LMFDB - Embedded newform 930.2.br.b.761.9

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			761.9
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.38456 + 1.04067i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.995214 - 1.41759i) q^{6} +(-0.249897 + 2.37761i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.834029 + 2.88173i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.38456 + 1.04067i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.995214 - 1.41759i) q^{6} +(-0.249897 + 2.37761i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.834029 + 2.88173i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.10532 + 0.492120i) q^{11} +(0.508447 + 1.65574i) q^{12} +(0.245675 - 1.15581i) q^{13} +(0.972390 - 2.18402i) q^{14} +(-0.678734 - 1.59352i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.53967 + 1.57596i) q^{17} +(0.0972966 - 2.99842i) q^{18} +(0.0990872 - 0.0210616i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-2.82030 + 3.03190i) q^{21} +(1.20329 - 0.126471i) q^{22} +(-3.15414 + 2.29162i) q^{23} +(0.0280908 - 1.73182i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.590815 + 1.02332i) q^{26} +(-1.84416 + 4.85789i) 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} +(-2.04252 - 0.468897i) q^{33} +(-2.87943 - 2.59265i) q^{34} +(1.40522 - 1.93413i) q^{35} +(-1.01910 + 2.82160i) q^{36} +(1.25459 - 0.724340i) q^{37} +(-0.100746 - 0.0105888i) q^{38} +(1.54296 - 1.34462i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-2.78603 + 2.50855i) q^{41} +(3.61917 - 2.01198i) q^{42} +(0.549332 + 2.58440i) q^{43} +(-1.18348 - 0.251557i) q^{44} +(0.718577 - 2.91267i) q^{45} +(3.70792 - 1.20478i) q^{46} +(2.54004 - 0.825307i) q^{47} +(-0.561879 + 1.63838i) q^{48} +(1.25643 + 0.267062i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(3.26084 + 5.86563i) q^{51} +(0.878122 - 0.790664i) q^{52} +(0.599254 + 5.70152i) q^{53} +(3.25507 - 4.05025i) q^{54} +(1.20329 + 0.126471i) q^{55} +(2.07042 - 1.19536i) q^{56} +(0.159111 + 0.0739555i) q^{57} +(3.31087 - 4.55702i) q^{58} +(-7.17722 - 6.46239i) q^{59} +(0.387543 - 1.68814i) 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} +(1.79765 + 1.07712i) q^{66} +(4.00396 - 6.93507i) q^{67} +(1.93732 + 3.35555i) q^{68} +(-6.75192 - 0.109519i) q^{69} +(-1.93413 + 1.40522i) q^{70} +(-10.6927 + 1.12385i) q^{71} +(1.84114 - 2.36858i) q^{72} +(-2.36384 - 5.30927i) q^{73} +(-1.41702 + 0.301198i) q^{74} +(-0.208962 + 1.71940i) q^{75} +(0.0925430 + 0.0412028i) q^{76} +(-0.893855 - 2.75100i) q^{77} +(-1.88296 + 0.802012i) q^{78} +(4.22491 - 9.48930i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-7.60879 + 4.80690i) q^{81} +(3.42485 - 1.52484i) q^{82} +(4.71135 + 5.23248i) q^{83} +(-4.06378 + 0.795125i) q^{84} +(-2.27746 - 3.13466i) q^{85} +(0.276179 - 2.62767i) q^{86} +(-7.98496 + 5.60583i) q^{87} +(1.04782 + 0.604961i) q^{88} +(4.63131 + 3.36485i) q^{89} +(-1.58347 + 2.54806i) q^{90} +(2.68667 + 0.872953i) q^{91} -3.89874 q^{92} +(-9.01765 - 3.41789i) q^{93} -2.67075 q^{94} +(-0.0963429 - 0.0313037i) q^{95} +(1.04067 - 1.38456i) q^{96} +(2.86853 + 2.08411i) q^{97} +(-1.11241 - 0.642250i) q^{98} +(-2.34003 - 2.77479i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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
$3$	1.38456	+	1.04067i	0.799378	+	0.600829i
$3$	1.38456	+	1.04067i	0.799378	+	0.600829i
$4$	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
$6$	−0.995214	−	1.41759i	−0.406294	−	0.578727i
$7$	−0.249897	+	2.37761i	−0.0944523	+	0.898654i	0.840005	+	0.542579i	$0.182552\pi$
$7$	−0.249897	+	2.37761i	−0.0944523	+	0.898654i	−0.934457	+	0.356075i	$0.884115\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.834029	+	2.88173i	0.278010	+	0.960578i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	−1.10532	+	0.492120i	−0.333266	+	0.148380i	−0.566546	−	0.824030i	$-0.691721\pi$
$11$	−1.10532	+	0.492120i	−0.333266	+	0.148380i	0.233280	+	0.972410i	$0.425054\pi$
$12$	0.508447	+	1.65574i	0.146776	+	0.477972i
$13$	0.245675	−	1.15581i	0.0681379	−	0.320563i	−0.930857	−	0.365383i	$-0.880938\pi$
$13$	0.245675	−	1.15581i	0.0681379	−	0.320563i	0.998995	+	0.0448197i	$0.0142713\pi$
$14$	0.972390	−	2.18402i	0.259882	−	0.583705i
$15$	−0.678734	−	1.59352i	−0.175248	−	0.411446i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.53967	+	1.57596i	0.858496	+	0.382227i	0.788289	−	0.615306i	$-0.210967\pi$
$17$	3.53967	+	1.57596i	0.858496	+	0.382227i	0.0702070	+	0.997532i	$0.477634\pi$
$18$	0.0972966	−	2.99842i	0.0229330	−	0.706735i
$19$	0.0990872	−	0.0210616i	0.0227322	−	0.00483187i	−0.196532	−	0.980497i	$-0.562968\pi$
$19$	0.0990872	−	0.0210616i	0.0227322	−	0.00483187i	0.219264	+	0.975666i	$0.429634\pi$
$20$	−0.406737	−	0.913545i	−0.0909491	−	0.204275i
$21$	−2.82030	+	3.03190i	−0.615440	+	0.661614i
$22$	1.20329	−	0.126471i	0.256543	−	0.0269638i
$23$	−3.15414	+	2.29162i	−0.657684	+	0.477836i	−0.865880	−	0.500251i	$-0.833241\pi$
$23$	−3.15414	+	2.29162i	−0.657684	+	0.477836i	0.208196	+	0.978087i	$0.433241\pi$
$24$	0.0280908	−	1.73182i	0.00573401	−	0.353507i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.590815	+	1.02332i	−0.115868	+	0.200690i
$27$	−1.84416	+	4.85789i	−0.354908	+	0.934901i
$28$	−1.59970	+	1.77664i	−0.302315	+	0.335754i
$29$	−1.74063	+	5.35710i	−0.323227	+	0.994789i	0.649008	+	0.760781i	$0.275184\pi$
$29$	−1.74063	+	5.35710i	−0.323227	+	0.994789i	−0.972235	+	0.234008i	$0.924816\pi$
$30$	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
$33$	−2.04252	−	0.468897i	−0.355556	−	0.0816245i
$34$	−2.87943	−	2.59265i	−0.493817	−	0.444635i
$35$	1.40522	−	1.93413i	0.237526	−	0.326927i
$36$	−1.01910	+	2.82160i	−0.169850	+	0.470267i
$37$	1.25459	−	0.724340i	0.206254	−	0.119081i	−0.393315	−	0.919404i	$-0.628672\pi$
$37$	1.25459	−	0.724340i	0.206254	−	0.119081i	0.599569	+	0.800323i	$0.295339\pi$
$38$	−0.100746	−	0.0105888i	−0.0163432	−	0.00171773i
$39$	1.54296	−	1.34462i	0.247072	−	0.215312i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−2.78603	+	2.50855i	−0.435104	+	0.391770i	−0.857368	−	0.514703i	$-0.827902\pi$
$41$	−2.78603	+	2.50855i	−0.435104	+	0.391770i	0.422264	+	0.906473i	$0.361235\pi$
$42$	3.61917	−	2.01198i	0.558451	−	0.310456i
$43$	0.549332	+	2.58440i	0.0837724	+	0.394118i	0.999978	−	0.00658976i	$-0.00209760\pi$
$43$	0.549332	+	2.58440i	0.0837724	+	0.394118i	−0.916206	+	0.400708i	$0.868764\pi$
$44$	−1.18348	−	0.251557i	−0.178417	−	0.0379236i
$45$	0.718577	−	2.91267i	0.107119	−	0.434195i
$46$	3.70792	−	1.20478i	0.546703	−	0.177634i
$47$	2.54004	−	0.825307i	0.370502	−	0.120383i	−0.117847	−	0.993032i	$-0.537599\pi$
$47$	2.54004	−	0.825307i	0.370502	−	0.120383i	0.488349	+	0.872648i	$0.337599\pi$
$48$	−0.561879	+	1.63838i	−0.0811002	+	0.236480i
$49$	1.25643	+	0.267062i	0.179490	+	0.0381518i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	3.26084	+	5.86563i	0.456609	+	0.821353i
$52$	0.878122	−	0.790664i	0.121774	−	0.109645i
$53$	0.599254	+	5.70152i	0.0823139	+	0.783164i	0.955344	+	0.295497i	$0.0954853\pi$
$53$	0.599254	+	5.70152i	0.0823139	+	0.783164i	−0.873030	+	0.487667i	$0.837848\pi$
$54$	3.25507	−	4.05025i	0.442959	−	0.551169i
$55$	1.20329	+	0.126471i	0.162252	+	0.0170534i
$56$	2.07042	−	1.19536i	0.276671	−	0.159736i
$57$	0.159111	+	0.0739555i	0.0210747	+	0.00979565i
$58$	3.31087	−	4.55702i	0.434739	−	0.598367i
$59$	−7.17722	−	6.46239i	−0.934394	−	0.841332i	0.0531642	−	0.998586i	$-0.483069\pi$
$59$	−7.17722	−	6.46239i	−0.934394	−	0.841332i	−0.987558	+	0.157254i	$0.949736\pi$
$60$	0.387543	−	1.68814i	0.0500316	−	0.217938i
$61$			11.3964i			1.45915i	0.683899	+	0.729577i	$0.260283\pi$
$61$			11.3964i			1.45915i	−0.683899	+	0.729577i	$0.739717\pi$
$62$	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
$66$	1.79765	+	1.07712i	0.221275	+	0.132584i
$67$	4.00396	−	6.93507i	0.489162	−	0.847253i	−0.510760	−	0.859723i	$-0.670636\pi$
$67$	4.00396	−	6.93507i	0.489162	−	0.847253i	0.999922	+	0.0124699i	$0.00396940\pi$
$68$	1.93732	+	3.35555i	0.234935	+	0.406920i
$69$	−6.75192	−	0.109519i	−0.812836	−	0.0131845i
$70$	−1.93413	+	1.40522i	−0.231172	+	0.167956i
$71$	−10.6927	+	1.12385i	−1.26899	+	0.133376i	−0.714987	−	0.699138i	$-0.753567\pi$
$71$	−10.6927	+	1.12385i	−1.26899	+	0.133376i	−0.554004	+	0.832514i	$0.686901\pi$
$72$	1.84114	−	2.36858i	0.216981	−	0.279140i
$73$	−2.36384	−	5.30927i	−0.276666	−	0.621403i	0.720754	−	0.693191i	$-0.243796\pi$
$73$	−2.36384	−	5.30927i	−0.276666	−	0.621403i	−0.997420	+	0.0717888i	$0.977129\pi$
$74$	−1.41702	+	0.301198i	−0.164726	+	0.0350135i
$75$	−0.208962	+	1.71940i	−0.0241288	+	0.198539i
$76$	0.0925430	+	0.0412028i	0.0106154	+	0.00472628i
$77$	−0.893855	−	2.75100i	−0.101864	−	0.313506i
$78$	−1.88296	+	0.802012i	−0.213203	+	0.0908099i
$79$	4.22491	−	9.48930i	0.475340	−	1.06763i	−0.503685	−	0.863887i	$-0.668023\pi$
