LMFDB - Embedded newform 336.2.bq.b.205.22

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			205.22
Character	$\chi$	$=$	336.205
Dual form			336.2.bq.b.277.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.918366 + 1.07546i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.313209 + 1.97532i) q^{4} +(0.157792 + 0.588887i) q^{5} +(-1.27650 + 0.608725i) q^{6} +(-2.58295 + 0.573024i) q^{7} +(-2.41201 + 1.47723i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.918366 + 1.07546i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.313209 + 1.97532i) q^{4} +(0.157792 + 0.588887i) q^{5} +(-1.27650 + 0.608725i) q^{6} +(-2.58295 + 0.573024i) q^{7} +(-2.41201 + 1.47723i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.488411 + 0.710511i) q^{10} +(-0.221946 - 0.0594702i) q^{11} +(-1.82695 - 0.813787i) q^{12} +(1.86885 + 1.86885i) q^{13} +(-2.98836 - 2.25160i) q^{14} -0.609660 q^{15} +(-3.80380 - 1.23738i) q^{16} +(1.70915 + 2.96034i) q^{17} +(-0.257600 - 1.39055i) q^{18} +(1.55898 - 0.417729i) q^{19} +(-1.21266 + 0.127245i) q^{20} +(0.115019 - 2.64325i) q^{21} +(-0.139870 - 0.293308i) q^{22} +(-2.65039 - 1.53020i) q^{23} +(-0.802617 - 2.71216i) q^{24} +(4.00824 - 2.31416i) q^{25} +(-0.293576 + 3.72615i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.322904 - 5.28164i) q^{28} +(4.50223 + 4.50223i) q^{29} +(-0.559891 - 0.655662i) q^{30} +(2.55841 + 4.43129i) q^{31} +(-2.16254 - 5.22718i) q^{32} +(0.114888 - 0.198991i) q^{33} +(-1.61408 + 4.55679i) q^{34} +(-0.745014 - 1.43065i) q^{35} +(1.25891 - 1.55408i) q^{36} +(-1.47652 - 5.51046i) q^{37} +(1.88097 + 1.29299i) q^{38} +(-2.28886 + 1.32147i) q^{39} +(-1.25051 - 1.18731i) q^{40} +6.64364i q^{41} +(2.94833 - 2.30377i) q^{42} +(1.27101 - 1.27101i) q^{43} +(0.186988 - 0.419788i) q^{44} +(0.157792 - 0.588887i) q^{45} +(-0.788362 - 4.25566i) q^{46} +(-3.46555 + 6.00251i) q^{47} +(2.17971 - 3.35393i) q^{48} +(6.34329 - 2.96019i) q^{49} +(6.16980 + 2.18544i) q^{50} +(-3.30183 + 0.884722i) q^{51} +(-4.27692 + 3.10624i) q^{52} +(-3.27047 - 0.876319i) q^{53} +(1.40984 + 0.111079i) q^{54} -0.140085i q^{55} +(5.38362 - 5.19775i) q^{56} +1.61398i q^{57} +(-0.707253 + 8.97664i) q^{58} +(7.01230 + 1.87894i) q^{59} +(0.190951 - 1.20428i) q^{60} +(7.21998 - 1.93459i) q^{61} +(-2.41610 + 6.82100i) q^{62} +(2.52341 + 0.795223i) q^{63} +(3.63560 - 7.12618i) q^{64} +(-0.805651 + 1.39543i) q^{65} +(0.319515 - 0.0591902i) q^{66} +(3.81546 - 14.2395i) q^{67} +(-6.38294 + 2.44892i) q^{68} +(2.16403 - 2.16403i) q^{69} +(0.854402 - 2.11509i) q^{70} +3.66497i q^{71} +(2.82748 - 0.0733105i) q^{72} +(11.2389 - 6.48880i) q^{73} +(4.57026 - 6.64855i) q^{74} +(1.19790 + 4.47061i) q^{75} +(0.336862 + 3.21033i) q^{76} +(0.607353 + 0.0264285i) q^{77} +(-3.52320 - 1.24797i) q^{78} +(-4.80570 + 8.32371i) q^{79} +(0.128466 - 2.43525i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-7.14494 + 6.10129i) q^{82} +(-8.15769 - 8.15769i) q^{83} +(5.18525 + 1.05509i) q^{84} +(-1.47361 + 1.47361i) q^{85} +(2.53417 + 0.199662i) q^{86} +(-5.51408 + 3.18356i) q^{87} +(0.623186 - 0.184421i) q^{88} +(10.9782 + 6.33826i) q^{89} +(0.778232 - 0.371115i) q^{90} +(-5.89804 - 3.75625i) q^{91} +(3.85277 - 4.75610i) q^{92} +(-4.94247 + 1.32433i) q^{93} +(-9.63808 + 1.78546i) q^{94} +(0.491990 + 0.852151i) q^{95} +(5.60878 - 0.735957i) q^{96} -11.7203 q^{97} +(9.00901 + 4.10339i) q^{98} +(0.162476 + 0.162476i) 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.918366	+	1.07546i	0.649383	+	0.760462i
$2$	0.918366	+	1.07546i	0.649383	+	0.760462i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	−0.313209	+	1.97532i	−0.156604	+	0.987661i
$5$	0.157792	+	0.588887i	0.0705666	+	0.263358i	0.992192	−	0.124724i	$-0.0398045\pi$
$5$	0.157792	+	0.588887i	0.0705666	+	0.263358i	−0.921625	+	0.388082i	$0.873138\pi$
$6$	−1.27650	+	0.608725i	−0.521129	+	0.248511i
$7$	−2.58295	+	0.573024i	−0.976264	+	0.216583i
$7$	−2.58295	+	0.573024i	−0.976264	+	0.216583i
$8$	−2.41201	+	1.47723i	−0.852775	+	0.522279i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.488411	+	0.710511i	−0.154449	+	0.224683i
$11$	−0.221946	−	0.0594702i	−0.0669191	−	0.0179309i	0.225204	−	0.974312i	$-0.427695\pi$
$11$	−0.221946	−	0.0594702i	−0.0669191	−	0.0179309i	−0.292123	+	0.956381i	$0.594362\pi$
$12$	−1.82695	−	0.813787i	−0.527395	−	0.234920i
$13$	1.86885	+	1.86885i	0.518325	+	0.518325i	0.917064	−	0.398739i	$-0.130552\pi$
$13$	1.86885	+	1.86885i	0.518325	+	0.518325i	−0.398739	+	0.917064i	$0.630552\pi$
$14$	−2.98836	−	2.25160i	−0.798672	−	0.601767i
$15$	−0.609660			−0.157414
$16$	−3.80380	−	1.23738i	−0.950950	−	0.309344i
$17$	1.70915	+	2.96034i	0.414530	+	0.717987i	0.995379	−	0.0960241i	$-0.0306126\pi$
$17$	1.70915	+	2.96034i	0.414530	+	0.717987i	−0.580849	+	0.814011i	$0.697279\pi$
$18$	−0.257600	−	1.39055i	−0.0607170	−	0.327757i
$19$	1.55898	−	0.417729i	0.357656	−	0.0958335i	−0.0755170	−	0.997145i	$-0.524061\pi$
$19$	1.55898	−	0.417729i	0.357656	−	0.0958335i	0.433173	+	0.901311i	$0.357394\pi$
$20$	−1.21266	+	0.127245i	−0.271160	+	0.0284529i
$21$	0.115019	−	2.64325i	0.0250992	−	0.576804i
$22$	−0.139870	−	0.293308i	−0.0298203	−	0.0625335i
$23$	−2.65039	−	1.53020i	−0.552645	−	0.319069i	0.197543	−	0.980294i	$-0.436704\pi$
$23$	−2.65039	−	1.53020i	−0.552645	−	0.319069i	−0.750188	+	0.661225i	$0.770037\pi$
$24$	−0.802617	−	2.71216i	−0.163834	−	0.553617i
$25$	4.00824	−	2.31416i	0.801648	−	0.462831i
$26$	−0.293576	+	3.72615i	−0.0575751	+	0.730758i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.322904	−	5.28164i	−0.0610232	−	0.998136i
$29$	4.50223	+	4.50223i	0.836043	+	0.836043i	0.988335	−	0.152292i	$-0.0486655\pi$
$29$	4.50223	+	4.50223i	0.836043	+	0.836043i	−0.152292	+	0.988335i	$0.548666\pi$
$30$	−0.559891	−	0.655662i	−0.102222	−	0.119707i
$31$	2.55841	+	4.43129i	0.459504	+	0.795884i	0.998935	−	0.0461461i	$-0.0146940\pi$
$31$	2.55841	+	4.43129i	0.459504	+	0.795884i	−0.539431	+	0.842030i	$0.681361\pi$
$32$	−2.16254	−	5.22718i	−0.382286	−	0.924044i
$33$	0.114888	−	0.198991i	0.0199994	−	0.0346399i
$34$	−1.61408	+	4.55679i	−0.276813	+	0.781483i
$35$	−0.745014	−	1.43065i	−0.125930	−	0.241824i
$36$	1.25891	−	1.55408i	0.209818	−	0.259013i
$37$	−1.47652	−	5.51046i	−0.242739	−	0.905913i	−0.974507	−	0.224359i	$-0.927971\pi$
$37$	−1.47652	−	5.51046i	−0.242739	−	0.905913i	0.731768	−	0.681554i	$-0.238696\pi$
$38$	1.88097	+	1.29299i	0.305133	+	0.209751i
$39$	−2.28886	+	1.32147i	−0.366511	+	0.211605i
$40$	−1.25051	−	1.18731i	−0.197724	−	0.187730i
$41$			6.64364i			1.03756i	0.854907	+	0.518781i	$0.173614\pi$
$41$			6.64364i			1.03756i	−0.854907	+	0.518781i	$0.826386\pi$
$42$	2.94833	−	2.30377i	0.454937	−	0.355480i
$43$	1.27101	−	1.27101i	0.193827	−	0.193827i	−0.603520	−	0.797348i	$-0.706236\pi$
$43$	1.27101	−	1.27101i	0.193827	−	0.193827i	0.797348	+	0.603520i	$0.206236\pi$
$44$	0.186988	−	0.419788i	0.0281895	−	0.0632854i
$45$	0.157792	−	0.588887i	0.0235222	−	0.0877860i
$46$	−0.788362	−	4.25566i	−0.116238	−	0.627463i
$47$	−3.46555	+	6.00251i	−0.505503	+	0.875557i	0.494477	+	0.869191i	$0.335360\pi$
$47$	−3.46555	+	6.00251i	−0.505503	+	0.875557i	−0.999980	+	0.00636583i	$0.997974\pi$
$48$	2.17971	−	3.35393i	0.314614	−	0.484099i
$49$	6.34329	−	2.96019i	0.906184	−	0.422884i
$50$	6.16980	+	2.18544i	0.872542	+	0.309068i
$51$	−3.30183	+	0.884722i	−0.462348	+	0.123886i
$52$	−4.27692	+	3.10624i	−0.593102	+	0.430758i
$53$	−3.27047	−	0.876319i	−0.449233	−	0.120372i	0.0271073	−	0.999633i	$-0.491370\pi$
$53$	−3.27047	−	0.876319i	−0.449233	−	0.120372i	−0.476341	+	0.879261i	$0.658037\pi$
$54$	1.40984	+	0.111079i	0.191856	+	0.0151160i
$55$		−	0.140085i		−	0.0188890i
$56$	5.38362	−	5.19775i	0.719417	−	0.694578i
$57$			1.61398i			0.213777i
$58$	−0.707253	+	8.97664i	−0.0928669	+	1.17869i
$59$	7.01230	+	1.87894i	0.912924	+	0.244617i	0.684558	−	0.728958i	$-0.259995\pi$
$59$	7.01230	+	1.87894i	0.912924	+	0.244617i	0.228366	+	0.973575i	$0.426662\pi$
$60$	0.190951	−	1.20428i	0.0246516	−	0.155471i
$61$	7.21998	−	1.93459i	0.924424	−	0.247699i	0.234949	−	0.972008i	$-0.424508\pi$
$61$	7.21998	−	1.93459i	0.924424	−	0.247699i	0.689475	+	0.724309i	$0.257841\pi$
$62$	−2.41610	+	6.82100i	−0.306845	+	0.866268i
$63$	2.52341	+	0.795223i	0.317920	+	0.100189i
$64$	3.63560	−	7.12618i	0.454450	−	0.890772i
$65$	−0.805651	+	1.39543i	−0.0999287	+	0.173082i
$66$	0.319515	−	0.0591902i	0.0393296	−	0.00728580i
$67$	3.81546	−	14.2395i	0.466132	−	1.73963i	−0.186976	−	0.982365i	$-0.559869\pi$
$67$	3.81546	−	14.2395i	0.466132	−	1.73963i	0.653108	−	0.757265i	$-0.273465\pi$
$68$	−6.38294	+	2.44892i	−0.774046	+	0.296976i
$69$	2.16403	−	2.16403i	0.260519	−	0.260519i
$70$	0.854402	−	2.11509i	0.102121	−	0.252801i
$71$			3.66497i			0.434952i	0.976066	+	0.217476i	$0.0697824\pi$
$71$			3.66497i			0.434952i	−0.976066	+	0.217476i	$0.930218\pi$
$72$	2.82748	−	0.0733105i	0.333221	−	0.00863973i
$73$	11.2389	−	6.48880i	1.31542	−	0.759456i	0.332430	−	0.943128i	$-0.392132\pi$
$73$	11.2389	−	6.48880i	1.31542	−	0.759456i	0.982988	+	0.183672i	$0.0587983\pi$
$74$	4.57026	−	6.64855i	0.531282	−	0.772878i
$75$	1.19790	+	4.47061i	0.138321	+	0.516221i
$76$	0.336862	+	3.21033i	0.0386407	+	0.368251i
$77$	0.607353	+	0.0264285i	0.0692143	+	0.00301180i
