LMFDB - Embedded newform 750.2.o.a.259.1

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			259.1
Character	$\chi$	$=$	750.259
Dual form			750.2.o.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.904827 - 0.425779i) q^{2} +(-0.998027 + 0.0627905i) q^{3} +(0.637424 + 0.770513i) q^{4} +(-1.94576 + 1.10182i) q^{5} +(0.929776 + 0.368125i) q^{6} +(1.63461 - 0.531117i) q^{7} +(-0.248690 - 0.968583i) q^{8} +(0.992115 - 0.125333i) q^{9} +O(q^{10})$	\(q+(-0.904827 - 0.425779i) q^{2} +(-0.998027 + 0.0627905i) q^{3} +(0.637424 + 0.770513i) q^{4} +(-1.94576 + 1.10182i) q^{5} +(0.929776 + 0.368125i) q^{6} +(1.63461 - 0.531117i) q^{7} +(-0.248690 - 0.968583i) q^{8} +(0.992115 - 0.125333i) q^{9} +(2.22971 - 0.168493i) q^{10} +(-1.40163 + 2.97862i) q^{11} +(-0.684547 - 0.728969i) q^{12} +(-0.112087 - 0.887260i) q^{13} +(-1.70518 - 0.215414i) q^{14} +(1.87274 - 1.22182i) q^{15} +(-0.187381 + 0.982287i) q^{16} +(0.986786 + 0.816341i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.0642121 - 1.02062i) q^{19} +(-2.08924 - 0.796908i) q^{20} +(-1.59804 + 0.632707i) q^{21} +(2.53647 - 2.09835i) q^{22} +(-1.27395 - 2.31731i) q^{23} +(0.309017 + 0.951057i) q^{24} +(2.57198 - 4.28776i) q^{25} +(-0.276357 + 0.850541i) q^{26} +(-0.982287 + 0.187381i) q^{27} +(1.45117 + 0.920942i) q^{28} +(-3.27630 + 5.16263i) q^{29} +(-2.21473 + 0.308165i) q^{30} +(-1.46026 + 1.76515i) q^{31} +(0.587785 - 0.809017i) q^{32} +(1.21184 - 3.06075i) q^{33} +(-0.545290 - 1.15880i) q^{34} +(-2.59537 + 2.83448i) q^{35} +(0.728969 + 0.684547i) q^{36} +(-5.48183 - 1.04572i) q^{37} +(-0.492661 + 0.896147i) q^{38} +(0.167577 + 0.878471i) q^{39} +(1.55110 + 1.61062i) q^{40} +(-8.29044 - 4.55771i) q^{41} +(1.71534 + 0.107920i) q^{42} +(-3.35445 - 4.61701i) q^{43} +(-3.18850 + 0.818668i) q^{44} +(-1.79232 + 1.33700i) q^{45} +(0.166044 + 2.63919i) q^{46} +(-0.804439 + 3.13308i) q^{47} +(0.125333 - 0.992115i) q^{48} +(-3.27325 + 2.37816i) q^{49} +(-4.15284 + 2.78459i) q^{50} +(-1.03610 - 0.752769i) q^{51} +(0.612198 - 0.651925i) q^{52} +(-1.79154 - 4.52492i) q^{53} +(0.968583 + 0.248690i) q^{54} +(-0.554664 - 7.34003i) q^{55} +(-0.920942 - 1.45117i) q^{56} +1.02264i q^{57} +(5.16263 - 3.27630i) q^{58} +(-6.17867 + 5.80216i) q^{59} +(2.13516 + 0.664151i) q^{60} +(-10.1165 + 5.56159i) q^{61} +(2.07285 - 0.975408i) q^{62} +(1.55515 - 0.731800i) q^{63} +(-0.876307 + 0.481754i) q^{64} +(1.19570 + 1.60290i) q^{65} +(-2.39971 + 2.25348i) q^{66} +(-2.61495 + 1.65950i) q^{67} +1.28069i q^{68} +(1.41694 + 2.23275i) q^{69} +(3.55522 - 1.45966i) q^{70} +(-2.19617 - 0.563882i) q^{71} +(-0.368125 - 0.929776i) q^{72} +(3.79615 - 4.04249i) q^{73} +(4.51486 + 3.28024i) q^{74} +(-2.29767 + 4.44080i) q^{75} +(0.827334 - 0.601093i) q^{76} +(-0.709126 + 5.61331i) q^{77} +(0.222406 - 0.866215i) q^{78} +(0.323266 + 5.13816i) q^{79} +(-0.717706 - 2.11776i) q^{80} +(0.968583 - 0.248690i) q^{81} +(5.56084 + 7.65383i) q^{82} +(-3.77622 - 0.237579i) q^{83} +(-1.50614 - 0.828005i) q^{84} +(-2.81951 - 0.501142i) q^{85} +(1.06937 + 5.60585i) q^{86} +(2.94567 - 5.35816i) q^{87} +(3.23361 + 0.616845i) q^{88} +(3.73703 + 3.50931i) q^{89} +(2.19101 - 0.446621i) q^{90} +(-0.654457 - 1.39079i) q^{91} +(0.973471 - 2.45871i) q^{92} +(1.34654 - 1.85336i) q^{93} +(2.06188 - 2.49238i) q^{94} +(0.999602 + 2.05664i) q^{95} +(-0.535827 + 0.844328i) q^{96} +(-2.10499 - 1.33587i) q^{97} +(3.97430 - 0.758138i) q^{98} +(-1.01726 + 3.13080i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{50}\right)$	$1$

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 $

$2$	−0.904827	−	0.425779i	−0.639809	−	0.301071i
$2$	−0.904827	−	0.425779i	−0.639809	−	0.301071i
$3$	−0.998027	+	0.0627905i	−0.576211	+	0.0362521i
$3$	−0.998027	+	0.0627905i	−0.576211	+	0.0362521i
$4$	0.637424	+	0.770513i	0.318712	+	0.385257i
$5$	−1.94576	+	1.10182i	−0.870171	+	0.492749i
$5$	−1.94576	+	1.10182i	−0.870171	+	0.492749i
$6$	0.929776	+	0.368125i	0.379580	+	0.150286i
$7$	1.63461	−	0.531117i	0.617825	−	0.200743i	0.0166504	−	0.999861i	$-0.494700\pi$
$7$	1.63461	−	0.531117i	0.617825	−	0.200743i	0.601174	+	0.799118i	$0.294700\pi$
$8$	−0.248690	−	0.968583i	−0.0879252	−	0.342446i
$9$	0.992115	−	0.125333i	0.330705	−	0.0417777i
$10$	2.22971	−	0.168493i	0.705096	−	0.0532820i
$11$	−1.40163	+	2.97862i	−0.422608	+	0.898088i	0.574235	+	0.818690i	$0.305300\pi$
$11$	−1.40163	+	2.97862i	−0.422608	+	0.898088i	−0.996843	+	0.0793971i	$0.974700\pi$
$12$	−0.684547	−	0.728969i	−0.197612	−	0.210435i
$13$	−0.112087	−	0.887260i	−0.0310873	−	0.246082i	0.968912	−	0.247406i	$-0.0795783\pi$
$13$	−0.112087	−	0.887260i	−0.0310873	−	0.246082i	−0.999999	+	0.00132488i	$0.999578\pi$
$14$	−1.70518	−	0.215414i	−0.455728	−	0.0575718i
$15$	1.87274	−	1.22182i	0.483539	−	0.315473i
$16$	−0.187381	+	0.982287i	−0.0468453	+	0.245572i
$17$	0.986786	+	0.816341i	0.239331	+	0.197992i	0.749355	−	0.662168i	$-0.230364\pi$
$17$	0.986786	+	0.816341i	0.239331	+	0.197992i	−0.510024	+	0.860160i	$0.670364\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	0.0642121	−	1.02062i	0.0147313	−	0.234147i	−0.983771	−	0.179430i	$-0.942575\pi$
$19$	0.0642121	−	1.02062i	0.0147313	−	0.234147i	0.998502	−	0.0547164i	$-0.0174255\pi$
$20$	−2.08924	−	0.796908i	−0.467169	−	0.178194i
$21$	−1.59804	+	0.632707i	−0.348720	+	0.138068i
$22$	2.53647	−	2.09835i	0.540777	−	0.447370i
$23$	−1.27395	−	2.31731i	−0.265638	−	0.483193i	0.709526	−	0.704679i	$-0.248909\pi$
$23$	−1.27395	−	2.31731i	−0.265638	−	0.483193i	−0.975163	+	0.221486i	$0.928909\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	2.57198	−	4.28776i	0.514396	−	0.857553i
$26$	−0.276357	+	0.850541i	−0.0541982	+	0.166805i
$27$	−0.982287	+	0.187381i	−0.189041	+	0.0360616i
$28$	1.45117	+	0.920942i	0.274246	+	0.174042i
$29$	−3.27630	+	5.16263i	−0.608394	+	0.958676i	0.390875	+	0.920444i	$0.372173\pi$
$29$	−3.27630	+	5.16263i	−0.608394	+	0.958676i	−0.999269	+	0.0382321i	$0.987827\pi$
$30$	−2.21473	+	0.308165i	−0.404353	+	0.0562629i
$31$	−1.46026	+	1.76515i	−0.262270	+	0.317030i	−0.885167	−	0.465274i	$-0.845956\pi$
$31$	−1.46026	+	1.76515i	−0.262270	+	0.317030i	0.622896	+	0.782304i	$0.285956\pi$
$32$	0.587785	−	0.809017i	0.103907	−	0.143015i
$33$	1.21184	−	3.06075i	0.210954	−	0.532808i
$34$	−0.545290	−	1.15880i	−0.0935165	−	0.198733i
$35$	−2.59537	+	2.83448i	−0.438697	+	0.479114i
$36$	0.728969	+	0.684547i	0.121495	+	0.114091i
$37$	−5.48183	−	1.04572i	−0.901207	−	0.171915i	−0.284101	−	0.958794i	$-0.591695\pi$
$37$	−5.48183	−	1.04572i	−0.901207	−	0.171915i	−0.617106	+	0.786880i	$0.711695\pi$
$38$	−0.492661	+	0.896147i	−0.0799201	+	0.145374i
$39$	0.167577	+	0.878471i	0.0268338	+	0.140668i
$40$	1.55110	+	1.61062i	0.245250	+	0.254661i
$41$	−8.29044	−	4.55771i	−1.29475	−	0.711794i	−0.322684	−	0.946507i	$-0.604585\pi$
$41$	−8.29044	−	4.55771i	−1.29475	−	0.711794i	−0.972065	+	0.234713i	$0.924585\pi$
$42$	1.71534	+	0.107920i	0.264683	+	0.0166524i
$43$	−3.35445	−	4.61701i	−0.511549	−	0.704087i	0.472631	−	0.881261i	$-0.343305\pi$
$43$	−3.35445	−	4.61701i	−0.511549	−	0.704087i	−0.984180	+	0.177174i	$0.943305\pi$
$44$	−3.18850	+	0.818668i	−0.480684	+	0.123419i
$45$	−1.79232	+	1.33700i	−0.267184	+	0.199308i
$46$	0.166044	+	2.63919i	0.0244818	+	0.389127i
$47$	−0.804439	+	3.13308i	−0.117339	+	0.457007i	−0.999913	−	0.0131668i	$-0.995809\pi$
$47$	−0.804439	+	3.13308i	−0.117339	+	0.457007i	0.882574	+	0.470174i	$0.155809\pi$
$48$	0.125333	−	0.992115i	0.0180903	−	0.143199i
$49$	−3.27325	+	2.37816i	−0.467608	+	0.339737i
$50$	−4.15284	+	2.78459i	−0.587300	+	0.393800i
$51$	−1.03610	−	0.752769i	−0.145083	−	0.105409i
$52$	0.612198	−	0.651925i	0.0848966	−	0.0904057i
$53$	−1.79154	−	4.52492i	−0.246087	−	0.621546i	0.753258	−	0.657725i	$-0.228481\pi$
$53$	−1.79154	−	4.52492i	−0.246087	−	0.621546i	−0.999345	+	0.0361795i	$0.988481\pi$
$54$	0.968583	+	0.248690i	0.131807	+	0.0338424i
$55$	−0.554664	−	7.34003i	−0.0747909	−	0.989730i
$56$	−0.920942	−	1.45117i	−0.123066	−	0.193921i
$57$			1.02264i			0.135452i
$58$	5.16263	−	3.27630i	0.677886	−	0.430200i
$59$	−6.17867	+	5.80216i	−0.804394	+	0.755377i	−0.973123	−	0.230286i	$-0.926034\pi$
$59$	−6.17867	+	5.80216i	−0.804394	+	0.755377i	0.168729	+	0.985663i	$0.446034\pi$
$60$	2.13516	+	0.664151i	0.275648	+	0.0857415i
$61$	−10.1165	+	5.56159i	−1.29528	+	0.712088i	−0.972171	−	0.234272i	$-0.924729\pi$
$61$	−10.1165	+	5.56159i	−1.29528	+	0.712088i	−0.323113	+	0.946361i	$0.604729\pi$
$62$	2.07285	−	0.975408i	0.263252	−	0.123877i
$63$	1.55515	−	0.731800i	0.195931	−	0.0921981i
$64$	−0.876307	+	0.481754i	−0.109538	+	0.0602192i
$65$	1.19570	+	1.60290i	0.148308	+	0.198815i
$66$	−2.39971	+	2.25348i	−0.295384	+	0.277384i
$67$	−2.61495	+	1.65950i	−0.319467	+	0.202740i	−0.685884	−	0.727711i	$-0.740584\pi$
$67$	−2.61495	+	1.65950i	−0.319467	+	0.202740i	0.366417	+	0.930451i	$0.380584\pi$
$68$			1.28069i			0.155306i
$69$	1.41694	+	2.23275i	0.170580	+	0.268791i
$70$	3.55522	−	1.45966i	0.424930	−	0.174462i
$71$	−2.19617	−	0.563882i	−0.260638	−	0.0669204i	0.116110	−	0.993236i	$-0.462958\pi$
$71$	−2.19617	−	0.563882i	−0.260638	−	0.0669204i	−0.376748	+	0.926316i	$0.622958\pi$
$72$	−0.368125	−	0.929776i	−0.0433839	−	0.109575i
$73$	3.79615	−	4.04249i	0.444305	−	0.473137i	−0.467362	−	0.884066i	$-0.654796\pi$
$73$	3.79615	−	4.04249i	0.444305	−	0.473137i	0.911667	+	0.410929i	$0.134796\pi$
$74$	4.51486	+	3.28024i	0.524842	+	0.381320i
$75$	−2.29767	+	4.44080i	−0.265312	+	0.512779i
