LMFDB - Embedded newform 336.2.bq.b.109.10

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			109.10
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.948203 + 1.04924i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.201821 - 1.98979i) q^{4} +(-2.71136 - 0.726506i) q^{5} +(0.644330 - 1.25890i) q^{6} +(-0.393486 - 2.61633i) q^{7} +(2.27914 + 1.67497i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.948203 + 1.04924i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.201821 - 1.98979i) q^{4} +(-2.71136 - 0.726506i) q^{5} +(0.644330 - 1.25890i) q^{6} +(-0.393486 - 2.61633i) q^{7} +(2.27914 + 1.67497i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.33320 - 2.15600i) q^{10} +(1.04416 + 3.89684i) q^{11} +(0.709940 + 1.86976i) q^{12} +(4.21026 + 4.21026i) q^{13} +(3.11827 + 2.06795i) q^{14} +2.80700 q^{15} +(-3.91854 + 0.803162i) q^{16} +(-2.10450 + 3.64510i) q^{17} +(-0.296547 + 1.38277i) q^{18} +(-0.0315900 + 0.117895i) q^{19} +(-0.898387 + 5.54166i) q^{20} +(1.05723 + 2.42534i) q^{21} +(-5.07881 - 2.59943i) q^{22} +(6.12209 - 3.53459i) q^{23} +(-2.63499 - 1.02801i) q^{24} +(2.49352 + 1.43963i) q^{25} +(-8.40977 + 0.425402i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-5.12653 + 1.31098i) q^{28} +(0.932475 + 0.932475i) q^{29} +(-2.66161 + 2.94523i) q^{30} +(0.233565 - 0.404546i) q^{31} +(2.87286 - 4.87306i) q^{32} +(-2.01716 - 3.49382i) q^{33} +(-1.82910 - 5.66442i) q^{34} +(-0.833897 + 7.37967i) q^{35} +(-1.16968 - 1.62230i) q^{36} +(10.5017 + 2.81392i) q^{37} +(-0.0937472 - 0.144934i) q^{38} +(-5.15649 - 2.97710i) q^{39} +(-4.96269 - 6.19724i) q^{40} +7.38316i q^{41} +(-3.54724 - 1.19042i) q^{42} +(-0.452297 + 0.452297i) q^{43} +(7.54317 - 2.86412i) q^{44} +(-2.71136 + 0.726506i) q^{45} +(-2.09634 + 9.77507i) q^{46} +(-0.826133 - 1.43090i) q^{47} +(3.57714 - 1.78999i) q^{48} +(-6.69034 + 2.05897i) q^{49} +(-3.87489 + 1.25124i) q^{50} +(1.08937 - 4.06558i) q^{51} +(7.52782 - 9.22725i) q^{52} +(2.86203 + 10.6812i) q^{53} +(-0.0714456 - 1.41241i) q^{54} -11.3243i q^{55} +(3.48545 - 6.62205i) q^{56} -0.122054i q^{57} +(-1.86257 + 0.0942167i) q^{58} +(-0.903261 - 3.37102i) q^{59} +(-0.566511 - 5.58535i) q^{60} +(-1.62128 + 6.05071i) q^{61} +(0.203000 + 0.628658i) q^{62} +(-1.64893 - 2.06906i) q^{63} +(2.38897 + 7.63497i) q^{64} +(-8.35674 - 14.4743i) q^{65} +(5.57853 + 1.19636i) q^{66} +(6.79088 - 1.81961i) q^{67} +(7.67771 + 3.45185i) q^{68} +(-4.99866 + 4.99866i) q^{69} +(-6.95236 - 7.87239i) q^{70} -0.947244i q^{71} +(2.81128 + 0.310994i) q^{72} +(8.20143 + 4.73510i) q^{73} +(-12.9102 + 8.35067i) q^{74} +(-2.78116 - 0.745209i) q^{75} +(0.240963 + 0.0390637i) q^{76} +(9.78456 - 4.26521i) q^{77} +(8.01311 - 2.58751i) q^{78} +(-1.03748 - 1.79696i) q^{79} +(11.2081 + 0.669181i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-7.74673 - 7.00074i) q^{82} +(-3.86567 - 3.86567i) q^{83} +(4.61254 - 2.59316i) q^{84} +(8.35422 - 8.35422i) q^{85} +(-0.0456998 - 0.903438i) q^{86} +(-1.14204 - 0.659359i) q^{87} +(-4.14731 + 10.6304i) q^{88} +(3.38120 - 1.95213i) q^{89} +(1.80864 - 3.53375i) q^{90} +(9.35874 - 12.6721i) q^{91} +(-8.26866 - 11.4683i) q^{92} +(-0.120902 + 0.451212i) q^{93} +(2.28471 + 0.489974i) q^{94} +(0.171303 - 0.296706i) q^{95} +(-1.51373 + 5.45056i) q^{96} -4.22876 q^{97} +(4.18344 - 8.97212i) q^{98} +(2.85269 + 2.85269i) 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 $

$2$	−0.948203	+	1.04924i	−0.670481	+	0.741927i
$2$	−0.948203	+	1.04924i	−0.670481	+	0.741927i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.201821	−	1.98979i	−0.100910	−	0.994896i
$5$	−2.71136	−	0.726506i	−1.21256	−	0.324903i	−0.404791	−	0.914409i	$-0.632656\pi$
$5$	−2.71136	−	0.726506i	−1.21256	−	0.324903i	−0.807764	+	0.589506i	$0.799323\pi$
$6$	0.644330	−	1.25890i	0.263047	−	0.513945i
$7$	−0.393486	−	2.61633i	−0.148724	−	0.988879i
$7$	−0.393486	−	2.61633i	−0.148724	−	0.988879i
$8$	2.27914	+	1.67497i	0.805798	+	0.592191i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	3.33320	−	2.15600i	1.05405	−	0.681786i
$11$	1.04416	+	3.89684i	0.314825	+	1.17494i	0.924152	+	0.382024i	$0.124773\pi$
$11$	1.04416	+	3.89684i	0.314825	+	1.17494i	−0.609327	+	0.792919i	$0.708560\pi$
$12$	0.709940	+	1.86976i	0.204942	+	0.539752i
$13$	4.21026	+	4.21026i	1.16772	+	1.16772i	0.982744	+	0.184972i	$0.0592195\pi$
$13$	4.21026	+	4.21026i	1.16772	+	1.16772i	0.184972	+	0.982744i	$0.440781\pi$
$14$	3.11827	+	2.06795i	0.833392	+	0.552682i
$15$	2.80700			0.724765
$16$	−3.91854	+	0.803162i	−0.979634	+	0.200790i
$17$	−2.10450	+	3.64510i	−0.510415	+	0.884065i	0.489512	+	0.871997i	$0.337175\pi$
$17$	−2.10450	+	3.64510i	−0.510415	+	0.884065i	−0.999927	+	0.0120687i	$0.996158\pi$
$18$	−0.296547	+	1.38277i	−0.0698968	+	0.325923i
$19$	−0.0315900	+	0.117895i	−0.00724724	+	0.0270471i	−0.969455	−	0.245270i	$-0.921123\pi$
$19$	−0.0315900	+	0.117895i	−0.00724724	+	0.0270471i	0.962208	+	0.272317i	$0.0877900\pi$
$20$	−0.898387	+	5.54166i	−0.200885	+	1.23915i
$21$	1.05723	+	2.42534i	0.230707	+	0.529252i
$22$	−5.07881	−	2.59943i	−1.08281	−	0.554200i
$23$	6.12209	−	3.53459i	1.27654	−	0.737013i	0.300332	−	0.953835i	$-0.402902\pi$
$23$	6.12209	−	3.53459i	1.27654	−	0.737013i	0.976211	+	0.216822i	$0.0695691\pi$
$24$	−2.63499	−	1.02801i	−0.537866	−	0.209842i
$25$	2.49352	+	1.43963i	0.498703	+	0.287927i
$26$	−8.40977	+	0.425402i	−1.64929	+	0.0834282i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−5.12653	+	1.31098i	−0.968823	+	0.247753i
$29$	0.932475	+	0.932475i	0.173156	+	0.173156i	0.788365	−	0.615208i	$-0.210928\pi$
