LMFDB - Embedded newform 550.2.bh.b.57.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(7,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("550.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.bh (of order $20$, degree $8$, 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.1
Character	$\chi$	$=$	550.57
Dual form			550.2.bh.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.256351 + 1.61854i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.55851 - 0.506390i) q^{6} +(0.753160 - 0.119289i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.299227 + 0.0972249i) q^{9} +(-1.49880 + 2.95865i) q^{11} +(-1.15874 - 1.15874i) q^{12} +(0.760418 - 0.387452i) q^{13} +(-0.448214 - 0.616914i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.29037 + 0.657479i) q^{17} +(-0.0492184 - 0.310753i) q^{18} +(-4.09783 + 2.97724i) q^{19} +1.24960i q^{21} +(3.31662 - 0.00776159i) q^{22} +(1.65567 - 1.65567i) q^{23} +(-0.506390 + 1.55851i) q^{24} +(-0.690445 - 0.501638i) q^{26} +(-2.46595 + 4.83969i) q^{27} +(-0.346189 + 0.679435i) q^{28} +(-0.552936 - 0.401731i) q^{29} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.40446 - 3.18431i) q^{33} -1.44822i q^{34} +(-0.254538 + 0.184933i) q^{36} +(1.26983 + 8.01741i) q^{37} +(4.51312 + 2.29955i) q^{38} +(0.432172 + 1.33009i) q^{39} +(7.30492 + 10.0544i) q^{41} +(1.11340 - 0.567304i) q^{42} +(7.61267 + 7.61267i) q^{43} +(-1.51263 - 2.95160i) q^{44} +(-2.22687 - 0.723555i) q^{46} +(-12.5361 - 1.98553i) q^{47} +(1.61854 - 0.256351i) q^{48} +(-6.10438 + 1.98343i) q^{49} +(-1.39494 + 1.91997i) q^{51} +(-0.133507 + 0.842930i) q^{52} +(-3.72862 - 7.31784i) q^{53} +5.43171 q^{54} +0.762548 q^{56} +(-3.76830 - 7.39570i) q^{57} +(-0.106918 + 0.675052i) q^{58} +(0.254349 - 0.350081i) q^{59} +(12.0627 - 3.91939i) q^{61} +(3.47761 - 0.550800i) q^{62} +(0.236964 + 0.0375314i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.837655 + 5.37005i) q^{66} +(3.82631 + 3.82631i) q^{67} +(-1.29037 + 0.657479i) q^{68} +(2.25533 + 3.10420i) q^{69} +(-2.45595 - 7.55864i) q^{71} +(0.280334 + 0.142837i) q^{72} +(0.179057 + 1.13052i) q^{73} +(6.56708 - 4.77126i) q^{74} -5.06519i q^{76} +(-0.775899 + 2.40712i) q^{77} +(0.988915 - 0.988915i) q^{78} +(3.11720 - 9.59376i) q^{79} +(-6.43745 - 4.67708i) q^{81} +(5.64213 - 11.0733i) q^{82} +(0.108440 - 0.212826i) q^{83} +(-1.01094 - 0.734494i) q^{84} +(3.32686 - 10.2390i) q^{86} +(0.791962 - 0.791962i) q^{87} +(-1.94318 + 2.68776i) q^{88} -11.2102i q^{89} +(0.526498 - 0.382523i) q^{91} +(0.366287 + 2.31265i) q^{92} +(-5.14097 - 2.61945i) q^{93} +(3.92217 + 12.0712i) q^{94} +(-0.963210 - 1.32575i) q^{96} +(12.6763 - 6.45889i) q^{97} +(4.53858 + 4.53858i) q^{98} +(-0.736135 + 0.739589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{26} - 8 q^{27} + 20 q^{28} + 16 q^{31} + 104 q^{33} - 4 q^{36} - 20 q^{37} + 36 q^{38} - 20 q^{41}+ \cdots - 72 q^{97}+O(q^{100}) $ 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^26 - 8 * q^27 + 20 * q^28 + 16 * q^31 + 104 * q^33 - 4 * q^36 - 20 * q^37 + 36 * q^38 - 20 * q^41 + 20 * q^42 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−0.256351	+	1.61854i	−0.148004	+	0.934462i	0.796184	+	0.605055i	$0.206849\pi$
$3$	−0.256351	+	1.61854i	−0.148004	+	0.934462i	−0.944188	+	0.329407i	$0.893151\pi$
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	1.55851	−	0.506390i	0.636258	−	0.206733i
$7$	0.753160	−	0.119289i	0.284668	−	0.0450869i	−0.0124678	−	0.999922i	$-0.503969\pi$
$7$	0.753160	−	0.119289i	0.284668	−	0.0450869i	0.297135	+	0.954835i	$0.403969\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	0.299227	+	0.0972249i	0.0997424	+	0.0324083i
$10$		0			0
$11$	−1.49880	+	2.95865i	−0.451904	+	0.892067i
$11$	−1.49880	+	2.95865i	−0.451904	+	0.892067i
$12$	−1.15874	−	1.15874i	−0.334500	−	0.334500i
$13$	0.760418	−	0.387452i	0.210902	−	0.107460i	−0.345349	−	0.938474i	$-0.612239\pi$
$13$	0.760418	−	0.387452i	0.210902	−	0.107460i	0.556251	+	0.831014i	$0.312239\pi$
$14$	−0.448214	−	0.616914i	−0.119790	−	0.164877i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.29037	+	0.657479i	0.312962	+	0.159462i	0.603415	−	0.797427i	$-0.293806\pi$
$17$	1.29037	+	0.657479i	0.312962	+	0.159462i	−0.290453	+	0.956889i	$0.593806\pi$
$18$	−0.0492184	−	0.310753i	−0.0116009	−	0.0732451i
$19$	−4.09783	+	2.97724i	−0.940106	+	0.683027i	−0.948446	−	0.316939i	$-0.897345\pi$
$19$	−4.09783	+	2.97724i	−0.940106	+	0.683027i	0.00834049	+	0.999965i	$0.497345\pi$
$20$		0			0
$21$			1.24960i			0.272684i
$22$	3.31662	−	0.00776159i	0.707105	−	0.00165478i
$23$	1.65567	−	1.65567i	0.345231	−	0.345231i	−0.513098	−	0.858330i	$-0.671502\pi$
$23$	1.65567	−	1.65567i	0.345231	−	0.345231i	0.858330	+	0.513098i	$0.171502\pi$
$24$	−0.506390	+	1.55851i	−0.103366	+	0.318129i
$25$		0			0
$26$	−0.690445	−	0.501638i	−0.135407	−	0.0983793i
$27$	−2.46595	+	4.83969i	−0.474572	+	0.931399i
$28$	−0.346189	+	0.679435i	−0.0654237	+	0.128401i
$29$	−0.552936	−	0.401731i	−0.102678	−	0.0745996i	0.535262	−	0.844686i	$-0.320213\pi$
$29$	−0.552936	−	0.401731i	−0.102678	−	0.0745996i	−0.637939	+	0.770087i	$0.720213\pi$
$30$		0			0
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	0.804554	+	0.593879i	$0.202404\pi$
$31$	−1.08804	+	3.34864i	−0.195417	+	0.601433i	−0.999971	+	0.00755335i	$0.997596\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−4.40446	−	3.18431i	−0.766719	−	0.554317i
$34$		−	1.44822i		−	0.248368i
$35$		0			0
$36$	−0.254538	+	0.184933i	−0.0424230	+	0.0308221i
$37$	1.26983	+	8.01741i	0.208759	+	1.31805i	0.840050	+	0.542509i	$0.182525\pi$
$37$	1.26983	+	8.01741i	0.208759	+	1.31805i	−0.631291	+	0.775546i	$0.717475\pi$
$38$	4.51312	+	2.29955i	0.732124	+	0.373036i
$39$	0.432172	+	1.33009i	0.0692029	+	0.212985i
$40$		0			0
$41$	7.30492	+	10.0544i	1.14084	+	1.57023i	0.765624	+	0.643288i	$0.222430\pi$
$41$	7.30492	+	10.0544i	1.14084	+	1.57023i	0.375212	+	0.926939i	$0.377570\pi$
$42$	1.11340	−	0.567304i	0.171801	−	0.0875370i
$43$	7.61267	+	7.61267i	1.16092	+	1.16092i	0.984274	+	0.176647i	$0.0565249\pi$
$43$	7.61267	+	7.61267i	1.16092	+	1.16092i	0.176647	+	0.984274i	$0.443475\pi$
$44$	−1.51263	−	2.95160i	−0.228037	−	0.444971i
$45$		0			0
$46$	−2.22687	−	0.723555i	−0.328335	−	0.106682i
$47$	−12.5361	−	1.98553i	−1.82858	−	0.289619i	−0.855114	−	0.518440i	$-0.826513\pi$
$47$	−12.5361	−	1.98553i	−1.82858	−	0.289619i	−0.973468	+	0.228821i	$0.926513\pi$
$48$	1.61854	−	0.256351i	0.233616	−	0.0370011i
$49$	−6.10438	+	1.98343i	−0.872054	+	0.283347i
$50$		0			0
$51$	−1.39494	+	1.91997i	−0.195331	+	0.268850i
$52$	−0.133507	+	0.842930i	−0.0185141	+	0.116893i
$53$	−3.72862	−	7.31784i	−0.512166	−	1.00518i	−0.991810	−	0.127719i	$-0.959234\pi$
$53$	−3.72862	−	7.31784i	−0.512166	−	1.00518i	0.479644	−	0.877463i	$-0.340766\pi$
$54$	5.43171			0.739163
$55$		0			0
$56$	0.762548			0.101900
$57$	−3.76830	−	7.39570i	−0.499123	−	0.979584i
$58$	−0.106918	+	0.675052i	−0.0140390	+	0.0886386i
$59$	0.254349	−	0.350081i	0.0331134	−	0.0455767i	−0.792139	−	0.610340i	$-0.791033\pi$
$59$	0.254349	−	0.350081i	0.0331134	−	0.0455767i	0.825253	+	0.564764i	$0.191033\pi$
$60$		0			0
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.591860	−	0.806040i	$-0.298394\pi$
$61$	12.0627	−	3.91939i	1.54446	−	0.501827i	0.952604	+	0.304214i	$0.0983937\pi$
$62$	3.47761	−	0.550800i	0.441657	−	0.0699517i
$63$	0.236964	+	0.0375314i	0.0298546	+	0.00472851i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$		0			0
$66$	−0.837655	+	5.37005i	−0.103108	+	0.661008i
$67$	3.82631	+	3.82631i	0.467458	+	0.467458i	0.901090	−	0.433632i	$-0.142768\pi$
$67$	3.82631	+	3.82631i	0.467458	+	0.467458i	−0.433632	+	0.901090i	$0.642768\pi$
$68$	−1.29037	+	0.657479i	−0.156481	+	0.0797310i
$69$	2.25533	+	3.10420i	0.271510	+	0.373701i
$70$		0			0
$71$	−2.45595	−	7.55864i	−0.291468	−	0.897045i	−0.984385	−	0.176028i	$-0.943675\pi$
$71$	−2.45595	−	7.55864i	−0.291468	−	0.897045i	0.692918	−	0.721017i	$-0.256325\pi$
$72$	0.280334	+	0.142837i	0.0330377	+	0.0168335i
$73$	0.179057	+	1.13052i	0.0209571	+	0.132318i	0.995949	−	0.0899243i	$-0.0286625\pi$
$73$	0.179057	+	1.13052i	0.0209571	+	0.132318i	−0.974992	+	0.222242i	$0.928663\pi$
$74$	6.56708	−	4.77126i	0.763407	−	0.554648i
$75$		0			0
$76$		−	5.06519i		−	0.581017i
$77$	−0.775899	+	2.40712i	−0.0884219	+	0.274317i
$78$	0.988915	−	0.988915i	0.111973	−	0.111973i
$79$	3.11720	−	9.59376i	0.350713	−	1.07938i	−0.607741	−	0.794135i	$-0.707924\pi$
