LMFDB - Embedded newform 130.2.m.a.69.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(49,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("130.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.m (of order $6$, 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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.3
Root			$-1.83766i$ of defining polynomial
Character	$\chi$	$=$	130.69
Dual form			130.2.m.a.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.59146 + 0.918829i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21022 + 0.339024i) q^{5} +(-1.59146 + 0.918829i) q^{6} +(2.39871 + 4.15469i) q^{7} +1.00000 q^{8} +(0.188495 + 0.326482i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.59146 + 0.918829i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21022 + 0.339024i) q^{5} +(-1.59146 + 0.918829i) q^{6} +(2.39871 + 4.15469i) q^{7} +1.00000 q^{8} +(0.188495 + 0.326482i) q^{9} +(0.811505 - 2.08362i) q^{10} +(1.43026 + 0.825763i) q^{11} -1.83766i q^{12} +(-1.09146 - 3.43638i) q^{13} -4.79742 q^{14} +(-3.82898 - 1.49127i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0697360 + 0.0402621i) q^{17} -0.376989 q^{18} +(3.67867 - 2.12388i) q^{19} +(1.39871 + 1.74459i) q^{20} +8.81603i q^{21} +(-1.43026 + 0.825763i) q^{22} +(-5.10893 - 2.94964i) q^{23} +(1.59146 + 0.918829i) q^{24} +(4.77013 - 1.49863i) q^{25} +(3.52172 + 0.772959i) q^{26} -4.82020i q^{27} +(2.39871 - 4.15469i) q^{28} +(2.21022 - 3.82821i) q^{29} +(3.20597 - 2.57036i) q^{30} +4.06163i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.51747 + 2.62834i) q^{33} -0.0805241i q^{34} +(-6.71022 - 8.36955i) q^{35} +(0.188495 - 0.326482i) q^{36} +(0.908541 - 1.57364i) q^{37} +4.24776i q^{38} +(1.42044 - 6.47172i) q^{39} +(-2.21022 + 0.339024i) q^{40} +(-5.87906 - 3.39427i) q^{41} +(-7.63491 - 4.40801i) q^{42} +(7.35733 - 4.24776i) q^{43} -1.65153i q^{44} +(-0.527300 - 0.657693i) q^{45} +(5.10893 - 2.94964i) q^{46} +0.448597 q^{47} +(-1.59146 + 0.918829i) q^{48} +(-8.00764 + 13.8696i) q^{49} +(-1.08721 + 4.88037i) q^{50} -0.147976 q^{51} +(-2.43026 + 2.66342i) q^{52} +11.5770i q^{53} +(4.17441 + 2.41010i) q^{54} +(-3.44115 - 1.34022i) q^{55} +(2.39871 + 4.15469i) q^{56} +7.80593 q^{57} +(2.21022 + 3.82821i) q^{58} +(1.82559 - 1.05400i) q^{59} +(0.623011 + 4.06163i) q^{60} +(1.56416 + 2.70920i) q^{61} +(-3.51747 - 2.03081i) q^{62} +(-0.904289 + 1.56627i) q^{63} +1.00000 q^{64} +(3.57738 + 7.22512i) q^{65} -3.03494 q^{66} +(-2.00000 + 3.46410i) q^{67} +(0.0697360 + 0.0402621i) q^{68} +(-5.42044 - 9.38847i) q^{69} +(10.6034 - 1.62644i) q^{70} +(-6.36584 + 3.67532i) q^{71} +(0.188495 + 0.326482i) q^{72} -10.5752 q^{73} +(0.908541 + 1.57364i) q^{74} +(8.96845 + 1.99792i) q^{75} +(-3.67867 - 2.12388i) q^{76} +7.92308i q^{77} +(4.89446 + 4.46600i) q^{78} -14.6468 q^{79} +(0.811505 - 2.08362i) q^{80} +(4.99442 - 8.65060i) q^{81} +(5.87906 - 3.39427i) q^{82} -12.4289 q^{83} +(7.63491 - 4.40801i) q^{84} +(0.140482 - 0.112630i) q^{85} +8.49552i q^{86} +(7.03494 - 4.06163i) q^{87} +(1.43026 + 0.825763i) q^{88} +(7.23958 + 4.17978i) q^{89} +(0.833228 - 0.127808i) q^{90} +(11.6590 - 12.7776i) q^{91} +5.89928i q^{92} +(-3.73194 + 6.46391i) q^{93} +(-0.224298 + 0.388496i) q^{94} +(-7.41061 + 5.94139i) q^{95} -1.83766i q^{96} +(-2.90296 - 5.02808i) q^{97} +(-8.00764 - 13.8696i) q^{98} +0.622608i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9} - 3 q^{11} + 4 q^{13} - 10 q^{14} - 2 q^{15} - 4 q^{16} - 15 q^{17} - 16 q^{18} + 9 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} + 5 q^{28} - 3 q^{29} + 10 q^{30} - 4 q^{32} - 10 q^{33} - 33 q^{35} + 8 q^{36} + 20 q^{37} - 30 q^{39} + 3 q^{40} + 21 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{45} + 6 q^{46} + 6 q^{47} - 15 q^{49} - q^{50} - 20 q^{51} - 5 q^{52} + 18 q^{54} - 23 q^{55} + 5 q^{56} + 24 q^{57} - 3 q^{58} + 30 q^{59} - 8 q^{60} - 5 q^{61} - 6 q^{62} - 25 q^{63} + 8 q^{64} - 6 q^{65} + 20 q^{66} - 16 q^{67} + 15 q^{68} - 2 q^{69} + 18 q^{70} + 8 q^{72} + 26 q^{73} + 20 q^{74} + 72 q^{75} - 9 q^{76} + 30 q^{78} + 4 q^{79} + 8 q^{81} - 21 q^{82} - 48 q^{83} - 6 q^{84} - 34 q^{85} + 12 q^{87} - 3 q^{88} - 39 q^{89} - 27 q^{90} + 19 q^{91} + 18 q^{93} - 3 q^{94} + 9 q^{95} - 4 q^{97} - 15 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9 - 3 * q^11 + 4 * q^13 - 10 * q^14 - 2 * q^15 - 4 * q^16 - 15 * q^17 - 16 * q^18 + 9 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 5 * q^25 + q^26 + 5 * q^28 - 3 * q^29 + 10 * q^30 - 4 * q^32 - 10 * q^33 - 33 * q^35 + 8 * q^36 + 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^45 + 6 * q^46 + 6 * q^47 - 15 * q^49 - q^50 - 20 * q^51 - 5 * q^52 + 18 * q^54 - 23 * q^55 + 5 * q^56 + 24 * q^57 - 3 * q^58 + 30 * q^59 - 8 * q^60 - 5 * q^61 - 6 * q^62 - 25 * q^63 + 8 * q^64 - 6 * q^65 + 20 * q^66 - 16 * q^67 + 15 * q^68 - 2 * q^69 + 18 * q^70 + 8 * q^72 + 26 * q^73 + 20 * q^74 + 72 * q^75 - 9 * q^76 + 30 * q^78 + 4 * q^79 + 8 * q^81 - 21 * q^82 - 48 * q^83 - 6 * q^84 - 34 * q^85 + 12 * q^87 - 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 + 18 * q^93 - 3 * q^94 + 9 * q^95 - 4 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.59146	+	0.918829i	0.918829	+	0.530486i	0.883261	−	0.468881i	$-0.155343\pi$
$3$	1.59146	+	0.918829i	0.918829	+	0.530486i	0.0355679	+	0.999367i	$0.488676\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.21022	+	0.339024i	−0.988439	+	0.151616i
$5$	−2.21022	+	0.339024i	−0.988439	+	0.151616i
$6$	−1.59146	+	0.918829i	−0.649710	+	0.375111i
$7$	2.39871	+	4.15469i	0.906628	+	1.57033i	0.818717	+	0.574198i	$0.194686\pi$
$7$	2.39871	+	4.15469i	0.906628	+	1.57033i	0.0879113	+	0.996128i	$0.471981\pi$
$8$	1.00000			0.353553
$9$	0.188495	+	0.326482i	0.0628316	+	0.108827i
$10$	0.811505	−	2.08362i	0.256621	−	0.658897i
$11$	1.43026	+	0.825763i	0.431241	+	0.248977i	0.699875	−	0.714265i	$-0.253239\pi$
$11$	1.43026	+	0.825763i	0.431241	+	0.248977i	−0.268634	+	0.963242i	$0.586572\pi$
$12$		−	1.83766i		−	0.530486i
$13$	−1.09146	−	3.43638i	−0.302716	−	0.953081i
$13$	−1.09146	−	3.43638i	−0.302716	−	0.953081i
$14$	−4.79742			−1.28217
$15$	−3.82898	−	1.49127i	−0.988637	−	0.385044i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0697360	+	0.0402621i	−0.0169135	+	0.00976499i	−0.508433	−	0.861102i	$-0.669775\pi$
$17$	−0.0697360	+	0.0402621i	−0.0169135	+	0.00976499i	0.491519	+	0.870867i	$0.336442\pi$
$18$	−0.376989			−0.0888572
$19$	3.67867	−	2.12388i	0.843944	−	0.487251i	−0.0146590	−	0.999893i	$-0.504666\pi$
$19$	3.67867	−	2.12388i	0.843944	−	0.487251i	0.858603	+	0.512641i	$0.171333\pi$
$20$	1.39871	+	1.74459i	0.312762	+	0.390103i
$21$			8.81603i			1.92382i
$22$	−1.43026	+	0.825763i	−0.304933	+	0.176053i
$23$	−5.10893	−	2.94964i	−1.06529	−	0.615043i	−0.138396	−	0.990377i	$-0.544195\pi$
$23$	−5.10893	−	2.94964i	−1.06529	−	0.615043i	−0.926890	+	0.375334i	$0.877528\pi$
$24$	1.59146	+	0.918829i	0.324855	+	0.187555i
$25$	4.77013	−	1.49863i	0.954025	−	0.299727i
$26$	3.52172	+	0.772959i	0.690667	+	0.151590i
$27$		−	4.82020i		−	0.927648i
$28$	2.39871	−	4.15469i	0.453314	−	0.785163i
$29$	2.21022	−	3.82821i	0.410427	−	0.710881i	−0.584509	−	0.811387i	$-0.698713\pi$
$29$	2.21022	−	3.82821i	0.410427	−	0.710881i	0.994936	+	0.100506i	$0.0320463\pi$
$30$	3.20597	−	2.57036i	0.585327	−	0.469281i
$31$			4.06163i			0.729490i	0.931108	+	0.364745i	$0.118844\pi$
$31$			4.06163i			0.729490i	−0.931108	+	0.364745i	$0.881156\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.51747	+	2.62834i	0.264158	+	0.457535i
$34$		−	0.0805241i		−	0.0138098i
$35$	−6.71022	−	8.36955i	−1.13423	−	1.41471i
$36$	0.188495	−	0.326482i	0.0314158	−	0.0544137i
$37$	0.908541	−	1.57364i	0.149363	−	0.258705i	−0.781629	−	0.623744i	$-0.785611\pi$
$37$	0.908541	−	1.57364i	0.149363	−	0.258705i	0.930992	+	0.365039i	$0.118944\pi$
$38$			4.24776i			0.689077i
$39$	1.42044	−	6.47172i	0.227452	−	1.03631i
$40$	−2.21022	+	0.339024i	−0.349466	+	0.0536044i
$41$	−5.87906	−	3.39427i	−0.918154	−	0.530097i	−0.0351085	−	0.999384i	$-0.511178\pi$
$41$	−5.87906	−	3.39427i	−0.918154	−	0.530097i	−0.883046	+	0.469287i	$0.844511\pi$
$42$	−7.63491	−	4.40801i	−1.17809	−	0.680171i
$43$	7.35733	−	4.24776i	1.12198	−	0.647777i	0.180076	−	0.983653i	$-0.442366\pi$
$43$	7.35733	−	4.24776i	1.12198	−	0.647777i	0.941906	+	0.335876i	$0.109032\pi$
$44$		−	1.65153i		−	0.248977i
$45$	−0.527300	−	0.657693i	−0.0786052	−	0.0980431i
$46$	5.10893	−	2.94964i	0.753271	−	0.434901i
$47$	0.448597			0.0654345			0.0327173	−	0.999465i	$-0.489584\pi$
$47$	0.448597			0.0654345			0.0327173	+	0.999465i	$0.489584\pi$
$48$	−1.59146	+	0.918829i	−0.229707	+	0.132622i
$49$	−8.00764	+	13.8696i	−1.14395	+	1.98138i
$50$	−1.08721	+	4.88037i	−0.153754	+	0.690188i
$51$	−0.147976			−0.0207208
$52$	−2.43026	+	2.66342i	−0.337017	+	0.369350i
$53$			11.5770i			1.59022i	0.606463	+	0.795112i	$0.292588\pi$
$53$			11.5770i			1.59022i	−0.606463	+	0.795112i	$0.707412\pi$
$54$	4.17441	+	2.41010i	0.568066	+	0.327973i
$55$	−3.44115	−	1.34022i	−0.464004	−	0.180716i
$56$	2.39871	+	4.15469i	0.320541	+	0.555194i
$57$	7.80593			1.03392
$58$	2.21022	+	3.82821i	0.290216	+	0.502669i
$59$	1.82559	−	1.05400i	0.237671	−	0.137219i	−0.376435	−	0.926443i	$-0.622850\pi$
$59$	1.82559	−	1.05400i	0.237671	−	0.137219i	0.614106	+	0.789224i	$0.289517\pi$
