LMFDB - Embedded newform 825.2.bx.h.724.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 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:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.4
Root			$0.701538 + 0.227943i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.h.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.33569 + 0.758911i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.26145 + 2.36959i) q^{4} +(0.758911 + 2.33569i) q^{6} +(1.93196 - 2.65911i) q^{7} +(2.93237 + 4.03606i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(2.33569 + 0.758911i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.26145 + 2.36959i) q^{4} +(0.758911 + 2.33569i) q^{6} +(1.93196 - 2.65911i) q^{7} +(2.93237 + 4.03606i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(2.96813 - 1.47994i) q^{11} +4.03138i q^{12} +(0.297808 + 0.0967635i) q^{13} +(6.53048 - 4.74467i) q^{14} +(1.29455 + 3.98423i) q^{16} +(-4.75528 + 1.54508i) q^{17} +(-1.44353 + 1.98685i) q^{18} +(-6.03048 + 4.38140i) q^{19} +3.28684 q^{21} +(8.05576 - 1.20413i) q^{22} -1.07392i q^{23} +(-1.54164 + 4.74467i) q^{24} +(0.622150 + 0.452019i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(12.6020 - 4.09463i) q^{28} +(-4.07459 - 2.96036i) q^{29} +(1.06580 - 3.28018i) q^{31} +0.310680i q^{32} +(2.94192 + 1.53138i) q^{33} -12.2794 q^{34} +(-3.26145 + 2.36959i) q^{36} +(1.54839 - 2.13118i) q^{37} +(-17.4104 + 5.65698i) q^{38} +(0.0967635 + 0.297808i) q^{39} +(-8.77557 + 6.37583i) q^{41} +(7.67703 + 2.49442i) q^{42} +5.51468i q^{43} +(13.1873 + 2.20648i) q^{44} +(0.815010 - 2.50834i) q^{46} +(7.05236 + 9.70674i) q^{47} +(-2.46239 + 3.38919i) q^{48} +(-1.17529 - 3.61718i) q^{49} +(-4.04508 - 2.93893i) q^{51} +(0.741996 + 1.02127i) q^{52} +(-4.69387 - 1.52513i) q^{53} -2.45589 q^{54} +16.3975 q^{56} +(-7.08925 - 2.30344i) q^{57} +(-7.27031 - 10.0067i) q^{58} +(-7.41391 - 5.38652i) q^{59} +(2.83811 + 8.73480i) q^{61} +(4.97873 - 6.85264i) q^{62} +(1.93196 + 2.65911i) q^{63} +(2.35333 - 7.24280i) q^{64} +(5.70922 + 5.80948i) q^{66} -15.2739i q^{67} +(-19.1704 - 6.22882i) q^{68} +(0.868820 - 0.631235i) q^{69} +(0.949335 + 2.92175i) q^{71} +(-4.74467 + 1.54164i) q^{72} +(5.08592 - 7.00018i) q^{73} +(5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(1.79898 - 10.7518i) q^{77} +0.769020i q^{78} +(-1.67316 + 5.14946i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-25.3357 + 8.23206i) q^{82} +(15.4503 - 5.02011i) q^{83} +(10.7199 + 7.78845i) q^{84} +(-4.18515 + 12.8806i) q^{86} -5.03647i q^{87} +(14.6768 + 7.63981i) q^{88} -1.62118 q^{89} +(0.832656 - 0.604960i) q^{91} +(2.54475 - 3.50254i) q^{92} +(3.28018 - 1.06580i) q^{93} +(9.10556 + 28.0240i) q^{94} +(-0.251345 + 0.182613i) q^{96} +(0.213115 + 0.0692451i) q^{97} -9.34054i q^{98} +(0.490303 + 3.28018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

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 $

$2$	2.33569	+	0.758911i	1.65158	+	0.536631i	0.979082	−	0.203468i	$-0.0652211\pi$
$2$	2.33569	+	0.758911i	1.65158	+	0.536631i	0.672499	+	0.740098i	$0.265221\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	3.26145	+	2.36959i	1.63073	+	1.18479i
$5$		0			0
$5$		0			0
$6$	0.758911	+	2.33569i	0.309824	+	0.953540i
$7$	1.93196	−	2.65911i	0.730211	−	1.00505i	−0.268911	−	0.963165i	$-0.586664\pi$
$7$	1.93196	−	2.65911i	0.730211	−	1.00505i	0.999122	−	0.0418845i	$-0.0133361\pi$
$8$	2.93237	+	4.03606i	1.03675	+	1.42696i
$9$	−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
$12$			4.03138i			1.16376i
$13$	0.297808	+	0.0967635i	0.0825970	+	0.0268374i	0.350024	−	0.936741i	$-0.386173\pi$
$13$	0.297808	+	0.0967635i	0.0825970	+	0.0268374i	−0.267427	+	0.963578i	$0.586173\pi$
$14$	6.53048	−	4.74467i	1.74534	−	1.26807i
$15$		0			0
$16$	1.29455	+	3.98423i	0.323638	+	0.996057i
$17$	−4.75528	+	1.54508i	−1.15333	+	0.374738i	−0.822395	−	0.568917i	$-0.807363\pi$
$17$	−4.75528	+	1.54508i	−1.15333	+	0.374738i	−0.330930	+	0.943655i	$0.607363\pi$
$18$	−1.44353	+	1.98685i	−0.340244	+	0.468306i
$19$	−6.03048	+	4.38140i	−1.38349	+	1.00516i	−0.386941	+	0.922104i	$0.626468\pi$
$19$	−6.03048	+	4.38140i	−1.38349	+	1.00516i	−0.996545	+	0.0830568i	$0.973532\pi$
$20$		0			0
$21$	3.28684			0.717248
$22$	8.05576	−	1.20413i	1.71749	−	0.256721i
$23$		−	1.07392i		−	0.223928i	−0.993712	−	0.111964i	$-0.964286\pi$
$23$		−	1.07392i		−	0.223928i	0.993712	−	0.111964i	$-0.0357141\pi$
$24$	−1.54164	+	4.74467i	−0.314685	+	0.968501i
$25$		0			0
$26$	0.622150	+	0.452019i	0.122014	+	0.0886482i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	12.6020	−	4.09463i	2.38155	−	0.773813i
$29$	−4.07459	−	2.96036i	−0.756632	−	0.549725i	0.141243	−	0.989975i	$-0.454890\pi$
$29$	−4.07459	−	2.96036i	−0.756632	−	0.549725i	−0.897875	+	0.440250i	$0.854890\pi$
$30$		0			0
$31$	1.06580	−	3.28018i	0.191423	−	0.589138i	−0.808577	−	0.588390i	$-0.799762\pi$
$31$	1.06580	−	3.28018i	0.191423	−	0.589138i	1.00000		0.000748050i	$-0.000238112\pi$
$32$			0.310680i			0.0549210i
$33$	2.94192	+	1.53138i	0.512122	+	0.266579i
$34$	−12.2794			−2.10591
$35$		0			0
$36$	−3.26145	+	2.36959i	−0.543576	+	0.394931i
$37$	1.54839	−	2.13118i	0.254554	−	0.350364i	−0.662546	−	0.749022i	$-0.730524\pi$
$37$	1.54839	−	2.13118i	0.254554	−	0.350364i	0.917100	+	0.398658i	$0.130524\pi$
$38$	−17.4104	+	5.65698i	−2.82434	+	0.917683i
$39$	0.0967635	+	0.297808i	0.0154946	+	0.0476874i
$40$		0			0
$41$	−8.77557	+	6.37583i	−1.37051	+	0.995737i	−0.372817	+	0.927905i	$0.621608\pi$
$41$	−8.77557	+	6.37583i	−1.37051	+	0.995737i	−0.997697	+	0.0678321i	$0.978392\pi$
$42$	7.67703	+	2.49442i	1.18459	+	0.384897i
$43$			5.51468i			0.840980i	0.907297	+	0.420490i	$0.138142\pi$
$43$			5.51468i			0.840980i	−0.907297	+	0.420490i	$0.861858\pi$
$44$	13.1873	+	2.20648i	1.98805	+	0.332640i
$45$		0			0
$46$	0.815010	−	2.50834i	0.120167	−	0.369835i
$47$	7.05236	+	9.70674i	1.02869	+	1.41587i	0.905925	+	0.423438i	$0.139177\pi$
$47$	7.05236	+	9.70674i	1.02869	+	1.41587i	0.122767	+	0.992435i	$0.460823\pi$
$48$	−2.46239	+	3.38919i	−0.355415	+	0.489187i
$49$	−1.17529	−	3.61718i	−0.167899	−	0.516740i
$50$		0			0
$51$	−4.04508	−	2.93893i	−0.566425	−	0.411532i
$52$	0.741996	+	1.02127i	0.102896	+	0.141625i
$53$	−4.69387	−	1.52513i	−0.644753	−	0.209493i	−0.0316539	−	0.999499i	$-0.510077\pi$
$53$	−4.69387	−	1.52513i	−0.644753	−	0.209493i	−0.613099	+	0.790006i	$0.710077\pi$
$54$	−2.45589			−0.334204
$55$		0			0
$56$	16.3975			2.19121
$57$	−7.08925	−	2.30344i	−0.938994	−	0.305098i
$58$	−7.27031	−	10.0067i	−0.954639	−	1.31395i
$59$	−7.41391	−	5.38652i	−0.965208	−	0.701265i	−0.0108537	−	0.999941i	$-0.503455\pi$
$59$	−7.41391	−	5.38652i	−0.965208	−	0.701265i	−0.954354	+	0.298676i	$0.903455\pi$
$60$		0			0
$61$	2.83811	+	8.73480i	0.363382	+	1.11838i	0.950988	+	0.309229i	$0.100071\pi$
$61$	2.83811	+	8.73480i	0.363382	+	1.11838i	−0.587605	+	0.809148i	$0.699929\pi$
$62$	4.97873	−	6.85264i	0.632300	−	0.870286i
$63$	1.93196	+	2.65911i	0.243404	+	0.335016i
$64$	2.35333	−	7.24280i	0.294166	−	0.905350i
$65$		0			0
$66$	5.70922	+	5.80948i	0.702756	+	0.715097i
$67$		−	15.2739i		−	1.86600i	−0.359876	−	0.933000i	$-0.617181\pi$
$67$		−	15.2739i		−	1.86600i	0.359876	−	0.933000i	$-0.382819\pi$
$68$	−19.1704	−	6.22882i	−2.32475	−	0.755356i
$69$	0.868820	−	0.631235i	0.104594	−	0.0759917i
$70$		0			0
$71$	0.949335	+	2.92175i	0.112665	+	0.346748i	0.991453	−	0.130465i	$-0.0416470\pi$
$71$	0.949335	+	2.92175i	0.112665	+	0.346748i	−0.878788	+	0.477213i	$0.841647\pi$
$72$	−4.74467	+	1.54164i	−0.559164	+	0.181684i
$73$	5.08592	−	7.00018i	0.595262	−	0.819309i	−0.400002	−	0.916514i	$-0.630991\pi$
$73$	5.08592	−	7.00018i	0.595262	−	0.819309i	0.995264	+	0.0972058i	$0.0309905\pi$
$74$	5.23394	−	3.80268i	0.608433	−	0.442052i
$75$		0			0
$76$	−30.0502			−3.44700
$77$	1.79898	−	10.7518i	0.205012	−	1.22528i
$78$			0.769020i			0.0870744i
$79$	−1.67316	+	5.14946i	−0.188245	+	0.579360i	−0.999989	−	0.00465401i	$-0.998519\pi$