$76$	0.827334	−	0.601093i	0.0949017	−	0.0689501i
$77$	−0.709126	+	5.61331i	−0.0808124	+	0.639696i
$78$	0.222406	−	0.866215i	0.0251825	−	0.0980795i
$79$	0.323266	+	5.13816i	0.0363702	+	0.578088i	0.973439	+	0.228945i	$0.0735275\pi$
$79$	0.323266	+	5.13816i	0.0363702	+	0.578088i	−0.937069	+	0.349144i	$0.886472\pi$
$80$	−0.717706	−	2.11776i	−0.0802419	−	0.236773i
$81$	0.968583	−	0.248690i	0.107620	−	0.0276322i
$82$	5.56084	+	7.65383i	0.614092	+	0.845224i
$83$	−3.77622	−	0.237579i	−0.414494	−	0.0260777i	−0.145825	−	0.989310i	$-0.546584\pi$
$83$	−3.77622	−	0.237579i	−0.414494	−	0.0260777i	−0.268669	+	0.963233i	$0.586584\pi$
$84$	−1.50614	−	0.828005i	−0.164333	−	0.0903427i
$85$	−2.81951	−	0.501142i	−0.305819	−	0.0543565i
$86$	1.06937	+	5.60585i	0.115313	+	0.604494i
$87$	2.94567	−	5.35816i	0.315809	−	0.574455i
$88$	3.23361	+	0.616845i	0.344704	+	0.0657559i
$89$	3.73703	+	3.50931i	0.396125	+	0.371986i	0.856858	−	0.515553i	$-0.172413\pi$
$89$	3.73703	+	3.50931i	0.396125	+	0.371986i	−0.460733	+	0.887539i	$0.652413\pi$
$90$	2.19101	−	0.446621i	0.230953	−	0.0470780i
$91$	−0.654457	−	1.39079i	−0.0686057	−	0.145795i
$92$	0.973471	−	2.45871i	0.101491	−	0.256338i
$93$	1.34654	−	1.85336i	0.139630	−	0.192184i
$94$	2.06188	−	2.49238i	0.212667	−	0.257070i
$95$	0.999602	+	2.05664i	0.102557	+	0.211007i
$96$	−0.535827	+	0.844328i	−0.0546876	+	0.0861739i
$97$	−2.10499	−	1.33587i	−0.213730	−	0.135637i	0.424653	−	0.905356i	$-0.360396\pi$
$97$	−2.10499	−	1.33587i	−0.213730	−	0.135637i	−0.638383	+	0.769719i	$0.720396\pi$
$98$	3.97430	−	0.758138i	0.401465	−	0.0765835i
$99$	−1.01726	+	3.13080i	−0.102238	+	0.314658i
$100$	4.94322	−	0.751380i	0.494322	−	0.0751380i
$101$	−3.30579	−	10.1742i	−0.328938	−	1.01237i	−0.969631	−	0.244571i	$-0.921353\pi$
$101$	−3.30579	−	10.1742i	−0.328938	−	1.01237i	0.640693	−	0.767797i	$-0.278647\pi$
$102$	0.616976	+	1.12227i	0.0610897	+	0.111122i
$103$	−3.57480	+	2.95733i	−0.352236	+	0.291395i	−0.796667	−	0.604418i	$-0.793406\pi$
$103$	−3.57480	+	2.95733i	−0.352236	+	0.291395i	0.444432	+	0.895813i	$0.353406\pi$
$104$	−0.831510	+	0.329218i	−0.0815362	+	0.0322825i
$105$	2.41227	−	2.99185i	0.235413	−	0.291974i
$106$	−0.305581	+	4.85707i	−0.0296807	+	0.471761i
$107$	9.91057	+	3.22014i	0.958091	+	0.311303i	0.745999	−	0.665947i	$-0.231972\pi$
$107$	9.91057	+	3.22014i	0.958091	+	0.311303i	0.212092	+	0.977250i	$0.431972\pi$
$108$	−0.770513	−	0.637424i	−0.0741427	−	0.0613362i
$109$	0.200768	−	1.05246i	0.0192301	−	0.100808i	−0.971378	−	0.237538i	$-0.923659\pi$
$109$	0.200768	−	1.05246i	0.0192301	−	0.100808i	0.990608	+	0.136731i	$0.0436595\pi$
$110$	−2.62336	+	6.87762i	−0.250127	+	0.655756i
$111$	5.53667	+	0.699445i	0.525518	+	0.0663883i
$112$	0.215414	+	1.70518i	0.0203547	+	0.161124i
$113$	−10.4576	−	11.1362i	−0.983766	−	1.04760i	−0.998861	−	0.0477180i	$-0.984805\pi$
$113$	−10.4576	−	11.1362i	−0.983766	−	1.04760i	0.0150952	−	0.999886i	$-0.495195\pi$
$114$	0.435419	−	0.925313i	0.0407807	−	0.0866635i
$115$	5.03207	+	3.10527i	0.469243	+	0.289568i
$116$	−6.06627	+	0.766348i	−0.563239	+	0.0711536i
$117$	−0.222406	−	0.866215i	−0.0205615	−	0.0800816i
$118$	8.06107	−	2.61920i	0.742081	−	0.241117i
$119$	2.04658	+	0.810300i	0.187610	+	0.0742801i
$120$	−1.64917	−	1.51005i	−0.150548	−	0.137848i
$121$	0.104062	+	0.125789i	0.00946016	+	0.0114354i
$122$	11.5217	−	0.724883i	1.04312	−	0.0656278i
$123$	8.56026	+	4.02815i	0.771853	+	0.363206i
$124$	−2.29088			−0.205727
$125$	−0.280110	+	11.1768i	−0.0250538	+	0.999686i
$126$	−1.71873			−0.153117
$127$	12.0127	+	5.65273i	1.06595	+	0.501599i	0.877051	−	0.480398i	$-0.159508\pi$
$127$	12.0127	+	5.65273i	1.06595	+	0.501599i	0.188901	+	0.981996i	$0.439508\pi$
$128$	0.998027	−	0.0627905i	0.0882139	−	0.00554995i
$129$	3.63774	+	4.39727i	0.320285	+	0.387158i
$130$	−0.399418	−	1.95945i	−0.0350313	−	0.171855i
$131$	−12.2738	−	4.85953i	−1.07236	−	0.424579i	−0.235435	−	0.971890i	$-0.575651\pi$
$131$	−12.2738	−	4.85953i	−1.07236	−	0.424579i	−0.836929	+	0.547311i	$0.815651\pi$
$132$	3.13080	−	1.01726i	0.272501	−	0.0885411i
$133$	−0.437108	−	1.70242i	−0.0379021	−	0.147619i
$134$	3.07266	−	0.388167i	0.265437	−	0.0335325i
$135$	1.70484	−	1.44690i	0.146729	−	0.124530i
$136$	0.545290	−	1.15880i	0.0467582	−	0.0993663i
$137$	−15.1614	−	16.1452i	−1.29532	−	1.37938i	−0.883718	−	0.468019i	$-0.844968\pi$
$137$	−15.1614	−	16.1452i	−1.29532	−	1.37938i	−0.411607	−	0.911362i	$-0.635032\pi$
$138$	−0.331432	−	2.62356i	−0.0282134	−	0.223332i
$139$	−2.59751	−	0.328142i	−0.220318	−	0.0278327i	0.0143991	−	0.999896i	$-0.495416\pi$
$139$	−2.59751	−	0.328142i	−0.220318	−	0.0278327i	−0.234717	+	0.972064i	$0.575416\pi$
$140$	−3.83835	−	0.193001i	−0.324400	−	0.0163116i
$141$	0.606123	−	3.17741i	0.0510448	−	0.267586i
$142$	1.74707	+	1.44530i	0.146611	+	0.121287i
$143$	2.79991	+	0.909747i	0.234141	+	0.0760769i
$144$	−0.0627905	+	0.998027i	−0.00523254	+	0.0831689i
$145$	0.686613	−	13.6551i	0.0570201	−	1.13400i
$146$	−5.15606	+	2.04143i	−0.426719	+	0.168950i
$147$	3.11747	−	2.57899i	0.257125	−	0.212712i
$148$	−2.68851	−	4.89039i	−0.220994	−	0.401987i
$149$	2.00096	+	6.15832i	0.163925	+	0.504509i	0.998955	−	0.0456944i	$-0.0145500\pi$
$149$	2.00096	+	6.15832i	0.163925	+	0.504509i	−0.835030	+	0.550204i	$0.814550\pi$
$150$	3.96980	−	3.03985i	0.324133	−	0.248203i
$151$	3.40998	−	10.4948i	0.277500	−	0.854057i	−0.711047	−	0.703144i	$-0.751779\pi$
$151$	3.40998	−	10.4948i	0.277500	−	0.854057i	0.988547	−	0.150913i	$-0.0482213\pi$
$152$	−1.00453	+	0.191624i	−0.0814779	+	0.0155427i
$153$	1.08132	+	0.686226i	0.0874195	+	0.0554781i
$154$	3.03167	−	4.77715i	0.244299	−	0.384953i
$155$	0.896437	−	5.04351i	0.0720035	−	0.405104i
$156$	−0.570056	+	0.689079i	−0.0456410	+	0.0551705i
$157$	2.81515	−	3.87473i	0.224674	−	0.309237i	−0.681767	−	0.731569i	$-0.738788\pi$
$157$	2.81515	−	3.87473i	0.224674	−	0.309237i	0.906441	+	0.422332i	$0.138788\pi$
$158$	1.89522	−	4.78679i	0.150776	−	0.380816i
$159$	2.07213	+	4.40350i	0.164331	+	0.349220i
$160$	−0.252298	+	2.22179i	−0.0199459	+	0.175648i
$161$	−3.31318	−	3.11128i	−0.261115	−	0.245204i
$162$	−0.982287	−	0.187381i	−0.0771758	−	0.0147221i
$163$	−6.28260	+	11.4280i	−0.492091	+	0.895111i	0.507352	+	0.861739i	$0.330624\pi$
$163$	−6.28260	+	11.4280i	−0.492091	+	0.895111i	−0.999443	+	0.0333716i	$0.989376\pi$
$164$	−1.77275	−	9.29308i	−0.138429	−	0.725668i
$165$	1.01445	+	7.29072i	0.0789752	+	0.567582i
$166$	3.31567	+	1.82280i	0.257346	+	0.141477i
$167$	12.3789	+	0.778814i	0.957907	+	0.0602664i	0.534041	−	0.845458i	$-0.320673\pi$
$167$	12.3789	+	0.778814i	0.957907	+	0.0602664i	0.423866	+	0.905725i	$0.360673\pi$
$168$	1.01024	+	1.39048i	0.0779421	+	0.107278i
$169$	11.8169	−	3.03407i	0.908993	−	0.233390i
$170$	2.33780	+	1.65394i	0.179301	+	0.126851i
$171$	−0.0642121	−	1.02062i	−0.00491042	−	0.0780490i
$172$	1.41926	−	5.52764i	0.108217	−	0.421479i
$173$	0.958811	−	7.58977i	0.0728971	−	0.577040i	−0.912787	−	0.408436i	$-0.866074\pi$
$173$	0.958811	−	7.58977i	0.0728971	−	0.577040i	0.985684	−	0.168603i	$-0.0539257\pi$
$174$	−4.94672	+	3.59400i	−0.375010	+	0.272461i
$175$	1.92688	−	8.37484i	0.145658	−	0.633079i
$176$	−2.66322	−	1.93494i	−0.200748	−	0.145852i
$177$	5.80216	−	6.17867i	0.436117	−	0.464417i
$178$	−1.88718	−	4.76647i	−0.141450	−	0.357262i
$179$	24.7437	+	6.35311i	1.84943	+	0.474854i	0.998711	−	0.0507626i	$-0.0161652\pi$
$179$	24.7437	+	6.35311i	1.84943	+	0.474854i	0.850722	+	0.525616i	$0.176165\pi$
$180$	−2.17265	−	0.528773i	−0.161940	−	0.0394124i
$181$	−0.560584	−	0.883339i	−0.0416679	−	0.0656581i	0.822856	−	0.568251i	$-0.192380\pi$
$181$	−0.560584	−	0.883339i	−0.0416679	−	0.0656581i	−0.864523	+	0.502593i	$0.832380\pi$
$182$			1.53708i			0.113936i
$183$	9.74731	−	6.18583i	0.720542	−	0.457270i
$184$	−1.92769	+	1.81022i	−0.142111	+	0.133451i
$185$	11.8185	−	4.00529i	0.868916	−	0.294474i
$186$	−2.00751	+	1.10364i	−0.147198	+	0.0809227i
$187$	−3.81468	+	1.79505i	−0.278957	+	0.131267i
$188$	−2.92685	+	1.37727i	−0.213462	+	0.100448i
$189$	−1.50614	+	0.828005i	−0.109555	+	0.0602285i
$190$	−0.0287929	−	2.28651i	−0.00208886	−	0.165881i
$191$	2.31157	−	2.17071i	0.167259	−	0.157067i	−0.596398	−	0.802689i	$-0.703402\pi$
$191$	2.31157	−	2.17071i	0.167259	−	0.157067i	0.763657	+	0.645622i	$0.223402\pi$
$192$	0.844328	−	0.535827i	0.0609341	−	0.0386700i
$193$		−	2.10885i		−	0.151799i	−0.997115	−	0.0758993i	$-0.975817\pi$
$193$		−	2.10885i		−	0.151799i	0.997115	−	0.0758993i	$-0.0241827\pi$
$194$	1.33587	+	2.10499i	0.0959099	+	0.151130i
$195$	−1.29398	−	1.52465i	−0.0926641	−	0.109183i
$196$	−3.91885	−	1.00619i	−0.279918	−	0.0718707i
$197$	1.48522	+	3.75124i	0.105818	+	0.267265i	0.973032	−	0.230670i	$-0.0740918\pi$
$197$	1.48522	+	3.75124i	0.105818	+	0.267265i	−0.867214	+	0.497935i	$0.834092\pi$
$198$	2.25348	−	2.39971i	0.160148	−	0.170540i
$199$	20.4900	+	14.8868i	1.45250	+	1.05530i	0.985240	+	0.171179i	$0.0547575\pi$
$199$	20.4900	+	14.8868i	1.45250	+	1.05530i	0.467256	+	0.884122i	$0.345243\pi$
$200$	−4.79268	−	1.42485i	−0.338894	−	0.100752i
$201$	2.50559	−	1.82042i	0.176731	−	0.128402i
$202$	−1.34078	+	10.6134i	−0.0943373	+	0.746756i
$203$	−2.61352	+	10.1790i	−0.183433	+	0.714425i
$204$	−0.0804150	−	1.27816i	−0.00563018	−	0.0894891i
$205$	21.1530	−	0.266369i	1.47739	−	0.0186040i
$206$	4.49375	−	1.15380i	0.313094	−	0.0803889i
$207$	−1.55434	−	2.13937i	−0.108034	−	0.148697i
$208$	0.892547	+	0.0561543i	0.0618870	+	0.00389360i