$60$	0.623011	+	4.06163i	0.0804303	+	0.524354i
$61$	1.56416	+	2.70920i	0.200270	+	0.346878i	0.948615	−	0.316431i	$-0.102485\pi$
$61$	1.56416	+	2.70920i	0.200270	+	0.346878i	−0.748345	+	0.663309i	$0.769151\pi$
$62$	−3.51747	−	2.03081i	−0.446719	−	0.257913i
$63$	−0.904289	+	1.56627i	−0.113930	+	0.197332i
$64$	1.00000			0.125000
$65$	3.57738	+	7.22512i	0.443719	+	0.896166i
$66$	−3.03494			−0.373576
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	0.0697360	+	0.0402621i	0.00845673	+	0.00488249i
$69$	−5.42044	−	9.38847i	−0.652544	−	1.13024i
$70$	10.6034	−	1.62644i	1.26734	−	0.194397i
$71$	−6.36584	+	3.67532i	−0.755486	+	0.436180i	−0.827673	−	0.561211i	$-0.810336\pi$
$71$	−6.36584	+	3.67532i	−0.755486	+	0.436180i	0.0721869	+	0.997391i	$0.477002\pi$
$72$	0.188495	+	0.326482i	0.0222143	+	0.0384763i
$73$	−10.5752			−1.23773			−0.618866	−	0.785496i	$-0.712408\pi$
$73$	−10.5752			−1.23773			−0.618866	+	0.785496i	$0.712408\pi$
$74$	0.908541	+	1.57364i	0.105616	+	0.182932i
$75$	8.96845	+	1.99792i	1.03559	+	0.230699i
$76$	−3.67867	−	2.12388i	−0.421972	−	0.243626i
$77$			7.92308i			0.902918i
$78$	4.89446	+	4.46600i	0.554189	+	0.505674i
$79$	−14.6468			−1.64789			−0.823947	−	0.566667i	$-0.808233\pi$
$79$	−14.6468			−1.64789			−0.823947	+	0.566667i	$0.808233\pi$
$80$	0.811505	−	2.08362i	0.0907291	−	0.232955i
$81$	4.99442	−	8.65060i	0.554936	−	0.961177i
$82$	5.87906	−	3.39427i	0.649233	−	0.374835i
$83$	−12.4289			−1.36425			−0.682127	−	0.731234i	$-0.738945\pi$
$83$	−12.4289			−1.36425			−0.682127	+	0.731234i	$0.738945\pi$
$84$	7.63491	−	4.40801i	0.833036	−	0.480954i
$85$	0.140482	−	0.112630i	0.0152374	−	0.0122165i
$86$			8.49552i			0.916095i
$87$	7.03494	−	4.06163i	0.754225	−	0.435452i
$88$	1.43026	+	0.825763i	0.152467	+	0.0880267i
$89$	7.23958	+	4.17978i	0.767394	+	0.443055i	0.831944	−	0.554859i	$-0.187228\pi$
$89$	7.23958	+	4.17978i	0.767394	+	0.443055i	−0.0645500	+	0.997914i	$0.520561\pi$
$90$	0.833228	−	0.127808i	0.0878300	−	0.0134722i
$91$	11.6590	−	12.7776i	1.22220	−	1.33945i
$92$			5.89928i			0.615043i
$93$	−3.73194	+	6.46391i	−0.386984	+	0.670276i
$94$	−0.224298	+	0.388496i	−0.0231346	+	0.0400703i
$95$	−7.41061	+	5.94139i	−0.760312	+	0.609574i
$96$		−	1.83766i		−	0.187555i
$97$	−2.90296	−	5.02808i	−0.294751	−	0.510524i	0.680176	−	0.733049i	$-0.261903\pi$
$97$	−2.90296	−	5.02808i	−0.294751	−	0.510524i	−0.974927	+	0.222525i	$0.928570\pi$
$98$	−8.00764	−	13.8696i	−0.808894	−	1.40105i
$99$			0.622608i			0.0625744i
$100$	−3.68292	−	3.38173i	−0.368292	−	0.338173i
$101$	−0.618759	+	1.07172i	−0.0615688	+	0.106640i	−0.895167	−	0.445731i	$-0.852944\pi$
$101$	−0.618759	+	1.07172i	−0.0615688	+	0.106640i	0.833598	+	0.552372i	$0.186277\pi$
$102$	0.0739879	−	0.128151i	0.00732590	−	0.0126888i
$103$		−	9.38847i		−	0.925073i	−0.886600	−	0.462537i	$-0.846939\pi$
$103$		−	9.38847i		−	0.925073i	0.886600	−	0.462537i	$-0.153061\pi$
$104$	−1.09146	−	3.43638i	−0.107026	−	0.336965i
$105$	−2.98885	−	19.4853i	−0.291682	−	1.90157i
$106$	−10.0260	−	5.78850i	−0.973809	−	0.562229i
$107$	16.0272	+	9.25330i	1.54941	+	0.894550i	0.998187	+	0.0601893i	$0.0191704\pi$
$107$	16.0272	+	9.25330i	1.54941	+	0.894550i	0.551219	+	0.834361i	$0.314163\pi$
$108$	−4.17441	+	2.41010i	−0.401683	+	0.231912i
$109$			9.08638i			0.870317i	0.900354	+	0.435158i	$0.143308\pi$
$109$			9.08638i			0.870317i	−0.900354	+	0.435158i	$0.856692\pi$
$110$	2.88124	−	2.31001i	0.274716	−	0.220251i
$111$	2.89181	−	1.66959i	0.274479	−	0.158470i
$112$	−4.79742			−0.453314
$113$	13.8051	−	7.97036i	1.29867	−	0.749788i	0.318497	−	0.947924i	$-0.396822\pi$
$113$	13.8051	−	7.97036i	1.29867	−	0.749788i	0.980175	+	0.198136i	$0.0634886\pi$
$114$	−3.90296	+	6.76013i	−0.365546	+	0.633144i
$115$	12.2918	+	4.78730i	1.14622	+	0.446418i
$116$	−4.42044			−0.410427
$117$	0.916184	−	1.00408i	0.0847012	−	0.0928274i
$118$			2.10800i			0.194058i
$119$	−0.334553	−	0.193154i	−0.0306684	−	0.0177064i
$120$	−3.82898	−	1.49127i	−0.349536	−	0.136134i
$121$	−4.13623	−	7.16416i	−0.376021	−	0.651287i
$122$	−3.12832			−0.283225
$123$	−6.23752	−	10.8037i	−0.562418	−	0.974137i
$124$	3.51747	−	2.03081i	0.315878	−	0.182372i
$125$	−10.0349	+	4.92950i	−0.897553	+	0.440908i
$126$	−0.904289	−	1.56627i	−0.0805605	−	0.139535i
$127$	0.773321	+	0.446477i	0.0686211	+	0.0396184i	0.533918	−	0.845536i	$-0.320719\pi$
$127$	0.773321	+	0.446477i	0.0686211	+	0.0396184i	−0.465297	+	0.885155i	$0.654052\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	15.6119			1.37455
$130$	−8.04583	−	0.514459i	−0.705666	−	0.0451211i
$131$	−1.11770			−0.0976541			−0.0488271	−	0.998807i	$-0.515548\pi$
$131$	−1.11770			−0.0976541			−0.0488271	+	0.998807i	$0.515548\pi$
$132$	1.51747	−	2.62834i	0.132079	−	0.228767i
$133$	17.6481	+	10.1891i	1.53029	+	0.883511i
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$	1.63416	+	10.6537i	0.140646	+	0.916923i
$136$	−0.0697360	+	0.0402621i	−0.00597981	+	0.00345244i
$137$	−4.10468	−	7.10951i	−0.350686	−	0.607407i	0.635684	−	0.771950i	$-0.280718\pi$
$137$	−4.10468	−	7.10951i	−0.350686	−	0.607407i	−0.986370	+	0.164543i	$0.947385\pi$
$138$	10.8409			0.922836
$139$	2.55885	+	4.43206i	0.217039	+	0.375922i	0.953901	−	0.300120i	$-0.0970268\pi$
$139$	2.55885	+	4.43206i	0.217039	+	0.375922i	−0.736862	+	0.676043i	$0.763693\pi$
$140$	−3.89314	+	9.99600i	−0.329030	+	0.844816i
$141$	0.713923	+	0.412184i	0.0601232	+	0.0347121i
$142$		−	7.35063i		−	0.616852i
$143$	1.27656	−	5.81622i	0.106752	−	0.486377i
$144$	−0.376989			−0.0314158
$145$	−3.58721	+	9.21049i	−0.297901	+	0.764890i
$146$	5.28760	−	9.15839i	0.437605	−	0.757953i
$147$	−25.4877	+	14.7153i	−2.10219	+	1.21370i
$148$	−1.81708			−0.149363
$149$	3.58721	−	2.07107i	0.293875	−	0.169669i	−0.345813	−	0.938304i	$-0.612397\pi$
$149$	3.58721	−	2.07107i	0.293875	−	0.169669i	0.639688	+	0.768634i	$0.279063\pi$
$150$	−6.21447	+	6.76795i	−0.507409	+	0.552601i
$151$			4.43389i			0.360825i	0.983591	+	0.180412i	$0.0577432\pi$
$151$			4.43389i			0.360825i	−0.983591	+	0.180412i	$0.942257\pi$
$152$	3.67867	−	2.12388i	0.298379	−	0.172269i
$153$	−0.0262897	−	0.0151784i	−0.00212540	−	0.00122710i
$154$	−6.86158	−	3.96154i	−0.552922	−	0.319230i
$155$	−1.37699	−	8.97708i	−0.110602	−	0.721056i
$156$	−6.31490	+	2.00573i	−0.505596	+	0.160587i
$157$		−	8.32411i		−	0.664337i	−0.943220	−	0.332168i	$-0.892220\pi$
$157$		−	8.32411i		−	0.664337i	0.943220	−	0.332168i	$-0.107780\pi$
$158$	7.32340	−	12.6845i	0.582618	−	1.00912i
$159$	−10.6373	+	18.4243i	−0.843592	+	1.46114i
$160$	1.39871	+	1.74459i	0.110578	+	0.137922i
$161$		−	28.3014i		−	2.23046i
$162$	4.99442	+	8.65060i	0.392399	+	0.679655i
$163$	−0.471644	−	0.816912i	−0.0369420	−	0.0639855i	0.846963	−	0.531651i	$-0.178428\pi$
$163$	−0.471644	−	0.816912i	−0.0369420	−	0.0639855i	−0.883905	+	0.467666i	$0.845095\pi$
$164$			6.78855i			0.530097i
$165$	−4.24501	−	5.29474i	−0.330474	−	0.412195i
$166$	6.21447	−	10.7638i	0.482336	−	0.835431i
$167$	2.15031	−	3.72445i	0.166396	−	0.288206i	−0.770754	−	0.637133i	$-0.780120\pi$
$167$	2.15031	−	3.72445i	0.166396	−	0.288206i	0.937150	+	0.348926i	$0.113454\pi$
$168$			8.81603i			0.680171i
$169$	−10.6174	+	7.50134i	−0.816726	+	0.577026i
$170$	0.0272996	+	0.177976i	0.00209379	+	0.0136501i
$171$	1.38682	+	0.800680i	0.106053	+	0.0612295i
$172$	−7.35733	−	4.24776i	−0.560991	−	0.323888i
$173$	−0.861584	+	0.497436i	−0.0655050	+	0.0378194i	−0.532395	−	0.846496i	$-0.678708\pi$
$173$	−0.861584	+	0.497436i	−0.0655050	+	0.0378194i	0.466890	+	0.884316i	$0.345374\pi$
$174$			8.12325i			0.615822i
$175$	17.6685	+	16.2236i	1.33561	+	1.22639i
$176$	−1.43026	+	0.825763i	−0.107810	+	0.0622443i
$177$	3.87379			0.291172
$178$	−7.23958	+	4.17978i	−0.542630	+	0.313287i
$179$	10.2179	−	17.6979i	0.763719	−	1.32280i	−0.177203	−	0.984174i	$-0.556705\pi$
$179$	10.2179	−	17.6979i	0.763719	−	1.32280i	0.940921	−	0.338625i	$-0.109962\pi$
$180$	−0.305929	+	0.785501i	−0.0228026	+	0.0585478i
$181$	−19.9522			−1.48303			−0.741517	−	0.670934i	$-0.765893\pi$
$181$	−19.9522			−1.48303			−0.741517	+	0.670934i	$0.765893\pi$
$182$	5.23619	+	16.4858i	0.388132	+	1.22201i
$183$			5.74878i			0.424962i
$184$	−5.10893	−	2.94964i	−0.376635	−	0.217451i
$185$	−1.47457	+	3.78610i	−0.108413	+	0.278360i
$186$	−3.73194	−	6.46391i	−0.273639	−	0.473957i
$187$	−0.132988			−0.00972503
$188$	−0.224298	−	0.388496i	−0.0163586	−	0.0283340i
$189$	20.0264	−	11.5623i	1.45671	−	0.841031i
$190$	−1.44009	−	9.38847i	−0.104475	−	0.681111i
$191$	3.83986	+	6.65083i	0.277843	+	0.481238i	0.970848	−	0.239695i	$-0.0770473\pi$
$191$	3.83986	+	6.65083i	0.277843	+	0.481238i	−0.693006	+	0.720932i	$0.743714\pi$
$192$	1.59146	+	0.918829i	0.114854	+	0.0663108i
$193$	−7.59571	+	13.1562i	−0.546751	+	0.947001i	0.451743	+	0.892148i	$0.350802\pi$
$193$	−7.59571	+	13.1562i	−0.546751	+	0.947001i	−0.998494	+	0.0548529i	$0.982531\pi$
$194$	5.80593			0.416841
$195$	−0.945401	+	14.7855i	−0.0677016	+	1.05881i
$196$	16.0153			1.14395
$197$	1.50663	−	2.60956i	0.107343	−	0.185924i	−0.807350	−	0.590073i	$-0.799099\pi$
$197$	1.50663	−	2.60956i	0.107343	−	0.185924i	0.914693	+	0.404149i	$0.132432\pi$
$198$	−0.539194	−	0.311304i	−0.0383189	−	0.0221234i
$199$	4.86053	+	8.41868i	0.344554	+	0.596785i	0.985273	−	0.170991i	$-0.0546969\pi$
