	0.143024i
$739$	12.9424	−	14.3739i	0.476092	−	0.528754i	−0.456482	−	0.889733i	$-0.650891\pi$
$739$	12.9424	−	14.3739i	0.476092	−	0.528754i	0.932574	+	0.360979i	$0.117557\pi$
$740$	−0.251742	+	0.112083i	−0.00925423	+	0.00412025i
$741$	3.77312	−	2.74133i	0.138609	−	0.100705i
$742$	−9.73853	−	5.77239i	−0.357513	−	0.211911i
$743$	7.59037	−	23.3608i	0.278464	−	0.857023i	−0.709818	−	0.704385i	$-0.751223\pi$
$743$	7.59037	−	23.3608i	0.278464	−	0.857023i	0.988282	−	0.152638i	$-0.0487769\pi$
$744$	0.178628	+	1.69953i	0.00654882	+	0.0623078i
$745$	−0.218230	+	2.07632i	−0.00799532	+	0.0760704i
$746$	−11.9002	+	13.2165i	−0.435699	+	0.483892i
$747$	−5.64358	+	9.77496i	−0.206488	+	0.357647i
$748$	−10.0881	+	3.09951i	−0.368857	+	0.113329i
$749$	3.15331	+	2.90540i	0.115220	+	0.106161i
$750$	−0.490985	−	1.51110i	−0.0179282	−	0.0551774i
$751$	−22.3090	+	9.93259i	−0.814066	+	0.362446i	−0.771166	−	0.636634i	$-0.780326\pi$
$751$	−22.3090	+	9.93259i	−0.814066	+	0.362446i	−0.0428998	+	0.999079i	$0.513660\pi$
$752$	28.5151	+	12.6957i	1.03984	+	0.462966i
$753$	−27.7479	+	5.89800i	−1.01119	+	0.214935i
$754$	−1.92775	−	2.14098i	−0.0702044	−	0.0779699i
$755$	−2.35956	+	1.71432i	−0.0858730	+	0.0623904i
$756$	1.16916	+	0.394758i	0.0425220	+	0.0143572i
$757$	−14.8702	−	45.7656i	−0.540465	−	1.66338i	−0.731535	−	0.681804i	$-0.761196\pi$
$757$	−14.8702	−	45.7656i	−0.540465	−	1.66338i	0.191070	−	0.981576i	$-0.438804\pi$
$758$	−20.1489	+	34.8989i	−0.731841	+	1.26759i
$759$	2.75098	+	0.333915i	0.0998544	+	0.0121203i
$760$	0.407141	+	0.705189i	0.0147686	+	0.0255799i
$761$	−25.5150	−	5.42338i	−0.924918	−	0.196597i	−0.279252	−	0.960218i	$-0.590087\pi$
$761$	−25.5150	−	5.42338i	−0.924918	−	0.196597i	−0.645665	+	0.763620i	$0.723420\pi$
$762$	−9.92895	−	7.21381i	−0.359688	−	0.261329i
$763$	14.8532	−	19.9585i	0.537723	−	0.722547i
$764$	2.53038	−	7.78771i	0.0915460	−	0.281750i
$765$	−0.586667	−	0.651560i	−0.0212110	−	0.0235572i
$766$	−4.53494	−	2.01909i	−0.163854	−	0.0729525i
$767$	0.478497	−	4.55259i	0.0172775	−	0.164385i
$768$	10.3075	+	2.19092i	0.371939	+	0.0790582i
$769$	14.2293			0.513123			0.256561	−	0.966528i	$-0.417410\pi$
$769$	14.2293			0.513123			0.256561	+	0.966528i	$0.417410\pi$
$770$	−0.184157	+	1.38433i	−0.00663654	+	0.0498878i
$771$	−10.5246			−0.379034
$772$	11.0199	+	2.34234i	0.396613	+	0.0843028i
$773$	2.43655	−	23.1822i	0.0876367	−	0.833808i	−0.859102	−	0.511805i	$-0.828977\pi$
$773$	2.43655	−	23.1822i	0.0876367	−	0.833808i	0.946739	−	0.322003i	$-0.104356\pi$
$774$	−0.355517	−	0.158287i	−0.0127788	−	0.00568949i
$775$	−1.86569	−	2.07206i	−0.0670175	−	0.0744304i
$776$	−7.41169	+	22.8108i	−0.266064	+	0.818861i
