LMFDB - Embedded newform 483.2.bf.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(10,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	483.61
Dual form			483.2.bf.a.388.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93407 - 1.52097i) q^{2} +(0.814576 + 0.580057i) q^{3} +(0.955758 + 3.93969i) q^{4} +(2.26903 - 0.437319i) q^{5} +(-0.693197 - 2.36081i) q^{6} +(2.27494 - 1.35080i) q^{7} +(2.09940 - 4.59704i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(-1.93407 - 1.52097i) q^{2} +(0.814576 + 0.580057i) q^{3} +(0.955758 + 3.93969i) q^{4} +(2.26903 - 0.437319i) q^{5} +(-0.693197 - 2.36081i) q^{6} +(2.27494 - 1.35080i) q^{7} +(2.09940 - 4.59704i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-5.05360 - 2.60531i) q^{10} +(-3.37740 - 4.29472i) q^{11} +(-1.50671 + 3.76357i) q^{12} +(1.63226 + 2.53985i) q^{13} +(-6.45440 - 0.847579i) q^{14} +(2.10196 + 0.959935i) q^{15} +(-3.84571 + 1.98260i) q^{16} +(2.54757 + 2.42911i) q^{17} +(0.804744 - 2.32516i) q^{18} +(-0.307530 + 0.293230i) q^{19} +(3.89154 + 8.52128i) q^{20} +(2.63665 + 0.219269i) q^{21} +13.4432i q^{22} +(1.29572 - 4.61748i) q^{23} +(4.37666 - 2.52687i) q^{24} +(0.315393 - 0.126264i) q^{25} +(0.706122 - 7.39485i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(7.49600 + 7.67152i) q^{28} +(8.46859 - 2.48660i) q^{29} +(-2.60531 - 5.05360i) q^{30} +(0.321182 + 3.36357i) q^{31} +(0.528522 + 0.101864i) q^{32} +(-0.259971 - 5.45746i) q^{33} +(-1.23259 - 8.57283i) q^{34} +(4.57117 - 4.05987i) q^{35} +(-3.41041 + 2.19174i) q^{36} +(4.10018 - 1.41909i) q^{37} +(1.04078 - 0.0993822i) q^{38} +(-0.143656 + 3.01570i) q^{39} +(2.75321 - 11.3489i) q^{40} +(-6.43137 + 5.57281i) q^{41} +(-4.76596 - 4.43434i) q^{42} +(-0.852373 + 0.389266i) q^{43} +(13.6919 - 17.4106i) q^{44} +(1.15539 + 2.00120i) q^{45} +(-9.52904 + 6.95978i) q^{46} +(-3.54815 - 2.04853i) q^{47} +(-4.28264 - 0.615751i) q^{48} +(3.35070 - 6.14596i) q^{49} +(-0.802036 - 0.235499i) q^{50} +(0.666172 + 3.45643i) q^{51} +(-8.44615 + 8.85807i) q^{52} +(5.08321 + 0.242143i) q^{53} +(2.00425 - 1.42722i) q^{54} +(-9.54158 - 8.26782i) q^{55} +(-1.43366 - 13.2938i) q^{56} +(-0.420597 + 0.0604727i) q^{57} +(-20.1609 - 8.07120i) q^{58} +(-2.72684 + 5.28934i) q^{59} +(-1.77287 + 9.19855i) q^{60} +(-3.60032 - 5.05594i) q^{61} +(4.49470 - 6.99388i) q^{62} +(2.02056 + 1.70802i) q^{63} +(4.79948 + 5.53890i) q^{64} +(4.81436 + 5.04916i) q^{65} +(-7.79782 + 10.9505i) q^{66} +(-1.94424 - 4.85649i) q^{67} +(-7.13506 + 12.3583i) q^{68} +(3.73386 - 3.00970i) q^{69} +(-15.0159 + 0.899454i) q^{70} +(1.96863 - 13.6922i) q^{71} +(5.03085 + 0.480388i) q^{72} +(-7.99707 + 1.94007i) q^{73} +(-10.0884 - 3.49164i) q^{74} +(0.330152 + 0.0800941i) q^{75} +(-1.44916 - 0.931317i) q^{76} +(-13.4847 - 5.20804i) q^{77} +(4.86462 - 5.61408i) q^{78} +(14.1029 - 0.671805i) q^{79} +(-7.85898 + 6.18037i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(20.9148 - 0.996294i) q^{82} +(1.19745 - 1.38193i) q^{83} +(1.65615 + 10.5971i) q^{84} +(6.84281 + 4.39760i) q^{85} +(2.24061 + 0.543565i) q^{86} +(8.34068 + 2.88674i) q^{87} +(-26.8335 + 6.50973i) q^{88} +(7.77947 + 0.742850i) q^{89} +(0.809151 - 5.62777i) q^{90} +(7.14411 + 3.57315i) q^{91} +(19.4298 + 0.691521i) q^{92} +(-1.68944 + 2.92619i) q^{93} +(3.74663 + 9.35862i) q^{94} +(-0.569560 + 0.799835i) q^{95} +(0.371434 + 0.389549i) q^{96} +(0.0813483 + 0.0938809i) q^{97} +(-15.8283 + 6.79039i) q^{98} +(2.95387 - 4.59631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−1.93407	−	1.52097i	−1.36759	−	1.07549i	−0.988678	−	0.150055i	$-0.952055\pi$
$2$	−1.93407	−	1.52097i	−1.36759	−	1.07549i	−0.378915	−	0.925432i	$-0.623703\pi$
$3$	0.814576	+	0.580057i	0.470296	+	0.334896i
$3$	0.814576	+	0.580057i	0.470296	+	0.334896i
$4$	0.955758	+	3.93969i	0.477879	+	1.96984i
$5$	2.26903	−	0.437319i	1.01474	−	0.195575i	0.345340	−	0.938478i	$-0.387764\pi$
$5$	2.26903	−	0.437319i	1.01474	−	0.195575i	0.669399	+	0.742903i	$0.266551\pi$
$6$	−0.693197	−	2.36081i	−0.282997	−	0.963798i
$7$	2.27494	−	1.35080i	0.859846	−	0.510553i
$7$	2.27494	−	1.35080i	0.859846	−	0.510553i
$8$	2.09940	−	4.59704i	0.742248	−	1.62530i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	−5.05360	−	2.60531i	−1.59809	−	0.823872i
$11$	−3.37740	−	4.29472i	−1.01833	−	1.29491i	−0.954903	−	0.296919i	$-0.904041\pi$
$11$	−3.37740	−	4.29472i	−1.01833	−	1.29491i	−0.0634228	−	0.997987i	$-0.520202\pi$
$12$	−1.50671	+	3.76357i	−0.434948	+	1.08645i
$13$	1.63226	+	2.53985i	0.452707	+	0.704427i	0.990326	−	0.138762i	$-0.0443122\pi$
$13$	1.63226	+	2.53985i	0.452707	+	0.704427i	−0.537618	+	0.843188i	$0.680676\pi$
$14$	−6.45440	−	0.847579i	−1.72501	−	0.226525i
$15$	2.10196	+	0.959935i	0.542725	+	0.247854i
$16$	−3.84571	+	1.98260i	−0.961427	+	0.495650i
$17$	2.54757	+	2.42911i	0.617877	+	0.589145i	0.932987	−	0.359910i	$-0.117193\pi$
$17$	2.54757	+	2.42911i	0.617877	+	0.589145i	−0.315109	+	0.949055i	$0.602041\pi$
$18$	0.804744	−	2.32516i	0.189680	−	0.548044i
$19$	−0.307530	+	0.293230i	−0.0705523	+	0.0672715i	−0.724535	−	0.689238i	$-0.757945\pi$
$19$	−0.307530	+	0.293230i	−0.0705523	+	0.0672715i	0.653983	+	0.756510i	$0.273097\pi$
$20$	3.89154	+	8.52128i	0.870175	+	1.90542i
$21$	2.63665	+	0.219269i	0.575364	+	0.0478484i
$22$			13.4432i			2.86610i
$23$	1.29572	−	4.61748i	0.270175	−	0.962811i
$23$	1.29572	−	4.61748i	0.270175	−	0.962811i
$24$	4.37666	−	2.52687i	0.893382	−	0.515794i
$25$	0.315393	−	0.126264i	0.0630786	−	0.0252529i
$26$	0.706122	−	7.39485i	0.138482	−	1.45025i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	7.49600	+	7.67152i	1.41661	+	1.44978i
$29$	8.46859	−	2.48660i	1.57258	−	0.461751i	0.624827	−	0.780763i	$-0.285169\pi$
$29$	8.46859	−	2.48660i	1.57258	−	0.461751i	0.947751	+	0.319012i	$0.103351\pi$
$30$	−2.60531	−	5.05360i	−0.475663	−	0.922657i
$31$	0.321182	+	3.36357i	0.0576860	+	0.604115i	0.977382	+	0.211483i	$0.0678293\pi$
$31$	0.321182	+	3.36357i	0.0576860	+	0.604115i	−0.919696	+	0.392632i	$0.871565\pi$
$32$	0.528522	+	0.101864i	0.0934304	+	0.0180072i
$33$	−0.259971	−	5.45746i	−0.0452551	−	0.950022i
$34$	−1.23259	−	8.57283i	−0.211387	−	1.47023i
$35$	4.57117	−	4.05987i	0.772669	−	0.686243i
$36$	−3.41041	+	2.19174i	−0.568402	+	0.365290i
$37$	4.10018	−	1.41909i	0.674066	−	0.233297i	0.0314736	−	0.999505i	$-0.489980\pi$
$37$	4.10018	−	1.41909i	0.674066	−	0.233297i	0.642593	+	0.766208i	$0.277859\pi$
$38$	1.04078	−	0.0993822i	0.168836	−	0.0161219i
$39$	−0.143656	+	3.01570i	−0.0230033	+	0.482899i
$40$	2.75321	−	11.3489i	0.435321	−	1.79442i
$41$	−6.43137	+	5.57281i	−1.00441	+	0.870327i	−0.991568	−	0.129590i	$-0.958634\pi$
$41$	−6.43137	+	5.57281i	−1.00441	+	0.870327i	−0.0128438	+	0.999918i	$0.504088\pi$
$42$	−4.76596	−	4.43434i	−0.735403	−	0.684233i
$43$	−0.852373	+	0.389266i	−0.129986	+	0.0593624i	−0.479346	−	0.877626i	$-0.659126\pi$
$43$	−0.852373	+	0.389266i	−0.129986	+	0.0593624i	0.349360	+	0.936988i	$0.386399\pi$
$44$	13.6919	−	17.4106i	2.06413	−	2.62475i
$45$	1.15539	+	2.00120i	0.172236	+	0.298321i
$46$	−9.52904	+	6.95978i	−1.40498	+	1.02616i
$47$	−3.54815	−	2.04853i	−0.517552	−	0.298809i	0.218381	−	0.975864i	$-0.429923\pi$
$47$	−3.54815	−	2.04853i	−0.517552	−	0.298809i	−0.735932	+	0.677055i	$0.763256\pi$
$48$	−4.28264	−	0.615751i	−0.618146	−	0.0888760i
$49$	3.35070	−	6.14596i	0.478672	−	0.877994i
$50$	−0.802036	−	0.235499i	−0.113425	−	0.0333046i
$51$	0.666172	+	3.45643i	0.0932828	+	0.483997i
$52$	−8.44615	+	8.85807i	−1.17127	+	1.22839i
$53$	5.08321	+	0.242143i	0.698232	+	0.0332609i	0.393697	−	0.919240i	$-0.371196\pi$
$53$	5.08321	+	0.242143i	0.698232	+	0.0332609i	0.304535	+	0.952501i	$0.401499\pi$
$54$	2.00425	−	1.42722i	0.272744	−	0.194220i
$55$	−9.54158	−	8.26782i	−1.28659	−	1.11483i
$56$	−1.43366	−	13.2938i	−0.191581	−	1.77646i
$57$	−0.420597	+	0.0604727i	−0.0557094	+	0.00800980i
$58$	−20.1609	−	8.07120i	−2.64725	−	1.05980i
$59$	−2.72684	+	5.28934i	−0.355005	+	0.688613i	−0.996942	−	0.0781439i	$-0.975101\pi$
$59$	−2.72684	+	5.28934i	−0.355005	+	0.688613i	0.641937	+	0.766757i	$0.278131\pi$
$60$	−1.77287	+	9.19855i	−0.228877	+	1.18753i
$61$	−3.60032	−	5.05594i	−0.460974	−	0.647347i	0.517022	−	0.855972i	$-0.327041\pi$
$61$	−3.60032	−	5.05594i	−0.460974	−	0.647347i	−0.977996	+	0.208625i	$0.933101\pi$
$62$	4.49470	−	6.99388i	0.570827	−	0.888224i
$63$	2.02056	+	1.70802i	0.254567	+	0.215190i
$64$	4.79948	+	5.53890i	0.599935	+	0.692362i
$65$	4.81436	+	5.04916i	0.597148	+	0.626271i
$66$	−7.79782	+	10.9505i	−0.959845	+	1.34791i
$67$	−1.94424	−	4.85649i	−0.237527	−	0.593314i	0.760930	−	0.648833i	$-0.224743\pi$
$67$	−1.94424	−	4.85649i	−0.237527	−	0.593314i	−0.998458	+	0.0555192i	$0.982319\pi$
$68$	−7.13506	+	12.3583i	−0.865253	+	1.49866i
$69$	3.73386	−	3.00970i	0.449504	−	0.362325i
$70$	−15.0159	+	0.899454i	−1.79474	+	0.107505i
$71$	1.96863	−	13.6922i	0.233634	−	1.62496i	−0.448535	−	0.893765i	$-0.648054\pi$
$71$	1.96863	−	13.6922i	0.233634	−	1.62496i	0.682169	−	0.731194i	$-0.261037\pi$
$72$	5.03085	+	0.480388i	0.592891	+	0.0566142i
$73$	−7.99707	+	1.94007i	−0.935987	+	0.227068i	−0.674615	−	0.738170i	$-0.735690\pi$
$73$	−7.99707	+	1.94007i	−0.935987	+	0.227068i	−0.261372	+	0.965238i	$0.584175\pi$
$74$	−10.0884	−	3.49164i	−1.17276	−	0.405895i
$75$	0.330152	+	0.0800941i	0.0381227	+	0.00924847i
$76$	−1.44916	−	0.931317i	−0.166230	−	0.106829i