$29$	0.932475	+	0.932475i	0.173156	+	0.173156i	−0.615208	+	0.788365i	$0.710928\pi$
$30$	−2.66161	+	2.94523i	−0.485941	+	0.537723i
$31$	0.233565	−	0.404546i	0.0419495	−	0.0726586i	−0.844288	−	0.535889i	$-0.819976\pi$
$31$	0.233565	−	0.404546i	0.0419495	−	0.0726586i	0.886238	+	0.463231i	$0.153310\pi$
$32$	2.87286	−	4.87306i	0.507854	−	0.861443i
$33$	−2.01716	−	3.49382i	−0.351142	−	0.608195i
$34$	−1.82910	−	5.66442i	−0.313688	−	0.971440i
$35$	−0.833897	+	7.37967i	−0.140954	+	1.24739i
$36$	−1.16968	−	1.62230i	−0.194946	−	0.270383i
$37$	10.5017	+	2.81392i	1.72647	+	0.462606i	0.979365	−	0.202100i	$-0.0647765\pi$
$37$	10.5017	+	2.81392i	1.72647	+	0.462606i	0.747105	+	0.664706i	$0.231443\pi$
$38$	−0.0937472	−	0.144934i	−0.0152078	−	0.0235115i
$39$	−5.15649	−	2.97710i	−0.825700	−	0.476718i
$40$	−4.96269	−	6.19724i	−0.784670	−	0.979870i
$41$			7.38316i			1.15306i	0.817077	+	0.576528i	$0.195593\pi$
$41$			7.38316i			1.15306i	−0.817077	+	0.576528i	$0.804407\pi$
$42$	−3.54724	−	1.19042i	−0.547351	−	0.183685i
$43$	−0.452297	+	0.452297i	−0.0689746	+	0.0689746i	−0.740753	−	0.671778i	$-0.765531\pi$
$43$	−0.452297	+	0.452297i	−0.0689746	+	0.0689746i	0.671778	+	0.740753i	$0.265531\pi$
$44$	7.54317	−	2.86412i	1.13718	−	0.431782i
$45$	−2.71136	+	0.726506i	−0.404185	+	0.108301i
$46$	−2.09634	+	9.77507i	−0.309089	+	1.44125i
$47$	−0.826133	−	1.43090i	−0.120504	−	0.208719i	0.799463	−	0.600716i	$-0.205118\pi$
$47$	−0.826133	−	1.43090i	−0.120504	−	0.208719i	−0.919966	+	0.391997i	$0.871784\pi$
$48$	3.57714	−	1.78999i	0.516316	−	0.258362i
$49$	−6.69034	+	2.05897i	−0.955763	+	0.294139i
$50$	−3.87489	+	1.25124i	−0.547992	+	0.176952i
$51$	1.08937	−	4.06558i	0.152542	−	0.569294i
$52$	7.52782	−	9.22725i	1.04392	−	1.27959i
$53$	2.86203	+	10.6812i	0.393130	+	1.46718i	0.824942	+	0.565218i	$0.191208\pi$
$53$	2.86203	+	10.6812i	0.393130	+	1.46718i	−0.431812	+	0.901964i	$0.642126\pi$
$54$	−0.0714456	−	1.41241i	−0.00972252	−	0.192204i
$55$		−	11.3243i		−	1.52697i
$56$	3.48545	−	6.62205i	0.465763	−	0.884909i
$57$		−	0.122054i		−	0.0161665i
$58$	−1.86257	+	0.0942167i	−0.244567	+	0.0123713i
$59$	−0.903261	−	3.37102i	−0.117595	−	0.438869i	0.881873	−	0.471486i	$-0.156282\pi$
$59$	−0.903261	−	3.37102i	−0.117595	−	0.438869i	−0.999468	+	0.0326175i	$0.989616\pi$
$60$	−0.566511	−	5.58535i	−0.0731363	−	0.721066i
$61$	−1.62128	+	6.05071i	−0.207584	+	0.774714i	0.781062	+	0.624453i	$0.214678\pi$
$61$	−1.62128	+	6.05071i	−0.207584	+	0.774714i	−0.988646	+	0.150261i	$0.951989\pi$
$62$	0.203000	+	0.628658i	0.0257810	+	0.0798396i
$63$	−1.64893	−	2.06906i	−0.207746	−	0.260677i
$64$	2.38897	+	7.63497i	0.298621	+	0.954372i
$65$	−8.35674	−	14.4743i	−1.03653	−	1.79532i
$66$	5.57853	+	1.19636i	0.686670	+	0.147262i
$67$	6.79088	−	1.81961i	0.829639	−	0.222301i	0.181083	−	0.983468i	$-0.442040\pi$
$67$	6.79088	−	1.81961i	0.829639	−	0.222301i	0.648556	+	0.761167i	$0.275373\pi$
$68$	7.67771	+	3.45185i	0.931059	+	0.418599i
$69$	−4.99866	+	4.99866i	−0.601768	+	0.601768i
$70$	−6.95236	−	7.87239i	−0.830966	−	0.940930i
$71$		−	0.947244i		−	0.112417i	−0.998419	−	0.0562086i	$-0.982099\pi$
$71$		−	0.947244i		−	0.112417i	0.998419	−	0.0562086i	$-0.0179012\pi$
$72$	2.81128	+	0.310994i	0.331312	+	0.0366510i
$73$	8.20143	+	4.73510i	0.959905	+	0.554201i	0.896144	−	0.443764i	$-0.146357\pi$
$73$	8.20143	+	4.73510i	0.959905	+	0.554201i	0.0637610	+	0.997965i	$0.479690\pi$
$74$	−12.9102	+	8.35067i	−1.50079	+	0.970745i
$75$	−2.78116	−	0.745209i	−0.321140	−	0.0860493i
$76$	0.240963	+	0.0390637i	0.0276403	+	0.00448092i
$77$	9.78456	−	4.26521i	1.11505	−	0.486065i
$78$	8.01311	−	2.58751i	0.907306	−	0.292978i
$79$	−1.03748	−	1.79696i	−0.116725	−	0.202174i	0.801743	−	0.597669i	$-0.203906\pi$
$79$	−1.03748	−	1.79696i	−0.116725	−	0.202174i	−0.918468	+	0.395495i	$0.870573\pi$
$80$	11.2081	+	0.669181i	1.25310	+	0.0748167i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−7.74673	−	7.00074i	−0.855483	−	0.773103i
$83$	−3.86567	−	3.86567i	−0.424313	−	0.424313i	0.462373	−	0.886686i	$-0.346998\pi$
$83$	−3.86567	−	3.86567i	−0.424313	−	0.424313i	−0.886686	+	0.462373i	$0.846998\pi$
$84$	4.61254	−	2.59316i	0.503270	−	0.282937i
$85$	8.35422	−	8.35422i	0.906143	−	0.906143i
$86$	−0.0456998	−	0.903438i	−0.00492793	−	0.0974202i
$87$	−1.14204	−	0.659359i	−0.122440	−	0.0706908i
$88$	−4.14731	+	10.6304i	−0.442105	+	1.13320i
$89$	3.38120	−	1.95213i	0.358406	−	0.206926i	−0.309975	−	0.950745i	$-0.600321\pi$
$89$	3.38120	−	1.95213i	0.358406	−	0.206926i	0.668381	+	0.743819i	$0.266987\pi$
$90$	1.80864	−	3.53375i	0.190647	−	0.372490i
$91$	9.35874	−	12.6721i	0.981063	−	1.32840i
$92$	−8.26866	−	11.4683i	−0.862067	−	1.19566i
$93$	−0.120902	+	0.451212i	−0.0125370	+	0.0467885i
$94$	2.28471	+	0.489974i	0.235650	+	0.0505370i
$95$	0.171303	−	0.296706i	0.0175754	−	0.0304414i
$96$	−1.51373	+	5.45056i	−0.154494	+	0.556296i
$97$	−4.22876			−0.429365			−0.214683	−	0.976684i	$-0.568872\pi$
$97$	−4.22876			−0.429365			−0.214683	+	0.976684i	$0.568872\pi$
$98$	4.18344	−	8.97212i	0.422591	−	0.906321i
$99$	2.85269	+	2.85269i	0.286706	+	0.286706i
$100$	2.36133	−	5.25213i	0.236133	−	0.525213i
$101$	−4.20901	−	15.7082i	−0.418812	−	1.56303i	−0.777075	−	0.629408i	$-0.783298\pi$
$101$	−4.20901	−	15.7082i	−0.418812	−	1.56303i	0.358263	−	0.933621i	$-0.383369\pi$
$102$	3.23283	+	4.99800i	0.320098	+	0.494876i
$103$	−7.00686	+	4.04541i	−0.690406	+	0.398606i	−0.803764	−	0.594948i	$-0.797173\pi$
$103$	−7.00686	+	4.04541i	−0.690406	+	0.398606i	0.113358	+	0.993554i	$0.463839\pi$
$104$	2.54373	+	16.6478i	0.249433	+	1.63245i
$105$	−1.10452	−	7.34404i	−0.107790	−	0.716705i
