LMFDB - Embedded newform 825.2.n.k.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.k.526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +(2.96813 + 1.47994i) q^{11} -4.03138 q^{12} +(0.0967635 + 0.297808i) q^{13} +(-6.53048 - 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(1.98685 - 1.44353i) q^{18} +(6.03048 + 4.38140i) q^{19} +3.28684 q^{21} +(1.20413 - 8.05576i) q^{22} -1.07392 q^{23} +(1.54164 + 4.74467i) q^{24} +(0.622150 - 0.452019i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.09463 + 12.6020i) q^{28} +(4.07459 - 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680 q^{32} +(1.53138 + 2.94192i) q^{33} +12.2794 q^{34} +(-3.26145 - 2.36959i) q^{36} +(2.13118 - 1.54839i) q^{37} +(5.65698 - 17.4104i) q^{38} +(-0.0967635 + 0.297808i) q^{39} +(-8.77557 - 6.37583i) q^{41} +(-2.49442 - 7.67703i) q^{42} +5.51468 q^{43} +(-13.1873 + 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(-9.70674 - 7.05236i) q^{47} +(3.38919 - 2.46239i) q^{48} +(1.17529 - 3.61718i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(-1.02127 - 0.741996i) q^{52} +(-1.52513 - 4.69387i) q^{53} +2.45589 q^{54} +16.3975 q^{56} +(2.30344 + 7.08925i) q^{57} +(-10.0067 - 7.27031i) q^{58} +(7.41391 - 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(6.85264 - 4.97873i) q^{62} +(2.65911 + 1.93196i) q^{63} +(-2.35333 - 7.24280i) q^{64} +(5.70922 - 5.80948i) q^{66} +15.2739 q^{67} +(-6.22882 - 19.1704i) q^{68} +(-0.868820 - 0.631235i) q^{69} +(0.949335 - 2.92175i) q^{71} +(-1.54164 + 4.74467i) q^{72} +(-7.00018 + 5.08592i) q^{73} +(-5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 - 1.79898i) q^{77} +0.769020 q^{78} +(1.67316 + 5.14946i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-8.23206 + 25.3357i) q^{82} +(-5.02011 + 15.4503i) q^{83} +(-10.7199 + 7.78845i) q^{84} +(-4.18515 - 12.8806i) q^{86} +5.03647 q^{87} +(7.63981 + 14.6768i) q^{88} +1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(3.50254 - 2.54475i) q^{92} +(-1.06580 + 3.28018i) q^{93} +(-9.10556 + 28.0240i) q^{94} +(-0.251345 - 0.182613i) q^{96} +(-0.0692451 - 0.213115i) q^{97} -9.34054 q^{98} +(-0.490303 + 3.28018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.758911	−	2.33569i	−0.536631	−	1.65158i	−0.740098	−	0.672499i	$-0.765221\pi$
$2$	−0.758911	−	2.33569i	−0.536631	−	1.65158i	0.203468	−	0.979082i	$-0.434779\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−3.26145	+	2.36959i	−1.63073	+	1.18479i
$5$		0			0
$5$		0			0
$6$	0.758911	−	2.33569i	0.309824	−	0.953540i
$7$	2.65911	−	1.93196i	1.00505	−	0.730211i	0.0418845	−	0.999122i	$-0.486664\pi$
$7$	2.65911	−	1.93196i	1.00505	−	0.730211i	0.963165	+	0.268911i	$0.0866639\pi$
$8$	4.03606	+	2.93237i	1.42696	+	1.03675i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	2.96813	+	1.47994i	0.894924	+	0.446218i
$11$	2.96813	+	1.47994i	0.894924	+	0.446218i
$12$	−4.03138			−1.16376
$13$	0.0967635	+	0.297808i	0.0268374	+	0.0825970i	0.963578	−	0.267427i	$-0.0861734\pi$
$13$	0.0967635	+	0.297808i	0.0268374	+	0.0825970i	−0.936741	+	0.350024i	$0.886173\pi$
$14$	−6.53048	−	4.74467i	−1.74534	−	1.26807i
$15$		0			0
$16$	1.29455	−	3.98423i	0.323638	−	0.996057i
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	0.568917	+	0.822395i	$0.307363\pi$
$17$	−1.54508	+	4.75528i	−0.374738	+	1.15333i	−0.943655	+	0.330930i	$0.892637\pi$
$18$	1.98685	−	1.44353i	0.468306	−	0.340244i
$19$	6.03048	+	4.38140i	1.38349	+	1.00516i	0.996545	+	0.0830568i	$0.0264683\pi$
$19$	6.03048	+	4.38140i	1.38349	+	1.00516i	0.386941	+	0.922104i	$0.373532\pi$
$20$		0			0
$21$	3.28684			0.717248
$22$	1.20413	−	8.05576i	0.256721	−	1.71749i
$23$	−1.07392			−0.223928			−0.111964	−	0.993712i	$-0.535714\pi$
$23$	−1.07392			−0.223928			−0.111964	+	0.993712i	$0.535714\pi$
$24$	1.54164	+	4.74467i	0.314685	+	0.968501i
$25$		0			0
$26$	0.622150	−	0.452019i	0.122014	−	0.0886482i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−4.09463	+	12.6020i	−0.773813	+	2.38155i
$29$	4.07459	−	2.96036i	0.756632	−	0.549725i	−0.141243	−	0.989975i	$-0.545110\pi$
$29$	4.07459	−	2.96036i	0.756632	−	0.549725i	0.897875	+	0.440250i	$0.145110\pi$
$30$		0			0
$31$	1.06580	+	3.28018i	0.191423	+	0.589138i	1.00000		0.000748050i	$0.000238112\pi$
$31$	1.06580	+	3.28018i	0.191423	+	0.589138i	−0.808577	+	0.588390i	$0.799762\pi$
$32$	−0.310680			−0.0549210
$33$	1.53138	+	2.94192i	0.266579	+	0.512122i
$34$	12.2794			2.10591
$35$		0			0
$36$	−3.26145	−	2.36959i	−0.543576	−	0.394931i
$37$	2.13118	−	1.54839i	0.350364	−	0.254554i	−0.398658	−	0.917100i	$-0.630524\pi$
$37$	2.13118	−	1.54839i	0.350364	−	0.254554i	0.749022	+	0.662546i	$0.230524\pi$
$38$	5.65698	−	17.4104i	0.917683	−	2.82434i
$39$	−0.0967635	+	0.297808i	−0.0154946	+	0.0476874i
$40$		0			0
$41$	−8.77557	−	6.37583i	−1.37051	−	0.995737i	−0.997697	−	0.0678321i	$-0.978392\pi$
$41$	−8.77557	−	6.37583i	−1.37051	−	0.995737i	−0.372817	−	0.927905i	$-0.621608\pi$
$42$	−2.49442	−	7.67703i	−0.384897	−	1.18459i
$43$	5.51468			0.840980			0.420490	−	0.907297i	$-0.361858\pi$
$43$	5.51468			0.840980			0.420490	+	0.907297i	$0.361858\pi$
$44$	−13.1873	+	2.20648i	−1.98805	+	0.332640i
$45$		0			0
$46$	0.815010	+	2.50834i	0.120167	+	0.369835i
$47$	−9.70674	−	7.05236i	−1.41587	−	1.02869i	−0.992435	−	0.122767i	$-0.960823\pi$
$47$	−9.70674	−	7.05236i	−1.41587	−	1.02869i	−0.423438	−	0.905925i	$-0.639177\pi$
$48$	3.38919	−	2.46239i	0.489187	−	0.355415i
$49$	1.17529	−	3.61718i	0.167899	−	0.516740i
$50$		0			0
$51$	−4.04508	+	2.93893i	−0.566425	+	0.411532i
$52$	−1.02127	−	0.741996i	−0.141625	−	0.102896i
$53$	−1.52513	−	4.69387i	−0.209493	−	0.644753i	−0.999499	−	0.0316539i	$-0.989923\pi$
$53$	−1.52513	−	4.69387i	−0.209493	−	0.644753i	0.790006	−	0.613099i	$-0.210077\pi$
$54$	2.45589			0.334204
$55$		0			0
$56$	16.3975			2.19121
$57$	2.30344	+	7.08925i	0.305098	+	0.938994i
$58$	−10.0067	−	7.27031i	−1.31395	−	0.954639i
$59$	7.41391	−	5.38652i	0.965208	−	0.701265i	0.0108537	−	0.999941i	$-0.496545\pi$
$59$	7.41391	−	5.38652i	0.965208	−	0.701265i	0.954354	+	0.298676i	$0.0965451\pi$
$60$		0			0
$61$	2.83811	−	8.73480i	0.363382	−	1.11838i	−0.587605	−	0.809148i	$-0.699929\pi$
$61$	2.83811	−	8.73480i	0.363382	−	1.11838i	0.950988	−	0.309229i	$-0.100071\pi$
$62$	6.85264	−	4.97873i	0.870286	−	0.632300i
$63$	2.65911	+	1.93196i	0.335016	+	0.243404i
$64$	−2.35333	−	7.24280i	−0.294166	−	0.905350i
$65$		0			0
$66$	5.70922	−	5.80948i	0.702756	−	0.715097i
$67$	15.2739			1.86600			0.933000	−	0.359876i	$-0.117181\pi$
$67$	15.2739			1.86600			0.933000	+	0.359876i	$0.117181\pi$
$68$	−6.22882	−	19.1704i	−0.755356	−	2.32475i
$69$	−0.868820	−	0.631235i	−0.104594	−	0.0759917i
$70$		0			0
$71$	0.949335	−	2.92175i	0.112665	−	0.346748i	−0.878788	−	0.477213i	$-0.841647\pi$
$71$	0.949335	−	2.92175i	0.112665	−	0.346748i	0.991453	+	0.130465i	$0.0416470\pi$
$72$	−1.54164	+	4.74467i	−0.181684	+	0.559164i
$73$	−7.00018	+	5.08592i	−0.819309	+	0.595262i	−0.916514	−	0.400002i	$-0.869009\pi$
$73$	−7.00018	+	5.08592i	−0.819309	+	0.595262i	0.0972058	+	0.995264i	$0.469009\pi$
$74$	−5.23394	−	3.80268i	−0.608433	−	0.442052i
$75$		0			0
$76$	−30.0502			−3.44700
$77$	10.7518	−	1.79898i	1.22528	−	0.205012i
$78$	0.769020			0.0870744
$79$	1.67316	+	5.14946i	0.188245	+	0.579360i	0.999989	−	0.00465401i	$-0.00148142\pi$
$79$	1.67316	+	5.14946i	0.188245	+	0.579360i	−0.811744	+	0.584014i	$0.801481\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−8.23206	+	25.3357i	−0.909079	+	2.79786i
$83$	−5.02011	+	15.4503i	−0.551029	+	1.69589i	0.155178	+	0.987887i	$0.450405\pi$
$83$	−5.02011	+	15.4503i	−0.551029	+	1.69589i	−0.706207	+	0.708006i	$0.749595\pi$
$84$	−10.7199	+	7.78845i	−1.16964	+	0.849790i
$85$		0			0
$86$	−4.18515	−	12.8806i	−0.451296	−	1.38895i
$87$	5.03647			0.539966
$88$	7.63981	+	14.6768i	0.814406	+	1.56455i
$89$	1.62118			0.171845			0.0859223	−	0.996302i	$-0.472616\pi$
$89$	1.62118			0.171845			0.0859223	+	0.996302i	$0.472616\pi$
