LMFDB - Embedded newform 725.2.k.a.291.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(146,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("725.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.k (of order $5$, degree $4$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			291.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	725.291
Dual form			725.2.k.a.436.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.118034 + 0.363271i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-0.690983 + 2.12663i) q^{5} -3.00000 q^{7} +(2.30902 - 1.67760i) q^{9} +(2.11803 + 1.53884i) q^{11} +(0.618034 - 0.449028i) q^{12} +(0.809017 - 0.587785i) q^{13} -0.854102 q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.00000 - 3.07768i) q^{17} +(2.57295 - 7.91872i) q^{19} +4.47214 q^{20} +(-0.354102 - 1.08981i) q^{21} +(6.73607 + 4.89404i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.80902 + 1.31433i) q^{27} +(1.85410 + 5.70634i) q^{28} +(0.309017 + 0.951057i) q^{29} +(2.80902 - 8.64527i) q^{31} +(-0.309017 + 0.951057i) q^{33} +(2.07295 - 6.37988i) q^{35} +(-4.61803 - 3.35520i) q^{36} +(8.85410 - 6.43288i) q^{37} +(0.309017 + 0.224514i) q^{39} +(-0.500000 + 0.363271i) q^{41} -6.70820 q^{43} +(1.61803 - 4.97980i) q^{44} +(1.97214 + 6.06961i) q^{45} +(1.50000 + 4.61653i) q^{47} +(-1.23607 - 0.898056i) q^{48} +2.00000 q^{49} +1.23607 q^{51} +(-1.61803 - 1.17557i) q^{52} +(-3.00000 - 9.23305i) q^{53} +(-4.73607 + 3.44095i) q^{55} +3.18034 q^{57} +(6.28115 - 4.56352i) q^{59} +(0.527864 + 1.62460i) q^{60} +(7.92705 + 5.75934i) q^{61} +(-6.92705 + 5.03280i) q^{63} +(6.47214 + 4.70228i) q^{64} +(0.690983 + 2.12663i) q^{65} +(-3.78115 + 11.6372i) q^{67} -6.47214 q^{68} +(-0.982779 + 3.02468i) q^{69} +(1.95492 + 6.01661i) q^{71} +(-6.35410 - 4.61653i) q^{73} +(0.590170 - 1.81636i) q^{75} -16.6525 q^{76} +(-6.35410 - 4.61653i) q^{77} +(-4.30902 - 13.2618i) q^{79} +(-2.76393 - 8.50651i) q^{80} +(2.38197 - 7.33094i) q^{81} +(-2.78115 + 8.55951i) q^{83} +(-1.85410 + 1.34708i) q^{84} +(5.85410 + 4.25325i) q^{85} +(-0.309017 + 0.224514i) q^{87} +(-3.61803 - 2.62866i) q^{89} +(-2.42705 + 1.76336i) q^{91} +(5.14590 - 15.8374i) q^{92} +3.47214 q^{93} +(15.0623 + 10.9434i) q^{95} +(0.927051 + 2.85317i) q^{97} +7.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 2 q^{4} - 5 q^{5} - 12 q^{7} + 7 q^{9} + 4 q^{11} - 2 q^{12} + q^{13} + 10 q^{15} - 4 q^{16} + 4 q^{17} + 17 q^{19} + 12 q^{21} + 18 q^{23} - 5 q^{25} + 5 q^{27} - 6 q^{28} - q^{29} + 9 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 2 * q^4 - 5 * q^5 - 12 * q^7 + 7 * q^9 + 4 * q^11 - 2 * q^12 + q^13 + 10 * q^15 - 4 * q^16 + 4 * q^17 + 17 * q^19 + 12 * q^21 + 18 * q^23 - 5 * q^25 + 5 * q^27 - 6 * q^28 - q^29 + 9 * q^31 + q^33 + 15 * q^35 - 14 * q^36 + 22 * q^37 - q^39 - 2 * q^41 + 2 * q^44 - 10 * q^45 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 4 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 - 32 * q^57 + 5 * q^59 + 20 * q^60 + 25 * q^61 - 21 * q^63 + 8 * q^64 + 5 * q^65 + 5 * q^67 - 8 * q^68 - 33 * q^69 + 19 * q^71 - 12 * q^73 - 20 * q^75 - 4 * q^76 - 12 * q^77 - 15 * q^79 - 20 * q^80 + 14 * q^81 + 9 * q^83 + 6 * q^84 + 10 * q^85 + q^87 - 10 * q^89 - 3 * q^91 + 34 * q^92 - 4 * q^93 + 20 * q^95 - 3 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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			0		0.587785	−	0.809017i	$-0.300000\pi$
$2$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	0.979331	−	0.202265i	$-0.0648303\pi$
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	−0.911184	+	0.412000i	$0.864830\pi$
$4$	−0.618034	−	1.90211i	−0.309017	−	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$		0			0
$9$	2.30902	−	1.67760i	0.769672	−	0.559200i
$10$		0			0
$11$	2.11803	+	1.53884i	0.638611	+	0.463978i	0.859373	−	0.511350i	$-0.170854\pi$
$11$	2.11803	+	1.53884i	0.638611	+	0.463978i	−0.220762	+	0.975328i	$0.570854\pi$
$12$	0.618034	−	0.449028i	0.178411	−	0.129623i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i	−0.469916	−	0.882711i	$-0.655716\pi$
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i	0.694297	+	0.719689i	$0.255716\pi$
$14$		0			0
$15$	−0.854102			−0.220528
$16$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$17$	1.00000	−	3.07768i	0.242536	−	0.746448i	−0.753496	−	0.657452i	$-0.771634\pi$
$17$	1.00000	−	3.07768i	0.242536	−	0.746448i	0.996032	−	0.0889958i	$-0.0283658\pi$
$18$		0			0
$19$	2.57295	−	7.91872i	0.590275	−	1.81668i	0.0133090	−	0.999911i	$-0.495763\pi$
$19$	2.57295	−	7.91872i	0.590275	−	1.81668i	0.576966	−	0.816768i	$-0.304237\pi$
$20$	4.47214			1.00000
$21$	−0.354102	−	1.08981i	−0.0772714	−	0.237817i
$22$		0			0
$23$	6.73607	+	4.89404i	1.40457	+	1.02048i	0.994084	+	0.108610i	$0.0346398\pi$
$23$	6.73607	+	4.89404i	1.40457	+	1.02048i	0.410483	+	0.911868i	$0.365360\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$		0			0
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$	1.85410	+	5.70634i	0.350392	+	1.07840i
$29$	0.309017	+	0.951057i	0.0573830	+	0.176607i
$29$	0.309017	+	0.951057i	0.0573830	+	0.176607i
$30$		0			0
$31$	2.80902	−	8.64527i	0.504514	−	1.55274i	−0.297071	−	0.954855i	$-0.596010\pi$
$31$	2.80902	−	8.64527i	0.504514	−	1.55274i	0.801586	−	0.597880i	$-0.203990\pi$
$32$		0			0
$33$	−0.309017	+	0.951057i	−0.0537930	+	0.165558i
$34$		0			0
$35$	2.07295	−	6.37988i	0.350392	−	1.07840i
$36$	−4.61803	−	3.35520i	−0.769672	−	0.559200i
$37$	8.85410	−	6.43288i	1.45561	−	1.05756i	0.471125	−	0.882067i	$-0.343848\pi$
$37$	8.85410	−	6.43288i	1.45561	−	1.05756i	0.984481	−	0.175493i	$-0.0561518\pi$
$38$		0			0
$39$	0.309017	+	0.224514i	0.0494823	+	0.0359510i
$40$		0			0
$41$	−0.500000	+	0.363271i	−0.0780869	+	0.0567334i	−0.626144	−	0.779708i	$-0.715368\pi$
$41$	−0.500000	+	0.363271i	−0.0780869	+	0.0567334i	0.548057	+	0.836441i	$0.315368\pi$
$42$		0			0
$43$	−6.70820			−1.02299			−0.511496	−	0.859286i	$-0.670908\pi$
$43$	−6.70820			−1.02299			−0.511496	+	0.859286i	$0.670908\pi$
$44$	1.61803	−	4.97980i	0.243928	−	0.750733i
$45$	1.97214	+	6.06961i	0.293989	+	0.904804i
$46$		0			0
$47$	1.50000	+	4.61653i	0.218797	+	0.673389i	0.998862	+	0.0476905i	$0.0151861\pi$
$47$	1.50000	+	4.61653i	0.218797	+	0.673389i	−0.780065	+	0.625699i	$0.784814\pi$
$48$	−1.23607	−	0.898056i	−0.178411	−	0.129623i
$49$	2.00000			0.285714
$50$		0			0
$51$	1.23607			0.173084
$52$	−1.61803	−	1.17557i	−0.224381	−	0.163022i
$53$	−3.00000	−	9.23305i	−0.412082	−	1.26826i	−0.914835	−	0.403827i	$-0.867680\pi$
$53$	−3.00000	−	9.23305i	−0.412082	−	1.26826i	0.502754	−	0.864430i	$-0.332320\pi$
$54$		0			0
$55$	−4.73607	+	3.44095i	−0.638611	+	0.463978i
$56$		0			0
$57$	3.18034			0.421246
$58$		0			0
$59$	6.28115	−	4.56352i	0.817736	−	0.594120i	−0.0983268	−	0.995154i	$-0.531349\pi$
$59$	6.28115	−	4.56352i	0.817736	−	0.594120i	0.916063	+	0.401034i	$0.131349\pi$
$60$	0.527864	+	1.62460i	0.0681470	+	0.209735i
$61$	7.92705	+	5.75934i	1.01495	+	0.737408i	0.965243	−	0.261356i	$-0.0841696\pi$
$61$	7.92705	+	5.75934i	1.01495	+	0.737408i	0.0497123	+	0.998764i	$0.484170\pi$
$62$		0			0
$63$	−6.92705	+	5.03280i	−0.872726	+	0.634073i
$64$	6.47214	+	4.70228i	0.809017	+	0.587785i
$65$	0.690983	+	2.12663i	0.0857059	+	0.263776i
$66$		0			0
$67$	−3.78115	+	11.6372i	−0.461941	+	1.42171i	0.400847	+	0.916145i	$0.368716\pi$
$67$	−3.78115	+	11.6372i	−0.461941	+	1.42171i	−0.862789	+	0.505564i	$0.831284\pi$
