LMFDB - Embedded newform 228.2.m.a.11.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(11,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.m (of order $6$, degree $2$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	228.11
Dual form			228.2.m.a.83.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.315760 - 1.37851i) q^{2} +(1.70639 - 0.297045i) q^{3} +(-1.80059 + 0.870557i) q^{4} +(-3.23446 - 1.86742i) q^{5} +(-0.948290 - 2.25848i) q^{6} -2.36238i q^{7} +(1.76863 + 2.20725i) q^{8} +(2.82353 - 1.01375i) q^{9} +(-1.55295 + 5.04840i) q^{10} -3.84074 q^{11} +(-2.81392 + 2.02037i) q^{12} +(-1.36018 - 2.35591i) q^{13} +(-3.25657 + 0.745944i) q^{14} +(-6.07396 - 2.22576i) q^{15} +(2.48426 - 3.13503i) q^{16} +(6.40975 + 3.70067i) q^{17} +(-2.28902 - 3.57217i) q^{18} +(-0.632062 - 4.31283i) q^{19} +(7.44964 + 0.546674i) q^{20} +(-0.701734 - 4.03114i) q^{21} +(1.21275 + 5.29450i) q^{22} +(-0.930547 - 1.61175i) q^{23} +(3.67362 + 3.24107i) q^{24} +(4.47450 + 7.75007i) q^{25} +(-2.81816 + 2.61893i) q^{26} +(4.51691 - 2.56857i) q^{27} +(2.05659 + 4.25368i) q^{28} +(3.80366 - 2.19604i) q^{29} +(-1.15033 + 9.07584i) q^{30} +3.87048i q^{31} +(-5.10611 - 2.43467i) q^{32} +(-6.55379 + 1.14087i) q^{33} +(3.07748 - 10.0044i) q^{34} +(-4.41155 + 7.64103i) q^{35} +(-4.20149 + 4.28339i) q^{36} +5.90265 q^{37} +(-5.74571 + 2.23312i) q^{38} +(-3.02081 - 3.61606i) q^{39} +(-1.59870 - 10.4420i) q^{40} +(-1.45030 - 0.837331i) q^{41} +(-5.33539 + 2.24022i) q^{42} +(0.284264 + 0.164120i) q^{43} +(6.91560 - 3.34358i) q^{44} +(-11.0257 - 1.99377i) q^{45} +(-1.92799 + 1.79170i) q^{46} +(2.14829 + 3.72095i) q^{47} +(3.30787 - 6.08753i) q^{48} +1.41916 q^{49} +(9.27070 - 8.61532i) q^{50} +(12.0368 + 4.41079i) q^{51} +(4.50009 + 3.05791i) q^{52} +(-0.615760 + 0.355509i) q^{53} +(-4.96706 - 5.41556i) q^{54} +(12.4227 + 7.17227i) q^{55} +(5.21436 - 4.17817i) q^{56} +(-2.35965 - 7.17161i) q^{57} +(-4.22832 - 4.54997i) q^{58} +(1.31559 - 2.27867i) q^{59} +(12.8744 - 1.28004i) q^{60} +(2.39802 + 4.15349i) q^{61} +(5.33551 - 1.22214i) q^{62} +(-2.39486 - 6.67024i) q^{63} +(-1.74392 + 7.80761i) q^{64} +10.1601i q^{65} +(3.64213 + 8.67424i) q^{66} +(-2.11293 + 1.21990i) q^{67} +(-14.7630 - 1.08335i) q^{68} +(-2.06664 - 2.47387i) q^{69} +(11.9262 + 3.66865i) q^{70} +(5.00633 - 8.67122i) q^{71} +(7.23137 + 4.43929i) q^{72} +(2.50204 - 4.33365i) q^{73} +(-1.86382 - 8.13687i) q^{74} +(9.93737 + 11.8955i) q^{75} +(4.89265 + 7.21540i) q^{76} +9.07328i q^{77} +(-4.03093 + 5.30603i) q^{78} +(-10.6070 - 6.12393i) q^{79} +(-13.8897 + 5.50100i) q^{80} +(6.94462 - 5.72471i) q^{81} +(-0.696325 + 2.26365i) q^{82} -4.62119 q^{83} +(4.77287 + 6.64754i) q^{84} +(-13.8214 - 23.9394i) q^{85} +(0.136482 - 0.443684i) q^{86} +(5.83820 - 4.87717i) q^{87} +(-6.79283 - 8.47747i) q^{88} +(4.48641 - 2.59023i) q^{89} +(0.733033 + 15.8286i) q^{90} +(-5.56555 + 3.21327i) q^{91} +(3.07866 + 2.09202i) q^{92} +(1.14971 + 6.60455i) q^{93} +(4.45103 - 4.13637i) q^{94} +(-6.00948 + 15.1300i) q^{95} +(-9.43622 - 2.63774i) q^{96} +(-4.18678 + 7.25172i) q^{97} +(-0.448114 - 1.95633i) q^{98} +(-10.8444 + 3.89355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) $ 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.315760	−	1.37851i	−0.223276	−	0.974755i
$2$	−0.315760	−	1.37851i	−0.223276	−	0.974755i
$3$	1.70639	−	0.297045i	0.985184	−	0.171499i
$3$	1.70639	−	0.297045i	0.985184	−	0.171499i
$4$	−1.80059	+	0.870557i	−0.900296	+	0.435278i
$5$	−3.23446	−	1.86742i	−1.44650	−	0.835135i	−0.448226	−	0.893920i	$-0.647944\pi$
$5$	−3.23446	−	1.86742i	−1.44650	−	0.835135i	−0.998271	+	0.0587855i	$0.981277\pi$
$6$	−0.948290	−	2.25848i	−0.387138	−	0.922022i
$7$		−	2.36238i		−	0.892896i	−0.894810	−	0.446448i	$-0.852689\pi$
$7$		−	2.36238i		−	0.892896i	0.894810	−	0.446448i	$-0.147311\pi$
$8$	1.76863	+	2.20725i	0.625304	+	0.780381i
$9$	2.82353	−	1.01375i	0.941176	−	0.337917i
$10$	−1.55295	+	5.04840i	−0.491085	+	1.59645i
$11$	−3.84074			−1.15803			−0.579013	−	0.815318i	$-0.696562\pi$
$11$	−3.84074			−1.15803			−0.579013	+	0.815318i	$0.696562\pi$
$12$	−2.81392	+	2.02037i	−0.812307	+	0.583230i
$13$	−1.36018	−	2.35591i	−0.377247	−	0.653411i	0.613414	−	0.789762i	$-0.289796\pi$
$13$	−1.36018	−	2.35591i	−0.377247	−	0.653411i	−0.990661	+	0.136351i	$0.956463\pi$
$14$	−3.25657	+	0.745944i	−0.870355	+	0.199362i
$15$	−6.07396	−	2.22576i	−1.56829	−	0.574689i
$16$	2.48426	−	3.13503i	0.621065	−	0.783759i
$17$	6.40975	+	3.70067i	1.55459	+	0.897544i	0.997758	+	0.0669195i	$0.0213171\pi$
$17$	6.40975	+	3.70067i	1.55459	+	0.897544i	0.556833	+	0.830624i	$0.312016\pi$
$18$	−2.28902	−	3.57217i	−0.539528	−	0.841968i
$19$	−0.632062	−	4.31283i	−0.145005	−	0.989431i
$19$	−0.632062	−	4.31283i	−0.145005	−	0.989431i
$20$	7.44964	+	0.546674i	1.66579	+	0.122240i
$21$	−0.701734	−	4.03114i	−0.153131	−	0.879667i
$22$	1.21275	+	5.29450i	0.258559	+	1.12879i
$23$	−0.930547	−	1.61175i	−0.194032	−	0.336074i	0.752550	−	0.658535i	$-0.228823\pi$
$23$	−0.930547	−	1.61175i	−0.194032	−	0.336074i	−0.946583	+	0.322460i	$0.895490\pi$
$24$	3.67362	+	3.24107i	0.749875	+	0.661580i
$25$	4.47450	+	7.75007i	0.894901	+	1.55001i
$26$	−2.81816	+	2.61893i	−0.552686	+	0.513614i
$27$	4.51691	−	2.56857i	0.869279	−	0.494321i
$28$	2.05659	+	4.25368i	0.388658	+	0.803870i
$29$	3.80366	−	2.19604i	0.706322	−	0.407795i	−0.103376	−	0.994642i	$-0.532964\pi$
$29$	3.80366	−	2.19604i	0.706322	−	0.407795i	0.809698	+	0.586847i	$0.199631\pi$
$30$	−1.15033	+	9.07584i	−0.210020	+	1.65701i
$31$			3.87048i			0.695159i	0.937651	+	0.347579i	$0.112996\pi$
$31$			3.87048i			0.695159i	−0.937651	+	0.347579i	$0.887004\pi$
$32$	−5.10611	−	2.43467i	−0.902642	−	0.430393i
$33$	−6.55379	+	1.14087i	−1.14087	+	0.198601i
$34$	3.07748	−	10.0044i	0.527783	−	1.71575i
$35$	−4.41155	+	7.64103i	−0.745688	+	1.29157i
$36$	−4.20149	+	4.28339i	−0.700249	+	0.713899i
$37$	5.90265			0.970389			0.485194	−	0.874406i	$-0.338749\pi$
$37$	5.90265			0.970389			0.485194	+	0.874406i	$0.338749\pi$
$38$	−5.74571	+	2.23312i	−0.932077	+	0.362260i
$39$	−3.02081	−	3.61606i	−0.483717	−	0.579033i
$40$	−1.59870	−	10.4420i	−0.252777	−	1.65103i
$41$	−1.45030	−	0.837331i	−0.226499	−	0.130769i	0.382457	−	0.923973i	$-0.375078\pi$
$41$	−1.45030	−	0.837331i	−0.226499	−	0.130769i	−0.608956	+	0.793204i	$0.708411\pi$
$42$	−5.33539	+	2.24022i	−0.823269	+	0.345673i
$43$	0.284264	+	0.164120i	0.0433499	+	0.0250281i	0.521518	−	0.853240i	$-0.325366\pi$
$43$	0.284264	+	0.164120i	0.0433499	+	0.0250281i	−0.478168	+	0.878268i	$0.658699\pi$
$44$	6.91560	−	3.34358i	1.04257	−	0.504064i
$45$	−11.0257	−	1.99377i	−1.64361	−	0.297214i
$46$	−1.92799	+	1.79170i	−0.284267	+	0.264171i
$47$	2.14829	+	3.72095i	0.313360	+	0.542756i	0.979088	−	0.203439i	$-0.0652120\pi$
$47$	2.14829	+	3.72095i	0.313360	+	0.542756i	−0.665727	+	0.746195i	$0.731879\pi$
$48$	3.30787	−	6.08753i	0.477450	−	0.878659i
$49$	1.41916			0.202738
$50$	9.27070	−	8.61532i	1.31107	−	1.21839i
$51$	12.0368	+	4.41079i	1.68549	+	0.617635i
$52$	4.50009	+	3.05791i	0.624050	+	0.424056i
$53$	−0.615760	+	0.355509i	−0.0845811	+	0.0488329i	−0.541694	−	0.840576i	$-0.682217\pi$
$53$	−0.615760	+	0.355509i	−0.0845811	+	0.0488329i	0.457113	+	0.889409i	$0.348884\pi$
$54$	−4.96706	−	5.41556i	−0.675931	−	0.736965i
$55$	12.4227	+	7.17227i	1.67508	+	0.967108i
$56$	5.21436	−	4.17817i	0.696799	−	0.558331i
$57$	−2.35965	−	7.17161i	−0.312543	−	0.949904i
$58$	−4.22832	−	4.54997i	−0.555205	−	0.597441i
$59$	1.31559	−	2.27867i	0.171275	−	0.296657i	−0.767591	−	0.640940i	$-0.778545\pi$
$59$	1.31559	−	2.27867i	0.171275	−	0.296657i	0.938866	+	0.344283i	$0.111878\pi$
$60$	12.8744	−	1.28004i	1.66208	−	0.165253i
$61$	2.39802	+	4.15349i	0.307035	+	0.531799i	0.977712	−	0.209949i	$-0.0673300\pi$
$61$	2.39802	+	4.15349i	0.307035	+	0.531799i	−0.670678	+	0.741749i	$0.733997\pi$
$62$	5.33551	−	1.22214i	0.677610	−	0.155212i
$63$	−2.39486	−	6.67024i	−0.301724	−	0.840372i
$64$	−1.74392	+	7.80761i	−0.217989	+	0.975951i
$65$			10.1601i			1.26021i
$66$	3.64213	+	8.67424i	0.448315	+	1.06773i
$67$	−2.11293	+	1.21990i	−0.258136	+	0.149035i	−0.623484	−	0.781836i	$-0.714283\pi$
$67$	−2.11293	+	1.21990i	−0.258136	+	0.149035i	0.365348	+	0.930871i	$0.380950\pi$
$68$	−14.7630	−	1.08335i	−1.79027	−	0.131375i
$69$	−2.06664	−	2.47387i	−0.248794	−	0.297818i
$70$	11.9262	+	3.66865i	1.42546	+	0.438487i
$71$	5.00633	−	8.67122i	0.594142	−	1.02908i	−0.399525	−	0.916722i	$-0.630825\pi$
$71$	5.00633	−	8.67122i	0.594142	−	1.02908i	0.993667	−	0.112362i	$-0.0358418\pi$
$72$	7.23137	+	4.43929i	0.852225	+	0.523175i
$73$	2.50204	−	4.33365i	0.292841	−	0.507216i	−0.681639	−	0.731688i	$-0.738733\pi$
$73$	2.50204	−	4.33365i	0.292841	−	0.507216i	0.974480	+	0.224473i	$0.0720660\pi$
$74$	−1.86382	−	8.13687i	−0.216664	−	0.945892i
$75$	9.93737	+	11.8955i	1.14747	+	1.37357i
$76$	4.89265	+	7.21540i	0.561225	+	0.827663i
$77$			9.07328i			1.03400i
$78$	−4.03093	+	5.30603i	−0.456413	+	0.600790i