$79$	4.22491	−	9.48930i	0.475340	−	1.06763i	0.979024	−	0.203743i	$-0.0653106\pi$
$80$	0.207912	−	0.978148i	0.0232452	−	0.109360i
$81$	−7.60879	+	4.80690i	−0.845421	+	0.534100i
$82$	3.42485	−	1.52484i	0.378212	−	0.168391i
$83$	4.71135	+	5.23248i	0.517138	+	0.574340i	0.943987	−	0.329983i	$-0.107043\pi$
$83$	4.71135	+	5.23248i	0.517138	+	0.574340i	−0.426849	+	0.904323i	$0.640376\pi$
$84$	−4.06378	+	0.795125i	−0.443394	+	0.0867553i
$85$	−2.27746	−	3.13466i	−0.247025	−	0.340001i
$86$	0.276179	−	2.62767i	0.0297811	−	0.283349i
$87$	−7.98496	+	5.60583i	−0.856078	+	0.601008i
$88$	1.04782	+	0.604961i	0.111698	+	0.0644891i
$89$	4.63131	+	3.36485i	0.490918	+	0.356673i	0.805537	−	0.592545i	$-0.201877\pi$
$89$	4.63131	+	3.36485i	0.490918	+	0.356673i	−0.314619	+	0.949218i	$0.601877\pi$
$90$	−1.58347	+	2.54806i	−0.166913	+	0.268589i
$91$	2.68667	+	0.872953i	0.281640	+	0.0915103i
$92$	−3.89874			−0.406471
$93$	−9.01765	−	3.41789i	−0.935087	−	0.354419i
$94$	−2.67075			−0.275467
$95$	−0.0963429	−	0.0313037i	−0.00988457	−	0.00321169i
$96$	1.04067	−	1.38456i	0.106213	−	0.141311i
$97$	2.86853	+	2.08411i	0.291255	+	0.211610i	0.723812	−	0.689997i	$-0.242388\pi$
$97$	2.86853	+	2.08411i	0.291255	+	0.211610i	−0.432556	+	0.901607i	$0.642388\pi$
$98$	−1.11241	−	0.642250i	−0.112370	−	0.0648770i
$99$	−2.34003	−	2.77479i	−0.235181	−	0.278877i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	4.17324	+	5.74397i	0.415253	+	0.571547i	0.964490	−	0.264120i	$-0.0850815\pi$
$101$	4.17324	+	5.74397i	0.415253	+	0.571547i	−0.549237	+	0.835667i	$0.685081\pi$
$102$	−1.28867	−	6.58620i	−0.127597	−	0.652131i
$103$	5.54621	+	6.15969i	0.546484	+	0.606933i	0.951602	−	0.307332i	$-0.0994362\pi$
$103$	5.54621	+	6.15969i	0.546484	+	0.606933i	−0.405118	+	0.914264i	$0.632770\pi$
$104$	−1.07947	+	0.480612i	−0.105851	+	0.0471279i
$105$	3.95840	−	1.21555i	0.386300	−	0.118625i
$106$	1.19194	−	5.60765i	0.115772	−	0.544663i
$107$	6.45963	−	14.5086i	0.624476	−	1.40260i	−0.273208	−	0.961955i	$-0.588085\pi$
$107$	6.45963	−	14.5086i	0.624476	−	1.40260i	0.897684	−	0.440640i	$-0.145249\pi$
$108$	−4.34735	+	2.84615i	−0.418324	+	0.273870i
$109$	1.60032	+	4.92527i	0.153282	+	0.471755i	0.997983	−	0.0634846i	$-0.0202214\pi$
$109$	1.60032	+	4.92527i	0.153282	+	0.471755i	−0.844700	+	0.535239i	$0.820221\pi$
$110$	−1.10532	−	0.492120i	−0.105388	−	0.0469218i
$111$	2.49086	+	0.302719i	0.236422	+	0.0287328i
$112$	−2.33847	+	0.497057i	−0.220965	+	0.0469675i
$113$	4.98372	+	11.1936i	0.468829	+	1.05301i	0.980979	+	0.194112i	$0.0621825\pi$
$113$	4.98372	+	11.1936i	0.468829	+	1.05301i	−0.512150	+	0.858896i	$0.671151\pi$
$114$	−0.128470	−	0.119504i	−0.0120323	−	0.0111926i
$115$	3.87738	−	0.407529i	0.361567	−	0.0380023i
$116$	−4.55702	+	3.31087i	−0.423109	+	0.307407i
$117$	3.53563	−	0.256008i	0.326869	−	0.0236680i
$118$	4.82895	+	8.36398i	0.444541	+	0.769967i
$119$	−4.63158	+	8.02214i	−0.424577	+	0.735388i
$120$	−0.890239	+	1.48576i	−0.0812673	+	0.135630i
$121$	−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
$126$	7.10478	+	0.980632i	0.632944	+	0.0873616i
$127$	−10.1235	−	9.11522i	−0.898314	−	0.808845i	0.0839268	−	0.996472i	$-0.473254\pi$
$127$	−10.1235	−	9.11522i	−0.898314	−	0.808845i	−0.982240	+	0.187627i	$0.939920\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−1.92892	+	4.14994i	−0.169832	+	0.365382i
$130$	1.02332	−	0.590815i	0.0897512	−	0.0518179i
$131$	1.28517	+	0.135076i	0.112286	+	0.0118017i	0.160505	−	0.987035i	$-0.448688\pi$
$131$	1.28517	+	0.135076i	0.112286	+	0.0118017i	−0.0482190	+	0.998837i	$0.515355\pi$
$132$	−1.37682	−	1.57991i	−0.119837	−	0.137513i
$133$	0.0253148	+	0.240854i	0.00219507	+	0.0208847i
$134$	−5.95105	+	5.35835i	−0.514092	+	0.462891i
$135$	4.02603	−	3.28498i	0.346506	−	0.282726i
$136$	−0.805585	−	3.78998i	−0.0690783	−	0.324988i
$137$	9.30604	+	1.97806i	0.795069	+	0.168997i	0.587501	−	0.809224i	$-0.300112\pi$
$137$	9.30604	+	1.97806i	0.795069	+	0.168997i	0.207568	+	0.978221i	$0.433445\pi$
$138$	6.38761	+	2.19062i	0.543750	+	0.186478i
$139$	13.9471	−	4.53168i	1.18298	−	0.384372i	0.349504	−	0.936935i	$-0.386350\pi$
$139$	13.9471	−	4.53168i	1.18298	−	0.384372i	0.833471	+	0.552563i	$0.186350\pi$
$140$	2.27370	−	0.738770i	0.192163	−	0.0624375i
$141$	4.37571	+	1.50064i	0.368501	+	0.126377i
$142$	10.5167	+	2.23538i	0.882538	+	0.187589i
$143$	0.297247	+	1.39844i	0.0248570	+	0.116943i
$144$	−2.48296	+	1.68371i	−0.206914	+	0.140309i
$145$	4.18598	−	3.76907i	0.347627	−	0.313004i
$146$	0.607490	+	5.77988i	0.0502762	+	0.478346i
$147$	1.46168	+	1.67729i	0.120558	+	0.138340i
$148$	1.44074	+	0.151428i	0.118428	+	0.0124473i
$149$	−1.63220	+	0.942354i	−0.133715	+	0.0772006i	−0.565365	−	0.824841i	$-0.691265\pi$
$149$	−1.63220	+	0.942354i	−0.133715	+	0.0772006i	0.431650	+	0.902041i	$0.357932\pi$
$150$	0.730058	−	1.57067i	0.0596090	−	0.128245i
$151$	−5.49870	+	7.56831i	−0.447478	+	0.615901i	−0.971853	−	0.235587i	$-0.924299\pi$
$151$	−5.49870	+	7.56831i	−0.447478	+	0.615901i	0.524375	+	0.851487i	$0.324299\pi$
$152$	−0.0752812	−	0.0677835i	−0.00610611	−	0.00549797i
$153$	−1.58932	+	11.5148i	−0.128489	+	0.930915i
$154$			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	−0.736114	−	0.676857i	$-0.763341\pi$
$157$	3.22348	−	9.92085i	0.257262	−	0.791770i	0.993376	−	0.114912i	$-0.0366587\pi$
$158$	−6.95049	+	7.71930i	−0.552951	+	0.614114i
$159$	−5.10367	+	8.51774i	−0.404748	+	0.675500i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−4.66038	−	8.07201i	−0.367289	−	0.636163i
$162$	8.72180	−	2.22039i	0.685250	−	0.174450i
$163$	13.3181	−	9.67618i	1.04316	−	0.757897i	0.0722564	−	0.997386i	$-0.476980\pi$
$163$	13.3181	−	9.67618i	1.04316	−	0.757897i	0.970899	+	0.239489i	$0.0769800\pi$
$164$	−3.72843	+	0.391874i	−0.291142	+	0.0306002i
$165$	1.53442	+	1.42733i	0.119455	+	0.111118i
$166$	−2.86383	−	6.43227i	−0.222277	−	0.499241i
$167$	−2.65771	+	0.564914i	−0.205660	+	0.0437144i	−0.309590	−	0.950870i	$-0.600192\pi$
$167$	−2.65771	+	0.564914i	−0.205660	+	0.0437144i	0.103930	+	0.994585i	$0.466858\pi$
$168$	4.11059	+	0.499567i	0.317139	+	0.0385424i
$169$	10.6006	+	4.71967i	0.815427	+	0.363052i
$170$	1.19733	+	3.68501i	0.0918312	+	0.282627i
$171$	0.143336	+	0.267977i	0.0109612	+	0.0204927i
$172$	−1.07466	+	2.41372i	−0.0819417	+	0.184044i
$173$	0.596310	−	2.80542i	0.0453366	−	0.213292i	−0.949648	−	0.313318i	$-0.898559\pi$
$173$	0.596310	−	2.80542i	0.0453366	−	0.213292i	0.994985	+	0.100026i	$0.0318927\pi$
$174$	9.32645	−	2.86397i	0.707036	−	0.217117i
$175$	−2.18402	+	0.972390i	−0.165097	+	0.0735058i
$176$	−0.809596	−	0.899147i	−0.0610256	−	0.0677758i
$177$	−3.21211	−	16.4167i	−0.241437	−	1.23395i
$178$	−3.36485	−	4.63131i	−0.252206	−	0.347132i
$179$	−0.861720	+	8.19872i	−0.0644080	+	0.612801i	0.913942	+	0.405845i	$0.133023\pi$
$179$	−0.861720	+	8.19872i	−0.0644080	+	0.612801i	−0.978350	+	0.206957i	$0.933644\pi$
$180$	2.29337	−	1.93403i	0.170937	−	0.144154i
$181$	6.24798	+	3.60727i	0.464408	+	0.268126i	0.713896	−	0.700252i	$-0.246929\pi$
$181$	6.24798	+	3.60727i	0.464408	+	0.268126i	−0.249488	+	0.968378i	$0.580262\pi$
$182$	−2.28542	−	1.66046i	−0.169407	−	0.123081i
$183$	−11.8598	+	15.7790i	−0.876701	+	1.16641i
$184$	3.70792	+	1.20478i	0.273351	+	0.0888172i
$185$	−1.44868			−0.106509
$186$	7.52011	+	6.03722i	0.551401	+	0.442670i
$187$	−4.68802			−0.342822
$188$	2.54004	+	0.825307i	0.185251	+	0.0601917i
$189$	−11.0893	−	5.59867i	−0.806631	−	0.407243i
$190$	0.0819541	+	0.0595432i	0.00594558	+	0.00431972i
$191$	−6.63369	−	3.82996i	−0.479997	−	0.277126i	0.240418	−	0.970669i	$-0.422715\pi$
$191$	−6.63369	−	3.82996i	−0.479997	−	0.277126i	−0.720415	+	0.693543i	$0.756049\pi$
$192$	−1.41759	+	0.995214i	−0.102305	+	0.0718234i
$193$	2.28405	−	21.7313i	0.164409	−	1.56425i	−0.532087	−	0.846690i	$-0.678592\pi$
$193$	2.28405	−	21.7313i	0.164409	−	1.56425i	0.696496	−	0.717560i	$-0.254741\pi$
$194$	−2.08411	−	2.86853i	−0.149631	−	0.205949i
$195$	−2.00856	+	0.392997i	−0.143836	+	0.0281431i
$196$	0.859498	+	0.954569i	0.0613927	+	0.0681835i
$197$	13.7483	−	6.12112i	0.979524	−	0.436112i	0.146416	−	0.989223i	$-0.453226\pi$
$197$	13.7483	−	6.12112i	0.979524	−	0.436112i	0.833108	+	0.553111i	$0.186559\pi$
$198$	1.36804	+	3.36209i	0.0972222	+	0.238934i
$199$	4.10633	−	19.3188i	0.291090	−	1.36947i	−0.552961	−	0.833207i	$-0.686502\pi$
$199$	4.10633	−	19.3188i	0.291090	−	1.36947i	0.844051	−	0.536264i	$-0.180165\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	12.7608	−	5.43525i	0.900079	−	0.383373i
$202$	−2.19400	−	6.75245i	−0.154370	−	0.475100i
$203$	−12.3021	−	5.47727i	−0.863442	−	0.384429i
$204$	−0.809653	+	6.66207i	−0.0566871	+	0.466438i
$205$	3.66705	−	0.779455i	0.256118	−	0.0544395i
$206$	−3.37131	−	7.57209i	−0.234890	−	0.527572i
$207$	−9.23449	−	7.17813i	−0.641841	−	0.498914i
$208$	1.17516	−	0.123514i	0.0814824	−	0.00856415i
$209$	−0.0991581	+	0.0720426i	−0.00685891	+	0.00498329i