$78$	−3.52320	−	1.24797i	−0.398924	−	0.141305i
$79$	−4.80570	+	8.32371i	−0.540683	+	0.936491i	0.458182	+	0.888859i	$0.348501\pi$
$79$	−4.80570	+	8.32371i	−0.540683	+	0.936491i	−0.998865	+	0.0476323i	$0.984832\pi$
$80$	0.128466	−	2.43525i	0.0143629	−	0.272270i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−7.14494	+	6.10129i	−0.789027	+	0.673775i
$83$	−8.15769	−	8.15769i	−0.895423	−	0.895423i	0.0996045	−	0.995027i	$-0.468242\pi$
$83$	−8.15769	−	8.15769i	−0.895423	−	0.895423i	−0.995027	+	0.0996045i	$0.968242\pi$
$84$	5.18525	+	1.05509i	0.565757	+	0.115119i
$85$	−1.47361	+	1.47361i	−0.159836	+	0.159836i
$86$	2.53417	+	0.199662i	0.273266	+	0.0215302i
$87$	−5.51408	+	3.18356i	−0.591172	+	0.341313i
$88$	0.623186	−	0.184421i	0.0664319	−	0.0196594i
$89$	10.9782	+	6.33826i	1.16369	+	0.671854i	0.952184	−	0.305524i	$-0.0988315\pi$
$89$	10.9782	+	6.33826i	1.16369	+	0.671854i	0.211501	+	0.977378i	$0.432165\pi$
$90$	0.778232	−	0.371115i	0.0820328	−	0.0391190i
$91$	−5.89804	−	3.75625i	−0.618282	−	0.393762i
$92$	3.85277	−	4.75610i	0.401679	−	0.495858i
$93$	−4.94247	+	1.32433i	−0.512510	+	0.137327i
$94$	−9.63808	+	1.78546i	−0.994092	+	0.184156i
$95$	0.491990	+	0.852151i	0.0504771	+	0.0874288i
$96$	5.60878	−	0.735957i	0.572443	−	0.0751133i
$97$	−11.7203			−1.19001			−0.595007	−	0.803720i	$-0.702851\pi$
$97$	−11.7203			−1.19001			−0.595007	+	0.803720i	$0.702851\pi$
$98$	9.00901	+	4.10339i	0.910047	+	0.414505i
$99$	0.162476	+	0.162476i	0.0163294	+	0.0163294i
$100$	3.31579	+	8.64238i	0.331579	+	0.864238i
$101$	−9.34415	−	2.50376i	−0.929778	−	0.249133i	−0.238018	−	0.971261i	$-0.576498\pi$
$101$	−9.34415	−	2.50376i	−0.929778	−	0.249133i	−0.691760	+	0.722127i	$0.743164\pi$
$102$	−3.98376	−	2.73847i	−0.394451	−	0.271149i
$103$	2.61757	+	1.51126i	0.257917	+	0.148908i	0.623384	−	0.781916i	$-0.285757\pi$
$103$	2.61757	+	1.51126i	0.257917	+	0.148908i	−0.365467	+	0.930824i	$0.619091\pi$
$104$	−7.26839	−	1.74697i	−0.712725	−	0.171304i
$105$	1.57472	−	0.349350i	0.153677	−	0.0340931i
$106$	−2.06104	−	4.32202i	−0.200186	−	0.419792i
$107$	1.72849	+	6.45081i	0.167099	+	0.623623i	0.997763	+	0.0668490i	$0.0212946\pi$
$107$	1.72849	+	6.45081i	0.167099	+	0.623623i	−0.830664	+	0.556774i	$0.812039\pi$
$108$	1.17529	+	1.61824i	0.113093	+	0.155715i
$109$	3.80856	−	14.2138i	0.364794	−	1.36143i	−0.502905	−	0.864342i	$-0.667736\pi$
$109$	3.80856	−	14.2138i	0.364794	−	1.36143i	0.867699	−	0.497089i	$-0.165598\pi$
$110$	0.150655	−	0.128649i	0.0143644	−	0.0122662i
$111$	5.70484			0.541480
$112$	10.5341	+	1.01641i	0.995377	+	0.0960421i
$113$	7.65867			0.720467			0.360234	−	0.932862i	$-0.382697\pi$
$113$	7.65867			0.720467			0.360234	+	0.932862i	$0.382697\pi$
$114$	−1.73576	+	1.48222i	−0.162569	+	0.138823i
$115$	0.482907	−	1.80223i	0.0450313	−	0.168059i
$116$	−10.3035	+	7.48322i	−0.956656	+	0.694800i
$117$	−0.684046	−	2.55289i	−0.0632400	−	0.236015i
$118$	4.41914	+	9.26698i	0.406815	+	0.853094i
$119$	−6.11100	−	6.66703i	−0.560195	−	0.611165i
$120$	1.47051	−	0.900607i	0.134238	−	0.0822138i
$121$	−9.48056	−	5.47360i	−0.861869	−	0.497600i
$122$	8.71115	+	5.98811i	0.788670	+	0.542138i
$123$	−6.41726	−	1.71950i	−0.578625	−	0.155042i
$124$	−9.55455	+	3.66576i	−0.858024	+	0.329195i
$125$	4.15072	+	4.15072i	0.371251	+	0.371251i
$126$	1.46219	+	3.44413i	0.130262	+	0.306827i
$127$	−7.49596			−0.665159			−0.332580	−	0.943075i	$-0.607919\pi$
$127$	−7.49596			−0.665159			−0.332580	+	0.943075i	$0.607919\pi$
$128$	11.0027	−	2.63451i	0.972510	−	0.232860i
$129$	0.898740	+	1.55666i	0.0791296	+	0.137057i
$130$	−2.24060	+	0.415072i	−0.196514	+	0.0364042i
$131$	−4.95415	+	1.32746i	−0.432846	+	0.115981i	−0.468662	−	0.883378i	$-0.655264\pi$
$131$	−4.95415	+	1.32746i	−0.432846	+	0.115981i	0.0358158	+	0.999358i	$0.488597\pi$
$132$	0.357088	+	0.289266i	0.0310805	+	0.0251773i
$133$	−3.78741	+	1.97231i	−0.328410	+	0.171021i
$134$	18.8179	−	8.97370i	1.62562	−	0.775209i
$135$	0.527981	+	0.304830i	0.0454414	+	0.0262356i
$136$	−8.49559	−	4.61556i	−0.728490	−	0.395781i
$137$	−5.55639	+	3.20798i	−0.474714	+	0.274076i	−0.718211	−	0.695825i	$-0.755039\pi$
$137$	−5.55639	+	3.20798i	−0.474714	+	0.274076i	0.243497	+	0.969902i	$0.421705\pi$
$138$	4.31470	+	0.339947i	0.367291	+	0.0289382i
$139$	1.46518	−	1.46518i	0.124275	−	0.124275i	−0.642234	−	0.766509i	$-0.721992\pi$
$139$	1.46518	−	1.46518i	0.124275	−	0.124275i	0.766509	+	0.642234i	$0.221992\pi$
$140$	3.05934	−	1.02355i	0.258561	−	0.0865060i
$141$	−4.90103	−	4.90103i	−0.412741	−	0.412741i
$142$	−3.94151	+	3.36579i	−0.330765	+	0.282450i
$143$	−0.303642	−	0.525923i	−0.0253918	−	0.0439799i
$144$	2.67550	+	2.97350i	0.222958	+	0.247792i
$145$	−1.94089	+	3.36172i	−0.161182	+	0.279175i
$146$	17.2999	+	6.12788i	1.43175	+	0.507147i
$147$	1.21756	+	6.89330i	0.100422	+	0.568550i
$148$	11.3474	−	1.19069i	0.932750	−	0.0978738i
$149$	−5.59793	−	20.8918i	−0.458600	−	1.71152i	−0.677282	−	0.735724i	$-0.736842\pi$
$149$	−5.59793	−	20.8918i	−0.458600	−	1.71152i	0.218681	−	0.975796i	$-0.429825\pi$
$150$	−3.70783	+	5.39394i	−0.302743	+	0.440413i
$151$	−15.9876	+	9.23046i	−1.30105	+	0.751164i	−0.980585	−	0.196095i	$-0.937174\pi$
$151$	−15.9876	+	9.23046i	−1.30105	+	0.751164i	−0.320469	+	0.947259i	$0.603840\pi$
$152$	−3.14321	+	3.31054i	−0.254948	+	0.268520i
$153$		−	3.41830i		−	0.276353i
$154$	0.529350	+	0.677452i	0.0426562	+	0.0545906i
$155$	−2.20583	+	2.20583i	−0.177177	+	0.177177i
$156$	−1.89345	−	4.93514i	−0.151597	−	0.395127i
$157$	1.12198	−	4.18729i	0.0895437	−	0.334182i	−0.906592	−	0.422008i	$-0.861325\pi$
$157$	1.12198	−	4.18729i	0.0895437	−	0.334182i	0.996136	+	0.0878263i	$0.0279920\pi$
$158$	−13.3652	+	2.47590i	−1.06328	+	0.196972i
$159$	1.69292	−	2.93222i	0.134257	−	0.232540i
$160$	2.73699	−	2.09830i	0.216378	−	0.165885i
$161$	7.72267	+	2.43371i	0.608632	+	0.191803i
$162$	−0.472189	+	1.33306i	−0.0370987	+	0.104735i
$163$	18.1403	−	4.86068i	1.42086	−	0.380718i	0.535070	−	0.844808i	$-0.320285\pi$
$163$	18.1403	−	4.86068i	1.42086	−	0.380718i	0.885788	+	0.464090i	$0.153619\pi$
$164$	−13.1233	−	2.08084i	−1.02476	−	0.162487i
$165$	0.135311	+	0.0362566i	0.0105340	+	0.00282257i
$166$	1.28149	−	16.2650i	0.0994627	−	1.26241i
$167$		−	20.7942i		−	1.60910i	−0.593882	−	0.804552i	$-0.702406\pi$
$167$		−	20.7942i		−	1.60910i	0.593882	−	0.804552i	$-0.297594\pi$
$168$	3.62725	+	6.54546i	0.279849	+	0.504993i
$169$		−	6.01482i		−	0.462678i
$170$	−2.93812	−	0.231489i	−0.225344	−	0.0177544i
$171$	−1.55898	−	0.417729i	−0.119219	−	0.0319445i
$172$	2.11256	+	2.90875i	0.161082	+	0.221790i
$173$	−17.1270	+	4.58916i	−1.30214	+	0.348907i	−0.842259	−	0.539074i	$-0.818774\pi$
$173$	−17.1270	+	4.58916i	−1.30214	+	0.348907i	−0.459880	+	0.887981i	$0.652108\pi$
$174$	−8.48772	−	3.00648i	−0.643452	−	0.227921i
$175$	−9.02702	+	8.27417i	−0.682379	+	0.625469i
$176$	0.770650	+	0.500843i	0.0580899	+	0.0377525i
$177$	−3.62984	+	6.28706i	−0.272835	+	0.472564i
$178$	3.26548	+	17.6274i	0.244758	+	1.32123i
$179$	2.97340	−	11.0969i	0.222242	−	0.829419i	−0.761249	−	0.648460i	$-0.775413\pi$
$179$	2.97340	−	11.0969i	0.222242	−	0.829419i	0.983491	−	0.180959i	$-0.0579201\pi$
$180$	1.11382	+	0.496134i	0.0830192	+	0.0369796i
$181$	−13.9231	+	13.9231i	−1.03490	+	1.03490i	−0.0355297	+	0.999369i	$0.511312\pi$
$181$	−13.9231	+	13.9231i	−1.03490	+	1.03490i	−0.999369	+	0.0355297i	$0.988688\pi$
$182$	−1.37688	−	9.79269i	−0.102061	−	0.725882i
$183$			7.47468i			0.552544i
$184$	8.65323	−	0.224360i	0.637925	−	0.0165400i
$185$	3.01205	−	1.73901i	0.221450	−	0.127854i
$186$	−5.96325	−	4.09918i	−0.437247	−	0.300567i
$187$	−0.203287	−	0.758678i	−0.0148658	−	0.0554800i
$188$	−10.7715	−	8.72562i	−0.785590	−	0.636382i
$189$	−1.42123	+	2.23161i	−0.103380	+	0.162326i
$190$	−0.464624	+	1.31170i	−0.0337074	+	0.0951606i
$191$	1.24159	−	2.15049i	0.0898381	−	0.155604i	−0.817604	−	0.575780i	$-0.804698\pi$
$191$	1.24159	−	2.15049i	0.0898381	−	0.155604i	0.907443	+	0.420176i	$0.138032\pi$
$192$	5.94240	+	5.35611i	0.428856	+	0.386544i
$193$	0.637380	+	1.10397i	0.0458796	+	0.0794658i	0.888053	−	0.459741i	$-0.152058\pi$
$193$	0.637380	+	1.10397i	0.0458796	+	0.0794658i	−0.842174	+	0.539206i	$0.818724\pi$
$194$	−10.7635	−	12.6046i	−0.772775	−	0.904961i
$195$	−1.13936	−	1.13936i	−0.0815914	−	0.0815914i
$196$	3.86055	+	13.4572i	0.275754	+	0.961228i
$197$	−17.0554	+	17.0554i	−1.21515	+	1.21515i	−0.245833	+	0.969312i	$0.579062\pi$
$197$	−17.0554	+	17.0554i	−1.21515	+	1.21515i	−0.969312	+	0.245833i	$0.920938\pi$
$198$	−0.0255232	+	0.323947i	−0.00181386	+	0.0230219i
$199$	12.6311	−	7.29259i	0.895397	−	0.516958i	0.0196933	−	0.999806i	$-0.493731\pi$
$199$	12.6311	−	7.29259i	0.895397	−	0.516958i	0.875704	+	0.482848i	$0.160398\pi$
$200$	−6.24938	+	11.5029i	−0.441898	+	0.813374i
$201$	12.7668	+	7.37090i	0.900498	+	0.519903i
$202$	−5.88867	−	12.3486i	−0.414325	−	0.868844i
$203$	−14.2089	−	9.04916i	−0.997272	−	0.635127i
$204$	−0.713451	−	6.79928i	−0.0499516	−	0.476045i
$205$	−3.91235	+	1.04831i	−0.273250	+	0.0732172i
$206$	0.778600	+	4.20297i	0.0542476	+	0.292835i
$207$	1.53020	+	2.65039i	0.106356	+	0.184215i
$208$	−4.79626	−	9.42119i	−0.332561	−	0.653242i
$209$	−0.370852			−0.0256524
$210$	1.82188	+	1.37271i	0.125722	+	0.0947262i
