LMFDB - Embedded newform 605.2.g.k.251.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(81,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.1
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.k.511.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.147481 + 0.453901i) q^{2} +(-0.261370 + 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0476470 - 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +0.477260 q^{10} -0.572554 q^{12} +(1.44244 - 4.43939i) q^{13} +(-1.03679 + 0.753275i) q^{14} +(0.261370 + 0.189896i) q^{15} +(0.829779 + 2.55380i) q^{16} +(1.42961 + 4.39990i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(-3.51149 + 2.55125i) q^{19} +(0.547647 - 1.68548i) q^{20} -0.867517 q^{21} +2.77222 q^{23} +(0.179735 - 0.553168i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(1.80231 + 1.30945i) q^{26} +(-0.588587 - 1.81148i) q^{27} +(1.47055 + 4.52590i) q^{28} +(-2.43790 - 1.77124i) q^{29} +(-0.124741 + 0.0906300i) q^{30} +(0.737407 - 2.26951i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(0.829779 - 2.55380i) q^{35} +(-4.15163 + 3.01633i) q^{36} +(8.61029 + 6.25574i) q^{37} +(-0.640135 - 1.97013i) q^{38} +(0.466012 + 1.43424i) q^{39} +(1.45650 + 1.05821i) q^{40} +(-1.78826 + 1.29924i) q^{41} +(0.127943 - 0.393767i) q^{42} +7.06719 q^{43} +2.89563 q^{45} +(-0.408851 + 1.25832i) q^{46} +(-3.52905 + 2.56401i) q^{47} +(-0.701836 - 0.509914i) q^{48} +(0.0650188 + 0.200107i) q^{49} +(-0.147481 - 0.453901i) q^{50} +(-1.20918 - 0.878523i) q^{51} +(6.69257 - 4.86243i) q^{52} +(-1.95733 + 6.02403i) q^{53} +0.909040 q^{54} -4.83428 q^{56} +(0.433326 - 1.33364i) q^{57} +(1.16351 - 0.845342i) q^{58} +(-9.50375 - 6.90488i) q^{59} +(0.176929 + 0.544531i) q^{60} +(1.23070 + 3.78770i) q^{61} +(0.921378 + 0.669420i) q^{62} +(-6.29042 + 4.57026i) q^{63} +(-0.939522 + 2.89155i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(-2.53359 + 7.79760i) q^{68} +(-0.724576 + 0.526435i) q^{69} +(1.03679 + 0.753275i) q^{70} +(0.369495 + 1.13719i) q^{71} +(-1.61093 - 4.95794i) q^{72} +(0.826577 + 0.600544i) q^{73} +(-4.10935 + 2.98562i) q^{74} +(0.0998345 - 0.307259i) q^{75} -7.69223 q^{76} -0.719730 q^{78} +(-1.08222 + 3.33073i) q^{79} +(2.17239 - 1.57833i) q^{80} +(-6.53000 - 4.74432i) q^{81} +(-0.325994 - 1.00331i) q^{82} +(-3.43498 - 10.5718i) q^{83} +(-1.24381 - 0.903681i) q^{84} +(3.74278 - 2.71929i) q^{85} +(-1.04228 + 3.20780i) q^{86} +0.973547 q^{87} +2.76978 q^{89} +(-0.427051 + 1.31433i) q^{90} +(10.1404 - 7.36742i) q^{91} +(3.97470 + 2.88779i) q^{92} +(0.238235 + 0.733212i) q^{93} +(-0.643336 - 1.97998i) q^{94} +(3.51149 + 2.55125i) q^{95} +(1.27606 - 0.927114i) q^{96} +(5.72738 - 17.6271i) q^{97} -0.100418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23}+ \cdots - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * q^98

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.147481	+	0.453901i	−0.104285	+	0.320957i	−0.989562	−	0.144108i	$-0.953969\pi$
$2$	−0.147481	+	0.453901i	−0.104285	+	0.320957i	0.885277	+	0.465064i	$0.153969\pi$
$3$	−0.261370	+	0.189896i	−0.150902	+	0.109637i	−0.660674	−	0.750673i	$-0.729730\pi$
$3$	−0.261370	+	0.189896i	−0.150902	+	0.109637i	0.509772	+	0.860309i	$0.329730\pi$
$4$	1.43376	+	1.04169i	0.716879	+	0.520843i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.0476470	−	0.146642i	−0.0194518	−	0.0598665i
$7$	2.17239	+	1.57833i	0.821086	+	0.596554i	0.917023	−	0.398834i	$-0.130585\pi$
$7$	2.17239	+	1.57833i	0.821086	+	0.596554i	−0.0959376	+	0.995387i	$0.530585\pi$
$8$	−1.45650	+	1.05821i	−0.514950	+	0.374133i
$9$	−0.894797	+	2.75390i	−0.298266	+	0.917968i
$10$	0.477260			0.150923
$11$		0			0
$11$		0			0
$12$	−0.572554			−0.165282
$13$	1.44244	−	4.43939i	0.400062	−	1.23126i	−0.524886	−	0.851172i	$-0.675892\pi$
$13$	1.44244	−	4.43939i	0.400062	−	1.23126i	0.924949	−	0.380092i	$-0.124108\pi$
$14$	−1.03679	+	0.753275i	−0.277095	+	0.201321i
$15$	0.261370	+	0.189896i	0.0674854	+	0.0490310i
$16$	0.829779	+	2.55380i	0.207445	+	0.638449i
$17$	1.42961	+	4.39990i	0.346732	+	1.06713i	0.960650	+	0.277762i	$0.0895926\pi$
$17$	1.42961	+	4.39990i	0.346732	+	1.06713i	−0.613918	+	0.789370i	$0.710407\pi$
$18$	−1.11803	−	0.812299i	−0.263523	−	0.191461i
$19$	−3.51149	+	2.55125i	−0.805592	+	0.585297i	−0.912549	−	0.408967i	$-0.865889\pi$
$19$	−3.51149	+	2.55125i	−0.805592	+	0.585297i	0.106958	+	0.994264i	$0.465889\pi$
$20$	0.547647	−	1.68548i	0.122458	−	0.376886i
$21$	−0.867517			−0.189308
$22$		0			0
$23$	2.77222			0.578048			0.289024	−	0.957322i	$-0.406669\pi$
$23$	2.77222			0.578048			0.289024	+	0.957322i	$0.406669\pi$
$24$	0.179735	−	0.553168i	0.0366883	−	0.112915i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	1.80231	+	1.30945i	0.353462	+	0.256805i
$27$	−0.588587	−	1.81148i	−0.113274	−	0.348620i
$28$	1.47055	+	4.52590i	0.277908	+	0.855314i
$29$	−2.43790	−	1.77124i	−0.452707	−	0.328911i	0.337956	−	0.941162i	$-0.390264\pi$
$29$	−2.43790	−	1.77124i	−0.452707	−	0.328911i	−0.790664	+	0.612251i	$0.790264\pi$
$30$	−0.124741	+	0.0906300i	−0.0227746	+	0.0165467i
$31$	0.737407	−	2.26951i	0.132442	−	0.407615i	−0.862741	−	0.505646i	$-0.831254\pi$
$31$	0.737407	−	2.26951i	0.132442	−	0.407615i	0.995183	+	0.0980305i	$0.0312543\pi$
$32$	−4.88221			−0.863061
$33$		0			0
$34$	−2.20796			−0.378662
$35$	0.829779	−	2.55380i	0.140258	−	0.431670i
$36$	−4.15163	+	3.01633i	−0.691938	+	0.502722i
$37$	8.61029	+	6.25574i	1.41552	+	1.02844i	0.992490	+	0.122324i	$0.0390346\pi$
$37$	8.61029	+	6.25574i	1.41552	+	1.02844i	0.423033	+	0.906114i	$0.360965\pi$
$38$	−0.640135	−	1.97013i	−0.103844	−	0.319598i
$39$	0.466012	+	1.43424i	0.0746217	+	0.229662i
$40$	1.45650	+	1.05821i	0.230293	+	0.167317i
$41$	−1.78826	+	1.29924i	−0.279279	+	0.202908i	−0.718603	−	0.695421i	$-0.755218\pi$
$41$	−1.78826	+	1.29924i	−0.279279	+	0.202908i	0.439324	+	0.898329i	$0.355218\pi$
$42$	0.127943	−	0.393767i	0.0197420	−	0.0607596i
$43$	7.06719			1.07774			0.538868	−	0.842390i	$-0.318852\pi$
$43$	7.06719			1.07774			0.538868	+	0.842390i	$0.318852\pi$
$44$		0			0
$45$	2.89563			0.431654
$46$	−0.408851	+	1.25832i	−0.0602819	+	0.185528i
$47$	−3.52905	+	2.56401i	−0.514765	+	0.373999i	−0.814628	−	0.579983i	$-0.803059\pi$
$47$	−3.52905	+	2.56401i	−0.514765	+	0.373999i	0.299863	+	0.953982i	$0.403059\pi$
$48$	−0.701836	−	0.509914i	−0.101301	−	0.0735997i
$49$	0.0650188	+	0.200107i	0.00928840	+	0.0285868i
$50$	−0.147481	−	0.453901i	−0.0208570	−	0.0641913i
$51$	−1.20918	−	0.878523i	−0.169319	−	0.123018i
$52$	6.69257	−	4.86243i	0.928092	−	0.674298i
$53$	−1.95733	+	6.02403i	−0.268859	+	0.827464i	0.721920	+	0.691977i	$0.243260\pi$
$53$	−1.95733	+	6.02403i	−0.268859	+	0.827464i	−0.990779	+	0.135487i	$0.956740\pi$
$54$	0.909040			0.123705
$55$		0			0
$56$	−4.83428			−0.646008
$57$	0.433326	−	1.33364i	0.0573954	−	0.176645i
$58$	1.16351	−	0.845342i	0.152777	−	0.110999i
$59$	−9.50375	−	6.90488i	−1.23728	−	0.898939i	−0.239869	−	0.970805i	$-0.577104\pi$
$59$	−9.50375	−	6.90488i	−1.23728	−	0.898939i	−0.997414	+	0.0718667i	$0.977104\pi$
$60$	0.176929	+	0.544531i	0.0228414	+	0.0702987i
$61$	1.23070	+	3.78770i	0.157575	+	0.484966i	0.998413	−	0.0563214i	$-0.0179372\pi$
$61$	1.23070	+	3.78770i	0.157575	+	0.484966i	−0.840838	+	0.541287i	$0.817937\pi$
$62$	0.921378	+	0.669420i	0.117015	+	0.0850164i
$63$	−6.29042	+	4.57026i	−0.792519	+	0.575799i
$64$	−0.939522	+	2.89155i	−0.117440	+	0.361444i
$65$	−4.66785			−0.578975
$66$		0			0
$67$	7.31984			0.894260			0.447130	−	0.894469i	$-0.352446\pi$
$67$	7.31984			0.894260			0.447130	+	0.894469i	$0.352446\pi$
$68$	−2.53359	+	7.79760i	−0.307243	+	0.945598i
$69$	−0.724576	+	0.526435i	−0.0872287	+	0.0633754i
$70$	1.03679	+	0.753275i	0.123921	+	0.0900336i
$71$	0.369495	+	1.13719i	0.0438510	+	0.134960i	0.970585	−	0.240758i	$-0.0773961\pi$
$71$	0.369495	+	1.13719i	0.0438510	+	0.134960i	−0.926734	+	0.375718i	$0.877396\pi$
$72$	−1.61093	−	4.95794i	−0.189850	−	0.584299i
$73$	0.826577	+	0.600544i	0.0967436	+	0.0702883i	0.635105	−	0.772425i	$-0.280957\pi$
$73$	0.826577	+	0.600544i	0.0967436	+	0.0702883i	−0.538362	+	0.842714i	$0.680957\pi$
$74$	−4.10935	+	2.98562i	−0.477702	+	0.347071i
$75$	0.0998345	−	0.307259i	0.0115279	−	0.0354792i
$76$	−7.69223			−0.882360
$77$		0			0
$78$	−0.719730			−0.0814934
$79$	−1.08222	+	3.33073i	−0.121759	+	0.374736i	−0.993297	−	0.115593i	$-0.963123\pi$
$79$	−1.08222	+	3.33073i	−0.121759	+	0.374736i	0.871538	+	0.490329i	$0.163123\pi$
$80$	2.17239	−	1.57833i	0.242880	−	0.176463i
$81$	−6.53000	−	4.74432i	−0.725555	−	0.527147i
