LMFDB - Embedded newform 574.2.r.c.319.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(9,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("574.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.r (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.3
Character	$\chi$	$=$	574.319
Dual form			574.2.r.c.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.552179 - 2.06076i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.83592 - 1.05997i) q^{5} +(-1.50858 - 1.50858i) q^{6} +(0.869194 + 2.49890i) q^{7} -1.00000i q^{8} +(-1.34375 + 0.775813i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.552179 - 2.06076i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.83592 - 1.05997i) q^{5} +(-1.50858 - 1.50858i) q^{6} +(0.869194 + 2.49890i) q^{7} -1.00000i q^{8} +(-1.34375 + 0.775813i) q^{9} +(1.05997 - 1.83592i) q^{10} +(-1.19774 - 4.47004i) q^{11} +(-2.06076 - 0.552179i) q^{12} +(2.41363 - 2.41363i) q^{13} +(2.00219 + 1.72951i) q^{14} +(-3.19810 - 3.19810i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.09543 + 0.293519i) q^{17} +(-0.775813 + 1.34375i) q^{18} +(-1.70352 + 6.35761i) q^{19} -2.11994i q^{20} +(4.66968 - 3.17104i) q^{21} +(-3.27230 - 3.27230i) q^{22} +(2.44201 + 4.22969i) q^{23} +(-2.06076 + 0.552179i) q^{24} +(-0.252927 + 0.438083i) q^{25} +(0.883452 - 3.29709i) q^{26} +(-2.18499 - 2.18499i) q^{27} +(2.59871 + 0.496706i) q^{28} +(6.09739 - 6.09739i) q^{29} +(-4.36868 - 1.17059i) q^{30} +(-1.72813 + 2.99321i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-8.55030 + 4.93652i) q^{33} +(-0.801910 + 0.801910i) q^{34} +(4.24453 + 3.66647i) q^{35} +1.55163i q^{36} +(-4.75466 - 8.23531i) q^{37} +(1.70352 + 6.35761i) q^{38} +(-6.30667 - 3.64116i) q^{39} +(-1.05997 - 1.83592i) q^{40} +(-5.82799 - 2.65228i) q^{41} +(2.45854 - 5.08104i) q^{42} +10.4482i q^{43} +(-4.47004 - 1.19774i) q^{44} +(-1.64468 + 2.84866i) q^{45} +(4.22969 + 2.44201i) q^{46} +(-1.09867 + 4.10031i) q^{47} +(-1.50858 + 1.50858i) q^{48} +(-5.48900 + 4.34406i) q^{49} +0.505855i q^{50} +(1.20975 + 2.09534i) q^{51} +(-0.883452 - 3.29709i) q^{52} +(1.21988 + 4.55265i) q^{53} +(-2.98475 - 0.799761i) q^{54} +(-6.93707 - 6.93707i) q^{55} +(2.49890 - 0.869194i) q^{56} +14.0421 q^{57} +(2.23180 - 8.32918i) q^{58} +(-0.246544 + 0.427027i) q^{59} +(-4.36868 + 1.17059i) q^{60} +(-4.29663 + 2.48066i) q^{61} +3.45627i q^{62} +(-3.10666 - 2.68356i) q^{63} -1.00000 q^{64} +(1.87286 - 6.98962i) q^{65} +(-4.93652 + 8.55030i) q^{66} +(14.2998 - 3.83161i) q^{67} +(-0.293519 + 1.09543i) q^{68} +(7.36794 - 7.36794i) q^{69} +(5.50910 + 1.05299i) q^{70} +(6.37202 - 6.37202i) q^{71} +(0.775813 + 1.34375i) q^{72} +(9.76092 + 5.63547i) q^{73} +(-8.23531 - 4.75466i) q^{74} +(1.04244 + 0.279322i) q^{75} +(4.65409 + 4.65409i) q^{76} +(10.1291 - 6.87837i) q^{77} -7.28232 q^{78} +(10.1910 + 2.73068i) q^{79} +(-1.83592 - 1.05997i) q^{80} +(-5.62367 + 9.74048i) q^{81} +(-6.37332 + 0.617052i) q^{82} +2.57544 q^{83} +(-0.411359 - 5.62958i) q^{84} +(-1.70000 + 1.70000i) q^{85} +(5.22408 + 9.04837i) q^{86} +(-15.9321 - 9.19839i) q^{87} +(-4.47004 + 1.19774i) q^{88} +(2.46427 + 0.660298i) q^{89} +3.28935i q^{90} +(8.12935 + 3.93352i) q^{91} +4.88402 q^{92} +(7.12253 + 1.90848i) q^{93} +(1.09867 + 4.10031i) q^{94} +(3.61135 + 13.4778i) q^{95} +(-0.552179 + 2.06076i) q^{96} +(-3.28490 - 3.28490i) q^{97} +(-2.58159 + 6.50657i) q^{98} +(5.07738 + 5.07738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7	$ 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7} + 12 q^{10} - 4 q^{12} - 28 q^{13} + 12 q^{14} + 20 q^{15} - 20 q^{16} + 14 q^{17} - 16 q^{18} + 24 q^{23} - 4 q^{24} - 20 q^{25} + 14 q^{26} + 4 q^{27} + 44 q^{29} + 10 q^{30} - 8 q^{31} + 28 q^{34} - 2 q^{35} - 16 q^{37} - 12 q^{40} + 4 q^{41} - 64 q^{42} - 36 q^{45} + 2 q^{47} - 8 q^{48} + 28 q^{51} - 14 q^{52} + 20 q^{53} + 2 q^{54} - 44 q^{55} + 12 q^{56} - 40 q^{57} - 22 q^{58} - 8 q^{59} + 10 q^{60} + 24 q^{63} - 40 q^{64} + 36 q^{65} - 48 q^{66} + 6 q^{67} - 14 q^{68} - 36 q^{69} + 8 q^{70} + 40 q^{71} + 16 q^{72} + 36 q^{75} - 26 q^{79} + 84 q^{81} - 22 q^{82} - 24 q^{83} + 164 q^{85} - 28 q^{86} + 16 q^{89} + 48 q^{92} + 46 q^{93} - 2 q^{94} - 18 q^{95} + 4 q^{96} + 8 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7 + 12 * q^10 - 4 * q^12 - 28 * q^13 + 12 * q^14 + 20 * q^15 - 20 * q^16 + 14 * q^17 - 16 * q^18 + 24 * q^23 - 4 * q^24 - 20 * q^25 + 14 * q^26 + 4 * q^27 + 44 * q^29 + 10 * q^30 - 8 * q^31 + 28 * q^34 - 2 * q^35 - 16 * q^37 - 12 * q^40 + 4 * q^41 - 64 * q^42 - 36 * q^45 + 2 * q^47 - 8 * q^48 + 28 * q^51 - 14 * q^52 + 20 * q^53 + 2 * q^54 - 44 * q^55 + 12 * q^56 - 40 * q^57 - 22 * q^58 - 8 * q^59 + 10 * q^60 + 24 * q^63 - 40 * q^64 + 36 * q^65 - 48 * q^66 + 6 * q^67 - 14 * q^68 - 36 * q^69 + 8 * q^70 + 40 * q^71 + 16 * q^72 + 36 * q^75 - 26 * q^79 + 84 * q^81 - 22 * q^82 - 24 * q^83 + 164 * q^85 - 28 * q^86 + 16 * q^89 + 48 * q^92 + 46 * q^93 - 2 * q^94 - 18 * q^95 + 4 * q^96 + 8 * q^97 + 24 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.552179	−	2.06076i	−0.318800	−	1.18978i	−0.920399	−	0.390981i	$-0.872136\pi$
$3$	−0.552179	−	2.06076i	−0.318800	−	1.18978i	0.601598	−	0.798799i	$-0.294531\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.83592	−	1.05997i	0.821049	−	0.474033i	−0.0297289	−	0.999558i	$-0.509464\pi$
$5$	1.83592	−	1.05997i	0.821049	−	0.474033i	0.850778	+	0.525525i	$0.176131\pi$
$6$	−1.50858	−	1.50858i	−0.615875	−	0.615875i
$7$	0.869194	+	2.49890i	0.328524	+	0.944496i
$7$	0.869194	+	2.49890i	0.328524	+	0.944496i
$8$		−	1.00000i		−	0.353553i
$9$	−1.34375	+	0.775813i	−0.447916	+	0.258604i
$10$	1.05997	−	1.83592i	0.335192	−	0.580569i
$11$	−1.19774	−	4.47004i	−0.361133	−	1.34777i	−0.872588	−	0.488457i	$-0.837560\pi$
$11$	−1.19774	−	4.47004i	−0.361133	−	1.34777i	0.511454	−	0.859310i	$-0.329107\pi$
$12$	−2.06076	−	0.552179i	−0.594890	−	0.159400i
$13$	2.41363	−	2.41363i	0.669422	−	0.669422i	−0.288160	−	0.957582i	$-0.593044\pi$
$13$	2.41363	−	2.41363i	0.669422	−	0.669422i	0.957582	+	0.288160i	$0.0930436\pi$
$14$	2.00219	+	1.72951i	0.535109	+	0.462232i
$15$	−3.19810	−	3.19810i	−0.825745	−	0.825745i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.09543	+	0.293519i	−0.265681	+	0.0711889i	−0.389200	−	0.921153i	$-0.627249\pi$
$17$	−1.09543	+	0.293519i	−0.265681	+	0.0711889i	0.123519	+	0.992342i	$0.460582\pi$
$18$	−0.775813	+	1.34375i	−0.182861	+	0.316724i
$19$	−1.70352	+	6.35761i	−0.390814	+	1.45854i	0.437982	+	0.898984i	$0.355693\pi$
$19$	−1.70352	+	6.35761i	−0.390814	+	1.45854i	−0.828795	+	0.559552i	$0.810973\pi$
$20$		−	2.11994i		−	0.474033i
$21$	4.66968	−	3.17104i	1.01901	−	0.691977i
$22$	−3.27230	−	3.27230i	−0.697656	−	0.697656i
$23$	2.44201	+	4.22969i	0.509194	+	0.881951i	0.999943	+	0.0106495i	$0.00338990\pi$
$23$	2.44201	+	4.22969i	0.509194	+	0.881951i	−0.490749	+	0.871301i	$0.663277\pi$
$24$	−2.06076	+	0.552179i	−0.420651	+	0.112713i
$25$	−0.252927	+	0.438083i	−0.0505855	+	0.0876166i
$26$	0.883452	−	3.29709i	0.173259	−	0.646612i
$27$	−2.18499	−	2.18499i	−0.420501	−	0.420501i
$28$	2.59871	+	0.496706i	0.491110	+	0.0938687i
$29$	6.09739	−	6.09739i	1.13226	−	1.13226i	0.142455	−	0.989801i	$-0.454500\pi$
$29$	6.09739	−	6.09739i	1.13226	−	1.13226i	0.989801	−	0.142455i	$-0.0454995\pi$
$30$	−4.36868	−	1.17059i	−0.797609	−	0.213719i
$31$	−1.72813	+	2.99321i	−0.310382	+	0.537597i	−0.978445	−	0.206507i	$-0.933790\pi$
$31$	−1.72813	+	2.99321i	−0.310382	+	0.537597i	0.668063	+	0.744105i	$0.267124\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−8.55030	+	4.93652i	−1.48842	+	0.859338i
$34$	−0.801910	+	0.801910i	−0.137526	+	0.137526i
$35$	4.24453	+	3.66647i	0.717457	+	0.619746i
$36$			1.55163i			0.258604i
$37$	−4.75466	−	8.23531i	−0.781661	−	1.35388i	−0.930974	−	0.365086i	$-0.881039\pi$
$37$	−4.75466	−	8.23531i	−0.781661	−	1.35388i	0.149313	−	0.988790i	$-0.452294\pi$
$38$	1.70352	+	6.35761i	0.276347	+	1.03134i
$39$	−6.30667	−	3.64116i	−1.00988	−	0.583052i
$40$	−1.05997	−	1.83592i	−0.167596	−	0.290285i
$41$	−5.82799	−	2.65228i	−0.910178	−	0.414216i
$41$	−5.82799	−	2.65228i	−0.910178	−	0.414216i
$42$	2.45854	−	5.08104i	0.379361	−	0.784021i
$43$			10.4482i			1.59333i	0.604421	+	0.796665i	$0.293404\pi$
$43$			10.4482i			1.59333i	−0.604421	+	0.796665i	$0.706596\pi$
$44$	−4.47004	−	1.19774i	−0.673884	−	0.180567i
$45$	−1.64468	+	2.84866i	−0.245174	+	0.424654i
$46$	4.22969	+	2.44201i	0.623633	+	0.360055i
$47$	−1.09867	+	4.10031i	−0.160258	+	0.598091i	0.838340	+	0.545148i	$0.183527\pi$
$47$	−1.09867	+	4.10031i	−0.160258	+	0.598091i	−0.998598	+	0.0529426i	$0.983140\pi$
$48$	−1.50858	+	1.50858i	−0.217745	+	0.217745i
$49$	−5.48900	+	4.34406i	−0.784144	+	0.620580i
$50$			0.505855i			0.0715387i
$51$	1.20975	+	2.09534i	0.169398	+	0.293406i
$52$	−0.883452	−	3.29709i	−0.122513	−	0.457224i
$53$	1.21988	+	4.55265i	0.167563	+	0.625354i	0.997699	+	0.0677935i	$0.0215959\pi$
$53$	1.21988	+	4.55265i	0.167563	+	0.625354i	−0.830136	+	0.557561i	$0.811737\pi$
$54$	−2.98475	−	0.799761i	−0.406173	−	0.108834i
$55$	−6.93707	−	6.93707i	−0.935395	−	0.935395i
$56$	2.49890	−	0.869194i	0.333930	−	0.116151i
$57$	14.0421			1.85993
$58$	2.23180	−	8.32918i	0.293049	−	1.09368i
$59$	−0.246544	+	0.427027i	−0.0320973	+	0.0555941i	−0.881628	−	0.471945i	$-0.843552\pi$
$59$	−0.246544	+	0.427027i	−0.0320973	+	0.0555941i	0.849531	+	0.527539i	$0.176885\pi$
