LMFDB - Embedded newform 525.2.bb.a.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (of order $10$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35055 + 1.85887i) q^{2} +(-1.51070 - 0.847225i) q^{3} +(-1.01339 - 3.11890i) q^{4} +(-2.19863 + 0.407466i) q^{5} +(3.61516 - 1.66398i) q^{6} +(2.35939 + 1.19720i) q^{7} +(2.79580 + 0.908411i) q^{8} +(1.56442 + 2.55980i) q^{9} +O(q^{10})$	\(q+(-1.35055 + 1.85887i) q^{2} +(-1.51070 - 0.847225i) q^{3} +(-1.01339 - 3.11890i) q^{4} +(-2.19863 + 0.407466i) q^{5} +(3.61516 - 1.66398i) q^{6} +(2.35939 + 1.19720i) q^{7} +(2.79580 + 0.908411i) q^{8} +(1.56442 + 2.55980i) q^{9} +(2.21193 - 4.63728i) q^{10} +(1.42134 - 1.95631i) q^{11} +(-1.11148 + 5.57029i) q^{12} +(2.42900 + 3.34323i) q^{13} +(-5.41192 + 2.76892i) q^{14} +(3.66668 + 1.24718i) q^{15} +(-0.158310 + 0.115019i) q^{16} +(-0.861743 + 2.65217i) q^{17} +(-6.87118 - 0.549089i) q^{18} +(-2.98390 - 0.969528i) q^{19} +(3.49892 + 6.44438i) q^{20} +(-2.55002 - 3.80754i) q^{21} +(1.71694 + 5.28419i) q^{22} +(-0.572578 + 0.788086i) q^{23} +(-3.45398 - 3.74101i) q^{24} +(4.66794 - 1.79173i) q^{25} -9.49514 q^{26} +(-0.194634 - 5.19251i) q^{27} +(1.34297 - 8.57192i) q^{28} +(-5.37086 + 1.74510i) q^{29} +(-7.27039 + 5.13153i) q^{30} +(-7.14169 - 2.32047i) q^{31} +5.42974i q^{32} +(-3.80465 + 1.75120i) q^{33} +(-3.76623 - 5.18377i) q^{34} +(-5.67524 - 1.67083i) q^{35} +(6.39840 - 7.47335i) q^{36} +(-3.46327 + 2.51621i) q^{37} +(5.83214 - 4.23730i) q^{38} +(-0.837016 - 7.10853i) q^{39} +(-6.51708 - 0.858064i) q^{40} +(3.03574 - 2.20559i) q^{41} +(10.5217 + 0.402112i) q^{42} -10.9179 q^{43} +(-7.54190 - 2.45051i) q^{44} +(-4.48261 - 4.99061i) q^{45} +(-0.691657 - 2.12870i) q^{46} +(1.98639 + 6.11348i) q^{47} +(0.336605 - 0.0396346i) q^{48} +(4.13341 + 5.64933i) q^{49} +(-2.97369 + 11.0969i) q^{50} +(3.54882 - 3.27654i) q^{51} +(7.96567 - 10.9638i) q^{52} +(-6.42995 + 2.08922i) q^{53} +(9.91508 + 6.65095i) q^{54} +(-2.32787 + 4.88035i) q^{55} +(5.50883 + 5.49043i) q^{56} +(3.68637 + 3.99270i) q^{57} +(4.00971 - 12.3406i) q^{58} +(7.08247 - 5.14571i) q^{59} +(0.174031 - 12.6999i) q^{60} +(-1.26409 + 1.73988i) q^{61} +(13.9587 - 10.1416i) q^{62} +(0.626467 + 7.91249i) q^{63} +(-10.4098 - 7.56319i) q^{64} +(-6.70273 - 6.36079i) q^{65} +(1.88313 - 9.43745i) q^{66} +(-3.42580 + 10.5435i) q^{67} +9.14514 q^{68} +(1.53268 - 0.705458i) q^{69} +(10.7706 - 8.29301i) q^{70} +(-4.78411 + 1.55445i) q^{71} +(2.04845 + 8.57784i) q^{72} +(3.09494 - 4.25982i) q^{73} -9.83605i q^{74} +(-8.56986 - 1.24803i) q^{75} +10.2890i q^{76} +(5.69559 - 2.91406i) q^{77} +(14.3443 + 8.04452i) q^{78} +(1.21671 + 3.74464i) q^{79} +(0.301198 - 0.317390i) q^{80} +(-4.10519 + 8.00921i) q^{81} +8.62183i q^{82} +(2.51003 - 7.72508i) q^{83} +(-9.29117 + 11.8118i) q^{84} +(0.813983 - 6.18228i) q^{85} +(14.7452 - 20.2950i) q^{86} +(9.59225 + 1.91401i) q^{87} +(5.75092 - 4.17829i) q^{88} +(1.68543 + 1.22454i) q^{89} +(15.3309 - 1.59253i) q^{90} +(1.72843 + 10.7960i) q^{91} +(3.03821 + 0.987173i) q^{92} +(8.82297 + 9.55615i) q^{93} +(-14.0469 - 4.56412i) q^{94} +(6.95554 + 0.915794i) q^{95} +(4.60022 - 8.20270i) q^{96} +(-15.3450 + 4.98588i) q^{97} +(-16.0838 + 0.0537950i) q^{98} +(7.23134 + 0.577869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.35055	+	1.85887i	−0.954984	+	1.31442i	−0.00570642	+	0.999984i	$0.501816\pi$
$2$	−1.35055	+	1.85887i	−0.954984	+	1.31442i	−0.949278	+	0.314439i	$0.898184\pi$
$3$	−1.51070	−	0.847225i	−0.872202	−	0.489146i
$3$	−1.51070	−	0.847225i	−0.872202	−	0.489146i
$4$	−1.01339	−	3.11890i	−0.506696	−	1.55945i
$5$	−2.19863	+	0.407466i	−0.983257	+	0.182224i
$5$	−2.19863	+	0.407466i	−0.983257	+	0.182224i
$6$	3.61516	−	1.66398i	1.47588	−	0.679316i
$7$	2.35939	+	1.19720i	0.891764	+	0.452500i
$7$	2.35939	+	1.19720i	0.891764	+	0.452500i
$8$	2.79580	+	0.908411i	0.988465	+	0.321172i
$9$	1.56442	+	2.55980i	0.521473	+	0.853268i
$10$	2.21193	−	4.63728i	0.699475	−	1.46644i
$11$	1.42134	−	1.95631i	0.428550	−	0.589849i	−0.539069	−	0.842261i	$-0.681224\pi$
$11$	1.42134	−	1.95631i	0.428550	−	0.589849i	0.967620	+	0.252412i	$0.0812239\pi$
$12$	−1.11148	+	5.57029i	−0.320857	+	1.60800i
$13$	2.42900	+	3.34323i	0.673684	+	0.927246i	0.999837	−	0.0180711i	$-0.00575251\pi$
$13$	2.42900	+	3.34323i	0.673684	+	0.927246i	−0.326153	+	0.945317i	$0.605753\pi$
$14$	−5.41192	+	2.76892i	−1.44640	+	0.740025i
$15$	3.66668	+	1.24718i	0.946733	+	0.322019i
$16$	−0.158310	+	0.115019i	−0.0395775	+	0.0287547i
$17$	−0.861743	+	2.65217i	−0.209003	+	0.643246i	0.790522	+	0.612434i	$0.209809\pi$
$17$	−0.861743	+	2.65217i	−0.209003	+	0.643246i	−0.999525	+	0.0308124i	$0.990191\pi$
$18$	−6.87118	−	0.549089i	−1.61955	−	0.129421i
$19$	−2.98390	−	0.969528i	−0.684554	−	0.222425i	−0.0539659	−	0.998543i	$-0.517186\pi$
$19$	−2.98390	−	0.969528i	−0.684554	−	0.222425i	−0.630588	+	0.776118i	$0.717186\pi$
$20$	3.49892	+	6.44438i	0.782382	+	1.44101i
$21$	−2.55002	−	3.80754i	−0.556460	−	0.830874i
$22$	1.71694	+	5.28419i	0.366052	+	1.12659i
$23$	−0.572578	+	0.788086i	−0.119391	+	0.164327i	−0.864529	−	0.502582i	$-0.832383\pi$
$23$	−0.572578	+	0.788086i	−0.119391	+	0.164327i	0.745139	+	0.666910i	$0.232383\pi$
$24$	−3.45398	−	3.74101i	−0.705042	−	0.763630i
$25$	4.66794	−	1.79173i	0.933588	−	0.358347i
$26$	−9.49514			−1.86215
$27$	−0.194634	−	5.19251i	−0.0374573	−	0.999298i
$28$	1.34297	−	8.57192i	0.253797	−	1.61994i
$29$	−5.37086	+	1.74510i	−0.997344	+	0.324057i	−0.761804	−	0.647808i	$-0.775686\pi$
$29$	−5.37086	+	1.74510i	−0.997344	+	0.324057i	−0.235540	+	0.971865i	$0.575686\pi$
$30$	−7.27039	+	5.13153i	−1.32738	+	0.936884i
$31$	−7.14169	−	2.32047i	−1.28268	−	0.416770i	−0.413160	−	0.910659i	$-0.635575\pi$
$31$	−7.14169	−	2.32047i	−1.28268	−	0.416770i	−0.869525	+	0.493889i	$0.835575\pi$
$32$			5.42974i			0.959852i
$33$	−3.80465	+	1.75120i	−0.662305	+	0.304844i
$34$	−3.76623	−	5.18377i	−0.645903	−	0.889009i
$35$	−5.67524	−	1.67083i	−0.959290	−	0.282422i
$36$	6.39840	−	7.47335i	1.06640	−	1.24556i
$37$	−3.46327	+	2.51621i	−0.569357	+	0.413662i	−0.834872	−	0.550445i	$-0.814458\pi$
$37$	−3.46327	+	2.51621i	−0.569357	+	0.413662i	0.265514	+	0.964107i	$0.414458\pi$
$38$	5.83214	−	4.23730i	0.946099	−	0.687381i
$39$	−0.837016	−	7.10853i	−0.134030	−	1.13828i
$40$	−6.51708	−	0.858064i	−1.03044	−	0.135672i
$41$	3.03574	−	2.20559i	0.474103	−	0.344456i	−0.324935	−	0.945736i	$-0.605343\pi$
$41$	3.03574	−	2.20559i	0.474103	−	0.344456i	0.799038	+	0.601280i	$0.205343\pi$
$42$	10.5217	+	0.402112i	1.62353	+	0.0620472i
$43$	−10.9179			−1.66496			−0.832481	−	0.554054i	$-0.813080\pi$
$43$	−10.9179			−1.66496			−0.832481	+	0.554054i	$0.813080\pi$
$44$	−7.54190	−	2.45051i	−1.13698	−	0.369429i
$45$	−4.48261	−	4.99061i	−0.668228	−	0.743956i
$46$	−0.691657	−	2.12870i	−0.101979	−	0.313860i
$47$	1.98639	+	6.11348i	0.289745	+	0.891742i	0.984936	+	0.172918i	$0.0553195\pi$
$47$	1.98639	+	6.11348i	0.289745	+	0.891742i	−0.695192	+	0.718824i	$0.744681\pi$
$48$	0.336605	−	0.0396346i	0.0485848	−	0.00572077i
$49$	4.13341	+	5.64933i	0.590488	+	0.807047i
$50$	−2.97369	+	11.0969i	−0.420543	+	1.56935i
$51$	3.54882	−	3.27654i	0.496934	−	0.458808i
$52$	7.96567	−	10.9638i	1.10464	−	1.52041i
$53$	−6.42995	+	2.08922i	−0.883221	+	0.286976i	−0.715294	−	0.698823i	$-0.753707\pi$
$53$	−6.42995	+	2.08922i	−0.883221	+	0.286976i	−0.167927	+	0.985799i	$0.553707\pi$
$54$	9.91508	+	6.65095i	1.34927	+	0.905079i
$55$	−2.32787	+	4.88035i	−0.313890	+	0.658066i
$56$	5.50883	+	5.49043i	0.736148	+	0.733690i
$57$	3.68637	+	3.99270i	0.488271	+	0.528846i
$58$	4.00971	−	12.3406i	0.526500	−	1.62040i
$59$	7.08247	−	5.14571i	0.922059	−	0.669915i	−0.0219767	−	0.999758i	$-0.506996\pi$
$59$	7.08247	−	5.14571i	0.922059	−	0.669915i	0.944036	+	0.329843i	$0.106996\pi$
$60$	0.174031	−	12.6999i	0.0224673	−	1.63955i
$61$	−1.26409	+	1.73988i	−0.161851	+	0.222768i	−0.882238	−	0.470804i	$-0.843964\pi$
$61$	−1.26409	+	1.73988i	−0.161851	+	0.222768i	0.720387	+	0.693572i	$0.243964\pi$
$62$	13.9587	−	10.1416i	1.77275	−	1.28798i
$63$	0.626467	+	7.91249i	0.0789274	+	0.996880i
$64$	−10.4098	−	7.56319i	−1.30123	−	0.945398i
$65$	−6.70273	−	6.36079i	−0.831371	−	0.788959i
$66$	1.88313	−	9.43745i	0.231797	−	1.16167i
$67$	−3.42580	+	10.5435i	−0.418528	+	1.28810i	0.490529	+	0.871425i	$0.336804\pi$
$67$	−3.42580	+	10.5435i	−0.418528	+	1.28810i	−0.909057	+	0.416672i	$0.863196\pi$
$68$	9.14514			1.10901
$69$	1.53268	−	0.705458i	0.184513	−	0.0849271i
$70$	10.7706	−	8.29301i	1.28733	−	0.991204i
$71$	−4.78411	+	1.55445i	−0.567770	+	0.184480i	−0.578814	−	0.815460i	$-0.696484\pi$
$71$	−4.78411	+	1.55445i	−0.567770	+	0.184480i	0.0110446	+	0.999939i	$0.496484\pi$
$72$	2.04845	+	8.57784i	0.241412	+	1.01091i
$73$	3.09494	−	4.25982i	0.362235	−	0.498574i	−0.588535	−	0.808472i	$-0.700295\pi$
$73$	3.09494	−	4.25982i	0.362235	−	0.498574i	0.950770	+	0.309898i	$0.100295\pi$
$74$		−	9.83605i		−	1.14342i
$75$	−8.56986	−	1.24803i	−0.989562	−	0.144110i
$76$			10.2890i			1.18023i
$77$	5.69559	−	2.91406i	0.649073	−	0.332087i
$78$	14.3443	+	8.04452i	1.62417	+	0.910863i
