LMFDB - Embedded newform 770.2.o.a.439.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.18
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.732537 + 1.26879i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68971 - 1.46454i) q^{5} -1.46507 q^{6} +(-1.43527 - 2.22261i) q^{7} +1.00000 q^{8} +(0.426780 - 0.739205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.732537 + 1.26879i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68971 - 1.46454i) q^{5} -1.46507 q^{6} +(-1.43527 - 2.22261i) q^{7} +1.00000 q^{8} +(0.426780 - 0.739205i) q^{9} +(0.423475 + 2.19560i) q^{10} +(-2.72740 - 1.88714i) q^{11} +(0.732537 - 1.26879i) q^{12} +5.37574i q^{13} +(2.64247 - 0.131675i) q^{14} +(3.09597 + 1.07106i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.664625 - 0.383721i) q^{17} +(0.426780 + 0.739205i) q^{18} +(2.96023 - 5.12727i) q^{19} +(-2.11318 - 0.731061i) q^{20} +(1.76864 - 3.44920i) q^{21} +(2.99801 - 1.41842i) q^{22} +(3.06514 + 1.76966i) q^{23} +(0.732537 + 1.26879i) q^{24} +(0.710237 - 4.94930i) q^{25} +(-4.65553 - 2.68787i) q^{26} +5.64575 q^{27} +(-1.20720 + 2.35429i) q^{28} -7.08660i q^{29} +(-2.47555 + 2.14566i) q^{30} +(6.08099 - 3.51086i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.396473 - 4.84290i) q^{33} +0.767442i q^{34} +(-5.68030 - 1.65355i) q^{35} -0.853561 q^{36} +(0.614161 + 0.354586i) q^{37} +(2.96023 + 5.12727i) q^{38} +(-6.82069 + 3.93793i) q^{39} +(1.68971 - 1.46454i) q^{40} +10.5798 q^{41} +(2.10278 + 3.25629i) q^{42} -4.71918 q^{43} +(-0.270617 + 3.30557i) q^{44} +(-0.361462 - 1.87408i) q^{45} +(-3.06514 + 1.76966i) q^{46} +(0.259449 - 0.449378i) q^{47} -1.46507 q^{48} +(-2.88000 + 6.38009i) q^{49} +(3.93110 + 3.08973i) q^{50} +(0.973724 + 0.562180i) q^{51} +(4.65553 - 2.68787i) q^{52} +(3.48230 - 2.01051i) q^{53} +(-2.82287 + 4.88936i) q^{54} +(-7.37231 + 0.805660i) q^{55} +(-1.43527 - 2.22261i) q^{56} +8.67390 q^{57} +(6.13717 + 3.54330i) q^{58} +(-11.6286 + 6.71375i) q^{59} +(-0.620422 - 3.21672i) q^{60} +(0.529405 - 0.916956i) q^{61} +7.02172i q^{62} +(-2.25551 + 0.112393i) q^{63} +1.00000 q^{64} +(7.87299 + 9.08344i) q^{65} +(3.99583 + 2.76480i) q^{66} +(6.11463 - 3.53028i) q^{67} +(-0.664625 - 0.383721i) q^{68} +5.18536i q^{69} +(4.27217 - 4.09250i) q^{70} -10.5373 q^{71} +(0.426780 - 0.739205i) q^{72} +(-4.58904 + 2.64949i) q^{73} +(-0.614161 + 0.354586i) q^{74} +(6.79990 - 2.72440i) q^{75} -5.92046 q^{76} +(-0.279836 + 8.77050i) q^{77} -7.87585i q^{78} +(-3.17925 - 1.83554i) q^{79} +(0.423475 + 2.19560i) q^{80} +(2.85538 + 4.94566i) q^{81} +(-5.28989 + 9.16236i) q^{82} -1.73341i q^{83} +(-3.87142 + 0.192914i) q^{84} +(0.561047 - 1.62175i) q^{85} +(2.35959 - 4.08693i) q^{86} +(8.99141 - 5.19119i) q^{87} +(-2.72740 - 1.88714i) q^{88} +(11.2117 + 6.47308i) q^{89} +(1.80373 + 0.624005i) q^{90} +(11.9482 - 7.71564i) q^{91} -3.53932i q^{92} +(8.90909 + 5.14367i) q^{93} +(0.259449 + 0.449378i) q^{94} +(-2.50717 - 12.9990i) q^{95} +(0.732537 - 1.26879i) q^{96} -18.1758 q^{97} +(-4.08532 - 5.68420i) q^{98} +(-2.55899 + 1.21071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.732537	+	1.26879i	0.422930	+	0.732537i	0.996225	−	0.0868129i	$-0.0276682\pi$
$3$	0.732537	+	1.26879i	0.422930	+	0.732537i	−0.573294	+	0.819349i	$0.694335\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.68971	−	1.46454i	0.755661	−	0.654963i
$5$	1.68971	−	1.46454i	0.755661	−	0.654963i
$6$	−1.46507			−0.598114
$7$	−1.43527	−	2.22261i	−0.542481	−	0.840068i
$7$	−1.43527	−	2.22261i	−0.542481	−	0.840068i
$8$	1.00000			0.353553
$9$	0.426780	−	0.739205i	0.142260	−	0.246402i
$10$	0.423475	+	2.19560i	0.133915	+	0.694310i
$11$	−2.72740	−	1.88714i	−0.822341	−	0.568995i
$11$	−2.72740	−	1.88714i	−0.822341	−	0.568995i
$12$	0.732537	−	1.26879i	0.211465	−	0.366268i
$13$			5.37574i			1.49096i	0.666527	+	0.745481i	$0.267780\pi$
$13$			5.37574i			1.49096i	−0.666527	+	0.745481i	$0.732220\pi$
$14$	2.64247	−	0.131675i	0.706231	−	0.0351916i
$15$	3.09597	+	1.07106i	0.799376	+	0.276546i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.664625	−	0.383721i	0.161195	−	0.0930661i	−0.417232	−	0.908800i	$-0.637000\pi$
$17$	0.664625	−	0.383721i	0.161195	−	0.0930661i	0.578428	+	0.815734i	$0.303667\pi$
$18$	0.426780	+	0.739205i	0.100593	+	0.174232i
$19$	2.96023	−	5.12727i	0.679123	−	1.17628i	−0.296122	−	0.955150i	$-0.595694\pi$
$19$	2.96023	−	5.12727i	0.679123	−	1.17628i	0.975245	−	0.221125i	$-0.0709730\pi$
$20$	−2.11318	−	0.731061i	−0.472523	−	0.163470i
$21$	1.76864	−	3.44920i	0.385949	−	0.752677i
$22$	2.99801	−	1.41842i	0.639178	−	0.302409i
$23$	3.06514	+	1.76966i	0.639126	+	0.368999i	0.784278	−	0.620410i	$-0.213034\pi$
$23$	3.06514	+	1.76966i	0.639126	+	0.368999i	−0.145152	+	0.989409i	$0.546367\pi$
$24$	0.732537	+	1.26879i	0.149528	+	0.258991i
$25$	0.710237	−	4.94930i	0.142047	−	0.989860i
$26$	−4.65553	−	2.68787i	−0.913024	−	0.527135i
$27$	5.64575			1.08652
$28$	−1.20720	+	2.35429i	−0.228140	+	0.444918i
$29$		−	7.08660i		−	1.31595i	−0.753041	−	0.657974i	$-0.771414\pi$
$29$		−	7.08660i		−	1.31595i	0.753041	−	0.657974i	$-0.228586\pi$
$30$	−2.47555	+	2.14566i	−0.451971	+	0.391742i
$31$	6.08099	−	3.51086i	1.09218	−	0.630569i	0.158022	−	0.987436i	$-0.449488\pi$
$31$	6.08099	−	3.51086i	1.09218	−	0.630569i	0.934155	+	0.356867i	$0.116155\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.396473	−	4.84290i	0.0690171	−	0.843040i
$34$			0.767442i			0.131615i
$35$	−5.68030	−	1.65355i	−0.960145	−	0.279502i
$36$	−0.853561			−0.142260
$37$	0.614161	+	0.354586i	0.100967	+	0.0582936i	0.549633	−	0.835406i	$-0.314767\pi$
$37$	0.614161	+	0.354586i	0.100967	+	0.0582936i	−0.448666	+	0.893700i	$0.648101\pi$
$38$	2.96023	+	5.12727i	0.480212	+	0.831752i
$39$	−6.82069	+	3.93793i	−1.09218	+	0.630573i
$40$	1.68971	−	1.46454i	0.267167	−	0.231564i
$41$	10.5798			1.65228			0.826142	−	0.563462i	$-0.190531\pi$
$41$	10.5798			1.65228			0.826142	+	0.563462i	$0.190531\pi$
$42$	2.10278	+	3.25629i	0.324465	+	0.502456i
$43$	−4.71918			−0.719668			−0.359834	−	0.933016i	$-0.617167\pi$
$43$	−4.71918			−0.719668			−0.359834	+	0.933016i	$0.617167\pi$
$44$	−0.270617	+	3.30557i	−0.0407970	+	0.498333i
$45$	−0.361462	−	1.87408i	−0.0538836	−	0.279371i
$46$	−3.06514	+	1.76966i	−0.451930	+	0.260922i
$47$	0.259449	−	0.449378i	0.0378445	−	0.0655485i	−0.846483	−	0.532416i	$-0.821284\pi$
$47$	0.259449	−	0.449378i	0.0378445	−	0.0655485i	0.884327	+	0.466868i	$0.154618\pi$
$48$	−1.46507			−0.211465
$49$	−2.88000	+	6.38009i	−0.411428	+	0.911442i
$50$	3.93110	+	3.08973i	0.555942	+	0.436954i
$51$	0.973724	+	0.562180i	0.136349	+	0.0787209i
$52$	4.65553	−	2.68787i	0.645605	−	0.372741i
$53$	3.48230	−	2.01051i	0.478331	−	0.276164i	−0.241390	−	0.970428i	$-0.577603\pi$
$53$	3.48230	−	2.01051i	0.478331	−	0.276164i	0.719721	+	0.694264i	$0.244270\pi$
$54$	−2.82287	+	4.88936i	−0.384145	+	0.665358i
$55$	−7.37231	+	0.805660i	−0.994082	+	0.108635i
$56$	−1.43527	−	2.22261i	−0.191796	−	0.297009i
$57$	8.67390			1.14889
$58$	6.13717	+	3.54330i	0.805850	+	0.465258i
$59$	−11.6286	+	6.71375i	−1.51391	+	0.874056i	−0.514042	+	0.857765i	$0.671852\pi$
$59$	−11.6286	+	6.71375i	−1.51391	+	0.874056i	−0.999867	+	0.0162910i	$0.994814\pi$
$60$	−0.620422	−	3.21672i	−0.0800962	−	0.415276i
$61$	0.529405	−	0.916956i	0.0677834	−	0.117404i	−0.830142	−	0.557552i	$-0.811741\pi$
$61$	0.529405	−	0.916956i	0.0677834	−	0.117404i	0.897925	+	0.440148i	$0.145074\pi$
$62$			7.02172i			0.891759i
$63$	−2.25551	+	0.112393i	−0.284168	+	0.0141601i
$64$	1.00000			0.125000
$65$	7.87299	+	9.08344i	0.976525	+	1.12666i
$66$	3.99583	+	2.76480i	0.491853	+	0.340324i
$67$	6.11463	−	3.53028i	0.747020	−	0.431292i	−0.0775959	−	0.996985i	$-0.524724\pi$
$67$	6.11463	−	3.53028i	0.747020	−	0.431292i	0.824616	+	0.565692i	$0.191391\pi$
$68$	−0.664625	−	0.383721i	−0.0805976	−	0.0465330i
$69$			5.18536i			0.624244i
$70$	4.27217	−	4.09250i	0.510622	−	0.489148i
$71$	−10.5373			−1.25055			−0.625275	−	0.780404i	$-0.715013\pi$
$71$	−10.5373			−1.25055			−0.625275	+	0.780404i	$0.715013\pi$
$72$	0.426780	−	0.739205i	0.0502966	−	0.0871162i
$73$	−4.58904	+	2.64949i	−0.537107	+	0.310099i	−0.743906	−	0.668285i	$-0.767029\pi$
$73$	−4.58904	+	2.64949i	−0.537107	+	0.310099i	0.206799	+	0.978384i	$0.433695\pi$
$74$	−0.614161	+	0.354586i	−0.0713948	+	0.0412198i
$75$	6.79990	−	2.72440i	0.785185	−	0.314587i
$76$	−5.92046			−0.679123
$77$	−0.279836	+	8.77050i	−0.0318903	+	0.999491i
$78$		−	7.87585i		−	0.891765i
$79$	−3.17925	−	1.83554i	−0.357694	−	0.206515i	0.310375	−	0.950614i	$-0.399545\pi$
$79$	−3.17925	−	1.83554i	−0.357694	−	0.206515i	−0.668069	+	0.744100i	$0.732879\pi$
$80$	0.423475	+	2.19560i	0.0473460	+	0.245476i
$81$	2.85538	+	4.94566i	0.317264	+	0.549517i
