LMFDB - Embedded newform 260.2.o.a.27.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.17
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +O(q^{10})$	\(q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +(2.92509 + 1.20159i) q^{10} +0.497041i q^{11} +(-3.60941 - 2.88234i) q^{12} +(0.707107 - 0.707107i) q^{13} +(4.54342 + 4.06297i) q^{14} +(-4.86888 + 1.72154i) q^{15} +(3.90089 - 0.884894i) q^{16} +(-2.41342 - 2.41342i) q^{17} +(3.29556 - 0.183975i) q^{18} +5.62862 q^{19} +(1.46609 - 4.22499i) q^{20} -9.95385 q^{21} +(0.701829 - 0.0391797i) q^{22} +(4.41675 + 4.41675i) q^{23} +(-3.78540 + 5.32375i) q^{24} +(-3.14287 - 3.88875i) q^{25} +(-1.05418 - 0.942707i) q^{26} +(1.08773 - 1.08773i) q^{27} +(5.37884 - 6.73565i) q^{28} -5.13981i q^{29} +(2.81463 + 6.73924i) q^{30} +3.14912i q^{31} +(-1.55698 - 5.43837i) q^{32} +(-0.811710 + 0.811710i) q^{33} +(-3.21754 + 3.59802i) q^{34} +(-3.21261 - 9.08599i) q^{35} +(-0.519552 - 4.63888i) q^{36} +(4.40088 + 4.40088i) q^{37} +(-0.443681 - 7.94770i) q^{38} +2.30953 q^{39} +(-6.08132 - 1.73711i) q^{40} +8.49850 q^{41} +(0.784621 + 14.0550i) q^{42} +(5.16698 + 5.16698i) q^{43} +(-0.110645 - 0.987905i) q^{44} +(-4.70939 - 2.24903i) q^{45} +(5.88836 - 6.58467i) q^{46} +(-0.110788 + 0.110788i) q^{47} +(7.81560 + 4.92539i) q^{48} -11.5752i q^{49} +(-5.24323 + 4.74432i) q^{50} -7.88265i q^{51} +(-1.24802 + 1.56283i) q^{52} +(0.203180 - 0.203180i) q^{53} +(-1.62163 - 1.45015i) q^{54} +(-1.00292 - 0.478958i) q^{55} +(-9.93483 - 7.06405i) q^{56} +(9.19203 + 9.19203i) q^{57} +(-7.25749 + 0.405150i) q^{58} -7.36019 q^{59} +(9.29404 - 4.50552i) q^{60} -6.43106 q^{61} +(4.44661 - 0.248232i) q^{62} +(-7.11283 - 7.11283i) q^{63} +(-7.55632 + 2.62716i) q^{64} +(0.745404 + 2.10817i) q^{65} +(1.21013 + 1.08216i) q^{66} +(-7.40905 + 7.40905i) q^{67} +(5.33409 + 4.25960i) q^{68} +14.4259i q^{69} +(-12.5763 + 5.25247i) q^{70} -0.618858i q^{71} +(-6.50922 + 1.09928i) q^{72} +(-11.5363 + 11.5363i) q^{73} +(5.86720 - 6.56101i) q^{74} +(1.21807 - 11.4832i) q^{75} +(-11.1873 + 1.25297i) q^{76} +(-1.51476 - 1.51476i) q^{77} +(-0.182051 - 3.26110i) q^{78} -2.69514 q^{79} +(-1.97345 + 8.72385i) q^{80} +10.5545 q^{81} +(-0.669902 - 12.0000i) q^{82} +(-5.93375 - 5.93375i) q^{83} +(19.7840 - 2.21579i) q^{84} +(7.19537 - 2.54413i) q^{85} +(6.88856 - 7.70314i) q^{86} +(8.39376 - 8.39376i) q^{87} +(-1.38621 + 0.234104i) q^{88} -12.7437i q^{89} +(-2.80445 + 6.82701i) q^{90} +4.30990i q^{91} +(-9.76181 - 7.79541i) q^{92} +(-5.14279 + 5.14279i) q^{93} +(0.165168 + 0.147702i) q^{94} +(-5.42385 + 11.3573i) q^{95} +(6.33865 - 11.4240i) q^{96} +(8.15212 + 8.15212i) q^{97} +(-16.3444 + 0.912426i) q^{98} -1.16007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0788259	−	1.41202i	−0.0557383	−	0.998445i
$2$	−0.0788259	−	1.41202i	−0.0557383	−	0.998445i
$3$	1.63309	+	1.63309i	0.942863	+	0.942863i	0.998454	−	0.0555906i	$-0.0177042\pi$
$3$	1.63309	+	1.63309i	0.942863	+	0.942863i	−0.0555906	+	0.998454i	$0.517704\pi$
$4$	−1.98757	+	0.222607i	−0.993786	+	0.111303i
$5$	−0.963620	+	2.01778i	−0.430944	+	0.902379i
$5$	−0.963620	+	2.01778i	−0.430944	+	0.902379i
$6$	2.17721	−	2.43467i	0.888844	−	0.993951i
$7$	−3.04756	+	3.04756i	−1.15187	+	1.15187i	−0.165690	+	0.986178i	$0.552985\pi$
$7$	−3.04756	+	3.04756i	−1.15187	+	1.15187i	−0.986178	+	0.165690i	$0.947015\pi$
$8$	0.470996	+	2.78894i	0.166522	+	0.986038i
$9$			2.33394i			0.777981i
$10$	2.92509	+	1.20159i	0.924996	+	0.379977i
$11$			0.497041i			0.149863i	0.997189	+	0.0749317i	$0.0238739\pi$
$11$			0.497041i			0.149863i	−0.997189	+	0.0749317i	$0.976126\pi$
$12$	−3.60941	−	2.88234i	−1.04195	−	0.832061i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	4.54342	+	4.06297i	1.21428	+	1.08587i
$15$	−4.86888	+	1.72154i	−1.25714	+	0.444499i
$16$	3.90089	−	0.884894i	0.975223	−	0.221224i
$17$	−2.41342	−	2.41342i	−0.585340	−	0.585340i	0.351026	−	0.936366i	$-0.385833\pi$
$17$	−2.41342	−	2.41342i	−0.585340	−	0.585340i	−0.936366	+	0.351026i	$0.885833\pi$
$18$	3.29556	−	0.183975i	0.776772	−	0.0433634i
$19$	5.62862			1.29129			0.645647	−	0.763636i	$-0.276588\pi$
$19$	5.62862			1.29129			0.645647	+	0.763636i	$0.276588\pi$
$20$	1.46609	−	4.22499i	0.327828	−	0.944737i
$21$	−9.95385			−2.17211
$22$	0.701829	−	0.0391797i	0.149630	−	0.00835314i
$23$	4.41675	+	4.41675i	0.920956	+	0.920956i	0.997097	−	0.0761410i	$-0.0242599\pi$
$23$	4.41675	+	4.41675i	0.920956	+	0.920956i	−0.0761410	+	0.997097i	$0.524260\pi$
$24$	−3.78540	+	5.32375i	−0.772691	+	1.08671i
$25$	−3.14287	−	3.88875i	−0.628575	−	0.777749i
$26$	−1.05418	−	0.942707i	−0.206742	−	0.184880i
$27$	1.08773	−	1.08773i	0.209333	−	0.209333i
$28$	5.37884	−	6.73565i	1.01650	−	1.27292i
$29$		−	5.13981i		−	0.954439i	−0.878784	−	0.477220i	$-0.841645\pi$
$29$		−	5.13981i		−	0.954439i	0.878784	−	0.477220i	$-0.158355\pi$
$30$	2.81463	+	6.73924i	0.513878	+	1.23041i
$31$			3.14912i			0.565599i	0.959179	+	0.282800i	$0.0912631\pi$
$31$			3.14912i			0.565599i	−0.959179	+	0.282800i	$0.908737\pi$
$32$	−1.55698	−	5.43837i	−0.275237	−	0.961376i
$33$	−0.811710	+	0.811710i	−0.141301	+	0.141301i
$34$	−3.21754	+	3.59802i	−0.551804	+	0.617056i
$35$	−3.21261	−	9.08599i	−0.543031	−	1.53581i
$36$	−0.519552	−	4.63888i	−0.0865919	−	0.773147i
$37$	4.40088	+	4.40088i	0.723500	+	0.723500i	0.969316	−	0.245817i	$-0.0790561\pi$
$37$	4.40088	+	4.40088i	0.723500	+	0.723500i	−0.245817	+	0.969316i	$0.579056\pi$
$38$	−0.443681	−	7.94770i	−0.0719746	−	1.28929i
$39$	2.30953			0.369821
$40$	−6.08132	−	1.73711i	−0.961541	−	0.274661i
$41$	8.49850			1.32724			0.663621	−	0.748069i	$-0.269019\pi$
$41$	8.49850			1.32724			0.663621	+	0.748069i	$0.269019\pi$
$42$	0.784621	+	14.0550i	0.121070	+	2.16873i
$43$	5.16698	+	5.16698i	0.787957	+	0.787957i	0.981159	−	0.193202i	$-0.0618873\pi$
$43$	5.16698	+	5.16698i	0.787957	+	0.787957i	−0.193202	+	0.981159i	$0.561887\pi$
$44$	−0.110645	−	0.987905i	−0.0166803	−	0.148932i
$45$	−4.70939	−	2.24903i	−0.702034	−	0.335266i
$46$	5.88836	−	6.58467i	0.868192	−	0.970857i
$47$	−0.110788	+	0.110788i	−0.0161601	+	0.0161601i	−0.715141	−	0.698981i	$-0.753637\pi$
$47$	−0.110788	+	0.110788i	−0.0161601	+	0.0161601i	0.698981	+	0.715141i	$0.253637\pi$
$48$	7.81560	+	4.92539i	1.12809	+	0.710918i
$49$		−	11.5752i		−	1.65360i
$50$	−5.24323	+	4.74432i	−0.741504	+	0.670948i
$51$		−	7.88265i		−	1.10379i
$52$	−1.24802	+	1.56283i	−0.173069	+	0.216726i
$53$	0.203180	−	0.203180i	0.0279090	−	0.0279090i	−0.693015	−	0.720924i	$-0.743718\pi$
$53$	0.203180	−	0.203180i	0.0279090	−	0.0279090i	0.720924	+	0.693015i	$0.243718\pi$
$54$	−1.62163	−	1.45015i	−0.220676	−	0.197340i
$55$	−1.00292	−	0.478958i	−0.135234	−	0.0645827i
$56$	−9.93483	−	7.06405i	−1.32760	−	0.943974i
$57$	9.19203	+	9.19203i	1.21751	+	1.21751i
$58$	−7.25749	+	0.405150i	−0.952955	+	0.0531988i
