LMFDB - Embedded newform 390.2.bh.b.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(11,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("390.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bh (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.7
Character	$\chi$	$=$	390.71
Dual form			390.2.bh.b.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.05814 + 1.37125i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.667179 + 1.59840i) q^{6} +(1.27100 - 4.74345i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.760676 - 2.90196i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.05814 + 1.37125i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.667179 + 1.59840i) q^{6} +(1.27100 - 4.74345i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.760676 - 2.90196i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.174045 + 0.649546i) q^{11} +(-0.230750 + 1.71661i) q^{12} +(0.528886 - 3.56655i) q^{13} -4.91078i q^{14} +(1.71784 - 0.221404i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.91056 + 6.77329i) q^{17} +(-1.48584 - 2.60620i) q^{18} +(1.01500 + 0.271969i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(5.15957 + 6.76210i) q^{21} +(0.336230 + 0.582367i) q^{22} +(1.67128 - 2.89473i) q^{23} +(0.221404 + 1.71784i) q^{24} +1.00000i q^{25} +(-0.412226 - 3.58191i) q^{26} +(4.78423 + 2.02760i) q^{27} +(-1.27100 - 4.74345i) q^{28} +(-5.85497 - 3.38037i) q^{29} +(1.60200 - 0.658470i) q^{30} +(1.25448 - 1.25448i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.07486 - 0.448651i) q^{33} +(5.53037 + 5.53037i) q^{34} +(-4.25286 + 2.45539i) q^{35} +(-2.10974 - 2.13283i) q^{36} +(2.23093 - 0.597776i) q^{37} +1.05081 q^{38} +(4.33101 + 4.49915i) q^{39} -1.00000 q^{40} +(-7.70998 + 2.06588i) q^{41} +(6.73393 + 5.19630i) q^{42} +(-2.63868 + 1.52344i) q^{43} +(0.475501 + 0.475501i) q^{44} +(-1.51412 + 2.58987i) q^{45} +(0.865116 - 3.22866i) q^{46} +(4.77336 - 4.77336i) q^{47} +(0.658470 + 1.60200i) q^{48} +(-14.8227 - 8.55787i) q^{49} +(0.258819 + 0.965926i) q^{50} +(-13.4258 - 1.80472i) q^{51} +(-1.32525 - 3.35317i) q^{52} +13.3055i q^{53} +(5.14599 + 0.720265i) q^{54} +(0.336230 - 0.582367i) q^{55} +(-2.45539 - 4.25286i) q^{56} +(-1.44696 + 1.10405i) q^{57} +(-6.53037 - 1.74981i) q^{58} +(0.859565 + 0.230320i) q^{59} +(1.37699 - 1.05066i) q^{60} +(3.16591 + 5.48352i) q^{61} +(0.887052 - 1.53642i) q^{62} +(-14.7321 - 0.0801745i) q^{63} -1.00000i q^{64} +(-2.89591 + 2.14795i) q^{65} +(-1.15435 - 0.155170i) q^{66} +(1.47371 + 5.49997i) q^{67} +(6.77329 + 3.91056i) q^{68} +(2.20097 + 5.35478i) q^{69} +(-3.47244 + 3.47244i) q^{70} +(3.56633 - 13.3097i) q^{71} +(-2.58987 - 1.51412i) q^{72} +(6.70607 + 6.70607i) q^{73} +(2.00020 - 1.15481i) q^{74} +(-1.37125 - 1.05814i) q^{75} +(1.01500 - 0.271969i) q^{76} +3.30230 q^{77} +(5.34790 + 3.22490i) q^{78} -6.32216 q^{79} +(-0.965926 + 0.258819i) q^{80} +(-7.84274 + 4.41490i) q^{81} +(-6.91257 + 3.99098i) q^{82} +(3.44219 + 3.44219i) q^{83} +(7.84937 + 3.27637i) q^{84} +(2.02426 - 7.55463i) q^{85} +(-2.15447 + 2.15447i) q^{86} +(10.8307 - 4.45175i) q^{87} +(0.582367 + 0.336230i) q^{88} +(2.97431 + 11.1003i) q^{89} +(-0.792216 + 2.89351i) q^{90} +(-16.2455 - 7.04184i) q^{91} -3.34255i q^{92} +(0.392794 + 3.04763i) q^{93} +(3.37528 - 5.84615i) q^{94} +(-0.525404 - 0.910027i) q^{95} +(1.05066 + 1.37699i) q^{96} +(10.5715 + 2.83261i) q^{97} +(-16.5325 - 4.42988i) q^{98} +(1.75256 - 0.999166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 32 * q - 8 * q^6 + 4 * q^9	$ 32 q - 8 q^{6} + 4 q^{9} + 16 q^{13} + 4 q^{15} + 16 q^{16} + 24 q^{18} + 32 q^{19} + 36 q^{21} + 8 q^{22} - 8 q^{24} + 12 q^{30} - 24 q^{31} - 28 q^{33} - 8 q^{34} - 12 q^{36} + 16 q^{37} - 4 q^{39} - 32 q^{40} - 12 q^{42} + 48 q^{43} - 24 q^{45} + 24 q^{46} - 48 q^{49} - 16 q^{52} - 20 q^{54} + 8 q^{55} + 4 q^{57} - 24 q^{58} + 4 q^{60} + 32 q^{61} - 48 q^{63} - 48 q^{66} - 64 q^{67} - 36 q^{69} - 40 q^{73} - 12 q^{75} + 32 q^{76} + 4 q^{78} - 32 q^{79} + 16 q^{81} + 12 q^{84} + 40 q^{85} - 72 q^{87} - 48 q^{88} - 144 q^{91} + 56 q^{94} - 4 q^{96} + 112 q^{97} + 72 q^{99}+O(q^{100}) $ 32 * q - 8 * q^6 + 4 * q^9 + 16 * q^13 + 4 * q^15 + 16 * q^16 + 24 * q^18 + 32 * q^19 + 36 * q^21 + 8 * q^22 - 8 * q^24 + 12 * q^30 - 24 * q^31 - 28 * q^33 - 8 * q^34 - 12 * q^36 + 16 * q^37 - 4 * q^39 - 32 * q^40 - 12 * q^42 + 48 * q^43 - 24 * q^45 + 24 * q^46 - 48 * q^49 - 16 * q^52 - 20 * q^54 + 8 * q^55 + 4 * q^57 - 24 * q^58 + 4 * q^60 + 32 * q^61 - 48 * q^63 - 48 * q^66 - 64 * q^67 - 36 * q^69 - 40 * q^73 - 12 * q^75 + 32 * q^76 + 4 * q^78 - 32 * q^79 + 16 * q^81 + 12 * q^84 + 40 * q^85 - 72 * q^87 - 48 * q^88 - 144 * q^91 + 56 * q^94 - 4 * q^96 + 112 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.05814	+	1.37125i	−0.610918	+	0.791694i
$3$	−1.05814	+	1.37125i	−0.610918	+	0.791694i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.667179	+	1.59840i	−0.272375	+	0.652543i
$7$	1.27100	−	4.74345i	0.480394	−	1.79285i	−0.119568	−	0.992826i	$-0.538151\pi$
$7$	1.27100	−	4.74345i	0.480394	−	1.79285i	0.599962	−	0.800029i	$-0.295182\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.760676	−	2.90196i	−0.253559	−	0.967320i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	0.174045	+	0.649546i	0.0524766	+	0.195845i	0.987188	−	0.159563i	$-0.0510085\pi$
$11$	0.174045	+	0.649546i	0.0524766	+	0.195845i	−0.934711	+	0.355408i	$0.884342\pi$
$12$	−0.230750	+	1.71661i	−0.0666117	+	0.495543i
$13$	0.528886	−	3.56655i	0.146687	−	0.989183i
$13$	0.528886	−	3.56655i	0.146687	−	0.989183i
$14$		−	4.91078i		−	1.31246i
$15$	1.71784	−	0.221404i	0.443545	−	0.0571664i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.91056	+	6.77329i	0.948451	+	1.64277i	0.748690	+	0.662920i	$0.230683\pi$
$17$	3.91056	+	6.77329i	0.948451	+	1.64277i	0.199761	+	0.979845i	$0.435983\pi$
$18$	−1.48584	−	2.60620i	−0.350216	−	0.614287i
$19$	1.01500	+	0.271969i	0.232858	+	0.0623941i	0.373361	−	0.927686i	$-0.378205\pi$
$19$	1.01500	+	0.271969i	0.232858	+	0.0623941i	−0.140503	+	0.990080i	$0.544872\pi$
$20$	−0.965926	−	0.258819i	−0.215988	−	0.0578737i
$21$	5.15957	+	6.76210i	1.12591	+	1.47561i
$22$	0.336230	+	0.582367i	0.0716844	+	0.124161i
$23$	1.67128	−	2.89473i	0.348485	−	0.603594i	−0.637496	−	0.770454i	$-0.720030\pi$
$23$	1.67128	−	2.89473i	0.348485	−	0.603594i	0.985981	+	0.166860i	$0.0533629\pi$
$24$	0.221404	+	1.71784i	0.0451940	+	0.350653i
$25$			1.00000i			0.200000i
$26$	−0.412226	−	3.58191i	−0.0808443	−	0.702470i
$27$	4.78423	+	2.02760i	0.920725	+	0.390212i
$28$	−1.27100	−	4.74345i	−0.240197	−	0.896427i
$29$	−5.85497	−	3.38037i	−1.08724	−	0.627719i	−0.154400	−	0.988008i	$-0.549345\pi$
$29$	−5.85497	−	3.38037i	−1.08724	−	0.627719i	−0.932840	+	0.360290i	$0.882678\pi$
$30$	1.60200	−	0.658470i	0.292485	−	0.120220i
$31$	1.25448	−	1.25448i	0.225311	−	0.225311i	−0.585419	−	0.810731i	$-0.699070\pi$
$31$	1.25448	−	1.25448i	0.225311	−	0.225311i	0.810731	+	0.585419i	$0.199070\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−1.07486	−	0.448651i	−0.187109	−	0.0781001i
$34$	5.53037	+	5.53037i	0.948451	+	0.948451i
$35$	−4.25286	+	2.45539i	−0.718864	+	0.415037i
$36$	−2.10974	−	2.13283i	−0.351624	−	0.355472i
$37$	2.23093	−	0.597776i	0.366763	−	0.0982737i	−0.0707306	−	0.997495i	$-0.522533\pi$
$37$	2.23093	−	0.597776i	0.366763	−	0.0982737i	0.437493	+	0.899222i	$0.355866\pi$
$38$	1.05081			0.170464
$39$	4.33101	+	4.49915i	0.693517	+	0.720441i
$40$	−1.00000			−0.158114
$41$	−7.70998	+	2.06588i	−1.20410	+	0.322637i	−0.804443	−	0.594030i	$-0.797536\pi$
$41$	−7.70998	+	2.06588i	−1.20410	+	0.322637i	−0.399653	+	0.916667i	$0.630869\pi$
$42$	6.73393	+	5.19630i	1.03907	+	0.801806i
$43$	−2.63868	+	1.52344i	−0.402395	+	0.232323i	−0.687517	−	0.726168i	$-0.741299\pi$
$43$	−2.63868	+	1.52344i	−0.402395	+	0.232323i	0.285122	+	0.958491i	$0.407966\pi$
$44$	0.475501	+	0.475501i	0.0716844	+	0.0716844i
$45$	−1.51412	+	2.58987i	−0.225711	+	0.386076i
$46$	0.865116	−	3.22866i	0.127554	−	0.476039i
$47$	4.77336	−	4.77336i	0.696267	−	0.696267i	−0.267336	−	0.963603i	$-0.586144\pi$
$47$	4.77336	−	4.77336i	0.696267	−	0.696267i	0.963603	+	0.267336i	$0.0861435\pi$
$48$	0.658470	+	1.60200i	0.0950420	+	0.231229i
$49$	−14.8227	−	8.55787i	−2.11752	−	1.22255i
$50$	0.258819	+	0.965926i	0.0366025	+	0.136603i
$51$	−13.4258	−	1.80472i	−1.87999	−	0.252712i
$52$	−1.32525	−	3.35317i	−0.183779	−	0.465000i
$53$			13.3055i			1.82765i	0.406110	+	0.913824i	$0.366885\pi$
$53$			13.3055i			1.82765i	−0.406110	+	0.913824i	$0.633115\pi$
$54$	5.14599	+	0.720265i	0.700281	+	0.0980157i
$55$	0.336230	−	0.582367i	0.0453372	−	0.0785263i
$56$	−2.45539	−	4.25286i	−0.328115	−	0.568312i
$57$	−1.44696	+	1.10405i	−0.191654	+	0.146234i
$58$	−6.53037	−	1.74981i	−0.857480	−	0.229761i
$59$	0.859565	+	0.230320i	0.111906	+	0.0299851i	0.314337	−	0.949311i	$-0.398218\pi$
$59$	0.859565	+	0.230320i	0.111906	+	0.0299851i	−0.202432	+	0.979296i	$0.564884\pi$
$60$	1.37699	−	1.05066i	0.177769	−	0.135640i
$61$	3.16591	+	5.48352i	0.405354	+	0.702093i	0.994363	−	0.106033i	$-0.0338150\pi$
$61$	3.16591	+	5.48352i	0.405354	+	0.702093i	−0.589009	+	0.808127i	$0.700482\pi$
$62$	0.887052	−	1.53642i	0.112656	−	0.195125i
$63$	−14.7321	−	0.0801745i	−1.85607	−	0.0101010i
$64$		−	1.00000i		−	0.125000i
$65$	−2.89591	+	2.14795i	−0.359194	+	0.266421i
$66$	−1.15435	−	0.155170i	−0.142091	−	0.0191001i
