LMFDB - Embedded newform 750.2.o.a.19.1

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			19.1
Character	$\chi$	$=$	750.19
Dual form			750.2.o.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844328 - 0.535827i) q^{2} +(-0.684547 - 0.728969i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-2.22361 - 0.235684i) q^{5} +(0.187381 + 0.982287i) q^{6} +(1.43168 + 1.97054i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.0627905 + 0.998027i) q^{9} +O(q^{10})$	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.684547 - 0.728969i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-2.22361 - 0.235684i) q^{5} +(0.187381 + 0.982287i) q^{6} +(1.43168 + 1.97054i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.0627905 + 0.998027i) q^{9} +(1.75117 + 1.39047i) q^{10} +(1.28780 - 2.02925i) q^{11} +(0.368125 - 0.929776i) q^{12} +(-2.03194 - 0.127839i) q^{13} +(-0.152940 - 2.43092i) q^{14} +(1.35036 + 1.78228i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.267381 + 0.125820i) q^{17} +(0.587785 - 0.809017i) q^{18} +(1.54181 + 1.44785i) q^{19} +(-0.733515 - 2.11233i) q^{20} +(0.456410 - 2.39258i) q^{21} +(-2.17465 + 1.02331i) q^{22} +(1.66525 - 6.48573i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(4.88891 + 1.04814i) q^{25} +(1.64712 + 1.19670i) q^{26} +(0.770513 - 0.637424i) q^{27} +(-1.17342 + 2.13444i) q^{28} +(-2.73974 - 1.50619i) q^{29} +(-0.185154 - 2.22839i) q^{30} +(1.20837 - 2.56792i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-2.36082 + 0.450350i) q^{33} +(-0.158339 - 0.249503i) q^{34} +(-2.71908 - 4.71915i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(-6.38094 - 5.27877i) q^{37} +(-0.525992 - 2.04860i) q^{38} +(1.29777 + 1.56873i) q^{39} +(-0.512518 + 2.17654i) q^{40} +(7.40169 - 1.90043i) q^{41} +(-1.66737 + 1.77557i) q^{42} +(-5.62839 - 1.82878i) q^{43} +(2.38443 + 0.301224i) q^{44} +(0.374841 - 2.20443i) q^{45} +(-4.88125 + 4.58380i) q^{46} +(-1.09437 - 8.66286i) q^{47} +(0.998027 - 0.0627905i) q^{48} +(0.329795 - 1.01500i) q^{49} +(-3.56622 - 3.50458i) q^{50} +(-0.0913160 - 0.281042i) q^{51} +(-0.749485 - 1.89298i) q^{52} +(-11.7105 - 2.23390i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(-3.34183 + 4.20874i) q^{55} +(2.13444 - 1.17342i) q^{56} -2.11505i q^{57} +(1.50619 + 2.73974i) q^{58} +(-3.13869 - 1.24270i) q^{59} +(-1.03770 + 1.98070i) q^{60} +(4.00798 + 1.02908i) q^{61} +(-2.39622 + 1.52069i) q^{62} +(-2.05655 + 1.30513i) q^{63} +(-0.968583 - 0.248690i) q^{64} +(4.48811 + 0.763159i) q^{65} +(2.23461 + 0.884745i) q^{66} +(1.55089 + 2.82105i) q^{67} +0.295505i q^{68} +(-5.86784 + 3.22587i) q^{69} +(-0.232848 + 5.44147i) q^{70} +(-3.40151 + 0.429710i) q^{71} +(0.982287 + 0.187381i) q^{72} +(-2.46346 - 6.22199i) q^{73} +(2.55910 + 7.87610i) q^{74} +(-2.58263 - 4.28136i) q^{75} +(-0.653587 + 2.01153i) q^{76} +(5.84244 - 0.367575i) q^{77} +(-0.255173 - 2.01990i) q^{78} +(6.27100 - 5.88886i) q^{79} +(1.59898 - 1.56309i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-7.26776 - 2.36144i) q^{82} +(-9.41895 + 10.0302i) q^{83} +(2.35920 - 0.605740i) q^{84} +(-0.564897 - 0.342792i) q^{85} +(3.77230 + 4.55993i) q^{86} +(0.777521 + 3.02824i) q^{87} +(-1.85184 - 1.53198i) q^{88} +(1.42179 - 0.562926i) q^{89} +(-1.49768 + 1.66041i) q^{90} +(-2.65718 - 4.18705i) q^{91} +(6.57749 - 1.25472i) q^{92} +(-2.69912 + 0.876997i) q^{93} +(-3.71778 + 7.90069i) q^{94} +(-3.08714 - 3.58284i) q^{95} +(-0.876307 - 0.481754i) q^{96} +(6.12338 - 11.1384i) q^{97} +(-0.822322 + 0.680284i) q^{98} +(1.94438 + 1.41267i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{50}\right)$	$1$

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 $

$2$	−0.844328	−	0.535827i	−0.597030	−	0.378887i
$2$	−0.844328	−	0.535827i	−0.597030	−	0.378887i
$3$	−0.684547	−	0.728969i	−0.395223	−	0.420870i
$3$	−0.684547	−	0.728969i	−0.395223	−	0.420870i
$4$	0.425779	+	0.904827i	0.212890	+	0.452414i
$5$	−2.22361	−	0.235684i	−0.994430	−	0.105401i
$5$	−2.22361	−	0.235684i	−0.994430	−	0.105401i
$6$	0.187381	+	0.982287i	0.0764981	+	0.401017i
$7$	1.43168	+	1.97054i	0.541126	+	0.744795i	0.988775	−	0.149414i	$-0.0477386\pi$
$7$	1.43168	+	1.97054i	0.541126	+	0.744795i	−0.447649	+	0.894209i	$0.647739\pi$
$8$	0.125333	−	0.992115i	0.0443120	−	0.350766i
$9$	−0.0627905	+	0.998027i	−0.0209302	+	0.332676i
$10$	1.75117	+	1.39047i	0.553769	+	0.439704i
$11$	1.28780	−	2.02925i	0.388286	−	0.611841i	−0.592815	−	0.805339i	$-0.701983\pi$
$11$	1.28780	−	2.02925i	0.388286	−	0.611841i	0.981101	+	0.193498i	$0.0619834\pi$
$12$	0.368125	−	0.929776i	0.106268	−	0.268403i
$13$	−2.03194	−	0.127839i	−0.563558	−	0.0354561i	−0.221543	−	0.975151i	$-0.571109\pi$
$13$	−2.03194	−	0.127839i	−0.563558	−	0.0354561i	−0.342015	+	0.939694i	$0.611109\pi$
$14$	−0.152940	−	2.43092i	−0.0408751	−	0.649691i
$15$	1.35036	+	1.78228i	0.348662	+	0.460183i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	0.267381	+	0.125820i	0.0648493	+	0.0305158i	0.457930	−	0.888988i	$-0.348591\pi$
$17$	0.267381	+	0.125820i	0.0648493	+	0.0305158i	−0.393081	+	0.919504i	$0.628591\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	1.54181	+	1.44785i	0.353715	+	0.332160i	0.840952	−	0.541109i	$-0.181995\pi$
$19$	1.54181	+	1.44785i	0.353715	+	0.332160i	−0.487238	+	0.873269i	$0.661995\pi$
$20$	−0.733515	−	2.11233i	−0.164019	−	0.472332i
$21$	0.456410	−	2.39258i	0.0995967	−	0.522104i
$22$	−2.17465	+	1.02331i	−0.463637	+	0.218171i
$23$	1.66525	−	6.48573i	0.347229	−	1.35237i	−0.519875	−	0.854242i	$-0.674022\pi$
$23$	1.66525	−	6.48573i	0.347229	−	1.35237i	0.867105	−	0.498126i	$-0.165978\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	4.88891	+	1.04814i	0.977781	+	0.209628i
$26$	1.64712	+	1.19670i	0.323027	+	0.234693i
$27$	0.770513	−	0.637424i	0.148285	−	0.122672i
$28$	−1.17342	+	2.13444i	−0.221756	+	0.403372i
$29$	−2.73974	−	1.50619i	−0.508758	−	0.279692i	0.206631	−	0.978419i	$-0.433750\pi$
$29$	−2.73974	−	1.50619i	−0.508758	−	0.279692i	−0.715388	+	0.698727i	$0.753750\pi$
$30$	−0.185154	−	2.22839i	−0.0338044	−	0.406846i
$31$	1.20837	−	2.56792i	0.217030	−	0.461212i	−0.766433	−	0.642325i	$-0.777970\pi$
$31$	1.20837	−	2.56792i	0.217030	−	0.461212i	0.983462	+	0.181113i	$0.0579700\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	−2.36082	+	0.450350i	−0.410965	+	0.0783958i
$34$	−0.158339	−	0.249503i	−0.0271550	−	0.0427894i
$35$	−2.71908	−	4.71915i	−0.459609	−	0.797682i
$36$	−0.929776	+	0.368125i	−0.154963	+	0.0613541i
$37$	−6.38094	−	5.27877i	−1.04902	−	0.867825i	−0.0575743	−	0.998341i	$-0.518337\pi$
$37$	−6.38094	−	5.27877i	−1.04902	−	0.867825i	−0.991446	+	0.130516i	$0.958337\pi$
$38$	−0.525992	−	2.04860i	−0.0853271	−	0.332327i
$39$	1.29777	+	1.56873i	0.207809	+	0.251198i
$40$	−0.512518	+	2.17654i	−0.0810362	+	0.344141i
$41$	7.40169	−	1.90043i	1.15595	−	0.296798i	0.378415	−	0.925636i	$-0.376469\pi$
$41$	7.40169	−	1.90043i	1.15595	−	0.296798i	0.777536	+	0.628839i	$0.216469\pi$
$42$	−1.66737	+	1.77557i	−0.257281	+	0.273976i
$43$	−5.62839	−	1.82878i	−0.858322	−	0.278886i	−0.153394	−	0.988165i	$-0.549021\pi$
$43$	−5.62839	−	1.82878i	−0.858322	−	0.278886i	−0.704928	+	0.709279i	$0.749021\pi$
$44$	2.38443	+	0.301224i	0.359467	+	0.0454112i
$45$	0.374841	−	2.20443i	0.0558779	−	0.328616i
$46$	−4.88125	+	4.58380i	−0.719701	+	0.675844i
$47$	−1.09437	−	8.66286i	−0.159631	−	1.26361i	−0.844744	−	0.535171i	$-0.820247\pi$
$47$	−1.09437	−	8.66286i	−0.159631	−	1.26361i	0.685113	−	0.728437i	$-0.259753\pi$
$48$	0.998027	−	0.0627905i	0.144053	−	0.00906303i
$49$	0.329795	−	1.01500i	0.0471136	−	0.145001i
$50$	−3.56622	−	3.50458i	−0.504339	−	0.495623i
$51$	−0.0913160	−	0.281042i	−0.0127868	−	0.0393537i
$52$	−0.749485	−	1.89298i	−0.103935	−	0.262510i
$53$	−11.7105	−	2.23390i	−1.60856	−	0.306850i	−0.696706	−	0.717357i	$-0.745352\pi$
$53$	−11.7105	−	2.23390i	−1.60856	−	0.306850i	−0.911858	+	0.410507i	$0.865352\pi$
$54$	−0.992115	+	0.125333i	−0.135010	+	0.0170557i
$55$	−3.34183	+	4.20874i	−0.450612	+	0.567507i
$56$	2.13444	−	1.17342i	0.285227	−	0.156805i
$57$		−	2.11505i		−	0.280145i
$58$	1.50619	+	2.73974i	0.197772	+	0.359746i
$59$	−3.13869	−	1.24270i	−0.408623	−	0.161785i	0.154815	−	0.987943i	$-0.450522\pi$
$59$	−3.13869	−	1.24270i	−0.408623	−	0.161785i	−0.563438	+	0.826158i	$0.690522\pi$
$60$	−1.03770	+	1.98070i	−0.133966	+	0.255707i
$61$	4.00798	+	1.02908i	0.513170	+	0.131760i	0.496390	−	0.868100i	$-0.334659\pi$
$61$	4.00798	+	1.02908i	0.513170	+	0.131760i	0.0167796	+	0.999859i	$0.494659\pi$
$62$	−2.39622	+	1.52069i	−0.304320	+	0.193128i
$63$	−2.05655	+	1.30513i	−0.259101	+	0.164431i
$64$	−0.968583	−	0.248690i	−0.121073	−	0.0310862i
$65$	4.48811	+	0.763159i	0.556682	+	0.0946582i
$66$	2.23461	+	0.884745i	0.275062	+	0.108905i
$67$	1.55089	+	2.82105i	0.189471	+	0.344647i	0.953932	−	0.300024i	$-0.0969946\pi$
$67$	1.55089	+	2.82105i	0.189471	+	0.344647i	−0.764461	+	0.644670i	$0.776995\pi$
$68$			0.295505i			0.0358352i
$69$	−5.86784	+	3.22587i	−0.706405	+	0.388349i
$70$	−0.232848	+	5.44147i	−0.0278307	+	0.650380i
$71$	−3.40151	+	0.429710i	−0.403685	+	0.0509972i	−0.324554	−	0.945867i	$-0.605214\pi$
$71$	−3.40151	+	0.429710i	−0.403685	+	0.0509972i	−0.0791303	+	0.996864i	$0.525214\pi$
$72$	0.982287	+	0.187381i	0.115764	+	0.0220831i
$73$	−2.46346	−	6.22199i	−0.288326	−	0.728229i	−0.999678	−	0.0253925i	$-0.991916\pi$
$73$	−2.46346	−	6.22199i	−0.288326	−	0.728229i	0.711351	−	0.702837i	$-0.248084\pi$
