LMFDB - Embedded newform 84.2.o.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$1.40376 - 0.171630i$ of defining polynomial
Character	$\chi$	$=$	84.19
Dual form			84.2.o.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.850516 - 1.12988i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.553244 - 1.92196i) q^{4} +(0.834598 + 0.481855i) q^{5} +(-1.40376 - 0.171630i) q^{6} +(-1.20103 + 2.35744i) q^{7} +(-2.64212 - 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.850516 - 1.12988i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.553244 - 1.92196i) q^{4} +(0.834598 + 0.481855i) q^{5} +(-1.40376 - 0.171630i) q^{6} +(-1.20103 + 2.35744i) q^{7} +(-2.64212 - 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25428 - 0.533167i) q^{10} +(4.74861 - 2.74161i) q^{11} +(-1.38784 + 1.44010i) q^{12} +3.75117i q^{13} +(1.64212 + 3.36206i) q^{14} -0.963711i q^{15} +(-3.38784 + 2.12662i) q^{16} +(-0.594545 + 0.343260i) q^{17} +(0.553244 + 1.30151i) q^{18} +(-2.44109 + 4.22809i) q^{19} +(0.464369 - 1.87065i) q^{20} +(2.64212 - 0.138595i) q^{21} +(0.941086 - 7.69713i) q^{22} +(-1.07465 - 0.620450i) q^{23} +(0.446756 + 2.79292i) q^{24} +(-2.03563 - 3.52582i) q^{25} +(4.23836 + 3.19043i) q^{26} +1.00000 q^{27} +(5.19536 + 1.00409i) q^{28} -2.48011 q^{29} +(-1.08887 - 0.819652i) q^{30} +(-2.41401 - 4.18119i) q^{31} +(-0.478592 + 5.63657i) q^{32} +(-4.74861 - 2.74161i) q^{33} +(-0.117828 + 0.963711i) q^{34} +(-2.13832 + 1.38879i) q^{35} +(1.94109 + 0.481855i) q^{36} +(1.36643 - 2.36673i) q^{37} +(2.70103 + 6.35418i) q^{38} +(3.24861 - 1.87558i) q^{39} +(-1.71865 - 2.11569i) q^{40} -9.42976i q^{41} +(2.09057 - 3.10315i) q^{42} +5.97437i q^{43} +(-7.89640 - 7.60984i) q^{44} +(-0.834598 + 0.481855i) q^{45} +(-1.61504 + 0.686521i) q^{46} +(-1.80752 + 3.13072i) q^{47} +(3.53563 + 1.87065i) q^{48} +(-4.11504 - 5.66272i) q^{49} +(-5.71508 - 0.698752i) q^{50} +(0.594545 + 0.343260i) q^{51} +(7.20959 - 2.07531i) q^{52} +(2.04757 + 3.54650i) q^{53} +(0.850516 - 1.12988i) q^{54} +5.28424 q^{55} +(5.55324 - 5.01612i) q^{56} +4.88217 q^{57} +(-2.10937 + 2.80222i) q^{58} +(-6.34315 - 10.9867i) q^{59} +(-1.85221 + 0.533167i) q^{60} +(9.01711 + 5.20603i) q^{61} +(-6.77738 - 0.828634i) q^{62} +(-1.44109 - 2.21884i) q^{63} +(5.96158 + 5.33475i) q^{64} +(-1.80752 + 3.13072i) q^{65} +(-7.13645 + 3.03356i) q^{66} +(8.17396 - 4.71924i) q^{67} +(0.988660 + 0.952783i) q^{68} +1.24090i q^{69} +(-0.249518 + 3.59723i) q^{70} +10.1163i q^{71} +(2.19536 - 1.78336i) q^{72} +(-5.76850 + 3.33044i) q^{73} +(-1.51194 - 3.55685i) q^{74} +(-2.03563 + 3.52582i) q^{75} +(9.47672 + 2.35250i) q^{76} +(0.759946 + 14.4873i) q^{77} +(0.643814 - 5.26574i) q^{78} +(1.22492 + 0.707208i) q^{79} +(-3.85221 + 0.142425i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.6545 - 8.02016i) q^{82} +0.543780 q^{83} +(-1.72811 - 5.00136i) q^{84} -0.661608 q^{85} +(6.75030 + 5.08130i) q^{86} +(1.24005 + 2.14784i) q^{87} +(-15.3142 + 2.44966i) q^{88} +(0.480107 + 0.277190i) q^{89} +(-0.165402 + 1.35282i) q^{90} +(-8.84315 - 4.50528i) q^{91} +(-0.597935 + 2.40870i) q^{92} +(-2.41401 + 4.18119i) q^{93} +(2.00000 + 4.70500i) q^{94} +(-4.07465 + 2.35250i) q^{95} +(5.12071 - 2.40381i) q^{96} +10.8747i q^{97} +(-9.89809 - 0.166748i) q^{98} +5.48322i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.850516	−	1.12988i	0.601406	−	0.798944i
$2$	0.850516	−	1.12988i	0.601406	−	0.798944i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.553244	−	1.92196i	−0.276622	−	0.960979i
$5$	0.834598	+	0.481855i	0.373244	+	0.215492i	0.674875	−	0.737932i	$-0.264198\pi$
$5$	0.834598	+	0.481855i	0.373244	+	0.215492i	−0.301631	+	0.953425i	$0.597531\pi$
$6$	−1.40376	−	0.171630i	−0.573083	−	0.0700677i
$7$	−1.20103	+	2.35744i	−0.453948	+	0.891028i
$7$	−1.20103	+	2.35744i	−0.453948	+	0.891028i
$8$	−2.64212	−	1.00956i	−0.934130	−	0.356933i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.25428	−	0.533167i	0.396637	−	0.168602i
$11$	4.74861	−	2.74161i	1.43176	−	0.826626i	0.434504	−	0.900670i	$-0.356924\pi$
$11$	4.74861	−	2.74161i	1.43176	−	0.826626i	0.997255	+	0.0740437i	$0.0235904\pi$
$12$	−1.38784	+	1.44010i	−0.400636	+	0.415722i
$13$			3.75117i			1.04039i	0.854048	+	0.520193i	$0.174140\pi$
$13$			3.75117i			1.04039i	−0.854048	+	0.520193i	$0.825860\pi$
$14$	1.64212	+	3.36206i	0.438875	+	0.898548i
$15$		−	0.963711i		−	0.248829i
$16$	−3.38784	+	2.12662i	−0.846961	+	0.531656i
$17$	−0.594545	+	0.343260i	−0.144198	+	0.0832529i	−0.570363	−	0.821393i	$-0.693198\pi$
$17$	−0.594545	+	0.343260i	−0.144198	+	0.0832529i	0.426165	+	0.904645i	$0.359864\pi$
$18$	0.553244	+	1.30151i	0.130401	+	0.306768i
$19$	−2.44109	+	4.22809i	−0.560024	+	0.969989i	0.437470	+	0.899233i	$0.355875\pi$
$19$	−2.44109	+	4.22809i	−0.560024	+	0.969989i	−0.997494	+	0.0707563i	$0.977459\pi$
$20$	0.464369	−	1.87065i	0.103836	−	0.418289i
$21$	2.64212	−	0.138595i	0.576558	−	0.0302439i
$22$	0.941086	−	7.69713i	0.200640	−	1.64103i
$23$	−1.07465	−	0.620450i	−0.224080	−	0.129373i	0.383758	−	0.923434i	$-0.374630\pi$
$23$	−1.07465	−	0.620450i	−0.224080	−	0.129373i	−0.607838	+	0.794061i	$0.707963\pi$
$24$	0.446756	+	2.79292i	0.0911937	+	0.570103i
$25$	−2.03563	−	3.52582i	−0.407126	−	0.705163i
$26$	4.23836	+	3.19043i	0.831210	+	0.625695i
$27$	1.00000			0.192450
$28$	5.19536	+	1.00409i	0.981831	+	0.189756i
$29$	−2.48011			−0.460544			−0.230272	−	0.973126i	$-0.573962\pi$
$29$	−2.48011			−0.460544			−0.230272	+	0.973126i	$0.573962\pi$
$30$	−1.08887	−	0.819652i	−0.198800	−	0.149647i
$31$	−2.41401	−	4.18119i	−0.433569	−	0.750963i	0.563609	−	0.826042i	$-0.309413\pi$
$31$	−2.41401	−	4.18119i	−0.433569	−	0.750963i	−0.997178	+	0.0750787i	$0.976079\pi$
$32$	−0.478592	+	5.63657i	−0.0846040	+	0.996415i
$33$	−4.74861	−	2.74161i	−0.826626	−	0.477253i
$34$	−0.117828	+	0.963711i	−0.0202073	+	0.165275i
$35$	−2.13832	+	1.38879i	−0.361443	+	0.234748i
$36$	1.94109	+	0.481855i	0.323514	+	0.0803092i
$37$	1.36643	−	2.36673i	0.224640	−	0.389089i	−0.731571	−	0.681765i	$-0.761213\pi$
$37$	1.36643	−	2.36673i	0.224640	−	0.389089i	0.956212	+	0.292677i	$0.0945459\pi$
$38$	2.70103	+	6.35418i	0.438165	+	1.03078i
$39$	3.24861	−	1.87558i	0.520193	−	0.300334i
$40$	−1.71865	−	2.11569i	−0.271742	−	0.334521i
$41$		−	9.42976i		−	1.47268i	−0.676611	−	0.736340i	$-0.736552\pi$
$41$		−	9.42976i		−	1.47268i	0.676611	−	0.736340i	$-0.263448\pi$
$42$	2.09057	−	3.10315i	0.322582	−	0.478826i
$43$			5.97437i			0.911083i	0.890215	+	0.455541i	$0.150554\pi$
$43$			5.97437i			0.911083i	−0.890215	+	0.455541i	$0.849446\pi$
$44$	−7.89640	−	7.60984i	−1.19043	−	1.14723i
$45$	−0.834598	+	0.481855i	−0.124415	+	0.0718308i
$46$	−1.61504	+	0.686521i	−0.238125	+	0.101222i
$47$	−1.80752	+	3.13072i	−0.263654	+	0.456662i	−0.967210	−	0.253978i	$-0.918261\pi$
$47$	−1.80752	+	3.13072i	−0.263654	+	0.456662i	0.703556	+	0.710640i	$0.251594\pi$
$48$	3.53563	+	1.87065i	0.510324	+	0.270004i
$49$	−4.11504	−	5.66272i	−0.587863	−	0.808960i
$50$	−5.71508	−	0.698752i	−0.808234	−	0.0988184i
$51$	0.594545	+	0.343260i	0.0832529	+	0.0480661i
$52$	7.20959	−	2.07531i	0.999790	−	0.287794i
$53$	2.04757	+	3.54650i	0.281256	+	0.487150i	0.971694	−	0.236242i	$-0.0759157\pi$
$53$	2.04757	+	3.54650i	0.281256	+	0.487150i	−0.690438	+	0.723391i	$0.742582\pi$
$54$	0.850516	−	1.12988i	0.115741	−	0.153757i
$55$	5.28424			0.712526
$56$	5.55324	−	5.01612i	0.742083	−	0.670308i
$57$	4.88217			0.646660
$58$	−2.10937	+	2.80222i	−0.276974	+	0.367949i
$59$	−6.34315	−	10.9867i	−0.825808	−	1.43034i	−0.901300	−	0.433195i	$-0.857386\pi$
$59$	−6.34315	−	10.9867i	−0.825808	−	1.43034i	0.0754923	−	0.997146i	$-0.475947\pi$
$60$	−1.85221	+	0.533167i	−0.239119	+	0.0688316i
$61$	9.01711	+	5.20603i	1.15452	+	0.666564i	0.949985	−	0.312295i	$-0.101098\pi$
$61$	9.01711	+	5.20603i	1.15452	+	0.666564i	0.204537	+	0.978859i	$0.434431\pi$
$62$	−6.77738	−	0.828634i	−0.860728	−	0.105237i
$63$	−1.44109	−	2.21884i	−0.181560	−	0.279548i
$64$	5.96158	+	5.33475i	0.745198	+	0.666843i
$65$	−1.80752	+	3.13072i	−0.224195	+	0.388318i
$66$	−7.13645	+	3.03356i	−0.878436	+	0.373405i
$67$	8.17396	−	4.71924i	0.998608	−	0.576546i	0.0907716	−	0.995872i	$-0.471067\pi$
$67$	8.17396	−	4.71924i	0.998608	−	0.576546i	0.907836	+	0.419325i	$0.137733\pi$
$68$	0.988660	+	0.952783i	0.119893	+	0.115542i
$69$			1.24090i			0.149387i
$70$	−0.249518	+	3.59723i	−0.0298231	+	0.429952i
$71$			10.1163i			1.20058i	0.799782	+	0.600291i	$0.204948\pi$
$71$			10.1163i			1.20058i	−0.799782	+	0.600291i	$0.795052\pi$
$72$	2.19536	−	1.78336i	0.258726	−	0.210171i
$73$	−5.76850	+	3.33044i	−0.675152	+	0.389799i	−0.798026	−	0.602623i	$-0.794122\pi$
$73$	−5.76850	+	3.33044i	−0.675152	+	0.389799i	0.122874	+	0.992422i	$0.460789\pi$
$74$	−1.51194	−	3.55685i	−0.175760	−	0.413475i
$75$	−2.03563	+	3.52582i	−0.235054	+	0.407126i
$76$	9.47672	+	2.35250i	1.08705	+	0.269850i
$77$	0.759946	+	14.4873i	0.0866039	+	1.65098i
$78$	0.643814	−	5.26574i	0.0728976	−	0.596228i
$79$	1.22492	+	0.707208i	0.137814	+	0.0795671i	0.567322	−	0.823496i	$-0.307980\pi$
