LMFDB - Embedded newform 750.2.o.a.469.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.11
Character	$\chi$	$=$	750.469
Dual form			750.2.o.a.379.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.89198 - 1.19180i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.52211 + 3.47139i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.89198 - 1.19180i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.52211 + 3.47139i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.81342 - 1.30825i) q^{10} +(0.185304 + 2.94532i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-2.06998 - 1.71244i) q^{13} +(2.73510 + 3.30617i) q^{14} +(-1.20447 + 1.88394i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.0331730 - 0.262591i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-1.89036 + 4.01721i) q^{19} +(1.72769 - 1.41953i) q^{20} +(-3.76012 - 2.06714i) q^{21} +(0.369876 + 2.92787i) q^{22} +(-0.891511 - 2.25170i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(2.15921 - 4.50975i) q^{25} +(-2.17343 - 1.57909i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(2.93730 + 3.12791i) q^{28} +(4.44237 - 4.17166i) q^{29} +(-1.08380 + 1.95586i) q^{30} +(1.23119 + 0.155535i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-1.42172 - 2.58610i) q^{33} +(0.0166193 - 0.264156i) q^{34} +(8.90901 + 3.56195i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.68331 + 6.55607i) q^{37} +(-1.63438 + 4.12798i) q^{38} +(2.60210 + 0.668106i) q^{39} +(1.63515 - 1.52522i) q^{40} +(3.23394 + 1.28041i) q^{41} +(-3.88250 - 1.82696i) q^{42} +(-1.43314 - 0.465656i) q^{43} +(0.552989 + 2.89887i) q^{44} +(0.287695 - 2.21748i) q^{45} +(-1.03114 - 2.19128i) q^{46} +(-5.74495 - 1.09591i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.52637 + 10.8530i) q^{49} +(1.87178 - 4.63643i) q^{50} +(0.0817901 + 0.251724i) q^{51} +(-2.26829 - 1.43950i) q^{52} +(4.89135 - 8.89733i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(3.86083 + 5.35165i) q^{55} +(3.12791 + 2.93730i) q^{56} -4.43976i q^{57} +(4.17166 - 4.44237i) q^{58} +(4.49260 + 7.07921i) q^{59} +(-0.958855 + 2.02005i) q^{60} +(0.0151556 - 0.00600053i) q^{61} +(1.23852 + 0.0779214i) q^{62} +(4.28240 + 0.269426i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-5.95727 - 0.772894i) q^{65} +(-1.58130 - 2.49173i) q^{66} +(4.88445 - 5.20141i) q^{67} -0.264678i q^{68} +(1.76539 + 1.65781i) q^{69} +(9.11508 + 2.99552i) q^{70} +(0.522593 - 2.73953i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-11.8861 - 7.54317i) q^{73} +(2.09165 + 6.43743i) q^{74} +(-0.0335518 + 4.99989i) q^{75} +(-1.37196 + 4.22246i) q^{76} +(-9.75698 + 8.07167i) q^{77} +(2.63892 + 0.503400i) q^{78} +(-6.18230 - 13.1381i) q^{79} +(1.53615 - 1.62488i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(3.30795 + 1.07482i) q^{82} +(-2.19328 - 1.03208i) q^{83} +(-3.98955 - 1.57957i) q^{84} +(-0.250195 - 0.536354i) q^{85} +(-1.45955 - 0.374750i) q^{86} +(-2.24337 + 5.66610i) q^{87} +(0.733919 + 2.85842i) q^{88} +(-4.00885 + 6.31694i) q^{89} +(0.147891 - 2.23117i) q^{90} +(0.723813 - 11.5047i) q^{91} +(-1.16669 - 2.12221i) q^{92} +(-1.18024 + 0.383482i) q^{93} +(-5.80243 - 0.733017i) q^{94} +(1.21121 + 9.85344i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-7.32227 - 7.79743i) q^{97} +(-2.83794 + 11.0531i) q^{98} +(2.38752 + 1.73464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$2$	0.998027	−	0.0627905i	0.705711	−	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	1.89198	−	1.19180i	0.846121	−	0.532991i
$5$	1.89198	−	1.19180i	0.846121	−	0.532991i
$6$	−0.876307	+	0.481754i	−0.357751	+	0.196675i
$7$	2.52211	+	3.47139i	0.953268	+	1.31206i	0.950060	+	0.312066i	$0.101021\pi$
$7$	2.52211	+	3.47139i	0.953268	+	1.31206i	0.00320776	+	0.999995i	$0.498979\pi$
$8$	0.982287	−	0.187381i	0.347291	−	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	1.81342	−	1.30825i	0.573453	−	0.413705i
$11$	0.185304	+	2.94532i	0.0558711	+	0.888046i	0.921748	+	0.387789i	$0.126761\pi$
$11$	0.185304	+	2.94532i	0.0558711	+	0.888046i	−0.865877	+	0.500257i	$0.833239\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	−2.06998	−	1.71244i	−0.574110	−	0.474945i	0.304482	−	0.952518i	$-0.401517\pi$
$13$	−2.06998	−	1.71244i	−0.574110	−	0.474945i	−0.878592	+	0.477573i	$0.841517\pi$
$14$	2.73510	+	3.30617i	0.730987	+	0.883612i
$15$	−1.20447	+	1.88394i	−0.310994	+	0.486432i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.0331730	−	0.262591i	0.00804563	−	0.0636877i	−0.987581	−	0.157113i	$-0.949781\pi$
$17$	0.0331730	−	0.262591i	0.00804563	−	0.0636877i	0.995626	+	0.0934248i	$0.0297815\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−1.89036	+	4.01721i	−0.433678	+	0.921612i	0.561859	+	0.827233i	$0.310087\pi$
$19$	−1.89036	+	4.01721i	−0.433678	+	0.921612i	−0.995536	+	0.0943789i	$0.969913\pi$
$20$	1.72769	−	1.41953i	0.386324	−	0.317418i
$21$	−3.76012	−	2.06714i	−0.820525	−	0.451088i
$22$	0.369876	+	2.92787i	0.0788578	+	0.624224i
$23$	−0.891511	−	2.25170i	−0.185893	−	0.469512i	0.806706	−	0.590953i	$-0.201248\pi$
$23$	−0.891511	−	2.25170i	−0.185893	−	0.469512i	−0.992599	+	0.121442i	$0.961248\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	2.15921	−	4.50975i	0.431841	−	0.901950i
$26$	−2.17343	−	1.57909i	−0.426244	−	0.309684i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	2.93730	+	3.12791i	0.555098	+	0.591119i
$29$	4.44237	−	4.17166i	0.824927	−	0.774658i	−0.151967	−	0.988386i	$-0.548561\pi$
$29$	4.44237	−	4.17166i	0.824927	−	0.774658i	0.976893	+	0.213728i	$0.0685606\pi$
$30$	−1.08380	+	1.95586i	−0.197874	+	0.357089i
$31$	1.23119	+	0.155535i	0.221128	+	0.0279350i	0.235116	−	0.971967i	$-0.424453\pi$
$31$	1.23119	+	0.155535i	0.221128	+	0.0279350i	−0.0139885	+	0.999902i	$0.504453\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	−1.42172	−	2.58610i	−0.247490	−	0.450183i
$34$	0.0166193	−	0.264156i	0.00285018	−	0.0453024i
$35$	8.90901	+	3.56195i	1.50590	+	0.602079i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	1.68331	+	6.55607i	0.276735	+	1.07781i	0.943187	+	0.332263i	$0.107812\pi$
$37$	1.68331	+	6.55607i	0.276735	+	1.07781i	−0.666452	+	0.745548i	$0.732188\pi$
$38$	−1.63438	+	4.12798i	−0.265132	+	0.669647i
$39$	2.60210	+	0.668106i	0.416669	+	0.106983i
$40$	1.63515	−	1.52522i	0.258540	−	0.241158i
$41$	3.23394	+	1.28041i	0.505056	+	0.199966i	0.606815	−	0.794843i	$-0.292447\pi$
$41$	3.23394	+	1.28041i	0.505056	+	0.199966i	−0.101759	+	0.994809i	$0.532447\pi$
$42$	−3.88250	−	1.82696i	−0.599082	−	0.281907i
$43$	−1.43314	−	0.465656i	−0.218552	−	0.0710119i	0.197694	−	0.980264i	$-0.436655\pi$
$43$	−1.43314	−	0.465656i	−0.218552	−	0.0710119i	−0.416247	+	0.909252i	$0.636655\pi$
$44$	0.552989	+	2.89887i	0.0833662	+	0.437021i
$45$	0.287695	−	2.21748i	0.0428871	−	0.330563i
$46$	−1.03114	−	2.19128i	−0.152033	−	0.323086i
$47$	−5.74495	−	1.09591i	−0.837987	−	0.159855i	−0.249514	−	0.968371i	$-0.580271\pi$
$47$	−5.74495	−	1.09591i	−0.837987	−	0.159855i	−0.588473	+	0.808517i	$0.700271\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	−3.52637	+	10.8530i	−0.503767	+	1.55044i
$50$	1.87178	−	4.63643i	0.264709	−	0.655690i
$51$	0.0817901	+	0.251724i	0.0114529	+	0.0352484i
$52$	−2.26829	−	1.43950i	−0.314555	−	0.199623i
$53$	4.89135	−	8.89733i	0.671879	−	1.22214i	−0.292157	−	0.956370i	$-0.594373\pi$
$53$	4.89135	−	8.89733i	0.671879	−	1.22214i	0.964036	−	0.265772i	$-0.0856270\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	3.86083	+	5.35165i	0.520594	+	0.721616i
$56$	3.12791	+	2.93730i	0.417985	+	0.392514i
$57$		−	4.43976i		−	0.588061i
$58$	4.17166	−	4.44237i	0.547766	−	0.583311i
$59$	4.49260	+	7.07921i	0.584887	+	0.921634i	0.999930	+	0.0118324i	$0.00376646\pi$
$59$	4.49260	+	7.07921i	0.584887	+	0.921634i	−0.415043	+	0.909802i	$0.636234\pi$
$60$	−0.958855	+	2.02005i	−0.123788	+	0.260787i
$61$	0.0151556	−	0.00600053i	0.00194048	−	0.000768289i	−0.367154	−	0.930160i	$-0.619668\pi$
$61$	0.0151556	−	0.00600053i	0.00194048	−	0.000768289i	0.369095	+	0.929392i	$0.379668\pi$
$62$	1.23852	+	0.0779214i	0.157293	+	0.00989603i
$63$	4.28240	+	0.269426i	0.539532	+	0.0339445i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−5.95727	−	0.772894i	−0.738909	−	0.0958657i
$66$	−1.58130	−	2.49173i	−0.194645	−	0.306711i
$67$	4.88445	−	5.20141i	0.596730	−	0.635453i	−0.357718	−	0.933830i	$-0.616445\pi$
$67$	4.88445	−	5.20141i	0.596730	−	0.635453i	0.954448	+	0.298376i	$0.0964451\pi$
$68$		−	0.264678i		−	0.0320970i
$69$	1.76539	+	1.65781i	0.212528	+	0.199577i
$70$	9.11508	+	2.99552i	1.08946	+	0.358033i
$71$	0.522593	−	2.73953i	0.0620204	−	0.325122i	−0.937732	−	0.347359i	$-0.887079\pi$
$71$	0.522593	−	2.73953i	0.0620204	−	0.325122i	0.999753	+	0.0222364i	$0.00707866\pi$
$72$	0.481754	−	0.876307i	0.0567752	−	0.103274i
$73$	−11.8861	−	7.54317i	−1.39117	−	0.882861i	−0.391857	−	0.920026i	$-0.628167\pi$
$73$	−11.8861	−	7.54317i	−1.39117	−	0.882861i	−0.999309	+	0.0371650i	$0.988167\pi$
$74$	2.09165	+	6.43743i	0.243149	+	0.748336i
$75$	−0.0335518	+	4.99989i	−0.00387423	+	0.577337i
$76$	−1.37196	+	4.22246i	−0.157375	+	0.484350i
$77$	−9.75698	+	8.07167i	−1.11191	+	0.919853i
$78$	2.63892	+	0.503400i	0.298798	+	0.0569988i
$79$	−6.18230	−	13.1381i	−0.695563	−	1.47815i	−0.869780	−	0.493439i	$-0.835740\pi$
$79$	−6.18230	−	13.1381i	−0.695563	−	1.47815i	0.174217	−	0.984707i	$-0.444260\pi$