$67$	1.47371	+	5.49997i	0.180043	+	0.671928i	0.995638	+	0.0933047i	$0.0297431\pi$
$67$	1.47371	+	5.49997i	0.180043	+	0.671928i	−0.815595	+	0.578623i	$0.803590\pi$
$68$	6.77329	+	3.91056i	0.821383	+	0.474225i
$69$	2.20097	+	5.35478i	0.264966	+	0.644640i
$70$	−3.47244	+	3.47244i	−0.415037	+	0.415037i
$71$	3.56633	−	13.3097i	0.423246	−	1.57957i	−0.344479	−	0.938794i	$-0.611944\pi$
$71$	3.56633	−	13.3097i	0.423246	−	1.57957i	0.767724	−	0.640780i	$-0.221389\pi$
$72$	−2.58987	−	1.51412i	−0.305220	−	0.178440i
$73$	6.70607	+	6.70607i	0.784886	+	0.784886i	0.980651	−	0.195765i	$-0.0627190\pi$
$73$	6.70607	+	6.70607i	0.784886	+	0.784886i	−0.195765	+	0.980651i	$0.562719\pi$
$74$	2.00020	−	1.15481i	0.232518	−	0.134244i
$75$	−1.37125	−	1.05814i	−0.158339	−	0.122184i
$76$	1.01500	−	0.271969i	0.116429	−	0.0311970i
$77$	3.30230			0.376332
$78$	5.34790	+	3.22490i	0.605531	+	0.365148i
$79$	−6.32216			−0.711299			−0.355649	−	0.934619i	$-0.615740\pi$
$79$	−6.32216			−0.711299			−0.355649	+	0.934619i	$0.615740\pi$
$80$	−0.965926	+	0.258819i	−0.107994	+	0.0289368i
$81$	−7.84274	+	4.41490i	−0.871416	+	0.490545i
$82$	−6.91257	+	3.99098i	−0.763366	+	0.440730i
$83$	3.44219	+	3.44219i	0.377830	+	0.377830i	0.870319	−	0.492489i	$-0.163913\pi$
$83$	3.44219	+	3.44219i	0.377830	+	0.377830i	−0.492489	+	0.870319i	$0.663913\pi$
$84$	7.84937	+	3.27637i	0.856437	+	0.357481i
$85$	2.02426	−	7.55463i	0.219561	−	0.819414i
$86$	−2.15447	+	2.15447i	−0.232323	+	0.232323i
$87$	10.8307	−	4.45175i	1.16118	−	0.477277i
$88$	0.582367	+	0.336230i	0.0620805	+	0.0358422i
$89$	2.97431	+	11.1003i	0.315277	+	1.17663i	0.923732	+	0.383040i	$0.125123\pi$
$89$	2.97431	+	11.1003i	0.315277	+	1.17663i	−0.608455	+	0.793588i	$0.708210\pi$
$90$	−0.792216	+	2.89351i	−0.0835069	+	0.305003i
$91$	−16.2455	−	7.04184i	−1.70299	−	0.738185i
$92$		−	3.34255i		−	0.348485i
$93$	0.392794	+	3.04763i	0.0407309	+	0.316024i
$94$	3.37528	−	5.84615i	0.348133	−	0.602985i
$95$	−0.525404	−	0.910027i	−0.0539054	−	0.0933668i
$96$	1.05066	+	1.37699i	0.107233	+	0.140539i
$97$	10.5715	+	2.83261i	1.07337	+	0.287608i	0.751877	−	0.659304i	$-0.229149\pi$
$97$	10.5715	+	2.83261i	1.07337	+	0.287608i	0.321492	+	0.946912i	$0.395816\pi$
$98$	−16.5325	−	4.42988i	−1.67004	−	0.447486i
$99$	1.75256	−	0.999166i	0.176139	−	0.100420i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−2.53532	+	4.39130i	−0.252274	+	0.436951i	−0.964151	−	0.265353i	$-0.914512\pi$
$101$	−2.53532	+	4.39130i	−0.252274	+	0.436951i	0.711878	+	0.702303i	$0.247845\pi$
$102$	−13.4355	+	1.73163i	−1.33031	+	0.171457i
$103$		−	8.52836i		−	0.840325i	−0.907449	−	0.420162i	$-0.861973\pi$
$103$		−	8.52836i		−	0.840325i	0.907449	−	0.420162i	$-0.138027\pi$
$104$	−2.14795	−	2.89591i	−0.210624	−	0.283967i
$105$	1.13316	−	8.42990i	0.110585	−	0.822674i
$106$	3.44371	+	12.8521i	0.334483	+	1.24831i
$107$	0.667592	+	0.385435i	0.0645386	+	0.0372614i	0.531922	−	0.846793i	$-0.321470\pi$
$107$	0.667592	+	0.385435i	0.0645386	+	0.0372614i	−0.467383	+	0.884055i	$0.654803\pi$
$108$	5.15706	−	0.636158i	0.496239	−	0.0612143i
$109$	−7.62539	+	7.62539i	−0.730380	+	0.730380i	−0.970695	−	0.240315i	$-0.922749\pi$
$109$	−7.62539	+	7.62539i	−0.730380	+	0.730380i	0.240315	+	0.970695i	$0.422749\pi$
$110$	0.174045	−	0.649546i	0.0165946	−	0.0619318i
$111$	−1.54094	+	3.69170i	−0.146259	+	0.350401i
$112$	−3.47244	−	3.47244i	−0.328115	−	0.328115i
$113$	−5.55216	+	3.20554i	−0.522304	+	0.301552i	−0.737877	−	0.674936i	$-0.764171\pi$
$113$	−5.55216	+	3.20554i	−0.522304	+	0.301552i	0.215573	+	0.976488i	$0.430838\pi$
$114$	−1.11190	+	1.44093i	−0.104139	+	0.134955i
$115$	−3.22866	+	0.865116i	−0.301074	+	0.0806724i
$116$	−6.76074			−0.627719
$117$	−10.7523	+	1.17818i	−0.994050	+	0.108923i
$118$	0.889887			0.0819207
$119$	37.0991	−	9.94067i	3.40087	−	0.911260i
$120$	1.05814	−	1.37125i	0.0965946	−	0.125178i
$121$	9.13466	−	5.27390i	0.830424	−	0.479445i
$122$	4.47728	+	4.47728i	0.405354	+	0.405354i
$123$	5.32539	−	12.7583i	0.480174	−	1.15038i
$124$	0.459172	−	1.71365i	0.0412348	−	0.153890i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−14.2509	+	3.73551i	−1.26957	+	0.332786i
$127$	−1.26845	−	0.732338i	−0.112557	−	0.0649845i	0.442665	−	0.896687i	$-0.354033\pi$
$127$	−1.26845	−	0.732338i	−0.112557	−	0.0649845i	−0.555221	+	0.831703i	$0.687366\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.703068	−	5.23032i	0.0619017	−	0.460504i
$130$	−2.24130	+	2.82428i	−0.196575	+	0.247706i
$131$			9.87986i			0.863207i	0.902063	+	0.431604i	$0.142052\pi$
$131$			9.87986i			0.863207i	−0.902063	+	0.431604i	$0.857948\pi$
$132$	−1.15518	+	0.148886i	−0.100545	+	0.0129588i
$133$	2.58014	−	4.46894i	0.223727	−	0.387506i
$134$	2.84699	+	4.93113i	0.245943	+	0.425985i
$135$	−1.94923	−	4.81669i	−0.167763	−	0.414555i
$136$	7.55463	+	2.02426i	0.647804	+	0.173579i
$137$	6.18353	+	1.65687i	0.528295	+	0.141556i	0.513101	−	0.858328i	$-0.328497\pi$
$137$	6.18353	+	1.65687i	0.528295	+	0.141556i	0.0151941	+	0.999885i	$0.495163\pi$
$138$	3.51189	+	4.60267i	0.298952	+	0.391805i
$139$	11.1744	+	19.3546i	0.947797	+	1.64163i	0.750052	+	0.661378i	$0.230028\pi$
$139$	11.1744	+	19.3546i	0.947797	+	1.64163i	0.197744	+	0.980254i	$0.436638\pi$
$140$	−2.45539	+	4.25286i	−0.207518	+	0.359432i
$141$	1.49460	+	11.5964i	0.125868	+	0.976592i
$142$		−	13.7792i		−	1.15633i
$143$	2.40869	−	0.277206i	0.201425	−	0.0231811i
$144$	−2.89351	−	0.792216i	−0.241126	−	0.0660180i
$145$	1.74981	+	6.53037i	0.145314	+	0.542318i
$146$	8.21322	+	4.74191i	0.679731	+	0.392443i
$147$	27.4195	−	11.2702i	2.26152	−	0.929551i
$148$	1.63315	−	1.63315i	0.134244	−	0.134244i
$149$	−3.55295	+	13.2598i	−0.291069	+	1.08628i	0.653221	+	0.757168i	$0.273417\pi$
$149$	−3.55295	+	13.2598i	−0.291069	+	1.08628i	−0.944289	+	0.329116i	$0.893249\pi$
$150$	−1.59840	−	0.667179i	−0.130509	−	0.0544749i
$151$	−2.60236	−	2.60236i	−0.211777	−	0.211777i	0.593245	−	0.805022i	$-0.297847\pi$
$151$	−2.60236	−	2.60236i	−0.211777	−	0.211777i	−0.805022	+	0.593245i	$0.797847\pi$
$152$	0.910027	−	0.525404i	0.0738130	−	0.0426159i
$153$	16.6812	−	16.5006i	1.34859	−	1.33399i
$154$	3.18978	−	0.854698i	0.257039	−	0.0688735i
$155$	−1.77410			−0.142499
$156$	6.00034	+	1.73087i	0.480412	+	0.138581i
$157$	−3.10112			−0.247496			−0.123748	−	0.992314i	$-0.539492\pi$
$157$	−3.10112			−0.247496			−0.123748	+	0.992314i	$0.539492\pi$
$158$	−6.10674	+	1.63630i	−0.485826	+	0.130177i
$159$	−18.2452	−	14.0791i	−1.44694	−	1.11654i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−11.6068	−	11.6068i	−0.914746	−	0.914746i
$162$	−6.43285	+	6.29432i	−0.505412	+	0.494528i
$163$	0.668619	−	2.49532i	0.0523703	−	0.195449i	−0.934785	−	0.355215i	$-0.884408\pi$
$163$	0.668619	−	2.49532i	0.0523703	−	0.195449i	0.987155	+	0.159767i	$0.0510742\pi$
$164$	−5.64409	+	5.64409i	−0.440730	+	0.440730i
$165$	0.442795	+	1.07728i	0.0344715	+	0.0838663i
$166$	4.21581	+	2.43400i	0.327210	+	0.188915i
$167$	−4.08888	−	15.2599i	−0.316407	−	1.18085i	−0.922672	−	0.385585i	$-0.874000\pi$
$167$	−4.08888	−	15.2599i	−0.316407	−	1.18085i	0.606265	−	0.795263i	$-0.292667\pi$
$168$	8.42990	+	1.13316i	0.650381	+	0.0874253i
$169$	−12.4406	−	3.77260i	−0.956966	−	0.290200i
$170$		−	7.82113i		−	0.599853i
$171$	0.0171557	−	3.15238i	0.00131193	−	0.241069i
$172$	−1.52344	+	2.63868i	−0.116161	+	0.201198i
$173$	−4.69031	−	8.12385i	−0.356597	−	0.617645i	0.630793	−	0.775952i	$-0.282730\pi$
$173$	−4.69031	−	8.12385i	−0.356597	−	0.617645i	−0.987390	+	0.158307i	$0.949397\pi$
$174$	9.30948	−	7.10326i	0.705750	−	0.538496i
$175$	4.74345	+	1.27100i	0.358571	+	0.0960788i
$176$	0.649546	+	0.174045i	0.0489614	+	0.0131192i
$177$	−1.22537	+	0.934971i	−0.0921042	+	0.0702767i
$178$	5.74593	+	9.95225i	0.430676	+	0.745953i
$179$	−8.18472	+	14.1764i	−0.611755	+	1.05959i	0.379190	+	0.925319i	$0.376203\pi$
$179$	−8.18472	+	14.1764i	−0.611755	+	1.05959i	−0.990945	+	0.134271i	$0.957131\pi$
$180$	−0.0163262	+	2.99996i	−0.00121688	+	0.223603i
$181$		−	8.01719i		−	0.595913i	−0.954579	−	0.297956i	$-0.903695\pi$
$181$		−	8.01719i		−	0.595913i	0.954579	−	0.297956i	$-0.0963050\pi$
$182$	−17.5145	−	2.59724i	−1.29826	−	0.192520i
$183$	−10.8693	−	1.46107i	−0.803481	−	0.108005i
$184$	−0.865116	−	3.22866i	−0.0637772	−	0.238020i
$185$	−2.00020	−	1.15481i	−0.147057	−	0.0849036i
$186$	1.16819	+	2.84212i	0.0856562	+	0.208394i
$187$	−3.71895	+	3.71895i	−0.271957	+	0.271957i
$188$	1.74717	−	6.52054i	0.127426	−	0.475559i
$189$	15.6986	−	20.1166i	1.14190	−	1.46327i
$190$	−0.743034	−	0.743034i	−0.0539054	−	0.0539054i
$191$	−5.53512	+	3.19570i	−0.400507	+	0.231233i	−0.686703	−	0.726938i	$-0.740943\pi$
$191$	−5.53512	+	3.19570i	−0.400507	+	0.231233i	0.286196	+	0.958171i	$0.407609\pi$
$192$	1.37125	+	1.05814i	0.0989617	+	0.0763647i
$193$	4.48380	−	1.20143i	0.322751	−	0.0864808i	−0.0938061	−	0.995590i	$-0.529903\pi$
$193$	4.48380	−	1.20143i	0.322751	−	0.0864808i	0.416557	+	0.909110i	$0.363237\pi$
$194$	10.9444			0.785761
$195$	0.118892	−	6.24387i	0.00851405	−	0.447133i
$196$	−17.1157			−1.22255
$197$	−0.550371	+	0.147471i	−0.0392123	+	0.0105069i	−0.278372	−	0.960473i	$-0.589795\pi$
$197$	−0.550371	+	0.147471i	−0.0392123	+	0.0105069i	0.239160	+	0.970980i	$0.423128\pi$
$198$	1.43424	−	1.41872i	0.101927	−	0.100824i
$199$	6.62061	−	3.82241i	0.469323	−	0.270964i	−0.246633	−	0.969109i	$-0.579324\pi$
