LMFDB - Embedded newform 770.2.o.a.439.17

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			439.17
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.730155 + 1.26467i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.672229 - 2.13263i) q^{5} -1.46031 q^{6} +(-1.48697 + 2.18836i) q^{7} +1.00000 q^{8} +(0.433747 - 0.751273i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.730155 + 1.26467i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.672229 - 2.13263i) q^{5} -1.46031 q^{6} +(-1.48697 + 2.18836i) q^{7} +1.00000 q^{8} +(0.433747 - 0.751273i) q^{9} +(2.18303 + 0.484147i) q^{10} +(2.72526 - 1.89023i) q^{11} +(0.730155 - 1.26467i) q^{12} +4.41480i q^{13} +(-1.15169 - 2.38194i) q^{14} +(2.20623 - 2.40729i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.76243 - 3.90429i) q^{17} +(0.433747 + 0.751273i) q^{18} +(-0.986216 + 1.70818i) q^{19} +(-1.51080 + 1.64848i) q^{20} +(-3.85326 - 0.282684i) q^{21} +(0.274354 + 3.30526i) q^{22} +(0.107603 + 0.0621245i) q^{23} +(0.730155 + 1.26467i) q^{24} +(-4.09622 + 2.86723i) q^{25} +(-3.82333 - 2.20740i) q^{26} +5.64774 q^{27} +(2.63866 + 0.193578i) q^{28} +9.04548i q^{29} +(0.981663 + 3.11430i) q^{30} +(2.78401 - 1.60735i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.38037 + 2.06638i) q^{33} +7.80858i q^{34} +(5.66654 + 1.70009i) q^{35} -0.867495 q^{36} +(9.23676 + 5.33284i) q^{37} +(-0.986216 - 1.70818i) q^{38} +(-5.58324 + 3.22349i) q^{39} +(-0.672229 - 2.13263i) q^{40} -4.22292 q^{41} +(2.17144 - 3.19568i) q^{42} +4.97888 q^{43} +(-2.99961 - 1.41503i) q^{44} +(-1.89376 - 0.419995i) q^{45} +(-0.107603 + 0.0621245i) q^{46} +(1.30820 - 2.26586i) q^{47} -1.46031 q^{48} +(-2.57782 - 6.50806i) q^{49} +(-0.434987 - 4.98104i) q^{50} +(9.87525 + 5.70148i) q^{51} +(3.82333 - 2.20740i) q^{52} +(-8.19746 + 4.73280i) q^{53} +(-2.82387 + 4.89109i) q^{54} +(-5.86315 - 4.54131i) q^{55} +(-1.48697 + 2.18836i) q^{56} -2.88036 q^{57} +(-7.83362 - 4.52274i) q^{58} +(8.46792 - 4.88896i) q^{59} +(-3.18789 - 0.707005i) q^{60} +(-0.840243 + 1.45534i) q^{61} +3.21469i q^{62} +(0.999082 + 2.06632i) q^{63} +1.00000 q^{64} +(9.41512 - 2.96775i) q^{65} +(-3.97972 + 2.76032i) q^{66} +(2.21588 - 1.27934i) q^{67} +(-6.76243 - 3.90429i) q^{68} +0.181442i q^{69} +(-4.30559 + 4.05733i) q^{70} +11.5101 q^{71} +(0.433747 - 0.751273i) q^{72} +(-8.48316 + 4.89775i) q^{73} +(-9.23676 + 5.33284i) q^{74} +(-6.61696 - 3.08682i) q^{75} +1.97243 q^{76} +(0.0841024 + 8.77456i) q^{77} -6.44697i q^{78} +(-6.18481 - 3.57080i) q^{79} +(2.18303 + 0.484147i) q^{80} +(2.82248 + 4.88869i) q^{81} +(2.11146 - 3.65716i) q^{82} +3.51357i q^{83} +(1.68182 + 3.47836i) q^{84} +(-12.8723 - 11.7972i) q^{85} +(-2.48944 + 4.31183i) q^{86} +(-11.4395 + 6.60461i) q^{87} +(2.72526 - 1.89023i) q^{88} +(-0.291988 - 0.168580i) q^{89} +(1.31061 - 1.43005i) q^{90} +(-9.66115 - 6.56468i) q^{91} -0.124249i q^{92} +(4.06551 + 2.34722i) q^{93} +(1.30820 + 2.26586i) q^{94} +(4.30587 + 0.954947i) q^{95} +(0.730155 - 1.26467i) q^{96} -12.4310 q^{97} +(6.92506 + 1.02157i) q^{98} +(-0.238001 - 2.86729i) 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
$3$	0.730155	+	1.26467i	0.421555	+	0.730155i	0.996092	−	0.0883239i	$-0.0281511\pi$
$3$	0.730155	+	1.26467i	0.421555	+	0.730155i	−0.574537	+	0.818479i	$0.694818\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.672229	−	2.13263i	−0.300630	−	0.953741i
$5$	−0.672229	−	2.13263i	−0.300630	−	0.953741i
$6$	−1.46031			−0.596169
$7$	−1.48697	+	2.18836i	−0.562023	+	0.827122i
$7$	−1.48697	+	2.18836i	−0.562023	+	0.827122i
$8$	1.00000			0.353553
$9$	0.433747	−	0.751273i	0.144582	−	0.250424i
$10$	2.18303	+	0.484147i	0.690333	+	0.153101i
$11$	2.72526	−	1.89023i	0.821697	−	0.569925i
$11$	2.72526	−	1.89023i	0.821697	−	0.569925i
$12$	0.730155	−	1.26467i	0.210778	−	0.365077i
$13$			4.41480i			1.22444i	0.790686	+	0.612222i	$0.209724\pi$
$13$			4.41480i			1.22444i	−0.790686	+	0.612222i	$0.790276\pi$
$14$	−1.15169	−	2.38194i	−0.307801	−	0.636599i
$15$	2.20623	−	2.40729i	0.569646	−	0.621561i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.76243	−	3.90429i	1.64013	−	0.946930i	0.659345	−	0.751841i	$-0.270834\pi$
$17$	6.76243	−	3.90429i	1.64013	−	0.946930i	0.980786	−	0.195089i	$-0.0624996\pi$
$18$	0.433747	+	0.751273i	0.102235	+	0.177077i
$19$	−0.986216	+	1.70818i	−0.226253	+	0.391882i	−0.956695	−	0.291093i	$-0.905981\pi$
$19$	−0.986216	+	1.70818i	−0.226253	+	0.391882i	0.730441	+	0.682975i	$0.239314\pi$
$20$	−1.51080	+	1.64848i	−0.337824	+	0.368612i
$21$	−3.85326	−	0.282684i	−0.840851	−	0.0616866i
$22$	0.274354	+	3.30526i	0.0584925	+	0.704683i
$23$	0.107603	+	0.0621245i	0.0224367	+	0.0129539i	0.511176	−	0.859476i	$-0.329210\pi$
$23$	0.107603	+	0.0621245i	0.0224367	+	0.0129539i	−0.488740	+	0.872430i	$0.662543\pi$
$24$	0.730155	+	1.26467i	0.149042	+	0.258149i
$25$	−4.09622	+	2.86723i	−0.819243	+	0.573446i
$26$	−3.82333	−	2.20740i	−0.749816	−	0.432906i
$27$	5.64774			1.08691
$28$	2.63866	+	0.193578i	0.498660	+	0.0365828i
$29$			9.04548i			1.67970i	0.542815	+	0.839852i	$0.317358\pi$
$29$			9.04548i			1.67970i	−0.542815	+	0.839852i	$0.682642\pi$
$30$	0.981663	+	3.11430i	0.179226	+	0.568591i
$31$	2.78401	−	1.60735i	0.500022	−	0.288688i	−0.228700	−	0.973497i	$-0.573448\pi$
$31$	2.78401	−	1.60735i	0.500022	−	0.288688i	0.728723	+	0.684809i	$0.240114\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	4.38037	+	2.06638i	0.762524	+	0.359711i
$34$			7.80858i			1.33916i
$35$	5.66654	+	1.70009i	0.957821	+	0.287367i
$36$	−0.867495			−0.144582
$37$	9.23676	+	5.33284i	1.51851	+	0.876714i	0.999763	+	0.0217884i	$0.00693601\pi$
$37$	9.23676	+	5.33284i	1.51851	+	0.876714i	0.518751	+	0.854926i	$0.326397\pi$
$38$	−0.986216	−	1.70818i	−0.159985	−	0.277103i
$39$	−5.58324	+	3.22349i	−0.894034	+	0.516171i
$40$	−0.672229	−	2.13263i	−0.106289	−	0.337198i
$41$	−4.22292			−0.659510			−0.329755	−	0.944067i	$-0.606966\pi$
$41$	−4.22292			−0.659510			−0.329755	+	0.944067i	$0.606966\pi$
$42$	2.17144	−	3.19568i	0.335061	−	0.493104i
$43$	4.97888			0.759272			0.379636	−	0.925136i	$-0.376049\pi$
$43$	4.97888			0.759272			0.379636	+	0.925136i	$0.376049\pi$
$44$	−2.99961	−	1.41503i	−0.452209	−	0.213324i
$45$	−1.89376	−	0.419995i	−0.282306	−	0.0626092i
$46$	−0.107603	+	0.0621245i	−0.0158652	+	0.00915976i
$47$	1.30820	−	2.26586i	0.190820	−	0.330510i	−0.754702	−	0.656068i	$-0.772219\pi$
$47$	1.30820	−	2.26586i	0.190820	−	0.330510i	0.945522	+	0.325557i	$0.105552\pi$
$48$	−1.46031			−0.210778
$49$	−2.57782	−	6.50806i	−0.368260	−	0.929723i
$50$	−0.434987	−	4.98104i	−0.0615165	−	0.704426i
$51$	9.87525	+	5.70148i	1.38281	+	0.798366i
$52$	3.82333	−	2.20740i	0.530200	−	0.306111i
$53$	−8.19746	+	4.73280i	−1.12601	+	0.650101i	−0.942928	−	0.332997i	$-0.891940\pi$
$53$	−8.19746	+	4.73280i	−1.12601	+	0.650101i	−0.183080	+	0.983098i	$0.558607\pi$
$54$	−2.82387	+	4.89109i	−0.384280	+	0.665593i
$55$	−5.86315	−	4.54131i	−0.790587	−	0.612349i
$56$	−1.48697	+	2.18836i	−0.198705	+	0.292432i
$57$	−2.88036			−0.381513
$58$	−7.83362	−	4.52274i	−1.02860	−	0.593865i
$59$	8.46792	−	4.88896i	1.10243	−	0.636488i	0.165572	−	0.986198i	$-0.447053\pi$
$59$	8.46792	−	4.88896i	1.10243	−	0.636488i	0.936858	+	0.349710i	$0.113720\pi$
$60$	−3.18789	−	0.707005i	−0.411555	−	0.0912739i
$61$	−0.840243	+	1.45534i	−0.107582	+	0.186338i	−0.914790	−	0.403929i	$-0.867644\pi$
$61$	−0.840243	+	1.45534i	−0.107582	+	0.186338i	0.807208	+	0.590267i	$0.200978\pi$
$62$			3.21469i			0.408267i
$63$	0.999082	+	2.06632i	0.125873	+	0.260331i
$64$	1.00000			0.125000
$65$	9.41512	−	2.96775i	1.16780	−	0.368105i
$66$	−3.97972	+	2.76032i	−0.489870	+	0.339771i
$67$	2.21588	−	1.27934i	0.270713	−	0.156296i	−0.358499	−	0.933530i	$-0.616711\pi$
$67$	2.21588	−	1.27934i	0.270713	−	0.156296i	0.629211	+	0.777234i	$0.283378\pi$
$68$	−6.76243	−	3.90429i	−0.820065	−	0.473465i
$69$			0.181442i			0.0218431i
$70$	−4.30559	+	4.05733i	−0.514616	+	0.484943i
$71$	11.5101			1.36600			0.682999	−	0.730419i	$-0.260675\pi$
$71$	11.5101			1.36600			0.682999	+	0.730419i	$0.260675\pi$
$72$	0.433747	−	0.751273i	0.0511176	−	0.0885383i
$73$	−8.48316	+	4.89775i	−0.992879	+	0.573239i	−0.906134	−	0.422992i	$-0.860980\pi$
$73$	−8.48316	+	4.89775i	−0.992879	+	0.573239i	−0.0867451	+	0.996231i	$0.527647\pi$
$74$	−9.23676	+	5.33284i	−1.07375	+	0.619930i
$75$	−6.61696	−	3.08682i	−0.764061	−	0.356435i
$76$	1.97243			0.226253
$77$	0.0841024	+	8.77456i	0.00958436	+	0.999954i
$78$		−	6.44697i		−	0.729976i
$79$	−6.18481	−	3.57080i	−0.695846	−	0.401747i	0.109953	−	0.993937i	$-0.464930\pi$
$79$	−6.18481	−	3.57080i	−0.695846	−	0.401747i	−0.805798	+	0.592190i	$0.798263\pi$
$80$	2.18303	+	0.484147i	0.244070	+	0.0541293i
$81$	2.82248	+	4.88869i	0.313609	+	0.543187i