$79$	3.11720	−	9.59376i	0.350713	−	1.07938i	0.958454	−	0.285247i	$-0.0920757\pi$
$80$		0			0
$81$	−6.43745	−	4.67708i	−0.715273	−	0.519676i
$82$	5.64213	−	11.0733i	0.623070	−	1.22284i
$83$	0.108440	−	0.212826i	0.0119029	−	0.0233607i	−0.884979	−	0.465632i	$-0.845827\pi$
$83$	0.108440	−	0.212826i	0.0119029	−	0.0233607i	0.896881	+	0.442271i	$0.145827\pi$
$84$	−1.01094	−	0.734494i	−0.110303	−	0.0801398i
$85$		0			0
$86$	3.32686	−	10.2390i	0.358744	−	1.10410i
$87$	0.791962	−	0.791962i	0.0849073	−	0.0849073i
$88$	−1.94318	+	2.68776i	−0.207144	+	0.286516i
$89$		−	11.2102i		−	1.18828i	−0.804361	−	0.594141i	$-0.797492\pi$
$89$		−	11.2102i		−	1.18828i	0.804361	−	0.594141i	$-0.202508\pi$
$90$		0			0
$91$	0.526498	−	0.382523i	0.0551919	−	0.0400993i
$92$	0.366287	+	2.31265i	0.0381881	+	0.241110i
$93$	−5.14097	−	2.61945i	−0.533093	−	0.271625i
$94$	3.92217	+	12.0712i	0.404540	+	1.24505i
$95$		0			0
$96$	−0.963210	−	1.32575i	−0.0983072	−	0.135308i
$97$	12.6763	−	6.45889i	1.28708	−	0.655800i	0.329552	−	0.944137i	$-0.393102\pi$
$97$	12.6763	−	6.45889i	1.28708	−	0.655800i	0.957529	+	0.288337i	$0.0931023\pi$
$98$	4.53858	+	4.53858i	0.458466	+	0.458466i
$99$	−0.736135	+	0.739589i	−0.0739844	+	0.0743315i
$100$		0			0
$101$	−8.91281	−	2.89595i	−0.886858	−	0.288158i	−0.170056	−	0.985434i	$-0.554395\pi$
$101$	−8.91281	−	2.89595i	−0.886858	−	0.288158i	−0.716802	+	0.697277i	$0.754395\pi$
$102$	2.34400	+	0.371253i	0.232090	+	0.0367595i
$103$	−0.0976359	+	0.0154640i	−0.00962035	+	0.00152371i	−0.161243	−	0.986915i	$-0.551550\pi$
$103$	−0.0976359	+	0.0154640i	−0.00962035	+	0.00152371i	0.151622	+	0.988438i	$0.451550\pi$
$104$	0.811667	−	0.263727i	0.0795905	−	0.0258605i
$105$		0			0
$106$	−4.82748	+	6.64446i	−0.468886	+	0.645367i
$107$	−1.02130	+	6.44826i	−0.0987332	+	0.623377i	0.887852	+	0.460129i	$0.152197\pi$
$107$	−1.02130	+	6.44826i	−0.0987332	+	0.623377i	−0.986585	+	0.163248i	$0.947803\pi$
$108$	−2.46595	−	4.83969i	−0.237286	−	0.465700i
$109$	11.8125			1.13143			0.565716	−	0.824600i	$-0.308600\pi$
$109$	11.8125			1.13143			0.565716	+	0.824600i	$0.308600\pi$
$110$		0			0
$111$	−13.3020			−1.26257
$112$	−0.346189	−	0.679435i	−0.0327118	−	0.0642006i
$113$	1.80338	−	11.3861i	0.169647	−	1.07111i	−0.745061	−	0.666997i	$-0.767580\pi$
$113$	1.80338	−	11.3861i	0.169647	−	1.07111i	0.914708	−	0.404115i	$-0.132420\pi$
$114$	−4.87884	+	6.71515i	−0.456946	+	0.628932i
$115$		0			0
$116$	0.650015	−	0.211203i	0.0603524	−	0.0196097i
$117$	0.265208	−	0.0420048i	0.0245185	−	0.00388335i
$118$	−0.427397	−	0.0676930i	−0.0393451	−	0.00623165i
$119$	1.05029	+	0.341259i	0.0962797	+	0.0312832i
$120$		0			0
$121$	−6.50722	−	8.86883i	−0.591565	−	0.806257i
$122$	−8.96853	−	8.96853i	−0.811973	−	0.811973i
$123$	−18.1460	+	9.24583i	−1.63617	+	0.833668i
$124$	−2.06957	−	2.84852i	−0.185853	−	0.255805i
$125$		0			0
$126$	−0.0741386	−	0.228175i	−0.00660479	−	0.0203275i
$127$	5.78299	+	2.94658i	0.513157	+	0.261467i	0.691339	−	0.722531i	$-0.257021\pi$
$127$	5.78299	+	2.94658i	0.513157	+	0.261467i	−0.178181	+	0.983998i	$0.557021\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−14.2729	+	10.3699i	−1.25666	+	0.913015i
$130$		0			0
$131$			1.56355i			0.136608i	0.997665	+	0.0683040i	$0.0217588\pi$
$131$			1.56355i			0.136608i	−0.997665	+	0.0683040i	$0.978241\pi$
$132$	5.16504	−	1.69160i	0.449559	−	0.147235i
$133$	−2.73116	+	2.73116i	−0.236822	+	0.236822i
$134$	1.67216	−	5.14637i	0.144452	−	0.444579i
$135$		0			0
$136$	1.17164	+	0.851243i	0.100467	+	0.0729935i
$137$	0.766306	−	1.50396i	0.0654700	−	0.128492i	−0.855952	−	0.517055i	$-0.827028\pi$
$137$	0.766306	−	1.50396i	0.0654700	−	0.128492i	0.921422	+	0.388563i	$0.127028\pi$
$138$	1.74196	−	3.41879i	0.148286	−	0.291027i
$139$	7.01947	+	5.09995i	0.595384	+	0.432572i	0.844237	−	0.535969i	$-0.180054\pi$
$139$	7.01947	+	5.09995i	0.595384	+	0.432572i	−0.248854	+	0.968541i	$0.580054\pi$
$140$		0			0
$141$	6.42730	−	19.7812i	0.541276	−	1.66588i
$142$	−5.61982	+	5.61982i	−0.471605	+	0.471605i
$143$	0.00662403	+	2.83052i	0.000553929	+	0.236700i
$144$		−	0.314626i		−	0.0262189i
$145$		0			0
$146$	0.926013	−	0.672788i	0.0766374	−	0.0556803i
$147$	−1.64539	−	10.3886i	−0.135710	−	0.856838i
$148$	−7.23261	−	3.68520i	−0.594517	−	0.302922i
$149$	−4.55529	−	14.0197i	−0.373184	−	1.14854i	−0.944696	−	0.327948i	$-0.893643\pi$
$149$	−4.55529	−	14.0197i	−0.373184	−	1.14854i	0.571512	−	0.820594i	$-0.306357\pi$
$150$		0			0
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	0.989688	−	0.143240i	$-0.0457519\pi$
$151$	6.72937	+	9.26219i	0.547629	+	0.753746i	−0.442059	+	0.896986i	$0.645752\pi$
$152$	−4.51312	+	2.29955i	−0.366062	+	0.186518i
$153$	0.322192	+	0.322192i	0.0260477	+	0.0260477i
$154$	2.49701	−	0.401481i	0.201215	−	0.0323522i
$155$		0			0
$156$	−1.33009	−	0.432172i	−0.106492	−	0.0346014i
$157$	−0.814122	−	0.128944i	−0.0649740	−	0.0102909i	0.123863	−	0.992299i	$-0.460472\pi$
$157$	−0.814122	−	0.128944i	−0.0649740	−	0.0102909i	−0.188837	+	0.982008i	$0.560472\pi$
$158$	−9.96328	+	1.57803i	−0.792636	+	0.125541i
$159$	12.8000	−	4.15898i	1.01511	−	0.329828i
$160$		0			0
$161$	1.04948	−	1.44449i	0.0827108	−	0.113842i
$162$	−1.24477	+	7.85917i	−0.0977983	+	0.617474i
$163$	−4.05736	−	7.96301i	−0.317797	−	0.623711i	0.675750	−	0.737131i	$-0.263820\pi$
$163$	−4.05736	−	7.96301i	−0.317797	−	0.623711i	−0.993547	+	0.113419i	$0.963820\pi$
$164$	−12.4279			−0.970454
$165$		0			0
$166$	−0.238860			−0.0185391
$167$	−9.59049	−	18.8224i	−0.742134	−	1.45652i	−0.884418	−	0.466695i	$-0.845445\pi$
$167$	−9.59049	−	18.8224i	−0.742134	−	1.45652i	0.142284	−	0.989826i	$-0.454555\pi$
$168$	−0.195480	+	1.23421i	−0.0150816	+	0.0952214i
$169$	−7.21309	+	9.92797i	−0.554853	+	0.763690i
$170$		0			0
$171$	−1.51564	+	0.492462i	−0.115904	+	0.0376595i
$172$	−10.6334	+	1.68416i	−0.810788	+	0.128416i
$173$	−2.42835	−	0.384613i	−0.184624	−	0.0292416i	0.0634376	−	0.997986i	$-0.479794\pi$
$173$	−2.42835	−	0.384613i	−0.184624	−	0.0292416i	−0.248062	+	0.968744i	$0.579794\pi$
$174$	−1.06519	−	0.346100i	−0.0807516	−	0.0262378i
$175$		0			0
$176$	3.27700	+	0.511167i	0.247013	+	0.0385307i
$177$	0.501417	+	0.501417i	0.0376888	+	0.0376888i
$178$	−9.98839	+	5.08934i	−0.748661	+	0.381462i
$179$	9.35481	+	12.8758i	0.699211	+	0.962382i	0.999962	+	0.00867926i	$0.00276273\pi$
$179$	9.35481	+	12.8758i	0.699211	+	0.962382i	−0.300751	+	0.953703i	$0.597237\pi$
$180$		0			0
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	0.874358	−	0.485281i	$-0.161283\pi$
$181$	−1.59094	−	4.89640i	−0.118253	−	0.363947i	−0.992612	+	0.121334i	$0.961283\pi$
$182$	−0.579855	−	0.295451i	−0.0429817	−	0.0219003i
$183$	3.25141	+	20.5286i	0.240351	+	1.51752i
$184$	1.89429	−	1.37628i	0.139649	−	0.101461i
$185$		0			0
$186$			5.76984i			0.423065i
$187$	−3.87926	+	2.83234i	−0.283679	+	0.207121i
$188$	8.97488	−	8.97488i	0.654560	−	0.654560i
$189$	−1.27993	+	3.93922i	−0.0931012	+	0.286536i
$190$		0			0
$191$	21.7592	+	15.8090i	1.57444	+	1.14390i	0.922744	+	0.385413i	$0.125941\pi$
$191$	21.7592	+	15.8090i	1.57444	+	1.14390i	0.651693	+	0.758482i	$0.274059\pi$
$192$	−0.743959	+	1.46010i	−0.0536906	+	0.105374i
$193$	4.39692	−	8.62943i	0.316497	−	0.621160i	−0.676876	−	0.736097i	$-0.736667\pi$
$193$	4.39692	−	8.62943i	0.316497	−	0.621160i	0.993373	+	0.114937i	$0.0366666\pi$
$194$	−11.5098	−	8.36237i	−0.826357	−	0.600383i
$195$		0			0
$196$	1.98343	−	6.10438i	0.141674	−	0.436027i
$197$	5.96449	−	5.96449i	0.424952	−	0.424952i	−0.461952	−	0.886905i	$-0.652851\pi$
$197$	5.96449	−	5.96449i	0.424952	−	0.424952i	0.886905	+	0.461952i	$0.152851\pi$
$198$	0.993177	+	0.320135i	0.0705820	+	0.0227510i
$199$		−	0.826885i		−	0.0586163i	−0.999570	−	0.0293082i	$-0.990670\pi$
$199$		−	0.826885i		−	0.0586163i	0.999570	−	0.0293082i	$-0.00933042\pi$
$200$		0			0
$201$	−7.17389	+	5.21214i	−0.506007	+	0.367636i
$202$	1.46602	+	9.25610i	0.103149	+	0.651257i
$203$	−0.464371	−	0.236609i	−0.0325924	−	0.0166067i
$204$	−0.733364	−	2.25706i	−0.0513458	−	0.158026i
$205$		0			0
$206$	0.0581043	+	0.0799737i	0.00404832	+	0.00557203i
$207$	0.656395	−	0.334450i	0.0456226	−	0.0232459i
$208$	−0.603471	−	0.603471i	−0.0418432	−	0.0418432i
$209$	−2.66682	−	16.5863i	−0.184468	−	1.14730i
$210$		0			0
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.209440	−	0.977822i	$-0.567164\pi$
$211$	−13.8523	−	4.50087i	−0.953629	−	0.309853i	−0.744190	+	0.667969i	$0.767164\pi$
$212$	8.11188	+	1.28480i	0.557126	+	0.0882402i