$79$	1.22492	+	0.707208i	0.137814	+	0.0795671i	−0.429508	+	0.903063i	$0.641313\pi$
$80$	−3.85221	+	0.142425i	−0.430690	+	0.0159237i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.6545	−	8.02016i	−1.17659	−	0.885679i
$83$	0.543780			0.0596876			0.0298438	−	0.999555i	$-0.490499\pi$
$83$	0.543780			0.0596876			0.0298438	+	0.999555i	$0.490499\pi$
$84$	−1.72811	−	5.00136i	−0.188552	−	0.545693i
$85$	−0.661608			−0.0717614
$86$	6.75030	+	5.08130i	0.727904	+	0.547930i
$87$	1.24005	+	2.14784i	0.132948	+	0.230272i
$88$	−15.3142	+	2.44966i	−1.63250	+	0.261135i
$89$	0.480107	+	0.277190i	0.0508912	+	0.0293821i	0.525230	−	0.850960i	$-0.323979\pi$
$89$	0.480107	+	0.277190i	0.0508912	+	0.0293821i	−0.474339	+	0.880343i	$0.657313\pi$
$90$	−0.165402	+	1.35282i	−0.0174349	+	0.142600i
$91$	−8.84315	−	4.50528i	−0.927014	−	0.472281i
$92$	−0.597935	+	2.40870i	−0.0623390	+	0.251124i
$93$	−2.41401	+	4.18119i	−0.250321	+	0.433569i
$94$	2.00000	+	4.70500i	0.206284	+	0.485284i
$95$	−4.07465	+	2.35250i	−0.418050	+	0.241362i
$96$	5.12071	−	2.40381i	0.522630	−	0.245338i
$97$			10.8747i			1.10416i	0.833790	+	0.552081i	$0.186166\pi$
$97$			10.8747i			1.10416i	−0.833790	+	0.552081i	$0.813834\pi$
$98$	−9.89809	−	0.166748i	−0.999858	−	0.0168441i
$99$			5.48322i			0.551084i
$100$	−5.65027	+	5.86303i	−0.565027	+	0.586303i
$101$	12.4972	−	7.21527i	1.24352	−	0.717946i	0.273710	−	0.961812i	$-0.411749\pi$
$101$	12.4972	−	7.21527i	1.24352	−	0.717946i	0.969809	+	0.243866i	$0.0784157\pi$
$102$	0.893512	−	0.379814i	0.0884709	−	0.0376072i
$103$	7.51235	−	13.0118i	0.740214	−	1.28209i	−0.212184	−	0.977230i	$-0.568058\pi$
$103$	7.51235	−	13.0118i	0.740214	−	1.28209i	0.952398	−	0.304858i	$-0.0986090\pi$
$104$	3.78702	−	9.91103i	0.371348	−	0.971857i
$105$	2.27189	+	1.15745i	0.221714	+	0.112955i
$106$	5.74861	+	0.702851i	0.558354	+	0.0682669i
$107$	10.4925	+	6.05782i	1.01434	+	0.585632i	0.912461	−	0.409165i	$-0.134180\pi$
$107$	10.4925	+	6.05782i	1.01434	+	0.585632i	0.101883	+	0.994796i	$0.467513\pi$
$108$	−0.553244	−	1.92196i	−0.0532359	−	0.184940i
$109$	3.03563	+	5.25787i	0.290761	+	0.503612i	0.973990	−	0.226592i	$-0.0727583\pi$
$109$	3.03563	+	5.25787i	0.290761	+	0.503612i	−0.683229	+	0.730204i	$0.739425\pi$
$110$	4.49433	−	5.97054i	0.428518	−	0.569268i
$111$	−2.73287			−0.259392
$112$	−0.944476	−	10.5408i	−0.0892446	−	0.996010i
$113$	−7.37939			−0.694194			−0.347097	−	0.937829i	$-0.612833\pi$
$113$	−7.37939			−0.694194			−0.347097	+	0.937829i	$0.612833\pi$
$114$	4.15237	−	5.51625i	0.388905	−	0.516645i
$115$	−0.597935	−	1.03565i	−0.0557577	−	0.0965752i
$116$	1.37210	+	4.76666i	0.127397	+	0.442573i
$117$	−3.24861	−	1.87558i	−0.300334	−	0.173398i
$118$	−17.8085	−	2.17735i	−1.63941	−	0.200442i
$119$	−0.0951483	−	1.81387i	−0.00872223	−	0.166277i
$120$	−0.972923	+	2.54624i	−0.0888153	+	0.232439i
$121$	9.53284	−	16.5114i	0.866622	−	1.50103i
$122$	13.5514	−	5.76041i	1.22688	−	0.521523i
$123$	−8.16641	+	4.71488i	−0.736340	+	0.425126i
$124$	−6.70053	+	6.95284i	−0.601725	+	0.624383i
$125$		−	8.74207i		−	0.781915i
$126$	−3.73269	−	0.258913i	−0.332534	−	0.0230658i
$127$		−	11.6431i		−	1.03316i	−0.856240	−	0.516578i	$-0.827206\pi$
$127$		−	11.6431i		−	1.03316i	0.856240	−	0.516578i	$-0.172794\pi$
$128$	11.0980	−	2.19857i	0.980937	−	0.194328i
$129$	5.17396	−	2.98718i	0.455541	−	0.263007i
$130$	2.00000	+	4.70500i	0.175412	+	0.412656i
$131$	4.63078	−	8.02074i	0.404593	−	0.700776i	−0.589681	−	0.807636i	$-0.700747\pi$
$131$	4.63078	−	8.02074i	0.404593	−	0.700776i	0.994274	+	0.106861i	$0.0340798\pi$
$132$	−2.64212	+	10.6434i	−0.229967	+	0.926389i
$133$	−7.03563	−	10.8328i	−0.610067	−	0.939321i
$134$	1.61993	−	13.2494i	0.139940	−	1.14457i
$135$	0.834598	+	0.481855i	0.0718308	+	0.0414715i
$136$	1.91740	−	0.306707i	0.164416	−	0.0262999i
$137$	−3.61504	−	6.26144i	−0.308854	−	0.534951i	0.669258	−	0.743030i	$-0.266612\pi$
$137$	−3.61504	−	6.26144i	−0.308854	−	0.534951i	−0.978112	+	0.208080i	$0.933279\pi$
$138$	1.40207	+	1.05541i	0.119352	+	0.0898422i
$139$	−5.30812			−0.450229			−0.225115	−	0.974332i	$-0.572276\pi$
$139$	−5.30812			−0.450229			−0.225115	+	0.974332i	$0.572276\pi$
$140$	3.85221	+	3.34143i	0.325571	+	0.282402i
$141$	3.61504			0.304441
$142$	11.4302	+	8.60406i	0.959197	+	0.722037i
$143$	10.2842	+	17.8128i	0.860011	+	1.48958i
$144$	−0.147789	−	3.99727i	−0.0123157	−	0.333106i
$145$	−2.06989	−	1.19505i	−0.171895	−	0.0992438i
$146$	−1.14321	+	9.35029i	−0.0946127	+	0.773836i
$147$	−2.84654	+	6.39509i	−0.234779	+	0.527458i
$148$	−5.30473	−	1.31685i	−0.436046	−	0.108244i
$149$	−2.33080	+	4.03707i	−0.190947	+	0.330730i	−0.945564	−	0.325435i	$-0.894489\pi$
$149$	−2.33080	+	4.03707i	−0.190947	+	0.330730i	0.754617	+	0.656165i	$0.227822\pi$
$150$	2.25240	+	5.29878i	0.183908	+	0.432643i
$151$	−10.5709	+	6.10309i	−0.860244	+	0.496662i	−0.864094	−	0.503330i	$-0.832108\pi$
$151$	−10.5709	+	6.10309i	−0.860244	+	0.496662i	0.00384988	+	0.999993i	$0.498775\pi$
$152$	10.7181	−	8.70668i	0.869356	−	0.706205i
$153$		−	0.686521i		−	0.0555019i
$154$	17.0152	+	11.4631i	1.37113	+	0.923719i
$155$		−	4.65281i		−	0.373723i
$156$	−5.40207	−	5.20603i	−0.432511	−	0.416816i
$157$	−18.9944	+	10.9664i	−1.51592	+	0.875217i	−0.516095	+	0.856531i	$0.672615\pi$
$157$	−18.9944	+	10.9664i	−1.51592	+	0.875217i	−0.999825	+	0.0186856i	$0.994052\pi$
$158$	1.84087	−	0.782517i	0.146452	−	0.0622537i
$159$	2.04757	−	3.54650i	0.162383	−	0.281256i
$160$	−3.11545	+	4.47366i	−0.246298	+	0.353674i
$161$	2.75337	−	1.78824i	0.216996	−	0.140933i
$162$	−1.40376	−	0.171630i	−0.110290	−	0.0134845i
$163$	3.48011	+	2.00924i	0.272583	+	0.157376i	0.630061	−	0.776546i	$-0.283030\pi$
$163$	3.48011	+	2.00924i	0.272583	+	0.157376i	−0.357478	+	0.933922i	$0.616363\pi$
$164$	−18.1236	+	5.21696i	−1.41521	+	0.407376i
$165$	−2.64212	−	4.57628i	−0.205689	−	0.356263i
$166$	0.462494	−	0.614404i	0.0358965	−	0.0476870i
$167$	−14.7178			−1.13890			−0.569448	−	0.822027i	$-0.692843\pi$
$167$	−14.7178			−1.13890			−0.569448	+	0.822027i	$0.692843\pi$
$168$	−7.12071	−	2.30119i	−0.549375	−	0.177541i
$169$	−1.07126			−0.0824047
$170$	−0.562708	+	0.747535i	−0.0431577	+	0.0573333i
$171$	−2.44109	−	4.22809i	−0.186675	−	0.323330i
$172$	11.4825	−	3.30528i	0.875531	−	0.252026i
$173$	−10.0918	−	5.82648i	−0.767262	−	0.442979i	0.0646349	−	0.997909i	$-0.479412\pi$
$173$	−10.0918	−	5.82648i	−0.767262	−	0.442979i	−0.831897	+	0.554930i	$0.812745\pi$
$174$	3.48148	+	0.425661i	0.263930	+	0.0322693i
$175$	10.7568	−	0.564256i	0.813134	−	0.0426538i
$176$	−10.2572	+	19.3866i	−0.773163	+	1.46132i
$177$	−6.34315	+	10.9867i	−0.476780	+	0.825808i
$178$	0.721529	−	0.306707i	0.0540809	−	0.0229887i
$179$	2.24663	−	1.29709i	0.167921	−	0.0969494i	−0.413684	−	0.910421i	$-0.635758\pi$
$179$	2.24663	−	1.29709i	0.167921	−	0.0969494i	0.581605	+	0.813471i	$0.302425\pi$
$180$	1.38784	+	1.33748i	0.103444	+	0.0996898i
$181$		−	9.53343i		−	0.708615i	−0.935129	−	0.354307i	$-0.884717\pi$
$181$		−	9.53343i		−	0.708615i	0.935129	−	0.354307i	$-0.115283\pi$
$182$	−12.6117	+	6.15986i	−0.934838	+	0.456599i
$183$		−	10.4121i		−	0.769681i
$184$	2.21298	+	2.72423i	0.163143	+	0.200833i
$185$	2.28085	−	1.31685i	0.167691	−	0.0968166i
$186$	2.67107	+	6.28370i	0.195852	+	0.460743i
$187$	−1.88217	+	3.26002i	−0.137638	+	0.238396i
$188$	7.01711	+	1.74193i	0.511775	+	0.127043i
$189$	−1.20103	+	2.35744i	−0.0873623	+	0.171478i
$190$	−0.807521	+	6.60470i	−0.0585837	+	0.479155i
$191$	−7.21637	−	4.16637i	−0.522158	−	0.301468i	0.215659	−	0.976469i	$-0.430810\pi$
$191$	−7.21637	−	4.16637i	−0.522158	−	0.301468i	−0.737817	+	0.675001i	$0.764143\pi$
$192$	1.63924	−	7.83026i	0.118302	−	0.565100i
$193$	6.18630	+	10.7150i	0.445300	+	0.771282i	0.998073	−	0.0620498i	$-0.0197638\pi$
$193$	6.18630	+	10.7150i	0.445300	+	0.771282i	−0.552773	+	0.833332i	$0.686430\pi$
$194$	12.2871	+	9.24915i	0.882164	+	0.664050i
$195$	3.61504			0.258878
$196$	−8.60689	+	11.0418i	−0.614778	+	0.788700i
$197$	3.23686			0.230617			0.115308	−	0.993330i	$-0.463214\pi$
$197$	3.23686			0.230617			0.115308	+	0.993330i	$0.463214\pi$
$198$	6.19536	+	4.66357i	0.440285	+	0.331425i
$199$	9.61504	+	16.6537i	0.681592	+	1.18055i	0.974495	+	0.224410i	$0.0720455\pi$
$199$	9.61504	+	16.6537i	0.681592	+	1.18055i	−0.292903	+	0.956142i	$0.594621\pi$
$200$	1.81886	+	11.3707i	0.128613	+	0.804031i
$201$	−8.17396	−	4.71924i	−0.576546	−	0.332869i
$202$	2.47672	−	20.2570i	0.174261	−	1.42528i
$203$	2.97869	−	5.84670i	0.209063	−	0.410358i
$204$	0.330804	−	1.33260i	0.0231609	−	0.0933004i
$205$	4.54378	−	7.87006i	0.317351	−	0.549669i
$206$	−8.31232	−	19.5547i	−0.579147	−	1.36244i
$207$	1.07465	−	0.620450i	0.0746934	−	0.0431243i
$208$	−7.97732	−	12.7084i	−0.553128	−	0.881167i
$209$			26.7700i			1.85172i
$210$	3.24005	−	1.58253i	0.223585	−	0.109205i
$211$			9.24637i			0.636546i	0.947999	+	0.318273i	$0.103103\pi$
$211$			9.24637i			0.636546i	−0.947999	+	0.318273i	$0.896897\pi$
$212$	5.68342	−	5.89743i	0.390339	−	0.405037i
$213$	8.76095	−	5.05814i	0.600291	−	0.346578i
$214$	15.7686	−	6.70291i	1.07792	−	0.458201i
$215$	−2.87878	+	4.98620i	−0.196331	+	0.340056i