$77$	−13.4847	−	5.20804i	−1.53672	−	0.593511i
$78$	4.86462	−	5.61408i	0.550810	−	0.635669i
$79$	14.1029	−	0.671805i	1.58670	−	0.0755840i	0.764442	−	0.644693i	$-0.223015\pi$
$79$	14.1029	−	0.671805i	1.58670	−	0.0755840i	0.822262	+	0.569109i	$0.192712\pi$
$80$	−7.85898	+	6.18037i	−0.878661	+	0.690987i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	20.9148	−	0.996294i	2.30965	−	0.110022i
$83$	1.19745	−	1.38193i	0.131437	−	0.151687i	−0.686216	−	0.727398i	$-0.740729\pi$
$83$	1.19745	−	1.38193i	0.131437	−	0.151687i	0.817653	+	0.575712i	$0.195275\pi$
$84$	1.65615	+	10.5971i	0.180701	+	1.15624i
$85$	6.84281	+	4.39760i	0.742207	+	0.476987i
$86$	2.24061	+	0.543565i	0.241611	+	0.0586142i
$87$	8.34068	+	2.88674i	0.894215	+	0.309491i
$88$	−26.8335	+	6.50973i	−2.86046	+	0.693940i
$89$	7.77947	+	0.742850i	0.824623	+	0.0787419i	0.498831	−	0.866700i	$-0.333763\pi$
$89$	7.77947	+	0.742850i	0.824623	+	0.0787419i	0.325792	+	0.945441i	$0.394369\pi$
$90$	0.809151	−	5.62777i	0.0852920	−	0.593219i
$91$	7.14411	+	3.57315i	0.748906	+	0.374568i
$92$	19.4298	+	0.691521i	2.02570	+	0.0720960i
$93$	−1.68944	+	2.92619i	−0.175186	+	0.303432i
$94$	3.74663	+	9.35862i	0.386435	+	0.965268i
$95$	−0.569560	+	0.799835i	−0.0584356	+	0.0820613i
$96$	0.371434	+	0.389549i	0.0379093	+	0.0397582i
$97$	0.0813483	+	0.0938809i	0.00825967	+	0.00953216i	0.759864	−	0.650082i	$-0.225265\pi$
$97$	0.0813483	+	0.0938809i	0.00825967	+	0.00953216i	−0.751605	+	0.659614i	$0.770720\pi$
$98$	−15.8283	+	6.79039i	−1.59890	+	0.685933i
$99$	2.95387	−	4.59631i	0.296875	−	0.461947i
$100$	0.798882	+	1.12187i	0.0798882	+	0.112187i
$101$	−2.58505	+	13.4125i	−0.257222	+	1.33459i	0.591735	+	0.806132i	$0.298443\pi$
$101$	−2.58505	+	13.4125i	−0.257222	+	1.33459i	−0.848957	+	0.528462i	$0.822769\pi$
$102$	3.96870	−	7.69820i	0.392959	−	0.762235i
$103$	1.66031	+	0.664688i	0.163595	+	0.0654936i	0.452015	−	0.892011i	$-0.350705\pi$
$103$	1.66031	+	0.664688i	0.163595	+	0.0654936i	−0.288419	+	0.957504i	$0.593130\pi$
$104$	15.1025	−	2.17141i	1.48092	−	0.212925i
$105$	6.07852	−	0.655530i	0.593203	−	0.0639732i
$106$	−9.46297	−	8.19971i	−0.919125	−	0.796427i
$107$	−9.33808	+	6.64962i	−0.902746	+	0.642843i	−0.934234	−	0.356661i	$-0.883915\pi$
$107$	−9.33808	+	6.64962i	−0.902746	+	0.642843i	0.0314874	+	0.999504i	$0.489976\pi$
$108$	−4.04937	−	0.192895i	−0.389651	−	0.0185614i
$109$	10.1661	−	10.6619i	0.973733	−	1.02122i	−0.0260349	−	0.999661i	$-0.508288\pi$
$109$	10.1661	−	10.6619i	0.973733	−	1.02122i	0.999768	−	0.0215604i	$-0.00686342\pi$
$110$	5.87897	+	30.5030i	0.560537	+	2.90834i
$111$	4.16306	+	1.22239i	0.395141	+	0.116024i
$112$	−6.07066	+	9.70506i	−0.573624	+	0.917042i
$113$	−16.8043	−	2.41609i	−1.58081	−	0.227287i	−0.704741	−	0.709464i	$-0.748937\pi$
$113$	−16.8043	−	2.41609i	−1.58081	−	0.227287i	−0.876074	+	0.482178i	$0.839846\pi$
$114$	0.905440	+	0.522756i	0.0848022	+	0.0489606i
$115$	0.920701	−	11.0438i	0.0858558	−	1.02984i
$116$	17.8904	+	30.9870i	1.66108	+	2.87707i
$117$	−1.86630	+	2.37319i	−0.172539	+	0.219401i
$118$	13.3188	−	6.08250i	1.22610	−	0.559939i
$119$	9.07680	+	2.08482i	0.832069	+	0.191115i
$120$	8.82571	−	7.64752i	0.805673	−	0.698120i
$121$	−4.44440	+	18.3201i	−0.404036	+	1.66546i
$122$	−0.726662	+	15.2545i	−0.0657889	+	1.38108i
$123$	−8.47139	+	0.808920i	−0.763840	+	0.0729378i
$124$	−12.9444	+	4.48012i	−1.16245	+	0.402326i
$125$	−9.05936	+	5.82210i	−0.810294	+	0.520744i
$126$	−1.31007	−	6.37663i	−0.116710	−	0.568076i
$127$	1.28401	+	8.93050i	0.113938	+	0.792454i	0.964025	+	0.265812i	$0.0856401\pi$
$127$	1.28401	+	8.93050i	0.113938	+	0.792454i	−0.850087	+	0.526642i	$0.823451\pi$
$128$	−0.909261	−	19.0877i	−0.0803681	−	1.68713i
$129$	−0.920118	−	0.177338i	−0.0810119	−	0.0156138i
$130$	−1.63170	−	17.0879i	−0.143109	−	1.49871i
$131$	6.37835	+	12.3723i	0.557279	+	1.08097i	0.984263	+	0.176712i	$0.0565460\pi$
$131$	6.37835	+	12.3723i	0.557279	+	1.08097i	−0.426983	+	0.904260i	$0.640424\pi$
$132$	21.2522	−	6.24021i	1.84977	−	0.543141i
$133$	−0.303520	+	1.08249i	−0.0263185	+	0.0938638i
$134$	−3.62626	+	12.3499i	−0.313261	+	1.06687i
$135$	−0.219654	+	2.30032i	−0.0189048	+	0.197980i
$136$	16.5151	−	6.61163i	1.41615	−	0.566943i
$137$	−14.0506	+	8.11212i	−1.20042	+	0.693065i	−0.960650	−	0.277763i	$-0.910407\pi$
$137$	−14.0506	+	8.11212i	−1.20042	+	0.693065i	−0.239775	+	0.970829i	$0.577074\pi$
$138$	−11.7992	+	0.141883i	−1.00441	+	0.0120779i
$139$			20.0789i			1.70307i	0.524295	+	0.851537i	$0.324329\pi$
$139$			20.0789i			1.70307i	−0.524295	+	0.851537i	$0.675671\pi$
$140$	20.3635	+	14.1287i	1.72103	+	1.19410i
$141$	−1.70198	−	3.72681i	−0.143332	−	0.313854i
$142$	−24.6328	+	23.4873i	−2.06714	+	1.97101i
$143$	5.39512	−	15.5882i	0.451163	−	1.30355i
$144$	−3.13137	−	2.98575i	−0.260947	−	0.248813i
$145$	18.1280	−	9.34564i	1.50545	−	0.776113i
$146$	18.4177	+	8.41107i	1.52426	+	0.696105i
$147$	6.29441	−	3.06275i	0.519154	−	0.252612i
$148$	9.50954	+	14.7971i	0.781680	+	1.21632i
$149$	−4.88608	+	12.2048i	−0.400283	+	0.999859i	0.582123	+	0.813101i	$0.302222\pi$
$149$	−4.88608	+	12.2048i	−0.400283	+	0.999859i	−0.982406	+	0.186758i	$0.940202\pi$
$150$	−0.516716	−	0.657058i	−0.0421897	−	0.0536486i
$151$	1.89965	+	0.979339i	0.154591	+	0.0796974i	0.533786	−	0.845619i	$-0.320769\pi$
$151$	1.89965	+	0.979339i	0.154591	+	0.0796974i	−0.379195	+	0.925317i	$0.623799\pi$
$152$	0.702359	+	2.02933i	0.0569688	+	0.164601i
$153$	−1.46228	+	3.20194i	−0.118218	+	0.258862i
$154$	18.1590	+	30.5825i	1.46330	+	2.46440i
$155$	2.19972	+	7.49157i	0.176686	+	0.601738i
$156$	−12.0182	+	2.31632i	−0.962227	+	0.185454i
$157$	−1.62453	−	6.69640i	−0.129651	−	0.534431i	−0.999178	−	0.0405440i	$-0.987091\pi$
$157$	−1.62453	−	6.69640i	−0.129651	−	0.534431i	0.869526	−	0.493887i	$-0.164424\pi$
$158$	−28.2978	−	20.1508i	−2.25125	−	1.60311i
$159$	4.00020	+	3.14579i	0.317237	+	0.249478i
$160$	1.24378			0.0983292
$161$	−3.28960	−	12.2547i	−0.259257	−	0.965808i
$162$	2.46048			0.193314
$163$	−12.9287	−	10.1673i	−1.01266	−	0.796361i	−0.0334933	−	0.999439i	$-0.510663\pi$
$163$	−12.9287	−	10.1673i	−1.01266	−	0.796361i	−0.979163	+	0.203078i	$0.934906\pi$
$164$	−28.1020	−	20.0113i	−2.19440	−	1.56262i
$165$	−2.97653	−	12.2694i	−0.231723	−	0.955174i
$166$	−4.41782	+	0.851465i	−0.342889	+	0.0660865i
$167$	−5.61115	−	19.1098i	−0.434204	−	1.47876i	−0.828610	−	0.559826i	$-0.810868\pi$
$167$	−5.61115	−	19.1098i	−0.434204	−	1.47876i	0.394406	−	0.918936i	$-0.370950\pi$
$168$	6.54336	−	11.6604i	0.504831	−	0.899622i
$169$	1.61385	−	3.53384i	0.124142	−	0.271834i
$170$	−6.54584	−	18.9130i	−0.502043	−	1.45056i
$171$	−0.377686	−	0.194710i	−0.0288823	−	0.0148899i
$172$	−2.34825	−	2.98604i	−0.179052	−	0.227683i
$173$	−9.39021	+	23.4556i	−0.713924	+	1.78330i	−0.0984456	+	0.995142i	$0.531387\pi$
$173$	−9.39021	+	23.4556i	−0.713924	+	1.78330i	−0.615478	+	0.788154i	$0.711037\pi$
$174$	−11.7408	−	18.2691i	−0.890068	−	1.38497i
$175$	0.546943	−	0.713276i	0.0413450	−	0.0539186i
$176$	21.5032	+	9.82019i	1.62087	+	0.740224i
$177$	−5.28934	+	2.72684i	−0.397571	+	0.204962i
$178$	−13.9162	−	13.2691i	−1.04306	−	0.994558i
$179$	−3.27973	+	9.47616i	−0.245139	+	0.708281i	0.753565	+	0.657374i	$0.228333\pi$
$179$	−3.27973	+	9.47616i	−0.245139	+	0.708281i	−0.998703	+	0.0509077i	$0.983789\pi$
$180$	−6.77982	+	6.46455i	−0.505338	+	0.481839i
$181$	0.432694	+	0.947468i	0.0321619	+	0.0704247i	0.925031	−	0.379891i	$-0.124039\pi$
$181$	0.432694	+	0.947468i	0.0321619	+	0.0704247i	−0.892869	+	0.450316i	$0.851311\pi$
$182$	−8.38255	−	17.7767i	−0.621356	−	1.31769i
$183$		−	6.20684i		−	0.458823i
$184$	−18.5065	−	15.6504i	−1.36432	−	1.15376i
$185$	8.68283	−	5.01304i	0.638375	−	0.368566i
$186$	7.71812	−	3.08987i	0.565920	−	0.226560i
$187$	1.82814	−	19.1452i	0.133687	−	1.40003i
$188$	4.67938	−	15.9365i	0.341279	−	1.16229i
$189$	0.655155	+	2.56335i	0.0476555	+	0.186456i
$190$	2.31809	−	0.680653i	0.168172	−	0.0493797i
$191$	−2.54653	−	4.93957i	−0.184260	−	0.357415i	0.778555	−	0.627577i	$-0.215953\pi$
$191$	−2.54653	−	4.93957i	−0.184260	−	0.357415i	−0.962815	+	0.270162i	$0.912923\pi$
$192$	0.696667	+	7.29582i	0.0502776	+	0.526531i
$193$	1.07467	+	0.207125i	0.0773562	+	0.0149092i	0.227782	−	0.973712i	$-0.426852\pi$
$193$	1.07467	+	0.207125i	0.0773562	+	0.0149092i	−0.150426	+	0.988621i	$0.548065\pi$
$194$	−0.0145432	−	0.305300i	−0.00104414	−	0.0219193i
$195$	0.992865	+	6.90553i	0.0711006	+	0.494515i
$196$	27.4156	+	7.32667i	1.95826	+	0.523333i
$197$	1.88789	−	1.21327i	0.134507	−	0.0864421i	−0.471657	−	0.881782i	$-0.656344\pi$
$197$	1.88789	−	1.21327i	0.134507	−	0.0864421i	0.606164	+	0.795340i	$0.292708\pi$
$198$	−12.7038	+	4.39684i	−0.902822	+	0.312470i
$199$	14.8843	−	1.42128i	1.05512	−	0.100752i	0.446951	−	0.894558i	$-0.352510\pi$
$199$	14.8843	−	1.42128i	1.05512	−	0.100752i	0.608170	+	0.793807i	$0.291904\pi$
$200$	0.0816933	−	1.71495i	0.00577659	−	0.121265i
$201$	1.23330	−	5.08375i	0.0869906	−	0.358580i
$202$	25.3996	−	22.0089i	1.78711	−	1.54854i
$203$	15.9066	−	17.0962i	1.11643	−	1.19992i
$204$	−12.9805	+	5.92802i	−0.908820	+	0.415044i
$205$	−12.1559	+	15.4574i	−0.849002	+	1.07959i
$206$	−2.20018	−	3.81083i	−0.153294	−	0.265513i
$207$	4.78731	−	0.285778i	0.332741	−	0.0198629i
$208$	−11.3127	−	6.53139i	−0.784394	−	0.452870i
$209$	2.29799	+	0.330401i	0.158955	+	0.0228543i
$210$	−12.7533	−	7.97739i	−0.880062	−	0.550492i
