LMFDB - Embedded newform 784.2.x.o.165.4

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			165.4
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743894 + 1.20276i) q^{2} +(0.222846 + 0.831674i) q^{3} +(-0.893243 - 1.78945i) q^{4} +(-0.543265 + 2.02749i) q^{5} +(-1.16607 - 0.350647i) q^{6} +(2.81674 + 0.256804i) q^{8} +(1.95606 - 1.12933i) q^{9} +O(q^{10})$	\(q+(-0.743894 + 1.20276i) q^{2} +(0.222846 + 0.831674i) q^{3} +(-0.893243 - 1.78945i) q^{4} +(-0.543265 + 2.02749i) q^{5} +(-1.16607 - 0.350647i) q^{6} +(2.81674 + 0.256804i) q^{8} +(1.95606 - 1.12933i) q^{9} +(-2.03445 - 2.16165i) q^{10} +(-3.85837 + 1.03385i) q^{11} +(1.28918 - 1.14166i) q^{12} +(0.990473 - 0.990473i) q^{13} -1.80728 q^{15} +(-2.40423 + 3.19682i) q^{16} +(-3.07828 + 5.33174i) q^{17} +(-0.0967907 + 3.19276i) q^{18} +(-3.79274 - 1.01626i) q^{19} +(4.11335 - 0.838901i) q^{20} +(1.62675 - 5.40975i) q^{22} +(-5.91462 + 3.41481i) q^{23} +(0.414124 + 2.39984i) q^{24} +(0.514543 + 0.297072i) q^{25} +(0.454490 + 1.92810i) q^{26} +(3.20161 + 3.20161i) q^{27} +(-3.83574 + 3.83574i) q^{29} +(1.34442 - 2.17371i) q^{30} +(2.05131 - 3.55296i) q^{31} +(-2.05650 - 5.26980i) q^{32} +(-1.71965 - 2.97851i) q^{33} +(-4.12286 - 7.66866i) q^{34} +(-3.76811 - 2.49149i) q^{36} +(-0.0198548 + 0.0740993i) q^{37} +(4.04371 - 3.80575i) q^{38} +(1.04447 + 0.603027i) q^{39} +(-2.05091 + 5.57141i) q^{40} -8.68707i q^{41} +(0.713530 + 0.713530i) q^{43} +(5.29647 + 5.98086i) q^{44} +(1.22705 + 4.57941i) q^{45} +(0.292670 - 9.65410i) q^{46} +(-1.95337 - 3.38334i) q^{47} +(-3.19449 - 1.28714i) q^{48} +(-0.740070 + 0.397880i) q^{50} +(-5.12025 - 1.37197i) q^{51} +(-2.65713 - 0.887665i) q^{52} +(-7.06568 + 1.89324i) q^{53} +(-6.23242 + 1.46910i) q^{54} -8.38446i q^{55} -3.38079i q^{57} +(-1.76008 - 7.46685i) q^{58} +(-3.17831 + 0.851626i) q^{59} +(1.61434 + 3.23402i) q^{60} +(-8.84662 - 2.37044i) q^{61} +(2.74740 + 5.11025i) q^{62} +(7.86810 + 1.44670i) q^{64} +(1.47009 + 2.54627i) q^{65} +(4.86166 + 0.147385i) q^{66} +(0.401223 + 1.49739i) q^{67} +(12.2905 + 0.745876i) q^{68} +(-4.15805 - 4.15805i) q^{69} +2.86486i q^{71} +(5.79973 - 2.67871i) q^{72} +(8.95624 + 5.17089i) q^{73} +(-0.0743534 - 0.0790025i) q^{74} +(-0.132403 + 0.494133i) q^{75} +(1.56929 + 7.69467i) q^{76} +(-1.50227 + 0.807659i) q^{78} +(-3.33631 - 5.77865i) q^{79} +(-5.17539 - 6.61128i) q^{80} +(1.43876 - 2.49200i) q^{81} +(10.4484 + 6.46226i) q^{82} +(-10.2078 + 10.2078i) q^{83} +(-9.13773 - 9.13773i) q^{85} +(-1.38899 + 0.327412i) q^{86} +(-4.04486 - 2.33530i) q^{87} +(-11.1335 + 1.92124i) q^{88} +(-1.16348 + 0.671733i) q^{89} +(-6.42071 - 1.93076i) q^{90} +(11.3938 + 7.53363i) q^{92} +(3.41203 + 0.914251i) q^{93} +(5.52244 + 0.167417i) q^{94} +(4.12092 - 7.13765i) q^{95} +(3.92447 - 2.88469i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.743894	+	1.20276i	−0.526012	+	0.850477i
$2$	−0.743894	+	1.20276i	−0.526012	+	0.850477i
$3$	0.222846	+	0.831674i	0.128660	+	0.480167i	0.999944	−	0.0106134i	$-0.00337842\pi$
$3$	0.222846	+	0.831674i	0.128660	+	0.480167i	−0.871283	+	0.490780i	$0.836712\pi$
$4$	−0.893243	−	1.78945i	−0.446622	−	0.894723i
$5$	−0.543265	+	2.02749i	−0.242955	+	0.906722i	0.731445	+	0.681901i	$0.238846\pi$
$5$	−0.543265	+	2.02749i	−0.242955	+	0.906722i	−0.974400	+	0.224821i	$0.927820\pi$
$6$	−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
$10$	−2.03445	−	2.16165i	−0.643348	−	0.683575i
$11$	−3.85837	+	1.03385i	−1.16334	+	0.311716i	−0.788300	−	0.615291i	$-0.789038\pi$
$11$	−3.85837	+	1.03385i	−1.16334	+	0.311716i	−0.375042	+	0.927008i	$0.622372\pi$
$12$	1.28918	−	1.14166i	0.372154	−	0.329568i
$13$	0.990473	−	0.990473i	0.274708	−	0.274708i	−0.556284	−	0.830992i	$-0.687773\pi$
$13$	0.990473	−	0.990473i	0.274708	−	0.274708i	0.830992	+	0.556284i	$0.187773\pi$
$14$		0			0
$15$	−1.80728			−0.466636
$16$	−2.40423	+	3.19682i	−0.601058	+	0.799205i
$17$	−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	$0.898355\pi$
$18$	−0.0967907	+	3.19276i	−0.0228138	+	0.752540i
$19$	−3.79274	−	1.01626i	−0.870114	−	0.233146i	−0.203977	−	0.978976i	$-0.565387\pi$
$19$	−3.79274	−	1.01626i	−0.870114	−	0.233146i	−0.666137	+	0.745829i	$0.732053\pi$
$20$	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	−0.967713	−	0.252055i	$-0.918894\pi$
$23$	−5.91462	+	3.41481i	−1.23328	+	0.712036i	−0.265570	+	0.964092i	$0.585560\pi$
$24$	0.414124	+	2.39984i	0.0845327	+	0.489865i
$25$	0.514543	+	0.297072i	0.102909	+	0.0594143i
$26$	0.454490	+	1.92810i	0.0891329	+	0.378132i
$27$	3.20161	+	3.20161i	0.616151	+	0.616151i
$28$		0			0
$29$	−3.83574	+	3.83574i	−0.712279	+	0.712279i	−0.967012	−	0.254732i	$-0.918013\pi$
$29$	−3.83574	+	3.83574i	−0.712279	+	0.712279i	0.254732	+	0.967012i	$0.418013\pi$
$30$	1.34442	−	2.17371i	0.245457	−	0.396863i
$31$	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	$0.0465637\pi$
$32$	−2.05650	−	5.26980i	−0.363542	−	0.931578i
$33$	−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
$37$	−0.0198548	+	0.0740993i	−0.00326412	+	0.0121818i	−0.967539	−	0.252723i	$-0.918674\pi$
$37$	−0.0198548	+	0.0740993i	−0.00326412	+	0.0121818i	0.964275	+	0.264905i	$0.0853405\pi$
$38$	4.04371	−	3.80575i	0.655976	−	0.617374i
$39$	1.04447	+	0.603027i	0.167250	+	0.0965616i
$40$	−2.05091	+	5.57141i	−0.324277	+	0.880918i
$41$		−	8.68707i		−	1.35669i	−0.734742	−	0.678346i	$-0.762697\pi$
$41$		−	8.68707i		−	1.35669i	0.734742	−	0.678346i	$-0.237303\pi$
$42$		0			0
$43$	0.713530	+	0.713530i	0.108812	+	0.108812i	0.759417	−	0.650604i	$-0.225484\pi$
$43$	0.713530	+	0.713530i	0.108812	+	0.108812i	−0.650604	+	0.759417i	$0.725484\pi$
$44$	5.29647	+	5.98086i	0.798474	+	0.901649i
$45$	1.22705	+	4.57941i	0.182918	+	0.682658i
$46$	0.292670	−	9.65410i	0.0431519	−	1.42342i
$47$	−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
$51$	−5.12025	−	1.37197i	−0.716978	−	0.192114i
$52$	−2.65713	−	0.887665i	−0.368478	−	0.123097i
$53$	−7.06568	+	1.89324i	−0.970545	+	0.260057i	−0.709058	−	0.705150i	$-0.750880\pi$
$53$	−7.06568	+	1.89324i	−0.970545	+	0.260057i	−0.261487	+	0.965207i	$0.584213\pi$
$54$	−6.23242	+	1.46910i	−0.848125	+	0.199919i
$55$		−	8.38446i		−	1.13056i
$56$		0			0
$57$		−	3.38079i		−	0.447797i
$58$	−1.76008	−	7.46685i	−0.231109	−	0.980445i
$59$	−3.17831	+	0.851626i	−0.413781	+	0.110872i	−0.459703	−	0.888073i	$-0.652044\pi$
$59$	−3.17831	+	0.851626i	−0.413781	+	0.110872i	0.0459220	+	0.998945i	$0.485377\pi$
$60$	1.61434	+	3.23402i	0.208410	+	0.417510i
$61$	−8.84662	−	2.37044i	−1.13269	−	0.303504i	−0.356684	−	0.934225i	$-0.616093\pi$
$61$	−8.84662	−	2.37044i	−1.13269	−	0.303504i	−0.776010	+	0.630721i	$0.782759\pi$
$62$	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
$66$	4.86166	+	0.147385i	0.598429	+	0.0181418i
$67$	0.401223	+	1.49739i	0.0490172	+	0.182935i	0.986094	−	0.166189i	$-0.0531461\pi$
$67$	0.401223	+	1.49739i	0.0490172	+	0.182935i	−0.937077	+	0.349123i	$0.886479\pi$
$68$	12.2905	+	0.745876i	1.49044	+	0.0904507i
$69$	−4.15805	−	4.15805i	−0.500571	−	0.500571i
$70$		0			0
$71$			2.86486i			0.339997i	0.985444	+	0.169998i	$0.0543762\pi$
$71$			2.86486i			0.339997i	−0.985444	+	0.169998i	$0.945624\pi$
$72$	5.79973	−	2.67871i	0.683504	−	0.315689i
$73$	8.95624	+	5.17089i	1.04825	+	0.605207i	0.922159	−	0.386812i	$-0.126424\pi$