$777$	−4.81962	−	11.1679i	−0.172903	−	0.400645i
$778$	−3.48294	−	2.53051i	−0.124869	−	0.0907230i
$779$	7.35124	+	1.56255i	0.263386	+	0.0559843i
$780$	−0.0673790	−	0.116704i	−0.00241256	−	0.00417867i
$781$	6.92526	+	35.3660i	0.247805	+	1.26550i
$782$	−3.52959	+	6.11343i	−0.126218	+	0.218616i
$783$	0.319765	+	0.984134i	0.0114275	+	0.0351701i
$784$	19.9422	+	0.457299i	0.712222	+	0.0163321i
$785$	0.252047	−	0.183123i	0.00899594	−	0.00653594i
$786$	2.91632	+	3.23890i	0.104022	+	0.115528i
$787$	−13.3139	+	2.82996i	−0.474589	+	0.100877i	−0.438995	−	0.898489i	$-0.644666\pi$
$787$	−13.3139	+	2.82996i	−0.474589	+	0.100877i	−0.0355937	+	0.999366i	$0.511332\pi$
$788$	6.66557	+	2.96770i	0.237451	+	0.105720i
$789$	−4.27049	+	1.90134i	−0.152033	+	0.0676896i
$790$	0.642425	+	1.97718i	0.0228565	+	0.0703450i
$791$	3.90669	−	17.3965i	0.138906	−	0.618547i
$792$	−9.58281	−	3.28480i	−0.340510	−	0.116720i
$793$	13.2841	−	23.0088i	0.471733	−	0.817065i
$794$	1.74346	−	1.93631i	0.0618730	−	0.0687169i
$795$	0.0464147	−	0.441606i	0.00164616	−	0.0156622i
$796$	−0.808089	−	7.68846i	−0.0286420	−	0.272510i
$797$	−4.45172	+	13.7010i	−0.157688	+	0.485314i	−0.998423	−	0.0561325i	$-0.982123\pi$
$797$	−4.45172	+	13.7010i	−0.157688	+	0.485314i	0.840735	+	0.541446i	$0.182123\pi$
$798$	−5.92484	+	3.33074i	−0.209737	+	0.117907i
$799$	−60.4567	+	43.9244i	−2.13881	+	1.55393i
$800$	−11.7448	+	5.22912i	−0.415241	+	0.184877i
$801$	−5.01310	+	5.56761i	−0.177129	+	0.196722i
$802$	−14.4848	−	25.0884i	−0.511476	−	0.885903i
$803$	37.5823	−	3.34044i	1.32625	−	0.117882i
$804$	−6.73327			−0.237464
$805$	−0.164342	−	0.231738i	−0.00579230	−	0.00816769i
$806$	1.26021	+	0.915598i	0.0443891	+	0.0322506i
$807$	−0.138224	−	1.31511i	−0.00486570	−	0.0462940i
$808$	28.7965	−	6.12089i	1.01306	−	0.215332i
$809$	−15.6333	+	3.32296i	−0.549638	+	0.116829i	−0.474356	−	0.880333i	$-0.657319\pi$
$809$	−15.6333	+	3.32296i	−0.549638	+	0.116829i	−0.0752819	+	0.997162i	$0.523986\pi$
$810$	−0.0166356	−	0.158277i	−0.000584515	−	0.00556129i
$811$	−27.1719	−	19.7416i	−0.954136	−	0.693220i	−0.00235422	−	0.999997i	$-0.500749\pi$
$811$	−27.1719	−	19.7416i	−0.954136	−	0.693220i	−0.951781	+	0.306777i	$0.900749\pi$
$812$	−0.738667	−	1.04159i	−0.0259221	−	0.0365527i
$813$	5.76409			0.202155
$814$	7.40202	+	17.3712i	0.259441	+	0.608860i
$815$	−0.786403	−	1.36209i	−0.0275465	−	0.0477119i
$816$	13.0087	−	14.4476i	0.455394	−	0.505766i
$817$	−0.595542	+	0.265152i	−0.0208354	+	0.00927650i
$818$	5.45681	−	3.96460i	0.190793	−	0.138619i
$819$	5.18505	−	2.91486i	0.181180	−	0.101853i
$820$	0.0671044	−	0.206526i	0.00234339	−	0.00721220i
