LMFDB - Embedded newform 930.2.br.b.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(1.17969 - 1.26820i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.730058 - 1.57067i) q^{6} +(-0.249897 - 2.37761i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.216657 - 2.99217i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(1.17969 - 1.26820i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.730058 - 1.57067i) q^{6} +(-0.249897 - 2.37761i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.216657 - 2.99217i) q^{9} +(0.669131 - 0.743145i) q^{10} +(1.10532 + 0.492120i) q^{11} +(0.208962 - 1.71940i) q^{12} +(0.245675 + 1.15581i) q^{13} +(-0.972390 - 2.18402i) q^{14} +(0.387543 - 1.68814i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.53967 + 1.57596i) q^{17} +(-1.13068 - 2.77877i) q^{18} +(0.0990872 + 0.0210616i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-3.31009 - 2.48793i) q^{21} +(1.20329 + 0.126471i) q^{22} +(3.15414 + 2.29162i) q^{23} +(-0.332589 - 1.69982i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.590815 + 1.02332i) q^{26} +(-4.05025 - 3.25507i) q^{27} +(-1.59970 - 1.77664i) q^{28} +(1.74063 + 5.35710i) q^{29} +(-0.153088 - 1.72527i) q^{30} +(-5.34746 - 1.55069i) q^{31} -1.00000i q^{32} +(1.92804 - 0.821215i) q^{33} +(-2.87943 + 2.59265i) q^{34} +(-1.40522 - 1.93413i) q^{35} +(-1.93403 - 2.29337i) q^{36} +(1.25459 + 0.724340i) q^{37} +(0.100746 - 0.0105888i) q^{38} +(1.75561 + 1.05193i) q^{39} +(0.104528 - 0.994522i) q^{40} +(2.78603 + 2.50855i) q^{41} +(-3.91690 - 1.34329i) q^{42} +(0.549332 - 2.58440i) q^{43} +(1.18348 - 0.251557i) q^{44} +(-1.68371 - 2.48296i) q^{45} +(3.70792 + 1.20478i) q^{46} +(-2.54004 - 0.825307i) q^{47} +(-0.841584 - 1.51385i) q^{48} +(1.25643 - 0.267062i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-2.17708 + 6.34815i) q^{51} +(0.878122 + 0.790664i) q^{52} +(-0.599254 + 5.70152i) q^{53} +(-4.85789 - 1.84416i) q^{54} +(1.20329 - 0.126471i) q^{55} +(-2.07042 - 1.19536i) q^{56} +(0.143603 - 0.100816i) q^{57} +(3.31087 + 4.55702i) q^{58} +(7.17722 - 6.46239i) q^{59} +(-0.678734 - 1.59352i) q^{60} -11.3964i q^{61} +(-5.56493 + 0.177661i) q^{62} +(-7.06008 + 1.26286i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.790664 + 0.878122i) q^{65} +(1.57991 - 1.37682i) q^{66} +(4.00396 + 6.93507i) q^{67} +(-1.93732 + 3.35555i) q^{68} +(6.62715 - 1.29668i) q^{69} +(-1.93413 - 1.40522i) q^{70} +(10.6927 + 1.12385i) q^{71} +(-2.54806 - 1.58347i) q^{72} +(-2.36384 + 5.30927i) q^{73} +(1.41702 + 0.301198i) q^{74} +(-0.508447 - 1.65574i) q^{75} +(0.0925430 - 0.0412028i) q^{76} +(0.893855 - 2.75100i) q^{77} +(1.99475 + 0.457932i) q^{78} +(4.22491 + 9.48930i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.90612 + 1.29655i) q^{81} +(3.42485 + 1.52484i) q^{82} +(-4.71135 + 5.23248i) q^{83} +(-4.14029 - 0.0671570i) q^{84} +(-2.27746 + 3.13466i) q^{85} +(-0.276179 - 2.62767i) q^{86} +(8.84728 + 4.11226i) q^{87} +(1.04782 - 0.604961i) q^{88} +(-4.63131 + 3.36485i) q^{89} +(-2.36858 - 1.84114i) q^{90} +(2.68667 - 0.872953i) q^{91} +3.89874 q^{92} +(-8.27494 + 4.95231i) q^{93} -2.67075 q^{94} +(0.0963429 - 0.0313037i) q^{95} +(-1.26820 - 1.17969i) q^{96} +(2.86853 - 2.08411i) q^{97} +(1.11241 - 0.642250i) q^{98} +(1.23303 - 3.41392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

Coefficient data

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

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

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

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	1.17969	−	1.26820i	0.681095	−	0.732195i
$3$	1.17969	−	1.26820i	0.681095	−	0.732195i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.730058	−	1.57067i	0.298045	−	0.641225i
$7$	−0.249897	−	2.37761i	−0.0944523	−	0.898654i	−0.934457	−	0.356075i	$-0.884115\pi$
$7$	−0.249897	−	2.37761i	−0.0944523	−	0.898654i	0.840005	−	0.542579i	$-0.182552\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−0.216657	−	2.99217i	−0.0722189	−	0.997389i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	1.10532	+	0.492120i	0.333266	+	0.148380i	0.566546	−	0.824030i	$-0.308279\pi$
$11$	1.10532	+	0.492120i	0.333266	+	0.148380i	−0.233280	+	0.972410i	$0.574946\pi$
$12$	0.208962	−	1.71940i	0.0603221	−	0.496348i
$13$	0.245675	+	1.15581i	0.0681379	+	0.320563i	0.998995	−	0.0448197i	$-0.0142713\pi$
$13$	0.245675	+	1.15581i	0.0681379	+	0.320563i	−0.930857	+	0.365383i	$0.880938\pi$
$14$	−0.972390	−	2.18402i	−0.259882	−	0.583705i
$15$	0.387543	−	1.68814i	0.100063	−	0.435875i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.53967	+	1.57596i	−0.858496	+	0.382227i	−0.788289	−	0.615306i	$-0.789033\pi$
$17$	−3.53967	+	1.57596i	−0.858496	+	0.382227i	−0.0702070	+	0.997532i	$0.522366\pi$
$18$	−1.13068	−	2.77877i	−0.266505	−	0.654962i
$19$	0.0990872	+	0.0210616i	0.0227322	+	0.00483187i	0.219264	−	0.975666i	$-0.429634\pi$
$19$	0.0990872	+	0.0210616i	0.0227322	+	0.00483187i	−0.196532	+	0.980497i	$0.562968\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	−3.31009	−	2.48793i	−0.722321	−	0.542911i
$22$	1.20329	+	0.126471i	0.256543	+	0.0269638i
$23$	3.15414	+	2.29162i	0.657684	+	0.477836i	0.865880	−	0.500251i	$-0.166759\pi$
$23$	3.15414	+	2.29162i	0.657684	+	0.477836i	−0.208196	+	0.978087i	$0.566759\pi$
$24$	−0.332589	−	1.69982i	−0.0678895	−	0.346974i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.590815	+	1.02332i	0.115868	+	0.200690i
$27$	−4.05025	−	3.25507i	−0.779471	−	0.626438i
$28$	−1.59970	−	1.77664i	−0.302315	−	0.335754i
$29$	1.74063	+	5.35710i	0.323227	+	0.994789i	0.972235	+	0.234008i	$0.0751841\pi$
$29$	1.74063	+	5.35710i	0.323227	+	0.994789i	−0.649008	+	0.760781i	$0.724816\pi$
$30$	−0.153088	−	1.72527i	−0.0279499	−	0.314990i
$31$	−5.34746	−	1.55069i	−0.960433	−	0.278512i
$31$	−5.34746	−	1.55069i	−0.960433	−	0.278512i
$32$		−	1.00000i		−	0.176777i
$33$	1.92804	−	0.821215i	0.335629	−	0.142955i
$34$	−2.87943	+	2.59265i	−0.493817	+	0.444635i
$35$	−1.40522	−	1.93413i	−0.237526	−	0.326927i
$36$	−1.93403	−	2.29337i	−0.322338	−	0.382228i
$37$	1.25459	+	0.724340i	0.206254	+	0.119081i	0.599569	−	0.800323i	$-0.295339\pi$
$37$	1.25459	+	0.724340i	0.206254	+	0.119081i	−0.393315	+	0.919404i	$0.628672\pi$
$38$	0.100746	−	0.0105888i	0.0163432	−	0.00171773i
$39$	1.75561	+	1.05193i	0.281123	+	0.168444i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	2.78603	+	2.50855i	0.435104	+	0.391770i	0.857368	−	0.514703i	$-0.172098\pi$
$41$	2.78603	+	2.50855i	0.435104	+	0.391770i	−0.422264	+	0.906473i	$0.638765\pi$
$42$	−3.91690	−	1.34329i	−0.604390	−	0.207274i
$43$	0.549332	−	2.58440i	0.0837724	−	0.394118i	−0.916206	−	0.400708i	$-0.868764\pi$
$43$	0.549332	−	2.58440i	0.0837724	−	0.394118i	0.999978	+	0.00658976i	$0.00209760\pi$
$44$	1.18348	−	0.251557i	0.178417	−	0.0379236i
$45$	−1.68371	−	2.48296i	−0.250993	−	0.370138i
$46$	3.70792	+	1.20478i	0.546703	+	0.177634i
$47$	−2.54004	−	0.825307i	−0.370502	−	0.120383i	0.117847	−	0.993032i	$-0.462401\pi$
$47$	−2.54004	−	0.825307i	−0.370502	−	0.120383i	−0.488349	+	0.872648i	$0.662401\pi$
$48$	−0.841584	−	1.51385i	−0.121472	−	0.218505i
$49$	1.25643	−	0.267062i	0.179490	−	0.0381518i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−2.17708	+	6.34815i	−0.304853	+	0.888919i
$52$	0.878122	+	0.790664i	0.121774	+	0.109645i
$53$	−0.599254	+	5.70152i	−0.0823139	+	0.783164i	0.873030	+	0.487667i	$0.162152\pi$
$53$	−0.599254	+	5.70152i	−0.0823139	+	0.783164i	−0.955344	+	0.295497i	$0.904515\pi$
$54$	−4.85789	−	1.84416i	−0.661075	−	0.250958i
$55$	1.20329	−	0.126471i	0.162252	−	0.0170534i
$56$	−2.07042	−	1.19536i	−0.276671	−	0.159736i
$57$	0.143603	−	0.100816i	0.0190206	−	0.0133534i
$58$	3.31087	+	4.55702i	0.434739	+	0.598367i
$59$	7.17722	−	6.46239i	0.934394	−	0.841332i	−0.0531642	−	0.998586i	$-0.516931\pi$
$59$	7.17722	−	6.46239i	0.934394	−	0.841332i	0.987558	+	0.157254i	$0.0502640\pi$
$60$	−0.678734	−	1.59352i	−0.0876241	−	0.205723i
$61$		−	11.3964i		−	1.45915i	−0.683899	−	0.729577i	$-0.739717\pi$
$61$		−	11.3964i		−	1.45915i	0.683899	−	0.729577i	$-0.260283\pi$
$62$	−5.56493	+	0.177661i	−0.706747	+	0.0225630i
$63$	−7.06008	+	1.26286i	−0.889486	+	0.159106i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.790664	+	0.878122i	0.0980699	+	0.108918i
$66$	1.57991	−	1.37682i	0.194473	−	0.169475i
$67$	4.00396	+	6.93507i	0.489162	+	0.847253i	0.999922	−	0.0124699i	$-0.00396940\pi$
$67$	4.00396	+	6.93507i	0.489162	+	0.847253i	−0.510760	+	0.859723i	$0.670636\pi$
$68$	−1.93732	+	3.35555i	−0.234935	+	0.406920i
$69$	6.62715	−	1.29668i	0.797815	−	0.156102i
$70$	−1.93413	−	1.40522i	−0.231172	−	0.167956i
$71$	10.6927	+	1.12385i	1.26899	+	0.133376i	0.714987	−	0.699138i	$-0.246433\pi$
$71$	10.6927	+	1.12385i	1.26899	+	0.133376i	0.554004	+	0.832514i	$0.313099\pi$
$72$	−2.54806	−	1.58347i	−0.300292	−	0.186614i
$73$	−2.36384	+	5.30927i	−0.276666	+	0.621403i	−0.997420	−	0.0717888i	$-0.977129\pi$
$73$	−2.36384	+	5.30927i	−0.276666	+	0.621403i	0.720754	+	0.693191i	$0.243796\pi$
$74$	1.41702	+	0.301198i	0.164726	+	0.0350135i
$75$	−0.508447	−	1.65574i	−0.0587104	−	0.191189i
$76$	0.0925430	−	0.0412028i	0.0106154	−	0.00472628i
$77$	0.893855	−	2.75100i	0.101864	−	0.313506i
$78$	1.99475	+	0.457932i	0.225861	+	0.0518506i
$79$	4.22491	+	9.48930i	0.475340	+	1.06763i	0.979024	+	0.203743i	$0.0653106\pi$