$60$	−4.36868	+	1.17059i	−0.563995	+	0.151122i
$61$	−4.29663	+	2.48066i	−0.550127	+	0.317616i	−0.749173	−	0.662374i	$-0.769549\pi$
$61$	−4.29663	+	2.48066i	−0.550127	+	0.317616i	0.199046	+	0.979990i	$0.436216\pi$
$62$			3.45627i			0.438946i
$63$	−3.10666	−	2.68356i	−0.391402	−	0.338097i
$64$	−1.00000			−0.125000
$65$	1.87286	−	6.98962i	0.232300	−	0.866956i
$66$	−4.93652	+	8.55030i	−0.607644	+	1.05247i
$67$	14.2998	−	3.83161i	1.74699	−	0.468106i	0.763013	−	0.646383i	$-0.223719\pi$
$67$	14.2998	−	3.83161i	1.74699	−	0.468106i	0.983980	+	0.178277i	$0.0570524\pi$
$68$	−0.293519	+	1.09543i	−0.0355945	+	0.132840i
$69$	7.36794	−	7.36794i	0.886995	−	0.886995i
$70$	5.50910	+	1.05299i	0.658464	+	0.125856i
$71$	6.37202	−	6.37202i	0.756219	−	0.756219i	−0.219413	−	0.975632i	$-0.570414\pi$
$71$	6.37202	−	6.37202i	0.756219	−	0.756219i	0.975632	+	0.219413i	$0.0704141\pi$
$72$	0.775813	+	1.34375i	0.0914304	+	0.158362i
$73$	9.76092	+	5.63547i	1.14243	+	0.659582i	0.947031	−	0.321142i	$-0.104067\pi$
$73$	9.76092	+	5.63547i	1.14243	+	0.659582i	0.195398	+	0.980724i	$0.437400\pi$
$74$	−8.23531	−	4.75466i	−0.957335	−	0.552718i
$75$	1.04244	+	0.279322i	0.120371	+	0.0322533i
$76$	4.65409	+	4.65409i	0.533861	+	0.533861i
$77$	10.1291	−	6.87837i	1.15432	−	0.783863i
$78$	−7.28232			−0.824560
$79$	10.1910	+	2.73068i	1.14658	+	0.307226i	0.781595	−	0.623787i	$-0.214407\pi$
$79$	10.1910	+	2.73068i	1.14658	+	0.307226i	0.364988	+	0.931012i	$0.381073\pi$
$80$	−1.83592	−	1.05997i	−0.205262	−	0.118508i
$81$	−5.62367	+	9.74048i	−0.624852	+	1.08228i
$82$	−6.37332	+	0.617052i	−0.703816	+	0.0681420i
$83$	2.57544			0.282691			0.141345	−	0.989960i	$-0.454857\pi$
$83$	2.57544			0.282691			0.141345	+	0.989960i	$0.454857\pi$
$84$	−0.411359	−	5.62958i	−0.0448830	−	0.614237i
$85$	−1.70000	+	1.70000i	−0.184391	+	0.184391i
$86$	5.22408	+	9.04837i	0.563327	+	0.975711i
$87$	−15.9321	−	9.19839i	−1.70810	−	0.986171i
$88$	−4.47004	+	1.19774i	−0.476508	+	0.127680i
$89$	2.46427	+	0.660298i	0.261212	+	0.0699915i	0.387048	−	0.922060i	$-0.373495\pi$
$89$	2.46427	+	0.660298i	0.261212	+	0.0699915i	−0.125836	+	0.992051i	$0.540161\pi$
$90$			3.28935i			0.346728i
$91$	8.12935	+	3.93352i	0.852187	+	0.412345i
$92$	4.88402			0.509194
$93$	7.12253	+	1.90848i	0.738572	+	0.197900i
$94$	1.09867	+	4.10031i	0.113320	+	0.422914i
$95$	3.61135	+	13.4778i	0.370517	+	1.38279i
$96$	−0.552179	+	2.06076i	−0.0563565	+	0.210325i
$97$	−3.28490	−	3.28490i	−0.333531	−	0.333531i	0.520395	−	0.853926i	$-0.325785\pi$
$97$	−3.28490	−	3.28490i	−0.333531	−	0.333531i	−0.853926	+	0.520395i	$0.825785\pi$
$98$	−2.58159	+	6.50657i	−0.260780	+	0.657262i
$99$	5.07738	+	5.07738i	0.510296	+	0.510296i
$100$	0.252927	+	0.438083i	0.0252927	+	0.0438083i
$101$	6.28677	−	1.68454i	0.625557	−	0.167618i	0.0679045	−	0.997692i	$-0.478369\pi$
$101$	6.28677	−	1.68454i	0.625557	−	0.167618i	0.557653	+	0.830074i	$0.311702\pi$
$102$	2.09534	+	1.20975i	0.207470	+	0.119783i
$103$	−6.11679	+	3.53153i	−0.602705	+	0.347972i	−0.770105	−	0.637917i	$-0.779796\pi$
$103$	−6.11679	+	3.53153i	−0.602705	+	0.347972i	0.167400	+	0.985889i	$0.446463\pi$
$104$	−2.41363	−	2.41363i	−0.236676	−	0.236676i
$105$	5.21196	−	10.7715i	0.508635	−	1.05119i
$106$	3.33277	+	3.33277i	0.323707	+	0.323707i
$107$	−3.33283	−	5.77263i	−0.322197	−	0.558062i	0.658744	−	0.752367i	$-0.271088\pi$
$107$	−3.33283	−	5.77263i	−0.322197	−	0.558062i	−0.980941	+	0.194306i	$0.937755\pi$
$108$	−2.98475	+	0.799761i	−0.287208	+	0.0769570i
$109$	10.5428	−	2.82493i	1.00982	−	0.270579i	0.284263	−	0.958746i	$-0.408251\pi$
$109$	10.5428	−	2.82493i	1.00982	−	0.270579i	0.725552	+	0.688167i	$0.241584\pi$
$110$	−9.47622	−	2.53914i	−0.903522	−	0.242098i
$111$	−14.3456	+	14.3456i	−1.36162	+	1.36162i
$112$	1.72951	−	2.00219i	0.163424	−	0.189190i
$113$	12.1713			1.14498			0.572491	−	0.819911i	$-0.305977\pi$
$113$	12.1713			1.14498			0.572491	+	0.819911i	$0.305977\pi$
$114$	12.1609	−	7.02107i	1.13897	−	0.657584i
$115$	8.96668	+	5.17692i	0.836147	+	0.482750i
$116$	−2.23180	−	8.32918i	−0.207217	−	0.773345i
$117$	−1.37079	+	5.11584i	−0.126729	+	0.472960i
$118$			0.493088i			0.0453924i
$119$	−1.68562	−	2.48224i	−0.154520	−	0.227547i
$120$	−3.19810	+	3.19810i	−0.291945	+	0.291945i
$121$	−9.02039	+	5.20792i	−0.820035	+	0.473448i
$122$	−2.48066	+	4.29663i	−0.224589	+	0.388999i
$123$	−2.24762	+	13.4746i	−0.202661	+	1.21496i
$124$	1.72813	+	2.99321i	0.155191	+	0.268799i
$125$			11.6721i			1.04398i
$126$	−4.03222	−	0.770702i	−0.359219	−	0.0686596i
$127$	−6.90177			−0.612433			−0.306216	−	0.951962i	$-0.599063\pi$
$127$	−6.90177			−0.612433			−0.306216	+	0.951962i	$0.599063\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	21.5311	−	5.76925i	1.89571	−	0.507954i
$130$	−1.87286	−	6.98962i	−0.164261	−	0.613031i
$131$	−13.9868	+	8.07527i	−1.22203	+	0.705539i	−0.965350	−	0.260957i	$-0.915962\pi$
$131$	−13.9868	+	8.07527i	−1.22203	+	0.705539i	−0.256680	+	0.966497i	$0.582628\pi$
$132$			9.87304i			0.859338i
$133$	−17.3677	+	1.26908i	−1.50597	+	0.110043i
$134$	10.4681	−	10.4681i	0.904310	−	0.904310i
$135$	−6.32749	−	1.69545i	−0.544583	−	0.145921i
$136$	0.293519	+	1.09543i	0.0251691	+	0.0939323i
$137$	−5.21089	+	1.39625i	−0.445196	+	0.119290i	−0.474451	−	0.880282i	$-0.657353\pi$
$137$	−5.21089	+	1.39625i	−0.445196	+	0.119290i	0.0292546	+	0.999572i	$0.490687\pi$
$138$	2.69685	−	10.0648i	0.229571	−	0.856772i
$139$	12.3474			1.04730			0.523648	−	0.851935i	$-0.324571\pi$
$139$	12.3474			1.04730			0.523648	+	0.851935i	$0.324571\pi$
$140$	5.29752	−	1.84264i	0.447722	−	0.155731i
$141$	9.05640			0.762687
$142$	2.33232	−	8.70434i	0.195724	−	0.730452i
$143$	−13.6800	−	7.89813i	−1.14398	−	0.660475i
$144$	1.34375	+	0.775813i	0.111979	+	0.0646511i
$145$	4.73128	−	17.6574i	0.392911	−	1.46636i
$146$	11.2709			0.932789
$147$	11.9830	+	8.91282i	0.988338	+	0.735117i
$148$	−9.50932			−0.781661
$149$	−1.61742	+	6.03630i	−0.132504	+	0.494513i	−0.999996	−	0.00293917i	$-0.999064\pi$
$149$	−1.61742	+	6.03630i	−0.132504	+	0.494513i	0.867491	+	0.497452i	$0.165731\pi$
$150$	1.04244	−	0.279322i	0.0851152	−	0.0228066i
$151$	4.14152	+	15.4564i	0.337032	+	1.25782i	0.901649	+	0.432468i	$0.142357\pi$
$151$	4.14152	+	15.4564i	0.337032	+	1.25782i	−0.564617	+	0.825353i	$0.690976\pi$
$152$	6.35761	+	1.70352i	0.515670	+	0.138173i
$153$	1.24426	−	1.24426i	0.100593	−	0.100593i
$154$	5.33288	−	11.0214i	0.429736	−	0.888130i
$155$			7.32708i			0.588525i
$156$	−6.30667	+	3.64116i	−0.504938	+	0.291526i
$157$	−4.37295	−	16.3201i	−0.349000	−	1.30248i	−0.887869	−	0.460095i	$-0.847815\pi$
$157$	−4.37295	−	16.3201i	−0.349000	−	1.30248i	0.538870	−	0.842389i	$-0.318851\pi$
$158$	10.1910	−	2.73068i	0.810756	−	0.217241i
$159$	8.70831	−	5.02775i	0.690614	−	0.398726i
$160$	−2.11994			−0.167596
$161$	−8.44698	+	9.77876i	−0.665716	+	0.770674i
$162$			11.2473i			0.883674i
$163$	−5.24646	−	9.08714i	−0.410935	−	0.711759i	0.584058	−	0.811712i	$-0.301464\pi$
$163$	−5.24646	−	9.08714i	−0.410935	−	0.711759i	−0.994992	+	0.0999527i	$0.968131\pi$
$164$	−5.21093	+	3.72104i	−0.406906	+	0.290565i
$165$	−10.4651	+	18.1261i	−0.814709	+	1.41112i
$166$	2.23039	−	1.28772i	0.173112	−	0.0999463i
$167$	0.603224	−	0.603224i	0.0466789	−	0.0466789i	−0.683382	−	0.730061i	$-0.739492\pi$
$167$	0.603224	−	0.603224i	0.0466789	−	0.0466789i	0.730061	+	0.683382i	$0.239492\pi$
$168$	−3.17104	−	4.66968i	−0.244651	−	0.360274i
$169$			1.34874i			0.103749i
$170$	−0.622244	+	2.32224i	−0.0477239	+	0.178108i
$171$	−2.64322	−	9.86463i	−0.202132	−	0.754367i
$172$	9.04837	+	5.22408i	0.689932	+	0.398332i
$173$	10.4267	−	6.01987i	0.792729	−	0.457682i	−0.0481933	−	0.998838i	$-0.515346\pi$
$173$	10.4267	−	6.01987i	0.792729	−	0.457682i	0.840922	+	0.541156i	$0.182013\pi$
$174$	−18.3968			−1.39466
$175$	−1.31457	−	0.251261i	−0.0993721	−	0.0189936i
$176$	−3.27230	+	3.27230i	−0.246659	+	0.246659i
$177$	1.01614	+	0.272273i	0.0763774	+	0.0204653i
$178$	2.46427	−	0.660298i	0.184705	−	0.0494914i
$179$	−13.7234	+	3.67718i	−1.02574	+	0.274845i	−0.732190	−	0.681100i	$-0.761502\pi$
$179$	−13.7234	+	3.67718i	−1.02574	+	0.274845i	−0.293545	+	0.955945i	$0.594835\pi$
$180$	1.64468	+	2.84866i	0.122587	+	0.212327i
$181$	−7.46883	−	7.46883i	−0.555154	−	0.555154i	0.372770	−	0.927924i	$-0.378408\pi$
$181$	−7.46883	−	7.46883i	−0.555154	−	0.555154i	−0.927924	+	0.372770i	$0.878408\pi$
$182$	9.00698	−	0.658149i	0.667642	−	0.0487853i
$183$	7.48455	+	7.48455i	0.553274	+	0.553274i
$184$	4.22969	−	2.44201i	0.311817	−	0.180027i
$185$	−17.4584	−	10.0796i	−1.28356	−	0.741066i
$186$	7.12253	−	1.90848i	0.522249	−	0.139936i
$187$	2.62409	+	4.54505i	0.191892	+	0.332367i
$188$	3.00163	+	3.00163i	0.218916	+	0.218916i
$189$	3.56089	−	7.35924i	0.259017	−	0.535306i
$190$	9.86640	+	9.86640i	0.715784	+	0.715784i
$191$	5.35458	−	19.9836i	0.387444	−	1.44596i	−0.446834	−	0.894617i	$-0.647449\pi$
$191$	5.35458	−	19.9836i	0.387444	−	1.44596i	0.834278	−	0.551344i	$-0.185885\pi$
$192$	0.552179	+	2.06076i	0.0398501	+	0.148722i
$193$	−4.22799	−	15.7791i	−0.304337	−	1.13580i	−0.933514	−	0.358540i	$-0.883275\pi$
$193$	−4.22799	−	15.7791i	−0.304337	−	1.13580i	0.629177	−	0.777262i	$-0.283392\pi$
$194$	−4.48725	−	1.20236i	−0.322166	−	0.0863241i
$195$	−15.4381			−1.10554
$196$	1.01756	+	6.92565i	0.0726829	+	0.494689i
$197$			17.3220i			1.23414i	0.786906	+	0.617072i	$0.211681\pi$