$82$	2.11146	−	3.65716i	0.233172	−	0.403866i
$83$			3.51357i			0.385664i	0.981232	+	0.192832i	$0.0617673\pi$
$83$			3.51357i			0.385664i	−0.981232	+	0.192832i	$0.938233\pi$
$84$	1.68182	+	3.47836i	0.183502	+	0.379521i
$85$	−12.8723	−	11.7972i	−1.39620	−	1.27958i
$86$	−2.48944	+	4.31183i	−0.268443	+	0.464957i
$87$	−11.4395	+	6.60461i	−1.22644	+	0.708088i
$88$	2.72526	−	1.89023i	0.290514	−	0.201499i
$89$	−0.291988	−	0.168580i	−0.0309507	−	0.0178694i	0.484445	−	0.874822i	$-0.339022\pi$
$89$	−0.291988	−	0.168580i	−0.0309507	−	0.0178694i	−0.515396	+	0.856952i	$0.672355\pi$
$90$	1.31061	−	1.43005i	0.138150	−	0.150740i
$91$	−9.66115	−	6.56468i	−1.01276	−	0.688166i
$92$		−	0.124249i		−	0.0129539i
$93$	4.06551	+	2.34722i	0.421574	+	0.243396i
$94$	1.30820	+	2.26586i	0.134930	+	0.233706i
$95$	4.30587	+	0.954947i	0.441773	+	0.0979755i
$96$	0.730155	−	1.26467i	0.0745211	−	0.129074i
$97$	−12.4310			−1.26218			−0.631088	−	0.775711i	$-0.717391\pi$
$97$	−12.4310			−1.26218			−0.631088	+	0.775711i	$0.717391\pi$
$98$	6.92506	+	1.02157i	0.699536	+	0.103194i
$99$	−0.238001	−	2.86729i	−0.0239200	−	0.288174i
$100$	4.53120	+	2.11381i	0.453120	+	0.211381i
$101$	−5.63762	−	9.76465i	−0.560964	−	0.971619i	−0.997413	−	0.0718894i	$-0.977097\pi$
$101$	−5.63762	−	9.76465i	−0.560964	−	0.971619i	0.436448	−	0.899729i	$-0.356236\pi$
$102$	−9.87525	+	5.70148i	−0.977795	+	0.564530i
$103$	4.79161	−	8.29932i	0.472132	−	0.817756i	−0.527360	−	0.849642i	$-0.676818\pi$
$103$	4.79161	−	8.29932i	0.472132	−	0.817756i	0.999492	+	0.0318860i	$0.0101513\pi$
$104$			4.41480i			0.432906i
$105$	1.98742	+	8.40761i	0.193952	+	0.820498i
$106$		−	9.46561i		−	0.919381i
$107$	7.20778	−	12.4842i	0.696802	−	1.20690i	−0.272767	−	0.962080i	$-0.587939\pi$
$107$	7.20778	−	12.4842i	0.696802	−	1.20690i	0.969569	−	0.244817i	$-0.0787278\pi$
$108$	−2.82387	−	4.89109i	−0.271727	−	0.470645i
$109$	1.76313	−	1.01794i	0.168877	−	0.0975014i	−0.413179	−	0.910650i	$-0.635582\pi$
$109$	1.76313	−	1.01794i	0.168877	−	0.0975014i	0.582056	+	0.813148i	$0.302248\pi$
$110$	6.86446	−	2.80699i	0.654501	−	0.267636i
$111$			15.5752i			1.47833i
$112$	−1.15169	−	2.38194i	−0.108824	−	0.225072i
$113$			19.4573i			1.83039i	0.403013	+	0.915194i	$0.367963\pi$
$113$			19.4573i			1.83039i	−0.403013	+	0.915194i	$0.632037\pi$
$114$	1.44018	−	2.49447i	0.134885	−	0.233628i
$115$	0.0601548	−	0.271239i	0.00560947	−	0.0252932i
$116$	7.83362	−	4.52274i	0.727333	−	0.419926i
$117$	3.31672	+	1.91491i	0.306630	+	0.177033i
$118$			9.77792i			0.900130i
$119$	−1.51157	+	20.6042i	−0.138565	+	1.88878i
$120$	2.20623	−	2.40729i	0.201400	−	0.219755i
$121$	3.85409	−	10.3027i	0.350372	−	0.936611i
$122$	−0.840243	−	1.45534i	−0.0760720	−	0.131761i
$123$	−3.08339	−	5.34058i	−0.278020	−	0.481544i
$124$	−2.78401	−	1.60735i	−0.250011	−	0.144344i
$125$	8.86834	+	6.80827i	0.793208	+	0.608951i
$126$	−2.28902	−	0.167928i	−0.203922	−	0.0149602i
$127$	−0.485146			−0.0430497			−0.0215249	−	0.999768i	$-0.506852\pi$
$127$	−0.485146			−0.0430497			−0.0215249	+	0.999768i	$0.506852\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.63535	+	6.29661i	0.320075	+	0.554386i
$130$	−2.13741	+	9.63761i	−0.187463	+	0.845275i
$131$	2.57772	−	4.46474i	0.225216	−	0.390086i	−0.731168	−	0.682197i	$-0.761024\pi$
$131$	2.57772	−	4.46474i	0.225216	−	0.390086i	0.956384	+	0.292111i	$0.0943578\pi$
$132$	−0.400642	−	4.82670i	−0.0348714	−	0.420110i
$133$	−2.27162	−	4.69821i	−0.196975	−	0.407386i
$134$			2.55868i			0.221036i
$135$	−3.79658	−	12.0445i	−0.326757	−	1.03663i
$136$	6.76243	−	3.90429i	0.579874	−	0.334790i
$137$	−8.14857	+	4.70458i	−0.696179	+	0.401939i	−0.805923	−	0.592021i	$-0.798330\pi$
$137$	−8.14857	+	4.70458i	−0.696179	+	0.401939i	0.109744	+	0.993960i	$0.464997\pi$
$138$	−0.157133	−	0.0907211i	−0.0133761	−	0.00772269i
$139$	−14.1545			−1.20057			−0.600284	−	0.799787i	$-0.704946\pi$
$139$	−14.1545			−1.20057			−0.600284	+	0.799787i	$0.704946\pi$
$140$	−1.36095	−	5.75741i	−0.115022	−	0.486590i
$141$	3.82075			0.321765
$142$	−5.75506	+	9.96805i	−0.482954	+	0.836500i
$143$	8.34496	+	12.0315i	0.697841	+	1.00612i
$144$	0.433747	+	0.751273i	0.0361456	+	0.0626061i
$145$	19.2907	−	6.08064i	1.60200	−	0.504970i
$146$		−	9.79551i		−	0.810682i
$147$	6.34831	−	8.01197i	0.523600	−	0.660816i
$148$		−	10.6657i		−	0.876714i
$149$	−1.54892	−	0.894267i	−0.126892	−	0.0732612i	0.435210	−	0.900329i	$-0.356674\pi$
$149$	−1.54892	−	0.894267i	−0.126892	−	0.0732612i	−0.562102	+	0.827068i	$0.690007\pi$
$150$	5.98174	−	4.18705i	0.488407	−	0.341871i
$151$	18.9077	−	10.9164i	1.53869	−	0.888363i	0.539774	−	0.841810i	$-0.318510\pi$
$151$	18.9077	−	10.9164i	1.53869	−	0.888363i	0.998916	−	0.0465532i	$-0.0148237\pi$
$152$	−0.986216	+	1.70818i	−0.0799927	+	0.138551i
$153$		−	6.77391i		−	0.547638i
$154$	−7.64104	−	4.31445i	−0.615733	−	0.347668i
$155$	−5.29937	−	4.85675i	−0.425655	−	0.390103i
$156$	5.58324	+	3.22349i	0.447017	+	0.258085i
$157$	−2.49371	−	4.31924i	−0.199020	−	0.344713i	0.749191	−	0.662354i	$-0.230443\pi$
$157$	−2.49371	−	4.31924i	−0.199020	−	0.344713i	−0.948211	+	0.317641i	$0.897109\pi$
$158$	6.18481	−	3.57080i	0.492037	−	0.284078i
$159$	−11.9708	−	6.91136i	−0.949349	−	0.548107i
$160$	−1.51080	+	1.64848i	−0.119439	+	0.130324i
$161$	−0.295953	+	0.143096i	−0.0233244	+	0.0112775i
$162$	−5.64497			−0.443511
$163$	19.0189	+	10.9806i	1.48968	+	0.860066i	0.999930	−	0.0117980i	$-0.00375549\pi$
$163$	19.0189	+	10.9806i	1.48968	+	0.860066i	0.489748	+	0.871864i	$0.337089\pi$
$164$	2.11146	+	3.65716i	0.164877	+	0.285576i
$165$	1.46222	−	10.7308i	0.113834	−	0.835390i
$166$	−3.04284	−	1.75678i	−0.236170	−	0.136353i
$167$			4.67123i			0.361471i	0.983532	+	0.180735i	$0.0578477\pi$
$167$			4.67123i			0.361471i	−0.983532	+	0.180735i	$0.942152\pi$
$168$	−3.85326	−	0.282684i	−0.297286	−	0.0218095i
$169$	−6.49042			−0.499263
$170$	16.6528	−	5.24916i	1.27721	−	0.402592i
$171$	0.855537	+	1.48183i	0.0654246	+	0.113319i
$172$	−2.48944	−	4.31183i	−0.189818	−	0.328774i
$173$	−0.723732	−	0.417847i	−0.0550243	−	0.0317683i	0.472235	−	0.881472i	$-0.343447\pi$
$173$	−0.723732	−	0.417847i	−0.0550243	−	0.0317683i	−0.527260	+	0.849704i	$0.676781\pi$
$174$		−	13.2092i		−	1.00139i
$175$	−0.183564	−	13.2275i	−0.0138761	−	0.999904i
$176$	0.274354	+	3.30526i	0.0206802	+	0.249143i
$177$	12.3658	+	7.13939i	0.929470	+	0.536630i
$178$	0.291988	−	0.168580i	0.0218855	−	0.0126356i
$179$	−6.99856	−	12.1219i	−0.523097	−	0.906031i	−0.999639	−	0.0268789i	$-0.991443\pi$
$179$	−6.99856	−	12.1219i	−0.523097	−	0.906031i	0.476542	−	0.879152i	$-0.341890\pi$
$180$	0.583155	+	1.85005i	0.0434658	+	0.137894i
$181$		−	16.6154i		−	1.23501i	−0.786565	−	0.617507i	$-0.788143\pi$
$181$		−	16.6154i		−	1.23501i	0.786565	−	0.617507i	$-0.211857\pi$
$182$	10.5158	−	5.08446i	0.779480	−	0.376885i
$183$	−2.45403			−0.181407
$184$	0.107603	+	0.0621245i	0.00793259	+	0.00457988i
$185$	5.16376	−	23.2835i	0.379647	−	1.71183i
$186$	−4.06551	+	2.34722i	−0.298098	+	0.172107i
$187$	11.0494	−	23.4227i	0.808011	−	1.71284i
$188$	−2.61639			−0.190820
$189$	−8.39804	+	12.3593i	−0.610868	+	0.899005i
$190$	−2.97994	+	3.25152i	−0.216188	+	0.235890i
$191$	−0.0981228	+	0.169954i	−0.00709992	+	0.0122974i	−0.869554	−	0.493839i	$-0.835593\pi$
$191$	−0.0981228	+	0.169954i	−0.00709992	+	0.0122974i	0.862454	+	0.506136i	$0.168927\pi$
$192$	0.730155	+	1.26467i	0.0526944	+	0.0912694i
$193$	−11.2573	−	19.4983i	−0.810320	−	1.40352i	−0.912640	−	0.408764i	$-0.865960\pi$
$193$	−11.2573	−	19.4983i	−0.810320	−	1.40352i	0.102320	−	0.994752i	$-0.467373\pi$
$194$	6.21550	−	10.7656i	0.446247	−	0.772922i
$195$	10.6277	+	9.74006i	0.761067	+	0.697500i
$196$	−4.34723	+	5.48649i	−0.310517	+	0.391892i
$197$	−16.4940			−1.17515			−0.587574	−	0.809171i	$-0.699917\pi$
$197$	−16.4940			−1.17515			−0.587574	+	0.809171i	$0.699917\pi$
$198$	2.60215	+	1.22753i	0.184927	+	0.0872369i
$199$	−8.20306	+	4.73604i	−0.581499	+	0.335729i	−0.761729	−	0.647896i	$-0.775649\pi$
$199$	−8.20306	+	4.73604i	−0.581499	+	0.335729i	0.180230	+	0.983625i	$0.442316\pi$
$200$	−4.09622	+	2.86723i	−0.289646	+	0.202744i
$201$	3.23587	+	1.86823i	0.228241	+	0.131775i
$202$	11.2752			0.793323
$203$	−19.7948	−	13.4504i	−1.38932	−	0.944033i
$204$		−	11.4030i		−	0.798366i
$205$	2.83877	+	9.00593i	0.198268	+	0.629001i
$206$	4.79161	+	8.29932i	0.333848	+	0.578241i
$207$	0.0933449	−	0.0538927i	0.00648792	−	0.00374580i
$208$	−3.82333	−	2.20740i	−0.265100	−	0.153056i
$209$	0.541144	+	6.51940i	0.0374317	+	0.450956i
$210$	−8.27491	−	2.48265i	−0.571023	−	0.171319i
$211$		−	3.93203i		−	0.270692i	−0.990798	−	0.135346i	$-0.956785\pi$
$211$		−	3.93203i		−	0.270692i	0.990798	−	0.135346i	$-0.0432146\pi$
$212$	8.19746	+	4.73280i	0.563004	+	0.325050i
$213$	8.40416	+	14.5564i	0.575844	+	0.997391i
