LMFDB - Embedded newform 605.2.m.f.118.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.7
Character	$\chi$	$=$	605.118
Dual form			605.2.m.f.282.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25054 + 0.198066i) q^{2} +(1.03183 - 2.02507i) q^{3} +(-0.377491 - 0.122654i) q^{4} +(1.65288 - 1.50599i) q^{5} +(1.69144 - 2.32807i) q^{6} +(2.28322 - 1.16336i) q^{7} +(-2.70403 - 1.37777i) q^{8} +(-1.27290 - 1.75200i) q^{9} +O(q^{10})$	\(q+(1.25054 + 0.198066i) q^{2} +(1.03183 - 2.02507i) q^{3} +(-0.377491 - 0.122654i) q^{4} +(1.65288 - 1.50599i) q^{5} +(1.69144 - 2.32807i) q^{6} +(2.28322 - 1.16336i) q^{7} +(-2.70403 - 1.37777i) q^{8} +(-1.27290 - 1.75200i) q^{9} +(2.36528 - 1.55592i) q^{10} +(-0.637889 + 0.637889i) q^{12} +(-0.779496 + 4.92155i) q^{13} +(3.08568 - 1.00260i) q^{14} +(-1.34425 - 4.90112i) q^{15} +(-2.46639 - 1.79193i) q^{16} +(-0.0470767 - 0.297231i) q^{17} +(-1.24481 - 2.44307i) q^{18} +(1.87958 + 5.78475i) q^{19} +(-0.808662 + 0.365764i) q^{20} -5.82406i q^{21} +(-5.07364 - 5.07364i) q^{23} +(-5.58019 + 4.05424i) q^{24} +(0.464008 - 4.97842i) q^{25} +(-1.94958 + 6.00020i) q^{26} +(1.87308 - 0.296667i) q^{27} +(-1.00458 + 0.159110i) q^{28} +(1.23121 - 3.78926i) q^{29} +(-0.710296 - 6.39530i) q^{30} +(-6.14370 + 4.46366i) q^{31} +(1.56247 + 1.56247i) q^{32} -0.381023i q^{34} +(2.02188 - 5.36138i) q^{35} +(0.265619 + 0.817492i) q^{36} +(2.92965 + 5.74976i) q^{37} +(1.20473 + 7.60634i) q^{38} +(9.16219 + 6.65672i) q^{39} +(-6.54434 + 1.79495i) q^{40} +(2.30661 - 0.749464i) q^{41} +(1.15355 - 7.28323i) q^{42} +(1.43561 - 1.43561i) q^{43} +(-4.74245 - 0.978869i) q^{45} +(-5.33988 - 7.34971i) q^{46} +(3.14697 + 1.60346i) q^{47} +(-6.17369 + 3.14565i) q^{48} +(-0.254823 + 0.350734i) q^{49} +(1.56632 - 6.13382i) q^{50} +(-0.650489 - 0.211357i) q^{51} +(0.897901 - 1.76223i) q^{52} +(8.68003 + 1.37478i) q^{53} +2.40113 q^{54} -7.77673 q^{56} +(13.6539 + 2.16257i) q^{57} +(2.29020 - 4.49476i) q^{58} +(-1.11721 - 0.363002i) q^{59} +(-0.0937000 + 2.01501i) q^{60} +(0.0546362 - 0.0752003i) q^{61} +(-8.56705 + 4.36513i) q^{62} +(-4.94452 - 2.51936i) q^{63} +(5.22833 + 7.19618i) q^{64} +(6.12337 + 9.30862i) q^{65} +(7.07364 - 7.07364i) q^{67} +(-0.0186856 + 0.117976i) q^{68} +(-15.5096 + 5.03938i) q^{69} +(3.59035 - 6.30416i) q^{70} +(-9.09599 - 6.60862i) q^{71} +(1.02811 + 6.49125i) q^{72} +(1.80175 + 3.53613i) q^{73} +(2.52481 + 7.77058i) q^{74} +(-9.60290 - 6.07652i) q^{75} -2.41423i q^{76} +(10.1392 + 10.1392i) q^{78} +(-1.90794 + 1.38620i) q^{79} +(-6.77527 + 0.752497i) q^{80} +(3.33954 - 10.2781i) q^{81} +(3.03296 - 0.480373i) q^{82} +(-8.19874 + 1.29855i) q^{83} +(-0.714346 + 2.19853i) q^{84} +(-0.525437 - 0.420389i) q^{85} +(2.07963 - 1.51094i) q^{86} +(-6.40314 - 6.40314i) q^{87} -2.55325i q^{89} +(-5.73675 - 2.16343i) q^{90} +(3.94575 + 12.1438i) q^{91} +(1.29295 + 2.53756i) q^{92} +(2.70001 + 17.0472i) q^{93} +(3.61783 + 2.62850i) q^{94} +(11.8185 + 6.73086i) q^{95} +(4.77631 - 1.55192i) q^{96} +(-1.17781 + 7.43640i) q^{97} +(-0.388135 + 0.388135i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^5	$ 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.25054	+	0.198066i	0.884266	+	0.140054i	0.582018	−	0.813176i	$-0.302263\pi$
$2$	1.25054	+	0.198066i	0.884266	+	0.140054i	0.302247	+	0.953230i	$0.402263\pi$
$3$	1.03183	−	2.02507i	0.595726	−	1.16918i	−0.374557	−	0.927204i	$-0.622205\pi$
$3$	1.03183	−	2.02507i	0.595726	−	1.16918i	0.970283	−	0.241974i	$-0.0777947\pi$
$4$	−0.377491	−	0.122654i	−0.188745	−	0.0613271i
$5$	1.65288	−	1.50599i	0.739189	−	0.673498i
$5$	1.65288	−	1.50599i	0.739189	−	0.673498i
$6$	1.69144	−	2.32807i	0.690528	−	0.950430i
$7$	2.28322	−	1.16336i	0.862974	−	0.439707i	0.0342822	−	0.999412i	$-0.489085\pi$
$7$	2.28322	−	1.16336i	0.862974	−	0.439707i	0.828692	+	0.559705i	$0.189085\pi$
$8$	−2.70403	−	1.37777i	−0.956020	−	0.487116i
$9$	−1.27290	−	1.75200i	−0.424302	−	0.584001i
$10$	2.36528	−	1.55592i	0.747966	−	0.492025i
$11$		0			0
$11$		0			0
$12$	−0.637889	+	0.637889i	−0.184143	+	0.184143i
$13$	−0.779496	+	4.92155i	−0.216193	+	1.36499i	0.605856	+	0.795575i	$0.292831\pi$
$13$	−0.779496	+	4.92155i	−0.216193	+	1.36499i	−0.822049	+	0.569417i	$0.807169\pi$
$14$	3.08568	−	1.00260i	0.824681	−	0.267955i
$15$	−1.34425	−	4.90112i	−0.347084	−	1.26546i
$16$	−2.46639	−	1.79193i	−0.616597	−	0.447984i
$17$	−0.0470767	−	0.297231i	−0.0114178	−	0.0720890i	0.981322	−	0.192375i	$-0.0616189\pi$
$17$	−0.0470767	−	0.297231i	−0.0114178	−	0.0720890i	−0.992739	+	0.120286i	$0.961619\pi$
$18$	−1.24481	−	2.44307i	−0.293404	−	0.575837i
$19$	1.87958	+	5.78475i	0.431205	+	1.32711i	0.896926	+	0.442180i	$0.145795\pi$
$19$	1.87958	+	5.78475i	0.431205	+	1.32711i	−0.465721	+	0.884931i	$0.654205\pi$
$20$	−0.808662	+	0.365764i	−0.180822	+	0.0817873i
$21$		−	5.82406i		−	1.27091i
$22$		0			0
$23$	−5.07364	−	5.07364i	−1.05793	−	1.05793i	−0.998216	−	0.0597111i	$-0.980982\pi$
$23$	−5.07364	−	5.07364i	−1.05793	−	1.05793i	−0.0597111	−	0.998216i	$-0.519018\pi$
$24$	−5.58019	+	4.05424i	−1.13905	+	0.827569i
$25$	0.464008	−	4.97842i	0.0928015	−	0.995685i
$26$	−1.94958	+	6.00020i	−0.382345	+	1.17674i
$27$	1.87308	−	0.296667i	0.360475	−	0.0570936i
$28$	−1.00458	+	0.159110i	−0.189848	+	0.0300690i
$29$	1.23121	−	3.78926i	0.228629	−	0.703648i	−0.769274	−	0.638919i	$-0.779382\pi$
$29$	1.23121	−	3.78926i	0.228629	−	0.703648i	0.997903	−	0.0647286i	$-0.0206182\pi$
$30$	−0.710296	−	6.39530i	−0.129682	−	1.16762i
$31$	−6.14370	+	4.46366i	−1.10344	+	0.801697i	−0.981618	−	0.190855i	$-0.938874\pi$
$31$	−6.14370	+	4.46366i	−1.10344	+	0.801697i	−0.121823	+	0.992552i	$0.538874\pi$
$32$	1.56247	+	1.56247i	0.276208	+	0.276208i
$33$		0			0
$34$		−	0.381023i		−	0.0653449i
$35$	2.02188	−	5.36138i	0.341759	−	0.906238i
$36$	0.265619	+	0.817492i	0.0442699	+	0.136249i
$37$	2.92965	+	5.74976i	0.481632	+	0.945255i	0.996141	+	0.0877705i	$0.0279742\pi$
$37$	2.92965	+	5.74976i	0.481632	+	0.945255i	−0.514509	+	0.857485i	$0.672026\pi$
$38$	1.20473	+	7.60634i	0.195432	+	1.23391i
$39$	9.16219	+	6.65672i	1.46713	+	1.06593i
$40$	−6.54434	+	1.79495i	−1.03475	+	0.283806i
$41$	2.30661	−	0.749464i	0.360233	−	0.117047i	−0.123308	−	0.992368i	$-0.539350\pi$
$41$	2.30661	−	0.749464i	0.360233	−	0.117047i	0.483541	+	0.875322i	$0.339350\pi$
$42$	1.15355	−	7.28323i	0.177997	−	1.12383i
$43$	1.43561	−	1.43561i	0.218928	−	0.218928i	−0.589119	−	0.808047i	$-0.700525\pi$
$43$	1.43561	−	1.43561i	0.218928	−	0.218928i	0.808047	+	0.589119i	$0.200525\pi$
$44$		0			0
$45$	−4.74245	−	0.978869i	−0.706963	−	0.145921i
$46$	−5.33988	−	7.34971i	−0.787322	−	1.08366i
$47$	3.14697	+	1.60346i	0.459033	+	0.233889i	0.668187	−	0.743994i	$-0.267071\pi$
$47$	3.14697	+	1.60346i	0.459033	+	0.233889i	−0.209153	+	0.977883i	$0.567071\pi$
$48$	−6.17369	+	3.14565i	−0.891095	+	0.454036i
$49$	−0.254823	+	0.350734i	−0.0364033	+	0.0501048i
$50$	1.56632	−	6.13382i	0.221511	−	0.867453i
$51$	−0.650489	−	0.211357i	−0.0910867	−	0.0295959i
$52$	0.897901	−	1.76223i	0.124516	−	0.244377i
$53$	8.68003	+	1.37478i	1.19229	+	0.188841i	0.720873	−	0.693067i	$-0.243741\pi$
$53$	8.68003	+	1.37478i	1.19229	+	0.188841i	0.471421	+	0.881908i	$0.343741\pi$
$54$	2.40113			0.326752
$55$		0			0
$56$	−7.77673			−1.03921
$57$	13.6539	+	2.16257i	1.80851	+	0.286440i
$58$	2.29020	−	4.49476i	0.300718	−	0.590191i
$59$	−1.11721	−	0.363002i	−0.145448	−	0.0472588i	0.235388	−	0.971901i	$-0.424364\pi$
$59$	−1.11721	−	0.363002i	−0.145448	−	0.0472588i	−0.380836	+	0.924643i	$0.624364\pi$
$60$	−0.0937000	+	2.01501i	−0.0120966	+	0.260136i
$61$	0.0546362	−	0.0752003i	0.00699545	−	0.00962842i	−0.805505	−	0.592589i	$-0.798106\pi$
$61$	0.0546362	−	0.0752003i	0.00699545	−	0.00962842i	0.812500	+	0.582961i	$0.198106\pi$
$62$	−8.56705	+	4.36513i	−1.08802	+	0.554372i
$63$	−4.94452	−	2.51936i	−0.622951	−	0.317409i
$64$	5.22833	+	7.19618i	0.653541	+	0.899522i
$65$	6.12337	+	9.30862i	0.759511	+	1.15459i
$66$		0			0
$67$	7.07364	−	7.07364i	0.864183	−	0.864183i	−0.127638	−	0.991821i	$-0.540740\pi$
$67$	7.07364	−	7.07364i	0.864183	−	0.864183i	0.991821	+	0.127638i	$0.0407397\pi$
$68$	−0.0186856	+	0.117976i	−0.00226596	+	0.0143067i
$69$	−15.5096	+	5.03938i	−1.86714	+	0.606670i
$70$	3.59035	−	6.30416i	0.429128	−	0.753491i
$71$	−9.09599	−	6.60862i	−1.07950	−	0.784299i	−0.101900	−	0.994795i	$-0.532492\pi$
$71$	−9.09599	−	6.60862i	−1.07950	−	0.784299i	−0.977595	+	0.210495i	$0.932492\pi$
$72$	1.02811	+	6.49125i	0.121164	+	0.765001i
$73$	1.80175	+	3.53613i	0.210879	+	0.413873i	0.972082	−	0.234640i	$-0.0753912\pi$
$73$	1.80175	+	3.53613i	0.210879	+	0.413873i	−0.761204	+	0.648513i	$0.775391\pi$
$74$	2.52481	+	7.77058i	0.293504	+	0.903312i
$75$	−9.60290	−	6.07652i	−1.10885	−	0.701656i
$76$		−	2.41423i		−	0.276931i
$77$		0			0
$78$	10.1392	+	10.1392i	1.14804	+	1.14804i
$79$	−1.90794	+	1.38620i	−0.214660	+	0.155959i	−0.689919	−	0.723886i	$-0.742354\pi$
$79$	−1.90794	+	1.38620i	−0.214660	+	0.155959i	0.475260	+	0.879846i	$0.342354\pi$
$80$	−6.77527	+	0.752497i	−0.757498	+	0.0841317i