$197$			17.3220i			1.23414i	−0.786906	+	0.617072i	$0.788319\pi$
$198$	6.93583	+	1.85845i	0.492908	+	0.132074i
$199$	−18.8004	+	5.03755i	−1.33273	+	0.357103i	−0.853731	−	0.520715i	$-0.825665\pi$
$199$	−18.8004	+	5.03755i	−1.33273	+	0.357103i	−0.478995	+	0.877818i	$0.658999\pi$
$200$	0.438083	+	0.252927i	0.0309772	+	0.0178847i
$201$	−15.7920	−	27.3526i	−1.11388	−	1.92930i
$202$	4.60224	−	4.60224i	0.323812	−	0.323812i
$203$	20.5366	+	9.93695i	1.44138	+	0.697437i
$204$	2.41949			0.169398
$205$	−13.5111	+	1.30811i	−0.943653	+	0.0913626i
$206$	−3.53153	+	6.11679i	−0.246053	+	0.426177i
$207$	−6.56289	−	3.78909i	−0.456152	−	0.263360i
$208$	−3.29709	−	0.883452i	−0.228612	−	0.0612563i
$209$	30.4591			2.10690
$210$	−0.872057	−	11.9344i	−0.0601776	−	0.823550i
$211$	−11.5930	−	11.5930i	−0.798097	−	0.798097i	0.184698	−	0.982795i	$-0.440869\pi$
$211$	−11.5930	−	11.5930i	−0.798097	−	0.798097i	−0.982795	+	0.184698i	$0.940869\pi$
$212$	4.55265	+	1.21988i	0.312677	+	0.0837816i
$213$	−16.6497	−	9.61270i	−1.14082	−	0.658651i
$214$	−5.77263	−	3.33283i	−0.394609	−	0.227828i
$215$	11.0747	+	19.1820i	0.755291	+	1.30820i
$216$	−2.18499	+	2.18499i	−0.148670	+	0.148670i
$217$	−8.98183	−	1.71675i	−0.609726	−	0.116541i
$218$	7.71785	−	7.71785i	0.522719	−	0.522719i
$219$	6.22357	−	23.2267i	0.420550	−	1.56951i
$220$	−9.47622	+	2.53914i	−0.638886	+	0.171189i
$221$	−1.93552	+	3.35241i	−0.130197	+	0.225508i
$222$	−5.25084	+	19.5964i	−0.352413	+	1.31522i
$223$	−24.3878			−1.63313			−0.816564	−	0.577256i	$-0.804124\pi$
$223$	−24.3878			−1.63313			−0.816564	+	0.577256i	$0.804124\pi$
$224$	0.496706	−	2.59871i	0.0331876	−	0.173633i
$225$		−	0.784897i		−	0.0523265i
$226$	10.5407	−	6.08566i	0.701155	−	0.404812i
$227$	−9.93677	+	2.66255i	−0.659526	+	0.176720i	−0.573032	−	0.819533i	$-0.694233\pi$
$227$	−9.93677	+	2.66255i	−0.659526	+	0.176720i	−0.0864941	+	0.996252i	$0.527566\pi$
$228$	7.02107	−	12.1609i	0.464982	−	0.805372i
$229$	−7.20314	+	26.8825i	−0.475997	+	1.77644i	0.141573	+	0.989928i	$0.454784\pi$
$229$	−7.20314	+	26.8825i	−0.475997	+	1.77644i	−0.617570	+	0.786516i	$0.711883\pi$
$230$	10.3538			0.682711
$231$	−19.7677	−	17.0756i	−1.30062	−	1.12349i
$232$	−6.09739	−	6.09739i	−0.400313	−	0.400313i
$233$	−6.27358	−	1.68100i	−0.410996	−	0.110126i	0.0473959	−	0.998876i	$-0.484908\pi$
$233$	−6.27358	−	1.68100i	−0.410996	−	0.110126i	−0.458392	+	0.888750i	$0.651574\pi$
$234$	1.37079	+	5.11584i	0.0896111	+	0.334433i
$235$	2.32912	+	8.69240i	0.151935	+	0.567030i
$236$	0.246544	+	0.427027i	0.0160486	+	0.0277971i
$237$		−	22.5091i		−	1.46212i
$238$	−2.70091	−	1.30688i	−0.175074	−	0.0847123i
$239$	−18.7204	+	18.7204i	−1.21092	+	1.21092i	−0.240199	+	0.970724i	$0.577213\pi$
$239$	−18.7204	+	18.7204i	−1.21092	+	1.21092i	−0.970724	+	0.240199i	$0.922787\pi$
$240$	−1.17059	+	4.36868i	−0.0755610	+	0.281997i
$241$	10.5239	+	6.07598i	0.677904	+	0.391388i	0.799065	−	0.601245i	$-0.205328\pi$
$241$	10.5239	+	6.07598i	0.677904	+	0.391388i	−0.121161	+	0.992633i	$0.538662\pi$
$242$	−5.20792	+	9.02039i	−0.334778	+	0.579852i
$243$	14.2238	+	3.81125i	0.912457	+	0.244492i
$244$			4.96132i			0.317616i
$245$	−5.47281	+	13.7935i	−0.349645	+	0.881236i
$246$	4.79081	+	12.7932i	0.305451	+	0.815662i
$247$	11.2333	+	19.4566i	0.714757	+	1.23799i
$248$	2.99321	+	1.72813i	0.190069	+	0.109737i
$249$	−1.42210	−	5.30735i	−0.0901220	−	0.336340i
$250$	5.83604	+	10.1083i	0.369104	+	0.639306i
$251$			4.47096i			0.282204i	0.989995	+	0.141102i	$0.0450646\pi$
$251$			4.47096i			0.282204i	−0.989995	+	0.141102i	$0.954935\pi$
$252$	−3.87736	+	1.34866i	−0.244251	+	0.0849578i
$253$	15.9820	−	15.9820i	1.00478	−	1.00478i
$254$	−5.97710	+	3.45088i	−0.375037	+	0.216528i
$255$	4.44200	+	2.56459i	0.278169	+	0.160601i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.94165	+	1.32411i	0.308252	+	0.0825958i	0.409629	−	0.912252i	$-0.365658\pi$
$257$	4.94165	+	1.32411i	0.308252	+	0.0825958i	−0.101377	+	0.994848i	$0.532325\pi$
$258$	15.7619	−	15.7619i	0.981292	−	0.981292i
$259$	16.4465	−	19.0395i	1.02194	−	1.18306i
$260$	−5.11676	−	5.11676i	−0.317328	−	0.317328i
$261$	−3.46292	+	12.9238i	−0.214349	+	0.799962i
$262$	−8.07527	+	13.9868i	−0.498892	+	0.864106i
$263$	17.5195	−	4.69435i	1.08030	−	0.289466i	0.325582	−	0.945514i	$-0.394440\pi$
$263$	17.5195	−	4.69435i	1.08030	−	0.289466i	0.754719	+	0.656048i	$0.227773\pi$
$264$	4.93652	+	8.55030i	0.303822	+	0.526235i
$265$	7.06527	+	7.06527i	0.434016	+	0.434016i
$266$	−14.4063	+	9.78291i	−0.883310	+	0.599829i
$267$		−	5.44286i		−	0.333098i
$268$	3.83161	−	14.2998i	0.234053	−	0.873497i
$269$	1.45833	−	2.52591i	0.0889161	−	0.154007i	−0.818137	−	0.575023i	$-0.804993\pi$
$269$	1.45833	−	2.52591i	0.0889161	−	0.154007i	0.907053	+	0.421016i	$0.138326\pi$
$270$	−6.32749	+	1.69545i	−0.385079	+	0.103182i
$271$	−4.37049	−	7.56991i	−0.265488	−	0.459839i	0.702203	−	0.711977i	$-0.252200\pi$
$271$	−4.37049	−	7.56991i	−0.265488	−	0.459839i	−0.967691	+	0.252138i	$0.918866\pi$
$272$	0.801910	+	0.801910i	0.0486229	+	0.0486229i
$273$	3.61717	−	18.9246i	0.218921	−	1.14537i
$274$	−3.81464	+	3.81464i	−0.230451	+	0.230451i
$275$	2.26119	+	0.605884i	0.136355	+	0.0365362i
$276$	−2.69685	−	10.0648i	−0.162331	−	0.605829i
$277$	13.5150	−	23.4086i	0.812036	−	1.40649i	−0.0994001	−	0.995048i	$-0.531692\pi$
$277$	13.5150	−	23.4086i	0.812036	−	1.40649i	0.911437	−	0.411441i	$-0.134974\pi$
$278$	10.6932	−	6.17372i	0.641335	−	0.370275i
$279$		−	5.36283i		−	0.321064i
$280$	3.66647	−	4.24453i	0.219113	−	0.253659i
$281$	9.99732	+	9.99732i	0.596390	+	0.596390i	0.939350	−	0.342960i	$-0.111429\pi$
$281$	9.99732	+	9.99732i	0.596390	+	0.596390i	−0.342960	+	0.939350i	$0.611429\pi$
$282$	7.84307	−	4.52820i	0.467048	−	0.269650i
$283$	−5.98291	+	10.3627i	−0.355647	+	0.615999i	−0.987228	−	0.159311i	$-0.949073\pi$
$283$	−5.98291	+	10.3627i	−0.355647	+	0.615999i	0.631582	+	0.775309i	$0.282406\pi$
$284$	−2.33232	−	8.70434i	−0.138398	−	0.516508i
$285$	25.7803	−	14.8843i	1.52709	−	0.881667i
$286$	−15.7963			−0.934052
$287$	1.56213	−	16.8689i	0.0922097	−	0.995740i
$288$	1.55163			0.0914304
$289$	−13.6086	+	7.85694i	−0.800507	+	0.462173i
$290$	−4.73128	−	17.6574i	−0.277830	−	1.03688i
$291$	−4.95553	+	8.58323i	−0.290498	+	0.503158i
$292$	9.76092	−	5.63547i	0.571215	−	0.329791i
$293$	−3.32158	−	3.32158i	−0.194049	−	0.194049i	0.603394	−	0.797443i	$-0.293815\pi$
$293$	−3.32158	−	3.32158i	−0.194049	−	0.194049i	−0.797443	+	0.603394i	$0.793815\pi$
$294$	14.8340	+	1.72725i	0.865134	+	0.100735i
$295$			1.04532i			0.0608607i
$296$	−8.23531	+	4.75466i	−0.478668	+	0.276359i
$297$	−7.14993	+	12.3840i	−0.414881	+	0.718595i
$298$	1.61742	+	6.03630i	0.0936948	+	0.349674i
$299$	16.1030	+	4.31480i	0.931263	+	0.249531i
$300$	0.763122	−	0.763122i	0.0440589	−	0.0440589i
$301$	−26.1089	+	9.08148i	−1.50489	+	0.523448i
$302$	11.3148	+	11.3148i	0.651096	+	0.651096i
$303$	−6.94284	−	12.0254i	−0.398856	−	0.690839i
$304$	6.35761	−	1.70352i	0.364634	−	0.0977034i
$305$	−5.25885	+	9.10860i	−0.301121	+	0.521557i
$306$	0.455432	−	1.69970i	0.0260353	−	0.0971652i
$307$		−	10.0797i		−	0.575278i	−0.957739	−	0.287639i	$-0.907130\pi$
$307$		−	10.0797i		−	0.575278i	0.957739	−	0.287639i	$-0.0928704\pi$
$308$	−0.892289	−	12.2113i	−0.0508429	−	0.695801i
$309$	10.6552	+	10.6552i	0.606153	+	0.606153i
$310$	3.66354	+	6.34543i	0.208075	+	0.360396i
$311$	0.902085	−	0.241713i	0.0511526	−	0.0137063i	−0.233152	−	0.972440i	$-0.574904\pi$
$311$	0.902085	−	0.241713i	0.0511526	−	0.0137063i	0.284305	+	0.958734i	$0.408237\pi$
$312$	−3.64116	+	6.30667i	−0.206140	+	0.357045i
$313$	−7.59022	+	28.3271i	−0.429025	+	1.60114i	0.325950	+	0.945387i	$0.394316\pi$
$313$	−7.59022	+	28.3271i	−0.429025	+	1.60114i	−0.754974	+	0.655754i	$0.772351\pi$
$314$	−11.9471	−	11.9471i	−0.674216	−	0.674216i
$315$	−8.54807	−	1.63384i	−0.481629	−	0.0920566i
$316$	7.46036	−	7.46036i	0.419678	−	0.419678i
$317$	18.7256	+	5.01751i	1.05173	+	0.281811i	0.742968	−	0.669327i	$-0.233417\pi$
$317$	18.7256	+	5.01751i	1.05173	+	0.281811i	0.308766	+	0.951138i	$0.400084\pi$
$318$	5.02775	−	8.70831i	0.281942	−	0.488338i
$319$	−34.5587	−	19.9525i	−1.93491	−	1.11712i
$320$	−1.83592	+	1.05997i	−0.102631	+	0.0592541i
$321$	−10.0557	+	10.0557i	−0.561254	+	0.561254i
$322$	−2.42592	+	12.6921i	−0.135191	+	0.707306i
$323$		−	7.46433i		−	0.415326i
$324$	5.62367	+	9.74048i	0.312426	+	0.541138i
$325$	0.446898	+	1.66785i	0.0247894	+	0.0925155i
$326$	−9.08714	−	5.24646i	−0.503290	−	0.290575i
$327$	−11.6430	−	20.1663i	−0.643859	−	1.11520i
$328$	−2.65228	+	5.82799i	−0.146448	+	0.321797i
$329$	−11.2012	+	0.818484i	−0.617543	+	0.0451245i
$330$			20.9303i			1.15217i
$331$	−10.1850	−	2.72907i	−0.559820	−	0.150003i	−0.0321961	−	0.999482i	$-0.510250\pi$
$331$	−10.1850	−	2.72907i	−0.559820	−	0.150003i	−0.527623	+	0.849478i	$0.676917\pi$
$332$	1.28772	−	2.23039i	0.0706727	−	0.122409i
$333$	12.7781	+	7.37745i	0.700237	+	0.404282i
$334$	0.220795	−	0.824019i	0.0120814	−	0.0450883i
$335$	22.1918	−	22.1918i	1.21247	−	1.21247i
$336$	−5.08104	−	2.45854i	−0.277193	−	0.134124i
$337$			4.39999i			0.239683i	0.992793	+	0.119841i	$0.0382386\pi$
$337$			4.39999i			0.239683i	−0.992793	+	0.119841i	$0.961761\pi$
$338$	0.674368	+	1.16804i	0.0366808	+	0.0635330i
$339$	−6.72074	−	25.0822i	−0.365021	−	1.36228i
$340$	0.622244	+	2.32224i	0.0337459	+	0.125941i
$341$	15.4496	+	4.13972i	0.836645	+	0.224178i
