LMFDB - Embedded newform 585.2.i.h.196.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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			196.2
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26000 + 2.18239i) q^{2} +(-1.67966 + 0.422782i) q^{3} +(-2.17520 - 3.76756i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.19370 - 4.19837i) q^{6} +(-1.50610 + 2.60865i) q^{7} +5.92303 q^{8} +(2.64251 - 1.42026i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	−0.0522229	+	0.998635i	$0.516631\pi$
$2$	−1.26000	+	2.18239i	−0.890955	+	1.54318i	−0.838732	+	0.544544i	$0.816703\pi$
$3$	−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	0.427386	+	0.904069i	$0.359434\pi$
$7$	−1.50610	+	2.60865i	−0.569254	+	0.985976i	−0.996640	+	0.0819073i	$0.973899\pi$
$8$	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	0.00108088	−	0.999999i	$-0.499656\pi$
$11$	2.87407	−	4.97804i	0.866565	−	1.50094i	0.865484	−	0.500936i	$-0.167011\pi$
$12$	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	−0.856933	−	0.515427i	$-0.827633\pi$
$23$	−4.19558	−	7.26696i	−0.874840	−	1.51527i	−0.0179064	−	0.999840i	$-0.505700\pi$
$24$	−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	−0.979084	−	0.203458i	$-0.934782\pi$
$29$	−1.68740	+	2.92266i	−0.313342	+	0.542724i	0.665742	+	0.746182i	$0.268115\pi$
$30$	4.23274	−	1.06541i	0.772790	−	0.194516i
$31$	2.14772	+	3.71995i	0.385741	+	0.668123i	0.991872	−	0.127242i	$-0.0406124\pi$
$31$	2.14772	+	3.71995i	0.385741	+	0.668123i	−0.606131	+	0.795365i	$0.707279\pi$
$32$	−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	0.999896	+	0.0144329i	$0.00459429\pi$
$41$	3.28126	+	5.68331i	0.512447	+	0.887585i	−0.487449	+	0.873152i	$0.662072\pi$
$42$	9.15423	+	9.43712i	1.41253	+	1.45618i
$43$	0.327030	−	0.566432i	0.0498716	−	0.0863801i	−0.840012	−	0.542568i	$-0.817452\pi$
$43$	0.327030	−	0.566432i	0.0498716	−	0.0863801i	0.889884	+	0.456188i	$0.150785\pi$
$44$	−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	−0.184012	−	0.982924i	$-0.558909\pi$
$47$	5.20502	−	9.01537i	0.759231	−	1.31503i	0.943243	−	0.332103i	$-0.107758\pi$
$48$	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	0.507927	−	0.861400i	$-0.330412\pi$
$59$	−3.77936	−	6.54605i	−0.492031	−	0.852223i	−0.999958	+	0.00917755i	$0.997079\pi$
$60$	−2.06075	+	7.24786i	−0.266041	+	0.935695i
$61$	−3.01078	+	5.21482i	−0.385490	+	0.667689i	−0.991837	−	0.127512i	$-0.959301\pi$
$61$	−3.01078	+	5.21482i	−0.385490	+	0.667689i	0.606347	+	0.795200i	$0.292634\pi$
$62$	−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	0.637923	−	0.770100i	$-0.279794\pi$
$67$	−2.84821	−	4.93325i	−0.347965	−	0.602693i	−0.985888	+	0.167407i	$0.946460\pi$
$68$	−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	0.171074	+	0.985258i	$0.445276\pi$
$79$	−6.82366	+	11.8189i	−0.767721	+	1.32973i	−0.938796	+	0.344474i	$0.888057\pi$
$80$	−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	−0.645885	−	0.763434i	$-0.723512\pi$
$83$	3.08125	−	5.33688i	0.338211	−	0.585799i	0.984096	+	0.177636i	$0.0568449\pi$
$84$	−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	−0.979916	−	0.199411i	$-0.936097\pi$
$97$	−3.12468	+	5.41211i	−0.317263	+	0.549516i	0.662653	+	0.748927i	$0.269431\pi$
$98$	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	−0.678978	−	0.734159i	$-0.737577\pi$
$101$	2.97789	−	5.15786i	0.296311	−	0.513226i	0.975289	+	0.220933i	$0.0709101\pi$
$102$	6.52089	−	22.9346i	0.645664	−	2.27087i
$103$	3.18407	+	5.51497i	0.313736	+	0.543406i	0.979168	−	0.203052i	$-0.0650861\pi$
$103$	3.18407	+	5.51497i	0.313736	+	0.543406i	−0.665432	+	0.746458i	$0.731753\pi$
$104$	−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	0.984791	+	0.173742i	$0.0555858\pi$
$113$	6.83370	+	11.8363i	0.642860	+	1.11347i	−0.341931	+	0.939725i	$0.611081\pi$
$114$	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	0.995532	+	0.0944275i	$0.0301021\pi$