$79$	−10.6070	−	6.12393i	−1.19338	−	0.688996i	−0.234306	−	0.972163i	$-0.575282\pi$
$79$	−10.6070	−	6.12393i	−1.19338	−	0.688996i	−0.959071	+	0.283167i	$0.908615\pi$
$80$	−13.8897	+	5.50100i	−1.55291	+	0.615031i
$81$	6.94462	−	5.72471i	0.771624	−	0.636078i
$82$	−0.696325	+	2.26365i	−0.0768962	+	0.249978i
$83$	−4.62119			−0.507241			−0.253621	−	0.967304i	$-0.581621\pi$
$83$	−4.62119			−0.507241			−0.253621	+	0.967304i	$0.581621\pi$
$84$	4.77287	+	6.64754i	0.520763	+	0.725306i
$85$	−13.8214	−	23.9394i	−1.49914	−	2.59659i
$86$	0.136482	−	0.443684i	0.0147173	−	0.0478437i
$87$	5.83820	−	4.87717i	0.625921	−	0.522887i
$88$	−6.79283	−	8.47747i	−0.724119	−	0.903702i
$89$	4.48641	−	2.59023i	0.475558	−	0.274564i	−0.243005	−	0.970025i	$-0.578133\pi$
$89$	4.48641	−	2.59023i	0.475558	−	0.274564i	0.718564	+	0.695461i	$0.244800\pi$
$90$	0.733033	+	15.8286i	0.0772685	+	1.66848i
$91$	−5.56555	+	3.21327i	−0.583428	+	0.336842i
$92$	3.07866	+	2.09202i	0.320972	+	0.218108i
$93$	1.14971	+	6.60455i	0.119219	+	0.684860i
$94$	4.45103	−	4.13637i	0.459088	−	0.426634i
$95$	−6.00948	+	15.1300i	−0.616559	+	1.55231i
$96$	−9.43622	−	2.63774i	−0.963081	−	0.269213i
$97$	−4.18678	+	7.25172i	−0.425104	+	0.736301i	−0.996430	−	0.0844219i	$-0.973096\pi$
$97$	−4.18678	+	7.25172i	−0.425104	+	0.736301i	0.571327	+	0.820723i	$0.306429\pi$
$98$	−0.448114	−	1.95633i	−0.0452664	−	0.197620i
$99$	−10.8444	+	3.89355i	−1.08991	+	0.391317i
$100$	−14.8036	−	10.0594i	−1.48036	−	1.00594i
$101$	3.51449	−	2.02909i	0.349705	−	0.201902i	−0.314851	−	0.949141i	$-0.601954\pi$
$101$	3.51449	−	2.02909i	0.349705	−	0.201902i	0.664555	+	0.747239i	$0.268621\pi$
$102$	2.27960	−	17.9856i	0.225714	−	1.78084i
$103$		−	4.70851i		−	0.463943i	−0.972723	−	0.231971i	$-0.925482\pi$
$103$		−	4.70851i		−	0.463943i	0.972723	−	0.231971i	$-0.0745176\pi$
$104$	2.79442	−	7.16899i	0.274015	−	0.702977i
$105$	−5.25809	+	14.3490i	−0.513137	+	1.40032i
$106$	0.684505	+	0.736577i	0.0664850	+	0.0715427i
$107$	−1.66148			−0.160621			−0.0803105	−	0.996770i	$-0.525591\pi$
$107$	−1.66148			−0.160621			−0.0803105	+	0.996770i	$0.525591\pi$
$108$	−5.89702	+	8.55717i	−0.567441	+	0.823414i
$109$	−7.97654	+	13.8158i	−0.764014	+	1.32331i	0.176752	+	0.984255i	$0.443441\pi$
$109$	−7.97654	+	13.8158i	−0.764014	+	1.32331i	−0.940766	+	0.339056i	$0.889893\pi$
$110$	5.96446	−	19.3896i	0.568689	−	1.84873i
$111$	10.0722	−	1.75335i	0.956012	−	0.166421i
$112$	−7.40614	−	5.86877i	−0.699815	−	0.554547i
$113$			6.98736i			0.657315i	0.944449	+	0.328658i	$0.106596\pi$
$113$			6.98736i			0.657315i	−0.944449	+	0.328658i	$0.893404\pi$
$114$	−9.14108	+	5.51731i	−0.856140	+	0.516744i
$115$			6.95088i			0.648173i
$116$	−4.93706	+	7.26548i	−0.458394	+	0.674583i
$117$	−6.22882	−	5.27308i	−0.575854	−	0.487497i
$118$	−3.55658	−	1.09404i	−0.327410	−	0.100715i
$119$	8.74238	−	15.1423i	0.801413	−	1.38809i
$120$	−5.82976	−	17.3433i	−0.532182	−	1.58322i
$121$	3.75127			0.341025
$122$	4.96843	−	4.61720i	0.449821	−	0.418021i
$123$	−2.72350	−	0.998007i	−0.245570	−	0.0899873i
$124$	−3.36947	−	6.96916i	−0.302588	−	0.625849i
$125$		−	14.7489i		−	1.31918i
$126$	−8.43881	+	5.40754i	−0.751789	+	0.481742i
$127$	−13.7413	+	7.93357i	−1.21935	+	0.703991i	−0.964778	−	0.263064i	$-0.915267\pi$
$127$	−13.7413	+	7.93357i	−1.21935	+	0.703991i	−0.254569	+	0.967055i	$0.581934\pi$
$128$	11.3135	−	0.0613189i	0.999985	−	0.00541988i
$129$	0.533817	+	0.195613i	0.0469999	+	0.0172228i
$130$	14.0059	−	3.20816i	1.22840	−	0.281374i
$131$	−4.10729	+	7.11403i	−0.358856	+	0.621556i	−0.987770	−	0.155919i	$-0.950166\pi$
$131$	−4.10729	+	7.11403i	−0.358856	+	0.621556i	0.628914	+	0.777475i	$0.283500\pi$
$132$	10.8075	−	7.75970i	0.940673	−	0.675395i
$133$	−10.1885	+	1.49317i	−0.883458	+	0.129474i
$134$	2.34883	+	2.52751i	0.202908	+	0.218344i
$135$	−19.4064	−	0.127013i	−1.67023	−	0.0109316i
$136$	3.16815	+	20.6930i	0.271666	+	1.77441i
$137$	−14.8502	+	8.57374i	−1.26873	+	0.732504i	−0.974749	−	0.223305i	$-0.928315\pi$
$137$	−14.8502	+	8.57374i	−1.26873	+	0.732504i	−0.293986	+	0.955810i	$0.594982\pi$
$138$	−2.75769	+	3.63004i	−0.234750	+	0.309009i
$139$	13.4814	−	7.78347i	1.14348	−	0.660186i	0.196186	−	0.980567i	$-0.437144\pi$
$139$	13.4814	−	7.78347i	1.14348	−	0.660186i	0.947289	+	0.320381i	$0.103811\pi$
$140$	1.29145	−	17.5989i	0.109148	−	1.48738i
$141$	4.77111	+	5.71124i	0.401800	+	0.480973i
$142$	−13.5342	−	4.16327i	−1.13576	−	0.349374i
$143$	5.22411	+	9.04842i	0.436862	+	0.756667i
$144$	3.83624	−	11.3703i	0.319687	−	0.947523i
$145$	−16.4037			−1.36226
$146$	−6.76403	−	2.08069i	−0.559795	−	0.172199i
$147$	2.42164	−	0.421556i	0.199734	−	0.0347694i
$148$	−10.6283	+	5.13859i	−0.873637	+	0.422389i
$149$	11.5433	+	6.66452i	0.945662	+	0.545978i	0.891731	−	0.452566i	$-0.149491\pi$
$149$	11.5433	+	6.66452i	0.945662	+	0.545978i	0.0539316	+	0.998545i	$0.482825\pi$
$150$	13.2603	−	17.4549i	1.08270	−	1.42519i
$151$			11.0745i			0.901231i	0.892718	+	0.450616i	$0.148796\pi$
$151$			11.0745i			0.901231i	−0.892718	+	0.450616i	$0.851204\pi$
$152$	8.40162	−	9.02291i	0.681461	−	0.731854i
$153$	21.8496	+	3.95106i	1.76644	+	0.319424i
$154$	12.5076	−	2.86498i	1.00789	−	0.230866i
$155$	7.22781	−	12.5189i	0.580552	−	1.00554i
$156$	8.58724	+	3.88125i	0.687529	+	0.310749i
$157$	1.70510	−	2.95333i	0.136082	−	0.235701i	−0.789928	−	0.613199i	$-0.789882\pi$
$157$	1.70510	−	2.95333i	0.136082	−	0.235701i	0.926010	+	0.377498i	$0.123216\pi$
$158$	−5.09266	+	16.5555i	−0.405151	+	1.31709i
$159$	−0.945123	+	0.789545i	−0.0749531	+	0.0626150i
$160$	11.9690	+	17.4101i	0.946232	+	1.37639i
$161$	−3.80758	+	2.19831i	−0.300079	+	0.173251i
$162$	−10.0844	−	7.76561i	−0.792306	−	0.610124i
$163$		−	2.10197i		−	0.164639i	−0.996606	−	0.0823196i	$-0.973767\pi$
$163$		−	2.10197i		−	0.164639i	0.996606	−	0.0823196i	$-0.0262328\pi$
$164$	3.34034	+	0.245123i	0.260837	+	0.0191409i
$165$	23.3285	+	8.54856i	1.81612	+	0.665505i
$166$	1.45918	+	6.37036i	0.113255	+	0.494436i
$167$	4.89901	+	8.48534i	0.379097	+	0.656615i	0.990931	−	0.134371i	$-0.0429014\pi$
$167$	4.89901	+	8.48534i	0.379097	+	0.656615i	−0.611834	+	0.790986i	$0.709568\pi$
$168$	7.65663	−	8.67849i	0.590722	−	0.669560i
$169$	2.79980	−	4.84940i	0.215369	−	0.373031i
$170$	−28.6365	+	26.6120i	−2.19632	+	2.04105i
$171$	−6.15678	−	11.5366i	−0.470820	−	0.882229i
$172$	−0.654720	−	0.0480450i	−0.0499219	−	0.00366340i
$173$	8.34733	+	4.81933i	0.634636	+	0.366407i	0.782545	−	0.622594i	$-0.213921\pi$
$173$	8.34733	+	4.81933i	0.634636	+	0.366407i	−0.147909	+	0.989001i	$0.547254\pi$
$174$	−8.56670	−	6.50802i	−0.649440	−	0.493372i
$175$	18.3086	−	10.5705i	1.38400	−	0.799053i
$176$	−9.54140	+	12.0408i	−0.719210	+	0.907613i
$177$	1.56804	−	4.27908i	0.117861	−	0.321636i
$178$	−4.98729	−	5.36668i	−0.373813	−	0.402250i
$179$	−0.357736			−0.0267384			−0.0133692	−	0.999911i	$-0.504256\pi$
$179$	−0.357736			−0.0267384			−0.0133692	+	0.999911i	$0.504256\pi$
$180$	21.5885	−	6.00853i	1.60911	−	0.447849i
$181$	0.816222	+	1.41374i	0.0606693	+	0.105082i	0.894765	−	0.446538i	$-0.147343\pi$
$181$	0.816222	+	1.41374i	0.0606693	+	0.105082i	−0.834095	+	0.551620i	$0.814010\pi$
$182$	6.18691	+	6.65755i	0.458604	+	0.493491i
$183$	5.32572	+	6.37514i	0.393689	+	0.471264i
$184$	1.91176	−	4.90454i	0.140937	−	0.361568i
$185$	−19.0919	−	11.0227i	−1.40366	−	0.810406i
$186$	8.74142	−	3.67034i	0.640952	−	0.269122i
$187$	−24.6182	−	14.2133i	−1.80026	−	1.03938i
$188$	−7.10749	−	4.82970i	−0.518367	−	0.352242i
$189$	−6.06793	−	10.6706i	−0.441377	−	0.776176i
$190$	22.7545	+	3.50669i	1.65078	+	0.254402i
$191$	−11.0076			−0.796481			−0.398240	−	0.917281i	$-0.630379\pi$
$191$	−11.0076			−0.796481			−0.398240	+	0.917281i	$0.630379\pi$
$192$	−0.656583	+	13.8408i	−0.0473848	+	0.998877i
$193$	13.3078	−	23.0498i	0.957918	−	1.65916i	0.230372	−	0.973103i	$-0.426006\pi$
$193$	13.3078	−	23.0498i	0.957918	−	1.65916i	0.727545	−	0.686060i	$-0.240661\pi$
$194$	11.3186	+	3.48173i	0.812629	+	0.249974i
$195$	3.01802	+	17.3371i	0.216125	+	1.24154i
$196$	−2.55533	+	1.23546i	−0.182524	+	0.0882473i
$197$		−	22.5682i		−	1.60792i	−0.594686	−	0.803958i	$-0.702723\pi$
$197$		−	22.5682i		−	1.60792i	0.594686	−	0.803958i	$-0.297277\pi$
$198$	8.79154	+	13.7198i	0.624788	+	0.975021i
$199$	5.56762	−	3.21447i	0.394678	−	0.227868i	−0.289507	−	0.957176i	$-0.593491\pi$
$199$	5.56762	−	3.21447i	0.394678	−	0.227868i	0.684185	+	0.729308i	$0.260158\pi$
$200$	−9.19262	+	23.5833i	−0.650016	+	1.66759i
$201$	−3.24312	+	2.70927i	−0.228752	+	0.191097i
$202$	−3.90686	−	4.20406i	−0.274886	−	0.295797i
$203$	−5.18789	−	8.98569i	−0.364119	−	0.630672i
$204$	−25.5132	+	2.53667i	−1.78628	+	0.177602i
$205$	3.12729	+	5.41663i	0.218420	+	0.378314i
$206$	−6.49073	+	1.48676i	−0.452231	+	0.103587i
$207$	−4.26134	−	3.60749i	−0.296184	−	0.250738i
$208$	−10.7649	−	1.58847i	−0.746412	−	0.110140i
$209$	2.42758	+	16.5644i	0.167919	+	1.14579i
$210$	21.4406	+	2.71751i	1.47954	+	0.187526i
$211$	8.84094	+	5.10432i	0.608636	+	0.351396i	0.772431	−	0.635098i	$-0.219040\pi$
