LMFDB - Embedded newform 336.2.bq.b.109.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.20
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.608093 + 1.27680i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.26045 + 1.55283i) q^{4} +(2.60505 + 0.698021i) q^{5} +(0.917833 + 1.07591i) q^{6} +(2.64133 + 0.152886i) q^{7} +(-2.74912 - 0.665077i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.608093 + 1.27680i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.26045 + 1.55283i) q^{4} +(2.60505 + 0.698021i) q^{5} +(0.917833 + 1.07591i) q^{6} +(2.64133 + 0.152886i) q^{7} +(-2.74912 - 0.665077i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.692877 + 3.75059i) q^{10} +(-0.429396 - 1.60253i) q^{11} +(-0.815596 + 1.82614i) q^{12} +(-4.38976 - 4.38976i) q^{13} +(1.41097 + 3.46542i) q^{14} +2.69694 q^{15} +(-0.822550 - 3.91451i) q^{16} +(0.139323 - 0.241314i) q^{17} +(1.16502 + 0.801697i) q^{18} +(-1.76788 + 6.59783i) q^{19} +(-4.36743 + 3.16538i) q^{20} +(2.59090 - 0.535950i) q^{21} +(1.78500 - 1.52274i) q^{22} +(-1.62941 + 0.940743i) q^{23} +(-2.82758 + 0.0691103i) q^{24} +(1.96892 + 1.13676i) q^{25} +(2.93547 - 8.27423i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.56666 + 3.90883i) q^{28} +(1.52435 + 1.52435i) q^{29} +(1.63999 + 3.44346i) q^{30} +(-4.10364 + 7.10771i) q^{31} +(4.49787 - 3.43062i) q^{32} +(-0.829530 - 1.43679i) q^{33} +(0.392831 + 0.0311462i) q^{34} +(6.77408 + 2.24198i) q^{35} +(-0.315165 + 1.97501i) q^{36} +(-2.25734 - 0.604852i) q^{37} +(-9.49915 + 1.75486i) q^{38} +(-5.37633 - 3.10403i) q^{39} +(-6.69736 - 3.65150i) q^{40} -9.20821i q^{41} +(2.25981 + 2.98216i) q^{42} +(2.19581 - 2.19581i) q^{43} +(3.02968 + 1.35312i) q^{44} +(2.60505 - 0.698021i) q^{45} +(-2.19198 - 1.50838i) q^{46} +(-4.05167 - 7.01770i) q^{47} +(-1.80767 - 3.56824i) q^{48} +(6.95325 + 0.807646i) q^{49} +(-0.254127 + 3.20517i) q^{50} +(0.0721187 - 0.269150i) q^{51} +(12.3496 - 1.28348i) q^{52} +(-1.09437 - 4.08426i) q^{53} +(1.33282 + 0.472849i) q^{54} -4.47439i q^{55} +(-7.15966 - 2.17699i) q^{56} +6.83057i q^{57} +(-1.01935 + 2.87324i) q^{58} +(-2.97454 - 11.1011i) q^{59} +(-3.39935 + 4.18789i) q^{60} +(-0.490196 + 1.82944i) q^{61} +(-11.5705 - 0.917387i) q^{62} +(2.36390 - 1.18826i) q^{63} +(7.11535 + 3.65675i) q^{64} +(-8.37139 - 14.4997i) q^{65} +(1.33006 - 1.93285i) q^{66} +(-3.94597 + 1.05732i) q^{67} +(0.199110 + 0.520507i) q^{68} +(-1.33041 + 1.33041i) q^{69} +(1.25670 + 10.0125i) q^{70} +14.1982i q^{71} +(-2.71335 + 0.798588i) q^{72} +(4.55318 + 2.62878i) q^{73} +(-0.600395 - 3.24998i) q^{74} +(2.19604 + 0.588428i) q^{75} +(-8.01697 - 11.0614i) q^{76} +(-0.889173 - 4.29846i) q^{77} +(0.693919 - 8.75205i) q^{78} +(7.68741 + 13.3150i) q^{79} +(0.589628 - 10.7717i) q^{80} +(0.500000 - 0.866025i) q^{81} +(11.7571 - 5.59944i) q^{82} +(2.79010 + 2.79010i) q^{83} +(-2.43345 + 4.69876i) q^{84} +(0.531384 - 0.531384i) q^{85} +(4.13888 + 1.46836i) q^{86} +(1.86694 + 1.07788i) q^{87} +(0.114658 + 4.69113i) q^{88} +(15.5724 - 8.99075i) q^{89} +(2.47535 + 2.90167i) q^{90} +(-10.9237 - 12.2659i) q^{91} +(0.592978 - 3.71596i) q^{92} +(-2.12420 + 7.92762i) q^{93} +(6.49642 - 9.44059i) q^{94} +(-9.21084 + 15.9536i) q^{95} +(3.45670 - 4.47786i) q^{96} -4.17533 q^{97} +(3.19702 + 9.36905i) q^{98} +(-1.17313 - 1.17313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.608093	+	1.27680i	0.429987	+	0.902835i
$2$	0.608093	+	1.27680i	0.429987	+	0.902835i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−1.26045	+	1.55283i	−0.630223	+	0.776414i
$5$	2.60505	+	0.698021i	1.16501	+	0.312164i	0.788966	−	0.614436i	$-0.210617\pi$
$5$	2.60505	+	0.698021i	1.16501	+	0.312164i	0.376047	+	0.926601i	$0.377283\pi$
$6$	0.917833	+	1.07591i	0.374704	+	0.439238i
$7$	2.64133	+	0.152886i	0.998329	+	0.0577856i
$7$	2.64133	+	0.152886i	0.998329	+	0.0577856i
$8$	−2.74912	−	0.665077i	−0.971961	−	0.235140i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	0.692877	+	3.75059i	0.219107	+	1.18604i
$11$	−0.429396	−	1.60253i	−0.129468	−	0.483181i	0.870492	−	0.492183i	$-0.163801\pi$
$11$	−0.429396	−	1.60253i	−0.129468	−	0.483181i	−0.999959	+	0.00900264i	$0.997134\pi$
$12$	−0.815596	+	1.82614i	−0.235442	+	0.527162i
$13$	−4.38976	−	4.38976i	−1.21750	−	1.21750i	−0.968505	−	0.248995i	$-0.919900\pi$
$13$	−4.38976	−	4.38976i	−1.21750	−	1.21750i	−0.248995	−	0.968505i	$-0.580100\pi$
$14$	1.41097	+	3.46542i	0.377097	+	0.926174i
$15$	2.69694			0.696348
$16$	−0.822550	−	3.91451i	−0.205638	−	0.978628i
$17$	0.139323	−	0.241314i	0.0337907	−	0.0585272i	−0.848636	−	0.528978i	$-0.822575\pi$
$17$	0.139323	−	0.241314i	0.0337907	−	0.0585272i	0.882426	+	0.470451i	$0.155909\pi$
$18$	1.16502	+	0.801697i	0.274599	+	0.188962i
$19$	−1.76788	+	6.59783i	−0.405580	+	1.51365i	0.397403	+	0.917644i	$0.369911\pi$
$19$	−1.76788	+	6.59783i	−0.405580	+	1.51365i	−0.802983	+	0.596001i	$0.796755\pi$
$20$	−4.36743	+	3.16538i	−0.976587	+	0.707799i
$21$	2.59090	−	0.535950i	0.565381	−	0.116954i
$22$	1.78500	−	1.52274i	0.380563	−	0.324649i
$23$	−1.62941	+	0.940743i	−0.339756	+	0.196159i	−0.660164	−	0.751121i	$-0.729513\pi$
$23$	−1.62941	+	0.940743i	−0.339756	+	0.196159i	0.320408	+	0.947280i	$0.396180\pi$
$24$	−2.82758	+	0.0691103i	−0.577178	+	0.0141071i
$25$	1.96892	+	1.13676i	0.393784	+	0.227351i
$26$	2.93547	−	8.27423i	0.575693	−	1.62271i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−3.56666	+	3.90883i	−0.674036	+	0.738699i
$29$	1.52435	+	1.52435i	0.283065	+	0.283065i	0.834330	−	0.551265i	$-0.185855\pi$
$29$	1.52435	+	1.52435i	0.283065	+	0.283065i	−0.551265	+	0.834330i	$0.685855\pi$
$30$	1.63999	+	3.44346i	0.299420	+	0.628688i
$31$	−4.10364	+	7.10771i	−0.737036	+	1.27658i	0.216789	+	0.976218i	$0.430442\pi$
$31$	−4.10364	+	7.10771i	−0.737036	+	1.27658i	−0.953824	+	0.300365i	$0.902892\pi$
$32$	4.49787	−	3.43062i	0.795119	−	0.606454i
$33$	−0.829530	−	1.43679i	−0.144403	−	0.250113i
$34$	0.392831	+	0.0311462i	0.0673699	+	0.00534152i
$35$	6.77408	+	2.24198i	1.14503	+	0.378964i
$36$	−0.315165	+	1.97501i	−0.0525274	+	0.329169i
$37$	−2.25734	−	0.604852i	−0.371104	−	0.0994371i	0.0684466	−	0.997655i	$-0.478196\pi$
$37$	−2.25734	−	0.604852i	−0.371104	−	0.0994371i	−0.439551	+	0.898218i	$0.644862\pi$
$38$	−9.49915	+	1.75486i	−1.54097	+	0.284675i
$39$	−5.37633	−	3.10403i	−0.860902	−	0.497042i
$40$	−6.69736	−	3.65150i	−1.05895	−	0.577353i
$41$		−	9.20821i		−	1.43808i	−0.694969	−	0.719040i	$-0.744582\pi$
$41$		−	9.20821i		−	1.43808i	0.694969	−	0.719040i	$-0.255418\pi$
$42$	2.25981	+	2.98216i	0.348696	+	0.460157i
$43$	2.19581	−	2.19581i	0.334859	−	0.334859i	−0.519570	−	0.854428i	$-0.673908\pi$
$43$	2.19581	−	2.19581i	0.334859	−	0.334859i	0.854428	+	0.519570i	$0.173908\pi$
$44$	3.02968	+	1.35312i	0.456742	+	0.203991i
$45$	2.60505	−	0.698021i	0.388338	−	0.104055i
$46$	−2.19198	−	1.50838i	−0.323190	−	0.222399i
$47$	−4.05167	−	7.01770i	−0.590997	−	1.02364i	−0.994098	−	0.108481i	$-0.965401\pi$
$47$	−4.05167	−	7.01770i	−0.590997	−	1.02364i	0.403102	−	0.915155i	$-0.367932\pi$
$48$	−1.80767	−	3.56824i	−0.260915	−	0.515031i
$49$	6.95325	+	0.807646i	0.993322	+	0.115378i
$50$	−0.254127	+	3.20517i	−0.0359389	+	0.453280i
$51$	0.0721187	−	0.269150i	0.0100986	−	0.0376886i
$52$	12.3496	−	1.28348i	1.71258	−	0.177987i
$53$	−1.09437	−	4.08426i	−0.150324	−	0.561016i	−0.999461	−	0.0328431i	$-0.989544\pi$
$53$	−1.09437	−	4.08426i	−0.150324	−	0.561016i	0.849137	−	0.528173i	$-0.177123\pi$
$54$	1.33282	+	0.472849i	0.181374	+	0.0643466i
$55$		−	4.47439i		−	0.603327i
$56$	−7.15966	−	2.17699i	−0.956750	−	0.290913i
$57$			6.83057i			0.904731i
$58$	−1.01935	+	2.87324i	−0.133847	+	0.377275i
$59$	−2.97454	−	11.1011i	−0.387252	−	1.44524i	−0.834587	−	0.550876i	$-0.814294\pi$
$59$	−2.97454	−	11.1011i	−0.387252	−	1.44524i	0.447335	−	0.894366i	$-0.352373\pi$
$60$	−3.39935	+	4.18789i	−0.438855	+	0.540654i
$61$	−0.490196	+	1.82944i	−0.0627632	+	0.234235i	−0.990181	−	0.139792i	$-0.955357\pi$
$61$	−0.490196	+	1.82944i	−0.0627632	+	0.234235i	0.927418	+	0.374027i	$0.122023\pi$
$62$	−11.5705	−	0.917387i	−1.46946	−	0.116508i
$63$	2.36390	−	1.18826i	0.297824	−	0.149707i
$64$	7.11535	+	3.65675i	0.889418	+	0.457094i
$65$	−8.37139	−	14.4997i	−1.03834	−	1.79846i
$66$	1.33006	−	1.93285i	0.163719	−	0.237917i
$67$	−3.94597	+	1.05732i	−0.482077	+	0.129172i	−0.491670	−	0.870782i	$-0.663613\pi$
$67$	−3.94597	+	1.05732i	−0.482077	+	0.129172i	0.00959239	+	0.999954i	$0.496947\pi$
$68$	0.199110	+	0.520507i	0.0241456	+	0.0631207i
$69$	−1.33041	+	1.33041i	−0.160163	+	0.160163i
$70$	1.25670	+	10.0125i	0.150205	+	1.19672i
$71$			14.1982i			1.68502i	0.538682	+	0.842509i	$0.318923\pi$
$71$			14.1982i			1.68502i	−0.538682	+	0.842509i	$0.681077\pi$
$72$	−2.71335	+	0.798588i	−0.319771	+	0.0941145i
$73$	4.55318	+	2.62878i	0.532909	+	0.307675i	0.742200	−	0.670178i	$-0.233782\pi$
$73$	4.55318	+	2.62878i	0.532909	+	0.307675i	−0.209291	+	0.977853i	$0.567116\pi$
$74$	−0.600395	−	3.24998i	−0.0697945	−	0.377803i
$75$	2.19604	+	0.588428i	0.253577	+	0.0679458i
$76$	−8.01697	−	11.0614i	−0.919609	−	1.26883i
$77$	−0.889173	−	4.29846i	−0.101331	−	0.489855i
$78$	0.693919	−	8.75205i	0.0785708	−	0.990974i
