LMFDB - Embedded newform 465.2.bt.a.38.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(38,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.38"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([30, 45, 56])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.bt (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$60$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			38.17
Character	$\chi$	$=$	465.38
Dual form			465.2.bt.a.257.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.603653 + 1.18474i) q^{2} +(1.50094 - 0.864394i) q^{3} +(0.136370 + 0.187697i) q^{4} +(2.06692 - 0.853147i) q^{5} +(0.118032 + 2.30001i) q^{6} +(-1.30223 + 0.499878i) q^{7} +(-2.93127 + 0.464267i) q^{8} +(1.50564 - 2.59481i) q^{9} +(-0.236946 + 2.96375i) q^{10} +(4.20988 - 0.442477i) q^{11} +(0.366927 + 0.163845i) q^{12} +(-0.286746 + 5.47143i) q^{13} +(0.193870 - 1.84455i) q^{14} +(2.36486 - 3.06715i) q^{15} +(1.07605 - 3.31173i) q^{16} +(-2.23343 + 1.80859i) q^{17} +(2.16528 + 3.35015i) q^{18} +(-0.500863 - 0.450979i) q^{19} +(0.441998 + 0.271610i) q^{20} +(-1.52247 + 1.87593i) q^{21} +(-2.01709 + 5.25470i) q^{22} +(7.80172 - 1.23567i) q^{23} +(-3.99835 + 3.23061i) q^{24} +(3.54428 - 3.52677i) q^{25} +(-6.30910 - 3.64256i) q^{26} +(0.0169438 - 5.19612i) q^{27} +(-0.271410 - 0.176256i) q^{28} +(-2.43865 - 7.50539i) q^{29} +(2.20621 + 4.65323i) q^{30} +(-0.526685 + 5.54280i) q^{31} +(-0.923148 - 0.923148i) q^{32} +(5.93631 - 4.30313i) q^{33} +(-0.794490 - 3.73778i) q^{34} +(-2.26512 + 2.14420i) q^{35} +(0.692362 - 0.0712488i) q^{36} +(-0.252364 - 0.0676207i) q^{37} +(0.836638 - 0.321155i) q^{38} +(4.29909 + 8.46016i) q^{39} +(-5.66260 + 3.46040i) q^{40} +(1.29335 - 6.08475i) q^{41} +(-1.30343 - 2.93613i) q^{42} +(6.00689 - 0.314808i) q^{43} +(0.657152 + 0.729842i) q^{44} +(0.898286 - 6.64779i) q^{45} +(-3.24559 + 9.98889i) q^{46} +(-10.3430 + 5.27000i) q^{47} +(-1.24756 - 5.90084i) q^{48} +(-3.75610 + 3.38200i) q^{49} +(2.03877 + 6.32798i) q^{50} +(-1.78890 + 4.64515i) q^{51} +(-1.06607 + 0.692317i) q^{52} +(-1.69617 + 4.41867i) q^{53} +(6.14580 + 3.15673i) q^{54} +(8.32398 - 4.50621i) q^{55} +(3.58510 - 2.06986i) q^{56} +(-1.14159 - 0.243950i) q^{57} +(10.3640 + 1.64149i) q^{58} +(-13.8923 + 2.95289i) q^{59} +(0.898191 + 0.0256102i) q^{60} +0.784815 q^{61} +(-6.24881 - 3.96991i) q^{62} +(-0.663602 + 4.13167i) q^{63} +(8.27441 - 2.68852i) q^{64} +(4.07526 + 11.5536i) q^{65} +(1.51460 + 9.63055i) q^{66} +(-1.90750 - 7.11888i) q^{67} +(-0.644039 - 0.172570i) q^{68} +(10.6418 - 8.59843i) q^{69} +(-1.17296 - 3.97792i) q^{70} +(-1.87105 - 4.20245i) q^{71} +(-3.20876 + 8.30511i) q^{72} +(-1.41094 + 1.74237i) q^{73} +(0.232453 - 0.258165i) q^{74} +(2.27124 - 8.35712i) q^{75} +(0.0163448 - 0.155510i) q^{76} +(-5.26104 + 2.68063i) q^{77} +(-12.6182 - 0.0137153i) q^{78} +(-10.6005 - 1.11416i) q^{79} +(-0.601296 - 7.76310i) q^{80} +(-4.46607 - 7.81372i) q^{81} +(6.42808 + 5.20535i) q^{82} +(-11.5174 + 7.47950i) q^{83} +(-0.559725 - 0.0299440i) q^{84} +(-3.07331 + 5.64365i) q^{85} +(-3.25311 + 7.30661i) q^{86} +(-10.1479 - 9.15718i) q^{87} +(-12.1349 + 3.25153i) q^{88} +(9.08817 - 6.60294i) q^{89} +(7.33361 + 5.07719i) q^{90} +(-2.36164 - 7.26839i) q^{91} +(1.29585 + 1.29585i) q^{92} +(4.00064 + 8.77467i) q^{93} -15.4349i q^{94} +(-1.41999 - 0.504826i) q^{95} +(-2.18355 - 0.587626i) q^{96} +(0.237045 - 1.49664i) q^{97} +(-1.73940 - 6.49154i) q^{98} +(5.19045 - 11.5901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 14 q^{3} - 16 q^{6} - 60 q^{7} - 44 q^{10} - 64 q^{12} - 36 q^{13} + 4 q^{15} + 176 q^{16} - 14 q^{18} - 36 q^{21} - 88 q^{22} - 20 q^{25} - 8 q^{27} - 56 q^{28} - 200 q^{30} - 56 q^{31} + 44 q^{33}+ \cdots + 44 q^{97}+O(q^{100}) $ 960 * q - 14 * q^3 - 16 * q^6 - 60 * q^7 - 44 * q^10 - 64 * q^12 - 36 * q^13 + 4 * q^15 + 176 * q^16 - 14 * q^18 - 36 * q^21 - 88 * q^22 - 20 * q^25 - 8 * q^27 - 56 * q^28 - 200 * q^30 - 56 * q^31 + 44 * q^33 - 32 * q^36 - 80 * q^37 - 52 * q^40 - 30 * q^42 - 36 * q^43 - 8 * q^45 - 164 * q^46 - 28 * q^48 - 44 * q^51 - 100 * q^52 - 88 * q^55 + 24 * q^57 + 64 * q^58 - 124 * q^60 - 176 * q^61 - 116 * q^63 + 48 * q^66 - 28 * q^67 - 36 * q^70 - 154 * q^72 - 12 * q^73 - 178 * q^75 + 112 * q^76 + 54 * q^78 - 52 * q^81 - 92 * q^82 - 24 * q^85 - 32 * q^87 + 52 * q^88 - 20 * q^90 + 40 * q^91 + 134 * q^93 + 8 * q^96 + 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{14}{15}\right)$

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 $

$2$	−0.603653	+	1.18474i	−0.426847	+	0.837734i	0.572988	+	0.819564i	$0.305784\pi$
$2$	−0.603653	+	1.18474i	−0.426847	+	0.837734i	−0.999835	+	0.0181705i	$0.994216\pi$
$3$	1.50094	−	0.864394i	0.866568	−	0.499058i
$3$	1.50094	−	0.864394i	0.866568	−	0.499058i
$4$	0.136370	+	0.187697i	0.0681849	+	0.0938484i
$5$	2.06692	−	0.853147i	0.924353	−	0.381539i
$5$	2.06692	−	0.853147i	0.924353	−	0.381539i
$6$	0.118032	+	2.30001i	0.0481863	+	0.938976i
$7$	−1.30223	+	0.499878i	−0.492196	+	0.188936i	−0.591790	−	0.806092i	$-0.701579\pi$
$7$	−1.30223	+	0.499878i	−0.492196	+	0.188936i	0.0995948	+	0.995028i	$0.468245\pi$
$8$	−2.93127	+	0.464267i	−1.03636	+	0.164143i
$9$	1.50564	−	2.59481i	0.501881	−	0.864936i
$10$	−0.236946	+	2.96375i	−0.0749289	+	0.937221i
$11$	4.20988	−	0.442477i	1.26933	−	0.133412i	0.554187	−	0.832392i	$-0.313029\pi$
$11$	4.20988	−	0.442477i	1.26933	−	0.133412i	0.715141	+	0.698981i	$0.246363\pi$
$12$	0.366927	+	0.163845i	0.105923	+	0.0472979i
$13$	−0.286746	+	5.47143i	−0.0795289	+	1.51750i	0.609510	+	0.792778i	$0.291366\pi$
$13$	−0.286746	+	5.47143i	−0.0795289	+	1.51750i	−0.689039	+	0.724724i	$0.741967\pi$
$14$	0.193870	−	1.84455i	0.0518139	−	0.492976i
$15$	2.36486	−	3.06715i	0.610605	−	0.791936i
$16$	1.07605	−	3.31173i	0.269012	−	0.827933i
$17$	−2.23343	+	1.80859i	−0.541686	+	0.438648i	−0.860708	−	0.509099i	$-0.829979\pi$
$17$	−2.23343	+	1.80859i	−0.541686	+	0.438648i	0.319023	+	0.947747i	$0.396645\pi$
$18$	2.16528	+	3.35015i	0.510360	+	0.789639i
$19$	−0.500863	−	0.450979i	−0.114906	−	0.103462i	0.609675	−	0.792651i	$-0.291300\pi$
$19$	−0.500863	−	0.450979i	−0.114906	−	0.103462i	−0.724581	+	0.689190i	$0.757967\pi$
$20$	0.441998	+	0.271610i	0.0988337	+	0.0607339i
$21$	−1.52247	+	1.87593i	−0.332231	+	0.409360i
$22$	−2.01709	+	5.25470i	−0.430045	+	1.12031i
$23$	7.80172	−	1.23567i	1.62677	−	0.257655i	0.724643	−	0.689124i	$-0.242004\pi$
$23$	7.80172	−	1.23567i	1.62677	−	0.257655i	0.902128	+	0.431469i	$0.142004\pi$
$24$	−3.99835	+	3.23061i	−0.816160	+	0.659446i
$25$	3.54428	−	3.52677i	0.708856	−	0.705353i
$26$	−6.30910	−	3.64256i	−1.23732	−	0.714365i
$27$	0.0169438	−	5.19612i	0.00326084	−	0.999995i
$28$	−0.271410	−	0.176256i	−0.0512917	−	0.0333092i
$29$	−2.43865	−	7.50539i	−0.452846	−	1.39372i	−0.873646	−	0.486562i	$-0.838251\pi$
$29$	−2.43865	−	7.50539i	−0.452846	−	1.39372i	0.420800	−	0.907153i	$-0.361749\pi$
$30$	2.20621	+	4.65323i	0.402797	+	0.849560i
$31$	−0.526685	+	5.54280i	−0.0945954	+	0.995516i
$31$	−0.526685	+	5.54280i	−0.0945954	+	0.995516i
$32$	−0.923148	−	0.923148i	−0.163191	−	0.163191i
$33$	5.93631	−	4.30313i	1.03338	−	0.749079i
$34$	−0.794490	−	3.73778i	−0.136254	−	0.641024i
$35$	−2.26512	+	2.14420i	−0.382876	+	0.362435i
$36$	0.692362	−	0.0712488i	0.115394	−	0.0118748i
$37$	−0.252364	−	0.0676207i	−0.0414884	−	0.0111168i	0.238015	−	0.971261i	$-0.423503\pi$
$37$	−0.252364	−	0.0676207i	−0.0414884	−	0.0111168i	−0.279504	+	0.960145i	$0.590170\pi$
$38$	0.836638	−	0.321155i	0.135721	−	0.0520983i
$39$	4.29909	+	8.46016i	0.688405	+	1.35471i
$40$	−5.66260	+	3.46040i	−0.895335	+	0.547138i
$41$	1.29335	−	6.08475i	0.201988	−	0.950278i	−0.754001	−	0.656874i	$-0.771879\pi$
$41$	1.29335	−	6.08475i	0.201988	−	0.950278i	0.955988	−	0.293404i	$-0.0947882\pi$
$42$	−1.30343	−	2.93613i	−0.201123	−	0.453055i
$43$	6.00689	−	0.314808i	0.916043	−	0.0480078i	0.411515	−	0.911403i	$-0.365000\pi$
$43$	6.00689	−	0.314808i	0.916043	−	0.0480078i	0.504528	+	0.863395i	$0.331667\pi$
$44$	0.657152	+	0.729842i	0.0990694	+	0.110028i
$45$	0.898286	−	6.64779i	0.133909	−	0.990994i
$46$	−3.24559	+	9.98889i	−0.478536	+	1.47278i
$47$	−10.3430	+	5.27000i	−1.50868	+	0.768709i	−0.995956	−	0.0898471i	$-0.971362\pi$
$47$	−10.3430	+	5.27000i	−1.50868	+	0.768709i	−0.512720	+	0.858556i	$0.671362\pi$
$48$	−1.24756	−	5.90084i	−0.180070	−	0.851713i
$49$	−3.75610	+	3.38200i	−0.536585	+	0.483144i
$50$	2.03877	+	6.32798i	0.288325	+	0.894911i
$51$	−1.78890	+	4.64515i	−0.250496	+	0.650451i
$52$	−1.06607	+	0.692317i	−0.147838	+	0.0960071i
$53$	−1.69617	+	4.41867i	−0.232987	+	0.606951i	−0.999372	−	0.0354298i	$-0.988720\pi$
$53$	−1.69617	+	4.41867i	−0.232987	+	0.606951i	0.766385	+	0.642381i	$0.222053\pi$
$54$	6.14580	+	3.15673i	0.836338	+	0.429576i
$55$	8.32398	−	4.50621i	1.12240	−	0.607617i
$56$	3.58510	−	2.06986i	0.479079	−	0.276597i
$57$	−1.14159	−	0.243950i	−0.151207	−	0.0323119i
$58$	10.3640	+	1.64149i	1.36086	+	0.215539i
$59$	−13.8923	+	2.95289i	−1.80862	+	0.384433i	−0.983555	−	0.180608i	$-0.942193\pi$
$59$	−13.8923	+	2.95289i	−1.80862	+	0.384433i	−0.825062	+	0.565042i	$0.808860\pi$
$60$	0.898191	+	0.0256102i	0.115956	+	0.00330626i
$61$	0.784815			0.100485			0.0502427	−	0.998737i	$-0.484001\pi$
$61$	0.784815			0.100485			0.0502427	+	0.998737i	$0.484001\pi$
$62$	−6.24881	−	3.96991i	−0.793600	−	0.504179i
$63$	−0.663602	+	4.13167i	−0.0836060	+	0.520541i
$64$	8.27441	−	2.68852i	1.03430	−	0.336065i
$65$	4.07526	+	11.5536i	0.505473	+	1.43305i
$66$	1.51460	+	9.63055i	0.186434	+	1.18544i
$67$	−1.90750	−	7.11888i	−0.233038	−	0.869710i	−0.979023	−	0.203748i	$-0.934688\pi$
$67$	−1.90750	−	7.11888i	−0.233038	−	0.869710i	0.745985	−	0.665962i	$-0.231979\pi$