$821$	−5.24283	−	49.8822i	−0.182976	−	1.74090i	−0.572517	−	0.819893i	$-0.694033\pi$
$821$	−5.24283	−	49.8822i	−0.182976	−	1.74090i	0.389541	−	0.921009i	$-0.372634\pi$
$822$	−1.12535	+	10.7070i	−0.0392510	+	0.373449i
$823$	−20.5339	+	22.8052i	−0.715766	+	0.794939i	−0.985802	−	0.167911i	$-0.946298\pi$
$823$	−20.5339	+	22.8052i	−0.715766	+	0.794939i	0.270036	+	0.962850i	$0.412964\pi$
$824$	14.5621	−	25.2222i	0.507294	−	0.878658i
$825$	15.7994	−	4.85429i	0.550066	−	0.169005i
$826$	−1.46176	+	6.50920i	−0.0508610	+	0.226484i
$827$	14.2568	+	43.8781i	0.495759	+	1.52579i	0.815770	+	0.578376i	$0.196313\pi$
$827$	14.2568	+	43.8781i	0.495759	+	1.52579i	−0.320011	+	0.947414i	$0.603687\pi$
$828$	0.356014	−	0.158508i	0.0123723	−	0.00550852i
$829$	−32.1203	−	14.3009i	−1.11558	−	0.496690i	−0.235675	−	0.971832i	$-0.575730\pi$
$829$	−32.1203	−	14.3009i	−1.11558	−	0.496690i	−0.879909	+	0.475142i	$0.842397\pi$
$830$	−1.75708	+	0.373480i	−0.0609893	+	0.0129637i
$831$	14.4026	+	15.9957i	0.499619	+	0.554883i
$832$	16.1768	−	11.7531i	0.560830	−	0.407467i
$833$	−24.8200	+	40.7998i	−0.859961	+	1.41363i
$834$	−5.38837	−	16.5837i	−0.186584	−	0.574247i
$835$	−1.53817	+	2.66419i	−0.0532305	+	0.0921980i
$836$	−2.80451	+	1.55964i	−0.0969959	+	0.0539413i
$837$	−0.279747	−	0.484535i	−0.00966946	−	0.0167480i
$838$	−1.53633	−	0.326558i	−0.0530718	−	0.0112808i
$839$	−18.9410	−	13.7615i	−0.653917	−	0.475099i	0.210686	−	0.977554i	$-0.432430\pi$
$839$	−18.9410	−	13.7615i	−0.653917	−	0.475099i	−0.864603	+	0.502455i	$0.832430\pi$
$840$	0.411504	+	0.953522i	0.0141982	+	0.0328996i
$841$	−8.63061	+	26.5623i	−0.297607	+	0.915941i
$842$	6.66727	+	7.40476i	0.229769	+	0.255185i
$843$	9.36209	+	4.16827i	0.322448	+	0.143563i
$844$	−1.02783	+	9.77915i	−0.0353794	+	0.336612i
$845$	0.998798	+	0.212301i	0.0343597	+	0.00730338i
$846$	−13.5647			−0.466363
$847$	−28.7837	−	4.30086i	−0.989020	−	0.147779i
$848$	9.84604			0.338114
$849$	−1.17020	−	0.248734i	−0.0401612	−	0.00853653i
$850$	−4.40103	+	41.8730i	−0.150954	+	1.43623i
$851$	−3.50918	−	1.56239i	−0.120293	−	0.0535580i
$852$	3.39110	+	3.76619i	0.116177	+	0.129028i
$853$	1.01568	−	3.12594i	0.0347762	−	0.107030i	−0.932162	−	0.362042i	$-0.882080\pi$
$853$	1.01568	−	3.12594i	0.0347762	−	0.107030i	0.966938	+	0.255012i	$0.0820795\pi$
$854$	−23.1163	+	31.0618i	−0.791024	+	1.06291i
$855$	−0.215681	−	0.156702i	−0.00737614	−	0.00535908i
$856$	−4.84176	−	1.02915i	−0.165488	−	0.0351756i
$857$	17.6953	+	30.6492i	0.604461	+	1.04696i	0.992136	+	0.125161i	$0.0399449\pi$
$857$	17.6953	+	30.6492i	0.604461	+	1.04696i	−0.387675	+	0.921796i	$0.626722\pi$
$858$	−8.06999	+	4.48788i	−0.275505	+	0.153214i