$59$	−7.36019			−0.958216			−0.479108	−	0.877756i	$-0.659040\pi$
$59$	−7.36019			−0.958216			−0.479108	+	0.877756i	$0.659040\pi$
$60$	9.29404	−	4.50552i	1.19986	−	0.581661i
$61$	−6.43106			−0.823413			−0.411707	−	0.911316i	$-0.635067\pi$
$61$	−6.43106			−0.823413			−0.411707	+	0.911316i	$0.635067\pi$
$62$	4.44661	−	0.248232i	0.564720	−	0.0315256i
$63$	−7.11283	−	7.11283i	−0.896132	−	0.896132i
$64$	−7.55632	+	2.62716i	−0.944541	+	0.328395i
$65$	0.745404	+	2.10817i	0.0924560	+	0.261486i
$66$	1.21013	+	1.08216i	0.148957	+	0.133205i
$67$	−7.40905	+	7.40905i	−0.905159	+	0.905159i	−0.995877	−	0.0907174i	$-0.971084\pi$
$67$	−7.40905	+	7.40905i	−0.905159	+	0.905159i	0.0907174	+	0.995877i	$0.471084\pi$
$68$	5.33409	+	4.25960i	0.646853	+	0.516553i
$69$			14.4259i			1.73667i
$70$	−12.5763	+	5.25247i	−1.50316	+	0.627790i
$71$		−	0.618858i		−	0.0734449i	−0.999326	−	0.0367225i	$-0.988308\pi$
$71$		−	0.618858i		−	0.0734449i	0.999326	−	0.0367225i	$-0.0116917\pi$
$72$	−6.50922	+	1.09928i	−0.767119	+	0.129551i
$73$	−11.5363	+	11.5363i	−1.35023	+	1.35023i	−0.464820	+	0.885405i	$0.653881\pi$
$73$	−11.5363	+	11.5363i	−1.35023	+	1.35023i	−0.885405	+	0.464820i	$0.846119\pi$
$74$	5.86720	−	6.56101i	0.682048	−	0.762701i
$75$	1.21807	−	11.4832i	0.140651	−	1.32597i
$76$	−11.1873	+	1.25297i	−1.28327	+	0.143725i
$77$	−1.51476	−	1.51476i	−0.172623	−	0.172623i
$78$	−0.182051	−	3.26110i	−0.0206132	−	0.369246i
$79$	−2.69514			−0.303227			−0.151613	−	0.988440i	$-0.548447\pi$
$79$	−2.69514			−0.303227			−0.151613	+	0.988440i	$0.548447\pi$
$80$	−1.97345	+	8.72385i	−0.220639	+	0.975356i
$81$	10.5545			1.17273
$82$	−0.669902	−	12.0000i	−0.0739783	−	1.32518i
$83$	−5.93375	−	5.93375i	−0.651314	−	0.651314i	0.301995	−	0.953309i	$-0.402347\pi$
$83$	−5.93375	−	5.93375i	−0.651314	−	0.651314i	−0.953309	+	0.301995i	$0.902347\pi$
$84$	19.7840	−	2.21579i	2.15861	−	0.241763i
$85$	7.19537	−	2.54413i	0.780447	−	0.275950i
$86$	6.88856	−	7.70314i	0.742812	−	0.830651i
$87$	8.39376	−	8.39376i	0.899905	−	0.899905i
$88$	−1.38621	+	0.234104i	−0.147771	+	0.0249556i
$89$		−	12.7437i		−	1.35083i	−0.737440	−	0.675413i	$-0.763965\pi$
$89$		−	12.7437i		−	1.35083i	0.737440	−	0.675413i	$-0.236035\pi$
$90$	−2.80445	+	6.82701i	−0.295615	+	0.719630i
$91$			4.30990i			0.451800i
$92$	−9.76181	−	7.79541i	−1.01774	−	0.812728i
$93$	−5.14279	+	5.14279i	−0.533282	+	0.533282i
$94$	0.165168	+	0.147702i	0.0170357	+	0.0152343i
$95$	−5.42385	+	11.3573i	−0.556476	+	1.16524i
$96$	6.33865	−	11.4240i	0.646936	−	1.16596i
$97$	8.15212	+	8.15212i	0.827723	+	0.827723i	0.987201	−	0.159479i	$-0.0509814\pi$
$97$	8.15212	+	8.15212i	0.827723	+	0.827723i	−0.159479	+	0.987201i	$0.550981\pi$
$98$	−16.3444	+	0.912426i	−1.65103	+	0.0921690i
$99$	−1.16007			−0.116591
$100$	7.11235	+	7.02954i	0.711235	+	0.702954i
$101$	−4.18013			−0.415938			−0.207969	−	0.978135i	$-0.566685\pi$
$101$	−4.18013			−0.415938			−0.207969	+	0.978135i	$0.566685\pi$
$102$	−11.1304	+	0.621357i	−1.10208	+	0.0615235i
$103$	3.46965	+	3.46965i	0.341875	+	0.341875i	0.857072	−	0.515197i	$-0.172281\pi$
$103$	3.46965	+	3.46965i	0.341875	+	0.341875i	−0.515197	+	0.857072i	$0.672281\pi$
$104$	2.30512	+	1.63903i	0.226036	+	0.160720i
$105$	9.59172	−	20.0847i	0.936056	−	1.96006i
$106$	−0.302910	−	0.270878i	−0.0294212	−	0.0263100i
$107$	9.43408	−	9.43408i	0.912027	−	0.912027i	−0.0844046	−	0.996432i	$-0.526899\pi$
$107$	9.43408	−	9.43408i	0.912027	−	0.912027i	0.996432	+	0.0844046i	$0.0268988\pi$
$108$	−1.91980	+	2.40407i	−0.184733	+	0.231332i
$109$		−	10.2008i		−	0.977061i	−0.872547	−	0.488531i	$-0.837533\pi$
$109$		−	10.2008i		−	0.977061i	0.872547	−	0.488531i	$-0.162467\pi$
$110$	−0.597240	+	1.45389i	−0.0569446	+	0.138623i
$111$			14.3740i			1.36432i
$112$	−9.19143	+	14.5850i	−0.868508	+	1.37815i
$113$	9.50714	−	9.50714i	0.894357	−	0.894357i	−0.100573	−	0.994930i	$-0.532068\pi$
$113$	9.50714	−	9.50714i	0.894357	−	0.894357i	0.994930	+	0.100573i	$0.0320676\pi$
$114$	12.2547	−	13.7039i	1.14776	−	1.28348i
$115$	−13.1681	+	4.65596i	−1.22793	+	0.434171i
$116$	1.14416	+	10.2158i	0.106232	+	0.948509i
$117$	1.65035	+	1.65035i	0.152575	+	0.152575i
$118$	0.580174	+	10.3927i	0.0534093	+	0.956726i
$119$	14.7101			1.34847
$120$	−7.09448	−	12.7682i	−0.647634	−	1.16557i
$121$	10.7530			0.977541
$122$	0.506934	+	9.08076i	0.0458957	+	0.822133i
$123$	13.8788	+	13.8788i	1.25141	+	1.25141i
$124$	−0.701016	−	6.25911i	−0.0629531	−	0.562085i
$125$	10.8752	−	2.59436i	0.972705	−	0.232046i
$126$	−9.48274	+	10.6041i	−0.844790	+	0.944688i
$127$	−0.0846773	+	0.0846773i	−0.00751389	+	0.00751389i	−0.710854	−	0.703340i	$-0.751691\pi$
$127$	−0.0846773	+	0.0846773i	−0.00751389	+	0.00751389i	0.703340	+	0.710854i	$0.251691\pi$
$128$	4.30522	+	10.4626i	0.380531	+	0.924768i
$129$			16.8762i			1.48587i
$130$	2.91801	−	1.21870i	0.255926	−	0.106887i
$131$		−	12.2879i		−	1.07360i	−0.843709	−	0.536801i	$-0.819633\pi$
$131$		−	12.2879i		−	1.07360i	0.843709	−	0.536801i	$-0.180367\pi$
$132$	1.43264	−	1.79403i	0.124695	−	0.156150i
$133$	−17.1536	+	17.1536i	−1.48740	+	1.48740i
$134$	11.0457	+	9.87766i	0.954204	+	0.853300i
$135$	1.14664	+	3.24295i	0.0986870	+	0.279109i
$136$	5.59416	−	7.86758i	0.479695	−	0.674640i
$137$	−2.43793	−	2.43793i	−0.208286	−	0.208286i	0.595253	−	0.803539i	$-0.297052\pi$
$137$	−2.43793	−	2.43793i	−0.208286	−	0.208286i	−0.803539	+	0.595253i	$0.797052\pi$
$138$	20.3695	−	1.13713i	1.73397	−	0.0967991i
$139$	2.17145			0.184180			0.0920899	−	0.995751i	$-0.470645\pi$
$139$	2.17145			0.184180			0.0920899	+	0.995751i	$0.470645\pi$
$140$	8.40791	+	17.3439i	0.710598	+	1.46583i
$141$	−0.361854			−0.0304736
$142$	−0.873837	+	0.0487820i	−0.0733307	+	0.00409370i
$143$	0.351461	+	0.351461i	0.0293906	+	0.0293906i
$144$	2.06529	+	9.10446i	0.172108	+	0.758705i
$145$	10.3710	+	4.95282i	0.861266	+	0.411310i
$146$	17.1988	+	15.3801i	1.42339	+	1.27287i
$147$	18.9033	−	18.9033i	1.55912	−	1.55912i
$148$	−9.72673	−	7.76740i	−0.799532	−	0.638476i
$149$			0.402191i			0.0329488i	0.999864	+	0.0164744i	$0.00524420\pi$
$149$			0.402191i			0.0329488i	−0.999864	+	0.0164744i	$0.994756\pi$
$150$	−16.3105	−	0.814759i	−1.33175	−	0.0665248i
$151$		−	11.5532i		−	0.940189i	−0.882616	−	0.470095i	$-0.844220\pi$
$151$		−	11.5532i		−	0.940189i	0.882616	−	0.470095i	$-0.155780\pi$
$152$	2.65106	+	15.6979i	0.215029	+	1.27327i
$153$	5.63279	−	5.63279i	0.455384	−	0.455384i
$154$	−2.01946	+	2.25827i	−0.162733	+	0.181976i
$155$	−6.35424	−	3.03456i	−0.510385	−	0.243741i
$156$	−4.59037	+	0.514118i	−0.367523	+	0.0411624i
$157$	10.9364	+	10.9364i	0.872818	+	0.872818i	0.992779	−	0.119960i	$-0.0382767\pi$
$157$	10.9364	+	10.9364i	0.872818	+	0.872818i	−0.119960	+	0.992779i	$0.538277\pi$
$158$	0.212447	+	3.80557i	0.0169013	+	0.302755i
$159$	0.663622			0.0526287
$160$	12.4738	+	2.09888i	0.986137	+	0.165931i
$161$	−26.9206			−2.12164