$79$	4.22491	+	9.48930i	0.475340	+	1.06763i	−0.503685	+	0.863887i	$0.668023\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	−8.90612	+	1.29655i	−0.989569	+	0.144061i
$82$	3.42485	+	1.52484i	0.378212	+	0.168391i
$83$	−4.71135	+	5.23248i	−0.517138	+	0.574340i	−0.943987	−	0.329983i	$-0.892957\pi$
$83$	−4.71135	+	5.23248i	−0.517138	+	0.574340i	0.426849	+	0.904323i	$0.359624\pi$
$84$	−4.14029	−	0.0671570i	−0.451743	−	0.00732743i
$85$	−2.27746	+	3.13466i	−0.247025	+	0.340001i
$86$	−0.276179	−	2.62767i	−0.0297811	−	0.283349i
$87$	8.84728	+	4.11226i	0.948527	+	0.440881i
$88$	1.04782	−	0.604961i	0.111698	−	0.0644891i
$89$	−4.63131	+	3.36485i	−0.490918	+	0.356673i	−0.805537	−	0.592545i	$-0.798123\pi$
$89$	−4.63131	+	3.36485i	−0.490918	+	0.356673i	0.314619	+	0.949218i	$0.398123\pi$
$90$	−2.36858	−	1.84114i	−0.249671	−	0.194073i
$91$	2.68667	−	0.872953i	0.281640	−	0.0915103i
$92$	3.89874			0.406471
$93$	−8.27494	+	4.95231i	−0.858071	+	0.513530i
$94$	−2.67075			−0.275467
$95$	0.0963429	−	0.0313037i	0.00988457	−	0.00321169i
$96$	−1.26820	−	1.17969i	−0.129435	−	0.120402i
$97$	2.86853	−	2.08411i	0.291255	−	0.211610i	−0.432556	−	0.901607i	$-0.642388\pi$
$97$	2.86853	−	2.08411i	0.291255	−	0.211610i	0.723812	+	0.689997i	$0.242388\pi$
$98$	1.11241	−	0.642250i	0.112370	−	0.0648770i
$99$	1.23303	−	3.41392i	0.123924	−	0.343112i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−4.17324	+	5.74397i	−0.415253	+	0.571547i	−0.964490	−	0.264120i	$-0.914919\pi$
$101$	−4.17324	+	5.74397i	−0.415253	+	0.571547i	0.549237	+	0.835667i	$0.314919\pi$
$102$	−0.108842	+	6.71021i	−0.0107770	+	0.664410i
$103$	5.54621	−	6.15969i	0.546484	−	0.606933i	−0.405118	−	0.914264i	$-0.632770\pi$
$103$	5.54621	−	6.15969i	0.546484	−	0.606933i	0.951602	+	0.307332i	$0.0994362\pi$
$104$	1.07947	+	0.480612i	0.105851	+	0.0471279i
$105$	−4.11059	−	0.499567i	−0.401152	−	0.0487528i
$106$	1.19194	+	5.60765i	0.115772	+	0.544663i
$107$	−6.45963	−	14.5086i	−0.624476	−	1.40260i	−0.897684	−	0.440640i	$-0.854751\pi$
$107$	−6.45963	−	14.5086i	−0.624476	−	1.40260i	0.273208	−	0.961955i	$-0.411915\pi$
$108$	−5.19000	−	0.252729i	−0.499408	−	0.0243188i
$109$	1.60032	−	4.92527i	0.153282	−	0.471755i	−0.844700	−	0.535239i	$-0.820221\pi$
$109$	1.60032	−	4.92527i	0.153282	−	0.471755i	0.997983	+	0.0634846i	$0.0202214\pi$
$110$	1.10532	−	0.492120i	0.105388	−	0.0469218i
$111$	2.39864	−	0.736577i	0.227669	−	0.0699128i
$112$	−2.33847	−	0.497057i	−0.220965	−	0.0469675i
$113$	−4.98372	+	11.1936i	−0.468829	+	1.05301i	0.512150	+	0.858896i	$0.328849\pi$
$113$	−4.98372	+	11.1936i	−0.468829	+	1.05301i	−0.980979	+	0.194112i	$0.937818\pi$
$114$	0.105420	−	0.140257i	0.00987352	−	0.0131363i
$115$	3.87738	+	0.407529i	0.361567	+	0.0380023i
$116$	4.55702	+	3.31087i	0.423109	+	0.307407i
$117$	3.40514	−	0.985513i	0.314806	−	0.0911107i
$118$	4.82895	−	8.36398i	0.444541	−	0.769967i
$119$	4.63158	+	8.02214i	0.424577	+	0.735388i
$120$	−1.13794	−	1.30579i	−0.103879	−	0.119202i
$121$	−6.38089	−	7.08670i	−0.580081	−	0.644245i
$122$	−3.52167	−	10.8386i	−0.318837	−	0.981279i
$123$	6.46799	−	0.573922i	0.583199	−	0.0517488i
$124$	−5.23766	+	1.88862i	−0.470356	+	0.169603i
$125$		−	1.00000i		−	0.0894427i
$126$	−6.32429	+	3.38274i	−0.563412	+	0.301358i
$127$	−10.1235	+	9.11522i	−0.898314	+	0.808845i	−0.982240	−	0.187627i	$-0.939920\pi$
$127$	−10.1235	+	9.11522i	−0.898314	+	0.808845i	0.0839268	+	0.996472i	$0.473254\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−2.62950	−	3.74546i	−0.231514	−	0.329770i
$130$	1.02332	+	0.590815i	0.0897512	+	0.0518179i
$131$	−1.28517	+	0.135076i	−0.112286	+	0.0118017i	−0.160505	−	0.987035i	$-0.551312\pi$
$131$	−1.28517	+	0.135076i	−0.112286	+	0.0118017i	0.0482190	+	0.998837i	$0.484645\pi$
$132$	1.07712	−	1.79765i	0.0937512	−	0.156465i
$133$	0.0253148	−	0.240854i	0.00219507	−	0.0208847i
$134$	5.95105	+	5.35835i	0.514092	+	0.462891i
$135$	−5.13515	−	0.793847i	−0.441964	−	0.0683235i
$136$	−0.805585	+	3.78998i	−0.0690783	+	0.324988i
$137$	−9.30604	+	1.97806i	−0.795069	+	0.168997i	−0.587501	−	0.809224i	$-0.699888\pi$
$137$	−9.30604	+	1.97806i	−0.795069	+	0.168997i	−0.207568	+	0.978221i	$0.566555\pi$
$138$	5.90209	−	3.28111i	0.502420	−	0.279307i
$139$	13.9471	+	4.53168i	1.18298	+	0.384372i	0.833471	−	0.552563i	$-0.186350\pi$
$139$	13.9471	+	4.53168i	1.18298	+	0.384372i	0.349504	+	0.936935i	$0.386350\pi$
$140$	−2.27370	−	0.738770i	−0.192163	−	0.0624375i
$141$	−4.04311	+	2.24766i	−0.340491	+	0.189287i
$142$	10.5167	−	2.23538i	0.882538	−	0.187589i
$143$	−0.297247	+	1.39844i	−0.0248570	+	0.116943i
$144$	−2.91267	−	0.718577i	−0.242723	−	0.0598814i
$145$	4.18598	+	3.76907i	0.347627	+	0.313004i
$146$	−0.607490	+	5.77988i	−0.0502762	+	0.478346i
$147$	1.14351	−	1.90845i	0.0943152	−	0.157407i
$148$	1.44074	−	0.151428i	0.118428	−	0.0124473i
$149$	1.63220	+	0.942354i	0.133715	+	0.0772006i	0.565365	−	0.824841i	$-0.308735\pi$
$149$	1.63220	+	0.942354i	0.133715	+	0.0772006i	−0.431650	+	0.902041i	$0.642068\pi$
$150$	−0.995214	−	1.41759i	−0.0812589	−	0.115745i
$151$	−5.49870	−	7.56831i	−0.447478	−	0.615901i	0.524375	−	0.851487i	$-0.324299\pi$
$151$	−5.49870	−	7.56831i	−0.447478	−	0.615901i	−0.971853	+	0.235587i	$0.924299\pi$
$152$	0.0752812	−	0.0677835i	0.00610611	−	0.00549797i
$153$	5.48243	+	10.2498i	0.443229	+	0.828650i
$154$		−	2.89257i		−	0.233090i
$155$	−5.40638	+	1.33079i	−0.434251	+	0.106892i
$156$	2.03863	−	0.180893i	0.163221	−	0.0144830i
$157$	3.22348	+	9.92085i	0.257262	+	0.791770i	0.993376	+	0.114912i	$0.0366587\pi$
$157$	3.22348	+	9.92085i	0.257262	+	0.791770i	−0.736114	+	0.676857i	$0.763341\pi$
$158$	6.95049	+	7.71930i	0.552951	+	0.614114i
$159$	6.52373	+	7.48601i	0.517365	+	0.593679i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	4.66038	−	8.07201i	0.367289	−	0.636163i
$162$	−8.06957	+	3.98523i	−0.634005	+	0.313109i
$163$	13.3181	+	9.67618i	1.04316	+	0.757897i	0.970899	−	0.239489i	$-0.0769800\pi$
$163$	13.3181	+	9.67618i	1.04316	+	0.757897i	0.0722564	+	0.997386i	$0.476980\pi$
$164$	3.72843	+	0.391874i	0.291142	+	0.0306002i
$165$	1.25912	−	1.67521i	0.0980227	−	0.130415i
$166$	−2.86383	+	6.43227i	−0.222277	+	0.499241i
$167$	2.65771	+	0.564914i	0.205660	+	0.0437144i	0.309590	−	0.950870i	$-0.399808\pi$
$167$	2.65771	+	0.564914i	0.205660	+	0.0437144i	−0.103930	+	0.994585i	$0.533142\pi$
$168$	−3.95840	+	1.21555i	−0.305397	+	0.0937817i
$169$	10.6006	−	4.71967i	0.815427	−	0.363052i
$170$	−1.19733	+	3.68501i	−0.0918312	+	0.282627i
$171$	0.0415520	−	0.301049i	0.00317756	−	0.0230218i
$172$	−1.07466	−	2.41372i	−0.0819417	−	0.184044i
$173$	−0.596310	−	2.80542i	−0.0453366	−	0.213292i	0.949648	−	0.313318i	$-0.101441\pi$
$173$	−0.596310	−	2.80542i	−0.0453366	−	0.213292i	−0.994985	+	0.100026i	$0.968107\pi$
$174$	9.68502	+	1.17704i	0.734219	+	0.0892310i
$175$	−2.18402	−	0.972390i	−0.165097	−	0.0735058i
$176$	0.809596	−	0.899147i	0.0610256	−	0.0677758i
$177$	0.271298	−	16.7258i	0.0203920	−	1.25719i
$178$	−3.36485	+	4.63131i	−0.252206	+	0.347132i
$179$	0.861720	+	8.19872i	0.0644080	+	0.612801i	0.978350	+	0.206957i	$0.0663559\pi$
$179$	0.861720	+	8.19872i	0.0644080	+	0.612801i	−0.913942	+	0.405845i	$0.866977\pi$
$180$	−2.82160	−	1.01910i	−0.210310	−	0.0759591i
$181$	6.24798	−	3.60727i	0.464408	−	0.268126i	−0.249488	−	0.968378i	$-0.580262\pi$
$181$	6.24798	−	3.60727i	0.464408	−	0.268126i	0.713896	+	0.700252i	$0.246929\pi$
$182$	2.28542	−	1.66046i	0.169407	−	0.123081i
$183$	−14.4528	−	13.4442i	−1.06838	−	0.993822i
$184$	3.70792	−	1.20478i	0.273351	−	0.0888172i
$185$	1.44868			0.106509
$186$	−6.33959	+	7.26702i	−0.464841	+	0.532844i
$187$	−4.68802			−0.342822
$188$	−2.54004	+	0.825307i	−0.185251	+	0.0601917i
$189$	−6.72715	+	10.4434i	−0.489328	+	0.759643i
$190$	0.0819541	−	0.0595432i	0.00594558	−	0.00431972i
$191$	6.63369	−	3.82996i	0.479997	−	0.277126i	−0.240418	−	0.970669i	$-0.577285\pi$
$191$	6.63369	−	3.82996i	0.479997	−	0.277126i	0.720415	+	0.693543i	$0.243951\pi$
$192$	−1.57067	−	0.730058i	−0.113354	−	0.0526874i
$193$	2.28405	+	21.7313i	0.164409	+	1.56425i	0.696496	+	0.717560i	$0.254741\pi$
$193$	2.28405	+	21.7313i	0.164409	+	1.56425i	−0.532087	+	0.846690i	$0.678592\pi$
$194$	2.08411	−	2.86853i	0.149631	−	0.205949i
$195$	2.04637	+	0.0331929i	0.146544	+	0.00237699i
$196$	0.859498	−	0.954569i	0.0613927	−	0.0681835i
$197$	−13.7483	−	6.12112i	−0.979524	−	0.436112i	−0.146416	−	0.989223i	$-0.546774\pi$
$197$	−13.7483	−	6.12112i	−0.979524	−	0.436112i	−0.833108	+	0.553111i	$0.813441\pi$
$198$	0.117721	−	3.62786i	0.00836609	−	0.257821i
$199$	4.10633	+	19.3188i	0.291090	+	1.36947i	0.844051	+	0.536264i	$0.180165\pi$
$199$	4.10633	+	19.3188i	0.291090	+	1.36947i	−0.552961	+	0.833207i	$0.686502\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	13.5185	+	3.10342i	0.953520	+	0.218898i
$202$	−2.19400	+	6.75245i	−0.154370	+	0.475100i
$203$	12.3021	−	5.47727i	0.863442	−	0.384429i
$204$	1.97005	+	6.41542i	0.137931	+	0.449169i
$205$	3.66705	+	0.779455i	0.256118	+	0.0544395i
$206$	3.37131	−	7.57209i	0.234890	−	0.527572i
$207$	6.17354	−	9.93422i	0.429091	−	0.690476i
$208$	1.17516	+	0.123514i	0.0814824	+	0.00856415i
$209$	0.0991581	+	0.0720426i	0.00685891	+	0.00498329i
$210$	−4.06378	+	0.795125i	−0.280427	+	0.0548688i
$211$	−1.01522	+	1.75841i	−0.0698904	+	0.121054i	−0.898853	−	0.438250i	$-0.855598\pi$