$68$	−6.47214			−0.784862
$69$	−0.982779	+	3.02468i	−0.118313	+	0.364129i
$70$		0			0
$71$	1.95492	+	6.01661i	0.232006	+	0.714040i	0.997505	+	0.0706029i	$0.0224923\pi$
$71$	1.95492	+	6.01661i	0.232006	+	0.714040i	−0.765499	+	0.643437i	$0.777508\pi$
$72$		0			0
$73$	−6.35410	−	4.61653i	−0.743691	−	0.540323i	0.150174	−	0.988660i	$-0.452017\pi$
$73$	−6.35410	−	4.61653i	−0.743691	−	0.540323i	−0.893865	+	0.448336i	$0.852017\pi$
$74$		0			0
$75$	0.590170	−	1.81636i	0.0681470	−	0.209735i
$76$	−16.6525			−1.91017
$77$	−6.35410	−	4.61653i	−0.724117	−	0.526102i
$78$		0			0
$79$	−4.30902	−	13.2618i	−0.484802	−	1.49207i	−0.832267	−	0.554375i	$-0.812957\pi$
$79$	−4.30902	−	13.2618i	−0.484802	−	1.49207i	0.347465	−	0.937693i	$-0.387043\pi$
$80$	−2.76393	−	8.50651i	−0.309017	−	0.951057i
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$		0			0
$83$	−2.78115	+	8.55951i	−0.305271	+	0.939528i	0.674305	+	0.738453i	$0.264443\pi$
$83$	−2.78115	+	8.55951i	−0.305271	+	0.939528i	−0.979576	+	0.201075i	$0.935557\pi$
$84$	−1.85410	+	1.34708i	−0.202299	+	0.146979i
$85$	5.85410	+	4.25325i	0.634967	+	0.461330i
$86$		0			0
$87$	−0.309017	+	0.224514i	−0.0331301	+	0.0240704i
$88$		0			0
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	0.379280	−	0.925282i	$-0.376172\pi$
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	−0.762791	+	0.646645i	$0.776172\pi$
$90$		0			0
$91$	−2.42705	+	1.76336i	−0.254424	+	0.184850i
$92$	5.14590	−	15.8374i	0.536497	−	1.65117i
$93$	3.47214			0.360044
$94$		0			0
$95$	15.0623	+	10.9434i	1.54536	+	1.12277i
$96$		0			0
$97$	0.927051	+	2.85317i	0.0941278	+	0.289695i	0.987025	−	0.160564i	$-0.0513314\pi$
$97$	0.927051	+	2.85317i	0.0941278	+	0.289695i	−0.892898	+	0.450260i	$0.851331\pi$
$98$		0			0
$99$	7.47214			0.750978
$100$	−3.09017	+	9.51057i	−0.309017	+	0.951057i
$101$	3.70820			0.368980			0.184490	−	0.982834i	$-0.440937\pi$
$101$	3.70820			0.368980			0.184490	+	0.982834i	$0.440937\pi$
$102$		0			0
$103$	2.80902	+	8.64527i	0.276781	+	0.851843i	0.988743	+	0.149625i	$0.0478068\pi$
$103$	2.80902	+	8.64527i	0.276781	+	0.851843i	−0.711962	+	0.702218i	$0.752193\pi$
$104$		0			0
$105$	2.56231			0.250055
$106$		0			0
$107$	2.47214			0.238990			0.119495	−	0.992835i	$-0.461872\pi$
$107$	2.47214			0.238990			0.119495	+	0.992835i	$0.461872\pi$
$108$	1.38197	−	4.25325i	0.132980	−	0.409270i
$109$	1.69098	−	1.22857i	0.161967	−	0.117676i	−0.503850	−	0.863791i	$-0.668083\pi$
$109$	1.69098	−	1.22857i	0.161967	−	0.117676i	0.665816	+	0.746116i	$0.268083\pi$
$110$		0			0
$111$	3.38197	+	2.45714i	0.321002	+	0.233222i
$112$	9.70820	−	7.05342i	0.917339	−	0.666486i
$113$	4.92705	−	3.57971i	0.463498	−	0.336751i	−0.331404	−	0.943489i	$-0.607522\pi$
$113$	4.92705	−	3.57971i	0.463498	−	0.336751i	0.794902	+	0.606738i	$0.207522\pi$
$114$		0			0
$115$	−15.0623	+	10.9434i	−1.40457	+	1.02048i
$116$	1.61803	−	1.17557i	0.150231	−	0.109149i
$117$	0.881966	−	2.71441i	0.0815378	−	0.250948i
$118$		0			0
$119$	−3.00000	+	9.23305i	−0.275010	+	0.846392i
$120$		0			0
$121$	−1.28115	−	3.94298i	−0.116468	−	0.358453i
$122$		0			0
$123$	−0.190983	−	0.138757i	−0.0172204	−	0.0125113i
$124$	−18.1803			−1.63264
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$		0			0
$127$	4.97214	+	3.61247i	0.441206	+	0.320555i	0.786114	−	0.618082i	$-0.212090\pi$
$127$	4.97214	+	3.61247i	0.441206	+	0.320555i	−0.344908	+	0.938636i	$0.612090\pi$
$128$		0			0
$129$	−0.791796	−	2.43690i	−0.0697138	−	0.214557i
$130$		0			0
$131$	−4.38197	+	13.4863i	−0.382854	+	1.17830i	0.555171	+	0.831736i	$0.312653\pi$
$131$	−4.38197	+	13.4863i	−0.382854	+	1.17830i	−0.938025	+	0.346568i	$0.887347\pi$
$132$	2.00000			0.174078
$133$	−7.71885	+	23.7562i	−0.669309	+	2.05992i
$134$		0			0
$135$	−4.04508	+	2.93893i	−0.348145	+	0.252942i
$136$		0			0
$137$	−1.00000	+	0.726543i	−0.0854358	+	0.0620727i	−0.629683	−	0.776852i	$-0.716815\pi$
$137$	−1.00000	+	0.726543i	−0.0854358	+	0.0620727i	0.544247	+	0.838925i	$0.316815\pi$
$138$		0			0
$139$	1.69098	+	1.22857i	0.143427	+	0.104206i	0.657185	−	0.753729i	$-0.271747\pi$
$139$	1.69098	+	1.22857i	0.143427	+	0.104206i	−0.513758	+	0.857935i	$0.671747\pi$
$140$	−13.4164			−1.13389
$141$	−1.50000	+	1.08981i	−0.126323	+	0.0917789i
$142$		0			0
$143$	2.61803			0.218931
$144$	−3.52786	+	10.8576i	−0.293989	+	0.904804i
$145$	−2.23607			−0.185695
$146$		0			0
$147$	0.236068	+	0.726543i	0.0194706	+	0.0599242i
$148$	−17.7082	−	12.8658i	−1.45561	−	1.05756i
$149$	−14.7639			−1.20951			−0.604754	−	0.796412i	$-0.706729\pi$
$149$	−14.7639			−1.20951			−0.604754	+	0.796412i	$0.706729\pi$
$150$		0			0
$151$	−4.41641			−0.359402			−0.179701	−	0.983721i	$-0.557513\pi$
$151$	−4.41641			−0.359402			−0.179701	+	0.983721i	$0.557513\pi$
$152$		0			0
$153$	−2.85410	−	8.78402i	−0.230740	−	0.710146i
$154$		0			0
$155$	16.4443	+	11.9475i	1.32084	+	0.959643i
$156$	0.236068	−	0.726543i	0.0189006	−	0.0581700i
$157$	14.3820			1.14781			0.573903	−	0.818923i	$-0.305429\pi$
$157$	14.3820			1.14781			0.573903	+	0.818923i	$0.305429\pi$
$158$		0			0
$159$	3.00000	−	2.17963i	0.237915	−	0.172856i
$160$		0			0
$161$	−20.2082	−	14.6821i	−1.59263	−	1.15711i
$162$		0			0
$163$	−7.66312	+	5.56758i	−0.600222	+	0.436087i	−0.845958	−	0.533250i	$-0.820970\pi$
$163$	−7.66312	+	5.56758i	−0.600222	+	0.436087i	0.245736	+	0.969337i	$0.420970\pi$
$164$	1.00000	+	0.726543i	0.0780869	+	0.0567334i
$165$	−1.80902	−	1.31433i	−0.140832	−	0.102320i
$166$		0			0
$167$	−3.16312	+	9.73508i	−0.244769	+	0.753323i	0.750905	+	0.660410i	$0.229618\pi$
$167$	−3.16312	+	9.73508i	−0.244769	+	0.753323i	−0.995674	+	0.0929126i	$0.970382\pi$
$168$		0			0
$169$	−3.70820	+	11.4127i	−0.285246	+	0.877898i
$170$		0			0
$171$	−7.34346	−	22.6008i	−0.561568	−	1.72833i
$172$	4.14590	+	12.7598i	0.316122	+	0.972923i
$173$	2.92705	+	2.12663i	0.222540	+	0.161684i	0.693469	−	0.720486i	$-0.256081\pi$
$173$	2.92705	+	2.12663i	0.222540	+	0.161684i	−0.470930	+	0.882171i	$0.656081\pi$
$174$		0			0
$175$	12.1353	+	8.81678i	0.917339	+	0.666486i
$176$	−10.4721			−0.789367
$177$	2.39919	+	1.74311i	0.180334	+	0.131020i
$178$		0			0
$179$	−8.00000	−	24.6215i	−0.597948	−	1.84029i	−0.539468	−	0.842006i	$-0.681374\pi$
$179$	−8.00000	−	24.6215i	−0.597948	−	1.84029i	−0.0584805	−	0.998289i	$-0.518626\pi$
$180$	10.3262	−	7.50245i	0.769672	−	0.559200i
$181$	3.09017	−	9.51057i	0.229691	−	0.706915i	−0.768091	−	0.640341i	$-0.778793\pi$
$181$	3.09017	−	9.51057i	0.229691	−	0.706915i	0.997781	−	0.0665740i	$-0.0212068\pi$
$182$		0			0
$183$	−1.15654	+	3.55947i	−0.0854940	+	0.263123i
$184$		0			0
$185$	7.56231	+	23.2744i	0.555992	+	1.71117i
$186$		0			0
$187$	6.85410	−	4.97980i	0.501222	−	0.364159i
$188$	7.85410	−	5.70634i	0.572819	−	0.416178i
$189$	−5.42705	−	3.94298i	−0.394760	−	0.286810i
$190$		0			0
$191$	−21.7984	+	15.8374i	−1.57727	+	1.14596i	−0.657539	+	0.753421i	$0.728402\pi$
$191$	−21.7984	+	15.8374i	−1.57727	+	1.14596i	−0.919736	+	0.392536i	$0.871598\pi$
$192$	−0.944272	+	2.90617i	−0.0681470	+	0.209735i
$193$	−20.2705			−1.45910			−0.729552	−	0.683926i	$-0.760271\pi$
$193$	−20.2705			−1.45910			−0.729552	+	0.683926i	$0.760271\pi$
$194$		0			0
$195$	−0.690983	+	0.502029i	−0.0494823	+	0.0359510i
$196$	−1.23607	−	3.80423i	−0.0882906	−	0.271730i
$197$	−3.79180	−	11.6699i	−0.270154	−	0.831449i	−0.990461	−	0.137794i	$-0.955999\pi$