$79$	7.68741	+	13.3150i	0.864901	+	1.49805i	0.867145	+	0.498055i	$0.165952\pi$
$79$	7.68741	+	13.3150i	0.864901	+	1.49805i	−0.00224413	+	0.999997i	$0.500714\pi$
$80$	0.589628	−	10.7717i	0.0659224	−	1.20431i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	11.7571	−	5.59944i	1.29835	−	0.618355i
$83$	2.79010	+	2.79010i	0.306254	+	0.306254i	0.843454	−	0.537201i	$-0.180518\pi$
$83$	2.79010	+	2.79010i	0.306254	+	0.306254i	−0.537201	+	0.843454i	$0.680518\pi$
$84$	−2.43345	+	4.69876i	−0.265511	+	0.512676i
$85$	0.531384	−	0.531384i	0.0576367	−	0.0576367i
$86$	4.13888	+	1.46836i	0.446307	+	0.158337i
$87$	1.86694	+	1.07788i	0.200157	+	0.115561i
$88$	0.114658	+	4.69113i	0.0122226	+	0.500076i
$89$	15.5724	−	8.99075i	1.65067	−	0.953017i	0.673879	−	0.738842i	$-0.264627\pi$
$89$	15.5724	−	8.99075i	1.65067	−	0.953017i	0.976795	−	0.214175i	$-0.0687064\pi$
$90$	2.47535	+	2.90167i	0.260924	+	0.305863i
$91$	−10.9237	−	12.2659i	−1.14511	−	1.28582i
$92$	0.592978	−	3.71596i	0.0618222	−	0.387415i
$93$	−2.12420	+	7.92762i	−0.220269	+	0.822056i
$94$	6.49642	−	9.44059i	0.670054	−	0.973723i
$95$	−9.21084	+	15.9536i	−0.945012	+	1.63681i
$96$	3.45670	−	4.47786i	0.352798	−	0.457020i
$97$	−4.17533			−0.423940			−0.211970	−	0.977276i	$-0.567988\pi$
$97$	−4.17533			−0.423940			−0.211970	+	0.977276i	$0.567988\pi$
$98$	3.19702	+	9.36905i	0.322948	+	0.946417i
$99$	−1.17313	−	1.17313i	−0.117904	−	0.117904i
$100$	−4.24690	+	1.62457i	−0.424690	+	0.162457i
$101$	−1.49805	−	5.59080i	−0.149062	−	0.556306i	−0.999541	−	0.0302972i	$-0.990355\pi$
$101$	−1.49805	−	5.59080i	−0.149062	−	0.556306i	0.850479	−	0.526009i	$-0.176312\pi$
$102$	0.387507	−	0.0715872i	0.0383689	−	0.00708819i
$103$	0.235772	−	0.136123i	0.0232313	−	0.0134126i	−0.488339	−	0.872654i	$-0.662397\pi$
$103$	0.235772	−	0.136123i	0.0232313	−	0.0134126i	0.511571	+	0.859241i	$0.329064\pi$
$104$	9.14845	+	14.9875i	0.897080	+	1.46965i
$105$	7.12352	+	0.412326i	0.695185	+	0.0402389i
$106$	4.54931	−	3.88091i	0.441868	−	0.376947i
$107$	6.58275	+	1.76384i	0.636379	+	0.170517i	0.562563	−	0.826755i	$-0.309816\pi$
$107$	6.58275	+	1.76384i	0.636379	+	0.170517i	0.0738161	+	0.997272i	$0.476482\pi$
$108$	0.206745	+	1.98929i	0.0198941	+	0.191419i
$109$	−11.3663	+	3.04558i	−1.08869	+	0.291714i	−0.758151	−	0.652079i	$-0.773897\pi$
$109$	−11.3663	+	3.04558i	−1.08869	+	0.291714i	−0.330539	+	0.943792i	$0.607230\pi$
$110$	5.71291	−	2.72085i	0.544705	−	0.259422i
$111$	−2.33697			−0.221815
$112$	−1.57415	−	10.4653i	−0.148743	−	0.988876i
$113$	7.15803			0.673371			0.336685	−	0.941617i	$-0.390694\pi$
$113$	7.15803			0.673371			0.336685	+	0.941617i	$0.390694\pi$
$114$	−8.72129	+	4.15362i	−0.816824	+	0.389022i
$115$	−4.90136	+	1.31332i	−0.457054	+	0.122467i
$116$	−4.28841	+	0.445692i	−0.398169	+	0.0413815i
$117$	−5.99652	−	1.60676i	−0.554378	−	0.148545i
$118$	12.3651	−	10.5484i	1.13830	−	0.971059i
$119$	0.404890	−	0.616089i	0.0371162	−	0.0564768i
$120$	−7.41423	−	1.79368i	−0.676824	−	0.163739i
$121$	7.14256	−	4.12376i	0.649324	−	0.374887i
$122$	−2.63391	+	0.486584i	−0.238463	+	0.0440532i
$123$	−2.38326	−	8.89444i	−0.214891	−	0.801985i
$124$	−5.86464	−	15.3311i	−0.526660	−	1.37678i
$125$	−5.19949	−	5.19949i	−0.465057	−	0.465057i
$126$	2.95465	+	2.29566i	0.263221	+	0.204514i
$127$	−0.120662			−0.0107071			−0.00535353	−	0.999986i	$-0.501704\pi$
$127$	−0.120662			−0.0107071			−0.00535353	+	0.999986i	$0.501704\pi$
$128$	−0.342161	+	11.3085i	−0.0302431	+	0.999543i
$129$	1.55268	−	2.68931i	0.136705	−	0.236781i
$130$	13.4226	−	19.5058i	1.17724	−	1.71077i
$131$	0.953110	−	3.55706i	0.0832736	−	0.310781i	−0.911708	−	0.410839i	$-0.865236\pi$
$131$	0.953110	−	3.55706i	0.0832736	−	0.310781i	0.994982	+	0.100057i	$0.0319026\pi$
$132$	3.27666	+	0.522877i	0.285197	+	0.0455106i
$133$	−5.67828	+	17.1568i	−0.492369	+	1.48768i
$134$	−3.74951	−	4.39528i	−0.323908	−	0.379694i
$135$	2.33562	−	1.34847i	0.201018	−	0.116058i
$136$	−0.543507	+	0.570741i	−0.0466053	+	0.0489406i
$137$	5.81770	+	3.35885i	0.497040	+	0.286966i	0.727490	−	0.686118i	$-0.240687\pi$
$137$	5.81770	+	3.35885i	0.497040	+	0.286966i	−0.230450	+	0.973084i	$0.574020\pi$
$138$	−2.50769	−	0.889658i	−0.213468	−	0.0757328i
$139$	−10.7685	+	10.7685i	−0.913375	+	0.913375i	−0.996536	−	0.0831615i	$-0.973498\pi$
$139$	−10.7685	+	10.7685i	−0.913375	+	0.913375i	0.0831615	+	0.996536i	$0.473498\pi$
$140$	−12.0198	+	7.69308i	−1.01586	+	0.650184i
$141$	−5.72993	−	5.72993i	−0.482547	−	0.482547i
$142$	−18.1283	+	8.63383i	−1.52129	+	0.724535i
$143$	−5.14977	+	8.91966i	−0.430645	+	0.745899i
$144$	−2.66961	−	2.97879i	−0.222467	−	0.248233i
$145$	2.90698	+	5.03503i	0.241411	+	0.418137i
$146$	−0.587675	+	7.41205i	−0.0486363	+	0.613426i
$147$	6.92536	−	1.01951i	0.571194	−	0.0840876i
$148$	3.78449	−	2.74288i	0.311083	−	0.225463i
$149$	−8.05631	−	2.15868i	−0.659999	−	0.176846i	−0.0867534	−	0.996230i	$-0.527649\pi$
$149$	−8.05631	−	2.15868i	−0.659999	−	0.176846i	−0.573246	+	0.819384i	$0.694316\pi$
$150$	0.584092	+	3.16173i	0.0476909	+	0.258154i
$151$	12.1093	+	6.99133i	0.985444	+	0.568946i	0.903909	−	0.427724i	$-0.140685\pi$
$151$	12.1093	+	6.99133i	0.985444	+	0.568946i	0.0815344	+	0.996671i	$0.474018\pi$
$152$	9.24819	−	16.9625i	0.750127	−	1.37584i
$153$		−	0.278645i		−	0.0225271i
$154$	4.94758	−	3.74916i	0.398687	−	0.302116i
$155$	−15.6515	+	15.6515i	−1.25716	+	1.25716i
$156$	11.5966	−	4.43606i	0.928471	−	0.355169i
$157$	−5.13162	+	1.37501i	−0.409548	+	0.109738i	−0.457710	−	0.889101i	$-0.651330\pi$
$157$	−5.13162	+	1.37501i	−0.409548	+	0.109738i	0.0481621	+	0.998840i	$0.484664\pi$
$158$	−12.3259	+	17.9120i	−0.980599	+	1.42501i
$159$	−2.11417	−	3.66185i	−0.167665	−	0.290403i
$160$	14.1118	−	5.79733i	1.11564	−	0.458319i
$161$	−4.44765	+	2.23570i	−0.350524	+	0.176198i
$162$	1.40979	+	0.111777i	0.110764	+	0.00878204i
$163$	4.56160	−	17.0241i	0.357292	−	1.33343i	−0.520284	−	0.853993i	$-0.674174\pi$
$163$	4.56160	−	17.0241i	0.357292	−	1.33343i	0.877576	−	0.479438i	$-0.159159\pi$
$164$	14.2988	+	11.6065i	1.11655	+	0.906312i
$165$	−1.15806	−	4.32193i	−0.0901547	−	0.336462i
$166$	−1.86577	+	5.25905i	−0.144812	+	0.408182i
$167$			19.2278i			1.48789i	0.668239	+	0.743947i	$0.267048\pi$
$167$			19.2278i			1.48789i	−0.668239	+	0.743947i	$0.732952\pi$
$168$	−7.47915	−	0.249755i	−0.577029	−	0.0192690i
$169$			25.5399i			1.96461i
$170$	1.00160	+	0.355341i	0.0768194	+	0.0272534i
$171$	1.76788	+	6.59783i	0.135193	+	0.504548i
$172$	0.642016	+	6.17743i	0.0489533	+	0.471025i
$173$	−6.04270	+	22.5517i	−0.459418	+	1.71457i	0.215347	+	0.976538i	$0.430912\pi$
$173$	−6.04270	+	22.5517i	−0.459418	+	1.71457i	−0.674765	+	0.738033i	$0.735755\pi$
$174$	−0.240964	+	3.03916i	−0.0182675	+	0.230398i
$175$	5.02677	+	3.30357i	0.379988	+	0.249726i
$176$	−5.91992	+	2.99904i	−0.446231	+	0.226061i
$177$	−5.74636	−	9.95299i	−0.431923	−	0.748113i
$178$	20.9489	+	14.4157i	1.57019	+	1.08050i
$179$	1.46411	−	0.392307i	0.109433	−	0.0293224i	−0.203687	−	0.979036i	$-0.565293\pi$
$179$	1.46411	−	0.392307i	0.109433	−	0.0293224i	0.313120	+	0.949714i	$0.398626\pi$
$180$	−2.19962	+	4.92501i	−0.163950	+	0.367089i
$181$	7.28203	−	7.28203i	0.541269	−	0.541269i	−0.382632	−	0.923901i	$-0.624982\pi$
$181$	7.28203	−	7.28203i	0.541269	−	0.541269i	0.923901	+	0.382632i	$0.124982\pi$
$182$	9.01856	−	21.4062i	0.668500	−	1.58673i
$183$			1.89397i			0.140006i
$184$	5.10513	−	1.50253i	0.376355	−	0.110768i
$185$	−5.45828	−	3.15134i	−0.401301	−	0.231691i
$186$	−11.4137	+	2.10855i	−0.836894	+	0.154606i
$187$	−0.446537	−	0.119649i	−0.0326540	−	0.00874961i
$188$	16.0042	+	2.55389i	1.16723	+	0.186261i
$189$	1.97581	−	1.75960i	0.143719	−	0.127992i
$190$	−25.9707	−	2.05912i	−1.88411	−	0.149384i
$191$	0.0269765	+	0.0467247i	0.00195195	+	0.00338088i	0.867000	−	0.498309i	$-0.166045\pi$
$191$	0.0269765	+	0.0467247i	0.00195195	+	0.00338088i	−0.865048	+	0.501689i	$0.832712\pi$
$192$	7.81933	+	1.69057i	0.564312	+	0.122006i
$193$	−10.8305	+	18.7590i	−0.779599	+	1.35030i	0.152575	+	0.988292i	$0.451244\pi$
$193$	−10.8305	+	18.7590i	−0.779599	+	1.35030i	−0.932173	+	0.362013i	$0.882090\pi$
$194$	−2.53899	−	5.33107i	−0.182289	−	0.382748i
$195$	−11.8389	−	11.8389i	−0.847804	−	0.847804i
$196$	−10.0183	+	9.77921i	−0.715595	+	0.698515i
$197$	14.4504	−	14.4504i	1.02955	−	1.02955i	0.0299975	−	0.999550i	$-0.490450\pi$
$197$	14.4504	−	14.4504i	1.02955	−	1.02955i	0.999550	−	0.0299975i	$-0.00954992\pi$
$198$	0.784484	−	2.21123i	0.0557509	−	0.157145i
$199$	−18.0972	−	10.4484i	−1.28288	−	0.740671i	−0.305506	−	0.952190i	$-0.598826\pi$
$199$	−18.0972	−	10.4484i	−1.28288	−	0.740671i	−0.977374	+	0.211519i	$0.932159\pi$
$200$	−4.65677	−	4.43456i	−0.329283	−	0.313571i
$201$	−3.53786	+	2.04259i	−0.249542	+	0.144073i
$202$	6.22740	−	5.31244i	0.438158	−	0.373782i
$203$	3.79326	+	4.25936i	0.266235	+	0.298949i
$204$	0.327043	+	0.451238i	0.0228976	+	0.0315930i
$205$	6.42752	−	23.9878i	0.448917	−	1.67538i
$206$	0.317173	+	0.218258i	0.0220985	+	0.0152068i
$207$	−0.940743	+	1.62941i	−0.0653862	+	0.113252i
$208$	−13.5730	+	20.7946i	−0.941116	+	1.44184i
$209$	11.3323			0.783874
$210$	3.80530	+	9.34606i	0.262591	+	0.644939i
$211$	7.24944	+	7.24944i	0.499072	+	0.499072i	0.911149	−	0.412077i	$-0.135197\pi$