$210$	−4.14029	−	0.0671570i	−0.285707	−	0.00463427i
$211$	−1.01522	−	1.75841i	−0.0698904	−	0.121054i	0.828962	−	0.559304i	$-0.188932\pi$
$211$	−1.01522	−	1.75841i	−0.0698904	−	0.121054i	−0.898853	+	0.438250i	$0.855598\pi$
$212$	−2.86646	+	4.96486i	−0.196869	+	0.340988i
$213$	−15.9743	−	9.57150i	−1.09454	−	0.655828i
$214$	−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
$219$	2.25229	−	9.81098i	0.152196	−	0.662964i
$220$	0.899147	+	0.809596i	0.0606205	+	0.0545829i
$221$	2.69112	−	3.70400i	0.181024	−	0.249158i
$222$	−2.27540	−	1.05762i	−0.152715	−	0.0709829i
$223$	7.44401	−	4.29780i	0.498488	−	0.287802i	−0.229601	−	0.973285i	$-0.573742\pi$
$223$	7.44401	−	4.29780i	0.498488	−	0.287802i	0.728089	+	0.685483i	$0.240409\pi$
$224$	2.37761	+	0.249897i	0.158861	+	0.0166970i
$225$	−2.07864	+	2.16316i	−0.138576	+	0.144211i
$226$	−1.28078	−	12.1858i	−0.0851963	−	0.810589i
$227$	16.4788	−	14.8376i	1.09374	−	0.984805i	0.0937951	−	0.995592i	$-0.470100\pi$
$227$	16.4788	−	14.8376i	1.09374	−	0.984805i	0.999942	+	0.0107864i	$0.00343347\pi$
$228$	0.0852532	+	0.153354i	0.00564603	+	0.0101561i
$229$	−2.31325	−	10.8830i	−0.152864	−	0.719167i	−0.986087	−	0.166231i	$-0.946840\pi$
$229$	−2.31325	−	10.8830i	−0.152864	−	0.719167i	0.833223	−	0.552937i	$-0.186493\pi$
$230$	−3.81354	−	0.810593i	−0.251457	−	0.0534489i
$231$	1.62528	−	4.73914i	0.106935	−	0.311812i
$232$	5.35710	−	1.74063i	0.351711	−	0.114278i
$233$	3.65792	−	1.18853i	0.239638	−	0.0778631i	−0.186736	−	0.982410i	$-0.559791\pi$
$233$	3.65792	−	1.18853i	0.239638	−	0.0778631i	0.426374	+	0.904547i	$0.359791\pi$
$234$	−3.44170	−	0.849092i	−0.224991	−	0.0555069i
$235$	−2.61239	−	0.555280i	−0.170413	−	0.0362225i
$236$	−2.00799	−	9.44685i	−0.130709	−	0.614938i
$237$	15.7249	−	8.74182i	1.02144	−	0.567842i
$238$	6.88388	−	6.19827i	0.446215	−	0.401774i
$239$	0.622640	+	5.92403i	0.0402753	+	0.383194i	0.996029	+	0.0890264i	$0.0283756\pi$
$239$	0.622640	+	5.92403i	0.0402753	+	0.383194i	−0.955754	+	0.294167i	$0.904958\pi$
$240$	1.30579	−	1.13794i	0.0842885	−	0.0734537i
$241$	−20.7000	−	2.17565i	−1.33340	−	0.140146i	−0.589138	−	0.808032i	$-0.700533\pi$
$241$	−20.7000	−	2.17565i	−1.33340	−	0.140146i	−0.744264	+	0.667886i	$0.767199\pi$
$242$	8.25850	−	4.76804i	0.530876	−	0.306502i
$243$	−15.5372	−	1.26276i	−0.996714	−	0.0810059i
$244$	−6.69861	+	9.21984i	−0.428834	+	0.590240i
$245$	−0.954569	−	0.859498i	−0.0609852	−	0.0549113i
$246$	6.32878	+	1.45289i	0.403508	+	0.0926327i
$247$		−	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	$-0.735394\pi$
$251$	2.07968	−	2.30971i	0.131268	−	0.145788i	0.805195	+	0.593010i	$0.202061\pi$
$252$	−6.45401	−	3.12813i	−0.406565	−	0.197054i
$253$	2.35858	−	4.08519i	0.148283	−	0.256833i
$254$	6.81124	+	11.7974i	0.427375	+	0.740236i
$255$	0.108842	−	6.71021i	0.00681595	−	0.420209i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	28.3682	−	2.98162i	1.76956	−	0.185988i	0.837050	−	0.547127i	$-0.184279\pi$
$257$	28.3682	−	2.98162i	1.76956	−	0.185988i	0.932512	+	0.361139i	$0.117612\pi$
$258$	3.11691	−	3.35076i	0.194050	−	0.208609i
$259$	1.40868	+	3.16395i	0.0875312	+	0.196598i
$260$	−1.15581	+	0.245675i	−0.0716802	+	0.0152361i
$261$	−16.8895	−	0.548051i	−1.04543	−	0.0339235i
$262$	−1.18053	−	0.525604i	−0.0729331	−	0.0324719i
$263$	−5.09252	−	15.6732i	−0.314018	−	0.966449i	−0.976157	−	0.217068i	$-0.930351\pi$
$263$	−5.09252	−	15.6732i	−0.314018	−	0.966449i	0.662138	−	0.749382i	$-0.269649\pi$
$264$	0.821215	+	1.92804i	0.0505423	+	0.118663i
$265$	2.33179	−	5.23729i	0.143241	−	0.321724i
$266$	0.0503523	−	0.236889i	0.00308730	−	0.0145246i
$267$	2.91066	+	9.47849i	0.178130	+	0.580074i
$268$	7.31560	−	3.25712i	0.446872	−	0.198960i
$269$	−5.37081	−	5.96489i	−0.327464	−	0.363686i	0.556821	−	0.830632i	$-0.312021\pi$
$269$	−5.37081	−	5.96489i	−0.327464	−	0.363686i	−0.884286	+	0.466946i	$0.845354\pi$
$270$	−4.84410	+	1.88009i	−0.294802	+	0.114418i
$271$	3.77590	+	5.19708i	0.229369	+	0.315700i	0.908153	−	0.418638i	$-0.137493\pi$
$271$	3.77590	+	5.19708i	0.229369	+	0.315700i	−0.678784	+	0.734338i	$0.737493\pi$
$272$	−0.405011	+	3.85342i	−0.0245574	+	0.233648i
$273$	2.81142	+	4.00459i	0.170155	+	0.242369i
$274$	−8.23932	−	4.75697i	−0.497755	−	0.287379i
$275$	−0.978847	−	0.711174i	−0.0590267	−	0.0428854i
$276$	−5.39805	−	4.05728i	−0.324924	−	0.244220i
$277$	3.61479	+	1.17452i	0.217192	+	0.0705698i	0.415592	−	0.909551i	$-0.363575\pi$
$277$	3.61479	+	1.17452i	0.217192	+	0.0705698i	−0.198400	+	0.980121i	$0.563575\pi$
$278$	−14.6648			−0.879538
$279$	−8.92862	−	14.1166i	−0.534543	−	0.845142i
$280$	−2.39071			−0.142872
$281$	1.64265	+	0.533730i	0.0979925	+	0.0318397i	0.357603	−	0.933874i	$-0.383594\pi$
$281$	1.64265	+	0.533730i	0.0979925	+	0.0318397i	−0.259610	+	0.965713i	$0.583594\pi$
$282$	−3.69782	−	2.77936i	−0.220202	−	0.165508i
$283$	−10.5851	−	7.69052i	−0.629219	−	0.457154i	0.226911	−	0.973916i	$-0.427137\pi$
$283$	−10.5851	−	7.69052i	−0.629219	−	0.457154i	−0.856129	+	0.516761i	$0.827137\pi$
$284$	−9.31116	−	5.37580i	−0.552516	−	0.318995i
$285$	−0.100816	−	0.143603i	−0.00597183	−	0.00850629i
$286$	0.149442	−	1.42185i	0.00883670	−	0.0840756i
$287$	−5.26815	−	7.25098i	−0.310969	−	0.428012i
$288$	2.88173	−	0.834029i	0.169808	−	0.0491456i
$289$	−1.32962	−	1.47670i	−0.0782131	−	0.0868645i
$290$	−5.14581	+	2.29106i	−0.302172	+	0.134536i
$291$	1.80280	+	5.87077i	0.105682	+	0.344151i
$292$	1.20832	−	5.68471i	0.0707118	−	0.332673i
$293$	5.83737	−	13.1109i	0.341023	−	0.765950i	−0.658883	−	0.752245i	$-0.728971\pi$
$293$	5.83737	−	13.1109i	0.341023	−	0.765950i	0.999906	−	0.0137045i	$-0.00436242\pi$
$294$	−0.871833	−	2.04688i	−0.0508463	−	0.119377i
$295$	2.98445	+	9.18521i	0.173762	+	0.534783i
$296$	−1.32344	−	0.589231i	−0.0769231	−	0.0342484i
$297$	−0.352280	−	6.27706i	−0.0204413	−	0.364232i
$298$	1.84352	−	0.391853i	0.106792	−	0.0226994i
$299$	1.87378	+	4.20858i	0.108363	+	0.243388i
$300$	−1.17969	+	1.26820i	−0.0681095	+	0.0732195i
$301$	−6.28200	+	0.660264i	−0.362088	+	0.0380570i
$302$	7.56831	−	5.49870i	0.435508	−	0.316415i
$303$	−0.199443	+	12.2958i	−0.0114577	+	0.706378i
$304$	0.0506504	+	0.0877291i	0.00290500	+	0.00503161i
$305$	5.69818	−	9.86953i	0.326277	−	0.565128i
$306$	5.06980	−	10.4601i	0.289821	−	0.597963i
$307$	−18.1743	+	20.1847i	−1.03726	+	1.15200i	−0.0490698	+	0.998795i	$0.515626\pi$
$307$	−18.1743	+	20.1847i	−1.03726	+	1.15200i	−0.988195	+	0.153204i	$0.951041\pi$
$308$	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	$0.887320\pi$
$312$	−1.99475	−	0.457932i	−0.112931	−	0.0259253i
$313$	−6.40966	−	5.77128i	−0.362295	−	0.326212i	0.467799	−	0.883835i	$-0.345047\pi$
$313$	−6.40966	−	5.77128i	−0.362295	−	0.326212i	−0.830095	+	0.557623i	$0.811714\pi$
$314$	−6.13142	+	8.43917i	−0.346016	+	0.476250i
$315$	6.74564	+	2.43637i	0.380074	+	0.137274i
$316$	8.99570	−	5.19367i	0.506048	−	0.292167i
$317$	18.7212	+	1.96767i	1.05148	+	0.110515i	0.614471	−	0.788939i	$-0.289369\pi$
$317$	18.7212	+	1.96767i	1.05148	+	0.110515i	0.437014	+	0.899455i	$0.356036\pi$
$318$	7.48601	−	6.52373i	0.419794	−	0.365832i
$319$	−0.712386	−	6.77790i	−0.0398860	−	0.379490i
$320$	0.743145	−	0.669131i	0.0415431	−	0.0374055i
$321$	24.0423	−	13.3657i	1.34191	−	0.746000i
$322$	1.93789	+	9.11707i	0.107995	+	0.508075i
$323$	0.383928	+	0.0816065i	0.0213623	+	0.00454071i
$324$	−8.98107	−	0.583472i	−0.498948	−	0.0324151i
$325$	1.12380	−	0.365144i	0.0623370	−	0.0202545i
$326$	−15.6564	+	5.08707i	−0.867127	+	0.281747i
$327$	−2.90982	+	8.48473i	−0.160913	+	0.469207i
$328$	3.66705	+	0.779455i	0.202479	+	0.0430382i
$329$	1.32752	+	6.24547i	0.0731883	+	0.344324i
$330$	−1.01825	−	1.83164i	−0.0560529	−	0.100828i
$331$	23.5319	−	21.1882i	1.29343	−	1.16461i	0.317083	−	0.948398i	$-0.397297\pi$
$331$	23.5319	−	21.1882i	1.29343	−	1.16461i	0.976347	−	0.216211i	$-0.0693700\pi$
$332$	0.735985	+	7.00243i	0.0403924	+	0.384308i
$333$	3.13372	+	3.01129i	0.171727	+	0.165017i
$334$	2.70220	+	0.284013i	0.147858	+	0.0155405i
$335$	−6.93507	+	4.00396i	−0.378903	+	0.218760i
$336$	−3.75503	−	1.74536i	−0.204854	−	0.0952171i
$337$	−2.84275	+	3.91270i	−0.154854	+	0.213139i	−0.879394	−	0.476094i	$-0.842052\pi$
$337$	−2.84275	+	3.91270i	−0.154854	+	0.213139i	0.724540	+	0.689233i	$0.242052\pi$
$338$	−8.62327	−	7.76443i	−0.469044	−	0.422329i
$339$	−4.74855	+	20.6847i	−0.257906	+	1.12344i
$340$		−	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
$345$	5.79258	+	3.47081i	0.311862	+	0.186862i
$346$	−1.43405	+	2.48384i	−0.0770948	+	0.133532i
$347$	−9.62366	−	16.6687i	−0.516625	−	0.894821i	−0.999814	−	0.0193048i	$-0.993855\pi$
$347$	−9.62366	−	16.6687i	−0.516625	−	0.894821i	0.483188	−	0.875516i	$-0.339479\pi$
$348$	−9.75500	−	0.158230i	−0.522923	−	0.00848200i
$349$	7.89177	−	5.73371i	0.422437	−	0.306918i	−0.356181	−	0.934417i	$-0.615921\pi$
$349$	7.89177	−	5.73371i	0.422437	−	0.306918i	0.778618	+	0.627499i	$0.215921\pi$