$214$	7.20778	+	12.4842i	0.492713	+	0.853405i
$215$	−3.34695	−	10.6181i	−0.228260	−	0.724148i
$216$	5.64774			0.384280
$217$	−0.622293	+	8.48248i	−0.0422440	+	0.575829i
$218$			2.03589i			0.137888i
$219$	−12.3880	−	7.15224i	−0.837106	−	0.483304i
$220$	−1.00131	+	7.34829i	−0.0675083	+	0.495422i
$221$	17.2367	+	29.8548i	1.15946	+	2.00825i
$222$	−13.4885	−	7.78760i	−0.905291	−	0.522670i
$223$	−20.3402			−1.36208			−0.681039	−	0.732247i	$-0.738472\pi$
$223$	−20.3402			−1.36208			−0.681039	+	0.732247i	$0.738472\pi$
$224$	2.63866	+	0.193578i	0.176303	+	0.0129340i
$225$	0.377349	+	4.32103i	0.0251566	+	0.288069i
$226$	−16.8505	−	9.72865i	−1.12088	−	0.647140i
$227$	−6.03141	+	3.48223i	−0.400318	+	0.231124i	−0.686621	−	0.727015i	$-0.740907\pi$
$227$	−6.03141	+	3.48223i	−0.400318	+	0.231124i	0.286303	+	0.958139i	$0.407574\pi$
$228$	1.44018	+	2.49447i	0.0953783	+	0.165200i
$229$	1.17550	+	0.678674i	0.0776790	+	0.0448480i	0.538336	−	0.842730i	$-0.319053\pi$
$229$	1.17550	+	0.678674i	0.0776790	+	0.0448480i	−0.460657	+	0.887578i	$0.652386\pi$
$230$	0.204822	+	0.187715i	0.0135056	+	0.0123776i
$231$	−11.0355	+	6.51315i	−0.726081	+	0.428534i
$232$			9.04548i			0.593865i
$233$	3.52389	−	6.10356i	0.230858	−	0.399858i	−0.727203	−	0.686423i	$-0.759180\pi$
$233$	3.52389	−	6.10356i	0.230858	−	0.399858i	0.958061	+	0.286565i	$0.0925134\pi$
$234$	−3.31672	+	1.91491i	−0.216820	+	0.125181i
$235$	−5.71165	−	1.26672i	−0.372587	−	0.0826317i
$236$	−8.46792	−	4.88896i	−0.551215	−	0.318244i
$237$		−	10.4290i		−	0.677434i
$238$	−17.0880	−	11.6112i	−1.10765	−	0.752639i
$239$			23.5383i			1.52257i	0.648420	+	0.761283i	$0.275430\pi$
$239$			23.5383i			1.52257i	−0.648420	+	0.761283i	$0.724570\pi$
$240$	0.981663	+	3.11430i	0.0633661	+	0.201027i
$241$	−0.598243	−	1.03619i	−0.0385362	−	0.0667466i	0.846114	−	0.533002i	$-0.178936\pi$
$241$	−0.598243	−	1.03619i	−0.0385362	−	0.0667466i	−0.884650	+	0.466255i	$0.845603\pi$
$242$	6.99537	+	8.48910i	0.449680	+	0.545700i
$243$	4.34991	−	7.53427i	0.279047	−	0.483323i
$244$	1.68049			0.107582
$245$	−12.1464	+	9.87244i	−0.776005	+	0.630727i
$246$	6.16678			0.393179
$247$	−7.54125	−	4.35394i	−0.479838	−	0.277035i
$248$	2.78401	−	1.60735i	0.176785	−	0.102067i
$249$	−4.44349	+	2.56545i	−0.281595	+	0.162579i
$250$	−10.3303	+	4.27607i	−0.653346	+	0.270442i
$251$		−	21.4843i		−	1.35608i	−0.735027	−	0.678038i	$-0.762830\pi$
$251$		−	21.4843i		−	1.35608i	0.735027	−	0.678038i	$-0.237170\pi$
$252$	1.28994	−	1.89839i	0.0812587	−	0.119587i
$253$	0.410675	−	0.0340882i	0.0258189	−	0.00214311i
$254$	0.242573	−	0.420148i	0.0152204	−	0.0263625i
$255$	5.52071	−	24.8929i	0.345720	−	1.55886i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.843568	+	1.46110i	−0.0526203	+	0.0911410i	−0.891136	−	0.453737i	$-0.850091\pi$
$257$	−0.843568	+	1.46110i	−0.0526203	+	0.0911410i	0.838515	+	0.544878i	$0.183424\pi$
$258$	−7.27070			−0.452654
$259$	−25.4050	+	12.2835i	−1.57859	+	0.763261i
$260$	−7.27771	−	6.66986i	−0.451345	−	0.413647i
$261$	6.79562	+	3.92346i	0.420639	+	0.242856i
$262$	2.57772	+	4.46474i	0.159252	+	0.275832i
$263$	−0.567151	−	0.982334i	−0.0349720	−	0.0605733i	0.848010	−	0.529981i	$-0.177801\pi$
$263$	−0.567151	−	0.982334i	−0.0349720	−	0.0605733i	−0.882982	+	0.469407i	$0.844468\pi$
$264$	4.38037	+	2.06638i	0.269593	+	0.127177i
$265$	15.6039	+	14.3006i	0.958539	+	0.878480i
$266$	5.20458	+	0.381819i	0.319113	+	0.0234108i
$267$		−	0.492357i		−	0.0301318i
$268$	−2.21588	−	1.27934i	−0.135356	−	0.0781480i
$269$	9.31286	−	5.37678i	0.567815	−	0.327828i	−0.188461	−	0.982081i	$-0.560350\pi$
$269$	9.31286	−	5.37678i	0.567815	−	0.327828i	0.756276	+	0.654252i	$0.227017\pi$
$270$	12.3292	+	2.73434i	0.750329	+	0.166407i
$271$	−6.82810	+	11.8266i	−0.414777	+	0.718415i	−0.995405	−	0.0957538i	$-0.969474\pi$
$271$	−6.82810	+	11.8266i	−0.414777	+	0.718415i	0.580628	+	0.814169i	$0.302807\pi$
$272$			7.80858i			0.473465i
$273$	1.24799	−	17.0114i	0.0755318	−	1.02957i
$274$		−	9.40916i		−	0.568428i
$275$	−5.74354	+	15.5567i	−0.346348	+	0.938106i
$276$	0.157133	−	0.0907211i	0.00945832	−	0.00546077i
$277$	5.57442	+	9.65519i	0.334935	+	0.580124i	0.983472	−	0.181059i	$-0.0579524\pi$
$277$	5.57442	+	9.65519i	0.334935	+	0.580124i	−0.648538	+	0.761183i	$0.724619\pi$
$278$	7.07724	−	12.2581i	0.424465	−	0.735194i
$279$		−	2.78873i		−	0.166957i
$280$	5.66654	+	1.70009i	0.338641	+	0.101600i
$281$		−	7.41203i		−	0.442165i	−0.975255	−	0.221082i	$-0.929041\pi$
$281$		−	7.41203i		−	0.442165i	0.975255	−	0.221082i	$-0.0709590\pi$
$282$	−1.91037	+	3.30886i	−0.113761	+	0.197040i
$283$	−20.1809	+	11.6515i	−1.19963	+	0.692607i	−0.960473	−	0.278373i	$-0.910205\pi$
$283$	−20.1809	+	11.6515i	−1.19963	+	0.692607i	−0.239158	+	0.970981i	$0.576871\pi$
$284$	−5.75506	−	9.96805i	−0.341500	−	0.591495i
$285$	1.93626	+	6.14274i	0.114694	+	0.363865i
$286$	−14.5920	+	1.21122i	−0.862845	+	0.0716207i
$287$	6.27937	−	9.24127i	0.370660	−	0.545495i
$288$	−0.867495			−0.0511176
$289$	21.9870	−	38.0826i	1.29335	−	2.24015i
$290$	−4.37935	+	19.7465i	−0.257164	+	1.15956i
$291$	−9.07655	−	15.7211i	−0.532077	−	0.921584i
$292$	8.48316	+	4.89775i	0.496439	+	0.286619i
$293$		−	9.67275i		−	0.565088i	−0.959254	−	0.282544i	$-0.908822\pi$
$293$		−	9.67275i		−	0.565088i	0.959254	−	0.282544i	$-0.0911783\pi$
$294$	3.76442	+	9.50378i	0.219545	+	0.554272i
$295$	−16.1187	−	14.7724i	−0.938468	−	0.860085i
$296$	9.23676	+	5.33284i	0.536875	+	0.309965i
$297$	15.3916	−	10.6755i	0.893109	−	0.619456i
$298$	1.54892	−	0.894267i	0.0897263	−	0.0518035i
$299$	−0.274267	+	0.475045i	−0.0158613	+	0.0274725i
$300$	0.635216	+	7.27387i	0.0366742	+	0.419957i
$301$	−7.40346	+	10.8956i	−0.426728	+	0.628010i
$302$			21.8328i			1.25634i
$303$	8.23267	−	14.2594i	0.472955	−	0.819182i
$304$	−0.986216	−	1.70818i	−0.0565634	−	0.0979706i
$305$	3.66854	+	0.813602i	0.210060	+	0.0465867i
$306$	5.86637	+	3.38695i	0.335358	+	0.193619i
$307$			7.39236i			0.421905i	0.977496	+	0.210952i	$0.0676565\pi$
$307$			7.39236i			0.421905i	−0.977496	+	0.210952i	$0.932344\pi$
$308$	7.55694	−	4.46012i	0.430597	−	0.254139i
$309$	13.9945			0.796118
$310$	6.85575	−	2.16101i	0.389380	−	0.122737i
$311$	−10.3756	+	5.99037i	−0.588347	+	0.339682i	−0.764444	−	0.644690i	$-0.776986\pi$
$311$	−10.3756	+	5.99037i	−0.588347	+	0.339682i	0.176096	+	0.984373i	$0.443653\pi$
$312$	−5.58324	+	3.22349i	−0.316089	+	0.182494i
$313$	−13.9771	+	24.2091i	−0.790034	+	1.36838i	0.135911	+	0.990721i	$0.456604\pi$
$313$	−13.9771	+	24.2091i	−0.790034	+	1.36838i	−0.925945	+	0.377658i	$0.876729\pi$
$314$	4.98743			0.281457
$315$	3.73508	−	3.51971i	0.210448	−	0.198313i
$316$			7.14161i			0.401747i
$317$	−5.75467	−	3.32246i	−0.323214	−	0.186608i	0.329610	−	0.944117i	$-0.393083\pi$
$317$	−5.75467	−	3.32246i	−0.323214	−	0.186608i	−0.652824	+	0.757509i	$0.726416\pi$
$318$	11.9708	−	6.91136i	0.671291	−	0.387570i
$319$	17.0980	+	24.6513i	0.957305	+	1.38021i
$320$	−0.672229	−	2.13263i	−0.0375788	−	0.119218i
$321$	21.0512			1.17496
$322$	0.0240519	−	0.327851i	0.00134036	−	0.0182704i
$323$			15.4019i			0.856984i
$324$	2.82248	−	4.88869i	0.156805	−	0.271594i
$325$	−12.6582	−	18.0840i	−0.702153	−	1.00312i
$326$	−19.0189	+	10.9806i	−1.05336	+	0.608159i
$327$	2.57472	+	1.48651i	0.142382	+	0.0822044i
$328$	−4.22292			−0.233172
$329$	3.01327	+	6.23208i	0.166127	+	0.343586i
$330$	8.56202	+	6.63171i	0.471324	+	0.365064i
$331$	−4.18329	+	7.24567i	−0.229934	+	0.398258i	−0.957788	−	0.287474i	$-0.907184\pi$
$331$	−4.18329	+	7.24567i	−0.229934	+	0.398258i	0.727854	+	0.685732i	$0.240518\pi$
$332$	3.04284	−	1.75678i	0.166997	−	0.0964160i
$333$	8.01284	−	4.62621i	0.439101	−	0.253515i
$334$	−4.04540	−	2.33561i	−0.221355	−	0.127799i
$335$	−4.21793	−	3.86564i	−0.230450	−	0.211202i
$336$	2.17144	−	3.19568i	0.118462	−	0.174339i
$337$	13.1416			0.715867			0.357933	−	0.933747i	$-0.383481\pi$
$337$	13.1416			0.715867			0.357933	+	0.933747i	$0.383481\pi$
$338$	3.24521	−	5.62087i	0.176516	−	0.305735i
$339$	−24.6070	+	14.2068i	−1.33647	+	0.771610i
$340$	−3.78050	+	17.0463i	−0.205027	+	0.924467i
$341$	4.54889	−	9.64284i	0.246336	−	0.522189i
$342$	−1.71107			−0.0925243
$343$	18.0751	+	4.03612i	0.975964	+	0.217930i
$344$	4.97888			0.268443
$345$	0.386949	−	0.121971i	0.0208326	−	0.00656668i
$346$	0.723732	−	0.417847i	0.0389081	−	0.0224636i
$347$	1.81644	+	3.14616i	0.0975115	+	0.168895i	0.910654	−	0.413170i	$-0.135578\pi$
$347$	1.81644	+	3.14616i	0.0975115	+	0.168895i	−0.813143	+	0.582065i	$0.802245\pi$
$348$	11.4395	+	6.60461i	0.613222	+	0.354044i
$349$	−21.8165			−1.16781			−0.583905	−	0.811822i	$-0.698476\pi$
$349$	−21.8165			−1.16781			−0.583905	+	0.811822i	$0.698476\pi$
$350$	11.5471	+	6.45477i	0.617219	+	0.345022i
$351$			24.9336i			1.33086i