$79$	−1.67316	+	5.14946i	−0.188245	+	0.579360i	0.811744	+	0.584014i	$0.198519\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−25.3357	+	8.23206i	−2.79786	+	0.909079i
$83$	15.4503	−	5.02011i	1.69589	−	0.551029i	0.708006	−	0.706207i	$-0.249595\pi$
$83$	15.4503	−	5.02011i	1.69589	−	0.551029i	0.987887	+	0.155178i	$0.0495952\pi$
$84$	10.7199	+	7.78845i	1.16964	+	0.849790i
$85$		0			0
$86$	−4.18515	+	12.8806i	−0.451296	+	1.38895i
$87$		−	5.03647i		−	0.539966i
$88$	14.6768	+	7.63981i	1.56455	+	0.814406i
$89$	−1.62118			−0.171845			−0.0859223	−	0.996302i	$-0.527384\pi$
$89$	−1.62118			−0.171845			−0.0859223	+	0.996302i	$0.527384\pi$
$90$		0			0
$91$	0.832656	−	0.604960i	0.0872861	−	0.0634171i
$92$	2.54475	−	3.50254i	0.265308	−	0.365165i
$93$	3.28018	−	1.06580i	0.340139	−	0.110518i
$94$	9.10556	+	28.0240i	0.939166	+	2.89046i
$95$		0			0
$96$	−0.251345	+	0.182613i	−0.0256528	+	0.0186379i
$97$	0.213115	+	0.0692451i	0.0216385	+	0.00703078i	0.319816	−	0.947480i	$-0.396379\pi$
$97$	0.213115	+	0.0692451i	0.0216385	+	0.00703078i	−0.298178	+	0.954510i	$0.596379\pi$
$98$		−	9.34054i		−	0.943537i
$99$	0.490303	+	3.28018i	0.0492773	+	0.329671i
$100$		0			0
$101$	−0.156154	+	0.480593i	−0.0155379	+	0.0478208i	−0.958525	−	0.285009i	$-0.908003\pi$
$101$	−0.156154	+	0.480593i	−0.0155379	+	0.0478208i	0.942987	+	0.332830i	$0.108003\pi$
$102$	−7.21767	−	9.93427i	−0.714656	−	0.983639i
$103$	3.76298	−	5.17930i	0.370778	−	0.510332i	−0.582334	−	0.812949i	$-0.697861\pi$
$103$	3.76298	−	5.17930i	0.370778	−	0.510332i	0.953112	+	0.302618i	$0.0978605\pi$
$104$	0.482738	+	1.48571i	0.0473363	+	0.145686i
$105$		0			0
$106$	−9.80598	−	7.12446i	−0.952441	−	0.691989i
$107$	−1.22993	−	1.69286i	−0.118902	−	0.163655i	0.745417	−	0.666598i	$-0.232250\pi$
$107$	−1.22993	−	1.69286i	−0.118902	−	0.163655i	−0.864319	+	0.502943i	$0.832250\pi$
$108$	−3.83407	−	1.24576i	−0.368934	−	0.119874i
$109$	6.69278			0.641052			0.320526	−	0.947240i	$-0.396140\pi$
$109$	6.69278			0.641052			0.320526	+	0.947240i	$0.396140\pi$
$110$		0			0
$111$	2.63428			0.250035
$112$	13.0955	+	4.25499i	1.23741	+	0.402059i
$113$	−6.34462	−	8.73262i	−0.596852	−	0.821496i	0.398564	−	0.917141i	$-0.369509\pi$
$113$	−6.34462	−	8.73262i	−0.596852	−	0.821496i	−0.995416	+	0.0956448i	$0.969509\pi$
$114$	−14.8102	−	10.7602i	−1.38710	−	1.00779i
$115$		0			0
$116$	−6.27426	−	19.3102i	−0.582550	−	1.79290i
$117$	−0.184055	+	0.253330i	−0.0170159	+	0.0234204i
$118$	−13.2287	−	18.2077i	−1.21780	−	1.67616i
$119$	−5.07845	+	15.6299i	−0.465541	+	1.43279i
$120$		0			0
$121$	6.61956	−	8.78529i	0.601779	−	0.798663i
$122$			22.5556i			2.04209i
$123$	−10.3163	−	3.35197i	−0.930190	−	0.302237i
$124$	11.2487	−	8.17267i	1.01017	−	0.733928i
$125$		0			0
$126$	2.49442	+	7.67703i	0.222221	+	0.683925i
$127$	16.1711	−	5.25430i	1.43495	−	0.466244i	0.514632	−	0.857411i	$-0.327929\pi$
$127$	16.1711	−	5.25430i	1.43495	−	0.466244i	0.920320	+	0.391167i	$0.127929\pi$
$128$	11.3585	−	15.6336i	1.00396	−	1.38183i
$129$	−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	$0.500599\pi$
$132$	5.96619	+	11.9657i	0.519291	+	1.04148i
$133$			24.5004i			2.12445i
$134$	11.5915	−	35.6750i	1.00135	−	3.08185i
$135$		0			0
$136$	−20.1803	−	14.6618i	−1.73044	−	1.25724i
$137$	−7.00222	+	2.27516i	−0.598240	+	0.194380i	−0.592455	−	0.805603i	$-0.701841\pi$
$137$	−7.00222	+	2.27516i	−0.598240	+	0.194380i	−0.00578480	+	0.999983i	$0.501841\pi$
$138$	2.50834	−	0.815010i	0.213524	−	0.0693783i
$139$	10.7109	+	7.78189i	0.908483	+	0.660052i	0.940631	−	0.339432i	$-0.110235\pi$
$139$	10.7109	+	7.78189i	0.908483	+	0.660052i	−0.0321478	+	0.999483i	$0.510235\pi$
$140$		0			0
$141$	−3.70764	+	11.4110i	−0.312240	+	0.960976i
$142$			7.54476i			0.633142i
$143$	1.02713	−	0.153530i	0.0858933	−	0.0128388i
$144$	−4.18926			−0.349105
$145$		0			0
$146$	17.1916	−	12.4905i	1.42279	−	1.03372i
$147$	2.23554	−	3.07696i	0.184384	−	0.253783i
$148$	10.1000	−	3.28170i	0.830217	−	0.269754i
$149$	1.81658	+	5.59087i	0.148820	+	0.458022i	0.997482	−	0.0709136i	$-0.0225915\pi$
$149$	1.81658	+	5.59087i	0.148820	+	0.458022i	−0.848662	+	0.528935i	$0.822591\pi$
$150$		0			0
$151$	−6.17135	+	4.48375i	−0.502217	+	0.364882i	−0.809863	−	0.586619i	$-0.800459\pi$
$151$	−6.17135	+	4.48375i	−0.502217	+	0.364882i	0.307646	+	0.951501i	$0.400459\pi$
$152$	−35.3671	−	11.4915i	−2.86865	−	0.932082i
$153$		−	5.00000i		−	0.404226i
$154$	12.3615	−	23.7475i	0.996116	−	1.91363i
$155$		0			0
$156$	−0.390091	+	1.20058i	−0.0312322	+	0.0961230i
$157$	5.95616	+	8.19795i	0.475353	+	0.654267i	0.977604	−	0.210455i	$-0.0674945\pi$
$157$	5.95616	+	8.19795i	0.475353	+	0.654267i	−0.502250	+	0.864722i	$0.667494\pi$
$158$	−7.81596	+	10.7578i	−0.621805	+	0.855841i
$159$	−1.52513	−	4.69387i	−0.120951	−	0.372248i
$160$		0			0
$161$	−2.85567	−	2.07477i	−0.225059	−	0.163515i
$162$	−1.44353	−	1.98685i	−0.113415	−	0.156102i
$163$	4.78292	+	1.55407i	0.374627	+	0.121724i	0.490278	−	0.871566i	$-0.336895\pi$
$163$	4.78292	+	1.55407i	0.374627	+	0.121724i	−0.115651	+	0.993290i	$0.536895\pi$
$164$	−43.7292			−3.41468
$165$		0			0
$166$	39.8969			3.09660
$167$	5.50761	+	1.78953i	0.426192	+	0.138478i	0.514256	−	0.857637i	$-0.328068\pi$
$167$	5.50761	+	1.78953i	0.426192	+	0.138478i	−0.0880642	+	0.996115i	$0.528068\pi$
$168$	9.63822	+	13.2659i	0.743605	+	1.02348i
$169$	−10.4379	−	7.58357i	−0.802915	−	0.583352i
$170$		0			0
$171$	−2.30344	−	7.08925i	−0.176148	−	0.542128i
$172$	−13.0675	+	17.9859i	−0.996387	+	1.37141i
$173$	9.44290	+	12.9970i	0.717930	+	0.988146i	0.999590	+	0.0286316i	$0.00911498\pi$
$173$	9.44290	+	12.9970i	0.717930	+	0.988146i	−0.281660	+	0.959514i	$0.590885\pi$
$174$	3.82223	−	11.7636i	0.289762	−	0.891797i
$175$		0			0
$176$	9.73881	+	9.90983i	0.734090	+	0.746982i
$177$		−	9.16409i		−	0.688815i
$178$	−3.78657	−	1.23033i	−0.283815	−	0.0922171i
$179$	−6.71734	+	4.88043i	−0.502078	+	0.364781i	−0.809810	−	0.586692i	$-0.800430\pi$
$179$	−6.71734	+	4.88043i	−0.502078	+	0.364781i	0.307732	+	0.951473i	$0.400430\pi$
$180$		0			0
$181$	−1.99756	−	6.14787i	−0.148478	−	0.456968i	0.848964	−	0.528451i	$-0.177227\pi$
$181$	−1.99756	−	6.14787i	−0.148478	−	0.456968i	−0.997442	+	0.0714830i	$0.977227\pi$
$182$	2.40394	−	0.781086i	0.178192	−	0.0578980i
$183$	−5.39840	+	7.43026i	−0.399061	+	0.549261i
$184$	4.33440	−	3.14913i	0.319536	−	0.232157i
$185$		0			0
$186$	8.47033			0.621074
$187$	−11.8277	+	11.6235i	−0.864924	+	0.849997i
$188$			48.3693i			3.52769i
$189$	−1.01569	+	3.12597i	−0.0738806	+	0.227381i
$190$		0			0
$191$	−12.4340	−	9.03384i	−0.899694	−	0.653666i	0.0386935	−	0.999251i	$-0.487680\pi$
$191$	−12.4340	−	9.03384i	−0.899694	−	0.653666i	−0.938387	+	0.345585i	$0.887680\pi$
$192$	7.24280	−	2.35333i	0.522704	−	0.169837i
$193$	14.9808	−	4.86757i	1.07834	−	0.350375i	0.284612	−	0.958643i	$-0.408135\pi$
$193$	14.9808	−	4.86757i	1.07834	−	0.350375i	0.793732	+	0.608267i	$0.208135\pi$
$194$	0.445218	+	0.323470i	0.0319648	+	0.0232238i
$195$		0			0
$196$	4.73805	−	14.5822i	0.338432	−	1.04159i
$197$			16.3940i			1.16802i	0.811746	+	0.584010i	$0.198517\pi$
$197$			16.3940i			1.16802i	−0.811746	+	0.584010i	$0.801483\pi$
$198$	−1.34417	+	8.03358i	−0.0955261	+	0.570922i
$199$	−6.96500			−0.493736			−0.246868	−	0.969049i	$-0.579401\pi$
$199$	−6.96500			−0.493736			−0.246868	+	0.969049i	$0.579401\pi$
$200$		0			0
$201$	12.3568	−	8.97776i	0.871583	−	0.633242i
$202$	−0.729455	+	1.00401i	−0.0513242	+	0.0706418i
$203$	−15.7439	+	5.11549i	−1.10500	+	0.359037i
$204$	−6.22882	−	19.1704i	−0.436105	−	1.34219i
$205$		0			0
$206$	12.7198	−	9.24146i	0.886229	−	0.643883i
$207$	1.02136	+	0.331860i	0.0709894	+	0.0230658i
$208$			1.31180i			0.0909569i
$209$	−11.4150	+	21.9293i	−0.789594	+	1.51688i
$210$		0			0
$211$	−6.16585	+	18.9765i	−0.424475	+	1.30640i	0.479022	+	0.877803i	$0.340992\pi$
$211$	−6.16585	+	18.9765i	−0.424475	+	1.30640i	−0.903496	+	0.428596i	$0.859008\pi$