$79$	1.21671	+	3.74464i	0.136890	+	0.421305i	0.995879	−	0.0906893i	$-0.0289070\pi$
$79$	1.21671	+	3.74464i	0.136890	+	0.421305i	−0.858989	+	0.511994i	$0.828907\pi$
$80$	0.301198	−	0.317390i	0.0336750	−	0.0354852i
$81$	−4.10519	+	8.00921i	−0.456132	+	0.889912i
$82$			8.62183i			0.952122i
$83$	2.51003	−	7.72508i	0.275512	−	0.847937i	−0.713572	−	0.700582i	$-0.752924\pi$
$83$	2.51003	−	7.72508i	0.275512	−	0.847937i	0.989084	−	0.147355i	$-0.0470761\pi$
$84$	−9.29117	+	11.8118i	−1.01375	+	1.28877i
$85$	0.813983	−	6.18228i	0.0882888	−	0.670562i
$86$	14.7452	−	20.2950i	1.59001	−	2.18846i
$87$	9.59225	+	1.91401i	1.02840	+	0.205204i
$88$	5.75092	−	4.17829i	0.613050	−	0.445407i
$89$	1.68543	+	1.22454i	0.178655	+	0.129801i	0.673519	−	0.739170i	$-0.264782\pi$
$89$	1.68543	+	1.22454i	0.178655	+	0.129801i	−0.494864	+	0.868971i	$0.664782\pi$
$90$	15.3309	−	1.59253i	1.61602	−	0.167868i
$91$	1.72843	+	10.7960i	0.181189	+	1.13173i
$92$	3.03821	+	0.987173i	0.316755	+	0.102920i
$93$	8.82297	+	9.55615i	0.914899	+	0.990927i
$94$	−14.0469	−	4.56412i	−1.44883	−	0.470753i
$95$	6.95554	+	0.915794i	0.713624	+	0.0939585i
$96$	4.60022	−	8.20270i	0.469508	−	0.837185i
$97$	−15.3450	+	4.98588i	−1.55805	+	0.506240i	−0.956285	−	0.292437i	$-0.905534\pi$
$97$	−15.3450	+	4.98588i	−1.55805	+	0.506240i	−0.601760	+	0.798677i	$0.705534\pi$
$98$	−16.0838	+	0.0537950i	−1.62471	+	0.00543411i
$99$	7.23134	+	0.577869i	0.726777	+	0.0580781i
$100$	−10.3187	−	12.7431i	−1.03187	−	1.27431i
$101$	−13.2358			−1.31701			−0.658506	−	0.752575i	$-0.728811\pi$
$101$	−13.2358			−1.31701			−0.658506	+	0.752575i	$0.728811\pi$
$102$	1.29781	+	11.0220i	0.128503	+	1.09134i
$103$	1.61603	−	0.525079i	0.159232	−	0.0517376i	−0.228316	−	0.973587i	$-0.573322\pi$
$103$	1.61603	−	0.525079i	0.159232	−	0.0517376i	0.387548	+	0.921849i	$0.373322\pi$
$104$	3.75398	+	11.5535i	0.368108	+	1.13292i
$105$	7.15800	+	7.33233i	0.698549	+	0.715562i
$106$	4.80038	−	14.7741i	0.466255	−	1.43498i
$107$		−	4.40795i		−	0.426133i	−0.977038	−	0.213066i	$-0.931655\pi$
$107$		−	4.40795i		−	0.426133i	0.977038	−	0.213066i	$-0.0683451\pi$
$108$	−15.9977	+	5.86908i	−1.53938	+	0.564753i
$109$	−14.3207	+	10.4046i	−1.37167	+	0.996576i	−0.374065	+	0.927402i	$0.622036\pi$
$109$	−14.3207	+	10.4046i	−1.37167	+	0.996576i	−0.997605	+	0.0691739i	$0.977964\pi$
$110$	−5.92804	−	10.9184i	−0.565216	−	1.04103i
$111$	7.36375	−	0.867067i	0.698936	−	0.0822984i
$112$	−0.511215	+	0.0818451i	−0.0483053	+	0.00773363i
$113$	9.62075	+	13.2418i	0.905044	+	1.24569i	0.968831	+	0.247723i	$0.0796824\pi$
$113$	9.62075	+	13.2418i	0.905044	+	1.24569i	−0.0637863	+	0.997964i	$0.520318\pi$
$114$	−12.4006	+	1.46014i	−1.16142	+	0.136755i
$115$	0.937768	−	1.96602i	0.0874474	−	0.183332i
$116$	10.8856	+	14.9827i	1.01070	+	1.39111i
$117$	−4.75805	+	11.4480i	−0.439881	+	1.05837i
$118$			20.1150i			1.85173i
$119$	−5.20837	+	5.22582i	−0.477451	+	0.479050i
$120$	9.11837	+	6.81771i	0.832389	+	0.622369i
$121$	1.59226	+	4.90046i	0.144751	+	0.445496i
$122$	−1.52699	−	4.69959i	−0.138247	−	0.425481i
$123$	−6.45472	+	0.760031i	−0.582003	+	0.0685297i
$124$			24.6257i			2.21146i
$125$	−9.53300	+	5.84139i	−0.852658	+	0.522470i
$126$	−15.5544	−	9.52170i	−1.38570	−	0.848261i
$127$	−15.5510	−	11.2985i	−1.37993	−	1.00258i	−0.996887	−	0.0788466i	$-0.974876\pi$
$127$	−15.5510	−	11.2985i	−1.37993	−	1.00258i	−0.383042	−	0.923731i	$-0.625124\pi$
$128$	17.7900	−	5.78033i	1.57243	−	0.510914i
$129$	16.4936	+	9.24990i	1.45218	+	0.814409i
$130$	20.8763	−	3.86895i	1.83097	−	0.339329i
$131$	−4.06277	+	12.5039i	−0.354965	+	1.09247i	0.601064	+	0.799201i	$0.294744\pi$
$131$	−4.06277	+	12.5039i	−0.354965	+	1.09247i	−0.956029	+	0.293271i	$0.905256\pi$
$132$	9.31740	+	10.0917i	0.810976	+	0.878368i
$133$	−5.87946	−	5.85983i	−0.509814	−	0.508111i
$134$	−14.9724	−	20.6077i	−1.29342	−	1.78024i
$135$	2.54370	+	11.3371i	0.218927	+	0.975741i
$136$	−4.81853	+	6.63213i	−0.413185	+	0.568701i
$137$	−6.37596	−	8.77576i	−0.544735	−	0.749764i	0.444551	−	0.895754i	$-0.353363\pi$
$137$	−6.37596	−	8.77576i	−0.544735	−	0.749764i	−0.989286	+	0.145990i	$0.953363\pi$
$138$	−0.758605	+	3.80181i	−0.0645767	+	0.323632i
$139$	−1.56875	+	2.15920i	−0.133060	+	0.183141i	−0.870348	−	0.492438i	$-0.836106\pi$
$139$	−1.56875	+	2.15920i	−0.133060	+	0.183141i	0.737288	+	0.675578i	$0.236106\pi$
$140$	0.540080	+	19.3937i	0.0456451	+	1.63907i
$141$	2.17866	−	10.9185i	0.183476	−	0.919507i
$142$	3.57166	−	10.9924i	0.299727	−	0.922464i
$143$	9.99283			0.835643
$144$	−0.542088	−	0.225305i	−0.0451740	−	0.0187754i
$145$	11.0975	−	6.02527i	0.921595	−	0.500372i
$146$	3.73859	+	11.5062i	0.309408	+	0.952261i
$147$	−1.45809	−	12.0364i	−0.120261	−	0.992742i
$148$	11.3574	+	8.25167i	0.933576	+	0.678283i
$149$		−	0.497460i		−	0.0407535i	−0.999792	−	0.0203768i	$-0.993513\pi$
$149$		−	0.497460i		−	0.0407535i	0.999792	−	0.0203768i	$-0.00648657\pi$
$150$	13.8940	−	14.2448i	1.13444	−	1.16308i
$151$	19.6939			1.60267			0.801333	−	0.598218i	$-0.204124\pi$
$151$	19.6939			1.60267			0.801333	+	0.598218i	$0.204124\pi$
$152$	−7.46167	−	5.42122i	−0.605221	−	0.439719i
$153$	−8.13717	+	1.94321i	−0.657851	+	0.157100i
$154$	−2.27532	+	14.5230i	−0.183351	+	1.17029i
$155$	16.6474	+	2.19187i	1.33715	+	0.176055i
$156$	−21.3225	+	9.81429i	−1.70717	+	0.785772i
$157$		−	20.8316i		−	1.66254i	−0.555868	−	0.831270i	$-0.687614\pi$
$157$		−	20.8316i		−	1.66254i	0.555868	−	0.831270i	$-0.312386\pi$
$158$	−8.60404	−	2.79562i	−0.684500	−	0.222408i
$159$	11.4838	+	2.29144i	0.910721	+	0.181723i
$160$	−2.21244	−	11.9380i	−0.174909	−	0.943781i
$161$	−2.29443	+	1.17391i	−0.180827	+	0.0925170i
$162$	−9.34384	−	18.4479i	−0.734122	−	1.44940i
$163$	7.59429	−	5.51757i	0.594831	−	0.432170i	−0.249210	−	0.968450i	$-0.580171\pi$
$163$	7.59429	−	5.51757i	0.594831	−	0.432170i	0.844040	+	0.536280i	$0.180171\pi$
$164$	−9.95542	−	7.23303i	−0.777387	−	0.564805i
$165$	7.65147	−	5.40050i	0.595666	−	0.420428i
$166$	10.9700	+	15.0989i	0.851439	+	1.17191i
$167$	−5.56844	+	17.1379i	−0.430899	+	1.32617i	0.466333	+	0.884609i	$0.345575\pi$
$167$	−5.56844	+	17.1379i	−0.430899	+	1.32617i	−0.897231	+	0.441561i	$0.854425\pi$
$168$	−3.67054	−	12.9616i	−0.283188	−	1.00001i
$169$	−1.25994	+	3.87769i	−0.0969184	+	0.298284i
$170$	10.3927	+	9.86257i	0.797087	+	0.756425i
$171$	−2.18627	−	9.15495i	−0.167188	−	0.700097i
$172$	11.0641	+	34.0518i	0.843629	+	2.59642i
$173$	11.2556	+	8.17767i	0.855747	+	0.621737i	0.926725	−	0.375741i	$-0.122612\pi$
$173$	11.2556	+	8.17767i	0.855747	+	0.621737i	−0.0709773	+	0.997478i	$0.522612\pi$
$174$	−16.5127	+	15.2458i	−1.25183	+	1.15578i
$175$	13.1586	+	1.36107i	0.994693	+	0.102888i
$176$			0.473184i			0.0356676i
$177$	−15.0591	+	1.77318i	−1.13191	+	0.133280i
$178$	−4.55252	+	1.47920i	−0.341226	+	0.110871i
$179$	22.5022	−	7.31141i	1.68189	−	0.546480i	0.696616	−	0.717444i	$-0.254688\pi$
$179$	22.5022	−	7.31141i	1.68189	−	0.546480i	0.985277	+	0.170964i	$0.0546880\pi$
$180$	−11.0226	+	19.0382i	−0.821574	+	1.41903i
$181$	−12.3068	−	3.99873i	−0.914759	−	0.297223i	−0.186444	−	0.982466i	$-0.559696\pi$
$181$	−12.3068	−	3.99873i	−0.914759	−	0.297223i	−0.728315	+	0.685243i	$0.759696\pi$
$182$	−22.4027	−	11.3676i	−1.66060	−	0.842623i
$183$	3.38373	−	1.55746i	0.250133	−	0.115131i
$184$	−2.31672	+	1.68320i	−0.170791	+	0.124087i
$185$	6.58917	−	6.94338i	0.484445	−	0.510487i
$186$	−29.6796	+	3.49471i	−2.17621	+	0.256245i
$187$	3.96364	+	5.45548i	0.289850	+	0.398944i
$188$	17.0543	−	12.3907i	1.24381	−	0.903684i
$189$	5.75726	−	12.4841i	0.418779	−	0.908088i
$190$	−11.0962	+	11.6927i	−0.805000	+	0.848274i
$191$	−7.50959	−	10.3361i	−0.543375	−	0.747892i	0.445720	−	0.895173i	$-0.352948\pi$
$191$	−7.50959	−	10.3361i	−0.543375	−	0.747892i	−0.989095	+	0.147281i	$0.952948\pi$
$192$	9.31839	+	20.2452i	0.672497	+	1.46107i
$193$	−11.2803			−0.811977			−0.405989	−	0.913878i	$-0.633073\pi$
$193$	−11.2803			−0.811977			−0.405989	+	0.913878i	$0.633073\pi$
$194$	11.4560	−	35.2581i	0.822495	−	2.53138i
$195$	4.73677	+	15.2880i	0.339207	+	1.09479i
$196$	13.4309	−	18.6167i	0.959350	−	1.32976i
$197$	−20.3181	+	6.60177i	−1.44761	+	0.470356i	−0.924260	−	0.381763i	$-0.875317\pi$
$197$	−20.3181	+	6.60177i	−1.44761	+	0.470356i	−0.523348	+	0.852119i	$0.675317\pi$
$198$	−10.8405	+	12.6617i	−0.770399	+	0.899828i
$199$			8.28469i			0.587286i	0.955915	+	0.293643i	$0.0948677\pi$
$199$			8.28469i			0.587286i	−0.955915	+	0.293643i	$0.905132\pi$
$200$	14.6783	−	0.768924i	1.03791	−	0.0543712i
$201$	14.1081	−	13.0257i	0.995108	−	0.918760i
$202$	17.8756	−	24.6037i	1.25773	−	1.73111i
$203$	−14.7612	−	2.31264i	−1.03603	−	0.162316i
$204$	−13.8155	−	7.74799i	−0.967282	−	0.542468i
$205$	−5.77576	+	6.08625i	−0.403397	+	0.425082i
$206$	−1.20647	+	3.71314i	−0.0840589	+	0.258707i
$207$	−2.91310	−	0.232791i	−0.202474	−	0.0161801i
$208$	−0.769069	−	0.249886i	−0.0533254	−	0.0173265i
$209$	−6.13784	+	4.45940i	−0.424563	+	0.308463i
$210$	−23.2971	+	3.40314i	−1.60765	+	0.234839i
$211$	13.0080	+	9.45086i	0.895507	+	0.650624i	0.937308	−	0.348502i	$-0.113310\pi$
$211$	13.0080	+	9.45086i	0.895507	+	0.650624i	−0.0418011	+	0.999126i	$0.513310\pi$
