LMFDB - Embedded newform 250.2.h.a.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(9,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.h (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:	$1.99626005053$
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			229.3
Character	$\chi$	$=$	250.229
Dual form			250.2.h.a.119.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(-0.618597 + 0.118004i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.24690 + 1.85614i) q^{5} +(0.268135 + 0.569817i) q^{6} +(-1.17418 + 1.61612i) q^{7} +(0.684547 + 0.728969i) q^{8} +(-2.42059 + 0.958380i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.618597 + 0.118004i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.24690 + 1.85614i) q^{5} +(0.268135 + 0.569817i) q^{6} +(-1.17418 + 1.61612i) q^{7} +(0.684547 + 0.728969i) q^{8} +(-2.42059 + 0.958380i) q^{9} +(1.48773 - 1.66933i) q^{10} +(-0.991515 + 0.254578i) q^{11} +(0.485232 - 0.401419i) q^{12} +(2.18423 + 5.51674i) q^{13} +(1.85735 + 0.735376i) q^{14} +(-0.990360 - 1.00106i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.30104 + 2.36659i) q^{17} +(1.53025 + 2.10620i) q^{18} +(0.898568 - 4.71046i) q^{19} +(-1.98687 - 1.02585i) q^{20} +(0.535635 - 1.13828i) q^{21} +(0.493160 + 0.897054i) q^{22} +(8.35072 + 0.525382i) q^{23} +(-0.509480 - 0.370159i) q^{24} +(-1.89049 + 4.62883i) q^{25} +(4.80023 - 3.48757i) q^{26} +(2.97943 - 1.89080i) q^{27} +(0.250369 - 1.98188i) q^{28} +(-2.27248 - 0.287081i) q^{29} +(-0.723320 + 1.20820i) q^{30} +(1.45131 + 0.797863i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(0.583308 - 0.274484i) q^{33} +(2.61579 + 0.671621i) q^{34} +(-4.46381 - 0.164299i) q^{35} +(1.65948 - 2.00596i) q^{36} +(-4.10862 - 2.60741i) q^{37} +(-4.78594 + 0.301106i) q^{38} +(-2.00216 - 3.15490i) q^{39} +(-0.499504 + 2.17956i) q^{40} +(-0.348091 - 5.53276i) q^{41} +(-1.23573 - 0.235728i) q^{42} +(-8.83413 + 2.87038i) q^{43} +(0.746228 - 0.700754i) q^{44} +(-4.79712 - 3.29795i) q^{45} +(-1.56786 - 8.21902i) q^{46} +(0.0116713 - 0.0124286i) q^{47} +(-0.231827 + 0.585529i) q^{48} +(0.929980 + 2.86218i) q^{49} +(4.95355 + 0.679949i) q^{50} +(0.525555 - 1.61749i) q^{51} +(-4.57177 - 3.78210i) q^{52} +(10.3908 + 4.88952i) q^{53} +(-2.57236 - 2.41560i) q^{54} +(-1.70885 - 1.52296i) q^{55} +(-1.98188 + 0.250369i) q^{56} +3.01991i q^{57} +(0.287081 + 2.27248i) q^{58} +(-5.64160 - 6.81952i) q^{59} +(1.35012 + 0.400128i) q^{60} +(-0.0705046 + 1.12064i) q^{61} +(0.411871 - 1.60413i) q^{62} +(1.29335 - 5.03726i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-7.51631 + 10.9331i) q^{65} +(-0.410923 - 0.496721i) q^{66} +(-0.339933 - 2.69085i) q^{67} -2.70064i q^{68} +(-5.22773 + 0.660416i) q^{69} +(0.950967 + 4.36443i) q^{70} +(5.20074 + 4.88382i) q^{71} +(-2.35564 - 1.10848i) q^{72} +(-3.08252 - 2.55008i) q^{73} +(-1.50372 + 4.62797i) q^{74} +(0.623230 - 3.08647i) q^{75} +(1.48186 + 4.56069i) q^{76} +(0.752787 - 1.90132i) q^{77} +(-2.55786 + 2.72385i) q^{78} +(-1.61194 - 8.45006i) q^{79} +(2.23531 - 0.0582240i) q^{80} +(4.07347 - 3.82524i) q^{81} +(-5.27237 + 1.71310i) q^{82} +(12.1133 + 2.31074i) q^{83} +(0.0789912 + 1.25553i) q^{84} +(-6.01498 + 0.535983i) q^{85} +(4.97716 + 7.84275i) q^{86} +(1.43963 - 0.0905738i) q^{87} +(-0.864318 - 0.548513i) q^{88} +(10.9869 - 13.2808i) q^{89} +(-2.00134 + 5.46657i) q^{90} +(-11.4804 - 2.94766i) q^{91} +(-7.57089 + 3.56259i) q^{92} +(-0.991926 - 0.322296i) q^{93} +(-0.0149407 - 0.00821371i) q^{94} +(9.86368 - 4.20560i) q^{95} +(0.624786 + 0.0789289i) q^{96} +(-1.09970 + 8.70503i) q^{97} +(2.54099 - 1.61256i) q^{98} +(2.15607 - 1.56648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 10 q^{5}+O(q^{10}) $ 240 * q + 10 * q^5	$ 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) $ 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

Coefficient data

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

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

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

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	−0.618597	+	0.118004i	−0.357147	+	0.0681295i	−0.362833	−	0.931854i	$-0.618190\pi$
$3$	−0.618597	+	0.118004i	−0.357147	+	0.0681295i	0.00568522	+	0.999984i	$0.498190\pi$
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	1.24690	+	1.85614i	0.557630	+	0.830089i
$5$	1.24690	+	1.85614i	0.557630	+	0.830089i
$6$	0.268135	+	0.569817i	0.109466	+	0.232627i
$7$	−1.17418	+	1.61612i	−0.443797	+	0.610834i	−0.971051	−	0.238874i	$-0.923222\pi$
$7$	−1.17418	+	1.61612i	−0.443797	+	0.610834i	0.527253	+	0.849708i	$0.323222\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	−2.42059	+	0.958380i	−0.806864	+	0.319460i
$10$	1.48773	−	1.66933i	0.470462	−	0.527888i
$11$	−0.991515	+	0.254578i	−0.298953	+	0.0767581i	−0.395187	−	0.918601i	$-0.629320\pi$
$11$	−0.991515	+	0.254578i	−0.298953	+	0.0767581i	0.0962340	+	0.995359i	$0.469320\pi$
$12$	0.485232	−	0.401419i	0.140075	−	0.115880i
$13$	2.18423	+	5.51674i	0.605797	+	1.53007i	0.831298	+	0.555827i	$0.187598\pi$
$13$	2.18423	+	5.51674i	0.605797	+	1.53007i	−0.225501	+	0.974243i	$0.572402\pi$
$14$	1.85735	+	0.735376i	0.496397	+	0.196538i
$15$	−0.990360	−	1.00106i	−0.255710	−	0.258473i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−1.30104	+	2.36659i	−0.315549	+	0.573982i	−0.985754	−	0.168195i	$-0.946206\pi$
$17$	−1.30104	+	2.36659i	−0.315549	+	0.573982i	0.670205	+	0.742176i	$0.266206\pi$
$18$	1.53025	+	2.10620i	0.360683	+	0.496437i
$19$	0.898568	−	4.71046i	0.206146	−	1.08065i	−0.717254	−	0.696812i	$-0.754601\pi$
$19$	0.898568	−	4.71046i	0.206146	−	1.08065i	0.923399	−	0.383841i	$-0.125399\pi$
$20$	−1.98687	−	1.02585i	−0.444277	−	0.229386i
$21$	0.535635	−	1.13828i	0.116885	−	0.248394i
$22$	0.493160	+	0.897054i	0.105142	+	0.191253i
$23$	8.35072	+	0.525382i	1.74124	+	0.109550i	0.901320	−	0.433154i	$-0.142599\pi$
$23$	8.35072	+	0.525382i	1.74124	+	0.109550i	0.839924	+	0.542703i	$0.182599\pi$
$24$	−0.509480	−	0.370159i	−0.103997	−	0.0755584i
$25$	−1.89049	+	4.62883i	−0.378097	+	0.925766i
$26$	4.80023	−	3.48757i	0.941402	−	0.683969i
$27$	2.97943	−	1.89080i	0.573392	−	0.363885i
$28$	0.250369	−	1.98188i	0.0473154	−	0.374540i
$29$	−2.27248	−	0.287081i	−0.421990	−	0.0533097i	−0.0885287	−	0.996074i	$-0.528217\pi$
$29$	−2.27248	−	0.287081i	−0.421990	−	0.0533097i	−0.333461	+	0.942764i	$0.608217\pi$
$30$	−0.723320	+	1.20820i	−0.132060	+	0.220586i
$31$	1.45131	+	0.797863i	0.260662	+	0.143300i	0.606727	−	0.794910i	$-0.292482\pi$
$31$	1.45131	+	0.797863i	0.260662	+	0.143300i	−0.346064	+	0.938211i	$0.612482\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	0.583308	−	0.274484i	0.101541	−	0.0477815i
$34$	2.61579	+	0.671621i	0.448605	+	0.115182i
$35$	−4.46381	−	0.164299i	−0.754522	−	0.0277717i
$36$	1.65948	−	2.00596i	0.276580	−	0.334327i
$37$	−4.10862	−	2.60741i	−0.675452	−	0.428655i	0.153368	−	0.988169i	$-0.450988\pi$
$37$	−4.10862	−	2.60741i	−0.675452	−	0.428655i	−0.828821	+	0.559514i	$0.810988\pi$
$38$	−4.78594	+	0.301106i	−0.776381	+	0.0488458i
$39$	−2.00216	−	3.15490i	−0.320602	−	0.505188i
$40$	−0.499504	+	2.17956i	−0.0789785	+	0.344619i
$41$	−0.348091	−	5.53276i	−0.0543628	−	0.864071i	−0.926849	−	0.375433i	$-0.877494\pi$
$41$	−0.348091	−	5.53276i	−0.0543628	−	0.864071i	0.872487	−	0.488638i	$-0.162506\pi$
$42$	−1.23573	−	0.235728i	−0.190677	−	0.0363736i
$43$	−8.83413	+	2.87038i	−1.34719	+	0.437729i	−0.891747	−	0.452535i	$-0.850520\pi$
$43$	−8.83413	+	2.87038i	−1.34719	+	0.437729i	−0.455445	+	0.890264i	$0.650520\pi$
$44$	0.746228	−	0.700754i	0.112498	−	0.105643i
$45$	−4.79712	−	3.29795i	−0.715112	−	0.491629i
$46$	−1.56786	−	8.21902i	−0.231169	−	1.21183i
$47$	0.0116713	−	0.0124286i	0.00170243	−	0.00181290i	−0.728117	−	0.685453i	$-0.759604\pi$
$47$	0.0116713	−	0.0124286i	0.00170243	−	0.00181290i	0.729819	+	0.683640i	$0.239604\pi$
$48$	−0.231827	+	0.585529i	−0.0334614	+	0.0845138i
$49$	0.929980	+	2.86218i	0.132854	+	0.408883i
$50$	4.95355	+	0.679949i	0.700538	+	0.0961594i
$51$	0.525555	−	1.61749i	0.0735925	−	0.226494i
$52$	−4.57177	−	3.78210i	−0.633990	−	0.524483i
$53$	10.3908	+	4.88952i	1.42728	+	0.671628i	0.975398	−	0.220449i	$-0.0707523\pi$
$53$	10.3908	+	4.88952i	1.42728	+	0.671628i	0.451883	+	0.892077i	$0.350752\pi$
$54$	−2.57236	−	2.41560i	−0.350053	−	0.328722i
$55$	−1.70885	−	1.52296i	−0.230421	−	0.205355i
$56$	−1.98188	+	0.250369i	−0.264840	+	0.0334570i
$57$			3.01991i			0.399997i
$58$	0.287081	+	2.27248i	0.0376956	+	0.298392i
$59$	−5.64160	−	6.81952i	−0.734474	−	0.887826i	0.262550	−	0.964918i	$-0.415436\pi$
$59$	−5.64160	−	6.81952i	−0.734474	−	0.887826i	−0.997024	+	0.0770922i	$0.975436\pi$
$60$	1.35012	+	0.400128i	0.174300	+	0.0516564i
$61$	−0.0705046	+	1.12064i	−0.00902719	+	0.143483i	0.990931	+	0.134370i	$0.0429009\pi$
$61$	−0.0705046	+	1.12064i	−0.00902719	+	0.143483i	−0.999958	+	0.00911345i	$0.997099\pi$
$62$	0.411871	−	1.60413i	0.0523077	−	0.203725i
$63$	1.29335	−	5.03726i	0.162947	−	0.634636i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−7.51631	+	10.9331i	−0.932284	+	1.35608i
$66$	−0.410923	−	0.496721i	−0.0505811	−	0.0611421i
$67$	−0.339933	−	2.69085i	−0.0415294	−	0.328739i	−0.999169	−	0.0407685i	$-0.987019\pi$
$67$	−0.339933	−	2.69085i	−0.0415294	−	0.328739i	0.957639	−	0.287971i	$-0.0929806\pi$
$68$		−	2.70064i		−	0.327501i
$69$	−5.22773	+	0.660416i	−0.629345	+	0.0795047i
$70$	0.950967	+	4.36443i	0.113662	+	0.521650i