$199$	6.62061	−	3.82241i	0.469323	−	0.270964i	0.715956	+	0.698145i	$0.245991\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−9.10125	−	3.79891i	−0.641952	−	0.267954i
$202$	−1.31238	+	4.89786i	−0.0923386	+	0.344612i
$203$	−23.4763	+	23.4763i	−1.64771	+	1.64771i
$204$	−12.5295	+	5.14998i	−0.877239	+	0.360571i
$205$	6.91257	+	3.99098i	0.482795	+	0.278742i
$206$	−2.20730	−	8.23777i	−0.153790	−	0.573952i
$207$	−9.67170	−	2.64802i	−0.672230	−	0.184050i
$208$	−2.82428	−	2.24130i	−0.195829	−	0.155406i
$209$			0.706626i			0.0488784i
$210$	−1.08727	−	8.43594i	−0.0750286	−	0.582135i
$211$	4.55259	−	7.88532i	0.313414	−	0.542848i	−0.665685	−	0.746232i	$-0.731861\pi$
$211$	4.55259	−	7.88532i	0.313414	−	0.542848i	0.979099	+	0.203384i	$0.0651941\pi$
$212$	6.65274	+	11.5229i	0.456912	+	0.791395i
$213$	14.4773	+	18.9739i	0.991971	+	1.30007i
$214$	0.744603	+	0.199516i	0.0509000	+	0.0136386i
$215$	2.94307	+	0.788592i	0.200715	+	0.0537815i
$216$	4.81669	−	1.94923i	0.327734	−	0.132628i
$217$	−4.35611	−	7.54501i	−0.295712	−	0.512189i
$218$	−5.39196	+	9.33916i	−0.365190	+	0.632527i
$219$	−16.2917	+	2.09976i	−1.10089	+	0.141889i
$220$		−	0.672459i		−	0.0453372i
$221$	26.2255	−	10.3649i	1.76412	−	0.697220i
$222$	−0.532946	+	3.96473i	−0.0357690	+	0.266096i
$223$	3.03834	+	11.3392i	0.203462	+	0.759332i	0.989913	+	0.141679i	$0.0452500\pi$
$223$	3.03834	+	11.3392i	0.203462	+	0.759332i	−0.786450	+	0.617654i	$0.788083\pi$
$224$	−4.25286	−	2.45539i	−0.284156	−	0.164058i
$225$	2.90196	−	0.760676i	0.193464	−	0.0507117i
$226$	−4.53332	+	4.53332i	−0.301552	+	0.301552i
$227$	4.92103	−	18.3655i	0.326620	−	1.21896i	−0.586052	−	0.810273i	$-0.699319\pi$
$227$	4.92103	−	18.3655i	0.326620	−	1.21896i	0.912673	−	0.408691i	$-0.134015\pi$
$228$	−0.701078	+	1.67961i	−0.0464300	+	0.111235i
$229$	11.0904	+	11.0904i	0.732876	+	0.732876i	0.971189	−	0.238312i	$-0.0765942\pi$
$229$	11.0904	+	11.0904i	0.732876	+	0.732876i	−0.238312	+	0.971189i	$0.576594\pi$
$230$	−2.89473	+	1.67128i	−0.190873	+	0.110201i
$231$	−3.49430	+	4.52829i	−0.229908	+	0.297940i
$232$	−6.53037	+	1.74981i	−0.428740	+	0.114881i
$233$	2.66213			0.174402			0.0872011	−	0.996191i	$-0.472208\pi$
$233$	2.66213			0.174402			0.0872011	+	0.996191i	$0.472208\pi$
$234$	−10.0810	+	3.92094i	−0.659015	+	0.256320i
$235$	−6.75056			−0.440358
$236$	0.859565	−	0.230320i	0.0559529	−	0.0149925i
$237$	6.68974	−	8.66929i	0.434545	−	0.563131i
$238$	33.2621	−	19.2039i	2.15606	−	1.24480i
$239$	−13.6438	−	13.6438i	−0.882542	−	0.882542i	0.111250	−	0.993792i	$-0.464515\pi$
$239$	−13.6438	−	13.6438i	−0.882542	−	0.882542i	−0.993792	+	0.111250i	$0.964515\pi$
$240$	0.667179	−	1.59840i	0.0430662	−	0.103176i
$241$	−2.24088	+	8.36309i	−0.144348	+	0.538714i	0.855436	+	0.517909i	$0.173290\pi$
$241$	−2.24088	+	8.36309i	−0.144348	+	0.538714i	−0.999784	+	0.0208047i	$0.993377\pi$
$242$	7.45842	−	7.45842i	0.479445	−	0.479445i
$243$	2.24478	−	15.4260i	0.144003	−	0.989577i
$244$	5.48352	+	3.16591i	0.351047	+	0.202677i
$245$	4.42988	+	16.5325i	0.283015	+	1.05623i
$246$	1.84183	−	13.7019i	0.117431	−	0.873602i
$247$	1.50681	−	3.47622i	0.0958762	−	0.221187i
$248$		−	1.77410i		−	0.112656i
$249$	−8.36245	+	1.07780i	−0.529949	+	0.0683026i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−10.2794	−	17.8044i	−0.648830	−	1.12381i	−0.983403	−	0.181436i	$-0.941925\pi$
$251$	−10.2794	−	17.8044i	−0.648830	−	1.12381i	0.334573	−	0.942370i	$-0.391408\pi$
$252$	−12.7985	+	7.29663i	−0.806228	+	0.459644i
$253$	2.17114	+	0.581755i	0.136498	+	0.0365746i
$254$	−1.41477	−	0.379086i	−0.0887705	−	0.0237860i
$255$	8.21737	+	10.7696i	0.514591	+	0.674420i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.90976	−	11.9681i	0.431019	−	0.746547i	−0.565942	−	0.824445i	$-0.691487\pi$
$257$	6.90976	−	11.9681i	0.431019	−	0.746547i	0.996961	+	0.0778979i	$0.0248208\pi$
$258$	−0.674594	−	5.23407i	−0.0419984	−	0.325859i
$259$		−	11.3421i		−	0.704762i
$260$	−1.43396	+	3.30814i	−0.0889302	+	0.205162i
$261$	−5.35596	+	19.5623i	−0.331526	+	1.21087i
$262$	2.55709	+	9.54321i	0.157978	+	0.589581i
$263$	15.1100	+	8.72375i	0.931721	+	0.537929i	0.887355	−	0.461086i	$-0.152540\pi$
$263$	15.1100	+	8.72375i	0.931721	+	0.537929i	0.0443656	+	0.999015i	$0.485873\pi$
$264$	−1.07728	+	0.442795i	−0.0663022	+	0.0272521i
$265$	9.40840	−	9.40840i	0.577953	−	0.577953i
$266$	1.33558	−	4.98446i	0.0818897	−	0.305617i
$267$	−18.3686	−	7.66713i	−1.12414	−	0.469221i
$268$	4.02625	+	4.02625i	0.245943	+	0.245943i
$269$	20.4762	−	11.8220i	1.24846	−	0.720798i	0.277657	−	0.960680i	$-0.410442\pi$
$269$	20.4762	−	11.8220i	1.24846	−	0.720798i	0.970802	+	0.239882i	$0.0771089\pi$
$270$	−3.12946	−	4.14807i	−0.190453	−	0.252443i
$271$	14.4576	−	3.87391i	0.878237	−	0.235323i	0.208591	−	0.978003i	$-0.433112\pi$
$271$	14.4576	−	3.87391i	0.878237	−	0.235323i	0.669647	+	0.742680i	$0.266446\pi$
$272$	7.82113			0.474225
$273$	26.8462	−	14.8255i	1.62481	−	0.897279i
$274$	6.40166			0.386739
$275$	−0.649546	+	0.174045i	−0.0391691	+	0.0104953i
$276$	4.58349	+	3.53689i	0.275893	+	0.212896i
$277$	6.03963	−	3.48698i	0.362886	−	0.209512i	−0.307460	−	0.951561i	$-0.599479\pi$
$277$	6.03963	−	3.48698i	0.362886	−	0.209512i	0.670346	+	0.742049i	$0.266146\pi$
$278$	15.8029	+	15.8029i	0.947797	+	0.947797i
$279$	−4.59470	−	2.68620i	−0.275078	−	0.160819i
$280$	−1.27100	+	4.74345i	−0.0759570	+	0.283475i
$281$	16.0529	−	16.0529i	0.957637	−	0.957637i	−0.0415012	−	0.999138i	$-0.513214\pi$
$281$	16.0529	−	16.0529i	0.957637	−	0.957637i	0.999138	+	0.0415012i	$0.0132140\pi$
$282$	4.44504	+	10.8144i	0.264698	+	0.643989i
$283$	14.7346	+	8.50704i	0.875883	+	0.505691i	0.869299	−	0.494287i	$-0.164571\pi$
$283$	14.7346	+	8.50704i	0.875883	+	0.505691i	0.00658414	+	0.999978i	$0.497904\pi$
$284$	−3.56633	−	13.3097i	−0.211623	−	0.789787i
$285$	1.80383	+	0.242474i	0.106850	+	0.0143629i
$286$	2.25487	−	0.891174i	0.133333	−	0.0526962i
$287$			39.1976i			2.31376i
$288$	−2.99996	−	0.0163262i	−0.176774	−	0.000962032i
$289$	−22.0850	+	38.2524i	−1.29912	+	2.25014i
$290$	3.38037	+	5.85497i	0.198502	+	0.343816i
$291$	−15.0703	+	11.4989i	−0.883438	+	0.674075i
$292$	9.16066	+	2.45459i	0.536087	+	0.143644i
$293$	−20.5651	−	5.51039i	−1.20142	−	0.321921i	−0.398032	−	0.917371i	$-0.630307\pi$
$293$	−20.5651	−	5.51039i	−1.20142	−	0.321921i	−0.803392	+	0.595451i	$0.796973\pi$
$294$	23.5682	−	17.9829i	1.37453	−	1.04878i
$295$	−0.444943	−	0.770664i	−0.0259056	−	0.0448698i
$296$	1.15481	−	2.00020i	0.0671222	−	0.116259i
$297$	−0.484349	+	3.46047i	−0.0281048	+	0.200797i
$298$			13.7275i			0.795215i
$299$	−9.44030	−	7.49167i	−0.545947	−	0.433254i
$300$	−1.71661	−	0.230750i	−0.0991086	−	0.0133223i
$301$	3.87260	+	14.4527i	0.223213	+	0.833042i
$302$	−3.18723	−	1.84015i	−0.183404	−	0.105889i
$303$	−3.33886	−	8.12318i	−0.191813	−	0.466665i
$304$	0.743034	−	0.743034i	0.0426159	−	0.0426159i
$305$	1.63880	−	6.11608i	0.0938373	−	0.350206i
$306$	11.8421	−	20.2557i	0.676968	−	1.15794i
$307$	21.3686	+	21.3686i	1.21957	+	1.21957i	0.967782	+	0.251791i	$0.0810194\pi$
$307$	21.3686	+	21.3686i	1.21957	+	1.21957i	0.251791	+	0.967782i	$0.418981\pi$
$308$	2.85987	−	1.65115i	0.162956	−	0.0940830i
$309$	11.6946	+	9.02421i	0.665280	+	0.513369i
$310$	−1.71365	+	0.459172i	−0.0973289	+	0.0260792i
$311$	−3.85067			−0.218351			−0.109176	−	0.994022i	$-0.534821\pi$
$311$	−3.85067			−0.218351			−0.109176	+	0.994022i	$0.534821\pi$
$312$	6.24387	+	0.118892i	0.353489	+	0.00673094i
$313$	−20.6012			−1.16445			−0.582225	−	0.813028i	$-0.697818\pi$
$313$	−20.6012			−1.16445			−0.582225	+	0.813028i	$0.697818\pi$
$314$	−2.99545	+	0.802629i	−0.169043	+	0.0452950i
$315$	10.3605	+	10.4739i	0.583747	+	0.590136i
$316$	−5.47515	+	3.16108i	−0.308001	+	0.177825i
$317$	−11.9355	−	11.9355i	−0.670367	−	0.670367i	0.287434	−	0.957801i	$-0.407198\pi$
$317$	−11.9355	−	11.9355i	−0.670367	−	0.670367i	−0.957801	+	0.287434i	$0.907198\pi$
$318$	−21.2674	−	8.87714i	−1.19262	−	0.497805i
$319$	1.17667	−	4.39141i	0.0658811	−	0.245872i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	−1.23494	+	0.507595i	−0.0689274	+	0.0283312i
$322$	−14.2154	−	8.20726i	−0.792193	−	0.457373i
$323$	2.12711	+	7.93847i	0.118355	+	0.441708i
$324$	−4.58457	+	7.74479i	−0.254698	+	0.430266i
$325$	3.56655	+	0.528886i	0.197837	+	0.0293373i
$326$		−	2.58335i		−	0.143078i
$327$	−2.38761	−	18.5251i	−0.132035	−	1.02444i
$328$	−3.99098	+	6.91257i	−0.220365	+	0.381683i
$329$	−16.5752	−	28.7092i	−0.913823	−	1.58279i
$330$	0.706528	+	0.925971i	0.0388931	+	0.0509730i
$331$	−9.51447	−	2.54939i	−0.522962	−	0.140127i	−0.0123259	−	0.999924i	$-0.503924\pi$
$331$	−9.51447	−	2.54939i	−0.522962	−	0.140127i	−0.510637	+	0.859797i	$0.670590\pi$
$332$	4.70212	+	1.25993i	0.258063	+	0.0691477i
$333$	−3.43174	−	6.01936i	−0.188058	−	0.329859i
$334$	−7.89911	−	13.6817i	−0.432220	−	0.748627i
$335$	2.84699	−	4.93113i	0.155548	−	0.269417i
$336$	8.43594	−	1.08727i	0.460218	−	0.0593154i
$337$		−	13.3736i		−	0.728506i	−0.931300	−	0.364253i	$-0.881324\pi$
$337$		−	13.3736i		−	0.728506i	0.931300	−	0.364253i	$-0.118676\pi$
$338$	−12.9931	−	0.424195i	−0.706730	−	0.0230732i
$339$	1.47936	−	11.0053i	0.0803476	−	0.597728i
$340$	−2.02426	−	7.55463i	−0.109781	−	0.409707i
$341$	1.03318	+	0.596506i	0.0559498	+	0.0323026i
$342$	−0.799325	−	3.04941i	−0.0432225	−	0.164893i
$343$	−35.1264	+	35.1264i	−1.89665	+	1.89665i
$344$	−0.788592	+	2.94307i	−0.0425180	+	0.158679i
$345$	2.23008	−	5.34272i	0.120063	−	0.287642i
$346$	−6.63310	−	6.63310i	−0.356597	−	0.356597i
