LMFDB - Embedded newform 784.2.x.o.557.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.12
Character	$\chi$	$=$	784.557
Dual form			784.2.x.o.373.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41356 - 0.0428532i) q^{2} +(-0.831674 + 0.222846i) q^{3} +(1.99633 - 0.121151i) q^{4} +(2.02749 + 0.543265i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} +(-1.95606 + 1.12933i) q^{9} +O(q^{10})$	\(q+(1.41356 - 0.0428532i) q^{2} +(-0.831674 + 0.222846i) q^{3} +(1.99633 - 0.121151i) q^{4} +(2.02749 + 0.543265i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} +(-1.95606 + 1.12933i) q^{9} +(2.88927 + 0.681055i) q^{10} +(1.03385 + 3.85837i) q^{11} +(-1.63329 + 0.545632i) q^{12} +(0.990473 + 0.990473i) q^{13} -1.80728 q^{15} +(3.97064 - 0.483716i) q^{16} +(-3.07828 + 5.33174i) q^{17} +(-2.71662 + 1.68020i) q^{18} +(1.01626 - 3.79274i) q^{19} +(4.11335 + 0.838901i) q^{20} +(1.62675 + 5.40975i) q^{22} +(5.91462 - 3.41481i) q^{23} +(-2.28538 + 0.841278i) q^{24} +(-0.514543 - 0.297072i) q^{25} +(1.44254 + 1.35765i) q^{26} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(-2.55470 + 0.0774475i) q^{30} +(2.05131 - 3.55296i) q^{31} +(5.59203 - 0.853918i) q^{32} +(-1.71965 - 2.97851i) q^{33} +(-4.12286 + 7.66866i) q^{34} +(-3.76811 + 2.49149i) q^{36} +(0.0740993 + 0.0198548i) q^{37} +(1.27402 - 5.40483i) q^{38} +(-1.04447 - 0.603027i) q^{39} +(5.85044 + 1.00957i) q^{40} +8.68707i q^{41} +(0.713530 - 0.713530i) q^{43} +(2.53134 + 7.57731i) q^{44} +(-4.57941 + 1.22705i) q^{45} +(8.21436 - 5.08051i) q^{46} +(-1.95337 - 3.38334i) q^{47} +(-3.19449 + 1.28714i) q^{48} +(-0.740070 - 0.397880i) q^{50} +(1.37197 - 5.12025i) q^{51} +(2.09731 + 1.85731i) q^{52} +(1.89324 + 7.06568i) q^{53} +(4.38849 - 4.66289i) q^{54} +8.38446i q^{55} +3.38079i q^{57} +(-5.58644 - 5.25769i) q^{58} +(0.851626 + 3.17831i) q^{59} +(-3.60791 + 0.218954i) q^{60} +(2.37044 - 8.84662i) q^{61} +(2.74740 - 5.11025i) q^{62} +(7.86810 - 1.44670i) q^{64} +(1.47009 + 2.54627i) q^{65} +(-2.55847 - 4.13663i) q^{66} +(-1.49739 + 0.401223i) q^{67} +(-5.49930 + 11.0168i) q^{68} +(-4.15805 + 4.15805i) q^{69} -2.86486i q^{71} +(-5.21969 + 3.68336i) q^{72} +(-8.95624 - 5.17089i) q^{73} +(0.105595 + 0.0248907i) q^{74} +(0.494133 + 0.132403i) q^{75} +(1.56929 - 7.69467i) q^{76} +(-1.50227 - 0.807659i) q^{78} +(-3.33631 - 5.77865i) q^{79} +(8.31323 + 1.17638i) q^{80} +(1.43876 - 2.49200i) q^{81} +(0.372269 + 12.2797i) q^{82} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(0.978044 - 1.03920i) q^{86} +(4.04486 + 2.33530i) q^{87} +(3.90293 + 10.6025i) q^{88} +(1.16348 - 0.671733i) q^{89} +(-6.42071 + 1.93076i) q^{90} +(11.3938 - 7.53363i) q^{92} +(-0.914251 + 3.41203i) q^{93} +(-2.90621 - 4.69887i) q^{94} +(4.12092 - 7.13765i) q^{95} +(-4.46045 + 1.95634i) q^{96} +18.7539 q^{97} +(-6.37963 - 6.37963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.41356	−	0.0428532i	0.999541	−	0.0303018i
$2$	1.41356	−	0.0428532i	0.999541	−	0.0303018i
$3$	−0.831674	+	0.222846i	−0.480167	+	0.128660i	−0.490780	−	0.871283i	$-0.663288\pi$
$3$	−0.831674	+	0.222846i	−0.480167	+	0.128660i	0.0106134	+	0.999944i	$0.496622\pi$
$4$	1.99633	−	0.121151i	0.998164	−	0.0605757i
$5$	2.02749	+	0.543265i	0.906722	+	0.242955i	0.681901	−	0.731445i	$-0.261154\pi$
$5$	2.02749	+	0.543265i	0.906722	+	0.242955i	0.224821	+	0.974400i	$0.427820\pi$
$6$	−1.16607	+	0.350647i	−0.476048	+	0.143151i
$7$		0			0
$7$		0			0
$8$	2.81674	−	0.256804i	0.995870	−	0.0907940i
$9$	−1.95606	+	1.12933i	−0.652019	+	0.376443i
$10$	2.88927	+	0.681055i	0.913667	+	0.215368i
$11$	1.03385	+	3.85837i	0.311716	+	1.16334i	0.927008	+	0.375042i	$0.122372\pi$
$11$	1.03385	+	3.85837i	0.311716	+	1.16334i	−0.615291	+	0.788300i	$0.710962\pi$
$12$	−1.63329	+	0.545632i	−0.471491	+	0.157511i
$13$	0.990473	+	0.990473i	0.274708	+	0.274708i	0.830992	−	0.556284i	$-0.187773\pi$
$13$	0.990473	+	0.990473i	0.274708	+	0.274708i	−0.556284	+	0.830992i	$0.687773\pi$
$14$		0			0
$15$	−1.80728			−0.466636
$16$	3.97064	−	0.483716i	0.992661	−	0.120929i
$17$	−3.07828	+	5.33174i	−0.746592	+	1.29314i	0.202855	+	0.979209i	$0.434978\pi$
$17$	−3.07828	+	5.33174i	−0.746592	+	1.29314i	−0.949447	+	0.313927i	$0.898355\pi$
$18$	−2.71662	+	1.68020i	−0.640312	+	0.396028i
$19$	1.01626	−	3.79274i	0.233146	−	0.870114i	−0.745829	−	0.666137i	$-0.767947\pi$
$19$	1.01626	−	3.79274i	0.233146	−	0.870114i	0.978976	−	0.203977i	$-0.0653867\pi$
$20$	4.11335	+	0.838901i	0.919774	+	0.187584i
$21$		0			0
$22$	1.62675	+	5.40975i	0.346825	+	1.15336i
$23$	5.91462	−	3.41481i	1.23328	−	0.712036i	0.265570	−	0.964092i	$-0.414440\pi$
$23$	5.91462	−	3.41481i	1.23328	−	0.712036i	0.967713	+	0.252055i	$0.0811065\pi$
$24$	−2.28538	+	0.841278i	−0.466502	+	0.171725i
$25$	−0.514543	−	0.297072i	−0.102909	−	0.0594143i
$26$	1.44254	+	1.35765i	0.282906	+	0.266258i
$27$	3.20161	−	3.20161i	0.616151	−	0.616151i
$28$		0			0
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	0.254732	−	0.967012i	$-0.418013\pi$
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	−0.967012	+	0.254732i	$0.918013\pi$
$30$	−2.55470	+	0.0774475i	−0.466422	+	0.0141399i
$31$	2.05131	−	3.55296i	0.368425	−	0.638131i	−0.620894	−	0.783894i	$-0.713230\pi$
$31$	2.05131	−	3.55296i	0.368425	−	0.638131i	0.989320	+	0.145763i	$0.0465637\pi$
$32$	5.59203	−	0.853918i	0.988541	−	0.150953i
$33$	−1.71965	−	2.97851i	−0.299352	−	0.518493i
$34$	−4.12286	+	7.66866i	−0.707065	+	1.31516i
$35$		0			0
$36$	−3.76811	+	2.49149i	−0.628018	+	0.415248i
$37$	0.0740993	+	0.0198548i	0.0121818	+	0.00326412i	0.264905	−	0.964275i	$-0.414659\pi$
$37$	0.0740993	+	0.0198548i	0.0121818	+	0.00326412i	−0.252723	+	0.967539i	$0.581326\pi$
$38$	1.27402	−	5.40483i	0.206673	−	0.876779i
$39$	−1.04447	−	0.603027i	−0.167250	−	0.0965616i
$40$	5.85044	+	1.00957i	0.925035	+	0.159627i
$41$			8.68707i			1.35669i	0.734742	+	0.678346i	$0.237303\pi$
$41$			8.68707i			1.35669i	−0.734742	+	0.678346i	$0.762697\pi$
$42$		0			0
$43$	0.713530	−	0.713530i	0.108812	−	0.108812i	−0.650604	−	0.759417i	$-0.725484\pi$
$43$	0.713530	−	0.713530i	0.108812	−	0.108812i	0.759417	+	0.650604i	$0.225484\pi$
$44$	2.53134	+	7.57731i	0.381614	+	1.14232i
$45$	−4.57941	+	1.22705i	−0.682658	+	0.182918i
$46$	8.21436	−	5.08051i	1.21114	−	0.749080i
$47$	−1.95337	−	3.38334i	−0.284929	−	0.493511i	0.687663	−	0.726030i	$-0.258637\pi$
$47$	−1.95337	−	3.38334i	−0.284929	−	0.493511i	−0.972592	+	0.232519i	$0.925303\pi$
$48$	−3.19449	+	1.28714i	−0.461084	+	0.185782i
$49$		0			0
$50$	−0.740070	−	0.397880i	−0.104662	−	0.0562687i
$51$	1.37197	−	5.12025i	0.192114	−	0.716978i
$52$	2.09731	+	1.85731i	0.290844	+	0.257563i
$53$	1.89324	+	7.06568i	0.260057	+	0.970545i	0.965207	+	0.261487i	$0.0842129\pi$
$53$	1.89324	+	7.06568i	0.260057	+	0.970545i	−0.705150	+	0.709058i	$0.749120\pi$
$54$	4.38849	−	4.66289i	0.597198	−	0.634539i
$55$			8.38446i			1.13056i
$56$		0			0
$57$			3.38079i			0.447797i
$58$	−5.58644	−	5.25769i	−0.733535	−	0.690369i
$59$	0.851626	+	3.17831i	0.110872	+	0.413781i	0.998945	−	0.0459220i	$-0.0146226\pi$
$59$	0.851626	+	3.17831i	0.110872	+	0.413781i	−0.888073	+	0.459703i	$0.847956\pi$
$60$	−3.60791	+	0.218954i	−0.465780	+	0.0282668i
$61$	2.37044	−	8.84662i	0.303504	−	1.13269i	−0.630721	−	0.776010i	$-0.717241\pi$
$61$	2.37044	−	8.84662i	0.303504	−	1.13269i	0.934225	−	0.356684i	$-0.116093\pi$
$62$	2.74740	−	5.11025i	0.348920	−	0.649002i
$63$		0			0
$64$	7.86810	−	1.44670i	0.983513	−	0.180838i
$65$	1.47009	+	2.54627i	0.182342	+	0.315825i
$66$	−2.55847	−	4.13663i	−0.314926	−	0.509184i
$67$	−1.49739	+	0.401223i	−0.182935	+	0.0490172i	−0.349123	−	0.937077i	$-0.613521\pi$
$67$	−1.49739	+	0.401223i	−0.182935	+	0.0490172i	0.166189	+	0.986094i	$0.446854\pi$
$68$	−5.49930	+	11.0168i	−0.666889	+	1.33599i
$69$	−4.15805	+	4.15805i	−0.500571	+	0.500571i
$70$		0			0
$71$		−	2.86486i		−	0.339997i	−0.985444	−	0.169998i	$-0.945624\pi$
$71$		−	2.86486i		−	0.339997i	0.985444	−	0.169998i	$-0.0543762\pi$
$72$	−5.21969	+	3.68336i	−0.615147	+	0.434088i
$73$	−8.95624	−	5.17089i	−1.04825	−	0.605207i	−0.126090	−	0.992019i	$-0.540243\pi$
$73$	−8.95624	−	5.17089i	−1.04825	−	0.605207i	−0.922159	+	0.386812i	$0.873576\pi$
$74$	0.105595	+	0.0248907i	0.0122752	+	0.00289349i
$75$	0.494133	+	0.132403i	0.0570576	+	0.0152885i
$76$	1.56929	−	7.69467i	0.180010	−	0.882639i
$77$		0			0
$78$	−1.50227	−	0.807659i	−0.170099	−	0.0914493i
$79$	−3.33631	−	5.77865i	−0.375364	−	0.650149i	0.615018	−	0.788513i	$-0.289149\pi$
$79$	−3.33631	−	5.77865i	−0.375364	−	0.650149i	−0.990381	+	0.138364i	$0.955816\pi$
$80$	8.31323	+	1.17638i	0.929448	+	0.131523i
$81$	1.43876	−	2.49200i	0.159862	−	0.276889i