$211$	−26.9576	−	7.91548i	−1.85584	−	0.544924i	−0.999598	−	0.0283508i	$-0.990974\pi$
$211$	−26.9576	−	7.91548i	−1.85584	−	0.544924i	−0.856243	−	0.516573i	$-0.827207\pi$
$212$	3.90435	+	20.2577i	0.268152	+	1.39130i
$213$	9.54583	−	10.0114i	0.654070	−	0.685968i
$214$	28.1743	+	1.34211i	1.92596	+	0.0917447i
$215$	−1.76382	+	1.25601i	−0.120292	+	0.0856593i
$216$	3.81935	+	3.30949i	0.259874	+	0.225182i
$217$	5.27417	+	7.21807i	0.358034	+	0.489995i
$218$	−35.8782	+	5.15851i	−2.42998	+	0.349378i
$219$	−7.63957	−	3.05842i	−0.516235	−	0.206669i
$220$	23.4532	−	45.4929i	1.58121	−	3.06713i
$221$	−2.01125	+	10.4354i	−0.135292	+	0.701959i
$222$	−6.19244	−	8.69606i	−0.415609	−	0.583642i
$223$	−1.12405	+	1.74906i	−0.0752720	+	0.117125i	−0.876849	−	0.480767i	$-0.840358\pi$
$223$	−1.12405	+	1.74906i	−0.0752720	+	0.117125i	0.801577	+	0.597892i	$0.203995\pi$
$224$	1.33995	−	0.482190i	0.0895294	−	0.0322177i
$225$	0.222475	+	0.256750i	0.0148317	+	0.0171167i
$226$	28.8258	+	30.2317i	1.91747	+	2.01098i
$227$	−16.5384	+	23.2249i	−1.09769	+	1.54149i	−0.285246	+	0.958454i	$0.592075\pi$
$227$	−16.5384	+	23.2249i	−1.09769	+	1.54149i	−0.812445	+	0.583038i	$0.801864\pi$
$228$	−0.640232	−	1.59922i	−0.0424004	−	0.105911i
$229$	−5.89719	+	10.2142i	−0.389697	+	0.674975i	−0.992409	−	0.122984i	$-0.960754\pi$
$229$	−5.89719	+	10.2142i	−0.389697	+	0.674975i	0.602712	+	0.797959i	$0.294087\pi$
$230$	−18.5780	+	19.9592i	−1.22500	+	1.31607i
$231$	−7.96333	−	12.0642i	−0.523949	−	0.793768i
$232$	6.34792	−	44.1508i	0.416762	−	2.89864i
$233$	−0.958500	−	0.0915257i	−0.0627934	−	0.00599605i	0.0636120	−	0.997975i	$-0.479738\pi$
$233$	−0.958500	−	0.0915257i	−0.0627934	−	0.00599605i	−0.126405	+	0.991979i	$0.540344\pi$
$234$	7.21909	−	1.75133i	0.471927	−	0.114488i
$235$	−8.94672	−	3.09649i	−0.583619	−	0.201993i
$236$	−23.4445	−	5.68758i	−1.52611	−	0.370230i
$237$	11.8776	+	7.63327i	0.771533	+	0.495834i
$238$	−14.3842	−	17.8377i	−0.932390	−	1.15625i
$239$	−2.64946	+	3.05764i	−0.171379	+	0.197782i	−0.834941	−	0.550339i	$-0.814498\pi$
$239$	−2.64946	+	3.05764i	−0.171379	+	0.197782i	0.663562	+	0.748121i	$0.269044\pi$
$240$	−9.98671	+	0.475725i	−0.644639	+	0.0307079i
$241$	−22.0484	+	17.3391i	−1.42026	+	1.11691i	−0.445084	+	0.895489i	$0.646826\pi$
$241$	−22.0484	+	17.3391i	−1.42026	+	1.11691i	−0.975179	+	0.221418i	$0.928931\pi$
$242$	36.4600	−	28.6724i	2.34374	−	1.84313i
$243$	−0.998867	+	0.0475819i	−0.0640774	+	0.00305238i
$244$	16.4778	−	19.0164i	1.05488	−	1.21740i
$245$	4.91509	−	15.4107i	0.314013	−	0.984551i
$246$	17.6146	+	11.3202i	1.12306	+	0.721750i
$247$	−1.24673	−	0.302453i	−0.0793274	−	0.0192446i
$248$	16.1367	+	5.58498i	1.02468	+	0.354647i
$249$	1.77701	−	0.431098i	0.112614	−	0.0273197i
$250$	26.3767	+	2.51866i	1.66821	+	0.159294i
$251$	3.82013	−	26.5696i	0.241124	−	1.67706i	−0.405382	−	0.914147i	$-0.632862\pi$
$251$	3.82013	−	26.5696i	0.241124	−	1.67706i	0.646507	−	0.762908i	$-0.276229\pi$
$252$	−4.79789	+	9.59284i	−0.302238	+	0.604292i
$253$	−24.2069	+	10.0304i	−1.52188	+	0.630603i
$254$	11.0996	−	19.2251i	0.696453	−	1.20629i
$255$	3.02312	+	7.55140i	0.189315	+	0.472887i
$256$	−18.7708	+	26.3599i	−1.17317	+	1.64749i
$257$	12.6310	+	13.2470i	0.787900	+	0.826325i	0.988162	−	0.153417i	$-0.0490278\pi$
$257$	12.6310	+	13.2470i	0.787900	+	0.826325i	−0.200262	+	0.979742i	$0.564179\pi$
$258$	1.50985	+	1.74245i	0.0939989	+	0.108480i
$259$	7.41078	−	8.76685i	0.460483	−	0.544746i
$260$	−15.2907	+	23.7929i	−0.948291	+	1.47557i
$261$	5.11965	+	7.18954i	0.316898	+	0.445021i
$262$	6.48167	−	33.6301i	0.400439	−	2.07767i
$263$	−6.67262	+	12.9431i	−0.411451	+	0.798104i	−0.999946	−	0.0103970i	$-0.996690\pi$
$263$	−6.67262	+	12.9431i	−0.411451	+	0.798104i	0.588495	+	0.808501i	$0.299721\pi$
$264$	−25.6339	−	10.2623i	−1.57766	−	0.631599i
$265$	11.6398	−	1.67355i	0.715029	−	0.102806i
$266$	2.23346	−	1.63197i	0.136942	−	0.100062i
$267$	5.90608	+	5.11765i	0.361446	+	0.313195i
$268$	17.2748	−	12.3013i	1.05523	−	0.751424i
$269$	−21.9116	−	1.04378i	−1.33598	−	0.0636404i	−0.632611	−	0.774470i	$-0.718017\pi$
$269$	−21.9116	−	1.04378i	−1.33598	−	0.0636404i	−0.703365	+	0.710829i	$0.748320\pi$
$270$	3.92354	−	4.11489i	0.238779	−	0.250424i
$271$	3.76061	+	19.5119i	0.228441	+	1.18526i	0.897145	+	0.441735i	$0.145637\pi$
$271$	3.76061	+	19.5119i	0.228441	+	1.18526i	−0.668705	+	0.743528i	$0.733151\pi$
$272$	−14.6132	−	4.29081i	−0.886053	−	0.260169i
$273$	3.74679	+	7.05459i	0.226766	+	0.426963i
$274$	39.5131	+	5.68113i	2.38707	+	0.343209i
$275$	−1.60748	−	0.928079i	−0.0969347	−	0.0559653i
$276$	15.4259	+	11.8337i	0.928532	+	0.712305i
$277$	−4.20565	−	7.28439i	−0.252693	−	0.437677i	0.711574	−	0.702612i	$-0.247983\pi$
$277$	−4.20565	−	7.28439i	−0.252693	−	0.437677i	−0.964266	+	0.264935i	$0.914650\pi$
$278$	30.5394	−	38.8340i	1.83163	−	2.32911i
$279$	−3.07353	+	1.40363i	−0.184007	+	0.0840333i
$280$	−9.06665	−	29.5371i	−0.541836	−	1.76518i
$281$	11.5252	−	9.98667i	0.687538	−	0.595755i	−0.239422	−	0.970916i	$-0.576958\pi$
$281$	11.5252	−	9.98667i	0.687538	−	0.595755i	0.926960	+	0.375161i	$0.122413\pi$
$282$	−2.37662	+	9.79656i	−0.141526	+	0.583377i
$283$	−0.113112	+	2.37451i	−0.00672380	+	0.141150i	0.993009	+	0.118038i	$0.0376604\pi$
$283$	−0.113112	+	2.37451i	−0.00672380	+	0.141150i	−0.999733	+	0.0231119i	$0.992643\pi$
$284$	55.8243	−	5.33058i	3.31256	−	0.316312i
$285$	−0.927899	+	0.321149i	−0.0549640	+	0.0190232i
$286$	−34.1436	+	21.9428i	−2.01896	+	1.29750i
$287$	−7.10325	+	21.3653i	−0.419291	+	1.26115i
$288$	0.0766008	+	0.532770i	0.00451374	+	0.0313938i
$289$	−0.219320	−	4.60409i	−0.0129012	−	0.270829i
$290$	−49.2752	−	9.49702i	−2.89354	−	0.557684i
$291$	0.0118081	+	0.123660i	0.000692202	+	0.00724906i
$292$	−15.2865	−	29.6517i	−0.894576	−	1.73524i
$293$	11.6762	−	3.42844i	0.682130	−	0.200292i	0.0777326	−	0.996974i	$-0.475232\pi$
$293$	11.6762	−	3.42844i	0.682130	−	0.200292i	0.604398	+	0.796683i	$0.293414\pi$
$294$	−16.8322	−	3.65002i	−0.981671	−	0.212873i
$295$	−3.87415	+	13.1942i	−0.225562	+	0.768193i
$296$	2.08431	−	21.8279i	0.121148	−	1.26872i
$297$	5.07228	−	2.03063i	0.294323	−	0.117829i
$298$	28.0132	−	16.1734i	1.62276	−	0.936901i
$299$	13.8426	−	4.24601i	0.800540	−	0.245553i
$300$			1.37725i			0.0795154i
$301$	−1.41328	+	2.03694i	−0.0814600	+	0.117407i
$302$	−2.18451	−	4.78342i	−0.125705	−	0.275255i
$303$	−9.88573	+	9.42603i	−0.567920	+	0.541511i
$304$	0.601315	−	1.73738i	0.0344878	−	0.0996459i
$305$	−10.3803	−	9.89758i	−0.594373	−	0.566734i
$306$	7.69820	−	3.96870i	0.440077	−	0.226875i
$307$	−15.4562	−	7.05863i	−0.882135	−	0.402857i	−0.0777547	−	0.996973i	$-0.524775\pi$
$307$	−15.4562	−	7.05863i	−0.882135	−	0.402857i	−0.804380	+	0.594115i	$0.797502\pi$
$308$	7.62997	−	58.1030i	0.434758	−	3.31073i
$309$	0.966892	+	1.50451i	0.0550046	+	0.0855888i
$310$	7.14002	−	17.8349i	0.405526	−	1.01296i
$311$	7.46398	+	9.49122i	0.423243	+	0.538198i	0.950178	−	0.311708i	$-0.100901\pi$
$311$	7.46398	+	9.49122i	0.423243	+	0.538198i	−0.526934	+	0.849906i	$0.676659\pi$
$312$	13.5617	+	6.99154i	0.767780	+	0.395818i
$313$	−3.60572	−	10.4180i	−0.203807	−	0.588862i	0.796059	−	0.605219i	$-0.206914\pi$
$313$	−3.60572	−	10.4180i	−0.203807	−	0.588862i	−0.999866	+	0.0163568i	$0.994793\pi$
$314$	−7.04306	+	15.4221i	−0.397463	+	0.870322i
$315$	5.33166	+	2.99191i	0.300405	+	0.168575i
$316$	16.1257	+	54.9190i	0.907141	+	3.08944i
$317$	13.9290	−	2.68460i	0.782332	−	0.150782i	0.217580	−	0.976043i	$-0.430184\pi$
$317$	13.9290	−	2.68460i	0.782332	−	0.150782i	0.564752	+	0.825260i	$0.308972\pi$
$318$	−2.95201	−	12.1684i	−0.165541	−	0.682367i
$319$	−39.2811	−	27.9719i	−2.19932	−	1.56613i
$320$	13.3124	+	10.4690i	0.744187	+	0.585235i
$321$	−11.4637			−0.639843
$322$	−12.2768	+	28.7049i	−0.684157	+	1.59966i
$323$	−1.49574			−0.0832253
$324$	−3.18663	−	2.50599i	−0.177035	−	0.139222i
$325$	0.835496	+	0.594954i	0.0463450	+	0.0330021i
$326$	9.54095	+	39.3283i	0.528425	+	2.17820i
$327$	14.4655	−	2.78800i	0.799945	−	0.154177i
$328$	12.1164	+	41.2648i	0.669018	+	2.27847i
$329$	−10.8390	+	0.132555i	−0.597572	+	0.00730798i
$330$	−12.9046	+	28.2571i	−0.710374	+	1.55550i
$331$	0.427134	+	1.23412i	0.0234774	+	0.0678336i	0.956131	−	0.292940i	$-0.0946338\pi$
$331$	0.427134	+	1.23412i	0.0234774	+	0.0678336i	−0.932653	+	0.360774i	$0.882513\pi$
$332$	6.58884	+	3.39678i	0.361610	+	0.186423i
$333$	2.68208	+	3.41054i	0.146977	+	0.186896i
$334$	−18.2131	+	45.4941i	−0.996575	+	2.48932i
$335$	−6.53537	−	10.1692i	−0.357066	−	0.555605i
$336$	−10.5745	+	4.38418i	−0.576886	+	0.239177i
$337$	0.445252	+	0.203340i	0.0242544	+	0.0110766i	0.427505	−	0.904013i	$-0.359393\pi$
$337$	0.445252	+	0.203340i	0.0242544	+	0.0110766i	−0.403251	+	0.915089i	$0.632120\pi$
$338$	−8.49615	+	4.38007i	−0.462130	+	0.238244i
$339$	−12.2869	−	11.7155i	−0.667333	−	0.636301i
$340$	−10.7851	+	31.1616i	−0.584905	+	1.68997i
$341$	13.3608	−	12.7395i	0.723529	−	0.689884i
$342$	0.434321	+	0.951031i	0.0234854	+	0.0514259i
$343$	−0.679291	−	18.5078i	−0.0366783	−	0.999327i
$344$			4.73561i			0.255327i
$345$	7.15603	−	8.46198i	0.385268	−	0.455577i
$346$	53.8365	−	31.0825i	2.89427	−	1.67101i
$347$	10.7008	−	4.28396i	0.574450	−	0.229975i	−0.0662023	−	0.997806i	$-0.521088\pi$
$347$	10.7008	−	4.28396i	0.574450	−	0.229975i	0.640652	+	0.767831i	$0.278664\pi$
$348$	−3.40117	+	35.6187i	−0.182322	+	1.90936i