$73$	8.95624	+	5.17089i	1.04825	+	0.605207i	0.126090	+	0.992019i	$0.459757\pi$
$74$	−0.0743534	−	0.0790025i	−0.00864341	−	0.00918386i
$75$	−0.132403	+	0.494133i	−0.0152885	+	0.0570576i
$76$	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	$0.955816\pi$
$80$	−5.17539	−	6.61128i	−0.578626	−	0.739164i
$81$	1.43876	−	2.49200i	0.159862	−	0.276889i
$82$	10.4484	+	6.46226i	1.15384	+	0.713637i
$83$	−10.2078	+	10.2078i	−1.12045	+	1.12045i	−0.128776	+	0.991674i	$0.541105\pi$
$83$	−10.2078	+	10.2078i	−1.12045	+	1.12045i	−0.991674	+	0.128776i	$0.958895\pi$
$84$		0			0
$85$	−9.13773	−	9.13773i	−0.991126	−	0.991126i
$86$	−1.38899	+	0.327412i	−0.149779	+	0.0353057i
$87$	−4.04486	−	2.33530i	−0.433655	−	0.250371i
$88$	−11.1335	+	1.92124i	−1.18684	+	0.204805i
$89$	−1.16348	+	0.671733i	−0.123328	+	0.0712036i	−0.560395	−	0.828225i	$-0.689351\pi$
$89$	−1.16348	+	0.671733i	−0.123328	+	0.0712036i	0.437067	+	0.899429i	$0.356017\pi$
$90$	−6.42071	−	1.93076i	−0.676802	−	0.203519i
$91$		0			0
$92$	11.3938	+	7.53363i	1.18789	+	0.785436i
$93$	3.41203	+	0.914251i	0.353811	+	0.0948034i
$94$	5.52244	+	0.167417i	0.569596	+	0.0172677i
$95$	4.12092	−	7.13765i	0.422798	−	0.732307i
$96$	3.92447	−	2.88469i	0.400540	−	0.294418i
$97$	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
$100$	0.0719813	−	1.18610i	0.00719813	−	0.118610i
$101$	4.29719	−	1.15143i	0.427587	−	0.114571i	−0.0386065	−	0.999254i	$-0.512292\pi$
$101$	4.29719	−	1.15143i	0.427587	−	0.114571i	0.466193	+	0.884683i	$0.345625\pi$
$102$	5.45906	−	5.13781i	0.540527	−	0.508719i
$103$	−7.76159	+	4.48115i	−0.764772	+	0.441541i	−0.831006	−	0.556263i	$-0.812235\pi$
$103$	−7.76159	+	4.48115i	−0.764772	+	0.441541i	0.0662345	+	0.997804i	$0.478901\pi$
$104$	3.04427	−	2.53555i	0.298515	−	0.248631i
$105$		0			0
$106$	2.97901	−	9.90665i	0.289347	−	0.962219i
$107$	3.28789	−	12.2706i	0.317852	−	1.18624i	−0.603453	−	0.797399i	$-0.706209\pi$
$107$	3.28789	−	12.2706i	0.317852	−	1.18624i	0.921305	−	0.388841i	$-0.127125\pi$
$108$	2.86929	−	8.58894i	0.276098	−	0.826471i
$109$	3.74605	+	13.9805i	0.358807	+	1.33909i	0.875626	+	0.482990i	$0.160449\pi$
$109$	3.74605	+	13.9805i	0.358807	+	1.33909i	−0.516819	+	0.856095i	$0.672884\pi$
$110$	10.0845	+	6.23715i	0.961515	+	0.594689i
$111$	−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	$0.460812\pi$
$114$	4.06627	+	2.51495i	0.380841	+	0.235547i
$115$	−3.71029	−	13.8470i	−0.345986	−	1.29124i
$116$	10.2901	+	3.43760i	0.955412	+	0.319173i
$117$	0.818851	−	3.05599i	0.0757028	−	0.282527i
$118$	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
$122$	9.43201	−	8.87696i	0.853934	−	0.803682i
$123$	7.22481	−	1.93588i	0.651439	−	0.174553i
$124$	−8.19015	−	0.497037i	−0.735497	−	0.0446352i
$125$	−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	$0.641396\pi$
$128$	−7.59307	+	8.38721i	−0.671139	+	0.741332i
$129$	−0.434417	+	0.752432i	−0.0382483	+	0.0662479i
$130$	−4.15612	−	0.125996i	−0.364516	−	0.0110506i
$131$	13.3711	+	3.58278i	1.16824	+	0.313029i	0.790252	−	0.612782i	$-0.209950\pi$
$131$	13.3711	+	3.58278i	1.16824	+	0.313029i	0.377987	+	0.925811i	$0.376616\pi$
$132$	−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
$136$	−10.0399	+	14.2276i	−0.860918	+	1.22001i
$137$	9.80462	+	5.66070i	0.837665	+	0.483626i	0.856470	−	0.516197i	$-0.172653\pi$
$137$	9.80462	+	5.66070i	0.837665	+	0.483626i	−0.0188049	+	0.999823i	$0.505986\pi$
$138$	8.09428	−	1.90797i	0.689031	−	0.162417i
$139$	−2.29276	−	2.29276i	−0.194469	−	0.194469i	0.603155	−	0.797624i	$-0.293910\pi$
$139$	−2.29276	−	2.29276i	−0.194469	−	0.194469i	−0.797624	+	0.603155i	$0.793910\pi$
$140$		0			0
$141$	2.37854	−	2.37854i	0.200309	−	0.200309i
$142$	−3.44573	−	2.13115i	−0.289159	−	0.178842i
$143$	−2.79761	+	4.84561i	−0.233948	+	0.405210i
$144$	−1.09255	+	8.96833i	−0.0910457	+	0.747361i
$145$	−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
$149$	−0.488473	+	1.82301i	−0.0400172	+	0.149346i	−0.983044	−	0.183371i	$-0.941299\pi$
$149$	−0.488473	+	1.82301i	−0.0400172	+	0.149346i	0.943026	+	0.332718i	$0.107966\pi$
$150$	−0.495828	−	0.526831i	−0.0404842	−	0.0430155i
$151$	−12.3236	−	7.11503i	−1.00288	−	0.579013i	−0.0937803	−	0.995593i	$-0.529895\pi$
$151$	−12.3236	−	7.11503i	−1.00288	−	0.579013i	−0.909099	+	0.416580i	$0.863228\pi$
$152$	−10.4222	−	3.83654i	−0.845352	−	0.311184i
$153$			13.9056i			1.12420i
$154$		0			0
$155$	6.08920	+	6.08920i	0.489097	+	0.489097i
$156$	0.146115	−	2.40768i	0.0116986	−	0.192769i
$157$	5.01921	+	18.7320i	0.400577	+	1.49497i	0.812070	+	0.583560i	$0.198341\pi$
$157$	5.01921	+	18.7320i	0.400577	+	1.49497i	−0.411493	+	0.911413i	$0.634993\pi$
$158$	9.43216	+	0.285943i	0.750383	+	0.0227484i
$159$	−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
$163$	4.10438	+	1.09977i	0.321480	+	0.0861403i	0.415950	−	0.909387i	$-0.363449\pi$
$163$	4.10438	+	1.09977i	0.321480	+	0.0861403i	−0.0944702	+	0.995528i	$0.530116\pi$
$164$	−15.5450	+	7.75967i	−1.21386	+	0.605928i
$165$	6.97313	−	1.86845i	0.542858	−	0.145458i
$166$	−4.68396	−	19.8710i	−0.363546	−	1.54229i
$167$			12.2720i			0.949638i	0.880084	+	0.474819i	$0.157486\pi$
$167$			12.2720i			0.949638i	−0.880084	+	0.474819i	$0.842514\pi$
$168$		0			0
$169$			11.0379i			0.849071i
$170$	17.7880	−	4.19295i	1.36427	−	0.321585i
$171$	−8.56650	+	2.29539i	−0.655097	+	0.175533i
$172$	0.639467	−	1.91418i	0.0487589	−	0.145955i
$173$	14.4207	+	3.86401i	1.09639	+	0.293776i	0.761292	−	0.648409i	$-0.224565\pi$
$173$	14.4207	+	3.86401i	1.09639	+	0.293776i	0.335093	+	0.942185i	$0.391232\pi$
$174$	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
$178$	0.0575718	−	1.89908i	0.00431519	−	0.142342i
$179$	1.76822	+	6.59910i	0.132163	+	0.493240i	0.999993	−	0.00362111i	$-0.00115264\pi$
$179$	1.76822	+	6.59910i	0.132163	+	0.493240i	−0.867830	+	0.496861i	$0.834486\pi$
$180$	7.09855	−	6.28627i	0.529095	−	0.468551i
$181$	−5.61848	−	5.61848i	−0.417618	−	0.417618i	0.466764	−	0.884382i	$-0.345420\pi$
$181$	−5.61848	−	5.61848i	−0.417618	−	0.417618i	−0.884382	+	0.466764i	$0.845420\pi$
$182$		0			0
$183$		−	7.88574i		−	0.582931i
$184$	−17.5369	+	8.09974i	−1.29284	+	0.597121i
$185$	−0.139449	−	0.0805110i	−0.0102525	−	0.00591929i
$186$	−3.63781	+	3.42374i	−0.266737	+	0.251040i
$187$	6.36494	−	23.7543i	0.465450	−	1.73708i
$188$	−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	$0.758970\pi$
$192$	0.550192	+	6.86609i	0.0397067	+	0.495517i
$193$	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	$0.0517403\pi$
$194$	−13.9509	+	22.5564i	−1.00162	+	1.61945i
$195$	−1.79006	+	1.79006i	−0.128189	+	0.128189i
$196$		0			0
$197$	14.8073	+	14.8073i	1.05498	+	1.05498i	0.998398	+	0.0565783i	$0.0180191\pi$
$197$	14.8073	+	14.8073i	1.05498	+	1.05498i	0.0565783	+	0.998398i	$0.481981\pi$
$198$	−2.92737	−	12.4189i	−0.208039	−	0.882573i
$199$	3.76329	+	2.17274i	0.266772	+	0.154021i	0.627420	−	0.778681i	$-0.284111\pi$
$199$	3.76329	+	2.17274i	0.266772	+	0.154021i	−0.360648	+	0.932702i	$0.617444\pi$
$200$	1.37305	+	0.968912i	0.0970891	+	0.0685124i
$201$	−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
$205$	17.6130	+	4.71938i	1.23014	+	0.329616i
$206$	0.384063	−	12.6688i	0.0267590	−	0.882677i
$207$	−7.71288	+	13.3591i	−0.536082	+	0.928522i
$208$	0.785038	+	5.54769i	0.0544326	+	0.384663i
$209$	15.6844			1.08492
$210$		0			0
$211$	−14.5998	+	14.5998i	−1.00509	+	1.00509i	−0.00510394	+	0.999987i	$0.501625\pi$