$106$	−13.9210	−	7.12502i	−1.35213	−	0.692044i
$107$	−7.72337	−	2.06947i	−0.746646	−	0.200063i	−0.134616	−	0.990898i	$-0.542980\pi$
$107$	−7.72337	−	2.06947i	−0.746646	−	0.200063i	−0.612030	+	0.790835i	$0.709647\pi$
$108$	1.54970	+	1.26429i	0.149120	+	0.121656i
$109$	−19.0587	+	5.10676i	−1.82549	+	0.489139i	−0.997440	−	0.0715115i	$-0.977218\pi$
$109$	−19.0587	+	5.10676i	−1.82549	+	0.489139i	−0.828052	+	0.560651i	$0.810551\pi$
$110$	11.8820	+	10.7378i	1.13290	+	1.02381i
$111$	−10.8722			−1.03194
$112$	3.64322	+	9.93614i	0.344252	+	0.938877i
$113$	10.5590			0.993311			0.496655	−	0.867948i	$-0.334561\pi$
$113$	10.5590			0.993311			0.496655	+	0.867948i	$0.334561\pi$
$114$	0.128065	+	0.115732i	0.0119943	+	0.0108393i
$115$	−19.1671	+	5.13580i	−1.78734	+	0.478916i
$116$	1.66724	−	2.04362i	0.154799	−	0.189746i
$117$	5.75132	+	1.54106i	0.531710	+	0.142471i
$118$	4.39349	+	2.24867i	0.404453	+	0.207007i
$119$	10.3649	+	4.07176i	0.950144	+	0.373258i
$120$	6.39756	+	4.70164i	0.584014	+	0.429199i
$121$	−4.56885	+	2.63783i	−0.415350	+	0.239803i
$122$	−4.81136	−	7.43843i	−0.435600	−	0.673444i
$123$	−1.91090	−	7.13159i	−0.172300	−	0.643034i
$124$	−0.852100	−	0.383099i	−0.0765209	−	0.0344033i
$125$	4.20934	+	4.20934i	0.376495	+	0.376495i
$126$	3.73447	+	0.231762i	0.332693	+	0.0206470i
$127$	21.8647			1.94018			0.970088	−	0.242755i	$-0.0780511\pi$
$127$	21.8647			1.94018			0.970088	+	0.242755i	$0.0780511\pi$
$128$	−10.2762	−	4.73290i	−0.908293	−	0.418334i
$129$	0.319822	−	0.553948i	0.0281588	−	0.0487724i
$130$	23.1109	+	4.95633i	2.02696	+	0.434699i
$131$	−3.31427	+	12.3690i	−0.289569	+	1.08069i	0.655866	+	0.754877i	$0.272304\pi$
$131$	−3.31427	+	12.3690i	−0.289569	+	1.08069i	−0.945435	+	0.325810i	$0.894363\pi$
$132$	−6.54486	+	4.71884i	−0.569657	+	0.410722i
$133$	0.320883	+	0.0362596i	0.0278241	+	0.00314410i
$134$	−4.52993	+	8.85065i	−0.391326	+	0.764580i
$135$	2.43094	−	1.40350i	0.209222	−	0.120794i
$136$	−10.9019	+	4.78272i	−0.934827	+	0.410115i
$137$	−5.82192	−	3.36129i	−0.497400	−	0.287174i	0.230239	−	0.973134i	$-0.426049\pi$
$137$	−5.82192	−	3.36129i	−0.497400	−	0.287174i	−0.727639	+	0.685960i	$0.759383\pi$
$138$	−0.505062	−	9.98456i	−0.0429937	−	0.849942i
$139$	−9.82296	+	9.82296i	−0.833173	+	0.833173i	−0.987950	−	0.154777i	$-0.950534\pi$
$139$	−9.82296	+	9.82296i	−0.833173	+	0.833173i	0.154777	+	0.987950i	$0.450534\pi$
$140$	14.8523	+	0.169912i	1.25525	+	0.0143602i
$141$	1.16833	+	1.16833i	0.0983910	+	0.0983910i
$142$	0.993889	+	0.898180i	0.0834053	+	0.0753736i
$143$	−12.0106	+	20.8029i	−1.00437	+	1.73963i
$144$	−2.99197	+	2.65483i	−0.249331	+	0.221236i
$145$	−1.85082	−	3.20572i	−0.153703	−	0.266221i
$146$	−12.7449	+	4.11545i	−1.05477	+	0.340597i
$147$	5.92947	−	3.72040i	0.489054	−	0.306854i
$148$	3.47966	−	21.4641i	0.286026	−	1.76434i
$149$	−18.3547	−	4.91813i	−1.50368	−	0.402909i	−0.589347	−	0.807880i	$-0.700615\pi$
$149$	−18.3547	−	4.91813i	−1.50368	−	0.402909i	−0.914329	+	0.404971i	$0.867282\pi$
$150$	3.41901	−	2.21150i	0.279161	−	0.180568i
$151$	7.61103	+	4.39423i	0.619377	+	0.357598i	0.776626	−	0.629961i	$-0.216929\pi$
$151$	7.61103	+	4.39423i	0.619377	+	0.357598i	−0.157249	+	0.987559i	$0.550263\pi$
$152$	−0.269469	+	0.215788i	−0.0218568	+	0.0175027i
$153$			4.20899i			0.340277i
$154$	−4.80252	+	14.3107i	−0.386998	+	1.15319i
$155$	−0.927182	+	0.927182i	−0.0744731	+	0.0744731i
$156$	−4.88313	+	10.8612i	−0.390963	+	0.869591i
$157$	8.61027	−	2.30711i	0.687174	−	0.184128i	0.101696	−	0.994816i	$-0.467573\pi$
$157$	8.61027	−	2.30711i	0.687174	−	0.184128i	0.585479	+	0.810688i	$0.300907\pi$
$158$	2.86919	+	0.615321i	0.228261	+	0.0489523i
$159$	−5.52902	−	9.57654i	−0.438480	−	0.759469i
$160$	−11.3296	+	11.1254i	−0.895687	+	0.879544i
$161$	−11.6566	−	14.6266i	−0.918668	−	1.15274i
$162$	0.434569	+	1.34579i	0.0341430	+	0.105735i
$163$	−5.26097	+	19.6342i	−0.412071	+	1.53787i	0.378559	+	0.925577i	$0.376420\pi$
$163$	−5.26097	+	19.6342i	−0.412071	+	1.53787i	−0.790630	+	0.612294i	$0.790247\pi$
$164$	14.6910	−	1.49008i	1.14717	−	0.116355i
$165$	2.93095	+	10.9385i	0.228174	+	0.851557i
$166$	7.72147	−	0.390585i	0.599303	−	0.0303153i
$167$		−	23.2981i		−	1.80286i	−0.432920	−	0.901432i	$-0.642517\pi$
$167$		−	23.2981i		−	1.80286i	0.432920	−	0.901432i	$-0.357483\pi$
$168$	−1.65278	+	7.29852i	−0.127515	+	0.563093i
$169$			22.4526i			1.72712i
$170$	0.844105	+	16.6871i	0.0647399	+	1.27984i
$171$	0.0315900	+	0.117895i	0.00241575	+	0.00901569i
$172$	0.991259	+	0.808693i	0.0755828	+	0.0616623i
$173$	−1.44525	+	5.39375i	−0.109880	+	0.410079i	−0.998853	−	0.0478810i	$-0.984753\pi$
$173$	−1.44525	+	5.39375i	−0.109880	+	0.410079i	0.888973	+	0.457960i	$0.151420\pi$
$174$	1.77472	−	0.573075i	0.134541	−	0.0434447i
$175$	2.78539	−	7.09033i	0.210556	−	0.535979i
$176$	−7.22136	−	14.4313i	−0.544331	−	1.08780i
$177$	1.74497	+	3.02237i	0.131160	+	0.227175i
$178$	−1.15780	+	5.39872i	−0.0867807	+	0.404651i
$179$	9.14675	−	2.45086i	0.683660	−	0.183186i	0.0997600	−	0.995012i	$-0.468193\pi$
$179$	9.14675	−	2.45086i	0.683660	−	0.183186i	0.583900	+	0.811825i	$0.301526\pi$
$180$	1.99280	+	5.24841i	0.148535	+	0.391193i
$181$	10.6838	−	10.6838i	0.794123	−	0.794123i	−0.188038	−	0.982162i	$-0.560213\pi$
$181$	10.6838	−	10.6838i	0.794123	−	0.794123i	0.982162	+	0.188038i	$0.0602129\pi$
$182$	4.42211	+	21.8353i	0.327789	+	1.61854i
$183$		−	6.26416i		−	0.463060i
$184$	19.8734	+	2.19847i	1.46509	+	0.162074i
$185$	−26.4295	−	15.2591i	−1.94314	−	1.12187i
$186$	−0.358792	−	0.554697i	−0.0263079	−	0.0406723i
$187$	−16.4018	−	4.39485i	−1.19942	−	0.321383i