$80$	1.53615	−	1.62488i	0.171747	−	0.181667i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	3.30795	+	1.07482i	0.365302	+	0.118694i
$83$	−2.19328	−	1.03208i	−0.240743	−	0.113285i	0.301623	−	0.953427i	$-0.402472\pi$
$83$	−2.19328	−	1.03208i	−0.240743	−	0.113285i	−0.542367	+	0.840142i	$0.682472\pi$
$84$	−3.98955	−	1.57957i	−0.435296	−	0.172346i
$85$	−0.250195	−	0.536354i	−0.0271374	−	0.0581758i
$86$	−1.45955	−	0.374750i	−0.157388	−	0.0404103i
$87$	−2.24337	+	5.66610i	−0.240514	+	0.607469i
$88$	0.733919	+	2.85842i	0.0782360	+	0.304709i
$89$	−4.00885	+	6.31694i	−0.424938	+	0.669594i	−0.987582	−	0.157105i	$-0.949784\pi$
$89$	−4.00885	+	6.31694i	−0.424938	+	0.669594i	0.562644	+	0.826699i	$0.309784\pi$
$90$	0.147891	−	2.23117i	0.0155891	−	0.235186i
$91$	0.723813	−	11.5047i	0.0758762	−	1.20602i
$92$	−1.16669	−	2.12221i	−0.121636	−	0.221256i
$93$	−1.18024	+	0.383482i	−0.122385	+	0.0397652i
$94$	−5.80243	−	0.733017i	−0.598475	−	0.0756049i
$95$	1.21121	+	9.85344i	0.124267	+	1.01094i
$96$	−0.728969	+	0.684547i	−0.0744000	+	0.0698663i
$97$	−7.32227	−	7.79743i	−0.743464	−	0.791709i	0.240391	−	0.970676i	$-0.422724\pi$
$97$	−7.32227	−	7.79743i	−0.743464	−	0.791709i	−0.983855	+	0.178967i	$0.942724\pi$
$98$	−2.83794	+	11.0531i	−0.286675	+	1.11653i
$99$	2.38752	+	1.73464i	0.239955	+	0.174338i
$100$	1.57696	−	4.74481i	0.157696	−	0.474481i
$101$	11.0187	−	8.00558i	1.09640	−	0.796585i	0.115935	−	0.993257i	$-0.463013\pi$
$101$	11.0187	−	8.00558i	1.09640	−	0.796585i	0.980469	+	0.196672i	$0.0630135\pi$
$102$	0.0974346	+	0.246092i	0.00964746	+	0.0243667i
$103$	0.297562	+	2.35545i	0.0293197	+	0.232089i	0.999964	−	0.00842832i	$-0.00268285\pi$
$103$	0.297562	+	2.35545i	0.0293197	+	0.232089i	−0.970645	+	0.240518i	$0.922683\pi$
$104$	−2.35420	−	1.29423i	−0.230848	−	0.126910i
$105$	−9.57771	+	0.570323i	−0.934689	+	0.0556578i
$106$	4.32303	−	9.18691i	0.419890	−	0.892311i
$107$	1.27848	−	1.75968i	0.123596	−	0.170115i	−0.742735	−	0.669585i	$-0.766472\pi$
$107$	1.27848	−	1.75968i	0.123596	−	0.170115i	0.866331	+	0.499470i	$0.166472\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	−18.1415	+	4.65796i	−1.73765	+	0.446151i	−0.978749	−	0.205061i	$-0.934261\pi$
$109$	−18.1415	+	4.65796i	−1.73765	+	0.446151i	−0.758896	+	0.651212i	$0.774261\pi$
$110$	4.18925	+	5.09866i	0.399429	+	0.486138i
$111$	−4.31454	−	5.21539i	−0.409518	−	0.495023i
$112$	3.30617	+	2.73510i	0.312404	+	0.258443i
$113$	−11.8270	+	7.50566i	−1.11259	+	0.706073i	−0.959379	−	0.282120i	$-0.908962\pi$
$113$	−11.8270	+	7.50566i	−1.11259	+	0.706073i	−0.153214	+	0.988193i	$0.548962\pi$
$114$	−0.278775	−	4.43100i	−0.0261097	−	0.415001i
$115$	−4.37031	−	3.19767i	−0.407533	−	0.298185i
$116$	3.88449	−	4.69554i	0.360666	−	0.435970i
$117$	−2.63892	+	0.503400i	−0.243968	+	0.0465394i
$118$	4.92824	+	6.78314i	0.453682	+	0.624439i
$119$	0.995222	−	0.547128i	0.0912318	−	0.0501551i
$120$	−0.830122	+	2.07627i	−0.0757795	+	0.189537i
$121$	2.27271	−	0.287110i	0.206610	−	0.0261009i
$122$	0.0147489	−	0.00694032i	0.00133530	−	0.000628347i
$123$	−3.47133	+	0.218397i	−0.312999	+	0.0196922i
$124$	1.24097			0.111443
$125$	−1.28955	−	11.1057i	−0.115341	−	0.993326i
$126$	4.29087			0.382261
$127$	−14.1050	+	0.887413i	−1.25162	+	0.0787452i	−0.674722	−	0.738072i	$-0.735737\pi$
$127$	−14.1050	+	0.887413i	−1.25162	+	0.0787452i	−0.576897	+	0.816817i	$0.695737\pi$
$128$	0.904827	−	0.425779i	0.0799762	−	0.0376339i
$129$	1.49501	−	0.188864i	0.131629	−	0.0166286i
$130$	−5.99405	−	0.397309i	−0.525713	−	0.0348463i
$131$	10.4849	−	5.76414i	0.916073	−	0.503616i	0.0473306	−	0.998879i	$-0.484929\pi$
$131$	10.4849	−	5.76414i	0.916073	−	0.503616i	0.868743	+	0.495264i	$0.164929\pi$
$132$	−1.73464	−	2.38752i	−0.150981	−	0.207807i
$133$	−18.7130	+	3.56970i	−1.62262	+	0.309532i
$134$	4.54821	−	5.49784i	0.392906	−	0.474941i
$135$	0.683844	+	2.12893i	0.0588559	+	0.183229i
$136$	−0.0166193	−	0.264156i	−0.00142509	−	0.0226512i
$137$	−4.65177	+	2.95210i	−0.397427	+	0.252215i	−0.719489	−	0.694504i	$-0.755624\pi$
$137$	−4.65177	+	2.95210i	−0.397427	+	0.252215i	0.322062	+	0.946719i	$0.395624\pi$
$138$	1.86600	+	1.54369i	0.158845	+	0.131408i
$139$	12.7110	+	15.3649i	1.07813	+	1.30323i	0.950265	+	0.311443i	$0.100812\pi$
$139$	12.7110	+	15.3649i	1.07813	+	1.30323i	0.127865	+	0.991792i	$0.459188\pi$
$140$	9.28519	+	2.41727i	0.784741	+	0.204296i
$141$	5.66480	−	1.45447i	0.477062	−	0.122489i
$142$	0.349545	−	2.76694i	0.0293332	−	0.232196i
$143$	4.66010	−	6.41408i	0.389697	−	0.536372i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	3.43309	−	13.1871i	0.285102	−	1.09513i
$146$	−12.3363	−	6.78195i	−1.02096	−	0.561278i
$147$	−1.43025	−	11.3216i	−0.117965	−	0.933789i
$148$	2.49173	+	6.29340i	0.204819	+	0.517314i
$149$	15.5440	−	11.2934i	1.27341	−	0.925189i	0.274080	−	0.961707i	$-0.411627\pi$
$149$	15.5440	−	11.2934i	1.27341	−	0.925189i	0.999333	+	0.0365184i	$0.0116268\pi$
$150$	0.280460	+	4.99213i	0.0228995	+	0.407606i
$151$	−13.1681	−	9.56716i	−1.07160	−	0.778565i	−0.0954028	−	0.995439i	$-0.530414\pi$
$151$	−13.1681	−	9.56716i	−1.07160	−	0.778565i	−0.976200	+	0.216874i	$0.930414\pi$
$152$	−1.10412	+	4.30028i	−0.0895562	+	0.348798i
$153$	−0.181185	−	0.192942i	−0.0146479	−	0.0155985i
$154$	−9.23090	+	8.66839i	−0.743847	+	0.698519i
$155$	2.51476	−	1.17306i	0.201990	−	0.0942228i
$156$	2.66532	+	0.336708i	0.213396	+	0.0269582i
$157$	−14.9595	+	4.86063i	−1.19390	+	0.387920i	−0.837512	−	0.546419i	$-0.815991\pi$
$157$	−14.9595	+	4.86063i	−1.19390	+	0.387920i	−0.356384	+	0.934339i	$0.615991\pi$
$158$	−6.99504	−	12.7239i	−0.556496	−	1.01226i
$159$	−0.637526	+	10.1332i	−0.0505591	+	0.803614i
$160$	1.43110	−	1.71813i	0.113138	−	0.135830i
$161$	5.56803	−	8.77382i	0.438823	−	0.691474i
$162$	−0.248690	−	0.968583i	−0.0195389	−	0.0760991i
$163$	3.40085	−	8.58957i	0.266375	−	0.672787i	−0.733602	−	0.679580i	$-0.762162\pi$
$163$	3.40085	−	8.58957i	0.266375	−	0.672787i	0.999977	+	0.00679280i	$0.00216223\pi$
$164$	3.36892	+	0.864990i	0.263068	+	0.0675444i
$165$	−5.77200	−	3.19845i	−0.449350	−	0.248999i
$166$	−2.25375	−	0.892324i	−0.174925	−	0.0692578i
$167$	−6.89254	−	3.24338i	−0.533361	−	0.250980i	0.140186	−	0.990125i	$-0.455230\pi$
$167$	−6.89254	−	3.24338i	−0.533361	−	0.250980i	−0.673547	+	0.739145i	$0.735230\pi$
$168$	−4.08086	−	1.32595i	−0.314845	−	0.102299i
$169$	−1.08357	−	5.68028i	−0.0833517	−	0.436945i
$170$	−0.283379	−	0.519586i	−0.0217342	−	0.0398504i
$171$	1.89036	+	4.01721i	0.144559	+	0.307204i
$172$	−1.48020	−	0.282364i	−0.112865	−	0.0215301i
$173$	−3.36587	+	2.78449i	−0.255902	+	0.211701i	−0.756525	−	0.653965i	$-0.773104\pi$
$173$	−3.36587	+	2.78449i	−0.255902	+	0.211701i	0.500623	+	0.865666i	$0.333104\pi$
$174$	−1.88316	+	5.79578i	−0.142762	+	0.439377i
$175$	21.1008	−	3.87864i	1.59507	−	0.293197i
$176$	0.911952	+	2.80670i	0.0687410	+	0.211563i
$177$	−7.07921	−	4.49260i	−0.532106	−	0.337685i
$178$	−3.60430	+	6.55619i	−0.270154	+	0.491408i
$179$	3.00670	−	15.7617i	0.224731	−	1.17808i	−0.673712	−	0.738994i	$-0.735301\pi$
$179$	3.00670	−	15.7617i	0.224731	−	1.17808i	0.898443	−	0.439089i	$-0.144699\pi$
$180$	0.00750245	−	2.23606i	0.000559200	−	0.166666i
$181$	−17.0340	−	15.9960i	−1.26613	−	1.18897i	−0.972461	−	0.233064i	$-0.925125\pi$
$181$	−17.0340	−	15.9960i	−1.26613	−	1.18897i	−0.293666	−	0.955908i	$-0.594875\pi$
$182$		−	11.5274i		−	0.854470i
$183$	−0.0111583	+	0.0118824i	−0.000824845	+	0.000878371i
$184$	−1.29765	−	2.04476i	−0.0956638	−	0.150742i
$185$	10.9983	+	10.3978i	0.808614	+	0.764461i
$186$	−1.15383	+	0.456833i	−0.0846028	+	0.0334966i
$187$	0.779562	+	0.0490459i	0.0570072	+	0.00358659i
$188$	−5.83700	−	0.367233i	−0.425707	−	0.0267832i
$189$	−3.98955	+	1.57957i	−0.290197	+	0.114897i
$190$	1.82752	+	9.75795i	0.132582	+	0.707916i
$191$	−3.25247	−	5.12507i	−0.235340	−	0.370837i	0.706047	−	0.708165i	$-0.250477\pi$
$191$	−3.25247	−	5.12507i	−0.235340	−	0.370837i	−0.941387	+	0.337328i	$0.890477\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$			9.67880i			0.696695i	0.937365	+	0.348348i	$0.113257\pi$
$193$			9.67880i			0.696695i	−0.937365	+	0.348348i	$0.886743\pi$
$194$	−7.79743	−	7.32227i	−0.559823	−	0.525708i
$195$	5.71938	−	1.83715i	0.409573	−	0.131561i
$196$	−2.13831	+	11.2094i	−0.152737	+	0.800674i
$197$	−3.89452	+	7.08410i	−0.277473	+	0.504721i	−0.977919	−	0.208984i	$-0.932984\pi$
$197$	−3.89452	+	7.08410i	−0.277473	+	0.504721i	0.700446	+	0.713705i	$0.252984\pi$
$198$	2.49173	+	1.58130i	0.177080	+	0.112378i
$199$	6.48738	+	19.9661i	0.459879	+	1.41536i	0.865311	+	0.501236i	$0.167121\pi$
$199$	6.48738	+	19.9661i	0.459879	+	1.41536i	−0.405432	+	0.914125i	$0.632879\pi$
$200$	1.27592	−	4.83446i	0.0902211	−	0.341848i
$201$	−2.20493	+	6.78607i	−0.155524	+	0.478653i
$202$	10.4943	−	8.68165i	0.738377	−	0.610839i
$203$	25.6856	+	4.89979i	1.80277	+	0.343898i
$204$	0.112695	+	0.239488i	0.00789020	+	0.0167675i
$205$	7.64455	−	1.43171i	0.533919	−	0.0999950i
$206$	0.444875	+	2.33212i	0.0309959	+	0.162486i
$207$	−2.30324	−	0.748367i	−0.160086	−	0.0520151i
$208$	−2.43082	−	1.14386i	−0.168547	−	0.0793122i
$209$	−12.1823	−	4.82330i	−0.842665	−	0.333634i
$210$	−9.52300	+	1.17059i	−0.657150	+	0.0807782i
$211$	−8.39476	−	2.15541i	−0.577919	−	0.148384i	−0.0515946	−	0.998668i	$-0.516430\pi$
$211$	−8.39476	−	2.15541i	−0.577919	−	0.148384i	−0.526325	+	0.850284i	$0.676430\pi$
