LMFDB - Embedded newform 625.2.e.a.374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.1
Root			$-0.983224 - 0.644389i$ of defining polynomial
Character	$\chi$	$=$	625.374
Dual form			625.2.e.a.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +O(q^{10})$	\(q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(3.03472 - 4.17693i) q^{12} +(-1.98322 + 2.72967i) q^{13} +(-1.67421 + 1.21638i) q^{14} +(2.57411 + 1.87020i) q^{16} +(2.75284 - 0.894453i) q^{17} -3.82309i q^{18} +(0.798649 + 2.45799i) q^{19} +(-0.674207 + 2.07500i) q^{21} +(3.96645 + 1.28878i) q^{22} +(2.67421 + 3.68073i) q^{23} -1.59730 q^{24} +7.03588 q^{26} +(1.50757 + 2.07500i) q^{27} +(2.21650 + 0.720183i) q^{28} +(1.66384 - 5.12077i) q^{29} +(0.0421925 + 0.129855i) q^{31} -8.08800i q^{32} +(4.18178 - 1.35874i) q^{33} +(-4.88313 - 3.54780i) q^{34} +(-3.48322 + 2.53071i) q^{36} +(1.26321 - 1.73866i) q^{37} +(3.16780 - 4.36010i) q^{38} +(6.00116 - 4.36010i) q^{39} +(-6.98439 - 5.07446i) q^{41} +(4.32696 - 1.40591i) q^{42} +4.64398i q^{43} +(-1.45140 - 4.46695i) q^{44} +(2.93173 - 9.02294i) q^{46} +(-9.44047 - 3.06739i) q^{47} +(-4.11163 - 5.65917i) q^{48} +6.01515 q^{49} -6.36356 q^{51} +(-4.65743 - 6.41040i) q^{52} +(7.19494 + 2.33778i) q^{53} +(1.65275 - 5.08664i) q^{54} +(-0.222807 - 0.685730i) q^{56} -5.68196i q^{57} +(-10.6783 + 3.46958i) q^{58} +(3.97854 + 2.89058i) q^{59} +(2.24075 - 1.62800i) q^{61} +(0.167354 - 0.230343i) q^{62} +(1.06943 - 1.47195i) q^{63} +(-8.49648 + 6.17306i) q^{64} +(-7.41785 - 5.38938i) q^{66} +(2.07879 - 0.675441i) q^{67} +6.79751i q^{68} +(-3.09089 - 9.51278i) q^{69} +(2.97971 - 9.17060i) q^{71} +(1.26682 + 0.411616i) q^{72} +(-0.456080 - 0.627740i) q^{73} -4.48150 q^{74} -6.06943 q^{76} +(1.16663 + 1.60573i) q^{77} +(-14.7113 - 4.77998i) q^{78} +(-4.89818 + 15.0750i) q^{79} +(-3.44210 - 10.5937i) q^{81} +18.0026i q^{82} +(1.68442 - 0.547301i) q^{83} +(-4.14518 - 3.01165i) q^{84} +(7.83453 - 5.69212i) q^{86} +(-6.95781 + 9.57660i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(11.7372 - 8.52760i) q^{89} +(2.70892 + 1.96815i) q^{91} +(-10.1615 + 3.30167i) q^{92} -0.300177i q^{93} +(6.39639 + 19.6861i) q^{94} +(-5.49476 + 16.9111i) q^{96} +(16.1956 + 5.26228i) q^{97} +(-7.37276 - 10.1477i) q^{98} -3.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.22570	−	1.68703i	−0.866701	−	1.19291i	−0.979930	−	0.199342i	$-0.936119\pi$
$2$	−1.22570	−	1.68703i	−0.866701	−	1.19291i	0.113229	−	0.993569i	$-0.463881\pi$
$3$	−2.09089	−	0.679371i	−1.20718	−	0.392235i	−0.364780	−	0.931094i	$-0.618856\pi$
$3$	−2.09089	−	0.679371i	−1.20718	−	0.392235i	−0.842396	+	0.538859i	$0.818856\pi$
$4$	−0.725700	+	2.23347i	−0.362850	+	1.11674i
$5$		0			0
$5$		0			0
$6$	1.41668	+	4.36010i	0.578358	+	1.78000i
$7$		−	0.992398i		−	0.375091i	−0.982256	−	0.187546i	$-0.939947\pi$
$7$		−	0.992398i		−	0.375091i	0.982256	−	0.187546i	$-0.0600533\pi$
$8$	0.690983	−	0.224514i	0.244299	−	0.0793777i
$9$	1.48322	+	1.07763i	0.494408	+	0.359208i
$10$		0			0
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	3.03472	−	4.17693i	0.876047	−	1.20578i
$13$	−1.98322	+	2.72967i	−0.550047	+	0.757075i	−0.990019	−	0.140937i	$-0.954989\pi$
$13$	−1.98322	+	2.72967i	−0.550047	+	0.757075i	0.439971	+	0.898012i	$0.354989\pi$
$14$	−1.67421	+	1.21638i	−0.447451	+	0.325092i
$15$		0			0
$16$	2.57411	+	1.87020i	0.643528	+	0.467551i
$17$	2.75284	−	0.894453i	0.667663	−	0.216937i	0.0444767	−	0.999010i	$-0.485838\pi$
$17$	2.75284	−	0.894453i	0.667663	−	0.216937i	0.623186	+	0.782074i	$0.285838\pi$
$18$		−	3.82309i		−	0.901111i
$19$	0.798649	+	2.45799i	0.183223	+	0.563901i	0.999913	−	0.0131746i	$-0.00419372\pi$
$19$	0.798649	+	2.45799i	0.183223	+	0.563901i	−0.816691	+	0.577076i	$0.804194\pi$
$20$		0			0
$21$	−0.674207	+	2.07500i	−0.147124	+	0.452801i
$22$	3.96645	+	1.28878i	0.845650	+	0.274768i
$23$	2.67421	+	3.68073i	0.557611	+	0.767485i	0.991020	−	0.133712i	$-0.0426896\pi$
$23$	2.67421	+	3.68073i	0.557611	+	0.767485i	−0.433410	+	0.901197i	$0.642690\pi$
$24$	−1.59730			−0.326047
$25$		0			0
$26$	7.03588			1.37985
$27$	1.50757	+	2.07500i	0.290132	+	0.399333i
$28$	2.21650	+	0.720183i	0.418878	+	0.136102i
$29$	1.66384	−	5.12077i	0.308967	−	0.950903i	−0.669200	−	0.743082i	$-0.733363\pi$
$29$	1.66384	−	5.12077i	0.308967	−	0.950903i	0.978167	−	0.207821i	$-0.0666370\pi$
$30$		0			0
$31$	0.0421925	+	0.129855i	0.00757799	+	0.0233227i	0.954774	−	0.297332i	$-0.0960970\pi$
$31$	0.0421925	+	0.129855i	0.00757799	+	0.0233227i	−0.947196	+	0.320655i	$0.896097\pi$
$32$		−	8.08800i		−	1.42977i
$33$	4.18178	−	1.35874i	0.727954	−	0.236527i
$34$	−4.88313	−	3.54780i	−0.837450	−	0.608443i
$35$		0			0
$36$	−3.48322	+	2.53071i	−0.580537	+	0.421785i
$37$	1.26321	−	1.73866i	0.207671	−	0.285834i	−0.692458	−	0.721458i	$-0.743472\pi$
$37$	1.26321	−	1.73866i	0.207671	−	0.285834i	0.900129	+	0.435624i	$0.143472\pi$
$38$	3.16780	−	4.36010i	0.513885	−	0.707302i
$39$	6.00116	−	4.36010i	0.960955	−	0.698175i
$40$		0			0
$41$	−6.98439	−	5.07446i	−1.09078	−	0.792497i	−0.111248	−	0.993793i	$-0.535485\pi$
$41$	−6.98439	−	5.07446i	−1.09078	−	0.792497i	−0.979530	+	0.201296i	$0.935485\pi$
$42$	4.32696	−	1.40591i	0.667664	−	0.216937i
$43$			4.64398i			0.708200i	0.935208	+	0.354100i	$0.115213\pi$
$43$			4.64398i			0.708200i	−0.935208	+	0.354100i	$0.884787\pi$
$44$	−1.45140	−	4.46695i	−0.218807	−	0.673418i
$45$		0			0
$46$	2.93173	−	9.02294i	0.432260	−	1.33036i
$47$	−9.44047	−	3.06739i	−1.37703	−	0.447425i	−0.475341	−	0.879802i	$-0.657675\pi$
$47$	−9.44047	−	3.06739i	−1.37703	−	0.447425i	−0.901693	+	0.432376i	$0.857675\pi$
$48$	−4.11163	−	5.65917i	−0.593462	−	0.816831i
$49$	6.01515			0.859306
$50$		0			0
$51$	−6.36356			−0.891077
$52$	−4.65743	−	6.41040i	−0.645869	−	0.888963i
$53$	7.19494	+	2.33778i	0.988301	+	0.321119i	0.758181	−	0.652044i	$-0.226088\pi$
$53$	7.19494	+	2.33778i	0.988301	+	0.321119i	0.230120	+	0.973162i	$0.426088\pi$
$54$	1.65275	−	5.08664i	0.224911	−	0.692205i
$55$		0			0
$56$	−0.222807	−	0.685730i	−0.0297739	−	0.0916346i
$57$		−	5.68196i		−	0.752594i
$58$	−10.6783	+	3.46958i	−1.40212	+	0.455578i
$59$	3.97854	+	2.89058i	0.517962	+	0.376322i	0.815836	−	0.578284i	$-0.196277\pi$
$59$	3.97854	+	2.89058i	0.517962	+	0.376322i	−0.297873	+	0.954605i	$0.596277\pi$
$60$		0			0
$61$	2.24075	−	1.62800i	0.286898	−	0.208444i	−0.435022	−	0.900420i	$-0.643260\pi$
$61$	2.24075	−	1.62800i	0.286898	−	0.208444i	0.721921	+	0.691976i	$0.243260\pi$
$62$	0.167354	−	0.230343i	0.0212540	−	0.0292536i
$63$	1.06943	−	1.47195i	0.134736	−	0.185448i
$64$	−8.49648	+	6.17306i	−1.06206	+	0.771632i
$65$		0			0
$66$	−7.41785	−	5.38938i	−0.913074	−	0.663387i
$67$	2.07879	−	0.675441i	0.253965	−	0.0825183i	−0.179268	−	0.983800i	$-0.557373\pi$
$67$	2.07879	−	0.675441i	0.253965	−	0.0825183i	0.433233	+	0.901282i	$0.357373\pi$
$68$			6.79751i			0.824319i
$69$	−3.09089	−	9.51278i	−0.372099	−	1.14520i
$70$		0			0
$71$	2.97971	−	9.17060i	0.353626	−	1.08835i	−0.603175	−	0.797609i	$-0.706098\pi$
$71$	2.97971	−	9.17060i	0.353626	−	1.08835i	0.956802	−	0.290741i	$-0.0939019\pi$
$72$	1.26682	+	0.411616i	0.149297	+	0.0485094i
$73$	−0.456080	−	0.627740i	−0.0533801	−	0.0734714i	0.781492	−	0.623915i	$-0.214459\pi$
$73$	−0.456080	−	0.627740i	−0.0533801	−	0.0734714i	−0.834873	+	0.550443i	$0.814459\pi$
$74$	−4.48150			−0.520963
$75$		0			0
$76$	−6.06943			−0.696212
$77$	1.16663	+	1.60573i	0.132950	+	0.182990i
$78$	−14.7113	−	4.77998i	−1.66572	−	0.541226i
$79$	−4.89818	+	15.0750i	−0.551088	+	1.69608i	0.154968	+	0.987919i	$0.450473\pi$
$79$	−4.89818	+	15.0750i	−0.551088	+	1.69608i	−0.706056	+	0.708156i	$0.749527\pi$
$80$		0			0
$81$	−3.44210	−	10.5937i	−0.382455	−	1.17708i
$82$			18.0026i			1.98806i
$83$	1.68442	−	0.547301i	0.184889	−	0.0600740i	−0.215109	−	0.976590i	$-0.569011\pi$
$83$	1.68442	−	0.547301i	0.184889	−	0.0600740i	0.399998	+	0.916516i	$0.369011\pi$
$84$	−4.14518	−	3.01165i	−0.452276	−	0.328598i
$85$		0			0