$162$	−0.831971	−	14.9032i	−0.0653658	−	1.17090i
$163$	−5.15794	−	5.15794i	−0.404001	−	0.404001i	0.475639	−	0.879640i	$-0.342217\pi$
$163$	−5.15794	−	5.15794i	−0.404001	−	0.404001i	−0.879640	+	0.475639i	$0.842217\pi$
$164$	−16.8914	+	1.89182i	−1.31900	+	0.147727i
$165$	−0.855673	−	2.42003i	−0.0666141	−	0.188399i
$166$	−7.91081	+	8.84628i	−0.613998	+	0.686605i
$167$	4.88399	−	4.88399i	0.377935	−	0.377935i	−0.492422	−	0.870357i	$-0.663888\pi$
$167$	4.88399	−	4.88399i	0.377935	−	0.377935i	0.870357	+	0.492422i	$0.163888\pi$
$168$	−4.68823	−	27.7606i	−0.361705	−	2.14178i
$169$		−	1.00000i		−	0.0769231i
$170$	−4.15953	−	9.95942i	−0.319022	−	0.763853i
$171$			13.1369i			1.00460i
$172$	−11.4200	−	9.11954i	−0.870763	−	0.695359i
$173$	11.3759	−	11.3759i	0.864896	−	0.864896i	−0.127006	−	0.991902i	$-0.540537\pi$
$173$	11.3759	−	11.3759i	0.864896	−	0.864896i	0.991902	+	0.127006i	$0.0405367\pi$
$174$	−12.5138	−	11.1905i	−0.948666	−	0.848347i
$175$	21.4293	+	2.27308i	1.61990	+	0.171829i
$176$	0.439828	+	1.93890i	0.0331533	+	0.146150i
$177$	−12.0198	−	12.0198i	−0.903466	−	0.903466i
$178$	−17.9942	+	1.00453i	−1.34873	+	0.0752928i
$179$	−14.2199			−1.06285			−0.531423	−	0.847106i	$-0.678343\pi$
$179$	−14.2199			−1.06285			−0.531423	+	0.847106i	$0.678343\pi$
$180$	9.86090	+	3.42178i	0.734988	+	0.255044i
$181$	−10.4080			−0.773624			−0.386812	−	0.922159i	$-0.626424\pi$
$181$	−10.4080			−0.773624			−0.386812	+	0.922159i	$0.626424\pi$
$182$	6.08564	−	0.339732i	0.451098	−	0.0251826i
$183$	−10.5025	−	10.5025i	−0.776366	−	0.776366i
$184$	−10.2378	+	14.3983i	−0.754738	+	1.06146i
$185$	−13.1208	+	4.63923i	−0.964658	+	0.341083i
$186$	7.66708	+	6.85631i	0.562178	+	0.502729i
$187$	1.19957	−	1.19957i	0.0877211	−	0.0877211i
$188$	0.195538	−	0.244862i	0.0142610	−	0.0178584i
$189$			6.62982i			0.482249i
$190$	16.4643	+	6.76331i	1.19444	+	0.490662i
$191$		−	7.07244i		−	0.511744i	−0.966711	−	0.255872i	$-0.917637\pi$
$191$		−	7.07244i		−	0.511744i	0.966711	−	0.255872i	$-0.0823626\pi$
$192$	−16.6305	−	8.04976i	−1.20020	−	0.580941i
$193$	15.3297	−	15.3297i	1.10345	−	1.10345i	0.109464	−	0.993991i	$-0.465087\pi$
$193$	15.3297	−	15.3297i	1.10345	−	1.10345i	0.993991	−	0.109464i	$-0.0349134\pi$
$194$	10.8683	−	12.1535i	0.780300	−	0.872572i
$195$	−2.22551	+	4.66013i	−0.159372	+	0.333719i
$196$	2.57672	+	23.0066i	0.184051	+	1.64333i
$197$	−3.85661	−	3.85661i	−0.274772	−	0.274772i	0.556246	−	0.831018i	$-0.312241\pi$
$197$	−3.85661	−	3.85661i	−0.274772	−	0.274772i	−0.831018	+	0.556246i	$0.812241\pi$
$198$	0.0914432	+	1.63803i	0.00649858	+	0.116410i
$199$	3.17819			0.225296			0.112648	−	0.993635i	$-0.464067\pi$
$199$	3.17819			0.225296			0.112648	+	0.993635i	$0.464067\pi$
$200$	9.36518	−	10.5969i	0.662218	−	0.749311i
$201$	−24.1992			−1.70688
$202$	0.329502	+	5.90240i	0.0231837	+	0.415292i
$203$	15.6639	+	15.6639i	1.09939	+	1.09939i
$204$	1.75473	+	15.6673i	0.122856	+	1.09693i
$205$	−8.18932	+	17.1481i	−0.571967	+	1.19768i
$206$	4.62570	−	5.17269i	0.322288	−	0.360399i
$207$	−10.3084	+	10.3084i	−0.716487	+	0.716487i
$208$	2.13263	−	3.38406i	0.147871	−	0.234642i
$209$			2.79766i			0.193518i
$210$	−29.1159	−	11.9605i	−2.00919	−	0.825351i
$211$			10.6465i			0.732937i	0.930430	+	0.366469i	$0.119433\pi$
$211$			10.6465i			0.732937i	−0.930430	+	0.366469i	$0.880567\pi$
$212$	−0.358606	+	0.449065i	−0.0246292	+	0.0308419i
$213$	1.01065	−	1.01065i	0.0692485	−	0.0692485i
$214$	−14.0647	−	12.5774i	−0.961444	−	0.859774i
$215$	−15.4048	+	5.44683i	−1.05060	+	0.371470i
$216$	3.54592	+	2.52129i	0.241269	+	0.171552i
$217$	−9.59713	−	9.59713i	−0.651496	−	0.651496i
$218$	−14.4037	+	0.804089i	−0.975542	+	0.0544598i
$219$	−37.6796			−2.54615
$220$	2.09999	+	0.728708i	0.141582	+	0.0491295i
$221$	−3.41309			−0.229589
$222$	20.2963	−	1.13305i	1.36220	−	0.0760450i
$223$	−13.3536	−	13.3536i	−0.894220	−	0.894220i	0.100697	−	0.994917i	$-0.467893\pi$
$223$	−13.3536	−	13.3536i	−0.894220	−	0.894220i	−0.994917	+	0.100697i	$0.967893\pi$
$224$	21.3187	+	11.8288i	1.42442	+	0.790342i
$225$	9.07611	−	7.33529i	0.605074	−	0.489020i
$226$	−14.1736	−	12.6748i	−0.942816	−	0.843116i
$227$	−5.71415	+	5.71415i	−0.379262	+	0.379262i	−0.870836	−	0.491574i	$-0.836422\pi$
$227$	−5.71415	+	5.71415i	−0.379262	+	0.379262i	0.491574	+	0.870836i	$0.336422\pi$
$228$	−20.3160	−	16.2236i	−1.34546	−	1.07444i
$229$			12.9982i			0.858948i	0.903079	+	0.429474i	$0.141301\pi$
$229$			12.9982i			0.858948i	−0.903079	+	0.429474i	$0.858699\pi$
$230$	7.61228	+	18.2265i	0.501939	+	1.20182i
$231$		−	4.94747i		−	0.325519i
$232$	14.3346	−	2.42083i	0.941113	−	0.158935i
$233$	0.881833	−	0.881833i	0.0577708	−	0.0577708i	−0.677631	−	0.735402i	$-0.736993\pi$
$233$	0.881833	−	0.881833i	0.0577708	−	0.0577708i	0.735402	+	0.677631i	$0.236993\pi$
$234$	2.20023	−	2.46041i	0.143833	−	0.160842i
$235$	−0.116789	−	0.330304i	−0.00761845	−	0.0215467i
$236$	14.6289	−	1.63843i	0.952262	−	0.106653i
$237$	−4.40139	−	4.40139i	−0.285901	−	0.285901i
$238$	−1.15953	−	20.7708i	−0.0751614	−	1.34637i
$239$	6.13684			0.396960			0.198480	−	0.980105i	$-0.436400\pi$
$239$	6.13684			0.396960			0.198480	+	0.980105i	$0.436400\pi$
$240$	−17.4696	+	11.0240i	−1.12766	+	0.711594i
$241$	23.7790			1.53174			0.765869	−	0.642997i	$-0.222309\pi$
$241$	23.7790			1.53174			0.765869	+	0.642997i	$0.222309\pi$
$242$	−0.847611	−	15.1833i	−0.0544865	−	0.976021i
$243$	13.9733	+	13.9733i	0.896387	+	0.896387i
$244$	12.7822	−	1.43160i	0.818297	−	0.0916487i
$245$	23.3562	+	11.1541i	1.49217	+	0.712609i
$246$	18.5030	−	20.6911i	1.17971	−	1.31921i
$247$	3.98004	−	3.98004i	0.253244	−	0.253244i
$248$	−8.78270	+	1.48323i	−0.557702	+	0.0941849i
$249$		−	19.3807i		−	1.22820i
$250$	−4.52052	−	15.1514i	−0.285903	−	0.958259i
$251$			21.3919i			1.35025i	0.737705	+	0.675124i	$0.235910\pi$
$251$			21.3919i			1.35025i	−0.737705	+	0.675124i	$0.764090\pi$
$252$	15.7206	+	12.5539i	0.990306	+	0.790821i
$253$	−2.19530	+	2.19530i	−0.138018	+	0.138018i
$254$	0.126240	+	0.112891i	0.00792103	+	0.00708340i
$255$	15.9054	+	7.59587i	0.996038	+	0.475672i
$256$	14.4339	−	6.90375i	0.902120	−	0.431485i
$257$	11.7799	+	11.7799i	0.734811	+	0.734811i	0.971569	−	0.236758i	$-0.0760847\pi$
$257$	11.7799	+	11.7799i	0.734811	+	0.734811i	−0.236758	+	0.971569i	$0.576085\pi$
$258$	23.8295	−	1.33029i	1.48356	−	0.0828200i
$259$	−26.8238			−1.66675
$260$	−1.95084	−	4.02421i	−0.120986	−	0.249571i
$261$	11.9960			0.742536
$262$	−17.3508	+	0.968608i	−1.07193	+	0.0598408i
$263$	−11.1802	−	11.1802i	−0.689398	−	0.689398i	0.272701	−	0.962099i	$-0.412083\pi$
$263$	−11.1802	−	11.1802i	−0.689398	−	0.689398i	−0.962099	+	0.272701i	$0.912083\pi$
$264$	−2.64612	−	1.88150i	−0.162857	−	0.115798i
$265$	0.214185	+	0.605762i	0.0131573	+	0.0372117i
$266$	25.5732	+	22.8689i	1.56799	+	1.40218i
$267$	20.8115	−	20.8115i	1.27364	−	1.27364i
$268$	13.0767	−	16.3753i	0.798788	−	1.00028i