$82$	−0.325994	−	1.00331i	−0.0360000	−	0.110797i
$83$	−3.43498	−	10.5718i	−0.377038	−	1.16040i	−0.942093	−	0.335351i	$-0.891145\pi$
$83$	−3.43498	−	10.5718i	−0.377038	−	1.16040i	0.565055	−	0.825053i	$-0.308855\pi$
$84$	−1.24381	−	0.903681i	−0.135711	−	0.0985996i
$85$	3.74278	−	2.71929i	0.405961	−	0.294948i
$86$	−1.04228	+	3.20780i	−0.112392	+	0.345906i
$87$	0.973547			0.104375
$88$		0			0
$89$	2.76978			0.293596			0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978			0.293596			0.146798	+	0.989167i	$0.453103\pi$
$90$	−0.427051	+	1.31433i	−0.0450151	+	0.138542i
$91$	10.1404	−	7.36742i	1.06300	−	0.772315i
$92$	3.97470	+	2.88779i	0.414391	+	0.301073i
$93$	0.238235	+	0.733212i	0.0247038	+	0.0760305i
$94$	−0.643336	−	1.97998i	−0.0663550	−	0.204220i
$95$	3.51149	+	2.55125i	0.360271	+	0.261753i
$96$	1.27606	−	0.927114i	0.130238	−	0.0946232i
$97$	5.72738	−	17.6271i	0.581528	−	1.78976i	−0.0312615	−	0.999511i	$-0.509952\pi$
$97$	5.72738	−	17.6271i	0.581528	−	1.78976i	0.612789	−	0.790247i	$-0.290048\pi$
$98$	−0.100418			−0.0101438
$99$		0			0
$100$	−1.77222			−0.177222
$101$	2.19852	−	6.76634i	0.218761	−	0.673276i	−0.780104	−	0.625649i	$-0.784834\pi$
$101$	2.19852	−	6.76634i	0.218761	−	0.673276i	0.998865	−	0.0476270i	$-0.0151659\pi$
$102$	0.577094	−	0.419284i	0.0571409	−	0.0415153i
$103$	−6.09056	−	4.42505i	−0.600121	−	0.436014i	0.245801	−	0.969320i	$-0.420949\pi$
$103$	−6.09056	−	4.42505i	−0.600121	−	0.436014i	−0.845922	+	0.533307i	$0.820949\pi$
$104$	2.59688	+	7.99237i	0.254645	+	0.783716i
$105$	0.268077	+	0.825058i	0.0261617	+	0.0805174i
$106$	−2.44565	−	1.77687i	−0.237542	−	0.172584i
$107$	14.5859	−	10.5973i	1.41008	−	1.02448i	0.416764	−	0.909015i	$-0.363164\pi$
$107$	14.5859	−	10.5973i	1.41008	−	1.02448i	0.993312	−	0.115465i	$-0.0368358\pi$
$108$	1.04311	−	3.21035i	0.100373	−	0.308916i
$109$	16.3653			1.56751			0.783756	−	0.621068i	$-0.213301\pi$
$109$	16.3653			1.56751			0.783756	+	0.621068i	$0.213301\pi$
$110$		0			0
$111$	−3.43842			−0.326360
$112$	−2.22814	+	6.85750i	−0.210539	+	0.647973i
$113$	1.66154	−	1.20718i	0.156304	−	0.113562i	−0.506884	−	0.862014i	$-0.669203\pi$
$113$	1.66154	−	1.20718i	0.156304	−	0.113562i	0.663188	+	0.748453i	$0.269203\pi$
$114$	0.541433	+	0.393374i	0.0507099	+	0.0368429i
$115$	−0.856664	−	2.63654i	−0.0798843	−	0.245859i
$116$	−1.65029	−	5.07906i	−0.153225	−	0.471579i
$117$	10.9349	+	7.94470i	1.01094	+	0.734488i
$118$	4.53576	−	3.29542i	0.417551	−	0.303368i
$119$	−3.83883	+	11.8147i	−0.351905	+	1.08305i
$120$	−0.581635			−0.0530958
$121$		0			0
$122$	−1.90075			−0.172086
$123$	0.220675	−	0.679167i	0.0198976	−	0.0612384i
$124$	3.42138	−	2.48578i	0.307249	−	0.223229i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−1.14673	−	3.52926i	−0.102158	−	0.314411i
$127$	0.0235677	+	0.0725340i	0.00209130	+	0.00643635i	0.952097	−	0.305797i	$-0.0989229\pi$
$127$	0.0235677	+	0.0725340i	0.00209130	+	0.00643635i	−0.950005	+	0.312233i	$0.898923\pi$
$128$	−9.07350	−	6.59228i	−0.801992	−	0.582681i
$129$	−1.84715	+	1.34203i	−0.162633	+	0.118159i
$130$	0.688421	−	2.11874i	0.0603785	−	0.185826i
$131$	11.4831			1.00328			0.501642	−	0.865075i	$-0.332730\pi$
$131$	11.4831			1.00328			0.501642	+	0.865075i	$0.332730\pi$
$132$		0			0
$133$	−11.6550			−1.01062
$134$	−1.07954	+	3.32248i	−0.0932580	+	0.287019i
$135$	−1.54094	+	1.11956i	−0.132623	+	0.0963562i
$136$	−6.73823	−	4.89561i	−0.577799	−	0.419795i
$137$	−5.66406	−	17.4322i	−0.483914	−	1.48933i	−0.833548	−	0.552447i	$-0.813694\pi$
$137$	−5.66406	−	17.4322i	−0.483914	−	1.48933i	0.349635	−	0.936886i	$-0.386306\pi$
$138$	−0.132088	−	0.406525i	−0.0112441	−	0.0346057i
$139$	−18.7590	−	13.6292i	−1.59111	−	1.15601i	−0.902330	−	0.431046i	$-0.858145\pi$
$139$	−18.7590	−	13.6292i	−1.59111	−	1.15601i	−0.688785	−	0.724966i	$-0.741855\pi$
$140$	3.84996	−	2.79716i	0.325381	−	0.236403i
$141$	0.435493	−	1.34031i	0.0366751	−	0.112874i
$142$	−0.570666			−0.0478892
$143$		0			0
$144$	−7.77539			−0.647949
$145$	−0.931196	+	2.86593i	−0.0773317	+	0.238002i
$146$	−0.394492	+	0.286615i	−0.0326484	+	0.0237205i
$147$	−0.0549936	−	0.0399552i	−0.00453580	−	0.00329545i
$148$	5.82856	+	17.9385i	0.479104	+	1.47453i
$149$	−4.53161	−	13.9469i	−0.371244	−	1.14257i	−0.945978	−	0.324232i	$-0.894894\pi$
$149$	−4.53161	−	13.9469i	−0.371244	−	1.14257i	0.574733	−	0.818341i	$-0.305106\pi$
$150$	0.124741	+	0.0906300i	0.0101851	+	0.00739991i
$151$	−6.08301	+	4.41957i	−0.495028	+	0.359659i	−0.807115	−	0.590394i	$-0.798972\pi$
$151$	−6.08301	+	4.41957i	−0.495028	+	0.359659i	0.312086	+	0.950054i	$0.398972\pi$
$152$	2.41473	−	7.43178i	0.195861	−	0.602797i
$153$	−13.3961			−1.08301
$154$		0			0
$155$	−2.38630			−0.191672
$156$	−0.825877	+	2.54179i	−0.0661231	+	0.203506i
$157$	10.8262	−	7.86568i	0.864023	−	0.627750i	−0.0649531	−	0.997888i	$-0.520690\pi$
$157$	10.8262	−	7.86568i	0.864023	−	0.627750i	0.928977	+	0.370139i	$0.120690\pi$
$158$	−1.35221	−	0.982441i	−0.107576	−	0.0781588i
$159$	−0.632355	−	1.94619i	−0.0501491	−	0.154343i
$160$	1.50869	+	4.64326i	0.119272	+	0.367082i
$161$	6.02234	+	4.37549i	0.474627	+	0.344837i
$162$	3.11651	−	2.26427i	0.244856	−	0.177898i
$163$	−0.238558	+	0.734206i	−0.0186853	+	0.0575075i	−0.959964	−	0.280122i	$-0.909625\pi$
$163$	−0.238558	+	0.734206i	−0.0186853	+	0.0575075i	0.941279	+	0.337629i	$0.109625\pi$
$164$	−3.91733			−0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	2.62118	−	8.06716i	0.202833	−	0.624256i	−0.796962	−	0.604029i	$-0.793561\pi$
$167$	2.62118	−	8.06716i	0.202833	−	0.624256i	0.999795	−	0.0202268i	$-0.00643884\pi$
$168$	1.26354	−	0.918013i	0.0974840	−	0.0708263i
$169$	−7.11029	−	5.16593i	−0.546946	−	0.397379i
$170$	0.682297	+	2.09989i	0.0523298	+	0.161055i
$171$	−3.88382	−	11.9532i	−0.297003	−	0.914081i
$172$	10.1326	+	7.36179i	0.772606	+	0.561331i
$173$	4.10876	−	2.98519i	0.312384	−	0.226960i	−0.420535	−	0.907276i	$-0.638158\pi$
$173$	4.10876	−	2.98519i	0.312384	−	0.226960i	0.732919	+	0.680316i	$0.238158\pi$
$174$	−0.143580	+	0.441894i	−0.0108848	+	0.0334999i
$175$	−2.68522			−0.202984
$176$		0			0
$177$	3.79521			0.285265
$178$	−0.408491	+	1.25721i	−0.0306177	+	0.0942315i
$179$	9.15568	−	6.65199i	0.684328	−	0.497193i	−0.190463	−	0.981694i	$-0.560999\pi$
$179$	9.15568	−	6.65199i	0.684328	−	0.497193i	0.874791	+	0.484501i	$0.160999\pi$
$180$	4.15163	+	3.01633i	0.309444	+	0.224824i
$181$	2.28674	+	7.03787i	0.169972	+	0.523121i	0.999368	−	0.0355402i	$-0.0113152\pi$
$181$	2.28674	+	7.03787i	0.169972	+	0.523121i	−0.829396	+	0.558661i	$0.811315\pi$
$182$	1.84856	+	5.68929i	0.137025	+	0.421718i
$183$	−1.04094	−	0.756287i	−0.0769485	−	0.0559063i
$184$	−4.03774	+	2.93359i	−0.297666	+	0.216267i
$185$	3.28884	−	10.1220i	0.241800	−	0.744185i
$186$	−0.367941			−0.0269787
$187$		0			0
$188$	−7.73070			−0.563819
$189$	1.58048	−	4.86423i	0.114963	−	0.353821i
$190$	−1.67589	+	1.21761i	−0.121582	+	0.0883346i
$191$	4.17135	+	3.03067i	0.301829	+	0.219291i	0.728382	−	0.685171i	$-0.240272\pi$
$191$	4.17135	+	3.03067i	0.301829	+	0.219291i	−0.426554	+	0.904462i	$0.640272\pi$
$192$	−0.303532	−	0.934176i	−0.0219056	−	0.0674184i
$193$	1.24605	+	3.83494i	0.0896925	+	0.276045i	0.985834	−	0.167723i	$-0.0536414\pi$
$193$	1.24605	+	3.83494i	0.0896925	+	0.276045i	−0.896142	+	0.443768i	$0.853641\pi$
$194$	7.15627	+	5.19933i	0.513790	+	0.373290i
$195$	1.22004	−	0.886408i	0.0873686	−	0.0634770i
$196$	−0.115228	+	0.354635i	−0.00823056	+	0.0253311i
$197$	−11.4176			−0.813469			−0.406734	−	0.913547i	$-0.633333\pi$
$197$	−11.4176			−0.813469			−0.406734	+	0.913547i	$0.633333\pi$
$198$		0			0
$199$	−7.16644			−0.508015			−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644			−0.508015			−0.254008	+	0.967202i	$0.581749\pi$
$200$	0.556333	−	1.71222i	0.0393387	−	0.121072i
$201$	−1.91319	+	1.39001i	−0.134946	+	0.0980438i
$202$	2.74701	+	1.99582i	0.193279	+	0.140425i
$203$	−2.50047	−	7.69565i	−0.175498	−	0.540128i
$204$	−0.818531	−	2.51918i	−0.0573086	−	0.176378i
$205$	1.78826	+	1.29924i	0.124897	+	0.0907431i
$206$	2.90678	−	2.11190i	0.202525	−	0.147143i
$207$	−2.48058	+	7.63443i	−0.172412	+	0.530630i
$208$	12.5342			0.869090
$209$		0			0
$210$	−0.414031			−0.0285709
$211$	−1.07649	+	3.31309i	−0.0741086	+	0.228083i	−0.981249	−	0.192746i	$-0.938261\pi$
$211$	−1.07649	+	3.31309i	−0.0741086	+	0.228083i	0.907140	+	0.420829i	$0.138261\pi$
$212$	−9.08148	+	6.59808i	−0.623719	+	0.453158i
$213$	−0.312523	−	0.227061i	−0.0214137	−	0.0155580i
$214$	2.65897	+	8.18348i	0.181764	+	0.559411i
$215$	−2.18388	−	6.72129i	−0.148939	−	0.458388i