$213$	12.8635	−	2.03738i	0.881393	−	0.139599i
$214$	6.20910	−	2.01746i	0.424446	−	0.137911i
$215$		0			0
$216$	−3.19268	+	4.39435i	−0.217234	+	0.298998i
$217$	−0.420011	+	2.65185i	−0.0285122	+	0.180019i
$218$	−5.36276	−	10.5250i	−0.363212	−	0.712844i
$219$	−1.87569			−0.126748
$220$		0			0
$221$	1.23597			0.0831401
$222$	6.03898	+	11.8522i	0.405310	+	0.795465i
$223$	0.210549	−	1.32935i	0.0140994	−	0.0890201i	−0.979635	−	0.200786i	$-0.935651\pi$
$223$	0.210549	−	1.32935i	0.0140994	−	0.0890201i	0.993735	+	0.111766i	$0.0356506\pi$
$224$	−0.448214	+	0.616914i	−0.0299476	+	0.0412193i
$225$		0			0
$226$	−10.9638	+	3.56235i	−0.729300	+	0.236964i
$227$	−2.02684	+	0.321020i	−0.134526	+	0.0213068i	−0.223334	−	0.974742i	$-0.571694\pi$
$227$	−2.02684	+	0.321020i	−0.134526	+	0.0213068i	0.0888083	+	0.996049i	$0.471694\pi$
$228$	8.19819	+	1.29847i	0.542939	+	0.0859930i
$229$	17.0466	+	5.53877i	1.12647	+	0.366012i	0.812234	−	0.583332i	$-0.198251\pi$
$229$	17.0466	+	5.53877i	1.12647	+	0.366012i	0.314237	+	0.949345i	$0.398251\pi$
$230$		0			0
$231$	−3.69712	−	1.87289i	−0.243252	−	0.123227i
$232$	−0.483284	−	0.483284i	−0.0317291	−	0.0317291i
$233$	21.9042	−	11.1608i	1.43499	−	0.731166i	0.448320	−	0.893873i	$-0.352023\pi$
$233$	21.9042	−	11.1608i	1.43499	−	0.731166i	0.986674	+	0.162707i	$0.0520226\pi$
$234$	−0.157828	−	0.217232i	−0.0103176	−	0.0142009i
$235$		0			0
$236$	0.133719	+	0.411545i	0.00870438	+	0.0267893i
$237$	14.7287	+	7.50467i	0.956735	+	0.487481i
$238$	−0.172757	−	1.09074i	−0.0111981	−	0.0707023i
$239$	2.40071	−	1.74422i	0.155289	−	0.112824i	−0.507427	−	0.861695i	$-0.669403\pi$
$239$	2.40071	−	1.74422i	0.155289	−	0.112824i	0.662717	+	0.748870i	$0.269403\pi$
$240$		0			0
$241$			21.2858i			1.37114i	0.728007	+	0.685570i	$0.240447\pi$
$241$			21.2858i			1.37114i	−0.728007	+	0.685570i	$0.759553\pi$
$242$	−4.94797	+	9.82434i	−0.318067	+	0.631532i
$243$	−2.30213	+	2.30213i	−0.147682	+	0.147682i
$244$	−3.91939	+	12.0627i	−0.250913	+	0.772232i
$245$		0			0
$246$	16.4762	+	11.9707i	1.05048	+	0.763221i
$247$	−1.96252	+	3.85166i	−0.124872	+	0.245075i
$248$	−1.59848	+	3.13720i	−0.101504	+	0.199212i
$249$	0.316667	+	0.230072i	0.0200680	+	0.0145802i
$250$		0			0
$251$	4.10394	−	12.6306i	0.259038	−	0.797238i	−0.733969	−	0.679183i	$-0.762334\pi$
$251$	4.10394	−	12.6306i	0.259038	−	0.797238i	0.993007	−	0.118055i	$-0.0376658\pi$
$252$	−0.169647	+	0.169647i	−0.0106868	+	0.0106868i
$253$	2.41704	+	7.38007i	0.151958	+	0.463981i
$254$		−	6.49040i		−	0.407244i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.89548	−	18.2813i	−0.180615	−	1.14036i	−0.896796	−	0.442444i	$-0.854112\pi$
$257$	−2.89548	−	18.2813i	−0.180615	−	1.14036i	0.716181	−	0.697914i	$-0.245888\pi$
$258$	15.7194	+	8.00942i	0.978645	+	0.498645i
$259$	1.91277	+	5.88692i	0.118854	+	0.365795i
$260$		0			0
$261$	−0.126395	−	0.173968i	−0.00782367	−	0.0107684i
$262$	1.39313	−	0.709837i	0.0860681	−	0.0438539i
$263$	17.4405	+	17.4405i	1.07543	+	1.07543i	0.996913	+	0.0785172i	$0.0250185\pi$
$263$	17.4405	+	17.4405i	1.07543	+	1.07543i	0.0785172	+	0.996913i	$0.474981\pi$
$264$	−3.85210	−	3.83411i	−0.237080	−	0.235973i
$265$		0			0
$266$	3.67341	+	1.19356i	0.225231	+	0.0731820i
$267$	18.1442	+	2.87375i	1.11040	+	0.175871i
$268$	−5.34459	+	0.846501i	−0.326473	+	0.0517083i
$269$	−19.3677	+	6.29294i	−1.18087	+	0.383687i	−0.832689	−	0.553741i	$-0.813200\pi$
$269$	−19.3677	+	6.29294i	−1.18087	+	0.383687i	−0.348179	+	0.937428i	$0.613200\pi$
$270$		0			0
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	−0.654853	−	0.755756i	$-0.727269\pi$
$271$	4.38344	−	6.03328i	0.266275	−	0.366496i	0.921128	+	0.389261i	$0.127269\pi$
$272$	0.226552	−	1.43039i	0.0137367	−	0.0867302i
$273$	0.484159	+	0.950215i	0.0293026	+	0.0575096i
$274$	−1.68793			−0.101972
$275$		0			0
$276$	−3.83700			−0.230960
$277$	7.43406	+	14.5902i	0.446669	+	0.876638i	0.999072	+	0.0430609i	$0.0137110\pi$
$277$	7.43406	+	14.5902i	0.446669	+	0.876638i	−0.552403	+	0.833577i	$0.686289\pi$
$278$	1.35731	−	8.56972i	0.0814061	−	0.513978i
$279$	−0.651141	+	0.896219i	−0.0389828	+	0.0536552i
$280$		0			0
$281$	3.98244	−	1.29397i	0.237572	−	0.0771919i	−0.187811	−	0.982205i	$-0.560139\pi$
$281$	3.98244	−	1.29397i	0.237572	−	0.0771919i	0.425383	+	0.905013i	$0.360139\pi$
$282$	−20.5431	+	3.25371i	−1.22332	+	0.193755i
$283$	27.3003	+	4.32395i	1.62284	+	0.257032i	0.900611	−	0.434626i	$-0.143119\pi$
$283$	27.3003	+	4.32395i	1.62284	+	0.257032i	0.722225	+	0.691658i	$0.243119\pi$
$284$	7.55864	+	2.45595i	0.448523	+	0.145734i
$285$		0			0
$286$	2.51901	−	1.29093i	0.148952	−	0.0763345i
$287$	6.70114	+	6.70114i	0.395556	+	0.395556i
$288$	−0.280334	+	0.142837i	−0.0165188	+	0.00841677i
$289$	−8.75956	−	12.0565i	−0.515268	−	0.709206i
$290$		0			0
$291$	7.20436	+	22.1727i	0.422327	+	1.29979i
$292$	−1.01986	−	0.519644i	−0.0596827	−	0.0304099i
$293$	2.92476	+	18.4662i	0.170866	+	1.07881i	0.912822	+	0.408357i	$0.133898\pi$
$293$	2.92476	+	18.4662i	0.170866	+	1.07881i	−0.741956	+	0.670448i	$0.766102\pi$
$294$	−8.50932	+	6.18238i	−0.496274	+	0.360564i
$295$		0			0
$296$			8.11735i			0.471812i
$297$	−10.6230	−	14.5496i	−0.616409	−	0.844253i
$298$	−10.4236	+	10.4236i	−0.603824	+	0.603824i
$299$	0.617509	−	1.90050i	0.0357115	−	0.109909i
$300$		0			0
$301$	6.64166	+	4.82545i	0.382819	+	0.278134i
$302$	5.19760	−	10.2009i	0.299088	−	0.586994i
$303$	6.97200	−	13.6833i	0.400531	−	0.786086i
$304$	4.09783	+	2.97724i	0.235026	+	0.170757i
$305$		0			0
$306$	0.140803	−	0.433347i	0.00804918	−	0.0247728i
$307$	−7.13262	+	7.13262i	−0.407080	+	0.407080i	−0.880719	−	0.473639i	$-0.842940\pi$
$307$	−7.13262	+	7.13262i	−0.407080	+	0.407080i	0.473639	+	0.880719i	$0.342940\pi$
$308$	−1.49134	−	2.04259i	−0.0849771	−	0.116387i
$309$		−	0.161991i		−	0.00921537i
$310$		0			0
$311$	18.5344	−	13.4660i	1.05099	−	0.763589i	0.0785899	−	0.996907i	$-0.474958\pi$
$311$	18.5344	−	13.4660i	1.05099	−	0.763589i	0.972401	+	0.233318i	$0.0749582\pi$
$312$	0.218779	+	1.38132i	0.0123859	+	0.0782018i
$313$	−12.9044	−	6.57514i	−0.729402	−	0.371649i	0.0495173	−	0.998773i	$-0.484232\pi$
$313$	−12.9044	−	6.57514i	−0.729402	−	0.371649i	−0.778919	+	0.627125i	$0.784232\pi$
$314$	0.254714	+	0.783928i	0.0143743	+	0.0442396i
$315$		0			0
$316$	5.92927	+	8.16094i	0.333547	+	0.459089i
$317$	1.99314	−	1.01556i	0.111946	−	0.0570393i	−0.397121	−	0.917766i	$-0.629991\pi$
$317$	1.99314	−	1.01556i	0.111946	−	0.0570393i	0.509067	+	0.860727i	$0.329991\pi$
$318$	−9.51676	−	9.51676i	−0.533673	−	0.533673i
$319$	2.01732	−	1.03383i	0.112948	−	0.0578834i
$320$		0			0
$321$	−10.1749	−	3.30603i	−0.567909	−	0.184525i
$322$	−1.76350	−	0.279311i	−0.0982762	−	0.0155654i
$323$	−7.24520	+	1.14753i	−0.403134	+	0.0638501i
$324$	7.56768	−	2.45889i	0.420427	−	0.136605i
$325$		0			0
$326$	−5.25310	+	7.23027i	−0.290942	+	0.400447i
$327$	−3.02815	+	19.1190i	−0.167457	+	1.05728i
$328$	5.64213	+	11.0733i	0.311535	+	0.611421i
$329$	−9.67856			−0.533596
$330$		0			0
$331$	1.96672			0.108101			0.0540503	−	0.998538i	$-0.482787\pi$
$331$	1.96672			0.108101			0.0540503	+	0.998538i	$0.482787\pi$
$332$	0.108440	+	0.212826i	0.00595143	+	0.0116803i
$333$	−0.399523	+	2.52249i	−0.0218937	+	0.138232i
$334$	−12.4169	+	17.0904i	−0.679422	+	0.935144i
$335$		0			0
$336$	1.18844	−	0.386146i	0.0648345	−	0.0210660i
$337$	0.400422	−	0.0634205i	0.0218123	−	0.00345474i	−0.145519	−	0.989355i	$-0.546485\pi$
$337$	0.400422	−	0.0634205i	0.0218123	−	0.00345474i	0.167331	+	0.985901i	$0.446485\pi$
$338$	12.1206	+	1.91971i	0.659272	+	0.104418i
$339$	17.9665	+	5.83766i	0.975805	+	0.317058i
$340$		0			0
$341$	−8.27669	−	8.23804i	−0.448208	−	0.446115i
$342$	1.12687	+	1.12687i	0.0609344	+	0.0609344i
$343$	−9.11701	+	4.64535i	−0.492272	+	0.250825i
$344$	6.32806	+	8.70983i	0.341186	+	0.469602i
$345$		0			0
$346$	0.759756	+	2.33829i	0.0408447	+	0.125707i
$347$	−9.52619	−	4.85384i	−0.511393	−	0.260568i	0.179198	−	0.983813i	$-0.442650\pi$
$347$	−9.52619	−	4.85384i	−0.511393	−	0.260568i	−0.690591	+	0.723245i	$0.742650\pi$
$348$	0.175207	+	1.10621i	0.00939209	+	0.0592993i
$349$	−6.50852	+	4.72872i	−0.348393	+	0.253123i	−0.748195	−	0.663479i	$-0.769079\pi$
$349$	−6.50852	+	4.72872i	−0.348393	+	0.253123i	0.399801	+	0.916602i	$0.369079\pi$
$350$		0			0
$351$			4.63563i			0.247432i
$352$	−1.03227	−	3.15189i	−0.0550203	−	0.167996i
$353$	−17.8934	+	17.8934i	−0.952372	+	0.952372i	−0.998916	−	0.0465446i	$-0.985179\pi$