$82$	−5.28989	+	9.16236i	−0.584170	+	1.01181i
$83$		−	1.73341i		−	0.190267i	−0.995465	−	0.0951334i	$-0.969672\pi$
$83$		−	1.73341i		−	0.190267i	0.995465	−	0.0951334i	$-0.0303278\pi$
$84$	−3.87142	+	0.192914i	−0.422406	+	0.0210486i
$85$	0.561047	−	1.62175i	0.0608541	−	0.175903i
$86$	2.35959	−	4.08693i	0.254441	−	0.440705i
$87$	8.99141	−	5.19119i	0.963980	−	0.556554i
$88$	−2.72740	−	1.88714i	−0.290741	−	0.201170i
$89$	11.2117	+	6.47308i	1.18844	+	0.686145i	0.957951	−	0.286930i	$-0.0926348\pi$
$89$	11.2117	+	6.47308i	1.18844	+	0.686145i	0.230487	+	0.973075i	$0.425968\pi$
$90$	1.80373	+	0.624005i	0.190130	+	0.0657759i
$91$	11.9482	−	7.71564i	1.25251	−	0.808819i
$92$		−	3.53932i		−	0.368999i
$93$	8.90909	+	5.14367i	0.923830	+	0.533373i
$94$	0.259449	+	0.449378i	0.0267601	+	0.0463498i
$95$	−2.50717	−	12.9990i	−0.257230	−	1.33367i
$96$	0.732537	−	1.26879i	0.0747642	−	0.129495i
$97$	−18.1758			−1.84547			−0.922734	−	0.385437i	$-0.874051\pi$
$97$	−18.1758			−1.84547			−0.922734	+	0.385437i	$0.874051\pi$
$98$	−4.08532	−	5.68420i	−0.412680	−	0.574191i
$99$	−2.55899	+	1.21071i	−0.257188	+	0.121681i
$100$	−4.64134	+	1.85957i	−0.464134	+	0.185957i
$101$	1.85447	+	3.21204i	0.184527	+	0.319610i	0.943417	−	0.331609i	$-0.107591\pi$
$101$	1.85447	+	3.21204i	0.184527	+	0.319610i	−0.758890	+	0.651219i	$0.774258\pi$
$102$	−0.973724	+	0.562180i	−0.0964130	+	0.0556641i
$103$	−5.97746	+	10.3533i	−0.588976	+	1.02014i	0.405390	+	0.914144i	$0.367136\pi$
$103$	−5.97746	+	10.3533i	−0.588976	+	1.02014i	−0.994367	+	0.105993i	$0.966198\pi$
$104$			5.37574i			0.527135i
$105$	−2.06301	−	8.41839i	−0.201329	−	0.821551i
$106$			4.02101i			0.390555i
$107$	−1.26159	+	2.18513i	−0.121962	+	0.211244i	−0.920541	−	0.390645i	$-0.872252\pi$
$107$	−1.26159	+	2.18513i	−0.121962	+	0.211244i	0.798579	+	0.601890i	$0.205585\pi$
$108$	−2.82287	−	4.88936i	−0.271631	−	0.470479i
$109$	−1.36565	+	0.788460i	−0.130806	+	0.0755207i	−0.563975	−	0.825792i	$-0.690729\pi$
$109$	−1.36565	+	0.788460i	−0.130806	+	0.0755207i	0.433169	+	0.901313i	$0.357395\pi$
$110$	2.98843	−	6.78744i	0.284936	−	0.647157i
$111$			1.03899i			0.0986165i
$112$	2.64247	−	0.131675i	0.249690	−	0.0124421i
$113$			8.51970i			0.801466i	0.916195	+	0.400733i	$0.131244\pi$
$113$			8.51970i			0.801466i	−0.916195	+	0.400733i	$0.868756\pi$
$114$	−4.33695	+	7.51182i	−0.406193	+	0.703546i
$115$	7.77093	−	1.49881i	0.724643	−	0.139765i
$116$	−6.13717	+	3.54330i	−0.569822	+	0.328987i
$117$	3.97378	+	2.29426i	0.367376	+	0.212105i
$118$		−	13.4275i		−	1.23610i
$119$	−1.80678	−	0.926458i	−0.165627	−	0.0849283i
$120$	3.09597	+	1.07106i	0.282622	+	0.0977737i
$121$	3.87738	+	10.2940i	0.352489	+	0.935816i
$122$	0.529405	+	0.916956i	0.0479301	+	0.0830173i
$123$	7.75007	+	13.4235i	0.698801	+	1.21036i
$124$	−6.08099	−	3.51086i	−0.546089	−	0.315285i
$125$	−6.04836	−	9.40305i	−0.540982	−	0.841034i
$126$	1.03042	−	2.00953i	0.0917972	−	0.179023i
$127$	2.25516			0.200113			0.100056	−	0.994982i	$-0.468098\pi$
$127$	2.25516			0.200113			0.100056	+	0.994982i	$0.468098\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.45697	−	5.98765i	−0.304369	−	0.527183i
$130$	−11.8030	+	2.27649i	−1.03519	+	0.199662i
$131$	9.16864	−	15.8805i	0.801068	−	1.38749i	−0.117846	−	0.993032i	$-0.537599\pi$
$131$	9.16864	−	15.8805i	0.801068	−	1.38749i	0.918914	−	0.394458i	$-0.129068\pi$
$132$	−4.39231	+	2.07809i	−0.382301	+	0.180875i
$133$	−15.6446	+	0.779576i	−1.35656	+	0.0675979i
$134$			7.06056i			0.609940i
$135$	9.53967	−	8.26843i	0.821044	−	0.711633i
$136$	0.664625	−	0.383721i	0.0569911	−	0.0329038i
$137$	−2.89385	+	1.67076i	−0.247238	+	0.142743i	−0.618499	−	0.785786i	$-0.712259\pi$
$137$	−2.89385	+	1.67076i	−0.247238	+	0.142743i	0.371261	+	0.928529i	$0.378926\pi$
$138$	−4.49065	−	2.59268i	−0.382270	−	0.220704i
$139$	−14.1702			−1.20190			−0.600950	−	0.799287i	$-0.705211\pi$
$139$	−14.1702			−1.20190			−0.600950	+	0.799287i	$0.705211\pi$
$140$	1.40813	+	5.74606i	0.119009	+	0.485630i
$141$	0.760222			0.0640223
$142$	5.26866	−	9.12559i	0.442136	−	0.765803i
$143$	10.1448	−	14.6618i	0.848350	−	1.22608i
$144$	0.426780	+	0.739205i	0.0355650	+	0.0616005i
$145$	−10.3786	−	11.9743i	−0.861897	−	0.994411i
$146$		−	5.29897i		−	0.438546i
$147$	−10.2047	+	1.01954i	−0.841670	+	0.0840901i
$148$		−	0.709172i		−	0.0582936i
$149$	18.4525	+	10.6536i	1.51169	+	0.872774i	0.999907	+	0.0136590i	$0.00434793\pi$
$149$	18.4525	+	10.6536i	1.51169	+	0.872774i	0.511782	+	0.859115i	$0.328985\pi$
$150$	−1.04055	+	7.25109i	−0.0849604	+	0.592049i
$151$	−9.70140	+	5.60111i	−0.789489	+	0.455812i	−0.839783	−	0.542923i	$-0.817318\pi$
$151$	−9.70140	+	5.60111i	−0.789489	+	0.455812i	0.0502936	+	0.998734i	$0.483984\pi$
$152$	2.96023	−	5.12727i	0.240106	−	0.415876i
$153$		−	0.655059i		−	0.0529584i
$154$	−7.45556	−	4.62760i	−0.600786	−	0.372902i
$155$	5.13330	−	14.8382i	0.412317	−	1.19183i
$156$	6.82069	+	3.93793i	0.546092	+	0.315286i
$157$	8.20784	+	14.2164i	0.655057	+	1.13459i	0.981880	+	0.189506i	$0.0606887\pi$
$157$	8.20784	+	14.2164i	0.655057	+	1.13459i	−0.326823	+	0.945086i	$0.605978\pi$
$158$	3.17925	−	1.83554i	0.252928	−	0.146028i
$159$	5.10182	+	2.94554i	0.404601	+	0.233596i
$160$	−2.11318	−	0.731061i	−0.167062	−	0.0577954i
$161$	−0.466040	−	9.35255i	−0.0367291	−	0.737084i
$162$	−5.71075			−0.448679
$163$	−12.4021	−	7.16037i	−0.971410	−	0.560844i	−0.0717441	−	0.997423i	$-0.522856\pi$
$163$	−12.4021	−	7.16037i	−0.971410	−	0.560844i	−0.899666	+	0.436579i	$0.856190\pi$
$164$	−5.28989	−	9.16236i	−0.413071	−	0.715460i
$165$	−6.42270	−	8.76374i	−0.500006	−	0.682256i
$166$	1.50118	+	0.866706i	0.116514	+	0.0672695i
$167$		−	18.0946i		−	1.40020i	−0.714043	−	0.700102i	$-0.753138\pi$
$167$		−	18.0946i		−	1.40020i	0.714043	−	0.700102i	$-0.246862\pi$
$168$	1.76864	−	3.44920i	0.136454	−	0.266112i
$169$	−15.8986			−1.22297
$170$	1.12395	+	1.29675i	0.0862031	+	0.0994566i
$171$	−2.52674	−	4.37643i	−0.193224	−	0.334674i
$172$	2.35959	+	4.08693i	0.179917	+	0.311625i
$173$	7.42565	+	4.28720i	0.564562	+	0.325950i	0.754974	−	0.655754i	$-0.227649\pi$
$173$	7.42565	+	4.28720i	0.564562	+	0.325950i	−0.190413	+	0.981704i	$0.560983\pi$
$174$			10.3824i			0.787086i
$175$	−12.0197	+	5.52500i	−0.908608	+	0.417651i
$176$	2.99801	−	1.41842i	0.225984	−	0.106918i
$177$	−17.0367	−	9.83614i	−1.28056	−	0.739329i
$178$	−11.2117	+	6.47308i	−0.840353	+	0.485178i
$179$	1.38069	+	2.39143i	0.103198	+	0.178744i	0.913001	−	0.407958i	$-0.133759\pi$
$179$	1.38069	+	2.39143i	0.103198	+	0.178744i	−0.809803	+	0.586702i	$0.800426\pi$
$180$	−1.44227	+	1.25008i	−0.107500	+	0.0931751i
$181$			1.57584i			0.117131i	0.998284	+	0.0585655i	$0.0186527\pi$
$181$			1.57584i			0.117131i	−0.998284	+	0.0585655i	$0.981347\pi$
$182$	0.707851	+	14.2052i	0.0524694	+	1.05296i
$183$	1.55123			0.114671
$184$	3.06514	+	1.76966i	0.225965	+	0.130461i
$185$	1.55706	−	0.300317i	0.114477	−	0.0220797i
$186$	−8.90909	+	5.14367i	−0.653246	+	0.377152i
$187$	−2.53683	−	0.207683i	−0.185512	−	0.0151873i
$188$	−0.518897			−0.0378445
$189$	−8.10317	−	12.5483i	−0.589419	−	0.912755i
$190$	12.5110	+	4.32821i	0.907645	+	0.314002i
$191$	−2.26142	+	3.91689i	−0.163631	+	0.283416i	−0.936168	−	0.351553i	$-0.885654\pi$
$191$	−2.26142	+	3.91689i	−0.163631	+	0.283416i	0.772538	+	0.634969i	$0.218987\pi$
$192$	0.732537	+	1.26879i	0.0528663	+	0.0915671i
$193$	0.959084	+	1.66118i	0.0690364	+	0.119575i	0.898477	−	0.439020i	$-0.144674\pi$
$193$	0.959084	+	1.66118i	0.0690364	+	0.119575i	−0.829441	+	0.558594i	$0.811341\pi$
$194$	9.08788	−	15.7407i	0.652471	−	1.13011i
$195$	−5.75773	+	16.6431i	−0.412319	+	1.19184i
$196$	6.96532	−	0.695896i	0.497523	−	0.0497068i
$197$	−3.25969			−0.232243			−0.116121	−	0.993235i	$-0.537046\pi$
$197$	−3.25969			−0.232243			−0.116121	+	0.993235i	$0.537046\pi$
$198$	0.230988	−	2.82150i	0.0164156	−	0.200515i
$199$	−17.9730	+	10.3767i	−1.27407	+	0.735585i	−0.975752	−	0.218881i	$-0.929759\pi$
$199$	−17.9730	+	10.3767i	−1.27407	+	0.735585i	−0.298320	+	0.954466i	$0.596426\pi$
$200$	0.710237	−	4.94930i	0.0502213	−	0.349968i
$201$	8.95837	+	5.17212i	0.631875	+	0.364813i
$202$	−3.70895			−0.260961
$203$	−15.7507	+	10.1712i	−1.10549	+	0.713877i
$204$		−	1.12436i		−	0.0787209i
$205$	17.8768	−	15.4945i	1.24857	−	1.08218i
$206$	−5.97746	−	10.3533i	−0.416469	−	0.721346i
$207$	2.61628	−	1.51051i	0.181844	−	0.104988i
$208$	−4.65553	−	2.68787i	−0.322803	−	0.186370i
$209$	−17.7496	+	8.39771i	−1.22777	+	0.580882i
$210$	8.32205	+	2.42258i	0.574276	+	0.167174i
$211$			13.1991i			0.908663i	0.890833	+	0.454331i	$0.150122\pi$
$211$			13.1991i			0.908663i	−0.890833	+	0.454331i	$0.849878\pi$
$212$	−3.48230	−	2.01051i	−0.239165	−	0.138082i
$213$	−7.71898	−	13.3697i	−0.528896	−	0.916074i
$214$	−1.26159	−	2.18513i	−0.0862402	−	0.149372i