$86$	7.83453	−	5.69212i	0.844819	−	0.613797i
$87$	−6.95781	+	9.57660i	−0.745955	+	1.02672i
$88$	−0.854102	+	1.17557i	−0.0910476	+	0.125316i
$89$	11.7372	−	8.52760i	1.24414	−	0.903924i	0.246277	−	0.969200i	$-0.420793\pi$
$89$	11.7372	−	8.52760i	1.24414	−	0.903924i	0.997867	+	0.0652758i	$0.0207927\pi$
$90$		0			0
$91$	2.70892	+	1.96815i	0.283972	+	0.206318i
$92$	−10.1615	+	3.30167i	−1.05941	+	0.344223i
$93$		−	0.300177i		−	0.0311269i
$94$	6.39639	+	19.6861i	0.659737	+	2.03046i
$95$		0			0
$96$	−5.49476	+	16.9111i	−0.560806	+	1.72598i
$97$	16.1956	+	5.26228i	1.64442	+	0.534304i	0.977520	−	0.210844i	$-0.0676214\pi$
$97$	16.1956	+	5.26228i	1.64442	+	0.534304i	0.666899	+	0.745148i	$0.267621\pi$
$98$	−7.37276	−	10.1477i	−0.744761	−	1.02508i
$99$	−3.66673			−0.368520
$100$		0			0
$101$	−2.54716			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$102$	7.79981	+	10.7355i	0.772297	+	1.06298i
$103$	9.66790	+	3.14129i	0.952606	+	0.309520i	0.743774	−	0.668431i	$-0.233034\pi$
$103$	9.66790	+	3.14129i	0.952606	+	0.309520i	0.208832	+	0.977952i	$0.433034\pi$
$104$	−0.757524	+	2.33142i	−0.0742814	+	0.228615i
$105$		0			0
$106$	−4.87494	−	15.0035i	−0.473496	−	1.45727i
$107$			4.81720i			0.465697i	0.972513	+	0.232848i	$0.0748046\pi$
$107$			4.81720i			0.465697i	−0.972513	+	0.232848i	$0.925195\pi$
$108$	−5.72850	+	1.86130i	−0.551225	+	0.179104i
$109$	13.1662	+	9.56578i	1.26109	+	0.916236i	0.998811	−	0.0487563i	$-0.0155258\pi$
$109$	13.1662	+	9.56578i	1.26109	+	0.916236i	0.262280	+	0.964992i	$0.415526\pi$
$110$		0			0
$111$	−3.82243	+	2.77716i	−0.362809	+	0.263596i
$112$	1.85599	−	2.55455i	0.175374	−	0.241382i
$113$	3.97169	−	5.46656i	0.373625	−	0.514251i	−0.580256	−	0.814434i	$-0.697048\pi$
$113$	3.97169	−	5.46656i	0.373625	−	0.514251i	0.953882	+	0.300183i	$0.0970477\pi$
$114$	−9.58565	+	6.96438i	−0.897778	+	0.652274i
$115$		0			0
$116$	10.2297	+	7.43228i	0.949800	+	0.690070i
$117$	−5.88313	+	1.91155i	−0.543896	+	0.176722i
$118$		−	10.2549i		−	0.944041i
$119$	−0.887654	−	2.73192i	−0.0813711	−	0.250435i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	−5.49297	−	1.78477i	−0.497310	−	0.161586i
$123$	11.1561	+	15.3551i	1.00592	+	1.38452i
$124$	−0.320647			−0.0287950
$125$		0			0
$126$	−3.79403			−0.337999
$127$	−0.876278	−	1.20609i	−0.0777571	−	0.107023i	0.768367	−	0.640010i	$-0.221070\pi$
$127$	−0.876278	−	1.20609i	−0.0777571	−	0.107023i	−0.846124	+	0.532986i	$0.821070\pi$
$128$	5.44398	+	1.76886i	0.481185	+	0.156346i
$129$	3.15498	−	9.71004i	0.277781	−	0.854921i
$130$		0			0
$131$	4.36167	+	13.4239i	0.381081	+	1.17285i	0.939283	+	0.343143i	$0.111491\pi$
$131$	4.36167	+	13.4239i	0.381081	+	1.17285i	−0.558202	+	0.829705i	$0.688509\pi$
$132$			10.3259i			0.898757i
$133$	2.43930	−	0.792578i	0.211514	−	0.0687252i
$134$	−3.68747	−	2.67910i	−0.318549	−	0.231439i
$135$		0			0
$136$	1.70135	−	1.23610i	0.145890	−	0.105995i
$137$	0.405247	−	0.557775i	0.0346226	−	0.0476539i	−0.791355	−	0.611357i	$-0.790624\pi$
$137$	0.405247	−	0.557775i	0.0346226	−	0.0476539i	0.825977	+	0.563703i	$0.190624\pi$
$138$	−12.2599	+	16.8742i	−1.04363	+	1.43643i
$139$	−13.4069	+	9.74070i	−1.13716	+	0.826195i	−0.986721	−	0.162424i	$-0.948069\pi$
$139$	−13.4069	+	9.74070i	−1.13716	+	0.826195i	−0.150439	+	0.988619i	$0.548069\pi$
$140$		0			0
$141$	17.6551	+	12.8272i	1.48683	+	1.08024i
$142$	−19.1233	+	6.21354i	−1.60479	+	0.521429i
$143$		−	6.74812i		−	0.564307i
$144$	1.80261	+	5.54786i	0.150217	+	0.462322i
$145$		0			0
$146$	−0.500000	+	1.53884i	−0.0413803	+	0.127355i
$147$	−12.5770	−	4.08652i	−1.03733	−	0.337050i
$148$	2.96655	+	4.08310i	0.243849	+	0.335629i
$149$	−3.21156			−0.263101			−0.131551	−	0.991309i	$-0.541996\pi$
$149$	−3.21156			−0.263101			−0.131551	+	0.991309i	$0.541996\pi$
$150$		0			0
$151$	17.6863			1.43929			0.719647	−	0.694340i	$-0.244304\pi$
$151$	17.6863			1.43929			0.719647	+	0.694340i	$0.244304\pi$
$152$	1.10371	+	1.51912i	0.0895223	+	0.123217i
$153$	5.04697	+	1.63986i	0.408023	+	0.132575i
$154$	1.27898	−	3.93630i	0.103063	−	0.317196i
$155$		0			0
$156$	5.38313	+	16.5676i	0.430995	+	1.32647i
$157$		−	1.65512i		−	0.132093i	−0.997817	−	0.0660465i	$-0.978961\pi$
$157$		−	1.65512i		−	0.132093i	0.997817	−	0.0660465i	$-0.0210386\pi$
$158$	31.4358	−	10.2141i	2.50090	−	0.812590i
$159$	−13.4556	−	9.77608i	−1.06710	−	0.775293i
$160$		0			0
$161$	3.65275	−	2.65388i	0.287877	−	0.209155i
$162$	−13.6529	+	18.7916i	−1.07267	+	1.47641i
$163$	0.524854	−	0.722399i	0.0411097	−	0.0565827i	−0.787967	−	0.615717i	$-0.788866\pi$
$163$	0.524854	−	0.722399i	0.0411097	−	0.0565827i	0.829077	+	0.559134i	$0.188866\pi$
$164$	16.4022	−	11.9169i	1.28080	−	0.930555i
$165$		0			0
$166$	−2.98790	−	2.17084i	−0.231906	−	0.168490i
$167$	4.94129	−	1.60552i	0.382368	−	0.124239i	−0.111525	−	0.993762i	$-0.535573\pi$
$167$	4.94129	−	1.60552i	0.382368	−	0.124239i	0.493893	+	0.869523i	$0.335573\pi$
$168$			1.58516i			0.122297i
$169$	0.499280	+	1.53663i	0.0384062	+	0.118202i
$170$		0			0
$171$	−1.46422	+	4.50639i	−0.111971	+	0.344612i
$172$	−10.3722	−	3.37013i	−0.790873	−	0.256970i
$173$	3.38837	+	4.66370i	0.257613	+	0.354574i	0.918159	−	0.396211i	$-0.129675\pi$
$173$	3.38837	+	4.66370i	0.257613	+	0.354574i	−0.660546	+	0.750785i	$0.729675\pi$
$174$	24.6842			1.87130
$175$		0			0
$176$	−6.36356			−0.479671
$177$	−6.35492	−	8.74680i	−0.477665	−	0.657449i
$178$	−28.7726	−	9.34880i	−2.15660	−	0.700722i
$179$	−2.67883	+	8.24458i	−0.200225	+	0.616229i	0.799651	+	0.600465i	$0.205018\pi$
$179$	−2.67883	+	8.24458i	−0.200225	+	0.616229i	−0.999876	+	0.0157637i	$0.994982\pi$
$180$		0			0
$181$	4.41612	+	13.5914i	0.328248	+	1.01024i	0.969953	+	0.243291i	$0.0782271\pi$
$181$	4.41612	+	13.5914i	0.328248	+	1.01024i	−0.641706	+	0.766951i	$0.721773\pi$
$182$		−	6.98240i		−	0.517570i
$183$	−5.79117	+	1.88167i	−0.428096	+	0.139097i
$184$	2.67421	+	1.94293i	0.197145	+	0.143234i
$185$		0			0
$186$	−0.506408	+	0.367927i	−0.0371316	+	0.0269777i
$187$	−3.40270	+	4.68342i	−0.248830	+	0.342485i
$188$	13.7019	−	18.8590i	0.999313	−	1.37544i
$189$	2.05922	−	1.49611i	0.149786	−	0.108826i
$190$		0			0
$191$	1.02451	+	0.744347i	0.0741306	+	0.0538591i	0.624233	−	0.781238i	$-0.285411\pi$
$191$	1.02451	+	0.744347i	0.0741306	+	0.0538591i	−0.550103	+	0.835097i	$0.685411\pi$
$192$	21.9590	−	7.13492i	1.58476	−	0.514918i
$193$			21.1730i			1.52406i	0.647540	+	0.762031i	$0.275798\pi$
$193$			21.1730i			1.52406i	−0.647540	+	0.762031i	$0.724202\pi$
$194$	−10.9734	−	33.7725i	−0.787841	−	2.42473i
$195$		0			0
$196$	−4.36519	+	13.4347i	−0.311799	+	0.959620i
$197$	11.6042	+	3.77042i	0.826761	+	0.268631i	0.691681	−	0.722203i	$-0.256871\pi$
$197$	11.6042	+	3.77042i	0.826761	+	0.268631i	0.135081	+	0.990835i	$0.456871\pi$
$198$	4.49431	+	6.18589i	0.319397	+	0.439612i
$199$	−10.4065			−0.737695			−0.368848	−	0.929490i	$-0.620248\pi$
$199$	−10.4065			−0.737695			−0.368848	+	0.929490i	$0.620248\pi$
$200$		0			0
$201$	−4.80540			−0.338947
$202$	3.12205	+	4.29714i	0.219667	+	0.302346i
$203$	−5.08184	−	1.65119i	−0.356675	−	0.115891i
$204$	4.61803	−	14.2128i	0.323327	−	0.995098i
$205$		0			0
$206$	−6.55049	−	20.1603i	−0.456394	−	1.40464i
$207$			8.34114i			0.579749i
$208$	−10.2101	+	3.31746i	−0.707942	+	0.230024i
$209$	−4.18178	−	3.03824i	−0.289260	−	0.210160i
$210$		0			0
$211$	7.00421	−	5.08886i	0.482190	−	0.350332i	−0.319983	−	0.947423i	$-0.603677\pi$
$211$	7.00421	−	5.08886i	0.482190	−	0.350332i	0.802173	+	0.597092i	$0.203677\pi$
$212$	−10.4427	+	14.3732i	−0.717210	+	0.987155i
$213$	−12.4605	+	17.1504i	−0.853778	+	1.17513i
$214$	8.12677	−	5.90445i	0.555535	−	0.403620i
$215$		0			0
$216$	1.50757	+	1.09532i	0.102577	+	0.0745268i
$217$	0.128868	−	0.0418717i	0.00874813	−	0.00284244i
$218$		−	33.9365i		−	2.29847i
$219$	0.527144	+	1.62238i	0.0356211	+	0.109630i
$220$		0			0
$221$	−3.01794	+	9.28827i	−0.203009	+	0.624796i
$222$	9.37032	+	3.04460i	0.628894	+	0.204340i
$223$	−16.6598	−	22.9303i	−1.11562	−	1.53552i	−0.812860	−	0.582459i	$-0.802091\pi$
