LMFDB - Embedded newform 930.2.br.a.11.18

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			11.18
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.928002 + 1.46247i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.33451 + 1.10412i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.27762 + 2.71435i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.928002 + 1.46247i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.33451 + 1.10412i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.27762 + 2.71435i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.26789 + 1.45496i) q^{11} +(1.61039 + 0.637695i) q^{12} +(-0.192024 - 0.903403i) q^{13} +(0.217038 + 0.487475i) q^{14} +(-1.53491 - 0.802533i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.44802 + 1.98039i) q^{17} +(-0.376313 + 2.97630i) q^{18} +(6.98823 + 1.48540i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-0.724348 + 0.574049i) q^{21} +(3.55756 + 0.373915i) q^{22} +(2.96422 + 2.15363i) q^{23} +(1.72863 + 0.108847i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.461793 - 0.799848i) q^{26} +(-5.15528 + 0.650438i) q^{27} +(0.357053 + 0.396548i) q^{28} +(1.61663 + 4.97546i) q^{29} +(-1.70778 - 0.288942i) q^{30} +(-2.08585 + 5.16229i) q^{31} -1.00000i q^{32} +(0.904781 + 6.12940i) q^{33} +(-3.61835 + 3.25797i) q^{34} +(-0.313647 - 0.431698i) q^{35} +(0.561834 + 2.94692i) q^{36} +(-6.62694 - 3.82607i) q^{37} +(7.10522 - 0.746789i) q^{38} +(1.14300 - 1.11919i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.30633 - 6.57865i) q^{41} +(-0.511505 + 0.769789i) q^{42} +(0.884595 - 4.16169i) q^{43} +(3.49899 - 0.743733i) q^{44} +(-0.250719 - 2.98950i) q^{45} +(3.48465 + 1.13223i) q^{46} +(10.3560 + 3.36487i) q^{47} +(1.67766 - 0.430655i) q^{48} +(6.56852 - 1.39618i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-7.02402 - 4.66728i) q^{51} +(-0.686358 - 0.617999i) q^{52} +(-0.214537 + 2.04118i) q^{53} +(-4.70197 + 2.21167i) q^{54} +(-3.55756 + 0.373915i) q^{55} +(0.462118 + 0.266804i) q^{56} +(4.31276 + 11.5985i) q^{57} +(3.07501 + 4.23238i) q^{58} +(-5.93713 + 5.34582i) q^{59} +(-1.71348 + 0.252933i) q^{60} -2.90278i q^{61} +(-0.388526 + 5.55419i) q^{62} +(-1.51172 - 0.526616i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.617999 + 0.686358i) q^{65} +(2.75459 + 5.54981i) q^{66} +(-7.79547 - 13.5021i) q^{67} +(-2.43448 + 4.21665i) q^{68} +(-0.398813 + 6.33364i) q^{69} +(-0.431698 - 0.313647i) q^{70} +(10.3864 + 1.09165i) q^{71} +(1.44498 + 2.62907i) q^{72} +(6.67127 - 14.9839i) q^{73} +(-7.48492 - 1.59097i) q^{74} +(1.73054 - 0.0724398i) q^{75} +(6.52669 - 2.90587i) q^{76} +(-0.589851 + 1.81538i) q^{77} +(0.741208 - 1.41762i) q^{78} +(-3.95429 - 8.88148i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-5.73536 - 6.93583i) q^{81} +(-8.98165 - 3.99889i) q^{82} +(2.52325 - 2.80236i) q^{83} +(-0.248592 + 0.890176i) q^{84} +(2.86191 - 3.93907i) q^{85} +(-0.444734 - 4.23136i) q^{86} +(-5.77622 + 6.98151i) q^{87} +(3.09791 - 1.78858i) q^{88} +(-1.09614 + 0.796391i) q^{89} +(-1.16226 - 2.76571i) q^{90} +(0.468711 - 0.152294i) q^{91} +3.66397 q^{92} +(-9.48535 + 1.74013i) q^{93} +10.8890 q^{94} +(-6.79469 + 2.20773i) q^{95} +(1.46247 - 0.928002i) q^{96} +(6.70459 - 4.87117i) q^{97} +(5.81559 - 3.35763i) q^{98} +(-8.12441 + 7.01131i) 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} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 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 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * 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
$3$	0.928002	+	1.46247i	0.535782	+	0.844356i
$3$	0.928002	+	1.46247i	0.535782	+	0.844356i
$4$	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
$6$	1.33451	+	1.10412i	0.544811	+	0.450755i
$7$	0.0557772	+	0.530685i	0.0210818	+	0.200580i	0.999993	−	0.00370565i	$-0.00117955\pi$
$7$	0.0557772	+	0.530685i	0.0210818	+	0.200580i	−0.978911	+	0.204286i	$0.934513\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.27762	+	2.71435i	−0.425874	+	0.904782i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	3.26789	+	1.45496i	0.985307	+	0.438687i	0.835178	−	0.549979i	$-0.185364\pi$
$11$	3.26789	+	1.45496i	0.985307	+	0.438687i	0.150129	+	0.988666i	$0.452031\pi$
$12$	1.61039	+	0.637695i	0.464879	+	0.184087i
$13$	−0.192024	−	0.903403i	−0.0532579	−	0.250559i	0.943463	−	0.331479i	$-0.107548\pi$
$13$	−0.192024	−	0.903403i	−0.0532579	−	0.250559i	−0.996721	+	0.0809199i	$0.974214\pi$
$14$	0.217038	+	0.487475i	0.0580058	+	0.130283i
$15$	−1.53491	−	0.802533i	−0.396311	−	0.207213i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.44802	+	1.98039i	−1.07880	+	0.480314i	−0.867669	−	0.497143i	$-0.834383\pi$
$17$	−4.44802	+	1.98039i	−1.07880	+	0.480314i	−0.211135	+	0.977457i	$0.567716\pi$
$18$	−0.376313	+	2.97630i	−0.0886977	+	0.701522i
$19$	6.98823	+	1.48540i	1.60321	+	0.340773i	0.920751	−	0.390150i	$-0.127577\pi$
$19$	6.98823	+	1.48540i	1.60321	+	0.340773i	0.682460	+	0.730923i	$0.260910\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	−0.724348	+	0.574049i	−0.158066	+	0.125268i
$22$	3.55756	+	0.373915i	0.758474	+	0.0797189i
$23$	2.96422	+	2.15363i	0.618082	+	0.449063i	0.852251	−	0.523133i	$-0.175237\pi$
$23$	2.96422	+	2.15363i	0.618082	+	0.449063i	−0.234169	+	0.972196i	$0.575237\pi$
$24$	1.72863	+	0.108847i	0.352855	+	0.0222184i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.461793	−	0.799848i	−0.0905650	−	0.156863i
$27$	−5.15528	+	0.650438i	−0.992134	+	0.125177i
$28$	0.357053	+	0.396548i	0.0674767	+	0.0749405i
$29$	1.61663	+	4.97546i	0.300200	+	0.923921i	0.981425	+	0.191846i	$0.0614476\pi$
$29$	1.61663	+	4.97546i	0.300200	+	0.923921i	−0.681225	+	0.732074i	$0.738552\pi$
$30$	−1.70778	−	0.288942i	−0.311797	−	0.0527533i
$31$	−2.08585	+	5.16229i	−0.374630	+	0.927175i
$31$	−2.08585	+	5.16229i	−0.374630	+	0.927175i
$32$		−	1.00000i		−	0.176777i
$33$	0.904781	+	6.12940i	0.157502	+	1.06699i
$34$	−3.61835	+	3.25797i	−0.620541	+	0.558738i
$35$	−0.313647	−	0.431698i	−0.0530160	−	0.0729702i
$36$	0.561834	+	2.94692i	0.0936390	+	0.491153i
$37$	−6.62694	−	3.82607i	−1.08946	−	0.629002i	−0.156029	−	0.987752i	$-0.549869\pi$
$37$	−6.62694	−	3.82607i	−1.08946	−	0.629002i	−0.933433	+	0.358751i	$0.883203\pi$
$38$	7.10522	−	0.746789i	1.15262	−	0.121145i
$39$	1.14300	−	1.11919i	0.183026	−	0.179214i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−7.30633	−	6.57865i	−1.14106	−	1.02741i	−0.999296	−	0.0375114i	$-0.988057\pi$
$41$	−7.30633	−	6.57865i	−1.14106	−	1.02741i	−0.141761	−	0.989901i	$-0.545276\pi$
$42$	−0.511505	+	0.769789i	−0.0789269	+	0.118781i
$43$	0.884595	−	4.16169i	0.134899	−	0.634652i	−0.857795	−	0.513993i	$-0.828166\pi$
$43$	0.884595	−	4.16169i	0.134899	−	0.634652i	0.992694	−	0.120659i	$-0.0385008\pi$
$44$	3.49899	−	0.743733i	0.527492	−	0.112122i
$45$	−0.250719	−	2.98950i	−0.0373750	−	0.445649i
$46$	3.48465	+	1.13223i	0.513783	+	0.166938i
$47$	10.3560	+	3.36487i	1.51058	+	0.490817i	0.943083	−	0.332558i	$-0.107912\pi$
$47$	10.3560	+	3.36487i	1.51058	+	0.490817i	0.567497	+	0.823375i	$0.307912\pi$
$48$	1.67766	−	0.430655i	0.242149	−	0.0621597i
$49$	6.56852	−	1.39618i	0.938360	−	0.199455i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−7.02402	−	4.66728i	−0.983560	−	0.653550i
$52$	−0.686358	−	0.617999i	−0.0951807	−	0.0857011i
$53$	−0.214537	+	2.04118i	−0.0294689	+	0.280378i	0.969857	+	0.243674i	$0.0783526\pi$
$53$	−0.214537	+	2.04118i	−0.0294689	+	0.280378i	−0.999326	+	0.0367043i	$0.988314\pi$
$54$	−4.70197	+	2.21167i	−0.639857	+	0.300971i
$55$	−3.55756	+	0.373915i	−0.479701	+	0.0504186i
$56$	0.462118	+	0.266804i	0.0617531	+	0.0356532i
$57$	4.31276	+	11.5985i	0.571238	+	1.53626i
$58$	3.07501	+	4.23238i	0.403768	+	0.555739i
$59$	−5.93713	+	5.34582i	−0.772949	+	0.695966i	−0.958002	−	0.286763i	$-0.907421\pi$
$59$	−5.93713	+	5.34582i	−0.772949	+	0.695966i	0.185053	+	0.982729i	$0.440754\pi$
$60$	−1.71348	+	0.252933i	−0.221210	+	0.0326535i
$61$		−	2.90278i		−	0.371663i	−0.982582	−	0.185831i	$-0.940502\pi$
$61$		−	2.90278i		−	0.371663i	0.982582	−	0.185831i	$-0.0594978\pi$
$62$	−0.388526	+	5.55419i	−0.0493428	+	0.705383i
$63$	−1.51172	−	0.526616i	−0.190459	−	0.0663474i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.617999	+	0.686358i	0.0766534	+	0.0851322i
$66$	2.75459	+	5.54981i	0.339066	+	0.683134i
$67$	−7.79547	−	13.5021i	−0.952368	−	1.64955i	−0.740280	−	0.672299i	$-0.765307\pi$
$67$	−7.79547	−	13.5021i	−0.952368	−	1.64955i	−0.212088	−	0.977251i	$-0.568026\pi$
$68$	−2.43448	+	4.21665i	−0.295224	+	0.511344i
$69$	−0.398813	+	6.33364i	−0.0480115	+	0.762481i
$70$	−0.431698	−	0.313647i	−0.0515978	−	0.0374880i
$71$	10.3864	+	1.09165i	1.23264	+	0.129555i	0.698356	−	0.715751i	$-0.253915\pi$
$71$	10.3864	+	1.09165i	1.23264	+	0.129555i	0.534282	+	0.845306i	$0.320582\pi$
$72$	1.44498	+	2.62907i	0.170293	+	0.309839i
$73$	6.67127	−	14.9839i	0.780813	−	1.75373i	0.134147	−	0.990961i	$-0.457171\pi$
$73$	6.67127	−	14.9839i	0.780813	−	1.75373i	0.646666	−	0.762773i	$-0.276163\pi$
$74$	−7.48492	−	1.59097i	−0.870104	−	0.184946i
$75$	1.73054	−	0.0724398i	0.199825	−	0.00836463i
$76$	6.52669	−	2.90587i	0.748663	−	0.333326i
$77$	−0.589851	+	1.81538i	−0.0672198	+	0.206881i
$78$	0.741208	−	1.41762i	0.0839252	−	0.160514i