$71$	5.20074	+	4.88382i	0.617214	+	0.579603i	0.928784	−	0.370621i	$-0.120855\pi$
$71$	5.20074	+	4.88382i	0.617214	+	0.579603i	−0.311570	+	0.950223i	$0.600855\pi$
$72$	−2.35564	−	1.10848i	−0.277615	−	0.130636i
$73$	−3.08252	−	2.55008i	−0.360782	−	0.298465i	0.439318	−	0.898332i	$-0.355220\pi$
$73$	−3.08252	−	2.55008i	−0.360782	−	0.298465i	−0.800100	+	0.599867i	$0.795220\pi$
$74$	−1.50372	+	4.62797i	−0.174804	+	0.537991i
$75$	0.623230	−	3.08647i	0.0719644	−	0.356394i
$76$	1.48186	+	4.56069i	0.169981	+	0.523148i
$77$	0.752787	−	1.90132i	0.0857881	−	0.216676i
$78$	−2.55786	+	2.72385i	−0.289621	+	0.308415i
$79$	−1.61194	−	8.45006i	−0.181357	−	0.950706i	−0.950287	−	0.311374i	$-0.899211\pi$
$79$	−1.61194	−	8.45006i	−0.181357	−	0.950706i	0.768930	−	0.639332i	$-0.220789\pi$
$80$	2.23531	−	0.0582240i	0.249915	−	0.00650964i
$81$	4.07347	−	3.82524i	0.452608	−	0.425027i
$82$	−5.27237	+	1.71310i	−0.582236	+	0.189180i
$83$	12.1133	+	2.31074i	1.32961	+	0.253637i	0.802750	−	0.596315i	$-0.203369\pi$
$83$	12.1133	+	2.31074i	1.32961	+	0.253637i	0.526860	+	0.849952i	$0.323369\pi$
$84$	0.0789912	+	1.25553i	0.00861864	+	0.136989i
$85$	−6.01498	+	0.535983i	−0.652416	+	0.0581355i
$86$	4.97716	+	7.84275i	0.536701	+	0.845706i
$87$	1.43963	−	0.0905738i	0.154344	−	0.00971053i
$88$	−0.864318	−	0.548513i	−0.0921366	−	0.0584717i
$89$	10.9869	−	13.2808i	1.16460	−	1.40776i	0.268868	−	0.963177i	$-0.413350\pi$
$89$	10.9869	−	13.2808i	1.16460	−	1.40776i	0.895736	−	0.444587i	$-0.146650\pi$
$90$	−2.00134	+	5.46657i	−0.210960	+	0.576227i
$91$	−11.4804	−	2.94766i	−1.20347	−	0.308999i
$92$	−7.57089	+	3.56259i	−0.789320	+	0.371426i
$93$	−0.991926	−	0.322296i	−0.102858	−	0.0334206i
$94$	−0.0149407	−	0.00821371i	−0.00154101	−	0.000847179i
$95$	9.86368	−	4.20560i	1.01199	−	0.431486i
$96$	0.624786	+	0.0789289i	0.0637670	+	0.00805564i
$97$	−1.09970	+	8.70503i	−0.111658	+	0.883862i	0.832421	+	0.554143i	$0.186954\pi$
$97$	−1.09970	+	8.70503i	−0.111658	+	0.883862i	−0.944079	+	0.329719i	$0.893046\pi$
$98$	2.54099	−	1.61256i	0.256678	−	0.162893i
$99$	2.15607	−	1.56648i	0.216693	−	0.157437i
$100$	−0.573311	−	4.96702i	−0.0573311	−	0.496702i
$101$	14.7788	+	10.7374i	1.47055	+	1.06841i	0.980455	+	0.196743i	$0.0630366\pi$
$101$	14.7788	+	10.7374i	1.47055	+	1.06841i	0.490091	+	0.871671i	$0.336963\pi$
$102$	−1.69738	−	0.106790i	−0.168065	−	0.0105738i
$103$	−8.81237	−	16.0296i	−0.868309	−	1.57945i	−0.813956	−	0.580926i	$-0.802691\pi$
$103$	−8.81237	−	16.0296i	−0.868309	−	1.57945i	−0.0543522	−	0.998522i	$-0.517309\pi$
$104$	−2.52632	+	5.36871i	−0.247726	+	0.526445i
$105$	2.78069	−	0.425112i	0.271368	−	0.0414866i
$106$	2.15183	−	11.2803i	0.209004	−	1.09564i
$107$	7.43971	+	10.2399i	0.719224	+	0.989927i	0.999549	+	0.0300219i	$0.00955770\pi$
$107$	7.43971	+	10.2399i	0.719224	+	0.989927i	−0.280325	+	0.959905i	$0.590442\pi$
$108$	−1.69999	+	3.09228i	−0.163582	+	0.297554i
$109$	0.927907	−	1.46215i	0.0888774	−	0.140048i	−0.796980	−	0.604005i	$-0.793571\pi$
$109$	0.927907	−	1.46215i	0.0888774	−	0.140048i	0.885858	+	0.463957i	$0.153571\pi$
$110$	−1.05013	+	2.03391i	−0.100126	+	0.193925i
$111$	2.84926	+	1.12810i	0.270440	+	0.107075i
$112$	0.735376	+	1.85735i	0.0694865	+	0.175503i
$113$	4.69687	−	3.88559i	0.441844	−	0.365525i	−0.389739	−	0.920925i	$-0.627435\pi$
$113$	4.69687	−	3.88559i	0.441844	−	0.365525i	0.831583	+	0.555400i	$0.187435\pi$
$114$	2.92504	−	0.751022i	0.273955	−	0.0703396i
$115$	9.43732	+	16.1552i	0.880034	+	1.50648i
$116$	2.12969	−	0.843206i	0.197737	−	0.0782897i
$117$	−10.5743	−	11.2605i	−0.977592	−	1.04103i
$118$	−5.20227	+	7.16030i	−0.478907	+	0.659159i
$119$	−2.29703	−	4.88143i	−0.210568	−	0.447480i
$120$	0.0517953	−	1.40722i	0.00472824	−	0.128461i
$121$	−8.72108	+	4.79445i	−0.792826	+	0.435860i
$122$	1.10297	−	0.210402i	0.0998578	−	0.0190489i
$123$	0.868215	+	3.38147i	0.0782843	+	0.304897i
$124$	−1.65616			−0.148728
$125$	−10.9490	+	2.26268i	−0.979307	+	0.202381i
$126$	−5.20065			−0.463311
$127$	1.97035	+	7.67401i	0.174840	+	0.680959i	0.994188	+	0.107661i	$0.0343361\pi$
$127$	1.97035	+	7.67401i	0.174840	+	0.680959i	−0.819347	+	0.573298i	$0.805664\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	5.12605	−	2.81807i	0.451324	−	0.248117i
$130$	12.4588	+	4.56123i	1.09271	+	0.400047i
$131$	1.56539	+	3.32662i	0.136769	+	0.290648i	0.961465	−	0.274928i	$-0.0886539\pi$
$131$	1.56539	+	3.32662i	0.136769	+	0.290648i	−0.824696	+	0.565576i	$0.808654\pi$
$132$	−0.378923	+	0.521543i	−0.0329810	+	0.0453945i
$133$	6.55757	+	6.98310i	0.568613	+	0.605512i
$134$	−2.52177	+	0.998440i	−0.217848	+	0.0862521i
$135$	7.22464	+	3.17259i	0.621798	+	0.273053i
$136$	−2.61579	+	0.671621i	−0.224302	+	0.0575911i
$137$	6.00996	−	4.97187i	0.513465	−	0.424775i	−0.344267	−	0.938872i	$-0.611873\pi$
$137$	6.00996	−	4.97187i	0.513465	−	0.424775i	0.857732	+	0.514096i	$0.171873\pi$
$138$	1.93975	+	4.89925i	0.165123	+	0.417052i
$139$	14.8130	+	5.86488i	1.25642	+	0.497452i	0.899598	−	0.436720i	$-0.143860\pi$
$139$	14.8130	+	5.86488i	1.25642	+	0.497452i	0.356823	+	0.934172i	$0.383860\pi$
$140$	3.99082	−	2.00648i	0.337286	−	0.169579i
$141$	−0.00575318	+	0.00906557i	−0.000484505	+	0.000763458i
$142$	3.43701	−	6.25190i	0.288428	−	0.524648i
$143$	−3.57014	−	4.91388i	−0.298550	−	0.410919i
$144$	−0.487831	+	2.55730i	−0.0406526	+	0.213108i
$145$	−2.30069	−	4.57600i	−0.191062	−	0.380016i
$146$	−1.70338	+	3.61986i	−0.140972	+	0.299582i
$147$	−0.913031	−	1.66080i	−0.0753056	−	0.136980i
$148$	4.85654	+	0.305547i	0.399205	+	0.0251158i
$149$	13.1828	+	9.57784i	1.07997	+	0.784648i	0.977679	−	0.210106i	$-0.0673810\pi$
$149$	13.1828	+	9.57784i	1.07997	+	0.784648i	0.102296	+	0.994754i	$0.467381\pi$
$150$	−3.14449	+	0.163923i	−0.256747	+	0.0133842i
$151$	7.74682	−	5.62840i	0.630427	−	0.458032i	−0.226121	−	0.974099i	$-0.572604\pi$
$151$	7.74682	−	5.62840i	0.630427	−	0.458032i	0.856548	+	0.516067i	$0.172604\pi$
$152$	4.04889	−	2.56950i	0.328408	−	0.208414i
$153$	0.881202	−	6.97544i	0.0712410	−	0.563930i
$154$	−2.02880	−	0.256297i	−0.163485	−	0.0206530i
$155$	0.328691	+	3.68868i	0.0264011	+	0.296282i
$156$	3.27439	+	1.80011i	0.262161	+	0.144124i
$157$	8.39229	+	2.72682i	0.669778	+	0.217624i	0.624114	−	0.781333i	$-0.285460\pi$
$157$	8.39229	+	2.72682i	0.669778	+	0.217624i	0.0456631	+	0.998957i	$0.485460\pi$
$158$	−7.78372	+	3.66274i	−0.619239	+	0.291392i
$159$	−7.00469	−	1.79850i	−0.555508	−	0.142630i
$160$	−0.612294	−	2.15060i	−0.0484061	−	0.170020i
$161$	−10.6543	+	12.8788i	−0.839676	+	1.01499i
$162$	−4.71810	−	2.99420i	−0.370689	−	0.235246i
$163$	5.17816	−	0.325782i	0.405585	−	0.0255172i	0.141312	−	0.989965i	$-0.454868\pi$
$163$	5.17816	−	0.325782i	0.405585	−	0.0255172i	0.264273	+	0.964448i	$0.414868\pi$
$164$	2.97046	+	4.68070i	0.231954	+	0.365501i
$165$	1.23681	+	0.740445i	0.0962852	+	0.0576436i
$166$	−0.774318	−	12.3074i	−0.0600987	−	0.955241i
$167$	−15.9835	−	3.04901i	−1.23684	−	0.235939i	−0.472834	−	0.881152i	$-0.656769\pi$
$167$	−15.9835	−	3.04901i	−1.23684	−	0.235939i	−0.764003	+	0.645212i	$0.776769\pi$
$168$	1.19644	−	0.388747i	0.0923073	−	0.0299925i
$169$	−16.1870	+	15.2006i	−1.24515	+	1.16928i
$170$	2.01501	+	5.69271i	0.154544	+	0.436611i
$171$	2.33934	+	12.2633i	0.178894	+	0.937795i
$172$	6.35859	−	6.77121i	0.484838	−	0.516300i
$173$	1.16859	−	2.95151i	0.0888460	−	0.224399i	−0.878559	−	0.477634i	$-0.841494\pi$
$173$	1.16859	−	2.95151i	0.0888460	−	0.224399i	0.967405	+	0.253235i	$0.0814945\pi$
$174$	−0.445749	−	1.37188i	−0.0337922	−	0.104002i
$175$	−5.26096	−	8.49031i	−0.397691	−	0.641807i
$176$	−0.316333	+	0.973574i	−0.0238445	+	0.0733859i
$177$	4.29461	+	3.55281i	0.322803	+	0.267045i
$178$	−15.5959	−	7.33887i	−1.16896	−	0.550072i
$179$	−11.5197	−	10.8177i	−0.861021	−	0.808552i	0.121907	−	0.992541i	$-0.461099\pi$
$179$	−11.5197	−	10.8177i	−0.861021	−	0.808552i	−0.982928	+	0.183989i	$0.941099\pi$
$180$	5.79254	+	0.578983i	0.431751	+	0.0431548i
$181$	−19.8796	+	2.51137i	−1.47764	+	0.186669i	−0.822467	−	0.568813i	$-0.807403\pi$
$181$	−19.8796	+	2.51137i	−1.47764	+	0.186669i	−0.655169	+	0.755482i	$0.727403\pi$
$182$			11.8528i			0.878584i
$183$	−0.0886256	−	0.701544i	−0.00655139	−	0.0518596i
$184$	5.33347	+	6.44706i	0.393189	+	0.475283i
$185$	−0.283326	−	10.8773i	−0.0208305	−	0.799717i
$186$	−0.0654888	+	1.04091i	−0.00480187	+	0.0763235i
$187$	0.687523	−	2.67772i	0.0502766	−	0.195815i
$188$	−0.00424006	+	0.0165140i	−0.000309238	+	0.00120440i
$189$	−0.442620	+	7.03525i	−0.0321959	+	0.511739i
$190$	−6.52647	−	8.50790i	−0.473480	−	0.617228i
$191$	−2.89665	−	3.50145i	−0.209594	−	0.253356i	0.655231	−	0.755428i	$-0.272571\pi$
$191$	−2.89665	−	3.50145i	−0.209594	−	0.253356i	−0.864826	+	0.502072i	$0.832571\pi$
$192$	−0.0789289	−	0.624786i	−0.00569620	−	0.0450901i
$193$			2.65963i			0.191444i	0.995408	+	0.0957222i	$0.0305161\pi$
$193$			2.65963i			0.191444i	−0.995408	+	0.0957222i	$0.969484\pi$
$194$	8.70503	−	1.09970i	0.624985	−	0.0789539i
$195$	3.35943	−	7.65012i	0.240574	−	0.547836i
$196$	−2.19381	−	2.06013i	−0.156701	−	0.147152i
$197$	14.1943	+	6.67932i	1.01130	+	0.475882i	0.858740	−	0.512412i	$-0.171248\pi$
$197$	14.1943	+	6.67932i	1.01130	+	0.475882i	0.152561	+	0.988294i	$0.451248\pi$
$198$	−2.05346	−	1.69877i	−0.145933	−	0.120726i
$199$	0.875557	−	2.69469i	0.0620666	−	0.191021i	−0.915215	−	0.402965i	$-0.867979\pi$
$199$	0.875557	−	2.69469i	0.0620666	−	0.191021i	0.977282	+	0.211944i	$0.0679795\pi$
$200$	−4.66840	+	1.79055i	−0.330106	+	0.126611i
$201$	0.527812	+	1.62444i	0.0372290	+	0.114579i