$216$	−2.64212	−	1.00956i	−0.179773	−	0.0686918i
$217$	12.7562	−	0.669139i	0.865947	−	0.0454241i
$218$	8.52260	+	1.04201i	0.577223	+	0.0705740i
$219$	5.76850	+	3.33044i	0.389799	+	0.225051i
$220$	−2.92347	−	10.1561i	−0.197100	−	0.684723i
$221$	−1.28763	−	2.23024i	−0.0866152	−	0.150022i
$222$	−2.32435	+	3.08781i	−0.156000	+	0.207240i
$223$	−1.94585			−0.130303			−0.0651517	−	0.997875i	$-0.520753\pi$
$223$	−1.94585			−0.130303			−0.0651517	+	0.997875i	$0.520753\pi$
$224$	−12.7131	−	7.89796i	−0.849428	−	0.527705i
$225$	4.07126			0.271417
$226$	−6.27629	+	8.33780i	−0.417492	+	0.554622i
$227$	−4.32265	−	7.48706i	−0.286905	−	0.496933i	0.686165	−	0.727446i	$-0.259293\pi$
$227$	−4.32265	−	7.48706i	−0.286905	−	0.496933i	−0.973069	+	0.230513i	$0.925960\pi$
$228$	−2.70103	−	9.38333i	−0.178880	−	0.621426i
$229$	14.5396	+	8.39446i	0.960805	+	0.554721i	0.896421	−	0.443204i	$-0.146158\pi$
$229$	14.5396	+	8.39446i	0.960805	+	0.554721i	0.0643846	+	0.997925i	$0.479492\pi$
$230$	−1.67871	−	0.205247i	−0.110691	−	0.0135336i
$231$	12.1664	−	7.90179i	0.800491	−	0.519900i
$232$	6.55274	+	2.50381i	0.430208	+	0.164383i
$233$	0.523283	−	0.906353i	0.0342814	−	0.0593772i	−0.848376	−	0.529395i	$-0.822419\pi$
$233$	0.523283	−	0.906353i	0.0342814	−	0.0593772i	0.882657	+	0.470018i	$0.155752\pi$
$234$	−4.88217	+	2.07531i	−0.319158	+	0.135667i
$235$	−3.01711	+	1.74193i	−0.196814	+	0.113631i
$236$	−17.6066	+	18.2696i	−1.14609	+	1.18925i
$237$		−	1.41442i		−	0.0918761i
$238$	−2.13037	−	1.43522i	−0.138092	−	0.0930315i
$239$		−	19.2479i		−	1.24505i	−0.782602	−	0.622523i	$-0.786108\pi$
$239$		−	19.2479i		−	1.24505i	0.782602	−	0.622523i	$-0.213892\pi$
$240$	2.04945	+	3.26490i	0.132291	+	0.210748i
$241$	−2.38754	+	1.37844i	−0.153795	+	0.0887934i	−0.574922	−	0.818208i	$-0.694968\pi$
$241$	−2.38754	+	1.37844i	−0.153795	+	0.0887934i	0.421128	+	0.907001i	$0.361634\pi$
$242$	−10.5480	−	24.8141i	−0.678050	−	1.59511i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	5.01711	−	20.2107i	0.321187	−	1.29386i
$245$	−0.705792	−	6.70895i	−0.0450914	−	0.428619i
$246$	−1.61843	+	13.2371i	−0.103187	+	0.843968i
$247$	−15.8603	−	9.15692i	−1.00916	−	0.582641i
$248$	2.15695	+	13.4843i	0.136966	+	0.856252i
$249$	−0.271890	−	0.470927i	−0.0172303	−	0.0298438i
$250$	−9.87747	−	7.43528i	−0.624706	−	0.470248i
$251$	20.7493			1.30968			0.654841	−	0.755767i	$-0.272736\pi$
$251$	20.7493			1.30968			0.654841	+	0.755767i	$0.272736\pi$
$252$	−3.46725	+	3.99727i	−0.218416	+	0.251804i
$253$	−6.80413			−0.427772
$254$	−13.1553	−	9.90263i	−0.825434	−	0.621346i
$255$	0.330804	+	0.572969i	0.0207157	+	0.0358807i
$256$	6.95495	−	14.4093i	0.434684	−	0.900583i
$257$	6.45283	+	3.72554i	0.402516	+	0.232393i	0.687569	−	0.726119i	$-0.258678\pi$
$257$	6.45283	+	3.72554i	0.402516	+	0.232393i	−0.285053	+	0.958512i	$0.592011\pi$
$258$	1.02538	−	8.38658i	0.0638375	−	0.522126i
$259$	3.93830	+	6.06381i	0.244714	+	0.376787i
$260$	7.01711	+	1.74193i	0.435182	+	0.108030i
$261$	1.24005	−	2.14784i	0.0767574	−	0.132948i
$262$	−5.12390	−	12.0540i	−0.316556	−	0.744698i
$263$	−25.7034	+	14.8399i	−1.58494	+	0.915066i	−0.590818	+	0.806805i	$0.701195\pi$
$263$	−25.7034	+	14.8399i	−1.58494	+	0.915066i	−0.994123	+	0.108260i	$0.965472\pi$
$264$	9.77857	+	12.0377i	0.601829	+	0.740866i
$265$			3.94654i			0.242434i
$266$	−18.2236	−	1.26406i	−1.11736	−	0.0775045i
$267$		−	0.554380i		−	0.0339275i
$268$	−13.5924	−	13.0991i	−0.830286	−	0.800155i
$269$	−3.73727	+	2.15771i	−0.227865	+	0.131558i	−0.609587	−	0.792719i	$-0.708665\pi$
$269$	−3.73727	+	2.15771i	−0.227865	+	0.131558i	0.381722	+	0.924277i	$0.375331\pi$
$270$	1.25428	−	0.533167i	0.0763328	−	0.0324475i
$271$	−6.79142	+	11.7631i	−0.412550	+	0.714557i	−0.995168	−	0.0981892i	$-0.968695\pi$
$271$	−6.79142	+	11.7631i	−0.412550	+	0.714557i	0.582618	+	0.812746i	$0.302028\pi$
$272$	1.28424	−	2.42728i	0.0778683	−	0.147176i
$273$	0.519893	+	9.91103i	0.0314654	+	0.599843i
$274$	−10.1493	−	1.24090i	−0.613142	−	0.0749656i
$275$	−19.3328	−	11.1618i	−1.16581	−	0.673082i
$276$	2.38496	−	0.686521i	0.143558	−	0.0413237i
$277$	−1.03563	−	1.79376i	−0.0622250	−	0.107777i	0.833235	−	0.552920i	$-0.186486\pi$
$277$	−1.03563	−	1.79376i	−0.0622250	−	0.107777i	−0.895460	+	0.445143i	$0.853153\pi$
$278$	−4.51465	+	5.99753i	−0.270770	+	0.359708i
$279$	4.82802			0.289046
$280$	7.05177	−	1.51059i	0.421424	−	0.0902747i
$281$	23.7122			1.41455			0.707276	−	0.706938i	$-0.249924\pi$
$281$	23.7122			1.41455			0.707276	+	0.706938i	$0.249924\pi$
$282$	3.07465	−	4.08455i	0.183093	−	0.243232i
$283$	6.12739	+	10.6129i	0.364235	+	0.630874i	0.988653	−	0.150216i	$-0.0479970\pi$
$283$	6.12739	+	10.6129i	0.364235	+	0.630874i	−0.624418	+	0.781091i	$0.714664\pi$
$284$	19.4431	−	5.59677i	1.15373	−	0.332107i
$285$	4.07465	+	2.35250i	0.241362	+	0.139350i
$286$	28.8732	+	3.53017i	1.70731	+	0.208743i
$287$	22.2301	+	11.3254i	1.31220	+	0.668520i
$288$	−4.64212	−	3.23276i	−0.273539	−	0.190492i
$289$	−8.26434	+	14.3143i	−0.486138	+	0.842016i
$290$	−3.11074	+	1.32231i	−0.182669	+	0.0776488i
$291$	9.41780	−	5.43737i	0.552081	−	0.318744i
$292$	9.59236	+	9.24426i	0.561351	+	0.540980i
$293$		−	10.7090i		−	0.625626i	−0.949815	−	0.312813i	$-0.898729\pi$
$293$		−	10.7090i		−	0.625626i	0.949815	−	0.312813i	$-0.101271\pi$
$294$	4.80464	+	8.65537i	0.280212	+	0.504792i
$295$		−	12.2259i		−	0.711821i
$296$	−5.99964	+	4.87370i	−0.348722	+	0.283278i
$297$	4.74861	−	2.74161i	0.275542	−	0.159084i
$298$	2.57901	+	6.06712i	0.149398	+	0.351459i
$299$	2.32741	−	4.03120i	0.134598	−	0.233130i
$300$	7.90267	+	1.96176i	0.456261	+	0.113262i
$301$	−14.0842	−	7.17541i	−0.811801	−	0.413584i
$302$	−2.09495	+	17.1345i	−0.120551	+	0.985982i
$303$	−12.4972	−	7.21527i	−0.717946	−	0.414506i
$304$	−0.721529	−	19.5154i	−0.0413825	−	1.11928i
$305$	5.01711	+	8.68988i	0.287279	+	0.497581i
$306$	−0.775684	−	0.583897i	−0.0443429	−	0.0333792i
$307$	−4.22056			−0.240880			−0.120440	−	0.992721i	$-0.538431\pi$
$307$	−4.22056			−0.240880			−0.120440	+	0.992721i	$0.538431\pi$
$308$	27.4236	−	9.47561i	1.56260	−	0.539923i
$309$	−15.0247			−0.854725
$310$	−5.25711	−	3.95729i	−0.298584	−	0.224759i
$311$	4.85070	+	8.40165i	0.275058	+	0.476414i	0.970150	−	0.242507i	$-0.0779697\pi$
$311$	4.85070	+	8.40165i	0.275058	+	0.476414i	−0.695092	+	0.718921i	$0.744636\pi$
$312$	−10.4767	+	1.67586i	−0.593127	+	0.0948767i
$313$	11.8328	+	6.83168i	0.668831	+	0.386149i	0.795633	−	0.605778i	$-0.207138\pi$
$313$	11.8328	+	6.83168i	0.668831	+	0.386149i	−0.126803	+	0.991928i	$0.540472\pi$
$314$	−3.76434	+	30.7885i	−0.212434	+	1.73750i
$315$	−0.133565	−	2.54624i	−0.00752556	−	0.143464i
$316$	0.681544	−	2.74550i	0.0383398	−	0.154447i
$317$	−10.0442	+	17.3970i	−0.564138	+	0.977115i	0.432992	+	0.901398i	$0.357458\pi$
$317$	−10.0442	+	17.3970i	−0.564138	+	0.977115i	−0.997129	+	0.0757171i	$0.975875\pi$
$318$	−2.26562	−	5.32987i	−0.127049	−	0.298884i
$319$	−11.7771	+	6.79948i	−0.659388	+	0.380698i
$320$	2.40495	+	7.32499i	0.134441	+	0.409479i
$321$		−	12.1156i		−	0.676229i
$322$	0.321286	−	4.63190i	0.0179046	−	0.258125i
$323$		−	3.35171i		−	0.186494i
$324$	−1.38784	+	1.44010i	−0.0771023	+	0.0800057i
$325$	13.2259	−	7.63599i	0.733642	−	0.423569i
$326$	5.23008	−	2.22320i	0.289667	−	0.123132i
$327$	3.03563	−	5.25787i	0.167871	−	0.290761i
$328$	−9.51989	+	24.9145i	−0.525648	+	1.37568i
$329$	−5.20959	−	8.02121i	−0.287214	−	0.442224i
$330$	−7.41780	−	0.906935i	−0.408337	−	0.0499251i
$331$	−8.15886	−	4.71052i	−0.448452	−	0.258914i	0.258724	−	0.965951i	$-0.416698\pi$
$331$	−8.15886	−	4.71052i	−0.448452	−	0.258914i	−0.707176	+	0.707037i	$0.750031\pi$
$332$	−0.300843	−	1.04512i	−0.0165109	−	0.0573585i
$333$	1.36643	+	2.36673i	0.0748802	+	0.129696i
$334$	−12.5177	+	16.6293i	−0.684939	+	0.909914i
$335$	9.09596			0.496965
$336$	−8.65634	+	6.08833i	−0.472242	+	0.332146i
$337$	−13.4411			−0.732185			−0.366092	−	0.930578i	$-0.619305\pi$
$337$	−13.4411			−0.732185			−0.366092	+	0.930578i	$0.619305\pi$
$338$	−0.911125	+	1.21039i	−0.0495587	+	0.0658367i
$339$	3.68969	+	6.39074i	0.200397	+	0.347097i
$340$	0.366030	+	1.27158i	0.0198508	+	0.0689612i
$341$	−22.9264	−	13.2365i	−1.24153	−	0.716799i
$342$	−6.85340	−	0.837928i	−0.370589	−	0.0453100i
$343$	18.2918	−	2.89985i	0.987666	−	0.156577i
$344$	6.03148	−	15.7850i	0.325195	−	0.851070i
$345$	−0.597935	+	1.03565i	−0.0321917	+	0.0557577i
$346$	−15.1664	+	6.44693i	−0.815351	+	0.346589i
$347$	19.5890	−	11.3097i	1.05159	−	0.607136i	0.128497	−	0.991710i	$-0.458985\pi$
$347$	19.5890	−	11.3097i	1.05159	−	0.607136i	0.923094	+	0.384574i	$0.125651\pi$
$348$	3.44200	−	3.57161i	0.184510	−	0.191458i
$349$		−	2.48180i		−	0.132848i	−0.997791	−	0.0664239i	$-0.978841\pi$
$349$		−	2.48180i		−	0.132848i	0.997791	−	0.0664239i	$-0.0211590\pi$
$350$	8.51126	−	12.6337i	0.454946	−	0.675301i
$351$			3.75117i			0.200223i
$352$	13.1806	+	28.0780i	0.702530	+	1.49656i
$353$	−7.89315	+	4.55711i	−0.420110	+	0.242551i	−0.695124	−	0.718889i	$-0.744651\pi$
$353$	−7.89315	+	4.55711i	−0.420110	+	0.242551i	0.275014	+	0.961440i	$0.411317\pi$