$342$	−7.22141	−	7.22141i	−0.390489	−	0.390489i
$343$	−15.6264	−	9.94065i	−0.843745	−	0.536745i
$344$	10.4482			0.563327
$345$	5.71716	−	21.3367i	0.307802	−	1.14873i
$346$	6.01987	−	10.4267i	0.323630	−	0.560544i
$347$	4.57983	−	1.22716i	0.245858	−	0.0658775i	−0.133785	−	0.991010i	$-0.542713\pi$
$347$	4.57983	−	1.22716i	0.245858	−	0.0658775i	0.379644	+	0.925133i	$0.376047\pi$
$348$	−15.9321	+	9.19839i	−0.854049	+	0.493086i
$349$			24.4435i			1.30843i	0.756308	+	0.654215i	$0.227001\pi$
$349$			24.4435i			1.30843i	−0.756308	+	0.654215i	$0.772999\pi$
$350$	−1.26408	+	0.439686i	−0.0675679	+	0.0235022i
$351$	−10.5475			−0.562985
$352$	−1.19774	+	4.47004i	−0.0638399	+	0.238254i
$353$	−5.73919	+	9.94056i	−0.305466	+	0.529083i	−0.977365	−	0.211560i	$-0.932146\pi$
$353$	−5.73919	+	9.94056i	−0.305466	+	0.529083i	0.671899	+	0.740643i	$0.265479\pi$
$354$	1.01614	−	0.272273i	0.0540070	−	0.0144711i
$355$	4.94438	−	18.4527i	0.262420	−	0.979366i
$356$	1.80397	−	1.80397i	0.0956101	−	0.0956101i
$357$	−4.18454	+	4.84429i	−0.221470	+	0.256387i
$358$	−10.0462	+	10.0462i	−0.530960	+	0.530960i
$359$	−6.94261	−	12.0250i	−0.366417	−	0.634653i	0.622585	−	0.782552i	$-0.286082\pi$
$359$	−6.94261	−	12.0250i	−0.366417	−	0.634653i	−0.989002	+	0.147899i	$0.952749\pi$
$360$	2.84866	+	1.64468i	0.150138	+	0.0866821i
$361$	−21.0628	−	12.1606i	−1.10857	−	0.640031i
$362$	−10.2026	−	2.73378i	−0.536237	−	0.143684i
$363$	15.7131	+	15.7131i	0.824726	+	0.824726i
$364$	7.47120	−	5.07346i	0.391597	−	0.265922i
$365$	23.8937			1.25065
$366$	10.2241	+	2.73954i	0.534422	+	0.143198i
$367$	−0.787789	−	0.454830i	−0.0411222	−	0.0237419i	0.479298	−	0.877652i	$-0.340891\pi$
$367$	−0.787789	−	0.454830i	−0.0411222	−	0.0237419i	−0.520420	+	0.853910i	$0.674225\pi$
$368$	2.44201	−	4.22969i	0.127299	−	0.220488i
$369$	9.88901	−	0.957434i	0.514801	−	0.0498420i
$370$	−20.1592			−1.04803
$371$	−10.3163	+	7.00549i	−0.535596	+	0.363707i
$372$	5.21405	−	5.21405i	0.270336	−	0.270336i
$373$	−13.6681	−	23.6738i	−0.707706	−	1.22578i	−0.965706	−	0.259638i	$-0.916397\pi$
$373$	−13.6681	−	23.6738i	−0.707706	−	1.22578i	0.258000	−	0.966145i	$-0.416936\pi$
$374$	4.54505	+	2.62409i	0.235019	+	0.135688i
$375$	24.0533	−	6.44507i	1.24211	−	0.332822i
$376$	4.10031	+	1.09867i	0.211457	+	0.0566598i
$377$		−	29.4337i		−	1.51591i
$378$	−0.595802	−	8.15374i	−0.0306447	−	0.419383i
$379$	−24.4233			−1.25454			−0.627269	−	0.778802i	$-0.715827\pi$
$379$	−24.4233			−1.25454			−0.627269	+	0.778802i	$0.715827\pi$
$380$	13.4778	+	3.61135i	0.691394	+	0.185258i
$381$	3.81101	+	14.2229i	0.195244	+	0.728660i
$382$	−5.35458	−	19.9836i	−0.273964	−	1.02245i
$383$	4.83616	−	18.0488i	0.247116	−	0.922250i	−0.725192	−	0.688547i	$-0.758249\pi$
$383$	4.83616	−	18.0488i	0.247116	−	0.922250i	0.972308	−	0.233703i	$-0.0750844\pi$
$384$	1.50858	+	1.50858i	0.0769844	+	0.0769844i
$385$	11.3054	−	23.3647i	0.576176	−	1.19078i
$386$	−11.5511	−	11.5511i	−0.587934	−	0.587934i
$387$	−8.10582	−	14.0397i	−0.412042	−	0.713678i
$388$	−4.48725	+	1.20236i	−0.227806	+	0.0610404i
$389$	4.18788	+	2.41787i	0.212334	+	0.122591i	0.602396	−	0.798198i	$-0.294213\pi$
$389$	4.18788	+	2.41787i	0.212334	+	0.122591i	−0.390062	+	0.920789i	$0.627546\pi$
$390$	−13.3698	+	7.71904i	−0.677005	+	0.390869i
$391$	−3.91655	−	3.91655i	−0.198068	−	0.198068i
$392$	4.34406	+	5.48900i	0.219408	+	0.277237i
$393$	24.3644	+	24.3644i	1.22902	+	1.22902i
$394$	8.66102	+	15.0013i	0.436336	+	0.755756i
$395$	21.6044	−	5.78888i	1.08704	−	0.291270i
$396$	6.93583	−	1.85845i	0.348539	−	0.0933906i
$397$	−22.9922	−	6.16074i	−1.15395	−	0.309199i	−0.369400	−	0.929270i	$-0.620437\pi$
$397$	−22.9922	−	6.16074i	−1.15395	−	0.309199i	−0.784545	+	0.620072i	$0.787103\pi$
$398$	−13.7629	+	13.7629i	−0.689869	+	0.689869i
$399$	12.2053	+	35.0899i	0.611031	+	1.75669i
$400$	0.505855			0.0252927
$401$	−6.63886	+	3.83295i	−0.331529	+	0.191408i	−0.656520	−	0.754309i	$-0.727972\pi$
$401$	−6.63886	+	3.83295i	−0.331529	+	0.191408i	0.324991	+	0.945717i	$0.394639\pi$
$402$	−27.3526	−	15.7920i	−1.36422	−	0.787635i
$403$	3.05344	+	11.3956i	0.152103	+	0.567656i
$404$	1.68454	−	6.28677i	0.0838088	−	0.312779i
$405$			23.8437i			1.18480i
$406$	22.7537	−	1.66263i	1.12925	−	0.0825151i
$407$	−31.1173	+	31.1173i	−1.54243	+	1.54243i
$408$	2.09534	−	1.20975i	0.103735	−	0.0598913i
$409$	−4.05133	+	7.01710i	−0.200325	+	0.346973i	−0.948633	−	0.316378i	$-0.897533\pi$
$409$	−4.05133	+	7.01710i	−0.200325	+	0.346973i	0.748308	+	0.663351i	$0.230867\pi$
$410$	−11.0469	+	7.88839i	−0.545566	+	0.389580i
$411$	5.75468	+	9.96740i	0.283858	+	0.491656i
$412$			7.06306i			0.347972i
$413$	−1.28139	−	0.244920i	−0.0630532	−	0.0120517i
$414$	−7.57817			−0.372447
$415$	4.72830	−	2.72989i	0.232103	−	0.134005i
$416$	−3.29709	+	0.883452i	−0.161653	+	0.0433148i
$417$	−6.81799	−	25.4451i	−0.333878	−	1.24605i
$418$	26.3784	−	15.2296i	1.29021	−	0.744903i
$419$		−	26.3572i		−	1.28763i	−0.765180	−	0.643817i	$-0.777350\pi$
$419$		−	26.3572i		−	1.28763i	0.765180	−	0.643817i	$-0.222650\pi$
$420$	−6.72241	−	9.89944i	−0.328020	−	0.483043i
$421$	−6.81394	+	6.81394i	−0.332091	+	0.332091i	−0.853380	−	0.521289i	$-0.825451\pi$
$421$	−6.81394	+	6.81394i	−0.332091	+	0.332091i	0.521289	+	0.853380i	$0.325451\pi$
$422$	−15.8364	−	4.24334i	−0.770902	−	0.206563i
$423$	−1.70473	−	6.36214i	−0.0828868	−	0.309338i
$424$	4.55265	−	1.21988i	0.221096	−	0.0592425i
$425$	0.148478	−	0.554128i	0.00720225	−	0.0268792i
$426$	−19.2254			−0.931474
$427$	−9.93353	−	8.58068i	−0.480717	−	0.415248i
$428$	−6.66566			−0.322197
$429$	−8.72235	+	32.5523i	−0.421119	+	1.57164i
$430$	19.1820	+	11.0747i	0.925039	+	0.534071i
$431$	−14.0013	−	8.08366i	−0.674420	−	0.389376i	0.123330	−	0.992366i	$-0.460643\pi$
$431$	−14.0013	−	8.08366i	−0.674420	−	0.389376i	−0.797749	+	0.602989i	$0.793976\pi$
$432$	−0.799761	+	2.98475i	−0.0384785	+	0.143604i
$433$	30.5827			1.46971			0.734856	−	0.678223i	$-0.237249\pi$
$433$	30.5827			1.46971			0.734856	+	0.678223i	$0.237249\pi$
$434$	−8.63686	+	3.00416i	−0.414583	+	0.144205i
$435$	−39.0001			−1.86991
$436$	2.82493	−	10.5428i	0.135290	−	0.504908i
$437$	−31.0507	+	8.32001i	−1.48536	+	0.398000i
$438$	−6.22357	−	23.2267i	−0.297374	−	1.10981i
$439$	−1.88726	−	0.505691i	−0.0900742	−	0.0241353i	0.213500	−	0.976943i	$-0.431514\pi$
$439$	−1.88726	−	0.505691i	−0.0900742	−	0.0241353i	−0.303575	+	0.952808i	$0.598180\pi$
$440$	−6.93707	+	6.93707i	−0.330712	+	0.330712i
$441$	4.00566	−	10.0958i	0.190746	−	0.480750i
$442$			3.87104i			0.184126i
$443$	−24.2442	+	13.9974i	−1.15188	+	0.665035i	−0.949343	−	0.314240i	$-0.898250\pi$
$443$	−24.2442	+	13.9974i	−1.15188	+	0.665035i	−0.202532	+	0.979276i	$0.564917\pi$
$444$	5.25084	+	19.5964i	0.249194	+	0.930004i
$445$	5.22410	−	1.39979i	0.247646	−	0.0663565i
$446$	−21.1204	+	12.1939i	−1.00008	+	0.577398i
$447$	13.3325			0.630604
$448$	−0.869194	−	2.49890i	−0.0410655	−	0.118062i
$449$		−	1.06642i		−	0.0503275i	−0.999683	−	0.0251638i	$-0.991989\pi$
$449$		−	1.06642i		−	0.0503275i	0.999683	−	0.0251638i	$-0.00801072\pi$
$450$	−0.392449	−	0.679741i	−0.0185002	−	0.0320433i
$451$	−4.87536	+	29.2281i	−0.229572	+	1.37630i
$452$	6.08566	−	10.5407i	0.286245	−	0.495792i
$453$	29.5650	−	17.0693i	1.38908	−	0.801987i
$454$	−7.27422	+	7.27422i	−0.341396	+	0.341396i
$455$	19.0943	−	1.39524i	0.895153	−	0.0654097i
$456$		−	14.0421i		−	0.657584i
$457$	9.24397	−	34.4990i	0.432415	−	1.61379i	−0.314763	−	0.949170i	$-0.601925\pi$
$457$	9.24397	−	34.4990i	0.432415	−	1.61379i	0.747178	−	0.664624i	$-0.231408\pi$
$458$	7.20314	+	26.8825i	0.336580	+	1.25614i
$459$	3.03484	+	1.75216i	0.141654	+	0.0817840i
$460$	8.96668	−	5.17692i	0.418074	−	0.241375i
$461$	4.19652			0.195451			0.0977256	−	0.995213i	$-0.468843\pi$
$461$	4.19652			0.195451			0.0977256	+	0.995213i	$0.468843\pi$
$462$	−25.6571	−	4.90400i	−1.19368	−	0.228155i
$463$	20.0888	−	20.0888i	0.933607	−	0.933607i	−0.0643223	−	0.997929i	$-0.520489\pi$
$463$	20.0888	−	20.0888i	0.933607	−	0.933607i	0.997929	+	0.0643223i	$0.0204886\pi$
$464$	−8.32918	−	2.23180i	−0.386673	−	0.103609i
$465$	15.0993	−	4.04585i	0.700215	−	0.187622i
$466$	−6.27358	+	1.68100i	−0.290618	+	0.0778709i
$467$	2.46726	+	4.27341i	0.114171	+	0.197750i	0.917448	−	0.397856i	$-0.130246\pi$
$467$	2.46726	+	4.27341i	0.114171	+	0.197750i	−0.803277	+	0.595606i	$0.796912\pi$
$468$	3.74506	+	3.74506i	0.173115	+	0.173115i
$469$	22.0041	+	32.4033i	1.01605	+	1.49624i
$470$	6.36328	+	6.36328i	0.293516	+	0.293516i
$471$	−31.2171	+	18.0232i	−1.43841	+	0.830465i
$472$	0.427027	+	0.246544i	0.0196555	+	0.0113481i
$473$	46.7037	−	12.5142i	2.14744	−	0.575404i
$474$	−11.2546	−	19.4935i	−0.516939	−	0.895364i
$475$	−2.35430	−	2.35430i	−0.108022	−	0.108022i
$476$	−2.99249	+	0.218665i	−0.137161	+	0.0100225i
$477$	−5.17121	−	5.17121i	−0.236773	−	0.236773i
$478$	−6.85215	+	25.5726i	−0.313410	+	1.16966i
$479$	1.06851	+	3.98774i	0.0488215	+	0.182204i	0.986031	−	0.166563i	$-0.0532670\pi$
$479$	1.06851	+	3.98774i	0.0488215	+	0.182204i	−0.937209	+	0.348767i	$0.886600\pi$
$480$	1.17059	+	4.36868i	0.0534297	+	0.199402i
$481$	−31.3530	−	8.40102i	−1.42958	−	0.383054i
$482$	12.1520			0.553506
$483$	24.8159	+	12.0076i	1.12916	+	0.546363i
$484$			10.4158i			0.473448i
$485$	−9.51271	−	2.54892i	−0.431950	−	0.115741i
$486$	14.2238	−	3.81125i	0.645204	−	0.172882i