$216$	2.77420	+	2.01558i	0.188760	+	0.137143i
$217$	5.18397	−	3.76638i	0.351911	−	0.255678i
$218$	−2.41358	+	7.42824i	−0.163468	+	0.503104i
$219$	−0.330084			−0.0223050
$220$		0			0
$221$	21.5950			1.45264
$222$	0.507102	−	1.56070i	0.0340345	−	0.104747i
$223$	−8.53103	+	6.19816i	−0.571280	+	0.415059i	−0.835570	−	0.549384i	$-0.814862\pi$
$223$	−8.53103	+	6.19816i	−0.571280	+	0.415059i	0.264290	+	0.964443i	$0.414862\pi$
$224$	−10.6061	−	7.70575i	−0.708647	−	0.514862i
$225$	−0.894797	−	2.75390i	−0.0596532	−	0.183594i
$226$	0.302893	+	0.932209i	0.0201481	+	0.0620096i
$227$	0.174762	+	0.126972i	0.0115994	+	0.00842743i	0.593570	−	0.804782i	$-0.297718\pi$
$227$	0.174762	+	0.126972i	0.0115994	+	0.00842743i	−0.581970	+	0.813210i	$0.697718\pi$
$228$	2.01052	−	1.46073i	0.133150	−	0.0967390i
$229$	−0.0233956	+	0.0720042i	−0.00154602	+	0.00475817i	−0.951827	−	0.306637i	$-0.900796\pi$
$229$	−0.0233956	+	0.0720042i	−0.00154602	+	0.00475817i	0.950281	+	0.311395i	$0.100796\pi$
$230$	1.32307			0.0872407
$231$		0			0
$232$	5.42514			0.356178
$233$	−4.67235	+	14.3800i	−0.306096	+	0.942067i	0.673170	+	0.739488i	$0.264932\pi$
$233$	−4.67235	+	14.3800i	−0.306096	+	0.942067i	−0.979266	+	0.202579i	$0.935068\pi$
$234$	−5.21881	+	3.79169i	−0.341164	+	0.247870i
$235$	3.52905	+	2.56401i	0.230210	+	0.167257i
$236$	−6.43336	−	19.7999i	−0.418776	−	1.28886i
$237$	−0.349634	−	1.07606i	−0.0227111	−	0.0698977i
$238$	−4.79655	−	3.48489i	−0.310914	−	0.225892i
$239$	−18.7406	+	13.6158i	−1.21223	+	0.880734i	−0.995431	−	0.0954825i	$-0.969561\pi$
$239$	−18.7406	+	13.6158i	−1.21223	+	0.880734i	−0.216796	+	0.976217i	$0.569561\pi$
$240$	−0.268077	+	0.825058i	−0.0173043	+	0.0532572i
$241$	21.3349			1.37430			0.687151	−	0.726515i	$-0.258861\pi$
$241$	21.3349			1.37430			0.687151	+	0.726515i	$0.258861\pi$
$242$		0			0
$243$	8.32179			0.533843
$244$	−2.18107	+	6.71266i	−0.139629	+	0.429734i
$245$	0.170221	−	0.123673i	0.0108750	−	0.00790119i
$246$	0.275729	+	0.200329i	0.0175798	+	0.0127725i
$247$	6.26085	+	19.2689i	0.398368	+	1.22605i
$248$	1.32758	+	4.08586i	0.0843012	+	0.259453i
$249$	2.90535	+	2.11086i	0.184119	+	0.133770i
$250$	−0.386111	+	0.280526i	−0.0244198	+	0.0177420i
$251$	−1.92266	+	5.91734i	−0.121357	+	0.373499i	−0.993220	−	0.116251i	$-0.962912\pi$
$251$	−1.92266	+	5.91734i	−0.121357	+	0.373499i	0.871863	+	0.489751i	$0.162912\pi$
$252$	−13.7797			−0.868041
$253$		0			0
$254$	−0.0363991			−0.00228388
$255$	−0.461867	+	1.42148i	−0.0289232	+	0.0890165i
$256$	−0.588982	+	0.427920i	−0.0368113	+	0.0267450i
$257$	11.5611	+	8.39964i	0.721163	+	0.523955i	0.886755	−	0.462239i	$-0.152954\pi$
$257$	11.5611	+	8.39964i	0.721163	+	0.523955i	−0.165593	+	0.986194i	$0.552954\pi$
$258$	−0.336730	−	1.03635i	−0.0209639	−	0.0645203i
$259$	8.83126	+	27.1798i	0.548748	+	1.68887i
$260$	−6.69257	−	4.86243i	−0.415055	−	0.301555i
$261$	7.05926	−	5.12885i	0.436957	−	0.317468i
$262$	−1.69355	+	5.21220i	−0.104628	+	0.322011i
$263$	−4.13132			−0.254748			−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132			−0.254748			−0.127374	+	0.991855i	$0.540655\pi$
$264$		0			0
$265$	6.33404			0.389097
$266$	1.71890	−	5.29024i	0.105393	−	0.324365i
$267$	−0.723937	+	0.525971i	−0.0443042	+	0.0321889i
$268$	10.4949	+	7.62497i	0.641077	+	0.465769i
$269$	−0.520367	−	1.60152i	−0.0317273	−	0.0976466i	0.933939	−	0.357433i	$-0.116348\pi$
$269$	−0.520367	−	1.60152i	−0.0317273	−	0.0976466i	−0.965666	+	0.259786i	$0.916348\pi$
$270$	−0.280909	−	0.864548i	−0.0170956	−	0.0526147i
$271$	−14.9110	−	10.8335i	−0.905778	−	0.658086i	0.0341657	−	0.999416i	$-0.489123\pi$
$271$	−14.9110	−	10.8335i	−0.905778	−	0.658086i	−0.939943	+	0.341330i	$0.889123\pi$
$272$	−10.0502	+	7.30188i	−0.609381	+	0.442741i
$273$	−1.25134	+	3.85124i	−0.0757348	+	0.233088i
$274$	8.74784			0.528476
$275$		0			0
$276$	−1.58725			−0.0955411
$277$	1.05914	−	3.25969i	0.0636375	−	0.195856i	−0.914183	−	0.405303i	$-0.867166\pi$
$277$	1.05914	−	3.25969i	0.0636375	−	0.195856i	0.977820	+	0.209446i	$0.0671662\pi$
$278$	8.95290	−	6.50466i	0.536959	−	0.390124i
$279$	5.59017	+	4.06150i	0.334675	+	0.243155i
$280$	1.49388	+	4.59768i	0.0892762	+	0.274764i
$281$	7.05230	+	21.7048i	0.420705	+	1.29480i	0.907047	+	0.421029i	$0.138331\pi$
$281$	7.05230	+	21.7048i	0.420705	+	1.29480i	−0.486342	+	0.873769i	$0.661669\pi$
$282$	0.544141	+	0.395341i	0.0324031	+	0.0235422i
$283$	−23.5416	+	17.1040i	−1.39941	+	1.01673i	−0.404647	+	0.914473i	$0.632606\pi$
$283$	−23.5416	+	17.1040i	−1.39941	+	1.01673i	−0.994758	+	0.102255i	$0.967394\pi$
$284$	−0.654828	+	2.01535i	−0.0388569	+	0.119589i
$285$	−1.40227			−0.0830634
$286$		0			0
$287$	−5.93542			−0.350357
$288$	4.36859	−	13.4451i	0.257422	−	0.792262i
$289$	−3.56201	+	2.58795i	−0.209530	+	0.152232i
$290$	−1.16351	−	0.845342i	−0.0683239	−	0.0496402i
$291$	1.85035	+	5.69480i	0.108470	+	0.333835i
$292$	0.559534	+	1.72207i	0.0327443	+	0.100776i
$293$	17.1621	+	12.4690i	1.00262	+	0.728448i	0.962649	−	0.270753i	$-0.0872725\pi$
$293$	17.1621	+	12.4690i	1.00262	+	0.728448i	0.0399740	+	0.999201i	$0.487273\pi$
$294$	0.0262463	−	0.0190690i	0.00153071	−	0.00111213i
$295$	−3.63011	+	11.1723i	−0.211353	+	0.650478i
$296$	−19.1608			−1.11370
$297$		0			0
$298$	6.99883			0.405432
$299$	3.99878	−	12.3070i	0.231255	−	0.711731i
$300$	0.463206	−	0.336539i	0.0267432	−	0.0194301i
$301$	15.3527	+	11.1544i	0.884913	+	0.642927i
$302$	−1.10892	−	3.41289i	−0.0638109	−	0.196390i
$303$	0.710278	+	2.18601i	0.0408044	+	0.125583i
$304$	−9.42913	−	6.85066i	−0.540798	−	0.392912i
$305$	3.22201	−	2.34093i	0.184492	−	0.134041i
$306$	1.97568	−	6.08051i	0.112942	−	0.347599i
$307$	6.87520			0.392388			0.196194	−	0.980565i	$-0.437142\pi$
$307$	6.87520			0.392388			0.196194	+	0.980565i	$0.437142\pi$
$308$		0			0
$309$	2.43219			0.138363
$310$	0.351935	−	1.08314i	0.0199886	−	0.0615185i
$311$	−20.3530	+	14.7873i	−1.15411	+	0.838511i	−0.989022	−	0.147768i	$-0.952791\pi$
$311$	−20.3530	+	14.7873i	−1.15411	+	0.838511i	−0.165089	+	0.986279i	$0.552791\pi$
$312$	−2.19647	−	1.59583i	−0.124350	−	0.0903459i
$313$	−3.57821	−	11.0126i	−0.202252	−	0.622469i	−0.999815	−	0.0192328i	$-0.993878\pi$
$313$	−3.57821	−	11.0126i	−0.202252	−	0.622469i	0.797563	−	0.603236i	$-0.206122\pi$
$314$	1.97358	+	6.07406i	0.111376	+	0.342779i
$315$	6.29042	+	4.57026i	0.354425	+	0.257505i
$316$	−5.02121	+	3.64812i	−0.282465	+	0.205223i
$317$	6.40940	−	19.7261i	0.359988	−	1.10793i	−0.593073	−	0.805149i	$-0.702085\pi$
$317$	6.40940	−	19.7261i	0.359988	−	1.10793i	0.953061	−	0.302780i	$-0.0979146\pi$
$318$	0.976639			0.0547672
$319$		0			0
$320$	3.04036			0.169961
$321$	−1.79994	+	5.53963i	−0.100463	+	0.309192i
$322$	−2.87422	+	2.08825i	−0.160174	+	0.116373i
$323$	−16.2453	−	11.8029i	−0.903913	−	0.656731i
$324$	−4.42034	−	13.6044i	−0.245575	−	0.755801i
$325$	1.44244	+	4.43939i	0.0800124	+	0.246253i
$326$	−0.298074	−	0.216564i	−0.0165088	−	0.0119943i
$327$	−4.27740	+	3.10771i	−0.236541	+	0.171857i
$328$	1.22972	−	3.78469i	0.0679000	−	0.208975i
$329$	−11.7133			−0.645777
$330$		0			0
$331$	−32.1415			−1.76665			−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415			−1.76665			−0.883327	+	0.468757i	$0.844702\pi$
$332$	6.08755	−	18.7356i	0.334098	−	1.02825i
$333$	−24.9322	+	18.1143i	−1.36627	+	0.992657i
$334$	3.27512	+	2.37951i	0.179207	+	0.130201i
$335$	−2.26195	−	6.96158i	−0.123584	−	0.380352i
$336$	−0.719847	−	2.21546i	−0.0392709	−	0.120863i
$337$	−14.5594	−	10.5780i	−0.793100	−	0.576221i	0.115782	−	0.993275i	$-0.463063\pi$
$337$	−14.5594	−	10.5780i	−0.793100	−	0.576221i	−0.908882	+	0.417054i	$0.863063\pi$
$338$	3.39346	−	2.46549i	0.184580	−	0.134105i
$339$	−0.205037	+	0.631039i	−0.0111361	+	0.0342734i
$340$	8.19888			0.444647
$341$		0			0
$342$	5.99834			0.324353
$343$	5.63386	−	17.3392i	0.304200	−	0.936231i
$344$	−10.2933	+	7.47855i	−0.554980	+	0.403217i
$345$	0.724576	+	0.526435i	0.0390099	+	0.0283423i
$346$	0.749016	+	2.30523i	0.0402673	+	0.123930i
$347$	2.48753	+	7.65583i	0.133538	+	0.410986i	0.995360	−	0.0962243i	$-0.0306766\pi$
$347$	2.48753	+	7.65583i	0.133538	+	0.410986i	−0.861822	+	0.507211i	$0.830677\pi$
$348$	1.39583	+	1.01413i	0.0748244	+	0.0543631i
$349$	15.5569	−	11.3027i	0.832741	−	0.605022i	−0.0875926	−	0.996156i	$-0.527917\pi$
$349$	15.5569	−	11.3027i	0.832741	−	0.605022i	0.920333	+	0.391135i	$0.127917\pi$
$350$	0.396020	−	1.21882i	0.0211682	−	0.0651489i
$351$	−8.89088			−0.474560
$352$		0			0
$353$	14.8497			0.790371			0.395186	−	0.918601i	$-0.370680\pi$
$353$	14.8497			0.790371			0.395186	+	0.918601i	$0.370680\pi$
$354$	−0.559723	+	1.72265i	−0.0297489	+	0.0915578i