$215$	−7.97404	+	6.91143i	−0.543825	+	0.471356i
$216$	5.64575			0.384145
$217$	−16.5311	−	8.47664i	−1.12221	−	0.575432i
$218$		−	1.57692i		−	0.106802i
$219$	−6.72329	−	3.88169i	−0.454318	−	0.262300i
$220$	4.38388	+	5.98178i	0.295561	+	0.403291i
$221$	2.06279	+	3.57285i	0.138758	+	0.240336i
$222$	−0.899791	−	0.519495i	−0.0603900	−	0.0348662i
$223$	2.07351			0.138852			0.0694261	−	0.997587i	$-0.477883\pi$
$223$	2.07351			0.138852			0.0694261	+	0.997587i	$0.477883\pi$
$224$	−1.20720	+	2.35429i	−0.0806596	+	0.157302i
$225$	−3.35543	−	2.63728i	−0.223696	−	0.175818i
$226$	−7.37828	−	4.25985i	−0.490796	−	0.283361i
$227$	−2.32184	+	1.34051i	−0.154106	+	0.0889731i	−0.575070	−	0.818104i	$-0.695025\pi$
$227$	−2.32184	+	1.34051i	−0.154106	+	0.0889731i	0.420964	+	0.907077i	$0.361692\pi$
$228$	−4.33695	−	7.51182i	−0.287222	−	0.497482i
$229$	16.2306	+	9.37074i	1.07255	+	0.619236i	0.928876	−	0.370390i	$-0.120776\pi$
$229$	16.2306	+	9.37074i	1.07255	+	0.619236i	0.143671	+	0.989625i	$0.454109\pi$
$230$	−2.58746	+	7.47923i	−0.170612	+	0.493166i
$231$	−11.3329	+	6.06966i	−0.745651	+	0.399354i
$232$		−	7.08660i		−	0.465258i
$233$	3.42464	−	5.93166i	0.224356	−	0.388596i	−0.731770	−	0.681552i	$-0.761306\pi$
$233$	3.42464	−	5.93166i	0.224356	−	0.388596i	0.956126	+	0.292956i	$0.0946388\pi$
$234$	−3.97378	+	2.29426i	−0.259774	+	0.149981i
$235$	−0.219740	−	1.13929i	−0.0143343	−	0.0743192i
$236$	11.6286	+	6.71375i	0.756955	+	0.437028i
$237$		−	5.37841i		−	0.349365i
$238$	1.70573	−	1.10149i	0.110566	−	0.0713988i
$239$			2.46292i			0.159313i	0.996822	+	0.0796566i	$0.0253824\pi$
$239$			2.46292i			0.159313i	−0.996822	+	0.0796566i	$0.974618\pi$
$240$	−2.47555	+	2.14566i	−0.159796	+	0.138502i
$241$	8.09203	+	14.0158i	0.521254	+	0.902838i	0.999694	+	0.0247181i	$0.00786880\pi$
$241$	8.09203	+	14.0158i	0.521254	+	0.902838i	−0.478441	+	0.878120i	$0.658798\pi$
$242$	−10.8535	−	1.78908i	−0.697692	−	0.115007i
$243$	4.28529	−	7.42234i	0.274901	−	0.476143i
$244$	−1.05881			−0.0677834
$245$	4.47755	+	14.9984i	0.286060	+	0.958212i
$246$	−15.5001			−0.988253
$247$	27.5628	+	15.9134i	1.75378	+	1.01255i
$248$	6.08099	−	3.51086i	0.386143	−	0.222940i
$249$	2.19934	−	1.26979i	0.139377	−	0.0804696i
$250$	11.1675	−	0.536510i	0.706292	−	0.0339318i
$251$		−	9.85444i		−	0.622006i	−0.950409	−	0.311003i	$-0.899335\pi$
$251$		−	9.85444i		−	0.622006i	0.950409	−	0.311003i	$-0.100665\pi$
$252$	1.22509	+	1.89713i	0.0771735	+	0.119508i
$253$	−5.02025	−	10.6109i	−0.315620	−	0.667103i
$254$	−1.12758	+	1.95302i	−0.0707505	+	0.122544i
$255$	2.46865	−	0.476138i	0.154593	−	0.0298169i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5008	−	18.1879i	0.655021	−	1.13453i	−0.326867	−	0.945070i	$-0.605993\pi$
$257$	10.5008	−	18.1879i	0.655021	−	1.13453i	0.981888	−	0.189460i	$-0.0606737\pi$
$258$	6.91394			0.430443
$259$	−0.0933803	−	1.87397i	−0.00580237	−	0.116443i
$260$	3.92999	−	11.3599i	0.243728	−	0.704513i
$261$	−5.23845	−	3.02442i	−0.324252	−	0.187207i
$262$	9.16864	+	15.8805i	0.566440	+	0.981103i
$263$	12.9102	+	22.3611i	0.796075	+	1.37884i	0.922154	+	0.386822i	$0.126427\pi$
$263$	12.9102	+	22.3611i	0.796075	+	1.37884i	−0.126080	+	0.992020i	$0.540240\pi$
$264$	0.396473	−	4.84290i	0.0244012	−	0.298060i
$265$	2.93960	−	8.49714i	0.180578	−	0.521975i
$266$	7.14719	−	13.9384i	0.438222	−	0.854621i
$267$			18.9671i			1.16077i
$268$	−6.11463	−	3.53028i	−0.373510	−	0.215646i
$269$	11.4272	−	6.59750i	0.696729	−	0.402256i	−0.109399	−	0.993998i	$-0.534893\pi$
$269$	11.4272	−	6.59750i	0.696729	−	0.402256i	0.806128	+	0.591741i	$0.201559\pi$
$270$	2.39084	+	12.3958i	0.145502	+	0.754385i
$271$	9.39635	−	16.2749i	0.570787	−	0.988633i	−0.425698	−	0.904865i	$-0.639971\pi$
$271$	9.39635	−	16.2749i	0.570787	−	0.988633i	0.996485	−	0.0837674i	$-0.0266953\pi$
$272$			0.767442i			0.0465330i
$273$	18.5420	+	9.50775i	1.12221	+	0.575435i
$274$		−	3.34153i		−	0.201869i
$275$	−11.2771	+	12.1584i	−0.680037	+	0.733178i
$276$	4.49065	−	2.59268i	0.270306	−	0.156061i
$277$	4.88924	+	8.46841i	0.293766	+	0.508818i	0.974697	−	0.223530i	$-0.0717580\pi$
$277$	4.88924	+	8.46841i	0.293766	+	0.508818i	−0.680931	+	0.732347i	$0.738425\pi$
$278$	7.08509	−	12.2717i	0.424936	−	0.736010i
$279$		−	5.99347i		−	0.358819i
$280$	−5.68030	−	1.65355i	−0.339463	−	0.0988187i
$281$			21.0606i			1.25637i	0.778064	+	0.628185i	$0.216202\pi$
$281$			21.0606i			1.25637i	−0.778064	+	0.628185i	$0.783798\pi$
$282$	−0.380111	+	0.658372i	−0.0226353	+	0.0392055i
$283$	−21.1211	+	12.1943i	−1.25552	+	0.724875i	−0.972200	−	0.234150i	$-0.924769\pi$
$283$	−21.1211	+	12.1943i	−1.25552	+	0.724875i	−0.283320	+	0.959025i	$0.591436\pi$
$284$	5.26866	+	9.12559i	0.312638	+	0.541504i
$285$	14.6564	−	12.7033i	0.868169	−	0.752478i
$286$	7.62507	+	16.1165i	0.450880	+	0.952991i
$287$	−15.1848	−	23.5147i	−0.896333	−	1.38803i
$288$	−0.853561			−0.0502966
$289$	−8.20552	+	14.2124i	−0.482677	+	0.836022i
$290$	15.5593	−	3.00100i	0.913676	−	0.176225i
$291$	−13.3144	−	23.0612i	−0.780504	−	1.35187i
$292$	4.58904	+	2.64949i	0.268554	+	0.155049i
$293$		−	21.8313i		−	1.27540i	−0.770286	−	0.637698i	$-0.779887\pi$
$293$		−	21.8313i		−	1.27540i	0.770286	−	0.637698i	$-0.220113\pi$
$294$	4.21941	−	9.34730i	0.246081	−	0.545146i
$295$	−9.81632	+	28.3748i	−0.571528	+	1.65204i
$296$	0.614161	+	0.354586i	0.0356974	+	0.0206099i
$297$	−15.3982	−	10.6543i	−0.893494	−	0.618227i
$298$	−18.4525	+	10.6536i	−1.06893	+	0.617144i
$299$	−9.51323	+	16.4774i	−0.550164	+	0.952912i
$300$	−5.75935	−	4.52668i	−0.332516	−	0.261348i
$301$	6.77330	+	10.4889i	0.390406	+	0.604570i
$302$		−	11.2022i		−	0.644615i
$303$	−2.71694	+	4.70588i	−0.156084	+	0.270346i
$304$	2.96023	+	5.12727i	0.169781	+	0.294069i
$305$	−0.448380	−	2.32473i	−0.0256742	−	0.133113i
$306$	0.567298	+	0.327529i	0.0324302	+	0.0187236i
$307$		−	9.19859i		−	0.524991i	−0.964933	−	0.262496i	$-0.915454\pi$
$307$		−	9.19859i		−	0.524991i	0.964933	−	0.262496i	$-0.0845455\pi$
$308$	7.73539	−	4.14291i	0.440765	−	0.236064i
$309$	−17.5148			−0.996384
$310$	10.2836	+	11.8647i	0.584069	+	0.673868i
$311$	1.48350	−	0.856499i	0.0841216	−	0.0485676i	−0.457349	−	0.889287i	$-0.651201\pi$
$311$	1.48350	−	0.856499i	0.0841216	−	0.0485676i	0.541471	+	0.840720i	$0.317868\pi$
$312$	−6.82069	+	3.93793i	−0.386145	+	0.222941i
$313$	−13.8799	+	24.0407i	−0.784537	+	1.35886i	0.144738	+	0.989470i	$0.453766\pi$
$313$	−13.8799	+	24.0407i	−0.784537	+	1.35886i	−0.929275	+	0.369388i	$0.879567\pi$
$314$	−16.4157			−0.926390
$315$	−3.64656	+	3.49320i	−0.205460	+	0.196820i
$316$			3.67108i			0.206515i
$317$	26.8418	+	15.4971i	1.50759	+	0.870406i	0.999961	+	0.00882863i	$0.00281028\pi$
$317$	26.8418	+	15.4971i	1.50759	+	0.870406i	0.507626	+	0.861577i	$0.330523\pi$
$318$	−5.10182	+	2.94554i	−0.286096	+	0.165178i
$319$	−13.3734	+	19.3280i	−0.748768	+	1.08216i
$320$	1.68971	−	1.46454i	0.0944576	−	0.0818704i
$321$	−3.69663			−0.206326
$322$	8.33257	+	4.27267i	0.464356	+	0.238107i
$323$		−	4.54361i		−	0.252813i
$324$	2.85538	−	4.94566i	0.158632	−	0.274759i
$325$	26.6061	+	3.81805i	1.47584	+	0.211787i
$326$	12.4021	−	7.16037i	0.686890	−	0.396576i
$327$	−2.00078	−	1.15515i	−0.110643	−	0.0638800i
$328$	10.5798			0.584170
$329$	−1.37117	+	0.0683258i	−0.0755951	+	0.00376692i
$330$	10.8010	−	1.18035i	0.594574	−	0.0649761i
$331$	15.8081	−	27.3804i	0.868892	−	1.50496i	0.00576167	−	0.999983i	$-0.498166\pi$
$331$	15.8081	−	27.3804i	0.868892	−	1.50496i	0.863130	−	0.504981i	$-0.168501\pi$
$332$	−1.50118	+	0.866706i	−0.0823879	+	0.0475667i
$333$	0.524224	−	0.302661i	0.0287273	−	0.0165857i
$334$	15.6704	+	9.04731i	0.857447	+	0.495047i
$335$	5.16170	−	14.9203i	0.282014	−	0.815181i
$336$	2.10278	+	3.25629i	0.114716	+	0.177645i
$337$	−26.9419			−1.46762			−0.733808	−	0.679357i	$-0.762259\pi$
$337$	−26.9419			−1.46762			−0.733808	+	0.679357i	$0.762259\pi$
$338$	7.94929	−	13.7686i	0.432384	−	0.748912i
$339$	−10.8097	+	6.24099i	−0.587103	+	0.338964i
$340$	−1.68500	+	0.324993i	−0.0913819	+	0.0176252i
$341$	−23.2108	−	1.90019i	−1.25693	−	0.102901i
$342$	5.05347			0.273260
$343$	18.3140	−	2.75604i	0.988865	−	0.148812i
$344$	−4.71918			−0.254441
$345$	7.59417	+	8.76175i	0.408857	+	0.471717i
$346$	−7.42565	+	4.28720i	−0.399206	+	0.230481i
$347$	1.26565	+	2.19218i	0.0679438	+	0.117682i	0.897996	−	0.440004i	$-0.145023\pi$
$347$	1.26565	+	2.19218i	0.0679438	+	0.117682i	−0.830052	+	0.557686i	$0.811689\pi$
$348$	−8.99141	−	5.19119i	−0.481990	−	0.278277i
$349$	12.7075			0.680218			0.340109	−	0.940386i	$-0.389536\pi$
$349$	12.7075			0.680218			0.340109	+	0.940386i	$0.389536\pi$
$350$	1.22508	−	13.1719i	0.0654833	−	0.704068i
$351$			30.3501i			1.61997i
$352$	−0.270617	+	3.30557i	−0.0144239	+	0.176187i