$197$	−3.79180	−	11.6699i	−0.270154	−	0.831449i	0.720307	−	0.693656i	$-0.244001\pi$
$198$		0			0
$199$	10.8541			0.769427			0.384713	−	0.923036i	$-0.374300\pi$
$199$	10.8541			0.769427			0.384713	+	0.923036i	$0.374300\pi$
$200$		0			0
$201$	−4.67376			−0.329662
$202$		0			0
$203$	−0.927051	−	2.85317i	−0.0650662	−	0.200253i
$204$	−0.763932	−	2.35114i	−0.0534859	−	0.164613i
$205$	−0.427051	−	1.31433i	−0.0298265	−	0.0917966i
$206$		0			0
$207$	23.7639			1.65171
$208$	−1.23607	+	3.80423i	−0.0857059	+	0.263776i
$209$	17.6353	−	12.8128i	1.21986	−	0.886277i
$210$		0			0
$211$	−2.85410	−	2.07363i	−0.196484	−	0.142754i	0.485193	−	0.874407i	$-0.338749\pi$
$211$	−2.85410	−	2.07363i	−0.196484	−	0.142754i	−0.681678	+	0.731653i	$0.738749\pi$
$212$	−15.7082	+	11.4127i	−1.07884	+	0.783826i
$213$	−1.95492	+	1.42033i	−0.133949	+	0.0973193i
$214$		0			0
$215$	4.63525	−	14.2658i	0.316122	−	0.972923i
$216$		0			0
$217$	−8.42705	+	25.9358i	−0.572065	+	1.76064i
$218$		0			0
$219$	0.927051	−	2.85317i	0.0626443	−	0.192799i
$220$	9.47214	+	6.88191i	0.638611	+	0.463978i
$221$	−1.00000	−	3.07768i	−0.0672673	−	0.207027i
$222$		0			0
$223$	7.50000	+	5.44907i	0.502237	+	0.364897i	0.809871	−	0.586608i	$-0.199537\pi$
$223$	7.50000	+	5.44907i	0.502237	+	0.364897i	−0.307634	+	0.951505i	$0.599537\pi$
$224$		0			0
$225$	−14.2705			−0.951367
$226$		0			0
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.288934	−	0.957349i	$-0.593301\pi$
$227$	−19.4164	−	14.1068i	−1.28871	−	0.936304i	−0.999779	+	0.0210448i	$0.993301\pi$
$228$	−1.96556	−	6.04937i	−0.130172	−	0.400629i
$229$	1.01722	+	3.13068i	0.0672199	+	0.206881i	0.979024	−	0.203743i	$-0.0653107\pi$
$229$	1.01722	+	3.13068i	0.0672199	+	0.206881i	−0.911805	+	0.410624i	$0.865311\pi$
$230$		0			0
$231$	0.927051	−	2.85317i	0.0609955	−	0.187725i
$232$		0			0
$233$	−4.36475	+	13.4333i	−0.285944	+	0.880045i	0.700170	+	0.713976i	$0.253107\pi$
$233$	−4.36475	+	13.4333i	−0.285944	+	0.880045i	−0.986114	+	0.166069i	$0.946893\pi$
$234$		0			0
$235$	−10.8541			−0.708044
$236$	−12.5623	−	9.12705i	−0.817736	−	0.594120i
$237$	4.30902	−	3.13068i	0.279901	−	0.203360i
$238$		0			0
$239$	11.9271	+	8.66551i	0.771497	+	0.560525i	0.902415	−	0.430868i	$-0.141793\pi$
$239$	11.9271	+	8.66551i	0.771497	+	0.560525i	−0.130918	+	0.991393i	$0.541793\pi$
$240$	2.76393	−	2.00811i	0.178411	−	0.129623i
$241$	−8.00000	+	5.81234i	−0.515325	+	0.374406i	−0.814840	−	0.579686i	$-0.803175\pi$
$241$	−8.00000	+	5.81234i	−0.515325	+	0.374406i	0.299515	+	0.954092i	$0.403175\pi$
$242$		0			0
$243$	9.65248			0.619207
$244$	6.05573	−	18.6376i	0.387678	−	1.19315i
$245$	−1.38197	+	4.25325i	−0.0882906	+	0.271730i
$246$		0			0
$247$	−2.57295	−	7.91872i	−0.163713	−	0.503856i
$248$		0			0
$249$	−3.43769			−0.217855
$250$		0			0
$251$	7.38197			0.465946			0.232973	−	0.972483i	$-0.425155\pi$
$251$	7.38197			0.465946			0.232973	+	0.972483i	$0.425155\pi$
$252$	13.8541	+	10.0656i	0.872726	+	0.634073i
$253$	6.73607	+	20.7315i	0.423493	+	1.30338i
$254$		0			0
$255$	−0.854102	+	2.62866i	−0.0534859	+	0.164613i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	2.05573			0.128233			0.0641164	−	0.997942i	$-0.479577\pi$
$257$	2.05573			0.128233			0.0641164	+	0.997942i	$0.479577\pi$
$258$		0			0
$259$	−26.5623	+	19.2986i	−1.65050	+	1.19916i
$260$	3.61803	−	2.62866i	0.224381	−	0.163022i
$261$	2.30902	+	1.67760i	0.142925	+	0.103841i
$262$		0			0
$263$	12.3992	−	9.00854i	0.764567	−	0.555490i	−0.135741	−	0.990744i	$-0.543341\pi$
$263$	12.3992	−	9.00854i	0.764567	−	0.555490i	0.900308	+	0.435254i	$0.143341\pi$
$264$		0			0
$265$	21.7082			1.33352
$266$		0			0
$267$	0.527864	−	1.62460i	0.0323048	−	0.0994238i
$268$	24.4721			1.49487
$269$	4.34346	−	13.3678i	0.264825	−	0.815049i	−0.726908	−	0.686735i	$-0.759043\pi$
$269$	4.34346	−	13.3678i	0.264825	−	0.815049i	0.991734	−	0.128314i	$-0.0409565\pi$
$270$		0			0
$271$	7.54508	+	23.2214i	0.458331	+	1.41060i	0.867179	+	0.497996i	$0.165931\pi$
$271$	7.54508	+	23.2214i	0.458331	+	1.41060i	−0.408848	+	0.912602i	$0.634069\pi$
$272$	4.00000	+	12.3107i	0.242536	+	0.746448i
$273$	−0.927051	−	0.673542i	−0.0561077	−	0.0407646i
$274$		0			0
$275$	−4.04508	−	12.4495i	−0.243928	−	0.750733i
$276$	6.36068			0.382868
$277$	−4.42705	−	3.21644i	−0.265996	−	0.193257i	0.446790	−	0.894639i	$-0.352567\pi$
$277$	−4.42705	−	3.21644i	−0.265996	−	0.193257i	−0.712786	+	0.701381i	$0.752567\pi$
$278$		0			0
$279$	−8.01722	−	24.6745i	−0.479978	−	1.47722i
$280$		0			0
$281$	1.60081	−	4.92680i	0.0954965	−	0.293908i	−0.891886	−	0.452260i	$-0.850618\pi$
$281$	1.60081	−	4.92680i	0.0954965	−	0.293908i	0.987383	+	0.158352i	$0.0506180\pi$
$282$		0			0
$283$	−4.10081	+	12.6210i	−0.243768	+	0.750241i	0.752069	+	0.659085i	$0.229056\pi$
$283$	−4.10081	+	12.6210i	−0.243768	+	0.750241i	−0.995837	+	0.0911560i	$0.970944\pi$
$284$	10.2361	−	7.43694i	0.607399	−	0.441301i
$285$	−2.19756	+	6.76340i	−0.130172	+	0.400629i
$286$		0			0
$287$	1.50000	−	1.08981i	0.0885422	−	0.0643297i
$288$		0			0
$289$	5.28115	+	3.83698i	0.310656	+	0.225705i
$290$		0			0
$291$	−0.927051	+	0.673542i	−0.0543447	+	0.0394837i
$292$	−4.85410	+	14.9394i	−0.284065	+	0.874262i
$293$	−10.4164			−0.608533			−0.304267	−	0.952587i	$-0.598411\pi$
$293$	−10.4164			−0.608533			−0.304267	+	0.952587i	$0.598411\pi$
$294$		0			0
$295$	5.36475	+	16.5110i	0.312348	+	0.961307i
$296$		0			0
$297$	1.80902	+	5.56758i	0.104970	+	0.323064i
$298$		0			0
$299$	8.32624			0.481519
$300$	−3.81966			−0.220528
$301$	20.1246			1.15996
$302$		0			0
$303$	0.437694	+	1.34708i	0.0251449	+	0.0773879i
$304$	10.2918	+	31.6749i	0.590275	+	1.81668i
$305$	−17.7254	+	12.8783i	−1.01495	+	0.737408i
$306$		0			0
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	−4.85410	+	14.9394i	−0.276588	+	0.851251i
$309$	−2.80902	+	2.04087i	−0.159799	+	0.116101i
$310$		0			0
$311$	4.07295	+	2.95917i	0.230956	+	0.167799i	0.697244	−	0.716833i	$-0.254409\pi$
$311$	4.07295	+	2.95917i	0.230956	+	0.167799i	−0.466289	+	0.884633i	$0.654409\pi$
$312$		0			0
$313$	25.4164	−	18.4661i	1.43662	−	1.04377i	0.447885	−	0.894091i	$-0.352177\pi$
$313$	25.4164	−	18.4661i	1.43662	−	1.04377i	0.988735	−	0.149675i	$-0.0478226\pi$
$314$		0			0
$315$	−5.91641	−	18.2088i	−0.333352	−	1.02595i
$316$	−22.5623	+	16.3925i	−1.26923	+	0.922149i
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	−0.447539	−	0.894264i	$-0.647699\pi$
$317$	7.83688	−	24.1194i	0.440163	−	1.35468i	0.887702	−	0.460418i	$-0.152301\pi$
$318$		0			0
$319$	−0.809017	+	2.48990i	−0.0452963	+	0.139408i
$320$	−14.4721	+	10.5146i	−0.809017	+	0.587785i
$321$	0.291796	+	0.898056i	0.0162865	+	0.0501246i
$322$		0			0
$323$	−21.7984	−	15.8374i	−1.21289	−	0.881219i
$324$	−15.4164			−0.856467
$325$	−5.00000			−0.277350
$326$		0			0
$327$	0.645898	+	0.469272i	0.0357182	+	0.0259508i
$328$		0			0
$329$	−4.50000	−	13.8496i	−0.248093	−	0.763552i
$330$		0			0
$331$	5.91641	−	18.2088i	0.325195	−	1.00085i	−0.646157	−	0.763204i	$-0.723625\pi$
$331$	5.91641	−	18.2088i	0.325195	−	1.00085i	0.971352	−	0.237644i	$-0.0763750\pi$
$332$	18.0000			0.987878
$333$	9.65248	−	29.7073i	0.528952	−	1.62795i
$334$		0			0
$335$	−22.1353	−	16.0822i	−1.20938	−	0.878665i
$336$	3.70820	+	2.69417i	0.202299	+	0.146979i
$337$	−0.809017	+	0.587785i	−0.0440700	+	0.0320187i	−0.609602	−	0.792708i	$-0.708671\pi$
$337$	−0.809017	+	0.587785i	−0.0440700	+	0.0320187i	0.565532	+	0.824726i	$0.308671\pi$
$338$		0			0