$188$	−2.68047	+	1.93262i	−0.195493	+	0.140951i
$189$	2.12826	+	1.57179i	0.154808	+	0.114331i
$190$	0.148886	+	0.461077i	0.0108013	+	0.0334500i
$191$	1.80409	+	3.12478i	0.130540	+	0.226101i	0.923885	−	0.382671i	$-0.124996\pi$
$191$	1.80409	+	3.12478i	0.130540	+	0.226101i	−0.793345	+	0.608772i	$0.791662\pi$
$192$	−4.28364	−	6.75651i	−0.309145	−	0.487609i
$193$	−2.55513	+	4.42561i	−0.183922	+	0.318562i	−0.943213	−	0.332189i	$-0.892213\pi$
$193$	−2.55513	+	4.42561i	−0.183922	+	0.318562i	0.759291	+	0.650752i	$0.225546\pi$
$194$	4.00972	−	4.43699i	0.287881	−	0.318558i
$195$	11.8182	+	11.8182i	0.846320	+	0.846320i
$196$	5.44718	+	12.8968i	0.389084	+	0.921202i
$197$	1.32975	−	1.32975i	0.0947411	−	0.0947411i	−0.658148	−	0.752889i	$-0.728660\pi$
$197$	1.32975	−	1.32975i	0.0947411	−	0.0947411i	0.752889	+	0.658148i	$0.228660\pi$
$198$	−5.69809	+	0.288234i	−0.404946	+	0.0204839i
$199$	17.7364	+	10.2401i	1.25730	+	0.725902i	0.972549	−	0.232700i	$-0.0747561\pi$
$199$	17.7364	+	10.2401i	1.25730	+	0.725902i	0.284750	+	0.958602i	$0.408089\pi$
$200$	3.27174	+	7.45769i	0.231347	+	0.527338i
$201$	−6.08854	+	3.51522i	−0.429453	+	0.247945i
$202$	20.4728	+	10.4783i	1.44046	+	0.737253i
$203$	2.07274	−	2.80658i	0.145478	−	0.196983i
$204$	−8.30950	−	1.34710i	−0.581782	−	0.0943156i
$205$	5.36391	−	20.0184i	0.374632	−	1.39815i
$206$	2.39931	−	11.1878i	0.167168	−	0.779489i
$207$	3.53459	−	6.12209i	0.245671	−	0.425515i
$208$	−19.8796	−	13.1165i	−1.37840	−	0.909468i
$209$	−0.492405			−0.0340604
$210$	8.75298	+	5.80474i	0.604013	+	0.400565i
$211$	3.44225	+	3.44225i	0.236974	+	0.236974i	0.815596	−	0.578622i	$-0.196409\pi$
$211$	3.44225	+	3.44225i	0.236974	+	0.236974i	−0.578622	+	0.815596i	$0.696409\pi$
$212$	20.6758	−	7.85054i	1.42002	−	0.539177i
$213$	0.245165	+	0.914967i	0.0167984	+	0.0626925i
$214$	9.49470	−	6.14141i	0.649044	−	0.419818i
$215$	1.55493	−	0.897741i	0.106046	−	0.0612255i
$216$	−2.79598	+	0.427215i	−0.190242	+	0.0290683i
$217$	−1.15033	−	0.451899i	−0.0780894	−	0.0306769i
$218$	12.7133	−	24.8395i	0.861053	−	1.68234i
$219$	−9.14751	−	2.45107i	−0.618131	−	0.165628i
$220$	−22.5330	+	2.28548i	−1.51918	+	0.154087i
$221$	−24.2073	+	6.48632i	−1.62836	+	0.436317i
$222$	10.3090	−	11.4075i	0.691896	−	0.765624i
$223$	8.80744			0.589790			0.294895	−	0.955530i	$-0.404715\pi$
$223$	8.80744			0.589790			0.294895	+	0.955530i	$0.404715\pi$
$224$	−13.8799	−	5.59886i	−0.927393	−	0.374090i
$225$	2.87927			0.191951
$226$	−10.0121	+	11.0790i	−0.665996	+	0.736964i
$227$	14.3935	−	3.85673i	0.955331	−	0.255980i	0.252708	−	0.967543i	$-0.418679\pi$
$227$	14.3935	−	3.85673i	0.955331	−	0.255980i	0.702623	+	0.711562i	$0.252012\pi$
$228$	−0.242863	+	0.0246331i	−0.0160840	+	0.00163137i
$229$	−1.17629	−	0.315185i	−0.0777313	−	0.0208280i	0.219744	−	0.975558i	$-0.429478\pi$
$229$	−1.17629	−	0.315185i	−0.0777313	−	0.0208280i	−0.297475	+	0.954730i	$0.596145\pi$
$230$	12.7856	−	24.9807i	0.843056	−	1.64718i
$231$	−8.34724	+	6.65230i	−0.549208	+	0.437689i
$232$	0.563376	+	3.68711i	0.0369875	+	0.242070i
$233$	8.06076	−	4.65388i	0.528078	−	0.304886i	−0.212155	−	0.977236i	$-0.568048\pi$
$233$	8.06076	−	4.65388i	0.528078	−	0.304886i	0.740234	+	0.672350i	$0.234715\pi$
$234$	−7.07037	+	4.57329i	−0.462205	+	0.298965i
$235$	1.20038	+	4.47988i	0.0783042	+	0.292235i
$236$	−6.52532	+	2.47764i	−0.424762	+	0.161281i
$237$	1.46721	+	1.46721i	0.0953058	+	0.0953058i
$238$	−14.1003	+	7.01439i	−0.913984	+	0.454675i
$239$	−14.9611			−0.967754			−0.483877	−	0.875136i	$-0.660772\pi$
$239$	−14.9611			−0.967754			−0.483877	+	0.875136i	$0.660772\pi$
$240$	−10.9993	+	2.25448i	−0.710005	+	0.145526i
$241$	−5.42802	+	9.40161i	−0.349650	+	0.605611i	−0.986187	−	0.165635i	$-0.947033\pi$
$241$	−5.42802	+	9.40161i	−0.349650	+	0.605611i	0.636538	+	0.771246i	$0.280366\pi$
$242$	1.56448	−	7.29504i	0.100569	−	0.468943i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	12.3669	+	2.00486i	0.791707	+	0.128348i
$245$	19.6357	−	0.722045i	1.25448	−	0.0461297i
$246$	9.29469	+	4.75720i	0.592608	+	0.303308i
$247$	−0.629372	+	0.363368i	−0.0400460	+	0.0231206i
$248$	1.20993	−	0.530804i	0.0768305	−	0.0337061i
$249$	4.73446	+	2.73344i	0.300034	+	0.173225i
$250$	−8.40793	+	0.425309i	−0.531764	+	0.0268989i
$251$	−19.2758	+	19.2758i	−1.21668	+	1.21668i	−0.247892	+	0.968788i	$0.579738\pi$
$251$	−19.2758	+	19.2758i	−1.21668	+	1.21668i	−0.968788	+	0.247892i	$0.920262\pi$
$252$	−3.78421	+	3.69861i	−0.238383	+	0.232991i
$253$	20.1662	+	20.1662i	1.26784	+	1.26784i
$254$	−20.7322	+	22.9413i	−1.30085	+	1.43947i
$255$	−5.90733	+	10.2318i	−0.369931	+	0.640740i
$256$	14.7099	−	6.29444i	0.919366	−	0.393402i
$257$	9.13658	+	15.8250i	0.569924	+	0.987137i	0.996573	+	0.0827199i	$0.0263607\pi$
$257$	9.13658	+	15.8250i	0.569924	+	0.987137i	−0.426649	+	0.904417i	$0.640306\pi$
$258$	0.277970	+	0.860826i	0.0173056	+	0.0535927i
$259$	3.22988	−	28.5831i	0.200695	−	1.77607i
$260$	−27.1143	+	19.5494i	−1.68155	+	1.21240i
$261$	1.27378	+	0.341310i	0.0788453	+	0.0211265i
$262$	−9.83551	−	15.2058i	−0.607640	−	0.939420i
$263$	−2.87490	−	1.65983i	−0.177274	−	0.102349i	0.408737	−	0.912652i	$-0.365969\pi$
$263$	−2.87490	−	1.65983i	−0.177274	−	0.102349i	−0.586011	+	0.810303i	$0.699303\pi$
$264$	1.25465	−	11.3416i	0.0772182	−	0.698025i
$265$		−	31.0399i		−	1.90677i
$266$	−0.342308	+	0.302303i	−0.0209882	+	0.0185354i
$267$	−2.76073	+	2.76073i	−0.168954	+	0.168954i
$268$	−4.99119	−	13.1452i	−0.304885	−	0.802971i
$269$	16.3450	−	4.37963i	0.996572	−	0.267031i	0.276563	−	0.960996i	$-0.410804\pi$
