LMFDB - Embedded newform 418.2.n.d.159.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			159.4
Character	$\chi$	$=$	418.159
Dual form			418.2.n.d.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(0.0789616 - 0.751269i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(4.07114 - 0.865348i) q^{5} +(0.505466 + 0.561377i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37627 + 0.505092i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(0.0789616 - 0.751269i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(4.07114 - 0.865348i) q^{5} +(0.505466 + 0.561377i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37627 + 0.505092i) q^{9} +(-2.08105 + 3.60448i) q^{10} +(-2.71302 - 1.90776i) q^{11} -0.755407 q^{12} +(-5.22365 - 1.11032i) q^{13} +(-0.232129 + 2.20856i) q^{14} +(-0.328646 - 3.12685i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(3.02460 - 0.642899i) q^{17} +(-1.96539 + 1.42794i) q^{18} +(-4.29394 + 0.749698i) q^{19} +(-1.28616 - 3.95839i) q^{20} +(-0.838775 - 1.45280i) q^{21} +(3.23310 - 0.739626i) q^{22} +(-3.27816 + 5.67793i) q^{23} +(0.505466 - 0.561377i) q^{24} +(11.2577 - 5.01223i) q^{25} +(4.32043 - 3.13898i) q^{26} +(1.26740 - 3.90064i) q^{27} +(-1.48595 - 1.65032i) q^{28} +(-0.498341 - 4.74139i) q^{29} +(2.54361 + 1.84804i) q^{30} +(2.93603 + 9.03617i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.64746 + 1.88757i) q^{33} +(-1.54609 + 2.67790i) q^{34} +(6.18468 - 6.86878i) q^{35} +(0.253937 - 2.41605i) q^{36} +(1.55807 - 1.13201i) q^{37} +(2.31608 - 3.69267i) q^{38} +(-1.24662 + 3.83669i) q^{39} +(3.80226 + 1.69288i) q^{40} +(-0.606770 + 5.77303i) q^{41} +(1.64089 + 0.348782i) q^{42} +(0.172924 + 0.299514i) q^{43} +(-1.61372 + 2.89757i) q^{44} +10.1112 q^{45} +(-2.02601 - 6.23542i) q^{46} +(1.97362 - 0.878714i) q^{47} +(0.0789616 + 0.751269i) q^{48} +(-0.639168 + 1.96716i) q^{49} +(-3.80803 + 11.7199i) q^{50} +(-0.244163 - 2.32305i) q^{51} +(-0.558218 + 5.31109i) q^{52} +(3.46365 + 0.736222i) q^{53} +(2.05069 + 3.55190i) q^{54} +(-12.6960 - 5.41905i) q^{55} +2.22072 q^{56} +(0.224168 + 3.28510i) q^{57} +(3.85700 + 2.80227i) q^{58} +(-6.14881 - 2.73763i) q^{59} +(-3.07537 + 0.653690i) q^{60} +(-0.997391 - 1.10772i) q^{61} +(-8.67977 - 3.86448i) q^{62} +(4.92852 - 2.19432i) q^{63} +(0.309017 + 0.951057i) q^{64} -22.2270 q^{65} +(-0.300367 - 2.48733i) q^{66} +(-0.202754 + 0.351181i) q^{67} +(-0.955534 - 2.94083i) q^{68} +(4.00681 + 2.91111i) q^{69} +(0.966142 + 9.19223i) q^{70} +(-2.84814 + 0.605392i) q^{71} +(1.62556 + 1.80537i) q^{72} +(12.0191 + 5.35126i) q^{73} +(-0.201310 + 1.91533i) q^{74} +(-2.87661 - 8.85330i) q^{75} +(1.19443 + 4.19206i) q^{76} +(-7.36442 + 0.113842i) q^{77} +(-2.01707 - 3.49366i) q^{78} +(6.41873 - 7.12872i) q^{79} +(-3.80226 + 1.69288i) q^{80} +(3.82764 + 1.70417i) q^{81} +(-3.88419 - 4.31383i) q^{82} +(-2.21429 + 6.81490i) q^{83} +(-1.35717 + 0.986039i) q^{84} +(11.7573 - 5.23467i) q^{85} +(-0.338291 - 0.0719060i) q^{86} -3.60141 q^{87} +(-1.07353 - 3.13808i) q^{88} +(0.0638976 - 0.110674i) q^{89} +(-6.76573 + 7.51411i) q^{90} +(-10.8341 + 4.82366i) q^{91} +(5.98949 + 2.66669i) q^{92} +(7.02043 - 1.49224i) q^{93} +(-0.667601 + 2.05466i) q^{94} +(-16.8325 + 6.76789i) q^{95} +(-0.611137 - 0.444017i) q^{96} +(-7.18964 + 7.98491i) q^{97} +(-1.03419 - 1.79128i) q^{98} +(-5.48328 - 5.90368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	0.0789616	−	0.751269i	0.0455885	−	0.433745i	−0.947793	−	0.318886i	$-0.896691\pi$
$3$	0.0789616	−	0.751269i	0.0455885	−	0.433745i	0.993382	−	0.114860i	$-0.0366419\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	4.07114	−	0.865348i	1.82067	−	0.386996i	0.834271	−	0.551355i	$-0.185889\pi$
$5$	4.07114	−	0.865348i	1.82067	−	0.386996i	0.986400	+	0.164360i	$0.0525558\pi$
$6$	0.505466	+	0.561377i	0.206356	+	0.229181i
$7$	1.79660	−	1.30531i	0.679052	−	0.493360i	−0.193991	−	0.981003i	$-0.562143\pi$
$7$	1.79660	−	1.30531i	0.679052	−	0.493360i	0.873043	+	0.487643i	$0.162143\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	2.37627	+	0.505092i	0.792091	+	0.168364i
$10$	−2.08105	+	3.60448i	−0.658085	+	1.13984i
$11$	−2.71302	−	1.90776i	−0.818005	−	0.575210i
$11$	−2.71302	−	1.90776i	−0.818005	−	0.575210i
$12$	−0.755407			−0.218067
$13$	−5.22365	−	1.11032i	−1.44878	−	0.307947i	−0.584678	−	0.811266i	$-0.698779\pi$
$13$	−5.22365	−	1.11032i	−1.44878	−	0.307947i	−0.864101	+	0.503318i	$0.832112\pi$
$14$	−0.232129	+	2.20856i	−0.0620390	+	0.590262i
$15$	−0.328646	−	3.12685i	−0.0848559	−	0.807350i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	3.02460	−	0.642899i	0.733574	−	0.155926i	0.174046	−	0.984738i	$-0.444316\pi$
$17$	3.02460	−	0.642899i	0.733574	−	0.155926i	0.559528	+	0.828812i	$0.310983\pi$
$18$	−1.96539	+	1.42794i	−0.463248	+	0.336569i
$19$	−4.29394	+	0.749698i	−0.985098	+	0.171993i
$19$	−4.29394	+	0.749698i	−0.985098	+	0.171993i
$20$	−1.28616	−	3.95839i	−0.287594	−	0.885123i
$21$	−0.838775	−	1.45280i	−0.183036	−	0.317027i
$22$	3.23310	−	0.739626i	0.689300	−	0.157689i
$23$	−3.27816	+	5.67793i	−0.683543	+	1.18393i	0.290350	+	0.956921i	$0.406228\pi$
$23$	−3.27816	+	5.67793i	−0.683543	+	1.18393i	−0.973892	+	0.227010i	$0.927105\pi$
$24$	0.505466	−	0.561377i	0.103178	−	0.114591i
$25$	11.2577	−	5.01223i	2.25153	−	1.00245i
$26$	4.32043	−	3.13898i	0.847306	−	0.615604i
$27$	1.26740	−	3.90064i	0.243910	−	0.750679i
$28$	−1.48595	−	1.65032i	−0.280819	−	0.311881i
$29$	−0.498341	−	4.74139i	−0.0925395	−	0.880455i	−0.938051	−	0.346497i	$-0.887371\pi$
$29$	−0.498341	−	4.74139i	−0.0925395	−	0.880455i	0.845511	−	0.533957i	$-0.179296\pi$
$30$	2.54361	+	1.84804i	0.464398	+	0.337405i
$31$	2.93603	+	9.03617i	0.527327	+	1.62294i	0.759668	+	0.650311i	$0.225361\pi$
$31$	2.93603	+	9.03617i	0.527327	+	1.62294i	−0.232342	+	0.972634i	$0.574639\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.64746	+	1.88757i	−0.286786	+	0.328583i
$34$	−1.54609	+	2.67790i	−0.265152	+	0.459256i
$35$	6.18468	−	6.86878i	1.04540	−	1.16104i
$36$	0.253937	−	2.41605i	0.0423229	−	0.402675i
$37$	1.55807	−	1.13201i	0.256145	−	0.186101i	−0.452301	−	0.891866i	$-0.649397\pi$
$37$	1.55807	−	1.13201i	0.256145	−	0.186101i	0.708446	+	0.705765i	$0.249397\pi$
$38$	2.31608	−	3.69267i	0.375717	−	0.599030i
$39$	−1.24662	+	3.83669i	−0.199618	+	0.614362i
$40$	3.80226	+	1.69288i	0.601191	+	0.267667i
$41$	−0.606770	+	5.77303i	−0.0947615	+	0.901596i	0.839104	+	0.543971i	$0.183080\pi$
$41$	−0.606770	+	5.77303i	−0.0947615	+	0.901596i	−0.933865	+	0.357625i	$0.883587\pi$
$42$	1.64089	+	0.348782i	0.253195	+	0.0538183i
$43$	0.172924	+	0.299514i	0.0263707	+	0.0456754i	0.878910	−	0.476988i	$-0.158272\pi$
$43$	0.172924	+	0.299514i	0.0263707	+	0.0456754i	−0.852539	+	0.522664i	$0.824938\pi$
$44$	−1.61372	+	2.89757i	−0.243277	+	0.436825i
$45$	10.1112			1.50729
$46$	−2.02601	−	6.23542i	−0.298719	−	0.919363i
$47$	1.97362	−	0.878714i	0.287883	−	0.128174i	−0.257715	−	0.966221i	$-0.582969\pi$
$47$	1.97362	−	0.878714i	0.287883	−	0.128174i	0.545597	+	0.838047i	$0.316303\pi$
$48$	0.0789616	+	0.751269i	0.0113971	+	0.108436i
$49$	−0.639168	+	1.96716i	−0.0913097	+	0.281022i
$50$	−3.80803	+	11.7199i	−0.538537	+	1.65745i
$51$	−0.244163	−	2.32305i	−0.0341896	−	0.325293i
$52$	−0.558218	+	5.31109i	−0.0774109	+	0.736516i
$53$	3.46365	+	0.736222i	0.475769	+	0.101128i	0.439554	−	0.898216i	$-0.355136\pi$
$53$	3.46365	+	0.736222i	0.475769	+	0.101128i	0.0362152	+	0.999344i	$0.488470\pi$
$54$	2.05069	+	3.55190i	0.279063	+	0.483352i
$55$	−12.6960	−	5.41905i	−1.71192	−	0.730704i
$56$	2.22072			0.296757
$57$	0.224168	+	3.28510i	0.0296918	+	0.435123i
$58$	3.85700	+	2.80227i	0.506449	+	0.367956i
$59$	−6.14881	−	2.73763i	−0.800507	−	0.356409i	−0.0346335	−	0.999400i	$-0.511026\pi$
$59$	−6.14881	−	2.73763i	−0.800507	−	0.356409i	−0.765873	+	0.642991i	$0.777693\pi$
$60$	−3.07537	+	0.653690i	−0.397029	+	0.0843911i
$61$	−0.997391	−	1.10772i	−0.127703	−	0.141828i	0.675902	−	0.736991i	$-0.263754\pi$
$61$	−0.997391	−	1.10772i	−0.127703	−	0.141828i	−0.803605	+	0.595163i	$0.797088\pi$
$62$	−8.67977	−	3.86448i	−1.10233	−	0.490790i
$63$	4.92852	−	2.19432i	0.620935	−	0.276458i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−22.2270			−2.75692
$66$	−0.300367	−	2.48733i	−0.0369727	−	0.306169i
$67$	−0.202754	+	0.351181i	−0.0247704	+	0.0429036i	−0.878145	−	0.478395i	$-0.841219\pi$
$67$	−0.202754	+	0.351181i	−0.0247704	+	0.0429036i	0.853374	+	0.521298i	$0.174552\pi$
$68$	−0.955534	−	2.94083i	−0.115876	−	0.356628i
$69$	4.00681	+	2.91111i	0.482363	+	0.350457i
$70$	0.966142	+	9.19223i	0.115476	+	1.09868i
$71$	−2.84814	+	0.605392i	−0.338013	+	0.0718468i	−0.373791	−	0.927513i	$-0.621942\pi$
$71$	−2.84814	+	0.605392i	−0.338013	+	0.0718468i	0.0357784	+	0.999360i	$0.488609\pi$
$72$	1.62556	+	1.80537i	0.191574	+	0.212764i
$73$	12.0191	+	5.35126i	1.40673	+	0.626318i	0.962917	−	0.269799i	$-0.0869573\pi$
$73$	12.0191	+	5.35126i	1.40673	+	0.626318i	0.443817	+	0.896117i	$0.353624\pi$
$74$	−0.201310	+	1.91533i	−0.0234018	+	0.222653i
$75$	−2.87661	−	8.85330i	−0.332163	−	1.02229i
$76$	1.19443	+	4.19206i	0.137011	+	0.480862i
$77$	−7.36442	+	0.113842i	−0.839254	+	0.0129735i
$78$	−2.01707	−	3.49366i	−0.228388	−	0.395580i
$79$	6.41873	−	7.12872i	0.722163	−	0.802044i	−0.264575	−	0.964365i	$-0.585232\pi$