$131$	6.63317	+	11.4890i	0.579542	+	1.00380i	−0.415989	+	0.909370i	$0.636565\pi$
$132$	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	−0.544888	−	0.838509i	$-0.683428\pi$
$137$	5.31072	−	9.19844i	0.453725	−	0.785876i	0.998614	+	0.0526330i	$0.0167613\pi$
$138$	−35.5177	+	8.94003i	−3.02346	+	0.761026i
$139$	−2.22628	−	3.85603i	−0.188831	−	0.327064i	0.756030	−	0.654537i	$-0.227136\pi$
$139$	−2.22628	−	3.85603i	−0.188831	−	0.327064i	−0.944861	+	0.327473i	$0.893803\pi$
$140$	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	0.977848	+	0.209318i	$0.0671242\pi$
$149$	8.18081	+	14.1696i	0.670198	+	1.16082i	−0.307650	+	0.951500i	$0.599542\pi$
$150$	3.03904	+	3.13296i	0.248137	+	0.255805i
$151$	2.99210	−	5.18246i	0.243493	−	0.421743i	−0.718214	−	0.695823i	$-0.755040\pi$
$151$	2.99210	−	5.18246i	0.243493	−	0.421743i	0.961707	+	0.274080i	$0.0883733\pi$
$152$	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	0.714563	−	0.699571i	$-0.246626\pi$
$157$	−3.11451	−	5.39449i	−0.248565	−	0.430527i	−0.963128	+	0.269044i	$0.913292\pi$
$158$	−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	0.753850	−	0.657046i	$-0.228194\pi$
$167$	−2.48240	−	4.29964i	−0.192094	−	0.332716i	−0.945944	+	0.324330i	$0.894861\pi$
$168$	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	−0.810849	−	0.585256i	$-0.800994\pi$
$173$	1.33399	−	2.31055i	0.101422	−	0.175668i	0.912271	+	0.409588i	$0.134328\pi$
$174$	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	−0.878619	−	0.477523i	$-0.841535\pi$
$191$	−0.356045	+	0.616689i	−0.0257625	+	0.0446220i	0.852857	+	0.522145i	$0.174868\pi$
$192$	4.65230	−	1.17102i	0.335751	−	0.0845108i
$193$	10.3493	+	17.9256i	0.744961	+	1.29031i	0.950213	+	0.311602i	$0.100865\pi$
$193$	10.3493	+	17.9256i	0.744961	+	1.29031i	−0.205251	+	0.978709i	$0.565801\pi$
$194$	−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	0.798467	−	0.602039i	$-0.205645\pi$
$211$	−1.77430	−	3.07318i	−0.122148	−	0.211566i	−0.920614	+	0.390473i	$0.872312\pi$
$212$	−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	−0.853672	−	0.520811i	$-0.825630\pi$
$223$	0.361381	−	0.625930i	0.0241999	−	0.0419154i	0.877872	+	0.478896i	$0.158963\pi$
$224$	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	−0.329485	−	0.944161i	$-0.606875\pi$
$227$	9.83730	−	17.0387i	0.652925	−	1.13090i	0.982410	−	0.186738i	$-0.0597915\pi$
$228$	30.9354	+	31.8914i	2.04875	+	2.11206i
$229$	−2.25838	−	3.91162i	−0.149238	−	0.258487i	0.781708	−	0.623644i	$-0.214349\pi$
$229$	−2.25838	−	3.91162i	−0.149238	−	0.258487i	−0.930946	+	0.365157i	$0.881015\pi$
$230$	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	0.636614	−	0.771182i	$-0.280334\pi$
$239$	−5.40401	−	9.36002i	−0.349556	−	0.605450i	−0.986171	+	0.165733i	$0.947001\pi$
$240$	10.4563	−	2.63191i	0.674950	−	0.169889i
$241$	3.81756	−	6.61222i	0.245911	−	0.425930i	−0.716476	−	0.697611i	$-0.754246\pi$
$241$	3.81756	−	6.61222i	0.245911	−	0.425930i	0.962387	+	0.271681i	$0.0875796\pi$
$242$	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	−0.967490	−	0.252908i	$-0.918613\pi$
$257$	−11.2663	−	19.5137i	−0.702770	−	1.21723i	0.264720	−	0.964325i	$-0.414720\pi$
$258$	−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	−0.996646	−	0.0818391i	$-0.973921\pi$
$263$	−6.93204	+	12.0066i	−0.427448	+	0.740362i	0.569198	+	0.822201i	$0.307254\pi$
$264$	−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	−0.618888	−	0.785479i	$-0.712416\pi$
$277$	6.17136	−	10.6891i	0.370801	−	0.642247i	0.989689	+	0.143233i	$0.0457498\pi$
$278$	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	−0.786894	−	0.617088i	$-0.788312\pi$
$281$	2.36303	−	4.09288i	0.140966	−	0.244161i	0.927861	+	0.372927i	$0.121646\pi$
$282$	−31.6366	−	32.6143i	−1.88393	−	1.94215i
$283$	6.43592	+	11.1473i	0.382576	+	0.662640i	0.991430	−	0.130642i	$-0.0417038\pi$
$283$	6.43592	+	11.1473i	0.382576	+	0.662640i	−0.608854	+	0.793282i	$0.708370\pi$