$90$		0			0
$91$	0.832656	+	0.604960i	0.0872861	+	0.0634171i
$92$	3.50254	−	2.54475i	0.365165	−	0.265308i
$93$	−1.06580	+	3.28018i	−0.110518	+	0.340139i
$94$	−9.10556	+	28.0240i	−0.939166	+	2.89046i
$95$		0			0
$96$	−0.251345	−	0.182613i	−0.0256528	−	0.0186379i
$97$	−0.0692451	−	0.213115i	−0.00703078	−	0.0216385i	0.947480	−	0.319816i	$-0.103621\pi$
$97$	−0.0692451	−	0.213115i	−0.00703078	−	0.0216385i	−0.954510	+	0.298178i	$0.903621\pi$
$98$	−9.34054			−0.943537
$99$	−0.490303	+	3.28018i	−0.0492773	+	0.329671i
$100$		0			0
$101$	−0.156154	−	0.480593i	−0.0155379	−	0.0478208i	0.942987	−	0.332830i	$-0.108003\pi$
$101$	−0.156154	−	0.480593i	−0.0155379	−	0.0478208i	−0.958525	+	0.285009i	$0.908003\pi$
$102$	9.93427	+	7.21767i	0.983639	+	0.714656i
$103$	−5.17930	+	3.76298i	−0.510332	+	0.370778i	−0.812949	−	0.582334i	$-0.802139\pi$
$103$	−5.17930	+	3.76298i	−0.510332	+	0.370778i	0.302618	+	0.953112i	$0.402139\pi$
$104$	−0.482738	+	1.48571i	−0.0473363	+	0.145686i
$105$		0			0
$106$	−9.80598	+	7.12446i	−0.952441	+	0.691989i
$107$	1.69286	+	1.22993i	0.163655	+	0.118902i	0.666598	−	0.745417i	$-0.267750\pi$
$107$	1.69286	+	1.22993i	0.163655	+	0.118902i	−0.502943	+	0.864319i	$0.667750\pi$
$108$	−1.24576	−	3.83407i	−0.119874	−	0.368934i
$109$	−6.69278			−0.641052			−0.320526	−	0.947240i	$-0.603860\pi$
$109$	−6.69278			−0.641052			−0.320526	+	0.947240i	$0.603860\pi$
$110$		0			0
$111$	2.63428			0.250035
$112$	−4.25499	−	13.0955i	−0.402059	−	1.23741i
$113$	−8.73262	−	6.34462i	−0.821496	−	0.596852i	0.0956448	−	0.995416i	$-0.469509\pi$
$113$	−8.73262	−	6.34462i	−0.821496	−	0.596852i	−0.917141	+	0.398564i	$0.869509\pi$
$114$	14.8102	−	10.7602i	1.38710	−	1.00779i
$115$		0			0
$116$	−6.27426	+	19.3102i	−0.582550	+	1.79290i
$117$	−0.253330	+	0.184055i	−0.0234204	+	0.0170159i
$118$	−18.2077	−	13.2287i	−1.67616	−	1.21780i
$119$	5.07845	+	15.6299i	0.465541	+	1.43279i
$120$		0			0
$121$	6.61956	+	8.78529i	0.601779	+	0.798663i
$122$	−22.5556			−2.04209
$123$	−3.35197	−	10.3163i	−0.302237	−	0.930190i
$124$	−11.2487	−	8.17267i	−1.01017	−	0.733928i
$125$		0			0
$126$	2.49442	−	7.67703i	0.222221	−	0.683925i
$127$	5.25430	−	16.1711i	0.466244	−	1.43495i	−0.391167	−	0.920320i	$-0.627929\pi$
$127$	5.25430	−	16.1711i	0.466244	−	1.43495i	0.857411	−	0.514632i	$-0.172071\pi$
$128$	−15.6336	+	11.3585i	−1.38183	+	1.00396i
$129$	4.46147	+	3.24145i	0.392810	+	0.285393i
$130$		0			0
$131$	−0.0430508			−0.00376136			−0.00188068	−	0.999998i	$-0.500599\pi$
$131$	−0.0430508			−0.00376136			−0.00188068	+	0.999998i	$0.500599\pi$
$132$	−11.9657	−	5.96619i	−1.04148	−	0.519291i
$133$	24.5004			2.12445
$134$	−11.5915	−	35.6750i	−1.00135	−	3.08185i
$135$		0			0
$136$	−20.1803	+	14.6618i	−1.73044	+	1.25724i
$137$	−2.27516	+	7.00222i	−0.194380	+	0.598240i	0.805603	+	0.592455i	$0.201841\pi$
$137$	−2.27516	+	7.00222i	−0.194380	+	0.598240i	−0.999983	+	0.00578480i	$0.998159\pi$
$138$	−0.815010	+	2.50834i	−0.0693783	+	0.213524i
$139$	−10.7109	+	7.78189i	−0.908483	+	0.660052i	−0.940631	−	0.339432i	$-0.889765\pi$
$139$	−10.7109	+	7.78189i	−0.908483	+	0.660052i	0.0321478	+	0.999483i	$0.489765\pi$
$140$		0			0
$141$	−3.70764	−	11.4110i	−0.312240	−	0.960976i
$142$	−7.54476			−0.633142
$143$	−0.153530	+	1.02713i	−0.0128388	+	0.0858933i
$144$	4.18926			0.349105
$145$		0			0
$146$	17.1916	+	12.4905i	1.42279	+	1.03372i
$147$	3.07696	−	2.23554i	0.253783	−	0.184384i
$148$	−3.28170	+	10.1000i	−0.269754	+	0.830217i
$149$	−1.81658	+	5.59087i	−0.148820	+	0.458022i	−0.997482	−	0.0709136i	$-0.977409\pi$
$149$	−1.81658	+	5.59087i	−0.148820	+	0.458022i	0.848662	+	0.528935i	$0.177409\pi$
$150$		0			0
$151$	−6.17135	−	4.48375i	−0.502217	−	0.364882i	0.307646	−	0.951501i	$-0.400459\pi$
$151$	−6.17135	−	4.48375i	−0.502217	−	0.364882i	−0.809863	+	0.586619i	$0.800459\pi$
$152$	11.4915	+	35.3671i	0.932082	+	2.86865i
$153$	−5.00000			−0.404226
$154$	−12.3615	−	23.7475i	−0.996116	−	1.91363i
$155$		0			0
$156$	−0.390091	−	1.20058i	−0.0312322	−	0.0961230i
$157$	−8.19795	−	5.95616i	−0.654267	−	0.475353i	0.210455	−	0.977604i	$-0.432506\pi$
$157$	−8.19795	−	5.95616i	−0.654267	−	0.475353i	−0.864722	+	0.502250i	$0.832506\pi$
$158$	10.7578	−	7.81596i	0.855841	−	0.621805i
$159$	1.52513	−	4.69387i	0.120951	−	0.372248i
$160$		0			0
$161$	−2.85567	+	2.07477i	−0.225059	+	0.163515i
$162$	1.98685	+	1.44353i	0.156102	+	0.113415i
$163$	1.55407	+	4.78292i	0.121724	+	0.374627i	0.993290	−	0.115651i	$-0.0368953\pi$
$163$	1.55407	+	4.78292i	0.121724	+	0.374627i	−0.871566	+	0.490278i	$0.836895\pi$
$164$	43.7292			3.41468
$165$		0			0
$166$	39.8969			3.09660
$167$	−1.78953	−	5.50761i	−0.138478	−	0.426192i	0.857637	−	0.514256i	$-0.171932\pi$
$167$	−1.78953	−	5.50761i	−0.138478	−	0.426192i	−0.996115	+	0.0880642i	$0.971932\pi$
$168$	13.2659	+	9.63822i	1.02348	+	0.743605i
$169$	10.4379	−	7.58357i	0.802915	−	0.583352i
$170$		0			0
$171$	−2.30344	+	7.08925i	−0.176148	+	0.542128i
$172$	−17.9859	+	13.0675i	−1.37141	+	0.996387i
$173$	12.9970	+	9.44290i	0.988146	+	0.717930i	0.959514	−	0.281660i	$-0.0908850\pi$
$173$	12.9970	+	9.44290i	0.988146	+	0.717930i	0.0286316	+	0.999590i	$0.490885\pi$
$174$	−3.82223	−	11.7636i	−0.289762	−	0.891797i
$175$		0			0
$176$	9.73881	−	9.90983i	0.734090	−	0.746982i
$177$	9.16409			0.688815
$178$	−1.23033	−	3.78657i	−0.0922171	−	0.283815i
$179$	6.71734	+	4.88043i	0.502078	+	0.364781i	0.809810	−	0.586692i	$-0.199570\pi$
$179$	6.71734	+	4.88043i	0.502078	+	0.364781i	−0.307732	+	0.951473i	$0.599570\pi$
$180$		0			0
$181$	−1.99756	+	6.14787i	−0.148478	+	0.456968i	−0.997442	−	0.0714830i	$-0.977227\pi$
$181$	−1.99756	+	6.14787i	−0.148478	+	0.456968i	0.848964	+	0.528451i	$0.177227\pi$
$182$	0.781086	−	2.40394i	0.0578980	−	0.178192i
$183$	7.43026	−	5.39840i	0.549261	−	0.399061i
$184$	−4.33440	−	3.14913i	−0.319536	−	0.232157i
$185$		0			0
$186$	8.47033			0.621074
$187$	−11.6235	+	11.8277i	−0.849997	+	0.864924i
$188$	48.3693			3.52769
$189$	1.01569	+	3.12597i	0.0738806	+	0.227381i
$190$		0			0
$191$	−12.4340	+	9.03384i	−0.899694	+	0.653666i	−0.938387	−	0.345585i	$-0.887680\pi$
$191$	−12.4340	+	9.03384i	−0.899694	+	0.653666i	0.0386935	+	0.999251i	$0.487680\pi$
$192$	2.35333	−	7.24280i	0.169837	−	0.522704i
$193$	−4.86757	+	14.9808i	−0.350375	+	1.07834i	0.608267	+	0.793732i	$0.291865\pi$
$193$	−4.86757	+	14.9808i	−0.350375	+	1.07834i	−0.958643	+	0.284612i	$0.908135\pi$
$194$	−0.445218	+	0.323470i	−0.0319648	+	0.0232238i
$195$		0			0
$196$	4.73805	+	14.5822i	0.338432	+	1.04159i
$197$	−16.3940			−1.16802			−0.584010	−	0.811746i	$-0.698517\pi$
$197$	−16.3940			−1.16802			−0.584010	+	0.811746i	$0.698517\pi$
$198$	8.03358	−	1.34417i	0.570922	−	0.0955261i
$199$	6.96500			0.493736			0.246868	−	0.969049i	$-0.420599\pi$
$199$	6.96500			0.493736			0.246868	+	0.969049i	$0.420599\pi$
$200$		0			0
$201$	12.3568	+	8.97776i	0.871583	+	0.633242i
$202$	−1.00401	+	0.729455i	−0.0706418	+	0.0513242i
$203$	5.11549	−	15.7439i	0.359037	−	1.10500i
$204$	6.22882	−	19.1704i	0.436105	−	1.34219i
$205$		0			0
$206$	12.7198	+	9.24146i	0.886229	+	0.643883i
$207$	−0.331860	−	1.02136i	−0.0230658	−	0.0709894i
$208$	1.31180			0.0909569
$209$	11.4150	+	21.9293i	0.789594	+	1.51688i
$210$		0			0
$211$	−6.16585	−	18.9765i	−0.424475	−	1.30640i	−0.903496	−	0.428596i	$-0.859008\pi$
$211$	−6.16585	−	18.9765i	−0.424475	−	1.30640i	0.479022	−	0.877803i	$-0.340992\pi$
$212$	16.0967	+	11.6949i	1.10552	+	0.803211i
$213$	2.48539	−	1.80574i	0.170296	−	0.123727i
$214$	1.58801	−	4.88740i	0.108554	−	0.334096i
$215$		0			0
$216$	−4.03606	+	2.93237i	−0.274619	+	0.199522i
$217$	9.17124	+	6.66330i	0.622585	+	0.452334i
$218$	5.07922	+	15.6322i	0.344008	+	1.05875i
$219$	−8.65269			−0.584695
$220$		0			0
$221$	−1.56567			−0.105318
$222$	−1.99919	−	6.15286i	−0.134177	−	0.412953i
$223$	−16.2990	−	11.8419i	−1.09146	−	0.792992i	−0.111815	−	0.993729i	$-0.535666\pi$
$223$	−16.2990	−	11.8419i	−1.09146	−	0.792992i	−0.979645	+	0.200737i	$0.935666\pi$