$353$	−17.8934	+	17.8934i	−0.952372	+	0.952372i	0.0465446	+	0.998916i	$0.485179\pi$
$354$	0.219127	−	0.674404i	0.0116465	−	0.0358442i
$355$		0			0
$356$	9.06926	+	6.58921i	0.480670	+	0.349227i
$357$	−0.821582	+	1.61245i	−0.0434828	+	0.0853397i
$358$	7.22542	−	14.1807i	0.381875	−	0.749473i
$359$	−13.1469	−	9.55175i	−0.693864	−	0.504122i	0.184064	−	0.982914i	$-0.441075\pi$
$359$	−13.1469	−	9.55175i	−0.693864	−	0.504122i	−0.877928	+	0.478792i	$0.841075\pi$
$360$		0			0
$361$	2.05687	−	6.33038i	0.108256	−	0.333178i
$362$	−3.64046	+	3.64046i	−0.191338	+	0.191338i
$363$	16.0226	−	8.25863i	0.840971	−	0.433466i
$364$			0.650787i			0.0341105i
$365$		0			0
$366$	16.8150	−	12.2168i	0.878933	−	0.638582i
$367$	−1.34090	−	8.46611i	−0.0699944	−	0.441927i	−0.997652	−	0.0684942i	$-0.978181\pi$
$367$	−1.34090	−	8.46611i	−0.0699944	−	0.441927i	0.927657	−	0.373433i	$-0.121819\pi$
$368$	−2.08627	−	1.06301i	−0.108754	−	0.0554131i
$369$	1.20830	+	3.71876i	0.0629015	+	0.193591i
$370$		0			0
$371$	−3.68118	−	5.06672i	−0.191118	−	0.263051i
$372$	5.14097	−	2.61945i	0.266547	−	0.135812i
$373$	−23.2440	−	23.2440i	−1.20353	−	1.20353i	−0.973085	−	0.230446i	$-0.925982\pi$
$373$	−23.2440	−	23.2440i	−1.20353	−	1.20353i	−0.230446	−	0.973085i	$-0.574018\pi$
$374$	4.28478	+	2.17059i	0.221561	+	0.112238i
$375$		0			0
$376$	−12.0712	−	3.92217i	−0.622524	−	0.202270i
$377$	−0.576114	−	0.0912475i	−0.0296714	−	0.00469949i
$378$	4.09095	−	0.647942i	0.210416	−	0.0333266i
$379$	−12.1822	+	3.95823i	−0.625757	+	0.203321i	−0.604695	−	0.796457i	$-0.706705\pi$
$379$	−12.1822	+	3.95823i	−0.625757	+	0.203321i	−0.0210622	+	0.999778i	$0.506705\pi$
$380$		0			0
$381$	−6.25162	+	8.60462i	−0.320280	+	0.440828i
$382$	4.20743	−	26.5647i	0.215271	−	1.35917i
$383$	−10.1184	−	19.8586i	−0.517028	−	1.01473i	−0.990959	−	0.134163i	$-0.957165\pi$
$383$	−10.1184	−	19.8586i	−0.517028	−	1.01473i	0.473931	−	0.880562i	$-0.342835\pi$
$384$	1.63871			0.0836251
$385$		0			0
$386$	−9.68504			−0.492955
$387$	1.53778	+	3.01806i	0.0781696	+	0.153417i
$388$	−2.22558	+	14.0518i	−0.112987	+	0.713370i
$389$	8.06422	−	11.0995i	0.408872	−	0.562765i	−0.554071	−	0.832470i	$-0.686926\pi$
$389$	8.06422	−	11.0995i	0.408872	−	0.562765i	0.962943	+	0.269705i	$0.0869262\pi$
$390$		0			0
$391$	3.22501	−	1.04787i	0.163096	−	0.0529930i
$392$	−6.33950	+	1.00408i	−0.320193	+	0.0507136i
$393$	−2.53066	−	0.400817i	−0.127655	−	0.0202186i
$394$	−8.02222	−	2.60658i	−0.404154	−	0.131318i
$395$		0			0
$396$	−0.165650	−	1.03027i	−0.00832425	−	0.0517728i
$397$	0.807418	+	0.807418i	0.0405232	+	0.0405232i	0.727078	−	0.686555i	$-0.240878\pi$
$397$	0.807418	+	0.807418i	0.0405232	+	0.0405232i	−0.686555	+	0.727078i	$0.740878\pi$
$398$	−0.736760	+	0.375398i	−0.0369304	+	0.0188170i
$399$	−3.72035	−	5.12062i	−0.186251	−	0.256352i
$400$		0			0
$401$	4.25930	+	13.1088i	0.212700	+	0.654622i	0.999309	+	0.0371709i	$0.0118346\pi$
$401$	4.25930	+	13.1088i	0.212700	+	0.654622i	−0.786609	+	0.617451i	$0.788165\pi$
$402$	7.90093	+	4.02572i	0.394062	+	0.200785i
$403$	0.470073	+	2.96793i	0.0234160	+	0.147843i
$404$	7.58169	−	5.50842i	0.377203	−	0.274054i
$405$		0			0
$406$			0.521176i			0.0258655i
$407$	−25.6239	−	8.25948i	−1.27013	−	0.409407i
$408$	−1.67812	+	1.67812i	−0.0830792	+	0.0830792i
$409$	6.24805	−	19.2295i	0.308946	−	0.950839i	−0.669229	−	0.743056i	$-0.733375\pi$
$409$	6.24805	−	19.2295i	0.308946	−	0.950839i	0.978175	−	0.207782i	$-0.0666246\pi$
$410$		0			0
$411$	2.23777	+	1.62584i	0.110381	+	0.0801966i
$412$	0.0448783	−	0.0880786i	0.00221099	−	0.00433932i
$413$	0.149805	−	0.294008i	0.00737140	−	0.0144672i
$414$	−0.595994	−	0.433015i	−0.0292915	−	0.0212815i
$415$		0			0
$416$	−0.263727	+	0.811667i	−0.0129303	+	0.0397953i
$417$	−10.0539	+	10.0539i	−0.492341	+	0.492341i
$418$	−13.5678	+	9.90618i	−0.663623	+	0.484527i
$419$			19.4960i			0.952442i	0.879326	+	0.476221i	$0.157994\pi$
$419$			19.4960i			0.952442i	−0.879326	+	0.476221i	$0.842006\pi$
$420$		0			0
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	−0.642720	−	0.766101i	$-0.722194\pi$
$421$	−2.31295	+	1.68045i	−0.112726	+	0.0819003i	0.529994	+	0.848001i	$0.322194\pi$
$422$	2.27849	+	14.3858i	0.110915	+	0.700290i
$423$	−3.55811	−	1.81295i	−0.173001	−	0.0881485i
$424$	−2.53796	−	7.81103i	−0.123254	−	0.379337i
$425$		0			0
$426$	−7.65523	−	10.5365i	−0.370897	−	0.510496i
$427$	8.61756	−	4.39087i	0.417033	−	0.212489i
$428$	−4.61644	−	4.61644i	−0.223144	−	0.223144i
$429$	−4.58300	−	0.714886i	−0.221269	−	0.0345150i
$430$		0			0
$431$	−15.3238	−	4.97899i	−0.738120	−	0.239830i	−0.0842582	−	0.996444i	$-0.526852\pi$
$431$	−15.3238	−	4.97899i	−0.738120	−	0.239830i	−0.653861	+	0.756614i	$0.726852\pi$
$432$	5.36484	+	0.849707i	0.258116	+	0.0408816i
$433$	24.1225	−	3.82063i	1.15925	−	0.183608i	0.452963	−	0.891529i	$-0.350367\pi$
$433$	24.1225	−	3.82063i	1.15925	−	0.183608i	0.706291	+	0.707922i	$0.250367\pi$
$434$	2.55349	−	0.829681i	0.122572	−	0.0398259i
$435$		0			0
$436$	−6.94322	+	9.55652i	−0.332520	+	0.457674i
$437$	−1.85531	+	11.7140i	−0.0887517	+	0.560356i
$438$	0.851547	+	1.67125i	0.0406885	+	0.0798556i
$439$	−13.2566			−0.632702			−0.316351	−	0.948642i	$-0.602458\pi$
$439$	−13.2566			−0.632702			−0.316351	+	0.948642i	$0.602458\pi$
$440$		0			0
$441$	−2.01944			−0.0961636
$442$	−0.561117	−	1.10125i	−0.0266896	−	0.0523813i
$443$	0.340637	−	2.15069i	0.0161841	−	0.102183i	−0.978274	−	0.207316i	$-0.933527\pi$
$443$	0.340637	−	2.15069i	0.0161841	−	0.102183i	0.994458	+	0.105134i	$0.0335271\pi$
$444$	7.81872	−	10.7615i	0.371060	−	0.510720i
$445$		0			0
$446$	−1.28005	+	0.415913i	−0.0606121	+	0.0196941i
$447$	23.8592	−	3.77893i	1.12850	−	0.178737i
$448$	0.753160	+	0.119289i	0.0355834	+	0.00563586i
$449$	−4.58948	−	1.49121i	−0.216591	−	0.0703747i	0.198712	−	0.980058i	$-0.436324\pi$
$449$	−4.58948	−	1.49121i	−0.216591	−	0.0703747i	−0.415303	+	0.909683i	$0.636324\pi$
$450$		0			0
$451$	−40.6959	+	6.54326i	−1.91630	+	0.308110i
$452$	8.15153	+	8.15153i	0.383416	+	0.383416i
$453$	−16.7163	+	8.51736i	−0.785399	+	0.400181i
$454$	1.20620	+	1.66019i	0.0566096	+	0.0779164i
$455$		0			0
$456$	−2.56496	−	7.89413i	−0.120115	−	0.369677i
$457$	−18.2443	−	9.29594i	−0.853433	−	0.434846i	−0.0281758	−	0.999603i	$-0.508970\pi$
$457$	−18.2443	−	9.29594i	−0.853433	−	0.434846i	−0.825257	+	0.564757i	$0.808970\pi$
$458$	−2.80391	−	17.7032i	−0.131018	−	0.827215i
$459$	−6.36399	+	4.62371i	−0.297046	+	0.215816i
$460$		0			0
$461$			0.616244i			0.0287013i	0.999897	+	0.0143507i	$0.00456812\pi$
$461$			0.616244i			0.0287013i	−0.999897	+	0.0143507i	$0.995432\pi$
$462$	0.00969884	+	4.14443i	0.000451231	+	0.192816i
$463$	13.5983	−	13.5983i	0.631968	−	0.631968i	−0.316593	−	0.948561i	$-0.602539\pi$
$463$	13.5983	−	13.5983i	0.631968	−	0.631968i	0.948561	+	0.316593i	$0.102539\pi$
$464$	−0.211203	+	0.650015i	−0.00980484	+	0.0301762i
$465$		0			0
$466$	−19.8886	−	14.4499i	−0.921323	−	0.669380i
$467$	−0.705649	+	1.38491i	−0.0326535	+	0.0640862i	−0.906757	−	0.421654i	$-0.861450\pi$
$467$	−0.705649	+	1.38491i	−0.0326535	+	0.0640862i	0.874103	+	0.485740i	$0.161450\pi$
$468$	−0.121903	+	0.239248i	−0.00563495	+	0.0110592i
$469$	3.33825	+	2.42538i	0.154146	+	0.111994i
$470$		0			0
$471$	0.417402	−	1.28463i	0.0192329	−	0.0591927i
$472$	0.305982	−	0.305982i	0.0140840	−	0.0140840i
$473$	−33.9331	+	11.1134i	−1.56024	+	0.510994i
$474$		−	16.5305i		−	0.759269i
$475$		0			0
$476$	−0.893428	+	0.649114i	−0.0409502	+	0.0297521i
$477$	−0.404231	−	2.55221i	−0.0185084	−	0.116858i
$478$	−2.64401	−	1.34719i	−0.120934	−	0.0616191i
$479$	7.47583	+	23.0082i	0.341579	+	1.05127i	0.963390	+	0.268105i	$0.0863975\pi$
$479$	7.47583	+	23.0082i	0.341579	+	1.05127i	−0.621810	+	0.783168i	$0.713603\pi$
$480$		0			0
$481$	4.07197	+	5.60459i	0.185666	+	0.255547i
$482$	18.9658	−	9.66356i	0.863869	−	0.440163i
$483$	2.06892	+	2.06892i	0.0941391	+	0.0941391i
$484$	10.9999	−	0.0514844i	0.499995	−	0.00234020i
$485$		0			0
$486$	3.09636	+	1.00607i	0.140454	+	0.0456362i
$487$	18.5340	+	2.93550i	0.839857	+	0.133020i	0.561520	−	0.827463i	$-0.310217\pi$
$487$	18.5340	+	2.93550i	0.839857	+	0.133020i	0.278337	+	0.960483i	$0.410217\pi$
$488$	12.5273	−	1.98412i	0.567083	−	0.0898171i
$489$	13.9285	−	4.52565i	0.629870	−	0.204657i
$490$		0			0
$491$	14.9190	−	20.5343i	0.673285	−	0.926698i	−0.326544	−	0.945182i	$-0.605884\pi$
$491$	14.9190	−	20.5343i	0.673285	−	0.926698i	0.999829	+	0.0184843i	$0.00588406\pi$
$492$	3.18590	−	20.1150i	0.143631	−	0.906852i