$212$	3.73765	−	9.44022i	0.256703	−	0.648357i
$213$	0.693578	+	2.70131i	0.0475232	+	0.185091i
$214$	1.16547	−	1.83649i	0.0796699	−	0.125540i
$215$	−3.26645	+	0.827011i	−0.222770	+	0.0564017i
$216$	−0.0627905	+	0.998027i	−0.00427235	+	0.0679071i
$217$	2.56527	+	4.66621i	0.174142	+	0.316763i
$218$	−17.8133	+	5.78788i	−1.20647	+	0.392005i
$219$	13.9666	+	1.76439i	0.943777	+	0.119227i
$220$	4.50113	+	4.82556i	0.303466	+	0.325339i
$221$	−0.518339	+	0.486753i	−0.0348673	+	0.0327426i
$222$	−4.63351	−	4.93418i	−0.310981	−	0.331161i
$223$	−0.956873	+	3.72678i	−0.0640770	+	0.249563i	−0.992550	−	0.121836i	$-0.961122\pi$
$223$	−0.956873	+	3.72678i	−0.0640770	+	0.249563i	0.928473	+	0.371399i	$0.121122\pi$
$224$	3.47139	+	2.52211i	0.231942	+	0.168516i
$225$	−2.09849	−	4.53832i	−0.139899	−	0.302555i
$226$	−11.3324	+	8.23347i	−0.753820	+	0.547682i
$227$	−0.882687	−	2.22941i	−0.0585860	−	0.147971i	0.897535	−	0.440943i	$-0.145356\pi$
$227$	−0.882687	−	2.22941i	−0.0585860	−	0.147971i	−0.956121	+	0.292972i	$0.905356\pi$
$228$	−0.556449	−	4.40475i	−0.0368518	−	0.291712i
$229$	20.4388	+	11.2363i	1.35063	+	0.742517i	0.982324	−	0.187187i	$-0.0599371\pi$
$229$	20.4388	+	11.2363i	1.35063	+	0.742517i	0.368308	+	0.929704i	$0.379937\pi$
$230$	−4.56247	−	2.91695i	−0.300840	−	0.192338i
$231$	5.39163	−	11.4578i	0.354743	−	0.753867i
$232$	3.58199	−	4.93018i	0.235169	−	0.323682i
$233$	−3.11919	+	24.6910i	−0.204345	+	1.61756i	0.472429	+	0.881369i	$0.343377\pi$
$233$	−3.11919	+	24.6910i	−0.204345	+	1.61756i	−0.676775	+	0.736190i	$0.736623\pi$
$234$	−2.60210	+	0.668106i	−0.170105	+	0.0436754i
$235$	−12.1755	+	4.77341i	−0.794240	+	0.311383i
$236$	5.34443	+	6.46031i	0.347893	+	0.420531i
$237$	11.1878	+	9.25537i	0.726727	+	0.601201i
$238$	0.958904	−	0.608539i	0.0621565	−	0.0394457i
$239$	1.09157	+	17.3501i	0.0706081	+	1.12228i	0.860639	+	0.509216i	$0.170065\pi$
$239$	1.09157	+	17.3501i	0.0706081	+	1.12228i	−0.790031	+	0.613067i	$0.789935\pi$
$240$	−0.698114	+	2.12430i	−0.0450631	+	0.137123i
$241$	−16.5475	+	20.0025i	−1.06592	+	1.28847i	−0.110287	+	0.993900i	$0.535177\pi$
$241$	−16.5475	+	20.0025i	−1.06592	+	1.28847i	−0.955629	+	0.294572i	$0.904823\pi$
$242$	2.25020	−	0.429248i	0.144648	−	0.0275931i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	0.0142840	−	0.00785272i	0.000914442	−	0.000502719i
$245$	6.26287	+	24.7365i	0.400120	+	1.58036i
$246$	−3.45076	+	0.435933i	−0.220013	+	0.0277941i
$247$	10.7923	−	5.07845i	0.686695	−	0.323134i
$248$	1.23852	−	0.0779214i	0.0786464	−	0.00494801i
$249$	2.42397			0.153613
$250$	−1.98434	−	11.0028i	−0.125501	−	0.695880i
$251$	16.0980			1.01610			0.508049	−	0.861328i	$-0.330367\pi$
$251$	16.0980			1.01610			0.508049	+	0.861328i	$0.330367\pi$
$252$	4.28240	−	0.269426i	0.269766	−	0.0169722i
$253$	6.46677	−	3.04303i	0.406562	−	0.191314i
$254$	−14.0215	+	1.77132i	−0.879786	+	0.111143i
$255$	0.454751	+	0.378780i	0.0284776	+	0.0237201i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	8.07292	+	11.1114i	0.503575	+	0.693112i	0.982819	−	0.184570i	$-0.0590892\pi$
$257$	8.07292	+	11.1114i	0.503575	+	0.693112i	−0.479244	+	0.877682i	$0.659089\pi$
$258$	1.48020	−	0.282364i	0.0921535	−	0.0175792i
$259$	−18.5131	+	22.3786i	−1.15035	+	1.39054i
$260$	−6.00717	−	0.0201554i	−0.372549	−	0.00124998i
$261$	−0.382648	−	6.08202i	−0.0236853	−	0.376467i
$262$	10.1023	−	6.41112i	0.624123	−	0.396081i
$263$	−6.29784	−	5.21003i	−0.388342	−	0.321264i	0.422681	−	0.906278i	$-0.361089\pi$
$263$	−6.29784	−	5.21003i	−0.388342	−	0.321264i	−0.811023	+	0.585014i	$0.801089\pi$
$264$	−1.88113	−	2.27389i	−0.115775	−	0.139948i
$265$	−1.34952	−	22.6631i	−0.0829003	−	1.39219i
$266$	−18.4519	+	4.73765i	−1.13136	+	0.290484i
$267$	0.937696	−	7.42263i	0.0573860	−	0.454257i
$268$	4.19402	−	5.77258i	0.256191	−	0.352616i
$269$	3.49671	−	7.43089i	0.213198	−	0.453069i	−0.769411	−	0.638754i	$-0.779450\pi$
$269$	3.49671	−	7.43089i	0.213198	−	0.453069i	0.982609	+	0.185685i	$0.0594503\pi$
$270$	0.816171	+	2.08179i	0.0496706	+	0.126694i
$271$	−9.76395	−	5.36778i	−0.593118	−	0.326069i	0.156769	−	0.987635i	$-0.449892\pi$
$271$	−9.76395	−	5.36778i	−0.593118	−	0.326069i	−0.749887	+	0.661566i	$0.769892\pi$
$272$	−0.0331730	−	0.262591i	−0.00201141	−	0.0159219i
$273$	4.24353	+	10.7179i	0.256830	+	0.648679i
$274$	−4.45722	+	3.23836i	−0.269271	+	0.195637i
$275$	13.6827	+	5.52388i	0.825101	+	0.333102i
$276$	1.95925	+	1.42348i	0.117933	+	0.0856833i
$277$	2.61044	−	10.1670i	0.156846	−	0.610874i	−0.840741	−	0.541438i	$-0.817880\pi$
$277$	2.61044	−	10.1670i	0.156846	−	0.610874i	0.997586	−	0.0694361i	$-0.0221200\pi$
$278$	13.6506	+	14.5365i	0.818711	+	0.871839i
$279$	0.904631	−	0.849505i	0.0541588	−	0.0508585i
$280$	9.41864	+	1.82948i	0.562872	+	0.109332i
$281$	32.4630	+	4.10103i	1.93658	+	0.244647i	0.995592	−	0.0937938i	$-0.0298994\pi$
$281$	32.4630	+	4.10103i	1.93658	+	0.244647i	0.940988	+	0.338441i	$0.109899\pi$
$282$	5.56230	−	1.80730i	0.331230	−	0.107623i
$283$	−13.0072	−	23.6600i	−0.773199	−	1.40644i	−0.909469	−	0.415771i	$-0.863512\pi$
$283$	−13.0072	−	23.6600i	−0.773199	−	1.40644i	0.136271	−	0.990672i	$-0.456488\pi$
$284$	0.175118	−	2.78342i	0.0103914	−	0.165166i
$285$	−5.29132	−	8.39995i	−0.313431	−	0.497570i
$286$	4.24816	−	6.69404i	0.251199	−	0.395827i
$287$	3.71156	+	14.4556i	0.219087	+	0.853286i
$288$	0.368125	−	0.929776i	0.0216919	−	0.0547876i
$289$	16.3981	+	4.21031i	0.964592	+	0.247665i
$290$	2.59828	−	13.3767i	0.152576	−	0.785506i
$291$	9.94537	+	3.93765i	0.583008	+	0.230829i
$292$	−12.7378	−	5.99396i	−0.745424	−	0.350770i
$293$	−24.7603	−	8.04512i	−1.44651	−	0.470001i	−0.522593	−	0.852582i	$-0.675035\pi$
$293$	−24.7603	−	8.04512i	−1.44651	−	0.470001i	−0.923922	+	0.382581i	$0.875035\pi$
$294$	−2.13831	−	11.2094i	−0.124709	−	0.653748i
$295$	16.9370	+	8.03945i	0.986108	+	0.468075i
$296$	2.88198	+	6.12452i	0.167512	+	0.355980i
$297$	−2.89887	−	0.552989i	−0.168209	−	0.0320876i
$298$	14.8042	−	12.2471i	0.857584	−	0.709455i
$299$	−2.01049	+	6.18764i	−0.116270	+	0.357841i
$300$	0.593365	+	4.96467i	0.0342579	+	0.286635i
$301$	−1.99807	−	6.14943i	−0.115167	−	0.354447i
$302$	−13.7428	−	8.72145i	−0.790810	−	0.501863i
$303$	−6.56144	+	11.9352i	−0.376945	+	0.685660i
$304$	−0.831928	+	4.36112i	−0.0477143	+	0.250127i
$305$	0.0215227	−	0.0294154i	0.00123239	−	0.00168432i
$306$	−0.192942	−	0.181185i	−0.0110298	−	0.0103576i
$307$			18.6547i			1.06468i	0.846531	+	0.532339i	$0.178687\pi$
$307$			18.6547i			1.06468i	−0.846531	+	0.532339i	$0.821313\pi$
$308$	−8.66839	+	9.23090i	−0.493928	+	0.525979i
$309$	−1.27214	−	2.00458i	−0.0723697	−	0.114036i
$310$	2.43614	−	1.32865i	0.138363	−	0.0754624i
$311$	−29.4915	+	11.6765i	−1.67231	+	0.662115i	−0.997142	−	0.0755482i	$-0.975929\pi$
$311$	−29.4915	+	11.6765i	−1.67231	+	0.662115i	−0.675169	+	0.737663i	$0.735929\pi$
$312$	2.68120	+	0.168687i	0.151793	+	0.00955001i
$313$	6.21104	+	0.390766i	0.351069	+	0.0220874i	0.237346	−	0.971425i	$-0.423722\pi$
$313$	6.21104	+	0.390766i	0.351069	+	0.0220874i	0.113723	+	0.993513i	$0.463722\pi$
$314$	−14.6248	+	5.79035i	−0.825323	+	0.326768i
$315$	8.42334	−	4.59404i	0.474602	−	0.258845i
$316$	−7.78018	−	12.2596i	−0.437670	−	0.689657i
$317$	18.8424	−	20.0651i	1.05829	−	1.12697i	0.0666751	−	0.997775i	$-0.478761\pi$
$317$	18.8424	−	20.0651i	1.05829	−	1.12697i	0.991619	−	0.129194i	$-0.0412391\pi$
$318$			10.1532i			0.569364i
$319$	13.1100	+	12.3112i	0.734022	+	0.689292i
$320$	1.32039	−	1.80460i	0.0738120	−	0.100880i
$321$	−0.407571	+	2.13656i	−0.0227484	+	0.119251i
$322$	5.00613	−	9.10612i	0.278981	−	0.507464i
$323$	0.992177	+	0.629655i	0.0552062	+	0.0350349i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−12.1922	+	5.63760i	−0.676302	+	0.312718i
$326$	2.85480	−	8.78616i	0.158113	−	0.486620i
$327$	14.4317	−	11.9389i	0.798075	−	0.660225i
$328$	3.41658	+	0.651748i	0.188649	+	0.0359867i
$329$	−10.6851	−	22.7069i	−0.589087	−	1.25187i
$330$	−5.96145	−	2.82971i	−0.328167	−	0.155771i
$331$	−1.45394	−	7.62180i	−0.0799155	−	0.418932i	−0.999652	−	0.0263945i	$-0.991597\pi$
$331$	−1.45394	−	7.62180i	−0.0799155	−	0.418932i	0.919736	−	0.392537i	$-0.128403\pi$
$332$	−2.30534	−	0.749049i	−0.126522	−	0.0411094i
$333$	6.12452	+	2.88198i	0.335622	+	0.157932i
$334$	−7.08259	−	2.80420i	−0.387542	−	0.153439i
$335$	3.04224	−	15.6623i	0.166215	−	0.855722i
$336$	−4.15606	−	1.06710i	−0.226732	−	0.0582149i
$337$	3.03627	−	7.66875i	0.165396	−	0.417743i	−0.823313	−	0.567587i	$-0.807877\pi$
$337$	3.03627	−	7.66875i	0.165396	−	0.417743i	0.988710	+	0.149844i	$0.0478770\pi$
$338$	−1.43810	−	5.60104i	−0.0782224	−	0.304656i
$339$	7.50566	−	11.8270i	0.407651	−	0.642356i
$340$	−0.315445	−	0.500767i	−0.0171074	−	0.0271579i
$341$	−0.229957	+	3.65506i	−0.0124529	+	0.197933i
$342$	2.13887	+	3.89059i	0.115657	+	0.210379i
$343$	−18.0030	+	5.84953i	−0.972071	+	0.315845i
$344$	−1.49501	−	0.188864i	−0.0806057	−	0.0101829i
$345$	5.31588	+	1.03255i	0.286197	+	0.0555909i
$346$	−3.18439	+	2.99034i	−0.171194	+	0.160762i
$347$	10.3923	+	11.0667i	0.557890	+	0.594093i	0.944647	−	0.328089i	$-0.106405\pi$
$347$	10.3923	+	11.0667i	0.557890	+	0.594093i	−0.386756	+	0.922182i	$0.626405\pi$
$348$	−1.51553	+	5.90259i	−0.0812408	+	0.316412i
$349$	13.4323	+	9.75911i	0.719012	+	0.522393i	0.886068	−	0.463554i	$-0.153426\pi$