$211$	13.2500	+	13.2500i	0.912169	+	0.912169i	0.996443	−	0.0842733i	$-0.0268569\pi$
$211$	13.2500	+	13.2500i	0.912169	+	0.912169i	−0.0842733	+	0.996443i	$0.526857\pi$
$212$	2.75535	−	6.18576i	0.189238	−	0.424840i
$213$	−3.54009	−	0.948565i	−0.242563	−	0.0649946i
$214$	−5.35017	+	7.78312i	−0.365730	+	0.532043i
$215$	0.949036	+	0.547926i	0.0647237	+	0.0373682i
$216$	−0.660992	+	2.75011i	−0.0449748	+	0.187121i
$217$	−9.14748	−	9.97979i	−0.620972	−	0.677472i
$218$	18.7839	−	8.95748i	1.27221	−	0.606677i
$219$	3.35885	+	12.5354i	0.226970	+	0.847064i
$220$	0.276713	+	0.0438757i	0.0186560	+	0.00295810i
$221$	−2.33828	+	8.72656i	−0.157289	+	0.587012i
$222$	5.23913	+	6.13530i	0.351628	+	0.411775i
$223$	−2.09867			−0.140537			−0.0702685	−	0.997528i	$-0.522386\pi$
$223$	−2.09867			−0.140537			−0.0702685	+	0.997528i	$0.522386\pi$
$224$	8.58103	+	12.2624i	0.573344	+	0.819314i
$225$	−4.62831			−0.308554
$226$	7.03346	+	8.23656i	0.467859	+	0.547888i
$227$	3.90626	−	14.5784i	0.259268	−	0.967600i	−0.706399	−	0.707814i	$-0.749681\pi$
$227$	3.90626	−	14.5784i	0.259268	−	0.967600i	0.965666	−	0.259786i	$-0.0836520\pi$
$228$	−3.18813	−	0.505512i	−0.211139	−	0.0334784i
$229$	1.52274	+	5.68295i	0.100626	+	0.375540i	0.997812	−	0.0661117i	$-0.0210594\pi$
$229$	1.52274	+	5.68295i	0.100626	+	0.375540i	−0.897187	+	0.441652i	$0.854393\pi$
$230$	2.38171	−	1.13576i	0.157045	−	0.0748901i
$231$	−0.182722	+	0.579818i	−0.0120223	+	0.0381492i
$232$	−17.5102	−	4.20861i	−1.14960	−	0.276309i
$233$	−3.35266	−	1.93566i	−0.219640	−	0.126809i	0.386143	−	0.922439i	$-0.373807\pi$
$233$	−3.35266	−	1.93566i	−0.219640	−	0.126809i	−0.605784	+	0.795629i	$0.707140\pi$
$234$	2.11732	−	3.08015i	0.138413	−	0.201356i
$235$	−4.08163	−	1.09367i	−0.266256	−	0.0713432i
$236$	−5.90783	+	13.2631i	−0.384567	+	0.863352i
$237$	−6.79628	−	6.79628i	−0.441466	−	0.441466i
$238$	1.55795	−	12.6949i	0.100987	−	0.822887i
$239$	17.2703			1.11712			0.558560	−	0.829464i	$-0.311354\pi$
$239$	17.2703			1.11712			0.558560	+	0.829464i	$0.311354\pi$
$240$	2.31903	+	0.754379i	0.149692	+	0.0486949i
$241$	9.87354	+	17.1015i	0.636010	+	1.10160i	0.986300	+	0.164961i	$0.0527498\pi$
$241$	9.87354	+	17.1015i	0.636010	+	1.10160i	−0.350290	+	0.936641i	$0.613917\pi$
$242$	−2.82000	−	15.2227i	−0.181277	−	0.978551i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	1.56008	+	14.8677i	0.0998737	+	0.951809i
$245$	2.74413	+	3.26838i	0.175316	+	0.208809i
$246$	−4.04415	−	8.48061i	−0.257846	−	0.540704i
$247$	3.69418	+	2.13283i	0.235055	+	0.135709i
$248$	−12.7169	−	6.90898i	−0.807526	−	0.438721i
$249$	9.99109	−	5.76836i	0.633159	−	0.365555i
$250$	−0.652034	+	8.27579i	−0.0412383	+	0.523407i
$251$	8.31713	−	8.31713i	0.524972	−	0.524972i	−0.394097	−	0.919069i	$-0.628942\pi$
$251$	8.31713	−	8.31713i	0.524972	−	0.524972i	0.919069	+	0.394097i	$0.128942\pi$
$252$	−2.36118	+	4.73549i	−0.148740	+	0.298308i
$253$	0.497241	+	0.497241i	0.0312613	+	0.0312613i
$254$	−6.88404	−	8.06157i	−0.431943	−	0.505828i
$255$	−1.04200	−	1.80480i	−0.0652527	−	0.113021i
$256$	12.9378	+	9.41346i	0.808613	+	0.588341i
$257$	−12.9914	+	22.5018i	−0.810381	+	1.40362i	0.102216	+	0.994762i	$0.467407\pi$
$257$	−12.9914	+	22.5018i	−0.810381	+	1.40362i	−0.912597	+	0.408859i	$0.865927\pi$
$258$	−0.848750	+	2.39614i	−0.0528409	+	0.149177i
$259$	6.97141	+	13.3872i	0.433182	+	0.831838i
$260$	−2.50408	−	2.02848i	−0.155297	−	0.125801i
$261$	−1.64793	−	6.15016i	−0.102004	−	0.380685i
$262$	−5.97735	−	4.10887i	−0.369282	−	0.253847i
$263$	−16.1568	+	9.32812i	−0.996270	+	0.575197i	−0.907143	−	0.420824i	$-0.861741\pi$
$263$	−16.1568	+	9.32812i	−0.996270	+	0.575197i	−0.0891274	+	0.996020i	$0.528408\pi$
$264$	0.0168449	+	0.649684i	0.00103673	+	0.0399853i
$265$		−	2.06421i		−	0.126803i
$266$	−5.59936	−	2.26189i	−0.343319	−	0.138686i
$267$	−8.96365	+	8.96365i	−0.548567	+	0.548567i
$268$	26.9325	+	11.9967i	1.64517	+	0.732814i
$269$	2.88664	−	10.7731i	0.176002	−	0.656848i	−0.820377	−	0.571823i	$-0.806236\pi$
$269$	2.88664	−	10.7731i	0.176002	−	0.656848i	0.996379	−	0.0850247i	$-0.0270969\pi$
$270$	0.157049	+	0.847766i	0.00955768	+	0.0515934i
$271$	4.60089	−	7.96898i	0.279484	−	0.484081i	−0.691772	−	0.722116i	$-0.743170\pi$
$271$	4.60089	−	7.96898i	0.279484	−	0.484081i	0.971257	+	0.238035i	$0.0765032\pi$
$272$	−2.83822	−	13.3754i	−0.172093	−	0.811003i
$273$	5.15478	−	4.72488i	0.311982	−	0.285963i
$274$	−8.55283	−	3.02955i	−0.516696	−	0.183022i
$275$	−1.02723	+	0.275247i	−0.0619446	+	0.0165980i
$276$	3.59687	+	4.95246i	0.216506	+	0.298103i
$277$	22.2164	+	5.95287i	1.33485	+	0.357673i	0.854523	−	0.519414i	$-0.173850\pi$
$277$	22.2164	+	5.95287i	1.33485	+	0.357673i	0.480332	+	0.877087i	$0.340516\pi$
$278$	2.92131	+	0.230165i	0.175209	+	0.0138044i
$279$		−	5.11682i		−	0.306336i
$280$	3.91037	+	2.35018i	0.233690	+	0.140450i
$281$			21.5167i			1.28358i	0.766881	+	0.641790i	$0.221808\pi$
$281$			21.5167i			1.28358i	−0.766881	+	0.641790i	$0.778192\pi$
$282$	0.769901	−	9.77178i	0.0458469	−	0.581901i
$283$	13.9350	+	3.73386i	0.828348	+	0.221955i	0.647993	−	0.761647i	$-0.275609\pi$
$283$	13.9350	+	3.73386i	0.828348	+	0.221955i	0.180355	+	0.983602i	$0.442275\pi$
$284$	−7.23950	−	1.14790i	−0.429586	−	0.0681154i
$285$	−0.950451	+	0.254673i	−0.0562998	+	0.0150855i
$286$	0.286753	−	0.809543i	0.0169560	−	0.0478693i
$287$	−3.80696	−	17.1602i	−0.224718	−	1.01294i
$288$	−0.740778	+	5.60814i	−0.0436508	+	0.330463i
$289$	2.65760	−	4.60310i	0.156329	−	0.270771i
$290$	−5.39782	+	0.999947i	−0.316971	+	0.0587189i
$291$	3.03343	−	11.3209i	0.177823	−	0.663645i
$292$	9.29734	+	24.2329i	0.544086	+	1.41812i
$293$	16.2870	−	16.2870i	0.951494	−	0.951494i	−0.0473826	−	0.998877i	$-0.515088\pi$
$293$	16.2870	−	16.2870i	0.951494	−	0.951494i	0.998877	+	0.0473826i	$0.0150880\pi$
$294$	−6.29527	+	7.64000i	−0.367148	+	0.445574i
$295$			4.42593i			0.257688i
$296$	11.7016	+	11.1101i	0.680141	+	0.645763i
$297$	−0.198991	+	0.114888i	−0.0115466	+	0.00666645i
$298$	17.3272	−	25.2066i	1.00374	−	1.46018i
$299$	−2.09346	−	7.81289i	−0.121068	−	0.451831i
$300$	−9.20609	+	0.965999i	−0.531514	+	0.0557720i
$301$	−2.55464	+	4.01128i	−0.147247	+	0.231206i
$302$	−24.6094	−	8.71703i	−1.41611	−	0.501609i
$303$	4.83689	−	8.37774i	0.277872	−	0.481289i
$304$	−6.44695	−	0.340093i	−0.369758	−	0.0195057i
$305$	2.27851	+	3.94649i	0.130467	+	0.225975i
$306$	3.67623	−	3.13925i	0.210156	−	0.179459i
$307$	8.46457	+	8.46457i	0.483098	+	0.483098i	0.906120	−	0.423021i	$-0.139030\pi$
$307$	8.46457	+	8.46457i	0.483098	+	0.483098i	−0.423021	+	0.906120i	$0.639030\pi$
$308$	−0.242433	+	1.19144i	−0.0138139	+	0.0678886i
$309$	−2.13724	+	2.13724i	−0.121583	+	0.121583i
$310$	−4.39804	−	0.346513i	−0.249792	−	0.0196806i
$311$	19.0709	−	11.0106i	1.08141	−	0.624355i	0.150137	−	0.988665i	$-0.452029\pi$
$311$	19.0709	−	11.0106i	1.08141	−	0.624355i	0.931278	+	0.364311i	$0.118695\pi$
$312$	3.56864	−	6.56858i	0.202035	−	0.371873i
$313$	−14.6029	−	8.43098i	−0.825404	−	0.476547i	0.0268722	−	0.999639i	$-0.491445\pi$
$313$	−14.6029	−	8.43098i	−0.825404	−	0.476547i	−0.852277	+	0.523091i	$0.824779\pi$
$314$	5.53363	−	2.63882i	0.312281	−	0.148917i
$315$	−0.0701224	+	1.61148i	−0.00395095	+	0.0907969i
$316$	−14.9368	−	12.0999i	−0.840263	−	0.680670i
$317$	−4.16639	+	1.11638i	−0.234008	+	0.0627022i	−0.373917	−	0.927462i	$-0.621986\pi$
$317$	−4.16639	+	1.11638i	−0.234008	+	0.0627022i	0.139909	+	0.990164i	$0.455319\pi$
$318$	4.70819	−	0.872193i	0.264022	−	0.0489102i
$319$	−0.731502	−	1.26700i	−0.0409563	−	0.0709383i
$320$	4.77018	+	1.01650i	0.266661	+	0.0568243i
$321$	−6.67837			−0.372750
$322$	4.47490	+	10.5404i	0.249376	+	0.587395i
$323$	3.90116	+	3.90116i	0.217066	+	0.217066i
$324$	−1.86728	+	0.716415i	−0.103738	+	0.0398008i
$325$	11.8156	+	3.16598i	0.655411	+	0.175617i
$326$	21.8869	+	15.0452i	1.21220	+	0.833276i
$327$	12.7437	+	7.35758i	0.704728	+	0.406875i
$328$	−9.81417	−	16.0245i	−0.541897	−	0.884807i
$329$	5.51178	−	17.4901i	0.303874	−	0.964258i
$330$	0.0852731	+	0.178818i	0.00469413	+	0.00984362i
$331$	−4.83600	−	18.0482i	−0.265811	−	0.992019i	−0.961752	−	0.273921i	$-0.911679\pi$
$331$	−4.83600	−	18.0482i	−0.265811	−	0.992019i	0.695941	−	0.718099i	$-0.254987\pi$
$332$	18.6691	−	13.5590i	1.02460	−	0.744147i
$333$	−1.47652	+	5.51046i	−0.0809129	+	0.301971i
$334$	22.3632	−	19.0967i	1.22366	−	1.04492i
$335$	8.98749			0.491039
$336$	−3.70820	+	9.91208i	−0.202299	+	0.540748i
$337$	1.83390			0.0998988			0.0499494	−	0.998752i	$-0.484094\pi$
$337$	1.83390			0.0998988			0.0499494	+	0.998752i	$0.484094\pi$
$338$	6.46867	−	5.52380i	0.351849	−	0.300455i
$339$	−1.98221	+	7.39771i	−0.107659	+	0.401788i
$340$	−2.44931	−	3.37241i	−0.132833	−	0.182895i
$341$	−0.304298	−	1.13566i	−0.0164787	−	0.0614992i
$342$	−0.982470	−	2.06025i	−0.0531259	−	0.111405i
$343$	−14.6882	+	11.2809i	−0.793086	+	0.609110i
$344$	−1.18812	+	4.94326i	−0.0640592	+	0.266523i
$345$	1.61584	+	0.932904i	0.0869938	+	0.0502259i
$346$	−20.6642	−	14.2048i	−1.11092	−	0.763653i
$347$	19.6286	+	5.25948i	1.05372	+	0.282344i	0.743789	−	0.668415i	$-0.233027\pi$
$347$	19.6286	+	5.25948i	1.05372	+	0.282344i	0.309932	+	0.950759i	$0.399694\pi$
$348$	−4.56150	−	11.8892i	−0.244522	−	0.637329i
$349$	5.94895	+	5.94895i	0.318440	+	0.318440i	0.848168	−	0.529728i	$-0.177706\pi$