$211$	8.84094	+	5.10432i	0.608636	+	0.351396i	−0.163796	+	0.986494i	$0.552374\pi$
$212$	0.799241	−	1.17618i	0.0548921	−	0.0807804i
$213$	5.96700	−	16.2836i	0.408852	−	1.11573i
$214$	0.524627	+	2.29037i	0.0358628	+	0.156566i
$215$	−0.612962	−	1.06168i	−0.0418037	−	0.0724061i
$216$	13.6582	+	5.42711i	0.929323	+	0.369268i
$217$	9.14355			0.620704
$218$	21.5639	+	6.63330i	1.46049	+	0.449263i
$219$	2.98215	−	8.13811i	0.201515	−	0.549923i
$220$	−28.6121	−	2.09963i	−1.92903	−	0.141557i
$221$		−	20.1344i		−	1.35438i
$222$	−5.59742	−	13.3310i	−0.375674	−	0.894720i
$223$	20.6444	+	11.9190i	1.38245	+	0.798158i	0.992449	−	0.122656i	$-0.0391411\pi$
$223$	20.6444	+	11.9190i	1.38245	+	0.798158i	0.390002	+	0.920814i	$0.372474\pi$
$224$	−5.75161	+	12.0626i	−0.384296	+	0.805965i
$225$	20.4905	+	17.3465i	1.36604	+	1.15643i
$226$	9.63216	−	2.20633i	0.640722	−	0.146763i
$227$	−0.541353			−0.0359308			−0.0179654	−	0.999839i	$-0.505719\pi$
$227$	−0.541353			−0.0359308			−0.0179654	+	0.999839i	$0.505719\pi$
$228$	10.4921	+	10.8589i	0.694854	+	0.719151i
$229$	−13.6361			−0.901099			−0.450550	−	0.892751i	$-0.648772\pi$
$229$	−13.6361			−0.901099			−0.450550	+	0.892751i	$0.648772\pi$
$230$	9.58188	−	2.19481i	0.631810	−	0.144721i
$231$	2.69518	+	15.4825i	0.177330	+	1.01868i
$232$	11.5745	+	4.51165i	0.759902	+	0.296204i
$233$	−12.5270	−	7.23246i	−0.820671	−	0.473814i	0.0299771	−	0.999551i	$-0.490457\pi$
$233$	−12.5270	−	7.23246i	−0.820671	−	0.473814i	−0.850648	+	0.525736i	$0.823790\pi$
$234$	−5.30220	+	10.2515i	−0.346616	+	0.670163i
$235$		−	16.0470i		−	1.04679i
$236$	−0.385130	+	5.24825i	−0.0250698	+	0.341632i
$237$	−19.9187	−	7.29906i	−1.29386	−	0.474125i
$238$	−23.6343	−	7.27017i	−1.53198	−	0.471255i
$239$	5.29819			0.342711			0.171356	−	0.985209i	$-0.445185\pi$
$239$	5.29819			0.342711			0.171356	+	0.985209i	$0.445185\pi$
$240$	−22.0671	+	13.5127i	−1.42443	+	0.872242i
$241$	7.52688	+	13.0369i	0.484849	+	0.839784i	0.999848	−	0.0174071i	$-0.00554114\pi$
$241$	7.52688	+	13.0369i	0.484849	+	0.839784i	−0.514999	+	0.857191i	$0.672208\pi$
$242$	−1.18450	−	5.17117i	−0.0761425	−	0.332416i
$243$	10.1497	−	11.8314i	0.651105	−	0.758987i
$244$	−7.93369	−	5.39112i	−0.507903	−	0.345131i
$245$	−4.59023	−	2.65017i	−0.293259	−	0.169313i
$246$	−0.515794	+	4.06951i	−0.0328858	+	0.259462i
$247$	−9.30091	+	7.35532i	−0.591802	+	0.468008i
$248$	−8.54312	+	6.84544i	−0.542489	+	0.434686i
$249$	−7.88554	+	1.37270i	−0.499726	+	0.0869915i
$250$	−20.3315	+	4.65711i	−1.28588	+	0.294541i
$251$	12.5993	+	21.8226i	0.795260	+	1.37743i	0.922674	+	0.385580i	$0.125999\pi$
$251$	12.5993	+	21.8226i	0.795260	+	1.37743i	−0.127415	+	0.991850i	$0.540668\pi$
$252$	10.1190	+	9.92552i	0.637437	+	0.625249i
$253$	3.57399	+	6.19033i	0.224695	+	0.389183i
$254$	15.2755	+	16.4375i	0.958469	+	1.03138i
$255$	−30.6958	−	36.7443i	−1.92224	−	2.30102i
$256$	−3.65689	−	15.5765i	−0.228556	−	0.973531i
$257$	3.79344	−	2.19015i	0.236628	−	0.136618i	−0.376998	−	0.926214i	$-0.623044\pi$
$257$	3.79344	−	2.19015i	0.236628	−	0.136618i	0.613626	+	0.789597i	$0.289710\pi$
$258$	0.101098	−	0.797640i	0.00629406	−	0.0496589i
$259$		−	13.9443i		−	0.866456i
$260$	−8.84497	−	18.2942i	−0.548542	−	1.13456i
$261$	8.51350	−	10.0566i	0.526973	−	0.622485i
$262$	11.1037	+	3.41562i	0.685989	+	0.211018i
$263$	0.198768	−	0.344276i	0.0122566	−	0.0212290i	−0.859832	−	0.510577i	$-0.829432\pi$
$263$	0.198768	−	0.344276i	0.0122566	−	0.0212290i	0.872089	+	0.489348i	$0.162765\pi$
$264$	−14.1094	−	12.4481i	−0.868374	−	0.766127i
$265$	2.65554			0.163128
$266$	5.27548	+	13.5735i	0.323460	+	0.832247i
$267$	6.88614	−	5.75261i	0.421425	−	0.352054i
$268$	2.74254	−	4.03598i	0.167527	−	0.246537i
$269$	5.12862	+	2.96101i	0.312698	+	0.180536i	0.648133	−	0.761527i	$-0.275550\pi$
$269$	5.12862	+	2.96101i	0.312698	+	0.180536i	−0.335435	+	0.942063i	$0.608883\pi$
$270$	5.95266	+	26.7920i	0.362267	+	1.63051i
$271$	17.8051	+	10.2798i	1.08158	+	0.624452i	0.931323	−	0.364194i	$-0.118656\pi$
$271$	17.8051	+	10.2798i	1.08158	+	0.624452i	0.150260	+	0.988646i	$0.451989\pi$
$272$	27.5252	−	10.9013i	1.66896	−	0.660991i
$273$	−8.54250	+	7.13631i	−0.517016	+	0.431909i
$274$	16.5081	+	17.7639i	0.997290	+	1.07316i
$275$	−17.1854	−	29.7660i	−1.03632	−	1.79496i
$276$	5.87482	+	2.65530i	0.353622	+	0.159830i
$277$	6.19023			0.371935			0.185967	−	0.982556i	$-0.440458\pi$
$277$	6.19023			0.371935			0.185967	+	0.982556i	$0.440458\pi$
$278$	−14.9865	−	16.1265i	−0.898830	−	0.967205i
$279$	3.92370	+	10.9284i	0.234906	+	0.654267i
$280$	−24.6681	+	3.77673i	−1.47420	+	0.225703i
$281$	21.0458	−	12.1508i	1.25549	−	0.724856i	0.283293	−	0.959033i	$-0.408573\pi$
$281$	21.0458	−	12.1508i	1.25549	−	0.724856i	0.972194	+	0.234177i	$0.0752396\pi$
$282$	6.36649	−	8.38041i	0.379119	−	0.499046i
$283$	−11.9928	−	6.92403i	−0.712897	−	0.411591i	0.0992360	−	0.995064i	$-0.468360\pi$
$283$	−11.9928	−	6.92403i	−0.712897	−	0.411591i	−0.812133	+	0.583473i	$0.801693\pi$
$284$	−1.46557	+	19.9716i	−0.0869656	+	1.18510i
$285$	−5.76021	+	27.6028i	−0.341205	+	1.63505i
$286$	10.8238	−	10.0586i	0.640025	−	0.594779i
$287$	−1.97809	+	3.42616i	−0.116763	+	0.202240i
$288$	−16.8854	−	1.69803i	−0.994982	−	0.100057i
$289$	18.8899	+	32.7182i	1.11117	+	1.92460i
$290$	5.17964	+	22.6128i	0.304159	+	1.32787i
$291$	−4.99019	+	13.6179i	−0.292530	+	0.798297i
$292$	−0.732454	+	9.98130i	−0.0428636	+	0.584112i
$293$			12.5992i			0.736054i	0.929815	+	0.368027i	$0.119967\pi$
$293$			12.5992i			0.736054i	−0.929815	+	0.368027i	$0.880033\pi$
$294$	−1.34578	−	3.20516i	−0.0784873	−	0.186929i
$295$	−8.51045	+	4.91351i	−0.495498	+	0.286076i
$296$	10.4396	+	13.0286i	0.606788	+	0.757273i
$297$	−17.3483	+	9.86520i	−1.00665	+	0.572437i
$298$	5.54222	−	18.0169i	0.321052	−	1.04369i
$299$	−2.53143	+	4.38456i	−0.146396	+	0.253566i
$300$	−28.2489	−	12.7679i	−1.63095	−	0.737155i
$301$	0.387714	−	0.671540i	0.0223475	−	0.0387069i
$302$	15.2664	−	3.49688i	0.878480	−	0.201223i
$303$	5.39435	−	4.50638i	0.309897	−	0.258885i
$304$	−15.0911	−	8.73266i	−0.865533	−	0.500853i
$305$		−	17.9124i		−	1.02566i
$306$	−1.45265	−	31.3676i	−0.0830427	−	1.79317i
$307$	−1.01353	−	0.585163i	−0.0578453	−	0.0333970i	0.470798	−	0.882241i	$-0.343966\pi$
$307$	−1.01353	−	0.585163i	−0.0578453	−	0.0333970i	−0.528644	+	0.848844i	$0.677299\pi$
$308$	−7.89881	−	16.3373i	−0.450076	−	0.930903i
$309$	−1.39864	−	8.03454i	−0.0795659	−	0.457069i
$310$	−19.5397	−	6.01065i	−1.10978	−	0.341382i
$311$	−13.2234			−0.749829			−0.374914	−	0.927059i	$-0.622328\pi$
$311$	−13.2234			−0.749829			−0.374914	+	0.927059i	$0.622328\pi$
$312$	2.63885	−	13.0632i	0.149396	−	0.739555i
$313$	6.40165	+	11.0880i	0.361843	+	0.626730i	0.988264	−	0.152754i	$-0.0488144\pi$
$313$	6.40165	+	11.0880i	0.361843	+	0.626730i	−0.626421	+	0.779485i	$0.715481\pi$
$314$	−4.60960	−	1.41796i	−0.260135	−	0.0800204i
$315$	−4.71004	+	26.0469i	−0.265381	+	1.46758i
$316$	24.4300	+	1.79274i	1.37430	+	0.100849i
$317$	−19.0314	+	10.9878i	−1.06891	+	0.617135i	−0.927883	−	0.372871i	$-0.878373\pi$
$317$	−19.0314	+	10.9878i	−1.06891	+	0.617135i	−0.141025	+	0.990006i	$0.545040\pi$
$318$	1.38683	+	1.05356i	0.0777695	+	0.0590806i
$319$	−14.6089	+	8.43443i	−0.817940	+	0.472238i
$320$	20.2207	−	21.9968i	1.13037	−	1.22966i
$321$	−2.83513	+	0.493534i	−0.158241	+	0.0275464i
$322$	4.23267	+	4.55465i	0.235877	+	0.253821i
$323$	11.9090	−	29.9832i	0.662634	−	1.66831i
$324$	−7.52074	+	16.3535i	−0.417819	+	0.908530i
$325$	12.1723	−	21.0830i	0.675197	−	1.16948i
$326$	−2.89759	+	0.663718i	−0.160483	+	0.0367599i
$327$	−9.50717	+	25.9445i	−0.525748	+	1.43473i
$328$	−0.716840	−	4.68210i	−0.0395809	−	0.258526i
$329$	8.79029	−	5.07507i	0.484624	−	0.279798i
$330$	4.41810	−	34.8579i	0.243208	−	1.91886i
$331$			23.0599i			1.26749i	0.773542	+	0.633745i	$0.218483\pi$
$331$			23.0599i			1.26749i	−0.773542	+	0.633745i	$0.781517\pi$
$332$	8.32087	−	4.02301i	0.456667	−	0.220791i
$333$	16.6663	−	5.98381i	0.913307	−	0.327911i
$334$	10.1502	−	9.43267i	0.555396	−	0.516133i
$335$	9.11228			0.497857
$336$	−14.3811	−	7.81444i	−0.784551	−	0.426313i
$337$	9.92175	−	17.1850i	0.540472	−	0.936125i	−0.458405	−	0.888744i	$-0.651579\pi$
$337$	9.92175	−	17.1850i	0.540472	−	0.936125i	0.998877	−	0.0473815i	$-0.0150877\pi$
$338$	−7.56902	−	2.32832i	−0.411700	−	0.126644i
$339$	2.07556	+	11.9232i	0.112729	+	0.647577i
$340$	45.7273	+	31.0727i	2.47991	+	1.68515i
$341$		−	14.8655i		−	0.805012i
$342$	−13.9593	+	12.1300i	−0.754835	+	0.655915i
$343$		−	19.8893i		−	1.07392i
$344$	0.140503	+	0.917710i	0.00757544	+	0.0494796i
$345$	2.06473	+	11.8609i	0.111161	+	0.638570i
$346$	4.00776	−	13.0286i	0.215459	−	0.700424i
$347$	16.8453	−	29.1769i	0.904301	−	1.56630i	0.0824489	−	0.996595i	$-0.473726\pi$
$347$	16.8453	−	29.1769i	0.904301	−	1.56630i	0.821852	−	0.569700i	$-0.192941\pi$
$348$	−6.26637	+	13.8643i	−0.335912	+	0.743203i
$349$	−21.2363			−1.13675			−0.568375	−	0.822769i	$-0.692428\pi$
$349$	−21.2363			−1.13675			−0.568375	+	0.822769i	$0.692428\pi$