$347$	7.46309	−	4.30882i	0.400640	−	0.231309i	−0.286120	−	0.958194i	$-0.592366\pi$
$347$	7.46309	−	4.30882i	0.400640	−	0.231309i	0.686760	+	0.726884i	$0.259032\pi$
$348$	7.15381	−	9.27069i	0.383485	−	0.496961i
$349$	−19.2413	+	5.15568i	−1.02996	+	0.275977i	−0.733947	−	0.679207i	$-0.762324\pi$
$349$	−19.2413	+	5.15568i	−1.02996	+	0.275977i	−0.296013	+	0.955184i	$0.595657\pi$
$350$	4.91078			0.262492
$351$	9.76186	−	15.9908i	0.521049	−	0.853527i
$352$	0.672459			0.0358422
$353$	−11.6723	+	3.12758i	−0.621252	+	0.166464i	−0.555697	−	0.831385i	$-0.687549\pi$
$353$	−11.6723	+	3.12758i	−0.621252	+	0.166464i	−0.0655554	+	0.997849i	$0.520882\pi$
$354$	−0.941626	+	1.22026i	−0.0500468	+	0.0648561i
$355$	−11.9332	+	6.88962i	−0.633347	+	0.365663i
$356$	8.12598	+	8.12598i	0.430676	+	0.430676i
$357$	−25.6249	+	61.3909i	−1.35621	+	3.24915i
$358$	−4.23672	+	15.8117i	−0.223918	+	0.835673i
$359$	−19.8462	+	19.8462i	−1.04744	+	1.04744i	−0.0486248	+	0.998817i	$0.515484\pi$
$359$	−19.8462	+	19.8462i	−1.04744	+	1.04744i	−0.998817	+	0.0486248i	$0.984516\pi$
$360$	0.760676	+	2.90196i	0.0400911	+	0.152947i
$361$	−15.4982	−	8.94790i	−0.815696	−	0.470942i
$362$	−2.07500	−	7.74401i	−0.109060	−	0.407016i
$363$	−2.43390	+	18.1065i	−0.127747	+	0.950343i
$364$	−17.5900	+	2.02435i	−0.921964	+	0.106105i
$365$		−	9.48381i		−	0.496405i
$366$	−10.8771	+	1.40190i	−0.568554	+	0.0732782i
$367$	−15.7064	+	27.2043i	−0.819868	+	1.42005i	0.0859107	+	0.996303i	$0.472620\pi$
$367$	−15.7064	+	27.2043i	−0.819868	+	1.42005i	−0.905779	+	0.423751i	$0.860713\pi$
$368$	−1.67128	−	2.89473i	−0.0871212	−	0.150898i
$369$	11.8599	+	20.8026i	0.617402	+	1.08294i
$370$	−2.23093	−	0.597776i	−0.115981	−	0.0310769i
$371$	63.1139	+	16.9113i	3.27671	+	0.877991i
$372$	1.86398	+	2.44293i	0.0966431	+	0.126660i
$373$	−16.6404	−	28.8220i	−0.861608	−	1.49235i	−0.870376	−	0.492387i	$-0.836124\pi$
$373$	−16.6404	−	28.8220i	−0.861608	−	1.49235i	0.00876839	−	0.999962i	$-0.497209\pi$
$374$	−2.62969	+	4.55476i	−0.135978	+	0.235521i
$375$	0.221404	+	1.71784i	0.0114333	+	0.0887090i
$376$		−	6.75056i		−	0.348133i
$377$	−15.1529	+	19.0942i	−0.780412	+	0.983402i
$378$	9.95711	−	23.4943i	0.512138	−	1.20842i
$379$	−4.85522	−	18.1199i	−0.249396	−	0.930758i	−0.971123	−	0.238580i	$-0.923318\pi$
$379$	−4.85522	−	18.1199i	−0.249396	−	0.930758i	0.721727	−	0.692178i	$-0.243349\pi$
$380$	−0.910027	−	0.525404i	−0.0466834	−	0.0269527i
$381$	2.34642	−	0.964447i	0.120211	−	0.0494101i
$382$	−4.51941	+	4.51941i	−0.231233	+	0.231233i
$383$	−1.07660	+	4.01791i	−0.0550115	+	0.205306i	−0.987961	−	0.154700i	$-0.950559\pi$
$383$	−1.07660	+	4.01791i	−0.0550115	+	0.205306i	0.932950	+	0.360006i	$0.117225\pi$
$384$	1.59840	+	0.667179i	0.0815678	+	0.0340468i
$385$	−2.33508	−	2.33508i	−0.119007	−	0.119007i
$386$	4.02006	−	2.32098i	0.204616	−	0.118135i
$387$	6.42815	+	6.49850i	0.326761	+	0.330337i
$388$	10.5715	−	2.83261i	0.536684	−	0.143804i
$389$	−6.01112			−0.304776			−0.152388	−	0.988321i	$-0.548696\pi$
$389$	−6.01112			−0.304776			−0.152388	+	0.988321i	$0.548696\pi$
$390$	−1.50119	−	6.06188i	−0.0760157	−	0.306955i
$391$	26.1425			1.32208
$392$	−16.5325	+	4.42988i	−0.835019	+	0.223743i
$393$	−13.5478	−	10.4543i	−0.683396	−	0.527349i
$394$	−0.493449	+	0.284893i	−0.0248596	+	0.0143527i
$395$	4.47044	+	4.47044i	0.224932	+	0.224932i
$396$	1.01818	−	1.74159i	0.0511656	−	0.0875180i
$397$	−6.42226	+	23.9682i	−0.322324	+	1.20293i	0.594650	+	0.803984i	$0.297290\pi$
$397$	−6.42226	+	23.9682i	−0.322324	+	1.20293i	−0.916975	+	0.398946i	$0.869376\pi$
$398$	5.40571	−	5.40571i	0.270964	−	0.270964i
$399$	3.39790	+	8.26680i	0.170108	+	0.413858i
$400$	0.866025	+	0.500000i	0.0433013	+	0.0250000i
$401$	5.02288	+	18.7456i	0.250830	+	0.936112i	0.970363	+	0.241653i	$0.0776896\pi$
$401$	5.02288	+	18.7456i	0.250830	+	0.936112i	−0.719532	+	0.694459i	$0.755644\pi$
$402$	−9.77436	−	1.31389i	−0.487501	−	0.0655307i
$403$	−3.81069	−	5.13764i	−0.189824	−	0.255924i
$404$			5.07064i			0.252274i
$405$	8.66746	+	2.42385i	0.430690	+	0.120442i
$406$	−16.6002	+	28.7525i	−0.823856	+	1.42696i
$407$	0.776566	+	1.34505i	0.0384929	+	0.0666717i
$408$	−10.7696	+	8.21737i	−0.533176	+	0.406820i
$409$	29.8016	+	7.98531i	1.47359	+	0.394848i	0.904162	−	0.427190i	$-0.140497\pi$
$409$	29.8016	+	7.98531i	1.47359	+	0.394848i	0.569432	+	0.822039i	$0.307163\pi$
$410$	7.70998	+	2.06588i	0.380769	+	0.102027i
$411$	−8.81504	+	6.72599i	−0.434814	+	0.331769i
$412$	−4.26418	−	7.38578i	−0.210081	−	0.363871i
$413$	2.18502	−	3.78456i	0.107518	−	0.186226i
$414$	−10.0275	−	0.0545712i	−0.492825	−	0.00268203i
$415$		−	4.86800i		−	0.238961i
$416$	−3.30814	−	1.43396i	−0.162195	−	0.0703055i
$417$	−38.3641	−	5.15696i	−1.87870	−	0.252538i
$418$	0.182888	+	0.682549i	0.00894536	+	0.0333845i
$419$	5.56782	+	3.21458i	0.272006	+	0.157043i	0.629799	−	0.776758i	$-0.283137\pi$
$419$	5.56782	+	3.21458i	0.272006	+	0.157043i	−0.357793	+	0.933801i	$0.616471\pi$
$420$	−3.23360	−	7.86709i	−0.157784	−	0.383875i
$421$	−7.68239	+	7.68239i	−0.374417	+	0.374417i	−0.869083	−	0.494666i	$-0.835290\pi$
$421$	−7.68239	+	7.68239i	−0.374417	+	0.374417i	0.494666	+	0.869083i	$0.335290\pi$
$422$	2.35660	−	8.79494i	0.114717	−	0.428131i
$423$	−17.4831	−	10.2211i	−0.850057	−	0.496968i
$424$	9.40840	+	9.40840i	0.456912	+	0.456912i
$425$	−6.77329	+	3.91056i	−0.328553	+	0.189690i
$426$	18.8948	+	14.5804i	0.915458	+	0.706422i
$427$	30.0347	−	8.04777i	1.45348	−	0.389459i
$428$	0.770869			0.0372614
$429$	−2.16861	+	3.59625i	−0.104702	+	0.173628i
$430$	3.04689			0.146934
$431$	11.6153	−	3.11231i	0.559489	−	0.149915i	0.0320175	−	0.999487i	$-0.489807\pi$
$431$	11.6153	−	3.11231i	0.559489	−	0.149915i	0.527472	+	0.849573i	$0.323140\pi$
$432$	4.14807	−	3.12946i	0.199574	−	0.150566i
$433$	8.33984	−	4.81501i	0.400787	−	0.231395i	−0.286036	−	0.958219i	$-0.592338\pi$
$433$	8.33984	−	4.81501i	0.400787	−	0.231395i	0.686824	+	0.726824i	$0.259005\pi$
$434$	−6.16048	−	6.16048i	−0.295712	−	0.295712i
$435$	−10.8063	−	4.51062i	−0.518124	−	0.216268i
$436$	−2.79109	+	10.4165i	−0.133669	+	0.498859i
$437$	2.48363	−	2.48363i	0.118808	−	0.118808i
$438$	−15.1931	+	6.24481i	−0.725955	+	0.298389i
$439$	−14.8040	−	8.54709i	−0.706556	−	0.407930i	0.103229	−	0.994658i	$-0.467083\pi$
$439$	−14.8040	−	8.54709i	−0.706556	−	0.407930i	−0.809784	+	0.586728i	$0.800416\pi$
$440$	−0.174045	−	0.649546i	−0.00829728	−	0.0309659i
$441$	−13.5594	+	49.5246i	−0.645684	+	2.35831i
$442$	22.6493	−	16.7994i	1.07732	−	0.799066i
$443$		−	34.3968i		−	1.63424i	−0.576467	−	0.817120i	$-0.695569\pi$
$443$		−	34.3968i		−	1.63424i	0.576467	−	0.817120i	$-0.304431\pi$
$444$	0.511362	+	3.96758i	0.0242682	+	0.188293i
$445$	5.74593	−	9.95225i	0.272383	−	0.471782i
$446$	5.86963	+	10.1665i	0.277935	+	0.481397i
$447$	−14.4230	−	18.9027i	−0.682185	−	0.894068i
$448$	−4.74345	−	1.27100i	−0.224107	−	0.0600492i
$449$	−29.4387	−	7.88808i	−1.38930	−	0.372261i	−0.514809	−	0.857305i	$-0.672137\pi$
$449$	−29.4387	−	7.88808i	−1.38930	−	0.372261i	−0.874490	+	0.485044i	$0.838804\pi$
$450$	2.60620	−	1.48584i	0.122857	−	0.0700431i
$451$	−2.68377	−	4.64843i	−0.126374	−	0.218886i
$452$	−3.20554	+	5.55216i	−0.150776	+	0.261152i
$453$	6.32216	−	0.814834i	0.297041	−	0.0382842i
$454$		−	19.0134i		−	0.892344i
$455$	6.50799	+	16.4667i	0.305099	+	0.771969i
$456$	−0.242474	+	1.80383i	−0.0113549	+	0.0844721i
$457$	2.92897	+	10.9310i	0.137011	+	0.511333i	0.999982	+	0.00607823i	$0.00193477\pi$
$457$	2.92897	+	10.9310i	0.137011	+	0.511333i	−0.862970	+	0.505255i	$0.831399\pi$
$458$	13.5829	+	7.84212i	0.634690	+	0.366438i
$459$	4.97547	+	40.3340i	0.232235	+	1.88263i
$460$	−2.36354	+	2.36354i	−0.110201	+	0.110201i
$461$	−4.98234	+	18.5944i	−0.232051	+	0.866025i	0.747405	+	0.664368i	$0.231299\pi$
$461$	−4.98234	+	18.5944i	−0.232051	+	0.866025i	−0.979456	+	0.201657i	$0.935367\pi$
$462$	−2.20322	+	5.27838i	−0.102503	+	0.245573i
$463$	−4.95617	−	4.95617i	−0.230333	−	0.230333i	0.582499	−	0.812832i	$-0.302075\pi$
$463$	−4.95617	−	4.95617i	−0.230333	−	0.230333i	−0.812832	+	0.582499i	$0.802075\pi$
$464$	−5.85497	+	3.38037i	−0.271810	+	0.156930i
$465$	1.87725	−	2.43275i	0.0870554	−	0.112816i
$466$	2.57142	−	0.689011i	0.119119	−	0.0319178i
$467$	−6.76016			−0.312823			−0.156411	−	0.987692i	$-0.549993\pi$
$467$	−6.76016			−0.312823			−0.156411	+	0.987692i	$0.549993\pi$
$468$	−8.72267	+	6.39648i	−0.403206	+	0.295678i
$469$	27.9619			1.29116
$470$	−6.52054	+	1.74717i	−0.300770	+	0.0805911i
$471$	3.28142	−	4.25242i	0.151200	−	0.195941i
$472$	0.770664	−	0.444943i	0.0354727	−	0.0204802i
$473$	−1.44880	−	1.44880i	−0.0666157	−	0.0666157i
$474$	4.21801	−	10.1053i	0.193740	−	0.464153i
$475$	−0.271969	+	1.01500i	−0.0124788	+	0.0465716i
$476$	27.1584	−	27.1584i	1.24480	−	1.24480i
$477$	38.6120	−	10.1212i	1.76792	−	0.463416i
$478$	−16.7101	−	9.64761i	−0.764304	−	0.441271i
$479$	3.08895	+	11.5281i	0.141138	+	0.526734i	0.999897	+	0.0143541i	$0.00456920\pi$
$479$	3.08895	+	11.5281i	0.141138	+	0.526734i	−0.858759	+	0.512379i	$0.828764\pi$
$480$	0.230750	−	1.71661i	0.0105322	−	0.0783522i
$481$	−0.952090	−	8.27288i	−0.0434116	−	0.377211i
$482$			8.65811i			0.394366i
$483$	28.1976	−	3.63425i	1.28303	−	0.165364i
$484$	5.27390	−	9.13466i	0.239723	−	0.415212i
$485$	−5.47219	−	9.47811i	−0.248479	−	0.430379i
$486$	−1.82425	−	15.4813i	−0.0827496	−	0.702248i
$487$	−16.9145	−	4.53223i	−0.766470	−	0.205375i	−0.145659	−	0.989335i	$-0.546530\pi$