$269$	16.3450	−	4.37963i	0.996572	−	0.267031i	0.720009	+	0.693965i	$0.244138\pi$
$270$	−0.832408	+	3.88145i	−0.0506587	+	0.236217i
$271$	−8.02891	−	13.9065i	−0.487721	−	0.844758i	0.512179	−	0.858879i	$-0.328838\pi$
$271$	−8.02891	−	13.9065i	−0.487721	−	0.844758i	−0.999900	+	0.0141205i	$0.995505\pi$
$272$	5.31895	−	15.9737i	0.322508	−	0.968547i
$273$	−5.76007	+	14.6625i	−0.348615	+	0.887416i
$274$	9.04717	−	2.92142i	0.546560	−	0.176490i
$275$	−3.00640	+	11.2201i	−0.181293	+	0.676595i
$276$	10.9551	+	8.93746i	0.659421	+	0.537972i
$277$	−3.72231	−	13.8918i	−0.223652	−	0.834680i	−0.982940	−	0.183926i	$-0.941119\pi$
$277$	−3.72231	−	13.8918i	−0.223652	−	0.834680i	0.759288	−	0.650754i	$-0.225547\pi$
$278$	−0.992506	−	19.6208i	−0.0595266	−	1.17678i
$279$		−	0.467129i		−	0.0279663i
$280$	−14.2613	+	15.4225i	−0.852274	+	0.921674i
$281$		−	14.4083i		−	0.859525i	−0.902942	−	0.429762i	$-0.858597\pi$
$281$		−	14.4083i		−	0.859525i	0.902942	−	0.429762i	$-0.141403\pi$
$282$	−2.33367	+	0.118047i	−0.138968	+	0.00702960i
$283$	0.748313	+	2.79274i	0.0444826	+	0.166011i	0.984594	−	0.174856i	$-0.0559460\pi$
$283$	0.748313	+	2.79274i	0.0444826	+	0.166011i	−0.940111	+	0.340867i	$0.889279\pi$
$284$	−1.88482	+	0.191173i	−0.111843	+	0.0113441i
$285$	−0.0886732	+	0.330933i	−0.00525254	+	0.0196028i
$286$	−10.4388	−	32.3274i	−0.617261	−	1.91156i
$287$	19.3168	−	2.90517i	1.14023	−	0.171487i
$288$	0.0514394	−	5.65662i	0.00303110	−	0.333320i
$289$	−0.357812	−	0.619749i	−0.0210478	−	0.0364558i
$290$	5.11854	+	1.09771i	0.300571	+	0.0644599i
$291$	4.08467	−	1.09448i	0.239447	−	0.0641597i
$292$	7.76664	−	17.2748i	0.454508	−	1.01093i
$293$	2.20355	−	2.20355i	0.128733	−	0.128733i	−0.639805	−	0.768537i	$-0.720985\pi$
$293$	2.20355	−	2.20355i	0.128733	−	0.128733i	0.768537	+	0.639805i	$0.220985\pi$
$294$	−1.71874	+	9.74915i	−0.100239	+	0.568582i
$295$			9.79625i			0.570360i
$296$	19.2216	+	24.0033i	1.11723	+	1.39517i
$297$	−3.49382	−	2.01716i	−0.202732	−	0.117047i
$298$	22.5643	−	14.5952i	1.30712	−	0.845475i
$299$	40.6571	+	10.8940i	2.35126	+	0.630019i
$300$	−0.921515	+	5.68432i	−0.0532037	+	0.328184i
$301$	1.36133	+	1.00538i	0.0784657	+	0.0579494i
$302$	−11.8274	+	3.81920i	−0.680592	+	0.219770i
$303$	8.13118	+	14.0836i	0.467124	+	0.809083i
$304$	0.0290974	−	0.487349i	0.00166885	−	0.0279514i
$305$	8.79176	−	15.2278i	0.503415	−	0.871940i
$306$	−4.41626	−	3.99098i	−0.252461	−	0.228149i
$307$	−22.8932	−	22.8932i	−1.30658	−	1.30658i	−0.923865	−	0.382719i	$-0.874988\pi$
$307$	−22.8932	−	22.8932i	−1.30658	−	1.30658i	−0.382719	−	0.923865i	$-0.625012\pi$
$308$	−10.4616	−	18.6084i	−0.596105	−	1.06031i
$309$	5.72108	−	5.72108i	0.325461	−	0.325461i
$310$	−0.0936819	−	1.85200i	−0.00532077	−	0.105186i
$311$	−11.1220	−	6.42131i	−0.630673	−	0.364119i	0.150340	−	0.988634i	$-0.451963\pi$
$311$	−11.1220	−	6.42131i	−0.630673	−	0.364119i	−0.781013	+	0.624515i	$0.785297\pi$
$312$	−6.76582	−	15.4222i	−0.383039	−	0.873110i
$313$	5.76549	−	3.32871i	0.325885	−	0.188150i	−0.328128	−	0.944633i	$-0.606418\pi$
$313$	5.76549	−	3.32871i	0.325885	−	0.188150i	0.654013	+	0.756484i	$0.273084\pi$
$314$	−5.74356	+	11.2219i	−0.324128	+	0.633287i
$315$	2.96766	+	6.80793i	0.167209	+	0.383583i
$316$	−3.36620	+	2.42703i	−0.189363	+	0.136531i
$317$	−0.110898	+	0.413875i	−0.00622863	+	0.0232456i	−0.968970	−	0.247178i	$-0.920497\pi$
$317$	−0.110898	+	0.413875i	−0.00622863	+	0.0232456i	0.962742	+	0.270423i	$0.0871636\pi$
$318$	15.2907	+	3.27923i	0.857462	+	0.183890i
$319$	−2.66006	+	4.60736i	−0.148935	+	0.257963i
$320$	−0.930486	−	22.4367i	−0.0520157	−	1.25425i
$321$	7.99582			0.446283
$322$	26.3997	+	1.63837i	1.47120	+	0.0913028i
$323$	−0.363259	−	0.363259i	−0.0202123	−	0.0202123i
$324$	−1.82412	−	0.820114i	−0.101340	−	0.0455619i
$325$	4.43713	+	16.5596i	0.246128	+	0.918560i
$326$	−15.6126	−	24.1373i	−0.864701	−	1.33684i
$327$	17.0876	−	9.86551i	0.944944	−	0.545564i
$328$	−12.3666	+	16.8273i	−0.682829	+	0.929131i
$329$	−3.41864	+	2.72447i	−0.188476	+	0.150205i
$330$	−14.2562	−	7.29660i	−0.784780	−	0.401665i
$331$	−5.82859	−	1.56176i	−0.320368	−	0.0858424i	0.0950513	−	0.995472i	$-0.469698\pi$
$331$	−5.82859	−	1.56176i	−0.320368	−	0.0858424i	−0.415419	+	0.909630i	$0.636365\pi$
$332$	−6.91171	+	8.47205i	−0.379329	+	0.464964i
$333$	10.5017	−	2.81392i	0.575490	−	0.154202i
$334$	24.4454	+	22.0914i	1.33759	+	1.20879i
$335$	−19.7345			−1.07821
$336$	−6.09075	−	8.65464i	−0.332277	−	0.472149i
$337$	−15.0923			−0.822129			−0.411065	−	0.911606i	$-0.634843\pi$
$337$	−15.0923			−0.822129			−0.411065	+	0.911606i	$0.634843\pi$
$338$	−23.5582	−	21.2896i	−1.28140	−	1.15800i
$339$	−10.1992	+	2.73288i	−0.553947	+	0.148430i
$340$	−18.3092	−	14.9371i	−0.992957	−	0.810078i
$341$	1.82033	+	0.487756i	0.0985764	+	0.0264135i
$342$	−0.153655	−	0.0786433i	−0.00830869	−	0.00425254i
$343$	8.01950	+	16.6939i	0.433012	+	0.901388i
$344$	−1.78843	+	0.273265i	−0.0964257	+	0.0147335i
$345$	17.1847	−	9.92160i	0.925194	−	0.534161i
$346$	−4.28896	−	6.63079i	−0.230576	−	0.356474i
$347$	4.79889	+	17.9097i	0.257618	+	0.961443i	0.966615	+	0.256232i	$0.0824810\pi$
$347$	4.79889	+	17.9097i	0.257618	+	0.961443i	−0.708998	+	0.705211i	$0.750852\pi$
$348$	−1.08150	+	2.40550i	−0.0579745	+	0.128948i
$349$	−20.7287	−	20.7287i	−1.10958	−	1.10958i	−0.993205	−	0.116378i	$-0.962872\pi$
$349$	−20.7287	−	20.7287i	−1.10958	−	1.10958i	−0.116378	−	0.993205i	$-0.537128\pi$
$350$	4.79837	+	9.64563i	0.256483	+	0.515580i
$351$	−5.95421			−0.317812
$352$	21.9893	+	6.10685i	1.17203	+	0.325496i
$353$	8.93700	−	15.4793i	0.475669	−	0.823882i	−0.523943	−	0.851753i	$-0.675539\pi$