$224$	−0.826133	+	0.600220i	−0.0551983	+	0.0401039i
$225$		0			0
$226$	−8.19177	+	25.2117i	−0.544908	+	1.67706i
$227$	0.431964	−	0.313840i	0.0286705	−	0.0208303i	−0.573358	−	0.819305i	$-0.694359\pi$
$227$	0.431964	−	0.313840i	0.0286705	−	0.0208303i	0.602028	+	0.798475i	$0.294359\pi$
$228$	−24.3111	−	17.6631i	−1.61004	−	1.16977i
$229$	−6.85803	−	21.1068i	−0.453191	−	1.39478i	−0.873245	−	0.487281i	$-0.837989\pi$
$229$	−6.85803	−	21.1068i	−0.453191	−	1.39478i	0.420054	−	0.907499i	$-0.362011\pi$
$230$		0			0
$231$	9.75577	+	4.86432i	0.641882	+	0.320049i
$232$	25.1261			1.64961
$233$	1.41087	+	4.34221i	0.0924291	+	0.284467i	0.986575	−	0.163308i	$-0.0522164\pi$
$233$	1.41087	+	4.34221i	0.0924291	+	0.284467i	−0.894146	+	0.447775i	$0.852216\pi$
$234$	0.622150	+	0.452019i	0.0406712	+	0.0295494i
$235$		0			0
$236$	−11.4163	+	35.1358i	−0.743138	+	2.28714i
$237$	−1.67316	+	5.14946i	−0.108684	+	0.334493i
$238$	32.6524	−	23.7233i	2.11654	−	1.53776i
$239$	4.74126	+	3.44473i	0.306687	+	0.222821i	0.730474	−	0.682941i	$-0.239299\pi$
$239$	4.74126	+	3.44473i	0.306687	+	0.222821i	−0.423787	+	0.905762i	$0.639299\pi$
$240$		0			0
$241$	9.96074			0.641628			0.320814	−	0.947142i	$-0.396044\pi$
$241$	9.96074			0.641628			0.320814	+	0.947142i	$0.396044\pi$
$242$	15.4960	−	22.1285i	0.996123	−	1.42247i
$243$	−1.00000			−0.0641500
$244$	11.4415	+	35.2133i	0.732466	+	2.25430i
$245$		0			0
$246$	−21.5518	+	15.6583i	−1.37409	+	0.998337i
$247$	−0.721283	+	2.21988i	−0.0458941	+	0.141248i
$248$	−5.31709	+	16.3643i	−0.337635	+	1.03913i
$249$	−13.1428	+	9.54882i	−0.832892	+	0.605132i
$250$		0			0
$251$	−5.21584	−	16.0527i	−0.329221	−	1.01324i	−0.969499	−	0.245094i	$-0.921181\pi$
$251$	−5.21584	−	16.0527i	−0.329221	−	1.01324i	0.640279	−	0.768143i	$-0.278819\pi$
$252$	−13.2505			−0.834704
$253$	−3.18753	−	1.58934i	−0.200399	−	0.0999207i
$254$	−41.7581			−2.62014
$255$		0			0
$256$	26.0723	+	18.9426i	1.62952	+	1.18391i
$257$	9.01534	−	6.55003i	0.562362	−	0.408580i	−0.269961	−	0.962871i	$-0.587011\pi$
$257$	9.01534	−	6.55003i	0.562362	−	0.408580i	0.832323	+	0.554292i	$0.187011\pi$
$258$	4.18515	−	12.8806i	0.260556	−	0.801909i
$259$	2.67561	−	8.23470i	0.166255	−	0.511679i
$260$		0			0
$261$	4.07459	+	2.96036i	0.252211	+	0.183242i
$262$	0.0326717	+	0.100553i	0.00201846	+	0.00621220i
$263$	26.8726			1.65704			0.828519	−	0.559961i	$-0.189184\pi$
$263$	26.8726			1.65704			0.828519	+	0.559961i	$0.189184\pi$
$264$	−2.44604	+	16.3643i	−0.150544	+	1.00715i
$265$		0			0
$266$	−18.5936	−	57.2252i	−1.14005	−	3.50870i
$267$	1.31156	+	0.952905i	0.0802662	+	0.0583168i
$268$	−49.8150	+	36.1927i	−3.04294	+	2.21082i
$269$	−3.10961	+	9.57038i	−0.189596	+	0.583516i	−0.999997	−	0.00235886i	$-0.999249\pi$
$269$	−3.10961	+	9.57038i	−0.189596	+	0.583516i	0.810401	+	0.585875i	$0.199249\pi$
$270$		0			0
$271$	−8.53037	+	6.19767i	−0.518183	+	0.376482i	−0.815919	−	0.578166i	$-0.803768\pi$
$271$	−8.53037	+	6.19767i	−0.518183	+	0.376482i	0.297736	+	0.954648i	$0.403768\pi$
$272$	16.9459	+	12.3119i	1.02750	+	0.746521i
$273$	0.318046	+	0.978846i	0.0192490	+	0.0592425i
$274$	18.0816			1.09235
$275$		0			0
$276$	4.32938			0.260598
$277$	5.54302	+	17.0597i	0.333048	+	1.02502i	0.967676	+	0.252198i	$0.0811534\pi$
$277$	5.54302	+	17.0597i	0.333048	+	1.02502i	−0.634628	+	0.772818i	$0.718847\pi$
$278$	26.3047	+	19.1114i	1.57765	+	1.14623i
$279$	−2.79029	+	2.02726i	−0.167050	+	0.121369i
$280$		0			0
$281$	2.29013	−	7.04830i	0.136618	−	0.420467i	−0.859220	−	0.511606i	$-0.829051\pi$
$281$	2.29013	−	7.04830i	0.136618	−	0.420467i	0.995838	+	0.0911392i	$0.0290508\pi$
$282$	−23.8387	+	17.3198i	−1.41957	+	1.03138i
$283$	4.35804	+	3.16630i	0.259059	+	0.188217i	0.709732	−	0.704472i	$-0.248816\pi$
$283$	4.35804	+	3.16630i	0.259059	+	0.188217i	−0.450673	+	0.892689i	$0.648816\pi$
$284$	3.82713	+	11.7787i	0.227098	+	0.698937i
$285$		0			0
$286$	2.51558	−	0.420905i	0.148749	−	0.0248886i
$287$	−35.6530			−2.10453
$288$	−0.0960054	−	0.295474i	−0.00565717	−	0.0174110i
$289$	−6.47214	−	4.70228i	−0.380714	−	0.276605i
$290$		0			0
$291$	0.0692451	−	0.213115i	0.00405922	−	0.0124930i
$292$	10.7792	−	33.1750i	0.630806	−	1.94142i
$293$	−1.40774	+	1.02278i	−0.0822409	+	0.0597515i	−0.628146	−	0.778096i	$-0.716186\pi$
$293$	−1.40774	+	1.02278i	−0.0822409	+	0.0597515i	0.545905	+	0.837847i	$0.316186\pi$
$294$	−7.55666	−	5.49023i	−0.440713	−	0.320197i
$295$		0			0
$296$	13.1420			0.763864
$297$	−2.32471	+	2.36553i	−0.134893	+	0.137262i
$298$	14.4371			0.836321
$299$	−0.103916	−	0.319822i	−0.00600964	−	0.0184958i
$300$		0			0
$301$	14.6641	−	10.6541i	0.845227	−	0.614093i
$302$	−5.78913	+	17.8171i	−0.333127	+	1.02526i
$303$	0.156154	−	0.480593i	0.00897082	−	0.0276094i
$304$	25.2633	−	18.3548i	1.44895	−	1.05272i
$305$		0			0
$306$	3.79455	+	11.6784i	0.216920	+	0.667612i
$307$	−21.3566			−1.21889			−0.609444	−	0.792829i	$-0.708607\pi$
$307$	−21.3566			−1.21889			−0.609444	+	0.792829i	$0.708607\pi$
$308$	−30.8035	+	31.3445i	−1.75519	+	1.78602i
$309$	−6.40197			−0.364195
$310$		0			0
$311$	−26.5435	−	19.2850i	−1.50514	−	1.09355i	−0.968275	−	0.249886i	$-0.919607\pi$
$311$	−26.5435	−	19.2850i	−1.50514	−	1.09355i	−0.536870	−	0.843665i	$-0.680393\pi$
$312$	−1.26382	+	0.918222i	−0.0715499	+	0.0519841i
$313$	1.06874	−	3.28925i	0.0604089	−	0.185919i	−0.916298	−	0.400497i	$-0.868837\pi$
$313$	1.06874	−	3.28925i	0.0604089	−	0.185919i	0.976707	+	0.214578i	$0.0688375\pi$
$314$	−7.69021	+	23.6680i	−0.433984	+	1.33566i
$315$		0			0
$316$	−17.6590	−	12.8300i	−0.993398	−	0.721746i
$317$	0.888626	+	2.73491i	0.0499102	+	0.153608i	0.972905	−	0.231204i	$-0.0742664\pi$
$317$	0.888626	+	2.73491i	0.0499102	+	0.153608i	−0.922995	+	0.384812i	$0.874266\pi$
$318$	−12.1209			−0.679704
$319$	16.4751	−	2.75659i	0.922426	−	0.154340i
$320$		0			0
$321$	0.646615	+	1.99008i	0.0360905	+	0.111075i
$322$	7.01321	+	5.09540i	0.390831	+	0.283955i
$323$	−30.1524	+	21.9070i	−1.67772	+	1.21894i
$324$	1.24576	−	3.83407i	0.0692092	−	0.213004i
$325$		0			0
$326$	9.99201	−	7.25962i	0.553406	−	0.402073i
$327$	−5.41457	−	3.93392i	−0.299427	−	0.217546i
$328$	−16.7224	−	51.4664i	−0.923342	−	2.84176i
$329$	−39.4362			−2.17419
$330$		0			0
$331$	−14.1221			−0.776219			−0.388109	−	0.921613i	$-0.626872\pi$
$331$	−14.1221			−0.776219			−0.388109	+	0.921613i	$0.626872\pi$
$332$	−20.2380	−	62.2861i	−1.11070	−	3.41839i
$333$	2.13118	+	1.54839i	0.116788	+	0.0848514i
$334$	−11.5060	+	8.35958i	−0.629579	+	0.457416i
$335$		0			0
$336$	4.25499	−	13.0955i	0.232129	−	0.714419i
$337$	12.9030	−	9.37457i	0.702870	−	0.510665i	−0.177995	−	0.984031i	$-0.556961\pi$
$337$	12.9030	−	9.37457i	0.702870	−	0.510665i	0.880866	+	0.473366i	$0.156961\pi$
$338$	−25.6343	−	18.6244i	−1.39432	−	1.01303i
$339$	−3.33556	−	10.2658i	−0.181163	−	0.557562i
$340$		0			0
$341$	−1.69105	+	11.3133i	−0.0915755	+	0.612650i
$342$	18.3064			0.989895
$343$	3.24683	+	9.99271i	0.175312	+	0.539555i
$344$	22.2575	+	16.1711i	1.20005	+	0.871885i
$345$		0			0
$346$	12.1921	−	37.5233i	0.655449	−	2.01727i
$347$	−9.17166	+	28.2275i	−0.492360	+	1.51533i	0.328670	+	0.944445i	$0.393400\pi$
$347$	−9.17166	+	28.2275i	−0.492360	+	1.51533i	−0.821030	+	0.570884i	$0.806600\pi$
$348$	−16.4262	+	11.9343i	−0.880537	+	0.639748i
$349$	−25.6408	−	18.6291i	−1.37252	−	0.997194i	−0.997536	−	0.0701620i	$-0.977648\pi$
$349$	−25.6408	−	18.6291i	−1.37252	−	0.997194i	−0.374984	−	0.927031i	$-0.622352\pi$
$350$		0			0
$351$	−0.313133			−0.0167138
$352$	−0.922138	−	0.459787i	−0.0491501	−	0.0245067i
$353$	−1.20189			−0.0639703			−0.0319852	−	0.999488i	$-0.510183\pi$
$353$	−1.20189			−0.0639703			−0.0319852	+	0.999488i	$0.510183\pi$
$354$	−6.95473	−	21.4044i	−0.369640	−	1.13763i
$355$		0			0
$356$	−5.28740	+	3.84152i	−0.280232	+	0.203600i
$357$	−5.07845	+	15.6299i	−0.268780	+	0.827220i
$358$	6.30130	−	19.3934i	0.333034	−	1.02497i
$359$	9.43239	−	6.85304i	0.497823	−	0.361689i	−0.310362	−	0.950618i	$-0.600450\pi$