$487$	27.5117	+	15.8839i	1.24667	+	0.719767i	0.970444	−	0.241325i	$-0.0775818\pi$
$487$	27.5117	+	15.8839i	1.24667	+	0.719767i	0.276229	+	0.961092i	$0.410915\pi$
$488$	2.48066	+	4.29663i	0.112294	+	0.194499i
$489$	−15.8294	+	15.8294i	−0.715831	+	0.715831i
$490$	2.15717	+	14.6820i	0.0974509	+	0.663263i
$491$	21.3288			0.962554			0.481277	−	0.876569i	$-0.340173\pi$
$491$	21.3288			0.962554			0.481277	+	0.876569i	$0.340173\pi$
$492$	10.5455	+	8.68379i	0.475430	+	0.391496i
$493$	−4.88955	+	8.46896i	−0.220214	+	0.381423i
$494$	19.4566	+	11.2333i	0.875395	+	0.505409i
$495$	14.7035	+	3.93980i	0.660875	+	0.177081i
$496$	3.45627			0.155191
$497$	21.4616	+	10.3845i	0.962682	+	0.465809i
$498$	−3.88525	−	3.88525i	−0.174102	−	0.174102i
$499$	−8.05489	−	2.15830i	−0.360586	−	0.0966188i	0.0739773	−	0.997260i	$-0.476431\pi$
$499$	−8.05489	−	2.15830i	−0.360586	−	0.0966188i	−0.434564	+	0.900641i	$0.643097\pi$
$500$	10.1083	+	5.83604i	0.452058	+	0.260996i
$501$	−1.57619	−	0.910011i	−0.0704188	−	0.0406563i
$502$	2.23548	+	3.87196i	0.0997743	+	0.172814i
$503$	27.0372	−	27.0372i	1.20553	−	1.20553i	0.233069	−	0.972460i	$-0.425123\pi$
$503$	27.0372	−	27.0372i	1.20553	−	1.20553i	0.972460	−	0.233069i	$-0.0748769\pi$
$504$	−2.68356	+	3.10666i	−0.119535	+	0.138381i
$505$	9.75647	−	9.75647i	0.434157	−	0.434157i
$506$	5.84980	−	21.8318i	0.260056	−	0.970540i
$507$	2.77942	−	0.744743i	0.123438	−	0.0330752i
$508$	−3.45088	+	5.97710i	−0.153108	+	0.265191i
$509$	−6.14741	+	22.9425i	−0.272479	+	1.01691i	0.685032	+	0.728513i	$0.259788\pi$
$509$	−6.14741	+	22.9425i	−0.272479	+	1.01691i	−0.957512	+	0.288394i	$0.906879\pi$
$510$	5.12917			0.227124
$511$	−5.59835	+	29.2899i	−0.247656	+	1.29571i
$512$			1.00000i			0.0441942i
$513$	17.6135	−	10.1691i	0.777653	−	0.448978i
$514$	4.94165	−	1.32411i	0.217967	−	0.0584041i
$515$	−7.48663	+	12.9672i	−0.329900	+	0.571404i
$516$	5.76925	−	21.5311i	0.253977	−	0.947855i
$517$	19.6445			0.863962
$518$	4.72334	−	24.7119i	0.207531	−	1.08578i
$519$	−18.1629	−	18.1629i	−0.797263	−	0.797263i
$520$	−6.98962	−	1.87286i	−0.306515	−	0.0821305i
$521$	0.841174	+	3.13930i	0.0368525	+	0.137535i	0.981901	−	0.189395i	$-0.0606525\pi$
$521$	0.841174	+	3.13930i	0.0368525	+	0.137535i	−0.945049	+	0.326930i	$0.893986\pi$
$522$	3.46292	+	12.9238i	0.151568	+	0.565658i
$523$	−4.52386	−	7.83555i	−0.197814	−	0.342625i	0.750005	−	0.661432i	$-0.230051\pi$
$523$	−4.52386	−	7.83555i	−0.197814	−	0.342625i	−0.947820	+	0.318807i	$0.896718\pi$
$524$			16.1505i			0.705539i
$525$	0.208088	+	2.84775i	0.00908170	+	0.124286i
$526$	12.8252	−	12.8252i	0.559205	−	0.559205i
$527$	1.01448	−	3.78610i	0.0441915	−	0.164925i
$528$	8.55030	+	4.93652i	0.372104	+	0.214834i
$529$	−0.426830	+	0.739292i	−0.0185578	+	0.0321431i
$530$	9.65134	+	2.58607i	0.419227	+	0.112332i
$531$		−	0.765088i		−	0.0332020i
$532$	−7.58481	+	15.6754i	−0.328843	+	0.679616i
$533$	−20.4683	+	7.66500i	−0.886579	+	0.332008i
$534$	−2.72143	−	4.71365i	−0.117768	−	0.203980i
$535$	−12.2376	−	7.06540i	−0.529079	−	0.305464i
$536$	−3.83161	−	14.2998i	−0.165500	−	0.617655i
$537$	15.1555	+	26.2502i	0.654010	+	1.13278i
$538$		−	2.91666i		−	0.125746i
$539$	25.9925	+	19.3330i	1.11958	+	0.832731i
$540$	−4.63204	+	4.63204i	−0.199331	+	0.199331i
$541$	−9.35914	+	5.40350i	−0.402381	+	0.232315i	−0.687511	−	0.726174i	$-0.741297\pi$
$541$	−9.35914	+	5.40350i	−0.402381	+	0.232315i	0.285130	+	0.958489i	$0.407963\pi$
$542$	−7.56991	−	4.37049i	−0.325155	−	0.187728i
$543$	−11.2673	+	19.5156i	−0.483527	+	0.837494i
$544$	1.09543	+	0.293519i	0.0469661	+	0.0125845i
$545$	16.3614	−	16.3614i	0.700845	−	0.700845i
$546$	−6.32975	−	18.1978i	−0.270888	−	0.778794i
$547$	−11.3214	−	11.3214i	−0.484069	−	0.484069i	0.422359	−	0.906428i	$-0.361202\pi$
$547$	−11.3214	−	11.3214i	−0.484069	−	0.484069i	−0.906428	+	0.422359i	$0.861202\pi$
$548$	−1.39625	+	5.21089i	−0.0596450	+	0.222598i
$549$	3.84906	−	6.66677i	0.164274	−	0.284531i
$550$	2.26119	−	0.605884i	0.0964175	−	0.0258350i
$551$	28.3778	+	49.1518i	1.20894	+	2.09394i
$552$	−7.36794	−	7.36794i	−0.313600	−	0.313600i
$553$	2.03429	+	27.8399i	0.0865068	+	1.18387i
$554$		−	27.0300i		−	1.14839i
$555$	−11.1315	+	41.5432i	−0.472504	+	1.76341i
$556$	6.17372	−	10.6932i	0.261824	−	0.453492i
$557$	10.0181	−	2.68435i	0.424481	−	0.113739i	−0.0402531	−	0.999190i	$-0.512816\pi$
$557$	10.0181	−	2.68435i	0.424481	−	0.113739i	0.464735	+	0.885450i	$0.346150\pi$
$558$	−2.68142	−	4.64435i	−0.113513	−	0.196611i
$559$	25.2180	+	25.2180i	1.06661	+	1.06661i
$560$	1.05299	−	5.50910i	0.0444968	−	0.232802i
$561$	7.91729	−	7.91729i	0.334268	−	0.334268i
$562$	13.6566	+	3.65927i	0.576069	+	0.154357i
$563$	−0.594054	−	2.21704i	−0.0250364	−	0.0934371i	0.952277	−	0.305235i	$-0.0987349\pi$
$563$	−0.594054	−	2.21704i	−0.0250364	−	0.0934371i	−0.977314	+	0.211798i	$0.932068\pi$
$564$	4.52820	−	7.84307i	0.190672	−	0.330253i
$565$	22.3456	−	12.9012i	0.940086	−	0.542759i
$566$			11.9658i			0.502961i
$567$	−29.2285	−	5.58662i	−1.22748	−	0.234616i
$568$	−6.37202	−	6.37202i	−0.267364	−	0.267364i
$569$	−18.9448	+	10.9378i	−0.794205	+	0.458535i	−0.841441	−	0.540349i	$-0.818292\pi$
$569$	−18.9448	+	10.9378i	−0.794205	+	0.458535i	0.0472356	+	0.998884i	$0.484959\pi$
$570$	14.8843	−	25.7803i	0.623433	−	1.07982i
$571$	−3.29200	−	12.2859i	−0.137766	−	0.514150i	−0.999971	−	0.00759063i	$-0.997584\pi$
$571$	−3.29200	−	12.2859i	−0.137766	−	0.514150i	0.862205	−	0.506559i	$-0.169083\pi$
$572$	−13.6800	+	7.89813i	−0.571988	+	0.330237i
$573$	−44.1380			−1.84389
$574$	−7.08160	−	15.3900i	−0.295580	−	0.642365i
$575$	−2.47061			−0.103031
$576$	1.34375	−	0.775813i	0.0559895	−	0.0323255i
$577$	2.47562	+	9.23916i	0.103062	+	0.384631i	0.998118	−	0.0613218i	$-0.0195316\pi$
$577$	2.47562	+	9.23916i	0.103062	+	0.384631i	−0.895056	+	0.445953i	$0.852865\pi$
$578$	−7.85694	+	13.6086i	−0.326806	+	0.566044i
$579$	−30.1822	+	17.4257i	−1.25433	+	0.724188i
$580$	−12.9261	−	12.9261i	−0.536727	−	0.536727i
$581$	2.23855	+	6.43576i	0.0928708	+	0.267000i
$582$			9.91106i			0.410827i
$583$	18.8894	−	10.9058i	0.782319	−	0.451672i
$584$	5.63547	−	9.76092i	0.233197	−	0.403910i
$585$	2.90598	+	10.8453i	0.120148	+	0.448397i
$586$	−4.53737	−	1.21578i	−0.187437	−	0.0502236i
$587$	8.66154	−	8.66154i	0.357500	−	0.357500i	−0.505391	−	0.862891i	$-0.668652\pi$
$587$	8.66154	−	8.66154i	0.357500	−	0.357500i	0.862891	+	0.505391i	$0.168652\pi$
$588$	13.7102	−	5.92114i	0.565399	−	0.244184i
$589$	−16.0858	−	16.0858i	−0.662803	−	0.662803i
$590$	0.522658	+	0.905271i	0.0215175	+	0.0372694i
$591$	35.6966	−	9.56486i	1.46836	−	0.393446i
$592$	−4.75466	+	8.23531i	−0.195415	+	0.338469i
$593$	11.8181	−	44.1059i	0.485312	−	1.81121i	−0.0933381	−	0.995634i	$-0.529754\pi$
$593$	11.8181	−	44.1059i	0.485312	−	1.81121i	0.578650	−	0.815576i	$-0.303580\pi$
$594$			14.2999i			0.586730i
$595$	−5.72576	−	2.77050i	−0.234733	−	0.113580i
$596$	4.41888	+	4.41888i	0.181004	+	0.181004i
$597$	20.7624	+	35.9615i	0.849747	+	1.47180i
$598$	16.1030	−	4.31480i	0.658502	−	0.176445i
$599$	−6.44386	+	11.1611i	−0.263289	+	0.456030i	−0.967114	−	0.254344i	$-0.918141\pi$
$599$	−6.44386	+	11.1611i	−0.263289	+	0.456030i	0.703825	+	0.710373i	$0.251474\pi$
$600$	0.279322	−	1.04244i	0.0114033	−	0.0425576i
$601$	−27.6279	−	27.6279i	−1.12697	−	1.12697i	−0.990668	−	0.136300i	$-0.956479\pi$
$601$	−27.6279	−	27.6279i	−1.12697	−	1.12697i	−0.136300	−	0.990668i	$-0.543521\pi$
$602$	−18.0702	+	20.9192i	−0.736488	+	0.852605i
$603$	−16.2427	+	16.2427i	−0.661452	+	0.661452i
$604$	15.4564	+	4.14152i	0.628910	+	0.168516i
$605$	−11.0405	+	19.1227i	−0.448860	+	0.777448i
$606$	−12.0254	−	6.94284i	−0.488497	−	0.282034i
$607$	−16.7172	+	9.65170i	−0.678532	+	0.391750i	−0.799302	−	0.600930i	$-0.794797\pi$
$607$	−16.7172	+	9.65170i	−0.678532	+	0.391750i	0.120770	+	0.992681i	$0.461464\pi$
$608$	4.65409	−	4.65409i	0.188748	−	0.188748i
$609$	9.13780	−	47.8079i	0.370282	−	1.93727i
$610$			10.5177i			0.425850i
$611$	7.24484	+	12.5484i	0.293095	+	0.507655i
$612$	−0.455432	−	1.69970i	−0.0184098	−	0.0687062i
$613$	8.91886	+	5.14931i	0.360230	+	0.207979i	0.669181	−	0.743099i	$-0.266645\pi$
$613$	8.91886	+	5.14931i	0.360230	+	0.207979i	−0.308952	+	0.951078i	$0.599978\pi$
$614$	−5.03984	−	8.72927i	−0.203392	−	0.352284i
$615$	10.1562	+	27.1207i	0.409538	+	1.09361i
$616$	−6.87837	−	10.1291i	−0.277138	−	0.408114i
$617$		−	35.9025i		−	1.44538i	−0.691172	−	0.722690i	$-0.742905\pi$
$617$		−	35.9025i		−	1.44538i	0.691172	−	0.722690i	$-0.257095\pi$
$618$	14.5553	+	3.90007i	0.585498	+	0.156884i
$619$	14.9831	−	25.9514i	0.602220	−	1.04308i	−0.390264	−	0.920703i	$-0.627616\pi$
$619$	14.9831	−	25.9514i	0.602220	−	1.04308i	0.992484	−	0.122373i	$-0.0390503\pi$
$620$	6.34543	+	3.66354i	0.254839	+	0.147131i
$621$	3.90605	−	14.5776i	0.156744	−	0.584978i
$622$	0.660372	−	0.660372i	0.0264785	−	0.0264785i
$623$	0.491905	+	6.73188i	0.0197078	+	0.269707i
$624$			7.28232i			0.291526i
$625$	11.1074	+	19.2386i	0.444297	+	0.769545i
$626$	7.59022	+	28.3271i	0.303366	+	1.13218i
$627$	−16.8189	−	62.7689i	−0.671682	−	2.50675i
$628$	−16.3201	−	4.37295i	−0.651242	−	0.174500i
$629$	7.62562	+	7.62562i	0.304053	+	0.304053i
$630$	−8.21977	+	2.85909i	−0.327483	+	0.113909i
$631$	11.6027			0.461896			0.230948	−	0.972966i	$-0.425817\pi$
$631$	11.6027			0.461896			0.230948	+	0.972966i	$0.425817\pi$
$632$	2.73068	−	10.1910i	0.108621	−	0.405378i