$209$	2.95004	+	1.62180i	0.204059	+	0.112182i
$210$	−3.45655	+	1.68001i	−0.238525	+	0.115932i
$211$	1.91789	+	10.0539i	0.132033	+	0.692140i	0.985322	+	0.170703i	$0.0546039\pi$
$211$	1.91789	+	10.0539i	0.132033	+	0.692140i	−0.853290	+	0.521437i	$0.825396\pi$
$212$	2.34454	−	4.26470i	0.161024	−	0.292901i
$213$	2.22725	+	0.424870i	0.152608	+	0.0291116i
$214$	−7.59628	−	7.13339i	−0.519271	−	0.487628i
$215$	11.6141	+	5.28759i	0.792074	+	0.360611i
$216$	0.425779	+	0.904827i	0.0289706	+	0.0615657i
$217$	−1.44945	+	3.66090i	−0.0983953	+	0.248518i
$218$	−0.629778	+	0.866815i	−0.0426539	+	0.0587081i
$219$	−3.53483	+	4.27287i	−0.238861	+	0.288734i
$220$	5.30204	−	5.10609i	0.357463	−	0.344252i
$221$	0.613700	−	0.967037i	0.0412819	−	0.0650499i
$222$	−4.71192	−	2.99028i	−0.316244	−	0.200694i
$223$	−19.3618	+	3.69345i	−1.29656	+	0.247332i	−0.789058	−	0.614319i	$-0.789431\pi$
$223$	−19.3618	+	3.69345i	−1.29656	+	0.247332i	−0.507501	+	0.861651i	$0.669431\pi$
$224$	0.531117	−	1.63461i	0.0354867	−	0.109217i
$225$	2.01430	−	4.57631i	0.134287	−	0.305087i
$226$	4.72074	+	14.5289i	0.314019	+	0.966451i
$227$	10.3990	+	18.9158i	0.690209	+	1.25548i	0.956539	+	0.291603i	$0.0941887\pi$
$227$	10.3990	+	18.9158i	0.690209	+	1.25548i	−0.266331	+	0.963882i	$0.585811\pi$
$228$	−0.787958	+	0.651856i	−0.0521838	+	0.0431702i
$229$	−15.0222	+	5.94770i	−0.992694	+	0.393035i	−0.807629	−	0.589691i	$-0.799250\pi$
$229$	−15.0222	+	5.94770i	−0.992694	+	0.393035i	−0.185065	+	0.982726i	$0.559250\pi$
$230$	−3.23100	−	4.95228i	−0.213046	−	0.326544i
$231$	0.355264	−	5.64676i	0.0233747	−	0.371530i
$232$	5.81522	+	1.88948i	0.381788	+	0.124050i
$233$	−15.5490	−	12.8632i	−1.01865	−	0.842698i	−0.0310199	−	0.999519i	$-0.509876\pi$
$233$	−15.5490	−	12.8632i	−1.01865	−	0.842698i	−0.987627	+	0.156821i	$0.949876\pi$
$234$	−0.167577	+	0.878471i	−0.0109549	+	0.0574274i
$235$	−1.88685	−	6.98258i	−0.123085	−	0.455493i
$236$	−8.40907	−	1.06231i	−0.547384	−	0.0691507i
$237$	−0.645256	−	5.10773i	−0.0419139	−	0.331782i
$238$	−1.50680	−	1.60457i	−0.0976710	−	0.104009i
$239$	−1.22964	+	2.61313i	−0.0795390	+	0.169029i	−0.940641	−	0.339403i	$-0.889775\pi$
$239$	−1.22964	+	2.61313i	−0.0795390	+	0.169029i	0.861102	+	0.508432i	$0.169775\pi$
$240$	0.849265	+	2.06851i	0.0548198	+	0.133522i
$241$	8.82267	−	1.11456i	0.568318	−	0.0717953i	0.164077	−	0.986448i	$-0.447536\pi$
$241$	8.82267	−	1.11456i	0.568318	−	0.0717953i	0.404241	+	0.914652i	$0.367536\pi$
$242$	−0.0405995	−	0.158125i	−0.00260984	−	0.0101646i
$243$	−0.951057	+	0.309017i	−0.0610103	+	0.0198234i
$244$	−10.7338	−	4.24980i	−0.687159	−	0.272066i
$245$	3.74867	−	8.23387i	0.239494	−	0.526043i
$246$	−6.03045	−	7.28956i	−0.384487	−	0.464766i
$247$	−0.912755	+	0.0574256i	−0.0580772	+	0.00365391i
$248$	2.07285	+	0.975408i	0.131626	+	0.0619385i
$249$	3.78368			0.239781
$250$	5.01231	−	9.99383i	0.317007	−	0.632066i
$251$	−2.67028			−0.168546			−0.0842732	−	0.996443i	$-0.526857\pi$
$251$	−2.67028			−0.168546			−0.0842732	+	0.996443i	$0.526857\pi$
$252$	1.55515	+	0.731800i	0.0979655	+	0.0460991i
$253$	8.68800	−	0.546603i	0.546210	−	0.0343646i
$254$	−8.46257	−	10.2295i	−0.530989	−	0.641855i
$255$	2.84542	+	0.323115i	0.178187	+	0.0202342i
$256$	−0.929776	−	0.368125i	−0.0581110	−	0.0230078i
$257$	7.11522	−	2.31187i	0.443835	−	0.144211i	−0.0785693	−	0.996909i	$-0.525035\pi$
$257$	7.11522	−	2.31187i	0.443835	−	0.144211i	0.522404	+	0.852698i	$0.325035\pi$
$258$	−1.41926	−	5.52764i	−0.0883591	−	0.344136i
$259$	−9.51605	+	1.20216i	−0.591299	+	0.0746984i
$260$	−0.472887	+	1.94302i	−0.0293272	+	0.120501i
$261$	−2.60342	+	5.53255i	−0.161148	+	0.342456i
$262$	9.03655	+	9.62295i	0.558280	+	0.594508i
$263$	1.29331	+	10.2376i	0.0797490	+	0.631278i	0.980440	+	0.196818i	$0.0630608\pi$
$263$	1.29331	+	10.2376i	0.0797490	+	0.631278i	−0.900691	+	0.434460i	$0.856939\pi$
$264$	−3.26596	−	0.412587i	−0.201006	−	0.0253930i
$265$	8.47157	+	6.83046i	0.520405	+	0.419592i
$266$	−0.329350	+	1.72651i	−0.0201937	+	0.105859i
$267$	−3.95001	−	3.26773i	−0.241737	−	0.199982i
$268$	−2.94550	−	0.957050i	−0.179925	−	0.0584611i
$269$	0.876219	−	13.9271i	0.0534240	−	0.849150i	−0.876501	−	0.481400i	$-0.840128\pi$
$269$	0.876219	−	13.9271i	0.0534240	−	0.849150i	0.929925	−	0.367750i	$-0.119872\pi$
$270$	−2.15864	+	0.583314i	−0.131371	+	0.0354994i
$271$	−4.38313	+	1.73540i	−0.266256	+	0.105418i	−0.497460	−	0.867487i	$-0.665734\pi$
$271$	−4.38313	+	1.73540i	−0.266256	+	0.105418i	0.231203	+	0.972905i	$0.425734\pi$
$272$	−0.986786	+	0.816341i	−0.0598327	+	0.0494979i
$273$	0.740494	+	1.34695i	0.0448168	+	0.0815214i
$274$	6.84413	+	21.0641i	0.413469	+	1.27253i
$275$	9.16665	+	13.6708i	0.552770	+	0.824381i
$276$	−0.817167	+	2.51498i	−0.0491877	+	0.151384i
$277$	−11.4355	+	2.18144i	−0.687094	+	0.131070i	−0.519094	−	0.854717i	$-0.673731\pi$
$277$	−11.4355	+	2.18144i	−0.687094	+	0.131070i	−0.167999	+	0.985787i	$0.553731\pi$
$278$	2.21059	+	1.40288i	0.132582	+	0.0841391i
$279$	−1.22751	+	1.93425i	−0.0734893	+	0.115801i
$280$	3.39087	+	1.80892i	0.202643	+	0.108104i
$281$	8.47973	−	10.2502i	0.505858	−	0.611478i	−0.454329	−	0.890834i	$-0.650121\pi$
$281$	8.47973	−	10.2502i	0.505858	−	0.611478i	0.960188	+	0.279356i	$0.0901210\pi$
$282$	−1.90131	+	2.61693i	−0.113222	+	0.155836i
$283$	−2.42701	+	6.12993i	−0.144271	+	0.364387i	−0.983886	−	0.178794i	$-0.942780\pi$
$283$	−2.42701	+	6.12993i	−0.144271	+	0.364387i	0.839616	+	0.543181i	$0.182780\pi$
$284$	−0.965416	−	2.05161i	−0.0572869	−	0.121741i
$285$	−1.12677	−	1.98982i	−0.0667439	−	0.117866i
$286$	−2.14609	−	2.01531i	−0.126901	−	0.119168i
$287$	−15.9723	−	3.04688i	−0.942816	−	0.179852i
$288$	0.481754	−	0.876307i	0.0283876	−	0.0516369i
$289$	−2.87815	−	15.0878i	−0.169303	−	0.887516i
$290$	−6.43535	+	12.0632i	−0.377896	+	0.708376i
$291$	2.18472	+	1.20106i	0.128071	+	0.0704074i
$292$	5.53454	+	0.348204i	0.323885	+	0.0203771i
$293$	−9.60075	−	13.2143i	−0.560882	−	0.771987i	0.430557	−	0.902564i	$-0.358317\pi$
$293$	−9.60075	−	13.2143i	−0.560882	−	0.771987i	−0.991438	+	0.130576i	$0.958317\pi$
$294$	−3.91885	+	1.00619i	−0.228552	+	0.0586822i
$295$	5.62928	−	18.0974i	0.327749	−	1.05367i
$296$	0.350414	+	5.56967i	0.0203674	+	0.323730i
$297$	0.818668	−	3.18850i	0.0475039	−	0.185016i
$298$	0.811563	−	6.42418i	0.0470126	−	0.372143i
$299$	−1.91326	+	1.39007i	−0.110647	+	0.0803897i
$300$	−4.88629	+	1.06028i	−0.282110	+	0.0612155i
$301$	−7.93539	−	5.76540i	−0.457388	−	0.332312i
$302$	−7.55392	+	8.04411i	−0.434679	+	0.462886i
$303$	3.93811	+	9.94652i	0.226238	+	0.571413i
$304$	0.990512	+	0.254320i	0.0568098	+	0.0145863i
$305$	13.5564	−	21.9681i	0.776237	−	1.25789i
$306$	−0.686226	−	1.08132i	−0.0392290	−	0.0618149i
$307$			9.63792i			0.550065i	0.961435	+	0.275033i	$0.0886886\pi$
$307$			9.63792i			0.550065i	−0.961435	+	0.275033i	$0.911311\pi$
$308$	−4.77715	+	3.03167i	−0.272203	+	0.172745i
$309$	3.38205	−	3.17596i	0.192398	−	0.180674i
$310$	−2.95854	+	4.18182i	−0.168034	+	0.237511i
$311$	−21.7460	+	11.9549i	−1.23310	+	0.677903i	−0.958893	−	0.283768i	$-0.908415\pi$
$311$	−21.7460	+	11.9549i	−1.23310	+	0.677903i	−0.274207	+	0.961671i	$0.588415\pi$
$312$	0.809197	−	0.380779i	0.0458118	−	0.0215574i
$313$	−30.1317	+	14.1789i	−1.70314	+	0.801439i	−0.707656	+	0.706557i	$0.750247\pi$
$313$	−30.1317	+	14.1789i	−1.70314	+	0.801439i	−0.995489	+	0.0948820i	$0.969753\pi$
$314$	−4.19701	+	2.30732i	−0.236851	+	0.130210i
$315$	−2.21965	+	3.13741i	−0.125063	+	0.176773i
$316$	−3.75296	+	3.52427i	−0.211121	+	0.198256i
$317$	−0.564705	+	0.358373i	−0.0317170	+	0.0201282i	−0.551591	−	0.834115i	$-0.685979\pi$
$317$	−0.564705	+	0.358373i	−0.0317170	+	0.0201282i	0.519874	+	0.854243i	$0.325979\pi$
$318$		−	4.86668i		−	0.272910i
$319$	−10.7853	−	16.9950i	−0.603863	−	0.951536i
$320$	1.17428	−	1.90291i	0.0656441	−	0.106376i
$321$	−10.0932	−	2.59150i	−0.563348	−	0.144643i
$322$	1.67314	+	4.22586i	0.0932402	+	0.235498i
$323$	0.896539	−	0.954718i	0.0498848	−	0.0531219i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−4.09265	−	1.80141i	−0.227019	−	0.0999243i
$326$	10.5505	−	7.66537i	0.584337	−	0.424546i
$327$	−0.134287	+	1.06299i	−0.00742610	+	0.0587837i
$328$	−2.35277	+	9.16343i	−0.129910	+	0.505966i
$329$	0.349089	+	5.54862i	0.0192459	+	0.305905i
$330$	2.18633	−	7.02878i	0.120354	−	0.386921i
$331$	5.03827	−	1.29361i	0.276928	−	0.0711031i	−0.107671	−	0.994187i	$-0.534339\pi$
$331$	5.03827	−	1.29361i	0.276928	−	0.0711031i	0.384600	+	0.923083i	$0.374339\pi$
$332$	−2.22399	−	3.06106i	−0.122057	−	0.167998i
$333$	−5.56967	−	0.350414i	−0.305216	−	0.0192026i
$334$	−10.8692	−	5.97537i	−0.594733	−	0.326958i
$335$	3.25960	−	6.11020i	0.178091	−	0.333836i
$336$	−0.322058	−	1.68829i	−0.0175697	−	0.0921036i
$337$	−14.0536	+	25.5633i	−0.765546	+	1.39252i	0.149330	+	0.988787i	$0.452288\pi$
$337$	−14.0536	+	25.5633i	−0.765546	+	1.39252i	−0.914876	+	0.403735i	$0.867712\pi$
$338$	−11.9841	−	2.28609i	−0.651850	−	0.124347i
$339$	11.1362	+	10.4576i	0.604834	+	0.567977i
$340$	−1.41109	−	2.49191i	−0.0765270	−	0.135143i
$341$	−3.21097	−	6.82365i	−0.173884	−	0.369521i
$342$	−0.376459	+	0.950827i	−0.0203566	+	0.0514148i
$343$	−11.1591	+	15.3592i	−0.602536	+	0.829320i
$344$	−3.63774	+	4.39727i	−0.196134	+	0.237085i
$345$	−5.21713	−	2.78317i	−0.280881	−	0.149841i
$346$	−4.09913	+	6.45919i	−0.220370	+	0.347248i
$347$	20.6365	+	13.0963i	1.10782	+	0.703046i	0.958315	−	0.285715i	$-0.0922310\pi$