$284$	−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	0.950486	+	0.310766i	$0.100586\pi$
$293$	12.7416	+	22.0692i	0.744375	+	1.28929i	−0.206112	+	0.978528i	$0.566081\pi$
$294$	−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	0.939253	−	0.343224i	$-0.111519\pi$
$311$	3.04005	+	5.26553i	0.172386	+	0.298581i	−0.766868	+	0.641805i	$0.778186\pi$
$312$	7.14300	+	7.36373i	0.404392	+	0.416889i
$313$	3.93739	−	6.81976i	0.222554	−	0.385476i	−0.733029	−	0.680198i	$-0.761894\pi$
$313$	3.93739	−	6.81976i	0.222554	−	0.385476i	0.955583	+	0.294722i	$0.0952272\pi$
$314$	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	−0.446755	−	0.894656i	$-0.647420\pi$
$317$	9.81771	−	17.0048i	0.551418	−	0.955083i	0.998173	−	0.0604269i	$-0.0192462\pi$
$318$	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	−0.816695	−	0.577070i	$-0.804196\pi$
$331$	1.66306	−	2.88051i	0.0914102	−	0.158327i	0.908105	+	0.418743i	$0.137529\pi$
$332$	−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	0.950216	+	0.311591i	$0.100862\pi$
$337$	13.6755	+	23.6867i	0.744954	+	1.29030i	−0.205263	+	0.978707i	$0.565805\pi$
$338$	−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	0.978786	+	0.204885i	$0.0656819\pi$
$347$	12.4216	+	21.5149i	0.666828	+	1.15498i	−0.311958	+	0.950096i	$0.600985\pi$
$348$	−24.6603	+	6.20716i	−1.32193	+	0.332739i
$349$	0.915567	−	1.58581i	0.0490092	−	0.0848864i	−0.840480	−	0.541842i	$-0.817727\pi$
$349$	0.915567	−	1.58581i	0.0490092	−	0.0848864i	0.889489	+	0.456956i	$0.151060\pi$
$350$	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	0.431188	+	0.902262i	$0.358095\pi$
$353$	−10.6302	+	18.4120i	−0.565788	+	0.979974i	−0.996976	+	0.0777117i	$0.975239\pi$
$354$	−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	0.396504	+	0.918033i	$0.370223\pi$
$367$	−11.4328	+	19.8022i	−0.596788	+	1.03367i	−0.993292	+	0.115634i	$0.963110\pi$
$368$	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	0.537216	−	0.843445i	$-0.319476\pi$
$373$	−8.91954	−	15.4491i	−0.461836	−	0.799924i	−0.999053	+	0.0435205i	$0.986143\pi$
$374$	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	0.902485	+	0.430722i	$0.141741\pi$
$383$	16.1311	+	27.9398i	0.824258	+	1.42766i	−0.0782265	+	0.996936i	$0.524926\pi$
$384$	−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	−0.496501	−	0.868036i	$-0.665382\pi$
$389$	9.93039	−	17.1999i	0.503491	−	0.872072i	0.999992	−	0.00403561i	$-0.00128458\pi$
$390$	−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	0.529797	−	0.848124i	$-0.322268\pi$
$401$	−9.40370	−	16.2877i	−0.469598	−	0.813368i	−0.999396	+	0.0347560i	$0.988935\pi$
$402$	−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	0.850235	−	0.526403i	$-0.176460\pi$
$409$	−0.622094	−	1.07750i	−0.0307606	−	0.0532789i	−0.880996	+	0.473124i	$0.843126\pi$
$410$	−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	−0.898021	−	0.439952i	$-0.854995\pi$
$419$	−16.9901	−	29.4277i	−0.830020	−	1.43764i	0.0680010	−	0.997685i	$-0.478338\pi$
$420$	−15.8034	−	16.2918i	−0.771128	−	0.794958i
$421$	5.53112	−	9.58019i	0.269570	−	0.466910i	−0.699180	−	0.714945i	$-0.746452\pi$
$421$	5.53112	−	9.58019i	0.269570	−	0.466910i	0.968751	+	0.248035i	$0.0797849\pi$
$422$	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	−0.910297	−	0.413956i	$-0.864147\pi$
$439$	−2.02508	+	3.50754i	−0.0966517	+	0.167406i	0.813645	+	0.581362i	$0.197480\pi$
$440$	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	−0.805179	−	0.593032i	$-0.797931\pi$
$443$	2.33610	−	4.04624i	0.110991	−	0.192242i	0.916170	+	0.400789i	$0.131264\pi$
$444$	−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	−0.881124	−	0.472885i	$-0.843212\pi$
$457$	−0.663373	+	1.14900i	−0.0310313	+	0.0537477i	0.850093	+	0.526633i	$0.176546\pi$
$458$	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	−0.941841	−	0.336058i	$-0.890906\pi$