$353$	8.93700	−	15.4793i	0.475669	−	0.823882i	0.999612	+	0.0278711i	$0.00887280\pi$
$354$	−4.82578	−	1.03493i	−0.256487	−	0.0550058i
$355$	−0.688178	+	2.56832i	−0.0365247	+	0.136312i
$356$	−4.56673	−	6.33389i	−0.242036	−	0.335696i
$357$	−11.0655	−	1.25040i	−0.585650	−	0.0661780i
$358$	−6.10143	+	11.9211i	−0.322471	+	0.630049i
$359$	11.3931	−	6.57782i	0.601306	−	0.347164i	−0.168249	−	0.985744i	$-0.553811\pi$
$359$	11.3931	−	6.57782i	0.601306	−	0.347164i	0.769555	+	0.638580i	$0.220478\pi$
$360$	−7.39644	−	2.88563i	−0.389826	−	0.152086i
$361$	16.4416	+	9.49255i	0.865346	+	0.499608i
$362$	1.07949	+	21.3404i	0.0567366	+	1.12163i
$363$	3.73045	−	3.73045i	0.195798	−	0.195798i
$364$	−27.1036	−	16.0644i	−1.42061	−	0.842006i
$365$	−18.7969	−	18.7969i	−0.983876	−	0.983876i
$366$	6.57262	+	5.93970i	0.343557	+	0.310473i
$367$	8.56687	−	14.8383i	0.447187	−	0.774550i	−0.551015	−	0.834496i	$-0.685759\pi$
$367$	8.56687	−	14.8383i	0.447187	−	0.774550i	0.998202	+	0.0599450i	$0.0190925\pi$
$368$	−21.1508	+	18.7674i	−1.10256	+	0.978321i
$369$	3.69158	+	6.39401i	0.192176	+	0.332859i
$370$	41.0711	−	13.2623i	2.13518	−	0.689473i
$371$	26.8195	−	11.6909i	1.39240	−	0.606962i
$372$	0.922219	+	0.149506i	0.0478148	+	0.00775151i
$373$	−25.5633	−	6.84965i	−1.32362	−	0.354662i	−0.473284	−	0.880910i	$-0.656932\pi$
$373$	−25.5633	−	6.84965i	−1.32362	−	0.354662i	−0.850331	+	0.526248i	$0.823598\pi$
$374$	20.1635	−	13.0423i	1.04263	−	0.674399i
$375$	−5.15537	−	2.97645i	−0.266222	−	0.153703i
$376$	0.513845	−	4.64498i	0.0264995	−	0.239546i
$377$			7.85192i			0.404395i
$378$	−3.66721	+	0.742687i	−0.188621	+	0.0381997i
$379$	−9.63202	+	9.63202i	−0.494763	+	0.494763i	−0.909803	−	0.415040i	$-0.863768\pi$
$379$	−9.63202	+	9.63202i	−0.494763	+	0.494763i	0.415040	+	0.909803i	$0.363768\pi$
$380$	−0.624956	−	0.280976i	−0.0320596	−	0.0144138i
$381$	−21.1196	+	5.65899i	−1.08199	+	0.289919i
$382$	−4.98930	−	1.07000i	−0.255275	−	0.0547457i
$383$	8.38804	+	14.5285i	0.428609	+	0.742373i	0.996750	−	0.0805588i	$-0.0256705\pi$
$383$	8.38804	+	14.5285i	0.428609	+	0.742373i	−0.568141	+	0.822931i	$0.692337\pi$
$384$	11.1510	+	1.91197i	0.569046	+	0.0975696i
$385$	−29.6281	+	4.45596i	−1.50999	+	0.227097i
$386$	−2.22076	−	6.87733i	−0.113034	−	0.350047i
$387$	−0.165552	+	0.617849i	−0.00841548	+	0.0314070i
$388$	0.853451	+	8.41434i	0.0433274	+	0.427174i
$389$	4.04522	+	15.0970i	0.205101	+	0.765446i	0.989419	+	0.145088i	$0.0463464\pi$
$389$	4.04522	+	15.0970i	0.205101	+	0.765446i	−0.784318	+	0.620359i	$0.786987\pi$
$390$	−23.6062	+	1.19410i	−1.19535	+	0.0604658i
$391$			29.7541i			1.50473i
$392$	−18.6969	−	6.51341i	−0.944338	−	0.328977i
$393$		−	12.8054i		−	0.645945i
$394$	0.134358	+	2.65611i	0.00676884	+	0.133813i
$395$	1.50747	+	5.62594i	0.0758489	+	0.283072i
$396$	5.10052	−	6.25198i	0.256311	−	0.314174i
$397$	−0.359299	+	1.34092i	−0.0180327	+	0.0672989i	−0.974356	−	0.225013i	$-0.927758\pi$
$397$	−0.359299	+	1.34092i	−0.0180327	+	0.0672989i	0.956323	+	0.292311i	$0.0944244\pi$
$398$	−27.5620	+	8.90007i	−1.38156	+	0.446120i
$399$	−0.319334	+	0.0480266i	−0.0159867	+	0.00240434i
$400$	−10.9272	−	3.63856i	−0.546360	−	0.181928i
$401$	−6.55328	−	11.3506i	−0.327255	−	0.566822i	0.654711	−	0.755879i	$-0.272790\pi$
$401$	−6.55328	−	11.3506i	−0.327255	−	0.566822i	−0.981966	+	0.189057i	$0.939457\pi$
$402$	2.08486	−	9.72150i	0.103983	−	0.484864i
$403$	2.68661	−	0.719875i	0.133830	−	0.0358595i
$404$	−30.4066	+	11.5453i	−1.51279	+	0.574400i
$405$	−1.98485	+	1.98485i	−0.0986280	+	0.0986280i
$406$	0.979396	+	4.83602i	0.0486066	+	0.240007i
$407$			43.8617i			2.17414i
$408$	9.29253	−	7.44136i	0.460049	−	0.368402i
$409$	−1.93173	−	1.11529i	−0.0955179	−	0.0551473i	0.451480	−	0.892281i	$-0.350896\pi$
$409$	−1.93173	−	1.11529i	−0.0955179	−	0.0551473i	−0.546998	+	0.837134i	$0.684230\pi$
$410$	15.9181	+	24.6096i	0.786138	+	1.21538i
$411$	6.49351	+	1.73993i	0.320301	+	0.0858244i
$412$	9.46365	+	13.1257i	0.466241	+	0.646659i
$413$	−8.46426	+	3.68967i	−0.416499	+	0.181557i
$414$	3.07205	+	9.51363i	0.150983	+	0.467569i
$415$	7.67278	+	13.2897i	0.376642	+	0.652363i
$416$	32.6123	−	8.42136i	1.59895	−	0.412891i
$417$	6.94588	−	12.0306i	0.340141	−	0.589142i
$418$	0.466900	−	0.516652i	0.0228368	−	0.0252703i
$419$	3.07109	+	3.07109i	0.150033	+	0.150033i	0.778133	−	0.628100i	$-0.216167\pi$
$419$	3.07109	+	3.07109i	0.150033	+	0.150033i	−0.628100	+	0.778133i	$0.716167\pi$
$420$	−14.3902	+	3.67993i	−0.702169	+	0.179562i
$421$	17.7216	−	17.7216i	0.863697	−	0.863697i	−0.128068	−	0.991765i	$-0.540878\pi$
$421$	17.7216	−	17.7216i	0.863697	−	0.863697i	0.991765	+	0.128068i	$0.0408776\pi$
$422$	−6.87570	+	0.347803i	−0.334704	+	0.0169308i
$423$	−1.43090	−	0.826133i	−0.0695729	−	0.0401679i
$424$	−11.3678	+	29.1379i	−0.552067	+	1.41506i
$425$	−10.4952	+	6.05941i	−0.509092	+	0.293924i
$426$	−1.19249	−	0.610338i	−0.0577763	−	0.0295710i
$427$	16.4686	+	1.86094i	0.796971	+	0.0900572i
$428$	−2.55908	+	15.7855i	−0.123698	+	0.763023i
$429$	6.21712	−	23.2026i	0.300165	−	1.12023i
$430$	−0.532445	+	2.48274i	−0.0256768	+	0.119729i
$431$	4.76805	−	8.25851i	0.229669	−	0.397798i	−0.728041	−	0.685534i	$-0.759569\pi$
$431$	4.76805	−	8.25851i	0.229669	−	0.397798i	0.957710	+	0.287735i	$0.0929023\pi$
$432$	2.20290	−	3.33875i	0.105987	−	0.160635i
$433$	13.4371			0.645748			0.322874	−	0.946442i	$-0.395351\pi$
$433$	13.4371			0.645748			0.322874	+	0.946442i	$0.395351\pi$
$434$	1.56490	−	0.778483i	0.0751175	−	0.0373684i
$435$	2.61746	+	2.61746i	0.125498	+	0.125498i
$436$	14.0078	+	36.8922i	0.670853	+	1.76681i