$352$	−2.99961	−	1.41503i	−0.159880	−	0.0754214i
$353$	−1.17432	−	2.03399i	−0.0625030	−	0.108258i	0.833081	−	0.553152i	$-0.186575\pi$
$353$	−1.17432	−	2.03399i	−0.0625030	−	0.108258i	−0.895584	+	0.444893i	$0.853242\pi$
$354$	−12.3658	+	7.13939i	−0.657234	+	0.379454i
$355$	−7.73743	−	24.5468i	−0.410660	−	1.30281i
$356$			0.337159i			0.0178694i
$357$	−27.1611	+	13.1326i	−1.43752	+	0.695052i
$358$	13.9971			0.739771
$359$	21.0487	+	12.1525i	1.11091	+	0.641383i	0.939064	−	0.343742i	$-0.111694\pi$
$359$	21.0487	+	12.1525i	1.11091	+	0.641383i	0.171843	+	0.985124i	$0.445028\pi$
$360$	−1.89376	−	0.419995i	−0.0998101	−	0.0221357i
$361$	7.55476	+	13.0852i	0.397619	+	0.688696i
$362$	14.3894	+	8.30771i	0.756289	+	0.436644i
$363$	15.8436	−	2.64845i	0.831572	−	0.139008i
$364$	−0.854606	+	11.6491i	−0.0447935	+	0.610581i
$365$	16.1477	+	14.7990i	0.845210	+	0.774616i
$366$	1.22701	−	2.12525i	0.0641371	−	0.111089i
$367$	−13.8179	−	23.9333i	−0.721289	−	1.24931i	−0.960483	−	0.278337i	$-0.910217\pi$
$367$	−13.8179	−	23.9333i	−0.721289	−	1.24931i	0.239195	−	0.970972i	$-0.423117\pi$
$368$	−0.107603	+	0.0621245i	−0.00560919	+	0.00323846i
$369$	−1.83168	+	3.17257i	−0.0953536	+	0.165157i
$370$	17.5822	+	16.1137i	0.914055	+	0.837710i
$371$	1.83233	−	24.9765i	0.0951299	−	1.29672i
$372$		−	4.69445i		−	0.243396i
$373$	−3.58546	+	6.21019i	−0.185648	+	0.321552i	−0.943795	−	0.330532i	$-0.892772\pi$
$373$	−3.58546	+	6.21019i	−0.185648	+	0.321552i	0.758147	+	0.652084i	$0.226105\pi$
$374$	14.7600	+	21.2804i	0.763221	+	1.10038i
$375$	−2.13493	+	16.1866i	−0.110247	+	0.835871i
$376$	1.30820	−	2.26586i	0.0674651	−	0.116853i
$377$	−39.9340			−2.05670
$378$	−6.50443	−	13.4526i	−0.334552	−	0.691925i
$379$	−19.0629			−0.979196			−0.489598	−	0.871948i	$-0.662856\pi$
$379$	−19.0629			−0.979196			−0.489598	+	0.871948i	$0.662856\pi$
$380$	−1.32593	−	4.20647i	−0.0680186	−	0.215787i
$381$	−0.354231	−	0.613547i	−0.0181478	−	0.0314330i
$382$	−0.0981228	−	0.169954i	−0.00502040	−	0.00869558i
$383$	−5.40700	+	9.36519i	−0.276285	+	0.478539i	−0.970458	−	0.241268i	$-0.922437\pi$
$383$	−5.40700	+	9.36519i	−0.276285	+	0.478539i	0.694174	+	0.719807i	$0.255770\pi$
$384$	−1.46031			−0.0745211
$385$	18.6564	−	6.07787i	0.950816	−	0.309757i
$386$	22.5147			1.14597
$387$	2.15958	−	3.74049i	0.109777	−	0.190140i
$388$	6.21550	+	10.7656i	0.315544	+	0.546538i
$389$	9.66479	+	16.7399i	0.490024	+	0.848747i	0.999934	−	0.0114811i	$-0.00365461\pi$
$389$	9.66479	+	16.7399i	0.490024	+	0.848747i	−0.509910	+	0.860228i	$0.670321\pi$
$390$	−13.7490	+	4.33384i	−0.696208	+	0.219453i
$391$	0.970209			0.0490656
$392$	−2.57782	−	6.50806i	−0.130200	−	0.328707i
$393$	7.52854			0.379764
$394$	8.24699	−	14.2842i	0.415477	−	0.719628i
$395$	−3.45759	+	15.5903i	−0.173970	+	0.784434i
$396$	−2.36415	+	1.63976i	−0.118803	+	0.0824011i
$397$	−0.274448	+	0.475357i	−0.0137741	+	0.0238575i	−0.872830	−	0.488024i	$-0.837718\pi$
$397$	−0.274448	+	0.475357i	−0.0137741	+	0.0238575i	0.859056	+	0.511881i	$0.171051\pi$
$398$		−	9.47208i		−	0.474792i
$399$	4.28302	−	6.30326i	0.214419	−	0.315558i
$400$	−0.434987	−	4.98104i	−0.0217493	−	0.249052i
$401$	−5.86262	+	10.1544i	−0.292765	+	0.507085i	−0.974463	−	0.224550i	$-0.927909\pi$
$401$	−5.86262	+	10.1544i	−0.292765	+	0.507085i	0.681697	+	0.731634i	$0.261242\pi$
$402$	−3.23587	+	1.86823i	−0.161391	+	0.0931789i
$403$	7.09611	+	12.2908i	0.353482	+	0.612249i
$404$	−5.63762	+	9.76465i	−0.280482	+	0.485809i
$405$	8.52840	−	9.30563i	0.423780	−	0.462400i
$406$	21.5458	−	10.4176i	1.06930	−	0.517015i
$407$	35.2528	−	2.92617i	1.74742	−	0.145045i
$408$	9.87525	+	5.70148i	0.488897	+	0.282265i
$409$	−8.92186	−	15.4531i	−0.441158	−	0.764107i	0.556618	−	0.830769i	$-0.312099\pi$
$409$	−8.92186	−	15.4531i	−0.441158	−	0.764107i	−0.997776	+	0.0666611i	$0.978765\pi$
$410$	−9.21875	−	2.04452i	−0.455282	−	0.100971i
$411$	−11.8994	−	6.87014i	−0.586956	−	0.338879i
$412$	−9.58323			−0.472132
$413$	−1.89279	+	25.8006i	−0.0931380	+	1.26956i
$414$			0.107785i			0.00529736i
$415$	7.49314	−	2.36192i	0.367824	−	0.115942i
$416$	3.82333	−	2.20740i	0.187454	−	0.108227i
$417$	−10.3350	−	17.9007i	−0.506105	−	0.876600i
$418$	−5.91653	−	2.79105i	−0.289387	−	0.136515i
$419$		−	10.8557i		−	0.530336i	−0.964202	−	0.265168i	$-0.914573\pi$
$419$		−	10.8557i		−	0.530336i	0.964202	−	0.265168i	$-0.0854275\pi$
$420$	6.28749	−	5.92496i	0.306798	−	0.289108i
$421$	4.35912			0.212451			0.106225	−	0.994342i	$-0.466124\pi$
$421$	4.35912			0.212451			0.106225	+	0.994342i	$0.466124\pi$
$422$	3.40523	+	1.96601i	0.165764	+	0.0957040i
$423$	−1.13485	−	1.96562i	−0.0551785	−	0.0955719i
$424$	−8.19746	+	4.73280i	−0.398104	+	0.229845i
$425$	−16.5059	+	35.3823i	−0.800652	+	1.71629i
$426$	−16.8083			−0.814366
$427$	−1.93539	−	4.00281i	−0.0936602	−	0.193709i
$428$	−14.4156			−0.696802
$429$	−9.12267	+	19.3384i	−0.440446	+	0.933668i
$430$	10.8690	+	2.41051i	0.524151	+	0.116245i
$431$	−27.8164	+	16.0598i	−1.33987	+	0.773575i	−0.986788	−	0.162018i	$-0.948200\pi$
$431$	−27.8164	+	16.0598i	−1.33987	+	0.773575i	−0.353083	+	0.935592i	$0.614867\pi$
$432$	−2.82387	+	4.89109i	−0.135864	+	0.235323i
$433$	−12.8796			−0.618952			−0.309476	−	0.950907i	$-0.600154\pi$
$433$	−12.8796			−0.618952			−0.309476	+	0.950907i	$0.600154\pi$
$434$	−7.03490	−	4.78016i	−0.337686	−	0.229455i
$435$	21.7751	+	19.9564i	1.04404	+	0.956838i
$436$	−1.76313	−	1.01794i	−0.0844387	−	0.0487507i
$437$	−0.212239	+	0.122536i	−0.0101528	+	0.00586171i
$438$	12.3880	−	7.15224i	0.591923	−	0.341747i
$439$	7.92080	−	13.7192i	0.378039	−	0.654783i	−0.612738	−	0.790286i	$-0.709932\pi$
$439$	7.92080	−	13.7192i	0.378039	−	0.654783i	0.990777	+	0.135503i	$0.0432651\pi$
$440$	−5.86315	−	4.54131i	−0.279515	−	0.216498i
$441$	−6.00745	−	0.886208i	−0.286069	−	0.0422004i
$442$	−34.4733			−1.63973
$443$	−0.732234	−	0.422755i	−0.0347895	−	0.0200857i	0.482504	−	0.875894i	$-0.339727\pi$
$443$	−0.732234	−	0.422755i	−0.0347895	−	0.0200857i	−0.517294	+	0.855808i	$0.673061\pi$
$444$	13.4885	−	7.78760i	0.640137	−	0.369583i
$445$	−0.163235	+	0.736027i	−0.00773807	+	0.0348910i
$446$	10.1701	−	17.6151i	0.481567	−	0.834099i
$447$		−	2.61181i		−	0.123535i
$448$	−1.48697	+	2.18836i	−0.0702529	+	0.103390i
$449$	7.21835			0.340655			0.170328	−	0.985387i	$-0.445517\pi$
$449$	7.21835			0.340655			0.170328	+	0.985387i	$0.445517\pi$
$450$	−3.93080	−	1.83372i	−0.185299	−	0.0864424i
$451$	−11.5086	+	7.98228i	−0.541917	+	0.375871i
$452$	16.8505	−	9.72865i	0.792582	−	0.457597i
$453$	27.6112	+	15.9413i	1.29729	+	0.748988i
$454$		−	6.96447i		−	0.326859i
$455$	−7.50553	+	25.0166i	−0.351865	+	1.17280i
$456$	−2.88036			−0.134885
$457$	−17.2505	+	29.8787i	−0.806944	+	1.39767i	0.108027	+	0.994148i	$0.465547\pi$
$457$	−17.2505	+	29.8787i	−0.806944	+	1.39767i	−0.914971	+	0.403520i	$0.867787\pi$
$458$	−1.17550	+	0.678674i	−0.0549274	+	0.0317123i
$459$	38.1925	−	22.0504i	1.78267	−	1.02923i
$460$	−0.264977	+	0.0835238i	−0.0123546	+	0.00389432i
$461$	3.10550			0.144637			0.0723187	−	0.997382i	$-0.476960\pi$
$461$	3.10550			0.144637			0.0723187	+	0.997382i	$0.476960\pi$
$462$	−0.122816	−	12.8136i	−0.00571390	−	0.596142i
$463$			19.1575i			0.890325i	0.895450	+	0.445162i	$0.146854\pi$
$463$			19.1575i			0.890325i	−0.895450	+	0.445162i	$0.853146\pi$
$464$	−7.83362	−	4.52274i	−0.363667	−	0.209963i
$465$	2.27280	−	10.2481i	0.105399	−	0.475244i
$466$	3.52389	+	6.10356i	0.163241	+	0.282742i
$467$	8.65141	−	14.9847i	0.400339	−	0.693408i	−0.593427	−	0.804888i	$-0.702226\pi$
$467$	8.65141	−	14.9847i	0.400339	−	0.693408i	0.993767	+	0.111479i	$0.0355589\pi$
$468$		−	3.82981i		−	0.177033i
$469$	−0.495303	+	6.75148i	−0.0228710	+	0.311754i
$470$	3.95284	−	4.31308i	0.182331	−	0.198947i
$471$	3.64159	−	6.30743i	0.167796	−	0.290631i
$472$	8.46792	−	4.88896i	0.389768	−	0.225033i
$473$	13.5687	−	9.41121i	0.623891	−	0.432728i
$474$	9.03174	+	5.21448i	0.414842	+	0.239509i
$475$	−0.857982	−	9.82477i	−0.0393669	−	0.450791i
$476$	18.5995	−	8.99304i	0.852509	−	0.412195i
$477$			8.21137i			0.375973i
$478$	−20.3848	−	11.7691i	−0.932377	−	0.538308i
$479$	16.4937	+	28.5680i	0.753618	+	1.30530i	0.946058	+	0.323996i	$0.105026\pi$
$479$	16.4937	+	28.5680i	0.753618	+	1.30530i	−0.192440	+	0.981309i	$0.561640\pi$
$480$	−3.18789	−	0.707005i	−0.145507	−	0.0322702i
$481$	−23.5434	+	40.7784i	−1.07349	+	1.85933i
$482$	1.19649			0.0544984
$483$	−0.397060	−	0.269800i	−0.0180669	−	0.0122763i
$484$	−10.8495	+	1.81362i	−0.493157	+	0.0824373i
$485$	8.35648	+	26.5107i	0.379448	+	1.20379i
$486$	4.34991	+	7.53427i	0.197316	+	0.341761i
$487$	−14.8045	+	8.54738i	−0.670855	+	0.387319i	−0.796401	−	0.604769i	$-0.793265\pi$
$487$	−14.8045	+	8.54738i	−0.670855	+	0.387319i	0.125545	+	0.992088i	$0.459932\pi$
$488$	−0.840243	+	1.45534i	−0.0380360	+	0.0658803i