$211$	7.24944	+	7.24944i	0.499072	+	0.499072i	−0.412077	+	0.911149i	$0.635197\pi$
$212$	7.72155	+	3.44862i	0.530319	+	0.236852i
$213$	3.67477	+	13.7144i	0.251791	+	0.939697i
$214$	1.75085	+	9.47745i	0.119685	+	0.647865i
$215$	7.25293	−	4.18748i	0.494646	−	0.285584i
$216$	−2.41420	+	1.47364i	−0.164266	+	0.100269i
$217$	−11.9257	+	18.1464i	−0.809572	+	1.23186i
$218$	−10.8003	−	12.6605i	−0.731492	−	0.857475i
$219$	5.07841	+	1.36076i	0.343167	+	0.0919514i
$220$	6.94796	+	5.63973i	0.468432	+	0.380231i
$221$	−1.67090	+	0.447716i	−0.112397	+	0.0301167i
$222$	−1.42109	−	2.98385i	−0.0953776	−	0.200263i
$223$	−7.66663			−0.513395			−0.256698	−	0.966492i	$-0.582634\pi$
$223$	−7.66663			−0.513395			−0.256698	+	0.966492i	$0.582634\pi$
$224$	12.4049	−	8.37374i	0.828834	−	0.559494i
$225$	2.27351			0.151567
$226$	4.35275	+	9.13939i	0.289540	+	0.607943i
$227$	0.992793	−	0.266018i	0.0658940	−	0.0176562i	−0.225721	−	0.974192i	$-0.572474\pi$
$227$	0.992793	−	0.266018i	0.0658940	−	0.0176562i	0.291615	+	0.956536i	$0.405807\pi$
$228$	−10.6067	−	8.60957i	−0.702446	−	0.570183i
$229$	−19.0284	−	5.09865i	−1.25743	−	0.336928i	−0.432230	−	0.901763i	$-0.642273\pi$
$229$	−19.0284	−	5.09865i	−1.25743	−	0.336928i	−0.825204	+	0.564835i	$0.808940\pi$
$230$	−4.65733	−	5.45945i	−0.307095	−	0.359986i
$231$	−1.97140	−	3.92186i	−0.129708	−	0.258039i
$232$	−3.17681	−	5.20443i	−0.208568	−	0.341688i
$233$	−12.4040	+	7.16142i	−0.812610	+	0.469161i	−0.847861	−	0.530218i	$-0.822110\pi$
$233$	−12.4040	+	7.16142i	−0.812610	+	0.469161i	0.0352515	+	0.999378i	$0.488777\pi$
$234$	−1.59492	−	8.63343i	−0.104263	−	0.564385i
$235$	−5.65630	−	21.1096i	−0.368976	−	1.37704i
$236$	20.9874	+	9.37342i	1.36616	+	0.610158i
$237$	10.8716	+	10.8716i	0.706189	+	0.706189i
$238$	1.03283	+	0.142326i	0.0669487	+	0.00922561i
$239$	23.6067			1.52699			0.763495	−	0.645814i	$-0.223482\pi$
$239$	23.6067			1.52699			0.763495	+	0.645814i	$0.223482\pi$
$240$	−2.21837	−	10.5572i	−0.143195	−	0.681466i
$241$	1.44073	−	2.49542i	0.0928056	−	0.160744i	−0.815885	−	0.578214i	$-0.803750\pi$
$241$	1.44073	−	2.49542i	0.0928056	−	0.160744i	0.908691	+	0.417470i	$0.137083\pi$
$242$	9.60857	+	6.61201i	0.617662	+	0.425036i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−2.22293	−	3.06710i	−0.142309	−	0.196351i
$245$	17.5498	+	6.95747i	1.12122	+	0.444497i
$246$	9.90720	−	8.45160i	0.631660	−	0.538854i
$247$	36.7234	−	21.2023i	2.33666	−	1.34907i
$248$	16.0086	−	16.8107i	1.01655	−	1.06748i
$249$	3.41717	+	1.97290i	0.216554	+	0.125028i
$250$	3.47695	−	9.80049i	0.219901	−	0.619838i
$251$	4.78248	−	4.78248i	0.301867	−	0.301867i	−0.539877	−	0.841744i	$-0.681529\pi$
$251$	4.78248	−	4.78248i	0.301867	−	0.301867i	0.841744	+	0.539877i	$0.181529\pi$
$252$	−1.13441	+	5.16847i	−0.0714608	+	0.325583i
$253$	2.20723	+	2.20723i	0.138768	+	0.138768i
$254$	−0.0733739	−	0.154062i	−0.00460389	−	0.00966671i
$255$	0.375745	−	0.650810i	0.0235301	−	0.0407553i
$256$	−14.6468	+	6.43977i	−0.915426	+	0.402485i
$257$	1.97514	+	3.42105i	0.123206	+	0.213399i	0.921030	−	0.389491i	$-0.127349\pi$
$257$	1.97514	+	3.42105i	0.123206	+	0.213399i	−0.797824	+	0.602890i	$0.794016\pi$
$258$	4.37789	+	0.347107i	0.272556	+	0.0216100i
$259$	−5.86990	−	1.94273i	−0.364738	−	0.120715i
$260$	33.0672	+	5.27673i	2.05074	+	0.327249i
$261$	2.08230	+	0.557951i	0.128891	+	0.0345363i
$262$	5.12124	−	0.946087i	0.316391	−	0.0584494i
$263$	−2.21417	−	1.27835i	−0.136532	−	0.0788266i	0.430178	−	0.902744i	$-0.358451\pi$
$263$	−2.21417	−	1.27835i	−0.136532	−	0.0788266i	−0.566710	+	0.823917i	$0.691784\pi$
$264$	1.32490	+	4.50161i	0.0815423	+	0.277055i
$265$		−	11.4036i		−	0.700517i
$266$	−25.3587	+	3.18286i	−1.55484	+	0.195154i
$267$	12.7148	−	12.7148i	0.778135	−	0.778135i
$268$	3.33185	−	7.46011i	0.203525	−	0.455699i
$269$	−30.1180	+	8.07009i	−1.83633	+	0.492042i	−0.998543	−	0.0539617i	$-0.982815\pi$
$269$	−30.1180	+	8.07009i	−1.83633	+	0.492042i	−0.837783	+	0.546004i	$0.816148\pi$
$270$	3.14201	+	2.16213i	0.191216	+	0.131583i
$271$	−11.8446	−	20.5155i	−0.719509	−	1.24623i	−0.961195	−	0.275872i	$-0.911034\pi$
$271$	−11.8446	−	20.5155i	−0.719509	−	1.24623i	0.241685	−	0.970355i	$-0.422300\pi$
$272$	−1.05923	−	0.346887i	−0.0642250	−	0.0210331i
$273$	−13.7261	−	9.02073i	−0.830742	−	0.545959i
$274$	−0.750886	+	9.47055i	−0.0453627	+	0.572137i
$275$	0.976237	−	3.64337i	0.0588693	−	0.219703i
$276$	−0.388988	−	3.74281i	−0.0234143	−	0.225291i
$277$	1.90451	+	7.10774i	0.114431	+	0.427063i	0.999244	−	0.0388843i	$-0.0123804\pi$
$277$	1.90451	+	7.10774i	0.114431	+	0.427063i	−0.884813	+	0.465947i	$0.845714\pi$
$278$	−20.2975	−	7.20101i	−1.21737	−	0.431888i
$279$			8.20728i			0.491357i
$280$	−17.1317	−	10.6688i	−1.02381	−	0.637580i
$281$			23.4339i			1.39795i	0.715147	+	0.698974i	$0.246360\pi$
$281$			23.4339i			1.39795i	−0.715147	+	0.698974i	$0.753640\pi$
$282$	3.83165	−	10.8003i	0.228172	−	0.643149i
$283$	−1.87869	−	7.01137i	−0.111677	−	0.416783i	0.887340	−	0.461115i	$-0.152551\pi$
$283$	−1.87869	−	7.01137i	−0.111677	−	0.416783i	−0.999017	+	0.0443325i	$0.985884\pi$
$284$	−22.0474	−	17.8961i	−1.30827	−	1.06194i
$285$	−4.76788	+	17.7940i	−0.282425	+	1.05402i
$286$	−14.5202	−	1.15125i	−0.858596	−	0.0680750i
$287$	1.40781	−	24.3219i	0.0831003	−	1.43568i
$288$	2.17996	−	5.21994i	0.128455	−	0.307588i
$289$	8.46118	+	14.6552i	0.497716	+	0.862070i
$290$	−4.66103	+	6.77340i	−0.273705	+	0.397748i
$291$	−4.03306	+	1.08065i	−0.236422	+	0.0633491i
$292$	−9.82108	+	3.75687i	−0.574735	+	0.219854i
$293$	4.76217	−	4.76217i	0.278209	−	0.278209i	−0.554185	−	0.832394i	$-0.686970\pi$
$293$	4.76217	−	4.76217i	0.278209	−	0.278209i	0.832394	+	0.554185i	$0.186970\pi$
$294$	5.51297	+	8.22236i	0.321523	+	0.479538i
$295$		−	30.9952i		−	1.80461i
$296$	5.80343	+	3.16412i	0.337317	+	0.183911i
$297$	−1.43679	−	0.829530i	−0.0833709	−	0.0481342i
$298$	−2.14278	−	11.5990i	−0.124128	−	0.671912i
$299$	11.2824	+	3.02310i	0.652476	+	0.174830i
$300$	−3.68172	+	2.66840i	−0.212564	+	0.154060i
$301$	6.13558	−	5.46416i	0.353649	−	0.314949i
$302$	−1.56294	+	19.7126i	−0.0899372	+	1.13433i
$303$	−2.89401	−	5.01258i	−0.166257	−	0.287965i
$304$	27.2814	+	1.49336i	1.56470	+	0.0856498i
$305$	−2.55397	+	4.42360i	−0.146240	+	0.253295i
$306$	0.355775	−	0.169442i	0.0203383	−	0.00968636i
$307$	−3.80890	−	3.80890i	−0.217385	−	0.217385i	0.590010	−	0.807396i	$-0.299124\pi$
$307$	−3.80890	−	3.80890i	−0.217385	−	0.217385i	−0.807396	+	0.590010i	$0.799124\pi$
$308$	7.79552	+	4.03724i	0.444191	+	0.230043i
$309$	0.192507	−	0.192507i	0.0109513	−	0.0109513i
$310$	−29.5015	−	10.4663i	−1.67557	−	0.594446i
$311$	4.59975	+	2.65566i	0.260828	+	0.150589i	0.624712	−	0.780855i	$-0.285216\pi$
$311$	4.59975	+	2.65566i	0.260828	+	0.150589i	−0.363884	+	0.931444i	$0.618550\pi$
$312$	12.7158	+	12.1090i	0.719889	+	0.685538i
$313$	6.70050	−	3.86854i	0.378735	−	0.218663i	−0.298533	−	0.954399i	$-0.596497\pi$
$313$	6.70050	−	3.86854i	0.378735	−	0.218663i	0.677268	+	0.735737i	$0.263164\pi$
$314$	−4.87612	−	5.71593i	−0.275176	−	0.322569i
$315$	6.98751	−	1.44543i	0.393702	−	0.0814406i
$316$	−30.3654	−	4.84560i	−1.70819	−	0.272586i
$317$	−0.127287	+	0.475043i	−0.00714918	+	0.0266811i	−0.969408	−	0.245454i	$-0.921063\pi$
$317$	−0.127287	+	0.475043i	−0.00714918	+	0.0266811i	0.962259	+	0.272135i	$0.0877297\pi$
$318$	3.38984	−	4.92612i	0.190093	−	0.276243i
$319$	1.78826	−	3.09736i	0.100124	−	0.173419i
$320$	15.9833	+	14.4927i	0.893495	+	0.810166i
$321$	6.81497			0.380374
$322$	−5.55913	−	4.31926i	−0.309798	−	0.240703i
$323$	1.34584	+	1.34584i	0.0748846	+	0.0748846i
$324$	0.714565	+	1.86799i	0.0396981	+	0.103777i
$325$	−3.65299	−	13.6332i	−0.202632	−	0.756231i
$326$	24.5103	−	4.52798i	1.35750	−	0.250782i
$327$	−10.1907	+	5.88361i	−0.563548	+	0.325364i
$328$	−6.12416	+	25.3145i	−0.338150	+	1.39776i
$329$	−9.62889	−	19.1555i	−0.530858	−	1.05608i
$330$	4.81404	−	4.10675i	0.265004	−	0.226069i
$331$	8.24658	+	2.20967i	0.453273	+	0.121454i	0.478231	−	0.878234i	$-0.341278\pi$
$331$	8.24658	+	2.20967i	0.453273	+	0.121454i	−0.0249573	+	0.999689i	$0.507945\pi$
$332$	−7.84933	+	0.815775i	−0.430788	+	0.0447715i
$333$	−2.25734	+	0.604852i	−0.123701	+	0.0331457i
$334$	−24.5501	+	11.6923i	−1.34332	+	0.639774i
$335$	−11.0175			−0.601949
$336$	−4.22913	−	9.70126i	−0.230718	−	0.529247i
$337$	16.3123			0.888588			0.444294	−	0.895881i	$-0.353455\pi$
$337$	16.3123			0.888588			0.444294	+	0.895881i	$0.353455\pi$
$338$	−32.6094	+	15.5306i	−1.77372	+	0.844756i
$339$	6.91413	−	1.85263i	0.375524	−	0.100621i
$340$	0.155367	+	1.49493i	0.00842596	+	0.0810739i
$341$	13.1524	+	3.52418i	0.712243	+	0.190845i
$342$	−7.34908	+	6.26933i	−0.397393	+	0.339006i
$343$	18.2424	+	3.19632i	0.984995	+	0.172585i
$344$	−7.49695	+	4.57618i	−0.404208	+	0.246731i
$345$	−4.39444	+	2.53713i	−0.236589	+	0.136595i
$346$	−32.4685	+	5.99817i	−1.74552	+	0.322464i
$347$	−6.09553	−	22.7488i	−0.327225	−	1.22122i	−0.912056	−	0.410065i	$-0.865506\pi$
$347$	−6.09553	−	22.7488i	−0.327225	−	1.22122i	0.584831	−	0.811155i	$-0.301161\pi$
$348$	−4.02694	+	1.54043i	−0.215866	+	0.0825756i
$349$	23.6096	+	23.6096i	1.26379	+	1.26379i	0.949240	+	0.314552i	$0.101854\pi$