$359$	9.43239	−	6.85304i	0.497823	−	0.361689i	0.808185	+	0.588929i	$0.200450\pi$
$360$		0			0
$361$	11.2987	+	34.7737i	0.594667	+	1.83020i
$362$	15.8755			0.834396
$363$	0.191475	+	10.9983i	0.0100498	+	0.577263i
$364$	−4.14918			−0.217476
$365$		0			0
$366$	−18.2479	−	13.2579i	−0.953832	−	0.693000i
$367$	12.9330	−	9.39636i	0.675096	−	0.490486i	−0.196631	−	0.980478i	$-0.563000\pi$
$367$	12.9330	−	9.39636i	0.675096	−	0.490486i	0.871727	+	0.489991i	$0.163000\pi$
$368$	−1.39025	+	4.27874i	−0.0724717	+	0.223045i
$369$	3.35197	−	10.3163i	0.174497	−	0.537045i
$370$		0			0
$371$	−13.1239	−	9.53504i	−0.681357	−	0.495035i
$372$	−4.29663	−	13.2237i	−0.222770	−	0.685615i
$373$	−0.321975			−0.0166712			−0.00833561	−	0.999965i	$-0.502653\pi$
$373$	−0.321975			−0.0166712			−0.00833561	+	0.999965i	$0.502653\pi$
$374$	36.4469	+	18.1728i	1.88463	+	0.939693i
$375$		0			0
$376$	−18.4968	−	56.9274i	−0.953902	−	2.93581i
$377$	1.27589	+	0.926988i	0.0657117	+	0.0477423i
$378$	6.53048	−	4.74467i	0.335891	−	0.244039i
$379$	3.52819	−	10.8586i	0.181231	−	0.557771i	−0.818632	−	0.574318i	$-0.805267\pi$
$379$	3.52819	−	10.8586i	0.181231	−	0.557771i	0.999863	+	0.0165471i	$0.00526734\pi$
$380$		0			0
$381$	13.7559	−	9.99428i	0.704738	−	0.512022i
$382$	30.5365	+	22.1861i	1.56239	+	1.13514i
$383$	−8.76597	−	26.9789i	−0.447920	−	1.37856i	−0.879249	−	0.476362i	$-0.841955\pi$
$383$	−8.76597	−	26.9789i	−0.447920	−	1.37856i	0.431329	−	0.902195i	$-0.358045\pi$
$384$	−19.3242			−0.986136
$385$		0			0
$386$	38.6846			1.96899
$387$	1.70413	+	5.24477i	0.0866257	+	0.266607i
$388$	0.730833	+	0.530981i	0.0371024	+	0.0269565i
$389$	−12.2810	+	8.92269i	−0.622673	+	0.452398i	−0.853854	−	0.520513i	$-0.825741\pi$
$389$	−12.2810	+	8.92269i	−0.622673	+	0.452398i	0.231181	+	0.972911i	$0.425741\pi$
$390$		0			0
$391$	1.65930	−	5.10680i	0.0839143	−	0.258262i
$392$	15.3504	−	11.1528i	0.775315	−	0.563299i
$393$	−0.0348288	−	0.0253046i	−0.00175688	−	0.00127645i
$394$	12.4415	+	38.2911i	0.626796	+	1.92908i
$395$		0			0
$396$	−6.17357	−	11.8600i	−0.310234	−	0.595987i
$397$	−5.22461			−0.262216			−0.131108	−	0.991368i	$-0.541853\pi$
$397$	−5.22461			−0.262216			−0.131108	+	0.991368i	$0.541853\pi$
$398$	−5.28581	−	16.2681i	−0.264954	−	0.815444i
$399$	19.8212	+	14.4010i	0.992302	+	0.720950i
$400$		0			0
$401$	4.32644	−	13.3154i	0.216052	−	0.664941i	−0.783025	−	0.621990i	$-0.786324\pi$
$401$	4.32644	−	13.3154i	0.216052	−	0.664941i	0.999077	−	0.0429502i	$-0.0136757\pi$
$402$	11.5915	−	35.6750i	0.578132	−	1.77931i
$403$	−0.873733	+	0.634804i	−0.0435238	+	0.0316219i
$404$	1.64810	+	1.19741i	0.0819959	+	0.0595735i
$405$		0			0
$406$	−40.6549			−2.01767
$407$	8.61714	−	1.44181i	0.427136	−	0.0714680i
$408$	−24.9442			−1.23492
$409$	10.2937	+	31.6809i	0.508993	+	1.56652i	0.793953	+	0.607979i	$0.208020\pi$
$409$	10.2937	+	31.6809i	0.508993	+	1.56652i	−0.284960	+	0.958539i	$0.591980\pi$
$410$		0			0
$411$	−5.95645	+	4.32761i	−0.293810	+	0.213465i
$412$	7.97535	−	24.5456i	0.392917	−	1.20927i
$413$	9.30787	−	28.6467i	0.458011	−	1.40961i
$414$	−2.13372	+	1.55024i	−0.104867	+	0.0761902i
$415$		0			0
$416$	−0.0300625	−	0.0925229i	−0.00147394	−	0.00453631i
$417$	−13.2393			−0.648334
$418$	42.5569	−	43.3043i	2.08153	−	2.11808i
$419$	−5.28460			−0.258170			−0.129085	−	0.991634i	$-0.541204\pi$
$419$	−5.28460			−0.258170			−0.129085	+	0.991634i	$0.541204\pi$
$420$		0			0
$421$	24.9023	+	18.0926i	1.21367	+	0.881780i	0.995558	−	0.0941452i	$-0.0300118\pi$
$421$	24.9023	+	18.0926i	1.21367	+	0.881780i	0.218107	+	0.975925i	$0.430012\pi$
$422$	−39.6439	+	28.8030i	−1.92984	+	1.40211i
$423$	3.70764	−	11.4110i	0.180272	−	0.554820i
$424$	7.60864	−	23.4170i	0.369508	−	1.13723i
$425$		0			0
$426$	−6.10384	−	4.43470i	−0.295732	−	0.214862i
$427$	−9.32841	−	28.7099i	−0.451433	−	1.38937i
$428$	−8.43562			−0.407751
$429$	−0.727943	+	0.740727i	−0.0351454	+	0.0357626i
$430$		0			0
$431$	3.81656	+	11.7462i	0.183837	+	0.565793i	0.999926	−	0.0121333i	$-0.00386225\pi$
$431$	3.81656	+	11.7462i	0.183837	+	0.565793i	−0.816089	+	0.577926i	$0.803862\pi$
$432$	3.38919	+	2.46239i	0.163062	+	0.118472i
$433$	1.14304	−	0.830465i	0.0549308	−	0.0399096i	−0.559981	−	0.828505i	$-0.689192\pi$
$433$	1.14304	−	0.830465i	0.0549308	−	0.0399096i	0.614912	+	0.788596i	$0.289192\pi$
$434$	8.60323	−	26.4780i	0.412968	−	1.27098i
$435$		0			0
$436$	21.8282	−	15.8591i	1.04538	−	0.759514i
$437$	−6.47625	−	4.70527i	−0.309801	−	0.225084i
$438$	6.56662	+	20.2100i	0.313765	+	0.965670i
$439$	−7.58532			−0.362028			−0.181014	−	0.983481i	$-0.557938\pi$
$439$	−7.58532			−0.362028			−0.181014	+	0.983481i	$0.557938\pi$
$440$		0			0
$441$	3.80333			0.181111
$442$	1.18820	+	3.65691i	0.0565170	+	0.173941i
$443$	8.95274	+	6.50455i	0.425358	+	0.309040i	0.779790	−	0.626041i	$-0.215326\pi$
$443$	8.95274	+	6.50455i	0.425358	+	0.309040i	−0.354432	+	0.935082i	$0.615326\pi$
$444$	−8.59160	+	6.24216i	−0.407739	+	0.296240i
$445$		0			0
$446$	−15.2895	+	47.0562i	−0.723979	+	2.22818i
$447$	−4.75587	+	3.45534i	−0.224945	+	0.163432i
$448$	−20.2505	−	14.7129i	−0.956748	−	0.695118i
$449$	1.95563	+	6.01882i	0.0922920	+	0.284045i	0.986538	−	0.163529i	$-0.0522878\pi$
$449$	1.95563	+	6.01882i	0.0922920	+	0.284045i	−0.894247	+	0.447575i	$0.852288\pi$
$450$		0			0
$451$	−16.6112	−	31.9116i	−0.782190	−	1.50266i
$452$	43.5152			2.04678
$453$	−2.35725	−	7.25486i	−0.110753	−	0.340863i
$454$	−1.06085	−	0.770756i	−0.0497884	−	0.0361734i
$455$		0			0
$456$	−11.4915	+	35.3671i	−0.538138	+	1.65622i
$457$	0.0585832	−	0.180300i	0.00274040	−	0.00843410i	−0.949677	−	0.313231i	$-0.898589\pi$
$457$	0.0585832	−	0.180300i	0.00274040	−	0.00843410i	0.952417	+	0.304797i	$0.0985886\pi$
$458$	−44.0944	+	32.0364i	−2.06039	+	1.49696i
$459$	−4.04508	−	2.93893i	−0.188808	−	0.137177i
$460$		0			0
$461$	−26.6198			−1.23981			−0.619904	−	0.784678i	$-0.712828\pi$
$461$	−26.6198			−1.23981			−0.619904	+	0.784678i	$0.712828\pi$
$462$	3.95778	−	26.4780i	0.184133	−	1.23187i
$463$	−20.9935			−0.975652			−0.487826	−	0.872941i	$-0.662210\pi$
$463$	−20.9935			−0.975652			−0.487826	+	0.872941i	$0.662210\pi$
$464$	−6.51998	−	20.0664i	−0.302682	−	0.931561i
$465$		0			0
$466$	9.07131	−	6.59070i	0.420221	−	0.305308i
$467$	−2.44120	+	7.51324i	−0.112965	+	0.347671i	−0.991517	−	0.129976i	$-0.958510\pi$
$467$	−2.44120	+	7.51324i	−0.112965	+	0.347671i	0.878552	+	0.477647i	$0.158510\pi$
$468$	0.390091	−	1.20058i	0.0180319	−	0.0554966i
$469$	40.6149	−	29.5085i	1.87542	−	1.36257i
$470$		0			0
$471$	−3.13134	−	9.63727i	−0.144284	−	0.444062i
$472$	45.7182			2.10435
$473$	16.3683	+	8.16138i	0.752614	+	0.375261i
$474$	13.2973			0.610766
$475$		0			0
$476$	−53.5994	−	38.9423i	−2.45673	−	1.78492i
$477$	3.99285	−	2.90097i	0.182820	−	0.132826i
$478$	4.44762	−	13.6884i	0.203429	−	0.626091i
$479$	12.3523	−	38.0164i	0.564389	−	1.73701i	−0.105369	−	0.994433i	$-0.533602\pi$
$479$	12.3523	−	38.0164i	0.564389	−	1.73701i	0.669758	−	0.742579i	$-0.266398\pi$
$480$		0			0
$481$	0.667344	+	0.484854i	0.0304282	+	0.0221074i
$482$	−7.55931	−	23.2652i	−0.344317	−	1.05970i
$483$	−3.52981			−0.160612
$484$	−42.4069	−	12.9672i	−1.92759	−	0.589419i
$485$		0			0
$486$	0.758911	+	2.33569i	0.0344249	+	0.105949i
$487$	−8.03804	−	5.83998i	−0.364238	−	0.264635i	0.390579	−	0.920569i	$-0.372275\pi$
$487$	−8.03804	−	5.83998i	−0.364238	−	0.264635i	−0.754818	+	0.655935i	$0.772275\pi$
$488$	37.0684	−	26.9318i	1.67801	−	1.21914i
$489$	−1.55407	+	4.78292i	−0.0702773	+	0.216291i
$490$		0			0
$491$	−4.02364	+	2.92335i	−0.181584	+	0.131929i	−0.674864	−	0.737942i	$-0.735798\pi$
$491$	−4.02364	+	2.92335i	−0.181584	+	0.131929i	0.493280	+	0.869871i	$0.335798\pi$
$492$	35.3777	+	25.7034i	1.59495	+	1.15880i
$493$	7.78177	+	23.9498i	0.350473	+	1.07865i
$494$	5.73234			0.257910
$495$		0			0
$496$	14.4487			0.648767
$497$	−3.12031	−	9.60333i	−0.139965	−	0.430768i
$498$	32.2773	+	23.4508i	1.44638	+	1.05086i