$269$		−	1.87020i		−	0.114028i	−0.998373	−	0.0570141i	$-0.981842\pi$
$269$		−	1.87020i		−	0.114028i	0.998373	−	0.0570141i	$-0.0181580\pi$
$270$	4.48871	−	1.87470i	0.273174	−	0.114091i
$271$		−	23.6707i		−	1.43789i	−0.695066	−	0.718946i	$-0.744625\pi$
$271$		−	23.6707i		−	1.43789i	0.695066	−	0.718946i	$-0.255375\pi$
$272$	−11.5501	−	7.27887i	−0.700328	−	0.441346i
$273$	−7.03843	+	7.03843i	−0.425985	+	0.425985i
$274$	−3.25022	+	3.63456i	−0.196353	+	0.219572i
$275$	1.93286	−	1.56214i	0.116556	−	0.0942004i
$276$	−3.21130	−	28.6725i	−0.193297	−	1.72588i
$277$	−11.2334	−	11.2334i	−0.674949	−	0.674949i	0.283903	−	0.958853i	$-0.408370\pi$
$277$	−11.2334	−	11.2334i	−0.674949	−	0.674949i	−0.958853	+	0.283903i	$0.908370\pi$
$278$	−0.171166	−	3.06612i	−0.0102659	−	0.183893i
$279$	−7.34988			−0.440026
$280$	23.8271	−	13.2392i	1.42394	−	0.791196i
$281$	5.48143			0.326995			0.163497	−	0.986544i	$-0.447723\pi$
$281$	5.48143			0.326995			0.163497	+	0.986544i	$0.447723\pi$
$282$	0.0285234	+	0.510943i	0.00169855	+	0.0304262i
$283$	7.89795	+	7.89795i	0.469484	+	0.469484i	0.901747	−	0.432263i	$-0.142285\pi$
$283$	7.89795	+	7.89795i	0.469484	+	0.469484i	−0.432263	+	0.901747i	$0.642285\pi$
$284$	0.137762	+	1.23003i	0.00817467	+	0.0729886i
$285$	−27.4051	+	9.68988i	−1.62334	+	0.573979i
$286$	0.468564	−	0.523972i	0.0277068	−	0.0309831i
$287$	−25.8997	+	25.8997i	−1.52881	+	1.52881i
$288$	12.6928	−	3.63389i	0.747933	−	0.214129i
$289$		−	5.35082i		−	0.314754i
$290$	6.17596	−	15.0344i	0.362665	−	0.882852i
$291$			26.6262i			1.56086i
$292$	20.3612	−	25.4974i	1.19155	−	1.49212i
$293$	−12.2389	+	12.2389i	−0.715005	+	0.715005i	−0.967578	−	0.252573i	$-0.918723\pi$
$293$	−12.2389	+	12.2389i	−0.715005	+	0.715005i	0.252573	+	0.967578i	$0.418723\pi$
$294$	−28.1818	−	25.2017i	−1.64360	−	1.46979i
$295$	7.09243	−	14.8513i	0.412937	−	0.864673i
$296$	−10.2010	+	14.3466i	−0.592919	+	0.833877i
$297$	0.540645	+	0.540645i	0.0313714	+	0.0313714i
$298$	0.567900	−	0.0317031i	0.0328976	−	0.00183651i
$299$	6.24623			0.361229
$300$	0.135241	+	23.0949i	0.00780812	+	1.33339i
$301$	−31.4933			−1.81524
$302$	−16.3133	+	0.910695i	−0.938728	+	0.0524046i
$303$	−6.82651	−	6.82651i	−0.392173	−	0.392173i
$304$	21.9567	−	4.98074i	1.25930	−	0.285665i
$305$	6.19710	−	12.9765i	0.354845	−	0.743031i
$306$	−8.39759	−	7.50957i	−0.480058	−	0.429293i
$307$	−4.60280	+	4.60280i	−0.262696	+	0.262696i	−0.826148	−	0.563453i	$-0.809473\pi$
$307$	−4.60280	+	4.60280i	−0.262696	+	0.262696i	0.563453	+	0.826148i	$0.309473\pi$
$308$	3.34789	+	2.67350i	0.190764	+	0.152337i
$309$			11.3325i			0.644682i
$310$	−3.78396	+	9.21148i	−0.214915	+	0.523177i
$311$			32.5052i			1.84320i	0.388141	+	0.921600i	$0.373118\pi$
$311$			32.5052i			1.84320i	−0.388141	+	0.921600i	$0.626882\pi$
$312$	1.08778	+	6.44114i	0.0615835	+	0.364658i
$313$	−19.2039	+	19.2039i	−1.08547	+	1.08547i	−0.0894769	+	0.995989i	$0.528520\pi$
$313$	−19.2039	+	19.2039i	−1.08547	+	1.08547i	−0.995989	+	0.0894769i	$0.971480\pi$
$314$	14.5803	−	16.3044i	0.822812	−	0.920111i
$315$	21.2062	−	7.49806i	1.19483	−	0.422468i
$316$	5.35678	−	0.599956i	0.301342	−	0.0337501i
$317$	−8.28473	−	8.28473i	−0.465317	−	0.465317i	0.435077	−	0.900393i	$-0.356721\pi$
$317$	−8.28473	−	8.28473i	−0.465317	−	0.465317i	−0.900393	+	0.435077i	$0.856721\pi$
$318$	−0.0523106	−	0.937045i	−0.00293343	−	0.0525469i
$319$	2.55470			0.143035
$320$	1.98040	−	17.7786i	0.110708	−	0.993853i
$321$	30.8133			1.71983
$322$	2.12204	+	38.0123i	0.118257	+	2.11834i
$323$	−13.5842	−	13.5842i	−0.755847	−	0.755847i
$324$	−20.9779	+	2.34951i	−1.16544	+	0.130528i
$325$	−4.97211	−	0.527410i	−0.275803	−	0.0292555i
$326$	−6.87651	+	7.68967i	−0.380855	+	0.425891i
$327$	16.6588	−	16.6588i	0.921235	−	0.921235i
$328$	4.00276	+	23.7018i	0.221015	+	1.30871i
$329$		−	0.675267i		−	0.0372287i
$330$	−3.34967	+	1.39898i	−0.184394	+	0.0770116i
$331$			2.91495i			0.160220i	0.996786	+	0.0801102i	$0.0255272\pi$
$331$			2.91495i			0.160220i	−0.996786	+	0.0801102i	$0.974473\pi$
$332$	13.1147	+	10.4729i	0.719760	+	0.574774i
$333$	−10.2714	+	10.2714i	−0.562869	+	0.562869i
$334$	−7.28126	−	6.51129i	−0.398413	−	0.356282i
$335$	−7.81033	−	22.0893i	−0.426724	−	1.20687i
$336$	−38.8289	+	8.80810i	−2.11829	+	0.480521i
$337$	−4.32305	−	4.32305i	−0.235492	−	0.235492i	0.579489	−	0.814980i	$-0.303252\pi$
$337$	−4.32305	−	4.32305i	−0.235492	−	0.235492i	−0.814980	+	0.579489i	$0.803252\pi$
$338$	−1.41202	+	0.0788259i	−0.0768035	+	0.00428756i
$339$	31.0520			1.68651
$340$	−13.7350	+	6.65838i	−0.744884	+	0.361102i
$341$	−1.56524			−0.0847626
$342$	18.5495	−	1.03553i	1.00304	−	0.0559949i
$343$	13.9432	+	13.9432i	0.752862	+	0.752862i
$344$	−11.9767	+	16.8440i	−0.645743	+	0.908168i
$345$	−29.1082	−	13.9011i	−1.56713	−	0.748408i
$346$	−16.9597	−	15.1663i	−0.911760	−	0.815344i
$347$	−16.3762	+	16.3762i	−0.879119	+	0.879119i	−0.993443	−	0.114324i	$-0.963530\pi$
$347$	−16.3762	+	16.3762i	−0.879119	+	0.879119i	0.114324	+	0.993443i	$0.463530\pi$
$348$	−14.8147	+	18.5517i	−0.794151	+	0.994476i
$349$		−	24.6174i		−	1.31774i	−0.752258	−	0.658869i	$-0.771035\pi$
$349$		−	24.6174i		−	1.31774i	0.752258	−	0.658869i	$-0.228965\pi$
$350$	1.52045	−	30.4376i	0.0812714	−	1.62696i
$351$		−	1.53828i		−	0.0821072i
$352$	2.70309	−	0.773880i	0.144075	−	0.0412479i
$353$	5.78094	−	5.78094i	0.307688	−	0.307688i	−0.536324	−	0.844012i	$-0.680187\pi$
$353$	5.78094	−	5.78094i	0.307688	−	0.307688i	0.844012	+	0.536324i	$0.180187\pi$
$354$	−16.0247	+	17.9197i	−0.851704	+	0.952419i
$355$	1.24872	+	0.596344i	0.0662751	+	0.0316506i
$356$	2.83683	+	25.3290i	0.150351	+	1.34243i
$357$	24.0228	+	24.0228i	1.27142	+	1.27142i
$358$	1.12090	+	20.0787i	0.0592413	+	1.06119i
$359$	6.42788			0.339251			0.169625	−	0.985509i	$-0.445744\pi$
$359$	6.42788			0.339251			0.169625	+	0.985509i	$0.445744\pi$
$360$	4.05431	−	14.1935i	0.213681	−	0.748061i
$361$	12.6814			0.667443
$362$	0.820424	+	14.6963i	0.0431205	+	0.772422i
$363$	17.5605	+	17.5605i	0.921687	+	0.921687i
$364$	−0.959412	−	8.56623i	−0.0502869	−	0.448993i
$365$	−12.1611	−	34.3944i	−0.636543	−	1.80029i
$366$	−14.0018	+	15.6575i	−0.731886	+	0.818432i
$367$	−11.7313	+	11.7313i	−0.612371	+	0.612371i	−0.943563	−	0.331192i	$-0.892549\pi$
$367$	−11.7313	+	11.7313i	−0.612371	+	0.612371i	0.331192	+	0.943563i	$0.392549\pi$
$368$	21.1376	+	13.3209i	1.10187	+	0.694400i
$369$			19.8350i			1.03257i
$370$	7.58492	+	18.1610i	0.394321	+	0.944147i
$371$			1.23841i			0.0642949i
$372$	9.07685	−	11.3665i	0.470613	−	0.589325i
$373$	15.7227	−	15.7227i	0.814091	−	0.814091i	−0.171154	−	0.985244i	$-0.554749\pi$
$373$	15.7227	−	15.7227i	0.814091	−	0.814091i	0.985244	+	0.171154i	$0.0547494\pi$
$374$	−1.78836	−	1.59925i	−0.0924741	−	0.0826953i
$375$	21.9969	+	13.5233i	1.13592	+	0.698339i
$376$	−0.361162	−	0.256800i	−0.0186255	−	0.0132435i