$349$	23.6096	+	23.6096i	1.26379	+	1.26379i	0.314552	+	0.949240i	$0.398146\pi$
$350$	−1.16126	+	8.42707i	−0.0620719	+	0.450446i
$351$	−6.20805			−0.331361
$352$	−7.42904	−	5.73487i	−0.395969	−	0.305670i
$353$	11.5964	−	20.0855i	0.617212	−	1.06904i	−0.372780	−	0.927920i	$-0.621595\pi$
$353$	11.5964	−	20.0855i	0.617212	−	1.06904i	0.989992	−	0.141123i	$-0.0450714\pi$
$354$	9.21368	−	13.3893i	0.489701	−	0.711634i
$355$	−9.91065	+	36.9871i	−0.526003	+	1.96307i
$356$	−5.66713	+	35.5137i	−0.300357	+	1.88222i
$357$	0.231639	−	0.699889i	0.0122596	−	0.0370421i
$358$	1.39121	+	1.63082i	0.0735278	+	0.0861914i
$359$	−10.1815	+	5.87831i	−0.537360	+	0.310245i	−0.744008	−	0.668170i	$-0.767078\pi$
$359$	−10.1815	+	5.87831i	−0.537360	+	0.310245i	0.206648	+	0.978415i	$0.433744\pi$
$360$	−7.62583	+	0.186387i	−0.401917	+	0.00982345i
$361$	−23.9514	−	13.8284i	−1.26060	−	0.727809i
$362$	13.7259	+	4.86956i	0.721415	+	0.255938i
$363$	5.83188	−	5.83188i	0.306094	−	0.306094i
$364$	32.8156	−	1.50202i	1.72000	−	0.0787275i
$365$	10.0263	+	10.0263i	0.524801	+	0.524801i
$366$	−2.41823	+	1.15171i	−0.126403	+	0.0602009i
$367$	5.80568	−	10.0557i	0.303054	−	0.524905i	−0.673772	−	0.738939i	$-0.735327\pi$
$367$	5.80568	−	10.0557i	0.303054	−	0.524905i	0.976826	+	0.214034i	$0.0686603\pi$
$368$	5.02283	+	5.60456i	0.261833	+	0.292158i
$369$	−4.60410	−	7.97454i	−0.239680	−	0.415138i
$370$	0.704495	−	8.88545i	0.0366250	−	0.461932i
$371$	−2.26618	−	10.9552i	−0.117654	−	0.568765i
$372$	−9.63280	−	13.2909i	−0.499437	−	0.689099i
$373$	−31.7047	−	8.49524i	−1.64160	−	0.439867i	−0.684360	−	0.729144i	$-0.739918\pi$
$373$	−31.7047	−	8.49524i	−1.64160	−	0.439867i	−0.957245	+	0.289278i	$0.906585\pi$
$374$	−0.118767	−	0.642897i	−0.00614132	−	0.0332434i
$375$	−6.36805	−	3.67659i	−0.328845	−	0.189859i
$376$	6.47123	+	21.9872i	0.333728	+	1.13390i
$377$		−	13.3830i		−	0.689262i
$378$	3.44813	+	1.45272i	0.177353	+	0.0747199i
$379$	−12.7248	+	12.7248i	−0.653627	+	0.653627i	−0.953864	−	0.300238i	$-0.902934\pi$
$379$	−12.7248	+	12.7248i	−0.653627	+	0.653627i	0.300238	+	0.953864i	$0.402934\pi$
$380$	−13.1635	−	34.4116i	−0.675273	−	1.76528i
$381$	−0.116551	+	0.0312297i	−0.00597108	+	0.00159995i
$382$	−0.0432540	+	0.0628566i	−0.00221307	+	0.00321602i
$383$	−3.53131	−	6.11640i	−0.180441	−	0.312534i	0.761590	−	0.648060i	$-0.224419\pi$
$383$	−3.53131	−	6.11640i	−0.180441	−	0.312534i	−0.942031	+	0.335526i	$0.891086\pi$
$384$	2.59636	+	11.0118i	0.132495	+	0.561942i
$385$	0.684073	−	11.8183i	0.0348636	−	0.602319i
$386$	−30.5375	−	2.42121i	−1.55432	−	0.123236i
$387$	0.803724	−	2.99954i	0.0408556	−	0.152475i
$388$	5.26278	−	6.48357i	0.267177	−	0.329153i
$389$	3.33144	+	12.4331i	0.168910	+	0.630382i	0.997509	+	0.0705392i	$0.0224720\pi$
$389$	3.33144	+	12.4331i	0.168910	+	0.630382i	−0.828599	+	0.559843i	$0.810861\pi$
$390$	7.91680	−	22.3151i	0.400883	−	1.12997i
$391$			0.524267i			0.0265133i
$392$	−18.5782	−	6.84476i	−0.938340	−	0.345713i
$393$		−	3.68254i		−	0.185759i
$394$	27.2375	+	9.66311i	1.37220	+	0.486820i
$395$	10.7319	+	40.0522i	0.539983	+	2.01524i
$396$	3.30034	−	0.343002i	0.165848	−	0.0172365i
$397$	6.27871	−	23.4325i	0.315120	−	1.17604i	−0.608759	−	0.793356i	$-0.708332\pi$
$397$	6.27871	−	23.4325i	0.315120	−	1.17604i	0.923878	−	0.382687i	$-0.125001\pi$
$398$	2.33580	−	29.4602i	0.117083	−	1.47671i
$399$	−1.04430	+	18.0418i	−0.0522804	+	0.903220i
$400$	2.83031	−	8.64240i	0.141516	−	0.432120i
$401$	−2.17848	−	3.77324i	−0.108788	−	0.188427i	0.806491	−	0.591246i	$-0.201364\pi$
$401$	−2.17848	−	3.77324i	−0.108788	−	0.188427i	−0.915280	+	0.402819i	$0.868030\pi$
$402$	−4.75933	−	3.27507i	−0.237374	−	0.163346i
$403$	49.2151	−	13.1872i	2.45158	−	0.656899i
$404$	10.5698	+	4.72069i	0.525866	+	0.234863i
$405$	1.90703	−	1.90703i	0.0947610	−	0.0947610i
$406$	−3.13171	+	7.43333i	−0.155424	+	0.368910i
$407$			3.87717i			0.192184i
$408$	−0.377269	+	0.691963i	−0.0186776	+	0.0342573i
$409$	−26.8149	−	15.4816i	−1.32591	−	0.765516i	−0.341248	−	0.939973i	$-0.610850\pi$
$409$	−26.8149	−	15.4816i	−1.32591	−	0.765516i	−0.984665	+	0.174457i	$0.944183\pi$
$410$	34.5362	−	6.38016i	1.70562	−	0.315093i
$411$	6.48881	+	1.73867i	0.320069	+	0.0857623i
$412$	−0.0858021	+	0.537688i	−0.00422717	+	0.0264900i
$413$	−6.15952	−	29.7765i	−0.303090	−	1.46521i
$414$	−2.65250	−	0.210307i	−0.130363	−	0.0103360i
$415$	5.32081	+	9.21591i	0.261188	+	0.452391i
$416$	−34.8041	−	4.68497i	−1.70641	−	0.229700i
$417$	−7.61450	+	13.1887i	−0.372884	+	0.645853i
$418$	6.89111	+	14.4691i	0.337055	+	0.707709i
$419$	−14.0924	−	14.0924i	−0.688460	−	0.688460i	0.273432	−	0.961891i	$-0.411841\pi$
$419$	−14.0924	−	14.0924i	−0.688460	−	0.688460i	−0.961891	+	0.273432i	$0.911841\pi$
$420$	−9.61909	+	10.5419i	−0.469363	+	0.514392i
$421$	15.0600	−	15.0600i	0.733979	−	0.733979i	−0.237427	−	0.971405i	$-0.576304\pi$
$421$	15.0600	−	15.0600i	0.733979	−	0.733979i	0.971405	+	0.237427i	$0.0763040\pi$
$422$	−4.84777	+	13.6644i	−0.235986	+	0.665174i
$423$	−7.01770	−	4.05167i	−0.341212	−	0.196999i
$424$	0.292222	+	11.9560i	0.0141915	+	0.580633i
$425$	0.548629	−	0.316751i	0.0266124	−	0.0153647i
$426$	−15.2760	+	13.0316i	−0.740125	+	0.631383i
$427$	−1.57447	+	4.75720i	−0.0761937	+	0.230217i
$428$	−11.0362	+	7.99865i	−0.533453	+	0.386629i
$429$	−2.66572	+	9.94858i	−0.128702	+	0.480322i
$430$	9.75704	+	6.71418i	0.470526	+	0.323786i
$431$	6.82531	−	11.8218i	0.328763	−	0.569435i	−0.653503	−	0.756924i	$-0.726701\pi$
$431$	6.82531	−	11.8218i	0.328763	−	0.569435i	0.982267	+	0.187489i	$0.0600348\pi$
$432$	−3.34961	−	2.18635i	−0.161158	−	0.105191i
$433$	29.1963			1.40308			0.701542	−	0.712628i	$-0.252495\pi$
$433$	29.1963			1.40308			0.701542	+	0.712628i	$0.252495\pi$
$434$	−30.4214	−	4.19210i	−1.46027	−	0.201227i
$435$	4.11109	+	4.11109i	0.197112	+	0.197112i
$436$	9.59730	−	21.4886i	0.459627	−	1.02912i
$437$	−3.32625	−	12.4137i	−0.159116	−	0.593829i
$438$	1.35073	+	7.31159i	0.0645403	+	0.349361i
$439$	−20.6686	+	11.9330i	−0.986457	+	0.569531i	−0.904213	−	0.427081i	$-0.859542\pi$
$439$	−20.6686	+	11.9330i	−0.986457	+	0.569531i	−0.0822435	+	0.996612i	$0.526209\pi$
$440$	−2.97581	+	12.3007i	−0.141866	+	0.586411i
$441$	6.42552	−	2.77718i	0.305977	−	0.132247i
$442$	−1.58771	−	1.86116i	−0.0755196	−	0.0885262i
$443$	20.6289	+	5.52749i	0.980107	+	0.262619i	0.713090	−	0.701073i	$-0.247295\pi$
$443$	20.6289	+	5.52749i	0.980107	+	0.262619i	0.267017	+	0.963692i	$0.413962\pi$
$444$	2.94562	−	3.62891i	0.139793	−	0.172221i
$445$	46.8427	−	12.5515i	2.22056	−	0.594996i
$446$	−4.66202	−	9.78876i	−0.220753	−	0.463511i
$447$	−8.34051			−0.394493
$448$	18.2349	+	10.7465i	0.861519	+	0.507726i
$449$	−9.15371			−0.431990			−0.215995	−	0.976394i	$-0.569300\pi$
$449$	−9.15371			−0.431990			−0.215995	+	0.976394i	$0.569300\pi$
$450$	1.38251	+	2.90282i	0.0651720	+	0.136840i
$451$	−14.7564	+	3.95397i	−0.694852	+	0.186185i
$452$	−9.02231	+	11.1152i	−0.424374	+	0.522815i
$453$	13.5062	+	3.61898i	0.634577	+	0.170034i
$454$	0.943362	+	1.10584i	0.0442742	+	0.0518995i
$455$	−19.8948	−	39.5783i	−0.932683	−	1.85546i
$456$	4.54286	−	18.7781i	0.212739	−	0.879364i
$457$	11.1210	−	6.42072i	0.520219	−	0.300348i	−0.216805	−	0.976215i	$-0.569564\pi$
$457$	11.1210	−	6.42072i	0.520219	−	0.300348i	0.737024	+	0.675866i	$0.236230\pi$
$458$	−5.06108	−	27.3960i	−0.236489	−	1.28013i
$459$	−0.0721187	−	0.269150i	−0.00336621	−	0.0125629i
$460$	4.13855	−	9.26634i	0.192961	−	0.432045i
$461$	7.54954	+	7.54954i	0.351617	+	0.351617i	0.860711	−	0.509094i	$-0.170019\pi$
$461$	7.54954	+	7.54954i	0.351617	+	0.351617i	−0.509094	+	0.860711i	$0.670019\pi$
$462$	3.80864	−	4.90194i	0.177194	−	0.228059i
$463$	22.4612			1.04386			0.521930	−	0.852988i	$-0.325212\pi$
$463$	22.4612			1.04386			0.521930	+	0.852988i	$0.325212\pi$
$464$	4.71323	−	7.22094i	0.218806	−	0.335224i
$465$	−11.0673	+	19.1691i	−0.513233	+	0.888946i
$466$	−16.6865	−	11.4826i	−0.772986	−	0.531920i
$467$	1.67577	−	6.25407i	0.0775455	−	0.289404i	−0.916253	−	0.400600i	$-0.868802\pi$
$467$	1.67577	−	6.25407i	0.0775455	−	0.289404i	0.993798	+	0.111196i	$0.0354683\pi$
$468$	10.0533	−	7.28633i	0.464715	−	0.336811i
$469$	−10.5843	+	2.18945i	−0.488736	+	0.101099i
$470$	23.5132	−	20.0586i	1.08458	−	0.925233i
$471$	−4.60089	+	2.65632i	−0.211998	+	0.122397i
$472$	0.794266	+	32.4966i	0.0365591	+	1.49578i
$473$	−4.46173	−	2.57598i	−0.205151	−	0.118444i
$474$	−7.26996	+	20.4919i	−0.333921	+	0.941224i
$475$	−10.9809	+	10.9809i	−0.503840	+	0.503840i
$476$	0.446337	+	1.40527i	0.0204578	+	0.0644105i
$477$	−2.98989	−	2.98989i	−0.136897	−	0.136897i
$478$	14.3551	+	30.1411i	0.656585	+	1.37862i
$479$	−10.9878	+	19.0315i	−0.502046	+	0.869569i	0.497951	+	0.867205i	$0.334086\pi$
$479$	−10.9878	+	19.0315i	−0.502046	+	0.869569i	−0.999997	+	0.00236419i	$0.999247\pi$
$480$	12.1305	−	9.25219i	0.553679	−	0.422303i
$481$	7.25402	+	12.5643i	0.330755	+	0.572884i
$482$	4.06225	+	0.322082i	0.185031	+	0.0146704i
$483$	−3.71746	+	3.31066i	−0.169150	+	0.150640i
$484$	−2.59933	+	16.2889i	−0.118151	+	0.740407i
$485$	−10.8769	−	2.91447i	−0.493896	−	0.132339i
$486$	1.39068	−	0.256912i	0.0630826	−	0.0116538i
$487$	11.5101	+	6.64536i	0.521572	+	0.301130i	0.737578	−	0.675262i	$-0.235970\pi$
