LMFDB - Embedded newform 585.2.i.h.391.2

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.2
Character	$\chi$	$=$	585.391
Dual form			585.2.i.h.196.2

$q$-expansion

$f(q)$	$=$	$q+(-1.26000 - 2.18239i) q^{2} +(-1.67966 - 0.422782i) q^{3} +(-2.17520 + 3.76756i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.19370 + 4.19837i) q^{6} +(-1.50610 - 2.60865i) q^{7} +5.92303 q^{8} +(2.64251 + 1.42026i) q^{9} +O(q^{10})$	\(q+(-1.26000 - 2.18239i) q^{2} +(-1.67966 - 0.422782i) q^{3} +(-2.17520 + 3.76756i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.19370 + 4.19837i) q^{6} +(-1.50610 - 2.60865i) q^{7} +5.92303 q^{8} +(2.64251 + 1.42026i) q^{9} -2.52000 q^{10} +(2.87407 + 4.97804i) q^{11} +(5.24646 - 5.40859i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-3.79538 + 6.57380i) q^{14} +(-1.20597 + 1.24324i) q^{15} +(-3.11262 - 5.39121i) q^{16} +5.46275 q^{17} +(-0.230017 - 7.55650i) q^{18} +5.89643 q^{19} +(2.17520 + 3.76756i) q^{20} +(1.42685 + 5.01839i) q^{21} +(7.24267 - 12.5447i) q^{22} +(-4.19558 + 7.26696i) q^{23} +(-9.94868 - 2.50415i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.52000 q^{26} +(-3.83806 - 3.50275i) q^{27} +13.1043 q^{28} +(-1.68740 - 2.92266i) q^{29} +(4.23274 + 1.06541i) q^{30} +(2.14772 - 3.71995i) q^{31} +(-1.92077 + 3.32687i) q^{32} +(-2.72284 - 9.57651i) q^{33} +(-6.88307 - 11.9218i) q^{34} -3.01221 q^{35} +(-11.0989 + 6.86648i) q^{36} -4.29747 q^{37} +(-7.42951 - 12.8683i) q^{38} +(1.20597 - 1.24324i) q^{39} +(2.96152 - 5.12950i) q^{40} +(3.28126 - 5.68331i) q^{41} +(9.15423 - 9.43712i) q^{42} +(0.327030 + 0.566432i) q^{43} -25.0068 q^{44} +(2.55124 - 1.57835i) q^{45} +21.1458 q^{46} +(5.20502 + 9.01537i) q^{47} +(2.94883 + 10.3714i) q^{48} +(-1.03670 + 1.79561i) q^{49} +(-1.26000 + 2.18239i) q^{50} +(-9.17556 - 2.30955i) q^{51} +(-2.17520 - 3.76756i) q^{52} +6.03463 q^{53} +(-2.80840 + 12.7896i) q^{54} +5.74814 q^{55} +(-8.92070 - 15.4511i) q^{56} +(-9.90399 - 2.49290i) q^{57} +(-4.25224 + 7.36510i) q^{58} +(-3.77936 + 6.54605i) q^{59} +(-2.06075 - 7.24786i) q^{60} +(-3.01078 - 5.21482i) q^{61} -10.8245 q^{62} +(-0.274943 - 9.03244i) q^{63} -2.76979 q^{64} +(0.500000 + 0.866025i) q^{65} +(-17.4689 + 18.0087i) q^{66} +(-2.84821 + 4.93325i) q^{67} +(-11.8826 + 20.5813i) q^{68} +(10.1195 - 10.4322i) q^{69} +(3.79538 + 6.57380i) q^{70} +2.00130 q^{71} +(15.6517 + 8.41223i) q^{72} +12.4518 q^{73} +(5.41482 + 9.37874i) q^{74} +(0.473690 + 1.66602i) q^{75} +(-12.8259 + 22.2152i) q^{76} +(8.65730 - 14.9949i) q^{77} +(-4.23274 - 1.06541i) q^{78} +(-6.82366 - 11.8189i) q^{79} -6.22524 q^{80} +(4.96574 + 7.50610i) q^{81} -16.5376 q^{82} +(3.08125 + 5.33688i) q^{83} +(-22.0108 - 5.54027i) q^{84} +(2.73138 - 4.73088i) q^{85} +(0.824115 - 1.42741i) q^{86} +(1.59861 + 5.62247i) q^{87} +(17.0232 + 29.4851i) q^{88} +2.25804 q^{89} +(-6.65913 - 3.57905i) q^{90} +3.01221 q^{91} +(-18.2525 - 31.6143i) q^{92} +(-5.18016 + 5.34024i) q^{93} +(13.1167 - 22.7187i) q^{94} +(2.94822 - 5.10646i) q^{95} +(4.63278 - 4.77594i) q^{96} +(-3.12468 - 5.41211i) q^{97} +5.22496 q^{98} +(0.524670 + 17.2364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−1.26000	−	2.18239i	−0.890955	−	1.54318i	−0.838732	−	0.544544i	$-0.816703\pi$
$2$	−1.26000	−	2.18239i	−0.890955	−	1.54318i	−0.0522229	−	0.998635i	$-0.516631\pi$
$3$	−1.67966	−	0.422782i	−0.969752	−	0.244093i
$3$	−1.67966	−	0.422782i	−0.969752	−	0.244093i
$4$	−2.17520	+	3.76756i	−1.08760	+	1.88378i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.19370	+	4.19837i	0.487326	+	1.71398i
$7$	−1.50610	−	2.60865i	−0.569254	−	0.985976i	−0.996640	−	0.0819073i	$-0.973899\pi$
$7$	−1.50610	−	2.60865i	−0.569254	−	0.985976i	0.427386	−	0.904069i	$-0.359434\pi$
$8$	5.92303			2.09411
$9$	2.64251	+	1.42026i	0.880837	+	0.473419i
$10$	−2.52000			−0.796894
$11$	2.87407	+	4.97804i	0.866565	+	1.50094i	0.865484	+	0.500936i	$0.167011\pi$
$11$	2.87407	+	4.97804i	0.866565	+	1.50094i	0.00108088	+	0.999999i	$0.499656\pi$
$12$	5.24646	−	5.40859i	1.51452	−	1.56132i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−3.79538	+	6.57380i	−1.01436	+	1.75692i
$15$	−1.20597	+	1.24324i	−0.311380	+	0.321002i
$16$	−3.11262	−	5.39121i	−0.778154	−	1.34780i
$17$	5.46275			1.32491			0.662456	−	0.749101i	$-0.269514\pi$
$17$	5.46275			1.32491			0.662456	+	0.749101i	$0.269514\pi$
$18$	−0.230017	−	7.55650i	−0.0542154	−	1.78109i
$19$	5.89643			1.35273			0.676367	−	0.736565i	$-0.263553\pi$
$19$	5.89643			1.35273			0.676367	+	0.736565i	$0.263553\pi$
$20$	2.17520	+	3.76756i	0.486390	+	0.842453i
$21$	1.42685	+	5.01839i	0.311365	+	1.09510i
$22$	7.24267	−	12.5447i	1.54414	−	2.67453i
$23$	−4.19558	+	7.26696i	−0.874840	+	1.51527i	−0.0179064	+	0.999840i	$0.505700\pi$
$23$	−4.19558	+	7.26696i	−0.874840	+	1.51527i	−0.856933	+	0.515427i	$0.827633\pi$
$24$	−9.94868	−	2.50415i	−2.03077	−	0.511157i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.52000			0.494213
$27$	−3.83806	−	3.50275i	−0.738635	−	0.674105i
$28$	13.1043			2.47649
$29$	−1.68740	−	2.92266i	−0.313342	−	0.542724i	0.665742	−	0.746182i	$-0.268115\pi$
$29$	−1.68740	−	2.92266i	−0.313342	−	0.542724i	−0.979084	+	0.203458i	$0.934782\pi$
$30$	4.23274	+	1.06541i	0.772790	+	0.194516i
$31$	2.14772	−	3.71995i	0.385741	−	0.668123i	−0.606131	−	0.795365i	$-0.707279\pi$
$31$	2.14772	−	3.71995i	0.385741	−	0.668123i	0.991872	+	0.127242i	$0.0406124\pi$
$32$	−1.92077	+	3.32687i	−0.339547	+	0.588113i
$33$	−2.72284	−	9.57651i	−0.473986	−	1.66706i
$34$	−6.88307	−	11.9218i	−1.18044	−	2.04458i
$35$	−3.01221			−0.509156
$36$	−11.0989	+	6.86648i	−1.84982	+	1.14441i
$37$	−4.29747			−0.706500			−0.353250	−	0.935529i	$-0.614923\pi$
$37$	−4.29747			−0.706500			−0.353250	+	0.935529i	$0.614923\pi$
$38$	−7.42951	−	12.8683i	−1.20523	−	2.08751i
$39$	1.20597	−	1.24324i	0.193110	−	0.199077i
$40$	2.96152	−	5.12950i	0.468257	−	0.811045i
$41$	3.28126	−	5.68331i	0.512447	−	0.887585i	−0.487449	−	0.873152i	$-0.662072\pi$
$41$	3.28126	−	5.68331i	0.512447	−	0.887585i	0.999896	−	0.0144329i	$-0.00459429\pi$
$42$	9.15423	−	9.43712i	1.41253	−	1.45618i
$43$	0.327030	+	0.566432i	0.0498716	+	0.0863801i	0.889884	−	0.456188i	$-0.150785\pi$
$43$	0.327030	+	0.566432i	0.0498716	+	0.0863801i	−0.840012	+	0.542568i	$0.817452\pi$
$44$	−25.0068			−3.76991
$45$	2.55124	−	1.57835i	0.380316	−	0.235287i
$46$	21.1458			3.11777
$47$	5.20502	+	9.01537i	0.759231	+	1.31503i	0.943243	+	0.332103i	$0.107758\pi$
$47$	5.20502	+	9.01537i	0.759231	+	1.31503i	−0.184012	+	0.982924i	$0.558909\pi$
$48$	2.94883	+	10.3714i	0.425627	+	1.49698i
$49$	−1.03670	+	1.79561i	−0.148100	+	0.256516i
$50$	−1.26000	+	2.18239i	−0.178191	+	0.308636i
$51$	−9.17556	−	2.30955i	−1.28484	−	0.323402i
$52$	−2.17520	−	3.76756i	−0.301647	−	0.522467i
$53$	6.03463			0.828920			0.414460	−	0.910068i	$-0.363970\pi$
$53$	6.03463			0.828920			0.414460	+	0.910068i	$0.363970\pi$