$79$	6.41873	−	7.12872i	0.722163	−	0.802044i	0.986738	+	0.162322i	$0.0518982\pi$
$80$	−3.80226	+	1.69288i	−0.425106	+	0.189269i
$81$	3.82764	+	1.70417i	0.425293	+	0.189353i
$82$	−3.88419	−	4.31383i	−0.428937	−	0.476383i
$83$	−2.21429	+	6.81490i	−0.243050	+	0.748032i	0.752901	+	0.658134i	$0.228654\pi$
$83$	−2.21429	+	6.81490i	−0.243050	+	0.748032i	−0.995951	+	0.0898979i	$0.971346\pi$
$84$	−1.35717	+	0.986039i	−0.148079	+	0.107586i
$85$	11.7573	−	5.23467i	1.27525	−	0.567780i
$86$	−0.338291	−	0.0719060i	−0.0364789	−	0.00775383i
$87$	−3.60141			−0.386112
$88$	−1.07353	−	3.13808i	−0.114438	−	0.334520i
$89$	0.0638976	−	0.110674i	0.00677313	−	0.0117314i	−0.862619	−	0.505854i	$-0.831177\pi$
$89$	0.0638976	−	0.110674i	0.00677313	−	0.0117314i	0.869392	+	0.494123i	$0.164511\pi$
$90$	−6.76573	+	7.51411i	−0.713171	+	0.792057i
$91$	−10.8341	+	4.82366i	−1.13572	+	0.505657i
$92$	5.98949	+	2.66669i	0.624447	+	0.278022i
$93$	7.02043	−	1.49224i	0.727985	−	0.154738i
$94$	−0.667601	+	2.05466i	−0.0688577	+	0.211922i
$95$	−16.8325	+	6.76789i	−1.72698	+	0.694370i
$96$	−0.611137	−	0.444017i	−0.0623739	−	0.0453173i
$97$	−7.18964	+	7.98491i	−0.729998	+	0.810745i	−0.987845	−	0.155441i	$-0.950320\pi$
$97$	−7.18964	+	7.98491i	−0.729998	+	0.810745i	0.257847	+	0.966186i	$0.416987\pi$
$98$	−1.03419	−	1.79128i	−0.104469	−	0.180946i
$99$	−5.48328	−	5.90368i	−0.551090	−	0.593342i
$100$	−6.16152	−	10.6721i	−0.616152	−	1.06721i
$101$	−15.1329	−	3.21660i	−1.50578	−	0.320064i	−0.620161	−	0.784475i	$-0.712933\pi$
$101$	−15.1329	−	3.21660i	−1.50578	−	0.320064i	−0.885620	+	0.464411i	$0.846266\pi$
$102$	1.88974	+	1.37298i	0.187112	+	0.135945i
$103$	5.82684	−	4.23345i	0.574135	−	0.417134i	−0.262470	−	0.964940i	$-0.584537\pi$
$103$	5.82684	−	4.23345i	0.574135	−	0.417134i	0.836605	+	0.547806i	$0.184537\pi$
$104$	−3.57339	−	3.96865i	−0.350400	−	0.389158i
$105$	−4.67195	−	5.18873i	−0.455936	−	0.506368i
$106$	−2.86476	+	2.08137i	−0.278250	+	0.202160i
$107$	2.46545	+	1.79126i	0.238344	+	0.173167i	0.700545	−	0.713608i	$-0.252940\pi$
$107$	2.46545	+	1.79126i	0.238344	+	0.173167i	−0.462201	+	0.886775i	$0.652940\pi$
$108$	−4.01175	−	0.852724i	−0.386031	−	0.0820534i
$109$	7.61223	+	13.1848i	0.729119	+	1.26287i	0.957256	+	0.289243i	$0.0934034\pi$
$109$	7.61223	+	13.1848i	0.729119	+	1.26287i	−0.228136	+	0.973629i	$0.573263\pi$
$110$	12.5224	−	5.80888i	1.19396	−	0.553855i
$111$	−0.727413	−	1.25992i	−0.0690430	−	0.119586i
$112$	−1.48595	+	1.65032i	−0.140409	+	0.155940i
$113$	−5.83454	−	4.23904i	−0.548867	−	0.398775i	0.278501	−	0.960436i	$-0.410163\pi$
$113$	−5.83454	−	4.23904i	−0.548867	−	0.398775i	−0.827368	+	0.561661i	$0.810163\pi$
$114$	−2.59131	−	2.03157i	−0.242698	−	0.190274i
$115$	−8.43245	+	25.9524i	−0.786330	+	2.42008i
$116$	−4.66333	+	0.991221i	−0.432979	+	0.0920326i
$117$	−11.8520	−	5.27685i	−1.09572	−	0.487845i
$118$	6.14881	−	2.73763i	0.566044	−	0.252019i
$119$	4.59483	−	5.10307i	0.421207	−	0.467798i
$120$	1.57204	−	2.72285i	0.143507	−	0.248561i
$121$	3.72093	+	10.3516i	0.338266	+	0.941051i
$122$	1.49058			0.134951
$123$	4.28919	+	0.911695i	0.386743	+	0.0822047i
$124$	8.67977	−	3.86448i	0.779467	−	0.347041i
$125$	24.6582	−	17.9152i	2.20550	−	1.60239i
$126$	−1.66713	+	5.13089i	−0.148519	+	0.457096i
$127$	−5.85010	−	6.49720i	−0.519113	−	0.576533i	0.425401	−	0.905005i	$-0.360133\pi$
$127$	−5.85010	−	6.49720i	−0.519113	−	0.576533i	−0.944514	+	0.328472i	$0.893466\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	0.238670	−	0.106263i	0.0210137	−	0.00935591i
$130$	14.8728	−	16.5179i	1.30443	−	1.44872i
$131$	1.21127	+	2.09798i	0.105829	+	0.183301i	0.914077	−	0.405542i	$-0.132917\pi$
$131$	1.21127	+	2.09798i	0.105829	+	0.183301i	−0.808248	+	0.588843i	$0.799584\pi$
$132$	2.04943	+	1.44113i	0.178380	+	0.125435i
$133$	−6.73592	+	6.95183i	−0.584079	+	0.602800i
$134$	−0.125309	−	0.385662i	−0.0108251	−	0.0333161i
$135$	1.78434	−	16.9768i	0.153571	−	1.46113i
$136$	2.82484	+	1.25770i	0.242228	+	0.107847i
$137$	−11.4819	−	12.7519i	−0.980963	−	1.08947i	−0.995979	−	0.0895828i	$-0.971447\pi$
$137$	−11.4819	−	12.7519i	−0.980963	−	1.08947i	0.0150161	−	0.999887i	$-0.495220\pi$
$138$	−4.84446	+	1.02972i	−0.412387	+	0.0876557i
$139$	0.385645	+	3.66917i	0.0327100	+	0.311215i	0.998628	+	0.0523663i	$0.0166764\pi$
$139$	0.385645	+	3.66917i	0.0327100	+	0.311215i	−0.965918	+	0.258848i	$0.916657\pi$
$140$	−7.47763	−	5.43282i	−0.631975	−	0.459157i
$141$	−0.504310	−	1.55211i	−0.0424706	−	0.130711i
$142$	1.45589	−	2.52167i	0.122175	−	0.211614i
$143$	12.0536	+	12.9778i	1.00797	+	1.08526i
$144$	−2.42936			−0.202447
$145$	−6.13177	−	18.8717i	−0.509216	−	1.56721i
$146$	−12.0191	+	5.35126i	−0.994711	+	0.442874i
$147$	1.42739	+	0.635516i	0.117729	+	0.0524165i
$148$	−1.28867	−	1.43121i	−0.105928	−	0.117645i
$149$	−21.0540	+	4.47516i	−1.72481	+	0.366619i	−0.960510	−	0.278245i	$-0.910247\pi$
$149$	−21.0540	+	4.47516i	−1.72481	+	0.366619i	−0.764297	+	0.644865i	$0.776914\pi$
$150$	8.50412	+	3.78628i	0.694358	+	0.309148i
$151$	6.18935	+	4.49683i	0.503682	+	0.365947i	0.810422	−	0.585847i	$-0.199238\pi$
$151$	6.18935	+	4.49683i	0.503682	+	0.365947i	−0.306739	+	0.951794i	$0.599238\pi$
$152$	−3.91453	−	1.91740i	−0.317511	−	0.155522i
$153$	7.51200			0.607310
$154$	4.84316	−	5.54901i	0.390273	−	0.447152i
$155$	19.7724	+	34.2469i	1.58816	+	2.75078i
$156$	3.94598	+	0.838744i	0.315931	+	0.0671533i
$157$	−0.0578688	+	0.550585i	−0.00461843	+	0.0439415i	−0.996588	−	0.0825322i	$-0.973699\pi$
$157$	−0.0578688	+	0.550585i	−0.00461843	+	0.0439415i	0.991970	+	0.126474i	$0.0403659\pi$
$158$	1.00270	+	9.54009i	0.0797708	+	0.758969i
$159$	0.826596	−	2.54400i	0.0655534	−	0.201752i
$160$	1.28616	−	3.95839i	0.101680	−	0.312938i
$161$	1.52191	+	14.4800i	0.119943	+	1.14118i
$162$	−3.82764	+	1.70417i	−0.300728	+	0.133893i
$163$	0.0373625	+	0.114990i	0.00292646	+	0.00900672i	0.952509	−	0.304510i	$-0.0984928\pi$
$163$	0.0373625	+	0.114990i	0.00292646	+	0.00900672i	−0.949583	+	0.313517i	$0.898493\pi$
$164$	5.80483			0.453281
$165$	−5.07366	+	9.11018i	−0.394984	+	0.709227i
$166$	−3.58280	−	6.20560i	−0.278080	−	0.481648i
$167$	6.85300	+	1.45665i	0.530301	+	0.112719i	0.465278	−	0.885165i	$-0.345954\pi$
$167$	6.85300	+	1.45665i	0.530301	+	0.112719i	0.0650234	+	0.997884i	$0.479288\pi$
$168$	0.175352	−	1.66836i	0.0135287	−	0.128717i
$169$	14.1776	+	6.31226i	1.09058	+	0.485559i
$170$	−3.97703	+	12.2400i	−0.305024	+	0.938767i
$171$	−10.5822	−	0.387351i	−0.809245	−	0.0296215i
$172$	0.279798	−	0.203285i	0.0213344	−	0.0155003i
$173$	−1.19071	+	11.3289i	−0.0905283	+	0.861319i	0.851177	+	0.524879i	$0.175890\pi$
$173$	−1.19071	+	11.3289i	−0.0905283	+	0.861319i	−0.941705	+	0.336440i	$0.890777\pi$
$174$	2.40982	−	2.67637i	0.182688	−	0.202895i
$175$	13.6830	−	23.6997i	1.03434	−	1.79153i
$176$	3.05038	+	1.30200i	0.229931	+	0.0981419i
$177$	−2.54221	+	4.40324i	−0.191084	+	0.330968i
$178$	0.0394909	+	0.121540i	0.00295997	+	0.00910984i
$179$	−15.8751	−	11.5340i	−1.18656	−	0.862088i	−0.193666	−	0.981067i	$-0.562038\pi$
$179$	−15.8751	−	11.5340i	−1.18656	−	0.862088i	−0.992897	+	0.118979i	$0.962038\pi$
$180$	−1.05691	−	10.0558i	−0.0787775	−	0.749518i
$181$	11.4946	+	12.7660i	0.854386	+	0.948892i	0.999177	−	0.0405703i	$-0.0129175\pi$
$181$	11.4946	+	12.7660i	0.854386	+	0.948892i	−0.144791	+	0.989462i	$0.546251\pi$
$182$	3.66476	−	11.2790i	0.271650	−	0.836054i
$183$	−0.910948	+	0.661842i	−0.0673392	+	0.0489248i
$184$	−5.98949	+	2.66669i	−0.441551	+	0.196591i
$185$	5.36355	−	5.95683i	0.394336	−	0.437955i
$186$	−3.58864	+	6.21570i	−0.263132	+	0.455757i
$187$	−9.43229	−	4.02601i	−0.689758	−	0.294411i
$188$	−1.08020	−	1.87096i	−0.0787817	−	0.136454i
$189$	−2.81453	−	8.66224i	−0.204727	−	0.630086i
$190$	6.23363	−	17.0376i	0.452235	−	1.23604i
$191$	−20.0450	+	14.5635i	−1.45040	+	1.05378i	−0.464667	+	0.885485i	$0.653826\pi$
$191$	−20.0450	+	14.5635i	−1.45040	+	1.05378i	−0.985737	+	0.168295i	$0.946174\pi$
$192$	0.738900	−	0.157058i	0.0533255	−	0.0113347i
$193$	14.8081	−	3.14755i	1.06591	−	0.226566i	0.358614	−	0.933486i	$-0.383249\pi$
$193$	14.8081	−	3.14755i	1.06591	−	0.226566i	0.707293	+	0.706920i	$0.249916\pi$
$194$	−1.12313	−	10.6859i	−0.0806362	−	0.767202i
$195$	−1.75508	+	16.6985i	−0.125684	+	1.19580i
$196$	2.02319	+	0.430042i	0.144514	+	0.0307173i
$197$	10.5835			0.754041			0.377020	−	0.926205i	$-0.376949\pi$
$197$	10.5835			0.754041			0.377020	+	0.926205i	$0.376949\pi$
$198$	8.05631	−	0.124538i	0.572537	−	0.00885050i
$199$	3.53822	−	6.12838i	0.250818	−	0.434429i	−0.712933	−	0.701232i	$-0.752634\pi$
$199$	3.53822	−	6.12838i	0.250818	−	0.434429i	0.963751	+	0.266802i	$0.0859671\pi$
$200$	12.0538	+	2.56210i	0.852329	+	0.181168i
$201$	0.247822	+	0.180053i	0.0174800	+	0.0127000i
$202$	12.5163	−	9.09362i	0.880643	−	0.639825i
$203$	−7.08430	−	7.86791i	−0.497220	−	0.552219i
$204$	−2.28481	+	0.485651i	−0.159968	+	0.0340023i
$205$	2.52543	+	24.0279i	0.176384	+	1.67818i
$206$	−0.752852	+	7.16291i	−0.0524537	+	0.499064i
$207$	−10.6577	+	11.8365i	−0.740759	+	0.822697i
$208$	5.34035			0.370286
$209$	13.0798	+	6.15786i	0.904748	+	0.425948i
$210$	6.98212			0.481812
$211$	−5.87040	+	6.51974i	−0.404135	+	0.448837i	−0.910517	−	0.413472i	$-0.864316\pi$