$339$	1.88197	+	1.36733i	0.102214	+	0.0742631i
$340$	4.47214	−	13.7638i	0.242536	−	0.746448i
$341$	19.2533	−	13.9883i	1.04262	−	0.757511i
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	−5.75329	−	4.18001i	−0.309747	−	0.225044i
$346$		0			0
$347$	−5.10081	−	15.6987i	−0.273826	−	0.842750i	−0.989528	−	0.144344i	$-0.953893\pi$
$347$	−5.10081	−	15.6987i	−0.273826	−	0.842750i	0.715702	−	0.698406i	$-0.246107\pi$
$348$	0.618034	+	0.449028i	0.0331301	+	0.0240704i
$349$	23.3607			1.25047			0.625234	−	0.780437i	$-0.285003\pi$
$349$	23.3607			1.25047			0.625234	+	0.780437i	$0.285003\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$		0			0
$353$	8.04508	+	24.7602i	0.428197	+	1.31785i	0.899900	+	0.436096i	$0.143639\pi$
$353$	8.04508	+	24.7602i	0.428197	+	1.31785i	−0.471703	+	0.881757i	$0.656361\pi$
$354$		0			0
$355$	−14.1459			−0.750786
$356$	−2.76393	+	8.50651i	−0.146488	+	0.450844i
$357$	−3.70820			−0.196259
$358$		0			0
$359$	9.73607	−	7.07367i	0.513850	−	0.373334i	−0.300432	−	0.953803i	$-0.597131\pi$
$359$	9.73607	−	7.07367i	0.513850	−	0.373334i	0.814282	+	0.580469i	$0.197131\pi$
$360$		0			0
$361$	−40.7148	−	29.5810i	−2.14288	−	1.55690i
$362$		0			0
$363$	1.28115	−	0.930812i	0.0672431	−	0.0488550i
$364$	4.85410	+	3.52671i	0.254424	+	0.184850i
$365$	14.2082	−	10.3229i	0.743691	−	0.540323i
$366$		0			0
$367$	1.68034	−	5.17155i	0.0877130	−	0.269953i	−0.897573	−	0.440866i	$-0.854672\pi$
$367$	1.68034	−	5.17155i	0.0877130	−	0.269953i	0.985286	+	0.170913i	$0.0546716\pi$
$368$	−33.3050			−1.73614
$369$	−0.545085	+	1.67760i	−0.0283760	+	0.0873323i
$370$		0			0
$371$	9.00000	+	27.6992i	0.467257	+	1.43807i
$372$	−2.14590	−	6.60440i	−0.111260	−	0.342422i
$373$	4.51722	+	3.28195i	0.233893	+	0.169933i	0.698558	−	0.715553i	$-0.253825\pi$
$373$	4.51722	+	3.28195i	0.233893	+	0.169933i	−0.464665	+	0.885486i	$0.653825\pi$
$374$		0			0
$375$	3.45492	+	2.51014i	0.178411	+	0.129623i
$376$		0			0
$377$	0.809017	+	0.587785i	0.0416665	+	0.0302725i
$378$		0			0
$379$	5.63525	+	17.3435i	0.289464	+	0.890877i	0.985025	+	0.172411i	$0.0551557\pi$
$379$	5.63525	+	17.3435i	0.289464	+	0.890877i	−0.695562	+	0.718467i	$0.744844\pi$
$380$	11.5066	−	35.4136i	0.590275	−	1.81668i
$381$	−0.725425	+	2.23263i	−0.0371646	+	0.114381i
$382$		0			0
$383$	3.59017	−	11.0494i	0.183449	−	0.564598i	−0.816469	−	0.577389i	$-0.804072\pi$
$383$	3.59017	−	11.0494i	0.183449	−	0.564598i	0.999918	+	0.0127908i	$0.00407156\pi$
$384$		0			0
$385$	14.2082	−	10.3229i	0.724117	−	0.526102i
$386$		0			0
$387$	−15.4894	+	11.2537i	−0.787368	+	0.572057i
$388$	4.85410	−	3.52671i	0.246430	−	0.179042i
$389$	−1.59017	−	1.15533i	−0.0806248	−	0.0585774i	0.546743	−	0.837301i	$-0.315868\pi$
$389$	−1.59017	−	1.15533i	−0.0806248	−	0.0585774i	−0.627367	+	0.778723i	$0.715868\pi$
$390$		0			0
$391$	21.7984	−	15.8374i	1.10239	−	0.800934i
$392$		0			0
$393$	−5.41641			−0.273222
$394$		0			0
$395$	31.1803			1.56885
$396$	−4.61803	−	14.2128i	−0.232065	−	0.714222i
$397$	−0.291796	−	0.898056i	−0.0146448	−	0.0450721i	0.943467	−	0.331466i	$-0.107543\pi$
$397$	−0.291796	−	0.898056i	−0.0146448	−	0.0450721i	−0.958112	+	0.286394i	$0.907543\pi$
$398$		0			0
$399$	−9.54102			−0.477648
$400$	20.0000			1.00000
$401$	12.2361			0.611040			0.305520	−	0.952186i	$-0.401170\pi$
$401$	12.2361			0.611040			0.305520	+	0.952186i	$0.401170\pi$
$402$		0			0
$403$	−2.80902	−	8.64527i	−0.139927	−	0.430651i
$404$	−2.29180	−	7.05342i	−0.114021	−	0.350921i
$405$	13.9443	+	10.1311i	0.692896	+	0.503419i
$406$		0			0
$407$	28.6525			1.42025
$408$		0			0
$409$	9.70820	−	7.05342i	0.480040	−	0.348769i	−0.321301	−	0.946977i	$-0.604120\pi$
$409$	9.70820	−	7.05342i	0.480040	−	0.348769i	0.801341	+	0.598208i	$0.204120\pi$
$410$		0			0
$411$	−0.381966	−	0.277515i	−0.0188410	−	0.0136888i
$412$	14.7082	−	10.6861i	0.724621	−	0.526468i
$413$	−18.8435	+	13.6906i	−0.927226	+	0.673669i
$414$		0			0
$415$	−16.2812	−	11.8290i	−0.799210	−	0.580660i
$416$		0			0
$417$	−0.246711	+	0.759299i	−0.0120815	+	0.0371830i
$418$		0			0
$419$	−2.36475	+	7.27794i	−0.115525	+	0.355550i	−0.992056	−	0.125795i	$-0.959852\pi$
$419$	−2.36475	+	7.27794i	−0.115525	+	0.355550i	0.876531	+	0.481346i	$0.159852\pi$
$420$	−1.58359	−	4.87380i	−0.0772714	−	0.237817i
$421$	1.84752	+	5.68609i	0.0900428	+	0.277123i	0.985930	−	0.167158i	$-0.0534590\pi$
$421$	1.84752	+	5.68609i	0.0900428	+	0.277123i	−0.895887	+	0.444281i	$0.853459\pi$
$422$		0			0
$423$	11.2082	+	8.14324i	0.544962	+	0.395938i
$424$		0			0
$425$	−13.0902	+	9.51057i	−0.634967	+	0.461330i
$426$		0			0
$427$	−23.7812	−	17.2780i	−1.15085	−	0.836142i
$428$	−1.52786	−	4.70228i	−0.0738521	−	0.227293i
$429$	0.309017	+	0.951057i	0.0149195	+	0.0459174i
$430$		0			0
$431$	−11.2082	+	34.4953i	−0.539880	+	1.66158i	0.192981	+	0.981202i	$0.438184\pi$
$431$	−11.2082	+	34.4953i	−0.539880	+	1.66158i	−0.732861	+	0.680378i	$0.761816\pi$
$432$	−8.94427			−0.430331
$433$	6.48278	−	19.9519i	0.311542	−	0.958829i	−0.665612	−	0.746298i	$-0.731829\pi$
$433$	6.48278	−	19.9519i	0.311542	−	0.958829i	0.977154	−	0.212531i	$-0.0681707\pi$
$434$		0			0
$435$	−0.263932	−	0.812299i	−0.0126546	−	0.0389468i
$436$	−3.38197	−	2.45714i	−0.161967	−	0.117676i
$437$	56.0861	−	40.7489i	2.68296	−	1.94929i
$438$		0			0
$439$	−4.47214	−	3.24920i	−0.213443	−	0.155076i	0.475927	−	0.879485i	$-0.342113\pi$
$439$	−4.47214	−	3.24920i	−0.213443	−	0.155076i	−0.689370	+	0.724409i	$0.742113\pi$
$440$		0			0
$441$	4.61803	−	3.35520i	0.219906	−	0.159771i
$442$		0			0
$443$	−4.52786			−0.215125			−0.107563	−	0.994198i	$-0.534305\pi$
$443$	−4.52786			−0.215125			−0.107563	+	0.994198i	$0.534305\pi$
$444$	2.58359	−	7.95148i	0.122612	−	0.377360i
$445$	8.09017	−	5.87785i	0.383511	−	0.278637i
$446$		0			0
$447$	−1.74265	−	5.36331i	−0.0824243	−	0.253676i
$448$	−19.4164	−	14.1068i	−0.917339	−	0.666486i
$449$	−8.23607			−0.388684			−0.194342	−	0.980934i	$-0.562257\pi$
$449$	−8.23607			−0.388684			−0.194342	+	0.980934i	$0.562257\pi$
$450$		0			0
$451$	−1.61803			−0.0761902
$452$	−9.85410	−	7.15942i	−0.463498	−	0.336751i
$453$	−0.521286	−	1.60435i	−0.0244922	−	0.0753791i
$454$		0			0
$455$	−2.07295	−	6.37988i	−0.0971813	−	0.299093i
$456$		0			0
$457$	−39.3607			−1.84121			−0.920607	−	0.390489i	$-0.872306\pi$
$457$	−39.3607			−1.84121			−0.920607	+	0.390489i	$0.872306\pi$
$458$		0			0
$459$	5.85410	−	4.25325i	0.273246	−	0.198525i
$460$	30.1246	+	21.8868i	1.40457	+	1.02048i
$461$	0.545085	+	0.396027i	0.0253871	+	0.0184448i	0.600406	−	0.799695i	$-0.295005\pi$
$461$	0.545085	+	0.396027i	0.0253871	+	0.0184448i	−0.575019	+	0.818140i	$0.695005\pi$
$462$		0			0
$463$	−13.1803	+	9.57608i	−0.612542	+	0.445038i	−0.850309	−	0.526284i	$-0.823585\pi$
$463$	−13.1803	+	9.57608i	−0.612542	+	0.445038i	0.237766	+	0.971322i	$0.423585\pi$
$464$	−3.23607	−	2.35114i	−0.150231	−	0.109149i
$465$	−2.39919	+	7.38394i	−0.111260	+	0.342422i
$466$		0			0
$467$	−9.00000	+	27.6992i	−0.416470	+	1.28176i	0.494459	+	0.869201i	$0.335366\pi$
$467$	−9.00000	+	27.6992i	−0.416470	+	1.28176i	−0.910929	+	0.412563i	$0.864634\pi$
$468$	−5.70820			−0.263862
$469$	11.3435	−	34.9116i	0.523792	−	1.61207i
$470$		0			0
$471$	1.69756	+	5.22455i	0.0782195	+	0.240735i
$472$		0			0
$473$	−14.2082	−	10.3229i	−0.653294	−	0.474646i
$474$		0			0
$475$	−33.6803	+	24.4702i	−1.54536	+	1.12277i
$476$	19.4164			0.889950
$477$	−22.4164	−	16.2865i	−1.02638	−	0.745706i
$478$		0			0