$353$	−14.4475	−	25.0238i	−0.768964	−	1.33188i	−0.938125	−	0.346296i	$-0.887439\pi$
$353$	−14.4475	−	25.0238i	−0.768964	−	1.33188i	0.169161	−	0.985588i	$-0.445894\pi$
$354$	17.0367	−	9.83614i	0.905490	−	0.522785i
$355$	−17.8050	+	15.4324i	−0.944992	+	0.819064i
$356$		−	12.9462i		−	0.686145i
$357$	−0.148050	−	2.97109i	−0.00783564	−	0.157247i
$358$	−2.76139			−0.145944
$359$	26.1847	+	15.1177i	1.38198	+	0.797884i	0.992393	−	0.123108i	$-0.0392860\pi$
$359$	26.1847	+	15.1177i	1.38198	+	0.797884i	0.389582	+	0.920992i	$0.372619\pi$
$360$	−0.361462	−	1.87408i	−0.0190507	−	0.0987727i
$361$	−8.02590	−	13.9013i	−0.422416	−	0.731646i
$362$	−1.36471	−	0.787918i	−0.0717278	−	0.0414121i
$363$	−10.2206	+	12.4603i	−0.536441	+	0.653996i
$364$	−12.6560	−	6.48961i	−0.663356	−	0.340148i
$365$	−3.87387	+	11.1977i	−0.202768	+	0.586115i
$366$	−0.775617	+	1.34341i	−0.0405421	+	0.0702211i
$367$	−3.68740	−	6.38676i	−0.192481	−	0.333386i	0.753591	−	0.657344i	$-0.228320\pi$
$367$	−3.68740	−	6.38676i	−0.192481	−	0.333386i	−0.946072	+	0.323957i	$0.894987\pi$
$368$	−3.06514	+	1.76966i	−0.159781	+	0.0922499i
$369$	4.51524	−	7.82063i	0.235054	−	0.407126i
$370$	−0.518448	+	1.49861i	−0.0269528	+	0.0779091i
$371$	−9.46661	−	4.85418i	−0.491482	−	0.252016i
$372$		−	10.2873i		−	0.533373i
$373$	−0.593341	+	1.02770i	−0.0307220	+	0.0532121i	−0.880978	−	0.473158i	$-0.843114\pi$
$373$	−0.593341	+	1.02770i	−0.0307220	+	0.0532121i	0.850256	+	0.526370i	$0.176447\pi$
$374$	1.44827	−	2.09312i	0.0748885	−	0.108233i
$375$	7.49985	−	14.5622i	0.387291	−	0.751988i
$376$	0.259449	−	0.449378i	0.0133800	−	0.0231749i
$377$	38.0957			1.96203
$378$	14.9187	−	0.743404i	0.767337	−	0.0382366i
$379$	31.1564			1.60040			0.800199	−	0.599734i	$-0.204727\pi$
$379$	31.1564			1.60040			0.800199	+	0.599734i	$0.204727\pi$
$380$	−10.0039	+	8.67075i	−0.513187	+	0.444800i
$381$	1.65198	+	2.86132i	0.0846337	+	0.146590i
$382$	−2.26142	−	3.91689i	−0.115704	−	0.200406i
$383$	12.0676	−	20.9017i	0.616627	−	1.06803i	−0.373470	−	0.927642i	$-0.621832\pi$
$383$	12.0676	−	20.9017i	0.616627	−	1.06803i	0.990097	−	0.140387i	$-0.0448346\pi$
$384$	−1.46507			−0.0747642
$385$	12.3719	+	15.2294i	0.630531	+	0.776164i
$386$	−1.91817			−0.0976322
$387$	−2.01405	+	3.48844i	−0.102380	+	0.177328i
$388$	9.08788	+	15.7407i	0.461367	+	0.799111i
$389$	−6.10537	−	10.5748i	−0.309555	−	0.536164i	0.668710	−	0.743523i	$-0.266847\pi$
$389$	−6.10537	−	10.5748i	−0.309555	−	0.536164i	−0.978265	+	0.207359i	$0.933513\pi$
$390$	−11.5345	−	13.3079i	−0.584073	−	0.673872i
$391$	2.71622			0.137365
$392$	−2.88000	+	6.38009i	−0.145462	+	0.322243i
$393$	26.8654			1.35518
$394$	1.62984	−	2.82297i	0.0821103	−	0.142219i
$395$	−8.06024	+	1.55461i	−0.405555	+	0.0782211i
$396$	2.32800	+	1.61079i	0.116986	+	0.0809454i
$397$	−5.65530	+	9.79526i	−0.283831	+	0.491610i	−0.972325	−	0.233632i	$-0.924939\pi$
$397$	−5.65530	+	9.79526i	−0.283831	+	0.491610i	0.688494	+	0.725242i	$0.258272\pi$
$398$		−	20.7534i		−	1.04027i
$399$	−12.4494	−	19.2787i	−0.623249	−	0.965143i
$400$	3.93110	+	3.08973i	0.196555	+	0.154487i
$401$	−3.34756	+	5.79814i	−0.167169	+	0.289545i	−0.937423	−	0.348192i	$-0.886796\pi$
$401$	−3.34756	+	5.79814i	−0.167169	+	0.289545i	0.770254	+	0.637737i	$0.220129\pi$
$402$	−8.95837	+	5.17212i	−0.446803	+	0.257962i
$403$	18.8735	+	32.6898i	0.940154	+	1.62840i
$404$	1.85447	−	3.21204i	0.0922635	−	0.159805i
$405$	12.0679	+	4.17490i	0.599657	+	0.207453i
$406$	−0.933128	−	18.7261i	−0.0463104	−	0.929363i
$407$	−1.00591	−	2.12611i	−0.0498609	−	0.105387i
$408$	0.973724	+	0.562180i	0.0482065	+	0.0278320i
$409$	−3.84541	−	6.66045i	−0.190143	−	0.329338i	0.755154	−	0.655547i	$-0.227562\pi$
$409$	−3.84541	−	6.66045i	−0.190143	−	0.329338i	−0.945298	+	0.326209i	$0.894229\pi$
$410$	4.48028	+	23.2290i	0.221265	+	1.14720i
$411$	−4.23970	−	2.44779i	−0.209129	−	0.120741i
$412$	11.9549			0.588976
$413$	31.6122	+	16.2097i	1.55553	+	0.797628i
$414$			3.02102i			0.148475i
$415$	−2.53866	−	2.92896i	−0.124618	−	0.143777i
$416$	4.65553	−	2.68787i	0.228256	−	0.131784i
$417$	−10.3802	−	17.9790i	−0.508320	−	0.880435i
$418$	1.60217	−	19.5705i	0.0783649	−	0.957222i
$419$			14.8582i			0.725870i	0.931814	+	0.362935i	$0.118225\pi$
$419$			14.8582i			0.725870i	−0.931814	+	0.362935i	$0.881775\pi$
$420$	−6.25904	+	5.99582i	−0.305410	+	0.292566i
$421$	19.0633			0.929086			0.464543	−	0.885551i	$-0.346219\pi$
$421$	19.0633			0.929086			0.464543	+	0.885551i	$0.346219\pi$
$422$	−11.4307	−	6.59954i	−0.556440	−	0.321261i
$423$	−0.221455	−	0.383572i	−0.0107675	−	0.0186499i
$424$	3.48230	−	2.01051i	0.169115	−	0.0976388i
$425$	−1.42711	−	3.56196i	−0.0692250	−	0.172780i
$426$	15.4380			0.747971
$427$	−2.79788	+	0.139419i	−0.135399	+	0.00674695i
$428$	2.52317			0.121962
$429$	26.0341	+	2.13134i	1.25694	+	0.102902i
$430$	−1.99846	−	10.3614i	−0.0963741	−	0.499673i
$431$	−12.7977	+	7.38876i	−0.616444	+	0.355904i	−0.775483	−	0.631368i	$-0.782494\pi$
$431$	−12.7977	+	7.38876i	−0.616444	+	0.355904i	0.159039	+	0.987272i	$0.449160\pi$
$432$	−2.82287	+	4.88936i	−0.135816	+	0.235240i
$433$	11.1228			0.534527			0.267264	−	0.963623i	$-0.413881\pi$
$433$	11.1228			0.534527			0.267264	+	0.963623i	$0.413881\pi$
$434$	15.6065	−	10.0781i	0.749138	−	0.483763i
$435$	7.59015	−	21.9399i	0.363920	−	1.05194i
$436$	1.36565	+	0.788460i	0.0654029	+	0.0377604i
$437$	18.1470	−	10.4772i	0.868090	−	0.501192i
$438$	6.72329	−	3.88169i	0.321251	−	0.185474i
$439$	5.09007	−	8.81626i	0.242936	−	0.420777i	−0.718613	−	0.695410i	$-0.755223\pi$
$439$	5.09007	−	8.81626i	0.242936	−	0.420777i	0.961549	+	0.274633i	$0.0885563\pi$
$440$	−7.37231	+	0.805660i	−0.351461	+	0.0384083i
$441$	3.48707	+	4.85181i	0.166051	+	0.231039i
$442$	−4.12557			−0.196233
$443$	30.3841	+	17.5423i	1.44359	+	0.833459i	0.998087	−	0.0618195i	$-0.0196903\pi$
$443$	30.3841	+	17.5423i	1.44359	+	0.833459i	0.445506	+	0.895279i	$0.353024\pi$
$444$	0.899791	−	0.519495i	0.0427022	−	0.0246541i
$445$	28.4246	−	5.48238i	1.34746	−	0.259890i
$446$	−1.03675	+	1.79571i	−0.0490917	+	0.0850293i
$447$			31.2165i			1.47649i
$448$	−1.43527	−	2.22261i	−0.0678101	−	0.105008i
$449$	−10.8598			−0.512505			−0.256252	−	0.966610i	$-0.582488\pi$
$449$	−10.8598			−0.512505			−0.256252	+	0.966610i	$0.582488\pi$
$450$	3.96166	−	1.58725i	0.186755	−	0.0748239i
$451$	−28.8552	−	19.9656i	−1.35874	−	0.940142i
$452$	7.37828	−	4.25985i	0.347045	−	0.200366i
$453$	−14.2133	−	8.20603i	−0.667797	−	0.385553i
$454$		−	2.68103i		−	0.125827i
$455$	8.88908	−	30.5358i	0.416726	−	1.43154i
$456$	8.67390			0.406193
$457$	−10.8625	+	18.8144i	−0.508125	+	0.880098i	0.491831	+	0.870691i	$0.336328\pi$
$457$	−10.8625	+	18.8144i	−0.508125	+	0.880098i	−0.999956	+	0.00940744i	$0.997005\pi$
$458$	−16.2306	+	9.37074i	−0.758406	+	0.437866i
$459$	3.75230	−	2.16639i	0.175143	−	0.101119i
$460$	−5.18348	−	5.98042i	−0.241681	−	0.278839i
$461$	39.2471			1.82792			0.913959	−	0.405806i	$-0.133009\pi$
$461$	39.2471			1.82792			0.913959	+	0.405806i	$0.133009\pi$
$462$	0.409980	−	12.8494i	0.0190740	−	0.597809i
$463$			22.9110i			1.06476i	0.846504	+	0.532382i	$0.178703\pi$
$463$			22.9110i			1.06476i	−0.846504	+	0.532382i	$0.821297\pi$
$464$	6.13717	+	3.54330i	0.284911	+	0.164494i
$465$	22.5869	−	4.35643i	1.04744	−	0.202025i
$466$	3.42464	+	5.93166i	0.158644	+	0.274779i
$467$	3.29578	−	5.70845i	0.152510	−	0.264156i	−0.779639	−	0.626229i	$-0.784598\pi$
$467$	3.29578	−	5.70845i	0.152510	−	0.264156i	0.932150	+	0.362073i	$0.117931\pi$
$468$		−	4.58852i		−	0.212105i
$469$	−16.6226	−	8.52353i	−0.767559	−	0.393580i
$470$	1.09653	+	0.379345i	0.0505790	+	0.0174979i
$471$	−12.0251	+	20.8281i	−0.554087	+	0.959706i
$472$	−11.6286	+	6.71375i	−0.535248	+	0.309025i
$473$	12.8711	+	8.90577i	0.591812	+	0.409488i
$474$	4.65784	+	2.68920i	0.213942	+	0.123519i
$475$	−23.2739	−	18.2926i	−1.06788	−	0.839323i
$476$	0.101053	+	2.02795i	0.00463176	+	0.0929507i
$477$		−	3.43218i		−	0.157149i
$478$	−2.13295	−	1.23146i	−0.0975590	−	0.0563257i
$479$	5.20270	+	9.01134i	0.237718	+	0.411739i	0.960059	−	0.279798i	$-0.0902674\pi$
$479$	5.20270	+	9.01134i	0.237718	+	0.411739i	−0.722341	+	0.691537i	$0.756934\pi$
$480$	−0.620422	−	3.21672i	−0.0283183	−	0.146822i
$481$	−1.90616	+	3.30157i	−0.0869135	+	0.150539i
$482$	−16.1841			−0.737164
$483$	11.5250	−	7.44239i	0.524407	−	0.338641i
$484$	6.97616	−	8.50489i	0.317098	−	0.386586i
$485$	−30.7117	+	26.6191i	−1.39455	+	1.20871i
$486$	4.28529	+	7.42234i	0.194385	+	0.336684i
$487$	−11.7349	+	6.77515i	−0.531759	+	0.307011i	−0.741733	−	0.670696i	$-0.765996\pi$
$487$	−11.7349	+	6.77515i	−0.531759	+	0.307011i	0.209973	+	0.977707i	$0.432662\pi$
$488$	0.529405	−	0.916956i	0.0239650	−	0.0415087i
$489$		−	20.9809i		−	0.948791i
$490$	−15.2278	−	3.62152i	−0.687920	−	0.163603i