$212$	−11.6949	−	16.0967i	−0.803211	−	1.10552i
$213$	−1.80574	+	2.48539i	−0.123727	+	0.170296i
$214$	−1.58801	−	4.88740i	−0.108554	−	0.334096i
$215$		0			0
$216$	−4.03606	−	2.93237i	−0.274619	−	0.199522i
$217$	−6.66330	−	9.17124i	−0.452334	−	0.622585i
$218$	15.6322	+	5.07922i	1.05875	+	0.344008i
$219$	8.65269			0.584695
$220$		0			0
$221$	−1.56567			−0.105318
$222$	6.15286	+	1.99919i	0.412953	+	0.134177i
$223$	−11.8419	−	16.2990i	−0.792992	−	1.09146i	−0.993729	−	0.111815i	$-0.964334\pi$
$223$	−11.8419	−	16.2990i	−0.792992	−	1.09146i	0.200737	−	0.979645i	$-0.435666\pi$
$224$	0.826133	+	0.600220i	0.0551983	+	0.0401039i
$225$		0			0
$226$	−8.19177	−	25.2117i	−0.544908	−	1.67706i
$227$	0.313840	−	0.431964i	0.0208303	−	0.0286705i	−0.798475	−	0.602028i	$-0.794359\pi$
$227$	0.313840	−	0.431964i	0.0208303	−	0.0286705i	0.819305	+	0.573358i	$0.194359\pi$
$228$	−17.6631	−	24.3111i	−1.16977	−	1.61004i
$229$	6.85803	−	21.1068i	0.453191	−	1.39478i	−0.420054	−	0.907499i	$-0.637989\pi$
$229$	6.85803	−	21.1068i	0.453191	−	1.39478i	0.873245	−	0.487281i	$-0.162011\pi$
$230$		0			0
$231$	9.75577	−	4.86432i	0.641882	−	0.320049i
$232$		−	25.1261i		−	1.64961i
$233$	4.34221	+	1.41087i	0.284467	+	0.0924291i	0.447775	−	0.894146i	$-0.352216\pi$
$233$	4.34221	+	1.41087i	0.284467	+	0.0924291i	−0.163308	+	0.986575i	$0.552216\pi$
$234$	−0.622150	+	0.452019i	−0.0406712	+	0.0295494i
$235$		0			0
$236$	−11.4163	−	35.1358i	−0.743138	−	2.28714i
$237$	−5.14946	+	1.67316i	−0.334493	+	0.108684i
$238$	−23.7233	+	32.6524i	−1.53776	+	2.11654i
$239$	−4.74126	+	3.44473i	−0.306687	+	0.222821i	−0.730474	−	0.682941i	$-0.760701\pi$
$239$	−4.74126	+	3.44473i	−0.306687	+	0.222821i	0.423787	+	0.905762i	$0.360701\pi$
$240$		0			0
$241$	9.96074			0.641628			0.320814	−	0.947142i	$-0.396044\pi$
$241$	9.96074			0.641628			0.320814	+	0.947142i	$0.396044\pi$
$242$	22.1285	−	15.4960i	1.42247	−	0.996123i
$243$		−	1.00000i		−	0.0641500i
$244$	−11.4415	+	35.2133i	−0.732466	+	2.25430i
$245$		0			0
$246$	−21.5518	−	15.6583i	−1.37409	−	0.998337i
$247$	−2.21988	+	0.721283i	−0.141248	+	0.0458941i
$248$	16.3643	−	5.31709i	1.03913	−	0.337635i
$249$	13.1428	+	9.54882i	0.832892	+	0.605132i
$250$		0			0
$251$	−5.21584	+	16.0527i	−0.329221	+	1.01324i	0.640279	+	0.768143i	$0.278819\pi$
$251$	−5.21584	+	16.0527i	−0.329221	+	1.01324i	−0.969499	+	0.245094i	$0.921181\pi$
$252$			13.2505i			0.834704i
$253$	−1.58934	−	3.18753i	−0.0999207	−	0.200399i
$254$	41.7581			2.62014
$255$		0			0
$256$	26.0723	−	18.9426i	1.62952	−	1.18391i
$257$	6.55003	−	9.01534i	0.408580	−	0.562362i	−0.554292	−	0.832323i	$-0.687011\pi$
$257$	6.55003	−	9.01534i	0.408580	−	0.562362i	0.962871	+	0.269961i	$0.0870108\pi$
$258$	−12.8806	+	4.18515i	−0.801909	+	0.260556i
$259$	−2.67561	−	8.23470i	−0.166255	−	0.511679i
$260$		0			0
$261$	4.07459	−	2.96036i	0.252211	−	0.183242i
$262$	−0.100553	−	0.0326717i	−0.00621220	−	0.00201846i
$263$			26.8726i			1.65704i	0.559961	+	0.828519i	$0.310816\pi$
$263$			26.8726i			1.65704i	−0.559961	+	0.828519i	$0.689184\pi$
$264$	2.44604	+	16.3643i	0.150544	+	1.00715i
$265$		0			0
$266$	−18.5936	+	57.2252i	−1.14005	+	3.50870i
$267$	−0.952905	−	1.31156i	−0.0583168	−	0.0802662i
$268$	36.1927	−	49.8150i	2.21082	−	3.04294i
$269$	3.10961	+	9.57038i	0.189596	+	0.583516i	0.999997	−	0.00235886i	$-0.000750850\pi$
$269$	3.10961	+	9.57038i	0.189596	+	0.583516i	−0.810401	+	0.585875i	$0.800751\pi$
$270$		0			0
$271$	−8.53037	−	6.19767i	−0.518183	−	0.376482i	0.297736	−	0.954648i	$-0.403768\pi$
$271$	−8.53037	−	6.19767i	−0.518183	−	0.376482i	−0.815919	+	0.578166i	$0.803768\pi$
$272$	−12.3119	−	16.9459i	−0.746521	−	1.02750i
$273$	0.978846	+	0.318046i	0.0592425	+	0.0192490i
$274$	−18.0816			−1.09235
$275$		0			0
$276$	4.32938			0.260598
$277$	−17.0597	−	5.54302i	−1.02502	−	0.333048i	−0.252198	−	0.967676i	$-0.581153\pi$
$277$	−17.0597	−	5.54302i	−1.02502	−	0.333048i	−0.772818	+	0.634628i	$0.781153\pi$
$278$	19.1114	+	26.3047i	1.14623	+	1.57765i
$279$	2.79029	+	2.02726i	0.167050	+	0.121369i
$280$		0			0
$281$	2.29013	+	7.04830i	0.136618	+	0.420467i	0.995838	−	0.0911392i	$-0.0290508\pi$
$281$	2.29013	+	7.04830i	0.136618	+	0.420467i	−0.859220	+	0.511606i	$0.829051\pi$
$282$	−17.3198	+	23.8387i	−1.03138	+	1.41957i
$283$	3.16630	+	4.35804i	0.188217	+	0.259059i	0.892689	−	0.450673i	$-0.148816\pi$
$283$	3.16630	+	4.35804i	0.188217	+	0.259059i	−0.704472	+	0.709732i	$0.748816\pi$
$284$	−3.82713	+	11.7787i	−0.227098	+	0.698937i
$285$		0			0
$286$	2.51558	+	0.420905i	0.148749	+	0.0248886i
$287$			35.6530i			2.10453i
$288$	−0.295474	−	0.0960054i	−0.0174110	−	0.00565717i
$289$	6.47214	−	4.70228i	0.380714	−	0.276605i
$290$		0			0
$291$	0.0692451	+	0.213115i	0.00405922	+	0.0124930i
$292$	33.1750	−	10.7792i	1.94142	−	0.630806i
$293$	1.02278	−	1.40774i	0.0597515	−	0.0822409i	−0.778096	−	0.628146i	$-0.783814\pi$
$293$	1.02278	−	1.40774i	0.0597515	−	0.0822409i	0.837847	+	0.545905i	$0.183814\pi$
$294$	7.55666	−	5.49023i	0.440713	−	0.320197i
$295$		0			0
$296$	13.1420			0.763864
$297$	−2.36553	+	2.32471i	−0.137262	+	0.134893i
$298$			14.4371i			0.836321i
$299$	0.103916	−	0.319822i	0.00600964	−	0.0184958i
$300$		0			0
$301$	14.6641	+	10.6541i	0.845227	+	0.614093i
$302$	−17.8171	+	5.78913i	−1.02526	+	0.333127i
$303$	−0.480593	+	0.156154i	−0.0276094	+	0.00897082i
$304$	−25.2633	−	18.3548i	−1.44895	−	1.05272i
$305$		0			0
$306$	3.79455	−	11.6784i	0.216920	−	0.667612i
$307$			21.3566i			1.21889i	0.792829	+	0.609444i	$0.208607\pi$
$307$			21.3566i			1.21889i	−0.792829	+	0.609444i	$0.791393\pi$
$308$	31.3445	−	30.8035i	1.78602	−	1.75519i
$309$	6.40197			0.364195
$310$		0			0
$311$	−26.5435	+	19.2850i	−1.50514	+	1.09355i	−0.536870	+	0.843665i	$0.680393\pi$
$311$	−26.5435	+	19.2850i	−1.50514	+	1.09355i	−0.968275	+	0.249886i	$0.919607\pi$
$312$	−0.918222	+	1.26382i	−0.0519841	+	0.0715499i
$313$	−3.28925	+	1.06874i	−0.185919	+	0.0604089i	−0.400497	−	0.916298i	$-0.631163\pi$
$313$	−3.28925	+	1.06874i	−0.185919	+	0.0604089i	0.214578	+	0.976707i	$0.431163\pi$
$314$	7.69021	+	23.6680i	0.433984	+	1.33566i
$315$		0			0
$316$	−17.6590	+	12.8300i	−0.993398	+	0.721746i
$317$	−2.73491	−	0.888626i	−0.153608	−	0.0499102i	0.231204	−	0.972905i	$-0.425734\pi$
$317$	−2.73491	−	0.888626i	−0.153608	−	0.0499102i	−0.384812	+	0.922995i	$0.625734\pi$
$318$		−	12.1209i		−	0.679704i
$319$	−16.4751	−	2.75659i	−0.922426	−	0.154340i
$320$		0			0
$321$	0.646615	−	1.99008i	0.0360905	−	0.111075i
$322$	−5.09540	−	7.01321i	−0.283955	−	0.390831i
$323$	21.9070	−	30.1524i	1.21894	−	1.67772i
$324$	−1.24576	−	3.83407i	−0.0692092	−	0.213004i
$325$		0			0
$326$	9.99201	+	7.25962i	0.553406	+	0.402073i
$327$	3.93392	+	5.41457i	0.217546	+	0.299427i
$328$	−51.4664	−	16.7224i	−2.84176	−	0.923342i
$329$	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	$0.626872\pi$
$332$	62.2861	+	20.2380i	3.41839	+	1.11070i
$333$	1.54839	+	2.13118i	0.0848514	+	0.116788i
$334$	11.5060	+	8.35958i	0.629579	+	0.457416i
$335$		0			0
$336$	4.25499	+	13.0955i	0.232129	+	0.714419i
$337$	9.37457	−	12.9030i	0.510665	−	0.702870i	−0.473366	−	0.880866i	$-0.656961\pi$
$337$	9.37457	−	12.9030i	0.510665	−	0.702870i	0.984031	+	0.177995i	$0.0569612\pi$
$338$	−18.6244	−	25.6343i	−1.01303	−	1.39432i
$339$	3.33556	−	10.2658i	0.181163	−	0.557562i
$340$		0			0
$341$	−1.69105	−	11.3133i	−0.0915755	−	0.612650i
$342$		−	18.3064i		−	0.989895i
$343$	9.99271	+	3.24683i	0.539555	+	0.175312i
$344$	−22.2575	+	16.1711i	−1.20005	+	0.871885i
$345$		0			0
$346$	12.1921	+	37.5233i	0.655449	+	2.01727i
$347$	−28.2275	+	9.17166i	−1.51533	+	0.492360i	−0.944445	−	0.328670i	$-0.893400\pi$
$347$	−28.2275	+	9.17166i	−1.51533	+	0.492360i	−0.570884	+	0.821030i	$0.693400\pi$
$348$	11.9343	−	16.4262i	0.639748	−	0.880537i
$349$	25.6408	−	18.6291i	1.37252	−	0.997194i	0.374984	−	0.927031i	$-0.377648\pi$
$349$	25.6408	−	18.6291i	1.37252	−	0.997194i	0.997536	−	0.0701620i	$-0.0223516\pi$
$350$		0			0
$351$	−0.313133			−0.0167138
