LMFDB - Embedded newform 525.2.bb.a.41.10

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			41.10
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.10

$q$-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} +(-0.961025 + 6.00269i) 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} +(4.57862 + 0.190322i) 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} +(-6.12493 - 6.14545i) 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} +(4.69960 - 3.59357i) 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} +(-6.53745 + 8.25404i) 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} +(7.68393 - 1.20385i) 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} +(6.75567 + 4.16664i) 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} +(0.332954 + 13.5893i) 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} +(1.01140 - 6.31732i) 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} +(-4.04634 - 14.4731i) 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} +(-9.73348 - 4.97998i) 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} +(4.91900 + 15.3132i) 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	0.326153	−	0.945317i	$-0.394247\pi$
$13$	−2.42900	−	3.34323i	−0.673684	−	0.927246i	−0.999837	+	0.0180711i	$0.994247\pi$
$14$	−0.961025	+	6.00269i	−0.256845	+	1.60429i
$15$	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	$-0.790191\pi$
$17$	0.861743	−	2.65217i	0.209003	−	0.643246i	0.999525	−	0.0308124i	$-0.00980944\pi$
$18$	−6.87118	−	0.549089i	−1.61955	−	0.129421i
$19$	2.98390	+	0.969528i	0.684554	+	0.222425i	0.630588	−	0.776118i	$-0.282814\pi$
$19$	2.98390	+	0.969528i	0.684554	+	0.222425i	0.0539659	+	0.998543i	$0.482814\pi$
$20$	−3.49892	−	6.44438i	−0.782382	−	1.44101i
$21$	4.57862	+	0.190322i	0.999137	+	0.0415316i
$22$	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
$28$	−6.12493	−	6.14545i	−1.15750	−	1.16138i
$29$	−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	0.869525	−	0.493889i	$-0.164425\pi$
$31$	7.14169	+	2.32047i	1.28268	+	0.416770i	0.413160	+	0.910659i	$0.364425\pi$
$32$			5.42974i			0.959852i
$33$	3.80465	−	1.75120i	0.662305	−	0.304844i
$34$	3.76623	+	5.18377i	0.645903	+	0.889009i
$35$	4.69960	−	3.59357i	0.794377	−	0.607425i
$36$	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	−0.799038	−	0.601280i	$-0.794657\pi$
$41$	−3.03574	+	2.20559i	−0.474103	+	0.344456i	0.324935	+	0.945736i	$0.394657\pi$
$42$	−6.53745	+	8.25404i	−1.00875	+	1.27363i
$43$	−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	$-0.944681\pi$
$47$	−1.98639	−	6.11348i	−0.289745	−	0.891742i	0.695192	−	0.718824i	$-0.255319\pi$
$48$	−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
$56$	7.68393	−	1.20385i	1.02681	−	0.160871i
$57$	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	−0.944036	−	0.329843i	$-0.893004\pi$
$59$	−7.08247	+	5.14571i	−0.922059	+	0.669915i	0.0219767	+	0.999758i	$0.493004\pi$
$60$	0.174031	−	12.6999i	0.0224673	−	1.63955i
$61$	1.26409	−	1.73988i	0.161851	−	0.222768i	−0.720387	−	0.693572i	$-0.756036\pi$
$61$	1.26409	−	1.73988i	0.161851	−	0.222768i	0.882238	+	0.470804i	$0.156036\pi$
$62$	−13.9587	+	10.1416i	−1.77275	+	1.28798i
$63$	6.75567	+	4.16664i	0.851135	+	0.524948i
$64$	−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
$70$	0.332954	+	13.5893i	0.0397956	+	1.62423i
$71$	−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	−0.950770	−	0.309898i	$-0.899705\pi$
$73$	−3.09494	+	4.25982i	−0.362235	+	0.498574i	0.588535	+	0.808472i	$0.299705\pi$
$74$		−	9.83605i		−	1.14342i
$75$	8.56986	+	1.24803i	0.989562	+	0.144110i
$76$		−	10.2890i		−	1.18023i
$77$	1.01140	−	6.31732i	0.115259	−	0.719925i
$78$	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	$0.247076\pi$