$211$	−14.5998	+	14.5998i	−1.00509	+	1.00509i	−0.999987	+	0.00510394i	$0.998375\pi$
$212$	9.69922	+	10.9525i	0.666145	+	0.752222i
$213$	−2.38263	+	0.638424i	−0.163255	+	0.0437441i
$214$	12.3127	+	13.0825i	0.841676	+	0.894303i
$215$	−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
$219$	−2.30463	+	8.60098i	−0.155732	+	0.581201i
$220$	−15.0035	+	7.48936i	−1.01154	+	0.504933i
$221$	2.23199	+	8.32990i	0.150140	+	0.560329i
$222$	0.0491349	−	0.0794432i	0.00329772	−	0.00533188i
$223$	−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
$226$	−1.94217	+	3.14017i	−0.129191	+	0.208881i
$227$	−2.95285	−	11.0202i	−0.195988	−	0.731436i	−0.992009	−	0.126167i	$-0.959732\pi$
$227$	−2.95285	−	11.0202i	−0.195988	−	0.731436i	0.796021	−	0.605268i	$-0.206934\pi$
$228$	−6.04974	+	3.01987i	−0.400654	+	0.199996i
$229$	−4.06690	+	15.1779i	−0.268748	+	1.00298i	0.691168	+	0.722694i	$0.257097\pi$
$229$	−4.06690	+	15.1779i	−0.268748	+	1.00298i	−0.959916	+	0.280288i	$0.909570\pi$
$230$	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	−0.328752	−	0.944416i	$-0.606628\pi$
$233$	4.95726	−	2.86207i	0.324761	−	0.187501i	0.653513	+	0.756916i	$0.273295\pi$
$234$	3.06647	+	3.25821i	0.200462	+	0.212996i
$235$	7.92090	−	2.12240i	0.516703	−	0.138450i
$236$	4.36294	+	4.92671i	0.284003	+	0.320701i
$237$	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	$0.344126\pi$
$240$	4.34511	−	5.77754i	0.280476	−	0.372938i
$241$	−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	$0.197659\pi$
$242$	−0.212374	+	7.00540i	−0.0136519	+	0.450324i
$243$	15.5136	+	4.15686i	0.995199	+	0.266663i
$244$	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
$248$	6.69042	−	9.48101i	0.424842	−	0.602045i
$249$	−10.7643	−	6.21478i	−0.682160	−	0.393845i
$250$	−3.80992	−	16.1630i	−0.240960	−	1.02224i
$251$	13.5264	+	13.5264i	0.853777	+	0.853777i	0.990596	−	0.136819i	$-0.0436880\pi$
$251$	13.5264	+	13.5264i	0.853777	+	0.853777i	−0.136819	+	0.990596i	$0.543688\pi$
$252$		0			0
$253$	19.2904	−	19.2904i	1.21278	−	1.21278i
$254$	7.20531	−	11.6498i	0.452101	−	0.730974i
$255$	5.56330	−	9.63591i	0.348387	−	0.603424i
$256$	−4.43933	−	15.3718i	−0.277458	−	0.960738i
$257$	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
$261$	−3.17111	+	11.8347i	−0.196287	+	0.732552i
$262$	−14.2559	+	13.4170i	−0.880732	+	0.828903i
$263$	−23.3754	−	13.4958i	−1.44139	−	0.832188i	−0.443449	−	0.896300i	$-0.646245\pi$
$263$	−23.3754	−	13.4958i	−1.44139	−	0.832188i	−0.997943	+	0.0641116i	$0.979579\pi$
$264$	−4.07891	−	8.83133i	−0.251039	−	0.543531i
$265$		−	15.3541i		−	0.943197i
$266$		0			0
$267$	−0.817939	−	0.817939i	−0.0500570	−	0.0500570i
$268$	2.32110	−	2.05550i	0.141784	−	0.125560i
$269$	−4.71013	−	17.5785i	−0.287182	−	1.07178i	−0.947230	−	0.320554i	$-0.896131\pi$
$269$	−4.71013	−	17.5785i	−0.287182	−	1.07178i	0.660048	−	0.751223i	$-0.270536\pi$
$270$	0.407270	−	13.4343i	0.0247856	−	0.817585i
$271$	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
$275$	−2.29242	−	0.614253i	−0.138238	−	0.0370408i
$276$	−3.72646	+	11.1548i	−0.224306	+	0.671438i
$277$	−15.9023	+	4.26100i	−0.955476	+	0.256019i	−0.702684	−	0.711502i	$-0.748015\pi$
$277$	−15.9023	+	4.26100i	−0.955476	+	0.256019i	−0.252792	+	0.967521i	$0.581349\pi$
$278$	4.46320	−	1.05206i	0.267685	−	0.0630983i
$279$		−	9.26640i		−	0.554765i
$280$		0			0
$281$		−	25.4166i		−	1.51622i	−0.652124	−	0.758112i	$-0.726122\pi$
$281$		−	25.4166i		−	1.51622i	0.652124	−	0.758112i	$-0.273878\pi$
$282$	1.09142	+	4.63018i	0.0649931	+	0.275723i
$283$	6.01181	−	1.61086i	0.357365	−	0.0957556i	−0.0756698	−	0.997133i	$-0.524109\pi$
$283$	6.01181	−	1.61086i	0.357365	−	0.0957556i	0.433035	+	0.901377i	$0.357443\pi$
$284$	5.12652	−	2.55902i	0.304203	−	0.151850i
$285$	6.85452	+	1.83666i	0.406027	+	0.108795i
$286$	−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
$290$	16.0951	+	0.487935i	0.945140	+	0.0286526i
$291$	4.17924	+	15.5971i	0.244991	+	0.914320i
$292$	1.25292	−	20.6456i	0.0733216	−	1.20819i
$293$	−18.5820	−	18.5820i	−1.08557	−	1.08557i	−0.995979	−	0.0895915i	$-0.971444\pi$
$293$	−18.5820	−	18.5820i	−1.08557	−	1.08557i	−0.0895915	−	0.995979i	$-0.528556\pi$
$294$		0			0
$295$		−	6.90666i		−	0.402121i
$296$	−0.0749550	+	0.203620i	−0.00435667	+	0.0118352i
$297$	−15.6630	−	9.04303i	−0.908859	−	0.524730i
$298$	−1.82926	−	1.94364i	−0.105966	−	0.112592i
$299$	−2.47600	+	9.24055i	−0.143191	+	0.534395i
$300$	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
$304$	12.3674	−	9.68138i	0.709321	−	0.555265i
$305$	9.61211	−	16.6487i	0.550388	−	0.953300i
$306$	−16.7250	−	10.3443i	−0.956104	−	0.591342i
$307$	−19.0620	+	19.0620i	−1.08792	+	1.08792i	−0.0921822	+	0.995742i	$0.529384\pi$
$307$	−19.0620	+	19.0620i	−1.08792	+	1.08792i	−0.995742	+	0.0921822i	$0.970616\pi$
$308$		0			0
$309$	−5.45650	−	5.45650i	−0.310409	−	0.310409i
$310$	−11.8535	+	2.79410i	−0.673236	+	0.158694i
$311$	−5.95180	−	3.43627i	−0.337496	−	0.194853i	0.321668	−	0.946852i	$-0.395756\pi$
$311$	−5.95180	−	3.43627i	−0.337496	−	0.194853i	−0.659164	+	0.751999i	$0.729090\pi$
$312$	2.78716	+	1.96680i	0.157792	+	0.111348i
$313$	6.94756	−	4.01118i	0.392699	−	0.226725i	−0.290630	−	0.956836i	$-0.593865\pi$
$313$	6.94756	−	4.01118i	0.392699	−	0.226725i	0.683329	+	0.730110i	$0.260531\pi$
$314$	−26.2637	−	7.89770i	−1.48215	−	0.445693i
$315$		0			0
$316$	−7.36045	+	11.1319i	−0.414058	+	0.626217i
$317$	−2.68620	−	0.719764i	−0.150872	−	0.0404260i	0.182593	−	0.983189i	$-0.441551\pi$
$317$	−2.68620	−	0.719764i	−0.150872	−	0.0404260i	−0.333464	+	0.942763i	$0.608218\pi$
$318$	8.90296	+	0.269899i	0.499253	+	0.0151352i
$319$	10.8341	−	18.7653i	0.606595	−	1.05065i
$320$	−7.20764	+	15.1666i	−0.402919	+	0.847837i
$321$	10.9378			0.610488
$322$		0			0
$323$	17.0935	−	17.0935i	0.951110	−	0.951110i
$324$	−5.74446	−	0.348615i	−0.319137	−	0.0193675i
$325$	0.803883	−	0.215400i	0.0445914	−	0.0119482i
$326$	−4.37598	+	4.11846i	−0.242363	+	0.228100i
$327$	−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
$331$	−2.78135	+	10.3801i	−0.152877	+	0.570544i	0.846401	+	0.532546i	$0.178765\pi$
$331$	−2.78135	+	10.3801i	−0.152877	+	0.570544i	−0.999278	+	0.0379979i	$0.987902\pi$
$332$	27.3843	+	9.14824i	1.50291	+	0.502075i
$333$	0.0448453	+	0.167365i	0.00245751	+	0.00917154i
$334$	−14.7602	−	9.12908i	−0.807645	−	0.499521i
$335$	−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	$0.352545\pi$
$338$	−13.2759	−	8.21105i	−0.722115	−	0.446622i
$339$	0.581810	+	2.17134i	0.0315996	+	0.117931i
$340$	−8.18925	+	24.5137i	−0.444125	+	1.32944i
$341$	−4.24147	+	15.8294i	−0.229688	+	0.857209i
$342$	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
$346$	−15.3749	+	14.4702i	−0.826562	+	0.777921i
$347$	35.0535	−	9.39255i	1.88177	−	0.504219i	0.882334	−	0.470623i	$-0.155971\pi$
$347$	35.0535	−	9.39255i	1.88177	−	0.504219i	0.999436	−	0.0335953i	$-0.0106957\pi$
$348$	−0.565851	+	9.32406i	−0.0303328	+	0.499822i
$349$	−10.3424	+	10.3424i	−0.553614	+	0.553614i	−0.927482	−	0.373868i	$-0.878031\pi$
$349$	−10.3424	+	10.3424i	−0.553614	+	0.553614i	0.373868	+	0.927482i	$0.378031\pi$
$350$		0			0
$351$	6.34223			0.338523
$352$	13.3829	+	18.2067i	0.713311	+	0.970422i
$353$	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	$0.0883703\pi$
$354$	4.00477	+	0.121407i	0.212851	+	0.00645272i