$349$	1.61774	−	5.50950i	0.0865954	−	0.294917i	−0.904797	−	0.425844i	$-0.859977\pi$
$349$	1.61774	−	5.50950i	0.0865954	−	0.294917i	0.991392	+	0.130927i	$0.0417954\pi$
$350$	−2.14269	+	0.547641i	−0.114532	+	0.0292726i
$351$	−2.89683	+	0.850585i	−0.154621	+	0.0454008i
$352$	−1.34755	−	2.61389i	−0.0718248	−	0.139321i
$353$	−0.0352952	−	0.369628i	−0.00187858	−	0.0196733i	0.994484	−	0.104888i	$-0.0334484\pi$
$353$	−0.0352952	−	0.369628i	−0.00187858	−	0.0196733i	−0.996363	+	0.0852147i	$0.972842\pi$
$354$	14.3774	+	2.77101i	0.764149	+	0.147278i
$355$	−1.52096	−	31.9288i	−0.0807239	−	1.69460i
$356$	4.50870	+	31.3587i	0.238960	+	1.66201i
$357$	6.18443	+	6.96331i	0.327315	+	0.368537i
$358$	20.7562	−	13.3392i	1.09700	−	0.704997i
$359$	−11.1428	+	3.85655i	−0.588093	+	0.203541i	−0.604878	−	0.796318i	$-0.706778\pi$
$359$	−11.1428	+	3.85655i	−0.588093	+	0.203541i	0.0167851	+	0.999859i	$0.494657\pi$
$360$	11.6252	−	1.11007i	0.612702	−	0.0585060i
$361$	−0.895465	+	18.7981i	−0.0471297	+	0.989375i
$362$	0.604208	−	2.49058i	0.0317565	−	0.130902i
$363$	−14.2470	+	12.3451i	−0.747772	+	0.647948i
$364$	−7.24904	+	31.5606i	−0.379953	+	1.65423i
$365$	−17.2971	+	7.89934i	−0.905374	+	0.413470i
$366$	−9.44041	+	12.0045i	−0.493458	+	0.627483i
$367$	−7.92980	−	13.7348i	−0.413932	−	0.716951i	0.581384	−	0.813630i	$-0.302512\pi$
$367$	−7.92980	−	13.7348i	−0.413932	−	0.716951i	−0.995316	+	0.0966782i	$0.969178\pi$
$368$	4.17167	+	20.3264i	0.217463	+	1.05958i
$369$	−7.36981	−	4.25496i	−0.383657	−	0.221504i
$370$	−24.4179	−	3.51076i	−1.26942	−	0.182516i
$371$	11.8911	−	6.31551i	0.617354	−	0.327885i
$372$	−13.1430	−	3.85912i	−0.681430	−	0.200086i
$373$	0.0951210	+	0.493535i	0.00492518	+	0.0255542i	0.984308	−	0.176458i	$-0.0564640\pi$
$373$	0.0951210	+	0.493535i	0.00492518	+	0.0255542i	−0.979383	+	0.202012i	$0.935252\pi$
$374$	−32.6550	+	34.2475i	−1.68855	+	1.77090i
$375$	−10.7567	−	0.512404i	−0.555473	−	0.0264604i
$376$	−16.8661	+	12.0103i	−0.869805	+	0.619385i
$377$	20.1385	+	17.4501i	1.03719	+	0.898728i
$378$	2.63166	−	5.95417i	0.135358	−	0.306249i
$379$	18.1478	−	2.60925i	0.932187	−	0.134028i	0.340544	−	0.940228i	$-0.389389\pi$
$379$	18.1478	−	2.60925i	0.932187	−	0.134028i	0.591643	+	0.806200i	$0.298480\pi$
$380$	−3.69546	−	1.47944i	−0.189573	−	0.0758936i
$381$	−4.13427	+	8.01937i	−0.211805	+	0.410845i
$382$	−2.58777	+	13.4266i	−0.132402	+	0.686967i
$383$	11.5102	+	16.1638i	0.588142	+	0.825929i	0.996206	−	0.0870236i	$-0.0277356\pi$
$383$	11.5102	+	16.1638i	0.588142	+	0.825929i	−0.408065	+	0.912953i	$0.633796\pi$
$384$	10.3313	−	16.0758i	0.527218	−	0.820367i
$385$	−32.8747	−	5.92008i	−1.67545	−	0.301715i
$386$	−1.76345	−	2.03513i	−0.0897571	−	0.103585i
$387$	−0.646640	−	0.678177i	−0.0328706	−	0.0344737i
$388$	−0.292112	+	0.410214i	−0.0148297	+	0.0208255i
$389$	12.9798	+	32.4220i	0.658103	+	1.64386i	0.760673	+	0.649135i	$0.224869\pi$
$389$	12.9798	+	32.4220i	0.658103	+	1.64386i	−0.102571	+	0.994726i	$0.532707\pi$
$390$	8.58282	−	14.8659i	0.434608	−	0.752763i
$391$	14.5173	−	8.61594i	0.734170	−	0.435727i
$392$	−21.2187	−	28.3061i	−1.07171	−	1.42967i
$393$	−1.98097	+	13.7780i	−0.0999269	+	0.695007i
$394$	−5.49665	−	0.524867i	−0.276917	−	0.0264424i
$395$	31.7061	−	7.69182i	1.59531	−	0.387018i
$396$	20.9312	+	7.24437i	1.05183	+	0.364043i
$397$	−10.7172	−	2.59997i	−0.537882	−	0.130489i	−0.0423900	−	0.999101i	$-0.513497\pi$
$397$	−10.7172	−	2.59997i	−0.537882	−	0.130489i	−0.495492	+	0.868612i	$0.665012\pi$
$398$	−30.9490	−	19.8897i	−1.55133	−	0.996981i
$399$	−0.875146	+	0.705712i	−0.0438121	+	0.0353298i
$400$	−0.962578	+	1.11087i	−0.0481289	+	0.0555437i
$401$	24.7270	−	1.17789i	1.23481	−	0.0588211i	0.579999	−	0.814617i	$-0.303053\pi$
$401$	24.7270	−	1.17789i	1.23481	−	0.0588211i	0.654807	+	0.755796i	$0.272750\pi$
$402$	−10.1175	+	7.95650i	−0.504616	+	0.396834i
$403$	−8.01870	+	6.30598i	−0.399440	+	0.314123i
$404$	−55.3117	+	2.63482i	−2.75186	+	0.131087i
$405$	−1.51324	+	1.74637i	−0.0751936	+	0.0867781i
$406$	−56.7673	+	8.87174i	−2.81731	+	0.440297i
$407$	−19.9426	−	12.8163i	−0.988516	−	0.635281i
$408$	17.2879	+	4.19400i	0.855878	+	0.207634i
$409$	1.10213	+	0.381452i	0.0544970	+	0.0188616i	0.354180	−	0.935177i	$-0.384760\pi$
$409$	1.10213	+	0.381452i	0.0544970	+	0.0188616i	−0.299683	+	0.954039i	$0.596881\pi$
$410$	47.0205	−	11.4070i	2.32218	−	0.563354i
$411$	−16.1508	−	1.54221i	−0.796659	−	0.0760717i
$412$	−1.03181	+	7.17638i	−0.0508335	+	0.353555i
$413$	0.941412	+	15.7163i	0.0463238	+	0.773350i
$414$	−9.69364	−	6.72863i	−0.476416	−	0.330694i
$415$	2.11270	−	3.65930i	0.103708	−	0.179628i
$416$	0.603966	+	1.50863i	0.0296119	+	0.0739668i
$417$	−11.6469	+	16.3558i	−0.570352	+	0.800948i
$418$	−3.94194	−	4.13419i	−0.192807	−	0.202210i
$419$	−10.4425	−	12.0513i	−0.510148	−	0.588742i	0.440988	−	0.897513i	$-0.354628\pi$
$419$	−10.4425	−	12.0513i	−0.510148	−	0.588742i	−0.951137	+	0.308770i	$0.900083\pi$
$420$	8.39217	+	23.3209i	0.409496	+	1.13794i
$421$	18.7024	−	29.1015i	0.911500	−	1.41832i	0.00320369	−	0.999995i	$-0.498980\pi$
$421$	18.7024	−	29.1015i	0.911500	−	1.41832i	0.908296	−	0.418327i	$-0.137383\pi$
$422$	40.0987	+	56.3108i	1.95198	+	2.74117i
$423$	0.775373	−	4.02302i	0.0376999	−	0.195606i
$424$	11.7848	−	22.8593i	0.572321	−	1.11015i
$425$	1.11020	+	0.444456i	0.0538525	+	0.0215593i
$426$	−33.6893	+	4.84379i	−1.63225	+	0.234682i
$427$	−15.0201	−	6.63867i	−0.726872	−	0.321268i
$428$	−35.1224	−	30.4337i	−1.69770	−	1.47107i
$429$	13.4368	−	9.56828i	0.648733	−	0.461961i
$430$	5.32171	+	0.253504i	0.256636	+	0.0122251i
$431$	−8.71842	+	9.14361i	−0.419951	+	0.440432i	−0.899393	−	0.437142i	$-0.855991\pi$
$431$	−8.71842	+	9.14361i	−0.419951	+	0.440432i	0.479441	+	0.877574i	$0.340839\pi$
$432$	−0.818830	−	4.24849i	−0.0393960	−	0.204406i
$433$	4.07350	+	1.19609i	0.195760	+	0.0574803i	0.378143	−	0.925747i	$-0.376563\pi$
$433$	4.07350	+	1.19609i	0.195760	+	0.0574803i	−0.182383	+	0.983228i	$0.558381\pi$
$434$	0.777854	−	21.9821i	0.0373382	−	1.05517i
$435$	20.1877	+	2.90255i	0.967924	+	0.139166i
$436$	51.7207	+	29.8610i	2.47697	+	1.43008i
$437$	0.955510	+	1.79996i	0.0457082	+	0.0861036i
$438$	10.1237	+	17.5347i	0.483729	+	0.837843i
$439$	0.248206	−	0.315619i	0.0118462	−	0.0150637i	−0.780094	−	0.625662i	$-0.784829\pi$
$439$	0.248206	−	0.315619i	0.0118462	−	0.0150637i	0.791940	+	0.610599i	$0.209071\pi$
$440$	−58.0390	+	26.5055i	−2.76690	+	1.26360i
$441$	6.90384	+	1.15627i	0.328754	+	0.0550605i
$442$	19.7618	−	17.1237i	0.939972	−	0.814490i
$443$	−2.52110	+	10.3921i	−0.119781	+	0.493744i	0.880041	+	0.474897i	$0.157515\pi$
$443$	−2.52110	+	10.3921i	−0.119781	+	0.493744i	−0.999822	+	0.0188468i	$0.994001\pi$
$444$	−0.836937	+	17.5695i	−0.0397193	+	0.833810i
$445$	17.9767	−	1.71657i	0.852177	−	0.0813731i
$446$	4.83425	−	1.67315i	0.228908	−	0.0792259i
$447$	−11.0596	+	7.10756i	−0.523100	+	0.336176i
$448$	18.4004	+	6.11754i	0.869340	+	0.289026i
$449$	0.693546	+	4.82372i	0.0327304	+	0.227645i	0.999620	−	0.0275481i	$-0.00876995\pi$
$449$	0.693546	+	4.82372i	0.0327304	+	0.227645i	−0.966890	+	0.255193i	$0.917861\pi$
$450$	−0.0397735	−	0.834949i	−0.00187494	−	0.0393599i
$451$	45.6550	+	8.79928i	2.14981	+	0.414342i
$452$	−6.54218	−	68.5128i	−0.307718	−	3.22257i
$453$	0.979339	+	1.89965i	0.0460133	+	0.0892534i
$454$	67.3107	−	19.7642i	3.15905	−	0.927580i
$455$	17.7728	+	4.98331i	0.833200	+	0.233621i
$456$	−0.605004	+	2.06045i	−0.0283319	+	0.0964896i
$457$	−1.21733	+	12.7485i	−0.0569444	+	0.596349i	0.921294	+	0.388866i	$0.127133\pi$
$457$	−1.21733	+	12.7485i	−0.0569444	+	0.596349i	−0.978239	+	0.207483i	$0.933473\pi$
$458$	26.9411	−	10.7856i	1.25887	−	0.503977i
$459$	−3.04845	+	1.76002i	−0.142289	+	0.0821507i
$460$	44.3892	−	6.92795i	2.06966	−	0.323017i
$461$		−	14.8496i		−	0.691614i	−0.938306	−	0.345807i	$-0.887605\pi$
$461$		−	14.8496i		−	0.691614i	0.938306	−	0.345807i	$-0.112395\pi$
$462$	−2.94767	+	35.4450i	−0.137138	+	1.64905i
$463$	−1.58805	−	3.47734i	−0.0738028	−	0.161606i	0.869135	−	0.494576i	$-0.164676\pi$
$463$	−1.58805	−	3.47734i	−0.0738028	−	0.161606i	−0.942937	+	0.332970i	$0.891949\pi$
$464$	−27.6378	+	26.3526i	−1.28305	+	1.22339i
$465$	−2.55370	+	7.37842i	−0.118425	+	0.342166i
$466$	1.71460	+	1.63486i	0.0794272	+	0.0757337i
$467$	−22.6616	+	11.6829i	−1.04865	+	0.540618i	−0.894333	−	0.447403i	$-0.852349\pi$
$467$	−22.6616	+	11.6829i	−1.04865	+	0.540618i	−0.154320	+	0.988021i	$0.549319\pi$
$468$	−11.1333	−	5.08443i	−0.514639	−	0.235028i
$469$	−10.9832	−	8.42194i	−0.507155	−	0.388889i
$470$	12.5939	+	19.5965i	0.580913	+	0.903919i
$471$	2.56099	−	6.39704i	0.118004	−	0.294760i
$472$	18.5906	+	23.6398i	0.855700	+	1.08811i
$473$	4.55059	+	2.34599i	0.209236	+	0.107869i
$474$	−11.3621	−	32.8287i	−0.521879	−	1.50787i
$475$	−0.0599685	+	0.131313i	−0.00275154	+	0.00602504i
$476$	0.461690	+	37.7523i	0.0211615	+	1.73038i
$477$	1.43373	+	4.88283i	0.0656459	+	0.223569i
$478$	9.77480	−	1.88394i	0.447089	−	0.0861693i
$479$	−7.86074	−	32.4024i	−0.359166	−	1.48050i	−0.809222	−	0.587503i	$-0.800111\pi$
$479$	−7.86074	−	32.4024i	−0.359166	−	1.48050i	0.450055	−	0.893001i	$-0.351404\pi$
$480$	1.01315	+	0.721462i	0.0462438	+	0.0329301i
$481$	10.2968	+	8.09752i	0.469495	+	0.369215i
$482$	69.0153			3.14356
$483$	4.42882	−	11.8906i	0.201518	−	0.541040i
$484$	−76.4231			−3.47378
$485$	0.225637	+	0.177443i	0.0102457	+	0.00805728i