$479$	9.51064	+	29.2707i	0.434552	+	1.33741i	0.893545	+	0.448974i	$0.148211\pi$
$479$	9.51064	+	29.2707i	0.434552	+	1.33741i	−0.458992	+	0.888440i	$0.651789\pi$
$480$		0			0
$481$	3.38197	−	10.4086i	0.154204	−	0.474592i
$482$		0			0
$483$	2.94834	−	9.07405i	0.134154	−	0.412884i
$484$	−6.70820	+	4.87380i	−0.304918	+	0.221536i
$485$	−6.70820			−0.304604
$486$		0			0
$487$	−4.33688	+	3.15093i	−0.196523	+	0.142782i	−0.681695	−	0.731636i	$-0.738757\pi$
$487$	−4.33688	+	3.15093i	−0.196523	+	0.142782i	0.485172	+	0.874419i	$0.338757\pi$
$488$		0			0
$489$	−2.92705	−	2.12663i	−0.132366	−	0.0961694i
$490$		0			0
$491$	8.51722	−	6.18812i	0.384377	−	0.279266i	−0.378771	−	0.925491i	$-0.623653\pi$
$491$	8.51722	−	6.18812i	0.384377	−	0.279266i	0.763147	+	0.646225i	$0.223653\pi$
$492$	−0.145898	+	0.449028i	−0.00657759	+	0.0202437i
$493$	3.23607			0.145745
$494$		0			0
$495$	−5.16312	+	15.8904i	−0.232065	+	0.714222i
$496$	11.2361	+	34.5811i	0.504514	+	1.55274i
$497$	−5.86475	−	18.0498i	−0.263070	−	0.809646i
$498$		0			0
$499$	−28.2148			−1.26307			−0.631534	−	0.775349i	$-0.717574\pi$
$499$	−28.2148			−1.26307			−0.631534	+	0.775349i	$0.717574\pi$
$500$	−18.0902	−	13.1433i	−0.809017	−	0.587785i
$501$	−3.90983			−0.174678
$502$		0			0
$503$	11.2812	+	34.7198i	0.503002	+	1.54808i	0.804104	+	0.594488i	$0.202645\pi$
$503$	11.2812	+	34.7198i	0.503002	+	1.54808i	−0.301102	+	0.953592i	$0.597355\pi$
$504$		0			0
$505$	−2.56231	+	7.88597i	−0.114021	+	0.350921i
$506$		0			0
$507$	−4.58359			−0.203564
$508$	3.79837	−	11.6902i	0.168526	−	0.518668i
$509$	−16.3262	+	11.8617i	−0.723648	+	0.525761i	−0.887548	−	0.460716i	$-0.847593\pi$
$509$	−16.3262	+	11.8617i	−0.723648	+	0.525761i	0.163900	+	0.986477i	$0.447593\pi$
$510$		0			0
$511$	19.0623	+	13.8496i	0.843267	+	0.612669i
$512$		0			0
$513$	15.0623	−	10.9434i	0.665017	−	0.483163i
$514$		0			0
$515$	−20.3262			−0.895681
$516$	−4.14590	+	3.01217i	−0.182513	+	0.132603i
$517$	−3.92705	+	12.0862i	−0.172712	+	0.531551i
$518$		0			0
$519$	−0.427051	+	1.31433i	−0.0187455	+	0.0576926i
$520$		0			0
$521$	7.36475	+	22.6664i	0.322655	+	0.993031i	0.972488	+	0.232954i	$0.0748390\pi$
$521$	7.36475	+	22.6664i	0.322655	+	0.993031i	−0.649833	+	0.760077i	$0.725161\pi$
$522$		0			0
$523$	18.6353	+	13.5393i	0.814863	+	0.592032i	0.915236	−	0.402917i	$-0.132004\pi$
$523$	18.6353	+	13.5393i	0.814863	+	0.592032i	−0.100374	+	0.994950i	$0.532004\pi$
$524$	28.3607			1.23894
$525$	−1.77051	+	5.44907i	−0.0772714	+	0.237817i
$526$		0			0
$527$	−23.7984	−	17.2905i	−1.03667	−	0.753187i
$528$	−1.23607	−	3.80423i	−0.0537930	−	0.165558i
$529$	14.3156	+	44.0589i	0.622417	+	1.91560i
$530$		0			0
$531$	6.84752	−	21.0745i	0.297157	−	0.914556i
$532$	49.9574			2.16593
$533$	−0.190983	+	0.587785i	−0.00827239	+	0.0254598i
$534$		0			0
$535$	−1.70820	+	5.25731i	−0.0738521	+	0.227293i
$536$		0			0
$537$	8.00000	−	5.81234i	0.345225	−	0.250821i
$538$		0			0
$539$	4.23607	+	3.07768i	0.182460	+	0.132565i
$540$	8.09017	+	5.87785i	0.348145	+	0.252942i
$541$	−4.66312	+	3.38795i	−0.200483	+	0.145660i	−0.683497	−	0.729953i	$-0.739542\pi$
$541$	−4.66312	+	3.38795i	−0.200483	+	0.145660i	0.483014	+	0.875613i	$0.339542\pi$
$542$		0			0
$543$	3.81966			0.163917
$544$		0			0
$545$	1.44427	+	4.44501i	0.0618658	+	0.190403i
$546$		0			0
$547$	10.4894	+	32.2829i	0.448493	+	1.38032i	0.878608	+	0.477544i	$0.158473\pi$
$547$	10.4894	+	32.2829i	0.448493	+	1.38032i	−0.430115	+	0.902774i	$0.641527\pi$
$548$	2.00000	+	1.45309i	0.0854358	+	0.0620727i
$549$	27.9656			1.19354
$550$		0			0
$551$	8.32624			0.354710
$552$		0			0
$553$	12.9271	+	39.7854i	0.549714	+	1.69185i
$554$		0			0
$555$	−7.56231	+	5.49434i	−0.321002	+	0.233222i
$556$	1.29180	−	3.97574i	0.0547844	−	0.168609i
$557$	−9.43769			−0.399888			−0.199944	−	0.979807i	$-0.564076\pi$
$557$	−9.43769			−0.399888			−0.199944	+	0.979807i	$0.564076\pi$
$558$		0			0
$559$	−5.42705	+	3.94298i	−0.229540	+	0.166770i
$560$	8.29180	+	25.5195i	0.350392	+	1.07840i
$561$	2.61803	+	1.90211i	0.110533	+	0.0803073i
$562$		0			0
$563$	−33.7984	+	24.5560i	−1.42443	+	1.03491i	−0.433412	+	0.901196i	$0.642690\pi$
$563$	−33.7984	+	24.5560i	−1.42443	+	1.03491i	−0.991020	+	0.133714i	$0.957310\pi$
$564$	3.00000	+	2.17963i	0.126323	+	0.0917789i
$565$	4.20820	+	12.9515i	0.177040	+	0.544875i
$566$		0			0
$567$	−7.14590	+	21.9928i	−0.300100	+	0.923611i
$568$		0			0
$569$	2.59017	−	7.97172i	0.108586	−	0.334192i	−0.881970	−	0.471306i	$-0.843783\pi$
$569$	2.59017	−	7.97172i	0.108586	−	0.334192i	0.990555	+	0.137114i	$0.0437827\pi$
$570$		0			0
$571$	−11.3435	−	34.9116i	−0.474709	−	1.46100i	−0.846350	−	0.532627i	$-0.821205\pi$
$571$	−11.3435	−	34.9116i	−0.474709	−	1.46100i	0.371641	−	0.928377i	$-0.378795\pi$
$572$	−1.61803	−	4.97980i	−0.0676534	−	0.208216i
$573$	−8.32624	−	6.04937i	−0.347834	−	0.252716i
$574$		0			0
$575$	−12.8647	−	39.5936i	−0.536497	−	1.65117i
$576$	22.8328			0.951367
$577$	−35.0066	−	25.4338i	−1.45734	−	1.05882i	−0.984045	−	0.177919i	$-0.943063\pi$
$577$	−35.0066	−	25.4338i	−1.45734	−	1.05882i	−0.473298	−	0.880902i	$-0.656937\pi$
$578$		0			0
$579$	−2.39261	−	7.36369i	−0.0994334	−	0.306025i
$580$	1.38197	+	4.25325i	0.0573830	+	0.176607i
$581$	8.34346	−	25.6785i	0.346145	−	1.06532i
$582$		0			0
$583$	7.85410	−	24.1724i	0.325284	−	1.00112i
$584$		0			0
$585$	5.16312	+	3.75123i	0.213469	+	0.155094i
$586$		0			0
$587$	6.76393	−	4.91428i	0.279177	−	0.202834i	−0.439381	−	0.898301i	$-0.644802\pi$
$587$	6.76393	−	4.91428i	0.279177	−	0.202834i	0.718559	+	0.695467i	$0.244802\pi$
$588$	1.23607	−	0.898056i	0.0509746	−	0.0370352i
$589$	−61.2320	−	44.4877i	−2.52302	−	1.83308i
$590$		0			0
$591$	3.79180	−	2.75490i	0.155974	−	0.113321i
$592$	−13.5279	+	41.6345i	−0.555992	+	1.71117i
$593$	24.6738			1.01323			0.506615	−	0.862172i	$-0.330897\pi$
$593$	24.6738			1.01323			0.506615	+	0.862172i	$0.330897\pi$
$594$		0			0
$595$	−17.5623	−	12.7598i	−0.719984	−	0.523099i
$596$	9.12461	+	28.0827i	0.373759	+	1.15031i
$597$	1.28115	+	3.94298i	0.0524341	+	0.161376i
$598$		0			0
$599$	7.90983			0.323187			0.161593	−	0.986857i	$-0.448337\pi$
$599$	7.90983			0.323187			0.161593	+	0.986857i	$0.448337\pi$
$600$		0			0
$601$	38.4164			1.56704			0.783519	−	0.621368i	$-0.213423\pi$
$601$	38.4164			1.56704			0.783519	+	0.621368i	$0.213423\pi$
$602$		0			0
$603$	10.7918	+	33.2137i	0.439476	+	1.35257i
$604$	2.72949	+	8.40051i	0.111061	+	0.341812i
$605$	9.27051			0.376900
$606$		0			0
$607$	−30.0344			−1.21906			−0.609530	−	0.792763i	$-0.708642\pi$
$607$	−30.0344			−1.21906			−0.609530	+	0.792763i	$0.708642\pi$
$608$		0			0
$609$	0.927051	−	0.673542i	0.0375660	−	0.0272933i
$610$		0			0
$611$	3.92705	+	2.85317i	0.158871	+	0.115427i
$612$	−14.9443	+	10.8576i	−0.604086	+	0.438894i
$613$	−20.9721	+	15.2371i	−0.847057	+	0.615423i	−0.924333	−	0.381587i	$-0.875378\pi$
$613$	−20.9721	+	15.2371i	−0.847057	+	0.615423i	0.0772763	+	0.997010i	$0.475378\pi$
$614$		0			0
$615$	0.427051	−	0.310271i	0.0172204	−	0.0125113i
$616$		0			0
$617$	−6.21885	+	19.1396i	−0.250361	+	0.770533i	0.744347	+	0.667793i	$0.232761\pi$
$617$	−6.21885	+	19.1396i	−0.250361	+	0.770533i	−0.994708	+	0.102740i	$0.967239\pi$
$618$		0			0
$619$	3.21885	−	9.90659i	0.129376	−	0.398180i	−0.865297	−	0.501260i	$-0.832870\pi$
$619$	3.21885	−	9.90659i	0.129376	−	0.398180i	0.994673	+	0.103081i	$0.0328700\pi$
$620$	12.5623	−	38.6628i	0.504514	−	1.55274i