$68$	−0.644039	−	0.172570i	−0.0781012	−	0.0209272i
$69$	10.6418	−	8.59843i	1.28112	−	1.03513i
$70$	−1.17296	−	3.97792i	−0.140195	−	0.475453i
$71$	−1.87105	−	4.20245i	−0.222053	−	0.498739i	0.767825	−	0.640659i	$-0.221339\pi$
$71$	−1.87105	−	4.20245i	−0.222053	−	0.498739i	−0.989878	+	0.141921i	$0.954672\pi$
$72$	−3.20876	+	8.30511i	−0.378156	+	0.978766i
$73$	−1.41094	+	1.74237i	−0.165138	+	0.203929i	−0.852997	−	0.521916i	$-0.825217\pi$
$73$	−1.41094	+	1.74237i	−0.165138	+	0.203929i	0.687859	+	0.725844i	$0.258551\pi$
$74$	0.232453	−	0.258165i	0.0270221	−	0.0300111i
$75$	2.27124	−	8.35712i	0.262260	−	0.964997i
$76$	0.0163448	−	0.155510i	0.00187488	−	0.0178383i
$77$	−5.26104	+	2.68063i	−0.599551	+	0.305487i
$78$	−12.6182	−	0.0137153i	−1.42873	−	0.00155296i
$79$	−10.6005	−	1.11416i	−1.19265	−	0.125353i	−0.512672	−	0.858585i	$-0.671344\pi$
$79$	−10.6005	−	1.11416i	−1.19265	−	0.125353i	−0.679979	+	0.733232i	$0.738011\pi$
$80$	−0.601296	−	7.76310i	−0.0672269	−	0.867941i
$81$	−4.46607	−	7.81372i	−0.496230	−	0.868191i
$82$	6.42808	+	5.20535i	0.709862	+	0.574835i
$83$	−11.5174	+	7.47950i	−1.26420	+	0.820982i	−0.990052	−	0.140705i	$-0.955063\pi$
$83$	−11.5174	+	7.47950i	−1.26420	+	0.820982i	−0.274150	+	0.961687i	$0.588396\pi$
$84$	−0.559725	−	0.0299440i	−0.0610710	−	0.00326716i
$85$	−3.07331	+	5.64365i	−0.333347	+	0.612140i
$86$	−3.25311	+	7.30661i	−0.350792	+	0.787892i
$87$	−10.1479	−	9.15718i	−1.08797	−	0.981753i
$88$	−12.1349	+	3.25153i	−1.29358	+	0.346614i
$89$	9.08817	−	6.60294i	0.963344	−	0.699910i	0.00941910	−	0.999956i	$-0.497002\pi$
$89$	9.08817	−	6.60294i	0.963344	−	0.699910i	0.953925	+	0.300045i	$0.0970018\pi$
$90$	7.33361	+	5.07719i	0.773031	+	0.535182i
$91$	−2.36164	−	7.26839i	−0.247567	−	0.761934i
$92$	1.29585	+	1.29585i	0.135102	+	0.135102i
$93$	4.00064	+	8.77467i	0.414847	+	0.909891i
$94$		−	15.4349i		−	1.59199i
$95$	−1.41999	−	0.504826i	−0.145688	−	0.0517941i
$96$	−2.18355	−	0.587626i	−0.222858	−	0.0599743i
$97$	0.237045	−	1.49664i	0.0240683	−	0.151961i	−0.972727	−	0.231951i	$-0.925489\pi$
$97$	0.237045	−	1.49664i	0.0240683	−	0.151961i	0.996796	+	0.0799904i	$0.0254890\pi$
$98$	−1.73940	−	6.49154i	−0.175706	−	0.655744i
$99$	5.19045	−	11.5901i	0.521659	−	1.16484i
$100$	1.14530	+	0.184306i	0.114530	+	0.0184306i
$101$	4.84753	−	6.67205i	0.482347	−	0.663893i	−0.496607	−	0.867976i	$-0.665421\pi$
$101$	4.84753	−	6.67205i	0.482347	−	0.663893i	0.978954	+	0.204082i	$0.0654209\pi$
$102$	−4.42340	−	4.92343i	−0.437982	−	0.487493i
$103$	−2.36990	−	3.64933i	−0.233514	−	0.359579i	0.702416	−	0.711767i	$-0.252105\pi$
$103$	−2.36990	−	3.64933i	−0.233514	−	0.359579i	−0.935930	+	0.352187i	$0.885438\pi$
$104$	−1.69968	−	16.1714i	−0.166667	−	1.58573i
$105$	−1.54638	+	5.17627i	−0.150912	+	0.505152i
$106$	−4.21106	−	4.67685i	−0.409014	−	0.454256i
$107$	7.41985	−	6.00847i	0.717304	−	0.580861i	−0.199644	−	0.979869i	$-0.563979\pi$
$107$	7.41985	−	6.00847i	0.717304	−	0.580861i	0.916948	+	0.399007i	$0.130645\pi$
$108$	0.977607	−	0.705414i	0.0940703	−	0.0678785i
$109$	7.51416	+	2.44150i	0.719726	+	0.233853i	0.645904	−	0.763418i	$-0.276480\pi$
$109$	7.51416	+	2.44150i	0.719726	+	0.233853i	0.0738215	+	0.997271i	$0.476480\pi$
$110$	0.313876	+	12.5819i	0.0299269	+	1.19964i
$111$	−0.437234	+	0.116647i	−0.0415004	+	0.0110717i
$112$	0.254205	+	4.85052i	0.0240201	+	0.458331i
$113$	−5.45804	−	4.41983i	−0.513449	−	0.415783i	0.337267	−	0.941409i	$-0.390498\pi$
$113$	−5.45804	−	4.41983i	−0.513449	−	0.415783i	−0.850715	+	0.525627i	$0.823831\pi$
$114$	0.978139	−	1.20522i	0.0916111	−	0.112879i
$115$	15.0713	−	9.21004i	1.40541	−	0.858841i
$116$	1.07618	−	1.48123i	0.0999208	−	0.137529i
$117$	13.7656	+	8.98208i	1.27263	+	0.830394i
$118$	4.88770	−	18.2412i	0.449950	−	1.67923i
$119$	2.00435	−	3.47164i	0.183739	−	0.318245i
$120$	−5.50807	+	10.0886i	−0.502815	+	0.920957i
$121$	6.76771	−	1.43852i	0.615246	−	0.130775i
$122$	−0.473756	+	0.929798i	−0.0428918	+	0.0841800i
$123$	−3.31838	−	10.2508i	−0.299208	−	0.924284i
$124$	−1.11219	+	0.657013i	−0.0998776	+	0.0590015i
$125$	4.31688	−	10.3133i	0.386113	−	0.922451i
$126$	−4.49435	−	3.28029i	−0.400388	−	0.292231i
$127$	−6.69513	+	10.3096i	−0.594097	+	0.914829i	0.405903	+	0.913916i	$0.366957\pi$
$127$	−6.69513	+	10.3096i	−0.594097	+	0.914829i	−1.00000		0.000912556i	$0.999710\pi$
$128$	−1.40123	+	8.84701i	−0.123852	+	0.781972i
$129$	8.74387	−	5.66483i	0.769855	−	0.498761i
$130$	−16.1480	−	2.14628i	−1.41628	−	0.188241i
$131$	−1.34956	+	3.03115i	−0.117911	+	0.264833i	−0.962853	−	0.270025i	$-0.912968\pi$
$131$	−1.34956	+	3.03115i	−0.117911	+	0.264833i	0.844942	+	0.534858i	$0.179635\pi$
$132$	1.61722	+	0.527410i	0.140761	+	0.0459051i
$133$	0.877672	+	0.336907i	0.0761038	+	0.0292135i
$134$	9.58546	+	2.03745i	0.828057	+	0.176009i
$135$	−4.39804	−	10.7544i	−0.378523	−	0.925592i
$136$	5.70710	−	6.33838i	0.489380	−	0.543512i
$137$	0.844857	−	16.1208i	0.0721810	−	1.37730i	−0.687114	−	0.726550i	$-0.741123\pi$
$137$	0.844857	−	16.1208i	0.0721810	−	1.37730i	0.759295	−	0.650747i	$-0.225544\pi$
$138$	3.76291	+	17.7982i	0.320320	+	1.51508i
$139$	−7.99736	−	2.59850i	−0.678328	−	0.220402i	−0.0504645	−	0.998726i	$-0.516070\pi$
$139$	−7.99736	−	2.59850i	−0.678328	−	0.220402i	−0.627863	+	0.778324i	$0.716070\pi$
$140$	−0.711354	−	0.132753i	−0.0601203	−	0.0112197i
$141$	−10.9688	+	16.8504i	−0.923740	+	1.41906i
$142$	6.10825	+	0.320120i	0.512593	+	0.0268639i
$143$	1.21382	+	23.1610i	0.101504	+	1.93682i
$144$	−6.97317	−	7.77843i	−0.581097	−	0.648202i
$145$	−11.4437	−	13.4325i	−0.950346	−	1.11551i
$146$	−1.21252	−	2.72337i	−0.100349	−	0.225388i
$147$	−2.71429	+	8.32294i	−0.223871	+	0.686464i
$148$	−0.0217226	−	0.0565893i	−0.00178559	−	0.00465162i
$149$	4.32119	+	7.48453i	0.354006	+	0.613156i	0.986947	−	0.161043i	$-0.0514859\pi$
$149$	4.32119	+	7.48453i	0.354006	+	0.613156i	−0.632941	+	0.774200i	$0.718153\pi$
$150$	8.52994	+	7.73561i	0.696466	+	0.631610i
$151$	−4.82779	+	3.50760i	−0.392880	+	0.285444i	−0.766635	−	0.642084i	$-0.778070\pi$
$151$	−4.82779	+	3.50760i	−0.392880	+	0.285444i	0.373755	+	0.927528i	$0.378070\pi$
$152$	1.67754	+	1.08941i	0.136066	+	0.0883626i
$153$	1.33021	+	8.51841i	0.107541	+	0.688673i
$154$		−	7.85111i		−	0.632660i
$155$	3.64021	+	11.9058i	0.292388	+	0.956300i
$156$	−1.00168	+	1.96064i	−0.0801985	+	0.156976i
$157$	7.08113	+	3.60802i	0.565136	+	0.287951i	0.713124	−	0.701038i	$-0.247280\pi$
$157$	7.08113	+	3.60802i	0.565136	+	0.287951i	−0.147988	+	0.988989i	$0.547280\pi$
$158$	7.71901	−	11.8862i	0.614091	−	0.945618i
$159$	1.27363	+	8.09832i	0.101005	+	0.642239i
$160$	−2.69565	−	1.12049i	−0.213110	−	0.0885823i
$161$	−9.54193	+	5.50903i	−0.752009	+	0.434173i
$162$	11.9531	−	0.574337i	0.939128	−	0.0451242i
$163$	−2.77333	−	17.5101i	−0.217224	−	1.37150i	−0.819440	−	0.573165i	$-0.805715\pi$
$163$	−2.77333	−	17.5101i	−0.217224	−	1.37150i	0.602216	−	0.798333i	$-0.294285\pi$
$164$	1.31846	−	0.587017i	0.102955	−	0.0458383i
$165$	8.59865	−	13.9588i	0.669404	−	1.08669i
$166$	−1.90870	−	18.1601i	−0.148144	−	1.40950i
$167$	−18.6730	+	0.978612i	−1.44496	+	0.0757272i	−0.758611	−	0.651544i	$-0.774122\pi$
$167$	−18.6730	+	0.978612i	−1.44496	+	0.0757272i	−0.686351	+	0.727271i	$0.740788\pi$
$168$	3.59185	−	6.20568i	0.277117	−	0.478778i
$169$	−16.9256	−	1.77895i	−1.30197	−	0.136842i
$170$	−4.83102	−	7.04786i	−0.370522	−	0.540546i
$171$	−1.92433	+	0.620630i	−0.147157	+	0.0474608i
$172$	0.878247	+	1.08454i	0.0669657	+	0.0826958i
$173$	−14.0080	−	0.734131i	−1.06501	−	0.0558149i	−0.488232	−	0.872714i	$-0.662358\pi$
$173$	−14.0080	−	0.734131i	−1.06501	−	0.0558149i	−0.576781	+	0.816899i	$0.695691\pi$
$174$	16.9746	−	6.49479i	1.28684	−	0.492369i
$175$	−2.85250	+	6.36436i	−0.215629	+	0.481100i
$176$	3.06467	−	14.4181i	0.231008	−	1.08681i
$177$	−18.2990	+	16.4405i	−1.37544	+	1.23574i
$178$	2.33664	+	14.7530i	0.175138	+	1.10578i
$179$	2.30436	+	1.02597i	0.172236	+	0.0766844i	0.491043	−	0.871135i	$-0.336616\pi$
$179$	2.30436	+	1.02597i	0.172236	+	0.0766844i	−0.318807	+	0.947820i	$0.603282\pi$
$180$	1.37027	−	0.737952i	0.102134	−	0.0550037i
$181$	6.07252	−	10.5179i	0.451367	−	0.781791i	−0.547104	−	0.837064i	$-0.684270\pi$
$181$	6.07252	−	10.5179i	0.451367	−	0.781791i	0.998471	+	0.0552740i	$0.0176032\pi$
$182$	10.0367	+	1.58966i	0.743971	+	0.117833i
$183$	1.17796	−	0.678390i	0.0870774	−	0.0501480i
$184$	−22.2953	+	7.24417i	−1.64363	+	0.534047i
$185$	−0.579305	+	0.0755372i	−0.0425914	+	0.00555361i
$186$	−12.8107	−	0.557155i	−0.939323	−	0.0408526i
$187$	−8.60221	+	8.60221i	−0.629056	+	0.629056i
$188$	−2.39963	−	1.22267i	−0.175011	−	0.0891726i
$189$	2.57536	+	6.77500i	0.187330	+	0.492809i
$190$	1.45527	−	1.37758i	0.105576	−	0.0999399i
$191$	14.7512	+	8.51663i	1.06736	+	0.616242i	0.927459	−	0.373924i	$-0.121988\pi$
$191$	14.7512	+	8.51663i	1.06736	+	0.616242i	0.139902	+	0.990165i	$0.455321\pi$
$192$	10.0955	−	11.1877i	0.728577	−	0.807400i
$193$	−0.961862	−	2.50574i	−0.0692364	−	0.180367i	0.894596	−	0.446875i	$-0.147463\pi$
$193$	−0.961862	−	2.50574i	−0.0692364	−	0.180367i	−0.963833	+	0.266509i	$0.914130\pi$
$194$	1.63003	+	1.18429i	0.117030	+	0.0850269i
$195$	16.1036	+	13.8187i	1.15320	+	0.989576i
$196$	−1.14701	−	0.243804i	−0.0819293	−	0.0174146i
$197$	3.47717	−	4.29394i	0.247738	−	0.305931i	−0.638074	−	0.769975i	$-0.720269\pi$
$197$	3.47717	−	4.29394i	0.247738	−	0.305931i	0.885812	+	0.464044i	$0.153602\pi$
$198$	10.5979	+	13.1457i	0.753161	+	0.934222i
$199$	0.199088	−	0.179260i	0.0141130	−	0.0127074i	−0.662044	−	0.749465i	$-0.730311\pi$
$199$	0.199088	−	0.179260i	0.0141130	−	0.0127074i	0.676157	+	0.736758i	$0.263644\pi$
$200$	−8.75188	+	11.9834i	−0.618851	+	0.847354i