$211$	−1.01522	+	1.75841i	−0.0698904	+	0.121054i	0.828962	+	0.559304i	$0.188932\pi$
$212$	2.86646	+	4.96486i	0.196869	+	0.340988i
$213$	14.0394	−	12.2347i	0.961961	−	0.838307i
$214$	−10.6269	−	11.8023i	−0.726437	−	0.806790i
$215$	−0.816467	−	2.51283i	−0.0556826	−	0.171373i
$216$	−5.01408	+	1.36344i	−0.341165	+	0.0927703i
$217$	−2.35063	+	13.1017i	−0.159571	+	0.889403i
$218$		−	5.17873i		−	0.350748i
$219$	3.94461	+	9.26111i	0.266552	+	0.625808i
$220$	0.899147	−	0.809596i	0.0606205	−	0.0545829i
$221$	−2.69112	−	3.70400i	−0.181024	−	0.249158i
$222$	2.05363	−	1.44175i	0.137831	−	0.0967637i
$223$	7.44401	+	4.29780i	0.498488	+	0.287802i	0.728089	−	0.685483i	$-0.240409\pi$
$223$	7.44401	+	4.29780i	0.498488	+	0.287802i	−0.229601	+	0.973285i	$0.573742\pi$
$224$	−2.37761	+	0.249897i	−0.158861	+	0.0166970i
$225$	−2.69962	−	1.30845i	−0.179975	−	0.0872302i
$226$	−1.28078	+	12.1858i	−0.0851963	+	0.810589i
$227$	−16.4788	−	14.8376i	−1.09374	−	0.984805i	−0.0937951	−	0.995592i	$-0.529900\pi$
$227$	−16.4788	−	14.8376i	−1.09374	−	0.984805i	−0.999942	+	0.0107864i	$0.996567\pi$
$228$	0.0569188	−	0.165969i	0.00376954	−	0.0109916i
$229$	−2.31325	+	10.8830i	−0.152864	+	0.719167i	0.833223	+	0.552937i	$0.186493\pi$
$229$	−2.31325	+	10.8830i	−0.152864	+	0.719167i	−0.986087	+	0.166231i	$0.946840\pi$
$230$	3.81354	−	0.810593i	0.251457	−	0.0534489i
$231$	−2.43434	−	4.37892i	−0.160168	−	0.288112i
$232$	5.35710	+	1.74063i	0.351711	+	0.114278i
$233$	−3.65792	−	1.18853i	−0.239638	−	0.0778631i	0.186736	−	0.982410i	$-0.440209\pi$
$233$	−3.65792	−	1.18853i	−0.239638	−	0.0778631i	−0.426374	+	0.904547i	$0.640209\pi$
$234$	2.93394	−	1.98953i	0.191798	−	0.130059i
$235$	−2.61239	+	0.555280i	−0.170413	+	0.0362225i
$236$	2.00799	−	9.44685i	0.130709	−	0.614938i
$237$	17.0184	+	5.83642i	1.10546	+	0.379116i
$238$	6.88388	+	6.19827i	0.446215	+	0.401774i
$239$	−0.622640	+	5.92403i	−0.0402753	+	0.383194i	0.955754	+	0.294167i	$0.0950422\pi$
$239$	−0.622640	+	5.92403i	−0.0402753	+	0.383194i	−0.996029	+	0.0890264i	$0.971624\pi$
$240$	−1.48576	−	0.890239i	−0.0959052	−	0.0574647i
$241$	−20.7000	+	2.17565i	−1.33340	+	0.140146i	−0.744264	−	0.667886i	$-0.767199\pi$
$241$	−20.7000	+	2.17565i	−1.33340	+	0.140146i	−0.589138	+	0.808032i	$0.700533\pi$
$242$	−8.25850	−	4.76804i	−0.530876	−	0.306502i
$243$	−8.86219	+	12.8243i	−0.568510	+	0.822676i
$244$	−6.69861	−	9.21984i	−0.428834	−	0.590240i
$245$	0.954569	−	0.859498i	0.0609852	−	0.0549113i
$246$	5.97408	−	2.54455i	0.380893	−	0.162235i
$247$			0.119700i			0.00761634i
$248$	−4.39770	+	3.41471i	−0.279254	+	0.216835i
$249$	1.07789	+	12.1476i	0.0683086	+	0.769826i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−2.07968	−	2.30971i	−0.131268	−	0.145788i	0.673927	−	0.738798i	$-0.264606\pi$
$251$	−2.07968	−	2.30971i	−0.131268	−	0.145788i	−0.805195	+	0.593010i	$0.797939\pi$
$252$	−4.96943	+	5.17149i	−0.313045	+	0.325773i
$253$	2.35858	+	4.08519i	0.148283	+	0.256833i
$254$	−6.81124	+	11.7974i	−0.427375	+	0.740236i
$255$	1.28867	+	6.58620i	0.0806995	+	0.412444i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−28.3682	−	2.98162i	−1.76956	−	0.185988i	−0.837050	−	0.547127i	$-0.815721\pi$
$257$	−28.3682	−	2.98162i	−1.76956	−	0.185988i	−0.932512	+	0.361139i	$0.882388\pi$
$258$	−3.65821	−	2.74959i	−0.227750	−	0.171182i
$259$	1.40868	−	3.16395i	0.0875312	−	0.196598i
$260$	1.15581	+	0.245675i	0.0716802	+	0.0152361i
$261$	15.6522	−	6.36890i	0.968848	−	0.394225i
$262$	−1.18053	+	0.525604i	−0.0729331	+	0.0324719i
$263$	5.09252	−	15.6732i	0.314018	−	0.966449i	−0.662138	−	0.749382i	$-0.730351\pi$
$263$	5.09252	−	15.6732i	0.314018	−	0.966449i	0.976157	−	0.217068i	$-0.0696492\pi$
$264$	0.468897	−	2.04252i	0.0288586	−	0.125708i
$265$	2.33179	+	5.23729i	0.143241	+	0.321724i
$266$	−0.0503523	−	0.236889i	−0.00308730	−	0.0145246i
$267$	−1.19623	+	9.84291i	−0.0732079	+	0.602376i
$268$	7.31560	+	3.25712i	0.446872	+	0.198960i
$269$	5.37081	−	5.96489i	0.327464	−	0.363686i	−0.556821	−	0.830632i	$-0.687979\pi$
$269$	5.37081	−	5.96489i	0.327464	−	0.363686i	0.884286	+	0.466946i	$0.154646\pi$
$270$	−5.12913	+	0.831856i	−0.312149	+	0.0506252i
$271$	3.77590	−	5.19708i	0.229369	−	0.315700i	−0.678784	−	0.734338i	$-0.737493\pi$
$271$	3.77590	−	5.19708i	0.229369	−	0.315700i	0.908153	+	0.418638i	$0.137493\pi$
$272$	0.405011	+	3.85342i	0.0245574	+	0.233648i
$273$	2.06237	−	4.43705i	0.124820	−	0.268543i
$274$	−8.23932	+	4.75697i	−0.497755	+	0.287379i
$275$	0.978847	−	0.711174i	0.0590267	−	0.0428854i
$276$	4.59930	−	4.94437i	0.276846	−	0.297616i
$277$	3.61479	−	1.17452i	0.217192	−	0.0705698i	−0.198400	−	0.980121i	$-0.563575\pi$
$277$	3.61479	−	1.17452i	0.217192	−	0.0705698i	0.415592	+	0.909551i	$0.363575\pi$
$278$	14.6648			0.879538
$279$	−3.48136	+	16.3365i	−0.208424	+	0.978039i
$280$	−2.39071			−0.142872
$281$	−1.64265	+	0.533730i	−0.0979925	+	0.0318397i	−0.357603	−	0.933874i	$-0.616406\pi$
$281$	−1.64265	+	0.533730i	−0.0979925	+	0.0318397i	0.259610	+	0.965713i	$0.416406\pi$
$282$	−3.15066	+	3.38704i	−0.187619	+	0.201696i
$283$	−10.5851	+	7.69052i	−0.629219	+	0.457154i	−0.856129	−	0.516761i	$-0.827137\pi$
$283$	−10.5851	+	7.69052i	−0.629219	+	0.457154i	0.226911	+	0.973916i	$0.427137\pi$
$284$	9.31116	−	5.37580i	0.552516	−	0.318995i
$285$	0.0739555	−	0.159111i	0.00438075	−	0.00942490i
$286$	0.149442	+	1.42185i	0.00883670	+	0.0840756i
$287$	5.26815	−	7.25098i	0.310969	−	0.428012i
$288$	−2.99217	+	0.216657i	−0.176315	+	0.0127666i
$289$	−1.32962	+	1.47670i	−0.0782131	+	0.0868645i
$290$	5.14581	+	2.29106i	0.302172	+	0.134536i
$291$	0.740916	−	6.09648i	0.0434333	−	0.357382i
$292$	1.20832	+	5.68471i	0.0707118	+	0.332673i
$293$	−5.83737	−	13.1109i	−0.341023	−	0.765950i	−0.999906	−	0.0137045i	$-0.995638\pi$
$293$	−5.83737	−	13.1109i	−0.341023	−	0.765950i	0.658883	−	0.752245i	$-0.271029\pi$
$294$	0.497799	−	2.16841i	0.0290322	−	0.126464i
$295$	2.98445	−	9.18521i	0.173762	−	0.534783i
$296$	1.32344	−	0.589231i	0.0769231	−	0.0342484i
$297$	−2.87493	−	5.59110i	−0.166821	−	0.324428i
$298$	1.84352	+	0.391853i	0.106792	+	0.0226994i
$299$	−1.87378	+	4.20858i	−0.108363	+	0.243388i
$300$	−1.38456	−	1.04067i	−0.0799378	−	0.0600829i
$301$	−6.28200	−	0.660264i	−0.362088	−	0.0380570i
$302$	−7.56831	−	5.49870i	−0.435508	−	0.316415i
$303$	2.36136	+	12.0686i	0.135657	+	0.693324i
$304$	0.0506504	−	0.0877291i	0.00290500	−	0.00503161i
$305$	−5.69818	−	9.86953i	−0.326277	−	0.565128i
$306$	8.38148	+	8.05401i	0.479137	+	0.460417i
$307$	−18.1743	−	20.1847i	−1.03726	−	1.15200i	−0.988195	−	0.153204i	$-0.951041\pi$
$307$	−18.1743	−	20.1847i	−1.03726	−	1.15200i	−0.0490698	−	0.998795i	$-0.515626\pi$
$308$	−0.893855	−	2.75100i	−0.0509321	−	0.156753i
$309$	−1.26890	−	14.3002i	−0.0721850	−	0.813512i
$310$	−4.73054	+	2.93632i	−0.268677	+	0.166772i
$311$			12.2264i			0.693293i	0.937996	+	0.346647i	$0.112680\pi$
$311$			12.2264i			0.693293i	−0.937996	+	0.346647i	$0.887320\pi$
$312$	1.88296	−	0.802012i	0.106601	−	0.0454050i
$313$	−6.40966	+	5.77128i	−0.362295	+	0.326212i	−0.830095	−	0.557623i	$-0.811714\pi$
$313$	−6.40966	+	5.77128i	−0.362295	+	0.326212i	0.467799	+	0.883835i	$0.345047\pi$
$314$	6.13142	+	8.43917i	0.346016	+	0.476250i
$315$	−5.48278	+	4.62371i	−0.308919	+	0.260516i
$316$	8.99570	+	5.19367i	0.506048	+	0.292167i
$317$	−18.7212	+	1.96767i	−1.05148	+	0.110515i	−0.614471	−	0.788939i	$-0.710631\pi$
$317$	−18.7212	+	1.96767i	−1.05148	+	0.110515i	−0.437014	+	0.899455i	$0.643964\pi$
$318$	8.51774	+	5.10367i	0.477651	+	0.286200i
$319$	−0.712386	+	6.77790i	−0.0398860	+	0.379490i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−26.0201	−	8.92353i	−1.45230	−	0.498063i
$322$	1.93789	−	9.11707i	0.107995	−	0.508075i
$323$	−0.383928	+	0.0816065i	−0.0213623	+	0.00454071i
$324$	−6.44311	+	6.28381i	−0.357951	+	0.349101i
$325$	1.12380	+	0.365144i	0.0623370	+	0.0202545i
$326$	15.6564	+	5.08707i	0.867127	+	0.281747i
$327$	−4.35834	−	7.83981i	−0.241017	−	0.433543i
$328$	3.66705	−	0.779455i	0.202479	−	0.0430382i
$329$	−1.32752	+	6.24547i	−0.0731883	+	0.344324i
$330$	0.679829	−	1.98231i	0.0374234	−	0.109123i
$331$	23.5319	+	21.1882i	1.29343	+	1.16461i	0.976347	+	0.216211i	$0.0693700\pi$
$331$	23.5319	+	21.1882i	1.29343	+	1.16461i	0.317083	+	0.948398i	$0.397297\pi$
$332$	−0.735985	+	7.00243i	−0.0403924	+	0.384308i
$333$	1.89553	−	3.91089i	0.103874	−	0.214315i
$334$	2.70220	−	0.284013i	0.147858	−	0.0155405i
$335$	6.93507	+	4.00396i	0.378903	+	0.218760i
$336$	−3.38904	+	2.37927i	−0.184887	+	0.129800i
$337$	−2.84275	−	3.91270i	−0.154854	−	0.213139i	0.724540	−	0.689233i	$-0.242052\pi$
$337$	−2.84275	−	3.91270i	−0.154854	−	0.213139i	−0.879394	+	0.476094i	$0.842052\pi$
$338$	8.62327	−	7.76443i	0.469044	−	0.422329i
$339$	8.31649	+	19.5254i	0.451690	+	1.06047i
$340$			3.87465i			0.210132i
$341$	−5.14752	−	4.34560i	−0.278754	−	0.235327i
$342$	−0.0535108	−	0.299155i	−0.00289353	−	0.0161764i
$343$	−6.12034	−	18.8365i	−0.330467	−	1.01707i
$344$	−1.76794	−	1.96349i	−0.0953208	−	0.105865i
$345$	5.09094	−	4.43653i	0.274087	−	0.238855i
$346$	−1.43405	−	2.48384i	−0.0770948	−	0.133532i
$347$	9.62366	−	16.6687i	0.516625	−	0.894821i	−0.483188	−	0.875516i	$-0.660521\pi$
$347$	9.62366	−	16.6687i	0.516625	−	0.894821i	0.999814	−	0.0193048i	$-0.00614528\pi$
$348$	9.57472	−	1.87341i	0.513259	−	0.100425i
$349$	7.89177	+	5.73371i	0.422437	+	0.306918i	0.778618	−	0.627499i	$-0.215921\pi$