$355$	−5.80848	−	1.55638i	−0.308282	−	0.0826040i
$356$	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	−0.294851	−	0.955543i	$-0.595270\pi$
$359$	7.29942	−	4.21432i	0.385248	−	0.222423i	0.680099	+	0.733120i	$0.261937\pi$
$360$	2.28027	+	13.2141i	0.120181	+	0.696446i
$361$	−3.10240	−	1.79117i	−0.163284	−	0.0942723i
$362$	10.9372	−	2.57811i	0.574847	−	0.135502i
$363$	3.01725	+	3.01725i	0.158365	+	0.158365i
$364$		0			0
$365$	−15.3495	+	15.3495i	−0.803432	+	0.803432i
$366$	9.48462	+	5.86616i	0.495769	+	0.306629i
$367$	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	$0.0885933\pi$
$368$	3.30359	−	27.1180i	0.172212	−	1.41362i
$369$	−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
$373$	5.31370	−	19.8310i	0.275133	−	1.02681i	−0.680620	−	0.732637i	$-0.738289\pi$
$373$	5.31370	−	19.8310i	0.275133	−	1.02681i	0.955752	−	0.294172i	$-0.0950440\pi$
$374$	23.8357	+	25.3261i	1.23252	+	1.30958i
$375$	−8.75565	−	5.05508i	−0.452140	−	0.261043i
$376$	−4.63330	−	10.0317i	−0.238944	−	0.517343i
$377$			7.59840i			0.391337i
$378$		0			0
$379$	−9.02290	−	9.02290i	−0.463475	−	0.463475i	0.436317	−	0.899793i	$-0.356282\pi$
$379$	−9.02290	−	9.02290i	−0.463475	−	0.463475i	−0.899793	+	0.436317i	$0.856282\pi$
$380$	−16.4534	−	0.998511i	−0.844042	−	0.0512225i
$381$	−2.15847	−	8.05554i	−0.110582	−	0.412698i
$382$	−9.04514	−	0.274209i	−0.462789	−	0.0140298i
$383$	−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
$387$	2.20152	+	0.589894i	0.111909	+	0.0299860i
$388$	−16.7518	−	33.5591i	−0.850444	−	1.70371i
$389$	−16.6947	+	4.47334i	−0.846457	+	0.226807i	−0.655880	−	0.754865i	$-0.727702\pi$
$389$	−16.6947	+	4.47334i	−0.846457	+	0.226807i	−0.190577	+	0.981672i	$0.561036\pi$
$390$	−0.821389	−	3.48462i	−0.0415927	−	0.176450i
$391$		−	42.0469i		−	2.12640i
$392$		0			0
$393$			11.9188i			0.601224i
$394$	−28.8246	+	6.79451i	−1.45216	+	0.342302i
$395$	13.5287	−	3.62499i	0.680701	−	0.182393i
$396$	17.1146	+	5.71744i	0.860039	+	0.287312i
$397$	27.3900	+	7.33912i	1.37466	+	0.368340i	0.869179	−	0.494497i	$-0.164648\pi$
$397$	27.3900	+	7.33912i	1.37466	+	0.368340i	0.505483	+	0.862837i	$0.331314\pi$
$398$	−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	$0.643182\pi$
$402$	0.0571982	−	1.88675i	0.00285278	−	0.0941026i
$403$	−1.48735	−	5.55088i	−0.0740904	−	0.276509i
$404$	−5.89886	−	6.66109i	−0.293479	−	0.331401i
$405$	4.27088	+	4.27088i	0.212222	+	0.212222i
$406$		0			0
$407$		−	0.306429i		−	0.0151891i
$408$	−14.0701	−	5.17938i	−0.696574	−	0.256417i
$409$	26.7305	+	15.4328i	1.32174	+	0.763105i	0.984006	−	0.178138i	$-0.0570073\pi$
$409$	26.7305	+	15.4328i	1.32174	+	0.763105i	0.337731	+	0.941243i	$0.390341\pi$
$410$	−18.7784	+	17.6734i	−0.927401	+	0.872826i
$411$	−2.52293	+	9.41570i	−0.124447	+	0.464442i
$412$	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
$416$	−7.25651	−	3.18269i	−0.355780	−	0.156044i
$417$	1.39589	−	2.41776i	0.0683572	−	0.118398i
$418$	−11.6676	+	18.8646i	−0.570679	+	0.922695i
$419$	7.74947	−	7.74947i	0.378586	−	0.378586i	−0.492006	−	0.870592i	$-0.663736\pi$
$419$	7.74947	−	7.74947i	0.378586	−	0.378586i	0.870592	+	0.492006i	$0.163736\pi$
$420$		0			0
$421$	−12.7552	−	12.7552i	−0.621651	−	0.621651i	0.324302	−	0.945953i	$-0.394870\pi$
$421$	−12.7552	−	12.7552i	−0.621651	−	0.621651i	−0.945953	+	0.324302i	$0.894870\pi$
$422$	−6.69929	−	28.4207i	−0.326116	−	1.38350i
$423$	−7.64182	−	4.41201i	−0.371558	−	0.214519i
$424$	−20.3884	+	3.51828i	−0.990148	+	0.170863i
$425$	−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
$429$	−4.65340	−	1.24688i	−0.224668	−	0.0601997i
$430$	0.0907665	−	2.99404i	0.00437715	−	0.144386i
$431$	−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	$0.242934\pi$
$432$	−17.9324	+	2.53756i	−0.862774	+	0.122089i
$433$	−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
$436$	21.6711	−	19.1913i	1.03786	−	0.919097i
$437$	25.9029	−	6.94067i	1.23911	−	0.332017i
$438$	−8.63049	−	9.17012i	−0.412381	−	0.438165i
$439$	−8.04703	+	4.64596i	−0.384064	+	0.221739i	−0.679585	−	0.733597i	$-0.737840\pi$
$439$	−8.04703	+	4.64596i	−0.384064	+	0.221739i	0.295521	+	0.955336i	$0.404507\pi$
$440$	2.15316	−	23.6169i	0.102648	−	1.12589i
$441$		0			0
$442$	−11.6792	−	3.51202i	−0.555523	−	0.167050i
$443$	2.63496	−	9.83379i	0.125191	−	0.467217i	−0.874656	−	0.484744i	$-0.838913\pi$
$443$	2.63496	−	9.83379i	0.125191	−	0.467217i	0.999846	+	0.0175270i	$0.00557931\pi$
$444$	0.0589996	+	0.118195i	0.00280000	+	0.00560927i
$445$	−0.729858	−	2.72387i	−0.0345986	−	0.129124i
$446$	0.202874	−	0.328014i	0.00960635	−	0.0155319i
$447$	−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	$0.471259\pi$
$450$	−0.998281	+	1.61406i	−0.0470594	+	0.0760874i
$451$	8.98110	+	33.5179i	0.422904	+	1.57830i
$452$	−2.33209	−	4.67191i	−0.109692	−	0.219748i
$453$	3.17111	−	11.8348i	0.148992	−	0.556045i
$454$	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	−0.913092	−	0.407753i	$-0.866312\pi$
$457$	−21.7306	+	12.5462i	−1.01651	+	0.586885i	−0.103422	+	0.994638i	$0.532979\pi$
$458$	−15.2299	−	16.1822i	−0.711648	−	0.756145i
$459$	−26.9256	+	7.21470i	−1.25678	+	0.336753i
$460$	−21.4642	+	19.0081i	−1.00077	+	0.886256i
$461$	7.13847	−	7.13847i	0.332472	−	0.332472i	−0.521053	−	0.853524i	$-0.674461\pi$
$461$	7.13847	−	7.13847i	0.332472	−	0.332472i	0.853524	+	0.521053i	$0.174461\pi$
$462$		0			0
$463$	3.67655			0.170864			0.0854320	−	0.996344i	$-0.472773\pi$
$463$	3.67655			0.170864			0.0854320	+	0.996344i	$0.472773\pi$
$464$	−3.04017	−	21.4842i	−0.141136	−	0.997379i
$465$	−3.70727	+	6.42118i	−0.171921	+	0.297775i
$466$	−0.245298	+	8.09145i	−0.0113632	+	0.374829i
$467$	9.39910	+	2.51848i	0.434938	+	0.116541i	0.469643	−	0.882856i	$-0.344383\pi$
$467$	9.39910	+	2.51848i	0.434938	+	0.116541i	−0.0347050	+	0.999398i	$0.511049\pi$
$468$	−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
$472$	−9.17119	+	1.58261i	−0.422138	+	0.0728455i
$473$	−3.49074	−	2.01538i	−0.160505	−	0.0926673i
$474$	1.86411	+	7.90820i	0.0856215	+	0.363236i
$475$	−1.64963	−	1.64963i	−0.0756900	−	0.0756900i
$476$		0			0
$477$	−11.6828	+	11.6828i	−0.534917	+	0.534917i
$478$	−10.8184	+	17.4917i	−0.494824	+	0.800050i
$479$	−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	$0.286823\pi$
$480$	3.71666	+	9.52398i	0.169642	+	0.434708i
$481$	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
$485$	−10.1883	+	38.0234i	−0.462629	+	1.72655i
$486$	−16.5402	+	15.5668i	−0.750278	+	0.706126i
$487$	11.3224	+	6.53697i	0.513065	+	0.296218i	0.734093	−	0.679049i	$-0.237608\pi$
$487$	11.3224	+	6.53697i	0.513065	+	0.296218i	−0.221027	+	0.975268i	$0.570941\pi$
$488$	−24.3099	−	8.94878i	−1.10046	−	0.405092i
$489$			3.65859i			0.165447i
$490$		0			0
$491$	10.1749	+	10.1749i	0.459188	+	0.459188i	0.898389	−	0.439201i	$-0.144738\pi$
$491$	10.1749	+	10.1749i	0.459188	+	0.459188i	−0.439201	+	0.898389i	$0.644738\pi$
$492$	−9.91767	−	11.1992i	−0.447123	−	0.504898i
$493$	−8.64368	−	32.2586i	−0.389292	−	1.45286i
$494$	0.235695	−	7.77468i	0.0106044	−	0.349799i
$495$	−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
$499$	40.2131	+	10.7751i	1.80019	+	0.482358i	0.994007	−	0.109313i	$-0.0348651\pi$
$499$	40.2131	+	10.7751i	1.80019	+	0.482358i	0.806179	+	0.591672i	$0.201532\pi$
$500$	22.2743	+	7.44115i	0.996137	+	0.332778i