$377$	−3.63440	−	3.63440i	−0.187181	−	0.187181i
$378$	9.36141	−	0.522602i	0.481499	−	0.0268797i
$379$	28.9807			1.48864			0.744319	−	0.667825i	$-0.232774\pi$
$379$	28.9807			1.48864			0.744319	+	0.667825i	$0.232774\pi$
$380$	8.25209	−	23.7809i	0.423323	−	1.21993i
$381$	−0.276571			−0.0141691
$382$	−9.98640	+	0.557492i	−0.510948	+	0.0285238i
$383$	−22.7875	−	22.7875i	−1.16439	−	1.16439i	−0.983505	−	0.180882i	$-0.942105\pi$
$383$	−22.7875	−	22.7875i	−1.16439	−	1.16439i	−0.180882	−	0.983505i	$-0.557895\pi$
$384$	−10.0555	+	24.1171i	−0.513141	+	1.23072i
$385$	4.51610	−	1.59680i	0.230162	−	0.0813805i
$386$	−22.8541	−	20.4374i	−1.16324	−	1.04023i
$387$	−12.0594	+	12.0594i	−0.613016	+	0.613016i
$388$	−18.0177	−	14.3882i	−0.914708	−	0.730451i
$389$		−	1.60674i		−	0.0814649i	−0.999170	−	0.0407324i	$-0.987031\pi$
$389$		−	1.60674i		−	0.0814649i	0.999170	−	0.0407324i	$-0.0129691\pi$
$390$	6.75560	+	2.77512i	0.342083	+	0.140524i
$391$		−	21.3189i		−	1.07815i
$392$	32.2825	−	5.45188i	1.63051	−	0.275362i
$393$	20.0673	−	20.0673i	1.01226	−	1.01226i
$394$	−5.14160	+	5.74960i	−0.259030	+	0.289661i
$395$	2.59709	−	5.43819i	0.130674	−	0.273625i
$396$	2.30571	−	0.258238i	0.115866	−	0.0129770i
$397$	−12.8728	−	12.8728i	−0.646069	−	0.646069i	0.305971	−	0.952041i	$-0.401019\pi$
$397$	−12.8728	−	12.8728i	−0.646069	−	0.646069i	−0.952041	+	0.305971i	$0.901019\pi$
$398$	−0.250524	−	4.48766i	−0.0125576	−	0.224946i
$399$	−56.0265			−2.80483
$400$	−15.7011	−	12.3885i	−0.785057	−	0.619423i
$401$	−9.91973			−0.495367			−0.247684	−	0.968841i	$-0.579669\pi$
$401$	−9.91973			−0.495367			−0.247684	+	0.968841i	$0.579669\pi$
$402$	1.90753	+	34.1697i	0.0951388	+	1.70423i
$403$	2.22677	+	2.22677i	0.110923	+	0.110923i
$404$	8.30831	−	0.930524i	0.413354	−	0.0462953i
$405$	−10.1706	+	21.2967i	−0.505379	+	1.05824i
$406$	20.8829	−	23.3523i	1.03640	−	1.15896i
$407$	−2.18741	+	2.18741i	−0.108426	+	0.108426i
$408$	21.9842	−	3.71270i	1.08838	−	0.183806i
$409$			22.7557i			1.12520i	0.826730	+	0.562599i	$0.190198\pi$
$409$			22.7557i			1.12520i	−0.826730	+	0.562599i	$0.809802\pi$
$410$	24.8589	+	10.2117i	1.22769	+	0.504321i
$411$		−	7.96269i		−	0.392770i
$412$	−7.66855	−	6.12381i	−0.377802	−	0.301699i
$413$	22.4306	−	22.4306i	1.10374	−	1.10374i
$414$	15.3683	+	13.7431i	0.755309	+	0.675437i
$415$	17.6909	−	6.25513i	0.868412	−	0.307052i
$416$	−4.94645	−	2.74456i	−0.242520	−	0.134563i
$417$	3.54616	+	3.54616i	0.173656	+	0.173656i
$418$	3.95033	−	0.220528i	0.193217	−	0.0107864i
$419$	6.93899			0.338992			0.169496	−	0.985531i	$-0.445786\pi$
$419$	6.93899			0.338992			0.169496	+	0.985531i	$0.445786\pi$
$420$	−14.5933	+	42.0550i	−0.712079	+	2.05207i
$421$	−3.45189			−0.168235			−0.0841173	−	0.996456i	$-0.526807\pi$
$421$	−3.45189			−0.168235			−0.0841173	+	0.996456i	$0.526807\pi$
$422$	15.0331	−	0.839222i	0.731798	−	0.0408527i
$423$	−0.258574	−	0.258574i	−0.0125723	−	0.0125723i
$424$	0.662354	+	0.470960i	0.0321668	+	0.0228718i
$425$	−1.80010	+	16.9702i	−0.0873176	+	0.823178i
$426$	−1.50672	−	1.34739i	−0.0730006	−	0.0652810i
$427$	19.5990	−	19.5990i	0.948463	−	0.948463i
$428$	−16.6508	+	20.8510i	−0.804848	+	1.00787i
$429$			1.14793i			0.0554227i
$430$	8.90530	+	21.3225i	0.429452	+	1.02826i
$431$		−	5.69174i		−	0.274161i	−0.990560	−	0.137081i	$-0.956228\pi$
$431$		−	5.69174i		−	0.274161i	0.990560	−	0.137081i	$-0.0437720\pi$
$432$	3.28058	−	5.20563i	0.157837	−	0.250456i
$433$	−22.4844	+	22.4844i	−1.08053	+	1.08053i	−0.0840698	+	0.996460i	$0.526792\pi$
$433$	−22.4844	+	22.4844i	−1.08053	+	1.08053i	−0.996460	+	0.0840698i	$0.973208\pi$
$434$	−12.7948	+	14.3078i	−0.614170	+	0.686796i
$435$	8.84837	+	25.0252i	0.424247	+	1.19986i
$436$	2.27077	+	20.2749i	0.108750	+	0.970990i
$437$	24.8602	+	24.8602i	1.18923	+	1.18923i
$438$	2.97013	+	53.2042i	0.141918	+	2.54220i
$439$	18.8063			0.897574			0.448787	−	0.893639i	$-0.351856\pi$
$439$	18.8063			0.897574			0.448787	+	0.893639i	$0.351856\pi$
$440$	0.863412	−	3.02266i	0.0411616	−	0.144100i
$441$	27.0159			1.28647
$442$	0.269040	+	4.81933i	0.0127969	+	0.229232i
$443$	−27.8526	−	27.8526i	−1.32332	−	1.32332i	−0.911073	−	0.412246i	$-0.864744\pi$
$443$	−27.8526	−	27.8526i	−1.32332	−	1.32332i	−0.412246	−	0.911073i	$-0.635256\pi$
$444$	−3.19975	−	28.5694i	−0.151854	−	1.35584i
$445$	25.7139	+	12.2800i	1.21896	+	0.582130i
$446$	−17.8028	+	19.9080i	−0.842988	+	0.942672i
$447$	−0.656813	+	0.656813i	−0.0310662	+	0.0310662i
$448$	15.0219	−	31.0347i	0.709719	−	1.46625i
$449$			18.0953i			0.853970i	0.904259	+	0.426985i	$0.140424\pi$
$449$			18.0953i			0.853970i	−0.904259	+	0.426985i	$0.859576\pi$
$450$	−11.0730	−	12.2374i	−0.521985	−	0.576876i
$451$			4.22410i			0.198905i
$452$	−16.7798	+	21.0125i	−0.789255	+	0.988344i
$453$	18.8674	−	18.8674i	0.886470	−	0.886470i
$454$	8.51890	+	7.61805i	0.399812	+	0.357533i
$455$	−8.69642	−	4.15310i	−0.407695	−	0.194700i
$456$	−21.3066	+	29.9654i	−0.997772	+	1.40326i
$457$	19.6055	+	19.6055i	0.917105	+	0.917105i	0.996818	−	0.0797133i	$-0.0254005\pi$
$457$	19.6055	+	19.6055i	0.917105	+	0.917105i	−0.0797133	+	0.996818i	$0.525400\pi$
$458$	18.3537	−	1.02460i	0.857613	−	0.0478763i
$459$	−5.25028			−0.245062
$460$	25.1361	−	12.1854i	1.17198	−	0.568146i
$461$	−34.9245			−1.62660			−0.813298	−	0.581848i	$-0.802330\pi$
$461$	−34.9245			−1.62660			−0.813298	+	0.581848i	$0.802330\pi$
$462$	−6.98590	+	0.389989i	−0.325013	+	0.0181439i
$463$	21.6671	+	21.6671i	1.00695	+	1.00695i	0.999976	+	0.00697798i	$0.00222118\pi$
$463$	21.6671	+	21.6671i	1.00695	+	1.00695i	0.00697798	+	0.999976i	$0.497779\pi$
$464$	−4.54819	−	20.0499i	−0.211144	−	0.930791i
$465$	−5.42133	−	15.3327i	−0.251408	−	0.711038i
$466$	−1.31467	−	1.17565i	−0.0609010	−	0.0544609i
$467$	1.42697	−	1.42697i	0.0660321	−	0.0660321i	−0.673320	−	0.739352i	$-0.735132\pi$
$467$	1.42697	−	1.42697i	0.0660321	−	0.0660321i	0.739352	+	0.673320i	$0.235132\pi$
$468$	−3.64756	−	2.91281i	−0.168609	−	0.134645i
$469$		−	45.1590i		−	2.08525i
$470$	−0.457188	+	0.190944i	−0.0210885	+	0.00880758i
$471$			35.7201i			1.64590i
$472$	−3.46662	−	20.5271i	−0.159564	−	0.944837i
$473$	−2.56820	+	2.56820i	−0.118086	+	0.118086i
$474$	−5.86789	+	6.56178i	−0.269521	+	0.301392i
$475$	−17.6901	−	21.8883i	−0.811676	−	1.00430i
$476$	−29.2373	+	3.27456i	−1.34009	+	0.150089i
$477$	0.474212	+	0.474212i	0.0217127	+	0.0217127i
$478$	−0.483742	−	8.66532i	−0.0221259	−	0.396342i
$479$	27.3934			1.25163			0.625817	−	0.779970i	$-0.284765\pi$
$479$	27.3934			1.25163			0.625817	+	0.779970i	$0.284765\pi$
$480$	16.9431	+	23.7984i	0.773342	+	1.08624i
$481$	6.22378			0.283780
$482$	−1.87440	−	33.5763i	−0.0853765	−	1.52936i
$483$	−43.9637	−	43.9637i	−2.00042	−	2.00042i
$484$	−21.3723	+	2.39368i	−0.971467	+	0.108804i
$485$	−24.3047	+	8.59365i	−1.10362	+	0.390217i
$486$	18.6290	−	20.8320i	0.845030	−	0.944957i