$347$	20.6365	+	13.0963i	1.10782	+	0.703046i	0.149508	+	0.988760i	$0.452231\pi$
$348$	6.00618	−	1.14574i	0.321965	−	0.0614181i
$349$	−8.29400	+	25.5263i	−0.443968	+	1.36639i	0.439644	+	0.898172i	$0.355105\pi$
$349$	−8.29400	+	25.5263i	−0.443968	+	1.36639i	−0.883612	+	0.468220i	$0.844895\pi$
$350$	−5.30933	+	6.75736i	−0.283796	+	0.361196i
$351$	0.276357	+	0.850541i	0.0147509	+	0.0453985i
$352$	1.58590	+	2.88473i	0.0845285	+	0.153757i
$353$	10.2654	−	8.49231i	0.546374	−	0.452000i	−0.322827	−	0.946458i	$-0.604633\pi$
$353$	10.2654	−	8.49231i	0.546374	−	0.452000i	0.869202	+	0.494458i	$0.164633\pi$
$354$	−7.88070	+	3.12019i	−0.418854	+	0.165836i
$355$	4.89453	−	1.32261i	0.259775	−	0.0701969i
$356$	−0.321894	+	5.11635i	−0.0170603	+	0.271166i
$357$	−2.09342	−	0.680195i	−0.110796	−	0.0359997i
$358$	−19.6838	−	16.2838i	−1.04032	−	0.860627i
$359$	−6.90811	+	36.2136i	−0.364596	+	1.91128i	0.0449472	+	0.998989i	$0.485688\pi$
$359$	−6.90811	+	36.2136i	−0.364596	+	1.91128i	−0.409543	+	0.912291i	$0.634312\pi$
$360$	1.74073	+	1.40352i	0.0917445	+	0.0739718i
$361$	17.8126	+	2.25026i	0.937507	+	0.118435i
$362$	0.131124	+	1.03795i	0.00689173	+	0.0545537i
$363$	−0.111755	−	0.119007i	−0.00586561	−	0.00624624i
$364$	0.654457	−	1.39079i	0.0343029	−	0.0728973i
$365$	−2.93230	+	12.0484i	−0.153484	+	0.630642i
$366$	−11.4534	+	1.44690i	−0.598680	+	0.0756309i
$367$	0.458999	+	1.78768i	0.0239596	+	0.0933163i	0.979438	−	0.201743i	$-0.0646606\pi$
$367$	0.458999	+	1.78768i	0.0239596	+	0.0933163i	−0.955479	+	0.295059i	$0.904661\pi$
$368$	2.51498	−	0.817167i	0.131102	−	0.0425978i
$369$	−8.79630	−	3.48270i	−0.457917	−	0.181302i
$370$	−12.3991	−	1.40799i	−0.644598	−	0.0731981i
$371$	−5.33174	−	6.44496i	−0.276810	−	0.334606i
$372$	2.28636	−	0.143845i	0.118542	−	0.00745803i
$373$	−4.34462	−	2.04442i	−0.224956	−	0.105856i	0.309999	−	0.950737i	$-0.399671\pi$
$373$	−4.34462	−	2.04442i	−0.224956	−	0.105856i	−0.534955	+	0.844881i	$0.679671\pi$
$374$	4.21592			0.218000
$375$	−0.422242	−	11.1724i	−0.0218045	−	0.576938i
$376$	3.23471			0.166817
$377$	4.94782	+	2.32827i	0.254826	+	0.119912i
$378$	1.71534	−	0.107920i	0.0882275	−	0.00555081i
$379$	−17.7247	−	21.4254i	−0.910454	−	1.10055i	−0.994567	−	0.104094i	$-0.966806\pi$
$379$	−17.7247	−	21.4254i	−0.910454	−	1.10055i	0.0841130	−	0.996456i	$-0.473194\pi$
$380$	−0.947497	+	2.08116i	−0.0486056	+	0.106761i
$381$	−12.3439	−	4.88729i	−0.632397	−	0.250384i
$382$	−3.01582	+	0.979898i	−0.154303	+	0.0501359i
$383$	5.48247	+	21.3528i	0.280141	+	1.09108i	0.940408	+	0.340047i	$0.110443\pi$
$383$	5.48247	+	21.3528i	0.280141	+	1.09108i	−0.660267	+	0.751031i	$0.729557\pi$
$384$	−0.992115	+	0.125333i	−0.0506286	+	0.00639588i
$385$	−4.80508	−	11.7035i	−0.244889	−	0.596466i
$386$	−0.897906	+	1.90815i	−0.0457022	+	0.0971221i
$387$	−3.90666	−	4.16018i	−0.198587	−	0.211474i
$388$	−0.312468	−	2.47344i	−0.0158632	−	0.125570i
$389$	31.8389	+	4.02218i	1.61429	+	0.203933i	0.880025	−	0.474927i	$-0.157525\pi$
$389$	31.8389	+	4.02218i	1.61429	+	0.203933i	0.734268	+	0.678859i	$0.237525\pi$
$390$	0.521665	+	1.93050i	0.0264155	+	0.0977547i
$391$	0.634597	−	3.32667i	0.0320929	−	0.168237i
$392$	3.11747	+	2.57899i	0.157456	+	0.130259i
$393$	12.5547	+	4.07926i	0.633300	+	0.205772i
$394$	0.253332	−	4.02660i	0.0127627	−	0.202857i
$395$	−6.29034	−	9.64146i	−0.316501	−	0.485114i
$396$	−3.06075	+	1.21184i	−0.153809	+	0.0608971i
$397$	−26.2408	+	21.7083i	−1.31699	+	1.08951i	−0.327506	+	0.944849i	$0.606208\pi$
$397$	−26.2408	+	21.7083i	−1.31699	+	1.08951i	−0.989482	+	0.144658i	$0.953792\pi$
$398$	−12.2014	−	22.1942i	−0.611600	−	1.11250i
$399$	0.543142	+	1.67162i	0.0271911	+	0.0836856i
$400$	3.72988	+	3.32987i	0.186494	+	0.166493i
$401$	4.15362	−	12.7835i	0.207422	−	0.638378i	−0.792184	−	0.610283i	$-0.791056\pi$
$401$	4.15362	−	12.7835i	0.207422	−	0.638378i	0.999605	−	0.0280955i	$-0.00894425\pi$
$402$	−3.04222	+	0.580335i	−0.151732	+	0.0289445i
$403$	1.72982	+	1.09778i	0.0861686	+	0.0546843i
$404$	5.73215	−	9.03242i	0.285185	−	0.449379i
$405$	−1.61062	+	1.55110i	−0.0800324	+	0.0770746i
$406$	6.69878	−	8.09744i	0.332455	−	0.401869i
$407$	10.7983	−	14.8626i	0.535252	−	0.736711i
$408$	−0.471452	+	1.19075i	−0.0233404	+	0.0589510i
$409$	−5.12873	−	10.8991i	−0.253599	−	0.538926i	0.736972	−	0.675923i	$-0.236255\pi$
$409$	−5.12873	−	10.8991i	−0.253599	−	0.538926i	−0.990571	+	0.136997i	$0.956255\pi$
$410$	−19.2532	−	8.76549i	−0.950849	−	0.432897i
$411$	16.1452	+	15.1614i	0.796386	+	0.747856i
$412$	−4.55733	−	0.869357i	−0.224523	−	0.0428301i
$413$	−7.01809	+	12.7659i	−0.345338	+	0.628167i
$414$	0.495513	+	2.59757i	0.0243531	+	0.127663i
$415$	7.60939	−	3.69844i	0.373530	−	0.181549i
$416$	−0.783691	−	0.430838i	−0.0384236	−	0.0211236i
$417$	2.61299	+	0.164396i	0.127959	+	0.00805049i
$418$	−1.97875	−	2.72352i	−0.0967839	−	0.133212i
$419$	−1.71977	+	0.441562i	−0.0840163	+	0.0215717i	−0.290464	−	0.956886i	$-0.593810\pi$
$419$	−1.71977	+	0.441562i	−0.0840163	+	0.0215717i	0.206448	+	0.978458i	$0.433810\pi$
$420$	3.84289	−	0.0483916i	0.187514	−	0.00236127i
$421$	0.489702	+	7.78360i	0.0238666	+	0.379349i	0.991770	+	0.128029i	$0.0408649\pi$
$421$	0.489702	+	7.78360i	0.0238666	+	0.379349i	−0.967904	+	0.251321i	$0.919135\pi$
$422$	2.54539	−	9.91366i	0.123908	−	0.482589i
$423$	−0.405416	+	3.20920i	−0.0197120	+	0.156037i
$424$	−3.93722	+	2.86056i	−0.191209	+	0.138921i
$425$	6.03827	−	2.13150i	0.292899	−	0.103393i
$426$	−1.83437	−	1.33275i	−0.0888756	−	0.0645719i
$427$	−13.5827	+	14.4641i	−0.657311	+	0.699965i
$428$	3.83608	+	9.68882i	0.185424	+	0.468327i
$429$	−2.85151	−	0.732144i	−0.137672	−	0.0353482i
$430$	−8.25739	−	9.72939i	−0.398207	−	0.469193i
$431$	−6.29640	−	9.92155i	−0.303287	−	0.477904i	0.658166	−	0.752873i	$-0.271332\pi$
$431$	−6.29640	−	9.92155i	−0.303287	−	0.477904i	−0.961453	+	0.274969i	$0.911332\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	21.0459	−	13.3561i	1.01140	−	0.641854i	0.0766120	−	0.997061i	$-0.475590\pi$
$433$	21.0459	−	13.3561i	1.01140	−	0.641854i	0.934788	+	0.355207i	$0.115590\pi$
$434$	2.87024	−	2.69534i	0.137776	−	0.129380i
$435$	0.172156	+	13.6713i	0.00825424	+	0.655489i
$436$	0.938912	−	0.516171i	0.0449657	−	0.0247201i
$437$	−2.44690	+	1.15143i	−0.117051	+	0.0550802i
$438$	5.01771	−	2.36115i	0.239755	−	0.112820i
$439$	6.99110	−	3.84339i	0.333667	−	0.183435i	−0.306109	−	0.951997i	$-0.599027\pi$
$439$	6.99110	−	3.84339i	0.333667	−	0.183435i	0.639776	+	0.768562i	$0.279027\pi$
$440$	−6.97149	+	2.36263i	−0.332353	+	0.112634i
$441$	−2.94938	+	2.76965i	−0.140447	+	0.131888i
$442$	−0.967037	+	0.613700i	−0.0459972	+	0.0291907i
$443$			7.55067i			0.358743i	0.983781	+	0.179371i	$0.0574064\pi$
$443$			7.55067i			0.358743i	−0.983781	+	0.179371i	$0.942594\pi$
$444$	2.99028	+	4.71192i	0.141912	+	0.223618i
$445$	−11.1380	−	2.71074i	−0.527992	−	0.128501i
$446$	19.0916	+	4.90190i	0.904015	+	0.232112i
$447$	−2.38370	−	6.02053i	−0.112745	−	0.284761i
$448$	−1.17655	+	1.25290i	−0.0555869	+	0.0591940i
$449$	13.3529	+	9.70149i	0.630165	+	0.457841i	0.856457	−	0.516218i	$-0.172661\pi$
$449$	13.3529	+	9.70149i	0.630165	+	0.457841i	−0.226293	+	0.974059i	$0.572661\pi$
$450$	−3.77109	+	3.28312i	−0.177771	+	0.154768i
$451$	25.1958	−	18.3058i	1.18642	−	0.861988i
$452$	1.91467	−	15.1562i	0.0900585	−	0.712886i
$453$	−2.74427	+	10.6882i	−0.128937	+	0.502177i
$454$	−1.35538	−	21.5432i	−0.0636113	−	1.01107i
$455$	2.80582	+	1.98506i	0.131539	+	0.0930608i
$456$	0.990512	−	0.254320i	0.0463850	−	0.0119096i
$457$	5.96015	+	8.20344i	0.278804	+	0.383741i	0.925337	−	0.379145i	$-0.123782\pi$
$457$	5.96015	+	8.20344i	0.278804	+	0.383741i	−0.646533	+	0.762886i	$0.723782\pi$
$458$	16.1249	+	1.01449i	0.753467	+	0.0474041i
$459$	−1.12227	−	0.616976i	−0.0523833	−	0.0287980i
$460$	0.814913	+	5.85665i	0.0379955	+	0.273068i
$461$	3.00349	+	15.7448i	0.139886	+	0.733309i	0.981235	+	0.192817i	$0.0617622\pi$
$461$	3.00349	+	15.7448i	0.139886	+	0.733309i	−0.841349	+	0.540493i	$0.818238\pi$
$462$	−2.72573	+	4.95808i	−0.126812	+	0.230671i
$463$	−41.6768	−	7.95027i	−1.93688	−	0.369480i	−0.999792	−	0.0203960i	$-0.993507\pi$
$463$	−41.6768	−	7.95027i	−1.93688	−	0.369480i	−0.937091	−	0.349084i	$-0.886493\pi$
$464$	−4.45727	−	4.18565i	−0.206923	−	0.194314i
$465$	−0.577984	+	5.08984i	−0.0268033	+	0.236036i
$466$	8.59223	+	18.2594i	0.398028	+	0.845852i
$467$	8.56295	−	21.6275i	0.396246	−	1.00080i	−0.585511	−	0.810664i	$-0.699106\pi$
$467$	8.56295	−	21.6275i	0.396246	−	1.00080i	0.981757	−	0.190139i	$-0.0608939\pi$
$468$	0.525663	−	0.723513i	0.0242988	−	0.0334444i
$469$	−3.39304	+	4.10148i	−0.156676	+	0.189389i
$470$	−1.26576	+	7.12141i	−0.0583854	+	0.328486i
$471$	−2.56630	+	4.04385i	−0.118249	+	0.186331i
$472$	7.15645	+	4.54162i	0.329402	+	0.209045i
$473$	18.4540	−	3.52029i	0.848516	−	0.161863i
$474$	−1.59092	+	4.89634i	−0.0730733	+	0.224897i
$475$	−4.21104	−	2.90035i	−0.193216	−	0.133077i
$476$	0.680195	+	2.09342i	0.0311767	+	0.0959519i
$477$	−2.34454	−	4.26470i	−0.107349	−	0.195267i
$478$	2.22523	−	1.84087i	0.101780	−	0.0841994i
$479$	14.1091	−	5.58618i	0.644660	−	0.255239i	−0.0229654	−	0.999736i	$-0.507311\pi$
$479$	14.1091	−	5.58618i	0.644660	−	0.255239i	0.667625	+	0.744497i	$0.267311\pi$
$480$	0.112293	−	2.23325i	0.00512544	−	0.101933i
$481$	−0.313379	+	4.98102i	−0.0142889	+	0.227115i
$482$	−8.45755	−	2.74802i	−0.385231	−	0.125169i
$483$	3.50200	+	2.89711i	0.159347	+	0.131823i