$354$	7.01862	+	16.5113i	0.373036	+	0.877566i
$355$	−4.87458	+	8.44303i	−0.258716	+	0.448109i
$356$	0.267131	−	1.07610i	0.0141579	−	0.0570331i
$357$	−1.52328	+	0.989336i	−0.0806207	+	0.0523612i
$358$	0.445241	−	3.64162i	0.0235317	−	0.192466i
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$	2.69157	−	0.430544i	0.141858	−	0.0226916i
$361$	−2.41780	−	4.18776i	−0.127253	−	0.220408i
$362$	−10.7716	−	8.10834i	−0.566143	−	0.426165i
$363$	−19.0657			−1.00069
$364$	−3.76653	+	19.4887i	−0.197420	+	1.02148i
$365$	−6.41917			−0.335995
$366$	−11.7643	−	8.85562i	−0.614932	−	0.462891i
$367$	1.91680	+	3.31999i	0.100056	+	0.173302i	0.911707	−	0.410840i	$-0.134765\pi$
$367$	1.91680	+	3.31999i	0.100056	+	0.173302i	−0.811652	+	0.584142i	$0.801431\pi$
$368$	4.96021	−	0.183391i	0.258569	−	0.00955992i
$369$	8.16641	+	4.71488i	0.425126	+	0.245447i
$370$	0.452022	−	3.69708i	0.0234995	−	0.192202i
$371$	−10.8199	+	0.567567i	−0.561740	+	0.0294666i
$372$	9.37160	+	2.32641i	0.485895	+	0.120619i
$373$	13.4150	−	23.2355i	0.694603	−	1.20309i	−0.275711	−	0.961241i	$-0.588913\pi$
$373$	13.4150	−	23.2355i	0.694603	−	1.20309i	0.970314	−	0.241848i	$-0.0777534\pi$
$374$	2.08260	+	4.89932i	0.107689	+	0.253338i
$375$	−7.57086	+	4.37104i	−0.390957	+	0.225719i
$376$	7.93633	−	6.44693i	0.409285	−	0.332475i
$377$		−	9.30330i		−	0.479144i
$378$	1.64212	+	3.36206i	0.0844615	+	0.172926i
$379$			6.93692i			0.356325i	0.984001	+	0.178163i	$0.0570153\pi$
$379$			6.93692i			0.356325i	−0.984001	+	0.178163i	$0.942985\pi$
$380$	6.77568	+	6.52980i	0.347585	+	0.334972i
$381$	−10.0832	+	5.82154i	−0.516578	+	0.298247i
$382$	−10.8451	+	4.61004i	−0.554885	+	0.235870i
$383$	−1.12881	+	1.95515i	−0.0576793	+	0.0999035i	−0.893423	−	0.449216i	$-0.851703\pi$
$383$	−1.12881	+	1.95515i	−0.0576793	+	0.0999035i	0.835744	+	0.549119i	$0.185037\pi$
$384$	−7.45303	−	8.51189i	−0.380336	−	0.434371i
$385$	−6.34654	+	12.4573i	−0.323450	+	0.634881i
$386$	17.3682	+	2.12351i	0.884017	+	0.108084i
$387$	−5.17396	−	2.98718i	−0.263007	−	0.151847i
$388$	20.9008	−	6.01639i	1.06108	−	0.305436i
$389$	−15.3047	−	26.5086i	−0.775981	−	1.34404i	−0.934242	−	0.356641i	$-0.883922\pi$
$389$	−15.3047	−	26.5086i	−0.775981	−	1.34404i	0.158261	−	0.987397i	$-0.449411\pi$
$390$	3.07465	−	4.08455i	0.155691	−	0.206829i
$391$	0.851904			0.0430827
$392$	5.15558	+	19.1160i	0.260396	+	0.965502i
$393$	−9.26156			−0.467184
$394$	2.75300	−	3.65726i	0.138694	−	0.184250i
$395$	0.681544	+	1.18047i	0.0342922	+	0.0593958i
$396$	10.5385	−	3.03356i	0.529580	−	0.152442i
$397$	−12.0368	−	6.94947i	−0.604112	−	0.348784i	0.166546	−	0.986034i	$-0.446739\pi$
$397$	−12.0368	−	6.94947i	−0.604112	−	0.348784i	−0.770657	+	0.637250i	$0.780072\pi$
$398$	26.9944	+	3.30046i	1.35311	+	0.165437i
$399$	−5.86365	+	11.5094i	−0.293550	+	0.576192i
$400$	14.3945	+	7.61589i	0.719724	+	0.380794i
$401$	5.13832	−	8.89984i	0.256596	−	0.444437i	−0.708732	−	0.705478i	$-0.750732\pi$
$401$	5.13832	−	8.89984i	0.256596	−	0.444437i	0.965328	+	0.261041i	$0.0840658\pi$
$402$	−12.2842	+	5.22178i	−0.612682	+	0.260439i
$403$	15.6843	−	9.05535i	0.781292	−	0.451079i
$404$	−20.7815	−	20.0273i	−1.03392	−	0.996396i
$405$		−	0.963711i		−	0.0478872i
$406$	−4.07263	−	8.33827i	−0.202121	−	0.413821i
$407$		−	14.9849i		−	0.742775i
$408$	−1.22432	−	1.50716i	−0.0606127	−	0.0746157i
$409$	10.5342	−	6.08193i	0.520883	−	0.300732i	−0.216413	−	0.976302i	$-0.569436\pi$
$409$	10.5342	−	6.08193i	0.520883	−	0.300732i	0.737296	+	0.675570i	$0.236102\pi$
$410$	−5.02764	−	11.8275i	−0.248297	−	0.584120i
$411$	−3.61504	+	6.26144i	−0.178317	+	0.308854i
$412$	−29.1642	−	7.23973i	−1.43682	−	0.356676i
$413$	33.5187	−	1.75826i	1.64935	−	0.0865182i
$414$	0.212976	−	1.74193i	0.0104672	−	0.0856111i
$415$	0.453838	+	0.262023i	0.0222780	+	0.0128622i
$416$	−21.1437	−	1.79528i	−1.03666	−	0.0880209i
$417$	2.65406	+	4.59697i	0.129970	+	0.225115i
$418$	30.2468	+	22.7683i	1.47942	+	1.11364i
$419$	−16.2245			−0.792619			−0.396310	−	0.918117i	$-0.629709\pi$
$419$	−16.2245			−0.792619			−0.396310	+	0.918117i	$0.629709\pi$
$420$	0.967657	−	5.00683i	0.0472168	−	0.244308i
$421$	−9.58477			−0.467133			−0.233567	−	0.972341i	$-0.575040\pi$
$421$	−9.58477			−0.467133			−0.233567	+	0.972341i	$0.575040\pi$
$422$	10.4473	+	7.86419i	0.508565	+	0.382823i
$423$	−1.80752	−	3.13072i	−0.0878847	−	0.152221i
$424$	−1.82953	−	11.4374i	−0.0888499	−	0.555451i
$425$	2.42055	+	1.39750i	0.117414	+	0.0677889i
$426$	1.73626	−	14.2008i	0.0841220	−	0.688032i
$427$	−23.1027	+	15.0047i	−1.11802	+	0.726127i
$428$	5.83799	−	23.5175i	0.282190	−	1.13676i
$429$	10.2842	−	17.8128i	0.496528	−	0.860011i
$430$	3.18534	+	7.49351i	0.153611	+	0.361369i
$431$	0.131544	−	0.0759470i	0.00633626	−	0.00365824i	−0.496829	−	0.867849i	$-0.665502\pi$
$431$	0.131544	−	0.0759470i	0.00633626	−	0.00365824i	0.503165	+	0.864190i	$0.332169\pi$
$432$	−3.38784	+	2.12662i	−0.162998	+	0.102317i
$433$		−	9.46997i		−	0.455098i	−0.973767	−	0.227549i	$-0.926929\pi$
$433$		−	9.46997i		−	0.455098i	0.973767	−	0.227549i	$-0.0730711\pi$
$434$	10.0933	−	14.9820i	0.484494	−	0.719161i
$435$			2.39011i			0.114597i
$436$	8.42595	−	8.74324i	0.403530	−	0.418725i
$437$	5.24663	−	3.02915i	0.250981	−	0.144904i
$438$	8.66920	−	3.68510i	0.414230	−	0.176081i
$439$	16.7373	−	28.9898i	0.798826	−	1.38361i	−0.121555	−	0.992585i	$-0.538788\pi$
$439$	16.7373	−	28.9898i	0.798826	−	1.38361i	0.920381	−	0.391023i	$-0.127879\pi$
$440$	−13.9616	−	5.33475i	−0.665592	−	0.254324i
$441$	6.96158	−	0.732369i	0.331504	−	0.0348747i
$442$	−3.61504	−	0.441992i	−0.171950	−	0.0210234i
$443$	22.6513	+	13.0777i	1.07619	+	0.621341i	0.929867	−	0.367895i	$-0.119921\pi$
$443$	22.6513	+	13.0777i	1.07619	+	0.621341i	0.146327	+	0.989236i	$0.453255\pi$
$444$	1.51194	+	5.25246i	0.0717537	+	0.249271i
$445$	0.267131	+	0.462684i	0.0126632	+	0.0219333i
$446$	−1.65497	+	2.19857i	−0.0783652	+	0.104105i
$447$	4.66161			0.220486
$448$	−19.7364	+	7.64686i	−0.932457	+	0.361280i
$449$	10.2918			0.485701			0.242851	−	0.970064i	$-0.421918\pi$
$449$	10.2918			0.485701			0.242851	+	0.970064i	$0.421918\pi$
$450$	3.46267	−	4.60002i	0.163232	−	0.216847i
$451$	−25.8527	−	44.7782i	−1.21736	−	2.10852i
$452$	4.08260	+	14.1829i	0.192029	+	0.667106i
$453$	10.5709	+	6.10309i	0.496662	+	0.286748i
$454$	−12.1359	−	1.48380i	−0.569568	−	0.0696380i
$455$	−5.20959	−	8.02121i	−0.244229	−	0.376040i
$456$	−12.8993	−	4.92884i	−0.604064	−	0.230814i
$457$	−5.96574	+	10.3330i	−0.279065	+	0.483356i	−0.971153	−	0.238458i	$-0.923358\pi$
$457$	−5.96574	+	10.3330i	−0.279065	+	0.483356i	0.692087	+	0.721814i	$0.256691\pi$
$458$	21.8509	−	9.28837i	1.02103	−	0.434017i
$459$	−0.594545	+	0.343260i	−0.0277510	+	0.0160220i
$460$	−1.65968	+	1.72217i	−0.0773829	+	0.0802968i
$461$			30.0093i			1.39767i	0.715281	+	0.698837i	$0.246299\pi$
$461$			30.0093i			1.39767i	−0.715281	+	0.698837i	$0.753701\pi$
$462$	1.41968	−	20.4671i	0.0660494	−	0.952218i
$463$		−	13.2736i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$463$		−	13.2736i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$464$	8.40221	−	5.27425i	0.390063	−	0.244851i
$465$	−4.02945	+	2.32641i	−0.186861	+	0.107885i
$466$	−0.579007	−	1.36211i	−0.0268220	−	0.0630987i
$467$	−14.8246	+	25.6770i	−0.686002	+	1.18819i	0.287119	+	0.957895i	$0.407303\pi$
$467$	−14.8246	+	25.6770i	−0.686002	+	1.18819i	−0.973121	+	0.230295i	$0.926031\pi$
$468$	−1.80752	+	7.28134i	−0.0835527	+	0.336580i
$469$	1.30812	+	24.9376i	0.0604036	+	1.15151i
$470$	−0.597935	+	4.89050i	−0.0275807	+	0.225582i
$471$	18.9944	+	10.9664i	0.875217	+	0.505307i
$472$	5.66768	+	35.4318i	0.260876	+	1.63088i
$473$	16.3794	+	28.3699i	0.753125	+	1.30445i
$474$	−1.59812	−	1.20298i	−0.0734039	−	0.0552549i
$475$	19.8766			0.912001
$476$	−3.43354	+	1.18638i	−0.157376	+	0.0543778i
$477$	−4.09515			−0.187504
$478$	−21.7478	−	16.3707i	−0.994721	−	0.748777i
$479$	5.76773	+	9.99001i	0.263535	+	0.456455i	0.967179	−	0.254097i	$-0.0817784\pi$
$479$	5.76773	+	9.99001i	0.263535	+	0.456455i	−0.703644	+	0.710553i	$0.748445\pi$
$480$	5.43203	+	0.461225i	0.247937	+	0.0210519i
$481$	8.87802	+	5.12573i	0.404803	+	0.233713i
$482$	−0.473165	+	3.87001i	−0.0215521	+	0.176274i
$483$	−2.92535	−	1.49036i	−0.133108	−	0.0678138i
$484$	−37.0081	−	9.18691i	−1.68219	−	0.417587i
$485$	−5.24005	+	9.07604i	−0.237939	+	0.412122i
$486$	0.553244	+	1.30151i	0.0250957	+	0.0590376i
$487$	8.44822	−	4.87758i	0.382825	−	0.221024i	−0.296221	−	0.955119i	$-0.595727\pi$
$487$	8.44822	−	4.87758i	0.382825	−	0.221024i	0.679047	+	0.734095i	$0.262393\pi$
$488$	−18.5685	−	22.8582i	−0.840555	−	1.03474i
$489$		−	4.01848i		−	0.181722i
$490$	−8.18058	−	4.90862i	−0.369561	−	0.221749i
$491$			40.4736i			1.82655i	0.407346	+	0.913274i	$0.366454\pi$
$491$			40.4736i			1.82655i	−0.407346	+	0.913274i	$0.633546\pi$
$492$	13.5798	+	13.0870i	0.612225	+	0.590008i
$493$	1.47453	−	0.851323i	0.0664097	−	0.0383416i
$494$	−23.8356	+	10.1320i	−1.07241	+	0.455861i
$495$	−2.64212	+	4.57628i	−0.118754	+	0.205689i
$496$	17.0701	+	9.03151i	0.766470	+	0.405527i
$497$	−23.8485	−	12.1500i	−1.06975	−	0.545001i