$201$	−9.01656	−	9.03619i	−0.635979	−	0.637364i
$202$	4.97839	+	9.77063i	0.350278	+	0.687459i
$203$	6.92745	+	8.55469i	0.486212	+	0.600422i
$204$	−1.11583	+	0.297687i	−0.0781239	+	0.0208423i
$205$	−2.51793	−	13.6801i	−0.175860	−	0.955458i
$206$	5.75409	−	0.604779i	0.400907	−	0.0421370i
$207$	8.54029	−	22.1045i	0.593591	−	1.53637i
$208$	17.8114	+	6.83714i	1.23500	+	0.474071i
$209$	−2.30812	−	1.67695i	−0.159656	−	0.115997i
$210$	−5.19903	−	4.95673i	−0.358767	−	0.342047i
$211$	13.4612	+	23.3155i	0.926710	+	1.60511i	0.788788	+	0.614665i	$0.210709\pi$
$211$	13.4612	+	23.3155i	0.926710	+	1.60511i	0.137922	+	0.990443i	$0.455958\pi$
$212$	−1.06068	+	0.284208i	−0.0728476	+	0.0195195i
$213$	−6.44090	−	4.69030i	−0.441323	−	0.321374i
$214$	2.63944	+	12.4176i	0.180428	+	0.848849i
$215$	12.1472	−	5.77544i	0.828430	−	0.393882i
$216$	2.36272	+	15.2391i	0.160763	+	1.03689i
$217$	−2.08486	−	7.48126i	−0.141529	−	0.507861i
$218$	−7.42847	+	7.42847i	−0.503119	+	0.503119i
$219$	−0.611646	+	3.83480i	−0.0413312	+	0.259132i
$220$	1.98094	+	0.947874i	0.133555	+	0.0639056i
$221$	−9.25517	−	12.7387i	−0.622570	−	0.856894i
$222$	0.125741	−	0.588421i	0.00843921	−	0.0394922i
$223$	−1.34681	+	5.02636i	−0.0901891	+	0.336590i	−0.996246	−	0.0865652i	$-0.972411\pi$
$223$	−1.34681	+	5.02636i	−0.0901891	+	0.336590i	0.906057	+	0.423155i	$0.139078\pi$
$224$	1.66361	+	0.740686i	0.111155	+	0.0494892i
$225$	−3.81486	−	14.5068i	−0.254324	−	0.967119i
$226$	8.53109	−	3.79828i	0.567479	−	0.252658i
$227$	12.3351	+	18.9943i	0.818706	+	1.26070i	0.962552	+	0.271097i	$0.0873865\pi$
$227$	12.3351	+	18.9943i	0.818706	+	1.26070i	−0.143846	+	0.989600i	$0.545947\pi$
$228$	−0.109890	−	0.247540i	−0.00727763	−	0.0163937i
$229$	19.9657	+	17.9772i	1.31937	+	1.18797i	0.967776	+	0.251813i	$0.0810267\pi$
$229$	19.9657	+	17.9772i	1.31937	+	1.18797i	0.351593	+	0.936153i	$0.385640\pi$
$230$	1.81364	+	23.4152i	0.119588	+	1.54395i
$231$	−5.57938	+	8.57108i	−0.367096	+	0.563936i
$232$	10.6328	+	20.8681i	0.698080	+	1.37006i
$233$	0.497075	+	0.975565i	0.0325645	+	0.0639114i	0.906716	−	0.421743i	$-0.138581\pi$
$233$	0.497075	+	0.975565i	0.0325645	+	0.0639114i	−0.874151	+	0.485654i	$0.838581\pi$
$234$	−18.9510	+	10.8865i	−1.23887	+	0.711674i
$235$	−16.8819	+	19.7167i	−1.10126	+	1.28618i
$236$	−2.44873	−	2.20485i	−0.159399	−	0.143523i
$237$	−16.8738	+	7.49074i	−1.09607	+	0.486576i
$238$	2.90304	+	4.47029i	0.188176	+	0.289766i
$239$	10.1053	−	4.49918i	0.653658	−	0.291027i	−0.0529872	−	0.998595i	$-0.516874\pi$
$239$	10.1053	−	4.49918i	0.653658	−	0.291027i	0.706646	+	0.707568i	$0.250208\pi$
$240$	−7.61289	−	11.1322i	−0.491410	−	0.718580i
$241$	3.45302	+	1.53738i	0.222429	+	0.0990316i	0.514926	−	0.857235i	$-0.327820\pi$
$241$	3.45302	+	1.53738i	0.222429	+	0.0990316i	−0.292497	+	0.956266i	$0.594486\pi$
$242$	−2.38108	+	8.88631i	−0.153062	+	0.571234i
$243$	−13.4574	−	7.86748i	−0.863295	−	0.504699i
$244$	0.107025	+	0.147307i	0.00685158	+	0.00943039i
$245$	−4.87819	+	10.1948i	−0.311656	+	0.651323i
$246$	14.1476	+	2.25653i	0.902021	+	0.143871i
$247$	2.61112	−	2.61112i	0.166142	−	0.166142i
$248$	−1.02948	−	16.4920i	−0.0653723	−	1.04724i
$249$	−10.8217	+	21.1819i	−0.685799	+	1.34235i
$250$	9.61266	+	11.3400i	0.607958	+	0.717206i
$251$	−2.77563	−	13.0583i	−0.175196	−	0.824233i	−0.974690	−	0.223559i	$-0.928232\pi$
$251$	−2.77563	−	13.0583i	−0.175196	−	0.824233i	0.799494	−	0.600674i	$-0.205101\pi$
$252$	−0.865997	+	0.438879i	−0.0545527	+	0.0276468i
$253$	32.2976	−	8.65411i	2.03053	−	0.544079i
$254$	−8.17261	−	14.1554i	−0.512795	−	0.888187i
$255$	0.265487	+	11.1273i	0.0166255	+	0.696821i
$256$	4.44176	+	3.22713i	0.277610	+	0.201696i
$257$	12.8176	+	4.92023i	0.799542	+	0.306915i	0.723620	−	0.690199i	$-0.242477\pi$
$257$	12.8176	+	4.92023i	0.799542	+	0.306915i	0.0759215	+	0.997114i	$0.475810\pi$
$258$	1.43307	+	13.7788i	0.0892188	+	0.857828i
$259$	0.362437	−	0.0380937i	0.0225208	−	0.00236703i
$260$	−1.61284	+	2.34048i	−0.100024	+	0.145150i
$261$	−23.1468	−	4.97262i	−1.43275	−	0.307797i
$262$	−2.77645	−	3.42863i	−0.171530	−	0.211821i
$263$	−7.34273	−	14.4109i	−0.452772	−	0.888615i	−0.998709	−	0.0507890i	$-0.983826\pi$
$263$	−7.34273	−	14.4109i	−0.452772	−	0.888615i	0.545937	−	0.837826i	$-0.316174\pi$
$264$	−15.4031	+	15.3697i	−0.947996	+	0.945938i
$265$	0.263938	+	10.5801i	0.0162136	+	0.649931i
$266$	−0.928954	+	0.836434i	−0.0569578	+	0.0512851i
$267$	7.93326	−	17.7664i	0.485507	−	1.08729i
$268$	1.07607	−	1.32883i	0.0657313	−	0.0811713i
$269$	10.9720	+	2.33216i	0.668972	+	0.142194i	0.529864	−	0.848083i	$-0.322243\pi$
$269$	10.9720	+	2.33216i	0.668972	+	0.142194i	0.139108	+	0.990277i	$0.455576\pi$
$270$	15.3960	+	1.28142i	0.936971	+	0.0779846i
$271$	2.25736	+	1.64007i	0.137125	+	0.0996270i	0.654233	−	0.756293i	$-0.272992\pi$
$271$	2.25736	+	1.64007i	0.137125	+	0.0996270i	−0.517108	+	0.855920i	$0.672992\pi$
$272$	3.58630	+	9.34264i	0.217452	+	0.566481i
$273$	−9.82744	−	8.86802i	−0.594783	−	0.536717i
$274$	18.5889	+	10.7323i	1.12300	+	0.648363i
$275$	13.3605	−	16.4155i	0.805668	−	0.989894i
$276$	3.06512	+	0.824868i	0.184499	+	0.0496512i
$277$	19.2402	+	9.80337i	1.15603	+	0.589027i	0.923514	−	0.383565i	$-0.125304\pi$
$277$	19.2402	+	9.80337i	1.15603	+	0.589027i	0.232518	+	0.972592i	$0.425304\pi$
$278$	7.90617	−	7.90617i	0.474180	−	0.474180i
$279$	13.5895	+	9.71213i	0.813582	+	0.581450i
$280$	5.64421	−	7.33684i	0.337306	−	0.438460i
$281$	−1.63683	+	0.531838i	−0.0976450	+	0.0317268i	−0.357432	−	0.933939i	$-0.616348\pi$
$281$	−1.63683	+	0.531838i	−0.0976450	+	0.0317268i	0.259787	+	0.965666i	$0.416348\pi$
$282$	−13.3419	−	23.1669i	−0.794496	−	1.37957i
$283$	2.29921	+	0.364159i	0.136674	+	0.0216470i	0.224397	−	0.974498i	$-0.427959\pi$
$283$	2.29921	+	0.364159i	0.136674	+	0.0216470i	−0.0877226	+	0.996145i	$0.527959\pi$
$284$	0.533631	−	0.924277i	0.0316652	−	0.0548457i
$285$	−2.56769	+	0.469720i	−0.152097	+	0.0278238i
$286$	−28.1723	−	12.5431i	−1.66587	−	0.741691i
$287$	1.35739	+	8.57024i	0.0801244	+	0.505885i
$288$	−3.78532	+	1.00546i	−0.223052	+	0.0592473i
$289$	−1.81731	+	8.54979i	−0.106901	+	0.502929i
$290$	22.8219	−	5.44918i	1.34015	−	0.319987i
$291$	−0.937900	−	2.45127i	−0.0549806	−	0.143696i
$292$	−0.519446	−	0.0272230i	−0.0303983	−	0.00159311i
$293$	7.80963	+	9.64409i	0.456243	+	0.563414i	0.952412	−	0.304812i	$-0.0985937\pi$
$293$	7.80963	+	9.64409i	0.456243	+	0.563414i	−0.496169	+	0.868226i	$0.665260\pi$
$294$	−8.22199	−	8.23988i	−0.479516	−	0.480560i
$295$	−26.1949	+	17.9555i	−1.52512	+	1.04541i
$296$	0.771141	+	0.0810501i	0.0448216	+	0.00471094i
$297$	−2.22783	−	21.8826i	−0.129272	−	1.26976i
$298$	−11.4757	+	0.601415i	−0.664768	+	0.0348390i
$299$	4.52378	+	43.0409i	0.261617	+	2.48912i
$300$	1.87833	−	0.713355i	0.108446	−	0.0411855i
$301$	−7.66497	+	3.41267i	−0.441802	+	0.196703i
$302$	−1.24126	−	7.83702i	−0.0714266	−	0.450970i
$303$	1.50857	−	14.2045i	0.0866649	−	0.816028i
$304$	−2.03247	+	1.17345i	−0.116570	+	0.0673019i
$305$	1.62215	−	0.669563i	0.0928839	−	0.0383391i
$306$	−10.8950	−	3.56622i	−0.622829	−	0.203867i
$307$	−7.90071	+	12.1660i	−0.450917	+	0.694352i	−0.988896	−	0.148607i	$-0.952521\pi$
$307$	−7.90071	+	12.1660i	−0.450917	+	0.694352i	0.537979	+	0.842958i	$0.319188\pi$
$308$	−1.22059	−	0.621923i	−0.0695498	−	0.0354374i
$309$	−6.71155	−	3.42890i	−0.381807	−	0.195063i
$310$	−16.3027	−	2.87431i	−0.925930	−	0.163250i
$311$			18.4571i			1.04661i	0.852146	+	0.523303i	$0.175301\pi$
$311$			18.4571i			1.04661i	−0.852146	+	0.523303i	$0.824699\pi$
$312$	−16.5296	−	22.8031i	−0.935802	−	1.29097i
$313$	1.18023	+	0.766447i	0.0667103	+	0.0433222i	0.577563	−	0.816346i	$-0.304004\pi$
$313$	1.18023	+	0.766447i	0.0667103	+	0.0433222i	−0.510853	+	0.859668i	$0.670670\pi$
$314$	−8.54909	+	6.21128i	−0.482453	+	0.350523i
$315$	2.15331	+	9.10596i	0.121325	+	0.513063i
$316$	−1.23647	−	2.14162i	−0.0695566	−	0.120476i
$317$	−1.08214	−	2.81906i	−0.0607788	−	0.158334i	0.899828	−	0.436244i	$-0.143692\pi$
$317$	−1.08214	−	2.81906i	−0.0607788	−	0.158334i	−0.960607	+	0.277910i	$0.910358\pi$
$318$	−10.3632	−	3.37966i	−0.581139	−	0.189522i
$319$	−13.5874	−	30.5178i	−0.760747	−	1.70867i
$320$	14.8088	−	12.6162i	0.827837	−	0.705269i
$321$	5.94306	−	15.4320i	0.331709	−	0.861332i
$322$	−0.766736	−	14.6302i	−0.0427285	−	0.815309i
$323$	1.93428	+	0.101371i	0.107626	+	0.00564045i
$324$	0.857574	−	1.90382i	0.0476430	−	0.105768i
$325$	18.2802	+	20.4036i	1.01400	+	1.13179i
$326$	22.4190	+	7.28437i	1.24167	+	0.403444i
$327$	13.3887	−	2.83065i	0.740398	−	0.156535i
$328$	−0.966216	+	18.4365i	−0.0533503	+	1.01798i
$329$	10.8345	−	12.0330i	0.597327	−	0.663398i
$330$	11.3468	+	18.6134i	0.624622	+	1.02463i
$331$	−16.3653	−	3.47856i	−0.899519	−	0.191199i	−0.265130	−	0.964213i	$-0.585415\pi$
$331$	−16.3653	−	3.47856i	−0.899519	−	0.191199i	−0.634389	+	0.773014i	$0.718748\pi$
$332$	−2.97451	−	1.14181i	−0.163247	−	0.0626648i
$333$	−0.555433	+	0.553023i	−0.0304375	+	0.0303055i
$334$	10.1126	−	22.7133i	0.553338	−	1.24282i
$335$	−10.0161	−	13.0868i	−0.547238	−	0.715006i
$336$	4.57431	+	7.06061i	0.249549	+	0.385188i
$337$	2.06078	−	13.0112i	0.112258	−	0.708767i	−0.865793	−	0.500402i	$-0.833186\pi$
$337$	2.06078	−	13.0112i	0.112258	−	0.708767i	0.978051	−	0.208365i	$-0.0668143\pi$
$338$	12.3247	−	18.9784i	0.670378	−	1.03229i
$339$	−12.0127	−	1.91601i	−0.652438	−	0.104063i
$340$	−1.47840	+	0.192773i	−0.0801776	+	0.0104546i
$341$	0.235276	+	23.5676i	0.0127409	+	1.27626i
$342$	0.426343	−	2.65446i	0.0230540	−	0.143537i
$343$	7.63352	−	14.9816i	0.412171	−	0.808931i
$344$	−17.4617	+	3.71159i	−0.941470	+	0.200116i
$345$	14.6600	−	26.8513i	0.789268	−	1.44562i