$81$	3.33954	−	10.2781i	0.371060	−	1.14201i
$82$	3.03296	−	0.480373i	0.334934	−	0.0530484i
$83$	−8.19874	+	1.29855i	−0.899928	+	0.142535i	−0.589222	−	0.807971i	$-0.700566\pi$
$83$	−8.19874	+	1.29855i	−0.899928	+	0.142535i	−0.310706	+	0.950506i	$0.600566\pi$
$84$	−0.714346	+	2.19853i	−0.0779415	+	0.239879i
$85$	−0.525437	−	0.420389i	−0.0569917	−	0.0455976i
$86$	2.07963	−	1.51094i	0.224252	−	0.162929i
$87$	−6.40314	−	6.40314i	−0.686489	−	0.686489i
$88$		0			0
$89$		−	2.55325i		−	0.270644i	−0.990802	−	0.135322i	$-0.956793\pi$
$89$		−	2.55325i		−	0.270644i	0.990802	−	0.135322i	$-0.0432069\pi$
$90$	−5.73675	−	2.16343i	−0.604706	−	0.228046i
$91$	3.94575	+	12.1438i	0.413627	+	1.27301i
$92$	1.29295	+	2.53756i	0.134799	+	0.264558i
$93$	2.70001	+	17.0472i	0.279978	+	1.76771i
$94$	3.61783	+	2.62850i	0.373150	+	0.271110i
$95$	11.8185	+	6.73086i	1.21255	+	0.690571i
$96$	4.77631	−	1.55192i	0.487480	−	0.158392i
$97$	−1.17781	+	7.43640i	−0.119588	+	0.755052i	0.852895	+	0.522082i	$0.174844\pi$
$97$	−1.17781	+	7.43640i	−0.119588	+	0.755052i	−0.972484	+	0.232970i	$0.925156\pi$
$98$	−0.388135	+	0.388135i	−0.0392076	+	0.0392076i
$99$		0			0
$100$	−0.785783	+	1.82240i	−0.0785783	+	0.182240i
$101$	9.42579	+	12.9735i	0.937901	+	1.29091i	0.956697	+	0.291087i	$0.0940168\pi$
$101$	9.42579	+	12.9735i	0.937901	+	1.29091i	−0.0187957	+	0.999823i	$0.505983\pi$
$102$	−0.771601	−	0.393150i	−0.0763998	−	0.0389277i
$103$	1.28238	−	0.653404i	0.126356	−	0.0643818i	−0.389670	−	0.920955i	$-0.627411\pi$
$103$	1.28238	−	0.653404i	0.126356	−	0.0643818i	0.516026	+	0.856573i	$0.327411\pi$
$104$	8.88856	−	12.2341i	0.871595	−	1.19965i
$105$	−8.77096	−	9.62646i	−0.855958	−	0.939447i
$106$	10.5824	+	3.43844i	1.02786	+	0.333971i
$107$	−5.07693	+	9.96405i	−0.490806	+	0.963261i	0.504214	+	0.863579i	$0.331782\pi$
$107$	−5.07693	+	9.96405i	−0.490806	+	0.963261i	−0.995019	+	0.0996816i	$0.968218\pi$
$108$	−0.743459	−	0.117752i	−0.0715394	−	0.0113307i
$109$	−16.2607			−1.55749			−0.778746	−	0.627339i	$-0.784144\pi$
$109$	−16.2607			−1.55749			−0.778746	+	0.627339i	$0.784144\pi$
$110$		0			0
$111$	14.6666			1.39209
$112$	−7.71595	−	1.22209i	−0.729089	−	0.115476i
$113$	0.871944	−	1.71129i	0.0820256	−	0.160984i	−0.846350	−	0.532626i	$-0.821205\pi$
$113$	0.871944	−	1.71129i	0.0820256	−	0.160984i	0.928376	+	0.371642i	$0.121205\pi$
$114$	16.6465	+	5.40877i	1.55909	+	0.506578i
$115$	−16.0269	−	0.745270i	−1.49452	−	0.0694968i
$116$	−0.929537	+	1.27940i	−0.0863054	+	0.118789i
$117$	9.61479	−	4.89898i	0.888888	−	0.452911i
$118$	−1.32521	−	0.675230i	−0.121996	−	0.0621599i
$119$	−0.453271	−	0.623874i	−0.0415513	−	0.0571905i
$120$	−3.11773	+	15.1049i	−0.284608	+	1.37888i
$121$		0			0
$122$	0.0832195	−	0.0832195i	0.00753434	−	0.00753434i
$123$	0.862306	−	5.44438i	0.0777515	−	0.490904i
$124$	2.86668	−	0.931440i	0.257435	−	0.0836457i
$125$	−6.73049	−	8.92751i	−0.601993	−	0.798501i
$126$	−5.68432	−	4.12990i	−0.506400	−	0.367921i
$127$	−0.394254	−	2.48922i	−0.0349844	−	0.220883i	0.964002	−	0.265895i	$-0.0856674\pi$
$127$	−0.394254	−	2.48922i	−0.0349844	−	0.220883i	−0.998986	+	0.0450121i	$0.985667\pi$
$128$	3.10659	+	6.09702i	0.274586	+	0.538905i
$129$	−1.42591	−	4.38851i	−0.125545	−	0.386387i
$130$	5.81380	+	12.8536i	0.509904	+	1.12734i
$131$			13.8354i			1.20880i	0.796680	+	0.604401i	$0.206588\pi$
$131$			13.8354i			1.20880i	−0.796680	+	0.604401i	$0.793412\pi$
$132$		0			0
$133$	11.0212	+	11.0212i	0.955659	+	0.955659i
$134$	10.2469	−	7.44483i	0.885199	−	0.643135i
$135$	2.64920	−	3.31119i	0.228007	−	0.284982i
$136$	−0.282219	+	0.868582i	−0.0242001	+	0.0744803i
$137$	1.93754	−	0.306877i	0.165535	−	0.0262182i	−0.0731165	−	0.997323i	$-0.523294\pi$
$137$	1.93754	−	0.306877i	0.165535	−	0.0262182i	0.238652	+	0.971105i	$0.423294\pi$
$138$	−20.3935	+	3.23002i	−1.73601	+	0.274958i
$139$	2.67729	−	8.23984i	0.227084	−	0.698894i	−0.770989	−	0.636849i	$-0.780238\pi$
$139$	2.67729	−	8.23984i	0.227084	−	0.698894i	0.998073	−	0.0620453i	$-0.0197623\pi$
$140$	−1.42084	+	1.77588i	−0.120082	+	0.150089i
$141$	6.49426	−	4.71836i	0.546916	−	0.397357i
$142$	−10.0660	−	10.0660i	−0.844717	−	0.844717i
$143$		0			0
$144$			6.60208i			0.550173i
$145$	−3.67154	−	8.11736i	−0.304905	−	0.674110i
$146$	1.55277	+	4.77894i	0.128508	+	0.395508i
$147$	0.447329	+	0.877932i	0.0368951	+	0.0724106i
$148$	−0.400684	−	2.52982i	−0.0329360	−	0.207950i
$149$	−6.88899	−	5.00515i	−0.564368	−	0.410038i	0.268687	−	0.963228i	$-0.413410\pi$
$149$	−6.88899	−	5.00515i	−0.564368	−	0.410038i	−0.833055	+	0.553190i	$0.813410\pi$
$150$	−10.8053	−	9.50095i	−0.882247	−	0.775749i
$151$	6.55520	−	2.12991i	0.533454	−	0.173330i	−0.0298882	−	0.999553i	$-0.509515\pi$
$151$	6.55520	−	2.12991i	0.533454	−	0.173330i	0.563343	+	0.826223i	$0.309515\pi$
$152$	2.88763	−	18.2318i	0.234218	−	1.47879i
$153$	−0.460825	+	0.460825i	−0.0372555	+	0.0372555i
$154$		0			0
$155$	−3.43257	+	16.6302i	−0.275711	+	1.33577i
$156$	−2.64217	−	3.63663i	−0.211543	−	0.291164i
$157$	4.85901	+	2.47579i	0.387791	+	0.197589i	0.637006	−	0.770859i	$-0.280173\pi$
$157$	4.85901	+	2.47579i	0.387791	+	0.197589i	−0.249215	+	0.968448i	$0.580173\pi$
$158$	−2.66051	+	1.35560i	−0.211659	+	0.107846i
$159$	11.7403	−	16.1592i	0.931069	−	1.28151i
$160$	4.93563	+	0.229512i	0.390196	+	0.0181445i
$161$	−17.4867	−	5.68176i	−1.37814	−	0.447785i
$162$	6.21197	−	12.1917i	0.488058	−	0.957868i
$163$	2.21277	+	0.350469i	0.173318	+	0.0274508i	0.242490	−	0.970154i	$-0.422036\pi$
$163$	2.21277	+	0.350469i	0.173318	+	0.0274508i	−0.0691723	+	0.997605i	$0.522036\pi$
$164$	−0.962651			−0.0751704
$165$		0			0
$166$	−10.5101			−0.815738
$167$	−8.30924	−	1.31605i	−0.642988	−	0.101839i	−0.173579	−	0.984820i	$-0.555533\pi$
$167$	−8.30924	−	1.31605i	−0.642988	−	0.101839i	−0.469409	+	0.882981i	$0.655533\pi$
$168$	−8.02424	+	15.7485i	−0.619084	+	1.21502i
$169$	−11.2503	−	3.65544i	−0.865406	−	0.281187i
$170$	−0.573816	−	0.629785i	−0.0440097	−	0.0483023i
$171$	7.74237	−	10.6565i	0.592074	−	0.814920i
$172$	−0.718012	+	0.365845i	−0.0547479	+	0.0278954i
$173$	−12.3025	−	6.26846i	−0.935345	−	0.476582i	−0.0812468	−	0.996694i	$-0.525890\pi$
$173$	−12.3025	−	6.26846i	−0.935345	−	0.476582i	−0.854098	+	0.520112i	$0.825890\pi$
$174$	−6.73915	−	9.27564i	−0.510893	−	0.703184i
$175$	−4.73225	−	11.9066i	−0.357725	−	0.900056i
$176$		0			0
$177$	−1.88787	+	1.88787i	−0.141901	+	0.141901i
$178$	0.505712	−	3.19294i	0.0379047	−	0.239321i
$179$	−6.55220	+	2.12894i	−0.489734	+	0.159124i	−0.543466	−	0.839431i	$-0.682888\pi$
$179$	−6.55220	+	2.12894i	−0.489734	+	0.159124i	0.0537320	+	0.998555i	$0.482888\pi$
$180$	1.67017	+	0.951195i	0.124487	+	0.0708979i
$181$	18.8254	+	13.6775i	1.39928	+	1.01664i	0.994774	+	0.102106i	$0.0325580\pi$
$181$	18.8254	+	13.6775i	1.39928	+	1.01664i	0.404510	+	0.914533i	$0.367442\pi$
$182$	2.52905	+	15.9678i	0.187466	+	1.18361i
$183$	−0.0959111	−	0.188236i	−0.00708996	−	0.0139148i
$184$	6.72896	+	20.7096i	0.496065	+	1.52673i
$185$	13.5014	+	5.09164i	0.992644	+	0.374345i
$186$			21.8530i			1.60234i
$187$		0			0
$188$	−0.991282	−	0.991282i	−0.0722967	−	0.0722967i
$189$	3.93152	−	2.85642i	0.285976	−	0.207774i
$190$	13.4463	+	10.7580i	0.975498	+	0.780471i
$191$	2.32799	−	7.16480i	0.168447	−	0.518427i	−0.830827	−	0.556531i	$-0.812132\pi$
$191$	2.32799	−	7.16480i	0.168447	−	0.518427i	0.999274	+	0.0381043i	$0.0121319\pi$
$192$	19.9675	−	3.16255i	1.44103	−	0.228237i
$193$	−24.9586	+	3.95305i	−1.79656	+	0.284547i	−0.963317	−	0.268365i	$-0.913517\pi$
$193$	−24.9586	+	3.95305i	−1.79656	+	0.284547i	−0.833240	+	0.552912i	$0.813517\pi$
$194$	−2.94580	+	9.06624i	−0.211496	+	0.650918i
$195$	25.1689	−	2.79540i	1.80238	−	0.200182i
$196$	0.139212	−	0.101144i	0.00994374	−	0.00722455i
$197$	10.3579	+	10.3579i	0.737967	+	0.737967i	0.972184	−	0.234217i	$-0.0752527\pi$
$197$	10.3579	+	10.3579i	0.737967	+	0.737967i	−0.234217	+	0.972184i	$0.575253\pi$
$198$		0			0
$199$		−	8.62950i		−	0.611729i	−0.952075	−	0.305865i	$-0.901055\pi$
$199$		−	8.62950i		−	0.611729i	0.952075	−	0.305865i	$-0.0989455\pi$
$200$	−8.11383	+	12.8225i	−0.573734	+	0.906689i
$201$	−7.02588	−	21.6234i	−0.495567	−	1.52520i
$202$	9.21772	+	18.0908i	0.648557	+	1.27286i
$203$	−1.59715	−	10.0840i	−0.112098	−	0.707760i
$204$	0.219630	+	0.159570i	0.0153772	+	0.0111722i
$205$	2.68387	−	4.71250i	0.187449	−	0.329135i
$206$	1.73308	−	0.563113i	0.120750	−	0.0392339i
$207$	−2.43077	+	15.3473i	−0.168950	+	1.06671i
$208$	10.7416	−	10.7416i	0.744798	−	0.744798i
$209$		0			0
$210$	−9.06177	−	13.7755i	−0.625322	−	0.950601i
$211$	−9.94032	−	13.6817i	−0.684320	−	0.941885i	0.315656	−	0.948874i	$-0.397775\pi$
$211$	−9.94032	−	13.6817i	−0.684320	−	0.941885i	−0.999976	+	0.00698866i	$0.997775\pi$
$212$	−3.10801	−	1.58361i	−0.213459	−	0.108763i
$213$	−22.7684	+	11.6011i	−1.56007	+	0.794894i
$214$	−8.32245	+	11.4549i	−0.568911	+	0.783039i
$215$	0.210877	−	4.53489i	0.0143817	−	0.309277i
$216$	−5.47362	−	1.77849i	−0.372433	−	0.121011i
$217$	−8.83456	+	17.3388i	−0.599729	+	1.17703i