$633$	−17.4890	+	30.2918i	−0.695126	+	1.20399i
$634$	18.7256	−	5.01751i	0.743689	−	0.199271i
$635$	−12.6711	+	7.31566i	−0.502837	+	0.290313i
$636$		−	10.0555i		−	0.398726i
$637$	−2.76349	+	23.7334i	−0.109493	+	0.940352i
$638$	−39.9049			−1.57985
$639$	−3.61889	+	13.5059i	−0.143161	+	0.534284i
$640$	−1.05997	+	1.83592i	−0.0418990	+	0.0725712i
$641$	−16.5772	+	4.44186i	−0.654762	+	0.175443i	−0.570881	−	0.821033i	$-0.693398\pi$
$641$	−16.5772	+	4.44186i	−0.654762	+	0.175443i	−0.0838810	+	0.996476i	$0.526732\pi$
$642$	−3.68064	+	13.7363i	−0.145263	+	0.542129i
$643$	16.2223	−	16.2223i	0.639743	−	0.639743i	−0.310749	−	0.950492i	$-0.600580\pi$
$643$	16.2223	−	16.2223i	0.639743	−	0.639743i	0.950492	+	0.310749i	$0.100580\pi$
$644$	4.24516	+	12.2047i	0.167283	+	0.480932i
$645$	33.4142	−	33.4142i	1.31568	−	1.31568i
$646$	−3.73216	−	6.46430i	−0.146840	−	0.254334i
$647$	27.4319	+	15.8378i	1.07846	+	0.622649i	0.930481	−	0.366341i	$-0.119390\pi$
$647$	27.4319	+	15.8378i	1.07846	+	0.622649i	0.147980	+	0.988990i	$0.452723\pi$
$648$	9.74048	+	5.62367i	0.382642	+	0.220919i
$649$	2.20412	+	0.590593i	0.0865194	+	0.0231828i
$650$	1.22095	+	1.22095i	0.0478895	+	0.0478895i
$651$	1.42177	+	19.4573i	0.0557234	+	0.762593i
$652$	−10.4929			−0.410935
$653$	−14.9047	−	3.99370i	−0.583265	−	0.156285i	−0.0448919	−	0.998992i	$-0.514294\pi$
$653$	−14.9047	−	3.99370i	−0.583265	−	0.156285i	−0.538373	+	0.842706i	$0.680961\pi$
$654$	−20.1663	−	11.6430i	−0.788563	−	0.455277i
$655$	−17.1191	+	29.6511i	−0.668898	+	1.15856i
$656$	0.617052	+	6.37332i	0.0240918	+	0.248836i
$657$	−17.4883			−0.682283
$658$	−9.29129	+	6.30943i	−0.362212	+	0.245967i
$659$	−9.90890	+	9.90890i	−0.385996	+	0.385996i	−0.873257	−	0.487261i	$-0.837996\pi$
$659$	−9.90890	+	9.90890i	−0.385996	+	0.385996i	0.487261	+	0.873257i	$0.337996\pi$
$660$	10.4651	+	18.1261i	0.407354	+	0.705559i
$661$	−23.1526	−	13.3672i	−0.900534	−	0.519923i	−0.0231603	−	0.999732i	$-0.507373\pi$
$661$	−23.1526	−	13.3672i	−0.900534	−	0.519923i	−0.877373	+	0.479808i	$0.840706\pi$
$662$	−10.1850	+	2.72907i	−0.395852	+	0.106068i
$663$	7.97727	+	2.13750i	0.309811	+	0.0830137i
$664$		−	2.57544i		−	0.0999463i
$665$	−30.5406	+	20.7392i	−1.18431	+	0.804231i
$666$	14.7549			0.571741
$667$	40.6799	+	10.9001i	1.57513	+	0.422055i
$668$	−0.220795	−	0.824019i	−0.00854282	−	0.0318823i
$669$	13.4664	+	50.2573i	0.520642	+	1.94306i
$670$	8.12278	−	30.3146i	0.313810	−	1.17116i
$671$	16.2349	+	16.2349i	0.626742	+	0.626742i
$672$	−5.62958	+	0.411359i	−0.217166	+	0.0158685i
$673$	5.71979	+	5.71979i	0.220482	+	0.220482i	0.808701	−	0.588220i	$-0.200171\pi$
$673$	5.71979	+	5.71979i	0.220482	+	0.220482i	−0.588220	+	0.808701i	$0.700171\pi$
$674$	2.20000	+	3.81051i	0.0847407	+	0.146775i
$675$	1.50985	−	0.404563i	0.0581141	−	0.0155716i
$676$	1.16804	+	0.674368i	0.0449246	+	0.0259372i
$677$	−40.9650	+	23.6512i	−1.57441	+	0.908988i	−0.578795	+	0.815473i	$0.696477\pi$
$677$	−40.9650	+	23.6512i	−1.57441	+	0.908988i	−0.995618	+	0.0935151i	$0.970190\pi$
$678$	−18.3614	−	18.3614i	−0.705166	−	0.705166i
$679$	5.35342	−	11.0638i	0.205445	−	0.424591i
$680$	1.70000	+	1.70000i	0.0651921	+	0.0651921i
$681$	10.9737	+	19.0071i	0.420515	+	0.728353i
$682$	15.4496	−	4.13972i	0.591598	−	0.158518i
$683$	−33.4605	+	8.96572i	−1.28033	+	0.343064i	−0.833980	−	0.551794i	$-0.813943\pi$
$683$	−33.4605	+	8.96572i	−1.28033	+	0.343064i	−0.446351	+	0.894858i	$0.647277\pi$
$684$	−9.86463	−	2.64322i	−0.377184	−	0.101066i
$685$	−8.08680	+	8.08680i	−0.308981	+	0.308981i
$686$	−18.5032	−	0.795668i	−0.706454	−	0.0303787i
$687$	59.3757			2.26532
$688$	9.04837	−	5.22408i	0.344966	−	0.199166i
$689$	13.9328	+	8.04409i	0.530796	+	0.306455i
$690$	−5.71716	−	21.3367i	−0.217649	−	0.812276i
$691$	−8.15024	+	30.4171i	−0.310050	+	1.15712i	0.618461	+	0.785815i	$0.287756\pi$
$691$	−8.15024	+	30.4171i	−0.310050	+	1.15712i	−0.928511	+	0.371306i	$0.878910\pi$
$692$		−	12.0397i		−	0.457682i
$693$	−8.27464	+	17.1011i	−0.314328	+	0.649617i
$694$	3.35267	−	3.35267i	0.127266	−	0.127266i
$695$	22.6689	−	13.0879i	0.859882	−	0.496453i
$696$	−9.19839	+	15.9321i	−0.348664	+	0.603904i
$697$	7.16264	+	1.19476i	0.271304	+	0.0452546i
$698$	12.2217	+	21.1687i	0.462600	+	0.801247i
$699$			13.8566i			0.524103i
$700$	−0.874883	+	1.01282i	−0.0330675	+	0.0382810i
$701$	−27.6406			−1.04397			−0.521986	−	0.852954i	$-0.674809\pi$
$701$	−27.6406			−1.04397			−0.521986	+	0.852954i	$0.674809\pi$
$702$	−9.13442	+	5.27376i	−0.344757	+	0.199045i
$703$	60.4565	−	16.1993i	2.28016	−	0.610967i
$704$	1.19774	+	4.47004i	0.0451417	+	0.168471i
$705$	16.6268	−	9.59951i	0.626203	−	0.361539i
$706$			11.4784i			0.431994i
$707$	9.67391	+	14.2458i	0.363825	+	0.535770i
$708$	0.743862	−	0.743862i	0.0279561	−	0.0279561i
$709$	−12.1134	−	3.24577i	−0.454928	−	0.121897i	0.0240765	−	0.999710i	$-0.492335\pi$
$709$	−12.1134	−	3.24577i	−0.454928	−	0.121897i	−0.479004	+	0.877813i	$0.659002\pi$
$710$	−4.94438	−	18.4527i	−0.185559	−	0.692517i
$711$	−15.8127	+	4.23700i	−0.593022	+	0.158900i
$712$	0.660298	−	2.46427i	0.0247457	−	0.0923523i
$713$	−16.8805			−0.632179
$714$	−1.20178	+	6.28755i	−0.0449753	+	0.235306i
$715$	−33.4871			−1.25235
$716$	−3.67718	+	13.7234i	−0.137422	+	0.512868i
$717$	48.9153	+	28.2412i	1.82677	+	1.05469i
$718$	−12.0250	−	6.94261i	−0.448767	−	0.259096i
$719$	1.64005	−	6.12073i	0.0611634	−	0.228265i	−0.928578	−	0.371138i	$-0.878968\pi$
$719$	1.64005	−	6.12073i	0.0611634	−	0.228265i	0.989741	+	0.142874i	$0.0456342\pi$
$720$	3.28935			0.122587
$721$	−14.1416	−	12.2157i	−0.526661	−	0.454935i
$722$	−24.3212			−0.905141
$723$	6.71005	−	25.0422i	0.249549	−	0.931331i
$724$	−10.2026	+	2.73378i	−0.379177	+	0.101600i
$725$	1.12897	+	4.21336i	0.0419287	+	0.156480i
$726$	21.4645	+	5.75141i	0.796624	+	0.213455i
$727$	17.1340	−	17.1340i	0.635465	−	0.635465i	−0.313968	−	0.949433i	$-0.601659\pi$
$727$	17.1340	−	17.1340i	0.635465	−	0.635465i	0.949433	+	0.313968i	$0.101659\pi$
$728$	3.93352	−	8.12935i	0.145786	−	0.301294i
$729$			2.32571i			0.0861376i
$730$	20.6926	−	11.9469i	0.765866	−	0.442173i
$731$	−3.06674	−	11.4452i	−0.113427	−	0.423317i
$732$	10.2241	−	2.73954i	0.377893	−	0.101256i
$733$	−4.23448	+	2.44478i	−0.156404	+	0.0902999i	−0.576159	−	0.817337i	$-0.695449\pi$
$733$	−4.23448	+	2.44478i	−0.156404	+	0.0902999i	0.419755	+	0.907637i	$0.362116\pi$
$734$	−0.909660			−0.0335762
$735$	31.4471	+	3.66166i	1.15994	+	0.135062i
$736$		−	4.88402i		−	0.180027i
$737$	−34.2549	−	59.3312i	−1.26180	−	2.18549i
$738$	8.08542	−	5.77367i	0.297628	−	0.212532i
$739$	12.0799	−	20.9230i	0.444367	−	0.769666i	−0.553641	−	0.832755i	$-0.686762\pi$
$739$	12.0799	−	20.9230i	0.444367	−	0.769666i	0.998008	+	0.0630897i	$0.0200954\pi$
$740$	−17.4584	+	10.0796i	−0.641782	+	0.370533i
$741$	33.8926	−	33.8926i	1.24508	−	1.24508i
$742$	−5.43143	+	11.2251i	−0.199394	+	0.412086i
$743$			11.5997i			0.425551i	0.977101	+	0.212775i	$0.0682502\pi$
$743$			11.5997i			0.425551i	−0.977101	+	0.212775i	$0.931750\pi$
$744$	1.90848	−	7.12253i	0.0699681	−	0.261125i
$745$	3.42884	+	12.7966i	0.125623	+	0.468831i
$746$	−23.6738	−	13.6681i	−0.866759	−	0.500424i
$747$	−3.46074	+	1.99806i	−0.126622	+	0.0731051i
$748$	5.24817			0.191892
$749$	11.5284	−	13.3460i	0.421237	−	0.487650i
$750$	17.6083	−	17.6083i	0.642963	−	0.642963i
$751$	−36.8318	−	9.86905i	−1.34401	−	0.360127i	−0.486090	−	0.873909i	$-0.661577\pi$
$751$	−36.8318	−	9.86905i	−1.34401	−	0.360127i	−0.857921	+	0.513782i	$0.828244\pi$
$752$	4.10031	−	1.09867i	0.149523	−	0.0400645i
$753$	9.21356	−	2.46877i	0.335761	−	0.0899669i
$754$	−14.7169	−	25.4903i	−0.535956	−	0.928304i
$755$	23.9868	+	23.9868i	0.872968	+	0.872968i
$756$	−4.59285	−	6.76344i	−0.167040	−	0.245984i
$757$	−16.3302	−	16.3302i	−0.593532	−	0.593532i	0.345052	−	0.938584i	$-0.387861\pi$
$757$	−16.3302	−	16.3302i	−0.593532	−	0.593532i	−0.938584	+	0.345052i	$0.887861\pi$
$758$	−21.1512	+	12.2116i	−0.768245	+	0.443546i
$759$	−41.7599	−	24.1101i	−1.51579	−	0.875140i
$760$	13.4778	−	3.61135i	0.488889	−	0.130998i
$761$	−1.84905	−	3.20264i	−0.0670278	−	0.116096i	0.830564	−	0.556923i	$-0.188018\pi$
$761$	−1.84905	−	3.20264i	−0.0670278	−	0.116096i	−0.897592	+	0.440828i	$0.854685\pi$
$762$	10.4119	+	10.4119i	0.377182	+	0.377182i
$763$	16.2229	+	23.8899i	0.587310	+	0.864874i
$764$	−14.6290	−	14.6290i	−0.529258	−	0.529258i
$765$	0.965489	−	3.60325i	0.0349073	−	0.130276i
$766$	−4.83616	−	18.0488i	−0.174737	−	0.652129i
$767$	0.435619	+	1.62575i	0.0157293	+	0.0587025i
$768$	2.06076	+	0.552179i	0.0743612	+	0.0199250i
$769$	12.0760			0.435470			0.217735	−	0.976008i	$-0.430133\pi$
$769$	12.0760			0.435470			0.217735	+	0.976008i	$0.430133\pi$
$770$	−1.89160	−	25.8871i	−0.0681685	−	0.932907i
$771$		−	10.9147i		−	0.393083i
$772$	−15.7791	−	4.22799i	−0.567901	−	0.152169i
$773$	28.9167	−	7.74821i	1.04006	−	0.278684i	0.301923	−	0.953332i	$-0.402372\pi$
$773$	28.9167	−	7.74821i	1.04006	−	0.278684i	0.738139	+	0.674649i	$0.235705\pi$
$774$	−14.0397	−	8.10582i	−0.504646	−	0.291358i
$775$	−0.874184	−	1.51413i	−0.0314016	−	0.0543892i
$776$	−3.28490	+	3.28490i	−0.117921	+	0.117921i
$777$	−48.3172	−	23.3791i	−1.73337	−	0.838719i
$778$	4.83575			0.173370
$779$	26.7902	−	32.5339i	0.959859	−	1.16565i
$780$	−7.71904	+	13.3698i	−0.276386	+	0.478715i
$781$	−36.1152	−	20.8511i	−1.29230	−	0.746112i
$782$	−5.35010	−	1.43356i	−0.191319	−	0.0512638i