$349$	7.89177	+	5.73371i	0.422437	+	0.306918i	−0.356181	+	0.934417i	$0.615921\pi$
$350$	−2.37761	−	0.249897i	−0.127089	−	0.0133576i
$351$	2.76719	−	5.48100i	0.147702	−	0.292554i
$352$	0.492120	−	1.10532i	0.0262301	−	0.0589137i
$353$	−25.7648	−	5.47648i	−1.37132	−	0.291484i	−0.537382	−	0.843339i	$-0.680587\pi$
$353$	−25.7648	−	5.47648i	−1.37132	−	0.291484i	−0.833940	+	0.551855i	$0.813920\pi$
$354$	−4.91053	−	15.9910i	−0.260992	−	0.849911i
$355$	9.82208	−	4.37307i	0.521302	−	0.232099i
$356$	−1.76900	+	5.44444i	−0.0937571	+	0.288555i
$357$	15.6375	+	3.58988i	0.827625	+	0.189996i
$358$	3.35309	+	7.53116i	0.177216	+	0.398034i
$359$	6.70560	+	31.5474i	0.353908	+	1.66501i	0.690482	+	0.723349i	$0.257398\pi$
$359$	6.70560	+	31.5474i	0.353908	+	1.66501i	−0.336574	+	0.941657i	$0.609268\pi$
$360$	−2.99842	−	0.0972966i	−0.158031	−	0.00512798i
$361$	−17.3480	−	7.72382i	−0.913052	−	0.406517i
$362$	4.82747	−	5.36145i	0.253726	−	0.281792i
$363$	−16.5148	−	0.267876i	−0.866803	−	0.0140599i
$364$	1.66046	−	2.28542i	0.0870315	−	0.119789i
$365$	0.607490	+	5.77988i	0.0317975	+	0.302533i
$366$	−17.9000	−	8.32000i	−0.935645	−	0.434893i
$367$	20.0262	−	11.5621i	1.04536	−	0.603537i	0.124011	−	0.992281i	$-0.460424\pi$
$367$	20.0262	−	11.5621i	1.04536	−	0.603537i	0.921346	+	0.388743i	$0.127091\pi$
$368$	3.15414	−	2.29162i	0.164421	−	0.119459i
$369$	6.90239	−	8.87975i	0.359324	−	0.462261i
$370$	1.37778	−	0.447667i	0.0716272	−	0.0232731i
$371$	13.7058			0.711568
$372$	−3.78367	+	8.87039i	−0.196174	+	0.459908i
$373$	−9.82687			−0.508816			−0.254408	−	0.967097i	$-0.581881\pi$
$373$	−9.82687			−0.508816			−0.254408	+	0.967097i	$0.581881\pi$
$374$	−4.45858	+	1.44868i	−0.230547	+	0.0749094i
$375$	−1.26820	−	1.17969i	−0.0654895	−	0.0609190i
$376$	−2.16068	+	1.56983i	−0.111429	+	0.0809577i
$377$	−5.76415	+	3.32794i	−0.296869	+	0.171397i
$378$	−3.17072	+	12.0110i	−0.163084	+	0.617781i
$379$	−1.98672	−	18.9024i	−0.102051	−	0.970949i	−0.919005	−	0.394246i	$-0.871006\pi$
$379$	−1.98672	−	18.9024i	−0.102051	−	0.970949i	0.816954	−	0.576703i	$-0.195661\pi$
$380$	0.0595432	−	0.0819541i	0.00305450	−	0.00420416i
$381$	−0.382667	+	23.5917i	−0.0196046	+	1.20864i
$382$	5.12549	−	5.69243i	0.262243	−	0.291250i
$383$	12.8005	+	5.69917i	0.654077	+	0.291214i	0.706819	−	0.707394i	$-0.250129\pi$
$383$	12.8005	+	5.69917i	0.654077	+	0.291214i	−0.0527421	+	0.998608i	$0.516796\pi$
$384$	−1.71940	−	0.208962i	−0.0877427	−	0.0106635i
$385$	−0.601400	−	2.82936i	−0.0306502	−	0.144198i
$386$	8.88758	+	19.9618i	0.452366	+	1.01603i
$387$	−7.85199	−	1.08376i	−0.399139	−	0.0550908i
$388$	1.09568	−	3.37216i	0.0556249	−	0.171196i
$389$	−24.7962	+	11.0400i	−1.25722	+	0.559750i	−0.923744	−	0.383010i	$-0.874888\pi$
$389$	−24.7962	+	11.0400i	−1.25722	+	0.559750i	−0.333474	+	0.942759i	$0.608221\pi$
$390$	1.95647	−	0.600796i	0.0990699	−	0.0304225i
$391$	−14.7761	−	3.14076i	−0.747261	−	0.158835i
$392$	0.522453	−	1.17345i	0.0263879	−	0.0592681i
$393$	−1.34480	+	1.78920i	−0.0678360	+	0.0902530i
$394$	−14.9669	−	1.57309i	−0.754022	−	0.0792509i
$395$	8.40353	+	6.10552i	0.422828	+	0.307202i
$396$	−1.00911	−	3.48667i	−0.0507097	−	0.175212i
$397$	17.8009	−	30.8321i	0.893401	−	1.54742i	0.0576304	−	0.998338i	$-0.481646\pi$
$397$	17.8009	−	30.8321i	0.893401	−	1.54742i	0.835771	−	0.549078i	$-0.185021\pi$
$398$	9.87518	+	17.1043i	0.494998	+	0.857362i
$399$	−0.275588	−	0.316238i	−0.0137966	−	0.0158317i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−6.80493	−	20.9434i	−0.339822	−	1.04586i	−0.964298	−	0.264820i	$-0.914687\pi$
$401$	−6.80493	−	20.9434i	−0.339822	−	1.04586i	0.624476	−	0.781044i	$-0.285313\pi$
$402$	13.8159	−	1.22592i	0.689072	−	0.0611431i
$403$	0.478567	−	6.56161i	0.0238391	−	0.326857i
$404$			7.09994i			0.353235i
$405$	−7.06465	+	5.57590i	−0.351045	+	0.277069i
$406$	10.0075	−	9.01077i	0.496662	−	0.447197i
$407$	1.03026	+	1.41804i	0.0510683	+	0.0702895i
$408$	3.85611	+	5.49265i	0.190906	+	0.271927i
$409$	−5.53408	−	3.19510i	−0.273643	−	0.157988i	0.356899	−	0.934143i	$-0.383834\pi$
$409$	−5.53408	−	3.19510i	−0.273643	−	0.157988i	−0.630542	+	0.776155i	$0.717167\pi$
$410$	3.72843	−	0.391874i	0.184134	−	0.0193533i
$411$	−8.46968	+	14.1354i	−0.417779	+	0.697248i
$412$	0.866403	−	8.24328i	0.0426846	−	0.406117i
$413$	−17.1587	−	15.4497i	−0.844322	−	0.760231i
$414$	2.80154	−	11.3557i	0.137688	−	0.558104i
$415$	−1.46391	+	6.88714i	−0.0718603	+	0.338076i
$416$	1.15581	−	0.245675i	0.0566682	−	0.0120452i
$417$	22.2003	−	12.3417i	1.08715	−	0.604375i
$418$	0.116567	+	0.0378750i	0.00570150	+	0.00185253i
$419$	−20.0618	−	6.51848i	−0.980084	−	0.318449i	−0.225204	−	0.974312i	$-0.572305\pi$
$419$	−20.0618	−	6.51848i	−0.980084	−	0.318449i	−0.754880	+	0.655863i	$0.772305\pi$
$420$	−3.61917	+	2.01198i	−0.176598	+	0.0981748i
$421$	5.89085	−	1.25214i	0.287102	−	0.0610255i	−0.0621093	−	0.998069i	$-0.519783\pi$
$421$	5.89085	−	1.25214i	0.287102	−	0.0610255i	0.349212	+	0.937044i	$0.386449\pi$
$422$	−0.422151	+	1.98606i	−0.0205500	+	0.0966801i
$423$	−1.91914	+	7.77902i	−0.0933118	+	0.378229i
$424$	4.26039	+	3.83608i	0.206903	+	0.186296i
$425$	−0.405011	+	3.85342i	−0.0196459	+	0.186919i
$426$	9.57150	−	15.9743i	0.463741	−	0.773956i
$427$	−27.0961	+	2.84792i	−1.31127	+	0.137820i
$428$	−13.7539	−	7.94080i	−0.664818	−	0.383833i
$429$	1.42284	+	2.02669i	0.0686952	+	0.0978497i
$430$	−1.55301	−	2.13754i	−0.0748929	−	0.103081i
$431$	20.2822	−	18.2622i	0.976958	−	0.879657i	−0.0157892	−	0.999875i	$-0.505026\pi$
$431$	20.2822	−	18.2622i	0.976958	−	0.879657i	0.992747	+	0.120218i	$0.0383594\pi$
$432$	−4.34735	+	2.84615i	−0.209162	+	0.136935i
$433$		−	37.0346i		−	1.77977i	−0.456184	−	0.889886i	$-0.650784\pi$
$433$		−	37.0346i		−	1.77977i	0.456184	−	0.889886i	$-0.349216\pi$
$434$	1.81307	+	13.1869i	0.0870302	+	0.632990i
$435$	9.71810	−	0.862312i	0.465947	−	0.0413447i
$436$	−1.60032	−	4.92527i	−0.0766412	−	0.235877i
$437$	0.264270	+	0.293502i	0.0126418	+	0.0140401i
$438$	6.61338	+	7.58889i	0.316000	+	0.362611i
$439$	4.78973	+	8.29605i	0.228601	+	0.395949i	0.957394	−	0.288786i	$-0.0932515\pi$
$439$	4.78973	+	8.29605i	0.228601	+	0.395949i	−0.728793	+	0.684735i	$0.759918\pi$
$440$	0.604961	−	1.04782i	0.0288404	−	0.0499530i
$441$	−1.07131	−	3.70159i	−0.0510147	−	0.176266i
$442$	−3.70400	−	2.69112i	−0.176181	−	0.128003i
$443$	−4.45924	−	0.468685i	−0.211865	−	0.0222679i	−0.00199861	−	0.999998i	$-0.500636\pi$
$443$	−4.45924	−	0.468685i	−0.211865	−	0.0222679i	−0.209866	+	0.977730i	$0.567303\pi$
$444$	1.50759	−	2.00579i	0.0715472	−	0.0951905i
$445$	−2.32841	+	5.22970i	−0.110377	+	0.247912i
$446$	8.40777	+	1.78713i	0.398120	+	0.0846229i
$447$	3.12059	−	0.958273i	0.147599	−	0.0453248i
$448$	−2.18402	+	0.972390i	−0.103185	+	0.0459411i
$449$	7.55873	−	23.2634i	0.356718	−	1.09787i	−0.598288	−	0.801281i	$-0.704152\pi$
$449$	7.55873	−	23.2634i	0.356718	−	1.09787i	0.955006	−	0.296585i	$-0.0958479\pi$
$450$	−2.97183	−	0.410184i	−0.140093	−	0.0193363i
$451$	1.84494	+	4.14381i	0.0868749	+	0.195124i
$452$	2.54753	+	11.9852i	0.119826	+	0.563736i
$453$	−16.0849	−	1.95483i	−0.755734	−	0.0918458i
$454$	−20.2573	−	9.01915i	−0.950724	−	0.423290i
$455$	1.89025	−	2.09934i	0.0886163	−	0.0984184i
$456$	0.00284562	−	0.175435i	0.000133259	−	0.00821551i
$457$	9.71077	−	13.3657i	0.454251	−	0.625223i	−0.519053	−	0.854742i	$-0.673715\pi$
$457$	9.71077	−	13.3657i	0.454251	−	0.625223i	0.973304	+	0.229519i	$0.0737154\pi$
$458$	1.16300	+	11.0652i	0.0543432	+	0.517041i
$459$	19.4664	+	5.13882i	0.908614	+	0.239860i
$460$	3.37640	−	1.94937i	0.157426	−	0.0908898i
$461$	6.00865	−	4.36554i	0.279851	−	0.203323i	−0.439002	−	0.898486i	$-0.644668\pi$
$461$	6.00865	−	4.36554i	0.279851	−	0.203323i	0.718852	+	0.695163i	$0.244668\pi$
$462$	−3.66836	−	3.41234i	−0.170668	−	0.158757i
$463$	13.0676	−	4.24593i	0.607304	−	0.197325i	0.0108089	−	0.999942i	$-0.496559\pi$
$463$	13.0676	−	4.24593i	0.607304	−	0.197325i	0.596495	+	0.802616i	$0.296559\pi$
$464$	5.63279			0.261496
$465$	−4.69015	+	8.42630i	−0.217501	+	0.390760i
$466$	−3.84616			−0.178170
$467$	−31.9309	+	10.3750i	−1.47758	+	0.480096i	−0.933390	−	0.358863i	$-0.883165\pi$
$467$	−31.9309	+	10.3750i	−1.47758	+	0.480096i	−0.544194	+	0.838959i	$0.683165\pi$
$468$	2.17555	−	2.79879i	0.100565	−	0.129374i
$469$	15.4883	−	11.2529i	0.715185	−	0.519612i
$470$	−2.31294	+	1.33538i	−0.106688	+	0.0615963i
$471$	16.3843	+	7.61552i	0.754949	+	0.350905i
$472$	−1.00953	−	9.60499i	−0.0464672	−	0.442106i
$473$	1.87902	−	2.58625i	0.0863976	−	0.118916i
$474$	17.9890	+	0.291789i	0.826263	+	0.0134023i
$475$	0.0677835	−	0.0752812i	0.00311012	−	0.00345414i
$476$	8.46233	+	3.76767i	0.387870	+	0.172691i
$477$	17.1897	+	0.557794i	0.787064	+	0.0255396i
$478$	1.23846	+	5.82649i	0.0566458	+	0.266498i
$479$	−0.359545	−	0.807552i	−0.0164280	−	0.0368980i	0.905145	−	0.425103i	$-0.139762\pi$
$479$	−0.359545	−	0.807552i	−0.0164280	−	0.0368980i	−0.921573	+	0.388205i	$0.873095\pi$
$480$	−1.68814	−	0.387543i	−0.0770526	−	0.0176888i
$481$	−0.528976	+	1.62802i	−0.0241192	+	0.0742314i
$482$	−19.0145	+	8.46581i	−0.866088	+	0.385607i
$483$	−4.73911	−	15.4328i	−0.215637	−	0.702215i
$484$	−9.32770	−	1.98266i	−0.423986	−	0.0901211i
$485$	1.44217	−	3.23916i	0.0654854	−	0.147083i
$486$	−4.46553	+	14.9352i	−0.202561	+	0.677473i