$461$	−3.86232	+	6.68973i	−0.179886	+	0.311572i	0.761955	+	0.647630i	$0.224240\pi$
$462$	73.2883	−	18.4472i	3.40968	−	0.858239i
$463$	5.34129	+	9.25138i	0.248231	+	0.429948i	0.963035	−	0.269376i	$-0.0868176\pi$
$463$	5.34129	+	9.25138i	0.248231	+	0.429948i	−0.714804	+	0.699325i	$0.753484\pi$
$464$	−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	−0.880124	−	0.474743i	$-0.842541\pi$
$479$	−0.633003	+	1.09639i	−0.0289226	+	0.0500955i	0.851202	+	0.524839i	$0.175874\pi$
$480$	−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	0.969785	−	0.243962i	$-0.0784471\pi$
$491$	6.06292	+	10.5013i	0.273616	+	0.473916i	−0.696169	+	0.717878i	$0.745114\pi$
$492$	−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	0.756899	−	0.653532i	$-0.226713\pi$
$499$	−4.18901	−	7.25557i	−0.187526	−	0.324804i	−0.944425	+	0.328728i	$0.893380\pi$
$500$	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	0.715911	−	0.698192i	$-0.246012\pi$
$509$	−5.56573	−	9.64012i	−0.246697	−	0.427291i	−0.962607	+	0.270901i	$0.912678\pi$
$510$	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	−0.553217	−	0.833037i	$-0.686600\pi$
$547$	10.4035	−	18.0194i	0.444822	−	0.770455i	0.998040	+	0.0625819i	$0.0199335\pi$
$548$	−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	−0.965461	−	0.260548i	$-0.916097\pi$
$563$	−16.8080	−	29.1123i	−0.708372	−	1.22694i	0.257089	−	0.966388i	$-0.417237\pi$
$564$	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	0.0825545	+	0.996587i	$0.473692\pi$
$569$	−19.6028	+	33.9530i	−0.821792	+	1.42339i	−0.904347	+	0.426799i	$0.859641\pi$
$570$	24.9581	−	6.28212i	1.04538	−	0.263129i
$571$	6.88909	+	11.9322i	0.288299	+	0.499349i	0.973404	−	0.229096i	$-0.0735769\pi$
$571$	6.88909	+	11.9322i	0.288299	+	0.499349i	−0.685105	+	0.728445i	$0.740244\pi$
$572$	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	−0.355042	−	0.934850i	$-0.615534\pi$
$587$	15.3142	−	26.5249i	0.632083	−	1.09480i	0.987125	−	0.159949i	$-0.0511331\pi$
$588$	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	0.852964	−	0.521971i	$-0.174803\pi$
$599$	−0.625518	−	1.08343i	−0.0255580	−	0.0442677i	−0.878521	+	0.477703i	$0.841470\pi$
$600$	2.80568	−	9.86788i	0.114542	−	0.402855i
$601$	5.36808	−	9.29779i	0.218969	−	0.379265i	−0.735524	−	0.677498i	$-0.763064\pi$
$601$	5.36808	−	9.29779i	0.218969	−	0.379265i	0.954493	+	0.298234i	$0.0963974\pi$
$602$	−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	−0.959360	−	0.282184i	$-0.908941\pi$
$607$	−17.8389	−	30.8979i	−0.724059	−	1.25411i	0.235302	−	0.971922i	$-0.424392\pi$
$608$	−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	0.943282	−	0.331991i	$-0.107721\pi$
$617$	4.57365	+	7.92179i	0.184128	+	0.318919i	−0.759154	+	0.650911i	$0.774387\pi$
$618$	26.9547	−	6.78468i	1.08428	−	0.272920i
$619$	19.2689	−	33.3747i	0.774481	−	1.34144i	−0.160604	−	0.987019i	$-0.551344\pi$
$619$	19.2689	−	33.3747i	0.774481	−	1.34144i	0.935086	−	0.354422i	$-0.115322\pi$
$620$	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	−0.811745	−	0.584012i	$-0.801482\pi$
$641$	2.52917	−	4.38065i	0.0998962	−	0.173025i	0.911642	+	0.410986i	$0.134816\pi$
$642$	15.2785	−	53.7360i	0.602993	−	2.12079i
$643$	−0.555778	−	0.962636i	−0.0219177	−	0.0379627i	0.854858	−	0.518861i	$-0.173644\pi$
$643$	−0.555778	−	0.962636i	−0.0219177	−	0.0379627i	−0.876776	+	0.480899i	$0.840311\pi$
$644$	−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	0.986825	−	0.161790i	$-0.0517268\pi$
$653$	9.02813	+	15.6372i	0.353298	+	0.611930i	−0.633527	+	0.773720i	$0.718393\pi$
$654$	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	−0.369421	−	0.929262i	$-0.620444\pi$
$659$	15.9174	−	27.5698i	0.620054	−	1.07397i	0.989475	−	0.144703i	$-0.0462228\pi$
$660$	30.1574	+	31.0893i	1.17388	+	1.21015i
$661$	−6.91126	−	11.9706i	−0.268817	−	0.465604i	0.699740	−	0.714398i	$-0.253299\pi$
$661$	−6.91126	−	11.9706i	−0.268817	−	0.465604i	−0.968557	+	0.248794i	$0.919966\pi$