$83$	−2.51003	+	7.72508i	−0.275512	+	0.847937i	−0.989084	+	0.147355i	$0.952924\pi$
$84$	−4.04634	−	14.4731i	−0.441492	−	1.57915i
$85$	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	0.494864	−	0.868971i	$-0.335218\pi$
$89$	−1.68543	−	1.22454i	−0.178655	−	0.129801i	−0.673519	+	0.739170i	$0.735218\pi$
$90$	−15.3309	+	1.59253i	−1.61602	+	0.167868i
$91$	−9.73348	−	4.97998i	−1.02035	−	0.522043i
$92$	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	0.601760	−	0.798677i	$-0.294466\pi$
$97$	15.3450	−	4.98588i	1.55805	−	0.506240i	0.956285	+	0.292437i	$0.0944662\pi$
$98$	4.91900	+	15.3132i	0.496894	+	1.54687i
$99$	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	$-0.271189\pi$
$101$	13.2358			1.31701			0.658506	+	0.752575i	$0.271189\pi$
$102$	1.29781	+	11.0220i	0.128503	+	1.09134i
$103$	−1.61603	+	0.525079i	−0.159232	+	0.0517376i	−0.387548	−	0.921849i	$-0.626678\pi$
$103$	−1.61603	+	0.525079i	−0.159232	+	0.0517376i	0.228316	+	0.973587i	$0.426678\pi$
$104$	−3.75398	−	11.5535i	−0.368108	−	1.13292i
$105$	10.1442	−	1.44719i	0.989977	−	0.141231i
$106$	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
$112$	−0.235813	+	0.460903i	−0.0222823	+	0.0435512i
$113$	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
$119$	−1.14200	−	7.28918i	−0.104687	−	0.668198i
$120$	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
$126$	−16.8691	+	6.93068i	−1.50282	+	0.617434i
$127$	−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	$-0.705256\pi$
$131$	4.06277	−	12.5039i	0.354965	−	1.09247i	0.956029	−	0.293271i	$-0.0947437\pi$
$132$	−9.31740	−	10.0917i	−0.810976	−	0.878368i
$133$	8.20090	−	1.28484i	0.711108	−	0.111410i
$134$	−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	−0.737288	−	0.675578i	$-0.763894\pi$
$139$	1.56875	−	2.15920i	0.133060	−	0.183141i	0.870348	+	0.492438i	$0.163894\pi$
$140$	−15.9705	−	11.0159i	−1.34976	−	0.931011i
$141$	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
$147$	11.0306	−	5.03249i	0.909788	−	0.415073i
$148$	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
$154$	10.3772	+	10.4119i	0.836216	+	0.839017i
$155$	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	$0.312386\pi$
$157$			20.8316i			1.66254i	−0.555868	+	0.831270i	$0.687614\pi$
$158$	−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
$161$	−0.407435	+	2.54489i	−0.0321104	+	0.200566i
$162$	−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	$-0.654425\pi$
$167$	5.56844	−	17.1379i	0.430899	−	1.32617i	0.897231	−	0.441561i	$-0.145575\pi$
$168$	12.6280	+	4.69137i	0.974274	+	0.361947i
$169$	−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	0.0709773	−	0.997478i	$-0.477388\pi$
$173$	−11.2556	−	8.17767i	−0.855747	−	0.621737i	−0.926725	+	0.375741i	$0.877388\pi$
$174$	16.5127	−	15.2458i	1.25183	−	1.15578i
$175$	8.86842	−	9.81587i	0.670389	−	0.742010i
$176$			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	0.728315	−	0.685243i	$-0.240304\pi$
$181$	12.3068	+	3.99873i	0.914759	+	0.297223i	0.186444	+	0.982466i	$0.440304\pi$
$182$	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
$189$	6.67569	+	12.0181i	0.485585	+	0.874189i
$190$	−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
$196$	−21.8084	−	7.16672i	−1.55775	−	0.511909i
$197$	−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	$-0.905132\pi$
$199$		−	8.28469i		−	0.587286i	0.955915	−	0.293643i	$-0.0948677\pi$
$200$	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
$203$	−10.5827	+	10.5474i	−0.742761	+	0.740280i
$204$	−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
$210$	−11.0102	+	20.8114i	−0.759775	+	1.43612i
$211$	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
$217$	19.6281	−	3.07514i	1.33244	−	0.208754i
$218$		−	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	−0.999865	−	0.0164365i	$-0.994768\pi$