$493$	−0.449365	−	0.881928i	−0.0202384	−	0.0397200i
$494$	4.32282			0.194493
$495$		0			0
$496$	3.52096			0.158096
$497$	−2.75138	−	5.39989i	−0.123416	−	0.242218i
$498$	0.0612320	−	0.386603i	0.00274387	−	0.0173241i
$499$	5.36524	−	7.38462i	0.240181	−	0.330581i	−0.671861	−	0.740677i	$-0.734505\pi$
$499$	5.36524	−	7.38462i	0.240181	−	0.330581i	0.912042	+	0.410096i	$0.134505\pi$
$500$		0			0
$501$	32.9232	−	10.6974i	1.47090	−	0.477925i
$502$	−13.1171	+	2.07755i	−0.585446	+	0.0927255i
$503$	−22.1939	−	3.51517i	−0.989577	−	0.156734i	−0.359399	−	0.933184i	$-0.617018\pi$
$503$	−22.1939	−	3.51517i	−0.989577	−	0.156734i	−0.630178	+	0.776451i	$0.717018\pi$
$504$	0.228175	+	0.0741386i	0.0101637	+	0.00330240i
$505$		0			0
$506$	5.47838	−	5.50408i	0.243544	−	0.244686i
$507$	−14.2197	−	14.2197i	−0.631519	−	0.631519i
$508$	−5.78299	+	2.94658i	−0.256579	+	0.130733i
$509$	16.8593	+	23.2049i	0.747276	+	1.02854i	0.998167	+	0.0605220i	$0.0192765\pi$
$509$	16.8593	+	23.2049i	0.747276	+	1.02854i	−0.250891	+	0.968015i	$0.580723\pi$
$510$		0			0
$511$	0.269717	+	0.830104i	0.0119316	+	0.0367217i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−4.30393	−	27.1739i	−0.190023	−	1.19976i
$514$	−14.9743	+	10.8794i	−0.660486	+	0.479871i
$515$		0			0
$516$		−	17.6423i		−	0.776657i
$517$	24.6636	−	34.1141i	1.08470	−	1.50034i
$518$	4.37690	−	4.37690i	0.192310	−	0.192310i
$519$	1.24502	−	3.83178i	0.0546503	−	0.168196i
$520$		0			0
$521$	−27.5311	−	20.0025i	−1.20616	−	0.876325i	−0.211282	−	0.977425i	$-0.567764\pi$
$521$	−27.5311	−	20.0025i	−1.20616	−	0.876325i	−0.994876	+	0.101100i	$0.967764\pi$
$522$	−0.0976245	+	0.191599i	−0.00427291	+	0.00838605i
$523$	−12.9583	+	25.4321i	−0.566628	+	1.11207i	0.412903	+	0.910775i	$0.364515\pi$
$523$	−12.9583	+	25.4321i	−0.566628	+	1.11207i	−0.979531	+	0.201295i	$0.935485\pi$
$524$	−1.26494	−	0.919032i	−0.0552591	−	0.0401481i
$525$		0			0
$526$	7.62180	−	23.4575i	0.332326	−	1.02279i
$527$	−3.60563	+	3.60563i	−0.157064	+	0.157064i
$528$	−1.66740	+	5.17290i	−0.0725644	+	0.225122i
$529$			17.5175i			0.761630i
$530$		0			0
$531$	0.110145	−	0.0800249i	0.00477988	−	0.00347278i
$532$	−0.604220	−	3.81490i	−0.0261963	−	0.165397i
$533$	9.45038	+	4.81521i	0.409341	+	0.208570i
$534$	−5.67674	−	17.4712i	−0.245657	−	0.756053i
$535$		0			0
$536$	3.18063	+	4.37777i	0.137382	+	0.189091i
$537$	−23.2380	+	11.8404i	−1.00280	+	0.510950i
$538$	14.3998	+	14.3998i	0.620819	+	0.620819i
$539$	3.28094	−	21.0335i	0.141320	−	0.905976i
$540$		0			0
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.858151	−	0.513398i	$-0.171613\pi$
$541$	29.0892	+	9.45165i	1.25064	+	0.406358i	0.392491	+	0.919756i	$0.371613\pi$
$542$	−7.36573	−	1.16662i	−0.316385	−	0.0501105i
$543$	8.33284	−	1.31979i	0.357596	−	0.0566377i
$544$	−1.37734	+	0.447525i	−0.0590530	+	0.0191875i
$545$		0			0
$546$	0.626844	−	0.862777i	0.0268265	−	0.0369235i
$547$	−0.0192582	+	0.121591i	−0.000823420	+	0.00519887i	−0.988097	−	0.153834i	$-0.950838\pi$
$547$	−0.0192582	+	0.121591i	−0.000823420	+	0.00519887i	0.987273	+	0.159033i	$0.0508377\pi$
$548$	0.766306	+	1.50396i	0.0327350	+	0.0642460i
$549$	3.99054			0.170312
$550$		0			0
$551$	3.46189			0.147481
$552$	1.74196	+	3.41879i	0.0741428	+	0.145513i
$553$	1.20332	−	7.59748i	0.0511705	−	0.323078i
$554$	9.62494	−	13.2476i	0.408924	−	0.562836i
$555$		0			0
$556$	−8.25188	+	2.68120i	−0.349958	+	0.113708i
$557$	35.5695	−	5.63365i	1.50713	−	0.238705i	0.652436	−	0.757844i	$-0.273747\pi$
$557$	35.5695	−	5.63365i	1.50713	−	0.238705i	0.854690	+	0.519138i	$0.173747\pi$
$558$	1.09415	+	0.173296i	0.0463190	+	0.00733621i
$559$	8.73836	+	2.83926i	0.369593	+	0.120088i
$560$		0			0
$561$	−3.58979	−	7.00479i	−0.151561	−	0.295743i
$562$	−2.96093	−	2.96093i	−0.124899	−	0.124899i
$563$	−10.5592	+	5.38016i	−0.445015	+	0.226747i	−0.662114	−	0.749403i	$-0.730341\pi$
$563$	−10.5592	+	5.38016i	−0.445015	+	0.226747i	0.217099	+	0.976150i	$0.430341\pi$
$564$	12.2254	+	16.8269i	0.514784	+	0.708539i
$565$		0			0
$566$	−8.54143	−	26.2878i	−0.359023	−	1.10496i
$567$	−5.40635	−	2.75467i	−0.227046	−	0.115685i
$568$	−1.24328	−	7.84977i	−0.0521669	−	0.329369i
$569$	28.8735	−	20.9778i	1.21044	−	0.879435i	0.215168	−	0.976577i	$-0.430970\pi$
$569$	28.8735	−	20.9778i	1.21044	−	0.879435i	0.995270	+	0.0971424i	$0.0309702\pi$
$570$		0			0
$571$		−	31.2536i		−	1.30792i	−0.756528	−	0.653961i	$-0.773106\pi$
$571$		−	31.2536i		−	1.30792i	0.756528	−	0.653961i	$-0.226894\pi$
$572$	−2.29384	−	1.65838i	−0.0959101	−	0.0693404i
$573$	−31.1653	+	31.1653i	−1.30195	+	1.30195i
$574$	2.92851	−	9.01301i	0.122233	−	0.376196i
$575$		0			0
$576$	0.254538	+	0.184933i	0.0106057	+	0.00770553i
$577$	−20.9695	+	41.1550i	−0.872972	+	1.71330i	−0.191454	+	0.981502i	$0.561320\pi$
$577$	−20.9695	+	41.1550i	−0.872972	+	1.71330i	−0.681518	+	0.731801i	$0.738680\pi$
$578$	−6.76566	+	13.2784i	−0.281415	+	0.552307i
$579$	12.8399	+	9.32873i	0.533608	+	0.387689i
$580$		0			0
$581$	0.0562850	−	0.173227i	0.00233510	−	0.00718668i
$582$	16.4854	−	16.4854i	0.683340	−	0.683340i
$583$	27.2394	−	0.0637459i	1.12814	−	0.00264009i
$584$			1.14461i			0.0473645i
$585$		0			0
$586$	15.1257	−	10.9894i	0.624836	−	0.453970i
$587$	4.82637	+	30.4725i	0.199205	+	1.25773i	0.861216	+	0.508239i	$0.169703\pi$
$587$	4.82637	+	30.4725i	0.199205	+	1.25773i	−0.662011	+	0.749494i	$0.730297\pi$
$588$	9.37170	+	4.77512i	0.386482	+	0.196923i
$589$	−5.51112	−	16.9615i	−0.227082	−	0.698885i
$590$		0			0
$591$	8.12474	+	11.1827i	0.334207	+	0.459997i
$592$	7.23261	−	3.68520i	0.297259	−	0.151461i
$593$	−3.14365	−	3.14365i	−0.129094	−	0.129094i	0.639607	−	0.768702i	$-0.279097\pi$
$593$	−3.14365	−	3.14365i	−0.129094	−	0.129094i	−0.768702	+	0.639607i	$0.779097\pi$
$594$	−8.14103	+	16.0705i	−0.334031	+	0.659382i
$595$		0			0
$596$	14.0197	+	4.55529i	0.574271	+	0.186592i
$597$	1.33834	+	0.211973i	0.0547747	+	0.00867547i
$598$	−1.97370	+	0.312603i	−0.0807105	+	0.0127833i
$599$	8.63991	−	2.80728i	0.353017	−	0.114702i	−0.127140	−	0.991885i	$-0.540580\pi$
$599$	8.63991	−	2.80728i	0.353017	−	0.114702i	0.480157	+	0.877183i	$0.340580\pi$
$600$		0			0
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	0.284705	+	0.958615i	$0.408105\pi$
$601$	−17.5277	+	24.1249i	−0.714971	+	0.984074i	−0.999676	+	0.0254583i	$0.991895\pi$
$602$	1.28426	−	8.10847i	0.0523423	−	0.330476i
$603$	0.772923	+	1.51695i	0.0314759	+	0.0617749i
$604$	−11.4487			−0.465841
$605$		0			0
$606$	−15.3572			−0.623842
$607$	−9.38932	−	18.4276i	−0.381101	−	0.747952i	0.618174	−	0.786041i	$-0.287873\pi$
$607$	−9.38932	−	18.4276i	−0.381101	−	0.747952i	−0.999274	+	0.0380895i	$0.987873\pi$
$608$	0.792370	−	5.00283i	0.0321349	−	0.202892i
$609$	0.502002	−	0.690946i	0.0203421	−	0.0279985i
$610$		0			0
$611$	−10.3020	+	3.34732i	−0.416774	+	0.135418i
$612$	−0.450039	+	0.0712791i	−0.0181917	+	0.00288129i
$613$	12.4538	+	1.97249i	0.503005	+	0.0796682i	0.402780	−	0.915297i	$-0.368044\pi$
$613$	12.4538	+	1.97249i	0.503005	+	0.0796682i	0.100225	+	0.994965i	$0.468044\pi$
$614$	9.59336	+	3.11707i	0.387156	+	0.125795i
$615$		0			0
$616$	−1.14290	+	2.25611i	−0.0460489	+	0.0909013i
$617$	−6.47501	−	6.47501i	−0.260674	−	0.260674i	0.564654	−	0.825328i	$-0.309010\pi$
$617$	−6.47501	−	6.47501i	−0.260674	−	0.260674i	−0.825328	+	0.564654i	$0.809010\pi$
$618$	−0.144335	+	0.0735426i	−0.00580602	+	0.00295832i
$619$	−23.3769	−	32.1756i	−0.939598	−	1.29325i	−0.955996	−	0.293380i	$-0.905220\pi$
$619$	−23.3769	−	32.1756i	−0.939598	−	1.29325i	0.0163985	−	0.999866i	$-0.494780\pi$
$620$		0			0
$621$	3.93015	+	12.0957i	0.157711	+	0.485385i
$622$	−20.4128	−	10.4008i	−0.818478	−	0.417035i
$623$	−1.33725	−	8.44309i	−0.0535759	−	0.338265i
$624$	1.13144	−	0.822040i	0.0452939	−	0.0329079i
$625$		0			0
$626$			14.4830i			0.578857i
$627$	27.5292	−	0.0644241i	1.09941	−	0.00257285i
$628$	0.582847	−	0.582847i	0.0232581	−	0.0232581i
$629$	−3.63272	+	11.1804i	−0.144846	+	0.445790i
$630$		0			0
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	0.0667657	−	0.997769i	$-0.478732\pi$
$631$	−21.6416	−	15.7235i	−0.861537	−	0.625943i	−0.928303	+	0.371825i	$0.878732\pi$
$632$	4.57962	−	8.98801i	0.182167	−	0.357524i
$633$	10.8359	−	21.2666i	0.430687	−	0.845271i
$634$	−1.80973	−	1.31485i	−0.0718737	−	0.0522193i
$635$		0			0
$636$	−4.15898	+	12.8000i	−0.164914	+	0.507554i
$637$	−3.87339	+	3.87339i	−0.153469	+	0.153469i
$638$	−1.83699	−	1.32810i	−0.0727273	−	0.0525799i