$486$	2.00425	+	1.42722i	0.0909145	+	0.0647399i
$487$	−1.08573	−	4.47543i	−0.0491990	−	0.202801i	0.941907	−	0.335873i	$-0.109031\pi$
$487$	−1.08573	−	4.47543i	−0.0491990	−	0.202801i	−0.991106	+	0.133071i	$0.957516\pi$
$488$	−30.8009	+	5.93638i	−1.39429	+	0.268727i
$489$	−4.63384	−	15.7814i	−0.209549	−	0.713660i
$490$	−32.9452	+	22.3296i	−1.48831	+	1.00875i
$491$	4.78218	−	10.4715i	0.215817	−	0.472573i	−0.770499	−	0.637442i	$-0.779993\pi$
$491$	4.78218	−	10.4715i	0.215817	−	0.472573i	0.986316	+	0.164869i	$0.0527200\pi$
$492$	−11.2835	−	32.6015i	−0.508699	−	1.46979i
$493$	27.6146	+	14.2363i	1.24370	+	0.641171i
$494$	1.95123	+	2.48120i	0.0877902	+	0.111634i
$495$	4.69236	−	11.7209i	0.210906	−	0.526817i
$496$	−7.90379	−	12.2985i	−0.354891	−	0.552220i
$497$	−14.0168	−	33.8080i	−0.628738	−	1.51650i
$498$	−4.09255	−	1.86900i	−0.183391	−	0.0837520i
$499$	−4.40621	+	2.27156i	−0.197249	+	0.101689i	−0.554021	−	0.832502i	$-0.686907\pi$
$499$	−4.40621	+	2.27156i	−0.197249	+	0.101689i	0.356772	+	0.934191i	$0.383877\pi$
$500$	−31.5958	−	30.1265i	−1.41301	−	1.34730i
$501$	6.51407	−	18.8212i	0.291027	−	0.840868i
$502$	−47.7998	+	45.5770i	−2.13341	+	2.03420i
$503$	−0.155690	−	0.340913i	−0.00694187	−	0.0152006i	0.906129	−	0.423001i	$-0.139023\pi$
$503$	−0.155690	−	0.340913i	−0.00694187	−	0.0152006i	−0.913071	+	0.407800i	$0.866296\pi$
$504$	12.0938	−	5.70279i	0.538700	−	0.254023i
$505$			31.5638i			1.40457i
$506$	62.0737	+	17.4186i	2.75951	+	0.774349i
$507$	3.36443	−	1.94245i	0.149420	−	0.0862674i
$508$	−33.9562	+	13.5940i	−1.50656	+	0.603136i
$509$	3.50614	−	36.7180i	0.155407	−	1.62750i	−0.495688	−	0.868501i	$-0.665084\pi$
$509$	3.50614	−	36.7180i	0.155407	−	1.62750i	0.651095	−	0.758996i	$-0.274310\pi$
$510$	5.63851	−	19.2030i	0.249677	−	0.850323i
$511$	−15.5722	+	15.2160i	−0.688875	+	0.673114i
$512$	39.7258	−	11.6646i	1.75565	−	0.515505i
$513$	−0.194710	−	0.377686i	−0.00859668	−	0.0166752i
$514$	−4.28093	−	44.8319i	−0.188824	−	1.97745i
$515$	4.05797	+	0.782109i	0.178815	+	0.0344639i
$516$	−0.180753	−	3.79447i	−0.00795720	−	0.167042i
$517$	3.18570	+	22.1570i	0.140107	+	0.974465i
$518$	−27.6670	+	5.68414i	−1.21562	+	0.249747i
$519$	−21.2546	+	13.6595i	−0.932974	+	0.599586i
$520$	33.3184	−	11.5316i	1.46111	−	0.505695i
$521$	20.9227	−	1.99788i	0.916642	−	0.0875287i	0.373939	−	0.927453i	$-0.378007\pi$
$521$	20.9227	−	1.99788i	0.916642	−	0.0875287i	0.542703	+	0.839925i	$0.317401\pi$
$522$	1.03331	−	21.6919i	0.0452268	−	0.949427i
$523$	3.72306	−	15.3466i	0.162798	−	0.671062i	−0.830652	−	0.556792i	$-0.812032\pi$
$523$	3.72306	−	15.3466i	0.162798	−	0.671062i	0.993450	−	0.114270i	$-0.0364528\pi$
$524$	−42.6467	+	36.9536i	−1.86303	+	1.61433i
$525$	0.859267	−	0.263759i	0.0375015	−	0.0115114i
$526$	32.5913	−	14.8839i	1.42105	−	0.648971i
$527$	−7.35224	+	9.34913i	−0.320268	+	0.407255i
$528$	11.8197	+	20.4724i	0.514388	+	0.890946i
$529$	−19.6422	−	11.9659i	−0.854011	−	0.520256i
$530$	−25.0576	−	14.4670i	−1.08843	−	0.628408i
$531$	−5.89029	−	0.846896i	−0.255617	−	0.0367522i
$532$	−4.55476	−	0.161174i	−0.197474	−	0.00698778i
$533$	−24.6518	−	7.23841i	−1.06779	−	0.313530i
$534$	−3.63898	−	18.8808i	−0.157474	−	0.817053i
$535$	−18.2803	+	19.1719i	−0.790328	+	0.828873i
$536$	−26.4072	−	1.25793i	−1.14062	−	0.0543343i
$537$	−8.16830	+	5.81662i	−0.352488	+	0.251006i
$538$	40.7910	+	35.3456i	1.75863	+	1.52386i
$539$	−37.7118	+	6.36706i	−1.62436	+	0.274249i
$540$	−9.27248	+	1.33318i	−0.399024	+	0.0573710i
$541$	−16.9899	−	6.80172i	−0.730452	−	0.292429i	−0.0235325	−	0.999723i	$-0.507491\pi$
$541$	−16.9899	−	6.80172i	−0.730452	−	0.292429i	−0.706919	+	0.707294i	$0.749916\pi$
$542$	22.4037	−	43.4571i	0.962321	−	1.86664i
$543$	−0.197123	+	1.02277i	−0.00845936	+	0.0438913i
$544$	1.09901	+	1.54334i	0.0471196	+	0.0661703i
$545$	18.4044	−	28.6379i	0.788360	−	1.22671i
$546$	3.48326	−	19.3428i	0.149070	−	0.827795i
$547$	−14.7191	−	16.9868i	−0.629344	−	0.726302i	0.348109	−	0.937454i	$-0.386824\pi$
$547$	−14.7191	−	16.9868i	−0.629344	−	0.726302i	−0.977453	+	0.211152i	$0.932279\pi$
$548$	−45.3882	−	47.6018i	−1.93889	−	2.03345i
$549$	3.60032	−	5.05594i	0.153658	−	0.215782i
$550$	1.69740	+	4.23989i	0.0723773	+	0.180790i
$551$	−1.87520	+	3.24795i	−0.0798864	+	0.138367i
$552$	−5.99685	−	23.4832i	−0.255243	−	0.999513i
$553$	31.1758	−	20.5785i	1.32573	−	0.875087i
$554$	−2.94532	+	20.4852i	−0.125135	+	0.870331i
$555$	9.98067	+	0.953039i	0.423656	+	0.0404542i
$556$	−79.1047	+	19.1906i	−3.35479	+	0.813863i
$557$	−26.5554	−	9.19092i	−1.12519	−	0.389432i	−0.299803	−	0.954001i	$-0.596921\pi$
$557$	−26.5554	−	9.19092i	−1.12519	−	0.389432i	−0.825386	+	0.564569i	$0.809042\pi$
$558$	8.07930	+	1.96002i	0.342024	+	0.0829741i
$559$	−2.37997	−	1.52951i	−0.100662	−	0.0646915i
$560$	−9.53029	+	24.6759i	−0.402728	+	1.04275i
$561$	12.5945	−	14.5348i	0.531738	−	0.613659i
$562$	−37.4800	+	1.78539i	−1.58100	+	0.0753122i
$563$	22.8113	−	17.9390i	0.961382	−	0.756039i	−0.00841233	−	0.999965i	$-0.502678\pi$
$563$	22.8113	−	17.9390i	0.961382	−	0.756039i	0.969794	+	0.243926i	$0.0784353\pi$
$564$	13.0558	−	10.2672i	0.549748	−	0.432327i
$565$	−39.1860	+	1.86666i	−1.64857	+	0.0785309i
$566$	3.83032	−	4.42042i	0.161000	−	0.185804i
$567$	−0.953217	+	2.46807i	−0.0400313	+	0.103649i
$568$	−58.8104	−	37.7951i	−2.46763	−	1.58585i
$569$	15.3643	+	3.72734i	0.644105	+	0.156258i	0.544489	−	0.838768i	$-0.316724\pi$
$569$	15.3643	+	3.72734i	0.644105	+	0.156258i	0.0996156	+	0.995026i	$0.468239\pi$
$570$	2.28308	+	0.790181i	0.0956276	+	0.0330970i
$571$	14.0793	−	3.41561i	0.589202	−	0.142939i	0.0699359	−	0.997551i	$-0.477721\pi$
$571$	14.0793	−	3.41561i	0.589202	−	0.142939i	0.519266	+	0.854613i	$0.326205\pi$
$572$	66.5690	+	6.35657i	2.78339	+	0.265781i
$573$	0.790893	−	5.50078i	0.0330400	−	0.229799i
$574$	46.2341	−	30.5181i	1.92977	−	1.27380i
$575$	−0.174363	−	1.61992i	−0.00727146	−	0.0675555i
$576$	−3.66451	+	6.34711i	−0.152688	+	0.264463i
$577$	12.3126	+	30.7553i	0.512578	+	1.28036i	0.928626	+	0.371016i	$0.120991\pi$
$577$	12.3126	+	30.7553i	0.512578	+	1.28036i	−0.416048	+	0.909343i	$0.636585\pi$
$578$	−6.57849	+	9.23820i	−0.273629	+	0.384258i
$579$	0.755253	+	0.792086i	0.0313872	+	0.0329180i
$580$	54.1449	+	62.4865i	2.24824	+	2.59461i
$581$	0.857419	−	4.76132i	0.0355717	−	0.197533i
$582$	0.165245	−	0.257126i	0.00684962	−	0.0106582i
$583$	−16.1281	−	22.6487i	−0.667958	−	0.938015i
$584$	−7.87046	+	40.8358i	−0.325682	+	1.68980i
$585$	−3.19684	+	6.20100i	−0.132173	+	0.256380i
$586$	−27.7971	−	11.1283i	−1.14829	−	0.459705i
$587$	−16.5758	+	2.38324i	−0.684157	+	0.0983669i	−0.475624	−	0.879648i	$-0.657778\pi$
$587$	−16.5758	+	2.38324i	−0.684157	+	0.0983669i	−0.208533	+	0.978015i	$0.566869\pi$
$588$	18.0822	+	21.8707i	0.745698	+	0.901934i
$589$	−1.08507	−	0.940220i	−0.0447096	−	0.0387411i
$590$	27.5607	−	19.6259i	1.13466	−	0.807986i
$591$	2.24160	+	0.106780i	0.0922070	+	0.00439236i
$592$	−12.9546	+	13.5864i	−0.532432	+	0.558398i
$593$	−7.84658	−	40.7119i	−0.322220	−	1.67184i	−0.676303	−	0.736624i	$-0.736419\pi$
$593$	−7.84658	−	40.7119i	−0.322220	−	1.67184i	0.354083	−	0.935214i	$-0.384793\pi$
$594$	−12.8987	−	3.78739i	−0.529238	−	0.155398i
$595$	21.5072	+	0.761051i	0.881711	+	0.0312001i
$596$	−52.7532	−	7.58476i	−2.16085	−	0.310684i
$597$	12.9488	+	7.47601i	0.529960	+	0.305973i
$598$	−33.2306	−	12.8421i	−1.35890	−	0.525154i
$599$	0.0341618	+	0.0591700i	0.00139581	+	0.00241762i	0.866722	−	0.498791i	$-0.166222\pi$
$599$	0.0341618	+	0.0591700i	0.00139581	+	0.00241762i	−0.865327	+	0.501208i	$0.832889\pi$
$600$	1.06132	−	1.34957i	0.0433280	−	0.0550961i
$601$	8.60233	−	3.92855i	0.350896	−	0.160249i	−0.232167	−	0.972676i	$-0.574581\pi$
$601$	8.60233	−	3.92855i	0.350896	−	0.160249i	0.583063	+	0.812427i	$0.301854\pi$
$602$	5.83149	−	1.79002i	0.237674	−	0.0729559i
$603$	3.95348	−	3.42571i	0.160998	−	0.139506i
$604$	−2.04268	+	8.42004i	−0.0831155	+	0.342607i
$605$	−2.07275	+	43.5123i	−0.0842692	+	1.76903i
$606$	33.4564	−	3.19469i	1.35907	−	0.129776i
$607$	26.7193	−	9.24763i	1.08450	−	0.375350i	0.274386	−	0.961620i	$-0.411525\pi$
$607$	26.7193	−	9.24763i	1.08450	−	0.375350i	0.810116	+	0.586270i	$0.199404\pi$
$608$	−0.192406	+	0.123652i	−0.00780310	+	0.00501475i
$609$	22.8739	−	4.69940i	0.926899	−	0.190429i
$610$	5.02227	+	34.9307i	0.203346	+	1.41430i
$611$	−0.588565	−	12.3555i	−0.0238108	−	0.499850i
$612$	−14.0122	−	2.70064i	−0.566411	−	0.109167i
$613$	3.68503	+	38.5914i	0.148837	+	1.55869i	0.693761	+	0.720205i	$0.255952\pi$
$613$	3.68503	+	38.5914i	0.148837	+	1.55869i	−0.544924	+	0.838485i	$0.683442\pi$
$614$	19.1575	+	37.1603i	0.773133	+	1.49967i
$615$	−18.8681	+	5.54016i	−0.760833	+	0.223401i
$616$	−52.2512	+	51.0558i	−2.10526	+	2.05710i
$617$	−4.45249	+	15.1638i	−0.179251	+	0.610472i	0.820022	+	0.572332i	$0.193961\pi$
$617$	−4.45249	+	15.1638i	−0.179251	+	0.610472i	−0.999272	+	0.0381393i	$0.987857\pi$
$618$	0.418282	−	4.38044i	0.0168258	−	0.176207i
$619$	−8.88755	+	3.55804i	−0.357221	+	0.143010i	−0.543329	−	0.839520i	$-0.682837\pi$
$619$	−8.88755	+	3.55804i	−0.357221	+	0.143010i	0.186109	+	0.982529i	$0.440412\pi$
$620$	−27.4120	+	15.8264i	−1.10089	+	0.635602i
$621$	4.06539	+	2.54412i	0.163139	+	0.102092i
$622$		−	29.7091i		−	1.19123i
$623$	18.7013	−	8.81854i	0.749251	−	0.353307i
$624$	−5.42647	−	11.8823i	−0.217233	−	0.475673i
$625$	−19.2392	+	18.3445i	−0.769567	+	0.733781i