$349$	5.94895	+	5.94895i	0.318440	+	0.318440i	−0.529728	+	0.848168i	$0.677706\pi$
$350$	−17.1886	−	2.10944i	−0.918770	−	0.112754i
$351$	2.64295			0.141070
$352$	0.169105	+	1.28876i	0.00901331	+	0.0686910i
$353$	−12.8295	−	22.2213i	−0.682843	−	1.18272i	−0.974109	−	0.226077i	$-0.927410\pi$
$353$	−12.8295	−	22.2213i	−0.682843	−	1.18272i	0.291266	−	0.956642i	$-0.405923\pi$
$354$	−10.0950	+	1.87009i	−0.536542	+	0.0993944i
$355$	−2.15825	+	0.578302i	−0.114548	+	0.0306931i
$356$	−15.9586	+	19.7003i	−0.845803	+	1.04411i
$357$	8.02150	−	4.17722i	0.424543	−	0.221082i
$358$	14.6649	−	6.99323i	0.775062	−	0.369604i
$359$	23.4074	+	13.5143i	1.23539	+	0.713255i	0.968149	−	0.250374i	$-0.0805534\pi$
$359$	23.4074	+	13.5143i	1.23539	+	0.713255i	0.267245	+	0.963629i	$0.413887\pi$
$360$	0.489324	+	1.65350i	0.0257896	+	0.0871469i
$361$	−14.1985	+	8.19754i	−0.747292	+	0.431449i
$362$	−27.7602	−	2.18718i	−1.45905	−	0.114956i
$363$	7.74084	−	7.74084i	0.406289	−	0.406289i
$364$	9.26712	−	10.4740i	0.485729	−	0.548989i
$365$	5.59458	+	5.59458i	0.292833	+	0.292833i
$366$	−8.03868	+	6.86449i	−0.420189	+	0.358812i
$367$	14.6163	+	25.3162i	0.762967	+	1.32150i	0.941315	+	0.337529i	$0.109591\pi$
$367$	14.6163	+	25.3162i	0.762967	+	1.32150i	−0.178348	+	0.983967i	$0.557075\pi$
$368$	8.18812	+	9.10012i	0.426835	+	0.474376i
$369$	3.32182	−	5.75356i	0.172927	−	0.299518i
$370$	4.63639	+	1.64228i	0.241034	+	0.0853781i
$371$	8.94961	+	0.389435i	0.464641	+	0.0202185i
$372$	−1.06796	−	10.1778i	−0.0553710	−	0.527692i
$373$	−3.71871	−	13.8784i	−0.192548	−	0.718597i	−0.992888	−	0.119051i	$-0.962015\pi$
$373$	−3.71871	−	13.8784i	−0.192548	−	0.718597i	0.800341	−	0.599546i	$-0.204652\pi$
$374$	0.629232	−	0.915370i	0.0325368	−	0.0473326i
$375$	−5.08357	+	2.93500i	−0.262514	+	0.151563i
$376$	−0.508123	−	19.5975i	−0.0262044	−	1.01067i
$377$			16.8280i			0.866684i
$378$	−3.70521	+	0.520962i	−0.190576	+	0.0267954i
$379$	12.0509	−	12.0509i	0.619013	−	0.619013i	−0.326265	−	0.945278i	$-0.605790\pi$
$379$	12.0509	−	12.0509i	0.619013	−	0.619013i	0.945278	+	0.326265i	$0.105790\pi$
$380$	−1.83737	+	0.704937i	−0.0942550	+	0.0361625i
$381$	1.94010	−	7.24054i	0.0993942	−	0.370944i
$382$	3.45299	−	0.639667i	0.176670	−	0.0327282i
$383$	14.8885	−	25.7877i	0.760768	−	1.31769i	−0.181687	−	0.983356i	$-0.558156\pi$
$383$	14.8885	−	25.7877i	0.760768	−	1.31769i	0.942455	−	0.334333i	$-0.108511\pi$
$384$	−0.302963	+	11.3097i	−0.0154605	+	0.577143i
$385$	0.0802719	+	0.361832i	0.00409103	+	0.0184407i
$386$	−0.601927	+	1.69933i	−0.0306373	+	0.0864934i
$387$	−1.73623	+	0.465222i	−0.0882576	+	0.0236486i
$388$	3.67089	−	23.1514i	0.186361	−	1.17533i
$389$	24.9988	+	6.69840i	1.26749	+	0.339622i	0.829068	−	0.559148i	$-0.188872\pi$
$389$	24.9988	+	6.69840i	1.26749	+	0.339622i	0.438420	+	0.898770i	$0.355538\pi$
$390$	0.178982	−	2.27168i	0.00906310	−	0.115031i
$391$		−	10.4614i		−	0.529056i
$392$	−10.9272	+	16.5105i	−0.551908	+	0.833905i
$393$		−	5.12891i		−	0.258719i
$394$	−34.0054	−	2.67922i	−1.71317	−	0.134977i
$395$	−5.66002	−	1.51660i	−0.284787	−	0.0763083i
$396$	−0.371830	+	0.270053i	−0.0186852	+	0.0135707i
$397$	7.62425	−	2.04291i	0.382650	−	0.102531i	−0.0623659	−	0.998053i	$-0.519865\pi$
$397$	7.62425	−	2.04291i	0.382650	−	0.102531i	0.445016	+	0.895523i	$0.353198\pi$
$398$	19.4429	+	6.88696i	0.974582	+	0.345212i
$399$	−0.924849	−	4.16883i	−0.0463003	−	0.208703i
$400$	−18.1100	+	3.84290i	−0.905501	+	0.192145i
$401$	4.70377	−	8.14717i	0.234895	−	0.406850i	−0.724347	−	0.689436i	$-0.757859\pi$
$401$	4.70377	−	8.14717i	0.234895	−	0.406850i	0.959242	+	0.282585i	$0.0911920\pi$
$402$	3.79749	+	20.4993i	0.189402	+	1.02241i
$403$	−3.50014	+	13.0627i	−0.174354	+	0.650699i
$404$	7.87240	−	17.6735i	0.391667	−	0.879291i
$405$	−0.431095	+	0.431095i	−0.0214213	+	0.0214213i
$406$	−3.31703	−	23.5915i	−0.164621	−	1.17083i
$407$			1.31083i			0.0649755i
$408$	6.65711	−	7.01151i	0.329576	−	0.347121i
$409$	−6.42055	+	3.70690i	−0.317476	+	0.183295i	−0.650267	−	0.759706i	$-0.725343\pi$
$409$	−6.42055	+	3.70690i	−0.317476	+	0.183295i	0.332791	+	0.943001i	$0.392010\pi$
$410$	−4.72038	−	3.24483i	−0.233123	−	0.160251i
$411$	−1.66057	−	6.19734i	−0.0819100	−	0.305692i
$412$	−3.80506	+	4.69721i	−0.187462	+	0.231415i
$413$	−19.1891	−	0.834999i	−0.944235	−	0.0410876i
$414$	−1.44509	+	4.07969i	−0.0710223	+	0.200506i
$415$	3.51674	−	6.09117i	0.172630	−	0.299004i
$416$	5.72735	−	13.8103i	0.280807	−	0.677104i
$417$	1.03604	+	1.79447i	0.0507351	+	0.0878758i
$418$	−0.340578	−	0.398835i	−0.0166582	−	0.0195077i
$419$	−3.25454	−	3.25454i	−0.158995	−	0.158995i	0.623126	−	0.782121i	$-0.285862\pi$
$419$	−3.25454	−	3.25454i	−0.158995	−	0.158995i	−0.782121	+	0.623126i	$0.785862\pi$
$420$	0.196862	+	3.22001i	0.00960588	+	0.157120i
$421$	−5.54370	+	5.54370i	−0.270183	+	0.270183i	−0.829174	−	0.558991i	$-0.811189\pi$
$421$	−5.54370	+	5.54370i	−0.270183	+	0.270183i	0.558991	+	0.829174i	$0.311189\pi$
$422$	−2.08144	+	26.4182i	−0.101323	+	1.28602i
$423$	6.00251	−	3.46555i	0.291852	−	0.168501i
$424$	9.18293	−	2.71753i	0.445962	−	0.131975i
$425$	13.7014	+	7.91049i	0.664614	+	0.383715i
$426$	−2.23096	−	4.67834i	−0.108090	−	0.226666i
$427$	−17.5403	+	9.13417i	−0.848835	+	0.442034i
$428$	−13.2838	+	1.39388i	−0.642097	+	0.0673755i
$429$	0.586591	−	0.157177i	0.0283209	−	0.00758856i
$430$	0.282292	+	1.52384i	0.0136133	+	0.0734862i
$431$	16.0025	+	27.7171i	0.770813	+	1.33509i	0.937118	+	0.349013i	$0.113483\pi$
$431$	16.0025	+	27.7171i	0.770813	+	1.33509i	−0.166305	+	0.986074i	$0.553184\pi$
$432$	−3.56465	+	1.81474i	−0.171504	+	0.0873116i
$433$	−29.7217			−1.42833			−0.714166	−	0.699976i	$-0.753194\pi$
$433$	−29.7217			−1.42833			−0.714166	+	0.699976i	$0.753194\pi$
$434$	2.33208	−	19.0028i	0.111944	−	0.912164i
$435$	−2.74483	−	2.74483i	−0.131605	−	0.131605i
$436$	26.8839	+	11.9750i	1.28750	+	0.573499i
$437$	−4.77113	−	1.27842i	−0.228234	−	0.0611551i
$438$	−10.3966	+	15.1244i	−0.496769	+	0.722670i
$439$	7.00658	+	4.04525i	0.334406	+	0.193069i	0.657795	−	0.753197i	$-0.271489\pi$
$439$	7.00658	+	4.04525i	0.334406	+	0.193069i	−0.323390	+	0.946266i	$0.604822\pi$
$440$	0.206937	+	0.337886i	0.00986533	+	0.0161081i
$441$	−6.97354	−	0.608047i	−0.332073	−	0.0289546i
$442$	−11.5324	+	5.49947i	−0.548541	+	0.261583i
$443$	9.88009	+	36.8730i	0.469417	+	1.75189i	0.641813	+	0.766861i	$0.278182\pi$
$443$	9.88009	+	36.8730i	0.469417	+	1.75189i	−0.172396	+	0.985028i	$0.555151\pi$
$444$	−1.78681	+	11.2689i	−0.0847980	+	0.534799i
$445$	−2.00025	+	7.46503i	−0.0948209	+	0.353876i
$446$	−1.92734	−	2.25702i	−0.0912623	−	0.106873i
$447$	21.6287			1.02300
$448$	−5.30711	+	20.4899i	−0.250737	+	0.968055i
$449$	−3.41547			−0.161186			−0.0805930	−	0.996747i	$-0.525681\pi$
$449$	−3.41547			−0.161186			−0.0805930	+	0.996747i	$0.525681\pi$
$450$	−4.25049	−	4.97755i	−0.200370	−	0.234644i
$451$	0.395098	−	1.47453i	0.0186045	−	0.0694328i
$452$	−2.39876	+	15.1283i	−0.112828	+	0.711578i
$453$	−4.77804	−	17.8319i	−0.224492	−	0.837814i
$454$	19.2658	−	9.18726i	0.904187	−	0.431180i
$455$	1.28134	−	4.06598i	0.0600703	−	0.190616i
$456$	−2.38421	−	3.89294i	−0.111651	−	0.182303i
$457$	−34.8281	−	20.1080i	−1.62919	−	0.940614i	−0.984335	−	0.176310i	$-0.943584\pi$
$457$	−34.8281	−	20.1080i	−1.62919	−	0.940614i	−0.644856	−	0.764304i	$-0.723083\pi$
$458$	−4.71333	+	6.85667i	−0.220239	+	0.320391i
$459$	3.30183	+	0.884722i	0.154116	+	0.0412953i
$460$	3.40874	+	1.51837i	0.158933	+	0.0707944i
$461$	12.6102	+	12.6102i	0.587314	+	0.587314i	0.936903	−	0.349589i	$-0.113679\pi$
$461$	12.6102	+	12.6102i	0.587314	+	0.587314i	−0.349589	+	0.936903i	$0.613679\pi$
$462$	−0.791374	+	0.335975i	−0.0368181	+	0.0156310i
$463$	−35.5662			−1.65290			−0.826451	−	0.563009i	$-0.809644\pi$
$463$	−35.5662			−1.65290			−0.826451	+	0.563009i	$0.809644\pi$
$464$	−11.5546	−	22.6965i	−0.536411	−	1.05366i
$465$	−1.55976	−	2.70158i	−0.0723321	−	0.125283i
$466$	−0.997255	−	5.38329i	−0.0461969	−	0.249376i
$467$	−36.4702	+	9.77215i	−1.68764	+	0.452201i	−0.969778	−	0.243987i	$-0.921544\pi$
$467$	−36.4702	+	9.77215i	−1.68764	+	0.452201i	−0.717859	+	0.696188i	$0.754878\pi$
$468$	5.25704	−	0.551623i	0.243007	−	0.0254988i
$469$	−1.69558	+	38.9662i	−0.0782948	+	1.79929i
$470$	−2.57224	−	5.39401i	−0.118649	−	0.248807i
$471$	3.75422	+	2.16750i	0.172985	+	0.0998731i
$472$	−19.6894	+	5.82674i	−0.906277	+	0.268197i
$473$	−0.357682	+	0.206508i	−0.0164463	+	0.00949525i
$474$	1.06763	−	13.5506i	0.0490377	−	0.622398i
$475$	5.28209	−	5.28209i	0.242359	−	0.242359i
$476$	15.0835	−	9.98303i	0.691353	−	0.457572i
$477$	2.39415	+	2.39415i	0.109621	+	0.109621i
$478$	15.8604	+	18.5734i	0.725439	+	0.849528i
$479$	−20.0556	−	34.7372i	−0.916362	−	1.58719i	−0.804895	−	0.593417i	$-0.797779\pi$
$479$	−20.0556	−	34.7372i	−0.916362	−	1.58719i	−0.111467	−	0.993768i	$-0.535555\pi$
$480$	1.31841	+	3.18680i	0.0601771	+	0.145457i
$481$	7.53881	−	13.0576i	0.343740	−	0.595375i
$482$	−9.32435	+	26.3240i	−0.424712	+	1.19902i
$483$	−4.34955	+	6.82964i	−0.197912	+	0.310759i
$484$	13.7815	−	17.0128i	0.626433	−	0.773308i
$485$	−1.84936	−	6.90192i	−0.0839753	−	0.313400i
$486$	−1.16542	−	0.801120i	−0.0528646	−	0.0363395i