$621$	5.75329	+	17.7068i	0.230872	+	0.710550i
$622$		0			0
$623$	10.8541	+	7.88597i	0.434860	+	0.315945i
$624$	−1.52786			−0.0611635
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$	6.73607	+	4.89404i	0.269013	+	0.195449i
$628$	−8.88854	−	27.3561i	−0.354692	−	1.09163i
$629$	−10.9443	−	33.6830i	−0.436377	−	1.34303i
$630$		0			0
$631$	−8.89261	+	27.3686i	−0.354009	+	1.08953i	0.602573	+	0.798064i	$0.294142\pi$
$631$	−8.89261	+	27.3686i	−0.354009	+	1.08953i	−0.956582	+	0.291464i	$0.905858\pi$
$632$		0			0
$633$	0.416408	−	1.28157i	0.0165507	−	0.0509379i
$634$		0			0
$635$	−11.1180	+	8.07772i	−0.441206	+	0.320555i
$636$	−6.00000	−	4.35926i	−0.237915	−	0.172856i
$637$	1.61803	−	1.17557i	0.0641088	−	0.0465778i
$638$		0			0
$639$	14.6074	+	10.6129i	0.577859	+	0.419839i
$640$		0			0
$641$	20.0344	−	14.5559i	0.791313	−	0.574922i	−0.117040	−	0.993127i	$-0.537341\pi$
$641$	20.0344	−	14.5559i	0.791313	−	0.574922i	0.908353	+	0.418205i	$0.137341\pi$
$642$		0			0
$643$	17.2148			0.678885			0.339442	−	0.940627i	$-0.389762\pi$
$643$	17.2148			0.678885			0.339442	+	0.940627i	$0.389762\pi$
$644$	−15.4377	+	47.5123i	−0.608330	+	1.87225i
$645$	5.72949			0.225598
$646$		0			0
$647$	−9.72542	−	29.9318i	−0.382346	−	1.17674i	−0.938387	−	0.345585i	$-0.887680\pi$
$647$	−9.72542	−	29.9318i	−0.382346	−	1.17674i	0.556041	−	0.831155i	$-0.312320\pi$
$648$		0			0
$649$	20.3262			0.797875
$650$		0			0
$651$	−10.4164			−0.408251
$652$	15.3262	+	11.1352i	0.600222	+	0.436087i
$653$	7.01064	+	21.5765i	0.274348	+	0.844355i	0.989391	+	0.145275i	$0.0464068\pi$
$653$	7.01064	+	21.5765i	0.274348	+	0.844355i	−0.715044	+	0.699080i	$0.753593\pi$
$654$		0			0
$655$	−25.6525	−	18.6376i	−1.00233	−	0.728232i
$656$	0.763932	−	2.35114i	0.0298265	−	0.0917966i
$657$	−22.4164			−0.874547
$658$		0			0
$659$	−16.8992	+	12.2780i	−0.658299	+	0.478282i	−0.866088	−	0.499892i	$-0.833373\pi$
$659$	−16.8992	+	12.2780i	−0.658299	+	0.478282i	0.207789	+	0.978174i	$0.433373\pi$
$660$	−1.38197	+	4.25325i	−0.0537930	+	0.165558i
$661$	8.20820	+	5.96361i	0.319262	+	0.231958i	0.735861	−	0.677133i	$-0.236778\pi$
$661$	8.20820	+	5.96361i	0.319262	+	0.231958i	−0.416598	+	0.909091i	$0.636778\pi$
$662$		0			0
$663$	1.00000	−	0.726543i	0.0388368	−	0.0282166i
$664$		0			0
$665$	−45.1869	−	32.8302i	−1.75227	−	1.27310i
$666$		0			0
$667$	−2.57295	+	7.91872i	−0.0996250	+	0.306614i
$668$	20.4721			0.792091
$669$	−1.09424	+	3.36771i	−0.0423056	+	0.130203i
$670$		0			0
$671$	7.92705	+	24.3970i	0.306020	+	0.941834i
$672$		0			0
$673$	2.19098	+	1.59184i	0.0844562	+	0.0613610i	0.629212	−	0.777234i	$-0.283378\pi$
$673$	2.19098	+	1.59184i	0.0844562	+	0.0613610i	−0.544756	+	0.838595i	$0.683378\pi$
$674$		0			0
$675$	−3.45492	−	10.6331i	−0.132980	−	0.409270i
$676$	24.0000			0.923077
$677$	−29.9894	−	21.7885i	−1.15258	−	0.837402i	−0.163762	−	0.986500i	$-0.552363\pi$
$677$	−29.9894	−	21.7885i	−1.15258	−	0.837402i	−0.988822	+	0.149098i	$0.952363\pi$
$678$		0			0
$679$	−2.78115	−	8.55951i	−0.106731	−	0.328484i
$680$		0			0
$681$	2.83282	−	8.71851i	0.108554	−	0.334094i
$682$		0			0
$683$	12.5729	−	38.6956i	0.481091	−	1.48064i	−0.356474	−	0.934305i	$-0.616021\pi$
$683$	12.5729	−	38.6956i	0.481091	−	1.48064i	0.837564	−	0.546339i	$-0.183979\pi$
$684$	−38.4508	+	27.9362i	−1.47020	+	1.06817i
$685$	−0.854102	−	2.62866i	−0.0326336	−	0.100436i
$686$		0			0
$687$	−1.01722	+	0.739054i	−0.0388094	+	0.0281967i
$688$	21.7082	−	15.7719i	0.827618	−	0.601299i
$689$	−7.85410	−	5.70634i	−0.299217	−	0.217394i
$690$		0			0
$691$	−41.0238	+	29.8055i	−1.56062	+	1.13386i	−0.625119	+	0.780530i	$0.714949\pi$
$691$	−41.0238	+	29.8055i	−1.56062	+	1.13386i	−0.935500	+	0.353326i	$0.885051\pi$
$692$	2.23607	−	6.88191i	0.0850026	−	0.261611i
$693$	−22.4164			−0.851529
$694$		0			0
$695$	−3.78115	+	2.74717i	−0.143427	+	0.104206i
$696$		0			0
$697$	0.618034	+	1.90211i	0.0234097	+	0.0720477i
$698$		0			0
$699$	−5.39512			−0.204062
$700$	9.27051	−	28.5317i	0.350392	−	1.07840i
$701$	−12.5066			−0.472367			−0.236183	−	0.971708i	$-0.575897\pi$
$701$	−12.5066			−0.472367			−0.236183	+	0.971708i	$0.575897\pi$
$702$		0			0
$703$	−28.1591	−	86.6647i	−1.06204	−	3.26862i
$704$	6.47214	+	19.9192i	0.243928	+	0.750733i
$705$	−1.28115	−	3.94298i	−0.0482510	−	0.148501i
$706$		0			0
$707$	−11.1246			−0.418384
$708$	1.83282	−	5.64083i	0.0688814	−	0.211995i
$709$	−22.3992	+	16.2740i	−0.841219	+	0.611181i	−0.922711	−	0.385493i	$-0.874032\pi$
$709$	−22.3992	+	16.2740i	−0.841219	+	0.611181i	0.0814918	+	0.996674i	$0.474032\pi$
$710$		0			0
$711$	−32.1976	−	23.3929i	−1.20750	−	0.877302i
$712$		0			0
$713$	61.2320	−	44.4877i	2.29316	−	1.66608i
$714$		0			0
$715$	−1.80902	+	5.56758i	−0.0676534	+	0.208216i
$716$	−41.8885	+	30.4338i	−1.56545	+	1.13736i
$717$	−1.74013	+	5.35558i	−0.0649865	+	0.200008i
$718$		0			0
$719$	−12.4549	+	38.3323i	−0.464490	+	1.42955i	0.395133	+	0.918624i	$0.370699\pi$
$719$	−12.4549	+	38.3323i	−0.464490	+	1.42955i	−0.859623	+	0.510929i	$0.829301\pi$
$720$	−20.6525	−	15.0049i	−0.769672	−	0.559200i
$721$	−8.42705	−	25.9358i	−0.313840	−	0.965900i
$722$		0			0
$723$	−3.05573	−	2.22012i	−0.113644	−	0.0825670i
$724$	−20.0000			−0.743294
$725$	1.54508	−	4.75528i	0.0573830	−	0.176607i
$726$		0			0
$727$	7.18034	+	5.21682i	0.266304	+	0.193481i	0.712922	−	0.701244i	$-0.247372\pi$
$727$	7.18034	+	5.21682i	0.266304	+	0.193481i	−0.446618	+	0.894725i	$0.647372\pi$
$728$		0			0
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$		0			0
$731$	−6.70820	+	20.6457i	−0.248112	+	0.763610i
$732$	7.48529			0.276664
$733$	−8.36475	+	25.7440i	−0.308959	+	0.950878i	0.669211	+	0.743072i	$0.266632\pi$
$733$	−8.36475	+	25.7440i	−0.308959	+	0.950878i	−0.978170	+	0.207806i	$0.933368\pi$
$734$		0			0
$735$	−1.70820			−0.0630081
$736$		0			0
$737$	−25.9164	+	18.8294i	−0.954643	+	0.693589i
$738$		0			0
$739$	13.5172	+	9.82084i	0.497239	+	0.361265i	0.807961	−	0.589235i	$-0.200571\pi$
$739$	13.5172	+	9.82084i	0.497239	+	0.361265i	−0.310722	+	0.950501i	$0.600571\pi$
$740$	39.5967	−	28.7687i	1.45561	−	1.05756i
$741$	2.57295	−	1.86936i	0.0945196	−	0.0686725i
$742$		0			0
$743$	−29.9443			−1.09855			−0.549274	−	0.835642i	$-0.685096\pi$
$743$	−29.9443			−1.09855			−0.549274	+	0.835642i	$0.685096\pi$
$744$		0			0
$745$	10.2016	−	31.3974i	0.373759	−	1.15031i
$746$		0			0
$747$	7.93769	+	24.4297i	0.290425	+	0.893836i
$748$	−13.7082	−	9.95959i	−0.501222	−	0.364159i
$749$	−7.41641			−0.270990
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	−15.7082	−	11.4127i	−0.572819	−	0.416178i
$753$	0.871323	+	2.68166i	0.0317528	+	0.0977250i
$754$		0			0
$755$	3.05166	−	9.39205i	0.111061	−	0.341812i
$756$	−4.14590	+	12.7598i	−0.150785	+	0.464068i
$757$	−32.4721			−1.18022			−0.590110	−	0.807323i	$-0.700916\pi$
$757$	−32.4721			−1.18022			−0.590110	+	0.807323i	$0.700916\pi$
$758$		0			0
$759$	−6.73607	+	4.89404i	−0.244504	+	0.177642i
$760$		0			0
$761$	25.9164	+	18.8294i	0.939469	+	0.682564i	0.948293	−	0.317397i	$-0.102809\pi$
$761$	25.9164	+	18.8294i	0.939469	+	0.682564i	−0.00882375	+	0.999961i	$0.502809\pi$
$762$		0			0
$763$	−5.07295	+	3.68571i	−0.183653	+	0.133432i
$764$	43.5967	+	31.6749i	1.57727	+	1.14596i
$765$	20.6525			0.746692
$766$		0			0
$767$	2.39919	−	7.38394i	0.0866296	−	0.266619i
$768$	6.11146			0.220528
$769$	−5.73607	+	17.6538i	−0.206848	+	0.636612i	0.792785	+	0.609502i	$0.208631\pi$