$487$	11.5101	+	6.64536i	0.521572	+	0.301130i	−0.216005	+	0.976392i	$0.569303\pi$
$488$	2.56432	−	4.70333i	0.116082	−	0.212910i
$489$		−	17.6247i		−	0.797014i
$490$	1.78860	+	26.6384i	0.0808006	+	1.20340i
$491$	−20.5240	+	20.5240i	−0.926235	+	0.926235i	−0.997460	−	0.0712256i	$-0.977309\pi$
$491$	−20.5240	+	20.5240i	−0.926235	+	0.926235i	0.0712256	+	0.997460i	$0.477309\pi$
$492$	16.8155	+	7.51018i	0.758102	+	0.338585i
$493$	0.580223	−	0.155470i	0.0261319	−	0.00700203i
$494$	49.4024	+	33.9956i	2.22272	+	1.52953i
$495$	−2.23720	−	3.87494i	−0.100554	−	0.174166i
$496$	31.1987	+	10.2173i	1.40086	+	0.458770i
$497$	−2.17071	+	37.5022i	−0.0973698	+	1.68220i
$498$	−0.441051	+	5.56275i	−0.0197640	+	0.249273i
$499$	−2.75117	+	10.2675i	−0.123159	+	0.459637i	−0.999767	−	0.0215680i	$-0.993134\pi$
$499$	−2.75117	+	10.2675i	−0.123159	+	0.459637i	0.876608	+	0.481205i	$0.159801\pi$
$500$	14.6276	−	1.52024i	0.654166	−	0.0679870i
$501$	4.97652	+	18.5726i	0.222335	+	0.829765i
$502$	9.01447	+	3.19809i	0.402336	+	0.142738i
$503$			2.45217i			0.109337i	0.998505	+	0.0546684i	$0.0174102\pi$
$503$			2.45217i			0.109337i	−0.998505	+	0.0546684i	$0.982590\pi$
$504$	−7.28894	+	1.69450i	−0.324675	+	0.0754790i
$505$		−	15.6100i		−	0.694635i
$506$	−1.47600	+	4.16040i	−0.0656161	+	0.184952i
$507$	6.61022	+	24.6697i	0.293570	+	1.09562i
$508$	0.152088	−	0.187368i	0.00674784	−	0.00831311i
$509$	−4.18783	+	15.6292i	−0.185622	+	0.692751i	0.808874	+	0.587982i	$0.200077\pi$
$509$	−4.18783	+	15.6292i	−0.185622	+	0.692751i	−0.994497	+	0.104770i	$0.966589\pi$
$510$	1.05944	+	0.0839995i	0.0469129	+	0.00371956i
$511$	11.6245	+	7.63959i	0.514240	+	0.337956i
$512$	−17.1289	−	14.7851i	−0.756999	−	0.653416i
$513$	3.41529	+	5.91545i	0.150789	+	0.261173i
$514$	−3.16693	+	4.60218i	−0.139687	+	0.202993i
$515$	0.709213	−	0.190033i	0.0312517	−	0.00837386i
$516$	2.21898	+	5.80077i	0.0976850	+	0.255365i
$517$	−9.50629	+	9.50629i	−0.418086	+	0.418086i
$518$	−1.08896	−	8.67607i	−0.0478464	−	0.381204i
$519$			23.3472i			1.02483i
$520$	13.3706	+	45.4290i	0.586339	+	1.99219i
$521$	31.4566	+	18.1615i	1.37814	+	0.795668i	0.991935	−	0.126747i	$-0.0404536\pi$
$521$	31.4566	+	18.1615i	1.37814	+	0.795668i	0.386202	+	0.922414i	$0.373787\pi$
$522$	0.553839	+	2.99797i	0.0242409	+	0.131218i
$523$	17.3302	+	4.64363i	0.757799	+	0.203052i	0.616975	−	0.786983i	$-0.288358\pi$
$523$	17.3302	+	4.64363i	0.757799	+	0.203052i	0.140824	+	0.990035i	$0.455025\pi$
$524$	4.32215	+	5.96349i	0.188814	+	0.260516i
$525$	5.71051	+	1.88998i	0.249227	+	0.0824854i
$526$	0.285781	−	3.60441i	0.0124606	−	0.157160i
$527$	1.14346	+	1.98053i	0.0498099	+	0.0862732i
$528$	−4.94200	+	4.42904i	−0.215073	+	0.192749i
$529$	−9.73000	+	16.8529i	−0.423044	+	0.732733i
$530$	14.5601	−	6.93444i	0.632452	−	0.301213i
$531$	−8.12658	−	8.12658i	−0.352664	−	0.352664i
$532$	−19.4843	−	30.4426i	−0.844753	−	1.31985i
$533$	−40.4218	+	40.4218i	−1.75086	+	1.75086i
$534$	23.9661	+	8.50253i	1.03712	+	0.367940i
$535$	15.9172	+	9.18979i	0.688160	+	0.397309i
$536$	11.5512	−	0.282328i	0.498934	−	0.0121947i
$537$	1.31268	−	0.757878i	0.0566465	−	0.0327049i
$538$	−28.6184	−	33.5473i	−1.23383	−	1.44633i
$539$	−1.69142	−	11.4896i	−0.0728548	−	0.494891i
$540$	−0.849981	+	5.32650i	−0.0365774	+	0.229216i
$541$	−5.40170	+	20.1594i	−0.232237	+	0.866721i	0.747138	+	0.664669i	$0.231428\pi$
$541$	−5.40170	+	20.1594i	−0.232237	+	0.866721i	−0.979375	+	0.202052i	$0.935239\pi$
$542$	18.9916	−	27.5985i	0.815758	−	1.18546i
$543$	5.14917	−	8.91863i	0.220972	−	0.382735i
$544$	−0.201201	−	1.56336i	−0.00862642	−	0.0670285i
$545$	−31.7355			−1.35940
$546$	3.17094	−	23.0110i	0.135704	−	0.984778i
$547$	−20.3456	−	20.3456i	−0.869914	−	0.869914i	0.122549	−	0.992462i	$-0.460893\pi$
$547$	−20.3456	−	20.3456i	−0.869914	−	0.869914i	−0.992462	+	0.122549i	$0.960893\pi$
$548$	−12.5486	+	4.80024i	−0.536051	+	0.205056i
$549$	0.490196	+	1.82944i	0.0209211	+	0.0780785i
$550$	5.24550	−	0.969044i	0.223669	−	0.0413202i
$551$	−12.7523	+	7.36252i	−0.543265	+	0.313654i
$552$	4.54229	−	2.77264i	0.193333	−	0.118011i
$553$	18.2693	+	36.3446i	0.776890	+	1.54553i
$554$	−7.91706	+	6.75385i	−0.336364	+	0.286944i
$555$	−6.08792	−	1.63125i	−0.258418	−	0.0692428i
$556$	−3.14852	−	30.2948i	−0.133527	−	1.28479i
$557$	37.9572	−	10.1706i	1.60830	−	0.430942i	0.660762	−	0.750595i	$-0.270233\pi$
$557$	37.9572	−	10.1706i	1.60830	−	0.430942i	0.947535	+	0.319653i	$0.103566\pi$
$558$	−10.4791	+	4.99079i	−0.443614	+	0.211277i
$559$	−19.2782			−0.815380
$560$	3.20424	−	28.3613i	0.135404	−	1.19849i
$561$	−0.462289			−0.0195179
$562$	−29.9204	+	14.2500i	−1.26212	+	0.601099i
$563$	−7.27950	+	1.95054i	−0.306795	+	0.0822053i	−0.408932	−	0.912565i	$-0.634099\pi$
$563$	−7.27950	+	1.95054i	−0.306795	+	0.0822053i	0.102137	+	0.994770i	$0.467432\pi$
$564$	16.1199	−	1.67533i	0.678768	−	0.0705439i
$565$	18.6470	+	4.99645i	0.784486	+	0.210202i
$566$	7.80971	−	6.66228i	0.328267	−	0.280037i
$567$	1.45307	−	2.21102i	0.0610231	−	0.0928539i
$568$	9.44291	−	39.0326i	0.396216	−	1.63777i
$569$	−17.7057	+	10.2224i	−0.742262	+	0.428545i	−0.822891	−	0.568199i	$-0.807640\pi$
$569$	−17.7057	+	10.2224i	−0.742262	+	0.428545i	0.0806289	+	0.996744i	$0.474307\pi$
$570$	−25.6187	+	4.73275i	−1.07305	+	0.198233i
$571$	−6.16087	−	22.9927i	−0.257824	−	0.962214i	−0.966497	−	0.256677i	$-0.917372\pi$
$571$	−6.16087	−	22.9927i	−0.257824	−	0.962214i	0.708673	−	0.705537i	$-0.249294\pi$
$572$	−7.35969	−	19.2394i	−0.307724	−	0.804442i
$573$	0.0381506	+	0.0381506i	0.00159376	+	0.00159376i
$574$	31.9103	−	12.9925i	1.33191	−	0.542296i
$575$	−4.27758			−0.178387
$576$	7.99045	−	0.390830i	0.332935	−	0.0162846i
$577$	2.96510	−	5.13571i	0.123439	−	0.213802i	−0.797683	−	0.603077i	$-0.793941\pi$
$577$	2.96510	−	5.13571i	0.123439	−	0.213802i	0.921122	+	0.389275i	$0.127274\pi$
$578$	−13.5666	+	19.7150i	−0.564296	+	0.820034i
$579$	−5.60630	+	20.9230i	−0.232990	+	0.869529i
$580$	−11.4826	−	1.83235i	−0.476790	−	0.0760843i
$581$	6.94302	+	7.79616i	0.288045	+	0.323439i
$582$	−3.83226	−	4.49228i	−0.158852	−	0.186211i
$583$	−6.07522	+	3.50753i	−0.251610	+	0.145267i
$584$	−10.7689	−	10.2550i	−0.445620	−	0.424357i
$585$	−14.4997	−	8.37139i	−0.599488	−	0.346114i
$586$	8.97618	+	3.18451i	0.370803	+	0.131551i
$587$	−4.26798	+	4.26798i	−0.176158	+	0.176158i	−0.789679	−	0.613520i	$-0.789753\pi$
$587$	−4.26798	+	4.26798i	−0.176158	+	0.176158i	0.613520	+	0.789679i	$0.289753\pi$
$588$	−7.14592	+	12.0389i	−0.294693	+	0.496477i
$589$	−39.6407	−	39.6407i	−1.63337	−	1.63337i
$590$	39.5748	−	18.8480i	1.62927	−	0.775959i
$591$	10.2180	−	17.6980i	0.420311	−	0.728000i
$592$	−0.510927	+	9.33390i	−0.0209990	+	0.383621i
$593$	−16.5643	−	28.6903i	−0.680216	−	1.17817i	−0.974915	−	0.222579i	$-0.928553\pi$
$593$	−16.5643	−	28.6903i	−0.680216	−	1.17817i	0.294699	−	0.955590i	$-0.404781\pi$
$594$	0.185445	−	2.33892i	0.00760890	−	0.0959672i
$595$	1.48480	−	1.32232i	0.0608709	−	0.0542098i
$596$	13.5066	−	9.78917i	0.553252	−	0.400980i
$597$	−20.1849	−	5.40852i	−0.826111	−	0.221356i
$598$	3.00082	+	16.2437i	0.122713	+	0.664253i
$599$	−2.41360	−	1.39349i	−0.0986172	−	0.0569367i	0.449880	−	0.893089i	$-0.351467\pi$
$599$	−2.41360	−	1.39349i	−0.0986172	−	0.0569367i	−0.548497	+	0.836152i	$0.684800\pi$
$600$	−5.64584	−	3.07820i	−0.230491	−	0.125667i
$601$		−	1.22065i		−	0.0497914i	−0.999690	−	0.0248957i	$-0.992075\pi$
$601$		−	1.22065i		−	0.0497914i	0.999690	−	0.0248957i	$-0.00792537\pi$
$602$	10.7077	+	4.51120i	0.436411	+	0.183863i
$603$	−2.88865	+	2.88865i	−0.117635	+	0.117635i
$604$	−26.1195	+	9.99152i	−1.06279	+	0.406549i
$605$	21.4852	−	5.75694i	0.873497	−	0.234053i
$606$	4.64024	−	6.74319i	0.188497	−	0.273924i
$607$	3.84092	+	6.65267i	0.155898	+	0.270024i	0.933386	−	0.358875i	$-0.116839\pi$
$607$	3.84092	+	6.65267i	0.155898	+	0.270024i	−0.777487	+	0.628898i	$0.783506\pi$
$608$	14.6829	+	35.7411i	0.595472	+	1.44949i
$609$	4.76641	+	3.13246i	0.193145	+	0.126934i
$610$	−7.20112	−	0.570951i	−0.291565	−	0.0231171i
$611$	−13.0201	+	48.5918i	−0.526739	+	1.96582i
$612$	0.432688	+	0.351217i	0.0174904	+	0.0141971i
$613$	8.61710	+	32.1595i	0.348041	+	1.29891i	0.889019	+	0.457871i	$0.151388\pi$
$613$	8.61710	+	32.1595i	0.348041	+	1.29891i	−0.540977	+	0.841037i	$0.681945\pi$
$614$	2.54705	−	7.17938i	0.102790	−	0.289736i
$615$		−	24.8340i		−	1.00140i
$616$	−0.414359	+	12.4084i	−0.0166950	+	0.499947i
$617$		−	49.3280i		−	1.98587i	−0.118654	−	0.992936i	$-0.537858\pi$
$617$		−	49.3280i		−	1.98587i	0.118654	−	0.992936i	$-0.462142\pi$
$618$	0.362855	+	0.128731i	0.0145962	+	0.00517832i
$619$	−1.07742	−	4.02099i	−0.0433052	−	0.161617i	0.940887	−	0.338720i	$-0.109994\pi$
$619$	−1.07742	−	4.02099i	−0.0433052	−	0.161617i	−0.984192	+	0.177103i	$0.943327\pi$
$620$	−4.57622	−	44.0320i	−0.183785	−	1.76837i
$621$	−0.486964	+	1.81738i	−0.0195412	+	0.0729288i
$622$	−0.593685	+	7.48785i	−0.0238046	+	0.300236i
$623$	42.5065	−	21.3667i	1.70299	−	0.856040i
$624$	−7.72845	+	23.5989i	−0.309386	+	0.944714i
$625$	−15.5994	−	27.0189i	−0.623974	−	1.08075i
$626$	9.01388	+	6.20279i	0.360267	+	0.247913i
$627$	10.9462	−	2.93302i	0.437149	−	0.117134i