$487$	−7.04368	+	4.06667i	−0.319179	+	0.184278i	−0.651027	−	0.759055i	$-0.725661\pi$
$487$	−7.04368	+	4.06667i	−0.319179	+	0.184278i	0.331847	+	0.943333i	$0.392328\pi$
$488$	−14.5569	+	15.3318i	−0.658958	+	0.694038i
$489$			18.7802i			0.849271i
$490$	−0.994884	+	5.95276i	−0.0449443	+	0.268918i
$491$	2.80755	−	2.80755i	0.126703	−	0.126703i	−0.640912	−	0.767615i	$-0.721443\pi$
$491$	2.80755	−	2.80755i	0.126703	−	0.126703i	0.767615	+	0.640912i	$0.221443\pi$
$492$	5.40651	−	12.1376i	0.243744	−	0.547206i
$493$	−5.63313	+	21.0231i	−0.253703	+	0.946834i
$494$	1.09884	+	5.93164i	0.0494390	+	0.266877i
$495$	−0.0700424	+	0.121317i	−0.00314817	+	0.00545279i
$496$	−4.24850	−	20.0215i	−0.190763	−	0.898990i
$497$	−2.10012	−	9.46645i	−0.0942031	−	0.424628i
$498$	15.3791	+	5.44751i	0.689153	+	0.244109i
$499$	−17.8553	+	4.78431i	−0.799312	+	0.214175i	−0.635282	−	0.772280i	$-0.719116\pi$
$499$	−17.8553	+	4.78431i	−0.799312	+	0.214175i	−0.164030	+	0.986455i	$0.552449\pi$
$500$	−9.49905	+	6.89897i	−0.424810	+	0.308531i
$501$	20.0857	+	5.38194i	0.897361	+	0.240447i
$502$	16.5829	+	1.30653i	0.740129	+	0.0583135i
$503$			18.3324i			0.817403i	0.912668	+	0.408701i	$0.134018\pi$
$503$			18.3324i			0.817403i	−0.912668	+	0.408701i	$0.865982\pi$
$504$	−7.26123	+	1.80957i	−0.323441	+	0.0806046i
$505$		−	5.89772i		−	0.262445i
$506$	−0.0781114	+	0.991410i	−0.00347248	+	0.0440735i
$507$	5.80987	+	1.55675i	0.258025	+	0.0691377i
$508$	2.34780	−	14.8069i	0.104167	−	0.656952i
$509$	−1.06758	+	0.286058i	−0.0473199	+	0.0126793i	−0.282401	−	0.959296i	$-0.591131\pi$
$509$	−1.06758	+	0.286058i	−0.0473199	+	0.0126793i	0.235081	+	0.971976i	$0.424464\pi$
$510$	0.984043	−	2.77809i	0.0435742	−	0.123016i
$511$	−25.3114	+	23.2004i	−1.11971	+	1.02633i
$512$	1.75788	+	22.5590i	0.0776879	+	0.996978i
$513$	0.806990	−	1.39775i	0.0356295	−	0.0617121i
$514$	−36.1305	+	6.69318i	−1.59365	+	0.295223i
$515$	−0.476927	+	1.77992i	−0.0210159	+	0.0784325i
$516$	−3.35641	+	1.28774i	−0.147758	+	0.0566897i
$517$	1.12613	−	1.12613i	0.0495274	−	0.0495274i
$518$	−7.99499	+	19.7918i	−0.351280	+	0.869600i
$519$		−	17.7311i		−	0.778311i
$520$	−0.118125	−	4.55592i	−0.00518014	−	0.199790i
$521$	−14.6547	+	8.46087i	−0.642032	+	0.370677i	−0.785397	−	0.618993i	$-0.787541\pi$
$521$	−14.6547	+	8.46087i	−0.642032	+	0.370677i	0.143365	+	0.989670i	$0.454208\pi$
$522$	5.10082	−	7.42037i	0.223257	−	0.324781i
$523$	−7.65387	−	28.5646i	−0.334680	−	1.24904i	−0.904215	−	0.427077i	$-0.859543\pi$
$523$	−7.65387	−	28.5646i	−0.334680	−	1.24904i	0.569535	−	0.821967i	$-0.307123\pi$
$524$	−1.07048	−	10.2018i	−0.0467642	−	0.445668i
$525$	−5.65587	−	10.8609i	−0.246843	−	0.474011i
$526$	−24.8698	−	8.80927i	−1.08438	−	0.384102i
$527$	−8.74542	+	15.1475i	−0.380956	+	0.659836i
$528$	−0.683236	+	0.614763i	−0.0297340	+	0.0267541i
$529$	−6.81696	−	11.8073i	−0.296389	−	0.513361i
$530$	2.21997	−	1.89570i	0.0964292	−	0.0823439i
$531$	−5.13336	−	5.13336i	−0.222769	−	0.222769i
$532$	−2.70970	−	8.09911i	−0.117480	−	0.351141i
$533$	−12.4160	+	12.4160i	−0.537795	+	0.537795i
$534$	−17.8719	−	1.40810i	−0.773394	−	0.0609343i
$535$	−3.52605	+	2.03577i	−0.152445	+	0.0880139i
$536$	11.8320	+	39.9821i	0.511065	+	1.72696i
$537$	9.94918	+	5.74416i	0.429339	+	0.247879i
$538$	14.2370	−	6.78919i	0.613800	−	0.292703i
$539$	−1.58391	+	0.279764i	−0.0682237	+	0.0120503i
$540$	−0.767506	+	0.947458i	−0.0330282	+	0.0407721i
$541$	−0.255973	+	0.0685877i	−0.0110051	+	0.00294881i	−0.264317	−	0.964436i	$-0.585147\pi$
$541$	−0.255973	+	0.0685877i	−0.0110051	+	0.00294881i	0.253312	+	0.967385i	$0.418480\pi$
$542$	12.7956	−	2.37038i	0.549617	−	0.101817i
$543$	−9.84514	−	17.0523i	−0.422495	−	0.731784i
$544$	11.7781	−	15.3359i	0.504983	−	0.657521i
$545$	8.97125			0.384286
$546$	9.81537	+	1.20457i	0.420059	+	0.0515510i
$547$	9.31466	+	9.31466i	0.398266	+	0.398266i	0.877621	−	0.479355i	$-0.159129\pi$
$547$	9.31466	+	9.31466i	0.398266	+	0.398266i	−0.479355	+	0.877621i	$0.659129\pi$
$548$	−4.59649	−	11.9804i	−0.196352	−	0.511778i
$549$	−7.21998	−	1.93459i	−0.308141	−	0.0825662i
$550$	−1.23939	−	0.851968i	−0.0528479	−	0.0363280i
$551$	8.89962	+	5.13820i	0.379136	+	0.218895i
$552$	−2.02291	+	8.41645i	−0.0861006	+	0.358228i
$553$	7.64320	−	24.2535i	0.325022	−	1.03137i
$554$	14.0007	+	29.3597i	0.594835	+	1.24737i
$555$	0.900177	+	3.35951i	0.0382104	+	0.142603i
$556$	2.43530	+	3.35312i	0.103280	+	0.142204i
$557$	6.84813	−	25.5576i	0.290165	−	1.08291i	−0.654818	−	0.755787i	$-0.727255\pi$
$557$	6.84813	−	25.5576i	0.290165	−	1.08291i	0.944982	−	0.327122i	$-0.106079\pi$
$558$	5.50291	−	4.69911i	0.232957	−	0.198929i
$559$	4.75065			0.200931
$560$	1.06364	+	6.36376i	0.0449469	+	0.268918i
$561$	0.785441			0.0331613
$562$	−23.1403	+	19.7602i	−0.976113	+	0.833534i
$563$	−9.72916	+	36.3097i	−0.410035	+	1.53027i	0.384541	+	0.923108i	$0.374360\pi$
$563$	−9.72916	+	36.3097i	−0.410035	+	1.53027i	−0.794576	+	0.607165i	$0.792307\pi$
$564$	11.2162	−	8.14608i	0.472286	−	0.343012i
$565$	1.20847	+	4.51009i	0.0508409	+	0.189741i
$566$	8.78179	+	18.4155i	0.369126	+	0.774060i
$567$	−1.78773	−	1.95039i	−0.0750776	−	0.0819087i
$568$	−5.41400	−	8.83996i	−0.227166	−	0.370916i
$569$	−0.188299	−	0.108715i	−0.00789392	−	0.00455756i	0.496048	−	0.868295i	$-0.334784\pi$
$569$	−0.188299	−	0.108715i	−0.00789392	−	0.00455756i	−0.503942	+	0.863738i	$0.668117\pi$
$570$	−1.14675	−	0.788285i	−0.0480321	−	0.0330176i
$571$	−12.4603	−	3.33873i	−0.521448	−	0.139722i	−0.0115117	−	0.999934i	$-0.503664\pi$
$571$	−12.4603	−	3.33873i	−0.521448	−	0.139722i	−0.509936	+	0.860212i	$0.670331\pi$
$572$	1.13397	−	0.435067i	0.0474137	−	0.0181911i
$573$	1.75587	+	1.75587i	0.0733525	+	0.0733525i
$574$	14.9589	−	19.8536i	0.624370	−	0.828672i
$575$	−14.1645			−0.590702
$576$	−6.71161	+	4.35365i	−0.279650	+	0.181402i
$577$	3.12867	+	5.41901i	0.130248	+	0.225596i	0.923772	−	0.382943i	$-0.125089\pi$
$577$	3.12867	+	5.41901i	0.130248	+	0.225596i	−0.793524	+	0.608539i	$0.791756\pi$
$578$	7.39108	−	1.36920i	0.307428	−	0.0569511i
$579$	−1.23132	+	0.329932i	−0.0511721	+	0.0137115i
$580$	−6.03257	−	4.88680i	−0.250489	−	0.202913i
$581$	25.7455	+	16.3964i	1.06810	+	0.680236i
$582$	14.9610	−	7.13443i	0.620152	−	0.295732i
$583$	0.673751	+	0.388991i	0.0279039	+	0.0161103i
$584$	−17.5230	+	32.2535i	−0.725107	+	1.33466i
$585$	1.39543	−	0.805651i	0.0576938	−	0.0333096i
$586$	32.4733	+	2.55851i	1.34146	+	0.105691i
$587$	−21.1521	+	21.1521i	−0.873040	+	0.873040i	−0.992803	−	0.119763i	$-0.961787\pi$
$587$	−21.1521	+	21.1521i	−0.873040	+	0.873040i	0.119763	+	0.992803i	$0.461787\pi$
$588$	−13.9978	+	0.246029i	−0.577261	+	0.0101461i
$589$	5.83960	+	5.83960i	0.240616	+	0.240616i
$590$	−4.75989	+	4.06463i	−0.195962	+	0.167338i
$591$	−12.0600	−	20.8885i	−0.496081	−	0.859238i
$592$	−1.20211	+	22.7877i	−0.0494064	+	0.936568i
$593$	1.49024	−	2.58117i	0.0611967	−	0.105996i	−0.833804	−	0.552061i	$-0.813842\pi$
$593$	1.49024	−	2.58117i	0.0611967	−	0.105996i	0.895001	+	0.446065i	$0.147175\pi$
$594$	−0.306303	−	0.108497i	−0.0125678	−	0.00445169i
$595$	2.96186	−	4.65069i	0.121424	−	0.190660i
$596$	43.0213	−	4.51424i	1.76222	−	0.184911i
$597$	3.77492	+	14.0882i	0.154497	+	0.576592i
$598$	6.47986	−	9.42651i	0.264981	−	0.385479i
$599$	−4.29387	+	2.47907i	−0.175443	+	0.101292i	−0.585150	−	0.810925i	$-0.698964\pi$
$599$	−4.29387	+	2.47907i	−0.175443	+	0.101292i	0.409707	+	0.912217i	$0.365631\pi$
$600$	−9.49344	−	9.01359i	−0.387568	−	0.367978i
$601$			27.4349i			1.11909i	0.828799	+	0.559547i	$0.189025\pi$
$601$			27.4349i			1.11909i	−0.828799	+	0.559547i	$0.810975\pi$
$602$	−6.66004	+	0.936419i	−0.271443	+	0.0381656i
$603$	−10.4240	+	10.4240i	−0.424499	+	0.424499i
$604$	−13.2257	−	34.4718i	−0.538145	−	1.40264i
$605$	1.72738	−	6.44666i	0.0702279	−	0.262094i
$606$	13.4519	−	2.49197i	0.546447	−	0.101229i
$607$	5.95919	−	10.3216i	0.241876	−	0.418942i	−0.719373	−	0.694624i	$-0.755571\pi$
$607$	5.95919	−	10.3216i	0.241876	−	0.418942i	0.961249	+	0.275683i	$0.0889039\pi$
$608$	−5.55491	−	7.24574i	−0.225281	−	0.293854i
$609$	12.4184	−	11.3827i	0.503217	−	0.461249i
$610$	−2.15177	+	6.07475i	−0.0871226	+	0.245960i
$611$	−17.6944	+	4.74119i	−0.715838	+	0.191808i
$612$	6.75225	+	1.07064i	0.272944	+	0.0432781i
$613$	32.3133	+	8.65833i	1.30512	+	0.349706i	0.843385	−	0.537310i	$-0.180560\pi$
$613$	32.3133	+	8.65833i	1.30512	+	0.349706i	0.461738	+	0.887017i	$0.347226\pi$
$614$	−1.32969	+	16.8768i	−0.0536621	+	0.681093i
$615$		−	4.05036i		−	0.163326i
$616$	−1.50398	+	0.833453i	−0.0605972	+	0.0335808i
$617$		−	17.0517i		−	0.686477i	−0.939248	−	0.343238i	$-0.888476\pi$
$617$		−	17.0517i		−	0.686477i	0.939248	−	0.343238i	$-0.111524\pi$
$618$	−4.26127	−	0.335738i	−0.171413	−	0.0135054i
$619$	6.69840	+	1.79483i	0.269231	+	0.0721403i	0.390909	−	0.920429i	$-0.372161\pi$
$619$	6.69840	+	1.79483i	0.269231	+	0.0721403i	−0.121678	+	0.992570i	$0.538827\pi$
$620$	−3.66635	−	5.04812i	−0.147244	−	0.202737i
$621$	−2.95613	+	0.792092i	−0.118625	+	0.0317855i
$622$	29.3555	+	10.3982i	1.17705	+	0.416929i
$623$	−31.9881	−	10.0807i	−1.28158	−	0.403873i
$624$	10.3415	−	2.19445i	0.413993	−	0.0878481i
$625$	9.78143	−	16.9419i	0.391257	−	0.677678i
$626$	−4.34365	−	23.4475i	−0.173607	−	0.937150i
$627$	0.0959836	−	0.358216i	0.00383322	−	0.0143058i