$223$	−16.6598	−	22.9303i	−1.11562	−	1.53552i	−0.302764	−	0.953065i	$-0.597909\pi$
$224$	−8.02652			−0.536295
$225$		0			0
$226$	−14.0904			−0.937277
$227$	13.0732	+	17.9937i	0.867699	+	1.19429i	0.979678	+	0.200575i	$0.0642809\pi$
$227$	13.0732	+	17.9937i	0.867699	+	1.19429i	−0.111979	+	0.993711i	$0.535719\pi$
$228$	12.6905	+	4.12340i	0.840450	+	0.273079i
$229$	−0.765000	+	2.35443i	−0.0505526	+	0.155585i	−0.973146	−	0.230189i	$-0.926066\pi$
$229$	−0.765000	+	2.35443i	−0.0505526	+	0.155585i	0.922593	+	0.385774i	$0.126066\pi$
$230$		0			0
$231$	−1.34841	−	4.14999i	−0.0887191	−	0.273049i
$232$		−	3.91192i		−	0.256830i
$233$	−5.66454	+	1.84052i	−0.371096	+	0.120576i	−0.488627	−	0.872493i	$-0.662502\pi$
$233$	−5.66454	+	1.84052i	−0.371096	+	0.120576i	0.117531	+	0.993069i	$0.462502\pi$
$234$	10.4358	+	7.58204i	0.682209	+	0.495654i
$235$		0			0
$236$	−9.34327	+	6.78828i	−0.608195	+	0.441879i
$237$	20.4831	−	28.1926i	1.33052	−	1.83130i
$238$	−3.52083	+	4.84601i	−0.228222	+	0.314120i
$239$	−5.68935	+	4.13356i	−0.368014	+	0.267378i	−0.756387	−	0.654125i	$-0.773037\pi$
$239$	−5.68935	+	4.13356i	−0.368014	+	0.267378i	0.388373	+	0.921502i	$0.373037\pi$
$240$		0			0
$241$	−0.954449	−	0.693448i	−0.0614815	−	0.0446689i	0.556620	−	0.830767i	$-0.312098\pi$
$241$	−0.954449	−	0.693448i	−0.0614815	−	0.0446689i	−0.618102	+	0.786098i	$0.712098\pi$
$242$	13.8826	−	4.51072i	0.892405	−	0.289960i
$243$			16.7942i			1.07735i
$244$	2.00998	+	6.18609i	0.128676	+	0.396024i
$245$		0			0
$246$	12.2305	−	37.6415i	0.779787	−	2.39994i
$247$	−8.29341	−	2.69469i	−0.527697	−	0.171459i
$248$	0.0583086	+	0.0802548i	0.00370260	+	0.00509619i
$249$	−3.89375			−0.246757
$250$		0			0
$251$	4.60867			0.290897			0.145448	−	0.989366i	$-0.453538\pi$
$251$	4.60867			0.290897			0.145448	+	0.989366i	$0.453538\pi$
$252$	2.51147	+	3.45675i	0.158208	+	0.217755i
$253$	−8.65392	−	2.81183i	−0.544067	−	0.176778i
$254$	−0.960663	+	2.95662i	−0.0602774	+	0.185515i
$255$		0			0
$256$	2.80216	+	8.62417i	0.175135	+	0.539011i
$257$			9.75542i			0.608526i	0.952588	+	0.304263i	$0.0984102\pi$
$257$			9.75542i			0.608526i	−0.952588	+	0.304263i	$0.901590\pi$
$258$	−20.2482	+	6.57904i	−1.26060	+	0.409593i
$259$	−1.72545	−	1.25361i	−0.107214	−	0.0778955i
$260$		0			0
$261$	7.98612	−	5.80225i	0.494328	−	0.359150i
$262$	17.3004	−	23.8119i	1.06882	−	1.47110i
$263$	0.585333	−	0.805641i	0.0360932	−	0.0496780i	−0.790589	−	0.612347i	$-0.790225\pi$
$263$	0.585333	−	0.805641i	0.0360932	−	0.0496780i	0.826682	+	0.562669i	$0.190225\pi$
$264$	2.58448	−	1.87774i	0.159064	−	0.115567i
$265$		0			0
$266$	−4.32696	−	3.14372i	−0.265303	−	0.192754i
$267$	−30.3347	+	9.85633i	−1.85645	+	0.603198i
$268$			5.13310i			0.313554i
$269$	1.01621	+	3.12758i	0.0619596	+	0.190692i	0.977245	−	0.212114i	$-0.0680349\pi$
$269$	1.01621	+	3.12758i	0.0619596	+	0.190692i	−0.915285	+	0.402806i	$0.868035\pi$
$270$		0			0
$271$	3.75457	−	11.5554i	0.228074	−	0.701940i	−0.769891	−	0.638175i	$-0.779689\pi$
$271$	3.75457	−	11.5554i	0.228074	−	0.701940i	0.997965	−	0.0637642i	$-0.0203105\pi$
$272$	8.75894	+	2.84595i	0.531089	+	0.172561i
$273$	−4.32696	−	5.95555i	−0.261879	−	0.360446i
$274$	−1.43769			−0.0868543
$275$		0			0
$276$	23.4896			1.41391
$277$	−6.97499	−	9.60025i	−0.419087	−	0.576823i	0.546319	−	0.837577i	$-0.316029\pi$
$277$	−6.97499	−	9.60025i	−0.419087	−	0.576823i	−0.965405	+	0.260754i	$0.916029\pi$
$278$	32.8657	+	10.6787i	1.97115	+	0.640467i
$279$	−0.0773542	+	0.238072i	−0.00463108	+	0.0142530i
$280$		0			0
$281$	−7.61468	−	23.4356i	−0.454253	−	1.39805i	−0.872009	−	0.489489i	$-0.837183\pi$
$281$	−7.61468	−	23.4356i	−0.454253	−	1.39805i	0.417756	−	0.908559i	$-0.362817\pi$
$282$		−	45.5069i		−	2.70990i
$283$	3.19881	−	1.03936i	0.190150	−	0.0617833i	−0.212394	−	0.977184i	$-0.568126\pi$
$283$	3.19881	−	1.03936i	0.190150	−	0.0617833i	0.402544	+	0.915401i	$0.368126\pi$
$284$	18.3199	+	13.3102i	1.08709	+	0.789815i
$285$		0			0
$286$	−11.3843	+	8.27117i	−0.673168	+	0.489085i
$287$	−5.03588	+	6.93130i	−0.297259	+	0.409141i
$288$	8.71584	−	11.9963i	0.513586	−	0.706890i
$289$	−6.97519	+	5.06777i	−0.410305	+	0.298104i
$290$		0			0
$291$	−30.2883	−	22.0057i	−1.77553	−	1.29000i
$292$	1.73302	−	0.563092i	0.101417	−	0.0329525i
$293$		−	8.96340i		−	0.523647i	−0.965116	−	0.261824i	$-0.915676\pi$
$293$		−	8.96340i		−	0.523647i	0.965116	−	0.261824i	$-0.0843239\pi$
$294$	8.52155	+	26.2266i	0.496987	+	1.52957i
$295$		0			0
$296$	0.482504	−	1.48499i	0.0280450	−	0.0863136i
$297$	−4.87861	−	1.58516i	−0.283086	−	0.0919801i
$298$	3.93641	+	5.41801i	0.228030	+	0.313857i
$299$	−15.3507			−0.887756
$300$		0			0
$301$	4.60867			0.265640
$302$	−21.6781	−	29.8374i	−1.24744	−	1.71695i
$303$	5.32583	+	1.73047i	0.305961	+	0.0994128i
$304$	−2.54112	+	7.82078i	−0.145743	+	0.448552i
$305$		0			0
$306$	−3.41958	−	10.5244i	−0.195484	−	0.601638i
$307$		−	9.48133i		−	0.541128i	−0.962702	−	0.270564i	$-0.912790\pi$
$307$		−	9.48133i		−	0.541128i	0.962702	−	0.270564i	$-0.0872102\pi$
$308$	−4.43299	+	1.44037i	−0.252593	+	0.0820725i
$309$	−18.0804	−	13.1362i	−1.02856	−	0.747291i
$310$		0			0
$311$	−23.7301	+	17.2409i	−1.34561	+	0.977643i	−0.346393	+	0.938089i	$0.612594\pi$
$311$	−23.7301	+	17.2409i	−1.34561	+	0.977643i	−0.999217	+	0.0395541i	$0.987406\pi$
$312$	3.16780	−	4.36010i	0.179341	−	0.246842i
$313$	11.1033	−	15.2824i	0.627596	−	0.863811i	−0.370283	−	0.928919i	$-0.620739\pi$
$313$	11.1033	−	15.2824i	0.627596	−	0.863811i	0.997878	+	0.0651079i	$0.0207392\pi$
$314$	−2.79224	+	2.02868i	−0.157575	+	0.114485i
$315$		0			0
$316$	−30.1151	−	21.8799i	−1.69411	−	1.23084i
$317$	21.6739	−	7.04229i	1.21733	−	0.395534i	0.371221	−	0.928545i	$-0.378939\pi$
$317$	21.6739	−	7.04229i	1.21733	−	0.395534i	0.846109	+	0.533010i	$0.178939\pi$
$318$			34.6826i			1.94490i
$319$	3.32768	+	10.2415i	0.186314	+	0.573416i
$320$		0			0
$321$	3.27267	−	10.0722i	0.182663	−	0.562178i
$322$	−8.95435	−	2.90945i	−0.499007	−	0.162137i
$323$	4.39711	+	6.05210i	0.244662	+	0.336748i
$324$	26.1587			1.45326
$325$		0			0
$326$	−1.86202			−0.103128
$327$	−21.0303	−	28.9457i	−1.16298	−	1.60070i
$328$	−5.96538	−	1.93827i	−0.329383	−	0.107023i
$329$	−3.04408	+	9.36871i	−0.167825	+	0.516513i
$330$		0			0
$331$	0.915615	+	2.81797i	0.0503268	+	0.154890i	0.973061	−	0.230546i	$-0.0740512\pi$
$331$	0.915615	+	2.81797i	0.0503268	+	0.154890i	−0.922735	+	0.385436i	$0.874051\pi$
$332$			4.15928i			0.228270i
$333$	3.74725	−	1.21756i	0.205348	−	0.0667217i
$334$	−8.76510	−	6.36822i	−0.479605	−	0.348453i
$335$		0			0
$336$	−5.61615	+	4.08037i	−0.306386	+	0.222603i
$337$	11.0576	−	15.2195i	0.602345	−	0.829057i	−0.393575	−	0.919292i	$-0.628762\pi$
$337$	11.0576	−	15.2195i	0.602345	−	0.829057i	0.995920	+	0.0902353i	$0.0287619\pi$
$338$	1.98037	−	2.72574i	0.107718	−	0.148261i
$339$	−12.0182	+	8.73173i	−0.652739	+	0.474242i
$340$		0			0
$341$	−0.220923	−	0.160510i	−0.0119636	−	0.00869209i
$342$	9.39711	−	3.05331i	0.508138	−	0.165104i
$343$		−	12.9162i		−	0.697410i
$344$	1.04264	+	3.20891i	0.0562152	+	0.173013i
$345$		0			0
$346$	3.71467	−	11.4326i	0.199702	−	0.614620i
$347$	21.6253	+	7.02649i	1.16091	+	0.377201i	0.825242	−	0.564780i	$-0.191039\pi$
$347$	21.6253	+	7.02649i	1.16091	+	0.377201i	0.335665	+	0.941981i	$0.391039\pi$
$348$	−16.3398	−	22.4898i	−0.875906	−	1.20558i
$349$	−1.93849			−0.103765			−0.0518824	−	0.998653i	$-0.516522\pi$
$349$	−1.93849			−0.103765			−0.0518824	+	0.998653i	$0.516522\pi$
$350$		0			0
$351$	−8.65392			−0.461912
$352$	9.50802	+	13.0867i	0.506779	+	0.697522i
$353$	4.99252	+	1.62217i	0.265725	+	0.0863394i	0.438849	−	0.898561i	$-0.355386\pi$
$353$	4.99252	+	1.62217i	0.265725	+	0.0863394i	−0.173124	+	0.984900i	$0.555386\pi$
$354$	−6.96689	+	21.4419i	−0.370286	+	1.13962i
$355$		0			0
$356$	10.5285	+	32.4033i	0.558008	+	1.71737i
$357$			6.31519i			0.334235i
$358$	17.1923	−	5.58612i	0.908642	−	0.295236i