$202$	6.72476	−	16.9848i	0.473152	−	1.19505i
$203$	3.13225	−	3.33551i	0.219841	−	0.234107i
$204$	0.318686	+	1.67061i	0.0223125	+	0.116966i
$205$	9.83552	−	7.54489i	0.686942	−	0.526958i
$206$	−13.3345	+	12.5219i	−0.929058	+	0.872444i
$207$	−20.7172	+	6.73142i	−1.43994	+	0.467866i
$208$	5.82831	+	1.11181i	0.404121	+	0.0770902i
$209$	0.308235	+	4.89925i	0.0213210	+	0.338888i
$210$	−1.10329	−	2.58761i	−0.0761339	−	0.178562i
$211$	0.309414	+	0.487558i	0.0213009	+	0.0335649i	0.854812	−	0.518939i	$-0.173673\pi$
$211$	0.309414	+	0.487558i	0.0213009	+	0.0335649i	−0.833511	+	0.552503i	$0.813673\pi$
$212$	−11.4610	+	0.721068i	−0.787148	+	0.0495231i
$213$	−3.79347	−	2.40741i	−0.259924	−	0.164953i
$214$	8.06800	−	9.75253i	0.551517	−	0.666670i
$215$	−16.3431	−	12.8183i	−1.11459	−	0.874199i
$216$	3.41790	+	0.877567i	0.232559	+	0.0597109i
$217$	−2.99353	+	1.40865i	−0.203214	+	0.0956253i
$218$	−1.64697	−	0.535134i	−0.111547	−	0.0362438i
$219$	2.20776	+	1.21373i	0.149187	+	0.0820160i
$220$	2.23117	+	0.511330i	0.150425	+	0.0344739i
$221$	−15.8976	−	2.00834i	−1.06939	−	0.135095i
$222$	0.384079	−	3.04030i	0.0257777	−	0.204051i
$223$	−3.04118	+	1.92999i	−0.203653	+	0.129242i	−0.633742	−	0.773544i	$-0.718482\pi$
$223$	−3.04118	+	1.92999i	−0.203653	+	0.129242i	0.430090	+	0.902786i	$0.358482\pi$
$224$	1.61612	−	1.17418i	0.107981	−	0.0784530i
$225$	0.139916	−	13.0163i	0.00932772	−	0.867754i
$226$	−4.93158	−	3.58300i	−0.328044	−	0.238338i
$227$	−8.74234	−	0.550021i	−0.580249	−	0.0365062i	−0.230046	−	0.973180i	$-0.573888\pi$
$227$	−8.74234	−	0.550021i	−0.580249	−	0.0365062i	−0.350204	+	0.936674i	$0.613888\pi$
$228$	−1.45485	−	2.64637i	−0.0963500	−	0.175260i
$229$	0.965460	−	2.05171i	0.0637994	−	0.135581i	−0.870384	−	0.492373i	$-0.836130\pi$
$229$	0.965460	−	2.05171i	0.0637994	−	0.135581i	0.934184	+	0.356792i	$0.116130\pi$
$230$	13.3007	−	13.1585i	0.877019	−	0.867643i
$231$	−0.241309	+	1.26499i	−0.0158770	+	0.0832299i
$232$	−1.34635	−	1.85309i	−0.0883921	−	0.121661i
$233$	2.90430	−	5.28290i	0.190267	−	0.346094i	−0.763917	−	0.645314i	$-0.776726\pi$
$233$	2.90430	−	5.28290i	0.190267	−	0.346094i	0.954184	+	0.299220i	$0.0967264\pi$
$234$	−8.27698	+	13.0424i	−0.541083	+	0.852610i
$235$	0.0376221	+	0.00616620i	0.00245420	+	0.000402239i
$236$	8.22910	+	3.25813i	0.535669	+	0.212086i
$237$	1.99428	+	5.03697i	0.129542	+	0.327187i
$238$	−4.15682	+	3.43882i	−0.269447	+	0.222906i
$239$	−4.81108	+	1.23528i	−0.311203	+	0.0799033i	−0.401061	−	0.916051i	$-0.631359\pi$
$239$	−4.81108	+	1.23528i	−0.311203	+	0.0799033i	0.0898584	+	0.995955i	$0.471359\pi$
$240$	−1.37589	+	0.299792i	−0.0888131	+	0.0193515i
$241$	8.04646	−	3.18582i	0.518318	−	0.205217i	−0.0943761	−	0.995537i	$-0.530086\pi$
$241$	8.04646	−	3.18582i	0.518318	−	0.205217i	0.612694	+	0.790320i	$0.290086\pi$
$242$	6.81267	+	7.25476i	0.437935	+	0.466354i
$243$	−8.29091	+	11.4115i	−0.531862	+	0.732045i
$244$	−0.478088	−	1.01599i	−0.0306065	−	0.0650420i
$245$	−4.15301	+	5.29502i	−0.265326	+	0.338287i
$246$	3.05932	−	1.68188i	0.195055	−	0.107233i
$247$	27.9491	−	5.33157i	1.77836	−	0.339240i
$248$	0.411871	+	1.60413i	0.0261538	+	0.101862i
$249$	−7.76595			−0.492147
$250$	4.91450	+	10.0423i	0.310820	+	0.635131i
$251$	−3.25942			−0.205733			−0.102866	−	0.994695i	$-0.532801\pi$
$251$	−3.25942			−0.205733			−0.102866	+	0.994695i	$0.532801\pi$
$252$	1.29335	+	5.03726i	0.0814734	+	0.317318i
$253$	−8.41361	+	1.60498i	−0.528959	+	0.100904i
$254$	6.94291	−	3.81690i	0.435637	−	0.239494i
$255$	3.65760	−	1.04135i	0.229048	−	0.0652117i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	18.6385	−	25.6537i	1.16264	−	1.60023i	0.461638	−	0.887069i	$-0.347262\pi$
$257$	18.6385	−	25.6537i	1.16264	−	1.60023i	0.700999	−	0.713163i	$-0.252738\pi$
$258$	−4.00433	−	4.26418i	−0.249299	−	0.265476i
$259$	9.03812	−	3.57844i	0.561601	−	0.222354i
$260$	1.31955	−	13.2017i	0.0818352	−	0.818736i
$261$	5.77589	−	1.48300i	0.357518	−	0.0917951i
$262$	2.83281	−	2.34351i	0.175012	−	0.144782i
$263$	−9.56127	−	24.1490i	−0.589573	−	1.48909i	−0.851685	−	0.524054i	$-0.824419\pi$
$263$	−9.56127	−	24.1490i	−0.589573	−	1.48909i	0.262112	−	0.965038i	$-0.415581\pi$
$264$	0.599392	+	0.237316i	0.0368900	+	0.0146058i
$265$	3.88061	+	25.3834i	0.238384	+	1.55929i
$266$	5.13291	−	8.08818i	0.314719	−	0.495918i
$267$	−5.22925	+	9.51197i	−0.320025	+	0.582123i
$268$	1.59421	+	2.19424i	0.0973820	+	0.134035i
$269$	0.878973	−	4.60774i	0.0535919	−	0.280939i	−0.945396	−	0.325925i	$-0.894324\pi$
$269$	0.878973	−	4.60774i	0.0535919	−	0.280939i	0.998988	+	0.0449861i	$0.0143244\pi$
$270$	1.27622	−	7.78666i	0.0776683	−	0.473881i
$271$	−0.303497	+	0.644964i	−0.0184361	+	0.0391788i	−0.913833	−	0.406090i	$-0.866892\pi$
$271$	−0.303497	+	0.644964i	−0.0184361	+	0.0391788i	0.895397	+	0.445269i	$0.146892\pi$
$272$	1.30104	+	2.36659i	0.0788873	+	0.143495i
$273$	7.44957	+	0.468687i	0.450868	+	0.0283662i
$274$	−6.31028	−	4.58469i	−0.381218	−	0.276971i
$275$	0.696048	−	5.07083i	0.0419733	−	0.305783i
$276$	4.26294	−	3.09720i	0.256599	−	0.186430i
$277$	13.5002	−	8.56749i	0.811149	−	0.514771i	−0.0643864	−	0.997925i	$-0.520509\pi$
$277$	13.5002	−	8.56749i	0.811149	−	0.514771i	0.875535	+	0.483154i	$0.160509\pi$
$278$	1.99678	−	15.8061i	0.119759	−	0.947989i
$279$	−4.27768	−	0.540396i	−0.256098	−	0.0323527i
$280$	−2.93592	−	3.36645i	−0.175455	−	0.201184i
$281$	−18.8738	−	10.3760i	−1.12592	−	0.618978i	−0.193766	−	0.981048i	$-0.562070\pi$
$281$	−18.8738	−	10.3760i	−1.12592	−	0.618978i	−0.932151	+	0.362070i	$0.882070\pi$
$282$	0.0102115	+	0.00331792i	0.000608087	+	0.000197579i
$283$	−28.2473	+	13.2922i	−1.67913	+	0.790137i	−0.680791	+	0.732478i	$0.738364\pi$
$283$	−28.2473	+	13.2922i	−1.67913	+	0.790137i	−0.998336	+	0.0576593i	$0.981636\pi$
$284$	−6.91024	−	1.77425i	−0.410047	−	0.105282i
$285$	−5.60537	+	3.76553i	−0.332033	+	0.223050i
$286$	−3.87164	+	4.68001i	−0.228935	+	0.276735i
$287$	9.35030	+	5.93388i	0.551931	+	0.350266i
$288$	2.59828	−	0.163470i	0.153105	−	0.00963254i
$289$	5.20103	+	8.19551i	0.305943	+	0.482089i
$290$	−3.86008	+	3.36642i	−0.226672	+	0.197683i
$291$	−0.346954	−	5.51468i	−0.0203388	−	0.323276i
$292$	3.92975	+	0.749639i	0.229971	+	0.0438693i
$293$	−21.4926	+	6.98337i	−1.25561	+	0.407973i	−0.859929	−	0.510414i	$-0.829492\pi$
$293$	−21.4926	+	6.98337i	−1.25561	+	0.407973i	−0.395683	+	0.918387i	$0.629492\pi$
$294$	−1.38156	+	1.29737i	−0.0805742	+	0.0756642i
$295$	5.62346	−	18.9748i	0.327410	−	1.10476i
$296$	−0.911824	−	4.77995i	−0.0529987	−	0.277829i
$297$	−2.47279	+	2.63326i	−0.143486	+	0.152797i
$298$	5.99852	−	15.1505i	0.347485	−	0.877646i
$299$	15.3415	+	47.2163i	0.887223	+	2.73059i
$300$	0.940776	+	3.00493i	0.0543157	+	0.173490i
$301$	5.73396	−	17.6473i	0.330500	−	1.01717i
$302$	−7.37812	−	6.10372i	−0.424563	−	0.351229i
$303$	−10.4092	−	4.89819i	−0.597992	−	0.281394i
$304$	−3.49569	−	3.28268i	−0.200492	−	0.188274i
$305$	−2.16797	+	1.26646i	−0.124138	+	0.0725171i
$306$	−6.97544	+	0.881202i	−0.398759	+	0.0503750i
$307$			30.9989i			1.76920i	0.466348	+	0.884601i	$0.345569\pi$
$307$			30.9989i			1.76920i	−0.466348	+	0.884601i	$0.654431\pi$
$308$	0.256297	+	2.02880i	0.0146039	+	0.115602i
$309$	7.34287	+	8.87600i	0.417721	+	0.504938i
$310$	3.49105	−	1.23570i	0.198278	−	0.0701831i
$311$	−1.06616	+	16.9462i	−0.0604566	+	0.960930i	0.844535	+	0.535500i	$0.179877\pi$
$311$	−1.06616	+	16.9462i	−0.0604566	+	0.960930i	−0.904992	+	0.425430i	$0.860123\pi$
$312$	0.929249	−	3.61919i	0.0526084	−	0.204896i
$313$	3.75806	−	14.6367i	0.212418	−	0.827314i	−0.769600	−	0.638526i	$-0.779544\pi$
$313$	3.75806	−	14.6367i	0.212418	−	0.827314i	0.982018	−	0.188787i	$-0.0604557\pi$
$314$	0.554074	−	8.80676i	0.0312682	−	0.496994i
$315$	10.9625	−	3.88033i	0.617668	−	0.218632i
$316$	5.48340	+	6.62829i	0.308465	+	0.372871i
$317$	−0.497251	−	3.93614i	−0.0279284	−	0.221076i	0.971973	−	0.235091i	$-0.0755388\pi$
$317$	−0.497251	−	3.93614i	−0.0279284	−	0.221076i	−0.999902	+	0.0140150i	$0.995539\pi$
$318$			7.23189i			0.405544i
$319$	2.32629	−	0.293878i	0.130247	−	0.0164540i
$320$	−1.93077	+	1.12789i	−0.107933	+	0.0630510i
$321$	−5.81053	−	5.45645i	−0.324312	−	0.304549i
$322$	15.1238	+	7.11674i	0.842818	+	0.396600i
$323$	9.97864	+	8.25505i	0.555226	+	0.459323i
$324$	−1.72678	+	5.31450i	−0.0959325	+	0.295250i
$325$	−29.6653	−	0.318881i	−1.64554	−	0.0176883i
$326$	−1.60330	−	4.93446i	−0.0887987	−	0.273294i
$327$	−0.401462	+	1.01398i	−0.0222009	+	0.0560731i
$328$	3.79492	−	4.04118i	0.209539	−	0.223137i
$329$	0.00638198	+	0.0334555i	0.000351850	+	0.00184446i
$330$	0.409602	−	1.38209i	0.0225478	−	0.0760815i
$331$	8.54929	−	8.02832i	0.469912	−	0.441276i	−0.413059	−	0.910704i	$-0.635540\pi$
$331$	8.54929	−	8.02832i	0.469912	−	0.441276i	0.882971	+	0.469428i	$0.155540\pi$
$332$	−11.7282	+	3.81072i	−0.643669	+	0.209141i
$333$	12.4442	+	2.37385i	0.681936	+	0.130086i
$334$	1.02171	+	16.2396i	0.0559053	+	0.888590i
$335$	4.57072	−	3.98618i	0.249725	−	0.217788i
$336$	−0.674076	−	1.06217i	−0.0367739	−	0.0579463i
$337$	21.0078	−	1.32170i	1.14437	−	0.0719977i	0.520739	−	0.853716i	$-0.325657\pi$
$337$	21.0078	−	1.32170i	1.14437	−	0.0719977i	0.623631	+	0.781718i	$0.285657\pi$
$338$	18.7486	+	11.8982i	1.01979	+	0.647178i
$339$	−2.44696	+	2.95786i	−0.132900	+	0.160649i
$340$	5.01275	−	3.36742i	0.271855	−	0.182624i
$341$	−1.64211	−	0.421623i	−0.0889253	−	0.0228321i
$342$	11.2962	−	5.31560i	0.610830	−	0.287435i
$343$	−19.0166	−	6.17886i	−1.02680	−	0.333627i