$484$	−0.0305907	+	0.160362i	−0.00139049	+	0.00728918i
$485$	5.56771	+	0.279957i	0.252817	+	0.0127122i
$486$	0.992115	+	0.125333i	0.0450032	+	0.00568523i
$487$	−2.23323	−	17.6778i	−0.101197	−	0.801059i	−0.958270	−	0.285864i	$-0.907719\pi$
$487$	−2.23323	−	17.6778i	−0.101197	−	0.801059i	0.857073	−	0.515195i	$-0.172281\pi$
$488$	7.90273	+	8.41555i	0.357740	+	0.380954i
$489$	5.55263	−	11.7999i	0.251099	−	0.533612i
$490$	−6.89771	+	5.85412i	−0.311607	+	0.264462i
$491$	22.8381	−	2.88513i	1.03067	−	0.130204i	0.408236	−	0.912876i	$-0.366144\pi$
$491$	22.8381	−	2.88513i	1.03067	−	0.130204i	0.622434	+	0.782672i	$0.286144\pi$
$492$	2.35277	+	9.16343i	0.106071	+	0.413120i
$493$	−7.44748	+	2.41983i	−0.335417	+	0.108984i
$494$	0.850336	+	0.336672i	0.0382584	+	0.0151476i
$495$	−1.47024	−	7.21264i	−0.0660824	−	0.324184i
$496$	−1.46026	−	1.76515i	−0.0655676	−	0.0792576i
$497$	−3.88938	+	0.244699i	−0.174462	+	0.0109762i
$498$	−3.42358	−	1.61101i	−0.153414	−	0.0721912i
$499$	−6.66707			−0.298459			−0.149230	−	0.988803i	$-0.547679\pi$
$499$	−6.66707			−0.298459			−0.149230	+	0.988803i	$0.547679\pi$
$500$	−8.79044	+	6.90855i	−0.393121	+	0.308960i
$501$	−12.4034			−0.554141
$502$	2.41614	+	1.13695i	0.107838	+	0.0507445i
$503$	31.9281	−	2.00875i	1.42360	−	0.0895655i	0.667789	−	0.744351i	$-0.267241\pi$
$503$	31.9281	−	2.00875i	1.42360	−	0.0895655i	0.755815	+	0.654785i	$0.227241\pi$
$504$	−1.09556	−	1.32430i	−0.0488001	−	0.0589892i
$505$	17.6424	+	16.1541i	0.785076	+	0.718849i
$506$	−8.09387	−	3.20459i	−0.359817	−	0.142461i
$507$	−11.6031	+	3.77007i	−0.515311	+	0.167435i
$508$	3.30166	+	12.8591i	0.146487	+	0.570530i
$509$	−38.8382	+	4.90641i	−1.72147	+	0.217473i	−0.923065	−	0.384644i	$-0.874324\pi$
$509$	−38.8382	+	4.90641i	−1.72147	+	0.217473i	−0.798408	+	0.602116i	$0.794324\pi$
$510$	−2.43703	−	1.50388i	−0.107914	−	0.0665930i
$511$	4.05819	−	8.62409i	0.179524	−	0.381507i
$512$	0.684547	+	0.728969i	0.0302530	+	0.0322162i
$513$	0.128171	+	1.01458i	0.00565888	+	0.0447947i
$514$	−7.42239	−	0.937666i	−0.327388	−	0.0413587i
$515$	3.69726	−	9.69306i	0.162921	−	0.427127i
$516$	−1.06937	+	5.60585i	−0.0470765	+	0.246784i
$517$	−8.20473	−	6.78754i	−0.360844	−	0.298516i
$518$	9.12224	+	2.96399i	0.400808	+	0.130230i
$519$	−0.480353	+	7.63500i	−0.0210852	+	0.335139i
$520$	1.25518	−	1.55676i	0.0550433	−	0.0682682i
$521$	−21.5958	+	8.55037i	−0.946128	+	0.374599i	−0.789978	−	0.613135i	$-0.789908\pi$
$521$	−21.5958	+	8.55037i	−0.946128	+	0.374599i	−0.156150	+	0.987733i	$0.549908\pi$
$522$	4.71129	−	3.89752i	0.206208	−	0.170590i
$523$	−3.23586	−	5.88601i	−0.141494	−	0.257377i	0.796059	−	0.605219i	$-0.206915\pi$
$523$	−3.23586	−	5.88601i	−0.141494	−	0.257377i	−0.937553	+	0.347842i	$0.886915\pi$
$524$	−4.07926	−	12.5547i	−0.178203	−	0.548454i
$525$	−1.39722	+	8.47931i	−0.0609795	+	0.370067i
$526$	3.18874	−	9.81393i	0.139036	−	0.427908i
$527$	−2.88193	+	0.549757i	−0.125539	+	0.0239478i
$528$	2.77946	+	1.76390i	0.120961	+	0.0767639i
$529$	8.57704	−	13.5152i	0.372915	−	0.587619i
$530$	−4.75704	−	9.78740i	−0.206633	−	0.425138i
$531$	−5.40275	+	6.53080i	−0.234459	+	0.283413i
$532$	1.03312	−	1.42196i	0.0447913	−	0.0616499i
$533$	−3.11462	+	7.86663i	−0.134909	+	0.340742i
$534$	2.18274	+	4.63857i	0.0944566	+	0.200730i
$535$	−22.8316	+	4.65405i	−0.987097	+	0.201212i
$536$	2.25767	+	2.12010i	0.0975166	+	0.0915742i
$537$	−25.0938	−	4.78690i	−1.08288	−	0.206570i
$538$	−6.72270	+	12.2285i	−0.289836	+	0.527210i
$539$	−2.49573	−	13.0831i	−0.107499	−	0.563528i
$540$	2.20156	+	0.391307i	0.0947402	+	0.0168392i
$541$	27.5787	+	15.1615i	1.18570	+	0.651845i	0.947620	−	0.319400i	$-0.103482\pi$
$541$	27.5787	+	15.1615i	1.18570	+	0.651845i	0.238081	+	0.971245i	$0.423482\pi$
$542$	4.70488	+	0.296006i	0.202092	+	0.0127145i
$543$	0.614943	+	0.846397i	0.0263897	+	0.0363224i
$544$	1.24045	−	0.318494i	0.0531839	−	0.0136553i
$545$	0.768980	+	2.26905i	0.0329395	+	0.0971956i
$546$	−0.0965141	−	1.53405i	−0.00413042	−	0.0656512i
$547$	6.22826	−	24.2575i	0.266301	−	1.03718i	−0.684908	−	0.728629i	$-0.740158\pi$
$547$	6.22826	−	24.2575i	0.266301	−	1.03718i	0.951209	−	0.308546i	$-0.0998423\pi$
$548$	2.77589	−	21.9734i	0.118580	−	0.938658i
$549$	−9.33967	+	6.78566i	−0.398607	+	0.289605i
$550$	−2.47348	−	16.2727i	−0.105470	−	0.693870i
$551$	5.05872	+	3.67537i	0.215509	+	0.156576i
$552$	1.81022	−	1.92769i	0.0770481	−	0.0820479i
$553$	3.25738	+	8.22720i	0.138518	+	0.349856i
$554$	11.2760	+	2.89518i	0.479070	+	0.123004i
$555$	−11.5437	+	4.73947i	−0.490003	+	0.201179i
$556$	−1.40288	−	2.21059i	−0.0594954	−	0.0937497i
$557$		−	3.12849i		−	0.132558i	−0.997801	−	0.0662792i	$-0.978887\pi$
$557$		−	3.12849i		−	0.132558i	0.997801	−	0.0662792i	$-0.0211128\pi$
$558$	1.93425	−	1.22751i	0.0818834	−	0.0519648i
$559$	−3.72049	+	3.49377i	−0.157360	+	0.147771i
$560$	−2.29795	−	3.08052i	−0.0971060	−	0.130176i
$561$	3.69444	−	2.03104i	0.155979	−	0.0857504i
$562$	−12.0370	+	5.66419i	−0.507751	+	0.238930i
$563$	−15.2227	+	7.16325i	−0.641559	+	0.301895i	−0.718904	−	0.695110i	$-0.755356\pi$
$563$	−15.2227	+	7.16325i	−0.641559	+	0.301895i	0.0773446	+	0.997004i	$0.475356\pi$
$564$	2.83459	−	1.55833i	0.119358	−	0.0656176i
$565$	32.6180	+	10.1460i	1.37225	+	0.426845i
$566$	4.80602	−	4.51316i	0.202012	−	0.189702i
$567$	1.45117	−	0.920942i	0.0609435	−	0.0386759i
$568$			2.26741i			0.0951384i
$569$	−10.2184	−	16.1017i	−0.428379	−	0.675018i	0.559747	−	0.828664i	$-0.310898\pi$
$569$	−10.2184	−	16.1017i	−0.428379	−	0.675018i	−0.988126	+	0.153646i	$0.950898\pi$
$570$	0.172307	+	2.28019i	0.00721716	+	0.0955068i
$571$	−7.57146	−	1.94402i	−0.316856	−	0.0813548i	0.0869127	−	0.996216i	$-0.472300\pi$
$571$	−7.57146	−	1.94402i	−0.316856	−	0.0813548i	−0.403769	+	0.914861i	$0.632300\pi$
$572$	1.08376	+	2.73726i	0.0453143	+	0.114451i
$573$	−2.17071	+	2.31157i	−0.0906827	+	0.0965673i
$574$	13.1549	+	9.55758i	0.549074	+	0.398926i
$575$	−13.2127	−	0.497668i	−0.551006	−	0.0207542i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−0.613489	+	4.85626i	−0.0255399	+	0.202169i	−0.999722	−	0.0235965i	$-0.992488\pi$
$577$	−0.613489	+	4.85626i	−0.0255399	+	0.202169i	0.974182	+	0.225765i	$0.0724883\pi$
$578$	−3.81984	+	14.8773i	−0.158884	+	0.618813i
$579$	0.132416	+	2.10469i	0.00550302	+	0.0874680i
$580$	10.9591	−	8.17507i	0.455053	−	0.339452i
$581$	−6.29882	+	1.61726i	−0.261319	+	0.0670954i
$582$	−1.46541	−	2.01696i	−0.0607431	−	0.0836057i
$583$	15.9891	+	1.00595i	0.662201	+	0.0416622i
$584$	−4.85955	−	2.67156i	−0.201089	−	0.110550i
$585$	1.38716	+	1.44040i	0.0573522	+	0.0595531i
$586$	3.06064	+	16.0445i	0.126434	+	0.662790i
$587$	19.4077	−	35.3026i	0.801043	−	1.45709i	−0.0864419	−	0.996257i	$-0.527550\pi$
$587$	19.4077	−	35.3026i	0.801043	−	1.45709i	0.887485	−	0.460836i	$-0.152450\pi$
$588$	3.97430	+	0.758138i	0.163897	+	0.0312651i
$589$	1.70779	+	1.60372i	0.0703681	+	0.0660800i
$590$	−12.7990	+	13.9782i	−0.526928	+	0.575473i
$591$	−1.71783	−	3.65058i	−0.0706623	−	0.150165i
$592$	2.05439	−	5.18878i	0.0844347	−	0.213258i
$593$	1.73676	−	2.39044i	0.0713200	−	0.0981636i	−0.771867	−	0.635784i	$-0.780677\pi$
$593$	1.73676	−	2.39044i	0.0713200	−	0.0981636i	0.843187	+	0.537621i	$0.180677\pi$
$594$	−2.09835	+	2.53647i	−0.0860963	+	0.104073i
$595$	−4.87497	+	0.678319i	−0.199854	+	0.0278084i
$596$	−3.46961	+	5.46723i	−0.142121	+	0.223946i
$597$	−21.3843	−	13.5709i	−0.875201	−	0.555420i
$598$	2.32303	−	0.443143i	0.0949960	−	0.0181214i
$599$	6.26790	−	19.2906i	0.256099	−	0.788193i	−0.737512	−	0.675335i	$-0.763999\pi$
$599$	6.26790	−	19.2906i	0.256099	−	0.788193i	0.993611	−	0.112859i	$-0.0360007\pi$
$600$	4.87269	+	1.12111i	0.198927	+	0.0457690i
$601$	6.53501	+	20.1127i	0.266569	+	0.820414i	0.991328	+	0.131412i	$0.0419510\pi$
$601$	6.53501	+	20.1127i	0.266569	+	0.820414i	−0.724759	+	0.689002i	$0.758049\pi$
$602$	4.72537	+	8.59541i	0.192592	+	0.350323i
$603$	−2.38634	+	1.97415i	−0.0971793	+	0.0803937i
$604$	10.2600	−	4.06222i	0.417474	−	0.165290i
$605$	−0.341077	−	0.130098i	−0.0138667	−	0.00528924i
$606$	0.671718	−	10.6766i	0.0272867	−	0.433709i
$607$	−16.4948	−	5.35949i	−0.669504	−	0.217535i	−0.0455099	−	0.998964i	$-0.514491\pi$
$607$	−16.4948	−	5.35949i	−0.669504	−	0.217535i	−0.623995	+	0.781429i	$0.714491\pi$
$608$	−0.787958	−	0.651856i	−0.0319559	−	0.0264362i
$609$	1.96922	−	10.3230i	0.0797968	−	0.418309i
$610$	−21.6198	+	14.1053i	−0.875358	+	0.571106i
$611$	2.87002	+	0.362568i	0.116109	+	0.0146679i
$612$	0.160513	+	1.27059i	0.00648834	+	0.0513605i
$613$	−21.8968	−	23.3178i	−0.884405	−	0.941795i	0.114260	−	0.993451i	$-0.463550\pi$
$613$	−21.8968	−	23.3178i	−0.884405	−	0.941795i	−0.998665	+	0.0516555i	$0.983550\pi$
$614$	4.10363	−	8.72065i	0.165609	−	0.351937i
$615$	−21.0945	+	1.59405i	−0.850614	+	0.0642783i
$616$	5.61331	−	0.709126i	0.226167	−	0.0285715i
$617$	7.41930	+	28.8963i	0.298690	+	1.16332i	0.923828	+	0.382807i	$0.125042\pi$
$617$	7.41930	+	28.8963i	0.298690	+	1.16332i	−0.625138	+	0.780514i	$0.714958\pi$
$618$	−4.41243	+	1.43369i	−0.177494	+	0.0576713i
$619$	−26.6182	−	10.5389i	−1.06988	−	0.423594i	−0.233843	−	0.972274i	$-0.575130\pi$
$619$	−26.6182	−	10.5389i	−1.06988	−	0.423594i	−0.836032	+	0.548681i	$0.815130\pi$
$620$	4.45750	−	2.52414i	0.179018	−	0.101372i
$621$	1.68561	+	2.03755i	0.0676412	+	0.0817641i
$622$	24.7665	−	1.55818i	0.993046	−	0.0624772i
$623$	7.97245	+	3.75155i	0.319409	+	0.150303i
$624$	−0.894311			−0.0358011