$223$	−10.0837	+	13.8791i	−0.675258	+	0.929412i	0.324607	+	0.945849i	$0.394768\pi$
$224$	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	0.744636	−	0.667470i	$-0.232623\pi$
$227$	5.12171	+	3.72114i	0.339940	+	0.246981i	−0.404697	+	0.914451i	$0.632623\pi$
$228$	8.71710	−	15.5436i	0.577304	−	1.02940i
$229$	−16.5232	+	5.36871i	−1.09188	+	0.354775i	−0.798974	−	0.601365i	$-0.794624\pi$
$229$	−16.5232	+	5.36871i	−1.09188	+	0.354775i	−0.292910	+	0.956140i	$0.594624\pi$
$230$	−2.38807	−	4.39840i	−0.157465	−	0.290022i
$231$	6.88011	−	8.68668i	0.452678	−	0.571542i
$232$	−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
$238$	15.0920	+	7.72158i	0.978269	+	0.500516i
$239$	−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	0.803383	−	0.595463i	$-0.203031\pi$
$241$	−0.173801	−	0.239217i	−0.0111955	−	0.0154093i	−0.814578	+	0.580054i	$0.803031\pi$
$242$	−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
$245$	6.78594	−	14.1050i	0.433538	−	0.901135i
$246$	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	$-0.614707\pi$
$251$	−11.1729			−0.705228			−0.352614	+	0.935769i	$0.614707\pi$
$252$	6.14920	−	25.2927i	0.387363	−	1.59329i
$253$	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	$-0.422577\pi$
$257$	7.72197			0.481683			0.240842	+	0.970564i	$0.422577\pi$
$258$	39.4699	−	18.1671i	2.45729	−	1.13103i
$259$	−5.15877	+	10.0829i	−0.320551	+	0.626523i
$260$	−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
$266$	−8.68738	+	16.9797i	−0.532657	+	1.04109i
$267$	−1.50872	−	3.27785i	−0.0923321	−	0.200601i
$268$	36.3559			2.22079
$269$	0.267018	−	0.821797i	0.0162804	−	0.0501058i	−0.942586	−	0.333963i	$-0.891614\pi$
$269$	0.267018	−	0.821797i	0.0162804	−	0.0501058i	0.958867	+	0.283857i	$0.0916140\pi$
$270$	−24.5096	−	10.5829i	−1.49161	−	0.644055i
$271$	−4.12362	+	1.33985i	−0.250492	+	0.0813898i	−0.431572	−	0.902079i	$-0.642041\pi$
$271$	−4.12362	+	1.33985i	−0.250492	+	0.0813898i	0.181080	+	0.983468i	$0.442041\pi$
$272$	0.168627	+	0.518982i	0.0102245	+	0.0314679i
$273$	−10.4852	−	15.7697i	−0.634592	−	0.954425i
$274$	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
$280$	16.4036	−	5.77775i	0.980302	−	0.345287i
$281$	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	−0.0604148	−	0.998173i	$-0.519242\pi$
$283$	−11.7086	−	3.80435i	−0.696003	−	0.226145i	−0.635588	+	0.772028i	$0.719242\pi$
$284$	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
$287$	−4.52194	+	8.83824i	−0.266922	+	0.521705i
$288$	−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	$-0.117827\pi$
$293$	31.9157			1.86454			0.932268	+	0.361769i	$0.117827\pi$
$294$	−5.54261	+	27.3011i	−0.323252	+	1.59223i
$295$	−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	$-0.709015\pi$
$307$		−	27.7556i		−	1.58410i	0.610459	−	0.792048i	$-0.290985\pi$
$308$	−20.7280	+	3.24747i	−1.18109	+	0.185042i
$309$	−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	0.310225	−	0.950663i	$-0.399596\pi$
$311$	−8.78312	−	6.38131i	−0.498045	−	0.361851i	−0.808270	+	0.588812i	$0.799596\pi$
$312$	4.11733	−	20.6344i	0.233098	−	1.16819i
$313$	4.61902	+	6.35754i	0.261083	+	0.359349i	0.919354	−	0.393431i	$-0.128712\pi$
$313$	4.61902	+	6.35754i	0.261083	+	0.359349i	−0.658271	+	0.752781i	$0.728712\pi$
$314$	−38.7233	−	28.1341i	−2.18528	−	1.58770i
$315$	16.5510	+	6.40820i	0.932542	+	0.361061i
$316$	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
$322$	−4.18037	−	4.19438i	−0.232963	−	0.233744i
$323$	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
$329$	−12.0057	−	12.0459i	−0.661897	−	0.664115i
$330$	−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
$336$	−0.746731	+	0.496498i	−0.0407375	+	0.0270862i
$337$	−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	$-0.784764\pi$