$662$	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	−0.818449	−	0.574579i	$-0.805166\pi$
$673$	2.29266	−	3.97100i	0.0883754	−	0.153071i	0.906825	+	0.421508i	$0.138499\pi$
$674$	−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	−0.823125	−	0.567861i	$-0.807771\pi$
$677$	2.08724	−	3.61521i	0.0802193	−	0.138944i	0.903344	+	0.428917i	$0.141105\pi$
$678$	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	−0.848024	−	0.529958i	$-0.822208\pi$
$691$	0.918602	−	1.59106i	0.0349453	−	0.0605270i	0.882969	+	0.469431i	$0.155541\pi$
$692$	−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	−0.195585	−	0.980687i	$-0.562661\pi$
$709$	20.0104	−	34.6591i	0.751507	−	1.30165i	0.947092	−	0.320962i	$-0.104006\pi$
$710$	−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	0.279445	+	0.960162i	$0.409850\pi$
$727$	−18.6530	+	32.3080i	−0.691802	+	1.19824i	−0.971247	+	0.238074i	$0.923484\pi$
$728$	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	0.959476	−	0.281789i	$-0.0909277\pi$
$733$	6.38139	+	11.0529i	0.235702	+	0.408248i	−0.723774	+	0.690037i	$0.757594\pi$
$734$	−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	0.605769	−	0.795641i	$-0.292866\pi$
$743$	−10.5260	−	18.2315i	−0.386161	−	0.668850i	−0.991930	+	0.126790i	$0.959532\pi$
$744$	−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	0.782687	−	0.622415i	$-0.213849\pi$
$751$	−4.04719	−	7.00993i	−0.147684	−	0.255796i	−0.930371	+	0.366619i	$0.880515\pi$
$752$	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	−0.968426	−	0.249302i	$-0.919799\pi$
$761$	−19.3135	−	33.4520i	−0.700115	−	1.21263i	0.268311	−	0.963332i	$-0.413535\pi$
$762$	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	0.604331	−	0.796733i	$-0.293440\pi$
$769$	−10.7547	−	18.6277i	−0.387825	−	0.671733i	−0.992157	+	0.125000i	$0.960107\pi$
$770$	−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
$776$	−18.5076	+	32.0561i	−0.664384	+	1.15075i
$777$	−6.13186	+	21.5664i	−0.219979	+	0.773690i
$778$	25.0246	+	43.3439i	0.897176	+	1.55395i
$779$	19.3477	+	33.5113i	0.693205	+	1.20067i
$780$	7.30720	−	1.83927i	0.261640	−	0.0658565i
$781$	5.75189	−	9.96256i	0.205819	−	0.356488i
$782$	115.514			4.13077
$783$	−3.76102	−	17.1279i	−0.134408	−	0.612100i
$784$	12.9074			0.460978
$785$	3.11451	−	5.39449i	0.111162	−	0.192538i
$786$	56.1530	−	14.1341i	2.00291	−	0.504146i
$787$	−18.8610	−	32.6683i	−0.672324	−	1.16450i	−0.977244	−	0.212121i	$-0.931963\pi$
$787$	−18.8610	−	32.6683i	−0.672324	−	1.16450i	0.304920	−	0.952378i	$-0.401370\pi$
$788$	54.7987	+	94.9142i	1.95212	+	3.38118i
$789$	6.56728	−	23.0978i	0.233801	−	0.822304i
$790$	17.1956	−	29.7837i	0.611793	−	1.05966i
$791$	−41.1691			−1.46380
$792$	3.10764	−	102.092i	0.110425	−	3.62768i
$793$	6.02155			0.213832
$794$	−0.271800	+	0.470771i	−0.00964582	+	0.0167070i
$795$	−7.27758	−	7.50247i	−0.258109	−	0.266085i
$796$	1.50619	+	2.60880i	0.0533855	+	0.0924665i
$797$	16.8403	+	29.1682i	0.596513	+	1.03319i	0.993331	+	0.115294i	$0.0367810\pi$
$797$	16.8403	+	29.1682i	0.596513	+	1.03319i	−0.396818	+	0.917897i	$0.629886\pi$
$798$	53.9773	+	55.6453i	1.91078	+	1.96982i
$799$	28.4338	−	49.2487i	1.00591	−	1.74229i
$800$	3.84154			0.135819
$801$	5.96689	−	3.20699i	0.210830	−	0.113314i
$802$	47.3947			1.67356
$803$	35.7875	−	61.9857i	1.26291	−	2.18743i
$804$	11.7389	−	41.2869i	0.413999	−	1.45608i
$805$	12.6380	+	21.8896i	0.445430	+	0.771507i
$806$	5.41225	+	9.37429i	0.190638	+	0.330195i
$807$	−6.36477	+	1.60206i	−0.224051	+	0.0563951i
$808$	17.6381	−	30.5502i	0.620508	−	1.07475i
$809$	−27.7726			−0.976432			−0.488216	−	0.872723i	$-0.662352\pi$
$809$	−27.7726			−0.976432			−0.488216	+	0.872723i	$0.662352\pi$
$810$	−12.5137	+	18.9154i	−0.439685	+	0.664618i
$811$	19.6682			0.690645			0.345323	−	0.938484i	$-0.387770\pi$
$811$	19.6682			0.690645			0.345323	+	0.938484i	$0.387770\pi$
$812$	−22.1122	+	38.2995i	−0.775986	+	1.34405i