$349$	13.4323	+	9.75911i	0.719012	+	0.522393i	−0.167056	+	0.985947i	$0.553426\pi$
$350$	20.8157	−	5.19592i	1.11264	−	0.277733i
$351$	2.17343	−	1.57909i	0.116009	−	0.0842854i
$352$	1.08639	+	2.74390i	0.0579046	+	0.146250i
$353$	−0.508390	−	4.02432i	−0.0270589	−	0.214193i	0.972788	−	0.231697i	$-0.0744279\pi$
$353$	−0.508390	−	4.02432i	−0.0270589	−	0.214193i	−0.999847	+	0.0175043i	$0.994428\pi$
$354$	−7.34733	−	4.03923i	−0.390506	−	0.214683i
$355$	−2.27624	−	5.80597i	−0.120810	−	0.308149i
$356$	−3.18552	+	6.76957i	−0.168832	+	0.358787i
$357$	−0.667548	+	0.918801i	−0.0353304	+	0.0486281i
$358$	2.01108	−	15.9194i	0.106289	−	0.841365i
$359$	28.7165	−	7.37315i	1.51560	−	0.389140i	0.602916	−	0.797805i	$-0.294005\pi$
$359$	28.7165	−	7.37315i	1.51560	−	0.389140i	0.912685	+	0.408664i	$0.134005\pi$
$360$	−0.132915	−	2.23211i	−0.00700526	−	0.117643i
$361$	−0.453506	−	0.548195i	−0.0238687	−	0.0288523i
$362$	−18.0048	−	14.8948i	−0.946310	−	0.782856i
$363$	−1.93416	+	1.22746i	−0.101517	+	0.0644248i
$364$	−0.723813	−	11.5047i	−0.0379381	−	0.603009i
$365$	−31.4783	−	0.105617i	−1.64765	−	0.00552823i
$366$	−0.0103902	+	0.0125596i	−0.000543104	+	0.000656499i
$367$	−4.66470	+	0.889839i	−0.243495	+	0.0464492i	−0.307684	−	0.951489i	$-0.599554\pi$
$367$	−4.66470	+	0.889839i	−0.243495	+	0.0464492i	0.0641889	+	0.997938i	$0.479554\pi$
$368$	−1.42348	−	1.95925i	−0.0742039	−	0.102133i
$369$	3.04796	−	1.67563i	0.158670	−	0.0872298i
$370$	11.6295	+	9.68669i	0.604590	+	0.503587i
$371$	43.2226	−	5.46029i	2.24401	−	0.283484i
$372$	−1.12287	+	0.528381i	−0.0582179	+	0.0273953i
$373$	19.8834	−	1.25096i	1.02952	−	0.0647722i	0.460968	−	0.887417i	$-0.347502\pi$
$373$	19.8834	−	1.25096i	1.02952	−	0.0647722i	0.568556	+	0.822644i	$0.307502\pi$
$374$	0.781103			0.0403899
$375$	5.89541	+	9.49969i	0.304437	+	0.490562i
$376$	−5.84854			−0.301616
$377$	−16.3393	+	1.02798i	−0.841519	+	0.0529439i
$378$	−3.88250	+	1.82696i	−0.199694	+	0.0939689i
$379$	−16.0175	+	2.02348i	−0.822763	+	0.103939i	−0.525432	−	0.850835i	$-0.676096\pi$
$379$	−16.0175	+	2.02348i	−0.822763	+	0.103939i	−0.297331	+	0.954774i	$0.596096\pi$
$380$	2.43662	+	9.62394i	0.124996	+	0.493698i
$381$	12.3848	−	6.80859i	0.634491	−	0.348814i
$382$	−3.56786	−	4.91073i	−0.182547	−	0.251255i
$383$	−6.56493	+	1.25233i	−0.335452	+	0.0639910i	−0.352356	−	0.935866i	$-0.614619\pi$
$383$	−6.56493	+	1.25233i	−0.335452	+	0.0639910i	0.0169033	+	0.999857i	$0.494619\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	−8.84019	+	26.8999i	−0.450538	+	1.37095i
$386$	0.607737	+	9.65970i	0.0309330	+	0.491666i
$387$	−1.27231	+	0.807435i	−0.0646754	+	0.0410442i
$388$	−8.24181	−	6.81822i	−0.418414	−	0.346143i
$389$	−9.12782	−	11.0336i	−0.462799	−	0.559428i	0.486550	−	0.873653i	$-0.338255\pi$
$389$	−9.12782	−	11.0336i	−0.462799	−	0.559428i	−0.949348	+	0.314225i	$0.898255\pi$
$390$	5.59274	−	2.19265i	0.283199	−	0.111029i
$391$	−0.620851	+	0.159407i	−0.0313978	+	0.00806158i
$392$	−1.43025	+	11.3216i	−0.0722385	+	0.571826i
$393$	−7.03280	+	9.67982i	−0.354758	+	0.488282i
$394$	−3.44202	+	7.31466i	−0.173406	+	0.368507i
$395$	−27.3548	−	17.4889i	−1.37637	−	0.879962i
$396$	2.58610	+	1.42172i	0.129957	+	0.0714442i
$397$	1.04958	+	8.30824i	0.0526767	+	0.416979i	0.996299	+	0.0859549i	$0.0273941\pi$
$397$	1.04958	+	8.30824i	0.0526767	+	0.416979i	−0.943622	+	0.331024i	$0.892606\pi$
$398$	7.72827	+	19.5194i	0.387383	+	0.978418i
$399$	15.4121	−	11.1976i	0.771571	−	0.560579i
$400$	0.969843	−	4.90504i	0.0484921	−	0.245252i
$401$	−3.83124	−	2.78356i	−0.191323	−	0.139004i	0.488000	−	0.872843i	$-0.337726\pi$
$401$	−3.83124	−	2.78356i	−0.191323	−	0.139004i	−0.679323	+	0.733839i	$0.737726\pi$
$402$	−1.77448	+	6.91113i	−0.0885029	+	0.344696i
$403$	−2.28220	−	2.43029i	−0.113684	−	0.121061i
$404$	9.92848	−	9.32346i	0.493960	−	0.463860i
$405$	−1.52522	−	1.63515i	−0.0757886	−	0.0812513i
$406$	25.9426	+	3.27731i	1.28751	+	0.162650i
$407$	−18.9978	+	6.17275i	−0.941684	+	0.305972i
$408$	0.127510	+	0.231939i	0.00631267	+	0.0114827i
$409$	1.27541	−	20.2721i	0.0630650	−	1.00239i	−0.831521	−	0.555493i	$-0.812530\pi$
$409$	1.27541	−	20.2721i	0.0630650	−	1.00239i	0.894586	−	0.446896i	$-0.147470\pi$
$410$	7.53957	−	1.90889i	0.372353	−	0.0942734i
$411$	2.95210	−	4.65177i	0.145616	−	0.229455i
$412$	0.590432	+	2.29958i	0.0290885	+	0.113292i
$413$	−13.2438	+	33.4501i	−0.651686	+	1.64597i
$414$	−2.34568	−	0.602268i	−0.115284	−	0.0295999i
$415$	−5.37968	+	0.661281i	−0.264078	+	0.0324610i
$416$	−2.49785	−	0.988967i	−0.122467	−	0.0484881i
$417$	−18.0433	−	8.49052i	−0.883583	−	0.415783i
$418$	−12.4611	−	4.04885i	−0.609491	−	0.198036i
$419$	5.45504	+	28.5963i	0.266496	+	1.39702i	0.823879	+	0.566765i	$0.191805\pi$
$419$	5.45504	+	28.5963i	0.266496	+	1.39702i	−0.557383	+	0.830255i	$0.688195\pi$
$420$	−9.43071	+	1.76623i	−0.460171	+	0.0861833i
$421$	9.83314	+	20.8965i	0.479238	+	1.01843i	0.987557	+	0.157264i	$0.0502672\pi$
$421$	9.83314	+	20.8965i	0.479238	+	1.01843i	−0.508319	+	0.861169i	$0.669733\pi$
$422$	−8.51354	−	1.62404i	−0.414433	−	0.0790572i
$423$	−4.50638	+	3.72800i	−0.219108	+	0.181262i
$424$	3.13752	−	9.65628i	0.152371	−	0.468951i
$425$	−1.11259	−	0.716591i	−0.0539687	−	0.0347598i
$426$	0.861826	+	2.65243i	0.0417556	+	0.128511i
$427$	0.0590543	+	0.0374770i	0.00285784	+	0.00181364i
$428$	1.04786	−	1.90604i	0.0506500	−	0.0921321i
$429$	−1.48560	+	7.78781i	−0.0717257	+	0.375999i
$430$	−3.20808	+	1.03048i	−0.154707	+	0.0496942i
$431$	10.4097	+	9.77540i	0.501420	+	0.470864i	0.893498	−	0.449068i	$-0.148244\pi$
$431$	10.4097	+	9.77540i	0.501420	+	0.470864i	−0.392078	+	0.919932i	$0.628244\pi$
$432$			1.00000i			0.0481125i
$433$	5.28192	−	5.62467i	0.253833	−	0.270304i	−0.589414	−	0.807831i	$-0.700641\pi$
$433$	5.28192	−	5.62467i	0.253833	−	0.270304i	0.843247	+	0.537527i	$0.180641\pi$
$434$	2.85320	+	4.49593i	0.136958	+	0.215811i
$435$	2.50846	+	13.3938i	0.120272	+	0.642185i
$436$	−17.4147	+	6.89497i	−0.834013	+	0.330209i
$437$	10.7308	+	0.675127i	0.513326	+	0.0322957i
$438$	14.0498	+	0.883941i	0.671328	+	0.0422363i
$439$	−11.0886	+	4.39029i	−0.529230	+	0.209537i	−0.617516	−	0.786558i	$-0.711861\pi$
$439$	−11.0886	+	4.39029i	−0.529230	+	0.209537i	0.0882859	+	0.996095i	$0.471861\pi$
$440$	4.79524	+	4.53341i	0.228604	+	0.216122i
$441$	6.11462	+	9.63511i	0.291173	+	0.458815i
$442$	−0.486753	+	0.518339i	−0.0231525	+	0.0246549i
$443$		−	23.9348i		−	1.13717i	−0.822623	−	0.568587i	$-0.807490\pi$
$443$		−	23.9348i		−	1.13717i	0.822623	−	0.568587i	$-0.192510\pi$
$444$	−4.93418	−	4.63351i	−0.234166	−	0.219896i
$445$	−0.0561305	+	16.7293i	−0.00266084	+	0.793046i
$446$	−0.720979	+	3.77950i	−0.0341393	+	0.178965i
$447$	−9.25614	+	16.8368i	−0.437800	+	0.796356i
$448$	3.62290	+	2.29916i	0.171166	+	0.108625i
$449$	−10.6975	−	32.9234i	−0.504844	−	1.55375i	−0.801032	−	0.598622i	$-0.795715\pi$
$449$	−10.6975	−	32.9234i	−0.504844	−	1.55375i	0.296187	−	0.955130i	$-0.404285\pi$
$450$	−2.37931	−	4.39760i	−0.112162	−	0.207305i
$451$	−3.17194	+	9.76224i	−0.149361	+	0.459686i
$452$	−10.7931	+	8.92879i	−0.507663	+	0.419975i
$453$	15.9883	+	3.04994i	0.751197	+	0.143299i
$454$	−1.02093	−	2.16959i	−0.0479147	−	0.101824i
$455$	−12.3419	−	22.6293i	−0.578596	−	1.06088i
$456$	−0.831928	−	4.36112i	−0.0389586	−	0.204228i
$457$	25.0784	+	8.14846i	1.17312	+	0.381169i	0.829806	−	0.558053i	$-0.188451\pi$
$457$	25.0784	+	8.14846i	1.17312	+	0.381169i	0.343312	+	0.939221i	$0.388451\pi$
$458$	21.1040	+	9.93078i	0.986124	+	0.464035i
$459$	0.246092	+	0.0974346i	0.0114866	+	0.00454786i
$460$	−4.73662	−	2.62471i	−0.220846	−	0.122378i
$461$	14.6236	+	3.75469i	0.681088	+	0.174874i	0.573356	−	0.819306i	$-0.305641\pi$
$461$	14.6236	+	3.75469i	0.681088	+	0.174874i	0.107732	+	0.994180i	$0.465641\pi$
$462$	4.66155	−	11.7737i	0.216875	−	0.547763i
$463$	−6.12041	−	23.8374i	−0.284439	−	1.10782i	−0.936787	−	0.349899i	$-0.886216\pi$
$463$	−6.12041	−	23.8374i	−0.284439	−	1.10782i	0.652348	−	0.757920i	$-0.273784\pi$
$464$	3.26535	−	5.14537i	0.151590	−	0.238868i
$465$	−1.77595	+	2.13215i	−0.0823578	+	0.0988762i
$466$	−1.56268	+	24.8381i	−0.0723898	+	1.15060i
$467$	−8.24177	−	14.9917i	−0.381384	−	0.693734i	0.614042	−	0.789273i	$-0.289542\pi$
$467$	−8.24177	−	14.9917i	−0.381384	−	0.693734i	−0.995426	+	0.0955391i	$0.969542\pi$
$468$	−2.55501	+	0.830175i	−0.118106	+	0.0383748i
$469$	30.3752	+	3.83728i	1.40260	+	0.177189i
$470$	−11.8517	+	5.52850i	−0.546679	+	0.255011i
$471$	11.4662	−	10.7675i	0.528334	−	0.496139i
$472$	5.73954	+	6.11198i	0.264184	+	0.281327i
$473$	1.10594	−	4.30735i	0.0508511	−	0.198052i
$474$	11.7469	+	8.53462i	0.539553	+	0.392008i
$475$	14.0350	+	17.1990i	0.643968	+	0.789146i
$476$	0.918801	−	0.667548i	0.0421132	−	0.0305970i
$477$	−3.73765	−	9.44022i	−0.171135	−	0.432238i
$478$	2.17884	+	17.2473i	0.0996579	+	0.788873i
$479$	7.72257	+	4.24552i	0.352853	+	0.193983i	0.648316	−	0.761372i	$-0.275474\pi$
$479$	7.72257	+	4.24552i	0.352853	+	0.193983i	−0.295462	+	0.955354i	$0.595474\pi$
$480$	−0.563351	+	2.16394i	−0.0257133	+	0.0987699i
$481$	7.74244	−	16.4535i	0.353025	−	0.750216i
$482$	−15.2589	+	21.0020i	−0.695022	+	0.956616i
$483$	−1.30240	+	10.3095i	−0.0592612	+	0.469100i
$484$	2.21880	−	0.569692i	0.100855	−	0.0258951i
$485$	−23.1466	−	6.02590i	−1.05103	−	0.273622i
$486$	0.637424	+	0.770513i	0.0289141	+	0.0349512i