$352$	0.459787	+	0.922138i	0.0245067	+	0.0491501i
$353$		−	1.20189i		−	0.0639703i	−0.999488	−	0.0319852i	$-0.989817\pi$
$353$		−	1.20189i		−	0.0639703i	0.999488	−	0.0319852i	$-0.0101829\pi$
$354$	6.95473	−	21.4044i	0.369640	−	1.13763i
$355$		0			0
$356$	−5.28740	−	3.84152i	−0.280232	−	0.203600i
$357$	−15.6299	+	5.07845i	−0.827220	+	0.268780i
$358$	−19.3934	+	6.30130i	−1.02497	+	0.333034i
$359$	−9.43239	−	6.85304i	−0.497823	−	0.361689i	0.310362	−	0.950618i	$-0.399550\pi$
$359$	−9.43239	−	6.85304i	−0.497823	−	0.361689i	−0.808185	+	0.588929i	$0.799550\pi$
$360$		0			0
$361$	11.2987	−	34.7737i	0.594667	−	1.83020i
$362$		−	15.8755i		−	0.834396i
$363$	10.9983	+	0.191475i	0.577263	+	0.0100498i
$364$	4.14918			0.217476
$365$		0			0
$366$	−18.2479	+	13.2579i	−0.953832	+	0.693000i
$367$	9.39636	−	12.9330i	0.490486	−	0.675096i	−0.489991	−	0.871727i	$-0.663000\pi$
$367$	9.39636	−	12.9330i	0.490486	−	0.675096i	0.980478	+	0.196631i	$0.0630001\pi$
$368$	4.27874	−	1.39025i	0.223045	−	0.0724717i
$369$	−3.35197	−	10.3163i	−0.174497	−	0.537045i
$370$		0			0
$371$	−13.1239	+	9.53504i	−0.681357	+	0.495035i
$372$	13.2237	+	4.29663i	0.685615	+	0.222770i
$373$		−	0.321975i		−	0.0166712i	−0.999965	−	0.00833561i	$-0.997347\pi$
$373$		−	0.321975i		−	0.0166712i	0.999965	−	0.00833561i	$-0.00265334\pi$
$374$	−36.4469	+	18.1728i	−1.88463	+	0.939693i
$375$		0			0
$376$	−18.4968	+	56.9274i	−0.953902	+	2.93581i
$377$	−0.926988	−	1.27589i	−0.0477423	−	0.0657117i
$378$	−4.74467	+	6.53048i	−0.244039	+	0.335891i
$379$	−3.52819	−	10.8586i	−0.181231	−	0.557771i	0.818632	−	0.574318i	$-0.194733\pi$
$379$	−3.52819	−	10.8586i	−0.181231	−	0.557771i	−0.999863	+	0.0165471i	$0.994733\pi$
$380$		0			0
$381$	13.7559	+	9.99428i	0.704738	+	0.512022i
$382$	−22.1861	−	30.5365i	−1.13514	−	1.56239i
$383$	−26.9789	−	8.76597i	−1.37856	−	0.447920i	−0.476362	−	0.879249i	$-0.658045\pi$
$383$	−26.9789	−	8.76597i	−1.37856	−	0.447920i	−0.902195	+	0.431329i	$0.858045\pi$
$384$	19.3242			0.986136
$385$		0			0
$386$	38.6846			1.96899
$387$	−5.24477	−	1.70413i	−0.266607	−	0.0866257i
$388$	0.530981	+	0.730833i	0.0269565	+	0.0371024i
$389$	12.2810	+	8.92269i	0.622673	+	0.452398i	0.853854	−	0.520513i	$-0.174259\pi$
$389$	12.2810	+	8.92269i	0.622673	+	0.452398i	−0.231181	+	0.972911i	$0.574259\pi$
$390$		0			0
$391$	1.65930	+	5.10680i	0.0839143	+	0.258262i
$392$	11.1528	−	15.3504i	0.563299	−	0.775315i
$393$	−0.0253046	−	0.0348288i	−0.00127645	−	0.00175688i
$394$	−12.4415	+	38.2911i	−0.626796	+	1.92908i
$395$		0			0
$396$	−6.17357	+	11.8600i	−0.310234	+	0.595987i
$397$			5.22461i			0.262216i	0.991368	+	0.131108i	$0.0418534\pi$
$397$			5.22461i			0.262216i	−0.991368	+	0.131108i	$0.958147\pi$
$398$	−16.2681	−	5.28581i	−0.815444	−	0.264954i
$399$	−19.8212	+	14.4010i	−0.992302	+	0.720950i
$400$		0			0
$401$	4.32644	+	13.3154i	0.216052	+	0.664941i	0.999077	+	0.0429502i	$0.0136757\pi$
$401$	4.32644	+	13.3154i	0.216052	+	0.664941i	−0.783025	+	0.621990i	$0.786324\pi$
$402$	35.6750	−	11.5915i	1.77931	−	0.578132i
$403$	0.634804	−	0.873733i	0.0316219	−	0.0435238i
$404$	−1.64810	+	1.19741i	−0.0819959	+	0.0595735i
$405$		0			0
$406$	−40.6549			−2.01767
$407$	1.44181	−	8.61714i	0.0714680	−	0.427136i
$408$		−	24.9442i		−	1.23492i
$409$	−10.2937	+	31.6809i	−0.508993	+	1.56652i	0.284960	+	0.958539i	$0.408020\pi$
$409$	−10.2937	+	31.6809i	−0.508993	+	1.56652i	−0.793953	+	0.607979i	$0.791980\pi$
$410$		0			0
$411$	−5.95645	−	4.32761i	−0.293810	−	0.213465i
$412$	24.5456	−	7.97535i	1.20927	−	0.392917i
$413$	−28.6467	+	9.30787i	−1.40961	+	0.458011i
$414$	2.13372	+	1.55024i	0.104867	+	0.0761902i
$415$		0			0
$416$	−0.0300625	+	0.0925229i	−0.00147394	+	0.00453631i
$417$			13.2393i			0.648334i
$418$	−43.3043	+	42.5569i	−2.11808	+	2.08153i
$419$	5.28460			0.258170			0.129085	−	0.991634i	$-0.458796\pi$
$419$	5.28460			0.258170			0.129085	+	0.991634i	$0.458796\pi$
$420$		0			0
$421$	24.9023	−	18.0926i	1.21367	−	0.881780i	0.218107	−	0.975925i	$-0.430012\pi$
$421$	24.9023	−	18.0926i	1.21367	−	0.881780i	0.995558	+	0.0941452i	$0.0300118\pi$
$422$	−28.8030	+	39.6439i	−1.40211	+	1.92984i
$423$	−11.4110	+	3.70764i	−0.554820	+	0.180272i
$424$	−7.60864	−	23.4170i	−0.369508	−	1.13723i
$425$		0			0
$426$	−6.10384	+	4.43470i	−0.295732	+	0.214862i
$427$	28.7099	+	9.32841i	1.38937	+	0.451433i
$428$		−	8.43562i		−	0.407751i
$429$	0.727943	+	0.740727i	0.0351454	+	0.0357626i
$430$		0			0
$431$	3.81656	−	11.7462i	0.183837	−	0.565793i	−0.816089	−	0.577926i	$-0.803862\pi$
$431$	3.81656	−	11.7462i	0.183837	−	0.565793i	0.999926	+	0.0121333i	$0.00386225\pi$
$432$	−2.46239	−	3.38919i	−0.118472	−	0.163062i
$433$	−0.830465	+	1.14304i	−0.0399096	+	0.0549308i	−0.828505	−	0.559981i	$-0.810808\pi$
$433$	−0.830465	+	1.14304i	−0.0399096	+	0.0549308i	0.788596	+	0.614912i	$0.210808\pi$
$434$	−8.60323	−	26.4780i	−0.412968	−	1.27098i
$435$		0			0
$436$	21.8282	+	15.8591i	1.04538	+	0.759514i
$437$	4.70527	+	6.47625i	0.225084	+	0.309801i
$438$	20.2100	+	6.56662i	0.965670	+	0.313765i
$439$	7.58532			0.362028			0.181014	−	0.983481i	$-0.442062\pi$
$439$	7.58532			0.362028			0.181014	+	0.983481i	$0.442062\pi$
$440$		0			0
$441$	3.80333			0.181111
$442$	−3.65691	−	1.18820i	−0.173941	−	0.0565170i
$443$	6.50455	+	8.95274i	0.309040	+	0.425358i	0.935082	−	0.354432i	$-0.115326\pi$
$443$	6.50455	+	8.95274i	0.309040	+	0.425358i	−0.626041	+	0.779790i	$0.715326\pi$
$444$	8.59160	+	6.24216i	0.407739	+	0.296240i
$445$		0			0
$446$	−15.2895	−	47.0562i	−0.723979	−	2.22818i
$447$	−3.45534	+	4.75587i	−0.163432	+	0.224945i
$448$	−14.7129	−	20.2505i	−0.695118	−	0.956748i
$449$	−1.95563	+	6.01882i	−0.0922920	+	0.284045i	−0.986538	−	0.163529i	$-0.947712\pi$
$449$	−1.95563	+	6.01882i	−0.0922920	+	0.284045i	0.894247	+	0.447575i	$0.147712\pi$
$450$		0			0
$451$	−16.6112	+	31.9116i	−0.782190	+	1.50266i
$452$		−	43.5152i		−	2.04678i
$453$	−7.25486	−	2.35725i	−0.340863	−	0.110753i
$454$	1.06085	−	0.770756i	0.0497884	−	0.0361734i
$455$		0			0
$456$	−11.4915	−	35.3671i	−0.538138	−	1.65622i
$457$	0.180300	−	0.0585832i	0.00843410	−	0.00274040i	−0.304797	−	0.952417i	$-0.598589\pi$
$457$	0.180300	−	0.0585832i	0.00843410	−	0.00274040i	0.313231	+	0.949677i	$0.398589\pi$
$458$	32.0364	−	44.0944i	1.49696	−	2.06039i
$459$	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	$0.712828\pi$
$462$	26.4780	−	3.95778i	1.23187	−	0.184133i
$463$		−	20.9935i		−	0.975652i	−0.872941	−	0.487826i	$-0.837790\pi$
$463$		−	20.9935i		−	0.975652i	0.872941	−	0.487826i	$-0.162210\pi$
$464$	6.51998	−	20.0664i	0.302682	−	0.931561i
$465$		0			0
$466$	9.07131	+	6.59070i	0.420221	+	0.305308i
$467$	−7.51324	+	2.44120i	−0.347671	+	0.112965i	−0.477647	−	0.878552i	$-0.658510\pi$
$467$	−7.51324	+	2.44120i	−0.347671	+	0.112965i	0.129976	+	0.991517i	$0.458510\pi$
$468$	−1.20058	+	0.390091i	−0.0554966	+	0.0180319i
$469$	−40.6149	−	29.5085i	−1.87542	−	1.36257i
$470$		0			0
$471$	−3.13134	+	9.63727i	−0.144284	+	0.444062i
$472$		−	45.7182i		−	2.10435i
$473$	8.16138	+	16.3683i	0.375261	+	0.752614i
$474$	−13.2973			−0.610766
$475$		0			0
$476$	−53.5994	+	38.9423i	−2.45673	+	1.78492i
$477$	2.90097	−	3.99285i	0.132826	−	0.182820i
$478$	−13.6884	+	4.44762i	−0.626091	+	0.203429i
$479$	−12.3523	−	38.0164i	−0.564389	−	1.73701i	−0.669758	−	0.742579i	$-0.733602\pi$
$479$	−12.3523	−	38.0164i	−0.564389	−	1.73701i	0.105369	−	0.994433i	$-0.466398\pi$
$480$		0			0
$481$	0.667344	−	0.484854i	0.0304282	−	0.0221074i
$482$	23.2652	+	7.55931i	1.05970	+	0.344317i
$483$		−	3.52981i		−	0.160612i
$484$	42.4069	−	12.9672i	1.92759	−	0.589419i
$485$		0			0
$486$	0.758911	−	2.33569i	0.0344249	−	0.105949i
$487$	5.83998	+	8.03804i	0.264635	+	0.364238i	0.920569	−	0.390579i	$-0.127725\pi$
$487$	5.83998	+	8.03804i	0.264635	+	0.364238i	−0.655935	+	0.754818i	$0.727725\pi$
$488$	−26.9318	+	37.0684i	−1.21914	+	1.67801i
$489$	1.55407	+	4.78292i	0.0702773	+	0.216291i
$490$		0			0