$628$	4.33297	−	9.70166i	0.172904	−	0.387138i
$629$	−0.460457	+	0.460457i	−0.0183596	+	0.0183596i
$630$	6.09458	+	8.04271i	0.242814	+	0.320429i
$631$		−	14.5700i		−	0.580021i	−0.957023	−	0.290011i	$-0.906341\pi$
$631$		−	14.5700i		−	0.580021i	0.957023	−	0.290011i	$-0.0936588\pi$
$632$	−12.2781	−	41.7172i	−0.488398	−	1.65942i
$633$	8.87872	+	5.12613i	0.352897	+	0.203745i
$634$	−0.683939	+	0.126350i	−0.0271627	+	0.00501798i
$635$	−0.314331	−	0.0842249i	−0.0124739	−	0.00334236i
$636$	8.35102	+	1.33262i	0.331139	+	0.0528419i
$637$	−26.9777	−	34.0685i	−1.06890	−	1.34984i
$638$	5.04215	+	0.399774i	0.199621	+	0.0158272i
$639$	7.09911	+	12.2960i	0.280836	+	0.486423i
$640$	−8.78494	+	29.2204i	−0.347255	+	1.15504i
$641$	6.57108	−	11.3814i	0.259542	−	0.449540i	−0.706577	−	0.707636i	$-0.749762\pi$
$641$	6.57108	−	11.3814i	0.259542	−	0.449540i	0.966119	+	0.258096i	$0.0830950\pi$
$642$	4.14413	+	8.70136i	0.163556	+	0.343415i
$643$	19.5254	+	19.5254i	0.770006	+	0.770006i	0.978107	−	0.208102i	$-0.0667285\pi$
$643$	19.5254	+	19.5254i	0.770006	+	0.770006i	−0.208102	+	0.978107i	$0.566728\pi$
$644$	2.13437	−	9.72441i	0.0841059	−	0.383196i
$645$	5.92199	−	5.92199i	0.233178	−	0.233178i
$646$	−0.899976	+	2.53677i	−0.0354091	+	0.0998078i
$647$	−3.08275	−	1.77983i	−0.121195	−	0.0699722i	0.438177	−	0.898889i	$-0.355624\pi$
$647$	−3.08275	−	1.77983i	−0.121195	−	0.0699722i	−0.559372	+	0.828917i	$0.688958\pi$
$648$	−1.95053	+	2.04827i	−0.0766242	+	0.0804637i
$649$	−16.5126	+	9.53356i	−0.648177	+	0.374225i
$650$	15.1855	−	12.9544i	0.595624	−	0.508112i
$651$	−6.82274	+	20.6147i	−0.267404	+	0.807954i
$652$	20.6859	+	28.5414i	0.810121	+	1.11777i
$653$	6.45119	−	24.0762i	0.252455	−	0.942173i	−0.717034	−	0.697038i	$-0.754501\pi$
$653$	6.45119	−	24.0762i	0.252455	−	0.942173i	0.969489	−	0.245135i	$-0.0788324\pi$
$654$	−13.7091	−	9.43374i	−0.536068	−	0.368888i
$655$	4.96580	−	8.60101i	0.194030	−	0.336069i
$656$	−36.0456	+	7.57421i	−1.40735	+	0.295723i
$657$	5.25756			0.205117
$658$	18.6025	−	23.9425i	0.725202	−	0.933376i
$659$	−5.86961	−	5.86961i	−0.228647	−	0.228647i	0.583480	−	0.812127i	$-0.301691\pi$
$659$	−5.86961	−	5.86961i	−0.228647	−	0.228647i	−0.812127	+	0.583480i	$0.801691\pi$
$660$	8.17089	+	3.64930i	0.318051	+	0.142049i
$661$	−1.31949	−	4.92441i	−0.0513223	−	0.191537i	0.935505	−	0.353312i	$-0.114945\pi$
$661$	−1.31949	−	4.92441i	−0.0513223	−	0.191537i	−0.986828	+	0.161775i	$0.948278\pi$
$662$	2.19338	+	11.8729i	0.0852482	+	0.461455i
$663$	−1.49809	+	0.864922i	−0.0581809	+	0.0335908i
$664$	−5.81470	−	9.52597i	−0.225654	−	0.369679i
$665$	−26.7680	+	40.7306i	−1.03802	+	1.57947i
$666$	−2.14495	−	2.51437i	−0.0831150	−	0.0974298i
$667$	−3.91782	−	1.04978i	−0.151699	−	0.0406475i
$668$	−29.8575	−	24.2356i	−1.15522	−	0.937705i
$669$	−7.40539	+	1.98427i	−0.286309	+	0.0767163i
$670$	−6.69965	−	14.0671i	−0.258830	−	0.543461i
$671$	3.14221			0.121304
$672$	9.81489	−	11.2990i	0.378618	−	0.435869i
$673$	−1.90924			−0.0735960			−0.0367980	−	0.999323i	$-0.511716\pi$
$673$	−1.90924			−0.0735960			−0.0367980	+	0.999323i	$0.511716\pi$
$674$	9.91940	+	20.8276i	0.382081	+	0.802249i
$675$	2.19604	−	0.588428i	0.0845257	−	0.0226486i
$676$	−39.6591	−	32.1917i	−1.52535	−	1.23814i
$677$	−3.29262	−	0.882254i	−0.126546	−	0.0339078i	0.194990	−	0.980805i	$-0.437532\pi$
$677$	−3.29262	−	0.882254i	−0.126546	−	0.0339078i	−0.321536	+	0.946897i	$0.604199\pi$
$678$	6.56988	+	7.70140i	0.252315	+	0.295770i
$679$	−11.0284	−	0.638350i	−0.423232	−	0.0244976i
$680$	−1.81425	+	1.10743i	−0.0695733	+	0.0424679i
$681$	0.890114	−	0.513907i	0.0341092	−	0.0196930i
$682$	3.49821	+	18.9360i	0.133953	+	0.725098i
$683$	1.46470	+	5.46633i	0.0560451	+	0.209163i	0.988270	−	0.152716i	$-0.0488020\pi$
$683$	1.46470	+	5.46633i	0.0560451	+	0.209163i	−0.932225	+	0.361879i	$0.882135\pi$
$684$	−12.4736	−	5.57099i	−0.476940	−	0.213012i
$685$	12.8109	+	12.8109i	0.489478	+	0.489478i
$686$	7.01198	+	25.2355i	0.267719	+	0.963497i
$687$	−19.6997			−0.751590
$688$	−10.4017	−	6.78938i	−0.396562	−	0.258843i
$689$	−13.1249	+	22.7329i	−0.500018	+	0.866056i
$690$	−5.91164	−	4.06802i	−0.225052	−	0.154867i
$691$	5.26113	−	19.6348i	0.200143	−	0.746943i	−0.790732	−	0.612162i	$-0.790300\pi$
$691$	5.26113	−	19.6348i	0.200143	−	0.746943i	0.990875	−	0.134782i	$-0.0430333\pi$
$692$	−27.4023	−	37.8084i	−1.04168	−	1.43726i
$693$	−2.91927	−	3.27799i	−0.110894	−	0.124520i
$694$	25.3391	−	21.6162i	0.961858	−	0.820539i
$695$	−35.5692	+	20.5359i	−1.34922	+	0.778970i
$696$	−4.41557	−	4.20488i	−0.167372	−	0.159385i
$697$	−2.22207	−	1.28291i	−0.0841668	−	0.0485937i
$698$	−15.7879	+	44.5016i	−0.597583	+	1.68441i
$699$	−10.1278	+	10.1278i	−0.383068	+	0.383068i
$700$	−11.4658	+	3.64174i	−0.433368	+	0.137645i
$701$	4.63561	+	4.63561i	0.175084	+	0.175084i	0.789209	−	0.614125i	$-0.210491\pi$
$701$	4.63561	+	4.63561i	0.175084	+	0.175084i	−0.614125	+	0.789209i	$0.710491\pi$
$702$	−3.77507	−	7.92645i	−0.142481	−	0.299165i
$703$	7.98142	−	13.8242i	0.301025	−	0.521390i
$704$	2.80475	−	12.9727i	0.105708	−	0.488929i
$705$	−10.9271	−	18.9263i	−0.411540	−	0.712807i
$706$	32.6969	+	2.59242i	1.23056	+	0.0975670i
$707$	−3.10209	−	14.9962i	−0.116666	−	0.563990i
$708$	22.6983	+	3.62210i	0.853053	+	0.136127i
$709$	32.3487	+	8.66780i	1.21488	+	0.325526i	0.808675	−	0.588256i	$-0.200185\pi$
$709$	32.3487	+	8.66780i	1.21488	+	0.325526i	0.406205	+	0.913782i	$0.366852\pi$
$710$	−53.2517	+	9.83762i	−1.99850	+	0.369199i
$711$	13.3150	+	7.68741i	0.499351	+	0.288300i
$712$	−48.7900	+	14.3598i	−1.82848	+	0.538156i
$713$		−	15.4419i		−	0.578303i
$714$	1.03448	−	0.129841i	0.0387144	−	0.00485918i
$715$	−19.6415	+	19.6415i	−0.734550	+	0.734550i
$716$	−1.23625	+	2.76799i	−0.0462007	+	0.103445i
$717$	22.8023	−	6.10986i	0.851568	−	0.228177i
$718$	−13.6967	−	9.42524i	−0.511158	−	0.351747i
$719$	−22.0128	−	38.1273i	−0.820940	−	1.42191i	−0.904983	−	0.425447i	$-0.860117\pi$
$719$	−22.0128	−	38.1273i	−0.820940	−	1.42191i	0.0840435	−	0.996462i	$-0.473217\pi$
$720$	−4.87519	−	9.62334i	−0.181688	−	0.358641i
$721$	0.643562	−	0.323499i	0.0239675	−	0.0120477i
$722$	3.09139	−	38.9902i	0.115050	−	1.45106i
$723$	0.745777	−	2.78328i	0.0277357	−	0.103511i
$724$	2.12913	+	20.4863i	0.0791286	+	0.761369i
$725$	1.26851	+	4.73413i	0.0471112	+	0.175821i
$726$	10.9925	+	3.89983i	0.407969	+	0.144736i
$727$			40.9321i			1.51809i	0.651040	+	0.759043i	$0.274333\pi$
$727$			40.9321i			1.51809i	−0.651040	+	0.759043i	$0.725667\pi$
$728$	21.8727	+	40.9856i	0.810656	+	1.51903i
$729$		−	1.00000i		−	0.0370370i
$730$	−6.70469	+	18.8985i	−0.248152	+	0.699466i
$731$	−0.223954	−	0.835807i	−0.00828323	−	0.0309134i
$732$	−2.94101	−	2.38725i	−0.108703	−	0.0882353i
$733$	10.0185	−	37.3897i	0.370044	−	1.38102i	−0.490410	−	0.871492i	$-0.663153\pi$
$733$	10.0185	−	37.3897i	0.370044	−	1.38102i	0.860453	−	0.509529i	$-0.170180\pi$
$734$	16.3696	+	1.29789i	0.604212	+	0.0479058i
$735$	18.7525	+	2.17818i	0.691698	+	0.0803433i
$736$	−4.10157	+	9.82125i	−0.151186	+	0.362016i
$737$	3.38877	+	5.86953i	0.124827	+	0.216207i
$738$	7.38219	−	10.7278i	0.271742	−	0.394895i
$739$	−17.5719	+	4.70839i	−0.646395	+	0.173201i	−0.567098	−	0.823650i	$-0.691934\pi$
$739$	−17.5719	+	4.70839i	−0.646395	+	0.173201i	−0.0792964	+	0.996851i	$0.525267\pi$
$740$	11.7734	−	4.50367i	0.432797	−	0.165558i
$741$	29.9846	−	29.9846i	1.10151	−	1.10151i
$742$	12.6096	−	9.55524i	0.462912	−	0.350784i
$743$		−	22.8578i		−	0.838570i	−0.907855	−	0.419285i	$-0.862281\pi$
$743$		−	22.8578i		−	0.838570i	0.907855	−	0.419285i	$-0.137719\pi$
$744$	11.1122	−	20.3813i	0.407392	−	0.747213i
$745$	−19.4803	−	11.2469i	−0.713702	−	0.412056i
$746$	−8.43264	−	45.6465i	−0.308741	−	1.67124i
$747$	3.81135	+	1.02125i	0.139450	+	0.0373655i
$748$	0.748630	−	0.542583i	0.0273726	−	0.0198388i
$749$	17.1176	+	5.66530i	0.625462	+	0.207006i
$750$	0.821919	−	10.3664i	0.0300122	−	0.378529i
$751$	−16.7955	−	29.0907i	−0.612878	−	1.06154i	−0.990753	−	0.135679i	$-0.956678\pi$
$751$	−16.7955	−	29.0907i	−0.612878	−	1.06154i	0.377875	−	0.925857i	$-0.376655\pi$
$752$	−24.1382	+	21.6327i	−0.880228	+	0.788864i
$753$	3.38172	−	5.85732i	0.123237	−	0.213453i
$754$	17.0875	−	8.13814i	0.622290	−	0.296373i
$755$	26.6653	+	26.6653i	0.970450	+	0.970450i
$756$	0.241948	+	5.28597i	0.00879955	+	0.192249i
$757$	17.4929	−	17.4929i	0.635789	−	0.635789i	−0.313725	−	0.949514i	$-0.601577\pi$
$757$	17.4929	−	17.4929i	0.635789	−	0.635789i	0.949514	+	0.313725i	$0.101577\pi$
$758$	−23.9848	−	8.50916i	−0.871168	−	0.309067i
$759$	2.70330	+	1.56075i	0.0981235	+	0.0566516i
$760$	35.9321	−	37.7326i	1.30339	−	1.36871i
$761$	8.76696	−	5.06161i	0.317802	−	0.183483i	−0.332610	−	0.943064i	$-0.607929\pi$
$761$	8.76696	−	5.06161i	0.317802	−	0.183483i	0.650412	+	0.759581i	$0.274596\pi$
$762$	−0.110748	−	0.129822i	−0.00401198	−	0.00470295i
$763$	−30.4877	+	6.30664i	−1.10373	+	0.228316i
$764$	−0.106558	−	0.0170041i	−0.00385513	−	0.000615186i
$765$	0.194500	−	0.725884i	0.00703216	−	0.0262444i
$766$	5.66207	−	8.22812i	0.204579	−	0.297294i
$767$	−35.6737	+	61.7887i	−1.28810	+	2.23106i
$768$	−12.4810	+	10.0112i	−0.450370	+	0.361249i
$769$	3.80211			0.137108			0.0685539	−	0.997647i	$-0.478161\pi$