$487$	13.7207	+	11.3508i	0.621746	+	0.514353i	0.894114	−	0.447840i	$-0.147807\pi$
$487$	13.7207	+	11.3508i	0.621746	+	0.514353i	−0.272368	+	0.962193i	$0.587807\pi$
$488$	0.0137628	−	0.00873412i	0.000623011	−	0.000395375i
$489$	0.580078	+	9.22008i	0.0262321	+	0.416947i
$490$	7.80373	+	24.2945i	0.352537	+	1.09751i
$491$	−27.3620	+	33.0749i	−1.23483	+	1.49265i	−0.425869	+	0.904785i	$0.640031\pi$
$491$	−27.3620	+	33.0749i	−1.23483	+	1.49265i	−0.808959	+	0.587865i	$0.799969\pi$
$492$	−3.41658	+	0.651748i	−0.154031	+	0.0293831i
$493$	−0.948075	−	1.30491i	−0.0426991	−	0.0587703i
$494$	10.4521	−	5.74608i	0.470261	−	0.258528i
$495$	6.58450	+	0.436446i	0.295951	+	0.0196168i
$496$	1.23119	−	0.155535i	0.0552820	−	0.00698374i
$497$	10.8280	−	5.09527i	0.485702	−	0.228554i
$498$	2.41919	−	0.152203i	0.108407	−	0.00682036i
$499$	18.8075			0.841939			0.420970	−	0.907075i	$-0.361690\pi$
$499$	18.8075			0.841939			0.420970	+	0.907075i	$0.361690\pi$
$500$	−2.67130	−	10.8565i	−0.119464	−	0.485519i
$501$	7.61752			0.340326
$502$	16.0662	−	1.01080i	0.717072	−	0.0451143i
$503$	19.1080	−	8.99154i	0.851983	−	0.400913i	0.0503518	−	0.998732i	$-0.483966\pi$
$503$	19.1080	−	8.99154i	0.851983	−	0.400913i	0.801631	+	0.597819i	$0.203966\pi$
$504$	4.25704	−	0.537789i	0.189623	−	0.0239550i
$505$	11.3062	−	28.2786i	0.503119	−	1.25838i
$506$	6.26294	−	3.44308i	0.278421	−	0.153063i
$507$	3.39899	+	4.67831i	0.150955	+	0.207771i
$508$	−13.8826	+	2.64825i	−0.615940	+	0.117497i
$509$	12.9084	−	15.6035i	0.572153	−	0.691614i	−0.402479	−	0.915429i	$-0.631851\pi$
$509$	12.9084	−	15.6035i	0.572153	−	0.691614i	0.974632	+	0.223816i	$0.0718513\pi$
$510$	0.477638	+	0.349479i	0.0211502	+	0.0154752i
$511$	−3.79288	−	60.2861i	−0.167787	−	2.66690i
$512$	0.844328	−	0.535827i	0.0373144	−	0.0236804i
$513$	−3.42089	−	2.83001i	−0.151036	−	0.124948i
$514$	8.75468	+	10.5826i	0.386153	+	0.466778i
$515$	3.37022	+	4.10183i	0.148509	+	0.180748i
$516$	1.45955	−	0.374750i	0.0642533	−	0.0164974i
$517$	2.16324	−	17.1238i	0.0951390	−	0.753103i
$518$	−17.0715	+	23.4968i	−0.750077	+	1.03239i
$519$	1.85995	−	3.95260i	0.0816429	−	0.173500i
$520$	−5.99658	+	0.357077i	−0.262967	+	0.0156589i
$521$	8.69864	+	4.78212i	0.381094	+	0.209508i	0.660774	−	0.750585i	$-0.270228\pi$
$521$	8.69864	+	4.78212i	0.381094	+	0.209508i	−0.279680	+	0.960093i	$0.590228\pi$
$522$	−0.763786	−	6.04599i	−0.0334300	−	0.264626i
$523$	12.6506	+	31.9519i	0.553174	+	1.39716i	0.890160	+	0.455648i	$0.150593\pi$
$523$	12.6506	+	31.9519i	0.553174	+	1.39716i	−0.336986	+	0.941510i	$0.609407\pi$
$524$	9.67982	−	7.03280i	0.422865	−	0.307229i
$525$	−17.4412	+	12.4938i	−0.761195	+	0.545274i
$526$	−6.61256	−	4.80430i	−0.288321	−	0.209478i
$527$	0.0816844	−	0.318140i	0.00355823	−	0.0138584i
$528$	−2.02019	−	2.15129i	−0.0879177	−	0.0936228i
$529$	12.4909	−	11.7298i	0.543083	−	0.509989i
$530$	−2.76989	−	22.5337i	−0.120316	−	0.978801i
$531$	8.31831	+	1.05085i	0.360984	+	0.0456029i
$532$	−18.1180	+	5.88691i	−0.785517	+	0.255230i
$533$	−4.50158	−	8.18835i	−0.194985	−	0.354677i
$534$	0.469775	−	7.46686i	0.0203291	−	0.323123i
$535$	0.321675	−	4.85299i	0.0139072	−	0.209813i
$536$	3.82328	−	6.02453i	0.165141	−	0.260220i
$537$	3.99045	+	15.5418i	0.172201	+	0.670678i
$538$	3.02322	−	7.63578i	0.130340	−	0.329202i
$539$	−32.6191	−	8.37516i	−1.40500	−	0.360744i
$540$	0.945278	+	2.02644i	0.0406783	+	0.0872040i
$541$	36.1820	+	14.3255i	1.55559	+	0.615901i	0.979492	−	0.201482i	$-0.0645758\pi$
$541$	36.1820	+	14.3255i	1.55559	+	0.615901i	0.576095	+	0.817383i	$0.304576\pi$
$542$	−10.0817	−	4.74410i	−0.433047	−	0.203777i
$543$	22.2236	+	7.22088i	0.953705	+	0.309878i
$544$	−0.0495958	−	0.259990i	−0.00212640	−	0.0111470i
$545$	−28.7721	+	30.4339i	−1.23246	+	1.30365i
$546$	4.90814	+	10.4303i	0.210049	+	0.446377i
$547$	22.6257	+	4.31608i	0.967404	+	0.184542i	0.646790	−	0.762668i	$-0.276111\pi$
$547$	22.6257	+	4.31608i	0.967404	+	0.184542i	0.320614	+	0.947210i	$0.396111\pi$
$548$	−4.24509	+	3.51184i	−0.181341	+	0.150018i
$549$	0.00503706	−	0.0155025i	0.000214977	−	0.000661630i
$550$	14.0026	+	4.65383i	0.597072	+	0.198440i
$551$	8.36079	+	25.7319i	0.356182	+	1.09621i
$552$	2.04476	+	1.29765i	0.0870309	+	0.0552315i
$553$	30.0148	−	54.5968i	1.27636	−	2.32169i
$554$	1.96689	−	10.3108i	0.0835654	−	0.438065i
$555$	−14.3788	−	4.72534i	−0.610345	−	0.200579i
$556$	14.5365	+	13.6506i	0.616483	+	0.578916i
$557$			9.16447i			0.388311i	0.980971	+	0.194156i	$0.0621967\pi$
$557$			9.16447i			0.388311i	−0.980971	+	0.194156i	$0.937803\pi$
$558$	0.849505	−	0.904631i	0.0359624	−	0.0382961i
$559$	2.16918	+	3.41807i	0.0917463	+	0.144569i
$560$	9.51493	+	1.23446i	0.402079	+	0.0521656i
$561$	−0.726251	+	0.287543i	−0.0306623	+	0.0121401i
$562$	32.6564	+	2.05457i	1.37753	+	0.0866667i
$563$	−4.41724	−	0.277909i	−0.186165	−	0.0117125i	−0.0305654	−	0.999533i	$-0.509731\pi$
$563$	−4.41724	−	0.277909i	−0.186165	−	0.0117125i	−0.155599	+	0.987820i	$0.549731\pi$
$564$	5.43784	−	2.15299i	0.228974	−	0.0906574i
$565$	−13.4313	+	28.2961i	−0.565058	+	1.19042i
$566$	−14.4672	−	22.7966i	−0.608101	−	0.958213i
$567$	2.93730	−	3.12791i	0.123355	−	0.131360i
$568$		−	2.78893i		−	0.117021i
$569$	−1.72352	−	1.61849i	−0.0722537	−	0.0678507i	0.647579	−	0.761998i	$-0.275782\pi$
$569$	−1.72352	−	1.61849i	−0.0722537	−	0.0678507i	−0.719833	+	0.694148i	$0.755782\pi$
$570$	−5.80832	−	8.05113i	−0.243284	−	0.337225i
$571$	−2.02799	+	10.6311i	−0.0848687	+	0.444897i	0.914334	+	0.404962i	$0.132715\pi$
$571$	−2.02799	+	10.6311i	−0.0848687	+	0.444897i	−0.999202	+	0.0399354i	$0.987285\pi$
$572$	3.81946	−	6.94757i	0.159700	−	0.290493i
$573$	5.12507	+	3.25247i	0.214103	+	0.135874i
$574$	4.61191	+	14.1940i	0.192497	+	0.592446i
$575$	−12.0796	−	0.841397i	−0.503752	−	0.0350887i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−30.6255	+	25.3356i	−1.27496	+	1.05474i	−0.279438	+	0.960164i	$0.590148\pi$
$577$	−30.6255	+	25.3356i	−1.27496	+	1.05474i	−0.995518	+	0.0945715i	$0.969852\pi$
$578$	16.6301	+	3.17236i	0.691720	+	0.131953i
$579$	−4.12103	−	8.75764i	−0.171264	−	0.363955i
$580$	1.75323	−	13.5134i	0.0727988	−	0.561115i
$581$	−1.94895	−	10.2167i	−0.0808559	−	0.423861i
$582$	10.1730	+	3.30541i	0.421684	+	0.137013i
$583$	27.1118	+	12.7579i	1.12286	+	0.528377i
$584$	−13.0890	−	5.18232i	−0.541628	−	0.214446i
$585$	−4.39283	+	4.09750i	−0.181621	+	0.169411i
$586$	−25.2166	−	6.47453i	−1.04169	−	0.267461i
$587$	14.3498	−	36.2435i	0.592280	−	1.49593i	−0.256159	−	0.966635i	$-0.582457\pi$
$587$	14.3498	−	36.2435i	0.592280	−	1.49593i	0.848439	−	0.529293i	$-0.177543\pi$
$588$	−2.83794	−	11.0531i	−0.117035	−	0.455820i
$589$	−2.95220	+	4.65193i	−0.121643	+	0.191679i
$590$	17.4083	+	6.96010i	0.716690	+	0.286543i
$591$	0.507601	−	8.06809i	0.0208799	−	0.331877i
$592$	3.26086	+	5.93147i	0.134020	+	0.243782i
$593$	−16.5311	+	5.37128i	−0.678851	+	0.220572i	−0.628092	−	0.778139i	$-0.716164\pi$
$593$	−16.5311	+	5.37128i	−0.678851	+	0.220572i	−0.0507590	+	0.998711i	$0.516164\pi$
$594$	−2.92787	−	0.369876i	−0.120132	−	0.0151762i
$595$	1.23087	−	2.22127i	0.0504610	−	0.0910631i
$596$	14.0060	−	13.1525i	0.573707	−	0.538747i
$597$	−14.3711	−	15.3037i	−0.588171	−	0.626338i
$598$	−1.61799	+	6.30167i	−0.0661647	+	0.257695i
$599$	−16.1592	−	11.7404i	−0.660249	−	0.479699i	0.206498	−	0.978447i	$-0.433793\pi$
$599$	−16.1592	−	11.7404i	−0.660249	−	0.479699i	−0.866747	+	0.498748i	$0.833793\pi$
$600$	0.903928	+	4.91761i	0.0369027	+	0.200761i
$601$	−4.79021	+	3.48029i	−0.195397	+	0.141964i	−0.681182	−	0.732114i	$-0.738534\pi$
$601$	−4.79021	+	3.48029i	−0.195397	+	0.141964i	0.485785	+	0.874078i	$0.338534\pi$
$602$	−2.38025	−	6.01184i	−0.0970119	−	0.245024i
$603$	−0.894290	−	7.07904i	−0.0364183	−	0.288281i
$604$	−14.2633	−	7.84133i	−0.580366	−	0.319059i
$605$	3.95775	−	3.25183i	0.160905	−	0.132206i
$606$	−5.79907	+	12.3237i	−0.235571	+	0.500614i
$607$	−14.9527	+	20.5806i	−0.606909	+	0.835339i	−0.996319	−	0.0857257i	$-0.972679\pi$
$607$	−14.9527	+	20.5806i	−0.606909	+	0.835339i	0.389409	+	0.921065i	$0.372679\pi$
$608$	−0.556449	+	4.40475i	−0.0225670	+	0.178636i
$609$	−25.3272	+	6.50293i	−1.02631	+	0.263512i
$610$	0.0196332	−	0.0307088i	0.000794926	−	0.00124336i
$611$	10.0153	+	12.1064i	0.405175	+	0.489772i
$612$	−0.203938	−	0.168712i	−0.00824371	−	0.00681979i
$613$	37.5593	−	23.8358i	1.51700	−	0.962721i	0.523125	−	0.852256i	$-0.324766\pi$
$613$	37.5593	−	23.8358i	1.51700	−	0.962721i	0.993880	−	0.110465i	$-0.0352339\pi$
$614$	1.17134	+	18.6178i	0.0472713	+	0.751355i
$615$	−6.30741	+	4.55034i	−0.254339	+	0.183488i
$616$	−8.07167	+	9.75698i	−0.325217	+	0.393120i
$617$	−36.4433	+	6.95192i	−1.46715	+	0.279874i	−0.858192	−	0.513329i	$-0.828412\pi$
$617$	−36.4433	+	6.95192i	−1.46715	+	0.279874i	−0.608958	+	0.793202i	$0.708412\pi$
$618$	−1.39550	−	1.92074i	−0.0561353	−	0.0772636i
$619$	−33.5301	+	18.4333i	−1.34769	+	0.740898i	−0.981828	−	0.189772i	$-0.939225\pi$
$619$	−33.5301	+	18.4333i	−1.34769	+	0.740898i	−0.365860	+	0.930670i	$0.619225\pi$
$620$	2.34790	−	1.47900i	0.0942940	−	0.0593980i
$621$	2.40267	−	0.303528i	0.0964158	−	0.0121801i
$622$	−28.7002	+	13.5053i	−1.15077	+	0.541512i
$623$	−32.0393	+	2.01574i	−1.28363	+	0.0807590i
$624$	2.68650			0.107546
$625$	−15.6756	−	19.4750i	−0.627026	−	0.778998i
$626$	6.22332			0.248734
$627$	13.0765	−	0.822704i	0.522225	−	0.0328556i