$491$	−4.02364	−	2.92335i	−0.181584	−	0.131929i	0.493280	−	0.869871i	$-0.335798\pi$
$491$	−4.02364	−	2.92335i	−0.181584	−	0.131929i	−0.674864	+	0.737942i	$0.735798\pi$
$492$	−25.7034	−	35.3777i	−1.15880	−	1.59495i
$493$	23.9498	+	7.78177i	1.07865	+	0.350473i
$494$	−5.73234			−0.257910
$495$		0			0
$496$	14.4487			0.648767
$497$	9.60333	+	3.12031i	0.430768	+	0.139965i
$498$	23.4508	+	32.2773i	1.05086	+	1.44638i
$499$	35.4153	+	25.7307i	1.58541	+	1.15186i	0.910149	+	0.414281i	$0.135967\pi$
$499$	35.4153	+	25.7307i	1.58541	+	1.15186i	0.675256	+	0.737584i	$0.264033\pi$
$500$		0			0
$501$	1.78953	+	5.50761i	0.0799504	+	0.246062i
$502$	−24.3651	+	33.5357i	−1.08747	+	1.49677i
$503$	3.69268	+	5.08254i	0.164648	+	0.226619i	0.883367	−	0.468682i	$-0.155271\pi$
$503$	3.69268	+	5.08254i	0.164648	+	0.226619i	−0.718718	+	0.695301i	$0.755271\pi$
$504$	−5.06711	+	15.5950i	−0.225707	+	0.694655i
$505$		0			0
$506$	−1.29314	−	8.65125i	−0.0574870	−	0.384595i
$507$		−	12.9019i		−	0.572996i
$508$	65.1918	+	21.1821i	2.89242	+	0.939803i
$509$	20.0945	−	14.5995i	0.890671	−	0.647111i	−0.0453816	−	0.998970i	$-0.514450\pi$
$509$	20.0945	−	14.5995i	0.890671	−	0.647111i	0.936053	+	0.351859i	$0.114450\pi$
$510$		0			0
$511$	−8.78845	−	27.0481i	−0.388778	−	1.19654i
$512$	38.5155	−	12.5144i	1.70216	−	0.553066i
$513$	4.38140	−	6.03048i	0.193443	−	0.266252i
$514$	22.1407	−	16.0861i	0.976583	−	0.709529i
$515$		0			0
$516$	−22.2318			−0.978699
$517$	35.2977	+	18.3738i	1.55239	+	0.808078i
$518$		−	21.2642i		−	0.934296i
$519$	−4.96442	+	15.2789i	−0.217914	+	0.670670i
$520$		0			0
$521$	5.62161	+	4.08434i	0.246287	+	0.178938i	0.704080	−	0.710121i	$-0.251360\pi$
$521$	5.62161	+	4.08434i	0.246287	+	0.178938i	−0.457792	+	0.889059i	$0.651360\pi$
$522$	11.7636	−	3.82223i	0.514879	−	0.167294i
$523$	−25.4417	+	8.26650i	−1.11249	+	0.361469i	−0.806896	−	0.590694i	$-0.798854\pi$
$523$	−25.4417	+	8.26650i	−1.11249	+	0.361469i	−0.305591	+	0.952163i	$0.598854\pi$
$524$	−0.140408	−	0.102013i	−0.00613376	−	0.00445644i
$525$		0			0
$526$	−20.3939	+	62.7661i	−0.889218	+	2.73673i
$527$			17.2449i			0.751202i
$528$	−2.29290	+	13.7037i	−0.0997854	+	0.596378i
$529$	21.8467			0.949856
$530$		0			0
$531$	7.41391	−	5.38652i	0.321736	−	0.233755i
$532$	−58.0557	+	79.9069i	−2.51704	+	3.46440i
$533$	−3.23038	+	1.04961i	−0.139923	+	0.0454638i
$534$	−1.23033	−	3.78657i	−0.0532416	−	0.163861i
$535$		0			0
$536$	61.6462	−	44.7886i	2.66271	−	1.93457i
$537$	−7.89671	−	2.56580i	−0.340768	−	0.110722i
$538$			24.7133i			1.06547i
$539$	−8.84162	−	8.99689i	−0.380836	−	0.387524i
$540$		0			0
$541$	4.48336	−	13.7984i	0.192755	−	0.593237i	−0.807241	−	0.590222i	$-0.799040\pi$
$541$	4.48336	−	13.7984i	0.192755	−	0.593237i	0.999995	−	0.00301536i	$-0.000959822\pi$
$542$	−15.2208	−	20.9496i	−0.653789	−	0.899863i
$543$	3.79959	−	5.22969i	0.163056	−	0.224428i
$544$	−0.480027	−	1.47737i	−0.0205810	−	0.0633418i
$545$		0			0
$546$	2.04491	+	1.48571i	0.0875141	+	0.0635827i
$547$	15.7142	+	21.6287i	0.671890	+	0.924777i	0.999801	−	0.0199316i	$-0.00634485\pi$
$547$	15.7142	+	21.6287i	0.671890	+	0.924777i	−0.327912	+	0.944708i	$0.606345\pi$
$548$	−28.2286	−	9.17203i	−1.20587	−	0.391810i
$549$	−9.18431			−0.391977
$550$		0			0
$551$	37.5422			1.59935
$552$	5.09540	+	1.65559i	0.216875	+	0.0704668i
$553$	10.4605	+	14.3977i	0.444826	+	0.612251i
$554$	−35.6394	−	25.8935i	−1.51417	−	1.10011i
$555$		0			0
$556$	16.4931	+	50.7606i	0.699464	+	2.15273i
$557$	10.1360	−	13.9510i	0.429477	−	0.591125i	−0.538356	−	0.842718i	$-0.680954\pi$
$557$	10.1360	−	13.9510i	0.429477	−	0.591125i	0.967833	+	0.251593i	$0.0809544\pi$
$558$	4.97873	+	6.85264i	0.210767	+	0.290095i
$559$	−0.533620	+	1.64231i	−0.0225697	+	0.0694624i
$560$		0			0
$561$	−16.3558	−	2.73663i	−0.690541	−	0.115541i
$562$			18.2006i			0.767748i
$563$	0.791197	+	0.257075i	0.0333450	+	0.0108344i	0.325642	−	0.945493i	$-0.394420\pi$
$563$	0.791197	+	0.257075i	0.0333450	+	0.0108344i	−0.292297	+	0.956328i	$0.594420\pi$
$564$	−39.1316	+	28.4307i	−1.64774	+	1.19715i
$565$		0			0
$566$	4.08813	+	12.5820i	0.171837	+	0.528860i
$567$	−3.12597	+	1.01569i	−0.131278	+	0.0426550i
$568$	−9.00855	+	12.3992i	−0.377991	+	0.520259i
$569$	9.38141	−	6.81599i	0.393289	−	0.285741i	−0.373513	−	0.927625i	$-0.621847\pi$
$569$	9.38141	−	6.81599i	0.393289	−	0.285741i	0.766802	+	0.641884i	$0.221847\pi$
$570$		0			0
$571$	21.8414			0.914034			0.457017	−	0.889458i	$-0.348918\pi$
$571$	21.8414			0.914034			0.457017	+	0.889458i	$0.348918\pi$
$572$	3.71376	+	1.93315i	0.155280	+	0.0808292i
$573$		−	15.3693i		−	0.642061i
$574$	−27.0575	+	83.2744i	−1.12936	+	3.47580i
$575$		0			0
$576$	6.16110	+	4.47630i	0.256712	+	0.186512i
$577$	−9.26888	+	3.01164i	−0.385868	+	0.125376i	−0.495526	−	0.868593i	$-0.665025\pi$
$577$	−9.26888	+	3.01164i	−0.385868	+	0.125376i	0.109657	+	0.993969i	$0.465025\pi$
$578$	18.6855	−	6.07129i	0.777214	−	0.252532i
$579$	12.7435	+	9.25867i	0.529600	+	0.384777i
$580$		0			0
$581$	16.5003	−	50.7827i	0.684548	−	2.10682i
$582$			0.550320i			0.0228115i
$583$	−16.1891	+	2.41986i	−0.670485	+	0.100220i
$584$	43.1669			1.78626
$585$		0			0
$586$	3.45724	−	2.51183i	0.142817	−	0.103763i
$587$	13.4862	−	18.5622i	0.556635	−	0.766143i	−0.434258	−	0.900788i	$-0.642990\pi$
$587$	13.4862	−	18.5622i	0.556635	−	0.766143i	0.990894	+	0.134645i	$0.0429895\pi$
$588$	14.5822	−	4.73805i	0.601361	−	0.195394i
$589$	7.94453	+	24.4507i	0.327349	+	1.00748i
$590$		0			0
$591$	−13.2630	+	9.63612i	−0.545566	+	0.396377i
$592$	10.4956	+	3.41022i	0.431366	+	0.140159i
$593$		−	28.7819i		−	1.18193i	−0.806697	−	0.590965i	$-0.798747\pi$
$593$		−	28.7819i		−	1.18193i	0.806697	−	0.590965i	$-0.201253\pi$
$594$	−7.28939	+	3.63456i	−0.299087	+	0.149128i
$595$		0			0
$596$	−7.32333	+	22.5389i	−0.299975	+	0.923229i
$597$	−4.09392	−	5.63480i	−0.167553	−	0.230617i
$598$	0.485432	−	0.668140i	0.0198508	−	0.0273223i
$599$	9.02179	+	27.7662i	0.368620	+	1.13450i	0.947683	+	0.319214i	$0.103419\pi$
$599$	9.02179	+	27.7662i	0.368620	+	1.13450i	−0.579062	+	0.815283i	$0.696581\pi$
$600$		0			0
$601$	5.40494	+	3.92692i	0.220472	+	0.160182i	0.692539	−	0.721380i	$-0.256492\pi$
$601$	5.40494	+	3.92692i	0.220472	+	0.160182i	−0.472067	+	0.881563i	$0.656492\pi$
$602$	26.1653	+	36.0135i	1.06642	+	1.46780i
$603$	14.5263	+	4.71989i	0.591557	+	0.192209i
$604$	−30.7522			−1.25129
$605$		0			0
$606$	−1.24102			−0.0504131
$607$	−40.5252	−	13.1674i	−1.64487	−	0.534450i	−0.667250	−	0.744834i	$-0.732529\pi$
$607$	−40.5252	−	13.1674i	−1.64487	−	0.534450i	−0.977619	+	0.210384i	$0.932529\pi$
$608$	−1.36121	−	1.87355i	−0.0552044	−	0.0759824i
$609$	−13.3925	−	9.73024i	−0.542693	−	0.394289i
$610$		0			0
$611$	1.16099	+	3.57315i	0.0469685	+	0.144554i
$612$	11.8479	−	16.3073i	0.478924	−	0.659182i
$613$	−3.42771	−	4.71783i	−0.138444	−	0.190552i	0.734165	−	0.678971i	$-0.237574\pi$
$613$	−3.42771	−	4.71783i	−0.138444	−	0.190552i	−0.872609	+	0.488419i	$0.837574\pi$
$614$	−16.2078	+	49.8824i	−0.654093	+	2.01309i
$615$		0			0
$616$	48.6699	−	24.2673i	1.96097	−	0.977758i
$617$		−	33.6386i		−	1.35424i	−0.735874	−	0.677119i	$-0.763228\pi$
$617$		−	33.6386i		−	1.35424i	0.735874	−	0.677119i	$-0.236772\pi$
$618$	14.9530	+	4.85852i	0.601498	+	0.195438i
$619$	34.4331	−	25.0171i	1.38398	−	1.00552i	0.387488	−	0.921875i	$-0.373343\pi$
$619$	34.4331	−	25.0171i	1.38398	−	1.00552i	0.996495	−	0.0836477i	$-0.0266570\pi$
$620$		0			0
$621$	0.331860	+	1.02136i	0.0133171	+	0.0409857i
$622$	−76.6329	+	24.8996i	−3.07270	+	0.998381i
$623$	−3.13205	+	4.31089i	−0.125483	+	0.172712i
$624$	−1.06127	+	0.771056i	−0.0424847	+	0.0308669i
$625$		0			0
$626$	−8.49374			−0.339478
$627$	−24.4507	+	3.65476i	−0.976468	+	0.145957i
$628$			40.8509i			1.63013i
$629$	−4.07019	+	12.5268i	−0.162289	+	0.499475i
$630$		0			0
$631$	7.20016	+	5.23122i	0.286634	+	0.208252i	0.721806	−	0.692096i	$-0.243312\pi$
$631$	7.20016	+	5.23122i	0.286634	+	0.208252i	−0.435172	+	0.900347i	$0.643312\pi$