$769$	3.80211			0.137108			0.0685539	+	0.997647i	$0.478161\pi$
$770$	15.5057	−	6.31323i	0.558786	−	0.227513i
$771$	2.79327	+	2.79327i	0.100597	+	0.100597i
$772$	−15.4782	−	40.4627i	−0.557074	−	1.45628i
$773$	−3.77261	−	14.0796i	−0.135691	−	0.506407i	−0.999994	−	0.00343516i	$-0.998907\pi$
$773$	−3.77261	−	14.0796i	−0.135691	−	0.506407i	0.864303	−	0.502972i	$-0.167760\pi$
$774$	4.31856	−	0.797801i	0.155227	−	0.0286764i
$775$	−16.1595	+	9.32967i	−0.580465	+	0.335132i
$776$	11.4785	+	2.77691i	0.412054	+	0.0996854i
$777$	−6.17271	−	0.357290i	−0.221445	−	0.0128177i
$778$	−13.8488	+	11.8141i	−0.496502	+	0.423554i
$779$	60.7542	+	16.2790i	2.17674	+	0.583257i
$780$	33.3062	−	3.46149i	1.19255	−	0.123941i
$781$	22.7531	−	6.09666i	0.814168	−	0.218156i
$782$	−0.669385	+	0.318803i	−0.0239372	+	0.0114004i
$783$	2.15576			0.0770404
$784$	−2.55786	−	27.8829i	−0.0913520	−	0.995819i
$785$	−14.3279			−0.511385
$786$	4.70187	−	2.23932i	0.167710	−	0.0798740i
$787$	−29.4506	+	7.89128i	−1.04980	+	0.281294i	−0.742170	−	0.670212i	$-0.766203\pi$
$787$	−29.4506	+	7.89128i	−1.04980	+	0.281294i	−0.307632	+	0.951505i	$0.599537\pi$
$788$	4.22503	+	40.6529i	0.150510	+	1.44820i
$789$	−2.46959	−	0.661724i	−0.0879196	−	0.0235580i
$790$	−44.6126	+	38.0580i	−1.58725	+	1.35404i
$791$	18.9067	+	1.09436i	0.672246	+	0.0389111i
$792$	2.44486	+	4.00531i	0.0868744	+	0.142322i
$793$	10.1826	−	5.87894i	0.361596	−	0.208767i
$794$	33.7367	−	6.23245i	1.19727	−	0.221181i
$795$	−2.95147	−	11.0150i	−0.104678	−	0.390663i
$796$	39.0353	−	14.9322i	1.38357	−	0.529258i
$797$	−16.4756	−	16.4756i	−0.583597	−	0.583597i	0.352293	−	0.935890i	$-0.385402\pi$
$797$	−16.4756	−	16.4756i	−0.583597	−	0.583597i	−0.935890	+	0.352293i	$0.885402\pi$
$798$	−23.6708	+	9.63772i	−0.837938	+	0.341172i
$799$	−2.25796			−0.0798807
$800$	12.7557	−	1.64163i	0.450983	−	0.0580405i
$801$	8.99075	−	15.5724i	0.317672	−	0.550225i
$802$	3.49296	−	5.07597i	0.123341	−	0.179239i
$803$	2.25758	−	8.42539i	0.0796681	−	0.297325i
$804$	1.28750	−	8.06826i	0.0454067	−	0.284546i
$805$	−13.1469	+	2.71955i	−0.463368	+	0.0958516i
$806$	46.7647	+	54.8189i	1.64722	+	1.93091i
$807$	−27.0030	+	15.5902i	−0.950552	+	0.548802i
$808$	0.400012	+	16.3661i	0.0140724	+	0.575758i
$809$	−7.40093	−	4.27293i	−0.260203	−	0.150228i	0.364224	−	0.931311i	$-0.381334\pi$
$809$	−7.40093	−	4.27293i	−0.260203	−	0.150228i	−0.624427	+	0.781083i	$0.714667\pi$
$810$	3.59455	+	1.27525i	0.126300	+	0.0448076i
$811$	−20.9522	+	20.9522i	−0.735730	+	0.735730i	−0.971749	−	0.236018i	$-0.924158\pi$
$811$	−20.9522	+	20.9522i	−0.735730	+	0.735730i	0.236018	+	0.971749i	$0.424158\pi$
$812$	−11.3953	+	0.521580i	−0.399895	+	0.0183039i
$813$	−16.7508	−	16.7508i	−0.587477	−	0.587477i
$814$	−4.95038	+	2.35768i	−0.173511	+	0.0826366i
$815$	23.7664	−	41.1645i	0.832499	−	1.44193i
$816$	−1.11291	−	0.0609197i	−0.0389598	−	0.00213261i
$817$	10.6057	+	18.3695i	0.371045	+	0.642669i
$818$	3.46098	−	43.6516i	0.121010	−	1.52624i
$819$	−15.5931	−	5.16078i	−0.544868	−	0.180332i
$820$	29.1474	+	40.2162i	1.01787	+	1.40441i
$821$	20.5731	+	5.51255i	0.718007	+	0.192389i	0.599282	−	0.800538i	$-0.295453\pi$
$821$	20.5731	+	5.51255i	0.718007	+	0.192389i	0.118725	+	0.992927i	$0.462119\pi$
$822$	1.72586	+	9.34219i	0.0601962	+	0.325846i
$823$	−37.1621	−	21.4555i	−1.29539	−	0.747893i	−0.315785	−	0.948831i	$-0.602268\pi$
$823$	−37.1621	−	21.4555i	−1.29539	−	0.747893i	−0.979604	+	0.200938i	$0.935601\pi$
$824$	−0.738697	+	0.217412i	−0.0257337	+	0.00757390i
$825$		−	3.77189i		−	0.131320i
$826$	34.2731	−	25.9714i	1.19251	−	0.903659i
$827$	18.9114	−	18.9114i	0.657613	−	0.657613i	−0.297202	−	0.954815i	$-0.596053\pi$
$827$	18.9114	−	18.9114i	0.657613	−	0.657613i	0.954815	+	0.297202i	$0.0960534\pi$
$828$	−1.34444	−	3.51460i	−0.0467227	−	0.122141i
$829$	−12.4124	+	3.32589i	−0.431100	+	0.115513i	−0.467842	−	0.883812i	$-0.654968\pi$
$829$	−12.4124	+	3.32589i	−0.431100	+	0.115513i	0.0367427	+	0.999325i	$0.488302\pi$
$830$	−8.53134	+	12.3977i	−0.296127	+	0.430332i
$831$	3.67924	+	6.37263i	0.127631	+	0.221064i
$832$	−15.1824	−	47.2869i	−0.526354	−	1.63938i
$833$	1.16364	−	1.56539i	0.0403178	−	0.0542376i
$834$	−21.4697	−	1.70225i	−0.743434	−	0.0589442i
$835$	−13.4214	+	50.0894i	−0.464467	+	1.73341i
$836$	−14.2838	+	17.5972i	−0.494015	+	0.608610i
$837$	2.12420	+	7.92762i	0.0734231	+	0.274019i
$838$	9.42373	−	26.5627i	0.325537	−	0.917594i
$839$		−	1.08980i		−	0.0376240i	−0.999823	−	0.0188120i	$-0.994012\pi$
$839$		−	1.08980i		−	0.0376240i	0.999823	−	0.0188120i	$-0.00598840\pi$
$840$	−19.3092	−	5.87122i	−0.666231	−	0.202576i
$841$		−	24.3527i		−	0.839749i
$842$	28.3865	+	10.0707i	0.978263	+	0.347061i
$843$	6.06514	+	22.6354i	0.208894	+	0.779605i
$844$	−20.3947	+	2.11960i	−0.702013	+	0.0729598i
$845$	−17.8274	+	66.5328i	−0.613281	+	2.28880i
$846$	0.905768	−	11.4240i	0.0311410	−	0.392765i
$847$	19.4963	−	9.80021i	0.669902	−	0.336739i
$848$	−15.0877	+	7.64345i	−0.518114	+	0.262477i
$849$	−3.62935	−	6.28622i	−0.124559	−	0.215743i
$850$	0.738046	+	0.507877i	0.0253148	+	0.0174200i
$851$	4.24715	−	1.13802i	0.145590	−	0.0390109i
$852$	−25.9280	−	11.5800i	−0.888279	−	0.396725i
$853$	−14.8313	+	14.8313i	−0.507813	+	0.507813i	−0.913854	−	0.406042i	$-0.866909\pi$
$853$	−14.8313	+	14.8313i	−0.507813	+	0.507813i	0.406042	+	0.913854i	$0.366909\pi$
$854$	−7.03143	+	0.882540i	−0.240610	+	0.0301999i
$855$			18.4217i			0.630008i
$856$	−16.9237	−	9.22706i	−0.578440	−	0.315374i
$857$	−0.372411	−	0.215012i	−0.0127213	−	0.00734466i	0.493626	−	0.869674i	$-0.335671\pi$
$857$	−0.372411	−	0.215012i	−0.0127213	−	0.00734466i	−0.506347	+	0.862330i	$0.669005\pi$
$858$	−14.3234	+	2.64607i	−0.488992	+	0.0903354i
$859$	38.6374	+	10.3529i	1.31829	+	0.353235i	0.848337	−	0.529456i	$-0.177604\pi$
$859$	38.6374	+	10.3529i	1.31829	+	0.353235i	0.469954	+	0.882691i	$0.344271\pi$
$860$	−2.63949	+	16.5406i	−0.0900059	+	0.564031i
$861$	−4.93514	−	23.8575i	−0.168189	−	0.813063i
$862$	19.2445	+	1.52583i	0.655470	+	0.0519699i
$863$	0.769454	+	1.33273i	0.0261925	+	0.0453667i	0.878825	−	0.477145i	$-0.158328\pi$
$863$	0.769454	+	1.33273i	0.0261925	+	0.0453667i	−0.852632	+	0.522512i	$0.824995\pi$
$864$	0.754660	−	5.60629i	0.0256741	−	0.190730i
$865$	−31.4830	+	54.5302i	−1.07046	+	1.85408i
$866$	17.7541	+	37.2779i	0.603308	+	1.26675i
$867$	11.9659	+	11.9659i	0.406384	+	0.406384i
$868$	−13.1465	−	41.3912i	−0.446222	−	1.40491i
$869$	18.0367	−	18.0367i	0.611853	−	0.611853i
$870$	−2.74912	+	7.74897i	−0.0932039	+	0.262715i
$871$	21.9632	+	12.6805i	0.744196	+	0.429662i
$872$	33.2728	−	0.813236i	1.12676	−	0.0275397i
$873$	−3.61594	+	2.08766i	−0.122381	+	0.0706567i
$874$	13.8272	−	11.7957i	0.467712	−	0.398994i
$875$	−12.9386	−	14.5285i	−0.437406	−	0.491153i
$876$	−8.51409	+	6.17074i	−0.287664	+	0.208490i
$877$	−2.55312	+	9.52837i	−0.0862127	+	0.321750i	−0.995541	−	0.0943291i	$-0.969929\pi$
$877$	−2.55312	+	9.52837i	−0.0862127	+	0.321750i	0.909328	+	0.416079i	$0.136596\pi$
$878$	−27.8045	−	19.1333i	−0.938356	−	0.645717i
$879$	3.36736	−	5.83244i	0.113578	−	0.196723i
$880$	−17.5151	+	3.68041i	−0.590433	+	0.124067i
$881$	−12.0398			−0.405632			−0.202816	−	0.979217i	$-0.565009\pi$
$881$	−12.0398			−0.405632			−0.202816	+	0.979217i	$0.565009\pi$
$882$	7.45322	+	6.51533i	0.250963	+	0.219382i
$883$	25.7445	+	25.7445i	0.866373	+	0.866373i	0.992069	−	0.125696i	$-0.0401165\pi$
$883$	25.7445	+	25.7445i	0.866373	+	0.866373i	−0.125696	+	0.992069i	$0.540116\pi$
$884$	1.41085	−	3.15894i	0.0474521	−	0.106247i
$885$	−8.02216	−	29.9391i	−0.269662	−	1.00639i
$886$	5.48676	+	29.7002i	0.184331	+	0.997798i
$887$	3.43742	−	1.98459i	0.115417	−	0.0666361i	−0.441180	−	0.897419i	$-0.645440\pi$
$887$	3.43742	−	1.98459i	0.115417	−	0.0666361i	0.556597	+	0.830782i	$0.312107\pi$
$888$	6.42461	+	1.55426i	0.215596	+	0.0521577i
$889$	−0.318709	−	0.0184476i	−0.0106892	−	0.000618713i
$890$	44.5104	+	52.1764i	1.49199	+	1.74896i
$891$	−1.60253	−	0.429396i	−0.0536867	−	0.0143853i
$892$	9.66337	−	11.9050i	0.323554	−	0.398607i
$893$	53.4644	−	14.3258i	1.78912	−	0.479393i
$894$	−5.07180	−	10.6492i	−0.169626	−	0.356162i
$895$	4.08791			0.136644
$896$	−2.63268	+	29.8173i	−0.0879517	+	0.996125i
$897$	11.6804			0.389996
$898$	−5.56631	−	11.6875i	−0.185750	−	0.390016i
$899$	−17.0900	+	4.57926i	−0.569984	+	0.152727i
$900$	−2.86564	+	3.53037i	−0.0955213	+	0.117679i
$901$	−1.13806	−	0.304942i	−0.0379142	−	0.0101591i
$902$	−14.0217	−	16.4366i	−0.466872	−	0.547280i
$903$	4.51229	−	6.86598i	0.150160	−	0.228486i
$904$	−19.6783	−	4.76064i	−0.654490	−	0.158337i
$905$	24.0530	−	13.8870i	0.799550	−	0.461621i
$906$	3.59231	+	19.4454i	0.119347	+	0.646031i
$907$	7.53716	+	28.1291i	0.250267	+	0.934010i	0.970662	+	0.240446i	$0.0772938\pi$
$907$	7.53716	+	28.1291i	0.250267	+	0.934010i	−0.720395	+	0.693564i	$0.756040\pi$
$908$	−0.838282	+	1.87694i	−0.0278194	+	0.0622884i
$909$	−4.09275	−	4.09275i	−0.135748	−	0.135748i
$910$	38.4358	−	49.4690i	1.27413	−	1.63988i
$911$	−26.3721			−0.873747			−0.436873	−	0.899523i	$-0.643914\pi$
$911$	−26.3721			−0.873747			−0.436873	+	0.899523i	$0.643914\pi$
$912$	26.7384	−	5.61849i	0.885396	−	0.186047i
$913$	3.27316	−	5.66928i	0.108326	−	0.187626i