$498$	−0.763337	−	0.0933291i	−0.0342059	−	0.00418218i
$499$	27.6827	+	15.9826i	1.23925	+	0.715480i	0.968941	−	0.247294i	$-0.0795413\pi$
$499$	27.6827	+	15.9826i	1.23925	+	0.715480i	0.270307	+	0.962774i	$0.412875\pi$
$500$	−16.8019	+	4.83650i	−0.751404	+	0.216295i
$501$	7.35889	+	12.7460i	0.328771	+	0.569448i
$502$	17.6476	−	23.4441i	0.787650	−	1.04636i
$503$	−22.7110			−1.01263			−0.506317	−	0.862348i	$-0.668993\pi$
$503$	−22.7110			−1.01263			−0.506317	+	0.862348i	$0.668993\pi$
$504$	1.56747	+	7.31731i	0.0698205	+	0.325939i
$505$	13.9069			0.618847
$506$	−5.78702	+	7.68783i	−0.257265	+	0.341766i
$507$	0.535631	+	0.927740i	0.0237882	+	0.0412024i
$508$	−22.3775	+	6.44147i	−0.992841	+	0.285794i
$509$	−1.98947	−	1.14862i	−0.0881819	−	0.0509118i	0.455261	−	0.890358i	$-0.349546\pi$
$509$	−1.98947	−	1.14862i	−0.0881819	−	0.0509118i	−0.543443	+	0.839446i	$0.682879\pi$
$510$	0.928739	+	0.113552i	0.0411252	+	0.00502816i
$511$	−0.923166	−	17.5989i	−0.0408384	−	0.778528i
$512$	−10.3655	−	20.1136i	−0.458093	−	0.888904i
$513$	−2.44109	+	4.22809i	−0.107777	+	0.186675i
$514$	9.69764	−	4.12227i	0.427745	−	0.181825i
$515$	12.5396	−	7.23973i	0.552560	−	0.319021i
$516$	−8.60370	−	8.29148i	−0.378757	−	0.365012i
$517$			19.8221i			0.871773i
$518$	10.2009	+	0.707576i	0.448204	+	0.0310891i
$519$			11.6530i			0.511508i
$520$	7.93633	−	6.44693i	0.348031	−	0.282717i
$521$	−32.5712	+	18.8050i	−1.42697	+	0.823862i	−0.996881	−	0.0789240i	$-0.974852\pi$
$521$	−32.5712	+	18.8050i	−1.42697	+	0.823862i	−0.430090	+	0.902786i	$0.641518\pi$
$522$	−1.37210	−	3.22788i	−0.0600554	−	0.141280i
$523$	17.8444	−	30.9073i	0.780279	−	1.35148i	−0.151500	−	0.988457i	$-0.548410\pi$
$523$	17.8444	−	30.9073i	0.780279	−	1.35148i	0.931779	−	0.363026i	$-0.118256\pi$
$524$	−17.9775	−	4.46273i	−0.785350	−	0.194955i
$525$	−5.86704	−	9.03350i	−0.256059	−	0.394254i
$526$	−5.09394	+	41.6632i	−0.222106	+	1.81660i
$527$	2.87047	+	1.65727i	0.125040	+	0.0721917i
$528$	21.9179	−	0.810357i	0.953854	−	0.0352663i
$529$	−10.7301	−	18.5850i	−0.466525	−	0.808046i
$530$	4.45910	+	3.35660i	0.193691	+	0.145801i
$531$	12.6863			0.550539
$532$	−16.9277	+	19.5154i	−0.733910	+	0.846098i
$533$	35.3726			1.53216
$534$	−0.626381	−	0.471509i	−0.0271062	−	0.0204042i
$535$	5.83799	+	10.1117i	0.252398	+	0.437167i
$536$	−26.3609	+	4.21669i	−1.13862	+	0.182133i
$537$	−2.24663	−	1.29709i	−0.0969494	−	0.0559738i
$538$	−0.740657	+	6.05782i	−0.0319320	+	0.261171i
$539$	−35.0657	−	15.6082i	−1.51039	−	0.672293i
$540$	0.464369	−	1.87065i	0.0199833	−	0.0804998i
$541$	−18.5102	+	32.0605i	−0.795814	+	1.37839i	0.126507	+	0.991966i	$0.459623\pi$
$541$	−18.5102	+	32.0605i	−0.795814	+	1.37839i	−0.922321	+	0.386425i	$0.873710\pi$
$542$	7.51463	+	17.6782i	0.322781	+	0.759342i
$543$	−8.25620	+	4.76672i	−0.354307	+	0.204559i
$544$	−1.65027	−	3.51548i	−0.0707547	−	0.150725i
$545$			5.85094i			0.250627i
$546$	11.6404	+	7.84208i	0.498164	+	0.335610i
$547$			2.09106i			0.0894073i	0.999000	+	0.0447036i	$0.0142344\pi$
$547$			2.09106i			0.0894073i	−0.999000	+	0.0447036i	$0.985766\pi$
$548$	−10.0342	+	10.4121i	−0.428640	+	0.444781i
$549$	−9.01711	+	5.20603i	−0.384841	+	0.222188i
$550$	−29.0543	+	12.3504i	−1.23888	+	0.526623i
$551$	6.05415	−	10.4861i	0.257916	−	0.446723i
$552$	1.25276	−	3.27861i	0.0533211	−	0.139547i
$553$	−3.13837	+	2.03829i	−0.133457	+	0.0866771i
$554$	−2.90755	−	0.355491i	−0.123530	−	0.0151034i
$555$	−2.28085	−	1.31685i	−0.0968166	−	0.0558971i
$556$	2.93669	+	10.2020i	0.124543	+	0.432661i
$557$	8.39887	+	14.5473i	0.355872	+	0.616388i	0.987267	−	0.159073i	$-0.0508507\pi$
$557$	8.39887	+	14.5473i	0.355872	+	0.616388i	−0.631395	+	0.775461i	$0.717517\pi$
$558$	4.10631	−	5.45507i	0.173834	−	0.230931i
$559$	−22.4109			−0.947878
$560$	4.29087	−	9.25241i	0.181322	−	0.390986i
$561$	3.76434			0.158931
$562$	20.1676	−	26.7919i	0.850720	−	1.13015i
$563$	−8.69784	−	15.0651i	−0.366570	−	0.634918i	0.622456	−	0.782654i	$-0.286135\pi$
$563$	−8.69784	−	15.0651i	−0.366570	−	0.634918i	−0.989027	+	0.147736i	$0.952801\pi$
$564$	−2.00000	−	6.94796i	−0.0842152	−	0.292562i
$565$	−6.15882	−	3.55580i	−0.259104	−	0.149594i
$566$	17.2028	+	2.10329i	0.723086	+	0.0884079i
$567$	2.64212	−	0.138595i	0.110959	−	0.00582044i
$568$	10.2130	−	26.7284i	0.428527	−	1.12150i
$569$	17.1425	−	29.6917i	0.718652	−	1.24474i	−0.242882	−	0.970056i	$-0.578093\pi$
$569$	17.1425	−	29.6917i	0.718652	−	1.24474i	0.961534	−	0.274686i	$-0.0885739\pi$
$570$	6.12359	−	2.60301i	0.256489	−	0.109028i
$571$	−5.14176	+	2.96860i	−0.215176	+	0.124232i	−0.603715	−	0.797201i	$-0.706313\pi$
$571$	−5.14176	+	2.96860i	−0.215176	+	0.124232i	0.388539	+	0.921432i	$0.372980\pi$
$572$	28.5458	−	29.6207i	1.19356	−	1.23850i
$573$			8.33274i			0.348105i
$574$	31.7034	−	15.4848i	1.32327	−	0.646322i
$575$			5.05203i			0.210684i
$576$	−7.60082	+	2.49551i	−0.316701	+	0.103980i
$577$	33.7930	−	19.5104i	1.40682	−	0.812229i	0.411742	−	0.911300i	$-0.364920\pi$
$577$	33.7930	−	19.5104i	1.40682	−	0.812229i	0.995080	+	0.0990712i	$0.0315871\pi$
$578$	9.14440	+	21.5122i	0.380357	+	0.894790i
$579$	6.18630	−	10.7150i	0.257094	−	0.445300i
$580$	−1.15169	+	4.63940i	−0.0478211	+	0.192641i
$581$	−0.653097	+	1.28193i	−0.0270950	+	0.0531833i
$582$	1.86643	−	15.2655i	0.0773662	−	0.632777i
$583$	19.4462	+	11.2273i	0.805381	+	0.464987i
$584$	18.6033	−	2.97579i	0.769812	−	0.123139i
$585$	−1.80752	−	3.13072i	−0.0747318	−	0.129439i
$586$	−12.0999	−	9.10818i	−0.499840	−	0.376255i
$587$	7.71931			0.318610			0.159305	−	0.987229i	$-0.449075\pi$
$587$	7.71931			0.318610			0.159305	+	0.987229i	$0.449075\pi$
$588$	13.8659	+	1.93289i	0.571821	+	0.0797109i
$589$	23.5712			0.971235
$590$	−13.8138	−	10.3984i	−0.568705	−	0.428093i
$591$	−1.61843	−	2.80321i	−0.0665734	−	0.115308i
$592$	0.403887	+	10.9240i	0.0165996	+	0.448974i
$593$	0.336377	+	0.194207i	0.0138133	+	0.00797513i	0.506891	−	0.862010i	$-0.330795\pi$
$593$	0.336377	+	0.194207i	0.0138133	+	0.00797513i	−0.493077	+	0.869985i	$0.664128\pi$
$594$	0.941086	−	7.69713i	0.0386132	−	0.315817i
$595$	0.794612	−	1.55970i	0.0325759	−	0.0639415i
$596$	9.04858	+	2.24622i	0.370644	+	0.0920088i
$597$	9.61504	−	16.6537i	0.393517	−	0.681592i
$598$	−2.57526	−	6.05829i	−0.105310	−	0.247742i
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	−0.820416	−	0.571767i	$-0.806258\pi$
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	0.0849563	+	0.996385i	$0.472925\pi$
$600$	8.93790	−	7.26054i	0.364888	−	0.296410i
$601$		−	26.4110i		−	1.07733i	−0.842521	−	0.538664i	$-0.818929\pi$
$601$		−	26.4110i		−	1.07733i	0.842521	−	0.538664i	$-0.181071\pi$
$602$	−20.0862	+	9.81062i	−0.818652	+	0.399851i
$603$			9.43847i			0.384364i
$604$	17.5781	+	16.9402i	0.715244	+	0.689289i
$605$	15.9122	−	9.18691i	0.646922	−	0.373501i
$606$	−18.7815	+	7.98361i	−0.762944	+	0.324312i
$607$	−20.3531	+	35.2526i	−0.826106	+	1.43086i	0.0749655	+	0.997186i	$0.476115\pi$
$607$	−20.3531	+	35.2526i	−0.826106	+	1.43086i	−0.901071	+	0.433671i	$0.857218\pi$
$608$	−22.6636	−	15.7829i	−0.919131	−	0.640081i
$609$	−6.55274	+	0.343730i	−0.265530	+	0.0139287i
$610$	14.0856	+	1.72217i	0.570310	+	0.0697288i
$611$	−11.7438	−	6.78031i	−0.475105	−	0.274302i
$612$	−1.31946	+	0.379814i	−0.0533362	+	0.0153531i
$613$	−8.66920	−	15.0155i	−0.350146	−	0.606470i	0.636129	−	0.771583i	$-0.280535\pi$
$613$	−8.66920	−	15.0155i	−0.350146	−	0.606470i	−0.986275	+	0.165113i	$0.947201\pi$
$614$	−3.58966	+	4.76872i	−0.144867	+	0.192450i
$615$	−9.08756			−0.366446
$616$	12.6179	−	39.0444i	0.508391	−	1.57314i
$617$	−46.4753			−1.87103			−0.935513	−	0.353291i	$-0.885062\pi$
$617$	−46.4753			−1.87103			−0.935513	+	0.353291i	$0.885062\pi$
$618$	−12.7787	+	16.9761i	−0.514037	+	0.682877i
$619$	−13.1911	−	22.8476i	−0.530194	−	0.918322i	−0.999379	−	0.0352227i	$-0.988786\pi$
$619$	−13.1911	−	22.8476i	−0.530194	−	0.918322i	0.469186	−	0.883099i	$-0.344547\pi$
$620$	−8.94251	+	2.57414i	−0.359140	+	0.103380i
$621$	−1.07465	−	0.620450i	−0.0431243	−	0.0248978i
$622$	13.6184	+	1.66505i	0.546049	+	0.0667625i
$623$	−1.23008	+	0.798909i	−0.0492822	+	0.0320076i
$624$	−7.01711	+	13.2627i	−0.280909	+	0.530935i
$625$	−5.96574	+	10.3330i	−0.238630	+	0.413318i
$626$	17.7830	−	7.55917i	0.710750	−	0.302125i
$627$	23.1835	−	13.3850i	0.925860	−	0.534546i
$628$	31.5856	+	30.4394i	1.26040	+	1.21466i
$629$			1.87617i			0.0748079i
$630$	−2.99054	−	2.01470i	−0.119146	−	0.0802678i
$631$			41.0696i			1.63495i	0.575961	+	0.817477i	$0.304628\pi$
$631$			41.0696i			1.63495i	−0.575961	+	0.817477i	$0.695372\pi$
$632$	−2.52242	−	3.10515i	−0.100336	−	0.123516i
$633$	8.00759	−	4.62318i	0.318273	−	0.183755i
$634$	11.1138	+	26.1452i	0.441384	+	1.03836i
$635$	5.61028	−	9.71729i	0.222637	−	0.385619i
$636$	−7.94904	−	1.97327i	−0.315200	−	0.0782452i
$637$	21.2418	−	15.4362i	0.841632	−	0.611605i
$638$	−2.33399	+	19.0897i	−0.0924037	+	0.755768i
$639$	−8.76095	−	5.05814i	−0.346578	−	0.200097i
$640$	10.3218	+	3.51273i	0.408004	+	0.138853i
$641$	−22.7239	−	39.3590i	−0.897540	−	1.55459i	−0.830629	−	0.556827i	$-0.812019\pi$