$859$	−2.37427	+	4.11235i	−0.0810089	+	0.140312i	−0.903684	−	0.428201i	$-0.859148\pi$
$859$	−2.37427	+	4.11235i	−0.0810089	+	0.140312i	0.822675	+	0.568512i	$0.192481\pi$
$860$	0.00582072	+	0.0179143i	0.000198485	+	0.000610873i
$861$	9.08148	+	3.06629i	0.309496	+	0.104499i
$862$	−26.6279	+	19.3463i	−0.906949	+	0.658937i
$863$	−11.6872	−	12.9800i	−0.397838	−	0.441844i	0.510629	−	0.859801i	$-0.329413\pi$
$863$	−11.6872	−	12.9800i	−0.397838	−	0.441844i	−0.908466	+	0.417958i	$0.862746\pi$
$864$	−2.52340	+	0.536366i	−0.0858479	+	0.0182475i
$865$	0.0664292	+	0.0295762i	0.00225866	+	0.00100562i
$866$	15.8798	−	7.07014i	0.539618	−	0.240253i
$867$	9.12960	+	28.0980i	0.310057	+	0.954259i
$868$	0.507752	+	0.467832i	0.0172342	+	0.0158792i
$869$	−41.4138	+	12.7242i	−1.40487	+	0.431638i
$870$	−0.0823420	+	0.142621i	−0.00279166	+	0.00483529i
$871$	−21.7173	+	24.1195i	−0.735861	+	0.817256i
$872$	−3.00218	+	28.5639i	−0.101667	+	0.967295i
$873$	−0.820823	−	7.80960i	−0.0277806	−	0.264315i
$874$	−0.663301	+	2.04143i	−0.0224365	+	0.0690524i
$875$	−2.92010	−	1.73086i	−0.0987175	−	0.0585136i
$876$	4.29262	−	3.11877i	0.145034	−	0.105374i
$877$	0.0319309	−	0.0142165i	0.00107823	−	0.000480059i	−0.406197	−	0.913785i	$-0.633145\pi$
$877$	0.0319309	−	0.0142165i	0.00107823	−	0.000480059i	0.407276	+	0.913305i	$0.366479\pi$
$878$	28.2906	−	31.4198i	0.954760	−	1.06037i
$879$	9.09369	+	15.7507i	0.306723	+	0.531259i
$880$	−0.476131	−	1.11739i	−0.0160504	−	0.0376673i
$881$	−52.6530			−1.77392			−0.886962	−	0.461843i	$-0.847188\pi$
$881$	−52.6530			−1.77392			−0.886962	+	0.461843i	$0.847188\pi$
$882$	−7.99798	+	3.34339i	−0.269306	+	0.112578i
$883$	8.54792	+	6.21043i	0.287660	+	0.208997i	0.722252	−	0.691630i	$-0.243107\pi$
$883$	8.54792	+	6.21043i	0.287660	+	0.208997i	−0.434591	+	0.900628i	$0.643107\pi$
$884$	0.747777	+	7.11462i	0.0251505	+	0.239291i
$885$	−0.255953	+	0.0544046i	−0.00860378	+	0.00182879i
$886$	23.3005	−	4.95267i	0.782796	−	0.166388i
$887$	1.76297	+	16.7736i	0.0591948	+	0.563201i	0.983419	+	0.181350i	$0.0580466\pi$
$887$	1.76297	+	16.7736i	0.0591948	+	0.563201i	−0.924224	+	0.381851i	$0.875287\pi$
$888$	11.3602	+	8.25367i	0.381223	+	0.276975i
$889$	−26.1065	+	2.44168i	−0.875585	+	0.0818912i
$890$	−1.19234			−0.0399672
$891$	3.30360	−	0.293635i	0.110675	−	0.00983713i
$892$	0.961125	+	1.66472i	0.0321808	+	0.0557389i
$893$	−15.2045	+	16.8863i	−0.508799	+	0.565078i
$894$	18.3787	−	8.18273i	0.614676	−	0.273671i
$895$	−0.929536	+	0.675347i	−0.0310710	+	0.0225744i
$896$	−13.5026	+	7.59068i	−0.451089	+	0.253587i
$897$	0.580480	−	1.78653i	0.0193816	−	0.0596506i
$898$	1.21596	+	11.5691i	0.0405771	+	0.386065i