$487$	−23.4787	−	2.46771i	−1.06392	−	0.111823i	−0.443643	−	0.896203i	$-0.646314\pi$
$487$	−23.4787	−	2.46771i	−1.06392	−	0.111823i	−0.620280	+	0.784381i	$0.712981\pi$
$488$	−9.21984	−	6.69861i	−0.417363	−	0.303232i
$489$	27.9826	−	5.47512i	1.26542	−	0.247593i
$490$	0.642250	−	1.11241i	0.0290139	−	0.0502535i
$491$	18.1512	+	31.4388i	0.819151	+	1.41881i	0.906309	+	0.422617i	$0.138888\pi$
$491$	18.1512	+	31.4388i	0.819151	+	1.41881i	−0.0871575	+	0.996195i	$0.527778\pi$
$492$	4.89537	−	4.26610i	0.220700	−	0.192331i
$493$	−14.6038	−	16.2192i	−0.657724	−	0.730476i
$494$	0.0369894	+	0.113842i	0.00166423	+	0.00512197i
$495$	−0.639125	−	3.57305i	−0.0287265	−	0.160597i
$496$	−3.12725	+	4.60655i	−0.140418	+	0.206840i
$497$		−	25.7040i		−	1.15298i
$498$	4.77896	+	11.2200i	0.214151	+	0.502781i
$499$	−2.45437	+	2.20993i	−0.109873	+	0.0989299i	−0.722236	−	0.691647i	$-0.756886\pi$
$499$	−2.45437	+	2.20993i	−0.109873	+	0.0989299i	0.612363	+	0.790576i	$0.290219\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	3.85170	−	2.70408i	0.172081	−	0.120810i
$502$	−2.69163	−	1.55401i	−0.120133	−	0.0693590i
$503$	35.8585	−	3.76888i	1.59885	−	0.168046i	0.737246	−	0.675624i	$-0.236126\pi$
$503$	35.8585	−	3.76888i	1.59885	−	0.168046i	0.861606	+	0.507578i	$0.169459\pi$
$504$	−3.12813	+	6.45401i	−0.139338	+	0.287485i
$505$	−0.742146	+	7.06105i	−0.0330251	+	0.314213i
$506$	3.50554	+	3.15640i	0.155840	+	0.140319i
$507$	6.51990	−	19.0114i	0.289559	−	0.844324i
$508$	−2.83227	+	13.3248i	−0.125662	+	0.591192i
$509$	15.0848	−	3.20636i	0.668620	−	0.142120i	0.138919	−	0.990304i	$-0.455637\pi$
$509$	15.0848	−	3.20636i	0.668620	−	0.142120i	0.529701	+	0.848184i	$0.322304\pi$
$510$	3.26084	+	5.86563i	0.144393	+	0.259735i
$511$	13.2141	+	4.29352i	0.584558	+	0.189934i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−0.332771	−	0.407841i	−0.0146922	−	0.0180066i
$514$	−27.9012	+	5.93058i	−1.23067	+	0.261586i
$515$	1.72331	−	8.10756i	0.0759383	−	0.357262i
$516$	−4.32883	−	1.48456i	−0.190566	−	0.0653542i
$517$	−2.40140	−	2.16223i	−0.105613	−	0.0950947i
$518$	0.362021	−	3.44440i	0.0159063	−	0.151338i
$519$	−4.26129	−	2.55329i	−0.187050	−	0.112077i
$520$	1.17516	−	0.123514i	0.0515340	−	0.00541644i
$521$	−7.30055	−	4.21497i	−0.319843	−	0.184661i	0.331480	−	0.943462i	$-0.392452\pi$
$521$	−7.30055	−	4.21497i	−0.319843	−	0.184661i	−0.651323	+	0.758801i	$0.725786\pi$
$522$	12.9180	−	10.8940i	0.565408	−	0.476817i
$523$	−12.7735	−	17.5813i	−0.558548	−	0.768775i	0.432593	−	0.901589i	$-0.357599\pi$
$523$	−12.7735	−	17.5813i	−0.558548	−	0.768775i	−0.991141	+	0.132814i	$0.957599\pi$
$524$	−0.960326	+	0.864681i	−0.0419520	+	0.0377738i
$525$	−3.80966	+	1.62266i	−0.166267	+	0.0708185i
$526$		−	16.4798i		−	0.718551i
$527$	21.3721	−	2.93846i	0.930982	−	0.128001i
$528$	−0.185224	−	2.08744i	−0.00806086	−	0.0908444i
$529$	−2.41029	−	7.41811i	−0.104795	−	0.322526i
$530$	3.83608	+	4.26039i	0.166628	+	0.185060i
$531$	−20.8916	−	20.0753i	−0.906616	−	0.871194i
$532$	−0.121091	−	0.209735i	−0.00524994	−	0.00909317i
$533$	−2.21495	+	3.83640i	−0.0959400	+	0.166173i
$534$	1.90395	+	9.73082i	0.0823919	+	0.421094i
$535$	−12.8485	−	9.33497i	−0.555488	−	0.403586i
$536$	7.96406	+	0.837056i	0.343995	+	0.0361553i
$537$	11.4142	+	8.57913i	0.492558	+	0.370217i
$538$	3.26469	−	7.33262i	0.140751	−	0.316132i
$539$	1.52018	+	0.323125i	0.0654789	+	0.0139180i
$540$	−4.62104	+	2.37613i	−0.198858	+	0.102252i
$541$	−17.4557	+	7.77177i	−0.750478	+	0.334135i	−0.746080	−	0.665856i	$-0.768067\pi$
$541$	−17.4557	+	7.77177i	−0.750478	+	0.334135i	−0.00439797	+	0.999990i	$0.501400\pi$
$542$	1.98511	−	6.10953i	0.0852677	−	0.262427i
$543$	2.79595	−	12.1791i	0.119986	−	0.522657i
$544$	1.57596	+	3.53967i	0.0675688	+	0.151762i
$545$	−1.07672	−	5.06556i	−0.0461216	−	0.216985i
$546$	0.590303	−	4.85719i	0.0252626	−	0.207869i
$547$	−39.7825	−	17.7123i	−1.70098	−	0.757324i	−0.998980	−	0.0451451i	$-0.985625\pi$
$547$	−39.7825	−	17.7123i	−1.70098	−	0.757324i	−0.701998	−	0.712179i	$-0.747708\pi$
$548$	−6.36607	+	7.07024i	−0.271945	+	0.302026i
$549$	−34.0998	+	2.46910i	−1.45534	+	0.105379i
$550$	0.711174	−	0.978847i	0.0303246	−	0.0417382i
$551$	0.0596446	+	0.567481i	0.00254095	+	0.0241755i
$552$	2.84630	−	6.12364i	0.121147	−	0.260639i
$553$	21.5061	−	12.4166i	0.914533	−	0.528006i
$554$	3.07492	−	2.23406i	0.130641	−	0.0949162i
$555$	1.70900	−	1.83721i	0.0725428	−	0.0779854i
$556$	13.9471	−	4.53168i	0.591488	−	0.192186i
$557$	−17.2905			−0.732622			−0.366311	−	0.930493i	$-0.619379\pi$
$557$	−17.2905			−0.732622			−0.366311	+	0.930493i	$0.619379\pi$
$558$	1.73727	+	16.6127i	0.0735446	+	0.703272i
$559$	3.12203			0.132048
$560$	−2.27370	+	0.738770i	−0.0960814	+	0.0312187i
$561$	−5.53042	+	5.94535i	−0.233495	+	0.251013i
$562$	−1.39732	+	1.01522i	−0.0589426	+	0.0428243i
$563$	−17.2892	+	9.98194i	−0.728654	+	0.420689i	−0.817930	−	0.575318i	$-0.804878\pi$
$563$	−17.2892	+	9.98194i	−0.728654	+	0.420689i	0.0892754	+	0.996007i	$0.471545\pi$
$564$	−1.94980	+	4.19488i	−0.0821015	+	0.176636i
$565$	1.28078	+	12.1858i	0.0538829	+	0.512662i
$566$	−7.69052	+	10.5851i	−0.323257	+	0.444925i
$567$	5.30830	+	20.8513i	0.222928	+	0.875673i
$568$	7.19423	−	7.99000i	0.301863	−	0.335253i
$569$	−28.9104	−	12.8718i	−1.21199	−	0.539612i	−0.301627	−	0.953426i	$-0.597530\pi$
$569$	−28.9104	−	12.8718i	−1.21199	−	0.539612i	−0.910361	+	0.413814i	$0.864196\pi$
$570$	0.0211680	−	0.174177i	0.000886630	−	0.00729546i
$571$	0.981866	+	4.61931i	0.0410898	+	0.193312i	0.993905	−	0.110238i	$-0.0351613\pi$
$571$	0.981866	+	4.61931i	0.0410898	+	0.193312i	−0.952815	+	0.303550i	$0.901828\pi$
$572$	0.581503	+	1.30608i	0.0243139	+	0.0546098i
$573$	2.96855	−	12.9310i	0.124013	−	0.540201i
$574$	2.76963	−	8.52404i	0.115602	−	0.355787i
$575$	3.56167	−	1.58576i	0.148532	−	0.0661307i
$576$	−2.77877	+	1.13068i	−0.115782	+	0.0471118i
$577$	6.21112	+	1.32021i	0.258572	+	0.0549612i	0.335374	−	0.942085i	$-0.391137\pi$
$577$	6.21112	+	1.32021i	0.258572	+	0.0549612i	−0.0768015	+	0.997046i	$0.524471\pi$
$578$	−0.808222	+	1.81530i	−0.0336176	+	0.0755064i
$579$	30.2540	+	22.7395i	1.25731	+	0.945023i
$580$	5.60193	+	0.588787i	0.232608	+	0.0244480i
$581$	13.6182	+	9.89419i	0.564977	+	0.410480i
$582$	−1.17926	−	6.02705i	−0.0488820	−	0.249829i
$583$	−3.46820	+	6.00709i	−0.143638	+	0.248788i
$584$	2.90586	+	5.03309i	0.120245	+	0.208271i
$585$	2.45618	−	2.55605i	0.101551	−	0.105680i
$586$	−9.60317	−	10.6654i	−0.396703	−	0.440584i
$587$	11.4050	+	35.1008i	0.470733	+	1.44877i	0.851627	+	0.524148i	$0.175616\pi$
$587$	11.4050	+	35.1008i	0.470733	+	1.44877i	−0.380894	+	0.924619i	$0.624384\pi$
$588$	−0.196641	−	2.21611i	−0.00810935	−	0.0913909i
$589$	−0.497205	−	0.266280i	−0.0204870	−	0.0109719i
$590$		−	9.65790i		−	0.397609i
$591$	−23.9815	+	10.2145i	−0.986468	+	0.420169i
$592$	1.07658	−	0.969356i	0.0442471	−	0.0398403i
$593$	−17.7308	−	24.4044i	−0.728119	−	1.00217i	−0.999215	−	0.0396171i	$-0.987386\pi$
$593$	−17.7308	−	24.4044i	−0.728119	−	1.00217i	0.271096	−	0.962552i	$-0.412614\pi$
$594$	−4.46197	−	4.42904i	−0.183077	−	0.181726i
$595$	8.02214	+	4.63158i	0.328876	+	0.189876i
$596$	1.87438	−	0.197006i	0.0767777	−	0.00806966i
$597$	29.3442	+	17.5825i	1.20098	+	0.719605i
$598$	−0.481548	+	4.58162i	−0.0196920	+	0.187357i
$599$	−16.8780	−	15.1970i	−0.689616	−	0.620933i	0.247936	−	0.968776i	$-0.420248\pi$
$599$	−16.8780	−	15.1970i	−0.689616	−	0.620933i	−0.937553	+	0.347843i	$0.886914\pi$
$600$	−1.63838	−	0.561879i	−0.0668866	−	0.0229386i
$601$	0.472492	−	2.22290i	0.0192734	−	0.0906741i	−0.967460	−	0.253025i	$-0.918574\pi$
$601$	0.472492	−	2.22290i	0.0192734	−	0.0906741i	0.986733	+	0.162351i	$0.0519078\pi$
$602$	−6.17857	+	1.31329i	−0.251820	+	0.0535259i
$603$	19.8834	−	13.4831i	0.809714	−	0.549072i
$604$	−8.89709	−	2.89084i	−0.362017	−	0.117627i
$605$	−9.06936	−	2.94681i	−0.368722	−	0.119805i
$606$	5.97520	+	10.7482i	0.242726	+	0.436617i
$607$	−41.0463	+	8.72466i	−1.66602	+	0.354123i	−0.941988	−	0.335647i	$-0.891045\pi$
$607$	−41.0463	+	8.72466i	−1.66602	+	0.354123i	−0.724029	+	0.689769i	$0.757712\pi$
$608$	0.0210616	−	0.0990872i	0.000854162	−	0.00401852i
$609$	7.56647	−	22.0631i	0.306609	−	0.894040i
$610$	−8.46914	−	7.62565i	−0.342906	−	0.308754i
$611$	0.329875	−	3.13855i	0.0133453	−	0.126972i
$612$	10.4601	+	5.06980i	0.422824	+	0.204934i
$613$	2.40884	−	0.253180i	0.0972923	−	0.0102258i	−0.0557572	−	0.998444i	$-0.517757\pi$
$613$	2.40884	−	0.253180i	0.0972923	−	0.0102258i	0.153050	+	0.988219i	$0.451091\pi$
$614$	−23.5222	−	13.5806i	−0.949280	−	0.548067i
$615$	5.31449	−	3.73103i	0.214301	−	0.150450i
$616$	−1.70021	−	2.34014i	−0.0685035	−	0.0942870i
$617$	7.08510	−	6.37945i	0.285235	−	0.256827i	−0.514075	−	0.857745i	$-0.671865\pi$
$617$	7.08510	−	6.37945i	0.285235	−	0.256827i	0.799311	+	0.600918i	$0.205198\pi$
$618$	−5.62581	−	13.2082i	−0.226303	−	0.531313i
$619$		−	14.0896i		−	0.566311i	−0.959074	−	0.283155i	$-0.908619\pi$
$619$		−	14.0896i		−	0.566311i	0.959074	−	0.283155i	$-0.0913812\pi$
$620$	−3.59164	+	4.25443i	−0.144244	+	0.170862i
$621$	−5.31569	−	19.5486i	−0.213311	−	0.784458i
$622$	3.77815	+	11.6280i	0.151490	+	0.466239i
$623$	9.15766	+	10.1706i	0.366894	+	0.407477i
$624$	1.54296	−	1.34462i	0.0617679	−	0.0538280i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.31252	+	7.46951i	−0.172363	+	0.298542i
$627$	0.208340	−	0.0407642i	0.00832031	−	0.00162797i