$813$	14.5601	−	3.66488i	0.510646	−	0.128533i
$814$	−31.1251	−	53.9103i	−1.09094	−	1.88956i
$815$	−1.21170	−	2.09872i	−0.0424440	−	0.0735151i
$816$	16.1087	−	56.6561i	0.563919	−	1.98336i
$817$	1.92831	−	3.33993i	0.0674629	−	0.116849i
$818$	3.13536			0.109625
$819$	7.95979	−	4.27811i	0.278138	−	0.149489i
$820$	28.5497			0.996998
$821$	7.54642	−	13.0708i	0.263372	−	0.456173i	−0.703764	−	0.710434i	$-0.748499\pi$
$821$	7.54642	−	13.0708i	0.263372	−	0.456173i	0.967136	+	0.254260i	$0.0818321\pi$
$822$	−32.2790	−	33.2765i	−1.12586	−	1.16065i
$823$	8.26909	+	14.3225i	0.288242	+	0.499251i	0.973390	−	0.229153i	$-0.0735958\pi$
$823$	8.26909	+	14.3225i	0.288242	+	0.499251i	−0.685148	+	0.728404i	$0.740262\pi$
$824$	18.8594	+	32.6654i	0.656997	+	1.13795i
$825$	−6.93209	−	7.14631i	−0.241344	−	0.248802i
$826$	−28.6883	+	49.6895i	−0.998192	+	1.72892i
$827$	50.4211			1.75331			0.876656	−	0.481117i	$-0.159769\pi$
$827$	50.4211			1.75331			0.876656	+	0.481117i	$0.159769\pi$
$828$	−3.33205	+	109.464i	−0.115797	+	3.80415i
$829$	−27.0835			−0.940650			−0.470325	−	0.882493i	$-0.655863\pi$
$829$	−27.0835			−0.940650			−0.470325	+	0.882493i	$0.655863\pi$
$830$	−7.76475	+	13.4489i	−0.269518	+	0.466820i
$831$	−5.84663	+	20.5632i	−0.202817	+	0.713330i
$832$	1.38489	+	2.39871i	0.0480126	+	0.0831602i
$833$	−5.66322	−	9.80899i	−0.196219	−	0.339861i
$834$	−18.8465	+	4.74380i	−0.652602	+	0.164264i
$835$	2.48240	−	4.29964i	0.0859070	−	0.148795i
$836$	−147.451			−5.09969
$837$	−21.2731	−	6.75448i	−0.735308	−	0.233469i
$838$	85.6301			2.95804
$839$	−17.5713	+	30.4343i	−0.606628	+	1.05071i	0.385164	+	0.922848i	$0.374145\pi$
$839$	−17.5713	+	30.4343i	−0.606628	+	1.05071i	−0.991792	+	0.127862i	$0.959189\pi$
$840$	29.9675	−	7.54302i	1.03398	−	0.260259i
$841$	8.80539	+	15.2514i	0.303634	+	0.525910i
$842$	13.9384	+	24.1421i	0.480350	+	0.831991i
$843$	−2.23868	+	7.87369i	−0.0771044	+	0.271184i
$844$	−7.71893	+	13.3696i	−0.265697	+	0.460200i
$845$	−1.00000			−0.0344010
$846$	66.9274	+	41.4055i	2.30101	+	1.42355i
$847$	66.3926			2.28128
$848$	−18.7835	+	32.5340i	−0.645028	+	1.11722i
$849$	−15.5230	−	16.0027i	−0.532749	−	0.549213i
$850$	−6.88307	−	11.9218i	−0.236087	−	0.408915i
$851$	18.0304	+	31.2296i	0.618074	+	1.07054i
$852$	10.4997	+	10.8242i	0.359715	+	0.370832i
$853$	23.5824	−	40.8459i	0.807446	−	1.39854i	−0.107181	−	0.994240i	$-0.534182\pi$
$853$	23.5824	−	40.8459i	0.807446	−	1.39854i	0.914627	−	0.404298i	$-0.132484\pi$
$854$	45.7082			1.56410
$855$	15.0432	+	9.30665i	0.514466	+	0.318281i
$856$	75.8104			2.59115
$857$	−27.2409	+	47.1827i	−0.930532	+	1.61173i	−0.148120	+	0.988969i	$0.547322\pi$
$857$	−27.2409	+	47.1827i	−0.930532	+	1.61173i	−0.782413	+	0.622760i	$0.786011\pi$
$858$	−6.86156	+	24.1328i	−0.234250	+	0.823881i
$859$	13.2504	+	22.9503i	0.452096	+	0.783054i	0.998516	−	0.0544578i	$-0.0173430\pi$
$859$	13.2504	+	22.9503i	0.452096	+	0.783054i	−0.546420	+	0.837511i	$0.684010\pi$
$860$	−1.42271	−	2.46421i	−0.0485141	−	0.0840289i
$861$	33.2030	−	8.35741i	1.13155	−	0.284820i
$862$	37.0163	−	64.1142i	1.26078	−	2.18374i
$863$	−34.4594			−1.17301			−0.586506	−	0.809945i	$-0.699497\pi$
$863$	−34.4594			−1.17301			−0.586506	+	0.809945i	$0.699497\pi$
$864$	19.0252	+	6.04074i	0.647252	+	0.205510i
$865$	2.66799			0.0907144
$866$	41.2916	−	71.5191i	1.40314	−	2.43032i
$867$	−21.5696	+	5.42921i	−0.732542	+	0.184386i
$868$	28.1444	+	48.7475i	0.955283	+	1.65460i
$869$	39.2234	+	67.9369i	1.33056	+	2.30460i
$870$	−4.02849	+	14.1686i	−0.136579	+	0.480361i
$871$	−2.84821	+	4.93325i	−0.0965081	+	0.167157i
$872$	55.9541			1.89485
$873$	−0.570419	+	18.7394i	−0.0193058	+	0.634233i
$874$	124.684			4.21752
$875$	1.50610	−	2.60865i	0.0509156	−	0.0881884i
$876$	65.3280	+	67.3468i	2.20723	+	2.27544i
$877$	10.7961	+	18.6994i	0.364558	+	0.631433i	0.988705	−	0.149874i	$-0.0478867\pi$
$877$	10.7961	+	18.6994i	0.364558	+	0.631433i	−0.624147	+	0.781307i	$0.714553\pi$