$639$		−	2.50053i		−	0.0989194i
$640$		0			0
$641$	−10.9993	+	7.99147i	−0.434447	+	0.315644i	−0.783425	−	0.621487i	$-0.786529\pi$
$641$	−10.9993	+	7.99147i	−0.434447	+	0.315644i	0.348978	+	0.937131i	$0.386529\pi$
$642$	1.67362	+	10.5668i	0.0660526	+	0.417040i
$643$	−16.4511	−	8.38228i	−0.648770	−	0.330565i	0.0984497	−	0.995142i	$-0.468612\pi$
$643$	−16.4511	−	8.38228i	−0.648770	−	0.330565i	−0.747220	+	0.664577i	$0.768612\pi$
$644$	0.551745	+	1.69810i	0.0217418	+	0.0669144i
$645$		0			0
$646$	4.31171	+	5.93456i	0.169642	+	0.233492i
$647$	−16.0422	+	8.17393i	−0.630686	+	0.321350i	−0.739950	−	0.672662i	$-0.765151\pi$
$647$	−16.0422	+	8.17393i	−0.630686	+	0.321350i	0.109264	+	0.994013i	$0.465151\pi$
$648$	−5.62654	−	5.62654i	−0.221031	−	0.221031i
$649$	0.654551	+	1.27723i	0.0256934	+	0.0501357i
$650$		0			0
$651$	−4.18444	−	1.35961i	−0.164001	−	0.0532872i
$652$	8.82707	+	1.39807i	0.345695	+	0.0547527i
$653$	26.2280	−	4.15411i	1.02638	−	0.162563i	0.379531	−	0.925179i	$-0.376086\pi$
$653$	26.2280	−	4.15411i	1.02638	−	0.162563i	0.646851	+	0.762616i	$0.276086\pi$
$654$	18.4099	−	5.98173i	0.719883	−	0.233904i
$655$		0			0
$656$	7.30492	−	10.0544i	0.285209	−	0.392557i
$657$	−0.0563361	+	0.355692i	−0.00219788	+	0.0138769i
$658$	4.39397	+	8.62366i	0.171295	+	0.336185i
$659$	−36.6251			−1.42671			−0.713356	−	0.700802i	$-0.752826\pi$
$659$	−36.6251			−1.42671			−0.713356	+	0.700802i	$0.752826\pi$
$660$		0			0
$661$	7.39959			0.287811			0.143905	−	0.989591i	$-0.454034\pi$
$661$	7.39959			0.287811			0.143905	+	0.989591i	$0.454034\pi$
$662$	−0.892871	−	1.75236i	−0.0347024	−	0.0681073i
$663$	−0.316841	+	2.00046i	−0.0123051	+	0.0776912i
$664$	0.140398	−	0.193242i	0.00544851	−	0.00749923i
$665$		0			0
$666$	2.42893	−	0.789208i	0.0941193	−	0.0305812i
$667$	−1.58062	+	0.250345i	−0.0612017	+	0.00969339i
$668$	20.8648	+	3.30466i	0.807283	+	0.127861i
$669$	2.09763	+	0.681562i	0.0810991	+	0.0263507i
$670$		0			0
$671$	−6.48335	+	41.5635i	−0.250287	+	1.60454i
$672$	−0.883597	−	0.883597i	−0.0340855	−	0.0340855i
$673$	27.1875	−	13.8527i	1.04800	−	0.533983i	0.156818	−	0.987627i	$-0.449876\pi$
$673$	27.1875	−	13.8527i	1.04800	−	0.533983i	0.891183	+	0.453644i	$0.149876\pi$
$674$	−0.238296	−	0.327986i	−0.00917881	−	0.0126335i
$675$		0			0
$676$	−3.79215	−	11.6710i	−0.145852	−	0.448886i
$677$	26.6676	+	13.5878i	1.02492	+	0.522223i	0.883847	−	0.467776i	$-0.154945\pi$
$677$	26.6676	+	13.5878i	1.02492	+	0.522223i	0.141074	+	0.989999i	$0.454945\pi$
$678$	−2.95521	−	18.6585i	−0.113494	−	0.716575i
$679$	8.77679	−	6.37671i	0.336822	−	0.244716i
$680$		0			0
$681$		−	3.36280i		−	0.128863i
$682$	−3.58261	+	11.1146i	−0.137185	+	0.425599i
$683$	13.9351	−	13.9351i	0.533214	−	0.533214i	−0.388314	−	0.921527i	$-0.626942\pi$
$683$	13.9351	−	13.9351i	0.533214	−	0.533214i	0.921527	+	0.388314i	$0.126942\pi$
$684$	0.492462	−	1.51564i	0.0188298	−	0.0579521i
$685$		0			0
$686$	8.27807	+	6.01437i	0.316058	+	0.229630i
$687$	−13.3346	+	26.1706i	−0.508747	+	0.998472i
$688$	4.88763	−	9.59252i	0.186339	−	0.365711i
$689$	−5.67063	−	4.11995i	−0.216034	−	0.156958i
$690$		0			0
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	0.616827	+	0.787099i	$0.288418\pi$
$691$	−9.06481	+	27.8986i	−0.344841	+	1.06131i	−0.961669	+	0.274214i	$0.911582\pi$
$692$	1.73851	−	1.73851i	0.0660882	−	0.0660882i
$693$	−0.466203	+	0.644841i	−0.0177096	+	0.0244955i
$694$			10.6915i			0.405844i
$695$		0			0
$696$	0.906102	−	0.658322i	0.0343457	−	0.0249536i
$697$	2.81556	+	17.7767i	0.106647	+	0.673341i
$698$	7.16813	+	3.65234i	0.271318	+	0.138243i
$699$	12.4489	+	38.3139i	0.470862	+	1.44916i
$700$		0			0
$701$	4.36586	+	6.00910i	0.164896	+	0.226960i	0.883467	−	0.468494i	$-0.155203\pi$
$701$	4.36586	+	6.00910i	0.164896	+	0.226960i	−0.718570	+	0.695454i	$0.755203\pi$
$702$	4.13037	−	2.10453i	0.155891	−	0.0794304i
$703$	−29.0734	−	29.0734i	−1.09652	−	1.09652i
$704$	−2.33971	+	2.35069i	−0.0881813	+	0.0885950i
$705$		0			0
$706$	24.0666	+	7.81972i	0.905759	+	0.294299i
$707$	−7.05822	−	1.11791i	−0.265452	−	0.0420434i
$708$	−0.700380	+	0.110929i	−0.0263219	+	0.00416898i
$709$	−25.9291	+	8.42488i	−0.973788	+	0.316403i	−0.752344	−	0.658770i	$-0.771077\pi$
$709$	−25.9291	+	8.42488i	−0.973788	+	0.316403i	−0.221444	+	0.975173i	$0.571077\pi$
$710$		0			0
$711$	1.86550	−	2.56765i	0.0699619	−	0.0962942i
$712$	1.75367	−	11.0722i	0.0657214	−	0.414949i
$713$	3.74281	+	7.34567i	0.140169	+	0.275098i
$714$	1.80969			0.0677260
$715$		0			0
$716$	−15.9154			−0.594785
$717$	2.20766	+	4.33277i	0.0824464	+	0.161810i
$718$	−2.54212	+	16.0503i	−0.0948712	+	0.598993i
$719$	−1.00656	+	1.38541i	−0.0375383	+	0.0516670i	−0.827374	−	0.561652i	$-0.810166\pi$
$719$	−1.00656	+	1.38541i	−0.0375383	+	0.0516670i	0.789835	+	0.613319i	$0.210166\pi$
$720$		0			0
$721$	−0.0716907	+	0.0232937i	−0.00266990	+	0.000867504i
$722$	−6.57421	+	1.04125i	−0.244667	+	0.0387514i
$723$	−34.4519	−	5.45664i	−1.28128	−	0.202935i
$724$	4.89640	+	1.59094i	0.181973	+	0.0591267i
$725$		0			0
$726$	−14.6326	−	10.5269i	−0.543068	−	0.390691i
$727$	13.9556	+	13.9556i	0.517583	+	0.517583i	0.916839	−	0.399256i	$-0.130732\pi$
$727$	13.9556	+	13.9556i	0.517583	+	0.517583i	−0.399256	+	0.916839i	$0.630732\pi$
$728$	0.579855	−	0.295451i	0.0214909	−	0.0109501i
$729$	−17.1672	−	23.6286i	−0.635822	−	0.875133i
$730$		0			0
$731$	4.81803	+	14.8284i	0.178201	+	0.548447i
$732$	−18.5191	−	9.43595i	−0.684485	−	0.348763i
$733$	0.923038	+	5.82783i	0.0340932	+	0.215256i	0.998853	−	0.0478750i	$-0.0152449\pi$
$733$	0.923038	+	5.82783i	0.0340932	+	0.215256i	−0.964760	+	0.263131i	$0.915245\pi$
$734$	−6.93460	+	5.03828i	−0.255961	+	0.185966i
$735$		0			0
$736$			2.34147i			0.0863079i
$737$	−17.0556	+	5.58585i	−0.628250	+	0.205757i
$738$	2.76488	−	2.76488i	0.101777	−	0.101777i
$739$	10.0720	−	30.9985i	0.370505	−	1.14030i	−0.575956	−	0.817480i	$-0.695370\pi$
$739$	10.0720	−	30.9985i	0.370505	−	1.14030i	0.946461	−	0.322817i	$-0.104630\pi$
$740$		0			0
$741$	−5.73096	−	4.16379i	−0.210532	−	0.152961i
$742$	−2.84325	+	5.58020i	−0.104379	+	0.204856i
$743$	−19.3261	+	37.9296i	−0.709007	+	1.39150i	0.202113	+	0.979362i	$0.435219\pi$
$743$	−19.3261	+	37.9296i	−0.709007	+	1.39150i	−0.911120	+	0.412142i	$0.864781\pi$
$744$	−4.66790	−	3.39143i	−0.171134	−	0.124336i
$745$		0			0
$746$	−10.1580	+	31.2632i	−0.371911	+	1.14463i
$747$	0.0531402	−	0.0531402i	0.00194430	−	0.00194430i
$748$	−0.0112405	−	4.80319i	−0.000410993	−	0.175622i
$749$			4.97840i			0.181907i
$750$		0			0
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	−0.0983111	−	0.995156i	$-0.531344\pi$
$751$	22.4102	−	16.2819i	0.817758	−	0.594136i	0.916070	+	0.401019i	$0.131344\pi$
$752$	1.98553	+	12.5361i	0.0724047	+	0.457146i
$753$	19.3911	+	9.88024i	0.706650	+	0.360056i
$754$	0.180248	+	0.554747i	0.00656425	+	0.0202027i
$755$		0			0
$756$	−2.43457	−	3.35090i	−0.0885445	−	0.121871i
$757$	−14.2535	+	7.26251i	−0.518051	+	0.263960i	−0.693409	−	0.720544i	$-0.743892\pi$
$757$	−14.2535	+	7.26251i	−0.518051	+	0.263960i	0.175357	+	0.984505i	$0.443892\pi$
$758$	9.05740	+	9.05740i	0.328980	+	0.328980i
$759$	−12.5645	+	2.02018i	−0.456063	+	0.0733277i
$760$		0			0
$761$	6.47967	+	2.10537i	0.234888	+	0.0763197i	0.424096	−	0.905617i	$-0.360592\pi$
$761$	6.47967	+	2.10537i	0.234888	+	0.0763197i	−0.189208	+	0.981937i	$0.560592\pi$
$762$	10.5049	+	1.66382i	0.380554	+	0.0602738i
$763$	8.89670	−	1.40910i	0.322082	−	0.0510128i
$764$	−25.5794	+	8.31126i	−0.925431	+	0.300691i
$765$		0			0
$766$	−13.1004	+	18.0312i	−0.473338	+	0.651494i
$767$	0.0577717	−	0.364756i	0.00208602	−	0.0131706i
$768$	−0.743959	−	1.46010i	−0.0268453	−	0.0526869i
$769$	48.7563			1.75820			0.879098	−	0.476640i	$-0.158146\pi$
$769$	48.7563			1.75820			0.879098	+	0.476640i	$0.158146\pi$
$770$		0			0
$771$	30.3312			1.09235
$772$	4.39692	+	8.62943i	0.158248	+	0.310580i
$773$	−4.09258	+	25.8396i	−0.147200	+	0.929384i	0.797944	+	0.602731i	$0.205921\pi$
$773$	−4.09258	+	25.8396i	−0.147200	+	0.929384i	−0.945144	+	0.326653i	$0.894079\pi$
$774$	1.99097	−	2.74034i	0.0715641	−	0.0984995i
$775$		0			0
$776$	13.5306	−	4.39636i	0.485720	−	0.157820i
$777$	−10.0185	+	1.58678i	−0.359413	+	0.0569254i
$778$	−13.5508	−	2.14623i	−0.485818	−	0.0769461i
$779$	−59.8686	−	19.4525i	−2.14501	−	0.696957i
$780$		0			0
$781$	26.0443	+	4.06256i	0.931939	+	0.145370i
$782$	−2.39778	−	2.39778i	−0.0857444	−	0.0857444i
$783$	3.30777	−	1.68539i	0.118210	−	0.0602310i