$349$		−	23.3826i		−	1.25164i	0.779966	−	0.625821i	$-0.215236\pi$
$350$	6.26921	+	29.7421i	0.335103	+	1.58978i
$351$	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	0.951388	−	0.307995i	$-0.0996580\pi$
$353$	0.0124760	+	0.0383971i	0.000664030	+	0.00204367i	−0.950724	+	0.310039i	$0.899658\pi$
$354$	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
$357$	4.45036	−	11.9793i	0.235538	−	0.634011i
$358$	−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
$364$	−5.66821	+	35.4044i	−0.297095	+	1.85569i
$365$	−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	−0.204013	−	0.978968i	$-0.565398\pi$
$367$	−18.0937	−	5.87902i	−0.944486	−	0.306882i	−0.740473	+	0.672086i	$0.765398\pi$
$368$		−	0.190619i		−	0.00993670i
$369$	−10.3951	−	4.32043i	−0.541145	−	0.224912i
$370$	−4.00786	−	21.6258i	−0.208359	−	1.12427i
$371$	−12.6695	+	12.6272i	−0.657769	+	0.655573i
$372$	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
$378$	−31.3560	−	3.82180i	−1.61278	−	0.196572i
$379$	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	$-0.568708\pi$
$383$	10.4357	−	32.1178i	0.533240	−	1.64114i	0.747421	−	0.664350i	$-0.231292\pi$
$384$	31.7726	+	6.33983i	1.62139	+	0.323528i
$385$	−0.350406	−	14.3016i	−0.0178583	−	0.728875i
$386$	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
$392$	16.6881	−	12.0396i	0.842877	−	0.608089i
$393$	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	−0.345166	−	0.938542i	$-0.612177\pi$
$397$	−1.44952	+	0.470978i	−0.0727493	+	0.0236377i	0.272416	+	0.962180i	$0.412177\pi$
$398$	15.4002	+	11.1889i	0.771942	+	0.560849i
$399$	13.4776	+	5.00700i	0.674726	+	0.250664i
$400$	−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
$406$	−5.31375	−	33.9167i	−0.263717	−	1.68326i
$407$			10.3516i			0.513110i
$408$	12.8982	−	5.93677i	0.638558	−	0.293914i
$409$	−10.0896	−	13.8871i	−0.498898	−	0.686674i	0.483100	−	0.875565i	$-0.339511\pi$
$409$	−10.0896	−	13.8871i	−0.498898	−	0.686674i	−0.981998	+	0.188891i	$0.939511\pi$
$410$	−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
$413$	−10.5498	+	20.6199i	−0.519123	+	1.01464i
$414$	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	$0.381237\pi$
$419$	−9.77891	+	30.0964i	−0.477731	+	1.47030i	−0.842239	+	0.539104i	$0.818763\pi$
$420$	−14.7937	−	30.1723i	−0.721860	−	1.47226i
$421$	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
$427$	0.899505	−	5.61842i	0.0435301	−	0.271894i
$428$	−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	−0.0705494	−	0.997508i	$-0.522475\pi$
$433$	−14.8562	−	4.82709i	−0.713946	−	0.231975i	−0.643396	+	0.765533i	$0.722475\pi$
$434$	−20.7924	+	40.6393i	−0.998068	+	1.95075i
$435$	−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	−0.491072	−	0.871119i	$-0.663395\pi$
$439$	10.2491	−	14.1066i	0.489161	−	0.673272i	0.980233	+	0.197847i	$0.0633949\pi$
$440$	10.9416	−	11.5298i	0.521622	−	0.549662i
$441$	20.9276	+	1.74282i	0.996550	+	0.0829915i
$442$	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
$448$	−33.6155	−	5.38181i	−1.58818	−	0.254267i
$449$			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
$455$	−23.4295	−	6.98306i	−1.09839	−	0.327371i
$456$	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	0.658265	−	0.752786i	$-0.271290\pi$
$461$	3.12914	+	2.27346i	0.145739	+	0.105885i	−0.512527	+	0.858671i	$0.671290\pi$
$462$	6.85551	+	24.5211i	0.318947	+	1.14082i
$463$	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	$0.455180\pi$
$467$	−11.9972	+	36.9236i	−0.555165	+	1.70862i	−0.695507	+	0.718519i	$0.744820\pi$
$468$	−40.5268	−	3.23857i	−1.87335	−	0.149703i
$469$	4.53995	+	28.9776i	0.209635	+	1.33806i
$470$	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	$-0.863626\pi$
$479$	−9.14648	−	28.1500i	−0.417913	−	1.28621i	0.491705	−	0.870762i	$-0.336374\pi$