$218$	−20.3347	−	3.22069i	−1.37724	−	0.218133i
$219$	9.02002			0.609517
$220$		0			0
$221$	1.49953			0.100869
$222$	18.3412	+	2.90496i	1.23098	+	0.194968i
$223$	−3.42025	+	6.71262i	−0.229037	+	0.449510i	−0.976712	−	0.214554i	$-0.931170\pi$
$223$	−3.42025	+	6.71262i	−0.229037	+	0.449510i	0.747675	+	0.664065i	$0.231170\pi$
$224$	5.38516	+	1.74974i	0.359811	+	0.116910i
$225$	−9.31285	+	5.52412i	−0.620857	+	0.368274i
$226$	1.42935	−	1.96733i	0.0950789	−	0.130865i
$227$	5.23244	−	2.66606i	0.347289	−	0.176953i	−0.271641	−	0.962399i	$-0.587566\pi$
$227$	5.23244	−	2.66606i	0.347289	−	0.176953i	0.618930	+	0.785446i	$0.287566\pi$
$228$	−4.88899	−	2.49106i	−0.323781	−	0.164975i
$229$	−14.0925	−	19.3966i	−0.931256	−	1.28176i	−0.959368	−	0.282159i	$-0.908949\pi$
$229$	−14.0925	−	19.3966i	−0.931256	−	1.28176i	0.0281112	−	0.999605i	$-0.491051\pi$
$230$	−19.8947	−	4.10639i	−1.31182	−	0.270767i
$231$		0			0
$232$	−8.54996	+	8.54996i	−0.561332	+	0.561332i
$233$	−2.25466	+	14.2354i	−0.147708	+	0.932590i	0.796834	+	0.604198i	$0.206507\pi$
$233$	−2.25466	+	14.2354i	−0.147708	+	0.932590i	−0.944542	+	0.328392i	$0.893493\pi$
$234$	12.9940	−	4.22201i	0.849445	−	0.276001i
$235$	7.61635	−	2.08897i	0.496836	−	0.136269i
$236$	0.377211	+	0.274060i	0.0245544	+	0.0178398i
$237$	0.838492	+	5.29403i	0.0544659	+	0.343884i
$238$	−0.443266	−	0.869958i	−0.0287327	−	0.0563910i
$239$	−4.67164	−	14.3778i	−0.302183	−	0.930024i	−0.980713	−	0.195451i	$-0.937383\pi$
$239$	−4.67164	−	14.3778i	−0.302183	−	0.930024i	0.678530	−	0.734572i	$-0.262617\pi$
$240$	−5.46704	+	14.4969i	−0.352896	+	0.935769i
$241$		−	3.12966i		−	0.201599i	−0.994907	−	0.100800i	$-0.967860\pi$
$241$		−	3.12966i		−	0.201599i	0.994907	−	0.100800i	$-0.0321401\pi$
$242$		0			0
$243$	−13.3451	−	13.3451i	−0.856086	−	0.856086i
$244$	−0.0298483	+	0.0216861i	−0.00191084	+	0.00138831i
$245$	0.107009	+	0.963480i	0.00683657	+	0.0615545i
$246$	2.15670	−	6.63763i	0.137506	−	0.423200i
$247$	−29.9350	+	4.74124i	−1.90472	+	0.301678i
$248$	22.7627	−	3.60525i	1.44543	−	0.228934i
$249$	−5.83001	+	17.9429i	−0.369462	+	1.13709i
$250$	−6.64852	−	12.4973i	−0.420489	−	0.790399i
$251$	5.01370	−	3.64266i	0.316462	−	0.229923i	−0.418202	−	0.908354i	$-0.637340\pi$
$251$	5.01370	−	3.64266i	0.316462	−	0.229923i	0.734664	+	0.678431i	$0.237340\pi$
$252$	1.55750	+	1.55750i	0.0981133	+	0.0981133i
$253$		0			0
$254$		−	3.19096i		−	0.200219i
$255$	−1.39348	+	0.630281i	−0.0872631	+	0.0394697i
$256$	−2.82009	−	8.67935i	−0.176256	−	0.542459i
$257$	0.614905	+	1.20682i	0.0383567	+	0.0752793i	0.909390	−	0.415946i	$-0.136549\pi$
$257$	0.614905	+	1.20682i	0.0383567	+	0.0752793i	−0.871033	+	0.491225i	$0.836549\pi$
$258$	−0.913947	−	5.77043i	−0.0568999	−	0.359252i
$259$	13.3780	+	9.71972i	0.831271	+	0.603954i
$260$	−1.16977	−	4.26498i	−0.0725464	−	0.264503i
$261$	−8.20600	+	2.66629i	−0.507939	+	0.165039i
$262$	−2.74032	+	17.3017i	−0.169298	+	1.06890i
$263$	6.97161	−	6.97161i	0.429888	−	0.429888i	−0.458702	−	0.888590i	$-0.651686\pi$
$263$	6.97161	−	6.97161i	0.429888	−	0.429888i	0.888590	+	0.458702i	$0.151686\pi$
$264$		0			0
$265$	16.4174	−	10.7997i	1.00851	−	0.663418i
$266$	11.5995	+	15.9654i	0.711213	+	0.978901i
$267$	−5.17052	−	2.63451i	−0.316431	−	0.161230i
$268$	−3.53785	+	1.80262i	−0.216108	+	0.110113i
$269$	−7.96652	+	10.9650i	−0.485727	+	0.668547i	−0.979593	−	0.200992i	$-0.935584\pi$
$269$	−7.96652	+	10.9650i	−0.485727	+	0.668547i	0.493865	+	0.869538i	$0.335584\pi$
$270$	3.96877	−	3.61606i	0.241532	−	0.220067i
$271$	5.12570	+	1.66544i	0.311364	+	0.101168i	0.460531	−	0.887644i	$-0.347659\pi$
$271$	5.12570	+	1.66544i	0.311364	+	0.101168i	−0.149167	+	0.988812i	$0.547659\pi$
$272$	−0.416508	+	0.817444i	−0.0252545	+	0.0495648i
$273$	28.6634	+	4.53984i	1.73479	+	0.274763i
$274$	2.48376			0.150049
$275$		0			0
$276$	6.47284			0.389619
$277$	−28.1706	−	4.46178i	−1.69261	−	0.268082i	−0.765651	−	0.643256i	$-0.777583\pi$
$277$	−28.1706	−	4.46178i	−1.69261	−	0.268082i	−0.926955	+	0.375174i	$0.877583\pi$
$278$	4.98009	−	9.77397i	0.298686	−	0.586204i
$279$	15.6407	+	5.08197i	0.936383	+	0.304249i
$280$	−12.8540	+	11.7117i	−0.768172	+	0.699905i
$281$	6.70908	−	9.23425i	0.400230	−	0.550869i	−0.560572	−	0.828106i	$-0.689419\pi$
$281$	6.70908	−	9.23425i	0.400230	−	0.550869i	0.960802	+	0.277237i	$0.0894186\pi$
$282$	9.05589	−	4.61421i	0.539270	−	0.274772i
$283$	−1.65537	−	0.843455i	−0.0984018	−	0.0501382i	0.404097	−	0.914716i	$-0.367586\pi$
$283$	−1.65537	−	0.843455i	−0.0984018	−	0.0501382i	−0.502499	+	0.864578i	$0.667586\pi$
$284$	2.62308	+	3.61036i	0.155651	+	0.214235i
$285$	25.8251	−	16.9882i	1.52975	−	1.00629i
$286$		0			0
$287$	4.39460	−	4.39460i	0.259405	−	0.259405i
$288$	0.748576	−	4.72632i	0.0441103	−	0.278501i
$289$	16.0818	−	5.22530i	0.945990	−	0.307371i
$290$	−2.98364	−	10.8783i	−0.175205	−	0.638796i
$291$	13.8440	+	10.0582i	0.811548	+	0.589624i
$292$	−0.246422	−	1.55585i	−0.0144208	−	0.0910492i
$293$	8.12751	+	15.9511i	0.474814	+	0.931875i	0.996877	+	0.0789683i	$0.0251626\pi$
$293$	8.12751	+	15.9511i	0.474814	+	0.931875i	−0.522063	+	0.852907i	$0.674837\pi$
$294$	0.385514	+	1.18649i	0.0224836	+	0.0691976i
$295$	−2.39328	+	1.08250i	−0.139342	+	0.0630255i
$296$		−	19.5839i		−	1.13829i
$297$		0			0
$298$	−7.62362	−	7.62362i	−0.441624	−	0.441624i
$299$	28.9250	−	21.0153i	1.67278	−	1.21534i
$300$	2.87970	+	3.47167i	0.166259	+	0.200437i
$301$	1.60768	−	4.94792i	0.0926650	−	0.285193i
$302$	8.61941	−	1.36518i	0.495991	−	0.0785573i
$303$	35.9981	−	5.70153i	2.06803	−	0.327544i
$304$	5.73012	−	17.6355i	0.328645	−	1.01147i
$305$	−0.0229437	−	0.206578i	−0.00131375	−	0.0118286i
$306$	−0.667554	+	0.485006i	−0.0381615	+	0.0277260i
$307$	−9.10688	−	9.10688i	−0.519757	−	0.519757i	0.397741	−	0.917498i	$-0.369794\pi$
$307$	−9.10688	−	9.10688i	−0.519757	−	0.519757i	−0.917498	+	0.397741i	$0.869794\pi$
$308$		0			0
$309$		−	3.27111i		−	0.186087i
$310$	−7.58645	+	20.1169i	−0.430881	+	1.14256i
$311$	−5.82621	−	17.9312i	−0.330374	−	1.01679i	−0.968956	−	0.247233i	$-0.920479\pi$
$311$	−5.82621	−	17.9312i	−0.330374	−	1.01679i	0.638582	−	0.769554i	$-0.279521\pi$
$312$	−15.6034	−	30.6234i	−0.883369	−	1.73371i
$313$	−1.50145	−	9.47980i	−0.0848672	−	0.535830i	−0.993091	−	0.117346i	$-0.962561\pi$
$313$	−1.50145	−	9.47980i	−0.0848672	−	0.535830i	0.908224	−	0.418484i	$-0.137439\pi$
$314$	5.58602	+	4.05848i	0.315237	+	0.229033i
$315$	−11.9668	+	3.28219i	−0.674253	+	0.184930i
$316$	0.890252	−	0.289260i	0.0500806	−	0.0162722i
$317$	2.06475	−	13.0363i	0.115968	−	0.732193i	−0.859350	−	0.511388i	$-0.829132\pi$
$317$	2.06475	−	13.0363i	0.115968	−	0.732193i	0.975318	−	0.220805i	$-0.0708685\pi$
$318$	17.8823	−	17.8823i	1.00279	−	1.00279i
$319$		0			0
$320$	19.4791	+	4.02060i	1.08892	+	0.224759i
$321$	14.9394	+	20.5623i	0.833837	+	1.14768i
$322$	−20.7424	−	10.5688i	−1.15593	−	0.588976i
$323$	1.63092	−	0.830995i	0.0907468	−	0.0462378i
$324$	−2.52129	+	3.47026i	−0.140072	+	0.192792i
$325$	24.1398	+	6.16430i	1.33904	+	0.341934i
$326$	2.69775	+	0.876551i	0.149414	+	0.0485477i
$327$	−16.7782	+	32.9291i	−0.927838	+	1.82098i
$328$	−7.26975	−	1.15142i	−0.401405	−	0.0635763i
$329$	9.05061			0.498976
$330$		0			0
$331$	−12.7005			−0.698084			−0.349042	−	0.937107i	$-0.613493\pi$
$331$	−12.7005			−0.698084			−0.349042	+	0.937107i	$0.613493\pi$
$332$	3.25422	+	0.515418i	0.178599	+	0.0282872i
$333$	6.34444	−	12.4517i	0.347673	−	0.682347i
$334$	−10.1304	−	3.29156i	−0.554309	−	0.180106i
$335$	1.03905	−	22.3447i	0.0567694	−	1.22082i
$336$	−10.4363	+	14.3644i	−0.569349	+	0.783642i
$337$	−13.9105	+	7.08775i	−0.757753	+	0.386094i	−0.789778	−	0.613393i	$-0.789804\pi$
$337$	−13.9105	+	7.08775i	−0.757753	+	0.386094i	0.0320251	+	0.999487i	$0.489804\pi$
$338$	−13.3449	−	6.79957i	−0.725867	−	0.369848i
$339$	−2.56579	−	3.53150i	−0.139354	−	0.191805i
$340$	0.146785	+	0.223140i	0.00796055	+	0.0121015i
$341$		0			0
$342$	11.7928	−	11.7928i	0.637683	−	0.637683i
$343$	−2.97984	+	18.8140i	−0.160896	+	1.01586i
$344$	−5.85987	+	1.90399i	−0.315943	+	0.102656i
$345$	−18.0463	+	31.6868i	−0.971578	+	1.70596i
$346$	−14.1433	−	10.2757i	−0.760346	−	0.552424i
$347$	−0.373519	−	2.35831i	−0.0200516	−	0.126601i	0.975632	−	0.219413i	$-0.0704143\pi$
$347$	−0.373519	−	2.35831i	−0.0200516	−	0.126601i	−0.995684	+	0.0928126i	$0.970414\pi$
$348$	1.63176	+	3.20250i	0.0874713	+	0.171672i
$349$	−10.9107	−	33.5796i	−0.584034	−	1.79747i	−0.603115	−	0.797655i	$-0.706074\pi$
$349$	−10.9107	−	33.5796i	−0.584034	−	1.79747i	0.0190803	−	0.999818i	$-0.493926\pi$
$350$	−3.55957	−	15.8270i	−0.190267	−	0.845989i
$351$			9.44972i			0.504389i
$352$		0			0
$353$	−0.0520523	−	0.0520523i	−0.00277046	−	0.00277046i	0.705720	−	0.708491i	$-0.250624\pi$
$353$	−0.0520523	−	0.0520523i	−0.00277046	−	0.00277046i	−0.708491	+	0.705720i	$0.750624\pi$
$354$	−2.73478	+	1.98693i	−0.145352	+	0.105604i
$355$	−24.9871	+	2.77520i	−1.32617	+	0.147292i
$356$	−0.313167	+	0.963828i	−0.0165978	+	0.0510828i
$357$	−1.73109	+	0.274178i	−0.0916190	+	0.0145110i