$628$	8.43917	+	6.13142i	0.336760	+	0.244670i
$629$	−5.58238	−	0.586732i	−0.222584	−	0.0233945i
$630$	−3.78563	+	6.09168i	−0.150823	+	0.242698i
$631$	5.29306	−	11.8884i	0.210713	−	0.473270i	−0.777009	−	0.629489i	$-0.783264\pi$
$631$	5.29306	−	11.8884i	0.210713	−	0.473270i	0.987722	+	0.156220i	$0.0499308\pi$
$632$	10.1603	+	2.15965i	0.404157	+	0.0859062i
$633$	1.03237	+	3.36187i	0.0410329	+	0.133622i
$634$	−17.1968	+	7.65652i	−0.682973	+	0.304079i
$635$	−4.20958	+	12.9558i	−0.167052	+	0.514133i
$636$	9.67797	+	2.22176i	0.383756	+	0.0880984i
$637$	0.617346	+	1.38658i	0.0244601	+	0.0549383i
$638$	1.41697	+	6.66631i	0.0560983	+	0.263922i
$639$	1.04609	−	32.2378i	0.0413829	−	1.27531i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−19.2340	+	21.3615i	−0.759696	+	0.843728i	−0.991645	−	0.129000i	$-0.958823\pi$
$641$	−19.2340	+	21.3615i	−0.759696	+	0.843728i	0.231948	+	0.972728i	$0.425490\pi$
$642$	−27.5041	−	0.446127i	−1.08550	−	0.0176072i
$643$	5.26128	−	7.24153i	0.207485	−	0.285578i	−0.692574	−	0.721347i	$-0.743523\pi$
$643$	5.26128	−	7.24153i	0.207485	−	0.285578i	0.900059	+	0.435769i	$0.143523\pi$
$644$	−0.974284	−	9.26969i	−0.0383922	−	0.365277i
$645$	−4.14994	−	1.92892i	−0.163404	−	0.0759510i
$646$	−0.339920	+	0.196253i	−0.0133740	+	0.00772146i
$647$	17.5864	−	12.7773i	0.691394	−	0.502327i	−0.185724	−	0.982602i	$-0.559463\pi$
$647$	17.5864	−	12.7773i	0.691394	−	0.502327i	0.877118	+	0.480275i	$0.159463\pi$
$648$	−4.18596	+	7.96729i	−0.164440	+	0.312985i
$649$	11.1134	−	3.61096i	0.436238	−	0.141742i
$650$	1.18163			0.0463473
$651$	13.8426	+	18.4371i	0.542533	+	0.722605i
$652$	16.4621			0.644705
$653$	39.0457	−	12.6867i	1.52798	−	0.496469i	0.579947	−	0.814654i	$-0.303073\pi$
$653$	39.0457	−	12.6867i	1.52798	−	0.496469i	0.948029	+	0.318185i	$0.103073\pi$
$654$	−6.56766	−	6.10930i	−0.256816	−	0.238893i
$655$	−1.04545	+	0.759563i	−0.0408491	+	0.0296786i
$656$	3.24670	−	1.87448i	0.126762	−	0.0731863i
$657$	16.3983	+	5.92271i	0.639760	+	0.231067i
$658$	0.667414	+	6.35002i	0.0260185	+	0.247549i
$659$	3.20807	−	4.41553i	0.124969	−	0.172005i	−0.741948	−	0.670457i	$-0.766098\pi$
$659$	3.20807	−	4.41553i	0.124969	−	0.172005i	0.866917	+	0.498452i	$0.166098\pi$
$660$	0.0339877	−	2.09537i	0.00132297	−	0.0815622i
$661$	−20.5855	+	22.8626i	−0.800685	+	0.889250i	−0.995802	−	0.0915295i	$-0.970824\pi$
$661$	−20.5855	+	22.8626i	−0.800685	+	0.889250i	0.195118	+	0.980780i	$0.437491\pi$
$662$	28.9277	+	12.8794i	1.12431	+	0.500573i
$663$	−7.87210	−	0.956710i	−0.305727	−	0.0371556i
$664$	1.46391	+	6.88714i	0.0568106	+	0.267273i
$665$	−0.0985040	−	0.221244i	−0.00381982	−	0.00857946i
$666$	0.594226	−	4.30523i	0.0230258	−	0.166824i
$667$	−6.78625	+	20.8859i	−0.262765	+	0.808706i
$668$	2.48218	−	1.10514i	0.0960386	−	0.0427591i
$669$	14.2321	−	4.37041i	0.550245	−	0.168970i
$670$	7.83293	+	1.66494i	0.302613	+	0.0643223i
$671$	5.60837	−	12.5966i	0.216509	−	0.486286i
$672$	−2.48793	+	3.31009i	−0.0959741	+	0.127690i
$673$	−26.1640	−	2.74995i	−1.00855	−	0.106003i	−0.414179	−	0.910195i	$-0.635931\pi$
$673$	−26.1640	−	2.74995i	−1.00855	−	0.106003i	−0.594369	+	0.804193i	$0.702598\pi$
$674$	−3.91270	−	2.84275i	−0.150712	−	0.109498i
$675$	−4.84410	+	1.88009i	−0.186449	+	0.0723645i
$676$	5.80188	−	10.0491i	0.223149	−	0.386506i
$677$	3.20458	+	5.55050i	0.123162	+	0.213323i	0.921013	−	0.389532i	$-0.127363\pi$
$677$	3.20458	+	5.55050i	0.123162	+	0.213323i	−0.797851	+	0.602855i	$0.794030\pi$
$678$	13.9431	+	15.9998i	0.535482	+	0.614469i
$679$	−5.67205	−	6.29945i	−0.217673	−	0.241751i
$680$	1.19733	+	3.68501i	0.0459156	+	0.141314i
$681$	−38.2569	+	3.39464i	−1.46601	+	0.130083i
$682$	−6.23845	−	2.54224i	−0.238883	−	0.0973473i
$683$			12.0123i			0.459638i	0.973233	+	0.229819i	$0.0738134\pi$
$683$			12.0123i			0.459638i	−0.973233	+	0.229819i	$0.926187\pi$
$684$	−0.143336	−	0.267977i	−0.00548058	−	0.0102464i
$685$	−7.07024	+	6.36607i	−0.270140	+	0.243235i
$686$	−11.6416	−	16.0233i	−0.444478	−	0.611771i
$687$	11.0729	+	15.7722i	0.422456	+	0.601747i
$688$	−2.28816	−	1.32107i	−0.0872354	−	0.0503654i
$689$	−6.73708	+	0.708096i	−0.256662	+	0.0269763i
$690$	3.47081	−	5.79258i	0.132131	−	0.220520i
$691$	2.98513	−	28.4016i	0.113560	−	1.08045i	−0.778224	−	0.627986i	$-0.783879\pi$
$691$	2.98513	−	28.4016i	0.113560	−	1.08045i	0.891784	−	0.452461i	$-0.149454\pi$
$692$	−2.13141	−	1.91913i	−0.0810239	−	0.0729543i
$693$	−8.42511	−	2.07854i	−0.320044	−	0.0789571i
$694$	4.00174	−	18.8267i	0.151904	−	0.714653i
$695$	14.3444	−	3.04899i	0.544113	−	0.115655i
$696$	8.52719	−	4.74047i	0.323222	−	0.179687i
$697$	−13.8150	−	4.48876i	−0.523280	−	0.170024i
$698$	9.27733	+	3.01439i	0.351152	+	0.114096i
$699$	−5.82250	+	3.23687i	−0.220227	+	0.122430i
$700$	−2.33847	+	0.497057i	−0.0883858	+	0.0187870i
$701$	−9.39731	+	44.2109i	−0.354931	+	1.66982i	0.332139	+	0.943230i	$0.392230\pi$
$701$	−9.39731	+	44.2109i	−0.354931	+	1.66982i	−0.687071	+	0.726591i	$0.741104\pi$
$702$	0.938033	−	6.06785i	0.0354038	−	0.229016i
$703$	0.109058	+	0.0981967i	0.00411322	+	0.00370356i
$704$	0.126471	−	1.20329i	0.00476657	−	0.0453508i
$705$	−2.37761	+	3.96809i	−0.0895458	+	0.149447i
$706$	−26.1961	+	2.75332i	−0.985904	+	0.103623i
$707$	14.6998	+	8.48696i	0.552844	+	0.319185i
$708$	−9.61168	−	13.6909i	−0.361229	−	0.514535i
$709$	8.43616	+	11.6114i	0.316826	+	0.436074i	0.937495	−	0.347999i	$-0.113139\pi$
$709$	8.43616	+	11.6114i	0.316826	+	0.436074i	−0.620668	+	0.784073i	$0.713139\pi$
$710$	7.99000	−	7.19423i	0.299859	−	0.269995i
$711$	27.4782	−	14.6976i	1.03051	−	0.551202i
$712$			5.72462i			0.214539i
$713$	−13.3131	−	17.1455i	−0.498578	−	0.642102i
$714$	15.9815	−	1.41808i	0.598092	−	0.0530703i
$715$	0.441795	+	1.35971i	0.0165222	+	0.0508501i
$716$	5.51623	+	6.12640i	0.206151	+	0.228954i
$717$	6.77832	+	7.77816i	0.253141	+	0.290481i
$718$	16.1261	+	27.9312i	0.601820	+	1.04238i
$719$	26.4095	−	45.7426i	0.984909	−	1.70591i	0.342570	−	0.939492i	$-0.388703\pi$
$719$	26.4095	−	45.7426i	0.984909	−	1.70591i	0.642339	−	0.766421i	$-0.277964\pi$
$720$	−2.88173	+	0.834029i	−0.107396	+	0.0310824i
$721$	−16.0314	−	11.6475i	−0.597039	−	0.433774i
$722$	−18.8857	−	1.98497i	−0.702853	−	0.0738729i
$723$	−21.6604	+	28.8183i	−0.805559	+	1.07176i
$724$	2.93442	−	6.59081i	0.109057	−	0.244946i
$725$	5.50970	+	1.17112i	0.204625	+	0.0434944i
$726$	−15.7893	+	4.84859i	−0.585996	+	0.179948i
$727$	11.9850	−	5.33605i	0.444498	−	0.197903i	−0.172268	−	0.985050i	$-0.555109\pi$
$727$	11.9850	−	5.33605i	0.444498	−	0.197903i	0.616765	+	0.787147i	$0.288443\pi$
$728$	0.872953	−	2.68667i	0.0323538	−	0.0995747i
$729$	5.80905	+	26.3677i	0.215150	+	0.976581i
$730$	2.36384	+	5.30927i	0.0874895	+	0.196505i
$731$	2.12847	+	10.0137i	0.0787243	+	0.370369i
$732$	−19.5949	−	2.38140i	−0.724248	−	0.0880191i
$733$	−35.3453	−	15.7367i	−1.30551	−	0.581249i	−0.368197	−	0.929748i	$-0.620025\pi$
$733$	−35.3453	−	15.7367i	−1.30551	−	0.581249i	−0.937309	+	0.348499i	$0.886692\pi$
$734$	15.4731	−	17.1846i	0.571124	−	0.634297i
$735$	0.0360826	−	2.22453i	0.00133093	−	0.0820528i
$736$	2.29162	−	3.15414i	0.0844702	−	0.116263i
$737$	1.01277	+	9.63589i	0.0373060	+	0.354942i
$738$	3.82057	−	10.5781i	0.140637	−	0.389385i
$739$	27.8291	−	16.0671i	1.02371	−	0.591039i	0.108534	−	0.994093i	$-0.465385\pi$
$739$	27.8291	−	16.0671i	1.02371	−	0.591039i	0.915176	+	0.403054i	$0.132051\pi$
$740$	1.17201	−	0.851513i	0.0430838	−	0.0313022i
$741$	0.151804	+	0.141209i	0.00557664	+	0.00518745i
$742$	13.0350	−	4.23532i	0.478529	−	0.155483i
$743$	−2.39114			−0.0877225			−0.0438613	−	0.999038i	$-0.513966\pi$
$743$	−2.39114			−0.0877225			−0.0438613	+	0.999038i	$0.513966\pi$
$744$	−0.857387	+	9.60546i	−0.0314333	+	0.352153i
$745$	1.88471			0.0690503
$746$	−9.34591	+	3.03667i	−0.342178	+	0.111180i
$747$	16.6772	+	12.9635i	0.610187	+	0.474309i
$748$	−3.79269	+	2.75555i	−0.138674	+	0.100753i
$749$	−32.8815	+	18.9842i	−1.20146	+	0.693666i
$750$	−1.57067	−	0.730058i	−0.0573529	−	0.0266580i
$751$	4.20594	+	40.0168i	0.153477	+	1.46023i	0.752018	+	0.659143i	$0.229081\pi$
$751$	4.20594	+	40.0168i	0.153477	+	1.46023i	−0.598541	+	0.801092i	$0.704253\pi$
$752$	−1.56983	+	2.16068i	−0.0572457	+	0.0787920i
$753$	−5.38255	−	0.0873069i	−0.196151	−	0.00318164i
$754$	−4.45365	+	4.94628i	−0.162192	+	0.180133i
$755$	−8.54617	−	3.80500i	−0.311027	−	0.138478i
$756$	0.696077	+	12.4030i	0.0253161	+	0.451092i
$757$	1.68390	+	7.92213i	0.0612024	+	0.287935i	0.998096	−	0.0616801i	$-0.0196459\pi$
$757$	1.68390	+	7.92213i	0.0612024	+	0.287935i	−0.936894	+	0.349615i	$0.886313\pi$
$758$	−7.73063	−	17.3633i	−0.280789	−	0.630663i
$759$	7.96323	+	1.82811i	0.289047	+	0.0663560i
$760$	0.0313037	−	0.0963429i	0.00113550	−	0.00349472i
$761$	19.8233	−	8.82588i	0.718593	−	0.319938i	−0.0146617	−	0.999893i	$-0.504667\pi$
$761$	19.8233	−	8.82588i	0.718593	−	0.319938i	0.733254	+	0.679954i	$0.238000\pi$
$762$	6.92631	+	22.5553i	0.250914	+	0.817093i
$763$	−12.1103	−	2.57412i	−0.438422	−	0.0931895i
$764$	3.11557	−	6.99769i	0.112717	−	0.253168i
$765$	9.87284	+	6.13540i	0.356953	+	0.221826i
$766$	13.9352	+	1.46465i	0.503498	+	0.0529198i
$767$	9.23255	+	6.70784i	0.333368	+	0.242206i
$768$	−1.69982	+	0.332589i	−0.0613369	+	0.0120013i
$769$	−0.776312	+	1.34461i	−0.0279945	+	0.0484879i	−0.879683	−	0.475560i	$-0.842245\pi$