$499$	−35.4153	+	25.7307i	−1.58541	+	1.15186i	−0.675256	+	0.737584i	$0.735967\pi$
$499$	−35.4153	+	25.7307i	−1.58541	+	1.15186i	−0.910149	+	0.414281i	$0.864033\pi$
$500$		0			0
$501$	1.78953	−	5.50761i	0.0799504	−	0.246062i
$502$	−33.5357	+	24.3651i	−1.49677	+	1.08747i
$503$	5.08254	+	3.69268i	0.226619	+	0.164648i	0.695301	−	0.718718i	$-0.255271\pi$
$503$	5.08254	+	3.69268i	0.226619	+	0.164648i	−0.468682	+	0.883367i	$0.655271\pi$
$504$	5.06711	+	15.5950i	0.225707	+	0.694655i
$505$		0			0
$506$	−1.29314	+	8.65125i	−0.0574870	+	0.384595i
$507$	12.9019			0.572996
$508$	21.1821	+	65.1918i	0.939803	+	2.89242i
$509$	−20.0945	−	14.5995i	−0.890671	−	0.647111i	0.0453816	−	0.998970i	$-0.485550\pi$
$509$	−20.0945	−	14.5995i	−0.890671	−	0.647111i	−0.936053	+	0.351859i	$0.885550\pi$
$510$		0			0
$511$	−8.78845	+	27.0481i	−0.388778	+	1.19654i
$512$	12.5144	−	38.5155i	0.553066	−	1.70216i
$513$	−6.03048	+	4.38140i	−0.266252	+	0.193443i
$514$	−22.1407	−	16.0861i	−0.976583	−	0.709529i
$515$		0			0
$516$	−22.2318			−0.978699
$517$	−18.3738	−	35.2977i	−0.808078	−	1.55239i
$518$	−21.2642			−0.934296
$519$	4.96442	+	15.2789i	0.217914	+	0.670670i
$520$		0			0
$521$	5.62161	−	4.08434i	0.246287	−	0.178938i	−0.457792	−	0.889059i	$-0.651360\pi$
$521$	5.62161	−	4.08434i	0.246287	−	0.178938i	0.704080	+	0.710121i	$0.251360\pi$
$522$	3.82223	−	11.7636i	0.167294	−	0.514879i
$523$	8.26650	−	25.4417i	0.361469	−	1.11249i	−0.590694	−	0.806896i	$-0.701146\pi$
$523$	8.26650	−	25.4417i	0.361469	−	1.11249i	0.952163	−	0.305591i	$-0.0988541\pi$
$524$	0.140408	−	0.102013i	0.00613376	−	0.00445644i
$525$		0			0
$526$	−20.3939	−	62.7661i	−0.889218	−	2.73673i
$527$	−17.2449			−0.751202
$528$	13.7037	−	2.29290i	0.596378	−	0.0997854i
$529$	−21.8467			−0.949856
$530$		0			0
$531$	7.41391	+	5.38652i	0.321736	+	0.233755i
$532$	−79.9069	+	58.0557i	−3.46440	+	2.51704i
$533$	1.04961	−	3.23038i	0.0454638	−	0.139923i
$534$	1.23033	−	3.78657i	0.0532416	−	0.163861i
$535$		0			0
$536$	61.6462	+	44.7886i	2.66271	+	1.93457i
$537$	2.56580	+	7.89671i	0.110722	+	0.340768i
$538$	24.7133			1.06547
$539$	8.84162	−	8.99689i	0.380836	−	0.387524i
$540$		0			0
$541$	4.48336	+	13.7984i	0.192755	+	0.593237i	0.999995	+	0.00301536i	$0.000959822\pi$
$541$	4.48336	+	13.7984i	0.192755	+	0.593237i	−0.807241	+	0.590222i	$0.799040\pi$
$542$	20.9496	+	15.2208i	0.899863	+	0.653789i
$543$	−5.22969	+	3.79959i	−0.224428	+	0.163056i
$544$	0.480027	−	1.47737i	0.0205810	−	0.0633418i
$545$		0			0
$546$	2.04491	−	1.48571i	0.0875141	−	0.0635827i
$547$	−21.6287	−	15.7142i	−0.924777	−	0.671890i	0.0199316	−	0.999801i	$-0.493655\pi$
$547$	−21.6287	−	15.7142i	−0.924777	−	0.671890i	−0.944708	+	0.327912i	$0.893655\pi$
$548$	−9.17203	−	28.2286i	−0.391810	−	1.20587i
$549$	9.18431			0.391977
$550$		0			0
$551$	37.5422			1.59935
$552$	−1.65559	−	5.09540i	−0.0704668	−	0.216875i
$553$	14.3977	+	10.4605i	0.612251	+	0.444826i
$554$	35.6394	−	25.8935i	1.51417	−	1.10011i
$555$		0			0
$556$	16.4931	−	50.7606i	0.699464	−	2.15273i
$557$	13.9510	−	10.1360i	0.591125	−	0.429477i	−0.251593	−	0.967833i	$-0.580954\pi$
$557$	13.9510	−	10.1360i	0.591125	−	0.429477i	0.842718	+	0.538356i	$0.180954\pi$
$558$	6.85264	+	4.97873i	0.290095	+	0.210767i
$559$	0.533620	+	1.64231i	0.0225697	+	0.0694624i
$560$		0			0
$561$	−16.3558	+	2.73663i	−0.690541	+	0.115541i
$562$	−18.2006			−0.767748
$563$	0.257075	+	0.791197i	0.0108344	+	0.0333450i	0.956328	−	0.292297i	$-0.0944196\pi$
$563$	0.257075	+	0.791197i	0.0108344	+	0.0333450i	−0.945493	+	0.325642i	$0.894420\pi$
$564$	39.1316	+	28.4307i	1.64774	+	1.19715i
$565$		0			0
$566$	4.08813	−	12.5820i	0.171837	−	0.528860i
$567$	−1.01569	+	3.12597i	−0.0426550	+	0.131278i
$568$	12.3992	−	9.00855i	0.520259	−	0.377991i
$569$	−9.38141	−	6.81599i	−0.393289	−	0.285741i	0.373513	−	0.927625i	$-0.378153\pi$
$569$	−9.38141	−	6.81599i	−0.393289	−	0.285741i	−0.766802	+	0.641884i	$0.778153\pi$
$570$		0			0
$571$	21.8414			0.914034			0.457017	−	0.889458i	$-0.348918\pi$
$571$	21.8414			0.914034			0.457017	+	0.889458i	$0.348918\pi$
$572$	−1.93315	−	3.71376i	−0.0808292	−	0.155280i
$573$	−15.3693			−0.642061
$574$	27.0575	+	83.2744i	1.12936	+	3.47580i
$575$		0			0
$576$	6.16110	−	4.47630i	0.256712	−	0.186512i
$577$	−3.01164	+	9.26888i	−0.125376	+	0.385868i	−0.993969	−	0.109657i	$-0.965025\pi$
$577$	−3.01164	+	9.26888i	−0.125376	+	0.385868i	0.868593	+	0.495526i	$0.165025\pi$
$578$	−6.07129	+	18.6855i	−0.252532	+	0.777214i
$579$	−12.7435	+	9.25867i	−0.529600	+	0.384777i
$580$		0			0
$581$	16.5003	+	50.7827i	0.684548	+	2.10682i
$582$	−0.550320			−0.0228115
$583$	2.41986	−	16.1891i	0.100220	−	0.670485i
$584$	−43.1669			−1.78626
$585$		0			0
$586$	3.45724	+	2.51183i	0.142817	+	0.103763i
$587$	18.5622	−	13.4862i	0.766143	−	0.556635i	−0.134645	−	0.990894i	$-0.542990\pi$
$587$	18.5622	−	13.4862i	0.766143	−	0.556635i	0.900788	+	0.434258i	$0.142990\pi$
$588$	−4.73805	+	14.5822i	−0.195394	+	0.601361i
$589$	−7.94453	+	24.4507i	−0.327349	+	1.00748i
$590$		0			0
$591$	−13.2630	−	9.63612i	−0.545566	−	0.396377i
$592$	−3.41022	−	10.4956i	−0.140159	−	0.431366i
$593$	−28.7819			−1.18193			−0.590965	−	0.806697i	$-0.701253\pi$
$593$	−28.7819			−1.18193			−0.590965	+	0.806697i	$0.701253\pi$
$594$	7.28939	+	3.63456i	0.299087	+	0.149128i
$595$		0			0
$596$	−7.32333	−	22.5389i	−0.299975	−	0.923229i
$597$	5.63480	+	4.09392i	0.230617	+	0.167553i
$598$	−0.668140	+	0.485432i	−0.0273223	+	0.0198508i
$599$	−9.02179	+	27.7662i	−0.368620	+	1.13450i	0.579062	+	0.815283i	$0.303419\pi$
$599$	−9.02179	+	27.7662i	−0.368620	+	1.13450i	−0.947683	+	0.319214i	$0.896581\pi$
$600$		0			0
$601$	5.40494	−	3.92692i	0.220472	−	0.160182i	−0.472067	−	0.881563i	$-0.656492\pi$
$601$	5.40494	−	3.92692i	0.220472	−	0.160182i	0.692539	+	0.721380i	$0.256492\pi$
$602$	−36.0135	−	26.1653i	−1.46780	−	1.06642i
$603$	4.71989	+	14.5263i	0.192209	+	0.591557i
$604$	30.7522			1.25129
$605$		0			0
$606$	−1.24102			−0.0504131
$607$	13.1674	+	40.5252i	0.534450	+	1.64487i	0.744834	+	0.667250i	$0.232529\pi$
$607$	13.1674	+	40.5252i	0.534450	+	1.64487i	−0.210384	+	0.977619i	$0.567471\pi$
$608$	−1.87355	−	1.36121i	−0.0759824	−	0.0552044i
$609$	13.3925	−	9.73024i	0.542693	−	0.394289i
$610$		0			0
$611$	1.16099	−	3.57315i	0.0469685	−	0.144554i
$612$	16.3073	−	11.8479i	0.659182	−	0.478924i
$613$	−4.71783	−	3.42771i	−0.190552	−	0.138444i	0.488419	−	0.872609i	$-0.337574\pi$
$613$	−4.71783	−	3.42771i	−0.190552	−	0.138444i	−0.678971	+	0.734165i	$0.737574\pi$
$614$	16.2078	+	49.8824i	0.654093	+	2.01309i
$615$		0			0
$616$	48.6699	+	24.2673i	1.96097	+	0.977758i
$617$	33.6386			1.35424			0.677119	−	0.735874i	$-0.263228\pi$
$617$	33.6386			1.35424			0.677119	+	0.735874i	$0.263228\pi$
$618$	4.85852	+	14.9530i	0.195438	+	0.601498i
$619$	−34.4331	−	25.0171i	−1.38398	−	1.00552i	−0.996495	−	0.0836477i	$-0.973343\pi$
$619$	−34.4331	−	25.0171i	−1.38398	−	1.00552i	−0.387488	−	0.921875i	$-0.626657\pi$
$620$		0			0
$621$	0.331860	−	1.02136i	0.0133171	−	0.0409857i
$622$	−24.8996	+	76.6329i	−0.998381	+	3.07270i
$623$	4.31089	−	3.13205i	0.172712	−	0.125483i
$624$	1.06127	+	0.771056i	0.0424847	+	0.0308669i
$625$		0			0
$626$	−8.49374			−0.339478
$627$	−3.65476	+	24.4507i	−0.145957	+	0.976468i
$628$	40.8509			1.63013
$629$	4.07019	+	12.5268i	0.162289	+	0.499475i
$630$		0			0
$631$	7.20016	−	5.23122i	0.286634	−	0.208252i	−0.435172	−	0.900347i	$-0.643312\pi$
$631$	7.20016	−	5.23122i	0.286634	−	0.208252i	0.721806	+	0.692096i	$0.243312\pi$
$632$	−8.34713	+	25.6898i	−0.332031	+	1.02189i
$633$	6.16585	−	18.9765i	0.245071	−	0.754250i
$634$	5.71351	−	4.15111i	0.226912	−	0.164862i
$635$		0			0
$636$	6.14839	+	18.9228i	0.243799	+	0.750337i
$637$	1.19095			0.0471871
$638$	−18.9416	−	36.3886i	−0.749906	−	1.44064i
$639$	3.07211			0.121531
$640$		0			0
$641$	4.99007	+	3.62549i	0.197096	+	0.143198i	0.681956	−	0.731393i	$-0.261130\pi$
$641$	4.99007	+	3.62549i	0.197096	+	0.143198i	−0.484860	+	0.874592i	$0.661130\pi$