$74$	2.55910	+	7.87610i	0.297489	+	0.915578i
$75$	−2.58263	−	4.28136i	−0.298216	−	0.494369i
$76$	−0.653587	+	2.01153i	−0.0749715	+	0.230739i
$77$	5.84244	−	0.367575i	0.665808	−	0.0418891i
$78$	−0.255173	−	2.01990i	−0.0288926	−	0.228709i
$79$	6.27100	−	5.88886i	0.705542	−	0.662548i	−0.246280	−	0.969199i	$-0.579208\pi$
$79$	6.27100	−	5.88886i	0.705542	−	0.662548i	0.951822	+	0.306651i	$0.0992083\pi$
$80$	1.59898	−	1.56309i	0.178772	−	0.174759i
$81$	−0.992115	−	0.125333i	−0.110235	−	0.0139259i
$82$	−7.26776	−	2.36144i	−0.802590	−	0.260777i
$83$	−9.41895	+	10.0302i	−1.03386	+	1.10095i	−0.0390508	+	0.999237i	$0.512433\pi$
$83$	−9.41895	+	10.0302i	−1.03386	+	1.10095i	−0.994813	+	0.101716i	$0.967567\pi$
$84$	2.35920	−	0.605740i	0.257410	−	0.0660917i
$85$	−0.564897	−	0.342792i	−0.0612717	−	0.0371810i
$86$	3.77230	+	4.55993i	0.406778	+	0.491710i
$87$	0.777521	+	3.02824i	0.0833590	+	0.324662i
$88$	−1.85184	−	1.53198i	−0.197407	−	0.163309i
$89$	1.42179	−	0.562926i	0.150709	−	0.0596701i	−0.291559	−	0.956553i	$-0.594174\pi$
$89$	1.42179	−	0.562926i	0.150709	−	0.0596701i	0.442268	+	0.896883i	$0.354174\pi$
$90$	−1.49768	+	1.66041i	−0.157869	+	0.175022i
$91$	−2.65718	−	4.18705i	−0.278548	−	0.438922i
$92$	6.57749	−	1.25472i	0.685751	−	0.130814i
$93$	−2.69912	+	0.876997i	−0.279886	+	0.0909403i
$94$	−3.71778	+	7.90069i	−0.383460	+	0.814894i
$95$	−3.08714	−	3.58284i	−0.316734	−	0.367592i
$96$	−0.876307	−	0.481754i	−0.0894377	−	0.0491688i
$97$	6.12338	−	11.1384i	0.621735	−	1.13093i	−0.358581	−	0.933499i	$-0.616739\pi$
$97$	6.12338	−	11.1384i	0.621735	−	1.13093i	0.980316	−	0.197434i	$-0.0632607\pi$
$98$	−0.822322	+	0.680284i	−0.0830671	+	0.0687190i
$99$	1.94438	+	1.41267i	0.195418	+	0.141979i
$100$	1.13321	+	4.86989i	0.113321	+	0.486989i
$101$	12.6398	−	9.18335i	1.25771	−	0.913778i	0.259065	−	0.965860i	$-0.416586\pi$
$101$	12.6398	−	9.18335i	1.25771	−	0.913778i	0.998643	+	0.0520820i	$0.0165857\pi$
$102$	−0.0734890	+	0.286221i	−0.00727650	+	0.0283401i
$103$	4.80771	−	2.26233i	0.473717	−	0.222914i	−0.174074	−	0.984733i	$-0.555693\pi$
$103$	4.80771	−	2.26233i	0.473717	−	0.222914i	0.647791	+	0.761818i	$0.275693\pi$
$104$	−0.381500	+	1.99989i	−0.0374092	+	0.196106i
$105$	−1.57877	+	5.21261i	−0.154072	+	0.508698i
$106$	8.69054	+	8.16096i	0.844100	+	0.792662i
$107$	3.55285	−	4.89008i	0.343467	−	0.472742i	−0.601983	−	0.798509i	$-0.705623\pi$
$107$	3.55285	−	4.89008i	0.343467	−	0.472742i	0.945450	+	0.325767i	$0.105623\pi$
$108$	0.904827	+	0.425779i	0.0870670	+	0.0409706i
$109$	4.97196	−	6.01007i	0.476228	−	0.575661i	−0.476620	−	0.879110i	$-0.658138\pi$
$109$	4.97196	−	6.01007i	0.476228	−	0.575661i	0.952848	+	0.303449i	$0.0981382\pi$
$110$	5.07675	−	1.76292i	0.484050	−	0.168088i
$111$	0.519995	+	8.26508i	0.0493557	+	0.784486i
$112$	−2.43092	−	0.152940i	−0.229700	−	0.0144515i
$113$	0.568511	−	1.43590i	0.0534810	−	0.135078i	−0.900580	−	0.434691i	$-0.856858\pi$
$113$	0.568511	−	1.43590i	0.0534810	−	0.135078i	0.954061	+	0.299613i	$0.0968576\pi$
$114$	−1.13330	+	1.78580i	−0.106143	+	0.167255i
$115$	−5.23146	+	14.0293i	−0.487836	+	1.30824i
$116$	0.196312	−	3.12030i	0.0182272	−	0.289712i
$117$	0.255173	−	2.01990i	0.0235907	−	0.186740i
$118$	1.98422	+	2.73104i	0.182662	+	0.251413i
$119$	0.134871	+	0.707019i	0.0123636	+	0.0648124i
$120$	1.93747	−	1.11633i	0.176866	−	0.101907i
$121$	2.22416	+	4.72658i	0.202196	+	0.429689i
$122$	−2.83265	−	3.01646i	−0.256456	−	0.273098i
$123$	−6.45216	−	4.09467i	−0.581772	−	0.369204i
$124$	2.83802			0.254862
$125$	−10.6240	−	3.48289i	−0.950240	−	0.311519i
$126$	2.43573			0.216992
$127$	−11.6418	−	7.38809i	−1.03304	−	0.655587i	−0.0926547	−	0.995698i	$-0.529535\pi$
$127$	−11.6418	−	7.38809i	−1.03304	−	0.655587i	−0.940385	+	0.340111i	$0.889535\pi$
$128$	0.684547	+	0.728969i	0.0605060	+	0.0644323i
$129$	2.51978	+	5.35481i	0.221854	+	0.471464i
$130$	−3.38052	−	3.04921i	−0.296491	−	0.267433i
$131$	0.839882	+	4.40281i	0.0733808	+	0.384676i	0.999963	+	0.00858375i	$0.00273233\pi$
$131$	0.839882	+	4.40281i	0.0733808	+	0.384676i	−0.926582	+	0.376092i	$0.877268\pi$
$132$	−1.41267	−	1.94438i	−0.122958	−	0.169237i
$133$	−0.645677	+	5.11106i	−0.0559873	+	0.443185i
$134$	0.202139	−	3.21290i	0.0174621	−	0.277553i
$135$	−1.86355	+	1.23579i	−0.160389	+	0.106360i
$136$	0.158339	−	0.249503i	0.0135775	−	0.0213947i
$137$	1.56402	−	3.95027i	0.133624	−	0.337495i	−0.847523	−	0.530758i	$-0.821907\pi$
$137$	1.56402	−	3.95027i	0.133624	−	0.337495i	0.981147	+	0.193264i	$0.0619073\pi$
$138$	6.68289	+	0.420452i	0.568885	+	0.0357912i
$139$	0.644650	+	10.2464i	0.0546785	+	0.869090i	0.925798	+	0.378019i	$0.123395\pi$
$139$	0.644650	+	10.2464i	0.0546785	+	0.869090i	−0.871119	+	0.491071i	$0.836605\pi$
$140$	3.11229	−	4.46962i	0.263036	−	0.377752i
$141$	−5.56580	+	6.72790i	−0.468725	+	0.566591i
$142$	3.10224	+	1.45980i	0.260334	+	0.122504i
$143$	−2.87614	+	3.95867i	−0.240515	+	0.331041i
$144$	−0.728969	−	0.684547i	−0.0607474	−	0.0570456i
$145$	5.73714	+	3.99489i	0.476444	+	0.331758i
$146$	−1.25394	+	6.57339i	−0.103777	+	0.544018i
$147$	−0.965667	+	0.454408i	−0.0796469	+	0.0374790i
$148$	2.05951	−	8.02124i	0.169290	−	0.659342i
$149$	−1.86680	+	1.35631i	−0.152934	+	0.111113i	−0.661621	−	0.749839i	$-0.730131\pi$
$149$	−1.86680	+	1.35631i	−0.152934	+	0.111113i	0.508687	+	0.860952i	$0.330131\pi$
$150$	−0.113485	+	4.99871i	−0.00926597	+	0.408143i
$151$	3.89422	+	2.82932i	0.316907	+	0.230247i	0.734855	−	0.678225i	$-0.237250\pi$
$151$	3.89422	+	2.82932i	0.316907	+	0.230247i	−0.417947	+	0.908471i	$0.637250\pi$
$152$	1.62967	−	1.34818i	0.132184	−	0.109352i
$153$	−0.142360	+	0.258953i	−0.0115092	+	0.0209351i
$154$	−5.12989	−	2.82018i	−0.413378	−	0.227257i
$155$	−3.29217	+	5.42526i	−0.264433	+	0.435768i
$156$	−0.866868	+	1.84219i	−0.0694050	+	0.147493i
$157$	17.3574	−	5.63974i	1.38527	−	0.450101i	0.480870	−	0.876792i	$-0.340321\pi$
$157$	17.3574	−	5.63974i	1.38527	−	0.450101i	0.904397	+	0.426691i	$0.140321\pi$
$158$	−8.45018	+	1.61196i	−0.672261	+	0.128241i
$159$	6.38796	+	10.0658i	0.506598	+	0.798271i
$160$	−2.18761	+	0.462985i	−0.172946	+	0.0366022i
$161$	15.1645	−	6.00406i	1.19513	−	0.473186i
$162$	0.770513	+	0.637424i	0.0605372	+	0.0500808i
$163$	2.88083	+	11.2201i	0.225644	+	0.878826i	0.975996	+	0.217788i	$0.0698840\pi$
$163$	2.88083	+	11.2201i	0.225644	+	0.878826i	−0.750352	+	0.661039i	$0.770116\pi$
$164$	4.87105	+	5.88809i	0.380365	+	0.459782i
$165$	5.35568	−	0.444997i	0.416939	−	0.0346430i
$166$	13.3271	−	3.42182i	1.03438	−	0.265585i
$167$	10.9391	−	11.6490i	0.846495	−	0.901425i	−0.149687	−	0.988733i	$-0.547827\pi$
$167$	10.9391	−	11.6490i	0.846495	−	0.901425i	0.996181	+	0.0873083i	$0.0278265\pi$
$168$	−2.31651	−	0.752681i	−0.178723	−	0.0580706i
$169$	−8.78506	−	1.10981i	−0.675774	−	0.0853701i
$170$	0.293282	+	0.592116i	0.0224937	+	0.0454132i
$171$	−1.54181	+	1.44785i	−0.117905	+	0.110720i
$172$	−0.741727	−	5.87138i	−0.0565562	−	0.447688i
$173$	15.4623	−	0.972805i	1.17558	−	0.0739610i	0.537043	−	0.843555i	$-0.319541\pi$
$173$	15.4623	−	0.972805i	1.17558	−	0.0739610i	0.638533	+	0.769594i	$0.279541\pi$
$174$	0.966131	−	2.97345i	0.0732422	−	0.225416i
$175$	4.93396	+	11.1344i	0.372973	+	0.841682i
$176$	0.742687	+	2.28576i	0.0559821	+	0.172295i
$177$	1.24270	+	3.13869i	0.0934068	+	0.235919i
$178$	−1.50209	−	0.286539i	−0.112586	−	0.0214770i
$179$	−22.3514	+	2.82364i	−1.67062	+	0.211049i	−0.902936	−	0.429775i	$-0.858593\pi$
$179$	−22.3514	+	2.82364i	−1.67062	+	0.211049i	−0.767688	+	0.640824i	$0.778593\pi$
$180$	2.15422	−	0.599433i	0.160566	−	0.0446791i
$181$	7.15605	−	3.93407i	0.531905	−	0.292417i	−0.193079	−	0.981183i	$-0.561847\pi$
$181$	7.15605	−	3.93407i	0.531905	−	0.292417i	0.724984	+	0.688766i	$0.241847\pi$
$182$			4.95903i			0.367588i
$183$	−1.99349	−	3.62614i	−0.147363	−	0.268052i
$184$	−6.22588	−	2.46500i	−0.458978	−	0.181722i
$185$	12.9446	+	13.2418i	0.951708	+	0.973559i
$186$	2.74886	+	0.705787i	0.201556	+	0.0517508i
$187$	0.599652	−	0.380551i	0.0438509	−	0.0278286i
$188$	7.37243	−	4.67868i	0.537689	−	0.341228i
$189$	2.35920	+	0.605740i	0.171607	+	0.0440611i
$190$	0.686779	+	4.67927i	0.0498242	+	0.339470i
$191$	0.184628	+	0.0730994i	0.0133592	+	0.00528928i	0.374795	−	0.927108i	$-0.377713\pi$
$191$	0.184628	+	0.0730994i	0.0133592	+	0.00528928i	−0.361435	+	0.932397i	$0.617713\pi$
$192$	0.481754	+	0.876307i	0.0347676	+	0.0632420i
$193$			22.7780i			1.63960i	0.572652	+	0.819798i	$0.305915\pi$
$193$			22.7780i			1.63960i	−0.572652	+	0.819798i	$0.694085\pi$
$194$	−11.1384	+	6.12338i	−0.799690	+	0.439633i
$195$	−2.51601	−	3.79411i	−0.180175	−	0.271702i
$196$	1.05882	−	0.133761i	0.0756303	−	0.00955432i
$197$	20.3161	+	3.87551i	1.44746	+	0.276118i	0.850426	−	0.526095i	$-0.176344\pi$
$197$	20.3161	+	3.87551i	1.44746	+	0.276118i	0.597037	+	0.802214i	$0.296344\pi$
$198$	−0.884745	−	2.23461i	−0.0628761	−	0.158807i
$199$	1.96126	+	6.03613i	0.139030	+	0.427890i	0.996195	−	0.0871519i	$-0.0277765\pi$
$199$	1.96126	+	6.03613i	0.139030	+	0.427890i	−0.857165	+	0.515041i	$0.827777\pi$
$200$	1.65262	−	4.71899i	0.116858	−	0.333683i
$201$	0.994805	−	3.06169i	0.0701681	−	0.215955i
$202$	−15.5928	+	0.981018i	−1.09711	+	0.0690242i
$203$	−0.954440	−	7.55517i	−0.0669885	−	0.530269i
$204$	0.215414	−	0.202287i	0.0150820	−	0.0141629i
$205$	−16.9064	+	2.48136i	−1.18079	+	0.173306i
$206$	−5.27150	−	0.665945i	−0.367283	−	0.0463986i