$199$	4.86053	+	8.41868i	0.344554	+	0.596785i	−0.640719	+	0.767776i	$0.721364\pi$
$200$	4.77013	−	1.49863i	0.337299	−	0.105969i
$201$	−6.36584	+	3.67532i	−0.449011	+	0.259237i
$202$	−0.618759	−	1.07172i	−0.0435357	−	0.0754061i
$203$	21.2067			1.48842
$204$	0.0739879	+	0.128151i	0.00518019	+	0.00897236i
$205$	14.1447	+	5.50894i	0.987911	+	0.384761i
$206$	8.13065	+	4.69423i	0.566489	+	0.327063i
$207$		−	2.22397i		−	0.154576i
$208$	3.52172	+	0.772959i	0.244188	+	0.0535951i
$209$	7.01529			0.485257
$210$	18.3692	+	7.15425i	1.26760	+	0.493690i
$211$	2.39532	−	4.14882i	0.164901	−	0.285616i	−0.771719	−	0.635963i	$-0.780603\pi$
$211$	2.39532	−	4.14882i	0.164901	−	0.285616i	0.936620	+	0.350347i	$0.113936\pi$
$212$	10.0260	−	5.78850i	0.688587	−	0.397556i
$213$	−13.5080			−0.925550
$214$	−16.0272	+	9.25330i	−1.09560	+	0.632542i
$215$	−14.8212	+	11.8828i	−1.01080	+	0.810399i
$216$		−	4.82020i		−	0.327973i
$217$	−16.8748	+	9.74267i	−1.14554	+	0.661376i
$218$	−7.86903	−	4.54319i	−0.532958	−	0.307704i
$219$	−16.8300	−	9.71680i	−1.13727	−	0.656600i
$220$	0.559907	+	3.65023i	0.0377490	+	0.246099i
$221$	0.214470	+	0.195695i	0.0144268	+	0.0131639i
$222$			3.33918i			0.224111i
$223$	7.02172	−	12.1620i	0.470209	−	0.814426i	−0.529210	−	0.848491i	$-0.677512\pi$
$223$	7.02172	−	12.1620i	0.470209	−	0.814426i	0.999420	+	0.0340642i	$0.0108451\pi$
$224$	2.39871	−	4.15469i	0.160271	−	0.277597i
$225$	1.38842	+	1.27488i	0.0925614	+	0.0849918i
$226$			15.9407i			1.06036i
$227$	1.44009	+	2.49431i	0.0955823	+	0.165553i	0.909851	−	0.414934i	$-0.136195\pi$
$227$	1.44009	+	2.49431i	0.0955823	+	0.165553i	−0.814269	+	0.580487i	$0.802862\pi$
$228$	−3.90296	−	6.76013i	−0.258480	−	0.447701i
$229$		−	6.70802i		−	0.443279i	−0.975129	−	0.221639i	$-0.928859\pi$
$229$		−	6.70802i		−	0.443279i	0.975129	−	0.221639i	$-0.0711408\pi$
$230$	−10.2918	+	8.25140i	−0.678624	+	0.544081i
$231$	−7.27995	+	12.6092i	−0.478986	+	0.829628i
$232$	2.21022	−	3.82821i	0.145108	−	0.251334i
$233$			17.5959i			1.15275i	0.817186	+	0.576374i	$0.195533\pi$
$233$			17.5959i			1.15275i	−0.817186	+	0.576374i	$0.804467\pi$
$234$	0.411468	+	1.29548i	0.0268985	+	0.0846881i
$235$	−0.991496	+	0.152085i	−0.0646781	+	0.00992094i
$236$	−1.82559	−	1.05400i	−0.118836	−	0.0686097i
$237$	−23.3098	−	13.4579i	−1.51413	−	0.874185i
$238$	0.334553	−	0.193154i	0.0216858	−	0.0125203i
$239$			11.3119i			0.731708i	0.930672	+	0.365854i	$0.119223\pi$
$239$			11.3119i			0.731708i	−0.930672	+	0.365854i	$0.880777\pi$
$240$	3.20597	−	2.57036i	0.206944	−	0.165916i
$241$	−4.39957	+	2.54010i	−0.283401	+	0.163622i	−0.634962	−	0.772543i	$-0.718984\pi$
$241$	−4.39957	+	2.54010i	−0.283401	+	0.163622i	0.351561	+	0.936165i	$0.385651\pi$
$242$	8.27246			0.531774
$243$	3.37360	−	1.94775i	0.216416	−	0.124948i
$244$	1.56416	−	2.70920i	0.100135	−	0.173439i
$245$	12.9965	−	33.3697i	0.830315	−	2.13191i
$246$	12.4750			0.795379
$247$	−11.3136	−	10.3232i	−0.719865	−	0.656848i
$248$			4.06163i			0.257913i
$249$	−19.7801	−	11.4201i	−1.25352	−	0.723718i
$250$	0.748402	−	11.1553i	0.0473331	−	0.705521i
$251$	9.78522	+	16.9485i	0.617637	+	1.06978i	0.989916	+	0.141658i	$0.0452434\pi$
$251$	9.78522	+	16.9485i	0.617637	+	1.06978i	−0.372278	+	0.928121i	$0.621423\pi$
$252$	1.80858			0.113930
$253$	−4.87141	−	8.43753i	−0.306263	−	0.530463i
$254$	−0.773321	+	0.446477i	−0.0485225	+	0.0280145i
$255$	0.327059	−	0.0501674i	0.0204812	−	0.00314160i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.71818	+	0.991989i	0.107177	+	0.0618786i	0.552630	−	0.833427i	$-0.313624\pi$
$257$	1.71818	+	0.991989i	0.107177	+	0.0618786i	−0.445453	+	0.895305i	$0.646958\pi$
$258$	−7.80593	+	13.5203i	−0.485976	+	0.841735i
$259$	8.71731			0.541668
$260$	4.46845	−	6.71066i	0.277121	−	0.416178i
$261$	1.66646			0.103151
$262$	0.558851	−	0.967959i	0.0345259	−	0.0598007i
$263$	−0.527031	−	0.304282i	−0.0324981	−	0.0187628i	0.483663	−	0.875254i	$-0.339306\pi$
$263$	−0.527031	−	0.304282i	−0.0324981	−	0.0187628i	−0.516161	+	0.856492i	$0.672639\pi$
$264$	1.51747	+	2.62834i	0.0933939	+	0.161763i
$265$	−3.92488	−	25.5877i	−0.241104	−	1.57184i
$266$	−17.6481	+	10.1891i	−1.08208	+	0.624737i
$267$	7.68100	+	13.3039i	0.470070	+	0.814184i
$268$	4.00000			0.244339
$269$	−8.87242	−	15.3675i	−0.540961	−	0.936972i	−0.998849	−	0.0479623i	$-0.984727\pi$
$269$	−8.87242	−	15.3675i	−0.540961	−	0.936972i	0.457888	−	0.889010i	$-0.348606\pi$
$270$	−10.0434	−	3.91162i	−0.611225	−	0.238053i
$271$	−13.8806	−	8.01395i	−0.843185	−	0.486813i	0.0151607	−	0.999885i	$-0.495174\pi$
$271$	−13.8806	−	8.01395i	−0.843185	−	0.486813i	−0.858346	+	0.513072i	$0.828507\pi$
$272$		−	0.0805241i		−	0.00488249i
$273$	30.2952	−	9.62234i	1.83355	−	0.582370i
$274$	8.20936			0.495945
$275$	8.06006	+	1.79555i	0.486040	+	0.108276i
$276$	−5.42044	+	9.38847i	−0.326272	+	0.565119i
$277$	10.3093	−	5.95209i	0.619427	−	0.357626i	−0.157219	−	0.987564i	$-0.550253\pi$
$277$	10.3093	−	5.95209i	0.619427	−	0.357626i	0.776646	+	0.629937i	$0.216919\pi$
$278$	−5.11770			−0.306939
$279$	−1.32605	+	0.765595i	−0.0793885	+	0.0458350i
$280$	−6.71022	−	8.36955i	−0.401012	−	0.500176i
$281$		−	11.3975i		−	0.679920i	−0.940440	−	0.339960i	$-0.889587\pi$
$281$		−	11.3975i		−	0.679920i	0.940440	−	0.339960i	$-0.110413\pi$
$282$	−0.713923	+	0.412184i	−0.0425135	+	0.0245452i
$283$	−17.6776	−	10.2062i	−1.05082	−	0.606694i	−0.127945	−	0.991781i	$-0.540838\pi$
$283$	−17.6776	−	10.2062i	−1.05082	−	0.606694i	−0.922880	+	0.385087i	$0.874171\pi$
$284$	6.36584	+	3.67532i	0.377743	+	0.218090i
$285$	−17.2528	+	2.64640i	−1.02197	+	0.156759i
$286$	4.39871	+	4.01365i	0.260101	+	0.237332i
$287$		−	32.5676i		−	1.92240i
$288$	0.188495	−	0.326482i	0.0111072	−	0.0192382i
$289$	−8.49676	+	14.7168i	−0.499809	+	0.865695i
$290$	−6.18292	−	7.71186i	−0.363073	−	0.452856i
$291$		−	10.6693i		−	0.625446i
$292$	5.28760	+	9.15839i	0.309433	+	0.535954i
$293$	−2.09384	−	3.62664i	−0.122323	−	0.211870i	0.798360	−	0.602180i	$-0.205701\pi$
$293$	−2.09384	−	3.62664i	−0.122323	−	0.211870i	−0.920684	+	0.390310i	$0.872368\pi$
$294$		−	29.4306i		−	1.71643i
$295$	−3.67761	+	2.94849i	−0.214119	+	0.171668i
$296$	0.908541	−	1.57364i	0.0528079	−	0.0914659i
$297$	3.98034	−	6.89416i	0.230963	−	0.400040i
$298$			4.14215i			0.239948i
$299$	−4.55991	+	20.7756i	−0.263706	+	1.20149i
$300$	−2.75398	−	8.76586i	−0.159001	−	0.506097i
$301$	35.2962	+	20.3783i	2.03444	+	1.17459i
$302$	−3.83986	−	2.21694i	−0.220959	−	0.127571i
$303$	−1.96946	+	1.13707i	−0.113142	+	0.0653228i
$304$			4.24776i			0.243626i
$305$	−4.37562	−	5.45764i	−0.250547	−	0.312504i
$306$	0.0262897	−	0.0151784i	0.00150288	−	0.000867690i
$307$	−18.0170			−1.02828			−0.514142	−	0.857705i	$-0.671890\pi$
$307$	−18.0170			−1.02828			−0.514142	+	0.857705i	$0.671890\pi$
$308$	6.86158	−	3.96154i	0.390975	−	0.225730i
$309$	8.62640	−	14.9414i	0.490739	−	0.849985i
$310$	8.46287	+	3.29603i	0.480659	+	0.187202i
$311$	−5.17816			−0.293626			−0.146813	−	0.989164i	$-0.546902\pi$
$311$	−5.17816			−0.293626			−0.146813	+	0.989164i	$0.546902\pi$
$312$	1.42044	−	6.47172i	0.0804163	−	0.366389i
$313$			32.6333i			1.84455i	0.386539	+	0.922273i	$0.373670\pi$
$313$			32.6333i			1.84455i	−0.386539	+	0.922273i	$0.626330\pi$
$314$	7.20889	+	4.16206i	0.406821	+	0.234878i
$315$	1.46767	−	3.76838i	0.0826939	−	0.212324i
$316$	7.32340	+	12.6845i	0.411973	+	0.713559i
$317$	23.7385			1.33328			0.666642	−	0.745378i	$-0.267731\pi$
$317$	23.7385			1.33328			0.666642	+	0.745378i	$0.267731\pi$
$318$	−10.6373	−	18.4243i	−0.596509	−	1.03318i
$319$	6.32239	−	3.65023i	0.353986	−	0.204374i
$320$	−2.21022	+	0.339024i	−0.123555	+	0.0189520i
$321$	17.0044	+	29.4525i	0.949093	+	1.64388i
$322$	24.5097	+	14.1507i	1.36587	+	0.788587i
$323$	−0.171024	+	0.296221i	−0.00951600	+	0.0164822i
$324$	−9.98885			−0.554936
$325$	−10.3563	−	14.7563i	−0.574463	−	0.818531i
$326$	0.943288			0.0522439
$327$	−8.34883	+	14.4606i	−0.461691	+	0.799673i
$328$	−5.87906	−	3.39427i	−0.324617	−	0.187417i
$329$	1.07605	+	1.86378i	0.0593248	+	0.102754i
$330$	6.70788	−	1.02892i	0.369257	−	0.0566401i
$331$	26.3923	−	15.2376i	1.45065	−	0.837534i	0.452132	−	0.891951i	$-0.350663\pi$
$331$	26.3923	−	15.2376i	1.45065	−	0.837534i	0.998518	+	0.0544174i	$0.0173301\pi$
$332$	6.21447	+	10.7638i	0.341063	+	0.590739i
$333$	0.685020			0.0375389
$334$	2.15031	+	3.72445i	0.117660	+	0.203793i
$335$	3.24602	−	8.33447i	0.177349	−	0.455361i
$336$	−7.63491	−	4.40801i	−0.416518	−	0.240477i
$337$			19.2799i			1.05024i	0.851027	+	0.525121i	$0.175980\pi$
$337$			19.2799i			1.05024i	−0.851027	+	0.525121i	$0.824020\pi$
$338$	−1.18763	−	12.9456i	−0.0645987	−	0.704150i
$339$	29.2936			1.59101
$340$	−0.167781	−	0.0653458i	−0.00909923	−	0.00354387i
$341$	−3.35394	+	5.80920i	−0.181626	+	0.314586i
$342$	−1.38682	+	0.800680i	−0.0749905	+	0.0432958i
$343$	−43.2502			−2.33529
$344$	7.35733	−	4.24776i	0.396681	−	0.229024i
$345$	15.1633	+	18.9129i	0.816363	+	1.01824i
$346$		−	0.994872i		−	0.0534846i
$347$	−13.3125	+	7.68598i	−0.714653	+	0.412605i	−0.812782	−	0.582569i	$-0.802048\pi$
$347$	−13.3125	+	7.68598i	−0.714653	+	0.412605i	0.0981283	+	0.995174i	$0.468714\pi$
$348$	−7.03494	−	4.06163i	−0.377112	−	0.217726i
$349$	−13.1667	−	7.60177i	−0.704795	−	0.406913i	0.104336	−	0.994542i	$-0.466728\pi$
$349$	−13.1667	−	7.60177i	−0.704795	−	0.406913i	−0.809131	+	0.587629i	$0.800062\pi$