$487$	−16.9145	−	4.53223i	−0.766470	−	0.205375i	−0.620812	+	0.783960i	$0.713197\pi$
$488$	6.11608	+	1.63880i	0.276862	+	0.0741849i
$489$	2.71422	+	3.55725i	0.122741	+	0.160864i
$490$	8.55787	+	14.8227i	0.386605	+	0.669620i
$491$	−2.74555	+	4.75543i	−0.123905	+	0.214609i	−0.921304	−	0.388842i	$-0.872875\pi$
$491$	−2.74555	+	4.75543i	−0.123905	+	0.214609i	0.797399	+	0.603452i	$0.206208\pi$
$492$	−1.76724	−	13.7117i	−0.0796733	−	0.618173i
$493$		−	52.8766i		−	2.38144i
$494$	0.555758	−	3.74776i	0.0250047	−	0.168620i
$495$	−1.94577	−	0.532733i	−0.0874557	−	0.0239446i
$496$	−0.459172	−	1.71365i	−0.0206174	−	0.0769452i
$497$	−58.6012	−	33.8334i	−2.62862	−	1.51764i
$498$	−7.79855	+	3.20543i	−0.349461	+	0.143639i
$499$	15.0333	−	15.0333i	0.672982	−	0.672982i	−0.285420	−	0.958402i	$-0.592133\pi$
$499$	15.0333	−	15.0333i	0.672982	−	0.672982i	0.958402	+	0.285420i	$0.0921332\pi$
$500$	0.258819	−	0.965926i	0.0115747	−	0.0431975i
$501$	25.2518	+	10.5402i	1.12817	+	0.470903i
$502$	−14.5373	−	14.5373i	−0.648830	−	0.648830i
$503$	−28.2216	+	16.2938i	−1.25834	+	0.726503i	−0.972752	−	0.231849i	$-0.925522\pi$
$503$	−28.2216	+	16.2938i	−1.25834	+	0.726503i	−0.285589	+	0.958352i	$0.592189\pi$
$504$	−10.4739	+	10.3605i	−0.466543	+	0.461493i
$505$	4.89786	−	1.31238i	0.217952	−	0.0584000i
$506$	2.24773			0.0999237
$507$	18.3371	−	13.0672i	0.814377	−	0.580336i
$508$	−1.46468			−0.0649845
$509$	−24.7720	+	6.63764i	−1.09800	+	0.294208i	−0.761950	−	0.647636i	$-0.775758\pi$
$509$	−24.7720	+	6.63764i	−1.09800	+	0.294208i	−0.336050	+	0.941844i	$0.609091\pi$
$510$	10.7248	+	8.27585i	0.474900	+	0.366461i
$511$	40.3333	−	23.2865i	1.78424	−	1.03013i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.30456	+	3.35919i	0.190051	+	0.148312i
$514$	3.57676	−	13.3486i	0.157764	−	0.588783i
$515$	−6.03046	+	6.03046i	−0.265734	+	0.265734i
$516$	−2.00628	−	4.88112i	−0.0883218	−	0.214879i
$517$	3.93130	+	2.26974i	0.172898	+	0.0998229i
$518$	−2.93554	−	10.9556i	−0.128980	−	0.481362i
$519$	16.1029	+	2.16458i	0.706837	+	0.0950143i
$520$	−0.528886	+	3.56655i	−0.0231932	+	0.156404i
$521$		−	24.6166i		−	1.07847i	−0.842154	−	0.539236i	$-0.818713\pi$
$521$		−	24.6166i		−	1.07847i	0.842154	−	0.539236i	$-0.181287\pi$
$522$	−0.110377	+	20.2819i	−0.00483108	+	0.887715i
$523$	−10.6335	+	18.4177i	−0.464969	+	0.805350i	−0.999200	−	0.0399886i	$-0.987268\pi$
$523$	−10.6335	+	18.4177i	−0.464969	+	0.805350i	0.534231	+	0.845338i	$0.320601\pi$
$524$	4.93993	+	8.55621i	0.215802	+	0.373780i
$525$	−6.76210	+	5.15957i	−0.295122	+	0.225182i
$526$	16.8530	+	4.51575i	0.734825	+	0.196896i
$527$	13.4027	+	3.59124i	0.583830	+	0.156437i
$528$	−0.925971	+	0.706528i	−0.0402977	+	0.0307477i
$529$	5.91368	+	10.2428i	0.257116	+	0.445339i
$530$	6.65274	−	11.5229i	0.288977	−	0.500522i
$531$	0.0145285	−	2.66962i	0.000630483	−	0.115852i
$532$		−	5.16029i		−	0.223727i
$533$	3.29037	+	28.5906i	0.142522	+	1.23840i
$534$	−19.7271	−	2.65175i	−0.853674	−	0.114752i
$535$	−0.199516	−	0.744603i	−0.00862581	−	0.0321920i
$536$	4.93113	+	2.84699i	0.212993	+	0.122971i
$537$	−10.7788	−	26.2239i	−0.465139	−	1.13165i
$538$	16.7188	−	16.7188i	0.720798	−	0.720798i
$539$	2.97891	−	11.1175i	0.128311	−	0.478863i
$540$	−4.09643	−	3.19676i	−0.176282	−	0.137567i
$541$	−0.983681	−	0.983681i	−0.0422917	−	0.0422917i	0.685645	−	0.727936i	$-0.259520\pi$
$541$	−0.983681	−	0.983681i	−0.0422917	−	0.0422917i	−0.727936	+	0.685645i	$0.759520\pi$
$542$	12.9623	−	7.48381i	0.556780	−	0.321457i
$543$	10.9936	+	8.48331i	0.471781	+	0.364054i
$544$	7.55463	−	2.02426i	0.323902	−	0.0867893i
$545$	10.7839			0.461933
$546$	22.0943	−	21.2686i	0.945550	−	0.910214i
$547$	5.08638			0.217478			0.108739	−	0.994070i	$-0.465319\pi$
$547$	5.08638			0.217478			0.108739	+	0.994070i	$0.465319\pi$
$548$	6.18353	−	1.65687i	0.264147	−	0.0707781i
$549$	13.5047	−	13.3585i	0.576368	−	0.570129i
$550$	−0.582367	+	0.336230i	−0.0248322	+	0.0143369i
$551$	−5.02346	−	5.02346i	−0.214007	−	0.214007i
$552$	5.34272	+	2.23008i	0.227401	+	0.0949185i
$553$	−8.03549	+	29.9888i	−0.341704	+	1.27526i
$554$	4.93134	−	4.93134i	0.209512	−	0.209512i
$555$	3.70003	−	1.52082i	0.157058	−	0.0645553i
$556$	19.3546	+	11.1744i	0.820816	+	0.473898i
$557$	0.663312	+	2.47552i	0.0281054	+	0.104891i	0.978554	−	0.205992i	$-0.0660420\pi$
$557$	0.663312	+	2.47552i	0.0281054	+	0.104891i	−0.950448	+	0.310883i	$0.899375\pi$
$558$	−5.13338	−	1.40547i	−0.217313	−	0.0594984i
$559$	4.03787	+	10.2167i	0.170784	+	0.432121i
$560$			4.91078i			0.207518i
$561$	−1.16445	−	9.03480i	−0.0491632	−	0.381449i
$562$	11.3511	−	19.6607i	0.478819	−	0.829338i
$563$	6.40816	+	11.0993i	0.270072	+	0.467778i	0.968880	−	0.247531i	$-0.0796193\pi$
$563$	6.40816	+	11.0993i	0.270072	+	0.467778i	−0.698808	+	0.715309i	$0.746286\pi$
$564$	7.09256	+	9.29546i	0.298651	+	0.391410i
$565$	6.19263	+	1.65931i	0.260526	+	0.0698077i
$566$	16.4343	+	4.40357i	0.690787	+	0.185096i
$567$	10.9737	+	42.8130i	0.460852	+	1.79798i
$568$	−6.88962	−	11.9332i	−0.289082	−	0.500705i
$569$	9.88096	−	17.1143i	0.414231	−	0.717470i	−0.581116	−	0.813821i	$-0.697384\pi$
$569$	9.88096	−	17.1143i	0.414231	−	0.717470i	0.995347	+	0.0963509i	$0.0307171\pi$
$570$	1.80512	−	0.232654i	0.0756083	−	0.00974480i
$571$		−	29.9675i		−	1.25410i	−0.778979	−	0.627050i	$-0.784262\pi$
$571$		−	29.9675i		−	1.25410i	0.778979	−	0.627050i	$-0.215738\pi$
$572$	1.94738	−	1.44441i	0.0814241	−	0.0603939i
$573$	1.47482	−	10.9716i	0.0616113	−	0.458344i
$574$	10.1451	+	37.8620i	0.423448	+	1.58033i
$575$	2.89473	+	1.67128i	0.120719	+	0.0696970i
$576$	−2.90196	+	0.760676i	−0.120915	+	0.0316948i
$577$	21.1608	−	21.1608i	0.880938	−	0.880938i	−0.112692	−	0.993630i	$-0.535947\pi$
$577$	21.1608	−	21.1608i	0.880938	−	0.880938i	0.993630	+	0.112692i	$0.0359474\pi$
$578$	−11.4320	+	42.6650i	−0.475510	+	1.77463i
$579$	−3.09702	+	7.41971i	−0.128708	+	0.308352i
$580$	4.78056	+	4.78056i	0.198502	+	0.198502i
$581$	20.7029	−	11.9528i	0.858901	−	0.495887i
$582$	−11.5807	+	15.0075i	−0.480035	+	0.622082i
$583$	−8.64252	+	2.31576i	−0.357937	+	0.0959088i
$584$	9.48381			0.392443
$585$	8.43612	+	6.76992i	0.348791	+	0.279902i
$586$	−21.2905			−0.879503
$587$	−21.8846	+	5.86397i	−0.903275	+	0.242032i	−0.680422	−	0.732820i	$-0.738204\pi$
$587$	−21.8846	+	5.86397i	−0.903275	+	0.242032i	−0.222853	+	0.974852i	$0.571537\pi$
$588$	18.1109	−	23.4700i	0.746880	−	0.967888i
$589$	1.61448	−	0.932122i	0.0665236	−	0.0384074i
$590$	−0.629245	−	0.629245i	−0.0259056	−	0.0259056i
$591$	0.380149	−	0.910744i	0.0156372	−	0.0374630i
$592$	0.597776	−	2.23093i	0.0245684	−	0.0916907i
$593$	−8.32570	+	8.32570i	−0.341895	+	0.341895i	−0.857080	−	0.515184i	$-0.827724\pi$
$593$	−8.32570	+	8.32570i	−0.341895	+	0.341895i	0.515184	+	0.857080i	$0.327724\pi$
$594$	0.427790	+	3.46792i	0.0175524	+	0.142290i
$595$	−33.2621	−	19.2039i	−1.36362	−	0.787284i
$596$	3.55295	+	13.2598i	0.145534	+	0.543142i
$597$	−1.76404	+	13.1232i	−0.0721974	+	0.537097i
$598$	−11.0576	−	4.79307i	−0.452179	−	0.196003i
$599$			36.7193i			1.50031i	0.661262	+	0.750155i	$0.270021\pi$
$599$			36.7193i			1.50031i	−0.661262	+	0.750155i	$0.729979\pi$
$600$	−1.71784	+	0.221404i	−0.0701306	+	0.00903880i
$601$	15.5013	−	26.8491i	0.632312	−	1.09520i	−0.354765	−	0.934955i	$-0.615439\pi$
$601$	15.5013	−	26.8491i	0.632312	−	1.09520i	0.987078	−	0.160242i	$-0.0512274\pi$
$602$	7.48129	+	12.9580i	0.304915	+	0.528128i
$603$	14.8397	−	8.46034i	0.604318	−	0.344532i
$604$	−3.55489	−	0.952530i	−0.144646	−	0.0387579i
$605$	−10.1884	−	2.72997i	−0.414217	−	0.110989i
$606$	−5.32753	−	6.98223i	−0.216416	−	0.283634i
$607$	−14.6011	−	25.2898i	−0.592640	−	1.02648i	−0.993875	−	0.110508i	$-0.964752\pi$
$607$	−14.6011	−	25.2898i	−0.592640	−	1.02648i	0.401235	−	0.915975i	$-0.368581\pi$
$608$	0.525404	−	0.910027i	0.0213080	−	0.0369065i
$609$	−7.35074	−	57.0332i	−0.297867	−	2.31110i
$610$		−	6.33183i		−	0.256368i
$611$	−14.4999	−	19.5490i	−0.586602	−	0.790868i
$612$	6.19602	−	22.6305i	0.250459	−	0.914784i
$613$	1.30307	+	4.86313i	0.0526305	+	0.196420i	0.987235	−	0.159268i	$-0.0509134\pi$
$613$	1.30307	+	4.86313i	0.0526305	+	0.196420i	−0.934605	+	0.355688i	$0.884247\pi$
$614$	26.1711	+	15.1099i	1.05618	+	0.609786i
$615$	−12.7871	+	5.25588i	−0.515626	+	0.211938i
$616$	2.33508	−	2.33508i	0.0940830	−	0.0940830i
$617$	6.45361	−	24.0852i	0.259812	−	0.969633i	−0.705537	−	0.708673i	$-0.749294\pi$
$617$	6.45361	−	24.0852i	0.259812	−	0.969633i	0.965350	−	0.260960i	$-0.0840392\pi$
$618$	13.6317	+	5.68994i	0.548348	+	0.228883i
$619$	−21.4082	−	21.4082i	−0.860470	−	0.860470i	0.130922	−	0.991393i	$-0.458206\pi$
$619$	−21.4082	−	21.4082i	−0.860470	−	0.860470i	−0.991393	+	0.130922i	$0.958206\pi$
$620$	−1.53642	+	0.887052i	−0.0617040	+	0.0356248i
$621$	13.8651	−	10.4604i	0.556388	−	0.419761i
$622$	−3.71946	+	0.996626i	−0.149137	+	0.0399611i
$623$	56.4340			2.26098
$624$	6.06188	−	1.50119i	0.242670	−	0.0600957i
$625$	−1.00000			−0.0400000
$626$	−19.8992	+	5.33199i	−0.795334	+	0.213109i
$627$	−0.968964	−	0.747710i	−0.0386967	−	0.0298607i
$628$	−2.68565	+	1.55056i	−0.107169	+	0.0618741i
$629$	12.7731	+	12.7731i	0.509297	+	0.509297i
$630$	12.7183	+	7.43549i	0.506709	+	0.296237i
$631$	−3.30587	+	12.3377i	−0.131605	+	0.491155i	−0.999989	−	0.00473707i	$-0.998492\pi$
$631$	−3.30587	+	12.3377i	−0.131605	+	0.491155i	0.868384	+	0.495892i	$0.165159\pi$