$487$	−8.51241	+	8.51241i	−0.385734	+	0.385734i	−0.873163	−	0.487429i	$-0.837935\pi$
$487$	−8.51241	+	8.51241i	−0.385734	+	0.385734i	0.487429	+	0.873163i	$0.337935\pi$
$488$	−3.02901	−	17.9358i	−0.137117	−	0.811916i
$489$		−	16.8467i		−	0.761835i
$490$	13.9087	−	33.8586i	0.628330	−	1.52957i
$491$			14.9696i			0.675570i	0.941223	+	0.337785i	$0.109678\pi$
$491$			14.9696i			0.675570i	−0.941223	+	0.337785i	$0.890322\pi$
$492$	−30.6746	−	24.4956i	−1.38292	−	1.10435i
$493$	−12.4045	+	12.4045i	−0.558672	+	0.558672i
$494$	−5.93360	−	5.30614i	−0.266965	−	0.238735i
$495$	1.11786	−	2.34076i	0.0502441	−	0.105209i
$496$	2.78664	+	12.2844i	0.125124	+	0.551585i
$497$	1.88600	+	1.88600i	0.0845989	+	0.0845989i
$498$	−27.3658	+	1.52770i	−1.22629	+	0.0684578i
$499$	−15.5021			−0.693969			−0.346984	−	0.937871i	$-0.612794\pi$
$499$	−15.5021			−0.693969			−0.346984	+	0.937871i	$0.612794\pi$
$500$	−21.0377	+	7.57736i	−0.940833	+	0.338870i
$501$	15.9520			0.712682
$502$	30.2057	−	1.68624i	1.34815	−	0.0752605i
$503$	7.25339	+	7.25339i	0.323413	+	0.323413i	0.850075	−	0.526662i	$-0.176557\pi$
$503$	7.25339	+	7.25339i	0.323413	+	0.323413i	−0.526662	+	0.850075i	$0.676557\pi$
$504$	16.4871	−	23.1873i	0.734394	−	1.03285i
$505$	4.02805	−	8.43458i	0.179246	−	0.375334i
$506$	3.27285	+	2.92676i	0.145496	+	0.130110i
$507$	1.63309	−	1.63309i	0.0725279	−	0.0725279i
$508$	0.149453	−	0.187152i	0.00663089	−	0.00830353i
$509$		−	3.62150i		−	0.160520i	−0.996774	−	0.0802602i	$-0.974425\pi$
$509$		−	3.62150i		−	0.160520i	0.996774	−	0.0802602i	$-0.0255751\pi$
$510$	9.47172	−	23.0575i	0.419415	−	1.02100i
$511$		−	70.3152i		−	3.11056i
$512$	−10.8860	−	19.8367i	−0.481097	−	0.876668i
$513$	6.12241	−	6.12241i	0.270311	−	0.270311i
$514$	15.7049	−	17.5620i	0.692712	−	0.774626i
$515$	−10.3444	+	3.65757i	−0.455829	+	0.161172i
$516$	−3.75677	−	33.5428i	−0.165382	−	1.47664i
$517$	−0.0550663	−	0.0550663i	−0.00242181	−	0.00242181i
$518$	2.11441	+	37.8757i	0.0929020	+	1.66416i
$519$	37.1558			1.63096
$520$	−5.52846	+	3.07182i	−0.242439	+	0.134708i
$521$	35.8853			1.57216			0.786082	−	0.618123i	$-0.212107\pi$
$521$	35.8853			1.57216			0.786082	+	0.618123i	$0.212107\pi$
$522$	−0.945598	−	16.9386i	−0.0413877	−	0.741381i
$523$	18.4185	+	18.4185i	0.805384	+	0.805384i	0.983931	−	0.178548i	$-0.0571399\pi$
$523$	18.4185	+	18.4185i	0.805384	+	0.805384i	−0.178548	+	0.983931i	$0.557140\pi$
$524$	2.73538	+	24.4232i	0.119496	+	1.06693i
$525$	31.2837	+	38.7080i	1.36533	+	1.68936i
$526$	−14.9053	+	16.6678i	−0.649900	+	0.726752i
$527$	7.60015	−	7.60015i	0.331068	−	0.331068i
$528$	−2.44812	+	3.88467i	−0.106541	+	0.169059i
$529$			16.0154i			0.696320i
$530$	0.838462	−	0.350182i	0.0364204	−	0.0152109i
$531$		−	17.1783i		−	0.745474i
$532$	30.2754	−	37.9124i	1.31261	−	1.64371i
$533$	6.00935	−	6.00935i	0.260294	−	0.260294i
$534$	−31.0266	−	27.7457i	−1.34265	−	1.20067i
$535$	9.94504	+	28.1268i	0.429961	+	1.21603i
$536$	−24.1530	−	17.1737i	−1.04325	−	0.741792i
$537$	−23.2224	−	23.2224i	−1.00212	−	1.00212i
$538$	−2.64075	+	0.147420i	−0.113851	+	0.00635574i
$539$	5.75335			0.247814
$540$	−3.00093	−	6.19035i	−0.129140	−	0.266390i
$541$	−0.467513			−0.0200999			−0.0100500	−	0.999949i	$-0.503199\pi$
$541$	−0.467513			−0.0200999			−0.0100500	+	0.999949i	$0.503199\pi$
$542$	−33.4234	+	1.86586i	−1.43566	+	0.0801457i
$543$	−16.9972	−	16.9972i	−0.729422	−	0.729422i
$544$	−9.36742	+	16.8827i	−0.401625	+	0.723839i
$545$	20.5830	+	9.82971i	0.881679	+	0.421058i
$546$	10.4932	+	9.38356i	0.449067	+	0.401579i
$547$	−16.7318	+	16.7318i	−0.715402	+	0.715402i	−0.967660	−	0.252258i	$-0.918827\pi$
$547$	−16.7318	+	16.7318i	−0.715402	+	0.715402i	0.252258	+	0.967660i	$0.418827\pi$
$548$	5.38825	+	4.30286i	0.230175	+	0.183809i
$549$		−	15.0097i		−	0.640600i
$550$	−2.35812	−	2.60610i	−0.100551	−	0.111124i
$551$		−	28.9301i		−	1.23246i
$552$	−40.2328	+	6.79453i	−1.71242	+	0.289194i
$553$	8.21358	−	8.21358i	0.349277	−	0.349277i
$554$	−14.9762	+	16.7472i	−0.636280	+	0.711521i
$555$	−29.0036	−	13.8511i	−1.23114	−	0.587946i
$556$	−4.31591	+	0.483379i	−0.183035	+	0.0204998i
$557$	−26.5909	−	26.5909i	−1.12669	−	1.12669i	−0.990711	−	0.135981i	$-0.956581\pi$
$557$	−26.5909	−	26.5909i	−1.12669	−	1.12669i	−0.135981	−	0.990711i	$-0.543419\pi$
$558$	0.579361	+	10.3781i	0.0245263	+	0.439341i
$559$	7.30721			0.309062
$560$	−20.5722	−	32.6006i	−0.869334	−	1.37763i
$561$	3.91800			0.165418
$562$	−0.432078	−	7.73986i	−0.0182261	−	0.326486i
$563$	−0.168647	−	0.168647i	−0.00710764	−	0.00710764i	0.703544	−	0.710652i	$-0.251600\pi$
$563$	−0.168647	−	0.168647i	−0.00710764	−	0.00710764i	−0.710652	+	0.703544i	$0.751600\pi$
$564$	0.719211	−	0.0805511i	0.0302842	−	0.00339181i
$565$	10.0221	+	28.3446i	0.421631	+	1.19247i
$566$	10.5295	−	11.7746i	0.442586	−	0.494923i
$567$	−32.1656	+	32.1656i	−1.35083	+	1.35083i
$568$	1.72595	−	0.291480i	0.0724194	−	0.0122302i
$569$		−	3.52360i		−	0.147717i	−0.997269	−	0.0738586i	$-0.976469\pi$
$569$		−	3.52360i		−	0.147717i	0.997269	−	0.0738586i	$-0.0235313\pi$
$570$	15.8425	+	37.9326i	0.663569	+	1.58882i
$571$		−	29.6178i		−	1.23947i	−0.784812	−	0.619734i	$-0.787240\pi$
$571$		−	29.6178i		−	1.23947i	0.784812	−	0.619734i	$-0.212760\pi$
$572$	−0.776792	−	0.620316i	−0.0324793	−	0.0259367i
$573$	11.5499	−	11.5499i	0.482505	−	0.482505i
$574$	38.6123	+	34.5291i	1.61164	+	1.44122i
$575$	3.29433	−	31.0569i	0.137383	−	1.29516i
$576$	−6.13164	−	17.6360i	−0.255485	−	0.734835i
$577$	−6.92290	−	6.92290i	−0.288204	−	0.288204i	0.548166	−	0.836370i	$-0.315326\pi$
$577$	−6.92290	−	6.92290i	−0.288204	−	0.288204i	−0.836370	+	0.548166i	$0.815326\pi$
$578$	−7.55543	+	0.421783i	−0.314265	+	0.0175439i
$579$	50.0694			2.08081
$580$	−21.7157	−	7.53544i	−0.901694	−	0.312892i
$581$	36.1669			1.50046
$582$	37.5967	−	2.09884i	1.55843	−	0.0869996i
$583$	0.100989	+	0.100989i	0.00418253	+	0.00418253i
$584$	−37.6076	−	26.7405i	−1.55622	−	1.10653i
$585$	−4.92035	+	1.73973i	−0.203431	+	0.0719290i
$586$	18.2463	+	16.3168i	0.753747	+	0.674040i
$587$	−18.1217	+	18.1217i	−0.747961	+	0.747961i	−0.974096	−	0.226135i	$-0.927391\pi$
$587$	−18.1217	+	18.1217i	−0.747961	+	0.747961i	0.226135	+	0.974096i	$0.427391\pi$
$588$	−33.3637	+	41.7797i	−1.37590	+	1.72297i
$589$			17.7252i			0.730355i
$590$	−21.5293	−	8.84395i	−0.886346	−	0.364100i
$591$		−	12.5964i		−	0.518145i
$592$	21.0617	+	13.2730i	0.865629	+	0.545518i
$593$	−16.4896	+	16.4896i	−0.677147	+	0.677147i	−0.959354	−	0.282206i	$-0.908934\pi$
$593$	−16.4896	+	16.4896i	−0.677147	+	0.677147i	0.282206	+	0.959354i	$0.408934\pi$
$594$	0.720782	−	0.806015i	0.0295740	−	0.0330712i
$595$	−14.1749	+	29.6817i	−0.581115	+	1.21683i
$596$	−0.0895305	−	0.799385i	−0.00366731	−	0.0327441i
$597$	5.19027	+	5.19027i	0.212423	+	0.212423i
$598$	−0.492365	−	8.81977i	−0.0201343	−	0.360667i