$489$			32.0701i			1.45026i
$490$	−2.47659	−	15.4553i	−0.111881	−	0.698200i
$491$		−	23.9541i		−	1.08103i	−0.841333	−	0.540517i	$-0.818229\pi$
$491$		−	23.9541i		−	1.08103i	0.841333	−	0.540517i	$-0.181771\pi$
$492$	−3.08339	+	5.34058i	−0.139010	+	0.240772i
$493$	35.3162	+	61.1695i	1.59056	+	2.75493i
$494$	7.54125	−	4.35394i	0.339297	−	0.195893i
$495$	−5.95489	+	2.43505i	−0.267652	+	0.109447i
$496$			3.21469i			0.144344i
$497$	−17.1152	+	25.1882i	−0.767723	+	1.12985i
$498$		−	5.13090i		−	0.229921i
$499$	0.352884	−	0.611212i	0.0157972	−	0.0273616i	−0.858019	−	0.513618i	$-0.828305\pi$
$499$	0.352884	−	0.611212i	0.0157972	−	0.0273616i	0.873816	+	0.486257i	$0.161638\pi$
$500$	1.46197	−	11.0843i	0.0653813	−	0.495707i
$501$	−5.90754	+	3.41072i	−0.263930	+	0.152380i
$502$	18.6059	+	10.7421i	0.830424	+	0.479445i
$503$		−	29.2965i		−	1.30627i	−0.757244	−	0.653133i	$-0.773454\pi$
$503$		−	29.2965i		−	1.30627i	0.757244	−	0.653133i	$-0.226546\pi$
$504$	0.999082	+	2.06632i	0.0445027	+	0.0920411i
$505$	−17.0346	+	18.5870i	−0.758030	+	0.827112i
$506$	−0.175816	+	0.372699i	−0.00781599	+	0.0165685i
$507$	−4.73902	−	8.20822i	−0.210467	−	0.364540i
$508$	0.242573	+	0.420148i	0.0107624	+	0.0186411i
$509$	−35.1771	−	20.3095i	−1.55920	−	0.900202i	−0.997334	−	0.0729710i	$-0.976752\pi$
$509$	−35.1771	−	20.3095i	−1.55920	−	0.900202i	−0.561862	−	0.827231i	$-0.689915\pi$
$510$	18.7976	+	17.2275i	0.832370	+	0.762848i
$511$	1.89619	−	25.8470i	0.0838826	−	1.14340i
$512$	1.00000			0.0441942
$513$	−5.56989	+	9.64734i	−0.245917	+	0.425940i
$514$	−0.843568	−	1.46110i	−0.0372082	−	0.0644465i
$515$	−20.9204	−	4.63969i	−0.921864	−	0.204449i
$516$	3.63535	−	6.29661i	0.160037	−	0.277193i
$517$	−0.717818	−	8.64786i	−0.0315696	−	0.380332i
$518$	2.06464	−	28.1431i	0.0907151	−	1.23654i
$519$		−	1.22037i		−	0.0535684i
$520$	9.41512	−	2.96775i	0.412880	−	0.130145i
$521$	−29.6808	+	17.1362i	−1.30034	+	0.750752i	−0.980462	−	0.196706i	$-0.936975\pi$
$521$	−29.6808	+	17.1362i	−1.30034	+	0.750752i	−0.319879	+	0.947459i	$0.603642\pi$
$522$	−6.79562	+	3.92346i	−0.297436	+	0.171725i
$523$	−32.0175	−	18.4853i	−1.40003	−	0.808306i	−0.405633	−	0.914036i	$-0.632949\pi$
$523$	−32.0175	−	18.4853i	−1.40003	−	0.808306i	−0.994395	+	0.105730i	$0.966282\pi$
$524$	−5.15544			−0.225216
$525$	16.5943	−	9.89026i	0.724235	−	0.431646i
$526$	1.13430			0.0494579
$527$	12.5511	−	21.7391i	0.546735	−	0.946972i
$528$	−3.97972	+	2.76032i	−0.173195	+	0.120127i
$529$	−11.4923	−	19.9052i	−0.499664	−	0.865444i
$530$	−20.1866	+	6.36306i	−0.876851	+	0.276394i
$531$		−	8.48229i		−	0.368100i
$532$	−2.93295	+	4.31639i	−0.127160	+	0.187139i
$533$		−	18.6433i		−	0.807533i
$534$	0.426394	+	0.246178i	0.0184519	+	0.0106532i
$535$	−31.4695	−	6.97925i	−1.36055	−	0.301739i
$536$	2.21588	−	1.27934i	0.0957114	−	0.0552590i
$537$	10.2201	−	17.7017i	0.441029	−	0.763884i
$538$			10.7536i			0.463619i
$539$	−19.3269	−	12.8635i	−0.832470	−	0.554070i
$540$	−8.53259	+	9.31020i	−0.367184	+	0.400647i
$541$	−12.9849	−	7.49681i	−0.558262	−	0.322313i	0.194185	−	0.980965i	$-0.437794\pi$
$541$	−12.9849	−	7.49681i	−0.558262	−	0.322313i	−0.752448	+	0.658652i	$0.771127\pi$
$542$	−6.82810	−	11.8266i	−0.293292	−	0.507996i
$543$	21.0130	−	12.1318i	0.901752	−	0.520627i
$544$	−6.76243	−	3.90429i	−0.289937	−	0.167395i
$545$	−3.35613	−	3.07581i	−0.143761	−	0.131753i
$546$	14.1083	+	9.58647i	0.603779	+	0.410263i
$547$	23.9952			1.02596			0.512980	−	0.858400i	$-0.328541\pi$
$547$	23.9952			1.02596			0.512980	+	0.858400i	$0.328541\pi$
$548$	8.14857	+	4.70458i	0.348090	+	0.200970i
$549$	0.728906	+	1.26250i	0.0311090	+	0.0538823i
$550$	−10.6008	−	12.7524i	−0.452018	−	0.543765i
$551$	−15.4513	−	8.92080i	−0.658247	−	0.380039i
$552$			0.181442i			0.00772269i
$553$	17.0108	−	8.22489i	0.723375	−	0.349758i
$554$	−11.1488			−0.473669
$555$	33.2161	−	10.4701i	1.40995	−	0.444431i
$556$	7.07724	+	12.2581i	0.300142	+	0.519861i
$557$	−9.63488	−	16.6881i	−0.408243	−	0.707097i	0.586450	−	0.809985i	$-0.300525\pi$
$557$	−9.63488	−	16.6881i	−0.408243	−	0.707097i	−0.994693	+	0.102888i	$0.967192\pi$
$558$	2.41511	+	1.39437i	0.102240	+	0.0590282i
$559$			21.9807i			0.929686i
$560$	−4.30559	+	4.05733i	−0.181944	+	0.171453i
$561$	37.6897	−	3.12844i	1.59126	−	0.132083i
$562$	6.41901	+	3.70602i	0.270770	+	0.156329i
$563$	14.0283	−	8.09925i	0.591223	−	0.341343i	−0.174358	−	0.984682i	$-0.555785\pi$
$563$	14.0283	−	8.09925i	0.591223	−	0.341343i	0.765581	+	0.643340i	$0.222452\pi$
$564$	−1.91037	−	3.30886i	−0.0804412	−	0.139328i
$565$	41.4952	−	13.0798i	1.74572	−	0.550270i
$566$		−	23.3029i		−	0.979495i
$567$	−14.8952	−	1.09274i	−0.625538	−	0.0458908i
$568$	11.5101			0.482954
$569$	−35.1269	−	20.2805i	−1.47260	−	0.850205i	−0.473073	−	0.881023i	$-0.656855\pi$
$569$	−35.1269	−	20.2805i	−1.47260	−	0.850205i	−0.999525	+	0.0308185i	$0.990189\pi$
$570$	−6.28790	−	1.39452i	−0.263371	−	0.0584100i
$571$	−12.6019	+	7.27572i	−0.527374	+	0.304480i	−0.739946	−	0.672666i	$-0.765149\pi$
$571$	−12.6019	+	7.27572i	−0.527374	+	0.304480i	0.212572	+	0.977145i	$0.431816\pi$
$572$	6.24708	−	13.2427i	0.261203	−	0.553704i
$573$	−0.286579			−0.0119720
$574$	4.86348	+	10.0587i	0.202998	+	0.419843i
$575$	−0.618890	+	0.0540467i	−0.0258095	+	0.00225390i
$576$	0.433747	−	0.751273i	0.0180728	−	0.0313030i
$577$	6.83296	+	11.8350i	0.284460	+	0.492699i	0.972478	−	0.232995i	$-0.0748524\pi$
$577$	6.83296	+	11.8350i	0.284460	+	0.492699i	−0.688018	+	0.725693i	$0.741519\pi$
$578$	21.9870	+	38.0826i	0.914538	+	1.58403i
$579$	16.4392	−	28.4735i	0.683189	−	1.18332i
$580$	−14.9113	−	13.6659i	−0.619159	−	0.567445i
$581$	−7.68894	−	5.22458i	−0.318991	−	0.216752i
$582$	18.1531			0.752470
$583$	−13.3941	+	28.3932i	−0.554728	+	1.17593i
$584$	−8.48316	+	4.89775i	−0.351036	+	0.202671i
$585$	1.85419	−	8.36058i	0.0766615	−	0.345667i
$586$	8.37685	+	4.83637i	0.346044	+	0.199789i
$587$	12.6270			0.521172			0.260586	−	0.965451i	$-0.416084\pi$
$587$	12.6270			0.521172			0.260586	+	0.965451i	$0.416084\pi$
$588$	−10.1127	−	1.49181i	−0.417042	−	0.0615213i
$589$			6.34076i			0.261267i
$590$	20.8527	−	6.57300i	0.858491	−	0.270606i
$591$	−12.0432	−	20.8594i	−0.495389	−	0.858040i
$592$	−9.23676	+	5.33284i	−0.379628	+	0.219179i
$593$	−0.290961	−	0.167986i	−0.0119483	−	0.00689837i	0.494014	−	0.869454i	$-0.335529\pi$
$593$	−0.290961	−	0.167986i	−0.0119483	−	0.00689837i	−0.505962	+	0.862556i	$0.668863\pi$
$594$	1.54948	+	18.6672i	0.0635759	+	0.765926i
$595$	44.9572	−	10.6271i	1.84307	−	0.435670i
$596$			1.78853i			0.0732612i
$597$	−11.9790	−	6.91608i	−0.490268	−	0.283056i
$598$	−0.274267	−	0.475045i	−0.0112156	−	0.0194260i
$599$	14.8655	+	25.7479i	0.607390	+	1.05203i	0.991669	+	0.128813i	$0.0411167\pi$
$599$	14.8655	+	25.7479i	0.607390	+	1.05203i	−0.384279	+	0.923217i	$0.625550\pi$
$600$	−6.61696	−	3.08682i	−0.270136	−	0.126019i
$601$	15.9038			0.648730			0.324365	−	0.945932i	$-0.394849\pi$
$601$	15.9038			0.648730			0.324365	+	0.945932i	$0.394849\pi$
$602$	−5.73411	−	11.8594i	−0.233705	−	0.483352i
$603$		−	2.21964i		−	0.0903907i
$604$	−18.9077	−	10.9164i	−0.769345	−	0.444182i
$605$	−24.5627	−	1.29355i	−0.998616	−	0.0525904i
$606$	8.23267	+	14.2594i	0.334430	+	0.579249i
$607$	−37.6396	−	21.7312i	−1.52774	−	0.882043i	−0.999456	−	0.0329782i	$-0.989501\pi$
$607$	−37.6396	−	21.7312i	−1.52774	−	0.882043i	−0.528288	−	0.849065i	$-0.677166\pi$
$608$	1.97243			0.0799927
$609$	2.55701	−	34.8546i	0.103615	−	1.41238i
$610$	−2.53887	+	2.77025i	−0.102796	+	0.112164i
$611$	10.0033	+	5.77542i	0.404691	+	0.233649i
$612$	−5.86637	+	3.38695i	−0.237134	+	0.136909i
$613$	0.949984	+	1.64542i	0.0383695	+	0.0664579i	0.884572	−	0.466403i	$-0.154450\pi$
$613$	0.949984	+	1.64542i	0.0383695	+	0.0664579i	−0.846203	+	0.532861i	$0.821117\pi$
$614$	−6.40198	−	3.69618i	−0.258363	−	0.149166i
$615$	−9.31674	+	10.1658i	−0.375687	+	0.409925i
$616$	0.0841024	+	8.77456i	0.00338858	+	0.353537i
$617$			6.35764i			0.255949i	0.991777	+	0.127975i	$0.0408476\pi$
$617$			6.35764i			0.255949i	−0.991777	+	0.127975i	$0.959152\pi$
$618$	−6.99724	+	12.1196i	−0.281470	+	0.487521i
$619$	32.6004	−	18.8218i	1.31032	−	0.756513i	0.328171	−	0.944618i	$-0.393568\pi$
$619$	32.6004	−	18.8218i	1.31032	−	0.756513i	0.982149	+	0.188105i	$0.0602345\pi$
$620$	−1.55639	+	7.01776i	−0.0625059	+	0.281840i
$621$	0.607713	+	0.350863i	0.0243867	+	0.0140797i
$622$		−	11.9807i		−	0.480384i
$623$	0.803092	−	0.388302i	0.0321752	−	0.0155570i
$624$		−	6.44697i		−	0.258085i
$625$	8.55797	−	23.4896i	0.342319	−	0.939584i
$626$	−13.9771	−	24.2091i	−0.558638	−	0.967590i
$627$	−7.84973	+	5.44454i	−0.313488	+	0.217434i
$628$	−2.49371	+	4.31924i	−0.0995100	+	0.172356i
$629$	83.2839			3.32075
$630$	1.18062	+	4.99453i	0.0470371	+	0.198987i