$783$	−26.6454			−0.952230
$784$	6.50657	+	2.58159i	0.232377	+	0.0921996i
$785$	−25.3272	−	25.3272i	−0.903966	−	0.903966i
$786$	33.2823	+	8.91798i	1.18714	+	0.318094i
$787$	−23.4985	−	13.5669i	−0.837631	−	0.483606i	0.0188275	−	0.999823i	$-0.494007\pi$
$787$	−23.4985	−	13.5669i	−0.837631	−	0.483606i	−0.856458	+	0.516216i	$0.827340\pi$
$788$	15.0013	+	8.66102i	0.534400	+	0.308536i
$789$	−19.3478	−	33.5114i	−0.688801	−	1.19304i
$790$	15.8155	−	15.8155i	0.562691	−	0.562691i
$791$	10.5792	+	30.4149i	0.376154	+	1.08143i
$792$	5.07738	−	5.07738i	0.180417	−	0.180417i
$793$	−4.38309	+	16.3579i	−0.155648	+	0.580886i
$794$	−22.9922	+	6.16074i	−0.815962	+	0.218636i
$795$	10.6585	−	18.4611i	0.378019	−	0.654748i
$796$	−5.03755	+	18.8004i	−0.178551	+	0.666363i
$797$	−22.3661			−0.792248			−0.396124	−	0.918197i	$-0.629645\pi$
$797$	−22.3661			−0.792248			−0.396124	+	0.918197i	$0.629645\pi$
$798$	28.1151	+	24.2861i	0.995264	+	0.859718i
$799$		−	4.81408i		−	0.170310i
$800$	0.438083	−	0.252927i	0.0154886	−	0.00894233i
$801$	−3.82362	+	1.02454i	−0.135101	+	0.0362002i
$802$	−3.83295	+	6.63886i	−0.135346	+	0.234426i
$803$	13.4997	−	50.3815i	0.476394	−	1.77793i
$804$	−31.5841			−1.11388
$805$	−5.14281	+	26.9066i	−0.181260	+	0.948332i
$806$	8.34216	+	8.34216i	0.293840	+	0.293840i
$807$	−6.01054	−	1.61052i	−0.211581	−	0.0566930i
$808$	−1.68454	−	6.28677i	−0.0592618	−	0.221168i
$809$	−3.23980	−	12.0911i	−0.113905	−	0.425100i	0.885297	−	0.465025i	$-0.153955\pi$
$809$	−3.23980	−	12.0911i	−0.113905	−	0.425100i	−0.999203	+	0.0399252i	$0.987288\pi$
$810$	11.9218	+	20.6492i	0.418891	+	0.725540i
$811$			16.8971i			0.593336i	0.954981	+	0.296668i	$0.0958755\pi$
$811$			16.8971i			0.593336i	−0.954981	+	0.296668i	$0.904124\pi$
$812$	18.8739	−	12.8167i	0.662345	−	0.449779i
$813$	−13.1865	+	13.1865i	−0.462469	+	0.462469i
$814$	−11.3897	+	42.5070i	−0.399210	+	1.48987i
$815$	−19.2642	−	11.1222i	−0.674795	−	0.389593i
$816$	1.20975	−	2.09534i	0.0423496	−	0.0733516i
$817$	−66.4253	−	17.7986i	−2.32393	−	0.622695i
$818$			8.10265i			0.283303i
$819$	−13.9755	+	1.02120i	−0.488342	+	0.0356837i
$820$	−5.62267	+	12.3550i	−0.196352	+	0.431455i
$821$	−4.20233	−	7.27865i	−0.146662	−	0.254027i	0.783330	−	0.621607i	$-0.213520\pi$
$821$	−4.20233	−	7.27865i	−0.146662	−	0.254027i	−0.929992	+	0.367580i	$0.880186\pi$
$822$	9.96740	+	5.75468i	0.347653	+	0.200718i
$823$	6.10997	+	22.8027i	0.212980	+	0.794853i	0.986868	+	0.161530i	$0.0516428\pi$
$823$	6.10997	+	22.8027i	0.212980	+	0.794853i	−0.773888	+	0.633323i	$0.781691\pi$
$824$	3.53153	+	6.11679i	0.123027	+	0.213088i
$825$		−	4.99432i		−	0.173880i
$826$	−1.23218	+	0.428589i	−0.0428729	+	0.0149125i
$827$	−7.28926	+	7.28926i	−0.253472	+	0.253472i	−0.822393	−	0.568920i	$-0.807361\pi$
$827$	−7.28926	+	7.28926i	−0.253472	+	0.253472i	0.568920	+	0.822393i	$0.307361\pi$
$828$	−6.56289	+	3.78909i	−0.228076	+	0.131680i
$829$	42.4011	+	24.4803i	1.47265	+	0.850236i	0.999527	−	0.0307590i	$-0.00979242\pi$
$829$	42.4011	+	24.4803i	1.47265	+	0.850236i	0.473125	+	0.880995i	$0.343126\pi$
$830$	2.72989	−	4.72830i	0.0947557	−	0.164122i
$831$	−55.7022	−	14.9254i	−1.93229	−	0.517755i
$832$	−2.41363	+	2.41363i	−0.0836777	+	0.0836777i
$833$	4.73775	−	6.36974i	0.164153	−	0.220698i
$834$	−18.6271	−	18.6271i	−0.645004	−	0.645004i
$835$	0.468073	−	1.74687i	0.0161983	−	0.0604530i
$836$	15.2296	−	26.3784i	0.526726	−	0.912316i
$837$	10.3161	−	2.76419i	0.356576	−	0.0955443i
$838$	−13.1786	−	22.8260i	−0.455247	−	0.788511i
$839$	8.53420	+	8.53420i	0.294633	+	0.294633i	0.838907	−	0.544274i	$-0.183195\pi$
$839$	8.53420	+	8.53420i	0.294633	+	0.294633i	−0.544274	+	0.838907i	$0.683195\pi$
$840$	−10.7715	−	5.21196i	−0.371652	−	0.179830i
$841$		−	45.3562i		−	1.56401i
$842$	−2.49408	+	9.30802i	−0.0859515	+	0.320775i
$843$	15.0818	−	26.1224i	0.519443	−	0.899702i
$844$	−15.8364	+	4.24334i	−0.545110	+	0.146062i
$845$	1.42962	+	2.47618i	0.0491804	+	0.0851830i
$846$	−4.65741	−	4.65741i	−0.160125	−	0.160125i
$847$	−20.8545	−	18.0144i	−0.716571	−	0.618981i
$848$	3.33277	−	3.33277i	0.114448	−	0.114448i
$849$	24.6587	+	6.60727i	0.846283	+	0.226761i
$850$	−0.148478	−	0.554128i	−0.00509276	−	0.0190064i
$851$	23.2218	−	40.2214i	0.796035	−	1.37877i
$852$	−16.6497	+	9.61270i	−0.570409	+	0.329326i
$853$			8.11516i			0.277858i	0.990302	+	0.138929i	$0.0443660\pi$
$853$			8.11516i			0.277858i	−0.990302	+	0.138929i	$0.955634\pi$
$854$	−12.8930	−	2.46432i	−0.441190	−	0.0843273i
$855$	−15.3090	−	15.3090i	−0.523555	−	0.523555i
$856$	−5.77263	+	3.33283i	−0.197305	+	0.113914i
$857$	3.67268	−	6.36126i	0.125456	−	0.217297i	−0.796455	−	0.604698i	$-0.793294\pi$
$857$	3.67268	−	6.36126i	0.125456	−	0.217297i	0.921911	+	0.387401i	$0.126627\pi$
$858$	8.72235	+	32.5523i	0.297776	+	1.11132i
$859$	9.24793	−	5.33929i	0.315535	−	0.182174i	−0.333866	−	0.942621i	$-0.608353\pi$
$859$	9.24793	−	5.33929i	0.315535	−	0.182174i	0.649401	+	0.760446i	$0.275020\pi$
$860$	22.1495			0.755291
$861$	−35.6253	+	6.09547i	−1.21411	+	0.207733i
$862$	−16.1673			−0.550661
$863$	21.2822	−	12.2873i	0.724454	−	0.418264i	−0.0919359	−	0.995765i	$-0.529305\pi$
$863$	21.2822	−	12.2873i	0.724454	−	0.418264i	0.816390	+	0.577501i	$0.195972\pi$
$864$	0.799761	+	2.98475i	0.0272084	+	0.101543i
$865$	12.7618	−	22.1040i	0.433913	−	0.751559i
$866$	26.4854	−	15.2914i	0.900012	−	0.519622i
$867$	23.7056	+	23.7056i	0.805086	+	0.805086i
$868$	−5.97766	+	6.92012i	−0.202895	+	0.234884i
$869$		−	48.8250i		−	1.65628i
$870$	−33.7751	+	19.5000i	−1.14508	+	0.661113i
$871$	25.2663	−	43.7625i	0.856115	−	1.48284i
$872$	−2.82493	−	10.5428i	−0.0956642	−	0.357024i
$873$	6.96254	+	1.86561i	0.235646	+	0.0631412i
$874$	−22.7307	+	22.7307i	−0.768877	+	0.768877i
$875$	−29.1674	+	10.1453i	−0.986037	+	0.342974i
$876$	−17.0031	−	17.0031i	−0.574482	−	0.574482i
$877$	20.6606	+	35.7852i	0.697659	+	1.20838i	0.969276	+	0.245976i	$0.0791084\pi$
$877$	20.6606	+	35.7852i	0.697659	+	1.20838i	−0.271617	+	0.962406i	$0.587558\pi$
$878$	−1.88726	+	0.505691i	−0.0636921	+	0.0170662i
$879$	−5.01087	+	8.67909i	−0.169013	+	0.292738i
$880$	−2.53914	+	9.47622i	−0.0855945	+	0.319443i
$881$			19.1702i			0.645861i	0.946423	+	0.322930i	$0.104668\pi$
$881$			19.1702i			0.645861i	−0.946423	+	0.322930i	$0.895332\pi$
$882$	−1.57887	−	10.7460i	−0.0531635	−	0.361837i
$883$	−20.2359	−	20.2359i	−0.680992	−	0.680992i	0.279232	−	0.960224i	$-0.409920\pi$
$883$	−20.2359	−	20.2359i	−0.680992	−	0.680992i	−0.960224	+	0.279232i	$0.909920\pi$
$884$	1.93552	+	3.35241i	0.0650985	+	0.112754i
$885$	2.15415	−	0.577201i	0.0724108	−	0.0194024i
$886$	−13.9974	+	24.2442i	−0.470251	+	0.814499i
$887$	6.63073	−	24.7462i	0.222638	−	0.830897i	−0.760699	−	0.649105i	$-0.775144\pi$
$887$	6.63073	−	24.7462i	0.222638	−	0.830897i	0.983337	−	0.181792i	$-0.0581897\pi$
$888$	14.3456	+	14.3456i	0.481406	+	0.481406i
$889$	−5.99897	−	17.2468i	−0.201199	−	0.578440i
$890$	3.82430	−	3.82430i	0.128191	−	0.128191i
$891$	50.2760	+	13.4714i	1.68431	+	0.451310i
$892$	−12.1939	+	21.1204i	−0.408282	+	0.707165i
$893$	−24.1965	−	13.9699i	−0.809706	−	0.467484i
$894$	11.5463	−	6.66623i	0.386165	−	0.222952i
$895$	−21.2974	+	21.2974i	−0.711894	+	0.711894i
$896$	−2.00219	−	1.72951i	−0.0668886	−	0.0577790i
$897$		−	35.5670i		−	1.18755i
$898$	−0.533210	−	0.923548i	−0.0177935	−	0.0308192i
$899$	7.71369	+	28.7879i	0.257266	+	0.960129i
$900$	−0.679741	−	0.392449i	−0.0226580	−	0.0130816i
$901$	−2.67258	−	4.62905i	−0.0890366	−	0.154216i
$902$	10.3919	+	27.7499i	0.346011	+	0.923972i
$903$	33.1315	+	48.7896i	1.10255	+	1.62361i
$904$		−	12.1713i		−	0.404812i
$905$	−21.6289	−	5.79545i	−0.718970	−	0.192647i
$906$	17.0693	−	29.5650i	0.567091	−	0.982230i
$907$	31.3645	+	18.1083i	1.04144	+	0.601277i	0.920242	−	0.391351i	$-0.127992\pi$
$907$	31.3645	+	18.1083i	1.04144	+	0.601277i	0.121201	+	0.992628i	$0.461325\pi$
$908$	−2.66255	+	9.93677i	−0.0883598	+	0.329763i
$909$	−7.14095	+	7.14095i	−0.236850	+	0.236850i
$910$	15.8385	−	10.7554i	0.525041	−	0.356539i
$911$			27.0328i			0.895635i	0.894125	+	0.447818i	$0.147799\pi$
$911$			27.0328i			0.895635i	−0.894125	+	0.447818i	$0.852201\pi$
$912$	−7.02107	−	12.1609i	−0.232491	−	0.402686i
$913$	−3.08471	−	11.5123i	−0.102089	−	0.381002i
$914$	−9.24397	−	34.4990i	−0.305763	−	1.14112i
$915$	21.6745	+	5.80765i	0.716535	+	0.191995i
$916$	19.6793	+	19.6793i	0.650223	+	0.650223i
$917$	−32.3365	−	27.9326i	−1.06785	−	0.922415i
$918$	3.50433			0.115660
$919$	−7.54166	+	28.1459i	−0.248777	+	0.928447i	0.722671	+	0.691192i	$0.242914\pi$
$919$	−7.54166	+	28.1459i	−0.248777	+	0.928447i	−0.971448	+	0.237254i	$0.923752\pi$
$920$	5.17692	−	8.96668i	0.170678	−	0.295623i
$921$	−20.7718	+	5.56579i	−0.684454	+	0.183399i
$922$	3.63429	−	2.09826i	0.119689	−	0.0691025i
$923$		−	30.7594i		−	1.01246i
$924$	−24.6717	+	8.58158i	−0.811641	+	0.282313i
$925$	4.81033			0.158163
$926$	7.35302	−	27.4418i	0.241635	−	0.901795i
$927$	5.47961	−	9.49097i	0.179974	−	0.311724i
$928$	−8.32918	+	2.23180i	−0.273419	+	0.0732624i
$929$	8.37651	−	31.2615i	0.274824	−	1.02566i	−0.681135	−	0.732158i	$-0.738513\pi$
$929$	8.37651	−	31.2615i	0.274824	−	1.02566i	0.955959	−	0.293500i	$-0.0948201\pi$
$930$	11.0535	−	11.0535i	0.362458	−	0.362458i
$931$	−18.2672	−	42.2971i	−0.598684	−	1.38623i
$932$	−4.59258	+	4.59258i	−0.150435	+	0.150435i
$933$	−0.996224	−	1.72551i	−0.0326149	−	0.0564907i