$632$	−4.47044	+	4.47044i	−0.177825	+	0.177825i
$633$	5.99550	+	14.5865i	0.238300	+	0.579763i
$634$	−14.6180	−	8.43970i	−0.580555	−	0.335183i
$635$	0.379086	+	1.41477i	0.0150436	+	0.0561434i
$636$	−22.8403	−	3.07024i	−0.905678	−	0.121743i
$637$	−38.3616	+	48.3397i	−1.51994	+	1.91529i
$638$		−	4.54632i		−	0.179991i
$639$	−41.3371	−	0.224963i	−1.63527	−	0.00889940i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−16.4852	−	28.5531i	−0.651125	−	1.12778i	−0.982850	−	0.184405i	$-0.940964\pi$
$641$	−16.4852	−	28.5531i	−0.651125	−	1.12778i	0.331725	−	0.943376i	$-0.392369\pi$
$642$	−1.06148	+	0.809924i	−0.0418933	+	0.0319651i
$643$	18.9766	+	5.08477i	0.748364	+	0.200524i	0.612792	−	0.790244i	$-0.290046\pi$
$643$	18.9766	+	5.08477i	0.748364	+	0.200524i	0.135572	+	0.990768i	$0.456713\pi$
$644$	−15.8552	−	4.24839i	−0.624783	−	0.167410i
$645$	−4.19554	+	3.20125i	−0.165199	+	0.126049i
$646$	4.10925	+	7.11744i	0.161676	+	0.280032i
$647$	13.8371	−	23.9666i	0.543993	−	0.942223i	−0.454677	−	0.890657i	$-0.650245\pi$
$647$	13.8371	−	23.9666i	0.543993	−	0.942223i	0.998670	−	0.0515668i	$-0.0164215\pi$
$648$	−2.42385	+	8.66746i	−0.0952179	+	0.340490i
$649$			0.598413i			0.0234897i
$650$	3.58191	−	0.412226i	0.140494	−	0.0161689i
$651$	14.9555	+	2.01035i	0.586153	+	0.0787916i
$652$	−0.668619	−	2.49532i	−0.0261851	−	0.0977243i
$653$	13.0969	+	7.56151i	0.512522	+	0.295905i	0.733870	−	0.679290i	$-0.237712\pi$
$653$	13.0969	+	7.56151i	0.512522	+	0.295905i	−0.221348	+	0.975195i	$0.571046\pi$
$654$	−7.10090	−	17.2759i	−0.277667	−	0.675541i
$655$	6.98611	−	6.98611i	0.272970	−	0.272970i
$656$	−2.06588	+	7.70998i	−0.0806591	+	0.301024i
$657$	14.3596	−	24.5619i	0.560221	−	0.958250i
$658$	−23.4409	−	23.4409i	−0.913823	−	0.913823i
$659$	23.6214	−	13.6378i	0.920158	−	0.531253i	0.0364723	−	0.999335i	$-0.488388\pi$
$659$	23.6214	−	13.6378i	0.920158	−	0.531253i	0.883685	+	0.468081i	$0.155055\pi$
$660$	0.922113	+	0.711557i	0.0358932	+	0.0276973i
$661$	−14.3942	+	3.85690i	−0.559868	+	0.150016i	−0.527646	−	0.849465i	$-0.676925\pi$
$661$	−14.3942	+	3.85690i	−0.559868	+	0.150016i	−0.0322223	+	0.999481i	$0.510258\pi$
$662$	−9.85010			−0.382835
$663$	−13.5374	+	46.9294i	−0.525748	+	1.82259i
$664$	4.86800			0.188915
$665$	−4.98446	+	1.33558i	−0.193289	+	0.0517916i
$666$	−4.87273	−	4.92605i	−0.188814	−	0.190881i
$667$	−19.5705	+	11.2991i	−0.757774	+	0.437501i
$668$	−11.1710	−	11.1710i	−0.432220	−	0.432220i
$669$	−18.7640	−	7.83218i	−0.725458	−	0.302810i
$670$	1.47371	−	5.49997i	0.0569344	−	0.212482i
$671$	−3.01079	+	3.01079i	−0.116230	+	0.116230i
$672$	7.86709	−	3.23360i	0.303479	−	0.124739i
$673$	18.7397	+	10.8194i	0.722361	+	0.417055i	0.815621	−	0.578586i	$-0.196395\pi$
$673$	18.7397	+	10.8194i	0.722361	+	0.417055i	−0.0932599	+	0.995642i	$0.529729\pi$
$674$	−3.46134	−	12.9179i	−0.133326	−	0.497579i
$675$	−2.02760	+	4.78423i	−0.0780425	+	0.184145i
$676$	−12.6601	+	2.95312i	−0.486928	+	0.113581i
$677$		−	1.72927i		−	0.0664612i	−0.999448	−	0.0332306i	$-0.989420\pi$
$677$		−	1.72927i		−	0.0664612i	0.999448	−	0.0332306i	$-0.0105796\pi$
$678$	−1.41944	−	11.0132i	−0.0545134	−	0.422961i
$679$	26.8727	−	46.5449i	1.03128	−	1.78623i
$680$	−3.91056	−	6.77329i	−0.149963	−	0.259744i
$681$	19.9767	+	26.1813i	0.765508	+	1.00327i
$682$	1.15236	+	0.308774i	0.0441262	+	0.0118236i
$683$	−34.3225	−	9.19668i	−1.31331	−	0.351901i	−0.466844	−	0.884340i	$-0.654609\pi$
$683$	−34.3225	−	9.19668i	−1.31331	−	0.351901i	−0.846469	+	0.532438i	$0.821276\pi$
$684$	−1.56133	−	2.73862i	−0.0596990	−	0.104714i
$685$	−3.20083	−	5.54400i	−0.122298	−	0.211826i
$686$	−24.8381	+	43.0208i	−0.948323	+	1.64254i
$687$	−26.9430	+	3.47256i	−1.02794	+	0.132486i
$688$			3.04689i			0.116161i
$689$	47.4547	+	7.03708i	1.80788	+	0.268091i
$690$	0.771293	−	5.73786i	0.0293626	−	0.218437i
$691$	5.87881	+	21.9400i	0.223641	+	0.834638i	0.982945	+	0.183902i	$0.0588729\pi$
$691$	5.87881	+	21.9400i	0.223641	+	0.834638i	−0.759304	+	0.650736i	$0.774460\pi$
$692$	−8.12385	−	4.69031i	−0.308822	−	0.178299i
$693$	−2.51198	−	9.58314i	−0.0954222	−	0.364033i
$694$	6.09359	−	6.09359i	0.231309	−	0.231309i
$695$	5.78427	−	21.5872i	0.219410	−	0.818849i
$696$	4.51062	−	10.8063i	0.170975	−	0.409613i
$697$	−44.1432	−	44.1432i	−1.67204	−	1.67204i
$698$	−17.2512	+	9.96000i	−0.652969	+	0.376992i
$699$	−2.81691	+	3.65046i	−0.106545	+	0.138073i
$700$	4.74345	−	1.27100i	0.179285	−	0.0480394i
$701$	−17.1199			−0.646610			−0.323305	−	0.946295i	$-0.604794\pi$
$701$	−17.1199			−0.646610			−0.323305	+	0.946295i	$0.604794\pi$
$702$	5.29050	−	17.9725i	0.199677	−	0.678328i
$703$	2.42698			0.0915352
$704$	0.649546	−	0.174045i	0.0244807	−	0.00655958i
$705$	7.14304	−	9.25673i	0.269022	−	0.348629i
$706$	−10.4651	+	6.04201i	−0.393858	+	0.227394i
$707$	17.6075	+	17.6075i	0.662198	+	0.662198i
$708$	−0.593714	+	1.42239i	−0.0223131	+	0.0534568i
$709$	9.81956	−	36.6471i	0.368781	−	1.37631i	−0.493441	−	0.869779i	$-0.664261\pi$
$709$	9.81956	−	36.6471i	0.368781	−	1.37631i	0.862222	−	0.506531i	$-0.169072\pi$
$710$	−9.74340	+	9.74340i	−0.365663	+	0.365663i
$711$	4.80912	+	18.3467i	0.180356	+	0.688054i
$712$	9.95225	+	5.74593i	0.372976	+	0.215338i
$713$	−1.53480	−	5.72797i	−0.0574789	−	0.214514i
$714$	−8.86260	+	65.9313i	−0.331674	+	2.46742i
$715$	−1.89921	−	1.50719i	−0.0710266	−	0.0563655i
$716$			16.3694i			0.611755i
$717$	33.1461	−	4.27205i	1.23786	−	0.159542i
$718$	−14.0334	+	24.3065i	−0.523721	+	0.907111i
$719$	−14.5318	−	25.1698i	−0.541944	−	0.938675i	−0.998792	−	0.0491300i	$-0.984355\pi$
$719$	−14.5318	−	25.1698i	−0.541944	−	0.938675i	0.456848	−	0.889545i	$-0.348978\pi$
$720$	1.48584	+	2.60620i	0.0553739	+	0.0971274i
$721$	−40.4538	−	10.8396i	−1.50658	−	0.403687i
$722$	−17.2860	−	4.63177i	−0.643319	−	0.172377i
$723$	−9.09675	−	11.9221i	−0.338312	−	0.443389i
$724$	−4.00859	−	6.94309i	−0.148978	−	0.258038i
$725$	3.38037	−	5.85497i	0.125544	−	0.217448i
$726$	2.33533	+	18.1194i	0.0866722	+	0.672476i
$727$			33.7140i			1.25038i	0.780472	+	0.625191i	$0.214979\pi$
$727$			33.7140i			1.25038i	−0.780472	+	0.625191i	$0.785021\pi$
$728$	−16.4667	+	6.50799i	−0.610295	+	0.241202i
$729$	18.7777	+	19.4010i	0.695469	+	0.718556i
$730$	−2.45459	−	9.16066i	−0.0908485	−	0.339051i
$731$	−20.6375	−	11.9150i	−0.763304	−	0.440694i
$732$	−10.1436	+	4.16932i	−0.374919	+	0.154103i
$733$	27.6408	−	27.6408i	1.02093	−	1.02093i	0.0211584	−	0.999776i	$-0.493265\pi$
$733$	27.6408	−	27.6408i	1.02093	−	1.02093i	0.999776	−	0.0211584i	$-0.00673542\pi$
$734$	−8.13024	+	30.3425i	−0.300093	+	1.11996i
$735$	−27.3578	−	11.4193i	−1.00911	−	0.421206i
$736$	−2.36354	−	2.36354i	−0.0871212	−	0.0871212i
$737$	−3.31599	+	1.91449i	−0.122146	+	0.0705210i
$738$	16.8399	+	17.0242i	0.619885	+	0.626669i
$739$	−6.58406	+	1.76419i	−0.242199	+	0.0648969i	−0.377876	−	0.925856i	$-0.623346\pi$
$739$	−6.58406	+	1.76419i	−0.242199	+	0.0648969i	0.135678	+	0.990753i	$0.456679\pi$
$740$	−2.30963			−0.0849036
$741$	3.17236	+	5.74455i	0.116540	+	0.211031i
$742$	65.3403			2.39872
$743$	38.7916	−	10.3942i	1.42313	−	0.381326i	0.536535	−	0.843878i	$-0.319733\pi$
$743$	38.7916	−	10.3942i	1.42313	−	0.381326i	0.886592	+	0.462552i	$0.153066\pi$
$744$	2.43275	+	1.87725i	0.0891888	+	0.0688234i
$745$	11.8884	−	6.86377i	0.435557	−	0.251469i
$746$	−23.5331	−	23.5331i	−0.861608	−	0.861608i
$747$	7.37071	−	12.6075i	0.269680	−	0.461284i
$748$	−1.36123	+	5.08018i	−0.0497715	+	0.185750i
$749$	2.67680	−	2.67680i	0.0978082	−	0.0978082i
$750$	0.658470	+	1.60200i	0.0240439	+	0.0584969i
$751$	−1.44291	−	0.833065i	−0.0526526	−	0.0303990i	0.473443	−	0.880825i	$-0.343011\pi$
$751$	−1.44291	−	0.833065i	−0.0526526	−	0.0303990i	−0.526095	+	0.850426i	$0.676344\pi$
$752$	−1.74717	−	6.52054i	−0.0637128	−	0.237780i
$753$	35.2915	+	4.74394i	1.28609	+	0.172879i
$754$	−9.69460	+	22.3654i	−0.353056	+	0.814502i
$755$			3.68029i			0.133940i
$756$	3.53706	−	25.2708i	0.128642	−	0.919091i
$757$	−16.0809	+	27.8529i	−0.584469	+	1.01233i	0.410472	+	0.911873i	$0.365364\pi$
$757$	−16.0809	+	27.8529i	−0.584469	+	1.01233i	−0.994941	+	0.100457i	$0.967969\pi$
$758$	−9.37957	−	16.2459i	−0.340681	−	0.590077i
$759$	−3.09511	+	2.36161i	−0.112345	+	0.0857208i
$760$	−1.01500	−	0.271969i	−0.0368180	−	0.00986537i
$761$	18.5266	+	4.96420i	0.671590	+	0.179952i	0.578471	−	0.815703i	$-0.303650\pi$
$761$	18.5266	+	4.96420i	0.671590	+	0.179952i	0.0931190	+	0.995655i	$0.470316\pi$
$762$	2.01685	−	1.53888i	0.0730627	−	0.0557478i
$763$	26.4787	+	45.8625i	0.958595	+	1.66034i
$764$	−3.19570	+	5.53512i	−0.115617	+	0.200254i
$765$	−23.4630	−	0.127689i	−0.848308	−	0.00461662i
$766$			4.15965i			0.150294i
$767$	1.27606	−	2.94387i	0.0460758	−	0.106297i
$768$	1.71661	+	0.230750i	0.0619429	+	0.00832647i
$769$	7.90436	+	29.4995i	0.285039	+	1.06378i	0.948811	+	0.315844i	$0.102288\pi$
$769$	7.90436	+	29.4995i	0.285039	+	1.06378i	−0.663773	+	0.747934i	$0.731046\pi$
$770$	−2.85987	−	1.65115i	−0.103063	−	0.0595033i
$771$	9.09975	+	22.1389i	0.327719	+	0.797314i
$772$	3.28237	−	3.28237i	0.118135	−	0.118135i
$773$	1.17736	−	4.39397i	0.0423467	−	0.158040i	−0.941515	−	0.336972i	$-0.890597\pi$
$773$	1.17736	−	4.39397i	0.0423467	−	0.158040i	0.983862	+	0.178931i	$0.0572640\pi$
$774$	7.89105	+	4.61334i	0.283638	+	0.165823i
$775$	1.25448	+	1.25448i	0.0450623	+	0.0450623i
$776$	9.47811	−	5.47219i	0.340244	−	0.196440i
$777$	15.5529	+	12.0015i	0.557956	+	0.430552i
$778$	−5.80629	+	1.55579i	−0.208166	+	0.0557778i