$631$	0.241983			0.00963319			0.00481660	−	0.999988i	$-0.498467\pi$
$631$	0.241983			0.00963319			0.00481660	+	0.999988i	$0.498467\pi$
$632$	−6.18481	−	3.57080i	−0.246019	−	0.142039i
$633$	4.97270	−	2.87099i	0.197647	−	0.114112i
$634$	5.75467	−	3.32246i	0.228547	−	0.131952i
$635$	0.326129	+	1.03464i	0.0129420	+	0.0410583i
$636$			13.8227i			0.548107i
$637$	28.7318	−	11.3806i	1.13839	−	0.450914i
$638$	−29.8977	+	2.48166i	−1.18366	+	0.0982500i
$639$	4.99248	−	8.64723i	0.197499	−	0.342079i
$640$	2.18303	+	0.484147i	0.0862917	+	0.0191376i
$641$	−16.5014	−	28.5813i	−0.651767	−	1.12889i	−0.982694	−	0.185238i	$-0.940694\pi$
$641$	−16.5014	−	28.5813i	−0.651767	−	1.12889i	0.330926	−	0.943657i	$-0.392639\pi$
$642$	−10.5256	+	18.2309i	−0.415412	+	0.719514i
$643$	−45.3998			−1.79039			−0.895196	−	0.445672i	$-0.852965\pi$
$643$	−45.3998			−1.79039			−0.895196	+	0.445672i	$0.852965\pi$
$644$	0.271901	+	0.184755i	0.0107144	+	0.00728037i
$645$	10.9846	−	11.9856i	0.432516	−	0.471934i
$646$	−13.3384	−	7.70095i	−0.524794	−	0.302990i
$647$	−1.37791	−	2.38662i	−0.0541714	−	0.0938276i	0.837668	−	0.546180i	$-0.183918\pi$
$647$	−1.37791	−	2.38662i	−0.0541714	−	0.0938276i	−0.891839	+	0.452352i	$0.850585\pi$
$648$	2.82248	+	4.88869i	0.110878	+	0.192046i
$649$	13.8361	−	29.3300i	0.543113	−	1.15130i
$650$	21.9903	−	1.92038i	0.862530	−	0.0753235i
$651$	−11.1819	+	5.40654i	−0.438252	+	0.211899i
$652$		−	21.9612i		−	0.860066i
$653$	−26.9307	−	15.5484i	−1.05388	−	0.608457i	−0.130146	−	0.991495i	$-0.541545\pi$
$653$	−26.9307	−	15.5484i	−1.05388	−	0.608457i	−0.923733	+	0.383037i	$0.874878\pi$
$654$	−2.57472	+	1.48651i	−0.100679	+	0.0581273i
$655$	−11.2545	−	2.49599i	−0.439748	−	0.0975264i
$656$	2.11146	−	3.65716i	0.0824387	−	0.142788i
$657$			8.49755i			0.331521i
$658$	−6.90377	−	0.506476i	−0.269137	−	0.0197445i
$659$			34.3823i			1.33935i	0.742656	+	0.669673i	$0.233566\pi$
$659$			34.3823i			1.33935i	−0.742656	+	0.669673i	$0.766434\pi$
$660$	−10.0242	+	4.09907i	−0.390193	+	0.159556i
$661$	23.2597	−	13.4290i	0.904697	−	0.522327i	0.0259760	−	0.999663i	$-0.491731\pi$
$661$	23.2597	−	13.4290i	0.904697	−	0.522327i	0.878721	+	0.477335i	$0.158397\pi$
$662$	−4.18329	−	7.24567i	−0.162588	−	0.281611i
$663$	−25.1709	+	43.5972i	−0.977555	+	1.69317i
$664$			3.51357i			0.136353i
$665$	−8.49248	+	8.00280i	−0.329324	+	0.310335i
$666$			9.25243i			0.358524i
$667$	−0.561946	+	0.973320i	−0.0217587	+	0.0376871i
$668$	4.04540	−	2.33561i	0.156521	−	0.0903677i
$669$	−14.8515	−	25.7235i	−0.574191	−	0.994528i
$670$	5.45671	−	1.72002i	0.210811	−	0.0664501i
$671$	0.461048	+	5.55444i	0.0177986	+	0.214427i
$672$	1.68182	+	3.47836i	0.0648776	+	0.134181i
$673$	−8.81771			−0.339898			−0.169949	−	0.985453i	$-0.554360\pi$
$673$	−8.81771			−0.339898			−0.169949	+	0.985453i	$0.554360\pi$
$674$	−6.57078	+	11.3809i	−0.253097	+	0.438377i
$675$	−23.1344	+	16.1934i	−0.890442	+	0.623283i
$676$	3.24521	+	5.62087i	0.124816	+	0.216187i
$677$	−15.2660	−	8.81381i	−0.586719	−	0.338742i	0.177080	−	0.984196i	$-0.443335\pi$
$677$	−15.2660	−	8.81381i	−0.586719	−	0.338742i	−0.763799	+	0.645454i	$0.776668\pi$
$678$		−	28.4137i		−	1.09122i
$679$	18.4846	−	27.2035i	0.709372	−	1.04397i
$680$	−12.8723	−	11.7972i	−0.493631	−	0.452401i
$681$	−8.80772	−	5.08514i	−0.337513	−	0.194863i
$682$	6.07650	+	8.76088i	0.232681	+	0.335471i
$683$	38.5720	−	22.2696i	1.47592	−	0.852121i	0.476286	−	0.879290i	$-0.341983\pi$
$683$	38.5720	−	22.2696i	1.47592	−	0.852121i	0.999631	+	0.0271695i	$0.00864939\pi$
$684$	0.855537	−	1.48183i	0.0327123	−	0.0566593i
$685$	15.5108	+	14.2153i	0.592638	+	0.543139i
$686$	−12.5329	+	13.6354i	−0.478510	+	0.520604i
$687$			1.98215i			0.0756237i
$688$	−2.48944	+	4.31183i	−0.0949090	+	0.164387i
$689$	−20.8944	−	36.1901i	−0.796012	−	1.37873i
$690$	−0.0878447	+	0.396093i	−0.00334419	+	0.0150790i
$691$	15.6928	+	9.06023i	0.596982	+	0.344668i	0.767853	−	0.640626i	$-0.221325\pi$
$691$	15.6928	+	9.06023i	0.596982	+	0.344668i	−0.170872	+	0.985293i	$0.554658\pi$
$692$			0.835694i			0.0317683i
$693$	6.62857	+	3.74276i	0.251798	+	0.142176i
$694$	−3.63287			−0.137902
$695$	9.51506	+	30.1863i	0.360927	+	1.14503i
$696$	−11.4395	+	6.60461i	−0.433614	+	0.250347i
$697$	−28.5572	+	16.4875i	−1.08168	+	0.624509i
$698$	10.9083	−	18.8936i	0.412883	−	0.715135i
$699$	10.2920			0.389278
$700$	−11.3636	+	6.77271i	−0.429502	+	0.255984i
$701$		−	17.2719i		−	0.652351i	−0.945309	−	0.326175i	$-0.894240\pi$
$701$		−	17.2719i		−	0.652351i	0.945309	−	0.326175i	$-0.105760\pi$
$702$	−21.5932	−	12.4668i	−0.814981	−	0.470530i
$703$	−18.2189	+	10.5187i	−0.687138	+	0.396719i
$704$	2.72526	−	1.89023i	0.102712	−	0.0712406i
$705$	−2.56842	−	8.14823i	−0.0967322	−	0.306880i
$706$	2.34865			0.0883925
$707$	29.7515	+	2.18264i	1.11892	+	0.0820865i
$708$		−	14.2788i		−	0.536630i
$709$	−16.3336	+	28.2907i	−0.613423	+	1.06248i	0.377236	+	0.926117i	$0.376874\pi$
$709$	−16.3336	+	28.2907i	−0.613423	+	1.06248i	−0.990659	+	0.136362i	$0.956459\pi$
$710$	25.1269	+	5.57259i	0.942995	+	0.209135i
$711$	−5.36529	+	3.09765i	−0.201214	+	0.116171i
$712$	−0.291988	−	0.168580i	−0.0109427	−	0.00631779i
$713$	0.399423			0.0149585
$714$	2.20736	−	30.0885i	0.0826083	−	1.12603i
$715$	20.0489	−	25.8846i	0.749788	−	0.968030i
$716$	−6.99856	+	12.1219i	−0.261549	+	0.453015i
$717$	−29.7681	+	17.1866i	−1.11171	+	0.641845i
$718$	−21.0487	+	12.1525i	−0.785530	+	0.453526i
$719$	14.6959	+	8.48470i	0.548066	+	0.316426i	0.748341	−	0.663314i	$-0.230850\pi$
$719$	14.6959	+	8.48470i	0.548066	+	0.316426i	−0.200276	+	0.979740i	$0.564184\pi$
$720$	1.31061	−	1.43005i	0.0488435	−	0.0532948i
$721$	11.0369	+	22.8266i	0.411035	+	0.850108i
$722$	−15.1095			−0.562318
$723$	0.873620	−	1.51315i	0.0324903	−	0.0562748i
$724$	−14.3894	+	8.30771i	−0.534777	+	0.308754i
$725$	−25.9355	−	37.0523i	−0.963220	−	1.37609i
$726$	−5.62816	+	15.0452i	−0.208881	+	0.558378i
$727$	27.2181			1.00946			0.504732	−	0.863276i	$-0.331591\pi$
$727$	27.2181			1.00946			0.504732	+	0.863276i	$0.331591\pi$
$728$	−9.66115	−	6.56468i	−0.358066	−	0.243303i
$729$	29.6393			1.09775
$730$	−20.8902	+	6.58483i	−0.773181	+	0.243715i
$731$	33.6693	−	19.4390i	1.24530	−	0.718977i
$732$	1.22701	+	2.12525i	0.0453518	+	0.0785516i
$733$	31.2321	+	18.0319i	1.15358	+	0.666022i	0.949758	−	0.312985i	$-0.101329\pi$
$733$	31.2321	+	18.0319i	1.15358	+	0.666022i	0.203826	+	0.979007i	$0.434662\pi$
$734$	27.6358			1.02006
$735$	−21.3541	−	8.15271i	−0.787657	−	0.300717i
$736$		−	0.124249i		−	0.00457988i
$737$	3.62061	−	7.67504i	0.133367	−	0.282714i
$738$	−1.83168	−	3.17257i	−0.0674251	−	0.116784i
$739$	4.85390	−	2.80240i	0.178554	−	0.103088i	−0.408059	−	0.912955i	$-0.633794\pi$
$739$	4.85390	−	2.80240i	0.178554	−	0.103088i	0.586613	+	0.809867i	$0.300461\pi$
$740$	−22.7460	+	7.16978i	−0.836158	+	0.263567i
$741$		−	12.7162i		−	0.467142i
$742$	20.7141	+	14.0751i	0.760440	+	0.516713i
$743$	−0.213004			−0.00781436			−0.00390718	−	0.999992i	$-0.501244\pi$
$743$	−0.213004			−0.00781436			−0.00390718	+	0.999992i	$0.501244\pi$
$744$	4.06551	+	2.34722i	0.149049	+	0.0860534i
$745$	−0.865913	+	3.90441i	−0.0317246	+	0.143047i
$746$	−3.58546	−	6.21019i	−0.131273	−	0.227371i
$747$	2.63965	+	1.52400i	0.0965796	+	0.0557603i
$748$	−25.8094	+	2.14232i	−0.943684	+	0.0783308i
$749$	16.6022	+	34.3369i	0.606631	+	1.25464i
$750$	−12.9505	−	9.94219i	−0.472886	−	0.363037i
$751$	−19.6331	+	34.0055i	−0.716422	+	1.24088i	0.245987	+	0.969273i	$0.420888\pi$
$751$	−19.6331	+	34.0055i	−0.716422	+	1.24088i	−0.962409	+	0.271606i	$0.912445\pi$
$752$	1.30820	+	2.26586i	0.0477050	+	0.0826275i
$753$	27.1704	−	15.6869i	0.990146	−	0.571661i
$754$	19.9670	−	34.5838i	0.727155	−	1.25947i
$755$	−35.9909	−	32.9849i	−1.30984	−	1.20044i
$756$	14.9025	+	1.09328i	0.541998	+	0.0397621i
$757$		−	0.0600756i		−	0.00218348i	−0.999999	−	0.00109174i	$-0.999652\pi$
$757$		−	0.0600756i		−	0.00218348i	0.999999	−	0.00109174i	$-0.000347512\pi$
$758$	9.53146	−	16.5090i	0.346198	−	0.599633i
$759$	0.342967	+	0.494477i	0.0124489	+	0.0179484i
$760$	4.30587	+	0.954947i	0.156190	+	0.0346396i
$761$	14.3813	−	24.9091i	0.521321	−	0.902954i	−0.478372	−	0.878158i	$-0.658773\pi$
$761$	14.3813	−	24.9091i	0.521321	−	0.902954i	0.999693	−	0.0247969i	$-0.00789390\pi$
$762$	0.708463			0.0256649
$763$	−0.394103	+	5.37202i	−0.0142675	+	0.194480i
$764$	0.196246			0.00709992
$765$	−14.4462	+	4.55362i	−0.522305	+	0.164636i
$766$	−5.40700	−	9.36519i	−0.195363	−	0.338378i
$767$	21.5838	+	37.3842i	0.779344	+	1.34986i
$768$	0.730155	−	1.26467i	0.0263472	−	0.0456347i
$769$	32.0667			1.15635			0.578177	−	0.815911i	$-0.303764\pi$
$769$	32.0667			1.15635			0.578177	+	0.815911i	$0.303764\pi$
$770$	−4.06458	+	19.1958i	−0.146477	+	0.691769i
$771$	−2.46374			−0.0887295