$350$	−20.3527	−	21.9009i	−1.08789	−	1.17065i
$351$	−12.1951	−	7.14769i	−0.650928	−	0.381515i
$352$	19.6112	+	9.35092i	1.04528	+	0.498406i
$353$		−	13.0170i		−	0.692826i	−0.938082	−	0.346413i	$-0.887400\pi$
$353$		−	13.0170i		−	0.692826i	0.938082	−	0.346413i	$-0.112600\pi$
$354$	−6.39389	−	0.810400i	−0.339832	−	0.0430723i
$355$	−32.3856	+	18.6978i	−1.71885	+	0.992378i
$356$	−5.82325	+	8.56962i	−0.308632	+	0.454189i
$357$	10.4200	−	28.4355i	0.551483	−	1.50496i
$358$	0.112958	+	0.493143i	0.00597004	+	0.0260634i
$359$	17.1145	−	29.6432i	0.903270	−	1.56451i	0.0800474	−	0.996791i	$-0.474493\pi$
$359$	17.1145	−	29.6432i	0.903270	−	1.56451i	0.823223	−	0.567719i	$-0.192174\pi$
$360$	−15.0996	−	27.8627i	−0.795819	−	1.46849i
$361$	−18.2010	+	5.45195i	−0.957947	+	0.286945i
$362$	1.69112	−	1.57157i	0.0888835	−	0.0826000i
$363$	6.40113	−	1.11430i	0.335972	−	0.0584855i
$364$	7.22394	−	10.6309i	0.378638	−	0.557211i
$365$	−16.1855	+	9.34469i	−0.847187	+	0.489124i
$366$	7.10657	−	9.35459i	0.371466	−	0.488972i
$367$	−2.90921	+	1.67963i	−0.151860	+	0.0876762i	−0.574004	−	0.818852i	$-0.694611\pi$
$367$	−2.90921	+	1.67963i	−0.151860	+	0.0876762i	0.422145	+	0.906528i	$0.361277\pi$
$368$	−7.36463	−	1.08672i	−0.383908	−	0.0566494i
$369$	−4.94381	−	0.893985i	−0.257364	−	0.0465390i
$370$	−9.16649	+	29.7989i	−0.476543	+	1.54917i
$371$	0.839847	+	1.45466i	0.0436027	+	0.0755221i
$372$	−7.81979	−	10.8912i	−0.405437	−	0.564683i
$373$	−4.05547			−0.209984			−0.104992	−	0.994473i	$-0.533482\pi$
$373$	−4.05547			−0.209984			−0.104992	+	0.994473i	$0.533482\pi$
$374$	−11.8198	+	38.4244i	−0.611187	+	1.98688i
$375$	−4.38110	−	25.1674i	−0.226239	−	1.29964i
$376$	−4.41354	+	11.3228i	−0.227611	+	0.583928i
$377$	−10.3474	−	5.97405i	−0.532916	−	0.307679i
$378$	−12.7936	+	11.7341i	−0.658032	+	0.603536i
$379$		−	18.4922i		−	0.949880i	−0.880018	−	0.474940i	$-0.842470\pi$
$379$		−	18.4922i		−	0.949880i	0.880018	−	0.474940i	$-0.157530\pi$
$380$	−2.35092	−	32.4746i	−0.120600	−	1.66591i
$381$	−21.0915	+	17.6196i	−1.08055	+	0.902678i
$382$	3.47575	+	15.1741i	0.177835	+	0.776374i
$383$	−7.41020	+	12.8348i	−0.378644	+	0.655830i	−0.990865	−	0.134856i	$-0.956943\pi$
$383$	−7.41020	+	12.8348i	−0.378644	+	0.655830i	0.612222	+	0.790686i	$0.290276\pi$
$384$	19.2871	−	3.46527i	0.984240	−	0.176836i
$385$	16.9436	−	29.3472i	0.863527	−	1.49567i
$386$	−35.9765	−	11.0668i	−1.83116	−	0.563285i
$387$	0.969005	+	0.175225i	0.0492573	+	0.00890717i
$388$	1.22565	−	16.7022i	0.0622231	−	0.847927i
$389$	−2.81428	+	1.62482i	−0.142690	+	0.0823819i	−0.569645	−	0.821891i	$-0.692919\pi$
$389$	−2.81428	+	1.62482i	−0.142690	+	0.0823819i	0.426956	+	0.904273i	$0.359586\pi$
$390$	22.9465	−	9.63474i	1.16194	−	0.487874i
$391$		−	13.7746i		−	0.696611i
$392$	2.50997	+	3.13245i	0.126773	+	0.158213i
$393$	−4.89544	+	13.3594i	−0.246942	+	0.673891i
$394$	−31.1105	+	7.12612i	−1.56733	+	0.359009i
$395$	22.8719	+	39.6153i	1.15081	+	1.99326i
$396$	16.1368	−	16.4514i	0.810907	−	0.826713i
$397$	−3.28770	+	5.69446i	−0.165005	+	0.285797i	−0.936657	−	0.350248i	$-0.886097\pi$
$397$	−3.28770	+	5.69446i	−0.165005	+	0.285797i	0.771652	+	0.636045i	$0.219431\pi$
$398$	−6.18922	−	6.66004i	−0.310237	−	0.333838i
$399$	−16.9421	+	5.57439i	−0.848165	+	0.279068i
$400$	35.4126	+	5.22547i	1.77063	+	0.261274i
$401$	11.1576	+	6.44186i	0.557186	+	0.321691i	0.752015	−	0.659146i	$-0.229082\pi$
$401$	11.1576	+	6.44186i	0.557186	+	0.321691i	−0.194830	+	0.980837i	$0.562415\pi$
$402$	4.75881	+	3.61521i	0.237348	+	0.180310i
$403$	9.11849	−	5.26456i	0.454225	−	0.262247i
$404$	−4.56172	+	6.71312i	−0.226954	+	0.333990i
$405$	−33.1525	+	5.54784i	−1.64736	+	0.275674i
$406$	−10.7488	+	9.98889i	−0.533452	+	0.495740i
$407$	−22.6705			−1.12374
$408$	11.5529	+	34.3693i	0.571952	+	1.70153i
$409$	16.2230	+	28.0990i	0.802175	+	1.38941i	0.918182	+	0.396159i	$0.129657\pi$
$409$	16.2230	+	28.0990i	0.802175	+	1.38941i	−0.116008	+	0.993248i	$0.537010\pi$
$410$	6.47942	−	6.02137i	0.319996	−	0.297374i
$411$	−22.7934	+	19.0413i	−1.12431	+	0.939239i
$412$	4.09902	+	8.47810i	0.201944	+	0.417686i
$413$	−5.38308	−	3.10792i	−0.264884	−	0.152931i
$414$	−3.62741	+	7.01341i	−0.178278	+	0.344690i
$415$	14.9471	+	8.62969i	0.733722	+	0.423615i
$416$	1.20940	+	15.3411i	0.0592957	+	0.752160i
$417$	20.6924	−	17.2862i	1.01331	−	0.846510i
$418$	22.0678	−	8.57684i	1.07937	−	0.419507i
$419$	−13.7824			−0.673315			−0.336658	−	0.941627i	$-0.609296\pi$
$419$	−13.7824			−0.673315			−0.336658	+	0.941627i	$0.609296\pi$
$420$	−3.02395	−	30.4142i	−0.147554	−	1.48406i
$421$	−3.91435	+	6.77985i	−0.190774	+	0.330429i	−0.945507	−	0.325602i	$-0.894433\pi$
$421$	−3.91435	+	6.77985i	−0.190774	+	0.330429i	0.754733	+	0.656032i	$0.227766\pi$
$422$	4.24476	−	13.7991i	0.206632	−	0.671729i
$423$	9.83786	+	8.32836i	0.478333	+	0.404939i
$424$	−1.87375	−	0.730373i	−0.0909972	−	0.0354701i
$425$			66.2346i			3.21285i
$426$	−24.3313	−	3.08389i	−1.17885	−	0.149415i
$427$	9.81211	−	5.66502i	0.474841	−	0.274150i
$428$	2.99164	−	1.44641i	0.144606	−	0.0699149i
$429$	11.6022	+	13.8883i	0.560157	+	0.670535i
$430$	−1.26999	+	1.18021i	−0.0612444	+	0.0569148i
$431$	13.4343	+	23.2688i	0.647105	+	1.12082i	0.983811	+	0.179209i	$0.0573538\pi$
$431$	13.4343	+	23.2688i	0.647105	+	1.12082i	−0.336706	+	0.941610i	$0.609313\pi$
$432$	3.16863	−	20.5417i	0.152451	−	0.988311i
$433$	−9.78529	−	16.9486i	−0.470251	−	0.814498i	0.529170	−	0.848516i	$-0.322503\pi$
$433$	−9.78529	−	16.9486i	−0.470251	−	0.814498i	−0.999421	+	0.0340171i	$0.989170\pi$
$434$	−2.88716	−	12.6045i	−0.138588	−	0.605035i
$435$	−27.9912	+	4.87266i	−1.34207	+	0.233626i
$436$	2.33508	−	31.8206i	0.111830	−	1.52393i
$437$	−6.36306	+	5.03202i	−0.304386	+	0.240714i
$438$	−12.1601	−	1.54125i	−0.581034	−	0.0736437i
$439$	21.7265	+	12.5438i	1.03695	+	0.598682i	0.918967	−	0.394334i	$-0.129025\pi$
$439$	21.7265	+	12.5438i	1.03695	+	0.598682i	0.117980	+	0.993016i	$0.462358\pi$
$440$	6.14019	+	40.1052i	0.292722	+	1.91194i
$441$	4.00705	−	1.43868i	0.190812	−	0.0685084i
$442$	−27.7554	+	6.35761i	−1.32019	+	0.302401i
$443$	7.84798	+	13.5931i	0.372869	+	0.645827i	0.990006	−	0.141028i	$-0.0450409\pi$
$443$	7.84798	+	13.5931i	0.372869	+	0.645827i	−0.617137	+	0.786856i	$0.711708\pi$
$444$	−16.6095	+	11.9255i	−0.788254	+	0.565960i
$445$	−19.3482			−0.917191
$446$	9.91189	−	32.2221i	0.469341	−	1.52576i
$447$	21.6770	+	7.94338i	1.02529	+	0.375709i
$448$	18.4445	+	4.11979i	0.871422	+	0.194642i
$449$		−	1.84010i		−	0.0868397i	−0.999057	−	0.0434199i	$-0.986175\pi$
$449$		−	1.84010i		−	0.0868397i	0.999057	−	0.0434199i	$-0.0138253\pi$
$450$	17.4423	−	33.7238i	0.822238	−	1.58975i
$451$	5.57022	+	3.21597i	0.262291	+	0.151434i
$452$	−6.08289	−	12.5814i	−0.286115	−	0.591778i
$453$	3.28964	+	18.8974i	0.154561	+	0.887879i
$454$	0.170937	+	0.746261i	0.00802248	+	0.0350238i
$455$	24.0021			1.12523
$456$	11.6562	−	17.8923i	0.545852	−	0.837881i
$457$	−42.1797			−1.97308			−0.986540	−	0.163517i	$-0.947716\pi$
$457$	−42.1797			−1.97308			−0.986540	+	0.163517i	$0.947716\pi$
$458$	4.30573	+	18.7975i	0.201194	+	0.878351i
$459$	38.4576	+	0.251703i	1.79505	+	0.0117485i
$460$	−6.05114	−	12.5157i	−0.282136	−	0.583548i
$461$	−2.44396	−	1.41102i	−0.113826	−	0.0657177i	0.442006	−	0.897012i	$-0.354267\pi$
$461$	−2.44396	−	1.41102i	−0.113826	−	0.0657177i	−0.555832	+	0.831294i	$0.687600\pi$
$462$	20.4919	−	8.60410i	0.953367	−	0.400299i
$463$			34.5319i			1.60483i	0.596765	+	0.802416i	$0.296452\pi$
$463$			34.5319i			1.60483i	−0.596765	+	0.802416i	$0.703548\pi$
$464$	2.56461	−	17.3802i	0.119059	−	0.806854i
$465$	8.61476	−	23.5092i	0.399500	−	1.09021i
$466$	−6.01452	+	19.5523i	−0.278617	+	0.905744i
$467$	35.8768			1.66018			0.830091	−	0.557628i	$-0.188288\pi$
$467$	35.8768			1.66018			0.830091	+	0.557628i	$0.188288\pi$
$468$	15.8061	+	4.07213i	0.730636	+	0.188234i
$469$	2.88188	+	4.99155i	0.133073	+	0.230489i
$470$	−22.1210	+	5.06700i	−1.02037	+	0.233723i
$471$	2.03230	−	5.54602i	0.0936433	−	0.255547i
$472$	7.35638	−	1.12628i	0.338605	−	0.0518411i
$473$	−1.09179	−	0.630342i	−0.0502003	−	0.0289832i
$474$	−3.77233	+	29.7629i	−0.173269	+	1.36706i
$475$	30.5966	−	24.1963i	1.40387	−	1.11020i
$476$	−2.55927	+	34.8758i	−0.117304	+	1.59853i
$477$	−1.37822	+	1.62802i	−0.0631042	+	0.0745417i
$478$	−1.67295	−	7.30362i	−0.0765191	−	0.334060i
$479$	−20.9661	−	36.3143i	−0.957965	−	1.65924i	−0.727431	−	0.686181i	$-0.759286\pi$
$479$	−20.9661	−	36.3143i	−0.957965	−	1.65924i	−0.230534	−	0.973064i	$-0.574047\pi$
$480$	25.5954	+	26.1531i	1.16826	+	1.19372i
$481$	−8.02868	−	13.9061i	−0.366076	−	0.634063i
$482$	15.5949	−	14.4924i	0.710328	−	0.660113i
$483$	−5.84421	+	4.88219i	−0.265921	+	0.222147i
$484$	−6.75451	+	3.26569i	−0.307023	+	0.148441i
$485$	27.0840	−	15.6370i	1.22982	−	0.710038i
$486$	−19.5147	−	10.2556i	−0.885203	−	0.465205i
$487$		−	6.37445i		−	0.288854i	−0.989515	−	0.144427i	$-0.953866\pi$
$487$		−	6.37445i		−	0.288854i	0.989515	−	0.144427i	$-0.0461339\pi$