$82$	0.372269	+	12.2797i	0.0411102	+	1.35607i
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.991674	−	0.128776i	$-0.958895\pi$
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.128776	−	0.991674i	$-0.541105\pi$
$84$		0			0
$85$	−9.13773	+	9.13773i	−0.991126	+	0.991126i
$86$	0.978044	−	1.03920i	0.105465	−	0.112060i
$87$	4.04486	+	2.33530i	0.433655	+	0.250371i
$88$	3.90293	+	10.6025i	0.416053	+	1.13023i
$89$	1.16348	−	0.671733i	0.123328	−	0.0712036i	−0.437067	−	0.899429i	$-0.643983\pi$
$89$	1.16348	−	0.671733i	0.123328	−	0.0712036i	0.560395	+	0.828225i	$0.310649\pi$
$90$	−6.42071	+	1.93076i	−0.676802	+	0.203519i
$91$		0			0
$92$	11.3938	−	7.53363i	1.18789	−	0.785436i
$93$	−0.914251	+	3.41203i	−0.0948034	+	0.353811i
$94$	−2.90621	−	4.69887i	−0.299752	−	0.484651i
$95$	4.12092	−	7.13765i	0.422798	−	0.732307i
$96$	−4.46045	+	1.95634i	−0.455243	+	0.199669i
$97$	18.7539			1.90417			0.952086	−	0.305831i	$-0.0989343\pi$
$97$	18.7539			1.90417			0.952086	+	0.305831i	$0.0989343\pi$
$98$		0			0
$99$	−6.37963	−	6.37963i	−0.641177	−	0.641177i
$100$	−1.06319	−	0.530715i	−0.106319	−	0.0530715i
$101$	−1.15143	−	4.29719i	−0.114571	−	0.427587i	0.884683	−	0.466193i	$-0.154375\pi$
$101$	−1.15143	−	4.29719i	−0.114571	−	0.427587i	−0.999254	+	0.0386065i	$0.987708\pi$
$102$	1.71994	−	7.29659i	0.170300	−	0.722470i
$103$	7.76159	−	4.48115i	0.764772	−	0.441541i	−0.0662345	−	0.997804i	$-0.521099\pi$
$103$	7.76159	−	4.48115i	0.764772	−	0.441541i	0.831006	+	0.556263i	$0.187765\pi$
$104$	3.04427	+	2.53555i	0.298515	+	0.248631i
$105$		0			0
$106$	2.97901	+	9.90665i	0.289347	+	0.962219i
$107$	−12.2706	−	3.28789i	−1.18624	−	0.317852i	−0.388841	−	0.921305i	$-0.627125\pi$
$107$	−12.2706	−	3.28789i	−1.18624	−	0.317852i	−0.797399	+	0.603453i	$0.793791\pi$
$108$	6.00359	−	6.77935i	0.577696	−	0.652343i
$109$	−13.9805	+	3.74605i	−1.33909	+	0.358807i	−0.856095	−	0.516819i	$-0.827116\pi$
$109$	−13.9805	+	3.74605i	−1.33909	+	0.358807i	−0.482990	+	0.875626i	$0.660449\pi$
$110$	0.359301	+	11.8520i	0.0342580	+	1.13004i
$111$	−0.0660510			−0.00626928
$112$		0			0
$113$	2.61081			0.245605			0.122802	−	0.992431i	$-0.460812\pi$
$113$	2.61081			0.245605			0.122802	+	0.992431i	$0.460812\pi$
$114$	0.144878	+	4.77896i	0.0135690	+	0.447591i
$115$	13.8470	−	3.71029i	1.29124	−	0.345986i
$116$	−8.12210	−	7.19269i	−0.754118	−	0.667824i
$117$	−3.05599	−	0.818851i	−0.282527	−	0.0757028i
$118$	1.34003	+	4.45625i	0.123360	+	0.410231i
$119$		0			0
$120$	−5.09063	+	0.464116i	−0.464709	+	0.0423678i
$121$	−4.29189	+	2.47792i	−0.390171	+	0.225266i
$122$	2.97167	−	12.6068i	0.269042	−	1.14137i
$123$	−1.93588	−	7.22481i	−0.174553	−	0.651439i
$124$	3.66463	−	7.34140i	0.329093	−	0.659277i
$125$	−8.30298	−	8.30298i	−0.742641	−	0.742641i
$126$		0			0
$127$	−9.68594			−0.859488			−0.429744	−	0.902951i	$-0.641396\pi$
$127$	−9.68594			−0.859488			−0.429744	+	0.902951i	$0.641396\pi$
$128$	11.0601	−	2.38218i	0.977582	−	0.210557i
$129$	−0.434417	+	0.752432i	−0.0382483	+	0.0662479i
$130$	2.18718	+	3.53631i	0.191828	+	0.310155i
$131$	−3.58278	+	13.3711i	−0.313029	+	1.16824i	0.612782	+	0.790252i	$0.290050\pi$
$131$	−3.58278	+	13.3711i	−0.313029	+	1.16824i	−0.925811	+	0.377987i	$0.876616\pi$
$132$	−3.79383	−	5.73775i	−0.330210	−	0.499407i
$133$		0			0
$134$	−2.09946	+	0.631323i	−0.181366	+	0.0545380i
$135$	8.23057	−	4.75192i	0.708375	−	0.408980i
$136$	−7.30151	+	15.8087i	−0.626100	+	1.35558i
$137$	−9.80462	−	5.66070i	−0.837665	−	0.483626i	0.0188049	−	0.999823i	$-0.494014\pi$
$137$	−9.80462	−	5.66070i	−0.837665	−	0.483626i	−0.856470	+	0.516197i	$0.827347\pi$
$138$	−5.69949	+	6.05586i	−0.485173	+	0.515509i
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	−0.797624	−	0.603155i	$-0.793910\pi$
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	0.603155	+	0.797624i	$0.293910\pi$
$140$		0			0
$141$	2.37854	+	2.37854i	0.200309	+	0.200309i
$142$	−0.122768	−	4.04967i	−0.0103025	−	0.339840i
$143$	−2.79761	+	4.84561i	−0.233948	+	0.405210i
$144$	−7.22053	+	5.43034i	−0.601711	+	0.452528i
$145$	−5.69311	−	9.86075i	−0.472787	−	0.818891i
$146$	−12.8818	−	6.92558i	−1.06611	−	0.573165i
$147$		0			0
$148$	0.150332	+	0.0306595i	0.0123572	+	0.00252020i
$149$	1.82301	+	0.488473i	0.149346	+	0.0400172i	0.332718	−	0.943026i	$-0.392034\pi$
$149$	1.82301	+	0.488473i	0.149346	+	0.0400172i	−0.183371	+	0.983044i	$0.558701\pi$
$150$	0.704163	+	0.165984i	0.0574947	+	0.0135526i
$151$	12.3236	+	7.11503i	1.00288	+	0.579013i	0.909099	−	0.416580i	$-0.136772\pi$
$151$	12.3236	+	7.11503i	1.00288	+	0.579013i	0.0937803	+	0.995593i	$0.470105\pi$
$152$	1.88856	−	10.9442i	0.153182	−	0.887688i
$153$		−	13.9056i		−	1.12420i
$154$		0			0
$155$	6.08920	−	6.08920i	0.489097	−	0.489097i
$156$	−2.15817	−	1.07730i	−0.172792	−	0.0862530i
$157$	−18.7320	+	5.01921i	−1.49497	+	0.400577i	−0.911413	−	0.411493i	$-0.865007\pi$
$157$	−18.7320	+	5.01921i	−1.49497	+	0.400577i	−0.583560	+	0.812070i	$0.698341\pi$
$158$	−4.96372	−	8.02552i	−0.394892	−	0.638476i
$159$	−3.14912	−	5.45443i	−0.249741	−	0.432565i
$160$	11.8017	+	1.30664i	0.933006	+	0.103299i
$161$		0			0
$162$	1.92699	−	3.58426i	0.151398	−	0.281606i
$163$	−1.09977	+	4.10438i	−0.0861403	+	0.321480i	−0.995528	−	0.0944702i	$-0.969884\pi$
$163$	−1.09977	+	4.10438i	−0.0861403	+	0.321480i	0.909387	+	0.415950i	$0.136551\pi$
$164$	1.05245	+	17.3422i	0.0821826	+	1.35420i
$165$	−1.86845	−	6.97313i	−0.145458	−	0.542858i
$166$	−14.8668	−	13.9919i	−1.15389	−	1.08598i
$167$		−	12.2720i		−	0.949638i	−0.880084	−	0.474819i	$-0.842514\pi$
$167$		−	12.2720i		−	0.949638i	0.880084	−	0.474819i	$-0.157486\pi$
$168$		0			0
$169$		−	11.0379i		−	0.849071i
$170$	−12.5252	+	13.3083i	−0.960638	+	1.02070i
$171$	2.29539	+	8.56650i	0.175533	+	0.655097i
$172$	1.33799	−	1.51088i	0.102021	−	0.115204i
$173$	−3.86401	+	14.4207i	−0.293776	+	1.09639i	0.648409	+	0.761292i	$0.275435\pi$
$173$	−3.86401	+	14.4207i	−0.293776	+	1.09639i	−0.942185	+	0.335093i	$0.891232\pi$
$174$	5.81775	+	3.12777i	0.441043	+	0.237115i
$175$		0			0
$176$	5.97139	+	14.8201i	0.450110	+	1.11711i
$177$	−1.41655	−	2.45354i	−0.106474	−	0.184419i
$178$	1.61586	−	0.999396i	0.121114	−	0.0749079i
$179$	−6.59910	+	1.76822i	−0.493240	+	0.132163i	−0.496861	−	0.867830i	$-0.665514\pi$
$179$	−6.59910	+	1.76822i	−0.493240	+	0.132163i	0.00362111	+	0.999993i	$0.498847\pi$
$180$	−8.99334	+	3.00439i	−0.670324	+	0.223934i
$181$	−5.61848	+	5.61848i	−0.417618	+	0.417618i	−0.884382	−	0.466764i	$-0.845420\pi$
$181$	−5.61848	+	5.61848i	−0.417618	+	0.417618i	0.466764	+	0.884382i	$0.345420\pi$
$182$		0			0
$183$			7.88574i			0.582931i
$184$	15.7830	−	11.1375i	1.16354	−	0.821070i
$185$	0.139449	+	0.0805110i	0.0102525	+	0.00591929i
$186$	−1.14614	+	4.86230i	−0.0840388	+	0.356521i
$187$	−23.7543	−	6.36494i	−1.73708	−	0.465450i
$188$	−4.30947	−	6.51761i	−0.314301	−	0.475345i
$189$		0			0
$190$	5.51932	−	10.2661i	0.400413	−	0.744782i
$191$	3.19941	+	5.54154i	0.231501	+	0.400972i	0.958250	−	0.285932i	$-0.0923030\pi$
$191$	3.19941	+	5.54154i	0.231501	+	0.400972i	−0.726749	+	0.686903i	$0.758970\pi$
$192$	−6.22130	+	2.95656i	−0.448984	+	0.213372i
$193$	4.90762	−	8.50025i	0.353258	−	0.611861i	−0.633560	−	0.773694i	$-0.718407\pi$
$193$	4.90762	−	8.50025i	0.353258	−	0.611861i	0.986818	+	0.161832i	$0.0517403\pi$
$194$	26.5099	−	0.803665i	1.90330	−	0.0576998i
$195$	−1.79006	−	1.79006i	−0.128189	−	0.128189i
$196$		0			0
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.0565783	−	0.998398i	$-0.481981\pi$
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.998398	−	0.0565783i	$-0.0180191\pi$
$198$	−9.29140	−	8.74463i	−0.660311	−	0.621454i
$199$	−3.76329	−	2.17274i	−0.266772	−	0.154021i	0.360648	−	0.932702i	$-0.382556\pi$
$199$	−3.76329	−	2.17274i	−0.266772	−	0.154021i	−0.627420	+	0.778681i	$0.715889\pi$
$200$	−1.52563	−	0.704638i	−0.107878	−	0.0498254i
$201$	1.15593	−	0.667374i	0.0815327	−	0.0470729i
$202$	−1.81177	−	6.02501i	−0.127476	−	0.423919i
$203$		0			0
$204$	2.11857	−	10.3879i	0.148329	−	0.727299i
$205$	−4.71938	+	17.6130i	−0.329616	+	1.23014i
$206$	10.7795	−	6.66701i	0.751041	−	0.464512i
$207$	−7.71288	+	13.3591i	−0.536082	+	0.928522i
$208$	4.41193	+	3.45371i	0.305912	+	0.239472i
$209$	15.6844			1.08492
$210$		0			0
$211$	−14.5998	−	14.5998i	−1.00509	−	1.00509i	−0.999987	−	0.00510394i	$-0.998375\pi$
$211$	−14.5998	−	14.5998i	−1.00509	−	1.00509i	−0.00510394	−	0.999987i	$-0.501625\pi$
$212$	4.63555	+	13.8760i	0.318371	+	0.953010i
$213$	0.638424	+	2.38263i	0.0437441	+	0.163255i
$214$	−17.4861	−	4.12181i	−1.19533	−	0.281761i
$215$	1.83431	−	1.05904i	0.125099	−	0.0722260i