$628$	7.91983	+	3.52777i	0.316036	+	0.140773i
$629$	13.7892	−	13.7892i	0.549812	−	0.549812i
$630$	−1.79748	+	1.40452i	−0.0716132	+	0.0559574i
$631$		−	44.8926i		−	1.78715i	−0.448916	−	0.893574i	$-0.648190\pi$
$631$		−	44.8926i		−	1.78715i	0.448916	−	0.893574i	$-0.351810\pi$
$632$	−0.704616	−	27.1760i	−0.0280281	−	1.08100i
$633$	−16.2279	+	9.36918i	−0.645001	+	0.372392i
$634$	−5.02689	−	3.45552i	−0.199643	−	0.137236i
$635$	−1.18280	−	4.41427i	−0.0469380	−	0.175175i
$636$	5.26185	+	4.26246i	0.208646	+	0.169017i
$637$	17.3868	+	6.32250i	0.688889	+	0.250507i
$638$	0.690814	−	1.95027i	0.0273496	−	0.0772118i
$639$	1.83249	−	3.17396i	0.0724920	−	0.125560i
$640$	3.28756	+	6.06364i	0.129952	+	0.239686i
$641$	−22.5114	−	38.9909i	−0.889148	−	1.54005i	−0.840884	−	0.541215i	$-0.817964\pi$
$641$	−22.5114	−	38.9909i	−0.889148	−	1.54005i	−0.0482640	−	0.998835i	$-0.515369\pi$
$642$	−6.13319	−	7.18229i	−0.242058	−	0.283462i
$643$	−12.4240	−	12.4240i	−0.489955	−	0.489955i	0.418337	−	0.908292i	$-0.362613\pi$
$643$	−12.4240	−	12.4240i	−0.489955	−	0.489955i	−0.908292	+	0.418337i	$0.862613\pi$
$644$	−7.22616	+	14.4925i	−0.284751	+	0.571085i
$645$	−0.774884	+	0.774884i	−0.0305110	+	0.0305110i
$646$	−0.612831	+	7.77821i	−0.0241115	+	0.306030i
$647$	14.7418	−	8.51117i	0.579559	−	0.334609i	−0.181399	−	0.983410i	$-0.558063\pi$
$647$	14.7418	−	8.51117i	0.579559	−	0.334609i	0.760958	+	0.648801i	$0.224729\pi$
$648$	−2.48532	−	1.35025i	−0.0976327	−	0.0530428i
$649$	−1.44461	−	0.834046i	−0.0567059	−	0.0327392i
$650$	7.44617	+	15.6147i	0.292063	+	0.612458i
$651$	12.0073	−	6.25283i	0.470602	−	0.245068i
$652$	3.91971	+	37.3553i	0.153508	+	1.46295i
$653$	17.2583	−	4.62435i	0.675369	−	0.180965i	0.0951969	−	0.995458i	$-0.469652\pi$
$653$	17.2583	−	4.62435i	0.675369	−	0.180965i	0.580172	+	0.814494i	$0.302985\pi$
$654$	3.79063	+	20.4622i	0.148225	+	0.800137i
$655$	−1.56345	−	2.70797i	−0.0610889	−	0.105809i
$656$	8.22068	−	25.2711i	0.320964	−	0.986670i
$657$	−12.9776			−0.506304
$658$	23.8716	−	10.1346i	0.930612	−	0.395088i
$659$	6.59895	+	6.59895i	0.257058	+	0.257058i	0.823857	−	0.566798i	$-0.191818\pi$
$659$	6.59895	+	6.59895i	0.257058	+	0.257058i	−0.566798	+	0.823857i	$0.691818\pi$
$660$	−0.113999	+	0.255928i	−0.00443741	+	0.00996198i
$661$	−25.3884	−	6.80281i	−0.987495	−	0.264599i	−0.271297	−	0.962496i	$-0.587453\pi$
$661$	−25.3884	−	6.80281i	−0.987495	−	0.264599i	−0.716198	+	0.697897i	$0.754119\pi$
$662$	14.9688	−	21.7758i	0.581780	−	0.846339i
$663$	−7.82402	−	4.51720i	−0.303860	−	0.175434i
$664$	31.7272	+	7.62568i	1.23125	+	0.295934i
$665$	−1.75909	−	1.91914i	−0.0682145	−	0.0744212i
$666$	−7.28224	+	3.47268i	−0.282181	+	0.134564i
$667$	−5.04334	−	18.8220i	−0.195279	−	0.728791i
$668$	41.0753	+	6.51292i	1.58925	+	0.251992i
$669$	0.543175	−	2.02716i	0.0210003	−	0.0783744i
$670$	8.25380	+	9.66564i	0.318872	+	0.373416i
$671$	−1.71749			−0.0663031
$672$	−14.0655	+	5.11490i	−0.542588	+	0.197312i
$673$	35.1107			1.35342			0.676709	−	0.736250i	$-0.263405\pi$
$673$	35.1107			1.35342			0.676709	+	0.736250i	$0.263405\pi$
$674$	1.68419	+	1.97228i	0.0648726	+	0.0759692i
$675$	1.19790	−	4.47061i	0.0461070	−	0.172074i
$676$	11.8812	+	1.88389i	0.456970	+	0.0724574i
$677$	0.854664	+	3.18965i	0.0328474	+	0.122588i	0.980403	−	0.197003i	$-0.0631210\pi$
$677$	0.854664	+	3.18965i	0.0328474	+	0.122588i	−0.947555	+	0.319591i	$0.896454\pi$
$678$	−9.77630	+	4.66202i	−0.375457	+	0.179044i
$679$	30.2729	−	6.71600i	1.16177	−	0.257737i
$680$	1.37751	−	5.73123i	0.0528251	−	0.219783i
$681$	13.0706	+	7.54632i	0.500867	+	0.289176i
$682$	0.941890	−	1.37021i	0.0360668	−	0.0524679i
$683$	−16.3066	−	4.36934i	−0.623955	−	0.167188i	−0.0670298	−	0.997751i	$-0.521352\pi$
$683$	−16.3066	−	4.36934i	−0.623955	−	0.167188i	−0.556925	+	0.830563i	$0.688019\pi$
$684$	1.31344	−	2.94866i	0.0502205	−	0.112745i
$685$	−2.76589	−	2.76589i	−0.105679	−	0.105679i
$686$	−25.6212	−	5.43648i	−0.978221	−	0.207566i
$687$	−5.88342			−0.224467
$688$	−6.40739	+	3.26195i	−0.244279	+	0.124361i
$689$	−4.47430	−	7.74971i	−0.170457	−	0.295241i
$690$	0.480633	+	2.59451i	0.0182974	+	0.0987712i
$691$	−45.3538	+	12.1525i	−1.72534	+	0.462303i	−0.979101	−	0.203377i	$-0.934808\pi$
$691$	−45.3538	+	12.1525i	−1.72534	+	0.462303i	−0.746238	+	0.665680i	$0.768142\pi$
$692$	−3.70075	−	35.2686i	−0.140682	−	1.34071i
$693$	−0.512769	−	0.326564i	−0.0194785	−	0.0124051i
$694$	12.3699	+	25.9399i	0.469557	+	0.984664i
$695$	1.09402	+	0.631632i	0.0414985	+	0.0239592i
$696$	8.59720	−	15.8243i	0.325876	−	0.599820i
$697$	−19.6674	+	11.3550i	−0.744957	+	0.430101i
$698$	−0.934519	+	11.8612i	−0.0353721	+	0.448951i
$699$	2.73744	−	2.73744i	0.103539	−	0.103539i
$700$	−13.5168	−	20.4228i	−0.510888	−	0.771910i
$701$	−26.6000	−	26.6000i	−1.00467	−	1.00467i	−0.999989	−	0.00467922i	$-0.998511\pi$
$701$	−26.6000	−	26.6000i	−1.00467	−	1.00467i	−0.00467922	−	0.999989i	$-0.501489\pi$
$702$	2.42719	+	2.84237i	0.0916086	+	0.107279i
$703$	−4.60375	−	7.97393i	−0.173634	−	0.300742i
$704$	−1.23070	+	1.36541i	−0.0463838	+	0.0514610i
$705$	2.11281	−	3.65949i	0.0795730	−	0.137825i
$706$	12.1159	−	34.2048i	0.455986	−	1.28731i
$707$	25.5702	+	1.11267i	0.961667	+	0.0418461i
$708$	−11.2821	−	9.13926i	−0.424006	−	0.343474i
$709$	−3.38321	−	12.6263i	−0.127059	−	0.474191i	0.872846	−	0.487997i	$-0.162272\pi$
$709$	−3.38321	−	12.6263i	−0.127059	−	0.474191i	−0.999905	+	0.0138053i	$0.995605\pi$
$710$	−2.60400	−	1.79001i	−0.0977265	−	0.0671779i
$711$	8.32371	−	4.80570i	0.312164	−	0.180228i
$712$	−35.8426	+	0.929322i	−1.34326	+	0.0348278i
$713$		−	15.6595i		−	0.586454i
$714$	11.8591	+	4.79055i	0.443815	+	0.179282i
$715$	0.261797	−	0.261797i	0.00979065	−	0.00979065i
$716$	20.9886	+	9.34905i	0.784381	+	0.349391i
$717$	−4.46987	+	16.6818i	−0.166931	+	0.622993i
$718$	6.96256	+	37.5846i	0.259840	+	1.40265i
$719$	13.0465	−	22.5972i	0.486553	−	0.842735i	−0.513327	−	0.858193i	$-0.671587\pi$
$719$	13.0465	−	22.5972i	0.486553	−	0.842735i	0.999881	+	0.0154581i	$0.00492067\pi$
$720$	−1.32888	+	2.04476i	−0.0495245	+	0.0762037i
$721$	−7.62705	−	2.40357i	−0.284046	−	0.0895137i
$722$	−21.8555	−	7.74157i	−0.813379	−	0.288111i
$723$	−19.0742	+	5.11092i	−0.709377	+	0.190077i
$724$	−23.1418	−	31.8635i	−0.860060	−	1.18420i
$725$	28.4649	+	7.62714i	1.05716	+	0.283265i
$726$	15.4339	+	1.21601i	0.572804	+	0.0451302i
$727$		−	5.23353i		−	0.194101i	−0.995279	−	0.0970505i	$-0.969059\pi$
$727$		−	5.23353i		−	0.194101i	0.995279	−	0.0970505i	$-0.0309408\pi$
$728$	19.7750	+	0.347376i	0.732909	+	0.0128746i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.878850	+	11.1546i	−0.0325277	+	0.412850i
$731$	5.93497	+	1.59027i	0.219513	+	0.0588183i
$732$	−14.7649	−	2.34113i	−0.545726	−	0.0865307i
$733$	42.0435	−	11.2655i	1.55291	−	0.416102i	0.622501	−	0.782619i	$-0.286116\pi$
$733$	42.0435	−	11.2655i	1.55291	−	0.416102i	0.930411	+	0.366517i	$0.119450\pi$
$734$	−13.8033	+	38.9688i	−0.509491	+	1.43836i
$735$	−3.86725	+	1.80471i	−0.142646	+	0.0665677i
$736$	−2.26708	+	17.1632i	−0.0835657	+	0.632644i
$737$	−1.69365	+	2.93349i	−0.0623863	+	0.108056i
$738$	9.23835	−	1.71140i	0.340068	−	0.0629977i
$739$	8.98423	−	33.5296i	0.330490	−	1.23341i	−0.578186	−	0.815905i	$-0.696239\pi$
$739$	8.98423	−	33.5296i	0.330490	−	1.23341i	0.908676	−	0.417501i	$-0.137094\pi$
$740$	2.49170	+	6.49444i	0.0915968	+	0.238740i
$741$	−3.01628	+	3.01628i	−0.110806	+	0.110806i
$742$	7.80020	+	9.98255i	0.286354	+	0.366471i
$743$		−	17.9525i		−	0.658613i	−0.944223	−	0.329307i	$-0.893185\pi$
$743$		−	17.9525i		−	0.658613i	0.944223	−	0.329307i	$-0.106815\pi$
$744$	9.96495	−	10.4954i	0.365333	−	0.384782i
$745$	11.4196	−	6.59309i	0.418381	−	0.241552i
$746$	11.5105	−	16.7448i	0.421429	−	0.613070i
$747$	2.98592	+	11.1436i	0.109249	+	0.407723i
$748$	1.56230	−	0.163933i	0.0571235	−	0.00599400i
$749$	−8.16108	−	15.6717i	−0.298199	−	0.572630i
$750$	−7.82504	−	2.77175i	−0.285730	−	0.101210i
$751$	−11.5931	+	20.0798i	−0.423037	+	0.732721i	−0.996235	−	0.0866958i	$-0.972369\pi$
$751$	−11.5931	+	20.0798i	−0.423037	+	0.732721i	0.573198	+	0.819417i	$0.305703\pi$
$752$	20.6096	−	18.5442i	0.751556	−	0.676236i
$753$	5.88110	+	10.1864i	0.214319	+	0.371212i
$754$	−18.0977	+	15.4542i	−0.659080	+	0.562810i
$755$	−7.95840	−	7.95840i	−0.289636	−	0.289636i
$756$	−3.96301	−	3.50636i	−0.144133	−	0.127525i
$757$	−9.13432	+	9.13432i	−0.331993	+	0.331993i	−0.853343	−	0.521350i	$-0.825429\pi$
$757$	−9.13432	+	9.13432i	−0.331993	+	0.331993i	0.521350	+	0.853343i	$0.325429\pi$
$758$	24.0273	+	1.89307i	0.872712	+	0.0687594i
$759$	−0.608994	+	0.351603i	−0.0221051	+	0.0127624i
$760$	−2.44550	−	1.32862i	−0.0887078	−	0.0481940i
$761$	22.6330	+	13.0672i	0.820446	+	0.473685i	0.850570	−	0.525861i	$-0.176257\pi$
$761$	22.6330	+	13.0672i	0.820446	+	0.473685i	−0.0301242	+	0.999546i	$0.509590\pi$
$762$	9.56860	−	4.56298i	0.346634	−	0.165299i
$763$	−1.69252	+	38.8958i	−0.0612733	+	1.40812i
$764$	3.85904	+	3.12609i	0.139615	+	0.113098i
$765$	2.01299	−	0.539380i	0.0727799	−	0.0195013i
$766$	41.4066	−	7.67058i	1.49608	−	0.277149i
$767$	9.59347	+	16.6164i	0.346400	+	0.599983i
$768$	−12.4413	+	10.0606i	−0.448935	+	0.363030i
$769$	−10.1116			−0.364634			−0.182317	−	0.983240i	$-0.558360\pi$