$54$	−2.80840	+	12.7896i	−0.382175	+	1.74044i
$55$	5.74814			0.775080
$56$	−8.92070	−	15.4511i	−1.19208	−	2.06474i
$57$	−9.90399	−	2.49290i	−1.31182	−	0.330193i
$58$	−4.25224	+	7.36510i	−0.558347	+	0.967085i
$59$	−3.77936	+	6.54605i	−0.492031	+	0.852223i	−0.999958	−	0.00917755i	$-0.997079\pi$
$59$	−3.77936	+	6.54605i	−0.492031	+	0.852223i	0.507927	+	0.861400i	$0.330412\pi$
$60$	−2.06075	−	7.24786i	−0.266041	−	0.935695i
$61$	−3.01078	−	5.21482i	−0.385490	−	0.667689i	0.606347	−	0.795200i	$-0.292634\pi$
$61$	−3.01078	−	5.21482i	−0.385490	−	0.667689i	−0.991837	+	0.127512i	$0.959301\pi$
$62$	−10.8245			−1.37471
$63$	−0.274943	−	9.03244i	−0.0346396	−	1.13798i
$64$	−2.76979			−0.346224
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	−17.4689	+	18.0087i	−2.15027	+	2.21672i
$67$	−2.84821	+	4.93325i	−0.347965	+	0.602693i	−0.985888	−	0.167407i	$-0.946460\pi$
$67$	−2.84821	+	4.93325i	−0.347965	+	0.602693i	0.637923	+	0.770100i	$0.279794\pi$
$68$	−11.8826	+	20.5813i	−1.44098	+	2.49584i
$69$	10.1195	−	10.4322i	1.21824	−	1.25589i
$70$	3.79538	+	6.57380i	0.453635	+	0.785719i
$71$	2.00130			0.237511			0.118755	−	0.992924i	$-0.462110\pi$
$71$	2.00130			0.237511			0.118755	+	0.992924i	$0.462110\pi$
$72$	15.6517	+	8.41223i	1.84457	+	0.991391i
$73$	12.4518			1.45738			0.728689	−	0.684845i	$-0.240130\pi$
$73$	12.4518			1.45738			0.728689	+	0.684845i	$0.240130\pi$
$74$	5.41482	+	9.37874i	0.629460	+	1.09026i
$75$	0.473690	+	1.66602i	0.0546970	+	0.192375i
$76$	−12.8259	+	22.2152i	−1.47124	+	2.54826i
$77$	8.65730	−	14.9949i	0.986591	−	1.70883i
$78$	−4.23274	−	1.06541i	−0.479264	−	0.120634i
$79$	−6.82366	−	11.8189i	−0.767721	−	1.32973i	−0.938796	−	0.344474i	$-0.888057\pi$
$79$	−6.82366	−	11.8189i	−0.767721	−	1.32973i	0.171074	−	0.985258i	$-0.445276\pi$
$80$	−6.22524			−0.696002
$81$	4.96574	+	7.50610i	0.551748	+	0.834011i
$82$	−16.5376			−1.82627
$83$	3.08125	+	5.33688i	0.338211	+	0.585799i	0.984096	−	0.177636i	$-0.0568449\pi$
$83$	3.08125	+	5.33688i	0.338211	+	0.585799i	−0.645885	+	0.763434i	$0.723512\pi$
$84$	−22.0108	−	5.54027i	−2.40158	−	0.604493i
$85$	2.73138	−	4.73088i	0.296259	−	0.513136i
$86$	0.824115	−	1.42741i	0.0888666	−	0.153922i
$87$	1.59861	+	5.62247i	0.171389	+	0.602792i
$88$	17.0232	+	29.4851i	1.81468	+	3.14312i
$89$	2.25804			0.239351			0.119676	−	0.992813i	$-0.461815\pi$
$89$	2.25804			0.239351			0.119676	+	0.992813i	$0.461815\pi$
$90$	−6.65913	−	3.57905i	−0.701934	−	0.377265i
$91$	3.01221			0.315765
$92$	−18.2525	−	31.6143i	−1.90295	−	3.29601i
$93$	−5.18016	+	5.34024i	−0.537157	+	0.553757i
$94$	13.1167	−	22.7187i	1.35288	−	2.34326i
$95$	2.94822	−	5.10646i	0.302480	−	0.523912i
$96$	4.63278	−	4.77594i	0.472831	−	0.487443i
$97$	−3.12468	−	5.41211i	−0.317263	−	0.549516i	0.662653	−	0.748927i	$-0.269431\pi$
$97$	−3.12468	−	5.41211i	−0.317263	−	0.549516i	−0.979916	+	0.199411i	$0.936097\pi$
$98$	5.22496			0.527801
$99$	0.524670	+	17.2364i	0.0527313	+	1.73233i
$100$	4.35041			0.435041
$101$	2.97789	+	5.15786i	0.296311	+	0.513226i	0.975289	−	0.220933i	$-0.0709101\pi$
$101$	2.97789	+	5.15786i	0.296311	+	0.513226i	−0.678978	+	0.734159i	$0.737577\pi$
$102$	6.52089	+	22.9346i	0.645664	+	2.27087i
$103$	3.18407	−	5.51497i	0.313736	−	0.543406i	−0.665432	−	0.746458i	$-0.731753\pi$
$103$	3.18407	−	5.51497i	0.313736	−	0.543406i	0.979168	+	0.203052i	$0.0650861\pi$
$104$	−2.96152	+	5.12950i	−0.290401	+	0.502989i
$105$	5.05948	+	1.27351i	0.493755	+	0.124281i
$106$	−7.60364	−	13.1699i	−0.738531	−	1.27917i
$107$	12.7993			1.23735			0.618675	−	0.785647i	$-0.287670\pi$
$107$	12.7993			1.23735			0.618675	+	0.785647i	$0.287670\pi$
$108$	21.5454	−	6.84093i	2.07321	−	0.658269i
$109$	9.44687			0.904846			0.452423	−	0.891804i	$-0.350560\pi$
$109$	9.44687			0.904846			0.452423	+	0.891804i	$0.350560\pi$
$110$	−7.24267	−	12.5447i	−0.690561	−	1.19609i
$111$	7.21829	+	1.81689i	0.685129	+	0.172452i
$112$	−9.37585	+	16.2395i	−0.885935	+	1.53448i
$113$	6.83370	−	11.8363i	0.642860	−	1.11347i	−0.341931	−	0.939725i	$-0.611081\pi$
$113$	6.83370	−	11.8363i	0.642860	−	1.11347i	0.984791	−	0.173742i	$-0.0555858\pi$
$114$	7.03857	+	24.7554i	0.659222	+	2.31855i
$115$	4.19558	+	7.26696i	0.391240	+	0.677648i
$116$	14.6817			1.36316
$117$	−2.55124	+	1.57835i	−0.235862	+	0.145919i
$118$	19.0480			1.75351
$119$	−8.22747	−	14.2504i	−0.754211	−	1.30633i
$120$	−7.14300	+	7.36373i	−0.652063	+	0.672214i
$121$	−11.0206	+	19.0882i	−1.00187	+	1.73529i
$122$	−7.58716	+	13.1413i	−0.686909	+	1.18976i
$123$	−7.91420	+	8.15877i	−0.713600	+	0.735652i
$124$	9.34344	+	16.1833i	0.839066	+	1.45330i
$125$	−1.00000			−0.0894427
$126$	−19.3658	+	11.9809i	−1.72525	+	1.06734i
$127$	4.37449			0.388173			0.194086	−	0.980984i	$-0.437826\pi$
$127$	4.37449			0.388173			0.194086	+	0.980984i	$0.437826\pi$
$128$	7.33147	+	12.6985i	0.648017	+	1.12240i
$129$	−0.309821	−	1.08967i	−0.0272783	−	0.0959405i
$130$	1.26000	−	2.18239i	0.110509	−	0.191408i
$131$	6.63317	−	11.4890i	0.579542	−	1.00380i	−0.415989	−	0.909370i	$-0.636565\pi$
$131$	6.63317	−	11.4890i	0.579542	−	1.00380i	0.995532	−	0.0944275i	$-0.0301021\pi$
$132$	42.0029	+	10.5724i	3.65588	+	0.920209i
$133$	−8.88064	−	15.3817i	−0.770049	−	1.33376i
$134$	14.3550			1.24008
$135$	−4.95250	+	1.57248i	−0.426244	+	0.135338i
$136$	32.3560			2.77451
$137$	5.31072	+	9.19844i	0.453725	+	0.785876i	0.998614	−	0.0526330i	$-0.0167613\pi$
$137$	5.31072	+	9.19844i	0.453725	+	0.785876i	−0.544888	+	0.838509i	$0.683428\pi$
$138$	−35.5177	−	8.94003i	−3.02346	−	0.761026i
$139$	−2.22628	+	3.85603i	−0.188831	+	0.327064i	−0.944861	−	0.327473i	$-0.893803\pi$
$139$	−2.22628	+	3.85603i	−0.188831	+	0.327064i	0.756030	+	0.654537i	$0.227136\pi$
$140$	6.55217	−	11.3487i	0.553759	−	0.959139i
$141$	−4.93114	−	17.3433i	−0.415277	−	1.46057i
$142$	−2.52164	−	4.36761i	−0.211612	−	0.366522i
$143$	−5.74814			−0.480684
$144$	−0.568217	−	18.6671i	−0.0473514	−	1.55559i
$145$	−3.37479			−0.280261
$146$	−15.6893	−	27.1747i	−1.29846	−	2.24899i
$147$	2.50045	−	2.57772i	0.206234	−	0.212607i
$148$	9.34788	−	16.1910i	0.768391	−	1.33089i
$149$	8.18081	−	14.1696i	0.670198	−	1.16082i	−0.307650	−	0.951500i	$-0.599542\pi$
$149$	8.18081	−	14.1696i	0.670198	−	1.16082i	0.977848	−	0.209318i	$-0.0671242\pi$
$150$	3.03904	−	3.13296i	0.248137	−	0.255805i
$151$	2.99210	+	5.18246i	0.243493	+	0.421743i	0.961707	−	0.274080i	$-0.0883733\pi$
$151$	2.99210	+	5.18246i	0.243493	+	0.421743i	−0.718214	+	0.695823i	$0.755040\pi$
$152$	34.9247			2.83277
$153$	14.4354	+	7.75851i	1.16703	+	0.627239i
$154$	−43.6328			−3.51603
$155$	−2.14772	−	3.71995i	−0.172509	−	0.298794i
$156$	2.06075	+	7.24786i	0.164992	+	0.580293i
$157$	−3.11451	+	5.39449i	−0.248565	+	0.430527i	−0.963128	−	0.269044i	$-0.913292\pi$
$157$	−3.11451	+	5.39449i	−0.248565	+	0.430527i	0.714563	+	0.699571i	$0.246626\pi$