$216$	8.19594	−	9.84032i	0.557663	−	0.669549i
$217$		0			0
$218$	−19.6017	+	5.89439i	−1.32760	+	0.399219i
$219$	8.60098	+	2.30463i	0.581201	+	0.155732i
$220$	1.01579	+	16.7381i	0.0684845	+	1.12848i
$221$	−8.32990	+	2.23199i	−0.560329	+	0.150140i
$222$	−0.0933673	+	0.00283049i	−0.00626640	+	0.000189970i
$223$	−0.272719			−0.0182626			−0.00913130	−	0.999958i	$-0.502907\pi$
$223$	−0.272719			−0.0182626			−0.00913130	+	0.999958i	$0.502907\pi$
$224$		0			0
$225$	1.34197			0.0894645
$226$	3.69055	−	0.111882i	0.245492	−	0.00744225i
$227$	11.0202	−	2.95285i	0.731436	−	0.195988i	0.126167	−	0.992009i	$-0.459732\pi$
$227$	11.0202	−	2.95285i	0.731436	−	0.195988i	0.605268	+	0.796021i	$0.293066\pi$
$228$	0.409587	+	6.74916i	0.0271256	+	0.446974i
$229$	15.1779	+	4.06690i	1.00298	+	0.268748i	0.722694	−	0.691168i	$-0.242903\pi$
$229$	15.1779	+	4.06690i	1.00298	+	0.268748i	0.280288	+	0.959916i	$0.409570\pi$
$230$	19.4146	−	5.83812i	1.28016	−	0.384954i
$231$		0			0
$232$	−11.7893	−	9.81927i	−0.774008	−	0.644667i
$233$	−4.95726	+	2.86207i	−0.324761	+	0.187501i	−0.653513	−	0.756916i	$-0.726705\pi$
$233$	−4.95726	+	2.86207i	−0.324761	+	0.187501i	0.328752	+	0.944416i	$0.393372\pi$
$234$	−4.35493	−	1.02654i	−0.284691	−	0.0671069i
$235$	−2.12240	−	7.92090i	−0.138450	−	0.516703i
$236$	2.08518	+	6.24177i	0.135734	+	0.406305i
$237$	4.06247	+	4.06247i	0.263886	+	0.263886i
$238$		0			0
$239$	14.5430			0.940708			0.470354	−	0.882478i	$-0.344126\pi$
$239$	14.5430			0.940708			0.470354	+	0.882478i	$0.344126\pi$
$240$	−7.17605	+	0.874207i	−0.463212	+	0.0564298i
$241$	−1.50912	+	2.61387i	−0.0972111	+	0.168374i	−0.910529	−	0.413445i	$-0.864326\pi$
$241$	−1.50912	+	2.61387i	−0.0972111	+	0.168374i	0.813318	+	0.581819i	$0.197659\pi$
$242$	−5.96067	+	3.68662i	−0.383166	+	0.236985i
$243$	−4.15686	+	15.5136i	−0.266663	+	0.995199i
$244$	3.66040	−	17.9479i	0.234333	−	1.14900i
$245$		0			0
$246$	−3.04610	−	10.1298i	−0.194212	−	0.645851i
$247$	4.76319	−	2.75003i	0.303074	−	0.174980i
$248$	4.86559	−	10.5346i	0.308965	−	0.668946i
$249$	10.7643	+	6.21478i	0.682160	+	0.393845i
$250$	−12.0926	−	11.3810i	−0.764803	−	0.719796i
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	−0.136819	−	0.990596i	$-0.543688\pi$
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	0.990596	+	0.136819i	$0.0436880\pi$
$252$		0			0
$253$	19.2904	+	19.2904i	1.21278	+	1.21278i
$254$	−13.6917	+	0.415073i	−0.859093	+	0.0260440i
$255$	5.56330	−	9.63591i	0.348387	−	0.603424i
$256$	15.5320	−	3.84133i	0.970752	−	0.240083i
$257$	1.52413	+	2.63988i	0.0950728	+	0.164671i	0.909639	−	0.415400i	$-0.136358\pi$
$257$	1.52413	+	2.63988i	0.0950728	+	0.164671i	−0.814566	+	0.580071i	$0.803025\pi$
$258$	−0.581832	+	1.08223i	−0.0362233	+	0.0673765i
$259$		0			0
$260$	3.24326	+	4.90508i	0.201138	+	0.304200i
$261$	11.8347	+	3.17111i	0.732552	+	0.196287i
$262$	−4.49149	+	19.0545i	−0.277485	+	1.17719i
$263$	23.3754	+	13.4958i	1.44139	+	0.832188i	0.997943	−	0.0641116i	$-0.0204213\pi$
$263$	23.3754	+	13.4958i	1.44139	+	0.832188i	0.443449	+	0.896300i	$0.353755\pi$
$264$	−5.60870	−	7.94810i	−0.345192	−	0.489172i
$265$			15.3541i			0.943197i
$266$		0			0
$267$	−0.817939	+	0.817939i	−0.0500570	+	0.0500570i
$268$	−2.94066	+	0.982384i	−0.179630	+	0.0600086i
$269$	17.5785	−	4.71013i	1.07178	−	0.287182i	0.320554	−	0.947230i	$-0.396131\pi$
$269$	17.5785	−	4.71013i	1.07178	−	0.287182i	0.751223	+	0.660048i	$0.229464\pi$
$270$	11.4308	−	7.06985i	0.695657	−	0.430257i
$271$	15.6541	+	27.1137i	0.950917	+	1.64704i	0.743446	+	0.668796i	$0.233190\pi$
$271$	15.6541	+	27.1137i	0.950917	+	1.64704i	0.207472	+	0.978241i	$0.433477\pi$
$272$	−9.64371	+	22.6594i	−0.584736	+	1.37393i
$273$		0			0
$274$	−14.1020	−	7.58160i	−0.851935	−	0.458021i
$275$	0.614253	−	2.29242i	0.0370408	−	0.138238i
$276$	−7.79708	+	8.80459i	−0.469329	+	0.529974i
$277$	4.26100	+	15.9023i	0.256019	+	0.955476i	0.967521	+	0.252792i	$0.0813487\pi$
$277$	4.26100	+	15.9023i	0.256019	+	0.955476i	−0.711502	+	0.702684i	$0.751985\pi$
$278$	−3.14271	+	3.33921i	−0.188487	+	0.200273i
$279$			9.26640i			0.554765i
$280$		0			0
$281$			25.4166i			1.51622i	0.652124	+	0.758112i	$0.273878\pi$
$281$			25.4166i			1.51622i	−0.652124	+	0.758112i	$0.726122\pi$
$282$	3.46414	+	3.26028i	0.206287	+	0.194147i
$283$	−1.61086	−	6.01181i	−0.0957556	−	0.357365i	0.901377	−	0.433035i	$-0.142557\pi$
$283$	−1.61086	−	6.01181i	−0.0957556	−	0.357365i	−0.997133	+	0.0756698i	$0.975891\pi$
$284$	−0.347082	−	5.71920i	−0.0205955	−	0.339372i
$285$	−1.83666	+	6.85452i	−0.108795	+	0.406027i
$286$	−3.74696	+	6.96947i	−0.221562	+	0.412113i
$287$		0			0
$288$	−9.97397	+	7.98556i	−0.587722	+	0.470553i
$289$	−10.4516	−	18.1027i	−0.614800	−	1.06486i
$290$	−8.47014	−	13.6948i	−0.497384	−	0.804189i
$291$	−15.5971	+	4.17924i	−0.914320	+	0.244991i
$292$	−18.5061	−	9.23773i	−1.08298	−	0.540597i
$293$	−18.5820	+	18.5820i	−1.08557	+	1.08557i	−0.0895915	+	0.995979i	$0.528556\pi$
$293$	−18.5820	+	18.5820i	−1.08557	+	1.08557i	−0.995979	+	0.0895915i	$0.971444\pi$
$294$		0			0
$295$			6.90666i			0.402121i
$296$	0.213818	+	0.0368970i	0.0124279	+	0.00214460i
$297$	15.6630	+	9.04303i	0.908859	+	0.524730i
$298$	2.59787	+	0.612366i	0.150490	+	0.0354734i
$299$	9.24055	+	2.47600i	0.534395	+	0.143191i
$300$	1.00249	+	0.204454i	0.0578789	+	0.0118042i
$301$		0			0
$302$	17.7251	+	9.52944i	1.01996	+	0.548358i
$303$	1.91523	+	3.31727i	0.110027	+	0.190572i
$304$	2.20061	−	15.5512i	0.126213	−	0.891922i
$305$	9.61211	−	16.6487i	0.550388	−	0.953300i
$306$	−0.595897	−	19.6564i	−0.0340652	−	1.12368i
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.995742	−	0.0921822i	$-0.970616\pi$
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.0921822	−	0.995742i	$-0.529384\pi$
$308$		0			0
$309$	−5.45650	+	5.45650i	−0.310409	+	0.310409i
$310$	8.34654	−	8.86842i	0.474051	−	0.503692i
$311$	5.95180	+	3.43627i	0.337496	+	0.194853i	0.659164	−	0.751999i	$-0.270910\pi$
$311$	5.95180	+	3.43627i	0.337496	+	0.194853i	−0.321668	+	0.946852i	$0.604244\pi$
$312$	−3.09688	−	1.43035i	−0.175326	−	0.0809775i
$313$	−6.94756	+	4.01118i	−0.392699	+	0.226725i	−0.683329	−	0.730110i	$-0.739469\pi$
$313$	−6.94756	+	4.01118i	−0.392699	+	0.226725i	0.290630	+	0.956836i	$0.406135\pi$
$314$	−26.2637	+	7.89770i	−1.48215	+	0.445693i
$315$		0			0
$316$	−7.36045	−	11.1319i	−0.414058	−	0.626217i
$317$	0.719764	−	2.68620i	0.0404260	−	0.150872i	−0.942763	−	0.333464i	$-0.891782\pi$
$317$	0.719764	−	2.68620i	0.0404260	−	0.150872i	0.983189	+	0.182593i	$0.0584490\pi$
$318$	−4.68522	−	7.57524i	−0.262734	−	0.424798i
$319$	10.8341	−	18.7653i	0.606595	−	1.05065i
$320$	16.7385	+	1.34128i	0.935708	+	0.0749800i
$321$	10.9378			0.610488
$322$		0			0
$323$	17.0935	+	17.0935i	0.951110	+	0.951110i
$324$	2.57032	−	5.14916i	0.142796	−	0.286064i
$325$	−0.215400	−	0.803883i	−0.0119482	−	0.0445914i
$326$	−1.37870	+	5.84894i	−0.0763594	+	0.323943i
$327$	10.7924	−	6.23099i	0.596820	−	0.344574i
$328$	2.23088	+	24.4693i	0.123180	+	1.35109i
$329$		0			0
$330$	−2.93999	−	9.77690i	−0.161841	−	0.538201i
$331$	10.3801	+	2.78135i	0.570544	+	0.152877i	0.532546	−	0.846401i	$-0.321235\pi$
$331$	10.3801	+	2.78135i	0.570544	+	0.152877i	0.0379979	+	0.999278i	$0.487902\pi$
$332$	−21.6148	−	19.1414i	−1.18626	−	1.05052i
$333$	−0.167365	+	0.0448453i	−0.00917154	+	0.00245751i
$334$	−0.525895	−	17.3473i	−0.0287757	−	0.949201i
$335$	−3.25391			−0.177780
$336$		0			0
$337$	16.4062			0.893704			0.446852	−	0.894608i	$-0.352545\pi$
$337$	16.4062			0.893704			0.446852	+	0.894608i	$0.352545\pi$
$338$	−0.473010	−	15.6028i	−0.0257284	−	0.848681i
$339$	−2.17134	+	0.581810i	−0.117931	+	0.0315996i
$340$	−17.1348	+	19.3489i	−0.929267	+	1.04934i
$341$	15.8294	+	4.24147i	0.857209	+	0.229688i
$342$	3.61178	+	12.0109i	0.195303	+	0.649477i
$343$		0			0
$344$	1.82660	−	2.19307i	0.0984834	−	0.118242i
$345$	−10.6893	+	6.17149i	−0.575495	+	0.332262i
$346$	−4.84406	+	20.5502i	−0.260418	+	1.10478i
$347$	−9.39255	−	35.0535i	−0.504219	−	1.88177i	−0.470623	−	0.882334i	$-0.655971\pi$
$347$	−9.39255	−	35.0535i	−0.504219	−	1.88177i	−0.0335953	−	0.999436i	$-0.510696\pi$
$348$	8.35780	+	4.17199i	0.448025	+	0.223642i
$349$	−10.3424	−	10.3424i	−0.553614	−	0.553614i	0.373868	−	0.927482i	$-0.378031\pi$
$349$	−10.3424	−	10.3424i	−0.553614	−	0.553614i	−0.927482	+	0.373868i	$0.878031\pi$
$350$		0			0
$351$	6.34223			0.338523
$352$	9.07603	+	20.6933i	0.483754	+	1.10296i
$353$	4.57499	−	7.92412i	0.243502	−	0.421758i	−0.718207	−	0.695829i	$-0.755037\pi$
$353$	4.57499	−	7.92412i	0.243502	−	0.421758i	0.961709	+	0.274071i	$0.0883703\pi$
$354$	−2.10753	−	3.40753i	−0.112014	−	0.181108i