$769$	−10.1116			−0.364634			−0.182317	+	0.983240i	$0.558360\pi$
$770$	−0.315415	+	0.418623i	−0.0113668	+	0.0150861i
$771$	−18.3726	−	18.3726i	−0.661673	−	0.661673i
$772$	−2.38034	+	0.913257i	−0.0856703	+	0.0328688i
$773$	−10.4308	−	2.79494i	−0.375172	−	0.100527i	0.0663057	−	0.997799i	$-0.478879\pi$
$773$	−10.4308	−	2.79494i	−0.375172	−	0.100527i	−0.441477	+	0.897272i	$0.645545\pi$
$774$	−2.09482	−	1.44000i	−0.0752968	−	0.0517596i
$775$	20.5094	+	11.8411i	0.736720	+	0.425345i
$776$	28.2695	−	17.3135i	1.01481	−	0.621519i
$777$	−14.7353	+	3.26901i	−0.528627	+	0.117275i
$778$	15.7542	+	33.0366i	0.564815	+	1.18442i
$779$	2.77524	+	10.3573i	0.0994333	+	0.371090i
$780$	2.60747	−	1.89375i	0.0933622	−	0.0678071i
$781$	0.217957	−	0.813425i	0.00779910	−	0.0291066i
$782$	11.2508	−	9.60739i	0.402327	−	0.343560i
$783$	6.36712			0.227542
$784$	−27.7915	+	3.41093i	−0.992552	+	0.121819i
$785$	2.64288			0.0943283
$786$	5.51592	−	4.71022i	0.196746	−	0.168008i
$787$	−2.64310	+	9.86419i	−0.0942164	+	0.351621i	−0.996899	−	0.0786855i	$-0.974928\pi$
$787$	−2.64310	+	9.86419i	−0.0942164	+	0.351621i	0.902683	+	0.430306i	$0.141594\pi$
$788$	−28.3480	−	39.0318i	−1.00986	−	1.39045i
$789$	−4.82859	−	18.0205i	−0.171902	−	0.641549i
$790$	−3.56694	−	7.47989i	−0.126906	−	0.266123i
$791$	−19.7820	+	4.38860i	−0.703366	+	0.156041i
$792$	−0.631906	−	0.151880i	−0.0224538	−	0.00539681i
$793$	17.1085	+	9.87760i	0.607541	+	0.350764i
$794$	9.19892	+	6.32340i	0.326457	+	0.224409i
$795$	1.99387	+	0.534257i	0.0707154	+	0.0189481i
$796$	10.4490	+	27.2347i	0.370356	+	0.965307i
$797$	−3.09616	−	3.09616i	−0.109672	−	0.109672i	0.650141	−	0.759813i	$-0.274710\pi$
$797$	−3.09616	−	3.09616i	−0.109672	−	0.109672i	−0.759813	+	0.650141i	$0.774710\pi$
$798$	3.63404	−	4.82315i	0.128644	−	0.170738i
$799$	−23.6926			−0.838185
$800$	−20.7645	−	15.9473i	−0.734135	−	0.563823i
$801$	−6.33826	−	10.9782i	−0.223951	−	0.387895i
$802$	13.0817	−	2.42339i	0.461931	−	0.0855728i
$803$	−2.88032	+	0.771780i	−0.101644	+	0.0272355i
$804$	−18.5586	+	22.9099i	−0.654510	+	0.807969i
$805$	−0.214603	+	4.93180i	−0.00756376	+	0.173823i
$806$	−17.2627	+	8.23208i	−0.608054	+	0.289963i
$807$	9.65890	+	5.57657i	0.340009	+	0.196305i
$808$	26.2368	−	7.76434i	0.923008	−	0.273149i
$809$	5.99922	−	3.46365i	0.210922	−	0.121776i	−0.390818	−	0.920468i	$-0.627808\pi$
$809$	5.99922	−	3.46365i	0.210922	−	0.121776i	0.601740	+	0.798692i	$0.294475\pi$
$810$	−0.859526	−	0.0677205i	−0.0302007	−	0.00237946i
$811$	20.3073	−	20.3073i	0.713086	−	0.713086i	−0.254094	−	0.967180i	$-0.581777\pi$
$811$	20.3073	−	20.3073i	0.713086	−	0.713086i	0.967180	+	0.254094i	$0.0817772\pi$
$812$	22.3254	−	25.2330i	0.783467	−	0.885503i
$813$	6.50664	+	6.50664i	0.228198	+	0.228198i
$814$	−1.40974	+	1.20382i	−0.0494114	+	0.0421939i
$815$	5.72477	+	9.91560i	0.200530	+	0.347328i
$816$	13.6542	+	0.720295i	0.477994	+	0.0252154i
$817$	1.45055	−	2.51242i	0.0507482	−	0.0878985i
$818$	−9.88302	−	3.50072i	−0.345552	−	0.122400i
$819$	3.22973	+	6.20203i	0.112856	+	0.216716i
$820$	−0.845372	−	8.05650i	−0.0295217	−	0.281345i
$821$	−0.215358	−	0.803727i	−0.00751605	−	0.0280503i	0.962066	−	0.272817i	$-0.0879553\pi$
$821$	−0.215358	−	0.803727i	−0.00751605	−	0.0280503i	−0.969582	+	0.244767i	$0.921289\pi$
$822$	5.13995	−	7.47730i	0.179276	−	0.260801i
$823$	−33.0249	+	19.0669i	−1.15118	+	0.664632i	−0.949174	−	0.314753i	$-0.898078\pi$
$823$	−33.0249	+	19.0669i	−1.15118	+	0.664632i	−0.202003	+	0.979385i	$0.564745\pi$
$824$	−8.54608	+	0.221582i	−0.297717	+	0.00771917i
$825$		−	1.06347i		−	0.0370253i
$826$	−16.7246	−	21.4039i	−0.581924	−	0.744736i
$827$	−3.92430	+	3.92430i	−0.136461	+	0.136461i	−0.772038	−	0.635577i	$-0.780762\pi$
$827$	−3.92430	+	3.92430i	−0.136461	+	0.136461i	0.635577	+	0.772038i	$0.280762\pi$
$828$	−5.71465	+	2.19252i	−0.198598	+	0.0761954i
$829$	−4.74865	+	17.7222i	−0.164927	+	0.615517i	0.833122	+	0.553089i	$0.186551\pi$
$829$	−4.74865	+	17.7222i	−0.164927	+	0.615517i	−0.998049	+	0.0624283i	$0.980116\pi$
$830$	9.78043	−	1.81183i	0.339484	−	0.0628894i
$831$	−11.5001	+	19.9187i	−0.398933	+	0.690971i
$832$	20.1121	−	6.52336i	0.697262	−	0.226157i
$833$	19.6048	+	13.7189i	0.679266	+	0.475330i
$834$	−0.978413	+	2.76220i	−0.0338797	+	0.0956471i
$835$	12.2454	−	3.28115i	0.423770	−	0.113549i
$836$	0.116154	−	0.732553i	0.00401727	−	0.0253359i
$837$	4.94247	+	1.32433i	0.170837	+	0.0457755i
$838$	0.511255	−	6.48898i	0.0176610	−	0.224158i
$839$			18.8933i			0.652271i	0.945323	+	0.326135i	$0.105747\pi$
$839$			18.8933i			0.652271i	−0.945323	+	0.326135i	$0.894253\pi$
$840$	−3.28218	+	3.16886i	−0.113246	+	0.109336i
$841$			11.5402i			0.397936i
$842$	−11.0531	−	0.870857i	−0.380916	−	0.0300117i
$843$	−20.7835	−	5.56893i	−0.715823	−	0.191804i
$844$	−30.3231	+	22.0231i	−1.04376	+	0.758065i
$845$	3.54205	−	0.949088i	0.121850	−	0.0326496i
$846$	9.23955	+	3.27279i	0.317662	+	0.112521i
$847$	27.6243	+	8.70547i	0.949183	+	0.299123i
$848$	11.3559	+	7.38014i	0.389962	+	0.253435i
$849$	−7.21327	+	12.4937i	−0.247559	+	0.428784i
$850$	4.07549	+	21.9999i	0.139788	+	0.754592i
$851$	−4.51876	+	16.8642i	−0.154901	+	0.578099i
$852$	2.98251	−	6.69572i	0.102179	−	0.229392i
$853$	1.19503	−	1.19503i	0.0409172	−	0.0409172i	−0.686352	−	0.727269i	$-0.740789\pi$
$853$	1.19503	−	1.19503i	0.0409172	−	0.0409172i	0.727269	+	0.686352i	$0.240789\pi$
$854$	−25.9318	−	10.4753i	−0.887368	−	0.358458i
$855$		−	0.983979i		−	0.0336514i
$856$	−13.6985	−	13.0061i	−0.468203	−	0.444538i
$857$	−17.4611	+	10.0812i	−0.596460	+	0.344367i	−0.767648	−	0.640872i	$-0.778573\pi$
$857$	−17.4611	+	10.0812i	−0.596460	+	0.344367i	0.171187	+	0.985238i	$0.445240\pi$
$858$	0.707742	+	0.486507i	0.0241619	+	0.0166091i
$859$	14.5324	+	54.2356i	0.495839	+	1.85050i	0.525281	+	0.850929i	$0.323960\pi$
$859$	14.5324	+	54.2356i	0.495839	+	1.85050i	−0.0294418	+	0.999566i	$0.509373\pi$
$860$	−1.37958	+	1.70304i	−0.0470432	+	0.0580731i
$861$	17.5608	+	0.764144i	0.598471	+	0.0260419i
$862$	−15.1124	+	42.6644i	−0.514730	+	1.45316i
$863$	−0.730895	+	1.26595i	−0.0248800	+	0.0430933i	−0.878197	−	0.478299i	$-0.841254\pi$
$863$	−0.730895	+	1.26595i	−0.0248800	+	0.0430933i	0.853317	+	0.521392i	$0.174587\pi$
$864$	−5.22532	−	2.16703i	−0.177769	−	0.0737239i
$865$	−5.40498	−	9.36171i	−0.183775	−	0.318308i
$866$	−27.2954	−	31.9643i	−0.927534	−	1.08619i
$867$	3.75841	+	3.75841i	0.127642	+	0.127642i
$868$	22.5784	−	14.9435i	0.766360	−	0.507215i
$869$	1.56162	−	1.56162i	0.0529742	−	0.0529742i
$870$	0.431184	−	5.47270i	0.0146185	−	0.185542i
$871$	33.7419	−	19.4809i	1.14330	−	0.660085i
$872$	11.8106	+	39.9099i	0.399959	+	1.35152i
$873$	10.1501	+	5.86014i	0.343528	+	0.198336i
$874$	−3.00676	−	6.30519i	−0.101705	−	0.213276i
$875$	−13.0996	−	8.34264i	−0.442846	−	0.282033i
$876$	−25.8135	+	2.70862i	−0.872157	+	0.0915158i
$877$	16.5700	−	4.43992i	0.559530	−	0.149926i	0.0320394	−	0.999487i	$-0.489800\pi$
$877$	16.5700	−	4.43992i	0.559530	−	0.149926i	0.527490	+	0.849561i	$0.323133\pi$
$878$	2.08412	+	11.2503i	0.0703355	+	0.379679i
$879$	11.5166	+	19.9474i	0.388446	+	0.672808i
$880$	−0.173337	+	0.532854i	−0.00584320	+	0.0179625i
$881$	29.7588			1.00260			0.501299	−	0.865274i	$-0.332856\pi$
$881$	29.7588			1.00260			0.501299	+	0.865274i	$0.332856\pi$
$882$	−5.75033	−	8.05814i	−0.193624	−	0.271332i
$883$	13.6809	+	13.6809i	0.460400	+	0.460400i	0.898786	−	0.438387i	$-0.144450\pi$
$883$	13.6809	+	13.6809i	0.460400	+	0.460400i	−0.438387	+	0.898786i	$0.644450\pi$
$884$	−16.5054	−	7.35208i	−0.555137	−	0.247277i
$885$	−4.27512	−	1.14552i	−0.143707	−	0.0385061i
$886$	−30.5817	+	44.4885i	−1.02741	+	1.49462i
$887$	−6.85058	−	3.95518i	−0.230020	−	0.132802i	0.380561	−	0.924756i	$-0.375731\pi$
$887$	−6.85058	−	3.95518i	−0.230020	−	0.132802i	−0.610581	+	0.791954i	$0.709064\pi$
$888$	−13.7601	+	8.42735i	−0.461760	+	0.282803i
$889$	19.3617	−	4.29537i	0.649371	−	0.144062i
$890$	−9.86527	+	4.70445i	−0.330685	+	0.157694i
$891$	−0.0594702	−	0.221946i	−0.00199233	−	0.00743546i
$892$	0.657320	−	4.14554i	0.0220087	−	0.138803i
$893$	−2.89532	+	10.8055i	−0.0968882	+	0.361592i
$894$	19.8631	+	23.2608i	0.664322	+	0.777956i
$895$	7.00397			0.234117
$896$	−26.9098	+	13.1096i	−0.898993	+	0.437962i
$897$	8.08850			0.270067
$898$	−3.13665	−	3.67319i	−0.104671	−	0.122576i
$899$	−8.43216	+	31.4692i	−0.281228	+	1.04956i
$900$	1.44963	−	9.14242i	0.0483209	−	0.304747i
$901$	−2.99552	−	11.1795i	−0.0997954	−	0.372442i
$902$	1.94863	−	0.929245i	0.0648824	−	0.0309405i
$903$	−3.21341	−	3.50579i	−0.106936	−	0.116665i
$904$	−18.4728	+	11.3136i	−0.614396	+	0.376285i
$905$	−10.3961	−	6.00219i	−0.345578	−	0.199520i
$906$	14.7894	−	21.5147i	0.491345	−	0.714779i
$907$	−22.6534	−	6.06996i	−0.752194	−	0.201550i	−0.137703	−	0.990474i	$-0.543972\pi$
$907$	−22.6534	−	6.06996i	−0.752194	−	0.201550i	−0.614491	+	0.788924i	$0.710639\pi$
$908$	27.5735	+	12.2822i	0.915059	+	0.407599i
$909$	6.84040	+	6.84040i	0.226882	+	0.226882i
$910$	5.54952	−	2.35603i	0.183965	−	0.0781016i
$911$	23.3024			0.772042			0.386021	−	0.922490i	$-0.373849\pi$
$911$	23.3024			0.772042			0.386021	+	0.922490i	$0.373849\pi$
$912$	1.99710	−	6.13926i	0.0661306	−	0.203291i
$913$	1.32542	+	2.29570i	0.0438652	+	0.0759767i
$914$	−10.3597	−	55.9226i	−0.342667	−	1.84976i