$344$	−8.13979	−	4.47489i	−0.438868	−	0.241270i
$345$	−7.74427	−	8.87991i	−0.416938	−	0.478078i
$346$	−3.14940	−	0.397862i	−0.169313	−	0.0213892i
$347$	−1.90351	+	15.0679i	−0.102186	+	0.808886i	0.854842	+	0.518889i	$0.173654\pi$
$347$	−1.90351	+	15.0679i	−0.102186	+	0.808886i	−0.957028	+	0.289997i	$0.906346\pi$
$348$	−1.21792	+	0.772917i	−0.0652875	+	0.0414327i
$349$	−0.405731	+	0.294781i	−0.0217183	+	0.0157793i	−0.598591	−	0.801054i	$-0.704273\pi$
$349$	−0.405731	+	0.294781i	−0.0217183	+	0.0157793i	0.576873	+	0.816834i	$0.304273\pi$
$350$	−6.91522	+	7.20713i	−0.369634	+	0.385237i
$351$	16.9389	+	12.3068i	0.904129	+	0.656888i
$352$	1.02166	+	0.0642772i	0.0544545	+	0.00342598i
$353$	12.6726	+	23.0514i	0.674495	+	1.22690i	0.963020	+	0.269430i	$0.0868351\pi$
$353$	12.6726	+	23.0514i	0.674495	+	1.22690i	−0.288525	+	0.957472i	$0.593165\pi$
$354$	2.37317	−	5.04323i	0.126132	−	0.268045i
$355$	−2.58024	+	15.7429i	−0.136945	+	0.835547i
$356$	−3.22977	+	16.9310i	−0.171177	+	0.897343i
$357$	1.99696	+	2.74858i	0.105690	+	0.145470i
$358$	−7.61301	+	13.8480i	−0.402360	+	0.731890i
$359$	−10.0488	+	15.8343i	−0.530354	+	0.835705i	−0.998859	−	0.0477562i	$-0.984793\pi$
$359$	−10.0488	+	15.8343i	−0.530354	+	0.835705i	0.468505	+	0.883461i	$0.344793\pi$
$360$	−0.879754	−	5.75455i	−0.0463671	−	0.303291i
$361$	−3.71524	−	1.47097i	−0.195539	−	0.0774193i
$362$	7.37632	+	18.6304i	0.387691	+	0.979195i
$363$	4.82907	−	3.99496i	0.253461	−	0.209681i
$364$	11.4804	−	2.94766i	0.601735	−	0.154499i
$365$	0.889710	−	8.90128i	0.0465696	−	0.465914i
$366$	−0.657463	+	0.260308i	−0.0343662	+	0.0136065i
$367$	−2.65463	−	2.82689i	−0.138571	−	0.147563i	0.655940	−	0.754813i	$-0.272272\pi$
$367$	−2.65463	−	2.82689i	−0.138571	−	0.147563i	−0.794510	+	0.607250i	$0.792272\pi$
$368$	4.91813	−	6.76923i	0.256375	−	0.352870i
$369$	6.14507	+	13.0589i	0.319900	+	0.679821i
$370$	−10.4651	+	2.97951i	−0.544057	+	0.154897i
$371$	−20.1026	+	11.0515i	−1.04368	+	0.573766i
$372$	1.02450	−	0.195434i	0.0531178	−	0.0101328i
$373$	−0.578358	−	2.25256i	−0.0299463	−	0.116633i	0.951853	−	0.306555i	$-0.0991764\pi$
$373$	−0.578358	−	2.25256i	−0.0299463	−	0.116633i	−0.981799	+	0.189922i	$0.939176\pi$
$374$	−2.76458			−0.142953
$375$	6.50601	−	2.69171i	0.335969	−	0.138999i
$376$	0.0170496			0.000879266
$377$	−3.37988	−	13.1638i	−0.174073	−	0.677968i
$378$	6.92430	−	1.32088i	0.356147	−	0.0679387i
$379$	21.3843	−	11.7561i	1.09844	−	0.603872i	0.173824	−	0.984777i	$-0.444388\pi$
$379$	21.3843	−	11.7561i	1.09844	−	0.603872i	0.924614	+	0.380905i	$0.124388\pi$
$380$	−6.61754	+	8.43726i	−0.339473	+	0.432822i
$381$	−2.12442	−	4.51462i	−0.108837	−	0.231291i
$382$	−2.67107	+	3.67642i	−0.136664	+	0.188102i
$383$	6.61021	+	7.03916i	0.337766	+	0.359684i	0.875319	−	0.483546i	$-0.160651\pi$
$383$	6.61021	+	7.03916i	0.337766	+	0.359684i	−0.537553	+	0.843230i	$0.680651\pi$
$384$	−0.585529	+	0.231827i	−0.0298801	+	0.0118304i
$385$	4.46777	−	0.973483i	0.227698	−	0.0496133i
$386$	2.57607	−	0.661423i	0.131119	−	0.0336656i
$387$	18.6329	−	15.4145i	0.947163	−	0.783562i
$388$	−3.23001	−	8.15806i	−0.163979	−	0.414163i
$389$	−23.6590	−	9.36726i	−1.19956	−	0.474939i	−0.318490	−	0.947926i	$-0.603176\pi$
$389$	−23.6590	−	9.36726i	−1.19956	−	0.474939i	−0.881069	+	0.472987i	$0.843176\pi$
$390$	−8.24523	−	1.35138i	−0.417513	−	0.0684298i
$391$	−12.1080	+	19.0792i	−0.612328	+	0.964874i
$392$	−1.44983	+	2.63723i	−0.0732273	+	0.133200i
$393$	−1.36090	−	1.87312i	−0.0686483	−	0.0944863i
$394$	2.93951	−	15.4094i	0.148090	−	0.776316i
$395$	13.6746	−	13.5283i	0.688041	−	0.680685i
$396$	−1.13472	+	2.41141i	−0.0570220	+	0.121178i
$397$	−7.92086	−	14.4080i	−0.397537	−	0.723117i	0.599473	−	0.800395i	$-0.295377\pi$
$397$	−7.92086	−	14.4080i	−0.397537	−	0.723117i	−0.997010	+	0.0772785i	$0.975377\pi$
$398$	−2.82777	−	0.177908i	−0.141743	−	0.00891774i
$399$	−4.88053	−	3.54591i	−0.244332	−	0.177518i
$400$	2.89528	+	4.07644i	0.144764	+	0.203822i
$401$	19.4725	−	14.1476i	0.972413	−	0.706499i	0.0164126	−	0.999865i	$-0.494775\pi$
$401$	19.4725	−	14.1476i	0.972413	−	0.706499i	0.956000	+	0.293366i	$0.0947755\pi$
$402$	1.44214	−	0.915211i	0.0719275	−	0.0456466i
$403$	−1.23161	+	9.74921i	−0.0613509	+	0.485643i
$404$	−18.1236	−	2.28954i	−0.901681	−	0.113909i
$405$	12.1794	+	2.79123i	0.605198	+	0.138697i
$406$	−4.00968	−	2.20434i	−0.198997	−	0.109400i
$407$	4.73755	+	1.53932i	0.234831	+	0.0763013i
$408$	1.53887	−	0.724137i	0.0761854	−	0.0358501i
$409$	−19.6664	−	5.04946i	−0.972439	−	0.249680i	−0.271134	−	0.962541i	$-0.587399\pi$
$409$	−19.6664	−	5.04946i	−0.972439	−	0.249680i	−0.701305	+	0.712862i	$0.747399\pi$
$410$	−9.75385	−	7.65018i	−0.481708	−	0.377815i
$411$	−3.13105	+	3.78478i	−0.154443	+	0.186690i
$412$	15.4447	+	9.80149i	0.760905	+	0.482885i
$413$	17.6454	−	1.11015i	0.868272	−	0.0546271i
$414$	11.6721	+	18.3923i	0.573652	+	0.903931i
$415$	10.8150	+	25.3653i	0.530890	+	1.24513i
$416$	−0.372562	−	5.92170i	−0.0182663	−	0.290335i
$417$	−9.85535	−	1.88001i	−0.482619	−	0.0920644i
$418$	4.66867	−	1.51694i	0.228352	−	0.0741962i
$419$	−20.9029	+	19.6291i	−1.02117	+	0.958946i	−0.999167	−	0.0408117i	$-0.987006\pi$
$419$	−20.9029	+	19.6291i	−1.02117	+	0.958946i	−0.0220070	+	0.999758i	$0.507006\pi$
$420$	−2.23194	+	1.71214i	−0.108907	+	0.0835437i
$421$	6.55089	+	34.3410i	0.319271	+	1.67368i	0.674019	+	0.738714i	$0.264567\pi$
$421$	6.55089	+	34.3410i	0.319271	+	1.67368i	−0.354748	+	0.934962i	$0.615433\pi$
$422$	0.395292	−	0.420944i	0.0192425	−	0.0204912i
$423$	−0.0163400	+	0.0412701i	−0.000794478	+	0.00200662i
$424$	3.54866	+	10.9217i	0.172338	+	0.530402i
$425$	−8.49493	−	10.4963i	−0.412065	−	0.509146i
$426$	−1.38838	+	4.27299i	−0.0672672	+	0.207027i
$427$	−1.72830	−	1.42977i	−0.0836382	−	0.0691915i
$428$	−11.4526	−	5.38917i	−0.553581	−	0.260495i
$429$	2.78834	+	2.61842i	0.134622	+	0.126419i
$430$	−8.35120	+	19.0174i	−0.402731	+	0.917101i
$431$	20.3427	−	2.56988i	0.979871	−	0.123787i	0.380951	−	0.924595i	$-0.375597\pi$
$431$	20.3427	−	2.56988i	0.979871	−	0.123787i	0.598920	+	0.800809i	$0.295597\pi$
$432$		−	3.52876i		−	0.169778i
$433$	2.91620	+	23.0841i	0.140143	+	1.10935i	0.892645	+	0.450759i	$0.148847\pi$
$433$	2.91620	+	23.0841i	0.140143	+	1.10935i	−0.752502	+	0.658590i	$0.771153\pi$
$434$	2.10885	+	2.54917i	0.101228	+	0.122364i
$435$	1.96319	+	2.55921i	0.0941277	+	0.122705i
$436$	−0.108736	+	1.72831i	−0.00520752	+	0.0827712i
$437$	9.97848	−	38.8636i	0.477335	−	1.85910i
$438$	0.626547	−	2.44024i	0.0299376	−	0.116599i
$439$	2.08765	−	33.1823i	0.0996382	−	1.58370i	−0.557658	−	0.830071i	$-0.688300\pi$
$439$	2.08765	−	33.1823i	0.0996382	−	1.58370i	0.657296	−	0.753633i	$-0.271700\pi$
$440$	−0.0596025	−	2.28823i	−0.00284144	−	0.109087i
$441$	−4.99416	−	6.03690i	−0.237817	−	0.287472i
$442$	2.00834	+	15.8976i	0.0955269	+	0.756174i
$443$		−	4.13997i		−	0.196696i	−0.995152	−	0.0983479i	$-0.968644\pi$
$443$		−	4.13997i		−	0.196696i	0.995152	−	0.0983479i	$-0.0313558\pi$
$444$	−3.04030	+	0.384079i	−0.144286	+	0.0182276i
$445$	38.3505	+	3.83325i	1.81799	+	0.181714i
$446$	2.62567	+	2.46567i	0.124329	+	0.116753i
$447$	−9.28505	−	4.36921i	−0.439168	−	0.206657i
$448$	−1.53920	−	1.27334i	−0.0727204	−	0.0601595i
$449$	0.889985	−	2.73909i	0.0420010	−	0.129266i	−0.927857	−	0.372935i	$-0.878351\pi$
$449$	0.889985	−	2.73909i	0.0420010	−	0.129266i	0.969858	+	0.243670i	$0.0783513\pi$
$450$	−12.6422	+	3.10150i	−0.595958	+	0.146206i
$451$	1.75366	+	5.39720i	0.0825764	+	0.254144i
$452$	−2.24400	+	5.66770i	−0.105549	+	0.266586i
$453$	−4.12799	+	4.39587i	−0.193950	+	0.206536i
$454$	1.64139	+	8.60446i	0.0770342	+	0.403828i
$455$	−8.84361	−	24.9846i	−0.414595	−	1.17130i
$456$	−2.20142	+	2.06727i	−0.103091	+	0.0968089i
$457$	−12.1106	+	3.93498i	−0.566511	+	0.184071i	−0.578249	−	0.815861i	$-0.696264\pi$
$457$	−12.1106	+	3.93498i	−0.566511	+	0.184071i	0.0117378	+	0.999931i	$0.496264\pi$
$458$	−2.22735	−	0.424890i	−0.104077	−	0.0198538i
$459$	0.598388	+	9.51110i	0.0279304	+	0.443940i
$460$	−16.0528	−	9.61042i	−0.748465	−	0.448088i
$461$	−17.5315	−	27.6253i	−0.816525	−	1.28664i	−0.955099	−	0.296286i	$-0.904252\pi$
$461$	−17.5315	−	27.6253i	−0.816525	−	1.28664i	0.138574	−	0.990352i	$-0.455748\pi$
$462$	1.28525	−	0.0808614i	0.0597955	−	0.00376201i
$463$	−8.75649	−	5.55704i	−0.406948	−	0.258257i	0.316561	−	0.948572i	$-0.397472\pi$
$463$	−8.75649	−	5.55704i	−0.406948	−	0.258257i	−0.723509	+	0.690315i	$0.757472\pi$
$464$	−1.46005	+	1.76490i	−0.0677810	+	0.0819332i
$465$	−0.638605	−	2.24302i	−0.0296146	−	0.104018i
$466$	−5.83920	−	1.49925i	−0.270496	−	0.0694515i
$467$	−4.05138	+	1.90643i	−0.187475	+	0.0882193i	−0.517226	−	0.855849i	$-0.673035\pi$
$467$	−4.05138	+	1.90643i	−0.187475	+	0.0882193i	0.329751	+	0.944068i	$0.393035\pi$
$468$	14.6911	+	4.77342i	0.679095	+	0.220651i
$469$	4.74786	+	2.61016i	0.219236	+	0.120526i
$470$	−0.00338376	−	0.0379736i	−0.000156081	−	0.00175159i
$471$	−5.51322	−	0.696482i	−0.254036	−	0.0320922i
$472$	1.10928	−	8.78083i	0.0510586	−	0.404171i
$473$	8.02844	−	5.09500i	0.369148	−	0.234268i
$474$	4.38277	−	3.18427i	0.201307	−	0.146258i
$475$	20.1052	+	13.0644i	0.922489	+	0.599434i
$476$	4.36455	+	3.17103i	0.200049	+	0.145344i
$477$	−29.8378	−	1.87724i	−1.36618	−	0.0859528i
$478$	2.39293	+	4.35273i	0.109450	+	0.199089i
$479$	2.81439	−	5.98089i	0.128593	−	0.273274i	−0.830154	−	0.557534i	$-0.811748\pi$
$479$	2.81439	−	5.98089i	0.128593	−	0.273274i	0.958747	+	0.284260i	$0.0917478\pi$
$480$	0.632543	+	1.25811i	0.0288715	+	0.0574244i