$359$	18.2787	+	13.2803i	0.964713	+	0.700905i	0.954241	−	0.299040i	$-0.0966664\pi$
$359$	18.2787	+	13.2803i	0.964713	+	0.700905i	0.0104726	+	0.999945i	$0.496666\pi$
$360$		0			0
$361$	9.96746	−	7.24178i	0.524603	−	0.381146i
$362$	17.5163	−	24.1091i	0.920637	−	1.26715i
$363$	9.04569	−	12.4503i	0.474775	−	0.653472i
$364$	−6.36167	+	4.62203i	−0.333442	+	0.242260i
$365$		0			0
$366$	10.2727	+	7.46353i	0.536961	+	0.390125i
$367$	−6.94150	+	2.25543i	−0.362343	+	0.117732i	−0.484530	−	0.874775i	$-0.661009\pi$
$367$	−6.94150	+	2.25543i	−0.362343	+	0.117732i	0.122187	+	0.992507i	$0.461009\pi$
$368$			14.4759i			0.754610i
$369$	−4.89105	−	15.0531i	−0.254618	−	0.783634i
$370$		0			0
$371$	2.32001	−	7.14025i	0.120449	−	0.370703i
$372$	0.670438	+	0.217838i	0.0347606	+	0.0112944i
$373$	13.1119	+	18.0470i	0.678911	+	0.934440i	0.999920	−	0.0126358i	$-0.00402219\pi$
$373$	13.1119	+	18.0470i	0.678911	+	0.934440i	−0.321010	+	0.947076i	$0.604022\pi$
$374$	12.0718			0.624216
$375$		0			0
$376$	−7.21188			−0.371924
$377$	10.6783	+	14.6974i	0.549959	+	0.756953i
$378$	−5.04798	−	1.64019i	−0.259640	−	0.0843621i
$379$	10.1811	−	31.3341i	0.522966	−	1.60952i	−0.245337	−	0.969438i	$-0.578899\pi$
$379$	10.1811	−	31.3341i	0.522966	−	1.60952i	0.768303	−	0.640086i	$-0.221101\pi$
$380$		0			0
$381$	1.01282	+	3.11713i	0.0518881	+	0.159695i
$382$		−	2.64072i		−	0.135111i
$383$	19.6871	−	6.39671i	1.00596	−	0.326857i	0.240716	−	0.970595i	$-0.422618\pi$
$383$	19.6871	−	6.39671i	1.00596	−	0.326857i	0.765245	+	0.643739i	$0.222618\pi$
$384$	−10.1811	−	7.39697i	−0.519550	−	0.377475i
$385$		0			0
$386$	35.7194	−	25.9517i	1.81807	−	1.32091i
$387$	−5.00447	+	6.88806i	−0.254391	+	0.350140i
$388$	−23.5063	+	32.3537i	−1.19335	+	1.64251i
$389$	−0.925886	+	0.672696i	−0.0469443	+	0.0341070i	−0.611010	−	0.791623i	$-0.709236\pi$
$389$	−0.925886	+	0.672696i	−0.0469443	+	0.0341070i	0.564066	+	0.825730i	$0.309236\pi$
$390$		0			0
$391$	10.6539	+	7.74052i	0.538792	+	0.391455i
$392$	4.15636	−	1.35048i	0.209928	−	0.0682098i
$393$		−	31.0310i		−	1.56531i
$394$	−7.86239	−	24.1980i	−0.396102	−	1.21908i
$395$		0			0
$396$	2.66095	−	8.18955i	0.133718	−	0.411540i
$397$	4.45583	+	1.44779i	0.223631	+	0.0726623i	0.418690	−	0.908129i	$-0.362490\pi$
$397$	4.45583	+	1.44779i	0.223631	+	0.0726623i	−0.195058	+	0.980792i	$0.562490\pi$
$398$	12.7552	+	17.5560i	0.639361	+	0.880005i
$399$	−5.63877			−0.282292
$400$		0			0
$401$	−24.0851			−1.20275			−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851			−1.20275			−0.601376	+	0.798966i	$0.705381\pi$
$402$	5.88998	+	8.10687i	0.293766	+	0.404334i
$403$	−0.438139	−	0.142360i	−0.0218253	−	0.00709146i
$404$	1.84847	−	5.68902i	0.0919650	−	0.283039i
$405$		0			0
$406$	3.44320	+	10.5971i	0.170883	+	0.525925i
$407$			4.29821i			0.213054i
$408$	−4.39711	+	1.42871i	−0.217689	+	0.0707316i
$409$	−1.53660	−	1.11641i	−0.0759801	−	0.0552027i	0.549147	−	0.835726i	$-0.314953\pi$
$409$	−1.53660	−	1.11641i	−0.0759801	−	0.0552027i	−0.625127	+	0.780523i	$0.714953\pi$
$410$		0			0
$411$	−1.22626	+	0.890932i	−0.0604871	+	0.0439464i
$412$	−14.0320	+	19.3134i	−0.691306	+	0.951501i
$413$	2.86861	−	3.94830i	0.141155	−	0.194283i
$414$	14.0718	−	10.2237i	0.691589	−	0.502469i
$415$		0			0
$416$	22.0776	+	16.0403i	1.08244	+	0.786441i
$417$	34.6499	−	11.2584i	1.69681	−	0.551328i
$418$			10.7788i			0.527207i
$419$	0.719410	+	2.21412i	0.0351455	+	0.108167i	0.967090	−	0.254434i	$-0.0818890\pi$
$419$	0.719410	+	2.21412i	0.0351455	+	0.108167i	−0.931945	+	0.362600i	$0.881889\pi$
$420$		0			0
$421$	−7.40097	+	22.7779i	−0.360701	+	1.11012i	0.591928	+	0.805991i	$0.298367\pi$
$421$	−7.40097	+	22.7779i	−0.360701	+	1.11012i	−0.952629	+	0.304134i	$0.901633\pi$
$422$	−17.1701	−	5.57891i	−0.835829	−	0.271577i
$423$	−10.6968	−	14.7229i	−0.520098	−	0.715853i
$424$	5.49645			0.266931
$425$		0			0
$426$	44.2060			2.14179
$427$	−1.61562	−	2.22371i	−0.0781855	−	0.107613i
$428$	−10.7591	−	3.49584i	−0.520061	−	0.168978i
$429$	−4.58448	+	14.1096i	−0.221341	+	0.681217i
$430$		0			0
$431$	0.368430	+	1.13391i	0.0177467	+	0.0546186i	0.959538	−	0.281580i	$-0.0908586\pi$
$431$	0.368430	+	1.13391i	0.0177467	+	0.0546186i	−0.941791	+	0.336199i	$0.890859\pi$
$432$			8.16074i			0.392634i
$433$	−24.3602	+	7.91511i	−1.17068	+	0.380376i	−0.828895	−	0.559404i	$-0.811030\pi$
$433$	−24.3602	+	7.91511i	−1.17068	+	0.380376i	−0.341781	+	0.939780i	$0.611030\pi$
$434$	−0.228592	−	0.166082i	−0.0109728	−	0.00797219i
$435$		0			0
$436$	−30.9196	+	22.4644i	−1.48078	+	1.07585i
$437$	−6.91144	+	9.51278i	−0.330619	+	0.455058i
$438$	2.09089	−	2.87786i	0.0999066	−	0.137510i
$439$	15.6740	−	11.3878i	0.748079	−	0.543511i	−0.147152	−	0.989114i	$-0.547011\pi$
$439$	15.6740	−	11.3878i	0.748079	−	0.543511i	0.895231	+	0.445603i	$0.147011\pi$
$440$		0			0
$441$	8.92181	+	6.48207i	0.424848	+	0.308670i
$442$	19.3687	−	6.29327i	0.921274	−	0.299340i
$443$		−	2.46263i		−	0.117003i	−0.998287	−	0.0585016i	$-0.981368\pi$
$443$		−	2.46263i		−	0.117003i	0.998287	−	0.0585016i	$-0.0186323\pi$
$444$	−3.42878	−	10.5527i	−0.162723	−	0.500809i
$445$		0			0
$446$	−18.2641	+	56.2113i	−0.864833	+	2.66168i
$447$	6.71502	+	2.18184i	0.317610	+	0.103198i
$448$	6.12613	+	8.43190i	0.289433	+	0.398370i
$449$	14.3585			0.677618			0.338809	−	0.940855i	$-0.389976\pi$
$449$	14.3585			0.677618			0.338809	+	0.940855i	$0.389976\pi$
$450$		0			0
$451$	17.2664			0.813041
$452$	9.32717	+	12.8378i	0.438713	+	0.603837i
$453$	−36.9802	−	12.0156i	−1.73748	−	0.564542i
$454$	14.3321	−	44.1098i	0.672641	−	2.07018i
$455$		0			0
$456$	−1.27568	−	3.92614i	−0.0597392	−	0.183858i
$457$		−	25.1964i		−	1.17864i	−0.807901	−	0.589319i	$-0.799396\pi$
$457$		−	25.1964i		−	1.17864i	0.807901	−	0.589319i	$-0.200604\pi$
$458$	4.90965	−	1.59524i	0.229413	−	0.0745408i
$459$	6.00610	+	4.36369i	0.280341	+	0.203679i
$460$		0			0
$461$	−23.3203	+	16.9432i	−1.08614	+	0.789124i	−0.978743	−	0.205092i	$-0.934251\pi$
$461$	−23.3203	+	16.9432i	−1.08614	+	0.789124i	−0.107394	+	0.994217i	$0.534251\pi$
$462$	−5.34841	+	7.36146i	−0.248831	+	0.342486i
$463$	−18.7384	+	25.7911i	−0.870846	+	1.19862i	0.108028	+	0.994148i	$0.465547\pi$
$463$	−18.7384	+	25.7911i	−0.870846	+	1.19862i	−0.978873	+	0.204468i	$0.934453\pi$
$464$	13.8598	−	10.0697i	0.643425	−	0.467475i
$465$		0			0
$466$	10.0480	+	7.30033i	0.465466	+	0.338181i
$467$	−40.9902	+	13.3185i	−1.89680	+	0.616307i	−0.925314	+	0.379201i	$0.876199\pi$
$467$	−40.9902	+	13.3185i	−1.89680	+	0.616307i	−0.971484	+	0.237106i	$0.923801\pi$
$468$		−	14.5270i		−	0.671512i
$469$	−0.670307	−	2.06299i	−0.0309519	−	0.0952601i
$470$		0			0
$471$	−1.12444	+	3.46068i	−0.0518115	+	0.159460i
$472$	3.39808	+	1.10410i	0.156409	+	0.0508205i
$473$	−5.45932	−	7.51411i	−0.251020	−	0.345499i
$474$	−72.6679			−3.33775
$475$		0			0
$476$	6.74584			0.309195
$477$	8.15246	+	11.2209i	0.373276	+	0.513770i
$478$	13.9469	+	4.53161i	0.637915	+	0.207271i
$479$	−6.49749	+	19.9972i	−0.296878	+	0.913697i	0.685706	+	0.727878i	$0.259494\pi$
$479$	−6.49749	+	19.9972i	−0.296878	+	0.913697i	−0.982584	+	0.185818i	$0.940506\pi$
$480$		0			0
$481$	2.24075	+	6.89631i	0.102169	+	0.314445i
$482$			2.46014i			0.112057i
$483$	−9.44047	+	3.06739i	−0.429556	+	0.139571i
$484$	−13.2993	−	9.66254i	−0.604516	−	0.439206i
$485$		0			0
$486$	28.3323	−	20.5846i	1.28518	−	0.933739i
$487$	−16.4104	+	22.5869i	−0.743625	+	1.02351i	0.254777	+	0.967000i	$0.417998\pi$
$487$	−16.4104	+	22.5869i	−0.743625	+	1.02351i	−0.998402	+	0.0565121i	$0.982002\pi$
$488$	1.18281	−	1.62800i	0.0535433	−	0.0736960i
$489$	−1.58819	+	1.15389i	−0.0718204	+	0.0521805i
$490$		0			0
$491$	−12.1037	−	8.79389i	−0.546234	−	0.396862i	0.280161	−	0.959953i	$-0.409612\pi$
$491$	−12.1037	−	8.79389i	−0.546234	−	0.396862i	−0.826395	+	0.563091i	$0.809612\pi$
$492$	−42.3913	+	13.7738i	−1.91115	+	0.620969i
$493$		−	15.5849i		−	0.701909i
$494$	5.61920	+	17.2941i	0.252820	+	0.778099i
$495$		0			0
$496$	−0.134247	+	0.413170i	−0.00602787	+	0.0185519i
