LMFDB - Embedded newform 825.2.bx.h.49.4

Newspace parameters

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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			49.4
Root			$0.701538 - 0.227943i$ of defining polynomial
Character	$\chi$	$=$	825.49
Dual form			825.2.bx.h.724.4

$q$-expansion

$f(q)$	$=$	$q+(2.33569 - 0.758911i) q^{2} +(0.587785 - 0.809017i) q^{3} +(3.26145 - 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(1.93196 + 2.65911i) q^{7} +(2.93237 - 4.03606i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.33569	−	0.758911i	1.65158	−	0.536631i	0.672499	−	0.740098i	$-0.265221\pi$
$2$	2.33569	−	0.758911i	1.65158	−	0.536631i	0.979082	+	0.203468i	$0.0652211\pi$
$3$	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	0.999122	+	0.0418845i	$0.0133361\pi$
$7$	1.93196	+	2.65911i	0.730211	+	1.00505i	−0.268911	+	0.963165i	$0.586664\pi$
$8$	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	−0.267427	−	0.963578i	$-0.586173\pi$
$13$	0.297808	−	0.0967635i	0.0825970	−	0.0268374i	0.350024	+	0.936741i	$0.386173\pi$
$14$	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	−0.330930	−	0.943655i	$-0.607363\pi$
$17$	−4.75528	−	1.54508i	−1.15333	−	0.374738i	−0.822395	+	0.568917i	$0.807363\pi$
$18$	−1.44353	−	1.98685i	−0.340244	−	0.468306i
$19$	−6.03048	−	4.38140i	−1.38349	−	1.00516i	−0.996545	−	0.0830568i	$-0.973532\pi$
$19$	−6.03048	−	4.38140i	−1.38349	−	1.00516i	−0.386941	−	0.922104i	$-0.626468\pi$
$20$		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	$0.0357141\pi$
$23$			1.07392i			0.223928i	−0.993712	+	0.111964i	$0.964286\pi$
$24$	−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	−0.897875	−	0.440250i	$-0.854890\pi$
$29$	−4.07459	+	2.96036i	−0.756632	+	0.549725i	0.141243	+	0.989975i	$0.454890\pi$
$30$		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	$0.799762\pi$
$32$		−	0.310680i		−	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	0.917100	−	0.398658i	$-0.130524\pi$
$37$	1.54839	+	2.13118i	0.254554	+	0.350364i	−0.662546	+	0.749022i	$0.730524\pi$
$38$	−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	−0.997697	−	0.0678321i	$-0.978392\pi$
$41$	−8.77557	−	6.37583i	−1.37051	−	0.995737i	−0.372817	−	0.927905i	$-0.621608\pi$
$42$	7.67703	−	2.49442i	1.18459	−	0.384897i
$43$		−	5.51468i		−	0.840980i	−0.907297	−	0.420490i	$-0.861858\pi$
$43$		−	5.51468i		−	0.840980i	0.907297	−	0.420490i	$-0.138142\pi$
$44$	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	0.122767	−	0.992435i	$-0.460823\pi$
$47$	7.05236	−	9.70674i	1.02869	−	1.41587i	0.905925	−	0.423438i	$-0.139177\pi$
$48$	−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	−0.613099	−	0.790006i	$-0.710077\pi$
$53$	−4.69387	+	1.52513i	−0.644753	+	0.209493i	−0.0316539	+	0.999499i	$0.510077\pi$
$54$	−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	−0.954354	−	0.298676i	$-0.903455\pi$
$59$	−7.41391	+	5.38652i	−0.965208	+	0.701265i	−0.0108537	+	0.999941i	$0.503455\pi$
$60$		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	$-0.100071\pi$
$62$	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	$0.382819\pi$
$67$			15.2739i			1.86600i	−0.359876	+	0.933000i	$0.617181\pi$
$68$	−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	−0.878788	−	0.477213i	$-0.841647\pi$
$71$	0.949335	−	2.92175i	0.112665	−	0.346748i	0.991453	+	0.130465i	$0.0416470\pi$
$72$	−4.74467	−	1.54164i	−0.559164	−	0.181684i
$73$	5.08592	+	7.00018i	0.595262	+	0.819309i	0.995264	−	0.0972058i	$-0.0309905\pi$
$73$	5.08592	+	7.00018i	0.595262	+	0.819309i	−0.400002	+	0.916514i	$0.630991\pi$
$74$	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	0.811744	−	0.584014i	$-0.198519\pi$