$769$	−5.73607	+	17.6538i	−0.206848	+	0.636612i	−0.999632	+	0.0271104i	$0.991369\pi$
$770$		0			0
$771$	0.242646	+	0.746787i	0.00873867	+	0.0268949i
$772$	12.5279	+	38.5568i	0.450888	+	1.38769i
$773$	10.0623	+	7.31069i	0.361916	+	0.262947i	0.753851	−	0.657046i	$-0.228194\pi$
$773$	10.0623	+	7.31069i	0.361916	+	0.262947i	−0.391935	+	0.919993i	$0.628194\pi$
$774$		0			0
$775$	−36.7705	+	26.7153i	−1.32084	+	0.959643i
$776$		0			0
$777$	−10.1459	−	7.37143i	−0.363982	−	0.264448i
$778$		0			0
$779$	1.59017	+	4.89404i	0.0569738	+	0.175347i
$780$	1.38197	+	1.00406i	0.0494823	+	0.0359510i
$781$	−5.11803	+	15.7517i	−0.183138	+	0.563640i
$782$		0			0
$783$	−0.690983	+	2.12663i	−0.0246937	+	0.0759994i
$784$	−6.47214	+	4.70228i	−0.231148	+	0.167939i
$785$	−9.93769	+	30.5851i	−0.354692	+	1.09163i
$786$		0			0
$787$	−28.5344	+	20.7315i	−1.01714	+	0.738998i	−0.965695	−	0.259678i	$-0.916384\pi$
$787$	−28.5344	+	20.7315i	−1.01714	+	0.738998i	−0.0514478	+	0.998676i	$0.516384\pi$
$788$	−19.8541	+	14.4248i	−0.707273	+	0.513864i
$789$	4.73607	+	3.44095i	0.168608	+	0.122501i
$790$		0			0
$791$	−14.7812	+	10.7391i	−0.525557	+	0.381840i
$792$		0			0
$793$	9.79837			0.347950
$794$		0			0
$795$	2.56231	+	7.88597i	0.0908756	+	0.279686i
$796$	−6.70820	−	20.6457i	−0.237766	−	0.731768i
$797$	6.29180	+	19.3642i	0.222867	+	0.685914i	0.998501	+	0.0547310i	$0.0174301\pi$
$797$	6.29180	+	19.3642i	0.222867	+	0.685914i	−0.775634	+	0.631183i	$0.782570\pi$
$798$		0			0
$799$	15.7082			0.555716
$800$		0			0
$801$	−12.7639			−0.450991
$802$		0			0
$803$	−6.35410	−	19.5559i	−0.224231	−	0.690113i
$804$	2.88854	+	8.89002i	0.101871	+	0.313527i
$805$	45.1869	−	32.8302i	1.59263	−	1.15711i
$806$		0			0
$807$	5.36881			0.188991
$808$		0			0
$809$	35.3713	−	25.6988i	1.24359	−	0.903521i	0.245757	−	0.969331i	$-0.420963\pi$
$809$	35.3713	−	25.6988i	1.24359	−	0.903521i	0.997832	+	0.0658107i	$0.0209634\pi$
$810$		0			0
$811$	−32.0517	−	23.2869i	−1.12549	−	0.817714i	−0.140454	−	0.990087i	$-0.544856\pi$
$811$	−32.0517	−	23.2869i	−1.12549	−	0.817714i	−0.985032	+	0.172374i	$0.944856\pi$
$812$	−4.85410	+	3.52671i	−0.170346	+	0.123763i
$813$	−7.54508	+	5.48183i	−0.264618	+	0.192256i
$814$		0			0
$815$	−6.54508	−	20.1437i	−0.229264	−	0.705603i
$816$	−4.00000	+	2.90617i	−0.140028	+	0.101736i
$817$	−17.2599	+	53.1204i	−0.603846	+	1.85845i
$818$		0			0
$819$	−2.64590	+	8.14324i	−0.0924552	+	0.284548i
$820$	−2.23607	+	1.62460i	−0.0780869	+	0.0567334i
$821$	3.00000	+	9.23305i	0.104701	+	0.322236i	0.989660	−	0.143433i	$-0.0458140\pi$
$821$	3.00000	+	9.23305i	0.104701	+	0.322236i	−0.884959	+	0.465668i	$0.845814\pi$
$822$		0			0
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	0.895238	−	0.445589i	$-0.147006\pi$
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	−0.147137	+	0.989116i	$0.547006\pi$
$824$		0			0
$825$	4.04508	−	2.93893i	0.140832	−	0.102320i
$826$		0			0
$827$	10.1910	+	7.40418i	0.354375	+	0.257469i	0.750702	−	0.660641i	$-0.229715\pi$
$827$	10.1910	+	7.40418i	0.354375	+	0.257469i	−0.396327	+	0.918109i	$0.629715\pi$
$828$	−14.6869	−	45.2017i	−0.510406	−	1.57087i
$829$	2.55573	+	7.86572i	0.0887641	+	0.273188i	0.985578	−	0.169219i	$-0.0541246\pi$
$829$	2.55573	+	7.86572i	0.0887641	+	0.273188i	−0.896814	+	0.442407i	$0.854125\pi$
$830$		0			0
$831$	0.645898	−	1.98787i	0.0224060	−	0.0689584i
$832$	8.00000			0.277350
$833$	2.00000	−	6.15537i	0.0692959	−	0.213271i
$834$		0			0
$835$	−18.5172	−	13.4535i	−0.640815	−	0.465579i
$836$	−35.2705	−	25.6255i	−1.21986	−	0.886277i
$837$	16.4443	−	11.9475i	0.568397	−	0.412965i
$838$		0			0
$839$	25.7254	+	18.6906i	0.888140	+	0.645272i	0.935392	−	0.353611i	$-0.115046\pi$
$839$	25.7254	+	18.6906i	0.888140	+	0.645272i	−0.0472522	+	0.998883i	$0.515046\pi$
$840$		0			0
$841$	−0.809017	+	0.587785i	−0.0278971	+	0.0202685i
$842$		0			0
$843$	1.97871			0.0681505
$844$	−2.18034	+	6.71040i	−0.0750504	+	0.230981i
$845$	−21.7082	−	15.7719i	−0.746785	−	0.542571i
$846$		0			0
$847$	3.84346	+	11.8290i	0.132063	+	0.406448i
$848$	31.4164	+	22.8254i	1.07884	+	0.783826i
$849$	−5.06888			−0.173964
$850$		0			0
$851$	91.1246			3.12371
$852$	3.90983	+	2.84066i	0.133949	+	0.0973193i
$853$	−11.3435	−	34.9116i	−0.388393	−	1.19535i	−0.933989	−	0.357302i	$-0.883697\pi$
$853$	−11.3435	−	34.9116i	−0.388393	−	1.19535i	0.545596	−	0.838048i	$-0.316303\pi$
$854$		0			0
$855$	53.1378			1.81727
$856$		0			0
$857$	32.3262			1.10424			0.552122	−	0.833764i	$-0.313818\pi$
$857$	32.3262			1.10424			0.552122	+	0.833764i	$0.313818\pi$
$858$		0			0
$859$	10.0451	−	7.29818i	0.342734	−	0.249011i	−0.403081	−	0.915165i	$-0.632061\pi$
$859$	10.0451	−	7.29818i	0.342734	−	0.249011i	0.745814	+	0.666154i	$0.232061\pi$
$860$	−30.0000			−1.02299
$861$	0.572949	+	0.416272i	0.0195261	+	0.0141865i
$862$		0			0
$863$	−10.6353	+	7.72696i	−0.362028	+	0.263029i	−0.753898	−	0.656992i	$-0.771829\pi$
$863$	−10.6353	+	7.72696i	−0.362028	+	0.263029i	0.391869	+	0.920021i	$0.371829\pi$
$864$		0			0
$865$	−6.54508	+	4.75528i	−0.222540	+	0.161684i
$866$		0			0
$867$	−0.770510	+	2.37139i	−0.0261679	+	0.0805365i
$868$	54.5410			1.85124
$869$	11.2812	−	34.7198i	0.382687	−	1.17779i
$870$		0			0
$871$	3.78115	+	11.6372i	0.128119	+	0.394311i
$872$		0			0
$873$	6.92705	+	5.03280i	0.234445	+	0.170334i
$874$		0			0
$875$	−27.1353	+	19.7149i	−0.917339	+	0.666486i
$876$	−6.00000			−0.202721
$877$	−32.3156	−	23.4787i	−1.09122	−	0.792818i	−0.111615	−	0.993751i	$-0.535602\pi$
$877$	−32.3156	−	23.4787i	−1.09122	−	0.792818i	−0.979605	+	0.200934i	$0.935602\pi$
$878$		0			0
$879$	−1.22949	−	3.78398i	−0.0414697	−	0.127631i
$880$	7.23607	−	22.2703i	0.243928	−	0.750733i
$881$	−0.993422	+	3.05744i	−0.0334692	+	0.103008i	−0.966396	−	0.257060i	$-0.917246\pi$
$881$	−0.993422	+	3.05744i	−0.0334692	+	0.103008i	0.932926	+	0.360067i	$0.117246\pi$
$882$		0			0
$883$	4.98278	−	15.3354i	0.167684	−	0.516078i	−0.831540	−	0.555465i	$-0.812540\pi$
$883$	4.98278	−	15.3354i	0.167684	−	0.516078i	0.999224	+	0.0393867i	$0.0125404\pi$
$884$	−5.23607	+	3.80423i	−0.176108	+	0.127950i
$885$	−5.36475	+	3.89772i	−0.180334	+	0.131020i
$886$		0			0
$887$	−10.4271	+	7.57570i	−0.350106	+	0.254367i	−0.748914	−	0.662668i	$-0.769424\pi$
$887$	−10.4271	+	7.57570i	−0.350106	+	0.254367i	0.398807	+	0.917035i	$0.369424\pi$
$888$		0			0
$889$	−14.9164	−	10.8374i	−0.500280	−	0.363475i
$890$		0			0
$891$	16.3262	−	11.8617i	0.546950	−	0.397382i
$892$	5.72949	−	17.6336i	0.191838	−	0.590415i
$893$	40.4164			1.35248
$894$		0			0
$895$	57.8885			1.93500
$896$		0			0
$897$	0.982779	+	3.02468i	0.0328140	+	0.100991i
$898$		0			0
$899$	9.09017			0.303174
$900$	8.81966	+	27.1441i	0.293989	+	0.904804i
$901$	−31.4164			−1.04663
$902$		0			0
$903$	2.37539	+	7.31069i	0.0790480	+	0.243285i
$904$		0			0
$905$	18.0902	+	13.1433i	0.601338	+	0.436897i
$906$		0			0
$907$	19.4377			0.645418			0.322709	−	0.946498i	$-0.395406\pi$
$907$	19.4377			0.645418			0.322709	+	0.946498i	$0.395406\pi$
$908$	−14.8328	+	45.6507i	−0.492244	+	1.51497i
$909$	8.56231	−	6.22088i	0.283994	−	0.206334i
$910$		0			0
$911$	34.4164	+	25.0050i	1.14027	+	0.828452i	0.987156	−	0.159757i	$-0.0510711\pi$
$911$	34.4164	+	25.0050i	1.14027	+	0.828452i	0.153110	+	0.988209i	$0.451071\pi$
$912$	−10.2918	+	7.47743i	−0.340795	+	0.247602i
$913$	−19.0623	+	13.8496i	−0.630870	+	0.458354i
$914$		0			0
$915$	−6.77051	−	4.91906i	−0.223826	−	0.162619i