$355$	1.55638	−	5.80848i	0.0826040	−	0.308282i
$356$	2.24130	−	1.48196i	0.118789	−	0.0785435i
$357$		0			0
$358$	−9.25247	+	2.78229i	−0.489008	+	0.147049i
$359$	−7.29942	+	4.21432i	−0.385248	+	0.222423i	−0.680099	−	0.733120i	$-0.738063\pi$
$359$	−7.29942	+	4.21432i	−0.385248	+	0.222423i	0.294851	+	0.955543i	$0.404730\pi$
$360$	−12.5839	+	4.63230i	−0.663231	+	0.244143i
$361$	3.10240	+	1.79117i	0.163284	+	0.0942723i
$362$	−7.70131	+	8.18285i	−0.404772	+	0.430081i
$363$	3.01725	−	3.01725i	0.158365	−	0.158365i
$364$		0			0
$365$	−15.3495	−	15.3495i	−0.803432	−	0.803432i
$366$	0.337929	+	11.1470i	0.0176638	+	0.582663i
$367$	4.65182	−	8.05718i	0.242823	−	0.420582i	−0.718694	−	0.695326i	$-0.755260\pi$
$367$	4.65182	−	8.05718i	0.242823	−	0.420582i	0.961517	+	0.274745i	$0.0885933\pi$
$368$	21.8331	−	16.4200i	1.13813	−	0.855950i
$369$	−9.81057	−	16.9924i	−0.510718	−	0.884589i
$370$	0.200571	+	0.107832i	0.0104272	+	0.00560590i
$371$		0			0
$372$	−1.41177	+	6.92230i	−0.0731970	+	0.358904i
$373$	−19.8310	−	5.31370i	−1.02681	−	0.275133i	−0.294172	−	0.955752i	$-0.595044\pi$
$373$	−19.8310	−	5.31370i	−1.02681	−	0.275133i	−0.732637	+	0.680620i	$0.761711\pi$
$374$	−33.8509	−	7.97930i	−1.75039	−	0.412600i
$375$	8.75565	+	5.05508i	0.452140	+	0.261043i
$376$	−6.37102	−	9.02838i	−0.328560	−	0.465603i
$377$		−	7.59840i		−	0.391337i
$378$		0			0
$379$	−9.02290	+	9.02290i	−0.463475	+	0.463475i	−0.899793	−	0.436317i	$-0.856282\pi$
$379$	−9.02290	+	9.02290i	−0.463475	+	0.463475i	0.436317	+	0.899793i	$0.356282\pi$
$380$	7.36197	−	14.7483i	0.377661	−	0.756573i
$381$	8.05554	−	2.15847i	0.412698	−	0.110582i
$382$	4.76004	+	7.69621i	0.243545	+	0.393773i
$383$	−0.562798	−	0.974794i	−0.0287576	−	0.0498097i	0.851288	−	0.524698i	$-0.175822\pi$
$383$	−0.562798	−	0.974794i	−0.0287576	−	0.0498097i	−0.880046	+	0.474888i	$0.842488\pi$
$384$	−8.66751	+	4.44589i	−0.442312	+	0.226879i
$385$		0			0
$386$	6.57298	−	12.2260i	0.334556	−	0.622285i
$387$	−0.589894	+	2.20152i	−0.0299860	+	0.111909i
$388$	37.4390	−	2.27206i	1.90067	−	0.115347i
$389$	4.47334	+	16.6947i	0.226807	+	0.846457i	0.981672	+	0.190577i	$0.0610358\pi$
$389$	4.47334	+	16.6947i	0.226807	+	0.846457i	−0.754865	+	0.655880i	$0.772298\pi$
$390$	−2.60707	−	2.45365i	−0.132014	−	0.124246i
$391$			42.0469i			2.12640i
$392$		0			0
$393$		−	11.9188i		−	0.601224i
$394$	20.2965	−	21.5656i	1.02252	−	1.08646i
$395$	−3.62499	−	13.5287i	−0.182393	−	0.680701i
$396$	−13.5087	−	11.9629i	−0.678839	−	0.601160i
$397$	−7.33912	+	27.3900i	−0.368340	+	1.37466i	0.494497	+	0.869179i	$0.335352\pi$
$397$	−7.33912	+	27.3900i	−0.368340	+	1.37466i	−0.862837	+	0.505483i	$0.831314\pi$
$398$	−5.41276	−	2.91003i	−0.271317	−	0.145867i
$399$		0			0
$400$	−2.18677	−	0.930673i	−0.109338	−	0.0465337i
$401$	11.2636	+	19.5091i	0.562477	+	0.974238i	0.997280	+	0.0737127i	$0.0234848\pi$
$401$	11.2636	+	19.5091i	0.562477	+	0.974238i	−0.434803	+	0.900526i	$0.643182\pi$
$402$	1.60538	−	0.992911i	0.0800689	−	0.0495219i
$403$	5.55088	−	1.48735i	0.276509	−	0.0740904i
$404$	−2.81924	−	8.43910i	−0.140262	−	0.419861i
$405$	4.27088	−	4.27088i	0.212222	−	0.212222i
$406$		0			0
$407$			0.306429i			0.0151891i
$408$	2.54958	−	14.7748i	0.126223	−	0.731459i
$409$	−26.7305	−	15.4328i	−1.32174	−	0.763105i	−0.337731	−	0.941243i	$-0.609659\pi$
$409$	−26.7305	−	15.4328i	−1.32174	−	0.763105i	−0.984006	+	0.178138i	$0.942993\pi$
$410$	−5.91637	+	25.0993i	−0.292189	+	1.23957i
$411$	9.41570	+	2.52293i	0.464442	+	0.124447i
$412$	14.9518	−	9.88618i	0.736621	−	0.487057i
$413$		0			0
$414$	−10.3302	+	19.2145i	−0.507700	+	0.944340i
$415$	−15.1507	−	26.2417i	−0.743717	−	1.28816i
$416$	6.38454	+	4.69298i	0.313028	+	0.230092i
$417$	1.39589	−	2.41776i	0.0683572	−	0.118398i
$418$	22.1710	−	0.672128i	1.08442	−	0.0328748i
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	0.870592	−	0.492006i	$-0.163736\pi$
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	−0.492006	+	0.870592i	$0.663736\pi$
$420$		0			0
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	−0.945953	−	0.324302i	$-0.894870\pi$
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	0.324302	+	0.945953i	$0.394870\pi$
$422$	−21.2634	−	20.0121i	−1.03509	−	0.974173i
$423$	7.64182	+	4.41201i	0.371558	+	0.214519i
$424$	7.14728	+	19.4160i	0.347102	+	0.942925i
$425$	3.16781	−	1.82894i	0.153662	−	0.0887165i
$426$	1.00456	+	3.34064i	0.0486709	+	0.161855i
$427$		0			0
$428$	−24.8944	−	5.07710i	−1.20332	−	0.245411i
$429$	1.24688	−	4.65340i	0.0601997	−	0.224668i
$430$	2.54753	−	1.57563i	0.122853	−	0.0759835i
$431$	−4.92680	+	8.53348i	−0.237316	+	0.411043i	−0.959943	−	0.280195i	$-0.909601\pi$
$431$	−4.92680	+	8.53348i	−0.237316	+	0.411043i	0.722627	+	0.691238i	$0.242934\pi$
$432$	11.1638	−	14.2611i	0.537119	−	0.686140i
$433$	−14.9150			−0.716769			−0.358385	−	0.933574i	$-0.616672\pi$
$433$	−14.9150			−0.716769			−0.358385	+	0.933574i	$0.616672\pi$
$434$		0			0
$435$	6.93224	+	6.93224i	0.332375	+	0.332375i
$436$	−27.4557	+	9.17210i	−1.31489	+	0.439264i
$437$	−6.94067	−	25.9029i	−0.332017	−	1.23911i
$438$	12.2568	+	2.88916i	0.585653	+	0.138049i
$439$	8.04703	−	4.64596i	0.384064	−	0.221739i	−0.295521	−	0.955336i	$-0.595493\pi$
$439$	8.04703	−	4.64596i	0.384064	−	0.221739i	0.679585	+	0.733597i	$0.262160\pi$
$440$	2.15316	+	23.6169i	0.102648	+	1.12589i
$441$		0			0
$442$	−11.6792	+	3.51202i	−0.555523	+	0.167050i
$443$	−9.83379	−	2.63496i	−0.467217	−	0.125191i	0.0175270	−	0.999846i	$-0.494421\pi$
$443$	−9.83379	−	2.63496i	−0.467217	−	0.125191i	−0.484744	+	0.874656i	$0.661087\pi$
$444$	−0.131859	+	0.00800217i	−0.00625777	+	0.000379766i
$445$	2.72387	−	0.729858i	0.129124	−	0.0345986i
$446$	−0.385505	+	0.0116869i	−0.0182542	+	0.000553389i
$447$	−1.62500			−0.0768598
$448$		0			0
$449$	3.82136			0.180341			0.0901705	−	0.995926i	$-0.471259\pi$
$449$	3.82136			0.180341			0.0901705	+	0.995926i	$0.471259\pi$
$450$	1.89696	−	0.0575075i	0.0894234	−	0.00271093i
$451$	−33.5179	+	8.98110i	−1.57830	+	0.422904i
$452$	5.21204	−	0.316304i	0.245154	−	0.0148777i
$453$	−11.8348	−	3.17111i	−0.556045	−	0.148992i
$454$	15.4512	−	4.64629i	0.725161	−	0.218061i
$455$		0			0
$456$	0.868201	+	9.52282i	0.0406572	+	0.445947i
$457$	21.7306	−	12.5462i	1.01651	−	0.586885i	0.103422	−	0.994638i	$-0.467021\pi$
$457$	21.7306	−	12.5462i	1.01651	−	0.586885i	0.913092	+	0.407753i	$0.133688\pi$
$458$	21.6292	+	5.09840i	1.01066	+	0.238233i
$459$	7.21470	+	26.9256i	0.336753	+	1.25678i
$460$	27.1936	−	9.08453i	1.26791	−	0.423568i
$461$	7.13847	+	7.13847i	0.332472	+	0.332472i	0.853524	−	0.521053i	$-0.174461\pi$
$461$	7.13847	+	7.13847i	0.332472	+	0.332472i	−0.521053	+	0.853524i	$0.674461\pi$
$462$		0			0
$463$	3.67655			0.170864			0.0854320	−	0.996344i	$-0.472773\pi$
$463$	3.67655			0.170864			0.0854320	+	0.996344i	$0.472773\pi$
$464$	−17.0858	−	13.3750i	−0.793187	−	0.620917i
$465$	−3.70727	+	6.42118i	−0.171921	+	0.297775i
$466$	−6.88475	+	4.25816i	−0.318930	+	0.197255i
$467$	−2.51848	+	9.39910i	−0.116541	+	0.434938i	−0.999398	−	0.0347050i	$-0.988951\pi$
$467$	−2.51848	+	9.39910i	−0.116541	+	0.434938i	0.882856	+	0.469643i	$0.155617\pi$
$468$	−6.19996	−	1.26446i	−0.286593	−	0.0584495i
$469$		0			0
$470$	−3.33958	−	11.1057i	−0.154043	−	0.512270i
$471$	14.4604	−	8.34869i	0.666298	−	0.384687i
$472$	3.21502	+	8.73379i	0.147983	+	0.402005i
$473$	3.49074	+	2.01538i	0.160505	+	0.0926673i
$474$	5.91665	+	5.56847i	0.271761	+	0.255768i
$475$	−1.64963	+	1.64963i	−0.0756900	+	0.0756900i
$476$		0			0
$477$	−11.6828	−	11.6828i	−0.534917	−	0.534917i
$478$	20.5575	−	0.623213i	0.940276	−	0.0285051i
$479$	−8.06678	+	13.9721i	−0.368581	+	0.638400i	−0.989344	−	0.145598i	$-0.953490\pi$
$479$	−8.06678	+	13.9721i	−0.368581	+	0.638400i	0.620763	+	0.783998i	$0.286823\pi$
$480$	−10.1063	+	1.54326i	−0.461289	+	0.0704401i
$481$	0.0537277	+	0.0930591i	0.00244977	+	0.00424313i
$482$	−2.02123	+	3.75955i	−0.0920644	+	0.171243i
$483$		0			0
$484$	−8.26780	+	5.46671i	−0.375809	+	0.248487i
$485$	38.0234	+	10.1883i	1.72655	+	0.462629i
$486$	−5.21118	+	22.1076i	−0.236384	+	1.00282i
$487$	−11.3224	−	6.53697i	−0.513065	−	0.296218i	0.221027	−	0.975268i	$-0.429059\pi$
$487$	−11.3224	−	6.53697i	−0.513065	−	0.296218i	−0.734093	+	0.679049i	$0.762392\pi$
$488$	4.40509	−	25.5274i	0.199409	−	1.15557i
$489$		−	3.65859i		−	0.165447i
$490$		0			0
$491$	10.1749	−	10.1749i	0.459188	−	0.459188i	−0.439201	−	0.898389i	$-0.644738\pi$
$491$	10.1749	−	10.1749i	0.459188	−	0.459188i	0.898389	+	0.439201i	$0.144738\pi$
$492$	−4.73995	−	14.1885i	−0.213693	−	0.639669i
$493$	32.2586	−	8.64368i	1.45286	−	0.389292i
$494$	6.61522	−	4.09146i	0.297633	−	0.184083i