$346$	9.32575	−	16.1527i	0.501355	−	0.868373i
$347$	−0.133341	+	0.497637i	−0.00715814	+	0.0267146i	−0.969413	−	0.245437i	$-0.921069\pi$
$347$	−0.133341	+	0.497637i	−0.00715814	+	0.0267146i	0.962254	+	0.272152i	$0.0877352\pi$
$348$	0.334911	−	3.15349i	0.0179531	−	0.169045i
$349$	−5.96257	+	8.20677i	−0.319169	+	0.439299i	−0.938213	−	0.346058i	$-0.887520\pi$
$349$	−5.96257	+	8.20677i	−0.319169	+	0.439299i	0.619044	+	0.785356i	$0.287520\pi$
$350$	−5.81816	−	7.22132i	−0.310993	−	0.385996i
$351$	28.4254	+	1.58267i	1.51724	+	0.0844768i
$352$	−4.29481	−	3.47787i	−0.228914	−	0.185371i
$353$	0.404158	+	7.71180i	0.0215112	+	0.410458i	0.988069	+	0.154010i	$0.0492188\pi$
$353$	0.404158	+	7.71180i	0.0215112	+	0.410458i	−0.966558	+	0.256448i	$0.917448\pi$
$354$	−8.43141	−	31.6038i	−0.448124	−	1.67972i
$355$	−7.45260	−	7.08982i	−0.395543	−	0.376289i
$356$	2.47870	+	0.805380i	0.131371	+	0.0426850i
$357$	0.00754699	−	6.94328i	0.000399429	−	0.367477i
$358$	−2.60653	+	2.11073i	−0.137760	+	0.111556i
$359$	1.52453	+	1.69317i	0.0804618	+	0.0893619i	0.782031	−	0.623239i	$-0.214184\pi$
$359$	1.52453	+	1.69317i	0.0804618	+	0.0893619i	−0.701569	+	0.712601i	$0.747517\pi$
$360$	0.453232	+	19.9035i	0.0238874	+	1.04901i
$361$	−1.93856	−	18.4442i	−0.102029	−	0.970745i
$362$	8.79525	+	13.5435i	0.462268	+	0.711830i
$363$	8.91448	−	8.00911i	0.467889	−	0.420369i
$364$	1.04220	−	1.43446i	0.0546260	−	0.0751862i
$365$	−1.42980	+	4.80506i	−0.0748392	+	0.251509i
$366$	0.0926331	+	1.80508i	0.00484201	+	0.0943533i
$367$	2.48572	+	9.27682i	0.129753	+	0.484246i	0.999964	−	0.00843309i	$-0.00268437\pi$
$367$	2.48572	+	9.27682i	0.129753	+	0.484246i	−0.870211	+	0.492679i	$0.836018\pi$
$368$	4.30281	−	27.1668i	0.224299	−	1.41617i
$369$	−13.8414	−	12.5175i	−0.720556	−	0.651633i
$370$	0.260208	−	0.731922i	0.0135276	−	0.0380508i
$371$		−	6.60199i		−	0.342758i
$372$	−1.10141	+	1.94751i	−0.0571056	+	0.100974i
$373$	−11.0276	−	11.0276i	−0.570990	−	0.570990i	0.361415	−	0.932405i	$-0.382294\pi$
$373$	−11.0276	−	11.0276i	−0.570990	−	0.570990i	−0.932405	+	0.361415i	$0.882294\pi$
$374$	−4.99859	−	15.3841i	−0.258471	−	0.795492i
$375$	−2.43540	−	19.2112i	−0.125763	−	0.992060i
$376$	27.8713	−	20.2497i	1.43735	−	1.04430i
$377$	41.7645	−	11.1908i	2.15098	−	0.576354i
$378$	−9.58121	−	1.03862i	−0.492804	−	0.0534211i
$379$	3.65966	−	8.21972i	0.187984	−	0.422219i	−0.794826	−	0.606837i	$-0.792438\pi$
$379$	3.65966	−	8.21972i	0.187984	−	0.422219i	0.982810	+	0.184618i	$0.0591048\pi$
$380$	−0.0988899	−	0.335371i	−0.00507294	−	0.0172042i
$381$	−1.13743	+	21.2613i	−0.0582725	+	1.08925i
$382$	−18.9946	+	12.3352i	−0.971847	+	0.631125i
$383$	−13.9583	−	11.3032i	−0.713236	−	0.577567i	0.202532	−	0.979276i	$-0.435083\pi$
$383$	−13.9583	−	11.3032i	−0.713236	−	0.577567i	−0.915767	+	0.401709i	$0.868416\pi$
$384$	5.54414	+	14.4900i	0.282923	+	0.739442i
$385$	−8.58715	+	10.0291i	−0.437642	+	0.511129i
$386$	3.54927	+	0.373043i	0.180653	+	0.0189874i
$387$	8.22738	−	16.0607i	0.418221	−	0.816413i
$388$	0.313241	−	0.159604i	0.0159024	−	0.00810268i
$389$	2.13085	−	20.2737i	0.108038	−	1.02792i	−0.797404	−	0.603446i	$-0.793794\pi$
$389$	2.13085	−	20.2737i	0.108038	−	1.02792i	0.905442	−	0.424469i	$-0.139539\pi$
$390$	−26.0925	+	10.7368i	−1.32124	+	0.543681i
$391$	−15.1897	+	16.8699i	−0.768178	+	0.853149i
$392$	9.43998	−	11.6574i	0.476791	−	0.588788i
$393$	0.594508	+	5.71613i	0.0299890	+	0.288340i
$394$	2.98818	+	6.71157i	0.150543	+	0.338124i
$395$	−22.8609	+	6.74092i	−1.15026	+	0.339173i
$396$	2.88324	−	0.606303i	0.144888	−	0.0304679i
$397$	11.7865	+	3.15817i	0.591546	+	0.158504i	0.542160	−	0.840276i	$-0.317607\pi$
$397$	11.7865	+	3.15817i	0.591546	+	0.158504i	0.0493861	+	0.998780i	$0.484274\pi$
$398$	0.0921953	+	0.344078i	0.00462133	+	0.0172471i
$399$	1.60855	−	0.252978i	0.0805284	−	0.0126647i
$400$	−7.86589	−	15.5327i	−0.393294	−	0.776634i
$401$	−13.0510	+	4.24052i	−0.651734	+	0.211761i	−0.616179	−	0.787606i	$-0.711320\pi$
$401$	−13.0510	+	4.24052i	−0.651734	+	0.211761i	−0.0355555	+	0.999368i	$0.511320\pi$
$402$	16.1484	−	5.22752i	0.805407	−	0.260725i
$403$	−30.1760	−	4.47109i	−1.50317	−	0.222721i
$404$	1.91338			0.0951941
$405$	−15.8972	−	12.3401i	−0.789940	−	0.613184i
$406$	−14.3168	+	3.04313i	−0.710532	+	0.151028i
$407$	−1.09234	−	0.173010i	−0.0541454	−	0.00857580i
$408$	3.08716	−	14.4467i	0.152837	−	0.715219i
$409$	2.84154	−	1.64057i	0.140505	−	0.0811208i	−0.428099	−	0.903732i	$-0.640817\pi$
$409$	2.84154	−	1.64057i	0.140505	−	0.0811208i	0.568605	+	0.822611i	$0.307483\pi$
$410$	17.7272	+	5.27493i	0.875485	+	0.260510i
$411$	−12.6667	−	24.9267i	−0.624802	−	1.22954i
$412$	0.361785	−	0.942482i	0.0178239	−	0.0464328i
$413$	16.6148	−	10.7898i	0.817560	−	0.530930i
$414$	21.0326	+	23.4614i	1.03369	+	1.15306i
$415$	−17.4244	+	25.2855i	−0.855331	+	1.24122i
$416$	5.31565	−	4.78623i	0.260621	−	0.234664i
$417$	−14.2497	+	3.01268i	−0.697811	+	0.147532i
$418$	3.38005	−	1.72222i	0.165323	−	0.0842365i
$419$	−5.02662	+	15.4703i	−0.245566	+	0.755775i	0.749977	+	0.661464i	$0.230065\pi$
$419$	−5.02662	+	15.4703i	−0.245566	+	0.755775i	−0.995543	+	0.0943108i	$0.969935\pi$
$420$	−1.18245	+	0.415636i	−0.0576977	+	0.0202809i
$421$	20.7276	+	23.0203i	1.01020	+	1.12194i	0.992518	+	0.122098i	$0.0389624\pi$
$421$	20.7276	+	23.0203i	1.01020	+	1.12194i	0.0176832	+	0.999844i	$0.494371\pi$
$422$	−35.7487	+	1.87351i	−1.74022	+	0.0912009i
$423$	−1.89817	+	34.7728i	−0.0922923	+	1.69071i
$424$	2.92048	−	13.7398i	0.141831	−	0.667263i
$425$	−1.53741	+	14.2869i	−0.0745752	+	0.693018i
$426$	9.44483	−	4.79946i	0.457603	−	0.232534i
$427$	−1.02201	+	0.392312i	−0.0494584	+	0.0189853i
$428$	2.13961	+	0.573308i	0.103422	+	0.0277119i
$429$	21.8421	+	33.7140i	1.05455	+	1.62773i
$430$	−0.490297	+	17.8775i	−0.0236442	+	0.862131i
$431$	−0.177043	−	0.832921i	−0.00852785	−	0.0401204i	0.973678	−	0.227928i	$-0.0731951\pi$
$431$	−0.177043	−	0.832921i	−0.00852785	−	0.0401204i	−0.982206	+	0.187808i	$0.939862\pi$
$432$	−17.1899	−	5.64739i	−0.827051	−	0.271710i
$433$	−14.0761	−	14.0761i	−0.676454	−	0.676454i	0.282742	−	0.959196i	$-0.408756\pi$
$433$	−14.0761	−	14.0761i	−0.676454	−	0.676454i	−0.959196	+	0.282742i	$0.908756\pi$
$434$	10.1218	+	2.04608i	0.485864	+	0.0982148i
$435$	−28.7872	−	10.2695i	−1.38024	−	0.492385i
$436$	0.566442	+	1.74333i	0.0271277	+	0.0834904i
$437$	−4.46486	−	2.89951i	−0.213583	−	0.138702i
$438$	−4.17400	−	3.03952i	−0.199441	−	0.145234i
$439$	0.345039	+	0.199208i	0.0164678	+	0.00950770i	0.508211	−	0.861232i	$-0.330307\pi$
$439$	0.345039	+	0.199208i	0.0164678	+	0.00950770i	−0.491743	+	0.870740i	$0.663640\pi$
$440$	−22.3077	+	17.0735i	−1.06348	+	0.813946i
$441$	3.12031	+	14.8385i	0.148586	+	0.706593i
$442$	20.6788	−	3.27521i	0.983592	−	0.155786i
$443$	−12.4376	+	32.4012i	−0.590931	+	1.53943i	0.232847	+	0.972513i	$0.425196\pi$
$443$	−12.4376	+	32.4012i	−0.590931	+	1.53943i	−0.823778	+	0.566913i	$0.808137\pi$
$444$	−0.0815199	−	0.0661603i	−0.00386876	−	0.00313983i
$445$	13.1512	−	21.4013i	0.623427	−	1.01452i
$446$	−5.14191	−	4.62979i	−0.243476	−	0.219227i
$447$	12.9554	+	7.49861i	0.612771	+	0.354672i
$448$	−9.43123	+	7.63726i	−0.445584	+	0.360827i
$449$	−8.22277	+	25.3071i	−0.388056	+	1.19431i	0.546182	+	0.837666i	$0.316081\pi$
$449$	−8.22277	+	25.3071i	−0.388056	+	1.19431i	−0.934239	+	0.356649i	$0.883919\pi$
$450$	19.4895	+	4.23747i	0.918746	+	0.199756i
$451$	2.75251	−	26.1884i	0.129610	−	1.23316i
$452$	0.0852773	−	1.62719i	0.00401111	−	0.0765365i
$453$	−4.21428	+	9.43781i	−0.198004	+	0.443427i
$454$	−29.9493	+	3.14780i	−1.40559	+	0.147734i
$455$	−11.0823	−	13.0083i	−0.519547	−	0.609839i
$456$	3.45956	+	0.185079i	0.162009	+	0.00866712i
$457$	−5.19072	+	0.822129i	−0.242812	+	0.0384576i	−0.276654	−	0.960970i	$-0.589226\pi$
$457$	−5.19072	+	0.822129i	−0.242812	+	0.0384576i	0.0338424	+	0.999427i	$0.489226\pi$
$458$	−33.3505	+	12.8021i	−1.55837	+	0.598201i
$459$	9.35983	+	11.6358i	0.436880	+	0.543113i
$460$	3.78396	+	1.57286i	0.176428	+	0.0733351i
$461$	6.98335	+	9.61176i	0.325247	+	0.447664i	0.940060	−	0.341009i	$-0.110769\pi$
$461$	6.98335	+	9.61176i	0.325247	+	0.447664i	−0.614813	+	0.788673i	$0.710769\pi$
$462$	−6.78646	−	11.7840i	−0.315735	−	0.548244i
$463$	18.5091	−	36.3261i	0.860189	−	1.68822i	0.144833	−	0.989456i	$-0.453735\pi$
$463$	18.5091	−	36.3261i	0.860189	−	1.68822i	0.715356	−	0.698760i	$-0.246265\pi$
$464$	−27.4799			−1.27572
$465$	15.7551	+	14.7234i	0.730624	+	0.682780i
$466$	−1.45585			−0.0674408
$467$	5.04521	−	9.90179i	0.233465	−	0.458200i	−0.744317	−	0.667827i	$-0.767225\pi$
$467$	5.04521	−	9.90179i	0.233465	−	0.458200i	0.977782	+	0.209626i	$0.0672248\pi$
$468$	0.191301	+	3.80864i	0.00884290	+	0.176055i
$469$	6.04257	+	8.31688i	0.279020	+	0.384038i
$470$	−13.1683	−	31.9027i	−0.607406	−	1.47156i
$471$	13.7471	−	0.705473i	0.633433	−	0.0325065i
$472$	39.3510	−	15.1054i	1.81128	−	0.695284i
$473$	25.1490	−	3.98321i	1.15635	−	0.183148i
$474$	1.31138	−	24.5128i	0.0602337	−	1.12591i
$475$	−3.36570	+	0.168030i	−0.154429	+	0.00770975i
$476$	0.924949	−	0.0972161i	0.0423950	−	0.00445589i
$477$	8.91178	+	11.0542i	0.408043	+	0.506136i
$478$	−0.769768	+	14.6881i	−0.0352084	+	0.671816i
$479$	−3.65928	+	34.8157i	−0.167197	+	1.59077i	0.513423	+	0.858135i	$0.328377\pi$
$479$	−3.65928	+	34.8157i	−0.167197	+	1.59077i	−0.680620	+	0.732636i	$0.738290\pi$
$480$	−5.01455	+	0.648319i	−0.228882	+	0.0295916i
$481$	0.442346	−	1.36140i	0.0201693	−	0.0620746i
$482$	−3.90582	+	3.16287i	−0.177905	+	0.144065i
$483$	−9.55989	+	16.5167i	−0.434990	+	0.751537i
$484$	1.19292	+	1.07411i	0.0542235	+	0.0488231i
$485$	−0.786904	−	3.29567i	−0.0357315	−	0.149649i
$486$	17.4445	−	11.1943i	0.791299	−	0.507783i