$350$	−22.8843	+	7.18959i	−1.22322	+	0.384300i
$351$	−16.5640	+	5.26105i	−0.884123	+	0.280814i
$352$		−	1.65153i		−	0.0880267i
$353$	−13.4509	+	23.2976i	−0.715917	+	1.24000i	0.246688	+	0.969095i	$0.420658\pi$
$353$	−13.4509	+	23.2976i	−0.715917	+	1.24000i	−0.962605	+	0.270909i	$0.912676\pi$
$354$	−1.93690	+	3.35480i	−0.102945	+	0.178306i
$355$	12.8239	−	10.2814i	0.680620	−	0.545681i
$356$		−	8.35955i		−	0.443055i
$357$	−0.354952	−	0.614794i	−0.0187860	−	0.0325384i
$358$	10.2179	+	17.6979i	0.540031	+	0.935361i
$359$		−	20.8348i		−	1.09962i	−0.835291	−	0.549809i	$-0.814701\pi$
$359$		−	20.8348i		−	1.09962i	0.835291	−	0.549809i	$-0.185299\pi$
$360$	−0.527300	−	0.657693i	−0.0277911	−	0.0346635i
$361$	−0.478277	+	0.828400i	−0.0251725	+	0.0436000i
$362$	9.97609	−	17.2791i	0.524332	−	0.908169i
$363$		−	15.2020i		−	0.797896i
$364$	−16.8952	−	3.70821i	−0.885549	−	0.194363i
$365$	23.3735	−	3.58525i	1.22342	−	0.187660i
$366$	−4.97859	−	2.87439i	−0.260235	−	0.150247i
$367$	29.9410	+	17.2865i	1.56291	+	0.902346i	0.996961	+	0.0779051i	$0.0248231\pi$
$367$	29.9410	+	17.2865i	1.56291	+	0.902346i	0.565948	+	0.824441i	$0.308510\pi$
$368$	5.10893	−	2.94964i	0.266321	−	0.153761i
$369$		−	2.55921i		−	0.133227i
$370$	−2.54157	−	3.17007i	−0.132130	−	0.164804i
$371$	−48.0989	+	27.7699i	−2.49717	+	1.44174i
$372$	7.46388			0.386984
$373$	21.6562	−	12.5032i	1.12131	−	0.647391i	0.179578	−	0.983744i	$-0.442527\pi$
$373$	21.6562	−	12.5032i	1.12131	−	0.647391i	0.941736	+	0.336353i	$0.109194\pi$
$374$	0.0664939	−	0.115171i	0.00343832	−	0.00595534i
$375$	−20.4996	−	1.37531i	−1.05859	−	0.0710206i
$376$	0.448597			0.0231346
$377$	−15.5676	−	3.41682i	−0.801770	−	0.175975i
$378$			23.1245i			1.18940i
$379$	−3.25585	−	1.87977i	−0.167242	−	0.0965571i	0.414043	−	0.910257i	$-0.364116\pi$
$379$	−3.25585	−	1.87977i	−0.167242	−	0.0965571i	−0.581285	+	0.813700i	$0.697450\pi$
$380$	8.85070	+	3.44708i	0.454031	+	0.176831i
$381$	0.820472	+	1.42110i	0.0420341	+	0.0728052i
$382$	−7.67972			−0.392929
$383$	1.96946	+	3.41120i	0.100635	+	0.174304i	0.911946	−	0.410310i	$-0.134579\pi$
$383$	1.96946	+	3.41120i	0.100635	+	0.174304i	−0.811312	+	0.584614i	$0.801246\pi$
$384$	−1.59146	+	0.918829i	−0.0812138	+	0.0468888i
$385$	−2.68611	−	17.5117i	−0.136897	−	0.892480i
$386$	−7.59571	−	13.1562i	−0.386612	−	0.669631i
$387$	2.77364	+	1.60136i	0.140992	+	0.0814017i
$388$	−2.90296	+	5.02808i	−0.147376	+	0.255262i
$389$	−19.1589			−0.971394			−0.485697	−	0.874127i	$-0.661434\pi$
$389$	−19.1589			−0.971394			−0.485697	+	0.874127i	$0.661434\pi$
$390$	−12.3319	−	8.21148i	−0.624450	−	0.415805i
$391$	0.475035			0.0240235
$392$	−8.00764	+	13.8696i	−0.404447	+	0.700523i
$393$	−1.77878	−	1.02698i	−0.0897275	−	0.0518042i
$394$	1.50663	+	2.60956i	0.0759031	+	0.131468i
$395$	32.3726	−	4.96562i	1.62884	−	0.249847i
$396$	0.539194	−	0.311304i	0.0270955	−	0.0156436i
$397$	−3.22769	−	5.59052i	−0.161993	−	0.280580i	0.773590	−	0.633686i	$-0.218459\pi$
$397$	−3.22769	−	5.59052i	−0.161993	−	0.280580i	−0.935583	+	0.353106i	$0.885126\pi$
$398$	−9.72106			−0.487273
$399$	18.7242	+	32.4312i	0.937381	+	1.62359i
$400$	−1.08721	+	4.88037i	−0.0543604	+	0.244018i
$401$	30.0012	+	17.3212i	1.49819	+	0.864980i	0.999998	−	0.00208777i	$-0.000664557\pi$
$401$	30.0012	+	17.3212i	1.49819	+	0.864980i	0.498191	+	0.867067i	$0.333998\pi$
$402$		−	7.35063i		−	0.366616i
$403$	13.9573	−	4.43310i	0.695262	−	0.220828i
$404$	1.23752			0.0615688
$405$	−8.10600	+	20.8129i	−0.402791	+	1.03420i
$406$	−10.6034	+	18.3655i	−0.526236	+	0.911467i
$407$	2.59891	−	1.50048i	0.128823	−	0.0743760i
$408$	−0.147976			−0.00732590
$409$	−16.1142	+	9.30356i	−0.796798	+	0.460031i	−0.842350	−	0.538931i	$-0.818829\pi$
$409$	−16.1142	+	9.30356i	−0.796798	+	0.460031i	0.0455524	+	0.998962i	$0.485495\pi$
$410$	−11.8433	+	9.49523i	−0.584897	+	0.468936i
$411$		−	15.0860i		−	0.744137i
$412$	−8.13065	+	4.69423i	−0.400569	+	0.231268i
$413$	8.75811	+	5.05650i	0.430958	+	0.248814i
$414$	1.92601	+	1.11198i	0.0946583	+	0.0546510i
$415$	27.4707	−	4.21371i	1.34848	−	0.206843i
$416$	−2.43026	+	2.66342i	−0.119153	+	0.130585i
$417$			9.40459i			0.460545i
$418$	−3.50764	+	6.07542i	−0.171564	+	0.297158i
$419$	11.4748	−	19.8749i	0.560579	−	0.970951i	−0.436867	−	0.899526i	$-0.643912\pi$
$419$	11.4748	−	19.8749i	0.560579	−	0.970951i	0.997446	−	0.0714252i	$-0.0227547\pi$
$420$	−15.3804	+	12.3311i	−0.750486	+	0.601696i
$421$			34.8196i			1.69700i	0.529194	+	0.848501i	$0.322495\pi$
$421$			34.8196i			1.69700i	−0.529194	+	0.848501i	$0.677505\pi$
$422$	2.39532	+	4.14882i	0.116602	+	0.201961i
$423$	0.0845580	+	0.146459i	0.00411135	+	0.00712107i
$424$			11.5770i			0.562229i
$425$	−0.272311	+	0.296564i	−0.0132090	+	0.0143855i
$426$	6.75398	−	11.6982i	0.327231	−	0.566781i
$427$	−7.50394	+	12.9972i	−0.363141	+	0.628979i
$428$		−	18.5066i		−	0.894550i
$429$	7.37571	−	8.08333i	0.356103	−	0.390267i
$430$	−2.88019	−	18.7769i	−0.138895	−	0.905504i
$431$	17.7523	+	10.2493i	0.855100	+	0.493692i	0.862368	−	0.506281i	$-0.168980\pi$
$431$	17.7523	+	10.2493i	0.855100	+	0.493692i	−0.00726828	+	0.999974i	$0.502314\pi$
$432$	4.17441	+	2.41010i	0.200842	+	0.115956i
$433$	−1.85765	+	1.07251i	−0.0892728	+	0.0515417i	−0.543972	−	0.839103i	$-0.683080\pi$
$433$	−1.85765	+	1.07251i	−0.0892728	+	0.0515417i	0.454699	+	0.890645i	$0.349747\pi$
$434$		−	19.4853i		−	0.935326i
$435$	−14.1718	+	11.3621i	−0.679484	+	0.544771i
$436$	7.86903	−	4.54319i	0.376858	−	0.217579i
$437$	−25.0587			−1.19872
$438$	16.8300	−	9.71680i	0.804168	−	0.464287i
$439$	−0.525975	+	0.911016i	−0.0251034	+	0.0434804i	−0.878304	−	0.478102i	$-0.841325\pi$
$439$	−0.525975	+	0.911016i	−0.0251034	+	0.0434804i	0.853201	+	0.521583i	$0.174658\pi$
$440$	−3.44115	−	1.34022i	−0.164050	−	0.0638926i
$441$	−6.03759			−0.287504
$442$	−0.276712	+	0.0878888i	−0.0131618	+	0.00418044i
$443$			18.3043i			0.869665i	0.900511	+	0.434833i	$0.143193\pi$
$443$			18.3043i			0.869665i	−0.900511	+	0.434833i	$0.856807\pi$
$444$	−2.89181	−	1.66959i	−0.137239	−	0.0792351i
$445$	−17.4181	−	6.78382i	−0.825697	−	0.321584i
$446$	7.02172	+	12.1620i	0.332488	+	0.575887i
$447$	7.61186			0.360029
$448$	2.39871	+	4.15469i	0.113329	+	0.196291i
$449$	−12.0831	+	6.97618i	−0.570237	+	0.329226i	−0.757244	−	0.653132i	$-0.773455\pi$
$449$	−12.0831	+	6.97618i	−0.570237	+	0.329226i	0.187007	+	0.982359i	$0.440121\pi$
$450$	−1.79829	+	0.564969i	−0.0847720	+	0.0266329i
$451$	−5.60573	−	9.70942i	−0.263964	−	0.457199i
$452$	−13.8051	−	7.97036i	−0.649336	−	0.374894i
$453$	−4.07399	+	7.05635i	−0.191413	+	0.331536i
$454$	−2.88019			−0.135174
$455$	−21.4370	+	32.1939i	−1.00498	+	1.50927i
$456$	7.80593			0.365546
$457$	14.7165	−	25.4898i	0.688411	−	1.19236i	−0.283941	−	0.958842i	$-0.591642\pi$
$457$	14.7165	−	25.4898i	0.688411	−	1.19236i	0.972352	−	0.233520i	$-0.0750245\pi$
$458$	5.80932	+	3.35401i	0.271452	+	0.156723i
$459$	0.194071	+	0.336141i	0.00905847	+	0.0156897i
$460$	−2.00000	−	13.0387i	−0.0932505	−	0.607933i
$461$	7.87540	−	4.54686i	0.366794	−	0.211768i	−0.305263	−	0.952268i	$-0.598744\pi$
$461$	7.87540	−	4.54686i	0.366794	−	0.211768i	0.672057	+	0.740500i	$0.265411\pi$
$462$	−7.27995	−	12.6092i	−0.338694	−	0.586635i
$463$	41.6642			1.93630			0.968150	−	0.250372i	$-0.0805529\pi$
$463$	41.6642			1.93630			0.968150	+	0.250372i	$0.0805529\pi$
$464$	2.21022	+	3.82821i	0.102607	+	0.177720i
$465$	6.05698	−	15.5519i	0.280886	−	0.721201i
$466$	−15.2385	−	8.79797i	−0.705911	−	0.407558i
$467$		−	38.1079i		−	1.76342i	−0.471789	−	0.881712i	$-0.656391\pi$
$467$		−	38.1079i		−	1.76342i	0.471789	−	0.881712i	$-0.343609\pi$
$468$	−1.32765	−	0.291397i	−0.0613707	−	0.0134699i
$469$	−19.1897			−0.886098
$470$	0.364038	−	0.934703i	0.0167918	−	0.0431146i
$471$	7.64844	−	13.2475i	0.352421	−	0.610412i
$472$	1.82559	−	1.05400i	0.0840294	−	0.0485144i
$473$	14.0306			0.645126
$474$	23.3098	−	13.4579i	1.07065	−	0.618142i
$475$	14.3648	−	15.6441i	0.659101	−	0.717803i
$476$			0.386309i			0.0177064i
$477$	−3.77969	+	2.18220i	−0.173060	+	0.0999162i
$478$	−9.79641	−	5.65596i	−0.448078	−	0.258698i
$479$	−13.0228	−	7.51871i	−0.595026	−	0.343538i	0.172056	−	0.985087i	$-0.444959\pi$
$479$	−13.0228	−	7.51871i	−0.595026	−	0.343538i	−0.767082	+	0.641549i	$0.778292\pi$
$480$	0.623011	+	4.06163i	0.0284364	+	0.185387i
$481$	−6.39926	−	1.40453i	−0.291781	−	0.0640411i
$482$		−	5.08019i		−	0.231396i
$483$	26.0041	−	45.0405i	1.18323	−	2.04941i
$484$	−4.13623	+	7.16416i	−0.188010	+	0.325644i
$485$	8.12082	+	10.1290i	0.368748	+	0.459933i
$486$			3.89550i			0.176703i
$487$	−2.28128	−	3.95129i	−0.103375	−	0.179050i	0.809698	−	0.586846i	$-0.199631\pi$
$487$	−2.28128	−	3.95129i	−0.103375	−	0.179050i	−0.913073	+	0.407796i	$0.866297\pi$
$488$	1.56416	+	2.70920i	0.0708062	+	0.122640i
$489$		−	1.73344i		−	0.0783890i
$490$	22.4008	+	27.9401i	1.01196	+	1.26221i
$491$	4.20803	−	7.28853i	0.189906	−	0.328927i	−0.755313	−	0.655364i	$-0.772515\pi$
$491$	4.20803	−	7.28853i	0.189906	−	0.328927i	0.945219	+	0.326438i	$0.105848\pi$
$492$	−6.23752	+	10.8037i	−0.281209	+	0.487068i
$493$			0.355952i			0.0160313i
$494$	14.5969	−	4.63625i	0.656746	−	0.208595i
$495$	−0.211079	−	1.37610i	−0.00948730	−	0.0618511i
$496$	−3.51747	−	2.03081i	−0.157939	−	0.0911862i