$488$	−4.92659	+	12.6390i	−0.223016	+	0.572140i
$489$	−0.624381	−	3.58678i	−0.0282355	−	0.162200i
$490$	−2.20388	+	7.16451i	−0.0995613	+	0.323659i
$491$	−9.98477	+	17.2941i	−0.450606	+	0.780473i	−0.998424	−	0.0561249i	$-0.982125\pi$
$491$	−9.98477	+	17.2941i	−0.450606	+	0.780473i	0.547817	+	0.836598i	$0.315459\pi$
$492$	5.77274	−	0.573958i	0.260255	−	0.0258760i
$493$	32.5073			1.46406
$494$	13.0762	+	10.4989i	0.588328	+	0.472368i
$495$	42.3468	+	7.65755i	1.90335	+	0.344181i
$496$	12.1341	+	9.61529i	0.544837	+	0.431739i
$497$	−20.4847	−	11.8269i	−0.918865	−	0.530507i
$498$	4.38222	+	10.4369i	0.196372	+	0.467687i
$499$	−15.6461	−	9.03327i	−0.700415	−	0.404385i	0.107087	−	0.994250i	$-0.465848\pi$
$499$	−15.6461	−	9.03327i	−0.700415	−	0.404385i	−0.807502	+	0.589865i	$0.799181\pi$
$500$	12.8398	+	26.5568i	0.574212	+	1.18765i
$501$	10.8802	+	13.0241i	0.486089	+	0.581872i
$502$	26.1044	−	24.2590i	1.16510	−	1.08273i
$503$	10.8674	+	18.8229i	0.484553	+	0.839270i	0.999843	−	0.0177460i	$-0.00564902\pi$
$503$	10.8674	+	18.8229i	0.484553	+	0.839270i	−0.515290	+	0.857016i	$0.672316\pi$
$504$	10.4873	−	17.0832i	0.467141	−	0.760948i
$505$	−15.1566			−0.674462
$506$	7.40492	−	6.88144i	0.329189	−	0.305917i
$507$	3.33706	−	9.10663i	0.148204	−	0.404440i
$508$	17.8359	−	26.2477i	0.791342	−	1.16456i
$509$	−33.1500	+	19.1392i	−1.46935	+	0.848330i	−0.999409	−	0.0343682i	$-0.989058\pi$
$509$	−33.1500	+	19.1392i	−1.46935	+	0.848330i	−0.469941	+	0.882698i	$0.655725\pi$
$510$	−40.9600	+	53.9168i	−1.81374	+	2.38748i
$511$	−10.2377	−	5.91076i	−0.452891	−	0.261476i
$512$	−20.3177	+	9.95949i	−0.897924	+	0.440152i
$513$	−13.9328	−	17.8572i	−0.615147	−	0.788413i
$514$	−4.21696	−	4.53775i	−0.186002	−	0.200151i
$515$	−8.79275	+	15.2295i	−0.387455	+	0.671092i
$516$	−1.13148	+	0.112498i	−0.0498106	+	0.00495245i
$517$	−8.25102	−	14.2912i	−0.362879	−	0.628525i
$518$	−19.2224	+	4.40304i	−0.844583	+	0.193459i
$519$	15.6754	+	5.74412i	0.688072	+	0.252139i
$520$	−22.4260	+	17.9695i	−0.983443	+	0.788014i
$521$			23.1939i			1.01615i	0.861314	+	0.508073i	$0.169642\pi$
$521$			23.1939i			1.01615i	−0.861314	+	0.508073i	$0.830358\pi$
$522$	−16.5513	−	8.56051i	−0.724431	−	0.374683i
$523$	−34.0022	+	19.6312i	−1.48681	+	0.858411i	−0.999887	−	0.0150323i	$-0.995215\pi$
$523$	−34.0022	+	19.6312i	−1.48681	+	0.858411i	−0.486925	+	0.873444i	$0.661882\pi$
$524$	1.20238	−	16.3851i	0.0525263	−	0.715786i
$525$	28.1017	−	23.4758i	1.22646	−	1.02457i
$526$	−0.537352	−	0.165296i	−0.0234297	−	0.00720723i
$527$	−14.3234	+	24.8088i	−0.623936	+	1.08069i
$528$	−12.7047	+	23.3806i	−0.552899	+	1.01751i
$529$	9.76816	−	16.9190i	0.424703	−	0.735607i
$530$	−0.838511	−	3.66069i	−0.0364226	−	0.159010i
$531$	1.40460	−	7.76756i	0.0609546	−	0.337083i
$532$	17.0455	−	11.5583i	0.739017	−	0.501115i
$533$			4.55569i			0.197329i
$534$	−10.1044	−	7.67619i	−0.437260	−	0.332181i
$535$	5.37399	+	3.10267i	0.232338	+	0.134140i
$536$	−6.42963	−	2.50622i	−0.277718	−	0.108252i
$537$	−0.610436	+	0.106264i	−0.0263423	+	0.00458562i
$538$	2.46238	−	8.00484i	0.106161	−	0.345113i
$539$	−5.45063			−0.234775
$540$	35.0535	−	16.6656i	1.50846	−	0.717175i
$541$	12.1104	+	20.9758i	0.520666	+	0.901821i	0.999711	+	0.0240301i	$0.00764976\pi$
$541$	12.1104	+	20.9758i	0.520666	+	0.901821i	−0.479045	+	0.877790i	$0.659017\pi$
$542$	8.54867	−	27.7905i	0.367197	−	1.19370i
$543$	1.81274	+	2.16993i	0.0777920	+	0.0931207i
$544$	−23.7190	−	34.5016i	−1.01694	−	1.47925i
$545$	51.5997	−	29.7911i	2.21029	−	1.27611i
$546$	12.5349	+	9.52258i	0.536443	+	0.407529i
$547$	19.5350	−	11.2785i	0.835255	−	0.482235i	−0.0203936	−	0.999792i	$-0.506492\pi$
$547$	19.5350	−	11.2785i	0.835255	−	0.482235i	0.855649	+	0.517557i	$0.173159\pi$
$548$	19.2751	−	28.3657i	0.823393	−	1.21172i
$549$	10.9815	+	9.29649i	0.468677	+	0.396765i
$550$	−35.6063	+	33.0892i	−1.51826	+	1.41093i
$551$	−11.8753	−	15.0165i	−0.505905	−	0.639725i
$552$	1.80533	−	8.93694i	0.0768399	−	0.380381i
$553$	−14.4670	+	25.0577i	−0.615202	+	1.06556i
$554$	−1.95462	−	8.53331i	−0.0830440	−	0.362545i
$555$	−35.8524	−	13.1379i	−1.52185	−	0.557672i
$556$	−17.4985	+	25.7512i	−0.742101	+	1.09209i
$557$	7.28515	−	4.20608i	0.308682	−	0.178217i	−0.337655	−	0.941270i	$-0.609634\pi$
$557$	7.28515	−	4.20608i	0.308682	−	0.178217i	0.646336	+	0.763053i	$0.276300\pi$
$558$	13.8260	−	8.85962i	0.585301	−	0.375058i
$559$		−	0.892934i		−	0.0377671i
$560$	12.9955	+	32.8127i	0.549158	+	1.38659i
$561$	−46.2301	−	16.9407i	−1.95184	−	0.715237i
$562$	−23.3954	−	25.1752i	−0.986877	−	1.06195i
$563$	−13.7709			−0.580375			−0.290187	−	0.956970i	$-0.593718\pi$
$563$	−13.7709			−0.580375			−0.290187	+	0.956970i	$0.593718\pi$
$564$	−13.5628	−	6.13010i	−0.571096	−	0.258124i
$565$	13.0483	−	22.6004i	0.548947	−	0.950804i
$566$	−5.75803	+	18.7185i	−0.242028	+	0.786798i
$567$	−13.5239	−	16.4058i	−0.567952	−	0.688980i
$568$	27.9939	−	4.28593i	1.17460	−	0.179834i
$569$		−	30.1824i		−	1.26531i	−0.774433	−	0.632655i	$-0.781965\pi$
$569$		−	30.1824i		−	1.26531i	0.774433	−	0.632655i	$-0.218035\pi$
$570$	39.8696	−	0.775329i	1.66995	−	0.0324750i
$571$		−	32.1380i		−	1.34493i	−0.740127	−	0.672467i	$-0.765235\pi$
$571$		−	32.1380i		−	1.34493i	0.740127	−	0.672467i	$-0.234765\pi$
$572$	−17.2837	−	11.7446i	−0.722666	−	0.491068i
$573$	−18.7832	+	3.26975i	−0.784680	+	0.136596i
$574$	5.34760	+	1.64498i	0.223205	+	0.0686603i
$575$	8.32747	−	14.4236i	0.347280	−	0.601506i
$576$	2.99097	+	23.8129i	0.124624	+	0.992204i
$577$	3.72818			0.155206			0.0776031	−	0.996984i	$-0.475273\pi$
$577$	3.72818			0.155206			0.0776031	+	0.996984i	$0.475273\pi$
$578$	39.1378	−	36.3710i	1.62792	−	1.51284i
$579$	15.8615	−	43.2850i	0.659180	−	1.79886i
$580$	29.5364	−	14.2804i	1.22643	−	0.592961i
$581$			10.9170i			0.452913i
$582$	20.3482	+	2.57905i	0.843459	+	0.106905i
$583$	2.36497	−	1.36542i	0.0979471	−	0.0565498i
$584$	13.9906	−	2.14200i	0.578936	−	0.0886364i
$585$	10.2998	+	28.6874i	0.425846	+	1.18608i
$586$	17.3682	−	3.97832i	0.717473	−	0.164343i
$587$	−23.8026	+	41.2273i	−0.982439	+	1.70163i	−0.329633	+	0.944109i	$0.606925\pi$
$587$	−23.8026	+	41.2273i	−0.982439	+	1.70163i	−0.652806	+	0.757525i	$0.726408\pi$
$588$	−3.99341	+	2.86723i	−0.164685	+	0.118243i
$589$	16.6927	−	2.44638i	0.687812	−	0.100801i
$590$	9.46059	+	10.1803i	0.389486	+	0.419115i
$591$	−6.70378	−	38.5101i	−0.275757	−	1.58409i
$592$	14.6637	−	18.5050i	0.602675	−	0.760551i
$593$	13.1012	−	7.56396i	0.538000	−	0.310615i	−0.206268	−	0.978496i	$-0.566132\pi$
$593$	13.1012	−	7.56396i	0.538000	−	0.310615i	0.744268	+	0.667881i	$0.232798\pi$
$594$	19.0772	+	20.7998i	0.782746	+	0.853424i
$595$	−56.5538	+	32.6514i	−2.31848	+	1.33858i
$596$	−26.5866	−	1.95099i	−1.08903	−	0.0799157i
$597$	8.54569	−	7.13897i	0.349752	−	0.292179i
$598$	6.84350	+	2.10514i	0.279851	+	0.0860855i
$599$	−15.3550	−	26.5956i	−0.627387	−	1.08667i	−0.988074	−	0.153979i	$-0.950791\pi$
$599$	−15.3550	−	26.5956i	−0.627387	−	1.08667i	0.360688	−	0.932687i	$-0.382542\pi$
$600$	−8.68086	+	42.9730i	−0.354395	+	1.75436i
$601$	23.3220			0.951324			0.475662	−	0.879628i	$-0.342209\pi$
$601$	23.3220			0.951324			0.475662	+	0.879628i	$0.342209\pi$
$602$	−1.04815	−	0.322423i	−0.0427194	−	0.0131410i
$603$	−4.72925	+	5.58642i	−0.192590	+	0.227497i
$604$	−9.64100	−	19.9407i	−0.392287	−	0.811375i
$605$	−12.1334	−	7.00519i	−0.493291	−	0.284802i
$606$	−7.91542	−	6.01325i	−0.321542	−	0.244271i
$607$			41.5066i			1.68470i	0.538931	+	0.842350i	$0.318829\pi$
$607$			41.5066i			1.68470i	−0.538931	+	0.842350i	$0.681171\pi$
$608$	−7.27293	+	23.5607i	−0.294956	+	0.955511i
$609$	−11.5217	−	13.7920i	−0.466884	−	0.558882i
$610$	−24.6925	+	5.65601i	−0.999769	+	0.229005i
$611$	5.84413	−	10.1223i	0.236428	−	0.409506i
$612$	−42.7819	+	11.9071i	−1.72936	+	0.481317i
$613$	−9.70581	+	16.8110i	−0.392014	+	0.678988i	−0.992715	−	0.120486i	$-0.961555\pi$
$613$	−9.70581	+	16.8110i	−0.392014	+	0.678988i	0.600701	+	0.799474i	$0.294888\pi$
$614$	−0.486622	+	1.58194i	−0.0196385	+	0.0638418i
$615$	6.94537	+	8.31393i	0.280064	+	0.335250i
$616$	−20.0270	+	16.0473i	−0.806911	+	0.646562i
$617$	−37.5215	+	21.6631i	−1.51056	+	0.872122i	−0.510636	+	0.859797i	$0.670590\pi$
$617$	−37.5215	+	21.6631i	−1.51056	+	0.872122i	−0.999924	+	0.0123252i	$0.996077\pi$
$618$	−10.6341	+	4.46503i	−0.427765	+	0.179610i
$619$			30.2779i			1.21697i	0.793565	+	0.608486i	$0.208223\pi$
$619$			30.2779i			1.21697i	−0.793565	+	0.608486i	$0.791777\pi$
$620$	−2.11589	+	28.8337i	−0.0849762	+	1.15799i
$621$	−8.34310	−	4.88997i	−0.334797	−	0.196228i
$622$	4.17541	+	18.2286i	0.167419	+	0.730899i
$623$	−6.11910	−	10.5986i	−0.245157	−	0.424624i
$624$	−18.8410	+	0.487124i	−0.754242	+	0.0195006i
$625$	−5.16986	+	8.95446i	−0.206794	+	0.358178i
$626$	13.2635	−	12.3259i	0.530118	−	0.492642i
$627$	9.06280	+	27.5443i	0.361933	+	1.10001i
$628$	−0.499157	+	6.80212i	−0.0199185	+	0.271434i
$629$	37.8345	+	21.8437i	1.50856	+	0.870967i
$630$	37.3932	−	1.73170i	1.48978	−	0.0689927i