$480$	−6.77185	+	19.9091i	−0.309091	+	0.908724i
$481$	16.8245	+	5.46663i	0.767133	+	0.249257i
$482$	0.679401			0.0309459
$483$	−2.77161	+	3.49937i	−0.126113	+	0.159227i
$484$	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
$490$	17.0547	+	31.6637i	0.770451	+	1.43042i
$491$	−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
$497$	−9.42658	+	9.39510i	−0.422840	+	0.421428i
$498$	−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	0.957698	−	0.287775i	$-0.0929155\pi$
$503$	0.308477	+	0.949394i	0.0137543	+	0.0423314i	−0.943944	+	0.330106i	$0.892915\pi$
$504$	15.1025	+	17.7860i	0.672719	+	0.792253i
$505$	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	−0.216146	−	0.976361i	$-0.569349\pi$
$509$	14.5662	−	10.5830i	0.645636	−	0.469082i	0.861782	+	0.507279i	$0.169349\pi$
$510$	7.34449	+	23.7044i	0.325219	+	1.04965i
$511$	−2.20230	+	13.7558i	−0.0974239	+	0.608522i
$512$	−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	$0.188654\pi$
$521$	11.1100	+	34.1929i	0.486736	+	1.49802i	−0.342715	+	0.939440i	$0.611346\pi$
$522$	37.8624	−	9.04181i	1.65719	−	0.395749i
$523$	−12.9393	+	17.8094i	−0.565796	+	0.778752i	−0.992049	−	0.125852i	$-0.959833\pi$
$523$	−12.9393	+	17.8094i	−0.565796	+	0.778752i	0.426253	+	0.904604i	$0.359833\pi$
$524$	−43.1156			−1.88351
$525$	21.7137	−	7.31527i	0.947666	−	0.319264i
$526$	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
$539$	−5.17683	−	16.1159i	−0.222982	−	0.694159i
$540$	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
$546$	43.4747	+	1.80713i	1.86054	+	0.0773380i
$547$	−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
$553$	7.35377	+	7.37841i	0.312714	+	0.313762i
$554$	−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
$560$	−0.330664	+	1.10944i	−0.0139731	+	0.0468824i
$561$	−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	−0.708620	−	0.705590i	$-0.750682\pi$
$563$	−6.08707	+	4.42252i	−0.256540	+	0.186387i	0.452081	+	0.891977i	$0.350682\pi$
$564$	−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
$567$	−0.0970908	+	23.8116i	−0.00407743	+	0.999992i
$568$	−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	−0.537928	−	0.842991i	$-0.680793\pi$
$577$	10.3297	−	14.2177i	0.430033	−	0.591890i	0.967961	+	0.251101i	$0.0807927\pi$
$578$	−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
$581$	3.32635	+	21.2315i	0.138000	+	0.880829i
$582$	−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	$-0.367070\pi$
$587$	33.9250	−	24.6479i	1.40023	−	1.01733i	0.994653	−	0.103269i	$-0.0329302\pi$
$588$	−26.8741	−	29.3034i	−1.10827	−	1.20845i
$589$	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	$-0.593033\pi$
$593$	−14.0328			−0.576257			−0.288128	+	0.957592i	$0.593033\pi$
$594$	−27.1040	+	9.94369i	−1.11209	+	0.407995i
$595$	−5.48093	−	15.5609i	−0.224696	−	0.637934i
$596$	−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	$0.147373\pi$
$601$			21.8982i			0.893245i	−0.894723	+	0.446622i	$0.852627\pi$
$602$	10.4924	−	65.5366i	0.427637	−	2.67107i
$603$	−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	$-0.711120\pi$
$607$		−	38.8281i		−	1.57599i	0.615685	−	0.787993i	$-0.288880\pi$
$608$	−5.26429	+	16.2018i	−0.213495	+	0.657071i
$609$	−24.9233	+	6.96796i	−1.00994	+	0.282356i
$610$	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
$616$	8.56639	−	16.7432i	0.345150	−	0.674603i
$617$	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	0.223333	−	0.974742i	$-0.428306\pi$
$619$	−4.20284	−	1.36559i	−0.168926	−	0.0548875i	−0.392259	+	0.919855i	$0.628306\pi$
$620$	−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
$623$	−5.44260	−	0.871356i	−0.218053	−	0.0349102i
$624$	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
$630$	−34.2650	+	22.1116i	−1.36515	+	0.880947i
$631$	−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