$491$		−	0.904579i		−	0.0408231i	−0.999792	−	0.0204115i	$-0.993502\pi$
$491$		−	0.904579i		−	0.0408231i	0.999792	−	0.0204115i	$-0.00649765\pi$
$492$	7.75007	−	13.4235i	0.349400	−	0.605179i
$493$	−2.71928	−	4.70993i	−0.122470	−	0.212124i
$494$	−27.5628	+	15.9134i	−1.24011	+	0.715978i
$495$	−2.55081	+	5.79349i	−0.114650	+	0.260398i
$496$			7.02172i			0.315285i
$497$	15.1239	+	23.4204i	0.678400	+	1.05055i
$498$			2.53958i			0.113801i
$499$	−0.526196	+	0.911398i	−0.0235558	+	0.0407998i	−0.877563	−	0.479461i	$-0.840832\pi$
$499$	−0.526196	+	0.911398i	−0.0235558	+	0.0407998i	0.854007	+	0.520261i	$0.174165\pi$
$500$	−5.11910	+	9.93956i	−0.228933	+	0.444511i
$501$	22.9583	−	13.2550i	1.02570	−	0.592189i
$502$	8.53419	+	4.92722i	0.380900	+	0.219912i
$503$			28.1021i			1.25301i	0.779417	+	0.626505i	$0.215515\pi$
$503$			28.1021i			1.25301i	−0.779417	+	0.626505i	$0.784485\pi$
$504$	−2.25551	+	0.112393i	−0.100468	+	0.00500637i
$505$	7.83769	+	2.71147i	0.348773	+	0.120659i
$506$	11.6995	+	0.957798i	0.520104	+	0.0425793i
$507$	−11.6463	−	20.1720i	−0.517230	−	0.895869i
$508$	−1.12758	−	1.95302i	−0.0500282	−	0.0866513i
$509$	−6.18250	−	3.56947i	−0.274034	−	0.158214i	0.356685	−	0.934225i	$-0.383907\pi$
$509$	−6.18250	−	3.56947i	−0.274034	−	0.158214i	−0.630720	+	0.776011i	$0.717240\pi$
$510$	−0.821975	+	2.37598i	−0.0363977	+	0.105210i
$511$	12.4753	+	6.39693i	0.551875	+	0.282984i
$512$	1.00000			0.0441942
$513$	16.7127	−	28.9473i	0.737884	−	1.27805i
$514$	10.5008	+	18.1879i	0.463170	+	0.802234i
$515$	5.06261	+	26.2482i	0.223085	+	1.15664i
$516$	−3.45697	+	5.98765i	−0.152185	+	0.263592i
$517$	−1.55566	+	0.736015i	−0.0684179	+	0.0323699i
$518$	1.66959	+	0.856114i	0.0733578	+	0.0376155i
$519$			12.5621i			0.551416i
$520$	7.87299	+	9.08344i	0.345254	+	0.398335i
$521$	7.84033	−	4.52661i	0.343491	−	0.198315i	−0.318324	−	0.947982i	$-0.603120\pi$
$521$	7.84033	−	4.52661i	0.343491	−	0.198315i	0.661815	+	0.749667i	$0.269787\pi$
$522$	5.23845	−	3.02442i	0.229281	−	0.132375i
$523$	−32.4539	−	18.7373i	−1.41911	−	0.819325i	−0.422891	−	0.906181i	$-0.638985\pi$
$523$	−32.4539	−	18.7373i	−1.41911	−	0.819325i	−0.996221	+	0.0868560i	$0.972318\pi$
$524$	−18.3373			−0.801068
$525$	−15.8150	−	11.2033i	−0.690222	−	0.488951i
$526$	−25.8203			−1.12582
$527$	2.69438	−	4.66681i	0.117369	−	0.203289i
$528$	3.99583	+	2.76480i	0.173896	+	0.120323i
$529$	−5.23661	−	9.07008i	−0.227679	−	0.394351i
$530$	5.88894	+	6.79434i	0.255799	+	0.295127i
$531$			11.4612i			0.497373i
$532$	8.49745	+	13.1589i	0.368411	+	0.570509i
$533$			56.8741i			2.46349i
$534$	−16.4260	−	9.48354i	−0.710821	−	0.410393i
$535$	1.06850	+	5.53988i	0.0461953	+	0.239510i
$536$	6.11463	−	3.53028i	0.264112	−	0.152485i
$537$	−2.02282	+	3.50363i	−0.0872911	+	0.151193i
$538$			13.1950i			0.568876i
$539$	19.8951	−	11.9661i	0.856941	−	0.515415i
$540$	−11.9305	−	4.12738i	−0.513407	−	0.177614i
$541$	−35.0913	−	20.2600i	−1.50869	−	0.871045i	−0.999949	−	0.0101271i	$-0.996776\pi$
$541$	−35.0913	−	20.2600i	−1.50869	−	0.871045i	−0.508745	−	0.860917i	$-0.669890\pi$
$542$	9.39635	+	16.2749i	0.403608	+	0.699069i
$543$	−1.99941	+	1.15436i	−0.0858028	+	0.0495382i
$544$	−0.664625	−	0.383721i	−0.0284955	−	0.0164519i
$545$	−1.15282	+	3.33232i	−0.0493815	+	0.142741i
$546$	−17.5050	+	11.3040i	−0.749143	+	0.483766i
$547$	−27.4296			−1.17280			−0.586402	−	0.810020i	$-0.699456\pi$
$547$	−27.4296			−1.17280			−0.586402	+	0.810020i	$0.699456\pi$
$548$	2.89385	+	1.67076i	0.123619	+	0.0713715i
$549$	−0.451879	−	0.782678i	−0.0192857	−	0.0334039i
$550$	−4.89090	−	15.8455i	−0.208549	−	0.675653i
$551$	−36.3349	−	20.9779i	−1.54792	−	0.893691i
$552$			5.18536i			0.220704i
$553$	0.483390	+	9.70074i	0.0205558	+	0.412517i
$554$	−9.77848			−0.415448
$555$	1.52164	+	1.75559i	0.0645901	+	0.0745206i
$556$	7.08509	+	12.2717i	0.300475	+	0.520438i
$557$	12.6454	+	21.9025i	0.535805	+	0.928041i	0.999124	+	0.0418494i	$0.0133250\pi$
$557$	12.6454	+	21.9025i	0.535805	+	0.928041i	−0.463319	+	0.886191i	$0.653342\pi$
$558$	5.19049	+	2.99673i	0.219731	+	0.126862i
$559$		−	25.3691i		−	1.07300i
$560$	4.27217	−	4.09250i	0.180532	−	0.172940i
$561$	−1.59482	−	3.37084i	−0.0673332	−	0.142317i
$562$	−18.2390	−	10.5303i	−0.769367	−	0.444194i
$563$	−19.7958	+	11.4291i	−0.834292	+	0.481679i	−0.855320	−	0.518100i	$-0.826639\pi$
$563$	−19.7958	+	11.4291i	−0.834292	+	0.481679i	0.0210280	+	0.999779i	$0.493306\pi$
$564$	−0.380111	−	0.658372i	−0.0160056	−	0.0277225i
$565$	12.4775	+	14.3958i	0.524930	+	0.605637i
$566$		−	24.3886i		−	1.02513i
$567$	6.89403	−	13.4447i	0.289522	−	0.564626i
$568$	−10.5373			−0.442136
$569$	−10.1924	−	5.88461i	−0.427289	−	0.246696i	0.270902	−	0.962607i	$-0.412678\pi$
$569$	−10.1924	−	5.88461i	−0.427289	−	0.246696i	−0.698191	+	0.715911i	$0.746011\pi$
$570$	3.67318	+	19.0444i	0.153853	+	0.797684i
$571$	−22.8872	+	13.2140i	−0.957801	+	0.552987i	−0.895496	−	0.445071i	$-0.853179\pi$
$571$	−22.8872	+	13.2140i	−0.957801	+	0.552987i	−0.0623054	+	0.998057i	$0.519845\pi$
$572$	−17.7699	−	1.45476i	−0.742995	−	0.0608267i
$573$	−6.62629			−0.276817
$574$	27.9568	−	1.39309i	1.16689	−	0.0581466i
$575$	10.9355	−	13.9134i	0.456044	−	0.580230i
$576$	0.426780	−	0.739205i	0.0177825	−	0.0308002i
$577$	−13.2480	−	22.9461i	−0.551520	−	0.955260i	−0.998165	−	0.0605493i	$-0.980715\pi$
$577$	−13.2480	−	22.9461i	−0.551520	−	0.955260i	0.446645	−	0.894711i	$-0.352619\pi$
$578$	−8.20552	−	14.2124i	−0.341304	−	0.591157i
$579$	−1.40513	+	2.43375i	−0.0583951	+	0.101143i
$580$	−5.18073	+	14.9753i	−0.215118	+	0.621815i
$581$	−3.85270	+	2.48792i	−0.159837	+	0.103216i
$582$	26.6288			1.10380
$583$	−13.2917	−	1.08815i	−0.550487	−	0.0450667i
$584$	−4.58904	+	2.64949i	−0.189896	+	0.109637i
$585$	10.0746	−	1.94313i	0.416532	−	0.0803384i
$586$	18.9064	+	10.9156i	0.781018	+	0.450921i
$587$	5.65519			0.233415			0.116707	−	0.993166i	$-0.462766\pi$
$587$	5.65519			0.233415			0.116707	+	0.993166i	$0.462766\pi$
$588$	5.98530	+	8.32777i	0.246830	+	0.343431i
$589$		−	41.5718i		−	1.71294i
$590$	−19.6651	−	22.6886i	−0.809601	−	0.934074i
$591$	−2.38784	−	4.13586i	−0.0982226	−	0.170126i
$592$	−0.614161	+	0.354586i	−0.0252419	+	0.0145734i
$593$	−20.6104	−	11.8994i	−0.846367	−	0.488650i	0.0130561	−	0.999915i	$-0.495844\pi$
$593$	−20.6104	−	11.8994i	−0.846367	−	0.488650i	−0.859424	+	0.511264i	$0.829177\pi$
$594$	16.9260	−	8.00805i	0.694483	−	0.328574i
$595$	−4.40977	+	1.08066i	−0.180783	+	0.0443026i
$596$		−	21.3071i		−	0.872774i
$597$	−26.3317	−	15.2026i	−1.07769	−	0.622203i
$598$	−9.51323	−	16.4774i	−0.389025	−	0.673811i
$599$	11.3058	+	19.5823i	0.461944	+	0.800110i	0.999058	−	0.0433997i	$-0.0138189\pi$
$599$	11.3058	+	19.5823i	0.461944	+	0.800110i	−0.537114	+	0.843510i	$0.680486\pi$
$600$	6.79990	−	2.72440i	0.277605	−	0.111223i
$601$	−37.3053			−1.52172			−0.760858	−	0.648918i	$-0.775222\pi$
$601$	−37.3053			−1.52172			−0.760858	+	0.648918i	$0.775222\pi$
$602$	−12.4703	+	0.621398i	−0.508251	+	0.0253263i
$603$		−	6.02662i		−	0.245423i
$604$	9.70140	+	5.60111i	0.394744	+	0.227906i
$605$	21.6276	+	11.7153i	0.879287	+	0.476293i
$606$	−2.71694	−	4.70588i	−0.110368	−	0.191163i
$607$	14.0761	+	8.12685i	0.571332	+	0.329859i	0.757681	−	0.652625i	$-0.226332\pi$
$607$	14.0761	+	8.12685i	0.571332	+	0.329859i	−0.186349	+	0.982484i	$0.559666\pi$
$608$	−5.92046			−0.240106
$609$	−24.4431	−	12.5336i	−0.990484	−	0.507889i
$610$	2.23746	+	0.774054i	0.0905922	+	0.0313405i
$611$	2.41574	+	1.39473i	0.0977304	+	0.0564247i
$612$	−0.567298	+	0.327529i	−0.0229316	+	0.0132396i
$613$	11.8875	+	20.5898i	0.480133	+	0.831615i	0.999740	−	0.0227901i	$-0.00725495\pi$
$613$	11.8875	+	20.5898i	0.480133	+	0.831615i	−0.519607	+	0.854405i	$0.673922\pi$
$614$	7.96621	+	4.59929i	0.321490	+	0.185612i
$615$	32.7547	+	11.3315i	1.32080	+	0.456932i
$616$	−0.279836	+	8.77050i	−0.0112749	+	0.353374i
$617$			10.7811i			0.434030i	0.976168	+	0.217015i	$0.0696321\pi$
$617$			10.7811i			0.434030i	−0.976168	+	0.217015i	$0.930368\pi$
$618$	8.75741	−	15.1683i	0.352275	−	0.610158i
$619$	−13.8713	+	8.00858i	−0.557534	+	0.321892i	−0.752155	−	0.658986i	$-0.770986\pi$
$619$	−13.8713	+	8.00858i	−0.557534	+	0.321892i	0.194621	+	0.980878i	$0.437652\pi$
$620$	−15.4169	+	2.97353i	−0.619158	+	0.119420i
$621$	17.3050	+	9.99105i	0.694426	+	0.400927i
$622$			1.71300i			0.0686850i
$623$	−1.70469	−	34.2099i	−0.0682968	−	1.37059i
$624$		−	7.87585i		−	0.315286i
$625$	−23.9911	−	7.03035i	−0.959645	−	0.281214i
$626$	−13.8799	−	24.0407i	−0.554751	−	0.960858i
$627$	−23.6572	−	16.3689i	−0.944776	−	0.653711i
$628$	8.20784	−	14.2164i	0.327528	−	0.567296i
$629$	0.544249			0.0217006
$630$	−1.20192	−	4.90461i	−0.0478858	−	0.195404i
$631$	45.6361			1.81674			0.908372	−	0.418163i	$-0.137326\pi$