$878$	−5.10320	−	8.83900i	−0.172225	−	0.298302i
$879$	−30.7321	−	31.6818i	−1.03657	−	1.06860i
$880$	−17.8918	+	30.9895i	−0.603132	+	1.04465i
$881$	47.3112			1.59396			0.796978	−	0.604009i	$-0.206431\pi$
$881$	47.3112			1.59396			0.796978	+	0.604009i	$0.206431\pi$
$882$	13.8070	−	7.42079i	0.464906	−	0.249871i
$883$	−5.56289			−0.187206			−0.0936031	−	0.995610i	$-0.529838\pi$
$883$	−5.56289			−0.187206			−0.0936031	+	0.995610i	$0.529838\pi$
$884$	−11.8826	+	20.5813i	−0.399655	+	0.692223i
$885$	−3.58049	+	12.5930i	−0.120357	+	0.423308i
$886$	5.88696	+	10.1965i	0.197776	+	0.342559i
$887$	−18.2066	−	31.5348i	−0.611318	−	1.05883i	−0.991019	−	0.133724i	$-0.957306\pi$
$887$	−18.2066	−	31.5348i	−0.611318	−	1.05883i	0.379701	−	0.925109i	$-0.376027\pi$
$888$	42.7541	−	10.7615i	1.43474	−	0.361132i
$889$	−6.58843	+	11.4115i	−0.220969	+	0.382729i
$890$	−5.69026			−0.190738
$891$	−23.0938	−	46.2927i	−0.773670	−	1.55086i
$892$	−3.14431			−0.105279
$893$	30.6911	−	53.1585i	1.02704	−	1.77888i
$894$	69.2546	−	17.4318i	2.31622	−	0.583008i
$895$	−6.99643	−	12.1182i	−0.233865	−	0.405066i
$896$	22.0839	+	38.2505i	0.737772	+	1.27786i
$897$	3.97481	−	13.9798i	0.132715	−	0.466773i
$898$	31.9199	−	55.2869i	1.06518	−	1.84495i
$899$	−14.4962			−0.483475
$900$	11.4960	−	6.17870i	0.383200	−	0.205957i
$901$	32.9657			1.09825
$902$	−47.5302	+	82.3247i	−1.58258	+	2.74111i
$903$	−2.37596	−	2.44938i	−0.0790668	−	0.0815102i
$904$	40.4762	+	70.1069i	1.34622	+	2.33172i
$905$	4.14373	+	7.17715i	0.137742	+	0.238576i
$906$	−18.1862	−	18.7482i	−0.604197	−	0.622868i
$907$	−22.0460	+	38.1848i	−0.732025	+	1.26791i	0.223991	+	0.974591i	$0.428091\pi$
$907$	−22.0460	+	38.1848i	−0.732025	+	1.26791i	−0.956016	+	0.293314i	$0.905242\pi$
$908$	−85.5925			−2.84049
$909$	0.543622	−	17.8591i	0.0180308	−	0.592348i
$910$	−7.59077			−0.251632
$911$	11.3430	−	19.6466i	0.375810	−	0.650922i	−0.614638	−	0.788809i	$-0.710698\pi$
$911$	11.3430	−	19.6466i	0.375810	−	0.650922i	0.990448	+	0.137887i	$0.0440312\pi$
$912$	17.3876	−	61.1540i	0.575761	−	2.02501i
$913$	−17.7115	−	30.6772i	−0.586164	−	1.01527i
$914$	−1.67170	−	2.89547i	−0.0552949	−	0.0957737i
$915$	10.1142	−	2.54580i	0.334364	−	0.0841616i
$916$	−9.82486	+	17.0172i	−0.324622	+	0.562263i
$917$	−39.9610			−1.31963
$918$	−15.3416	−	69.8664i	−0.506348	−	2.30593i
$919$	−45.1040			−1.48784			−0.743922	−	0.668267i	$-0.767036\pi$
$919$	−45.1040			−1.48784			−0.743922	+	0.668267i	$0.767036\pi$
$920$	24.8506	−	43.0425i	0.819299	−	1.41907i
$921$	52.8300	−	13.2977i	1.74081	−	0.438173i
$922$	−9.73305	−	16.8581i	−0.320541	−	0.555193i
$923$	−1.00065	−	1.73318i	−0.0329368	−	0.0570483i
$924$	−35.6810	+	125.494i	−1.17382	+	4.12844i
$925$	2.14874	−	3.72172i	0.0706500	−	0.122369i
$926$	−26.9201			−0.884650
$927$	16.2466	+	10.0512i	0.533609	+	0.330124i
$928$	12.9644			0.425577
$929$	−17.5307	+	30.3640i	−0.575162	+	0.996210i	0.420862	+	0.907125i	$0.361728\pi$
$929$	−17.5307	+	30.3640i	−0.575162	+	0.996210i	−0.996024	+	0.0890855i	$0.971606\pi$
$930$	13.0540	+	13.4574i	0.428058	+	0.441286i
$931$	−6.11282	−	10.5877i	−0.200339	−	0.346998i
$932$	−2.46921	−	4.27679i	−0.0808816	−	0.140091i
$933$	−7.33242	−	7.55901i	−0.240053	−	0.247471i
$934$	−2.63231	+	4.55930i	−0.0861318	+	0.149185i
$935$	31.4007			1.02691
$936$	−15.1110	−	9.34864i	−0.493920	−	0.305570i
$937$	−41.2551			−1.34775			−0.673873	−	0.738847i	$-0.735370\pi$
$937$	−41.2551			−1.34775			−0.673873	+	0.738847i	$0.735370\pi$
$938$	−21.6201	+	37.4472i	−0.705922	+	1.22269i
$939$	−3.73021	+	13.1195i	−0.121731	+	0.428140i
$940$	−22.6440	−	39.2205i	−0.738565	−	1.27923i
$941$	−12.1782	−	21.0932i	−0.396998	−	0.687620i	0.596356	−	0.802720i	$-0.296615\pi$
$941$	−12.1782	−	21.0932i	−0.396998	−	0.687620i	−0.993354	+	0.115100i	$0.963281\pi$
$942$	−26.3659	+	6.63646i	−0.859046	+	0.216228i
$943$	27.5336	−	47.6896i	0.896618	−	1.55299i