$79$	−1.67316	−	5.14946i	−0.188245	−	0.579360i	−0.999989	+	0.00465401i	$0.998519\pi$
$80$		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	0.987887	−	0.155178i	$-0.0495952\pi$
$83$	15.4503	+	5.02011i	1.69589	+	0.551029i	0.708006	+	0.706207i	$0.249595\pi$
$84$	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	−0.298178	−	0.954510i	$-0.596379\pi$
$97$	0.213115	−	0.0692451i	0.0216385	−	0.00703078i	0.319816	+	0.947480i	$0.396379\pi$
$98$			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	0.942987	−	0.332830i	$-0.108003\pi$
$101$	−0.156154	−	0.480593i	−0.0155379	−	0.0478208i	−0.958525	+	0.285009i	$0.908003\pi$
$102$	−7.21767	+	9.93427i	−0.714656	+	0.983639i
$103$	3.76298	+	5.17930i	0.370778	+	0.510332i	0.953112	−	0.302618i	$-0.0978605\pi$
$103$	3.76298	+	5.17930i	0.370778	+	0.510332i	−0.582334	+	0.812949i	$0.697861\pi$
$104$	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	−0.864319	−	0.502943i	$-0.832250\pi$
$107$	−1.22993	+	1.69286i	−0.118902	+	0.163655i	0.745417	+	0.666598i	$0.232250\pi$
$108$	−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	−0.995416	−	0.0956448i	$-0.969509\pi$
$113$	−6.34462	+	8.73262i	−0.596852	+	0.821496i	0.398564	+	0.917141i	$0.369509\pi$
$114$	−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	0.920320	−	0.391167i	$-0.127929\pi$
$127$	16.1711	+	5.25430i	1.43495	+	0.466244i	0.514632	+	0.857411i	$0.327929\pi$
$128$	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	−0.00578480	−	0.999983i	$-0.501841\pi$
$137$	−7.00222	−	2.27516i	−0.598240	−	0.194380i	−0.592455	+	0.805603i	$0.701841\pi$
$138$	2.50834	+	0.815010i	0.213524	+	0.0693783i
$139$	10.7109	−	7.78189i	0.908483	−	0.660052i	−0.0321478	−	0.999483i	$-0.510235\pi$
$139$	10.7109	−	7.78189i	0.908483	−	0.660052i	0.940631	+	0.339432i	$0.110235\pi$
$140$		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	−0.848662	−	0.528935i	$-0.822591\pi$
$149$	1.81658	−	5.59087i	0.148820	−	0.458022i	0.997482	+	0.0709136i	$0.0225915\pi$
$150$		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	$0.800459\pi$
$152$	−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	−0.502250	−	0.864722i	$-0.667494\pi$
$157$	5.95616	−	8.19795i	0.475353	−	0.654267i	0.977604	+	0.210455i	$0.0674945\pi$
$158$	−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	−0.115651	−	0.993290i	$-0.536895\pi$
$163$	4.78292	−	1.55407i	0.374627	−	0.121724i	0.490278	+	0.871566i	$0.336895\pi$
$164$	−43.7292			−3.41468
$165$		0			0
$166$	39.8969			3.09660
$167$	5.50761	−	1.78953i	0.426192	−	0.138478i	−0.0880642	−	0.996115i	$-0.528068\pi$
$167$	5.50761	−	1.78953i	0.426192	−	0.138478i	0.514256	+	0.857637i	$0.328068\pi$
$168$	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	−0.281660	−	0.959514i	$-0.590885\pi$
$173$	9.44290	−	12.9970i	0.717930	−	0.988146i	0.999590	−	0.0286316i	$-0.00911498\pi$
$174$	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	0.307732	−	0.951473i	$-0.400430\pi$
$179$	−6.71734	−	4.88043i	−0.502078	−	0.364781i	−0.809810	+	0.586692i	$0.800430\pi$
$180$		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	$0.177227\pi$
$182$	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	−0.938387	−	0.345585i	$-0.887680\pi$
$191$	−12.4340	+	9.03384i	−0.899694	+	0.653666i	0.0386935	+	0.999251i	$0.487680\pi$
$192$	7.24280	+	2.35333i	0.522704	+	0.169837i
$193$	14.9808	+	4.86757i	1.07834	+	0.350375i	0.793732	−	0.608267i	$-0.208135\pi$
$193$	14.9808	+	4.86757i	1.07834	+	0.350375i	0.284612	+	0.958643i	$0.408135\pi$
$194$	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	$-0.801483\pi$
$197$		−	16.3940i		−	1.16802i	0.811746	−	0.584010i	$-0.198517\pi$
$198$	−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	−0.903496	−	0.428596i	$-0.859008\pi$