$637$	−28.9271	−	0.0967516i	−1.14613	−	0.00383344i
$638$	−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	$-0.850038\pi$
$643$		−	23.0187i		−	0.907770i	0.891060	−	0.453885i	$-0.149962\pi$
$644$	8.35015	−	1.30822i	0.329042	−	0.0515512i
$645$	−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	$0.204461\pi$
$647$	12.8464	+	39.5370i	0.505042	+	1.55436i	−0.295657	+	0.955294i	$0.595539\pi$
$648$	−18.7530	+	18.6630i	−0.736685	+	0.733150i
$649$			21.1693i			0.830968i
$650$	44.3228	−	17.0128i	1.73848	−	0.667296i
$651$	32.2574	+	11.9838i	1.26427	+	0.469682i
$652$	−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
$658$	38.6063	−	6.04847i	1.50503	−	0.235794i
$659$	−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	−0.993471	−	0.114087i	$-0.963606\pi$
$661$	−14.8595	+	20.4524i	−0.577969	+	0.795506i	0.415502	+	0.909592i	$0.363606\pi$
$662$	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
$665$	17.5072	−	6.16648i	0.678901	−	0.239126i
$666$	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
$672$	−1.03340	+	24.8607i	−0.0398642	+	0.959024i
$673$	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	0.780169	−	0.625569i	$-0.215133\pi$
$677$	11.0921	+	8.05887i	0.426303	+	0.309727i	−0.353866	+	0.935296i	$0.615133\pi$
$678$	−56.8147	−	31.8626i	−2.18196	−	1.22368i
$679$	30.2356	−	30.1346i	1.16034	−	1.15646i
$680$	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
$686$	29.9388	+	30.2407i	1.14307	+	1.15460i
$687$	−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	$-0.993665\pi$
$691$	−18.6577	−	25.6801i	−0.709772	−	0.976917i	0.290030	−	0.957018i	$-0.406335\pi$
$692$	−14.0990	+	43.3923i	−0.535963	+	1.64953i
$693$	17.7533	−	7.29395i	0.674394	−	0.277074i
$694$	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
$700$	−39.6019	−	17.7124i	−1.49681	−	0.669465i
$701$		−	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
$714$	16.2575	+	24.4513i	0.608423	+	0.915067i
$715$	−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	−0.949788	−	0.312895i	$-0.898701\pi$
$719$	0.0676134	−	0.208093i	0.00252155	−	0.00776055i	0.952309	+	0.305134i	$0.0987013\pi$
$720$	−1.28366	−	0.274478i	−0.0478390	−	0.0102292i
$721$	−3.18421	+	3.17358i	−0.118586	+	0.118190i
$722$	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	−0.651755	−	0.758430i	$-0.725967\pi$
$727$	7.30584	−	10.0556i	0.270958	−	0.372942i	0.922713	+	0.385488i	$0.125967\pi$
$728$	−22.6890	−	22.7650i	−0.840911	−	0.843728i
$729$	−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	0.790290	−	0.612733i	$-0.209930\pi$
$733$	28.9554	+	9.40818i	1.06949	+	0.347499i	0.279202	+	0.960232i	$0.409930\pi$
$734$	35.3649	−	25.6941i	1.30534	−	0.948386i
$735$	22.2016	−	15.5592i	0.818919	−	0.573909i
$736$	−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
$742$	−6.36157	−	40.6048i	−0.233541	−	1.49065i
$743$			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
$756$	30.7182	−	32.9999i	1.11721	−	1.20019i
$757$	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	0.437010	−	0.899457i	$-0.356038\pi$
$761$	−7.81741	−	5.67968i	−0.283381	−	0.205888i	−0.720391	+	0.693568i	$0.756038\pi$
$762$	75.0198	+	14.9693i	2.71768	+	0.542279i
$763$	−21.3316	+	41.6931i	−0.772256	+	1.50939i
$764$	−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	−0.158671	−	0.987332i	$-0.550721\pi$
$769$	−24.0531	−	7.81533i	−0.867377	−	0.281828i	−0.708706	+	0.705504i	$0.750721\pi$
$770$	27.0580	+	18.6636i	0.975104	+	0.672590i
$771$	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	0.0852321	−	0.996361i	$-0.472837\pi$
$773$	−23.2439	−	16.8877i	−0.836025	−	0.607408i	−0.921258	+	0.388953i	$0.872837\pi$
$774$	75.0187	+	5.99488i	2.69649	+	0.215482i
$775$	37.4947	−	1.96417i	1.34685	−	0.0705549i
$776$	47.4307			1.70266