$211$	−5.87040	+	6.51974i	−0.404135	+	0.448837i	0.506382	+	0.862309i	$0.330983\pi$
$212$	0.370139	−	3.52164i	0.0254212	−	0.241867i
$213$	0.229918	+	2.18753i	0.0157537	+	0.149887i
$214$	−2.98087	+	0.633604i	−0.203768	+	0.0433123i
$215$	0.963184	+	1.06972i	0.0656886	+	0.0729546i
$216$	3.31808	−	2.41073i	0.225767	−	0.164029i
$217$	17.0699	+	12.4020i	1.15878	+	0.841902i
$218$	−14.8918	−	3.16534i	−1.00860	−	0.214384i
$219$	4.96929	−	8.60706i	0.335793	−	0.581611i
$220$	−4.06227	+	13.1929i	−0.273878	+	0.889462i
$221$	−16.5133			−1.11080
$222$	1.42303	+	0.302475i	0.0955078	+	0.0203008i
$223$	1.60117	−	15.2341i	0.107222	−	1.02015i	−0.800143	−	0.599809i	$-0.795243\pi$
$223$	1.60117	−	15.2341i	0.107222	−	1.02015i	0.907366	−	0.420342i	$-0.138090\pi$
$224$	−0.232129	−	2.20856i	−0.0155098	−	0.147565i
$225$	29.2829	−	6.22427i	1.95219	−	0.414952i
$226$	7.05429	−	1.49943i	0.469244	−	0.0997409i
$227$	22.9125	−	16.6469i	1.52075	−	1.10489i	0.559640	−	0.828736i	$-0.310939\pi$
$227$	22.9125	−	16.6469i	1.52075	−	1.10489i	0.961113	−	0.276156i	$-0.0890607\pi$
$228$	3.24368	−	0.566327i	0.214818	−	0.0375059i
$229$	−7.93686	−	24.4271i	−0.524483	−	1.61419i	−0.765337	−	0.643630i	$-0.777428\pi$
$229$	−7.93686	−	24.4271i	−0.524483	−	1.61419i	0.240854	−	0.970561i	$-0.422572\pi$
$230$	−13.6440	−	23.6321i	−0.899658	−	1.55825i
$231$	−0.495980	+	5.54165i	−0.0326331	+	0.364614i
$232$	2.38376	−	4.12879i	0.156501	−	0.271068i
$233$	1.77924	−	1.97605i	0.116562	−	0.129455i	−0.682040	−	0.731315i	$-0.738907\pi$
$233$	1.77924	−	1.97605i	0.116562	−	0.129455i	0.798602	+	0.601860i	$0.205573\pi$
$234$	11.8520	−	5.27685i	0.774789	−	0.344958i
$235$	7.27451	−	5.28524i	0.474537	−	0.344771i
$236$	−2.07990	+	6.40129i	−0.135390	+	0.416688i
$237$	−4.84875	−	5.38509i	−0.314960	−	0.349799i
$238$	0.717782	+	6.82924i	0.0465269	+	0.442674i
$239$	−12.2233	−	8.88078i	−0.790662	−	0.574450i	0.117498	−	0.993073i	$-0.462513\pi$
$239$	−12.2233	−	8.88078i	−0.790662	−	0.574450i	−0.908160	+	0.418623i	$0.862513\pi$
$240$	0.971573	+	2.99020i	0.0627148	+	0.193016i
$241$	−1.08593	+	1.88088i	−0.0699507	+	0.121158i	−0.898879	−	0.438196i	$-0.855618\pi$
$241$	−1.08593	+	1.88088i	−0.0699507	+	0.121158i	0.828929	+	0.559354i	$0.188951\pi$
$242$	−10.1825	−	4.16136i	−0.654555	−	0.267502i
$243$	7.73460	−	13.3967i	0.496175	−	0.859399i
$244$	−0.997391	+	1.10772i	−0.0638514	+	0.0709142i
$245$	−0.899868	+	8.56168i	−0.0574905	+	0.546985i
$246$	−3.54755	+	2.57744i	−0.226183	+	0.164332i
$247$	23.2624	+	0.851496i	1.48015	+	0.0541794i
$248$	−2.93603	+	9.03617i	−0.186438	+	0.573798i
$249$	4.94498	+	2.20165i	0.313375	+	0.139524i
$250$	−3.18594	+	30.3122i	−0.201497	+	1.91711i
$251$	3.15551	+	0.670725i	0.199174	+	0.0423358i	0.306418	−	0.951897i	$-0.400869\pi$
$251$	3.15551	+	0.670725i	0.199174	+	0.0423358i	−0.107244	+	0.994233i	$0.534203\pi$
$252$	−2.69747	−	4.67215i	−0.169924	−	0.294318i
$253$	19.7258	−	9.15040i	1.24015	−	0.575281i
$254$	8.74284			0.548574
$255$	−3.00427	−	9.24620i	−0.188135	−	0.579020i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−2.52034	−	23.9794i	−0.157215	−	1.49580i	−0.734139	−	0.678999i	$-0.762414\pi$
$257$	−2.52034	−	23.9794i	−0.157215	−	1.49580i	0.576925	−	0.816797i	$-0.304253\pi$
$258$	−0.0807328	+	0.248470i	−0.00502620	+	0.0154691i
$259$	1.32162	−	4.06753i	0.0821214	−	0.252744i
$260$	2.32336	+	22.1053i	0.144089	+	1.37091i
$261$	1.21065	−	11.5186i	0.0749373	−	0.712981i
$262$	−2.36960	−	0.503674i	−0.146394	−	0.0311171i
$263$	12.4545	+	21.5718i	0.767977	+	1.33017i	0.938658	+	0.344849i	$0.112070\pi$
$263$	12.4545	+	21.5718i	0.767977	+	1.33017i	−0.170682	+	0.985326i	$0.554597\pi$
$264$	−2.44231	+	0.558719i	−0.150314	+	0.0343868i
$265$	14.7381			0.905356
$266$	−0.659003	−	9.65745i	−0.0404061	−	0.592136i
$267$	−0.0781004	−	0.0567432i	−0.00477966	−	0.00347263i
$268$	0.370451	+	0.164935i	0.0226289	+	0.0100750i
$269$	−5.23114	+	1.11191i	−0.318948	+	0.0677945i	−0.364604	−	0.931163i	$-0.618796\pi$
$269$	−5.23114	+	1.11191i	−0.318948	+	0.0677945i	0.0456559	+	0.998957i	$0.485462\pi$
$270$	11.4223	+	12.6857i	0.695138	+	0.772029i
$271$	−19.8209	−	8.82482i	−1.20403	−	0.536069i	−0.296087	−	0.955161i	$-0.595682\pi$
$271$	−19.8209	−	8.82482i	−1.20403	−	0.536069i	−0.907944	+	0.419091i	$0.862349\pi$
$272$	−2.82484	+	1.25770i	−0.171281	+	0.0762593i
$273$	2.76839	+	8.52023i	0.167551	+	0.515668i
$274$	17.1594			1.03664
$275$	−40.1043	−	7.87861i	−2.41838	−	0.475098i
$276$	2.47634	−	4.28915i	0.149058	−	0.258176i
$277$	2.97146	+	9.14520i	0.178538	+	0.549482i	0.999777	−	0.0211012i	$-0.00671721\pi$
$277$	2.97146	+	9.14520i	0.178538	+	0.549482i	−0.821240	+	0.570583i	$0.806717\pi$
$278$	−2.98477	−	2.16856i	−0.179015	−	0.130062i
$279$	2.41271	+	22.9554i	0.144445	+	1.37430i
$280$	9.04088	−	1.92170i	0.540296	−	0.114843i
$281$	−6.06708	−	6.73818i	−0.361932	−	0.401966i	0.534485	−	0.845178i	$-0.320506\pi$
$281$	−6.06708	−	6.73818i	−0.361932	−	0.401966i	−0.896417	+	0.443212i	$0.853839\pi$
$282$	1.49089	+	0.663787i	0.0887812	+	0.0395279i
$283$	0.688349	−	6.54920i	0.0409181	−	0.389310i	−0.954827	−	0.297162i	$-0.903960\pi$
$283$	0.688349	−	6.54920i	0.0409181	−	0.389310i	0.995745	−	0.0921482i	$-0.0293733\pi$
$284$	0.899788	+	2.76926i	0.0533926	+	0.164325i
$285$	3.75538	+	13.1801i	0.222450	+	0.780725i
$286$	−17.7098	+	0.273765i	−1.04720	+	0.0161881i
$287$	6.44546	+	11.1639i	0.380463	+	0.658982i
$288$	1.62556	−	1.80537i	0.0957870	−	0.106382i
$289$	−6.79537	+	3.02549i	−0.399728	+	0.177970i
$290$	18.1273	+	8.07081i	1.06447	+	0.473934i
$291$	5.43111	+	6.03186i	0.318377	+	0.353594i
$292$	4.06561	−	12.5127i	0.237922	−	0.732248i
$293$	−14.8286	+	10.7736i	−0.866293	+	0.629399i	−0.929590	−	0.368596i	$-0.879839\pi$
$293$	−14.8286	+	10.7736i	−0.866293	+	0.629399i	0.0632965	+	0.997995i	$0.479839\pi$
$294$	−1.42739	+	0.635516i	−0.0832473	+	0.0370641i
$295$	−27.4017	−	5.82441i	−1.59539	−	0.339110i
$296$	1.92588			0.111940
$297$	−10.8799	+	8.16463i	−0.631318	+	0.473760i
$298$	10.7622	−	18.6406i	0.623435	−	1.07982i
$299$	23.4282	−	26.0197i	1.35489	−	1.50476i
$300$	−8.50412	+	3.78628i	−0.490985	+	0.218601i
$301$	0.701634	+	0.312388i	0.0404415	+	0.0180057i
$302$	−7.48328	+	1.59062i	−0.430614	+	0.0915299i
$303$	−3.61145	+	11.1149i	−0.207472	+	0.638534i
$304$	4.04424	−	1.62608i	0.231953	−	0.0932619i
$305$	−5.01908	−	3.64658i	−0.287392	−	0.208802i
$306$	−5.02651	+	5.58251i	−0.287347	+	0.319131i
$307$	2.81014	+	4.86731i	0.160383	+	0.277792i	0.935006	−	0.354631i	$-0.115394\pi$
$307$	2.81014	+	4.86731i	0.160383	+	0.277792i	−0.774623	+	0.632423i	$0.782060\pi$
$308$	0.883011	+	7.31218i	0.0503142	+	0.416650i
$309$	−2.72036	−	4.71180i	−0.154756	−	0.268045i
$310$	−38.6807	−	8.22185i	−2.19692	−	0.466969i
$311$	−22.9886	−	16.7022i	−1.30356	−	0.947095i	−0.303580	−	0.952806i	$-0.598182\pi$
$311$	−22.9886	−	16.7022i	−1.30356	−	0.947095i	−0.999984	+	0.00571134i	$0.998182\pi$
$312$	−3.26368	+	2.37121i	−0.184770	+	0.134243i
$313$	−9.48205	−	10.5309i	−0.535957	−	0.595241i	0.412967	−	0.910746i	$-0.364493\pi$
$313$	−9.48205	−	10.5309i	−0.535957	−	0.595241i	−0.948924	+	0.315505i	$0.897826\pi$
$314$	−0.370443	−	0.411418i	−0.0209053	−	0.0232177i
$315$	18.1659	−	13.1983i	1.02353	−	0.743638i
$316$	−7.76061	−	5.63841i	−0.436568	−	0.317185i
$317$	17.7470	+	3.77225i	0.996774	+	0.211871i	0.677286	−	0.735720i	$-0.263156\pi$
$317$	17.7470	+	3.77225i	0.996774	+	0.211871i	0.319487	+	0.947591i	$0.396489\pi$
$318$	1.33746	+	2.31655i	0.0750011	+	0.129906i
$319$	−7.69342	+	13.8142i	−0.430749	+	0.773447i
$320$	2.08105	+	3.60448i	0.116334	+	0.201497i
$321$	1.54039	−	1.71078i	0.0859762	−	0.0954863i
$322$	−11.7791	−	8.55801i	−0.656423	−	0.476919i
$323$	−12.5055	+	5.02811i	−0.695824	+	0.279772i
$324$	1.29474	−	3.98480i	0.0719301	−	0.221378i
$325$	−64.3712	+	13.6825i	−3.57067	+	0.758970i
$326$	−0.110455	−	0.0491776i	−0.00611752	−	0.00272370i
$327$	10.5064	−	4.67774i	0.581004	−	0.258680i
$328$	−3.88419	+	4.31383i	−0.214468	+	0.238191i
$329$	2.39883	−	4.15489i	0.132252	−	0.229066i
$330$	−3.37525	−	9.86636i	−0.185801	−	0.543125i
$331$	−26.4436			−1.45347			−0.726735	−	0.686918i	$-0.758963\pi$
$331$	−26.4436			−1.45347			−0.726735	+	0.686918i	$0.758963\pi$
$332$	7.00902	+	1.48981i	0.384670	+	0.0817641i
$333$	4.27417	−	1.90298i	0.234223	−	0.104283i
$334$	−5.66806	+	4.11808i	−0.310142	+	0.225331i
$335$	−0.521549	+	1.60516i	−0.0284952	+	0.0876993i
$336$	1.12250	+	1.24666i	0.0612374	+	0.0680110i
$337$	−27.7750	−	12.3662i	−1.51300	−	0.673631i	−0.528487	−	0.848942i	$-0.677240\pi$
$337$	−27.7750	−	12.3662i	−1.51300	−	0.673631i	−0.984513	+	0.175311i	$0.943907\pi$
$338$	−14.1776	+	6.31226i	−0.771158	+	0.343342i
$339$	−3.64536	+	4.04858i	−0.197989	+	0.219889i
$340$	−6.43496	−	11.1457i	−0.348985	−	0.604459i
$341$	9.27332	−	30.1165i	0.502179	−	1.63090i
$342$	7.36876	−	7.60495i	0.398457	−	0.411229i
$343$	6.22310	+	19.1527i	0.336016	+	1.03415i
$344$	−0.0361510	+	0.343954i	−0.00194913	+	0.0185448i
$345$	18.8314	+	8.38428i	1.01385	+	0.451395i
$346$	−7.62226	−	8.46537i	−0.409775	−	0.455101i
$347$	15.5751	−	3.31059i	0.836115	−	0.177722i	0.230092	−	0.973169i	$-0.426097\pi$
$347$	15.5751	−	3.31059i	0.836115	−	0.177722i	0.606023	+	0.795447i	$0.292764\pi$
$348$	0.376450	+	3.58168i	0.0201798	+	0.191998i
$349$	11.4538	+	8.32167i	0.613108	+	0.445449i	0.850507	−	0.525963i	$-0.176295\pi$