$207$	6.36837	+	2.06921i	0.442632	+	0.143820i
$208$	1.39371	−	1.48415i	0.0966362	−	0.102907i
$209$	4.92358	−	1.26416i	0.340571	−	0.0874439i
$210$	4.12606	−	3.55520i	0.284725	−	0.245332i
$211$	7.24589	+	8.75878i	0.498828	+	0.602979i	0.958494	−	0.285113i	$-0.0920310\pi$
$211$	7.24589	+	8.75878i	0.498828	+	0.602979i	−0.459666	+	0.888092i	$0.652031\pi$
$212$	−2.96480	−	11.5471i	−0.203624	−	0.793061i
$213$	2.64174	+	2.18544i	0.181009	+	0.149744i
$214$	−5.62001	+	2.22512i	−0.384176	+	0.152106i
$215$	12.0844	+	5.39301i	0.824146	+	0.367800i
$216$	−0.535827	−	0.844328i	−0.0364584	−	0.0574492i
$217$	6.79020	−	1.29530i	0.460949	−	0.0879307i
$218$	−7.41833	+	2.41036i	−0.502433	+	0.163250i
$219$	−2.84928	+	6.05503i	−0.192537	+	0.409161i
$220$	−5.23106	−	1.23178i	−0.352678	−	0.0830465i
$221$	−0.527216	−	0.289840i	−0.0354644	−	0.0194967i
$222$	3.98960	−	7.25706i	0.267765	−	0.487062i
$223$	0.325241	−	0.269062i	0.0217797	−	0.0180178i	−0.626470	−	0.779445i	$-0.715501\pi$
$223$	0.325241	−	0.269062i	0.0217797	−	0.0180178i	0.648250	+	0.761427i	$0.275501\pi$
$224$	1.97054	+	1.43168i	0.131662	+	0.0956584i
$225$	−1.35305	+	4.81345i	−0.0902032	+	0.320896i
$226$	−1.24940	+	0.907743i	−0.0831089	+	0.0603822i
$227$	−5.44409	+	21.2033i	−0.361337	+	1.40732i	0.484928	+	0.874554i	$0.338846\pi$
$227$	−5.44409	+	21.2033i	−0.361337	+	1.40732i	−0.846265	+	0.532761i	$0.821154\pi$
$228$	1.91376	−	0.900545i	0.126742	−	0.0596400i
$229$	2.57808	−	13.5148i	0.170365	−	0.893083i	−0.789740	−	0.613442i	$-0.789785\pi$
$229$	2.57808	−	13.5148i	0.170365	−	0.893083i	0.960105	−	0.279641i	$-0.0902154\pi$
$230$	11.9343	−	9.04216i	0.786926	−	0.596222i
$231$	−4.26737	−	4.00733i	−0.280773	−	0.263663i
$232$	−1.83769	+	2.52936i	−0.120650	+	0.166061i
$233$	−6.90294	−	3.24827i	−0.452226	−	0.212802i	0.186157	−	0.982520i	$-0.440397\pi$
$233$	−6.90294	−	3.24827i	−0.452226	−	0.212802i	−0.638384	+	0.769718i	$0.720397\pi$
$234$	−1.29777	+	1.56873i	−0.0848377	+	0.102551i
$235$	0.391766	+	19.5208i	0.0255560	+	1.27339i
$236$	−0.211965	−	3.36909i	−0.0137978	−	0.219309i
$237$	−8.58558	−	0.540159i	−0.557694	−	0.0350871i
$238$	0.264964	−	0.669224i	0.0171751	−	0.0433793i
$239$	−6.95838	+	10.9647i	−0.450100	+	0.709244i	−0.991296	−	0.131652i	$-0.957972\pi$
$239$	−6.95838	+	10.9647i	−0.450100	+	0.709244i	0.541196	+	0.840897i	$0.317972\pi$
$240$	−2.23402	−	0.0955971i	−0.144206	−	0.00617077i
$241$	0.849196	−	13.4976i	0.0547015	−	0.869456i	−0.871020	−	0.491248i	$-0.836541\pi$
$241$	0.849196	−	13.4976i	0.0547015	−	0.869456i	0.925721	−	0.378207i	$-0.123459\pi$
$242$	0.654708	−	5.18255i	0.0420862	−	0.333147i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	0.775381	+	4.06469i	0.0496387	+	0.260215i
$245$	−0.972557	+	2.17925i	−0.0621344	+	0.139227i
$246$	3.25371	+	6.91448i	0.207449	+	0.440851i
$247$	−2.94776	−	3.13905i	−0.187562	−	0.199733i
$248$	−2.39622	−	1.52069i	−0.152160	−	0.0965638i
$249$	13.7594			0.871966
$250$	7.10392	+	8.63333i	0.449291	+	0.546020i
$251$	−12.6383			−0.797722			−0.398861	−	0.917011i	$-0.630594\pi$
$251$	−12.6383			−0.797722			−0.398861	+	0.917011i	$0.630594\pi$
$252$	−2.05655	−	1.30513i	−0.129551	−	0.0822153i
$253$	−11.0166	−	11.7315i	−0.692610	−	0.737554i
$254$	5.87073	+	12.4759i	0.368363	+	0.782810i
$255$	0.136814	+	0.646450i	0.00856765	+	0.0404822i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	17.2624	+	23.7596i	1.07680	+	1.48209i	0.862997	+	0.505209i	$0.168585\pi$
$257$	17.2624	+	23.7596i	1.07680	+	1.48209i	0.213802	+	0.976877i	$0.431415\pi$
$258$	0.741727	−	5.87138i	0.0461779	−	0.365536i
$259$	1.26656	−	20.1315i	0.0787005	−	1.25091i
$260$	1.22042	+	4.38590i	0.0756872	+	0.272002i
$261$	1.67524	−	2.63976i	0.103695	−	0.163397i
$262$	1.65001	−	4.16745i	0.101938	−	0.257466i
$263$	−17.3350	−	1.09063i	−1.06892	−	0.0672509i	−0.481433	−	0.876483i	$-0.659883\pi$
$263$	−17.3350	−	1.09063i	−1.06892	−	0.0672509i	−0.587489	+	0.809232i	$0.699883\pi$
$264$	0.150910	+	2.39864i	0.00928786	+	0.147626i
$265$	25.5132	+	7.72731i	1.56726	+	0.474685i
$266$	3.28381	−	3.96944i	0.201343	−	0.243382i
$267$	−1.38364	−	0.651090i	−0.0846772	−	0.0398461i
$268$	−1.89223	+	2.60443i	−0.115586	+	0.159091i
$269$	−10.1519	−	9.53323i	−0.618970	−	0.581251i	0.310307	−	0.950636i	$-0.399568\pi$
$269$	−10.1519	−	9.53323i	−0.618970	−	0.581251i	−0.929276	+	0.369385i	$0.879568\pi$
$270$	2.23562	−	0.0448670i	0.136055	−	0.00273052i
$271$	4.39098	−	23.0183i	0.266733	−	1.39826i	−0.556636	−	0.830756i	$-0.687908\pi$
$271$	4.39098	−	23.0183i	0.266733	−	1.39826i	0.823369	−	0.567506i	$-0.192092\pi$
$272$	−0.267381	+	0.125820i	−0.0162123	+	0.00762895i
$273$	−1.23326	+	4.80323i	−0.0746403	+	0.290705i
$274$	−3.43721	+	2.49728i	−0.207649	+	0.150866i
$275$	8.42286	−	8.57100i	0.507918	−	0.516851i
$276$	−5.41726	−	3.93587i	−0.326081	−	0.236911i
$277$	−11.9247	+	9.86494i	−0.716484	+	0.592727i	−0.922580	−	0.385805i	$-0.873924\pi$
$277$	−11.9247	+	9.86494i	−0.716484	+	0.592727i	0.206097	+	0.978532i	$0.433924\pi$
$278$	4.94601	−	8.99676i	0.296642	−	0.539590i
$279$	2.48698	+	1.36723i	0.148891	+	0.0818537i
$280$	−5.02273	+	2.10618i	−0.300166	+	0.125868i
$281$	−6.00355	+	12.7582i	−0.358142	+	0.761090i	−0.999983	−	0.00574734i	$-0.998171\pi$
$281$	−6.00355	+	12.7582i	−0.358142	+	0.761090i	0.641842	+	0.766837i	$0.278171\pi$
$282$	8.30435	−	2.69825i	0.494517	−	0.160678i
$283$	−10.9449	+	2.08785i	−0.650607	+	0.124110i	−0.502111	−	0.864803i	$-0.667443\pi$
$283$	−10.9449	+	2.08785i	−0.650607	+	0.124110i	−0.148496	+	0.988913i	$0.547443\pi$
$284$	−1.83710	−	2.89481i	−0.109012	−	0.171776i
$285$	−0.498484	+	4.70305i	−0.0295276	+	0.278585i
$286$	4.54957	−	1.80130i	0.269022	−	0.106513i
$287$	14.3418	+	11.8645i	0.846568	+	0.700342i
$288$	0.248690	+	0.968583i	0.0146542	+	0.0570743i
$289$	−10.7805	−	13.0314i	−0.634150	−	0.766555i
$290$	−2.70346	−	6.44711i	−0.158753	−	0.378587i
$291$	−12.3113	+	3.16100i	−0.721700	+	0.185301i
$292$	4.58094	−	4.87820i	0.268079	−	0.285475i
$293$	−8.62382	−	2.80205i	−0.503809	−	0.163697i	0.0460759	−	0.998938i	$-0.485328\pi$
$293$	−8.62382	−	2.80205i	−0.503809	−	0.163697i	−0.549885	+	0.835241i	$0.685328\pi$
$294$	1.05882	+	0.133761i	0.0617519	+	0.00780107i
$295$	6.68635	+	3.50302i	0.389295	+	0.203953i
$296$	−6.03689	+	5.66902i	−0.350887	+	0.329505i
$297$	−0.301224	−	2.38443i	−0.0174788	−	0.138359i
$298$	2.30293	−	0.144888i	0.133405	−	0.00839316i
$299$	−4.21282	+	12.9657i	−0.243634	+	0.749827i
$300$	2.77426	−	4.15974i	0.160172	−	0.240163i
$301$	−4.45440	−	13.7092i	−0.256747	−	0.790187i
$302$	−1.77198	−	4.47550i	−0.101966	−	0.257536i
$303$	−15.3469	−	2.92758i	−0.881657	−	0.168185i
$304$	−2.09837	+	0.265086i	−0.120350	+	0.0152037i
$305$	−8.66966	−	3.23288i	−0.496424	−	0.185114i
$306$	0.258953	−	0.142360i	0.0148033	−	0.00813821i
$307$		−	10.3208i		−	0.589041i	−0.955645	−	0.294520i	$-0.904840\pi$
$307$		−	10.3208i		−	0.589041i	0.955645	−	0.294520i	$-0.0951599\pi$
$308$	2.82018	+	5.12989i	0.160695	+	0.292303i
$309$	−4.94027	−	1.95599i	−0.281042	−	0.111272i
$310$	5.68667	−	2.81667i	0.322981	−	0.159976i
$311$	−7.15469	−	1.83701i	−0.405705	−	0.104167i	0.0403221	−	0.999187i	$-0.487162\pi$
$311$	−7.15469	−	1.83701i	−0.405705	−	0.104167i	−0.446027	+	0.895019i	$0.647162\pi$
$312$	1.71901	−	1.09092i	0.0973200	−	0.0617612i
$313$	8.54763	−	5.42449i	0.483141	−	0.306610i	−0.271857	−	0.962338i	$-0.587638\pi$
$313$	8.54763	−	5.42449i	0.483141	−	0.306610i	0.754998	+	0.655727i	$0.227638\pi$
$314$	−17.6772	−	4.53874i	−0.997583	−	0.256136i
$315$	4.88057	−	2.41740i	0.274989	−	0.136205i
$316$	7.99846	+	3.16681i	0.449948	+	0.178147i
$317$	−11.8121	−	21.4861i	−0.663434	−	1.20678i	−0.967195	−	0.254033i	$-0.918243\pi$
$317$	−11.8121	−	21.4861i	−0.663434	−	1.20678i	0.303762	−	0.952748i	$-0.401757\pi$
$318$		−	11.9217i		−	0.668535i
$319$	−6.58466	+	3.61995i	−0.368670	+	0.202678i
$320$	2.09514	+	0.781269i	0.117122	+	0.0436743i
$321$	−5.99681	+	0.757573i	−0.334709	+	0.0422836i
$322$	−16.0210	−	3.05616i	−0.892814	−	0.170313i
$323$	0.230081	+	0.581117i	0.0128020	+	0.0323342i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−9.79996	−	2.75475i	−0.543604	−	0.152806i
$326$	3.57966	−	11.0171i	0.198259	−	0.610179i
$327$	−7.78470	+	0.489772i	−0.430495	+	0.0270844i
$328$	−0.957768	−	7.58152i	−0.0528839	−	0.418619i
$329$	15.5037	−	14.5590i	0.854749	−	0.802663i
$330$	−4.76039	−	2.49399i	−0.262051	−	0.137290i
$331$	−21.0029	−	2.65328i	−1.15442	−	0.145837i	−0.475273	−	0.879838i	$-0.657651\pi$
$331$	−21.0029	−	2.65328i	−1.15442	−	0.145837i	−0.679149	+	0.734001i	$0.737651\pi$
$332$	−13.0860	−	4.25189i	−0.718185	−	0.233353i
$333$	5.66902	−	6.03689i	0.310660	−	0.330820i
$334$	−15.4780	+	3.97409i	−0.846921	+	0.217452i
$335$	−2.78370	−	6.63845i	−0.152090	−	0.362697i
$336$	1.55259	+	1.87676i	0.0847007	+	0.102386i
$337$	−1.37991	−	5.37440i	−0.0751686	−	0.292762i	0.919874	−	0.392215i	$-0.128291\pi$
$337$	−1.37991	−	5.37440i	−0.0751686	−	0.292762i	−0.995042	+	0.0994522i	$0.968291\pi$
$338$	6.82281	+	5.64432i	0.371112	+	0.307010i
$339$	−1.43590	+	0.568511i	−0.0779872	+	0.0308773i
$340$	0.0696457	−	0.657088i	0.00377707	−	0.0356356i
$341$	−3.65480	−	5.75904i	−0.197918	−	0.311870i
$342$	2.07759	−	0.396321i	0.112343	−	0.0214306i
$343$	18.6879	−	6.07206i	1.00905	−	0.327860i
$344$	−2.51978	+	5.35481i	−0.135857	+	0.288712i
$345$	13.8081	−	5.79013i	0.743402	−	0.311730i
$346$	−13.5765	−	7.46374i	−0.729877	−	0.401253i
$347$	−6.78158	+	12.3356i	−0.364054	+	0.662212i	−0.993373	−	0.114935i	$-0.963334\pi$