$79$	−3.95429	−	8.88148i	−0.444892	−	0.999245i	−0.987262	−	0.159105i	$-0.949139\pi$
$79$	−3.95429	−	8.88148i	−0.444892	−	0.999245i	0.542369	−	0.840140i	$-0.317527\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−5.73536	−	6.93583i	−0.637262	−	0.770647i
$82$	−8.98165	−	3.99889i	−0.991857	−	0.441603i
$83$	2.52325	−	2.80236i	0.276963	−	0.307599i	−0.588574	−	0.808443i	$-0.700310\pi$
$83$	2.52325	−	2.80236i	0.276963	−	0.307599i	0.865537	+	0.500844i	$0.166977\pi$
$84$	−0.248592	+	0.890176i	−0.0271236	+	0.0971262i
$85$	2.86191	−	3.93907i	0.310417	−	0.427253i
$86$	−0.444734	−	4.23136i	−0.0479569	−	0.456279i
$87$	−5.77622	+	6.98151i	−0.619276	+	0.748496i
$88$	3.09791	−	1.78858i	0.330238	−	0.190663i
$89$	−1.09614	+	0.796391i	−0.116190	+	0.0844173i	−0.644363	−	0.764720i	$-0.722877\pi$
$89$	−1.09614	+	0.796391i	−0.116190	+	0.0844173i	0.528173	+	0.849137i	$0.322877\pi$
$90$	−1.16226	−	2.76571i	−0.122513	−	0.291532i
$91$	0.468711	−	0.152294i	0.0491343	−	0.0159647i
$92$	3.66397			0.381996
$93$	−9.48535	+	1.74013i	−0.983585	+	0.180443i
$94$	10.8890			1.12311
$95$	−6.79469	+	2.20773i	−0.697120	+	0.226508i
$96$	1.46247	−	0.928002i	0.149262	−	0.0947138i
$97$	6.70459	−	4.87117i	0.680748	−	0.494592i	−0.192858	−	0.981227i	$-0.561776\pi$
$97$	6.70459	−	4.87117i	0.680748	−	0.494592i	0.873606	+	0.486634i	$0.161776\pi$
$98$	5.81559	−	3.35763i	0.587463	−	0.339172i
$99$	−8.12441	+	7.01131i	−0.816534	+	0.704663i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−8.20256	+	11.2899i	−0.816185	+	1.12338i	0.174155	+	0.984718i	$0.444281\pi$
$101$	−8.20256	+	11.2899i	−0.816185	+	1.12338i	−0.990340	+	0.138664i	$0.955719\pi$
$102$	−8.12251	−	2.26831i	−0.804249	−	0.224596i
$103$	−0.782332	+	0.868867i	−0.0770854	+	0.0856120i	−0.780454	−	0.625214i	$-0.785012\pi$
$103$	−0.782332	+	0.868867i	−0.0770854	+	0.0856120i	0.703368	+	0.710826i	$0.251679\pi$
$104$	−0.843737	−	0.375656i	−0.0827352	−	0.0368361i
$105$	0.340279	−	0.859315i	0.0332078	−	0.0838605i
$106$	0.426724	+	2.00758i	0.0414471	+	0.194993i
$107$	−2.11595	−	4.75251i	−0.204557	−	0.459442i	0.781912	−	0.623388i	$-0.214244\pi$
$107$	−2.11595	−	4.75251i	−0.204557	−	0.459442i	−0.986469	+	0.163946i	$0.947578\pi$
$108$	−3.78839	+	3.55641i	−0.364538	+	0.342216i
$109$	−4.04029	+	12.4347i	−0.386989	+	1.19103i	0.548038	+	0.836454i	$0.315375\pi$
$109$	−4.04029	+	12.4347i	−0.386989	+	1.19103i	−0.935027	+	0.354577i	$0.884625\pi$
$110$	−3.26789	+	1.45496i	−0.311582	+	0.138725i
$111$	−0.554319	−	13.2423i	−0.0526136	−	1.25690i
$112$	0.521947	+	0.110943i	0.0493194	+	0.0104832i
$113$	4.91174	−	11.0319i	0.462058	−	1.03780i	−0.520842	−	0.853653i	$-0.674382\pi$
$113$	4.91174	−	11.0319i	0.462058	−	1.03780i	0.982899	−	0.184145i	$-0.0589516\pi$
$114$	7.68581	+	9.69813i	0.719842	+	0.908313i
$115$	−3.64390	−	0.382990i	−0.339796	−	0.0357140i
$116$	4.23238	+	3.07501i	0.392967	+	0.285507i
$117$	2.69748	+	0.632988i	0.249382	+	0.0585198i
$118$	−3.99460	+	6.91885i	−0.367733	+	0.636932i
$119$	−1.29906	−	2.25004i	−0.119085	−	0.206260i
$120$	−1.55146	+	0.770049i	−0.141628	+	0.0702955i
$121$	1.20179	+	1.33472i	0.109254	+	0.121338i
$122$	−0.897008	−	2.76071i	−0.0812112	−	0.249943i
$123$	2.84077	−	16.7903i	0.256144	−	1.51393i
$124$	1.34683	+	5.40241i	0.120949	+	0.485151i
$125$			1.00000i			0.0894427i
$126$	−1.60047	−	0.0336934i	−0.142581	−	0.00300165i
$127$	2.07482	−	1.86818i	0.184111	−	0.165774i	−0.571922	−	0.820308i	$-0.693802\pi$
$127$	2.07482	−	1.86818i	0.184111	−	0.165774i	0.756032	+	0.654534i	$0.227135\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	6.90724	−	2.56837i	0.608149	−	0.226132i
$130$	0.799848	+	0.461793i	0.0701513	+	0.0405019i
$131$	2.06866	−	0.217425i	0.180740	−	0.0189965i	−0.0137261	−	0.999906i	$-0.504369\pi$
$131$	2.06866	−	0.217425i	0.180740	−	0.0189965i	0.194466	+	0.980909i	$0.437703\pi$
$132$	4.33475	+	4.42697i	0.377292	+	0.385318i
$133$	−0.398492	+	3.79140i	−0.0345537	+	0.328756i
$134$	−11.5863	−	10.4324i	−1.00091	−	0.901219i
$135$	4.13939	−	3.14094i	0.356262	−	0.270329i
$136$	−1.01231	+	4.76257i	−0.0868053	+	0.408387i
$137$	11.3232	−	2.40681i	0.967402	−	0.205628i	0.302990	−	0.952994i	$-0.402015\pi$
$137$	11.3232	−	2.40681i	0.967402	−	0.205628i	0.664413	+	0.747366i	$0.268682\pi$
$138$	1.57791	+	6.14689i	0.134321	+	0.523258i
$139$	4.29889	+	1.39679i	0.364627	+	0.118475i	0.485600	−	0.874181i	$-0.338601\pi$
$139$	4.29889	+	1.39679i	0.364627	+	0.118475i	−0.120973	+	0.992656i	$0.538601\pi$
$140$	−0.507491	−	0.164894i	−0.0428908	−	0.0139361i
$141$	4.68939	+	18.2679i	0.394918	+	1.53844i
$142$	10.2154	−	2.17135i	0.857256	−	0.182215i
$143$	0.686901	−	3.23161i	0.0574415	−	0.270241i
$144$	2.18669	+	2.05387i	0.182224	+	0.171156i
$145$	−3.88777	−	3.50057i	−0.322862	−	0.290706i
$146$	1.71447	−	16.3121i	0.141891	−	1.35000i
$147$	8.13747	+	8.31059i	0.671167	+	0.685446i
$148$	−7.61022	+	0.799866i	−0.625556	+	0.0657486i
$149$	15.5131	+	8.95649i	1.27088	+	0.733745i	0.975154	−	0.221527i	$-0.0711043\pi$
$149$	15.5131	+	8.95649i	1.27088	+	0.733745i	0.295729	+	0.955272i	$0.404438\pi$
$150$	1.62345	−	0.603659i	0.132554	−	0.0492886i
$151$	−10.5527	−	14.5246i	−0.858770	−	1.18200i	−0.981861	−	0.189600i	$-0.939281\pi$
$151$	−10.5527	−	14.5246i	−0.858770	−	1.18200i	0.123091	−	0.992395i	$-0.460719\pi$
$152$	5.30929	−	4.78051i	0.430640	−	0.387750i
$153$	0.307439	−	14.6037i	0.0248550	−	1.18064i
$154$			1.90880i			0.153815i
$155$	−0.774746	−	5.51360i	−0.0622291	−	0.442863i
$156$	0.266862	−	1.57728i	0.0213661	−	0.126284i
$157$	−4.78962	−	14.7409i	−0.382253	−	1.17645i	−0.938453	−	0.345406i	$-0.887741\pi$
$157$	−4.78962	−	14.7409i	−0.382253	−	1.17645i	0.556200	−	0.831048i	$-0.312259\pi$
$158$	−6.50528	−	7.22485i	−0.517532	−	0.574778i
$159$	−3.18426	+	1.58047i	−0.252528	+	0.125339i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−0.977562	+	1.69319i	−0.0770427	+	0.133442i
$162$	−7.59794	−	4.82404i	−0.596950	−	0.379012i
$163$	6.54365	+	4.75424i	0.512538	+	0.372381i	0.813786	−	0.581165i	$-0.197403\pi$
$163$	6.54365	+	4.75424i	0.512538	+	0.372381i	−0.301247	+	0.953546i	$0.597403\pi$
$164$	−9.77778	−	1.02769i	−0.763516	−	0.0802488i
$165$	−3.84826	−	4.85582i	−0.299587	−	0.378025i
$166$	1.53378	−	3.44493i	0.119045	−	0.267378i
$167$	−7.88557	−	1.67613i	−0.610204	−	0.129703i	−0.107563	−	0.994198i	$-0.534305\pi$
$167$	−7.88557	−	1.67613i	−0.610204	−	0.129703i	−0.502641	+	0.864496i	$0.667638\pi$
$168$	0.0386544	+	0.923427i	0.00298225	+	0.0712440i
$169$	11.0968	−	4.94063i	0.853602	−	0.380048i
$170$	1.50459	−	4.63066i	0.115397	−	0.355155i
$171$	−12.9602	+	17.0707i	−0.991092	+	1.30543i
$172$	−1.73053	−	3.88683i	−0.131952	−	0.296368i
$173$	0.334418	+	1.57332i	0.0254254	+	0.119617i	0.989030	−	0.147714i	$-0.0471916\pi$
$173$	0.334418	+	1.57332i	0.0254254	+	0.119617i	−0.963605	+	0.267331i	$0.913858\pi$
$174$	−3.33611	+	8.42476i	−0.252910	+	0.638679i
$175$	0.487475	+	0.217038i	0.0368496	+	0.0164065i
$176$	2.39358	−	2.65835i	0.180423	−	0.200380i
$177$	−13.3278	−	3.72193i	−1.00178	−	0.279757i
$178$	−0.796391	+	1.09614i	−0.0596920	+	0.0821590i
$179$	−1.99466	−	18.9780i	−0.149088	−	1.41848i	−0.771719	−	0.635964i	$-0.780603\pi$
$179$	−1.99466	−	18.9780i	−0.149088	−	1.41848i	0.622631	−	0.782516i	$-0.286064\pi$
$180$	−1.96002	−	2.27119i	−0.146091	−	0.169285i
$181$	7.82137	−	4.51567i	0.581358	−	0.335647i	−0.180315	−	0.983609i	$-0.557712\pi$
$181$	7.82137	−	4.51567i	0.581358	−	0.335647i	0.761673	+	0.647962i	$0.224378\pi$
$182$	0.398710	−	0.289680i	0.0295543	−	0.0214725i
$183$	4.24522	−	2.69378i	0.313816	−	0.199130i
$184$	3.48465	−	1.13223i	0.256892	−	0.0834691i
$185$	7.65214			0.562596
$186$	−8.48338	+	4.58610i	−0.622032	+	0.336269i
$187$	−17.4170			−1.27366
$188$	10.3560	−	3.36487i	0.755290	−	0.245409i
$189$	−0.632724	−	2.69955i	−0.0460239	−	0.196363i
$190$	−5.77991	+	4.19935i	−0.419318	+	0.304653i
$191$	−11.0534	+	6.38167i	−0.799795	+	0.461762i	−0.843399	−	0.537287i	$-0.819449\pi$
$191$	−11.0534	+	6.38167i	−0.799795	+	0.461762i	0.0436045	+	0.999049i	$0.486116\pi$
$192$	1.10412	−	1.33451i	0.0796831	−	0.0963100i
$193$	2.86137	+	27.2241i	0.205966	+	1.95963i	0.273377	+	0.961907i	$0.411859\pi$
$193$	2.86137	+	27.2241i	0.205966	+	1.95963i	−0.0674118	+	0.997725i	$0.521474\pi$
$194$	4.87117	−	6.70459i	0.349730	−	0.481362i
$195$	−0.430271	+	1.54075i	−0.0308124	+	0.110335i
$196$	4.49339	−	4.99041i	0.320956	−	0.356458i
$197$	−23.2027	−	10.3305i	−1.65312	−	0.736017i	−0.653343	−	0.757062i	$-0.726634\pi$
$197$	−23.2027	−	10.3305i	−1.65312	−	0.736017i	−0.999779	+	0.0210451i	$0.993301\pi$
$198$	−5.56016	+	9.17873i	−0.395143	+	0.652304i
$199$	1.28362	+	6.03897i	0.0909936	+	0.428091i	0.999938	+	0.0111730i	$0.00355654\pi$
$199$	1.28362	+	6.03897i	0.0909936	+	0.428091i	−0.908944	+	0.416918i	$0.863110\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	12.5122	−	23.9306i	0.882545	−	1.68794i
$202$	−4.31234	+	13.2720i	−0.303415	+	0.933816i
$203$	−2.55023	+	1.13544i	−0.178991	+	0.0796920i
$204$	−8.42591	+	0.352707i	−0.589932	+	0.0246944i
$205$	9.61679	+	2.04411i	0.671666	+	0.142767i
$206$	−0.475547	+	1.06810i	−0.0331329	+	0.0744178i
$207$	−9.63285	+	5.29439i	−0.669529	+	0.367985i
$208$	−0.918526	−	0.0965410i	−0.0636883	−	0.00669391i
$209$	20.6756	+	15.0217i	1.43016	+	1.03907i
$210$	0.0580817	−	0.922409i	0.00400802	−	0.0636523i
$211$	12.3160	−	21.3319i	0.847866	−	1.46855i	−0.0352432	−	0.999379i	$-0.511221\pi$