$212$	13.0321	+	17.9372i	0.895049	+	1.23193i
$213$	8.54432	+	1.70491i	0.585447	+	0.116819i
$214$	8.19383	+	5.95317i	0.560119	+	0.406950i
$215$	24.0044	−	4.44867i	1.63708	−	0.303397i
$216$	4.17277	−	14.6940i	0.283921	−	0.999802i
$217$	−14.0719	−	14.0249i	−0.955265	−	0.952075i
$218$		−	40.6722i		−	2.75467i
$219$	−8.28455	+	3.81319i	−0.559818	+	0.257671i
$220$	17.5803	+	2.31470i	1.18527	+	0.156057i
$221$	−10.9600	+	3.56112i	−0.737250	+	0.239547i
$222$	−8.33335	+	14.8593i	−0.559298	+	0.997291i
$223$	10.0837	−	13.8791i	0.675258	−	0.929412i	−0.324607	−	0.945849i	$-0.605232\pi$
$223$	10.0837	−	13.8791i	0.675258	−	0.929412i	0.999865	+	0.0164365i	$0.00523212\pi$
$224$	−6.50050	+	12.8109i	−0.434333	+	0.855962i
$225$	11.8891	+	9.14599i	0.792607	+	0.609733i
$226$	−37.6082			−2.50166
$227$	−5.12171	−	3.72114i	−0.339940	−	0.246981i	0.404697	−	0.914451i	$-0.367377\pi$
$227$	−5.12171	−	3.72114i	−0.339940	−	0.246981i	−0.744636	+	0.667470i	$0.767377\pi$
$228$	8.71710	−	15.5436i	0.577304	−	1.02940i
$229$	16.5232	−	5.36871i	1.09188	−	0.354775i	0.292910	−	0.956140i	$-0.405376\pi$
$229$	16.5232	−	5.36871i	1.09188	−	0.354775i	0.798974	+	0.601365i	$0.205376\pi$
$230$	2.38807	+	4.39840i	0.157465	+	0.290022i
$231$	−11.0732	−	0.423189i	−0.728562	−	0.0278438i
$232$	−16.6011			−1.08992
$233$	23.1513	+	7.52230i	1.51669	+	0.492802i	0.944833	−	0.327552i	$-0.106224\pi$
$233$	23.1513	+	7.52230i	1.51669	+	0.492802i	0.571856	+	0.820354i	$0.306224\pi$
$234$	−14.8544	−	24.3057i	−0.971061	−	1.58891i
$235$	−6.85837	−	12.6319i	−0.447391	−	0.824013i
$236$	−23.2263	−	16.8749i	−1.51190	−	1.09846i
$237$	1.33448	−	6.68784i	0.0866835	−	0.434422i
$238$	−2.67997	−	16.7394i	−0.173717	−	1.08506i
$239$	−2.12889	+	2.93017i	−0.137706	+	0.189537i	−0.872300	−	0.488970i	$-0.837373\pi$
$239$	−2.12889	+	2.93017i	−0.137706	+	0.189537i	0.734594	+	0.678507i	$0.237373\pi$
$240$	−0.723920	+	0.224297i	−0.0467289	+	0.0144783i
$241$	0.173801	+	0.239217i	0.0111955	+	0.0154093i	0.814578	−	0.580054i	$-0.196969\pi$
$241$	0.173801	+	0.239217i	0.0111955	+	0.0154093i	−0.803383	+	0.595463i	$0.796969\pi$
$242$	−11.2598	−	3.65852i	−0.723805	−	0.235178i
$243$	12.9873	−	8.62148i	0.833136	−	0.553068i
$244$	6.70752	+	2.17941i	0.429405	+	0.139522i
$245$	−11.3898	−	10.7365i	−0.727665	−	0.685933i
$246$	7.30463	−	13.0250i	0.465726	−	0.830442i
$247$	−4.00654	−	12.3309i	−0.254930	−	0.784594i
$248$	−17.8588	−	12.9752i	−1.13403	−	0.823924i
$249$	−10.3368	+	9.54370i	−0.655067	+	0.604807i
$250$	2.01640	−	25.6098i	0.127528	−	1.61970i
$251$	11.1729			0.705228			0.352614	−	0.935769i	$-0.385293\pi$
$251$	11.1729			0.705228			0.352614	+	0.935769i	$0.385293\pi$
$252$	24.0434	−	9.97234i	1.51459	−	0.628198i
$253$	0.727910	+	2.24028i	0.0457633	+	0.140845i
$254$	42.0049	−	13.6482i	2.63562	−	0.856365i
$255$	−6.46746	+	8.64993i	−0.405008	+	0.541679i
$256$	−5.32904	+	16.4011i	−0.333065	+	1.02507i
$257$	−7.72197			−0.481683			−0.240842	−	0.970564i	$-0.577423\pi$
$257$	−7.72197			−0.481683			−0.240842	+	0.970564i	$0.577423\pi$
$258$	−39.4699	+	18.1671i	−2.45729	+	1.13103i
$259$	−11.1836	+	1.79048i	−0.694915	+	0.111255i
$260$	−13.0462	+	27.3511i	−0.809090	+	1.69624i
$261$	−12.8694	−	11.0183i	−0.796595	−	0.682015i
$262$	−17.7562	−	24.4393i	−1.09698	−	1.50987i
$263$	−15.5843	−	21.4500i	−0.960972	−	1.32266i	−0.946478	−	0.322769i	$-0.895386\pi$
$263$	−15.5843	−	21.4500i	−0.960972	−	1.32266i	−0.0144939	−	0.999895i	$-0.504614\pi$
$264$	−12.2279	+	1.43981i	−0.752573	+	0.0886140i
$265$	13.2858	−	7.21340i	0.816140	−	0.443116i
$266$	18.8332	−	3.01518i	1.15474	−	0.184872i
$267$	−1.50872	−	3.27785i	−0.0923321	−	0.200601i
$268$	36.3559			2.22079
$269$	−0.267018	+	0.821797i	−0.0162804	+	0.0501058i	−0.958867	−	0.283857i	$-0.908386\pi$
$269$	−0.267018	+	0.821797i	−0.0162804	+	0.0501058i	0.942586	+	0.333963i	$0.108386\pi$
$270$	−24.5096	−	10.5829i	−1.49161	−	0.644055i
$271$	4.12362	−	1.33985i	0.250492	−	0.0813898i	−0.181080	−	0.983468i	$-0.557959\pi$
$271$	4.12362	−	1.33985i	0.250492	−	0.0813898i	0.431572	+	0.902079i	$0.357959\pi$
$272$	−0.168627	−	0.518982i	−0.0102245	−	0.0314679i
$273$	6.53550	−	17.7738i	0.395546	−	1.07572i
$274$	24.9241			1.50572
$275$	3.12955	−	11.6786i	0.188719	−	0.704246i
$276$	−3.75345	−	4.06537i	−0.225931	−	0.244706i
$277$	6.13093	+	4.45438i	0.368372	+	0.267638i	0.756535	−	0.653953i	$-0.226890\pi$
$277$	6.13093	+	4.45438i	0.368372	+	0.267638i	−0.388164	+	0.921590i	$0.626890\pi$
$278$	−1.89500	−	5.83222i	−0.113655	−	0.349793i
$279$	−5.23263	−	21.9115i	−0.313269	−	1.31181i
$280$	−14.3490	−	9.82677i	−0.857519	−	0.587262i
$281$	5.85788	+	1.90334i	0.349452	+	0.113544i	0.478483	−	0.878097i	$-0.341187\pi$
$281$	5.85788	+	1.90334i	0.349452	+	0.113544i	−0.129031	+	0.991641i	$0.541187\pi$
$282$	17.3538	+	18.7959i	1.03340	+	1.11928i
$283$	11.7086	+	3.80435i	0.696003	+	0.226145i	0.635588	−	0.772028i	$-0.280758\pi$
$283$	11.7086	+	3.80435i	0.696003	+	0.226145i	0.0604148	+	0.998173i	$0.480758\pi$
$284$	9.69636	+	13.3459i	0.575373	+	0.791933i
$285$	−9.73184	−	7.27640i	−0.576465	−	0.431017i
$286$	−13.4958	+	18.5754i	−0.798025	+	1.09839i
$287$	9.80303	−	1.56946i	0.578654	−	0.0926421i
$288$	−13.8991	+	8.49439i	−0.819011	+	0.500537i
$289$	7.46187	+	5.42137i	0.438934	+	0.318904i
$290$	−3.78748	+	28.7662i	−0.222408	+	1.68921i
$291$	27.4058	+	5.46848i	1.60656	+	0.320568i
$292$	−16.4223	−	5.33594i	−0.961044	−	0.312262i
$293$	−31.9157			−1.86454			−0.932268	−	0.361769i	$-0.882173\pi$
$293$	−31.9157			−1.86454			−0.932268	+	0.361769i	$0.882173\pi$
$294$	24.3433	+	13.5453i	1.41973	+	0.789979i
$295$	−13.4750	+	14.1994i	−0.784546	+	0.826720i
$296$	−11.9684	+	3.88875i	−0.695647	+	0.226029i
$297$	−10.4348	−	6.99956i	−0.605488	−	0.406156i
$298$	0.924716	+	0.671846i	0.0535674	+	0.0389190i
$299$	−4.02555			−0.232803
$300$	4.79214	+	27.9933i	0.276675	+	1.61619i
$301$	−25.7595	−	13.0709i	−1.48475	−	0.753395i
$302$	−26.5976	+	36.6085i	−1.53052	+	2.10658i
$303$	19.9953	+	11.2137i	1.14870	+	0.644211i
$304$	0.583895	−	0.189719i	0.0334887	−	0.0108811i
$305$	2.07033	−	4.34042i	0.118547	−	0.248532i
$306$	7.37747	−	17.7504i	0.421742	−	1.01472i
$307$			27.7556i			1.58410i	0.610459	+	0.792048i	$0.290985\pi$
$307$			27.7556i			1.58410i	−0.610459	+	0.792048i	$0.709015\pi$
$308$	−14.8605	−	14.8109i	−0.846756	−	0.843929i
$309$	−2.88619	−	0.575903i	−0.164190	−	0.0327620i
$310$	−26.5576	+	27.9853i	−1.50837	+	1.58946i
$311$	8.78312	+	6.38131i	0.498045	+	0.361851i	0.808270	−	0.588812i	$-0.200404\pi$
$311$	8.78312	+	6.38131i	0.498045	+	0.361851i	−0.310225	+	0.950663i	$0.600404\pi$
$312$	4.11733	−	20.6344i	0.233098	−	1.16819i
$313$	−4.61902	−	6.35754i	−0.261083	−	0.359349i	0.658271	−	0.752781i	$-0.271288\pi$
$313$	−4.61902	−	6.35754i	−0.261083	−	0.359349i	−0.919354	+	0.393431i	$0.871288\pi$
$314$	38.7233	+	28.1341i	2.18528	+	1.58770i
$315$	−4.60144	−	17.1414i	−0.259262	−	0.965807i
$316$	10.4461	−	7.58957i	0.587642	−	0.426947i
$317$	0.671917	+	0.218319i	0.0377386	+	0.0122620i	0.327825	−	0.944738i	$-0.393684\pi$
$317$	0.671917	+	0.218319i	0.0377386	+	0.0122620i	−0.290087	+	0.957000i	$0.593684\pi$
$318$	−19.7689	+	18.2521i	−1.10858	+	1.02353i
$319$	−4.21988	+	12.9874i	−0.236268	+	0.727157i
$320$	25.9691	+	12.3870i	1.45172	+	0.692454i
$321$	−3.73453	+	6.65909i	−0.208441	+	0.371674i
$322$	0.916599	−	5.85048i	0.0510801	−	0.326035i
$323$	5.14271	−	7.07834i	0.286148	−	0.393849i
$324$	29.1401	+	4.68720i	1.61889	+	0.260400i
$325$	17.3286	+	11.2539i	0.961219	+	0.624254i
$326$			21.5686i			1.19457i
$327$	30.4492	−	3.58534i	1.68384	−	0.198270i
$328$	10.4909	−	3.40870i	0.579264	−	0.188214i
$329$	−2.63241	+	16.8022i	−0.145129	+	0.926333i
$330$	−0.294852	+	21.5168i	−0.0162311	+	1.18446i
$331$	7.93201	−	24.4122i	0.435983	−	1.34182i	−0.456094	−	0.889932i	$-0.650752\pi$
$331$	7.93201	−	24.4122i	0.435983	−	1.34182i	0.892076	−	0.451885i	$-0.149248\pi$
$332$	−26.6374			−1.46192
$333$	−11.8590	−	4.92887i	−0.649869	−	0.270101i
$334$	−24.3367	−	33.4966i	−1.33165	−	1.83285i
$335$	3.23593	−	24.5772i	0.176798	−	1.34280i
$336$	0.841633	+	0.309471i	0.0459148	+	0.0168830i
$337$	−15.7941	+	11.4751i	−0.860362	+	0.625089i	−0.927983	−	0.372622i	$-0.878459\pi$
$337$	−15.7941	+	11.4751i	−0.860362	+	0.625089i	0.0676216	+	0.997711i	$0.478459\pi$
$338$	−5.50653	−	7.57909i	−0.299516	−	0.412248i
$339$	−3.31524	−	28.1554i	−0.180059	−	1.52919i
$340$	−20.1068	+	3.72634i	−1.09044	+	0.202089i
$341$	−14.6903	+	10.6732i	−0.795526	+	0.577984i
$342$	19.9706	+	8.30023i	1.07988	+	0.448825i
$343$	2.98894	+	18.2775i	0.161388	+	0.986891i
$344$	−30.5242	−	9.91792i	−1.64576	−	0.534739i
$345$	−3.08234	+	2.17555i	−0.165948	+	0.117128i
$346$	−30.4025	+	9.87838i	−1.63445	+	0.531065i
$347$	−13.8343	+	4.49505i	−0.742667	+	0.241307i	−0.655823	−	0.754915i	$-0.727678\pi$
$347$	−13.8343	+	4.49505i	−0.742667	+	0.241307i	−0.0868439	+	0.996222i	$0.527678\pi$
$348$	−3.75109	−	31.8569i	−0.201079	−	1.70771i
$349$			23.3826i			1.25164i	0.779966	+	0.625821i	$0.215236\pi$
$349$			23.3826i			1.25164i	−0.779966	+	0.625821i	$0.784764\pi$
$350$	−20.3014	+	22.6219i	−1.08515	+	1.20919i