$628$	−14.2323	+	6.69722i	−0.567931	+	0.267248i
$629$	1.77741	−	0.224539i	0.0708698	−	0.00895294i
$630$	8.11826	−	5.11388i	0.323439	−	0.203742i
$631$	−29.1924	+	16.0487i	−1.16213	+	0.638887i	−0.941680	−	0.336511i	$-0.890753\pi$
$631$	−29.1924	+	16.0487i	−1.16213	+	0.638887i	−0.220452	+	0.975398i	$0.570753\pi$
$632$	−8.53462	−	11.7469i	−0.339489	−	0.467266i
$633$	8.51354	−	1.62404i	0.338383	−	0.0645500i
$634$	17.5453	−	21.2086i	0.696814	−	0.842303i
$635$	−25.6289	+	18.4894i	−1.01705	+	0.733730i
$636$	0.637526	+	10.1332i	0.0252795	+	0.401807i
$637$	25.8847	−	16.4269i	1.02559	−	0.650859i
$638$	13.8572	+	11.4637i	0.548612	+	0.453851i
$639$	−1.77773	−	2.14891i	−0.0703259	−	0.0850094i
$640$	1.20447	−	1.88394i	0.0476110	−	0.0744694i
$641$	−43.2031	+	11.0927i	−1.70642	+	0.438134i	−0.970923	−	0.239393i	$-0.923052\pi$
$641$	−43.2031	+	11.0927i	−1.70642	+	0.438134i	−0.735498	+	0.677527i	$0.763052\pi$
$642$	−0.272611	+	2.15794i	−0.0107591	+	0.0851669i
$643$	−12.1210	+	16.6831i	−0.478004	+	0.657916i	−0.978120	−	0.208043i	$-0.933291\pi$
$643$	−12.1210	+	16.6831i	−0.478004	+	0.657916i	0.500116	+	0.865958i	$0.333291\pi$
$644$	4.42448	−	9.40249i	0.174349	−	0.370510i
$645$	2.60345	−	2.13909i	0.102511	−	0.0842266i
$646$	1.02976	+	0.566113i	0.0405152	+	0.0222734i
$647$	−0.443436	−	3.51016i	−0.0174333	−	0.137999i	0.980996	−	0.194029i	$-0.0621556\pi$
$647$	−0.443436	−	3.51016i	−0.0174333	−	0.137999i	−0.998429	+	0.0560305i	$0.982156\pi$
$648$	−0.368125	−	0.929776i	−0.0144613	−	0.0365251i
$649$	−20.0180	+	14.5439i	−0.785776	+	0.570899i
$650$	−11.8142	+	6.39203i	−0.463389	+	0.250716i
$651$	−4.30790	−	3.12987i	−0.168840	−	0.122669i
$652$	2.29748	−	8.94807i	0.0899761	−	0.350434i
$653$	−19.3302	−	20.5846i	−0.756451	−	0.805538i	0.229370	−	0.973339i	$-0.426333\pi$
$653$	−19.3302	−	20.5846i	−0.756451	−	0.805538i	−0.985821	+	0.167801i	$0.946333\pi$
$654$	13.6536	−	12.8216i	0.533897	−	0.501363i
$655$	12.9676	−	23.4017i	0.506686	−	0.914378i
$656$	3.45076	+	0.435933i	0.134730	+	0.0170203i
$657$	−13.3886	+	4.35022i	−0.522340	+	0.169718i
$658$	−12.0898	−	21.9912i	−0.471309	−	0.857307i
$659$	−2.09956	+	33.3715i	−0.0817872	+	1.29997i	0.716455	+	0.697633i	$0.245764\pi$
$659$	−2.09956	+	33.3715i	−0.0817872	+	1.29997i	−0.798242	+	0.602337i	$0.794236\pi$
$660$	−6.12736	−	2.44981i	−0.238507	−	0.0953586i
$661$	12.2427	−	19.2914i	0.476186	−	0.750349i	−0.518302	−	0.855197i	$-0.673436\pi$
$661$	12.2427	−	19.2914i	0.476186	−	0.750349i	0.994488	+	0.104849i	$0.0334358\pi$
$662$	−1.92964	−	7.51546i	−0.0749977	−	0.292097i
$663$	0.261758	−	0.661126i	0.0101658	−	0.0256760i
$664$	−2.34782	−	0.602818i	−0.0911131	−	0.0233939i
$665$	−31.1503	+	29.0560i	−1.20796	+	1.12674i
$666$	6.29340	+	2.49173i	0.243864	+	0.0965526i
$667$	−13.3537	−	6.28380i	−0.517059	−	0.243310i
$668$	−7.24469	−	2.35394i	−0.280306	−	0.0910768i
$669$	−0.720979	−	3.77950i	−0.0278747	−	0.146124i
$670$	2.05279	−	15.8224i	0.0793063	−	0.611273i
$671$	0.0204818	+	0.0435261i	0.000790693	+	0.00168031i
$672$	−4.21487	−	0.804029i	−0.162592	−	0.0310161i
$673$	1.42086	−	1.17544i	0.0547703	−	0.0453099i	−0.609636	−	0.792681i	$-0.708684\pi$
$673$	1.42086	−	1.17544i	0.0547703	−	0.0453099i	0.664406	+	0.747371i	$0.268684\pi$
$674$	2.54876	−	7.84427i	0.0981744	−	0.302150i
$675$	3.83109	+	3.21290i	0.147459	+	0.123665i
$676$	−1.78696	−	5.49969i	−0.0687291	−	0.211526i
$677$	−34.4096	−	21.8370i	−1.32247	−	0.839265i	−0.328040	−	0.944664i	$-0.606388\pi$
$677$	−34.4096	−	21.8370i	−1.32247	−	0.839265i	−0.994430	+	0.105399i	$0.966388\pi$
$678$	6.74822	−	12.2750i	0.259164	−	0.471417i
$679$	8.60031	−	45.0844i	0.330050	−	1.73018i
$680$	−0.346266	−	0.479972i	−0.0132787	−	0.0184061i
$681$	1.74792	+	1.64140i	0.0669803	+	0.0628987i
$682$			3.66229i			0.140236i
$683$	29.5730	−	31.4921i	1.13158	−	1.20501i	0.155446	−	0.987844i	$-0.450319\pi$
$683$	29.5730	−	31.4921i	1.13158	−	1.20501i	0.976135	−	0.217166i	$-0.0696814\pi$
$684$	2.37894	+	3.74861i	0.0909611	+	0.143332i
$685$	−5.28274	+	11.1293i	−0.201843	+	0.425229i
$686$	−17.6002	+	6.96840i	−0.671978	+	0.266055i
$687$	−23.2777	−	1.46451i	−0.888102	−	0.0558746i
$688$	−1.50392	−	0.0946188i	−0.0573365	−	0.00360731i
$689$	−25.3612	+	10.0412i	−0.966184	+	0.382539i
$690$	5.37022	+	0.696731i	0.204441	+	0.0265241i
$691$	2.41244	+	3.80140i	0.0917735	+	0.144612i	0.887113	−	0.461552i	$-0.152707\pi$
$691$	2.41244	+	3.80140i	0.0917735	+	0.144612i	−0.795339	+	0.606164i	$0.792707\pi$
$692$	−2.99034	+	3.18439i	−0.113676	+	0.121052i
$693$			12.6630i			0.481026i
$694$	11.0667	+	10.3923i	0.420087	+	0.394488i
$695$	42.3609	+	13.9212i	1.60684	+	0.528061i
$696$	−1.14191	+	5.98610i	−0.0432840	+	0.226903i
$697$	0.443503	−	0.806729i	0.0167989	−	0.0305570i
$698$	14.0185	+	8.89643i	0.530609	+	0.336735i
$699$	−7.69057	−	23.6691i	−0.290884	−	0.895249i
$700$	20.4483	−	6.49269i	0.772874	−	0.245401i
$701$	−12.6333	+	38.8814i	−0.477154	+	1.46853i	0.365876	+	0.930664i	$0.380769\pi$
$701$	−12.6333	+	38.8814i	−0.477154	+	1.46853i	−0.843030	+	0.537866i	$0.819231\pi$
$702$	2.06998	−	1.71244i	0.0781265	−	0.0646319i
$703$	−29.5192	−	5.63109i	−1.11334	−	0.212380i
$704$	1.25653	+	2.67027i	0.0473574	+	0.100640i
$705$	8.98427	−	9.50317i	0.338367	−	0.357910i
$706$	−0.760077	−	3.98446i	−0.0286059	−	0.149957i
$707$	55.5809	+	18.0593i	2.09034	+	0.679191i
$708$	−7.58646	−	3.56992i	−0.285116	−	0.134166i
$709$	−5.58850	−	2.21264i	−0.209881	−	0.0830976i	0.260832	−	0.965384i	$-0.416003\pi$
$709$	−5.58850	−	2.21264i	−0.209881	−	0.0830976i	−0.470713	+	0.882287i	$0.656003\pi$
$710$	−2.63631	−	5.65159i	−0.0989390	−	0.212100i
$711$	−14.0638	−	3.61097i	−0.527433	−	0.135422i
$712$	−2.75417	+	6.95624i	−0.103217	+	0.260696i
$713$	−0.747399	−	2.91093i	−0.0279903	−	0.109015i
$714$	−0.608539	+	0.958904i	−0.0227740	+	0.0358861i
$715$	1.17251	−	17.6893i	0.0438495	−	0.661541i
$716$	1.00753	−	16.0142i	0.0376532	−	0.598480i
$717$	−8.37499	−	15.2341i	−0.312770	−	0.568926i
$718$	28.1969	−	9.16173i	1.05230	−	0.341913i
$719$	−3.42595	−	0.432798i	−0.127766	−	0.0161407i	0.0611899	−	0.998126i	$-0.480510\pi$
$719$	−3.42595	−	0.432798i	−0.127766	−	0.0161407i	−0.188956	+	0.981985i	$0.560510\pi$
$720$	−0.272809	−	2.21936i	−0.0101670	−	0.0827108i
$721$	−7.42619	+	6.97365i	−0.276566	+	0.259712i
$722$	−0.487033	−	0.518637i	−0.0181255	−	0.0193017i
$723$	6.45597	−	25.1443i	0.240100	−	0.935128i
$724$	−18.9045	−	13.7349i	−0.702580	−	0.510455i
$725$	−9.22114	−	29.0414i	−0.342465	−	1.07857i
$726$	−1.85327	+	1.34648i	−0.0687814	+	0.0499726i
$727$	17.4363	+	44.0392i	0.646678	+	1.63332i	0.767803	+	0.640686i	$0.221350\pi$
$727$	17.4363	+	44.0392i	0.646678	+	1.63332i	−0.121125	+	0.992637i	$0.538650\pi$
$728$	−1.44477	−	11.4365i	−0.0535467	−	0.423866i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	−31.4229	+	1.87113i	−1.16301	+	0.0692538i
$731$	−0.169819	+	0.360884i	−0.00628098	+	0.0133478i
$732$	−0.00958106	+	0.0131872i	−0.000354126	+	0.000487413i
$733$	1.45752	−	11.5374i	0.0538347	−	0.426145i	−0.942047	−	0.335481i	$-0.891101\pi$
$733$	1.45752	−	11.5374i	0.0538347	−	0.426145i	0.995882	−	0.0906640i	$-0.0288989\pi$
$734$	−4.59962	+	1.18098i	−0.169775	+	0.0435908i
$735$	−16.1991	−	19.7157i	−0.597513	−	0.727224i
$736$	−1.54369	−	1.86600i	−0.0569012	−	0.0687817i
$737$	16.2249	+	13.4224i	0.597652	+	0.494421i
$738$	2.93673	−	1.86371i	0.108103	−	0.0686040i
$739$	1.18410	+	18.8207i	0.0435578	+	0.692332i	0.957849	+	0.287273i	$0.0927488\pi$
$739$	1.18410	+	18.8207i	0.0435578	+	0.692332i	−0.914291	+	0.405058i	$0.867251\pi$
$740$	12.2148	+	8.93735i	0.449025	+	0.328543i
$741$	−7.60282	+	9.19024i	−0.279297	+	0.337612i
$742$	42.7945	−	8.16348i	1.57103	−	0.299691i
$743$	2.27693	+	3.13393i	0.0835325	+	0.114973i	0.848738	−	0.528813i	$-0.177363\pi$
$743$	2.27693	+	3.13393i	0.0835325	+	0.114973i	−0.765206	+	0.643786i	$0.777363\pi$
$744$	−1.08747	+	0.597844i	−0.0398687	+	0.0219180i
$745$	15.9495	−	39.8922i	0.584344	−	1.46154i
$746$	19.7656	−	2.49698i	0.723672	−	0.0914210i
$747$	−2.19328	+	1.03208i	−0.0802478	+	0.0377618i
$748$	0.779562	−	0.0490459i	0.0285036	−	0.00179329i
$749$	9.33302			0.341021
$750$	6.48026	+	9.11077i	0.236626	+	0.332678i
$751$	34.9119			1.27395			0.636977	−	0.770883i	$-0.280185\pi$
$751$	34.9119			1.27395			0.636977	+	0.770883i	$0.280185\pi$
$752$	−5.83700	+	0.367233i	−0.212854	+	0.0133916i
$753$	−14.5659	+	6.85420i	−0.530812	+	0.249781i
$754$	−16.2426	+	2.05191i	−0.591519	+	0.0747262i
$755$	−36.3160	−	2.40716i	−1.32167	−	0.0876056i
$756$	−3.76012	+	2.06714i	−0.136754	+	0.0751813i
$757$	25.6852	+	35.3527i	0.933545	+	1.28491i	0.958461	+	0.285225i	$0.0920684\pi$
$757$	25.6852	+	35.3527i	0.933545	+	1.28491i	−0.0249154	+	0.999690i	$0.507932\pi$
$758$	−15.8588	+	3.02523i	−0.576019	+	0.109881i
$759$	−4.55565	+	5.50683i	−0.165360	+	0.199885i
$760$	3.03610	+	9.45195i	0.110131	+	0.342858i
$761$	−2.97535	−	47.2918i	−0.107856	−	1.71433i	−0.565130	−	0.825002i	$-0.691174\pi$
$761$	−2.97535	−	47.2918i	−0.107856	−	1.71433i	0.457274	−	0.889326i	$-0.348826\pi$
$762$	11.9328	−	7.57280i	0.432280	−	0.274334i
$763$	−61.9246	−	51.2284i	−2.24182	−	1.85459i
$764$	−3.86916	−	4.67702i	−0.139981	−	0.169209i
$765$	−0.572748	−	0.149107i	−0.0207077	−	0.00539097i
$766$	−6.47334	+	1.66207i	−0.233891	+	0.0600531i
$767$	2.82310	−	22.3472i	0.101936	−	0.806909i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−11.2844	+	23.9805i	−0.406925	+	0.864759i	0.591371	+	0.806400i	$0.298587\pi$