$211$	12.3160	−	21.3319i	0.847866	−	1.46855i	0.883109	−	0.469168i	$-0.155446\pi$
$212$	1.02621	+	1.77745i	0.0704806	+	0.122076i
$213$	8.04208	+	16.2028i	0.551035	+	1.11020i
$214$	−3.48100	−	3.86604i	−0.237956	−	0.264277i
$215$	1.31476	+	4.04643i	0.0896661	+	0.275964i
$216$	−2.50398	+	4.55303i	−0.170375	+	0.309794i
$217$	−2.85589	−	0.818990i	−0.193870	−	0.0555967i
$218$			13.0746i			0.885527i
$219$	28.1044	−	4.14859i	1.89912	−	0.280336i
$220$	−2.65835	+	2.39358i	−0.179226	+	0.161375i
$221$	2.64321	+	3.63807i	0.177802	+	0.244723i
$222$	−4.61928	−	12.4229i	−0.310026	−	0.833769i
$223$	11.6159	+	6.70641i	0.777855	+	0.449095i	0.835670	−	0.549233i	$-0.185080\pi$
$223$	11.6159	+	6.70641i	0.777855	+	0.449095i	−0.0578146	+	0.998327i	$0.518413\pi$
$224$	0.530685	−	0.0557772i	0.0354579	−	0.00372677i
$225$	1.71188	+	2.46363i	0.114125	+	0.164242i
$226$	1.26228	−	12.0098i	0.0839658	−	0.798881i
$227$	2.73661	+	2.46405i	0.181635	+	0.163545i	0.754933	−	0.655802i	$-0.227670\pi$
$227$	2.73661	+	2.46405i	0.181635	+	0.163545i	−0.573298	+	0.819347i	$0.694336\pi$
$228$	10.3065	+	6.84842i	0.682567	+	0.453548i
$229$	−2.26195	+	10.6416i	−0.149474	+	0.703219i	0.838030	+	0.545624i	$0.183707\pi$
$229$	−2.26195	+	10.6416i	−0.149474	+	0.703219i	−0.987504	+	0.157595i	$0.949626\pi$
$230$	−3.58391	+	0.761783i	−0.236316	+	0.0502305i
$231$	−3.20231	+	0.822034i	−0.210697	+	0.0540859i
$232$	4.97546	+	1.61663i	0.326655	+	0.106137i
$233$	−23.4239	−	7.61088i	−1.53455	−	0.498606i	−0.584684	−	0.811261i	$-0.698781\pi$
$233$	−23.4239	−	7.61088i	−1.53455	−	0.498606i	−0.949867	+	0.312656i	$0.898781\pi$
$234$	2.76106	−	0.231561i	0.180496	−	0.0151376i
$235$	−10.6510	+	2.26394i	−0.694795	+	0.147683i
$236$	−1.66105	+	7.81461i	−0.108125	+	0.508688i
$237$	9.31929	−	14.0251i	0.605353	−	0.911025i
$238$	−1.93078	−	1.73848i	−0.125154	−	0.112689i
$239$	0.491079	−	4.67230i	0.0317652	−	0.302226i	−0.967092	−	0.254428i	$-0.918113\pi$
$239$	0.491079	−	4.67230i	0.0317652	−	0.302226i	0.998857	−	0.0477982i	$-0.0152205\pi$
$240$	−1.23757	+	1.21179i	−0.0798846	+	0.0782205i
$241$	−15.1891	+	1.59644i	−0.978419	+	0.102836i	−0.580217	−	0.814462i	$-0.697032\pi$
$241$	−15.1891	+	1.59644i	−0.978419	+	0.102836i	−0.398202	+	0.917298i	$0.630366\pi$
$242$	1.55542	+	0.898024i	0.0999864	+	0.0577272i
$243$	4.82100	−	14.8242i	0.309267	−	0.950975i
$244$	−1.70621	−	2.34840i	−0.109229	−	0.150341i
$245$	−4.99041	+	4.49339i	−0.318826	+	0.287072i
$246$	−2.48675	−	16.8463i	−0.158549	−	1.07408i
$247$		−	6.59842i		−	0.419848i
$248$	2.95035	+	4.72181i	0.187347	+	0.299835i
$249$	6.43995	+	1.08958i	0.408115	+	0.0690495i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−7.59356	−	8.43350i	−0.479301	−	0.532318i	0.454196	−	0.890902i	$-0.349926\pi$
$251$	−7.59356	−	8.43350i	−0.479301	−	0.532318i	−0.933498	+	0.358584i	$0.883260\pi$
$252$	−1.53255	+	0.462528i	−0.0965415	+	0.0291365i
$253$	6.55330	+	11.3507i	0.412003	+	0.713610i
$254$	1.39597	−	2.41790i	0.0875912	−	0.151712i
$255$	8.41662	+	0.529973i	0.527069	+	0.0331882i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−19.0451	−	2.00172i	−1.18800	−	0.124864i	−0.510165	−	0.860077i	$-0.670415\pi$
$257$	−19.0451	−	2.00172i	−1.18800	−	0.124864i	−0.677836	+	0.735213i	$0.737082\pi$
$258$	5.77551	−	4.57712i	0.359567	−	0.284959i
$259$	1.66080	−	3.73022i	0.103197	−	0.231785i
$260$	0.903403	+	0.192024i	0.0560267	+	0.0119088i
$261$	−15.5706	−	1.96868i	−0.963794	−	0.121859i
$262$	1.90023	−	0.846036i	0.117396	−	0.0522682i
$263$	−2.13997	+	6.58614i	−0.131956	+	0.406119i	−0.995104	−	0.0988319i	$-0.968489\pi$
$263$	−2.13997	+	6.58614i	−0.131956	+	0.406119i	0.863148	+	0.504951i	$0.168489\pi$
$264$	5.49060	+	2.87079i	0.337923	+	0.176685i
$265$	−0.834797	−	1.87499i	−0.0512812	−	0.115179i
$266$	0.792618	+	3.72898i	0.0485986	+	0.228638i
$267$	−2.18192	−	0.864014i	−0.133531	−	0.0528768i
$268$	−14.2430	−	6.34140i	−0.870031	−	0.387363i
$269$	−4.02839	+	4.47398i	−0.245615	+	0.272784i	−0.853329	−	0.521373i	$-0.825420\pi$
$269$	−4.02839	+	4.47398i	−0.245615	+	0.272784i	0.607714	+	0.794156i	$0.292087\pi$
$270$	2.96619	−	4.26635i	0.180516	−	0.259642i
$271$	−11.6934	+	16.0947i	−0.710326	+	0.977681i	0.289464	+	0.957189i	$0.406523\pi$
$271$	−11.6934	+	16.0947i	−0.710326	+	0.977681i	−0.999790	+	0.0204915i	$0.993477\pi$
$272$	0.508945	+	4.84229i	0.0308593	+	0.293607i
$273$	0.657690	+	0.544147i	0.0398052	+	0.0329332i
$274$	10.0252	−	5.78806i	0.605645	−	0.349670i
$275$	2.89398	−	2.10260i	0.174514	−	0.126792i
$276$	3.40018	+	5.35844i	0.204667	+	0.322540i
$277$	13.1585	−	4.27544i	0.790615	−	0.256886i	0.114249	−	0.993452i	$-0.463554\pi$
$277$	13.1585	−	4.27544i	0.790615	−	0.256886i	0.676366	+	0.736566i	$0.263554\pi$
$278$	4.52012			0.271099
$279$	−11.3473	−	12.2572i	−0.679346	−	0.733818i
$280$	−0.533608			−0.0318892
$281$	−4.24780	+	1.38019i	−0.253403	+	0.0823355i	−0.432964	−	0.901411i	$-0.642532\pi$
$281$	−4.24780	+	1.38019i	−0.253403	+	0.0823355i	0.179561	+	0.983747i	$0.442532\pi$
$282$	10.1050	+	15.9247i	0.601743	+	0.948305i
$283$	−10.4808	+	7.61475i	−0.623019	+	0.452650i	−0.853975	−	0.520314i	$-0.825815\pi$
$283$	−10.4808	+	7.61475i	−0.623019	+	0.452650i	0.230956	+	0.972964i	$0.425815\pi$
$284$	9.04442	−	5.22180i	0.536688	−	0.309857i
$285$	−9.53422	−	7.88823i	−0.564758	−	0.467259i
$286$	−0.345342	−	3.28571i	−0.0204205	−	0.194288i
$287$	3.08366	−	4.24430i	0.182023	−	0.250533i
$288$	2.71435	+	1.27762i	0.159944	+	0.0752847i
$289$	4.48773	−	4.98413i	0.263984	−	0.293184i
$290$	−4.77923	−	2.12785i	−0.280646	−	0.124952i
$291$	13.3458	+	5.28479i	0.782345	+	0.309800i
$292$	−3.41015	−	16.0435i	−0.199564	−	0.938876i
$293$	−1.18132	−	2.65329i	−0.0690136	−	0.155007i	0.875745	−	0.482774i	$-0.160371\pi$
$293$	−1.18132	−	2.65329i	−0.0690136	−	0.155007i	−0.944759	+	0.327767i	$0.893704\pi$
$294$	10.3073	+	5.38922i	0.601134	+	0.314306i
$295$	2.46880	−	7.59818i	0.143739	−	0.442383i
$296$	−6.99057	+	3.11240i	−0.406319	+	0.180905i
$297$	−17.7933	−	5.37517i	−1.03247	−	0.311899i
$298$	17.5215	+	3.72432i	1.01500	+	0.215744i
$299$	1.37639	−	3.09143i	0.0795989	−	0.178782i
$300$	1.35745	−	1.07579i	0.0783726	−	0.0621107i
$301$	2.25789	+	0.237313i	0.130142	+	0.0136785i
$302$	−14.5246	−	10.5527i	−0.835797	−	0.607242i
$303$	−24.1230	−	1.51897i	−1.38583	−	0.0872623i
$304$	3.57218	−	6.18719i	0.204878	−	0.354860i
$305$	1.45139	+	2.51388i	0.0831063	+	0.143944i
$306$	−4.22039	−	13.9839i	−0.241263	−	0.799407i
$307$	−11.4054	−	12.6670i	−0.650941	−	0.722943i	0.323839	−	0.946112i	$-0.395026\pi$
$307$	−11.4054	−	12.6670i	−0.650941	−	0.722943i	−0.974780	+	0.223169i	$0.928360\pi$
$308$	0.589851	+	1.81538i	0.0336099	+	0.103441i
$309$	−1.99670	−	0.337824i	−0.113588	−	0.0192181i
$310$	−2.44062	−	5.00433i	−0.138618	−	0.284227i
$311$			8.73371i			0.495243i	0.968857	+	0.247622i	$0.0796490\pi$
$311$			8.73371i			0.495243i	−0.968857	+	0.247622i	$0.920351\pi$
$312$	−0.233605	−	1.58255i	−0.0132253	−	0.0895941i
$313$	−21.8884	+	19.7084i	−1.23721	+	1.11399i	−0.247801	+	0.968811i	$0.579708\pi$
$313$	−21.8884	+	19.7084i	−1.23721	+	1.11399i	−0.989406	+	0.145175i	$0.953625\pi$
$314$	−9.11040	−	12.5394i	−0.514129	−	0.707638i
$315$	1.57250	−	0.299799i	0.0886003	−	0.0168918i
$316$	−8.41949	−	4.86100i	−0.473633	−	0.273452i
$317$	20.1882	−	2.12187i	1.13388	−	0.119176i	0.481061	−	0.876687i	$-0.340252\pi$
$317$	20.1882	−	2.12187i	1.13388	−	0.119176i	0.652822	+	0.757511i	$0.273585\pi$
$318$	−2.54002	+	2.48711i	−0.142437	+	0.139470i
$319$	−1.95614	+	18.6114i	−0.109523	+	1.04204i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	4.98678	−	7.50485i	0.278335	−	0.418880i
$322$	−0.406493	+	1.91240i	−0.0226530	+	0.106574i
$323$	−34.0255	+	7.23234i	−1.89323	+	0.402418i
$324$	−8.71678	−	2.24004i	−0.484265	−	0.124447i
$325$	−0.878382	−	0.285404i	−0.0487239	−	0.0158313i
$326$	7.69252	+	2.49945i	0.426049	+	0.138432i
$327$	−21.9348	+	5.63066i	−1.21300	+	0.311376i
$328$	−9.61679	+	2.04411i	−0.530999	+	0.112867i
$329$	−1.20806	+	5.68346i	−0.0666023	+	0.313339i
$330$	−5.16045	−	3.42898i	−0.284073	−	0.188759i
$331$	6.53075	+	5.88032i	0.358963	+	0.323211i	0.828804	−	0.559540i	$-0.189022\pi$
$331$	6.53075	+	5.88032i	0.358963	+	0.323211i	−0.469841	+	0.882751i	$0.655689\pi$
$332$	0.394171	−	3.75029i	0.0216330	−	0.205824i
$333$	18.8520	−	13.0996i	1.03308	−	0.717851i
$334$	−8.01757	+	0.842681i	−0.438702	+	0.0461094i
$335$	13.5021	+	7.79547i	0.737701	+	0.425912i
$336$	0.322117	+	0.866287i	0.0175729	+	0.0472598i
$337$	1.37733	+	1.89573i	0.0750280	+	0.103267i	0.844882	−	0.534953i	$-0.179671\pi$
$337$	1.37733	+	1.89573i	0.0750280	+	0.103267i	−0.769854	+	0.638221i	$0.779671\pi$
$338$	9.02697	−	8.12792i	0.491003	−	0.442101i
$339$	20.6920	−	3.05441i	1.12383	−	0.165893i
$340$		−	4.86896i		−	0.264057i
$341$	−14.3273	+	13.8350i	−0.775865	+	0.749207i
$342$	−7.05075	+	20.2401i	−0.381261	+	1.09446i
$343$	2.26156	+	6.96037i	0.122113	+	0.375825i
$344$	−2.84693	−	3.16183i	−0.153496	−	0.170475i
$345$	−2.82144	−	5.68450i	−0.151901	−	0.306043i
$346$	0.804232	+	1.39297i	0.0432358	+	0.0748866i
$347$	−9.55161	+	16.5439i	−0.512757	+	0.888122i	0.487133	+	0.873328i	$0.338043\pi$
$347$	−9.55161	+	16.5439i	−0.512757	+	0.888122i	−0.999891	+	0.0147942i	$0.995291\pi$
$348$	−0.569436	+	9.04334i	−0.0305250	+	0.484774i
$349$	18.6175	+	13.5264i	0.996572	+	0.724052i	0.961350	−	0.275328i	$-0.0887864\pi$