$158$	−17.1956	+	29.7837i	−1.36801	+	2.36946i
$159$	−10.1361	−	2.55133i	−0.803847	−	0.202334i
$160$	1.92077	+	3.32687i	0.151850	+	0.263012i
$161$	25.2759			1.99202
$162$	10.1244	−	20.2948i	0.795445	−	1.59451i
$163$	−2.42340			−0.189815			−0.0949076	−	0.995486i	$-0.530256\pi$
$163$	−2.42340			−0.189815			−0.0949076	+	0.995486i	$0.530256\pi$
$164$	14.2748	+	24.7247i	1.11468	+	1.93068i
$165$	−9.65492	−	2.43021i	−0.751635	−	0.189192i
$166$	7.76475	−	13.4489i	0.602662	−	1.04384i
$167$	−2.48240	+	4.29964i	−0.192094	+	0.332716i	−0.945944	−	0.324330i	$-0.894861\pi$
$167$	−2.48240	+	4.29964i	−0.192094	+	0.332716i	0.753850	+	0.657046i	$0.228194\pi$
$168$	8.45130	+	29.7241i	0.652032	+	2.29326i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−13.7661			−1.05581
$171$	15.5814	+	8.37445i	1.19154	+	0.640410i
$172$	−2.84542			−0.216962
$173$	1.33399	+	2.31055i	0.101422	+	0.175668i	0.912271	−	0.409588i	$-0.134328\pi$
$173$	1.33399	+	2.31055i	0.101422	+	0.175668i	−0.810849	+	0.585256i	$0.800994\pi$
$174$	10.2561	−	10.5731i	0.777516	−	0.801544i
$175$	−1.50610	+	2.60865i	−0.113851	+	0.197195i
$176$	17.8918	−	30.9895i	1.34864	−	2.33592i
$177$	9.11559	−	9.39728i	0.685169	−	0.706343i
$178$	−2.84513	−	4.92791i	−0.213251	−	0.369362i
$179$	−13.9929			−1.04588			−0.522938	−	0.852371i	$-0.675164\pi$
$179$	−13.9929			−1.04588			−0.522938	+	0.852371i	$0.675164\pi$
$180$	0.397090	+	13.0452i	0.0295973	+	0.972330i
$181$	8.28746			0.616002			0.308001	−	0.951386i	$-0.400340\pi$
$181$	8.28746			0.616002			0.308001	+	0.951386i	$0.400340\pi$
$182$	−3.79538	−	6.57380i	−0.281333	−	0.487282i
$183$	2.85235	+	10.0320i	0.210852	+	0.741588i
$184$	−24.8506	+	43.0425i	−1.83201	+	3.17313i
$185$	−2.14874	+	3.72172i	−0.157978	+	0.273626i
$186$	18.1815	+	4.57640i	1.33313	+	0.335558i
$187$	15.7003	+	27.1938i	1.14812	+	1.98861i
$188$	−45.2880			−3.30296
$189$	−3.35694	+	15.2877i	−0.244181	+	1.11201i
$190$	−14.8590			−1.07799
$191$	−0.356045	−	0.616689i	−0.0257625	−	0.0446220i	0.852857	−	0.522145i	$-0.174868\pi$
$191$	−0.356045	−	0.616689i	−0.0257625	−	0.0446220i	−0.878619	+	0.477523i	$0.841535\pi$
$192$	4.65230	+	1.17102i	0.335751	+	0.0845108i
$193$	10.3493	−	17.9256i	0.744961	−	1.29031i	−0.205251	−	0.978709i	$-0.565801\pi$
$193$	10.3493	−	17.9256i	0.744961	−	1.29031i	0.950213	−	0.311602i	$-0.100865\pi$
$194$	−7.87420	+	13.6385i	−0.565335	+	0.979189i
$195$	−0.473690	−	1.66602i	−0.0339217	−	0.119306i
$196$	−4.51006	−	7.81165i	−0.322147	−	0.557975i
$197$	−25.1924			−1.79489			−0.897444	−	0.441129i	$-0.854578\pi$
$197$	−25.1924			−1.79489			−0.897444	+	0.441129i	$0.854578\pi$
$198$	36.9555	−	22.8630i	2.62631	−	1.62480i
$199$	−0.692437			−0.0490855			−0.0245428	−	0.999699i	$-0.507813\pi$
$199$	−0.692437			−0.0490855			−0.0245428	+	0.999699i	$0.507813\pi$
$200$	−2.96152	−	5.12950i	−0.209411	−	0.362710i
$201$	6.86972	−	7.08201i	0.484553	−	0.499527i
$202$	7.50429	−	12.9978i	0.528000	−	0.914523i
$203$	−5.08279	+	8.80365i	−0.356742	+	0.617895i
$204$	28.6601	−	29.5458i	2.00661	−	2.06862i
$205$	−3.28126	−	5.68331i	−0.229173	−	0.396940i
$206$	−16.0477			−1.11810
$207$	−21.4078	+	13.2442i	−1.48795	+	0.920537i
$208$	6.22524			0.431642
$209$	16.9468	+	29.3527i	1.17223	+	2.03037i
$210$	−3.59567	−	12.6464i	−0.248125	−	0.872682i
$211$	−1.77430	+	3.07318i	−0.122148	+	0.211566i	−0.920614	−	0.390473i	$-0.872312\pi$
$211$	−1.77430	+	3.07318i	−0.122148	+	0.211566i	0.798467	+	0.602039i	$0.205645\pi$
$212$	−13.1266	+	22.7359i	−0.901535	+	1.56150i
$213$	−3.36151	−	0.846114i	−0.230327	−	0.0579747i
$214$	−16.1271	−	27.9329i	−1.10242	−	1.90945i
$215$	0.654059			0.0446065
$216$	−22.7330	−	20.7469i	−1.54678	−	1.41165i
$217$	−12.9387			−0.878338
$218$	−11.9031	−	20.6167i	−0.806177	−	1.39634i
$219$	−20.9148	−	5.26441i	−1.41329	−	0.355736i
$220$	−12.5034	+	21.6565i	−0.842978	+	1.46008i
$221$	−2.73138	+	4.73088i	−0.183732	+	0.318233i
$222$	−5.12989	−	18.0424i	−0.344296	−	1.21092i
$223$	0.361381	+	0.625930i	0.0241999	+	0.0419154i	0.877872	−	0.478896i	$-0.158963\pi$
$223$	0.361381	+	0.625930i	0.0241999	+	0.0419154i	−0.853672	+	0.520811i	$0.825630\pi$
$224$	11.5715			0.773154
$225$	−0.0912764	−	2.99861i	−0.00608509	−	0.199907i
$226$	−34.4419			−2.29104
$227$	9.83730	+	17.0387i	0.652925	+	1.13090i	0.982410	+	0.186738i	$0.0597915\pi$
$227$	9.83730	+	17.0387i	0.652925	+	1.13090i	−0.329485	+	0.944161i	$0.606875\pi$
$228$	30.9354	−	31.8914i	2.04875	−	2.11206i
$229$	−2.25838	+	3.91162i	−0.149238	+	0.258487i	−0.930946	−	0.365157i	$-0.881015\pi$
$229$	−2.25838	+	3.91162i	−0.149238	+	0.258487i	0.781708	+	0.623644i	$0.214349\pi$
$230$	10.5729	−	18.3128i	0.697155	−	1.20751i
$231$	−20.8809	+	21.5262i	−1.37386	+	1.41632i
$232$	−9.99450	−	17.3110i	−0.656171	−	1.13652i
$233$	1.13516			0.0743669			0.0371835	−	0.999308i	$-0.488161\pi$
$233$	1.13516			0.0743669			0.0371835	+	0.999308i	$0.488161\pi$
$234$	6.65913	+	3.57905i	0.435321	+	0.233970i
$235$	10.4100			0.679077
$236$	−16.4418	−	28.4780i	−1.07027	−	1.85376i
$237$	6.46460	+	22.7367i	0.419921	+	1.47691i
$238$	−20.7332	+	35.9110i	−1.34394	+	2.32777i
$239$	−5.40401	+	9.36002i	−0.349556	+	0.605450i	−0.986171	−	0.165733i	$-0.947001\pi$
$239$	−5.40401	+	9.36002i	−0.349556	+	0.605450i	0.636614	+	0.771182i	$0.280334\pi$
$240$	10.4563	+	2.63191i	0.674950	+	0.169889i
$241$	3.81756	+	6.61222i	0.245911	+	0.425930i	0.962387	−	0.271681i	$-0.0875796\pi$
$241$	3.81756	+	6.61222i	0.245911	+	0.425930i	−0.716476	+	0.697611i	$0.754246\pi$
$242$	55.5438			3.57049
$243$	−5.16731	−	14.7071i	−0.331483	−	0.943461i
$244$	26.1962			1.67704
$245$	1.03670	+	1.79561i	0.0662322	+	0.114718i
$246$	27.7775	+	6.99178i	1.77103	+	0.445780i
$247$	−2.94822	+	5.10646i	−0.187590	+	0.324916i
$248$	12.7210	−	22.0334i	0.807784	−	1.39912i
$249$	−2.91911	−	10.2668i	−0.184991	−	0.650634i
$250$	1.26000	+	2.18239i	0.0796894	+	0.138026i
$251$	6.71696			0.423971			0.211985	−	0.977273i	$-0.432007\pi$
$251$	6.71696			0.423971			0.211985	+	0.977273i	$0.432007\pi$
$252$	34.6284	+	18.6115i	2.18138	+	1.17242i
$253$	−48.2336			−3.03242
$254$	−5.51185	−	9.54681i	−0.345845	−	0.599020i
$255$	−6.58791	+	6.79149i	−0.412551	+	0.425300i
$256$	15.7055	−	27.2028i	0.981596	−	1.70017i
$257$	−11.2663	+	19.5137i	−0.702770	+	1.21723i	0.264720	+	0.964325i	$0.414720\pi$
$257$	−11.2663	+	19.5137i	−0.702770	+	1.21723i	−0.967490	+	0.252908i	$0.918613\pi$
$258$	−1.98772	+	2.04914i	−0.123750	+	0.127574i
$259$	6.47244	+	11.2106i	0.402178	+	0.696592i
$260$	−4.35041			−0.269801
$261$	−0.308039	−	10.1197i	−0.0190671	−	0.626393i
$262$	−33.4312			−2.06539
$263$	−6.93204	−	12.0066i	−0.427448	−	0.740362i	0.569198	−	0.822201i	$-0.307254\pi$
$263$	−6.93204	−	12.0066i	−0.427448	−	0.740362i	−0.996646	+	0.0818391i	$0.973921\pi$
$264$	−16.1275	−	56.7220i	−0.992577	−	3.49100i
$265$	3.01731	−	5.22614i	0.185352	−	0.321039i
$266$	−22.3792	+	38.7619i	−1.37216	+	2.37665i