$351$	16.8870	−	13.2633i	0.901361	−	0.707943i
$352$	10.6223	+	7.71752i	0.566168	+	0.411345i
$353$	−0.0124760	−	0.0383971i	−0.000664030	−	0.00204367i	0.950724	−	0.310039i	$-0.100342\pi$
$353$	−0.0124760	−	0.0383971i	−0.000664030	−	0.00204367i	−0.951388	+	0.307995i	$0.900342\pi$
$354$	17.0419	−	30.3877i	0.905768	−	1.61509i
$355$	9.88510	−	5.36703i	0.524647	−	0.284852i
$356$	2.11121	−	6.49763i	0.111894	−	0.344373i
$357$	12.2957	−	3.48197i	0.650759	−	0.184286i
$358$	−16.7994	+	51.7032i	−0.887875	+	2.73260i
$359$	4.31895	+	5.94452i	0.227945	+	0.313740i	0.907635	−	0.419760i	$-0.137886\pi$
$359$	4.31895	+	5.94452i	0.227945	+	0.313740i	−0.679690	+	0.733499i	$0.737886\pi$
$360$	−7.99896	−	18.0248i	−0.421582	−	0.949991i
$361$	−7.40764	−	5.38197i	−0.389876	−	0.283261i
$362$	24.0541	−	17.4763i	1.26426	−	0.918536i
$363$	1.74638	−	8.75211i	0.0916609	−	0.459367i
$364$	31.9200	−	16.3314i	1.67306	−	0.855995i
$365$	−5.06889	+	10.6268i	−0.265318	+	0.556235i
$366$	−1.67479	+	8.39336i	−0.0875427	+	0.438728i
$367$	18.0937	+	5.87902i	0.944486	+	0.306882i	0.740473	−	0.672086i	$-0.234602\pi$
$367$	18.0937	+	5.87902i	0.944486	+	0.306882i	0.204013	+	0.978968i	$0.434602\pi$
$368$		−	0.190619i		−	0.00993670i
$369$	10.3951	+	4.32043i	0.541145	+	0.224912i
$370$	4.00786	+	21.6258i	0.208359	+	1.12427i
$371$	−17.6720	−	2.76868i	−0.917482	−	0.143742i
$372$	20.8636	−	37.2021i	1.08172	−	1.92884i
$373$	−8.47382	−	6.15659i	−0.438758	−	0.318776i	0.346383	−	0.938093i	$-0.387410\pi$
$373$	−8.47382	−	6.15659i	−0.438758	−	0.318776i	−0.785141	+	0.619317i	$0.787410\pi$
$374$	−15.4941			−0.801183
$375$	19.3505	−	0.747975i	0.999254	−	0.0386252i
$376$			18.8965i			0.974514i
$377$	−18.8801	−	13.7172i	−0.972375	−	0.706472i
$378$	15.4310	+	27.5625i	0.793684	+	1.41766i
$379$	0.294443	+	0.906202i	0.0151245	+	0.0465485i	0.958334	−	0.285650i	$-0.0922095\pi$
$379$	0.294443	+	0.906202i	0.0151245	+	0.0465485i	−0.943209	+	0.332199i	$0.892210\pi$
$380$	−4.19242	−	22.6217i	−0.215067	−	1.16047i
$381$	13.9205	+	30.2438i	0.713171	+	1.54944i
$382$	29.3555			1.50196
$383$	−10.4357	+	32.1178i	−0.533240	+	1.64114i	0.214181	+	0.976794i	$0.431292\pi$
$383$	−10.4357	+	32.1178i	−0.533240	+	1.64114i	−0.747421	+	0.664350i	$0.768708\pi$
$384$	−31.7726	−	6.33983i	−1.62139	−	0.323528i
$385$	−11.3351	+	8.72769i	−0.577691	+	0.444804i
$386$	15.2347	−	20.9688i	0.775425	−	1.06728i
$387$	−17.0801	−	27.9476i	−0.868232	−	1.42066i
$388$	31.1009	+	42.8067i	1.57891	+	2.17318i
$389$	9.87465	−	13.5913i	0.500664	−	0.689106i	−0.481646	−	0.876366i	$-0.659961\pi$
$389$	9.87465	−	13.5913i	0.500664	−	0.689106i	0.982310	+	0.187260i	$0.0599608\pi$
$390$	−34.8157	−	11.8421i	−1.76296	−	0.599649i
$391$	−1.59672	−	2.19770i	−0.0807499	−	0.111143i
$392$	6.42430	+	19.5492i	0.324476	+	0.987386i
$393$	16.7312	−	15.4476i	0.843979	−	0.779226i
$394$	15.1688	−	46.6849i	0.764196	−	2.35195i
$395$	−4.20090	−	7.73730i	−0.211370	−	0.389306i
$396$	−5.52586	−	23.1394i	−0.277685	−	1.16280i
$397$	1.44952	−	0.470978i	0.0727493	−	0.0236377i	−0.272416	−	0.962180i	$-0.587823\pi$
$397$	1.44952	−	0.470978i	0.0727493	−	0.0236377i	0.345166	+	0.938542i	$0.387823\pi$
$398$	−15.4002	−	11.1889i	−0.771942	−	0.560849i
$399$	3.91749	+	13.8337i	0.196120	+	0.692549i
$400$	−0.532898	+	0.820550i	−0.0266449	+	0.0410275i
$401$			17.5533i			0.876569i	0.898836	+	0.438285i	$0.144414\pi$
$401$			17.5533i			0.876569i	−0.898836	+	0.438285i	$0.855586\pi$
$402$	5.15937	+	43.8170i	0.257326	+	2.18539i
$403$	−9.58927	−	29.5128i	−0.477676	−	1.47013i
$404$	13.4131	+	41.2811i	0.667324	+	2.05381i
$405$	5.76231	−	19.2820i	0.286331	−	0.958131i
$406$	24.2346	−	24.3158i	1.20275	−	1.20677i
$407$			10.3516i			0.513110i
$408$	12.8982	−	5.93677i	0.638558	−	0.293914i
$409$	10.0896	+	13.8871i	0.498898	+	0.686674i	0.981998	−	0.188891i	$-0.0604892\pi$
$409$	10.0896	+	13.8871i	0.498898	+	0.686674i	−0.483100	+	0.875565i	$0.660489\pi$
$410$	−3.51310	−	18.9562i	−0.173500	−	0.936180i
$411$	2.19711	+	18.6594i	0.108375	+	0.920400i
$412$	−3.27534	−	4.50812i	−0.161364	−	0.222099i
$413$	22.8707	−	3.66159i	1.12540	−	0.180175i
$414$	4.36702	−	5.10069i	0.214627	−	0.250685i
$415$	−2.37092	+	18.0073i	−0.116384	+	0.883945i
$416$	−18.1529	+	13.1889i	−0.890019	+	0.646637i
$417$	4.19924	−	1.93281i	0.205637	−	0.0946503i
$418$		−	17.4321i		−	0.852633i
$419$	9.77891	−	30.0964i	0.477731	−	1.47030i	−0.364508	−	0.931200i	$-0.618763\pi$
$419$	9.77891	−	30.0964i	0.477731	−	1.47030i	0.842239	−	0.539104i	$-0.181237\pi$
$420$	15.6149	−	29.7556i	0.761931	−	1.45192i
$421$	4.64976	+	14.3105i	0.226616	+	0.697451i	0.998124	+	0.0612315i	$0.0195028\pi$
$421$	4.64976	+	14.3105i	0.226616	+	0.697451i	−0.771508	+	0.636220i	$0.780497\pi$
$422$	−35.1359	+	11.4164i	−1.71039	+	0.555739i
$423$	−12.5418	+	14.6488i	−0.609801	+	0.712249i
$424$	−19.8747			−0.965202
$425$	0.729422	+	13.9242i	0.0353822	+	0.675423i
$426$	−14.7088	+	13.5802i	−0.712642	+	0.657965i
$427$	−5.06547	+	2.59167i	−0.245135	+	0.125420i
$428$	−13.7480	+	4.46698i	−0.664533	+	0.215920i
$429$	−15.0962	−	8.46618i	−0.728849	−	0.408751i
$430$	−24.1496	+	50.6293i	−1.16460	+	2.44156i
$431$	−2.24870	−	0.730648i	−0.108316	−	0.0351941i	0.254357	−	0.967110i	$-0.418136\pi$
$431$	−2.24870	−	0.730648i	−0.108316	−	0.0351941i	−0.362674	+	0.931916i	$0.618136\pi$
$432$	0.628048	+	0.799638i	0.0302170	+	0.0384726i
$433$	14.8562	+	4.82709i	0.713946	+	0.231975i	0.643396	−	0.765533i	$-0.277525\pi$
$433$	14.8562	+	4.82709i	0.713946	+	0.231975i	0.0705494	+	0.997508i	$0.477525\pi$
$434$	45.0755	−	7.21654i	2.16369	−	0.346405i
$435$	−21.8697	−	0.299688i	−1.04857	−	0.0143690i
$436$	46.9632	+	34.1208i	2.24913	+	1.63409i
$437$	2.47259	−	1.79644i	0.118280	−	0.0859354i
$438$	4.10046	−	20.5498i	0.195928	−	0.981909i
$439$	−10.2491	+	14.1066i	−0.489161	+	0.673272i	−0.980233	−	0.197847i	$-0.936605\pi$
$439$	−10.2491	+	14.1066i	−0.489161	+	0.673272i	0.491072	+	0.871119i	$0.336605\pi$
$440$	−10.9416	+	11.5298i	−0.521622	+	0.549662i
$441$	−7.99477	+	19.4186i	−0.380704	+	0.924697i
$442$	8.18237	−	25.1827i	0.389196	−	1.19782i
$443$			30.0694i			1.42864i	0.699818	+	0.714321i	$0.253264\pi$
$443$			30.0694i			1.42864i	−0.699818	+	0.714321i	$0.746736\pi$
$444$	−10.1667	−	22.0881i	−0.482488	−	1.04825i
$445$	−4.20460	−	2.00555i	−0.199317	−	0.0950721i
$446$	12.1809	+	37.4888i	0.576781	+	1.77515i
$447$	−0.421461	+	0.751512i	−0.0199344	+	0.0355453i
$448$	−15.5062	−	30.3072i	−0.732597	−	1.43188i
$449$			6.41425i			0.302707i	0.988480	+	0.151354i	$0.0483632\pi$
$449$			6.41425i			0.302707i	−0.988480	+	0.151354i	$0.951637\pi$
$450$	−33.0581	+	9.74822i	−1.55837	+	0.459535i
$451$		−	9.07374i		−	0.427266i
$452$	31.5503	−	43.4253i	1.48400	−	2.04256i
$453$	−29.7515	−	16.6852i	−1.39785	−	0.783938i
$454$	13.8343	−	4.49502i	0.649274	−	0.210962i
$455$	−8.19917	−	23.0321i	−0.384383	−	1.07976i
$456$	6.67933	+	14.5115i	0.312788	+	0.679565i
$457$	11.2537			0.526424			0.263212	−	0.964738i	$-0.415218\pi$
$457$	11.2537			0.526424			0.263212	+	0.964738i	$0.415218\pi$
$458$	−12.3357	+	37.9653i	−0.576408	+	1.77400i
$459$	13.9391	+	3.95840i	0.650624	+	0.184762i
$460$	−7.08213	−	0.932461i	−0.330206	−	0.0434762i
$461$	−3.12914	−	2.27346i	−0.145739	−	0.105885i	0.512527	−	0.858671i	$-0.328710\pi$
$461$	−3.12914	−	2.27346i	−0.145739	−	0.105885i	−0.658265	+	0.752786i	$0.728710\pi$
$462$	15.7416	−	20.0121i	0.732363	−	0.931048i
$463$	10.5590	−	7.67158i	0.490720	−	0.356529i	−0.314741	−	0.949177i	$-0.601918\pi$
$463$	10.5590	−	7.67158i	0.490720	−	0.356529i	0.805461	+	0.592649i	$0.201918\pi$
$464$	0.649541	−	0.894017i	0.0301542	−	0.0415037i
$465$	−23.2922	−	17.4154i	−1.08015	−	0.807619i
$466$	−45.2500	+	32.8760i	−2.09616	+	1.52295i
$467$	11.9972	−	36.9236i	0.555165	−	1.70862i	−0.140342	−	0.990103i	$-0.544820\pi$
$467$	11.9972	−	36.9236i	0.555165	−	1.70862i	0.695507	−	0.718519i	$-0.255180\pi$
$468$	40.5268	+	3.23857i	1.87335	+	0.149703i
$469$	−20.7055	+	20.7749i	−0.956092	+	0.959296i
$470$	32.7437	+	4.31116i	1.51035	+	0.198859i
$471$	−17.6490	+	31.4702i	−0.813225	+	1.45007i
$472$	24.4756	−	7.95261i	1.12658	−	0.366048i
$473$	−15.5180	+	21.3587i	−0.713520	+	0.982076i
$474$	10.6296	+	11.5129i	0.488233	+	0.528805i
$475$	−15.6658	+	0.820657i	−0.718797	+	0.0376543i
$476$	21.5769	+	10.9486i	0.988977	+	0.501827i
$477$	−15.4071	−	13.1910i	−0.705443	−	0.603974i
$478$	−2.57164	−	7.91468i	−0.117624	−	0.362009i
$479$	9.14648	+	28.1500i	0.417913	+	1.28621i	0.909619	+	0.415444i	$0.136374\pi$
$479$	9.14648	+	28.1500i	0.417913	+	1.28621i	−0.491705	+	0.870762i	$0.663626\pi$
$480$	−6.77185	+	19.9091i	−0.309091	+	0.908724i
$481$	−16.8245	−	5.46663i	−0.767133	−	0.249257i
$482$	−0.679401			−0.0309459
$483$	4.46076	+	0.170479i	0.202972	+	0.00775705i
$484$	13.6705	−	9.93217i	0.621384	−	0.451462i
$485$	31.7063	−	17.2147i	1.43971	−	0.781677i
$486$	−1.51378	+	35.7855i	−0.0686665	+	1.62326i
$487$	7.60402	−	5.52464i	0.344571	−	0.250345i	−0.402017	−	0.915632i	$-0.631691\pi$
$487$	7.60402	−	5.52464i	0.344571	−	0.250345i	0.746588	+	0.665287i	$0.231691\pi$
$488$	−5.11468	+	3.71603i	−0.231531	+	0.168217i