$349$	18.6175	+	13.5264i	0.996572	+	0.724052i	0.0352212	+	0.999380i	$0.488786\pi$
$350$	0.530685	+	0.0557772i	0.0283663	+	0.00298142i
$351$	1.57755	+	4.53240i	0.0842032	+	0.241921i
$352$	1.45496	−	3.26789i	0.0775497	−	0.174179i
$353$	19.9966	+	4.25042i	1.06431	+	0.226227i	0.706606	−	0.707607i	$-0.250225\pi$
$353$	19.9966	+	4.25042i	1.06431	+	0.226227i	0.357707	+	0.933834i	$0.383558\pi$
$354$	−13.8256	+	0.578736i	−0.734822	+	0.0307595i
$355$	−9.54070	+	4.24779i	−0.506368	+	0.225450i
$356$	−0.418688	+	1.28859i	−0.0221904	+	0.0682950i
$357$	2.08507	−	3.98787i	0.110354	−	0.211060i
$358$	−7.76155	−	17.4327i	−0.410211	−	0.921348i
$359$	−0.567143	−	2.66820i	−0.0299327	−	0.140822i	0.960644	−	0.277783i	$-0.0895997\pi$
$359$	−0.567143	−	2.66820i	−0.0299327	−	0.140822i	−0.990576	+	0.136961i	$0.956266\pi$
$360$	−2.56593	−	1.55435i	−0.135236	−	0.0819215i
$361$	29.2717	+	13.0326i	1.54061	+	0.685926i
$362$	6.04314	−	6.71159i	0.317621	−	0.352753i
$363$	−0.836726	+	2.99621i	−0.0439167	+	0.157260i
$364$	0.289680	−	0.398710i	0.0151833	−	0.0208981i
$365$	1.71447	+	16.3121i	0.0897394	+	0.853814i
$366$	3.20502	−	3.87379i	0.167529	−	0.202486i
$367$	−20.5506	+	11.8649i	−1.07273	+	0.619343i	−0.928927	−	0.370263i	$-0.879268\pi$
$367$	−20.5506	+	11.8649i	−1.07273	+	0.619343i	−0.143806	+	0.989606i	$0.545934\pi$
$368$	2.96422	−	2.15363i	0.154520	−	0.112266i
$369$	27.1915	−	11.4269i	1.41553	−	0.594860i
$370$	7.27761	−	2.36464i	0.378345	−	0.122932i
$371$	−1.09519			−0.0568595
$372$	−6.65099	+	6.98315i	−0.344838	+	0.362059i
$373$	18.2194			0.943363			0.471681	−	0.881769i	$-0.343647\pi$
$373$	18.2194			0.943363			0.471681	+	0.881769i	$0.343647\pi$
$374$	−16.5646	+	5.38216i	−0.856535	+	0.278305i
$375$	−1.46247	+	0.928002i	−0.0755215	+	0.0479218i
$376$	8.80935	−	6.40037i	0.454308	−	0.330074i
$377$	4.18442	−	2.41587i	0.215508	−	0.124424i
$378$	−1.43596	−	2.37190i	−0.0738580	−	0.121997i
$379$	−0.109845	−	1.04510i	−0.00564235	−	0.0536834i	0.991338	−	0.131332i	$-0.0419254\pi$
$379$	−0.109845	−	1.04510i	−0.00564235	−	0.0536834i	−0.996981	+	0.0776487i	$0.975259\pi$
$380$	−4.19935	+	5.77991i	−0.215422	+	0.296503i
$381$	4.65759	+	1.30069i	0.238615	+	0.0666361i
$382$	−8.54035	+	9.48502i	−0.436962	+	0.485296i
$383$	−27.3267	−	12.1666i	−1.39633	−	0.621685i	−0.435844	−	0.900022i	$-0.643550\pi$
$383$	−27.3267	−	12.1666i	−1.39633	−	0.621685i	−0.960483	+	0.278337i	$0.910217\pi$
$384$	0.637695	−	1.61039i	0.0325422	−	0.0821797i
$385$	−0.396862	−	1.86709i	−0.0202259	−	0.0951555i
$386$	11.1340	+	25.0074i	0.566707	+	1.27284i
$387$	10.1661	+	7.71817i	0.516771	+	0.392337i
$388$	2.56093	−	7.88172i	0.130011	−	0.400134i
$389$	7.39136	−	3.29084i	0.374757	−	0.166852i	−0.210711	−	0.977548i	$-0.567578\pi$
$389$	7.39136	−	3.29084i	0.374757	−	0.166852i	0.585467	+	0.810696i	$0.300911\pi$
$390$	0.0669043	+	1.59830i	0.00338783	+	0.0809329i
$391$	−17.4499	−	3.70909i	−0.882480	−	0.187577i
$392$	2.73134	−	6.13470i	0.137954	−	0.309849i
$393$	2.23770	+	2.82358i	0.112877	+	0.142431i
$394$	−25.2593	−	2.65486i	−1.27255	−	0.133750i
$395$	7.86526	+	5.71444i	0.395744	+	0.287525i
$396$	−2.45164	+	10.4477i	−0.123199	+	0.525015i
$397$	10.1240	−	17.5354i	0.508111	−	0.880075i	−0.491845	−	0.870683i	$-0.663677\pi$
$397$	10.1240	−	17.5354i	0.508111	−	0.880075i	0.999956	−	0.00939159i	$-0.00298948\pi$
$398$	3.08694	+	5.34674i	0.154734	+	0.268008i
$399$	−5.91460	+	2.93565i	−0.296100	+	0.146966i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	1.74782	+	5.37923i	0.0872819	+	0.268626i	0.985166	−	0.171607i	$-0.0548959\pi$
$401$	1.74782	+	5.37923i	0.0872819	+	0.268626i	−0.897884	+	0.440233i	$0.854896\pi$
$402$	4.50487	−	26.6259i	0.224683	−	1.32798i
$403$	5.06416	+	0.893078i	0.252264	+	0.0444874i
$404$			13.9550i			0.694288i
$405$	8.43488	+	3.13892i	0.419132	+	0.155974i
$406$	−2.07455	+	1.86793i	−0.102958	+	0.0927038i
$407$	−16.0894	−	22.1451i	−0.797521	−	1.09769i
$408$	−7.90453	+	2.93919i	−0.391332	+	0.145512i
$409$	8.36292	+	4.82833i	0.413520	+	0.238746i	0.692301	−	0.721609i	$-0.256597\pi$
$409$	8.36292	+	4.82833i	0.413520	+	0.238746i	−0.278781	+	0.960355i	$0.589930\pi$
$410$	9.77778	−	1.02769i	0.482890	−	0.0507538i
$411$	14.0278	+	14.3262i	0.691940	+	0.706660i
$412$	−0.122212	+	1.16277i	−0.00602096	+	0.0572856i
$413$	−3.16810	−	2.85257i	−0.155892	−	0.140366i
$414$	−7.52533	+	8.01197i	−0.369850	+	0.393767i
$415$	−0.784024	+	3.68854i	−0.0384862	+	0.181063i
$416$	−0.903403	+	0.192024i	−0.0442930	+	0.00941476i
$417$	1.94661	+	7.58322i	0.0953261	+	0.371352i
$418$	24.3057	+	7.89739i	1.18883	+	0.386274i
$419$	23.1426	+	7.51949i	1.13059	+	0.367351i	0.813800	−	0.581145i	$-0.197395\pi$
$419$	23.1426	+	7.51949i	1.13059	+	0.367351i	0.316790	+	0.948496i	$0.397395\pi$
$420$	−0.229801	−	0.895211i	−0.0112131	−	0.0436818i
$421$	22.9900	−	4.88668i	1.12047	−	0.238162i	0.389801	−	0.920899i	$-0.372544\pi$
$421$	22.9900	−	4.88668i	1.12047	−	0.238162i	0.730664	+	0.682737i	$0.239210\pi$
$422$	5.12126	−	24.0937i	0.249299	−	1.17286i
$423$	−22.3645	+	23.8108i	−1.08740	+	1.15772i
$424$	1.52525	+	1.37334i	0.0740727	+	0.0666954i
$425$	−0.508945	+	4.84229i	−0.0246875	+	0.234886i
$426$	12.6554	+	12.9247i	0.613157	+	0.626201i
$427$	1.54046	−	0.161909i	0.0745481	−	0.00783532i
$428$	−4.50529	−	2.60113i	−0.217772	−	0.125730i
$429$	5.36358	−	1.99437i	0.258956	−	0.0962893i
$430$	2.50083	+	3.44210i	0.120601	+	0.165993i
$431$	6.09708	−	5.48983i	0.293686	−	0.264436i	−0.509095	−	0.860711i	$-0.670020\pi$
$431$	6.09708	−	5.48983i	0.293686	−	0.264436i	0.802781	+	0.596275i	$0.203353\pi$
$432$	−0.974467	+	5.10396i	−0.0468841	+	0.245564i
$433$			8.78818i			0.422333i	0.977450	+	0.211166i	$0.0677262\pi$
$433$			8.78818i			0.422333i	−0.977450	+	0.211166i	$0.932274\pi$
$434$	−2.96920	+	0.103613i	−0.142526	+	0.00497357i
$435$	1.51160	−	8.93427i	0.0724758	−	0.428366i
$436$	4.04029	+	12.4347i	0.193495	+	0.595515i
$437$	17.5157	+	19.4531i	0.837887	+	0.930568i
$438$	25.4469	−	12.6303i	1.21590	−	0.603499i
$439$	3.55757	+	6.16189i	0.169794	+	0.294091i	0.938347	−	0.345694i	$-0.112357\pi$
$439$	3.55757	+	6.16189i	0.169794	+	0.294091i	−0.768554	+	0.639785i	$0.779023\pi$
$440$	−1.78858	+	3.09791i	−0.0852671	+	0.147687i
$441$	−4.60237	+	19.6130i	−0.219160	+	0.933954i
$442$	3.63807	+	2.64321i	0.173045	+	0.125725i
$443$	−10.6857	−	1.12311i	−0.507691	−	0.0533604i	−0.152779	−	0.988260i	$-0.548822\pi$
$443$	−10.6857	−	1.12311i	−0.507691	−	0.0533604i	−0.354912	+	0.934900i	$0.615489\pi$
$444$	−8.23208	−	10.3874i	−0.390677	−	0.492965i
$445$	0.551088	−	1.23776i	0.0261241	−	0.0586756i
$446$	13.1197	+	2.78868i	0.621237	+	0.132048i
$447$	1.29761	+	30.9991i	0.0613750	+	1.46621i
$448$	0.487475	−	0.217038i	0.0230310	−	0.0102541i
$449$	3.51712	−	10.8246i	0.165983	−	0.510843i	−0.833124	−	0.553086i	$-0.813450\pi$
$449$	3.51712	−	10.8246i	0.165983	−	0.510843i	0.999107	+	0.0422426i	$0.0134503\pi$
$450$	2.38940	+	1.81405i	0.112637	+	0.0855151i
$451$	−14.3046	−	32.1288i	−0.673579	−	1.51288i
$452$	−2.51074	−	11.8121i	−0.118095	−	0.555594i
$453$	11.4488	−	28.9119i	0.537911	−	1.35840i
$454$	3.36410	+	1.49779i	0.157885	+	0.0702949i
$455$	−0.329769	+	0.366246i	−0.0154598	+	0.0171699i
$456$	11.9184	+	3.32834i	0.558129	+	0.155864i
$457$	5.07938	−	6.99117i	0.237603	−	0.327033i	−0.673518	−	0.739171i	$-0.735218\pi$
$457$	5.07938	−	6.99117i	0.237603	−	0.327033i	0.911122	+	0.412138i	$0.135218\pi$
$458$	1.13720	+	10.8198i	0.0531381	+	0.505575i
$459$	21.6427	−	13.1026i	1.01019	−	0.611577i
$460$	−3.17309	+	1.83199i	−0.147946	+	0.0854168i
$461$	−25.5208	+	18.5419i	−1.18862	+	0.863583i	−0.993118	−	0.117120i	$-0.962634\pi$
$461$	−25.5208	+	18.5419i	−1.18862	+	0.863583i	−0.195503	+	0.980703i	$0.562634\pi$
$462$	−2.79156	+	1.77137i	−0.129875	+	0.0824116i
$463$	8.93121	−	2.90193i	0.415069	−	0.134864i	−0.0940357	−	0.995569i	$-0.529977\pi$
$463$	8.93121	−	2.90193i	0.415069	−	0.134864i	0.509104	+	0.860705i	$0.329977\pi$
$464$	5.23151			0.242867
$465$	7.34449	−	6.24967i	0.340593	−	0.289822i
$466$	−24.6293			−1.14093
$467$	3.38397	−	1.09952i	0.156591	−	0.0508796i	−0.229672	−	0.973268i	$-0.573765\pi$
$467$	3.38397	−	1.09952i	0.156591	−	0.0508796i	0.386264	+	0.922388i	$0.373765\pi$
$468$	2.55437	−	1.07344i	0.118076	−	0.0496199i
$469$	6.73057	−	4.89005i	0.310789	−	0.225801i
$470$	−9.43011	+	5.44448i	−0.434979	+	0.251135i
$471$	17.1134	−	20.6843i	0.788542	−	0.953081i
$472$	0.835098	+	7.94543i	0.0384385	+	0.365718i
$473$	8.94586	−	12.3129i	0.411331	−	0.566148i
$474$	4.52919	−	16.2184i	0.208033	−	0.744938i
$475$	4.78051	−	5.30929i	0.219345	−	0.243607i
$476$	−2.37350	−	1.05675i	−0.108789	−	0.0484360i
$477$	−5.26638	−	3.19019i	−0.241131	−	0.146069i
$478$	−0.976777	−	4.59537i	−0.0446767	−	0.210188i
$479$	8.92492	+	20.0457i	0.407790	+	0.915911i	0.994364	+	0.106016i	$0.0338094\pi$
$479$	8.92492	+	20.0457i	0.407790	+	0.915911i	−0.586575	+	0.809895i	$0.699524\pi$
$480$	−0.802533	+	1.53491i	−0.0366305	+	0.0700586i
$481$	−2.18395	+	6.72150i	−0.0995794	+	0.306474i
$482$	−13.9524	+	6.21201i	−0.635515	+	0.282949i
$483$	−3.38341	+	0.141629i	−0.153951	+	0.00644433i
$484$	1.75680	+	0.373419i	0.0798545	+	0.0169736i
$485$	−3.37076	+	7.57085i	−0.153058	+	0.343775i
$486$	0.00409761	−	15.5885i	0.000185871	−	0.707107i
$487$	−30.6427	−	3.22068i	−1.38855	−	0.145943i	−0.619435	−	0.785048i	$-0.712638\pi$