$267$	−3.79273	−	0.954656i	−0.232111	−	0.0584240i
$268$	−12.3909	−	21.4617i	−0.756894	−	1.31098i
$269$	3.78932			0.231039			0.115520	−	0.993305i	$-0.463147\pi$
$269$	3.78932			0.231039			0.115520	+	0.993305i	$0.463147\pi$
$270$	9.67192	+	8.82695i	0.588614	+	0.537191i
$271$	−8.66850			−0.526574			−0.263287	−	0.964718i	$-0.584807\pi$
$271$	−8.66850			−0.526574			−0.263287	+	0.964718i	$0.584807\pi$
$272$	−17.0035	−	29.4508i	−1.03099	−	1.78572i
$273$	−5.05948	−	1.27351i	−0.306214	−	0.0770761i
$274$	13.3830	−	23.1801i	0.808498	−	1.40036i
$275$	2.87407	−	4.97804i	0.173313	−	0.300187i
$276$	17.2921	+	60.8180i	1.04086	+	3.66081i
$277$	6.17136	+	10.6891i	0.370801	+	0.642247i	0.989689	−	0.143233i	$-0.0457498\pi$
$277$	6.17136	+	10.6891i	0.370801	+	0.642247i	−0.618888	+	0.785479i	$0.712416\pi$
$278$	11.2205			0.672958
$279$	10.9587	−	6.77971i	0.656078	−	0.405891i
$280$	−17.8414			−1.06623
$281$	2.36303	+	4.09288i	0.140966	+	0.244161i	0.927861	−	0.372927i	$-0.121646\pi$
$281$	2.36303	+	4.09288i	0.140966	+	0.244161i	−0.786894	+	0.617088i	$0.788312\pi$
$282$	−31.6366	+	32.6143i	−1.88393	+	1.94215i
$283$	6.43592	−	11.1473i	0.382576	−	0.662640i	−0.608854	−	0.793282i	$-0.708370\pi$
$283$	6.43592	−	11.1473i	0.382576	−	0.662640i	0.991430	+	0.130642i	$0.0417038\pi$
$284$	−4.35324	+	7.54003i	−0.258317	+	0.447419i
$285$	−7.11091	+	7.33066i	−0.421214	+	0.434231i
$286$	7.24267	+	12.5447i	0.428268	+	0.741782i
$287$	−19.7677			−1.16685
$288$	−9.80067	+	6.06330i	−0.577510	+	0.357284i
$289$	12.8416			0.755391
$290$	4.25224	+	7.36510i	0.249700	+	0.432493i
$291$	2.96026	+	10.4116i	0.173534	+	0.610336i
$292$	−27.0853	+	46.9131i	−1.58505	+	2.74538i
$293$	12.7416	−	22.0692i	0.744375	−	1.28929i	−0.206112	−	0.978528i	$-0.566081\pi$
$293$	12.7416	−	22.0692i	0.744375	−	1.28929i	0.950486	−	0.310766i	$-0.100586\pi$
$294$	−8.77615	−	2.20902i	−0.511836	−	0.128832i
$295$	3.77936	+	6.54605i	0.220043	+	0.381126i
$296$	−25.4541			−1.47949
$297$	6.40599	−	29.1732i	0.371713	−	1.69280i
$298$	−41.2313			−2.38847
$299$	−4.19558	−	7.26696i	−0.242637	−	0.420259i
$300$	−7.30720	−	1.83927i	−0.421882	−	0.106190i
$301$	0.985081	−	1.70621i	0.0567791	−	0.0983444i
$302$	7.54009	−	13.0598i	0.433883	−	0.751508i
$303$	−2.82120	−	9.92244i	−0.162073	−	0.570029i
$304$	−18.3533	−	31.7889i	−1.05264	−	1.82322i
$305$	−6.02155			−0.344793
$306$	−1.25652	−	41.2793i	−0.0718307	−	2.35978i
$307$	−31.4528			−1.79511			−0.897553	−	0.440906i	$-0.854657\pi$
$307$	−31.4528			−1.79511			−0.897553	+	0.440906i	$0.854657\pi$
$308$	37.6628	+	65.2339i	2.14604	+	3.71705i
$309$	−7.67978	+	7.91711i	−0.436887	+	0.450388i
$310$	−5.41225	+	9.37429i	−0.307395	+	0.532424i
$311$	3.04005	−	5.26553i	0.172386	−	0.298581i	−0.766868	−	0.641805i	$-0.778186\pi$
$311$	3.04005	−	5.26553i	0.172386	−	0.298581i	0.939253	+	0.343224i	$0.111519\pi$
$312$	7.14300	−	7.36373i	0.404392	−	0.416889i
$313$	3.93739	+	6.81976i	0.222554	+	0.385476i	0.955583	−	0.294722i	$-0.0952272\pi$
$313$	3.93739	+	6.81976i	0.222554	+	0.385476i	−0.733029	+	0.680198i	$0.761894\pi$
$314$	15.6971			0.885841
$315$	−7.95979	−	4.27811i	−0.448484	−	0.241044i
$316$	59.3714			3.33990
$317$	9.81771	+	17.0048i	0.551418	+	0.955083i	0.998173	+	0.0604269i	$0.0192462\pi$
$317$	9.81771	+	17.0048i	0.551418	+	0.955083i	−0.446755	+	0.894656i	$0.647420\pi$
$318$	7.20354	+	25.3356i	0.403954	+	1.42075i
$319$	9.69940	−	16.7998i	0.543062	−	0.940611i
$320$	−1.38489	+	2.39871i	−0.0774180	+	0.134092i
$321$	−21.4984	−	5.41129i	−1.19992	−	0.302029i
$322$	−31.8477	−	55.1618i	−1.77480	−	3.07405i
$323$	32.2107			1.79225
$324$	−39.0812	+	2.38143i	−2.17118	+	0.132302i
$325$	1.00000			0.0554700
$326$	3.05348	+	5.28879i	0.169117	+	0.292919i
$327$	−15.8675	−	3.99396i	−0.877476	−	0.220867i
$328$	19.4350	−	33.6625i	1.07312	−	1.85870i
$329$	15.6786	−	27.1562i	0.864390	−	1.49717i
$330$	6.86156	+	24.1328i	0.377716	+	1.32847i
$331$	1.66306	+	2.88051i	0.0914102	+	0.158327i	0.908105	−	0.418743i	$-0.137529\pi$
$331$	1.66306	+	2.88051i	0.0914102	+	0.158327i	−0.816695	+	0.577070i	$0.804196\pi$
$332$	−26.8094			−1.47136
$333$	−11.3561	−	6.10352i	−0.622311	−	0.334471i
$334$	12.5113			0.684588
$335$	2.84821	+	4.93325i	0.155615	+	0.269532i
$336$	22.6140	−	23.3128i	1.23369	−	1.27182i
$337$	13.6755	−	23.6867i	0.744954	−	1.29030i	−0.205263	−	0.978707i	$-0.565805\pi$
$337$	13.6755	−	23.6867i	0.744954	−	1.29030i	0.950216	−	0.311591i	$-0.100862\pi$
$338$	−1.26000	+	2.18239i	−0.0685350	+	0.118706i
$339$	−16.4825	+	16.9918i	−0.895205	+	0.922869i
$340$	11.8826	+	20.5813i	0.644424	+	1.11618i
$341$	24.6908			1.33708
$342$	−1.35628	−	44.5564i	−0.0733391	−	2.40933i
$343$	−14.8400			−0.801282
$344$	1.93701	+	3.35499i	0.104436	+	0.180889i
$345$	−3.97481	−	13.9798i	−0.213997	−	0.752649i
$346$	3.36167	−	5.82258i	0.180724	−	0.313024i
$347$	12.4216	−	21.5149i	0.666828	−	1.15498i	−0.311958	−	0.950096i	$-0.600985\pi$
$347$	12.4216	−	21.5149i	0.666828	−	1.15498i	0.978786	−	0.204885i	$-0.0656819\pi$
$348$	−24.6603	−	6.20716i	−1.32193	−	0.332739i
$349$	0.915567	+	1.58581i	0.0490092	+	0.0848864i	0.889489	−	0.456956i	$-0.151060\pi$
$349$	0.915567	+	1.58581i	0.0490092	+	0.0848864i	−0.840480	+	0.541842i	$0.817727\pi$
$350$	7.59077			0.405744
$351$	4.95250	−	1.57248i	0.264345	−	0.0839328i
$352$	−22.0817			−1.17696
$353$	−10.6302	−	18.4120i	−0.565788	−	0.979974i	−0.996976	−	0.0777117i	$-0.975239\pi$
$353$	−10.6302	−	18.4120i	−0.565788	−	0.979974i	0.431188	−	0.902262i	$-0.358095\pi$
$354$	−31.9941	−	8.05314i	−1.70047	−	0.428020i
$355$	1.00065	−	1.73318i	0.0531090	−	0.0919876i
$356$	−4.91169	+	8.50730i	−0.260319	+	0.450886i
$357$	7.79454	+	27.4142i	0.412531	+	1.45092i
$358$	17.6310	+	30.5378i	0.931828	+	1.61397i
$359$	−4.46395			−0.235598			−0.117799	−	0.993037i	$-0.537584\pi$
$359$	−4.46395			−0.235598			−0.117799	+	0.993037i	$0.537584\pi$
$360$	15.1110	−	9.34864i	0.796422	−	0.492716i
$361$	15.7679			0.829889
$362$	−10.4422	−	18.0864i	−0.548830	−	0.950601i
$363$	26.5810	−	27.4024i	1.39514	−	1.43825i
$364$	−6.55217	+	11.3487i	−0.343427	+	0.594833i
$365$	6.22592	−	10.7836i	0.325879	−	0.564440i
$366$	18.2998	−	18.8653i	0.956544	−	0.986104i
$367$	−11.4328	−	19.8022i	−0.596788	−	1.03367i	−0.993292	−	0.115634i	$-0.963110\pi$
$367$	−11.4328	−	19.8022i	−0.596788	−	1.03367i	0.396504	−	0.918033i	$-0.370223\pi$
$368$	52.2370			2.72304
$369$	16.7425	−	10.3580i	0.871582	−	0.539215i
$370$	10.8296			0.563006
$371$	−9.08878	−	15.7422i	−0.471866	−	0.817296i
$372$	−8.85179	−	31.1327i	−0.458944	−	1.61415i
$373$	−8.91954	+	15.4491i	−0.461836	+	0.799924i	−0.999053	−	0.0435205i	$-0.986143\pi$
$373$	−8.91954	+	15.4491i	−0.461836	+	0.799924i	0.537216	+	0.843445i	$0.319476\pi$
$374$	39.5649	−	68.5284i	2.04585	−	3.54352i
$375$	1.67966	+	0.422782i	0.0867372	+	0.0218323i
$376$	30.8295	+	53.3983i	1.58991	+	2.75381i
$377$	3.37479			0.173811