$625$	−11.7698	−	22.0561i	−0.470794	−	0.882243i
$626$	33.3011			1.33098
$627$	−3.04606	−	1.43337i	−0.121648	−	0.0572431i
$628$	4.77998	−	0.300731i	0.190742	−	0.0120005i
$629$	−4.55574	−	5.50694i	−0.181649	−	0.219576i
$630$	3.34424	−	1.89373i	0.133238	−	0.0754482i
$631$	29.0514	+	11.5023i	1.15652	+	0.457898i	0.866526	−	0.499132i	$-0.166348\pi$
$631$	29.0514	+	11.5023i	1.15652	+	0.457898i	0.289991	+	0.957029i	$0.406348\pi$
$632$	4.89634	−	1.59092i	0.194766	−	0.0632834i
$633$	−2.54539	−	9.91366i	−0.101170	−	0.394032i
$634$	0.663548	−	0.0838256i	0.0263529	−	0.00332914i
$635$	−29.6021	+	2.23694i	−1.17472	+	0.0887703i
$636$	−2.07213	+	4.40350i	−0.0821653	+	0.174610i
$637$	2.47693	+	2.63767i	0.0981396	+	0.104508i
$638$	2.52276	+	19.9697i	0.0998769	+	0.790607i
$639$	−2.24953	−	0.284182i	−0.0889900	−	0.0112421i
$640$	−1.87274	+	1.22182i	−0.0740265	+	0.0482968i
$641$	8.64991	−	45.3444i	0.341651	−	1.79100i	−0.232871	−	0.972508i	$-0.574812\pi$
$641$	8.64991	−	45.3444i	0.341651	−	1.79100i	0.574522	−	0.818489i	$-0.305188\pi$
$642$	8.02920	+	6.64233i	0.316887	+	0.262152i
$643$	26.4706	+	8.60080i	1.04390	+	0.339183i	0.780270	−	0.625442i	$-0.215081\pi$
$643$	26.4706	+	8.60080i	1.04390	+	0.339183i	0.263626	+	0.964625i	$0.415081\pi$
$644$	0.285384	−	4.53606i	0.0112457	−	0.178746i
$645$	−11.9232	−	4.54790i	−0.469474	−	0.179073i
$646$	−1.21771	+	0.482126i	−0.0479102	+	0.0189690i
$647$	−5.79686	+	4.79558i	−0.227898	+	0.188534i	−0.744364	−	0.667774i	$-0.767247\pi$
$647$	−5.79686	+	4.79558i	−0.227898	+	0.188534i	0.516466	+	0.856308i	$0.327247\pi$
$648$	−0.481754	−	0.876307i	−0.0189251	−	0.0344246i
$649$	−8.62220	−	26.5364i	−0.338451	−	1.04164i
$650$	2.93613	+	3.37253i	0.115165	+	0.132281i
$651$	1.21672	−	3.74469i	0.0476872	−	0.146766i
$652$	−12.8101	+	2.44366i	−0.501683	+	0.0957011i
$653$	19.8066	+	12.5696i	0.775092	+	0.491888i	0.863594	−	0.504188i	$-0.168208\pi$
$653$	19.8066	+	12.5696i	0.775092	+	0.491888i	−0.0885024	+	0.996076i	$0.528208\pi$
$654$	0.574107	−	0.904648i	0.0224494	−	0.0353745i
$655$	29.2362	−	4.06801i	1.14235	−	0.158950i
$656$	6.03045	−	7.28956i	0.235450	−	0.284610i
$657$	3.25956	−	4.48639i	0.127167	−	0.175031i
$658$	2.04662	−	5.16917i	0.0797856	−	0.201515i
$659$	8.92119	+	18.9585i	0.347520	+	0.738518i	0.999811	−	0.0194507i	$-0.00619173\pi$
$659$	8.92119	+	18.9585i	0.347520	+	0.738518i	−0.652290	+	0.757969i	$0.726192\pi$
$660$	−4.97096	+	5.42893i	−0.193494	+	0.211321i
$661$	34.0214	+	31.9482i	1.32328	+	1.24264i	0.948981	+	0.315333i	$0.102116\pi$
$661$	34.0214	+	31.9482i	1.32328	+	1.24264i	0.374298	+	0.927309i	$0.377884\pi$
$662$	−5.10955	−	0.974699i	−0.198588	−	0.0378828i
$663$	−0.551768	+	1.00366i	−0.0214289	+	0.0389790i
$664$	0.708991	+	3.71666i	0.0275142	+	0.144234i
$665$	2.72628	+	2.83090i	0.105720	+	0.109777i
$666$	4.89039	+	2.68851i	0.189499	+	0.104178i
$667$	16.1373	+	1.01527i	0.624838	+	0.0393115i
$668$	7.29051	+	10.0345i	0.282078	+	0.388248i
$669$	19.0916	−	4.90190i	0.738125	−	0.189518i
$670$	−5.55097	+	4.14080i	−0.214453	+	0.159973i
$671$	−2.38626	−	37.9285i	−0.0921204	−	1.46421i
$672$	−0.427431	+	1.66473i	−0.0164885	+	0.0642185i
$673$	−4.57101	+	36.1833i	−0.176200	+	1.39476i	0.617556	+	0.786527i	$0.288123\pi$
$673$	−4.57101	+	36.1833i	−0.176200	+	1.39476i	−0.793756	+	0.608237i	$0.791877\pi$
$674$	23.6004	−	17.1467i	0.909052	−	0.660465i
$675$	−1.72298	+	4.69376i	−0.0663174	+	0.180663i
$676$	9.87017	+	7.17110i	0.379622	+	0.275812i
$677$	−21.8543	+	23.2724i	−0.839927	+	0.894431i	−0.995631	−	0.0933723i	$-0.970235\pi$
$677$	−21.8543	+	23.2724i	−0.839927	+	0.894431i	0.155704	+	0.987804i	$0.450235\pi$
$678$	−5.62370	−	14.2039i	−0.215977	−	0.545496i
$679$	−4.15035	−	1.06563i	−0.159276	−	0.0408951i
$680$	0.215786	+	2.85556i	0.00827503	+	0.109506i
$681$	−11.5663	−	18.2255i	−0.443220	−	0.698403i
$682$			7.54138i			0.288775i
$683$	37.5962	−	23.8593i	1.43858	−	0.912949i	0.438680	−	0.898643i	$-0.355446\pi$
$683$	37.5962	−	23.8593i	1.43858	−	0.912949i	0.999898	−	0.0143062i	$-0.00455396\pi$
$684$	0.745473	−	0.700046i	0.0285039	−	0.0267669i
$685$	47.2896	+	14.7097i	1.80684	+	0.562027i
$686$	16.6367	−	9.14611i	0.635193	−	0.349200i
$687$	14.6191	−	6.87922i	0.557753	−	0.262459i
$688$	5.16379	−	2.42989i	0.196868	−	0.0926388i
$689$	−3.81397	+	2.09675i	−0.145301	+	0.0798798i
$690$	3.53558	+	4.73964i	0.134597	+	0.180435i
$691$	16.6207	−	15.6079i	0.632283	−	0.593753i	−0.300680	−	0.953725i	$-0.597214\pi$
$691$	16.6207	−	15.6079i	0.632283	−	0.593753i	0.932963	+	0.359972i	$0.117214\pi$
$692$	6.45919	−	4.09913i	0.245541	−	0.155825i
$693$			5.65793i			0.214927i
$694$	−13.0963	−	20.6365i	−0.497128	−	0.783349i
$695$	5.41570	−	2.22351i	0.205429	−	0.0843425i
$696$	−5.92239	−	1.52061i	−0.224487	−	0.0576386i
$697$	−4.46025	−	11.2653i	−0.168944	−	0.426704i
$698$	18.3732	−	19.5655i	0.695436	−	0.740564i
$699$	16.3260	+	11.8615i	0.617505	+	0.448644i
$700$	7.68117	−	3.85364i	0.290321	−	0.145654i
$701$	4.73822	−	3.44252i	0.178960	−	0.130022i	−0.494699	−	0.869064i	$-0.664722\pi$
$701$	4.73822	−	3.44252i	0.178960	−	0.130022i	0.673659	+	0.739042i	$0.264722\pi$
$702$	0.112087	−	0.887260i	0.00423045	−	0.0334875i
$703$	−1.41928	+	5.52773i	−0.0535292	+	0.208482i
$704$	−0.206701	−	3.28543i	−0.00779035	−	0.123824i
$705$	2.32157	+	6.85032i	0.0874353	+	0.257998i
$706$	−12.9043	+	3.31326i	−0.485660	+	0.124696i
$707$	−10.8074	−	14.8750i	−0.406452	−	0.559434i
$708$	8.45918	+	0.532207i	0.317916	+	0.0200016i
$709$	8.64572	+	4.75303i	0.324697	+	0.178504i	0.635762	−	0.771885i	$-0.280686\pi$
$709$	8.64572	+	4.75303i	0.324697	+	0.178504i	−0.311065	+	0.950389i	$0.600686\pi$
$710$	−4.99184	−	0.887254i	−0.187341	−	0.0332980i
$711$	0.964699	+	5.05713i	0.0361790	+	0.189657i
$712$	2.46970	−	4.49236i	0.0925557	−	0.168358i
$713$	5.95071	+	1.13516i	0.222856	+	0.0425120i
$714$	1.60457	+	1.50680i	0.0600497	+	0.0563904i
$715$	−6.45034	+	1.31485i	−0.241229	+	0.0491727i
$716$	10.8771	+	23.1150i	0.406496	+	0.863848i
$717$	1.06314	−	2.68518i	0.0397036	−	0.100280i
$718$	21.6696	−	29.8257i	0.808704	−	1.11309i
$719$	−31.8151	+	38.4579i	−1.18650	+	1.43424i	−0.311417	+	0.950273i	$0.600804\pi$
$719$	−31.8151	+	38.4579i	−1.18650	+	1.43424i	−0.875088	+	0.483965i	$0.839196\pi$
$720$	−0.977472	−	2.01111i	−0.0364282	−	0.0749495i
$721$	−4.27272	+	6.73272i	−0.159124	+	0.250740i
$722$	−15.1592	−	9.62034i	−0.564168	−	0.358032i
$723$	−8.73528	+	1.66634i	−0.324868	+	0.0619720i
$724$	0.323295	−	0.994999i	0.0120152	−	0.0369789i
$725$	13.7095	+	27.3262i	0.509160	+	1.01487i
$726$	0.0504481	+	0.155263i	0.00187231	+	0.00576237i
$727$	−3.38443	−	6.15625i	−0.125521	−	0.228323i	0.806078	−	0.591809i	$-0.201586\pi$
$727$	−3.38443	−	6.15625i	−0.125521	−	0.228323i	−0.931599	+	0.363487i	$0.881586\pi$
$728$	−1.18434	+	0.979772i	−0.0438946	+	0.0363128i
$729$	0.929776	−	0.368125i	0.0344362	−	0.0136342i
$730$	7.78318	−	9.65320i	0.288068	−	0.357281i
$731$	0.458923	−	7.29437i	0.0169739	−	0.269792i
$732$	10.9794	+	3.56743i	0.405812	+	0.131856i
$733$	13.4374	+	11.1164i	0.496321	+	0.410593i	0.851620	−	0.524160i	$-0.175621\pi$
$733$	13.4374	+	11.1164i	0.496321	+	0.410593i	−0.355298	+	0.934753i	$0.615621\pi$
$734$	0.345844	−	1.81298i	0.0127653	−	0.0669182i
$735$	−3.22426	+	8.45300i	−0.118929	+	0.311794i
$736$	−2.62356	−	0.331432i	−0.0967055	−	0.0122168i
$737$	−1.27782	−	10.1149i	−0.0470689	−	0.372589i
$738$	6.47627	+	6.89652i	0.238395	+	0.253865i
$739$	18.9864	−	40.3483i	0.698428	−	1.48423i	−0.168448	−	0.985711i	$-0.553876\pi$
$739$	18.9864	−	40.3483i	0.698428	−	1.48423i	0.866876	−	0.498524i	$-0.166124\pi$
$740$	10.6195	+	6.55327i	0.390382	+	0.240903i
$741$	0.907348	−	0.114625i	0.0333322	−	0.00421084i
$742$	2.08017	+	8.10172i	0.0763654	+	0.297424i
$743$	4.58181	−	1.48872i	0.168090	−	0.0546158i	−0.223763	−	0.974644i	$-0.571834\pi$
$743$	4.58181	−	1.48872i	0.168090	−	0.0546158i	0.391853	+	0.920028i	$0.371834\pi$
$744$	−2.13000	−	0.843328i	−0.0780897	−	0.0309179i
$745$	−10.6788	−	9.77793i	−0.391240	−	0.358236i
$746$	3.06065	+	3.69970i	0.112059	+	0.135455i
$747$	−3.77622	+	0.237579i	−0.138165	+	0.00869257i
$748$	−3.81468	−	1.79505i	−0.139479	−	0.0656336i
$749$	17.9102			0.654424
$750$	−4.37491	+	10.2888i	−0.159749	+	0.375695i
$751$	3.48465			0.127157			0.0635783	−	0.997977i	$-0.479749\pi$
$751$	3.48465			0.127157			0.0635783	+	0.997977i	$0.479749\pi$
$752$	−2.92685	−	1.37727i	−0.106731	−	0.0502239i
$753$	2.66501	−	0.167668i	0.0971183	−	0.00611016i
$754$	−3.48560	−	4.21336i	−0.126938	−	0.153442i
$755$	4.92842	+	24.1776i	0.179364	+	0.879914i
$756$	−1.59804	−	0.632707i	−0.0581200	−	0.0230113i
$757$	50.0821	−	16.2727i	1.82027	−	0.591440i	0.820461	−	0.571703i	$-0.193717\pi$
$757$	50.0821	−	16.2727i	1.82027	−	0.591440i	0.999805	−	0.0197373i	$-0.00628298\pi$
$758$	6.91524	+	26.9331i	0.251173	+	0.978254i
$759$	−8.63654	+	1.09105i	−0.313487	+	0.0396026i
$760$	1.74343	−	1.47966i	0.0632410	−	0.0536730i
$761$	−14.3414	+	30.4770i	−0.519875	+	1.10479i	0.456702	+	0.889620i	$0.349031\pi$
$761$	−14.3414	+	30.4770i	−0.519875	+	1.10479i	−0.976576	+	0.215171i	$0.930969\pi$
$762$	9.08818	+	9.67793i	0.329230	+	0.350594i
$763$	−0.230804	−	1.82700i	−0.00835565	−	0.0661418i
$764$	3.14601	+	0.397434i	0.113819	+	0.0143786i
$765$	−2.86009	−	0.143812i	−0.103407	−	0.00519953i
$766$	4.13090	−	21.6549i	0.149255	−	0.782424i
$767$	5.84057	+	4.83174i	0.210891	+	0.174464i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	1.42933	−	22.7185i	0.0515429	−	0.819251i	−0.884319	−	0.466883i	$-0.845377\pi$