$501$	−10.2063	+	2.73477i	−0.455985	+	0.122181i
$502$	−26.3311	+	6.20673i	−1.17521	+	0.277020i
$503$		−	35.0535i		−	1.56296i	−0.623930	−	0.781480i	$-0.714465\pi$
$503$		−	35.0535i		−	1.56296i	0.623930	−	0.781480i	$-0.285535\pi$
$504$		0			0
$505$			9.33805i			0.415538i
$506$	8.85162	+	37.5516i	0.393503	+	1.66937i
$507$	−9.17995	+	2.45976i	−0.407696	+	0.109242i
$508$	8.65190	+	17.3325i	0.383866	+	0.769003i
$509$	2.87283	+	0.769772i	0.127336	+	0.0341195i	0.321924	−	0.946765i	$-0.395670\pi$
$509$	2.87283	+	0.769772i	0.127336	+	0.0341195i	−0.194588	+	0.980885i	$0.562337\pi$
$510$	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
$514$	−4.30892	−	0.130628i	−0.190058	−	0.00576175i
$515$	−4.86891	−	18.1710i	−0.214550	−	0.800710i
$516$	1.73448	+	0.105260i	0.0763560	+	0.00463383i
$517$	11.0347	+	11.0347i	0.485305	+	0.485305i
$518$		0			0
$519$			12.8544i			0.564245i
$520$	3.48697	+	7.54970i	0.152914	+	0.331076i
$521$	−21.8703	−	12.6268i	−0.958155	−	0.553191i	−0.0625503	−	0.998042i	$-0.519923\pi$
$521$	−21.8703	−	12.6268i	−0.958155	−	0.553191i	−0.895605	+	0.444851i	$0.853257\pi$
$522$	−11.8753	−	12.6179i	−0.519769	−	0.552269i
$523$	0.179826	−	0.671120i	0.00786324	−	0.0293460i	−0.961883	−	0.273462i	$-0.911831\pi$
$523$	0.179826	−	0.671120i	0.00786324	−	0.0293460i	0.969746	+	0.244116i	$0.0784978\pi$
$524$	−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
$528$	13.6562	+	1.66364i	0.594310	+	0.0724006i
$529$	11.8218	−	20.4760i	0.513991	−	0.890259i
$530$	18.4673	+	11.4218i	0.802167	+	0.496133i
$531$	−5.25519	+	5.25519i	−0.228056	+	0.228056i
$532$		0			0
$533$	−8.60431	−	8.60431i	−0.372694	−	0.372694i
$534$	1.59224	−	0.375321i	0.0689030	−	0.0162417i
$535$	23.0923	+	13.3323i	0.998366	+	0.576407i
$536$	0.745609	+	4.32079i	0.0322054	+	0.186630i
$537$	−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
$541$	11.2036	+	3.00200i	0.481681	+	0.129066i	0.491485	−	0.870886i	$-0.336454\pi$
$541$	11.2036	+	3.00200i	0.481681	+	0.129066i	−0.00980419	+	0.999952i	$0.503121\pi$
$542$	−44.2561	−	1.34165i	−1.90096	−	0.0576289i
$543$	3.42068	−	5.92480i	0.146796	−	0.254257i
$544$	34.4277	+	5.25719i	1.47607	+	0.225400i
$545$	−30.3804			−1.30135
$546$		0			0
$547$	8.29783	−	8.29783i	0.354790	−	0.354790i	−0.507098	−	0.861888i	$-0.669282\pi$
$547$	8.29783	−	8.29783i	0.354790	−	0.354790i	0.861888	+	0.507098i	$0.169282\pi$
$548$	1.37160	−	22.6012i	0.0585920	−	0.965476i
$549$	−19.9815	+	5.35402i	−0.852789	+	0.228504i
$550$	2.44412	−	2.30029i	0.104217	−	0.0980845i
$551$	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
$555$	0.0358832	−	0.133918i	0.00152316	−	0.00568449i
$556$	−2.05478	+	6.15076i	−0.0871419	+	0.260850i
$557$	−5.22346	−	19.4942i	−0.221325	−	0.825997i	−0.983844	−	0.179030i	$-0.942704\pi$
$557$	−5.22346	−	19.4942i	−0.221325	−	0.825997i	0.762518	−	0.646967i	$-0.223963\pi$
$558$	11.1452	+	6.89322i	0.471814	+	0.291813i
$559$	1.41347			0.0597832
$560$		0			0
$561$	21.1742			0.893975
$562$	30.5699	+	18.9072i	1.28951	+	0.797553i
$563$	−6.62929	−	24.7408i	−0.279391	−	1.04270i	−0.952841	−	0.303469i	$-0.901855\pi$
$563$	−6.62929	−	24.7408i	−0.279391	−	1.04270i	0.673450	−	0.739233i	$-0.264812\pi$
$564$	−6.38087	−	2.13165i	−0.268683	−	0.0897586i
$565$	−1.41836	+	5.29340i	−0.0596709	+	0.222695i
$566$	−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	−0.960558	−	0.278080i	$-0.910302\pi$
$569$	−28.6248	+	16.5265i	−1.20001	+	0.692828i	−0.239455	+	0.970908i	$0.576969\pi$
$570$	−7.30810	+	6.87803i	−0.306102	+	0.288089i
$571$	−14.4266	+	3.86560i	−0.603735	+	0.161770i	−0.547723	−	0.836660i	$-0.684505\pi$
$571$	−14.4266	+	3.86560i	−0.603735	+	0.161770i	−0.0560119	+	0.998430i	$0.517838\pi$
$572$	11.1699	+	0.677870i	0.467037	+	0.0283431i
$573$	−3.89577	+	3.89577i	−0.162748	+	0.162748i
$574$		0			0
$575$	−4.05777			−0.169221
$576$	17.0243	−	6.05585i	0.709344	−	0.252327i
$577$	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	$0.157832\pi$
$578$	29.5480	+	0.895768i	1.22904	+	0.0372590i
$579$	8.16308	+	2.18729i	0.339246	+	0.0909007i
$580$	−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
$584$	23.8995	+	16.8651i	0.988970	+	0.697882i
$585$	5.75114	+	3.32042i	0.237781	+	0.137283i
$586$	36.1726	−	8.52656i	1.49428	−	0.352229i
$587$	19.7266	+	19.7266i	0.814203	+	0.814203i	0.985261	−	0.171058i	$-0.0547186\pi$
$587$	19.7266	+	19.7266i	0.814203	+	0.814203i	−0.171058	+	0.985261i	$0.554719\pi$
$588$		0			0
$589$	−11.3908	+	11.3908i	−0.469350	+	0.469350i
$590$	8.30702	+	5.13782i	0.341995	+	0.211521i
$591$	−9.01509	+	15.6146i	−0.370831	+	0.642298i
$592$	−0.189147	−	0.241624i	−0.00777387	−	0.00993070i
$593$	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
$597$	−0.968372	+	3.61401i	−0.0396328	+	0.147912i
$598$	−9.27224	−	9.85201i	−0.379170	−	0.402879i
$599$	24.0798	+	13.9025i	0.983873	+	0.568039i	0.903437	−	0.428720i	$-0.141035\pi$
$599$	24.0798	+	13.9025i	0.983873	+	0.568039i	0.0804358	+	0.996760i	$0.474369\pi$
$600$	−0.499840	+	1.35785i	−0.0204059	+	0.0554338i
$601$			13.6372i			0.556271i	0.960542	+	0.278136i	$0.0897165\pi$
$601$			13.6372i			0.556271i	−0.960542	+	0.278136i	$0.910284\pi$
$602$		0			0
$603$	2.47586	+	2.47586i	0.100825	+	0.100825i
$604$	−1.72399	+	28.4078i	−0.0701482	+	1.15590i
$605$	2.69233	+	10.0479i	0.109459	+	0.408506i
$606$	−5.41459	−	0.164147i	−0.219953	−	0.00666802i
$607$	−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
$611$	−5.28588	−	1.41635i	−0.213844	−	0.0572993i
$612$	24.8832	−	12.4211i	1.00585	−	0.502091i
$613$	27.9879	−	7.49934i	1.13042	−	0.302895i	0.355327	−	0.934742i	$-0.384369\pi$
$613$	27.9879	−	7.49934i	1.13042	−	0.302895i	0.775094	+	0.631846i	$0.217703\pi$
$614$	−8.74681	−	37.1070i	−0.352993	−	1.49752i
$615$			15.6999i			0.633082i
$616$		0			0
$617$			5.44754i			0.219310i	0.993970	+	0.109655i	$0.0349745\pi$
$617$			5.44754i			0.219310i	−0.993970	+	0.109655i	$0.965025\pi$
$618$	10.6219	−	2.50378i	0.427275	−	0.100717i
$619$	5.86850	−	1.57246i	0.235875	−	0.0632025i	−0.138945	−	0.990300i	$-0.544371\pi$
$619$	5.86850	−	1.57246i	0.235875	−	0.0632025i	0.374820	+	0.927098i	$0.377705\pi$
$620$	5.45716	−	16.3354i	0.219165	−	0.656047i
$621$	−29.8692	−	8.00343i	−1.19861	−	0.321167i
$622$	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
$626$	−0.343783	+	11.3401i	−0.0137403	+	0.453242i
$627$	3.49522	+	13.0443i	0.139586	+	0.520941i
$628$	29.0364	−	25.7138i	1.15868	−	1.02609i
$629$	−0.333959	−	0.333959i	−0.0133158	−	0.0133158i
$630$		0			0
$631$		−	31.5326i		−	1.25529i	−0.778499	−	0.627646i	$-0.784018\pi$
$631$		−	31.5326i		−	1.25529i	0.778499	−	0.627646i	$-0.215982\pi$
$632$	−7.91354	−	17.1338i	−0.314784	−	0.681544i
$633$	−15.3958	−	8.88875i	−0.611927	−	0.353296i
$634$	2.86394	−	2.69541i	0.113742	−	0.107048i
$635$	5.26203	−	19.6381i	0.208817	−	0.779316i
$636$	−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
$640$	−12.8800	−	19.9514i	−0.509125	−	0.788646i
$641$	−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	$0.985963\pi$
$642$	−8.13656	+	13.1555i	−0.321125	+	0.519206i
$643$	8.13921	−	8.13921i	0.320979	−	0.320979i	−0.528164	−	0.849143i	$-0.677119\pi$
$643$	8.13921	−	8.13921i	0.320979	−	0.320979i	0.849143	+	0.528164i	$0.177119\pi$
$644$		0			0
$645$	−1.28955	−	1.28955i	−0.0507758	−	0.0507758i
$646$	7.84358	+	33.2751i	0.308601	+	1.30919i
$647$	6.70236	+	3.86961i	0.263497	+	0.152130i	0.625929	−	0.779880i	$-0.284720\pi$