$632$	−25.6898	+	8.34713i	−1.02189	+	0.332031i
$633$	−18.9765	+	6.16585i	−0.754250	+	0.245071i
$634$	−5.71351	−	4.15111i	−0.226912	−	0.164862i
$635$		0			0
$636$	6.14839	−	18.9228i	0.243799	−	0.750337i
$637$		−	1.19095i		−	0.0471871i
$638$	−36.3886	−	18.9416i	−1.44064	−	0.749906i
$639$	−3.07211			−0.121531
$640$		0			0
$641$	4.99007	−	3.62549i	0.197096	−	0.143198i	−0.484860	−	0.874592i	$-0.661130\pi$
$641$	4.99007	−	3.62549i	0.197096	−	0.143198i	0.681956	+	0.731393i	$0.261130\pi$
$642$	3.02058	−	4.15747i	0.119213	−	0.164082i
$643$	4.14029	−	1.34526i	0.163277	−	0.0530519i	−0.226238	−	0.974072i	$-0.572643\pi$
$643$	4.14029	−	1.34526i	0.163277	−	0.0530519i	0.389515	+	0.921020i	$0.372643\pi$
$644$	−4.39731	−	13.5335i	−0.173278	−	0.533296i
$645$		0			0
$646$	74.0508	−	53.8011i	2.91349	−	2.11677i
$647$	12.8329	+	4.16967i	0.504514	+	0.163927i	0.550206	−	0.835029i	$-0.314549\pi$
$647$	12.8329	+	4.16967i	0.504514	+	0.163927i	−0.0456916	+	0.998956i	$0.514549\pi$
$648$		−	4.98884i		−	0.195980i
$649$	−29.9771	−	5.01575i	−1.17671	−	0.196885i
$650$		0			0
$651$	3.50310	−	10.7814i	0.137297	−	0.422558i
$652$	11.9168	+	16.4021i	0.466697	+	0.642354i
$653$	−16.1336	+	22.2060i	−0.631357	+	0.868988i	−0.998118	−	0.0613270i	$-0.980467\pi$
$653$	−16.1336	+	22.2060i	−0.631357	+	0.868988i	0.366761	+	0.930315i	$0.380467\pi$
$654$	5.07922	+	15.6322i	0.198613	+	0.611269i
$655$		0			0
$656$	−36.7632	−	26.7100i	−1.43536	−	1.04285i
$657$	5.08592	+	7.00018i	0.198421	+	0.273103i
$658$	92.1105	+	29.9285i	3.59084	+	1.16674i
$659$	18.7768			0.731441			0.365721	−	0.930725i	$-0.380823\pi$
$659$	18.7768			0.731441			0.365721	+	0.930725i	$0.380823\pi$
$660$		0			0
$661$	−21.6525			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$662$	−32.9847	−	10.7174i	−1.28199	−	0.416543i
$663$	−0.920276	−	1.26665i	−0.0357406	−	0.0491927i
$664$	65.5674	+	47.6375i	2.54451	+	1.84869i
$665$		0			0
$666$	1.99919	+	6.15286i	0.0774669	+	0.238419i
$667$	−3.17919	+	4.37578i	−0.123099	+	0.169431i
$668$	13.7224	+	18.8872i	0.530935	+	0.730769i
$669$	6.22565	−	19.1606i	0.240698	−	0.740791i
$670$		0			0
$671$	21.3508	+	21.7258i	0.824240	+	0.838714i
$672$			1.02116i			0.0393919i
$673$	−22.1617	−	7.20076i	−0.854269	−	0.277569i	−0.151036	−	0.988528i	$-0.548261\pi$
$673$	−22.1617	−	7.20076i	−0.854269	−	0.277569i	−0.703233	+	0.710959i	$0.748261\pi$
$674$	31.6883	−	23.0229i	1.22059	−	0.886808i
$675$		0			0
$676$	−16.0728	−	49.4670i	−0.618184	−	1.90258i
$677$	−31.6519	+	10.2843i	−1.21648	+	0.395259i	−0.845800	−	0.533501i	$-0.820876\pi$
$677$	−31.6519	+	10.2843i	−1.21648	+	0.395259i	−0.370683	+	0.928760i	$0.620876\pi$
$678$	15.5817	−	21.4463i	0.598410	−	0.823641i
$679$	0.595859	−	0.432917i	0.0228670	−	0.0166138i
$680$		0			0
$681$	0.533937			0.0204605
$682$	4.63603	−	27.7077i	0.177523	−	1.06098i
$683$		−	16.9244i		−	0.647593i	−0.946127	−	0.323796i	$-0.895041\pi$
$683$		−	16.9244i		−	0.647593i	0.946127	−	0.323796i	$-0.104959\pi$
$684$	9.28603	−	28.5795i	0.355060	−	1.09276i
$685$		0			0
$686$	20.8758	+	15.1671i	0.797041	+	0.579084i
$687$	21.1068	−	6.85803i	0.805276	−	0.261650i
$688$	−21.9717	+	7.13905i	−0.837664	+	0.272174i
$689$	−1.25029	−	0.908392i	−0.0476324	−	0.0346070i
$690$		0			0
$691$	−14.9668	+	46.0630i	−0.569363	+	1.75232i	0.0852532	+	0.996359i	$0.472830\pi$
$691$	−14.9668	+	46.0630i	−0.569363	+	1.75232i	−0.654617	+	0.755961i	$0.727170\pi$
$692$			64.7650i			2.46200i
$693$	9.66962	+	5.03340i	0.367318	+	0.191203i
$694$	−72.8910			−2.76690
$695$		0			0
$696$	20.3275	−	14.7688i	0.770511	−	0.559809i
$697$	31.8791	−	43.8779i	1.20751	−	1.66199i
$698$	74.0267	−	24.0527i	2.80195	−	0.910409i
$699$	1.41087	+	4.34221i	0.0533640	+	0.164237i
$700$		0			0
$701$	36.7424	−	26.6949i	1.38774	−	1.00825i	0.391634	−	0.920121i	$-0.371910\pi$
$701$	36.7424	−	26.6949i	1.38774	−	1.00825i	0.996109	−	0.0881330i	$-0.0280900\pi$
$702$	−0.731382	−	0.237640i	−0.0276042	−	0.00896916i
$703$			19.6361i			0.740591i
$704$	−3.73392	−	24.9803i	−0.140727	−	0.941482i
$705$		0			0
$706$	0.912130	−	2.80725i	0.0343285	−	0.105652i
$707$	0.976267	+	1.34372i	0.0367163	+	0.0505357i
$708$	21.7151	−	29.8883i	0.816103	−	1.12327i
$709$	0.545405	+	1.67858i	0.0204831	+	0.0630406i	0.960776	−	0.277327i	$-0.0894485\pi$
$709$	0.545405	+	1.67858i	0.0204831	+	0.0630406i	−0.940292	+	0.340368i	$0.889449\pi$
$710$		0			0
$711$	−4.38039	−	3.18254i	−0.164278	−	0.119355i
$712$	−4.75389	−	6.54317i	−0.178160	−	0.245216i
$713$	−3.52266	−	1.14458i	−0.131925	−	0.0428649i
$714$	−40.3606			−1.51046
$715$		0			0
$716$	−33.4729			−1.25094
$717$	−5.57369	−	1.81100i	−0.208153	−	0.0676331i
$718$	−16.8303	−	23.1649i	−0.628100	−	0.864506i
$719$	−2.66974	−	1.93968i	−0.0995645	−	0.0723379i	0.536889	−	0.843653i	$-0.319599\pi$
$719$	−2.66974	−	1.93968i	−0.0995645	−	0.0723379i	−0.636454	+	0.771315i	$0.719599\pi$
$720$		0			0
$721$	−6.50241	−	20.0124i	−0.242163	−	0.745300i
$722$	52.7803	−	72.6459i	1.96428	−	2.70360i
$723$	5.85477	+	8.05841i	0.217741	+	0.299695i
$724$	8.05294	−	24.7844i	0.299285	−	0.921105i
$725$		0			0
$726$	25.5434	+	8.79398i	0.948003	+	0.326375i
$727$			11.7838i			0.437037i	0.975833	+	0.218519i	$0.0701225\pi$
$727$			11.7838i			0.437037i	−0.975833	+	0.218519i	$0.929878\pi$
$728$	4.88331	+	1.58668i	0.180987	+	0.0588064i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−8.52064	−	26.2238i	−0.315147	−	0.969924i
$732$	−35.2133	+	11.4415i	−1.30152	+	0.422890i
$733$	−3.36865	+	4.63654i	−0.124424	+	0.171255i	−0.866685	−	0.498856i	$-0.833754\pi$
$733$	−3.36865	+	4.63654i	−0.124424	+	0.171255i	0.742261	+	0.670111i	$0.233754\pi$
$734$	31.7619	−	23.0764i	1.17235	−	0.851765i
$735$		0			0
$736$	0.333646			0.0122983
$737$	−22.6044	−	45.3348i	−0.832643	−	1.66993i
$738$		−	26.6395i		−	0.980614i
$739$	6.50638	−	20.0246i	0.239341	−	0.736616i	−0.757175	−	0.653212i	$-0.773421\pi$
$739$	6.50638	−	20.0246i	0.239341	−	0.736616i	0.996516	−	0.0834038i	$-0.0265791\pi$
$740$		0			0
$741$	−1.88834	−	1.37196i	−0.0693700	−	0.0504003i
$742$	−37.8895	+	12.3110i	−1.39097	+	0.451952i
$743$	12.4857	−	4.05686i	0.458058	−	0.148832i	−0.0708942	−	0.997484i	$-0.522585\pi$
$743$	12.4857	−	4.05686i	0.458058	−	0.148832i	0.528952	+	0.848652i	$0.322585\pi$
$744$	13.9203	+	10.1137i	0.510343	+	0.370786i
$745$		0			0
$746$	0.244350	−	0.752032i	0.00894629	−	0.0275339i
$747$			16.2454i			0.594389i
$748$	−66.1183	+	9.88299i	−2.41753	+	0.361358i
$749$	−6.87768			−0.251305
$750$		0			0
$751$	−20.7311	+	15.0621i	−0.756490	+	0.549622i	−0.897832	−	0.440339i	$-0.854858\pi$
$751$	−20.7311	+	15.0621i	−0.756490	+	0.549622i	0.141342	+	0.989961i	$0.454858\pi$
$752$	−29.5442	+	40.6641i	−1.07737	+	1.48287i
$753$	−16.0527	+	5.21584i	−0.584993	+	0.190076i
$754$	−1.19687	−	3.68358i	−0.0435874	−	0.134148i
$755$		0			0
$756$	−10.7199	+	7.78845i	−0.389878	+	0.283263i
$757$	29.6701	+	9.64039i	1.07838	+	0.350386i	0.793745	−	0.608251i	$-0.208129\pi$
$757$	29.6701	+	9.64039i	1.07838	+	0.350386i	0.284632	+	0.958637i	$0.408129\pi$
$758$		−	28.0400i		−	1.01846i
$759$	1.64458	−	3.15939i	0.0596945	−	0.114678i
$760$		0			0
$761$	3.51539	−	10.8193i	0.127433	−	0.392198i	−0.866904	−	0.498476i	$-0.833893\pi$
$761$	3.51539	−	10.8193i	0.127433	−	0.392198i	0.994336	+	0.106278i	$0.0338932\pi$
$762$	24.5448	+	33.7830i	0.889165	+	1.22383i
$763$	12.9302	−	17.7968i	0.468103	−	0.644289i
$764$	−19.1465	−	58.9269i	−0.692697	−	2.13190i
$765$		0			0
$766$	−56.3617	−	40.9491i	−2.03643	−	1.47955i
$767$	−1.68670	−	2.32154i	−0.0609032	−	0.0838260i
$768$	30.6498	+	9.95872i	1.10598	+	0.359354i
$769$	−10.3938			−0.374811			−0.187405	−	0.982283i	$-0.560008\pi$
$769$	−10.3938			−0.374811			−0.187405	+	0.982283i	$0.560008\pi$
$770$		0			0
$771$	11.1436			0.401326
$772$	60.3935	+	19.6230i	2.17361	+	0.706248i
$773$	8.24944	+	11.3544i	0.296712	+	0.408389i	0.931180	−	0.364560i	$-0.118781\pi$
$773$	8.24944	+	11.3544i	0.296712	+	0.408389i	−0.634468	+	0.772949i	$0.718781\pi$