$497$	−30.5396	−	17.6321i	−1.36989	−	0.790906i
$498$	19.7801	−	11.4201i	0.886370	−	0.511746i
$499$		−	12.5587i		−	0.562206i	−0.959678	−	0.281103i	$-0.909300\pi$
$499$		−	12.5587i		−	0.562206i	0.959678	−	0.281103i	$-0.0907002\pi$
$500$	9.28654	+	6.22577i	0.415307	+	0.278425i
$501$	6.84426	−	3.95154i	0.305779	−	0.176542i
$502$	−19.5704			−0.873471
$503$	−6.79244	+	3.92162i	−0.302860	+	0.174856i	−0.643727	−	0.765255i	$-0.722613\pi$
$503$	−6.79244	+	3.92162i	−0.302860	+	0.174856i	0.340867	+	0.940112i	$0.389279\pi$
$504$	−0.904289	+	1.56627i	−0.0402802	+	0.0697674i
$505$	1.00425	−	2.57851i	0.0446886	−	0.114742i
$506$	9.74283			0.433121
$507$	−23.7897	+	2.18246i	−1.05654	+	0.0969267i
$508$		−	0.892954i		−	0.0396184i
$509$	31.4237	+	18.1425i	1.39283	+	0.804152i	0.993628	−	0.112711i	$-0.0359534\pi$
$509$	31.4237	+	18.1425i	1.39283	+	0.804152i	0.399203	+	0.916862i	$0.369287\pi$
$510$	−0.120083	+	0.308325i	−0.00531737	+	0.0136529i
$511$	−25.3668	−	43.9367i	−1.12216	−	1.94364i
$512$	1.00000			0.0441942
$513$	−10.2375	−	17.7319i	−0.451997	−	0.782883i
$514$	−1.71818	+	0.991989i	−0.0757855	+	0.0437548i
$515$	3.18292	+	20.7506i	0.140256	+	0.914379i
$516$	−7.80593	−	13.5203i	−0.343637	−	0.595196i
$517$	0.641611	+	0.370435i	0.0282180	+	0.0162917i
$518$	−4.35866	+	7.54942i	−0.191508	+	0.331702i
$519$	−1.82823			−0.0802506
$520$	3.57738	+	7.22512i	0.156878	+	0.316842i
$521$	1.95007			0.0854341			0.0427171	−	0.999087i	$-0.486399\pi$
$521$	1.95007			0.0854341			0.0427171	+	0.999087i	$0.486399\pi$
$522$	−0.833228	+	1.44319i	−0.0364694	+	0.0631669i
$523$	7.86903	+	4.54319i	0.344089	+	0.198660i	0.662079	−	0.749434i	$-0.269674\pi$
$523$	7.86903	+	4.54319i	0.344089	+	0.198660i	−0.317990	+	0.948094i	$0.603008\pi$
$524$	0.558851	+	0.967959i	0.0244135	+	0.0422855i
$525$	13.2120	+	42.0536i	0.576619	+	1.83537i
$526$	0.527031	−	0.304282i	0.0229797	−	0.0132673i
$527$	−0.163529	−	0.283241i	−0.00712346	−	0.0123382i
$528$	−3.03494			−0.132079
$529$	5.90078	+	10.2204i	0.256556	+	0.444367i
$530$	24.1220	+	9.39480i	1.04779	+	0.408084i
$531$	0.688226	+	0.397348i	0.0298665	+	0.0172434i
$532$		−	20.3783i		−	0.883511i
$533$	−5.24727	+	23.9074i	−0.227285	+	1.03554i
$534$	−15.3620			−0.664779
$535$	−38.5606	−	15.0182i	−1.66712	−	0.649293i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	32.5226	−	18.7769i	1.40345	−	0.810285i
$538$	17.7448			0.765035
$539$	−22.9061	+	13.2248i	−0.986635	+	0.569634i
$540$	8.40928	−	6.74207i	0.361878	−	0.290133i
$541$		−	35.7827i		−	1.53842i	−0.638997	−	0.769209i	$-0.720650\pi$
$541$		−	35.7827i		−	1.53842i	0.638997	−	0.769209i	$-0.279350\pi$
$542$	13.8806	−	8.01395i	0.596222	−	0.344229i
$543$	−31.7531	−	18.3326i	−1.36266	−	0.786729i
$544$	0.0697360	+	0.0402621i	0.00298990	+	0.00172622i
$545$	−3.08050	−	20.0829i	−0.131954	−	0.860256i
$546$	−6.81443	+	31.0476i	−0.291631	+	1.32872i
$547$			29.0584i			1.24245i	0.783634	+	0.621223i	$0.213364\pi$
$547$			29.0584i			1.24245i	−0.783634	+	0.621223i	$0.786636\pi$
$548$	−4.10468	+	7.10951i	−0.175343	+	0.303703i
$549$	−0.589671	+	1.02134i	−0.0251666	+	0.0435898i
$550$	−5.58502	+	6.08244i	−0.238146	+	0.259356i
$551$		−	18.7769i		−	0.799925i
$552$	−5.42044	−	9.38847i	−0.230709	−	0.399600i
$553$	−35.1335	−	60.8529i	−1.49403	−	2.58773i
$554$			11.9042i			0.505760i
$555$	−5.82550	+	4.67055i	−0.247279	+	0.198254i
$556$	2.55885	−	4.43206i	0.108519	−	0.187961i
$557$	−16.5492	+	28.6641i	−0.701213	+	1.21454i	0.266828	+	0.963744i	$0.414024\pi$
$557$	−16.5492	+	28.6641i	−0.701213	+	1.21454i	−0.968041	+	0.250792i	$0.919309\pi$
$558$		−	1.53119i		−	0.0648204i
$559$	−22.6271	−	20.6463i	−0.957026	−	0.873247i
$560$	10.6034	−	1.62644i	0.448073	−	0.0687298i
$561$	−0.211645	−	0.122193i	−0.00893564	−	0.00515899i
$562$	9.87055	+	5.69877i	0.416364	+	0.240388i
$563$	−9.06138	+	5.23159i	−0.381892	+	0.220485i	−0.678641	−	0.734470i	$-0.737431\pi$
$563$	−9.06138	+	5.23159i	−0.381892	+	0.220485i	0.296749	+	0.954955i	$0.404097\pi$
$564$		−	0.824367i		−	0.0347121i
$565$	−27.8101	+	22.2965i	−1.16998	+	0.938020i
$566$	17.6776	−	10.2062i	0.743045	−	0.428997i
$567$	47.9207			2.01248
$568$	−6.36584	+	3.67532i	−0.267105	+	0.154213i
$569$	−4.31622	+	7.47591i	−0.180945	+	0.313407i	−0.942203	−	0.335043i	$-0.891249\pi$
$569$	−4.31622	+	7.47591i	−0.180945	+	0.313407i	0.761257	+	0.648450i	$0.224582\pi$
$570$	6.33455	−	16.2646i	0.265325	−	0.681248i
$571$	14.3069			0.598724			0.299362	−	0.954140i	$-0.403226\pi$
$571$	14.3069			0.598724			0.299362	+	0.954140i	$0.403226\pi$
$572$	−5.67528	+	1.80257i	−0.237295	+	0.0753694i
$573$			14.1127i			0.589567i
$574$	28.2043	+	16.2838i	1.17723	+	0.679672i
$575$	−28.7907	−	6.41374i	−1.20065	−	0.267472i
$576$	0.188495	+	0.326482i	0.00785394	+	0.0136034i
$577$	11.9697			0.498306			0.249153	−	0.968464i	$-0.419848\pi$
$577$	11.9697			0.498306			0.249153	+	0.968464i	$0.419848\pi$
$578$	−8.49676	−	14.7168i	−0.353419	−	0.612139i
$579$	−24.1765	+	13.9583i	−1.00474	+	0.580088i
$580$	9.77013	−	1.49863i	0.405682	−	0.0622274i
$581$	−29.8135	−	51.6384i	−1.23687	−	2.14232i
$582$	9.23990	+	5.33466i	0.383006	+	0.221129i
$583$	−9.55986	+	16.5582i	−0.395929	+	0.685769i
$584$	−10.5752			−0.437605
$585$	−1.68456	+	2.52985i	−0.0696479	+	0.104596i
$586$	4.18768			0.172991
$587$	−2.75398	+	4.77003i	−0.113669	+	0.196880i	−0.917247	−	0.398319i	$-0.869594\pi$
$587$	−2.75398	+	4.77003i	−0.113669	+	0.196880i	0.803578	+	0.595199i	$0.202927\pi$
$588$	25.4877	+	14.7153i	1.05109	+	0.606849i
$589$	8.62640	+	14.9414i	0.355445	+	0.615648i
$590$	−0.714665	−	4.65915i	−0.0294223	−	0.191814i
$591$	4.79549	−	2.76868i	0.197260	−	0.113888i
$592$	0.908541	+	1.57364i	0.0373408	+	0.0646762i
$593$	−24.6037			−1.01035			−0.505177	−	0.863016i	$-0.668573\pi$
$593$	−24.6037			−1.01035			−0.505177	+	0.863016i	$0.668573\pi$
$594$	3.98034	+	6.89416i	0.163315	+	0.282871i
$595$	0.804919	+	0.313491i	0.0329985	+	0.0128519i
$596$	−3.58721	−	2.07107i	−0.146938	−	0.0848345i
$597$			17.8640i			0.731124i
$598$	−15.7123	−	14.3368i	−0.642523	−	0.586276i
$599$	35.3159			1.44297			0.721484	−	0.692431i	$-0.243460\pi$
$599$	35.3159			1.44297			0.721484	+	0.692431i	$0.243460\pi$
$600$	8.96845	+	1.99792i	0.366135	+	0.0815646i
$601$	−17.4607	+	30.2428i	−0.712236	+	1.23363i	0.251780	+	0.967785i	$0.418984\pi$
$601$	−17.4607	+	30.2428i	−0.712236	+	1.23363i	−0.964016	+	0.265845i	$0.914349\pi$
$602$	−35.2962	+	20.3783i	−1.43857	+	0.830557i
$603$	−1.50796			−0.0614088
$604$	3.83986	−	2.21694i	0.156242	−	0.0902062i
$605$	11.5708	+	14.4321i	0.470420	+	0.586747i
$606$		−	2.27413i		−	0.0923804i
$607$	21.6183	−	12.4813i	0.877461	−	0.506602i	0.00764039	−	0.999971i	$-0.497568\pi$
$607$	21.6183	−	12.4813i	0.877461	−	0.506602i	0.869820	+	0.493369i	$0.164235\pi$
$608$	−3.67867	−	2.12388i	−0.149190	−	0.0861347i
$609$	33.7496	+	19.4853i	1.36760	+	0.789586i
$610$	6.91427	−	1.06058i	0.279950	−	0.0429415i
$611$	−0.489625	−	1.54155i	−0.0198081	−	0.0623644i
$612$			0.0303567i			0.00122710i
$613$	8.06330	−	13.9660i	0.325674	−	0.564083i	−0.655975	−	0.754783i	$-0.727742\pi$
$613$	8.06330	−	13.9660i	0.325674	−	0.564083i	0.981648	+	0.190700i	$0.0610756\pi$
$614$	9.00850	−	15.6032i	0.363554	−	0.629693i
$615$	17.4490	+	21.7639i	0.703611	+	0.877603i
$616$			7.92308i			0.319230i
$617$	14.2537	+	24.6881i	0.573831	+	0.993904i	0.996168	+	0.0874652i	$0.0278767\pi$
$617$	14.2537	+	24.6881i	0.573831	+	0.993904i	−0.422337	+	0.906439i	$0.638790\pi$
$618$	8.62640	+	14.9414i	0.347005	+	0.601030i
$619$			0.338217i			0.0135941i	0.999977	+	0.00679705i	$0.00216358\pi$
$619$			0.338217i			0.0135941i	−0.999977	+	0.00679705i	$0.997836\pi$
$620$	−7.08588	+	5.68105i	−0.284576	+	0.228156i
$621$	−14.2179	+	24.6261i	−0.570543	+	0.988210i
$622$	2.58908	−	4.48442i	0.103813	−	0.179809i
$623$			40.1043i			1.60675i
$624$	4.89446	+	4.46600i	0.195935	+	0.178783i
$625$	20.5082	−	14.2973i	0.820328	−	0.571894i
$626$	−28.2613	−	16.3167i	−1.12955	−	0.652145i
$627$	11.1645	+	6.44585i	0.445869	+	0.257422i
$628$	−7.20889	+	4.16206i	−0.287666	+	0.166084i
$629$			0.146319i			0.00583412i
$630$	2.52968	+	3.15523i	0.100785	+	0.125707i
$631$	27.8799	−	16.0965i	1.10988	−	0.640791i	0.171084	−	0.985256i	$-0.445273\pi$
$631$	27.8799	−	16.0965i	1.10988	−	0.640791i	0.938799	+	0.344465i	$0.111940\pi$
$632$	−14.6468			−0.582618
$633$	7.62411	−	4.40178i	0.303031	−	0.174955i
$634$	−11.8692	+	20.5581i	−0.471387	+	0.816467i
$635$	−1.86057	−	0.724637i	−0.0738346	−	0.0287563i
$636$	21.2746			0.843592
$637$	56.4014	+	12.3792i	2.23470	+	0.490480i
$638$			7.30047i			0.289028i
$639$	−2.39985	−	1.38556i	−0.0949367	−	0.0548117i
$640$	0.811505	−	2.08362i	0.0320776	−	0.0823622i
$641$	6.29981	+	10.9116i	0.248827	+	0.430982i	0.963201	−	0.268783i	$-0.0866215\pi$
$641$	6.29981	+	10.9116i	0.248827	+	0.430982i	−0.714373	+	0.699765i	$0.753288\pi$
$642$	−34.0088			−1.34222
$643$	9.70277	+	16.8057i	0.382640	+	0.662752i	0.991439	−	0.130573i	$-0.0416817\pi$
$643$	9.70277	+	16.8057i	0.382640	+	0.662752i	−0.608799	+	0.793325i	$0.708348\pi$
$644$	−24.5097	+	14.1507i	−0.965818	+	0.557615i
$645$	−34.5056	+	5.29280i	−1.35866	+	0.208404i
$646$	−0.171024	−	0.296221i	−0.00672883	−	0.0116547i
$647$	16.1897	+	9.34715i	0.636485	+	0.367475i	0.783259	−	0.621695i	$-0.213556\pi$
$647$	16.1897	+	9.34715i	0.636485	+	0.367475i	−0.146774	+	0.989170i	$0.546889\pi$