$487$	−30.6427	−	3.22068i	−1.38855	−	0.145943i	−0.769119	+	0.639105i	$0.779305\pi$
$488$	−2.34840	−	1.70621i	−0.106307	−	0.0772365i
$489$	−0.880399	+	13.9818i	−0.0398130	+	0.632280i
$490$	−3.35763	+	5.81559i	−0.151682	+	0.262721i
$491$	16.9919	+	29.4308i	0.766834	+	1.32820i	0.939272	+	0.343175i	$0.111502\pi$
$491$	16.9919	+	29.4308i	0.766834	+	1.32820i	−0.172438	+	0.985020i	$0.555164\pi$
$492$	−7.57084	−	15.2534i	−0.341320	−	0.687675i
$493$	−17.0441	−	18.9294i	−0.767629	−	0.852538i
$494$	−2.03902	−	6.27547i	−0.0917401	−	0.282347i
$495$	3.53029	−	10.1342i	0.158675	−	0.455497i
$496$	4.26507	+	3.57900i	0.191507	+	0.160702i
$497$			5.57279i			0.249974i
$498$	6.46145	−	0.953797i	0.289545	−	0.0427407i
$499$	13.0651	−	11.7639i	0.584876	−	0.526624i	−0.322706	−	0.946499i	$-0.604593\pi$
$499$	13.0651	−	11.7639i	0.584876	−	0.526624i	0.907582	+	0.419875i	$0.137926\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	−4.86654	−	13.0878i	−0.217421	−	0.584722i
$502$	−9.82800	−	5.67420i	−0.438645	−	0.253252i
$503$	7.96026	−	0.836657i	0.354930	−	0.0373047i	0.0746143	−	0.997212i	$-0.476227\pi$
$503$	7.96026	−	0.836657i	0.354930	−	0.0373047i	0.280316	+	0.959908i	$0.409561\pi$
$504$	−1.31461	+	0.913473i	−0.0585574	+	0.0406893i
$505$	1.45870	−	13.8786i	0.0649112	−	0.617588i
$506$	9.74011	+	8.77003i	0.433001	+	0.389875i
$507$	17.5234	+	11.6438i	0.778241	+	0.517121i
$508$	0.580478	−	2.73094i	0.0257546	−	0.121166i
$509$	10.8782	−	2.31224i	0.482169	−	0.102488i	0.0395867	−	0.999216i	$-0.487396\pi$
$509$	10.8782	−	2.31224i	0.482169	−	0.102488i	0.442582	+	0.896728i	$0.354063\pi$
$510$	8.16846	−	2.09685i	0.361705	−	0.0928499i
$511$	8.32384	+	2.70458i	0.368225	+	0.119644i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−36.9925	−	3.11222i	−1.63326	−	0.137408i
$514$	−18.7315	+	3.98151i	−0.826213	+	0.175617i
$515$	0.243085	−	1.14363i	0.0107116	−	0.0503942i
$516$	4.07843	−	6.13783i	0.179543	−	0.270203i
$517$	28.9466	+	26.0636i	1.27307	+	1.14628i
$518$	0.426815	−	4.06087i	0.0187532	−	0.178424i
$519$	−1.99058	+	1.94912i	−0.0873768	+	0.0855567i
$520$	0.918526	−	0.0965410i	0.0402800	−	0.00423360i
$521$	35.2408	+	20.3463i	1.54393	+	0.891388i	0.998585	+	0.0531755i	$0.0169343\pi$
$521$	35.2408	+	20.3463i	1.54393	+	0.891388i	0.545344	+	0.838212i	$0.316399\pi$
$522$	−15.4169	+	2.93924i	−0.674777	+	0.128647i
$523$	12.0602	+	16.5995i	0.527357	+	0.725845i	0.986725	−	0.162401i	$-0.0519239\pi$
$523$	12.0602	+	16.5995i	0.527357	+	0.725845i	−0.459367	+	0.888246i	$0.651924\pi$
$524$	1.54578	−	1.39183i	0.0675279	−	0.0608024i
$525$	0.134967	+	0.914328i	0.00589045	+	0.0399045i
$526$			6.92508i			0.301948i
$527$	−0.945426	−	27.0928i	−0.0411834	−	1.18018i
$528$	6.10900	+	1.03359i	0.265860	+	0.0449812i
$529$	−2.95893	−	9.10665i	−0.128649	−	0.395941i
$530$	−1.37334	−	1.52525i	−0.0596542	−	0.0662527i
$531$	−6.92498	−	22.9454i	−0.300519	−	0.995744i
$532$	1.90614	+	3.30154i	0.0826417	+	0.143140i
$533$	−4.54018	+	7.86382i	−0.196657	+	0.340620i
$534$	−2.34212	−	0.147477i	−0.101353	−	0.00638197i
$535$	4.20872	+	3.05781i	0.181959	+	0.132201i
$536$	−15.5055	−	1.62970i	−0.669737	−	0.0703922i
$537$	25.9036	−	20.5287i	1.11782	−	0.885880i
$538$	−2.44869	+	5.49985i	−0.105571	+	0.237116i
$539$	23.4966	+	4.99436i	1.01207	+	0.215122i
$540$	1.50264	−	4.97414i	0.0646632	−	0.214053i
$541$	−20.1809	+	8.98512i	−0.867646	+	0.386301i	−0.791772	−	0.610817i	$-0.790841\pi$
$541$	−20.1809	+	8.98512i	−0.867646	+	0.386301i	−0.0758735	+	0.997117i	$0.524175\pi$
$542$	−6.14761	+	18.9204i	−0.264062	+	0.812701i
$543$	13.8623	+	7.24794i	0.594887	+	0.311039i
$544$	1.98039	+	4.44802i	0.0849084	+	0.190707i
$545$	−2.71837	−	12.7889i	−0.116442	−	0.547818i
$546$	0.793651	+	0.314277i	0.0339651	+	0.0134498i
$547$	7.81794	+	3.48077i	0.334271	+	0.148827i	0.567007	−	0.823713i	$-0.308101\pi$
$547$	7.81794	+	3.48077i	0.334271	+	0.148827i	−0.232736	+	0.972540i	$0.574768\pi$
$548$	7.74594	−	8.60273i	0.330890	−	0.367491i
$549$	7.87914	+	3.70866i	0.336274	+	0.158282i
$550$	2.10260	−	2.89398i	0.0896552	−	0.123400i
$551$	3.90683	+	37.1710i	0.166437	+	1.58354i
$552$	4.88961	+	4.04547i	0.208116	+	0.172187i
$553$	4.49271	−	2.59387i	0.191049	−	0.110302i
$554$	11.1933	−	8.13237i	0.475556	−	0.345511i
$555$	7.10120	+	11.1910i	0.301429	+	0.475032i
$556$	4.29889	−	1.39679i	0.182314	−	0.0592373i
$557$	27.3110			1.15721			0.578603	−	0.815610i	$-0.303598\pi$
$557$	27.3110			1.15721			0.578603	+	0.815610i	$0.303598\pi$
$558$	−14.5796	−	8.15076i	−0.617204	−	0.345049i
$559$	−3.92955			−0.166202
$560$	−0.507491	+	0.164894i	−0.0214454	+	0.00696804i
$561$	−16.1631	−	25.4719i	−0.682405	−	1.07542i
$562$	−3.61339	+	2.62529i	−0.152422	+	0.110741i
$563$	−16.7486	+	9.66979i	−0.705868	+	0.407533i	−0.809529	−	0.587080i	$-0.800277\pi$
$563$	−16.7486	+	9.66979i	−0.705868	+	0.407533i	0.103661	+	0.994613i	$0.466944\pi$
$564$	14.5314	+	12.0227i	0.611883	+	0.506248i
$565$	1.26228	+	12.0098i	0.0531046	+	0.505257i
$566$	−7.61475	+	10.4808i	−0.320072	+	0.440541i
$567$	3.36083	−	3.43053i	0.141142	−	0.144069i
$568$	6.98813	−	7.76111i	0.293216	−	0.325649i
$569$	−22.0126	−	9.80062i	−0.922814	−	0.410863i	−0.110362	−	0.993891i	$-0.535201\pi$
$569$	−22.0126	−	9.80062i	−0.922814	−	0.410863i	−0.812452	+	0.583028i	$0.801868\pi$
$570$	−11.5052	−	4.55592i	−0.481899	−	0.190827i
$571$	9.43585	+	44.3922i	0.394878	+	1.85776i	0.503966	+	0.863724i	$0.331874\pi$
$571$	9.43585	+	44.3922i	0.394878	+	1.85776i	−0.109087	+	0.994032i	$0.534793\pi$
$572$	−1.34378	−	3.01818i	−0.0561863	−	0.126196i
$573$	−19.5906	−	10.2430i	−0.818407	−	0.427908i
$574$	1.62118	−	4.98947i	0.0676666	−	0.208256i
$575$	3.34721	−	1.49027i	0.139588	−	0.0621487i
$576$	2.97630	+	0.376313i	0.124013	+	0.0156797i
$577$	−22.8442	−	4.85569i	−0.951017	−	0.202145i	−0.293817	−	0.955862i	$-0.594926\pi$
$577$	−22.8442	−	4.85569i	−0.951017	−	0.202145i	−0.657199	+	0.753717i	$0.728259\pi$
$578$	2.72791	−	6.12698i	0.113466	−	0.254849i
$579$	−37.1590	+	29.4487i	−1.54427	+	1.22384i
$580$	−5.20285	−	0.546842i	−0.216037	−	0.0227064i
$581$	1.62791	+	1.18274i	0.0675370	+	0.0490685i
$582$	14.3257	+	0.902053i	0.593820	+	0.0373913i
$583$	−3.67093	+	6.35823i	−0.152034	+	0.263331i
$584$	−8.20097	−	14.2045i	−0.339359	−	0.587786i
$585$	−2.65258	+	0.800558i	−0.109671	+	0.0330990i
$586$	−1.94342	−	2.15838i	−0.0802818	−	0.0891620i
$587$	−5.48446	−	16.8794i	−0.226368	−	0.696688i	−0.998150	−	0.0608012i	$-0.980634\pi$
$587$	−5.48446	−	16.8794i	−0.226368	−	0.696688i	0.771782	−	0.635887i	$-0.219366\pi$
$588$	11.4682	+	1.94032i	0.472940	+	0.0800174i
$589$	−22.2444	+	32.9770i	−0.916566	+	1.35879i
$590$		−	7.98920i		−	0.328910i
$591$	−6.42412	−	43.5199i	−0.264253	−	1.79017i
$592$	−5.68665	+	5.12028i	−0.233720	+	0.210442i
$593$	9.94222	+	13.6843i	0.408278	+	0.561947i	0.962797	−	0.270224i	$-0.0870979\pi$
$593$	9.94222	+	13.6843i	0.408278	+	0.561947i	−0.554519	+	0.832171i	$0.687098\pi$
$594$	−18.5834	+	0.386335i	−0.762488	+	0.0158515i
$595$	2.25004	+	1.29906i	0.0922425	+	0.0532562i
$596$	17.8149	−	1.87242i	0.729725	−	0.0766972i
$597$	−7.64059	+	7.48143i	−0.312709	+	0.306195i
$598$	0.353724	−	3.36545i	0.0144648	−	0.137624i
$599$	−28.1265	−	25.3252i	−1.14922	−	1.03476i	−0.998936	−	0.0461180i	$-0.985315\pi$
$599$	−28.1265	−	25.3252i	−1.14922	−	1.03476i	−0.150283	−	0.988643i	$-0.548018\pi$
$600$	0.958578	−	1.44261i	0.0391338	−	0.0588944i
$601$	−4.58335	+	21.5630i	−0.186959	+	0.879572i	0.780226	+	0.625498i	$0.215104\pi$
$601$	−4.58335	+	21.5630i	−0.186959	+	0.879572i	−0.967185	+	0.254074i	$0.918229\pi$
$602$	2.22071	−	0.472027i	0.0905094	−	0.0192384i
$603$	46.6092	−	3.90895i	1.89807	−	0.159185i
$604$	−17.0747	−	5.54791i	−0.694760	−	0.225741i
$605$	−1.70814	−	0.555009i	−0.0694459	−	0.0225643i
$606$	−23.4118	+	6.00980i	−0.951037	+	0.244132i
$607$	7.08341	−	1.50563i	0.287507	−	0.0611115i	−0.0619007	−	0.998082i	$-0.519716\pi$
$607$	7.08341	−	1.50563i	0.287507	−	0.0611115i	0.349408	+	0.936971i	$0.386383\pi$
$608$	1.48540	−	6.98823i	0.0602407	−	0.283410i
$609$	−4.02716	−	2.67594i	−0.163189	−	0.108435i
$610$	2.15718	+	1.94234i	0.0873418	+	0.0786429i
$611$	1.05123	−	10.0018i	0.0425282	−	0.404629i
$612$	−8.33509	−	11.9953i	−0.336926	−	0.484882i
$613$	−9.45474	+	0.993733i	−0.381873	+	0.0401365i	−0.293521	−	0.955953i	$-0.594827\pi$
$613$	−9.45474	+	0.993733i	−0.381873	+	0.0401365i	−0.0883527	+	0.996089i	$0.528160\pi$
$614$	−14.7615	−	8.52255i	−0.595725	−	0.343942i
$615$	5.93496	+	15.9612i	0.239321	+	0.643617i
$616$	1.12196	+	1.54425i	0.0452052	+	0.0622196i
$617$	8.53848	−	7.68808i	0.343746	−	0.309511i	−0.479116	−	0.877752i	$-0.659043\pi$
$617$	8.53848	−	7.68808i	0.343746	−	0.309511i	0.822862	+	0.568241i	$0.192376\pi$
$618$	−2.00336	+	0.295723i	−0.0805871	+	0.0118957i
$619$		−	10.9887i		−	0.441672i	−0.975311	−	0.220836i	$-0.929121\pi$
$619$		−	10.9887i		−	0.441672i	0.975311	−	0.220836i	$-0.0708785\pi$
$620$	−3.86759	−	4.00521i	−0.155326	−	0.160853i
$621$	−16.6822	−	9.17453i	−0.669433	−	0.368161i
$622$	2.69886	+	8.30625i	0.108215	+	0.333050i
$623$	−0.483772	−	0.537283i	−0.0193819	−	0.0215258i
$624$	−0.711206	−	1.43290i	−0.0284710	−	0.0573621i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.7269	+	25.5077i	−0.588605	+	1.01949i
$627$	−2.78175	+	44.1776i	−0.111092	+	1.76428i
$628$	−12.5394	−	9.11040i	−0.500376	−	0.363544i