$349$	11.4538	+	8.32167i	0.613108	+	0.445449i	−0.237399	+	0.971412i	$0.576295\pi$
$350$	8.45658	+	26.0267i	0.452023	+	1.39118i
$351$	−10.9514	+	18.9684i	−0.584542	+	1.01246i
$352$	−3.00867	+	1.39566i	−0.160363	+	0.0743891i
$353$	−20.8820			−1.11144			−0.555719	−	0.831370i	$-0.687557\pi$
$353$	−20.8820			−1.11144			−0.555719	+	0.831370i	$0.687557\pi$
$354$	−1.57117	−	4.83558i	−0.0835070	−	0.257008i
$355$	−11.0713	+	4.92928i	−0.587605	+	0.261619i
$356$	−0.116747	−	0.0519790i	−0.00618756	−	0.00275488i
$357$	−3.47097	−	3.85490i	−0.183703	−	0.204023i
$358$	19.1939	−	4.07980i	1.01443	−	0.215624i
$359$	−8.17196	−	3.63839i	−0.431300	−	0.192027i	0.179592	−	0.983741i	$-0.442522\pi$
$359$	−8.17196	−	3.63839i	−0.431300	−	0.192027i	−0.610892	+	0.791714i	$0.709189\pi$
$360$	8.18016	+	5.94323i	0.431132	+	0.313236i
$361$	17.8759	−	6.43832i	0.940837	−	0.338859i
$362$	−17.1784			−0.902876
$363$	8.07061	−	1.97804i	0.423597	−	0.103820i
$364$	5.92971	+	10.2706i	0.310801	+	0.538324i
$365$	53.5623	+	11.3850i	2.80358	+	0.595920i
$366$	0.117698	−	1.11982i	0.00615219	−	0.0585342i
$367$	−2.08955	−	19.8807i	−0.109073	−	1.03776i	−0.902968	−	0.429709i	$-0.858616\pi$
$367$	−2.08955	−	19.8807i	−0.109073	−	1.03776i	0.793894	−	0.608056i	$-0.208050\pi$
$368$	2.02601	−	6.23542i	0.105613	−	0.325044i
$369$	−4.35776	+	13.4118i	−0.226856	+	0.698191i
$370$	0.837870	+	7.97180i	0.0435588	+	0.414434i
$371$	7.18380	−	3.19844i	0.372965	−	0.166055i
$372$	−2.21790	−	6.82599i	−0.114993	−	0.353911i
$373$	−20.6017			−1.06672			−0.533359	−	0.845889i	$-0.679070\pi$
$373$	−20.6017			−1.06672			−0.533359	+	0.845889i	$0.679070\pi$
$374$	9.30335	−	4.31563i	0.481065	−	0.223156i
$375$	−11.5121	−	19.9396i	−0.594483	−	1.02967i
$376$	2.11319	+	0.449173i	0.108979	+	0.0231643i
$377$	−2.66131	+	25.3207i	−0.137064	+	1.30408i
$378$	8.32059	+	3.70457i	0.427965	+	0.190542i
$379$	−6.93233	+	21.3355i	−0.356090	+	1.09593i	0.599285	+	0.800536i	$0.295452\pi$
$379$	−6.93233	+	21.3355i	−0.356090	+	1.09593i	−0.955375	+	0.295396i	$0.904548\pi$
$380$	8.49029	+	16.0329i	0.435543	+	0.822469i
$381$	−5.34307	+	3.88197i	−0.273734	+	0.198879i
$382$	2.58990	−	24.6412i	0.132511	−	1.26075i
$383$	9.52187	−	10.5751i	0.486545	−	0.540363i	−0.449018	−	0.893523i	$-0.648226\pi$
$383$	9.52187	−	10.5751i	0.486545	−	0.540363i	0.935563	+	0.353160i	$0.114893\pi$
$384$	−0.377704	+	0.654202i	−0.0192746	+	0.0333846i
$385$	−29.8831	+	6.83626i	−1.52298	+	0.348408i
$386$	−7.56944	+	13.1107i	−0.385275	+	0.667315i
$387$	0.259633	+	0.799069i	0.0131979	+	0.0406190i
$388$	8.69269	+	6.31561i	0.441304	+	0.320626i
$389$	−0.910473	−	8.66258i	−0.0461628	−	0.439210i	−0.993054	−	0.117657i	$-0.962462\pi$
$389$	−0.910473	−	8.66258i	−0.0461628	−	0.439210i	0.946891	−	0.321553i	$-0.104205\pi$
$390$	−11.2350	−	12.4777i	−0.568907	−	0.631835i
$391$	−6.26478	+	19.2810i	−0.316824	+	0.975082i
$392$	−1.67336	+	1.21577i	−0.0845176	+	0.0614056i
$393$	1.67179	−	0.744329i	0.0843306	−	0.0375464i
$394$	−7.08172	+	7.86505i	−0.356772	+	0.396235i
$395$	19.9627	−	34.5765i	1.00443	−	1.73973i
$396$	−5.29818	+	6.07034i	−0.266243	+	0.305046i
$397$	16.0923	+	27.8727i	0.807651	+	1.39889i	0.914487	+	0.404616i	$0.132595\pi$
$397$	16.0923	+	27.8727i	0.807651	+	1.39889i	−0.106836	+	0.994277i	$0.534072\pi$
$398$	2.18674	+	6.73010i	0.109611	+	0.337349i
$399$	4.69081	+	5.60942i	0.234834	+	0.280822i
$400$	−9.96955	+	7.24330i	−0.498478	+	0.362165i
$401$	−24.2644	+	5.15756i	−1.21171	+	0.257556i	−0.769082	−	0.639150i	$-0.779286\pi$
$401$	−24.2644	+	5.15756i	−1.21171	+	0.257556i	−0.442626	+	0.896706i	$0.645953\pi$
$402$	−0.299630	+	0.0636884i	−0.0149442	+	0.00317649i
$403$	−5.30374	−	50.4617i	−0.264198	−	2.51368i
$404$	−1.61716	+	15.3862i	−0.0804566	+	0.765494i
$405$	17.0576	+	3.62570i	0.847597	+	0.180162i
$406$	10.5873			0.525440
$407$	−6.38667	+	0.0987276i	−0.316575	+	0.00489374i
$408$	1.16793	−	2.02291i	0.0578209	−	0.100149i
$409$	16.9050	+	3.59326i	0.835897	+	0.177675i	0.605925	−	0.795522i	$-0.292803\pi$
$409$	16.9050	+	3.59326i	0.835897	+	0.177675i	0.229972	+	0.973197i	$0.426136\pi$
$410$	−19.5461	−	14.2010i	−0.965311	−	0.701339i
$411$	−10.4867	+	7.61907i	−0.517273	+	0.375821i
$412$	−4.81932	−	5.35240i	−0.237431	−	0.263694i
$413$	−14.6204	+	3.10766i	−0.719423	+	0.152918i
$414$	−1.66489	−	15.8404i	−0.0818250	−	0.778512i
$415$	−3.11745	+	29.6606i	−0.153030	+	1.45598i
$416$	−3.57339	+	3.96865i	−0.175200	+	0.194579i
$417$	2.78698			0.136479
$418$	−13.3283	+	5.59976i	−0.651907	+	0.273893i
$419$	6.28016			0.306806			0.153403	−	0.988164i	$-0.450977\pi$
$419$	6.28016			0.306806			0.153403	+	0.988164i	$0.450977\pi$
$420$	−4.67195	+	5.18873i	−0.227968	+	0.253184i
$421$	−1.66410	+	15.8329i	−0.0811034	+	0.771647i	0.876080	+	0.482166i	$0.160150\pi$
$421$	−1.66410	+	15.8329i	−0.0811034	+	0.771647i	−0.957184	+	0.289482i	$0.906517\pi$
$422$	−0.917046	−	8.72511i	−0.0446411	−	0.424732i
$423$	5.13370	−	1.09120i	0.249609	−	0.0530560i
$424$	2.36941	+	2.63150i	0.115069	+	0.127797i
$425$	30.8276	−	22.3976i	1.49536	−	1.08644i
$426$	−1.77949	−	1.29288i	−0.0862167	−	0.0626401i
$427$	−3.23783	−	0.688221i	−0.156689	−	0.0333053i
$428$	1.52373	−	2.63918i	0.0736524	−	0.127570i
$429$	10.7016	−	8.03077i	0.516676	−	0.387729i
$430$	−1.43946			−0.0694167
$431$	23.5273	+	5.00088i	1.13327	+	0.240884i	0.736108	−	0.676864i	$-0.236662\pi$
$431$	23.5273	+	5.00088i	1.13327	+	0.240884i	0.397163	+	0.917748i	$0.369995\pi$
$432$	−0.428711	+	4.07891i	−0.0206264	+	0.196247i
$433$	−2.54882	−	24.2504i	−0.122488	−	1.16540i	−0.867182	−	0.497991i	$-0.834071\pi$
$433$	−2.54882	−	24.2504i	−0.122488	−	1.16540i	0.744694	−	0.667406i	$-0.232596\pi$
$434$	−20.6384	+	4.38684i	−0.990677	+	0.210575i
$435$	−14.6619	+	3.11648i	−0.702983	+	0.149424i
$436$	12.3168	−	8.94871i	0.589870	−	0.428566i
$437$	9.81948	−	26.8383i	0.469729	−	1.28385i
$438$	3.07119	+	9.45215i	0.146747	+	0.451641i
$439$	9.55875	+	16.5562i	0.456214	+	0.790187i	0.998757	−	0.0498416i	$-0.0158717\pi$
$439$	9.55875	+	16.5562i	0.456214	+	0.790187i	−0.542543	+	0.840028i	$0.682538\pi$
$440$	−7.08601	−	11.8466i	−0.337812	−	0.564765i
$441$	−2.51243	+	4.35166i	−0.119640	+	0.207222i
$442$	11.0495	−	12.2718i	0.525573	−	0.583708i
$443$	31.7366	−	14.1301i	1.50785	−	0.671339i	0.524229	−	0.851577i	$-0.324354\pi$
$443$	31.7366	−	14.1301i	1.50785	−	0.671339i	0.983623	+	0.180238i	$0.0576869\pi$
$444$	−1.17698	+	0.855125i	−0.0558569	+	0.0405824i
$445$	0.164365	−	0.505863i	0.00779164	−	0.0239802i
$446$	10.2498	+	11.3835i	0.485340	+	0.539025i
$447$	1.69959	+	16.1705i	0.0803880	+	0.764841i
$448$	1.79660	+	1.30531i	0.0848815	+	0.0616700i
$449$	−1.38286	−	4.25601i	−0.0652613	−	0.200854i	0.913109	−	0.407716i	$-0.133675\pi$
$449$	−1.38286	−	4.25601i	−0.0652613	−	0.200854i	−0.978370	+	0.206863i	$0.933675\pi$
$450$	−14.9686	+	25.9263i	−0.705624	+	1.22218i
$451$	12.6597	−	14.5048i	0.596123	−	0.683002i
$452$	−3.60594	+	6.24567i	−0.169609	+	0.293772i
$453$	3.86705	−	4.29479i	0.181690	−	0.201787i
$454$	−2.96039	+	28.1662i	−0.138938	+	1.32191i
$455$	−39.9331	+	29.0131i	−1.87209	+	1.36016i
$456$	−1.74958	+	2.78947i	−0.0819316	+	0.130629i
$457$	1.37148	−	4.22099i	0.0641552	−	0.197449i	−0.913841	−	0.406072i	$-0.866898\pi$
$457$	1.37148	−	4.22099i	0.0641552	−	0.197449i	0.977996	+	0.208623i	$0.0668981\pi$
$458$	23.4637	+	10.4467i	1.09639	+	0.488143i
$459$	1.32565	−	12.6127i	0.0618760	−	0.588710i
$460$	26.6917	+	5.67349i	1.24451	+	0.264528i
$461$	0.0100647	+	0.0174327i	0.000468762	+	0.000811920i	0.866260	−	0.499594i	$-0.166517\pi$
$461$	0.0100647	+	0.0174327i	0.000468762	+	0.000811920i	−0.865791	+	0.500406i	$0.833184\pi$
$462$	−3.78638	−	4.07667i	−0.176158	−	0.189664i
$463$	12.6734			0.588983			0.294491	−	0.955654i	$-0.404850\pi$
$463$	12.6734			0.588983			0.294491	+	0.955654i	$0.404850\pi$
$464$	1.47324	+	4.53417i	0.0683935	+	0.210494i
$465$	27.2899	−	12.1502i	1.26554	−	0.563454i
$466$	0.277945	+	2.64447i	0.0128756	+	0.122503i
$467$	7.21861	−	22.2166i	0.334037	−	1.02806i	−0.633157	−	0.774023i	$-0.718241\pi$
$467$	7.21861	−	22.2166i	0.334037	−	1.02806i	0.967194	−	0.254038i	$-0.0817587\pi$
$468$	−4.00907	+	12.3386i	−0.185319	+	0.570354i
$469$	0.0941303	+	0.895590i	0.00434653	+	0.0413545i
$470$	−0.939899	+	8.94254i	−0.0433543	+	0.412488i
$471$	0.409068	+	0.0869501i	0.0188489	+	0.00400645i
$472$	−3.36535	−	5.82897i	−0.154903	−	0.268300i
$473$	0.102253	−	1.14248i	0.00470159	−	0.0525315i
$474$	7.24635			0.332836
$475$	−44.5821	+	29.9621i	−2.04557	+	1.37476i
$476$	−5.55541	−	4.03624i	−0.254632	−	0.185001i
$477$	7.85872	+	3.49893i	0.359826	+	0.160205i
$478$	14.7787	−	3.14131i	0.675963	−	0.143680i
$479$	−2.02946	−	2.25395i	−0.0927285	−	0.102985i	0.694994	−	0.719015i	$-0.255407\pi$
$479$	−2.02946	−	2.25395i	−0.0927285	−	0.102985i	−0.787723	+	0.616030i	$0.788740\pi$
$480$	−2.87226	−	1.27881i	−0.131100	−	0.0583695i
$481$	−9.39570	+	4.18324i	−0.428407	+	0.190739i
$482$	−0.671139	−	2.06555i	−0.0305696	−	0.0940834i
$483$	10.9985			0.500451
$484$	9.90591	−	4.78257i	0.450268	−	0.217390i
$485$	−22.3604	+	38.7293i	−1.01533	+	1.75861i
$486$	4.78024	+	14.7121i	0.216836	+	0.667353i
$487$	−5.87128	−	4.26574i	−0.266053	−	0.193299i	0.446758	−	0.894655i	$-0.352578\pi$
$487$	−5.87128	−	4.26574i	−0.266053	−	0.193299i	−0.712811	+	0.701356i	$0.752578\pi$