$914$	14.9606	+	10.2949i	0.494852	+	0.340526i
$915$	−1.32203	+	4.93389i	−0.0437050	+	0.163109i
$916$	31.9016	−	23.1213i	1.05406	−	0.763949i
$917$	3.06130	−	9.24964i	0.101093	−	0.305450i
$918$	0.299797	−	0.255750i	0.00989478	−	0.00844100i
$919$	16.9360	−	9.77802i	0.558668	−	0.322547i	−0.193943	−	0.981013i	$-0.562128\pi$
$919$	16.9360	−	9.77802i	0.558668	−	0.322547i	0.752611	+	0.658466i	$0.228794\pi$
$920$	14.3479	−	0.350684i	0.473036	−	0.0115617i
$921$	−4.66493	−	2.69330i	−0.153715	−	0.0887472i
$922$	−5.04845	+	14.2301i	−0.166262	+	0.468643i
$923$	62.3267	−	62.3267i	2.05151	−	2.05151i
$924$	8.57481	+	1.88205i	0.282090	+	0.0619148i
$925$	−3.75695	−	3.75695i	−0.123528	−	0.123528i
$926$	13.6585	+	28.6785i	0.448846	+	0.942434i
$927$	0.136123	−	0.235772i	0.00447086	−	0.00774375i
$928$	12.0858	+	1.62686i	0.396736	+	0.0534044i
$929$	9.30235	+	16.1121i	0.305200	+	0.528622i	0.977306	−	0.211833i	$-0.0679433\pi$
$929$	9.30235	+	16.1121i	0.305200	+	0.528622i	−0.672106	+	0.740455i	$0.734610\pi$
$930$	−31.2051	−	2.47414i	−1.02326	−	0.0811303i
$931$	−17.6212	+	44.4485i	−0.577513	+	1.45674i
$932$	4.51405	−	28.2878i	0.147863	−	0.926598i
$933$	5.13035	+	1.37467i	0.167960	+	0.0450048i
$934$	9.00423	−	1.66342i	0.294627	−	0.0544289i
$935$	−1.07973	−	0.623384i	−0.0353110	−	0.0203868i
$936$	15.4165	+	8.40533i	0.503905	+	0.274737i
$937$			19.9977i			0.653295i	0.945146	+	0.326648i	$0.105919\pi$
$937$			19.9977i			0.653295i	−0.945146	+	0.326648i	$0.894081\pi$
$938$	−9.23171	−	12.1826i	−0.301426	−	0.397777i
$939$	5.47094	−	5.47094i	0.178537	−	0.178537i
$940$	39.9090	+	17.8243i	1.30169	+	0.581363i
$941$	22.9270	−	6.14327i	0.747399	−	0.200265i	0.135035	−	0.990841i	$-0.456885\pi$
$941$	22.9270	−	6.14327i	0.747399	−	0.200265i	0.612364	+	0.790576i	$0.290219\pi$
$942$	−6.18936	−	4.25913i	−0.201660	−	0.138770i
$943$	8.66256	+	15.0040i	0.282092	+	0.488597i
$944$	−41.0088	+	20.7751i	−1.33472	+	0.676172i
$945$	6.37531	−	3.20468i	0.207389	−	0.104248i
$946$	0.575872	−	7.26318i	0.0187232	−	0.236146i
$947$	8.79354	−	32.8179i	0.285751	−	1.06644i	−0.662537	−	0.749029i	$-0.730520\pi$
$947$	8.79354	−	32.8179i	0.285751	−	1.06644i	0.948288	−	0.317410i	$-0.102813\pi$
$948$	−30.5849	+	3.17867i	−0.993351	+	0.103238i
$949$	−8.44765	−	31.5270i	−0.274222	−	1.02341i
$950$	−20.6979	−	7.34305i	−0.671529	−	0.238240i
$951$			0.491801i			0.0159477i
$952$	−1.52284	+	1.42442i	−0.0493555	+	0.0461657i
$953$			54.0065i			1.74944i	0.484628	+	0.874720i	$0.338955\pi$
$953$			54.0065i			1.74944i	−0.484628	+	0.874720i	$0.661045\pi$
$954$	1.99936	−	5.63562i	0.0647318	−	0.182460i
$955$	0.0376603	+	0.140550i	0.00121866	+	0.00454810i
$956$	−29.7550	+	36.6571i	−0.962345	+	1.18558i
$957$	0.925674	−	3.45466i	0.0299228	−	0.111673i
$958$	−30.9810	−	2.45637i	−1.00095	−	0.0793618i
$959$	14.8530	+	9.76129i	0.479627	+	0.315208i
$960$	19.1897	+	9.86207i	0.619345	+	0.318297i
$961$	−18.1797	−	31.4882i	−0.586443	−	1.01575i
$962$	−11.6310	+	16.9022i	−0.375000	+	0.544949i
$963$	6.58275	−	1.76384i	0.212126	−	0.0568391i
$964$	2.05899	+	5.38255i	0.0663157	+	0.173360i
$965$	−41.3083	+	41.3083i	−1.32976	+	1.32976i
$966$	−6.48761	−	2.73327i	−0.208735	−	0.0879416i
$967$		−	25.9057i		−	0.833071i	−0.909119	−	0.416536i	$-0.863244\pi$
$967$		−	25.9057i		−	0.833071i	0.909119	−	0.416536i	$-0.136756\pi$
$968$	−22.3784	+	6.58637i	−0.719269	+	0.211694i
$969$	1.64831	+	0.951653i	0.0529514	+	0.0305715i
$970$	−2.89299	−	15.6600i	−0.0928883	−	0.502811i
$971$	−37.6946	−	10.1002i	−1.20968	−	0.324132i	−0.403042	−	0.915181i	$-0.632047\pi$
$971$	−37.6946	−	10.1002i	−1.20968	−	0.324132i	−0.806636	+	0.591049i	$0.798714\pi$
$972$	1.17369	+	1.61940i	0.0376461	+	0.0519423i
$973$	−30.0896	+	26.7969i	−0.964628	+	0.859068i
$974$	−1.48560	+	18.7371i	−0.0476016	+	0.600376i
$975$	−7.05704	−	12.2232i	−0.226006	−	0.391454i
$976$	7.56456	+	0.414076i	0.242136	+	0.0132542i
$977$	23.7796	−	41.1875i	0.760777	−	1.31770i	−0.181674	−	0.983359i	$-0.558152\pi$
$977$	23.7796	−	41.1875i	0.760777	−	1.31770i	0.942451	−	0.334345i	$-0.108515\pi$
$978$	22.5032	−	10.7174i	0.719573	−	0.342705i
$979$	−21.0947	−	21.0947i	−0.674189	−	0.674189i
$980$	−32.9243	+	18.4823i	−1.05173	+	0.590396i
$981$	−8.32068	+	8.32068i	−0.265659	+	0.265659i
$982$	−38.6856	−	13.7246i	−1.23451	−	0.437969i
$983$	0.793509	+	0.458133i	0.0253090	+	0.0146122i	0.512601	−	0.858627i	$-0.328682\pi$
$983$	0.793509	+	0.458133i	0.0253090	+	0.0146122i	−0.487292	+	0.873239i	$0.662015\pi$
$984$	0.636382	+	26.0370i	0.0202871	+	0.830028i
$985$	47.7306	−	27.5573i	1.52082	−	0.878048i
$986$	0.551334	+	0.646289i	0.0175580	+	0.0205820i
$987$	−14.2586	−	16.0107i	−0.453856	−	0.509625i
$988$	−13.3644	+	83.7495i	−0.425179	+	2.66443i
$989$	−1.51220	+	5.64359i	−0.0480850	+	0.179456i
$990$	3.58711	−	5.21278i	0.114006	−	0.165673i
$991$	−23.4494	+	40.6155i	−0.744894	+	1.29019i	0.205351	+	0.978688i	$0.434166\pi$
$991$	−23.4494	+	40.6155i	−0.744894	+	1.29019i	−0.950244	+	0.311505i	$0.899167\pi$
$992$	5.92622	+	46.0476i	0.188158	+	1.46201i
$993$	8.53749			0.270929
$994$	−49.2029	+	20.0332i	−1.56062	+	0.635416i
$995$	−39.8510	−	39.8510i	−1.26336	−	1.26336i
$996$	−7.37073	+	2.81953i	−0.233551	+	0.0893404i
$997$	−5.83714	−	21.7845i	−0.184864	−	0.689922i	−0.994660	−	0.103210i	$-0.967089\pi$
$997$	−5.83714	−	21.7845i	−0.184864	−	0.689922i	0.809795	−	0.586712i	$-0.199578\pi$
$998$	−14.7826	+	2.73090i	−0.467934	+	0.0864451i
$999$	−2.02387	+	1.16848i	−0.0640326	+	0.0369692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.20	yes	120
7.2	even	3	inner	336.2.bq.b.205.21	yes	120
16.5	even	4	inner	336.2.bq.b.277.21	yes	120
112.37	even	12	inner	336.2.bq.b.37.20	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.20	✓	120	112.37	even	12	inner
336.2.bq.b.109.20	yes	120	1.1	even	1	trivial
336.2.bq.b.205.21	yes	120	7.2	even	3	inner
336.2.bq.b.277.21	yes	120	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.608093 + 1.27680i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.26045 + 1.55283i) q^{4} +(2.60505 + 0.698021i) q^{5} +(0.917833 + 1.07591i) q^{6} +(2.64133 + 0.152886i) q^{7} +(-2.74912 - 0.665077i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.608093 + 1.27680i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.26045 + 1.55283i) q^{4} +(2.60505 + 0.698021i) q^{5} +(0.917833 + 1.07591i) q^{6} +(2.64133 + 0.152886i) q^{7} +(-2.74912 - 0.665077i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.692877 + 3.75059i) q^{10} +(-0.429396 - 1.60253i) q^{11} +(-0.815596 + 1.82614i) q^{12} +(-4.38976 - 4.38976i) q^{13} +(1.41097 + 3.46542i) q^{14} +2.69694 q^{15} +(-0.822550 - 3.91451i) q^{16} +(0.139323 - 0.241314i) q^{17} +(1.16502 + 0.801697i) q^{18} +(-1.76788 + 6.59783i) q^{19} +(-4.36743 + 3.16538i) q^{20} +(2.59090 - 0.535950i) q^{21} +(1.78500 - 1.52274i) q^{22} +(-1.62941 + 0.940743i) q^{23} +(-2.82758 + 0.0691103i) q^{24} +(1.96892 + 1.13676i) q^{25} +(2.93547 - 8.27423i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.56666 + 3.90883i) q^{28} +(1.52435 + 1.52435i) q^{29} +(1.63999 + 3.44346i) q^{30} +(-4.10364 + 7.10771i) q^{31} +(4.49787 - 3.43062i) q^{32} +(-0.829530 - 1.43679i) q^{33} +(0.392831 + 0.0311462i) q^{34} +(6.77408 + 2.24198i) q^{35} +(-0.315165 + 1.97501i) q^{36} +(-2.25734 - 0.604852i) q^{37} +(-9.49915 + 1.75486i) q^{38} +(-5.37633 - 3.10403i) q^{39} +(-6.69736 - 3.65150i) q^{40} -9.20821i q^{41} +(2.25981 + 2.98216i) q^{42} +(2.19581 - 2.19581i) q^{43} +(3.02968 + 1.35312i) q^{44} +(2.60505 - 0.698021i) q^{45} +(-2.19198 - 1.50838i) q^{46} +(-4.05167 - 7.01770i) q^{47} +(-1.80767 - 3.56824i) q^{48} +(6.95325 + 0.807646i) q^{49} +(-0.254127 + 3.20517i) q^{50} +(0.0721187 - 0.269150i) q^{51} +(12.3496 - 1.28348i) q^{52} +(-1.09437 - 4.08426i) q^{53} +(1.33282 + 0.472849i) q^{54} -4.47439i q^{55} +(-7.15966 - 2.17699i) q^{56} +6.83057i q^{57} +(-1.01935 + 2.87324i) q^{58} +(-2.97454 - 11.1011i) q^{59} +(-3.39935 + 4.18789i) q^{60} +(-0.490196 + 1.82944i) q^{61} +(-11.5705 - 0.917387i) q^{62} +(2.36390 - 1.18826i) q^{63} +(7.11535 + 3.65675i) q^{64} +(-8.37139 - 14.4997i) q^{65} +(1.33006 - 1.93285i) q^{66} +(-3.94597 + 1.05732i) q^{67} +(0.199110 + 0.520507i) q^{68} +(-1.33041 + 1.33041i) q^{69} +(1.25670 + 10.0125i) q^{70} +14.1982i q^{71} +(-2.71335 + 0.798588i) q^{72} +(4.55318 + 2.62878i) q^{73} +(-0.600395 - 3.24998i) q^{74} +(2.19604 + 0.588428i) q^{75} +(-8.01697 - 11.0614i) q^{76} +(-0.889173 - 4.29846i) q^{77} +(0.693919 - 8.75205i) q^{78} +(7.68741 + 13.3150i) q^{79} +(0.589628 - 10.7717i) q^{80} +(0.500000 - 0.866025i) q^{81} +(11.7571 - 5.59944i) q^{82} +(2.79010 + 2.79010i) q^{83} +(-2.43345 + 4.69876i) q^{84} +(0.531384 - 0.531384i) q^{85} +(4.13888 + 1.46836i) q^{86} +(1.86694 + 1.07788i) q^{87} +(0.114658 + 4.69113i) q^{88} +(15.5724 - 8.99075i) q^{89} +(2.47535 + 2.90167i) q^{90} +(-10.9237 - 12.2659i) q^{91} +(0.592978 - 3.71596i) q^{92} +(-2.12420 + 7.92762i) q^{93} +(6.49642 - 9.44059i) q^{94} +(-9.21084 + 15.9536i) q^{95} +(3.45670 - 4.47786i) q^{96} -4.17533 q^{97} +(3.19702 + 9.36905i) q^{98} +(-1.17313 - 1.17313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

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