$769$	−0.776312	+	1.34461i	−0.0279945	+	0.0484879i	0.851689	+	0.524048i	$0.175579\pi$
$770$	−1.44629	−	2.50504i	−0.0521206	−	0.0902755i
$771$	−37.2470	+	32.4592i	−1.34142	+	1.16899i
$772$	14.6211	+	16.2384i	0.526226	+	0.584434i
$773$	14.1794	+	43.6399i	0.509999	+	1.56962i	0.792200	+	0.610261i	$0.208935\pi$
$773$	14.1794	+	43.6399i	0.509999	+	1.56962i	−0.282201	+	0.959355i	$0.591065\pi$
$774$	−7.80258	+	1.39568i	−0.280458	+	0.0501665i
$775$	−4.01667	+	3.85569i	−0.144283	+	0.138501i
$776$		−	3.54570i		−	0.127283i
$777$	−2.35071	−	5.51898i	−0.0843313	−	0.197992i
$778$	−20.1711	+	18.1621i	−0.723168	+	0.651143i
$779$	0.223226	+	0.307244i	0.00799788	+	0.0110081i
$780$	1.67506	−	1.17597i	0.0599768	−	0.0421066i
$781$	11.2658	+	6.50430i	0.403121	+	0.232742i
$782$	−15.0235	+	1.57903i	−0.537239	+	0.0564661i
$783$	10.3878	−	27.3635i	0.371228	−	0.977891i
$784$	0.134267	−	1.27746i	0.00479524	−	0.0456237i
$785$	7.75204	+	6.97996i	0.276682	+	0.249126i
$786$	−0.726085	+	2.11719i	−0.0258986	+	0.0755177i
$787$	−1.04614	+	4.92170i	−0.0372909	+	0.175440i	−0.992852	−	0.119354i	$-0.961918\pi$
$787$	−1.04614	+	4.92170i	−0.0372909	+	0.175440i	0.955561	+	0.294794i	$0.0952510\pi$
$788$	−14.7205	+	3.12894i	−0.524396	+	0.111464i
$789$	−13.8691	−	24.9478i	−0.493753	−	0.888167i
$790$	9.87894	+	3.20986i	0.351477	+	0.114202i
$791$	27.8595	+	9.05212i	0.990572	+	0.321856i
$792$	−2.03716	−	3.00419i	−0.0723874	−	0.106749i
$793$	13.1720	−	2.79979i	0.467751	−	0.0994236i
$794$	7.40203	−	34.8238i	0.262688	−	1.23585i
$795$	9.39272	+	3.22121i	0.333125	+	0.114244i
$796$	14.6774	+	13.2156i	0.520226	+	0.468413i
$797$	0.179628	−	1.70905i	0.00636276	−	0.0605376i	−0.990880	−	0.134749i	$-0.956977\pi$
$797$	0.179628	−	1.70905i	0.00636276	−	0.0605376i	0.997243	+	0.0742112i	$0.0236439\pi$
$798$	−0.359822	−	0.215599i	−0.0127376	−	0.00763213i
$799$	10.2915	−	1.08168i	0.364088	−	0.0382672i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	11.0716	+	13.1286i	0.391195	+	0.463878i
$802$	−12.9437	−	17.8155i	−0.457059	−	0.629088i
$803$	−5.22559	+	4.70514i	−0.184407	+	0.166041i
$804$	12.7608	−	5.43525i	0.450040	−	0.191686i
$805$		−	9.32075i		−	0.328513i
$806$	−1.57250	−	6.38834i	−0.0553891	−	0.225020i
$807$	−1.22877	−	13.8480i	−0.0432547	−	0.487472i
$808$	2.19400	+	6.75245i	0.0771848	+	0.237550i
$809$	−16.6357	−	18.4759i	−0.584882	−	0.649577i	0.375973	−	0.926631i	$-0.377309\pi$
$809$	−16.6357	−	18.4759i	−0.584882	−	0.649577i	−0.960854	+	0.277054i	$0.910642\pi$
$810$	−4.99584	+	7.48610i	−0.175536	+	0.263035i
$811$	14.4885	+	25.0949i	0.508761	+	0.881201i	0.999949	+	0.0101465i	$0.00322980\pi$
$811$	14.4885	+	25.0949i	0.508761	+	0.881201i	−0.491187	+	0.871054i	$0.663437\pi$
$812$	6.73319	−	11.6622i	0.236289	−	0.409264i
$813$	−2.13653	−	10.9195i	−0.0749315	−	0.382965i
$814$	1.41804	+	1.03026i	0.0497022	+	0.0361107i
$815$	16.3719	+	1.72076i	0.573483	+	0.0602755i
$816$	5.36470	+	4.03222i	0.187802	+	0.141156i
$817$	0.108864	−	0.244512i	0.00380865	−	0.00855438i
$818$	−6.25057	−	1.32860i	−0.218546	−	0.0464534i
$819$	−3.19411	−	7.84984i	−0.111611	−	0.274296i
$820$	3.42485	−	1.52484i	0.119601	−	0.0532498i
$821$	−5.88112	+	18.1002i	−0.205252	+	0.631702i	0.794451	+	0.607329i	$0.207759\pi$
$821$	−5.88112	+	18.1002i	−0.205252	+	0.631702i	−0.999703	+	0.0243730i	$0.992241\pi$
$822$	−3.68706	+	16.0608i	−0.128601	+	0.560186i
$823$	7.40845	+	16.6396i	0.258242	+	0.580021i	0.995412	−	0.0956866i	$-0.0305047\pi$
$823$	7.40845	+	16.6396i	0.258242	+	0.580021i	−0.737169	+	0.675708i	$0.763838\pi$
$824$	−1.72331	−	8.10756i	−0.0600345	−	0.282440i
$825$	0.252827	−	2.08034i	0.00880232	−	0.0724281i
$826$	−21.0931	−	9.39124i	−0.733922	−	0.326763i
$827$	−7.02059	+	7.79715i	−0.244130	+	0.271134i	−0.852740	−	0.522336i	$-0.825061\pi$
$827$	−7.02059	+	7.79715i	−0.244130	+	0.271134i	0.608610	+	0.793469i	$0.291727\pi$
$828$	−0.844688	−	11.6657i	−0.0293549	−	0.405410i
$829$	26.4399	−	36.3914i	0.918296	−	1.26393i	−0.0459570	−	0.998943i	$-0.514634\pi$
$829$	26.4399	−	36.3914i	0.918296	−	1.26393i	0.964253	−	0.264983i	$-0.0853663\pi$
$830$	0.735985	+	7.00243i	0.0255464	+	0.243058i
$831$	2.77481	−	5.96984i	0.0962572	−	0.207091i
$832$	1.02332	−	0.590815i	0.0354773	−	0.0204828i
$833$	−4.02646	+	2.92540i	−0.139509	+	0.101359i
$834$	17.3000	−	18.5979i	0.599049	−	0.643993i
$835$	2.58410	−	0.839626i	0.0894266	−	0.0290565i
$836$	0.122566			0.00423904
$837$	16.6110	+	23.6870i	0.574159	+	0.818744i
$838$	−21.0943			−0.728689
$839$	11.4351	−	3.71549i	0.394783	−	0.128273i	−0.104896	−	0.994483i	$-0.533451\pi$
$839$	11.4351	−	3.71549i	0.394783	−	0.128273i	0.499680	+	0.866210i	$0.333451\pi$
$840$	−2.82030	+	3.03190i	−0.0973096	+	0.104610i
$841$	−2.20727	+	1.60367i	−0.0761127	+	0.0552991i
$842$	5.21560	−	3.01123i	0.179741	−	0.103774i
$843$	−1.26095	+	2.71285i	−0.0434293	+	0.0934355i
$844$	0.212238	+	2.01931i	0.00730554	+	0.0695075i
$845$	6.82051	−	9.38763i	0.234633	−	0.322944i
$846$	0.578636	+	7.99133i	0.0198939	+	0.274748i
$847$	−15.2549	+	16.9422i	−0.524163	+	0.582142i
$848$	5.23729	+	2.33179i	0.179849	+	0.0800740i
$849$	−2.73403	+	22.4965i	−0.0938318	+	0.772076i
$850$	0.805585	+	3.78998i	0.0276313	+	0.129995i
$851$	2.29726	+	5.15972i	0.0787490	+	0.176873i
$852$	4.16671	−	18.1502i	0.142749	−	0.621815i
$853$	−3.57940	+	11.0163i	−0.122556	+	0.377189i	−0.993448	−	0.114286i	$-0.963542\pi$
$853$	−3.57940	+	11.0163i	−0.122556	+	0.377189i	0.870892	+	0.491475i	$0.163542\pi$
$854$	−24.8899	+	11.0817i	−0.851715	+	0.379208i
$855$	−0.114539	−	0.281492i	−0.00391716	−	0.00962681i
$856$	−15.5345	−	3.30197i	−0.530960	−	0.112859i
$857$	−18.3768	+	41.2750i	−0.627740	+	1.40993i	0.267157	+	0.963653i	$0.413916\pi$
$857$	−18.3768	+	41.2750i	−0.627740	+	1.40993i	−0.894897	+	0.446274i	$0.852751\pi$
$858$	1.97948	+	1.48782i	0.0675784	+	0.0507933i
$859$	−33.6759	−	3.53948i	−1.14901	−	0.120766i	−0.489180	−	0.872183i	$-0.662704\pi$
$859$	−33.6759	−	3.53948i	−1.14901	−	0.120766i	−0.659828	+	0.751417i	$0.729371\pi$
$860$	−2.13754	−	1.55301i	−0.0728894	−	0.0529573i
$861$	−2.98090	−	15.2350i	−0.101589	−	0.519207i
$862$	13.6462	−	23.6359i	0.464791	−	0.805041i
$863$	−3.18409	−	5.51500i	−0.108388	−	0.187733i	0.806730	−	0.590921i	$-0.201235\pi$
$863$	−3.18409	−	5.51500i	−0.108388	−	0.187733i	−0.915117	+	0.403188i	$0.867902\pi$
$864$	−3.25507	+	4.05025i	−0.110740	+	0.137792i
$865$	−1.91913	−	2.13141i	−0.0652523	−	0.0724700i
$866$	−11.4443	−	35.2220i	−0.388894	−	1.19689i
$867$	0.304199	+	3.42827i	0.0103312	+	0.116430i
$868$	5.79930	+	11.9812i	0.196841	+	0.406668i
$869$			12.5679i			0.426336i
$870$	8.97599	−	3.82316i	0.304315	−	0.129617i
$871$	−7.03193	+	6.33158i	−0.238268	+	0.214537i
$872$	−3.04398	−	4.18968i	−0.103082	−	0.141881i
$873$	−6.85750	−	8.13159i	−0.232091	−	0.275213i
$874$	0.342033	+	0.197473i	0.0115694	+	0.00667961i
$875$	−2.37761	+	0.249897i	−0.0803781	+	0.00844807i
$876$	8.63480	+	5.17381i	0.291743	+	0.174807i
$877$	−4.45735	+	42.4089i	−0.150514	+	1.43205i	0.614949	+	0.788567i	$0.289177\pi$
$877$	−4.45735	+	42.4089i	−0.150514	+	1.43205i	−0.765463	+	0.643480i	$0.777490\pi$
$878$	7.11892	+	6.40991i	0.240252	+	0.216324i
$879$	−23.5136	−	8.06392i	−0.793093	−	0.271989i
$880$	0.251557	−	1.18348i	0.00847998	−	0.0398952i
$881$	48.7672	−	10.3658i	1.64301	−	0.349232i	0.708649	−	0.705561i	$-0.249305\pi$
$881$	48.7672	−	10.3658i	1.64301	−	0.349232i	0.934361	+	0.356329i	$0.115972\pi$
$882$	−2.16273	−	3.18936i	−0.0728229	−	0.107391i
$883$	43.6376	+	14.1787i	1.46852	+	0.477152i	0.930662	−	0.365881i	$-0.119232\pi$
$883$	43.6376	+	14.1787i	1.46852	+	0.477152i	0.537862	+	0.843033i	$0.319232\pi$
$884$	−4.35432	−	1.41480i	−0.146452	−	0.0475850i
$885$	−8.12793	−	14.6206i	−0.273217	−	0.491466i
$886$	−4.38582	+	0.932235i	−0.147344	+	0.0313190i
$887$	−6.89352	+	32.4314i	−0.231462	+	1.08894i	0.696873	+	0.717195i	$0.254574\pi$
$887$	−6.89352	+	32.4314i	−0.231462	+	1.08894i	−0.928334	+	0.371746i	$0.878759\pi$
$888$	0.813983	−	2.37349i	0.0273155	−	0.0796491i
$889$	24.2023	+	21.7919i	0.811720	+	0.730876i
$890$	−0.598386	+	5.69326i	−0.0200579	+	0.190839i
$891$	−10.4822	−	2.94978i	−0.351165	−	0.0988213i
$892$	8.54852	−	0.898486i	0.286226	−	0.0300835i
$893$	−0.234303	−	0.135275i	−0.00784064	−	0.00452680i
$894$	2.67173	−	1.87569i	0.0893561	−	0.0627324i
$895$	4.84563	+	6.66944i	0.161972	+	0.222935i
$896$	−1.77664	+	1.59970i	−0.0593535	+	0.0534422i
$897$	3.12683	+	7.34115i	0.104402	+	0.245114i
$898$		−	24.4606i		−	0.816259i
$899$	−1.00073	−	31.3461i	−0.0333762	−	1.04545i
$900$	−2.95313	+	0.528237i	−0.0984376	+	0.0176079i
$901$	−6.86422	−	21.1259i	−0.228680	−	0.703806i
$902$	3.03515	+	3.37088i	0.101059	+	0.112238i
$903$	−8.24816	+	7.18791i	−0.274482	+	0.239199i
$904$	6.12647	+	10.6114i	0.203764	+	0.352929i
$905$	3.60727	−	6.24798i	0.119910	−	0.207690i
$906$	−15.9017	+	3.11136i	−0.528299	+	0.103368i
$907$	−22.4220	−	16.2905i	−0.744510	−	0.540918i	0.149610	−	0.988745i	$-0.452198\pi$
$907$	−22.4220	−	16.2905i	−0.744510	−	0.540918i	−0.894120	+	0.447827i	$0.852198\pi$
$908$	−22.0530	−	2.31786i	−0.731853	−	0.0769208i
$909$	18.0911	+	11.2426i	0.600043	+	0.372892i
$910$	1.14900	−	2.58071i	0.0380891	−	0.0855496i
$911$	48.5643	+	10.3227i	1.60901	+	0.342005i	0.922764	−	0.385365i	$-0.125925\pi$
$911$	48.5643	+	10.3227i	1.60901	+	0.342005i	0.686245	+	0.727371i	$0.259258\pi$
$912$	−0.0515061	−	0.167728i	−0.00170554	−	0.00555403i