$599$	6.82062			0.278683			0.139341	−	0.990244i	$-0.455501\pi$
$599$	6.82062			0.278683			0.139341	+	0.990244i	$0.455501\pi$
$600$	32.5997	−	2.01144i	1.33088	−	0.0821167i
$601$	3.24618			0.132415			0.0662073	−	0.997806i	$-0.478910\pi$
$601$	3.24618			0.132415			0.0662073	+	0.997806i	$0.478910\pi$
$602$	2.48249	+	44.4690i	0.101179	+	1.81242i
$603$	−17.2923	−	17.2923i	−0.704197	−	0.704197i
$604$	2.57183	+	22.9629i	0.104646	+	0.934347i
$605$	−10.3618	+	21.6971i	−0.421265	+	0.882112i
$606$	−9.10103	+	10.1772i	−0.369704	+	0.413422i
$607$	−6.52615	+	6.52615i	−0.264888	+	0.264888i	−0.827036	−	0.562148i	$-0.809975\pi$
$607$	−6.52615	+	6.52615i	−0.264888	+	0.264888i	0.562148	+	0.827036i	$0.309975\pi$
$608$	−8.76363	−	30.6105i	−0.355412	−	1.24142i
$609$			51.1609i			2.07314i
$610$	−18.8115	−	7.72751i	−0.761654	−	0.312878i
$611$			0.156678i			0.00633852i
$612$	−9.94168	+	12.4495i	−0.401868	+	0.503240i
$613$	−5.59655	+	5.59655i	−0.226042	+	0.226042i	−0.811037	−	0.584995i	$-0.801097\pi$
$613$	−5.59655	+	5.59655i	−0.226042	+	0.226042i	0.584995	+	0.811037i	$0.301097\pi$
$614$	6.86205	+	6.13641i	0.276930	+	0.247645i
$615$	−41.3782	+	14.6305i	−1.66853	+	0.589957i
$616$	3.51112	−	4.93801i	0.141467	−	0.198958i
$617$	−26.4213	−	26.4213i	−1.06368	−	1.06368i	−0.997829	−	0.0658511i	$-0.979024\pi$
$617$	−26.4213	−	26.4213i	−1.06368	−	1.06368i	−0.0658511	−	0.997829i	$-0.520976\pi$
$618$	16.0016	−	0.893292i	0.643680	−	0.0359335i
$619$	−18.4631			−0.742093			−0.371046	−	0.928614i	$-0.621001\pi$
$619$	−18.4631			−0.742093			−0.371046	+	0.928614i	$0.621001\pi$
$620$	13.3050	+	4.61691i	0.534343	+	0.185419i
$621$	9.60844			0.385573
$622$	45.8978	−	2.56225i	1.84033	−	0.102737i
$623$	38.8370	+	38.8370i	1.55597	+	1.55597i
$624$	9.00924	−	2.04369i	0.360658	−	0.0818132i
$625$	−5.24468	+	24.4437i	−0.209787	+	0.977747i
$626$	28.6299	+	25.6024i	1.14428	+	1.02328i
$627$	−4.56881	+	4.56881i	−0.182461	+	0.182461i
$628$	−24.1714	−	19.3023i	−0.964543	−	0.770248i
$629$		−	21.2423i		−	0.846987i
$630$	−12.2590	−	29.3524i	−0.488409	−	1.16943i
$631$			23.4935i			0.935263i	0.883923	+	0.467632i	$0.154893\pi$
$631$			23.4935i			0.935263i	−0.883923	+	0.467632i	$0.845107\pi$
$632$	−1.26940	−	7.51656i	−0.0504940	−	0.298993i
$633$	−17.3867	+	17.3867i	−0.691059	+	0.691059i
$634$	−11.0451	+	12.3512i	−0.438657	+	0.490529i
$635$	−0.0892635	−	0.252457i	−0.00354231	−	0.0100184i
$636$	−1.31900	+	0.147727i	−0.0523017	+	0.00585775i
$637$	−8.18491	−	8.18491i	−0.324298	−	0.324298i
$638$	−0.201376	−	3.60727i	−0.00797256	−	0.142813i
$639$	1.44438			0.0571388
$640$	−25.2597	−	1.39494i	−0.998479	−	0.0551398i
$641$	23.5205			0.929004			0.464502	−	0.885572i	$-0.346233\pi$
$641$	23.5205			0.929004			0.464502	+	0.885572i	$0.346233\pi$
$642$	−2.42889	−	43.5089i	−0.0958606	−	1.71716i
$643$	−21.3805	−	21.3805i	−0.843165	−	0.843165i	0.146104	−	0.989269i	$-0.453326\pi$
$643$	−21.3805	−	21.3805i	−0.843165	−	0.843165i	−0.989269	+	0.146104i	$0.953326\pi$
$644$	53.5066	−	5.99271i	2.10846	−	0.236146i
$645$	−34.0526	−	16.2623i	−1.34082	−	0.640327i
$646$	−18.1103	+	20.2519i	−0.712542	+	0.796801i
$647$	20.7116	−	20.7116i	0.814255	−	0.814255i	−0.171013	−	0.985269i	$-0.554704\pi$
$647$	20.7116	−	20.7116i	0.814255	−	0.814255i	0.985269	+	0.171013i	$0.0547041\pi$
$648$	4.97115	+	29.4359i	0.195285	+	1.15635i
$649$		−	3.65832i		−	0.143601i
$650$	−0.352781	+	7.06226i	−0.0138372	+	0.277005i
$651$		−	31.3459i		−	1.22854i
$652$	11.4000	+	9.10359i	0.446457	+	0.356524i
$653$	18.3070	−	18.3070i	0.716410	−	0.716410i	−0.251458	−	0.967868i	$-0.580910\pi$
$653$	18.3070	−	18.3070i	0.716410	−	0.716410i	0.967868	+	0.251458i	$0.0809101\pi$
$654$	−24.8356	−	22.2094i	−0.971151	−	0.868455i
$655$	24.7944	+	11.8409i	0.968796	+	0.462662i
$656$	33.1517	−	7.52027i	1.29436	−	0.293617i
$657$	−26.9251	−	26.9251i	−1.05045	−	1.05045i
$658$	−0.953487	+	0.0532285i	−0.0371708	+	0.00207506i
$659$	21.7960			0.849050			0.424525	−	0.905416i	$-0.360441\pi$
$659$	21.7960			0.849050			0.424525	+	0.905416i	$0.360441\pi$
$660$	2.23943	+	4.61951i	0.0871696	+	0.179814i
$661$	−8.52927			−0.331750			−0.165875	−	0.986147i	$-0.553045\pi$
$661$	−8.52927			−0.331750			−0.165875	+	0.986147i	$0.553045\pi$
$662$	4.11596	−	0.229774i	0.159971	−	0.00893042i
$663$	−5.57387	−	5.57387i	−0.216471	−	0.216471i
$664$	13.7541	−	19.3436i	0.533762	−	0.750678i
$665$	−18.0826	−	51.1416i	−0.701213	−	1.98319i
$666$	15.3130	+	13.6937i	0.593367	+	0.530621i
$667$	22.7013	−	22.7013i	0.878997	−	0.878997i
$668$	−8.62009	+	10.7945i	−0.333521	+	0.417652i
$669$		−	43.6150i		−	1.68625i
$670$	−30.5748	+	12.7695i	−1.18121	+	0.493329i
$671$		−	3.19650i		−	0.123399i
$672$	15.4979	+	54.1327i	0.597844	+	2.08821i
$673$	12.3291	−	12.3291i	0.475250	−	0.475250i	−0.428358	−	0.903609i	$-0.640908\pi$
$673$	12.3291	−	12.3291i	0.475250	−	0.475250i	0.903609	+	0.428358i	$0.140908\pi$
$674$	−5.76344	+	6.44498i	−0.222000	+	0.248251i
$675$	−7.64848	−	0.811304i	−0.294390	−	0.0312271i
$676$	0.222607	+	1.98757i	0.00856180	+	0.0764451i
$677$	18.8117	+	18.8117i	0.722992	+	0.722992i	0.969213	−	0.246222i	$-0.0791892\pi$
$677$	18.8117	+	18.8117i	0.722992	+	0.722992i	−0.246222	+	0.969213i	$0.579189\pi$
$678$	−2.44770	−	43.8458i	−0.0940033	−	1.68389i
$679$	−49.6881			−1.90685
$680$	10.4844	+	18.8691i	0.402059	+	0.723599i
$681$	−18.6634			−0.715184
$682$	0.123382	+	2.21015i	0.00472453	+	0.0846308i
$683$	−29.2411	−	29.2411i	−1.11888	−	1.11888i	−0.991906	−	0.126973i	$-0.959474\pi$
$683$	−29.2411	−	29.2411i	−1.11888	−	1.11888i	−0.126973	−	0.991906i	$-0.540526\pi$
$684$	−2.92436	−	26.1105i	−0.111816	−	0.998361i
$685$	7.26843	−	2.56996i	0.277712	−	0.0981933i
$686$	18.5889	−	20.7871i	0.709729	−	0.793655i
$687$	−21.2273	+	21.2273i	−0.809870	+	0.809870i
$688$	24.7281	+	15.5836i	0.942748	+	0.594119i
$689$		−	0.287340i		−	0.0109468i
$690$	−17.3340	+	42.1970i	−0.659895	+	1.60641i
$691$		−	21.6953i		−	0.825329i	−0.910883	−	0.412664i	$-0.864598\pi$
$691$		−	21.6953i		−	0.825329i	0.910883	−	0.412664i	$-0.135402\pi$
$692$	−20.0781	+	25.1429i	−0.763256	+	0.955788i
$693$	3.53536	−	3.53536i	0.134297	−	0.134297i
$694$	24.4143	+	21.8325i	0.926753	+	0.828752i
$695$	−2.09245	+	4.38150i	−0.0793711	+	0.166200i
$696$	27.3631	+	19.4562i	1.03719	+	0.737486i
$697$	−20.5104	−	20.5104i	−0.776888	−	0.776888i
$698$	−34.7601	+	1.94049i	−1.31569	+	0.0734485i
$699$	2.88022			0.108940
$700$	−43.0982	+	0.252377i	−1.62896	+	0.00953896i
$701$	−1.18461			−0.0447420			−0.0223710	−	0.999750i	$-0.507122\pi$
$701$	−1.18461			−0.0447420			−0.0223710	+	0.999750i	$0.507122\pi$
$702$	−2.17207	+	0.121256i	−0.0819796	+	0.00457652i
$703$	24.7709	+	24.7709i	0.934251	+	0.934251i
$704$	−1.30580	−	3.75580i	−0.0492143	−	0.141552i
$705$	0.348689	−	0.730141i	0.0131324	−	0.0274987i
$706$	−8.61846	−	7.70709i	−0.324360	−	0.290060i
$707$	12.7392	−	12.7392i	0.479106	−	0.479106i