$495$	−9.46882	−	16.4005i	−0.425592	−	0.737146i
$496$	6.42638	−	15.0998i	0.288553	−	0.678001i
$497$		0			0
$498$	15.4824	+	8.32370i	0.693781	+	0.372994i
$499$	−10.7751	+	40.2131i	−0.482358	+	1.80019i	0.109313	+	0.994007i	$0.465135\pi$
$499$	−10.7751	+	40.2131i	−0.482358	+	1.80019i	−0.591672	+	0.806179i	$0.701532\pi$
$500$	−17.5814	−	15.5695i	−0.786263	−	0.696291i
$501$	2.73477	+	10.2063i	0.122181	+	0.455985i
$502$	18.5407	−	19.7000i	0.827514	−	0.879256i
$503$			35.0535i			1.56296i	0.623930	+	0.781480i	$0.285535\pi$
$503$			35.0535i			1.56296i	−0.623930	+	0.781480i	$0.714465\pi$
$504$		0			0
$505$		−	9.33805i		−	0.415538i
$506$	28.0949	+	26.4415i	1.24897	+	1.17547i
$507$	2.45976	+	9.17995i	0.109242	+	0.407696i
$508$	−19.3363	+	1.17346i	−0.857909	+	0.0520641i
$509$	−0.769772	+	2.87283i	−0.0341195	+	0.127336i	−0.980885	−	0.194588i	$-0.937663\pi$
$509$	−0.769772	+	2.87283i	−0.0341195	+	0.127336i	0.946765	+	0.321924i	$0.104330\pi$
$510$	7.45115	−	13.8594i	0.329942	−	0.613704i
$511$		0			0
$512$	21.7909	−	6.09556i	0.963032	−	0.269388i
$513$	−8.88921	−	15.3966i	−0.392468	−	0.679775i
$514$	2.26759	+	3.66632i	0.100019	+	0.161714i
$515$	18.1710	−	4.86891i	0.800710	−	0.214550i
$516$	−0.776080	+	1.55473i	−0.0341650	+	0.0684432i
$517$	11.0347	−	11.0347i	0.485305	−	0.485305i
$518$		0			0
$519$		−	12.8544i		−	0.564245i
$520$	4.79475	+	6.79465i	0.210264	+	0.297965i
$521$	21.8703	+	12.6268i	0.958155	+	0.553191i	0.895605	−	0.444851i	$-0.146743\pi$
$521$	21.8703	+	12.6268i	0.958155	+	0.553191i	0.0625503	+	0.998042i	$0.480077\pi$
$522$	16.8651	+	3.97541i	0.738163	+	0.173999i
$523$	−0.671120	−	0.179826i	−0.0293460	−	0.00786324i	0.244116	−	0.969746i	$-0.421502\pi$
$523$	−0.671120	−	0.179826i	−0.0293460	−	0.00786324i	−0.273462	+	0.961883i	$0.588169\pi$
$524$	−5.53247	+	27.1272i	−0.241687	+	1.18506i
$525$		0			0
$526$	33.6210	+	18.0755i	1.46595	+	0.788129i
$527$	12.6290	+	21.8740i	0.550127	+	0.952848i
$528$	−8.26886	−	10.9948i	−0.359856	−	0.478487i
$529$	11.8218	−	20.4760i	0.513991	−	0.890259i
$530$	0.657973	+	21.7040i	0.0285805	+	0.942763i
$531$	−5.25519	−	5.25519i	−0.228056	−	0.228056i
$532$		0			0
$533$	−8.60431	+	8.60431i	−0.372694	+	0.372694i
$534$	−1.12116	+	1.19126i	−0.0485172	+	0.0515509i
$535$	−23.0923	−	13.3323i	−0.998366	−	0.576407i
$536$	−4.11472	+	1.51468i	−0.177729	+	0.0654242i
$537$	5.09425	−	2.94117i	0.219833	−	0.126921i
$538$	24.6464	−	7.41137i	1.06258	−	0.319527i
$539$		0			0
$540$	15.8552	−	10.4835i	0.682300	−	0.451140i
$541$	−3.00200	+	11.2036i	−0.129066	+	0.481681i	−0.999952	−	0.00980419i	$-0.996879\pi$
$541$	−3.00200	+	11.2036i	−0.129066	+	0.481681i	0.870886	+	0.491485i	$0.163546\pi$
$542$	23.2899	+	37.6561i	1.00039	+	1.61747i
$543$	3.42068	−	5.92480i	0.146796	−	0.254257i
$544$	−12.6610	+	32.4438i	−0.542835	+	1.39102i
$545$	−30.3804			−1.30135
$546$		0			0
$547$	8.29783	+	8.29783i	0.354790	+	0.354790i	0.861888	−	0.507098i	$-0.169282\pi$
$547$	8.29783	+	8.29783i	0.354790	+	0.354790i	−0.507098	+	0.861888i	$0.669282\pi$
$548$	−20.2590	−	10.1128i	−0.865423	−	0.431996i
$549$	5.35402	+	19.9815i	0.228504	+	0.852789i
$550$	0.770048	−	3.26681i	0.0328350	−	0.139297i
$551$	−18.4461	+	10.6498i	−0.785829	+	0.453699i
$552$	−10.6444	+	12.7800i	−0.453055	+	0.543952i
$553$		0			0
$554$	6.70467	+	22.2963i	0.284854	+	0.947279i
$555$	−0.133918	−	0.0358832i	−0.00568449	−	0.00152316i
$556$	−4.29933	+	4.85487i	−0.182332	+	0.205892i
$557$	19.4942	−	5.22346i	0.825997	−	0.221325i	0.179030	−	0.983844i	$-0.442704\pi$
$557$	19.4942	−	5.22346i	0.825997	−	0.221325i	0.646967	+	0.762518i	$0.276037\pi$
$558$	0.397094	+	13.0986i	0.0168103	+	0.554510i
$559$	1.41347			0.0597832
$560$		0			0
$561$	21.1742			0.893975
$562$	1.08918	+	35.9279i	0.0459443	+	1.51553i
$563$	24.7408	−	6.62929i	1.04270	−	0.279391i	0.303469	−	0.952841i	$-0.401855\pi$
$563$	24.7408	−	6.62929i	1.04270	−	0.279391i	0.739233	+	0.673450i	$0.235188\pi$
$564$	5.03650	+	4.46017i	0.212075	+	0.187807i
$565$	5.29340	+	1.41836i	0.222695	+	0.0596709i
$566$	−2.53468	−	8.42904i	−0.106540	−	0.354299i
$567$		0			0
$568$	−0.735709	−	8.06959i	−0.0308697	−	0.338592i
$569$	28.6248	−	16.5265i	1.20001	−	0.692828i	0.239455	−	0.970908i	$-0.423031\pi$
$569$	28.6248	−	16.5265i	1.20001	−	0.692828i	0.960558	+	0.278080i	$0.0896980\pi$
$570$	−2.30250	+	9.76801i	−0.0964413	+	0.409137i
$571$	3.86560	+	14.4266i	0.161770	+	0.603735i	0.998430	+	0.0560119i	$0.0178385\pi$
$571$	3.86560	+	14.4266i	0.161770	+	0.603735i	−0.836660	+	0.547723i	$0.815495\pi$
$572$	−4.99790	+	10.0124i	−0.208973	+	0.418638i
$573$	−3.89577	−	3.89577i	−0.162748	−	0.162748i
$574$		0			0
$575$	−4.05777			−0.169221
$576$	−13.7566	+	11.7155i	−0.573193	+	0.488146i
$577$	0.666623	−	1.15463i	0.0277519	−	0.0480677i	−0.851816	−	0.523841i	$-0.824498\pi$
$577$	0.666623	−	1.15463i	0.0277519	−	0.0480677i	0.879568	+	0.475774i	$0.157832\pi$
$578$	−15.5498	−	25.1414i	−0.646785	−	1.04575i
$579$	−2.18729	+	8.16308i	−0.0909007	+	0.339246i
$580$	−12.5600	−	18.9956i	−0.521524	−	0.788748i
$581$		0			0
$582$	−21.8685	+	6.57601i	−0.906477	+	0.272584i
$583$	−25.3047	+	14.6097i	−1.04801	+	0.605070i
$584$	−26.5554	−	12.2651i	−1.09887	−	0.507532i
$585$	−5.75114	−	3.32042i	−0.237781	−	0.137283i
$586$	−25.4705	+	27.0631i	−1.05218	+	1.11797i
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	−0.171058	−	0.985261i	$-0.554719\pi$
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	0.985261	+	0.171058i	$0.0547186\pi$
$588$		0			0
$589$	−11.3908	−	11.3908i	−0.469350	−	0.469350i
$590$	0.295972	+	9.76300i	0.0121850	+	0.401936i
$591$	−9.01509	+	15.6146i	−0.370831	+	0.642298i
$592$	0.303826	+	0.0429935i	0.0124872	+	0.00176702i
$593$	9.40250	+	16.2856i	0.386114	+	0.668769i	0.991923	−	0.126841i	$-0.0404837\pi$
$593$	9.40250	+	16.2856i	0.386114	+	0.668769i	−0.605809	+	0.795610i	$0.707150\pi$
$594$	22.5282	+	12.1117i	0.924342	+	0.496949i
$595$		0			0
$596$	3.69849	+	0.754292i	0.151496	+	0.0308970i
$597$	3.61401	+	0.968372i	0.147912	+	0.0396328i
$598$	13.1682	+	3.10399i	0.538488	+	0.126932i
$599$	−24.0798	−	13.9025i	−0.983873	−	0.568039i	−0.0804358	−	0.996760i	$-0.525631\pi$
$599$	−24.0798	−	13.9025i	−0.983873	−	0.568039i	−0.903437	+	0.428720i	$0.858965\pi$
$600$	1.42585	+	0.246049i	0.0582100	+	0.0100449i
$601$		−	13.6372i		−	0.556271i	−0.960542	−	0.278136i	$-0.910284\pi$
$601$		−	13.6372i		−	0.556271i	0.960542	−	0.278136i	$-0.0897165\pi$
$602$		0			0
$603$	2.47586	−	2.47586i	0.100825	−	0.100825i
$604$	25.4639	+	12.7109i	1.03611	+	0.517199i
$605$	−10.0479	+	2.69233i	−0.408506	+	0.109459i
$606$	2.84945	+	4.60710i	0.115751	+	0.187151i
$607$	−14.5489	−	25.1994i	−0.590522	−	1.02281i	−0.994162	−	0.107896i	$-0.965589\pi$
$607$	−14.5489	−	25.1994i	−0.590522	−	1.02281i	0.403640	−	0.914918i	$-0.367745\pi$
$608$	2.44428	−	22.0769i	0.0991286	−	0.895337i
$609$		0			0
$610$	12.8739	−	23.9459i	0.521248	−	0.969539i
$611$	1.41635	−	5.28588i	0.0572993	−	0.213844i
$612$	−1.68468	−	27.7601i	−0.0680991	−	1.12213i
$613$	−7.49934	−	27.9879i	−0.302895	−	1.13042i	−0.934742	−	0.355327i	$-0.884369\pi$
$613$	−7.49934	−	27.9879i	−0.302895	−	1.13042i	0.631846	−	0.775094i	$-0.282297\pi$
$614$	−27.7622	−	26.1285i	−1.12039	−	1.05446i
$615$		−	15.6999i		−	0.633082i
$616$		0			0
$617$		−	5.44754i		−	0.219310i	−0.993970	−	0.109655i	$-0.965025\pi$
$617$		−	5.44754i		−	0.219310i	0.993970	−	0.109655i	$-0.0349745\pi$
$618$	−7.47928	+	7.94694i	−0.300861	+	0.319673i
$619$	−1.57246	−	5.86850i	−0.0632025	−	0.235875i	0.927098	−	0.374820i	$-0.122295\pi$
$619$	−1.57246	−	5.86850i	−0.0632025	−	0.235875i	−0.990300	+	0.138945i	$0.955629\pi$
$620$	11.4183	−	12.8938i	0.458571	−	0.517826i
$621$	8.00343	−	29.8692i	0.321167	−	1.19861i
$622$	8.56051	+	4.60234i	0.343245	+	0.184537i
$623$		0			0
$624$	−4.43893	−	1.88918i	−0.177699	−	0.0756277i
$625$	−10.8381	−	18.7722i	−0.433526	−	0.750888i
$626$	−9.64893	+	5.96778i	−0.385649	+	0.238521i
$627$	−13.0443	+	3.49522i	−0.520941	+	0.139586i
$628$	−36.7870	+	12.2894i	−1.46796	+	0.490400i
$629$	−0.333959	+	0.333959i	−0.0133158	+	0.0133158i
$630$		0			0
$631$			31.5326i			1.25529i	0.778499	+	0.627646i	$0.215982\pi$
$631$			31.5326i			1.25529i	−0.778499	+	0.627646i	$0.784018\pi$
$632$	−10.8815	−	15.4202i	−0.432843	−	0.613383i
$633$	15.3958	+	8.88875i	0.611927	+	0.353296i
$634$	0.902320	−	3.82795i	0.0358357	−	0.152027i
$635$	−19.6381	−	5.26203i	−0.779316	−	0.208817i
$636$	−6.94748	−	10.5073i	−0.275486	−	0.416642i
$637$		0			0
$638$	14.5106	−	26.9902i	0.574480	−	1.06855i
$639$	3.23537	+	5.60383i	0.127989	+	0.221684i
$640$	23.7184	+	1.17869i	0.937550	+	0.0465920i
$641$	−13.6133	+	23.5789i	−0.537691	+	0.931309i	0.461337	+	0.887225i	$0.347370\pi$