$642$	4.15747	−	3.02058i	0.164082	−	0.119213i
$643$	−1.34526	+	4.14029i	−0.0530519	+	0.163277i	−0.974072	−	0.226238i	$-0.927357\pi$
$643$	−1.34526	+	4.14029i	−0.0530519	+	0.163277i	0.921020	+	0.389515i	$0.127357\pi$
$644$	4.39731	−	13.5335i	0.173278	−	0.533296i
$645$		0			0
$646$	74.0508	+	53.8011i	2.91349	+	2.11677i
$647$	−4.16967	−	12.8329i	−0.163927	−	0.504514i	0.835029	−	0.550206i	$-0.185451\pi$
$647$	−4.16967	−	12.8329i	−0.163927	−	0.504514i	−0.998956	+	0.0456916i	$0.985451\pi$
$648$	−4.98884			−0.195980
$649$	29.9771	−	5.01575i	1.17671	−	0.196885i
$650$		0			0
$651$	3.50310	+	10.7814i	0.137297	+	0.422558i
$652$	−16.4021	−	11.9168i	−0.642354	−	0.466697i
$653$	22.2060	−	16.1336i	0.868988	−	0.631357i	−0.0613270	−	0.998118i	$-0.519533\pi$
$653$	22.2060	−	16.1336i	0.868988	−	0.631357i	0.930315	+	0.366761i	$0.119533\pi$
$654$	−5.07922	+	15.6322i	−0.198613	+	0.611269i
$655$		0			0
$656$	−36.7632	+	26.7100i	−1.43536	+	1.04285i
$657$	−7.00018	−	5.08592i	−0.273103	−	0.198421i
$658$	29.9285	+	92.1105i	1.16674	+	3.59084i
$659$	−18.7768			−0.731441			−0.365721	−	0.930725i	$-0.619177\pi$
$659$	−18.7768			−0.731441			−0.365721	+	0.930725i	$0.619177\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	10.7174	+	32.9847i	0.416543	+	1.28199i
$663$	−1.26665	−	0.920276i	−0.0491927	−	0.0357406i
$664$	−65.5674	+	47.6375i	−2.54451	+	1.84869i
$665$		0			0
$666$	1.99919	−	6.15286i	0.0774669	−	0.238419i
$667$	−4.37578	+	3.17919i	−0.169431	+	0.123099i
$668$	18.8872	+	13.7224i	0.730769	+	0.530935i
$669$	−6.22565	−	19.1606i	−0.240698	−	0.740791i
$670$		0			0
$671$	21.3508	−	21.7258i	0.824240	−	0.838714i
$672$	−1.02116			−0.0393919
$673$	−7.20076	−	22.1617i	−0.277569	−	0.854269i	−0.988528	−	0.151036i	$-0.951739\pi$
$673$	−7.20076	−	22.1617i	−0.277569	−	0.854269i	0.710959	−	0.703233i	$-0.248261\pi$
$674$	−31.6883	−	23.0229i	−1.22059	−	0.886808i
$675$		0			0
$676$	−16.0728	+	49.4670i	−0.618184	+	1.90258i
$677$	−10.2843	+	31.6519i	−0.395259	+	1.21648i	0.533501	+	0.845800i	$0.320876\pi$
$677$	−10.2843	+	31.6519i	−0.395259	+	1.21648i	−0.928760	+	0.370683i	$0.879124\pi$
$678$	−21.4463	+	15.5817i	−0.823641	+	0.598410i
$679$	−0.595859	−	0.432917i	−0.0228670	−	0.0166138i
$680$		0			0
$681$	0.533937			0.0204605
$682$	27.7077	−	4.63603i	1.06098	−	0.177523i
$683$	−16.9244			−0.647593			−0.323796	−	0.946127i	$-0.604959\pi$
$683$	−16.9244			−0.647593			−0.323796	+	0.946127i	$0.604959\pi$
$684$	−9.28603	−	28.5795i	−0.355060	−	1.09276i
$685$		0			0
$686$	20.8758	−	15.1671i	0.797041	−	0.579084i
$687$	6.85803	−	21.1068i	0.261650	−	0.805276i
$688$	7.13905	−	21.9717i	0.272174	−	0.837664i
$689$	1.25029	−	0.908392i	0.0476324	−	0.0346070i
$690$		0			0
$691$	−14.9668	−	46.0630i	−0.569363	−	1.75232i	−0.654617	−	0.755961i	$-0.727170\pi$
$691$	−14.9668	−	46.0630i	−0.569363	−	1.75232i	0.0852532	−	0.996359i	$-0.472830\pi$
$692$	−64.7650			−2.46200
$693$	5.03340	+	9.66962i	0.191203	+	0.367318i
$694$	72.8910			2.76690
$695$		0			0
$696$	20.3275	+	14.7688i	0.770511	+	0.559809i
$697$	43.8779	−	31.8791i	1.66199	−	1.20751i
$698$	−24.0527	+	74.0267i	−0.910409	+	2.80195i
$699$	−1.41087	+	4.34221i	−0.0533640	+	0.164237i
$700$		0			0
$701$	36.7424	+	26.6949i	1.38774	+	1.00825i	0.996109	+	0.0881330i	$0.0280900\pi$
$701$	36.7424	+	26.6949i	1.38774	+	1.00825i	0.391634	+	0.920121i	$0.371910\pi$
$702$	0.237640	+	0.731382i	0.00896916	+	0.0276042i
$703$	19.6361			0.740591
$704$	3.73392	−	24.9803i	0.140727	−	0.941482i
$705$		0			0
$706$	0.912130	+	2.80725i	0.0343285	+	0.105652i
$707$	−1.34372	−	0.976267i	−0.0505357	−	0.0367163i
$708$	−29.8883	+	21.7151i	−1.12327	+	0.816103i
$709$	−0.545405	+	1.67858i	−0.0204831	+	0.0630406i	−0.960776	−	0.277327i	$-0.910551\pi$
$709$	−0.545405	+	1.67858i	−0.0204831	+	0.0630406i	0.940292	+	0.340368i	$0.110551\pi$
$710$		0			0
$711$	−4.38039	+	3.18254i	−0.164278	+	0.119355i
$712$	6.54317	+	4.75389i	0.245216	+	0.178160i
$713$	−1.14458	−	3.52266i	−0.0428649	−	0.131925i
$714$	40.3606			1.51046
$715$		0			0
$716$	−33.4729			−1.25094
$717$	1.81100	+	5.57369i	0.0676331	+	0.208153i
$718$	−23.1649	−	16.8303i	−0.864506	−	0.628100i
$719$	2.66974	−	1.93968i	0.0995645	−	0.0723379i	−0.536889	−	0.843653i	$-0.680401\pi$
$719$	2.66974	−	1.93968i	0.0995645	−	0.0723379i	0.636454	+	0.771315i	$0.280401\pi$
$720$		0			0
$721$	−6.50241	+	20.0124i	−0.242163	+	0.745300i
$722$	72.6459	−	52.7803i	2.70360	−	1.96428i
$723$	8.05841	+	5.85477i	0.299695	+	0.217741i
$724$	−8.05294	−	24.7844i	−0.299285	−	0.921105i
$725$		0			0
$726$	25.5434	−	8.79398i	0.948003	−	0.326375i
$727$	−11.7838			−0.437037			−0.218519	−	0.975833i	$-0.570122\pi$
$727$	−11.7838			−0.437037			−0.218519	+	0.975833i	$0.570122\pi$
$728$	1.58668	+	4.88331i	0.0588064	+	0.180987i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−8.52064	+	26.2238i	−0.315147	+	0.969924i
$732$	−11.4415	+	35.2133i	−0.422890	+	1.30152i
$733$	4.63654	−	3.36865i	0.171255	−	0.124424i	−0.498856	−	0.866685i	$-0.666246\pi$
$733$	4.63654	−	3.36865i	0.171255	−	0.124424i	0.670111	+	0.742261i	$0.266246\pi$
$734$	−31.7619	−	23.0764i	−1.17235	−	0.851765i
$735$		0			0
$736$	0.333646			0.0122983
$737$	45.3348	+	22.6044i	1.66993	+	0.832643i
$738$	−26.6395			−0.980614
$739$	−6.50638	−	20.0246i	−0.239341	−	0.736616i	−0.996516	−	0.0834038i	$-0.973421\pi$
$739$	−6.50638	−	20.0246i	−0.239341	−	0.736616i	0.757175	−	0.653212i	$-0.226579\pi$
$740$		0			0
$741$	−1.88834	+	1.37196i	−0.0693700	+	0.0504003i
$742$	−12.3110	+	37.8895i	−0.451952	+	1.39097i
$743$	−4.05686	+	12.4857i	−0.148832	+	0.458058i	−0.997484	−	0.0708942i	$-0.977415\pi$
$743$	−4.05686	+	12.4857i	−0.148832	+	0.458058i	0.848652	+	0.528952i	$0.177415\pi$
$744$	−13.9203	+	10.1137i	−0.510343	+	0.370786i
$745$		0			0
$746$	0.244350	+	0.752032i	0.00894629	+	0.0275339i
$747$	−16.2454			−0.594389
$748$	9.88299	−	66.1183i	0.361358	−	2.41753i
$749$	6.87768			0.251305
$750$		0			0
$751$	−20.7311	−	15.0621i	−0.756490	−	0.549622i	0.141342	−	0.989961i	$-0.454858\pi$
$751$	−20.7311	−	15.0621i	−0.756490	−	0.549622i	−0.897832	+	0.440339i	$0.854858\pi$
$752$	−40.6641	+	29.5442i	−1.48287	+	1.07737i
$753$	5.21584	−	16.0527i	0.190076	−	0.584993i
$754$	1.19687	−	3.68358i	0.0435874	−	0.134148i
$755$		0			0
$756$	−10.7199	−	7.78845i	−0.389878	−	0.283263i
$757$	−9.64039	−	29.6701i	−0.350386	−	1.07838i	−0.958637	−	0.284632i	$-0.908129\pi$
$757$	−9.64039	−	29.6701i	−0.350386	−	1.07838i	0.608251	−	0.793745i	$-0.291871\pi$
$758$	−28.0400			−1.01846
$759$	−1.64458	−	3.15939i	−0.0596945	−	0.114678i
$760$		0			0
$761$	3.51539	+	10.8193i	0.127433	+	0.392198i	0.994336	−	0.106278i	$-0.0338932\pi$
$761$	3.51539	+	10.8193i	0.127433	+	0.392198i	−0.866904	+	0.498476i	$0.833893\pi$
$762$	−33.7830	−	24.5448i	−1.22383	−	0.889165i
$763$	−17.7968	+	12.9302i	−0.644289	+	0.468103i
$764$	19.1465	−	58.9269i	0.692697	−	2.13190i
$765$		0			0
$766$	−56.3617	+	40.9491i	−2.03643	+	1.47955i
$767$	2.32154	+	1.68670i	0.0838260	+	0.0609032i
$768$	9.95872	+	30.6498i	0.359354	+	1.10598i
$769$	10.3938			0.374811			0.187405	−	0.982283i	$-0.439992\pi$
$769$	10.3938			0.374811			0.187405	+	0.982283i	$0.439992\pi$
$770$		0			0
$771$	11.1436			0.401326
$772$	−19.6230	−	60.3935i	−0.706248	−	2.17361i
$773$	11.3544	+	8.24944i	0.408389	+	0.296712i	0.772949	−	0.634468i	$-0.218781\pi$
$773$	11.3544	+	8.24944i	0.408389	+	0.296712i	−0.364560	+	0.931180i	$0.618781\pi$
$774$	10.9569	−	7.96062i	0.393836	−	0.286139i
$775$		0			0
$776$	0.345453	−	1.06319i	0.0124010	−	0.0381665i
$777$	7.00485	−	5.08932i	0.251298	−	0.182578i
$778$	30.1608	+	21.9131i	1.08132	+	0.785623i
$779$	−24.9858	−	76.8985i	−0.895211	−	2.75518i
$780$		0			0
$781$	7.14176	−	7.26717i	0.255552	−	0.260040i
$782$	−13.1871			−0.471571
$783$	1.55635	+	4.78997i	0.0556196	+	0.171179i
$784$	−12.8902	−	9.36527i	−0.460364	−	0.334474i
$785$		0			0
$786$	−0.0326717	+	0.100553i	−0.00116536	+	0.00358661i
$787$	4.26988	−	13.1414i	0.152205	−	0.468439i	−0.845662	−	0.533719i	$-0.820794\pi$