$772$	−11.2573	+	19.4983i	−0.405160	+	0.701758i
$773$	7.96826	+	13.8014i	0.286598	+	0.496403i	0.972996	−	0.230824i	$-0.0741421\pi$
$773$	7.96826	+	13.8014i	0.286598	+	0.496403i	−0.686397	+	0.727227i	$0.740809\pi$
$774$	2.15958	+	3.74049i	0.0776243	+	0.134449i
$775$	−6.79526	+	14.5664i	−0.244093	+	0.523242i
$776$	−12.4310			−0.446247
$777$	−34.0841	−	23.1599i	−1.22276	−	0.830857i
$778$	−19.3296			−0.692999
$779$	4.16471	−	7.21350i	0.149216	−	0.258450i
$780$	3.12128	−	14.0739i	0.111760	−	0.503927i
$781$	31.3680	−	21.7567i	1.12244	−	0.778516i
$782$	−0.485104	+	0.840226i	−0.0173473	+	0.0300464i
$783$			51.0866i			1.82568i
$784$	6.92506	+	1.02157i	0.247323	+	0.0364847i
$785$	−7.53499	+	8.22168i	−0.268935	+	0.293444i
$786$	−3.76427	+	6.51990i	−0.134267	+	0.232557i
$787$	−22.9795	+	13.2672i	−0.819131	+	0.472925i	−0.850117	−	0.526594i	$-0.823469\pi$
$787$	−22.9795	+	13.2672i	−0.819131	+	0.472925i	0.0309858	+	0.999520i	$0.490135\pi$
$788$	8.24699	+	14.2842i	0.293787	+	0.508854i
$789$	0.828216	−	1.43451i	0.0294853	−	0.0510700i
$790$	−11.7728	−	10.7895i	−0.418858	−	0.383874i
$791$	−42.5795	−	28.9325i	−1.51395	−	1.02872i
$792$	−0.238001	−	2.86729i	−0.00845698	−	0.101885i
$793$	−6.42504	−	3.70950i	−0.228160	−	0.131728i
$794$	−0.274448	−	0.475357i	−0.00973978	−	0.0168698i
$795$	−6.69223	+	30.1754i	−0.237349	+	1.07021i
$796$	8.20306	+	4.73604i	0.290750	+	0.167864i
$797$	26.3548			0.933534			0.466767	−	0.884380i	$-0.345419\pi$
$797$	26.3548			0.933534			0.466767	+	0.884380i	$0.345419\pi$
$798$	3.31727	+	6.86084i	0.117430	+	0.242871i
$799$		−	20.4303i		−	0.722773i
$800$	4.53120	+	2.11381i	0.160202	+	0.0747345i
$801$	−0.253298	+	0.146242i	−0.00894986	+	0.00516720i
$802$	−5.86262	−	10.1544i	−0.207016	−	0.358563i
$803$	−13.8610	+	29.3827i	−0.489142	+	1.03689i
$804$		−	3.73646i		−	0.131775i
$805$	0.504119	+	0.534965i	0.0177679	+	0.0188550i
$806$	−14.1922			−0.499900
$807$	13.5997	+	7.85177i	0.478731	+	0.276395i
$808$	−5.63762	−	9.76465i	−0.198331	−	0.343519i
$809$	36.8195	−	21.2577i	1.29450	−	0.747382i	0.315055	−	0.949074i	$-0.397977\pi$
$809$	36.8195	−	21.2577i	1.29450	−	0.747382i	0.979449	+	0.201691i	$0.0646438\pi$
$810$	3.79471	+	12.0386i	0.133333	+	0.422994i
$811$	19.7912			0.694962			0.347481	−	0.937687i	$-0.387037\pi$
$811$	19.7912			0.694962			0.347481	+	0.937687i	$0.387037\pi$
$812$	−1.75100	+	23.8680i	−0.0614482	+	0.837601i
$813$	−19.9423			−0.699406
$814$	−15.0923	+	31.9929i	−0.528984	+	1.12135i
$815$	10.6324	−	47.9418i	0.372438	−	1.67933i
$816$	−9.87525	+	5.70148i	−0.345703	+	0.199592i
$817$	−4.91025	+	8.50480i	−0.171788	+	0.297545i
$818$	17.8437			0.623891
$819$	−9.12237	+	4.41075i	−0.318761	+	0.154124i
$820$	6.37998	−	6.96141i	0.222798	−	0.243103i
$821$	19.9437	+	11.5145i	0.696040	+	0.401859i	0.805871	−	0.592091i	$-0.201697\pi$
$821$	19.9437	+	11.5145i	0.696040	+	0.401859i	−0.109831	+	0.993950i	$0.535031\pi$
$822$	11.8994	−	6.87014i	0.415040	−	0.239624i
$823$	−8.70784	+	5.02747i	−0.303536	+	0.175247i	−0.644030	−	0.765000i	$-0.722739\pi$
$823$	−8.70784	+	5.02747i	−0.303536	+	0.175247i	0.340494	+	0.940247i	$0.389406\pi$
$824$	4.79161	−	8.29932i	0.166924	−	0.289120i
$825$	−23.8677	+	4.09517i	−0.830968	+	0.142575i
$826$	−21.3976	−	14.5395i	−0.744517	−	0.505894i
$827$	19.6991			0.685005			0.342502	−	0.939517i	$-0.388726\pi$
$827$	19.6991			0.685005			0.342502	+	0.939517i	$0.388726\pi$
$828$	−0.0933449	−	0.0538927i	−0.00324396	−	0.00187290i
$829$	48.1861	−	27.8203i	1.67357	−	0.966238i	0.707962	−	0.706250i	$-0.249615\pi$
$829$	48.1861	−	27.8203i	1.67357	−	0.966238i	0.965612	−	0.259988i	$-0.0837186\pi$
$830$	−1.70108	+	7.67021i	−0.0590455	+	0.266237i
$831$	−8.14039	+	14.0996i	−0.282387	+	0.489108i
$832$			4.41480i			0.153056i
$833$	−42.8417	−	33.9457i	−1.48438	−	1.17615i
$834$	20.6699			0.715741
$835$	9.96200	−	3.14014i	0.344749	−	0.108669i
$836$	5.37539	−	3.72834i	0.185912	−	0.128947i
$837$	15.7233	−	9.07788i	0.543478	−	0.313777i
$838$	9.40133	+	5.42786i	0.324763	+	0.187502i
$839$		−	24.2938i		−	0.838715i	−0.907821	−	0.419357i	$-0.862255\pi$
$839$		−	24.2938i		−	0.838715i	0.907821	−	0.419357i	$-0.137745\pi$
$840$	1.98742	+	8.40761i	0.0685724	+	0.290090i
$841$	−52.8208			−1.82141
$842$	−2.17956	+	3.77511i	−0.0751126	+	0.130099i
$843$	9.37374	−	5.41193i	0.322849	−	0.186397i
$844$	−3.40523	+	1.96601i	−0.117213	+	0.0676730i
$845$	4.36305	+	13.8417i	0.150094	+	0.476168i
$846$	2.26971			0.0780342
$847$	16.8151	+	23.7540i	0.577774	+	0.816197i
$848$		−	9.46561i		−	0.325050i
$849$	−29.4704	−	17.0147i	−1.01142	−	0.583944i
$850$	−22.3890	−	31.9856i	−0.767937	−	1.09710i
$851$	0.662601	+	1.14766i	0.0227137	+	0.0393412i
$852$	8.40416	−	14.5564i	0.287922	−	0.498695i
$853$		−	35.3196i		−	1.20932i	−0.796483	−	0.604661i	$-0.793309\pi$
$853$		−	35.3196i		−	1.20932i	0.796483	−	0.604661i	$-0.206691\pi$
$854$	4.43423	+	0.325305i	0.151736	+	0.0111317i
$855$	2.58509	−	2.82068i	0.0884081	−	0.0964651i
$856$	7.20778	−	12.4842i	0.246357	−	0.426702i
$857$	23.6108	−	13.6317i	0.806529	−	0.465650i	−0.0392200	−	0.999231i	$-0.512487\pi$
$857$	23.6108	−	13.6317i	0.806529	−	0.465650i	0.845749	+	0.533581i	$0.179154\pi$
$858$	−12.1862	−	17.5697i	−0.416031	−	0.599819i
$859$	31.6779	+	18.2892i	1.08083	+	0.624020i	0.931122	−	0.364709i	$-0.118832\pi$
$859$	31.6779	+	18.2892i	1.08083	+	0.624020i	0.149713	+	0.988729i	$0.452165\pi$
$860$	−7.52207	+	8.20759i	−0.256500	+	0.279877i
$861$	16.2720	+	1.19375i	0.554549	+	0.0406829i
$862$		−	32.1197i		−	1.09400i
$863$	−26.8185	−	15.4837i	−0.912913	−	0.527071i	−0.0315458	−	0.999502i	$-0.510043\pi$
$863$	−26.8185	−	15.4837i	−0.912913	−	0.527071i	−0.881367	+	0.472432i	$0.843376\pi$
$864$	−2.82387	−	4.89109i	−0.0960700	−	0.166398i
$865$	−0.404599	+	1.82434i	−0.0137568	+	0.0620295i
$866$	6.43978	−	11.1540i	0.218833	−	0.379029i
$867$	64.2156			2.18088
$868$	7.65719	−	3.70232i	0.259902	−	0.125665i
$869$	−23.6049	+	1.95933i	−0.800740	+	0.0664656i
$870$	−28.1704	+	8.87962i	−0.955064	+	0.301047i
$871$	5.64802	+	9.78265i	0.191376	+	0.331473i
$872$	1.76313	−	1.01794i	0.0597072	−	0.0344720i
$873$	−5.39191	+	9.33907i	−0.182489	+	0.316079i
$874$		−	0.245073i		−	0.00828971i
$875$	−28.0859	+	9.28337i	−0.949477	+	0.313835i
$876$			14.3045i			0.483304i
$877$	27.5345	−	47.6912i	0.929775	−	1.61042i	0.146078	−	0.989273i	$-0.453335\pi$
$877$	27.5345	−	47.6912i	0.929775	−	1.61042i	0.783696	−	0.621144i	$-0.213332\pi$
$878$	7.92080	+	13.7192i	0.267314	+	0.463002i
$879$	12.2328	−	7.06261i	0.412602	−	0.238216i
$880$	6.86446	−	2.80699i	0.231401	−	0.0946235i
$881$			4.33964i			0.146206i	0.997324	+	0.0731030i	$0.0232902\pi$
$881$			4.33964i			0.146206i	−0.997324	+	0.0731030i	$0.976710\pi$
$882$	3.77120	−	4.75950i	0.126983	−	0.160261i
$883$		−	3.16186i		−	0.106405i	−0.998584	−	0.0532025i	$-0.983057\pi$
$883$		−	3.16186i		−	0.106405i	0.998584	−	0.0532025i	$-0.0169429\pi$
$884$	17.2367	−	29.8548i	0.579731	−	1.00412i
$885$	6.91303	−	31.1710i	0.232379	−	1.04780i
$886$	0.732234	−	0.422755i	0.0245999	−	0.0142027i
$887$	−8.85625	−	5.11316i	−0.297364	−	0.171683i	0.343894	−	0.939008i	$-0.388254\pi$
$887$	−8.85625	−	5.11316i	−0.297364	−	0.171683i	−0.641258	+	0.767325i	$0.721587\pi$
$888$			15.5752i			0.522670i
$889$	0.721399	−	1.06167i	0.0241949	−	0.0356073i
$890$	−0.555801	−	0.509379i	−0.0186305	−	0.0170744i
$891$	16.9327	+	7.98781i	0.567268	+	0.267602i
$892$	10.1701	+	17.6151i	0.340520	+	0.589797i
$893$	2.58033	+	4.46926i	0.0863474	+	0.149558i
$894$	2.26190	+	1.30591i	0.0756491	+	0.0436761i
$895$	−21.1468	+	23.0740i	−0.706860	+	0.771279i
$896$	−1.15169	−	2.38194i	−0.0384752	−	0.0795749i
$897$	−0.801030			−0.0267456
$898$	−3.60918	+	6.25128i	−0.120440	+	0.208608i
$899$	14.5392	+	25.1827i	0.484911	+	0.839890i
$900$	3.55345	−	2.48731i	0.118448	−	0.0829103i
$901$	−36.9565	+	64.0105i	−1.23120	+	2.13250i
$902$	−1.15858	−	13.9578i	−0.0385763	−	0.464746i
$903$	−19.1849	−	1.40745i	−0.638434	−	0.0468369i
$904$			19.4573i			0.647140i
$905$	−35.4345	+	11.1694i	−1.17788	+	0.371283i
$906$	−27.6112	+	15.9413i	−0.917319	+	0.529615i
$907$	33.2462	−	19.1947i	1.10392	−	0.637349i	0.166673	−	0.986012i	$-0.446698\pi$
$907$	33.2462	−	19.1947i	1.10392	−	0.637349i	0.937248	+	0.348663i	$0.113364\pi$
$908$	6.03141	+	3.48223i	0.200159	+	0.115562i
$909$	−9.78122			−0.324422
$910$	−17.9123	−	19.0083i	−0.593786	−	0.630119i
$911$	19.6487			0.650991			0.325495	−	0.945544i	$-0.394469\pi$
$911$	19.6487			0.650991			0.325495	+	0.945544i	$0.394469\pi$
$912$	1.44018	−	2.49447i	0.0476891	−	0.0826000i
$913$	6.64144	+	9.57539i	0.219800	+	0.316899i
$914$	−17.2505	−	29.8787i	−0.570595	−	0.988300i
$915$	1.64967	+	5.23354i	0.0545364	+	0.173015i
$916$		−	1.35735i		−	0.0448480i
$917$	5.93745	+	12.2799i	0.196072	+	0.405519i