$481$	5.41022	−	28.3614i	0.246685	−	1.29317i
$482$	−5.08681	−	7.00139i	−0.231698	−	0.318905i
$483$	5.07097	−	9.22406i	0.230737	−	0.419709i
$484$	5.33260	−	8.40283i	0.242391	−	0.381947i
$485$	−17.5289	+	8.81310i	−0.795948	+	0.400182i
$486$	13.1148	+	5.19252i	0.594900	+	0.235537i
$487$	−6.06217	−	15.3113i	−0.274703	−	0.693821i	−0.999986	−	0.00536978i	$-0.998291\pi$
$487$	−6.06217	−	15.3113i	−0.274703	−	0.693821i	0.725282	−	0.688452i	$-0.241709\pi$
$488$	−0.865174	+	0.715734i	−0.0391646	+	0.0323998i
$489$	−3.16475	+	0.812570i	−0.143115	+	0.0367457i
$490$	6.16148	+	2.70572i	0.278347	+	0.122232i
$491$	32.5424	−	12.8844i	1.46862	−	0.581467i	0.508499	−	0.861062i	$-0.330200\pi$
$491$	32.5424	−	12.8844i	1.46862	−	0.581467i	0.960118	+	0.279596i	$0.0902004\pi$
$492$	−2.38986	−	2.54494i	−0.107743	−	0.114735i
$493$	3.63600	−	5.00453i	0.163757	−	0.225393i
$494$	−12.1147	−	25.7451i	−0.545067	−	1.15833i
$495$	5.59600	+	2.04872i	0.251521	+	0.0920833i
$496$	1.45131	−	0.797863i	0.0651656	−	0.0358251i
$497$	−13.9994	+	2.67053i	−0.627959	+	0.119790i
$498$	1.93131	+	7.52197i	0.0865442	+	0.337068i
$499$	14.4242			0.645716			0.322858	−	0.946447i	$-0.395356\pi$
$499$	14.4242			0.645716			0.322858	+	0.946447i	$0.395356\pi$
$500$	8.50461	−	7.25752i	0.380338	−	0.324566i
$501$	10.2471			0.457808
$502$	0.810585	+	3.15702i	0.0361782	+	0.140905i
$503$	−24.4841	+	4.67059i	−1.09169	+	0.208251i	−0.701632	−	0.712539i	$-0.747545\pi$
$503$	−24.4841	+	4.67059i	−1.09169	+	0.208251i	−0.390058	+	0.920790i	$0.627545\pi$
$504$	4.55737	−	2.50543i	0.203001	−	0.111601i
$505$	−1.50246	+	40.8200i	−0.0668586	+	1.81647i
$506$	3.64694	+	7.75014i	0.162126	+	0.344536i
$507$	8.21951	−	11.3132i	0.365041	−	0.502436i
$508$	−5.42362	−	5.77556i	−0.240634	−	0.256249i
$509$	15.4267	−	6.10787i	0.683777	−	0.270726i	−0.000445429	−	1.00000i	$-0.500142\pi$
$509$	15.4267	−	6.10787i	0.683777	−	0.270726i	0.684222	+	0.729273i	$0.260142\pi$
$510$	−1.91824	−	3.28372i	−0.0849411	−	0.145406i
$511$	7.74066	−	1.98746i	0.342427	−	0.0879202i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	−6.22933	−	15.7335i	−0.275032	−	0.694651i
$514$	−29.4829	−	11.6731i	−1.30044	−	0.514879i
$515$	18.7651	−	36.3443i	0.826888	−	1.60152i
$516$	−3.13438	+	4.93899i	−0.137983	+	0.217427i
$517$	−0.00840818	+	0.0152944i	−0.000369791	+	0.000672648i
$518$	−5.71371	−	7.86425i	−0.251046	−	0.345535i
$519$	−0.374595	+	1.96370i	−0.0164429	+	0.0861967i
$520$	−13.1151	+	2.00504i	−0.575136	+	0.0879267i
$521$	4.00531	−	8.51172i	0.175476	−	0.372905i	−0.797670	−	0.603094i	$-0.793934\pi$
$521$	4.00531	−	8.51172i	0.175476	−	0.372905i	0.973146	+	0.230189i	$0.0739344\pi$
$522$	−2.87281	−	5.22562i	−0.125739	−	0.228719i
$523$	−31.4136	−	1.97637i	−1.37362	−	0.0864208i	−0.641252	−	0.767331i	$-0.721585\pi$
$523$	−31.4136	−	1.97637i	−1.37362	−	0.0864208i	−0.732367	+	0.680910i	$0.761585\pi$
$524$	−2.97437	−	2.16101i	−0.129936	−	0.0944041i
$525$	4.25631	+	4.63127i	0.185760	+	0.202125i
$526$	−21.0125	+	15.2665i	−0.916190	+	0.665651i
$527$	−3.77642	+	2.39659i	−0.164504	+	0.104397i
$528$	0.0807976	−	0.639579i	0.00351626	−	0.0278341i
$529$	46.6398	+	5.89197i	2.02782	+	0.256173i
$530$	23.6209	−	10.0713i	1.02603	−	0.437469i
$531$	20.1917	+	11.1005i	0.876245	+	0.481720i
$532$	−9.11058	−	2.96021i	−0.394994	−	0.128341i
$533$	29.7625	−	14.0052i	1.28916	−	0.606631i
$534$	10.5136	+	2.69943i	0.454968	+	0.116816i
$535$	−9.73005	+	26.5772i	−0.420667	+	1.14903i
$536$	1.72884	−	2.08981i	0.0746747	−	0.0902661i
$537$	8.40257	+	5.33243i	0.362598	+	0.230111i
$538$	−4.68157	+	0.294539i	−0.201837	+	0.0126985i
$539$	−1.65074	−	2.60115i	−0.0711023	−	0.112039i
$540$	−7.85941	+	0.700337i	−0.338215	+	0.0301377i
$541$	−1.93041	−	30.6830i	−0.0829948	−	1.31916i	−0.790502	−	0.612459i	$-0.790180\pi$
$541$	−1.93041	−	30.6830i	−0.0829948	−	1.31916i	0.707507	−	0.706706i	$-0.249820\pi$
$542$	0.700178	+	0.133566i	0.0300752	+	0.00573716i
$543$	12.0011	−	3.89939i	0.515016	−	0.167339i
$544$	1.96868	−	1.84871i	0.0844065	−	0.0792630i
$545$	3.87095	−	0.100828i	0.165813	−	0.00431901i
$546$	−1.39867	−	7.33208i	−0.0598575	−	0.313784i
$547$	−27.3233	+	29.0964i	−1.16826	+	1.24407i	−0.204044	+	0.978962i	$0.565409\pi$
$547$	−27.3233	+	29.0964i	−1.16826	+	1.24407i	−0.964218	+	0.265111i	$0.914591\pi$
$548$	−2.87135	+	7.25220i	−0.122658	+	0.309799i
$549$	−0.903335	−	2.78018i	−0.0385534	−	0.118655i
$550$	−5.08462	+	0.586884i	−0.216809	+	0.0250248i
$551$	−3.39427	+	10.4465i	−0.144601	+	0.445035i
$552$	−4.06005	−	3.35876i	−0.172807	−	0.142959i
$553$	15.5490	+	7.31680i	0.661210	+	0.311142i
$554$	−11.6557	−	10.9454i	−0.495203	−	0.465027i
$555$	1.45883	+	6.69525i	0.0619239	+	0.284198i
$556$	−15.8061	+	1.99678i	−0.670330	+	0.0846823i
$557$			3.92992i			0.166516i	0.996528	+	0.0832580i	$0.0265325\pi$
$557$			3.92992i			0.166516i	−0.996528	+	0.0832580i	$0.973467\pi$
$558$	0.540396	+	4.27768i	0.0228768	+	0.181089i
$559$	−35.1310	−	42.4660i	−1.48588	−	1.79612i
$560$	−2.53055	+	3.68089i	−0.106935	+	0.155546i
$561$	−0.109318	+	1.73756i	−0.00461542	+	0.0733600i
$562$	−5.35626	+	20.8612i	−0.225940	+	0.879979i
$563$	−0.690365	+	2.68880i	−0.0290954	+	0.113319i	−0.981472	−	0.191604i	$-0.938631\pi$
$563$	−0.690365	+	2.68880i	−0.0290954	+	0.113319i	0.952377	+	0.304924i	$0.0986309\pi$
$564$	0.000674183	−	0.0107158i	2.83882e−5	−	0.000451218i
$565$	13.0687	+	3.87309i	0.549804	+	0.162942i
$566$	19.8994	+	24.0542i	0.836433	+	1.01107i
$567$	1.39906	+	11.0747i	0.0587551	+	0.465094i
$568$			7.13438i			0.299352i
$569$	−30.2810	+	3.82538i	−1.26944	+	0.160368i	−0.731049	−	0.682324i	$-0.760969\pi$
$569$	−30.2810	+	3.82538i	−1.26944	+	0.160368i	−0.538395	+	0.842693i	$0.680969\pi$
$570$	5.04122	+	4.49282i	0.211154	+	0.188183i
$571$	−0.0317914	−	0.0298542i	−0.00133043	−	0.00124936i	0.683882	−	0.729593i	$-0.260290\pi$
$571$	−0.0317914	−	0.0298542i	−0.00133043	−	0.00124936i	−0.685212	+	0.728344i	$0.740290\pi$
$572$	5.49582	+	2.58614i	0.229792	+	0.108132i
$573$	2.20504	+	1.82417i	0.0921170	+	0.0762058i
$574$	3.42213	−	10.5322i	0.142837	−	0.439607i
$575$	−18.2188	+	37.6608i	−0.759777	+	1.57056i
$576$	−0.804499	−	2.47599i	−0.0335208	−	0.103166i
$577$	1.43344	−	3.62047i	0.0596750	−	0.150722i	−0.896880	−	0.442274i	$-0.854172\pi$
$577$	1.43344	−	3.62047i	0.0596750	−	0.150722i	0.956555	+	0.291552i	$0.0941718\pi$
$578$	6.64459	−	7.07577i	0.276379	−	0.294313i
$579$	−0.313846	−	1.64524i	−0.0130430	−	0.0683739i
$580$	4.22062	+	2.90161i	0.175252	+	0.120483i
$581$	−17.9576	+	16.8633i	−0.745008	+	0.699609i
$582$	−5.25514	+	1.70750i	−0.217833	+	0.0707781i
$583$	−11.5474	−	2.20278i	−0.478243	−	0.0912298i
$584$	−0.251200	−	3.99271i	−0.0103947	−	0.165220i
$585$	7.71590	−	33.6680i	0.319013	−	1.39200i
$586$	12.1090	+	19.0807i	0.500217	+	0.788216i
$587$	−45.9041	+	2.88804i	−1.89467	+	0.119202i	−0.967091	−	0.254432i	$-0.918111\pi$
$587$	−45.9041	+	2.88804i	−1.89467	+	0.119202i	−0.927576	+	0.373634i	$0.878111\pi$
$588$	1.60019	+	1.01551i	0.0659908	+	0.0418790i
$589$	5.06240	−	6.11939i	0.208592	−	0.252145i
$590$	−19.7772	−	0.727939i	−0.814215	−	0.0299688i
$591$	−9.56874	−	2.45683i	−0.393605	−	0.101061i
$592$	−4.40301	+	2.07190i	−0.180963	+	0.0851546i
$593$	−26.8147	−	8.71263i	−1.10115	−	0.357785i	−0.298604	−	0.954377i	$-0.596521\pi$
$593$	−26.8147	−	8.71263i	−1.10115	−	0.357785i	−0.802545	+	0.596592i	$0.796521\pi$
$594$	3.16549	+	1.74024i	0.129882	+	0.0714030i
$595$	6.19644	−	10.3502i	0.254029	−	0.424319i
$596$	−16.1663	−	2.04228i	−0.662198	−	0.0836551i
$597$	−0.223634	+	1.77025i	−0.00915273	+	0.0724513i
$598$	41.9177	−	26.6018i	1.71414	−	1.08783i
$599$	31.0493	−	22.5586i	1.26864	−	0.921721i	0.269492	−	0.963003i	$-0.413144\pi$
$599$	31.0493	−	22.5586i	1.26864	−	0.921721i	0.999148	+	0.0412820i	$0.0131442\pi$
$600$	2.67657	−	1.65852i	0.109270	−	0.0677087i
$601$	−28.2270	−	20.5081i	−1.15140	−	0.836544i	−0.162737	−	0.986669i	$-0.552032\pi$
$601$	−28.2270	−	20.5081i	−1.15140	−	0.836544i	−0.988667	+	0.150125i	$0.952032\pi$
$602$	−18.5189	−	1.16511i	−0.754772	−	0.0474863i
$603$	3.40169	+	6.18766i	0.138528	+	0.251981i
$604$	−4.07709	+	8.66426i	−0.165894	+	0.352544i
$605$	−19.7735	−	10.2093i	−0.803906	−	0.415068i
$606$	−2.15565	+	11.3003i	−0.0875672	+	0.459043i
$607$	−13.9823	−	19.2450i	−0.567524	−	0.781129i	0.424735	−	0.905318i	$-0.360367\pi$
$607$	−13.9823	−	19.2450i	−0.567524	−	0.781129i	−0.992259	+	0.124188i	$0.960367\pi$
$608$	−2.31020	+	4.20224i	−0.0936910	+	0.170423i
$609$	−1.54400	+	2.43296i	−0.0625661	+	0.0985884i
$610$	1.76582	+	1.78490i	0.0714960	+	0.0722687i
$611$	0.0940583	+	0.0372403i	0.00380519	+	0.00150658i
$612$	2.58824	+	6.53714i	0.104623	+	0.264248i
$613$	−10.7205	+	8.86875i	−0.432996	+	0.358206i	−0.828243	−	0.560369i	$-0.810659\pi$
$613$	−10.7205	+	8.86875i	−0.432996	+	0.358206i	0.395247	+	0.918575i	$0.370659\pi$
$614$	30.0250	−	7.70912i	1.21171	−	0.311115i
$615$	−5.19390	+	5.82788i	−0.209438	+	0.235003i
$616$	1.90132	−	0.752787i	0.0766065	−	0.0303307i
$617$	−9.13342	−	9.72611i	−0.367698	−	0.391558i	0.518338	−	0.855176i	$-0.326551\pi$
$617$	−9.13342	−	9.72611i	−0.367698	−	0.391558i	−0.886035	+	0.463618i	$0.846551\pi$
$618$	6.77105	−	9.31955i	0.272372	−	0.374887i
$619$	−10.8435	−	23.0436i	−0.435838	−	0.926202i	−0.995254	−	0.0973152i	$-0.968975\pi$
$619$	−10.8435	−	23.0436i	−0.435838	−	0.926202i	0.559416	−	0.828887i	$-0.311025\pi$
$620$	−2.06507	−	3.07407i	−0.0829351	−	0.123457i
$621$	25.8738	−	14.2242i	1.03828	−	0.570799i
$622$	16.6789	−	3.18168i	0.668764	−	0.127574i