$769$	1.42933	−	22.7185i	0.0515429	−	0.819251i	0.935862	−	0.352367i	$-0.114623\pi$
$770$	−0.635345	+	12.6355i	−0.0228962	+	0.455353i
$771$	−6.95601	+	2.75408i	−0.250515	+	0.0991858i
$772$	1.62490	−	1.34423i	0.0584814	−	0.0483800i
$773$	−23.7258	−	43.1571i	−0.853357	−	1.55225i	−0.833548	−	0.552448i	$-0.813694\pi$
$773$	−23.7258	−	43.1571i	−0.853357	−	1.55225i	−0.0198098	−	0.999804i	$-0.506306\pi$
$774$	1.76354	+	5.42762i	0.0633891	+	0.195092i
$775$	3.81279	+	10.8012i	0.136960	+	0.387990i
$776$	−0.770411	+	2.37108i	−0.0276561	+	0.0851168i
$777$	9.42179	−	1.79730i	0.338005	−	0.0644779i
$778$	−27.0961	−	17.1957i	−0.971442	−	0.616496i
$779$	−5.18405	+	8.16875i	−0.185738	+	0.292676i
$780$	0.349951	−	1.96888i	0.0125302	−	0.0704973i
$781$	4.75782	−	5.75121i	0.170248	−	0.205795i
$782$	−1.99063	+	2.73986i	−0.0711847	+	0.0979774i
$783$	2.25089	−	5.68510i	0.0804403	−	0.203169i
$784$	−1.72269	−	3.66090i	−0.0615246	−	0.130746i
$785$	−1.20836	+	10.6411i	−0.0431283	+	0.379797i
$786$	−9.62295	−	9.03655i	−0.343239	−	0.322323i
$787$	−29.9354	−	5.71049i	−1.06708	−	0.203557i	−0.376211	−	0.926534i	$-0.622773\pi$
$787$	−29.9354	−	5.71049i	−1.06708	−	0.203557i	−0.690872	+	0.722977i	$0.742773\pi$
$788$	−1.94367	+	3.53552i	−0.0692403	+	0.125948i
$789$	−1.93358	−	10.1362i	−0.0688374	−	0.360858i
$790$	1.58653	+	11.4021i	0.0564463	+	0.405670i
$791$	−23.0087	−	12.6491i	−0.818094	−	0.449751i
$792$	3.28543	+	0.206701i	0.116743	+	0.00734482i
$793$	6.06850	+	8.35257i	0.215499	+	0.296608i
$794$	32.9863	−	8.46944i	1.17064	−	0.300569i
$795$	−8.88374	−	6.28505i	−0.315074	−	0.222908i
$796$	1.59030	+	25.2770i	0.0563666	+	0.895921i
$797$	6.58467	−	25.6456i	0.233241	−	0.908414i	−0.738862	−	0.673857i	$-0.764636\pi$
$797$	6.58467	−	25.6456i	0.233241	−	0.908414i	0.972103	−	0.234556i	$-0.0753637\pi$
$798$	0.220291	−	1.74378i	0.00779822	−	0.0617293i
$799$	−3.35147	+	2.43499i	−0.118567	+	0.0861436i
$800$	−1.95710	−	4.60106i	−0.0691940	−	0.162672i
$801$	4.14740	+	3.01326i	0.146541	+	0.106468i
$802$	−9.20126	+	9.79835i	−0.324908	+	0.345992i
$803$	6.72023	+	16.9734i	0.237152	+	0.598977i
$804$	2.99978	+	0.770212i	0.105794	+	0.0271633i
$805$	9.87474	+	2.40328i	0.348039	+	0.0847046i
$806$	−1.09778	−	1.72982i	−0.0386676	−	0.0609304i
$807$			13.9546i			0.491226i
$808$	−9.03242	+	5.73215i	−0.317759	+	0.201656i
$809$	−0.864622	+	0.811934i	−0.0303985	+	0.0285461i	−0.699598	−	0.714537i	$-0.746637\pi$
$809$	−0.864622	+	0.811934i	−0.0303985	+	0.0285461i	0.669199	+	0.743083i	$0.266637\pi$
$810$	2.11776	−	0.717706i	0.0744104	−	0.0252176i
$811$	8.06630	−	4.43449i	0.283246	−	0.155716i	−0.333798	−	0.942645i	$-0.608330\pi$
$811$	8.06630	−	4.43449i	0.283246	−	0.155716i	0.617044	+	0.786929i	$0.288330\pi$
$812$	−9.50896	+	4.47458i	−0.333699	+	0.157027i
$813$	4.26552	−	2.00720i	0.149598	−	0.0703956i
$814$	−16.0988	+	8.85037i	−0.564262	+	0.310205i
$815$	−0.367178	−	29.1585i	−0.0128617	−	1.02138i
$816$	0.933581	−	0.876691i	0.0326819	−	0.0306903i
$817$	−4.92762	+	3.12716i	−0.172396	+	0.109406i
$818$			12.0455i			0.421162i
$819$	−0.823609	−	1.29780i	−0.0287792	−	0.0453488i
$820$	13.6887	+	16.1289i	0.478029	+	0.563245i
$821$	24.3197	+	6.24425i	0.848765	+	0.217926i	0.647931	−	0.761699i	$-0.275635\pi$
$821$	24.3197	+	6.24425i	0.848765	+	0.217926i	0.200834	+	0.979625i	$0.435635\pi$
$822$	−8.15324	−	20.5927i	−0.284377	−	0.718254i
$823$	−7.01100	+	7.46596i	−0.244388	+	0.260247i	−0.839455	−	0.543429i	$-0.817126\pi$
$823$	−7.01100	+	7.46596i	−0.244388	+	0.260247i	0.595067	+	0.803676i	$0.297126\pi$
$824$	3.75344	+	2.72703i	0.130757	+	0.0950007i
$825$	−10.0070	−	13.0683i	−0.348398	−	0.454978i
$826$	11.7856	−	8.56274i	0.410074	−	0.297936i
$827$	−4.02928	+	31.8951i	−0.140112	+	1.10910i	0.752602	+	0.658476i	$0.228799\pi$
$827$	−4.02928	+	31.8951i	−0.140112	+	1.10910i	−0.892714	+	0.450624i	$0.851201\pi$
$828$	0.657637	−	2.56133i	0.0228545	−	0.0890123i
$829$	−2.70790	−	43.0408i	−0.0940492	−	1.49487i	−0.708386	−	0.705826i	$-0.750576\pi$
$829$	−2.70790	−	43.0408i	−0.0940492	−	1.49487i	0.614336	−	0.789044i	$-0.289424\pi$
$830$	−8.45990	+	0.106531i	−0.293647	+	0.00369775i
$831$	11.2760	−	2.89518i	0.391159	−	0.100433i
$832$	0.525663	+	0.723513i	0.0182241	+	0.0250833i
$833$	−5.17139	−	0.325356i	−0.179178	−	0.0112729i
$834$	−2.29431	−	1.26131i	−0.0794455	−	0.0436755i
$835$	−24.9445	+	12.1239i	−0.863240	+	0.419566i
$836$	0.630810	+	3.30682i	0.0218170	+	0.114369i
$837$	1.10364	−	2.00751i	0.0381473	−	0.0693897i
$838$	1.74410	+	0.332706i	0.0602491	+	0.0114931i
$839$	19.0786	+	17.9160i	0.658668	+	0.618530i	0.940038	−	0.341069i	$-0.110789\pi$
$839$	19.0786	+	17.9160i	0.658668	+	0.618530i	−0.281370	+	0.959599i	$0.590789\pi$
$840$	−3.49776	−	1.59244i	−0.120684	−	0.0549444i
$841$	−3.57097	−	7.58870i	−0.123137	−	0.261679i
$842$	2.87100	−	7.25132i	0.0989412	−	0.249897i
$843$	−7.81938	+	10.7625i	−0.269314	+	0.370679i
$844$	−6.52417	+	7.88637i	−0.224571	+	0.271460i
$845$	−19.6499	+	18.9237i	−0.675977	+	0.650995i
$846$	1.73324	−	2.73115i	0.0595901	−	0.0938990i
$847$	0.236909	+	0.150347i	0.00814029	+	0.00516599i
$848$	4.78047	−	0.911924i	0.164162	−	0.0313156i
$849$	2.03732	−	6.27023i	0.0699207	−	0.215194i
$850$	−6.37114	−	0.642335i	−0.218528	−	0.0220319i
$851$	4.56035	+	14.0353i	0.156327	+	0.481124i
$852$	1.09233	+	1.98695i	0.0374227	+	0.0680716i
$853$	−33.4471	+	27.6699i	−1.14521	+	0.947398i	−0.999123	−	0.0418738i	$-0.986667\pi$
$853$	−33.4471	+	27.6699i	−1.14521	+	0.947398i	−0.146085	+	0.989272i	$0.546667\pi$
$854$	18.4485	−	7.30426i	0.631293	−	0.249947i
$855$	1.24949	+	1.91514i	0.0427315	+	0.0654964i
$856$	0.654314	−	10.4000i	0.0223640	−	0.355466i
$857$	−19.6710	−	6.39148i	−0.671947	−	0.218329i	−0.0468808	−	0.998900i	$-0.514928\pi$
$857$	−19.6710	−	6.39148i	−0.671947	−	0.218329i	−0.625066	+	0.780572i	$0.714928\pi$
$858$	2.26839	+	1.87658i	0.0774417	+	0.0640653i
$859$	−0.765490	+	4.01284i	−0.0261182	+	0.136916i	−0.992958	−	0.118468i	$-0.962202\pi$
$859$	−0.765490	+	4.01284i	−0.0261182	+	0.136916i	0.966840	+	0.255384i	$0.0822018\pi$
$860$	3.32894	+	12.3192i	0.113516	+	0.420083i
$861$	16.1321	+	2.03796i	0.549781	+	0.0694535i
$862$	1.47277	+	11.6582i	0.0501627	+	0.397079i
$863$	−31.5031	−	33.5474i	−1.07238	−	1.14197i	−0.989370	−	0.145418i	$-0.953547\pi$
$863$	−31.5031	−	33.5474i	−1.07238	−	1.14197i	−0.0830079	−	0.996549i	$-0.526453\pi$
$864$	−0.425779	+	0.904827i	−0.0144853	+	0.0307828i
$865$	6.49695	+	15.8243i	0.220903	+	0.538043i
$866$	−24.7296	+	3.12408i	−0.840347	+	0.106160i
$867$	3.81984	+	14.8773i	0.129728	+	0.505259i
$868$	−3.74469	+	1.21672i	−0.127103	+	0.0412983i
$869$	−15.7577	−	6.23893i	−0.534544	−	0.211641i
$870$	5.66519	−	12.4435i	0.192068	−	0.421873i
$871$	1.76551	+	2.13413i	0.0598219	+	0.0723123i
$872$	−1.06933	+	0.0672764i	−0.0362120	+	0.00227827i
$873$	−2.25583	−	1.06151i	−0.0763481	−	0.0359267i
$874$	2.70428			0.0914736
$875$	5.47834	+	18.4185i	0.185202	+	0.622660i
$876$	−5.54549			−0.187365
$877$	−1.33729	−	0.629280i	−0.0451570	−	0.0212493i	0.403068	−	0.915170i	$-0.367944\pi$
$877$	−1.33729	−	0.629280i	−0.0451570	−	0.0212493i	−0.448225	+	0.893921i	$0.647944\pi$
$878$	−7.96217	+	0.500937i	−0.268710	+	0.0169058i
$879$	10.4115	+	12.5854i	0.351172	+	0.424494i
$880$	7.31395	+	0.830545i	0.246553	+	0.0279977i
$881$	−42.2425	−	16.7250i	−1.42318	−	0.563479i	−0.474656	−	0.880171i	$-0.657428\pi$
$881$	−42.2425	−	16.7250i	−1.42318	−	0.563479i	−0.948528	+	0.316692i	$0.897428\pi$
$882$	3.84794	−	1.25027i	0.129567	−	0.0420988i
$883$	4.04782	+	15.7652i	0.136220	+	0.530542i	0.999660	+	0.0260899i	$0.00830563\pi$
$883$	4.04782	+	15.7652i	0.136220	+	0.530542i	−0.863439	+	0.504452i	$0.831694\pi$
$884$	1.13630	−	0.143548i	0.0382180	−	0.00482805i
$885$	−4.48183	+	18.4152i	−0.150655	+	0.619019i
$886$	3.21492	−	6.83205i	0.108007	−	0.229527i
$887$	−32.1857	−	34.2743i	−1.08069	−	1.15082i	−0.987894	−	0.155132i	$-0.950420\pi$
$887$	−32.1857	−	34.2743i	−1.08069	−	1.15082i	−0.0927957	−	0.995685i	$-0.529580\pi$
$888$	−0.699445	−	5.53667i	−0.0234718	−	0.185799i
$889$	22.6383	+	2.85988i	0.759264	+	0.0959173i
$890$	8.92380	+	7.19508i	0.299126	+	0.241180i
$891$	−0.616845	+	3.23361i	−0.0206651	+	0.108330i
$892$	−15.1875	−	12.5642i	−0.508515	−	0.420680i
$893$	3.14604	+	1.02221i	0.105278	+	0.0342070i
$894$	−0.406584	+	6.46247i	−0.0135982	+	0.216137i
$895$	−55.1454	+	14.9015i	−1.84331	+	0.498103i
$896$	1.59804	−	0.632707i	0.0533866	−	0.0211373i
$897$	1.82221	−	1.50746i	0.0608417	−	0.0503326i
$898$	−7.95142	−	14.4636i	−0.265342	−	0.482656i
$899$	−4.32856	−	13.3219i	−0.144366	−	0.444312i
$900$	4.81007	−	1.36500i	0.160336	−	0.0455002i
$901$	1.92601	−	5.92764i	0.0641646	−	0.197478i
$902$	−30.5921	+	5.83576i	−1.01861	+	0.194309i
$903$	8.28174	+	5.25575i	0.275599	+	0.174901i
$904$	−8.18563	+	12.8985i	−0.272250	+	0.428997i
$905$	2.06405	+	1.10110i	0.0686112	+	0.0366020i
$906$	7.03392	−	8.50255i	0.233686	−	0.282478i
$907$	18.2223	−	25.0809i	0.605063	−	0.832798i	−0.391097	−	0.920350i	$-0.627904\pi$
$907$	18.2223	−	25.0809i	0.605063	−	0.832798i	0.996160	+	0.0875516i	$0.0279043\pi$
$908$	−7.94627	+	20.0700i	−0.263706	+	0.666046i
$909$	−4.55488	−	9.67962i	−0.151076	−	0.321053i
$910$	−1.69359	−	2.99079i	−0.0561419	−	0.0991438i
$911$	5.22383	+	4.90551i	0.173073	+	0.162527i	0.766243	−	0.642551i	$-0.222124\pi$
$911$	5.22383	+	4.90551i	0.173073	+	0.162527i	−0.593170	+	0.805077i	$0.702124\pi$