$784$	3.77271	+	5.19269i	0.134740	+	0.185453i
$785$		0			0
$786$	0.791765	+	2.43680i	0.0282413	+	0.0869179i
$787$	−20.7757	−	10.5858i	−0.740574	−	0.377341i	0.0426425	−	0.999090i	$-0.486422\pi$
$787$	−20.7757	−	10.5858i	−0.740574	−	0.377341i	−0.783217	+	0.621749i	$0.786422\pi$
$788$	1.31953	+	8.33122i	0.0470065	+	0.296787i
$789$	−32.6990	+	23.7572i	−1.16412	+	0.845780i
$790$		0			0
$791$		−	8.79065i		−	0.312560i
$792$	−0.842769	+	0.615326i	−0.0299465	+	0.0218647i
$793$	7.65408	−	7.65408i	0.271804	−	0.271804i
$794$	0.352855	−	1.08598i	0.0125223	−	0.0385398i
$795$		0			0
$796$	0.668964	+	0.486031i	0.0237108	+	0.0172269i
$797$	16.0427	−	31.4855i	0.568261	−	1.11527i	−0.410804	−	0.911724i	$-0.634752\pi$
$797$	16.0427	−	31.4855i	0.568261	−	1.11527i	0.979064	−	0.203551i	$-0.0652482\pi$
$798$	−2.87351	+	5.63957i	−0.101721	+	0.199639i
$799$	−14.8709	−	10.8043i	−0.526093	−	0.382229i
$800$		0			0
$801$	1.08991	−	3.35441i	0.0385102	−	0.118522i
$802$	9.74633	−	9.74633i	0.344155	−	0.344155i
$803$	−3.61319	−	1.16466i	−0.127507	−	0.0410998i
$804$		−	8.86742i		−	0.312730i
$805$		0			0
$806$	2.43103	−	1.76625i	0.0856295	−	0.0622135i
$807$	−5.22043	−	32.9605i	−0.183768	−	1.16026i
$808$	−8.35005	−	4.25456i	−0.293754	−	0.149675i
$809$	11.3255	+	34.8562i	0.398182	+	1.22548i	0.926455	+	0.376405i	$0.122840\pi$
$809$	11.3255	+	34.8562i	0.398182	+	1.22548i	−0.528273	+	0.849075i	$0.677160\pi$
$810$		0			0
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	0.984767	−	0.173878i	$-0.0556299\pi$
$811$	14.6687	+	20.1898i	0.515089	+	0.708960i	−0.469678	+	0.882838i	$0.655630\pi$
$812$	0.464371	−	0.236609i	0.0162962	−	0.00830334i
$813$	8.64138	+	8.64138i	0.303067	+	0.303067i
$814$	4.27378	+	26.5808i	0.149796	+	0.931657i
$815$		0			0
$816$	2.25706	+	0.733364i	0.0790130	+	0.0256729i
$817$	−53.8602	−	8.53061i	−1.88433	−	0.298448i
$818$	−19.9702	+	3.16297i	−0.698241	+	0.110591i
$819$	0.194733	−	0.0632726i	0.00680453	−	0.00221093i
$820$		0			0
$821$	7.96168	−	10.9583i	0.277865	−	0.382448i	−0.647160	−	0.762354i	$-0.724044\pi$
$821$	7.96168	−	10.9583i	0.277865	−	0.382448i	0.925025	+	0.379906i	$0.124044\pi$
$822$	0.432704	−	2.73198i	0.0150923	−	0.0952888i
$823$	−3.90905	−	7.67193i	−0.136261	−	0.267427i	0.812786	−	0.582563i	$-0.197950\pi$
$823$	−3.90905	−	7.67193i	−0.136261	−	0.267427i	−0.949047	+	0.315136i	$0.897950\pi$
$824$	−0.0988529			−0.00344371
$825$		0			0
$826$	−0.329973			−0.0114812
$827$	4.53336	+	8.89722i	0.157640	+	0.309387i	0.956295	−	0.292403i	$-0.0944547\pi$
$827$	4.53336	+	8.89722i	0.157640	+	0.309387i	−0.798655	+	0.601789i	$0.794455\pi$
$828$	−0.115244	+	0.727619i	−0.00400499	+	0.0252865i
$829$	−12.4310	+	17.1098i	−0.431746	+	0.594247i	−0.968353	−	0.249585i	$-0.919706\pi$
$829$	−12.4310	+	17.1098i	−0.431746	+	0.594247i	0.536607	+	0.843832i	$0.319706\pi$
$830$		0			0
$831$	−25.5204	+	8.29209i	−0.885294	+	0.287649i
$832$	0.842930	−	0.133507i	0.0292233	−	0.00462852i
$833$	−9.18100	−	1.45413i	−0.318103	−	0.0503825i
$834$	13.5225	+	4.39371i	0.468244	+	0.152142i
$835$		0			0
$836$	14.9861	+	7.59169i	0.518306	+	0.262564i
$837$	−13.5233	−	13.5233i	−0.467434	−	0.467434i
$838$	17.3711	−	8.85100i	0.600073	−	0.305753i
$839$	23.3328	+	32.1148i	0.805537	+	1.10873i	0.991997	+	0.126264i	$0.0402986\pi$
$839$	23.3328	+	32.1148i	0.805537	+	1.10873i	−0.186460	+	0.982463i	$0.559701\pi$
$840$		0			0
$841$	−8.81714	−	27.1364i	−0.304039	−	0.935737i
$842$	2.54735	+	1.29794i	0.0877875	+	0.0447300i
$843$	1.07344	+	6.77743i	0.0369712	+	0.233427i
$844$	11.7834	−	8.56117i	0.405603	−	0.294688i
$845$		0			0
$846$			3.99336i			0.137295i
$847$	−5.95893	−	5.90340i	−0.204751	−	0.202843i
$848$	−5.80747	+	5.80747i	−0.199429	+	0.199429i
$849$	−13.9969	+	43.0781i	−0.480373	+	1.47844i
$850$		0			0
$851$	15.3766	+	11.1718i	0.527104	+	0.382964i
$852$	−5.91271	+	11.6043i	−0.202566	+	0.397558i
$853$	−16.5238	+	32.4298i	−0.565764	+	1.11037i	0.414012	+	0.910272i	$0.364127\pi$
$853$	−16.5238	+	32.4298i	−0.565764	+	1.11037i	−0.979775	+	0.200102i	$0.935873\pi$
$854$	−7.82458	−	5.68489i	−0.267752	−	0.194533i
$855$		0			0
$856$	−2.01746	+	6.20910i	−0.0689554	+	0.212223i
$857$	10.3508	−	10.3508i	0.353576	−	0.353576i	−0.507862	−	0.861438i	$-0.669564\pi$
$857$	10.3508	−	10.3508i	0.353576	−	0.353576i	0.861438	+	0.507862i	$0.169564\pi$
$858$	1.44367	+	4.40804i	0.0492861	+	0.150488i
$859$		−	21.8229i		−	0.744588i	−0.928115	−	0.372294i	$-0.878571\pi$
$859$		−	21.8229i		−	0.744588i	0.928115	−	0.372294i	$-0.121429\pi$
$860$		0			0
$861$	−12.5639	+	9.12819i	−0.428176	+	0.311088i
$862$	2.52053	+	15.9140i	0.0858495	+	0.542032i
$863$	5.34286	+	2.72232i	0.181873	+	0.0926690i	0.542556	−	0.840019i	$-0.317456\pi$
$863$	5.34286	+	2.72232i	0.181873	+	0.0926690i	−0.360683	+	0.932688i	$0.617456\pi$
$864$	−1.67849	−	5.16587i	−0.0571035	−	0.175746i
$865$		0			0
$866$	−14.3556	−	19.7588i	−0.487823	−	0.671431i
$867$	21.7594	−	11.0870i	0.738988	−	0.376533i
$868$	−1.89851	−	1.89851i	−0.0644397	−	0.0644397i
$869$	23.7125	+	23.6018i	0.804392	+	0.800636i
$870$		0			0
$871$	4.39211	+	1.42708i	0.148821	+	0.0483548i
$872$	11.6671	+	1.84788i	0.395097	+	0.0625772i
$873$	4.42105	−	0.700226i	0.149630	−	0.0236991i
$874$	11.2795	−	3.66494i	0.381536	−	0.123969i
$875$		0			0
$876$	1.10250	−	1.51747i	0.0372502	−	0.0512705i
$877$	−4.44076	+	28.0379i	−0.149954	+	0.946771i	0.791876	+	0.610682i	$0.209105\pi$
$877$	−4.44076	+	28.0379i	−0.149954	+	0.946771i	−0.941830	+	0.336090i	$0.890895\pi$
$878$	6.01836	+	11.8117i	0.203110	+	0.398625i
$879$	−30.6379			−1.03339
$880$		0			0
$881$	−9.63291			−0.324541			−0.162270	−	0.986746i	$-0.551882\pi$
$881$	−9.63291			−0.324541			−0.162270	+	0.986746i	$0.551882\pi$
$882$	0.916804	+	1.79933i	0.0308704	+	0.0605866i
$883$	7.79859	−	49.2384i	0.262443	−	1.65700i	−0.406471	−	0.913663i	$-0.633241\pi$
$883$	7.79859	−	49.2384i	0.262443	−	1.65700i	0.668915	−	0.743339i	$-0.266759\pi$
$884$	−0.726483	+	0.999918i	−0.0244343	+	0.0336309i
$885$		0			0
$886$	−2.07093	+	0.672885i	−0.0695742	+	0.0226060i
$887$	33.0342	−	5.23210i	1.10918	−	0.175677i	0.425144	−	0.905126i	$-0.360223\pi$
$887$	33.0342	−	5.23210i	1.10918	−	0.175677i	0.684035	+	0.729449i	$0.260223\pi$
$888$	−13.1382	−	2.08089i	−0.440890	−	0.0698301i
$889$	4.70701	+	1.52940i	0.157868	+	0.0512944i
$890$		0			0
$891$	23.4863	−	12.0362i	0.786820	−	0.403227i
$892$	0.951712	+	0.951712i	0.0318657	+	0.0318657i
$893$	57.2823	−	29.1868i	1.91688	−	0.976698i
$894$	−14.1989	−	19.5431i	−0.474882	−	0.653619i
$895$		0			0
$896$	−0.235640	−	0.725226i	−0.00787219	−	0.0242281i
$897$	2.91772	+	1.48665i	0.0974200	+	0.0496380i
$898$	0.754900	+	4.76625i	0.0251913	+	0.159052i
$899$	1.94687	−	1.41448i	0.0649316	−	0.0471756i
$900$		0			0
$901$		−	11.8942i		−	0.396255i
$902$	24.3056	+	33.2897i	0.809289	+	1.10843i
$903$	−9.51275	+	9.51275i	−0.316565	+	0.316565i
$904$	3.56235	−	10.9638i	0.118482	−	0.364650i
$905$		0			0
$906$	15.1781	+	11.0275i	0.504257	+	0.366364i
$907$	19.2581	−	37.7962i	0.639456	−	1.25500i	−0.312833	−	0.949808i	$-0.601278\pi$
$907$	19.2581	−	37.7962i	0.639456	−	1.25500i	0.952290	−	0.305196i	$-0.0987218\pi$
$908$	0.931635	−	1.82844i	0.0309174	−	0.0606788i
$909$	−2.38540	−	1.73309i	−0.0791187	−	0.0574831i
$910$		0			0
$911$	−4.93516	+	15.1889i	−0.163509	+	0.503229i	−0.998923	−	0.0463915i	$-0.985228\pi$
$911$	−4.93516	+	15.1889i	−0.163509	+	0.503229i	0.835414	+	0.549621i	$0.185228\pi$
$912$	−5.86926	+	5.86926i	−0.194351	+	0.194351i
$913$	0.467147	+	0.639819i	0.0154603	+	0.0211749i
$914$			20.4761i			0.677288i
$915$		0			0
$916$	−14.5007	+	10.5354i	−0.479116	+	0.348098i
$917$	0.186514	+	1.17760i	0.00615923	+	0.0388879i
$918$	7.00895	+	3.57124i	0.231330	+	0.117868i
$919$	−7.78224	−	23.9513i	−0.256713	−	0.790080i	−0.993487	−	0.113942i	$-0.963652\pi$
$919$	−7.78224	−	23.9513i	−0.256713	−	0.790080i	0.736775	−	0.676138i	$-0.236348\pi$
$920$		0			0
$921$	−9.71595	−	13.3729i	−0.320151	−	0.440651i
$922$	0.549077	−	0.279769i	0.0180829	−	0.00921369i
$923$	−4.79616	−	4.79616i	−0.157868	−	0.157868i
$924$	3.68831	−	1.89017i	0.121336	−	0.0621821i
$925$		0			0
$926$	−18.2897	−	5.94269i	−0.601037	−	0.195289i
$927$	−0.0307188	−	0.00486538i	−0.00100894	−	0.000159800i
$928$	0.675052	−	0.106918i	0.0221597	−	0.00350974i
$929$	−8.61430	+	2.79896i	−0.282626	+	0.0918308i	−0.446900	−	0.894584i	$-0.647472\pi$
$929$	−8.61430	+	2.79896i	−0.282626	+	0.0918308i	0.164274	+	0.986415i	$0.447472\pi$
$930$		0			0
$931$	19.1095	−	26.3020i	0.626289	−	0.862012i