$647$	6.70236	+	3.86961i	0.263497	+	0.152130i	−0.362432	+	0.932010i	$0.618053\pi$
$648$	4.69257	−	6.64985i	0.184342	−	0.261231i
$649$	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
$653$	−9.73388	−	2.60819i	−0.380916	−	0.102066i	0.0632798	−	0.997996i	$-0.479844\pi$
$653$	−9.73388	−	2.60819i	−0.380916	−	0.102066i	−0.444196	+	0.895930i	$0.646511\pi$
$654$	0.534035	−	17.6158i	0.0208824	−	0.688832i
$655$	−14.5281	+	25.1634i	−0.567660	+	0.983216i
$656$	27.7710	+	20.8857i	1.08428	+	0.815451i
$657$	23.3585			0.911304
$658$		0			0
$659$	−4.61254	+	4.61254i	−0.179679	+	0.179679i	−0.791216	−	0.611537i	$-0.790552\pi$
$659$	−4.61254	+	4.61254i	−0.179679	+	0.179679i	0.611537	+	0.791216i	$0.290552\pi$
$660$	−9.57219	−	10.8091i	−0.372597	−	0.420742i
$661$	−18.8040	+	5.03853i	−0.731393	+	0.195976i	−0.605249	−	0.796036i	$-0.706927\pi$
$661$	−18.8040	+	5.03853i	−0.731393	+	0.195976i	−0.126143	+	0.992012i	$0.540260\pi$
$662$	−10.4157	−	11.0670i	−0.404819	−	0.430131i
$663$	−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
$667$	9.58863	−	35.7853i	0.371273	−	1.38561i
$668$	21.9601	−	10.9619i	0.849662	−	0.424129i
$669$	−0.0607743	−	0.226813i	−0.00234967	−	0.00876910i
$670$	2.42056	−	3.91366i	0.0935145	−	0.151198i
$671$	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	$0.684957\pi$
$674$	−12.2045	+	19.7327i	−0.470099	+	0.760075i
$675$	0.696260	+	2.59848i	0.0267991	+	0.100015i
$676$	19.7518	−	9.85955i	0.759683	−	0.379214i
$677$	−2.67980	+	10.0011i	−0.102993	+	0.384375i	−0.998110	−	0.0614567i	$-0.980425\pi$
$677$	−2.67980	+	10.0011i	−0.102993	+	0.384375i	0.895117	+	0.445832i	$0.147092\pi$
$678$	−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
$682$	−15.8837	−	16.8768i	−0.608217	−	0.646247i
$683$	9.01220	−	2.41481i	0.344842	−	0.0924002i	−0.0822411	−	0.996612i	$-0.526208\pi$
$683$	9.01220	−	2.41481i	0.344842	−	0.0924002i	0.427083	+	0.904212i	$0.359541\pi$
$684$	11.7594	+	13.2790i	0.449634	+	0.507733i
$685$	−16.8035	+	16.8035i	−0.642029	+	0.642029i
$686$		0			0
$687$	−13.5293			−0.516176
$688$	−3.99652	+	0.565536i	−0.152366	+	0.0215609i
$689$	−5.12316	+	8.87357i	−0.195177	+	0.338056i
$690$	−0.528936	+	17.4476i	−0.0201363	+	0.664219i
$691$	−24.9437	−	6.68364i	−0.948902	−	0.254258i	−0.249006	−	0.968502i	$-0.580104\pi$
$691$	−24.9437	−	6.68364i	−0.948902	−	0.254258i	−0.699896	+	0.714244i	$0.746770\pi$
$692$	−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
$696$	−10.7936	−	7.61669i	−0.409132	−	0.288710i
$697$	46.3172	+	26.7412i	1.75439	+	1.01290i
$698$	−4.74571	−	20.1330i	−0.179628	−	0.762044i
$699$	3.48502	+	3.48502i	0.131815	+	0.131815i
$700$		0			0
$701$	3.43743	−	3.43743i	0.129830	−	0.129830i	−0.639206	−	0.769036i	$-0.720737\pi$
$701$	3.43743	−	3.43743i	0.129830	−	0.129830i	0.769036	+	0.639206i	$0.220737\pi$
$702$	−4.71795	+	7.62815i	−0.178067	+	0.287906i
$703$	0.150608	−	0.260861i	0.00568031	−	0.00983858i
$704$	−31.8537	+	2.55250i	−1.20053	+	0.0962008i
$705$	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
$709$	7.74444	−	28.9026i	0.290849	−	1.08546i	−0.653610	−	0.756831i	$-0.726746\pi$
$709$	7.74444	−	28.9026i	0.290849	−	1.08546i	0.944459	−	0.328630i	$-0.106587\pi$
$710$	6.19284	−	5.82841i	0.232413	−	0.218736i
$711$	−13.0520	−	7.53558i	−0.489488	−	0.282606i
$712$	−3.44972	+	1.59332i	−0.129284	+	0.0597120i
$713$			28.0192i			1.04933i
$714$		0			0
$715$	−8.30458	−	8.30458i	−0.310574	−	0.310574i
$716$	10.2293	−	9.05874i	0.382286	−	0.338541i
$717$	3.24085	+	12.0950i	0.121032	+	0.451697i
$718$	−0.361194	+	11.9144i	−0.0134796	+	0.444642i
$719$	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
$723$	−2.51019	−	0.672604i	−0.0933551	−	0.0250144i
$724$	−5.03530	+	15.0726i	−0.187135	+	0.560170i
$725$	−3.11314	+	0.834164i	−0.115619	+	0.0309801i
$726$	−5.87353	+	1.38450i	−0.217987	+	0.0513837i
$727$			4.59798i			0.170530i	0.996358	+	0.0852648i	$0.0271736\pi$
$727$			4.59798i			0.170530i	−0.996358	+	0.0852648i	$0.972826\pi$
$728$		0			0
$729$			5.19606i			0.192447i
$730$	−7.04332	−	29.8802i	−0.260685	−	1.10592i
$731$	−6.00080	+	1.60791i	−0.221948	+	0.0594707i
$732$	−14.1111	+	7.04389i	−0.521562	+	0.260350i
$733$	−10.2337	−	2.74210i	−0.377989	−	0.101282i	0.0648221	−	0.997897i	$-0.479352\pi$
$733$	−10.2337	−	2.74210i	−0.377989	−	0.101282i	−0.442811	+	0.896615i	$0.646019\pi$
$734$	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
$738$	27.7357	+	0.840828i	1.02097	+	0.0309513i
$739$	12.2915	+	45.8723i	0.452149	+	1.68744i	0.696338	+	0.717714i	$0.254811\pi$
$739$	12.2915	+	45.8723i	0.452149	+	1.68744i	−0.244190	+	0.969728i	$0.578522\pi$
$740$	−0.0195080	+	0.321453i	−0.000717130	+	0.0118168i
$741$	−3.34858	−	3.34858i	−0.123013	−	0.123013i
$742$		0			0
$743$			17.5619i			0.644285i	0.946691	+	0.322142i	$0.104403\pi$
$743$			17.5619i			0.644285i	−0.946691	+	0.322142i	$0.895597\pi$
$744$	9.37604	+	3.45144i	0.343742	+	0.126536i
$745$	−3.43076	−	1.98075i	−0.125693	−	0.0725690i
$746$	19.8990	+	21.1432i	0.728554	+	0.774109i
$747$	−8.43904	+	31.4949i	−0.308768	+	1.15234i
$748$	−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	$0.726529\pi$
$752$	15.5123	+	1.88976i	0.565676	+	0.0689123i
$753$	−8.23522	+	14.2638i	−0.300108	+	0.519803i
$754$	−9.13902	−	5.65240i	−0.332823	−	0.205848i
$755$	21.1206	−	21.1206i	0.768658	−	0.768658i
$756$		0			0
$757$	18.4795	+	18.4795i	0.671647	+	0.671647i	0.958096	−	0.286448i	$-0.0924747\pi$
$757$	18.4795	+	18.4795i	0.671647	+	0.671647i	−0.286448	+	0.958096i	$0.592475\pi$
$758$	17.5644	−	4.14027i	0.637969	−	0.150381i
$759$	20.3421	+	11.7445i	0.738371	+	0.426299i
$760$	13.4406	−	19.0467i	0.487540	−	0.690895i
$761$	−5.61500	+	3.24182i	−0.203543	+	0.117516i	−0.598307	−	0.801267i	$-0.704160\pi$
$761$	−5.61500	+	3.24182i	−0.203543	+	0.117516i	0.394764	+	0.918783i	$0.370826\pi$
$762$	11.2945	+	3.39635i	0.409157	+	0.123037i
$763$		0			0
$764$	7.05843	−	10.6751i	0.255365	−	0.386212i
$765$	−28.1934	−	7.55440i	−1.01933	−	0.273130i
$766$	1.59110	+	0.0482353i	0.0574888	+	0.00174281i
$767$	−2.30452	+	3.99155i	−0.0832114	+	0.144126i
$768$	11.7950	−	7.11762i	0.425617	−	0.256835i
$769$	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
$772$	−19.5944	−	1.18913i	−0.705219	−	0.0427977i
$773$	−2.65554	+	0.711549i	−0.0955130	+	0.0255926i	−0.306259	−	0.951948i	$-0.599077\pi$
$773$	−2.65554	+	0.711549i	−0.0955130	+	0.0255926i	0.210746	+	0.977541i	$0.432411\pi$
$774$	−2.34719	+	2.20907i	−0.0843681	+	0.0794033i
$775$	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
$779$	−8.82834	+	32.9478i	−0.316308	+	1.18048i
$780$	4.80217	+	1.60425i	0.171945	+	0.0574415i
$781$	−2.96183	−	11.0537i	−0.105983	−	0.395532i
$782$	50.5722	+	31.2784i	1.80846	+	1.11851i
$783$	−24.5611			−0.877743
$784$		0			0
$785$	−40.7056			−1.45285
$786$	−14.3354	−	8.86633i	−0.511327	−	0.316251i
$787$	12.7513	+	47.5886i	0.454536	+	1.69635i	0.689449	+	0.724334i	$0.257853\pi$
$787$	12.7513	+	47.5886i	0.454536	+	1.69635i	−0.234913	+	0.972016i	$0.575481\pi$
$788$	13.2703	−	39.7234i	0.472736	−	1.41509i
$789$	6.01499	−	22.4482i	0.214139	−	0.799178i
$790$	−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
$794$	−29.2024	+	27.4839i	−1.03635	+	0.975367i
$795$	12.7696	−	3.42161i	0.452892	−	0.121352i
$796$	0.526460	−	8.67498i	0.0186599	−	0.307477i