$211$	−6.16585	−	18.9765i	−0.424475	−	1.30640i	0.479022	−	0.877803i	$-0.340992\pi$
$212$	−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	0.200737	+	0.979645i	$0.435666\pi$
$223$	−11.8419	+	16.2990i	−0.792992	+	1.09146i	−0.993729	+	0.111815i	$0.964334\pi$
$224$	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	0.819305	−	0.573358i	$-0.194359\pi$
$227$	0.313840	+	0.431964i	0.0208303	+	0.0286705i	−0.798475	+	0.602028i	$0.794359\pi$
$228$	−17.6631	+	24.3111i	−1.16977	+	1.61004i
$229$	6.85803	+	21.1068i	0.453191	+	1.39478i	0.873245	+	0.487281i	$0.162011\pi$
$229$	6.85803	+	21.1068i	0.453191	+	1.39478i	−0.420054	+	0.907499i	$0.637989\pi$
$230$		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	−0.163308	−	0.986575i	$-0.552216\pi$
$233$	4.34221	−	1.41087i	0.284467	−	0.0924291i	0.447775	+	0.894146i	$0.352216\pi$
$234$	−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	0.423787	−	0.905762i	$-0.360701\pi$
$239$	−4.74126	−	3.44473i	−0.306687	−	0.222821i	−0.730474	+	0.682941i	$0.760701\pi$
$240$		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	−0.969499	−	0.245094i	$-0.921181\pi$
$251$	−5.21584	−	16.0527i	−0.329221	−	1.01324i	0.640279	−	0.768143i	$-0.278819\pi$
$252$		−	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	0.962871	−	0.269961i	$-0.0870108\pi$
$257$	6.55003	+	9.01534i	0.408580	+	0.562362i	−0.554292	+	0.832323i	$0.687011\pi$
$258$	−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	$-0.689184\pi$
$263$		−	26.8726i		−	1.65704i	0.559961	−	0.828519i	$-0.310816\pi$
$264$	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	−0.810401	−	0.585875i	$-0.800751\pi$
$269$	3.10961	−	9.57038i	0.189596	−	0.583516i	0.999997	+	0.00235886i	$0.000750850\pi$
$270$		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	$0.403768\pi$
$272$	−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	−0.772818	−	0.634628i	$-0.781153\pi$
$277$	−17.0597	+	5.54302i	−1.02502	+	0.333048i	−0.252198	+	0.967676i	$0.581153\pi$
$278$	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	−0.859220	−	0.511606i	$-0.829051\pi$
$281$	2.29013	−	7.04830i	0.136618	−	0.420467i	0.995838	+	0.0911392i	$0.0290508\pi$
$282$	−17.3198	−	23.8387i	−1.03138	−	1.41957i
$283$	3.16630	−	4.35804i	0.188217	−	0.259059i	−0.704472	−	0.709732i	$-0.748816\pi$
$283$	3.16630	−	4.35804i	0.188217	−	0.259059i	0.892689	+	0.450673i	$0.148816\pi$
$284$	−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	0.837847	−	0.545905i	$-0.183814\pi$
$293$	1.02278	+	1.40774i	0.0597515	+	0.0822409i	−0.778096	+	0.628146i	$0.783814\pi$
$294$	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	$-0.791393\pi$
$307$		−	21.3566i		−	1.21889i	0.792829	−	0.609444i	$-0.208607\pi$
$308$	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	−0.968275	−	0.249886i	$-0.919607\pi$
$311$	−26.5435	−	19.2850i	−1.50514	−	1.09355i	−0.536870	−	0.843665i	$-0.680393\pi$
$312$	−0.918222	−	1.26382i	−0.0519841	−	0.0715499i
$313$	−3.28925	−	1.06874i	−0.185919	−	0.0604089i	0.214578	−	0.976707i	$-0.431163\pi$
$313$	−3.28925	−	1.06874i	−0.185919	−	0.0604089i	−0.400497	+	0.916298i	$0.631163\pi$
$314$	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	−0.384812	−	0.922995i	$-0.625734\pi$
$317$	−2.73491	+	0.888626i	−0.153608	+	0.0499102i	0.231204	+	0.972905i	$0.425734\pi$
$318$			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	0.984031	−	0.177995i	$-0.0569612\pi$
$337$	9.37457	+	12.9030i	0.510665	+	0.702870i	−0.473366	+	0.880866i	$0.656961\pi$
$338$	−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	−0.570884	−	0.821030i	$-0.693400\pi$
$347$	−28.2275	−	9.17166i	−1.51533	−	0.492360i	−0.944445	+	0.328670i	$0.893400\pi$