$918$			44.1009i			1.45555i
$919$	−23.2936	−	13.4486i	−0.768385	−	0.443627i	0.0639134	−	0.997955i	$-0.479642\pi$
$919$	−23.2936	−	13.4486i	−0.768385	−	0.443627i	−0.832298	+	0.554328i	$0.812975\pi$
$920$	0.0601548	−	0.271239i	0.00198325	−	0.00894248i
$921$	−9.34887	+	5.39757i	−0.308056	+	0.177856i
$922$	−1.55275	+	2.68944i	−0.0511371	+	0.0885720i
$923$			50.8148i			1.67259i
$924$	11.1583	+	6.30043i	0.367081	+	0.207269i
$925$	−53.1262	+	4.63943i	−1.74678	+	0.152544i
$926$	−16.5909	−	9.57875i	−0.545210	−	0.314777i
$927$	−4.15670	−	7.19962i	−0.136524	−	0.236466i
$928$	7.83362	−	4.52274i	0.257151	−	0.148466i
$929$	27.8727	+	16.0923i	0.914473	+	0.527971i	0.881868	−	0.471497i	$-0.156286\pi$
$929$	27.8727	+	16.0923i	0.914473	+	0.527971i	0.0326053	+	0.999468i	$0.489620\pi$
$930$	7.73872	+	7.09236i	0.253763	+	0.232568i
$931$	13.6592	+	2.01498i	0.447662	+	0.0660383i
$932$	−7.04779			−0.230858
$933$	−15.1516	−	8.74779i	−0.496042	−	0.286390i
$934$	8.65141	+	14.9847i	0.283083	+	0.490314i
$935$	−57.3797	−	7.81881i	−1.87652	−	0.255702i
$936$	3.31672	+	1.91491i	0.108410	+	0.0625907i
$937$			10.9849i			0.358862i	0.983771	+	0.179431i	$0.0574257\pi$
$937$			10.9849i			0.358862i	−0.983771	+	0.179431i	$0.942574\pi$
$938$	−5.59930	−	3.80468i	−0.182824	−	0.124227i
$939$	−40.8219			−1.33217
$940$	1.75882	+	5.57980i	0.0573662	+	0.181993i
$941$	−3.19451	−	5.53306i	−0.104138	−	0.180373i	0.809248	−	0.587468i	$-0.199875\pi$
$941$	−3.19451	−	5.53306i	−0.104138	−	0.180373i	−0.913386	+	0.407095i	$0.866542\pi$
$942$	3.64159	+	6.30743i	0.118650	+	0.205507i
$943$	−0.454398	−	0.262347i	−0.0147972	−	0.00854320i
$944$			9.77792i			0.318244i
$945$	32.0032	+	9.60164i	1.04106	+	0.312341i
$946$	1.36597	+	16.4565i	0.0444117	+	0.535046i
$947$	9.42556	+	5.44185i	0.306289	+	0.176836i	0.645265	−	0.763959i	$-0.276747\pi$
$947$	9.42556	+	5.44185i	0.306289	+	0.176836i	−0.338975	+	0.940795i	$0.610080\pi$
$948$	−9.03174	+	5.21448i	−0.293337	+	0.169358i
$949$	−21.6226	−	37.4514i	−0.701899	−	1.21572i
$950$	8.93749	+	4.16935i	0.289970	+	0.135272i
$951$		−	9.70364i		−	0.314662i
$952$	−1.51157	+	20.6042i	−0.0489902	+	0.667786i
$953$	38.7106			1.25396			0.626979	−	0.779036i	$-0.284291\pi$
$953$	38.7106			1.25396			0.626979	+	0.779036i	$0.284291\pi$
$954$	−7.11125	−	4.10568i	−0.230235	−	0.132926i
$955$	0.428409	+	0.0950117i	0.0138630	+	0.00307451i
$956$	20.3848	−	11.7691i	0.659290	−	0.380641i
$957$	−18.6914	+	39.6225i	−0.604209	+	1.28081i
$958$	−32.9875			−1.06578
$959$	1.82140	−	24.8276i	0.0588162	−	0.801724i
$960$	2.20623	−	2.40729i	0.0712058	−	0.0776951i
$961$	−10.3329	+	17.8971i	−0.333318	+	0.577324i
$962$	−23.5434	−	40.7784i	−0.759070	−	1.31475i
$963$	−6.25271	−	10.8300i	−0.201491	−	0.348992i
$964$	−0.598243	+	1.03619i	−0.0192681	+	0.0333733i
$965$	−34.0151	+	37.1150i	−1.09498	+	1.19477i
$966$	0.432183	−	0.208964i	0.0139053	−	0.00672332i
$967$	−18.1992			−0.585246			−0.292623	−	0.956228i	$-0.594528\pi$
$967$	−18.1992			−0.585246			−0.292623	+	0.956228i	$0.594528\pi$
$968$	3.85409	−	10.3027i	0.123875	−	0.331142i
$969$	−19.4782	+	11.2458i	−0.625731	+	0.361266i
$970$	−27.1372	−	6.01843i	−0.871322	−	0.193240i
$971$	35.2486	+	20.3508i	1.13118	+	0.653088i	0.944232	−	0.329281i	$-0.106806\pi$
$971$	35.2486	+	20.3508i	1.13118	+	0.653088i	0.186950	+	0.982369i	$0.440140\pi$
$972$	−8.69982			−0.279047
$973$	21.0473	−	30.9751i	0.674747	−	0.993015i
$974$		−	17.0948i		−	0.547751i
$975$	13.6277	−	29.2125i	0.436435	−	0.935550i
$976$	−0.840243	−	1.45534i	−0.0268955	−	0.0465844i
$977$	−33.2012	+	19.1687i	−1.06220	+	0.613262i	−0.926040	−	0.377425i	$-0.876810\pi$
$977$	−33.2012	+	19.1687i	−1.06220	+	0.613262i	−0.136161	+	0.990687i	$0.543476\pi$
$978$	−27.7735	−	16.0351i	−0.888100	−	0.512745i
$979$	−1.11440	+	0.0925010i	−0.0356163	+	0.00295634i
$980$	14.6230	+	5.58286i	0.467114	+	0.178338i
$981$		−	1.76612i		−	0.0563880i
$982$	20.7449	+	11.9771i	0.661996	+	0.382204i
$983$	11.6995	+	20.2641i	0.373156	+	0.646325i	0.990049	−	0.140722i	$-0.0449424\pi$
$983$	11.6995	+	20.2641i	0.373156	+	0.646325i	−0.616893	+	0.787047i	$0.711609\pi$
$984$	−3.08339	−	5.34058i	−0.0982948	−	0.170252i
$985$	11.0877	+	35.1755i	0.353285	+	1.12079i
$986$	−70.6324			−2.24939
$987$	−5.68135	+	8.36116i	−0.180839	+	0.266139i
$988$			8.70788i			0.277035i
$989$	0.535741	+	0.309310i	0.0170356	+	0.00983550i
$990$	0.868631	−	6.37460i	0.0276069	−	0.202598i
$991$	19.6635	+	34.0581i	0.624631	+	1.08189i	0.988612	+	0.150486i	$0.0480839\pi$
$991$	19.6635	+	34.0581i	0.624631	+	1.08189i	−0.363981	+	0.931406i	$0.618583\pi$
$992$	−2.78401	−	1.60735i	−0.0883923	−	0.0510333i
$993$	−12.2178			−0.387720
$994$	−13.2560	−	27.4163i	−0.420456	−	0.869594i
$995$	15.6145	+	14.3104i	0.495014	+	0.453670i
$996$	4.44349	+	2.56545i	0.140797	+	0.0812893i
$997$	−14.9230	+	8.61577i	−0.472615	+	0.272864i	−0.717334	−	0.696730i	$-0.754638\pi$
$997$	−14.9230	+	8.61577i	−0.472615	+	0.272864i	0.244719	+	0.969594i	$0.421304\pi$
$998$	0.352884	+	0.611212i	0.0111703	+	0.0193476i
$999$	52.1668	+	30.1185i	1.65048	+	0.952908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.439.17	yes	48
5.4	even	2		770.2.o.b.439.8	yes	48
7.3	odd	6	inner	770.2.o.a.549.8	yes	48
11.10	odd	2		770.2.o.b.439.17	yes	48
35.24	odd	6		770.2.o.b.549.17	yes	48
55.54	odd	2	inner	770.2.o.a.439.8	✓	48
77.10	even	6		770.2.o.b.549.8	yes	48
385.164	even	6	inner	770.2.o.a.549.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.8	✓	48	55.54	odd	2	inner
770.2.o.a.439.17	yes	48	1.1	even	1	trivial
770.2.o.a.549.8	yes	48	7.3	odd	6	inner
770.2.o.a.549.17	yes	48	385.164	even	6	inner
770.2.o.b.439.8	yes	48	5.4	even	2
770.2.o.b.439.17	yes	48	11.10	odd	2
770.2.o.b.549.8	yes	48	77.10	even	6
770.2.o.b.549.17	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.730155 + 1.26467i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.672229 - 2.13263i) q^{5} -1.46031 q^{6} +(-1.48697 + 2.18836i) q^{7} +1.00000 q^{8} +(0.433747 - 0.751273i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.730155 + 1.26467i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.672229 - 2.13263i) q^{5} -1.46031 q^{6} +(-1.48697 + 2.18836i) q^{7} +1.00000 q^{8} +(0.433747 - 0.751273i) q^{9} +(2.18303 + 0.484147i) q^{10} +(2.72526 - 1.89023i) q^{11} +(0.730155 - 1.26467i) q^{12} +4.41480i q^{13} +(-1.15169 - 2.38194i) q^{14} +(2.20623 - 2.40729i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.76243 - 3.90429i) q^{17} +(0.433747 + 0.751273i) q^{18} +(-0.986216 + 1.70818i) q^{19} +(-1.51080 + 1.64848i) q^{20} +(-3.85326 - 0.282684i) q^{21} +(0.274354 + 3.30526i) q^{22} +(0.107603 + 0.0621245i) q^{23} +(0.730155 + 1.26467i) q^{24} +(-4.09622 + 2.86723i) q^{25} +(-3.82333 - 2.20740i) q^{26} +5.64774 q^{27} +(2.63866 + 0.193578i) q^{28} +9.04548i q^{29} +(0.981663 + 3.11430i) q^{30} +(2.78401 - 1.60735i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(4.38037 + 2.06638i) q^{33} +7.80858i q^{34} +(5.66654 + 1.70009i) q^{35} -0.867495 q^{36} +(9.23676 + 5.33284i) q^{37} +(-0.986216 - 1.70818i) q^{38} +(-5.58324 + 3.22349i) q^{39} +(-0.672229 - 2.13263i) q^{40} -4.22292 q^{41} +(2.17144 - 3.19568i) q^{42} +4.97888 q^{43} +(-2.99961 - 1.41503i) q^{44} +(-1.89376 - 0.419995i) q^{45} +(-0.107603 + 0.0621245i) q^{46} +(1.30820 - 2.26586i) q^{47} -1.46031 q^{48} +(-2.57782 - 6.50806i) q^{49} +(-0.434987 - 4.98104i) q^{50} +(9.87525 + 5.70148i) q^{51} +(3.82333 - 2.20740i) q^{52} +(-8.19746 + 4.73280i) q^{53} +(-2.82387 + 4.89109i) q^{54} +(-5.86315 - 4.54131i) q^{55} +(-1.48697 + 2.18836i) q^{56} -2.88036 q^{57} +(-7.83362 - 4.52274i) q^{58} +(8.46792 - 4.88896i) q^{59} +(-3.18789 - 0.707005i) q^{60} +(-0.840243 + 1.45534i) q^{61} +3.21469i q^{62} +(0.999082 + 2.06632i) q^{63} +1.00000 q^{64} +(9.41512 - 2.96775i) q^{65} +(-3.97972 + 2.76032i) q^{66} +(2.21588 - 1.27934i) q^{67} +(-6.76243 - 3.90429i) q^{68} +0.181442i q^{69} +(-4.30559 + 4.05733i) q^{70} +11.5101 q^{71} +(0.433747 - 0.751273i) q^{72} +(-8.48316 + 4.89775i) q^{73} +(-9.23676 + 5.33284i) q^{74} +(-6.61696 - 3.08682i) q^{75} +1.97243 q^{76} +(0.0841024 + 8.77456i) q^{77} -6.44697i q^{78} +(-6.18481 - 3.57080i) q^{79} +(2.18303 + 0.484147i) q^{80} +(2.82248 + 4.88869i) q^{81} +(2.11146 - 3.65716i) q^{82} +3.51357i q^{83} +(1.68182 + 3.47836i) q^{84} +(-12.8723 - 11.7972i) q^{85} +(-2.48944 + 4.31183i) q^{86} +(-11.4395 + 6.60461i) q^{87} +(2.72526 - 1.89023i) q^{88} +(-0.291988 - 0.168580i) q^{89} +(1.31061 - 1.43005i) q^{90} +(-9.66115 - 6.56468i) q^{91} -0.124249i q^{92} +(4.06551 + 2.34722i) q^{93} +(1.30820 + 2.26586i) q^{94} +(4.30587 + 0.954947i) q^{95} +(0.730155 - 1.26467i) q^{96} -12.4310 q^{97} +(6.92506 + 1.02157i) q^{98} +(-0.238001 - 2.86729i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more