$626$	−8.87180	+	25.6334i	−0.354588	+	1.02452i
$627$	1.68024	+	1.60210i	0.0671022	+	0.0639818i
$628$	24.8291	−	12.8003i	0.990787	−	0.510786i
$629$	13.8926	+	6.34456i	0.553936	+	0.252974i
$630$	−5.76120	−	13.8958i	−0.229532	−	0.553623i
$631$	10.9899	+	17.1006i	0.437501	+	0.680764i	0.988067	−	0.154027i	$-0.0492244\pi$
$631$	10.9899	+	17.1006i	0.437501	+	0.680764i	−0.550566	+	0.834792i	$0.685588\pi$
$632$	26.5193	−	66.2421i	1.05488	−	2.63497i
$633$	−17.3676	−	22.0847i	−0.690301	−	0.877789i
$634$	−31.0229	−	15.9934i	−1.23208	−	0.635179i
$635$	6.81894	+	19.7020i	0.270601	+	0.781851i
$636$	−8.57021	+	18.7662i	−0.339831	+	0.744126i
$637$	21.0790	−	1.52154i	0.835180	−	0.0602854i
$638$	33.4279	+	113.845i	1.32342	+	4.50716i
$639$	13.5830	−	2.61790i	0.537334	−	0.103563i
$640$	−10.4106	−	42.9129i	−0.411514	−	1.69628i
$641$	−14.3145	−	10.1933i	−0.565389	−	0.402612i	0.261311	−	0.965255i	$-0.415845\pi$
$641$	−14.3145	−	10.1933i	−0.565389	−	0.402612i	−0.826700	+	0.562643i	$0.809785\pi$
$642$	22.1716	+	17.4360i	0.875045	+	0.688143i
$643$	8.69163			0.342764			0.171382	−	0.985205i	$-0.445177\pi$
$643$	8.69163			0.342764			0.171382	+	0.985205i	$0.445177\pi$
$644$	45.1358	−	24.6725i	1.77860	−	0.972234i
$645$	−2.16533			−0.0852596
$646$	2.89287	+	2.27498i	0.113818	+	0.0895077i
$647$	16.1531	+	11.5026i	0.635043	+	0.452212i	0.851696	−	0.524036i	$-0.175574\pi$
$647$	16.1531	+	11.5026i	0.635043	+	0.452212i	−0.216652	+	0.976249i	$0.569514\pi$
$648$	1.19146	+	4.91127i	0.0468051	+	0.192933i
$649$	31.9259	−	6.15321i	1.25320	−	0.241534i
$650$	−0.711000	−	2.42144i	−0.0278877	−	0.0949768i
$651$	0.109319	+	8.93898i	0.00428454	+	0.350346i
$652$	27.6991	−	60.6526i	1.08478	−	2.37534i
$653$	−3.69785	−	10.6842i	−0.144708	−	0.418107i	0.849233	−	0.528018i	$-0.177065\pi$
$653$	−3.69785	−	10.6842i	−0.144708	−	0.418107i	−0.993941	+	0.109911i	$0.964943\pi$
$654$	−32.2178	−	16.6094i	−1.25981	−	0.649479i
$655$	19.8833	+	25.2837i	0.776904	+	0.987914i
$656$	13.6845	−	34.1822i	0.534290	−	1.33459i
$657$	−4.44895	−	6.92271i	−0.173570	−	0.270081i
$658$	21.1649	+	16.2294i	0.825095	+	0.632687i
$659$	−15.7787	−	7.20590i	−0.614652	−	0.280702i	0.0836616	−	0.996494i	$-0.473339\pi$
$659$	−15.7787	−	7.20590i	−0.614652	−	0.280702i	−0.698313	+	0.715792i	$0.746066\pi$
$660$	45.4929	−	23.4532i	1.77081	−	0.912915i
$661$	−23.8981	−	22.7868i	−0.929527	−	0.886302i	0.0642223	−	0.997936i	$-0.479543\pi$
$661$	−23.8981	−	22.7868i	−0.929527	−	0.886302i	−0.993749	+	0.111633i	$0.964392\pi$
$662$	1.05096	−	3.03654i	0.0408465	−	0.118018i
$663$	−7.69143	+	7.33377i	−0.298710	+	0.284820i
$664$	−3.83886	−	8.40593i	−0.148977	−	0.326213i
$665$	−0.215301	+	2.58893i	−0.00834900	+	0.100395i
$666$		−	10.6756i		−	0.413670i
$667$	−0.508955	−	42.3255i	−0.0197068	−	1.63885i
$668$	69.9238	−	40.3705i	2.70543	−	1.56198i
$669$	−1.93018	+	0.772726i	−0.0746249	+	0.0298753i
$670$	−2.82723	+	29.6081i	−0.109225	+	1.14386i
$671$	−9.55412	+	32.5383i	−0.368833	+	1.25613i
$672$	1.37119	+	0.384469i	0.0528949	+	0.0148312i
$673$	6.23313	−	1.83021i	0.240270	−	0.0705495i	−0.159381	−	0.987217i	$-0.550950\pi$
$673$	6.23313	−	1.83021i	0.240270	−	0.0705495i	0.399650	+	0.916668i	$0.369132\pi$
$674$	−0.551875	−	1.07049i	−0.0212574	−	0.0412336i
$675$	0.0322933	+	0.338190i	0.00124297	+	0.0130170i
$676$	15.4647	+	2.98057i	0.594795	+	0.114637i
$677$	1.98169	+	41.6008i	0.0761625	+	1.59885i	0.636961	+	0.770896i	$0.280191\pi$
$677$	1.98169	+	41.6008i	0.0761625	+	1.59885i	−0.560799	+	0.827952i	$0.689506\pi$
$678$	5.94475	+	41.3466i	0.228307	+	1.58791i
$679$	0.311876	+	0.103689i	0.0119687	+	0.00397920i
$680$	34.5817	−	22.2243i	1.32615	−	0.852263i
$681$	−26.9435	+	9.32525i	−1.03248	+	0.357344i
$682$	−45.2171	+	4.31771i	−1.73145	+	0.165334i
$683$	2.27125	−	47.6795i	0.0869071	−	1.82440i	−0.363514	−	0.931589i	$-0.618423\pi$
$683$	2.27125	−	47.6795i	0.0869071	−	1.82440i	0.450421	−	0.892816i	$-0.351274\pi$
$684$	0.406122	−	1.67406i	0.0155285	−	0.0640092i
$685$	−28.3336	+	24.5512i	−1.08257	+	0.938054i
$686$	−26.8360	+	36.8285i	−1.02460	+	1.40612i
$687$	−10.7285	+	4.89956i	−0.409319	+	0.186930i
$688$	2.50622	−	3.18692i	0.0955487	−	0.121500i
$689$	7.68211	+	13.3058i	0.292665	+	0.506911i
$690$	−26.7106	+	5.48195i	−1.01686	+	0.208694i
$691$	2.28191	+	1.31746i	0.0868081	+	0.0501187i	0.542776	−	0.839878i	$-0.317373\pi$
$691$	2.28191	+	1.31746i	0.0868081	+	0.0501187i	−0.455968	+	0.889996i	$0.650707\pi$
$692$	−101.382	−	14.5766i	−3.85398	−	0.554119i
$693$	0.511198	−	14.4464i	0.0194188	−	0.548774i
$694$	−27.2119	−	7.99013i	−1.03295	−	0.303301i
$695$	8.78090	+	45.5596i	0.333079	+	1.72818i
$696$	30.7808	−	32.2820i	1.16674	−	1.22365i
$697$	−29.9214	−	1.42533i	−1.13335	−	0.0539882i
$698$	−11.5086	+	8.19523i	−0.435606	+	0.310194i
$699$	−0.727681	−	0.630539i	−0.0275234	−	0.0238492i
$700$	3.33283	+	1.47307i	0.125969	+	0.0556766i
$701$	17.1583	−	2.46699i	0.648059	−	0.0931768i	0.189556	−	0.981870i	$-0.439295\pi$
$701$	17.1583	−	2.46699i	0.648059	−	0.0931768i	0.458503	+	0.888693i	$0.348386\pi$
$702$	6.89637	+	2.76089i	0.260287	+	0.104203i
$703$	−0.844813	+	1.63871i	−0.0318627	+	0.0618051i
$704$	7.57821	−	39.3195i	0.285615	−	1.48191i
$705$	−5.49164	−	7.71193i	−0.206827	−	0.290448i
$706$	−0.493929	+	0.768569i	−0.0185893	+	0.0289255i
$707$	12.2367	+	34.0045i	0.460209	+	1.27887i
$708$	−15.7982	−	18.2321i	−0.593734	−	0.685206i
$709$	15.2875	+	16.0331i	0.574135	+	0.602136i	0.945208	−	0.326468i	$-0.105859\pi$
$709$	15.2875	+	16.0331i	0.574135	+	0.602136i	−0.371073	+	0.928604i	$0.621010\pi$
$710$	−45.6210	+	64.0657i	−1.71213	+	2.40434i
$711$	5.24747	+	13.1076i	0.196796	+	0.491572i
$712$	19.7471	−	34.2030i	0.740054	−	1.28181i
$713$	15.9474	+	2.87518i	0.597234	+	0.107676i
$714$	−1.37015	−	22.8738i	−0.0512765	−	0.856031i
$715$	5.42467	−	37.7294i	0.202871	−	1.41100i
$716$	−40.4677	−	3.86420i	−1.51235	−	0.144412i
$717$	−3.93179	+	0.953842i	−0.146835	+	0.0356219i
$718$	27.4166	+	9.48896i	1.02318	+	0.354125i
$719$	47.6638	+	11.5631i	1.77756	+	0.431232i	0.984133	−	0.177432i	$-0.0567790\pi$
$719$	47.6638	+	11.5631i	1.77756	+	0.431232i	0.793428	+	0.608664i	$0.208294\pi$
$720$	−8.41088	−	5.40534i	−0.313455	−	0.201445i
$721$	4.67496	−	0.730615i	0.174105	−	0.0272095i
$722$	30.3232	−	34.9949i	1.12851	−	1.30237i
$723$	−28.0177	+	1.33465i	−1.04199	+	0.0496362i
$724$	−3.31918	+	2.61023i	−0.123356	+	0.0970084i
$725$	2.35697	−	1.85354i	0.0875355	−	0.0688387i
$726$	46.3311	−	2.20702i	1.71951	−	0.0819102i
$727$	8.23267	−	9.50100i	0.305333	−	0.352373i	−0.582259	−	0.813003i	$-0.697831\pi$
$727$	8.23267	−	9.50100i	0.305333	−	0.352373i	0.887592	+	0.460630i	$0.152377\pi$
$728$	31.4242	−	25.3403i	1.16466	−	0.939173i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	45.4685	+	11.0305i	1.68286	+	0.408258i
$731$	−3.11705	−	1.07882i	−0.115288	−	0.0399016i
$732$	24.4530	−	5.93224i	0.903809	−	0.219262i
$733$	−9.43251	−	0.900696i	−0.348398	−	0.0332680i	−0.0806096	−	0.996746i	$-0.525687\pi$
$733$	−9.43251	−	0.900696i	−0.348398	−	0.0332680i	−0.267788	+	0.963478i	$0.586293\pi$
$734$	−5.55344	+	38.6250i	−0.204981	+	1.42568i
$735$	12.9428	−	9.70213i	0.477401	−	0.357868i
$736$	1.15517	−	2.30845i	0.0425801	−	0.0850907i
$737$	−14.2907	+	24.7523i	−0.526406	+	0.911762i
$738$	7.78205	+	19.4386i	0.286461	+	0.715546i
$739$	5.03575	−	7.07172i	0.185243	−	0.260138i	−0.711503	−	0.702683i	$-0.751985\pi$
$739$	5.03575	−	7.07172i	0.185243	−	0.260138i	0.896746	+	0.442546i	$0.145925\pi$
$740$	28.0485	+	29.4164i	1.03108	+	1.08137i
$741$	−0.840114	−	0.969544i	−0.0308624	−	0.0356171i
$742$	−32.6038	−	5.87131i	−1.19692	−	0.215543i
$743$	14.8204	−	23.0610i	0.543707	−	0.846025i	−0.455311	−	0.890333i	$-0.650472\pi$
$743$	14.8204	−	23.0610i	0.543707	−	0.846025i	0.999018	+	0.0443076i	$0.0141082\pi$
$744$	9.90500	+	13.9096i	0.363135	+	0.509951i
$745$	−5.74924	+	29.8299i	−0.210636	+	1.09288i
$746$	0.566680	−	1.09921i	0.0207476	−	0.0402448i
$747$	1.69757	+	0.679605i	0.0621109	+	0.0248655i
$748$	77.1733	−	11.0958i	2.82173	−	0.405704i
$749$	−12.2613	+	27.7413i	−0.448018	+	1.01365i
$750$	20.0248	+	17.3516i	0.731203	+	0.633591i
$751$	16.1844	−	11.5249i	0.590577	−	0.420548i	−0.245314	−	0.969444i	$-0.578891\pi$
$751$	16.1844	−	11.5249i	0.590577	−	0.420548i	0.835891	+	0.548896i	$0.184952\pi$
$752$	17.7066	+	0.843468i	0.645692	+	0.0307581i
$753$	18.5236	−	19.4270i	0.675039	−	0.707960i
$754$	−12.4082	−	64.3798i	−0.451880	−	2.34457i
$755$	4.73864	+	1.39139i	0.172457	+	0.0506379i
$756$	−9.47263	+	5.03105i	−0.344516	+	0.182977i
$757$	−22.5741	−	3.24567i	−0.820470	−	0.117966i	−0.280718	−	0.959790i	$-0.590573\pi$
$757$	−22.5741	−	3.24567i	−0.820470	−	0.117966i	−0.539751	+	0.841824i	$0.681482\pi$
$758$	−39.0676	−	22.5557i	−1.41900	−	0.819259i
$759$	−25.5366	−	5.87090i	−0.926918	−	0.213100i
$760$	2.48114	+	4.29746i	0.0900003	+	0.155885i
$761$	29.7954	−	37.8879i	1.08008	−	1.37344i	0.157552	−	0.987511i	$-0.449640\pi$
$761$	29.7954	−	37.8879i	1.08008	−	1.37344i	0.922530	−	0.385925i	$-0.126118\pi$
$762$	20.1932	−	9.22192i	0.731522	−	0.334075i
$763$	8.72519	−	37.9874i	0.315873	−	1.37524i
$764$	17.0265	−	14.7535i	0.615997	−	0.533764i
$765$	−1.91768	+	7.90477i	−0.0693338	+	0.285798i
$766$	2.32312	−	48.7684i	0.0839379	−	1.76207i
$767$	−17.8850	+	1.70781i	−0.645791	+	0.0616655i
$768$	−30.5804	+	10.5840i	−1.10348	+	0.381917i