$487$	−1.26364	+	3.29189i	−0.0572608	+	0.149170i	−0.959227	−	0.282638i	$-0.908791\pi$
$487$	−1.26364	+	3.29189i	−0.0572608	+	0.149170i	0.901966	+	0.431807i	$0.142124\pi$
$488$	−2.30051	+	0.364364i	−0.104139	+	0.0164940i
$489$	−19.2983	−	23.8844i	−0.872697	−	1.08009i
$490$	−9.13343	−	11.9335i	−0.412606	−	0.539100i
$491$	6.40341	+	3.69701i	0.288982	+	0.166844i	0.637483	−	0.770465i	$-0.279976\pi$
$491$	6.40341	+	3.69701i	0.288982	+	0.166844i	−0.348501	+	0.937309i	$0.613309\pi$
$492$	1.47152	−	2.02075i	0.0663412	−	0.0911024i
$493$	19.0207	+	12.3522i	0.856651	+	0.556315i
$494$	1.51728	+	4.66970i	0.0682655	+	0.210100i
$495$	0.840191	−	28.3839i	0.0377638	−	1.27576i
$496$	17.7895	+	7.70855i	0.798773	+	0.346124i
$497$	4.53724	+	4.53724i	0.203523	+	0.203523i
$498$	−18.5624	−	25.6074i	−0.831799	−	1.14749i
$499$	−0.884089	−	4.15931i	−0.0395773	−	0.186196i	0.953918	−	0.300066i	$-0.0970087\pi$
$499$	−0.884089	−	4.15931i	−0.0395773	−	0.186196i	−0.993496	+	0.113870i	$0.963675\pi$
$500$	2.52447	−	0.596160i	0.112898	−	0.0266611i
$501$	−27.1812	+	17.6097i	−1.21437	+	0.786743i
$502$	17.1462	+	4.59430i	0.765270	+	0.205054i
$503$	7.46432	−	2.86528i	0.332817	−	0.127757i	−0.186220	−	0.982508i	$-0.559624\pi$
$503$	7.46432	−	2.86528i	0.332817	−	0.127757i	0.519038	+	0.854751i	$0.326290\pi$
$504$	0.0269979	−	12.4191i	0.00120258	−	0.553192i
$505$	4.32719	−	17.9262i	0.192557	−	0.797706i
$506$	−9.24369	+	43.4882i	−0.410932	+	1.93328i
$507$	−26.9420	+	11.9603i	−1.19654	+	0.531174i
$508$	−2.84809	+	0.149262i	−0.126364	+	0.00662244i
$509$	−20.0773	−	22.2981i	−0.889909	−	0.988344i	0.110075	−	0.993923i	$-0.464891\pi$
$509$	−20.0773	−	22.2981i	−0.889909	−	0.988344i	−0.999984	+	0.00557884i	$0.998224\pi$
$510$	−13.3432	−	6.40251i	−0.590847	−	0.283508i
$511$	0.966394	−	2.97425i	0.0427508	−	0.131573i
$512$	−22.4666	+	11.4473i	−0.992892	+	0.505904i
$513$	−2.35183	+	2.59491i	−0.103836	+	0.114568i
$514$	−13.5666	+	12.2154i	−0.598395	+	0.538797i
$515$	−8.01181	−	5.52099i	−0.353043	−	0.243284i
$516$	2.25567	+	0.868685i	0.0993004	+	0.0382417i
$517$	−41.2108	+	26.7626i	−1.81245	+	1.17702i
$518$	−0.173655	+	0.452387i	−0.00762997	+	0.0198768i
$519$	−21.6598	+	11.0066i	−0.950761	+	0.483136i
$520$	−17.3096	−	31.9748i	−0.759078	−	1.40219i
$521$	3.88460	−	2.24278i	0.170188	−	0.0982579i	−0.412487	−	0.910964i	$-0.635340\pi$
$521$	3.88460	−	2.24278i	0.170188	−	0.0982579i	0.582674	+	0.812706i	$0.302006\pi$
$522$	19.8639	−	24.4211i	0.869417	−	1.06888i
$523$	31.8659	+	5.04707i	1.39340	+	0.220693i	0.807585	−	0.589752i	$-0.200774\pi$
$523$	31.8659	+	5.04707i	1.39340	+	0.220693i	0.585815	+	0.810445i	$0.300774\pi$
$524$	−0.752976	+	0.160050i	−0.0328939	+	0.00699182i
$525$	1.21988	+	12.0182i	0.0532397	+	0.524518i
$526$	21.5056			0.937687
$527$	−8.84835	−	13.3320i	−0.385440	−	0.580751i
$528$	−7.86307	−	24.2898i	−0.342196	−	1.05708i
$529$	37.4657	−	12.1733i	1.62894	−	0.529275i
$530$	−12.6939	−	6.07401i	−0.551390	−	0.263838i
$531$	−13.2546	+	40.4937i	−0.575201	+	1.75728i
$532$	0.0564516	+	0.210680i	0.00244749	+	0.00913415i
$533$	32.9214	+	8.82127i	1.42598	+	0.382091i
$534$	16.2595	+	20.1235i	0.703619	+	0.870830i
$535$	10.2101	−	18.7492i	0.441421	−	0.810600i
$536$	8.89646	+	19.9818i	0.384268	+	0.863081i
$537$	4.34555	−	0.451961i	0.187524	−	0.0195035i
$538$	−9.38625	+	11.5911i	−0.404670	+	0.499726i
$539$	−14.3163	+	15.8998i	−0.616646	+	0.684854i
$540$	1.41881	−	2.29207i	0.0610558	−	0.0986352i
$541$	−3.29005	+	31.3028i	−0.141450	+	1.34581i	0.661581	+	0.749874i	$0.269886\pi$
$541$	−3.29005	+	31.3028i	−0.141450	+	1.34581i	−0.803031	+	0.595937i	$0.796781\pi$
$542$	−3.30570	+	1.68434i	−0.141992	+	0.0723486i
$543$	0.0228649	−	21.0358i	0.000981225	−	0.902733i
$544$	3.73138	+	0.392184i	0.159982	+	0.0168147i
$545$	17.6141	−	1.36431i	0.754505	−	0.0584406i
$546$	16.4386	−	6.28970i	0.703508	−	0.269174i
$547$	−14.0477	−	11.3756i	−0.600635	−	0.486385i	0.280115	−	0.959967i	$-0.409627\pi$
$547$	−14.0477	−	11.3756i	−0.600635	−	0.486385i	−0.880750	+	0.473582i	$0.842961\pi$
$548$	3.14104	−	2.03982i	0.134179	−	0.0871367i
$549$	1.18165	−	2.03645i	0.0504317	−	0.0869134i
$550$	11.3830	+	25.7379i	0.485371	+	1.09747i
$551$	−2.16334	+	4.85895i	−0.0921616	+	0.206998i
$552$	−27.2020	+	30.1450i	−1.15780	+	1.28306i
$553$	14.3612	−	3.84808i	0.610701	−	0.163637i
$554$	−23.2288	+	16.8767i	−0.986897	+	0.717023i
$555$	−0.804209	+	0.614125i	−0.0341368	+	0.0260682i
$556$	−0.602868	−	1.85544i	−0.0255673	−	0.0786881i
$557$	1.44247	+	1.44247i	0.0611192	+	0.0611192i	0.737006	−	0.675886i	$-0.236239\pi$
$557$	1.44247	+	1.44247i	0.0611192	+	0.0611192i	−0.675886	+	0.737006i	$0.736239\pi$
$558$	−19.7096	+	10.2372i	−0.834376	+	0.433376i
$559$			32.9566i			1.39391i
$560$	4.66363	+	9.80874i	0.197074	+	0.414495i
$561$	−5.47570	+	20.3471i	−0.231184	+	0.859055i
$562$	0.357989	−	2.26025i	0.0151009	−	0.0953430i
$563$	−3.85369	−	14.3822i	−0.162414	−	0.606136i	−0.998356	−	0.0573187i	$-0.981745\pi$
$563$	−3.85369	−	14.3822i	−0.162414	−	0.606136i	0.835942	−	0.548817i	$-0.184922\pi$
$564$	−4.65857	+	0.239068i	−0.196161	+	0.0100666i
$565$	−15.0521	−	4.47891i	−0.633245	−	0.188429i
$566$	−1.81936	+	2.50413i	−0.0764733	+	0.105256i
$567$	9.72174	+	7.94275i	0.408275	+	0.333564i
$568$	7.43561	+	11.4498i	0.311991	+	0.480424i
$569$	−3.08019	−	29.3061i	−0.129128	−	1.22857i	−0.846693	−	0.532082i	$-0.821410\pi$
$569$	−3.08019	−	29.3061i	−0.129128	−	1.22857i	0.717565	−	0.696492i	$-0.245257\pi$
$570$	0.993501	−	3.32559i	0.0416132	−	0.139293i
$571$	−18.1832	−	20.1945i	−0.760945	−	0.845115i	0.230845	−	0.972990i	$-0.425851\pi$
$571$	−18.1832	−	20.1945i	−0.760945	−	0.845115i	−0.991790	+	0.127876i	$0.959184\pi$
$572$	−4.18172	+	3.38629i	−0.174846	+	0.141588i
$573$	29.5024	+	0.0320676i	1.23248	+	0.00133965i
$574$	−10.9729	−	3.56530i	−0.457998	−	0.148813i
$575$	23.2936	−	31.8944i	0.971409	−	1.33009i
$576$	5.48213	−	25.5185i	0.228422	−	1.06327i
$577$	1.40288	+	26.7685i	0.0584025	+	1.11439i	0.857933	+	0.513761i	$0.171748\pi$
$577$	1.40288	+	26.7685i	0.0584025	+	1.11439i	−0.799531	+	0.600625i	$0.794918\pi$
$578$	−9.03221	−	7.31414i	−0.375690	−	0.304228i
$579$	−3.60964	−	2.92953i	−0.150012	−	0.121747i
$580$	0.960662	−	3.97973i	0.0398893	−	0.165249i
$581$	11.2595	−	15.4973i	0.467121	−	0.642937i
$582$	3.47027	+	0.368555i	0.143847	+	0.0152771i
$583$	−5.18552	+	19.3526i	−0.214762	+	0.801503i
$584$	3.32692	−	5.76240i	0.137669	−	0.238450i
$585$	36.1153	+	6.82114i	1.49319	+	0.282019i
$586$	−16.1400	+	3.43066i	−0.666737	+	0.141719i
$587$	0.309791	−	0.607999i	0.0127865	−	0.0250948i	−0.884525	−	0.466493i	$-0.845517\pi$
$587$	0.309791	−	0.607999i	0.0127865	−	0.0250948i	0.897311	+	0.441398i	$0.145517\pi$
$588$	−1.93234	+	0.625533i	−0.0796882	+	0.0257965i
$589$	2.76348	−	2.53866i	0.113867	−	0.104604i
$590$	−5.45992	−	41.8729i	−0.224781	−	1.72388i
$591$	1.50736	−	9.45059i	0.0620045	−	0.388745i
$592$	−0.495497	+	0.762999i	−0.0203648	+	0.0313590i
$593$	4.23353	−	26.7295i	0.173850	−	1.09765i	−0.734245	−	0.678885i	$-0.762464\pi$
$593$	4.23353	−	26.7295i	0.173850	−	1.09765i	0.908095	−	0.418763i	$-0.137536\pi$
$594$	27.2699	+	10.5701i	1.11890	+	0.433696i
$595$	1.18101	−	8.88559i	0.0484166	−	0.364274i
$596$	−0.815542	+	1.83174i	−0.0334059	+	0.0750309i
$597$	0.143868	−	0.441149i	0.00588814	−	0.0180550i
$598$	−53.7229	−	20.6223i	−2.19689	−	0.843308i
$599$	19.4034	+	4.12432i	0.792801	+	0.168515i	0.586474	−	0.809968i	$-0.300516\pi$
$599$	19.4034	+	4.12432i	0.792801	+	0.168515i	0.206327	+	0.978483i	$0.433849\pi$
$600$	−2.77767	+	25.5514i	−0.113398	+	1.04313i
$601$	28.9660	−	32.1700i	1.18155	−	1.31224i	0.241820	−	0.970321i	$-0.422256\pi$
$601$	28.9660	−	32.1700i	1.18155	−	1.31224i	0.939729	−	0.341921i	$-0.111078\pi$
$602$	0.583877	−	11.1410i	0.0237970	−	0.454074i
$603$	−21.3442	−	5.76891i	−0.869201	−	0.234928i
$604$	−1.31673	−	0.427831i	−0.0535770	−	0.0174082i
$605$	12.7610	−	8.74715i	0.518809	−	0.355622i
$606$	15.9179	+	10.3618i	0.646622	+	0.420921i
$607$	16.3817	+	0.858531i	0.664914	+	0.0348467i	0.381808	−	0.924242i	$-0.375302\pi$
$607$	16.3817	+	0.858531i	0.664914	+	0.0348467i	0.283107	+	0.959088i	$0.408635\pi$
$608$	0.0460502	+	0.878691i	0.00186758	+	0.0356356i
$609$	17.7923	+	6.85203i	0.720981	+	0.277658i
$610$	−0.185959	+	2.32600i	−0.00752926	+	0.0941769i
$611$	−25.8687	−	58.1020i	−1.04653	−	2.35055i
$612$	−1.41748	+	1.41133i	−0.0572982	+	0.0570496i
$613$	−6.06205	−	15.7922i	−0.244844	−	0.637840i	0.754996	−	0.655729i	$-0.227639\pi$
$613$	−6.06205	−	15.7922i	−0.244844	−	0.637840i	−0.999840	+	0.0178893i	$0.994305\pi$
$614$	−9.64423	−	16.7043i	−0.389209	−	0.674131i
$615$	−15.6042	−	18.3565i	−0.629224	−	0.740205i
$616$	14.1770	−	10.3002i	0.571207	−	0.415006i
$617$	23.4957	+	15.2583i	0.945900	+	0.614275i	0.922726	−	0.385457i	$-0.125956\pi$
$617$	23.4957	+	15.2583i	0.945900	+	0.614275i	0.0231743	+	0.999731i	$0.492623\pi$
$618$	8.11378	−	5.88154i	0.326384	−	0.236590i
$619$		−	3.60885i		−	0.145052i	−0.997367	−	0.0725259i	$-0.976894\pi$
$619$		−	3.60885i		−	0.145052i	0.997367	−	0.0725259i	$-0.0231060\pi$
$620$	−1.73827	+	2.30685i	−0.0698108	+	0.0926454i
$621$	−6.28851	−	40.5597i	−0.252349	−	1.62760i
$622$	−21.8668	−	11.1417i	−0.876778	−	0.446741i
$623$	−8.53419	+	13.1415i	−0.341915	+	0.526503i
$624$	32.6438	−	5.13390i	1.30680	−	0.205521i
$625$	0.123849	−	24.9997i	0.00495397	−	0.999988i
$626$	−1.62048	+	0.935586i	−0.0647675	+	0.0373936i
$627$	−4.91390	−	0.521873i	−0.196242	−	0.0208416i
$628$	0.288439	+	1.82113i	0.0115100	+	0.0726710i
$629$	0.685935	−	0.305398i	0.0273500	−	0.0121770i
$630$	−12.0880	−	2.94574i	−0.481598	−	0.117361i
$631$	4.82514	+	45.9082i	0.192086	+	1.82758i	0.488555	+	0.872533i	$0.337524\pi$