$899$	−0.0605170	+	0.575781i	−0.00201836	+	0.0192034i
$900$	1.55530	−	1.72733i	0.0518432	−	0.0575777i
$901$	−11.7862	+	20.4143i	−0.392655	+	0.680098i
$902$	−14.0760	−	4.82497i	−0.468678	−	0.160654i
$903$	−0.793629	+	0.247844i	−0.0264103	+	0.00824774i
$904$	6.36060	+	19.5759i	0.211550	+	0.651085i
$905$	−2.69675	+	1.20067i	−0.0896431	+	0.0399117i
$906$	25.6749	+	11.4312i	0.852990	+	0.379776i
$907$	46.7484	−	9.93669i	1.55226	−	0.329942i	0.649591	−	0.760284i	$-0.274940\pi$
$907$	46.7484	−	9.93669i	1.55226	−	0.329942i	0.902666	+	0.430342i	$0.141607\pi$
$908$	7.01528	+	7.79126i	0.232810	+	0.258562i
$909$	−7.79782	+	5.66545i	−0.258637	+	0.187911i
$910$	0.896905	+	0.302832i	0.0297321	+	0.0100388i
$911$	12.5259	+	38.5507i	0.415001	+	1.27724i	0.912250	+	0.409635i	$0.134344\pi$
$911$	12.5259	+	38.5507i	0.415001	+	1.27724i	−0.497248	+	0.867608i	$0.665656\pi$
$912$	2.95573	−	5.11948i	0.0978742	−	0.169523i
$913$	−7.19383	−	36.7376i	−0.238081	−	1.21584i
$914$	−13.2710	−	22.9861i	−0.438967	−	0.760313i
$915$	−1.48552	−	0.315758i	−0.0491099	−	0.0104386i
$916$	−3.53193	−	2.56610i	−0.116698	−	0.0847863i
$917$	9.24870	+	1.07941i	0.305419	+	0.0356451i
$918$	−2.61077	+	8.03513i	−0.0861683	+	0.265199i
$919$	−10.7535	−	11.9430i	−0.354725	−	0.393962i	0.539201	−	0.842177i	$-0.318726\pi$
$919$	−10.7535	−	11.9430i	−0.354725	−	0.393962i	−0.893926	+	0.448215i	$0.852060\pi$
$920$	0.299617	+	0.133398i	0.00987809	+	0.00439801i
$921$	0.718237	−	6.83357i	0.0236667	−	0.225174i
$922$	35.9668	+	7.64498i	1.18450	+	0.251774i
$923$	24.4285			0.804075
$924$	−3.78331	+	1.56111i	−0.124462	+	0.0513566i
$925$	−22.9109			−0.753304
$926$	−31.1541	−	6.62200i	−1.02379	−	0.217612i
$927$	−0.996707	+	9.48304i	−0.0327362	+	0.311464i
$928$	2.43871	+	1.08578i	0.0800546	+	0.0356426i
$929$	2.66341	+	2.95802i	0.0873836	+	0.0970494i	0.785251	−	0.619178i	$-0.212534\pi$
$929$	2.66341	+	2.95802i	0.0873836	+	0.0970494i	−0.697867	+	0.716227i	$0.745867\pi$
$930$	0.0275157	−	0.0846847i	0.000902276	−	0.00277692i
$931$	−4.80274	+	13.7040i	−0.157403	+	0.449131i
$932$	−8.38807	−	6.09429i	−0.274760	−	0.199625i
$933$	−5.71441	−	1.21464i	−0.187082	−	0.0397654i
$934$	−24.9324	−	43.1842i	−0.815814	−	1.41303i
$935$	2.88670	+	0.350388i	0.0944051	+	0.0114589i
$936$	−3.43342	+	5.94686i	−0.112225	+	0.194379i
$937$	12.2180	+	37.6033i	0.399146	+	1.22844i	0.925685	+	0.378294i	$0.123489\pi$
$937$	12.2180	+	37.6033i	0.399146	+	1.22844i	−0.526539	+	0.850151i	$0.676511\pi$
$938$	35.5112	−	31.2448i	1.15948	−	1.02018i
$939$	−8.72113	+	6.33627i	−0.284603	+	0.206776i
$940$	0.439323	+	0.487918i	0.0143291	+	0.0159141i
$941$	46.0910	−	9.79694i	1.50252	−	0.319371i	0.618116	−	0.786087i	$-0.287896\pi$