$777$	−16.3359	+	10.8616i	−0.586046	+	0.389659i
$778$	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
$784$	−0.00458141	+	1.36976i	−0.000163622	+	0.0489202i
$785$	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	0.383348	−	0.923604i	$-0.374771\pi$
$787$	−17.2112	−	23.6892i	−0.613513	−	0.844428i	−0.996861	+	0.0791762i	$0.974771\pi$
$788$	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
$791$	38.5522	+	19.7246i	1.37076	+	0.701327i
$792$	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	$-0.820581\pi$
$797$	−13.4235	−	41.3132i	−0.475484	−	1.46339i	0.369821	−	0.929103i	$-0.379419\pi$
$798$	−27.5096	+	18.2910i	−0.973830	+	0.647495i
$799$	−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
$805$	0.141159	+	5.76129i	0.00497519	+	0.203059i
$806$	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	$0.418796\pi$
$811$	−21.2420	+	29.2370i	−0.745906	+	1.02665i	−0.998257	+	0.0590157i	$0.981204\pi$
$812$	43.6206	+	22.3178i	1.53078	+	0.783200i
$813$	−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
$819$	−2.47947	−	32.7066i	−0.0866398	−	1.14286i
$820$	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	−0.215068	−	0.976599i	$-0.568997\pi$
$829$	5.32569	−	1.73042i	0.184969	−	0.0601000i	0.400037	+	0.916499i	$0.368997\pi$
$830$	−30.2713	−	28.7271i	−1.05073	−	0.997131i
$831$	5.48812	+	11.9235i	0.190381	+	0.413622i
$832$			53.1735i			1.84346i
$833$	−11.4210	−	15.8308i	−0.395716	−	0.548505i
$834$	−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	−0.157044	−	0.987592i	$-0.550196\pi$
$839$	−33.1605	−	24.0925i	−1.14483	−	0.831767i	−0.987785	+	0.155825i	$0.950196\pi$
$840$	29.6759	+	5.16909i	1.02392	+	0.178351i
$841$	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
$847$	9.62359	+	9.65583i	0.330670	+	0.331778i
$848$	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	−0.396097	−	0.918209i	$-0.629636\pi$
$853$	−5.16471	+	1.67811i	−0.176836	+	0.0574576i	0.219261	+	0.975666i	$0.429636\pi$
$854$	9.22911	+	9.26003i	0.315814	+	0.316872i
$855$	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	$-0.828043\pi$
$857$	−50.2115			−1.71519			−0.857596	+	0.514324i	$0.828043\pi$
$858$	36.1257	−	16.6278i	1.23331	−	0.567665i
$859$	−5.67410	−	7.80973i	−0.193598	−	0.266465i	0.701172	−	0.712992i	$-0.252661\pi$
$859$	−5.67410	−	7.80973i	−0.193598	−	0.266465i	−0.894770	+	0.446527i	$0.852661\pi$
$860$	38.2008	+	70.3590i	1.30264	+	2.39922i
$861$	−14.3193	+	9.52081i	−0.488000	+	0.324468i
$862$	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
$875$	15.4987	−	25.1950i	0.523952	−	0.851747i
$876$	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	−0.980782	−	0.195109i	$-0.937494\pi$
$881$	−2.15579	+	6.63485i	−0.0726305	+	0.223534i	0.908151	+	0.418643i	$0.137494\pi$
$882$	−31.5034	+	36.5479i	−1.06078	+	1.23063i
$883$	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	−0.582956	−	0.812504i	$-0.698104\pi$
$887$	0.287017	−	0.208530i	0.00963708	−	0.00700175i	0.592593	+	0.805502i	$0.298104\pi$
$888$	−21.3752	−	4.26516i	−0.717306	−	0.143129i
$889$	−50.2174	−	8.03977i	−1.68424	−	0.269645i
$890$	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
$896$	35.0534	−	34.9363i	1.17105	−	1.16714i
$897$	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
$903$	−49.9888	−	2.07791i	−1.66352	−	0.0691484i
$904$	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
$910$	44.6233	−	34.1215i	1.47925	−	1.13112i
$911$	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
$917$	−5.38406	−	34.3655i	−0.177797	−	1.13485i
$918$	−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
$924$	−34.0651	−	12.6554i	−1.12066	−	0.416331i
$925$	−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	0.966143	−	0.258006i	$-0.0830655\pi$
$929$	1.00170	+	3.08291i	0.0328647	+	0.101147i	−0.933279	+	0.359153i	$0.883066\pi$