$708$	26.5660	+	21.2146i	0.998411	+	0.797294i
$709$			22.7803i			0.855532i	0.903890	+	0.427766i	$0.140699\pi$
$709$			22.7803i			0.855532i	−0.903890	+	0.427766i	$0.859301\pi$
$710$	0.743615	−	1.81022i	0.0279074	−	0.0679363i
$711$		−	6.29030i		−	0.235905i
$712$	35.5413	−	6.00222i	1.33197	−	0.224943i
$713$	−13.9089	+	13.9089i	−0.520892	+	0.520892i
$714$	32.0270	−	35.8142i	1.19858	−	1.34031i
$715$	−1.04785	+	0.370496i	−0.0391872	+	0.0138558i
$716$	28.2631	−	3.16545i	1.05624	−	0.118298i
$717$	10.0220	+	10.0220i	0.374278	+	0.374278i
$718$	−0.506684	−	9.07627i	−0.0189093	−	0.338723i
$719$	−11.1110			−0.414370			−0.207185	−	0.978302i	$-0.566430\pi$
$719$	−11.1110			−0.414370			−0.207185	+	0.978302i	$0.566430\pi$
$720$	−20.3610	−	4.60593i	−0.758808	−	0.171653i
$721$	−21.1479			−0.787589
$722$	−0.999624	−	17.9063i	−0.0372021	−	0.666405i
$723$	38.8331	+	38.8331i	1.44422	+	1.44422i
$724$	20.6868	−	2.31690i	0.768817	−	0.0861070i
$725$	−19.9874	+	16.1538i	−0.742314	+	0.599936i
$726$	23.4115	−	26.1799i	0.868881	−	0.971628i
$727$	−11.9420	+	11.9420i	−0.442904	+	0.442904i	−0.892987	−	0.450083i	$-0.851394\pi$
$727$	−11.9420	+	11.9420i	−0.442904	+	0.442904i	0.450083	+	0.892987i	$0.351394\pi$
$728$	−12.0200	+	2.02995i	−0.445492	+	0.0752348i
$729$			13.9756i			0.517614i
$730$	−47.6068	+	19.8829i	−1.76201	+	0.735899i
$731$		−	24.9402i		−	0.922445i
$732$	23.2124	+	18.5365i	0.857954	+	0.685130i
$733$	26.1775	−	26.1775i	0.966887	−	0.966887i	−0.0325820	−	0.999469i	$-0.510373\pi$
$733$	26.1775	−	26.1775i	0.966887	−	0.966887i	0.999469	+	0.0325820i	$0.0103730\pi$
$734$	17.4896	+	15.6401i	0.645552	+	0.577287i
$735$	19.9271	+	56.3584i	0.735023	+	2.07881i
$736$	17.1431	−	30.8967i	0.631904	−	1.13887i
$737$	−3.68260	−	3.68260i	−0.135650	−	0.135650i
$738$	28.0073	−	1.56351i	1.03096	−	0.0575537i
$739$	−4.47304			−0.164544			−0.0822718	−	0.996610i	$-0.526218\pi$
$739$	−4.47304			−0.164544			−0.0822718	+	0.996610i	$0.526218\pi$
$740$	25.0458	−	12.1416i	0.920701	−	0.446333i
$741$	12.9995			0.477548
$742$	1.74865	−	0.0976186i	0.0641950	−	0.00358369i
$743$	33.2249	+	33.2249i	1.21890	+	1.21890i	0.968017	+	0.250885i	$0.0807217\pi$
$743$	33.2249	+	33.2249i	1.21890	+	1.21890i	0.250885	+	0.968017i	$0.419278\pi$
$744$	−16.7651	−	11.9207i	−0.614640	−	0.437033i
$745$	−0.811534	−	0.387560i	−0.0297323	−	0.0141991i
$746$	−23.4401	−	20.9613i	−0.858201	−	0.767449i
$747$	13.8490	−	13.8490i	0.506710	−	0.506710i
$748$	−2.11720	+	2.65126i	−0.0774124	+	0.0969397i
$749$			57.5018i			2.10107i
$750$	17.3612	−	32.1259i	0.633940	−	1.17307i
$751$			20.1494i			0.735264i	0.929971	+	0.367632i	$0.119831\pi$
$751$			20.1494i			0.735264i	−0.929971	+	0.367632i	$0.880169\pi$
$752$	−0.334137	+	0.530209i	−0.0121847	+	0.0193347i
$753$	−34.9349	+	34.9349i	−1.27310	+	1.27310i
$754$	−4.84534	+	5.41831i	−0.176457	+	0.197323i
$755$	23.3119	+	11.1329i	0.848407	+	0.405169i
$756$	−1.47584	−	13.1773i	−0.0536759	−	0.479252i
$757$	0.215715	+	0.215715i	0.00784030	+	0.00784030i	0.711016	−	0.703176i	$-0.248235\pi$
$757$	0.215715	+	0.215715i	0.00784030	+	0.00784030i	−0.703176	+	0.711016i	$0.748235\pi$
$758$	−2.28443	−	40.9211i	−0.0829742	−	1.48632i
$759$	−7.17024			−0.260263
$760$	−34.2295	−	9.77752i	−1.24163	−	0.354668i
$761$	−44.7165			−1.62097			−0.810485	−	0.585759i	$-0.800796\pi$
$761$	−44.7165			−1.62097			−0.810485	+	0.585759i	$0.800796\pi$
$762$	0.0218009	+	0.390522i	0.000789765	+	0.0141471i
$763$	31.0876	+	31.0876i	1.12545	+	1.12545i
$764$	1.57437	+	14.0570i	0.0569588	+	0.508564i
$765$	5.93786	+	16.7936i	0.214684	+	0.607173i
$766$	−30.3801	+	33.9725i	−1.09768	+	1.22748i
$767$	−5.20444	+	5.20444i	−0.187922	+	0.187922i
$768$	34.8463	+	12.2974i	1.25741	+	0.443745i
$769$		−	10.5286i		−	0.379672i	−0.981816	−	0.189836i	$-0.939204\pi$
$769$		−	10.5286i		−	0.379672i	0.981816	−	0.189836i	$-0.0607956\pi$
$770$	−2.61069	−	6.25094i	−0.0940828	−	0.225268i
$771$			38.4753i			1.38565i
$772$	−27.0564	+	33.8814i	−0.973780	+	1.21942i

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +O(q^{10})\)	\(q+(-0.0788259 - 1.41202i) q^{2} +(1.63309 + 1.63309i) q^{3} +(-1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 - 2.43467i) q^{6} +(-3.04756 + 3.04756i) q^{7} +(0.470996 + 2.78894i) q^{8} +2.33394i q^{9} +(2.92509 + 1.20159i) q^{10} +0.497041i q^{11} +(-3.60941 - 2.88234i) q^{12} +(0.707107 - 0.707107i) q^{13} +(4.54342 + 4.06297i) q^{14} +(-4.86888 + 1.72154i) q^{15} +(3.90089 - 0.884894i) q^{16} +(-2.41342 - 2.41342i) q^{17} +(3.29556 - 0.183975i) q^{18} +5.62862 q^{19} +(1.46609 - 4.22499i) q^{20} -9.95385 q^{21} +(0.701829 - 0.0391797i) q^{22} +(4.41675 + 4.41675i) q^{23} +(-3.78540 + 5.32375i) q^{24} +(-3.14287 - 3.88875i) q^{25} +(-1.05418 - 0.942707i) q^{26} +(1.08773 - 1.08773i) q^{27} +(5.37884 - 6.73565i) q^{28} -5.13981i q^{29} +(2.81463 + 6.73924i) q^{30} +3.14912i q^{31} +(-1.55698 - 5.43837i) q^{32} +(-0.811710 + 0.811710i) q^{33} +(-3.21754 + 3.59802i) q^{34} +(-3.21261 - 9.08599i) q^{35} +(-0.519552 - 4.63888i) q^{36} +(4.40088 + 4.40088i) q^{37} +(-0.443681 - 7.94770i) q^{38} +2.30953 q^{39} +(-6.08132 - 1.73711i) q^{40} +8.49850 q^{41} +(0.784621 + 14.0550i) q^{42} +(5.16698 + 5.16698i) q^{43} +(-0.110645 - 0.987905i) q^{44} +(-4.70939 - 2.24903i) q^{45} +(5.88836 - 6.58467i) q^{46} +(-0.110788 + 0.110788i) q^{47} +(7.81560 + 4.92539i) q^{48} -11.5752i q^{49} +(-5.24323 + 4.74432i) q^{50} -7.88265i q^{51} +(-1.24802 + 1.56283i) q^{52} +(0.203180 - 0.203180i) q^{53} +(-1.62163 - 1.45015i) q^{54} +(-1.00292 - 0.478958i) q^{55} +(-9.93483 - 7.06405i) q^{56} +(9.19203 + 9.19203i) q^{57} +(-7.25749 + 0.405150i) q^{58} -7.36019 q^{59} +(9.29404 - 4.50552i) q^{60} -6.43106 q^{61} +(4.44661 - 0.248232i) q^{62} +(-7.11283 - 7.11283i) q^{63} +(-7.55632 + 2.62716i) q^{64} +(0.745404 + 2.10817i) q^{65} +(1.21013 + 1.08216i) q^{66} +(-7.40905 + 7.40905i) q^{67} +(5.33409 + 4.25960i) q^{68} +14.4259i q^{69} +(-12.5763 + 5.25247i) q^{70} -0.618858i q^{71} +(-6.50922 + 1.09928i) q^{72} +(-11.5363 + 11.5363i) q^{73} +(5.86720 - 6.56101i) q^{74} +(1.21807 - 11.4832i) q^{75} +(-11.1873 + 1.25297i) q^{76} +(-1.51476 - 1.51476i) q^{77} +(-0.182051 - 3.26110i) q^{78} -2.69514 q^{79} +(-1.97345 + 8.72385i) q^{80} +10.5545 q^{81} +(-0.669902 - 12.0000i) q^{82} +(-5.93375 - 5.93375i) q^{83} +(19.7840 - 2.21579i) q^{84} +(7.19537 - 2.54413i) q^{85} +(6.88856 - 7.70314i) q^{86} +(8.39376 - 8.39376i) q^{87} +(-1.38621 + 0.234104i) q^{88} -12.7437i q^{89} +(-2.80445 + 6.82701i) q^{90} +4.30990i q^{91} +(-9.76181 - 7.79541i) q^{92} +(-5.14279 + 5.14279i) q^{93} +(0.165168 + 0.147702i) q^{94} +(-5.42385 + 11.3573i) q^{95} +(6.33865 - 11.4240i) q^{96} +(8.15212 + 8.15212i) q^{97} +(-16.3444 + 0.912426i) q^{98} -1.16007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

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