$916$	5.32624	−	3.86974i	0.175984	−	0.127860i
$917$	13.1459	−	40.4589i	0.434116	−	1.33607i
$918$		0			0
$919$	−11.2361	+	34.5811i	−0.370644	+	1.14072i	0.575727	+	0.817642i	$0.304719\pi$
$919$	−11.2361	+	34.5811i	−0.370644	+	1.14072i	−0.946371	+	0.323082i	$0.895281\pi$
$920$		0			0
$921$	1.29837	+	3.99598i	0.0427829	+	0.131672i
$922$		0			0
$923$	5.11803	+	3.71847i	0.168462	+	0.122395i
$924$	−6.00000			−0.197386
$925$	−54.7214			−1.79923
$926$		0			0
$927$	20.9894	+	15.2497i	0.689381	+	0.500865i
$928$		0			0
$929$	9.91641	+	30.5196i	0.325347	+	1.00131i	0.971284	+	0.237924i	$0.0764668\pi$
$929$	9.91641	+	30.5196i	0.325347	+	1.00131i	−0.645937	+	0.763391i	$0.723533\pi$
$930$		0			0
$931$	5.14590	−	15.8374i	0.168650	−	0.519051i
$932$	28.2492			0.925334
$933$	−0.594235	+	1.82887i	−0.0194544	+	0.0598745i
$934$		0			0
$935$	5.85410	+	18.0171i	0.191450	+	0.589221i
$936$		0			0
$937$	40.7705	−	29.6215i	1.33191	−	0.967693i	0.332214	−	0.943204i	$-0.392204\pi$
$937$	40.7705	−	29.6215i	1.33191	−	0.967693i	0.999700	−	0.0244886i	$-0.00779575\pi$
$938$		0			0
$939$	9.70820	+	7.05342i	0.316815	+	0.230180i
$940$	6.70820	+	20.6457i	0.218797	+	0.673389i
$941$	7.23607	−	5.25731i	0.235889	−	0.171383i	−0.463561	−	0.886065i	$-0.653428\pi$
$941$	7.23607	−	5.25731i	0.235889	−	0.171383i	0.699450	+	0.714682i	$0.253428\pi$
$942$		0			0
$943$	−5.14590			−0.167573
$944$	−9.59675	+	29.5358i	−0.312348	+	0.961307i
$945$	12.1353	−	8.81678i	0.394760	−	0.286810i
$946$		0			0
$947$	10.0279	+	30.8626i	0.325862	+	1.00290i	0.971050	+	0.238876i	$0.0767789\pi$
$947$	10.0279	+	30.8626i	0.325862	+	1.00290i	−0.645188	+	0.764024i	$0.723221\pi$
$948$	−8.61803	−	6.26137i	−0.279901	−	0.203360i
$949$	−7.85410			−0.254955
$950$		0			0
$951$	9.68692			0.314120
$952$		0			0
$953$	−6.25329	−	19.2456i	−0.202564	−	0.623428i	−0.999805	−	0.0197661i	$-0.993708\pi$
$953$	−6.25329	−	19.2456i	−0.202564	−	0.623428i	0.797241	−	0.603662i	$-0.206292\pi$
$954$		0			0
$955$	−18.6180	−	57.3004i	−0.602465	−	1.85420i
$956$	9.11146	−	28.0422i	0.294686	−	0.906949i
$957$	−1.00000			−0.0323254
$958$		0			0
$959$	3.00000	−	2.17963i	0.0968751	−	0.0703838i
$960$	−5.52786	−	4.01623i	−0.178411	−	0.129623i
$961$	−41.7705	−	30.3481i	−1.34744	−	0.978969i
$962$		0			0
$963$	5.70820	−	4.14725i	0.183944	−	0.133643i
$964$	16.0000	+	11.6247i	0.515325	+	0.374406i
$965$	14.0066	−	43.1078i	0.450888	−	1.38769i
$966$		0			0
$967$	−12.4656	+	38.3650i	−0.400865	+	1.23374i	0.523433	+	0.852067i	$0.324651\pi$
$967$	−12.4656	+	38.3650i	−0.400865	+	1.23374i	−0.924299	+	0.381670i	$0.875349\pi$
$968$		0			0
$969$	3.18034	−	9.78808i	0.102167	−	0.314438i
$970$		0			0
$971$	12.8607	+	39.5811i	0.412719	+	1.27022i	0.914275	+	0.405093i	$0.132761\pi$
$971$	12.8607	+	39.5811i	0.412719	+	1.27022i	−0.501557	+	0.865125i	$0.667239\pi$
$972$	−5.96556	−	18.3601i	−0.191345	−	0.588900i
$973$	−5.07295	−	3.68571i	−0.162631	−	0.118159i
$974$		0			0
$975$	−0.590170	−	1.81636i	−0.0189006	−	0.0581700i
$976$	−39.1935			−1.25455
$977$	−14.9443	−	10.8576i	−0.478110	−	0.347367i	0.322484	−	0.946575i	$-0.395482\pi$
$977$	−14.9443	−	10.8576i	−0.478110	−	0.347367i	−0.800593	+	0.599208i	$0.795482\pi$
$978$		0			0
$979$	−3.61803	−	11.1352i	−0.115633	−	0.355881i
$980$	8.94427			0.285714
$981$	1.84346	−	5.67358i	0.0588571	−	0.181144i
$982$		0			0
$983$	−3.08359	+	9.49032i	−0.0983513	+	0.302694i	−0.988113	−	0.153732i	$-0.950871\pi$
$983$	−3.08359	+	9.49032i	−0.0983513	+	0.302694i	0.889761	+	0.456426i	$0.150871\pi$
$984$		0			0
$985$	27.4377			0.874238
$986$		0			0
$987$	4.50000	−	3.26944i	0.143237	−	0.104067i
$988$	−13.4721	+	9.78808i	−0.428606	+	0.311400i
$989$	−45.1869	−	32.8302i	−1.43686	−	1.04394i
$990$		0			0
$991$	24.3713	−	17.7068i	0.774181	−	0.562475i	−0.129046	−	0.991639i	$-0.541192\pi$
$991$	24.3713	−	17.7068i	0.774181	−	0.562475i	0.903227	+	0.429163i	$0.141192\pi$
$992$		0			0
$993$	7.31308			0.232074
$994$		0			0
$995$	−7.50000	+	23.0826i	−0.237766	+	0.731768i
$996$	2.12461	+	6.53888i	0.0673209	+	0.207192i
$997$	0.263932	+	0.812299i	0.00835881	+	0.0257258i	0.955149	−	0.296126i	$-0.0956948\pi$
$997$	0.263932	+	0.812299i	0.00835881	+	0.0257258i	−0.946790	+	0.321852i	$0.895695\pi$
$998$		0			0
$999$	24.4721			0.774264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.k.a.291.1	✓	4
25.11	even	5	inner	725.2.k.a.436.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.k.a.291.1	✓	4	1.1	even	1	trivial
725.2.k.a.436.1	yes	4	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.118034 + 0.363271i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-0.690983 + 2.12663i) q^{5} -3.00000 q^{7} +(2.30902 - 1.67760i) q^{9} +(2.11803 + 1.53884i) q^{11} +(0.618034 - 0.449028i) q^{12} +(0.809017 - 0.587785i) q^{13} -0.854102 q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.00000 - 3.07768i) q^{17} +(2.57295 - 7.91872i) q^{19} +4.47214 q^{20} +(-0.354102 - 1.08981i) q^{21} +(6.73607 + 4.89404i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.80902 + 1.31433i) q^{27} +(1.85410 + 5.70634i) q^{28} +(0.309017 + 0.951057i) q^{29} +(2.80902 - 8.64527i) q^{31} +(-0.309017 + 0.951057i) q^{33} +(2.07295 - 6.37988i) q^{35} +(-4.61803 - 3.35520i) q^{36} +(8.85410 - 6.43288i) q^{37} +(0.309017 + 0.224514i) q^{39} +(-0.500000 + 0.363271i) q^{41} -6.70820 q^{43} +(1.61803 - 4.97980i) q^{44} +(1.97214 + 6.06961i) q^{45} +(1.50000 + 4.61653i) q^{47} +(-1.23607 - 0.898056i) q^{48} +2.00000 q^{49} +1.23607 q^{51} +(-1.61803 - 1.17557i) q^{52} +(-3.00000 - 9.23305i) q^{53} +(-4.73607 + 3.44095i) q^{55} +3.18034 q^{57} +(6.28115 - 4.56352i) q^{59} +(0.527864 + 1.62460i) q^{60} +(7.92705 + 5.75934i) q^{61} +(-6.92705 + 5.03280i) q^{63} +(6.47214 + 4.70228i) q^{64} +(0.690983 + 2.12663i) q^{65} +(-3.78115 + 11.6372i) q^{67} -6.47214 q^{68} +(-0.982779 + 3.02468i) q^{69} +(1.95492 + 6.01661i) q^{71} +(-6.35410 - 4.61653i) q^{73} +(0.590170 - 1.81636i) q^{75} -16.6525 q^{76} +(-6.35410 - 4.61653i) q^{77} +(-4.30902 - 13.2618i) q^{79} +(-2.76393 - 8.50651i) q^{80} +(2.38197 - 7.33094i) q^{81} +(-2.78115 + 8.55951i) q^{83} +(-1.85410 + 1.34708i) q^{84} +(5.85410 + 4.25325i) q^{85} +(-0.309017 + 0.224514i) q^{87} +(-3.61803 - 2.62866i) q^{89} +(-2.42705 + 1.76336i) q^{91} +(5.14590 - 15.8374i) q^{92} +3.47214 q^{93} +(15.0623 + 10.9434i) q^{95} +(0.927051 + 2.85317i) q^{97} +7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 2 q^{4} - 5 q^{5} - 12 q^{7} + 7 q^{9} + 4 q^{11} - 2 q^{12} + q^{13} + 10 q^{15} - 4 q^{16} + 4 q^{17} + 17 q^{19} + 12 q^{21} + 18 q^{23} - 5 q^{25} + 5 q^{27} - 6 q^{28} - q^{29} + 9 q^{31}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 2 * q^4 - 5 * q^5 - 12 * q^7 + 7 * q^9 + 4 * q^11 - 2 * q^12 + q^13 + 10 * q^15 - 4 * q^16 + 4 * q^17 + 17 * q^19 + 12 * q^21 + 18 * q^23 - 5 * q^25 + 5 * q^27 - 6 * q^28 - q^29 + 9 * q^31 + q^33 + 15 * q^35 - 14 * q^36 + 22 * q^37 - q^39 - 2 * q^41 + 2 * q^44 - 10 * q^45 + 6 * q^47 + 4 * q^48 + 8 * q^49 - 4 * q^51 - 2 * q^52 - 12 * q^53 - 10 * q^55 - 32 * q^57 + 5 * q^59 + 20 * q^60 + 25 * q^61 - 21 * q^63 + 8 * q^64 + 5 * q^65 + 5 * q^67 - 8 * q^68 - 33 * q^69 + 19 * q^71 - 12 * q^73 - 20 * q^75 - 4 * q^76 - 12 * q^77 - 15 * q^79 - 20 * q^80 + 14 * q^81 + 9 * q^83 + 6 * q^84 + 10 * q^85 + q^87 - 10 * q^89 - 3 * q^91 + 34 * q^92 - 4 * q^93 + 20 * q^95 - 3 * q^97 + 12 * q^99

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