$641$	−13.6133	+	23.5789i	−0.537691	+	0.931309i	−0.999028	+	0.0440835i	$0.985963\pi$
$642$	15.4613	−	0.468719i	0.610208	−	0.0184989i
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	0.849143	−	0.528164i	$-0.177119\pi$
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	−0.528164	+	0.849143i	$0.677119\pi$
$644$		0			0
$645$	−1.28955	+	1.28955i	−0.0507758	+	0.0507758i
$646$	24.8953	+	23.4303i	0.979494	+	0.921853i
$647$	−6.70236	−	3.86961i	−0.263497	−	0.152130i	0.362432	−	0.932010i	$-0.381947\pi$
$647$	−6.70236	−	3.86961i	−0.263497	−	0.152130i	−0.625929	+	0.779880i	$0.715280\pi$
$648$	3.41266	−	7.38881i	0.134062	−	0.290260i
$649$	−11.3826	+	6.57177i	−0.446808	+	0.257965i
$650$	−0.338930	−	1.12711i	−0.0132939	−	0.0442089i
$651$		0			0
$652$	−1.69824	+	8.32693i	−0.0665083	+	0.326108i
$653$	2.60819	−	9.73388i	0.102066	−	0.380916i	−0.895930	−	0.444196i	$-0.853489\pi$
$653$	2.60819	−	9.73388i	0.102066	−	0.380916i	0.997996	+	0.0632798i	$0.0201561\pi$
$654$	14.9887	−	9.27039i	0.586105	−	0.362501i
$655$	−14.5281	+	25.1634i	−0.567660	+	0.983216i
$656$	4.20207	+	34.4933i	0.164063	+	1.34674i
$657$	23.3585			0.911304
$658$		0			0
$659$	−4.61254	−	4.61254i	−0.179679	−	0.179679i	0.611537	−	0.791216i	$-0.290552\pi$
$659$	−4.61254	−	4.61254i	−0.179679	−	0.179679i	−0.791216	+	0.611537i	$0.790552\pi$
$660$	−4.57483	−	13.6943i	−0.178075	−	0.533050i
$661$	5.03853	+	18.8040i	0.195976	+	0.731393i	0.992012	+	0.126143i	$0.0402599\pi$
$661$	5.03853	+	18.8040i	0.195976	+	0.731393i	−0.796036	+	0.605249i	$0.793073\pi$
$662$	14.7922	+	3.48679i	0.574914	+	0.135518i
$663$	6.43036	−	3.71257i	0.249735	−	0.144184i
$664$	−31.3741	−	26.1313i	−1.21755	−	1.01409i
$665$		0			0
$666$	−0.234659	+	0.0705638i	−0.00909287	+	0.00273429i
$667$	−35.7853	−	9.58863i	−1.38561	−	0.371273i
$668$	−1.48677	−	24.4990i	−0.0575250	−	0.947894i
$669$	0.226813	−	0.0607743i	0.00876910	−	0.00234967i
$670$	−4.59961	+	0.139440i	−0.177698	+	0.00538705i
$671$	36.5842			1.41232
$672$		0			0
$673$	−28.4799			−1.09782			−0.548910	−	0.835881i	$-0.684957\pi$
$673$	−28.4799			−1.09782			−0.548910	+	0.835881i	$0.684957\pi$
$674$	23.1913	−	0.703059i	0.893294	−	0.0270808i
$675$	−2.59848	+	0.696260i	−0.100015	+	0.0267991i
$676$	−1.33726	−	22.0353i	−0.0514331	−	0.847512i
$677$	10.0011	+	2.67980i	0.384375	+	0.102993i	0.445832	−	0.895117i	$-0.352908\pi$
$677$	10.0011	+	2.67980i	0.384375	+	0.102993i	−0.0614567	+	0.998110i	$0.519575\pi$
$678$	−3.04440	+	0.915474i	−0.116920	+	0.0351586i
$679$		0			0
$680$	−23.3920	+	28.0852i	−0.897044	+	1.07702i
$681$	−8.50717	+	4.91162i	−0.325995	+	0.188214i
$682$	22.5576	+	5.31725i	0.863775	+	0.203608i
$683$	−2.41481	−	9.01220i	−0.0924002	−	0.344842i	0.904212	−	0.427083i	$-0.140459\pi$
$683$	−2.41481	−	9.01220i	−0.0924002	−	0.344842i	−0.996612	+	0.0822411i	$0.973792\pi$
$684$	5.62019	+	16.8235i	0.214893	+	0.643261i
$685$	−16.8035	−	16.8035i	−0.642029	−	0.642029i
$686$		0			0
$687$	−13.5293			−0.516176
$688$	2.48803	−	3.17832i	0.0948552	−	0.121172i
$689$	−5.12316	+	8.87357i	−0.195177	+	0.338056i
$690$	−14.8456	+	9.18188i	−0.565162	+	0.349548i
$691$	6.68364	−	24.9437i	0.254258	−	0.948902i	−0.714244	−	0.699896i	$-0.753230\pi$
$691$	6.68364	−	24.9437i	0.254258	−	0.948902i	0.968502	−	0.249006i	$-0.0801038\pi$
$692$	−5.96675	+	29.2566i	−0.226822	+	1.11217i
$693$		0			0
$694$	−14.7791	−	49.1479i	−0.561008	−	1.86563i
$695$	−5.89412	+	3.40297i	−0.223577	+	0.129082i
$696$	11.9931	+	5.53922i	0.454596	+	0.209963i
$697$	−46.3172	−	26.7412i	−1.75439	−	1.01290i
$698$	−15.0628	−	14.1764i	−0.570135	−	0.536584i
$699$	3.48502	−	3.48502i	0.131815	−	0.131815i
$700$		0			0
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	0.769036	−	0.639206i	$-0.220737\pi$
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	−0.639206	+	0.769036i	$0.720737\pi$
$702$	8.96515	−	0.271785i	0.338368	−	0.0102578i
$703$	0.150608	−	0.260861i	0.00568031	−	0.00983858i
$704$	13.7163	+	28.8624i	0.516954	+	1.08779i
$705$	3.53029	+	6.11463i	0.132958	+	0.230290i
$706$	6.12747	−	11.3973i	0.230610	−	0.428943i
$707$		0			0
$708$	−3.12515	−	4.72644i	−0.117450	−	0.177631i
$709$	−28.9026	−	7.74444i	−1.08546	−	0.290849i	−0.328630	−	0.944459i	$-0.606587\pi$
$709$	−28.9026	−	7.74444i	−1.08546	−	0.290849i	−0.756831	+	0.653610i	$0.773254\pi$
$710$	1.95113	−	8.27736i	0.0732246	−	0.310644i
$711$	13.0520	+	7.53558i	0.489488	+	0.282606i
$712$	3.10471	−	2.19089i	0.116354	−	0.0821069i
$713$		−	28.0192i		−	1.04933i
$714$		0			0
$715$	−8.30458	+	8.30458i	−0.310574	+	0.310574i
$716$	−12.9597	+	4.32944i	−0.484328	+	0.161799i
$717$	−12.0950	+	3.24085i	−0.451697	+	0.121032i
$718$	−10.1376	+	6.27001i	−0.378332	+	0.233995i
$719$	2.49771	+	4.32616i	0.0931488	+	0.161339i	0.908835	−	0.417157i	$-0.136973\pi$
$719$	2.49771	+	4.32616i	0.0931488	+	0.161339i	−0.815686	+	0.578495i	$0.803640\pi$
$720$	−17.5897	+	7.08731i	−0.655528	+	0.264128i
$721$		0			0
$722$	4.46220	+	2.39899i	0.166066	+	0.0892812i
$723$	0.672604	−	2.51019i	0.0250144	−	0.0933551i
$724$	−10.5356	+	11.8970i	−0.391554	+	0.442149i
$725$	0.834164	+	3.11314i	0.0309801	+	0.115619i
$726$	4.13578	−	4.39438i	0.153493	−	0.163091i
$727$		−	4.59798i		−	0.170530i	−0.996358	−	0.0852648i	$-0.972826\pi$
$727$		−	4.59798i		−	0.170530i	0.996358	−	0.0852648i	$-0.0271736\pi$
$728$		0			0
$729$		−	5.19606i		−	0.192447i
$730$	−22.3553	−	21.0398i	−0.827408	−	0.778717i
$731$	1.60791	+	6.00080i	0.0594707	+	0.221948i
$732$	0.955369	+	15.7425i	0.0353114	+	0.581860i
$733$	2.74210	−	10.2337i	0.101282	−	0.377989i	−0.896615	−	0.442811i	$-0.853981\pi$
$733$	2.74210	−	10.2337i	0.101282	−	0.377989i	0.997897	+	0.0648221i	$0.0206480\pi$
$734$	6.23037	−	11.5887i	0.229967	−	0.427746i
$735$		0			0
$736$	30.1588	−	24.1463i	1.11167	−	0.890045i
$737$	−3.09614	−	5.36266i	−0.114048	−	0.197536i
$738$	−14.5960	−	23.5994i	−0.537288	−	0.868707i
$739$	−45.8723	+	12.2915i	−1.68744	+	0.452149i	−0.969728	−	0.244190i	$-0.921478\pi$
$739$	−45.8723	+	12.2915i	−1.68744	+	0.452149i	−0.717714	+	0.696338i	$0.754811\pi$
$740$	0.288140	+	0.143832i	0.0105922	+	0.00528737i
$741$	−3.34858	+	3.34858i	−0.123013	+	0.123013i
$742$		0			0
$743$		−	17.5619i		−	0.644285i	−0.946691	−	0.322142i	$-0.895597\pi$
$743$		−	17.5619i		−	0.644285i	0.946691	−	0.322142i	$-0.104403\pi$
$744$	−1.69899	+	9.84561i	−0.0622879	+	0.360957i
$745$	3.43076	+	1.98075i	0.125693	+	0.0725690i
$746$	−28.2601	−	6.66143i	−1.03467	−	0.243892i
$747$	31.4949	+	8.43904i	1.15234	+	0.308768i
$748$	−48.1924	−	9.82863i	−1.76209	−	0.359370i
$749$		0			0
$750$	12.5933	+	6.77047i	0.459842	+	0.247223i
$751$	9.02361	+	15.6293i	0.329276	+	0.570323i	0.982368	−	0.186955i	$-0.0598620\pi$
$751$	9.02361	+	15.6293i	0.329276	+	0.570323i	−0.653092	+	0.757278i	$0.726529\pi$
$752$	−9.39273	−	12.4892i	−0.342518	−	0.455434i
$753$	−8.23522	+	14.2638i	−0.300108	+	0.519803i
$754$	−0.325615	−	10.7408i	−0.0118582	−	0.391158i
$755$	21.1206	+	21.1206i	0.768658	+	0.768658i
$756$		0			0
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	−0.286448	−	0.958096i	$-0.592475\pi$
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	0.958096	+	0.286448i	$0.0924747\pi$
$758$	−12.3678	+	13.1411i	−0.449218	+	0.477307i
$759$	−20.3421	−	11.7445i	−0.738371	−	0.426299i
$760$	9.77461	−	21.1632i	0.354562	−	0.767670i
$761$	5.61500	−	3.24182i	0.203543	−	0.117516i	−0.394764	−	0.918783i	$-0.629174\pi$
$761$	5.61500	−	3.24182i	0.203543	−	0.117516i	0.598307	+	0.801267i	$0.295840\pi$
$762$	11.2945	−	3.39635i	0.409157	−	0.123037i
$763$		0			0
$764$	7.05843	+	10.6751i	0.255365	+	0.386212i
$765$	7.55440	−	28.1934i	0.273130	−	1.01933i
$766$	−0.837324	−	1.35382i	−0.0302537	−	0.0489154i
$767$	−2.30452	+	3.99155i	−0.0832114	+	0.144126i
$768$	−12.0616	+	6.65599i	−0.435234	+	0.240177i
$769$	23.9598			0.864014			0.432007	−	0.901870i	$-0.357806\pi$
$769$	23.9598			0.864014			0.432007	+	0.901870i	$0.357806\pi$
$770$		0			0
$771$	−1.85587	−	1.85587i	−0.0668374	−	0.0668374i
$772$	8.76740	−	17.5638i	0.315546	−	0.632137i
$773$	0.711549	+	2.65554i	0.0255926	+	0.0955130i	0.977541	−	0.210746i	$-0.0675893\pi$
$773$	0.711549	+	2.65554i	0.0255926	+	0.0955130i	−0.951948	+	0.306259i	$0.900923\pi$
$774$	−0.739512	+	3.13726i	−0.0265812	+	0.112767i
$775$	−2.11097	+	1.21877i	−0.0758283	+	0.0437795i
$776$	52.8250	−	4.81608i	1.89631	−	0.172887i
$777$		0			0
$778$	7.03878	+	23.4074i	0.252352	+	0.839196i
$779$	32.9478	+	8.82834i	1.18048	+	0.316308i
$780$	−3.79041	−	3.35667i	−0.135718	−	0.120188i
$781$	11.0537	−	2.96183i	0.395532	−	0.105983i
$782$	1.80184	+	59.4360i	0.0644338	+	2.12543i
$783$	−24.5611			−0.877743
$784$		0			0
$785$	−40.7056			−1.45285