$787$	4.26988	−	13.1414i	0.152205	−	0.468439i	0.997867	+	0.0652802i	$0.0207941\pi$
$788$	53.4681	−	38.8469i	1.90472	−	1.38386i
$789$	21.7404	+	15.7953i	0.773980	+	0.562329i
$790$		0			0
$791$	−35.4785			−1.26147
$792$	−11.5976	+	11.8013i	−0.412102	+	0.419339i
$793$	2.87591			0.102127
$794$	3.96502	+	12.2031i	0.140713	+	0.433070i
$795$		0			0
$796$	−22.7160	+	16.5042i	−0.805149	+	0.584975i
$797$	1.66435	−	5.12233i	0.0589541	−	0.181442i	−0.917243	−	0.398329i	$-0.869590\pi$
$797$	1.66435	−	5.12233i	0.0589541	−	0.181442i	0.976197	+	0.216887i	$0.0695902\pi$
$798$	18.5936	−	57.2252i	0.658206	−	2.02575i
$799$	48.5337	−	35.2618i	1.71700	−	1.24747i
$800$		0			0
$801$	0.500972	+	1.54183i	0.0177010	+	0.0544780i
$802$	−34.3840			−1.21414
$803$	−28.3043	+	4.73585i	−0.998836	+	0.167124i
$804$	−61.5748			−2.17157
$805$		0			0
$806$	2.14579	+	1.55901i	0.0755822	+	0.0549137i
$807$	−8.14105	+	5.91482i	−0.286579	+	0.208212i
$808$	0.779028	−	2.39760i	0.0274061	−	0.0843473i
$809$	7.34680	−	22.6111i	0.258300	−	0.794965i	−0.734862	−	0.678217i	$-0.762753\pi$
$809$	7.34680	−	22.6111i	0.258300	−	0.794965i	0.993162	−	0.116748i	$-0.0372470\pi$
$810$		0			0
$811$	−7.65601	−	5.56242i	−0.268839	−	0.195323i	0.445196	−	0.895433i	$-0.353134\pi$
$811$	−7.65601	−	5.56242i	−0.268839	−	0.195323i	−0.714035	+	0.700110i	$0.753134\pi$
$812$	20.6225	+	63.4695i	0.723707	+	2.22734i
$813$	−10.5441			−0.369798
$814$	−9.90726	−	19.0327i	−0.347249	−	0.667097i
$815$		0			0
$816$	6.47277	+	19.9211i	0.226592	+	0.697379i
$817$	33.2561	+	24.1620i	1.16348	+	0.845321i
$818$	66.1846	−	48.0859i	2.31409	−	1.68128i
$819$	−0.318046	+	0.978846i	−0.0111134	+	0.0342037i
$820$		0			0
$821$	8.42906	−	6.12407i	0.294176	−	0.213731i	−0.430901	−	0.902399i	$-0.641804\pi$
$821$	8.42906	−	6.12407i	0.294176	−	0.213731i	0.725077	+	0.688668i	$0.241804\pi$
$822$	14.6284	+	10.6281i	0.510223	+	0.370698i
$823$	−7.52581	−	23.1620i	−0.262333	−	0.807378i	−0.992296	−	0.123891i	$-0.960463\pi$
$823$	−7.52581	−	23.1620i	−0.262333	−	0.807378i	0.729963	−	0.683487i	$-0.239537\pi$
$824$	−31.9384			−1.11263
$825$		0			0
$826$	−73.9736			−2.57387
$827$	6.79857	+	20.9239i	0.236410	+	0.727594i	0.996931	+	0.0782813i	$0.0249432\pi$
$827$	6.79857	+	20.9239i	0.236410	+	0.727594i	−0.760522	+	0.649312i	$0.775057\pi$
$828$	3.50254	+	2.54475i	0.121722	+	0.0884361i
$829$	−2.45366	+	1.78269i	−0.0852191	+	0.0619153i	−0.629579	−	0.776936i	$-0.716773\pi$
$829$	−2.45366	+	1.78269i	−0.0852191	+	0.0619153i	0.544360	+	0.838852i	$0.316773\pi$
$830$		0			0
$831$	−5.54302	+	17.0597i	−0.192285	+	0.591793i
$832$	1.92924	−	1.40168i	0.0668845	−	0.0485945i
$833$	15.3848	+	11.1777i	0.533051	+	0.387284i
$834$	10.0475	+	30.9230i	0.347916	+	1.07077i
$835$		0			0
$836$	−89.1929	−	44.4725i	−3.08480	−	1.53811i
$837$	−3.44899			−0.119214
$838$	4.01054	+	12.3432i	0.138542	+	0.426388i
$839$	39.2683	+	28.5301i	1.35569	+	0.984968i	0.998706	+	0.0508591i	$0.0161960\pi$
$839$	39.2683	+	28.5301i	1.35569	+	0.984968i	0.356987	+	0.934109i	$0.383804\pi$
$840$		0			0
$841$	−1.12296	+	3.45613i	−0.0387229	+	0.119177i
$842$	23.3600	−	71.8947i	0.805039	−	2.47766i
$843$	5.99565	−	4.35609i	0.206501	−	0.150032i
$844$	65.0762	+	47.2806i	2.24001	+	1.62747i
$845$		0			0
$846$	−29.4662			−1.01307
$847$	34.5750	+	10.5723i	1.18801	+	0.363270i
$848$	−20.6758			−0.710011
$849$	1.66462	+	5.12319i	0.0571298	+	0.175827i
$850$		0			0
$851$	−2.28872	+	1.66285i	−0.0784563	+	0.0570018i
$852$	−3.82713	+	11.7787i	−0.131115	+	0.403531i
$853$	3.63504	−	11.1875i	0.124461	−	0.383053i	−0.869341	−	0.494213i	$-0.835456\pi$
$853$	3.63504	−	11.1875i	0.124461	−	0.383053i	0.993803	+	0.111160i	$0.0354565\pi$
$854$	−59.9779	+	43.5765i	−2.05240	+	1.49116i
$855$		0			0
$856$	3.22586	+	9.92817i	0.110258	+	0.339338i
$857$	−1.61311			−0.0551026			−0.0275513	−	0.999620i	$-0.508771\pi$
$857$	−1.61311			−0.0551026			−0.0275513	+	0.999620i	$0.508771\pi$
$858$	2.28255	+	1.13810i	0.0779250	+	0.0388542i
$859$	47.3263			1.61475			0.807376	−	0.590038i	$-0.200887\pi$
$859$	47.3263			1.61475			0.807376	+	0.590038i	$0.200887\pi$
$860$		0			0
$861$	−28.8439	−	20.9563i	−0.982998	−	0.714190i
$862$	24.5389	−	17.8286i	0.835799	−	0.607244i
$863$	3.08162	−	9.48425i	0.104900	−	0.322848i	−0.884807	−	0.465957i	$-0.845710\pi$
$863$	3.08162	−	9.48425i	0.104900	−	0.322848i	0.989707	+	0.143109i	$0.0457101\pi$
$864$	0.0960054	−	0.295474i	0.00326617	−	0.0100522i
$865$		0			0
$866$	−2.80717	−	2.03953i	−0.0953915	−	0.0693060i
$867$	−2.47214	−	7.60845i	−0.0839581	−	0.258397i
$868$	−45.7009			−1.55119
$869$	−2.65473	+	17.7604i	−0.0900555	+	0.602482i
$870$		0			0
$871$	1.47795	+	4.54867i	0.0500786	+	0.154126i
$872$	−27.0124	−	19.6257i	−0.914756	−	0.664609i
$873$	0.181286	−	0.131712i	0.00613560	−	0.00445778i
$874$	−6.07515	+	18.6974i	−0.205495	+	0.632448i
$875$		0			0
$876$	28.2204	−	20.5033i	0.953478	−	0.692742i
$877$	21.0391	+	15.2858i	0.710439	+	0.516164i	0.883315	−	0.468779i	$-0.155306\pi$
$877$	21.0391	+	15.2858i	0.710439	+	0.516164i	−0.172876	+	0.984944i	$0.555306\pi$
$878$	5.75658	+	17.7169i	0.194275	+	0.597918i
$879$	−1.74006			−0.0586907
$880$		0			0
$881$	10.4081			0.350657			0.175329	−	0.984510i	$-0.443901\pi$
$881$	10.4081			0.350657			0.175329	+	0.984510i	$0.443901\pi$
$882$	−2.88639	−	8.88338i	−0.0971897	−	0.299119i
$883$	−43.4671	−	31.5807i	−1.46279	−	1.06278i	−0.982626	−	0.185595i	$-0.940579\pi$
$883$	−43.4671	−	31.5807i	−1.46279	−	1.06278i	−0.480159	−	0.877181i	$-0.659421\pi$
$884$	5.10635	−	3.70998i	0.171745	−	0.124780i
$885$		0			0
$886$	8.39826	−	25.8472i	0.282145	−	0.868353i
$887$	−32.8660	+	23.8786i	−1.10353	+	0.801763i	−0.981633	−	0.190779i	$-0.938899\pi$
$887$	−32.8660	+	23.8786i	−1.10353	+	0.801763i	−0.121900	+	0.992542i	$0.538899\pi$
$888$	10.6321	+	7.72468i	0.356790	+	0.259223i
$889$	−17.2701	−	53.1518i	−0.579219	−	1.78265i
$890$		0			0
$891$	−3.27115	+	0.547326i	−0.109588	+	0.0183361i
$892$	81.2188			2.71941
$893$	−27.6371	−	85.0582i	−0.924839	−	2.84636i
$894$	11.6799	+	8.48594i	0.390634	+	0.283812i
$895$		0			0
$896$	−19.6274	+	60.4071i	−0.655707	+	2.01806i
$897$	0.103916	−	0.319822i	0.00346967	−	0.0106785i
$898$	12.5739	−	9.13549i	0.419597	−	0.304855i
$899$	14.0532	+	10.2103i	0.468701	+	0.340531i
$900$		0			0
$901$	24.6772			0.822115
$902$	−61.9290	+	63.0166i	−2.06201	+	2.09822i
$903$	18.1259			0.603191
$904$	−16.6406	−	51.2145i	−0.553458	−	1.70337i
$905$		0			0
$906$	−15.1561	+	11.0116i	−0.503529	+	0.365835i
$907$	5.99708	−	18.4571i	0.199130	−	0.612859i	−0.800774	−	0.598967i	$-0.795578\pi$
$907$	5.99708	−	18.4571i	0.199130	−	0.612859i	0.999904	−	0.0138917i	$-0.00442202\pi$
$908$	−0.665160	+	2.04715i	−0.0220741	+	0.0679371i
$909$	0.408817	−	0.297023i	0.0135596	−	0.00985163i
$910$		0			0
$911$	3.31290	+	10.1960i	0.109761	+	0.337810i	0.990818	−	0.135200i	$-0.0431676\pi$
$911$	3.31290	+	10.1960i	0.109761	+	0.337810i	−0.881057	+	0.473010i	$0.843168\pi$
$912$	31.2271			1.03403
$913$	−37.7658	+	38.4290i	−1.24987	+	1.27182i
$914$	−0.465585			−0.0154002
$915$		0			0
$916$	72.3816	+	52.5883i	2.39156	+	1.73757i
$917$	−0.114477	+	0.0831723i	−0.00378036	+	0.00274659i
$918$	−3.79455	+	11.6784i	−0.125239	+	0.385446i
$919$	−7.14787	+	21.9989i	−0.235787	+	0.725676i	0.761230	+	0.648483i	$0.224596\pi$
$919$	−7.14787	+	21.9989i	−0.235787	+	0.725676i	−0.997016	+	0.0771939i	$0.975404\pi$
$920$		0			0
$921$	−17.2779	−	12.5531i	−0.569325	−	0.413639i
$922$	20.2020	+	62.1755i	0.665319	+	2.04764i
$923$	0.961981			0.0316640
$924$	−43.3444	+	7.25235i	−1.42593	+	0.238585i
$925$		0			0
$926$	15.9322	+	49.0343i	0.523565	+	1.61137i
$927$	−5.17930	−	3.76298i	−0.170111	−	0.123593i
$928$	−1.26589	+	0.919725i	−0.0415550	+	0.0301915i
$929$	8.10467	−	24.9436i	0.265906	−	0.818374i	−0.725578	−	0.688140i	$-0.758427\pi$
$929$	8.10467	−	24.9436i	0.265906	−	0.818374i	0.991483	−	0.130233i	$-0.0415727\pi$
$930$		0			0
$931$	22.9359	−	16.6639i	0.751693	−	0.546137i