$437$	0.223315	+	0.833423i	0.0106826	+	0.0398681i
$438$	11.2455	−	7.27384i	0.537329	−	0.347558i
$439$	11.6133	−	6.70493i	0.554271	−	0.320009i	−0.196572	−	0.980489i	$-0.562981\pi$
$439$	11.6133	−	6.70493i	0.554271	−	0.320009i	0.750843	+	0.660481i	$0.229647\pi$
$440$	18.9679	−	25.8097i	0.904258	−	1.23043i
$441$	−4.76452	+	5.12829i	−0.226882	+	0.244204i
$442$	16.1477	−	31.5497i	0.768067	−	1.50066i
$443$	23.1879	+	6.21319i	1.10169	+	0.295198i	0.763454	−	0.645863i	$-0.223502\pi$
$443$	23.1879	+	6.21319i	1.10169	+	0.295198i	0.338239	+	0.941060i	$0.390169\pi$
$444$	2.19423	+	21.6333i	0.104133	+	1.02667i
$445$	−10.5859	+	2.83647i	−0.501818	+	0.134462i
$446$	−8.35124	+	9.24114i	−0.395443	+	0.437581i
$447$	19.0022			0.898773
$448$	19.0356	−	9.25457i	0.899346	−	0.437237i
$449$	4.78587			0.225859			0.112930	−	0.993603i	$-0.463977\pi$
$449$	4.78587			0.225859			0.112930	+	0.993603i	$0.463977\pi$
$450$	−2.73013	+	3.02105i	−0.128700	+	0.142414i
$451$	−28.7710	+	7.70918i	−1.35478	+	0.363011i
$452$	−2.13103	−	21.0103i	−0.100235	−	0.988240i
$453$	−8.48901	−	2.27462i	−0.398848	−	0.106871i
$454$	−9.60133	+	18.7593i	−0.450613	+	0.880416i
$455$	−34.5812	+	27.5594i	−1.62119	+	1.29200i
$456$	0.204437	−	0.278179i	0.00957364	−	0.0130269i
$457$	−1.88623	+	1.08901i	−0.0882340	+	0.0509419i	−0.543468	−	0.839430i	$-0.682889\pi$
$457$	−1.88623	+	1.08901i	−0.0882340	+	0.0509419i	0.455234	+	0.890372i	$0.349556\pi$
$458$	1.44607	−	0.935352i	0.0675703	−	0.0437061i
$459$	−1.08937	−	4.06558i	−0.0508473	−	0.189765i
$460$	14.0875	+	37.1019i	0.656832	+	1.72989i
$461$	17.1309	+	17.1309i	0.797867	+	0.797867i	0.982759	−	0.184892i	$-0.0591935\pi$
$461$	17.1309	+	17.1309i	0.797867	+	0.797867i	−0.184892	+	0.982759i	$0.559194\pi$
$462$	0.935002	−	15.0660i	0.0435002	−	0.700935i
$463$	−33.5855			−1.56085			−0.780426	−	0.625248i	$-0.784998\pi$
$463$	−33.5855			−1.56085			−0.780426	+	0.625248i	$0.784998\pi$
$464$	−4.40287	−	2.90501i	−0.204398	−	0.134862i
$465$	0.655617	−	1.13556i	0.0304035	−	0.0526604i
$466$	−2.76019	+	12.8705i	−0.127863	+	0.596216i
$467$	−1.00551	+	3.75262i	−0.0465295	+	0.173650i	−0.985280	−	0.170946i	$-0.945318\pi$
$467$	−1.00551	+	3.75262i	−0.0465295	+	0.173650i	0.938751	+	0.344597i	$0.111984\pi$
$468$	1.90566	−	11.7549i	0.0880890	−	0.543373i
$469$	−7.43282	−	17.0512i	−0.343216	−	0.787351i
$470$	−5.83869	−	2.98835i	−0.269319	−	0.137842i
$471$	−7.71976	+	4.45700i	−0.355708	+	0.205368i
$472$	3.58768	−	9.19595i	0.165137	−	0.423278i
$473$	−2.23480	−	1.29026i	−0.102756	−	0.0593263i
$474$	−2.93068	+	0.148246i	−0.134611	+	0.00680919i
$475$	−0.248496	+	0.248496i	−0.0114018	+	0.0114018i
$476$	6.01011	−	21.4457i	0.275473	−	0.982960i
$477$	7.81921	+	7.81921i	0.358017	+	0.358017i
$478$	14.1862	−	15.6978i	0.648861	−	0.718003i
$479$	−5.32313	+	9.21993i	−0.243220	+	0.421270i	−0.961630	−	0.274351i	$-0.911537\pi$
$479$	−5.32313	+	9.21993i	−0.243220	+	0.421270i	0.718410	+	0.695620i	$0.244870\pi$
$480$	8.06412	−	13.6787i	0.368075	−	0.624344i
$481$	32.3676	+	56.0623i	1.47583	+	2.55622i
$482$	−4.71770	−	14.6099i	−0.214885	−	0.665465i
$483$	15.0450	+	11.1112i	0.684573	+	0.505579i
$484$	6.17082	+	8.55870i	0.280492	+	0.389032i
$485$	11.4657	+	3.07222i	0.520629	+	0.139502i
$486$	−0.768078	−	1.18746i	−0.0348407	−	0.0538642i
$487$	−32.6243	−	18.8356i	−1.47835	−	0.853525i	−0.478648	−	0.878007i	$-0.658873\pi$
$487$	−32.6243	−	18.8356i	−1.47835	−	0.853525i	−0.999700	+	0.0244822i	$0.992206\pi$
$488$	−13.8299	+	11.0748i	−0.626049	+	0.501334i
$489$		−	20.3268i		−	0.919211i
$490$	−17.8611	+	21.2873i	−0.806882	+	0.961663i
$491$	24.2888	−	24.2888i	1.09614	−	1.09614i	0.101280	−	0.994858i	$-0.467706\pi$
$491$	24.2888	−	24.2888i	1.09614	−	1.09614i	0.994858	−	0.101280i	$-0.0322938\pi$
$492$	−13.8047	+	5.24160i	−0.622365	+	0.236310i
$493$	−5.36135	+	1.43657i	−0.241463	+	0.0646998i
$494$	0.215511	−	1.00491i	0.00969632	−	0.0452131i
$495$	−5.66216	−	9.80715i	−0.254495	−	0.440799i
$496$	−0.590316	+	1.77282i	−0.0265060	+	0.0796019i
$497$	−2.47830	+	0.372727i	−0.111167	+	0.0167191i
$498$	−7.35728	+	2.37574i	−0.329688	+	0.106459i
$499$	2.60953	−	9.73891i	0.116819	−	0.435974i	−0.882598	−	0.470129i	$-0.844207\pi$
$499$	2.60953	−	9.73891i	0.116819	−	0.435974i	0.999417	+	0.0341553i	$0.0108741\pi$
$500$	7.52618	−	9.22524i	0.336581	−	0.412565i
$501$	6.03000	+	22.5043i	0.269401	+	1.00542i
$502$	−1.94762	−	38.5024i	−0.0869264	−	1.71845i
$503$		−	11.6393i		−	0.518972i	−0.965747	−	0.259486i	$-0.916447\pi$
$503$		−	11.6393i		−	0.518972i	0.965747	−	0.259486i	$-0.0835532\pi$
$504$	−0.292535	−	7.47759i	−0.0130305	−	0.333079i
$505$			45.6485i			2.03133i
$506$	−40.2808	+	2.03758i	−1.79070	+	0.0905813i
$507$	−5.81115	−	21.6875i	−0.258082	−	0.963176i
$508$	−4.41274	−	43.5061i	−0.195784	−	1.93027i
$509$	5.44563	−	20.3234i	0.241373	−	0.900818i	−0.733798	−	0.679367i	$-0.762254\pi$
$509$	5.44563	−	20.3234i	0.241373	−	0.900818i	0.975172	−	0.221450i	$-0.0710791\pi$
$510$	−5.13429	−	15.9000i	−0.227350	−	0.704066i
$511$	9.16142	−	23.3208i	0.405277	−	1.03165i
$512$	−7.34355	+	21.4026i	−0.324542	+	0.945871i
$513$	−0.0610271	−	0.105702i	−0.00269441	−	0.00466686i
$514$	−25.2676	−	5.41885i	−1.11451	−	0.239015i
$515$	21.9371	−	5.87803i	0.966664	−	0.259017i
$516$	−1.16679	−	0.524581i	−0.0513650	−	0.0230934i
$517$	4.71340	−	4.71340i	0.207295	−	0.207295i
$518$	26.9281	+	30.4916i	1.18315	+	1.33972i
$519$		−	5.58402i		−	0.245111i
$520$	5.19779	−	46.9862i	0.227938	−	2.06048i
$521$	25.9644	+	14.9905i	1.13752	+	0.656748i	0.945815	−	0.324705i	$-0.105265\pi$
$521$	25.9644	+	14.9905i	1.13752	+	0.656748i	0.191705	+	0.981453i	$0.438598\pi$