$350$	2.37761	−	0.249897i	0.127089	−	0.0133576i
$351$	5.16172	+	3.32495i	0.275512	+	0.177473i
$352$	0.492120	+	1.10532i	0.0262301	+	0.0589137i
$353$	25.7648	−	5.47648i	1.37132	−	0.291484i	0.537382	−	0.843339i	$-0.319413\pi$
$353$	25.7648	−	5.47648i	1.37132	−	0.291484i	0.833940	+	0.551855i	$0.186080\pi$
$354$	−2.01813	+	16.6058i	−0.107262	+	0.882588i
$355$	9.82208	+	4.37307i	0.521302	+	0.232099i
$356$	1.76900	+	5.44444i	0.0937571	+	0.288555i
$357$	−14.7611	+	6.28722i	−0.781240	+	0.332755i
$358$	3.35309	−	7.53116i	0.177216	−	0.398034i
$359$	−6.70560	+	31.5474i	−0.353908	+	1.66501i	0.336574	+	0.941657i	$0.390732\pi$
$359$	−6.70560	+	31.5474i	−0.353908	+	1.66501i	−0.690482	+	0.723349i	$0.742602\pi$
$360$	−2.77877	+	1.13068i	−0.146454	+	0.0595922i
$361$	−17.3480	+	7.72382i	−0.913052	+	0.406517i
$362$	−4.82747	−	5.36145i	−0.253726	−	0.281792i
$363$	−16.2096	+	3.17160i	−0.850785	+	0.166466i
$364$	1.66046	+	2.28542i	0.0870315	+	0.119789i
$365$	−0.607490	+	5.77988i	−0.0317975	+	0.302533i
$366$	16.1553	−	11.3418i	0.844451	−	0.592846i
$367$	20.0262	+	11.5621i	1.04536	+	0.603537i	0.921346	−	0.388743i	$-0.127091\pi$
$367$	20.0262	+	11.5621i	1.04536	+	0.603537i	0.124011	+	0.992281i	$0.460424\pi$
$368$	−3.15414	−	2.29162i	−0.164421	−	0.119459i
$369$	−9.55260	−	5.93639i	−0.497289	−	0.309036i
$370$	1.37778	+	0.447667i	0.0716272	+	0.0232731i
$371$	−13.7058			−0.711568
$372$	−5.28645	−	8.06557i	−0.274089	−	0.418181i
$373$	−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
$375$	1.04067	−	1.38456i	0.0537398	−	0.0714985i
$376$	−2.16068	−	1.56983i	−0.111429	−	0.0809577i
$377$	5.76415	+	3.32794i	0.296869	+	0.171397i
$378$	8.81650	+	8.75145i	0.453472	+	0.450126i
$379$	−1.98672	+	18.9024i	−0.102051	+	0.970949i	0.816954	+	0.576703i	$0.195661\pi$
$379$	−1.98672	+	18.9024i	−0.102051	+	0.970949i	−0.919005	+	0.394246i	$0.871006\pi$
$380$	−0.0595432	−	0.0819541i	−0.00305450	−	0.00420416i
$381$	−4.53069	−	23.1558i	−0.232114	−	1.18631i
$382$	5.12549	+	5.69243i	0.262243	+	0.291250i
$383$	−12.8005	+	5.69917i	−0.654077	+	0.291214i	−0.706819	−	0.707394i	$-0.749871\pi$
$383$	−12.8005	+	5.69917i	−0.654077	+	0.291214i	0.0527421	+	0.998608i	$0.483204\pi$
$384$	1.65574	−	0.508447i	0.0844942	−	0.0259466i
$385$	−0.601400	+	2.82936i	−0.0306502	+	0.144198i
$386$	−8.88758	+	19.9618i	−0.452366	+	1.01603i
$387$	−6.98941	+	3.73850i	−0.355292	+	0.190039i
$388$	1.09568	+	3.37216i	0.0556249	+	0.171196i
$389$	24.7962	+	11.0400i	1.25722	+	0.559750i	0.923744	−	0.383010i	$-0.125112\pi$
$389$	24.7962	+	11.0400i	1.25722	+	0.559750i	0.333474	+	0.942759i	$0.391779\pi$
$390$	2.03169	+	0.246915i	0.102879	+	0.0125030i
$391$	−14.7761	+	3.14076i	−0.747261	+	0.158835i
$392$	−0.522453	−	1.17345i	−0.0263879	−	0.0592681i
$393$	1.63882	+	1.52445i	0.0826678	+	0.0768984i
$394$	−14.9669	+	1.57309i	−0.754022	+	0.0792509i
$395$	−8.40353	+	6.10552i	−0.422828	+	0.307202i
$396$	−0.262138	−	3.62029i	−0.0131729	−	0.181926i
$397$	17.8009	+	30.8321i	0.893401	+	1.54742i	0.835771	+	0.549078i	$0.185021\pi$
$397$	17.8009	+	30.8321i	0.893401	+	1.54742i	0.0576304	+	0.998338i	$0.481646\pi$
$398$	−9.87518	+	17.1043i	−0.494998	+	0.857362i
$399$	−0.215599	+	0.359822i	−0.0107935	+	0.0180137i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	6.80493	−	20.9434i	0.339822	−	1.04586i	−0.624476	−	0.781044i	$-0.714687\pi$
$401$	6.80493	−	20.9434i	0.339822	−	1.04586i	0.964298	−	0.264820i	$-0.0853126\pi$
$402$	−13.8159	+	1.22592i	−0.689072	+	0.0611431i
$403$	0.478567	+	6.56161i	0.0238391	+	0.326857i
$404$			7.09994i			0.353235i
$405$	8.99286	−	0.358501i	0.446859	−	0.0178141i
$406$	10.0075	+	9.01077i	0.496662	+	0.447197i
$407$	−1.03026	+	1.41804i	−0.0510683	+	0.0702895i
$408$	2.82872	−	6.08581i	0.140042	−	0.301292i
$409$	−5.53408	+	3.19510i	−0.273643	+	0.157988i	−0.630542	−	0.776155i	$-0.717167\pi$
$409$	−5.53408	+	3.19510i	−0.273643	+	0.157988i	0.356899	+	0.934143i	$0.383834\pi$
$410$	−3.72843	−	0.391874i	−0.184134	−	0.0193533i
$411$	10.8263	+	12.4232i	0.534022	+	0.612793i
$412$	0.866403	+	8.24328i	0.0426846	+	0.406117i
$413$	17.1587	−	15.4497i	0.844322	−	0.760231i
$414$	6.56435	+	9.68042i	0.322620	+	0.475767i
$415$	−1.46391	−	6.88714i	−0.0718603	−	0.338076i
$416$	−1.15581	−	0.245675i	−0.0566682	−	0.0120452i
$417$	24.0266	+	8.23985i	1.17659	+	0.403507i
$418$	0.116567	−	0.0378750i	0.00570150	−	0.00185253i
$419$	20.0618	−	6.51848i	0.980084	−	0.318449i	0.225204	−	0.974312i	$-0.427695\pi$
$419$	20.0618	−	6.51848i	0.980084	−	0.318449i	0.754880	+	0.655863i	$0.227695\pi$
$420$	3.91690	+	1.34329i	0.191125	+	0.0655458i
$421$	5.89085	+	1.25214i	0.287102	+	0.0610255i	0.349212	−	0.937044i	$-0.386449\pi$
$421$	5.89085	+	1.25214i	0.287102	+	0.0610255i	−0.0621093	+	0.998069i	$0.519783\pi$
$422$	0.422151	+	1.98606i	0.0205500	+	0.0966801i
$423$	4.49678	+	6.63138i	0.218641	+	0.322429i
$424$	4.26039	−	3.83608i	0.206903	−	0.186296i
$425$	0.405011	+	3.85342i	0.0196459	+	0.186919i
$426$	12.2347	+	14.0394i	0.592772	+	0.680209i
$427$	−27.0961	−	2.84792i	−1.31127	−	0.137820i
$428$	13.7539	−	7.94080i	0.664818	−	0.383833i
$429$	−1.04375	+	2.24556i	−0.0503927	+	0.108417i
$430$	−1.55301	+	2.13754i	−0.0748929	+	0.103081i
$431$	−20.2822	−	18.2622i	−0.976958	−	0.879657i	0.0157892	−	0.999875i	$-0.494974\pi$
$431$	−20.2822	−	18.2622i	−0.976958	−	0.879657i	−0.992747	+	0.120218i	$0.961641\pi$
$432$	−5.19000	−	0.252729i	−0.249704	−	0.0121594i
$433$			37.0346i			1.77977i	0.456184	+	0.889886i	$0.349216\pi$
$433$			37.0346i			1.77977i	−0.456184	+	0.889886i	$0.650784\pi$
$434$	−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
$438$	−5.17381	+	8.63480i	−0.247214	+	0.412587i
$439$	4.78973	−	8.29605i	0.228601	−	0.395949i	−0.728793	−	0.684735i	$-0.759918\pi$
$439$	4.78973	−	8.29605i	0.228601	−	0.395949i	0.957394	+	0.288786i	$0.0932515\pi$
$440$	−0.604961	−	1.04782i	−0.0288404	−	0.0499530i
$441$	0.278296	+	3.84344i	0.0132522	+	0.183021i
$442$	−3.70400	+	2.69112i	−0.176181	+	0.128003i
$443$	4.45924	−	0.468685i	0.211865	−	0.0222679i	0.00199861	−	0.999998i	$-0.499364\pi$
$443$	4.45924	−	0.468685i	0.211865	−	0.0222679i	0.209866	+	0.977730i	$0.432697\pi$
$444$	1.83721	+	1.70900i	0.0871904	+	0.0811053i
$445$	−2.32841	−	5.22970i	−0.110377	−	0.247912i
$446$	−8.40777	+	1.78713i	−0.398120	+	0.0846229i
$447$	−3.24056	−	0.393832i	−0.153273	−	0.0186276i
$448$	−2.18402	−	0.972390i	−0.103185	−	0.0459411i
$449$	−7.55873	−	23.2634i	−0.356718	−	1.09787i	−0.955006	−	0.296585i	$-0.904152\pi$
$449$	−7.55873	−	23.2634i	−0.356718	−	1.09787i	0.598288	−	0.801281i	$-0.295848\pi$
$450$	2.64536	−	1.41495i	0.124703	−	0.0667014i
$451$	1.84494	−	4.14381i	0.0868749	−	0.195124i
$452$	−2.54753	+	11.9852i	−0.119826	+	0.563736i
$453$	−15.4894	+	4.75649i	−0.727755	+	0.223480i
$454$	−20.2573	+	9.01915i	−0.950724	+	0.423290i
$455$	−1.89025	−	2.09934i	−0.0886163	−	0.0984184i
$456$	−0.0336916	−	0.172193i	−0.00157775	−	0.00806368i
$457$	9.71077	+	13.3657i	0.454251	+	0.625223i	0.973304	−	0.229519i	$-0.0737154\pi$
$457$	9.71077	+	13.3657i	0.454251	+	0.625223i	−0.519053	+	0.854742i	$0.673715\pi$
$458$	−1.16300	+	11.0652i	−0.0543432	+	0.517041i
$459$	−14.1836	+	14.2890i	−0.662032	+	0.666953i
$460$	3.37640	+	1.94937i	0.157426	+	0.0908898i
$461$	−6.00865	−	4.36554i	−0.279851	−	0.203323i	0.439002	−	0.898486i	$-0.355332\pi$
$461$	−6.00865	−	4.36554i	−0.279851	−	0.203323i	−0.718852	+	0.695163i	$0.755332\pi$
$462$	−3.01020	+	4.00495i	−0.140047	+	0.186327i
$463$	13.0676	+	4.24593i	0.607304	+	0.197325i	0.596495	−	0.802616i	$-0.296559\pi$
$463$	13.0676	+	4.24593i	0.607304	+	0.197325i	0.0108089	+	0.999942i	$0.496559\pi$
$464$	−5.63279			−0.261496
$465$	6.10057	+	7.46881i	0.282907	+	0.346358i
$466$	−3.84616			−0.178170
$467$	31.9309	+	10.3750i	1.47758	+	0.480096i	0.933390	−	0.358863i	$-0.116835\pi$
$467$	31.9309	+	10.3750i	1.47758	+	0.480096i	0.544194	+	0.838959i	$0.316835\pi$
$468$	3.01086	+	1.87108i	0.139177	+	0.0864906i
$469$	15.4883	+	11.2529i	0.715185	+	0.519612i
$470$	2.31294	+	1.33538i	0.106688	+	0.0615963i
$471$	14.7874	−	10.3815i	0.681367	−	0.478353i
$472$	−1.00953	+	9.60499i	−0.0464672	+	0.442106i
$473$	−1.87902	−	2.58625i	−0.0863976	−	0.118916i
$474$	−17.6566	+	3.45472i	−0.810994	+	0.158680i
$475$	0.0677835	+	0.0752812i	0.00311012	+	0.00345414i
$476$	−8.46233	+	3.76767i	−0.387870	+	0.172691i
$477$	−15.9305	+	6.48212i	−0.729406	+	0.296796i
$478$	1.23846	−	5.82649i	0.0566458	−	0.266498i
$479$	0.359545	−	0.807552i	0.0164280	−	0.0368980i	−0.905145	−	0.425103i	$-0.860238\pi$
$479$	0.359545	−	0.807552i	0.0164280	−	0.0368980i	0.921573	+	0.388205i	$0.126905\pi$
$480$	−1.59352	+	0.678734i	−0.0727341	+	0.0309798i
$481$	−0.528976	−	1.62802i	−0.0241192	−	0.0742314i
$482$	19.0145	+	8.46581i	0.866088	+	0.385607i
$483$	1.94768	−	16.0261i	0.0886225	−	0.729213i
$484$	−9.32770	+	1.98266i	−0.423986	+	0.0901211i