$797$	−22.5200	+	22.5200i	−0.797699	+	0.797699i	−0.982732	−	0.185033i	$-0.940761\pi$
$797$	−22.5200	+	22.5200i	−0.797699	+	0.797699i	0.185033	+	0.982732i	$0.440761\pi$
$798$		0			0
$799$	24.0521			0.850903
$800$	0.507349	−	3.32247i	0.0179375	−	0.117467i
$801$	−1.51722	+	2.62789i	−0.0536082	+	0.0928521i
$802$	−31.8436	−	0.965361i	−1.12444	−	0.0340881i
$803$	−39.9024	−	10.6918i	−1.40812	−	0.377306i
$804$	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
$808$	12.3998	−	2.13975i	0.436223	−	0.0752760i
$809$	−41.1059	−	23.7325i	−1.44521	−	0.834391i	−0.447017	−	0.894525i	$-0.647514\pi$
$809$	−41.1059	−	23.7325i	−1.44521	−	0.834391i	−0.998190	+	0.0601343i	$0.980847\pi$
$810$	−8.31392	+	1.95975i	−0.292121	+	0.0688585i
$811$	−39.0893	−	39.0893i	−1.37261	−	1.37261i	−0.856554	−	0.516058i	$-0.827399\pi$
$811$	−39.0893	−	39.0893i	−1.37261	−	1.37261i	−0.516058	−	0.856554i	$-0.672601\pi$
$812$		0			0
$813$	−19.0613	+	19.0613i	−0.668507	+	0.668507i
$814$	0.368559	+	0.227951i	0.0129180	+	0.00798967i
$815$	−4.45953	+	7.72414i	−0.156211	+	0.270565i
$816$	16.6962	−	13.0700i	0.584484	−	0.457541i
$817$	−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
$821$	3.25883	−	12.1621i	0.113734	−	0.424461i	−0.885455	−	0.464725i	$-0.846153\pi$
$821$	3.25883	−	12.1621i	0.113734	−	0.424461i	0.999189	+	0.0402639i	$0.0128199\pi$
$822$	−9.44800	−	10.0388i	−0.329537	−	0.350142i
$823$	4.29959	+	2.48237i	0.149874	+	0.0865300i	0.573062	−	0.819512i	$-0.305755\pi$
$823$	4.29959	+	2.48237i	0.149874	+	0.0865300i	−0.423187	+	0.906042i	$0.639089\pi$
$824$	−23.0132	+	10.6291i	−0.801703	+	0.370281i
$825$		−	2.04343i		−	0.0711432i
$826$		0			0
$827$	11.3168	+	11.3168i	0.393524	+	0.393524i	0.875942	−	0.482417i	$-0.160241\pi$
$827$	11.3168	+	11.3168i	0.393524	+	0.393524i	−0.482417	+	0.875942i	$0.660241\pi$
$828$	30.7949	+	1.86885i	1.07020	+	0.0649471i
$829$	−9.15557	−	34.1690i	−0.317986	−	1.18674i	−0.921177	−	0.389143i	$-0.872771\pi$
$829$	−9.15557	−	34.1690i	−0.317986	−	1.18674i	0.603191	−	0.797597i	$-0.293896\pi$
$830$	42.8329	+	1.29851i	1.48675	+	0.0450719i
$831$	−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
$835$	−24.8814	−	6.66696i	−0.861057	−	0.230719i
$836$	−14.0100	−	28.0665i	−0.484547	−	0.970699i
$837$	17.9427	−	4.80774i	0.620191	−	0.166180i
$838$	3.55594	+	15.0855i	0.122838	+	0.521120i
$839$			47.7342i			1.64797i	0.566614	+	0.823983i	$0.308253\pi$
$839$			47.7342i			1.64797i	−0.566614	+	0.823983i	$0.691747\pi$
$840$		0			0
$841$		−	0.425820i		−	0.0146834i
$842$	24.8299	−	5.85288i	0.855696	−	0.201704i
$843$	21.1383	−	5.66398i	0.728041	−	0.195078i
$844$	39.1667	+	13.0844i	1.34817	+	0.450382i
$845$	−22.3793	−	5.99651i	−0.769871	−	0.206286i
$846$	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
$850$	0.156752	−	5.17064i	0.00537654	−	0.177352i
$851$	−0.135601	−	0.506069i	−0.00464834	−	0.0173478i
$852$	3.27069	+	3.69332i	0.112052	+	0.126531i
$853$	−3.65043	−	3.65043i	−0.124988	−	0.124988i	0.641846	−	0.766834i	$-0.278169\pi$
$853$	−3.65043	−	3.65043i	−0.124988	−	0.124988i	−0.766834	+	0.641846i	$0.778169\pi$
$854$		0			0
$855$		−	18.6155i		−	0.636637i
$856$	12.4123	−	33.7187i	0.424243	−	1.15248i
$857$	−19.0400	−	10.9927i	−0.650394	−	0.375505i	0.138213	−	0.990402i	$-0.455864\pi$
$857$	−19.0400	−	10.9927i	−0.650394	−	0.375505i	−0.788607	+	0.614898i	$0.789197\pi$
$858$	4.96132	−	4.66936i	0.169377	−	0.159409i
$859$	3.20783	−	11.9718i	0.109450	−	0.408472i	−0.889362	−	0.457203i	$-0.848851\pi$
$859$	3.20783	−	11.9718i	0.109450	−	0.408472i	0.998812	+	0.0487316i	$0.0155179\pi$
$860$	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	$0.935100\pi$
$864$	10.2877	−	23.4560i	0.349996	−	0.797989i
$865$	−15.6685	+	27.1387i	−0.532745	+	0.922742i
$866$	11.0952	−	17.9391i	0.377029	−	0.609595i
$867$	12.7264	−	12.7264i	0.432213	−	0.432213i
$868$		0			0
$869$	18.8469	+	18.8469i	0.639338	+	0.639338i
$870$	3.18094	+	13.4946i	0.107844	+	0.457511i
$871$	1.88052	+	1.08572i	0.0637191	+	0.0367882i
$872$	6.96143	+	40.3414i	0.235744	+	1.36613i
$873$	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
$877$	−18.7288	−	5.01836i	−0.632426	−	0.169458i	−0.0716557	−	0.997429i	$-0.522828\pi$
$877$	−18.7288	−	5.01836i	−0.632426	−	0.169458i	−0.560770	+	0.827971i	$0.689495\pi$
$878$	0.398188	−	13.1347i	0.0134382	−	0.443275i
$879$	11.3132	−	19.5951i	0.381585	−	0.660925i
$880$	26.8036	+	20.1582i	0.903550	+	0.679532i
$881$	−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	−0.181589	+	0.983374i	$0.558124\pi$
$883$	−34.6173	+	34.6173i	−1.16496	+	1.16496i	−0.983374	+	0.181589i	$0.941876\pi$
$884$	12.9122	−	11.4346i	0.434284	−	0.384589i
$885$	5.74408	−	1.53912i	0.193085	−	0.0517370i
$886$	9.86752	+	10.4845i	0.331506	+	0.352234i
$887$	3.36305	−	1.94166i	0.112920	−	0.0651945i	−0.442476	−	0.896780i	$-0.645900\pi$
$887$	3.36305	−	1.94166i	0.112920	−	0.0651945i	0.555396	+	0.831586i	$0.312567\pi$
$888$	−0.186049	−	0.0169622i	−0.00624339	−	0.000569213i
$889$		0			0
$890$	3.81908	+	1.14843i	0.128016	+	0.0384954i
$891$	−2.97491	+	11.1025i	−0.0996632	+	0.371948i
$892$	0.243604	+	0.488015i	0.00815647	+	0.0163400i
$893$	3.97028	+	14.8173i	0.132860	+	0.495841i
$894$	1.20883	−	1.95448i	0.0404292	−	0.0653675i
$895$	−14.3402			−0.479341
$896$		0			0
$897$	−8.23688			−0.275022
$898$	−2.84268	+	4.59616i	−0.0948616	+	0.153376i
$899$	5.75998	+	21.4965i	0.192106	+	0.716949i
$900$	−1.19870	−	2.40138i	−0.0399568	−	0.0800459i
$901$	11.6559	−	43.5002i	0.388313	−	1.44920i
$902$	−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
$906$	11.8754	+	12.6179i	0.394532	+	0.419201i
$907$	−38.6836	+	10.3652i	−1.28447	+	0.344172i	−0.835557	−	0.549404i	$-0.814855\pi$
$907$	−38.6836	+	10.3652i	−1.28447	+	0.344172i	−0.448911	+	0.893577i	$0.648188\pi$
$908$	−17.0824	+	15.1277i	−0.566900	+	0.502030i
$909$	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	$0.667851\pi$
$912$	10.8078	+	8.12821i	0.357881	+	0.269152i
$913$	28.8321	−	49.9387i	0.954203	−	1.65273i
$914$	1.07529	−	35.4696i	0.0355673	−	1.17323i
$915$	15.9883	+	4.28404i	0.528556	+	0.141626i
$916$	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	−0.330497	−	0.943807i	$-0.607216\pi$
$919$	9.74979	−	5.62904i	0.321616	−	0.185685i	0.652113	+	0.758122i	$0.273883\pi$
$920$	−6.89497	−	39.9562i	−0.227320	−	1.31732i
$921$	−20.1012	−	11.6054i	−0.662358	−	0.382413i
$922$	3.27557	+	13.8961i	0.107875	+	0.457644i
$923$	2.83757	+	2.83757i	0.0933998	+	0.0933998i
$924$		0			0
$925$	−0.0322290	+	0.0322290i	−0.00105968	+	0.00105968i
$926$	−2.73497	+	4.42200i	−0.0898766	+	0.145316i
$927$	−10.1214	+	17.5308i	−0.332430	+	0.575786i
$928$	28.1018	+	12.3254i	0.922487	+	0.404601i
$929$	−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
$933$	1.53152	−	5.71572i	0.0501398	−	0.187124i
$934$	−10.0210	+	9.43134i	−0.327899	+	0.308603i
$935$	44.7037	+	25.8097i	1.46197	+	0.844068i
$936$	3.09128	−	8.39767i	0.101042	−	0.274486i
$937$		−	23.0570i		−	0.753238i	−0.926368	−	0.376619i	$-0.877087\pi$
$937$		−	23.0570i		−	0.753238i	0.926368	−	0.376619i	$-0.122913\pi$
$938$		0			0
$939$	4.88423	+	4.88423i	0.159391	+	0.159391i
$940$	−10.8732	−	12.2782i	−0.354645	−	0.400471i
$941$	8.27344	+	30.8769i	0.269706	+	1.00656i	0.959306	+	0.282367i	$0.0911197\pi$
$941$	8.27344	+	30.8769i	0.269706	+	1.00656i	−0.689600	+	0.724191i	$0.742214\pi$
$942$	0.715536	−	23.6028i	0.0233134	−	0.769022i