$631$	45.6361			1.81674			0.908372	+	0.418163i	$0.137326\pi$
$632$	−3.17925	−	1.83554i	−0.126464	−	0.0730139i
$633$	−16.7469	+	9.66882i	−0.665629	+	0.384301i
$634$	−26.8418	+	15.4971i	−1.06603	+	0.615470i
$635$	3.81056	−	3.30277i	0.151217	−	0.131066i
$636$		−	5.89108i		−	0.233596i
$637$	−34.2977	−	15.4821i	−1.35893	−	0.613424i
$638$	−10.0518	−	21.2457i	−0.397954	−	0.841126i
$639$	−4.49713	+	7.78925i	−0.177904	+	0.308138i
$640$	0.423475	+	2.19560i	0.0167393	+	0.0867888i
$641$	−23.7028	−	41.0545i	−0.936205	−	1.62155i	−0.772471	−	0.635050i	$-0.780979\pi$
$641$	−23.7028	−	41.0545i	−0.936205	−	1.62155i	−0.163734	−	0.986505i	$-0.552354\pi$
$642$	1.84831	−	3.20137i	0.0729471	−	0.126348i
$643$	5.84405			0.230467			0.115233	−	0.993338i	$-0.463238\pi$
$643$	5.84405			0.230467			0.115233	+	0.993338i	$0.463238\pi$
$644$	−7.86653	+	5.07988i	−0.309985	+	0.200175i
$645$	−14.6104	−	5.05451i	−0.575285	−	0.199021i
$646$	3.93488	+	2.27180i	0.154816	+	0.0893830i
$647$	14.1916	+	24.5805i	0.557928	+	0.966360i	0.997669	+	0.0682352i	$0.0217368\pi$
$647$	14.1916	+	24.5805i	0.557928	+	0.966360i	−0.439741	+	0.898125i	$0.644930\pi$
$648$	2.85538	+	4.94566i	0.112170	+	0.194284i
$649$	44.3855	+	3.63370i	1.74228	+	0.142635i
$650$	−16.6096	+	21.1326i	−0.651482	+	0.828888i
$651$	−1.35459	−	27.1840i	−0.0530904	−	1.06542i
$652$			14.3207i			0.560844i
$653$	−21.1314	−	12.2002i	−0.826936	−	0.477432i	0.0258665	−	0.999665i	$-0.491766\pi$
$653$	−21.1314	−	12.2002i	−0.826936	−	0.477432i	−0.852802	+	0.522234i	$0.825099\pi$
$654$	2.00078	−	1.15515i	0.0782367	−	0.0451700i
$655$	−7.76538	−	40.2614i	−0.303419	−	1.57314i
$656$	−5.28989	+	9.16236i	−0.206535	+	0.357730i
$657$			4.52300i			0.176459i
$658$	0.626414	−	1.22163i	0.0244202	−	0.0476242i
$659$			13.6753i			0.532716i	0.963874	+	0.266358i	$0.0858203\pi$
$659$			13.6753i			0.532716i	−0.963874	+	0.266358i	$0.914180\pi$
$660$	−4.37827	+	9.94409i	−0.170424	+	0.387073i
$661$	−23.8227	+	13.7540i	−0.926594	+	0.534970i	−0.885733	−	0.464195i	$-0.846344\pi$
$661$	−23.8227	+	13.7540i	−0.926594	+	0.534970i	−0.0408615	+	0.999165i	$0.513010\pi$
$662$	15.8081	+	27.3804i	0.614399	+	1.06417i
$663$	−3.02213	+	5.23449i	−0.117370	+	0.203291i
$664$		−	1.73341i		−	0.0672695i
$665$	−25.2932	+	24.2295i	−0.980827	+	0.939579i
$666$			0.605322i			0.0234557i
$667$	12.5409	−	21.7214i	0.485584	−	0.841056i
$668$	−15.6704	+	9.04731i	−0.606306	+	0.350051i
$669$	1.51892	+	2.63084i	0.0587248	+	0.101714i
$670$	10.3405	+	11.9303i	0.399488	+	0.460908i
$671$	−3.17433	+	1.50184i	−0.122543	+	0.0579779i
$672$	−3.87142	+	0.192914i	−0.149343	+	0.00744180i
$673$	−14.2968			−0.551102			−0.275551	−	0.961286i	$-0.588860\pi$
$673$	−14.2968			−0.551102			−0.275551	+	0.961286i	$0.588860\pi$
$674$	13.4709	−	23.3323i	0.518881	−	0.898728i
$675$	4.00982	−	27.9425i	0.154338	−	1.07551i
$676$	7.94929	+	13.7686i	0.305742	+	0.529561i
$677$	−10.0720	−	5.81508i	−0.387099	−	0.223492i	0.293804	−	0.955866i	$-0.405079\pi$
$677$	−10.0720	−	5.81508i	−0.387099	−	0.223492i	−0.680902	+	0.732374i	$0.738412\pi$
$678$		−	12.4820i		−	0.479368i
$679$	26.0871	+	40.3976i	1.00113	+	1.55032i
$680$	0.561047	−	1.62175i	0.0215152	−	0.0621912i
$681$	−3.40166	−	1.96395i	−0.130352	−	0.0752588i
$682$	13.2510	−	19.1510i	0.507407	−	0.733330i
$683$	−22.1051	+	12.7624i	−0.845826	+	0.488338i	−0.859240	−	0.511572i	$-0.829063\pi$
$683$	−22.1051	+	12.7624i	−0.845826	+	0.488338i	0.0134140	+	0.999910i	$0.495730\pi$
$684$	−2.52674	+	4.37643i	−0.0966121	+	0.167337i
$685$	−2.44286	+	7.06127i	−0.0933369	+	0.269797i
$686$	−6.77022	+	17.2384i	−0.258488	+	0.658167i
$687$			27.4576i			1.04757i
$688$	2.35959	−	4.08693i	0.0899585	−	0.155813i
$689$	10.8080	+	18.7199i	0.411750	+	0.713173i
$690$	−11.3850	+	2.19587i	−0.433419	+	0.0835954i
$691$	−9.11059	−	5.26000i	−0.346583	−	0.200100i	0.316596	−	0.948560i	$-0.397460\pi$
$691$	−9.11059	−	5.26000i	−0.346583	−	0.200100i	−0.663179	+	0.748461i	$0.730793\pi$
$692$		−	8.57440i		−	0.325950i
$693$	6.36377	+	3.94994i	0.241740	+	0.150046i
$694$	−2.53131			−0.0960871
$695$	−23.9435	+	20.7528i	−0.908229	+	0.787200i
$696$	8.99141	−	5.19119i	0.340818	−	0.196772i
$697$	7.03158	−	4.05968i	0.266340	−	0.153772i
$698$	−6.35376	+	11.0050i	−0.240493	+	0.416546i
$699$	10.0347			0.379548
$700$	10.7947	+	7.64691i	0.408000	+	0.289026i
$701$			3.39792i			0.128338i	0.997939	+	0.0641688i	$0.0204396\pi$
$701$			3.39792i			0.128338i	−0.997939	+	0.0641688i	$0.979560\pi$
$702$	−26.2839	−	15.1750i	−0.992023	−	0.572745i
$703$	3.63611	−	2.09931i	0.137139	−	0.0791770i
$704$	−2.72740	−	1.88714i	−0.102793	−	0.0711244i
$705$	1.28455	−	1.11338i	0.0483791	−	0.0419322i
$706$	28.8950			1.08748
$707$	4.47745	−	8.73192i	0.168392	−	0.328398i
$708$			19.6723i			0.739329i
$709$	24.0048	−	41.5775i	0.901519	−	1.56148i	0.0759972	−	0.997108i	$-0.475786\pi$
$709$	24.0048	−	41.5775i	0.901519	−	1.56148i	0.825522	−	0.564370i	$-0.190881\pi$
$710$	−4.46230	−	23.1358i	−0.167467	−	0.868270i
$711$	−2.71369	+	1.56675i	−0.101771	+	0.0587576i
$712$	11.2117	+	6.47308i	0.420176	+	0.242589i
$713$	24.8521			0.930718
$714$	2.64706	+	1.35733i	0.0990638	+	0.0507968i
$715$	−4.33102	−	39.6316i	−0.161971	−	1.48214i
$716$	1.38069	−	2.39143i	0.0515990	−	0.0893721i
$717$	−3.12493	+	1.80418i	−0.116703	+	0.0673784i
$718$	−26.1847	+	15.1177i	−0.977204	+	0.564189i
$719$	−26.4662	−	15.2802i	−0.987021	−	0.569857i	−0.0826387	−	0.996580i	$-0.526335\pi$
$719$	−26.4662	−	15.2802i	−0.987021	−	0.569857i	−0.904383	+	0.426723i	$0.859668\pi$
$720$	1.80373	+	0.624005i	0.0672211	+	0.0232553i
$721$	31.5905	−	1.57416i	1.17649	−	0.0586249i
$722$	16.0518			0.597386
$723$	−11.8554	+	20.5342i	−0.440908	+	0.763675i
$724$	1.36471	−	0.787918i	0.0507192	−	0.0292828i
$725$	−35.0737	−	5.03316i	−1.30260	−	0.186927i
$726$	−5.68064	−	15.0814i	−0.210828	−	0.559724i
$727$	7.61894			0.282571			0.141285	−	0.989969i	$-0.454876\pi$
$727$	7.61894			0.282571			0.141285	+	0.989969i	$0.454876\pi$
$728$	11.9482	−	7.71564i	0.442829	−	0.285961i
$729$	29.6888			1.09958
$730$	−7.76056	−	8.95372i	−0.287231	−	0.331392i
$731$	−3.13648	+	1.81085i	−0.116007	+	0.0669767i
$732$	−0.775617	−	1.34341i	−0.0286676	−	0.0496538i
$733$	9.65693	+	5.57543i	0.356687	+	0.205933i	0.667626	−	0.744496i	$-0.267310\pi$
$733$	9.65693	+	5.57543i	0.356687	+	0.205933i	−0.310940	+	0.950430i	$0.600644\pi$
$734$	7.37480			0.272209
$735$	−15.7498	+	16.6679i	−0.580941	+	0.614806i
$736$		−	3.53932i		−	0.130461i
$737$	−23.3392	−	1.91070i	−0.859709	−	0.0703817i
$738$	4.51524	+	7.82063i	0.166208	+	0.287881i
$739$	−4.10341	+	2.36911i	−0.150947	+	0.0871490i	−0.573571	−	0.819156i	$-0.694442\pi$
$739$	−4.10341	+	2.36911i	−0.150947	+	0.0871490i	0.422624	+	0.906305i	$0.361109\pi$
$740$	−1.03861	−	1.19829i	−0.0381801	−	0.0440502i
$741$			46.6286i			1.71295i
$742$	8.93715	−	5.77124i	0.328093	−	0.211869i
$743$	−9.62941			−0.353269			−0.176634	−	0.984277i	$-0.556521\pi$
$743$	−9.62941			−0.353269			−0.176634	+	0.984277i	$0.556521\pi$
$744$	8.90909	+	5.14367i	0.326623	+	0.188576i
$745$	46.7820	−	9.02305i	1.71396	−	0.330579i
$746$	−0.593341	−	1.02770i	−0.0217237	−	0.0376266i
$747$	−1.28135	−	0.739787i	−0.0468821	−	0.0270674i
$748$	1.08856	+	2.30080i	0.0398016	+	0.0841257i
$749$	6.66741	−	0.332239i	0.243622	−	0.0121397i
$750$	8.86129	+	13.7762i	0.323569	+	0.503034i
$751$	−18.5130	+	32.0655i	−0.675550	+	1.17009i	0.300757	+	0.953701i	$0.402761\pi$
$751$	−18.5130	+	32.0655i	−0.675550	+	1.17009i	−0.976308	+	0.216387i	$0.930573\pi$
$752$	0.259449	+	0.449378i	0.00946112	+	0.0163871i
$753$	12.5032	−	7.21873i	0.455642	−	0.263065i
$754$	−19.0479	+	32.9919i	−0.693682	+	1.20149i
$755$	−8.18950	+	23.6724i	−0.298046	+	0.861525i
$756$	−6.81556	+	13.2917i	−0.247880	+	0.483415i
$757$		−	25.5539i		−	0.928771i	−0.885633	−	0.464385i	$-0.846275\pi$
$757$		−	25.5539i		−	0.928771i	0.885633	−	0.464385i	$-0.153725\pi$
$758$	−15.5782	+	26.9823i	−0.565826	+	0.980040i
$759$	9.78552	−	14.1425i	0.355192	−	0.513341i
$760$	−2.50717	−	12.9990i	−0.0909445	−	0.471522i
$761$	−6.07258	+	10.5180i	−0.220131	+	0.381278i	−0.954848	−	0.297096i	$-0.903982\pi$
$761$	−6.07258	+	10.5180i	−0.220131	+	0.381278i	0.734717	+	0.678374i	$0.237315\pi$
$762$	−3.30397			−0.119690
$763$	3.71252	+	1.90366i	0.134402	+	0.0689171i
$764$	4.52284			0.163631
$765$	−0.959361	−	1.10686i	−0.0346858	−	0.0400186i
$766$	12.0676	+	20.9017i	0.436021	+	0.755211i
$767$	−36.0914	−	62.5121i	−1.30318	−	2.25718i
$768$	0.732537	−	1.26879i	0.0264331	−	0.0457835i
$769$	22.1664			0.799342			0.399671	−	0.916659i	$-0.369124\pi$
$769$	22.1664			0.799342			0.399671	+	0.916659i	$0.369124\pi$
$770$	−19.3750	+	3.09968i	−0.698228	+	0.111705i
$771$	30.7688			1.10811
$772$	0.959084	−	1.66118i	0.0345182	−	0.0597873i