$932$	−14.8907	−	10.8187i	−0.487762	−	0.354380i
$933$	−10.1387	−	31.2038i	−0.331927	−	1.02157i
$934$	19.4012			0.634828
$935$		0			0
$936$	−1.56217			−0.0510612
$937$	−7.23133	−	22.2557i	−0.236237	−	0.727063i	−0.996955	−	0.0779804i	$-0.975153\pi$
$937$	−7.23133	−	22.2557i	−0.236237	−	0.727063i	0.760718	−	0.649083i	$-0.224847\pi$
$938$	−99.7456	−	72.4694i	−3.25681	−	2.36621i
$939$	2.79800	−	2.03287i	0.0913094	−	0.0663401i
$940$		0			0
$941$	−3.38952	+	10.4319i	−0.110495	+	0.340069i	−0.990981	−	0.134004i	$-0.957217\pi$
$941$	−3.38952	+	10.4319i	−0.110495	+	0.340069i	0.880486	+	0.474073i	$0.157217\pi$
$942$	−20.1332	+	14.6276i	−0.655976	+	0.476595i
$943$	9.42427	+	6.84713i	0.306896	+	0.222973i
$944$	−11.8634	−	36.5118i	−0.386121	−	1.18836i
$945$		0			0
$946$	6.64038	−	44.4249i	0.215897	−	1.44438i
$947$	13.3652			0.434310			0.217155	−	0.976137i	$-0.430322\pi$
$947$	13.3652			0.434310			0.217155	+	0.976137i	$0.430322\pi$
$948$	−6.74515	−	20.7594i	−0.219072	−	0.674235i
$949$	−2.19199	−	1.59257i	−0.0711550	−	0.0516971i
$950$		0			0
$951$	−0.888626	+	2.73491i	−0.0288157	+	0.0886856i
$952$	−25.3356	+	77.9749i	−0.821130	+	2.52718i
$953$	−17.6562	+	12.8280i	−0.571939	+	0.415538i	−0.835809	−	0.549020i	$-0.815001\pi$
$953$	−17.6562	+	12.8280i	−0.571939	+	0.415538i	0.263870	+	0.964558i	$0.415001\pi$
$954$	−9.80598	−	7.12446i	−0.317480	−	0.230663i
$955$		0			0
$956$	−23.6260			−0.764120
$957$	14.9489	+	7.45366i	0.483229	+	0.240943i
$958$	−98.1686			−3.17168
$959$	7.47809	+	23.0152i	0.241480	+	0.743199i
$960$		0			0
$961$	15.4558	−	11.2293i	0.498576	−	0.362236i
$962$	0.626012	−	1.92667i	0.0201834	−	0.0621182i
$963$	−0.646615	+	1.99008i	−0.0208369	+	0.0641293i
$964$	−32.4865	+	23.6028i	−1.04632	+	0.760196i
$965$		0			0
$966$	2.67881	+	8.24453i	0.0861893	+	0.265263i
$967$	−16.6600			−0.535750			−0.267875	−	0.963454i	$-0.586321\pi$
$967$	−16.6600			−0.535750			−0.267875	+	0.963454i	$0.586321\pi$
$968$	0.955240	+	54.8689i	0.0307026	+	1.76355i
$969$	−37.2704			−1.19730
$970$		0			0
$971$	−8.98271	−	6.52632i	−0.288269	−	0.209440i	0.434247	−	0.900794i	$-0.357014\pi$
$971$	−8.98271	−	6.52632i	−0.288269	−	0.209440i	−0.722516	+	0.691354i	$0.757014\pi$
$972$	3.26145	−	2.36959i	0.104611	−	0.0760045i
$973$	−13.4471	+	41.3858i	−0.431093	+	1.32677i
$974$	−7.54021	+	23.2064i	−0.241604	+	0.743580i
$975$		0			0
$976$	−31.1273	−	22.6153i	−0.996362	−	0.723899i
$977$	−5.81397	−	17.8936i	−0.186005	−	0.572466i	0.813959	−	0.580923i	$-0.197308\pi$
$977$	−5.81397	−	17.8936i	−0.186005	−	0.572466i	−0.999964	+	0.00845665i	$0.997308\pi$
$978$	12.3508			0.394935
$979$	4.81187	+	2.39924i	0.153788	+	0.0766802i
$980$		0			0
$981$	−2.06818	−	6.36521i	−0.0660320	−	0.203226i
$982$	9.88160	+	7.17940i	0.315335	+	0.229104i
$983$	−1.11521	+	0.810250i	−0.0355698	+	0.0258430i	−0.605428	−	0.795900i	$-0.706998\pi$
$983$	−1.11521	+	0.810250i	−0.0355698	+	0.0258430i	0.569858	+	0.821743i	$0.306998\pi$
$984$	16.7224	−	51.4664i	0.533092	−	1.64069i
$985$		0			0
$986$	50.0336	−	36.3516i	1.59340	−	1.15767i
$987$	−31.9045	−	23.1800i	−1.01553	−	0.737827i
$988$	−2.90777	−	8.94918i	−0.0925083	−	0.284711i
$989$	−5.92233			−0.188319
$990$		0			0
$991$	−46.3186			−1.47136			−0.735680	−	0.677329i	$-0.763137\pi$
$991$	−46.3186			−1.47136			−0.735680	+	0.677329i	$0.763137\pi$
$992$	−0.331122	−	1.01909i	−0.0105131	−	0.0323561i
$993$	−11.4250	−	8.30074i	−0.362561	−	0.263416i
$994$	−20.0623	+	14.5761i	−0.636339	+	0.462327i
$995$		0			0
$996$	20.2380	−	62.2861i	0.641265	−	1.97361i
$997$	11.7688	−	8.55054i	0.372722	−	0.270798i	−0.385617	−	0.922659i	$-0.626011\pi$
$997$	11.7688	−	8.55054i	0.372722	−	0.270798i	0.758339	+	0.651861i	$0.226011\pi$
$998$	86.9759	+	63.1917i	2.75317	+	2.00030i
$999$	0.814038	+	2.50535i	0.0257550	+	0.0792658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.k.676.1		8
5.2	odd	4		825.2.bx.h.49.4		16
5.3	odd	4		825.2.bx.h.49.1		16
5.4	even	2		165.2.m.a.16.2	✓	8
11.3	even	5		9075.2.a.cl.1.2		4
11.8	odd	10		9075.2.a.dj.1.3		4
11.9	even	5	inner	825.2.n.k.526.1		8
15.14	odd	2		495.2.n.d.181.1		8
55.9	even	10		165.2.m.a.31.2	yes	8
55.14	even	10		1815.2.a.x.1.3		4
55.19	odd	10		1815.2.a.o.1.2		4
55.42	odd	20		825.2.bx.h.724.1		16
55.53	odd	20		825.2.bx.h.724.4		16
165.14	odd	10		5445.2.a.be.1.2		4
165.74	even	10		5445.2.a.bv.1.3		4
165.119	odd	10		495.2.n.d.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.2	✓	8	5.4	even	2
165.2.m.a.31.2	yes	8	55.9	even	10
495.2.n.d.181.1		8	15.14	odd	2
495.2.n.d.361.1		8	165.119	odd	10
825.2.n.k.526.1		8	11.9	even	5	inner
825.2.n.k.676.1		8	1.1	even	1	trivial
825.2.bx.h.49.1		16	5.3	odd	4
825.2.bx.h.49.4		16	5.2	odd	4
825.2.bx.h.724.1		16	55.42	odd	20
825.2.bx.h.724.4		16	55.53	odd	20
1815.2.a.o.1.2		4	55.19	odd	10
1815.2.a.x.1.3		4	55.14	even	10
5445.2.a.be.1.2		4	165.14	odd	10
5445.2.a.bv.1.3		4	165.74	even	10
9075.2.a.cl.1.2		4	11.3	even	5
9075.2.a.dj.1.3		4	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +(2.96813 + 1.47994i) q^{11} -4.03138 q^{12} +(0.0967635 + 0.297808i) q^{13} +(-6.53048 - 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(1.98685 - 1.44353i) q^{18} +(6.03048 + 4.38140i) q^{19} +3.28684 q^{21} +(1.20413 - 8.05576i) q^{22} -1.07392 q^{23} +(1.54164 + 4.74467i) q^{24} +(0.622150 - 0.452019i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.09463 + 12.6020i) q^{28} +(4.07459 - 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680 q^{32} +(1.53138 + 2.94192i) q^{33} +12.2794 q^{34} +(-3.26145 - 2.36959i) q^{36} +(2.13118 - 1.54839i) q^{37} +(5.65698 - 17.4104i) q^{38} +(-0.0967635 + 0.297808i) q^{39} +(-8.77557 - 6.37583i) q^{41} +(-2.49442 - 7.67703i) q^{42} +5.51468 q^{43} +(-13.1873 + 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(-9.70674 - 7.05236i) q^{47} +(3.38919 - 2.46239i) q^{48} +(1.17529 - 3.61718i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(-1.02127 - 0.741996i) q^{52} +(-1.52513 - 4.69387i) q^{53} +2.45589 q^{54} +16.3975 q^{56} +(2.30344 + 7.08925i) q^{57} +(-10.0067 - 7.27031i) q^{58} +(7.41391 - 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(6.85264 - 4.97873i) q^{62} +(2.65911 + 1.93196i) q^{63} +(-2.35333 - 7.24280i) q^{64} +(5.70922 - 5.80948i) q^{66} +15.2739 q^{67} +(-6.22882 - 19.1704i) q^{68} +(-0.868820 - 0.631235i) q^{69} +(0.949335 - 2.92175i) q^{71} +(-1.54164 + 4.74467i) q^{72} +(-7.00018 + 5.08592i) q^{73} +(-5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 - 1.79898i) q^{77} +0.769020 q^{78} +(1.67316 + 5.14946i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-8.23206 + 25.3357i) q^{82} +(-5.02011 + 15.4503i) q^{83} +(-10.7199 + 7.78845i) q^{84} +(-4.18515 - 12.8806i) q^{86} +5.03647 q^{87} +(7.63981 + 14.6768i) q^{88} +1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(3.50254 - 2.54475i) q^{92} +(-1.06580 + 3.28018i) q^{93} +(-9.10556 + 28.0240i) q^{94} +(-0.251345 - 0.182613i) q^{96} +(-0.0692451 - 0.213115i) q^{97} -9.34054 q^{98} +(-0.490303 + 3.28018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 - q^7 - 5 * q^8 - 2 * q^9 - 3 * q^11 - 18 * q^12 - 6 * q^13 - 10 * q^14 - 20 * q^16 + 10 * q^17 + 5 * q^18 + 6 * q^19 - 4 * q^21 + 25 * q^22 + 10 * q^23 - 20 * q^24 - 8 * q^26 + 2 * q^27 - 31 * q^28 + 3 * q^31 - 60 * q^32 - 2 * q^33 + 50 * q^34 - 2 * q^36 + 19 * q^37 + 28 * q^38 + 6 * q^39 - 25 * q^41 - 15 * q^42 + 4 * q^43 + 7 * q^44 - 6 * q^46 - 15 * q^47 - 5 * q^48 + 21 * q^49 - 10 * q^51 - 6 * q^52 - 7 * q^53 + 10 * q^54 + 20 * q^56 + 9 * q^57 + 2 * q^58 + 35 * q^59 + 21 * q^61 + 19 * q^62 - q^63 - 77 * q^64 + 25 * q^66 + 26 * q^67 + 35 * q^68 - 5 * q^69 + 25 * q^71 + 20 * q^72 - q^73 - 29 * q^74 - 14 * q^76 + 61 * q^77 - 12 * q^78 + 30 * q^79 - 2 * q^81 - 57 * q^82 - 11 * q^83 - 34 * q^84 - 34 * q^86 - 10 * q^87 + 85 * q^88 + 32 * q^89 + 37 * q^91 + 10 * q^92 - 3 * q^93 - 39 * q^94 + 10 * q^96 - 5 * q^97 - 50 * q^98 - 3 * q^99

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