$355$	0.967351	−	0.702822i	0.0513417	−	0.0373019i
$356$	3.97119	+	2.88524i	0.210473	+	0.152917i
$357$	−1.24021	−	3.81698i	−0.0656391	−	0.202016i
$358$	1.66905	+	5.13682i	0.0882123	+	0.271489i
$359$	8.27079	+	6.00908i	0.436516	+	0.317147i	0.784249	−	0.620446i	$-0.213048\pi$
$359$	8.27079	+	6.00908i	0.436516	+	0.317147i	−0.347733	+	0.937594i	$0.613048\pi$
$360$	−4.21747	+	3.06417i	−0.222280	+	0.161496i
$361$	−0.0496143	+	0.152697i	−0.00261128	+	0.00803670i
$362$	−3.53175			−0.185625
$363$		0			0
$364$	22.2134			1.16430
$365$	0.315724	−	0.971700i	0.0165258	−	0.0508611i
$366$	0.496799	−	0.360945i	0.0259681	−	0.0188669i
$367$	−11.4422	−	8.31327i	−0.597280	−	0.433949i	0.247632	−	0.968854i	$-0.420347\pi$
$367$	−11.4422	−	8.31327i	−0.597280	−	0.433949i	−0.844912	+	0.534905i	$0.820347\pi$
$368$	2.30033	+	7.07969i	0.119913	+	0.369054i
$369$	−1.97786	−	6.08724i	−0.102964	−	0.316889i
$370$	4.10935	+	2.98562i	0.213635	+	0.155215i
$371$	−13.7600	+	9.99722i	−0.714383	+	0.519030i
$372$	−0.422205	+	1.29941i	−0.0218903	+	0.0673715i
$373$	−12.4600			−0.645154			−0.322577	−	0.946543i	$-0.604549\pi$
$373$	−12.4600			−0.645154			−0.322577	+	0.946543i	$0.604549\pi$
$374$		0			0
$375$	−0.323071			−0.0166833
$376$	2.42681	−	7.46894i	0.125153	−	0.385181i
$377$	−11.3798	+	8.26788i	−0.586088	+	0.425818i
$378$	1.97479	+	1.43477i	0.101572	+	0.0737965i
$379$	5.04840	+	15.5374i	0.259319	+	0.798102i	0.992948	+	0.118552i	$0.0378251\pi$
$379$	5.04840	+	15.5374i	0.259319	+	0.798102i	−0.733629	+	0.679550i	$0.762175\pi$
$380$	2.37703	+	7.31575i	0.121939	+	0.375290i
$381$	−0.0199338	−	0.0144828i	−0.00102124	−	0.000741975i
$382$	−1.99082	+	1.44642i	−0.101859	+	0.0740051i
$383$	−0.251122	+	0.772874i	−0.0128317	+	0.0394920i	−0.957267	−	0.289204i	$-0.906609\pi$
$383$	−0.251122	+	0.772874i	−0.0128317	+	0.0394920i	0.944436	+	0.328696i	$0.106609\pi$
$384$	3.62339			0.184905
$385$		0			0
$386$	−1.92445			−0.0979522
$387$	−6.32370	+	19.4623i	−0.321452	+	0.989327i
$388$	26.5736	−	19.3068i	1.34907	−	0.980155i
$389$	24.5894	+	17.8652i	1.24673	+	0.905802i	0.998028	−	0.0627780i	$-0.0199960\pi$
$389$	24.5894	+	17.8652i	1.24673	+	0.905802i	0.248702	+	0.968580i	$0.419996\pi$
$390$	0.222409	+	0.684504i	0.0112621	+	0.0346612i
$391$	3.96321	+	12.1975i	0.200428	+	0.616854i
$392$	−0.306455	−	0.222653i	−0.0154783	−	0.0112457i
$393$	−3.00134	+	2.18060i	−0.151398	+	0.109997i
$394$	1.68388	−	5.18245i	0.0848327	−	0.261088i
$395$	3.50213			0.176211
$396$		0			0
$397$	−14.8996			−0.747789			−0.373894	−	0.927471i	$-0.621978\pi$
$397$	−14.8996			−0.747789			−0.373894	+	0.927471i	$0.621978\pi$
$398$	1.05692	−	3.25285i	0.0529784	−	0.163051i
$399$	3.04628	−	2.21325i	0.152505	−	0.110801i
$400$	−2.17239	−	1.57833i	−0.108619	−	0.0789166i
$401$	3.76049	+	11.5736i	0.187790	+	0.577957i	0.999985	−	0.00542792i	$-0.00172777\pi$
$401$	3.76049	+	11.5736i	0.187790	+	0.577957i	−0.812196	+	0.583385i	$0.801728\pi$
$402$	−0.348768	−	1.07340i	−0.0173950	−	0.0535362i
$403$	−9.01155	−	6.54727i	−0.448897	−	0.326143i
$404$	10.2006	−	7.41114i	0.507496	−	0.368718i
$405$	−2.49424	+	7.67647i	−0.123940	+	0.381447i
$406$	3.86184			0.191660
$407$		0			0
$408$	2.69083			0.133216
$409$	0.0809957	−	0.249279i	0.00400498	−	0.0123261i	−0.949034	−	0.315174i	$-0.897937\pi$
$409$	0.0809957	−	0.249279i	0.00400498	−	0.0123261i	0.953039	+	0.302847i	$0.0979373\pi$
$410$	−0.853463	+	0.620077i	−0.0421495	+	0.0306234i
$411$	4.79073	+	3.48067i	0.236309	+	0.171689i
$412$	−4.12288	−	12.6889i	−0.203120	−	0.625138i
$413$	−9.74764	−	30.0002i	−0.479650	−	1.47621i
$414$	−3.09944	−	2.25187i	−0.152329	−	0.110674i
$415$	−8.99290	+	6.53372i	−0.441444	+	0.320728i
$416$	−7.04232	+	21.6740i	−0.345278	+	1.06266i
$417$	7.49116			0.366844
$418$		0			0
$419$	−1.26916			−0.0620023			−0.0310012	−	0.999519i	$-0.509870\pi$
$419$	−1.26916			−0.0620023			−0.0310012	+	0.999519i	$0.509870\pi$
$420$	−0.475093	+	1.46219i	−0.0231822	+	0.0713474i
$421$	23.9999	−	17.4369i	1.16968	−	0.849824i	0.178712	−	0.983902i	$-0.442807\pi$
$421$	23.9999	−	17.4369i	1.16968	−	0.849824i	0.990971	+	0.134078i	$0.0428071\pi$
$422$	−1.34506	−	0.977240i	−0.0654763	−	0.0475713i
$423$	−3.90324	−	12.0129i	−0.189782	−	0.584089i
$424$	−3.52384	−	10.8452i	−0.171133	−	0.526692i
$425$	−3.74278	−	2.71929i	−0.181551	−	0.131905i
$426$	0.149155	−	0.108367i	0.00722658	−	0.00525041i
$427$	−3.30470	+	10.1708i	−0.159926	+	0.492200i
$428$	31.9518			1.54445
$429$		0			0
$430$	3.37289			0.162655
$431$	−9.68919	+	29.8203i	−0.466712	+	1.43639i	0.390105	+	0.920771i	$0.372439\pi$
$431$	−9.68919	+	29.8203i	−0.466712	+	1.43639i	−0.856817	+	0.515621i	$0.827561\pi$
$432$	4.13776	−	3.00626i	0.199078	−	0.144639i
$433$	21.0607	+	15.3015i	1.01212	+	0.735345i	0.964652	−	0.263528i	$-0.0848863\pi$
$433$	21.0607	+	15.3015i	1.01212	+	0.735345i	0.0474634	+	0.998873i	$0.484886\pi$
$434$	0.945023	+	2.90848i	0.0453625	+	0.139612i
$435$	−0.300843	−	0.925898i	−0.0144243	−	0.0443934i
$436$	23.4639	+	17.0475i	1.12372	+	0.816429i
$437$	−9.73464	+	7.07263i	−0.465671	+	0.338330i
$438$	0.0486812	−	0.149825i	0.00232608	−	0.00715893i
$439$	−14.4191			−0.688185			−0.344093	−	0.938936i	$-0.611813\pi$
$439$	−14.4191			−0.688185			−0.344093	+	0.938936i	$0.611813\pi$
$440$		0			0
$441$	−0.609255			−0.0290121
$442$	−3.18486	+	9.80199i	−0.151488	+	0.466233i
$443$	0.267467	−	0.194326i	0.0127078	−	0.00923273i	−0.581413	−	0.813608i	$-0.697500\pi$
$443$	0.267467	−	0.194326i	0.0127078	−	0.00923273i	0.594121	+	0.804376i	$0.297500\pi$
$444$	−4.92986	−	3.58175i	−0.233961	−	0.169982i
$445$	−0.855908	−	2.63421i	−0.0405739	−	0.124874i
$446$	−1.55518	−	4.78636i	−0.0736400	−	0.226641i
$447$	3.83289	+	2.78476i	0.181289	+	0.131715i
$448$	−6.60483	+	4.79869i	−0.312049	+	0.226717i
$449$	2.62920	−	8.09185i	0.124080	−	0.381878i	−0.869653	−	0.493664i	$-0.835657\pi$
$449$	2.62920	−	8.09185i	0.124080	−	0.381878i	0.993732	+	0.111786i	$0.0356571\pi$
$450$	1.38197			0.0651465
$451$		0			0
$452$	3.63974			0.171199
$453$	0.750657	−	2.31028i	0.0352689	−	0.108547i
$454$	−0.0834069	+	0.0605986i	−0.00391448	+	0.00284404i
$455$	−10.1404	−	7.36742i	−0.475388	−	0.345390i
$456$	0.780130	+	2.40099i	0.0365329	+	0.112437i
$457$	−0.351807	−	1.08275i	−0.0164569	−	0.0506490i	0.942491	−	0.334232i	$-0.108477\pi$
$457$	−0.351807	−	1.08275i	−0.0164569	−	0.0506490i	−0.958948	+	0.283583i	$0.908477\pi$
$458$	−0.0292324	−	0.0212386i	−0.00136594	−	0.000992413i
$459$	7.12889	−	5.17944i	0.332748	−	0.241756i
$460$	1.51820	−	4.67254i	0.0707864	−	0.217858i
$461$	−14.5073			−0.675670			−0.337835	−	0.941205i	$-0.609695\pi$
$461$	−14.5073			−0.675670			−0.337835	+	0.941205i	$0.609695\pi$
$462$		0			0
$463$	−4.89739			−0.227601			−0.113801	−	0.993504i	$-0.536302\pi$
$463$	−4.89739			−0.227601			−0.113801	+	0.993504i	$0.536302\pi$
$464$	2.50047	−	7.69565i	0.116081	−	0.357261i
$465$	0.623707	−	0.453150i	0.0289237	−	0.0210143i
$466$	−5.83803	−	4.24157i	−0.270441	−	0.196487i
$467$	10.0193	+	30.8361i	0.463637	+	1.42693i	0.860689	+	0.509131i	$0.170033\pi$
$467$	10.0193	+	30.8361i	0.463637	+	1.42693i	−0.397053	+	0.917796i	$0.629967\pi$
$468$	7.40218	+	22.7816i	0.342166	+	1.05308i
$469$	15.9015	+	11.5531i	0.734264	+	0.533474i
$470$	−1.68428	+	1.22370i	−0.0776898	+	0.0564450i
$471$	−1.33597	+	4.11171i	−0.0615585	+	0.189457i
$472$	21.1490			0.973461
$473$		0			0
$474$	0.539990			0.0248026
$475$	1.34127	−	4.12801i	0.0615417	−	0.189406i
$476$	−17.8111	+	12.9406i	−0.816373	+	0.593129i
$477$	−14.8382	−	10.7806i	−0.679394	−	0.493609i
$478$	−3.41635	−	10.5145i	−0.156260	−	0.480920i
$479$	−5.48054	−	16.8674i	−0.250412	−	0.770690i	−0.994699	−	0.102830i	$-0.967210\pi$
$479$	−5.48054	−	16.8674i	−0.250412	−	0.770690i	0.744287	−	0.667860i	$-0.232790\pi$
$480$	−1.27606	−	0.927114i	−0.0582441	−	0.0423168i
$481$	40.1915	−	29.2009i	1.83258	−	1.33144i
$482$	−3.14650	+	9.68394i	−0.143319	+	0.441091i
$483$	−2.40495			−0.109429
$484$		0			0
$485$	−18.5342			−0.841595
$486$	−1.22731	+	3.77727i	−0.0556719	+	0.171341i
$487$	14.9347	−	10.8507i	0.676754	−	0.491691i	−0.195525	−	0.980699i	$-0.562641\pi$
$487$	14.9347	−	10.8507i	0.676754	−	0.491691i	0.872279	+	0.489008i	$0.162641\pi$
$488$	−5.80069	−	4.21445i	−0.262585	−	0.190779i
$489$	−0.0770712	−	0.237201i	−0.00348528	−	0.0107266i
$490$	0.0310309	+	0.0955032i	0.00140183	+	0.00431440i
$491$	−9.25018	−	6.72065i	−0.417455	−	0.303299i	0.359158	−	0.933277i	$-0.383064\pi$
$491$	−9.25018	−	6.72065i	−0.417455	−	0.303299i	−0.776613	+	0.629978i	$0.783064\pi$
$492$	1.02387	−	0.743887i	0.0461597	−	0.0335370i