$769$	−11.2844	+	23.9805i	−0.406925	+	0.864759i	−0.998296	+	0.0583592i	$0.981413\pi$
$770$	−7.13369	+	27.4019i	−0.257080	+	0.987495i
$771$	−12.0356	−	6.61663i	−0.433452	−	0.238292i
$772$	1.21308	+	9.60248i	0.0436595	+	0.345601i
$773$	−2.33696	−	5.90250i	−0.0840548	−	0.212298i	0.881670	−	0.471867i	$-0.156420\pi$
$773$	−2.33696	−	5.90250i	−0.0840548	−	0.212298i	−0.965725	+	0.259569i	$0.916420\pi$
$774$	−1.21910	+	0.885731i	−0.0438198	+	0.0318369i
$775$	3.35982	−	5.21652i	0.120688	−	0.187383i
$776$	−8.65366	−	6.28726i	−0.310648	−	0.225699i
$777$	7.22287	−	28.1312i	0.259119	−	1.00920i
$778$	−9.80261	−	10.4387i	−0.351441	−	0.374246i
$779$	−11.2570	+	10.5710i	−0.403323	+	0.378745i
$780$	5.44403	−	2.53949i	0.194927	−	0.0909283i
$781$	8.16562	+	1.03156i	0.292189	+	0.0369120i
$782$	−0.609617	+	0.198076i	−0.0217998	+	0.00708320i
$783$	2.93583	+	5.34025i	0.104918	+	0.190845i
$784$	−0.716538	+	11.3891i	−0.0255907	+	0.406752i
$785$	−22.5102	+	27.0250i	−0.803423	+	0.964563i
$786$	−6.41112	+	10.1023i	−0.228677	+	0.360338i
$787$	8.08386	+	31.4846i	0.288159	+	1.12230i	0.933549	+	0.358450i	$0.116695\pi$
$787$	8.08386	+	31.4846i	0.288159	+	1.12230i	−0.645390	+	0.763853i	$0.723305\pi$
$788$	−2.97593	+	7.51635i	−0.106013	+	0.267759i
$789$	7.91678	+	2.03268i	0.281845	+	0.0723655i
$790$	−28.3989	−	15.7368i	−1.01039	−	0.559889i
$791$	−55.8841	−	22.1261i	−1.98701	−	0.786713i
$792$	2.67027	+	1.25653i	0.0948840	+	0.0446490i
$793$	−0.0416474	−	0.0135321i	−0.00147894	−	0.000480538i
$794$	1.56918	+	8.22595i	0.0556882	+	0.291928i
$795$	10.8706	+	19.9316i	0.385540	+	0.706902i
$796$	8.93865	+	18.9956i	0.316822	+	0.673281i
$797$	47.2275	+	9.00913i	1.67288	+	0.319120i	0.934689	−	0.355467i	$-0.115678\pi$
$797$	47.2275	+	9.00913i	1.67288	+	0.319120i	0.738196	+	0.674586i	$0.235678\pi$
$798$	14.6786	−	12.1432i	0.519617	−	0.429865i
$799$	−0.478353	+	1.47222i	−0.0169229	+	0.0520834i
$800$	0.659939	−	4.95626i	0.0233324	−	0.175230i
$801$	2.31195	+	7.11544i	0.0816887	+	0.251412i
$802$	−3.99846	−	2.53750i	−0.141190	−	0.0896021i
$803$	20.0145	−	36.4062i	0.706295	−	1.28475i
$804$	−1.33702	+	7.00891i	−0.0471531	+	0.247185i
$805$	0.0779616	−	23.2359i	0.00274779	−	0.818959i
$806$	−2.43029	−	2.28220i	−0.0856034	−	0.0803869i
$807$			8.21250i			0.289094i
$808$	9.32346	−	9.92848i	0.327998	−	0.349283i
$809$	−9.09276	−	14.3279i	−0.319684	−	0.503742i	0.646043	−	0.763301i	$-0.276423\pi$
$809$	−9.09276	−	14.3279i	−0.319684	−	0.503742i	−0.965727	+	0.259559i	$0.916423\pi$
$810$	−1.62488	−	1.53615i	−0.0570924	−	0.0539750i
$811$	−2.15398	+	0.852822i	−0.0756365	+	0.0299466i	−0.405638	−	0.914034i	$-0.632951\pi$
$811$	−2.15398	+	0.852822i	−0.0756365	+	0.0299466i	0.330002	+	0.943980i	$0.392951\pi$
$812$	26.0972	+	1.64189i	0.915830	+	0.0576192i
$813$	11.1202	+	0.699622i	0.390002	+	0.0245368i
$814$	−18.5727	+	7.35345i	−0.650972	+	0.257738i
$815$	−3.80272	−	20.3045i	−0.133204	−	0.711235i
$816$	0.141822	+	0.223475i	0.00496475	+	0.00782320i
$817$	4.57979	−	4.87699i	0.160227	−	0.170624i
$818$		−	20.3121i		−	0.710197i
$819$	−8.40313	−	7.89107i	−0.293629	−	0.275736i
$820$	7.40483	−	2.37854i	0.258588	−	0.0830622i
$821$	−6.89629	+	36.1516i	−0.240682	+	1.26170i	0.632598	+	0.774481i	$0.281989\pi$
$821$	−6.89629	+	36.1516i	−0.240682	+	1.26170i	−0.873280	+	0.487219i	$0.838011\pi$
$822$	2.65419	−	4.82795i	0.0925754	−	0.168394i
$823$	9.83804	+	6.24341i	0.342933	+	0.217632i	0.696128	−	0.717918i	$-0.254905\pi$
$823$	9.83804	+	6.24341i	0.342933	+	0.217632i	−0.353195	+	0.935550i	$0.614905\pi$
$824$	0.733659	+	2.25797i	0.0255582	+	0.0786601i
$825$	−14.7325	+	0.827677i	−0.512919	+	0.0288160i
$826$	−11.1173	+	34.2157i	−0.386822	+	1.19052i
$827$	−23.2585	+	19.2411i	−0.808777	+	0.669079i	−0.946968	−	0.321327i	$-0.895871\pi$
$827$	−23.2585	+	19.2411i	−0.808777	+	0.669079i	0.138191	+	0.990406i	$0.455871\pi$
$828$	−2.37887	−	0.453794i	−0.0826714	−	0.0157704i
$829$	−10.1106	−	21.4862i	−0.351157	−	0.746247i	0.648734	−	0.761016i	$-0.275299\pi$
$829$	−10.1106	−	21.4862i	−0.351157	−	0.746247i	−0.999891	+	0.0147682i	$0.995299\pi$
$830$	−5.32754	+	0.997769i	−0.184922	+	0.0346331i
$831$	1.96689	+	10.3108i	0.0682308	+	0.357679i
$832$	−2.55501	−	0.830175i	−0.0885792	−	0.0287811i
$833$	2.73294	+	1.28602i	0.0946906	+	0.0445580i
$834$	−18.5408	−	7.34082i	−0.642015	−	0.254192i
$835$	−16.9060	+	2.07813i	−0.585058	+	0.0719165i
$836$	−12.6907	−	3.25842i	−0.438918	−	0.112695i
$837$	−0.456833	+	1.15383i	−0.0157905	+	0.0398821i
$838$	7.23985	+	28.1973i	0.250096	+	0.974061i
$839$	4.32999	−	6.82297i	0.149488	−	0.235555i	−0.761329	−	0.648366i	$-0.775453\pi$
$839$	4.32999	−	6.82297i	0.149488	−	0.235555i	0.910817	+	0.412811i	$0.135453\pi$
$840$	−9.30120	+	2.35491i	−0.320922	+	0.0812520i
$841$	0.510949	−	8.12130i	0.0176189	−	0.280045i
$842$	11.1258	+	20.2378i	0.383422	+	0.697442i
$843$	−31.1195	+	10.1113i	−1.07181	+	0.348253i
$844$	−8.59871	−	1.08627i	−0.295980	−	0.0373910i
$845$	−8.81988	−	9.45560i	−0.303413	−	0.325283i
$846$	−4.26341	+	4.00360i	−0.146579	+	0.137647i
$847$	6.72869	+	7.16533i	0.231201	+	0.246204i
$848$	2.52500	−	9.83424i	0.0867090	−	0.337709i
$849$	21.8432	+	15.8700i	0.749658	+	0.544658i
$850$	−1.15539	−	0.645316i	−0.0396296	−	0.0221342i
$851$	13.2616	−	9.63512i	0.454602	−	0.330288i
$852$	1.02667	+	2.59308i	0.0351732	+	0.0888374i
$853$	0.176596	+	1.39790i	0.00604654	+	0.0478633i	0.994849	−	0.101365i	$-0.0323210\pi$
$853$	0.176596	+	1.39790i	0.00604654	+	0.0478633i	−0.988803	+	0.149228i	$0.952321\pi$
$854$	0.0612909	+	0.0336950i	0.00209733	+	0.00115302i
$855$	8.36426	+	5.34757i	0.286052	+	0.182883i
$856$	0.926107	−	1.96808i	0.0316537	−	0.0672675i
$857$	7.12078	−	9.80092i	0.243241	−	0.334793i	−0.669889	−	0.742462i	$-0.733658\pi$
$857$	7.12078	−	9.80092i	0.243241	−	0.334793i	0.913130	+	0.407669i	$0.133658\pi$
$858$	−0.993672	+	7.86572i	−0.0339234	+	0.268531i
$859$	−19.7156	+	5.06210i	−0.672687	+	0.172717i	−0.569558	−	0.821951i	$-0.692886\pi$
$859$	−19.7156	+	5.06210i	−0.672687	+	0.172717i	−0.103129	+	0.994668i	$0.532886\pi$
$860$	−3.13705	+	1.22989i	−0.106972	+	0.0419387i
$861$	−9.51321	−	11.4995i	−0.324209	−	0.391902i
$862$	11.0030	+	9.10248i	0.374764	+	0.310032i
$863$	27.9738	−	17.7527i	0.952239	−	0.604310i	0.0336123	−	0.999435i	$-0.489299\pi$
$863$	27.9738	−	17.7527i	0.952239	−	0.604310i	0.918627	+	0.395125i	$0.129299\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	−3.04961	+	9.27967i	−0.103690	+	0.315518i
$866$	4.91832	−	5.94523i	0.167131	−	0.202027i
$867$	−16.6301	+	3.17236i	−0.564787	+	0.107739i
$868$	3.12987	+	4.30790i	0.106235	+	0.146220i
$869$	37.5501	−	20.6434i	1.27380	−	0.700278i
$870$	3.34452	+	13.2099i	0.113390	+	0.447857i
$871$	−19.0178	+	2.40251i	−0.644395	+	0.0814060i
$872$	−16.9474	+	7.97484i	−0.573911	+	0.270062i
$873$	−10.6754	+	0.671640i	−0.361308	+	0.0227316i
$874$	10.7521			0.363694
$875$	35.2999	−	32.4864i	1.19335	−	1.09824i
$876$	14.0776			0.475639
$877$	16.9284	−	1.06505i	0.571633	−	0.0359641i	0.225656	−	0.974207i	$-0.427548\pi$
$877$	16.9284	−	1.06505i	0.571633	−	0.0359641i	0.345977	+	0.938243i	$0.387548\pi$
$878$	−10.7911	+	5.07789i	−0.364181	+	0.171370i
$879$	25.8293	−	3.26300i	0.871200	−	0.110058i
$880$	5.07044	+	4.22336i	0.170924	+	0.142370i
$881$	−44.9802	+	24.7281i	−1.51542	+	0.833111i	−0.999720	−	0.0236566i	$-0.992469\pi$
$881$	−44.9802	+	24.7281i	−1.51542	+	0.833111i	−0.515703	+	0.856767i	$0.672469\pi$
$882$	6.70755	+	9.23215i	0.225855	+	0.310863i
$883$	−27.4681	+	5.23981i	−0.924374	+	0.176334i	−0.627530	−	0.778592i	$-0.715934\pi$
$883$	−27.4681	+	5.23981i	−0.924374	+	0.176334i	−0.296844	+	0.954926i	$0.595934\pi$
$884$	−0.453246	+	0.547880i	−0.0152443	+	0.0184272i
$885$	−18.7480	−	0.0629038i	−0.630209	−	0.00211449i
$886$	−1.50288	−	23.8875i	−0.0504901	−	0.802517i
$887$	1.18228	−	0.750298i	0.0396971	−	0.0251925i	−0.515830	−	0.856691i	$-0.672516\pi$
$887$	1.18228	−	0.750298i	0.0396971	−	0.0251925i	0.555527	+	0.831498i	$0.312516\pi$
$888$	−5.21539	−	4.31454i	−0.175017	−	0.144787i
$889$	−38.6550	−	46.7259i	−1.29645	−	1.56714i
$890$	0.994423	+	16.6998i	0.0333331	+	0.559780i
$891$	2.85842	−	0.733919i	0.0957608	−	0.0245872i
$892$	−0.482239	+	3.81732i	−0.0161466	+	0.127813i
$893$	15.2625	−	21.0070i	0.510740	−	0.702974i
$894$	−8.18068	+	17.3848i	−0.273603	+	0.581435i
$895$	−13.0962	−	33.4042i	−0.437758	−	1.11658i
$896$	3.76012	+	2.06714i	0.125617	+	0.0690584i
$897$	−0.815427	−	6.45477i	−0.0272263	−	0.215519i
$898$	−12.7436	−	32.1867i	−0.425260	−	1.07409i
$899$	6.11823	−	4.44515i	0.204054	−	0.148254i
$900$	−2.65074	−	4.23952i	−0.0883582	−	0.141317i
$901$	−2.17410	−	1.57958i	−0.0724298	−	0.0526233i
$902$	−2.55271	+	9.94214i	−0.0849959	+	0.331037i
$903$	4.42621	+	4.71343i	0.147295	+	0.156853i
$904$	−10.2111	+	9.58887i	−0.339617	+	0.318921i
$905$	−51.2921	−	9.96297i	−1.70501	−	0.331180i
$906$	16.1483	+	2.04000i	0.536491	+	0.0677745i
$907$	5.41685	−	1.76004i	0.179864	−	0.0584412i	−0.217701	−	0.976016i	$-0.569856\pi$
$907$	5.41685	−	1.76004i	0.179864	−	0.0584412i	0.397564	+	0.917574i	$0.369856\pi$
$908$	−1.15515	−	2.10120i	−0.0383349	−	0.0697308i
$909$	0.855200	−	13.5930i	0.0283652	−	0.450852i
$910$	−13.7384	−	21.8097i	−0.455425	−	0.722985i
$911$	28.9212	−	45.5725i	0.958203	−	1.50989i	0.101013	−	0.994885i	$-0.467792\pi$