$348$	11.9343	+	16.4262i	0.639748	+	0.880537i
$349$	25.6408	+	18.6291i	1.37252	+	0.997194i	0.997536	+	0.0701620i	$0.0223516\pi$
$349$	25.6408	+	18.6291i	1.37252	+	0.997194i	0.374984	+	0.927031i	$0.377648\pi$
$350$		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	$0.0101829\pi$
$353$			1.20189i			0.0639703i	−0.999488	+	0.0319852i	$0.989817\pi$
$354$	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	−0.808185	−	0.588929i	$-0.799550\pi$
$359$	−9.43239	+	6.85304i	−0.497823	+	0.361689i	0.310362	+	0.950618i	$0.399550\pi$
$360$		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	0.980478	−	0.196631i	$-0.0630001\pi$
$367$	9.39636	+	12.9330i	0.490486	+	0.675096i	−0.489991	+	0.871727i	$0.663000\pi$
$368$	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	$0.00265334\pi$
$373$			0.321975i			0.0166712i	−0.999965	+	0.00833561i	$0.997347\pi$
$374$	−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	−0.999863	−	0.0165471i	$-0.994733\pi$
$379$	−3.52819	+	10.8586i	−0.181231	+	0.557771i	0.818632	+	0.574318i	$0.194733\pi$
$380$		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	−0.902195	−	0.431329i	$-0.858045\pi$
$383$	−26.9789	+	8.76597i	−1.37856	+	0.447920i	−0.476362	+	0.879249i	$0.658045\pi$
$384$	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	−0.231181	−	0.972911i	$-0.574259\pi$
$389$	12.2810	−	8.92269i	0.622673	−	0.452398i	0.853854	+	0.520513i	$0.174259\pi$
$390$		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	$-0.958147\pi$
$397$		−	5.22461i		−	0.262216i	0.991368	−	0.131108i	$-0.0418534\pi$
$398$	−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	−0.783025	−	0.621990i	$-0.786324\pi$
$401$	4.32644	−	13.3154i	0.216052	−	0.664941i	0.999077	−	0.0429502i	$-0.0136757\pi$
$402$	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	−0.793953	−	0.607979i	$-0.791980\pi$
$409$	−10.2937	−	31.6809i	−0.508993	−	1.56652i	0.284960	−	0.958539i	$-0.408020\pi$
$410$		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	0.995558	−	0.0941452i	$-0.0300118\pi$
$421$	24.9023	+	18.0926i	1.21367	+	0.881780i	0.218107	+	0.975925i	$0.430012\pi$
$422$	−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	0.999926	−	0.0121333i	$-0.00386225\pi$
$431$	3.81656	+	11.7462i	0.183837	+	0.565793i	−0.816089	+	0.577926i	$0.803862\pi$
$432$	−2.46239	+	3.38919i	−0.118472	+	0.163062i
$433$	−0.830465	−	1.14304i	−0.0399096	−	0.0549308i	0.788596	−	0.614912i	$-0.210808\pi$
$433$	−0.830465	−	1.14304i	−0.0399096	−	0.0549308i	−0.828505	+	0.559981i	$0.810808\pi$
$434$	−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	−0.626041	−	0.779790i	$-0.715326\pi$
$443$	6.50455	−	8.95274i	0.309040	−	0.425358i	0.935082	+	0.354432i	$0.115326\pi$
$444$	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	0.894247	−	0.447575i	$-0.147712\pi$
$449$	−1.95563	−	6.01882i	−0.0922920	−	0.284045i	−0.986538	+	0.163529i	$0.947712\pi$
$450$		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	0.313231	−	0.949677i	$-0.398589\pi$
$457$	0.180300	+	0.0585832i	0.00843410	+	0.00274040i	−0.304797	+	0.952417i	$0.598589\pi$
$458$	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	$0.162210\pi$
$463$			20.9935i			0.975652i	−0.872941	+	0.487826i	$0.837790\pi$
$464$	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	0.129976	−	0.991517i	$-0.458510\pi$
$467$	−7.51324	−	2.44120i	−0.347671	−	0.112965i	−0.477647	+	0.878552i	$0.658510\pi$
$468$	−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	0.105369	+	0.994433i	$0.466398\pi$
$479$	−12.3523	+	38.0164i	−0.564389	+	1.73701i	−0.669758	+	0.742579i	$0.733602\pi$
$480$		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	−0.655935	−	0.754818i	$-0.727725\pi$