$378$	37.5933	−	11.9363i	1.93359	−	0.613939i
$379$	24.4173			1.25423			0.627117	−	0.778925i	$-0.284235\pi$
$379$	24.4173			1.25423			0.627117	+	0.778925i	$0.284235\pi$
$380$	12.8259	+	22.2152i	0.657957	+	1.13961i
$381$	−7.34765	−	1.84945i	−0.376431	−	0.0947503i
$382$	−0.897235	+	1.55406i	−0.0459065	+	0.0795124i
$383$	16.1311	−	27.9398i	0.824258	−	1.42766i	−0.0782265	−	0.996936i	$-0.524926\pi$
$383$	16.1311	−	27.9398i	0.824258	−	1.42766i	0.902485	−	0.430722i	$-0.141741\pi$
$384$	−6.94569	−	24.4287i	−0.354446	−	1.24662i
$385$	−8.65730	−	14.9949i	−0.441217	−	0.764210i
$386$	−52.1607			−2.65491
$387$	0.0597002	+	1.96127i	0.00303473	+	0.0996969i
$388$	27.1873			1.38023
$389$	9.93039	+	17.1999i	0.503491	+	0.872072i	0.999992	+	0.00403561i	$0.00128458\pi$
$389$	9.93039	+	17.1999i	0.503491	+	0.872072i	−0.496501	+	0.868036i	$0.665382\pi$
$390$	−3.03904	+	3.13296i	−0.153888	+	0.158644i
$391$	−22.9194	+	39.6976i	−1.15909	+	2.00759i
$392$	−6.14039	+	10.6355i	−0.310137	+	0.537173i
$393$	−15.9988	+	16.4932i	−0.807032	+	0.831972i
$394$	31.7425	+	54.9796i	1.59916	+	2.76983i
$395$	−13.6473			−0.686671
$396$	−66.0807	−	35.5161i	−3.32068	−	1.78475i
$397$	0.215714			0.0108264			0.00541319	−	0.999985i	$-0.498277\pi$
$397$	0.215714			0.0108264			0.00541319	+	0.999985i	$0.498277\pi$
$398$	0.872471	+	1.51116i	0.0437330	+	0.0757478i
$399$	8.41334	+	29.5906i	0.421194	+	1.48138i
$400$	−3.11262	+	5.39121i	−0.155631	+	0.269561i
$401$	−9.40370	+	16.2877i	−0.469598	+	0.813368i	−0.999396	−	0.0347560i	$-0.988935\pi$
$401$	−9.40370	+	16.2877i	−0.469598	+	0.813368i	0.529797	+	0.848124i	$0.322268\pi$
$402$	−24.1115	−	6.06903i	−1.20257	−	0.302696i
$403$	2.14772	+	3.71995i	0.106985	+	0.185304i
$404$	−25.9101			−1.28907
$405$	8.98334	−	0.547405i	0.446386	−	0.0272008i
$406$	25.6173			1.27136
$407$	−12.3512	−	21.3930i	−0.612228	−	1.06041i
$408$	−54.3471	−	13.6795i	−2.69058	−	0.677238i
$409$	−0.622094	+	1.07750i	−0.0307606	+	0.0532789i	−0.880996	−	0.473124i	$-0.843126\pi$
$409$	−0.622094	+	1.07750i	−0.0307606	+	0.0532789i	0.850235	+	0.526403i	$0.176460\pi$
$410$	−8.26879	+	14.3220i	−0.408366	+	0.707311i
$411$	−5.03127	−	17.6955i	−0.248174	−	0.872856i
$412$	13.8520	+	23.9924i	0.682439	+	1.18202i
$413$	22.7684			1.12036
$414$	55.8779	+	30.0324i	2.74625	+	1.47601i
$415$	6.16250			0.302505
$416$	−1.92077	−	3.32687i	−0.0941734	−	0.163113i
$417$	5.36965	−	5.53558i	0.262953	−	0.271079i
$418$	42.7059	−	73.9687i	2.08881	−	3.61793i
$419$	−16.9901	+	29.4277i	−0.830020	+	1.43764i	0.0680010	+	0.997685i	$0.478338\pi$
$419$	−16.9901	+	29.4277i	−0.830020	+	1.43764i	−0.898021	+	0.439952i	$0.854995\pi$
$420$	−15.8034	+	16.2918i	−0.771128	+	0.794958i
$421$	5.53112	+	9.58019i	0.269570	+	0.466910i	0.968751	−	0.248035i	$-0.0797849\pi$
$421$	5.53112	+	9.58019i	0.269570	+	0.466910i	−0.699180	+	0.714945i	$0.746452\pi$
$422$	8.94248			0.435313
$423$	0.950192	+	31.2157i	0.0461999	+	1.51776i
$424$	35.7433			1.73585
$425$	−2.73138	−	4.73088i	−0.132491	−	0.229481i
$426$	2.38895	+	8.40221i	0.115745	+	0.407088i
$427$	−9.06908	+	15.7081i	−0.438884	+	0.760169i
$428$	−27.8410	+	48.2220i	−1.34575	+	2.33090i
$429$	9.65492	+	2.43021i	0.466144	+	0.117332i
$430$	−0.824115	−	1.42741i	−0.0397424	−	0.0688358i
$431$	−29.3780			−1.41509			−0.707545	−	0.706669i	$-0.750197\pi$
$431$	−29.3780			−1.41509			−0.707545	+	0.706669i	$0.750197\pi$
$432$	−6.93768	+	31.5945i	−0.333789	+	1.52009i
$433$	−32.7711			−1.57488			−0.787439	−	0.616393i	$-0.788593\pi$
$433$	−32.7711			−1.57488			−0.787439	+	0.616393i	$0.788593\pi$
$434$	16.3028	+	28.2373i	0.782560	+	1.35543i
$435$	5.66850	+	1.42680i	0.271784	+	0.0684098i
$436$	−20.5489	+	35.5917i	−0.984112	+	1.70453i
$437$	−24.7390	+	42.8492i	−1.18343	+	2.04975i
$438$	14.8638	+	52.2774i	0.710218	+	2.49791i
$439$	−2.02508	−	3.50754i	−0.0966517	−	0.167406i	0.813645	−	0.581362i	$-0.197480\pi$
$439$	−2.02508	−	3.50754i	−0.0966517	−	0.167406i	−0.910297	+	0.413956i	$0.864147\pi$
$440$	34.0464			1.62310
$441$	−5.28972	+	3.27255i	−0.251891	+	0.155836i
$442$	13.7661			0.654789
$443$	2.33610	+	4.04624i	0.110991	+	0.192242i	0.916170	−	0.400789i	$-0.131264\pi$
$443$	2.33610	+	4.04624i	0.110991	+	0.192242i	−0.805179	+	0.593032i	$0.797931\pi$
$444$	−22.5465	+	23.2432i	−1.07001	+	1.10308i
$445$	1.12902	−	1.95552i	0.0535206	−	0.0927004i
$446$	0.910680	−	1.57734i	0.0431220	−	0.0746894i
$447$	−19.7316	+	20.3414i	−0.933273	+	0.962114i
$448$	4.17159	+	7.22541i	0.197089	+	0.341368i
$449$	−25.3333			−1.19555			−0.597775	−	0.801664i	$-0.703948\pi$
$449$	−25.3333			−1.19555			−0.597775	+	0.801664i	$0.703948\pi$
$450$	−6.42912	+	3.97745i	−0.303071	+	0.187499i
$451$	37.7223			1.77628
$452$	29.7294	+	51.4928i	1.39835	+	2.42202i
$453$	−2.83465	−	9.96977i	−0.133184	−	0.468421i
$454$	24.7900	−	42.9376i	1.16345	−	2.01516i
$455$	1.50610	−	2.60865i	0.0706072	−	0.122295i
$456$	−58.6617	−	14.7655i	−2.74709	−	0.691460i
$457$	−0.663373	−	1.14900i	−0.0310313	−	0.0537477i	0.850093	−	0.526633i	$-0.176546\pi$
$457$	−0.663373	−	1.14900i	−0.0310313	−	0.0537477i	−0.881124	+	0.472885i	$0.843212\pi$
$458$	11.3822			0.531856
$459$	−20.9664	−	19.1347i	−0.978626	−	0.893130i
$460$	−36.5050			−1.70205
$461$	−3.86232	−	6.68973i	−0.179886	−	0.311572i	0.761955	−	0.647630i	$-0.224240\pi$
$461$	−3.86232	−	6.68973i	−0.179886	−	0.311572i	−0.941841	+	0.336058i	$0.890906\pi$
$462$	73.2883	+	18.4472i	3.40968	+	0.858239i
$463$	5.34129	−	9.25138i	0.248231	−	0.429948i	−0.714804	−	0.699325i	$-0.753484\pi$
$463$	5.34129	−	9.25138i	0.248231	−	0.429948i	0.963035	+	0.269376i	$0.0868176\pi$
$464$	−10.5044	+	18.1942i	−0.487656	+	0.844646i
$465$	2.03470	+	7.15627i	0.0943571	+	0.331864i
$466$	−1.43030	−	2.47736i	−0.0662576	−	0.114761i
$467$	2.08913			0.0966736			0.0483368	−	0.998831i	$-0.484608\pi$
$467$	2.08913			0.0966736			0.0483368	+	0.998831i	$0.484608\pi$
$468$	−0.397090	−	13.0452i	−0.0183555	−	0.603014i
$469$	17.1588			0.792321
$470$	−13.1167	−	22.7187i	−0.605027	−	1.04794i
$471$	7.51201	−	7.74415i	0.346135	−	0.356832i
$472$	−22.3853	+	38.7724i	−1.03037	+	1.78465i
$473$	−1.87981	+	3.25593i	−0.0864339	+	0.149708i
$474$	41.4748	−	42.7565i	1.90500	−	1.96387i
$475$	−2.94822	−	5.10646i	−0.135273	−	0.234300i
$476$	71.5857			3.28113
$477$	15.9466	+	8.57073i	0.730144	+	0.392427i
$478$	27.2362			1.24576
$479$	−0.633003	−	1.09639i	−0.0289226	−	0.0500955i	0.851202	−	0.524839i	$-0.175874\pi$
$479$	−0.633003	−	1.09639i	−0.0289226	−	0.0500955i	−0.880124	+	0.474743i	$0.842541\pi$
$480$	−1.81970	−	6.40007i	−0.0830575	−	0.292122i
$481$	2.14874	−	3.72172i	0.0979739	−	0.169696i
$482$	9.62027	−	16.6628i	0.438191	−	0.758969i
$483$	−42.4550	−	10.6862i	−1.93177	−	0.486239i
$484$	−47.9440	−	83.0415i	−2.17927	−	3.77461i
$485$	−6.24936			−0.283769
$486$	−25.5858	+	29.8080i	−1.16059	+	1.35212i
$487$	20.6599			0.936191			0.468096	−	0.883678i	$-0.344940\pi$