$488$	−0.155808	−	1.48241i	−0.00705309	−	0.0671056i
$489$	0.0893387	−	0.0189895i	0.00404003	−	0.000858736i
$490$	−5.76044	−	6.39761i	−0.260230	−	0.289015i
$491$	−12.7713	−	5.68615i	−0.576361	−	0.256612i	0.0977886	−	0.995207i	$-0.468823\pi$
$491$	−12.7713	−	5.68615i	−0.576361	−	0.256612i	−0.674150	+	0.738595i	$0.735490\pi$
$492$	0.458358	−	4.36099i	0.0206644	−	0.196609i
$493$	−4.55552	−	14.0205i	−0.205170	−	0.631449i
$494$	−16.1984	+	16.7176i	−0.728800	+	0.752161i
$495$	−27.4319	−	19.2898i	−1.23297	−	0.867011i
$496$	−4.75060	−	8.22828i	−0.213308	−	0.369461i
$497$	−4.32676	+	4.80536i	−0.194082	+	0.215550i
$498$	−4.94498	+	2.20165i	−0.221590	+	0.0986581i
$499$	−0.784459	−	0.349264i	−0.0351172	−	0.0156352i	0.389103	−	0.921194i	$-0.372785\pi$
$499$	−0.784459	−	0.349264i	−0.0351172	−	0.0156352i	−0.424220	+	0.905559i	$0.639452\pi$
$500$	−20.3946	−	22.6505i	−0.912073	−	1.01296i
$501$	1.63546	−	5.03343i	0.0730670	−	0.224877i
$502$	−2.60990	+	1.89620i	−0.116485	+	0.0846316i
$503$	6.68340	−	2.97564i	0.297998	−	0.132677i	−0.252291	−	0.967651i	$-0.581184\pi$
$503$	6.68340	−	2.97564i	0.297998	−	0.132677i	0.550289	+	0.834974i	$0.314517\pi$
$504$	5.27704	+	1.12167i	0.235058	+	0.0499632i
$505$	−64.3917			−2.86539
$506$	−6.39907	+	20.7819i	−0.284473	+	0.923870i
$507$	5.86169	−	10.1527i	0.260327	−	0.450899i
$508$	−5.85010	+	6.49720i	−0.259556	+	0.288266i
$509$	29.6149	−	13.1854i	1.31266	−	0.584432i	0.373407	−	0.927668i	$-0.378189\pi$
$509$	29.6149	−	13.1854i	1.31266	−	0.584432i	0.939249	+	0.343235i	$0.111523\pi$
$510$	8.88152	+	3.95431i	0.393280	+	0.175100i
$511$	28.5787	−	6.07458i	1.26425	−	0.268724i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−2.51782	+	17.6993i	−0.111165	+	0.781443i
$514$	19.5066	+	14.1724i	0.860401	+	0.625118i
$515$	20.0585	−	22.2772i	0.883883	−	0.981651i
$516$	−0.130628	−	0.226255i	−0.00575059	−	0.00996032i
$517$	−7.03085	−	1.38123i	−0.309216	−	0.0607464i
$518$	2.13843	+	3.70386i	0.0939570	+	0.162738i
$519$	8.41702	+	1.78909i	0.369466	+	0.0785324i
$520$	−17.9820	−	13.0647i	−0.788565	−	0.572926i
$521$	26.4120	−	19.1894i	1.15713	−	0.840704i	0.167718	−	0.985835i	$-0.446360\pi$
$521$	26.4120	−	19.1894i	1.15713	−	0.840704i	0.989413	+	0.145131i	$0.0463602\pi$
$522$	7.74987	+	8.60710i	0.339203	+	0.376723i
$523$	14.0074	+	15.5568i	0.612502	+	0.680253i	0.966992	−	0.254807i	$-0.0820120\pi$
$523$	14.0074	+	15.5568i	0.612502	+	0.680253i	−0.354489	+	0.935060i	$0.615345\pi$
$524$	1.95987	−	1.42393i	0.0856174	−	0.0622047i
$525$	−16.7244	−	12.1510i	−0.729914	−	0.530313i
$526$	−24.3647	−	5.17887i	−1.06235	−	0.225809i
$527$	14.6897	+	25.4433i	0.639892	+	1.10833i
$528$	1.21901	−	2.18885i	0.0530508	−	0.0952573i
$529$	−9.99260	−	17.3077i	−0.434461	−	0.752508i
$530$	−9.86173	+	10.9526i	−0.428366	+	0.475749i
$531$	−13.2285	−	9.61106i	−0.574068	−	0.417085i
$532$	7.61784	+	5.97236i	0.330275	+	0.258935i
$533$	9.57946	−	29.4826i	0.414933	−	1.27703i
$534$	0.0944278	−	0.0200712i	0.00408629	−	0.000868568i
$535$	11.5873	+	5.15899i	0.500961	+	0.223042i
$536$	−0.370451	+	0.164935i	−0.0160010	+	0.00712412i
$537$	−9.91863	+	11.0158i	−0.428020	+	0.475365i
$538$	2.67400	−	4.63151i	0.115284	−	0.199678i
$539$	5.48693	−	4.11755i	0.236339	−	0.177355i
$540$	−17.0703			−0.734590
$541$	−23.0307	−	4.89533i	−0.990168	−	0.210467i	−0.315771	−	0.948835i	$-0.602263\pi$
$541$	−23.0307	−	4.89533i	−0.990168	−	0.210467i	−0.674397	+	0.738369i	$0.735596\pi$
$542$	19.8209	−	8.82482i	0.851379	−	0.379058i
$543$	10.4984	−	7.62750i	0.450528	−	0.327327i
$544$	0.955534	−	2.94083i	0.0409682	−	0.126087i
$545$	42.3999	+	47.0899i	1.81621	+	2.01711i
$546$	−8.18418	−	3.64383i	−0.350250	−	0.155942i
$547$	16.3334	−	7.27211i	0.698366	−	0.310933i	−0.0266690	−	0.999644i	$-0.508490\pi$
$547$	16.3334	−	7.27211i	0.698366	−	0.310933i	0.725035	+	0.688712i	$0.241823\pi$
$548$	−11.4819	+	12.7519i	−0.490482	+	0.544735i
$549$	−1.81057	−	3.13601i	−0.0772735	−	0.133842i
$550$	32.6900	−	24.5315i	1.39391	−	1.04603i
$551$	5.69446	+	19.9857i	0.242592	+	0.851418i
$552$	1.53046	+	4.71028i	0.0651408	+	0.200483i
$553$	2.22673	−	21.1859i	0.0946901	−	0.900916i
$554$	−8.78450	−	3.91111i	−0.373218	−	0.166167i
$555$	−4.05167	−	4.49983i	−0.171984	−	0.191007i
$556$	3.60876	−	0.767065i	0.153045	−	0.0325308i
$557$	−1.79259	−	17.0553i	−0.0759544	−	0.722658i	−0.964538	−	0.263944i	$-0.914977\pi$
$557$	−1.79259	−	17.0553i	−0.0759544	−	0.722658i	0.888584	−	0.458715i	$-0.151690\pi$
$558$	−18.6736	−	13.5672i	−0.790516	−	0.574344i
$559$	−0.570740	−	1.75656i	−0.0241397	−	0.0742944i
$560$	−4.62143	+	8.00455i	−0.195291	+	0.338254i
$561$	−3.76941	+	6.76829i	−0.159144	+	0.285757i
$562$	9.06711			0.382473
$563$	−6.63993	−	20.4356i	−0.279840	−	0.861258i	−0.987898	−	0.155104i	$-0.950429\pi$
$563$	−6.63993	−	20.4356i	−0.279840	−	0.861258i	0.708058	−	0.706154i	$-0.249571\pi$
$564$	−1.49089	+	0.663787i	−0.0627778	+	0.0279505i
$565$	−27.4215	−	12.2088i	−1.15363	−	0.513629i
$566$	4.40641	+	4.89382i	0.185215	+	0.205702i
$567$	9.10121	−	1.93452i	0.382215	−	0.0812423i
$568$	−2.66004	−	1.18433i	−0.111613	−	0.0496932i
$569$	−6.95704	−	5.05459i	−0.291654	−	0.211899i	0.432330	−	0.901715i	$-0.357691\pi$
$569$	−6.95704	−	5.05459i	−0.291654	−	0.211899i	−0.723985	+	0.689816i	$0.757691\pi$
$570$	−12.3076	−	6.02845i	−0.515509	−	0.252504i
$571$	−0.814236			−0.0340747			−0.0170373	−	0.999855i	$-0.505423\pi$
$571$	−0.814236			−0.0340747			−0.0170373	+	0.999855i	$0.505423\pi$
$572$	11.6467	−	13.3441i	0.486974	−	0.557946i
$573$	9.35835	+	16.2091i	0.390951	+	0.677146i
$574$	−12.6092	−	2.68017i	−0.526299	−	0.111868i
$575$	−8.44524	+	80.3511i	−0.352191	+	3.35087i
$576$	0.253937	+	2.41605i	0.0105807	+	0.100669i
$577$	−5.61995	+	17.2964i	−0.233962	+	0.720060i	0.763296	+	0.646049i	$0.223580\pi$
$577$	−5.61995	+	17.2964i	−0.233962	+	0.720060i	−0.997257	+	0.0740109i	$0.976420\pi$
$578$	2.29861	−	7.07440i	0.0956096	−	0.294256i
$579$	−1.19539	−	11.3734i	−0.0496787	−	0.472661i
$580$	−18.1273	+	8.07081i	−0.752697	+	0.335122i
$581$	4.91733	+	15.1340i	0.204005	+	0.627864i
$582$	−8.11666			−0.336447
$583$	−7.99242	−	8.60519i	−0.331012	−	0.356391i
$584$	6.57829	+	11.3939i	0.272212	+	0.471484i
$585$	−52.8175	−	11.2267i	−2.18373	−	0.464167i
$586$	1.91591	−	18.2287i	0.0791456	−	0.753020i
$587$	7.19945	+	3.20540i	0.297153	+	0.132301i	0.549898	−	0.835232i	$-0.314667\pi$
$587$	7.19945	+	3.20540i	0.297153	+	0.132301i	−0.252745	+	0.967533i	$0.581333\pi$
$588$	0.482832	−	1.48600i	0.0199116	−	0.0612817i
$589$	−19.3816	−	36.5997i	−0.798603	−	1.50806i
$590$	22.6637	−	16.4661i	0.933049	−	0.677900i
$591$	0.835687	−	7.95103i	0.0343756	−	0.327062i
$592$	−1.28867	+	1.43121i	−0.0529639	+	0.0588223i
$593$	9.33780	−	16.1735i	0.383457	−	0.664168i	−0.608097	−	0.793863i	$-0.708067\pi$
$593$	9.33780	−	16.1735i	0.383457	−	0.664168i	0.991554	+	0.129695i	$0.0414000\pi$
$594$	1.21260	−	13.5486i	0.0497537	−	0.555905i
$595$	14.2903	−	24.7515i	0.585844	−	1.01471i
$596$	6.65138	+	20.4708i	0.272451	+	0.838518i
$597$	−4.32468	−	3.14206i	−0.176997	−	0.128596i
$598$	3.65985	+	34.8212i	0.149662	+	1.42394i
$599$	−15.9380	−	17.7009i	−0.651207	−	0.723239i	0.323623	−	0.946186i	$-0.395099\pi$
$599$	−15.9380	−	17.7009i	−0.651207	−	0.723239i	−0.974831	+	0.222947i	$0.928432\pi$
$600$	2.87661	−	8.85330i	0.117437	−	0.361435i
$601$	14.7921	−	10.7471i	0.603383	−	0.438383i	−0.243695	−	0.969852i	$-0.578360\pi$
$601$	14.7921	−	10.7471i	0.603383	−	0.438383i	0.847078	+	0.531469i	$0.178360\pi$
$602$	−0.701634	+	0.312388i	−0.0285965	+	0.0127320i
$603$	−0.659179	+	0.732092i	−0.0268438	+	0.0298131i
$604$	3.82523	−	6.62549i	0.155646	−	0.269588i
$605$	24.1061	+	38.9228i	0.980053	+	1.58244i
$606$	−5.84345	−	10.1211i	−0.237374	−	0.411144i
$607$	8.45422	+	26.0194i	0.343146	+	1.05609i	0.962569	+	0.271037i	$0.0873667\pi$
$607$	8.45422	+	26.0194i	0.343146	+	1.05609i	−0.619423	+	0.785058i	$0.712633\pi$
$608$	−1.49771	+	4.09351i	−0.0607403	+	0.166014i
$609$	−6.47031	+	4.70095i	−0.262190	+	0.190492i
$610$	6.06836	−	1.28987i	0.245701	−	0.0522253i
$611$	−11.2852	+	2.39874i	−0.456549	+	0.0970425i
$612$	−0.785218	−	7.47085i	−0.0317406	−	0.301991i
$613$	4.40746	−	41.9342i	0.178016	−	1.69371i	−0.432445	−	0.901660i	$-0.642349\pi$
$613$	4.40746	−	41.9342i	0.178016	−	1.69371i	0.610461	−	0.792046i	$-0.290984\pi$
$614$	−5.49747	−	1.16852i	−0.221860	−	0.0471578i
$615$	18.2508			0.735945
$616$	−6.02486	−	4.23660i	−0.242749	−	0.170697i
$617$	20.9170	−	36.2293i	0.842085	−	1.45853i	−0.0460429	−	0.998939i	$-0.514661\pi$
$617$	20.9170	−	36.2293i	0.842085	−	1.45853i	0.888128	−	0.459595i	$-0.152006\pi$
$618$	5.32183	+	1.13119i	0.214075	+	0.0455031i
$619$	27.7622	+	20.1704i	1.11586	+	0.810716i	0.983576	−	0.180496i	$-0.0577703\pi$
$619$	27.7622	+	20.1704i	1.11586	+	0.810716i	0.132280	+	0.991212i	$0.457770\pi$
$620$	31.9925	−	23.2439i	1.28485	−	0.933498i
$621$	17.9929	+	19.9831i	0.722028	+	0.801894i
$622$	27.7945	−	5.90791i	1.11446	−	0.236886i
$623$	−0.0296649	−	0.282243i	−0.00118850	−	0.0113078i
$624$	0.421682	−	4.01204i	0.0168808	−	0.160610i
$625$	43.6555	−	48.4844i	1.74622	−	1.93938i
$626$	14.1707			0.566375
$627$	5.65901	−	9.34020i	0.225999	−	0.373012i
$628$	0.553618			0.0220917
$629$	3.98478	−	4.42555i	0.158884	−	0.176458i