$358$	−8.61546	+	1.36455i	−0.455341	+	0.0721190i
$359$	5.01338	−	15.4296i	0.264596	−	0.814342i	−0.727190	−	0.686436i	$-0.759174\pi$
$359$	5.01338	−	15.4296i	0.264596	−	0.814342i	0.991786	−	0.127907i	$-0.0408258\pi$
$360$	11.4751	+	9.18091i	0.604790	+	0.483877i
$361$	−14.5591	+	10.5778i	−0.766271	+	0.556728i
$362$	20.8329	+	20.8329i	1.09495	+	1.09495i
$363$		0			0
$364$		−	5.06813i		−	0.265642i
$365$	8.30344	+	3.13138i	0.434622	+	0.163904i
$366$	−0.0826576	−	0.254394i	−0.00432058	−	0.0132974i
$367$	5.97071	+	11.7182i	0.311668	+	0.611683i	0.992705	−	0.120565i	$-0.0384708\pi$
$367$	5.97071	+	11.7182i	0.311668	+	0.611683i	−0.681037	+	0.732249i	$0.738471\pi$
$368$	3.42193	+	21.6052i	0.178380	+	1.12625i
$369$	−4.24916	−	3.08720i	−0.221203	−	0.160713i
$370$	15.8756	+	9.04148i	0.825333	+	0.470044i
$371$	21.4177	−	6.95905i	1.11195	−	0.361296i
$372$	1.07168	−	6.76632i	0.0555640	−	0.350817i
$373$	−18.8004	+	18.8004i	−0.973446	+	0.973446i	−0.999656	−	0.0262108i	$-0.991656\pi$
$373$	−18.8004	+	18.8004i	−0.973446	+	0.973446i	0.0262108	+	0.999656i	$0.491656\pi$
$374$		0			0
$375$	−25.0236	+	4.41810i	−1.29221	+	0.228150i
$376$	−6.30031	−	8.67163i	−0.324914	−	0.447205i
$377$	17.6893	+	9.01315i	0.911045	+	0.464201i
$378$	5.48229	−	2.79337i	0.281979	−	0.143675i
$379$	7.94654	−	10.9375i	0.408187	−	0.561821i	−0.554588	−	0.832125i	$-0.687124\pi$
$379$	7.94654	−	10.9375i	0.408187	−	0.561821i	0.962775	+	0.270304i	$0.0871243\pi$
$380$	−3.63579	−	3.99042i	−0.186512	−	0.204704i
$381$	−5.44766	−	1.77005i	−0.279092	−	0.0906825i
$382$	4.33035	−	8.49878i	0.221560	−	0.434836i
$383$	−18.0378	−	2.85690i	−0.921687	−	0.145981i	−0.322481	−	0.946576i	$-0.604517\pi$
$383$	−18.0378	−	2.85690i	−0.921687	−	0.145981i	−0.599206	+	0.800595i	$0.704517\pi$
$384$	15.5524			0.793654
$385$		0			0
$386$	−31.9947			−1.62849
$387$	−4.34258	−	0.687797i	−0.220746	−	0.0349627i
$388$	1.35672	−	2.66271i	0.0688769	−	0.135179i
$389$	16.8031	+	5.45965i	0.851950	+	0.276815i	0.702262	−	0.711918i	$-0.252173\pi$
$389$	16.8031	+	5.45965i	0.851950	+	0.276815i	0.149687	+	0.988733i	$0.452173\pi$
$390$	32.0284	+	1.48936i	1.62182	+	0.0754165i
$391$	−1.26919	+	1.74689i	−0.0641857	+	0.0883441i
$392$	1.17228	−	0.597307i	0.0592092	−	0.0301686i
$393$	28.0177	+	14.2757i	1.41330	+	0.720115i
$394$	10.9014	+	15.0045i	0.549204	+	0.755914i
$395$	−1.06599	+	5.16454i	−0.0536359	+	0.259856i
$396$		0			0
$397$	−11.7203	+	11.7203i	−0.588223	+	0.588223i	−0.937150	−	0.348927i	$-0.886546\pi$
$397$	−11.7203	+	11.7203i	−0.588223	+	0.588223i	0.348927	+	0.937150i	$0.386546\pi$
$398$	1.70921	−	10.7915i	0.0856751	−	0.540931i
$399$	33.6907	−	10.9468i	1.68665	−	0.548025i
$400$	−10.0654	+	11.4472i	−0.503272	+	0.572362i
$401$	17.6827	+	12.8472i	0.883032	+	0.641560i	0.934052	−	0.357137i	$-0.116247\pi$
$401$	17.6827	+	12.8472i	0.883032	+	0.641560i	−0.0510200	+	0.998698i	$0.516247\pi$
$402$	−4.50327	−	28.4326i	−0.224603	−	1.41809i
$403$	−17.1791	−	33.7159i	−0.855752	−	1.67951i
$404$	−1.96690	−	6.05348i	−0.0978567	−	0.301172i
$405$	−9.95876	−	22.0177i	−0.494855	−	1.09407i
$406$		−	12.9268i		−	0.641548i
$407$		0			0
$408$	1.46774	+	1.46774i	0.0726641	+	0.0726641i
$409$	−16.3385	+	11.8706i	−0.807886	+	0.586963i	−0.913217	−	0.407474i	$-0.866410\pi$
$409$	−16.3385	+	11.8706i	−0.807886	+	0.586963i	0.105331	+	0.994437i	$0.466410\pi$
$410$	4.28967	−	5.36159i	0.211852	−	0.264790i
$411$	1.37776	−	4.24031i	0.0679600	−	0.209159i
$412$	−0.564229	+	0.0893651i	−0.0277976	+	0.00440270i
$413$	−2.97312	+	0.470896i	−0.146298	+	0.0231713i
$414$	−6.07956	+	18.7110i	−0.298794	+	0.919593i
$415$	−11.5959	+	14.4935i	−0.569221	+	0.711460i
$416$	−8.90770	+	6.47182i	−0.436736	+	0.317307i
$417$	−13.9238	−	13.9238i	−0.681851	−	0.681851i
$418$		0			0
$419$		−	11.1391i		−	0.544179i	−0.962272	−	0.272090i	$-0.912285\pi$
$419$		−	11.1391i		−	0.544179i	0.962272	−	0.272090i	$-0.0877148\pi$
$420$	2.13023	+	4.70970i	0.103945	+	0.229810i
$421$	9.24113	+	28.4413i	0.450385	+	1.38614i	0.876469	+	0.481459i	$0.159893\pi$
$421$	9.24113	+	28.4413i	0.450385	+	1.38614i	−0.426084	+	0.904684i	$0.640107\pi$
$422$	−9.72089	−	19.0783i	−0.473206	−	0.928718i
$423$	−1.19652	−	7.55456i	−0.0581770	−	0.367315i
$424$	−21.5770	−	15.6766i	−1.04787	−	0.761322i
$425$	−1.50158	+	0.0964505i	−0.0728375	+	0.00467853i
$426$	−30.7707	+	9.99799i	−1.49084	+	0.484404i
$427$	0.0372615	−	0.235260i	0.00180321	−	0.0113850i
$428$	3.13863	−	3.13863i	0.151711	−	0.151711i
$429$		0			0
$430$	1.16192	−	5.62929i	0.0560327	−	0.271469i
$431$	−22.3851	−	30.8105i	−1.07825	−	1.48409i	−0.861428	−	0.507879i	$-0.830430\pi$
$431$	−22.3851	−	30.8105i	−1.07825	−	1.48409i	−0.216826	−	0.976210i	$-0.569570\pi$
$432$	−5.15136	−	2.62475i	−0.247845	−	0.126283i
$433$	−3.41540	+	1.74023i	−0.164134	+	0.0836302i	−0.534127	−	0.845404i	$-0.679360\pi$
$433$	−3.41540	+	1.74023i	−0.164134	+	0.0836302i	0.369994	+	0.929034i	$0.379360\pi$
$434$	−14.4822	+	19.9331i	−0.695168	+	0.956817i
$435$	−20.2267	−	0.940562i	−0.969794	−	0.0450965i
$436$	6.13826	+	1.99444i	0.293969	+	0.0955165i
$437$	19.8134	−	38.8860i	0.947804	−	1.86017i
$438$	11.2799	+	1.78656i	0.538975	+	0.0853652i
$439$	−17.8832			−0.853518			−0.426759	−	0.904365i	$-0.640345\pi$
$439$	−17.8832			−0.853518			−0.426759	+	0.904365i	$0.640345\pi$
$440$		0			0
$441$	0.938852			0.0447072
$442$	1.87522	+	0.297006i	0.0891953	+	0.0141271i
$443$	0.817427	−	1.60429i	0.0388372	−	0.0762222i	−0.870773	−	0.491686i	$-0.836381\pi$
$443$	0.817427	−	1.60429i	0.0388372	−	0.0762222i	0.909610	+	0.415464i	$0.136381\pi$
$444$	−5.53651	−	1.79892i	−0.262751	−	0.0853730i
$445$	−3.84516	−	4.22021i	−0.182278	−	0.200057i
$446$	−5.60671	+	7.71697i	−0.265485	+	0.365409i
$447$	−17.2440	+	8.78628i	−0.815615	+	0.415577i
$448$	20.3091	+	10.3480i	0.959516	+	0.488898i
$449$	8.51886	+	11.7252i	0.402030	+	0.553347i	0.961252	−	0.275671i	$-0.0889000\pi$
$449$	8.51886	+	11.7252i	0.402030	+	0.553347i	−0.559222	+	0.829018i	$0.688900\pi$
$450$	−12.7402	+	5.06357i	−0.600581	+	0.238699i
$451$		0			0
$452$	−0.539048	+	0.539048i	−0.0253547	+	0.0253547i
$453$	2.45060	−	15.4725i	0.115139	−	0.726960i
$454$	7.07143	−	2.29765i	0.331879	−	0.107834i
$455$	24.8102	+	14.1299i	1.16312	+	0.662421i
$456$	−33.9412	−	24.6597i	−1.58944	−	1.15480i
$457$	6.02553	+	38.0437i	0.281862	+	1.77961i	0.569622	+	0.821907i	$0.307090\pi$
$457$	6.02553	+	38.0437i	0.281862	+	1.77961i	−0.287759	+	0.957703i	$0.592910\pi$
$458$	−13.7814	−	27.0475i	−0.643962	−	1.26385i
$459$	−0.176357	−	0.542771i	−0.00823165	−	0.0253344i
$460$	5.95861	+	2.24710i	0.277822	+	0.104772i
$461$		−	19.2825i		−	0.898077i	−0.893512	−	0.449038i	$-0.851767\pi$
$461$		−	19.2825i		−	0.898077i	0.893512	−	0.449038i	$-0.148233\pi$
$462$		0			0
$463$	13.7252	+	13.7252i	0.637863	+	0.637863i	0.950028	−	0.312165i	$-0.101054\pi$
$463$	13.7252	+	13.7252i	0.637863	+	0.637863i	−0.312165	+	0.950028i	$0.601054\pi$
$464$	−9.82673	+	7.13954i	−0.456195	+	0.331445i
$465$	30.1356	+	24.1107i	1.39750	+	1.11811i
$466$	−5.63909	+	17.3553i	−0.261226	+	0.803970i
$467$	35.9024	−	5.68638i	1.66136	−	0.263134i	0.746055	−	0.665884i	$-0.231946\pi$
$467$	35.9024	−	5.68638i	1.66136	−	0.263134i	0.915310	+	0.402750i	$0.131946\pi$
$468$	−4.23038	+	0.670026i	−0.195549	+	0.0309719i
$469$	7.92148	−	24.3798i	0.365780	−	1.12575i
$470$	9.93832	−	1.10380i	0.458420	−	0.0509146i
$471$	10.0273	−	7.28527i	0.462034	−	0.335688i
$472$	2.52083	+	2.52083i	0.116030	+	0.116030i
$473$		0			0
$474$			6.78648i			0.311713i
$475$	29.6710	−	6.67317i	1.36140	−	0.306186i
$476$	0.0945849	+	0.291102i	0.00433529	+	0.0133427i
$477$	−8.64023	−	16.9574i	−0.395609	−	0.776426i
$478$	−2.99431	−	18.9053i	−0.136957	−	0.864710i
$479$	−6.89014	−	5.00598i	−0.314819	−	0.228729i	0.419143	−	0.907920i	$-0.362331\pi$
$479$	−6.89014	−	5.00598i	−0.314819	−	0.228729i	−0.733961	+	0.679191i	$0.762331\pi$
$480$	5.55749	−	9.75820i	0.253664	−	0.445399i
$481$	−30.5814	+	9.93649i	−1.39439	+	0.453065i
$482$	0.619880	−	3.91377i	0.0282348	−	0.178267i
$483$	−29.5492	+	29.5492i	−1.34454	+	1.34454i
$484$		0			0
$485$	9.25234	+	14.0652i	0.420127	+	0.638669i
$486$	−14.0453	−	19.3317i	−0.637109	−	0.876906i
$487$	−3.88834	−	1.98121i	−0.176198	−	0.0897772i	0.363667	−	0.931529i	$-0.381525\pi$
$487$	−3.88834	−	1.98121i	−0.176198	−	0.0897772i	−0.539865	+	0.841752i	$0.681525\pi$
$488$	−0.251347	+	0.128068i	−0.0113780	+	0.00579736i
$489$	2.99292	−	4.11941i	0.135345	−	0.186286i
$490$	−0.0570134	+	1.22607i	−0.00257560	+	0.0553880i
$491$	−16.5595	−	5.38049i	−0.747318	−	0.242818i	−0.0894911	−	0.995988i	$-0.528524\pi$
$491$	−16.5595	−	5.38049i	−0.747318	−	0.242818i	−0.657827	+	0.753169i	$0.728524\pi$
$492$	−0.993289	+	1.94944i	−0.0447809	+	0.0878875i
$493$	−1.18424	−	0.187566i	−0.0533357	−	0.00844755i
$494$	−38.3740			−1.72653
$495$		0			0
$496$	23.1513			1.03953
$497$	−28.4563	−	4.50703i	−1.27644	−	0.202168i
$498$	−10.8446	+	21.2836i	−0.485956	+	0.953743i
$499$	7.51710	+	2.44245i	0.336512	+	0.109339i	0.472398	−	0.881385i	$-0.343388\pi$
$499$	7.51710	+	2.44245i	0.336512	+	0.109339i	−0.135887	+	0.990724i	$0.543388\pi$