$915$	−4.40174	+	1.17944i	−0.145517	+	0.0389911i
$916$	−11.7026	+	1.22796i	−0.386665	+	0.0405729i
$917$	12.0357	−	6.26761i	0.397453	−	0.206975i
$918$	2.08081	+	4.36347i	0.0686768	+	0.144016i
$919$	−5.66767	−	3.27223i	−0.186959	−	0.107941i	0.403599	−	0.914936i	$-0.367759\pi$
$919$	−5.66767	−	3.27223i	−0.186959	−	0.107941i	−0.590558	+	0.806995i	$0.701092\pi$
$920$	1.49753	+	5.06037i	0.0493721	+	0.166835i
$921$	−10.3669	+	5.98535i	−0.341602	+	0.197224i
$922$	−1.98093	+	25.1424i	−0.0652383	+	0.828022i
$923$	−6.84927	+	6.84927i	−0.225447	+	0.225447i
$924$	−1.08810	−	0.542540i	−0.0357958	−	0.0178482i
$925$	−18.6703	−	18.6703i	−0.613876	−	0.613876i
$926$	−32.6628	−	38.2499i	−1.07337	−	1.25697i
$927$	−1.51126	−	2.61757i	−0.0496361	−	0.0859723i
$928$	13.7977	−	33.2702i	0.452933	−	1.09215i
$929$	−23.2456	+	40.2625i	−0.762663	+	1.32097i	0.178810	+	0.983884i	$0.442775\pi$
$929$	−23.2456	+	40.2625i	−0.762663	+	1.32097i	−0.941473	+	0.337087i	$0.890558\pi$
$930$	1.47300	−	4.15849i	0.0483016	−	0.136362i
$931$	8.65253	−	7.26466i	0.283575	−	0.238090i
$932$	4.87364	−	6.01633i	0.159641	−	0.197071i
$933$	5.69951	+	21.2709i	0.186594	+	0.696377i
$934$	−44.0025	−	30.2476i	−1.43980	−	0.989732i
$935$	0.414698	−	0.239426i	0.0135621	−	0.00783007i
$936$	5.42113	+	5.14712i	0.177195	+	0.168239i
$937$			43.7864i			1.43044i	0.698900	+	0.715219i	$0.253673\pi$
$937$			43.7864i			1.43044i	−0.698900	+	0.715219i	$0.746327\pi$
$938$	−43.4636	+	33.9617i	−1.41914	+	1.10889i
$939$	11.9232	−	11.9232i	0.389099	−	0.389099i
$940$	3.43876	−	7.72000i	0.112160	−	0.251799i
$941$	−4.88490	+	18.2307i	−0.159243	+	0.594303i	0.839461	+	0.543419i	$0.182871\pi$
$941$	−4.88490	+	18.2307i	−0.159243	+	0.594303i	−0.998705	+	0.0508841i	$0.983796\pi$
$942$	1.11670	+	6.02805i	0.0363840	+	0.196404i
$943$	10.1661	−	17.6082i	0.331054	−	0.573403i
$944$	−24.3485	−	15.8240i	−0.792475	−	0.515026i
$945$	−1.53843	−	0.484816i	−0.0500450	−	0.0157711i
$946$	−0.550573	−	0.195022i	−0.0179007	−	0.00634070i
$947$	1.14649	−	0.307202i	0.0372561	−	0.00998273i	−0.240143	−	0.970738i	$-0.577194\pi$
$947$	1.14649	−	0.307202i	0.0372561	−	0.00998273i	0.277399	+	0.960755i	$0.410528\pi$
$948$	15.5535	−	11.2962i	0.505154	−	0.366884i
$949$	33.1304	+	8.87727i	1.07546	+	0.288168i
$950$	10.5315	+	0.829761i	0.341688	+	0.0269210i
$951$		−	4.31337i		−	0.139870i
$952$	24.5885	+	7.05361i	0.796919	+	0.228609i
$953$		−	56.0870i		−	1.81684i	−0.418063	−	0.908418i	$-0.637291\pi$
$953$		−	56.0870i		−	1.81684i	0.418063	−	0.908418i	$-0.362709\pi$
$954$	−0.376096	+	4.77350i	−0.0121765	+	0.154548i
$955$	1.46231	+	0.391824i	0.0473192	+	0.0126791i
$956$	−5.40919	+	34.1144i	−0.174946	+	1.10334i
$957$	1.41315	−	0.378653i	0.0456808	−	0.0122401i
$958$	18.9400	−	53.4704i	0.611924	−	1.72755i
$959$	12.5136	−	11.4700i	0.404086	−	0.370386i
$960$	−2.21648	+	4.34455i	−0.0715366	+	0.140220i
$961$	2.40910	−	4.17268i	0.0777128	−	0.134602i
$962$	20.9662	−	3.88400i	0.675979	−	0.125225i
$963$	1.72849	−	6.45081i	0.0556998	−	0.207874i
$964$	−36.8734	+	14.1471i	−1.18761	+	0.455647i
$965$	−0.549542	+	0.549542i	−0.0176904	+	0.0176904i
$966$	−11.3395	+	1.59436i	−0.364841	+	0.0512976i
$967$		−	25.1251i		−	0.807970i	−0.914766	−	0.403985i	$-0.867625\pi$
$967$		−	25.1251i		−	0.807970i	0.914766	−	0.403985i	$-0.132375\pi$
$968$	30.9530	−	0.802545i	0.994866	−	0.0257948i
$969$	−4.77792	+	2.75854i	−0.153489	+	0.0886169i
$970$	5.72431	−	8.32739i	0.183797	−	0.267377i
$971$	−15.6063	−	58.2436i	−0.500831	−	1.86913i	−0.494555	−	0.869147i	$-0.664669\pi$
$971$	−15.6063	−	58.2436i	−0.500831	−	1.86913i	−0.00627639	−	0.999980i	$-0.501998\pi$
$972$	−0.208715	−	1.98908i	−0.00669454	−	0.0637998i
$973$	−2.94491	+	4.62408i	−0.0944095	+	0.148241i
$974$	−10.8422	−	3.84047i	−0.347406	−	0.123057i
$975$	−6.11620	+	10.5936i	−0.195875	+	0.339266i
$976$	−29.8572	−	1.57504i	−0.955705	−	0.0504159i
$977$	−12.3663	−	21.4191i	−0.395634	−	0.685258i	0.597548	−	0.801833i	$-0.296142\pi$
$977$	−12.3663	−	21.4191i	−0.395634	−	0.685258i	−0.993182	+	0.116575i	$0.962808\pi$
$978$	−20.1973	+	17.2471i	−0.645838	+	0.551502i
$979$	−2.05962	−	2.05962i	−0.0658259	−	0.0658259i
$980$	−7.31560	+	4.39686i	−0.233688	+	0.140453i
$981$	−10.4052	+	10.4052i	−0.332212	+	0.332212i
$982$	5.59776	+	0.441037i	0.178632	+	0.0140741i
$983$	−52.9362	+	30.5627i	−1.68840	+	0.974800i	−0.732662	+	0.680593i	$0.761722\pi$
$983$	−52.9362	+	30.5627i	−1.68840	+	0.974800i	−0.955742	+	0.294207i	$0.904944\pi$
$984$	18.0186	−	5.33230i	0.574412	−	0.169988i
$985$	−12.7349	−	7.35249i	−0.405767	−	0.234270i
$986$	−27.7827	+	13.2487i	−0.884781	+	0.421926i
$987$	15.4675	+	9.85072i	0.492337	+	0.313552i
$988$	−5.37008	+	6.62917i	−0.170845	+	0.210902i
$989$	−5.31358	+	1.42377i	−0.168962	+	0.0452732i
$990$	−0.194795	+	0.0360859i	−0.00619101	+	0.00114688i
$991$	−19.4798	−	33.7401i	−0.618798	−	1.07179i	−0.989705	−	0.143119i	$-0.954287\pi$
$991$	−19.4798	−	33.7401i	−0.618798	−	1.07179i	0.370908	−	0.928670i	$-0.379047\pi$
$992$	17.6305	−	22.9561i	0.559770	−	0.728857i
$993$	18.6849			0.592947
$994$	8.25207	−	10.9522i	0.261740	−	0.347384i
$995$	6.28760	+	6.28760i	0.199330	+	0.199330i
$996$	8.26507	+	21.5423i	0.261889	+	0.682595i
$997$	−5.47543	−	1.46714i	−0.173409	−	0.0464647i	0.171070	−	0.985259i	$-0.445278\pi$
$997$	−5.47543	−	1.46714i	−0.173409	−	0.0464647i	−0.344478	+	0.938794i	$0.611944\pi$
$998$	−21.5430	−	14.8088i	−0.681931	−	0.468765i
$999$	−4.94054	−	2.85242i	−0.156312	−	0.0902466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.205.22	yes	120
7.4	even	3	inner	336.2.bq.b.109.1	yes	120
16.5	even	4	inner	336.2.bq.b.37.1	✓	120
112.53	even	12	inner	336.2.bq.b.277.22	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.1	✓	120	16.5	even	4	inner
336.2.bq.b.109.1	yes	120	7.4	even	3	inner
336.2.bq.b.205.22	yes	120	1.1	even	1	trivial
336.2.bq.b.277.22	yes	120	112.53	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.918366 + 1.07546i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.313209 + 1.97532i) q^{4} +(0.157792 + 0.588887i) q^{5} +(-1.27650 + 0.608725i) q^{6} +(-2.58295 + 0.573024i) q^{7} +(-2.41201 + 1.47723i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.918366 + 1.07546i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.313209 + 1.97532i) q^{4} +(0.157792 + 0.588887i) q^{5} +(-1.27650 + 0.608725i) q^{6} +(-2.58295 + 0.573024i) q^{7} +(-2.41201 + 1.47723i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.488411 + 0.710511i) q^{10} +(-0.221946 - 0.0594702i) q^{11} +(-1.82695 - 0.813787i) q^{12} +(1.86885 + 1.86885i) q^{13} +(-2.98836 - 2.25160i) q^{14} -0.609660 q^{15} +(-3.80380 - 1.23738i) q^{16} +(1.70915 + 2.96034i) q^{17} +(-0.257600 - 1.39055i) q^{18} +(1.55898 - 0.417729i) q^{19} +(-1.21266 + 0.127245i) q^{20} +(0.115019 - 2.64325i) q^{21} +(-0.139870 - 0.293308i) q^{22} +(-2.65039 - 1.53020i) q^{23} +(-0.802617 - 2.71216i) q^{24} +(4.00824 - 2.31416i) q^{25} +(-0.293576 + 3.72615i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.322904 - 5.28164i) q^{28} +(4.50223 + 4.50223i) q^{29} +(-0.559891 - 0.655662i) q^{30} +(2.55841 + 4.43129i) q^{31} +(-2.16254 - 5.22718i) q^{32} +(0.114888 - 0.198991i) q^{33} +(-1.61408 + 4.55679i) q^{34} +(-0.745014 - 1.43065i) q^{35} +(1.25891 - 1.55408i) q^{36} +(-1.47652 - 5.51046i) q^{37} +(1.88097 + 1.29299i) q^{38} +(-2.28886 + 1.32147i) q^{39} +(-1.25051 - 1.18731i) q^{40} +6.64364i q^{41} +(2.94833 - 2.30377i) q^{42} +(1.27101 - 1.27101i) q^{43} +(0.186988 - 0.419788i) q^{44} +(0.157792 - 0.588887i) q^{45} +(-0.788362 - 4.25566i) q^{46} +(-3.46555 + 6.00251i) q^{47} +(2.17971 - 3.35393i) q^{48} +(6.34329 - 2.96019i) q^{49} +(6.16980 + 2.18544i) q^{50} +(-3.30183 + 0.884722i) q^{51} +(-4.27692 + 3.10624i) q^{52} +(-3.27047 - 0.876319i) q^{53} +(1.40984 + 0.111079i) q^{54} -0.140085i q^{55} +(5.38362 - 5.19775i) q^{56} +1.61398i q^{57} +(-0.707253 + 8.97664i) q^{58} +(7.01230 + 1.87894i) q^{59} +(0.190951 - 1.20428i) q^{60} +(7.21998 - 1.93459i) q^{61} +(-2.41610 + 6.82100i) q^{62} +(2.52341 + 0.795223i) q^{63} +(3.63560 - 7.12618i) q^{64} +(-0.805651 + 1.39543i) q^{65} +(0.319515 - 0.0591902i) q^{66} +(3.81546 - 14.2395i) q^{67} +(-6.38294 + 2.44892i) q^{68} +(2.16403 - 2.16403i) q^{69} +(0.854402 - 2.11509i) q^{70} +3.66497i q^{71} +(2.82748 - 0.0733105i) q^{72} +(11.2389 - 6.48880i) q^{73} +(4.57026 - 6.64855i) q^{74} +(1.19790 + 4.47061i) q^{75} +(0.336862 + 3.21033i) q^{76} +(0.607353 + 0.0264285i) q^{77} +(-3.52320 - 1.24797i) q^{78} +(-4.80570 + 8.32371i) q^{79} +(0.128466 - 2.43525i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-7.14494 + 6.10129i) q^{82} +(-8.15769 - 8.15769i) q^{83} +(5.18525 + 1.05509i) q^{84} +(-1.47361 + 1.47361i) q^{85} +(2.53417 + 0.199662i) q^{86} +(-5.51408 + 3.18356i) q^{87} +(0.623186 - 0.184421i) q^{88} +(10.9782 + 6.33826i) q^{89} +(0.778232 - 0.371115i) q^{90} +(-5.89804 - 3.75625i) q^{91} +(3.85277 - 4.75610i) q^{92} +(-4.94247 + 1.32433i) q^{93} +(-9.63808 + 1.78546i) q^{94} +(0.491990 + 0.852151i) q^{95} +(5.60878 - 0.735957i) q^{96} -11.7203 q^{97} +(9.00901 + 4.10339i) q^{98} +(0.162476 + 0.162476i) 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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