$487$	20.6599			0.936191			0.468096	+	0.883678i	$0.344940\pi$
$488$	−17.8329	−	30.8875i	−0.807258	−	1.39821i
$489$	4.07048	+	1.02457i	0.184074	+	0.0463326i
$490$	2.61248	−	4.52495i	0.118020	−	0.204416i
$491$	6.06292	−	10.5013i	0.273616	−	0.473916i	−0.696169	−	0.717878i	$-0.745114\pi$
$491$	6.06292	−	10.5013i	0.273616	−	0.473916i	0.969785	+	0.243962i	$0.0784471\pi$
$492$	−13.5237	−	47.5643i	−0.609695	−	2.14436i
$493$	−9.21783	−	15.9657i	−0.415150	−	0.719061i
$494$	14.8590			0.668539
$495$	15.1895	+	8.16385i	0.682719	+	0.366938i
$496$	−26.7401			−1.20066
$497$	−3.01417	−	5.22069i	−0.135204	−	0.234180i
$498$	−18.7281	+	19.3069i	−0.839226	+	0.865161i
$499$	−4.18901	+	7.25557i	−0.187526	+	0.324804i	−0.944425	−	0.328728i	$-0.893380\pi$
$499$	−4.18901	+	7.25557i	−0.187526	+	0.324804i	0.756899	+	0.653532i	$0.226713\pi$
$500$	2.17520	−	3.76756i	0.0972781	−	0.168491i
$501$	5.98740	−	6.17242i	0.267497	−	0.275764i
$502$	−8.46337	−	14.6590i	−0.377739	−	0.654263i
$503$	33.8591			1.50970			0.754851	−	0.655897i	$-0.227709\pi$
$503$	33.8591			1.50970			0.754851	+	0.655897i	$0.227709\pi$
$504$	−1.62850	−	53.4994i	−0.0725391	−	2.38305i
$505$	5.95578			0.265029
$506$	60.7744	+	105.264i	2.70175	+	4.67957i
$507$	0.473690	+	1.66602i	0.0210373	+	0.0739905i
$508$	−9.51540	+	16.4812i	−0.422178	+	0.731233i
$509$	−5.56573	+	9.64012i	−0.246697	+	0.427291i	−0.962607	−	0.270901i	$-0.912678\pi$
$509$	−5.56573	+	9.64012i	−0.246697	+	0.427291i	0.715911	+	0.698192i	$0.246012\pi$
$510$	23.1224	+	5.82007i	1.02388	+	0.257717i
$511$	−18.7538	−	32.4825i	−0.829617	−	1.43694i
$512$	−49.8301			−2.20220
$513$	−22.6309	−	20.6537i	−0.999177	−	0.911885i
$514$	56.7820			2.50455
$515$	−3.18407	−	5.51497i	−0.140307	−	0.243019i
$516$	4.77934	+	1.20299i	0.210399	+	0.0529588i
$517$	−29.9192	+	51.8216i	−1.31585	+	2.27911i
$518$	16.3106	−	28.2507i	0.716644	−	1.24126i
$519$	−1.26380	−	4.44492i	−0.0554747	−	0.195110i
$520$	2.96152	+	5.12950i	0.129871	+	0.224943i
$521$	−7.38081			−0.323359			−0.161679	−	0.986843i	$-0.551691\pi$
$521$	−7.38081			−0.323359			−0.161679	+	0.986843i	$0.551691\pi$
$522$	−21.6969	+	13.4231i	−0.949649	+	0.587512i
$523$	−27.1586			−1.18756			−0.593781	−	0.804626i	$-0.702366\pi$
$523$	−27.1586			−1.18756			−0.593781	+	0.804626i	$0.702366\pi$
$524$	28.8570	+	49.9818i	1.26062	+	2.18346i
$525$	3.63263	−	3.74489i	0.158541	−	0.163440i
$526$	−17.4688	+	30.2568i	−0.761674	+	1.31926i
$527$	11.7324	−	20.3212i	0.511073	−	0.885204i
$528$	−43.1539	+	44.4874i	−1.87803	+	1.93607i
$529$	−23.7058	−	41.0597i	−1.03069	−	1.78521i
$530$	−15.2073			−0.660562
$531$	−19.2841	+	11.9303i	−0.836858	+	0.517732i
$532$	77.2688			3.35003
$533$	3.28126	+	5.68331i	0.142127	+	0.246172i
$534$	2.69542	+	9.48007i	0.116642	+	0.410243i
$535$	6.39963	−	11.0845i	0.276680	−	0.479224i
$536$	−16.8701	+	29.2198i	−0.728676	+	1.26210i
$537$	23.5032	+	5.91592i	1.01424	+	0.255291i
$538$	−4.77455	−	8.26977i	−0.205846	−	0.356535i
$539$	−11.9182			−0.513352
$540$	4.84829	−	22.0793i	0.208637	−	0.950144i
$541$	17.0809			0.734365			0.367182	−	0.930149i	$-0.380322\pi$
$541$	17.0809			0.734365			0.367182	+	0.930149i	$0.380322\pi$
$542$	10.9223	+	18.9180i	0.469154	+	0.812598i
$543$	−13.9201	−	3.50378i	−0.597369	−	0.150362i
$544$	−10.4927	+	18.1739i	−0.449870	+	0.779198i
$545$	4.72343	−	8.18123i	0.202330	−	0.350445i
$546$	3.59567	+	12.6464i	0.153881	+	0.541214i
$547$	10.4035	+	18.0194i	0.444822	+	0.770455i	0.998040	−	0.0625819i	$-0.0199335\pi$
$547$	10.4035	+	18.0194i	0.444822	+	0.770455i	−0.553217	+	0.833037i	$0.686600\pi$
$548$	−46.2076			−1.97389
$549$	−0.549625	−	18.0563i	−0.0234574	−	0.770624i
$550$	−14.4853			−0.617657
$551$	−9.94962	−	17.2332i	−0.423868	−	0.734161i
$552$	59.9381	−	61.7903i	2.55113	−	2.62997i
$553$	−20.5543	+	35.6010i	−0.874057	+	1.51391i
$554$	15.5518	−	26.9366i	0.660735	−	1.14443i
$555$	5.18262	−	5.34277i	0.219990	−	0.226788i
$556$	−9.68522	−	16.7753i	−0.410745	−	0.711431i
$557$	−29.9187			−1.26770			−0.633848	−	0.773458i	$-0.718525\pi$
$557$	−29.9187			−1.26770			−0.633848	+	0.773458i	$0.718525\pi$
$558$	−28.6039	−	15.3736i	−1.21090	−	0.650815i
$559$	−0.654059			−0.0276638
$560$	9.37585	+	16.2395i	0.396202	+	0.686242i
$561$	−14.8742	−	52.3141i	−0.627989	−	2.20870i
$562$	5.95483	−	10.3141i	0.251189	−	0.435073i
$563$	−16.8080	+	29.1123i	−0.708372	+	1.22694i	0.257089	+	0.966388i	$0.417237\pi$
$563$	−16.8080	+	29.1123i	−0.708372	+	1.22694i	−0.965461	+	0.260548i	$0.916097\pi$
$564$	76.0684	+	19.1469i	3.20306	+	0.806231i
$565$	−6.83370	−	11.8363i	−0.287496	−	0.497958i
$566$	−32.4370			−1.36343
$567$	12.1019	−	24.2588i	0.508230	−	1.01877i
$568$	11.8538			0.497374
$569$	−19.6028	−	33.9530i	−0.821792	−	1.42339i	−0.904347	−	0.426799i	$-0.859641\pi$
$569$	−19.6028	−	33.9530i	−0.821792	−	1.42339i	0.0825545	−	0.996587i	$-0.473692\pi$
$570$	24.9581	+	6.28212i	1.04538	+	0.263129i
$571$	6.88909	−	11.9322i	0.288299	−	0.499349i	−0.685105	−	0.728445i	$-0.740244\pi$
$571$	6.88909	−	11.9322i	0.288299	−	0.499349i	0.973404	+	0.229096i	$0.0735769\pi$
$572$	12.5034	−	21.6565i	0.522793	−	0.905504i
$573$	0.337310	+	1.18636i	0.0140913	+	0.0495607i
$574$	24.9073	+	43.1407i	1.03961	+	1.80066i
$575$	8.39117			0.349936
$576$	−7.31920	−	3.93381i	−0.304967	−	0.163909i
$577$	25.4974			1.06147			0.530736	−	0.847537i	$-0.321916\pi$
$577$	25.4974			1.06147			0.530736	+	0.847537i	$0.321916\pi$
$578$	−16.1805	−	28.0254i	−0.673019	−	1.16570i
$579$	−24.9620	+	25.7334i	−1.03738	+	1.06944i
$580$	7.34086	−	12.7147i	0.304813	−	0.527951i
$581$	9.28136	−	16.0758i	0.385056	−	0.666936i
$582$	18.9921	−	19.5790i	0.787248	−	0.811576i
$583$	17.3440	+	30.0406i	0.718313	+	1.24416i
$584$	73.7526			3.05191
$585$	0.0912764	+	2.99861i	0.00377381	+	0.123977i
$586$	−64.2179			−2.65282
$587$	15.3142	+	26.5249i	0.632083	+	1.09480i	0.987125	+	0.159949i	$0.0511331\pi$
$587$	15.3142	+	26.5249i	0.632083	+	1.09480i	−0.355042	+	0.934850i	$0.615534\pi$
$588$	4.27274	+	15.0277i	0.176205	+	0.619731i
$589$	12.6639	−	21.9344i	0.521805	−	0.903793i
$590$	9.52400	−	16.4960i	0.392097	−	0.679131i
$591$	42.3147	+	10.6509i	1.74060	+	0.438119i
$592$	13.3764	+	23.1686i	0.549766	+	0.952222i
$593$	29.5710			1.21433			0.607167	−	0.794574i	$-0.292306\pi$
$593$	29.5710			1.21433			0.607167	+	0.794574i	$0.292306\pi$
$594$	−71.7387	+	22.7779i	−2.94347	+	0.934589i
$595$	−16.4549			−0.674587
$596$	35.5899	+	61.6435i	1.45782	+	2.52501i
$597$	1.16306	+	0.292749i	0.0476008	+	0.0119814i
$598$	−10.5729	+	18.3128i	−0.432357	+	0.748865i
$599$	−0.625518	+	1.08343i	−0.0255580	+	0.0442677i	−0.878521	−	0.477703i	$-0.841470\pi$
$599$	−0.625518	+	1.08343i	−0.0255580	+	0.0442677i	0.852964	+	0.521971i	$0.174803\pi$
$600$	2.80568	+	9.86788i	0.114542	+	0.402855i
$601$	5.36808	+	9.29779i	0.218969	+	0.379265i	0.954493	−	0.298234i	$-0.0963974\pi$