$773$	−8.93100	−	15.4689i	−0.321226	−	0.556379i	0.659516	−	0.751691i	$-0.270761\pi$
$773$	−8.93100	−	15.4689i	−0.321226	−	0.556379i	−0.980741	+	0.195312i	$0.937428\pi$
$774$	−2.01405	−	3.48844i	−0.0723937	−	0.125389i
$775$	−13.0574	−	32.5902i	−0.469034	−	1.17067i
$776$	−18.1758			−0.652471
$777$	2.30927	−	1.49123i	0.0828445	−	0.0534976i
$778$	12.2107			0.437776
$779$	31.3186	−	54.2453i	1.12210	−	1.94354i
$780$	17.2922	−	3.33523i	0.619161	−	0.119420i
$781$	28.7395	+	19.8855i	1.02838	+	0.711557i
$782$	−1.35811	+	2.35232i	−0.0485660	+	0.0841187i
$783$		−	40.0091i		−	1.42981i
$784$	−4.08532	−	5.68420i	−0.145904	−	0.203007i
$785$	34.6894	+	12.0009i	1.23812	+	0.428329i
$786$	−13.4327	+	23.2662i	−0.479129	+	0.829876i
$787$	44.5169	−	25.7018i	1.58686	−	0.916172i	0.593035	−	0.805177i	$-0.297930\pi$
$787$	44.5169	−	25.7018i	1.58686	−	0.916172i	0.993821	−	0.110995i	$-0.0354038\pi$
$788$	1.62984	+	2.82297i	0.0580607	+	0.100564i
$789$	−18.9143	+	32.7606i	−0.673368	+	1.16631i
$790$	2.68379	−	7.75768i	0.0954848	−	0.276006i
$791$	18.9360	−	12.2281i	0.673286	−	0.434780i
$792$	−2.55899	+	1.21071i	−0.0909296	+	0.0430207i
$793$	4.92932	+	2.84594i	0.175045	+	0.101062i
$794$	−5.65530	−	9.79526i	−0.200699	−	0.347621i
$795$	12.9345	−	2.49473i	0.458738	−	0.0884788i
$796$	17.9730	+	10.3767i	0.637036	+	0.367793i
$797$	−40.5056			−1.43478			−0.717392	−	0.696670i	$-0.754664\pi$
$797$	−40.5056			−1.43478			−0.717392	+	0.696670i	$0.754664\pi$
$798$	22.9205	−	1.14214i	0.811379	−	0.0404312i
$799$		−	0.398224i		−	0.0140881i
$800$	−4.64134	+	1.85957i	−0.164096	+	0.0657456i
$801$	9.56987	−	5.52517i	0.338135	−	0.195222i
$802$	−3.34756	−	5.79814i	−0.118206	−	0.204739i
$803$	17.5161	+	1.43399i	0.618130	+	0.0506044i
$804$		−	10.3442i		−	0.364813i
$805$	−14.4847	−	15.1206i	−0.510518	−	0.532930i
$806$	−37.7469			−1.32958
$807$	16.7417	+	9.66581i	0.589335	+	0.340253i
$808$	1.85447	+	3.21204i	0.0652402	+	0.112999i
$809$	32.5781	−	18.8090i	1.14539	−	0.661289i	0.197628	−	0.980277i	$-0.436676\pi$
$809$	32.5781	−	18.8090i	1.14539	−	0.661289i	0.947759	+	0.318988i	$0.103343\pi$
$810$	−9.64951	+	8.36363i	−0.339049	+	0.293868i
$811$	−12.6113			−0.442842			−0.221421	−	0.975178i	$-0.571069\pi$
$811$	−12.6113			−0.442842			−0.221421	+	0.975178i	$0.571069\pi$
$812$	16.6839	+	8.55496i	0.585489	+	0.300220i
$813$	27.5327			0.965613
$814$	2.34422	+	0.191914i	0.0821647	+	0.00672657i
$815$	−31.4427	+	6.06448i	−1.10139	+	0.212430i
$816$	−0.973724	+	0.562180i	−0.0340871	+	0.0196802i
$817$	−13.9698	+	24.1965i	−0.488743	+	0.846528i
$818$	7.69083			0.268903
$819$	−0.604194	−	12.1250i	−0.0211122	−	0.423683i
$820$	−22.3570	−	7.73446i	−0.780741	−	0.270099i
$821$	−11.0075	−	6.35516i	−0.384163	−	0.221797i	0.295465	−	0.955354i	$-0.404525\pi$
$821$	−11.0075	−	6.35516i	−0.384163	−	0.221797i	−0.679628	+	0.733557i	$0.737859\pi$
$822$	4.23970	−	2.44779i	0.147876	−	0.0853765i
$823$	−42.4201	+	24.4912i	−1.47867	+	0.853711i	−0.999709	−	0.0241245i	$-0.992320\pi$
$823$	−42.4201	+	24.4912i	−1.47867	+	0.853711i	−0.478962	+	0.877836i	$0.658987\pi$
$824$	−5.97746	+	10.3533i	−0.208235	+	0.360673i
$825$	−23.6874	−	5.40186i	−0.824688	−	0.188069i
$826$	−29.8441	+	19.2721i	−1.03841	+	0.670562i
$827$	14.1279			0.491274			0.245637	−	0.969362i	$-0.421003\pi$
$827$	14.1279			0.491274			0.245637	+	0.969362i	$0.421003\pi$
$828$	−2.61628	−	1.51051i	−0.0909221	−	0.0524939i
$829$	−9.70852	+	5.60522i	−0.337191	+	0.194677i	−0.659029	−	0.752117i	$-0.729033\pi$
$829$	−9.70852	+	5.60522i	−0.337191	+	0.194677i	0.321838	+	0.946795i	$0.395699\pi$
$830$	3.80589	−	0.734058i	0.132104	−	0.0254795i
$831$	−7.16309	+	12.4068i	−0.248485	+	0.430389i
$832$			5.37574i			0.186370i
$833$	0.534060	+	5.34548i	0.0185041	+	0.185210i
$834$	20.7604			0.718873
$835$	−26.5003	−	30.5747i	−0.917082	−	1.05808i
$836$	16.1474	+	11.1728i	0.558470	+	0.386418i
$837$	34.3317	−	19.8214i	1.18668	−	0.685129i
$838$	−12.8676	−	7.42909i	−0.444503	−	0.256634i
$839$			33.9318i			1.17146i	0.810508	+	0.585728i	$0.199191\pi$
$839$			33.9318i			1.17146i	−0.810508	+	0.585728i	$0.800809\pi$
$840$	−2.06301	−	8.41839i	−0.0711806	−	0.290462i
$841$	−21.2199			−0.731720
$842$	−9.53163	+	16.5093i	−0.328482	+	0.568947i
$843$	−26.7215	+	15.4277i	−0.920337	+	0.531357i
$844$	11.4307	−	6.59954i	0.393463	−	0.227166i
$845$	−26.8640	+	23.2841i	−0.924149	+	0.800998i
$846$	0.442910			0.0152276
$847$	17.3144	−	23.3925i	0.594931	−	0.803777i
$848$			4.02101i			0.138082i
$849$	−30.9440	−	17.8655i	−1.06200	−	0.613143i
$850$	3.79830	+	0.545066i	0.130281	+	0.0186956i
$851$	1.25499	+	2.17371i	0.0430206	+	0.0745139i
$852$	−7.71898	+	13.3697i	−0.264448	+	0.458037i
$853$		−	4.87480i		−	0.166910i	−0.996512	−	0.0834549i	$-0.973405\pi$
$853$		−	4.87480i		−	0.166910i	0.996512	−	0.0834549i	$-0.0265955\pi$
$854$	1.27820	−	2.49274i	0.0437390	−	0.0852999i
$855$	−10.6789	−	3.69439i	−0.365211	−	0.126346i
$856$	−1.26159	+	2.18513i	−0.0431201	+	0.0746862i
$857$	13.5423	−	7.81867i	0.462597	−	0.267081i	−0.250539	−	0.968107i	$-0.580608\pi$
$857$	13.5423	−	7.81867i	0.462597	−	0.267081i	0.713136	+	0.701026i	$0.247274\pi$
$858$	−14.8629	+	21.4806i	−0.507410	+	0.733334i
$859$	1.79847	+	1.03835i	0.0613631	+	0.0354280i	0.530368	−	0.847768i	$-0.322054\pi$
$859$	1.79847	+	1.03835i	0.0613631	+	0.0354280i	−0.469005	+	0.883196i	$0.655387\pi$
$860$	9.97250	+	3.45001i	0.340059	+	0.117644i
$861$	18.7118	−	36.4918i	0.637697	−	1.24364i
$862$		−	14.7775i		−	0.503324i
$863$	−4.05245	−	2.33968i	−0.137947	−	0.0796437i	0.429438	−	0.903096i	$-0.358712\pi$
$863$	−4.05245	−	2.33968i	−0.137947	−	0.0796437i	−0.567385	+	0.823453i	$0.692045\pi$
$864$	−2.82287	−	4.88936i	−0.0960361	−	0.166339i
$865$	18.8260	−	3.63105i	0.640103	−	0.123459i
$866$	−5.56140	+	9.63262i	−0.188984	+	0.327330i
$867$	−24.0434			−0.816555
$868$	0.924585	+	18.5547i	0.0313825	+	0.629788i
$869$	5.20715	+	11.0060i	0.176640	+	0.373352i
$870$	15.2054	+	17.5432i	0.515512	+	0.594771i
$871$	18.9779	+	32.8706i	0.643041	+	1.11378i
$872$	−1.36565	+	0.788460i	−0.0462468	+	0.0267006i
$873$	−7.75706	+	13.4356i	−0.262537	+	0.454727i
$874$			20.9544i			0.708792i
$875$	−12.2183	+	26.9391i	−0.413053	+	0.910707i
$876$			7.76338i			0.262300i
$877$	14.9097	−	25.8244i	0.503466	−	0.872029i	−0.496526	−	0.868022i	$-0.665391\pi$
$877$	14.9097	−	25.8244i	0.503466	−	0.872029i	0.999992	−	0.00400698i	$-0.00127546\pi$
$878$	5.09007	+	8.81626i	0.171781	+	0.297534i
$879$	27.6993	−	15.9922i	0.934274	−	0.539404i
$880$	2.98843	−	6.78744i	0.100740	−	0.228804i
$881$			21.7453i			0.732619i	0.930493	+	0.366310i	$0.119379\pi$
$881$			21.7453i			0.732619i	−0.930493	+	0.366310i	$0.880621\pi$
$882$	−5.94533	+	0.593989i	−0.200190	+	0.0200007i
$883$		−	38.5632i		−	1.29775i	−0.760893	−	0.648877i	$-0.775239\pi$
$883$		−	38.5632i		−	1.29775i	0.760893	−	0.648877i	$-0.224761\pi$
$884$	2.06279	−	3.57285i	0.0693790	−	0.120168i
$885$	−43.1925	+	8.33072i	−1.45190	+	0.280034i
$886$	−30.3841	+	17.5423i	−1.02077	+	0.589345i
$887$	42.4970	+	24.5357i	1.42691	+	0.823827i	0.996876	−	0.0789858i	$-0.0251682\pi$
$887$	42.4970	+	24.5357i	1.42691	+	0.823827i	0.430034	+	0.902813i	$0.358501\pi$
$888$			1.03899i			0.0348662i
$889$	−3.23676	−	5.01233i	−0.108557	−	0.168108i
$890$	−9.46443	+	27.3576i	−0.317248	+	0.917030i
$891$	1.54542	−	18.8773i	0.0517736	−	0.632412i
$892$	−1.03675	−	1.79571i	−0.0347131	−	0.0601248i
$893$	−1.53605	−	2.66052i	−0.0514021	−	0.0890310i
$894$	−27.0343	−	15.6083i	−0.904162	−	0.522018i
$895$	5.83533	+	2.01874i	0.195053	+	0.0674791i
$896$	2.64247	−	0.131675i	0.0882788	−	0.00439896i
$897$	−27.8751			−0.930724
$898$	5.42989	−	9.40484i	0.181198	−	0.313844i
$899$	−24.8800	−	43.0935i	−0.829796	−	1.43725i
$900$	−0.606230	+	4.22453i	−0.0202077	+	0.140818i
$901$	1.54295	−	2.67246i	0.0514031	−	0.0890327i
$902$	31.7183	−	15.0066i	1.05610	−	0.499665i
$903$	−8.34653	+	16.2774i	−0.277755	+	0.541678i
$904$			8.51970i			0.283361i
$905$	2.30788	+	2.66271i	0.0767165	+	0.0885114i
$906$	14.2133	−	8.20603i	0.472204	−	0.272627i
$907$	44.0172	−	25.4134i	1.46157	−	0.843837i	0.462484	−	0.886628i	$-0.346958\pi$
$907$	44.0172	−	25.4134i	1.46157	−	0.843837i	0.999084	+	0.0427912i	$0.0136250\pi$
$908$	2.32184	+	1.34051i	0.0770529	+	0.0444865i
$909$	3.16581			0.105003
$910$	22.0002	+	22.9661i	0.729301	+	0.761318i
$911$	−9.05570			−0.300029			−0.150014	−	0.988684i	$-0.547932\pi$
$911$	−9.05570			−0.300029			−0.150014	+	0.988684i	$0.547932\pi$
$912$	−4.33695	+	7.51182i	−0.143611	+	0.248741i
$913$	−3.27120	+	4.72770i	−0.108261	+	0.156464i
$914$	−10.8625	−	18.8144i	−0.359299	−	0.622323i
$915$	2.62113	−	2.27185i	0.0866520	−	0.0751049i
$916$		−	18.7415i		−	0.619236i
$917$	−48.4557	+	2.41456i	−1.60015	+	0.0797359i
$918$			4.33279i			0.143003i