$631$	4.82514	+	45.9082i	0.192086	+	1.82758i	−0.296470	+	0.955042i	$0.595809\pi$
$632$	31.5902	−	1.65557i	1.25659	−	0.0658552i
$633$	40.3583	+	23.3594i	1.60410	+	0.928454i
$634$	3.99307	+	0.419689i	0.158585	+	0.0166680i
$635$	−5.04267	+	27.0210i	−0.200112	+	1.07230i
$636$	−1.34635	+	1.34342i	−0.0533861	+	0.0532702i
$637$	−17.4274	−	21.5210i	−0.690497	−	0.852693i
$638$	44.3575	+	2.32468i	1.75613	+	0.0920349i
$639$	−13.7217	−	1.47237i	−0.542821	−	0.0582462i
$640$	4.65158	+	19.4815i	0.183870	+	0.770073i
$641$	−3.63152	+	17.0849i	−0.143436	+	0.674815i	0.846394	+	0.532558i	$0.178769\pi$
$641$	−3.63152	+	17.0849i	−0.143436	+	0.674815i	−0.989830	+	0.142257i	$0.954564\pi$
$642$	14.6953	+	16.3565i	0.579979	+	0.645541i
$643$	5.93462	+	37.4697i	0.234038	+	1.47766i	0.772502	+	0.635012i	$0.219005\pi$
$643$	5.93462	+	37.4697i	0.234038	+	1.47766i	−0.538464	+	0.842649i	$0.680995\pi$
$644$	−2.33526	−	1.03972i	−0.0920221	−	0.0409709i
$645$	13.2399	−	19.1685i	0.521321	−	0.754761i
$646$	−1.28773	+	2.23042i	−0.0506651	+	0.0877545i
$647$	8.05213	+	1.27533i	0.316562	+	0.0501385i	0.312694	−	0.949854i	$-0.398769\pi$
$647$	8.05213	+	1.27533i	0.316562	+	0.0501385i	0.00386834	+	0.999993i	$0.498769\pi$
$648$	16.7189	+	20.8307i	0.656781	+	0.818306i
$649$	−57.1782	+	18.5783i	−2.24444	+	0.729263i
$650$	−35.2077	+	9.34047i	−1.38096	+	0.366363i
$651$	−9.59601	−	9.42678i	−0.376097	−	0.369465i
$652$	2.90840	−	2.90840i	0.113902	−	0.113902i
$653$	−15.5010	−	7.89818i	−0.606603	−	0.309080i	0.123577	−	0.992335i	$-0.460564\pi$
$653$	−15.5010	−	7.89818i	−0.606603	−	0.309080i	−0.730179	+	0.683256i	$0.760564\pi$
$654$	−4.72856	+	17.5708i	−0.184901	+	0.687073i
$655$	−0.203400	+	7.41650i	−0.00794749	+	0.289787i
$656$	−18.7593	−	10.8307i	−0.732429	−	0.422868i
$657$	2.39673	+	6.28451i	0.0935055	+	0.245182i
$658$	7.71558	+	20.0998i	0.300785	+	0.783570i
$659$	21.5348	+	15.6459i	0.838876	+	0.609479i	0.922056	−	0.387055i	$-0.126508\pi$
$659$	21.5348	+	15.6459i	0.838876	+	0.609479i	−0.0831805	+	0.996534i	$0.526508\pi$
$660$	3.79261	−	0.289612i	0.147627	−	0.0112731i
$661$	17.0650	+	3.62727i	0.663750	+	0.141084i	0.527454	−	0.849584i	$-0.323147\pi$
$661$	17.0650	+	3.62727i	0.663750	+	0.141084i	0.136296	+	0.990668i	$0.456480\pi$
$662$	14.0001	−	17.2887i	0.544131	−	0.671946i
$663$	−24.9027	−	11.1198i	−0.967140	−	0.431859i
$664$	30.2882	−	27.2716i	1.17541	−	1.05834i
$665$	2.10151	−	0.0524254i	0.0814929	−	0.00203297i
$666$	−0.319898	−	0.991875i	−0.0123958	−	0.0384344i
$667$	−28.2998	−	55.5416i	−1.09577	−	2.15058i
$668$	−2.73012	−	3.37142i	−0.105631	−	0.130444i
$669$	2.32328	+	8.70845i	0.0898232	+	0.336688i
$670$	21.5506	−	3.96656i	0.832571	−	0.153242i
$671$	3.30398	−	0.347262i	0.127549	−	0.0134059i
$672$	3.13722	−	0.326288i	0.121021	−	0.0125868i
$673$	18.5029	+	7.10260i	0.713235	+	0.273785i	0.687809	−	0.725891i	$-0.258573\pi$
$673$	18.5029	+	7.10260i	0.713235	+	0.273785i	0.0254257	+	0.999677i	$0.491906\pi$
$674$	14.1709	+	10.2957i	0.545842	+	0.396577i
$675$	−18.2655	−	18.4763i	−0.703038	−	0.711152i
$676$	−1.97423	−	3.41947i	−0.0759320	−	0.131518i
$677$	−25.0951	+	6.72422i	−0.964484	+	0.258433i	−0.706497	−	0.707716i	$-0.749726\pi$
$677$	−25.0951	+	6.72422i	−0.964484	+	0.258433i	−0.257987	+	0.966148i	$0.583059\pi$
$678$	9.52144	−	13.0752i	0.365669	−	0.502151i
$679$	0.439453	+	2.06746i	0.0168646	+	0.0793419i
$680$	6.38853	−	17.9699i	0.244989	−	0.689114i
$681$	34.9328	+	17.8470i	1.33863	+	0.683898i
$682$	−28.0634	−	13.9479i	−1.07460	−	0.534092i
$683$	−19.7588	+	19.7588i	−0.756050	+	0.756050i	−0.975601	−	0.219551i	$-0.929541\pi$
$683$	−19.7588	+	19.7588i	−0.756050	+	0.756050i	0.219551	+	0.975601i	$0.429541\pi$
$684$	−0.378910	−	0.276555i	−0.0144880	−	0.0105743i
$685$	−12.0072	−	34.0412i	−0.458771	−	1.30065i
$686$	13.1413	+	18.0874i	0.501736	+	0.690580i
$687$	45.5067	+	9.72445i	1.73619	+	0.371011i
$688$	5.42114	−	20.2320i	0.206679	−	0.771337i
$689$	−23.6901	−	10.5475i	−0.902521	−	0.401828i
$690$	22.9621	+	33.5771i	0.874152	+	1.27826i
$691$	−3.05095	+	1.35837i	−0.116063	+	0.0516748i	−0.463947	−	0.885863i	$-0.653567\pi$
$691$	−3.05095	+	1.35837i	−0.116063	+	0.0516748i	0.347883	+	0.937538i	$0.386900\pi$
$692$	−1.77248	−	2.72938i	−0.0673796	−	0.103755i
$693$	−0.965522	+	17.6875i	−0.0366772	+	0.671892i
$694$	−0.509076	−	0.458374i	−0.0193243	−	0.0173996i
$695$	−18.7468	+	1.45204i	−0.711106	+	0.0550792i
$696$	33.9975	+	22.1308i	1.28867	+	0.838867i
$697$	8.11622	+	15.9290i	0.307424	+	0.603353i
$698$	−6.12353	−	12.0181i	−0.231779	−	0.454892i
$699$	1.58935	+	1.03460i	0.0601149	+	0.0391320i
$700$	−1.58357	+	0.332500i	−0.0598532	+	0.0125673i
$701$	1.40583	+	1.26582i	0.0530976	+	0.0478093i	0.695252	−	0.718766i	$-0.255293\pi$
$701$	1.40583	+	1.26582i	0.0530976	+	0.0478093i	−0.642155	+	0.766575i	$0.721959\pi$
$702$	−19.0341	+	32.7212i	−0.718396	+	1.23498i
$703$	0.0959042	+	0.147680i	0.00361710	+	0.00556984i
$704$	33.6447	−	14.9796i	1.26803	−	0.564564i
$705$	−8.29577	+	44.1863i	−0.312437	+	1.66415i
$706$	−9.38041	−	4.17643i	−0.353036	−	0.157182i
$707$	−2.97737	+	11.1117i	−0.111975	+	0.417898i
$708$	−5.58126	−	1.19268i	−0.209757	−	0.0448235i
$709$	10.8234	+	14.8971i	0.406481	+	0.559473i	0.962356	−	0.271793i	$-0.0876165\pi$
$709$	10.8234	+	14.8971i	0.406481	+	0.559473i	−0.555875	+	0.831266i	$0.687617\pi$
$710$	12.8983	−	4.54957i	0.484066	−	0.170742i
$711$	−18.8516	+	25.8288i	−0.706991	+	0.968655i
$712$	−23.5743	+	23.5743i	−0.883486	+	0.883486i
$713$	2.74003	+	43.8942i	0.102615	+	1.64385i
$714$	8.22139	+	4.20027i	0.307678	+	0.157191i
$715$	22.2686	+	46.8362i	0.832797	+	1.75158i
$716$	0.121674	+	0.572433i	0.00454718	+	0.0213928i
$717$	11.2784	−	15.4880i	0.421200	−	0.578409i
$718$	−2.92624	+	0.784085i	−0.109206	+	0.0292618i
$719$	7.45631	+	12.9147i	0.278073	+	0.481637i	0.970906	−	0.239461i	$-0.0769708\pi$
$719$	7.45631	+	12.9147i	0.278073	+	0.481637i	−0.692833	+	0.721099i	$0.743637\pi$
$720$	−21.0491	−	10.1282i	−0.784453	−	0.377456i
$721$	4.91038	+	3.56760i	0.182872	+	0.132864i
$722$	23.0217	+	8.83719i	0.856777	+	0.328886i
$723$	6.51168	−	0.677250i	0.242172	−	0.0251872i
$724$	2.80229	−	0.294532i	0.104146	−	0.0109462i
$725$	−35.1130	−	18.0007i	−1.30406	−	0.668528i
$726$	4.10742	+	15.3960i	0.152441	+	0.571400i
$727$	−17.0670	−	21.0759i	−0.632979	−	0.781664i	0.355230	−	0.934779i	$-0.384403\pi$
$727$	−17.0670	−	21.0759i	−0.632979	−	0.781664i	−0.988208	+	0.153116i	$0.951069\pi$
$728$	10.2971	+	20.2092i	0.381635	+	0.749001i
$729$	−26.9994	−	0.176084i	−0.999979	−	0.00652164i
$730$	−4.82963	−	4.59452i	−0.178752	−	0.170051i
$731$	−12.8466	+	11.5671i	−0.475149	+	0.427826i
$732$	0.287970	+	0.128588i	0.0106437	+	0.00475274i
$733$	9.61873	−	11.8781i	0.355276	−	0.438729i	−0.567906	−	0.823094i	$-0.692246\pi$
$733$	9.61873	−	11.8781i	0.355276	−	0.438729i	0.923181	+	0.384365i	$0.125579\pi$
$734$	−12.4911	−	2.65506i	−0.461054	−	0.0980001i
$735$	1.49048	+	19.5185i	0.0549771	+	0.719951i
$736$	−8.34285	−	6.06143i	−0.307521	−	0.223427i
$737$	−11.1803	−	29.1256i	−0.411831	−	1.07286i
$738$	23.1853	−	8.84222i	0.853463	−	0.325487i
$739$	−8.73374	−	5.04243i	−0.321276	−	0.185489i	0.330685	−	0.943741i	$-0.392720\pi$
$739$	−8.73374	−	5.04243i	−0.321276	−	0.185489i	−0.651961	+	0.758252i	$0.726053\pi$
$740$	−0.0931778	−	0.0984328i	−0.00342529	−	0.00361846i
$741$	1.66210	−	6.17618i	0.0610588	−	0.226888i
$742$	7.82161	+	3.98531i	0.287140	+	0.146305i
$743$	−2.86247	+	2.86247i	−0.105014	+	0.105014i	−0.757662	−	0.652648i	$-0.773658\pi$
$743$	−2.86247	+	2.86247i	−0.105014	+	0.105014i	0.652648	+	0.757662i	$0.273658\pi$
$744$	−15.8007	−	23.8636i	−0.579284	−	0.874881i
$745$	15.3169	+	11.7833i	0.561169	+	0.431706i
$746$	19.7217	−	6.40797i	0.722063	−	0.234612i
$747$	2.06674	+	41.1470i	0.0756179	+	1.50549i
$748$	−2.78769	−	0.441526i	−0.101928	−	0.0161438i
$749$	−6.65882	+	11.5334i	−0.243308	+	0.421422i
$750$	24.2303	+	8.71157i	0.884765	+	0.318102i
$751$	7.75023	+	3.45063i	0.282810	+	0.125915i	0.543240	−	0.839578i	$-0.317198\pi$
$751$	7.75023	+	3.45063i	0.282810	+	0.125915i	−0.260430	+	0.965493i	$0.583864\pi$
$752$	6.32332	+	39.9239i	0.230588	+	1.45587i
$753$	−15.4536	−	17.2005i	−0.563160	−	0.626821i
$754$	−11.9532	+	56.2352i	−0.435308	+	2.04796i
$755$	−6.98614	+	11.3687i	−0.254252	+	0.413750i
$756$	−0.920445	+	1.40729i	−0.0334763	+	0.0511828i
$757$	15.7054	+	0.823087i	0.570824	+	0.0299156i	0.335565	−	0.942017i	$-0.391073\pi$
$757$	15.7054	+	0.823087i	0.570824	+	0.0299156i	0.235259	+	0.971933i	$0.424406\pi$
$758$	7.52903	+	9.29758i	0.273467	+	0.337703i
$759$	40.9962	−	40.9072i	1.48807	−	1.48484i
$760$	4.39676	+	0.820524i	0.159487	+	0.0297635i
$761$	−24.4691	−	2.57181i	−0.887005	−	0.0932280i	−0.349943	−	0.936771i	$-0.613799\pi$
$761$	−24.4691	−	2.57181i	−0.887005	−	0.0932280i	−0.537062	+	0.843543i	$0.680466\pi$
$762$	−24.5024	−	14.1820i	−0.887629	−	0.513760i
$763$	−11.0056	+	0.576779i	−0.398429	+	0.0208808i
$764$	0.413078	+	3.93017i	0.0149446	+	0.142189i
$765$	10.0169	+	16.4720i	0.362161	+	0.595546i
$766$	21.8173	−	9.71367i	0.788290	−	0.350969i
$767$	−12.1730	−	76.8573i	−0.439541	−	2.77515i
$768$	9.45633	+	1.00429i	0.341226	+	0.0362393i
$769$	21.2253	−	12.2545i	0.765406	−	0.441907i	−0.0658276	−	0.997831i	$-0.520969\pi$
$769$	21.2253	−	12.2545i	0.765406	−	0.441907i	0.831233	+	0.555924i	$0.187635\pi$
$770$	−6.69815	−	16.2276i	−0.241385	−	0.584801i
$771$	23.4915	−	3.69452i	0.846026	−	0.133055i
$772$	0.339150	−	0.522245i	0.0122063	−	0.0187960i
$773$	−30.8496	−	15.7187i	−1.10958	−	0.565361i	−0.199546	−	0.979888i	$-0.563947\pi$
$773$	−30.8496	−	15.7187i	−1.10958	−	0.565361i	−0.910037	+	0.414528i	$0.863947\pi$
$774$	14.0612	+	19.4424i	0.505421	+	0.698842i