$912$	−1.00453	−	0.191624i	−0.0332632	−	0.00634530i
$913$	6.00052	−	10.9149i	0.198588	−	0.361231i
$914$	−1.90005	−	9.96041i	−0.0628480	−	0.329461i
$915$	−12.1503	+	22.7760i	−0.401675	+	0.752950i
$916$	−14.1583	−	7.78358i	−0.467803	−	0.257177i
$917$	−22.6438	−	1.42463i	−0.747764	−	0.0470453i
$918$	0.752769	+	1.03610i	0.0248451	+	0.0341963i
$919$	26.0720	−	6.69415i	0.860035	−	0.220820i	0.207181	−	0.978303i	$-0.433571\pi$
$919$	26.0720	−	6.69415i	0.860035	−	0.220820i	0.652855	+	0.757483i	$0.273571\pi$
$920$	1.75629	−	5.64623i	0.0579030	−	0.186151i
$921$	−0.605170	−	9.61890i	−0.0199410	−	0.316954i
$922$	3.98618	−	15.5252i	0.131278	−	0.511294i
$923$	−0.254147	+	2.01178i	−0.00836535	+	0.0662185i
$924$	4.57736	−	3.32565i	0.150584	−	0.109406i
$925$	−18.5829	+	20.8152i	−0.611003	+	0.684401i
$926$	34.3252	+	24.9387i	1.12800	+	0.819537i
$927$	−3.17596	+	3.38205i	−0.104312	+	0.111081i
$928$	2.25089	+	5.68510i	0.0738891	+	0.186623i
$929$	15.9851	+	4.10428i	0.524455	+	0.134657i	0.501630	−	0.865082i	$-0.332734\pi$
$929$	15.9851	+	4.10428i	0.524455	+	0.134657i	0.0228249	+	0.999739i	$0.492734\pi$
$930$	2.69013	−	4.35933i	0.0882127	−	0.142948i
$931$	2.21702	+	3.49346i	0.0726599	+	0.114494i
$932$		−	20.1800i		−	0.661018i
$933$	20.9524	−	13.2968i	0.685950	−	0.435317i
$934$	−16.9566	+	15.9233i	−0.554835	+	0.521025i
$935$	5.44463	−	7.69584i	0.178059	−	0.251681i
$936$	−0.783691	+	0.430838i	−0.0256157	+	0.0140824i
$937$	−38.5637	+	18.1467i	−1.25982	+	0.592826i	−0.935569	−	0.353144i	$-0.885112\pi$
$937$	−38.5637	+	18.1467i	−1.25982	+	0.592826i	−0.324252	+	0.945971i	$0.605112\pi$
$938$	4.81644	−	2.26644i	0.157262	−	0.0740020i
$939$	29.1819	−	16.0429i	0.952317	−	0.523541i
$940$	4.17745	−	5.90471i	0.136253	−	0.192590i
$941$	−8.59131	+	8.06778i	−0.280069	+	0.263002i	−0.811832	−	0.583891i	$-0.801530\pi$
$941$	−8.59131	+	8.06778i	−0.280069	+	0.263002i	0.531763	+	0.846893i	$0.321530\pi$
$942$	4.04385	−	2.56630i	0.131756	−	0.0836147i
$943$			25.0178i			0.814693i
$944$	−4.54162	−	7.15645i	−0.147817	−	0.232922i
$945$	2.01827	−	3.27059i	0.0656542	−	0.106392i
$946$	−18.1966	−	4.67208i	−0.591621	−	0.151902i
$947$	3.75282	+	9.47853i	0.121950	+	0.308011i	0.977908	−	0.209034i	$-0.0670320\pi$
$947$	3.75282	+	9.47853i	0.121950	+	0.308011i	−0.855958	+	0.517045i	$0.827032\pi$
$948$	3.52427	−	3.75296i	0.114463	−	0.121891i
$949$	−4.01223	−	2.91506i	−0.130243	−	0.0946268i
$950$	2.57535	+	4.41728i	0.0835555	+	0.143316i
$951$	0.541088	−	0.393124i	0.0175460	−	0.0127479i
$952$	0.275878	−	2.18380i	0.00894126	−	0.0707774i
$953$	−0.800728	+	3.11863i	−0.0259381	+	0.101022i	−0.980234	−	0.197840i	$-0.936607\pi$
$953$	−0.800728	+	3.11863i	−0.0259381	+	0.101022i	0.954296	+	0.298863i	$0.0966073\pi$
$954$	0.305581	+	4.85707i	0.00989356	+	0.157254i
$955$	−2.10603	+	6.77062i	−0.0681496	+	0.219092i
$956$	−2.79725	+	0.718212i	−0.0904696	+	0.0232286i
$957$	11.8312	+	16.2842i	0.382448	+	0.526394i
$958$	−15.1448	−	0.952827i	−0.489305	−	0.0307844i
$959$	−33.3580	−	18.3387i	−1.07719	−	0.592188i
$960$	−1.05248	+	1.97289i	−0.0339685	+	0.0636747i
$961$	4.82542	+	25.2957i	0.155659	+	0.815992i
$962$	2.40437	−	4.37353i	0.0775199	−	0.141008i
$963$	10.2360	+	1.95262i	0.329851	+	0.0629224i
$964$	6.48257	+	6.08753i	0.208789	+	0.196066i
$965$	2.32358	+	4.10333i	0.0747987	+	0.132091i
$966$	−1.93518	−	4.11246i	−0.0622633	−	0.132316i
$967$	−8.48404	+	21.4282i	−0.272828	+	0.689086i	0.727168	+	0.686459i	$0.240836\pi$
$967$	−8.48404	+	21.4282i	−0.272828	+	0.689086i	−0.999997	+	0.00262638i	$0.999164\pi$
$968$	0.0959581	−	0.132075i	0.00308421	−	0.00424505i
$969$	−0.834823	+	1.00913i	−0.0268184	+	0.0324179i
$970$	−4.91861	−	2.62393i	−0.157927	−	0.0842493i
$971$	−14.2329	+	22.4275i	−0.456756	+	0.719732i	−0.992175	−	0.124855i	$-0.960154\pi$
$971$	−14.2329	+	22.4275i	−0.456756	+	0.719732i	0.535420	+	0.844586i	$0.320154\pi$
$972$	−0.844328	−	0.535827i	−0.0270818	−	0.0171867i
$973$	−4.42021	+	0.843199i	−0.141705	+	0.0270317i
$974$	−5.50617	+	16.9462i	−0.176429	+	0.542993i
$975$	4.19768	+	1.54088i	0.134433	+	0.0493476i
$976$	−3.56743	−	10.9794i	−0.114191	−	0.351443i
$977$	2.78438	+	5.06477i	0.0890802	+	0.162036i	0.917094	−	0.398672i	$-0.130529\pi$
$977$	2.78438	+	5.06477i	0.0890802	+	0.162036i	−0.828013	+	0.560708i	$0.810529\pi$
$978$	−10.0483	+	8.31271i	−0.321311	+	0.265811i
$979$	−15.6908	+	6.21245i	−0.501482	+	0.198551i
$980$	8.73380	−	2.36007i	0.278991	−	0.0753896i
$981$	0.0672764	−	1.06933i	0.00214797	−	0.0341410i
$982$	−21.8930	−	7.11346i	−0.698633	−	0.227000i
$983$	27.9862	+	23.1522i	0.892622	+	0.738441i	0.965912	−	0.258869i	$-0.0833499\pi$
$983$	27.9862	+	23.1522i	0.892622	+	0.738441i	−0.0732900	+	0.997311i	$0.523350\pi$
$984$	1.77275	−	9.29308i	0.0565132	−	0.296253i
$985$	−7.02309	−	5.66258i	−0.223774	−	0.180425i
$986$	7.76899	+	0.981452i	0.247415	+	0.0312558i
$987$	−0.696801	−	5.51575i	−0.0221794	−	0.175568i
$988$	−0.626059	−	0.666685i	−0.0199176	−	0.0212101i
$989$	−6.42563	+	13.6552i	−0.204323	+	0.434209i
$990$	−1.74068	+	7.15219i	−0.0553224	+	0.227311i
$991$	17.4192	−	2.20056i	0.553339	−	0.0699030i	0.156308	−	0.987708i	$-0.450041\pi$
$991$	17.4192	−	2.20056i	0.553339	−	0.0699030i	0.397031	+	0.917805i	$0.370041\pi$
$992$	0.569718	+	2.21890i	0.0180886	+	0.0704503i
$993$	−4.94710	+	1.60741i	−0.156991	+	0.0510096i
$994$	3.62340	+	1.43461i	0.114927	+	0.0455029i
$995$	−56.2713	−	6.38995i	−1.78392	−	0.202575i
$996$	2.41181	+	2.91538i	0.0764211	+	0.0923773i
$997$	7.36127	−	0.463132i	0.233134	−	0.0146675i	0.0542061	−	0.998530i	$-0.482737\pi$
$997$	7.36127	−	0.463132i	0.233134	−	0.0146675i	0.178928	+	0.983862i	$0.442737\pi$
$998$	6.03255	+	2.83870i	0.190957	+	0.0898576i
$999$	5.58068			0.176565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.259.1	yes	240
125.14	even	50	inner	750.2.o.a.139.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.139.1	✓	240	125.14	even	50	inner
750.2.o.a.259.1	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)

\(f(q)\)	\(=\)	\(q+(-0.904827 - 0.425779i) q^{2} +(-0.998027 + 0.0627905i) q^{3} +(0.637424 + 0.770513i) q^{4} +(-1.94576 + 1.10182i) q^{5} +(0.929776 + 0.368125i) q^{6} +(1.63461 - 0.531117i) q^{7} +(-0.248690 - 0.968583i) q^{8} +(0.992115 - 0.125333i) q^{9} +O(q^{10})\)	\(q+(-0.904827 - 0.425779i) q^{2} +(-0.998027 + 0.0627905i) q^{3} +(0.637424 + 0.770513i) q^{4} +(-1.94576 + 1.10182i) q^{5} +(0.929776 + 0.368125i) q^{6} +(1.63461 - 0.531117i) q^{7} +(-0.248690 - 0.968583i) q^{8} +(0.992115 - 0.125333i) q^{9} +(2.22971 - 0.168493i) q^{10} +(-1.40163 + 2.97862i) q^{11} +(-0.684547 - 0.728969i) q^{12} +(-0.112087 - 0.887260i) q^{13} +(-1.70518 - 0.215414i) q^{14} +(1.87274 - 1.22182i) q^{15} +(-0.187381 + 0.982287i) q^{16} +(0.986786 + 0.816341i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.0642121 - 1.02062i) q^{19} +(-2.08924 - 0.796908i) q^{20} +(-1.59804 + 0.632707i) q^{21} +(2.53647 - 2.09835i) q^{22} +(-1.27395 - 2.31731i) q^{23} +(0.309017 + 0.951057i) q^{24} +(2.57198 - 4.28776i) q^{25} +(-0.276357 + 0.850541i) q^{26} +(-0.982287 + 0.187381i) q^{27} +(1.45117 + 0.920942i) q^{28} +(-3.27630 + 5.16263i) q^{29} +(-2.21473 + 0.308165i) q^{30} +(-1.46026 + 1.76515i) q^{31} +(0.587785 - 0.809017i) q^{32} +(1.21184 - 3.06075i) q^{33} +(-0.545290 - 1.15880i) q^{34} +(-2.59537 + 2.83448i) q^{35} +(0.728969 + 0.684547i) q^{36} +(-5.48183 - 1.04572i) q^{37} +(-0.492661 + 0.896147i) q^{38} +(0.167577 + 0.878471i) q^{39} +(1.55110 + 1.61062i) q^{40} +(-8.29044 - 4.55771i) q^{41} +(1.71534 + 0.107920i) q^{42} +(-3.35445 - 4.61701i) q^{43} +(-3.18850 + 0.818668i) q^{44} +(-1.79232 + 1.33700i) q^{45} +(0.166044 + 2.63919i) q^{46} +(-0.804439 + 3.13308i) q^{47} +(0.125333 - 0.992115i) q^{48} +(-3.27325 + 2.37816i) q^{49} +(-4.15284 + 2.78459i) q^{50} +(-1.03610 - 0.752769i) q^{51} +(0.612198 - 0.651925i) q^{52} +(-1.79154 - 4.52492i) q^{53} +(0.968583 + 0.248690i) q^{54} +(-0.554664 - 7.34003i) q^{55} +(-0.920942 - 1.45117i) q^{56} +1.02264i q^{57} +(5.16263 - 3.27630i) q^{58} +(-6.17867 + 5.80216i) q^{59} +(2.13516 + 0.664151i) q^{60} +(-10.1165 + 5.56159i) q^{61} +(2.07285 - 0.975408i) q^{62} +(1.55515 - 0.731800i) q^{63} +(-0.876307 + 0.481754i) q^{64} +(1.19570 + 1.60290i) q^{65} +(-2.39971 + 2.25348i) q^{66} +(-2.61495 + 1.65950i) q^{67} +1.28069i q^{68} +(1.41694 + 2.23275i) q^{69} +(3.55522 - 1.45966i) q^{70} +(-2.19617 - 0.563882i) q^{71} +(-0.368125 - 0.929776i) q^{72} +(3.79615 - 4.04249i) q^{73} +(4.51486 + 3.28024i) q^{74} +(-2.29767 + 4.44080i) q^{75} +(0.827334 - 0.601093i) q^{76} +(-0.709126 + 5.61331i) q^{77} +(0.222406 - 0.866215i) q^{78} +(0.323266 + 5.13816i) q^{79} +(-0.717706 - 2.11776i) q^{80} +(0.968583 - 0.248690i) q^{81} +(5.56084 + 7.65383i) q^{82} +(-3.77622 - 0.237579i) q^{83} +(-1.50614 - 0.828005i) q^{84} +(-2.81951 - 0.501142i) q^{85} +(1.06937 + 5.60585i) q^{86} +(2.94567 - 5.35816i) q^{87} +(3.23361 + 0.616845i) q^{88} +(3.73703 + 3.50931i) q^{89} +(2.19101 - 0.446621i) q^{90} +(-0.654457 - 1.39079i) q^{91} +(0.973471 - 2.45871i) q^{92} +(1.34654 - 1.85336i) q^{93} +(2.06188 - 2.49238i) q^{94} +(0.999602 + 2.05664i) q^{95} +(-0.535827 + 0.844328i) q^{96} +(-2.10499 - 1.33587i) q^{97} +(3.97430 - 0.758138i) q^{98} +(-1.01726 + 3.13080i) 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

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Database

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