$485$	−1.44217	−	3.23916i	−0.0654854	−	0.147083i
$486$	14.3866	+	6.00222i	0.652588	+	0.272266i
$487$	−23.4787	+	2.46771i	−1.06392	+	0.111823i	−0.620280	−	0.784381i	$-0.712981\pi$
$487$	−23.4787	+	2.46771i	−1.06392	+	0.111823i	−0.443643	+	0.896203i	$0.646314\pi$
$488$	9.21984	−	6.69861i	0.417363	−	0.303232i
$489$	28.5094	+	0.462433i	1.28924	+	0.0209120i
$490$	0.642250	+	1.11241i	0.0290139	+	0.0502535i
$491$	−18.1512	+	31.4388i	−0.819151	+	1.41881i	0.0871575	+	0.996195i	$0.472222\pi$
$491$	−18.1512	+	31.4388i	−0.819151	+	1.41881i	−0.906309	+	0.422617i	$0.861112\pi$
$492$	−5.57006	−	3.33748i	−0.251118	−	0.150465i
$493$	−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
$498$	2.72869	−	11.8862i	0.122276	−	0.532633i
$499$	−2.45437	−	2.20993i	−0.109873	−	0.0989299i	0.612363	−	0.790576i	$-0.290219\pi$
$499$	−2.45437	−	2.20993i	−0.109873	−	0.0989299i	−0.722236	+	0.691647i	$0.756886\pi$
$500$	0.587785	−	0.809017i	0.0262866	−	0.0361803i
$501$	−4.26766	−	1.98363i	−0.190665	−	0.0886221i
$502$	−2.69163	+	1.55401i	−0.120133	+	0.0693590i
$503$	−35.8585	−	3.76888i	−1.59885	−	0.168046i	−0.737246	−	0.675624i	$-0.763874\pi$
$503$	−35.8585	−	3.76888i	−1.59885	−	0.168046i	−0.861606	+	0.507578i	$0.830541\pi$
$504$	5.17149	+	4.96943i	0.230356	+	0.221356i
$505$	−0.742146	−	7.06105i	−0.0330251	−	0.314213i
$506$	−3.50554	+	3.15640i	−0.155840	+	0.140319i
$507$	9.76553	+	17.5663i	0.433703	+	0.780148i
$508$	−2.83227	−	13.3248i	−0.125662	−	0.591192i
$509$	−15.0848	−	3.20636i	−0.668620	−	0.142120i	−0.138919	−	0.990304i	$-0.544363\pi$
$509$	−15.0848	−	3.20636i	−0.668620	−	0.142120i	−0.529701	+	0.848184i	$0.677696\pi$
$510$	−2.17708	+	6.34815i	−0.0964029	+	0.281101i
$511$	13.2141	−	4.29352i	0.584558	−	0.189934i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−0.0804174	+	0.520196i	−0.00355052	+	0.0229672i
$514$	−27.9012	−	5.93058i	−1.23067	−	0.261586i
$515$	−1.72331	−	8.10756i	−0.0759383	−	0.357262i
$516$	−3.99980	+	2.22358i	−0.176081	+	0.0978879i
$517$	−2.40140	+	2.16223i	−0.105613	+	0.0950947i
$518$	−0.362021	−	3.44440i	−0.0159063	−	0.151338i
$519$	3.74513	−	3.26372i	0.164393	−	0.143261i
$520$	1.17516	+	0.123514i	0.0515340	+	0.00541644i
$521$	7.30055	−	4.21497i	0.319843	−	0.184661i	−0.331480	−	0.943462i	$-0.607548\pi$
$521$	7.30055	−	4.21497i	0.319843	−	0.184661i	0.651323	+	0.758801i	$0.274214\pi$
$522$	15.8935	+	5.74037i	0.695639	+	0.251249i
$523$	−12.7735	+	17.5813i	−0.558548	+	0.768775i	−0.991141	−	0.132814i	$-0.957599\pi$
$523$	−12.7735	+	17.5813i	−0.558548	+	0.768775i	0.432593	+	0.901589i	$0.357599\pi$
$524$	0.960326	+	0.864681i	0.0419520	+	0.0377738i
$525$	−4.03585	−	0.926504i	−0.176139	−	0.0404359i
$526$			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
$531$	12.6369	−	26.0727i	0.548395	−	1.13146i
$532$	−0.121091	+	0.209735i	−0.00524994	+	0.00909317i
$533$	2.21495	+	3.83640i	0.0959400	+	0.166173i
$534$	0.160809	−	9.91403i	0.00695889	−	0.429022i
$535$	−12.8485	+	9.33497i	−0.555488	+	0.403586i
$536$	−7.96406	+	0.837056i	−0.343995	+	0.0361553i
$537$	−9.72524	+	10.4549i	−0.419675	+	0.451161i
$538$	3.26469	+	7.33262i	0.140751	+	0.316132i
$539$	−1.52018	+	0.323125i	−0.0654789	+	0.0139180i
$540$	5.18799	−	0.291159i	0.223255	−	0.0125295i
$541$	−17.4557	−	7.77177i	−0.750478	−	0.334135i	−0.00439797	−	0.999990i	$-0.501400\pi$
$541$	−17.4557	−	7.77177i	−0.750478	−	0.334135i	−0.746080	+	0.665856i	$0.768067\pi$
$542$	−1.98511	−	6.10953i	−0.0852677	−	0.262427i
$543$	4.89675	+	11.4966i	0.210140	+	0.493364i
$544$	1.57596	−	3.53967i	0.0675688	−	0.151762i
$545$	1.07672	−	5.06556i	0.0461216	−	0.216985i
$546$	−1.43633	−	4.67736i	−0.0614692	−	0.200173i
$547$	−39.7825	+	17.7123i	−1.70098	+	0.757324i	−0.701998	+	0.712179i	$0.747708\pi$
$547$	−39.7825	+	17.7123i	−1.70098	+	0.757324i	−0.998980	+	0.0451451i	$0.985625\pi$
$548$	6.36607	+	7.07024i	0.271945	+	0.302026i
$549$	−32.8413	+	9.50489i	−1.40163	+	0.405659i
$550$	0.711174	+	0.978847i	0.0303246	+	0.0417382i
$551$	−0.0596446	+	0.567481i	−0.00254095	+	0.0241755i
$552$	3.88008	+	5.52679i	0.165147	+	0.235236i
$553$	21.5061	+	12.4166i	0.914533	+	0.528006i
$554$	−3.07492	−	2.23406i	−0.130641	−	0.0949162i
$555$	−2.00579	−	1.50759i	−0.0851410	−	0.0639937i
$556$	13.9471	+	4.53168i	0.591488	+	0.192186i
$557$	17.2905			0.732622			0.366311	−	0.930493i	$-0.380621\pi$
$557$	17.2905			0.732622			0.366311	+	0.930493i	$0.380621\pi$
$558$	4.12934	+	16.1848i	0.174809	+	0.685158i
$559$	3.12203			0.132048
$560$	2.27370	+	0.738770i	0.0960814	+	0.0312187i
$561$	−6.49086	−	4.87867i	−0.274044	−	0.205977i
$562$	−1.39732	−	1.01522i	−0.0589426	−	0.0428243i
$563$	17.2892	+	9.98194i	0.728654	+	0.420689i	0.817930	−	0.575318i	$-0.195122\pi$
$563$	17.2892	+	9.98194i	0.728654	+	0.420689i	−0.0892754	+	0.996007i	$0.528455\pi$
$564$	2.65797	+	3.78602i	0.111921	+	0.159420i
$565$	1.28078	−	12.1858i	0.0538829	−	0.512662i
$566$	7.69052	+	10.5851i	0.323257	+	0.444925i
$567$	−9.52754	−	19.2920i	−0.400119	−	0.810188i
$568$	7.19423	+	7.99000i	0.301863	+	0.335253i
$569$	28.9104	−	12.8718i	1.21199	−	0.539612i	0.301627	−	0.953426i	$-0.402470\pi$
$569$	28.9104	−	12.8718i	1.21199	−	0.539612i	0.910361	+	0.413814i	$0.135804\pi$
$570$	0.0515061	+	0.167728i	0.00215735	+	0.00702536i
$571$	0.981866	−	4.61931i	0.0410898	−	0.193312i	−0.952815	−	0.303550i	$-0.901828\pi$
$571$	0.981866	−	4.61931i	0.0410898	−	0.193312i	0.993905	+	0.110238i	$0.0351613\pi$
$572$	−0.581503	+	1.30608i	−0.0243139	+	0.0546098i
$573$	−5.19905	−	12.2063i	−0.217193	−	0.509925i
$574$	2.76963	+	8.52404i	0.115602	+	0.355787i
$575$	−3.56167	−	1.58576i	−0.148532	−	0.0661307i
$576$	−2.99842	−	0.0972966i	−0.124934	−	0.00405402i
$577$	6.21112	−	1.32021i	0.258572	−	0.0549612i	−0.0768015	−	0.997046i	$-0.524471\pi$
$577$	6.21112	−	1.32021i	0.258572	−	0.0549612i	0.335374	+	0.942085i	$0.391137\pi$
$578$	0.808222	+	1.81530i	0.0336176	+	0.0755064i
$579$	25.7774	−	27.7114i	1.07127	−	1.15164i
$580$	5.60193	−	0.588787i	0.232608	−	0.0244480i
$581$	−13.6182	+	9.89419i	−0.564977	+	0.410480i
$582$	0.0996016	−	6.14053i	0.00412862	−	0.254533i
$583$	−3.46820	−	6.00709i	−0.143638	−	0.248788i
$584$	−2.90586	+	5.03309i	−0.120245	+	0.208271i
$585$	−3.18995	−	1.54611i	−0.131888	−	0.0639236i
$586$	−9.60317	+	10.6654i	−0.396703	+	0.440584i
$587$	−11.4050	+	35.1008i	−0.470733	+	1.44877i	0.380894	+	0.924619i	$0.375616\pi$
$587$	−11.4050	+	35.1008i	−0.470733	+	1.44877i	−0.851627	+	0.524148i	$0.824384\pi$
$588$	0.196641	+	2.21611i	0.00810935	+	0.0913909i
$589$	−0.497205	+	0.266280i	−0.0204870	+	0.0109719i
$590$		−	9.65790i		−	0.397609i
$591$	25.4054	+	5.83228i	1.04504	+	0.239908i
$592$	1.07658	+	0.969356i	0.0442471	+	0.0398403i
$593$	17.7308	−	24.4044i	0.728119	−	1.00217i	−0.271096	−	0.962552i	$-0.587386\pi$
$593$	17.7308	−	24.4044i	0.728119	−	1.00217i	0.999215	−	0.0396171i	$-0.0126138\pi$
$594$	−1.60468	+	6.07870i	−0.0658408	+	0.249412i
$595$	8.02214	−	4.63158i	0.328876	−	0.189876i
$596$	−1.87438	−	0.197006i	−0.0767777	−	0.00806966i
$597$	25.7899	−	22.4747i	1.05551	−	0.919829i
$598$	−0.481548	−	4.58162i	−0.0196920	−	0.187357i
$599$	16.8780	−	15.1970i	0.689616	−	0.620933i	−0.247936	−	0.968776i	$-0.579752\pi$
$599$	16.8780	−	15.1970i	0.689616	−	0.620933i	0.937553	+	0.347843i	$0.113086\pi$
$600$	1.51385	−	0.841584i	0.0618026	−	0.0343575i
$601$	0.472492	+	2.22290i	0.0192734	+	0.0906741i	0.986733	−	0.162351i	$-0.0519078\pi$
$601$	0.472492	+	2.22290i	0.0192734	+	0.0906741i	−0.967460	+	0.253025i	$0.918574\pi$
$602$	6.17857	+	1.31329i	0.251820	+	0.0535259i
$603$	23.3244	+	5.75431i	0.949845	+	0.234334i
$604$	−8.89709	+	2.89084i	−0.362017	+	0.117627i
$605$	9.06936	−	2.94681i	0.368722	−	0.119805i
$606$	3.98931	−	11.6324i	0.162054	−	0.472534i
$607$	−41.0463	−	8.72466i	−1.66602	−	0.354123i	−0.724029	−	0.689769i	$-0.757712\pi$
$607$	−41.0463	−	8.72466i	−1.66602	−	0.354123i	−0.941988	+	0.335647i	$0.891045\pi$
$608$	−0.0210616	−	0.0990872i	−0.000854162	−	0.00401852i
$609$	−11.3331	−	20.3860i	−0.459240	−	0.826084i
$610$	−8.46914	+	7.62565i	−0.342906	+	0.308754i
$611$	−0.329875	−	3.13855i	−0.0133453	−	0.126972i
$612$	−8.05401	+	8.38148i	−0.325564	+	0.338801i
$613$	2.40884	+	0.253180i	0.0972923	+	0.0102258i	0.153050	−	0.988219i	$-0.451091\pi$
$613$	2.40884	+	0.253180i	0.0972923	+	0.0102258i	−0.0557572	+	0.998444i	$0.517757\pi$
$614$	23.5222	−	13.5806i	0.949280	−	0.548067i
$615$	5.88841	+	2.73697i	0.237444	+	0.110365i
$616$	−1.70021	+	2.34014i	−0.0685035	+	0.0942870i
$617$	−7.08510	−	6.37945i	−0.285235	−	0.256827i	0.514075	−	0.857745i	$-0.328135\pi$
$617$	−7.08510	−	6.37945i	−0.285235	−	0.256827i	−0.799311	+	0.600918i	$0.794802\pi$
$618$	3.21222	−	13.9924i	0.129215	−	0.562859i
$619$			14.0896i			0.566311i	0.959074	+	0.283155i	$0.0913812\pi$
$619$			14.0896i			0.566311i	−0.959074	+	0.283155i	$0.908619\pi$
$620$	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