$631$	16.7973	−	9.69793i	0.668690	−	0.386069i	−0.126890	−	0.991917i	$-0.540499\pi$
$631$	16.7973	−	9.69793i	0.668690	−	0.386069i	0.795580	+	0.605848i	$0.207166\pi$
$632$	−5.24270	−	34.2432i	−0.208544	−	1.36212i
$633$	16.6023	+	6.08380i	0.659882	+	0.241809i
$634$	21.1561	+	22.7655i	0.840217	+	0.904133i
$635$	59.2612			2.35171
$636$	1.01444	−	2.24443i	0.0402250	−	0.0889975i
$637$	−1.93032	−	3.34342i	−0.0764822	−	0.132471i
$638$	16.2399	+	17.4752i	0.642942	+	0.691852i
$639$	5.34506	−	29.5586i	0.211447	−	1.16932i
$640$	−36.7078	−	20.9288i	−1.45100	−	0.827283i
$641$	−21.9248	−	12.6583i	−0.865977	−	0.499972i	3.24300e−5	−	1.00000i	$-0.499990\pi$
$641$	−21.9248	−	12.6583i	−0.865977	−	0.499972i	−0.866009	+	0.500028i	$0.833323\pi$
$642$	1.57556	+	3.75242i	0.0621824	+	0.148096i
$643$	−18.3369	−	10.5868i	−0.723139	−	0.417504i	0.0927682	−	0.995688i	$-0.470428\pi$
$643$	−18.3369	−	10.5868i	−0.723139	−	0.417504i	−0.815907	+	0.578183i	$0.803762\pi$
$644$	4.94214	−	7.27296i	0.194748	−	0.286595i
$645$	−1.36132	−	1.62956i	−0.0536019	−	0.0641640i
$646$	−45.0926	−	6.94922i	−1.77414	−	0.273413i
$647$	−40.8362			−1.60544			−0.802718	−	0.596358i	$-0.796614\pi$
$647$	−40.8362			−1.60544			−0.802718	+	0.596358i	$0.796614\pi$
$648$	24.9183	+	5.20365i	0.978884	+	0.204419i
$649$	−5.05283	+	8.75177i	−0.198341	+	0.343537i
$650$	−32.9067	−	10.1225i	−1.29071	−	0.397037i
$651$	15.6024	−	2.71605i	0.611508	−	0.106450i
$652$	1.82989	+	3.78479i	0.0716639	+	0.148224i
$653$		−	23.4139i		−	0.916258i	−0.888886	−	0.458129i	$-0.848520\pi$
$653$		−	23.4139i		−	0.916258i	0.888886	−	0.458129i	$-0.151480\pi$
$654$	38.7668	+	4.91353i	1.51590	+	0.192134i
$655$	26.5698	−	15.3401i	1.03817	−	0.599386i
$656$	−6.22798	+	2.46659i	−0.243162	+	0.0963042i
$657$	2.67132	−	14.7726i	0.104218	−	0.576335i
$658$	−9.77167	−	10.5150i	−0.380939	−	0.409918i
$659$	12.5101	+	21.6681i	0.487324	+	0.844070i	0.999894	−	0.0145759i	$-0.00463981\pi$
$659$	12.5101	+	21.6681i	0.487324	+	0.844070i	−0.512570	+	0.858645i	$0.671306\pi$
$660$	−49.4471	+	4.91632i	−1.92473	+	0.191367i
$661$	14.5585	+	25.2160i	0.566259	+	0.980790i	0.996931	+	0.0782812i	$0.0249432\pi$
$661$	14.5585	+	25.2160i	0.566259	+	0.980790i	−0.430672	+	0.902508i	$0.641723\pi$
$662$	31.7884	−	7.28140i	1.23549	−	0.283000i
$663$	−5.98082	−	34.3570i	−0.232276	−	1.33432i
$664$	−8.17316	−	10.2001i	−0.317180	−	0.395841i
$665$	35.7428	+	14.1967i	1.38605	+	0.550523i
$666$	−13.5113	−	21.0852i	−0.523552	−	0.817036i
$667$	−7.07897	−	4.08705i	−0.274099	−	0.158251i
$668$	−16.2081	−	11.0138i	−0.627110	−	0.426135i
$669$	38.7679	+	14.2062i	1.49885	+	0.549244i
$670$	−2.87729	−	12.5614i	−0.111159	−	0.485289i
$671$	−9.21015	−	15.9525i	−0.355554	−	0.615838i
$672$	−6.23135	+	22.2919i	−0.240380	+	0.859930i
$673$	−49.9586			−1.92576			−0.962881	−	0.269926i	$-0.913001\pi$
$673$	−49.9586			−1.92576			−0.962881	+	0.269926i	$0.913001\pi$
$674$	−26.8226	−	8.25093i	−1.03317	−	0.317814i
$675$	40.1175	+	23.5133i	1.54412	+	0.905026i
$676$	−0.819623	+	11.1692i	−0.0315240	+	0.429584i
$677$			20.4835i			0.787246i	0.919272	+	0.393623i	$0.128778\pi$
$677$			20.4835i			0.787246i	−0.919272	+	0.393623i	$0.871222\pi$
$678$	15.7808	−	6.62604i	0.606059	−	0.254472i
$679$	17.1313	+	9.89077i	0.657440	+	0.379573i
$680$	28.3953	−	72.8471i	1.08891	−	2.79356i
$681$	−0.923758	+	0.160806i	−0.0353985	+	0.00616211i
$682$	−20.4923	+	4.69393i	−0.784690	+	0.179740i
$683$	−38.2792			−1.46471			−0.732357	−	0.680921i	$-0.761580\pi$
$683$	−38.2792			−1.46471			−0.732357	+	0.680921i	$0.761580\pi$
$684$	21.1291	+	15.4130i	0.807893	+	0.589329i
$685$	64.0431			2.44696
$686$	−27.4176	+	6.28022i	−1.04681	+	0.239780i
$687$	−23.2685	+	4.05054i	−0.887749	+	0.154538i
$688$	1.22071	−	0.483461i	0.0465391	−	0.0184318i
$689$	1.67509	+	0.967115i	0.0638159	+	0.0368441i
$690$	15.6985	−	6.59145i	0.597630	−	0.250932i
$691$		−	31.2219i		−	1.18774i	−0.804562	−	0.593868i	$-0.797600\pi$
$691$		−	31.2219i		−	1.18774i	0.804562	−	0.593868i	$-0.202400\pi$
$692$	−19.2256	−	1.41083i	−0.730849	−	0.0536316i
$693$	9.19804	+	25.6187i	0.349405	+	0.973173i
$694$	−45.5397	−	14.0085i	−1.72866	−	0.531757i
$695$	−58.1400			−2.20538
$696$	21.0907	+	4.26048i	0.799442	+	0.161493i
$697$	−6.19737	−	10.7342i	−0.234742	−	0.406585i
$698$	6.70555	+	29.2744i	0.253809	+	1.10805i
$699$	−23.5243	−	8.62031i	−0.889771	−	0.326050i
$700$	−23.7641	+	34.9718i	−0.898199	+	1.32181i
$701$	−11.8447	−	6.83853i	−0.447367	−	0.258288i	0.259350	−	0.965783i	$-0.416492\pi$
$701$	−11.8447	−	6.83853i	−0.447367	−	0.258288i	−0.706718	+	0.707496i	$0.749825\pi$
$702$	−6.00245	+	19.0681i	−0.226548	+	0.719679i
$703$	−3.73084	−	25.4571i	−0.140711	−	0.960133i
$704$	6.69792	−	29.9870i	0.252437	−	1.13018i
$705$	−4.76669	−	27.3825i	−0.179524	−	1.03128i
$706$	−17.9441	+	4.11025i	−0.675336	+	0.154691i
$707$	−4.79348	−	8.30255i	−0.180277	−	0.312250i
$708$	0.901786	+	9.06995i	0.0338912	+	0.340870i
$709$	−17.1909	−	29.7755i	−0.645617	−	1.11824i	−0.984159	−	0.177290i	$-0.943267\pi$
$709$	−17.1909	−	29.7755i	−0.645617	−	1.11824i	0.338542	−	0.940951i	$-0.390066\pi$
$710$	36.0013	+	38.7399i	1.35110	+	1.45388i
$711$	−36.1572	−	6.53828i	−1.35600	−	0.245205i
$712$	13.6521	+	5.32148i	0.511633	+	0.199431i
$713$	6.23827	−	3.60166i	0.233625	−	0.134883i
$714$	−42.4888	−	5.38529i	−1.59010	−	0.201539i
$715$		−	39.0224i		−	1.45935i
$716$	0.644136	−	0.311429i	0.0240725	−	0.0116387i
$717$	9.04077	−	1.57380i	0.337634	−	0.0587748i
$718$	−46.2676	−	14.2324i	−1.72669	−	0.531150i
$719$	−4.73255	+	8.19701i	−0.176494	+	0.305697i	−0.940677	−	0.339302i	$-0.889809\pi$
$719$	−4.73255	+	8.19701i	−0.176494	+	0.305697i	0.764183	+	0.644999i	$0.223142\pi$
$720$	−33.6413	+	29.6129i	−1.25374	+	1.10361i
$721$	−11.1233			−0.414252
$722$	13.2627	+	23.3688i	0.493587	+	0.869696i
$723$	16.7164	+	20.0103i	0.621688	+	0.744190i
$724$	−2.70042	−	1.83500i	−0.100360	−	0.0681971i
$725$	34.0390	+	19.6524i	1.26418	+	0.729873i
$726$	−3.55729	−	8.47218i	−0.132023	−	0.314432i
$727$	−34.9348	−	20.1696i	−1.29566	−	0.748050i	−0.316009	−	0.948756i	$-0.602343\pi$
$727$	−34.9348	−	20.1696i	−1.29566	−	0.748050i	−0.979652	+	0.200706i	$0.935676\pi$
$728$	−16.9359	−	6.60148i	−0.627685	−	0.244667i
$729$	13.8049	−	23.2040i	0.511293	−	0.859407i
$730$	17.9925	+	19.3612i	0.665932	+	0.716591i
$731$	1.21471	+	2.10394i	0.0449276	+	0.0778169i
$732$	−15.1394	−	6.84269i	−0.559568	−	0.252913i
$733$	2.23175			0.0824314			0.0412157	−	0.999150i	$-0.486877\pi$
$733$	2.23175			0.0824314			0.0412157	+	0.999150i	$0.486877\pi$
$734$	3.23401	+	3.48002i	0.119369	+	0.128450i
$735$	−8.61994	−	3.15872i	−0.317951	−	0.116511i
$736$	0.827391	+	10.4954i	0.0304980	+	0.386865i
$737$	8.11523	−	4.68533i	0.298928	−	0.172586i
$738$	0.328684	+	7.09738i	0.0120990	+	0.261258i
$739$	42.8726	+	24.7525i	1.57709	+	0.910535i	0.995262	+	0.0972254i	$0.0309968\pi$
$739$	42.8726	+	24.7525i	1.57709	+	0.910535i	0.581831	+	0.813310i	$0.302337\pi$
$740$	43.9726	+	3.22682i	1.61647	+	0.118620i
$741$	−13.6861	+	15.3138i	−0.502771	+	0.562567i
$742$	1.74007	−	1.61706i	0.0638801	−	0.0593642i
$743$	8.21323	−	14.2257i	0.301314	−	0.521892i	−0.675120	−	0.737708i	$-0.735908\pi$
$743$	8.21323	−	14.2257i	0.301314	−	0.521892i	0.976434	+	0.215817i	$0.0692413\pi$
$744$	−12.5445	+	14.2187i	−0.459903	+	0.521282i
$745$	−24.8909	−	43.1123i	−0.911931	−	1.57951i
$746$	1.28055	+	5.59051i	0.0468844	+	0.204683i
$747$	−13.0481	+	4.68473i	−0.477403	+	0.171405i
$748$	56.7007	+	4.16085i	2.07318	+	0.152136i
$749$			3.92504i			0.143418i
$750$	−33.3102	+	13.9862i	−1.21632	+	0.510705i
$751$	−18.2185	+	10.5185i	−0.664804	+	0.383825i	−0.794105	−	0.607781i	$-0.792060\pi$
$751$	−18.2185	+	10.5185i	−0.664804	+	0.383825i	0.129301	+	0.991605i	$0.458727\pi$
$752$	17.0022	+	2.50884i	0.620007	+	0.0914880i
$753$	27.9816	+	33.4953i	1.01971	+	1.22064i
$754$	−4.96802	+	16.1503i	−0.180925	+	0.588160i
$755$	20.6808	−	35.8201i	0.752650	−	1.30363i
$756$	20.2153	+	13.9310i	0.735223	+	0.506666i
$757$	−17.2476	+	29.8736i	−0.626873	+	1.08578i	0.361303	+	0.932449i	$0.382332\pi$
$757$	−17.2476	+	29.8736i	−0.626873	+	1.08578i	−0.988175	+	0.153327i	$0.951001\pi$
$758$	−25.4917	+	5.83909i	−0.925901	+	0.212085i
$759$	7.93742	+	9.50147i	0.288110	+	0.344882i
$760$	−44.0243	+	13.4949i	−1.59693	+	0.489513i
$761$		−	8.10513i		−	0.293811i	−0.989151	−	0.146905i	$-0.953069\pi$
$761$		−	8.10513i		−	0.293811i	0.989151	−	0.146905i	$-0.0469313\pi$
$762$	30.9486	+	23.5113i	1.12115	+	0.851724i
$763$	32.6381	+	18.8436i	1.18158	+	0.682185i
$764$	19.8202	−	9.58273i	0.717068	−	0.346691i
$765$	−63.2936	−	53.5820i	−2.28839	−	1.93726i
$766$	20.0328	+	6.16233i	0.723816	+	0.222654i
$767$	−7.15777			−0.258452
$768$	−10.8670	−	25.4933i	−0.392129	−	0.919910i
$769$	−12.5603	−	21.7550i	−0.452935	−	0.784507i	0.545632	−	0.838025i	$-0.316290\pi$
$769$	−12.5603	−	21.7550i	−0.452935	−	0.784507i	−0.998567	+	0.0535183i	$0.982956\pi$
$770$	−45.8056	−	14.0903i	−1.65072	−	0.507780i
$771$	5.82252	−	4.86407i	0.209693	−	0.175175i