$629$	37.0539	+	3.89452i	1.47743	+	0.155285i
$630$	1.40289	−	0.771055i	0.0558926	−	0.0307196i
$631$	1.81735	−	4.08185i	0.0723477	−	0.162496i	−0.873751	−	0.486373i	$-0.838320\pi$
$631$	1.81735	−	4.08185i	0.0723477	−	0.162496i	0.946099	+	0.323877i	$0.104986\pi$
$632$	−9.50954	−	2.02132i	−0.378269	−	0.0804036i
$633$	42.6264	−	1.78433i	1.69425	−	0.0709208i
$634$	18.5444	−	8.25651i	0.736494	−	0.327908i
$635$	−0.862759	+	2.65530i	−0.0342375	+	0.105372i
$636$	−1.64714	+	3.15029i	−0.0653134	+	0.124917i
$637$	−2.52263	−	5.66592i	−0.0999502	−	0.224492i
$638$	3.89085	+	18.3050i	0.154040	+	0.724702i
$639$	−16.2330	+	26.7975i	−0.642168	+	1.06009i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	7.79429	−	8.65644i	0.307856	−	0.341909i	−0.569286	−	0.822139i	$-0.692780\pi$
$641$	7.79429	−	8.65644i	0.307856	−	0.341909i	0.877142	+	0.480231i	$0.159447\pi$
$642$	2.42358	−	8.67853i	0.0956512	−	0.342514i
$643$	−14.3459	+	19.7454i	−0.565746	+	0.778683i	−0.992043	−	0.125901i	$-0.959818\pi$
$643$	−14.3459	+	19.7454i	−0.565746	+	0.778683i	0.426297	+	0.904583i	$0.359818\pi$
$644$	0.204366	+	1.94441i	0.00805316	+	0.0766207i
$645$	−4.69766	+	5.67789i	−0.184970	+	0.223567i
$646$	−30.1252	+	17.3928i	−1.18526	+	0.684311i
$647$	−33.9661	+	24.6778i	−1.33534	+	0.970184i	−0.335743	+	0.941954i	$0.608987\pi$
$647$	−33.9661	+	24.6778i	−1.33534	+	0.970184i	−0.999601	+	0.0282304i	$0.991013\pi$
$648$	−8.98236	+	0.563226i	−0.352860	+	0.0221256i
$649$	−27.1799	+	8.83127i	−1.06690	+	0.346658i
$650$	−0.923585			−0.0362260
$651$	−1.45253	−	4.93667i	−0.0569290	−	0.193483i
$652$	8.08839			0.316766
$653$	28.8170	−	9.36320i	1.12769	−	0.366410i	0.314995	−	0.949093i	$-0.397997\pi$
$653$	28.8170	−	9.36320i	1.12769	−	0.366410i	0.812700	+	0.582683i	$0.197997\pi$
$654$	−19.1212	+	12.1333i	−0.747700	+	0.474450i
$655$	−1.68280	+	1.22263i	−0.0657525	+	0.0477720i
$656$	−8.51445	+	4.91582i	−0.332433	+	0.191930i
$657$	32.1482	+	37.2519i	1.25422	+	1.45334i
$658$	0.607356	+	5.77860i	0.0236772	+	0.225273i
$659$	9.40858	−	12.9498i	0.366506	−	0.504453i	−0.585441	−	0.810715i	$-0.699079\pi$
$659$	9.40858	−	12.9498i	0.366506	−	0.504453i	0.951947	+	0.306263i	$0.0990786\pi$
$660$	−5.96749	−	1.66649i	−0.232284	−	0.0648681i
$661$	21.8829	−	24.3034i	0.851146	−	0.945293i	−0.147899	−	0.989003i	$-0.547251\pi$
$661$	21.8829	−	24.3034i	0.851146	−	0.945293i	0.999044	+	0.0437095i	$0.0139176\pi$
$662$	8.02823	+	3.57440i	0.312026	+	0.138923i
$663$	−2.86765	+	7.24175i	−0.111370	+	0.281246i
$664$	−0.784024	−	3.68854i	−0.0304260	−	0.143143i
$665$	−1.55060	−	3.48269i	−0.0601295	−	0.135053i
$666$	13.8813	−	18.2840i	0.537891	−	0.708491i
$667$	−5.92328	+	18.2300i	−0.229350	+	0.705867i
$668$	−7.36476	+	3.27900i	−0.284951	+	0.126868i
$669$	0.971622	+	23.2114i	0.0375651	+	0.897404i
$670$	15.2502	+	3.24154i	0.589168	+	0.125231i
$671$	4.22343	−	9.48597i	0.163044	−	0.366202i
$672$	0.574049	+	0.724348i	0.0221444	+	0.0279423i
$673$	−45.5304	−	4.78544i	−1.75507	−	0.184465i	−0.828348	−	0.560215i	$-0.810719\pi$
$673$	−45.5304	−	4.78544i	−1.75507	−	0.184465i	−0.926721	+	0.375749i	$0.877385\pi$
$674$	1.89573	+	1.37733i	0.0730210	+	0.0530528i
$675$	−2.01435	+	4.78982i	−0.0775322	+	0.184360i
$676$	6.07350	−	10.5196i	0.233596	−	0.404600i
$677$	−9.16902	−	15.8812i	−0.352394	−	0.610364i	0.634274	−	0.773108i	$-0.281299\pi$
$677$	−9.16902	−	15.8812i	−0.352394	−	0.610364i	−0.986668	+	0.162744i	$0.947966\pi$
$678$	18.7354	−	9.29909i	0.719527	−	0.357129i
$679$	2.95902	+	3.28632i	0.113557	+	0.126118i
$680$	−1.50459	−	4.63066i	−0.0576985	−	0.177578i
$681$	−1.06402	+	6.28884i	−0.0407733	+	0.240989i
$682$	−9.35079	+	17.5852i	−0.358060	+	0.673373i
$683$			3.32817i			0.127349i	0.997971	+	0.0636745i	$0.0202819\pi$
$683$			3.32817i			0.127349i	−0.997971	+	0.0636745i	$0.979718\pi$
$684$	−0.451113	+	21.4283i	−0.0172488	+	0.819332i
$685$	−8.60273	+	7.74594i	−0.328694	+	0.295957i
$686$	4.30175	+	5.92085i	0.164242	+	0.226059i
$687$	−17.6621	+	6.56744i	−0.673853	+	0.250563i
$688$	−3.68465	−	2.12733i	−0.140476	−	0.0811038i
$689$	1.88521	−	0.198143i	0.0718207	−	0.00754866i
$690$	−4.43996	−	4.53441i	−0.169026	−	0.172622i
$691$	−1.35809	+	12.9214i	−0.0516643	+	0.491553i	0.937842	+	0.347063i	$0.112821\pi$
$691$	−1.35809	+	12.9214i	−0.0516643	+	0.491553i	−0.989506	+	0.144490i	$0.953846\pi$
$692$	1.19532	+	1.07627i	0.0454393	+	0.0409137i
$693$	−4.17395	−	3.92043i	−0.158555	−	0.148925i
$694$	−3.97178	+	18.6858i	−0.150767	+	0.709302i
$695$	−4.42134	+	0.939786i	−0.167711	+	0.0356481i
$696$	2.25298	+	8.77669i	0.0853989	+	0.332680i
$697$	45.5270	+	14.7926i	1.72446	+	0.560310i
$698$	21.8862	+	7.11125i	0.828404	+	0.269165i
$699$	−10.6068	−	41.3196i	−0.401184	−	1.56285i
$700$	0.521947	−	0.110943i	0.0197277	−	0.00419326i
$701$	5.32543	−	25.0542i	0.201139	−	0.946283i	−0.755532	−	0.655112i	$-0.772622\pi$
$701$	5.32543	−	25.0542i	0.201139	−	0.946283i	0.956671	−	0.291172i	$-0.0940451\pi$
$702$	2.90092	+	3.82308i	0.109488	+	0.144293i
$703$	−40.6274	−	36.5811i	−1.53229	−	1.37968i
$704$	0.373915	−	3.55756i	0.0140924	−	0.134081i
$705$	−13.1951	−	13.4758i	−0.496956	−	0.507528i
$706$	20.3314	−	2.13692i	0.765182	−	0.0804239i
$707$	−6.44887	−	3.72325i	−0.242535	−	0.140027i
$708$	−12.9701	+	4.82275i	−0.487445	+	0.181250i
$709$	−11.3362	−	15.6030i	−0.425741	−	0.585983i	0.541228	−	0.840876i	$-0.317960\pi$
$709$	−11.3362	−	15.6030i	−0.425741	−	0.585983i	−0.966969	+	0.254893i	$0.917960\pi$
$710$	−7.76111	+	6.98813i	−0.291269	+	0.262260i
$711$	29.1595	+	0.613872i	1.09357	+	0.0230220i
$712$			1.35490i			0.0507771i
$713$	−17.3006	+	10.8100i	−0.647911	+	0.404838i
$714$	0.750705	−	4.43701i	0.0280944	−	0.166051i
$715$	1.02093	+	3.14211i	0.0381807	+	0.117508i
$716$	−12.7687	−	14.1811i	−0.477188	−	0.529971i
$717$	7.28881	−	3.61772i	0.272206	−	0.135106i
$718$	−1.36390	−	2.36235i	−0.0509004	−	0.0881621i
$719$	−15.2004	+	26.3279i	−0.566880	+	0.981864i	0.429992	+	0.902833i	$0.358516\pi$
$719$	−15.2004	+	26.3279i	−0.566880	+	0.981864i	−0.996872	+	0.0790319i	$0.974817\pi$
$720$	−2.92066	−	0.685360i	−0.108847	−	0.0255418i
$721$	−0.504731	−	0.366708i	−0.0187972	−	0.0136569i
$722$	31.8663	+	3.34928i	1.18594	+	0.124647i
$723$	−16.4303	−	20.7321i	−0.611050	−	0.771036i
$724$	3.67337	−	8.25054i	0.136520	−	0.306629i
$725$	5.11719	+	1.08769i	0.190048	+	0.0403959i
$726$	0.130105	+	3.10812i	0.00482866	+	0.115353i
$727$	−5.87174	+	2.61427i	−0.217771	+	0.0969578i	−0.512723	−	0.858554i	$-0.671363\pi$
$727$	−5.87174	+	2.61427i	−0.217771	+	0.0969578i	0.294952	+	0.955512i	$0.404696\pi$
$728$	0.152294	−	0.468711i	0.00564438	−	0.0173716i
$729$	26.1539	−	6.70638i	0.968662	−	0.248384i
$730$	6.67127	+	14.9839i	0.246915	+	0.554580i
$731$	4.30706	+	20.2631i	0.159302	+	0.749459i
$732$	1.85109	−	4.67459i	0.0684181	−	0.172778i
$733$	−2.19460	−	0.977098i	−0.0810593	−	0.0360899i	0.365807	−	0.930691i	$-0.380793\pi$
$733$	−2.19460	−	0.977098i	−0.0810593	−	0.0360899i	−0.446866	+	0.894601i	$0.647460\pi$
$734$	−15.8783	+	17.6347i	−0.586080	+	0.650908i
$735$	−11.2025	−	3.12844i	−0.413212	−	0.115394i
$736$	2.15363	−	2.96422i	0.0793838	−	0.109262i
$737$	−5.82968	−	55.4657i	−0.214739	−	2.04310i
$738$	22.3295	−	19.2702i	0.821961	−	0.709347i
$739$	9.71635	−	5.60974i	0.357422	−	0.206358i	−0.310527	−	0.950564i	$-0.600506\pi$
$739$	9.71635	−	5.60974i	0.357422	−	0.206358i	0.667949	+	0.744207i	$0.267172\pi$
$740$	6.19071	−	4.49781i	0.227575	−	0.165343i
$741$	9.64998	−	6.12335i	0.354501	−	0.224947i
$742$	−1.04159	+	0.338433i	−0.0382379	+	0.0124243i
$743$	5.98609			0.219608			0.109804	−	0.993953i	$-0.464978\pi$
$743$	5.98609			0.219608			0.109804	+	0.993953i	$0.464978\pi$
$744$	−4.16756	+	8.69664i	−0.152790	+	0.318834i
$745$	−17.9130			−0.656281
$746$	17.3276	−	5.63009i	0.634410	−	0.206132i
$747$	4.38280	+	10.4293i	0.160358	+	0.381590i
$748$	−14.0907	+	10.2375i	−0.515207	+	0.374319i
$749$	2.40406	−	1.38798i	0.0878424	−	0.0507159i
$750$	−1.10412	+	1.33451i	−0.0403168	+	0.0487294i
$751$	−2.20658	−	20.9942i	−0.0805192	−	0.766089i	−0.958056	−	0.286580i	$-0.907481\pi$
$751$	−2.20658	−	20.9942i	−0.0805192	−	0.766089i	0.877537	−	0.479509i	$-0.159185\pi$
$752$	6.40037	−	8.80935i	0.233397	−	0.321244i
$753$	5.28688	−	18.9316i	0.192665	−	0.689908i
$754$	3.23307	−	3.59069i	0.117742	−	0.130765i
$755$	16.4012	+	7.30231i	0.596902	+	0.265758i
$756$	−2.09864	−	1.81208i	−0.0763268	−	0.0659045i
$757$	−2.19536	−	10.3284i	−0.0797917	−	0.375390i	0.920075	−	0.391743i	$-0.128128\pi$
$757$	−2.19536	−	10.3284i	−0.0797917	−	0.375390i	−0.999866	+	0.0163528i	$0.994794\pi$
$758$	−0.427424	−	0.960009i	−0.0155247	−	0.0348691i
$759$	−10.5185	+	20.1174i	−0.381797	+	0.730216i
$760$	−2.20773	+	6.79469i	−0.0800827	+	0.246469i
$761$	−0.700532	+	0.311897i	−0.0253943	+	0.0113063i	−0.419394	−	0.907804i	$-0.637758\pi$
$761$	−0.700532	+	0.311897i	−0.0253943	+	0.0113063i	0.394000	+	0.919110i	$0.371091\pi$
$762$	4.83156	−	0.202248i	0.175029	−	0.00732667i
$763$	−6.82427	−	1.45054i	−0.247055	−	0.0525132i
$764$	−5.19132	+	11.6599i	−0.187815	+	0.421840i
$765$	7.03558	+	12.8009i	0.254372	+	0.462816i
$766$	−29.7489	−	3.12673i	−1.07487	−	0.112974i
$767$	5.96950	+	4.33709i	0.215546	+	0.156603i
$768$	0.108847	−	1.72863i	0.00392769	−	0.0623765i
$769$	−10.1381	+	17.5598i	−0.365591	+	0.633222i	−0.988871	−	0.148777i	$-0.952466\pi$