$624$	1.75561	+	1.05193i	0.0702808	+	0.0421110i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.31252	+	7.46951i	0.172363	+	0.298542i
$627$	−0.212263	−	0.00344298i	−0.00847696	−	0.000137499i
$628$	8.43917	−	6.13142i	0.336760	−	0.244670i
$629$	5.58238	−	0.586732i	0.222584	−	0.0233945i
$630$	−5.66260	−	4.40164i	−0.225603	−	0.175366i
$631$	5.29306	+	11.8884i	0.210713	+	0.473270i	0.987722	−	0.156220i	$-0.0499308\pi$
$631$	5.29306	+	11.8884i	0.210713	+	0.473270i	−0.777009	+	0.629489i	$0.783264\pi$
$632$	−10.1603	+	2.15965i	−0.404157	+	0.0859062i
$633$	0.424283	−	3.49113i	0.0168637	−	0.138760i
$634$	−17.1968	−	7.65652i	−0.682973	−	0.304079i
$635$	4.20958	+	12.9558i	0.167052	+	0.514133i
$636$	−9.13556	+	3.89113i	−0.362248	+	0.154293i
$637$	0.617346	−	1.38658i	0.0244601	−	0.0549383i
$638$	−1.41697	+	6.66631i	−0.0560983	+	0.263922i
$639$	−12.1567	−	29.8762i	−0.480910	−	1.18189i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	19.2340	+	21.3615i	0.759696	+	0.843728i	0.991645	−	0.129000i	$-0.0411767\pi$
$641$	19.2340	+	21.3615i	0.759696	+	0.843728i	−0.231948	+	0.972728i	$0.574510\pi$
$642$	−26.9958	+	5.28205i	−1.06544	+	0.208466i
$643$	5.26128	+	7.24153i	0.207485	+	0.285578i	0.900059	−	0.435769i	$-0.143523\pi$
$643$	5.26128	+	7.24153i	0.207485	+	0.285578i	−0.692574	+	0.721347i	$0.743523\pi$
$644$	0.974284	−	9.26969i	0.0383922	−	0.365277i
$645$	3.74546	−	2.62950i	0.147477	−	0.103536i
$646$	−0.339920	−	0.196253i	−0.0133740	−	0.00772146i
$647$	−17.5864	−	12.7773i	−0.691394	−	0.502327i	0.185724	−	0.982602i	$-0.440537\pi$
$647$	−17.5864	−	12.7773i	−0.691394	−	0.502327i	−0.877118	+	0.480275i	$0.840537\pi$
$648$	8.36120	+	3.33022i	0.328459	+	0.130823i
$649$	11.1134	+	3.61096i	0.436238	+	0.141742i
$650$	−1.18163			−0.0463473
$651$	10.3799	−	20.5864i	0.406821	−	0.806844i
$652$	16.4621			0.644705
$653$	−39.0457	−	12.6867i	−1.52798	−	0.496469i	−0.579947	−	0.814654i	$-0.696927\pi$
$653$	−39.0457	−	12.6867i	−1.52798	−	0.496469i	−0.948029	+	0.318185i	$0.896927\pi$
$654$	5.38933	−	7.17028i	0.210739	−	0.280380i
$655$	−1.04545	−	0.759563i	−0.0408491	−	0.0296786i
$656$	−3.24670	−	1.87448i	−0.126762	−	0.0731863i
$657$	13.3284	−	11.2400i	0.519990	−	0.438515i
$658$	0.667414	−	6.35002i	0.0260185	−	0.247549i
$659$	−3.20807	−	4.41553i	−0.124969	−	0.172005i	0.741948	−	0.670457i	$-0.233902\pi$
$659$	−3.20807	−	4.41553i	−0.124969	−	0.172005i	−0.866917	+	0.498452i	$0.833902\pi$
$660$	0.402407	+	2.05665i	0.0156637	+	0.0800549i
$661$	−20.5855	−	22.8626i	−0.800685	−	0.889250i	0.195118	−	0.980780i	$-0.437491\pi$
$661$	−20.5855	−	22.8626i	−0.800685	−	0.889250i	−0.995802	+	0.0915295i	$0.970824\pi$
$662$	−28.9277	+	12.8794i	−1.12431	+	0.500573i
$663$	7.58065	−	2.32787i	0.294408	−	0.0904071i
$664$	1.46391	−	6.88714i	0.0568106	−	0.267273i
$665$	0.0985040	−	0.221244i	0.00381982	−	0.00857946i
$666$	−2.04981	−	3.83228i	−0.0794285	−	0.148498i
$667$	−6.78625	−	20.8859i	−0.262765	−	0.808706i
$668$	−2.48218	−	1.10514i	−0.0960386	−	0.0427591i
$669$	14.7793	+	1.79615i	0.571400	+	0.0694433i
$670$	7.83293	−	1.66494i	0.302613	−	0.0643223i
$671$	−5.60837	−	12.5966i	−0.216509	−	0.486286i
$672$	3.03190	+	2.82030i	0.116958	+	0.108795i
$673$	−26.1640	+	2.74995i	−1.00855	+	0.106003i	−0.594369	−	0.804193i	$-0.702598\pi$
$673$	−26.1640	+	2.74995i	−1.00855	+	0.106003i	−0.414179	+	0.910195i	$0.635931\pi$
$674$	3.91270	−	2.84275i	0.150712	−	0.109498i
$675$	−5.12913	+	0.831856i	−0.197420	+	0.0320182i
$676$	5.80188	+	10.0491i	0.223149	+	0.386506i
$677$	−3.20458	+	5.55050i	−0.123162	+	0.213323i	−0.921013	−	0.389532i	$-0.872637\pi$
$677$	−3.20458	+	5.55050i	−0.123162	+	0.213323i	0.797851	+	0.602855i	$0.205970\pi$
$678$	10.9081	−	18.2049i	0.418921	−	0.699155i
$679$	−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	$0.926187\pi$
$684$	−0.0415520	+	0.301049i	−0.00158878	+	0.0115109i
$685$	−7.07024	−	6.36607i	−0.270140	−	0.243235i
$686$	11.6416	−	16.0233i	0.444478	−	0.611771i
$687$	8.12271	−	17.4755i	0.309901	−	0.666731i
$688$	−2.28816	+	1.32107i	−0.0872354	+	0.0503654i
$689$	6.73708	+	0.708096i	0.256662	+	0.0269763i
$690$	−4.43653	−	5.09094i	−0.168896	−	0.193809i
$691$	2.98513	+	28.4016i	0.113560	+	1.08045i	0.891784	+	0.452461i	$0.149454\pi$
$691$	2.98513	+	28.4016i	0.113560	+	1.08045i	−0.778224	+	0.627986i	$0.783879\pi$
$692$	2.13141	−	1.91913i	0.0810239	−	0.0729543i
$693$	7.18216	−	4.87027i	0.272828	−	0.185006i
$694$	4.00174	+	18.8267i	0.151904	+	0.714653i
$695$	−14.3444	−	3.04899i	−0.544113	−	0.115655i
$696$	9.22866	+	3.16495i	0.349811	+	0.119967i
$697$	−13.8150	+	4.48876i	−0.523280	+	0.170024i
$698$	−9.27733	+	3.01439i	−0.351152	+	0.114096i
$699$	6.30148	+	2.16108i	0.238344	+	0.0817394i
$700$	−2.33847	−	0.497057i	−0.0883858	−	0.0187870i
$701$	9.39731	+	44.2109i	0.354931	+	1.66982i	0.687071	+	0.726591i	$0.258896\pi$
$701$	9.39731	+	44.2109i	0.354931	+	1.66982i	−0.332139	+	0.943230i	$0.607770\pi$
$702$	−3.88162	−	4.75728i	−0.146502	−	0.179552i
$703$	0.109058	−	0.0981967i	0.00411322	−	0.00370356i
$704$	−0.126471	−	1.20329i	−0.00476657	−	0.0453508i
$705$	−3.03916	−	3.48744i	−0.114461	−	0.131345i
$706$	−26.1961	−	2.75332i	−0.985904	−	0.103623i
$707$	−14.6998	+	8.48696i	−0.552844	+	0.319185i
$708$	7.05083	−	15.1694i	0.264986	−	0.570101i
$709$	8.43616	−	11.6114i	0.316826	−	0.436074i	−0.620668	−	0.784073i	$-0.713139\pi$
$709$	8.43616	−	11.6114i	0.316826	−	0.436074i	0.937495	+	0.347999i	$0.113139\pi$
$710$	−7.99000	−	7.19423i	−0.299859	−	0.269995i
$711$	30.8694	+	4.26072i	1.15769	+	0.159789i
$712$		−	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
$717$	−5.30285	+	8.85015i	−0.198039	+	0.330515i
$718$	16.1261	−	27.9312i	0.601820	−	1.04238i
$719$	−26.4095	−	45.7426i	−0.984909	−	1.70591i	−0.642339	−	0.766421i	$-0.722036\pi$
$719$	−26.4095	−	45.7426i	−0.984909	−	1.70591i	−0.342570	−	0.939492i	$-0.611297\pi$
$720$	2.99217	−	0.216657i	0.111511	−	0.00807432i
$721$	−16.0314	+	11.6475i	−0.597039	+	0.433774i
$722$	18.8857	−	1.98497i	0.702853	−	0.0738729i
$723$	−26.3963	−	24.5541i	−0.981688	−	0.913176i
$724$	2.93442	+	6.59081i	0.109057	+	0.244946i
$725$	−5.50970	+	1.17112i	−0.204625	+	0.0434944i
$726$	16.3963	+	1.99268i	0.608526	+	0.0739552i
$727$	11.9850	+	5.33605i	0.444498	+	0.197903i	0.616765	−	0.787147i	$-0.288443\pi$
$727$	11.9850	+	5.33605i	0.444498	+	0.197903i	−0.172268	+	0.985050i	$0.555109\pi$
$728$	−0.872953	−	2.68667i	−0.0323538	−	0.0995747i
$729$	−20.1982	−	17.9174i	−0.748080	−	0.663609i
$730$	2.36384	−	5.30927i	0.0874895	−	0.196505i
$731$	−2.12847	+	10.0137i	−0.0787243	+	0.370369i
$732$	−18.8694	+	5.79444i	−0.697434	+	0.214169i
$733$	−35.3453	+	15.7367i	−1.30551	+	0.581249i	−0.937309	−	0.348499i	$-0.886692\pi$
$733$	−35.3453	+	15.7367i	−1.30551	+	0.581249i	−0.368197	+	0.929748i	$0.620025\pi$
$734$	−15.4731	−	17.1846i	−0.571124	−	0.634297i
$735$	−0.427211	−	2.18342i	−0.0157579	−	0.0805365i
$736$	2.29162	+	3.15414i	0.0844702	+	0.116263i
$737$	−1.01277	+	9.63589i	−0.0373060	+	0.354942i
$738$	7.25062	+	8.59776i	0.266899	+	0.316488i
$739$	27.8291	+	16.0671i	1.02371	+	0.591039i	0.915176	−	0.403054i	$-0.132051\pi$
$739$	27.8291	+	16.0671i	1.02371	+	0.591039i	0.108534	+	0.994093i	$0.465385\pi$
$740$	−1.17201	−	0.851513i	−0.0430838	−	0.0313022i
$741$	0.124568	−	0.165732i	0.00457611	−	0.00608833i
$742$	13.0350	+	4.23532i	0.478529	+	0.155483i
$743$	2.39114			0.0877225			0.0438613	−	0.999038i	$-0.486034\pi$
$743$	2.39114			0.0877225			0.0438613	+	0.999038i	$0.486034\pi$
$744$	2.53531	+	9.30442i	0.0929490	+	0.341117i
$745$	1.88471			0.0690503
$746$	9.34591	+	3.03667i	0.342178	+	0.111180i
$747$	−11.1492	+	17.9409i	−0.407929	+	0.656423i
$748$	−3.79269	−	2.75555i	−0.138674	−	0.100753i
$749$	32.8815	+	18.9842i	1.20146	+	0.693666i
$750$	−1.41759	+	0.995214i	−0.0517629	+	0.0363401i
$751$	4.20594	−	40.0168i	0.153477	−	1.46023i	−0.598541	−	0.801092i	$-0.704253\pi$
$751$	4.20594	−	40.0168i	0.153477	−	1.46023i	0.752018	−	0.659143i	$-0.229081\pi$
$752$	1.56983	+	2.16068i	0.0572457	+	0.0787920i
$753$	5.28308	−	1.03370i	0.192526	−	0.0376700i
$754$	−4.45365	−	4.94628i	−0.162192	−	0.180133i
$755$	8.54617	−	3.80500i	0.311027	−	0.138478i
$756$	−5.68065	−	11.0476i	−0.206603	−	0.401796i
$757$	1.68390	−	7.92213i	0.0612024	−	0.287935i	−0.936894	−	0.349615i	$-0.886313\pi$
$757$	1.68390	−	7.92213i	0.0612024	−	0.287935i	0.998096	+	0.0616801i	$0.0196459\pi$
$758$	7.73063	−	17.3633i	0.280789	−	0.630663i
$759$	7.51692	−	3.20170i	0.272847	−	0.116214i
$760$	0.0313037	+	0.0963429i	0.00113550	+	0.00349472i
$761$	−19.8233	−	8.82588i	−0.718593	−	0.319938i	0.0146617	−	0.999893i	$-0.495333\pi$
$761$	−19.8233	−	8.82588i	−0.718593	−	0.319938i	−0.733254	+	0.679954i	$0.762000\pi$
$762$	−2.84658	+	23.4225i	−0.103121	+	0.848508i
$763$	−12.1103	+	2.57412i	−0.438422	+	0.0931895i
$764$	−3.11557	−	6.99769i	−0.112717	−	0.253168i
$765$	7.13378	−	9.17744i	0.257922	−	0.331811i
$766$	13.9352	−	1.46465i	0.503498	−	0.0529198i