$772$	−3.89577	+	53.0885i	−0.140212	+	1.91070i
$773$	8.13627	−	4.69748i	0.292641	−	0.168956i	−0.346491	−	0.938053i	$-0.612627\pi$
$773$	8.13627	−	4.69748i	0.292641	−	0.168956i	0.639132	+	0.769097i	$0.279294\pi$
$774$	−0.0644234	−	1.39111i	−0.00231565	−	0.0500026i
$775$	−29.9965	+	17.3185i	−1.07751	+	0.622098i
$776$	−23.4112	+	3.58431i	−0.840414	+	0.128669i
$777$	−4.14209	−	23.7944i	−0.148597	−	0.853619i
$778$	3.12848	+	3.36646i	0.112161	+	0.120694i
$779$	−2.69459	+	6.78414i	−0.0965436	+	0.243067i
$780$	−20.5272	−	28.5897i	−0.734991	−	1.02368i
$781$	−19.2280	+	33.3039i	−0.688032	+	1.19171i
$782$	−18.9884	+	4.34946i	−0.679025	+	0.155536i
$783$	11.5401	−	19.6893i	0.412409	−	0.703638i
$784$	3.52557	−	4.44913i	0.125913	−	0.158897i
$785$	−11.0302	+	6.36828i	−0.393684	+	0.227294i
$786$	19.9618	+	2.53008i	0.712015	+	0.0902450i
$787$		−	0.570611i		−	0.0203401i	−0.999948	−	0.0101700i	$-0.996763\pi$
$787$		−	0.570611i		−	0.0203401i	0.999948	−	0.0101700i	$-0.00323728\pi$
$788$	19.6469	+	40.6361i	0.699891	+	1.44760i
$789$	0.236910	−	0.646512i	0.00843421	−	0.0230164i
$790$	47.3881	−	44.0381i	1.68599	−	1.56680i
$791$	16.5068			0.586914
$792$	−27.7738	−	17.0501i	−0.986899	−	0.605851i
$793$	6.52348	−	11.2990i	0.231656	−	0.401240i
$794$	8.88801	+	2.73405i	0.315423	+	0.0970279i
$795$	4.53138	−	0.788815i	0.160711	−	0.0279764i
$796$	−7.22664	+	10.6349i	−0.256141	+	0.376943i
$797$			33.0198i			1.16962i	0.811170	+	0.584811i	$0.198831\pi$
$797$			33.0198i			1.16962i	−0.811170	+	0.584811i	$0.801169\pi$
$798$	13.0340	+	21.5947i	0.461398	+	0.764444i
$799$			31.8004i			1.12502i
$800$	−3.97848	−	50.4667i	−0.140661	−	1.78427i
$801$	10.0417	−	11.8617i	0.354804	−	0.419112i
$802$	5.35706	−	17.4150i	0.189164	−	0.614945i
$803$	−9.60966	+	16.6444i	−0.339118	+	0.587369i
$804$	3.48097	−	7.70161i	0.122764	−	0.271615i
$805$	16.4206			0.578751
$806$	−10.1365	−	10.9076i	−0.357044	−	0.384204i
$807$	9.63098	+	3.52920i	0.339027	+	0.124234i
$808$	10.6945	+	4.16865i	0.376232	+	0.146653i
$809$		−	17.6248i		−	0.619654i	−0.950793	−	0.309827i	$-0.899729\pi$
$809$		−	17.6248i		−	0.619654i	0.950793	−	0.309827i	$-0.100271\pi$
$810$	18.1160	+	43.9494i	0.636531	+	1.54422i
$811$	37.4912	−	21.6456i	1.31650	−	0.760079i	0.333332	−	0.942809i	$-0.391827\pi$
$811$	37.4912	−	21.6456i	1.31650	−	0.760079i	0.983163	+	0.182731i	$0.0584936\pi$
$812$	17.1638	+	11.6632i	0.602332	+	0.409298i
$813$	33.4360	+	12.2524i	1.17265	+	0.429710i
$814$	7.15843	+	31.2516i	0.250903	+	1.09537i
$815$	−3.92526	+	6.79875i	−0.137496	+	0.238150i
$816$	43.7305	−	26.7782i	1.53087	−	0.937424i
$817$	0.528149	−	1.32972i	0.0184776	−	0.0465209i
$818$	33.6123	−	31.2361i	1.17523	−	1.09214i
$819$	−12.4570	+	14.7148i	−0.435284	+	0.514178i
$820$	−10.3465	−	7.03066i	−0.361314	−	0.245521i
$821$	26.2102	−	15.1325i	0.914743	−	0.528127i	0.0327891	−	0.999462i	$-0.489561\pi$
$821$	26.2102	−	15.1325i	0.914743	−	0.528127i	0.881954	+	0.471335i	$0.156228\pi$
$822$	33.4459	+	25.4084i	1.16656	+	0.886221i
$823$	29.9459	−	17.2893i	1.04385	−	0.602667i	0.122928	−	0.992416i	$-0.460772\pi$
$823$	29.9459	−	17.2893i	1.04385	−	0.602667i	0.920921	+	0.389749i	$0.127438\pi$
$824$	10.3929	−	8.32759i	0.362052	−	0.290105i
$825$	−38.1668	−	45.6875i	−1.32880	−	1.59064i
$826$	−2.58455	+	8.40199i	−0.0899280	+	0.292343i
$827$	−1.82513	−	3.16122i	−0.0634660	−	0.109926i	0.832546	−	0.553955i	$-0.186882\pi$
$827$	−1.82513	−	3.16122i	−0.0634660	−	0.109926i	−0.896013	+	0.444029i	$0.853549\pi$
$828$	10.8135	+	2.78588i	0.375794	+	0.0968160i
$829$	0.270509			0.00939515			0.00469758	−	0.999989i	$-0.498505\pi$
$829$	0.270509			0.00939515			0.00469758	+	0.999989i	$0.498505\pi$
$830$	7.17646	−	23.3296i	0.249098	−	0.809783i
$831$	10.5629	−	1.83878i	0.366424	−	0.0637866i
$832$	20.7660	−	6.51128i	0.719933	−	0.225738i
$833$	9.09647	+	5.25185i	0.315174	+	0.181966i
$834$	−30.3631	−	23.0665i	−1.05139	−	0.798726i
$835$		−	36.5940i		−	1.26639i
$836$	−18.7914	−	27.7125i	−0.649913	−	0.958456i
$837$	9.94160	+	17.4826i	0.343632	+	0.604287i
$838$	4.35193	+	18.9992i	0.150335	+	0.656317i
$839$	16.4553	−	28.5014i	0.568099	−	0.983976i	−0.428655	−	0.903468i	$-0.641012\pi$
$839$	16.4553	−	28.5014i	0.568099	−	0.983976i	0.996754	−	0.0805080i	$-0.0256543\pi$
$840$	−40.9715	+	13.7721i	−1.41365	+	0.475183i
$841$	−4.85477	+	8.40871i	−0.167406	+	0.289956i
$842$	10.5821	+	3.25517i	0.364683	+	0.112181i
$843$	32.3030	−	26.9856i	1.11257	−	0.929432i
$844$	−20.3625	−	1.49426i	−0.700907	−	0.0514344i
$845$	−18.1117	+	10.4568i	−0.623062	+	0.359725i
$846$	8.37435	−	16.1914i	0.287916	−	0.556671i
$847$		−	8.86193i		−	0.304499i
$848$	−0.415175	+	2.81361i	−0.0142572	+	0.0966196i
$849$	−22.5211	−	8.25269i	−0.772922	−	0.283232i
$850$	91.3052	−	20.9142i	3.13174	−	0.717352i
$851$	−5.49269	−	9.51362i	−0.188287	−	0.326123i
$852$	3.43165	+	34.5147i	0.117566	+	1.18245i
$853$	17.9948	−	31.1679i	0.616129	−	1.06717i	−0.374056	−	0.927406i	$-0.622033\pi$
$853$	17.9948	−	31.1679i	0.616129	−	1.06717i	0.990185	−	0.139761i	$-0.0446335\pi$
$854$	−10.9076	−	11.7373i	−0.373249	−	0.401643i
$855$	−1.62987	+	48.8121i	−0.0557404	+	1.66934i
$856$	−2.93853	−	3.66730i	−0.100437	−	0.125346i
$857$	−26.7953	−	15.4703i	−0.915310	−	0.528455i	−0.0331744	−	0.999450i	$-0.510562\pi$
$857$	−26.7953	−	15.4703i	−0.915310	−	0.528455i	−0.882136	+	0.470995i	$0.843895\pi$
$858$	15.4817	−	20.3791i	0.528538	−	0.695731i
$859$	−6.27083	+	3.62047i	−0.213958	+	0.123529i	−0.603150	−	0.797628i	$-0.706088\pi$
$859$	−6.27083	+	3.62047i	−0.213958	+	0.123529i	0.389191	+	0.921157i	$0.372754\pi$
$860$	2.02795	+	1.37804i	0.0691524	+	0.0469906i
$861$	−2.35767	+	6.43394i	−0.0803492	+	0.219268i
$862$	27.8343	−	25.8666i	0.948041	−	0.881021i
$863$	−0.317249			−0.0107993			−0.00539963	−	0.999985i	$-0.501719\pi$
$863$	−0.317249			−0.0107993			−0.00539963	+	0.999985i	$0.501719\pi$
$864$	−29.3175	+	2.11824i	−0.997400	+	0.0720638i
$865$	−17.9994	−	31.1759i	−0.611999	−	1.06001i
$866$	−20.2741	+	18.8408i	−0.688941	+	0.640237i
$867$	41.9523	+	50.2189i	1.42478	+	1.70552i
$868$	−16.4638	+	7.95998i	−0.558818	+	0.270179i
$869$	40.7386	+	23.5204i	1.38196	+	0.797876i
$870$	15.5555	+	37.0476i	0.527381	+	1.25603i
$871$	5.74796	+	3.31859i	0.194762	+	0.112446i
$872$	−44.6024	+	6.82872i	−1.51043	+	0.231250i
$873$	−4.47007	+	24.7198i	−0.151289	+	0.836638i
$874$	8.94590	+	7.18265i	0.302599	+	0.242957i
$875$	−34.8425			−1.17789
$876$	1.71505	+	17.2496i	0.0579462	+	0.582809i
$877$	4.70953	−	8.15714i	0.159030	−	0.275447i	−0.775489	−	0.631361i	$-0.782497\pi$
$877$	4.70953	−	8.15714i	0.159030	−	0.275447i	0.934519	+	0.355913i	$0.115830\pi$
$878$	10.4314	−	33.9110i	0.352043	−	1.14444i
$879$	3.74254	+	21.4992i	0.126233	+	0.725149i
$880$	53.3466	−	21.1279i	1.79831	−	0.712222i
$881$		−	21.5013i		−	0.724397i	−0.932101	−	0.362199i	$-0.882026\pi$
$881$		−	21.5013i		−	0.724397i	0.932101	−	0.362199i	$-0.117974\pi$
$882$	−3.24850	−	5.06949i	−0.109383	−	0.170699i
$883$	−29.1341	+	16.8206i	−0.980440	+	0.566057i	−0.902403	−	0.430893i	$-0.858199\pi$
$883$	−29.1341	+	16.8206i	−0.980440	+	0.566057i	−0.0780371	+	0.996950i	$0.524865\pi$
$884$	17.5281	+	36.2537i	0.589534	+	1.21935i
$885$	−13.0626	+	10.9124i	−0.439095	+	0.366815i
$886$	16.2602	−	15.1107i	0.546271	−	0.507653i
$887$	18.0099	+	31.1941i	0.604714	+	1.04740i	0.992097	+	0.125477i	$0.0400460\pi$
$887$	18.0099	+	31.1941i	0.604714	+	1.04740i	−0.387382	+	0.921919i	$0.626621\pi$
$888$	21.6841	+	19.1309i	0.727670	+	0.641990i
$889$	18.7421	+	32.4623i	0.628590	+	1.08875i
$890$	6.10937	+	26.6717i	0.204787	+	0.894037i
$891$	−26.6725	+	21.9871i	−0.893561	+	0.736595i
$892$	−47.5483	−	3.48922i	−1.59204	−	0.116828i
$893$	14.6900	−	11.6171i	0.491581	−	0.388750i
$894$	4.10533	−	32.3902i	0.137303	−	1.08329i
$895$	1.15708	+	0.668042i	0.0386770	+	0.0223302i
$896$	−0.144859	−	26.7269i	−0.00483939	−	0.892882i
$897$	−3.01719	+	8.23372i	−0.100741	+	0.274916i
$898$	−2.53660	+	0.581029i	−0.0846475	+	0.0193892i
$899$	8.49975	+	14.7220i	0.283483	+	0.491006i
$900$	−51.9962	−	13.3958i	−1.73321	−	0.446527i
$901$	−5.26248			−0.175319
$902$	2.67440	−	8.69409i	0.0890478	−	0.289482i
$903$	0.462113	−	1.26108i	0.0153782	−	0.0419660i
$904$	−15.4229	+	12.3580i	−0.512957	+	0.411022i
$905$		−	6.09691i		−	0.202668i
$906$	25.0116	−	10.5018i	0.830955	−	0.348901i
$907$	−44.6278	−	25.7659i	−1.48184	−	0.855542i	−0.482054	−	0.876142i	$-0.660109\pi$
$907$	−44.6278	−	25.7659i	−1.48184	−	0.855542i	−0.999788	+	0.0206000i	$0.993442\pi$
$908$	0.974755	−	0.471278i	0.0323484	−	0.0156399i
$909$	7.86626	−	9.29200i	0.260907	−	0.308196i
$910$	−7.57889	−	33.0872i	−0.251238	−	1.09683i
$911$	55.9410			1.85341			0.926703	−	0.375794i	$-0.122630\pi$
$911$	55.9410			1.85341			0.926703	+	0.375794i	$0.122630\pi$
$912$	−28.3452	−	10.4186i	−0.938605	−	0.344994i
$913$	17.7488			0.587399
$914$	13.3186	+	58.1452i	0.440541	+	1.92327i
$915$	−5.32080	−	30.5655i	−0.175900	−	1.01047i
$916$	24.5531	−	11.8710i	0.811256	−	0.392229i
$917$	16.8060	+	9.70298i	0.554985	+	0.320421i