$786$	−0.510758	−	16.8480i	−0.0182182	−	0.600948i
$787$	−47.5886	+	12.7513i	−1.69635	+	0.454536i	−0.972016	−	0.234913i	$-0.924519\pi$
$787$	−47.5886	+	12.7513i	−1.69635	+	0.454536i	−0.724334	+	0.689449i	$0.757853\pi$
$788$	27.7663	−	31.3541i	0.989133	−	1.11695i
$789$	−22.4482	−	6.01499i	−0.799178	−	0.214139i
$790$	−5.70391	−	18.9683i	−0.202936	−	0.674861i
$791$		0			0
$792$	−19.6081	−	16.3315i	−0.696744	−	0.580314i
$793$	11.1102	−	6.41448i	0.394535	−	0.227785i
$794$	−9.20057	+	39.0320i	−0.326516	+	1.38519i
$795$	−3.42161	−	12.7696i	−0.121352	−	0.452892i
$796$	−7.77598	−	3.88156i	−0.275612	−	0.137578i
$797$	−22.5200	−	22.5200i	−0.797699	−	0.797699i	0.185033	−	0.982732i	$-0.440761\pi$
$797$	−22.5200	−	22.5200i	−0.797699	−	0.797699i	−0.982732	+	0.185033i	$0.940761\pi$
$798$		0			0
$799$	24.0521			0.850903
$800$	−3.13102	−	1.22186i	−0.110698	−	0.0431992i
$801$	−1.51722	+	2.62789i	−0.0536082	+	0.0928521i
$802$	16.7578	+	27.0947i	0.591740	+	0.956747i
$803$	10.6918	−	39.9024i	0.377306	−	1.40812i
$804$	2.22675	−	1.47234i	0.0785315	−	0.0519254i
$805$		0			0
$806$	7.78279	−	2.34034i	0.274137	−	0.0824351i
$807$	−13.5699	+	7.83459i	−0.477683	+	0.275791i
$808$	−4.34682	−	11.8084i	−0.152921	−	0.415418i
$809$	41.1059	+	23.7325i	1.44521	+	0.834391i	0.998190	−	0.0601343i	$-0.0191529\pi$
$809$	41.1059	+	23.7325i	1.44521	+	0.834391i	0.447017	+	0.894525i	$0.352486\pi$
$810$	5.85415	−	6.22019i	0.205694	−	0.218555i
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.516058	+	0.856554i	$0.672601\pi$
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.856554	+	0.516058i	$0.827399\pi$
$812$		0			0
$813$	−19.0613	−	19.0613i	−0.668507	−	0.668507i
$814$	0.0131315	+	0.433157i	0.000460257	+	0.0151822i
$815$	−4.45953	+	7.72414i	−0.156211	+	0.270565i
$816$	2.97085	−	20.9943i	0.104000	−	0.734948i
$817$	−1.98110	−	3.43137i	−0.0693099	−	0.120048i
$818$	−38.4466	−	20.6698i	−1.34425	−	0.722703i
$819$		0			0
$820$	−7.28759	+	35.7330i	−0.254494	+	1.24785i
$821$	−12.1621	−	3.25883i	−0.424461	−	0.113734i	0.0402639	−	0.999189i	$-0.487180\pi$
$821$	−12.1621	−	3.25883i	−0.424461	−	0.113734i	−0.464725	+	0.885455i	$0.653847\pi$
$822$	13.4178	+	3.16283i	0.468000	+	0.110316i
$823$	−4.29959	−	2.48237i	−0.149874	−	0.0865300i	0.423187	−	0.906042i	$-0.360911\pi$
$823$	−4.29959	−	2.48237i	−0.149874	−	0.0865300i	−0.573062	+	0.819512i	$0.694245\pi$
$824$	20.7116	−	14.6155i	0.721524	−	0.509154i
$825$			2.04343i			0.0711432i
$826$		0			0
$827$	11.3168	−	11.3168i	0.393524	−	0.393524i	−0.482417	−	0.875942i	$-0.660241\pi$
$827$	11.3168	−	11.3168i	0.393524	−	0.393524i	0.875942	+	0.482417i	$0.160241\pi$
$828$	−13.7790	+	27.6036i	−0.478852	+	0.959290i
$829$	34.1690	−	9.15557i	1.18674	−	0.317986i	0.389143	−	0.921177i	$-0.372771\pi$
$829$	34.1690	−	9.15557i	1.18674	−	0.317986i	0.797597	+	0.603191i	$0.206104\pi$
$830$	−22.5410	−	36.4451i	−0.782409	−	1.26503i
$831$	−7.08753	−	12.2760i	−0.245864	−	0.425848i
$832$	9.22607	+	6.36023i	0.319856	+	0.220501i
$833$		0			0
$834$	1.86958	−	3.47748i	0.0647382	−	0.120415i
$835$	6.66696	−	24.8814i	0.230719	−	0.861057i
$836$	31.3113	−	1.90019i	1.08292	−	0.0657195i
$837$	−4.80774	−	17.9427i	−0.166180	−	0.620191i
$838$	11.2865	+	10.6223i	0.389884	+	0.366941i
$839$		−	47.7342i		−	1.64797i	−0.566614	−	0.823983i	$-0.691747\pi$
$839$		−	47.7342i		−	1.64797i	0.566614	−	0.823983i	$-0.308253\pi$
$840$		0			0
$841$			0.425820i			0.0146834i
$842$	−17.4837	+	18.5769i	−0.602528	+	0.640203i
$843$	−5.66398	−	21.1383i	−0.195078	−	0.728041i
$844$	−30.9147	−	27.3772i	−1.06413	−	0.942361i
$845$	5.99651	−	22.3793i	0.206286	−	0.769871i
$846$	10.9913	+	5.90918i	0.377888	+	0.203162i
$847$		0			0
$848$	10.9352	+	27.1395i	0.375515	+	0.931974i
$849$	2.67942	+	4.64089i	0.0919573	+	0.159275i
$850$	4.39953	−	2.72107i	0.150903	−	0.0933320i
$851$	0.506069	−	0.135601i	0.0173478	−	0.00464834i
$852$	1.56316	+	4.67916i	0.0535530	+	0.160306i
$853$	−3.65043	+	3.65043i	−0.124988	+	0.124988i	−0.766834	−	0.641846i	$-0.778169\pi$
$853$	−3.65043	+	3.65043i	−0.124988	+	0.124988i	0.641846	+	0.766834i	$0.278169\pi$
$854$		0			0
$855$			18.6155i			0.636637i
$856$	−35.4074	−	6.11001i	−1.21020	−	0.208836i
$857$	19.0400	+	10.9927i	0.650394	+	0.375505i	0.788607	−	0.614898i	$-0.210803\pi$
$857$	19.0400	+	10.9927i	0.650394	+	0.375505i	−0.138213	+	0.990402i	$0.544136\pi$
$858$	1.56313	−	6.63131i	0.0533642	−	0.226389i
$859$	−11.9718	−	3.20783i	−0.408472	−	0.109450i	0.0487316	−	0.998812i	$-0.484482\pi$
$859$	−11.9718	−	3.20783i	−0.408472	−	0.109450i	−0.457203	+	0.889362i	$0.651149\pi$
$860$	3.53358	−	2.33642i	0.120494	−	0.0796713i
$861$		0			0
$862$	−6.59867	+	12.2737i	−0.224752	+	0.418045i
$863$	−9.23283	−	15.9917i	−0.314289	−	0.544365i	0.664997	−	0.746846i	$-0.268433\pi$
$863$	−9.23283	−	15.9917i	−0.314289	−	0.544365i	−0.979286	+	0.202481i	$0.935100\pi$
$864$	15.1696	−	20.6374i	0.516081	−	0.702100i
$865$	−15.6685	+	27.1387i	−0.532745	+	0.922742i
$866$	−21.0833	+	0.639155i	−0.716440	+	0.0217194i
$867$	12.7264	+	12.7264i	0.432213	+	0.432213i
$868$		0			0
$869$	18.8469	−	18.8469i	0.639338	−	0.639338i
$870$	10.0962	+	9.50210i	0.342294	+	0.322151i
$871$	−1.88052	−	1.08572i	−0.0637191	−	0.0367882i
$872$	−38.4174	+	14.1419i	−1.30098	+	0.478906i
$873$	−36.6837	+	21.1793i	−1.24156	+	0.716812i
$874$	−10.9211	−	36.3180i	−0.369412	−	1.22848i
$875$		0			0
$876$	17.4496	+	3.55877i	0.589567	+	0.120240i
$877$	5.01836	−	18.7288i	0.169458	−	0.632426i	−0.827971	−	0.560770i	$-0.810505\pi$
$877$	5.01836	−	18.7288i	0.169458	−	0.632426i	0.997429	−	0.0716557i	$-0.0228283\pi$
$878$	11.1759	−	6.91220i	0.377169	−	0.233275i
$879$	11.3132	−	19.5951i	0.381585	−	0.660925i
$880$	4.05569	+	33.2917i	0.136717	+	1.12226i
$881$	−21.6393			−0.729046			−0.364523	−	0.931194i	$-0.618768\pi$
$881$	−21.6393			−0.729046			−0.364523	+	0.931194i	$0.618768\pi$
$882$		0			0
$883$	−34.6173	−	34.6173i	−1.16496	−	1.16496i	−0.983374	−	0.181589i	$-0.941876\pi$
$883$	−34.6173	−	34.6173i	−1.16496	−	1.16496i	−0.181589	−	0.983374i	$-0.558124\pi$
$884$	−16.3588	+	5.46496i	−0.550206	+	0.183806i
$885$	−1.53912	−	5.74408i	−0.0517370	−	0.193085i
$886$	−14.0136	−	3.30327i	−0.470796	−	0.110976i
$887$	−3.36305	+	1.94166i	−0.112920	+	0.0651945i	−0.555396	−	0.831586i	$-0.687433\pi$
$887$	−3.36305	+	1.94166i	−0.112920	+	0.0651945i	0.442476	+	0.896780i	$0.354100\pi$
$888$	−0.186049	+	0.0169622i	−0.00624339	+	0.000569213i
$889$		0			0
$890$	3.81908	−	1.14843i	0.128016	−	0.0384954i
$891$	11.1025	+	2.97491i	0.371948	+	0.0996632i
$892$	−0.544436	+	0.0330403i	−0.0182291	+	0.00110627i
$893$	−14.8173	+	3.97028i	−0.495841	+	0.132860i
$894$	−2.29704	+	0.0696364i	−0.0768245	+	0.00232899i
$895$	−14.3402			−0.479341
$896$		0			0
$897$	−8.23688			−0.275022
$898$	5.40173	−	0.163757i	0.180258	−	0.00546465i
$899$	−21.4965	+	5.75998i	−0.716949	+	0.192106i
$900$	2.67900	−	0.162581i	0.0893002	−	0.00541937i
$901$	−43.5002	−	11.6559i	−1.44920	−	0.388313i
$902$	−46.9949	+	14.1317i	−1.56476	+	0.470535i
$903$		0			0
$904$	7.35399	−	0.670468i	0.244590	−	0.0222994i
$905$	−14.4437	+	8.33910i	−0.480126	+	0.277201i
$906$	−16.8651	−	3.97542i	−0.560305	−	0.132074i
$907$	10.3652	+	38.6836i	0.344172	+	1.28447i	0.893577	+	0.448911i	$0.148188\pi$
$907$	10.3652	+	38.6836i	0.344172	+	1.28447i	−0.549404	+	0.835557i	$0.685145\pi$
$908$	21.6422	−	7.22997i	0.718220	−	0.239935i
$909$	7.10521	+	7.10521i	0.235665	+	0.235665i
$910$		0			0
$911$	−30.3771			−1.00644			−0.503218	−	0.864159i	$-0.667851\pi$
$911$	−30.3771			−1.00644			−0.503218	+	0.864159i	$0.667851\pi$
$912$	1.63534	+	13.4239i	0.0541516	+	0.444510i
$913$	28.8321	−	49.9387i	0.954203	−	1.65273i
$914$	30.1799	−	18.6660i	0.998263	−	0.617417i
$915$	−4.28404	+	15.9883i	−0.141626	+	0.528556i
$916$	30.7927	+	6.28004i	1.01742	+	0.207498i
$917$		0			0
$918$	11.3523	+	37.7519i	0.374681	+	1.24600i
$919$	−9.74979	+	5.62904i	−0.321616	+	0.185685i	−0.652113	−	0.758122i	$-0.726117\pi$
$919$	−9.74979	+	5.62904i	−0.321616	+	0.185685i	0.330497	+	0.943807i	$0.392784\pi$
$920$	38.0506	−	14.0069i	1.25449	−	0.461794i
$921$	20.1012	+	11.6054i	0.662358	+	0.382413i
$922$	10.3966	+	9.78478i	0.342393	+	0.322244i
$923$	2.83757	−	2.83757i	0.0933998	−	0.0933998i
$924$		0			0
$925$	−0.0322290	−	0.0322290i	−0.00105968	−	0.00105968i
$926$	5.19704	−	0.157552i	0.170785	−	0.00517748i
$927$	−10.1214	+	17.5308i	−0.332430	+	0.575786i
$928$	−24.7250	−	18.1742i	−0.811638	−	0.596597i
$929$	−12.8415	−	22.2420i	−0.421314	−	0.729738i	0.574754	−	0.818326i	$-0.305098\pi$
$929$	−12.8415	−	22.2420i	−0.421314	−	0.729738i	−0.996068	+	0.0885883i	$0.971764\pi$
$930$	−4.96530	+	9.23562i	−0.162819	+	0.302848i