$648$	4.99442	−	8.65060i	0.196199	−	0.339827i
$649$	3.48143			0.136658
$650$	17.9574	−	1.59066i	0.704349	−	0.0623909i
$651$	−35.8074			−1.40340
$652$	−0.471644	+	0.816912i	−0.0184710	+	0.0319927i
$653$	15.4758	+	8.93497i	0.605616	+	0.349652i	0.771248	−	0.636535i	$-0.219633\pi$
$653$	15.4758	+	8.93497i	0.605616	+	0.349652i	−0.165632	+	0.986188i	$0.552966\pi$
$654$	−8.34883	−	14.4606i	−0.326465	−	0.565454i
$655$	2.47037	−	0.378928i	0.0965252	−	0.0148059i
$656$	5.87906	−	3.39427i	0.229539	−	0.132524i
$657$	−1.99337	−	3.45261i	−0.0777687	−	0.134699i
$658$	−2.15211			−0.0838979
$659$	−19.5447	−	33.8523i	−0.761352	−	1.31870i	−0.942154	−	0.335180i	$-0.891203\pi$
$659$	−19.5447	−	33.8523i	−0.761352	−	1.31870i	0.180803	−	0.983519i	$-0.442130\pi$
$660$	−2.46287	+	6.32366i	−0.0958672	+	0.246148i
$661$	−34.9611	−	20.1848i	−1.35983	−	0.785098i	−0.370229	−	0.928941i	$-0.620721\pi$
$661$	−34.9611	−	20.1848i	−1.35983	−	0.785098i	−0.989601	+	0.143843i	$0.954054\pi$
$662$			30.4752i			1.18445i
$663$	0.161510	+	0.508502i	0.00627251	+	0.0197486i
$664$	−12.4289			−0.482336
$665$	−42.4606	−	16.5371i	−1.64655	−	0.641281i
$666$	−0.342510	+	0.593245i	−0.0132720	+	0.0229878i
$667$	−22.5837	+	13.0387i	−0.874444	+	0.504861i
$668$	−4.30062			−0.166396
$669$	22.3496	−	12.9035i	0.864084	−	0.498879i
$670$	5.59485	+	6.97837i	0.216148	+	0.269598i
$671$			5.16650i			0.199451i
$672$	7.63491	−	4.40801i	0.294523	−	0.170043i
$673$	18.3453	+	10.5917i	0.707160	+	0.408279i	0.810009	−	0.586418i	$-0.199462\pi$
$673$	18.3453	+	10.5917i	0.707160	+	0.408279i	−0.102849	+	0.994697i	$0.532796\pi$
$674$	−16.6969	−	9.63995i	−0.643140	−	0.371317i
$675$	−7.22372	−	22.9929i	−0.278041	−	0.884999i
$676$	11.8051	+	5.44430i	0.454041	+	0.209396i
$677$		−	2.48027i		−	0.0953245i	−0.998864	−	0.0476622i	$-0.984823\pi$
$677$		−	2.48027i		−	0.0953245i	0.998864	−	0.0476622i	$-0.0151771\pi$
$678$	−14.6468	+	25.3690i	−0.562507	+	0.974291i
$679$	13.9268	−	24.1218i	0.534460	−	0.925711i
$680$	0.140482	−	0.112630i	0.00538723	−	0.00431917i
$681$			5.29280i			0.202820i
$682$	−3.35394	−	5.80920i	−0.128429	−	0.222446i
$683$	6.42894	+	11.1352i	0.245997	+	0.426078i	0.962411	−	0.271596i	$-0.0875515\pi$
$683$	6.42894	+	11.1352i	0.245997	+	0.426078i	−0.716415	+	0.697675i	$0.754218\pi$
$684$		−	1.60136i		−	0.0612295i
$685$	11.4825	+	14.3220i	0.438725	+	0.547215i
$686$	21.6251	−	37.4557i	0.825649	−	1.43007i
$687$	6.16353	−	10.6755i	0.235153	−	0.407297i
$688$			8.49552i			0.323888i
$689$	39.7830	−	12.6358i	1.51561	−	0.481386i
$690$	−23.9607	+	3.67532i	−0.912168	+	0.139917i
$691$	0.975544	+	0.563231i	0.0371115	+	0.0214263i	0.518441	−	0.855113i	$-0.326513\pi$
$691$	0.975544	+	0.563231i	0.0371115	+	0.0214263i	−0.481329	+	0.876540i	$0.659846\pi$
$692$	0.861584	+	0.497436i	0.0327525	+	0.0189097i
$693$	−2.58674	+	1.49346i	−0.0982623	+	0.0567318i
$694$		−	15.3720i		−	0.583512i
$695$	−7.15819	−	8.92831i	−0.271526	−	0.338670i
$696$	7.03494	−	4.06163i	0.266659	−	0.153956i
$697$	0.546642			0.0207055
$698$	13.1667	−	7.60177i	0.498365	−	0.287731i
$699$	−16.1677	+	28.0032i	−0.611517	+	1.05918i
$700$	5.21579	−	23.4132i	0.197138	−	0.884936i
$701$	9.39602			0.354883			0.177441	−	0.984131i	$-0.443218\pi$
$701$	9.39602			0.354883			0.177441	+	0.984131i	$0.443218\pi$
$702$	3.72582	−	16.9754i	0.140622	−	0.640695i
$703$		−	7.71852i		−	0.291110i
$704$	1.43026	+	0.825763i	0.0539051	+	0.0311221i
$705$	−1.71767	−	0.668978i	−0.0646910	−	0.0251952i
$706$	−13.4509	−	23.2976i	−0.506230	−	0.876816i
$707$	−5.93690			−0.223280
$708$	−1.93690	−	3.35480i	−0.0727930	−	0.126081i
$709$	15.4770	−	8.93567i	0.581252	−	0.335586i	−0.180379	−	0.983597i	$-0.557732\pi$
$709$	15.4770	−	8.93567i	0.581252	−	0.335586i	0.761631	+	0.648011i	$0.224399\pi$
$710$	2.49204	+	16.2465i	0.0935247	+	0.609720i
$711$	−2.76084	−	4.78192i	−0.103540	−	0.179336i
$712$	7.23958	+	4.17978i	0.271315	+	0.156644i
$713$	11.9803	−	20.7506i	0.448667	−	0.777115i
$714$	0.709903			0.0265675
$715$	−0.849643	+	13.2879i	−0.0317749	+	0.496939i
$716$	−20.4357			−0.763719
$717$	−10.3937	+	18.0025i	−0.388161	+	0.672314i
$718$	18.0434	+	10.4174i	0.673375	+	0.388773i
$719$	1.15648	+	2.00308i	0.0431294	+	0.0747023i	0.886784	−	0.462184i	$-0.152934\pi$
$719$	1.15648	+	2.00308i	0.0431294	+	0.0747023i	−0.843655	+	0.536886i	$0.819601\pi$
$720$	0.833228	−	0.127808i	0.0310526	−	0.00476314i
$721$	39.0062	−	22.5202i	1.45267	−	0.838698i
$722$	−0.478277	−	0.828400i	−0.0177996	−	0.0308299i
$723$	−9.33566			−0.347197
$724$	9.97609	+	17.2791i	0.370759	+	0.642173i
$725$	4.80593	−	21.5733i	0.178488	−	0.801214i
$726$	13.1653	+	7.60098i	0.488609	+	0.282099i
$727$		−	17.9866i		−	0.667087i	−0.942735	−	0.333543i	$-0.891756\pi$
$727$		−	17.9866i		−	0.667087i	0.942735	−	0.333543i	$-0.108244\pi$
$728$	11.6590	−	12.7776i	0.432112	−	0.473568i
$729$	−22.8079			−0.844739
$730$	−8.58183	+	22.0346i	−0.317628	+	0.815539i
$731$	−0.342047	+	0.592443i	−0.0126511	+	0.0219123i
$732$	4.97859	−	2.87439i	0.184014	−	0.106241i
$733$	−45.2898			−1.67282			−0.836408	−	0.548108i	$-0.815348\pi$
$733$	−45.2898			−1.67282			−0.836408	+	0.548108i	$0.815348\pi$
$734$	−29.9410	+	17.2865i	−1.10514	+	0.638055i
$735$	51.3445	−	41.1650i	1.89387	−	1.51839i
$736$			5.89928i			0.217451i
$737$	−5.72106	+	3.30305i	−0.210738	+	0.121670i
$738$	2.21634	+	1.27961i	0.0815846	+	0.0471029i
$739$	38.9749	+	22.5022i	1.43372	+	0.827756i	0.997402	−	0.0720387i	$-0.0229505\pi$
$739$	38.9749	+	22.5022i	1.43372	+	0.827756i	0.436314	+	0.899795i	$0.356284\pi$
$740$	4.01615	−	0.616035i	0.147636	−	0.0226459i
$741$	−8.51985	−	26.8241i	−0.312985	−	0.985410i
$742$		−	55.5398i		−	2.03893i
$743$	3.28334	−	5.68692i	0.120454	−	0.208633i	−0.799493	−	0.600676i	$-0.794898\pi$
$743$	3.28334	−	5.68692i	0.120454	−	0.208633i	0.919947	+	0.392043i	$0.128232\pi$
$744$	−3.73194	+	6.46391i	−0.136820	+	0.236978i
$745$	−7.22636	+	5.79368i	−0.264754	+	0.212264i
$746$			25.0064i			0.915549i
$747$	−2.34279	−	4.05783i	−0.0857182	−	0.148468i
$748$	0.0664939	+	0.115171i	0.00243126	+	0.00421106i
$749$			88.7840i			3.24410i
$750$	11.4408	−	17.0655i	0.417760	−	0.623144i
$751$	−13.6750	+	23.6857i	−0.499006	+	0.864304i	−0.999999	−	0.00114692i	$-0.999635\pi$
$751$	−13.6750	+	23.6857i	−0.499006	+	0.864304i	0.500993	+	0.865451i	$0.332968\pi$
$752$	−0.224298	+	0.388496i	−0.00817932	+	0.0141670i
$753$			35.9638i			1.31059i
$754$	10.7428	−	11.7735i	0.391231	−	0.428765i
$755$	−1.50320	−	9.79986i	−0.0547069	−	0.356653i
$756$	−20.0264	−	11.5623i	−0.728355	−	0.420516i
$757$	−33.8205	−	19.5263i	−1.22923	−	0.709696i	−0.262360	−	0.964970i	$-0.584501\pi$
$757$	−33.8205	−	19.5263i	−1.22923	−	0.709696i	−0.966869	+	0.255275i	$0.917834\pi$
$758$	3.25585	−	1.87977i	0.118258	−	0.0682762i
$759$		−	17.9040i		−	0.649874i
$760$	−7.41061	+	5.94139i	−0.268811	+	0.215517i
$761$	−24.6247	+	14.2171i	−0.892645	+	0.515369i	−0.874807	−	0.484472i	$-0.839012\pi$
$761$	−24.6247	+	14.2171i	−0.892645	+	0.515369i	−0.0178384	+	0.999841i	$0.505678\pi$
$762$	−1.64094			−0.0594452
$763$	−37.7511	+	21.7956i	−1.36668	+	0.789054i
$764$	3.83986	−	6.65083i	0.138921	−	0.240619i
$765$	0.0632518	+	0.0246347i	0.00228687	+	0.000890668i
$766$	−3.93892			−0.142319
$767$	−5.61451	−	5.12301i	−0.202728	−	0.184981i
$768$		−	1.83766i		−	0.0663108i
$769$	−25.3247	−	14.6212i	−0.913231	−	0.527254i	−0.0317619	−	0.999495i	$-0.510112\pi$
$769$	−25.3247	−	14.6212i	−0.913231	−	0.527254i	−0.881469	+	0.472241i	$0.843445\pi$
$770$	16.5087	+	6.42962i	0.594931	+	0.231707i
$771$	1.82294	+	3.15742i	0.0656515	+	0.113712i
$772$	15.1914			0.546751
$773$	−10.4106	−	18.0317i	−0.374444	−	0.648555i	0.615800	−	0.787902i	$-0.288833\pi$
$773$	−10.4106	−	18.0317i	−0.374444	−	0.648555i	−0.990244	+	0.139347i	$0.955500\pi$
$774$	−2.77364	+	1.60136i	−0.0996963	+	0.0575597i
$775$	6.08689	+	19.3745i	0.218648	+	0.695951i
$776$	−2.90296	−	5.02808i	−0.104210	−	0.180498i
$777$	13.8732	+	8.00972i	0.497700	+	0.287347i
$778$	9.57944	−	16.5921i	0.343440	−	0.594855i
$779$	−28.8361			−1.03316
$780$	13.2773	−	6.57400i	0.475404	−	0.235387i
$781$	−12.1398			−0.434395
$782$	−0.237517	+	0.411392i	−0.00849361	+	0.0147114i
$783$	−18.4527	−	10.6537i	−0.659447	−	0.380732i
$784$	−8.00764	−	13.8696i	−0.285987	−	0.495344i
$785$	2.82208	+	18.3981i	0.100724	+	0.656656i
$786$	1.77878	−	1.02698i	0.0634469	−	0.0366311i
$787$	10.4784	+	18.1492i	0.373516	+	0.646948i	0.990104	−	0.140338i	$-0.0448189\pi$
$787$	10.4784	+	18.1492i	0.373516	+	0.646948i	−0.616588	+	0.787286i	$0.711486\pi$
$788$	−3.01327			−0.107343
$789$	−0.559166	−	0.968504i	−0.0199068	−	0.0344796i
$790$	−11.8860	+	30.5183i	−0.422883	+	1.08579i
$791$	66.2288	+	38.2372i	2.35482	+	1.35956i
$792$			0.622608i			0.0221234i
$793$	7.60264	−	8.33203i	0.269978	−	0.295879i
$794$	6.45538			0.229093
$795$	17.2644	−	44.3281i	0.612306	−	1.57215i
$796$	4.86053	−	8.41868i	0.172277	−	0.298392i
$797$	16.0855	−	9.28699i	0.569779	−	0.328962i	−0.187282	−	0.982306i	$-0.559968\pi$
$797$	16.0855	−	9.28699i	0.569779	−	0.328962i	0.757061	+	0.653344i	$0.226635\pi$
$798$	−37.4484			−1.32566
$799$	−0.0312833	+	0.0180614i	−0.00110672	+	0.000638967i
$800$	−3.68292	−	3.38173i	−0.130211	−	0.119562i
$801$			3.15146i			0.111351i
$802$	−30.0012	+	17.3212i	−1.05938	+	0.611633i
$803$	−15.1253	−	8.73261i	−0.533761	−	0.308167i