$493$	4.30802	−	13.2587i	0.194023	−	0.597142i
$494$	−9.66954			−0.435053
$495$		0			0
$496$	6.40774			0.287716
$497$	−0.992176	+	3.05360i	−0.0445052	+	0.136973i
$498$	−1.38661	+	1.00743i	−0.0621353	+	0.0451439i
$499$	−8.80335	−	6.39601i	−0.394092	−	0.286325i	0.373038	−	0.927816i	$-0.378316\pi$
$499$	−8.80335	−	6.39601i	−0.394092	−	0.286325i	−0.767130	+	0.641491i	$0.778316\pi$
$500$	0.547647	+	1.68548i	0.0244915	+	0.0753771i
$501$	0.846827	+	2.60627i	0.0378335	+	0.116439i
$502$	−2.40233	−	1.74540i	−0.107221	−	0.0779009i
$503$	36.1830	−	26.2885i	1.61332	−	1.17215i	0.761831	−	0.647776i	$-0.224301\pi$
$503$	36.1830	−	26.2885i	1.61332	−	1.17215i	0.851490	−	0.524371i	$-0.175699\pi$
$504$	4.32571	−	13.3132i	0.192682	−	0.593015i
$505$	−7.11455			−0.316594
$506$		0			0
$507$	2.83941			0.126103
$508$	−0.0417673	+	0.128546i	−0.00185312	+	0.00570332i
$509$	11.1720	−	8.11693i	0.495190	−	0.359777i	−0.311987	−	0.950086i	$-0.600994\pi$
$509$	11.1720	−	8.11693i	0.495190	−	0.359777i	0.807177	+	0.590310i	$0.200994\pi$
$510$	−0.577094	−	0.419284i	−0.0255542	−	0.0185662i
$511$	0.847790	+	2.60923i	0.0375040	+	0.115425i
$512$	−7.03891	−	21.6635i	−0.311079	−	0.957402i
$513$	6.68836	+	4.85938i	0.295298	+	0.214547i
$514$	−5.51766	+	4.00881i	−0.243374	+	0.176821i
$515$	−2.32639	+	7.15989i	−0.102513	+	0.315502i
$516$	−4.04635			−0.178130
$517$		0			0
$518$	−13.6394			−0.599281
$519$	−0.507030	+	1.56048i	−0.0222562	+	0.0684974i
$520$	6.79871	−	4.93955i	0.298143	−	0.216614i
$521$	2.95269	+	2.14525i	0.129360	+	0.0939852i	0.650584	−	0.759435i	$-0.274524\pi$
$521$	2.95269	+	2.14525i	0.129360	+	0.0939852i	−0.521224	+	0.853420i	$0.674524\pi$
$522$	1.28688	+	3.96061i	0.0563253	+	0.173351i
$523$	1.54109	+	4.74299i	0.0673872	+	0.207396i	0.979080	−	0.203476i	$-0.0652240\pi$
$523$	1.54109	+	4.74299i	0.0673872	+	0.207396i	−0.911693	+	0.410873i	$0.865224\pi$
$524$	16.4640	+	11.9618i	0.719233	+	0.522553i
$525$	0.701836	−	0.509914i	0.0306306	−	0.0222545i
$526$	0.609292	−	1.87521i	0.0265664	−	0.0817630i
$527$	11.0398			0.480901
$528$		0			0
$529$	−15.3148			−0.665860
$530$	−0.934153	+	2.87503i	−0.0405770	+	0.124883i
$531$	27.5193	−	19.9939i	1.19424	−	0.867663i
$532$	−16.7105	−	12.1409i	−0.724493	−	0.526375i
$533$	3.18839	+	9.81284i	0.138104	+	0.425041i
$534$	−0.131972	−	0.406167i	−0.00571097	−	0.0175766i
$535$	−14.5859	−	10.5973i	−0.630605	−	0.458161i
$536$	−10.6613	+	7.74591i	−0.460499	+	0.334572i
$537$	−1.12983	+	3.47726i	−0.0487558	+	0.150055i
$538$	0.803678			0.0346490
$539$		0			0
$540$	−3.37556			−0.145261
$541$	−0.0765109	+	0.235476i	−0.00328946	+	0.0101239i	−0.952688	−	0.303951i	$-0.901694\pi$
$541$	−0.0765109	+	0.235476i	−0.00328946	+	0.0101239i	0.949398	+	0.314075i	$0.101694\pi$
$542$	7.11642	−	5.17038i	0.305676	−	0.222087i
$543$	−1.93415	−	1.40524i	−0.0830025	−	0.0603048i
$544$	−6.97967	−	21.4812i	−0.299251	−	0.921000i
$545$	−5.05716	−	15.5643i	−0.216625	−	0.666703i
$546$	−1.56353	−	1.13597i	−0.0669131	−	0.0486152i
$547$	−20.4779	+	14.8780i	−0.875570	+	0.636139i	−0.932076	−	0.362263i	$-0.882004\pi$
$547$	−20.4779	+	14.8780i	−0.875570	+	0.636139i	0.0565056	+	0.998402i	$0.482004\pi$
$548$	10.0380	−	30.8937i	0.428801	−	1.31971i
$549$	−11.5322			−0.492182
$550$		0			0
$551$	13.0796			0.557208
$552$	0.498266	−	1.53350i	0.0212076	−	0.0652703i
$553$	−7.60799	+	5.52753i	−0.323525	+	0.235054i
$554$	1.32338	+	0.961489i	0.0562249	+	0.0408498i
$555$	1.06253	+	3.27013i	0.0451018	+	0.138809i
$556$	−12.6985	−	39.0819i	−0.538536	−	1.65744i
$557$	−31.2824	−	22.7280i	−1.32548	−	0.963015i	−0.999847	−	0.0175177i	$-0.994424\pi$
$557$	−31.2824	−	22.7280i	−1.32548	−	0.963015i	−0.325630	−	0.945497i	$-0.605576\pi$
$558$	−2.66796	+	1.93839i	−0.112944	+	0.0820586i
$559$	10.1940	−	31.3740i	0.431161	−	1.32698i
$560$	7.21041			0.304695
$561$		0			0
$562$	−10.8919			−0.459447
$563$	−4.30653	+	13.2541i	−0.181498	+	0.558595i	−0.999870	−	0.0160940i	$-0.994877\pi$
$563$	−4.30653	+	13.2541i	−0.181498	+	0.558595i	0.818372	+	0.574689i	$0.194877\pi$
$564$	2.02057	−	1.46803i	0.0850815	−	0.0618153i
$565$	−1.66154	−	1.20718i	−0.0699013	−	0.0507863i
$566$	−4.29157	−	13.2081i	−0.180388	−	0.555178i
$567$	−6.69757	−	20.6130i	−0.281272	−	0.865665i
$568$	−1.74155	−	1.26531i	−0.0730739	−	0.0530913i
$569$	22.5817	−	16.4065i	0.946672	−	0.687798i	−0.00334520	−	0.999994i	$-0.501065\pi$
$569$	22.5817	−	16.4065i	0.946672	−	0.687798i	0.950017	+	0.312197i	$0.101065\pi$
$570$	0.206809	−	0.636493i	0.00866228	−	0.0266598i
$571$	31.4113			1.31452			0.657261	−	0.753663i	$-0.271715\pi$
$571$	31.4113			1.31452			0.657261	+	0.753663i	$0.271715\pi$
$572$		0			0
$573$	−1.66578			−0.0695889
$574$	0.875365	−	2.69410i	0.0365370	−	0.112449i
$575$	−2.24278	+	1.62947i	−0.0935302	+	0.0679537i
$576$	−7.12237	−	5.17470i	−0.296765	−	0.215613i
$577$	6.40744	+	19.7201i	0.266745	+	0.820958i	0.991286	+	0.131726i	$0.0420519\pi$
$577$	6.40744	+	19.7201i	0.266745	+	0.820958i	−0.724541	+	0.689232i	$0.757948\pi$
$578$	−0.649343	−	1.99847i	−0.0270091	−	0.0831255i
$579$	−1.05392	−	0.765719i	−0.0437995	−	0.0318222i
$580$	−4.32051	+	3.13903i	−0.179399	+	0.130341i
$581$	9.22368	−	28.3876i	0.382663	−	1.17771i
$582$	−2.85777			−0.118458
$583$		0			0
$584$	−1.83941			−0.0761153
$585$	4.17678	−	12.8548i	0.172689	−	0.531481i
$586$	−8.19080	+	5.95097i	−0.338359	+	0.245832i
$587$	−12.3267	−	8.95591i	−0.508779	−	0.369650i	0.303581	−	0.952806i	$-0.401818\pi$
$587$	−12.3267	−	8.95591i	−0.508779	−	0.369650i	−0.812360	+	0.583156i	$0.801818\pi$
$588$	−0.0372268	−	0.114572i	−0.00153521	−	0.00472488i
$589$	3.20067	+	9.85066i	0.131881	+	0.405889i
$590$	−4.53576	−	3.29542i	−0.186734	−	0.135670i
$591$	2.98421	−	2.16816i	0.122754	−	0.0891860i
$592$	−8.83126	+	27.1798i	−0.362962	+	1.11708i
$593$	−27.5413			−1.13098			−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413			−1.13098			−0.565492	+	0.824754i	$0.691314\pi$
$594$		0			0
$595$	12.4227			0.509281
$596$	8.03103	−	24.7170i	0.328964	−	1.01245i
$597$	1.87309	−	1.36088i	0.0766605	−	0.0556971i
$598$	4.99640	+	3.63010i	0.204318	+	0.148446i
$599$	−8.26097	−	25.4247i	−0.337534	−	1.03882i	−0.965460	−	0.260551i	$-0.916096\pi$
$599$	−8.26097	−	25.4247i	−0.337534	−	1.03882i	0.627926	−	0.778273i	$-0.283904\pi$
$600$	0.179735	+	0.553168i	0.00733765	+	0.0225830i
$601$	1.94714	+	1.41468i	0.0794255	+	0.0577060i	0.626789	−	0.779189i	$-0.284369\pi$
$601$	1.94714	+	1.41468i	0.0794255	+	0.0577060i	−0.547364	+	0.836895i	$0.684369\pi$
$602$	−7.32722	+	5.32353i	−0.298635	+	0.216971i
$603$	−6.54977	+	20.1581i	−0.266727	+	0.820902i
$604$	−13.3254			−0.542202
$605$		0			0
$606$	−1.09699			−0.0445620
$607$	−3.18067	+	9.78909i	−0.129099	+	0.397327i	−0.994626	−	0.103536i	$-0.966984\pi$
$607$	−3.18067	+	9.78909i	−0.129099	+	0.397327i	0.865526	+	0.500864i	$0.166984\pi$
$608$	17.1438	−	12.4557i	0.695275	−	0.505147i
$609$	2.11492	+	1.53658i	0.0857010	+	0.0622654i
$610$	0.587364	+	1.80772i	0.0237817	+	0.0731924i
$611$	6.29216	+	19.3653i	0.254553	+	0.783435i
$612$	−19.2068	−	13.9545i	−0.776388	−	0.564079i
$613$	22.5519	−	16.3849i	0.910861	−	0.661779i	−0.0303715	−	0.999539i	$-0.509669\pi$
$613$	22.5519	−	16.3849i	0.910861	−	0.661779i	0.941232	+	0.337759i	$0.109669\pi$
$614$	−1.01396	+	3.12066i	−0.0409203	+	0.125940i
$615$	−0.714118			−0.0287960
$616$		0			0
$617$	−28.7216			−1.15629			−0.578143	−	0.815935i	$-0.696222\pi$
$617$	−28.7216			−1.15629			−0.578143	+	0.815935i	$0.696222\pi$
$618$	−0.358703	+	1.10398i	−0.0144292	+	0.0444084i
$619$	−18.3621	+	13.3408i	−0.738035	+	0.536214i	−0.892095	−	0.451848i	$-0.850765\pi$
$619$	−18.3621	+	13.3408i	−0.738035	+	0.536214i	0.154060	+	0.988061i	$0.450765\pi$
$620$	−3.42138	−	2.48578i	−0.137406	−	0.0998312i
$621$	−1.63169	−	5.02183i	−0.0654776	−	0.201519i
$622$	−3.71029	−	11.4191i	−0.148769	−	0.457864i
$623$	6.01703	+	4.37163i	0.241067	+	0.175146i
$624$	−3.27606	+	2.38020i	−0.131147	+	0.0952842i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	5.52635			0.220877
$627$		0			0
$628$	23.7157			0.946360
$629$	−15.2152	+	46.8277i	−0.606671	+	1.86714i
$630$	−3.00217	+	2.18120i	−0.119609	+	0.0869012i
$631$	−23.0864	−	16.7733i	−0.919056	−	0.667733i	0.0242327	−	0.999706i	$-0.492286\pi$
$631$	−23.0864	−	16.7733i	−0.919056	−	0.667733i	−0.943289	+	0.331973i	$0.892286\pi$
$632$	−1.94835	−	5.99641i	−0.0775013	−	0.238524i
$633$	−0.347783	−	1.07037i	−0.0138231	−	0.0425432i
$634$	8.00844	+	5.81847i	0.318056	+	0.231081i
$635$	0.0617011	−	0.0448285i	0.00244853	−	0.00177896i
$636$	1.12067	−	3.44908i	0.0444376	−	0.136765i
$637$	0.982140			0.0389138