$623$	8.56284	+	33.3501i	0.343063	+	1.33614i
$624$	−3.73658			−0.149583
$625$	−17.8521	−	17.5015i	−0.714085	−	0.700059i
$626$	−15.1114			−0.603974
$627$	−0.768803	−	2.99429i	−0.0307030	−	0.119580i
$628$	−8.66787	+	1.65349i	−0.345886	+	0.0659812i
$629$	11.5161	−	6.33105i	0.459179	−	0.252436i
$630$	−6.48469	−	9.65312i	−0.258356	−	0.384590i
$631$	−20.3064	−	43.1533i	−0.808385	−	1.71790i	−0.688644	−	0.725100i	$-0.741794\pi$
$631$	−20.3064	−	43.1533i	−0.808385	−	1.71790i	−0.119741	−	0.992805i	$-0.538206\pi$
$632$	5.05639	−	6.95952i	0.201132	−	0.276835i
$633$	−0.248936	−	0.265090i	−0.00989432	−	0.0105364i
$634$	−3.68882	+	1.46051i	−0.146502	+	0.0580042i
$635$	−11.7872	+	13.2260i	−0.467760	+	0.524856i
$636$	7.00469	−	1.79850i	0.277754	−	0.0713151i
$637$	−13.7586	+	11.3821i	−0.545137	+	0.450977i
$638$	−0.863170	−	2.18012i	−0.0341732	−	0.0863117i
$639$	−17.2694	−	6.83745i	−0.683168	−	0.270485i
$640$	1.57262	+	1.58961i	0.0621632	+	0.0628350i
$641$	−1.18568	+	1.86833i	−0.0468316	+	0.0737948i	−0.866937	−	0.498418i	$-0.833915\pi$
$641$	−1.18568	+	1.86833i	−0.0468316	+	0.0737948i	0.820106	+	0.572212i	$0.193915\pi$
$642$	−3.84001	+	6.98495i	−0.151553	+	0.275674i
$643$	26.9710	+	37.1223i	1.06363	+	1.46396i	0.876362	+	0.481654i	$0.159964\pi$
$643$	26.9710	+	37.1223i	1.06363	+	1.46396i	0.187269	+	0.982309i	$0.440036\pi$
$644$	3.13201	−	16.4186i	0.123418	−	0.646982i
$645$	11.6224	+	6.00080i	0.457631	+	0.236281i
$646$	5.51411	−	11.7181i	0.216950	−	0.461042i
$647$	10.7065	+	19.4751i	0.420917	+	0.765645i	0.998723	−	0.0505291i	$-0.0160908\pi$
$647$	10.7065	+	19.4751i	0.420917	+	0.765645i	−0.577805	+	0.816175i	$0.696091\pi$
$648$	5.57697	+	0.350873i	0.219084	+	0.0137836i
$649$	7.32983	+	5.32543i	0.287721	+	0.209042i
$650$	7.06861	+	28.8126i	0.277254	+	1.13012i
$651$	1.68556	−	1.22463i	0.0660625	−	0.0479972i
$652$	−4.38071	+	2.78008i	−0.171562	+	0.108876i
$653$	2.47354	−	19.5801i	0.0967969	−	0.766227i	−0.866760	−	0.498725i	$-0.833802\pi$
$653$	2.47354	−	19.5801i	0.0967969	−	0.766227i	0.963557	−	0.267502i	$-0.0861981\pi$
$654$	1.08196	+	0.136683i	0.0423080	+	0.00534475i
$655$	−4.22278	+	7.05354i	−0.164998	+	0.275605i
$656$	−4.85798	−	2.67070i	−0.189672	−	0.104273i
$657$	9.90547	+	3.21848i	0.386449	+	0.125565i
$658$	0.0308173	−	0.0145015i	0.00120138	−	0.000565328i
$659$	20.6674	+	5.30648i	0.805087	+	0.206711i	0.628739	−	0.777617i	$-0.283572\pi$
$659$	20.6674	+	5.30648i	0.805087	+	0.206711i	0.176348	+	0.984328i	$0.443572\pi$
$660$	−1.44053	−	0.0530216i	−0.0560727	−	0.00206386i
$661$	12.9021	−	15.5960i	0.501835	−	0.606614i	−0.457387	−	0.889268i	$-0.651215\pi$
$661$	12.9021	−	15.5960i	0.501835	−	0.606614i	0.959222	+	0.282653i	$0.0912146\pi$
$662$	−9.90222	−	6.28414i	−0.384861	−	0.244240i
$663$	10.0712	−	0.633628i	0.391134	−	0.0246081i
$664$	6.60769	+	10.4120i	0.256428	+	0.404066i
$665$	−4.78496	+	20.8790i	−0.185553	+	0.809652i
$666$	−0.795466	−	12.6436i	−0.0308237	−	0.489928i
$667$	−18.8260	−	3.59126i	−0.728947	−	0.139054i
$668$	15.4753	−	5.02823i	0.598757	−	0.194548i
$669$	1.65352	−	1.55276i	0.0639288	−	0.0600332i
$670$	−4.99764	−	3.43580i	−0.193076	−	0.132736i
$671$	−0.215383	−	1.12908i	−0.00831478	−	0.0435876i
$672$	−0.861168	+	0.917051i	−0.0332203	+	0.0353760i
$673$	−8.41327	+	21.2495i	−0.324308	+	0.819108i	0.672561	+	0.740041i	$0.265194\pi$
$673$	−8.41327	+	21.2495i	−0.324308	+	0.819108i	−0.996869	+	0.0790669i	$0.974806\pi$
$674$	−6.50462	−	20.0191i	−0.250548	−	0.771109i
$675$	3.11964	+	17.3658i	0.120075	+	0.668411i
$676$	6.86183	−	21.1185i	0.263916	−	0.812251i
$677$	−26.2432	−	21.7102i	−1.00861	−	0.834392i	−0.0223727	−	0.999750i	$-0.507122\pi$
$677$	−26.2432	−	21.7102i	−1.00861	−	0.834392i	−0.986234	+	0.165358i	$0.947122\pi$
$678$	3.47347	+	1.63449i	0.133398	+	0.0627722i
$679$	−12.7771	−	11.9985i	−0.490340	−	0.460460i
$680$	−4.50825	−	4.01782i	−0.172884	−	0.154077i
$681$	5.47289	−	0.691387i	0.209722	−	0.0264940i
$682$			1.69537i			0.0649193i
$683$	−0.212786	−	1.68437i	−0.00814203	−	0.0644508i	0.987520	−	0.157492i	$-0.0503410\pi$
$683$	−0.212786	−	1.68437i	−0.00814203	−	0.0644508i	−0.995662	+	0.0930417i	$0.970341\pi$
$684$	−7.95785	−	9.61939i	−0.304276	−	0.367807i
$685$	16.7223	+	4.95588i	0.638925	+	0.189355i
$686$	−1.25551	+	19.9558i	−0.0479356	+	0.761915i
$687$	−0.355122	+	1.38311i	−0.0135487	+	0.0527689i
$688$	−2.31002	+	8.99693i	−0.0880686	+	0.343005i
$689$	−4.27839	+	68.0031i	−0.162994	+	2.59071i
$690$	−6.67501	+	9.70931i	−0.254113	+	0.369627i
$691$	26.2571	+	31.7393i	0.998865	+	1.20742i	0.978207	+	0.207634i	$0.0665764\pi$
$691$	26.2571	+	31.7393i	0.998865	+	1.20742i	0.0206588	+	0.999787i	$0.493424\pi$
$692$	0.397862	+	3.14940i	0.0151244	+	0.119722i
$693$			5.32378i			0.202234i
$694$	15.0679	−	1.90351i	0.571968	−	0.0722564i
$695$	7.58429	+	34.8078i	0.287688	+	1.32034i
$696$	1.05152	+	0.987442i	0.0398577	+	0.0374289i
$697$	13.5466	+	6.37456i	0.513115	+	0.241454i
$698$	0.386421	+	0.319675i	0.0146263	+	0.0120999i
$699$	−1.17319	+	3.61071i	−0.0443741	+	0.136570i
$700$	8.70045	+	4.90563i	0.328846	+	0.185415i
$701$	1.90827	+	5.87304i	0.0720743	+	0.221822i	0.980604	−	0.195998i	$-0.0627945\pi$
$701$	1.90827	+	5.87304i	0.0720743	+	0.221822i	−0.908530	+	0.417819i	$0.862794\pi$
$702$	7.70764	−	19.4673i	0.290906	−	0.734745i
$703$	−15.9740	+	17.0105i	−0.602469	+	0.641565i
$704$	−0.191818	−	1.00554i	−0.00722940	−	0.0378979i
$705$	−0.0240006		0.000625152i	−0.000903914		2.35446e-5i
$706$	19.1756	−	18.0071i	0.721685	−	0.677707i
$707$	−34.7059	+	11.2766i	−1.30525	+	0.424101i
$708$	−5.47497	−	1.04441i	−0.205762	−	0.0392512i
$709$	2.62991	+	41.8012i	0.0987683	+	1.56988i	0.665767	+	0.746159i	$0.268104\pi$
$709$	2.62991	+	41.8012i	0.0987683	+	1.56988i	−0.566999	+	0.823718i	$0.691896\pi$
$710$	15.8900	−	1.41593i	0.596341	−	0.0531388i
$711$	12.0002	+	18.9093i	0.450043	+	0.709154i
$712$	17.2023	−	1.08228i	0.644684	−	0.0405601i
$713$	11.7003	+	7.42522i	0.438179	+	0.278077i
$714$	2.16561	−	2.61777i	0.0810458	−	0.0979675i
$715$	4.66922	−	12.7538i	0.174619	−	0.476964i
$716$	15.3062	+	3.92997i	0.572021	+	0.146870i
$717$	2.83035	−	1.33186i	0.105702	−	0.0497394i
$718$	17.8359	+	5.79524i	0.665630	+	0.216276i
$719$	11.1620	+	6.13637i	0.416273	+	0.228848i	0.676104	−	0.736806i	$-0.263667\pi$
$719$	11.1620	+	6.13637i	0.416273	+	0.228848i	−0.259831	+	0.965654i	$0.583667\pi$
$720$	−5.35497	+	2.28321i	−0.199568	+	0.0850903i
$721$	36.2530	+	4.57982i	1.35013	+	0.170562i
$722$	−0.500812	+	3.96433i	−0.0186383	+	0.147537i
$723$	−4.60158	+	2.92025i	−0.171135	+	0.108605i
$724$	16.2107	−	11.7778i	0.602467	−	0.437718i
$725$	5.62495	−	9.97621i	0.208905	−	0.370507i
$726$	−5.07039	−	3.68385i	−0.188180	−	0.136721i
$727$	22.5489	+	1.41866i	0.836292	+	0.0526150i	0.475160	−	0.879900i	$-0.342390\pi$
$727$	22.5489	+	1.41866i	0.836292	+	0.0526150i	0.361132	+	0.932515i	$0.382390\pi$
$728$	−5.71011	−	10.3866i	−0.211631	−	0.384955i
$729$	−3.35562	+	7.13105i	−0.124282	+	0.264113i
$730$	−8.84289	+	1.35190i	−0.327290	+	0.0500360i
$731$	4.70056	−	24.6412i	0.173857	−	0.911388i
$732$	0.415635	+	0.572072i	0.0153623	+	0.0211444i
$733$	−0.905492	+	1.64708i	−0.0334451	+	0.0608364i	−0.892501	−	0.451045i	$-0.851051\pi$
$733$	−0.905492	+	1.64708i	−0.0334451	+	0.0608364i	0.859056	+	0.511882i	$0.171051\pi$
$734$	−2.07790	+	3.27425i	−0.0766967	+	0.120855i
$735$	1.94421	−	3.76556i	0.0717133	−	0.138895i
$736$	−7.77965	−	3.08018i	−0.286762	−	0.113537i
$737$	1.02208	+	2.58148i	0.0376488	+	0.0950899i
$738$	11.1205	−	9.19964i	0.409349	−	0.338643i
$739$	−9.09056	+	2.33406i	−0.334402	+	0.0858597i	−0.412157	−	0.911113i	$-0.635225\pi$
$739$	−9.09056	+	2.33406i	−0.334402	+	0.0858597i	0.0777557	+	0.996972i	$0.475225\pi$
$740$	5.48847	+	9.39538i	0.201760	+	0.345381i
$741$	−16.6601	+	6.59619i	−0.612023	+	0.242317i
$742$	15.7036	+	16.7227i	0.576499	+	0.613909i
$743$	20.8420	−	28.6866i	0.764619	−	1.05241i	−0.232197	−	0.972669i	$-0.574591\pi$
$743$	20.8420	−	28.6866i	0.764619	−	1.05241i	0.996816	−	0.0797392i	$-0.0254087\pi$
$744$	−0.444076	−	0.943710i	−0.0162806	−	0.0345981i
$745$	−1.34020	+	36.4116i	−0.0491012	+	1.33402i
$746$	−2.03796	+	1.12038i	−0.0746149	+	0.0410199i
$747$	−31.5360	+	6.01581i	−1.15384	+	0.220107i
$748$	0.687523	+	2.67772i	0.0251383	+	0.0979073i
$749$	−25.2844			−0.923871
$750$	−4.22513	−	5.63221i	−0.154280	−	0.205659i
$751$	31.5752			1.15220			0.576098	−	0.817381i	$-0.304575\pi$
$751$	31.5752			1.15220			0.576098	+	0.817381i	$0.304575\pi$
$752$	−0.00424006	−	0.0165140i	−0.000154619	−	0.000602202i
$753$	2.01627	−	0.384624i	0.0734770	−	0.0140165i
$754$	−11.9097	+	6.54739i	−0.433724	+	0.238442i
$755$	20.1066	+	7.36112i	0.731753	+	0.267898i
$756$	−3.00138	−	6.37827i	−0.109159	−	0.231975i
$757$	20.6319	−	28.3973i	0.749878	−	1.03212i	−0.248111	−	0.968732i	$-0.579810\pi$
$757$	20.6319	−	28.3973i	0.749878	−	1.03212i	0.997989	−	0.0633865i	$-0.0201901\pi$
$758$	−16.7048	−	17.7889i	−0.606747	−	0.646120i
$759$	5.01525	−	1.98568i	0.182042	−	0.0720755i
$760$	9.81790	+	4.31138i	0.356133	+	0.156390i
$761$	21.9633	−	5.63921i	0.796167	−	0.204421i	0.171369	−	0.985207i	$-0.445181\pi$
$761$	21.9633	−	5.63921i	0.796167	−	0.204421i	0.624799	+	0.780786i	$0.285181\pi$
$762$	−3.84446	+	3.18041i	−0.139270	+	0.115214i
$763$	1.27347	+	3.21643i	0.0461028	+	0.116442i
$764$	4.22519	+	1.67287i	0.152862	+	0.0605223i
$765$	14.0461	−	7.06203i	0.507839	−	0.255328i
$766$	5.17412	−	8.15311i	0.186949	−	0.294584i
$767$	25.2990	−	46.0187i	0.913494	−	1.66164i