$630$	−2.34711	+	22.3312i	−0.0935110	+	0.889698i
$631$	3.53884	+	33.6698i	0.140879	+	1.34037i	0.805234	+	0.592957i	$0.202039\pi$
$631$	3.53884	+	33.6698i	0.140879	+	1.34037i	−0.664355	+	0.747417i	$0.731294\pi$
$632$	9.38302	−	1.99442i	0.373236	−	0.0793338i
$633$	4.43454	+	4.92506i	0.176257	+	0.195753i
$634$	−14.6784	+	10.6645i	−0.582955	+	0.423541i
$635$	−29.4389	−	21.3886i	−1.16825	−	0.848782i
$636$	−2.61647	−	0.556148i	−0.103750	−	0.0220527i
$637$	5.52296	−	9.56604i	0.218828	−	0.379020i
$638$	−5.11805	−	14.9608i	−0.202625	−	0.592305i
$639$	−7.07375			−0.279833
$640$	−4.07114	−	0.865348i	−0.160926	−	0.0342059i
$641$	0.396238	−	3.76996i	0.0156505	−	0.148904i	−0.983906	−	0.178687i	$-0.942815\pi$
$641$	0.396238	−	3.76996i	0.0156505	−	0.148904i	0.999556	+	0.0297830i	$0.00948162\pi$
$642$	0.240633	+	2.28947i	0.00949701	+	0.0903580i
$643$	38.6673	−	8.21898i	1.52489	−	0.324125i	0.632202	−	0.774804i	$-0.282151\pi$
$643$	38.6673	−	8.21898i	1.52489	−	0.324125i	0.892686	+	0.450679i	$0.148818\pi$
$644$	14.2416	−	3.02714i	0.561197	−	0.119286i
$645$	0.879705	−	0.639143i	0.0346384	−	0.0251662i
$646$	4.63119	−	12.6579i	0.182212	−	0.498017i
$647$	10.9737	+	33.7736i	0.431421	+	1.32778i	0.896710	+	0.442618i	$0.145950\pi$
$647$	10.9737	+	33.7736i	0.431421	+	1.32778i	−0.465290	+	0.885159i	$0.654050\pi$
$648$	2.09494	+	3.62853i	0.0822968	+	0.142542i
$649$	11.4591	+	19.1577i	0.449809	+	0.752004i
$650$	32.9047	−	56.9925i	1.29063	−	2.23543i
$651$	10.6651	−	11.8448i	0.417998	−	0.464234i
$652$	0.110455	−	0.0491776i	0.00432574	−	0.00192594i
$653$	−21.1852	+	15.3919i	−0.829040	+	0.602333i	−0.919288	−	0.393586i	$-0.871234\pi$
$653$	−21.1852	+	15.3919i	−0.829040	+	0.602333i	0.0902473	+	0.995919i	$0.471234\pi$
$654$	−3.55390	+	10.9378i	−0.138969	+	0.427701i
$655$	6.74673	+	7.49300i	0.263617	+	0.292776i
$656$	−0.606770	−	5.77303i	−0.0236904	−	0.225399i
$657$	25.8579	+	18.7868i	1.00881	+	0.732944i
$658$	1.48256	+	4.56284i	0.0577960	+	0.177878i
$659$	−9.33291	+	16.1651i	−0.363558	+	0.629702i	−0.988544	−	0.150935i	$-0.951772\pi$
$659$	−9.33291	+	16.1651i	−0.363558	+	0.629702i	0.624985	+	0.780637i	$0.285105\pi$
$660$	9.59062	+	4.09359i	0.373314	+	0.159343i
$661$	−21.4586	+	37.1673i	−0.834642	+	1.44564i	0.0596799	+	0.998218i	$0.480992\pi$
$661$	−21.4586	+	37.1673i	−0.834642	+	1.44564i	−0.894322	+	0.447424i	$0.852341\pi$
$662$	17.6942	−	19.6514i	0.687704	−	0.763773i
$663$	−1.30391	+	12.4059i	−0.0506398	+	0.481806i
$664$	−5.79710	+	4.21184i	−0.224971	+	0.163451i
$665$	−21.4072	+	34.1308i	−0.830134	+	1.32354i
$666$	−1.44579	+	4.44967i	−0.0560231	+	0.172421i
$667$	28.5549	+	12.7135i	1.10565	+	0.492268i
$668$	0.732337	−	6.96772i	0.0283350	−	0.269589i
$669$	−11.3185	−	2.40582i	−0.437598	−	0.0930142i
$670$	−0.843883	−	1.46165i	−0.0326021	−	0.0564684i
$671$	0.592688	+	4.90803i	0.0228805	+	0.189472i
$672$	−1.67755			−0.0647129
$673$	1.96225	+	6.03920i	0.0756394	+	0.232794i	0.981727	−	0.190297i	$-0.0609451\pi$
$673$	1.96225	+	6.03920i	0.0756394	+	0.232794i	−0.906087	+	0.423091i	$0.860945\pi$
$674$	27.7750	−	12.3662i	1.06985	−	0.476329i
$675$	−5.28302	−	50.2646i	−0.203344	−	1.93468i
$676$	4.79572	−	14.7597i	0.184451	−	0.567682i
$677$	2.30752	−	7.10183i	0.0886853	−	0.272945i	−0.896871	−	0.442292i	$-0.854166\pi$
$677$	2.30752	−	7.10183i	0.0886853	−	0.272945i	0.985557	+	0.169346i	$0.0541656\pi$
$678$	−0.569461	−	5.41806i	−0.0218700	−	0.208079i
$679$	−2.49417	+	23.7304i	−0.0957173	+	0.910690i
$680$	12.5887	+	2.67581i	0.482754	+	0.102613i
$681$	−10.6971	−	18.5279i	−0.409913	−	0.709990i
$682$	16.1759	+	27.0433i	0.619406	+	1.03554i
$683$	23.6992			0.906826			0.453413	−	0.891301i	$-0.350206\pi$
$683$	23.6992			0.906826			0.453413	+	0.891301i	$0.350206\pi$
$684$	0.720917	+	10.5648i	0.0275649	+	0.403954i
$685$	−57.7792	−	41.9791i	−2.20763	−	1.60394i
$686$	−18.3973	−	8.19102i	−0.702413	−	0.312734i
$687$	−18.9781	+	4.03391i	−0.724058	+	0.153903i
$688$	−0.231418	−	0.257016i	−0.00882273	−	0.00979863i
$689$	−17.2755	−	7.69153i	−0.658142	−	0.293024i
$690$	−18.8314	+	8.38428i	−0.716900	+	0.319184i
$691$	−0.286560	−	0.881940i	−0.0109012	−	0.0335506i	0.945458	−	0.325744i	$-0.105615\pi$
$691$	−0.286560	−	0.881940i	−0.0109012	−	0.0335506i	−0.956359	+	0.292194i	$0.905615\pi$
$692$	11.3913			0.433032
$693$	−17.5574	−	3.44919i	−0.666950	−	0.131024i
$694$	−7.96153	+	13.7898i	−0.302216	+	0.523453i
$695$	4.74513	+	14.6040i	0.179993	+	0.553961i
$696$	−2.91360	−	2.11686i	−0.110440	−	0.0802393i
$697$	1.87624	+	17.8512i	0.0710676	+	0.676163i
$698$	−13.8483	+	2.94355i	−0.524166	+	0.111415i
$699$	−1.34405	−	1.49272i	−0.0508368	−	0.0564599i
$700$	−25.0001	−	11.1308i	−0.944917	−	0.420704i
$701$	−0.691386	+	6.57810i	−0.0261133	+	0.248451i	0.973676	+	0.227935i	$0.0731975\pi$
$701$	−0.691386	+	6.57810i	−0.0261133	+	0.248451i	−0.999790	+	0.0205158i	$0.993469\pi$
$702$	−6.76833	−	20.8308i	−0.255454	−	0.786207i
$703$	−5.84161	+	6.02885i	−0.220320	+	0.227382i
$704$	0.976016	−	3.16976i	0.0367850	−	0.119465i
$705$	−3.39623	−	5.88245i	−0.127910	−	0.221546i
$706$	13.9728	−	15.5184i	0.525873	−	0.584041i
$707$	−31.3865	+	13.9742i	−1.18041	+	0.525552i
$708$	4.64485	+	2.06802i	0.174564	+	0.0777210i
$709$	−5.70795	−	6.33932i	−0.214366	−	0.238078i	0.626366	−	0.779529i	$-0.284542\pi$
$709$	−5.70795	−	6.33932i	−0.214366	−	0.238078i	−0.840732	+	0.541451i	$0.817875\pi$
$710$	3.74500	−	11.5259i	0.140547	−	0.432561i
$711$	18.8533	−	13.6977i	0.707054	−	0.513705i
$712$	0.116747	−	0.0519790i	0.00437527	−	0.00194799i
$713$	−60.9315	−	12.9514i	−2.28190	−	0.485034i
$714$	5.18728			0.194129
$715$	60.3023	+	42.4038i	2.25518	+	1.58581i
$716$	−9.81137	+	16.9938i	−0.366668	+	0.635088i
$717$	−7.63703	+	8.48178i	−0.285210	+	0.316758i
$718$	8.17196	−	3.63839i	0.304975	−	0.135784i
$719$	4.40953	+	1.96325i	0.164448	+	0.0732169i	0.487310	−	0.873229i	$-0.337978\pi$
$719$	4.40953	+	1.96325i	0.164448	+	0.0732169i	−0.322862	+	0.946446i	$0.604645\pi$
$720$	−9.89027	+	2.10224i	−0.368589	+	0.0783460i
$721$	4.94256	−	15.2116i	0.184071	−	0.566511i
$722$	−7.17671	+	17.5925i	−0.267090	+	0.654724i
$723$	1.32730	+	0.964340i	0.0493628	+	0.0358642i
$724$	11.4946	−	12.7660i	0.427193	−	0.474446i
$725$	−29.3751	−	50.8792i	−1.09096	−	1.88961i
$726$	−3.93032	+	7.32120i	−0.145868	+	0.271715i
$727$	−5.56558	−	9.63986i	−0.206416	−	0.357523i	0.744167	−	0.667993i	$-0.232847\pi$
$727$	−5.56558	−	9.63986i	−0.206416	−	0.357523i	−0.950583	+	0.310471i	$0.899513\pi$
$728$	−11.6003	−	2.46571i	−0.429935	−	0.0913854i
$729$	0.715230	+	0.519645i	0.0264900	+	0.0192461i
$730$	−44.3009	+	32.1865i	−1.63965	+	1.19128i
$731$	0.715585	+	0.794737i	0.0264669	+	0.0293944i
$732$	0.753436	+	0.836776i	0.0278478	+	0.0309281i
$733$	−38.7870	+	28.1804i	−1.43263	+	1.04087i	−0.443112	+	0.896466i	$0.646126\pi$
$733$	−38.7870	+	28.1804i	−1.43263	+	1.04087i	−0.989519	+	0.144402i	$0.953874\pi$
$734$	16.1724	+	11.7500i	0.596935	+	0.433699i
$735$	6.36107	+	1.35209i	0.234631	+	0.0498725i
$736$	3.27816	+	5.67793i	0.120834	+	0.209291i
$737$	1.22004	−	0.565954i	0.0449409	−	0.0208472i
$738$	−7.05101	−	12.2127i	−0.259551	−	0.449556i
$739$	26.2843	−	29.1916i	0.966882	−	1.07383i	−0.0303547	−	0.999539i	$-0.509664\pi$
$739$	26.2843	−	29.1916i	0.966882	−	1.07383i	0.997237	−	0.0742919i	$-0.0236697\pi$
$740$	−6.48484	−	4.71151i	−0.238388	−	0.173199i
$741$	2.47654	−	17.4091i	0.0909780	−	0.639540i
$742$	−2.43000	+	7.47878i	−0.0892082	+	0.274555i
$743$	0.351250	−	0.0746605i	0.0128861	−	0.00273903i	−0.201464	−	0.979496i	$-0.564570\pi$
$743$	0.351250	−	0.0746605i	0.0128861	−	0.00273903i	0.214350	+	0.976757i	$0.431237\pi$
$744$	6.55676	+	2.91926i	0.240383	+	0.107025i
$745$	−81.8411	+	36.4380i	−2.99843	+	1.33499i
$746$	13.7852	−	15.3101i	0.504714	−	0.560541i
$747$	−8.70392	+	15.0756i	−0.318460	+	0.551589i
$748$	−3.01801	+	9.80146i	−0.110349	+	0.358377i
$749$	6.76758			0.247282
$750$	22.5211	+	4.78700i	0.822353	+	0.174797i
$751$	2.43399	−	1.08368i	0.0888175	−	0.0395441i	−0.361847	−	0.932237i	$-0.617854\pi$
$751$	2.43399	−	1.08368i	0.0888175	−	0.0395441i	0.450665	+	0.892693i	$0.351187\pi$
$752$	−1.74780	+	1.26985i	−0.0637357	+	0.0463067i
$753$	0.753059	−	2.31768i	0.0274430	−	0.0844609i
$754$	−17.0362	−	18.9206i	−0.620421	−	0.689047i
$755$	29.0891	+	12.9513i	1.05866	+	0.471346i
$756$	−8.32059	+	3.70457i	−0.302617	+	0.134734i
$757$	−25.4419	+	28.2561i	−0.924703	+	1.02699i	0.0748535	+	0.997195i	$0.476151\pi$
$757$	−25.4419	+	28.2561i	−0.924703	+	1.02699i	−0.999556	+	0.0297918i	$0.990516\pi$
$758$	−11.2167	−	19.4280i	−0.407411	−	0.705656i
$759$	−5.31683	−	15.5419i	−0.192989	−	0.564136i
$760$	−17.5959	−	4.41857i	−0.638269	−	0.160278i
$761$	3.86870	+	11.9066i	0.140240	+	0.431615i	0.996368	−	0.0851486i	$-0.0271365\pi$
$761$	3.86870	+	11.9066i	0.140240	+	0.431615i	−0.856128	+	0.516764i	$0.827137\pi$
$762$	0.690348	−	6.56822i	0.0250087	−	0.237942i
$763$	30.8863	+	13.7515i	1.11816	+	0.497837i
$764$	16.5790	+	18.4129i	0.599808	+	0.666154i
$765$	30.5825	−	6.50050i	1.10571	−	0.235026i
$766$	1.48746	+	14.1523i	0.0537442	+	0.511342i
$767$	29.0796	+	21.1275i	1.05000	+	0.762871i
$768$	−0.233434	−	0.718435i	−0.00842331	−	0.0259243i
$769$	12.7193	−	22.0304i	0.458669	−	0.794438i	−0.540222	−	0.841522i	$-0.681660\pi$