$601$	5.36808	+	9.29779i	0.218969	+	0.379265i	−0.735524	+	0.677498i	$0.763064\pi$
$602$	−4.96481			−0.202351
$603$	−14.5329	+	8.99098i	−0.591827	+	0.366141i
$604$	−26.0337			−1.05930
$605$	11.0206	+	19.0882i	0.448050	+	0.776046i
$606$	−18.0999	+	18.6592i	−0.735258	+	0.757979i
$607$	−17.8389	+	30.8979i	−0.724059	+	1.25411i	0.235302	+	0.971922i	$0.424392\pi$
$607$	−17.8389	+	30.8979i	−0.724059	+	1.25411i	−0.959360	+	0.282184i	$0.908941\pi$
$608$	−11.3257	+	19.6167i	−0.459317	+	0.795560i
$609$	12.2594	−	12.6382i	0.496775	−	0.512127i
$610$	7.58716	+	13.1413i	0.307195	+	0.532078i
$611$	−10.4100			−0.421146
$612$	−60.6306	+	37.5099i	−2.45085	+	1.51625i
$613$	40.1588			1.62200			0.810999	−	0.585048i	$-0.198924\pi$
$613$	40.1588			1.62200			0.810999	+	0.585048i	$0.198924\pi$
$614$	39.6306	+	68.6422i	1.59936	+	2.77017i
$615$	3.10860	+	10.9333i	0.125351	+	0.440873i
$616$	51.2775	−	88.8152i	2.06603	−	3.57847i
$617$	4.57365	−	7.92179i	0.184128	−	0.318919i	−0.759154	−	0.650911i	$-0.774387\pi$
$617$	4.57365	−	7.92179i	0.184128	−	0.318919i	0.943282	+	0.331991i	$0.107721\pi$
$618$	26.9547	+	6.78468i	1.08428	+	0.272920i
$619$	19.2689	+	33.3747i	0.774481	+	1.34144i	0.935086	+	0.354422i	$0.115322\pi$
$619$	19.2689	+	33.3747i	0.774481	+	1.34144i	−0.160604	+	0.987019i	$0.551344\pi$
$620$	18.6869			0.750483
$621$	41.5573	−	13.1950i	1.66764	−	0.529495i
$622$	−15.3219			−0.614351
$623$	−3.40084	−	5.89042i	−0.136252	−	0.235995i
$624$	−10.4563	−	2.63191i	−0.418586	−	0.105361i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.92223	−	17.1858i	0.396572	−	0.686883i
$627$	−16.0550	−	56.4673i	−0.641176	−	2.25508i
$628$	−13.5494	−	23.4682i	−0.540680	−	0.936484i
$629$	−23.4760			−0.936050
$630$	0.692858	+	22.7618i	0.0276041	+	0.906850i
$631$	−20.8431			−0.829749			−0.414875	−	0.909879i	$-0.636175\pi$
$631$	−20.8431			−0.829749			−0.414875	+	0.909879i	$0.636175\pi$
$632$	−40.4167	−	70.0039i	−1.60769	−	2.78460i
$633$	4.27950	−	4.41175i	0.170095	−	0.175351i
$634$	24.7406	−	42.8521i	0.982577	−	1.70187i
$635$	2.18724	−	3.78842i	0.0867981	−	0.150339i
$636$	31.6604	−	32.6388i	1.25542	−	1.29421i
$637$	−1.03670	−	1.79561i	−0.0410755	−	0.0711448i
$638$	−48.8850			−1.93538
$639$	5.28846	+	2.84237i	0.209208	+	0.112442i
$640$	14.6629			0.579604
$641$	2.52917	+	4.38065i	0.0998962	+	0.173025i	0.911642	−	0.410986i	$-0.134816\pi$
$641$	2.52917	+	4.38065i	0.0998962	+	0.173025i	−0.811745	+	0.584012i	$0.801482\pi$
$642$	15.2785	+	53.7360i	0.602993	+	2.12079i
$643$	−0.555778	+	0.962636i	−0.0219177	+	0.0379627i	−0.876776	−	0.480899i	$-0.840311\pi$
$643$	−0.555778	+	0.962636i	−0.0219177	+	0.0379627i	0.854858	+	0.518861i	$0.173644\pi$
$644$	−54.9803	+	95.2287i	−2.16653	+	3.75254i
$645$	−1.09860	−	0.276524i	−0.0432572	−	0.0108881i
$646$	−40.5855	−	70.2962i	−1.59682	−	2.76577i
$647$	−4.82790			−0.189804			−0.0949022	−	0.995487i	$-0.530254\pi$
$647$	−4.82790			−0.189804			−0.0949022	+	0.995487i	$0.530254\pi$
$648$	29.4122	+	44.4589i	1.15542	+	1.74651i
$649$	−43.4486			−1.70551
$650$	−1.26000	−	2.18239i	−0.0494213	−	0.0856002i
$651$	21.7327	+	5.47026i	0.851770	+	0.214396i
$652$	5.27139	−	9.13031i	0.206443	−	0.357570i
$653$	9.02813	−	15.6372i	0.353298	−	0.611930i	−0.633527	−	0.773720i	$-0.718393\pi$
$653$	9.02813	−	15.6372i	0.353298	−	0.611930i	0.986825	+	0.161790i	$0.0517268\pi$
$654$	11.2767	+	39.6614i	0.440955	+	1.55089i
$655$	−6.63317	−	11.4890i	−0.259179	−	0.448912i
$656$	−40.8533			−1.59505
$657$	32.9041	+	17.6848i	1.28371	+	0.689950i
$658$	−79.0203			−3.08053
$659$	15.9174	+	27.5698i	0.620054	+	1.07397i	0.989475	+	0.144703i	$0.0462228\pi$
$659$	15.9174	+	27.5698i	0.620054	+	1.07397i	−0.369421	+	0.929262i	$0.620444\pi$
$660$	30.1574	−	31.0893i	1.17388	−	1.21015i
$661$	−6.91126	+	11.9706i	−0.268817	+	0.465604i	−0.968557	−	0.248794i	$-0.919966\pi$
$661$	−6.91126	+	11.9706i	−0.268817	+	0.465604i	0.699740	+	0.714398i	$0.253299\pi$
$662$	4.19092	−	7.25889i	0.162885	−	0.282125i
$663$	6.58791	−	6.79149i	0.255853	−	0.263760i
$664$	18.2503	+	31.6105i	0.708250	+	1.22673i
$665$	−17.7613			−0.688753
$666$	0.988490	+	32.4739i	0.0383032	+	1.25834i
$667$	28.3185			1.09649
$668$	−10.7995	−	18.7052i	−0.417843	−	0.723726i
$669$	−0.342365	−	1.20413i	−0.0132366	−	0.0465545i
$670$	7.17750	−	12.4318i	0.277291	−	0.480282i
$671$	17.3064	−	29.9755i	0.668105	−	1.15719i
$672$	−19.4362	−	4.89222i	−0.749768	−	0.188722i
$673$	2.29266	+	3.97100i	0.0883754	+	0.153071i	0.906825	−	0.421508i	$-0.138499\pi$
$673$	2.29266	+	3.97100i	0.0883754	+	0.153071i	−0.818449	+	0.574579i	$0.805166\pi$
$674$	−68.9247			−2.65488
$675$	−1.11444	+	5.07524i	−0.0428950	+	0.195346i
$676$	4.35041			0.167323
$677$	2.08724	+	3.61521i	0.0802193	+	0.138944i	0.903344	−	0.428917i	$-0.141105\pi$
$677$	2.08724	+	3.61521i	0.0802193	+	0.138944i	−0.823125	+	0.567861i	$0.807771\pi$
$678$	57.8506	+	14.5614i	2.22174	+	0.559227i
$679$	−9.41219	+	16.3024i	−0.361207	+	0.625628i
$680$	16.1780	−	28.0212i	0.620399	−	1.07456i
$681$	−9.31966	−	32.7782i	−0.357130	−	1.25607i
$682$	−31.1104	−	53.8848i	−1.19128	−	2.06335i
$683$	18.6465			0.713489			0.356744	−	0.934202i	$-0.383887\pi$
$683$	18.6465			0.713489			0.356744	+	0.934202i	$0.383887\pi$
$684$	−65.4440	+	40.4877i	−2.50231	+	1.54809i
$685$	10.6214			0.405824
$686$	18.6984	+	32.3865i	0.713907	+	1.23652i
$687$	5.44706	−	5.61539i	0.207818	−	0.214241i
$688$	2.03584	−	3.52617i	0.0776155	−	0.134434i
$689$	−3.01731	+	5.22614i	−0.114951	+	0.199100i
$690$	−25.5011	+	26.2892i	−0.970812	+	1.00081i
$691$	0.918602	+	1.59106i	0.0349453	+	0.0605270i	0.882969	−	0.469431i	$-0.155541\pi$
$691$	0.918602	+	1.59106i	0.0349453	+	0.0605270i	−0.848024	+	0.529958i	$0.822208\pi$
$692$	−11.6068			−0.441226
$693$	44.1736	−	27.3286i	1.67802	−	1.03813i
$694$	−62.6051			−2.37646
$695$	2.22628	+	3.85603i	0.0844476	+	0.146267i
$696$	9.46860	+	33.3021i	0.358906	+	1.26231i
$697$	17.9247	−	31.0465i	0.678947	−	1.17597i
$698$	2.30723	−	3.99624i	0.0873299	−	0.151260i
$699$	−1.90668	−	0.479925i	−0.0721174	−	0.0181524i
$700$	−6.55217	−	11.3487i	−0.247649	−	0.428940i
$701$	−48.5393			−1.83330			−0.916652	−	0.399687i	$-0.869119\pi$
$701$	−48.5393			−1.83330			−0.916652	+	0.399687i	$0.869119\pi$
$702$	−9.67192	−	8.82695i	−0.365043	−	0.333152i
$703$	−25.3397			−0.955706
$704$	−7.96057	−	13.7881i	−0.300025	−	0.519659i
$705$	−17.4853	−	4.40118i	−0.658536	−	0.165758i
$706$	−26.7881	+	46.3984i	−1.00818	+	1.74623i
$707$	8.97003	−	15.5365i	0.337353	−	0.584312i
$708$	15.5766	+	54.7846i	0.585405	+	2.05893i
$709$	20.0104	+	34.6591i	0.751507	+	1.30165i	0.947092	+	0.320962i	$0.104006\pi$
$709$	20.0104	+	34.6591i	0.751507	+	1.30165i	−0.195585	+	0.980687i	$0.562661\pi$
$710$	−5.04329			−0.189271
$711$	−1.24568	−	40.9230i	−0.0467166	−	1.53473i
$712$	13.3744			0.501228
$713$	18.0218	+	31.2148i	0.674923	+	1.16900i
$714$	50.0073	−	51.5527i	1.87148	−	1.92931i