$768$	0.370159	+	0.509480i	0.0133570	+	0.0183843i
$769$	6.19474	−	32.4740i	0.223388	−	1.17104i	−0.677010	−	0.735974i	$-0.736724\pi$
$769$	6.19474	−	32.4740i	0.223388	−	1.17104i	0.900398	−	0.435068i	$-0.143276\pi$
$770$	−2.05399	−	4.08531i	−0.0740205	−	0.147224i
$771$	−8.50248	+	18.0687i	−0.306209	+	0.650728i
$772$	−1.28129	−	2.33065i	−0.0461145	−	0.0838820i
$773$	13.2912	+	0.836213i	0.478052	+	0.0300765i	0.299989	−	0.953943i	$-0.403017\pi$
$773$	13.2912	+	0.836213i	0.478052	+	0.0300765i	0.178063	+	0.984019i	$0.443017\pi$
$774$	−19.5640	−	14.2141i	−0.703214	−	0.510915i
$775$	−6.43685	+	5.20950i	−0.231218	+	0.187131i
$776$	−7.09849	+	5.15736i	−0.254821	+	0.185138i
$777$	−5.16869	+	3.28015i	−0.185426	+	0.117675i
$778$	−3.18922	+	25.2453i	−0.114339	+	0.905086i
$779$	−26.3746	−	3.33189i	−0.944968	−	0.119377i
$780$	0.741581	+	8.32226i	0.0265529	+	0.297985i
$781$	−6.39992	−	3.51839i	−0.229007	−	0.125898i
$782$	21.4909	+	6.98281i	0.768512	+	0.249705i
$783$	−7.31352	+	3.44148i	−0.261364	+	0.122989i
$784$	2.91493	+	0.748427i	0.104105	+	0.0267295i
$785$	5.40299	+	18.9773i	0.192841	+	0.677329i
$786$	−1.47583	+	1.78397i	−0.0526411	+	0.0636321i
$787$	−0.882823	−	0.560256i	−0.0314692	−	0.0199710i	0.519999	−	0.854167i	$-0.325932\pi$
$787$	−0.882823	−	0.560256i	−0.0314692	−	0.0199710i	−0.551468	+	0.834196i	$0.685932\pi$
$788$	−15.6563	+	0.985013i	−0.557734	+	0.0350896i
$789$	8.76425	+	13.8103i	0.312016	+	0.491658i
$790$	−16.5041	−	9.88058i	−0.587188	−	0.351535i
$791$	0.764605	+	12.1530i	0.0271862	+	0.432113i
$792$	2.61785	+	0.499381i	0.0930211	+	0.0177447i
$793$	−6.33628	+	2.05878i	−0.225008	+	0.0731094i
$794$	−11.9855	+	11.2551i	−0.425350	+	0.399430i
$795$	−5.39588	−	15.2442i	−0.191372	−	0.540656i
$796$	0.530919	+	2.78318i	0.0188179	+	0.0986470i
$797$	−2.09321	+	2.22904i	−0.0741454	+	0.0789568i	−0.764972	−	0.644064i	$-0.777247\pi$
$797$	−2.09321	+	2.22904i	−0.0741454	+	0.0789568i	0.690826	+	0.723021i	$0.257247\pi$
$798$	−2.22077	+	5.60903i	−0.0786145	+	0.198557i
$799$	0.0142286	+	0.0437912i	0.000503373	+	0.00154922i
$800$	3.22835	−	3.81809i	0.114139	−	0.134990i
$801$	−13.8666	+	42.6770i	−0.489952	+	1.50792i
$802$	−18.5458	−	15.3424i	−0.654875	−	0.541759i
$803$	3.70556	+	1.74371i	0.130766	+	0.0615340i
$804$	−1.24510	−	1.16923i	−0.0439114	−	0.0412356i
$805$	−37.1897	−	3.71723i	−1.31076	−	0.131015i
$806$	9.74921	−	1.23161i	0.343401	−	0.0433817i
$807$			2.95406i			0.103988i
$808$	2.28954	+	18.1236i	0.0805457	+	0.637585i
$809$	3.92984	+	4.75035i	0.138166	+	0.167014i	0.835058	−	0.550163i	$-0.185434\pi$
$809$	3.92984	+	4.75035i	0.138166	+	0.167014i	−0.696892	+	0.717176i	$0.745434\pi$
$810$	−0.325355	−	12.4909i	−0.0114318	−	0.438885i
$811$	1.22104	−	19.4078i	0.0428764	−	0.681500i	−0.916617	−	0.399768i	$-0.869091\pi$
$811$	1.22104	−	19.4078i	0.0428764	−	0.681500i	0.959493	−	0.281733i	$-0.0909092\pi$
$812$	−1.13792	+	4.43191i	−0.0399332	+	0.155529i
$813$	0.111634	−	0.434787i	0.00391519	−	0.0152487i
$814$	0.312782	−	4.97152i	0.0109630	−	0.174252i
$815$	7.06133	+	9.20515i	0.247348	+	0.322442i
$816$	−1.08409	−	1.31044i	−0.0379507	−	0.0458745i
$817$	5.58275	+	44.1920i	0.195316	+	1.54608i
$818$			20.3043i			0.709922i
$819$	30.6143	−	3.86748i	1.06975	−	0.135141i
$820$	−4.98415	+	11.3499i	−0.174054	+	0.396357i
$821$	10.6699	+	10.0197i	0.372381	+	0.349689i	0.848032	−	0.529945i	$-0.177787\pi$
$821$	10.6699	+	10.0197i	0.372381	+	0.349689i	−0.475651	+	0.879634i	$0.657787\pi$
$822$	4.44454	+	2.09144i	0.155021	+	0.0729474i
$823$	8.58294	+	7.10042i	0.299182	+	0.247505i	0.774887	−	0.632100i	$-0.217807\pi$
$823$	8.58294	+	7.10042i	0.299182	+	0.247505i	−0.475704	+	0.879605i	$0.657807\pi$
$824$	5.65262	−	17.3970i	0.196918	−	0.606053i
$825$	0.167804	+	3.21894i	0.00584218	+	0.112069i
$826$	−5.46350	−	16.8149i	−0.190100	−	0.585066i
$827$	−17.8255	+	45.0221i	−0.619854	+	1.56557i	0.191801	+	0.981434i	$0.438567\pi$
$827$	−17.8255	+	45.0221i	−0.619854	+	1.56557i	−0.811654	+	0.584138i	$0.801433\pi$
$828$	14.9117	−	15.8794i	0.518218	−	0.551846i
$829$	2.35997	+	12.3714i	0.0819652	+	0.429677i	0.999488	+	0.0319937i	$0.0101856\pi$
$829$	2.35997	+	12.3714i	0.0819652	+	0.429677i	−0.917523	+	0.397683i	$0.869814\pi$
$830$	21.8788	−	16.7834i	0.759423	−	0.582559i
$831$	−7.34020	+	6.89290i	−0.254629	+	0.239112i
$832$	−5.64301	+	1.83352i	−0.195636	+	0.0635660i
$833$	−7.98355	−	1.52294i	−0.276614	−	0.0527669i
$834$	0.629981	+	10.0133i	0.0218145	+	0.346731i
$835$	−14.2704	−	33.4693i	−0.493847	−	1.15825i
$836$	−2.63034	−	4.14475i	−0.0909722	−	0.143349i
$837$	5.83267	−	0.366961i	0.201607	−	0.0126840i
$838$	24.2108	+	15.3646i	0.836348	+	0.530763i
$839$	14.5272	−	17.5603i	0.501534	−	0.606250i	−0.457616	−	0.889150i	$-0.651296\pi$
$839$	14.5272	−	17.5603i	0.501534	−	0.606250i	0.959149	+	0.282900i	$0.0912965\pi$
$840$	2.21341	+	1.73603i	0.0763698	+	0.0598986i
$841$	−23.0071	−	5.90723i	−0.793350	−	0.203698i
$842$	31.6329	−	14.8853i	1.09014	−	0.512982i
$843$	12.8997	+	4.19136i	0.444289	+	0.144358i
$844$	−0.506024	−	0.278189i	−0.0174181	−	0.00957566i
$845$	−48.3980	−	11.0917i	−1.66494	−	0.381565i
$846$	0.0440371	+	0.00556318i	0.00151403	+	0.000191266i
$847$	2.49170	−	19.7238i	0.0856157	−	0.677718i
$848$	9.69601	−	6.15328i	0.332962	−	0.211304i
$849$	15.9052	−	11.5558i	0.545864	−	0.396594i
$850$	−8.05394	+	10.8384i	−0.276248	+	0.371753i
$851$	−32.9400	−	23.9323i	−1.12917	−	0.820389i
$852$	4.48402	+	0.282111i	0.153620	+	0.00966496i
$853$	−3.61186	−	6.56995i	−0.123668	−	0.224951i	0.807225	−	0.590244i	$-0.200969\pi$
$853$	−3.61186	−	6.56995i	−0.123668	−	0.224951i	−0.930892	+	0.365293i	$0.880969\pi$
$854$	−0.955043	+	2.02957i	−0.0326809	+	0.0694504i
$855$	−19.8454	+	19.6332i	−0.678697	+	0.671441i
$856$	−2.37172	+	12.4330i	−0.0810638	+	0.424951i
$857$	−2.44173	−	3.36075i	−0.0834079	−	0.114801i	0.765274	−	0.643704i	$-0.222603\pi$
$857$	−2.44173	−	3.36075i	−0.0834079	−	0.114801i	−0.848682	+	0.528903i	$0.822603\pi$
$858$	1.84273	−	3.35191i	0.0629097	−	0.114432i
$859$	21.9887	−	34.6487i	0.750245	−	1.18220i	−0.227781	−	0.973712i	$-0.573147\pi$
$859$	21.9887	−	34.6487i	0.750245	−	1.18220i	0.978026	−	0.208485i	$-0.0668531\pi$
$860$	20.4968	+	3.35939i	0.698935	+	0.114554i
$861$	−6.48429	−	2.56731i	−0.220984	−	0.0874938i
$862$	−7.54815	−	19.0645i	−0.257091	−	0.649338i
$863$	1.60271	−	1.32587i	0.0545567	−	0.0451332i	−0.609746	−	0.792597i	$-0.708729\pi$
$863$	1.60271	−	1.32587i	0.0545567	−	0.0451332i	0.664303	+	0.747464i	$0.268729\pi$
$864$	−3.41790	+	0.877567i	−0.116279	+	0.0298554i
$865$	6.93552	−	1.51118i	0.235815	−	0.0513817i
$866$	21.6336	−	8.56535i	0.735140	−	0.291062i
$867$	−4.18445	−	4.45598i	−0.142111	−	0.151333i
$868$	1.94463	−	2.67655i	0.0660050	−	0.0908481i
$869$	3.74946	+	7.96801i	0.127192	+	0.270296i
$870$	1.99058	−	2.53796i	0.0674871	−	0.0860450i
$871$	14.1022	−	7.75276i	0.477836	−	0.262692i
$872$	1.70106	−	0.324494i	0.0576050	−	0.0109887i
$873$	−5.68080	−	22.1253i	−0.192266	−	0.748826i
$874$	−40.1242			−1.35722
$875$	9.19929	−	20.3516i	0.310993	−	0.688010i
$876$	−2.51939			−0.0851223
$877$	10.2078	+	39.7567i	0.344693	+	1.34249i	0.870619	+	0.491959i	$0.163719\pi$
$877$	10.2078	+	39.7567i	0.344693	+	1.34249i	−0.525926	+	0.850530i	$0.676281\pi$
$878$	−32.6590	+	6.23003i	−1.10219	+	0.210253i
$879$	12.4712	−	6.85611i	0.420644	−	0.231251i
$880$	−2.20152	+	0.626790i	−0.0742133	+	0.0211291i
$881$	2.11442	+	4.49336i	0.0712365	+	0.151385i	0.937274	−	0.348594i	$-0.113341\pi$
$881$	2.11442	+	4.49336i	0.0712365	+	0.151385i	−0.866037	+	0.499979i	$0.833341\pi$
$882$	−4.60524	+	6.33858i	−0.155067	+	0.213431i
$883$	−11.8593	−	12.6289i	−0.399098	−	0.424996i	0.497760	−	0.867315i	$-0.334156\pi$
$883$	−11.8593	−	12.6289i	−0.399098	−	0.424996i	−0.896858	+	0.442319i	$0.854156\pi$
$884$	14.8987	−	5.89883i	0.501099	−	0.198399i
$885$	−1.23956	+	12.4014i	−0.0416672	+	0.416868i
$886$	−4.00990	+	1.02957i	−0.134715	+	0.0345890i
$887$	11.2087	−	9.27262i	0.376350	−	0.311344i	−0.429947	−	0.902854i	$-0.641468\pi$
$887$	11.2087	−	9.27262i	0.376350	−	0.311344i	0.806298	+	0.591510i	$0.201468\pi$
$888$	1.12810	+	2.84926i	0.0378567	+	0.0956150i
$889$	−14.7156	−	5.82633i	−0.493547	−	0.195409i
$890$	−5.82456	−	38.0990i	−0.195240	−	1.27708i
$891$	−3.06509	+	4.82980i	−0.102684	+	0.161805i
$892$	1.73523	−	3.15637i	0.0580997	−	0.105683i
$893$	−0.0480571	−	0.0661449i	−0.00160817	−	0.00221346i
$894$	−1.92285	+	10.0799i	−0.0643097	+	0.337123i
$895$	5.71525	−	34.8707i	0.191040	−	1.16560i
$896$	−0.850549	+	1.80751i	−0.0284149	+	0.0603846i
$897$	−15.0619	−	27.3975i	−0.502903	−	0.914777i
$898$	−2.87437	−	0.180840i	−0.0959190	−	0.00603471i
$899$	−3.06902	−	2.22977i	−0.102358	−	0.0743671i
$900$	6.14805	+	11.4737i	0.204935	+	0.382456i
$901$	−25.0903	+	18.2292i	−0.835880	+	0.607302i
$902$	4.79152	−	3.04079i	0.159540	−	0.101247i
$903$	−1.46456	+	11.5932i	−0.0487376	+	0.385798i
$904$	6.04770	+	0.764002i	0.201143	+	0.0254103i
$905$	−29.4492	−	33.7677i	−0.978926	−	1.12248i
$906$	5.28435	+	2.90510i	0.175561	+	0.0965154i
$907$	21.8077	+	7.08574i	0.724112	+	0.235278i	0.647805	−	0.761806i	$-0.275687\pi$
$907$	21.8077	+	7.08574i	0.724112	+	0.235278i	0.0763068	+	0.997084i	$0.475687\pi$
$908$	7.92594	−	3.72967i	0.263032	−	0.123773i
$909$	−46.0640	−	11.8272i	−1.52785	−	0.392284i
$910$	−22.0003	+	14.7792i	−0.729304	+	0.489925i
$911$	27.6022	−	33.3653i	0.914501	−	1.10544i	−0.0795835	−	0.996828i	$-0.525359\pi$
$911$	27.6022	−	33.3653i	0.914501	−	1.10544i	0.994084	−	0.108613i	$-0.0346410\pi$