$769$	12.7193	−	22.0304i	0.458669	−	0.794438i	0.998891	+	0.0470848i	$0.0149931\pi$
$770$	14.9154	−	26.7818i	0.537513	−	0.965150i
$771$	−18.2140			−0.655962
$772$	−4.67817	−	14.3979i	−0.168371	−	0.518193i
$773$	−34.9796	+	15.5739i	−1.25813	+	0.560154i	−0.924007	−	0.382376i	$-0.875106\pi$
$773$	−34.9796	+	15.5739i	−1.25813	+	0.560154i	−0.334121	+	0.942530i	$0.608439\pi$
$774$	−0.767553	−	0.341737i	−0.0275891	−	0.0122835i
$775$	78.3443	+	87.0101i	2.81421	+	3.12550i
$776$	−10.5100	+	2.23396i	−0.377285	+	0.0801945i
$777$	−2.95145	−	1.31407i	−0.105883	−	0.0471420i
$778$	7.04677	+	5.11978i	0.252639	+	0.183553i
$779$	−1.72259	−	25.2440i	−0.0617183	−	0.904459i
$780$	16.7905			0.601195
$781$	8.88201	+	3.79113i	0.317823	+	0.135657i
$782$	−10.1366	−	17.5572i	−0.362485	−	0.627842i
$783$	−19.1261	−	4.06537i	−0.683510	−	0.145285i
$784$	0.216206	−	2.05706i	0.00772163	−	0.0734664i
$785$	0.240856	+	2.29159i	0.00859650	+	0.0817902i
$786$	−0.565501	+	1.74043i	−0.0201708	+	0.0620792i
$787$	7.04507	−	21.6825i	0.251130	−	0.772898i	−0.743438	−	0.668805i	$-0.766806\pi$
$787$	7.04507	−	21.6825i	0.251130	−	0.772898i	0.994568	−	0.104093i	$-0.0331939\pi$
$788$	−1.10627	−	10.5255i	−0.0394093	−	0.374955i
$789$	17.1897	−	7.65333i	0.611968	−	0.272466i
$790$	12.3377	+	37.9714i	0.438954	+	1.35096i
$791$	−16.0156			−0.569449
$792$	−0.965969	−	7.99916i	−0.0343242	−	0.284238i
$793$	3.98010	+	6.89374i	0.141337	+	0.244804i
$794$	−31.4814	−	6.69157i	−1.11723	−	0.237475i
$795$	1.16374	−	11.0723i	0.0412738	−	0.392694i
$796$	−6.46465	−	2.87825i	−0.229134	−	0.102017i
$797$	−4.51744	+	13.9033i	−0.160016	+	0.492479i	−0.998635	−	0.0522406i	$-0.983364\pi$
$797$	−4.51744	+	13.9033i	−0.160016	+	0.492479i	0.838619	+	0.544719i	$0.183364\pi$
$798$	−7.30738	−	0.267478i	−0.258678	−	0.00946863i
$799$	5.40450	−	3.92660i	0.191198	−	0.138913i
$800$	1.28811	−	12.2555i	0.0455415	−	0.433299i
$801$	0.207739	−	0.230717i	0.00734008	−	0.00815199i
$802$	12.4033	−	21.4831i	0.437974	−	0.758594i
$803$	−22.3992	−	37.4477i	−0.790451	−	1.32150i
$804$	0.153162	−	0.265285i	0.00540161	−	0.00935587i
$805$	18.7261	+	57.6331i	0.660010	+	2.03130i
$806$	41.0493	+	29.8240i	1.44590	+	1.05051i
$807$	0.422287	+	4.01779i	0.0148652	+	0.141433i
$808$	−10.3521	−	11.4972i	−0.364186	−	0.404470i
$809$	7.43677	−	22.8880i	0.261463	−	0.804701i	−0.731024	−	0.682352i	$-0.760957\pi$
$809$	7.43677	−	22.8880i	0.261463	−	0.804701i	0.992487	−	0.122349i	$-0.0390427\pi$
$810$	−14.1082	+	10.2502i	−0.495710	+	0.360154i
$811$	1.11666	−	0.497170i	0.0392113	−	0.0174580i	−0.387037	−	0.922064i	$-0.626502\pi$
$811$	1.11666	−	0.497170i	0.0392113	−	0.0174580i	0.426249	+	0.904606i	$0.359835\pi$
$812$	−7.08430	+	7.86791i	−0.248610	+	0.276110i
$813$	−8.19490	+	14.1940i	−0.287408	+	0.497804i
$814$	4.20014	−	4.81228i	0.147215	−	0.168670i
$815$	0.251615	+	0.435810i	0.00881368	+	0.0152657i
$816$	0.721817	+	2.22153i	0.0252687	+	0.0777690i
$817$	−0.967073	−	1.15645i	−0.0338336	−	0.0404592i
$818$	−13.9820	+	10.1585i	−0.488868	+	0.355183i
$819$	−28.1812	+	5.99011i	−0.984732	+	0.209311i
$820$	23.6323	−	5.02320i	0.825276	−	0.175418i
$821$	−3.49218	−	33.2259i	−0.121878	−	1.15959i	−0.868968	−	0.494868i	$-0.835216\pi$
$821$	−3.49218	−	33.2259i	−0.121878	−	1.15959i	0.747090	−	0.664723i	$-0.231450\pi$
$822$	1.35493	−	12.8913i	0.0472587	−	0.449637i
$823$	2.20654	+	0.469014i	0.0769151	+	0.0163488i	0.246208	−	0.969217i	$-0.420815\pi$
$823$	2.20654	+	0.469014i	0.0769151	+	0.0163488i	−0.169293	+	0.985566i	$0.554149\pi$
$824$	7.20237			0.250906
$825$	−9.08565	+	29.5070i	−0.316322	+	1.02730i
$826$	7.47352	−	12.9445i	0.260037	−	0.450397i
$827$	−20.4637	−	4.34970i	−0.711593	−	0.151254i	−0.162127	−	0.986770i	$-0.551836\pi$
$827$	−20.4637	−	4.34970i	−0.711593	−	0.151254i	−0.549466	+	0.835516i	$0.685169\pi$
$828$	12.8857	+	9.36203i	0.447810	+	0.325353i
$829$	25.6462	−	18.6330i	0.890729	−	0.647152i	−0.0453391	−	0.998972i	$-0.514437\pi$
$829$	25.6462	−	18.6330i	0.890729	−	0.647152i	0.936068	+	0.351819i	$0.114437\pi$
$830$	−19.9561	−	22.1635i	−0.692687	−	0.769307i
$831$	7.10514	−	1.51024i	0.246475	−	0.0523898i
$832$	−0.558218	−	5.31109i	−0.0193527	−	0.184129i
$833$	−0.668545	+	6.36078i	−0.0231637	+	0.220388i
$834$	−1.86486	+	2.07113i	−0.0645747	+	0.0717174i
$835$	29.1601			1.00913
$836$	4.75692	−	13.6518i	0.164521	−	0.472158i
$837$	38.9680			1.34693
$838$	−4.20225	+	4.66707i	−0.145164	+	0.161221i
$839$	−1.98466	+	18.8828i	−0.0685182	+	0.651907i	0.905330	+	0.424708i	$0.139623\pi$
$839$	−1.98466	+	18.8828i	−0.0685182	+	0.651907i	−0.973848	+	0.227199i	$0.927043\pi$
$840$	−0.729831	−	6.94388i	−0.0251816	−	0.239586i
$841$	6.13380	−	1.30378i	0.211510	−	0.0449579i
$842$	−10.6526	−	11.8309i	−0.367114	−	0.407721i
$843$	−5.54125	+	4.02595i	−0.190851	+	0.138661i
$844$	7.09765	+	5.15674i	0.244311	+	0.177502i
$845$	63.1813	+	13.4296i	2.17350	+	0.461992i
$846$	−2.62420	+	4.54524i	−0.0902217	+	0.156269i
$847$	20.1970	+	13.7407i	0.693977	+	0.472135i
$848$	−3.54103			−0.121600
$849$	−4.86586	−	1.03427i	−0.166996	−	0.0354961i
$850$	−3.98306	+	37.8962i	−0.136618	+	1.29983i
$851$	1.31985	+	12.5575i	0.0452438	+	0.430466i
$852$	2.15151	−	0.457317i	0.0737095	−	0.0156674i
$853$	0.0767825	−	0.0163206i	0.00262898	−	0.000558808i	−0.206597	−	0.978426i	$-0.566239\pi$
$853$	0.0767825	−	0.0163206i	0.00262898	−	0.000558808i	0.209226	+	0.977867i	$0.432906\pi$
$854$	2.67798	−	1.94566i	0.0916384	−	0.0665792i
$855$	−43.4171	+	7.58037i	−1.48483	+	0.259243i
$856$	0.941719	+	2.89831i	0.0321873	+	0.0990623i
$857$	1.78802	+	3.09694i	0.0610775	+	0.105789i	0.894947	−	0.446172i	$-0.147213\pi$
$857$	1.78802	+	3.09694i	0.0610775	+	0.105789i	−0.833870	+	0.551961i	$0.813880\pi$
$858$	−1.19272	+	13.3264i	−0.0407189	+	0.454957i
$859$	−0.339008	+	0.587179i	−0.0115668	+	0.0200343i	−0.871751	−	0.489949i	$-0.837015\pi$
$859$	−0.339008	+	0.587179i	−0.0115668	+	0.0200343i	0.860184	+	0.509984i	$0.170349\pi$
$860$	0.963184	−	1.06972i	0.0328443	−	0.0364773i
$861$	8.89601	−	3.96076i	0.303175	−	0.134982i
$862$	−19.4592	+	14.1380i	−0.662784	+	0.481541i
$863$	−0.483143	+	1.48696i	−0.0164464	+	0.0506167i	−0.958943	−	0.283599i	$-0.908471\pi$
$863$	−0.483143	+	1.48696i	−0.0164464	+	0.0506167i	0.942497	+	0.334216i	$0.108471\pi$
$864$	−2.74436	−	3.04792i	−0.0933649	−	0.103692i
$865$	4.95586	+	47.1519i	0.168504	+	1.60321i
$866$	19.7270	+	14.3325i	0.670351	+	0.487039i
$867$	1.73639	+	5.34405i	0.0589708	+	0.181493i
$868$	10.5498	−	18.2727i	0.358082	−	0.620217i
$869$	−31.0140	+	7.09496i	−1.05208	+	0.240680i
$870$	7.49471	−	12.9812i	0.254095	−	0.440105i
$871$	1.44904	−	1.60932i	0.0490989	−	0.0545298i
$872$	−1.59139	+	15.1411i	−0.0538912	+	0.512741i
$873$	−21.1177	+	15.3429i	−0.714725	+	0.519278i
$874$	13.3743	+	25.2557i	0.452391	+	0.854285i
$875$	20.9161	−	64.3731i	0.707093	−	2.17621i
$876$	−9.07934	−	4.04238i	−0.306763	−	0.136579i
$877$	5.79049	−	55.0928i	0.195531	−	1.86035i	−0.254154	−	0.967164i	$-0.581797\pi$
$877$	5.79049	−	55.0928i	0.195531	−	1.86035i	0.449685	−	0.893187i	$-0.351536\pi$
$878$	−18.6997	−	3.97475i	−0.631086	−	0.134141i
$879$	6.92297	+	11.9909i	0.233506	+	0.404444i
$880$	13.5452	+	2.66099i	0.456609	+	0.0897020i
$881$	−26.4871			−0.892373			−0.446187	−	0.894940i	$-0.647218\pi$
$881$	−26.4871			−0.892373			−0.446187	+	0.894940i	$0.647218\pi$
$882$	−1.55277	−	4.77893i	−0.0522844	−	0.160915i
$883$	−3.33408	+	1.48443i	−0.112201	+	0.0499549i	−0.462069	−	0.886844i	$-0.652893\pi$
$883$	−3.33408	+	1.48443i	−0.112201	+	0.0499549i	0.349869	+	0.936799i	$0.386226\pi$
$884$	1.72611	+	16.4228i	0.0580553	+	0.552359i
$885$	−6.53938	+	20.1261i	−0.219819	+	0.676533i
$886$	−10.7353	+	33.0398i	−0.360658	+	1.10999i
$887$	2.75298	+	26.1929i	0.0924360	+	0.879470i	0.938242	+	0.345979i	$0.112453\pi$
$887$	2.75298	+	26.1929i	0.0924360	+	0.879470i	−0.845806	+	0.533490i	$0.820880\pi$
$888$	0.152071	−	1.44686i	0.00510316	−	0.0485533i
$889$	−18.9911	−	4.03669i	−0.636943	−	0.135386i
$890$	0.265948	+	0.460635i	0.00891459	+	0.0154405i
$891$	−7.13330	−	11.9257i	−0.238974	−	0.399524i
$892$	−15.3180			−0.512885
$893$	−7.81586	+	5.25277i	−0.261548	+	0.175777i
$894$	−13.1543	−	9.55716i	−0.439946	−	0.319639i
$895$	−74.6108	−	33.2189i	−2.49397	−	1.11038i
$896$	−2.17219	+	0.461714i	−0.0725679	+	0.0154248i
$897$	−17.6979	−	19.6555i	−0.590914	−	0.656277i
$898$	4.08815	+	1.82016i	0.136423	+	0.0607396i
$899$	41.3809	−	18.4240i	1.38013	−	0.614474i
$900$	−9.25108	−	28.4719i	−0.308369	−	0.949063i
$901$	10.9495			0.364780
$902$	2.30813	+	19.1136i	0.0768524	+	0.636413i
$903$	0.290089	−	0.502450i	0.00965357	−	0.0167205i
$904$	−2.22859	−	6.85891i	−0.0741219	−	0.228124i
$905$	57.8432	+	42.0255i	1.92277	+	1.39698i
$906$	0.604092	+	5.74755i	0.0200696	+	0.190950i
$907$	−6.98501	+	1.48471i	−0.231933	+	0.0492990i	−0.322412	−	0.946599i	$-0.604494\pi$
$907$	−6.98501	+	1.48471i	−0.231933	+	0.0492990i	0.0904786	+	0.995898i	$0.471160\pi$
$908$	−18.9507	−	21.0469i	−0.628901	−	0.698465i
$909$	−34.3352	−	15.2870i	−1.13883	−	0.507039i
$910$	5.15953	−	49.0897i	0.171037	−	1.62731i
$911$	14.3326	+	44.1111i	0.474859	+	1.46147i	0.846148	+	0.532948i	$0.178916\pi$
$911$	14.3326	+	44.1111i	0.474859	+	1.46147i	−0.371289	+	0.928517i	$0.621084\pi$
$912$	−0.902281	−	3.16671i	−0.0298775	−	0.104860i
$913$	19.0086	−	14.2646i	0.629092	−	0.472089i