$641$	−22.7239	−	39.3590i	−0.897540	−	1.55459i	−0.0669115	−	0.997759i	$-0.521315\pi$
$642$	−13.6892	−	10.3046i	−0.540269	−	0.406688i
$643$	30.5534			1.20491			0.602454	−	0.798154i	$-0.294190\pi$
$643$	30.5534			1.20491			0.602454	+	0.798154i	$0.294190\pi$
$644$	−4.96021	−	4.30252i	−0.195460	−	0.169543i
$645$	5.75756			0.226704
$646$	−3.78702	−	2.85069i	−0.148998	−	0.112159i
$647$	−18.0896	−	31.3321i	−0.711175	−	1.23179i	−0.964417	−	0.264388i	$-0.914830\pi$
$647$	−18.0896	−	31.3321i	−0.711175	−	1.23179i	0.253242	−	0.967403i	$-0.418503\pi$
$648$	0.446756	+	2.79292i	0.0175502	+	0.109716i
$649$	−60.2423	−	34.7809i	−2.36472	−	1.36527i
$650$	2.62113	−	21.4382i	0.102809	−	0.840876i
$651$	−6.95759	−	10.7126i	−0.272689	−	0.419861i
$652$	1.93633	−	7.80022i	0.0758324	−	0.305480i
$653$	4.11545	−	7.12816i	0.161050	−	0.278946i	−0.774196	−	0.632946i	$-0.781845\pi$
$653$	4.11545	−	7.12816i	0.161050	−	0.278946i	0.935245	+	0.354000i	$0.115179\pi$
$654$	−3.35889	−	7.90179i	−0.131343	−	0.308984i
$655$	7.72968	−	4.46273i	0.302024	−	0.174373i
$656$	20.0535	+	31.9465i	0.782959	+	1.24730i
$657$		−	6.66089i		−	0.259866i
$658$	−13.4938	−	0.935982i	−0.526044	−	0.0364884i
$659$			22.8837i			0.891422i	0.895177	+	0.445711i	$0.147049\pi$
$659$			22.8837i			0.891422i	−0.895177	+	0.445711i	$0.852951\pi$
$660$	−7.33369	+	7.60984i	−0.285463	+	0.296213i
$661$	−17.7212	+	10.2313i	−0.689275	+	0.397953i	−0.803340	−	0.595520i	$-0.796946\pi$
$661$	−17.7212	+	10.2313i	−0.689275	+	0.397953i	0.114065	+	0.993473i	$0.463613\pi$
$662$	−12.2616	+	5.21214i	−0.476559	+	0.202575i
$663$	−1.28763	+	2.23024i	−0.0500073	+	0.0866152i
$664$	−1.43673	−	0.548978i	−0.0557560	−	0.0213045i
$665$	−0.652090	−	12.4312i	−0.0252870	−	0.482060i
$666$	3.83629	+	0.469043i	0.148653	+	0.0181750i
$667$	2.66525	+	1.53878i	0.103199	+	0.0595819i
$668$	8.14252	+	28.2869i	0.315044	+	1.09445i
$669$	0.972923	+	1.68515i	0.0376154	+	0.0651517i
$670$	7.73626	−	10.2773i	0.298878	−	0.397047i
$671$	57.0916			2.20400
$672$	−0.483297	+	14.9588i	−0.0186436	+	0.577049i
$673$	4.23008			0.163058			0.0815289	−	0.996671i	$-0.474020\pi$
$673$	4.23008			0.163058			0.0815289	+	0.996671i	$0.474020\pi$
$674$	−11.4319	+	15.1868i	−0.440340	+	0.584975i
$675$	−2.03563	−	3.52582i	−0.0783515	−	0.135709i
$676$	0.592669	+	2.05892i	0.0227950	+	0.0791892i
$677$	20.7962	+	12.0067i	0.799262	+	0.461454i	0.843213	−	0.537580i	$-0.180661\pi$
$677$	20.7962	+	12.0067i	0.799262	+	0.461454i	−0.0439511	+	0.999034i	$0.513995\pi$
$678$	10.3589	+	1.26653i	0.397831	+	0.0486406i
$679$	−25.6365	−	13.0609i	−0.983840	−	0.501232i
$680$	1.74805	+	0.667932i	0.0670345	+	0.0256140i
$681$	−4.32265	+	7.48706i	−0.165644	+	0.286905i
$682$	−34.4549	+	14.6461i	−1.31935	+	0.560827i
$683$	7.09951	−	4.09890i	0.271655	−	0.156840i	−0.357984	−	0.933728i	$-0.616536\pi$
$683$	7.09951	−	4.09890i	0.271655	−	0.156840i	0.629640	+	0.776887i	$0.283203\pi$
$684$	−6.77568	+	7.03083i	−0.259075	+	0.268830i
$685$		−	6.96771i		−	0.266222i
$686$	12.2810	−	23.1339i	0.468892	−	0.883256i
$687$		−	16.7889i		−	0.640537i
$688$	−12.7052	−	20.2402i	−0.484382	−	0.771651i
$689$	−13.3035	+	7.68079i	−0.506824	+	0.292615i
$690$	0.661608	+	1.55643i	0.0251870	+	0.0592524i
$691$	−17.9925	+	31.1638i	−0.684465	+	1.18553i	0.289139	+	0.957287i	$0.406631\pi$
$691$	−17.9925	+	31.1638i	−0.684465	+	1.18553i	−0.973605	+	0.228242i	$0.926702\pi$
$692$	−5.61504	+	22.6194i	−0.213452	+	0.859860i
$693$	−12.9264	−	6.58552i	−0.491032	−	0.250163i
$694$	3.88217	−	31.7522i	0.147365	−	1.20530i
$695$	−4.43015	−	2.55775i	−0.168045	−	0.0970209i
$696$	−1.10800	−	6.92674i	−0.0419987	−	0.262558i
$697$	3.23686	+	5.60641i	0.122605	+	0.212358i
$698$	−2.80413	−	2.11081i	−0.106138	−	0.0798954i
$699$	−1.04657			−0.0395848
$700$	−7.03559	−	20.3619i	−0.265920	−	0.769606i
$701$	−12.9471			−0.489003			−0.244502	−	0.969649i	$-0.578624\pi$
$701$	−12.9471			−0.489003			−0.244502	+	0.969649i	$0.578624\pi$
$702$	4.23836	+	3.19043i	0.159967	+	0.120415i
$703$	6.67117	+	11.5548i	0.251608	+	0.435798i
$704$	42.9350	+	8.98829i	1.61817	+	0.338759i
$705$	3.01711	+	1.74193i	0.113631	+	0.0656048i
$706$	−1.56428	+	12.7942i	−0.0588723	+	0.481516i
$707$	2.00000	+	38.1272i	0.0752177	+	1.43392i
$708$	24.6252	+	6.11296i	0.925472	+	0.229739i
$709$	−6.65603	+	11.5286i	−0.249973	+	0.432965i	−0.963518	−	0.267644i	$-0.913755\pi$
$709$	−6.65603	+	11.5286i	−0.249973	+	0.432965i	0.713545	+	0.700609i	$0.247088\pi$
$710$	5.39367	+	12.6886i	0.202421	+	0.476195i
$711$	−1.22492	+	0.707208i	−0.0459381	+	0.0265224i
$712$	−0.988660	−	1.21706i	−0.0370516	−	0.0456114i
$713$			5.99109i			0.224368i
$714$	−0.177749	+	2.56257i	−0.00665211	+	0.0959017i
$715$			19.8221i			0.741303i
$716$	−3.73590	−	3.60033i	−0.139617	−	0.134550i
$717$	−16.6692	+	9.62396i	−0.622523	+	0.359414i
$718$	9.01711	−	3.83299i	0.336515	−	0.143046i
$719$	23.7520	−	41.1397i	0.885800	−	1.53425i	0.0410056	−	0.999159i	$-0.486944\pi$
$719$	23.7520	−	41.1397i	0.885800	−	1.53425i	0.844794	−	0.535091i	$-0.179723\pi$
$720$	1.80276	−	3.40733i	0.0671850	−	0.126984i
$721$	21.6519	+	33.3375i	0.806358	+	1.24155i
$722$	−6.78803	−	0.829936i	−0.252624	−	0.0308870i
$723$	2.38754	+	1.37844i	0.0887934	+	0.0512649i
$724$	−18.3229	+	5.27431i	−0.680964	+	0.196018i
$725$	5.04858	+	8.74440i	0.187500	+	0.324759i
$726$	−16.2157	+	21.5419i	−0.601820	+	0.799494i
$727$	−24.3567			−0.903340			−0.451670	−	0.892185i	$-0.649172\pi$
$727$	−24.3567			−0.903340			−0.451670	+	0.892185i	$0.649172\pi$
$728$	18.8163	+	20.8312i	0.697379	+	0.772054i
$729$	1.00000			0.0370370
$730$	−5.45961	+	7.25287i	−0.202069	+	0.268441i
$731$	−2.05076	−	3.55203i	−0.0758503	−	0.131377i
$732$	−20.0115	+	5.76041i	−0.739648	+	0.212911i
$733$	3.35812	+	1.93881i	0.124035	+	0.0716117i	0.560734	−	0.827996i	$-0.310519\pi$
$733$	3.35812	+	1.93881i	0.124035	+	0.0716117i	−0.436699	+	0.899608i	$0.643852\pi$
$734$	5.38144	+	0.657960i	0.198633	+	0.0242857i
$735$	−5.45723	+	3.96571i	−0.201293	+	0.146277i
$736$	4.01153	−	5.76041i	0.147867	−	0.212331i
$737$	25.8766	−	44.8196i	0.953177	−	1.65095i
$738$	12.2729	−	5.21696i	0.451772	−	0.192039i
$739$	7.46497	−	4.30990i	0.274603	−	0.158542i	−0.356374	−	0.934343i	$-0.615987\pi$
$739$	7.46497	−	4.30990i	0.274603	−	0.158542i	0.630978	+	0.775801i	$0.282654\pi$
$740$	−3.79279	−	3.65515i	−0.139426	−	0.134366i
$741$			18.3138i			0.672776i
$742$	−8.56119	+	12.7078i	−0.314291	+	0.466520i
$743$		−	6.12929i		−	0.224862i	−0.993660	−	0.112431i	$-0.964136\pi$
$743$		−	6.12929i		−	0.224862i	0.993660	−	0.112431i	$-0.0358637\pi$
$744$	10.5992	−	8.61011i	0.388587	−	0.315662i
$745$	−3.89057	+	2.24622i	−0.142539	+	0.0822952i
$746$	−14.8436	−	34.9195i	−0.543461	−	1.27849i
$747$	−0.271890	+	0.470927i	−0.00994793	+	0.0172303i
$748$	7.30692	+	1.81387i	0.267167	+	0.0663216i
$749$	−26.8827	+	17.4597i	−0.982273	+	0.637963i
$750$	−1.50040	+	12.2718i	−0.0547870	+	0.448102i
$751$	−30.7146	−	17.7331i	−1.12079	−	0.647090i	−0.179190	−	0.983815i	$-0.557348\pi$
$751$	−30.7146	−	17.7331i	−1.12079	−	0.647090i	−0.941603	+	0.336725i	$0.890681\pi$
$752$	−0.534262	−	14.4503i	−0.0194825	−	0.526948i
$753$	−10.3746	−	17.9694i	−0.378072	−	0.654841i
$754$	−10.5116	−	7.91261i	−0.382809	−	0.288160i
$755$	−11.7632			−0.428108
$756$	5.19536	+	1.00409i	0.188954	+	0.0365186i
$757$	29.4204			1.06930			0.534651	−	0.845073i	$-0.320443\pi$
$757$	29.4204			1.06930			0.534651	+	0.845073i	$0.320443\pi$
$758$	7.83786	+	5.89996i	0.284684	+	0.214296i
$759$	3.40207	+	5.89255i	0.123487	+	0.213886i
$760$	13.1407	−	2.10199i	0.476663	−	0.0762471i
$761$	43.5568	+	25.1475i	1.57893	+	0.911597i	0.995009	+	0.0997877i	$0.0318164\pi$
$761$	43.5568	+	25.1475i	1.57893	+	0.911597i	0.583923	+	0.811809i	$0.301517\pi$
$762$	−1.99830	+	16.3441i	−0.0723909	+	0.592084i
$763$	−16.0410	+	0.841446i	−0.580723	+	0.0304624i
$764$	−4.01518	+	16.1746i	−0.145264	+	0.585175i
$765$	0.330804	−	0.572969i	0.0119602	−	0.0207157i
$766$	1.24901	+	2.93830i	0.0451286	+	0.106165i
$767$	41.2128	−	23.7942i	1.48811	−	0.859160i
$768$	−15.9563	+	1.18150i	−0.575774	+	0.0426338i
$769$		−	20.2817i		−	0.731377i	−0.930737	−	0.365689i	$-0.880833\pi$
$769$		−	20.2817i		−	0.731377i	0.930737	−	0.365689i	$-0.119167\pi$
$770$	8.67735	+	17.7659i	0.312710	+	0.640239i
$771$		−	7.45109i		−	0.268344i
$772$	17.1712	−	17.8178i	0.618006	−	0.641277i
$773$	−18.8149	+	10.8628i	−0.676723	+	0.390706i	−0.798619	−	0.601836i	$-0.794436\pi$
$773$	−18.8149	+	10.8628i	−0.676723	+	0.390706i	0.121896	+	0.992543i	$0.461103\pi$
$774$	−7.77568	+	3.30528i	−0.279491	+	0.118806i
$775$	−9.82806	+	17.0227i	−0.353034	+	0.611473i
$776$	10.9787	−	28.7324i	0.394112	−	1.03143i
$777$	3.28226	−	6.44257i	0.117751	−	0.231126i
$778$	−42.9684	−	5.25351i	−1.54049	−	0.188347i
$779$	39.8698	+	23.0189i	1.42848	+	0.824736i
$780$	−2.00000	−	6.94796i	−0.0716115	−	0.248777i
$781$	27.7349	+	48.0382i	0.992432	+	1.71894i
$782$	0.724559	−	0.962547i	0.0259102	−	0.0344206i
$783$	−2.48011			−0.0886318
$784$	25.9836	+	10.4333i	0.927985	+	0.372617i
$785$	−21.1369			−0.754410
$786$	−7.87711	+	10.4644i	−0.280967	+	0.373254i