$775$	17.6814	+	21.5027i	0.635136	+	0.772401i
$776$			4.49712i			0.161437i
$777$	0.511069	−	0.370465i	0.0183345	−	0.0132904i
$778$	22.7326	+	14.7627i	0.815004	+	0.529270i
$779$	−3.39189	+	2.46435i	−0.121527	+	0.0882945i
$780$	−0.397677	+	4.90705i	−0.0142391	+	0.175700i
$781$	−9.73638	−	16.8639i	−0.348395	−	0.603438i
$782$	−10.8171	−	28.1794i	−0.386817	−	1.00769i
$783$	−39.0402	+	12.5443i	−1.39518	+	0.448298i
$784$	7.15856	+	16.0784i	0.255663	+	0.574228i
$785$	17.7143	+	1.41622i	0.632249	+	0.0505471i
$786$	−7.13097	−	2.74622i	−0.254353	−	0.0979545i
$787$	0.744599	+	14.2078i	0.0265421	+	0.506453i	0.979261	+	0.202601i	$0.0649395\pi$
$787$	0.744599	+	14.2078i	0.0265421	+	0.506453i	−0.952719	+	0.303852i	$0.901727\pi$
$788$	1.28014	+	0.0670893i	0.0456031	+	0.00238996i
$789$	−23.4777	−	15.2829i	−0.835829	−	0.544086i
$790$	5.81384	−	31.1533i	0.206847	−	1.10838i
$791$	9.31698	+	3.02727i	0.331274	+	0.107637i
$792$	−9.83371	+	36.3833i	−0.349426	+	1.29283i
$793$	−0.225042	+	4.29406i	−0.00799149	+	0.152487i
$794$	−10.8565	+	12.0574i	−0.385284	+	0.427901i
$795$	9.54154	+	15.6520i	0.338404	+	0.555118i
$796$	0.0607962	+	0.0129226i	0.00215486	+	0.000458030i
$797$	39.0421	+	14.9868i	1.38294	+	0.530861i	0.932249	−	0.361818i	$-0.117844\pi$
$797$	39.0421	+	14.9868i	1.38294	+	0.530861i	0.450692	+	0.892679i	$0.351177\pi$
$798$	−0.671296	+	2.05842i	−0.0237636	+	0.0728673i
$799$	13.5690	−	30.4764i	0.480035	−	1.07818i
$800$	−6.52762	−	0.0161689i	−0.230786	−	0.000571658i
$801$	−3.44982	−	33.5238i	−0.121893	−	1.18450i
$802$	2.85436	−	18.0217i	0.100791	−	0.636370i
$803$	−5.16894	+	7.95947i	−0.182408	+	0.280884i
$804$	0.466477	−	2.92464i	0.0164514	−	0.103144i
$805$	−15.0223	+	19.5274i	−0.529468	+	0.688250i
$806$	23.5129	−	33.0516i	0.828207	−	1.16419i
$807$	18.4842	−	5.98367i	0.650674	−	0.210635i
$808$	−11.1118	+	21.8081i	−0.390911	+	0.767207i
$809$	25.6621	−	5.45464i	0.902230	−	0.191775i	0.266635	−	0.963798i	$-0.414088\pi$
$809$	25.6621	−	5.45464i	0.902230	−	0.191775i	0.635595	+	0.772023i	$0.280755\pi$
$810$	24.2161	−	11.3849i	0.850869	−	0.400024i
$811$	24.6444	−	42.6854i	0.865383	−	1.49889i	−0.00128398	−	0.999999i	$-0.500409\pi$
$811$	24.6444	−	42.6854i	0.865383	−	1.49889i	0.866667	−	0.498888i	$-0.166258\pi$
$812$	−0.660994	+	2.46686i	−0.0231963	+	0.0865699i
$813$	4.80582	+	0.510395i	0.168548	+	0.0179003i
$814$	0.864367	−	1.18970i	0.0302961	−	0.0416989i
$815$	−20.6709	−	33.8259i	−0.724072	−	1.18487i
$816$	13.4586	+	10.9228i	0.471144	+	0.382373i
$817$	−3.15060	−	2.55131i	−0.110226	−	0.0892590i
$818$	0.228331	+	4.35681i	0.00798340	+	0.152332i
$819$	−22.4159	−	4.81559i	−0.783274	−	0.168270i
$820$	2.22434	−	2.33816i	0.0776773	−	0.0816520i
$821$	−24.2980	−	7.89490i	−0.848006	−	0.275534i	−0.147395	−	0.989078i	$-0.547089\pi$
$821$	−24.2980	−	7.89490i	−0.848006	−	0.275534i	−0.700611	+	0.713544i	$0.747089\pi$
$822$	37.1778	+	0.0404104i	1.29673	+	0.00140947i
$823$	−34.2072	+	27.7005i	−1.19239	+	0.965577i	−0.999876	−	0.0157173i	$-0.994997\pi$
$823$	−34.2072	+	27.7005i	−1.19239	+	0.965577i	−0.192512	+	0.981295i	$0.561663\pi$
$824$	8.64109	+	9.59691i	0.301027	+	0.334324i
$825$	5.86381	−	36.1875i	0.204152	−	1.25989i
$826$	2.75346	+	26.1974i	0.0958050	+	0.911524i
$827$	−10.4632	−	16.1119i	−0.363840	−	0.560264i	0.608583	−	0.793491i	$-0.291738\pi$
$827$	−10.4632	−	16.1119i	−0.363840	−	0.560264i	−0.972423	+	0.233226i	$0.925072\pi$
$828$	5.31358	−	1.41139i	0.184660	−	0.0490494i
$829$	25.7915	−	35.4989i	0.895774	−	1.23293i	−0.0760219	−	0.997106i	$-0.524222\pi$
$829$	25.7915	−	35.4989i	0.895774	−	1.23293i	0.971796	−	0.235822i	$-0.0757781\pi$
$830$	−19.4384	−	35.9070i	−0.674716	−	1.24635i
$831$	37.3524	−	1.91685i	1.29574	−	0.0664946i
$832$	12.3374	+	46.0438i	0.427722	+	1.59628i
$833$	2.27230	−	14.3467i	0.0787304	−	0.497084i
$834$	5.03264	−	18.7007i	0.174266	−	0.647553i
$835$	−37.7607	+	17.9535i	−1.30676	+	0.621308i
$836$		−	0.661913i		−	0.0228927i
$837$	28.7921	+	2.83064i	0.995202	+	0.0978411i
$838$	−15.2939	−	15.2939i	−0.528320	−	0.528320i
$839$	10.8076	+	33.2624i	0.373120	+	1.14834i	0.944738	+	0.327825i	$0.106316\pi$
$839$	10.8076	+	33.2624i	0.373120	+	1.14834i	−0.571619	+	0.820520i	$0.693684\pi$
$840$	2.12969	−	15.8910i	0.0734814	−	0.548291i
$841$	−26.9223	+	19.5602i	−0.928356	+	0.674490i
$842$	−39.7853	+	10.6604i	−1.37109	+	0.367383i
$843$	−1.99706	+	2.21312i	−0.0687825	+	0.0762240i
$844$	−2.54055	+	5.70617i	−0.0874493	+	0.196414i
$845$	−36.5014	+	10.7631i	−1.25569	+	0.370261i
$846$	−40.0507	−	23.2395i	−1.37697	−	0.798990i
$847$	−8.09401	+	5.25631i	−0.278113	+	0.180609i
$848$	12.8083	+	10.3720i	0.439839	+	0.356174i
$849$	3.76576	−	1.44084i	0.129240	−	0.0494496i
$850$	−15.9982	−	10.4458i	−0.548733	−	0.358287i
$851$	−2.05243	−	0.215719i	−0.0703564	−	0.00739475i
$852$	0.00200928	−	1.84855i	6.88368e−5	−	0.0633304i
$853$	36.3687	−	18.5308i	1.24524	−	0.634482i	0.297866	−	0.954608i	$-0.403725\pi$
$853$	36.3687	−	18.5308i	1.24524	−	0.634482i	0.947375	+	0.320126i	$0.103725\pi$
$854$	0.152152	−	1.44763i	0.00520653	−	0.0495368i
$855$	−3.44793	+	2.92452i	−0.117917	+	0.100017i
$856$	−18.9600	+	21.0572i	−0.648041	+	0.719722i
$857$	23.9189	−	29.5374i	0.817054	−	1.00898i	−0.182613	−	0.983185i	$-0.558456\pi$
$857$	23.9189	−	29.5374i	0.817054	−	1.00898i	0.999667	−	0.0257928i	$-0.00821102\pi$
$858$	−53.1272	+	5.52552i	−1.81373	+	0.188638i
$859$	14.0389	+	31.5319i	0.479002	+	1.07586i	0.977877	+	0.209182i	$0.0670801\pi$
$859$	14.0389	+	31.5319i	0.479002	+	1.07586i	−0.498875	+	0.866674i	$0.666253\pi$
$860$	2.74054	+	1.49239i	0.0934516	+	0.0508900i
$861$	9.44543	+	11.6901i	0.321899	+	0.398397i
$862$	1.09366	+	0.293046i	0.0372503	+	0.00998119i
$863$	−3.74870	−	13.9903i	−0.127607	−	0.476236i	0.872312	−	0.488950i	$-0.162620\pi$
$863$	−3.74870	−	13.9903i	−0.127607	−	0.476236i	−0.999919	+	0.0127133i	$0.995953\pi$
$864$	−4.81243	+	4.78115i	−0.163722	+	0.162658i
$865$	−29.5798	+	10.4335i	−1.00574	+	0.354751i
$866$	25.1735	−	8.17937i	0.855431	−	0.277946i
$867$	4.66271	+	14.4036i	0.158354	+	0.489172i
$868$	1.11990	−	1.41154i	0.0380118	−	0.0479108i
$869$	−45.1199			−1.53059
$870$	29.5441	−	27.9060i	1.00164	−	0.946103i
$871$	39.4975	−	8.39544i	1.33832	−	0.284469i
$872$	−23.1595	−	3.66811i	−0.784281	−	0.124218i
$873$	−3.52660	−	2.86850i	−0.119357	−	0.0970840i
$874$	6.13038	−	3.53937i	0.207363	−	0.119721i
$875$	−0.466155	+	15.5882i	−0.0157589	+	0.526977i
$876$	−0.803190	+	0.408146i	−0.0271373	+	0.0137900i
$877$	11.0879	−	28.8850i	0.374413	−	0.975378i	−0.608866	−	0.793273i	$-0.708375\pi$
$877$	11.0879	−	28.8850i	0.374413	−	0.975378i	0.983279	−	0.182105i	$-0.0582912\pi$
$878$	−0.444293	+	0.288527i	−0.0149942	+	0.00973732i
$879$	20.0581	+	7.72460i	0.676543	+	0.260544i
$880$	−5.96637	−	32.4157i	−0.201126	−	1.09273i
$881$	−24.0561	+	21.6602i	−0.810471	+	0.729752i	−0.966129	−	0.258059i	$-0.916917\pi$
$881$	−24.0561	+	21.6602i	−0.810471	+	0.729752i	0.155658	+	0.987811i	$0.450250\pi$
$882$	−19.4632	−	5.26053i	−0.655361	−	0.177131i
$883$	4.21826	−	2.14931i	0.141956	−	0.0723300i	−0.381570	−	0.924340i	$-0.624616\pi$
$883$	4.21826	−	2.14931i	0.141956	−	0.0723300i	0.523526	+	0.852010i	$0.324616\pi$
$884$	1.12888	−	3.47433i	0.0379683	−	0.116854i
$885$	−23.7963	+	49.5928i	−0.799904	+	1.66705i
$886$	−30.8788	−	34.2944i	−1.03739	−	1.15214i
$887$	−30.4400	+	1.59529i	−1.02208	+	0.0535647i	−0.556002	−	0.831181i	$-0.687665\pi$
$887$	−30.4400	+	1.59529i	−1.02208	+	0.0535647i	−0.466074	+	0.884746i	$0.654332\pi$
$888$	1.22750	−	0.544918i	0.0411921	−	0.0182863i
$889$	3.56504	−	16.7722i	0.119568	−	0.562521i
$890$	17.4161	+	28.4996i	0.583788	+	0.955310i
$891$	−22.2590	−	30.9187i	−0.745705	−	1.03582i
$892$	−1.12710	+	0.432652i	−0.0377380	+	0.0144863i
$893$	7.55707	+	2.02491i	0.252888	+	0.0677610i
$894$	−16.7045	+	10.8222i	−0.558680	+	0.361949i
$895$	5.63822	+	0.154630i	0.188465	+	0.00516871i
$896$	−2.59771	−	12.2213i	−0.0867833	−	0.408283i
$897$	43.9943	+	60.6915i	1.46893	+	2.02643i
$898$	−25.0185	−	25.0185i	−0.834878	−	0.834878i
$899$	42.8852	−	9.56396i	1.43030	−	0.318976i
$900$	2.20265	−	2.69432i	0.0734216	−	0.0898108i
$901$	−4.20331	−	12.9365i	−0.140033	−	0.430976i
$902$	29.3647	+	19.0697i	0.977738	+	0.634950i
$903$	−8.55478	+	11.7478i	−0.284685	+	0.390941i
$904$	18.0510	+	10.4217i	0.600366	+	0.346621i
$905$	3.57806	−	26.9204i	0.118939	−	0.894864i
$906$	−8.63734	−	10.6900i	−0.286956	−	0.355150i
$907$	11.8880	−	1.88287i	0.394734	−	0.0625197i	0.0440876	−	0.999028i	$-0.485962\pi$
$907$	11.8880	−	1.88287i	0.394734	−	0.0625197i	0.350646	+	0.936508i	$0.385962\pi$
$908$	−1.88305	+	4.90550i	−0.0624911	+	0.162795i
$909$	−10.0140	−	22.6241i	−0.332145	−	0.750395i
$910$	22.1013	−	5.27710i	0.732650	−	0.174934i
$911$	13.0265	+	11.7292i	0.431589	+	0.388604i	0.856093	−	0.516822i	$-0.172885\pi$
$911$	13.0265	+	11.7292i	0.431589	+	0.388604i	−0.424504	+	0.905426i	$0.639552\pi$
$912$	−2.03630	+	3.51814i	−0.0674286	+	0.116497i
$913$	−45.1775	+	36.5840i	−1.49516	+	1.21075i
$914$	2.15939	−	6.64591i	0.0714262	−	0.219827i
$915$	1.85598	−	2.40715i	0.0613568	−	0.0795779i
$916$	−0.651545	+	6.19904i	−0.0215277	+	0.204822i
$917$	0.242221	−	4.62186i	0.00799886	−	0.152627i
$918$	−19.4354	+	4.06494i	−0.641465	+	0.134163i
$919$	−4.93293	+	0.518472i	−0.162722	+	0.0171028i	−0.185539	−	0.982637i	$-0.559403\pi$
$919$	−4.93293	+	0.518472i	−0.162722	+	0.0171028i	0.0228169	+	0.999740i	$0.492737\pi$
$920$	−39.9021	+	33.9942i	−1.31553	+	1.12076i
$921$	−1.34225	+	25.0898i	−0.0442286	+	0.826737i
$922$	−15.6029	+	2.47126i	−0.513854	+	0.0813865i
$923$	23.5299	−	9.03229i	0.774497	−	0.297301i
$924$	−2.36963	+	0.121604i	−0.0779549	+	0.00400048i
$925$	−1.13293	+	0.650362i	−0.0372505	+	0.0213838i