$911$	28.9212	−	45.5725i	0.958203	−	1.50989i	0.857190	−	0.515001i	$-0.172208\pi$
$912$	−1.10412	−	4.30028i	−0.0365612	−	0.142396i
$913$	2.63337	−	6.65114i	0.0871520	−	0.220121i
$914$	25.5405	+	6.55770i	0.844806	+	0.216909i
$915$	−0.00694986	+	0.0357798i	−0.000229755	+	0.00118284i
$916$	21.6859	+	8.58605i	0.716522	+	0.283691i
$917$	46.4537	+	21.8595i	1.53404	+	0.721863i
$918$	0.251724	+	0.0817901i	0.00830813	+	0.00269948i
$919$	−2.13068	−	11.1694i	−0.0702847	−	0.368445i	−1.00000		0.000166085i	$-0.999947\pi$
$919$	−2.13068	−	11.1694i	−0.0702847	−	0.368445i	0.929715	−	0.368279i	$-0.120053\pi$
$920$	−4.89208	−	2.32212i	−0.161287	−	0.0765580i
$921$	−7.94277	−	16.8792i	−0.261723	−	0.556190i
$922$	14.8305	+	2.82906i	0.488416	+	0.0931703i
$923$	−5.77304	+	4.77587i	−0.190022	+	0.157200i
$924$	3.91307	−	12.0432i	0.128731	−	0.396192i
$925$	33.2008	+	6.56459i	1.09164	+	0.215843i
$926$	−7.60509	−	23.4061i	−0.249919	−	0.769171i
$927$	2.00458	+	1.27214i	0.0658390	+	0.0417827i
$928$	2.93583	−	5.34025i	0.0963733	−	0.175302i
$929$	2.57159	−	13.4808i	0.0843712	−	0.442289i	−0.914885	−	0.403716i	$-0.867719\pi$
$929$	2.57159	−	13.4808i	0.0843712	−	0.442289i	0.999256	−	0.0385738i	$-0.0122815\pi$
$930$	−1.63857	+	2.23946i	−0.0537308	+	0.0734347i
$931$	−36.9329	−	34.6823i	−1.21043	−	1.13667i
$932$			24.8872i			0.815208i
$933$	21.7131	−	23.1221i	0.710855	−	0.756984i
$934$	−9.16684	−	14.4446i	−0.299948	−	0.472643i
$935$	1.53337	−	0.836291i	0.0501466	−	0.0273496i
$936$	−2.49785	+	0.988967i	−0.0816446	+	0.0323254i
$937$	−6.29200	−	0.395859i	−0.205551	−	0.0129321i	−0.0403186	−	0.999187i	$-0.512837\pi$
$937$	−6.29200	−	0.395859i	−0.205551	−	0.0129321i	−0.165232	+	0.986255i	$0.552837\pi$
$938$	30.5562	+	1.92244i	0.997696	+	0.0627697i
$939$	−5.78630	+	2.29096i	−0.188829	+	0.0747626i
$940$	−11.4812	+	6.26176i	−0.374475	+	0.204236i
$941$	22.2530	+	35.0652i	0.725428	+	1.14309i	0.984184	+	0.177149i	$0.0566876\pi$
$941$	22.2530	+	35.0652i	0.725428	+	1.14309i	−0.258756	+	0.965943i	$0.583312\pi$
$942$	10.7675	−	11.4662i	0.350823	−	0.373588i
$943$		−	8.42336i		−	0.274302i
$944$	6.11198	+	5.73954i	0.198928	+	0.186806i
$945$	−5.66562	+	7.74329i	−0.184303	+	0.251889i
$946$	0.833296	−	4.36829i	0.0270928	−	0.142025i
$947$	2.55548	−	4.64840i	0.0830419	−	0.151053i	−0.831525	−	0.555487i	$-0.812532\pi$
$947$	2.55548	−	4.64840i	0.0830419	−	0.151053i	0.914567	+	0.404435i	$0.132532\pi$
$948$	12.2596	+	7.78018i	0.398174	+	0.252689i
$949$	11.6869	+	35.9685i	0.379372	+	1.16759i
$950$	15.0872	+	16.2838i	0.489493	+	0.528317i
$951$	−8.50580	+	26.1782i	−0.275819	+	0.848885i
$952$	0.875072	−	0.723923i	0.0283613	−	0.0234625i
$953$	36.0552	+	6.87789i	1.16794	+	0.222797i	0.734643	−	0.678454i	$-0.237350\pi$
$953$	36.0552	+	6.87789i	1.16794	+	0.222797i	0.433298	+	0.901251i	$0.357350\pi$
$954$	−4.32303	−	9.18691i	−0.139963	−	0.297437i
$955$	−12.2617	−	5.82025i	−0.396779	−	0.188339i
$956$	3.25751	+	17.0765i	0.105355	+	0.552292i
$957$	−17.1042	−	5.55748i	−0.552899	−	0.179648i
$958$	7.97391	+	3.75224i	0.257625	+	0.121229i
$959$	−21.9801	−	8.70256i	−0.709776	−	0.281020i
$960$	−0.426365	+	2.19504i	−0.0137609	+	0.0708447i
$961$	−28.5344	−	7.32640i	−0.920466	−	0.236335i
$962$	6.69404	−	16.9072i	0.215824	−	0.545110i
$963$	−0.540922	−	2.10675i	−0.0174310	−	0.0678892i
$964$	−13.9100	+	21.9187i	−0.448012	+	0.705953i
$965$	11.5352	+	18.3121i	0.371332	+	0.589489i
$966$	−0.652486	+	10.3710i	−0.0209934	+	0.333681i
$967$	5.42061	+	9.86005i	0.174315	+	0.317078i	0.949004	−	0.315265i	$-0.102093\pi$
$967$	5.42061	+	9.86005i	0.174315	+	0.317078i	−0.774689	+	0.632343i	$0.782093\pi$
$968$	2.17865	−	0.707888i	0.0700246	−	0.0227524i
$969$	−1.16584	−	0.147280i	−0.0374522	−	0.00473132i
$970$	−23.4793	−	4.56062i	−0.753875	−	0.146433i
$971$	−18.0473	+	16.9475i	−0.579164	+	0.543871i	−0.917798	−	0.397047i	$-0.870035\pi$
$971$	−18.0473	+	16.9475i	−0.579164	+	0.543871i	0.338634	+	0.940918i	$0.390035\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	−21.2791	+	82.8767i	−0.682177	+	2.65690i
$974$	14.4064	+	10.4668i	0.461610	+	0.335379i
$975$	8.63146	−	10.2922i	0.276428	−	0.329615i
$976$	0.0131872	−	0.00958106i	0.000422112	−	0.000306682i
$977$	−7.53443	−	19.0298i	−0.241048	−	0.608817i	0.758009	−	0.652244i	$-0.226172\pi$
$977$	−7.53443	−	19.0298i	−0.241048	−	0.608817i	−0.999057	+	0.0434271i	$0.986172\pi$
$978$	1.15787	+	9.16547i	0.0370245	+	0.293079i
$979$	−19.3482	−	10.6368i	−0.618373	−	0.339953i
$980$	9.31380	+	23.7565i	0.297518	+	0.758875i
$981$	−7.97484	+	16.9474i	−0.254617	+	0.541089i
$982$	−25.2312	+	34.7277i	−0.805159	+	1.10821i
$983$	2.57778	−	20.4052i	0.0822184	−	0.650825i	−0.896120	−	0.443812i	$-0.853626\pi$
$983$	2.57778	−	20.4052i	0.0822184	−	0.650825i	0.978338	−	0.207013i	$-0.0663743\pi$
$984$	−3.36892	+	0.864990i	−0.107397	+	0.0275749i
$985$	1.07449	+	18.0445i	0.0342362	+	0.574946i
$986$	−1.02814	−	1.24281i	−0.0327427	−	0.0395791i
$987$	19.3363	+	15.9964i	0.615481	+	0.509170i
$988$	10.0707	−	6.39103i	0.320390	−	0.203326i
$989$	0.229144	+	3.64215i	0.00728637	+	0.115814i
$990$	6.59891	+	0.0221408i	0.209727	+	0.000703681i
$991$	−21.0833	+	25.4853i	−0.669732	+	0.809567i	−0.990489	−	0.137595i	$-0.956063\pi$
$991$	−21.0833	+	25.4853i	−0.669732	+	0.809567i	0.320757	+	0.947162i	$0.396063\pi$
$992$	1.21899	−	0.232535i	0.0387031	−	0.00738300i
$993$	4.56076	+	6.27735i	0.144731	+	0.199206i
$994$	10.4867	−	5.76511i	0.332618	−	0.182858i
$995$	36.0697	+	30.0439i	1.14349	+	0.952455i
$996$	2.40486	−	0.303804i	0.0762009	−	0.00962641i
$997$	−25.9369	+	12.2050i	−0.821429	+	0.386535i	−0.790103	−	0.612974i	$-0.789973\pi$
$997$	−25.9369	+	12.2050i	−0.821429	+	0.386535i	−0.0313259	+	0.999509i	$0.509973\pi$
$998$	18.7704	−	1.18093i	0.594166	−	0.0373818i
$999$	−6.76872			−0.214153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.469.11	yes	240
125.4	even	50	inner	750.2.o.a.379.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.379.11	✓	240	125.4	even	50	inner
750.2.o.a.469.11	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.89198 - 1.19180i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.52211 + 3.47139i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(0.998027 - 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.89198 - 1.19180i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(2.52211 + 3.47139i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.81342 - 1.30825i) q^{10} +(0.185304 + 2.94532i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-2.06998 - 1.71244i) q^{13} +(2.73510 + 3.30617i) q^{14} +(-1.20447 + 1.88394i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.0331730 - 0.262591i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-1.89036 + 4.01721i) q^{19} +(1.72769 - 1.41953i) q^{20} +(-3.76012 - 2.06714i) q^{21} +(0.369876 + 2.92787i) q^{22} +(-0.891511 - 2.25170i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(2.15921 - 4.50975i) q^{25} +(-2.17343 - 1.57909i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(2.93730 + 3.12791i) q^{28} +(4.44237 - 4.17166i) q^{29} +(-1.08380 + 1.95586i) q^{30} +(1.23119 + 0.155535i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-1.42172 - 2.58610i) q^{33} +(0.0166193 - 0.264156i) q^{34} +(8.90901 + 3.56195i) q^{35} +(0.535827 - 0.844328i) q^{36} +(1.68331 + 6.55607i) q^{37} +(-1.63438 + 4.12798i) q^{38} +(2.60210 + 0.668106i) q^{39} +(1.63515 - 1.52522i) q^{40} +(3.23394 + 1.28041i) q^{41} +(-3.88250 - 1.82696i) q^{42} +(-1.43314 - 0.465656i) q^{43} +(0.552989 + 2.89887i) q^{44} +(0.287695 - 2.21748i) q^{45} +(-1.03114 - 2.19128i) q^{46} +(-5.74495 - 1.09591i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.52637 + 10.8530i) q^{49} +(1.87178 - 4.63643i) q^{50} +(0.0817901 + 0.251724i) q^{51} +(-2.26829 - 1.43950i) q^{52} +(4.89135 - 8.89733i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(3.86083 + 5.35165i) q^{55} +(3.12791 + 2.93730i) q^{56} -4.43976i q^{57} +(4.17166 - 4.44237i) q^{58} +(4.49260 + 7.07921i) q^{59} +(-0.958855 + 2.02005i) q^{60} +(0.0151556 - 0.00600053i) q^{61} +(1.23852 + 0.0779214i) q^{62} +(4.28240 + 0.269426i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-5.95727 - 0.772894i) q^{65} +(-1.58130 - 2.49173i) q^{66} +(4.88445 - 5.20141i) q^{67} -0.264678i q^{68} +(1.76539 + 1.65781i) q^{69} +(9.11508 + 2.99552i) q^{70} +(0.522593 - 2.73953i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-11.8861 - 7.54317i) q^{73} +(2.09165 + 6.43743i) q^{74} +(-0.0335518 + 4.99989i) q^{75} +(-1.37196 + 4.22246i) q^{76} +(-9.75698 + 8.07167i) q^{77} +(2.63892 + 0.503400i) q^{78} +(-6.18230 - 13.1381i) q^{79} +(1.53615 - 1.62488i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(3.30795 + 1.07482i) q^{82} +(-2.19328 - 1.03208i) q^{83} +(-3.98955 - 1.57957i) q^{84} +(-0.250195 - 0.536354i) q^{85} +(-1.45955 - 0.374750i) q^{86} +(-2.24337 + 5.66610i) q^{87} +(0.733919 + 2.85842i) q^{88} +(-4.00885 + 6.31694i) q^{89} +(0.147891 - 2.23117i) q^{90} +(0.723813 - 11.5047i) q^{91} +(-1.16669 - 2.12221i) q^{92} +(-1.18024 + 0.383482i) q^{93} +(-5.80243 - 0.733017i) q^{94} +(1.21121 + 9.85344i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-7.32227 - 7.79743i) q^{97} +(-2.83794 + 11.0531i) q^{98} +(2.38752 + 1.73464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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