$347$	−6.78158	+	12.3356i	−0.364054	+	0.662212i	0.629319	+	0.777147i	$0.283334\pi$
$348$	−2.40898	+	1.99288i	−0.129135	+	0.106830i
$349$	1.17910	+	0.856669i	0.0631160	+	0.0458565i	0.618896	−	0.785473i	$-0.287580\pi$
$349$	1.17910	+	0.856669i	0.0631160	+	0.0458565i	−0.555780	+	0.831329i	$0.687580\pi$
$350$	1.80023	−	12.0448i	0.0962264	−	0.643824i
$351$	−1.64712	+	1.19670i	−0.0879169	+	0.0638754i
$352$	0.597698	−	2.32788i	0.0318574	−	0.124076i
$353$	−13.4725	+	6.33966i	−0.717067	+	0.337426i	−0.749460	−	0.662049i	$-0.769687\pi$
$353$	−13.4725	+	6.33966i	−0.717067	+	0.337426i	0.0323936	+	0.999475i	$0.489687\pi$
$354$	0.632552	−	3.31596i	0.0336198	−	0.176241i
$355$	7.66491	−	0.153829i	0.406811	−	0.00816437i
$356$	1.11472	+	1.04679i	0.0590800	+	0.0554798i
$357$	0.423069	−	0.582305i	0.0223912	−	0.0308188i
$358$	20.3849	+	9.59241i	1.07738	+	0.506975i
$359$	−9.04129	+	10.9290i	−0.477181	+	0.576813i	−0.953092	−	0.302681i	$-0.902118\pi$
$359$	−9.04129	+	10.9290i	−0.477181	+	0.576813i	0.475911	+	0.879493i	$0.342118\pi$
$360$	−2.14006	−	0.648173i	−0.112791	−	0.0341617i
$361$	−0.912130	−	14.4979i	−0.0480069	−	0.763047i
$362$	−8.15004	−	0.512757i	−0.428357	−	0.0269499i
$363$	1.92299	−	4.85691i	0.100931	−	0.254922i
$364$	2.65718	−	4.18705i	0.139274	−	0.219461i
$365$	4.01136	+	14.4159i	0.209964	+	0.754563i
$366$	−0.259826	+	4.12982i	−0.0135813	+	0.215869i
$367$	0.0995491	−	0.788013i	0.00519642	−	0.0411339i	−0.989303	−	0.145873i	$-0.953401\pi$
$367$	0.0995491	−	0.788013i	0.00519642	−	0.0411339i	0.994500	+	0.104739i	$0.0334008\pi$
$368$	3.93587	+	5.41726i	0.205171	+	0.282394i
$369$	1.43193	+	7.50642i	0.0745431	+	0.390769i
$370$	−3.83418	−	18.1165i	−0.199329	−	0.941833i
$371$	−12.3638	−	26.2743i	−0.641895	−	1.36410i
$372$	−1.94276	−	2.06883i	−0.100727	−	0.107264i
$373$	1.83784	+	1.16633i	0.0951596	+	0.0603901i	0.582555	−	0.812791i	$-0.302053\pi$
$373$	1.83784	+	1.16633i	0.0951596	+	0.0603901i	−0.487396	+	0.873181i	$0.662053\pi$
$374$	−0.710212			−0.0367242
$375$	4.73371	+	10.1288i	0.244448	+	0.523047i
$376$	−8.73171			−0.450304
$377$	5.37444	+	3.41072i	0.276798	+	0.175661i
$378$	−1.66737	−	1.77557i	−0.0857602	−	0.0913254i
$379$	−4.82407	−	10.2517i	−0.247796	−	0.526593i	0.741773	−	0.670651i	$-0.233985\pi$
$379$	−4.82407	−	10.2517i	−0.247796	−	0.526593i	−0.989569	+	0.144057i	$0.953985\pi$
$380$	1.92741	−	4.31883i	0.0988740	−	0.221551i
$381$	2.58365	+	13.5440i	0.132365	+	0.693879i
$382$	−0.116718	−	0.160648i	−0.00597181	−	0.00821949i
$383$	−2.22626	+	17.6227i	−0.113757	+	0.900476i	0.827190	+	0.561922i	$0.189938\pi$
$383$	−2.22626	+	17.6227i	−0.113757	+	0.900476i	−0.940947	+	0.338554i	$0.890062\pi$
$384$	0.0627905	−	0.998027i	0.00320427	−	0.0509303i
$385$	−13.0779	−	0.559624i	−0.666514	−	0.0285211i
$386$	12.2051	−	19.2321i	0.621222	−	0.978889i
$387$	2.17858	−	5.50246i	0.110743	−	0.279706i
$388$	12.6855	+	0.798106i	0.644010	+	0.0405177i
$389$	0.197067	+	3.13229i	0.00999169	+	0.158813i	0.999859	+	0.0168153i	$0.00535272\pi$
$389$	0.197067	+	3.13229i	0.00999169	+	0.158813i	−0.989867	+	0.141998i	$0.954647\pi$
$390$	0.0913473	+	4.55162i	0.00462555	+	0.230480i
$391$	1.26129	−	1.52464i	0.0637862	−	0.0771042i
$392$	−0.965667	−	0.454408i	−0.0487735	−	0.0229511i
$393$	2.63458	−	3.62618i	0.132897	−	0.182917i
$394$	−15.0769	−	14.1581i	−0.759561	−	0.713275i
$395$	−15.3322	+	11.6166i	−0.771445	+	0.584493i
$396$	−0.450350	+	2.36082i	−0.0226309	+	0.118635i
$397$	−22.9958	+	10.8210i	−1.15413	+	0.543091i	−0.905013	−	0.425384i	$-0.860139\pi$
$397$	−22.9958	+	10.8210i	−1.15413	+	0.543091i	−0.249113	+	0.968474i	$0.580139\pi$
$398$	1.57837	−	6.14736i	0.0791168	−	0.308139i
$399$	4.16780	−	3.02808i	0.208651	−	0.151594i
$400$	−3.92391	+	3.09886i	−0.196196	+	0.154943i
$401$	17.1490	+	12.4595i	0.856382	+	0.622198i	0.926898	−	0.375312i	$-0.122465\pi$
$401$	17.1490	+	12.4595i	0.856382	+	0.622198i	−0.0705160	+	0.997511i	$0.522465\pi$
$402$	−2.48048	+	2.05203i	−0.123715	+	0.102346i
$403$	−2.78361	+	5.06337i	−0.138662	+	0.252225i
$404$	13.6911	+	7.52675i	0.681158	+	0.374470i
$405$	2.17654	+	0.512518i	0.108153	+	0.0254672i
$406$	−3.24240	+	6.89045i	−0.160918	+	0.341967i
$407$	−18.9293	+	6.15050i	−0.938291	+	0.304869i
$408$	−0.290271	+	0.0553721i	−0.0143705	+	0.00274133i
$409$	−10.5804	−	16.6720i	−0.523166	−	0.824377i	0.475296	−	0.879826i	$-0.342341\pi$
$409$	−10.5804	−	16.6720i	−0.523166	−	0.824377i	−0.998462	+	0.0554487i	$0.982341\pi$
$410$	15.6041	+	6.96382i	0.770633	+	0.343918i
$411$	−3.95027	+	1.56402i	−0.194853	+	0.0771476i
$412$	4.09404	+	3.38689i	0.201699	+	0.166860i
$413$	−2.04483	−	7.96408i	−0.100619	−	0.391887i
$414$	−4.26826	−	5.15943i	−0.209773	−	0.253572i
$415$	23.3080	−	20.0833i	1.14415	−	0.985851i
$416$	−1.97199	+	0.506322i	−0.0966849	+	0.0248245i
$417$	7.02803	−	7.48409i	0.344164	−	0.366497i
$418$	−4.83449	−	1.57082i	−0.236463	−	0.0768314i
$419$	−13.0203	−	1.64485i	−0.636084	−	0.0803562i	−0.199323	−	0.979934i	$-0.563874\pi$
$419$	−13.0203	−	1.64485i	−0.636084	−	0.0803562i	−0.436761	+	0.899578i	$0.643874\pi$
$420$	−5.38872	+	0.790906i	−0.262942	+	0.0385922i
$421$	25.1527	−	23.6200i	1.22587	−	1.15117i	0.242382	−	0.970181i	$-0.422071\pi$
$421$	25.1527	−	23.6200i	1.22587	−	1.15117i	0.983486	−	0.180985i	$-0.0579286\pi$
$422$	−1.42472	−	11.2778i	−0.0693543	−	0.548996i
$423$	8.71448	−	0.548269i	0.423713	−	0.0266577i
$424$	−3.68400	+	11.3382i	−0.178911	+	0.550632i
$425$	1.17532	+	0.895373i	0.0570115	+	0.0434320i
$426$	−1.05948	−	3.26074i	−0.0513319	−	0.157983i
$427$	3.71033	+	9.37122i	0.179555	+	0.453505i
$428$	5.93741	+	1.13262i	0.286995	+	0.0547473i
$429$	4.85460	−	0.613279i	0.234382	−	0.0296094i
$430$	−7.31344	−	11.0286i	−0.352685	−	0.531846i
$431$	−27.1979	+	14.9522i	−1.31008	+	0.720221i	−0.975050	−	0.221988i	$-0.928746\pi$
$431$	−27.1979	+	14.9522i	−1.31008	+	0.720221i	−0.335027	+	0.942208i	$0.608746\pi$
$432$			1.00000i			0.0481125i
$433$	3.96725	+	7.21641i	0.190654	+	0.346798i	0.954307	−	0.298829i	$-0.0965960\pi$
$433$	3.96725	+	7.21641i	0.190654	+	0.346798i	−0.763653	+	0.645627i	$0.776596\pi$
$434$	−6.42721	−	2.54471i	−0.308516	−	0.122150i
$435$	−1.01520	−	6.91689i	−0.0486749	−	0.331639i
$436$	7.55504	+	1.93980i	0.361821	+	0.0928997i
$437$	11.9579	−	7.58870i	0.572023	−	0.363017i
$438$	5.65018	−	3.58571i	0.269976	−	0.171332i
$439$	21.1263	+	5.42431i	1.00830	+	0.258888i	0.716497	−	0.697590i	$-0.245744\pi$
$439$	21.1263	+	5.42431i	1.00830	+	0.258888i	0.291805	+	0.956478i	$0.405744\pi$
$440$	3.75671	+	3.84297i	0.179094	+	0.183206i
$441$	0.992294	+	0.392877i	0.0472521	+	0.0187084i
$442$	0.289840	+	0.527216i	0.0137863	+	0.0250771i
$443$		−	22.7610i		−	1.08141i	−0.841213	−	0.540704i	$-0.818158\pi$
$443$		−	22.7610i		−	1.08141i	0.841213	−	0.540704i	$-0.181842\pi$
$444$	−7.25706	+	3.98960i	−0.344405	+	0.189338i
$445$	−3.29418	+	0.916637i	−0.156159	+	0.0434528i
$446$	−0.418781	+	0.0529043i	−0.0198298	+	0.00250509i
$447$	2.26662	+	0.432380i	0.107207	+	0.0204509i
$448$	−0.896651	−	2.26468i	−0.0423628	−	0.106996i
$449$	10.7706	+	33.1485i	0.508297	+	1.56438i	0.795157	+	0.606404i	$0.207388\pi$
$449$	10.7706	+	33.1485i	0.508297	+	1.56438i	−0.286860	+	0.957972i	$0.592612\pi$
$450$	3.72159	−	3.33913i	0.175437	−	0.157408i
$451$	5.67545	−	17.4672i	0.267246	−	0.822500i
$452$	1.54130	−	0.0969702i	0.0724965	−	0.00456110i
$453$	−0.603294	−	4.77557i	−0.0283452	−	0.224376i
$454$	15.9579	−	14.9855i	0.748942	−	0.703304i
$455$	4.92172	+	9.93663i	0.230734	+	0.465836i
$456$	−2.09837	−	0.265086i	−0.0982653	−	0.0124138i
$457$	20.2005	+	6.56353i	0.944938	+	0.307029i	0.740657	−	0.671883i	$-0.234514\pi$
$457$	20.2005	+	6.56353i	0.944938	+	0.307029i	0.204281	+	0.978912i	$0.434514\pi$
$458$	−9.41834	+	10.0295i	−0.440090	+	0.468648i
$459$	0.286221	−	0.0734890i	0.0133596	−	0.00343017i
$460$	−14.9215	+	1.23981i	−0.695719	+	0.0578065i
$461$	24.7659	+	29.9368i	1.15346	+	1.39429i	0.904871	+	0.425686i	$0.139967\pi$
$461$	24.7659	+	29.9368i	1.15346	+	1.39429i	0.248590	+	0.968609i	$0.420033\pi$
$462$	1.45583	+	5.67008i	0.0677312	+	0.263796i
$463$	19.1819	+	15.8687i	0.891461	+	0.737480i	0.965673	−	0.259762i	$-0.0836441\pi$
$463$	19.1819	+	15.8687i	0.891461	+	0.737480i	−0.0742119	+	0.997242i	$0.523644\pi$
$464$	2.90692	−	1.15093i	0.134950	−	0.0534305i
$465$	6.20849	−	1.31396i	0.287912	−	0.0609335i
$466$	4.08783	+	6.44139i	0.189365	+	0.298391i
$467$	31.6208	−	6.03199i	1.46324	−	0.279127i	0.606582	−	0.795021i	$-0.292540\pi$
$467$	31.6208	−	6.03199i	1.46324	−	0.279127i	0.856653	+	0.515894i	$0.172540\pi$
$468$	1.93631	−	0.629145i	0.0895059	−	0.0290822i
$469$	−3.33863	+	7.09495i	−0.154164	+	0.327614i
$470$	10.1290	−	16.6918i	0.467215	−	0.769937i
$471$	−15.9931	−	8.79229i	−0.736924	−	0.405127i
$472$	−1.62628	+	2.95819i	−0.0748556	+	0.136162i
$473$	−10.9593	+	9.06630i	−0.503908	+	0.416869i
$474$	6.95962	+	5.05646i	0.319666	+	0.232251i
$475$	6.02019	+	8.69444i	0.276225	+	0.398928i
$476$	−0.582305	+	0.423069i	−0.0266899	+	0.0193913i
$477$	2.96480	−	11.5471i	0.135749	−	0.528707i
$478$	11.7503	−	5.52928i	0.537447	−	0.252903i
$479$	−0.403978	+	2.11773i	−0.0184582	+	0.0967614i	−0.990324	−	0.138773i	$-0.955684\pi$
$479$	−0.403978	+	2.11773i	−0.0184582	+	0.0967614i	0.971866	+	0.235535i	$0.0756841\pi$
$480$	1.83502	+	1.27776i	0.0837570	+	0.0583217i
$481$	12.2909	+	11.5419i	0.560415	+	0.526264i
$482$	−7.94936	+	10.9414i	−0.362084	+	0.498365i