$774$	−10.9569	−	7.96062i	−0.393836	−	0.286139i
$775$		0			0
$776$	0.345453	+	1.06319i	0.0124010	+	0.0381665i
$777$	5.08932	−	7.00485i	0.182578	−	0.251298i
$778$	21.9131	+	30.1608i	0.785623	+	1.08132i
$779$	24.9858	−	76.8985i	0.895211	−	2.75518i
$780$		0			0
$781$	7.14176	+	7.26717i	0.255552	+	0.260040i
$782$			13.1871i			0.471571i
$783$	4.78997	+	1.55635i	0.171179	+	0.0556196i
$784$	12.8902	−	9.36527i	0.460364	−	0.334474i
$785$		0			0
$786$	−0.0326717	−	0.100553i	−0.00116536	−	0.00358661i
$787$	13.1414	−	4.26988i	0.468439	−	0.152205i	−0.0652802	−	0.997867i	$-0.520794\pi$
$787$	13.1414	−	4.26988i	0.468439	−	0.152205i	0.533719	+	0.845662i	$0.320794\pi$
$788$	−38.8469	+	53.4681i	−1.38386	+	1.90472i
$789$	−21.7404	+	15.7953i	−0.773980	+	0.562329i
$790$		0			0
$791$	−35.4785			−1.26147
$792$	−11.8013	+	11.5976i	−0.419339	+	0.412102i
$793$			2.87591i			0.102127i
$794$	−3.96502	+	12.2031i	−0.140713	+	0.433070i
$795$		0			0
$796$	−22.7160	−	16.5042i	−0.805149	−	0.584975i
$797$	5.12233	−	1.66435i	0.181442	−	0.0589541i	−0.216887	−	0.976197i	$-0.569590\pi$
$797$	5.12233	−	1.66435i	0.181442	−	0.0589541i	0.398329	+	0.917243i	$0.369590\pi$
$798$	−57.2252	+	18.5936i	−2.02575	+	0.658206i
$799$	−48.5337	−	35.2618i	−1.71700	−	1.24747i
$800$		0			0
$801$	0.500972	−	1.54183i	0.0177010	−	0.0544780i
$802$			34.3840i			1.21414i
$803$	4.73585	−	28.3043i	0.167124	−	0.998836i
$804$	61.5748			2.17157
$805$		0			0
$806$	2.14579	−	1.55901i	0.0755822	−	0.0549137i
$807$	−5.91482	+	8.14105i	−0.208212	+	0.286579i
$808$	−2.39760	+	0.779028i	−0.0843473	+	0.0274061i
$809$	−7.34680	−	22.6111i	−0.258300	−	0.794965i	−0.993162	−	0.116748i	$-0.962753\pi$
$809$	−7.34680	−	22.6111i	−0.258300	−	0.794965i	0.734862	−	0.678217i	$-0.237247\pi$
$810$		0			0
$811$	−7.65601	+	5.56242i	−0.268839	+	0.195323i	−0.714035	−	0.700110i	$-0.753134\pi$
$811$	−7.65601	+	5.56242i	−0.268839	+	0.195323i	0.445196	+	0.895433i	$0.353134\pi$
$812$	−63.4695	−	20.6225i	−2.22734	−	0.723707i
$813$		−	10.5441i		−	0.369798i
$814$	9.90726	−	19.0327i	0.347249	−	0.667097i
$815$		0			0
$816$	6.47277	−	19.9211i	0.226592	−	0.697379i
$817$	−24.1620	−	33.2561i	−0.845321	−	1.16348i
$818$	−48.0859	+	66.1846i	−1.68128	+	2.31409i
$819$	0.318046	+	0.978846i	0.0111134	+	0.0342037i
$820$		0			0
$821$	8.42906	+	6.12407i	0.294176	+	0.213731i	0.725077	−	0.688668i	$-0.241804\pi$
$821$	8.42906	+	6.12407i	0.294176	+	0.213731i	−0.430901	+	0.902399i	$0.641804\pi$
$822$	−10.6281	−	14.6284i	−0.370698	−	0.510223i
$823$	−23.1620	−	7.52581i	−0.807378	−	0.262333i	−0.123891	−	0.992296i	$-0.539537\pi$
$823$	−23.1620	−	7.52581i	−0.807378	−	0.262333i	−0.683487	+	0.729963i	$0.739537\pi$
$824$	31.9384			1.11263
$825$		0			0
$826$	−73.9736			−2.57387
$827$	−20.9239	−	6.79857i	−0.727594	−	0.236410i	−0.0782813	−	0.996931i	$-0.524943\pi$
$827$	−20.9239	−	6.79857i	−0.727594	−	0.236410i	−0.649312	+	0.760522i	$0.724943\pi$
$828$	2.54475	+	3.50254i	0.0884361	+	0.121722i
$829$	2.45366	+	1.78269i	0.0852191	+	0.0619153i	0.629579	−	0.776936i	$-0.283227\pi$
$829$	2.45366	+	1.78269i	0.0852191	+	0.0619153i	−0.544360	+	0.838852i	$0.683227\pi$
$830$		0			0
$831$	−5.54302	−	17.0597i	−0.192285	−	0.591793i
$832$	1.40168	−	1.92924i	0.0485945	−	0.0668845i
$833$	11.1777	+	15.3848i	0.387284	+	0.533051i
$834$	−10.0475	+	30.9230i	−0.347916	+	1.07077i
$835$		0			0
$836$	−89.1929	+	44.4725i	−3.08480	+	1.53811i
$837$			3.44899i			0.119214i
$838$	12.3432	+	4.01054i	0.426388	+	0.138542i
$839$	−39.2683	+	28.5301i	−1.35569	+	0.984968i	−0.356987	+	0.934109i	$0.616196\pi$
$839$	−39.2683	+	28.5301i	−1.35569	+	0.984968i	−0.998706	+	0.0508591i	$0.983804\pi$
$840$		0			0
$841$	−1.12296	−	3.45613i	−0.0387229	−	0.119177i
$842$	71.8947	−	23.3600i	2.47766	−	0.805039i
$843$	−4.35609	+	5.99565i	−0.150032	+	0.206501i
$844$	−65.0762	+	47.2806i	−2.24001	+	1.62747i
$845$		0			0
$846$	−29.4662			−1.01307
$847$	−10.5723	−	34.5750i	−0.363270	−	1.18801i
$848$		−	20.6758i		−	0.710011i
$849$	−1.66462	+	5.12319i	−0.0571298	+	0.175827i
$850$		0			0
$851$	−2.28872	−	1.66285i	−0.0784563	−	0.0570018i
$852$	−11.7787	+	3.82713i	−0.403531	+	0.131115i
$853$	−11.1875	+	3.63504i	−0.383053	+	0.124461i	−0.494213	−	0.869341i	$-0.664544\pi$
$853$	−11.1875	+	3.63504i	−0.383053	+	0.124461i	0.111160	+	0.993803i	$0.464544\pi$
$854$	59.9779	+	43.5765i	2.05240	+	1.49116i
$855$		0			0
$856$	3.22586	−	9.92817i	0.110258	−	0.339338i
$857$			1.61311i			0.0551026i	0.999620	+	0.0275513i	$0.00877097\pi$
$857$			1.61311i			0.0551026i	−0.999620	+	0.0275513i	$0.991229\pi$
$858$	1.13810	+	2.28255i	0.0388542	+	0.0779250i
$859$	−47.3263			−1.61475			−0.807376	−	0.590038i	$-0.799113\pi$
$859$	−47.3263			−1.61475			−0.807376	+	0.590038i	$0.799113\pi$
$860$		0			0
$861$	−28.8439	+	20.9563i	−0.982998	+	0.714190i
$862$	17.8286	−	24.5389i	0.607244	−	0.835799i
$863$	−9.48425	+	3.08162i	−0.322848	+	0.104900i	−0.465957	−	0.884807i	$-0.654290\pi$
$863$	−9.48425	+	3.08162i	−0.322848	+	0.104900i	0.143109	+	0.989707i	$0.454290\pi$
$864$	−0.0960054	−	0.295474i	−0.00326617	−	0.0100522i
$865$		0			0
$866$	−2.80717	+	2.03953i	−0.0953915	+	0.0693060i
$867$	7.60845	+	2.47214i	0.258397	+	0.0839581i
$868$		−	45.7009i		−	1.55119i
$869$	2.65473	+	17.7604i	0.0900555	+	0.602482i
$870$		0			0
$871$	1.47795	−	4.54867i	0.0500786	−	0.154126i
$872$	19.6257	+	27.0124i	0.664609	+	0.914756i
$873$	−0.131712	+	0.181286i	−0.00445778	+	0.00613560i
$874$	6.07515	+	18.6974i	0.205495	+	0.632448i
$875$		0			0
$876$	28.2204	+	20.5033i	0.953478	+	0.692742i
$877$	−15.2858	−	21.0391i	−0.516164	−	0.710439i	0.468779	−	0.883315i	$-0.344694\pi$
$877$	−15.2858	−	21.0391i	−0.516164	−	0.710439i	−0.984944	+	0.172876i	$0.944694\pi$
$878$	17.7169	+	5.75658i	0.597918	+	0.194275i
$879$	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	$0.443901\pi$
$882$	8.88338	+	2.88639i	0.299119	+	0.0971897i
$883$	−31.5807	−	43.4671i	−1.06278	−	1.46279i	−0.877181	−	0.480159i	$-0.840579\pi$
$883$	−31.5807	−	43.4671i	−1.06278	−	1.46279i	−0.185595	−	0.982626i	$-0.559421\pi$
$884$	−5.10635	−	3.70998i	−0.171745	−	0.124780i
$885$		0			0
$886$	8.39826	+	25.8472i	0.282145	+	0.868353i
$887$	−23.8786	+	32.8660i	−0.801763	+	1.10353i	0.190779	+	0.981633i	$0.438899\pi$
$887$	−23.8786	+	32.8660i	−0.801763	+	1.10353i	−0.992542	+	0.121900i	$0.961101\pi$
$888$	7.72468	+	10.6321i	0.259223	+	0.356790i
$889$	17.2701	−	53.1518i	0.579219	−	1.78265i
$890$		0			0
$891$	−3.27115	−	0.547326i	−0.109588	−	0.0183361i
$892$		−	81.2188i		−	2.71941i
$893$	−85.0582	−	27.6371i	−2.84636	−	0.924839i
$894$	−11.6799	+	8.48594i	−0.390634	+	0.283812i
$895$		0			0
$896$	−19.6274	−	60.4071i	−0.655707	−	2.01806i
$897$	0.319822	−	0.103916i	0.0106785	−	0.00346967i
$898$	−9.13549	+	12.5739i	−0.304855	+	0.419597i
$899$	−14.0532	+	10.2103i	−0.468701	+	0.340531i
$900$		0			0
$901$	24.6772			0.822115
$902$	−63.0166	+	61.9290i	−2.09822	+	2.06201i
$903$			18.1259i			0.603191i
$904$	16.6406	−	51.2145i	0.553458	−	1.70337i
$905$		0			0
$906$	−15.1561	−	11.0116i	−0.503529	−	0.365835i
$907$	18.4571	−	5.99708i	0.612859	−	0.199130i	0.0138917	−	0.999904i	$-0.495578\pi$
$907$	18.4571	−	5.99708i	0.612859	−	0.199130i	0.598967	+	0.800774i	$0.295578\pi$
$908$	2.04715	−	0.665160i	0.0679371	−	0.0220741i
$909$	−0.408817	−	0.297023i	−0.0135596	−	0.00985163i
$910$		0			0
$911$	3.31290	−	10.1960i	0.109761	−	0.337810i	−0.881057	−	0.473010i	$-0.843168\pi$
$911$	3.31290	−	10.1960i	0.109761	−	0.337810i	0.990818	+	0.135200i	$0.0431676\pi$
$912$		−	31.2271i		−	1.03403i
$913$	38.4290	−	37.7658i	1.27182	−	1.24987i
$914$	0.465585			0.0154002
$915$		0			0
$916$	72.3816	−	52.5883i	2.39156	−	1.73757i
$917$	−0.0831723	+	0.114477i	−0.00274659	+	0.00378036i
$918$	11.6784	−	3.79455i	0.385446	−	0.125239i
$919$	7.14787	+	21.9989i	0.235787	+	0.725676i	0.997016	+	0.0771939i	$0.0245960\pi$
$919$	7.14787	+	21.9989i	0.235787	+	0.725676i	−0.761230	+	0.648483i	$0.775404\pi$
$920$		0			0
$921$	−17.2779	+	12.5531i	−0.569325	+	0.413639i