$489$	−16.1473	+	1.90132i	−0.730206	+	0.0859804i
$490$	35.3403	−	6.67187i	1.59651	−	0.301404i
$491$	−2.26767	−	3.12117i	−0.102338	−	0.140857i	0.754776	−	0.655982i	$-0.227745\pi$
$491$	−2.26767	−	3.12117i	−0.102338	−	0.140857i	−0.857115	+	0.515125i	$0.827745\pi$
$492$	8.91162	+	19.3614i	0.401767	+	0.872880i
$493$		−	15.7483i		−	0.709267i
$494$	28.3326	+	9.20581i	1.27474	+	0.414189i
$495$	−16.1345	+	1.67601i	−0.725192	+	0.0753308i
$496$	1.39750	−	0.454074i	0.0627495	−	0.0203885i
$497$	−13.1486	−	2.05999i	−0.589794	−	0.0924033i
$498$	−3.78019	−	32.1040i	−0.169394	−	1.43862i
$499$	−17.8450			−0.798853			−0.399427	−	0.916765i	$-0.630791\pi$
$499$	−17.8450			−0.798853			−0.399427	+	0.916765i	$0.630791\pi$
$500$	27.8794	+	23.8129i	1.24680	+	1.06494i
$501$	22.9319	−	21.1725i	1.02452	−	0.945916i
$502$	−15.0896	+	20.7690i	−0.673481	+	0.926967i
$503$	−0.308477	−	0.949394i	−0.0137543	−	0.0423314i	0.943944	−	0.330106i	$-0.107085\pi$
$503$	−0.308477	−	0.949394i	−0.0137543	−	0.0423314i	−0.957698	+	0.287775i	$0.907085\pi$
$504$	−5.43632	+	22.6909i	−0.242153	+	1.01073i
$505$	29.1006	−	5.39314i	1.29496	−	0.239992i
$506$	−5.14748	−	1.67252i	−0.228833	−	0.0743524i
$507$	5.18867	−	4.79057i	0.230437	−	0.212757i
$508$	−19.4795	+	59.9518i	−0.864264	+	2.65993i
$509$	−14.5662	+	10.5830i	−0.645636	+	0.469082i	−0.861782	−	0.507279i	$-0.830651\pi$
$509$	−14.5662	+	10.5830i	−0.645636	+	0.469082i	0.216146	+	0.976361i	$0.430651\pi$
$510$	−7.34449	−	23.7044i	−0.325219	−	1.04965i
$511$	12.4020	−	6.34529i	0.548633	−	0.280699i
$512$	−1.30076	−	1.79034i	−0.0574860	−	0.0791227i
$513$	−4.45351	+	15.6826i	−0.196627	+	0.692405i
$514$	10.4289	−	14.3542i	0.460000	−	0.633135i
$515$	−3.33909	+	1.81293i	−0.147138	+	0.0798873i
$516$	12.1350	−	60.8157i	0.534214	−	2.67726i
$517$	14.7832	+	4.80335i	0.650164	+	0.211251i
$518$	11.7757	−	23.2070i	0.517396	−	1.01966i
$519$	−10.0755	−	21.8900i	−0.442265	−	0.960865i
$520$	−12.9613	−	23.8724i	−0.568390	−	1.04687i
$521$	−11.1100	−	34.1929i	−0.486736	−	1.49802i	−0.829451	−	0.558580i	$-0.811346\pi$
$521$	−11.1100	−	34.1929i	−0.486736	−	1.49802i	0.342715	−	0.939440i	$-0.388654\pi$
$522$	37.8624	−	9.04181i	1.65719	−	0.395749i
$523$	12.9393	−	17.8094i	0.565796	−	0.778752i	−0.426253	−	0.904604i	$-0.640167\pi$
$523$	12.9393	−	17.8094i	0.565796	−	0.778752i	0.992049	+	0.125852i	$0.0401665\pi$
$524$	43.1156			1.88351
$525$	−18.7255	−	13.2044i	−0.817246	−	0.576289i
$526$	60.9203			2.65625
$527$	12.3086	−	16.9413i	0.536171	−	0.737976i
$528$	0.400893	−	0.714838i	0.0174466	−	0.0311093i
$529$	6.81416	+	20.9718i	0.296268	+	0.911818i
$530$	−4.53433	+	34.4387i	−0.196959	+	1.49592i
$531$	24.2520	+	10.0797i	1.05245	+	0.437421i
$532$	−12.3180	+	24.2757i	−0.534053	+	1.05249i
$533$	14.7476	+	4.79179i	0.638791	+	0.207556i
$534$	8.13071	+	1.62238i	0.351850	+	0.0702073i
$535$	1.79609	+	9.69146i	0.0776519	+	0.418998i
$536$	−19.1557	+	26.3656i	−0.827401	+	1.13882i
$537$	−40.1884	−	8.01910i	−1.73426	−	0.346050i
$538$	−1.16700	−	1.60623i	−0.0503127	−	0.0692496i
$539$	16.9268	−	0.0566146i	0.729090	−	0.00243857i
$540$	32.7815	−	19.4224i	1.41069	−	0.835809i
$541$	−9.66798	+	7.02420i	−0.415659	+	0.301994i	−0.775889	−	0.630870i	$-0.782698\pi$
$541$	−9.66798	+	7.02420i	−0.415659	+	0.301994i	0.360230	+	0.932864i	$0.382698\pi$
$542$	−3.07856	+	9.47483i	−0.132235	+	0.406979i
$543$	15.2041	+	16.4675i	0.652469	+	0.706689i
$544$	−14.4006	−	4.67904i	−0.617421	−	0.200612i
$545$	27.2463	−	28.7110i	1.16710	−	1.22984i
$546$	24.2128	+	36.1532i	1.03621	+	1.54721i
$547$	−10.1151	−	31.1312i	−0.432492	−	1.33107i	−0.895635	−	0.444790i	$-0.853278\pi$
$547$	−10.1151	−	31.1312i	−0.432492	−	1.33107i	0.463143	−	0.886283i	$-0.346722\pi$
$548$	−20.9094	+	28.7793i	−0.893203	+	1.22939i
$549$	−6.43132	−	0.513938i	−0.274482	−	0.0219344i
$550$	17.4824	+	21.5900i	0.745453	+	0.920601i
$551$	17.7181			0.754814
$552$	4.92591	−	0.580017i	0.209661	−	0.0246872i
$553$	−1.61241	+	10.2917i	−0.0685665	+	0.437647i
$554$	−16.5603	+	5.38076i	−0.703579	+	0.228607i
$555$	−15.8368	+	4.90684i	−0.672237	+	0.208284i
$556$	8.32408	+	2.70466i	0.353020	+	0.114703i
$557$		−	9.27773i		−	0.393110i	−0.980493	−	0.196555i	$-0.937025\pi$
$557$		−	9.27773i		−	0.393110i	0.980493	−	0.196555i	$-0.0629754\pi$
$558$	47.7977	+	19.8658i	2.02344	+	0.840987i
$559$	−26.5195	−	36.5010i	−1.12166	−	1.54383i
$560$	1.09062	−	0.388250i	0.0460872	−	0.0164066i
$561$	−1.36584	−	11.5997i	−0.0576658	−	0.489739i
$562$	−11.4494	+	8.31851i	−0.482966	+	0.350895i
$563$	6.08707	−	4.42252i	0.256540	−	0.186387i	−0.452081	−	0.891977i	$-0.649318\pi$
$563$	6.08707	−	4.42252i	0.256540	−	0.186387i	0.708620	+	0.705590i	$0.249318\pi$
$564$	−36.2616	+	4.26974i	−1.52689	+	0.179789i
$565$	−26.5481	−	25.1938i	−1.11689	−	1.05991i
$566$	−22.8849	+	16.6268i	−0.961922	+	0.698877i
$567$	−19.2744	+	13.9821i	−0.809447	+	0.587192i
$568$	−14.7875			−0.620470
$569$	−24.3067	−	7.89772i	−1.01899	−	0.331089i	−0.248561	−	0.968616i	$-0.579957\pi$
$569$	−24.3067	−	7.89772i	−1.01899	−	0.331089i	−0.770428	+	0.637527i	$0.779957\pi$
$570$	26.6693	−	8.26312i	1.11705	−	0.346104i
$571$	5.20835	+	16.0296i	0.217963	+	0.670820i	0.998930	+	0.0462481i	$0.0147265\pi$
$571$	5.20835	+	16.0296i	0.217963	+	0.670820i	−0.780967	+	0.624572i	$0.785274\pi$
$572$	−10.1267	−	31.1666i	−0.423417	−	1.30314i
$573$	2.58775	+	21.9770i	0.108105	+	0.918102i
$574$	−10.3221	+	20.3422i	−0.430835	+	0.849068i
$575$	−1.26072	+	4.70465i	−0.0525757	+	0.196197i
$576$	3.07494	−	38.4791i	0.128122	−	1.60330i
$577$	−10.3297	+	14.2177i	−0.430033	+	0.591890i	−0.967961	−	0.251101i	$-0.919207\pi$
$577$	−10.3297	+	14.2177i	−0.430033	+	0.591890i	0.537928	+	0.842991i	$0.319207\pi$
$578$	−20.1553	+	6.54885i	−0.838349	+	0.272396i
$579$	17.0412	+	9.55700i	0.708208	+	0.397175i
$580$	−30.0383	−	28.5059i	−1.24727	−	1.18364i
$581$	15.1706	−	15.2214i	0.629383	−	0.631491i
$582$	−47.1781	+	43.5584i	−1.95560	+	1.80556i
$583$	−5.05200	+	15.5485i	−0.209232	+	0.643951i
$584$	12.5225	−	9.09813i	0.518185	−	0.376483i
$585$	5.79651	−	27.1086i	0.239656	−	1.12080i
$586$	43.1038	−	59.3273i	1.78060	−	2.45079i
$587$	−33.9250	+	24.6479i	−1.40023	+	1.01733i	−0.405579	+	0.914060i	$0.632930\pi$
$587$	−33.9250	+	24.6479i	−1.40023	+	1.01733i	−0.994653	+	0.103269i	$0.967070\pi$
$588$	−36.0626	+	16.7452i	−1.48720	+	0.690560i
$589$	19.0603	+	13.8481i	0.785367	+	0.570602i
$590$	−8.19617	−	44.2254i	−0.337431	−	1.82073i
$591$	36.2878	+	7.24077i	1.49268	+	0.297846i
$592$	0.258857	−	0.796681i	0.0106390	−	0.0327434i
$593$	14.0328			0.576257			0.288128	−	0.957592i	$-0.406967\pi$
$593$	14.0328			0.576257			0.288128	+	0.957592i	$0.406967\pi$
$594$	27.1040	−	9.94369i	1.11209	−	0.407995i
$595$	9.32193	−	13.6119i	0.382162	−	0.558033i
$596$	−1.55153	+	0.504122i	−0.0635531	+	0.0206496i
$597$	7.01900	−	12.5157i	0.287268	−	0.512232i
$598$	5.43671	−	7.48299i	0.222324	−	0.306002i
$599$			13.3443i			0.545233i	0.962123	+	0.272617i	$0.0878891\pi$
$599$			13.3443i			0.545233i	−0.962123	+	0.272617i	$0.912111\pi$
$600$	−22.8259	−	11.2742i	−0.931863	−	0.460267i
$601$		−	21.8982i		−	0.893245i	−0.894723	−	0.446622i	$-0.852627\pi$
$601$		−	21.8982i		−	0.893245i	0.894723	−	0.446622i	$-0.147373\pi$
$602$	59.0867	−	30.2308i	2.40819	−	1.23211i
$603$	−32.3488	+	7.72512i	−1.31734	+	0.314591i
$604$	−19.9576	−	61.4233i	−0.812064	−	2.49928i
$605$	−5.49755	−	10.1255i	−0.223507	−	0.411660i
$606$	−47.8496	+	22.0241i	−1.94376	+	0.894667i
$607$			38.8281i			1.57599i	0.615685	+	0.787993i	$0.288880\pi$
$607$			38.8281i			1.57599i	−0.615685	+	0.787993i	$0.711120\pi$
$608$	5.26429	−	16.2018i	0.213495	−	0.657071i
$609$	20.3404	+	15.9998i	0.824233	+	0.648343i
$610$	5.27221	+	9.71046i	0.213465	+	0.393165i
$611$	−15.6138	+	21.4906i	−0.631668	+	0.869417i
$612$	14.3068	+	23.4098i	0.578319	+	0.946284i
$613$	21.3190	−	15.4891i	0.861066	−	0.625601i	−0.0671090	−	0.997746i	$-0.521378\pi$
$613$	21.3190	−	15.4891i	0.861066	−	0.625601i	0.928175	+	0.372145i	$0.121378\pi$
$614$	−51.5942	−	37.4854i	−2.08217	−	1.51279i
$615$	13.8819	−	4.30111i	0.559770	−	0.173437i
$616$	18.5709	−	2.97319i	0.748243	−	0.119793i
$617$	28.8262	+	9.36621i	1.16050	+	0.377069i	0.825089	−	0.565003i	$-0.191125\pi$
$617$	28.8262	+	9.36621i	1.16050	+	0.377069i	0.335411	+	0.942072i	$0.391125\pi$
$618$	4.96848	−	4.58728i	0.199862	−	0.184527i
$619$	4.20284	+	1.36559i	0.168926	+	0.0548875i	0.392259	−	0.919855i	$-0.371694\pi$
$619$	4.20284	+	1.36559i	0.168926	+	0.0548875i	−0.223333	+	0.974742i	$0.571694\pi$
$620$	−10.0342	−	54.1429i	−0.402982	−	2.17443i
$621$	4.20358	+	2.81973i	0.168684	+	0.113152i
$622$	−23.7241	+	7.70843i	−0.951251	+	0.309080i
$623$	2.51057	+	4.90696i	0.100584	+	0.196593i
$624$	0.950122	+	1.02908i	0.0380353	+	0.0411961i
$625$	18.5794	−	16.7274i	0.743175	−	0.669097i
$626$	18.0561			0.721667
$627$	13.0505	−	1.53668i	0.521188	−	0.0613690i
$628$	−64.9716	+	21.1105i	−2.59265	+	0.842402i
$629$	−3.68898	−	11.3535i	−0.147089	−	0.452694i
$630$	38.0782	+	14.5968i	1.51707	+	0.581551i
$631$	−2.87399	+	8.84524i	−0.114412	+	0.352124i	−0.991824	−	0.127614i	$-0.959268\pi$