$483$	−14.7576	−	6.94440i	−0.671494	−	0.315981i
$484$	−3.32973	+	4.02496i	−0.151352	+	0.182953i
$485$	−16.2412	+	23.3243i	−0.737474	+	1.05910i
$486$	−0.0627905	−	0.998027i	−0.00284824	−	0.0452714i
$487$	−40.1285	−	2.52467i	−1.81839	−	0.114404i	−0.883301	−	0.468806i	$-0.844684\pi$
$487$	−40.1285	−	2.52467i	−1.81839	−	0.114404i	−0.935093	+	0.354403i	$0.884684\pi$
$488$	1.52329	−	3.84740i	0.0689563	−	0.174164i
$489$	6.20704	−	9.78072i	0.280692	−	0.442300i
$490$	1.98886	−	1.31888i	0.0898474	−	0.0595809i
$491$	0.698591	−	11.1038i	0.0315270	−	0.501107i	−0.950301	−	0.311333i	$-0.899224\pi$
$491$	0.698591	−	11.1038i	0.0315270	−	0.501107i	0.981828	−	0.189774i	$-0.0607755\pi$
$492$	0.957768	−	7.58152i	0.0431795	−	0.341801i
$493$	−0.543046	−	0.747439i	−0.0244576	−	0.0336630i
$494$	0.806892	+	4.22988i	0.0363038	+	0.190311i
$495$	−3.99060	−	3.59950i	−0.179364	−	0.161786i
$496$	1.20837	+	2.56792i	0.0542574	+	0.115303i
$497$	−5.71665	−	6.08761i	−0.256427	−	0.273067i
$498$	−11.6174	−	7.37265i	−0.520590	−	0.330376i
$499$	22.3951			1.00254			0.501272	−	0.865290i	$-0.332866\pi$
$499$	22.3951			1.00254			0.501272	+	0.865290i	$0.332866\pi$
$500$	−1.37206	−	11.0958i	−0.0613606	−	0.496221i
$501$	−15.9801			−0.713938
$502$	10.6709	+	6.77194i	0.476264	+	0.302246i
$503$	−18.5577	−	19.7620i	−0.827448	−	0.881143i	0.167044	−	0.985949i	$-0.446578\pi$
$503$	−18.5577	−	19.7620i	−0.827448	−	0.881143i	−0.994493	+	0.104806i	$0.966578\pi$
$504$	1.03708	+	2.20391i	0.0461953	+	0.0981700i
$505$	−30.2704	+	17.4412i	−1.34701	+	0.776124i
$506$	3.01559	+	15.8083i	0.134059	+	0.702763i
$507$	5.20477	+	7.16375i	0.231152	+	0.318153i
$508$	1.72812	−	13.6795i	0.0766730	−	0.606929i
$509$	2.70261	−	42.9568i	0.119791	−	1.90403i	−0.239652	−	0.970859i	$-0.577033\pi$
$509$	2.70261	−	42.9568i	0.119791	−	1.90403i	0.359443	−	0.933167i	$-0.382967\pi$
$510$	0.230869	−	0.619124i	0.0102230	−	0.0274153i
$511$	8.73381	−	13.7623i	0.386361	−	0.608808i
$512$	−0.368125	+	0.929776i	−0.0162690	+	0.0410907i
$513$	2.11088	+	0.132805i	0.0931975	+	0.00586349i
$514$	−1.84407	−	29.3106i	−0.0813383	−	1.29283i
$515$	−11.2237	+	3.89746i	−0.494574	+	0.171742i
$516$	−3.77230	+	4.55993i	−0.166066	+	0.200740i
$517$	−18.9884	−	8.93526i	−0.835109	−	0.392972i
$518$	−11.8564	+	16.3189i	−0.520939	+	0.717011i
$519$	−11.2938	−	10.6056i	−0.495743	−	0.465534i
$520$	1.31965	−	4.35707i	0.0578705	−	0.191070i
$521$	−7.65240	+	40.1153i	−0.335258	+	1.75748i	0.271350	+	0.962481i	$0.412530\pi$
$521$	−7.65240	+	40.1153i	−0.335258	+	1.75748i	−0.606607	+	0.795002i	$0.707470\pi$
$522$	−2.82891	+	1.33118i	−0.123818	+	0.0582644i
$523$	8.62763	−	33.6024i	0.377260	−	1.46933i	−0.442576	−	0.896731i	$-0.645935\pi$
$523$	8.62763	−	33.6024i	0.377260	−	1.46933i	0.819835	−	0.572599i	$-0.194065\pi$
$524$	−3.62618	+	2.63458i	−0.158410	+	0.115092i
$525$	4.73910	−	11.2187i	0.206831	−	0.489626i
$526$	14.0520	+	10.2094i	0.612698	+	0.445151i
$527$	0.646190	−	0.534575i	0.0281485	−	0.0232864i
$528$	1.15784	−	2.10610i	0.0503885	−	0.0916564i
$529$	−19.1366	−	10.5204i	−0.832025	−	0.457410i
$530$	−17.4010	−	20.1950i	−0.755850	−	0.877216i
$531$	1.43732	−	3.05447i	0.0623746	−	0.132553i
$532$	−4.89954	+	1.59196i	−0.212422	+	0.0690201i
$533$	−15.2827	+	2.91534i	−0.661969	+	0.126277i
$534$	0.819372	+	1.29112i	0.0354577	+	0.0558724i
$535$	−9.05268	+	10.0363i	−0.391381	+	0.433907i
$536$	2.99319	−	1.18509i	0.129286	−	0.0511880i
$537$	17.3590	+	14.3606i	0.749094	+	0.619705i
$538$	3.46334	+	13.4888i	0.149315	+	0.581544i
$539$	−1.63498	−	1.97636i	−0.0704238	−	0.0851277i
$540$	−1.91164	−	1.16002i	−0.0822637	−	0.0499194i
$541$	3.55818	−	0.913586i	0.152978	−	0.0392781i	−0.171424	−	0.985197i	$-0.554837\pi$
$541$	3.55818	−	0.913586i	0.152978	−	0.0392781i	0.324402	+	0.945919i	$0.394837\pi$
$542$	−16.0412	+	17.0822i	−0.689031	+	0.733743i
$543$	−7.76647	−	2.52348i	−0.333291	−	0.108293i
$544$	0.293175	+	0.0370366i	0.0125698	+	0.00158793i
$545$	−12.4722	+	12.1923i	−0.534250	+	0.522259i
$546$	3.61498	−	3.39469i	0.154707	−	0.145279i
$547$	1.44641	+	11.4495i	0.0618438	+	0.489544i	0.992368	+	0.123313i	$0.0393520\pi$
$547$	1.44641	+	11.4495i	0.0618438	+	0.489544i	−0.930524	+	0.366231i	$0.880648\pi$
$548$	4.24024	−	0.266773i	0.181134	−	0.0113960i
$549$	−1.27871	+	3.93546i	−0.0545739	+	0.167961i
$550$	−11.7042	+	2.72354i	−0.499070	+	0.116132i
$551$	−2.04342	−	6.28899i	−0.0870525	−	0.267920i
$552$	2.46500	+	6.22588i	0.104917	+	0.264991i
$553$	20.5823	+	3.92629i	0.875250	+	0.166963i
$554$	15.3542	−	1.93969i	0.652339	−	0.0824095i
$555$	0.791680	−	18.5009i	0.0336049	−	0.785319i
$556$	−8.99676	+	4.94601i	−0.381548	+	0.209758i
$557$			44.8771i			1.90150i	0.309953	+	0.950752i	$0.399687\pi$
$557$			44.8771i			1.90150i	−0.309953	+	0.950752i	$0.600313\pi$
$558$	−1.36723	−	2.48698i	−0.0578793	−	0.105282i
$559$	11.2028	+	4.43549i	0.473826	+	0.187601i
$560$	5.36938	+	0.913009i	0.226898	+	0.0385817i
$561$	−0.687899	−	0.176623i	−0.0290431	−	0.00745701i
$562$	11.9051	−	7.55523i	0.502188	−	0.318698i
$563$	16.6105	−	10.5413i	0.700047	−	0.444263i	−0.137591	−	0.990489i	$-0.543936\pi$
$563$	16.6105	−	10.5413i	0.700047	−	0.444263i	0.837638	+	0.546226i	$0.183936\pi$
$564$	−8.45739	−	2.17149i	−0.356120	−	0.0914361i
$565$	−1.60257	+	3.05889i	−0.0674205	+	0.128688i
$566$	10.3598	+	4.10174i	0.435455	+	0.172409i
$567$	−1.17342	−	2.13444i	−0.0492790	−	0.0896382i
$568$			3.42854i			0.143858i
$569$	12.8021	−	7.03803i	0.536693	−	0.295050i	−0.190263	−	0.981733i	$-0.560934\pi$
$569$	12.8021	−	7.03803i	0.536693	−	0.295050i	0.726957	+	0.686684i	$0.240934\pi$
$570$	2.94091	−	3.70382i	0.123181	−	0.155136i
$571$	0.846527	−	0.106941i	0.0354260	−	0.00447535i	−0.107600	−	0.994194i	$-0.534317\pi$
$571$	0.846527	−	0.106941i	0.0354260	−	0.00447535i	0.143026	+	0.989719i	$0.454317\pi$
$572$	−4.80652	−	0.916892i	−0.200971	−	0.0383372i
$573$	−0.0730994	−	0.184628i	−0.00305377	−	0.00771294i
$574$	−5.75182	−	17.7023i	−0.240076	−	0.738878i
$575$	14.9392	−	29.9627i	0.623008	−	1.24953i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−42.5354	+	2.67610i	−1.77077	+	0.111408i	−0.914364	−	0.404892i	$-0.867309\pi$
$577$	−42.5354	+	2.67610i	−1.77077	+	0.111408i	−0.856408	+	0.516300i	$0.827309\pi$
$578$	2.11972	+	16.7793i	0.0881687	+	0.697928i
$579$	16.6045	−	15.5926i	0.690058	−	0.648007i
$580$	−1.17193	+	6.89206i	−0.0486616	+	0.286177i
$581$	−33.2498	−	4.20043i	−1.37944	−	0.174263i
$582$	12.0885	+	3.92779i	0.501085	+	0.162812i
$583$	−19.6139	+	20.8867i	−0.812326	+	0.865039i
$584$	−6.48168	+	1.66421i	−0.268214	+	0.0688656i
$585$	−1.04346	+	4.43134i	−0.0431419	+	0.183213i
$586$	5.77992	+	6.98672i	0.238766	+	0.288619i
$587$	8.33483	+	32.4620i	0.344015	+	1.33985i	0.871545	+	0.490315i	$0.163118\pi$
$587$	8.33483	+	32.4620i	0.344015	+	1.33985i	−0.527530	+	0.849536i	$0.676882\pi$
$588$	−0.822322	−	0.680284i	−0.0339120	−	0.0280544i
$589$	5.58104	−	2.20969i	0.229963	−	0.0910487i
$590$	−3.76847	−	6.54042i	−0.155145	−	0.269265i
$591$	−11.0822	−	17.4628i	−0.455861	−	0.718323i
$592$	8.13473	−	1.55178i	0.334335	−	0.0637779i
$593$	24.0977	−	7.82981i	0.989573	−	0.321532i	0.230881	−	0.972982i	$-0.425839\pi$
$593$	24.0977	−	7.82981i	0.989573	−	0.321532i	0.758691	+	0.651450i	$0.225839\pi$
$594$	−1.02331	+	2.17465i	−0.0419870	+	0.0892269i
$595$	−0.133268	−	1.60392i	−0.00546346	−	0.0657545i
$596$	−2.02207	−	1.11164i	−0.0828271	−	0.0455346i
$597$	3.05757	−	5.56171i	0.125138	−	0.227625i
$598$	10.5044	−	8.68998i	0.429556	−	0.355360i
$599$	7.14284	+	5.18958i	0.291848	+	0.212040i	0.724069	−	0.689728i	$-0.242270\pi$
$599$	7.14284	+	5.18958i	0.291848	+	0.212040i	−0.432220	+	0.901768i	$0.642270\pi$
$600$	−4.57129	+	2.02566i	−0.186622	+	0.0826974i
$601$	−21.7072	+	15.7712i	−0.885453	+	0.643320i	−0.934689	−	0.355468i	$-0.884322\pi$
$601$	−21.7072	+	15.7712i	−0.885453	+	0.643320i	0.0492352	+	0.998787i	$0.484322\pi$
$602$	−3.58480	+	13.9619i	−0.146105	+	0.569043i
$603$	−2.91287	+	1.37069i	−0.118621	+	0.0558189i
$604$	−0.901964	+	4.72826i	−0.0367004	+	0.192390i
$605$	−3.83169	−	11.0343i	−0.155780	−	0.448607i
$606$	11.3892	+	10.6951i	0.462653	+	0.434460i
$607$	−1.84350	+	2.53736i	−0.0748255	+	0.102988i	−0.844789	−	0.535099i	$-0.820274\pi$
$607$	−1.84350	+	2.53736i	−0.0748255	+	0.102988i	0.769964	+	0.638088i	$0.220274\pi$
$608$	1.91376	+	0.900545i	0.0776130	+	0.0365219i
$609$	−4.85412	+	5.86762i	−0.196699	+	0.237768i
$610$	5.58778	+	7.37505i	0.226242	+	0.298607i
$611$	1.11625	+	17.7423i	0.0451587	+	0.717776i
$612$	−0.294922	−	0.0185549i	−0.0119215	−	0.000750037i
$613$	−16.1884	+	40.8873i	−0.653844	+	1.65142i	0.100495	+	0.994938i	$0.467957\pi$
$613$	−16.1884	+	40.8873i	−0.653844	+	1.65142i	−0.754339	+	0.656485i	$0.772043\pi$
$614$	−5.53018	+	8.71416i	−0.223180	+	0.351675i
$615$	13.3821	+	10.6256i	0.539617	+	0.428467i
$616$	0.367575	−	5.84244i	0.0148100	−	0.235399i
$617$	4.09491	−	32.4146i	0.164855	−	1.30496i	−0.664941	−	0.746895i	$-0.731544\pi$
$617$	4.09491	−	32.4146i	0.164855	−	1.30496i	0.829796	−	0.558066i	$-0.188456\pi$
$618$	3.12314	+	4.29863i	0.125631	+	0.172916i
$619$	−0.971859	−	5.09466i	−0.0390623	−	0.204772i	0.957406	−	0.288747i	$-0.0932385\pi$
$619$	−0.971859	−	5.09466i	−0.0390623	−	0.204772i	−0.996468	+	0.0839748i	$0.973238\pi$
$620$	−6.31066	−	0.668876i	−0.253442	−	0.0268627i
$621$	−2.85106	−	6.05881i	−0.114409	−	0.243132i
$622$	5.05658	+	5.38471i	0.202751	+	0.215907i
$623$	3.14482	+	1.99577i	0.125995	+	0.0799587i
$624$	−2.03596			−0.0815035