$487$	5.83998	−	8.03804i	0.264635	−	0.364238i	0.920569	+	0.390579i	$0.127725\pi$
$488$	−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	−0.674864	−	0.737942i	$-0.735798\pi$
$491$	−4.02364	+	2.92335i	−0.181584	+	0.131929i	0.493280	+	0.869871i	$0.335798\pi$
$492$	−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	0.675256	−	0.737584i	$-0.264033\pi$
$499$	35.4153	−	25.7307i	1.58541	−	1.15186i	0.910149	−	0.414281i	$-0.135967\pi$
$500$		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	−0.718718	−	0.695301i	$-0.755271\pi$
$503$	3.69268	−	5.08254i	0.164648	−	0.226619i	0.883367	+	0.468682i	$0.155271\pi$
$504$	−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	0.936053	−	0.351859i	$-0.114450\pi$
$509$	20.0945	+	14.5995i	0.890671	+	0.647111i	−0.0453816	+	0.998970i	$0.514450\pi$
$510$		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	−0.457792	−	0.889059i	$-0.651360\pi$
$521$	5.62161	−	4.08434i	0.246287	−	0.178938i	0.704080	+	0.710121i	$0.251360\pi$
$522$	11.7636	+	3.82223i	0.514879	+	0.167294i
$523$	−25.4417	−	8.26650i	−1.11249	−	0.361469i	−0.305591	−	0.952163i	$-0.598854\pi$
$523$	−25.4417	−	8.26650i	−1.11249	−	0.361469i	−0.806896	+	0.590694i	$0.798854\pi$
$524$	−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	0.999995	+	0.00301536i	$0.000959822\pi$
$541$	4.48336	+	13.7984i	0.192755	+	0.593237i	−0.807241	+	0.590222i	$0.799040\pi$
$542$	−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	−0.327912	−	0.944708i	$-0.606345\pi$
$547$	15.7142	−	21.6287i	0.671890	−	0.924777i	0.999801	+	0.0199316i	$0.00634485\pi$
$548$	−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	0.967833	−	0.251593i	$-0.0809544\pi$
$557$	10.1360	+	13.9510i	0.429477	+	0.591125i	−0.538356	+	0.842718i	$0.680954\pi$
$558$	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	−0.292297	−	0.956328i	$-0.594420\pi$
$563$	0.791197	−	0.257075i	0.0333450	−	0.0108344i	0.325642	+	0.945493i	$0.394420\pi$
$564$	−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	0.766802	−	0.641884i	$-0.221847\pi$
$569$	9.38141	+	6.81599i	0.393289	+	0.285741i	−0.373513	+	0.927625i	$0.621847\pi$
$570$		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	0.109657	−	0.993969i	$-0.465025\pi$
$577$	−9.26888	−	3.01164i	−0.385868	−	0.125376i	−0.495526	+	0.868593i	$0.665025\pi$
$578$	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	0.990894	−	0.134645i	$-0.0429895\pi$
$587$	13.4862	+	18.5622i	0.556635	+	0.766143i	−0.434258	+	0.900788i	$0.642990\pi$
$588$	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	$0.201253\pi$
$593$			28.7819i			1.18193i	−0.806697	+	0.590965i	$0.798747\pi$
$594$	−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	−0.579062	−	0.815283i	$-0.696581\pi$
$599$	9.02179	−	27.7662i	0.368620	−	1.13450i	0.947683	−	0.319214i	$-0.103419\pi$
$600$		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	$0.256492\pi$
$602$	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	−0.977619	−	0.210384i	$-0.932529\pi$
$607$	−40.5252	+	13.1674i	−1.64487	+	0.534450i	−0.667250	+	0.744834i	$0.732529\pi$
$608$	−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	−0.872609	−	0.488419i	$-0.837574\pi$
$613$	−3.42771	+	4.71783i	−0.138444	+	0.190552i	0.734165	+	0.678971i	$0.237574\pi$
$614$	−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	$0.236772\pi$
$617$			33.6386i			1.35424i	−0.735874	+	0.677119i	$0.763228\pi$
$618$	14.9530	−	4.85852i	0.601498	−	0.195438i
$619$	34.4331	+	25.0171i	1.38398	+	1.00552i	0.996495	+	0.0836477i	$0.0266570\pi$
$619$	34.4331	+	25.0171i	1.38398	+	1.00552i	0.387488	+	0.921875i	$0.373343\pi$
$620$		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	−0.435172	−	0.900347i	$-0.643312\pi$