$638$		0			0
$639$	−3.46233			−0.136968
$640$	−3.46577	+	10.6665i	−0.136997	+	0.421632i
$641$	−1.92040	+	1.39526i	−0.0758514	+	0.0551093i	−0.625065	−	0.780573i	$-0.714927\pi$
$641$	−1.92040	+	1.39526i	−0.0758514	+	0.0551093i	0.549213	+	0.835682i	$0.314927\pi$
$642$	−2.24899	−	1.63399i	−0.0887605	−	0.0644883i
$643$	3.51053	+	10.8043i	0.138442	+	0.426080i	0.996109	−	0.0881244i	$-0.0280873\pi$
$643$	3.51053	+	10.8043i	0.138442	+	0.426080i	−0.857668	+	0.514204i	$0.828087\pi$
$644$	4.07670	+	12.5468i	0.160644	+	0.494413i
$645$	1.84715	+	1.34203i	0.0727315	+	0.0528425i
$646$	7.75323	−	5.63305i	0.305047	−	0.221630i
$647$	−14.9632	+	46.0520i	−0.588264	+	1.81049i	−0.00251822	+	0.999997i	$0.500802\pi$
$647$	−14.9632	+	46.0520i	−0.588264	+	1.81049i	−0.585746	+	0.810495i	$0.699198\pi$
$648$	14.5314			0.570848
$649$		0			0
$650$	−2.22778			−0.0873806
$651$	−0.639713	+	1.96883i	−0.0250723	+	0.0771647i
$652$	−1.10685	+	0.804171i	−0.0433475	+	0.0314938i
$653$	−24.0722	−	17.4894i	−0.942016	−	0.684415i	0.00688905	−	0.999976i	$-0.497807\pi$
$653$	−24.0722	−	17.4894i	−0.942016	−	0.684415i	−0.948905	+	0.315562i	$0.897807\pi$
$654$	−0.779758	−	2.39985i	−0.0304910	−	0.0938415i
$655$	−3.54847	−	10.9211i	−0.138650	−	0.426722i
$656$	−4.80186	−	3.48875i	−0.187481	−	0.136213i
$657$	−2.39346	+	1.73895i	−0.0933777	+	0.0678429i
$658$	1.72750	−	5.31669i	0.0673449	−	0.207266i
$659$	28.4931			1.10993			0.554966	−	0.831873i	$-0.312731\pi$
$659$	28.4931			1.10993			0.554966	+	0.831873i	$0.312731\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$	4.74027	−	14.5890i	0.184236	−	0.567019i
$663$	−5.64428	+	4.10081i	−0.219206	+	0.159262i
$664$	16.1902	+	11.7629i	0.628301	+	0.456488i
$665$	3.60161	+	11.0846i	0.139664	+	0.429843i
$666$	−4.54506	−	13.9883i	−0.176118	−	0.542034i
$667$	−6.75841	−	4.91027i	−0.261687	−	0.190127i
$668$	12.1616	−	8.83591i	0.470546	−	0.341872i
$669$	1.05275	−	3.24002i	0.0407016	−	0.125267i
$670$	3.49346			0.134964
$671$		0			0
$672$	4.23540			0.163384
$673$	−4.02863	+	12.3988i	−0.155292	+	0.477940i	−0.998190	−	0.0601327i	$-0.980848\pi$
$673$	−4.02863	+	12.3988i	−0.155292	+	0.477940i	0.842898	+	0.538073i	$0.180848\pi$
$674$	6.94861	−	5.04846i	0.267651	−	0.194459i
$675$	1.54094	+	1.11956i	0.0593108	+	0.0430918i
$676$	−4.81316	−	14.8134i	−0.185122	−	0.569746i
$677$	11.4665	+	35.2903i	0.440694	+	1.35632i	0.887138	+	0.461505i	$0.152690\pi$
$677$	11.4665	+	35.2903i	0.440694	+	1.35632i	−0.446444	+	0.894812i	$0.647310\pi$
$678$	−0.256190	−	0.186133i	−0.00983893	−	0.00714840i
$679$	40.2635	−	29.2531i	1.54517	−	1.12263i
$680$	−2.57378	+	7.92127i	−0.0986998	+	0.303767i
$681$	−0.0697890			−0.00267432
$682$		0			0
$683$	−32.8992			−1.25885			−0.629426	−	0.777061i	$-0.716710\pi$
$683$	−32.8992			−1.25885			−0.629426	+	0.777061i	$0.716710\pi$
$684$	6.88299	−	21.1837i	0.263178	−	0.809978i
$685$	−14.8287	+	10.7737i	−0.566576	+	0.411641i
$686$	7.03941	+	5.11443i	0.268766	+	0.195270i
$687$	−0.00755844	−	0.0232625i	−0.000288372	−	0.000887519i
$688$	5.86420	+	18.0481i	0.223570	+	0.688079i
$689$	23.9197	+	17.3787i	0.911267	+	0.662074i
$690$	−0.345811	+	0.251246i	−0.0131648	+	0.00956479i
$691$	11.3409	−	34.9036i	0.431427	−	1.32780i	−0.465277	−	0.885165i	$-0.654045\pi$
$691$	11.3409	−	34.9036i	0.431427	−	1.32780i	0.896704	−	0.442631i	$-0.145955\pi$
$692$	9.00061			0.342152
$693$		0			0
$694$	−3.84185			−0.145835
$695$	−7.16529	+	22.0525i	−0.271795	+	0.836498i
$696$	−1.41797	+	1.03022i	−0.0537480	+	0.0390502i
$697$	−8.27305	−	6.01072i	−0.313364	−	0.227672i
$698$	2.83597	+	8.72823i	0.107343	+	0.330368i
$699$	−1.50950	−	4.64577i	−0.0570946	−	0.175719i
$700$	−3.84996	−	2.79716i	−0.145515	−	0.105723i
$701$	−29.3266	+	21.3070i	−1.10765	+	0.804755i	−0.982292	−	0.187356i	$-0.940008\pi$
$701$	−29.3266	+	21.3070i	−1.10765	+	0.804755i	−0.125359	+	0.992111i	$0.540008\pi$
$702$	1.31124	−	4.03558i	0.0494895	−	0.152313i
$703$	−46.1949			−1.74227
$704$		0			0
$705$	−1.40928			−0.0530767
$706$	−2.19006	+	6.74031i	−0.0824240	+	0.253675i
$707$	15.4556	−	11.2291i	0.581267	−	0.422315i
$708$	5.44141	+	3.95342i	0.204501	+	0.148578i
$709$	−5.74811	−	17.6909i	−0.215875	−	0.664394i	−0.999090	−	0.0426440i	$-0.986422\pi$
$709$	−5.74811	−	17.6909i	−0.215875	−	0.664394i	0.783216	−	0.621750i	$-0.213578\pi$
$710$	0.176345	+	0.542735i	0.00661812	+	0.0203685i
$711$	−8.20413	−	5.96065i	−0.307679	−	0.223542i
$712$	−4.03418	+	2.93100i	−0.151187	+	0.109844i
$713$	2.04426	−	6.29158i	0.0765580	−	0.235621i
$714$	1.91544			0.0716836
$715$		0			0
$716$	20.0563			0.749540
$717$	2.31263	−	7.11754i	0.0863667	−	0.265809i
$718$	−3.94732	+	2.86790i	−0.147313	+	0.107029i
$719$	30.2799	+	21.9996i	1.12925	+	0.820447i	0.985585	−	0.169179i	$-0.0541117\pi$
$719$	30.2799	+	21.9996i	1.12925	+	0.820447i	0.143664	+	0.989627i	$0.454112\pi$
$720$	2.40273	+	7.39484i	0.0895444	+	0.275589i
$721$	−6.24687	−	19.2259i	−0.232645	−	0.716009i
$722$	−0.0619923	−	0.0450400i	−0.00230711	−	0.00167622i
$723$	−5.57630	+	4.05142i	−0.207385	+	0.150674i
$724$	−4.05262	+	12.4727i	−0.150614	+	0.463544i
$725$	3.01341			0.111915
$726$		0			0
$727$	14.6011			0.541526			0.270763	−	0.962646i	$-0.412724\pi$
$727$	14.6011			0.541526			0.270763	+	0.962646i	$0.412724\pi$
$728$	−6.97319	+	21.4613i	−0.258443	+	0.795407i
$729$	17.4149	−	12.6527i	0.644997	−	0.468618i
$730$	0.394492	+	0.286615i	0.0146008	+	0.0106081i
$731$	10.1033	+	31.0949i	0.373686	+	1.15009i
$732$	−0.704642	−	2.16867i	−0.0260443	−	0.0801562i
$733$	33.8468	+	24.5911i	1.25016	+	0.908293i	0.998231	−	0.0594528i	$-0.0189356\pi$
$733$	33.8468	+	24.5911i	1.25016	+	0.908293i	0.251927	+	0.967746i	$0.418936\pi$
$734$	5.46092	−	3.96759i	0.201566	−	0.146447i
$735$	−0.0210057	+	0.0646489i	−0.000774807	+	0.00238461i
$736$	−13.5346			−0.498891
$737$		0			0
$738$	3.05470			0.112445
$739$	3.68654	−	11.3460i	0.135612	−	0.417370i	−0.860073	−	0.510171i	$-0.829582\pi$
$739$	3.68654	−	11.3460i	0.135612	−	0.417370i	0.995685	+	0.0928012i	$0.0295821\pi$
$740$	15.2594	−	11.0866i	0.560945	−	0.407550i
$741$	−5.29549	−	3.84740i	−0.194535	−	0.141338i
$742$	−2.50841	−	7.72008i	−0.0920865	−	0.283413i
$743$	−14.4250	−	44.3956i	−0.529202	−	1.62872i	−0.755854	−	0.654740i	$-0.772778\pi$
$743$	−14.4250	−	44.3956i	−0.529202	−	1.62872i	0.226652	−	0.973976i	$-0.427222\pi$
$744$	−1.12288	−	0.815820i	−0.0411668	−	0.0299094i
$745$	−11.8639	+	8.61964i	−0.434660	+	0.315799i
$746$	1.83762	−	5.65561i	0.0672800	−	0.207067i
$747$	32.1873			1.17767
$748$		0			0
$749$	48.4124			1.76895
$750$	0.0476470	−	0.146642i	0.00173982	−	0.00535462i
$751$	−11.6530	+	8.46642i	−0.425225	+	0.308944i	−0.779737	−	0.626108i	$-0.784647\pi$
$751$	−11.6530	+	8.46642i	−0.425225	+	0.308944i	0.354512	+	0.935052i	$0.384647\pi$
$752$	−9.47628	−	6.88492i	−0.345564	−	0.251067i
$753$	−0.621156	−	1.91172i	−0.0226362	−	0.0696670i
$754$	−2.07450	−	6.38465i	−0.0755488	−	0.232515i
$755$	6.08301	+	4.41957i	0.221383	+	0.160845i
$756$	7.33304	−	5.32776i	0.266700	−	0.193769i
$757$	−4.96330	+	15.2755i	−0.180394	+	0.555196i	−0.999839	−	0.0179624i	$-0.994282\pi$
$757$	−4.96330	+	15.2755i	−0.180394	+	0.555196i	0.819444	+	0.573159i	$0.194282\pi$
$758$	−7.79698			−0.283199
$759$		0			0
$760$	−7.81423			−0.283452
$761$	12.0158	−	36.9809i	0.435573	−	1.34056i	−0.456925	−	0.889505i	$-0.651049\pi$
$761$	12.0158	−	36.9809i	0.435573	−	1.34056i	0.892498	−	0.451051i	$-0.148951\pi$
$762$	0.00951362	−	0.00691205i	0.000344642	−	0.000250397i
$763$	35.5518	+	25.8299i	1.28706	+	0.935106i
$764$	2.82371	+	8.69049i	0.102158	+	0.314411i
$765$	4.13962	+	12.7405i	0.149668	+	0.460632i
$766$	−0.313773	−	0.227969i	−0.0113371	−	0.00823686i
$767$	−44.3621	+	32.2309i	−1.60182	+	1.16379i
$768$	0.0726816	−	0.223691i	0.00262267	−	0.00807175i
$769$	−43.0017			−1.55068			−0.775341	−	0.631543i	$-0.782422\pi$
$769$	−43.0017			−1.55068			−0.775341	+	0.631543i	$0.782422\pi$
$770$		0			0
$771$	−4.61679			−0.166270
$772$	−2.20828	+	6.79637i	−0.0794776	+	0.244607i
$773$	6.35452	−	4.61683i	0.228556	−	0.166056i	−0.467613	−	0.883933i	$-0.654886\pi$
$773$	6.35452	−	4.61683i	0.228556	−	0.166056i	0.696170	+	0.717877i	$0.254886\pi$
$774$	−7.90135	−	5.74067i	−0.284008	−	0.206344i
$775$	0.737407	+	2.26951i	0.0264885	+	0.0815231i
$776$	10.3112	+	31.7346i	0.370150	+	1.13920i
$777$	−7.46957	−	5.42696i	−0.267969	−	0.194691i
$778$	−11.7355	+	8.52635i	−0.420739	+	0.305684i
$779$	2.96475	−	9.12457i	0.106223	−	0.326922i
$780$	2.67259			0.0956942
$781$		0			0
$782$	−6.12096			−0.218885
$783$	−1.77366	+	5.45875i	−0.0633853	+	0.195080i
$784$	−0.457082	+	0.332090i	−0.0163244	+	0.0118603i