$497$	−9.10089	−	2.95706i	−0.408231	−	0.132642i
$498$	4.77257	+	6.56888i	0.213864	+	0.294359i
$499$	44.3253			1.98427			0.992137	−	0.125160i	$-0.0399443\pi$
$499$	44.3253			1.98427			0.992137	+	0.125160i	$0.0399443\pi$
$500$		0			0
$501$	−11.4224			−0.510316
$502$	−5.64885	−	7.77498i	−0.252121	−	0.347014i
$503$	−22.4651	−	7.29936i	−1.00167	−	0.325462i	−0.238137	−	0.971232i	$-0.576537\pi$
$503$	−22.4651	−	7.29936i	−1.00167	−	0.325462i	−0.763532	+	0.645769i	$0.776537\pi$
$504$	0.408487	−	1.25719i	0.0181955	−	0.0559999i
$505$		0			0
$506$	5.86346	+	18.0459i	0.260663	+	0.802237i
$507$		−	3.55211i		−	0.157755i
$508$	3.32969	−	1.08188i	0.147731	−	0.0480008i
$509$	−21.6132	−	15.7029i	−0.957990	−	0.696020i	−0.00530682	−	0.999986i	$-0.501689\pi$
$509$	−21.6132	−	15.7029i	−0.957990	−	0.696020i	−0.952683	+	0.303966i	$0.901689\pi$
$510$		0			0
$511$	−0.622968	+	0.452613i	−0.0275585	+	0.0200224i
$512$	17.8438	−	24.5598i	0.788591	−	1.08540i
$513$	−3.89629	+	5.36279i	−0.172026	+	0.236773i
$514$	16.4577	−	11.9572i	0.725918	−	0.527410i
$515$		0			0
$516$	19.3976	+	14.0931i	0.853930	+	0.620416i
$517$	18.8809	−	6.13479i	0.830383	−	0.269808i
$518$			4.44743i			0.195409i
$519$	−3.91633	−	12.0532i	−0.171908	−	0.529078i
$520$		0			0
$521$	10.1071	−	31.1065i	0.442800	−	1.36280i	−0.442078	−	0.896977i	$-0.645759\pi$
$521$	10.1071	−	31.1065i	0.442800	−	1.36280i	0.884878	−	0.465822i	$-0.154241\pi$
$522$	−19.5772	−	6.36101i	−0.856869	−	0.278414i
$523$	−0.138697	−	0.190901i	−0.00606481	−	0.00834750i	0.805974	−	0.591951i	$-0.201642\pi$
$523$	−0.138697	−	0.190901i	−0.00606481	−	0.00834750i	−0.812039	+	0.583604i	$0.801642\pi$
$524$	−33.1471			−1.44804
$525$		0			0
$526$	−2.07658			−0.0905434
$527$	0.232299	+	0.319732i	0.0101191	+	0.0139277i
$528$	13.3055	+	4.32322i	0.579048	+	0.188144i
$529$	0.710999	−	2.18823i	0.0309130	−	0.0951405i
$530$		0			0
$531$	2.78611	+	8.57476i	0.120907	+	0.372113i
$532$			6.02330i			0.261143i
$533$	27.7032	−	9.00132i	1.19996	−	0.389890i
$534$	53.8091	+	39.0946i	2.32855	+	1.69179i
$535$		0			0
$536$	1.28477	−	0.933437i	0.0554934	−	0.0403183i
$537$	11.2023	−	15.4186i	0.483413	−	0.665361i
$538$	4.03076	−	5.54786i	0.173778	−	0.239185i
$539$	−9.73271	+	7.07123i	−0.419217	+	0.304579i
$540$		0			0
$541$	27.1484	+	19.7244i	1.16720	+	0.848020i	0.990671	−	0.136276i	$-0.0435133\pi$
$541$	27.1484	+	19.7244i	1.16720	+	0.848020i	0.176528	+	0.984296i	$0.443513\pi$
$542$	−24.0963	+	7.82935i	−1.03502	+	0.336299i
$543$		−	31.4183i		−	1.34829i
$544$	−7.23434	−	22.2650i	−0.310170	−	0.954604i
$545$		0			0
$546$	−4.74364	+	14.5994i	−0.203009	+	0.624798i
$547$	−36.6276	−	11.9010i	−1.56608	−	0.508851i	−0.607658	−	0.794199i	$-0.707891\pi$
$547$	−36.6276	−	11.9010i	−1.56608	−	0.508851i	−0.958424	+	0.285348i	$0.907891\pi$
$548$	0.951688	+	1.30989i	0.0406541	+	0.0559555i
$549$	5.07790			0.216720
$550$		0			0
$551$	13.9156			0.592825
$552$	−4.27150	−	5.87922i	−0.181807	−	0.250236i
$553$	14.9605	+	4.86095i	0.636183	+	0.206708i
$554$	−7.64668	+	23.5341i	−0.324876	+	0.999866i
$555$		0			0
$556$	−12.0262	−	37.0128i	−0.510024	−	1.56969i
$557$		−	4.33445i		−	0.183657i	−0.995775	−	0.0918283i	$-0.970729\pi$
$557$		−	4.33445i		−	0.183657i	0.995775	−	0.0918283i	$-0.0292711\pi$
$558$	0.496448	−	0.161306i	0.0210163	−	0.00682861i
$559$	−12.6765	−	9.21004i	−0.536160	−	0.389543i
$560$		0			0
$561$	10.2965	−	7.48081i	0.434717	−	0.315840i
$562$	−30.2032	+	41.5712i	−1.27405	+	1.75357i
$563$	−20.5148	+	28.2362i	−0.864595	+	1.19001i	0.115860	+	0.993266i	$0.463038\pi$
$563$	−20.5148	+	28.2362i	−0.864595	+	1.19001i	−0.980454	+	0.196747i	$0.936962\pi$
$564$	−41.4614	+	30.1235i	−1.74584	+	1.26843i
$565$		0			0
$566$	−5.67421	−	4.12255i	−0.238505	−	0.173284i
$567$	−10.5132	+	3.41593i	−0.441511	+	0.143456i
$568$		−	7.00572i		−	0.293953i
$569$	12.9678	+	39.9107i	0.543637	+	1.67314i	0.724208	+	0.689581i	$0.242205\pi$
$569$	12.9678	+	39.9107i	0.543637	+	1.67314i	−0.180571	+	0.983562i	$0.557795\pi$
$570$		0			0
$571$	−4.27469	+	13.1561i	−0.178890	+	0.550567i	−0.999790	−	0.0205055i	$-0.993472\pi$
$571$	−4.27469	+	13.1561i	−0.178890	+	0.550567i	0.820900	+	0.571072i	$0.193472\pi$
$572$	15.0718	+	4.89711i	0.630182	+	0.204759i
$573$	−1.63644	−	2.25237i	−0.0683633	−	0.0940940i
$574$	17.8658			0.745704
$575$		0			0
$576$	−19.2544			−0.802268
$577$	7.51147	+	10.3387i	0.312707	+	0.430404i	0.936223	−	0.351407i	$-0.114296\pi$
$577$	7.51147	+	10.3387i	0.312707	+	0.430404i	−0.623516	+	0.781810i	$0.714296\pi$
$578$	17.0990	+	5.55579i	0.711223	+	0.231090i
$579$	14.3843	−	44.2703i	0.597791	−	1.83981i
$580$		0			0
$581$	−0.543140	−	1.67161i	−0.0225333	−	0.0693502i
$582$			78.0696i			3.23609i
$583$	−14.3899	+	4.67556i	−0.595968	+	0.193642i
$584$	−0.456080	−	0.331361i	−0.0188727	−	0.0137118i
$585$		0			0
$586$	−15.1215	+	10.9864i	−0.624665	+	0.453845i
$587$	−7.16331	+	9.85945i	−0.295661	+	0.406943i	−0.930843	−	0.365420i	$-0.880925\pi$
$587$	−7.16331	+	9.85945i	−0.295661	+	0.406943i	0.635181	+	0.772363i	$0.280925\pi$
$588$	18.2543	−	25.1248i	0.752793	−	1.03613i
$589$	−0.285485	+	0.207417i	−0.0117632	+	0.00854648i
$590$		0			0
$591$	−21.7015	−	15.7671i	−0.892680	−	0.648570i
$592$	6.50330	−	2.11305i	0.267284	−	0.0868459i
$593$			31.2580i			1.28361i	0.766866	+	0.641807i	$0.221815\pi$
$593$			31.2580i			1.28361i	−0.766866	+	0.641807i	$0.778185\pi$
$594$	3.30550	+	10.1733i	0.135626	+	0.417415i
$595$		0			0
$596$	2.33063	−	7.17294i	0.0954663	−	0.293815i
$597$	21.7588	+	7.06986i	0.890528	+	0.289350i
$598$	18.8154	+	25.8972i	0.769419	+	1.05901i
$599$	33.3707			1.36349			0.681746	−	0.731589i	$-0.261221\pi$
$599$	33.3707			1.36349			0.681746	+	0.731589i	$0.261221\pi$
$600$		0			0
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$	−5.64885	−	7.77498i	−0.230230	−	0.316884i
$603$	3.81119	+	1.23833i	0.155204	+	0.0504287i
$604$	−12.8350	+	39.5020i	−0.522248	+	1.60731i
$605$		0			0
$606$	−3.60852	−	11.1059i	−0.146586	−	0.451145i
$607$			30.7401i			1.24770i	0.781543	+	0.623851i	$0.214433\pi$
$607$			30.7401i			1.24770i	−0.781543	+	0.623851i	$0.785567\pi$
$608$	19.8802	−	6.45947i	0.806249	−	0.261966i
$609$	9.50380	+	6.90492i	0.385114	+	0.279801i
$610$		0			0
$611$	27.0955	−	19.6861i	1.09617	−	0.796413i
$612$	−7.32517	+	10.0822i	−0.296102	+	0.407550i
$613$	22.5060	−	30.9768i	0.909008	−	1.25114i	−0.0584964	−	0.998288i	$-0.518631\pi$
$613$	22.5060	−	30.9768i	0.909008	−	1.25114i	0.967504	−	0.252854i	$-0.0813694\pi$
$614$	−15.9953	+	11.6213i	−0.645518	+	0.468996i
$615$		0			0
$616$	1.16663	+	0.847609i	0.0470050	+	0.0341512i
$617$	−0.404490	+	0.131427i	−0.0162842	+	0.00529104i	−0.317148	−	0.948376i	$-0.602725\pi$
$617$	−0.404490	+	0.131427i	−0.0162842	+	0.00529104i	0.300864	+	0.953667i	$0.402725\pi$
$618$			46.6032i			1.87466i
$619$	−2.32117	−	7.14384i	−0.0932958	−	0.287135i	0.893510	−	0.449043i	$-0.148235\pi$
$619$	−2.32117	−	7.14384i	−0.0932958	−	0.287135i	−0.986806	+	0.161908i	$0.948235\pi$
$620$		0			0
$621$	−3.60594	+	11.0979i	−0.144701	+	0.445345i
$622$	58.1720	+	18.9012i	2.33248	+	0.757870i
$623$	−8.46278	−	11.6480i	−0.339054	−	0.466668i
$624$	23.6020			0.944834
$625$		0			0
$626$	−39.3912			−1.57439
$627$	6.67955	+	9.19361i	0.266755	+	0.367157i
$628$	3.69667	+	1.20112i	0.147513	+	0.0479300i
$629$	1.92227	−	5.91615i	0.0766461	−	0.235892i
$630$		0			0
$631$	−3.48311	−	10.7199i	−0.138660	−	0.426752i	0.857481	−	0.514515i	$-0.172028\pi$
$631$	−3.48311	−	10.7199i	−0.138660	−	0.426752i	−0.996141	+	0.0877630i	$0.972028\pi$
$632$			11.5163i			0.458094i
$633$	−18.1023	+	5.88178i	−0.719500	+	0.233780i
$634$	−38.4463	−	27.9329i	−1.52690	−	1.10936i
$635$		0			0
$636$	31.5994	−	22.9583i	1.25300	−	0.910355i
$637$	−11.9294	+	16.4194i	−0.472659	+	0.650560i
$638$	13.1991	−	18.1669i	0.522556	−	0.719236i
$639$	14.3020	−	10.3910i	0.565780	−	0.411063i
$640$		0			0
$641$	−21.1012	−	15.3309i	−0.833447	−	0.605535i	0.0870851	−	0.996201i	$-0.472245\pi$