$941$	46.0910	−	9.79694i	1.50252	−	0.319371i	0.884407	+	0.466716i	$0.154563\pi$
$942$	−2.74258	−	1.22108i	−0.0893581	−	0.0397848i
$943$	2.76534	−	1.23121i	0.0900519	−	0.0400937i
$944$	−1.79300	−	5.51828i	−0.0583571	−	0.179605i
$945$	−0.250056	−	0.230396i	−0.00813431	−	0.00749478i
$946$	1.23378	−	0.379073i	0.0401138	−	0.0123247i
$947$	−11.7579	+	20.3654i	−0.382082	+	0.661785i	−0.991360	−	0.131172i	$-0.958126\pi$
$947$	−11.7579	+	20.3654i	−0.382082	+	0.661785i	0.609278	+	0.792957i	$0.291459\pi$
$948$	−4.07677	+	4.52771i	−0.132407	+	0.147053i
$949$	2.67342	−	25.4359i	0.0867830	−	0.825685i
$950$	1.33822	+	12.7323i	0.0434176	+	0.413091i
$951$	7.78037	−	23.9455i	0.252296	−	0.776487i
$952$	0.631993	−	55.1280i	0.0204830	−	1.78671i
$953$	11.2712	−	8.18899i	0.365109	−	0.265268i	−0.390071	−	0.920785i	$-0.627549\pi$
$953$	11.2712	−	8.18899i	0.365109	−	0.265268i	0.755180	+	0.655517i	$0.227549\pi$
$954$	−3.90892	+	1.74036i	−0.126556	+	0.0563463i
$955$	−1.50971	+	1.67671i	−0.0488532	+	0.0542570i
$956$	0.769153	+	1.33221i	0.0248762	+	0.0430868i
$957$	−2.94422	−	1.76353i	−0.0951732	−	0.0570067i
$958$	−19.9523			−0.644629
$959$	13.3055	+	18.7620i	0.429656	+	0.605856i
$960$	−0.924709	−	0.671840i	−0.0298449	−	0.0216836i
$961$	3.20766	+	30.5189i	0.103473	+	0.984479i
$962$	12.5200	−	2.66121i	0.403661	−	0.0858007i
$963$	1.58520	−	0.336944i	0.0510823	−	0.0108579i
$964$	0.319323	+	3.03816i	0.0102847	+	0.0978524i
$965$	−2.51136	−	1.82461i	−0.0808436	−	0.0587363i
$966$	−1.14208	+	2.48800i	−0.0367459	+	0.0800501i
$967$	4.61851			0.148521			0.0742606	−	0.997239i	$-0.476340\pi$
$967$	4.61851			0.148521			0.0742606	+	0.997239i	$0.476340\pi$
$968$	31.1165	−	12.6722i	1.00012	−	0.407299i
$969$	7.07632	+	12.2565i	0.227324	+	0.393737i
$970$	0.836237	−	0.928735i	0.0268499	−	0.0298199i
$971$	−17.9223	+	7.97951i	−0.575153	+	0.256075i	−0.673635	−	0.739064i	$-0.735268\pi$
$971$	−17.9223	+	7.97951i	−0.575153	+	0.256075i	0.0984817	+	0.995139i	$0.468601\pi$
$972$	0.377334	−	0.274150i	0.0121030	−	0.00879335i
$973$	−32.0470	−	18.9955i	−1.02738	−	0.608967i
$974$	−8.89808	+	27.3855i	−0.285113	+	0.877488i
$975$	−1.17113	−	11.1425i	−0.0375061	−	0.356847i
$976$	3.52006	−	33.4911i	0.112674	−	1.07203i
$977$	−6.51974	+	7.24090i	−0.208585	+	0.231657i	−0.838355	−	0.545124i	$-0.816482\pi$
$977$	−6.51974	+	7.24090i	−0.208585	+	0.231657i	0.629770	+	0.776781i	$0.283149\pi$
$978$	−7.57793	+	13.1254i	−0.242315	+	0.419703i
$979$	0.399278	−	24.8448i	0.0127610	−	0.794043i
$980$	0.379293	+	0.179402i	0.0121161	+	0.00573077i
$981$	−2.90580	−	8.94312i	−0.0927749	−	0.285532i
$982$	5.39011	−	2.39983i	0.172005	−	0.0765817i