$769$	−10.1381	+	17.5598i	−0.365591	+	0.633222i	0.623280	+	0.781999i	$0.285800\pi$
$770$	−0.954399	−	1.65307i	−0.0343942	−	0.0595724i
$771$	−14.7464	−	29.7104i	−0.531080	−	1.07000i
$772$	18.3168	+	20.3429i	0.659236	+	0.732156i
$773$	1.35939	+	4.18378i	0.0488940	+	0.150480i	0.972523	−	0.232808i	$-0.0747915\pi$
$773$	1.35939	+	4.18378i	0.0488940	+	0.150480i	−0.923629	+	0.383289i	$0.874791\pi$
$774$	12.0536	+	4.19892i	0.433257	+	0.150927i
$775$	3.42775	+	4.38754i	0.123128	+	0.157605i
$776$		−	8.28733i		−	0.297498i
$777$	6.99656	−	1.03279i	0.251000	−	0.0370510i
$778$	6.01267	−	5.41383i	0.215565	−	0.194095i
$779$	−41.2865	−	56.8259i	−1.47924	−	2.03600i
$780$	0.557531	+	1.49940i	0.0199628	+	0.0536870i
$781$	32.3533	+	18.6792i	1.15769	+	0.668394i
$782$	−17.7420	+	1.86476i	−0.634454	+	0.0666838i
$783$	−11.5704	−	24.5984i	−0.413492	−	0.879075i
$784$	0.701936	−	6.67848i	0.0250691	−	0.238517i
$785$	11.5184	+	10.3712i	0.411109	+	0.370164i
$786$	3.00071	+	1.99390i	0.107032	+	0.0711200i
$787$	−1.11269	+	5.23478i	−0.0396630	+	0.186600i	−0.993519	−	0.113664i	$-0.963741\pi$
$787$	−1.11269	+	5.23478i	−0.0396630	+	0.186600i	0.953856	+	0.300264i	$0.0970746\pi$
$788$	−24.8435	+	5.28064i	−0.885012	+	0.188115i
$789$	−11.6179	+	2.98232i	−0.413609	+	0.106174i
$790$	9.24616	+	3.00426i	0.328964	+	0.106887i
$791$	6.12845	+	1.99125i	0.217903	+	0.0708008i
$792$	0.896862	+	10.6939i	0.0318686	+	0.379992i
$793$	−2.62238	+	0.557403i	−0.0931233	+	0.0197940i
$794$	4.20982	−	19.8056i	0.149401	−	0.702875i
$795$	1.96741	−	2.96086i	0.0697769	−	0.105011i
$796$	4.58809	+	4.13113i	0.162621	+	0.146424i
$797$	3.87177	−	36.8374i	0.137145	−	1.30485i	−0.682038	−	0.731317i	$-0.738906\pi$
$797$	3.87177	−	36.8374i	0.137145	−	1.30485i	0.819183	−	0.573532i	$-0.194427\pi$
$798$	−4.71796	+	4.61968i	−0.167014	+	0.163535i
$799$	−52.7275	+	5.54188i	−1.86537	+	0.196058i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−0.761230	−	3.99279i	−0.0268967	−	0.141078i
$802$	3.32455	+	4.57585i	0.117394	+	0.161579i
$803$	43.6020	−	39.2594i	1.53868	−	1.38544i
$804$	−3.94346	−	26.7148i	−0.139075	−	0.942158i
$805$		−	1.95512i		−	0.0689091i
$806$	5.09228	−	0.715544i	0.179368	−	0.0252040i
$807$	−10.2814	−	1.73953i	−0.361923	−	0.0612343i
$808$	4.31234	+	13.2720i	0.151708	+	0.466908i
$809$	−20.9667	−	23.2859i	−0.737151	−	0.818689i	0.251668	−	0.967814i	$-0.419021\pi$
$809$	−20.9667	−	23.2859i	−0.737151	−	0.818689i	−0.988818	+	0.149125i	$0.952354\pi$
$810$	8.99203	+	0.378772i	0.315948	+	0.0133087i
$811$	−2.68607	−	4.65241i	−0.0943207	−	0.163368i	0.815004	−	0.579455i	$-0.196735\pi$
$811$	−2.68607	−	4.65241i	−0.0943207	−	0.163368i	−0.909325	+	0.416087i	$0.863401\pi$
$812$	−1.39579	+	2.41758i	−0.0489826	+	0.0848403i
$813$	−34.3895	−	2.16542i	−1.20609	−	0.0759445i
$814$	−22.1451	−	16.0894i	−0.776186	−	0.563932i
$815$	−8.04408	−	0.845467i	−0.281772	−	0.0296154i
$816$	−6.60939	+	5.23797i	−0.231375	+	0.183366i
$817$	12.3635	−	27.7689i	0.432544	−	0.971511i
$818$	9.44565	+	2.00773i	0.330259	+	0.0701988i
$819$	−0.185459	+	1.46682i	−0.00648046	+	0.0512548i
$820$	8.98165	−	3.99889i	0.313653	−	0.139647i
$821$	−13.7853	+	42.4267i	−0.481110	+	1.48070i	0.356428	+	0.934323i	$0.383995\pi$
$821$	−13.7853	+	42.4267i	−0.481110	+	1.48070i	−0.837537	+	0.546380i	$0.816005\pi$
$822$	17.7683	+	9.29022i	0.619740	+	0.324034i
$823$	12.6343	+	28.3772i	0.440405	+	0.989166i	0.988286	+	0.152610i	$0.0487679\pi$
$823$	12.6343	+	28.3772i	0.440405	+	0.989166i	−0.547881	+	0.836556i	$0.684565\pi$
$824$	0.243085	+	1.14363i	0.00846828	+	0.0398401i
$825$	5.76060	+	2.28114i	0.200559	+	0.0794189i
$826$	−3.89453	−	1.73396i	−0.135508	−	0.0603321i
$827$	2.85621	−	3.17214i	0.0993202	−	0.110306i	−0.691435	−	0.722438i	$-0.743021\pi$
$827$	2.85621	−	3.17214i	0.0993202	−	0.110306i	0.790755	+	0.612132i	$0.209688\pi$
$828$	−4.68118	+	9.94530i	−0.162682	+	0.345623i
$829$	−12.7413	+	17.5370i	−0.442525	+	0.609084i	−0.970771	−	0.240008i	$-0.922850\pi$
$829$	−12.7413	+	17.5370i	−0.442525	+	0.609084i	0.528246	+	0.849092i	$0.322850\pi$
$830$	0.394171	+	3.75029i	0.0136819	+	0.130174i
$831$	18.4638	+	15.2762i	0.640501	+	0.529925i
$832$	−0.799848	+	0.461793i	−0.0277298	+	0.0160098i
$833$	−26.4519	+	19.2184i	−0.916505	+	0.665880i
$834$	4.19468	+	6.61053i	0.145250	+	0.228904i
$835$	7.66717	−	2.49121i	0.265333	−	0.0862120i
$836$	25.5565			0.883889
$837$	7.39540	−	27.9698i	0.255622	−	0.966777i
$838$	24.3336			0.840589
$839$	−35.3767	+	11.4946i	−1.22134	+	0.396837i	−0.847570	−	0.530684i	$-0.821935\pi$
$839$	−35.3767	+	11.4946i	−1.22134	+	0.396837i	−0.373770	+	0.927521i	$0.621935\pi$
$840$	−0.495189	−	0.780384i	−0.0170857	−	0.0269258i
$841$	1.31972	−	0.958836i	0.0455078	−	0.0330633i
$842$	20.3547	−	11.7518i	0.701471	−	0.404994i
$843$	−5.96046	−	4.93145i	−0.205289	−	0.169848i
$844$	−2.57474	−	24.4970i	−0.0886261	−	0.843221i
$845$	−7.13982	+	9.82712i	−0.245617	+	0.338063i
$846$	−13.9120	+	29.5564i	−0.478304	+	1.01617i
$847$	−0.641285	+	0.712219i	−0.0220348	+	0.0244721i
$848$	1.87499	+	0.834797i	0.0643873	+	0.0286671i
$849$	−20.8625	−	8.26133i	−0.716001	−	0.283528i
$850$	1.01231	+	4.76257i	0.0347221	+	0.163355i
$851$	−11.4038	−	25.6133i	−0.390916	−	0.878012i
$852$	16.0300	+	8.38133i	0.549177	+	0.287140i
$853$	−11.9929	+	36.9102i	−0.410628	+	1.26378i	0.505476	+	0.862841i	$0.331317\pi$
$853$	−11.9929	+	36.9102i	−0.410628	+	1.26378i	−0.916104	+	0.400942i	$0.868683\pi$
$854$	1.41503	−	0.630013i	0.0484214	−	0.0215586i
$855$	2.68851	−	21.2638i	0.0919452	−	0.727206i
$856$	−5.08858	−	1.08161i	−0.173924	−	0.0369687i
$857$	3.04907	−	6.84833i	0.104154	−	0.233935i	−0.853949	−	0.520356i	$-0.825799\pi$
$857$	3.04907	−	6.84833i	0.104154	−	0.233935i	0.958104	+	0.286422i	$0.0924658\pi$
$858$	4.48477	−	3.55420i	0.153107	−	0.121338i
$859$	35.6297	+	3.74483i	1.21567	+	0.127772i	0.690567	−	0.723268i	$-0.257361\pi$
$859$	35.6297	+	3.74483i	1.21567	+	0.127772i	0.525101	+	0.851040i	$0.324028\pi$
$860$	3.44210	+	2.50083i	0.117374	+	0.0852776i
$861$	9.06879	+	0.571039i	0.309064	+	0.0194609i
$862$	4.10221	−	7.10524i	0.139722	−	0.242005i
$863$	−19.2181	−	33.2867i	−0.654192	−	1.13309i	−0.982096	−	0.188383i	$-0.939676\pi$
$863$	−19.2181	−	33.2867i	−0.654192	−	1.13309i	0.327904	−	0.944711i	$-0.393658\pi$
$864$	0.650438	+	5.15528i	0.0221283	+	0.175386i
$865$	−1.07627	−	1.19532i	−0.0365944	−	0.0406422i
$866$	2.71570	+	8.35805i	0.0922831	+	0.284018i
$867$	11.4538	+	1.93788i	0.388990	+	0.0658138i
$868$	−2.79185	+	1.01607i	−0.0947617	+	0.0344878i
$869$		−	34.7771i		−	1.17973i
$870$	−1.32322	−	8.96411i	−0.0448615	−	0.303912i
$871$	−10.7010	+	9.63518i	−0.362588	+	0.326476i
$872$	7.68508	+	10.5776i	0.260250	+	0.358203i
$873$	4.65610	+	24.4221i	0.157585	+	0.826563i
$874$	22.6697	+	13.0884i	0.766815	+	0.442721i
$875$	−0.530685	+	0.0557772i	−0.0179404	+	0.00188561i
$876$	20.2985	−	19.8757i	0.685823	−	0.671536i
$877$	−1.37193	+	13.0530i	−0.0463267	+	0.440769i	0.946633	+	0.322314i	$0.104461\pi$
$877$	−1.37193	+	13.0530i	−0.0463267	+	0.440769i	−0.992959	+	0.118455i	$0.962206\pi$
$878$	5.28758	+	4.76096i	0.178447	+	0.160675i
$879$	2.78409	−	4.18991i	0.0939049	−	0.141322i
$880$	−0.743733	+	3.49899i	−0.0250712	+	0.117951i
$881$	−48.3176	+	10.2702i	−1.62786	+	0.346013i	−0.929239	−	0.369478i	$-0.879536\pi$
$881$	−48.3176	+	10.2702i	−1.62786	+	0.346013i	−0.698622	+	0.715491i	$0.746203\pi$
$882$	1.68365	+	20.0753i	0.0566913	+	0.675971i
$883$	−14.7448	−	4.79088i	−0.496202	−	0.161226i	0.0502159	−	0.998738i	$-0.484009\pi$
$883$	−14.7448	−	4.79088i	−0.496202	−	0.161226i	−0.546418	+	0.837513i	$0.684009\pi$
$884$	4.27681	+	1.38962i	0.143845	+	0.0467380i
$885$	13.4031	−	3.44059i	0.450542	−	0.115654i
$886$	−10.5097	+	2.23391i	−0.353081	+	0.0750497i
$887$	11.5583	−	54.3773i	0.388088	−	1.82581i	−0.157203	−	0.987566i	$-0.550248\pi$
$887$	11.5583	−	54.3773i	0.388088	−	1.82581i	0.545292	−	0.838246i	$-0.316419\pi$
$888$	−11.0391	−	7.33517i	−0.370447	−	0.246152i
$889$	1.10714	+	0.996874i	0.0371323	+	0.0334341i
$890$	0.141626	−	1.34748i	0.00474731	−	0.0451676i
$891$	−8.65119	−	31.0103i	−0.289826	−	1.03888i
$892$	13.3394	−	1.40202i	0.446635	−	0.0469432i
$893$	67.3721	+	38.8973i	2.25452	+	1.30165i
$894$	10.8133	+	29.0809i	0.361652	+	0.972610i
$895$	11.2164	+	15.4381i	0.374923	+	0.516038i
$896$	0.396548	−	0.357053i	0.0132477	−	0.0119283i
$897$	5.79841	−	0.855924i	0.193603	−	0.0285785i
$898$		−	11.3816i		−	0.379810i
$899$	−29.0568	−	2.03258i	−0.969099	−	0.0677902i
$900$	2.83303	+	0.986898i	0.0944342	+	0.0328966i
$901$	−3.08807	−	9.50409i	−0.102878	−	0.316627i
$902$	−23.5329	−	26.1359i	−0.783558	−	0.870230i
$903$	1.74826	+	3.52231i	0.0581784	+	0.117215i
$904$	−6.03798	−	10.4581i	−0.200820	−	0.347831i
$905$	−4.51567	+	7.82137i	−0.150106	+	0.259991i
$906$	1.95418	−	31.0347i	0.0649232	−	1.03106i
$907$	44.8404	+	32.5785i	1.48890	+	1.08175i	0.974550	+	0.224171i	$0.0719674\pi$
$907$	44.8404	+	32.5785i	1.48890	+	1.08175i	0.514352	+	0.857579i	$0.328033\pi$
$908$	3.66229	+	0.384922i	0.121537	+	0.0127741i
$909$	−20.1648	−	36.6888i	−0.668824	−	1.21689i
$910$	−0.200453	+	0.450225i	−0.00664495	+	0.0149248i
$911$	41.9322	+	8.91297i	1.38928	+	0.295300i	0.841017	−	0.541009i	$-0.181957\pi$
$911$	41.9322	+	8.91297i	1.38928	+	0.295300i	0.548259	+	0.836308i	$0.315291\pi$
$912$	12.3636	−	0.517536i	0.409398	−	0.0171373i
$913$	12.3231	−	5.48658i	0.407834	−	0.181579i