$804$	6.36584	+	3.67532i	0.224506	+	0.129618i
$805$	9.59485	+	62.5522i	0.338174	+	2.20468i
$806$	−3.13947	+	14.3039i	−0.110583	+	0.503834i
$807$		−	32.6090i		−	1.14789i
$808$	−0.618759	+	1.07172i	−0.0217679	+	0.0377030i
$809$	14.0705	−	24.3708i	0.494692	−	0.856831i	−0.505290	−	0.862950i	$-0.668614\pi$
$809$	14.0705	−	24.3708i	0.494692	−	0.856831i	0.999981	+	0.00611875i	$0.00194767\pi$
$810$	−13.9715	−	17.4265i	−0.490909	−	0.612304i
$811$			17.1410i			0.601903i	0.953639	+	0.300952i	$0.0973043\pi$
$811$			17.1410i			0.601903i	−0.953639	+	0.300952i	$0.902696\pi$
$812$	−10.6034	−	18.3655i	−0.372105	−	0.644504i
$813$	−14.7269	−	25.5078i	−0.516495	−	0.894596i
$814$			3.00096i			0.105184i
$815$	1.31939	+	1.64565i	0.0462162	+	0.0576447i
$816$	0.0739879	−	0.128151i	0.00259010	−	0.00448618i
$817$	18.0434	−	31.2522i	0.631260	−	1.09337i
$818$		−	18.6071i		−	0.650583i
$819$	6.36931	+	1.39796i	0.222562	+	0.0488486i
$820$	−2.30148	−	15.0042i	−0.0803712	−	0.523968i
$821$	11.5893	+	6.69111i	0.404471	+	0.233521i	0.688411	−	0.725321i	$-0.258308\pi$
$821$	11.5893	+	6.69111i	0.404471	+	0.233521i	−0.283940	+	0.958842i	$0.591642\pi$
$822$	13.0649	+	7.54300i	0.455689	+	0.263092i
$823$	18.7144	−	10.8047i	0.652341	−	0.376629i	−0.137011	−	0.990569i	$-0.543750\pi$
$823$	18.7144	−	10.8047i	0.652341	−	0.376629i	0.789353	+	0.613940i	$0.210416\pi$
$824$		−	9.38847i		−	0.327063i
$825$	11.1774	+	10.2634i	0.389149	+	0.357324i
$826$	−8.75811	+	5.05650i	−0.304734	+	0.175938i
$827$	−5.85827			−0.203712			−0.101856	−	0.994799i	$-0.532478\pi$
$827$	−5.85827			−0.203712			−0.101856	+	0.994799i	$0.532478\pi$
$828$	−1.92601	+	1.11198i	−0.0669335	+	0.0386441i
$829$	10.6392	−	18.4276i	0.369513	−	0.640016i	−0.619976	−	0.784621i	$-0.712858\pi$
$829$	10.6392	−	18.4276i	0.369513	−	0.640016i	0.989489	+	0.144605i	$0.0461911\pi$
$830$	−10.0862	+	25.8971i	−0.350095	+	0.898903i
$831$	21.8758			0.758864
$832$	−1.09146	−	3.43638i	−0.0378395	−	0.119135i
$833$		−	1.28962i		−	0.0446826i
$834$	−8.14461	−	4.70230i	−0.282025	−	0.162827i
$835$	−3.48998	+	8.96085i	−0.120776	+	0.310103i
$836$	−3.50764	−	6.07542i	−0.121314	−	0.210123i
$837$	19.5778			0.676709
$838$	11.4748	+	19.8749i	0.396389	+	0.686566i
$839$	−16.9067	+	9.76109i	−0.583684	+	0.336990i	−0.762596	−	0.646875i	$-0.776076\pi$
$839$	−16.9067	+	9.76109i	−0.583684	+	0.336990i	0.178912	+	0.983865i	$0.442742\pi$
$840$	−2.98885	−	19.4853i	−0.103125	−	0.672308i
$841$	4.72987	+	8.19238i	0.163099	+	0.282496i
$842$	−30.1546	−	17.4098i	−1.03920	−	0.599981i
$843$	10.4724	−	18.1387i	0.360688	−	0.624730i
$844$	−4.79064			−0.164901
$845$	20.9237	−	20.1792i	0.719797	−	0.694184i
$846$	−0.169116			−0.00581433
$847$	19.8433	−	34.3695i	0.681822	−	1.18095i
$848$	−10.0260	−	5.78850i	−0.344293	−	0.198778i
$849$	−18.7555	−	32.4854i	−0.643686	−	1.11490i
$850$	−0.120676	−	0.384110i	−0.00413916	−	0.0131749i
$851$	−9.28334	+	5.35974i	−0.318229	+	0.183730i
$852$	6.75398	+	11.6982i	0.231387	+	0.400775i
$853$	33.3923			1.14333			0.571665	−	0.820487i	$-0.306298\pi$
$853$	33.3923			1.14333			0.571665	+	0.820487i	$0.306298\pi$
$854$	−7.50394	−	12.9972i	−0.256779	−	0.444755i
$855$	−3.33662	−	1.29951i	−0.114110	−	0.0444424i
$856$	16.0272	+	9.25330i	0.547798	+	0.316271i
$857$			22.7514i			0.777172i	0.921412	+	0.388586i	$0.127036\pi$
$857$			22.7514i			0.777172i	−0.921412	+	0.388586i	$0.872964\pi$
$858$	3.31252	+	10.4292i	0.113087	+	0.356048i
$859$	−7.99391			−0.272749			−0.136374	−	0.990657i	$-0.543545\pi$
$859$	−7.99391			−0.272749			−0.136374	+	0.990657i	$0.543545\pi$
$860$	17.7014	+	6.89416i	0.603613	+	0.235089i
$861$	29.9240	−	51.8299i	1.01981	−	1.76636i
$862$	−17.7523	+	10.2493i	−0.604647	+	0.349093i
$863$	−11.7205			−0.398971			−0.199486	−	0.979901i	$-0.563927\pi$
$863$	−11.7205			−0.398971			−0.199486	+	0.979901i	$0.563927\pi$
$864$	−4.17441	+	2.41010i	−0.142016	+	0.0819932i
$865$	1.73565	−	1.39154i	0.0590137	−	0.0473138i
$866$		−	2.14503i		−	0.0728909i
$867$	−27.0445	+	15.6141i	−0.918479	+	0.530284i
$868$	16.8748	+	9.74267i	0.572768	+	0.330688i
$869$	−20.9488	−	12.0948i	−0.710639	−	0.410288i
$870$	−2.75398	−	17.9542i	−0.0933686	−	0.608703i
$871$	14.0869	+	3.09184i	0.477316	+	0.104763i
$872$			9.08638i			0.307704i
$873$	1.09439	−	1.89553i	0.0370394	−	0.0641541i
$874$	12.5294	−	21.7015i	0.423812	−	0.734064i
$875$	−44.5515	−	29.8676i	−1.50611	−	1.00971i
$876$			19.4336i			0.656600i
$877$	−0.864038	−	1.49656i	−0.0291765	−	0.0505352i	0.851068	−	0.525055i	$-0.175955\pi$
$877$	−0.864038	−	1.49656i	−0.0291765	−	0.0505352i	−0.880245	+	0.474520i	$0.842622\pi$
$878$	−0.525975	−	0.911016i	−0.0177508	−	0.0307453i
$879$		−	7.69553i		−	0.259564i
$880$	2.88124	−	2.31001i	0.0971266	−	0.0778705i
$881$	−16.7831	+	29.0691i	−0.565436	+	0.979364i	0.431573	+	0.902078i	$0.357959\pi$
$881$	−16.7831	+	29.0691i	−0.565436	+	0.979364i	−0.997009	+	0.0772861i	$0.975375\pi$
$882$	3.01880	−	5.22871i	0.101648	−	0.176060i
$883$		−	18.2526i		−	0.614249i	−0.951669	−	0.307124i	$-0.900633\pi$
$883$		−	18.2526i		−	0.614249i	0.951669	−	0.307124i	$-0.0993667\pi$
$884$	0.0622419	−	0.283584i	0.00209342	−	0.00953795i
$885$	−8.56193	+	1.31331i	−0.287806	+	0.0441464i
$886$	−15.8520	−	9.15217i	−0.532559	−	0.307473i
$887$	−20.3335	−	11.7395i	−0.682732	−	0.394176i	0.118152	−	0.992996i	$-0.462303\pi$
$887$	−20.3335	−	11.7395i	−0.682732	−	0.394176i	−0.800884	+	0.598820i	$0.795636\pi$
$888$	2.89181	−	1.66959i	0.0970428	−	0.0560277i
$889$			4.28388i			0.143677i
$890$	14.5840	−	11.6926i	0.488857	−	0.391937i
$891$	14.2867	−	8.24842i	0.478622	−	0.276333i
$892$	−14.0434			−0.470209
$893$	1.65024	−	0.952765i	0.0552231	−	0.0318831i
$894$	−3.80593	+	6.59206i	−0.127289	+	0.220472i
$895$	−16.5837	+	42.5802i	−0.554332	+	1.42330i
$896$	−4.79742			−0.160271
$897$	−26.3462	+	28.8738i	−0.879673	+	0.964069i
$898$		−	13.9524i		−	0.465596i
$899$	15.5488	+	8.97708i	0.518580	+	0.299402i
$900$	0.409865	−	1.83985i	0.0136622	−	0.0613282i
$901$	−0.466114	−	0.807333i	−0.0155285	−	0.0268962i
$902$	11.2115			0.373301
$903$	37.4484	+	64.8625i	1.24620	+	2.15849i
$904$	13.8051	−	7.97036i	0.459150	−	0.265090i
$905$	44.0987	−	6.76427i	1.46589	−	0.224852i
$906$	−4.07399	−	7.05635i	−0.135349	−	0.234432i
$907$	−23.1056	−	13.3400i	−0.767208	−	0.442948i	0.0646698	−	0.997907i	$-0.479401\pi$
$907$	−23.1056	−	13.3400i	−0.767208	−	0.442948i	−0.831878	+	0.554959i	$0.812734\pi$
$908$	1.44009	−	2.49431i	0.0477911	−	0.0827767i
$909$	−0.466531			−0.0154739
$910$	−17.1622	−	34.6620i	−0.568922	−	1.14903i
$911$	−33.1591			−1.09861			−0.549305	−	0.835622i	$-0.685108\pi$
$911$	−33.1591			−1.09861			−0.549305	+	0.835622i	$0.685108\pi$
$912$	−3.90296	+	6.76013i	−0.129240	+	0.223850i
$913$	−17.7767	−	10.2634i	−0.588322	−	0.339668i
$914$	14.7165	+	25.4898i	0.486780	+	0.843127i
$915$	−1.94898	−	12.7061i	−0.0644312	−	0.420049i
$916$	−5.80932	+	3.35401i	−0.191945	+	0.110820i
$917$	−2.68105	−	4.64371i	−0.0885360	−	0.153349i
$918$	−0.388142			−0.0128106
$919$	−19.2895	−	33.4103i	−0.636301	−	1.10211i	−0.986238	−	0.165332i	$-0.947130\pi$
$919$	−19.2895	−	33.4103i	−0.636301	−	1.10211i	0.349937	−	0.936773i	$-0.386203\pi$
$920$	12.2918	+	4.78730i	0.405250	+	0.157833i
$921$	−28.6733	−	16.5546i	−0.944818	−	0.545491i
$922$			9.09372i			0.299486i
$923$	19.5778	+	17.8640i	0.644413	+	0.588000i
$924$	14.5599			0.478986
$925$	1.97554	−	8.86803i	0.0649555	−	0.291579i
$926$	−20.8321	+	36.0823i	−0.684585	+	1.18574i
$927$	3.06517	−	1.76968i	0.100673	−	0.0581238i
$928$	−4.42044			−0.145108
$929$	21.3019	−	12.2986i	0.698892	−	0.403505i	−0.108043	−	0.994146i	$-0.534458\pi$
$929$	21.3019	−	12.2986i	0.698892	−	0.403505i	0.806935	+	0.590641i	$0.201125\pi$
$930$	10.4398	+	13.0214i	0.342335	+	0.426990i
$931$			68.0291i			2.22956i
$932$	15.2385	−	8.79797i	0.499155	−	0.288187i
$933$	−8.24082	−	4.75784i	−0.269792	−	0.155765i
$934$	33.0024	+	19.0540i	1.07987	+	0.623464i
$935$	0.293932	−	0.0450861i	0.00961260	−	0.00147447i
$936$	0.916184	−	1.00408i	0.0299464	−	0.0328194i
$937$			25.6787i			0.838886i	0.907782	+	0.419443i	$0.137775\pi$
$937$			25.6787i			0.838886i	−0.907782	+	0.419443i	$0.862225\pi$
$938$	9.59485	−	16.6188i	0.313283	−	0.542622i
$939$	−29.9845	+	51.9346i	−0.978506	+	1.69482i
$940$	0.627458	+	0.782618i	0.0204654	+	0.0255262i
$941$		−	27.7630i		−	0.905047i	−0.891752	−	0.452524i	$-0.850524\pi$
$941$		−	27.7630i		−	0.905047i	0.891752	−	0.452524i	$-0.149476\pi$
$942$	7.64844	+	13.2475i	0.249200	+	0.431626i
$943$	20.0238	+	34.6822i	0.652064	+	1.12941i
$944$			2.10800i			0.0686097i
$945$	−40.3429	+	32.3446i	−1.31235	+	1.05217i
$946$	−7.01529	+	12.1508i	−0.228087	+	0.395058i
$947$	−5.01454	+	8.68544i	−0.162951	+	0.282239i	−0.935926	−	0.352198i	$-0.885435\pi$
$947$	−5.01454	+	8.68544i	−0.162951	+	0.282239i	0.772975	+	0.634437i	$0.218768\pi$
$948$			26.9158i			0.874185i
$949$	11.5424	+	36.3404i	0.374682	+	1.17966i
$950$	6.36584	+	20.2623i	0.206535	+	0.657397i
$951$	37.7788	+	21.8116i	1.22506	+	0.707289i
$952$	−0.334553	−	0.193154i	−0.0108429	−	0.00626017i
$953$	30.2756	−	17.4796i	0.980722	−	0.566220i	0.0782342	−	0.996935i	$-0.475072\pi$
$953$	30.2756	−	17.4796i	0.980722	−	0.566220i	0.902488	+	0.430715i	$0.141738\pi$
$954$		−	4.36440i		−	0.141303i
$955$	−10.7417	−	13.3980i	−0.347594	−	0.433549i
$956$	9.79641	−	5.65596i	0.316839	−	0.182927i