$641$	−21.1012	−	15.3309i	−0.833447	−	0.605535i	−0.920533	+	0.390666i	$0.872245\pi$
$642$	−21.0035	+	6.82445i	−0.828942	+	0.269340i
$643$			31.9492i			1.25995i	0.776614	+	0.629977i	$0.216936\pi$
$643$			31.9492i			1.25995i	−0.776614	+	0.629977i	$0.783064\pi$
$644$	3.27657	+	10.0842i	0.129115	+	0.397375i
$645$		0			0
$646$	4.82055	−	14.8361i	0.189662	−	0.583720i
$647$	−7.03243	−	2.28497i	−0.276473	−	0.0898316i	0.167499	−	0.985872i	$-0.446431\pi$
$647$	−7.03243	−	2.28497i	−0.276473	−	0.0898316i	−0.443972	+	0.896041i	$0.646431\pi$
$648$	−4.75686	−	6.54726i	−0.186867	−	0.257201i
$649$	−9.83550			−0.386077
$650$		0			0
$651$	−0.297895			−0.0116754
$652$	1.23257	+	1.69649i	0.0482713	+	0.0664398i
$653$	−17.7708	−	5.77407i	−0.695424	−	0.225957i	−0.0600882	−	0.998193i	$-0.519138\pi$
$653$	−17.7708	−	5.77407i	−0.695424	−	0.225957i	−0.635336	+	0.772236i	$0.719138\pi$
$654$	−23.0555	+	70.9575i	−0.901541	+	2.77466i
$655$		0			0
$656$	−8.48835	−	26.1245i	−0.331414	−	1.01999i
$657$		−	1.42256i		−	0.0554994i
$658$	19.5364	−	6.34777i	0.761609	−	0.247462i
$659$	7.92963	+	5.76122i	0.308895	+	0.224425i	0.731422	−	0.681925i	$-0.238857\pi$
$659$	7.92963	+	5.76122i	0.308895	+	0.224425i	−0.422527	+	0.906350i	$0.638857\pi$
$660$		0			0
$661$	22.7807	−	16.5511i	0.886066	−	0.643765i	−0.0487833	−	0.998809i	$-0.515534\pi$
$661$	22.7807	−	16.5511i	0.886066	−	0.643765i	0.934849	+	0.355045i	$0.115534\pi$
$662$	3.63174	−	4.99866i	0.141152	−	0.194278i
$663$	12.6204	−	17.3704i	0.490134	−	0.674612i
$664$	1.04103	−	0.756351i	0.0403997	−	0.0293521i
$665$		0			0
$666$	−6.64706	−	4.82937i	−0.257568	−	0.187134i
$667$	23.2976	−	7.56986i	0.902087	−	0.293106i
$668$			12.2014i			0.472085i
$669$	19.2557	+	59.2629i	0.744468	+	2.29124i
$670$		0			0
$671$	−1.71178	+	5.26831i	−0.0660825	+	0.203381i
$672$	16.7826	+	5.45299i	0.647402	+	0.210354i
$673$	−22.9385	−	31.5721i	−0.884214	−	1.21702i	−0.975236	−	0.221168i	$-0.929013\pi$
$673$	−22.9385	−	31.5721i	−0.884214	−	1.21702i	0.0910215	−	0.995849i	$-0.470987\pi$
$674$	−39.2290			−1.51104
$675$		0			0
$676$	−3.79434			−0.145936
$677$	−2.95969	−	4.07367i	−0.113750	−	0.156564i	0.748346	−	0.663309i	$-0.230848\pi$
$677$	−2.95969	−	4.07367i	−0.113750	−	0.156564i	−0.862096	+	0.506745i	$0.830848\pi$
$678$	29.4614	+	9.57259i	1.13146	+	0.367633i
$679$	5.22228	−	16.0725i	0.200413	−	0.616807i
$680$		0			0
$681$	−15.1102	−	46.5044i	−0.579025	−	1.78205i
$682$			0.569440i			0.0218050i
$683$	−28.8467	+	9.37285i	−1.10379	+	0.358642i	−0.803559	−	0.595225i	$-0.797063\pi$
$683$	−28.8467	+	9.37285i	−1.10379	+	0.358642i	−0.300228	+	0.953867i	$0.597063\pi$
$684$	−9.00233	−	6.54058i	−0.344213	−	0.250085i
$685$		0			0
$686$	−21.7900	+	15.8314i	−0.831948	+	0.604446i
$687$	3.19906	−	4.40313i	0.122052	−	0.167990i
$688$	−8.68518	+	11.9541i	−0.331119	+	0.455747i
$689$	−20.6506	+	15.0035i	−0.786724	+	0.571588i
$690$		0			0
$691$	17.1778	+	12.4804i	0.653474	+	0.474777i	0.864453	−	0.502714i	$-0.167665\pi$
$691$	17.1778	+	12.4804i	0.653474	+	0.474777i	−0.210979	+	0.977491i	$0.567665\pi$
$692$	−12.8752	+	4.18340i	−0.489441	+	0.159029i
$693$			3.63886i			0.138229i
$694$	−14.6522	−	45.0949i	−0.556191	−	1.71178i
$695$		0			0
$696$	−2.65765	+	8.17939i	−0.100738	+	0.310039i
$697$	−23.7658	−	7.72198i	−0.900194	−	0.292491i
$698$	2.37600	+	3.27029i	0.0899330	+	0.123782i
$699$	13.0943			0.495273
$700$		0			0
$701$	32.7698			1.23770			0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698			1.23770			0.618849	+	0.785510i	$0.287599\pi$
$702$	10.6071	+	14.5994i	0.400339	+	0.551020i
$703$	5.28247	+	1.71638i	0.199232	+	0.0647345i
$704$	6.49074	−	19.9764i	0.244629	−	0.752890i
$705$		0			0
$706$	−3.38269	−	10.4108i	−0.127309	−	0.391817i
$707$			2.52780i			0.0950676i
$708$	24.1475	−	7.84600i	0.907519	−	0.294871i
$709$	16.0557	+	11.6652i	0.602985	+	0.438094i	0.846937	−	0.531693i	$-0.178444\pi$
$709$	16.0557	+	11.6652i	0.602985	+	0.438094i	−0.243952	+	0.969787i	$0.578444\pi$
$710$		0			0
$711$	−23.5103	+	17.0813i	−0.881707	+	0.640598i
$712$	6.19566	−	8.52760i	0.232192	−	0.319585i
$713$	−0.365130	+	0.502558i	−0.0136742	+	0.0188210i
$714$	10.6539	−	7.74052i	0.398713	−	0.289682i
$715$		0			0
$716$	−16.4700	−	11.9662i	−0.615514	−	0.447197i
$717$	14.7040	−	4.77763i	0.549132	−	0.178424i
$718$		−	47.1144i		−	1.75829i
$719$	−7.48443	−	23.0347i	−0.279122	−	0.859049i	−0.988099	−	0.153818i	$-0.950843\pi$
$719$	−7.48443	−	23.0347i	−0.279122	−	0.859049i	0.708977	−	0.705231i	$-0.249157\pi$
$720$		0			0
$721$	3.11741	−	9.59440i	0.116098	−	0.357314i
$722$	−24.4342	−	7.93916i	−0.909347	−	0.295465i
$723$	1.52454	+	2.09835i	0.0566982	+	0.0780384i
$724$	−33.5609			−1.24728
$725$		0			0
$726$	−32.0914			−1.19102
$727$	3.44742	+	4.74496i	0.127858	+	0.175981i	0.868147	−	0.496308i	$-0.165311\pi$
$727$	3.44742	+	4.74496i	0.127858	+	0.175981i	−0.740289	+	0.672289i	$0.765311\pi$
$728$	2.31370	+	0.751766i	0.0857513	+	0.0278623i
$729$	1.08320	−	3.33374i	0.0401185	−	0.123472i
$730$		0			0
$731$	4.15382	+	12.7841i	0.153635	+	0.472838i
$732$		−	14.3000i		−	0.528542i
$733$	−32.8129	+	10.6615i	−1.21197	+	0.393793i	−0.844152	−	0.536104i	$-0.819895\pi$
$733$	−32.8129	+	10.6615i	−1.21197	+	0.393793i	−0.367819	+	0.929897i	$0.619895\pi$
$734$	12.3132	+	8.94604i	0.454487	+	0.330204i
$735$		0			0
$736$	29.7698	−	21.6290i	1.09733	−	0.797255i
$737$	−2.56953	+	3.53666i	−0.0946499	+	0.130274i
$738$	−19.4001	+	26.7019i	−0.714128	+	0.982912i
$739$	32.0138	−	23.2594i	1.17765	−	0.855611i	0.185743	−	0.982598i	$-0.440531\pi$
$739$	32.0138	−	23.2594i	1.17765	−	0.855611i	0.991904	+	0.126988i	$0.0405309\pi$
$740$		0			0
$741$	15.5099	+	11.2686i	0.569770	+	0.413962i
$742$	−14.8895	+	4.83788i	−0.546609	+	0.177604i
$743$		−	29.7058i		−	1.08980i	−0.838501	−	0.544900i	$-0.816567\pi$
$743$		−	29.7058i		−	1.08980i	0.838501	−	0.544900i	$-0.183433\pi$
$744$	−0.0673939	−	0.207417i	−0.00247078	−	0.00760428i
$745$		0			0
$746$	14.3746	−	44.2405i	0.526292	−	1.61976i
$747$	3.08815	+	1.00340i	0.112990	+	0.0367126i
$748$	−7.99095	−	10.9986i	−0.292178	−	0.402149i
$749$	4.78058			0.174679
$750$		0			0
$751$	26.8870			0.981122			0.490561	−	0.871407i	$-0.336792\pi$
$751$	26.8870			0.981122			0.490561	+	0.871407i	$0.336792\pi$
$752$	−18.5642	−	25.5514i	−0.676966	−	0.931764i
$753$	−9.63623	−	3.13100i	−0.351164	−	0.114100i
$754$	11.7066	−	36.0291i	0.426328	−	1.31210i
$755$		0			0
$756$	1.84715	+	5.68495i	0.0671803	+	0.206760i
$757$		−	44.6792i		−	1.62389i	−0.583731	−	0.811947i	$-0.698408\pi$
$757$		−	44.6792i		−	1.62389i	0.583731	−	0.811947i	$-0.301592\pi$
$758$	−65.3405	+	21.2304i	−2.37327	+	0.771123i
$759$	16.1841	+	11.7584i	0.587446	+	0.426804i
$760$		0			0
$761$	−16.4295	+	11.9367i	−0.595568	+	0.432706i	−0.844303	−	0.535866i	$-0.819985\pi$
$761$	−16.4295	+	11.9367i	−0.595568	+	0.432706i	0.248735	+	0.968572i	$0.419985\pi$
$762$	4.01728	−	5.52931i	0.145531	−	0.200306i
$763$	9.49307	−	13.0661i	0.343672	−	0.473024i
$764$	−2.40596	+	1.74803i	−0.0870447	+	0.0632417i
$765$		0			0
$766$	−34.9219	−	25.3722i	−1.26178	−	0.916736i
$767$	−15.7807	+	5.12746i	−0.569808	+	0.185142i
$768$		−	19.9359i		−	0.719375i
$769$	−8.05227	−	24.7823i	−0.290372	−	0.893674i	−0.984737	−	0.174051i	$-0.944314\pi$
$769$	−8.05227	−	24.7823i	−0.290372	−	0.893674i	0.694364	−	0.719624i	$-0.255686\pi$
$770$		0			0
$771$	6.62755	−	20.3975i	0.238685	−	0.734598i
$772$	−47.2892	−	15.3652i	−1.70198	−	0.553006i
$773$	−8.07058	−	11.1082i	−0.290278	−	0.399534i	0.638826	−	0.769351i	$-0.279420\pi$
$773$	−8.07058	−	11.1082i	−0.290278	−	0.399534i	−0.929105	+	0.369817i	$0.879420\pi$
$774$	17.7543			0.638166
$775$		0			0
$776$	12.3724			0.444142
$777$	2.75605	+	3.79338i	0.0988728	+	0.136087i
$778$	2.26972	+	0.737476i	0.0813733	+	0.0264398i
$779$	6.89488	−	21.2203i	0.247035	−	0.760295i
$780$		0			0
$781$	5.95942	+	18.3412i	0.213245	+	0.656300i
$782$		−	27.4610i		−	0.982005i
$783$	13.1339	−	4.26747i	0.469368	−	0.152507i
$784$	15.4837	+	11.2495i	0.552988	+	0.401769i
$785$		0			0