$631$	−2.87399	+	8.84524i	−0.114412	+	0.352124i	0.877412	+	0.479738i	$0.159268\pi$
$632$			11.5745i			0.460410i
$633$	−11.6441	−	25.2981i	−0.462813	−	1.00551i
$634$	−1.31329	+	0.954159i	−0.0521573	+	0.0378945i
$635$	38.7947	+	18.5046i	1.53952	+	0.734334i
$636$	−4.49077	−	38.1388i	−0.178071	−	1.51230i
$637$	−8.84694	+	27.5412i	−0.350529	+	1.09122i
$638$	−18.4429	−	25.3844i	−0.730160	−	1.00498i
$639$	−11.4634	−	9.81457i	−0.453487	−	0.388258i
$640$	−36.7584	+	19.9577i	−1.45300	+	0.788896i
$641$	−10.7676	−	14.8204i	−0.425296	−	0.585370i	0.541569	−	0.840656i	$-0.317830\pi$
$641$	−10.7676	−	14.8204i	−0.425296	−	0.585370i	−0.966866	+	0.255286i	$0.917830\pi$
$642$	−7.33474	−	15.9355i	−0.289479	−	0.628923i
$643$			23.0187i			0.907770i	0.891060	+	0.453885i	$0.149962\pi$
$643$			23.0187i			0.907770i	−0.891060	+	0.453885i	$0.850038\pi$
$644$	5.98646	+	5.96647i	0.235900	+	0.235112i
$645$	−40.0324	−	13.6165i	−1.57627	−	0.536150i
$646$	6.21224	+	19.1193i	0.244417	+	0.752239i
$647$	−12.8464	−	39.5370i	−0.505042	−	1.55436i	−0.800700	−	0.599066i	$-0.795539\pi$
$647$	−12.8464	−	39.5370i	−0.505042	−	1.55436i	0.295657	−	0.955294i	$-0.404461\pi$
$648$	−18.7530	+	18.6630i	−0.736685	+	0.733150i
$649$		−	21.1693i		−	0.830968i
$650$	−44.3228	+	17.0128i	−1.73848	+	0.667296i
$651$	9.37615	+	33.1095i	0.367480	+	1.29767i
$652$	−24.9047	−	18.0944i	−0.975345	−	0.708629i
$653$	22.2934	−	7.24355i	0.872407	−	0.283462i	0.161606	−	0.986855i	$-0.448333\pi$
$653$	22.2934	−	7.24355i	0.872407	−	0.283462i	0.710801	+	0.703393i	$0.248333\pi$
$654$	−34.4585	+	61.4434i	−1.34743	+	2.40263i
$655$	3.83760	−	29.1469i	0.149947	−	1.13886i
$656$	−0.226903	+	0.698334i	−0.00885906	+	0.0272654i
$657$	15.7461	+	1.25830i	0.614313	+	0.0490909i
$658$	−27.6779	−	27.5855i	−1.07900	−	1.07539i
$659$	−8.36626	−	11.5152i	−0.325903	−	0.448567i	0.614355	−	0.789030i	$-0.289416\pi$
$659$	−8.36626	−	11.5152i	−0.325903	−	0.448567i	−0.940258	+	0.340463i	$0.889416\pi$
$660$	−24.5975	−	18.3913i	−0.957458	−	0.715881i
$661$	14.8595	−	20.4524i	0.577969	−	0.795506i	−0.415502	−	0.909592i	$-0.636394\pi$
$661$	14.8595	−	20.4524i	0.577969	−	0.795506i	0.993471	+	0.114087i	$0.0363942\pi$
$662$	34.6667	+	47.7146i	1.34736	+	1.85448i
$663$	19.5743	+	3.90581i	0.760204	+	0.151689i
$664$	14.0351	−	19.3176i	0.544667	−	0.749670i
$665$	15.3144	+	10.4879i	0.593868	+	0.406703i
$666$	25.1783	−	15.3877i	0.975641	−	0.596261i
$667$	1.69995	−	5.23191i	0.0658223	−	0.202580i
$668$	59.0944			2.28643
$669$	−26.9922	+	12.4239i	−1.04358	+	0.480336i
$670$	41.3157	+	39.2080i	1.59616	+	1.51474i
$671$	1.60703	+	4.94592i	0.0620386	+	0.190935i
$672$	20.6740	−	13.8460i	0.797516	−	0.534120i
$673$	10.9902	+	7.98486i	0.423642	+	0.307794i	0.779102	−	0.626898i	$-0.215676\pi$
$673$	10.9902	+	7.98486i	0.423642	+	0.307794i	−0.355460	+	0.934692i	$0.615676\pi$
$674$		−	44.8571i		−	1.72783i
$675$	−10.2121	−	23.8896i	−0.393065	−	0.919511i
$676$	13.3709			0.514267
$677$	−11.0921	−	8.05887i	−0.426303	−	0.309727i	0.353866	−	0.935296i	$-0.384867\pi$
$677$	−11.0921	−	8.05887i	−0.426303	−	0.309727i	−0.780169	+	0.625569i	$0.784867\pi$
$678$	56.8147	+	31.8626i	2.18196	+	1.22368i
$679$	−42.1738	−	6.60740i	−1.61848	−	0.253569i
$680$	7.89178	−	16.5450i	0.302636	−	0.634471i
$681$	4.58471	+	9.96075i	0.175686	+	0.381697i
$682$		−	41.7221i		−	1.59762i
$683$	12.1221	+	3.93869i	0.463837	+	0.150710i	0.531607	−	0.846991i	$-0.321588\pi$
$683$	12.1221	+	3.93869i	0.463837	+	0.150710i	−0.0677697	+	0.997701i	$0.521588\pi$
$684$	−26.3378	+	16.0963i	−1.00705	+	0.615457i
$685$	17.5942	+	16.6967i	0.672240	+	0.637946i
$686$	−38.0123	−	19.1286i	−1.45131	−	0.730334i
$687$	−29.5101	−	5.88837i	−1.12588	−	0.224655i
$688$	1.72841	−	1.25576i	0.0658949	−	0.0478755i
$689$	−22.6031	−	16.4221i	−0.861109	−	0.625632i
$690$	0.118779	−	8.66789i	0.00452185	−	0.329981i
$691$	18.6577	+	25.6801i	0.709772	+	0.976917i	0.999802	+	0.0198998i	$0.00633473\pi$
$691$	18.6577	+	25.6801i	0.709772	+	0.976917i	−0.290030	+	0.957018i	$0.593665\pi$
$692$	14.0990	−	43.3923i	0.535963	−	1.64953i
$693$	16.3697	+	10.0208i	0.621833	+	0.380658i
$694$	10.3283	−	31.7871i	0.392055	−	1.20662i
$695$	2.56930	−	5.38649i	0.0974590	−	0.204321i
$696$	25.0793	+	14.0649i	0.950629	+	0.533129i
$697$	3.23359	+	9.95196i	0.122481	+	0.376957i
$698$	−43.4653	−	31.5794i	−1.64519	−	1.19530i
$699$	−28.6015	−	30.9783i	−1.08181	−	1.17171i
$700$	−9.08971	−	42.4195i	−0.343559	−	1.60331i
$701$		−	13.6546i		−	0.515727i	−0.966181	−	0.257863i	$-0.916982\pi$
$701$		−	13.6546i		−	0.515727i	0.966181	−	0.257863i	$-0.0830185\pi$
$702$	1.84808	+	49.3036i	0.0697511	+	1.86084i
$703$	12.7736	−	4.15039i	0.481765	−	0.156535i
$704$	−29.5918	+	9.61497i	−1.11528	+	0.362378i
$705$	−0.341125	+	24.8935i	−0.0128475	+	0.937545i
$706$	0.0882249	+	0.0286660i	0.00332039	+	0.00107886i
$707$	−31.2284	−	15.8459i	−1.17446	−	0.595948i
$708$	20.7911	+	45.1707i	0.781376	+	1.69762i
$709$	28.9801	−	21.0553i	1.08837	−	0.790749i	0.109249	−	0.994014i	$-0.465156\pi$
$709$	28.9801	−	21.0553i	1.08837	−	0.790749i	0.979124	+	0.203266i	$0.0651555\pi$
$710$	−3.37371	+	25.6236i	−0.126613	+	0.961637i
$711$	−7.68210	+	8.97271i	−0.288101	+	0.336503i
$712$	3.59975	+	4.95463i	0.134906	+	0.185683i
$713$	5.91791	−	4.29961i	0.221627	−	0.161022i
$714$	−10.1335	+	27.5588i	−0.379235	+	1.03136i
$715$	−21.9705	+	4.07174i	−0.821651	+	0.152275i
$716$	−45.6071	−	62.7728i	−1.70442	−	2.34593i
$717$	5.69862	−	2.62295i	0.212819	−	0.0979558i
$718$	−16.8831			−0.630071
$719$	−0.0676134	+	0.208093i	−0.00252155	+	0.00776055i	−0.952309	−	0.305134i	$-0.901299\pi$
$719$	−0.0676134	+	0.208093i	−0.00252155	+	0.00776055i	0.949788	+	0.312895i	$0.101299\pi$
$720$	1.28366	+	0.274478i	0.0478390	+	0.0102292i
$721$	4.44146	+	0.695847i	0.165409	+	0.0259147i
$722$	20.0088	−	6.50125i	0.744650	−	0.241952i
$723$	−0.0598906	−	0.508633i	−0.00222735	−	0.0189163i
$724$			42.4360i			1.57712i
$725$	−21.9441	+	17.7692i	−0.814984	+	0.659931i
$726$	13.9105	+	15.0665i	0.516268	+	0.559169i
$727$	−7.30584	+	10.0556i	−0.270958	+	0.372942i	−0.922713	−	0.385488i	$-0.874033\pi$
$727$	−7.30584	+	10.0556i	−0.270958	+	0.372942i	0.651755	+	0.758430i	$0.274033\pi$
$728$	−4.97485	+	31.7536i	−0.184380	+	1.17687i
$729$	−26.9242	+	2.02128i	−0.997194	+	0.0748620i
$730$	−12.9082	−	23.7745i	−0.477753	−	0.879935i
$731$	9.40841	−	28.9561i	0.347983	−	1.07098i
$732$	−8.28660	−	8.97521i	−0.306281	−	0.331733i
$733$	−28.9554	−	9.40818i	−1.06949	−	0.347499i	−0.279202	−	0.960232i	$-0.590070\pi$
$733$	−28.9554	−	9.40818i	−1.06949	−	0.347499i	−0.790290	+	0.612733i	$0.790070\pi$
$734$	−35.3649	+	25.6941i	−1.30534	+	0.948386i
$735$	8.11021	+	25.8694i	0.299150	+	0.954206i
$736$	−4.27910	−	3.10895i	−0.157730	−	0.114597i
$737$	15.7572	+	21.6879i	0.580423	+	0.798883i
$738$	−22.0702	+	13.4881i	−0.812415	+	0.496506i
$739$	4.30719	+	3.12936i	0.158443	+	0.115115i	0.664182	−	0.747571i	$-0.268780\pi$
$739$	4.30719	+	3.12936i	0.158443	+	0.115115i	−0.505739	+	0.862687i	$0.668780\pi$
$740$	−28.3331	−	13.5146i	−1.04155	−	0.496806i
$741$	−4.39435	+	22.0227i	−0.161430	+	0.809022i
$742$	29.0135	−	29.1107i	1.06512	−	1.06869i
$743$			25.7517i			0.944740i	0.881400	+	0.472370i	$0.156601\pi$
$743$			25.7517i			0.944740i	−0.881400	+	0.472370i	$0.843399\pi$
$744$	15.9864	+	34.7320i	0.586088	+	1.27334i
$745$	0.202698	+	1.09373i	0.00742629	+	0.0400712i
$746$	22.8887	−	7.43697i	0.838013	−	0.272287i
$747$	23.7014	−	5.66007i	0.867189	−	0.207091i
$748$	12.9984	−	17.8907i	0.475267	−	0.654149i
$749$	5.27721	−	10.4001i	0.192825	−	0.380010i
$750$	−24.7434	+	36.9803i	−0.903502	+	1.35033i
$751$	−33.2591			−1.21364			−0.606820	−	0.794839i	$-0.707555\pi$
$751$	−33.2591			−1.21364			−0.606820	+	0.794839i	$0.707555\pi$
$752$	−1.01763	−	0.739351i	−0.0371091	−	0.0269614i
$753$	−16.8789	−	9.46597i	−0.615101	−	0.344959i
$754$	50.9971	−	16.5700i	1.85720	−	0.603442i
$755$	−43.2996	+	8.02460i	−1.57583	+	0.292045i
$756$	−44.7711	−	5.30498i	−1.62831	−	0.192940i
$757$	9.85025			0.358014			0.179007	−	0.983848i	$-0.442712\pi$
$757$	9.85025			0.358014			0.179007	+	0.983848i	$0.442712\pi$
$758$	−2.08218	−	0.676540i	−0.0756281	−	0.0245730i
$759$	0.798367	−	4.00109i	0.0289789	−	0.145230i
$760$	18.6144	+	8.87887i	0.675215	+	0.322071i
$761$	7.81741	+	5.67968i	0.283381	+	0.205888i	0.720391	−	0.693568i	$-0.243962\pi$
$761$	7.81741	+	5.67968i	0.283381	+	0.205888i	−0.437010	+	0.899457i	$0.643962\pi$
$762$	−75.0198	−	14.9693i	−2.71768	−	0.542279i
$763$	−46.2443	+	7.40368i	−1.67416	+	0.268031i
$764$	−24.6270	+	33.8961i	−0.890973	+	1.22632i
$765$	17.0988	−	7.58803i	0.618209	−	0.274346i
$766$	−45.6090	−	62.7755i	−1.64792	−	2.26817i
$767$	34.4066	+	11.1794i	1.24235	+	0.403665i
$768$	21.9460	−	20.2622i	0.791909	−	0.731150i
$769$	24.0531	+	7.81533i	0.867377	+	0.281828i	0.708706	−	0.705504i	$-0.249279\pi$
$769$	24.0531	+	7.81533i	0.867377	+	0.281828i	0.158671	+	0.987332i	$0.449279\pi$
$770$	−0.915029	−	32.8577i	−0.0329754	−	1.18411i
$771$	11.6656	+	6.54225i	0.420125	+	0.235613i
$772$	11.4314	+	35.1823i	0.411425	+	1.26624i
$773$	23.2439	+	16.8877i	0.836025	+	0.607408i	0.921258	−	0.388953i	$-0.127163\pi$