$912$	2.54980	+	1.61815i	0.0844322	+	0.0535823i
$913$	−12.5988	+	0.792650i	−0.416960	+	0.0262329i
$914$	6.82314	+	10.7516i	0.225690	+	0.355630i
$915$	1.19165	−	1.03926i	0.0393949	−	0.0343567i
$916$	0.142378	+	2.26304i	0.00470431	+	0.0747729i
$917$	−7.21425	−	1.37619i	−0.238236	−	0.0454459i
$918$	9.06348	−	2.94490i	0.299139	−	0.0971963i
$919$	−41.8490	+	39.2988i	−1.38047	+	1.29635i	−0.470065	+	0.882632i	$0.655770\pi$
$919$	−41.8490	+	39.2988i	−1.38047	+	1.29635i	−0.910406	+	0.413717i	$0.864230\pi$
$920$	−5.31632	+	17.9385i	−0.175274	+	0.591414i
$921$	−3.65799	−	19.1759i	−0.120535	−	0.631866i
$922$	−22.3975	+	23.8509i	−0.737622	+	0.785487i
$923$	−15.5831	+	39.3585i	−0.512926	+	1.29550i
$924$	−0.397951	−	1.22477i	−0.0130916	−	0.0402919i
$925$	19.8365	−	14.0888i	0.652221	−	0.463238i
$926$	−3.20480	+	9.86336i	−0.105316	+	0.324130i
$927$	36.6936	+	30.3556i	1.20518	+	0.997009i
$928$	2.07255	+	0.975267i	0.0680347	+	0.0320147i
$929$	−14.3863	−	13.5096i	−0.471999	−	0.443236i	0.411681	−	0.911328i	$-0.364942\pi$
$929$	−14.3863	−	13.5096i	−0.471999	−	0.443236i	−0.883680	+	0.468092i	$0.844942\pi$
$930$	−2.01374	+	1.17636i	−0.0660330	+	0.0385743i
$931$	14.3178	−	1.80876i	0.469248	−	0.0592799i
$932$			6.02860i			0.197473i
$933$	−1.34019	−	10.6087i	−0.0438758	−	0.347313i
$934$	2.85408	+	3.44999i	0.0933883	+	0.112887i
$935$	5.82749	−	2.06272i	0.190579	−	0.0674580i
$936$	0.969932	−	15.4166i	0.0317032	−	0.503908i
$937$	5.92121	−	23.0616i	0.193437	−	0.753389i	−0.795612	−	0.605806i	$-0.792851\pi$
$937$	5.92121	−	23.0616i	0.193437	−	0.753389i	0.989050	−	0.147583i	$-0.0471493\pi$
$938$	1.34741	−	5.24782i	0.0439945	−	0.171347i
$939$	−0.597543	+	9.49767i	−0.0195001	+	0.309945i
$940$	−0.0359391	+	0.0127211i	−0.00117220	+	0.000414917i
$941$	26.0295	+	31.4643i	0.848538	+	1.02571i	0.999310	+	0.0371378i	$0.0118240\pi$
$941$	26.0295	+	31.4643i	0.848538	+	1.02571i	−0.150772	+	0.988569i	$0.548176\pi$
$942$	0.696482	+	5.51322i	0.0226926	+	0.179631i
$943$		−	46.3854i		−	1.51051i
$944$	−8.78083	+	1.10928i	−0.285792	+	0.0361039i
$945$	−13.6103	+	7.95068i	−0.442742	+	0.258636i
$946$	−6.93152	−	6.50913i	−0.225363	−	0.211630i
$947$	−8.93651	−	4.20520i	−0.290397	−	0.136651i	0.275063	−	0.961426i	$-0.411301\pi$
$947$	−8.93651	−	4.20520i	−0.290397	−	0.136651i	−0.565460	+	0.824776i	$0.691301\pi$
$948$	−4.17418	−	3.45318i	−0.135571	−	0.112154i
$949$	7.33521	−	22.5755i	0.238111	−	0.732830i
$950$	7.65398	−	22.7225i	0.248328	−	0.737216i
$951$	0.772078	+	2.37621i	0.0250363	+	0.0770539i
$952$	1.98599	−	5.01603i	0.0643662	−	0.162570i
$953$	0.794097	−	0.845628i	0.0257233	−	0.0273926i	−0.715978	−	0.698123i	$-0.754019\pi$
$953$	0.794097	−	0.845628i	0.0257233	−	0.0273926i	0.741702	+	0.670730i	$0.234019\pi$
$954$	5.60211	+	29.3673i	0.181375	+	0.950800i
$955$	2.88733	−	9.74252i	0.0934319	−	0.315261i
$956$	3.62088	−	3.40023i	0.117108	−	0.109971i
$957$	−1.40436	+	0.456303i	−0.0453964	+	0.0147502i
$958$	−6.49290	−	1.23859i	−0.209776	−	0.0400169i
$959$	0.978364	+	15.5506i	0.0315930	+	0.502156i
$960$	1.06127	−	0.925548i	0.0342524	−	0.0298719i
$961$	−15.1409	−	23.8583i	−0.488417	−	0.769622i
$962$	−28.8158	+	1.81294i	−0.929059	+	0.0584515i
$963$	−27.8222	−	17.6565i	−0.896558	−	0.568973i
$964$	−5.51639	+	6.66817i	−0.177671	+	0.214767i
$965$	−4.93664	+	3.31629i	−0.158916	+	0.106755i
$966$	−10.1954	−	2.61773i	−0.328031	−	0.0842239i
$967$	26.1614	−	12.3106i	0.841294	−	0.395883i	0.0436762	−	0.999046i	$-0.486093\pi$
$967$	26.1614	−	12.3106i	0.841294	−	0.395883i	0.797618	+	0.603163i	$0.206093\pi$
$968$	−9.46500	−	3.07536i	−0.304217	−	0.0988459i
$969$	−7.14689	−	3.92903i	−0.229591	−	0.126219i
$970$	12.8955	+	14.7865i	0.414049	+	0.474766i
$971$	−15.2531	−	1.92692i	−0.489496	−	0.0618378i	−0.123289	−	0.992371i	$-0.539344\pi$
$971$	−15.2531	−	1.92692i	−0.489496	−	0.0618378i	−0.366208	+	0.930533i	$0.619344\pi$
$972$	1.76787	−	13.9941i	0.0567044	−	0.448861i
$973$	−26.8714	+	17.0531i	−0.861457	+	0.546697i
$974$	−13.3227	+	9.67949i	−0.426886	+	0.310151i
$975$	18.3885	−	3.30336i	0.588904	−	0.105792i
$976$	0.908408	+	0.659997i	0.0290774	+	0.0211260i
$977$	15.0139	+	0.944593i	0.480336	+	0.0302202i	0.301113	−	0.953588i	$-0.402642\pi$
$977$	15.0139	+	0.944593i	0.480336	+	0.0302202i	0.179223	+	0.983809i	$0.442642\pi$
$978$	1.57408	+	2.86325i	0.0503336	+	0.0915565i
$979$	−7.51263	+	15.9651i	−0.240105	+	0.510248i
$980$	1.08842	−	6.64079i	0.0347682	−	0.212132i
$981$	−0.844791	+	4.42855i	−0.0269721	+	0.141393i
$982$	−20.5726	−	28.3158i	−0.656498	−	0.903593i
$983$	22.4171	−	40.7766i	0.714996	−	1.30057i	−0.229905	−	0.973213i	$-0.573841\pi$
$983$	22.4171	−	40.7766i	0.714996	−	1.30057i	0.944900	−	0.327359i	$-0.106159\pi$
$984$	−1.87065	+	2.94768i	−0.0596343	+	0.0939686i
$985$	5.30110	+	34.6750i	0.168907	+	1.10484i
$986$	−5.75154	−	2.27719i	−0.183166	−	0.0725206i
$987$	−0.00789575	−	0.0199424i	−0.000251325	−	0.000634773i
$988$	−21.9235	+	18.1367i	−0.697478	+	0.577004i
$989$	−75.2793	+	19.3284i	−2.39374	+	0.614609i
$990$	0.592691	−	5.92969i	0.0188369	−	0.188458i
$991$	−48.5003	+	19.2026i	−1.54066	+	0.609992i	−0.976471	−	0.215651i	$-0.930813\pi$
$991$	−48.5003	+	19.2026i	−1.54066	+	0.609992i	−0.564193	+	0.825643i	$0.690813\pi$
$992$	−1.13372	−	1.20729i	−0.0359957	−	0.0383315i
$993$	−4.34120	+	5.97515i	−0.137764	+	0.189616i
$994$	6.06814	+	12.8955i	0.192470	+	0.409019i
$995$	6.09344	−	1.73485i	0.193175	−	0.0549984i
$996$	6.80536	−	3.74128i	0.215636	−	0.118547i
$997$	−3.85719	+	0.735799i	−0.122159	+	0.0233030i	−0.248098	−	0.968735i	$-0.579805\pi$
$997$	−3.85719	+	0.735799i	−0.122159	+	0.0233030i	0.125939	+	0.992038i	$0.459805\pi$
$998$	−3.58715	−	13.9710i	−0.113549	−	0.442246i
$999$	−17.1714			−0.543280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.229.3	yes	240
125.119	even	50	inner	250.2.h.a.119.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.119.3	✓	240	125.119	even	50	inner
250.2.h.a.229.3	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.618597 + 0.118004i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.24690 + 1.85614i) q^{5} +(0.268135 + 0.569817i) q^{6} +(-1.17418 + 1.61612i) q^{7} +(0.684547 + 0.728969i) q^{8} +(-2.42059 + 0.958380i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.618597 + 0.118004i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.24690 + 1.85614i) q^{5} +(0.268135 + 0.569817i) q^{6} +(-1.17418 + 1.61612i) q^{7} +(0.684547 + 0.728969i) q^{8} +(-2.42059 + 0.958380i) q^{9} +(1.48773 - 1.66933i) q^{10} +(-0.991515 + 0.254578i) q^{11} +(0.485232 - 0.401419i) q^{12} +(2.18423 + 5.51674i) q^{13} +(1.85735 + 0.735376i) q^{14} +(-0.990360 - 1.00106i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.30104 + 2.36659i) q^{17} +(1.53025 + 2.10620i) q^{18} +(0.898568 - 4.71046i) q^{19} +(-1.98687 - 1.02585i) q^{20} +(0.535635 - 1.13828i) q^{21} +(0.493160 + 0.897054i) q^{22} +(8.35072 + 0.525382i) q^{23} +(-0.509480 - 0.370159i) q^{24} +(-1.89049 + 4.62883i) q^{25} +(4.80023 - 3.48757i) q^{26} +(2.97943 - 1.89080i) q^{27} +(0.250369 - 1.98188i) q^{28} +(-2.27248 - 0.287081i) q^{29} +(-0.723320 + 1.20820i) q^{30} +(1.45131 + 0.797863i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(0.583308 - 0.274484i) q^{33} +(2.61579 + 0.671621i) q^{34} +(-4.46381 - 0.164299i) q^{35} +(1.65948 - 2.00596i) q^{36} +(-4.10862 - 2.60741i) q^{37} +(-4.78594 + 0.301106i) q^{38} +(-2.00216 - 3.15490i) q^{39} +(-0.499504 + 2.17956i) q^{40} +(-0.348091 - 5.53276i) q^{41} +(-1.23573 - 0.235728i) q^{42} +(-8.83413 + 2.87038i) q^{43} +(0.746228 - 0.700754i) q^{44} +(-4.79712 - 3.29795i) q^{45} +(-1.56786 - 8.21902i) q^{46} +(0.0116713 - 0.0124286i) q^{47} +(-0.231827 + 0.585529i) q^{48} +(0.929980 + 2.86218i) q^{49} +(4.95355 + 0.679949i) q^{50} +(0.525555 - 1.61749i) q^{51} +(-4.57177 - 3.78210i) q^{52} +(10.3908 + 4.88952i) q^{53} +(-2.57236 - 2.41560i) q^{54} +(-1.70885 - 1.52296i) q^{55} +(-1.98188 + 0.250369i) q^{56} +3.01991i q^{57} +(0.287081 + 2.27248i) q^{58} +(-5.64160 - 6.81952i) q^{59} +(1.35012 + 0.400128i) q^{60} +(-0.0705046 + 1.12064i) q^{61} +(0.411871 - 1.60413i) q^{62} +(1.29335 - 5.03726i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-7.51631 + 10.9331i) q^{65} +(-0.410923 - 0.496721i) q^{66} +(-0.339933 - 2.69085i) q^{67} -2.70064i q^{68} +(-5.22773 + 0.660416i) q^{69} +(0.950967 + 4.36443i) q^{70} +(5.20074 + 4.88382i) q^{71} +(-2.35564 - 1.10848i) q^{72} +(-3.08252 - 2.55008i) q^{73} +(-1.50372 + 4.62797i) q^{74} +(0.623230 - 3.08647i) q^{75} +(1.48186 + 4.56069i) q^{76} +(0.752787 - 1.90132i) q^{77} +(-2.55786 + 2.72385i) q^{78} +(-1.61194 - 8.45006i) q^{79} +(2.23531 - 0.0582240i) q^{80} +(4.07347 - 3.82524i) q^{81} +(-5.27237 + 1.71310i) q^{82} +(12.1133 + 2.31074i) q^{83} +(0.0789912 + 1.25553i) q^{84} +(-6.01498 + 0.535983i) q^{85} +(4.97716 + 7.84275i) q^{86} +(1.43963 - 0.0905738i) q^{87} +(-0.864318 - 0.548513i) q^{88} +(10.9869 - 13.2808i) q^{89} +(-2.00134 + 5.46657i) q^{90} +(-11.4804 - 2.94766i) q^{91} +(-7.57089 + 3.56259i) q^{92} +(-0.991926 - 0.322296i) q^{93} +(-0.0149407 - 0.00821371i) q^{94} +(9.86368 - 4.20560i) q^{95} +(0.624786 + 0.0789289i) q^{96} +(-1.09970 + 8.70503i) q^{97} +(2.54099 - 1.61256i) q^{98} +(2.15607 - 1.56648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 10 q^{5}+O(q^{10}) \) 240 * q + 10 * q^5	\( 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) \) 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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