$786$	−52.3503	+	38.0347i	−1.86727	+	1.35665i
$787$	11.5594	−	15.9101i	0.412048	−	0.567136i	−0.551668	−	0.834064i	$-0.686009\pi$
$787$	11.5594	−	15.9101i	0.412048	−	0.567136i	0.963716	+	0.266928i	$0.0860086\pi$
$788$	−16.8423	+	23.1814i	−0.599981	+	0.825803i
$789$	−1.77120	+	1.28685i	−0.0630562	+	0.0458130i
$790$		0			0
$791$	−5.42501	−	3.94150i	−0.192891	−	0.140144i
$792$	−2.53365	+	0.823232i	−0.0900293	+	0.0292523i
$793$			9.34520i			0.331858i
$794$	−3.01905	−	9.29167i	−0.107142	−	0.329749i
$795$		0			0
$796$	7.55197	−	23.2426i	0.267673	−	0.823812i
$797$	−10.4085	−	3.38191i	−0.368686	−	0.119793i	0.118813	−	0.992917i	$-0.462091\pi$
$797$	−10.4085	−	3.38191i	−0.368686	−	0.119793i	−0.487500	+	0.873123i	$0.662091\pi$
$798$	6.91144	+	9.51278i	0.244662	+	0.336749i
$799$	−28.7318			−1.01646
$800$		0			0
$801$	26.5985			0.939812
$802$	29.5211	+	40.6323i	1.04243	+	1.43478i
$803$	1.47591	+	0.479551i	0.0520836	+	0.0169230i
$804$	3.48728	−	10.7327i	0.122987	−	0.378515i
$805$		0			0
$806$	0.296861	+	0.913645i	0.0104565	+	0.0321818i
$807$		−	7.22982i		−	0.254502i
$808$	−1.76004	+	0.571873i	−0.0619182	+	0.0201184i
$809$	13.3025	+	9.66480i	0.467689	+	0.339796i	0.796540	−	0.604586i	$-0.206661\pi$
$809$	13.3025	+	9.66480i	0.467689	+	0.339796i	−0.328851	+	0.944382i	$0.606661\pi$
$810$		0			0
$811$	−18.3220	+	13.3117i	−0.643373	+	0.467438i	−0.861007	−	0.508592i	$-0.830166\pi$
$811$	−18.3220	+	13.3117i	−0.643373	+	0.467438i	0.217634	+	0.976030i	$0.430166\pi$
$812$	7.37579	−	10.1519i	0.258839	−	0.356262i
$813$	−15.7008	+	21.6103i	−0.550651	+	0.757906i
$814$	7.25121	−	5.26831i	0.254155	−	0.184654i
$815$		0			0
$816$	−16.3805	−	11.9011i	−0.573433	−	0.416624i
$817$	−11.4148	+	3.70891i	−0.399355	+	0.129758i
$818$			3.96067i			0.138482i
$819$	1.89701	+	5.83841i	0.0662870	+	0.204011i
$820$		0			0
$821$	−12.2924	+	37.8322i	−0.429009	+	1.32035i	0.470094	+	0.882616i	$0.344220\pi$
$821$	−12.2924	+	37.8322i	−0.429009	+	1.32035i	−0.899103	+	0.437737i	$0.855780\pi$
$822$	3.00606	+	0.976728i	0.104848	+	0.0340673i
$823$	−9.73384	−	13.3975i	−0.339300	−	0.467007i	0.604937	−	0.796274i	$-0.293198\pi$
$823$	−9.73384	−	13.3975i	−0.339300	−	0.467007i	−0.944237	+	0.329267i	$0.893198\pi$
$824$	7.38562			0.257290
$825$		0			0
$826$	−10.1770			−0.354102
$827$	−15.3037	−	21.0637i	−0.532160	−	0.732456i	0.455297	−	0.890339i	$-0.349533\pi$
$827$	−15.3037	−	21.0637i	−0.532160	−	0.732456i	−0.987458	+	0.157884i	$0.949533\pi$
$828$	−18.6297	−	6.05316i	−0.647428	−	0.210362i
$829$	−1.58945	+	4.89182i	−0.0552039	+	0.169900i	−0.974857	−	0.222832i	$-0.928470\pi$
$829$	−1.58945	+	4.89182i	−0.0552039	+	0.169900i	0.919653	+	0.392732i	$0.128470\pi$
$830$		0			0
$831$	8.06180	+	24.8117i	0.279661	+	0.860708i
$832$		−	35.4352i		−	1.22849i
$833$	16.5588	−	5.38027i	0.573727	−	0.186415i
$834$	−61.4638	−	44.6560i	−2.12832	−	1.54631i
$835$		0			0
$836$	9.82055	−	7.13505i	0.339651	−	0.246771i
$837$	−0.205840	+	0.283315i	−0.00711489	+	0.00979280i
$838$	2.85350	−	3.92751i	0.0985726	−	0.135674i
$839$	31.2009	−	22.6688i	1.07717	−	0.782612i	0.0999856	−	0.994989i	$-0.468120\pi$
$839$	31.2009	−	22.6688i	1.07717	−	0.782612i	0.977188	+	0.212377i	$0.0681203\pi$
$840$		0			0
$841$	0.00757268	+	0.00550188i	0.000261127	+	0.000189720i
$842$	47.4983	−	15.4331i	1.63690	−	0.531861i
$843$			54.1744i			1.86586i
$844$	6.28288	+	19.3367i	0.216266	+	0.665597i
$845$		0			0
$846$	−11.7269	+	36.0918i	−0.403180	+	1.24086i
$847$	6.60679	+	2.14668i	0.227012	+	0.0737607i
$848$	14.1485	+	19.4737i	0.485861	+	0.668730i
$849$	−7.39447			−0.253777
$850$		0			0
$851$	9.77764			0.335173
$852$	−29.2624	−	40.2762i	−1.00251	−	1.37984i
$853$	8.69991	+	2.82677i	0.297879	+	0.0967868i	0.454144	−	0.890928i	$-0.349945\pi$
$853$	8.69991	+	2.82677i	0.297879	+	0.0967868i	−0.156265	+	0.987715i	$0.549945\pi$
$854$	−1.77121	+	5.45121i	−0.0606094	+	0.186537i
$855$		0			0
$856$	1.08153	+	3.32861i	0.0369659	+	0.113769i
$857$			13.6712i			0.466998i	0.972357	+	0.233499i	$0.0750176\pi$
$857$			13.6712i			0.466998i	−0.972357	+	0.233499i	$0.924982\pi$
$858$	29.4225	−	9.55995i	1.00447	−	0.326371i
$859$	−28.8460	−	20.9579i	−0.984213	−	0.715073i	−0.0255669	−	0.999673i	$-0.508139\pi$
$859$	−28.8460	−	20.9579i	−0.984213	−	0.715073i	−0.958646	+	0.284600i	$0.908139\pi$
$860$		0			0
$861$	15.2384	−	11.0713i	0.519323	−	0.377310i
$862$	1.46136	−	2.01139i	0.0497741	−	0.0685082i
$863$	19.9455	−	27.4526i	0.678953	−	0.934498i	−0.320968	−	0.947090i	$-0.604008\pi$
$863$	19.9455	−	27.4526i	0.678953	−	0.934498i	0.999921	+	0.0125918i	$0.00400820\pi$
$864$	16.7826	−	12.1933i	0.570955	−	0.414823i
$865$		0			0
$866$	43.2113	+	31.3949i	1.46838	+	1.06684i
$867$	18.0272	−	5.85741i	0.612237	−	0.198928i
$868$			0.318210i			0.0108007i
$869$	−9.79636	−	30.1501i	−0.332319	−	1.02277i
$870$		0			0
$871$	−2.27898	+	7.01398i	−0.0772203	+	0.237660i
$872$	11.2453	+	3.65380i	0.380812	+	0.123733i
$873$	18.3510	+	25.2580i	0.621087	+	0.854853i
$874$	24.5197			0.829391
$875$		0			0
$876$	−4.00610			−0.135354
$877$	16.8689	+	23.2181i	0.569622	+	0.784018i	0.992510	−	0.122164i	$-0.0389835\pi$
$877$	16.8689	+	23.2181i	0.569622	+	0.784018i	−0.422888	+	0.906182i	$0.638983\pi$
$878$	−38.4232	−	12.4845i	−1.29672	−	0.421330i
$879$	−6.08947	+	18.7415i	−0.205393	+	0.632134i
$880$		0			0
$881$	2.57423	+	7.92267i	0.0867281	+	0.266922i	0.985010	−	0.172498i	$-0.0551840\pi$
$881$	2.57423	+	7.92267i	0.0867281	+	0.266922i	−0.898282	+	0.439420i	$0.855184\pi$
$882$		−	22.9964i		−	0.774331i
$883$	47.8539	−	15.5487i	1.61041	−	0.523254i	0.640759	−	0.767742i	$-0.278620\pi$
$883$	47.8539	−	15.5487i	1.61041	−	0.523254i	0.969652	+	0.244488i	$0.0786200\pi$
$884$	−18.5550	−	13.4810i	−0.624072	−	0.453415i
$885$		0			0
$886$	−4.15454	+	3.01845i	−0.139574	+	0.101407i
$887$	−7.12315	+	9.80417i	−0.239172	+	0.329192i	−0.911682	−	0.410896i	$-0.865216\pi$
$887$	−7.12315	+	9.80417i	−0.239172	+	0.329192i	0.672510	+	0.740088i	$0.265216\pi$
$888$	−2.01773	+	2.77716i	−0.0677104	+	0.0931954i
$889$	−1.19693	+	0.869617i	−0.0401436	+	0.0291660i
$890$		0			0
$891$	18.0231	+	13.0945i	0.603795	+	0.438683i
$892$	63.3042	−	20.5688i	2.11958	−	0.688694i
$893$		−	25.6543i		−	0.858490i
$894$	−4.54977	−	14.0027i	−0.152167	−	0.468322i
$895$		0			0
$896$	1.75541	−	5.40260i	0.0586442	−	0.180488i
$897$	32.0967	+	10.4289i	1.07168	+	0.348209i
$898$	−17.5992	−	24.2232i	−0.587292	−	0.808338i
$899$	0.735159			0.0245189
$900$		0			0
$901$	21.8976			0.729514
$902$	−21.1634	−	29.1289i	−0.704663	−	0.969886i
$903$	−9.63623	−	3.13100i	−0.320674	−	0.104193i
$904$	1.51705	−	4.66900i	0.0504564	−	0.155289i
$905$		0			0
$906$	25.0559	+	77.1142i	0.832428	+	2.56195i
$907$			31.9105i			1.05957i	0.848132	+	0.529786i	$0.177728\pi$
$907$			31.9105i			1.05957i	−0.848132	+	0.529786i	$0.822272\pi$
$908$	−49.6757	+	16.1406i	−1.64855	+	0.535645i
$909$	−3.77801	−	2.74488i	−0.125309	−	0.0910421i
$910$		0			0
$911$	19.9730	−	14.5112i	0.661735	−	0.480778i	−0.205514	−	0.978654i	$-0.565886\pi$
$911$	19.9730	−	14.5112i	0.661735	−	0.480778i	0.867248	+	0.497876i	$0.165886\pi$
$912$	10.6264	−	14.6260i	0.351876	−	0.484316i
$913$	−2.08206	+	2.86570i	−0.0689060	+	0.0948409i
$914$	−42.5071	+	30.8832i	−1.40601	+	1.02153i
$915$		0			0
$916$	−4.70339	−	3.41721i	−0.155404	−	0.112908i
$917$	13.3218	−	4.32852i	0.439925	−	0.142940i
$918$		−	15.4810i		−	0.510951i
$919$	6.02121	+	18.5314i	0.198621	+	0.611293i	0.999915	+	0.0130225i	$0.00414530\pi$
$919$	6.02121	+	18.5314i	0.198621	+	0.611293i	−0.801294	+	0.598271i	$0.795855\pi$
$920$		0			0
$921$	−6.44134	+	19.8244i	−0.212249	+	0.653237i
$922$	57.1675	+	18.5748i	1.88271	+	0.611730i
$923$	19.1233	+	26.3210i	0.629452	+	0.866366i
$924$	10.2474			0.337116
$925$		0			0
$926$	66.4781			2.18461
$927$	10.9545	+	15.0776i	0.359794	+	0.495214i
$928$	−41.4168	−	13.4571i	−1.35957	−	0.441752i
$929$	−3.63535	+	11.1885i	−0.119272	+	0.367082i	−0.992814	−	0.119667i	$-0.961817\pi$
$929$	−3.63535	+	11.1885i	−0.119272	+	0.367082i	0.873542	+	0.486749i	$0.161817\pi$