$769$	−39.1744	+	25.1759i	−1.41267	+	0.907866i	−0.999995	−	0.00301417i	$-0.999041\pi$
$769$	−39.1744	+	25.1759i	−1.41267	+	0.907866i	−0.412671	+	0.910880i	$0.635404\pi$
$770$	54.5776	+	61.4511i	1.96684	+	2.21455i
$771$	2.60489	+	18.1174i	0.0938127	+	0.652482i
$772$	0.211113	+	4.43181i	0.00759813	+	0.159504i
$773$	43.2765	+	8.34086i	1.55655	+	0.300000i	0.893669	−	0.448727i	$-0.148123\pi$
$773$	43.2765	+	8.34086i	1.55655	+	0.300000i	0.662878	+	0.748727i	$0.269335\pi$
$774$	0.219161	+	2.29516i	0.00787758	+	0.0824978i
$775$	0.525998	+	1.02029i	0.0188944	+	0.0366500i
$776$	0.602356	−	0.176868i	0.0216233	−	0.00634918i
$777$	11.1219	−	2.84260i	0.398996	−	0.101978i
$778$	24.2090	−	82.4482i	0.867934	−	2.95591i
$779$	0.343728	−	3.59968i	0.0123153	−	0.128972i
$780$	−26.2567	+	10.5116i	−0.940140	+	0.376375i
$781$	−65.4528	+	37.7892i	−2.34209	+	1.35220i
$782$	−41.1820	−	5.41651i	−1.47266	−	0.193694i
$783$			8.82611i			0.315419i
$784$	−0.700840	+	30.2787i	−0.0250300	+	1.08138i
$785$	−6.61456	−	14.4839i	−0.236084	−	0.516951i
$786$	24.7872	−	23.6345i	0.884130	−	0.843016i
$787$	−11.0998	+	32.0708i	−0.395666	+	1.14320i	0.554696	+	0.832053i	$0.312835\pi$
$787$	−11.0998	+	32.0708i	−0.395666	+	1.14320i	−0.950362	+	0.311147i	$0.899287\pi$
$788$	6.58428	+	6.27810i	0.234555	+	0.223648i
$789$	−12.9431	+	6.67262i	−0.460786	+	0.237551i
$790$	−73.0208	−	33.3475i	−2.59796	−	1.18645i
$791$	−41.4924	+	17.2027i	−1.47530	+	0.611658i
$792$	−14.9281	−	23.2285i	−0.530446	−	0.825390i
$793$	6.96466	−	17.3969i	0.247322	−	0.617781i
$794$	16.7734	+	21.3291i	0.595265	+	0.756941i
$795$	10.4523	+	5.38852i	0.370704	+	0.191111i
$796$	19.8252	+	57.2811i	0.702686	+	2.03028i
$797$	2.71281	−	5.94022i	0.0960926	−	0.210413i	−0.855481	−	0.517834i	$-0.826739\pi$
$797$	2.71281	−	5.94022i	0.0960926	−	0.210413i	0.951574	+	0.307420i	$0.0994658\pi$
$798$	2.76596	−	0.0338261i	0.0979138	−	0.00119743i
$799$	−4.06309	−	13.8376i	−0.143742	−	0.489540i
$800$	0.179554	−	0.0346062i	0.00634819	−	0.00122351i
$801$	1.84242	+	7.59457i	0.0650988	+	0.268341i
$802$	−49.6152	−	35.3308i	−1.75197	−	1.24757i
$803$	35.3414	+	27.7928i	1.24717	+	0.980786i
$804$	21.2071			0.747917
$805$	−12.8234	−	26.3677i	−0.451966	−	0.929340i
$806$	25.0999			0.884106
$807$	−17.2432	−	13.5602i	−0.606991	−	0.477343i
$808$	56.2307	+	40.0417i	1.97819	+	1.40866i
$809$	9.95194	+	41.0225i	0.349892	+	1.44227i	0.826390	+	0.563098i	$0.190391\pi$
$809$	9.95194	+	41.0225i	0.349892	+	1.44227i	−0.476498	+	0.879175i	$0.658094\pi$
$810$	5.58289	−	1.07601i	0.196163	−	0.0378073i
$811$	−0.815652	−	2.77786i	−0.0286414	−	0.0975437i	0.943932	−	0.330140i	$-0.107096\pi$
$811$	−0.815652	−	2.77786i	−0.0286414	−	0.0975437i	−0.972573	+	0.232596i	$0.925278\pi$
$812$	82.5566	+	46.3274i	2.89717	+	1.62577i
$813$	−8.25471	+	18.0753i	−0.289505	+	0.633928i
$814$	19.0771	+	55.1196i	0.668651	+	1.93194i
$815$	−33.7820	−	17.4158i	−1.18333	−	0.610049i
$816$	−9.41462	−	11.9717i	−0.329578	−	0.419092i
$817$	0.147986	−	0.369652i	0.00517738	−	0.0129325i
$818$	−1.55142	−	2.41406i	−0.0542443	−	0.0844057i
$819$	−1.04002	+	7.91985i	−0.0363412	+	0.276742i
$820$	−72.5155	−	33.1167i	−2.53235	−	1.15649i
$821$	12.0734	−	6.22426i	0.421364	−	0.217228i	−0.234486	−	0.972119i	$-0.575341\pi$
$821$	12.0734	−	6.22426i	0.421364	−	0.217228i	0.655850	+	0.754891i	$0.272310\pi$
$822$	28.8911	+	27.5476i	1.00769	+	0.960832i
$823$	9.87333	−	28.5271i	0.344163	−	0.994393i	−0.631549	−	0.775336i	$-0.717581\pi$
$823$	9.87333	−	28.5271i	0.344163	−	0.994393i	0.975712	−	0.219057i	$-0.0702982\pi$
$824$	6.54124	−	6.23706i	0.227875	−	0.217278i
$825$	−0.771076	−	1.68842i	−0.0268454	−	0.0587833i
$826$	22.0833	−	31.8283i	0.768376	−	1.10745i
$827$		−	21.7602i		−	0.756677i	−0.925667	−	0.378339i	$-0.876495\pi$
$827$		−	21.7602i		−	0.756677i	0.925667	−	0.378339i	$-0.123505\pi$
$828$	5.70138	+	18.5874i	0.198137	+	0.645956i
$829$	−41.4218	+	23.9149i	−1.43864	+	0.830598i	−0.997755	−	0.0669676i	$-0.978668\pi$
$829$	−41.4218	+	23.9149i	−1.43864	+	0.830598i	−0.440882	+	0.897565i	$0.645334\pi$
$830$	−9.65179	+	3.86399i	−0.335018	+	0.134121i
$831$	0.799544	−	8.37321i	0.0277359	−	0.290463i
$832$	−6.23394	+	21.2309i	−0.216123	+	0.736048i
$833$	23.4653	−	7.51807i	0.813026	−	0.260486i
$834$	47.4026	−	13.9187i	1.64142	−	0.481964i
$835$	−21.0889	−	40.9068i	−0.729813	−	1.41564i
$836$	0.894646	+	9.36915i	0.0309420	+	0.324039i
$837$	−3.31781	−	0.639455i	−0.114680	−	0.0221028i
$838$	1.86688	+	39.1906i	0.0644903	+	1.35382i
$839$	1.55981	+	10.8487i	0.0538506	+	0.374539i	0.998870	+	0.0475249i	$0.0151333\pi$
$839$	1.55981	+	10.8487i	0.0538506	+	0.374539i	−0.945019	+	0.327014i	$0.893958\pi$
$840$	9.74772	−	29.3194i	0.336328	−	1.01161i
$841$	41.1375	−	26.4375i	1.41853	−	0.911637i
$842$	−80.4342	+	27.8386i	−2.77195	+	0.959380i
$843$	15.1810	−	1.44961i	0.522862	−	0.0499273i
$844$	5.41953	−	113.770i	0.186548	−	3.91612i
$845$	2.11645	−	8.72414i	0.0728082	−	0.300120i
$846$	−7.61850	+	6.60147i	−0.261930	+	0.226963i
$847$	14.6359	+	47.6805i	0.502896	+	1.63832i
$848$	−20.0286	+	9.14675i	−0.687785	+	0.314101i
$849$	−1.46949	+	1.86861i	−0.0504327	+	0.0641304i
$850$	−1.47119	−	2.54818i	−0.0504615	−	0.0874019i
$851$	−1.23994	−	20.7713i	−0.0425045	−	0.712029i
$852$	48.5652	+	28.0391i	1.66382	+	0.960605i
$853$	39.5795	+	5.69067i	1.35518	+	0.194845i	0.781330	−	0.624118i	$-0.214542\pi$
$853$	39.5795	+	5.69067i	1.35518	+	0.194845i	0.573846	+	0.818963i	$0.305451\pi$
$854$	18.9526	+	35.6847i	0.648545	+	1.22110i
$855$	−0.942129	−	0.276634i	−0.0322201	−	0.00946069i
$856$	10.9642	+	56.8877i	0.374749	+	1.94438i
$857$	22.6584	−	23.7634i	0.773996	−	0.811744i	−0.212217	−	0.977223i	$-0.568068\pi$
$857$	22.6584	−	23.7634i	0.773996	−	0.811744i	0.986213	+	0.165479i	$0.0529169\pi$
$858$	−40.5407	−	1.93119i	−1.38404	−	0.0659297i
$859$	−13.2669	+	9.44731i	−0.452661	+	0.322338i	−0.783547	−	0.621332i	$-0.786592\pi$
$859$	−13.2669	+	9.44731i	−0.452661	+	0.322338i	0.330886	+	0.943671i	$0.392652\pi$
$860$	−6.63408	−	5.74847i	−0.226220	−	0.196021i
$861$	−18.1792	+	13.2834i	−0.619546	+	0.452696i
$862$	30.7692	−	4.42394i	1.04800	−	0.150680i
$863$	−38.0535	−	15.2343i	−1.29536	−	0.518582i	−0.381405	−	0.924408i	$-0.624560\pi$
$863$	−38.0535	−	15.2343i	−1.29536	−	0.518582i	−0.913950	+	0.405826i	$0.866984\pi$
$864$	−0.246640	+	0.478415i	−0.00839086	+	0.0162760i
$865$	−11.0490	+	57.3279i	−0.375679	+	1.94921i
$866$	−6.05922	−	8.50898i	−0.205901	−	0.289147i
$867$	2.49198	−	3.87760i	0.0846321	−	0.131690i
$868$	−23.3961	+	27.6773i	−0.794116	+	0.939429i
$869$	−50.5165	−	58.2991i	−1.71365	−	1.97766i
$870$	−34.6296	−	36.3185i	−1.17405	−	1.23131i
$871$	9.16122	−	12.8651i	0.310416	−	0.435918i
$872$	−27.6704	−	69.1172i	−0.937037	−	2.34061i
$873$	−0.0621111	+	0.107580i	−0.00210214	+	0.00364102i
$874$	0.889656	−	4.93454i	0.0300931	−	0.166913i
$875$	−12.7450	+	25.4823i	−0.430861	+	0.861458i
$876$	4.74765	−	33.0206i	0.160408	−	1.11566i
$877$	−6.47645	−	0.618426i	−0.218694	−	0.0208828i	−0.0148663	−	0.999889i	$-0.504732\pi$
$877$	−6.47645	−	0.618426i	−0.218694	−	0.0208828i	−0.203828	+	0.979007i	$0.565338\pi$
$878$	−0.960094	+	0.232916i	−0.0324016	+	0.00786054i
$879$	11.4998	+	3.98013i	0.387880	+	0.134247i
$880$	53.0859	+	12.8785i	1.78953	+	0.434134i
$881$	−5.70090	−	3.66375i	−0.192068	−	0.123435i	0.441072	−	0.897472i	$-0.354598\pi$
$881$	−5.70090	−	3.66375i	−0.192068	−	0.123435i	−0.633141	+	0.774037i	$0.718235\pi$
$882$	−11.5939	−	12.7368i	−0.390385	−	0.428871i
$883$	−27.5302	+	31.7716i	−0.926467	+	1.06920i	0.0709583	+	0.997479i	$0.477394\pi$
$883$	−27.5302	+	31.7716i	−0.926467	+	1.06920i	−0.997425	+	0.0717201i	$0.977151\pi$
$884$	−43.0344	+	2.04998i	−1.44740	+	0.0689483i
$885$	−10.8091	+	8.50041i	−0.363346	+	0.285738i
$886$	20.6820	−	16.2645i	0.694826	−	0.546417i
$887$	−56.7905	+	2.70527i	−1.90684	+	0.0908340i	−0.967609	−	0.252453i	$-0.918763\pi$
$887$	−56.7905	+	2.70527i	−1.90684	+	0.0908340i	−0.939230	+	0.343287i	$0.888460\pi$
$888$	14.3593	−	16.5715i	0.481866	−	0.556102i
$889$	14.9843	+	18.5819i	0.502559	+	0.623218i
$890$	−37.3790	−	24.0220i	−1.25295	−	0.805220i
$891$	5.30964	+	1.28810i	0.177880	+	0.0431531i
$892$	−7.96505	−	2.75673i	−0.266690	−	0.0923022i
$893$	1.69185	−	0.410439i	0.0566158	−	0.0137348i
$894$	32.2004	+	3.07476i	1.07694	+	0.102835i
$895$	−3.29769	+	22.9359i	−0.110230	+	0.766664i
$896$	−27.8521	−	42.1952i	−0.930475	−	1.40964i
$897$	13.7388	+	4.57082i	0.458725	+	0.152615i
$898$	5.99535	−	10.3843i	0.200068	−	0.346527i
$899$	11.0838	+	27.6861i	0.369666	+	0.923382i
$900$	−0.798882	+	1.12187i	−0.0266294	+	0.0373957i
$901$	12.3617	+	12.9645i	0.411826	+	0.431911i
$902$	−74.9164	−	86.4582i	−2.49444	−	2.87874i
$903$	−2.33276	+	0.839458i	−0.0776295	+	0.0279354i
$904$	−46.3857	+	72.1776i	−1.54277	+	2.40059i
$905$	1.39614	+	1.96060i	0.0464093	+	0.0651727i
$906$	0.995202	−	5.16360i	0.0330634	−	0.171549i
$907$	21.6687	−	42.0314i	0.719497	−	1.39563i	−0.190782	−	0.981633i	$-0.561102\pi$
$907$	21.6687	−	42.0314i	0.719497	−	1.39563i	0.910278	−	0.413997i	$-0.135868\pi$
$908$	−107.306	−	42.9587i	−3.56106	−	1.42563i
$909$	−13.5203	+	1.94393i	−0.448440	+	0.0644760i
$910$	−26.7943	−	36.6699i	−0.888222	−	1.21559i
$911$	29.2393	+	25.3360i	0.968742	+	0.839420i	0.987050	−	0.160413i	$-0.0512825\pi$
$911$	29.2393	+	25.3360i	0.968742	+	0.839420i	−0.0183082	+	0.999832i	$0.505828\pi$
$912$	1.49760	−	1.06644i	0.0495904	−	0.0353132i