$787$	−0.299328	−	0.518452i	−0.0106699	−	0.0184808i	0.860641	−	0.509212i	$-0.170063\pi$
$787$	−0.299328	−	0.518452i	−0.0106699	−	0.0184808i	−0.871311	+	0.490731i	$0.836730\pi$
$788$	−1.79078	−	6.22111i	−0.0637937	−	0.221618i
$789$	25.7034	+	14.8399i	0.915066	+	0.528313i
$790$	1.91345	+	0.233947i	0.0680774	+	0.00832346i
$791$	8.86288	−	17.3965i	0.315128	−	0.618547i
$792$	5.53563	−	14.4873i	0.196700	−	0.514784i
$793$	−19.5287	+	33.8247i	−0.693484	+	1.20115i
$794$	−18.0896	+	7.68951i	−0.641975	+	0.272890i
$795$	3.41780	−	1.97327i	0.121217	−	0.0699847i
$796$	26.6883	−	27.6933i	0.945942	−	0.981562i
$797$		−	36.1789i		−	1.28152i	−0.767741	−	0.640760i	$-0.778619\pi$
$797$		−	36.1789i		−	1.28152i	0.767741	−	0.640760i	$-0.221381\pi$
$798$	8.01711	+	16.4142i	0.283802	+	0.581055i
$799$		−	2.48180i		−	0.0877998i
$800$	20.8478	−	9.78655i	0.737079	−	0.346007i
$801$	−0.480107	+	0.277190i	−0.0169637	+	0.00979402i
$802$	−5.68549	−	13.3751i	−0.200762	−	0.472292i
$803$	−18.2616	+	31.6299i	−0.644436	+	1.11620i
$804$	−4.54798	+	18.3209i	−0.160395	+	0.646128i
$805$	3.15963	−	0.165741i	0.111362	−	0.00584162i
$806$	3.10834	−	25.4231i	0.109487	−	0.895490i
$807$	3.73727	+	2.15771i	0.131558	+	0.0759551i
$808$	−40.3034	+	6.44693i	−1.41787	+	0.226802i
$809$	15.0603	+	26.0852i	0.529491	+	0.917106i	0.999408	+	0.0343953i	$0.0109505\pi$
$809$	15.0603	+	26.0852i	0.529491	+	0.917106i	−0.469917	+	0.882711i	$0.655716\pi$
$810$	−1.08887	−	0.819652i	−0.0382592	−	0.0287996i
$811$	−21.5947			−0.758292			−0.379146	−	0.925337i	$-0.623782\pi$
$811$	−21.5947			−0.758292			−0.379146	+	0.925337i	$0.623782\pi$
$812$	−12.8851	−	2.49026i	−0.452177	−	0.0873911i
$813$	13.5828			0.476371
$814$	−16.9311	−	12.7449i	−0.593435	−	0.446709i
$815$	1.93633	+	3.35382i	0.0678266	+	0.117479i
$816$	−2.74421	+	0.101460i	−0.0960665	+	0.00355181i
$817$	−25.2601	−	14.5839i	−0.883740	−	0.510228i
$818$	2.08769	−	17.0751i	0.0729942	−	0.597018i
$819$	8.32326	−	5.40576i	0.290838	−	0.188892i
$820$	−17.6397	−	4.37889i	−0.616006	−	0.152917i
$821$	−25.1264	+	43.5202i	−0.876918	+	1.51887i	−0.0222131	+	0.999753i	$0.507071\pi$
$821$	−25.1264	+	43.5202i	−0.876918	+	1.51887i	−0.854705	+	0.519114i	$0.826262\pi$
$822$	4.00000	+	9.41000i	0.139516	+	0.328212i
$823$	−2.87338	+	1.65894i	−0.100160	+	0.0578272i	−0.549243	−	0.835663i	$-0.685084\pi$
$823$	−2.87338	+	1.65894i	−0.100160	+	0.0578272i	0.449084	+	0.893490i	$0.351751\pi$
$824$	−32.9847	+	26.7945i	−1.14907	+	0.933430i
$825$			22.3236i			0.777209i
$826$	26.5216	−	39.3675i	0.922805	−	1.36977i
$827$		−	29.3948i		−	1.02216i	−0.859534	−	0.511078i	$-0.829246\pi$
$827$		−	29.3948i		−	1.02216i	0.859534	−	0.511078i	$-0.170754\pi$
$828$	−1.78702	−	1.72217i	−0.0621034	−	0.0598497i
$829$	28.2980	−	16.3379i	0.982830	−	0.567437i	0.0797067	−	0.996818i	$-0.474602\pi$
$829$	28.2980	−	16.3379i	0.982830	−	0.567437i	0.903123	+	0.429381i	$0.141268\pi$
$830$	0.682050	−	0.289926i	0.0236743	−	0.0100635i
$831$	−1.03563	+	1.79376i	−0.0359256	+	0.0622250i
$832$	−20.0115	+	22.3629i	−0.693775	+	0.775294i
$833$	4.39036	+	1.95421i	0.152117	+	0.0677094i
$834$	7.45133	+	0.911035i	0.258019	+	0.0315465i
$835$	−12.2834	−	7.09184i	−0.425086	−	0.245423i
$836$	51.4508	−	14.8104i	1.77946	−	0.512227i
$837$	−2.41401	−	4.18119i	−0.0834403	−	0.144523i
$838$	−13.7992	+	18.3317i	−0.476686	+	0.633258i
$839$	−8.66161			−0.299032			−0.149516	−	0.988759i	$-0.547772\pi$
$839$	−8.66161			−0.299032			−0.149516	+	0.988759i	$0.547772\pi$
$840$	−4.83409	−	5.35172i	−0.166792	−	0.184652i
$841$	−22.8491			−0.787899
$842$	−8.15201	+	10.8296i	−0.280937	+	0.373213i
$843$	−11.8561	−	20.5354i	−0.408346	−	0.707276i
$844$	17.7711	−	5.11550i	0.611707	−	0.176083i
$845$	−0.894073	−	0.516193i	−0.0307570	−	0.0177576i
$846$	−5.07465	−	0.620450i	−0.174470	−	0.0213315i
$847$	27.4753	+	42.3038i	0.944062	+	1.45358i
$848$	−14.4789	−	7.66057i	−0.497209	−	0.263065i
$849$	6.12739	−	10.6129i	0.210291	−	0.364235i
$850$	3.63772	−	1.54632i	0.124773	−	0.0530384i
$851$	−2.93688	+	1.69561i	−0.100675	+	0.0581248i
$852$	−14.5685	−	14.0398i	−0.499108	−	0.480996i
$853$			7.17809i			0.245773i	0.992421	+	0.122887i	$0.0392151\pi$
$853$			7.17809i			0.245773i	−0.992421	+	0.122887i	$0.960785\pi$
$854$	−2.69582	+	38.8650i	−0.0922491	+	1.32993i
$855$		−	4.70500i		−	0.160908i
$856$	−21.6066	−	26.5982i	−0.738498	−	0.909109i
$857$	39.5334	−	22.8246i	1.35044	−	0.779675i	0.362126	−	0.932129i	$-0.382051\pi$
$857$	39.5334	−	22.8246i	1.35044	−	0.779675i	0.988311	+	0.152454i	$0.0487176\pi$
$858$	−11.3794	−	26.7700i	−0.388486	−	0.913913i
$859$	6.77944	−	11.7423i	0.231311	−	0.400643i	−0.726883	−	0.686761i	$-0.759032\pi$
$859$	6.77944	−	11.7423i	0.231311	−	0.400643i	0.958194	+	0.286118i	$0.0923651\pi$
$860$	11.1759	+	2.77431i	0.381096	+	0.0946033i
$861$	−1.30692	−	24.9145i	−0.0445396	−	0.849085i
$862$	0.0260696	−	0.213223i	0.000887934	−	0.00726240i
$863$	−36.0550	−	20.8163i	−1.22733	−	0.708597i	−0.260856	−	0.965378i	$-0.584005\pi$
$863$	−36.0550	−	20.8163i	−1.22733	−	0.708597i	−0.966470	+	0.256781i	$0.917338\pi$
$864$	−0.478592	+	5.63657i	−0.0162820	+	0.191760i
$865$	−5.61504	−	9.72554i	−0.190917	−	0.330678i
$866$	−10.6999	−	8.05436i	−0.363597	−	0.273698i
$867$	16.5287			0.561344
$868$	−8.34335	−	24.1467i	−0.283192	−	0.819591i
$869$	7.75555			0.263089
$870$	2.70053	+	2.03282i	0.0915564	+	0.0689192i
$871$	17.7026	+	30.6619i	0.599831	+	1.03894i
$872$	−2.71237	−	16.9566i	−0.0918525	−	0.574221i
$873$	−9.41780	−	5.43737i	−0.318744	−	0.184027i
$874$	1.03979	−	8.50439i	0.0351713	−	0.287665i
$875$	20.6089	+	10.4995i	0.696708	+	0.354948i
$876$	3.20959	−	12.9294i	0.108442	−	0.436843i
$877$	9.84239	−	17.0475i	0.332354	−	0.575654i	−0.650619	−	0.759404i	$-0.725491\pi$
$877$	9.84239	−	17.0475i	0.332354	−	0.575654i	0.982973	+	0.183751i	$0.0588239\pi$
$878$	−18.5196	−	43.5673i	−0.625006	−	1.47033i
$879$	−9.27427	+	5.35450i	−0.312813	+	0.180603i
$880$	−17.9022	+	11.2376i	−0.603482	+	0.378819i
$881$		−	7.24606i		−	0.244126i	−0.992522	−	0.122063i	$-0.961049\pi$
$881$		−	7.24606i		−	0.244126i	0.992522	−	0.122063i	$-0.0389510\pi$
$882$	5.09345	−	8.48862i	0.171505	−	0.285827i
$883$		−	35.4533i		−	1.19310i	−0.802577	−	0.596549i	$-0.796538\pi$
$883$		−	35.4533i		−	1.19310i	0.802577	−	0.596549i	$-0.203462\pi$
$884$	−3.57405	+	3.70863i	−0.120208	+	0.124735i
$885$	−10.5880	+	6.11296i	−0.355911	+	0.205485i
$886$	34.0415	−	14.4703i	1.14365	−	0.486141i
$887$	−8.98684	+	15.5657i	−0.301749	+	0.522644i	−0.976532	−	0.215372i	$-0.930904\pi$
$887$	−8.98684	+	15.5657i	−0.301749	+	0.522644i	0.674784	+	0.738016i	$0.264237\pi$
$888$	7.22056	+	2.75899i	0.242306	+	0.0925857i
$889$	27.4479	+	13.9837i	0.920572	+	0.468999i
$890$	0.749976	+	0.0916955i	0.0251392	+	0.00307364i
$891$	−4.74861	−	2.74161i	−0.159084	−	0.0918474i
$892$	1.07653	+	3.73983i	0.0360448	+	0.125219i
$893$	−8.82463	−	15.2847i	−0.295305	−	0.511483i
$894$	3.96477	−	5.26704i	0.132602	−	0.176156i
$895$	2.50005			0.0835674
$896$	−8.14611	+	28.8035i	−0.272143	+	0.962257i
$897$	−4.65483			−0.155420
$898$	8.75337	−	11.6285i	0.292104	−	0.388048i
$899$	5.98700	+	10.3698i	0.199678	+	0.345852i
$900$	−2.25240	−	7.82479i	−0.0750800	−	0.260826i
$901$	−2.43475	−	1.40570i	−0.0811132	−	0.0468307i
$902$	−72.5820	−	8.87421i	−2.41672	−	0.295479i
$903$	0.828017	+	15.7850i	0.0275547	+	0.525292i
$904$	19.4972	+	7.44992i	0.648468	+	0.247781i
$905$	4.59374	−	7.95658i	0.152701	−	0.264486i
$906$	15.8864	−	6.75299i	0.527791	−	0.224353i
$907$	7.60870	−	4.39289i	0.252643	−	0.145863i	−0.368331	−	0.929695i	$-0.620071\pi$
$907$	7.60870	−	4.39289i	0.252643	−	0.145863i	0.620974	+	0.783831i	$0.286737\pi$
$908$	−11.9983	+	12.4501i	−0.398178	+	0.413172i
$909$			14.4305i			0.478631i
$910$	−13.4938	−	0.935982i	−0.447316	−	0.0310275i
$911$		−	21.5478i		−	0.713911i	−0.934121	−	0.356955i	$-0.883815\pi$
$911$		−	21.5478i		−	0.713911i	0.934121	−	0.356955i	$-0.116185\pi$
$912$	−16.5400	+	10.3825i	−0.547695	+	0.343800i
$913$	2.58220	−	1.49083i	0.0854582	−	0.0493393i
$914$	6.60102	+	15.5289i	0.218342	+	0.513650i
$915$	5.01711	−	8.68988i	0.165860	−	0.287279i
$916$	8.08983	−	32.5887i	0.267295	−	1.07676i
$917$	13.3467	+	20.5500i	0.440747	+	0.678619i
$918$	−0.117828	+	0.963711i	−0.00388890	+	0.0318072i
$919$	27.5939	+	15.9314i	0.910240	+	0.525527i	0.880508	−	0.474031i	$-0.157201\pi$
$919$	27.5939	+	15.9314i	0.910240	+	0.525527i	0.0297316	+	0.999558i	$0.490535\pi$
$920$	0.534262	+	3.33997i	0.0176141	+	0.110116i
$921$	2.11028	+	3.65512i	0.0695362	+	0.120440i
$922$	33.9069	+	25.5234i	1.11666	+	0.840570i
$923$	−37.9479			−1.24907
$924$	−21.9179	−	19.0117i	−0.721046	−	0.625439i
$925$	−11.1262			−0.365828
$926$	−14.9975	−	11.2894i	−0.492848	−	0.370992i
$927$	7.51235	+	13.0118i	0.246738	+	0.427363i
$928$	1.18696	−	13.9793i	0.0389639	−	0.458893i
$929$	44.1750	+	25.5044i	1.44933	+	0.836773i	0.998442	−	0.0558058i	$-0.0177728\pi$
$929$	44.1750	+	25.5044i	1.44933	+	0.836773i	0.450892	+	0.892579i	$0.351106\pi$
$930$	−0.798563	+	6.53143i	−0.0261859	+	0.214174i
$931$	33.9876	−	3.57555i	1.11390	−	0.117184i
$932$	−2.03148	−	0.504294i	−0.0665432	−	0.0165187i