$767$	−9.23255	+	6.70784i	−0.333368	+	0.242206i
$768$	−1.73182	−	0.0280908i	−0.0624918	−	0.00101364i
$769$	−0.776312	−	1.34461i	−0.0279945	−	0.0484879i	0.851689	−	0.524048i	$-0.175579\pi$
$769$	−0.776312	−	1.34461i	−0.0279945	−	0.0484879i	−0.879683	+	0.475560i	$0.842245\pi$
$770$	1.44629	−	2.50504i	0.0521206	−	0.0902755i
$771$	42.3805	+	25.3936i	1.52630	+	0.914529i
$772$	14.6211	−	16.2384i	0.526226	−	0.584434i
$773$	−14.1794	+	43.6399i	−0.509999	+	1.56962i	0.282201	+	0.959355i	$0.408935\pi$
$773$	−14.1794	+	43.6399i	−0.509999	+	1.56962i	−0.792200	+	0.610261i	$0.791065\pi$
$774$	7.80258	−	1.39568i	0.280458	−	0.0501665i
$775$	−4.01667	−	3.85569i	−0.144283	−	0.138501i
$776$		−	3.54570i		−	0.127283i
$777$	−1.34221	+	5.84666i	−0.0481514	+	0.209748i
$778$	−20.1711	−	18.1621i	−0.723168	−	0.651143i
$779$	−0.223226	+	0.307244i	−0.00799788	+	0.0110081i
$780$	−1.85595	−	0.862658i	−0.0664538	−	0.0308881i
$781$	11.2658	−	6.50430i	0.403121	−	0.232742i
$782$	15.0235	+	1.57903i	0.537239	+	0.0564661i
$783$	−22.8142	−	18.3351i	−0.815313	−	0.655244i
$784$	0.134267	+	1.27746i	0.00479524	+	0.0456237i
$785$	−7.75204	+	6.97996i	−0.276682	+	0.249126i
$786$	−1.08753	−	1.95626i	−0.0387910	−	0.0697776i
$787$	−1.04614	−	4.92170i	−0.0372909	−	0.175440i	0.955561	−	0.294794i	$-0.0952510\pi$
$787$	−1.04614	−	4.92170i	−0.0372909	−	0.175440i	−0.992852	+	0.119354i	$0.961918\pi$
$788$	14.7205	+	3.12894i	0.524396	+	0.111464i
$789$	9.25962	−	27.0001i	0.329651	−	0.961230i
$790$	9.87894	−	3.20986i	0.351477	−	0.114202i
$791$	−27.8595	+	9.05212i	−0.990572	+	0.321856i
$792$	−0.869422	+	3.52410i	−0.0308936	+	0.125224i
$793$	13.1720	+	2.79979i	0.467751	+	0.0994236i
$794$	−7.40203	−	34.8238i	−0.262688	−	1.23585i
$795$	8.67878	−	4.82474i	0.307805	−	0.171116i
$796$	14.6774	−	13.2156i	0.520226	−	0.468413i
$797$	−0.179628	−	1.70905i	−0.00636276	−	0.0605376i	0.990880	−	0.134749i	$-0.0430228\pi$
$797$	−0.179628	−	1.70905i	−0.00636276	−	0.0605376i	−0.997243	+	0.0742112i	$0.976356\pi$
$798$	0.316238	−	0.275588i	0.0111947	−	0.00975570i
$799$	10.2915	+	1.08168i	0.364088	+	0.0382672i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−5.83395	+	16.1526i	−0.206132	+	0.570724i
$802$	−12.9437	+	17.8155i	−0.457059	+	0.629088i
$803$	5.22559	+	4.70514i	0.184407	+	0.166041i
$804$	13.5185	+	3.10342i	0.476760	+	0.109449i
$805$			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	$-0.622691\pi$
$809$	16.6357	−	18.4759i	0.584882	−	0.649577i	0.960854	+	0.277054i	$0.0893580\pi$
$810$	−8.66350	−	2.43799i	−0.304404	−	0.0856623i
$811$	14.4885	−	25.0949i	0.508761	−	0.881201i	−0.491187	−	0.871054i	$-0.663437\pi$
$811$	14.4885	−	25.0949i	0.508761	−	0.881201i	0.999949	−	0.0101465i	$-0.00322980\pi$
$812$	−6.73319	−	11.6622i	−0.236289	−	0.409264i
$813$	−0.180454	+	11.1251i	−0.00632879	+	0.390175i
$814$	1.41804	−	1.03026i	0.0497022	−	0.0361107i
$815$	−16.3719	+	1.72076i	−0.573483	+	0.0602755i
$816$	−4.57089	+	4.91383i	−0.160013	+	0.172018i
$817$	0.108864	+	0.244512i	0.00380865	+	0.00855438i
$818$	6.25057	−	1.32860i	0.218546	−	0.0464534i
$819$	−0.274857	+	8.47035i	−0.00960426	+	0.295978i
$820$	3.42485	+	1.52484i	0.119601	+	0.0532498i
$821$	5.88112	+	18.1002i	0.205252	+	0.631702i	0.999703	+	0.0243730i	$0.00775893\pi$
$821$	5.88112	+	18.1002i	0.205252	+	0.631702i	−0.794451	+	0.607329i	$0.792241\pi$
$822$	−6.45743	−	15.1607i	−0.225229	−	0.528790i
$823$	7.40845	−	16.6396i	0.258242	−	0.580021i	−0.737169	−	0.675708i	$-0.763838\pi$
$823$	7.40845	−	16.6396i	0.258242	−	0.580021i	0.995412	+	0.0956866i	$0.0305047\pi$
$824$	1.72331	−	8.10756i	0.0600345	−	0.282440i
$825$	−0.615181	−	2.00332i	−0.0214178	−	0.0697466i
$826$	−21.0931	+	9.39124i	−0.733922	+	0.326763i
$827$	7.02059	+	7.79715i	0.244130	+	0.271134i	0.852740	−	0.522336i	$-0.174939\pi$
$827$	7.02059	+	7.79715i	0.244130	+	0.271134i	−0.608610	+	0.793469i	$0.708273\pi$
$828$	−3.25166	−	11.2351i	−0.113003	−	0.390448i
$829$	26.4399	+	36.3914i	0.918296	+	1.26393i	0.964253	+	0.264983i	$0.0853663\pi$
$829$	26.4399	+	36.3914i	0.918296	+	1.26393i	−0.0459570	+	0.998943i	$0.514634\pi$
$830$	−0.735985	+	7.00243i	−0.0255464	+	0.243058i
$831$	3.78262	+	5.38798i	0.131218	+	0.186907i
$832$	1.02332	+	0.590815i	0.0354773	+	0.0204828i
$833$	4.02646	+	2.92540i	0.139509	+	0.101359i
$834$	−20.3044	−	15.2612i	−0.703083	−	0.528452i
$835$	2.58410	+	0.839626i	0.0894266	+	0.0290565i
$836$	−0.122566			−0.00423904
$837$	2.32848	−	28.8371i	0.0804840	−	0.996756i
$838$	−21.0943			−0.728689
$839$	−11.4351	−	3.71549i	−0.394783	−	0.128273i	0.104896	−	0.994483i	$-0.466549\pi$
$839$	−11.4351	−	3.71549i	−0.394783	−	0.128273i	−0.499680	+	0.866210i	$0.666549\pi$
$840$	−3.31009	−	2.48793i	−0.114209	−	0.0858418i
$841$	−2.20727	−	1.60367i	−0.0761127	−	0.0552991i
$842$	−5.21560	−	3.01123i	−0.179741	−	0.103774i
$843$	1.71892	+	2.44844i	0.0592028	+	0.0843286i
$844$	0.212238	−	2.01931i	0.00730554	−	0.0695075i
$845$	−6.82051	−	9.38763i	−0.234633	−	0.322944i
$846$	−2.22748	−	7.69640i	−0.0765824	−	0.264608i
$847$	−15.2549	−	16.9422i	−0.524163	−	0.582142i
$848$	−5.23729	+	2.33179i	−0.179849	+	0.0800740i
$849$	−6.65247	−	21.6636i	−0.228312	−	0.743492i
$850$	0.805585	−	3.78998i	0.0276313	−	0.129995i
$851$	−2.29726	+	5.15972i	−0.0787490	+	0.176873i
$852$	−7.29748	−	17.1329i	−0.250007	−	0.586965i
$853$	−3.57940	−	11.0163i	−0.122556	−	0.377189i	0.870892	−	0.491475i	$-0.163542\pi$
$853$	−3.57940	−	11.0163i	−0.122556	−	0.377189i	−0.993448	+	0.114286i	$0.963542\pi$
$854$	24.8899	+	11.0817i	0.851715	+	0.379208i
$855$	0.00985623	−	0.303743i	0.000337076	−	0.0103878i
$856$	−15.5345	+	3.30197i	−0.530960	+	0.112859i
$857$	18.3768	+	41.2750i	0.627740	+	1.40993i	0.894897	+	0.446274i	$0.147249\pi$
$857$	18.3768	+	41.2750i	0.627740	+	1.40993i	−0.267157	+	0.963653i	$0.586084\pi$
$858$	1.68658	−	1.81312i	0.0575789	−	0.0618988i
$859$	−33.6759	+	3.53948i	−1.14901	+	0.120766i	−0.659828	−	0.751417i	$-0.729371\pi$
$859$	−33.6759	+	3.53948i	−1.14901	+	0.120766i	−0.489180	+	0.872183i	$0.662704\pi$
$860$	2.13754	−	1.55301i	0.0728894	−	0.0529573i
$861$	0.251770	−	15.5218i	0.00858028	−	0.528982i
$862$	13.6462	+	23.6359i	0.464791	+	0.805041i
$863$	3.18409	−	5.51500i	0.108388	−	0.187733i	−0.806730	−	0.590921i	$-0.798765\pi$
$863$	3.18409	−	5.51500i	0.108388	−	0.187733i	0.915117	+	0.403188i	$0.132098\pi$
$864$	4.85789	+	1.84416i	0.165269	+	0.0627395i
$865$	−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
$870$	−9.50893	−	2.18295i	−0.322383	−	0.0740089i
$871$	−7.03193	−	6.33158i	−0.238268	−	0.214537i
$872$	3.04398	−	4.18968i	0.103082	−	0.141881i
$873$	−3.61342	+	10.0046i	−0.122296	+	0.338603i
$874$	0.342033	−	0.197473i	0.0115694	−	0.00667961i
$875$	2.37761	+	0.249897i	0.0803781	+	0.00844807i
$876$	7.58889	−	6.61338i	0.256405	−	0.223446i
$877$	−4.45735	−	42.4089i	−0.150514	−	1.43205i	−0.765463	−	0.643480i	$-0.777490\pi$
$877$	−4.45735	−	42.4089i	−0.150514	−	1.43205i	0.614949	−	0.788567i	$-0.289177\pi$
$878$	−7.11892	+	6.40991i	−0.240252	+	0.216324i
$879$	21.7263	−	12.0782i	0.732811	−	0.407387i
$880$	0.251557	+	1.18348i	0.00847998	+	0.0398952i
$881$	−48.7672	−	10.3658i	−1.64301	−	0.349232i	−0.708649	−	0.705561i	$-0.750695\pi$
$881$	−48.7672	−	10.3658i	−1.64301	−	0.349232i	−0.934361	+	0.356329i	$0.884028\pi$
$882$	0.923012	−	3.74132i	0.0310794	−	0.125977i
$883$	43.6376	−	14.1787i	1.46852	−	0.477152i	0.537862	−	0.843033i	$-0.319232\pi$
$883$	43.6376	−	14.1787i	1.46852	−	0.477152i	0.930662	+	0.365881i	$0.119232\pi$
$884$	4.35432	−	1.41480i	0.146452	−	0.0475850i
$885$	−5.42657	+	15.8233i	−0.182412	+	0.531895i
$886$	−4.38582	−	0.932235i	−0.147344	−	0.0313190i
$887$	6.89352	+	32.4314i	0.231462	+	1.08894i	0.928334	+	0.371746i	$0.121241\pi$
$887$	6.89352	+	32.4314i	0.231462	+	1.08894i	−0.696873	+	0.717195i	$0.745426\pi$
$888$	−1.21919	−	2.19308i	−0.0409132	−	0.0735950i
$889$	24.2023	−	21.7919i	0.811720	−	0.730876i
$890$	0.598386	+	5.69326i	0.0200579	+	0.190839i
$891$	6.04457	−	9.05759i	0.202501	−	0.303441i
$892$	8.54852	+	0.898486i	0.286226	+	0.0300835i
$893$	0.234303	−	0.135275i	0.00784064	−	0.00452680i
$894$	2.96026	+	1.37595i	0.0990059	+	0.0460185i
$895$	4.84563	−	6.66944i	0.161972	−	0.222935i
$896$	1.77664	+	1.59970i	0.0593535	+	0.0534422i
$897$	−1.78536	+	7.77702i	−0.0596114	+	0.259667i
$898$			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
$903$	−9.38493	−	5.62328i	−0.312311	−	0.187131i
$904$	6.12647	−	10.6114i	0.203764	−	0.352929i
$905$	−3.60727	−	6.24798i	−0.119910	−	0.207690i
$906$	16.2011	+	0.262788i	0.538246	+	0.00873055i
$907$	−22.4220	+	16.2905i	−0.744510	+	0.540918i	−0.894120	−	0.447827i	$-0.852198\pi$
$907$	−22.4220	+	16.2905i	−0.744510	+	0.540918i	0.149610	+	0.988745i	$0.452198\pi$
$908$	22.0530	−	2.31786i	0.731853	−	0.0769208i
$909$	−13.0720	+	16.8168i	−0.433571	+	0.557779i
$910$	1.14900	+	2.58071i	0.0380891	+	0.0855496i