$914$	2.21910	+	3.84360i	0.0734014	+	0.127135i
$915$	−3.13587	+	3.48274i	−0.103669	+	0.115136i
$916$	−23.4637	+	10.4467i	−0.775263	+	0.345169i
$917$	4.91468	+	2.18815i	0.162297	+	0.0722592i
$918$	8.48603	+	9.42469i	0.280081	+	0.311061i
$919$	15.8711	−	48.8464i	0.523541	−	1.61129i	−0.243643	−	0.969865i	$-0.578342\pi$
$919$	15.8711	−	48.8464i	0.523541	−	1.61129i	0.767184	−	0.641428i	$-0.221658\pi$
$920$	−22.0764	+	16.0395i	−0.727839	+	0.528806i
$921$	3.87855	−	1.72684i	0.127803	−	0.0569014i
$922$	−0.0196896	−	0.00418516i	−0.000648443	−	0.000137831i
$923$	15.5499			0.511831
$924$	5.56314	−	0.0859972i	0.183014	−	0.00282910i
$925$	11.8664	−	20.5531i	0.390164	−	0.675783i
$926$	−8.48016	+	9.41817i	−0.278675	+	0.309500i
$927$	15.9844	−	7.11673i	0.524998	−	0.233744i
$928$	−4.35534	−	1.93912i	−0.142971	−	0.0636548i
$929$	17.1636	−	3.64823i	0.563119	−	0.119695i	0.0824473	−	0.996595i	$-0.473726\pi$
$929$	17.1636	−	3.64823i	0.563119	−	0.119695i	0.480671	+	0.876901i	$0.340393\pi$
$930$	−9.23111	+	28.4104i	−0.302700	+	0.931615i
$931$	1.26978	−	8.92604i	0.0416153	−	0.292539i
$932$	−2.15121	−	1.56294i	−0.0704651	−	0.0511959i
$933$	−14.3631	+	15.9518i	−0.470225	+	0.522238i
$934$	11.6800	+	20.2303i	0.382180	+	0.661955i
$935$	−41.8841	−	8.22825i	−1.36976	−	0.269093i
$936$	−6.48681	−	11.2355i	−0.212028	−	0.367243i
$937$	−32.9633	−	7.00657i	−1.07686	−	0.228895i	−0.364855	−	0.931064i	$-0.618881\pi$
$937$	−32.9633	−	7.00657i	−1.07686	−	0.228895i	−0.712010	+	0.702170i	$0.752215\pi$
$938$	−0.728538	−	0.529314i	−0.0237876	−	0.0172827i
$939$	−8.66025	+	6.29204i	−0.282616	+	0.205333i
$940$	−6.01669	−	6.68221i	−0.196243	−	0.217950i
$941$	21.9868	+	24.4188i	0.716750	+	0.796031i	0.985948	−	0.167053i	$-0.0534253\pi$
$941$	21.9868	+	24.4188i	0.716750	+	0.796031i	−0.269198	+	0.963085i	$0.586759\pi$
$942$	−0.338336	+	0.245816i	−0.0110236	+	0.00800911i
$943$	−30.7898	−	22.3701i	−1.00265	−	0.728470i
$944$	6.58363	+	1.39939i	0.214279	+	0.0455464i
$945$	−18.9542	−	32.8297i	−0.616581	−	1.06795i
$946$	0.780611	+	0.840460i	0.0253798	+	0.0273257i
$947$	−11.2681	−	19.5169i	−0.366164	−	0.634215i	0.622798	−	0.782383i	$-0.285996\pi$
$947$	−11.2681	−	19.5169i	−0.366164	−	0.634215i	−0.988962	+	0.148168i	$0.952663\pi$
$948$	−4.84875	+	5.38509i	−0.157480	+	0.174899i
$949$	−56.8421	−	41.2982i	−1.84517	−	1.34060i
$950$	7.56507	−	53.1795i	0.245443	−	1.72537i
$951$	4.23531	−	13.0349i	0.137339	−	0.422687i
$952$	6.71680	−	1.42770i	0.217693	−	0.0462720i
$953$	−1.37632	−	0.612778i	−0.0445835	−	0.0198498i	0.384324	−	0.923198i	$-0.374435\pi$
$953$	−1.37632	−	0.612778i	−0.0445835	−	0.0198498i	−0.428907	+	0.903349i	$0.641101\pi$
$954$	−7.85872	+	3.49893i	−0.254436	+	0.113282i
$955$	−69.0035	+	76.6361i	−2.23290	+	2.47989i
$956$	−7.55444	+	13.0847i	−0.244328	+	0.423189i
$957$	9.77069	+	6.87062i	0.315842	+	0.222096i
$958$	3.03298			0.0979913
$959$	−37.2736	−	7.92274i	−1.20363	−	0.255839i
$960$	2.87226	−	1.27881i	0.0927017	−	0.0412735i
$961$	−47.9526	+	34.8396i	−1.54686	+	1.12386i
$962$	3.17820	−	9.78150i	0.102469	−	0.315368i
$963$	4.95384	+	5.50179i	0.159635	+	0.177293i
$964$	1.98409	+	0.883372i	0.0639031	+	0.0284515i
$965$	57.5620	−	25.6283i	1.85299	−	0.825003i
$966$	−7.35946	+	8.17351i	−0.236787	+	0.262978i
$967$	−16.5341	−	28.6379i	−0.531701	−	0.920934i	−0.999315	−	0.0370009i	$-0.988220\pi$
$967$	−16.5341	−	28.6379i	−0.531701	−	0.920934i	0.467614	−	0.883933i	$-0.345114\pi$
$968$	−3.07420	+	10.5617i	−0.0988085	+	0.339466i
$969$	2.79001	+	9.79202i	0.0896281	+	0.314565i
$970$	−13.8195	−	42.5319i	−0.443716	−	1.36562i
$971$	−1.80587	+	17.1817i	−0.0579532	+	0.551388i	0.926569	+	0.376126i	$0.122744\pi$
$971$	−1.80587	+	17.1817i	−0.0579532	+	0.551388i	−0.984522	+	0.175262i	$0.943923\pi$
$972$	−14.1318	−	6.29189i	−0.453278	−	0.201812i
$973$	5.48225	+	6.08865i	0.175753	+	0.195193i
$974$	7.09871	−	1.50888i	0.227457	−	0.0483476i
$975$	5.19640	+	49.4405i	0.166418	+	1.58336i
$976$	1.20590	+	0.876140i	0.0386000	+	0.0280445i
$977$	−12.9606	−	39.8887i	−0.414647	−	1.27615i	−0.912566	−	0.408928i	$-0.865903\pi$
$977$	−12.9606	−	39.8887i	−0.414647	−	1.27615i	0.497920	−	0.867223i	$-0.334097\pi$
$978$	−0.0456673	+	0.0790980i	−0.00146028	+	0.00252928i
$979$	−0.384494	+	0.178359i	−0.0122885	+	0.00570038i
$980$	8.60884			0.274999
$981$	11.4292	+	35.1755i	0.364907	+	1.12307i
$982$	12.7713	−	5.68615i	0.407549	−	0.181452i
$983$	−38.8460	−	17.2953i	−1.23899	−	0.551636i	−0.320567	−	0.947226i	$-0.603873\pi$
$983$	−38.8460	−	17.2953i	−1.23899	−	0.551636i	−0.918427	+	0.395590i	$0.870540\pi$
$984$	2.93414	+	3.25870i	0.0935371	+	0.103883i
$985$	43.0868	−	9.15838i	1.37286	−	0.291810i
$986$	13.4675	+	5.99610i	0.428891	+	0.190955i
$987$	−2.93202	−	2.13024i	−0.0933273	−	0.0678063i
$988$	−1.58476	−	23.2240i	−0.0504178	−	0.738854i
$989$	−2.26749			−0.0721021
$990$	32.6906	−	7.47853i	1.03898	−	0.237683i
$991$	−2.30296	−	3.98884i	−0.0731559	−	0.126710i	0.827127	−	0.562015i	$-0.189974\pi$
$991$	−2.30296	−	3.98884i	−0.0731559	−	0.126710i	−0.900283	+	0.435305i	$0.856640\pi$
$992$	9.29357	+	1.97541i	0.295071	+	0.0627193i
$993$	−2.08802	+	19.8662i	−0.0662614	+	0.630435i
$994$	−0.675906	−	6.43082i	−0.0214385	−	0.203973i
$995$	9.10143	−	28.0113i	0.288535	−	0.888018i
$996$	1.67269	−	5.14802i	0.0530013	−	0.163121i
$997$	2.57404	+	24.4903i	0.0815205	+	0.775616i	0.956554	+	0.291554i	$0.0941724\pi$
$997$	2.57404	+	24.4903i	0.0815205	+	0.775616i	−0.875034	+	0.484062i	$0.839161\pi$
$998$	0.784459	−	0.349264i	0.0248316	−	0.0110557i
$999$	−2.44085	−	7.51218i	−0.0772252	−	0.237675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.159.4	yes	64
11.9	even	5	inner	418.2.n.d.273.5	yes	64
19.11	even	3	inner	418.2.n.d.49.5	✓	64
209.163	even	15	inner	418.2.n.d.163.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.5	✓	64	19.11	even	3	inner
418.2.n.d.159.4	yes	64	1.1	even	1	trivial
418.2.n.d.163.4	yes	64	209.163	even	15	inner
418.2.n.d.273.5	yes	64	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.0789616 - 0.751269i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(4.07114 - 0.865348i) q^{5} +(0.505466 + 0.561377i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37627 + 0.505092i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.0789616 - 0.751269i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(4.07114 - 0.865348i) q^{5} +(0.505466 + 0.561377i) q^{6} +(1.79660 - 1.30531i) q^{7} +(0.809017 + 0.587785i) q^{8} +(2.37627 + 0.505092i) q^{9} +(-2.08105 + 3.60448i) q^{10} +(-2.71302 - 1.90776i) q^{11} -0.755407 q^{12} +(-5.22365 - 1.11032i) q^{13} +(-0.232129 + 2.20856i) q^{14} +(-0.328646 - 3.12685i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(3.02460 - 0.642899i) q^{17} +(-1.96539 + 1.42794i) q^{18} +(-4.29394 + 0.749698i) q^{19} +(-1.28616 - 3.95839i) q^{20} +(-0.838775 - 1.45280i) q^{21} +(3.23310 - 0.739626i) q^{22} +(-3.27816 + 5.67793i) q^{23} +(0.505466 - 0.561377i) q^{24} +(11.2577 - 5.01223i) q^{25} +(4.32043 - 3.13898i) q^{26} +(1.26740 - 3.90064i) q^{27} +(-1.48595 - 1.65032i) q^{28} +(-0.498341 - 4.74139i) q^{29} +(2.54361 + 1.84804i) q^{30} +(2.93603 + 9.03617i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.64746 + 1.88757i) q^{33} +(-1.54609 + 2.67790i) q^{34} +(6.18468 - 6.86878i) q^{35} +(0.253937 - 2.41605i) q^{36} +(1.55807 - 1.13201i) q^{37} +(2.31608 - 3.69267i) q^{38} +(-1.24662 + 3.83669i) q^{39} +(3.80226 + 1.69288i) q^{40} +(-0.606770 + 5.77303i) q^{41} +(1.64089 + 0.348782i) q^{42} +(0.172924 + 0.299514i) q^{43} +(-1.61372 + 2.89757i) q^{44} +10.1112 q^{45} +(-2.02601 - 6.23542i) q^{46} +(1.97362 - 0.878714i) q^{47} +(0.0789616 + 0.751269i) q^{48} +(-0.639168 + 1.96716i) q^{49} +(-3.80803 + 11.7199i) q^{50} +(-0.244163 - 2.32305i) q^{51} +(-0.558218 + 5.31109i) q^{52} +(3.46365 + 0.736222i) q^{53} +(2.05069 + 3.55190i) q^{54} +(-12.6960 - 5.41905i) q^{55} +2.22072 q^{56} +(0.224168 + 3.28510i) q^{57} +(3.85700 + 2.80227i) q^{58} +(-6.14881 - 2.73763i) q^{59} +(-3.07537 + 0.653690i) q^{60} +(-0.997391 - 1.10772i) q^{61} +(-8.67977 - 3.86448i) q^{62} +(4.92852 - 2.19432i) q^{63} +(0.309017 + 0.951057i) q^{64} -22.2270 q^{65} +(-0.300367 - 2.48733i) q^{66} +(-0.202754 + 0.351181i) q^{67} +(-0.955534 - 2.94083i) q^{68} +(4.00681 + 2.91111i) q^{69} +(0.966142 + 9.19223i) q^{70} +(-2.84814 + 0.605392i) q^{71} +(1.62556 + 1.80537i) q^{72} +(12.0191 + 5.35126i) q^{73} +(-0.201310 + 1.91533i) q^{74} +(-2.87661 - 8.85330i) q^{75} +(1.19443 + 4.19206i) q^{76} +(-7.36442 + 0.113842i) q^{77} +(-2.01707 - 3.49366i) q^{78} +(6.41873 - 7.12872i) q^{79} +(-3.80226 + 1.69288i) q^{80} +(3.82764 + 1.70417i) q^{81} +(-3.88419 - 4.31383i) q^{82} +(-2.21429 + 6.81490i) q^{83} +(-1.35717 + 0.986039i) q^{84} +(11.7573 - 5.23467i) q^{85} +(-0.338291 - 0.0719060i) q^{86} -3.60141 q^{87} +(-1.07353 - 3.13808i) q^{88} +(0.0638976 - 0.110674i) q^{89} +(-6.76573 + 7.51411i) q^{90} +(-10.8341 + 4.82366i) q^{91} +(5.98949 + 2.66669i) q^{92} +(7.02043 - 1.49224i) q^{93} +(-0.667601 + 2.05466i) q^{94} +(-16.8325 + 6.76789i) q^{95} +(-0.611137 - 0.444017i) q^{96} +(-7.18964 + 7.98491i) q^{97} +(-1.03419 - 1.79128i) q^{98} +(-5.48328 - 5.90368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

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