$785$	−10.8262	−	7.86568i	−0.386403	−	0.280738i
$786$	−0.547135	−	1.68391i	−0.0195157	−	0.0600631i
$787$	3.53048	+	10.8657i	0.125848	+	0.387321i	0.994055	−	0.108882i	$-0.0347271\pi$
$787$	3.53048	+	10.8657i	0.125848	+	0.387321i	−0.868206	+	0.496203i	$0.834727\pi$
$788$	−16.3700	−	11.8935i	−0.583159	−	0.423690i
$789$	1.07980	−	0.784522i	0.0384420	−	0.0279297i
$790$	−0.516500	+	1.58962i	−0.0183762	+	0.0565562i
$791$	5.51483			0.196085
$792$		0			0
$793$	18.5903			0.660161
$794$	2.19741	−	6.76294i	0.0779832	−	0.240008i
$795$	−1.65553	+	1.20281i	−0.0587155	+	0.0426593i
$796$	−10.2749	−	7.46518i	−0.364186	−	0.264596i
$797$	−1.32414	−	4.07529i	−0.0469035	−	0.144354i	0.924862	−	0.380303i	$-0.124180\pi$
$797$	−1.32414	−	4.07529i	−0.0469035	−	0.144354i	−0.971766	+	0.235949i	$0.924180\pi$
$798$	0.555328	+	1.70912i	0.0196584	+	0.0605023i
$799$	−16.3265	−	11.8619i	−0.577592	−	0.419645i
$800$	3.94979	−	2.86969i	0.139646	−	0.101459i
$801$	−2.47839	+	7.62770i	−0.0875696	+	0.269511i
$802$	−5.80787			−0.205083
$803$		0			0
$804$	−4.19100			−0.147805
$805$	2.30033	−	7.07969i	0.0810760	−	0.249526i
$806$	4.30085	−	3.12475i	0.151491	−	0.110065i
$807$	0.440132	+	0.319774i	0.0154934	+	0.0112566i
$808$	3.95806	+	12.1817i	0.139244	+	0.428549i
$809$	6.13350	+	18.8770i	0.215642	+	0.663679i	0.999107	+	0.0422430i	$0.0134504\pi$
$809$	6.13350	+	18.8770i	0.215642	+	0.663679i	−0.783465	+	0.621436i	$0.786550\pi$
$810$	−3.11651	−	2.26427i	−0.109503	−	0.0795585i
$811$	−2.53899	+	1.84468i	−0.0891559	+	0.0647756i	−0.631470	−	0.775400i	$-0.717548\pi$
$811$	−2.53899	+	1.84468i	−0.0891559	+	0.0647756i	0.542314	+	0.840176i	$0.317548\pi$
$812$	4.43138	−	13.6384i	0.155511	−	0.478614i
$813$	5.95452			0.208834
$814$		0			0
$815$	0.771990			0.0270416
$816$	1.24021	−	3.81698i	0.0434162	−	0.133621i
$817$	−24.8164	+	18.0301i	−0.868215	+	0.630795i
$818$	0.101203	+	0.0735281i	0.00353847	+	0.00257085i
$819$	11.2156	+	34.5180i	0.391904	+	1.20616i
$820$	1.21052	+	3.72560i	0.0422733	+	0.130104i
$821$	19.0118	+	13.8129i	0.663516	+	0.482073i	0.867849	−	0.496829i	$-0.165502\pi$
$821$	19.0118	+	13.8129i	0.663516	+	0.482073i	−0.204332	+	0.978902i	$0.565502\pi$
$822$	−2.28642	+	1.66118i	−0.0797481	+	0.0579404i
$823$	−3.91103	+	12.0369i	−0.136330	+	0.419580i	−0.995795	−	0.0916150i	$-0.970797\pi$
$823$	−3.91103	+	12.0369i	−0.136330	+	0.419580i	0.859465	+	0.511195i	$0.170797\pi$
$824$	13.5535			0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−9.33959	+	28.7443i	−0.324770	+	0.999538i	0.646775	+	0.762681i	$0.276117\pi$
$827$	−9.33959	+	28.7443i	−0.324770	+	0.999538i	−0.971545	+	0.236857i	$0.923883\pi$
$828$	−11.5092	+	8.36195i	−0.399974	+	0.290598i
$829$	−1.61937	−	1.17654i	−0.0562432	−	0.0408630i	0.559308	−	0.828960i	$-0.311067\pi$
$829$	−1.61937	−	1.17654i	−0.0562432	−	0.0408630i	−0.615552	+	0.788097i	$0.711067\pi$
$830$	−1.63938	−	5.04549i	−0.0569037	−	0.175132i
$831$	0.342177	+	1.05311i	0.0118700	+	0.0365321i
$832$	11.4815	+	8.34180i	0.398050	+	0.289200i
$833$	−0.787500	+	0.572152i	−0.0272852	+	0.0198239i
$834$	−1.10481	+	3.40025i	−0.0382564	+	0.117741i
$835$	−8.48232			−0.293543
$836$		0			0
$837$	−4.54520			−0.157105
$838$	0.187177	−	0.576072i	0.00646592	−	0.0199001i
$839$	−28.6185	+	20.7925i	−0.988019	+	0.717838i	−0.959486	−	0.281755i	$-0.909083\pi$
$839$	−28.6185	+	20.7925i	−0.988019	+	0.717838i	−0.0285326	+	0.999593i	$0.509083\pi$
$840$	−1.26354	−	0.918013i	−0.0435962	−	0.0316745i
$841$	−6.15541	−	18.9444i	−0.212256	−	0.653255i
$842$	4.37511	+	13.4652i	0.150776	+	0.464041i
$843$	−5.96492	−	4.33377i	−0.205443	−	0.149263i
$844$	−4.99463	+	3.62881i	−0.171922	+	0.124909i
$845$	−2.71589	+	8.35865i	−0.0934295	+	0.287546i
$846$	6.02834			0.207259
$847$		0			0
$848$	−17.0083			−0.584067
$849$	2.90509	−	8.94095i	0.0997024	−	0.306853i
$850$	1.78628	−	1.29781i	0.0612688	−	0.0445144i
$851$	23.8696	+	17.3423i	0.818241	+	0.594487i
$852$	−0.211556	−	0.651102i	−0.00724779	−	0.0223064i
$853$	5.62515	+	17.3124i	0.192602	+	0.592767i	0.999996	+	0.00275489i	$0.000876911\pi$
$853$	5.62515	+	17.3124i	0.192602	+	0.592767i	−0.807395	+	0.590012i	$0.799123\pi$
$854$	−4.12917	−	3.00001i	−0.141297	−	0.102658i
$855$	−10.1680	+	7.38746i	−0.347737	+	0.252646i
$856$	−10.0302	+	30.8699i	−0.342827	+	1.05511i
$857$	29.2837			1.00031			0.500156	−	0.865935i	$-0.333276\pi$
$857$	29.2837			1.00031			0.500156	+	0.865935i	$0.333276\pi$
$858$		0			0
$859$	8.44030			0.287979			0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030			0.287979			0.143990	+	0.989579i	$0.454007\pi$
$860$	3.87032	−	11.9116i	0.131977	−	0.406183i
$861$	1.55134	−	1.12712i	0.0528696	−	0.0384120i
$862$	−12.1065	−	8.79587i	−0.412348	−	0.299589i
$863$	−5.97907	−	18.4017i	−0.203530	−	0.626400i	−0.999771	−	0.0214204i	$-0.993181\pi$
$863$	−5.97907	−	18.4017i	−0.203530	−	0.626400i	0.796241	−	0.604980i	$-0.206819\pi$
$864$	2.87360	+	8.84404i	0.0977620	+	0.300880i
$865$	−4.10876	−	2.98519i	−0.139702	−	0.101500i
$866$	−10.0515	+	7.30281i	−0.341562	+	0.248160i
$867$	0.439559	−	1.35282i	0.0149282	−	0.0459443i
$868$	11.3559			0.385446
$869$		0			0
$870$	0.464635			0.0157526
$871$	10.5585	−	32.4956i	0.357760	−	1.10107i
$872$	−23.8361	+	17.3179i	−0.807191	+	0.586458i
$873$	43.4184	+	31.5453i	1.46949	+	1.06765i
$874$	−1.77460	−	5.46165i	−0.0600266	−	0.184743i
$875$	0.829779	+	2.55380i	0.0280516	+	0.0863341i
$876$	−0.473260	−	0.343844i	−0.0159900	−	0.0116174i
$877$	14.1691	−	10.2945i	0.478456	−	0.347619i	−0.322271	−	0.946647i	$-0.604446\pi$
$877$	14.1691	−	10.2945i	0.478456	−	0.347619i	0.800728	+	0.599028i	$0.204446\pi$
$878$	2.12655	−	6.54484i	0.0717675	−	0.220878i
$879$	−6.85349			−0.231163
$880$		0			0
$881$	−20.0575			−0.675754			−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575			−0.675754			−0.337877	+	0.941190i	$0.609709\pi$
$882$	0.0898538	−	0.276542i	0.00302553	−	0.00931164i
$883$	−21.7609	+	15.8102i	−0.732313	+	0.532057i	−0.890294	−	0.455386i	$-0.849501\pi$
$883$	−21.7609	+	15.8102i	−0.732313	+	0.532057i	0.157981	+	0.987442i	$0.449501\pi$
$884$	30.9620	+	22.4952i	1.04136	+	0.756595i
$885$	−1.17278	−	3.60946i	−0.0394227	−	0.121331i
$886$	0.0487585	+	0.150063i	0.00163807	+	0.00504148i
$887$	5.50591	+	4.00028i	0.184870	+	0.134316i	0.676371	−	0.736561i	$-0.263552\pi$
$887$	5.50591	+	4.00028i	0.184870	+	0.134316i	−0.491501	+	0.870877i	$0.663552\pi$
$888$	5.00805	−	3.63856i	0.168059	−	0.122102i
$889$	−0.0632845	+	0.194770i	−0.00212249	+	0.00653237i
$890$	1.32190			0.0443103
$891$		0			0
$892$	−18.6880			−0.625720
$893$	5.85082	−	18.0070i	0.195790	−	0.602581i
$894$	−1.82928	+	1.32905i	−0.0611804	+	0.0444502i
$895$	−9.15568	−	6.65199i	−0.306041	−	0.222352i
$896$	−9.30635	−	28.6420i	−0.310903	−	0.956862i
$897$	1.29189	+	3.97603i	0.0431349	+	0.132756i
$898$	3.28514	+	2.38680i	0.109627	+	0.0796484i
$899$	−5.81757	+	4.22671i	−0.194027	+	0.140969i
$900$	1.58578	−	4.88053i	0.0528593	−	0.162684i
$901$	−29.3033			−0.976235
$902$		0			0
$903$	−6.13090			−0.204024
$904$	−1.14258	+	3.51650i	−0.0380017	+	0.116957i
$905$	5.98677	−	4.34965i	0.199007	−	0.144587i
$906$	0.937933	+	0.681448i	0.0311607	+	0.0226396i
$907$	−6.59174	−	20.2873i	−0.218875	−	0.673629i	−0.998856	−	0.0478248i	$-0.984771\pi$
$907$	−6.59174	−	20.2873i	−0.218875	−	0.673629i	0.779981	−	0.625804i	$-0.215229\pi$
$908$	0.118301	+	0.364094i	0.00392597	+	0.0120829i
$909$	16.6666	+	12.1090i	0.552797	+	0.401631i
$910$	4.83960	−	3.51617i	0.160431	−	0.116560i
$911$	−8.52542	+	26.2385i	−0.282460	+	0.869322i	0.704689	+	0.709516i	$0.251087\pi$
$911$	−8.52542	+	26.2385i	−0.282460	+	0.869322i	−0.987149	+	0.159805i	$0.948913\pi$
$912$	3.76541			0.124685
$913$		0			0
$914$	0.543347			0.0179723
$915$	−0.397604	+	1.22370i	−0.0131444	+	0.0404542i
$916$	−0.108549	+	0.0788658i	−0.00358657	+	0.00260580i
$917$	24.9458	+	18.1242i	0.823782	+	0.598512i
$918$	1.29958	+	3.99968i	0.0428924	+	0.132009i
$919$	1.85685	+	5.71479i	0.0612518	+	0.188514i	0.977000	−	0.213239i	$-0.0684012\pi$
$919$	1.85685	+	5.71479i	0.0612518	+	0.188514i	−0.915748	+	0.401752i	$0.868401\pi$
$920$	4.03774	+	2.93359i	0.133120	+	0.0967176i
$921$	−1.79697	+	1.30558i	−0.0592122	+	0.0430202i
$922$	2.13955	−	6.58486i	0.0704624	−	0.216861i
$923$	5.58140			0.183714
$924$		0			0
$925$	−10.6429			−0.349937
$926$	0.722274	−	2.22293i	0.0237354	−	0.0730501i
$927$	17.6360	−	12.8133i	0.579242	−	0.420844i
$928$	11.9024	+	8.64757i	0.390714	+	0.283870i
$929$	2.96576	+	9.12766i	0.0973034	+	0.299469i	0.987847	−	0.155429i	$-0.0496759\pi$
$929$	2.96576	+	9.12766i	0.0973034	+	0.299469i	−0.890544	+	0.454898i	$0.849676\pi$