$934$	4.27341	+	2.46726i	0.139830	+	0.0807311i
$935$	9.63524	+	5.56291i	0.315106	+	0.181927i
$936$	5.11584	+	1.37079i	0.167217	+	0.0448056i
$937$	−17.0678	−	17.0678i	−0.557582	−	0.557582i	0.371037	−	0.928618i	$-0.379002\pi$
$937$	−17.0678	−	17.0678i	−0.557582	−	0.557582i	−0.928618	+	0.371037i	$0.879002\pi$
$938$	35.2577	+	17.0600i	1.15121	+	0.557029i
$939$	62.5664			2.04178
$940$	8.69240	+	2.32912i	0.283515	+	0.0759676i
$941$	−30.7048	−	17.7274i	−1.00095	−	0.577897i	−0.0924181	−	0.995720i	$-0.529460\pi$
$941$	−30.7048	−	17.7274i	−1.00095	−	0.577897i	−0.908528	+	0.417824i	$0.862793\pi$
$942$	−18.0232	+	31.2171i	−0.587228	+	1.01711i
$943$	−3.01370	−	31.1274i	−0.0981394	−	1.01365i
$944$	0.493088			0.0160486
$945$	−1.26306	−	17.2854i	−0.0410875	−	0.562295i
$946$	34.1895	−	34.1895i	1.11160	−	1.11160i
$947$	−18.2838	−	31.6685i	−0.594145	−	1.02909i	−0.993667	−	0.112366i	$-0.964157\pi$
$947$	−18.2838	−	31.6685i	−0.594145	−	1.02909i	0.399522	−	0.916724i	$-0.369176\pi$
$948$	−19.4935	−	11.2546i	−0.633118	−	0.365531i
$949$	37.1613	−	9.95733i	1.20631	−	0.323229i
$950$	−3.21603	−	0.861732i	−0.104342	−	0.0279583i
$951$		−	41.3595i		−	1.34117i
$952$	−2.48224	+	1.68562i	−0.0804500	+	0.0546311i
$953$	33.4060			1.08213			0.541064	−	0.840982i	$-0.318022\pi$
$953$	33.4060			1.08213			0.541064	+	0.840982i	$0.318022\pi$
$954$	−7.06400	−	1.89279i	−0.228706	−	0.0612815i
$955$	−11.3514	−	42.3640i	−0.367323	−	1.37087i
$956$	6.85215	+	25.5726i	0.221614	+	0.827076i
$957$	−22.0346	+	82.2344i	−0.712278	+	2.65826i
$958$	2.91923	+	2.91923i	0.0943159	+	0.0943159i
$959$	−8.01837	−	11.8079i	−0.258927	−	0.381296i
$960$	3.19810	+	3.19810i	0.103218	+	0.103218i
$961$	9.52711	+	16.5014i	0.307326	+	0.532305i
$962$	−31.3530	+	8.40102i	−1.01086	+	0.270860i
$963$	8.95697	+	5.17131i	0.288634	+	0.166643i
$964$	10.5239	−	6.07598i	0.338952	−	0.195694i
$965$	−24.4876	−	24.4876i	−0.788283	−	0.788283i
$966$	27.4950	−	2.00909i	0.884637	−	0.0646413i
$967$	−13.3766	−	13.3766i	−0.430163	−	0.430163i	0.458521	−	0.888684i	$-0.348379\pi$
$967$	−13.3766	−	13.3766i	−0.430163	−	0.430163i	−0.888684	+	0.458521i	$0.848379\pi$
$968$	5.20792	+	9.02039i	0.167389	+	0.289926i
$969$	−15.3822	+	4.12164i	−0.494147	+	0.132406i
$970$	−9.51271	+	2.54892i	−0.305435	+	0.0818410i
$971$	37.6917	+	10.0995i	1.20959	+	0.324107i	0.806599	−	0.591099i	$-0.201306\pi$
$971$	37.6917	+	10.0995i	1.20959	+	0.324107i	0.402986	+	0.915206i	$0.367972\pi$
$972$	10.4125	−	10.4125i	0.333982	−	0.333982i
$973$	10.7323	+	30.8550i	0.344062	+	0.989166i
$974$	31.7678			1.01790
$975$	3.19026	−	1.84190i	0.102170	−	0.0589880i
$976$	4.29663	+	2.48066i	0.137532	+	0.0794040i
$977$	11.9868	+	44.7352i	0.383491	+	1.43121i	0.840532	+	0.541761i	$0.182242\pi$
$977$	11.9868	+	44.7352i	0.383491	+	1.43121i	−0.457042	+	0.889445i	$0.651091\pi$
$978$	−5.79397	+	21.6234i	−0.185271	+	0.691439i
$979$		−	11.8062i		−	0.377329i
$980$	9.20914	+	11.6364i	0.294175	+	0.371710i
$981$	−11.9752	+	11.9752i	−0.382339	+	0.382339i
$982$	18.4713	−	10.6644i	0.589441	−	0.340314i
$983$	11.5014	−	19.9210i	0.366837	−	0.635381i	−0.622232	−	0.782833i	$-0.713774\pi$
$983$	11.5014	−	19.9210i	0.366837	−	0.635381i	0.989069	+	0.147452i	$0.0471072\pi$
$984$	13.4746	+	2.24762i	0.429555	+	0.0716514i
$985$	18.3609	+	31.8019i	0.585025	+	1.01329i
$986$			9.77911i			0.311430i
$987$	7.87177	+	22.6310i	0.250561	+	0.720354i
$988$	22.4666			0.714757
$989$	−44.1924	+	25.5145i	−1.40524	+	0.811315i
$990$	14.7035	−	3.93980i	0.467309	−	0.125215i
$991$	0.279197	+	1.04198i	0.00886898	+	0.0330995i	0.970219	−	0.242231i	$-0.0778793\pi$
$991$	0.279197	+	1.04198i	0.00886898	+	0.0330995i	−0.961350	+	0.275331i	$0.911213\pi$
$992$	2.99321	−	1.72813i	0.0950347	−	0.0548683i
$993$			22.4958i			0.713883i
$994$	23.7785	−	1.73752i	0.754209	−	0.0551108i
$995$	−29.1764	+	29.1764i	−0.924955	+	0.924955i
$996$	−5.30735	−	1.42210i	−0.168170	−	0.0450610i
$997$	4.11717	+	15.3655i	0.130392	+	0.486630i	0.999974	−	0.00715786i	$-0.00227844\pi$
$997$	4.11717	+	15.3655i	0.130392	+	0.486630i	−0.869582	+	0.493788i	$0.835612\pi$
$998$	−8.05489	+	2.15830i	−0.254973	+	0.0683198i
$999$	−7.60518	+	28.3829i	−0.240617	+	0.897996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.r.c.319.3	yes	40
7.2	even	3	inner	574.2.r.c.401.8	yes	40
41.9	even	4	inner	574.2.r.c.501.8	yes	40
287.9	even	12	inner	574.2.r.c.9.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.r.c.9.3	✓	40	287.9	even	12	inner
574.2.r.c.319.3	yes	40	1.1	even	1	trivial
574.2.r.c.401.8	yes	40	7.2	even	3	inner
574.2.r.c.501.8	yes	40	41.9	even	4	inner

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.552179 - 2.06076i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.83592 - 1.05997i) q^{5} +(-1.50858 - 1.50858i) q^{6} +(0.869194 + 2.49890i) q^{7} -1.00000i q^{8} +(-1.34375 + 0.775813i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.552179 - 2.06076i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.83592 - 1.05997i) q^{5} +(-1.50858 - 1.50858i) q^{6} +(0.869194 + 2.49890i) q^{7} -1.00000i q^{8} +(-1.34375 + 0.775813i) q^{9} +(1.05997 - 1.83592i) q^{10} +(-1.19774 - 4.47004i) q^{11} +(-2.06076 - 0.552179i) q^{12} +(2.41363 - 2.41363i) q^{13} +(2.00219 + 1.72951i) q^{14} +(-3.19810 - 3.19810i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.09543 + 0.293519i) q^{17} +(-0.775813 + 1.34375i) q^{18} +(-1.70352 + 6.35761i) q^{19} -2.11994i q^{20} +(4.66968 - 3.17104i) q^{21} +(-3.27230 - 3.27230i) q^{22} +(2.44201 + 4.22969i) q^{23} +(-2.06076 + 0.552179i) q^{24} +(-0.252927 + 0.438083i) q^{25} +(0.883452 - 3.29709i) q^{26} +(-2.18499 - 2.18499i) q^{27} +(2.59871 + 0.496706i) q^{28} +(6.09739 - 6.09739i) q^{29} +(-4.36868 - 1.17059i) q^{30} +(-1.72813 + 2.99321i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-8.55030 + 4.93652i) q^{33} +(-0.801910 + 0.801910i) q^{34} +(4.24453 + 3.66647i) q^{35} +1.55163i q^{36} +(-4.75466 - 8.23531i) q^{37} +(1.70352 + 6.35761i) q^{38} +(-6.30667 - 3.64116i) q^{39} +(-1.05997 - 1.83592i) q^{40} +(-5.82799 - 2.65228i) q^{41} +(2.45854 - 5.08104i) q^{42} +10.4482i q^{43} +(-4.47004 - 1.19774i) q^{44} +(-1.64468 + 2.84866i) q^{45} +(4.22969 + 2.44201i) q^{46} +(-1.09867 + 4.10031i) q^{47} +(-1.50858 + 1.50858i) q^{48} +(-5.48900 + 4.34406i) q^{49} +0.505855i q^{50} +(1.20975 + 2.09534i) q^{51} +(-0.883452 - 3.29709i) q^{52} +(1.21988 + 4.55265i) q^{53} +(-2.98475 - 0.799761i) q^{54} +(-6.93707 - 6.93707i) q^{55} +(2.49890 - 0.869194i) q^{56} +14.0421 q^{57} +(2.23180 - 8.32918i) q^{58} +(-0.246544 + 0.427027i) q^{59} +(-4.36868 + 1.17059i) q^{60} +(-4.29663 + 2.48066i) q^{61} +3.45627i q^{62} +(-3.10666 - 2.68356i) q^{63} -1.00000 q^{64} +(1.87286 - 6.98962i) q^{65} +(-4.93652 + 8.55030i) q^{66} +(14.2998 - 3.83161i) q^{67} +(-0.293519 + 1.09543i) q^{68} +(7.36794 - 7.36794i) q^{69} +(5.50910 + 1.05299i) q^{70} +(6.37202 - 6.37202i) q^{71} +(0.775813 + 1.34375i) q^{72} +(9.76092 + 5.63547i) q^{73} +(-8.23531 - 4.75466i) q^{74} +(1.04244 + 0.279322i) q^{75} +(4.65409 + 4.65409i) q^{76} +(10.1291 - 6.87837i) q^{77} -7.28232 q^{78} +(10.1910 + 2.73068i) q^{79} +(-1.83592 - 1.05997i) q^{80} +(-5.62367 + 9.74048i) q^{81} +(-6.37332 + 0.617052i) q^{82} +2.57544 q^{83} +(-0.411359 - 5.62958i) q^{84} +(-1.70000 + 1.70000i) q^{85} +(5.22408 + 9.04837i) q^{86} +(-15.9321 - 9.19839i) q^{87} +(-4.47004 + 1.19774i) q^{88} +(2.46427 + 0.660298i) q^{89} +3.28935i q^{90} +(8.12935 + 3.93352i) q^{91} +4.88402 q^{92} +(7.12253 + 1.90848i) q^{93} +(1.09867 + 4.10031i) q^{94} +(3.61135 + 13.4778i) q^{95} +(-0.552179 + 2.06076i) q^{96} +(-3.28490 - 3.28490i) q^{97} +(-2.58159 + 6.50657i) q^{98} +(5.07738 + 5.07738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7	\( 40 q + 4 q^{3} + 20 q^{4} - 8 q^{6} - 12 q^{7} + 12 q^{10} - 4 q^{12} - 28 q^{13} + 12 q^{14} + 20 q^{15} - 20 q^{16} + 14 q^{17} - 16 q^{18} + 24 q^{23} - 4 q^{24} - 20 q^{25} + 14 q^{26} + 4 q^{27} + 44 q^{29} + 10 q^{30} - 8 q^{31} + 28 q^{34} - 2 q^{35} - 16 q^{37} - 12 q^{40} + 4 q^{41} - 64 q^{42} - 36 q^{45} + 2 q^{47} - 8 q^{48} + 28 q^{51} - 14 q^{52} + 20 q^{53} + 2 q^{54} - 44 q^{55} + 12 q^{56} - 40 q^{57} - 22 q^{58} - 8 q^{59} + 10 q^{60} + 24 q^{63} - 40 q^{64} + 36 q^{65} - 48 q^{66} + 6 q^{67} - 14 q^{68} - 36 q^{69} + 8 q^{70} + 40 q^{71} + 16 q^{72} + 36 q^{75} - 26 q^{79} + 84 q^{81} - 22 q^{82} - 24 q^{83} + 164 q^{85} - 28 q^{86} + 16 q^{89} + 48 q^{92} + 46 q^{93} - 2 q^{94} - 18 q^{95} + 4 q^{96} + 8 q^{97} + 24 q^{98} - 12 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 20 * q^4 - 8 * q^6 - 12 * q^7 + 12 * q^10 - 4 * q^12 - 28 * q^13 + 12 * q^14 + 20 * q^15 - 20 * q^16 + 14 * q^17 - 16 * q^18 + 24 * q^23 - 4 * q^24 - 20 * q^25 + 14 * q^26 + 4 * q^27 + 44 * q^29 + 10 * q^30 - 8 * q^31 + 28 * q^34 - 2 * q^35 - 16 * q^37 - 12 * q^40 + 4 * q^41 - 64 * q^42 - 36 * q^45 + 2 * q^47 - 8 * q^48 + 28 * q^51 - 14 * q^52 + 20 * q^53 + 2 * q^54 - 44 * q^55 + 12 * q^56 - 40 * q^57 - 22 * q^58 - 8 * q^59 + 10 * q^60 + 24 * q^63 - 40 * q^64 + 36 * q^65 - 48 * q^66 + 6 * q^67 - 14 * q^68 - 36 * q^69 + 8 * q^70 + 40 * q^71 + 16 * q^72 + 36 * q^75 - 26 * q^79 + 84 * q^81 - 22 * q^82 - 24 * q^83 + 164 * q^85 - 28 * q^86 + 16 * q^89 + 48 * q^92 + 46 * q^93 - 2 * q^94 - 18 * q^95 + 4 * q^96 + 8 * q^97 + 24 * q^98 - 12 * q^99

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