$773$	23.2439	+	16.8877i	0.836025	+	0.607408i	−0.0852321	+	0.996361i	$0.527163\pi$
$774$	75.0187	+	5.99488i	2.69649	+	0.215482i
$775$	−37.4947	+	1.96417i	−1.34685	+	0.0705549i
$776$	−47.4307			−1.70266
$777$	18.4120	+	6.77014i	0.660526	+	0.242878i
$778$	11.9283	+	36.7115i	0.427649	+	1.31617i
$779$	−11.1967	+	3.63804i	−0.401165	+	0.130346i
$780$	42.8814	−	30.2662i	1.53540	−	1.08370i
$781$	−3.75887	+	11.5686i	−0.134503	+	0.413957i
$782$	6.24171			0.223203
$783$	10.1068	+	27.5486i	0.361187	+	0.984506i
$784$	−1.30414	−	0.418923i	−0.0465764	−	0.0149615i
$785$	8.48816	+	45.8009i	0.302956	+	1.63470i
$786$	6.11866	+	51.9640i	0.218245	+	1.85349i
$787$	17.2112	+	23.6892i	0.613513	+	0.844428i	0.996861	−	0.0791762i	$-0.0252290\pi$
$787$	17.2112	+	23.6892i	0.613513	+	0.844428i	−0.383348	+	0.923604i	$0.625229\pi$
$788$	41.1805	+	56.6801i	1.46699	+	2.01914i
$789$	5.37025	+	45.6079i	0.191186	+	1.62369i
$790$	20.0562	+	2.64068i	0.713568	+	0.0939512i
$791$	6.84594	+	42.7606i	0.243413	+	1.52039i
$792$	19.6924	+	8.18464i	0.699741	+	0.290828i
$793$	−8.88730			−0.315597
$794$	−1.08216	+	3.33056i	−0.0384045	+	0.118197i
$795$	−26.1822	−	0.358784i	−0.928587	−	0.0127248i
$796$	25.8391	−	8.39563i	0.915843	−	0.297575i
$797$	13.4235	+	41.3132i	0.475484	+	1.46339i	0.845304	+	0.534285i	$0.179419\pi$
$797$	13.4235	+	41.3132i	0.475484	+	1.46339i	−0.369821	+	0.929103i	$0.620581\pi$
$798$	−31.0058	−	11.4009i	−1.09759	−	0.403589i
$799$	−17.9258			−0.634167
$800$	9.72866	+	25.3457i	0.343960	+	0.896107i
$801$	−0.497856	+	6.23006i	−0.0175909	+	0.220128i
$802$	−32.6294	−	23.7066i	−1.15218	−	0.837110i
$803$	−3.93455	−	12.1093i	−0.138847	−	0.427328i
$804$	−54.9228	−	30.8016i	−1.93698	−	1.08629i
$805$	4.56628	−	3.51589i	0.160940	−	0.123919i
$806$	67.8113	+	22.0332i	2.38855	+	0.776087i
$807$	1.09963	−	1.01526i	0.0387088	−	0.0357389i
$808$	−37.0047	−	12.0236i	−1.30182	−	0.422987i
$809$	2.44903	+	3.37080i	0.0861034	+	0.118511i	0.849896	−	0.526951i	$-0.176665\pi$
$809$	2.44903	+	3.37080i	0.0861034	+	0.118511i	−0.763792	+	0.645462i	$0.776665\pi$
$810$	28.0605	+	36.7527i	0.985947	+	1.29136i
$811$	21.2420	−	29.2370i	0.745906	−	1.02665i	−0.252351	−	0.967636i	$-0.581204\pi$
$811$	21.2420	−	29.2370i	0.745906	−	1.02665i	0.998257	−	0.0590157i	$-0.0187962\pi$
$812$	7.74596	+	48.3822i	0.271830	+	1.69788i
$813$	−7.36470	−	1.46953i	−0.258291	−	0.0515388i
$814$	−19.2423	−	13.9804i	−0.674444	−	0.490012i
$815$	−14.4488	+	15.2255i	−0.506119	+	0.533327i
$816$	−0.184949	+	0.926890i	−0.00647452	+	0.0324476i
$817$	32.5779	+	10.5852i	1.13976	+	0.370329i
$818$	−39.4409			−1.37902
$819$	−24.9316	+	21.3139i	−0.871181	+	0.744767i
$820$	24.8355	+	11.8463i	0.867293	+	0.413689i
$821$	2.74519	−	0.891968i	0.0958079	−	0.0311299i	−0.260721	−	0.965414i	$-0.583960\pi$
$821$	2.74519	−	0.891968i	0.0958079	−	0.0311299i	0.356529	+	0.934284i	$0.383960\pi$
$822$	−37.6528	−	21.1163i	−1.31329	−	0.736517i
$823$	19.6971	+	14.3108i	0.686597	+	0.498842i	0.875540	−	0.483146i	$-0.160506\pi$
$823$	19.6971	+	14.3108i	0.686597	+	0.498842i	−0.188943	+	0.981988i	$0.560506\pi$
$824$	4.99508			0.174012
$825$	−14.6222	+	14.9914i	−0.509080	+	0.521934i
$826$	−24.0817	+	47.4590i	−0.837909	+	1.65131i
$827$	16.5687	−	22.8048i	0.576149	−	0.793001i	−0.417118	−	0.908853i	$-0.636960\pi$
$827$	16.5687	−	22.8048i	0.576149	−	0.793001i	0.993267	+	0.115852i	$0.0369597\pi$
$828$	2.22606	+	9.32156i	0.0773608	+	0.323947i
$829$	−5.32569	+	1.73042i	−0.184969	+	0.0601000i	−0.400037	−	0.916499i	$-0.631003\pi$
$829$	−5.32569	+	1.73042i	−0.184969	+	0.0601000i	0.215068	+	0.976599i	$0.431003\pi$
$830$	−30.2713	−	28.7271i	−1.05073	−	0.997131i
$831$	−5.48812	−	11.9235i	−0.190381	−	0.413622i
$832$		−	53.1735i		−	1.84346i
$833$	−18.5449	+	6.09426i	−0.642544	+	0.211154i
$834$	−2.07843	+	10.4162i	−0.0719700	+	0.360684i
$835$	5.25982	−	39.9488i	0.182024	−	1.38249i
$836$	20.1284	+	14.6242i	0.696157	+	0.505788i
$837$	−10.6591	+	37.5349i	−0.368431	+	1.29740i
$838$	42.7385	+	58.8245i	1.47638	+	2.03206i
$839$	33.1605	+	24.0925i	1.14483	+	0.831767i	0.987785	−	0.155825i	$-0.0498035\pi$
$839$	33.1605	+	24.0925i	1.14483	+	0.831767i	0.157044	+	0.987592i	$0.449804\pi$
$840$	13.3516	+	27.0021i	0.460673	+	0.931663i
$841$	2.33931	−	1.69961i	0.0806658	−	0.0586072i
$842$	−32.8812	−	10.6837i	−1.13316	−	0.368186i
$843$	−7.23694	−	7.83832i	−0.249253	−	0.269966i
$844$	16.2941	−	50.1480i	0.560865	−	1.72617i
$845$	1.19011	−	9.03899i	0.0409410	−	0.310951i
$846$	−10.2920	−	43.0975i	−0.353846	−	1.48172i
$847$	−2.11009	+	13.4683i	−0.0725036	+	0.462777i
$848$	0.777625	−	1.07031i	0.0267037	−	0.0367546i
$849$	−14.4650	−	15.6670i	−0.496437	−	0.537691i
$850$	−26.8685	−	17.4494i	−0.921581	−	0.598511i
$851$		−	4.17008i		−	0.142948i
$852$	−3.34129	−	28.3766i	−0.114471	−	0.972167i
$853$	5.16471	−	1.67811i	0.176836	−	0.0574576i	−0.219261	−	0.975666i	$-0.570364\pi$
$853$	5.16471	−	1.67811i	0.176836	−	0.0574576i	0.396097	+	0.918209i	$0.370364\pi$
$854$	2.02360	−	12.9163i	0.0692461	−	0.441985i
$855$	8.53713	+	19.2375i	0.291964	+	0.657909i
$856$	4.00423	−	12.3238i	0.136862	−	0.421218i
$857$	50.2115			1.71519			0.857596	−	0.514324i	$-0.171957\pi$
$857$	50.2115			1.71519			0.857596	+	0.514324i	$0.171957\pi$
$858$	36.1257	−	16.6278i	1.23331	−	0.567665i
$859$	5.67410	+	7.80973i	0.193598	+	0.266465i	0.894770	−	0.446527i	$-0.147339\pi$
$859$	5.67410	+	7.80973i	0.193598	+	0.266465i	−0.701172	+	0.712992i	$0.747339\pi$
$860$	−38.2008	−	70.3590i	−1.30264	−	2.39922i
$861$	−16.1391	−	5.93440i	−0.550019	−	0.202244i
$862$	4.39517	−	3.19328i	0.149700	−	0.108763i
$863$	−18.8664	−	25.9674i	−0.642221	−	0.883941i	0.356511	−	0.934291i	$-0.383966\pi$
$863$	−18.8664	−	25.9674i	−0.642221	−	0.883941i	−0.998732	+	0.0503503i	$0.983966\pi$
$864$	28.1940	−	1.05681i	0.959178	−	0.0359535i
$865$	−28.0790	−	13.3934i	−0.954715	−	0.455389i
$866$	−29.0371	+	21.0967i	−0.986720	+	0.716894i
$867$	−6.67952	−	14.5119i	−0.226848	−	0.492851i
$868$	−29.4820	+	58.1017i	−1.00068	+	1.97210i
$869$	9.05502	+	2.94215i	0.307171	+	0.0998058i
$870$	30.0932	−	40.2483i	1.02026	−	1.36454i
$871$	−43.5707	+	14.1570i	−1.47634	+	0.479691i
$872$	−49.4893	+	16.0801i	−1.67592	+	0.544539i
$873$	−36.7688	−	31.4801i	−1.24444	−	1.06544i
$874$			7.02242i			0.237537i
$875$	−29.4854	+	2.36917i	−0.996787	+	0.0800925i
$876$	20.2884	+	21.9744i	0.685483	+	0.742446i
$877$	32.2510	+	23.4317i	1.08904	+	0.791234i	0.979237	−	0.202720i	$-0.0649781\pi$
$877$	32.2510	+	23.4317i	1.08904	+	0.791234i	0.109803	+	0.993953i	$0.464978\pi$
$878$	−12.3806	−	38.1034i	−0.417823	−	1.28593i
$879$	48.2150	+	27.0398i	1.62625	+	0.912030i
$880$	−0.192806	−	1.04036i	−0.00649950	−	0.0350704i
$881$	2.15579	−	6.63485i	0.0726305	−	0.223534i	−0.908151	−	0.418643i	$-0.862506\pi$
$881$	2.15579	−	6.63485i	0.0726305	−	0.223534i	0.980782	+	0.195109i	$0.0625060\pi$
$882$	−25.2995	−	41.0872i	−0.851877	−	1.38348i
$883$	3.13122	−	9.63691i	0.105374	−	0.324308i	−0.884444	−	0.466646i	$-0.845462\pi$
$883$	3.13122	−	9.63691i	0.105374	−	0.324308i	0.989818	+	0.142338i	$0.0454621\pi$
$884$	22.2135	+	30.5743i	0.747123	+	1.02833i
$885$	32.3868	−	10.0346i	1.08867	−	0.337310i
$886$	−55.8953	−	40.6103i	−1.87784	−	1.36433i
$887$	−0.287017	+	0.208530i	−0.00963708	+	0.00700175i	−0.592593	−	0.805502i	$-0.701896\pi$
$887$	−0.287017	+	0.208530i	−0.00963708	+	0.00700175i	0.582956	+	0.812504i	$0.301896\pi$
$888$	21.3752	+	4.26516i	0.717306	+	0.143129i
$889$	−23.1643	−	45.2752i	−0.776906	−	1.51848i
$890$	9.40659	−	5.10722i	0.315309	−	0.171194i
$891$	9.83361	+	19.4148i	0.329438	+	0.650421i
$892$	−53.5062	−	17.3852i	−1.79152	−	0.582101i
$893$		−	20.1679i		−	0.674892i
$894$	−0.827762	−	1.79840i	−0.0276845	−	0.0601475i
$895$	−46.4949	+	25.2440i	−1.55415	+	0.843813i
$896$	48.8938	+	7.66022i	1.63343	+	0.255910i
$897$	6.08139	+	3.41055i	0.203052	+	0.113875i
$898$	−11.9233	−	8.66278i	−0.397885	−	0.289081i
$899$	42.4065			1.41434
$900$	16.4771	−	46.3494i	0.549237	−	1.54498i
$901$		−	18.8537i		−	0.628108i
$902$	16.8670	+	12.2546i	0.561608	+	0.408032i
$903$	27.8408	+	41.5703i	0.926485	+	1.38337i
$904$	14.8687	+	45.7611i	0.494526	+	1.52199i
$905$	28.6875	+	3.77711i	0.953604	+	0.125555i
$906$	71.1966	−	32.7702i	2.36535	−	1.08872i
$907$	−3.59378			−0.119329			−0.0596647	−	0.998218i	$-0.519003\pi$
$907$	−3.59378			−0.119329			−0.0596647	+	0.998218i	$0.519003\pi$
$908$	−6.41556	+	19.7450i	−0.212908	+	0.655262i
$909$	−20.7063	−	33.8811i	−0.686786	−	1.12376i
$910$	53.8872	+	15.8648i	1.78634	+	0.525913i
$911$	19.6468	−	27.0415i	0.650928	−	0.895926i	−0.348210	−	0.937416i	$-0.613211\pi$
$911$	19.6468	−	27.0415i	0.650928	−	0.895926i	0.999139	+	0.0414902i	$0.0132105\pi$
$912$	−1.04282	−	0.208082i	−0.0345313	−	0.00689030i
$913$	−11.5450	−	15.8904i	−0.382084	−	0.525894i
$914$	−15.1987	+	20.9192i	−0.502727	+	0.691944i
$915$	−6.80497	+	4.80303i	−0.224965	+	0.158783i
$916$	−33.4889	−	46.0936i	−1.10651	−	1.52297i
$917$	−24.5553	+	24.6376i	−0.810889	+	0.813605i
$918$	−26.1837	+	20.5651i	−0.864191	+	0.678749i
$919$	11.0171	−	33.9072i	0.363421	−	1.11850i	−0.587542	−	0.809193i	$-0.699904\pi$