$715$	−2.87407	+	4.97804i	−0.107484	+	0.186168i
$716$	30.4373	−	52.7190i	1.13750	−	1.97020i
$717$	13.0341	−	13.4369i	0.486769	−	0.501812i
$718$	5.62459	+	9.74207i	0.209908	+	0.363571i
$719$	−28.6704			−1.06923			−0.534613	−	0.845097i	$-0.679543\pi$
$719$	−28.6704			−1.06923			−0.534613	+	0.845097i	$0.679543\pi$
$720$	−16.4503	−	8.84144i	−0.613065	−	0.329501i
$721$	−19.1822			−0.714381
$722$	−19.8676	−	34.4116i	−0.739394	−	1.28067i
$723$	−3.61669	−	12.7203i	−0.134506	−	0.473072i
$724$	−18.0269	+	31.2235i	−0.669965	+	1.16041i
$725$	−1.68740	+	2.92266i	−0.0626683	+	0.108545i
$726$	−93.2946	−	23.4829i	−3.46249	−	0.871531i
$727$	−18.6530	−	32.3080i	−0.691802	−	1.19824i	−0.971247	−	0.238074i	$-0.923484\pi$
$727$	−18.6530	−	32.3080i	−0.691802	−	1.19824i	0.279445	−	0.960162i	$-0.409850\pi$
$728$	17.8414			0.661246
$729$	2.46142	+	26.8876i	0.0911637	+	0.995836i
$730$	−31.3786			−1.16138
$731$	1.78648	+	3.09428i	0.0660754	+	0.114446i
$732$	−44.0007	−	11.0753i	−1.62631	−	0.409354i
$733$	6.38139	−	11.0529i	0.235702	−	0.408248i	−0.723774	−	0.690037i	$-0.757594\pi$
$733$	6.38139	−	11.0529i	0.235702	−	0.408248i	0.959476	+	0.281789i	$0.0909277\pi$
$734$	−28.8107	+	49.9016i	−1.06342	+	1.84190i
$735$	−0.982147	−	3.45432i	−0.0362270	−	0.127414i
$736$	−16.1175	−	27.9163i	−0.594099	−	1.02901i
$737$	−32.7439			−1.20614
$738$	−43.7007	−	23.4876i	−1.60865	−	0.864591i
$739$	20.5383			0.755512			0.377756	−	0.925905i	$-0.376696\pi$
$739$	20.5383			0.755512			0.377756	+	0.925905i	$0.376696\pi$
$740$	−9.34788	−	16.1910i	−0.343635	−	0.595193i
$741$	7.11091	−	7.33066i	0.261226	−	0.269299i
$742$	−22.9037	+	39.6704i	−0.840823	+	1.45635i
$743$	−10.5260	+	18.2315i	−0.386161	+	0.668850i	−0.991930	−	0.126790i	$-0.959532\pi$
$743$	−10.5260	+	18.2315i	−0.386161	+	0.668850i	0.605769	+	0.795641i	$0.292866\pi$
$744$	−30.6822	+	31.6304i	−1.12487	+	1.15963i
$745$	−8.18081	−	14.1696i	−0.299722	−	0.519133i
$746$	44.9545			1.64590
$747$	0.562491	+	18.4789i	0.0205805	+	0.676109i
$748$	−136.606			−4.99480
$749$	−19.2770	−	33.3888i	−0.704367	−	1.22000i
$750$	−1.19370	−	4.19837i	−0.0435878	−	0.153303i
$751$	−4.04719	+	7.00993i	−0.147684	+	0.255796i	−0.930371	−	0.366619i	$-0.880515\pi$
$751$	−4.04719	+	7.00993i	−0.147684	+	0.255796i	0.782687	+	0.622415i	$0.213849\pi$
$752$	32.4025	−	56.1228i	1.18160	−	2.04659i
$753$	−11.2822	−	2.83981i	−0.411146	−	0.103488i
$754$	−4.25224	−	7.36510i	−0.154858	−	0.268221i
$755$	5.98419			0.217787
$756$	−50.2952	−	45.9013i	−1.82922	−	1.66941i
$757$	16.9554			0.616254			0.308127	−	0.951345i	$-0.400298\pi$
$757$	16.9554			0.616254			0.308127	+	0.951345i	$0.400298\pi$
$758$	−30.7659	−	53.2880i	−1.11747	−	1.93551i
$759$	81.0161	+	20.3923i	2.94070	+	0.740193i
$760$	17.4624	−	30.2457i	0.633427	−	1.09713i
$761$	−19.3135	+	33.4520i	−0.700115	+	1.21263i	0.268311	+	0.963332i	$0.413535\pi$
$761$	−19.3135	+	33.4520i	−0.700115	+	1.21263i	−0.968426	+	0.249302i	$0.919799\pi$
$762$	5.22182	+	18.3657i	0.189167	+	0.665319i
$763$	−14.2280	−	24.6436i	−0.515087	−	0.892157i
$764$	3.09788			0.112078
$765$	13.9368	−	8.62215i	0.503885	−	0.311734i
$766$	−81.3006			−2.93751
$767$	−3.77936	−	6.54605i	−0.136465	−	0.236364i
$768$	−37.8808	+	39.0514i	−1.36691	+	1.40915i
$769$	−10.7547	+	18.6277i	−0.387825	+	0.671733i	−0.992157	−	0.125000i	$-0.960107\pi$
$769$	−10.7547	+	18.6277i	−0.387825	+	0.671733i	0.604331	+	0.796733i	$0.293440\pi$
$770$	−21.8164	+	37.7871i	−0.786209	+	1.36175i
$771$	27.1735	−	28.0133i	0.978631	−	1.00887i
$772$	45.0238	+	77.9836i	1.62044	+	2.80669i
$773$	−38.8254			−1.39645			−0.698226	−	0.715878i	$-0.746027\pi$
$773$	−38.8254			−1.39645			−0.698226	+	0.715878i	$0.746027\pi$
$774$	4.20502	−	2.60149i	0.151146	−	0.0935086i
$775$	−4.29543			−0.154296

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26000 - 2.18239i) q^{2} +(-1.67966 - 0.422782i) q^{3} +(-2.17520 + 3.76756i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.19370 + 4.19837i) q^{6} +(-1.50610 - 2.60865i) q^{7} +5.92303 q^{8} +(2.64251 + 1.42026i) q^{9} +O(q^{10})\)	\(q+(-1.26000 - 2.18239i) q^{2} +(-1.67966 - 0.422782i) q^{3} +(-2.17520 + 3.76756i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.19370 + 4.19837i) q^{6} +(-1.50610 - 2.60865i) q^{7} +5.92303 q^{8} +(2.64251 + 1.42026i) q^{9} -2.52000 q^{10} +(2.87407 + 4.97804i) q^{11} +(5.24646 - 5.40859i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-3.79538 + 6.57380i) q^{14} +(-1.20597 + 1.24324i) q^{15} +(-3.11262 - 5.39121i) q^{16} +5.46275 q^{17} +(-0.230017 - 7.55650i) q^{18} +5.89643 q^{19} +(2.17520 + 3.76756i) q^{20} +(1.42685 + 5.01839i) q^{21} +(7.24267 - 12.5447i) q^{22} +(-4.19558 + 7.26696i) q^{23} +(-9.94868 - 2.50415i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.52000 q^{26} +(-3.83806 - 3.50275i) q^{27} +13.1043 q^{28} +(-1.68740 - 2.92266i) q^{29} +(4.23274 + 1.06541i) q^{30} +(2.14772 - 3.71995i) q^{31} +(-1.92077 + 3.32687i) q^{32} +(-2.72284 - 9.57651i) q^{33} +(-6.88307 - 11.9218i) q^{34} -3.01221 q^{35} +(-11.0989 + 6.86648i) q^{36} -4.29747 q^{37} +(-7.42951 - 12.8683i) q^{38} +(1.20597 - 1.24324i) q^{39} +(2.96152 - 5.12950i) q^{40} +(3.28126 - 5.68331i) q^{41} +(9.15423 - 9.43712i) q^{42} +(0.327030 + 0.566432i) q^{43} -25.0068 q^{44} +(2.55124 - 1.57835i) q^{45} +21.1458 q^{46} +(5.20502 + 9.01537i) q^{47} +(2.94883 + 10.3714i) q^{48} +(-1.03670 + 1.79561i) q^{49} +(-1.26000 + 2.18239i) q^{50} +(-9.17556 - 2.30955i) q^{51} +(-2.17520 - 3.76756i) q^{52} +6.03463 q^{53} +(-2.80840 + 12.7896i) q^{54} +5.74814 q^{55} +(-8.92070 - 15.4511i) q^{56} +(-9.90399 - 2.49290i) q^{57} +(-4.25224 + 7.36510i) q^{58} +(-3.77936 + 6.54605i) q^{59} +(-2.06075 - 7.24786i) q^{60} +(-3.01078 - 5.21482i) q^{61} -10.8245 q^{62} +(-0.274943 - 9.03244i) q^{63} -2.76979 q^{64} +(0.500000 + 0.866025i) q^{65} +(-17.4689 + 18.0087i) q^{66} +(-2.84821 + 4.93325i) q^{67} +(-11.8826 + 20.5813i) q^{68} +(10.1195 - 10.4322i) q^{69} +(3.79538 + 6.57380i) q^{70} +2.00130 q^{71} +(15.6517 + 8.41223i) q^{72} +12.4518 q^{73} +(5.41482 + 9.37874i) q^{74} +(0.473690 + 1.66602i) q^{75} +(-12.8259 + 22.2152i) q^{76} +(8.65730 - 14.9949i) q^{77} +(-4.23274 - 1.06541i) q^{78} +(-6.82366 - 11.8189i) q^{79} -6.22524 q^{80} +(4.96574 + 7.50610i) q^{81} -16.5376 q^{82} +(3.08125 + 5.33688i) q^{83} +(-22.0108 - 5.54027i) q^{84} +(2.73138 - 4.73088i) q^{85} +(0.824115 - 1.42741i) q^{86} +(1.59861 + 5.62247i) q^{87} +(17.0232 + 29.4851i) q^{88} +2.25804 q^{89} +(-6.65913 - 3.57905i) q^{90} +3.01221 q^{91} +(-18.2525 - 31.6143i) q^{92} +(-5.18016 + 5.34024i) q^{93} +(13.1167 - 22.7187i) q^{94} +(2.94822 - 5.10646i) q^{95} +(4.63278 - 4.77594i) q^{96} +(-3.12468 - 5.41211i) q^{97} +5.22496 q^{98} +(0.524670 + 17.2364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

L-functions

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