$914$	2.67039	−	8.21861i	0.0883286	−	0.271848i
$915$	−2.32957	+	4.45549i	−0.0770134	+	0.147294i
$916$	4.42504	+	9.93881i	0.146208	+	0.328387i
$917$	0.230768	+	1.08568i	0.00762064	+	0.0358523i
$918$	16.5345	−	19.1493i	0.545719	−	0.632020i
$919$	−17.9198	−	7.97840i	−0.591119	−	0.263183i	0.0893020	−	0.996005i	$-0.471536\pi$
$919$	−17.9198	−	7.97840i	−0.591119	−	0.263183i	−0.680421	+	0.732822i	$0.738203\pi$
$920$	−2.45168	+	2.72286i	−0.0808294	+	0.0897701i
$921$	7.94081	−	28.4350i	0.261659	−	0.936966i
$922$	−18.5419	+	25.5208i	−0.610646	+	0.840482i
$923$	−1.00824	−	9.59272i	−0.0331865	−	0.315748i
$924$	−2.10754	+	2.54731i	−0.0693331	+	0.0838004i
$925$	−6.62694	+	3.82607i	−0.217893	+	0.125800i
$926$	7.59734	−	5.51979i	0.249664	−	0.181392i
$927$	−1.35888	−	3.23360i	−0.0446315	−	0.106206i
$928$	4.97546	−	1.61663i	0.163328	−	0.0530684i
$929$	12.5238			0.410893			0.205447	−	0.978668i	$-0.434135\pi$
$929$	12.5238			0.410893			0.205447	+	0.978668i	$0.434135\pi$
$930$	5.05377	−	8.21337i	0.165720	−	0.269327i
$931$	47.9762			1.57236
$932$	−23.4239	+	7.61088i	−0.767275	+	0.249303i
$933$	−12.7728	+	8.10490i	−0.418162	+	0.265343i
$934$	2.87857	−	2.09141i	0.0941898	−	0.0684329i
$935$	15.0836	−	8.70852i	0.493287	−	0.284799i
$936$	2.09764	−	1.81025i	0.0685635	−	0.0591698i
$937$	−3.63924	−	34.6251i	−0.118889	−	1.13115i	−0.877489	−	0.479596i	$-0.840783\pi$
$937$	−3.63924	−	34.6251i	−0.118889	−	1.13115i	0.758600	−	0.651556i	$-0.225884\pi$
$938$	4.89005	−	6.73057i	0.159666	−	0.219761i
$939$	−49.1355	−	13.7216i	−1.60347	−	0.447789i
$940$	−7.28613	+	8.09207i	−0.237648	+	0.263934i
$941$	−30.4726	−	13.5673i	−0.993377	−	0.442280i	−0.155321	−	0.987864i	$-0.549641\pi$
$941$	−30.4726	−	13.5673i	−0.993377	−	0.442280i	−0.838056	+	0.545584i	$0.816308\pi$
$942$	9.88398	−	24.9602i	0.322037	−	0.813249i
$943$	−7.48957	−	35.2357i	−0.243894	−	1.14743i
$944$	3.24950	+	7.29849i	0.105762	+	0.237546i
$945$	1.89773	+	2.02152i	0.0617332	+	0.0657599i
$946$	4.70312	−	14.4747i	0.152911	−	0.470613i
$947$	−29.3965	+	13.0882i	−0.955257	+	0.425308i	−0.824346	−	0.566086i	$-0.808457\pi$
$947$	−29.3965	+	13.0882i	−0.955257	+	0.425308i	−0.130911	+	0.991394i	$0.541790\pi$
$948$	−0.704259	−	16.8242i	−0.0228733	−	0.546426i
$949$	−14.8176	−	3.14957i	−0.480998	−	0.102239i
$950$	2.90587	−	6.52669i	0.0942789	−	0.211754i
$951$	21.8379	+	27.5555i	0.708141	+	0.893548i
$952$	−2.58388	−	0.271577i	−0.0837442	−	0.00880187i
$953$	−25.9178	−	18.8304i	−0.839561	−	0.609977i	0.0826870	−	0.996576i	$-0.473650\pi$
$953$	−25.9178	−	18.8304i	−0.839561	−	0.609977i	−0.922248	+	0.386599i	$0.873650\pi$
$954$	−5.99445	−	1.40665i	−0.194078	−	0.0455420i
$955$	6.38167	−	11.0534i	0.206506	−	0.357679i
$956$	−2.34902	−	4.06862i	−0.0759727	−	0.131589i
$957$	−29.0339	+	14.4107i	−0.938533	+	0.465830i
$958$	14.6826	+	16.3066i	0.474372	+	0.526843i
$959$	1.90883	+	5.87478i	0.0616394	+	0.189707i
$960$	−0.288942	+	1.70778i	−0.00932555	+	0.0551184i
$961$	−22.2985	−	21.5355i	−0.719305	−	0.694694i
$962$			7.06740i			0.227862i
$963$	15.6033	+	0.328485i	0.502811	+	0.0105853i
$964$	−11.3499	+	10.2195i	−0.365556	+	0.329148i
$965$	−16.0901	−	22.1461i	−0.517957	−	0.712907i
$966$	−3.17405	+	1.18023i	−0.102123	+	0.0379732i
$967$	−0.782812	−	0.451956i	−0.0251735	−	0.0145339i	0.487360	−	0.873201i	$-0.337960\pi$
$967$	−0.782812	−	0.451956i	−0.0251735	−	0.0145339i	−0.512534	+	0.858667i	$0.671293\pi$
$968$	1.78621	−	0.187738i	0.0574109	−	0.00603413i
$969$	−42.1528	−	43.0495i	−1.35414	−	1.38295i
$970$	−0.866262	+	8.24193i	−0.0278140	+	0.264632i
$971$	−20.1800	−	18.1702i	−0.647608	−	0.583108i	0.278468	−	0.960445i	$-0.410173\pi$
$971$	−20.1800	−	18.1702i	−0.647608	−	0.583108i	−0.926076	+	0.377337i	$0.876840\pi$
$972$	−4.81320	−	14.8268i	−0.154383	−	0.475569i
$973$	−0.501477	+	2.35926i	−0.0160766	+	0.0756345i
$974$	−30.1382	+	6.40607i	−0.965690	+	0.205264i
$975$	−0.397747	−	1.54946i	−0.0127381	−	0.0496224i
$976$	−2.76071	−	0.897008i	−0.0883680	−	0.0287125i
$977$	47.2521	+	15.3532i	1.51173	+	0.491191i	0.943413	−	0.331619i	$-0.107595\pi$
$977$	47.2521	+	15.3532i	1.51173	+	0.491191i	0.568317	+	0.822810i	$0.307595\pi$
$978$	3.48331	+	13.5696i	0.111384	+	0.433907i
$979$	−4.74078	+	1.00768i	−0.151516	+	0.0322057i
$980$	−1.39618	+	6.56852i	−0.0445994	+	0.209824i
$981$	−28.5902	−	26.8536i	−0.912815	−	0.857371i
$982$	25.2549	+	22.7396i	0.805916	+	0.725650i
$983$	4.20843	−	40.0405i	0.134228	−	1.27709i	−0.695337	−	0.718684i	$-0.744745\pi$
$983$	4.20843	−	40.0405i	0.134228	−	1.27709i	0.829565	−	0.558410i	$-0.188588\pi$
$984$	−11.9139	−	12.1673i	−0.379800	−	0.387880i
$985$	25.2593	−	2.65486i	0.804830	−	0.0845910i
$986$	−22.0594	−	12.7360i	−0.702516	−	0.405598i
$987$	−9.43296	+	3.50752i	−0.300254	+	0.111646i
$988$	−3.87846	−	5.33824i	−0.123390	−	0.169832i
$989$	11.5849	−	10.4311i	0.368377	−	0.331689i
$990$	0.225871	−	10.7291i	0.00717865	−	0.340993i
$991$		−	52.6598i		−	1.67279i	−0.548124	−	0.836397i	$-0.684658\pi$
$991$		−	52.6598i		−	1.67279i	0.548124	−	0.836397i	$-0.315342\pi$
$992$	5.16229	+	2.08585i	0.163903	+	0.0662258i
$993$	−2.53922	+	15.0080i	−0.0805797	+	0.476263i
$994$	1.72209	+	5.30003i	0.0546212	+	0.168107i
$995$	−4.13113	−	4.58809i	−0.130966	−	0.145452i
$996$	5.85047	−	2.90381i	0.185379	−	0.0920108i
$997$	−10.6734	−	18.4869i	−0.338031	−	0.585487i	0.646031	−	0.763311i	$-0.276428\pi$
$997$	−10.6734	−	18.4869i	−0.338031	−	0.585487i	−0.984062	+	0.177824i	$0.943094\pi$
$998$	8.79043	−	15.2255i	0.278256	−	0.481954i
$999$	36.6524	+	15.4140i	1.15963	+	0.487679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.18	yes	176
3.2	odd	2	inner	930.2.br.a.11.3	✓	176
31.17	odd	30	inner	930.2.br.a.761.3	yes	176
93.17	even	30	inner	930.2.br.a.761.18	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.3	✓	176	3.2	odd	2	inner
930.2.br.a.11.18	yes	176	1.1	even	1	trivial
930.2.br.a.761.3	yes	176	31.17	odd	30	inner
930.2.br.a.761.18	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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.928002 + 1.46247i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.33451 + 1.10412i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.27762 + 2.71435i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.928002 + 1.46247i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.33451 + 1.10412i) q^{6} +(0.0557772 + 0.530685i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.27762 + 2.71435i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.26789 + 1.45496i) q^{11} +(1.61039 + 0.637695i) q^{12} +(-0.192024 - 0.903403i) q^{13} +(0.217038 + 0.487475i) q^{14} +(-1.53491 - 0.802533i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.44802 + 1.98039i) q^{17} +(-0.376313 + 2.97630i) q^{18} +(6.98823 + 1.48540i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(-0.724348 + 0.574049i) q^{21} +(3.55756 + 0.373915i) q^{22} +(2.96422 + 2.15363i) q^{23} +(1.72863 + 0.108847i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.461793 - 0.799848i) q^{26} +(-5.15528 + 0.650438i) q^{27} +(0.357053 + 0.396548i) q^{28} +(1.61663 + 4.97546i) q^{29} +(-1.70778 - 0.288942i) q^{30} +(-2.08585 + 5.16229i) q^{31} -1.00000i q^{32} +(0.904781 + 6.12940i) q^{33} +(-3.61835 + 3.25797i) q^{34} +(-0.313647 - 0.431698i) q^{35} +(0.561834 + 2.94692i) q^{36} +(-6.62694 - 3.82607i) q^{37} +(7.10522 - 0.746789i) q^{38} +(1.14300 - 1.11919i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-7.30633 - 6.57865i) q^{41} +(-0.511505 + 0.769789i) q^{42} +(0.884595 - 4.16169i) q^{43} +(3.49899 - 0.743733i) q^{44} +(-0.250719 - 2.98950i) q^{45} +(3.48465 + 1.13223i) q^{46} +(10.3560 + 3.36487i) q^{47} +(1.67766 - 0.430655i) q^{48} +(6.56852 - 1.39618i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-7.02402 - 4.66728i) q^{51} +(-0.686358 - 0.617999i) q^{52} +(-0.214537 + 2.04118i) q^{53} +(-4.70197 + 2.21167i) q^{54} +(-3.55756 + 0.373915i) q^{55} +(0.462118 + 0.266804i) q^{56} +(4.31276 + 11.5985i) q^{57} +(3.07501 + 4.23238i) q^{58} +(-5.93713 + 5.34582i) q^{59} +(-1.71348 + 0.252933i) q^{60} -2.90278i q^{61} +(-0.388526 + 5.55419i) q^{62} +(-1.51172 - 0.526616i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.617999 + 0.686358i) q^{65} +(2.75459 + 5.54981i) q^{66} +(-7.79547 - 13.5021i) q^{67} +(-2.43448 + 4.21665i) q^{68} +(-0.398813 + 6.33364i) q^{69} +(-0.431698 - 0.313647i) q^{70} +(10.3864 + 1.09165i) q^{71} +(1.44498 + 2.62907i) q^{72} +(6.67127 - 14.9839i) q^{73} +(-7.48492 - 1.59097i) q^{74} +(1.73054 - 0.0724398i) q^{75} +(6.52669 - 2.90587i) q^{76} +(-0.589851 + 1.81538i) q^{77} +(0.741208 - 1.41762i) q^{78} +(-3.95429 - 8.88148i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-5.73536 - 6.93583i) q^{81} +(-8.98165 - 3.99889i) q^{82} +(2.52325 - 2.80236i) q^{83} +(-0.248592 + 0.890176i) q^{84} +(2.86191 - 3.93907i) q^{85} +(-0.444734 - 4.23136i) q^{86} +(-5.77622 + 6.98151i) q^{87} +(3.09791 - 1.78858i) q^{88} +(-1.09614 + 0.796391i) q^{89} +(-1.16226 - 2.76571i) q^{90} +(0.468711 - 0.152294i) q^{91} +3.66397 q^{92} +(-9.48535 + 1.74013i) q^{93} +10.8890 q^{94} +(-6.79469 + 2.20773i) q^{95} +(1.46247 - 0.928002i) q^{96} +(6.70459 - 4.87117i) q^{97} +(5.81559 - 3.35763i) q^{98} +(-8.12441 + 7.01131i) 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	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more