$930$	0.113700	+	0.349933i	0.00372837	+	0.0114747i
$931$	−0.738836	−	0.536796i	−0.0242144	−	0.0175928i
$932$	−21.6785	+	15.7504i	−0.710103	+	0.515920i
$933$	2.51160	−	7.72992i	0.0822261	−	0.253066i
$934$	−15.4742			−0.506332
$935$		0			0
$936$	−24.3339			−0.795378
$937$	11.9255	−	36.7029i	0.389589	−	1.19903i	−0.543507	−	0.839405i	$-0.682904\pi$
$937$	11.9255	−	36.7029i	0.389589	−	1.19903i	0.933096	−	0.359628i	$-0.117096\pi$
$938$	−7.58916	+	5.51385i	−0.247795	+	0.180034i
$939$	3.02649	+	2.19887i	0.0987658	+	0.0717575i
$940$	2.38892	+	7.35233i	0.0779179	+	0.239807i
$941$	9.01854	+	27.7562i	0.293996	+	0.904826i	0.983557	+	0.180599i	$0.0578035\pi$
$941$	9.01854	+	27.7562i	0.293996	+	0.904826i	−0.689561	+	0.724228i	$0.742196\pi$
$942$	−1.66928	−	1.21280i	−0.0543880	−	0.0395152i
$943$	−4.95744	+	3.60179i	−0.161437	+	0.117291i
$944$	9.74764	−	30.0002i	0.317259	−	0.976422i
$945$	−5.11455			−0.166376
$946$		0			0
$947$	46.7623			1.51957			0.759785	−	0.650174i	$-0.225304\pi$
$947$	46.7623			1.51957			0.759785	+	0.650174i	$0.225304\pi$
$948$	0.619629	−	1.90702i	0.0201246	−	0.0619371i
$949$	3.85834	−	2.80325i	0.125247	−	0.0909972i
$950$	1.67589	+	1.21761i	0.0543732	+	0.0395044i
$951$	2.07069	+	6.37293i	0.0671468	+	0.206657i
$952$	−6.91116	−	21.2704i	−0.223992	−	0.689376i
$953$	−4.97738	−	3.61628i	−0.161233	−	0.117143i	0.504243	−	0.863562i	$-0.331772\pi$
$953$	−4.97738	−	3.61628i	−0.161233	−	0.117143i	−0.665476	+	0.746419i	$0.731772\pi$
$954$	7.08167	−	5.14514i	0.229278	−	0.166580i
$955$	1.59332	−	4.90372i	0.0515585	−	0.158681i
$956$	−41.0529			−1.32774
$957$		0			0
$958$	8.46440			0.273472
$959$	15.2093	−	46.8093i	0.491132	−	1.51155i
$960$	−0.794658	+	0.577353i	−0.0256475	+	0.0186340i
$961$	20.4726	+	14.8742i	0.660408	+	0.479814i
$962$	7.32680	+	22.5496i	0.236226	+	0.727027i
$963$	16.1325	+	49.6507i	0.519862	+	1.59997i
$964$	30.5891	+	22.2243i	0.985209	+	0.715796i
$965$	3.26220	−	2.37013i	0.105014	−	0.0762970i
$966$	0.354686	−	1.09161i	0.0114118	−	0.0351220i
$967$	−3.39625			−0.109216			−0.0546080	−	0.998508i	$-0.517391\pi$
$967$	−3.39625			−0.109216			−0.0546080	+	0.998508i	$0.517391\pi$
$968$		0			0
$969$	6.48736			0.208404
$970$	2.73345	−	8.41270i	0.0877658	−	0.270115i
$971$	7.60072	−	5.52224i	0.243919	−	0.177217i	−0.459109	−	0.888380i	$-0.651831\pi$
$971$	7.60072	−	5.52224i	0.243919	−	0.177217i	0.703027	+	0.711163i	$0.251831\pi$
$972$	11.9314	+	8.66870i	0.382701	+	0.278049i
$973$	−19.2404	−	59.2158i	−0.616818	−	1.89837i
$974$	2.72255	+	8.37914i	0.0872360	+	0.268485i
$975$	−1.22004	−	0.886408i	−0.0390724	−	0.0283878i
$976$	−8.65182	+	6.28591i	−0.276938	+	0.201207i
$977$	−5.11585	+	15.7450i	−0.163671	+	0.503726i	−0.998936	−	0.0461210i	$-0.985314\pi$
$977$	−5.11585	+	15.7450i	−0.163671	+	0.503726i	0.835265	+	0.549847i	$0.185314\pi$
$978$	0.119032			0.00380623
$979$		0			0
$980$	0.372885			0.0119114
$981$	−14.6436	+	45.0685i	−0.467535	+	1.43893i
$982$	4.41474	−	3.20750i	0.140880	−	0.102355i
$983$	−41.1126	−	29.8701i	−1.31129	−	0.952707i	−0.999997	−	0.00239240i	$-0.999238\pi$
$983$	−41.1126	−	29.8701i	−1.31129	−	0.952707i	−0.311291	−	0.950315i	$-0.600762\pi$
$984$	0.397287	+	1.22272i	0.0126651	+	0.0389790i
$985$	3.52822	+	10.8588i	0.112419	+	0.345989i
$986$	5.38279	+	3.91083i	0.171423	+	0.124546i
$987$	3.06151	−	2.22432i	0.0974490	−	0.0708009i
$988$	−11.0956	+	34.1488i	−0.352999	+	1.08642i
$989$	19.5918			0.622983
$990$		0			0
$991$	11.3642			0.360996			0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642			0.360996			0.180498	+	0.983575i	$0.442229\pi$
$992$	−3.60018	+	11.0802i	−0.114306	+	0.351797i
$993$	8.40081	−	6.10355i	0.266592	−	0.193690i
$994$	−1.23971	−	0.900700i	−0.0393211	−	0.0285685i
$995$	2.21455	+	6.81569i	0.0702060	+	0.216072i
$996$	1.96671	+	6.05292i	0.0623177	+	0.191794i
$997$	−23.5945	−	17.1424i	−0.747246	−	0.542906i	0.147726	−	0.989028i	$-0.452805\pi$
$997$	−23.5945	−	17.1424i	−0.747246	−	0.542906i	−0.894972	+	0.446122i	$0.852805\pi$
$998$	4.20149	−	3.05256i	0.132996	−	0.0966271i
$999$	6.26427	−	19.2794i	0.198193	−	0.609975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.k.251.1		8
11.2	odd	10		605.2.g.m.366.1		8
11.3	even	5		605.2.g.e.81.2		8
11.4	even	5		605.2.a.k.1.2		4
11.5	even	5	inner	605.2.g.k.511.1		8
11.6	odd	10		55.2.g.b.16.2	✓	8
11.7	odd	10		605.2.a.j.1.3		4
11.8	odd	10		605.2.g.m.81.1		8
11.9	even	5		605.2.g.e.366.2		8
11.10	odd	2		55.2.g.b.31.2	yes	8
33.17	even	10		495.2.n.e.181.1		8
33.26	odd	10		5445.2.a.bi.1.3		4
33.29	even	10		5445.2.a.bp.1.2		4
33.32	even	2		495.2.n.e.361.1		8
44.7	even	10		9680.2.a.cn.1.3		4
44.15	odd	10		9680.2.a.cm.1.3		4
44.39	even	10		880.2.bo.h.401.1		8
44.43	even	2		880.2.bo.h.801.1		8
55.4	even	10		3025.2.a.w.1.3		4
55.17	even	20		275.2.z.a.49.2		16
55.28	even	20		275.2.z.a.49.3		16
55.29	odd	10		3025.2.a.bd.1.2		4
55.32	even	4		275.2.z.a.174.3		16
55.39	odd	10		275.2.h.a.126.1		8
55.43	even	4		275.2.z.a.174.2		16
55.54	odd	2		275.2.h.a.251.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	11.6	odd	10
55.2.g.b.31.2	yes	8	11.10	odd	2
275.2.h.a.126.1		8	55.39	odd	10
275.2.h.a.251.1		8	55.54	odd	2
275.2.z.a.49.2		16	55.17	even	20
275.2.z.a.49.3		16	55.28	even	20
275.2.z.a.174.2		16	55.43	even	4
275.2.z.a.174.3		16	55.32	even	4
495.2.n.e.181.1		8	33.17	even	10
495.2.n.e.361.1		8	33.32	even	2
605.2.a.j.1.3		4	11.7	odd	10
605.2.a.k.1.2		4	11.4	even	5
605.2.g.e.81.2		8	11.3	even	5
605.2.g.e.366.2		8	11.9	even	5
605.2.g.k.251.1		8	1.1	even	1	trivial
605.2.g.k.511.1		8	11.5	even	5	inner
605.2.g.m.81.1		8	11.8	odd	10
605.2.g.m.366.1		8	11.2	odd	10
880.2.bo.h.401.1		8	44.39	even	10
880.2.bo.h.801.1		8	44.43	even	2
3025.2.a.w.1.3		4	55.4	even	10
3025.2.a.bd.1.2		4	55.29	odd	10
5445.2.a.bi.1.3		4	33.26	odd	10
5445.2.a.bp.1.2		4	33.29	even	10
9680.2.a.cm.1.3		4	44.15	odd	10
9680.2.a.cn.1.3		4	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.147481 + 0.453901i) q^{2} +(-0.261370 + 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.0476470 - 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +0.477260 q^{10} -0.572554 q^{12} +(1.44244 - 4.43939i) q^{13} +(-1.03679 + 0.753275i) q^{14} +(0.261370 + 0.189896i) q^{15} +(0.829779 + 2.55380i) q^{16} +(1.42961 + 4.39990i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(-3.51149 + 2.55125i) q^{19} +(0.547647 - 1.68548i) q^{20} -0.867517 q^{21} +2.77222 q^{23} +(0.179735 - 0.553168i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(1.80231 + 1.30945i) q^{26} +(-0.588587 - 1.81148i) q^{27} +(1.47055 + 4.52590i) q^{28} +(-2.43790 - 1.77124i) q^{29} +(-0.124741 + 0.0906300i) q^{30} +(0.737407 - 2.26951i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(0.829779 - 2.55380i) q^{35} +(-4.15163 + 3.01633i) q^{36} +(8.61029 + 6.25574i) q^{37} +(-0.640135 - 1.97013i) q^{38} +(0.466012 + 1.43424i) q^{39} +(1.45650 + 1.05821i) q^{40} +(-1.78826 + 1.29924i) q^{41} +(0.127943 - 0.393767i) q^{42} +7.06719 q^{43} +2.89563 q^{45} +(-0.408851 + 1.25832i) q^{46} +(-3.52905 + 2.56401i) q^{47} +(-0.701836 - 0.509914i) q^{48} +(0.0650188 + 0.200107i) q^{49} +(-0.147481 - 0.453901i) q^{50} +(-1.20918 - 0.878523i) q^{51} +(6.69257 - 4.86243i) q^{52} +(-1.95733 + 6.02403i) q^{53} +0.909040 q^{54} -4.83428 q^{56} +(0.433326 - 1.33364i) q^{57} +(1.16351 - 0.845342i) q^{58} +(-9.50375 - 6.90488i) q^{59} +(0.176929 + 0.544531i) q^{60} +(1.23070 + 3.78770i) q^{61} +(0.921378 + 0.669420i) q^{62} +(-6.29042 + 4.57026i) q^{63} +(-0.939522 + 2.89155i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(-2.53359 + 7.79760i) q^{68} +(-0.724576 + 0.526435i) q^{69} +(1.03679 + 0.753275i) q^{70} +(0.369495 + 1.13719i) q^{71} +(-1.61093 - 4.95794i) q^{72} +(0.826577 + 0.600544i) q^{73} +(-4.10935 + 2.98562i) q^{74} +(0.0998345 - 0.307259i) q^{75} -7.69223 q^{76} -0.719730 q^{78} +(-1.08222 + 3.33073i) q^{79} +(2.17239 - 1.57833i) q^{80} +(-6.53000 - 4.74432i) q^{81} +(-0.325994 - 1.00331i) q^{82} +(-3.43498 - 10.5718i) q^{83} +(-1.24381 - 0.903681i) q^{84} +(3.74278 - 2.71929i) q^{85} +(-1.04228 + 3.20780i) q^{86} +0.973547 q^{87} +2.76978 q^{89} +(-0.427051 + 1.31433i) q^{90} +(10.1404 - 7.36742i) q^{91} +(3.97470 + 2.88779i) q^{92} +(0.238235 + 0.733212i) q^{93} +(-0.643336 - 1.97998i) q^{94} +(3.51149 + 2.55125i) q^{95} +(1.27606 - 0.927114i) q^{96} +(5.72738 - 17.6271i) q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23}+ \cdots - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * q^98

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