$913$	−7.78255	+	3.46501i	−0.257565	+	0.114675i
$914$	5.10526	−	15.7124i	0.168867	−	0.519719i
$915$	−19.2386	−	4.41658i	−0.636009	−	0.146008i
$916$	4.52540	+	10.1642i	0.149523	+	0.335835i
$917$	0.642319	+	3.02188i	0.0212113	+	0.0997911i
$918$	20.1016	−	1.12814i	0.663453	−	0.0372341i
$919$	0.372712	+	0.165942i	0.0122946	+	0.00547392i	0.412875	−	0.910788i	$-0.364525\pi$
$919$	0.372712	+	0.165942i	0.0122946	+	0.00547392i	−0.400580	+	0.916262i	$0.631191\pi$
$920$	2.60876	−	2.89733i	0.0860084	−	0.0955220i
$921$	−47.0383	−	0.762978i	−1.54996	−	0.0251410i
$922$	4.36554	−	6.00865i	0.143771	−	0.197884i
$923$	1.32797	+	12.6348i	0.0437108	+	0.415880i
$924$	−4.54329	−	2.11175i	−0.149463	−	0.0694714i
$925$	1.25459	−	0.724340i	0.0412508	−	0.0238162i
$926$	11.1160	−	8.07624i	0.365294	−	0.265402i
$927$	−19.6324	−	15.2606i	−0.644814	−	0.501225i
$928$	5.35710	−	1.74063i	0.175856	−	0.0571389i
$929$	−15.4813			−0.507925			−0.253962	−	0.967214i	$-0.581734\pi$
$929$	−15.4813			−0.507925			−0.253962	+	0.967214i	$0.581734\pi$
$930$	−1.85673	+	9.46322i	−0.0608847	+	0.310311i
$931$	0.130121			0.00426454
$932$	−3.65792	+	1.18853i	−0.119819	+	0.0389316i
$933$	15.5055	+	14.4233i	0.507626	+	0.472199i
$934$	−27.1620	+	19.7344i	−0.888769	+	0.645728i
$935$	−4.05995	+	2.34401i	−0.132774	+	0.0766574i
$936$	1.20420	−	3.33409i	0.0393604	−	0.108978i
$937$	−0.468153	−	4.45418i	−0.0152939	−	0.145512i	0.984210	−	0.177004i	$-0.0566406\pi$
$937$	−0.468153	−	4.45418i	−0.0152939	−	0.145512i	−0.999504	+	0.0314926i	$0.989974\pi$
$938$	11.2529	−	15.4883i	0.367421	−	0.505712i
$939$	−0.242284	+	14.9371i	−0.00790665	+	0.487452i
$940$	−1.78708	+	1.98475i	−0.0582882	+	0.0647356i
$941$	−14.6554	−	6.52501i	−0.477753	−	0.212709i	0.153709	−	0.988116i	$-0.450878\pi$
$941$	−14.6554	−	6.52501i	−0.477753	−	0.212709i	−0.631462	+	0.775407i	$0.717545\pi$
$942$	17.9357	+	2.17976i	0.584378	+	0.0710205i
$943$	3.03889	+	14.2968i	0.0989598	+	0.465569i
$944$	−3.92822	−	8.82293i	−0.127853	−	0.287162i
$945$	−0.604201	+	12.4078i	−0.0196547	+	0.403626i
$946$	0.987861	−	3.04032i	0.0321181	−	0.0988494i
$947$	−42.4357	+	18.8936i	−1.37897	+	0.613959i	−0.956317	−	0.292331i	$-0.905569\pi$
$947$	−42.4357	+	18.8936i	−1.37897	+	0.613959i	−0.422657	+	0.906290i	$0.638903\pi$
$948$	17.1988	−	5.28141i	0.558589	−	0.171532i
$949$	−6.71723	−	1.42779i	−0.218050	−	0.0463480i
$950$	0.0412028	−	0.0925430i	0.00133679	−	0.00300249i
$951$	−19.5898	+	26.0634i	−0.635242	+	0.845163i
$952$	9.21242	+	0.968265i	0.298576	+	0.0313816i
$953$	36.3641	+	26.4201i	1.17795	+	0.855831i	0.991939	−	0.126717i	$-0.0404439\pi$
$953$	36.3641	+	26.4201i	1.17795	+	0.855831i	0.186011	+	0.982548i	$0.440444\pi$
$954$	16.5208	−	4.78142i	0.534880	−	0.154804i
$955$	3.82996	−	6.63369i	0.123935	−	0.214661i
$956$	2.97833	+	5.15862i	0.0963261	+	0.166842i
$957$	7.75533	+	8.89928i	0.250694	+	0.287673i
$958$	−0.591495	−	0.656922i	−0.0191103	−	0.0212242i
$959$	7.02862	+	21.6319i	0.226966	+	0.698529i
$960$	−1.72527	+	0.153088i	−0.0556829	+	0.00494089i
$961$	26.1907	+	16.5845i	0.844862	+	0.534985i
$962$			1.71180i			0.0551908i
$963$	−42.0125	+	22.4717i	−1.35383	+	0.724139i
$964$	−15.4678	+	13.9273i	−0.498184	+	0.448567i
$965$	12.8437	+	17.6778i	0.413452	+	0.569068i
$966$	−9.27614	−	13.2130i	−0.298455	−	0.425120i
$967$	23.7376	+	13.7049i	0.763350	+	0.440720i	0.830497	−	0.557023i	$-0.188056\pi$
$967$	23.7376	+	13.7049i	0.763350	+	0.440720i	−0.0671475	+	0.997743i	$0.521390\pi$
$968$	−9.48385	+	0.996793i	−0.304822	+	0.0320381i
$969$	−0.349424	+	0.583168i	−0.0112251	+	0.0187340i
$970$	0.370627	−	3.52628i	0.0119001	−	0.113222i
$971$	−20.5955	−	18.5442i	−0.660940	−	0.595113i	0.268859	−	0.963179i	$-0.413353\pi$
$971$	−20.5955	−	18.5442i	−0.660940	−	0.595113i	−0.929800	+	0.368066i	$0.880020\pi$
$972$	0.368244	+	15.5841i	0.0118114	+	0.499860i
$973$	7.28925	−	34.2932i	0.233683	−	1.09939i
$974$	−23.0922	+	4.90839i	−0.739921	+	0.157275i
$975$	1.78881	−	0.994441i	0.0572877	−	0.0318476i
$976$	−10.8386	−	3.52167i	−0.346934	−	0.112726i
$977$	27.7450	+	9.01491i	0.887642	+	0.288412i	0.717127	−	0.696943i	$-0.245457\pi$
$977$	27.7450	+	9.01491i	0.887642	+	0.288412i	0.170515	+	0.985355i	$0.445457\pi$
$978$	24.9211	−	13.8542i	0.796889	−	0.443010i
$979$	−6.77499	+	1.44007i	−0.216529	+	0.0460248i
$980$	0.267062	−	1.25643i	0.00853100	−	0.0401352i
$981$	−15.0839	−	3.72132i	−0.481593	−	0.118813i
$982$	26.9779	+	24.2910i	0.860899	+	0.775157i
$983$	−4.30510	+	40.9603i	−0.137311	+	1.30643i	0.681267	+	0.732035i	$0.261429\pi$
$983$	−4.30510	+	40.9603i	−0.137311	+	1.30643i	−0.818578	+	0.574395i	$0.805237\pi$
$984$	3.33748	−	5.57006i	0.106395	−	0.177567i
$985$	−14.9669	+	1.57309i	−0.476886	+	0.0501227i
$986$	−18.9011	−	10.9125i	−0.601933	−	0.347526i
$987$	6.35444	+	9.05128i	0.202264	+	0.288105i
$988$	0.0703580	+	0.0968394i	0.00223838	+	0.00308087i
$989$	7.65514	−	6.89272i	0.243419	−	0.219176i
$990$	−1.71198	−	3.20068i	−0.0544102	−	0.101724i
$991$		−	43.6106i		−	1.38534i	−0.721256	−	0.692669i	$-0.756435\pi$
$991$		−	43.6106i		−	1.38534i	0.721256	−	0.692669i	$-0.243565\pi$
$992$	−1.55069	+	5.34746i	−0.0492345	+	0.169782i
$993$	54.6312	−	4.84757i	1.73367	−	0.153833i
$994$	−7.94297	−	24.4459i	−0.251936	−	0.775378i
$995$	13.2156	+	14.6774i	0.418962	+	0.465304i
$996$	8.01224	+	9.19408i	0.253877	+	0.291326i
$997$	28.5401	+	49.4330i	0.903875	+	1.56556i	0.822420	+	0.568881i	$0.192624\pi$
$997$	28.5401	+	49.4330i	0.903875	+	1.56556i	0.0814555	+	0.996677i	$0.474043\pi$
$998$	−1.65134	+	2.86021i	−0.0522723	+	0.0905383i
$999$	−2.72364	−	7.01755i	−0.0861722	−	0.222025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.20	yes	176
3.2	odd	2	inner	930.2.br.b.11.9	✓	176
31.17	odd	30	inner	930.2.br.b.761.9	yes	176
93.17	even	30	inner	930.2.br.b.761.20	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.9	✓	176	3.2	odd	2	inner
930.2.br.b.11.20	yes	176	1.1	even	1	trivial
930.2.br.b.761.9	yes	176	31.17	odd	30	inner
930.2.br.b.761.20	yes	176	93.17	even	30	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.17969 - 1.26820i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.730058 - 1.57067i) q^{6} +(-0.249897 - 2.37761i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.216657 - 2.99217i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.17969 - 1.26820i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.730058 - 1.57067i) q^{6} +(-0.249897 - 2.37761i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.216657 - 2.99217i) q^{9} +(0.669131 - 0.743145i) q^{10} +(1.10532 + 0.492120i) q^{11} +(0.208962 - 1.71940i) q^{12} +(0.245675 + 1.15581i) q^{13} +(-0.972390 - 2.18402i) q^{14} +(0.387543 - 1.68814i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.53967 + 1.57596i) q^{17} +(-1.13068 - 2.77877i) q^{18} +(0.0990872 + 0.0210616i) q^{19} +(0.406737 - 0.913545i) q^{20} +(-3.31009 - 2.48793i) q^{21} +(1.20329 + 0.126471i) q^{22} +(3.15414 + 2.29162i) q^{23} +(-0.332589 - 1.69982i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.590815 + 1.02332i) q^{26} +(-4.05025 - 3.25507i) q^{27} +(-1.59970 - 1.77664i) q^{28} +(1.74063 + 5.35710i) q^{29} +(-0.153088 - 1.72527i) q^{30} +(-5.34746 - 1.55069i) q^{31} -1.00000i q^{32} +(1.92804 - 0.821215i) q^{33} +(-2.87943 + 2.59265i) q^{34} +(-1.40522 - 1.93413i) q^{35} +(-1.93403 - 2.29337i) q^{36} +(1.25459 + 0.724340i) q^{37} +(0.100746 - 0.0105888i) q^{38} +(1.75561 + 1.05193i) q^{39} +(0.104528 - 0.994522i) q^{40} +(2.78603 + 2.50855i) q^{41} +(-3.91690 - 1.34329i) q^{42} +(0.549332 - 2.58440i) q^{43} +(1.18348 - 0.251557i) q^{44} +(-1.68371 - 2.48296i) q^{45} +(3.70792 + 1.20478i) q^{46} +(-2.54004 - 0.825307i) q^{47} +(-0.841584 - 1.51385i) q^{48} +(1.25643 - 0.267062i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-2.17708 + 6.34815i) q^{51} +(0.878122 + 0.790664i) q^{52} +(-0.599254 + 5.70152i) q^{53} +(-4.85789 - 1.84416i) q^{54} +(1.20329 - 0.126471i) q^{55} +(-2.07042 - 1.19536i) q^{56} +(0.143603 - 0.100816i) q^{57} +(3.31087 + 4.55702i) q^{58} +(7.17722 - 6.46239i) q^{59} +(-0.678734 - 1.59352i) q^{60} -11.3964i q^{61} +(-5.56493 + 0.177661i) q^{62} +(-7.06008 + 1.26286i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.790664 + 0.878122i) q^{65} +(1.57991 - 1.37682i) q^{66} +(4.00396 + 6.93507i) q^{67} +(-1.93732 + 3.35555i) q^{68} +(6.62715 - 1.29668i) q^{69} +(-1.93413 - 1.40522i) q^{70} +(10.6927 + 1.12385i) q^{71} +(-2.54806 - 1.58347i) q^{72} +(-2.36384 + 5.30927i) q^{73} +(1.41702 + 0.301198i) q^{74} +(-0.508447 - 1.65574i) q^{75} +(0.0925430 - 0.0412028i) q^{76} +(0.893855 - 2.75100i) q^{77} +(1.99475 + 0.457932i) q^{78} +(4.22491 + 9.48930i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.90612 + 1.29655i) q^{81} +(3.42485 + 1.52484i) q^{82} +(-4.71135 + 5.23248i) q^{83} +(-4.14029 - 0.0671570i) q^{84} +(-2.27746 + 3.13466i) q^{85} +(-0.276179 - 2.62767i) q^{86} +(8.84728 + 4.11226i) q^{87} +(1.04782 - 0.604961i) q^{88} +(-4.63131 + 3.36485i) q^{89} +(-2.36858 - 1.84114i) q^{90} +(2.68667 - 0.872953i) q^{91} +3.89874 q^{92} +(-8.27494 + 4.95231i) q^{93} -2.67075 q^{94} +(0.0963429 - 0.0313037i) q^{95} +(-1.26820 - 1.17969i) q^{96} +(2.86853 - 2.08411i) q^{97} +(1.11241 - 0.642250i) q^{98} +(1.23303 - 3.41392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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