$918$	−11.7964	−	53.0938i	−0.389339	−	1.75236i
$919$		−	1.59689i		−	0.0526764i	−0.999653	−	0.0263382i	$-0.991615\pi$
$919$		−	1.59689i		−	0.0526764i	0.999653	−	0.0263382i	$-0.00838468\pi$
$920$	−15.3423	+	12.2935i	−0.505822	+	0.405305i
$921$	−1.90330	−	0.697451i	−0.0627159	−	0.0229818i
$922$	−1.17340	+	3.81457i	−0.0386440	+	0.125626i
$923$	−27.2381			−0.896554
$924$	−18.3314	−	25.5314i	−0.603057	−	0.839923i
$925$	26.4114	+	45.7459i	0.868402	+	1.50412i
$926$	47.6026	−	10.9038i	1.56432	−	0.358320i
$927$	−4.77325	−	13.2946i	−0.156774	−	0.436652i
$928$	−24.7686	+	1.95260i	−0.813068	+	0.0640973i
$929$	22.6173	+	13.0581i	0.742049	+	0.428422i	0.822814	−	0.568311i	$-0.192403\pi$
$929$	22.6173	+	13.0581i	0.742049	+	0.428422i	−0.0807648	+	0.996733i	$0.525736\pi$
$930$	−35.1279	−	4.45231i	−1.15189	−	0.145997i
$931$	−0.896998	−	6.12061i	−0.0293979	−	0.200595i
$932$	28.8523	+	2.11725i	0.945088	+	0.0693530i
$933$	−22.5642	+	3.92794i	−0.738719	+	0.128595i
$934$	−11.3285	−	49.4567i	−0.370678	−	1.61827i
$935$	53.0844	+	91.9448i	1.73604	+	3.00692i
$936$	0.622560	−	23.0747i	0.0203490	−	0.754220i
$937$	2.71714	+	4.70623i	0.0887652	+	0.153746i	0.906989	−	0.421153i	$-0.138375\pi$
$937$	2.71714	+	4.70623i	0.0887652	+	0.153746i	−0.818224	+	0.574899i	$0.805041\pi$
$938$	5.97094	−	5.54883i	0.194958	−	0.181176i
$939$	14.2173	+	17.0188i	0.463966	+	0.555389i
$940$	13.9698	+	28.8941i	0.455646	+	0.942423i
$941$	−20.4438	+	11.8032i	−0.666450	+	0.384775i	−0.794730	−	0.606963i	$-0.792388\pi$
$941$	−20.4438	+	11.8032i	−0.666450	+	0.384775i	0.128280	+	0.991738i	$0.459054\pi$
$942$	−8.28697	−	1.05034i	−0.270004	−	0.0342219i
$943$			3.11670i			0.101494i
$944$	−3.87543	−	9.78522i	−0.126135	−	0.318482i
$945$	−0.300054	+	45.8452i	−0.00976075	+	1.49134i
$946$	−0.524193	+	1.70408i	−0.0170430	+	0.0554043i
$947$	−5.19580	+	8.99939i	−0.168841	+	0.292441i	−0.938013	−	0.346601i	$-0.887336\pi$
$947$	−5.19580	+	8.99939i	−0.168841	+	0.292441i	0.769172	+	0.639042i	$0.220669\pi$
$948$	42.2197	−	4.19772i	1.37123	−	0.136336i
$949$	−13.6129			−0.441894
$950$	−43.0160	−	34.5375i	−1.39562	−	1.12055i
$951$	−29.2111	+	24.4026i	−0.947234	+	0.791308i
$952$	48.8848	−	7.48436i	1.58436	−	0.242570i
$953$	−36.3084	−	20.9627i	−1.17614	−	0.679047i	−0.221025	−	0.975268i	$-0.570940\pi$
$953$	−36.3084	−	20.9627i	−1.17614	−	0.679047i	−0.955119	+	0.296221i	$0.904274\pi$
$954$	2.67943	+	1.38583i	0.0867496	+	0.0448678i
$955$	35.6036	+	20.5558i	1.15211	+	0.665169i
$956$	−9.53988	+	4.61238i	−0.308542	+	0.149175i
$957$	−22.4230	+	18.7319i	−0.724833	+	0.605517i
$958$	−43.4395	+	40.3686i	−1.40347	+	1.30425i
$959$	20.2544	+	35.0817i	0.654050	+	1.13285i
$960$	27.9703	−	43.5416i	0.902739	−	1.40530i
$961$	16.0194			0.516754
$962$	−16.6346	+	15.4586i	−0.536320	+	0.498406i
$963$	−4.69123	+	1.68432i	−0.151173	+	0.0542765i
$964$	−24.9022	−	16.9216i	−0.802047	−	0.545009i
$965$	−86.0873	+	49.7025i	−2.77125	+	1.59998i
$966$	8.57552	+	6.51472i	0.275913	+	0.209608i
$967$	36.4699	+	21.0559i	1.17279	+	0.677112i	0.954336	−	0.298735i	$-0.0965645\pi$
$967$	36.4699	+	21.0559i	1.17279	+	0.677112i	0.218456	+	0.975847i	$0.429898\pi$
$968$	6.63460	+	8.28000i	0.213244	+	0.266129i
$969$	11.4150	−	54.7005i	0.366703	−	1.75723i
$970$	−30.1078	−	32.3981i	−0.966702	−	1.04024i
$971$	0.633709	−	1.09762i	0.0203367	−	0.0352242i	−0.855678	−	0.517509i	$-0.826860\pi$
$971$	0.633709	−	1.09762i	0.0203367	−	0.0352242i	0.876015	+	0.482285i	$0.160193\pi$
$972$	−7.97557	+	30.1395i	−0.255817	+	0.966725i
$973$	−18.3875	−	31.8481i	−0.589477	−	1.02100i
$974$	−8.78726	+	2.01279i	−0.281562	+	0.0644941i
$975$	14.5081	−	39.5916i	0.464630	−	1.26795i
$976$	18.9786	+	2.80048i	0.607491	+	0.0896412i
$977$			30.4421i			0.973930i	0.873422	+	0.486965i	$0.161896\pi$
$977$			30.4421i			0.973930i	−0.873422	+	0.486965i	$0.838104\pi$
$978$	−4.74727	+	1.99328i	−0.151801	+	0.0637380i
$979$	−17.2311	+	9.94839i	−0.550709	+	0.317952i
$980$	10.5723	+	0.775820i	0.337718	+	0.0247826i
$981$	−8.51624	+	47.0954i	−0.271903	+	1.50364i
$982$	26.9929	+	8.30334i	0.861380	+	0.264970i
$983$	−10.0463	+	17.4007i	−0.320428	+	0.554997i	−0.980576	−	0.196138i	$-0.937160\pi$
$983$	−10.0463	+	17.4007i	−0.320428	+	0.554997i	0.660149	+	0.751135i	$0.270493\pi$
$984$	−2.61400	−	7.77655i	−0.0833314	−	0.247907i
$985$	−42.1442	+	72.9960i	−1.34283	+	2.32585i
$986$	−10.2645	−	44.8118i	−0.326888	−	1.42710i
$987$	13.4921	−	11.2712i	0.429459	−	0.358765i
$988$	10.3439	−	21.3409i	0.329084	−	0.678944i
$989$		−	0.610886i		−	0.0194250i
$990$	−2.81539	−	60.7935i	−0.0894789	−	1.93215i
$991$	−30.0503	−	17.3496i	−0.954580	−	0.551127i	−0.0600794	−	0.998194i	$-0.519135\pi$
$991$	−30.0503	−	17.3496i	−0.954580	−	0.551127i	−0.894501	+	0.447067i	$0.852469\pi$
$992$	9.42334	−	19.7631i	0.299191	−	0.627480i
$993$	6.84985	+	39.3492i	0.217373	+	1.24871i
$994$	−9.83522	+	31.9729i	−0.311954	+	1.01412i
$995$	−24.0110			−0.761201
$996$	13.0036	−	9.33649i	0.412036	−	0.295838i
$997$	18.2276	+	31.5711i	0.577274	+	0.999867i	0.995791	+	0.0916583i	$0.0292168\pi$
$997$	18.2276	+	31.5711i	0.577274	+	0.999867i	−0.418517	+	0.908209i	$0.637450\pi$
$998$	−7.51208	+	24.4207i	−0.237791	+	0.773023i
$999$	26.6617	−	15.1614i	0.843539	−	0.479684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.m.a.11.16	yes	72
3.2	odd	2	inner	228.2.m.a.11.21	yes	72
4.3	odd	2	inner	228.2.m.a.11.3	✓	72
12.11	even	2	inner	228.2.m.a.11.34	yes	72
19.7	even	3	inner	228.2.m.a.83.34	yes	72
57.26	odd	6	inner	228.2.m.a.83.3	yes	72
76.7	odd	6	inner	228.2.m.a.83.21	yes	72
228.83	even	6	inner	228.2.m.a.83.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.3	✓	72	4.3	odd	2	inner
228.2.m.a.11.16	yes	72	1.1	even	1	trivial
228.2.m.a.11.21	yes	72	3.2	odd	2	inner
228.2.m.a.11.34	yes	72	12.11	even	2	inner
228.2.m.a.83.3	yes	72	57.26	odd	6	inner
228.2.m.a.83.16	yes	72	228.83	even	6	inner
228.2.m.a.83.21	yes	72	76.7	odd	6	inner
228.2.m.a.83.34	yes	72	19.7	even	3	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.315760 - 1.37851i) q^{2} +(1.70639 - 0.297045i) q^{3} +(-1.80059 + 0.870557i) q^{4} +(-3.23446 - 1.86742i) q^{5} +(-0.948290 - 2.25848i) q^{6} -2.36238i q^{7} +(1.76863 + 2.20725i) q^{8} +(2.82353 - 1.01375i) q^{9} +(-1.55295 + 5.04840i) q^{10} -3.84074 q^{11} +(-2.81392 + 2.02037i) q^{12} +(-1.36018 - 2.35591i) q^{13} +(-3.25657 + 0.745944i) q^{14} +(-6.07396 - 2.22576i) q^{15} +(2.48426 - 3.13503i) q^{16} +(6.40975 + 3.70067i) q^{17} +(-2.28902 - 3.57217i) q^{18} +(-0.632062 - 4.31283i) q^{19} +(7.44964 + 0.546674i) q^{20} +(-0.701734 - 4.03114i) q^{21} +(1.21275 + 5.29450i) q^{22} +(-0.930547 - 1.61175i) q^{23} +(3.67362 + 3.24107i) q^{24} +(4.47450 + 7.75007i) q^{25} +(-2.81816 + 2.61893i) q^{26} +(4.51691 - 2.56857i) q^{27} +(2.05659 + 4.25368i) q^{28} +(3.80366 - 2.19604i) q^{29} +(-1.15033 + 9.07584i) q^{30} +3.87048i q^{31} +(-5.10611 - 2.43467i) q^{32} +(-6.55379 + 1.14087i) q^{33} +(3.07748 - 10.0044i) q^{34} +(-4.41155 + 7.64103i) q^{35} +(-4.20149 + 4.28339i) q^{36} +5.90265 q^{37} +(-5.74571 + 2.23312i) q^{38} +(-3.02081 - 3.61606i) q^{39} +(-1.59870 - 10.4420i) q^{40} +(-1.45030 - 0.837331i) q^{41} +(-5.33539 + 2.24022i) q^{42} +(0.284264 + 0.164120i) q^{43} +(6.91560 - 3.34358i) q^{44} +(-11.0257 - 1.99377i) q^{45} +(-1.92799 + 1.79170i) q^{46} +(2.14829 + 3.72095i) q^{47} +(3.30787 - 6.08753i) q^{48} +1.41916 q^{49} +(9.27070 - 8.61532i) q^{50} +(12.0368 + 4.41079i) q^{51} +(4.50009 + 3.05791i) q^{52} +(-0.615760 + 0.355509i) q^{53} +(-4.96706 - 5.41556i) q^{54} +(12.4227 + 7.17227i) q^{55} +(5.21436 - 4.17817i) q^{56} +(-2.35965 - 7.17161i) q^{57} +(-4.22832 - 4.54997i) q^{58} +(1.31559 - 2.27867i) q^{59} +(12.8744 - 1.28004i) q^{60} +(2.39802 + 4.15349i) q^{61} +(5.33551 - 1.22214i) q^{62} +(-2.39486 - 6.67024i) q^{63} +(-1.74392 + 7.80761i) q^{64} +10.1601i q^{65} +(3.64213 + 8.67424i) q^{66} +(-2.11293 + 1.21990i) q^{67} +(-14.7630 - 1.08335i) q^{68} +(-2.06664 - 2.47387i) q^{69} +(11.9262 + 3.66865i) q^{70} +(5.00633 - 8.67122i) q^{71} +(7.23137 + 4.43929i) q^{72} +(2.50204 - 4.33365i) q^{73} +(-1.86382 - 8.13687i) q^{74} +(9.93737 + 11.8955i) q^{75} +(4.89265 + 7.21540i) q^{76} +9.07328i q^{77} +(-4.03093 + 5.30603i) q^{78} +(-10.6070 - 6.12393i) q^{79} +(-13.8897 + 5.50100i) q^{80} +(6.94462 - 5.72471i) q^{81} +(-0.696325 + 2.26365i) q^{82} -4.62119 q^{83} +(4.77287 + 6.64754i) q^{84} +(-13.8214 - 23.9394i) q^{85} +(0.136482 - 0.443684i) q^{86} +(5.83820 - 4.87717i) q^{87} +(-6.79283 - 8.47747i) q^{88} +(4.48641 - 2.59023i) q^{89} +(0.733033 + 15.8286i) q^{90} +(-5.56555 + 3.21327i) q^{91} +(3.07866 + 2.09202i) q^{92} +(1.14971 + 6.60455i) q^{93} +(4.45103 - 4.13637i) q^{94} +(-6.00948 + 15.1300i) q^{95} +(-9.43622 - 2.63774i) q^{96} +(-4.18678 + 7.25172i) q^{97} +(-0.448114 - 1.95633i) q^{98} +(-10.8444 + 3.89355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) \) 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Introduction

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