$500$	1.44570	+	4.19558i	0.0646538	+	0.187632i
$501$	−11.2388	+	15.4689i	−0.502113	+	0.691099i
$502$	6.99132	−	3.56226i	0.312038	−	0.158991i
$503$	33.6124	+	17.1264i	1.49870	+	0.763628i	0.994965	−	0.100227i	$-0.0319569\pi$
$503$	33.6124	+	17.1264i	1.49870	+	0.763628i	0.503740	+	0.863855i	$0.331957\pi$
$504$	9.89904	+	13.6249i	0.440938	+	0.606899i
$505$	35.1176	+	7.24847i	1.56271	+	0.322553i
$506$		0			0
$507$	−19.0109	+	19.0109i	−0.844302	+	0.844302i
$508$	−0.156486	+	0.988015i	−0.00694295	+	0.0438361i
$509$	−39.0282	+	12.6810i	−1.72989	+	0.562077i	−0.993434	−	0.114405i	$-0.963504\pi$
$509$	−39.0282	+	12.6810i	−1.72989	+	0.562077i	−0.736460	+	0.676481i	$0.763504\pi$
$510$	−1.86744	+	0.512191i	−0.0826916	+	0.0226802i
$511$	8.22756	+	5.97767i	0.363966	+	0.264437i
$512$	−3.94847	−	24.9296i	−0.174499	−	1.10174i
$513$	5.23675	+	10.2777i	0.231208	+	0.453772i
$514$	0.529934	+	1.63097i	0.0233744	+	0.0719390i
$515$	1.13560	−	3.01124i	0.0500403	−	0.132691i
$516$			1.83152i			0.0806280i
$517$		0			0
$518$	14.8046	+	14.8046i	0.650479	+	0.650479i
$519$	−25.3882	+	18.4456i	−1.11442	+	0.809672i
$520$	−3.73262	−	33.6074i	−0.163686	−	1.47378i
$521$	−10.9751	+	33.7779i	−0.480828	+	1.47984i	0.357105	+	0.934064i	$0.383764\pi$
$521$	−10.9751	+	33.7779i	−0.480828	+	1.47984i	−0.837933	+	0.545772i	$0.816236\pi$
$522$	−10.7900	+	1.70897i	−0.472267	+	0.0747998i
$523$	33.2608	−	5.26800i	1.45439	−	0.230353i	0.621339	−	0.783542i	$-0.286589\pi$
$523$	33.2608	−	5.26800i	1.45439	−	0.230353i	0.833056	+	0.553189i	$0.186589\pi$
$524$	1.69697	−	5.22273i	0.0741324	−	0.228156i
$525$	−28.9947	−	2.70241i	−1.26543	−	0.117943i
$526$	10.0991	−	7.33744i	0.440343	−	0.319928i
$527$	1.61596	+	1.61596i	0.0703923	+	0.0703923i
$528$		0			0
$529$			28.4836i			1.23842i
$530$	22.6697	−	10.2537i	0.984710	−	0.445392i
$531$	0.786116	+	2.41941i	0.0341145	+	0.104994i
$532$	−2.80861	−	5.51220i	−0.121768	−	0.238984i
$533$	1.89053	+	11.9363i	0.0818878	+	0.517019i
$534$	−5.94414	−	4.31867i	−0.257228	−	0.186887i
$535$	6.61417	+	24.1151i	0.285955	+	1.04259i
$536$	−28.8732	+	9.38148i	−1.24713	+	0.405218i
$537$	−2.44948	+	15.4654i	−0.105703	+	0.667380i
$538$	−12.1343	+	12.1343i	−0.523145	+	0.523145i
$539$		0			0
$540$	−1.40618	+	0.925009i	−0.0605124	+	0.0398061i
$541$	−7.56741	−	10.4156i	−0.325348	−	0.447803i	0.614742	−	0.788728i	$-0.289260\pi$
$541$	−7.56741	−	10.4156i	−0.325348	−	0.447803i	−0.940091	+	0.340925i	$0.889260\pi$
$542$	6.08003	+	3.09793i	0.261160	+	0.133068i
$543$	47.1225	−	24.0101i	2.02222	−	1.03037i
$544$	0.390858	−	0.537969i	0.0167579	−	0.0230652i
$545$	−26.8769	+	24.4884i	−1.15128	+	1.04897i
$546$	34.9456	+	11.3545i	1.49553	+	0.485928i
$547$	9.83521	−	19.3027i	0.420523	−	0.825323i	−0.579424	−	0.815026i	$-0.696722\pi$
$547$	9.83521	−	19.3027i	0.420523	−	0.825323i	0.999947	−	0.0102966i	$-0.00327757\pi$
$548$	−0.769045	−	0.121805i	−0.0328520	−	0.00520324i
$549$	−0.201298			−0.00859119
$550$		0			0
$551$	24.2340			1.03241
$552$	48.8816	+	7.74209i	2.08054	+	0.329525i
$553$	−2.74359	+	5.38460i	−0.116669	+	0.228976i
$554$	−34.3447	−	11.1593i	−1.45917	−	0.474112i
$555$	24.2421	−	22.0877i	1.02902	−	0.937571i
$556$	−2.02130	+	2.78208i	−0.0857223	+	0.117987i
$557$	15.8706	−	8.08648i	0.672459	−	0.342635i	−0.0841961	−	0.996449i	$-0.526832\pi$
$557$	15.8706	−	8.08648i	0.672459	−	0.342635i	0.756655	+	0.653814i	$0.226832\pi$
$558$	18.5528	+	9.45310i	0.785401	+	0.400182i
$559$	5.94635	+	8.18445i	0.251504	+	0.346166i
$560$	−14.5940	+	9.60016i	−0.616708	+	0.405681i
$561$		0			0
$562$	10.2190	−	10.2190i	0.431061	−	0.431061i
$563$	−4.39761	+	27.7654i	−0.185337	+	1.17017i	0.703071	+	0.711120i	$0.251812\pi$
$563$	−4.39761	+	27.7654i	−0.185337	+	1.17017i	−0.888408	+	0.459054i	$0.848188\pi$
$564$	−3.03025	+	0.984588i	−0.127597	+	0.0414586i
$565$	−1.13596	−	4.14168i	−0.0477901	−	0.174242i
$566$	−1.90305	−	1.38265i	−0.0799913	−	0.0581171i
$567$	−4.33214	−	27.3521i	−0.181933	−	1.14868i
$568$	15.4907	+	30.4021i	0.649974	+	1.27565i
$569$	8.08585	+	24.8857i	0.338977	+	1.04326i	0.964730	+	0.263242i	$0.0847916\pi$
$569$	8.08585	+	24.8857i	0.338977	+	1.04326i	−0.625753	+	0.780021i	$0.715208\pi$
$570$	35.6601	−	16.1293i	1.49364	−	0.675584i
$571$			27.6158i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$571$			27.6158i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$572$		0			0
$573$	−12.1072	−	12.1072i	−0.505785	−	0.505785i
$574$	6.36605	−	4.62521i	0.265714	−	0.193052i
$575$	−27.6129	+	22.9045i	−1.15154	+	0.955184i
$576$	5.95256	−	18.3201i	0.248023	−	0.763337i
$577$	−29.2117	+	4.62667i	−1.21610	+	0.192611i	−0.731325	−	0.682029i	$-0.761098\pi$
$577$	−29.2117	+	4.62667i	−1.21610	+	0.192611i	−0.484772	+	0.874640i	$0.661098\pi$
$578$	21.1459	−	3.34919i	0.879555	−	0.139308i
$579$	−17.7477	+	54.6218i	−0.737570	+	2.27001i
$580$	0.390346	+	3.51456i	0.0162082	+	0.145934i
$581$	−17.2088	+	12.5029i	−0.713941	+	0.518709i
$582$	15.3203	+	15.3203i	0.635045	+	0.635045i
$583$		0			0
$584$		−	12.0442i		−	0.498393i
$585$	8.51427	−	22.5772i	0.352022	−	0.933451i
$586$	7.00440	+	21.5573i	0.289349	+	0.890525i
$587$	−3.28137	−	6.44005i	−0.135437	−	0.265809i	0.813320	−	0.581816i	$-0.197658\pi$
$587$	−3.28137	−	6.44005i	−0.135437	−	0.265809i	−0.948757	+	0.316007i	$0.897658\pi$
$588$	−0.0611805	−	0.386278i	−0.00252304	−	0.0159298i
$589$	−37.3687	−	27.1499i	−1.53975	−	1.11869i
$590$	−3.20730	+	0.879681i	−0.132043	+	0.0362159i
$591$	31.6630	−	10.2879i	1.30244	−	0.423189i
$592$	3.07755	−	19.4309i	0.126487	−	0.798605i
$593$	7.89832	−	7.89832i	0.324345	−	0.324345i	−0.526086	−	0.850431i	$-0.676341\pi$
$593$	7.89832	−	7.89832i	0.324345	−	0.324345i	0.850431	+	0.526086i	$0.176341\pi$
$594$		0			0
$595$	−1.68875	−	0.348567i	−0.0692319	−	0.0142899i
$596$	1.98663	+	2.73436i	0.0813755	+	0.112004i
$597$	−17.4754	−	8.90415i	−0.715220	−	0.364423i
$598$	40.3344	−	20.5514i	1.64939	−	0.840408i
$599$	−9.60915	+	13.2259i	−0.392619	+	0.540394i	−0.958872	−	0.283837i	$-0.908392\pi$
$599$	−9.60915	+	13.2259i	−0.392619	+	0.540394i	0.566253	+	0.824231i	$0.308392\pi$
$600$	17.5945	+	29.6617i	0.718292	+	1.21094i
$601$	30.9587	+	10.0591i	1.26283	+	0.410318i	0.862502	−	0.506054i	$-0.168896\pi$
$601$	30.9587	+	10.0591i	1.26283	+	0.410318i	0.400328	+	0.916372i	$0.368896\pi$
$602$	2.99048	−	5.86915i	0.121883	−	0.239209i
$603$	−21.3971	−	3.38897i	−0.871358	−	0.138009i
$604$	−2.73577			−0.111317
$605$		0			0
$606$	46.1463			1.87457
$607$	20.9027	+	3.31067i	0.848416	+	0.134376i	0.565479	−	0.824763i	$-0.308691\pi$
$607$	20.9027	+	3.31067i	0.848416	+	0.134376i	0.282937	+	0.959139i	$0.408691\pi$
$608$	−6.10170	+	11.9753i	−0.247457	+	0.485661i
$609$	−22.0689	−	7.17062i	−0.894277	−	0.290568i
$610$	0.0122242	−	0.262879i	0.000494942	−	0.0106437i
$611$	−10.3446	+	14.2381i	−0.418496	+	0.576011i
$612$	0.230479	−	0.117435i	0.00931657	−	0.00474703i
$613$	−26.6932	−	13.6009i	−1.07813	−	0.549333i	−0.177587	−	0.984105i	$-0.556829\pi$
$613$	−26.6932	−	13.6009i	−1.07813	−	0.549333i	−0.900541	+	0.434772i	$0.856829\pi$
$614$	−9.58476	−	13.1923i	−0.386809	−	0.532397i
$615$	−6.77388	−	10.2975i	−0.273149	−	0.415236i
$616$		0			0
$617$	16.8977	−	16.8977i	0.680276	−	0.680276i	−0.279786	−	0.960062i	$-0.590264\pi$
$617$	16.8977	−	16.8977i	0.680276	−	0.680276i	0.960062	+	0.279786i	$0.0902636\pi$
$618$	0.647897	−	4.09066i	0.0260622	−	0.164550i
$619$	−6.63527	+	2.15593i	−0.266694	+	0.0866541i	−0.439311	−	0.898335i	$-0.644778\pi$
$619$	−6.63527	+	2.15593i	−0.266694	+	0.0866541i	0.172617	+	0.984989i	$0.444778\pi$
$620$	3.33553	−	5.85673i	0.133958	−	0.235212i
$621$	−11.0085	−	7.99816i	−0.441757	−	0.320955i
$622$	−3.73435	−	23.5777i	−0.149734	−	0.945381i
$623$	−2.97034	−	5.82962i	−0.119004	−	0.233559i
$624$	−10.6691	−	32.8361i	−0.427106	−	1.31450i
$625$	−24.5694	−	4.62005i	−0.982776	−	0.184802i
$626$		−	12.1523i		−	0.485702i
$627$		0			0
$628$	−1.53057	−	1.53057i	−0.0610762	−	0.0610762i
$629$	1.57109	−	1.14146i	0.0626434	−	0.0455131i
$630$	−15.6151	+	1.73429i	−0.622119	+	0.0690959i
$631$	5.36729	−	16.5188i	0.213668	−	0.657604i	−0.785577	−	0.618764i	$-0.787634\pi$
$631$	5.36729	−	16.5188i	0.213668	−	0.657604i	0.999245	−	0.0388398i	$-0.0123662\pi$
$632$	7.06899	−	1.11962i	0.281189	−	0.0445360i
$633$	−37.9631	+	6.01276i	−1.50890	+	0.238986i
$634$	5.16411	−	15.8935i	0.205093	−	0.631212i
$635$	−4.40039	−	3.52064i	−0.174624	−	0.139712i
$636$	−6.41386	+	4.65994i	−0.254326	+	0.184779i
$637$	−1.52752	−	1.52752i	−0.0605225	−	0.0605225i
$638$		0			0
$639$			24.3483i			0.963206i
$640$	14.3168	+	5.39915i	0.565923	+	0.213420i
$641$	−8.61628	−	26.5182i	−0.340323	−	1.04741i	−0.964040	−	0.265756i	$-0.914379\pi$
$641$	−8.61628	−	26.5182i	−0.340323	−	1.04741i	0.623718	−	0.781650i	$-0.285621\pi$
$642$	14.6096	+	28.6730i	0.576597	+	1.13163i
$643$	2.61150	+	16.4884i	0.102988	+	0.650238i	0.984138	+	0.177403i	$0.0567695\pi$
$643$	2.61150	+	16.4884i	0.102988	+	0.650238i	−0.881151	+	0.472836i	$0.843230\pi$
$644$	5.90416	+	4.28962i	0.232657	+	0.169035i