$625$	22.8028	+	10.2485i	0.912112	+	0.409940i
$626$	−10.1236			−0.404620
$627$	−4.29196	−	2.72376i	−0.171404	−	0.108776i
$628$	12.4934	+	13.3041i	0.498541	+	0.530892i
$629$	−1.04197	−	2.21429i	−0.0415459	−	0.0882896i
$630$	−5.41611	−	0.574062i	−0.215783	−	0.0228712i
$631$	5.49502	+	28.8059i	0.218753	+	1.14674i	0.906956	+	0.421226i	$0.138400\pi$
$631$	5.49502	+	28.8059i	0.218753	+	1.14674i	−0.688202	+	0.725519i	$0.741600\pi$
$632$	−5.05646	−	6.95962i	−0.201135	−	0.276839i
$633$	1.42472	−	11.2778i	0.0566275	−	0.448253i
$634$	−1.53956	+	24.4706i	−0.0611437	+	0.971851i
$635$	24.1455	+	19.1720i	0.958186	+	0.760819i
$636$	−6.38796	+	10.0658i	−0.253299	+	0.399135i
$637$	−0.799880	+	2.02027i	−0.0316924	+	0.0800459i
$638$	7.49928	+	0.471815i	0.296899	+	0.0186793i
$639$	−0.215280	−	3.42178i	−0.00851634	−	0.135363i
$640$	−1.35036	−	1.78228i	−0.0533777	−	0.0704508i
$641$	0.631420	−	0.763255i	0.0249396	−	0.0301468i	−0.757896	−	0.652375i	$-0.773773\pi$
$641$	0.631420	−	0.763255i	0.0249396	−	0.0301468i	0.782836	+	0.622229i	$0.213773\pi$
$642$	5.46920	+	2.57361i	0.215852	+	0.101572i
$643$	22.3232	−	30.7253i	0.880341	−	1.21169i	−0.0959849	−	0.995383i	$-0.530600\pi$
$643$	22.3232	−	30.7253i	0.880341	−	1.21169i	0.976326	−	0.216303i	$-0.0693999\pi$
$644$	11.8894	+	11.1649i	0.468507	+	0.439958i
$645$	−4.34097	−	12.5009i	−0.170926	−	0.492222i
$646$	0.117115	−	0.613937i	0.00460782	−	0.0241550i
$647$	2.53644	−	1.19356i	0.0997178	−	0.0469236i	−0.375274	−	0.926914i	$-0.622451\pi$
$647$	2.53644	−	1.19356i	0.0997178	−	0.0469236i	0.474991	+	0.879991i	$0.342451\pi$
$648$	−0.248690	+	0.968583i	−0.00976946	+	0.0380495i
$649$	−6.56374	+	4.76884i	−0.257649	+	0.187193i
$650$	6.79832	+	7.57699i	0.266652	+	0.297194i
$651$	−5.59244	−	4.06315i	−0.219185	−	0.159247i
$652$	−8.92565	+	7.38394i	−0.349556	+	0.289177i
$653$	5.75379	−	10.4661i	0.225163	−	0.409570i	−0.739461	−	0.673199i	$-0.764920\pi$
$653$	5.75379	−	10.4661i	0.225163	−	0.409570i	0.964624	+	0.263629i	$0.0849196\pi$
$654$	6.83527	+	3.75772i	0.267280	+	0.146939i
$655$	−0.829899	−	9.98810i	−0.0324268	−	0.390267i
$656$	−3.25371	+	6.91448i	−0.127036	+	0.269965i
$657$	6.36440	−	2.06792i	0.248299	−	0.0806772i
$658$	−20.8913	+	3.98524i	−0.814429	+	0.155361i
$659$	−14.0119	−	22.0793i	−0.545827	−	0.860086i	0.453690	−	0.891160i	$-0.350107\pi$
$659$	−14.0119	−	22.0793i	−0.545827	−	0.860086i	−0.999517	+	0.0310734i	$0.990107\pi$
$660$	2.68298	+	4.65649i	0.104435	+	0.181254i
$661$	31.3087	−	12.3960i	1.21777	−	0.482148i	0.330677	−	0.943744i	$-0.392723\pi$
$661$	31.3087	−	12.3960i	1.21777	−	0.482148i	0.887091	+	0.461595i	$0.152723\pi$
$662$	16.3116	+	13.4941i	0.633969	+	0.524464i
$663$	0.149620	+	0.582733i	0.00581078	+	0.0226315i
$664$	8.77057	+	10.6018i	0.340364	+	0.411429i
$665$	2.64033	−	11.2128i	0.102388	−	0.434816i
$666$	−8.02124	+	2.05951i	−0.310817	+	0.0798042i
$667$	−14.3311	+	15.2611i	−0.554902	+	0.590911i
$668$	15.1980	+	4.93812i	0.588027	+	0.191062i
$669$	−0.418781	−	0.0529043i	−0.0161910	−	0.00204540i
$670$	−1.20671	+	7.09661i	−0.0466192	+	0.274166i
$671$	7.24972	−	6.80794i	0.279872	−	0.262818i
$672$	−0.305277	−	2.41652i	−0.0117763	−	0.0932193i
$673$	2.81993	−	0.177415i	0.108700	−	0.00683884i	−0.00834720	−	0.999965i	$-0.502657\pi$
$673$	2.81993	−	0.177415i	0.108700	−	0.00683884i	0.117047	+	0.993126i	$0.462657\pi$
$674$	−1.71465	+	5.27715i	−0.0660459	+	0.203268i
$675$	4.43508	−	2.30870i	0.170706	−	0.0888619i
$676$	−2.73631	−	8.42150i	−0.105243	−	0.323904i
$677$	−0.181707	−	0.458938i	−0.00698355	−	0.0176384i	0.926243	−	0.376927i	$-0.123019\pi$
$677$	−0.181707	−	0.458938i	−0.00698355	−	0.0176384i	−0.933226	+	0.359289i	$0.883019\pi$
$678$	1.51699	+	0.289381i	0.0582597	+	0.0111136i
$679$	30.7154	−	3.88026i	1.17875	−	0.148911i
$680$	−0.410889	+	0.517480i	−0.0157569	+	0.0198444i
$681$	19.1833	−	10.5461i	0.735106	−	0.404128i
$682$			6.82086i			0.261184i
$683$	18.9291	+	34.4320i	0.724303	+	1.31750i	0.940045	+	0.341052i	$0.110783\pi$
$683$	18.9291	+	34.4320i	0.724303	+	1.31750i	−0.215742	+	0.976451i	$0.569217\pi$
$684$	−1.96652	−	0.778602i	−0.0751919	−	0.0297706i
$685$	−4.40880	+	8.41526i	−0.168452	+	0.321531i
$686$	−19.0323	−	4.88665i	−0.726655	−	0.186573i
$687$	−11.6167	+	7.37217i	−0.443204	+	0.281266i
$688$	4.99677	−	3.17105i	0.190500	−	0.120895i
$689$	23.5095	+	6.03621i	0.895640	+	0.229961i
$690$	−14.7611	−	2.50997i	−0.561944	−	0.0955530i
$691$	1.42445	+	0.563981i	0.0541887	+	0.0214548i	0.395063	−	0.918654i	$-0.370723\pi$
$691$	1.42445	+	0.563981i	0.0541887	+	0.0214548i	−0.340874	+	0.940109i	$0.610723\pi$
$692$	7.46374	+	13.5765i	0.283729	+	0.516101i
$693$			5.85399i			0.222375i
$694$	12.3356	−	6.78158i	0.468255	−	0.257425i
$695$	0.981465	−	22.9360i	0.0372291	−	0.870012i
$696$	3.10181	−	0.391850i	0.117574	−	0.0148530i
$697$	2.21818	+	0.423141i	0.0840196	+	0.0160276i
$698$	−0.536524	−	1.35511i	−0.0203077	−	0.0512915i
$699$	2.35749	+	7.25562i	0.0891686	+	0.274433i
$700$	−7.97393	+	9.20518i	−0.301386	+	0.347923i
$701$	2.08848	−	6.42767i	0.0788807	−	0.242770i	−0.903838	−	0.427875i	$-0.859262\pi$
$701$	2.08848	−	6.42767i	0.0788807	−	0.242770i	0.982719	+	0.185105i	$0.0592625\pi$
$702$	2.03194	−	0.127839i	0.0766906	−	0.00482496i
$703$	−2.19529	−	17.3775i	−0.0827969	−	0.655405i
$704$	−1.75199	+	1.64523i	−0.0660307	+	0.0620070i
$705$	13.9618	−	13.6485i	0.525833	−	0.514031i
$706$	14.7721	+	1.86615i	0.555957	+	0.0702337i
$707$	36.1924	+	11.7596i	1.36116	+	0.442266i
$708$	−2.31086	+	2.46082i	−0.0868474	+	0.0924831i
$709$	18.1521	−	4.66067i	0.681717	−	0.175035i	0.108077	−	0.994143i	$-0.465531\pi$
$709$	18.1521	−	4.66067i	0.681717	−	0.175035i	0.573640	+	0.819107i	$0.305531\pi$
$710$	−6.55412	−	3.97718i	−0.245972	−	0.149261i
$711$	5.48348	+	6.62839i	0.205646	+	0.248584i
$712$	−0.380290	−	1.48113i	−0.0142520	−	0.0555078i
$713$	−14.6426	−	12.1134i	−0.548369	−	0.453650i
$714$	−0.669224	+	0.264964i	−0.0250451	+	0.00991605i
$715$	7.32842	−	8.12469i	0.274068	−	0.303846i
$716$	−12.0717	−	19.0219i	−0.451140	−	0.710883i
$717$	12.7562	−	2.43338i	0.476390	−	0.0908762i
$718$	13.4899	−	4.38313i	0.503438	−	0.163577i
$719$	8.04847	−	17.1039i	0.300157	−	0.637867i	−0.696676	−	0.717386i	$-0.745338\pi$
$719$	8.04847	−	17.1039i	0.300157	−	0.637867i	0.996833	+	0.0795192i	$0.0253385\pi$
$720$	1.45961	+	1.69397i	0.0543963	+	0.0631307i
$721$	11.3411	+	6.23485i	0.422366	+	0.232198i
$722$	−6.99822	+	12.7297i	−0.260447	+	0.473751i
$723$	−10.4206	+	8.62069i	−0.387547	+	0.320607i
$724$	6.60656	+	4.79994i	0.245531	+	0.178389i
$725$	−11.8157	−	10.2352i	−0.438822	−	0.380127i
$726$	−4.22609	+	3.07044i	−0.156845	+	0.113955i
$727$	−13.0812	+	50.9478i	−0.485154	+	1.88955i	−0.0291412	+	0.999575i	$0.509277\pi$
$727$	−13.0812	+	50.9478i	−0.485154	+	1.88955i	−0.456012	+	0.889973i	$0.650723\pi$
$728$	−4.48706	+	2.11145i	−0.166302	+	0.0782556i
$729$	0.187381	−	0.982287i	0.00694005	−	0.0363810i
$730$	4.33752	−	14.3211i	0.160539	−	0.530049i
$731$	−1.27483	−	1.19714i	−0.0471512	−	0.0442779i
$732$	2.43225	−	3.34770i	0.0898984	−	0.123735i
$733$	18.9832	+	8.93282i	0.701161	+	0.329941i	0.743101	−	0.669179i	$-0.233354\pi$
$733$	18.9832	+	8.93282i	0.701161	+	0.329941i	−0.0419406	+	0.999120i	$0.513354\pi$
$734$	−0.506290	+	0.612000i	−0.0186875	+	0.0225893i
$735$	2.25437	−	0.782836i	0.0831535	−	0.0288753i
$736$	−0.420452	−	6.68289i	−0.0154981	−	0.246335i
$737$	7.72184	+	0.485817i	0.284438	+	0.0178953i
$738$	2.81312	−	7.10514i	0.103553	−	0.261544i
$739$	−4.75579	+	7.49392i	−0.174944	+	0.275668i	−0.920474	−	0.390805i	$-0.872197\pi$
$739$	−4.75579	+	7.49392i	−0.174944	+	0.275668i	0.745529	+	0.666473i	$0.232197\pi$
$740$	−6.47002	+	17.3507i	−0.237843	+	0.637826i
$741$	−0.270385	+	4.29765i	−0.00993286	+	0.157878i
$742$	−3.63942	+	28.8090i	−0.133607	+	1.05761i
$743$	23.1329	+	31.8398i	0.848665	+	1.16809i	0.984155	+	0.177309i	$0.0567392\pi$
$743$	23.1329	+	31.8398i	0.848665	+	1.16809i	−0.135490	+	0.990779i	$0.543261\pi$
$744$	0.531792	+	2.78775i	0.0194964	+	0.102204i
$745$	4.47069	−	2.57593i	0.163794	−	0.0943747i
$746$	−0.926788	−	1.96953i	−0.0339321	−	0.0721094i
$747$	−9.41895	−	10.0302i	−0.344621	−	0.366985i
$748$	0.599652	+	0.380551i	0.0219254	+	0.0139143i
$749$	14.7227			0.537955
$750$	1.43046	−	11.0885i	0.0522331	−	0.404893i
$751$	−33.5928			−1.22582			−0.612909	−	0.790154i	$-0.710001\pi$
$751$	−33.5928			−1.22582			−0.612909	+	0.790154i	$0.710001\pi$
$752$	7.37243	+	4.67868i	0.268845	+	0.170614i
$753$	8.65151	+	9.21292i	0.315278	+	0.335737i
$754$	−2.71023	−	5.75954i	−0.0987009	−	0.209750i
$755$	−7.99242	−	7.20911i	−0.290874	−	0.262366i
$756$	0.456410	+	2.39258i	0.0165995	+	0.0870174i
$757$	−12.5202	−	17.2326i	−0.455054	−	0.626328i	0.518420	−	0.855126i	$-0.326520\pi$
$757$	−12.5202	−	17.2326i	−0.455054	−	0.626328i	−0.973474	+	0.228798i	$0.926520\pi$
$758$	−1.42002	+	11.2406i	−0.0515776	+	0.408279i
$759$	−1.01051	+	16.0616i	−0.0366791	+	0.582998i
$760$	−3.94151	+	2.61375i	−0.142974	+	0.0948107i
$761$	−11.1456	+	17.5627i	−0.404029	+	0.636649i	−0.984037	−	0.177962i	$-0.943049\pi$
$761$	−11.1456	+	17.5627i	−0.404029	+	0.636649i	0.580008	+	0.814611i	$0.303049\pi$
$762$	5.07578	−	12.8200i	0.183876	−	0.464418i
$763$	18.9614	+	1.19295i	0.686449	+	0.0431877i
$764$	0.0124685	+	0.198181i	0.000451093	+	0.00716992i
$765$	0.377586	−	0.542259i	0.0136516	−	0.0196054i
$766$	11.3224	−	13.6864i	0.409094	−	0.494510i