$922$	−62.1755	−	20.2020i	−2.04764	−	0.665319i
$923$			0.961981i			0.0316640i
$924$	43.3444	+	7.25235i	1.42593	+	0.238585i
$925$		0			0
$926$	15.9322	−	49.0343i	0.523565	−	1.61137i
$927$	3.76298	+	5.17930i	0.123593	+	0.170111i
$928$	0.919725	−	1.26589i	0.0301915	−	0.0415550i
$929$	−8.10467	−	24.9436i	−0.265906	−	0.818374i	−0.991483	−	0.130233i	$-0.958427\pi$
$929$	−8.10467	−	24.9436i	−0.265906	−	0.818374i	0.725578	−	0.688140i	$-0.241573\pi$
$930$		0			0
$931$	22.9359	+	16.6639i	0.751693	+	0.546137i
$932$	10.8187	+	14.8907i	0.354380	+	0.487762i
$933$	−31.2038	−	10.1387i	−1.02157	−	0.331927i
$934$	−19.4012			−0.634828
$935$		0			0
$936$	−1.56217			−0.0510612
$937$	22.2557	+	7.23133i	0.727063	+	0.236237i	0.649083	−	0.760718i	$-0.275153\pi$
$937$	22.2557	+	7.23133i	0.727063	+	0.236237i	0.0779804	+	0.996955i	$0.475153\pi$
$938$	−72.4694	−	99.7456i	−2.36621	−	3.25681i
$939$	−2.79800	−	2.03287i	−0.0913094	−	0.0663401i
$940$		0			0
$941$	−3.38952	−	10.4319i	−0.110495	−	0.340069i	0.880486	−	0.474073i	$-0.157217\pi$
$941$	−3.38952	−	10.4319i	−0.110495	−	0.340069i	−0.990981	+	0.134004i	$0.957217\pi$
$942$	−14.6276	+	20.1332i	−0.476595	+	0.655976i
$943$	6.84713	+	9.42427i	0.222973	+	0.306896i
$944$	11.8634	−	36.5118i	0.386121	−	1.18836i
$945$		0			0
$946$	6.64038	+	44.4249i	0.215897	+	1.44438i
$947$		−	13.3652i		−	0.434310i	−0.976137	−	0.217155i	$-0.930322\pi$
$947$		−	13.3652i		−	0.434310i	0.976137	−	0.217155i	$-0.0696777\pi$
$948$	−20.7594	−	6.74515i	−0.674235	−	0.219072i
$949$	2.19199	−	1.59257i	0.0711550	−	0.0516971i
$950$		0			0
$951$	−0.888626	−	2.73491i	−0.0288157	−	0.0886856i
$952$	−77.9749	+	25.3356i	−2.52718	+	0.821130i
$953$	12.8280	−	17.6562i	0.415538	−	0.571939i	−0.549020	−	0.835809i	$-0.684999\pi$
$953$	12.8280	−	17.6562i	0.415538	−	0.571939i	0.964558	+	0.263870i	$0.0849990\pi$
$954$	9.80598	−	7.12446i	0.317480	−	0.230663i
$955$		0			0
$956$	−23.6260			−0.764120
$957$	−7.45366	−	14.9489i	−0.240943	−	0.483229i
$958$		−	98.1686i		−	3.17168i
$959$	−7.47809	+	23.0152i	−0.241480	+	0.743199i
$960$		0			0
$961$	15.4558	+	11.2293i	0.498576	+	0.362236i
$962$	1.92667	−	0.626012i	0.0621182	−	0.0201834i
$963$	1.99008	−	0.646615i	0.0641293	−	0.0208369i
$964$	32.4865	+	23.6028i	1.04632	+	0.760196i
$965$		0			0
$966$	2.67881	−	8.24453i	0.0861893	−	0.265263i
$967$			16.6600i			0.535750i	0.963454	+	0.267875i	$0.0863214\pi$
$967$			16.6600i			0.535750i	−0.963454	+	0.267875i	$0.913679\pi$
$968$	54.8689	+	0.955240i	1.76355	+	0.0307026i
$969$	37.2704			1.19730
$970$		0			0
$971$	−8.98271	+	6.52632i	−0.288269	+	0.209440i	−0.722516	−	0.691354i	$-0.757014\pi$
$971$	−8.98271	+	6.52632i	−0.288269	+	0.209440i	0.434247	+	0.900794i	$0.357014\pi$
$972$	2.36959	−	3.26145i	0.0760045	−	0.104611i
$973$	41.3858	−	13.4471i	1.32677	−	0.431093i
$974$	7.54021	+	23.2064i	0.241604	+	0.743580i
$975$		0			0
$976$	−31.1273	+	22.6153i	−0.996362	+	0.723899i
$977$	17.8936	+	5.81397i	0.572466	+	0.186005i	0.580923	−	0.813959i	$-0.302692\pi$
$977$	17.8936	+	5.81397i	0.572466	+	0.186005i	−0.00845665	+	0.999964i	$0.502692\pi$
$978$			12.3508i			0.394935i
$979$	−4.81187	+	2.39924i	−0.153788	+	0.0766802i
$980$		0			0
$981$	−2.06818	+	6.36521i	−0.0660320	+	0.203226i
$982$	−7.17940	−	9.88160i	−0.229104	−	0.315335i
$983$	0.810250	−	1.11521i	0.0258430	−	0.0355698i	−0.795900	−	0.605428i	$-0.793002\pi$
$983$	0.810250	−	1.11521i	0.0258430	−	0.0355698i	0.821743	+	0.569858i	$0.193002\pi$
$984$	−16.7224	−	51.4664i	−0.533092	−	1.64069i
$985$		0			0
$986$	50.0336	+	36.3516i	1.59340	+	1.15767i
$987$	23.1800	+	31.9045i	0.737827	+	1.01553i
$988$	−8.94918	−	2.90777i	−0.284711	−	0.0925083i
$989$	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	$0.763137\pi$
$992$	1.01909	+	0.331122i	0.0323561	+	0.0105131i
$993$	−8.30074	−	11.4250i	−0.263416	−	0.362561i
$994$	20.0623	+	14.5761i	0.636339	+	0.462327i
$995$		0			0
$996$	20.2380	+	62.2861i	0.641265	+	1.97361i
$997$	8.55054	−	11.7688i	0.270798	−	0.372722i	−0.651861	−	0.758339i	$-0.726011\pi$
$997$	8.55054	−	11.7688i	0.270798	−	0.372722i	0.922659	+	0.385617i	$0.126011\pi$
$998$	63.1917	+	86.9759i	2.00030	+	2.75317i
$999$	−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.bx.h.724.4		16
5.2	odd	4		825.2.n.k.526.1		8
5.3	odd	4		165.2.m.a.31.2	yes	8
5.4	even	2	inner	825.2.bx.h.724.1		16
11.5	even	5	inner	825.2.bx.h.49.1		16
15.8	even	4		495.2.n.d.361.1		8
55.7	even	20		9075.2.a.dj.1.3		4
55.18	even	20		1815.2.a.o.1.2		4
55.27	odd	20		825.2.n.k.676.1		8
55.37	odd	20		9075.2.a.cl.1.2		4
55.38	odd	20		165.2.m.a.16.2	✓	8
55.48	odd	20		1815.2.a.x.1.3		4
55.49	even	10	inner	825.2.bx.h.49.4		16
165.38	even	20		495.2.n.d.181.1		8
165.128	odd	20		5445.2.a.bv.1.3		4
165.158	even	20		5445.2.a.be.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.2	✓	8	55.38	odd	20
165.2.m.a.31.2	yes	8	5.3	odd	4
495.2.n.d.181.1		8	165.38	even	20
495.2.n.d.361.1		8	15.8	even	4
825.2.n.k.526.1		8	5.2	odd	4
825.2.n.k.676.1		8	55.27	odd	20
825.2.bx.h.49.1		16	11.5	even	5	inner
825.2.bx.h.49.4		16	55.49	even	10	inner
825.2.bx.h.724.1		16	5.4	even	2	inner
825.2.bx.h.724.4		16	1.1	even	1	trivial
1815.2.a.o.1.2		4	55.18	even	20
1815.2.a.x.1.3		4	55.48	odd	20
5445.2.a.be.1.2		4	165.158	even	20
5445.2.a.bv.1.3		4	165.128	odd	20
9075.2.a.cl.1.2		4	55.37	odd	20
9075.2.a.dj.1.3		4	55.7	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.33569 + 0.758911i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.26145 + 2.36959i) q^{4} +(0.758911 + 2.33569i) q^{6} +(1.93196 - 2.65911i) q^{7} +(2.93237 + 4.03606i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(2.33569 + 0.758911i) q^{2} +(0.587785 + 0.809017i) q^{3} +(3.26145 + 2.36959i) q^{4} +(0.758911 + 2.33569i) q^{6} +(1.93196 - 2.65911i) q^{7} +(2.93237 + 4.03606i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(2.96813 - 1.47994i) q^{11} +4.03138i q^{12} +(0.297808 + 0.0967635i) q^{13} +(6.53048 - 4.74467i) q^{14} +(1.29455 + 3.98423i) q^{16} +(-4.75528 + 1.54508i) q^{17} +(-1.44353 + 1.98685i) q^{18} +(-6.03048 + 4.38140i) q^{19} +3.28684 q^{21} +(8.05576 - 1.20413i) q^{22} -1.07392i q^{23} +(-1.54164 + 4.74467i) q^{24} +(0.622150 + 0.452019i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(12.6020 - 4.09463i) q^{28} +(-4.07459 - 2.96036i) q^{29} +(1.06580 - 3.28018i) q^{31} +0.310680i q^{32} +(2.94192 + 1.53138i) q^{33} -12.2794 q^{34} +(-3.26145 + 2.36959i) q^{36} +(1.54839 - 2.13118i) q^{37} +(-17.4104 + 5.65698i) q^{38} +(0.0967635 + 0.297808i) q^{39} +(-8.77557 + 6.37583i) q^{41} +(7.67703 + 2.49442i) q^{42} +5.51468i q^{43} +(13.1873 + 2.20648i) q^{44} +(0.815010 - 2.50834i) q^{46} +(7.05236 + 9.70674i) q^{47} +(-2.46239 + 3.38919i) q^{48} +(-1.17529 - 3.61718i) q^{49} +(-4.04508 - 2.93893i) q^{51} +(0.741996 + 1.02127i) q^{52} +(-4.69387 - 1.52513i) q^{53} -2.45589 q^{54} +16.3975 q^{56} +(-7.08925 - 2.30344i) q^{57} +(-7.27031 - 10.0067i) q^{58} +(-7.41391 - 5.38652i) q^{59} +(2.83811 + 8.73480i) q^{61} +(4.97873 - 6.85264i) q^{62} +(1.93196 + 2.65911i) q^{63} +(2.35333 - 7.24280i) q^{64} +(5.70922 + 5.80948i) q^{66} -15.2739i q^{67} +(-19.1704 - 6.22882i) q^{68} +(0.868820 - 0.631235i) q^{69} +(0.949335 + 2.92175i) q^{71} +(-4.74467 + 1.54164i) q^{72} +(5.08592 - 7.00018i) q^{73} +(5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(1.79898 - 10.7518i) q^{77} +0.769020i q^{78} +(-1.67316 + 5.14946i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-25.3357 + 8.23206i) q^{82} +(15.4503 - 5.02011i) q^{83} +(10.7199 + 7.78845i) q^{84} +(-4.18515 + 12.8806i) q^{86} -5.03647i q^{87} +(14.6768 + 7.63981i) q^{88} -1.62118 q^{89} +(0.832656 - 0.604960i) q^{91} +(2.54475 - 3.50254i) q^{92} +(3.28018 - 1.06580i) q^{93} +(9.10556 + 28.0240i) q^{94} +(-0.251345 + 0.182613i) q^{96} +(0.213115 + 0.0692451i) q^{97} -9.34054i q^{98} +(0.490303 + 3.28018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

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