$957$	13.4158			0.433670
$958$	13.0228	−	7.51871i	0.420747	−	0.242918i
$959$	19.6919	−	34.1073i	0.635884	−	1.10138i
$960$	−3.82898	−	1.49127i	−0.123580	−	0.0481305i
$961$	14.5032			0.467845
$962$	4.41599	−	4.83966i	0.142377	−	0.156037i
$963$			6.97679i			0.224824i
$964$	4.39957	+	2.54010i	0.141701	+	0.0818110i
$965$	12.3279	−	31.6531i	0.396850	−	1.01895i
$966$	26.0041	+	45.0405i	0.836669	+	1.44915i
$967$	−8.61013			−0.276883			−0.138442	−	0.990371i	$-0.544209\pi$
$967$	−8.61013			−0.276883			−0.138442	+	0.990371i	$0.544209\pi$
$968$	−4.13623	−	7.16416i	−0.132943	−	0.230265i
$969$	−0.544354	+	0.314283i	−0.0174872	+	0.0100962i
$970$	−12.8324	+	1.96835i	−0.412022	+	0.0631999i
$971$	14.2447	+	24.6725i	0.457134	+	0.791779i	0.998808	−	0.0488092i	$-0.0155426\pi$
$971$	14.2447	+	24.6725i	0.457134	+	0.791779i	−0.541674	+	0.840589i	$0.682209\pi$
$972$	−3.37360	−	1.94775i	−0.108208	−	0.0624740i
$973$	−12.2759	+	21.2625i	−0.393547	+	0.681644i
$974$	4.56256			0.146194
$975$	−2.92309	−	32.9997i	−0.0936140	−	1.05683i
$976$	−3.12832			−0.100135
$977$	11.5564	−	20.0163i	0.369722	−	0.640377i	−0.619800	−	0.784760i	$-0.712786\pi$
$977$	11.5564	−	20.0163i	0.369722	−	0.640377i	0.989522	+	0.144383i	$0.0461196\pi$
$978$	1.50120	+	0.866721i	0.0480032	+	0.0277147i
$979$	6.90301	+	11.9564i	0.220621	+	0.382127i
$980$	−35.3973	+	5.42957i	−1.13072	+	0.173441i
$981$	−2.96654	+	1.71273i	−0.0947144	+	0.0546834i
$982$	4.20803	+	7.28853i	0.134284	+	0.232586i
$983$	28.0211			0.893736			0.446868	−	0.894600i	$-0.352539\pi$
$983$	28.0211			0.893736			0.446868	+	0.894600i	$0.352539\pi$
$984$	−6.23752	−	10.8037i	−0.198845	−	0.344409i
$985$	−2.44528	+	6.27849i	−0.0779131	+	0.200049i
$986$	−0.308263	−	0.177976i	−0.00981710	−	0.00566791i
$987$			3.95484i			0.125884i
$988$	−3.28334	+	14.9594i	−0.104457	+	0.475923i
$989$	−50.1175			−1.59364
$990$	1.29728	+	0.505250i	0.0412301	+	0.0160579i
$991$	−12.4357	+	21.5393i	−0.395034	+	0.684218i	−0.993105	−	0.117224i	$-0.962600\pi$
$991$	−12.4357	+	21.5393i	−0.395034	+	0.684218i	0.598072	+	0.801443i	$0.295934\pi$
$992$	3.51747	−	2.03081i	0.111680	−	0.0644784i
$993$	56.0030			1.77720
$994$	30.5396	−	17.6321i	0.968658	−	0.559255i
$995$	−13.5970	−	16.9593i	−0.431053	−	0.537645i
$996$			22.8401i			0.723718i
$997$	−23.1135	+	13.3446i	−0.732012	+	0.422627i	−0.819158	−	0.573568i	$-0.805559\pi$
$997$	−23.1135	+	13.3446i	−0.732012	+	0.422627i	0.0871459	+	0.996196i	$0.472225\pi$
$998$	10.8762	+	6.27936i	0.344279	+	0.198770i
$999$	−7.58525	−	4.37935i	−0.239987	−	0.138556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.m.a.69.3	yes	8
3.2	odd	2		1170.2.bj.b.199.4		8
4.3	odd	2		1040.2.df.c.849.2		8
5.2	odd	4		650.2.m.e.251.3		16
5.3	odd	4		650.2.m.e.251.6		16
5.4	even	2		130.2.m.b.69.2	yes	8
13.4	even	6		1690.2.c.e.1689.3		8
13.6	odd	12		1690.2.b.e.339.3		16
13.7	odd	12		1690.2.b.e.339.11		16
13.9	even	3		1690.2.c.f.1689.3		8
13.10	even	6		130.2.m.b.49.2	yes	8
15.14	odd	2		1170.2.bj.a.199.1		8
20.19	odd	2		1040.2.df.a.849.3		8
39.23	odd	6		1170.2.bj.a.829.1		8
52.23	odd	6		1040.2.df.a.49.3		8
65.4	even	6		1690.2.c.f.1689.6		8
65.7	even	12		8450.2.a.cr.1.3		8
65.9	even	6		1690.2.c.e.1689.6		8
65.19	odd	12		1690.2.b.e.339.14		16
65.23	odd	12		650.2.m.e.101.6		16
65.32	even	12		8450.2.a.cs.1.3		8
65.33	even	12		8450.2.a.cs.1.6		8
65.49	even	6	inner	130.2.m.a.49.3	✓	8
65.58	even	12		8450.2.a.cr.1.6		8
65.59	odd	12		1690.2.b.e.339.6		16
65.62	odd	12		650.2.m.e.101.3		16
195.179	odd	6		1170.2.bj.b.829.4		8
260.179	odd	6		1040.2.df.c.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.3	✓	8	65.49	even	6	inner
130.2.m.a.69.3	yes	8	1.1	even	1	trivial
130.2.m.b.49.2	yes	8	13.10	even	6
130.2.m.b.69.2	yes	8	5.4	even	2
650.2.m.e.101.3		16	65.62	odd	12
650.2.m.e.101.6		16	65.23	odd	12
650.2.m.e.251.3		16	5.2	odd	4
650.2.m.e.251.6		16	5.3	odd	4
1040.2.df.a.49.3		8	52.23	odd	6
1040.2.df.a.849.3		8	20.19	odd	2
1040.2.df.c.49.2		8	260.179	odd	6
1040.2.df.c.849.2		8	4.3	odd	2
1170.2.bj.a.199.1		8	15.14	odd	2
1170.2.bj.a.829.1		8	39.23	odd	6
1170.2.bj.b.199.4		8	3.2	odd	2
1170.2.bj.b.829.4		8	195.179	odd	6
1690.2.b.e.339.3		16	13.6	odd	12
1690.2.b.e.339.6		16	65.59	odd	12
1690.2.b.e.339.11		16	13.7	odd	12
1690.2.b.e.339.14		16	65.19	odd	12
1690.2.c.e.1689.3		8	13.4	even	6
1690.2.c.e.1689.6		8	65.9	even	6
1690.2.c.f.1689.3		8	13.9	even	3
1690.2.c.f.1689.6		8	65.4	even	6
8450.2.a.cr.1.3		8	65.7	even	12
8450.2.a.cr.1.6		8	65.58	even	12
8450.2.a.cs.1.3		8	65.32	even	12
8450.2.a.cs.1.6		8	65.33	even	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.59146 + 0.918829i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21022 + 0.339024i) q^{5} +(-1.59146 + 0.918829i) q^{6} +(2.39871 + 4.15469i) q^{7} +1.00000 q^{8} +(0.188495 + 0.326482i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.59146 + 0.918829i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.21022 + 0.339024i) q^{5} +(-1.59146 + 0.918829i) q^{6} +(2.39871 + 4.15469i) q^{7} +1.00000 q^{8} +(0.188495 + 0.326482i) q^{9} +(0.811505 - 2.08362i) q^{10} +(1.43026 + 0.825763i) q^{11} -1.83766i q^{12} +(-1.09146 - 3.43638i) q^{13} -4.79742 q^{14} +(-3.82898 - 1.49127i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0697360 + 0.0402621i) q^{17} -0.376989 q^{18} +(3.67867 - 2.12388i) q^{19} +(1.39871 + 1.74459i) q^{20} +8.81603i q^{21} +(-1.43026 + 0.825763i) q^{22} +(-5.10893 - 2.94964i) q^{23} +(1.59146 + 0.918829i) q^{24} +(4.77013 - 1.49863i) q^{25} +(3.52172 + 0.772959i) q^{26} -4.82020i q^{27} +(2.39871 - 4.15469i) q^{28} +(2.21022 - 3.82821i) q^{29} +(3.20597 - 2.57036i) q^{30} +4.06163i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.51747 + 2.62834i) q^{33} -0.0805241i q^{34} +(-6.71022 - 8.36955i) q^{35} +(0.188495 - 0.326482i) q^{36} +(0.908541 - 1.57364i) q^{37} +4.24776i q^{38} +(1.42044 - 6.47172i) q^{39} +(-2.21022 + 0.339024i) q^{40} +(-5.87906 - 3.39427i) q^{41} +(-7.63491 - 4.40801i) q^{42} +(7.35733 - 4.24776i) q^{43} -1.65153i q^{44} +(-0.527300 - 0.657693i) q^{45} +(5.10893 - 2.94964i) q^{46} +0.448597 q^{47} +(-1.59146 + 0.918829i) q^{48} +(-8.00764 + 13.8696i) q^{49} +(-1.08721 + 4.88037i) q^{50} -0.147976 q^{51} +(-2.43026 + 2.66342i) q^{52} +11.5770i q^{53} +(4.17441 + 2.41010i) q^{54} +(-3.44115 - 1.34022i) q^{55} +(2.39871 + 4.15469i) q^{56} +7.80593 q^{57} +(2.21022 + 3.82821i) q^{58} +(1.82559 - 1.05400i) q^{59} +(0.623011 + 4.06163i) q^{60} +(1.56416 + 2.70920i) q^{61} +(-3.51747 - 2.03081i) q^{62} +(-0.904289 + 1.56627i) q^{63} +1.00000 q^{64} +(3.57738 + 7.22512i) q^{65} -3.03494 q^{66} +(-2.00000 + 3.46410i) q^{67} +(0.0697360 + 0.0402621i) q^{68} +(-5.42044 - 9.38847i) q^{69} +(10.6034 - 1.62644i) q^{70} +(-6.36584 + 3.67532i) q^{71} +(0.188495 + 0.326482i) q^{72} -10.5752 q^{73} +(0.908541 + 1.57364i) q^{74} +(8.96845 + 1.99792i) q^{75} +(-3.67867 - 2.12388i) q^{76} +7.92308i q^{77} +(4.89446 + 4.46600i) q^{78} -14.6468 q^{79} +(0.811505 - 2.08362i) q^{80} +(4.99442 - 8.65060i) q^{81} +(5.87906 - 3.39427i) q^{82} -12.4289 q^{83} +(7.63491 - 4.40801i) q^{84} +(0.140482 - 0.112630i) q^{85} +8.49552i q^{86} +(7.03494 - 4.06163i) q^{87} +(1.43026 + 0.825763i) q^{88} +(7.23958 + 4.17978i) q^{89} +(0.833228 - 0.127808i) q^{90} +(11.6590 - 12.7776i) q^{91} +5.89928i q^{92} +(-3.73194 + 6.46391i) q^{93} +(-0.224298 + 0.388496i) q^{94} +(-7.41061 + 5.94139i) q^{95} -1.83766i q^{96} +(-2.90296 - 5.02808i) q^{97} +(-8.00764 - 13.8696i) q^{98} +0.622608i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9} - 3 q^{11} + 4 q^{13} - 10 q^{14} - 2 q^{15} - 4 q^{16} - 15 q^{17} - 16 q^{18} + 9 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} + 5 q^{28} - 3 q^{29} + 10 q^{30} - 4 q^{32} - 10 q^{33} - 33 q^{35} + 8 q^{36} + 20 q^{37} - 30 q^{39} + 3 q^{40} + 21 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{45} + 6 q^{46} + 6 q^{47} - 15 q^{49} - q^{50} - 20 q^{51} - 5 q^{52} + 18 q^{54} - 23 q^{55} + 5 q^{56} + 24 q^{57} - 3 q^{58} + 30 q^{59} - 8 q^{60} - 5 q^{61} - 6 q^{62} - 25 q^{63} + 8 q^{64} - 6 q^{65} + 20 q^{66} - 16 q^{67} + 15 q^{68} - 2 q^{69} + 18 q^{70} + 8 q^{72} + 26 q^{73} + 20 q^{74} + 72 q^{75} - 9 q^{76} + 30 q^{78} + 4 q^{79} + 8 q^{81} - 21 q^{82} - 48 q^{83} - 6 q^{84} - 34 q^{85} + 12 q^{87} - 3 q^{88} - 39 q^{89} - 27 q^{90} + 19 q^{91} + 18 q^{93} - 3 q^{94} + 9 q^{95} - 4 q^{97} - 15 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9 - 3 * q^11 + 4 * q^13 - 10 * q^14 - 2 * q^15 - 4 * q^16 - 15 * q^17 - 16 * q^18 + 9 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 5 * q^25 + q^26 + 5 * q^28 - 3 * q^29 + 10 * q^30 - 4 * q^32 - 10 * q^33 - 33 * q^35 + 8 * q^36 + 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^45 + 6 * q^46 + 6 * q^47 - 15 * q^49 - q^50 - 20 * q^51 - 5 * q^52 + 18 * q^54 - 23 * q^55 + 5 * q^56 + 24 * q^57 - 3 * q^58 + 30 * q^59 - 8 * q^60 - 5 * q^61 - 6 * q^62 - 25 * q^63 + 8 * q^64 - 6 * q^65 + 20 * q^66 - 16 * q^67 + 15 * q^68 - 2 * q^69 + 18 * q^70 + 8 * q^72 + 26 * q^73 + 20 * q^74 + 72 * q^75 - 9 * q^76 + 30 * q^78 + 4 * q^79 + 8 * q^81 - 21 * q^82 - 48 * q^83 - 6 * q^84 - 34 * q^85 + 12 * q^87 - 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 + 18 * q^93 - 3 * q^94 + 9 * q^95 - 4 * q^97 - 15 * q^98

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