$919$	51.0816	+	29.4920i	1.68503	+	0.972850i	0.958231	+	0.285994i	$0.0923238\pi$
$919$	51.0816	+	29.4920i	1.68503	+	0.972850i	0.726794	+	0.686856i	$0.241010\pi$
$920$	7.77093	−	1.49881i	0.256200	−	0.0494144i
$921$	11.6711	−	6.73830i	0.384575	−	0.222035i
$922$	−19.6235	+	33.9890i	−0.646267	+	1.11937i
$923$		−	56.6459i		−	1.86452i
$924$	10.9229	+	6.77977i	0.359338	+	0.223038i
$925$	2.19115	−	2.78783i	0.0720446	−	0.0916632i
$926$	−19.8415	−	11.4555i	−0.652032	−	0.376451i
$927$	5.10212	+	8.83714i	0.167576	+	0.290250i
$928$	−6.13717	+	3.54330i	−0.201463	+	0.116314i
$929$	35.4437	+	20.4635i	1.16287	+	0.671384i	0.951991	−	0.306127i	$-0.0990334\pi$
$929$	35.4437	+	20.4635i	1.16287	+	0.671384i	0.210881	+	0.977512i	$0.432367\pi$
$930$	−7.52066	+	21.7390i	−0.246612	+	0.712851i
$931$	24.1870	+	33.6531i	0.792696	+	1.10293i
$932$	−6.84929			−0.224356
$933$	2.17344	+	1.25483i	0.0711551	+	0.0410814i
$934$	3.29578	+	5.70845i	0.107841	+	0.186786i
$935$	−4.59067	+	3.36437i	−0.150131	+	0.110027i
$936$	3.97378	+	2.29426i	0.129887	+	0.0749903i
$937$			48.4254i			1.58199i	0.611823	+	0.790995i	$0.290436\pi$
$937$			48.4254i			1.58199i	−0.611823	+	0.790995i	$0.709564\pi$
$938$	15.6929	−	10.1338i	0.512391	−	0.330881i
$939$	−40.6701			−1.32722
$940$	−0.876786	+	0.759946i	−0.0285976	+	0.0247867i
$941$	−24.5130	−	42.4578i	−0.799101	−	1.38408i	−0.920202	−	0.391443i	$-0.871976\pi$
$941$	−24.5130	−	42.4578i	−0.799101	−	1.38408i	0.121102	−	0.992640i	$-0.461357\pi$
$942$	−12.0251	−	20.8281i	−0.391798	−	0.678615i
$943$	32.4285	+	18.7226i	1.05602	+	0.609692i
$944$		−	13.4275i		−	0.437028i
$945$	−32.0695	−	9.33555i	−1.04322	−	0.303685i
$946$	−14.1482	+	6.69379i	−0.459996	+	0.217634i
$947$	34.9526	+	20.1799i	1.13581	+	0.655759i	0.945389	−	0.325944i	$-0.105682\pi$
$947$	34.9526	+	20.1799i	1.13581	+	0.655759i	0.190419	+	0.981703i	$0.439015\pi$
$948$	−4.65784	+	2.68920i	−0.151280	+	0.0873413i
$949$	−14.2429	−	24.6695i	−0.462346	−	0.800806i
$950$	27.4788	−	11.0095i	0.891531	−	0.357195i
$951$			45.4089i			1.47248i
$952$	−1.80678	−	0.926458i	−0.0585580	−	0.0300267i
$953$	−30.1532			−0.976757			−0.488378	−	0.872632i	$-0.662411\pi$
$953$	−30.1532			−0.976757			−0.488378	+	0.872632i	$0.662411\pi$
$954$	2.97235	+	1.71609i	0.0962335	+	0.0555605i
$955$	1.91531	+	9.93035i	0.0619780	+	0.321339i
$956$	2.13295	−	1.23146i	0.0689846	−	0.0398283i
$957$	−34.3197	−	2.80964i	−1.10940	−	0.0908229i
$958$	−10.4054			−0.336183
$959$	7.86691	+	4.03390i	0.254036	+	0.130261i
$960$	3.09597	+	1.07106i	0.0999220	+	0.0345682i
$961$	9.15227	−	15.8522i	0.295235	−	0.511361i
$962$	−1.90616	−	3.30157i	−0.0614571	−	0.106447i
$963$	1.07684	+	1.86514i	0.0347007	+	0.0601033i
$964$	8.09203	−	14.0158i	0.260627	−	0.451419i
$965$	4.05344	+	1.40230i	0.130485	+	0.0451415i
$966$	0.682783	+	13.7022i	0.0219682	+	0.440860i
$967$	0.368529			0.0118511			0.00592554	−	0.999982i	$-0.498114\pi$
$967$	0.368529			0.0118511			0.00592554	+	0.999982i	$0.498114\pi$
$968$	3.87738	+	10.2940i	0.124624	+	0.330861i
$969$	5.76489	−	3.32836i	0.185195	−	0.106922i
$970$	−7.69698	−	39.9067i	−0.247135	−	1.28133i
$971$	26.9686	+	15.5704i	0.865465	+	0.499676i	0.865838	−	0.500324i	$-0.166786\pi$
$971$	26.9686	+	15.5704i	0.865465	+	0.499676i	−0.000373717		1.00000i	$0.500119\pi$
$972$	−8.57058			−0.274901
$973$	20.3381	+	31.4948i	0.652008	+	1.00968i
$974$		−	13.5503i		−	0.434180i
$975$	14.6457	+	36.5545i	0.469037	+	1.17068i
$976$	0.529405	+	0.916956i	0.0169458	+	0.0293511i
$977$	−14.1713	+	8.18183i	−0.453381	+	0.261760i	−0.709257	−	0.704950i	$-0.750969\pi$
$977$	−14.1713	+	8.18183i	−0.453381	+	0.261760i	0.255876	+	0.966710i	$0.417636\pi$
$978$	18.1700	+	10.4905i	0.581013	+	0.335448i
$979$	−18.3631	−	38.8128i	−0.586888	−	1.24046i
$980$	10.7502	−	11.3769i	0.343403	−	0.363421i
$981$			1.34600i			0.0429744i
$982$	0.783389	+	0.452290i	0.0249989	+	0.0144331i
$983$	6.06297	+	10.5014i	0.193379	+	0.334942i	0.946368	−	0.323091i	$-0.104722\pi$
$983$	6.06297	+	10.5014i	0.193379	+	0.334942i	−0.752989	+	0.658033i	$0.771389\pi$
$984$	7.75007	+	13.4235i	0.247063	+	0.427926i
$985$	−5.50792	+	4.77394i	−0.175497	+	0.152111i
$986$	5.43856			0.173199
$987$	−1.09112	−	1.68968i	−0.0347309	−	0.0537831i
$988$		−	31.8268i		−	1.01255i
$989$	−14.4649	−	8.35134i	−0.459958	−	0.265557i
$990$	−3.74190	−	5.10581i	−0.118926	−	0.162273i
$991$	16.1444	+	27.9629i	0.512843	+	0.888269i	0.999889	+	0.0148934i	$0.00474090\pi$
$991$	16.1444	+	27.9629i	0.512843	+	0.888269i	−0.487046	+	0.873376i	$0.661926\pi$
$992$	−6.08099	−	3.51086i	−0.193072	−	0.111470i
$993$	46.3200			1.46992
$994$	−27.8446	+	1.38750i	−0.883177	+	0.0440089i
$995$	−15.1720	+	43.8558i	−0.480985	+	1.39032i
$996$	−2.19934	−	1.26979i	−0.0696887	−	0.0402348i
$997$	−19.0180	+	10.9800i	−0.602306	+	0.347741i	−0.769948	−	0.638107i	$-0.779718\pi$
$997$	−19.0180	+	10.9800i	−0.602306	+	0.347741i	0.167642	+	0.985848i	$0.446385\pi$
$998$	−0.526196	−	0.911398i	−0.0166564	−	0.0288498i
$999$	3.46740	+	2.00190i	0.109704	+	0.0633374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.439.18	yes	48
5.4	even	2		770.2.o.b.439.7	yes	48
7.3	odd	6	inner	770.2.o.a.549.7	yes	48
11.10	odd	2		770.2.o.b.439.18	yes	48
35.24	odd	6		770.2.o.b.549.18	yes	48
55.54	odd	2	inner	770.2.o.a.439.7	✓	48
77.10	even	6		770.2.o.b.549.7	yes	48
385.164	even	6	inner	770.2.o.a.549.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.7	✓	48	55.54	odd	2	inner
770.2.o.a.439.18	yes	48	1.1	even	1	trivial
770.2.o.a.549.7	yes	48	7.3	odd	6	inner
770.2.o.a.549.18	yes	48	385.164	even	6	inner
770.2.o.b.439.7	yes	48	5.4	even	2
770.2.o.b.439.18	yes	48	11.10	odd	2
770.2.o.b.549.7	yes	48	77.10	even	6
770.2.o.b.549.18	yes	48	35.24	odd	6

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.732537 + 1.26879i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68971 - 1.46454i) q^{5} -1.46507 q^{6} +(-1.43527 - 2.22261i) q^{7} +1.00000 q^{8} +(0.426780 - 0.739205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.732537 + 1.26879i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.68971 - 1.46454i) q^{5} -1.46507 q^{6} +(-1.43527 - 2.22261i) q^{7} +1.00000 q^{8} +(0.426780 - 0.739205i) q^{9} +(0.423475 + 2.19560i) q^{10} +(-2.72740 - 1.88714i) q^{11} +(0.732537 - 1.26879i) q^{12} +5.37574i q^{13} +(2.64247 - 0.131675i) q^{14} +(3.09597 + 1.07106i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.664625 - 0.383721i) q^{17} +(0.426780 + 0.739205i) q^{18} +(2.96023 - 5.12727i) q^{19} +(-2.11318 - 0.731061i) q^{20} +(1.76864 - 3.44920i) q^{21} +(2.99801 - 1.41842i) q^{22} +(3.06514 + 1.76966i) q^{23} +(0.732537 + 1.26879i) q^{24} +(0.710237 - 4.94930i) q^{25} +(-4.65553 - 2.68787i) q^{26} +5.64575 q^{27} +(-1.20720 + 2.35429i) q^{28} -7.08660i q^{29} +(-2.47555 + 2.14566i) q^{30} +(6.08099 - 3.51086i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.396473 - 4.84290i) q^{33} +0.767442i q^{34} +(-5.68030 - 1.65355i) q^{35} -0.853561 q^{36} +(0.614161 + 0.354586i) q^{37} +(2.96023 + 5.12727i) q^{38} +(-6.82069 + 3.93793i) q^{39} +(1.68971 - 1.46454i) q^{40} +10.5798 q^{41} +(2.10278 + 3.25629i) q^{42} -4.71918 q^{43} +(-0.270617 + 3.30557i) q^{44} +(-0.361462 - 1.87408i) q^{45} +(-3.06514 + 1.76966i) q^{46} +(0.259449 - 0.449378i) q^{47} -1.46507 q^{48} +(-2.88000 + 6.38009i) q^{49} +(3.93110 + 3.08973i) q^{50} +(0.973724 + 0.562180i) q^{51} +(4.65553 - 2.68787i) q^{52} +(3.48230 - 2.01051i) q^{53} +(-2.82287 + 4.88936i) q^{54} +(-7.37231 + 0.805660i) q^{55} +(-1.43527 - 2.22261i) q^{56} +8.67390 q^{57} +(6.13717 + 3.54330i) q^{58} +(-11.6286 + 6.71375i) q^{59} +(-0.620422 - 3.21672i) q^{60} +(0.529405 - 0.916956i) q^{61} +7.02172i q^{62} +(-2.25551 + 0.112393i) q^{63} +1.00000 q^{64} +(7.87299 + 9.08344i) q^{65} +(3.99583 + 2.76480i) q^{66} +(6.11463 - 3.53028i) q^{67} +(-0.664625 - 0.383721i) q^{68} +5.18536i q^{69} +(4.27217 - 4.09250i) q^{70} -10.5373 q^{71} +(0.426780 - 0.739205i) q^{72} +(-4.58904 + 2.64949i) q^{73} +(-0.614161 + 0.354586i) q^{74} +(6.79990 - 2.72440i) q^{75} -5.92046 q^{76} +(-0.279836 + 8.77050i) q^{77} -7.87585i q^{78} +(-3.17925 - 1.83554i) q^{79} +(0.423475 + 2.19560i) q^{80} +(2.85538 + 4.94566i) q^{81} +(-5.28989 + 9.16236i) q^{82} -1.73341i q^{83} +(-3.87142 + 0.192914i) q^{84} +(0.561047 - 1.62175i) q^{85} +(2.35959 - 4.08693i) q^{86} +(8.99141 - 5.19119i) q^{87} +(-2.72740 - 1.88714i) q^{88} +(11.2117 + 6.47308i) q^{89} +(1.80373 + 0.624005i) q^{90} +(11.9482 - 7.71564i) q^{91} -3.53932i q^{92} +(8.90909 + 5.14367i) q^{93} +(0.259449 + 0.449378i) q^{94} +(-2.50717 - 12.9990i) q^{95} +(0.732537 - 1.26879i) q^{96} -18.1758 q^{97} +(-4.08532 - 5.68420i) q^{98} +(-2.55899 + 1.21071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

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