$767$	6.21877	+	2.92633i	0.224547	+	0.105664i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	20.0719	+	18.8487i	0.723810	+	0.679703i	0.956132	−	0.292936i	$-0.0946322\pi$
$769$	20.0719	+	18.8487i	0.723810	+	0.679703i	−0.232322	+	0.972639i	$0.574632\pi$
$770$	10.7422	+	7.48002i	0.387123	+	0.269561i
$771$	5.50312	−	28.8483i	0.198190	−	1.03895i
$772$	−20.6102	+	9.69840i	−0.741776	+	0.349053i
$773$	5.00126	−	19.4786i	0.179883	−	0.700598i	−0.813078	−	0.582155i	$-0.802210\pi$
$773$	5.00126	−	19.4786i	0.179883	−	0.700598i	0.992961	−	0.118443i	$-0.0377903\pi$
$774$	−4.78780	+	3.47854i	−0.172094	+	0.125033i
$775$	8.59915	−	11.2878i	0.308890	−	0.405469i
$776$	−10.2831	−	7.47111i	−0.369142	−	0.268197i
$777$	−15.5422	+	12.8576i	−0.557574	+	0.461266i
$778$	1.51198	−	2.75027i	0.0542070	−	0.0986021i
$779$	14.1635	+	7.78646i	0.507461	+	0.278979i
$780$	2.36175	−	3.89201i	0.0845643	−	0.139356i
$781$	−3.50847	+	7.45587i	−0.125543	+	0.266792i
$782$	−1.88188	+	0.611461i	−0.0672960	+	0.0218658i
$783$	−3.07109	+	0.585841i	−0.109752	+	0.0209363i
$784$	0.571855	+	0.901100i	0.0204234	+	0.0321821i
$785$	−39.9252	+	8.44976i	−1.42499	+	0.301585i
$786$	−4.16745	+	1.65001i	−0.148648	+	0.0588539i
$787$	27.7810	+	22.9824i	0.990285	+	0.819235i	0.983530	−	0.180742i	$-0.0578500\pi$
$787$	27.7810	+	22.9824i	0.990285	+	0.819235i	0.00675434	+	0.999977i	$0.497850\pi$
$788$	5.14352	+	20.0327i	0.183230	+	0.713635i
$789$	11.0716	+	13.3833i	0.394159	+	0.476456i
$790$	19.1698	−	1.59280i	0.682033	−	0.0566692i
$791$	3.64342	−	0.935472i	0.129545	−	0.0332616i
$792$	1.64523	−	1.75199i	0.0584607	−	0.0622544i
$793$	−8.01242	−	2.60339i	−0.284529	−	0.0924492i
$794$	25.2142	+	3.18529i	0.894818	+	0.113042i
$795$	−11.8320	−	23.8880i	−0.419638	−	0.847220i
$796$	−4.62659	+	4.34465i	−0.163985	+	0.153992i
$797$	−4.41861	−	34.9769i	−0.156515	−	1.23894i	−0.853206	−	0.521574i	$-0.825345\pi$
$797$	−4.41861	−	34.9769i	−0.156515	−	1.23894i	0.696691	−	0.717371i	$-0.254655\pi$
$798$	−5.14152	+	0.323477i	−0.182008	+	0.0114510i
$799$	0.797345	−	2.45397i	0.0282080	−	0.0868154i
$800$	4.97352	−	0.513915i	0.175840	−	0.0181696i
$801$	0.472541	+	1.45433i	0.0166964	+	0.0513862i
$802$	−7.80328	−	19.7088i	−0.275543	−	0.695943i
$803$	−15.7984	−	3.01370i	−0.557513	−	0.106351i
$804$	3.19387	−	0.403480i	0.112639	−	0.0142296i
$805$	−35.1351	+	9.77667i	−1.23835	+	0.344582i
$806$	5.06337	−	2.78361i	0.178350	−	0.0980486i
$807$			13.9263i			0.490230i
$808$	−7.52675	−	13.6911i	−0.264790	−	0.481652i
$809$	9.61813	+	3.80809i	0.338156	+	0.133885i	0.531064	−	0.847331i	$-0.321792\pi$
$809$	9.61813	+	3.80809i	0.338156	+	0.133885i	−0.192909	+	0.981217i	$0.561792\pi$
$810$	−1.56309	−	1.59898i	−0.0549215	−	0.0561825i
$811$	−18.1795	−	4.66770i	−0.638368	−	0.163905i	−0.0843855	−	0.996433i	$-0.526893\pi$
$811$	−18.1795	−	4.66770i	−0.638368	−	0.163905i	−0.553983	+	0.832528i	$0.686893\pi$
$812$	6.42974	−	4.08044i	0.225640	−	0.143195i
$813$	−19.7855	+	12.5562i	−0.693906	+	0.440366i
$814$	19.2781	+	4.94979i	0.675698	+	0.173490i
$815$	−3.76146	−	25.6281i	−0.131758	−	0.897714i
$816$	0.274753	+	0.108783i	0.00961829	+	0.00380815i
$817$	−6.03009	−	10.9687i	−0.210966	−	0.383746i
$818$			19.7459i			0.690399i
$819$	4.34563	−	2.38903i	0.151849	−	0.0834795i
$820$	−9.44360	−	14.2409i	−0.329785	−	0.497312i
$821$	−28.2229	+	3.56538i	−0.984986	+	0.124433i	−0.601293	−	0.799028i	$-0.705348\pi$
$821$	−28.2229	+	3.56538i	−0.984986	+	0.124433i	−0.383692	+	0.923461i	$0.625348\pi$
$822$	4.17337	+	0.796113i	0.145563	+	0.0277676i
$823$	14.1073	+	35.6309i	0.491749	+	1.24201i	0.937853	+	0.347034i	$0.112811\pi$
$823$	14.1073	+	35.6309i	0.491749	+	1.24201i	−0.446104	+	0.894981i	$0.647189\pi$
$824$	−1.64193	−	5.05334i	−0.0571993	−	0.176041i
$825$	−12.0138	−	0.272747i	−0.418268	−	0.00949583i
$826$	−2.54086	+	7.81997i	−0.0884079	+	0.272092i
$827$	45.2263	−	2.84540i	1.57267	−	0.0989442i	0.747669	−	0.664071i	$-0.231173\pi$
$827$	45.2263	−	2.84540i	1.57267	−	0.0989442i	0.825004	+	0.565127i	$0.191173\pi$
$828$	0.839244	+	6.64330i	0.0291657	+	0.230871i
$829$	0.836110	−	0.785159i	0.0290393	−	0.0272697i	−0.669892	−	0.742459i	$-0.733659\pi$
$829$	0.836110	−	0.785159i	0.0290393	−	0.0272697i	0.698931	+	0.715189i	$0.253659\pi$
$830$	−30.4408	+	4.46782i	−1.05662	+	0.155080i
$831$	15.3542	+	1.93969i	0.532632	+	0.0672871i
$832$	1.93631	+	0.629145i	0.0671294	+	0.0218117i
$833$	0.215889	−	0.229898i	0.00748009	−	0.00796549i
$834$	−9.94413	+	2.55322i	−0.344337	+	0.0884107i
$835$	−27.0698	+	23.3246i	−0.936791	+	0.807183i
$836$	3.24021	+	3.91674i	0.112065	+	0.135463i
$837$	−0.705787	−	2.74886i	−0.0243956	−	0.0950145i
$838$	10.1121	+	8.36543i	0.349316	+	0.288979i
$839$	−39.7324	+	15.7312i	−1.37172	+	0.543101i	−0.934406	−	0.356210i	$-0.884069\pi$
$839$	−39.7324	+	15.7312i	−1.37172	+	0.543101i	−0.437310	+	0.899311i	$0.644069\pi$
$840$	4.97363	+	2.21964i	0.171607	+	0.0765847i
$841$	−10.3014	−	16.2324i	−0.355220	−	0.559737i
$842$	−33.8933	+	6.46550i	−1.16804	+	0.222816i
$843$	13.4100	−	4.35718i	0.461866	−	0.150069i
$844$	−4.84003	+	10.2856i	−0.166601	+	0.354044i
$845$	19.2730	+	4.53829i	0.663012	+	0.156122i
$846$	−7.65166	−	4.20653i	−0.263069	−	0.144624i
$847$	−6.12964	+	11.1498i	−0.210617	+	0.383111i
$848$	9.18582	−	7.59917i	0.315442	−	0.260957i
$849$	9.01428	+	6.54926i	0.309369	+	0.224770i
$850$	−0.512592	−	1.38576i	−0.0175818	−	0.0475311i
$851$	−44.8626	+	32.5946i	−1.53787	+	1.11733i
$852$	−0.852644	+	3.32083i	−0.0292111	+	0.113770i
$853$	−5.41266	+	2.54700i	−0.185326	+	0.0872077i	−0.516204	−	0.856466i	$-0.672655\pi$
$853$	−5.41266	+	2.54700i	−0.185326	+	0.0872077i	0.330878	+	0.943674i	$0.392655\pi$
$854$	1.88862	−	9.90047i	0.0646271	−	0.338787i
$855$	3.76961	−	2.85608i	0.128918	−	0.0976760i
$856$	−4.40623	−	4.13772i	−0.150602	−	0.141425i
$857$	−13.8149	+	19.0145i	−0.471907	+	0.649524i	−0.976925	−	0.213585i	$-0.931486\pi$
$857$	−13.8149	+	19.0145i	−0.471907	+	0.649524i	0.505017	+	0.863109i	$0.331486\pi$
$858$	−4.42749	−	2.08342i	−0.151152	−	0.0711267i
$859$	16.2088	−	19.5931i	0.553039	−	0.668509i	−0.417718	−	0.908577i	$-0.637170\pi$
$859$	16.2088	−	19.5931i	0.553039	−	0.668509i	0.970756	+	0.240068i	$0.0771698\pi$
$860$	0.265525	+	13.2305i	0.00905433	+	0.451156i
$861$	−1.16874	−	18.5765i	−0.0398304	−	0.633087i
$862$	30.9757	+	1.94883i	1.05504	+	0.0663773i
$863$	19.7774	−	49.9520i	0.673230	−	1.70038i	−0.0397594	−	0.999209i	$-0.512659\pi$
$863$	19.7774	−	49.9520i	0.673230	−	1.70038i	0.712989	−	0.701175i	$-0.247341\pi$
$864$	0.535827	−	0.844328i	0.0182292	−	0.0287246i
$865$	−34.6114	−	1.48107i	−1.17682	−	0.0503580i
$866$	0.517081	−	8.21877i	0.0175711	−	0.279285i
$867$	−2.11972	+	16.7793i	−0.0719895	+	0.569855i
$868$	4.06315	+	5.59244i	0.137912	+	0.189820i
$869$	−3.87416	−	20.3091i	−0.131422	−	0.688937i
$870$	−2.84910	+	6.38409i	−0.0965934	+	0.216441i
$871$	−2.79067	−	5.93047i	−0.0945582	−	0.200946i
$872$	−5.33953	−	5.68602i	−0.180819	−	0.192553i
$873$	10.7319	+	6.81068i	0.363221	+	0.230507i
$874$	−14.1626			−0.479057
$875$	−8.34702	−	25.9215i	−0.282181	−	0.876305i
$876$	−6.69192			−0.226099
$877$	−42.8074	−	27.1664i	−1.44550	−	0.917344i	−0.999754	−	0.0221868i	$-0.992937\pi$
$877$	−42.8074	−	27.1664i	−1.44550	−	0.917344i	−0.445750	−	0.895158i	$-0.647063\pi$
$878$	−14.9310	−	15.8999i	−0.503897	−	0.536596i
$879$	3.86081	+	8.20463i	0.130222	+	0.276735i
$880$	−1.11273	−	5.25767i	−0.0375102	−	0.177236i
$881$	0.959667	+	5.03075i	0.0323320	+	0.169490i	0.994791	−	0.101938i	$-0.0325042\pi$
$881$	0.959667	+	5.03075i	0.0323320	+	0.169490i	−0.962459	+	0.271428i	$0.912504\pi$
$882$	−0.627307	−	0.863415i	−0.0211225	−	0.0290727i
$883$	−4.53116	+	35.8678i	−0.152486	+	1.20705i	0.711190	+	0.703000i	$0.248157\pi$
$883$	−4.53116	+	35.8678i	−0.152486	+	1.20705i	−0.863675	+	0.504049i	$0.831843\pi$
$884$	0.0377769	−	0.600447i	0.00127058	−	0.0201952i
$885$	−2.02354	−	7.27212i	−0.0680204	−	0.244450i
$886$	−12.1960	+	19.2178i	−0.409731	+	0.645633i
$887$	−2.58923	+	6.53965i	−0.0869378	+	0.219580i	−0.966741	−	0.255759i	$-0.917675\pi$
$887$	−2.58923	+	6.53965i	−0.0869378	+	0.219580i	0.879803	+	0.475339i	$0.157675\pi$
$888$	8.26508	+	0.519995i	0.277358	+	0.0174499i
$889$	−2.10878	−	33.5180i	−0.0707261	−	1.12416i
$890$	3.27253	+	0.991169i	0.109695	+	0.0332241i
$891$	−1.53198	+	1.85184i	−0.0513231	+	0.0620390i
$892$	0.381936	+	0.179725i	0.0127882	+	0.00601765i
$893$	10.8552	−	14.9409i	0.363256	−	0.499979i
$894$	−1.68209	−	1.57958i	−0.0562574	−	0.0528292i
$895$	50.3664	−	1.01081i	1.68356	−	0.0337878i
$896$	−0.456410	+	2.39258i	−0.0152476	+	0.0799306i
$897$	12.3355	−	5.80463i	0.411870	−	0.193811i
$898$	8.66795	−	33.7594i	0.289253	−	1.12657i
$899$	−7.17839	+	5.21541i	−0.239413	+	0.173944i
$900$	−4.93144	+	0.825191i	−0.164381	+	0.0275064i
$901$	−2.85010	−	2.07072i	−0.0949505	−	0.0689856i
$902$	−14.1513	+	11.7070i	−0.471188	+	0.389801i
$903$	−6.94435	+	12.6317i	−0.231093	+	0.420357i
$904$	−1.35332	−	0.743994i	−0.0450107	−	0.0247449i
$905$	−16.8395	+	7.06129i	−0.559764	+	0.234725i
$906$	−2.04950	+	4.35541i	−0.0680900	+	0.144699i
$907$	13.6541	−	4.43650i	0.453378	−	0.147311i	−0.0734216	−	0.997301i	$-0.523392\pi$
$907$	13.6541	−	4.43650i	0.453378	−	0.147311i	0.526800	+	0.849990i	$0.323392\pi$
$908$	−21.5033	+	4.10198i	−0.713613	+	0.136129i
$909$	8.37157	+	13.1915i	0.277668	+	0.437534i
$910$	1.16876	−	11.0270i	0.0387441	−	0.365540i
$911$	24.4462	−	9.67892i	0.809938	−	0.320677i	0.0735970	−	0.997288i	$-0.476552\pi$