$911$	−48.5643	+	10.3227i	−1.60901	+	0.342005i	−0.922764	−	0.385365i	$-0.874075\pi$
$911$	−48.5643	+	10.3227i	−1.60901	+	0.342005i	−0.686245	+	0.727371i	$0.740742\pi$
$912$	−0.0211680	+	0.174177i	−0.000700943	+	0.00576757i
$913$	−7.78255	−	3.46501i	−0.257565	−	0.114675i
$914$	−5.10526	−	15.7124i	−0.168867	−	0.519719i
$915$	18.1604	−	7.73509i	0.600363	−	0.255714i
$916$	4.52540	−	10.1642i	0.149523	−	0.335835i
$917$	−0.642319	+	3.02188i	−0.0212113	+	0.0997911i
$918$	17.9049	−	9.20668i	0.590950	−	0.303866i
$919$	0.372712	−	0.165942i	0.0122946	−	0.00547392i	−0.400580	−	0.916262i	$-0.631191\pi$
$919$	0.372712	−	0.165942i	0.0122946	−	0.00547392i	0.412875	+	0.910788i	$0.364525\pi$
$920$	−2.60876	−	2.89733i	−0.0860084	−	0.0955220i
$921$	−46.1690	+	9.03350i	−1.52132	+	0.297664i
$922$	4.36554	+	6.00865i	0.143771	+	0.197884i
$923$	−1.32797	+	12.6348i	−0.0437108	+	0.415880i
$924$	4.10047	−	2.87873i	0.134896	−	0.0947033i
$925$	1.25459	+	0.724340i	0.0412508	+	0.0238162i
$926$	−11.1160	−	8.07624i	−0.365294	−	0.265402i
$927$	−13.1249	+	21.1201i	−0.431078	+	0.693674i
$928$	5.35710	+	1.74063i	0.175856	+	0.0571389i
$929$	15.4813			0.507925			0.253962	−	0.967214i	$-0.418266\pi$
$929$	15.4813			0.507925			0.253962	+	0.967214i	$0.418266\pi$
$930$	−3.49400	−	8.98844i	−0.114573	−	0.294742i
$931$	0.130121			0.00426454
$932$	3.65792	+	1.18853i	0.119819	+	0.0389316i
$933$	−12.7236	+	16.9282i	−0.416551	+	0.554203i
$934$	−27.1620	−	19.7344i	−0.888769	−	0.645728i
$935$	4.05995	+	2.34401i	0.132774	+	0.0766574i
$936$	−2.28531	−	2.70991i	−0.0746976	−	0.0885761i
$937$	−0.468153	+	4.45418i	−0.0152939	+	0.145512i	−0.999504	−	0.0314926i	$-0.989974\pi$
$937$	−0.468153	+	4.45418i	−0.0152939	+	0.145512i	0.984210	+	0.177004i	$0.0566406\pi$
$938$	−11.2529	−	15.4883i	−0.367421	−	0.505712i
$939$	−2.86860	−	14.6610i	−0.0936132	−	0.478444i
$940$	−1.78708	−	1.98475i	−0.0582882	−	0.0647356i
$941$	14.6554	−	6.52501i	0.477753	−	0.212709i	−0.153709	−	0.988116i	$-0.549122\pi$
$941$	14.6554	−	6.52501i	0.477753	−	0.212709i	0.631462	+	0.775407i	$0.282455\pi$
$942$	−17.2717	+	5.30381i	−0.562742	+	0.172807i
$943$	3.03889	−	14.2968i	0.0989598	−	0.465569i
$944$	3.92822	−	8.82293i	0.127853	−	0.287162i
$945$	6.80431	+	10.3933i	0.221344	+	0.338093i
$946$	0.987861	+	3.04032i	0.0321181	+	0.0988494i
$947$	42.4357	+	18.8936i	1.37897	+	0.613959i	0.956317	−	0.292331i	$-0.0944308\pi$
$947$	42.4357	+	18.8936i	1.37897	+	0.613959i	0.422657	+	0.906290i	$0.361097\pi$
$948$	17.8600	+	2.17056i	0.580065	+	0.0704964i
$949$	−6.71723	+	1.42779i	−0.218050	+	0.0463480i
$950$	−0.0412028	−	0.0925430i	−0.00133679	−	0.00300249i
$951$	23.8729	+	22.2068i	0.774133	+	0.720106i
$952$	9.21242	−	0.968265i	0.298576	−	0.0313816i
$953$	−36.3641	+	26.4201i	−1.17795	+	0.855831i	−0.991939	−	0.126717i	$-0.959556\pi$
$953$	−36.3641	+	26.4201i	−1.17795	+	0.855831i	−0.186011	+	0.982548i	$0.559556\pi$
$954$	17.1539	−	1.24208i	0.555377	−	0.0402137i
$955$	3.82996	+	6.63369i	0.123935	+	0.214661i
$956$	−2.97833	+	5.15862i	−0.0963261	+	0.166842i
$957$	6.06719	−	10.1258i	0.196124	−	0.327320i
$958$	−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
$963$	47.1973	+	6.51438i	1.52091	+	0.209923i
$964$	−15.4678	−	13.9273i	−0.498184	−	0.448567i
$965$	−12.8437	+	17.6778i	−0.413452	+	0.569068i
$966$	−6.80469	+	14.6399i	−0.218937	+	0.471030i
$967$	23.7376	−	13.7049i	0.763350	−	0.440720i	−0.0671475	−	0.997743i	$-0.521390\pi$
$967$	23.7376	−	13.7049i	0.763350	−	0.440720i	0.830497	+	0.557023i	$0.188056\pi$
$968$	9.48385	+	0.996793i	0.304822	+	0.0320381i
$969$	0.446648	+	0.512530i	0.0143484	+	0.0164648i
$970$	0.370627	+	3.52628i	0.0119001	+	0.113222i
$971$	20.5955	−	18.5442i	0.660940	−	0.595113i	−0.268859	−	0.963179i	$-0.586647\pi$
$971$	20.5955	−	18.5442i	0.660940	−	0.595113i	0.929800	+	0.368066i	$0.119980\pi$
$972$	−11.8277	−	10.1541i	−0.379372	−	0.325694i
$973$	7.28925	+	34.2932i	0.233683	+	1.09939i
$974$	23.0922	+	4.90839i	0.739921	+	0.157275i
$975$	1.93596	+	0.663932i	0.0620003	+	0.0212629i
$976$	−10.8386	+	3.52167i	−0.346934	+	0.112726i
$977$	−27.7450	+	9.01491i	−0.887642	+	0.288412i	−0.717127	−	0.696943i	$-0.754543\pi$
$977$	−27.7450	+	9.01491i	−0.887642	+	0.288412i	−0.170515	+	0.985355i	$0.554543\pi$
$978$	−26.9712	−	9.24970i	−0.862443	−	0.295773i
$979$	−6.77499	−	1.44007i	−0.216529	−	0.0460248i
$980$	−0.267062	−	1.25643i	−0.00853100	−	0.0401352i
$981$	−12.8586	+	8.71950i	−0.410544	+	0.278392i
$982$	26.9779	−	24.2910i	0.860899	−	0.775157i
$983$	4.30510	+	40.9603i	0.137311	+	1.30643i	0.818578	+	0.574395i	$0.194763\pi$
$983$	4.30510	+	40.9603i	0.137311	+	1.30643i	−0.681267	+	0.732035i	$0.738571\pi$
$984$	4.26610	+	4.89537i	0.135998	+	0.156059i
$985$	−14.9669	−	1.57309i	−0.476886	−	0.0501227i
$986$	18.9011	−	10.9125i	0.601933	−	0.347526i
$987$	−4.66142	+	10.0287i	−0.148375	+	0.319218i
$988$	0.0703580	−	0.0968394i	0.00223838	−	0.00308087i
$989$	−7.65514	−	6.89272i	−0.243419	−	0.219176i
$990$	0.496291	−	3.59568i	0.0157732	−	0.114278i
$991$			43.6106i			1.38534i	0.721256	+	0.692669i	$0.243565\pi$
$991$			43.6106i			1.38534i	−0.721256	+	0.692669i	$0.756435\pi$
$992$	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
$996$	−6.26817	+	10.4612i	−0.198615	+	0.331476i
$997$	28.5401	−	49.4330i	0.903875	−	1.56556i	0.0814555	−	0.996677i	$-0.474043\pi$
$997$	28.5401	−	49.4330i	0.903875	−	1.56556i	0.822420	−	0.568881i	$-0.192624\pi$
$998$	1.65134	+	2.86021i	0.0522723	+	0.0905383i
$999$	1.20509	+	7.43048i	0.0381275	+	0.235090i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.9	✓	176	93.11	even	30	inner
930.2.br.b.11.20	yes	176	31.11	odd	30	inner
930.2.br.b.761.9	yes	176	1.1	even	1	trivial
930.2.br.b.761.20	yes	176	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.38456 + 1.04067i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.995214 - 1.41759i) q^{6} +(-0.249897 + 2.37761i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.834029 + 2.88173i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.38456 + 1.04067i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.995214 - 1.41759i) q^{6} +(-0.249897 + 2.37761i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.834029 + 2.88173i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-1.10532 + 0.492120i) q^{11} +(0.508447 + 1.65574i) q^{12} +(0.245675 - 1.15581i) q^{13} +(0.972390 - 2.18402i) q^{14} +(-0.678734 - 1.59352i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.53967 + 1.57596i) q^{17} +(0.0972966 - 2.99842i) q^{18} +(0.0990872 - 0.0210616i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(-2.82030 + 3.03190i) q^{21} +(1.20329 - 0.126471i) q^{22} +(-3.15414 + 2.29162i) q^{23} +(0.0280908 - 1.73182i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.590815 + 1.02332i) q^{26} +(-1.84416 + 4.85789i) 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} +(-2.04252 - 0.468897i) q^{33} +(-2.87943 - 2.59265i) q^{34} +(1.40522 - 1.93413i) q^{35} +(-1.01910 + 2.82160i) q^{36} +(1.25459 - 0.724340i) q^{37} +(-0.100746 - 0.0105888i) q^{38} +(1.54296 - 1.34462i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-2.78603 + 2.50855i) q^{41} +(3.61917 - 2.01198i) q^{42} +(0.549332 + 2.58440i) q^{43} +(-1.18348 - 0.251557i) q^{44} +(0.718577 - 2.91267i) q^{45} +(3.70792 - 1.20478i) q^{46} +(2.54004 - 0.825307i) q^{47} +(-0.561879 + 1.63838i) q^{48} +(1.25643 + 0.267062i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(3.26084 + 5.86563i) q^{51} +(0.878122 - 0.790664i) q^{52} +(0.599254 + 5.70152i) q^{53} +(3.25507 - 4.05025i) q^{54} +(1.20329 + 0.126471i) q^{55} +(2.07042 - 1.19536i) q^{56} +(0.159111 + 0.0739555i) q^{57} +(3.31087 - 4.55702i) q^{58} +(-7.17722 - 6.46239i) q^{59} +(0.387543 - 1.68814i) 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} +(1.79765 + 1.07712i) q^{66} +(4.00396 - 6.93507i) q^{67} +(1.93732 + 3.35555i) q^{68} +(-6.75192 - 0.109519i) q^{69} +(-1.93413 + 1.40522i) q^{70} +(-10.6927 + 1.12385i) q^{71} +(1.84114 - 2.36858i) q^{72} +(-2.36384 - 5.30927i) q^{73} +(-1.41702 + 0.301198i) q^{74} +(-0.208962 + 1.71940i) q^{75} +(0.0925430 + 0.0412028i) q^{76} +(-0.893855 - 2.75100i) q^{77} +(-1.88296 + 0.802012i) q^{78} +(4.22491 - 9.48930i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-7.60879 + 4.80690i) q^{81} +(3.42485 - 1.52484i) q^{82} +(4.71135 + 5.23248i) q^{83} +(-4.06378 + 0.795125i) q^{84} +(-2.27746 - 3.13466i) q^{85} +(0.276179 - 2.62767i) q^{86} +(-7.98496 + 5.60583i) q^{87} +(1.04782 + 0.604961i) q^{88} +(4.63131 + 3.36485i) q^{89} +(-1.58347 + 2.54806i) q^{90} +(2.68667 + 0.872953i) q^{91} -3.89874 q^{92} +(-9.01765 - 3.41789i) q^{93} -2.67075 q^{94} +(-0.0963429 - 0.0313037i) q^{95} +(1.04067 - 1.38456i) q^{96} +(2.86853 + 2.08411i) q^{97} +(-1.11241 - 0.642250i) q^{98} +(-2.34003 - 2.77479i) 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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