$645$	−8.96589	−	5.10626i	−0.353032	−	0.201059i
$646$	2.20412	−	0.716163i	0.0867200	−	0.0281771i
$647$	−3.10713	+	19.6176i	−0.122154	+	0.771249i	0.848221	+	0.529643i	$0.177674\pi$
$647$	−3.10713	+	19.6176i	−0.122154	+	0.771249i	−0.970374	+	0.241606i	$0.922326\pi$
$648$	−23.1911	+	23.1911i	−0.911031	+	0.911031i
$649$		0			0
$650$	28.9669	+	12.4900i	1.13618	+	0.489898i
$651$	25.9966	+	35.7813i	1.01889	+	1.40238i
$652$	−0.792315	−	0.403705i	−0.0310294	−	0.0158103i
$653$	33.0414	−	16.8354i	1.29301	−	0.658821i	0.334101	−	0.942537i	$-0.391567\pi$
$653$	33.0414	−	16.8354i	1.29301	−	0.658821i	0.958908	+	0.283716i	$0.0915673\pi$
$654$	−27.5040	+	37.8560i	−1.07549	+	1.48029i
$655$	20.8359	+	22.8682i	0.814126	+	0.893534i
$656$	−7.03199	−	2.28483i	−0.274553	−	0.0892078i
$657$	3.90186	−	7.65783i	0.152226	−	0.298760i
$658$	11.3182	+	1.79262i	0.441228	+	0.0698836i
$659$	25.1740			0.980641			0.490320	−	0.871542i	$-0.336880\pi$
$659$	25.1740			0.980641			0.490320	+	0.871542i	$0.336880\pi$
$660$		0			0
$661$	−25.7739			−1.00249			−0.501244	−	0.865306i	$-0.667124\pi$
$661$	−25.7739			−1.00249			−0.501244	+	0.865306i	$0.667124\pi$
$662$	−15.8825	−	2.51555i	−0.617292	−	0.0977694i
$663$	1.54726	−	3.03666i	0.0600904	−	0.117934i
$664$	23.9588	+	7.78467i	0.929780	+	0.302104i
$665$	34.8145	+	1.61891i	1.35005	+	0.0627787i
$666$	10.4002	−	14.3147i	0.403001	−	0.554683i
$667$	−25.4720	+	12.9786i	−0.986281	+	0.502535i
$668$	2.97524	+	1.51596i	0.115116	+	0.0586543i
$669$	10.0644	+	13.8525i	0.389114	+	0.535569i
$670$	5.72510	−	27.7371i	0.221180	−	1.07158i
$671$		0			0
$672$	9.09992	−	9.09992i	0.351037	−	0.351037i
$673$	3.53962	−	22.3483i	0.136442	−	0.861464i	−0.820597	−	0.571507i	$-0.806359\pi$
$673$	3.53962	−	22.3483i	0.136442	−	0.861464i	0.957040	−	0.289957i	$-0.0936410\pi$
$674$	−18.7995	+	6.10832i	−0.724129	+	0.235284i
$675$	−0.607810	−	9.46266i	−0.0233946	−	0.364218i
$676$	3.79852	+	2.75979i	0.146097	+	0.106146i
$677$	4.38246	+	27.6698i	0.168432	+	1.06344i	0.916565	+	0.399887i	$0.130950\pi$
$677$	4.38246	+	27.6698i	0.168432	+	1.06344i	−0.748133	+	0.663549i	$0.769050\pi$
$678$	−2.50915	−	4.92449i	−0.0963634	−	0.189124i
$679$	5.96199	+	18.3491i	0.228800	+	0.704174i
$680$	0.841599	+	1.86068i	0.0322738	+	0.0713538i
$681$		−	13.3470i		−	0.511458i
$682$		0			0
$683$	−27.8670	−	27.8670i	−1.06630	−	1.06630i	−0.997640	−	0.0686610i	$-0.978127\pi$
$683$	−27.8670	−	27.8670i	−1.06630	−	1.06630i	−0.0686610	−	0.997640i	$-0.521873\pi$
$684$	−4.22973	+	3.07308i	−0.161728	+	0.117502i
$685$	2.74037	−	3.42514i	0.104704	−	0.130868i
$686$	−7.45283	+	22.9375i	−0.284551	+	0.875756i
$687$	−53.8206	+	8.52434i	−2.05338	+	0.325224i
$688$	−6.11327	+	0.968248i	−0.233066	+	0.0369141i
$689$	−13.5321	+	41.6475i	−0.515532	+	1.58665i
$690$	−28.8437	+	36.0512i	−1.09806	+	1.37245i
$691$	37.8254	−	27.4817i	1.43895	−	1.04545i	0.450683	−	0.892684i	$-0.351180\pi$
$691$	37.8254	−	27.4817i	1.43895	−	1.04545i	0.988262	−	0.152771i	$-0.0488197\pi$
$692$	3.87524	+	3.87524i	0.147315	+	0.147315i
$693$		0			0
$694$		−	3.02314i		−	0.114757i
$695$	−7.98386	−	17.6514i	−0.302845	−	0.669556i
$696$	8.49223	+	26.1364i	0.321897	+	0.990697i
$697$	−0.331351	−	0.650314i	−0.0125508	−	0.0246324i
$698$	−6.99325	−	44.1536i	−0.264698	−	1.67124i
$699$	26.5013	+	19.2543i	1.00237	+	0.728264i
$700$	0.325984	+	5.07507i	0.0123211	+	0.191820i
$701$	21.8504	−	7.09961i	0.825277	−	0.268149i	0.134222	−	0.990951i	$-0.457146\pi$
$701$	21.8504	−	7.09961i	0.825277	−	0.268149i	0.691055	+	0.722803i	$0.257146\pi$
$702$	−1.87167	+	11.8173i	−0.0706416	+	0.446014i
$703$	−27.7544	+	27.7544i	−1.04678	+	1.04678i
$704$		0			0
$705$	3.62844	−	17.5791i	0.136655	−	0.662069i
$706$	−0.0547837	−	0.0754033i	−0.00206181	−	0.00283784i
$707$	36.6139	+	18.6557i	1.37701	+	0.701620i
$708$	0.944209	−	0.481098i	0.0354855	−	0.0180808i
$709$	−6.42747	+	8.84666i	−0.241389	+	0.332243i	−0.912472	−	0.409139i	$-0.865829\pi$
$709$	−6.42747	+	8.84666i	−0.241389	+	0.332243i	0.671083	+	0.741382i	$0.265829\pi$
$710$	−31.7970	−	1.47860i	−1.19332	−	0.0554907i
$711$	4.85725	+	1.57821i	0.182161	+	0.0591877i
$712$	−3.51780	+	6.90407i	−0.131835	+	0.258741i
$713$	53.8179	+	8.52392i	2.01550	+	0.319223i
$714$	−2.21910			−0.0830479
$715$		0			0
$716$	2.73452			0.102194
$717$	−33.9365	−	5.37501i	−1.26738	−	0.200733i
$718$	9.32551	−	18.3023i	0.348025	−	0.683038i
$719$	−43.5254	−	14.1423i	−1.62322	−	0.527417i	−0.650524	−	0.759485i	$-0.725451\pi$
$719$	−43.5254	−	14.1423i	−1.62322	−	0.527417i	−0.972700	+	0.232068i	$0.925451\pi$
$720$	9.94265	+	10.9124i	0.370541	+	0.406682i
$721$	2.16780	−	2.98372i	0.0807332	−	0.111120i
$722$	−20.3019	+	10.3443i	−0.755559	+	0.384977i
$723$	−6.33780	−	3.22927i	−0.235705	−	0.120098i
$724$	−5.42883	−	7.47214i	−0.201761	−	0.277700i
$725$	−18.2932	−	7.88770i	−0.679394	−	0.292942i
$726$		0			0
$727$	−36.0611	+	36.0611i	−1.33743	+	1.33743i	−0.438893	+	0.898539i	$0.644629\pi$
$727$	−36.0611	+	36.0611i	−1.33743	+	1.33743i	−0.898539	+	0.438893i	$0.855371\pi$
$728$	6.06193	−	38.2735i	0.224670	−	1.41851i
$729$	−9.96037	+	3.23632i	−0.368903	+	0.119864i
$730$	9.76357	+	5.56055i	0.361366	+	0.205805i
$731$	−0.494290	−	0.359123i	−0.0182820	−	0.0132826i
$732$	0.0131176	+	0.0828213i	0.000484841	+	0.00306117i
$733$	1.80175	+	3.53613i	0.0665491	+	0.130610i	0.921885	−	0.387464i	$-0.126649\pi$
$733$	1.80175	+	3.53613i	0.0665491	+	0.130610i	−0.855336	+	0.518074i	$0.826649\pi$
$734$	5.14564	+	15.8366i	0.189929	+	0.584541i
$735$	2.06153	+	0.777443i	0.0760408	+	0.0286764i
$736$		−	15.8548i		−	0.584416i
$737$		0			0
$738$	−4.70228	−	4.70228i	−0.173093	−	0.173093i
$739$	−1.27220	+	0.924310i	−0.0467988	+	0.0340013i	−0.610939	−	0.791678i	$-0.709208\pi$
$739$	−1.27220	+	0.924310i	−0.0467988	+	0.0340013i	0.564140	+	0.825679i	$0.309208\pi$
$740$	−4.47215	−	3.57805i	−0.164400	−	0.131532i
$741$	−21.2864	+	65.5128i	−0.781975	+	2.40667i
$742$	28.1621	−	4.46044i	1.03386	−	0.163748i
$743$	42.1322	−	6.67308i	1.54568	−	0.244812i	0.675431	−	0.737423i	$-0.263958\pi$
$743$	42.1322	−	6.67308i	1.54568	−	0.244812i	0.870249	+	0.492612i	$0.163958\pi$
$744$	16.1862	−	49.8161i	0.593416	−	1.82635i
$745$	−18.9243	+	2.10184i	−0.693334	+	0.0770054i
$746$	−27.2343	+	19.7869i	−0.997120	+	0.724450i
$747$	12.7113	+	12.7113i	0.465081	+	0.465081i
$748$		0			0
$749$			28.6563i			1.04708i
$750$	−32.1681	+	0.568687i	−1.17461	+	0.0207655i
$751$	12.1618	+	37.4301i	0.443789	+	1.36584i	0.883806	+	0.467853i	$0.154972\pi$
$751$	12.1618	+	37.4301i	0.443789	+	1.36584i	−0.440017	+	0.897989i	$0.645028\pi$
$752$	−4.88835	−	9.59393i	−0.178260	−	0.349855i
$753$	−2.20340	−	13.9117i	−0.0802963	−	0.506971i
$754$	20.3360	+	14.7750i	0.740593	+	0.538072i
$755$	7.62732	−	13.3925i	0.277587	−	0.487404i
$756$	−1.83447	+	0.596054i	−0.0667189	+	0.0216783i
$757$	−2.40077	+	15.1579i	−0.0872575	+	0.550922i	0.904870	+	0.425688i	$0.139968\pi$
$757$	−2.40077	+	15.1579i	−0.0872575	+	0.550922i	−0.992127	+	0.125234i	$0.960032\pi$
$758$	12.1038	−	12.1038i	0.439631	−	0.439631i
$759$		0			0
$760$	−22.6839	−	34.4836i	−0.822832	−	1.25085i
$761$	2.34728	+	3.23075i	0.0850888	+	0.117115i	0.849439	−	0.527686i	$-0.176940\pi$
$761$	2.34728	+	3.23075i	0.0850888	+	0.117115i	−0.764351	+	0.644801i	$0.776940\pi$
$762$	−6.46193	−	3.29252i	−0.234091	−	0.119275i
$763$	−37.1267	+	18.9170i	−1.34408	+	0.684841i
$764$	−1.75759	+	2.41911i	−0.0635872	+	0.0875203i
$765$	−0.0676908	+	1.45568i	−0.00244737	+	0.0526303i
$766$	−21.9911	−	7.14535i	−0.794571	−	0.258172i
$767$	2.65739	−	5.21542i	0.0959528	−	0.188318i
$768$	−20.4862	−	3.24469i	−0.739231	−	0.117083i
$769$	43.6566			1.57430			0.787148	−	0.616764i	$-0.211557\pi$
$769$	43.6566			1.57430			0.787148	+	0.616764i	$0.211557\pi$
$770$		0			0
$771$	3.07838			0.110865
$772$	9.90649	+	1.56903i	0.356542	+	0.0564708i
$773$	2.28464	−	4.48387i	0.0821730	−	0.161274i	−0.846264	−	0.532764i	$-0.821153\pi$
$773$	2.28464	−	4.48387i	0.0821730	−	0.161274i	0.928437	+	0.371491i	$0.121153\pi$
$774$	−5.29434	−	1.72024i	−0.190301	−	0.0618326i
$775$	19.3713	+	32.6571i	0.695836	+	1.17308i
$776$	13.4305	−	18.4855i	0.482127	−	0.663591i
$777$	33.4870	−	17.0625i	1.20134	−	0.612113i
$778$	19.9316	+	10.1556i	0.714581	+	0.364097i
$779$	8.67092	+	11.9345i	0.310668	+	0.427598i
$780$	−9.84390	−	2.03184i	−0.352468	−	0.0727515i
$781$		0			0
$782$	−1.93317	+	1.93317i	−0.0691302	+	0.0691302i
$783$	1.18200	−	7.46286i	0.0422412	−	0.266701i
$784$	1.25698	−	0.408419i	0.0448923	−	0.0145864i
$785$	11.7599	−	3.22543i	0.419727	−	0.115120i
$786$	32.2097	+	23.4017i	1.14888	+	0.834712i
$787$	−6.63165	−	41.8706i	−0.236393	−	1.49253i	−0.765205	−	0.643787i	$-0.777362\pi$
$787$	−6.63165	−	41.8706i	−0.236393	−	1.49253i	0.528812	−	0.848739i	$-0.322638\pi$
$788$	−2.63956	−	5.18043i	−0.0940305	−	0.184545i
$789$	−6.92453	−	21.3115i	−0.246520	−	0.758710i
$790$	−2.35599	+	6.24734i	−0.0838223	+	0.222270i
$791$		−	4.92162i		−	0.174993i
$792$		0			0
$793$	0.327513	+	0.327513i	0.0116303	+	0.0116303i
$794$	−16.9781	+	12.3353i	−0.602529	+	0.437763i
$795$	−4.93018	−	44.3899i	−0.174856	−	1.57435i