$944$	47.0548			1.53150
$945$	11.5610	−	10.5510i	0.376081	−	0.343225i
$946$	9.47427			0.308035
$947$	−26.8071	+	46.4313i	−0.871114	+	1.50881i	−0.0102687	+	0.999947i	$0.503269\pi$
$947$	−26.8071	+	46.4313i	−0.871114	+	1.50881i	−0.860845	+	0.508867i	$0.830065\pi$
$948$	−99.7237	+	25.1011i	−3.23888	+	0.815247i
$949$	−6.22592	−	10.7836i	−0.202102	−	0.350051i
$950$	−7.42951	−	12.8683i	−0.241045	−	0.417502i
$951$	−9.30111	+	32.7130i	−0.301609	+	1.06079i
$952$	−48.7316	+	84.4056i	−1.57940	+	2.73560i
$953$	49.0812			1.58990			0.794948	−	0.606677i	$-0.207498\pi$
$953$	49.0812			1.58990			0.794948	+	0.606677i	$0.207498\pi$
$954$	−1.38807	+	45.6007i	−0.0449403	+	1.47638i
$955$	−0.712091			−0.0230427
$956$	−23.5097	+	40.7199i	−0.760357	+	1.31698i
$957$	−23.3944	−	24.1173i	−0.756232	−	0.779602i
$958$	−1.59517	−	2.76291i	−0.0515376	−	0.0892657i
$959$	15.9970	+	27.7076i	0.516570	+	0.894725i
$960$	3.34028	+	3.44350i	0.107807	+	0.111139i
$961$	6.27463	−	10.8680i	0.202408	−	0.350580i
$962$	−10.8296			−0.349161
$963$	33.8222	−	18.1782i	1.08990	−	0.585786i
$964$	−33.2159			−1.06981
$965$	−10.3493	+	17.9256i	−0.333157	+	0.577045i
$966$	30.1719	−	106.118i	0.970765	−	3.41428i
$967$	2.85399	+	4.94326i	0.0917782	+	0.158965i	0.908259	−	0.418407i	$-0.137412\pi$
$967$	2.85399	+	4.94326i	0.0917782	+	0.158965i	−0.816481	+	0.577372i	$0.804078\pi$
$968$	−65.2753	−	113.060i	−2.09803	−	3.63389i
$969$	−54.1031	+	13.6181i	−1.73804	+	0.437476i
$970$	7.87420	−	13.6385i	0.252825	−	0.437906i
$971$	−14.0392			−0.450538			−0.225269	−	0.974297i	$-0.572326\pi$
$971$	−14.0392			−0.450538			−0.225269	+	0.974297i	$0.572326\pi$
$972$	66.6499	−	12.5228i	2.13780	−	0.401669i
$973$	13.4120			0.429970
$974$	−26.0315	+	45.0880i	−0.834105	+	1.44471i
$975$	−1.67966	+	0.422782i	−0.0537922	+	0.0135398i
$976$	−18.7428	−	32.4635i	−0.599942	−	1.03913i
$977$	−4.67090	−	8.09023i	−0.149435	−	0.258830i	0.781584	−	0.623801i	$-0.214412\pi$
$977$	−4.67090	−	8.09023i	−0.149435	−	0.258830i	−0.931019	+	0.364971i	$0.881079\pi$
$978$	−2.89281	+	10.1743i	−0.0925019	+	0.325339i
$979$	6.48976	−	11.2406i	0.207414	−	0.359251i
$980$	−9.02012			−0.288137
$981$	24.9635	−	13.4170i	0.797022	−	0.428371i
$982$	−30.5571			−0.975117
$983$	−16.0956	+	27.8784i	−0.513370	+	0.889183i	0.486510	+	0.873675i	$0.338270\pi$
$983$	−16.0956	+	27.8784i	−0.513370	+	0.889183i	−0.999880	+	0.0155076i	$0.995064\pi$
$984$	−46.8761	−	48.3247i	−1.49436	−	1.54053i
$985$	−12.5962	−	21.8173i	−0.401349	−	0.695157i
$986$	−23.2289	−	40.2337i	−0.739760	−	1.28130i
$987$	−37.8159	−	38.9845i	−1.20369	−	1.24089i
$988$	−12.8259	+	22.2152i	−0.408047	+	0.706759i
$989$	−5.48832			−0.174518
$990$	−1.32217	+	43.4359i	−0.0420213	+	1.38048i
$991$	13.6054			0.432189			0.216095	−	0.976372i	$-0.430668\pi$
$991$	13.6054			0.432189			0.216095	+	0.976372i	$0.430668\pi$
$992$	8.25053	−	14.2903i	0.261955	−	0.453719i
$993$	−1.57555	+	5.54139i	−0.0499987	+	0.175851i
$994$	−7.59571	−	13.1562i	−0.240921	−	0.417288i
$995$	−0.346218	−	0.599668i	−0.0109759	−	0.0190107i
$996$	45.0306	−	11.3345i	1.42685	−	0.359148i
$997$	−4.94972	+	8.57317i	−0.156759	+	0.271515i	−0.933698	−	0.358061i	$-0.883438\pi$
$997$	−4.94972	+	8.57317i	−0.156759	+	0.271515i	0.776939	+	0.629576i	$0.216771\pi$
$998$	21.1126			0.668308
$999$	16.4940	−	15.0530i	0.521846	−	0.476255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.2	✓	30
3.2	odd	2		1755.2.i.h.586.14		30
9.2	odd	6		5265.2.a.bl.1.2		15
9.4	even	3	inner	585.2.i.h.391.2	yes	30
9.5	odd	6		1755.2.i.h.1171.14		30
9.7	even	3		5265.2.a.bk.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.2	✓	30	1.1	even	1	trivial
585.2.i.h.391.2	yes	30	9.4	even	3	inner
1755.2.i.h.586.14		30	3.2	odd	2
1755.2.i.h.1171.14		30	9.5	odd	6
5265.2.a.bk.1.14		15	9.7	even	3
5265.2.a.bl.1.2		15	9.2	odd	6

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

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