$983$	22.3953	+	9.97103i	0.714299	+	0.318026i	0.731515	−	0.681825i	$-0.238814\pi$
$983$	22.3953	+	9.97103i	0.714299	+	0.318026i	−0.0172159	+	0.999852i	$0.505480\pi$
$984$	−10.8237	+	2.30064i	−0.345046	+	0.0733419i
$985$	−1.34524	−	1.49404i	−0.0428628	−	0.0476040i
$986$	7.07281	−	5.13870i	0.225244	−	0.163649i
$987$	−21.7575	+	19.1435i	−0.692549	+	0.609345i
$988$	0.672192	+	2.06880i	0.0213853	+	0.0658172i
$989$	−0.131285	+	0.227392i	−0.00417461	+	0.00723064i
$990$	0.386533	+	0.359449i	0.0122848	+	0.0114241i
$991$	−18.3651	−	31.8092i	−0.583385	−	1.01045i	−0.995075	−	0.0991284i	$-0.968395\pi$
$991$	−18.3651	−	31.8092i	−0.583385	−	1.01045i	0.411690	−	0.911324i	$-0.364939\pi$
$992$	−1.41183	−	0.300093i	−0.0448255	−	0.00952796i
$993$	−18.9136	−	13.7416i	−0.600206	−	0.436075i
$994$	−35.3611	−	4.12696i	−1.12159	−	0.130899i
$995$	−0.658245	+	2.02587i	−0.0208678	+	0.0642244i
$996$	−3.52261	−	3.91225i	−0.111618	−	0.123964i
$997$	−51.1835	−	22.7884i	−1.62100	−	0.721715i	−0.622838	−	0.782351i	$-0.714020\pi$
$997$	−51.1835	−	22.7884i	−1.62100	−	0.721715i	−0.998160	+	0.0606363i	$0.980687\pi$
$998$	−2.11934	+	20.1642i	−0.0670866	+	0.638286i
$999$	−4.49689	−	0.955844i	−0.142275	−	0.0302416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.16.3	✓	64
3.2	odd	2		693.2.by.c.478.6		64
7.4	even	3	inner	231.2.y.b.214.6	yes	64
11.9	even	5	inner	231.2.y.b.163.6	yes	64
21.11	odd	6		693.2.by.c.676.3		64
33.20	odd	10		693.2.by.c.163.3		64
77.53	even	15	inner	231.2.y.b.130.3	yes	64
231.53	odd	30		693.2.by.c.361.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.3	✓	64	1.1	even	1	trivial
231.2.y.b.130.3	yes	64	77.53	even	15	inner
231.2.y.b.163.6	yes	64	11.9	even	5	inner
231.2.y.b.214.6	yes	64	7.4	even	3	inner
693.2.by.c.163.3		64	33.20	odd	10
693.2.by.c.361.6		64	231.53	odd	30
693.2.by.c.478.6		64	3.2	odd	2
693.2.by.c.676.3		64	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21132 - 0.257474i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.426088 - 0.189706i) q^{4} +(0.0859924 + 0.0955042i) q^{5} +(0.382681 - 1.17777i) q^{6} +(-1.04835 - 2.42919i) q^{7} +(2.47103 + 1.79531i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-1.21132 - 0.257474i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.426088 - 0.189706i) q^{4} +(0.0859924 + 0.0955042i) q^{5} +(0.382681 - 1.17777i) q^{6} +(-1.04835 - 2.42919i) q^{7} +(2.47103 + 1.79531i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.0795744 - 0.137827i) q^{10} +(2.89856 - 1.61194i) q^{11} +(0.233206 - 0.403924i) q^{12} +(-0.694735 - 2.13817i) q^{13} +(0.644429 + 3.21245i) q^{14} +(-0.103970 + 0.0755384i) q^{15} +(-1.90678 - 2.11769i) q^{16} +(6.67323 - 1.41844i) q^{17} +(1.13132 + 0.503695i) q^{18} +(1.89512 - 0.843760i) q^{19} +(-0.0185225 - 0.0570065i) q^{20} +(2.52547 - 0.788684i) q^{21} +(-3.92611 + 1.20628i) q^{22} +(0.417771 - 0.723600i) q^{23} +(-2.04376 + 2.26983i) q^{24} +(0.520916 - 4.95618i) q^{25} +(0.291022 + 2.76889i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0141459 + 1.23393i) q^{28} +(-0.837155 + 0.608228i) q^{29} +(0.145390 - 0.0647317i) q^{30} +(0.374374 - 0.415785i) q^{31} +(-1.28989 - 2.23415i) q^{32} +(1.30013 + 3.05117i) q^{33} -8.44863 q^{34} +(0.141848 - 0.309013i) q^{35} +(0.377334 + 0.274150i) q^{36} +(-0.480555 - 4.57217i) q^{37} +(-2.51284 + 0.534120i) q^{38} +(2.19908 - 0.467429i) q^{39} +(0.0410302 + 0.390376i) q^{40} +(2.93095 + 2.12946i) q^{41} +(-3.26221 + 0.305106i) q^{42} -0.314251 q^{43} +(-1.54084 + 0.136954i) q^{44} +(-0.0642568 - 0.111296i) q^{45} +(-0.692362 + 0.768946i) q^{46} +(-10.0066 + 4.45521i) q^{47} +(2.30541 - 1.67498i) q^{48} +(-4.80194 + 5.09327i) q^{49} +(-1.90708 + 5.86940i) q^{50} +(0.713126 + 6.78494i) q^{51} +(-0.109607 + 1.04285i) q^{52} +(-2.31197 + 2.56770i) q^{53} +(-0.619191 + 1.07247i) q^{54} +(0.403201 + 0.138210i) q^{55} +(1.77065 - 7.88470i) q^{56} +(0.641044 + 1.97293i) q^{57} +(1.17067 - 0.521214i) q^{58} +(1.86011 + 0.828173i) q^{59} +(0.0586303 - 0.0124623i) q^{60} +(7.90746 + 8.78212i) q^{61} +(-0.560541 + 0.407257i) q^{62} +(0.520380 + 2.59407i) q^{63} +(2.74840 + 8.45872i) q^{64} +(0.144463 - 0.250217i) q^{65} +(-0.789278 - 4.03070i) q^{66} +(-7.21817 - 12.5022i) q^{67} +(-3.11247 - 0.661576i) q^{68} +(0.675967 + 0.491119i) q^{69} +(-0.251386 + 0.337792i) q^{70} +(-3.35771 + 10.3340i) q^{71} +(-2.04376 - 2.26983i) q^{72} +(10.3927 + 4.62711i) q^{73} +(-0.595110 + 5.66209i) q^{74} +(4.87458 + 1.03612i) q^{75} -0.967552 q^{76} +(-6.95441 - 5.35128i) q^{77} -2.78414 q^{78} +(-12.7774 - 2.71591i) q^{79} +(0.0382801 - 0.364211i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-3.00204 - 3.33410i) q^{82} +(3.48792 - 10.7347i) q^{83} +(-1.22569 - 0.143049i) q^{84} +(0.709314 + 0.515347i) q^{85} +(0.380658 + 0.0809114i) q^{86} +(-0.517390 - 0.896146i) q^{87} +(10.0563 + 1.22064i) q^{88} +(3.74598 - 6.48822i) q^{89} +(0.0491797 + 0.151360i) q^{90} +(-4.46571 + 3.92919i) q^{91} +(-0.315278 + 0.229063i) q^{92} +(0.374374 + 0.415785i) q^{93} +(13.2683 - 2.82026i) q^{94} +(0.243548 + 0.108435i) q^{95} +(2.35674 - 1.04929i) q^{96} +(2.42659 + 7.46829i) q^{97} +(7.12807 - 4.93320i) q^{98} +(-3.17036 + 0.974075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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