$926$	31.8637	+	43.8567i	1.04711	+	1.44122i
$927$	−13.0376	+	0.654852i	−0.428210	+	0.0215082i
$928$	−4.67735	+	9.17981i	−0.153541	+	0.301342i
$929$	−42.5370			−1.39559			−0.697797	−	0.716295i	$-0.745836\pi$
$929$	−42.5370			−1.39559			−0.697797	+	0.716295i	$0.745836\pi$
$930$	−26.9539	+	9.77778i	−0.883853	+	0.320626i
$931$	3.40650			0.111644
$932$	−0.115325	+	0.226337i	−0.00377758	+	0.00741392i
$933$	15.9542	+	27.7030i	0.522318	+	0.906956i
$934$	8.68544	+	11.9545i	0.284196	+	0.391163i
$935$	−10.4411	+	25.1190i	−0.341460	+	0.821479i
$936$	−44.5207	−	19.9380i	−1.45521	−	0.651693i
$937$	15.1086	−	5.79964i	0.493576	−	0.189466i	−0.0988320	−	0.995104i	$-0.531511\pi$
$937$	15.1086	−	5.79964i	0.493576	−	0.189466i	0.592408	+	0.805638i	$0.298177\pi$
$938$	−13.5009	+	2.13834i	−0.440821	+	0.0698191i
$939$	2.43396	+	0.130211i	0.0794293	+	0.00424929i
$940$	−6.00295	−	0.479924i	−0.195795	−	0.0156534i
$941$	−37.3614	+	3.92684i	−1.21795	+	0.128011i	−0.691614	−	0.722267i	$-0.743100\pi$
$941$	−37.3614	+	3.92684i	−1.21795	+	0.128011i	−0.526333	+	0.850278i	$0.676434\pi$
$942$	−7.46268	+	16.7125i	−0.243147	+	0.544524i
$943$	2.57163	−	49.0697i	0.0837438	−	1.59793i
$944$	−5.16954	+	49.1849i	−0.168254	+	1.60083i
$945$	11.1031	+	11.8062i	0.361185	+	0.384056i
$946$	−10.4622	+	32.1994i	−0.340156	+	1.04689i
$947$	−9.44592	+	7.64916i	−0.306951	+	0.248564i	−0.770402	−	0.637559i	$-0.779944\pi$
$947$	−9.44592	+	7.64916i	−0.306951	+	0.248564i	0.463451	+	0.886123i	$0.346611\pi$
$948$	−3.70707	−	2.14565i	−0.120400	−	0.0696875i
$949$	−9.12866	−	8.21948i	−0.296329	−	0.266816i
$950$	1.83264	−	4.08889i	0.0594587	−	0.132661i
$951$	−4.06100	−	3.29585i	−0.131687	−	0.106875i
$952$	−4.26353	+	11.1069i	−0.138182	+	0.359976i
$953$	22.6914	−	3.59397i	0.735048	−	0.116420i	0.222323	−	0.974973i	$-0.428636\pi$
$953$	22.6914	−	3.59397i	0.735048	−	0.116420i	0.512725	+	0.858553i	$0.328636\pi$
$954$	−18.4759	+	3.88521i	−0.598179	+	0.125788i
$955$	37.7555	+	5.01818i	1.22174	+	0.162385i
$956$	2.22254	+	1.28318i	0.0718821	+	0.0415011i
$957$	−46.7732	−	34.0605i	−1.51196	−	1.10102i
$958$	−39.0385	−	25.3519i	−1.26128	−	0.819083i
$959$	6.95826	+	21.4153i	0.224694	+	0.691537i
$960$	11.3217	−	31.7369i	0.365407	−	1.02430i
$961$	−30.4452	−	5.83862i	−0.982103	−	0.188342i
$962$	1.34588	+	1.34588i	0.0433928	+	0.0433928i
$963$	−4.41919	−	28.2997i	−0.142406	−	0.911946i
$964$	0.182325	+	0.857774i	0.00587231	+	0.0276270i
$965$	−4.12585	−	4.35854i	−0.132816	−	0.140306i
$966$	−13.7971	−	21.2963i	−0.443914	−	0.685197i
$967$	39.6636	+	10.6278i	1.27550	+	0.341768i	0.832134	−	0.554574i	$-0.187119\pi$
$967$	39.6636	+	10.6278i	1.27550	+	0.341768i	0.443362	+	0.896342i	$0.353785\pi$
$968$	−19.1701	+	7.35872i	−0.616151	+	0.236518i
$969$	2.99086	−	1.51983i	0.0960803	−	0.0488239i
$970$	4.37951	+	1.05717i	0.140618	+	0.0339436i
$971$	10.3957	−	48.9081i	0.333615	−	1.56954i	−0.417069	−	0.908875i	$-0.636943\pi$
$971$	10.3957	−	48.9081i	0.333615	−	1.56954i	0.750684	−	0.660661i	$-0.229724\pi$
$972$	−0.358486	−	3.59881i	−0.0114985	−	0.115432i
$973$	11.7133	−	0.613869i	0.375512	−	0.0196797i
$974$	−3.13722	−	3.48423i	−0.100523	−	0.111642i
$975$	45.0742	+	14.8233i	1.44353	+	0.474725i
$976$	0.844498	−	2.59910i	0.0270317	−	0.0831951i
$977$	−39.7617	+	20.2596i	−1.27209	+	0.648162i	−0.953974	−	0.299890i	$-0.903050\pi$
$977$	−39.7617	+	20.2596i	−1.27209	+	0.648162i	−0.318115	+	0.948052i	$0.603050\pi$
$978$	39.9461	−	8.44544i	1.27734	−	0.270055i
$979$	35.3385	−	31.8189i	1.12942	−	1.01694i
$980$	−2.57877	+	0.474645i	−0.0823759	+	0.0151620i
$981$	17.6489	−	15.8218i	0.563485	−	0.505150i
$982$	−8.24542	+	5.35464i	−0.263122	+	0.170873i
$983$	0.218436	−	0.569045i	0.00696702	−	0.0181497i	−0.930053	−	0.367426i	$-0.880239\pi$
$983$	0.218436	−	0.569045i	0.00696702	−	0.0181497i	0.937020	+	0.349276i	$0.113572\pi$
$984$	14.4862	+	28.5073i	0.461802	+	0.908778i
$985$	3.52364	−	11.8417i	0.112273	−	0.377310i
$986$	−26.1160	+	15.0781i	−0.831703	+	0.480184i
$987$	5.86075	−	27.4261i	0.186550	−	0.872981i
$988$	0.846178	+	0.134021i	0.0269205	+	0.00426379i
$989$	46.4751	−	9.87859i	1.47782	−	0.314121i
$990$	33.1202	+	18.1294i	1.05263	+	0.576191i
$991$	−40.2788			−1.27950			−0.639750	−	0.768583i	$-0.720962\pi$
$991$	−40.2788			−1.27950			−0.639750	+	0.768583i	$0.720962\pi$
$992$	5.60303	−	4.63061i	0.177896	−	0.147022i
$993$	−27.5702	+	8.92499i	−0.874914	+	0.283226i
$994$	−8.11435	+	2.63651i	−0.257371	+	0.0836251i
$995$	0.258564	−	0.540367i	0.00819702	−	0.0171308i
$996$	−5.45153	+	0.857364i	−0.172738	+	0.0271666i
$997$	5.76791	+	21.5261i	0.182671	+	0.681739i	0.995117	+	0.0987020i	$0.0314691\pi$
$997$	5.76791	+	21.5261i	0.182671	+	0.681739i	−0.812446	+	0.583037i	$0.801864\pi$
$998$	5.46137	+	1.46337i	0.172877	+	0.0463221i
$999$	−0.355642	+	1.31017i	−0.0112520	+	0.0414519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.bt.a.38.17	✓	960
3.2	odd	2	inner	465.2.bt.a.38.44	yes	960
5.2	odd	4	inner	465.2.bt.a.317.17	yes	960
15.2	even	4	inner	465.2.bt.a.317.44	yes	960
31.9	even	15	inner	465.2.bt.a.443.44	yes	960
93.71	odd	30	inner	465.2.bt.a.443.17	yes	960
155.102	odd	60	inner	465.2.bt.a.257.44	yes	960
465.257	even	60	inner	465.2.bt.a.257.17	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.bt.a.38.17	✓	960	1.1	even	1	trivial
465.2.bt.a.38.44	yes	960	3.2	odd	2	inner
465.2.bt.a.257.17	yes	960	465.257	even	60	inner
465.2.bt.a.257.44	yes	960	155.102	odd	60	inner
465.2.bt.a.317.17	yes	960	5.2	odd	4	inner
465.2.bt.a.317.44	yes	960	15.2	even	4	inner
465.2.bt.a.443.17	yes	960	93.71	odd	30	inner
465.2.bt.a.443.44	yes	960	31.9	even	15	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.bt (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.603653 + 1.18474i) q^{2} +(1.50094 - 0.864394i) q^{3} +(0.136370 + 0.187697i) q^{4} +(2.06692 - 0.853147i) q^{5} +(0.118032 + 2.30001i) q^{6} +(-1.30223 + 0.499878i) q^{7} +(-2.93127 + 0.464267i) q^{8} +(1.50564 - 2.59481i) q^{9} +(-0.236946 + 2.96375i) q^{10} +(4.20988 - 0.442477i) q^{11} +(0.366927 + 0.163845i) q^{12} +(-0.286746 + 5.47143i) q^{13} +(0.193870 - 1.84455i) q^{14} +(2.36486 - 3.06715i) q^{15} +(1.07605 - 3.31173i) q^{16} +(-2.23343 + 1.80859i) q^{17} +(2.16528 + 3.35015i) q^{18} +(-0.500863 - 0.450979i) q^{19} +(0.441998 + 0.271610i) q^{20} +(-1.52247 + 1.87593i) q^{21} +(-2.01709 + 5.25470i) q^{22} +(7.80172 - 1.23567i) q^{23} +(-3.99835 + 3.23061i) q^{24} +(3.54428 - 3.52677i) q^{25} +(-6.30910 - 3.64256i) q^{26} +(0.0169438 - 5.19612i) q^{27} +(-0.271410 - 0.176256i) q^{28} +(-2.43865 - 7.50539i) q^{29} +(2.20621 + 4.65323i) q^{30} +(-0.526685 + 5.54280i) q^{31} +(-0.923148 - 0.923148i) q^{32} +(5.93631 - 4.30313i) q^{33} +(-0.794490 - 3.73778i) q^{34} +(-2.26512 + 2.14420i) q^{35} +(0.692362 - 0.0712488i) q^{36} +(-0.252364 - 0.0676207i) q^{37} +(0.836638 - 0.321155i) q^{38} +(4.29909 + 8.46016i) q^{39} +(-5.66260 + 3.46040i) q^{40} +(1.29335 - 6.08475i) q^{41} +(-1.30343 - 2.93613i) q^{42} +(6.00689 - 0.314808i) q^{43} +(0.657152 + 0.729842i) q^{44} +(0.898286 - 6.64779i) q^{45} +(-3.24559 + 9.98889i) q^{46} +(-10.3430 + 5.27000i) q^{47} +(-1.24756 - 5.90084i) q^{48} +(-3.75610 + 3.38200i) q^{49} +(2.03877 + 6.32798i) q^{50} +(-1.78890 + 4.64515i) q^{51} +(-1.06607 + 0.692317i) q^{52} +(-1.69617 + 4.41867i) q^{53} +(6.14580 + 3.15673i) q^{54} +(8.32398 - 4.50621i) q^{55} +(3.58510 - 2.06986i) q^{56} +(-1.14159 - 0.243950i) q^{57} +(10.3640 + 1.64149i) q^{58} +(-13.8923 + 2.95289i) q^{59} +(0.898191 + 0.0256102i) q^{60} +0.784815 q^{61} +(-6.24881 - 3.96991i) q^{62} +(-0.663602 + 4.13167i) q^{63} +(8.27441 - 2.68852i) q^{64} +(4.07526 + 11.5536i) q^{65} +(1.51460 + 9.63055i) q^{66} +(-1.90750 - 7.11888i) q^{67} +(-0.644039 - 0.172570i) q^{68} +(10.6418 - 8.59843i) q^{69} +(-1.17296 - 3.97792i) q^{70} +(-1.87105 - 4.20245i) q^{71} +(-3.20876 + 8.30511i) q^{72} +(-1.41094 + 1.74237i) q^{73} +(0.232453 - 0.258165i) q^{74} +(2.27124 - 8.35712i) q^{75} +(0.0163448 - 0.155510i) q^{76} +(-5.26104 + 2.68063i) q^{77} +(-12.6182 - 0.0137153i) q^{78} +(-10.6005 - 1.11416i) q^{79} +(-0.601296 - 7.76310i) q^{80} +(-4.46607 - 7.81372i) q^{81} +(6.42808 + 5.20535i) q^{82} +(-11.5174 + 7.47950i) q^{83} +(-0.559725 - 0.0299440i) q^{84} +(-3.07331 + 5.64365i) q^{85} +(-3.25311 + 7.30661i) q^{86} +(-10.1479 - 9.15718i) q^{87} +(-12.1349 + 3.25153i) q^{88} +(9.08817 - 6.60294i) q^{89} +(7.33361 + 5.07719i) q^{90} +(-2.36164 - 7.26839i) q^{91} +(1.29585 + 1.29585i) q^{92} +(4.00064 + 8.77467i) q^{93} -15.4349i q^{94} +(-1.41999 - 0.504826i) q^{95} +(-2.18355 - 0.587626i) q^{96} +(0.237045 - 1.49664i) q^{97} +(-1.73940 - 6.49154i) q^{98} +(5.19045 - 11.5901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 14 q^{3} - 16 q^{6} - 60 q^{7} - 44 q^{10} - 64 q^{12} - 36 q^{13} + 4 q^{15} + 176 q^{16} - 14 q^{18} - 36 q^{21} - 88 q^{22} - 20 q^{25} - 8 q^{27} - 56 q^{28} - 200 q^{30} - 56 q^{31} + 44 q^{33}+ \cdots + 44 q^{97}+O(q^{100}) \) 960 * q - 14 * q^3 - 16 * q^6 - 60 * q^7 - 44 * q^10 - 64 * q^12 - 36 * q^13 + 4 * q^15 + 176 * q^16 - 14 * q^18 - 36 * q^21 - 88 * q^22 - 20 * q^25 - 8 * q^27 - 56 * q^28 - 200 * q^30 - 56 * q^31 + 44 * q^33 - 32 * q^36 - 80 * q^37 - 52 * q^40 - 30 * q^42 - 36 * q^43 - 8 * q^45 - 164 * q^46 - 28 * q^48 - 44 * q^51 - 100 * q^52 - 88 * q^55 + 24 * q^57 + 64 * q^58 - 124 * q^60 - 176 * q^61 - 116 * q^63 + 48 * q^66 - 28 * q^67 - 36 * q^70 - 154 * q^72 - 12 * q^73 - 178 * q^75 + 112 * q^76 + 54 * q^78 - 52 * q^81 - 92 * q^82 - 24 * q^85 - 32 * q^87 + 52 * q^88 - 20 * q^90 + 40 * q^91 + 134 * q^93 + 8 * q^96 + 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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