$631$	7.20016	−	5.23122i	0.286634	−	0.208252i	0.721806	+	0.692096i	$0.243312\pi$
$632$	−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	0.681956	−	0.731393i	$-0.261130\pi$
$641$	4.99007	+	3.62549i	0.197096	+	0.143198i	−0.484860	+	0.874592i	$0.661130\pi$
$642$	3.02058	+	4.15747i	0.119213	+	0.164082i
$643$	4.14029	+	1.34526i	0.163277	+	0.0530519i	0.389515	−	0.921020i	$-0.372643\pi$
$643$	4.14029	+	1.34526i	0.163277	+	0.0530519i	−0.226238	+	0.974072i	$0.572643\pi$
$644$	−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	−0.0456916	−	0.998956i	$-0.514549\pi$
$647$	12.8329	−	4.16967i	0.504514	−	0.163927i	0.550206	+	0.835029i	$0.314549\pi$
$648$			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	0.366761	−	0.930315i	$-0.380467\pi$
$653$	−16.1336	−	22.2060i	−0.631357	−	0.868988i	−0.998118	+	0.0613270i	$0.980467\pi$
$654$	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	−0.703233	−	0.710959i	$-0.748261\pi$
$673$	−22.1617	+	7.20076i	−0.854269	+	0.277569i	−0.151036	+	0.988528i	$0.548261\pi$
$674$	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	−0.370683	−	0.928760i	$-0.620876\pi$
$677$	−31.6519	−	10.2843i	−1.21648	−	0.395259i	−0.845800	+	0.533501i	$0.820876\pi$
$678$	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	$0.104959\pi$
$683$			16.9244i			0.647593i	−0.946127	+	0.323796i	$0.895041\pi$
$684$	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	−0.654617	−	0.755961i	$-0.727170\pi$
$691$	−14.9668	−	46.0630i	−0.569363	−	1.75232i	0.0852532	−	0.996359i	$-0.472830\pi$
$692$		−	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	0.996109	+	0.0881330i	$0.0280900\pi$
$701$	36.7424	+	26.6949i	1.38774	+	1.00825i	0.391634	+	0.920121i	$0.371910\pi$
$702$	−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	−0.940292	−	0.340368i	$-0.889449\pi$
$709$	0.545405	−	1.67858i	0.0204831	−	0.0630406i	0.960776	+	0.277327i	$0.0894485\pi$
$710$		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	−0.636454	−	0.771315i	$-0.719599\pi$
$719$	−2.66974	+	1.93968i	−0.0995645	+	0.0723379i	0.536889	+	0.843653i	$0.319599\pi$
$720$		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	$-0.929878\pi$
$727$		−	11.7838i		−	0.437037i	0.975833	−	0.218519i	$-0.0701225\pi$
$728$	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	0.742261	−	0.670111i	$-0.233754\pi$
$733$	−3.36865	−	4.63654i	−0.124424	−	0.171255i	−0.866685	+	0.498856i	$0.833754\pi$
$734$	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	0.996516	+	0.0834038i	$0.0265791\pi$
$739$	6.50638	+	20.0246i	0.239341	+	0.736616i	−0.757175	+	0.653212i	$0.773421\pi$
$740$		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	0.528952	−	0.848652i	$-0.322585\pi$
$743$	12.4857	+	4.05686i	0.458058	+	0.148832i	−0.0708942	+	0.997484i	$0.522585\pi$
$744$	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	0.141342	−	0.989961i	$-0.454858\pi$
$751$	−20.7311	−	15.0621i	−0.756490	−	0.549622i	−0.897832	+	0.440339i	$0.854858\pi$
$752$	−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	0.284632	−	0.958637i	$-0.408129\pi$
$757$	29.6701	−	9.64039i	1.07838	−	0.350386i	0.793745	+	0.608251i	$0.208129\pi$
$758$			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	0.994336	−	0.106278i	$-0.0338932\pi$
$761$	3.51539	+	10.8193i	0.127433	+	0.392198i	−0.866904	+	0.498476i	$0.833893\pi$
$762$	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	−0.634468	−	0.772949i	$-0.718781\pi$
$773$	8.24944	−	11.3544i	0.296712	−	0.408389i	0.931180	+	0.364560i	$0.118781\pi$
$774$	−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

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

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