$943$	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
$947$	10.3884	+	2.78357i	0.337578	+	0.0904539i	0.423626	−	0.905837i	$-0.360757\pi$
$947$	10.3884	+	2.78357i	0.337578	+	0.0904539i	−0.0860477	+	0.996291i	$0.527424\pi$
$948$	−10.8983	−	3.64079i	−0.353962	−	0.118247i
$949$	13.9925	−	3.74929i	0.454217	−	0.121707i
$950$	3.21124	−	0.756950i	0.104186	−	0.0245587i
$951$		−	2.39443i		−	0.0776449i
$952$		0			0
$953$		−	2.60332i		−	0.0843297i	−0.999111	−	0.0421649i	$-0.986575\pi$
$953$		−	2.60332i		−	0.0843297i	0.999111	−	0.0421649i	$-0.0134255\pi$
$954$	−5.36077	−	22.7422i	−0.173561	−	0.736307i
$955$	−12.9735	+	3.47625i	−0.419814	+	0.112489i
$956$	−12.9904	−	26.0239i	−0.420141	−	0.841673i
$957$	18.0209	+	4.82869i	0.582534	+	0.156089i
$958$	−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
$962$	−0.151895	−	0.00460480i	−0.00489729	−	0.000148465i
$963$	−7.42622	−	27.7150i	−0.239307	−	0.893104i
$964$	6.02540	+	0.365664i	0.194065	+	0.0117773i
$965$	14.5680	+	14.5680i	0.468962	+	0.468962i
$966$		0			0
$967$		−	10.6383i		−	0.342106i	−0.985262	−	0.171053i	$-0.945283\pi$
$967$		−	10.6383i		−	0.342106i	0.985262	−	0.171053i	$-0.0547169\pi$
$968$	12.7255	−	5.87750i	0.409013	−	0.188910i
$969$	18.0255	+	10.4070i	0.579062	+	0.334322i
$970$	−38.1538	−	40.5395i	−1.22505	−	1.30164i
$971$	0.481257	−	1.79607i	0.0154443	−	0.0576388i	−0.957774	−	0.287523i	$-0.907168\pi$
$971$	0.481257	−	1.79607i	0.0154443	−	0.0576388i	0.973218	+	0.229884i	$0.0738348\pi$
$972$	−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
$976$	28.8472	−	22.5820i	0.923377	−	0.722831i
$977$	−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	$0.199367\pi$
$978$	−4.40039	−	2.72160i	−0.140709	−	0.0870272i
$979$	3.79465	−	3.79465i	0.121278	−	0.121278i
$980$		0			0
$981$	23.1160	+	23.1160i	0.738038	+	0.738038i
$982$	−19.8070	+	4.66889i	−0.632067	+	0.148990i
$983$	16.6011	+	9.58464i	0.529492	+	0.305702i	0.740810	−	0.671715i	$-0.234442\pi$
$983$	16.6011	+	9.58464i	0.529492	+	0.305702i	−0.211317	+	0.977417i	$0.567775\pi$
$984$	20.8476	−	3.59752i	0.664597	−	0.114685i
$985$	−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
$989$	−6.65683	−	1.78369i	−0.211675	−	0.0567181i
$990$	26.7696	+	0.811537i	0.850792	+	0.0257924i
$991$	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	$0.0839295\pi$
$992$	−22.9419	−	3.50329i	−0.728407	−	0.111230i
$993$	−9.25270			−0.293626
$994$		0			0
$995$	−6.44966	+	6.44966i	−0.204468	+	0.204468i
$996$	−1.50586	+	24.8135i	−0.0477149	+	0.786244i
$997$	25.9655	−	6.95744i	0.822336	−	0.220344i	0.176969	−	0.984217i	$-0.443371\pi$
$997$	25.9655	−	6.95744i	0.822336	−	0.220344i	0.645368	+	0.763872i	$0.276704\pi$
$998$	−42.8741	+	40.3511i	−1.35716	+	1.27729i
$999$	−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.165.4		48
7.2	even	3	inner	784.2.x.o.373.12		48
7.3	odd	6		784.2.m.j.197.4		24
7.4	even	3		784.2.m.k.197.4		24
7.5	odd	6		112.2.w.c.37.12	✓	48
7.6	odd	2		112.2.w.c.53.4	yes	48
16.13	even	4	inner	784.2.x.o.557.12		48
28.19	even	6		448.2.ba.c.177.5		48
28.27	even	2		448.2.ba.c.305.8		48
56.5	odd	6		896.2.ba.f.737.5		48
56.13	odd	2		896.2.ba.f.865.8		48
56.19	even	6		896.2.ba.e.737.8		48
56.27	even	2		896.2.ba.e.865.5		48
112.5	odd	12		896.2.ba.f.289.8		48
112.13	odd	4		112.2.w.c.109.12	yes	48
112.19	even	12		448.2.ba.c.401.8		48
112.27	even	4		896.2.ba.e.417.8		48
112.45	odd	12		784.2.m.j.589.4		24
112.61	odd	12		112.2.w.c.93.4	yes	48
112.69	odd	4		896.2.ba.f.417.5		48
112.75	even	12		896.2.ba.e.289.5		48
112.83	even	4		448.2.ba.c.81.5		48
112.93	even	12	inner	784.2.x.o.765.4		48
112.109	even	12		784.2.m.k.589.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.12	✓	48	7.5	odd	6
112.2.w.c.53.4	yes	48	7.6	odd	2
112.2.w.c.93.4	yes	48	112.61	odd	12
112.2.w.c.109.12	yes	48	112.13	odd	4
448.2.ba.c.81.5		48	112.83	even	4
448.2.ba.c.177.5		48	28.19	even	6
448.2.ba.c.305.8		48	28.27	even	2
448.2.ba.c.401.8		48	112.19	even	12
784.2.m.j.197.4		24	7.3	odd	6
784.2.m.j.589.4		24	112.45	odd	12
784.2.m.k.197.4		24	7.4	even	3
784.2.m.k.589.4		24	112.109	even	12
784.2.x.o.165.4		48	1.1	even	1	trivial
784.2.x.o.373.12		48	7.2	even	3	inner
784.2.x.o.557.12		48	16.13	even	4	inner
784.2.x.o.765.4		48	112.93	even	12	inner
896.2.ba.e.289.5		48	112.75	even	12
896.2.ba.e.417.8		48	112.27	even	4
896.2.ba.e.737.8		48	56.19	even	6
896.2.ba.e.865.5		48	56.27	even	2
896.2.ba.f.289.8		48	112.5	odd	12
896.2.ba.f.417.5		48	112.69	odd	4
896.2.ba.f.737.5		48	56.5	odd	6
896.2.ba.f.865.8		48	56.13	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.743894 + 1.20276i) q^{2} +(0.222846 + 0.831674i) q^{3} +(-0.893243 - 1.78945i) q^{4} +(-0.543265 + 2.02749i) q^{5} +(-1.16607 - 0.350647i) q^{6} +(2.81674 + 0.256804i) q^{8} +(1.95606 - 1.12933i) q^{9} +O(q^{10})\)	\(q+(-0.743894 + 1.20276i) q^{2} +(0.222846 + 0.831674i) q^{3} +(-0.893243 - 1.78945i) q^{4} +(-0.543265 + 2.02749i) q^{5} +(-1.16607 - 0.350647i) q^{6} +(2.81674 + 0.256804i) q^{8} +(1.95606 - 1.12933i) q^{9} +(-2.03445 - 2.16165i) q^{10} +(-3.85837 + 1.03385i) q^{11} +(1.28918 - 1.14166i) q^{12} +(0.990473 - 0.990473i) q^{13} -1.80728 q^{15} +(-2.40423 + 3.19682i) q^{16} +(-3.07828 + 5.33174i) q^{17} +(-0.0967907 + 3.19276i) q^{18} +(-3.79274 - 1.01626i) q^{19} +(4.11335 - 0.838901i) q^{20} +(1.62675 - 5.40975i) q^{22} +(-5.91462 + 3.41481i) q^{23} +(0.414124 + 2.39984i) q^{24} +(0.514543 + 0.297072i) q^{25} +(0.454490 + 1.92810i) q^{26} +(3.20161 + 3.20161i) q^{27} +(-3.83574 + 3.83574i) q^{29} +(1.34442 - 2.17371i) q^{30} +(2.05131 - 3.55296i) q^{31} +(-2.05650 - 5.26980i) q^{32} +(-1.71965 - 2.97851i) q^{33} +(-4.12286 - 7.66866i) q^{34} +(-3.76811 - 2.49149i) q^{36} +(-0.0198548 + 0.0740993i) q^{37} +(4.04371 - 3.80575i) q^{38} +(1.04447 + 0.603027i) q^{39} +(-2.05091 + 5.57141i) q^{40} -8.68707i q^{41} +(0.713530 + 0.713530i) q^{43} +(5.29647 + 5.98086i) q^{44} +(1.22705 + 4.57941i) q^{45} +(0.292670 - 9.65410i) q^{46} +(-1.95337 - 3.38334i) q^{47} +(-3.19449 - 1.28714i) q^{48} +(-0.740070 + 0.397880i) q^{50} +(-5.12025 - 1.37197i) q^{51} +(-2.65713 - 0.887665i) q^{52} +(-7.06568 + 1.89324i) q^{53} +(-6.23242 + 1.46910i) q^{54} -8.38446i q^{55} -3.38079i q^{57} +(-1.76008 - 7.46685i) q^{58} +(-3.17831 + 0.851626i) q^{59} +(1.61434 + 3.23402i) q^{60} +(-8.84662 - 2.37044i) q^{61} +(2.74740 + 5.11025i) q^{62} +(7.86810 + 1.44670i) q^{64} +(1.47009 + 2.54627i) q^{65} +(4.86166 + 0.147385i) q^{66} +(0.401223 + 1.49739i) q^{67} +(12.2905 + 0.745876i) q^{68} +(-4.15805 - 4.15805i) q^{69} +2.86486i q^{71} +(5.79973 - 2.67871i) q^{72} +(8.95624 + 5.17089i) q^{73} +(-0.0743534 - 0.0790025i) q^{74} +(-0.132403 + 0.494133i) q^{75} +(1.56929 + 7.69467i) q^{76} +(-1.50227 + 0.807659i) q^{78} +(-3.33631 - 5.77865i) q^{79} +(-5.17539 - 6.61128i) q^{80} +(1.43876 - 2.49200i) q^{81} +(10.4484 + 6.46226i) q^{82} +(-10.2078 + 10.2078i) q^{83} +(-9.13773 - 9.13773i) q^{85} +(-1.38899 + 0.327412i) q^{86} +(-4.04486 - 2.33530i) q^{87} +(-11.1335 + 1.92124i) q^{88} +(-1.16348 + 0.671733i) q^{89} +(-6.42071 - 1.93076i) q^{90} +(11.3938 + 7.53363i) q^{92} +(3.41203 + 0.914251i) q^{93} +(5.52244 + 0.167417i) q^{94} +(4.12092 - 7.13765i) q^{95} +(3.92447 - 2.88469i) 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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