$931$		0			0
$932$	−9.54957	+	6.31422i	−0.312806	+	0.206829i
$933$	−5.71572	−	1.53152i	−0.187124	−	0.0501398i
$934$	−3.15725	+	13.3942i	−0.103308	+	0.438270i
$935$	−44.7037	−	25.8097i	−1.46197	−	0.844068i
$936$	−8.81823	−	1.52170i	−0.288233	−	0.0497384i
$937$			23.0570i			0.753238i	0.926368	+	0.376619i	$0.122913\pi$
$937$			23.0570i			0.753238i	−0.926368	+	0.376619i	$0.877087\pi$
$938$		0			0
$939$	4.88423	−	4.88423i	0.159391	−	0.159391i
$940$	−5.19663	−	15.5556i	−0.169495	−	0.507367i
$941$	−30.8769	+	8.27344i	−1.00656	+	0.269706i	−0.724191	−	0.689600i	$-0.757786\pi$
$941$	−30.8769	+	8.27344i	−1.00656	+	0.269706i	−0.282367	+	0.959306i	$0.591120\pi$
$942$	20.0829	−	12.4211i	0.654336	−	0.404701i
$943$	29.6647	+	51.3807i	0.966015	+	1.67319i
$944$	4.91890	+	12.2080i	0.160097	+	0.397337i
$945$		0			0
$946$	5.02075	+	2.69928i	0.163239	+	0.0877612i
$947$	−2.78357	+	10.3884i	−0.0904539	+	0.337578i	−0.996291	−	0.0860477i	$-0.972576\pi$
$947$	−2.78357	+	10.3884i	−0.0904539	+	0.337578i	0.905837	+	0.423626i	$0.139243\pi$
$948$	8.60219	+	7.61784i	0.279386	+	0.247416i
$949$	−3.74929	−	13.9925i	−0.121707	−	0.454217i
$950$	−2.26116	+	2.40254i	−0.0733617	+	0.0779488i
$951$			2.39443i			0.0776449i
$952$		0			0
$953$			2.60332i			0.0843297i	0.999111	+	0.0421649i	$0.0134255\pi$
$953$			2.60332i			0.0843297i	−0.999111	+	0.0421649i	$0.986575\pi$
$954$	−17.0150	−	16.0137i	−0.550880	−	0.518462i
$955$	3.47625	+	12.9735i	0.112489	+	0.419814i
$956$	29.0326	−	1.76190i	0.938980	−	0.0569840i
$957$	−4.82869	+	18.0209i	−0.156089	+	0.582534i
$958$	−10.8042	+	20.0961i	−0.349067	+	0.649276i
$959$		0			0
$960$	−14.2198	+	2.61459i	−0.458943	+	0.0843856i
$961$	7.08430	+	12.2704i	0.228526	+	0.395818i
$962$	0.0799354	+	0.129243i	0.00257722	+	0.00416695i
$963$	27.7150	−	7.42622i	0.893104	−	0.239307i
$964$	−2.69603	+	5.40098i	−0.0868331	+	0.173954i
$965$	14.5680	−	14.5680i	0.468962	−	0.468962i
$966$		0			0
$967$			10.6383i			0.342106i	0.985262	+	0.171053i	$0.0547169\pi$
$967$			10.6383i			0.342106i	−0.985262	+	0.171053i	$0.945283\pi$
$968$	−11.4528	+	8.08185i	−0.368107	+	0.259760i
$969$	−18.0255	−	10.4070i	−0.579062	−	0.334322i
$970$	54.1851	+	12.7724i	1.73978	+	0.410099i
$971$	−1.79607	−	0.481257i	−0.0576388	−	0.0154443i	0.229884	−	0.973218i	$-0.426165\pi$
$971$	−1.79607	−	0.481257i	−0.0576388	−	0.0154443i	−0.287523	+	0.957774i	$0.592832\pi$
$972$	−6.41896	+	31.4739i	−0.205888	+	1.00952i
$973$		0			0
$974$	−16.2850	−	8.75523i	−0.521806	−	0.280536i
$975$	0.358285	+	0.620567i	0.0114743	+	0.0198741i
$976$	5.13294	−	36.2734i	0.164302	−	1.16108i
$977$	−3.20547	+	5.55203i	−0.102552	+	0.177625i	−0.912735	−	0.408551i	$-0.866034\pi$
$977$	−3.20547	+	5.55203i	−0.102552	+	0.177625i	0.810183	+	0.586176i	$0.199367\pi$
$978$	−0.156782	−	5.17165i	−0.00501333	−	0.165371i
$979$	3.79465	+	3.79465i	0.121278	+	0.121278i
$980$		0			0
$981$	23.1160	−	23.1160i	0.738038	−	0.738038i
$982$	13.9469	−	14.8189i	0.445063	−	0.472891i
$983$	−16.6011	−	9.58464i	−0.529492	−	0.305702i	0.211317	−	0.977417i	$-0.432225\pi$
$983$	−16.6011	−	9.58464i	−0.529492	−	0.305702i	−0.740810	+	0.671715i	$0.765558\pi$
$984$	−7.30825	−	19.8533i	−0.232978	−	0.632900i
$985$	38.0660	−	21.9774i	1.21288	−	0.700258i
$986$	45.2292	−	13.6008i	1.44039	−	0.433137i
$987$		0			0
$988$	9.17571	−	6.06702i	0.291918	−	0.193018i
$989$	1.78369	−	6.65683i	0.0567181	−	0.211675i
$990$	−14.0876	−	22.7773i	−0.447733	−	0.723912i
$991$	8.09070	−	14.0135i	0.257009	−	0.445153i	−0.708430	−	0.705781i	$-0.750596\pi$
$991$	8.09070	−	14.0135i	0.257009	−	0.445153i	0.965439	+	0.260628i	$0.0839295\pi$
$992$	8.43702	−	21.6199i	0.267876	−	0.686434i
$993$	−9.25270			−0.293626
$994$		0			0
$995$	−6.44966	−	6.44966i	−0.204468	−	0.204468i
$996$	22.2420	+	11.1026i	0.704765	+	0.351800i
$997$	−6.95744	−	25.9655i	−0.220344	−	0.822336i	−0.984217	−	0.176969i	$-0.943371\pi$
$997$	−6.95744	−	25.9655i	−0.220344	−	0.822336i	0.763872	−	0.645368i	$-0.223296\pi$
$998$	−13.5080	+	57.3056i	−0.427588	+	1.81398i
$999$	0.300805	−	0.173670i	0.00951705	−	0.00549467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.557.12		48
7.2	even	3	inner	784.2.x.o.765.4		48
7.3	odd	6		784.2.m.j.589.4		24
7.4	even	3		784.2.m.k.589.4		24
7.5	odd	6		112.2.w.c.93.4	yes	48
7.6	odd	2		112.2.w.c.109.12	yes	48
16.5	even	4	inner	784.2.x.o.165.4		48
28.19	even	6		448.2.ba.c.401.8		48
28.27	even	2		448.2.ba.c.81.5		48
56.5	odd	6		896.2.ba.f.289.8		48
56.13	odd	2		896.2.ba.f.417.5		48
56.19	even	6		896.2.ba.e.289.5		48
56.27	even	2		896.2.ba.e.417.8		48
112.5	odd	12		112.2.w.c.37.12	✓	48
112.13	odd	4		896.2.ba.f.865.8		48
112.19	even	12		896.2.ba.e.737.8		48
112.27	even	4		448.2.ba.c.305.8		48
112.37	even	12	inner	784.2.x.o.373.12		48
112.53	even	12		784.2.m.k.197.4		24
112.61	odd	12		896.2.ba.f.737.5		48
112.69	odd	4		112.2.w.c.53.4	yes	48
112.75	even	12		448.2.ba.c.177.5		48
112.83	even	4		896.2.ba.e.865.5		48
112.101	odd	12		784.2.m.j.197.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.12	✓	48	112.5	odd	12
112.2.w.c.53.4	yes	48	112.69	odd	4
112.2.w.c.93.4	yes	48	7.5	odd	6
112.2.w.c.109.12	yes	48	7.6	odd	2
448.2.ba.c.81.5		48	28.27	even	2
448.2.ba.c.177.5		48	112.75	even	12
448.2.ba.c.305.8		48	112.27	even	4
448.2.ba.c.401.8		48	28.19	even	6
784.2.m.j.197.4		24	112.101	odd	12
784.2.m.j.589.4		24	7.3	odd	6
784.2.m.k.197.4		24	112.53	even	12
784.2.m.k.589.4		24	7.4	even	3
784.2.x.o.165.4		48	16.5	even	4	inner
784.2.x.o.373.12		48	112.37	even	12	inner
784.2.x.o.557.12		48	1.1	even	1	trivial
784.2.x.o.765.4		48	7.2	even	3	inner
896.2.ba.e.289.5		48	56.19	even	6
896.2.ba.e.417.8		48	56.27	even	2
896.2.ba.e.737.8		48	112.19	even	12
896.2.ba.e.865.5		48	112.83	even	4
896.2.ba.f.289.8		48	56.5	odd	6
896.2.ba.f.417.5		48	56.13	odd	2
896.2.ba.f.737.5		48	112.61	odd	12
896.2.ba.f.865.8		48	112.13	odd	4

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41356 - 0.0428532i) q^{2} +(-0.831674 + 0.222846i) q^{3} +(1.99633 - 0.121151i) q^{4} +(2.02749 + 0.543265i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} +(-1.95606 + 1.12933i) q^{9} +O(q^{10})\)	\(q+(1.41356 - 0.0428532i) q^{2} +(-0.831674 + 0.222846i) q^{3} +(1.99633 - 0.121151i) q^{4} +(2.02749 + 0.543265i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} +(-1.95606 + 1.12933i) q^{9} +(2.88927 + 0.681055i) q^{10} +(1.03385 + 3.85837i) q^{11} +(-1.63329 + 0.545632i) q^{12} +(0.990473 + 0.990473i) q^{13} -1.80728 q^{15} +(3.97064 - 0.483716i) q^{16} +(-3.07828 + 5.33174i) q^{17} +(-2.71662 + 1.68020i) q^{18} +(1.01626 - 3.79274i) q^{19} +(4.11335 + 0.838901i) q^{20} +(1.62675 + 5.40975i) q^{22} +(5.91462 - 3.41481i) q^{23} +(-2.28538 + 0.841278i) q^{24} +(-0.514543 - 0.297072i) q^{25} +(1.44254 + 1.35765i) q^{26} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(-2.55470 + 0.0774475i) q^{30} +(2.05131 - 3.55296i) q^{31} +(5.59203 - 0.853918i) q^{32} +(-1.71965 - 2.97851i) q^{33} +(-4.12286 + 7.66866i) q^{34} +(-3.76811 + 2.49149i) q^{36} +(0.0740993 + 0.0198548i) q^{37} +(1.27402 - 5.40483i) q^{38} +(-1.04447 - 0.603027i) q^{39} +(5.85044 + 1.00957i) q^{40} +8.68707i q^{41} +(0.713530 - 0.713530i) q^{43} +(2.53134 + 7.57731i) q^{44} +(-4.57941 + 1.22705i) q^{45} +(8.21436 - 5.08051i) q^{46} +(-1.95337 - 3.38334i) q^{47} +(-3.19449 + 1.28714i) q^{48} +(-0.740070 - 0.397880i) q^{50} +(1.37197 - 5.12025i) q^{51} +(2.09731 + 1.85731i) q^{52} +(1.89324 + 7.06568i) q^{53} +(4.38849 - 4.66289i) q^{54} +8.38446i q^{55} +3.38079i q^{57} +(-5.58644 - 5.25769i) q^{58} +(0.851626 + 3.17831i) q^{59} +(-3.60791 + 0.218954i) q^{60} +(2.37044 - 8.84662i) q^{61} +(2.74740 - 5.11025i) q^{62} +(7.86810 - 1.44670i) q^{64} +(1.47009 + 2.54627i) q^{65} +(-2.55847 - 4.13663i) q^{66} +(-1.49739 + 0.401223i) q^{67} +(-5.49930 + 11.0168i) q^{68} +(-4.15805 + 4.15805i) q^{69} -2.86486i q^{71} +(-5.21969 + 3.68336i) q^{72} +(-8.95624 - 5.17089i) q^{73} +(0.105595 + 0.0248907i) q^{74} +(0.494133 + 0.132403i) q^{75} +(1.56929 - 7.69467i) q^{76} +(-1.50227 - 0.807659i) q^{78} +(-3.33631 - 5.77865i) q^{79} +(8.31323 + 1.17638i) q^{80} +(1.43876 - 2.49200i) q^{81} +(0.372269 + 12.2797i) q^{82} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(0.978044 - 1.03920i) q^{86} +(4.04486 + 2.33530i) q^{87} +(3.90293 + 10.6025i) q^{88} +(1.16348 - 0.671733i) q^{89} +(-6.42071 + 1.93076i) q^{90} +(11.3938 - 7.53363i) q^{92} +(-0.914251 + 3.41203i) q^{93} +(-2.90621 - 4.69887i) q^{94} +(4.12092 - 7.13765i) q^{95} +(-4.46045 + 1.95634i) q^{96} +18.7539 q^{97} +(-6.37963 - 6.37963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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