$913$	−9.97927	−	0.475371i	−0.330266	−	0.0157325i
$914$	21.7444	−	22.8049i	0.719242	−	0.754319i
$915$	−2.71437	−	14.0835i	−0.0897343	−	0.465586i
$916$	−45.8771	−	13.4707i	−1.51582	−	0.445086i
$917$	31.2228	+	19.5303i	1.03107	+	0.644949i
$918$	8.57283	+	1.23259i	0.282946	+	0.0406814i
$919$	3.26634	+	1.88582i	0.107747	+	0.0622076i	0.552905	−	0.833244i	$-0.313519\pi$
$919$	3.26634	+	1.88582i	0.107747	+	0.0622076i	−0.445158	+	0.895452i	$0.646853\pi$
$920$	−48.8359	−	27.4179i	−1.61007	−	0.903940i
$921$	−8.49588	−	14.7153i	−0.279949	−	0.484886i
$922$	−22.5857	+	28.7201i	−0.743822	+	0.945846i
$923$	37.9893	−	17.3491i	1.25043	−	0.571053i
$924$	39.9182	−	42.9035i	1.31321	−	1.41142i
$925$	1.11399	−	0.965278i	0.0366278	−	0.0317381i
$926$	−2.21753	+	9.14077i	−0.0728725	+	0.300384i
$927$	−0.0850964	+	1.78639i	−0.00279493	+	0.0586728i
$928$	4.72913	−	0.451577i	0.155241	−	0.0148238i
$929$	45.4085	−	15.7160i	1.48980	−	0.515626i	0.543642	−	0.839317i	$-0.317045\pi$
$929$	45.4085	−	15.7160i	1.48980	−	0.515626i	0.946163	+	0.323691i	$0.104924\pi$
$930$	16.1614	−	10.3863i	0.529952	−	0.340579i
$931$	0.771735	+	2.87259i	0.0252926	+	0.0941455i
$932$	−0.555511	−	3.86367i	−0.0181964	−	0.126559i
$933$	0.574529	+	12.0609i	0.0188092	+	0.394855i
$934$	61.5983	+	11.8721i	2.01556	+	0.388467i
$935$	−4.22445	−	44.2404i	−0.138154	−	1.44682i
$936$	6.99154	+	13.5617i	0.228526	+	0.443278i
$937$	−16.9796	+	4.98566i	−0.554699	+	0.162874i	−0.547055	−	0.837097i	$-0.684251\pi$
$937$	−16.9796	+	4.98566i	−0.554699	+	0.162874i	−0.00764359	+	0.999971i	$0.502433\pi$
$938$	8.43268	+	32.9936i	0.275337	+	1.07728i
$939$	3.10592	−	10.5778i	0.101358	−	0.345194i
$940$	3.64830	−	38.2068i	0.118995	−	1.24617i
$941$	−27.9223	+	11.1784i	−0.910241	+	0.364406i	−0.779057	−	0.626952i	$-0.784302\pi$
$941$	−27.9223	+	11.1784i	−0.910241	+	0.364406i	−0.131184	+	0.991358i	$0.541878\pi$
$942$	−14.6828	+	8.47713i	−0.478392	+	0.276200i
$943$	17.3991	+	36.9175i	0.566594	+	1.20220i
$944$		−	25.7475i		−	0.838009i
$945$	2.60757	+	5.52980i	0.0848241	+	0.179884i
$946$	−5.23297	−	11.4586i	−0.170139	−	0.372552i
$947$	−5.15289	+	4.91327i	−0.167446	+	0.159660i	−0.769169	−	0.639045i	$-0.779330\pi$
$947$	−5.15289	+	4.91327i	−0.167446	+	0.159660i	0.601723	+	0.798705i	$0.294481\pi$
$948$	−18.7206	+	54.0895i	−0.608016	+	1.75675i
$949$	−17.9808	−	17.1446i	−0.583681	−	0.556539i
$950$	0.315706	−	0.162758i	0.0102428	−	0.00528055i
$951$	12.9035	+	5.89282i	0.418424	+	0.191088i
$952$	28.6398	−	37.3495i	0.928221	−	1.21051i
$953$	7.02746	+	10.9349i	0.227642	+	0.354218i	0.936220	−	0.351415i	$-0.114299\pi$
$953$	7.02746	+	10.9349i	0.227642	+	0.354218i	−0.708578	+	0.705632i	$0.750663\pi$
$954$	4.65370	−	11.6244i	0.150669	−	0.376353i
$955$	−7.93830	−	10.0944i	−0.256877	−	0.326646i
$956$	−14.5784	−	7.51567i	−0.471498	−	0.243074i
$957$	−15.7721	−	45.5706i	−0.509840	−	1.47309i
$958$	−34.0798	+	74.6244i	−1.10107	+	2.41100i
$959$	−21.0065	+	37.4341i	−0.678334	+	1.20881i
$960$	4.77136	+	16.2498i	0.153995	+	0.524459i
$961$	19.2293	−	3.70615i	0.620301	−	0.119553i
$962$	−7.59871	−	31.3223i	−0.244992	−	1.00987i
$963$	−9.33808	−	6.64962i	−0.300915	−	0.214281i
$964$	−89.3834	−	70.2919i	−2.87885	−	2.26395i
$965$	2.52903			0.0814122
$966$	−26.6508	+	16.2611i	−0.857475	+	0.523192i
$967$	−44.9486			−1.44545			−0.722725	−	0.691135i	$-0.757111\pi$
$967$	−44.9486			−1.44545			−0.722725	+	0.691135i	$0.757111\pi$
$968$	74.8874	+	58.8921i	2.40697	+	1.89286i
$969$	−1.21840	−	0.867616i	−0.0391405	−	0.0278718i
$970$	−0.166513	−	0.686374i	−0.00534640	−	0.0220381i
$971$	−34.6532	+	6.67885i	−1.11207	+	0.214335i	−0.712021	−	0.702158i	$-0.752220\pi$
$971$	−34.6532	+	6.67885i	−1.11207	+	0.214335i	−0.400052	+	0.916492i	$0.631008\pi$
$972$	−1.14213	−	3.88975i	−0.0366339	−	0.124764i
$973$	27.1225	+	45.6784i	0.869509	+	1.46438i
$974$	−4.70711	+	10.3071i	−0.150826	+	0.330262i
$975$	0.335468	+	0.969270i	0.0107436	+	0.0310415i
$976$	23.8697	+	12.3057i	0.764050	+	0.393895i
$977$	21.4835	+	27.3186i	0.687320	+	0.873998i	0.997044	−	0.0768283i	$-0.0244793\pi$
$977$	21.4835	+	27.3186i	0.687320	+	0.873998i	−0.309725	+	0.950826i	$0.600237\pi$
$978$	−15.0408	+	37.5702i	−0.480953	+	1.20136i
$979$	−23.0841	−	35.9196i	−0.737771	−	1.14799i
$980$	65.4108	+	4.63503i	2.08947	+	0.148061i
$981$	13.4005	+	6.11979i	0.427844	+	0.195390i
$982$	−25.1759	+	12.9791i	−0.803395	+	0.414179i
$983$	−18.5856	−	17.7213i	−0.592787	−	0.565222i	0.333162	−	0.942870i	$-0.391884\pi$
$983$	−18.5856	−	17.7213i	−0.592787	−	0.565222i	−0.925949	+	0.377648i	$0.876733\pi$
$984$	−14.0662	+	40.6415i	−0.448413	+	1.29560i
$985$	3.75308	−	3.57856i	0.119583	−	0.114022i
$986$	−31.7555	−	69.5349i	−1.01130	−	2.21444i
$987$	−8.90606	−	6.17925i	−0.283483	−	0.196688i
$988$		−	5.20079i		−	0.165459i
$989$	0.692994	+	4.44019i	0.0220359	+	0.141190i
$990$	−26.9025	+	15.5322i	−0.855018	+	0.493645i
$991$	38.3584	−	15.3564i	1.21849	−	0.487812i	0.328814	−	0.944395i	$-0.393351\pi$
$991$	38.3584	−	15.3564i	1.21849	−	0.487812i	0.889681	+	0.456583i	$0.150927\pi$
$992$	−0.172876	+	1.81044i	−0.00548881	+	0.0574815i
$993$	−0.367929	+	1.25305i	−0.0116759	+	0.0397643i
$994$	−24.3115	+	86.7061i	−0.771115	+	2.75015i
$995$	33.1514	−	9.73412i	1.05097	−	0.308592i
$996$	3.39678	+	6.58884i	0.107631	+	0.208775i
$997$	−0.516743	−	5.41157i	−0.0163654	−	0.171386i	0.983594	−	0.180396i	$-0.0577380\pi$
$997$	−0.516743	−	5.41157i	−0.0163654	−	0.171386i	−0.999959	+	0.00901009i	$0.997132\pi$
$998$	11.9769	+	2.30835i	0.379121	+	0.0730696i
$999$	0.206449	+	4.33390i	0.00653176	+	0.137119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.61.4	✓	640
7.3	odd	6	inner	483.2.bf.a.199.29	yes	640
23.20	odd	22	inner	483.2.bf.a.250.29	yes	640
161.66	even	66	inner	483.2.bf.a.388.4	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.61.4	✓	640	1.1	even	1	trivial
483.2.bf.a.199.29	yes	640	7.3	odd	6	inner
483.2.bf.a.250.29	yes	640	23.20	odd	22	inner
483.2.bf.a.388.4	yes	640	161.66	even	66	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93407 - 1.52097i) q^{2} +(0.814576 + 0.580057i) q^{3} +(0.955758 + 3.93969i) q^{4} +(2.26903 - 0.437319i) q^{5} +(-0.693197 - 2.36081i) q^{6} +(2.27494 - 1.35080i) q^{7} +(2.09940 - 4.59704i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(-1.93407 - 1.52097i) q^{2} +(0.814576 + 0.580057i) q^{3} +(0.955758 + 3.93969i) q^{4} +(2.26903 - 0.437319i) q^{5} +(-0.693197 - 2.36081i) q^{6} +(2.27494 - 1.35080i) q^{7} +(2.09940 - 4.59704i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-5.05360 - 2.60531i) q^{10} +(-3.37740 - 4.29472i) q^{11} +(-1.50671 + 3.76357i) q^{12} +(1.63226 + 2.53985i) q^{13} +(-6.45440 - 0.847579i) q^{14} +(2.10196 + 0.959935i) q^{15} +(-3.84571 + 1.98260i) q^{16} +(2.54757 + 2.42911i) q^{17} +(0.804744 - 2.32516i) q^{18} +(-0.307530 + 0.293230i) q^{19} +(3.89154 + 8.52128i) q^{20} +(2.63665 + 0.219269i) q^{21} +13.4432i q^{22} +(1.29572 - 4.61748i) q^{23} +(4.37666 - 2.52687i) q^{24} +(0.315393 - 0.126264i) q^{25} +(0.706122 - 7.39485i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(7.49600 + 7.67152i) q^{28} +(8.46859 - 2.48660i) q^{29} +(-2.60531 - 5.05360i) q^{30} +(0.321182 + 3.36357i) q^{31} +(0.528522 + 0.101864i) q^{32} +(-0.259971 - 5.45746i) q^{33} +(-1.23259 - 8.57283i) q^{34} +(4.57117 - 4.05987i) q^{35} +(-3.41041 + 2.19174i) q^{36} +(4.10018 - 1.41909i) q^{37} +(1.04078 - 0.0993822i) q^{38} +(-0.143656 + 3.01570i) q^{39} +(2.75321 - 11.3489i) q^{40} +(-6.43137 + 5.57281i) q^{41} +(-4.76596 - 4.43434i) q^{42} +(-0.852373 + 0.389266i) q^{43} +(13.6919 - 17.4106i) q^{44} +(1.15539 + 2.00120i) q^{45} +(-9.52904 + 6.95978i) q^{46} +(-3.54815 - 2.04853i) q^{47} +(-4.28264 - 0.615751i) q^{48} +(3.35070 - 6.14596i) q^{49} +(-0.802036 - 0.235499i) q^{50} +(0.666172 + 3.45643i) q^{51} +(-8.44615 + 8.85807i) q^{52} +(5.08321 + 0.242143i) q^{53} +(2.00425 - 1.42722i) q^{54} +(-9.54158 - 8.26782i) q^{55} +(-1.43366 - 13.2938i) q^{56} +(-0.420597 + 0.0604727i) q^{57} +(-20.1609 - 8.07120i) q^{58} +(-2.72684 + 5.28934i) q^{59} +(-1.77287 + 9.19855i) q^{60} +(-3.60032 - 5.05594i) q^{61} +(4.49470 - 6.99388i) q^{62} +(2.02056 + 1.70802i) q^{63} +(4.79948 + 5.53890i) q^{64} +(4.81436 + 5.04916i) q^{65} +(-7.79782 + 10.9505i) q^{66} +(-1.94424 - 4.85649i) q^{67} +(-7.13506 + 12.3583i) q^{68} +(3.73386 - 3.00970i) q^{69} +(-15.0159 + 0.899454i) q^{70} +(1.96863 - 13.6922i) q^{71} +(5.03085 + 0.480388i) q^{72} +(-7.99707 + 1.94007i) q^{73} +(-10.0884 - 3.49164i) q^{74} +(0.330152 + 0.0800941i) q^{75} +(-1.44916 - 0.931317i) q^{76} +(-13.4847 - 5.20804i) q^{77} +(4.86462 - 5.61408i) q^{78} +(14.1029 - 0.671805i) q^{79} +(-7.85898 + 6.18037i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(20.9148 - 0.996294i) q^{82} +(1.19745 - 1.38193i) q^{83} +(1.65615 + 10.5971i) q^{84} +(6.84281 + 4.39760i) q^{85} +(2.24061 + 0.543565i) q^{86} +(8.34068 + 2.88674i) q^{87} +(-26.8335 + 6.50973i) q^{88} +(7.77947 + 0.742850i) q^{89} +(0.809151 - 5.62777i) q^{90} +(7.14411 + 3.57315i) q^{91} +(19.4298 + 0.691521i) q^{92} +(-1.68944 + 2.92619i) q^{93} +(3.74663 + 9.35862i) q^{94} +(-0.569560 + 0.799835i) q^{95} +(0.371434 + 0.389549i) q^{96} +(0.0813483 + 0.0938809i) q^{97} +(-15.8283 + 6.79039i) q^{98} +(2.95387 - 4.59631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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