$930$	−63.8304	+	19.7770i	−2.09308	+	0.648513i
$931$	17.8109	−	12.8496i	0.583728	−	0.421128i
$932$		−	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	$0.112841\pi$
$937$	29.9416	+	41.2111i	0.978150	+	1.34631i	0.0403295	+	0.999186i	$0.487159\pi$
$938$	−59.9972	−	30.6966i	−1.95898	−	1.00228i
$939$	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	−0.292385	−	0.956301i	$-0.594449\pi$
$941$	16.1587	−	11.7400i	0.526760	−	0.382713i	0.819144	+	0.573587i	$0.194449\pi$
$942$	−34.6633	−	75.3095i	−1.12939	−	2.45372i
$943$		−	3.65530i		−	0.119033i
$944$	0.529370	−	1.62923i	0.0172295	−	0.0530271i
$945$	19.5744	+	23.7033i	0.636754	+	0.771067i
$946$	−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
$952$	3.42877	−	21.4165i	0.111127	−	0.694113i
$953$	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
$959$	−25.5497	−	13.0721i	−0.825043	−	0.422120i
$960$	−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
$966$	−2.76170	−	9.87816i	−0.0888562	−	0.317824i
$967$	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	$0.0324144\pi$
$971$	7.78231	+	23.9515i	0.249746	+	0.768639i	−0.745073	+	0.666982i	$0.767586\pi$
$972$	40.0507	+	31.7692i	1.28463	+	1.01900i
$973$	1.11629	−	6.97250i	0.0357866	−	0.223528i
$974$			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
$980$	−50.8689	−	6.87076i	−1.62495	−	0.219478i
$981$	−49.0371	−	20.3810i	−1.56564	−	0.650714i
$982$	8.86447			0.282877
$983$	−3.69633	+	11.3761i	−0.117895	+	0.362843i	−0.992540	−	0.121921i	$-0.961094\pi$
$983$	−3.69633	+	11.3761i	−0.117895	+	0.362843i	0.874645	+	0.484764i	$0.161094\pi$
$984$	−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
$987$	−7.93140	−	28.3693i	−0.252459	−	0.903006i
$988$	−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
$994$	−4.73324	−	30.2114i	−0.150129	−	0.958247i
$995$	−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	−0.814179	−	0.580615i	$-0.802812\pi$
$997$	−35.7302	+	11.6094i	−1.13159	+	0.367675i	−0.317408	+	0.948289i	$0.602812\pi$
$998$	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.41.10	yes	304
3.2	odd	2	inner	525.2.bb.a.41.68	yes	304
7.6	odd	2	inner	525.2.bb.a.41.9	✓	304
21.20	even	2	inner	525.2.bb.a.41.67	yes	304
25.11	even	5	inner	525.2.bb.a.461.67	yes	304
75.11	odd	10	inner	525.2.bb.a.461.9	yes	304
175.111	odd	10	inner	525.2.bb.a.461.68	yes	304
525.461	even	10	inner	525.2.bb.a.461.10	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.9	✓	304	7.6	odd	2	inner
525.2.bb.a.41.10	yes	304	1.1	even	1	trivial
525.2.bb.a.41.67	yes	304	21.20	even	2	inner
525.2.bb.a.41.68	yes	304	3.2	odd	2	inner
525.2.bb.a.461.9	yes	304	75.11	odd	10	inner
525.2.bb.a.461.10	yes	304	525.461	even	10	inner
525.2.bb.a.461.67	yes	304	25.11	even	5	inner
525.2.bb.a.461.68	yes	304	175.111	odd	10	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} +(-0.961025 + 6.00269i) 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} +(4.57862 + 0.190322i) 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} +(-6.12493 - 6.14545i) 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} +(4.69960 - 3.59357i) 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} +(-6.53745 + 8.25404i) 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} +(7.68393 - 1.20385i) 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} +(6.75567 + 4.16664i) 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} +(0.332954 + 13.5893i) 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} +(1.01140 - 6.31732i) 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} +(-4.04634 - 14.4731i) 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} +(-9.73348 - 4.97998i) 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} +(4.91900 + 15.3132i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more