$932$	−3.84574	+	24.2810i	−0.125971	+	0.795352i
$933$	17.0440	+	33.4507i	0.557994	+	1.09513i
$934$	1.55432			0.0508591
$935$		0			0
$936$	0.268514			0.00877665
$937$	10.0962	+	19.8149i	0.329829	+	0.647326i	0.995056	−	0.0993152i	$-0.0316652\pi$
$937$	10.0962	+	19.8149i	0.329829	+	0.647326i	−0.665227	+	0.746641i	$0.731665\pi$
$938$	0.645497	−	4.07551i	0.0210762	−	0.133070i
$939$	13.9502	−	19.2007i	0.455246	−	0.626593i
$940$		0			0
$941$	−20.9430	+	6.80478i	−0.682721	+	0.221829i	−0.629786	−	0.776769i	$-0.716857\pi$
$941$	−20.9430	+	6.80478i	−0.682721	+	0.221829i	−0.0529346	+	0.998598i	$0.516857\pi$
$942$	−1.33411	+	0.211302i	−0.0434677	+	0.00688461i
$943$	28.7413	+	4.55217i	0.935944	+	0.148239i
$944$	−0.411545	−	0.133719i	−0.0133947	−	0.00435219i
$945$		0			0
$946$	25.3074	+	25.1892i	0.822814	+	0.818972i
$947$	2.70333	+	2.70333i	0.0878464	+	0.0878464i	0.749664	−	0.661818i	$-0.230215\pi$
$947$	2.70333	+	2.70333i	0.0878464	+	0.0878464i	−0.661818	+	0.749664i	$0.730215\pi$
$948$	−14.7287	+	7.50467i	−0.478367	+	0.243740i
$949$	0.574182	+	0.790294i	0.0186387	+	0.0256540i
$950$		0			0
$951$	1.13277	+	3.48631i	0.0367326	+	0.113051i
$952$	0.983972	+	0.501359i	0.0318907	+	0.0162491i
$953$	5.80899	+	36.6765i	0.188172	+	1.18807i	0.883168	+	0.469056i	$0.155406\pi$
$953$	5.80899	+	36.6765i	0.188172	+	1.18807i	−0.694997	+	0.719013i	$0.744594\pi$
$954$	−2.09052	+	1.51885i	−0.0676831	+	0.0491746i
$955$		0			0
$956$			2.96744i			0.0959740i
$957$	1.15615	+	3.53013i	0.0373730	+	0.114113i
$958$	17.1065	−	17.1065i	0.552687	−	0.552687i
$959$	0.397745	−	1.22413i	0.0128439	−	0.0395294i
$960$		0			0
$961$	15.0500	+	10.9345i	0.485484	+	0.352725i
$962$	3.14509	−	6.17258i	0.101402	−	0.199012i
$963$	−0.932533	+	1.83020i	−0.0300505	+	0.0589773i
$964$	−17.2206	−	12.5115i	−0.554638	−	0.402968i
$965$		0			0
$966$	0.904151	−	2.78269i	0.0290906	−	0.0895316i
$967$	16.6994	−	16.6994i	0.537017	−	0.537017i	−0.385634	−	0.922652i	$-0.626017\pi$
$967$	16.6994	−	16.6994i	0.537017	−	0.537017i	0.922652	+	0.385634i	$0.126017\pi$
$968$	−5.03971	−	9.77759i	−0.161983	−	0.314264i
$969$		−	12.0208i		−	0.386163i
$970$		0			0
$971$	−21.9153	+	15.9224i	−0.703294	+	0.510973i	−0.881003	−	0.473110i	$-0.843131\pi$
$971$	−21.9153	+	15.9224i	−0.703294	+	0.510973i	0.177709	+	0.984083i	$0.443131\pi$
$972$	−0.509304	−	3.21562i	−0.0163359	−	0.103141i
$973$	5.89515	+	3.00373i	0.188990	+	0.0962951i
$974$	−5.79872	−	17.8466i	−0.185803	−	0.571843i
$975$		0			0
$976$	−7.45513	−	10.2611i	−0.238633	−	0.328450i
$977$	−36.0042	+	18.3451i	−1.15188	+	0.586911i	−0.922336	−	0.386388i	$-0.873722\pi$
$977$	−36.0042	+	18.3451i	−1.15188	+	0.586911i	−0.229541	+	0.973299i	$0.573722\pi$
$978$	−10.3558	−	10.3558i	−0.331142	−	0.331142i
$979$	33.1671	+	16.8018i	1.06003	+	0.536989i
$980$		0			0
$981$	3.53462	+	1.14847i	0.112852	+	0.0366678i
$982$	−25.0692	−	3.97058i	−0.799992	−	0.126706i
$983$	−23.7573	+	3.76279i	−0.757740	+	0.120014i	−0.523338	−	0.852125i	$-0.675313\pi$
$983$	−23.7573	+	3.76279i	−0.757740	+	0.120014i	−0.234402	+	0.972140i	$0.575313\pi$
$984$	−19.3689	+	6.29334i	−0.617459	+	0.200624i
$985$		0			0
$986$	−0.581796	+	0.800773i	−0.0185282	+	0.0255018i
$987$	2.48111	−	15.6651i	0.0789745	−	0.498625i
$988$	−1.96252	−	3.85166i	−0.0624361	−	0.122538i
$989$	25.2082			0.801573
$990$		0			0
$991$	−4.81752			−0.153034			−0.0765169	−	0.997068i	$-0.524380\pi$
$991$	−4.81752			−0.153034			−0.0765169	+	0.997068i	$0.524380\pi$
$992$	−1.59848	−	3.13720i	−0.0507519	−	0.0996062i
$993$	−0.504170	+	3.18320i	−0.0159993	+	0.101016i
$994$	−3.56224	+	4.90300i	−0.112987	+	0.155514i
$995$		0			0
$996$	−0.372265	+	0.120956i	−0.0117957	+	0.00383264i
$997$	36.3270	−	5.75364i	1.15049	−	0.182219i	0.448080	−	0.893993i	$-0.352108\pi$
$997$	36.3270	−	5.75364i	1.15049	−	0.182219i	0.702409	+	0.711774i	$0.252108\pi$
$998$	−9.01551	−	1.42792i	−0.285381	−	0.0451999i
$999$	−41.9332	−	13.6249i	−1.32671	−	0.431073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.bh.b.57.1		48
5.2	odd	4		110.2.k.a.13.6	✓	48
5.3	odd	4	inner	550.2.bh.b.343.1		48
5.4	even	2		110.2.k.a.57.6	yes	48
11.6	odd	10	inner	550.2.bh.b.457.1		48
15.2	even	4		990.2.bh.c.343.3		48
15.14	odd	2		990.2.bh.c.937.1		48
20.7	even	4		880.2.cm.c.673.2		48
20.19	odd	2		880.2.cm.c.497.2		48
55.17	even	20		110.2.k.a.83.6	yes	48
55.28	even	20	inner	550.2.bh.b.193.1		48
55.39	odd	10		110.2.k.a.17.6	yes	48
165.17	odd	20		990.2.bh.c.523.1		48
165.149	even	10		990.2.bh.c.127.3		48
220.39	even	10		880.2.cm.c.17.2		48
220.127	odd	20		880.2.cm.c.193.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.6	✓	48	5.2	odd	4
110.2.k.a.17.6	yes	48	55.39	odd	10
110.2.k.a.57.6	yes	48	5.4	even	2
110.2.k.a.83.6	yes	48	55.17	even	20
550.2.bh.b.57.1		48	1.1	even	1	trivial
550.2.bh.b.193.1		48	55.28	even	20	inner
550.2.bh.b.343.1		48	5.3	odd	4	inner
550.2.bh.b.457.1		48	11.6	odd	10	inner
880.2.cm.c.17.2		48	220.39	even	10
880.2.cm.c.193.2		48	220.127	odd	20
880.2.cm.c.497.2		48	20.19	odd	2
880.2.cm.c.673.2		48	20.7	even	4
990.2.bh.c.127.3		48	165.149	even	10
990.2.bh.c.343.3		48	15.2	even	4
990.2.bh.c.523.1		48	165.17	odd	20
990.2.bh.c.937.1		48	15.14	odd	2

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.256351 + 1.61854i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.55851 - 0.506390i) q^{6} +(0.753160 - 0.119289i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.299227 + 0.0972249i) q^{9} +(-1.49880 + 2.95865i) q^{11} +(-1.15874 - 1.15874i) q^{12} +(0.760418 - 0.387452i) q^{13} +(-0.448214 - 0.616914i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(1.29037 + 0.657479i) q^{17} +(-0.0492184 - 0.310753i) q^{18} +(-4.09783 + 2.97724i) q^{19} +1.24960i q^{21} +(3.31662 - 0.00776159i) q^{22} +(1.65567 - 1.65567i) q^{23} +(-0.506390 + 1.55851i) q^{24} +(-0.690445 - 0.501638i) q^{26} +(-2.46595 + 4.83969i) q^{27} +(-0.346189 + 0.679435i) q^{28} +(-0.552936 - 0.401731i) q^{29} +(-1.08804 + 3.34864i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.40446 - 3.18431i) q^{33} -1.44822i q^{34} +(-0.254538 + 0.184933i) q^{36} +(1.26983 + 8.01741i) q^{37} +(4.51312 + 2.29955i) q^{38} +(0.432172 + 1.33009i) q^{39} +(7.30492 + 10.0544i) q^{41} +(1.11340 - 0.567304i) q^{42} +(7.61267 + 7.61267i) q^{43} +(-1.51263 - 2.95160i) q^{44} +(-2.22687 - 0.723555i) q^{46} +(-12.5361 - 1.98553i) q^{47} +(1.61854 - 0.256351i) q^{48} +(-6.10438 + 1.98343i) q^{49} +(-1.39494 + 1.91997i) q^{51} +(-0.133507 + 0.842930i) q^{52} +(-3.72862 - 7.31784i) q^{53} +5.43171 q^{54} +0.762548 q^{56} +(-3.76830 - 7.39570i) q^{57} +(-0.106918 + 0.675052i) q^{58} +(0.254349 - 0.350081i) q^{59} +(12.0627 - 3.91939i) q^{61} +(3.47761 - 0.550800i) q^{62} +(0.236964 + 0.0375314i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.837655 + 5.37005i) q^{66} +(3.82631 + 3.82631i) q^{67} +(-1.29037 + 0.657479i) q^{68} +(2.25533 + 3.10420i) q^{69} +(-2.45595 - 7.55864i) q^{71} +(0.280334 + 0.142837i) q^{72} +(0.179057 + 1.13052i) q^{73} +(6.56708 - 4.77126i) q^{74} -5.06519i q^{76} +(-0.775899 + 2.40712i) q^{77} +(0.988915 - 0.988915i) q^{78} +(3.11720 - 9.59376i) q^{79} +(-6.43745 - 4.67708i) q^{81} +(5.64213 - 11.0733i) q^{82} +(0.108440 - 0.212826i) q^{83} +(-1.01094 - 0.734494i) q^{84} +(3.32686 - 10.2390i) q^{86} +(0.791962 - 0.791962i) q^{87} +(-1.94318 + 2.68776i) q^{88} -11.2102i q^{89} +(0.526498 - 0.382523i) q^{91} +(0.366287 + 2.31265i) q^{92} +(-5.14097 - 2.61945i) q^{93} +(3.92217 + 12.0712i) q^{94} +(-0.963210 - 1.32575i) q^{96} +(12.6763 - 6.45889i) q^{97} +(4.53858 + 4.53858i) q^{98} +(-0.736135 + 0.739589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} + 20 q^{7} + 12 q^{11} + 16 q^{12} + 12 q^{16} + 20 q^{17} + 4 q^{22} + 8 q^{23} + 8 q^{26} - 8 q^{27} + 20 q^{28} + 16 q^{31} + 104 q^{33} - 4 q^{36} - 20 q^{37} + 36 q^{38} - 20 q^{41}+ \cdots - 72 q^{97}+O(q^{100}) \) 48 * q + 4 * q^3 + 20 * q^7 + 12 * q^11 + 16 * q^12 + 12 * q^16 + 20 * q^17 + 4 * q^22 + 8 * q^23 + 8 * q^26 - 8 * q^27 + 20 * q^28 + 16 * q^31 + 104 * q^33 - 4 * q^36 - 20 * q^37 + 36 * q^38 - 20 * q^41 + 20 * q^42 + 40 * q^46 - 40 * q^47 - 4 * q^48 + 40 * q^51 - 40 * q^52 - 8 * q^56 - 48 * q^58 + 80 * q^61 - 40 * q^62 - 100 * q^63 + 24 * q^66 - 20 * q^68 - 56 * q^71 + 20 * q^73 + 96 * q^77 - 16 * q^78 - 68 * q^81 - 56 * q^86 + 4 * q^88 - 68 * q^91 + 12 * q^92 - 76 * q^93 - 72 * q^97

Introduction

L-functions

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