$779$	−8.38751			−0.300514
$780$	−3.01897	−	5.46679i	−0.108096	−	0.195743i
$781$	9.26598			0.331563
$782$	25.2517	−	6.76618i	0.903000	−	0.241958i
$783$	−21.1575	−	28.0440i	−0.756106	−	1.00221i
$784$	−14.8227	+	8.55787i	−0.529381	+	0.305638i
$785$	2.19282	+	2.19282i	0.0782652	+	0.0782652i
$786$	−15.7919	−	6.59163i	−0.563279	−	0.235116i
$787$	0.203545	−	0.759639i	0.00725559	−	0.0270782i	−0.962203	−	0.272333i	$-0.912205\pi$
$787$	0.203545	−	0.759639i	0.00725559	−	0.0270782i	0.969459	+	0.245255i	$0.0788715\pi$
$788$	−0.402899	+	0.402899i	−0.0143527	+	0.0143527i
$789$	−27.9510	+	11.4887i	−0.995081	+	0.409007i
$790$	5.47515	+	3.16108i	0.194797	+	0.112466i
$791$	8.14851	+	30.4107i	0.289728	+	1.08128i
$792$	0.532733	−	1.94577i	0.0189298	−	0.0691398i
$793$	21.2317	−	8.39123i	0.753959	−	0.297981i
$794$			24.8137i			0.880606i
$795$	2.94589	+	22.8567i	0.104480	+	0.810644i
$796$	3.82241	−	6.62061i	0.135482	−	0.234661i
$797$	13.6759	+	23.6873i	0.484425	+	0.839048i	0.999840	−	0.0178923i	$-0.00569561\pi$
$797$	13.6759	+	23.6873i	0.484425	+	0.839048i	−0.515415	+	0.856941i	$0.672362\pi$
$798$	5.42172	+	7.10568i	0.191927	+	0.251538i
$799$	50.9979	+	13.6649i	1.80418	+	0.483428i
$800$	0.965926	+	0.258819i	0.0341506	+	0.00915064i
$801$	29.9501	−	17.0751i	1.05824	−	0.603318i
$802$	9.70345	+	16.8069i	0.342641	+	0.593471i
$803$	−3.18874	+	5.52306i	−0.112528	+	0.194904i
$804$	−9.78136	+	1.26067i	−0.344962	+	0.0444605i
$805$			16.4145i			0.578536i
$806$	−5.01056	−	3.97630i	−0.176490	−	0.140059i
$807$	−5.45583	+	40.5874i	−0.192054	+	1.42875i
$808$	1.31238	+	4.89786i	0.0461693	+	0.172306i
$809$	9.72753	+	5.61619i	0.342002	+	0.197455i	0.661157	−	0.750248i	$-0.270066\pi$
$809$	9.72753	+	5.61619i	0.342002	+	0.197455i	−0.319155	+	0.947702i	$0.603399\pi$
$810$	8.99947	+	0.0979559i	0.316209	+	0.00344182i
$811$	21.0137	−	21.0137i	0.737892	−	0.737892i	−0.234278	−	0.972170i	$-0.575273\pi$
$811$	21.0137	−	21.0137i	0.737892	−	0.737892i	0.972170	+	0.234278i	$0.0752726\pi$
$812$	−8.59292	+	32.0692i	−0.301552	+	1.12541i
$813$	−9.98608	+	23.9242i	−0.350227	+	0.839058i
$814$	1.09823	+	1.09823i	0.0384929	+	0.0384929i
$815$	−2.23724	+	1.29167i	−0.0783672	+	0.0452453i
$816$	−8.27585	+	10.7248i	−0.289713	+	0.375441i
$817$	−3.09260	+	0.828660i	−0.108196	+	0.0289911i
$818$	30.8529			1.07875
$819$	−8.07756	+	52.5004i	−0.282253	+	1.83451i
$820$	7.98195			0.278742
$821$	−32.9168	+	8.82004i	−1.14880	+	0.307821i	−0.782486	−	0.622668i	$-0.786049\pi$
$821$	−32.9168	+	8.82004i	−1.14880	+	0.307821i	−0.366319	+	0.930489i	$0.619382\pi$
$822$	−6.77386	+	8.77831i	−0.236266	+	0.306179i
$823$	−41.5282	+	23.9763i	−1.44758	+	0.835762i	−0.998337	−	0.0576465i	$-0.981640\pi$
$823$	−41.5282	+	23.9763i	−1.44758	+	0.835762i	−0.449245	+	0.893409i	$0.648307\pi$
$824$	−6.03046	−	6.03046i	−0.210081	−	0.210081i
$825$	0.448651	−	1.07486i	0.0156200	−	0.0374217i
$826$	1.13105	−	4.22113i	0.0393542	−	0.146872i
$827$	−4.00303	+	4.00303i	−0.139199	+	0.139199i	−0.773273	−	0.634074i	$-0.781382\pi$
$827$	−4.00303	+	4.00303i	−0.139199	+	0.139199i	0.634074	+	0.773273i	$0.281382\pi$
$828$	−9.69995	+	2.54260i	−0.337096	+	0.0883613i
$829$	−43.2301	−	24.9589i	−1.50144	−	0.866858i	−0.999999	−	0.00166758i	$-0.999469\pi$
$829$	−43.2301	−	24.9589i	−1.50144	−	0.866858i	−0.501443	−	0.865190i	$-0.667197\pi$
$830$	−1.25993	−	4.70212i	−0.0437328	−	0.163213i
$831$	−1.60924	+	11.9716i	−0.0558239	+	0.415290i
$832$	−3.56655	−	0.528886i	−0.123648	−	0.0183358i
$833$		−	133.864i		−	4.63813i
$834$	−38.3916	+	4.94811i	−1.32939	+	0.171339i
$835$	−7.89911	+	13.6817i	−0.273360	+	0.473473i
$836$	0.353313	+	0.611956i	0.0122196	+	0.0211650i
$837$	8.54531	−	3.45813i	0.295369	−	0.119530i
$838$	6.21009	+	1.66399i	0.214524	+	0.0574815i
$839$	14.1508	+	3.79170i	0.488540	+	0.130904i	0.494676	−	0.869077i	$-0.335287\pi$
$839$	14.1508	+	3.79170i	0.488540	+	0.130904i	−0.00613628	+	0.999981i	$0.501953\pi$
$840$	−5.15957	−	6.76210i	−0.178022	−	0.233315i
$841$	8.35379	+	14.4692i	0.288062	+	0.498937i
$842$	−5.43227	+	9.40897i	−0.187208	+	0.324255i
$843$	5.02638	+	38.9989i	0.173118	+	1.34319i
$844$		−	9.10519i		−	0.313414i
$845$	6.12918	+	11.4644i	0.210850	+	0.394388i
$846$	−19.5328	−	5.34790i	−0.671551	−	0.183864i
$847$	−13.4063	−	50.0329i	−0.460645	−	1.71915i
$848$	11.5229	+	6.65274i	0.395697	+	0.228456i
$849$	−27.2566	+	11.2033i	−0.935445	+	0.384495i
$850$	−5.53037	+	5.53037i	−0.189690	+	0.189690i
$851$	1.99810	−	7.45699i	0.0684938	−	0.255622i
$852$	22.0247	+	9.19322i	0.754554	+	0.314955i
$853$	−8.07743	−	8.07743i	−0.276566	−	0.276566i	0.555171	−	0.831737i	$-0.312653\pi$
$853$	−8.07743	−	8.07743i	−0.276566	−	0.276566i	−0.831737	+	0.555171i	$0.812653\pi$
$854$	26.9284	−	15.5471i	0.921470	−	0.532011i
$855$	−2.24120	+	2.21694i	−0.0766474	+	0.0758177i
$856$	0.744603	−	0.199516i	0.0254500	−	0.00681930i
$857$	−9.82720			−0.335691			−0.167845	−	0.985813i	$-0.553681\pi$
$857$	−9.82720			−0.335691			−0.167845	+	0.985813i	$0.553681\pi$
$858$	−1.16394	+	4.03498i	−0.0397363	+	0.137752i
$859$	−40.1892			−1.37124			−0.685619	−	0.727960i	$-0.740468\pi$
$859$	−40.1892			−1.37124			−0.685619	+	0.727960i	$0.740468\pi$
$860$	2.94307	−	0.788592i	0.100358	−	0.0268908i
$861$	−53.7499	−	41.4766i	−1.83179	−	1.41352i
$862$	10.4140	−	6.01252i	0.354702	−	0.204787i
$863$	−2.13318	−	2.13318i	−0.0726145	−	0.0726145i	0.669867	−	0.742481i	$-0.266351\pi$
$863$	−2.13318	−	2.13318i	−0.0726145	−	0.0726145i	−0.742481	+	0.669867i	$0.766351\pi$
$864$	3.19676	−	4.09643i	0.108756	−	0.139363i
$865$	−2.42788	+	9.06098i	−0.0825504	+	0.308082i
$866$	6.80945	−	6.80945i	0.231395	−	0.231395i
$867$	−29.0846	−	70.7605i	−0.987766	−	2.40315i
$868$	−7.54501	−	4.35611i	−0.256094	−	0.147856i
$869$	−1.10034	−	4.10653i	−0.0373266	−	0.139305i
$870$	−11.6056	−	1.56004i	−0.393465	−	0.0528903i
$871$	20.3953	−	2.34721i	0.691069	−	0.0795322i
$872$			10.7839i			0.365190i
$873$	0.178680	−	32.8326i	0.00604741	−	1.11122i
$874$	1.75619	−	3.04181i	0.0594040	−	0.102891i
$875$	−2.45539	−	4.25286i	−0.0830073	−	0.143773i
$876$	−13.0591	+	9.96429i	−0.441227	+	0.336662i
$877$	−5.48085	−	1.46859i	−0.185075	−	0.0495907i	0.165091	−	0.986278i	$-0.447208\pi$
$877$	−5.48085	−	1.46859i	−0.185075	−	0.0495907i	−0.350166	+	0.936688i	$0.613875\pi$
$878$	−16.5117	−	4.42430i	−0.557243	−	0.149313i
$879$	29.3169	−	22.3692i	0.988834	−	0.754493i
$880$	−0.336230	−	0.582367i	−0.0113343	−	0.0196316i
$881$	−24.1079	+	41.7562i	−0.812217	+	1.40680i	0.0990917	+	0.995078i	$0.468406\pi$
$881$	−24.1079	+	41.7562i	−0.812217	+	1.40680i	−0.911309	+	0.411723i	$0.864927\pi$
$882$	−0.279435	+	51.3465i	−0.00940908	+	1.72893i
$883$		−	9.10360i		−	0.306361i	−0.988198	−	0.153180i	$-0.951048\pi$
$883$		−	9.10360i		−	0.306361i	0.988198	−	0.153180i	$-0.0489515\pi$
$884$	17.5295	−	22.0891i	0.589582	−	0.742935i
$885$	1.52759	+	0.205341i	0.0513494	+	0.00690247i
$886$	−8.90254	−	33.2247i	−0.299087	−	1.11621i
$887$	14.4541	+	8.34511i	0.485323	+	0.280201i	0.722632	−	0.691233i	$-0.242932\pi$
$887$	14.4541	+	8.34511i	0.485323	+	0.280201i	−0.237309	+	0.971434i	$0.576265\pi$
$888$	1.52082	+	3.70003i	0.0510354	+	0.124165i
$889$	−5.08601	+	5.08601i	−0.170579	+	0.170579i
$890$	2.97431	−	11.1003i	0.0996992	−	0.372083i
$891$	−4.23267	−	4.32583i	−0.141800	−	0.144921i
$892$	8.30091	+	8.30091i	0.277935	+	0.277935i
$893$	6.14319	−	3.54677i	0.205574	−	0.118688i
$894$	−18.8239	−	14.5257i	−0.629567	−	0.485811i
$895$	15.8117	−	4.23672i	0.528526	−	0.141618i
$896$	−4.91078			−0.164058
$897$	20.2621	−	5.01780i	0.676533	−	0.167540i
$898$	−30.4772			−1.01704
$899$	−11.5856	+	3.10434i	−0.386400	+	0.103536i
$900$	2.13283	−	2.10974i	0.0710944	−	0.0703248i
$901$	−90.1219	+	52.0319i	−3.00240	+	1.73343i
$902$	−3.79542	−	3.79542i	−0.126374	−	0.126374i
$903$	−23.9161	−	9.98272i	−0.795879	−	0.332204i
$904$	−1.65931	+	6.19263i	−0.0551879	+	0.205964i
$905$	−5.66901	+	5.66901i	−0.188444	+	0.188444i
$906$	5.89585	−	2.42337i	0.195876	−	0.0805109i
$907$	−10.9523	−	6.32330i	−0.363664	−	0.209962i	0.307023	−	0.951702i	$-0.400667\pi$
$907$	−10.9523	−	6.32330i	−0.363664	−	0.209962i	−0.670687	+	0.741741i	$0.734001\pi$
$908$	−4.92103	−	18.3655i	−0.163310	−	0.609482i
$909$	14.6719	+	4.01704i	0.486637	+	0.133237i
$910$	10.5481	+	14.2212i	0.349667	+	0.471427i
$911$			33.7068i			1.11676i	0.829587	+	0.558378i	$0.188576\pi$
$911$			33.7068i			1.11676i	−0.829587	+	0.558378i	$0.811424\pi$
$912$	0.232654	+	1.80512i	0.00770394	+	0.0597736i
$913$	−1.63676	+	2.83496i	−0.0541690	+	0.0938235i
$914$	5.65833	+	9.80051i	0.187161	+	0.324172i
$915$	6.65262	+	8.71888i	0.219929	+	0.288237i
$916$	15.1498	+	4.05938i	0.500564	+	0.134126i
$917$	46.8646	+	12.5573i	1.54760	+	0.414679i
$918$	15.2452	+	37.6719i	0.503165	+	1.24336i
$919$	10.9448	+	18.9569i	0.361034	+	0.625329i	0.988131	−	0.153612i	$-0.0490904\pi$
$919$	10.9448	+	18.9569i	0.361034	+	0.625329i	−0.627097	+	0.778941i	$0.715757\pi$
$920$	−1.67128	+	2.89473i	−0.0551003	+	0.0954365i
$921$	−51.9129	+	6.69080i	−1.71059	+	0.220469i
$922$			19.2503i			0.633974i
$923$	−45.5836	−	19.7588i	−1.50040	−	0.650370i
$924$	−0.762005	+	5.66876i	−0.0250681	+	0.186489i
$925$	0.597776	+	2.23093i	0.0196547	+	0.0733525i
$926$	−6.07005	−	3.50454i	−0.199474	−	0.115166i
$927$	−24.7490	+	6.48732i	−0.812863	+	0.213072i
$928$	−4.78056	+	4.78056i	−0.156930	+	0.156930i
$929$	8.30922	−	31.0104i	0.272617	−	1.01742i	−0.684805	−	0.728726i	$-0.740113\pi$