$919$	11.0171	−	33.9072i	0.363421	−	1.11850i	0.950964	−	0.309302i	$-0.100096\pi$
$920$	4.40776	−	4.64471i	0.145320	−	0.153132i
$921$	23.5152	−	41.9303i	0.774853	−	1.38165i
$922$	8.45214	−	2.74627i	0.278356	−	0.0904435i
$923$	−16.8175	−	12.2186i	−0.553555	−	0.402181i
$924$	9.90158	+	34.9650i	0.325738	+	1.15026i
$925$	−11.6579	+	17.9508i	−0.383311	+	0.590218i
$926$			29.9888i			0.985492i
$927$	3.87224	+	3.31527i	0.127181	+	0.108888i
$928$	−9.47544	−	29.1624i	−0.311047	−	0.957303i
$929$	−1.00170	−	3.08291i	−0.0328647	−	0.101147i	0.933279	−	0.359153i	$-0.116934\pi$
$929$	−1.00170	−	3.08291i	−0.0328647	−	0.101147i	−0.966143	+	0.258006i	$0.916934\pi$
$930$	63.8304	−	19.7770i	2.09308	−	0.648513i
$931$	−6.85652	−	20.8645i	−0.224713	−	0.683806i
$932$		−	79.8295i		−	2.61490i
$933$	−7.86224	−	17.0815i	−0.257398	−	0.559224i
$934$	52.4335	+	72.1686i	1.71568	+	2.36143i
$935$	−10.9375	−	10.3795i	−0.357694	−	0.339447i
$936$	−23.7020	+	27.6840i	−0.774725	+	0.904881i
$937$	−29.9416	−	41.2111i	−0.978150	−	1.34631i	−0.937820	−	0.347121i	$-0.887159\pi$
$937$	−29.9416	−	41.2111i	−0.978150	−	1.34631i	−0.0403295	−	0.999186i	$-0.512841\pi$
$938$	−10.6540	−	66.5465i	−0.347867	−	2.17282i
$939$	1.59168	+	13.5177i	0.0519426	+	0.441133i
$940$	−32.4473	+	34.1916i	−1.05832	+	1.11521i
$941$	−16.1587	+	11.7400i	−0.526760	+	0.382713i	−0.819144	−	0.573587i	$-0.805551\pi$
$941$	−16.1587	+	11.7400i	−0.526760	+	0.382713i	0.292385	+	0.956301i	$0.405551\pi$
$942$	−34.6633	−	75.3095i	−1.12939	−	2.45372i
$943$			3.65530i			0.119033i
$944$	−0.529370	+	1.62923i	−0.0172295	+	0.0530271i
$945$	−7.57122	+	29.7939i	−0.246292	+	0.969196i
$946$	−18.7453	−	57.6921i	−0.609463	−	1.87573i
$947$	−35.4465	+	11.5173i	−1.15186	+	0.374261i	−0.821843	−	0.569715i	$-0.807054\pi$
$947$	−35.4465	+	11.5173i	−1.15186	+	0.374261i	−0.330015	+	0.943976i	$0.607054\pi$
$948$	−22.2110	+	2.61531i	−0.721381	+	0.0849413i
$949$	21.7592			0.706333
$950$	19.6320	−	30.2291i	0.636946	−	0.980762i
$951$	−0.830099	−	0.899080i	−0.0269178	−	0.0291547i
$952$	−19.3088	+	9.87902i	−0.625801	+	0.320181i
$953$	52.1220	−	16.9355i	1.68840	−	0.548594i	0.701887	−	0.712288i	$-0.252341\pi$
$953$	52.1220	−	16.9355i	1.68840	−	0.548594i	0.986511	+	0.163695i	$0.0523412\pi$
$954$	45.3285	−	10.8248i	1.46756	−	0.350465i
$955$	20.7224	+	19.6653i	0.670562	+	0.636354i
$956$	11.2963	+	3.67039i	0.365348	+	0.118709i
$957$	17.3783	−	16.0449i	0.561759	−	0.518659i
$958$	−64.6801	−	21.0158i	−2.08972	−	0.678991i
$959$	−4.53701	−	28.3387i	−0.146508	−	0.915105i
$960$	−28.7369	−	40.7147i	−0.927480	−	1.31406i
$961$	20.5396	+	14.9229i	0.662566	+	0.481383i
$962$	32.8842	−	23.8918i	1.06023	−	0.770301i
$963$	11.2835	−	6.89588i	0.363606	−	0.222217i
$964$	0.569964	−	0.784488i	0.0183573	−	0.0252667i
$965$	24.8013	−	4.59636i	0.798382	−	0.147962i
$966$	−6.34138	+	8.06175i	−0.204031	+	0.259383i
$967$	0.495187	−	1.52403i	0.0159242	−	0.0490095i	−0.942779	−	0.333419i	$-0.891798\pi$
$967$	0.495187	−	1.52403i	0.0159242	−	0.0490095i	0.958703	+	0.284410i	$0.0917976\pi$
$968$			15.1471i			0.486847i
$969$	−13.7660	+	6.33619i	−0.442229	+	0.203548i
$970$	−10.8211	+	82.1873i	−0.347445	+	2.63888i
$971$	−7.78231	−	23.9515i	−0.249746	−	0.768639i	−0.994820	−	0.101657i	$-0.967586\pi$
$971$	−7.78231	−	23.9515i	−0.249746	−	0.768639i	0.745073	−	0.666982i	$-0.232414\pi$
$972$	−40.0507	−	31.7692i	−1.28463	−	1.01900i
$973$	−6.28628	+	3.21628i	−0.201529	+	0.103109i
$974$			21.5962i			0.691988i
$975$	−16.6437	−	31.6825i	−0.533026	−	1.01465i
$976$		−	0.420834i		−	0.0134706i
$977$	1.93356	−	2.66132i	0.0618602	−	0.0851433i	−0.776966	−	0.629543i	$-0.783242\pi$
$977$	1.93356	−	2.66132i	0.0618602	−	0.0851433i	0.838826	+	0.544399i	$0.183242\pi$
$978$	18.2735	−	32.5836i	0.584321	−	1.04191i
$979$	4.79115	−	1.55674i	0.153126	−	0.0497536i
$980$	−21.9439	+	46.4038i	−0.700973	+	1.48232i
$981$	−49.0371	−	20.3810i	−1.56564	−	0.650714i
$982$	8.86447			0.282877
$983$	3.69633	−	11.3761i	0.117895	−	0.362843i	−0.874645	−	0.484764i	$-0.838906\pi$
$983$	3.69633	−	11.3761i	0.117895	−	0.362843i	0.992540	+	0.121921i	$0.0389055\pi$
$984$	−18.7365	−	3.73864i	−0.597299	−	0.119184i
$985$	41.9821	−	22.7938i	1.33766	−	0.726271i
$986$	29.2741	+	21.2689i	0.932277	+	0.677339i
$987$	18.2120	−	23.1528i	0.579694	−	0.736961i
$988$	−34.3985	+	24.9920i	−1.09436	+	0.795101i
$989$	6.25134	−	8.60423i	0.198781	−	0.273599i
$990$	18.6750	−	32.2555i	0.593530	−	1.02515i
$991$	9.95388	−	7.23192i	0.316196	−	0.229730i	−0.418355	−	0.908284i	$-0.637393\pi$
$991$	9.95388	−	7.23192i	0.316196	−	0.229730i	0.734550	+	0.678554i	$0.237393\pi$
$992$	12.5996	−	38.7775i	0.400037	−	1.23119i
$993$	−32.6655	+	30.1593i	−1.03661	+	0.957076i
$994$	21.5871	−	21.6594i	0.684701	−	0.686995i
$995$	−3.37573	−	18.2150i	−0.107018	−	0.577453i
$996$	40.2410	+	22.5679i	1.27509	+	0.715090i
$997$	35.7302	−	11.6094i	1.13159	−	0.367675i	0.317408	−	0.948289i	$-0.397188\pi$
$997$	35.7302	−	11.6094i	1.13159	−	0.367675i	0.814179	+	0.580615i	$0.197188\pi$
$998$	24.1006	−	33.1717i	0.762892	−	1.05003i
$999$	13.7395	+	17.4933i	0.434699	+	0.553463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.9	✓	304
3.2	odd	2	inner	525.2.bb.a.41.67	yes	304
7.6	odd	2	inner	525.2.bb.a.41.10	yes	304
21.20	even	2	inner	525.2.bb.a.41.68	yes	304
25.11	even	5	inner	525.2.bb.a.461.68	yes	304
75.11	odd	10	inner	525.2.bb.a.461.10	yes	304
175.111	odd	10	inner	525.2.bb.a.461.67	yes	304
525.461	even	10	inner	525.2.bb.a.461.9	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.9	✓	304	1.1	even	1	trivial
525.2.bb.a.41.10	yes	304	7.6	odd	2	inner
525.2.bb.a.41.67	yes	304	3.2	odd	2	inner
525.2.bb.a.41.68	yes	304	21.20	even	2	inner
525.2.bb.a.461.9	yes	304	525.461	even	10	inner
525.2.bb.a.461.10	yes	304	75.11	odd	10	inner
525.2.bb.a.461.67	yes	304	175.111	odd	10	inner
525.2.bb.a.461.68	yes	304	25.11	even	5	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35055 + 1.85887i) q^{2} +(-1.51070 - 0.847225i) q^{3} +(-1.01339 - 3.11890i) q^{4} +(-2.19863 + 0.407466i) q^{5} +(3.61516 - 1.66398i) q^{6} +(2.35939 + 1.19720i) q^{7} +(2.79580 + 0.908411i) q^{8} +(1.56442 + 2.55980i) q^{9} +O(q^{10})\)	\(q+(-1.35055 + 1.85887i) q^{2} +(-1.51070 - 0.847225i) q^{3} +(-1.01339 - 3.11890i) q^{4} +(-2.19863 + 0.407466i) q^{5} +(3.61516 - 1.66398i) q^{6} +(2.35939 + 1.19720i) q^{7} +(2.79580 + 0.908411i) q^{8} +(1.56442 + 2.55980i) q^{9} +(2.21193 - 4.63728i) q^{10} +(1.42134 - 1.95631i) q^{11} +(-1.11148 + 5.57029i) q^{12} +(2.42900 + 3.34323i) q^{13} +(-5.41192 + 2.76892i) q^{14} +(3.66668 + 1.24718i) q^{15} +(-0.158310 + 0.115019i) q^{16} +(-0.861743 + 2.65217i) q^{17} +(-6.87118 - 0.549089i) q^{18} +(-2.98390 - 0.969528i) q^{19} +(3.49892 + 6.44438i) q^{20} +(-2.55002 - 3.80754i) q^{21} +(1.71694 + 5.28419i) q^{22} +(-0.572578 + 0.788086i) q^{23} +(-3.45398 - 3.74101i) q^{24} +(4.66794 - 1.79173i) q^{25} -9.49514 q^{26} +(-0.194634 - 5.19251i) q^{27} +(1.34297 - 8.57192i) q^{28} +(-5.37086 + 1.74510i) q^{29} +(-7.27039 + 5.13153i) q^{30} +(-7.14169 - 2.32047i) q^{31} +5.42974i q^{32} +(-3.80465 + 1.75120i) q^{33} +(-3.76623 - 5.18377i) q^{34} +(-5.67524 - 1.67083i) q^{35} +(6.39840 - 7.47335i) q^{36} +(-3.46327 + 2.51621i) q^{37} +(5.83214 - 4.23730i) q^{38} +(-0.837016 - 7.10853i) q^{39} +(-6.51708 - 0.858064i) q^{40} +(3.03574 - 2.20559i) q^{41} +(10.5217 + 0.402112i) q^{42} -10.9179 q^{43} +(-7.54190 - 2.45051i) q^{44} +(-4.48261 - 4.99061i) q^{45} +(-0.691657 - 2.12870i) q^{46} +(1.98639 + 6.11348i) q^{47} +(0.336605 - 0.0396346i) q^{48} +(4.13341 + 5.64933i) q^{49} +(-2.97369 + 11.0969i) q^{50} +(3.54882 - 3.27654i) q^{51} +(7.96567 - 10.9638i) q^{52} +(-6.42995 + 2.08922i) q^{53} +(9.91508 + 6.65095i) q^{54} +(-2.32787 + 4.88035i) q^{55} +(5.50883 + 5.49043i) q^{56} +(3.68637 + 3.99270i) q^{57} +(4.00971 - 12.3406i) q^{58} +(7.08247 - 5.14571i) q^{59} +(0.174031 - 12.6999i) q^{60} +(-1.26409 + 1.73988i) q^{61} +(13.9587 - 10.1416i) q^{62} +(0.626467 + 7.91249i) q^{63} +(-10.4098 - 7.56319i) q^{64} +(-6.70273 - 6.36079i) q^{65} +(1.88313 - 9.43745i) q^{66} +(-3.42580 + 10.5435i) q^{67} +9.14514 q^{68} +(1.53268 - 0.705458i) q^{69} +(10.7706 - 8.29301i) q^{70} +(-4.78411 + 1.55445i) q^{71} +(2.04845 + 8.57784i) q^{72} +(3.09494 - 4.25982i) q^{73} -9.83605i q^{74} +(-8.56986 - 1.24803i) q^{75} +10.2890i q^{76} +(5.69559 - 2.91406i) q^{77} +(14.3443 + 8.04452i) q^{78} +(1.21671 + 3.74464i) q^{79} +(0.301198 - 0.317390i) q^{80} +(-4.10519 + 8.00921i) q^{81} +8.62183i q^{82} +(2.51003 - 7.72508i) q^{83} +(-9.29117 + 11.8118i) q^{84} +(0.813983 - 6.18228i) q^{85} +(14.7452 - 20.2950i) q^{86} +(9.59225 + 1.91401i) q^{87} +(5.75092 - 4.17829i) q^{88} +(1.68543 + 1.22454i) q^{89} +(15.3309 - 1.59253i) q^{90} +(1.72843 + 10.7960i) q^{91} +(3.03821 + 0.987173i) q^{92} +(8.82297 + 9.55615i) q^{93} +(-14.0469 - 4.56412i) q^{94} +(6.95554 + 0.915794i) q^{95} +(4.60022 - 8.20270i) q^{96} +(-15.3450 + 4.98588i) q^{97} +(-16.0838 + 0.0537950i) q^{98} +(7.23134 + 0.577869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

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