$796$	−1.05844	+	3.25756i	−0.0375156	+	0.115461i
$797$	−45.1079	+	7.14438i	−1.59780	+	0.253067i	−0.890885	−	0.454229i	$-0.849915\pi$
$797$	−45.1079	+	7.14438i	−1.59780	+	0.253067i	−0.706918	+	0.707296i	$0.749915\pi$
$798$	44.2998	−	7.01640i	1.56820	−	0.248378i
$799$	0.328449	−	1.01086i	0.0116197	−	0.0357617i
$800$	8.50363	−	7.05363i	0.300649	−	0.249384i
$801$	−4.47330	+	3.25004i	−0.158056	+	0.114835i
$802$	19.5683	+	19.5683i	0.690982	+	0.690982i
$803$		0			0
$804$			9.02440i			0.318266i
$805$	−37.4600	+	16.9434i	−1.32029	+	0.597177i
$806$	−14.8052	−	45.5657i	−0.521491	−	1.60498i
$807$	13.9848	+	27.4468i	0.492289	+	0.966172i
$808$	−7.61312	−	48.0673i	−0.267828	−	1.69100i
$809$	−25.7494	−	18.7081i	−0.905302	−	0.657740i	0.0345205	−	0.999404i	$-0.489010\pi$
$809$	−25.7494	−	18.7081i	−0.905302	−	0.657740i	−0.939822	+	0.341664i	$0.889010\pi$
$810$	−8.09288	−	29.5065i	−0.284355	−	1.03675i
$811$	30.1488	−	9.79593i	1.05867	−	0.343982i	0.272603	−	0.962127i	$-0.412116\pi$
$811$	30.1488	−	9.79593i	1.05867	−	0.343982i	0.786064	+	0.618145i	$0.212116\pi$
$812$	−0.633938	+	4.00252i	−0.0222468	+	0.140461i
$813$	8.66148	−	8.66148i	0.303772	−	0.303772i
$814$		0			0
$815$	4.18524	−	2.75312i	0.146603	−	0.0964377i
$816$	1.22562	+	1.68692i	0.0429053	+	0.0590541i
$817$	11.0030	+	5.60628i	0.384945	+	0.196139i
$818$	−22.7831	+	11.6086i	−0.796592	+	0.405884i
$819$	16.2534	−	22.3709i	0.567939	−	0.781701i
$820$	−1.59114	+	1.44974i	−0.0555651	+	0.0506271i
$821$	−29.5072	−	9.58747i	−1.02981	−	0.334605i	−0.255094	−	0.966916i	$-0.582106\pi$
$821$	−29.5072	−	9.58747i	−1.02981	−	0.334605i	−0.774714	+	0.632311i	$0.782106\pi$
$822$	2.56281	−	5.02980i	0.0893883	−	0.175434i
$823$	−39.6889	−	6.28610i	−1.38347	−	0.219120i	−0.580071	−	0.814566i	$-0.696975\pi$
$823$	−39.6889	−	6.28610i	−1.38347	−	0.219120i	−0.803395	+	0.595446i	$0.796975\pi$
$824$	−4.36783			−0.152161
$825$		0			0
$826$	−3.81128			−0.132611
$827$	2.77897	+	0.440146i	0.0966344	+	0.0153054i	0.204564	−	0.978853i	$-0.434422\pi$
$827$	2.77897	+	0.440146i	0.0966344	+	0.0153054i	−0.107930	+	0.994158i	$0.534422\pi$
$828$	2.80000	−	5.49532i	0.0973069	−	0.190975i
$829$	−26.5360	−	8.62206i	−0.921633	−	0.299457i	−0.190496	−	0.981688i	$-0.561010\pi$
$829$	−26.5360	−	8.62206i	−0.921633	−	0.299457i	−0.731136	+	0.682231i	$0.761010\pi$
$830$	−17.3718	+	15.8280i	−0.602985	+	0.549398i
$831$	−38.1026	+	52.4437i	−1.32176	+	1.81925i
$832$	−39.4918	+	20.1221i	−1.36913	+	0.697607i
$833$	0.116245	+	0.0592298i	0.00402765	+	0.00205219i
$834$	−14.6544	−	20.1701i	−0.507442	−	0.698433i
$835$	−15.7161	+	10.3383i	−0.543878	+	0.357772i
$836$		0			0
$837$	−10.1834	+	10.1834i	−0.351991	+	0.351991i
$838$	2.20627	−	13.9299i	0.0762145	−	0.481199i
$839$	41.0512	−	13.3384i	1.41725	−	0.460491i	0.502520	−	0.864566i	$-0.332406\pi$
$839$	41.0512	−	13.3384i	1.41725	−	0.460491i	0.914726	+	0.404075i	$0.132406\pi$
$840$	10.4539	+	38.1147i	0.360693	+	1.31508i
$841$	10.6189	+	7.71506i	0.366168	+	0.266037i
$842$	5.92315	+	37.3973i	0.204125	+	1.28880i
$843$	−11.7774	−	23.1145i	−0.405637	−	0.796107i
$844$	2.07426	+	6.38393i	0.0713991	+	0.219744i
$845$	−24.1004	+	10.9008i	−0.829078	+	0.374998i
$846$		−	9.68428i		−	0.332952i
$847$		0			0
$848$	−18.9448	−	18.9448i	−0.650567	−	0.650567i
$849$	−3.41612	+	2.48196i	−0.117241	+	0.0851805i
$850$	−1.89690	−	0.176798i	−0.0650630	−	0.00606411i
$851$	14.3082	−	44.0362i	0.490480	−	1.50954i
$852$	10.0178	−	1.58666i	0.343204	−	0.0543582i
$853$	6.48289	−	1.02679i	0.221970	−	0.0351566i	−0.0444587	−	0.999011i	$-0.514156\pi$
$853$	6.48289	−	1.02679i	0.221970	−	0.0351566i	0.266429	+	0.963855i	$0.414156\pi$
$854$	0.0931941	−	0.286822i	0.00318904	−	0.00981484i
$855$	−3.25130	−	29.2737i	−0.111192	−	1.00114i
$856$	27.4564	−	19.9482i	0.938440	−	0.681817i
$857$	−16.3855	−	16.3855i	−0.559717	−	0.559717i	0.369510	−	0.929227i	$-0.379526\pi$
$857$	−16.3855	−	16.3855i	−0.559717	−	0.559717i	−0.929227	+	0.369510i	$0.879526\pi$
$858$		0			0
$859$		−	44.6723i		−	1.52420i	−0.647461	−	0.762099i	$-0.724169\pi$
$859$		−	44.6723i		−	1.52420i	0.647461	−	0.762099i	$-0.275831\pi$
$860$	−0.635827	+	1.68601i	−0.0216815	+	0.0574926i
$861$	−4.36493	−	13.4339i	−0.148756	−	0.457825i
$862$	−21.8910	−	42.9635i	−0.745611	−	1.46334i
$863$	1.86588	+	11.7807i	0.0635152	+	0.401019i	0.998879	+	0.0473326i	$0.0150721\pi$
$863$	1.86588	+	11.7807i	0.0635152	+	0.401019i	−0.935364	+	0.353687i	$0.884928\pi$
$864$	3.39017	+	2.46310i	0.115336	+	0.0837964i
$865$	−29.7748	+	8.16647i	−1.01237	+	0.277668i
$866$	−4.61578	+	1.49976i	−0.156850	+	0.0509638i
$867$	6.01204	−	37.9585i	0.204180	−	1.28914i
$868$	5.46164	−	5.46164i	0.185380	−	0.185380i
$869$		0			0
$870$	−25.1080	−	5.18243i	−0.851240	−	0.175701i
$871$	29.2994	+	40.3271i	0.992771	+	1.36643i
$872$	43.9694	+	22.4036i	1.48899	+	0.758680i
$873$	14.5278	−	7.40230i	0.491693	−	0.250530i
$874$	32.4795	−	44.7042i	1.09863	−	1.51214i
$875$	−25.7530	−	12.5535i	−0.870612	−	0.424385i
$876$	−3.40498	−	1.10634i	−0.115043	−	0.0373799i
$877$	7.23153	−	14.1927i	0.244191	−	0.479253i	−0.736084	−	0.676891i	$-0.763327\pi$
$877$	7.23153	−	14.1927i	0.244191	−	0.479253i	0.980275	+	0.197638i	$0.0633270\pi$
$878$	−22.3637	−	3.54206i	−0.754737	−	0.119539i
$879$	40.6884			1.37239
$880$		0			0
$881$	−35.9869			−1.21243			−0.606214	−	0.795301i	$-0.707313\pi$
$881$	−35.9869			−1.21243			−0.606214	+	0.795301i	$0.707313\pi$
$882$	1.17407	+	0.185955i	0.0395331	+	0.00626143i
$883$	7.38117	−	14.4864i	0.248396	−	0.487505i	−0.732818	−	0.680424i	$-0.761796\pi$
$883$	7.38117	−	14.4864i	0.248396	−	0.487505i	0.981215	+	0.192919i	$0.0617955\pi$
$884$	−0.566059	−	0.183924i	−0.0190386	−	0.00618602i
$885$	−0.277310	+	5.96352i	−0.00932169	+	0.200462i
$886$	1.33998	−	1.84433i	0.0450176	−	0.0619614i
$887$	27.7666	−	14.1478i	0.932310	−	0.475036i	0.0792538	−	0.996854i	$-0.474746\pi$
$887$	27.7666	−	14.1478i	0.932310	−	0.475036i	0.853056	+	0.521819i	$0.174746\pi$
$888$	−39.6590	−	20.2072i	−1.33087	−	0.678111i
$889$	−3.79602	−	5.22477i	−0.127314	−	0.175233i
$890$	−3.97265	−	6.03914i	−0.133163	−	0.202432i
$891$		0			0
$892$	2.11444	−	2.11444i	0.0707968	−	0.0707968i
$893$	−3.36064	+	21.2183i	−0.112460	+	0.710042i
$894$	−23.3046	+	7.57214i	−0.779424	+	0.253250i
$895$	−7.62382	+	13.3864i	−0.254836	+	0.447458i
$896$	14.1860	+	10.3067i	0.473921	+	0.344324i
$897$	−12.7119	−	80.2595i	−0.424436	−	2.67979i
$898$	8.33082	+	16.3502i	0.278003	+	0.545612i
$899$	9.34981	+	28.7757i	0.311833	+	0.959725i
$900$	4.19307	−	0.943043i	0.139769	−	0.0314348i
$901$		−	2.64469i		−	0.0881074i
$902$		0			0
$903$	−8.36106	−	8.36106i	−0.278239	−	0.278239i
$904$	−4.71553	+	3.42603i	−0.156836	+	0.113948i
$905$	51.7142	−	5.74366i	1.71904	−	0.190926i
$906$	6.12915	−	18.8636i	0.203627	−	0.626700i
$907$	34.2037	−	5.41733i	1.13571	−	0.179879i	0.439862	−	0.898065i	$-0.355027\pi$
$907$	34.2037	−	5.41733i	1.13571	−	0.179879i	0.695851	+	0.718186i	$0.255027\pi$
$908$	−2.30220	+	0.364633i	−0.0764012	+	0.0121008i
$909$	10.7315	−	33.0280i	0.355940	−	1.09547i
$910$	28.2275	+	22.5841i	0.935734	+	0.748656i
$911$	24.8232	−	18.0351i	0.822428	−	0.597529i	−0.0949790	−	0.995479i	$-0.530278\pi$
$911$	24.8232	−	18.0351i	0.822428	−	0.597529i	0.917407	+	0.397950i	$0.130278\pi$
$912$	−29.8007	−	29.8007i	−0.986800	−	0.986800i
$913$		0			0
$914$			48.7687i			1.61312i
$915$	−0.442011	−	0.166690i	−0.0146124	−	0.00551062i
$916$	2.94070	+	9.05054i	0.0971635	+	0.299038i
$917$	16.0955	+	31.5891i	0.531519	+	1.04317i
$918$	−0.113037	−	0.713688i	−0.00373078	−	0.0235552i
$919$	−21.6741	−	15.7472i	−0.714963	−	0.519451i	0.169808	−	0.985477i	$-0.445685\pi$
$919$	−21.6741	−	15.7472i	−0.714963	−	0.519451i	−0.884771	+	0.466026i	$0.845685\pi$
$920$	42.3105	+	24.0967i	1.39494	+	0.794445i
$921$	−27.8388	+	9.04538i	−0.917321	+	0.298056i
$922$	3.81922	−	24.1136i	0.125779	−	0.794139i
$923$	39.6149	−	39.6149i	1.30394	−	1.30394i
$924$		0			0
$925$	29.9841	−	11.9171i	0.985872	−	0.391832i
$926$	14.4454	+	19.8824i	0.474706	+	0.653376i
$927$	−2.77711	−	1.41501i	−0.0912123	−	0.0464750i
$928$	7.84432	−	3.99688i	0.257502	−	0.131204i
$929$	14.9610	−	20.5921i	0.490856	−	0.675605i	−0.489690	−	0.871897i	$-0.662890\pi$
$929$	14.9610	−	20.5921i	0.490856	−	0.675605i	0.980546	+	0.196292i	$0.0628899\pi$
$930$	32.9103	+	36.1203i	1.07917	+	1.18443i
$931$	−2.50787	−	0.814855i	−0.0821920	−	0.0267058i
$932$	2.59714	−	5.09718i	0.0850722	−	0.166964i
$933$	−42.3238	−	6.70342i	−1.38562	−	0.219460i
$934$	46.0237			1.50594
$935$		0			0
$936$	−32.7484			−1.07041
$937$	39.0588	+	6.18631i	1.27600	+	0.202098i	0.757417	−	0.652931i	$-0.226461\pi$
$937$	39.0588	+	6.18631i	1.27600	+	0.202098i	0.518579	+	0.855029i	$0.326461\pi$
$938$	14.7349	−	28.9190i	0.481113	−	0.944238i
$939$	−20.7466	−	6.74096i	−0.677038	−	0.219983i
$940$	−3.13132	−	0.145610i	−0.102133	−	0.00474928i
$941$	24.1047	−	33.1773i	0.785791	−	1.08155i	−0.208829	−	0.977952i	$-0.566965\pi$
$941$	24.1047	−	33.1773i	0.785791	−	1.08155i	0.994619	−	0.103596i	$-0.0330348\pi$
$942$	13.9825	−	7.12446i	0.455576	−	0.232127i