$930$		0			0
$931$	4.80399	+	14.7852i	0.157444	+	0.484564i
$932$		−	13.9873i		−	0.458168i
$933$	61.3300	−	19.9273i	2.00786	−	0.652392i
$934$	72.7104	+	52.8272i	2.37916	+	1.72856i
$935$		0			0
$936$	−3.63597	+	2.64169i	−0.118846	+	0.0863463i
$937$	12.3836	−	17.0446i	0.404556	−	0.556823i	−0.557324	−	0.830295i	$-0.688172\pi$
$937$	12.3836	−	17.0446i	0.404556	−	0.556823i	0.961880	+	0.273472i	$0.0881720\pi$
$938$	−2.65874	+	3.65944i	−0.0868108	+	0.119485i
$939$	−33.5982	+	24.4105i	−1.09644	+	0.796607i
$940$		0			0
$941$	1.81791	+	1.32079i	0.0592622	+	0.0430565i	0.617022	−	0.786946i	$-0.288339\pi$
$941$	1.81791	+	1.32079i	0.0592622	+	0.0430565i	−0.557760	+	0.830002i	$0.688339\pi$
$942$	7.21650	−	2.34478i	0.235126	−	0.0763971i
$943$		−	39.2778i		−	1.27906i
$944$	4.83525	+	14.8814i	0.157374	+	0.484347i
$945$		0			0
$946$	−5.98505	+	18.4201i	−0.194591	+	0.598889i
$947$	6.42557	+	2.08780i	0.208803	+	0.0678442i	0.411551	−	0.911387i	$-0.364987\pi$
$947$	6.42557	+	2.08780i	0.208803	+	0.0678442i	−0.202748	+	0.979231i	$0.564987\pi$
$948$	48.1028	+	66.2078i	1.56231	+	2.15033i
$949$	2.61803			0.0849850
$950$		0			0
$951$	−50.1021			−1.62467
$952$	−1.22671	−	1.68842i	−0.0397578	−	0.0547219i
$953$	57.0190	+	18.5266i	1.84703	+	0.600136i	0.997343	+	0.0728437i	$0.0232074\pi$
$953$	57.0190	+	18.5266i	1.84703	+	0.600136i	0.849684	+	0.527292i	$0.176793\pi$
$954$	8.93754	−	27.5069i	0.289364	−	0.890569i
$955$		0			0
$956$	−5.10343	−	15.7067i	−0.165057	−	0.507992i
$957$		−	23.6747i		−	0.765293i
$958$	41.6999	−	13.5491i	1.34726	−	0.437752i
$959$	−0.553535	−	0.402166i	−0.0178746	−	0.0129866i
$960$		0			0
$961$	25.0644	−	18.2104i	0.808530	−	0.587432i
$962$	8.88781	−	12.2330i	0.286555	−	0.394408i
$963$	−5.19114	+	7.14499i	−0.167282	+	0.230244i
$964$	2.24144	−	1.62850i	0.0721920	−	0.0524505i
$965$		0			0
$966$	16.7460	+	12.1667i	0.538793	+	0.391456i
$967$	−8.61276	+	2.79845i	−0.276968	+	0.0899922i	−0.444207	−	0.895924i	$-0.646515\pi$
$967$	−8.61276	+	2.79845i	−0.276968	+	0.0899922i	0.167240	+	0.985916i	$0.446515\pi$
$968$			5.08580i			0.163464i
$969$	−5.08225	−	15.6416i	−0.163265	−	0.502479i
$970$		0			0
$971$	14.6322	−	45.0333i	0.469570	−	1.44519i	−0.383573	−	0.923511i	$-0.625307\pi$
$971$	14.6322	−	45.0333i	0.469570	−	1.44519i	0.853143	−	0.521677i	$-0.174693\pi$
$972$	−37.5094	−	12.1875i	−1.20312	−	0.390916i
$973$	9.66665	+	13.3050i	0.309899	+	0.426539i
$974$	58.2191			1.86546
$975$		0			0
$976$	8.81263			0.282085
$977$	−2.78885	−	3.83852i	−0.0892231	−	0.122805i	0.762072	−	0.647492i	$-0.224182\pi$
$977$	−2.78885	−	3.83852i	−0.0892231	−	0.122805i	−0.851295	+	0.524687i	$0.824182\pi$
$978$	3.89328	+	1.26500i	0.124493	+	0.0404504i
$979$	−8.96645	+	27.5959i	−0.286569	+	0.881968i
$980$		0			0
$981$	9.22005	+	28.3764i	0.294374	+	0.905988i
$982$			31.1981i			0.995570i
$983$	−17.6569	+	5.73708i	−0.563168	+	0.182984i	−0.576746	−	0.816924i	$-0.695678\pi$
$983$	−17.6569	+	5.73708i	−0.563168	+	0.182984i	0.0135783	+	0.999908i	$0.495678\pi$
$984$	11.1561	+	8.10542i	0.355645	+	0.258391i
$985$		0			0
$986$	−26.2922	+	19.1024i	−0.837315	+	0.608345i
$987$	12.7297	−	17.5209i	0.405190	−	0.557696i
$988$	12.0370	−	16.5676i	0.382949	−	0.527085i
$989$	−17.0932	+	12.4190i	−0.543533	+	0.394900i
$990$		0			0
$991$	32.1340	+	23.3467i	1.02077	+	0.741634i	0.966441	−	0.256889i	$-0.0826976\pi$
$991$	32.1340	+	23.3467i	1.02077	+	0.741634i	0.0543304	+	0.998523i	$0.482698\pi$
$992$	1.05027	−	0.341253i	0.0333460	−	0.0108348i
$993$		−	6.51411i		−	0.206719i
$994$	6.16631	+	18.9779i	0.195583	+	0.601944i
$995$		0			0
$996$	2.82570	−	8.69660i	0.0895356	−	0.275562i
$997$	−28.8088	−	9.36056i	−0.912385	−	0.296452i	−0.185046	−	0.982730i	$-0.559243\pi$
$997$	−28.8088	−	9.36056i	−0.912385	−	0.296452i	−0.727339	+	0.686278i	$0.759243\pi$
$998$	−54.3295	−	74.7782i	−1.71977	−	2.36706i
$999$	5.51210			0.174395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.a.374.1		8
5.2	odd	4		625.2.d.o.251.4		16
5.3	odd	4		625.2.d.o.251.1		16
5.4	even	2		625.2.e.i.374.2		8
25.2	odd	20		125.2.d.b.26.1		16
25.3	odd	20		625.2.a.f.1.7		8
25.4	even	10		625.2.b.c.624.2		8
25.6	even	5		125.2.e.b.24.2		8
25.8	odd	20		125.2.d.b.101.4		16
25.9	even	10	inner	625.2.e.a.249.1		8
25.11	even	5		25.2.e.a.19.1	yes	8
25.12	odd	20		625.2.d.o.376.4		16
25.13	odd	20		625.2.d.o.376.1		16
25.14	even	10		125.2.e.b.99.2		8
25.16	even	5		625.2.e.i.249.2		8
25.17	odd	20		125.2.d.b.101.1		16
25.19	even	10		25.2.e.a.4.1	✓	8
25.21	even	5		625.2.b.c.624.7		8
25.22	odd	20		625.2.a.f.1.2		8
25.23	odd	20		125.2.d.b.26.4		16
75.11	odd	10		225.2.m.a.19.2		8
75.44	odd	10		225.2.m.a.154.2		8
75.47	even	20		5625.2.a.x.1.7		8
75.53	even	20		5625.2.a.x.1.2		8
100.3	even	20		10000.2.a.bj.1.2		8
100.11	odd	10		400.2.y.c.369.1		8
100.19	odd	10		400.2.y.c.129.1		8
100.47	even	20		10000.2.a.bj.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	25.19	even	10
25.2.e.a.19.1	yes	8	25.11	even	5
125.2.d.b.26.1		16	25.2	odd	20
125.2.d.b.26.4		16	25.23	odd	20
125.2.d.b.101.1		16	25.17	odd	20
125.2.d.b.101.4		16	25.8	odd	20
125.2.e.b.24.2		8	25.6	even	5
125.2.e.b.99.2		8	25.14	even	10
225.2.m.a.19.2		8	75.11	odd	10
225.2.m.a.154.2		8	75.44	odd	10
400.2.y.c.129.1		8	100.19	odd	10
400.2.y.c.369.1		8	100.11	odd	10
625.2.a.f.1.2		8	25.22	odd	20
625.2.a.f.1.7		8	25.3	odd	20
625.2.b.c.624.2		8	25.4	even	10
625.2.b.c.624.7		8	25.21	even	5
625.2.d.o.251.1		16	5.3	odd	4
625.2.d.o.251.4		16	5.2	odd	4
625.2.d.o.376.1		16	25.13	odd	20
625.2.d.o.376.4		16	25.12	odd	20
625.2.e.a.249.1		8	25.9	even	10	inner
625.2.e.a.374.1		8	1.1	even	1	trivial
625.2.e.i.249.2		8	25.16	even	5
625.2.e.i.374.2		8	5.4	even	2
5625.2.a.x.1.2		8	75.53	even	20
5625.2.a.x.1.7		8	75.47	even	20
10000.2.a.bj.1.2		8	100.3	even	20
10000.2.a.bj.1.7		8	100.47	even	20

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +O(q^{10})\)	\(q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(3.03472 - 4.17693i) q^{12} +(-1.98322 + 2.72967i) q^{13} +(-1.67421 + 1.21638i) q^{14} +(2.57411 + 1.87020i) q^{16} +(2.75284 - 0.894453i) q^{17} -3.82309i q^{18} +(0.798649 + 2.45799i) q^{19} +(-0.674207 + 2.07500i) q^{21} +(3.96645 + 1.28878i) q^{22} +(2.67421 + 3.68073i) q^{23} -1.59730 q^{24} +7.03588 q^{26} +(1.50757 + 2.07500i) q^{27} +(2.21650 + 0.720183i) q^{28} +(1.66384 - 5.12077i) q^{29} +(0.0421925 + 0.129855i) q^{31} -8.08800i q^{32} +(4.18178 - 1.35874i) q^{33} +(-4.88313 - 3.54780i) q^{34} +(-3.48322 + 2.53071i) q^{36} +(1.26321 - 1.73866i) q^{37} +(3.16780 - 4.36010i) q^{38} +(6.00116 - 4.36010i) q^{39} +(-6.98439 - 5.07446i) q^{41} +(4.32696 - 1.40591i) q^{42} +4.64398i q^{43} +(-1.45140 - 4.46695i) q^{44} +(2.93173 - 9.02294i) q^{46} +(-9.44047 - 3.06739i) q^{47} +(-4.11163 - 5.65917i) q^{48} +6.01515 q^{49} -6.36356 q^{51} +(-4.65743 - 6.41040i) q^{52} +(7.19494 + 2.33778i) q^{53} +(1.65275 - 5.08664i) q^{54} +(-0.222807 - 0.685730i) q^{56} -5.68196i q^{57} +(-10.6783 + 3.46958i) q^{58} +(3.97854 + 2.89058i) q^{59} +(2.24075 - 1.62800i) q^{61} +(0.167354 - 0.230343i) q^{62} +(1.06943 - 1.47195i) q^{63} +(-8.49648 + 6.17306i) q^{64} +(-7.41785 - 5.38938i) q^{66} +(2.07879 - 0.675441i) q^{67} +6.79751i q^{68} +(-3.09089 - 9.51278i) q^{69} +(2.97971 - 9.17060i) q^{71} +(1.26682 + 0.411616i) q^{72} +(-0.456080 - 0.627740i) q^{73} -4.48150 q^{74} -6.06943 q^{76} +(1.16663 + 1.60573i) q^{77} +(-14.7113 - 4.77998i) q^{78} +(-4.89818 + 15.0750i) q^{79} +(-3.44210 - 10.5937i) q^{81} +18.0026i q^{82} +(1.68442 - 0.547301i) q^{83} +(-4.14518 - 3.01165i) q^{84} +(7.83453 - 5.69212i) q^{86} +(-6.95781 + 9.57660i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(11.7372 - 8.52760i) q^{89} +(2.70892 + 1.96815i) q^{91} +(-10.1615 + 3.30167i) q^{92} -0.300177i q^{93} +(6.39639 + 19.6861i) q^{94} +(-5.49476 + 16.9111i) q^{96} +(16.1956 + 5.26228i) q^{97} +(-7.37276 - 10.1477i) q^{98} -3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more