$929$	8.30922	−	31.0104i	0.272617	−	1.01742i	0.957422	−	0.288693i	$-0.0932206\pi$
$930$	1.18364	−	2.83572i	0.0388132	−	0.0929869i
$931$	−12.7176	−	12.7176i	−0.416802	−	0.416802i
$932$	2.30547	−	1.33107i	0.0755183	−	0.0436005i
$933$	4.07455	−	5.28025i	0.133395	−	0.172867i
$934$	−6.52981	+	1.74966i	−0.213662	+	0.0572506i
$935$	5.25939			0.172000
$936$	−6.76992	+	8.43612i	−0.221282	+	0.275743i
$937$	−9.10870			−0.297568			−0.148784	−	0.988870i	$-0.547536\pi$
$937$	−9.10870			−0.297568			−0.148784	+	0.988870i	$0.547536\pi$
$938$	27.0091	−	7.23707i	0.881879	−	0.236299i
$939$	21.7990	−	28.2495i	0.711383	−	0.921888i
$940$	−5.84615	+	3.37528i	−0.190681	+	0.110089i
$941$	−20.6194	−	20.6194i	−0.672175	−	0.672175i	0.286042	−	0.958217i	$-0.407660\pi$
$941$	−20.6194	−	20.6194i	−0.672175	−	0.672175i	−0.958217	+	0.286042i	$0.907660\pi$
$942$	2.06900	−	4.95682i	0.0674117	−	0.161502i
$943$	−6.90531	+	25.7710i	−0.224868	+	0.839219i
$944$	0.629245	−	0.629245i	0.0204802	−	0.0204802i
$945$	−25.3252	+	3.12403i	−0.823829	+	0.101625i
$946$	−1.77441	−	1.02445i	−0.0576909	−	0.0333079i
$947$	5.61133	+	20.9418i	0.182344	+	0.680516i	0.995184	+	0.0980285i	$0.0312536\pi$
$947$	5.61133	+	20.9418i	0.182344	+	0.680516i	−0.812840	+	0.582487i	$0.802080\pi$
$948$	1.45884	−	10.8527i	0.0473808	−	0.352479i
$949$	27.4643	−	20.3708i	0.891528	−	0.661264i
$950$			1.05081i			0.0340927i
$951$	28.9962	−	3.73718i	0.940265	−	0.121186i
$952$	19.2039	−	33.2621i	0.622402	−	1.07803i
$953$	10.8849	+	18.8533i	0.352598	+	0.610718i	0.986704	−	0.162529i	$-0.0519650\pi$
$953$	10.8849	+	18.8533i	0.352598	+	0.610718i	−0.634106	+	0.773246i	$0.718632\pi$
$954$	34.6768	−	19.7698i	1.12270	−	0.640071i
$955$	6.17363	+	1.65422i	0.199774	+	0.0535292i
$956$	−18.6377	−	4.99397i	−0.602788	−	0.161516i
$957$	4.77665	+	6.26025i	0.154407	+	0.202365i
$958$	5.96740	+	10.3358i	0.192798	+	0.333936i
$959$	15.7186	−	27.2254i	0.507579	−	0.879153i
$960$	−0.221404	−	1.71784i	−0.00714580	−	0.0554431i
$961$			27.8526i			0.898470i
$962$	−3.06083	−	7.74457i	−0.0986850	−	0.249695i
$963$	0.610695	−	2.23052i	0.0196794	−	0.0718774i
$964$	2.24088	+	8.36309i	0.0721740	+	0.269357i
$965$	−4.02006	−	2.32098i	−0.129410	−	0.0747151i
$966$	26.2961	−	10.8085i	0.846064	−	0.347757i
$967$	−2.45515	+	2.45515i	−0.0789524	+	0.0789524i	−0.745480	−	0.666528i	$-0.767780\pi$
$967$	−2.45515	+	2.45515i	−0.0789524	+	0.0789524i	0.666528	+	0.745480i	$0.267780\pi$
$968$	2.72997	−	10.1884i	0.0877446	−	0.327467i
$969$	−13.1364	−	5.48322i	−0.422003	−	0.176146i
$970$	−7.73884	−	7.73884i	−0.248479	−	0.248479i
$971$	−26.0692	+	15.0510i	−0.836599	+	0.483011i	−0.856107	−	0.516799i	$-0.827124\pi$
$971$	−26.0692	+	15.0510i	−0.836599	+	0.483011i	0.0195075	+	0.999810i	$0.493790\pi$
$972$	−5.76896	−	14.4817i	−0.185039	−	0.464500i
$973$	106.010	−	28.4053i	3.39852	−	0.910632i
$974$	−17.5112			−0.561095
$975$	−4.49915	+	4.33101i	−0.144088	+	0.138703i
$976$	6.33183			0.202677
$977$	30.3048	−	8.12015i	0.969537	−	0.259787i	0.260905	−	0.965365i	$-0.415979\pi$
$977$	30.3048	−	8.12015i	0.969537	−	0.259787i	0.708632	+	0.705578i	$0.249313\pi$
$978$	3.54242	+	2.73354i	0.113274	+	0.0874091i
$979$	−6.69248	+	3.86391i	−0.213893	+	0.123491i
$980$	12.1027	+	12.1027i	0.386605	+	0.386605i
$981$	27.9290	+	16.3281i	0.891705	+	0.521317i
$982$	−1.42120	+	5.30399i	−0.0453523	+	0.169257i
$983$	−13.8106	+	13.8106i	−0.440490	+	0.440490i	−0.892177	−	0.451686i	$-0.850823\pi$
$983$	−13.8106	+	13.8106i	−0.440490	+	0.440490i	0.451686	+	0.892177i	$0.350823\pi$
$984$	−5.25588	−	12.7871i	−0.167551	−	0.407639i
$985$	0.493449	+	0.284893i	0.0157226	+	0.00907744i
$986$	−13.6855	−	51.0749i	−0.435834	−	1.62655i
$987$	56.9065	+	7.64947i	1.81135	+	0.243485i
$988$	−0.433171	−	3.76390i	−0.0137810	−	0.119746i
$989$			10.1844i			0.323844i
$990$	−2.01735	−	0.0109787i	−0.0641155	−	0.000348927i
$991$	−25.2547	+	43.7425i	−0.802243	+	1.38953i	0.115894	+	0.993262i	$0.463027\pi$
$991$	−25.2547	+	43.7425i	−0.802243	+	1.38953i	−0.918137	+	0.396264i	$0.870306\pi$
$992$	−0.887052	−	1.53642i	−0.0281639	−	0.0487813i
$993$	13.5635	−	10.3491i	0.430425	−	0.328420i
$994$	−65.3611	−	17.5135i	−2.07313	−	0.555493i
$995$	−7.38433	−	1.97863i	−0.234099	−	0.0627267i
$996$	−6.70319	+	5.11462i	−0.212399	+	0.162063i
$997$	17.9270	+	31.0505i	0.567754	+	0.983379i	0.996788	+	0.0800903i	$0.0255209\pi$
$997$	17.9270	+	31.0505i	0.567754	+	0.983379i	−0.429034	+	0.903289i	$0.641146\pi$
$998$	10.6301	−	18.4119i	0.336491	−	0.582820i
$999$	11.8853	+	1.66354i	0.376035	+	0.0526322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bh.b.71.7	yes	32
3.2	odd	2	inner	390.2.bh.b.71.1	yes	32
13.11	odd	12	inner	390.2.bh.b.11.1	✓	32
39.11	even	12	inner	390.2.bh.b.11.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bh.b.11.1	✓	32	13.11	odd	12	inner
390.2.bh.b.11.7	yes	32	39.11	even	12	inner
390.2.bh.b.71.1	yes	32	3.2	odd	2	inner
390.2.bh.b.71.7	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.05814 + 1.37125i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.667179 + 1.59840i) q^{6} +(1.27100 - 4.74345i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.760676 - 2.90196i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.05814 + 1.37125i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.667179 + 1.59840i) q^{6} +(1.27100 - 4.74345i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.760676 - 2.90196i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.174045 + 0.649546i) q^{11} +(-0.230750 + 1.71661i) q^{12} +(0.528886 - 3.56655i) q^{13} -4.91078i q^{14} +(1.71784 - 0.221404i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.91056 + 6.77329i) q^{17} +(-1.48584 - 2.60620i) q^{18} +(1.01500 + 0.271969i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(5.15957 + 6.76210i) q^{21} +(0.336230 + 0.582367i) q^{22} +(1.67128 - 2.89473i) q^{23} +(0.221404 + 1.71784i) q^{24} +1.00000i q^{25} +(-0.412226 - 3.58191i) q^{26} +(4.78423 + 2.02760i) q^{27} +(-1.27100 - 4.74345i) q^{28} +(-5.85497 - 3.38037i) q^{29} +(1.60200 - 0.658470i) q^{30} +(1.25448 - 1.25448i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.07486 - 0.448651i) q^{33} +(5.53037 + 5.53037i) q^{34} +(-4.25286 + 2.45539i) q^{35} +(-2.10974 - 2.13283i) q^{36} +(2.23093 - 0.597776i) q^{37} +1.05081 q^{38} +(4.33101 + 4.49915i) q^{39} -1.00000 q^{40} +(-7.70998 + 2.06588i) q^{41} +(6.73393 + 5.19630i) q^{42} +(-2.63868 + 1.52344i) q^{43} +(0.475501 + 0.475501i) q^{44} +(-1.51412 + 2.58987i) q^{45} +(0.865116 - 3.22866i) q^{46} +(4.77336 - 4.77336i) q^{47} +(0.658470 + 1.60200i) q^{48} +(-14.8227 - 8.55787i) q^{49} +(0.258819 + 0.965926i) q^{50} +(-13.4258 - 1.80472i) q^{51} +(-1.32525 - 3.35317i) q^{52} +13.3055i q^{53} +(5.14599 + 0.720265i) q^{54} +(0.336230 - 0.582367i) q^{55} +(-2.45539 - 4.25286i) q^{56} +(-1.44696 + 1.10405i) q^{57} +(-6.53037 - 1.74981i) q^{58} +(0.859565 + 0.230320i) q^{59} +(1.37699 - 1.05066i) q^{60} +(3.16591 + 5.48352i) q^{61} +(0.887052 - 1.53642i) q^{62} +(-14.7321 - 0.0801745i) q^{63} -1.00000i q^{64} +(-2.89591 + 2.14795i) q^{65} +(-1.15435 - 0.155170i) q^{66} +(1.47371 + 5.49997i) q^{67} +(6.77329 + 3.91056i) q^{68} +(2.20097 + 5.35478i) q^{69} +(-3.47244 + 3.47244i) q^{70} +(3.56633 - 13.3097i) q^{71} +(-2.58987 - 1.51412i) q^{72} +(6.70607 + 6.70607i) q^{73} +(2.00020 - 1.15481i) q^{74} +(-1.37125 - 1.05814i) q^{75} +(1.01500 - 0.271969i) q^{76} +3.30230 q^{77} +(5.34790 + 3.22490i) q^{78} -6.32216 q^{79} +(-0.965926 + 0.258819i) q^{80} +(-7.84274 + 4.41490i) q^{81} +(-6.91257 + 3.99098i) q^{82} +(3.44219 + 3.44219i) q^{83} +(7.84937 + 3.27637i) q^{84} +(2.02426 - 7.55463i) q^{85} +(-2.15447 + 2.15447i) q^{86} +(10.8307 - 4.45175i) q^{87} +(0.582367 + 0.336230i) q^{88} +(2.97431 + 11.1003i) q^{89} +(-0.792216 + 2.89351i) q^{90} +(-16.2455 - 7.04184i) q^{91} -3.34255i q^{92} +(0.392794 + 3.04763i) q^{93} +(3.37528 - 5.84615i) q^{94} +(-0.525404 - 0.910027i) q^{95} +(1.05066 + 1.37699i) q^{96} +(10.5715 + 2.83261i) q^{97} +(-16.5325 - 4.42988i) q^{98} +(1.75256 - 0.999166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 32 * q - 8 * q^6 + 4 * q^9	\( 32 q - 8 q^{6} + 4 q^{9} + 16 q^{13} + 4 q^{15} + 16 q^{16} + 24 q^{18} + 32 q^{19} + 36 q^{21} + 8 q^{22} - 8 q^{24} + 12 q^{30} - 24 q^{31} - 28 q^{33} - 8 q^{34} - 12 q^{36} + 16 q^{37} - 4 q^{39} - 32 q^{40} - 12 q^{42} + 48 q^{43} - 24 q^{45} + 24 q^{46} - 48 q^{49} - 16 q^{52} - 20 q^{54} + 8 q^{55} + 4 q^{57} - 24 q^{58} + 4 q^{60} + 32 q^{61} - 48 q^{63} - 48 q^{66} - 64 q^{67} - 36 q^{69} - 40 q^{73} - 12 q^{75} + 32 q^{76} + 4 q^{78} - 32 q^{79} + 16 q^{81} + 12 q^{84} + 40 q^{85} - 72 q^{87} - 48 q^{88} - 144 q^{91} + 56 q^{94} - 4 q^{96} + 112 q^{97} + 72 q^{99}+O(q^{100}) \) 32 * q - 8 * q^6 + 4 * q^9 + 16 * q^13 + 4 * q^15 + 16 * q^16 + 24 * q^18 + 32 * q^19 + 36 * q^21 + 8 * q^22 - 8 * q^24 + 12 * q^30 - 24 * q^31 - 28 * q^33 - 8 * q^34 - 12 * q^36 + 16 * q^37 - 4 * q^39 - 32 * q^40 - 12 * q^42 + 48 * q^43 - 24 * q^45 + 24 * q^46 - 48 * q^49 - 16 * q^52 - 20 * q^54 + 8 * q^55 + 4 * q^57 - 24 * q^58 + 4 * q^60 + 32 * q^61 - 48 * q^63 - 48 * q^66 - 64 * q^67 - 36 * q^69 - 40 * q^73 - 12 * q^75 + 32 * q^76 + 4 * q^78 - 32 * q^79 + 16 * q^81 + 12 * q^84 + 40 * q^85 - 72 * q^87 - 48 * q^88 - 144 * q^91 + 56 * q^94 - 4 * q^96 + 112 * q^97 + 72 * q^99

Introduction

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