$943$	−15.5054	−	7.90042i	−0.504927	−	0.257273i
$944$	2.10499	+	2.89726i	0.0685114	+	0.0942979i
$945$	2.19660	−	10.6421i	0.0714553	−	0.346188i
$946$		0			0
$947$	42.9022	−	42.9022i	1.39413	−	1.39413i	0.578336	−	0.815799i	$-0.303702\pi$
$947$	42.9022	−	42.9022i	1.39413	−	1.39413i	0.815799	−	0.578336i	$-0.196298\pi$
$948$	0.332812	−	2.10129i	0.0108092	−	0.0682468i
$949$	−18.8077	+	6.11099i	−0.610523	+	0.198371i
$950$	38.4266	−	2.46824i	1.24672	−	0.0800802i
$951$	−24.2691	−	17.6325i	−0.786978	−	0.571773i
$952$	0.366103	+	2.31148i	0.0118655	+	0.0749155i
$953$	2.07080	+	4.06417i	0.0670797	+	0.131651i	0.922112	−	0.386924i	$-0.126463\pi$
$953$	2.07080	+	4.06417i	0.0670797	+	0.131651i	−0.855032	+	0.518576i	$0.826463\pi$
$954$	−7.44627	−	22.9173i	−0.241082	−	0.741974i
$955$	−6.94222	−	15.3485i	−0.224645	−	0.496664i
$956$			6.00049i			0.194070i
$957$		0			0
$958$	−7.62489	−	7.62489i	−0.246349	−	0.246349i
$959$	4.06682	−	2.95472i	0.131325	−	0.0954128i
$960$	28.2411	−	35.2981i	0.911478	−	1.13924i
$961$	8.24126	−	25.3640i	0.265847	−	0.818193i
$962$	−40.2114	+	6.36885i	−1.29647	+	0.205340i
$963$	23.9195	−	3.78848i	0.770795	−	0.122082i
$964$	−0.383866	+	1.18142i	−0.0123635	+	0.0380509i
$965$	−35.3002	+	44.1212i	−1.13635	+	1.42031i
$966$	−42.8052	+	31.0998i	−1.37723	+	1.00062i
$967$	−27.0023	−	27.0023i	−0.868336	−	0.868336i	0.123952	−	0.992288i	$-0.460443\pi$
$967$	−27.0023	−	27.0023i	−0.868336	−	0.868336i	−0.992288	+	0.123952i	$0.960443\pi$
$968$		0			0
$969$		−	4.16018i		−	0.133644i
$970$	8.78459	+	19.4217i	0.282056	+	0.623594i
$971$	−12.2539	−	37.7137i	−0.393247	−	1.21029i	−0.930318	−	0.366753i	$-0.880469\pi$
$971$	−12.2539	−	37.7137i	−0.393247	−	1.21029i	0.537071	−	0.843537i	$-0.319531\pi$
$972$	3.40081	+	6.67446i	0.109081	+	0.214084i
$973$	−3.47305	−	21.9280i	−0.111341	−	0.702978i
$974$	−4.47012	−	3.24773i	−0.143232	−	0.104064i
$975$	37.3913	−	42.5245i	1.19748	−	1.36187i
$976$	−0.269508	+	0.0875685i	−0.00862675	+	0.00280300i
$977$	0.994498	−	6.27901i	0.0318168	−	0.200883i	−0.966660	−	0.256065i	$-0.917574\pi$
$977$	0.994498	−	6.27901i	0.0318168	−	0.200883i	0.998476	+	0.0551818i	$0.0175738\pi$
$978$	4.55869	−	4.55869i	0.145771	−	0.145771i
$979$		0			0
$980$	0.0777799	−	0.376830i	0.00248459	−	0.0120374i
$981$	20.6983	+	28.4888i	0.660846	+	0.909577i
$982$	−19.6426	−	10.0084i	−0.626820	−	0.319381i
$983$	1.06922	−	0.544795i	0.0341028	−	0.0173763i	−0.436856	−	0.899531i	$-0.643908\pi$
$983$	1.06922	−	0.544795i	0.0341028	−	0.0173763i	0.470959	+	0.882155i	$0.343908\pi$
$984$	−9.83283	+	13.5337i	−0.313459	+	0.431439i
$985$	32.7191	+	1.52147i	1.04252	+	0.0484782i
$986$	−1.44380	−	0.469118i	−0.0459798	−	0.0149398i
$987$	9.33867	−	18.3282i	0.297253	−	0.583392i
$988$	11.8817	+	1.88188i	0.378008	+	0.0598706i
$989$	−14.5675			−0.463220
$990$		0			0
$991$	9.57879			0.304280			0.152140	−	0.988359i	$-0.451383\pi$
$991$	9.57879			0.304280			0.152140	+	0.988359i	$0.451383\pi$
$992$	−16.5737	−	2.62501i	−0.526214	−	0.0833442i
$993$	−13.1047	+	25.7195i	−0.415867	+	0.816184i
$994$	−34.6930	−	11.2725i	−1.10040	−	0.357541i
$995$	−12.9959	−	14.2635i	−0.411998	−	0.452184i
$996$	4.40155	−	6.05822i	0.139469	−	0.191962i
$997$	15.0259	−	7.65608i	0.475875	−	0.242470i	−0.199566	−	0.979884i	$-0.563953\pi$
$997$	15.0259	−	7.65608i	0.475875	−	0.242470i	0.675441	+	0.737414i	$0.263953\pi$
$998$	8.91667	+	4.54327i	0.282252	+	0.143815i
$999$	7.19325	+	9.90065i	0.227584	+	0.313243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.f.118.7		80
5.2	odd	4	inner	605.2.m.f.602.4		80
11.2	odd	10		605.2.e.a.483.7	yes	20
11.3	even	5	inner	605.2.m.f.578.7		80
11.4	even	5	inner	605.2.m.f.403.7		80
11.5	even	5	inner	605.2.m.f.233.4		80
11.6	odd	10	inner	605.2.m.f.233.7		80
11.7	odd	10	inner	605.2.m.f.403.4		80
11.8	odd	10	inner	605.2.m.f.578.4		80
11.9	even	5		605.2.e.a.483.4	yes	20
11.10	odd	2	inner	605.2.m.f.118.4		80
55.2	even	20		605.2.e.a.362.4	✓	20
55.7	even	20	inner	605.2.m.f.282.7		80
55.17	even	20	inner	605.2.m.f.112.7		80
55.27	odd	20	inner	605.2.m.f.112.4		80
55.32	even	4	inner	605.2.m.f.602.7		80
55.37	odd	20	inner	605.2.m.f.282.4		80
55.42	odd	20		605.2.e.a.362.7	yes	20
55.47	odd	20	inner	605.2.m.f.457.7		80
55.52	even	20	inner	605.2.m.f.457.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.4	✓	20	55.2	even	20
605.2.e.a.362.7	yes	20	55.42	odd	20
605.2.e.a.483.4	yes	20	11.9	even	5
605.2.e.a.483.7	yes	20	11.2	odd	10
605.2.m.f.112.4		80	55.27	odd	20	inner
605.2.m.f.112.7		80	55.17	even	20	inner
605.2.m.f.118.4		80	11.10	odd	2	inner
605.2.m.f.118.7		80	1.1	even	1	trivial
605.2.m.f.233.4		80	11.5	even	5	inner
605.2.m.f.233.7		80	11.6	odd	10	inner
605.2.m.f.282.4		80	55.37	odd	20	inner
605.2.m.f.282.7		80	55.7	even	20	inner
605.2.m.f.403.4		80	11.7	odd	10	inner
605.2.m.f.403.7		80	11.4	even	5	inner
605.2.m.f.457.4		80	55.52	even	20	inner
605.2.m.f.457.7		80	55.47	odd	20	inner
605.2.m.f.578.4		80	11.8	odd	10	inner
605.2.m.f.578.7		80	11.3	even	5	inner
605.2.m.f.602.4		80	5.2	odd	4	inner
605.2.m.f.602.7		80	55.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25054 + 0.198066i) q^{2} +(1.03183 - 2.02507i) q^{3} +(-0.377491 - 0.122654i) q^{4} +(1.65288 - 1.50599i) q^{5} +(1.69144 - 2.32807i) q^{6} +(2.28322 - 1.16336i) q^{7} +(-2.70403 - 1.37777i) q^{8} +(-1.27290 - 1.75200i) q^{9} +O(q^{10})\)	\(q+(1.25054 + 0.198066i) q^{2} +(1.03183 - 2.02507i) q^{3} +(-0.377491 - 0.122654i) q^{4} +(1.65288 - 1.50599i) q^{5} +(1.69144 - 2.32807i) q^{6} +(2.28322 - 1.16336i) q^{7} +(-2.70403 - 1.37777i) q^{8} +(-1.27290 - 1.75200i) q^{9} +(2.36528 - 1.55592i) q^{10} +(-0.637889 + 0.637889i) q^{12} +(-0.779496 + 4.92155i) q^{13} +(3.08568 - 1.00260i) q^{14} +(-1.34425 - 4.90112i) q^{15} +(-2.46639 - 1.79193i) q^{16} +(-0.0470767 - 0.297231i) q^{17} +(-1.24481 - 2.44307i) q^{18} +(1.87958 + 5.78475i) q^{19} +(-0.808662 + 0.365764i) q^{20} -5.82406i q^{21} +(-5.07364 - 5.07364i) q^{23} +(-5.58019 + 4.05424i) q^{24} +(0.464008 - 4.97842i) q^{25} +(-1.94958 + 6.00020i) q^{26} +(1.87308 - 0.296667i) q^{27} +(-1.00458 + 0.159110i) q^{28} +(1.23121 - 3.78926i) q^{29} +(-0.710296 - 6.39530i) q^{30} +(-6.14370 + 4.46366i) q^{31} +(1.56247 + 1.56247i) q^{32} -0.381023i q^{34} +(2.02188 - 5.36138i) q^{35} +(0.265619 + 0.817492i) q^{36} +(2.92965 + 5.74976i) q^{37} +(1.20473 + 7.60634i) q^{38} +(9.16219 + 6.65672i) q^{39} +(-6.54434 + 1.79495i) q^{40} +(2.30661 - 0.749464i) q^{41} +(1.15355 - 7.28323i) q^{42} +(1.43561 - 1.43561i) q^{43} +(-4.74245 - 0.978869i) q^{45} +(-5.33988 - 7.34971i) q^{46} +(3.14697 + 1.60346i) q^{47} +(-6.17369 + 3.14565i) q^{48} +(-0.254823 + 0.350734i) q^{49} +(1.56632 - 6.13382i) q^{50} +(-0.650489 - 0.211357i) q^{51} +(0.897901 - 1.76223i) q^{52} +(8.68003 + 1.37478i) q^{53} +2.40113 q^{54} -7.77673 q^{56} +(13.6539 + 2.16257i) q^{57} +(2.29020 - 4.49476i) q^{58} +(-1.11721 - 0.363002i) q^{59} +(-0.0937000 + 2.01501i) q^{60} +(0.0546362 - 0.0752003i) q^{61} +(-8.56705 + 4.36513i) q^{62} +(-4.94452 - 2.51936i) q^{63} +(5.22833 + 7.19618i) q^{64} +(6.12337 + 9.30862i) q^{65} +(7.07364 - 7.07364i) q^{67} +(-0.0186856 + 0.117976i) q^{68} +(-15.5096 + 5.03938i) q^{69} +(3.59035 - 6.30416i) q^{70} +(-9.09599 - 6.60862i) q^{71} +(1.02811 + 6.49125i) q^{72} +(1.80175 + 3.53613i) q^{73} +(2.52481 + 7.77058i) q^{74} +(-9.60290 - 6.07652i) q^{75} -2.41423i q^{76} +(10.1392 + 10.1392i) q^{78} +(-1.90794 + 1.38620i) q^{79} +(-6.77527 + 0.752497i) q^{80} +(3.33954 - 10.2781i) q^{81} +(3.03296 - 0.480373i) q^{82} +(-8.19874 + 1.29855i) q^{83} +(-0.714346 + 2.19853i) q^{84} +(-0.525437 - 0.420389i) q^{85} +(2.07963 - 1.51094i) q^{86} +(-6.40314 - 6.40314i) q^{87} -2.55325i q^{89} +(-5.73675 - 2.16343i) q^{90} +(3.94575 + 12.1438i) q^{91} +(1.29295 + 2.53756i) q^{92} +(2.70001 + 17.0472i) q^{93} +(3.61783 + 2.62850i) q^{94} +(11.8185 + 6.73086i) q^{95} +(4.77631 - 1.55192i) q^{96} +(-1.17781 + 7.43640i) q^{97} +(-0.388135 + 0.388135i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{5}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^5	\( 80 q - 4 q^{3} - 4 q^{5} - 64 q^{12} - 16 q^{15} - 12 q^{16} - 16 q^{20} + 48 q^{23} - 16 q^{25} - 56 q^{26} + 20 q^{27} + 16 q^{31} + 20 q^{36} + 72 q^{37} + 32 q^{38} + 32 q^{42} - 112 q^{45} - 16 q^{47} + 104 q^{48} + 52 q^{53} - 128 q^{56} - 12 q^{58} - 112 q^{60} + 112 q^{67} - 104 q^{70} - 24 q^{71} - 64 q^{75} + 416 q^{78} - 44 q^{80} - 100 q^{81} + 124 q^{82} - 128 q^{86} + 16 q^{92} + 132 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^5 - 64 * q^12 - 16 * q^15 - 12 * q^16 - 16 * q^20 + 48 * q^23 - 16 * q^25 - 56 * q^26 + 20 * q^27 + 16 * q^31 + 20 * q^36 + 72 * q^37 + 32 * q^38 + 32 * q^42 - 112 * q^45 - 16 * q^47 + 104 * q^48 + 52 * q^53 - 128 * q^56 - 12 * q^58 - 112 * q^60 + 112 * q^67 - 104 * q^70 - 24 * q^71 - 64 * q^75 + 416 * q^78 - 44 * q^80 - 100 * q^81 + 124 * q^82 - 128 * q^86 + 16 * q^92 + 132 * q^93 - 32 * q^97

Introduction

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