$911$	24.4462	−	9.67892i	0.809938	−	0.320677i	0.736341	+	0.676611i	$0.236552\pi$
$912$	1.62967	+	1.34818i	0.0539639	+	0.0446428i
$913$	8.22396	+	32.0302i	0.272173	+	1.06004i
$914$	−13.5389	−	16.3657i	−0.447827	−	0.541330i
$915$	3.57812	+	8.53297i	0.118289	+	0.282091i
$916$	13.3262	−	3.42160i	0.440311	−	0.113053i
$917$	−7.47349	+	7.95846i	−0.246797	+	0.262812i
$918$	−0.281042	−	0.0913160i	−0.00927576	−	0.00301388i
$919$	−49.8587	−	6.29862i	−1.64469	−	0.207772i	−0.752229	−	0.658901i	$-0.771021\pi$
$919$	−49.8587	−	6.29862i	−1.64469	−	0.207772i	−0.892459	+	0.451129i	$0.851021\pi$
$920$	13.2630	+	6.94854i	0.437267	+	0.229087i
$921$	−7.52356	+	7.06509i	−0.247910	+	0.232803i
$922$	−4.86958	−	38.5467i	−0.160371	−	1.26947i
$923$	6.96659	−	0.438300i	0.229308	−	0.0144268i
$924$	1.80898	−	5.56747i	0.0595111	−	0.183156i
$925$	−25.6629	−	32.4956i	−0.843792	−	1.06845i
$926$	−7.69299	−	23.6766i	−0.252807	−	0.778061i
$927$	1.95599	+	4.94027i	0.0642432	+	0.162260i
$928$	−3.07109	−	0.585841i	−0.100813	−	0.0192312i
$929$	31.1765	−	3.93850i	1.02287	−	0.129218i	0.404036	−	0.914743i	$-0.367607\pi$
$929$	31.1765	−	3.93850i	1.02287	−	0.129218i	0.618830	+	0.785525i	$0.287607\pi$
$930$	−5.94606	−	2.21726i	−0.194979	−	0.0727068i
$931$	1.97806	−	1.08745i	0.0648282	−	0.0356396i
$932$		−	7.62901i		−	0.249897i
$933$	3.55860	+	6.47306i	0.116503	+	0.211919i
$934$	−29.9304	−	11.8503i	−0.979353	−	0.387753i
$935$	−1.42308	+	0.704869i	−0.0465398	+	0.0230517i
$936$	−1.97199	−	0.506322i	−0.0644566	−	0.0165496i
$937$	2.39397	−	1.51926i	0.0782076	−	0.0496321i	−0.496148	−	0.868238i	$-0.665253\pi$
$937$	2.39397	−	1.51926i	0.0782076	−	0.0496321i	0.574356	+	0.818606i	$0.305253\pi$
$938$	6.62056	−	4.20154i	0.216169	−	0.137185i
$939$	−9.80554	−	2.51763i	−0.319992	−	0.0821599i
$940$	−17.4961	+	8.66602i	−0.570660	+	0.282654i
$941$	2.78751	+	1.10365i	0.0908701	+	0.0359780i	0.413120	−	0.910677i	$-0.364439\pi$
$941$	2.78751	+	1.10365i	0.0908701	+	0.0359780i	−0.322250	+	0.946655i	$0.604439\pi$
$942$	8.79229	+	15.9931i	0.286468	+	0.521084i
$943$		−	51.1701i		−	1.66633i
$944$	2.95819	−	1.62628i	0.0962810	−	0.0529309i
$945$	−5.10319	−	1.90296i	−0.166007	−	0.0619032i
$946$	14.1112	−	1.78266i	0.458794	−	0.0579592i
$947$	−3.35352	−	0.639719i	−0.108975	−	0.0207881i	0.132605	−	0.991169i	$-0.457666\pi$
$947$	−3.35352	−	0.639719i	−0.108975	−	0.0207881i	−0.241580	+	0.970381i	$0.577666\pi$
$948$	−3.16681	−	7.99846i	−0.102853	−	0.259778i
$949$	4.21019	+	12.9576i	0.136669	+	0.420622i
$950$	−0.424303	−	10.5667i	−0.0137662	−	0.342830i
$951$	−7.57678	+	23.3189i	−0.245694	+	0.756168i
$952$	0.718348	−	0.0451946i	0.0232818	−	0.00146477i
$953$	−2.01834	−	15.9768i	−0.0653803	−	0.517539i	−0.990464	−	0.137774i	$-0.956005\pi$
$953$	−2.01834	−	15.9768i	−0.0653803	−	0.517539i	0.925083	−	0.379764i	$-0.123995\pi$
$954$	−8.69054	+	8.16096i	−0.281367	+	0.264221i
$955$	−0.393313	−	0.206059i	−0.0127273	−	0.00666790i
$956$	−12.8838	−	1.62761i	−0.416693	−	0.0526406i
$957$	7.14634	+	2.32199i	0.231008	+	0.0750592i
$958$	1.47582	−	1.57159i	0.0476817	−	0.0507759i
$959$	10.0234	−	2.57356i	0.323672	−	0.0831047i
$960$	−0.864702	−	2.06211i	−0.0279081	−	0.0665543i
$961$	14.6261	+	17.6799i	0.471810	+	0.570320i
$962$	−4.19306	−	16.3309i	−0.135190	−	0.526529i
$963$	4.65734	+	3.85289i	0.150081	+	0.124158i
$964$	12.5745	−	4.97861i	0.404999	−	0.160350i
$965$	5.36841	−	50.6495i	0.172815	−	1.63046i
$966$	8.73926	+	13.7709i	0.281181	+	0.443071i
$967$	44.9346	−	8.57174i	1.44500	−	0.275648i	0.595550	−	0.803318i	$-0.296934\pi$
$967$	44.9346	−	8.57174i	1.44500	−	0.275648i	0.849450	+	0.527670i	$0.176934\pi$
$968$	4.96807	−	1.61422i	0.159680	−	0.0518831i
$969$	0.266115	−	0.565524i	0.00854885	−	0.0181672i
$970$	26.2107	−	10.9909i	0.841573	−	0.352896i
$971$	−22.1245	−	12.1631i	−0.710011	−	0.390332i	0.0854456	−	0.996343i	$-0.472769\pi$
$971$	−22.1245	−	12.1631i	−0.710011	−	0.390332i	−0.795456	+	0.606011i	$0.792769\pi$
$972$	−0.481754	+	0.876307i	−0.0154523	+	0.0281075i
$973$	−19.2681	+	15.9399i	−0.617706	+	0.511011i
$974$	32.5288	+	23.6336i	1.04229	+	0.757268i
$975$	4.70041	+	9.02962i	0.150534	+	0.289179i
$976$	−3.34770	+	2.43225i	−0.107157	+	0.0778543i
$977$	11.9985	−	46.7310i	0.383865	−	1.49506i	−0.423985	−	0.905669i	$-0.639369\pi$
$977$	11.9985	−	46.7310i	0.383865	−	1.49506i	0.807851	−	0.589387i	$-0.200631\pi$
$978$	−10.4815	+	4.93224i	−0.335163	+	0.157716i
$979$	0.688663	−	3.61010i	0.0220098	−	0.115379i
$980$	−2.38594	+	0.0478839i	−0.0762160	+	0.00152959i
$981$	5.68602	+	5.33953i	0.181541	+	0.170478i
$982$	−6.53955	+	9.00092i	−0.208685	+	0.287231i
$983$	1.23159	+	0.579543i	0.0392817	+	0.0184845i	0.445320	−	0.895372i	$-0.353090\pi$
$983$	1.23159	+	0.579543i	0.0392817	+	0.0184845i	−0.406038	+	0.913856i	$0.633090\pi$
$984$	−4.87105	+	5.88809i	−0.155283	+	0.187705i
$985$	−44.2618	−	13.4058i	−1.41030	−	0.427144i
$986$	0.0580113	+	0.922063i	0.00184745	+	0.0293645i
$987$	−21.2261	−	1.33543i	−0.675634	−	0.0425073i
$988$	1.58520	−	4.00376i	0.0504319	−	0.127376i
$989$	−21.2336	+	33.4589i	−0.675191	+	1.06393i
$990$	1.44067	+	5.17743i	0.0457875	+	0.164550i
$991$	2.96637	−	47.1491i	0.0942299	−	1.49774i	−0.612619	−	0.790378i	$-0.709884\pi$
$991$	2.96637	−	47.1491i	0.0942299	−	1.49774i	0.706849	−	0.707364i	$-0.250116\pi$
$992$	0.355698	−	2.81564i	0.0112934	−	0.0893967i
$993$	12.4433	+	17.1267i	0.394876	+	0.543500i
$994$	1.56482	+	8.20307i	0.0496331	+	0.260186i
$995$	−2.93846	−	13.8842i	−0.0931553	−	0.440160i
$996$	5.85846	+	12.4499i	0.185633	+	0.394489i
$997$	−26.8491	−	28.5914i	−0.850319	−	0.905498i	0.146166	−	0.989260i	$-0.453307\pi$
$997$	−26.8491	−	28.5914i	−0.850319	−	0.905498i	−0.996486	+	0.0837617i	$0.973307\pi$
$998$	−18.9088	−	11.9999i	−0.598549	−	0.379851i
$999$	−8.28142			−0.262012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.19.1	✓	240
125.79	even	50	inner	750.2.o.a.79.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.19.1	✓	240	1.1	even	1	trivial
750.2.o.a.79.1	yes	240	125.79	even	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.684547 - 0.728969i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-2.22361 - 0.235684i) q^{5} +(0.187381 + 0.982287i) q^{6} +(1.43168 + 1.97054i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.0627905 + 0.998027i) q^{9} +O(q^{10})\)	\(q+(-0.844328 - 0.535827i) q^{2} +(-0.684547 - 0.728969i) q^{3} +(0.425779 + 0.904827i) q^{4} +(-2.22361 - 0.235684i) q^{5} +(0.187381 + 0.982287i) q^{6} +(1.43168 + 1.97054i) q^{7} +(0.125333 - 0.992115i) q^{8} +(-0.0627905 + 0.998027i) q^{9} +(1.75117 + 1.39047i) q^{10} +(1.28780 - 2.02925i) q^{11} +(0.368125 - 0.929776i) q^{12} +(-2.03194 - 0.127839i) q^{13} +(-0.152940 - 2.43092i) q^{14} +(1.35036 + 1.78228i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(0.267381 + 0.125820i) q^{17} +(0.587785 - 0.809017i) q^{18} +(1.54181 + 1.44785i) q^{19} +(-0.733515 - 2.11233i) q^{20} +(0.456410 - 2.39258i) q^{21} +(-2.17465 + 1.02331i) q^{22} +(1.66525 - 6.48573i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(4.88891 + 1.04814i) q^{25} +(1.64712 + 1.19670i) q^{26} +(0.770513 - 0.637424i) q^{27} +(-1.17342 + 2.13444i) q^{28} +(-2.73974 - 1.50619i) q^{29} +(-0.185154 - 2.22839i) q^{30} +(1.20837 - 2.56792i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-2.36082 + 0.450350i) q^{33} +(-0.158339 - 0.249503i) q^{34} +(-2.71908 - 4.71915i) q^{35} +(-0.929776 + 0.368125i) q^{36} +(-6.38094 - 5.27877i) q^{37} +(-0.525992 - 2.04860i) q^{38} +(1.29777 + 1.56873i) q^{39} +(-0.512518 + 2.17654i) q^{40} +(7.40169 - 1.90043i) q^{41} +(-1.66737 + 1.77557i) q^{42} +(-5.62839 - 1.82878i) q^{43} +(2.38443 + 0.301224i) q^{44} +(0.374841 - 2.20443i) q^{45} +(-4.88125 + 4.58380i) q^{46} +(-1.09437 - 8.66286i) q^{47} +(0.998027 - 0.0627905i) q^{48} +(0.329795 - 1.01500i) q^{49} +(-3.56622 - 3.50458i) q^{50} +(-0.0913160 - 0.281042i) q^{51} +(-0.749485 - 1.89298i) q^{52} +(-11.7105 - 2.23390i) q^{53} +(-0.992115 + 0.125333i) q^{54} +(-3.34183 + 4.20874i) q^{55} +(2.13444 - 1.17342i) q^{56} -2.11505i q^{57} +(1.50619 + 2.73974i) q^{58} +(-3.13869 - 1.24270i) q^{59} +(-1.03770 + 1.98070i) q^{60} +(4.00798 + 1.02908i) q^{61} +(-2.39622 + 1.52069i) q^{62} +(-2.05655 + 1.30513i) q^{63} +(-0.968583 - 0.248690i) q^{64} +(4.48811 + 0.763159i) q^{65} +(2.23461 + 0.884745i) q^{66} +(1.55089 + 2.82105i) q^{67} +0.295505i q^{68} +(-5.86784 + 3.22587i) q^{69} +(-0.232848 + 5.44147i) q^{70} +(-3.40151 + 0.429710i) q^{71} +(0.982287 + 0.187381i) q^{72} +(-2.46346 - 6.22199i) q^{73} +(2.55910 + 7.87610i) q^{74} +(-2.58263 - 4.28136i) q^{75} +(-0.653587 + 2.01153i) q^{76} +(5.84244 - 0.367575i) q^{77} +(-0.255173 - 2.01990i) q^{78} +(6.27100 - 5.88886i) q^{79} +(1.59898 - 1.56309i) q^{80} +(-0.992115 - 0.125333i) q^{81} +(-7.26776 - 2.36144i) q^{82} +(-9.41895 + 10.0302i) q^{83} +(2.35920 - 0.605740i) q^{84} +(-0.564897 - 0.342792i) q^{85} +(3.77230 + 4.55993i) q^{86} +(0.777521 + 3.02824i) q^{87} +(-1.85184 - 1.53198i) q^{88} +(1.42179 - 0.562926i) q^{89} +(-1.49768 + 1.66041i) q^{90} +(-2.65718 - 4.18705i) q^{91} +(6.57749 - 1.25472i) q^{92} +(-2.69912 + 0.876997i) q^{93} +(-3.71778 + 7.90069i) q^{94} +(-3.08714 - 3.58284i) q^{95} +(-0.876307 - 0.481754i) q^{96} +(6.12338 - 11.1384i) q^{97} +(-0.822322 + 0.680284i) q^{98} +(1.94438 + 1.41267i) 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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