$933$	4.85070	−	8.40165i	0.158805	−	0.275058i
$934$	16.4033	+	38.5887i	0.536731	+	1.26266i
$935$	−3.14171	+	1.81387i	−0.102745	+	0.0593199i
$936$	6.68969	+	8.23517i	0.218659	+	0.269175i
$937$		−	2.65742i		−	0.0868141i	−0.999057	−	0.0434071i	$-0.986179\pi$
$937$		−	2.65742i		−	0.0868141i	0.999057	−	0.0434071i	$-0.0138212\pi$
$938$	29.2890	+	19.7318i	0.956318	+	0.644266i
$939$		−	13.6634i		−	0.445887i
$940$	5.01711	+	4.83504i	0.163640	+	0.157702i
$941$	26.2920	−	15.1797i	0.857096	−	0.494844i	−0.00594304	−	0.999982i	$-0.501892\pi$
$941$	26.2920	−	15.1797i	0.857096	−	0.494844i	0.863039	+	0.505138i	$0.168558\pi$
$942$	28.5458	−	12.1342i	0.930072	−	0.395355i
$943$	−5.85070	+	10.1337i	−0.190525	+	0.329999i
$944$	44.8541	+	23.7316i	1.45988	+	0.772397i
$945$	−2.13832	+	1.38879i	−0.0695597	+	0.0451774i
$946$	45.9855	+	5.62240i	1.49512	+	0.182800i
$947$	−37.6505	−	21.7375i	−1.22348	−	0.706374i	−0.257818	−	0.966193i	$-0.583004\pi$
$947$	−37.6505	−	21.7375i	−1.22348	−	0.706374i	−0.965657	+	0.259819i	$0.916337\pi$
$948$	−2.71845	+	0.782517i	−0.0882910	+	0.0254150i
$949$	−12.4931	−	21.6386i	−0.405542	−	0.702419i
$950$	16.9054	−	22.4581i	0.548483	−	0.728637i
$951$	20.0884			0.651410
$952$	−1.57981	+	4.88852i	−0.0512021	+	0.158438i
$953$	−53.8683			−1.74497			−0.872483	−	0.488645i	$-0.837491\pi$
$953$	−53.8683			−1.74497			−0.872483	+	0.488645i	$0.837491\pi$
$954$	−3.48299	+	4.62701i	−0.112766	+	0.149805i
$955$	−4.01518	−	6.95449i	−0.129928	−	0.225042i
$956$	−36.9937	+	10.6488i	−1.19646	+	0.344407i
$957$	11.7771	+	6.79948i	0.380698	+	0.219796i
$958$	16.1930	+	1.97984i	0.523173	+	0.0639656i
$959$	19.1027	−	1.00205i	0.616860	−	0.0323580i
$960$	5.14115	−	5.74524i	0.165930	−	0.185427i
$961$	3.84512	−	6.65995i	0.124036	−	0.214837i
$962$	13.3423	−	5.67155i	0.430174	−	0.182858i
$963$	−10.4925	+	6.05782i	−0.338115	+	0.195211i
$964$	3.97020	+	3.82613i	0.127872	+	0.123231i
$965$			11.9236i			0.383835i
$966$	−4.17198	+	2.03771i	−0.134231	+	0.0655621i
$967$		−	44.9529i		−	1.44559i	−0.691064	−	0.722794i	$-0.742858\pi$
$967$		−	44.9529i		−	1.44559i	0.691064	−	0.722794i	$-0.257142\pi$
$968$	−41.8561	+	34.0010i	−1.34531	+	1.09283i
$969$	−2.90267	+	1.67586i	−0.0932472	+	0.0538363i
$970$	5.79806	+	13.6399i	0.186164	+	0.437952i
$971$	−0.641758	+	1.11156i	−0.0205950	+	0.0356716i	−0.876139	−	0.482058i	$-0.839889\pi$
$971$	−0.641758	+	1.11156i	−0.0205950	+	0.0356716i	0.855544	+	0.517730i	$0.173223\pi$
$972$	1.94109	+	0.481855i	0.0622604	+	0.0154555i
$973$	6.37523	−	12.5136i	0.204381	−	0.401167i
$974$	1.67428	−	13.6939i	0.0536474	−	0.438781i
$975$	−13.2259	−	7.63599i	−0.423569	−	0.244547i
$976$	−41.6198	+	1.53878i	−1.33222	+	0.0492553i
$977$	−9.67678	−	16.7607i	−0.309588	−	0.536222i	0.668684	−	0.743546i	$-0.266858\pi$
$977$	−9.67678	−	16.7607i	−0.309588	−	0.536222i	−0.978272	+	0.207325i	$0.933524\pi$
$978$	−4.54039	−	3.41778i	−0.145186	−	0.109289i
$979$	3.03979			0.0971520
$980$	−12.5038	+	5.06819i	−0.399421	+	0.161897i
$981$	−6.07126			−0.193840
$982$	45.7302	+	34.4234i	1.45931	+	1.09850i
$983$	4.21637	+	7.30296i	0.134481	+	0.232928i	0.925399	−	0.378994i	$-0.123730\pi$
$983$	4.21637	+	7.30296i	0.134481	+	0.232928i	−0.790918	+	0.611922i	$0.790397\pi$
$984$	26.3366	−	4.21280i	0.839579	−	0.134299i
$985$	2.70148	+	1.55970i	0.0860763	+	0.0496962i
$986$	0.292225	−	2.39011i	0.00930635	−	0.0761165i
$987$	−4.34178	+	8.52224i	−0.138200	+	0.271266i
$988$	−8.82463	+	35.5488i	−0.280749	+	1.13096i
$989$	3.70680	−	6.42036i	0.117869	−	0.204156i
$990$	2.92347	+	6.87747i	0.0929141	+	0.218580i
$991$	−21.1967	+	12.2379i	−0.673334	+	0.388750i	−0.797339	−	0.603532i	$-0.793760\pi$
$991$	−21.1967	+	12.2379i	−0.673334	+	0.388750i	0.124005	+	0.992282i	$0.460426\pi$
$992$	24.7229	−	11.6057i	0.784952	−	0.368480i
$993$			9.42104i			0.298968i
$994$	−34.0115	+	16.6121i	−1.07878	+	0.526905i
$995$			18.5322i			0.587511i
$996$	−0.754681	+	0.783099i	−0.0239130	+	0.0248134i
$997$	−29.0273	+	16.7589i	−0.919304	+	0.530761i	−0.883413	−	0.468595i	$-0.844760\pi$
$997$	−29.0273	+	16.7589i	−0.919304	+	0.530761i	−0.0358914	+	0.999356i	$0.511427\pi$
$998$	41.6030	−	17.6846i	1.31692	−	0.559795i
$999$	1.36643	−	2.36673i	0.0432321	−	0.0748802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.o.a.19.3	✓	8
3.2	odd	2		252.2.bf.g.19.2		8
4.3	odd	2		84.2.o.b.19.3	yes	8
7.2	even	3		588.2.b.b.391.1		8
7.3	odd	6		84.2.o.b.31.3	yes	8
7.4	even	3		588.2.o.b.31.3		8
7.5	odd	6		588.2.b.a.391.1		8
7.6	odd	2		588.2.o.d.19.3		8
8.3	odd	2		1344.2.bl.i.1279.2		8
8.5	even	2		1344.2.bl.j.1279.2		8
12.11	even	2		252.2.bf.f.19.2		8
21.2	odd	6		1764.2.b.i.1567.8		8
21.5	even	6		1764.2.b.j.1567.8		8
21.17	even	6		252.2.bf.f.199.2		8
28.3	even	6	inner	84.2.o.a.31.3	yes	8
28.11	odd	6		588.2.o.d.31.3		8
28.19	even	6		588.2.b.b.391.2		8
28.23	odd	6		588.2.b.a.391.2		8
28.27	even	2		588.2.o.b.19.3		8
56.3	even	6		1344.2.bl.j.703.2		8
56.45	odd	6		1344.2.bl.i.703.2		8
84.23	even	6		1764.2.b.j.1567.7		8
84.47	odd	6		1764.2.b.i.1567.7		8
84.59	odd	6		252.2.bf.g.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.3	✓	8	1.1	even	1	trivial
84.2.o.a.31.3	yes	8	28.3	even	6	inner
84.2.o.b.19.3	yes	8	4.3	odd	2
84.2.o.b.31.3	yes	8	7.3	odd	6
252.2.bf.f.19.2		8	12.11	even	2
252.2.bf.f.199.2		8	21.17	even	6
252.2.bf.g.19.2		8	3.2	odd	2
252.2.bf.g.199.2		8	84.59	odd	6
588.2.b.a.391.1		8	7.5	odd	6
588.2.b.a.391.2		8	28.23	odd	6
588.2.b.b.391.1		8	7.2	even	3
588.2.b.b.391.2		8	28.19	even	6
588.2.o.b.19.3		8	28.27	even	2
588.2.o.b.31.3		8	7.4	even	3
588.2.o.d.19.3		8	7.6	odd	2
588.2.o.d.31.3		8	28.11	odd	6
1344.2.bl.i.703.2		8	56.45	odd	6
1344.2.bl.i.1279.2		8	8.3	odd	2
1344.2.bl.j.703.2		8	56.3	even	6
1344.2.bl.j.1279.2		8	8.5	even	2
1764.2.b.i.1567.7		8	84.47	odd	6
1764.2.b.i.1567.8		8	21.2	odd	6
1764.2.b.j.1567.7		8	84.23	even	6
1764.2.b.j.1567.8		8	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.850516 - 1.12988i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.553244 - 1.92196i) q^{4} +(0.834598 + 0.481855i) q^{5} +(-1.40376 - 0.171630i) q^{6} +(-1.20103 + 2.35744i) q^{7} +(-2.64212 - 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.850516 - 1.12988i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.553244 - 1.92196i) q^{4} +(0.834598 + 0.481855i) q^{5} +(-1.40376 - 0.171630i) q^{6} +(-1.20103 + 2.35744i) q^{7} +(-2.64212 - 1.00956i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.25428 - 0.533167i) q^{10} +(4.74861 - 2.74161i) q^{11} +(-1.38784 + 1.44010i) q^{12} +3.75117i q^{13} +(1.64212 + 3.36206i) q^{14} -0.963711i q^{15} +(-3.38784 + 2.12662i) q^{16} +(-0.594545 + 0.343260i) q^{17} +(0.553244 + 1.30151i) q^{18} +(-2.44109 + 4.22809i) q^{19} +(0.464369 - 1.87065i) q^{20} +(2.64212 - 0.138595i) q^{21} +(0.941086 - 7.69713i) q^{22} +(-1.07465 - 0.620450i) q^{23} +(0.446756 + 2.79292i) q^{24} +(-2.03563 - 3.52582i) q^{25} +(4.23836 + 3.19043i) q^{26} +1.00000 q^{27} +(5.19536 + 1.00409i) q^{28} -2.48011 q^{29} +(-1.08887 - 0.819652i) q^{30} +(-2.41401 - 4.18119i) q^{31} +(-0.478592 + 5.63657i) q^{32} +(-4.74861 - 2.74161i) q^{33} +(-0.117828 + 0.963711i) q^{34} +(-2.13832 + 1.38879i) q^{35} +(1.94109 + 0.481855i) q^{36} +(1.36643 - 2.36673i) q^{37} +(2.70103 + 6.35418i) q^{38} +(3.24861 - 1.87558i) q^{39} +(-1.71865 - 2.11569i) q^{40} -9.42976i q^{41} +(2.09057 - 3.10315i) q^{42} +5.97437i q^{43} +(-7.89640 - 7.60984i) q^{44} +(-0.834598 + 0.481855i) q^{45} +(-1.61504 + 0.686521i) q^{46} +(-1.80752 + 3.13072i) q^{47} +(3.53563 + 1.87065i) q^{48} +(-4.11504 - 5.66272i) q^{49} +(-5.71508 - 0.698752i) q^{50} +(0.594545 + 0.343260i) q^{51} +(7.20959 - 2.07531i) q^{52} +(2.04757 + 3.54650i) q^{53} +(0.850516 - 1.12988i) q^{54} +5.28424 q^{55} +(5.55324 - 5.01612i) q^{56} +4.88217 q^{57} +(-2.10937 + 2.80222i) q^{58} +(-6.34315 - 10.9867i) q^{59} +(-1.85221 + 0.533167i) q^{60} +(9.01711 + 5.20603i) q^{61} +(-6.77738 - 0.828634i) q^{62} +(-1.44109 - 2.21884i) q^{63} +(5.96158 + 5.33475i) q^{64} +(-1.80752 + 3.13072i) q^{65} +(-7.13645 + 3.03356i) q^{66} +(8.17396 - 4.71924i) q^{67} +(0.988660 + 0.952783i) q^{68} +1.24090i q^{69} +(-0.249518 + 3.59723i) q^{70} +10.1163i q^{71} +(2.19536 - 1.78336i) q^{72} +(-5.76850 + 3.33044i) q^{73} +(-1.51194 - 3.55685i) q^{74} +(-2.03563 + 3.52582i) q^{75} +(9.47672 + 2.35250i) q^{76} +(0.759946 + 14.4873i) q^{77} +(0.643814 - 5.26574i) q^{78} +(1.22492 + 0.707208i) q^{79} +(-3.85221 + 0.142425i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.6545 - 8.02016i) q^{82} +0.543780 q^{83} +(-1.72811 - 5.00136i) q^{84} -0.661608 q^{85} +(6.75030 + 5.08130i) q^{86} +(1.24005 + 2.14784i) q^{87} +(-15.3142 + 2.44966i) q^{88} +(0.480107 + 0.277190i) q^{89} +(-0.165402 + 1.35282i) q^{90} +(-8.84315 - 4.50528i) q^{91} +(-0.597935 + 2.40870i) q^{92} +(-2.41401 + 4.18119i) q^{93} +(2.00000 + 4.70500i) q^{94} +(-4.07465 + 2.35250i) q^{95} +(5.12071 - 2.40381i) q^{96} +10.8747i q^{97} +(-9.89809 - 0.166748i) q^{98} +5.48322i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

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