$522$	−1.56592	+	1.01288i	−0.0685386	+	0.0443325i
$523$	−8.14129	−	2.18145i	−0.355994	−	0.0953882i	0.0763898	−	0.997078i	$-0.475661\pi$
$523$	−8.14129	−	2.18145i	−0.355994	−	0.0953882i	−0.432384	+	0.901690i	$0.642327\pi$
$524$	25.2807	+	4.09838i	1.10439	+	0.179039i
$525$	−0.855365	+	7.56965i	−0.0373312	+	0.330366i
$526$	4.46755	−	1.44262i	0.194795	−	0.0629011i
$527$	0.983072	+	1.70273i	0.0428233	+	0.0741721i
$528$	10.7104	+	12.0705i	0.466110	+	0.525303i
$529$	13.4866	−	23.3595i	0.586376	−	1.01563i
$530$	32.5684	+	29.4322i	1.41468	+	1.27845i
$531$	−2.46775	−	2.46775i	−0.107091	−	0.107091i
$532$	0.00738812	−	0.645808i	0.000320316	−	0.0279993i
$533$	−31.0850	+	31.0850i	−1.34644	+	1.34644i
$534$	−0.278943	−	5.51442i	−0.0120710	−	0.238632i
$535$	19.4373	+	11.2221i	0.840349	+	0.485176i
$536$	18.5252	+	7.22736i	0.800166	+	0.312174i
$537$	−8.20075	+	4.73471i	−0.353889	+	0.204318i
$538$	−10.9031	+	21.3026i	−0.470065	+	0.918422i
$539$	−15.0093	−	23.9213i	−0.646495	−	1.03036i
$540$	−3.28329	−	4.55380i	−0.141290	−	0.195964i
$541$	2.66747	−	9.95514i	0.114684	−	0.428005i	−0.884579	−	0.466389i	$-0.845555\pi$
$541$	2.66747	−	9.95514i	0.114684	−	0.428005i	0.999263	+	0.0383846i	$0.0122212\pi$
$542$	22.2043	+	4.76189i	0.953757	+	0.204541i
$543$	−7.55461	+	13.0850i	−0.324199	+	0.561530i
$544$	11.7168	+	20.7272i	0.502355	+	0.888670i
$545$	55.3850			2.37243
$546$	−9.92283	−	19.9468i	−0.424658	−	0.853643i
$547$	−15.5215	−	15.5215i	−0.663652	−	0.663652i	0.292587	−	0.956239i	$-0.405484\pi$
$547$	−15.5215	−	15.5215i	−0.663652	−	0.663652i	−0.956239	+	0.292587i	$0.905484\pi$
$548$	−5.51328	+	12.2628i	−0.235515	+	0.523840i
$549$	1.62128	+	6.05071i	0.0691947	+	0.258238i
$550$	−8.92188	−	13.7933i	−0.380430	−	0.588150i
$551$	−0.139391	+	0.0804776i	−0.00593827	+	0.00342846i
$552$	−19.7653	+	3.02006i	−0.841265	+	0.128542i
$553$	−4.29321	+	3.42146i	−0.182566	+	0.145495i
$554$	18.1054	+	9.26669i	0.769226	+	0.393704i
$555$	29.4783	+	7.89869i	1.25129	+	0.335281i
$556$	21.5281	+	17.5632i	0.912996	+	0.744844i
$557$	−21.3515	+	5.72113i	−0.904694	+	0.242412i	−0.681031	−	0.732255i	$-0.738468\pi$
$557$	−21.3515	+	5.72113i	−0.904694	+	0.242412i	−0.223663	+	0.974667i	$0.571801\pi$
$558$	0.490132	+	0.442934i	0.0207490	+	0.0187509i
$559$	−3.80857			−0.161085
$560$	−2.65941	−	29.5872i	−0.112381	−	1.25029i
$561$	16.9804			0.716912
$562$	15.1178	+	13.6620i	0.637705	+	0.576295i
$563$	−6.47783	+	1.73573i	−0.273008	+	0.0731523i	−0.392726	−	0.919656i	$-0.628468\pi$
$563$	−6.47783	+	1.73573i	−0.273008	+	0.0731523i	0.119718	+	0.992808i	$0.461801\pi$
$564$	2.08894	−	2.56052i	0.0879601	−	0.107817i
$565$	−28.6293	−	7.67120i	−1.20444	−	0.322730i
$566$	−3.63982	−	1.86292i	−0.152993	−	0.0783046i
$567$	−2.46255	−	0.967395i	−0.103417	−	0.0406268i
$568$	1.58660	−	2.15890i	0.0665724	−	0.0905855i
$569$	22.5200	−	13.0019i	0.944088	−	0.545069i	0.0528484	−	0.998603i	$-0.483170\pi$
$569$	22.5200	−	13.0019i	0.944088	−	0.545069i	0.891239	+	0.453533i	$0.149837\pi$
$570$	−0.263149	−	0.406831i	−0.0110221	−	0.0170403i
$571$	−5.10889	−	19.0666i	−0.213800	−	0.797914i	−0.986585	−	0.163246i	$-0.947804\pi$
$571$	−5.10889	−	19.0666i	−0.213800	−	0.797914i	0.772785	−	0.634668i	$-0.218863\pi$
$572$	43.8174	+	19.7000i	1.83210	+	0.823700i
$573$	−2.55137	−	2.55137i	−0.106585	−	0.106585i
$574$	−15.2680	+	23.0227i	−0.637274	+	0.960948i
$575$	20.3540			0.848822
$576$	5.88639	+	5.41760i	0.245266	+	0.225733i
$577$	10.2689	−	17.7863i	0.427501	−	0.740454i	−0.569149	−	0.822234i	$-0.692727\pi$
$577$	10.2689	−	17.7863i	0.427501	−	0.740454i	0.996650	+	0.0817805i	$0.0260607\pi$
$578$	0.989545	+	0.212216i	0.0411597	+	0.00882703i
$579$	1.32263	−	4.93613i	0.0549667	−	0.205138i
$580$	−6.00518	+	4.32973i	−0.249352	+	0.179782i
$581$	−8.59278	+	11.6350i	−0.356489	+	0.482699i
$582$	−2.72472	+	5.32360i	−0.112943	+	0.220670i
$583$	−38.6347	+	22.3058i	−1.60009	+	0.923811i
$584$	10.7611	+	24.5291i	0.445297	+	1.01502i
$585$	−14.4743	−	8.35674i	−0.598438	−	0.345509i
$586$	0.222645	+	4.40147i	0.00919739	+	0.181823i
$587$	7.03464	−	7.03464i	0.290351	−	0.290351i	−0.546868	−	0.837219i	$-0.684180\pi$
$587$	7.03464	−	7.03464i	0.290351	−	0.290351i	0.837219	+	0.546868i	$0.184180\pi$
$588$	−8.59952	−	11.0475i	−0.354638	−	0.455593i
$589$	0.0403158	+	0.0403158i	0.00166118	+	0.00166118i
$590$	−10.2786	−	9.28884i	−0.423165	−	0.382415i
$591$	−0.940279	+	1.62861i	−0.0386779	+	0.0669921i
$592$	−43.4114	−	2.59189i	−1.78420	−	0.106526i
$593$	17.0053	+	29.4540i	0.698324	+	1.20953i	0.969047	+	0.246875i	$0.0794037\pi$
$593$	17.0053	+	29.4540i	0.698324	+	1.20953i	−0.270724	+	0.962657i	$0.587263\pi$
$594$	5.42933	−	1.75319i	0.222768	−	0.0719341i
$595$	−25.1447	−	18.5701i	−1.03083	−	0.761301i
$596$	−6.08169	+	37.5146i	−0.249116	+	1.53666i
$597$	−19.7824	−	5.30067i	−0.809638	−	0.216942i
$598$	−49.9817	+	32.3294i	−2.04390	+	1.32205i
$599$	−29.6323	−	17.1082i	−1.21074	−	0.699023i	−0.247822	−	0.968806i	$-0.579715\pi$
$599$	−29.6323	−	17.1082i	−1.21074	−	0.699023i	−0.962921	+	0.269783i	$0.913048\pi$
$600$	−5.09045	−	6.35678i	−0.207817	−	0.259515i
$601$			32.0896i			1.30896i	0.756079	+	0.654480i	$0.227113\pi$
$601$			32.0896i			1.30896i	−0.756079	+	0.654480i	$0.772887\pi$
$602$	−2.34571	+	0.475055i	−0.0956039	+	0.0193618i
$603$	4.97127	−	4.97127i	0.202446	−	0.202446i
$604$	7.20754	−	16.0312i	0.293271	−	0.652301i
$605$	14.3042	−	3.83280i	0.581548	−	0.155825i
$606$	−22.4872	−	4.82255i	−0.913478	−	0.195903i
$607$	7.18534	+	12.4454i	0.291644	+	0.505142i	0.974199	−	0.225692i	$-0.0724644\pi$
$607$	7.18534	+	12.4454i	0.291644	+	0.505142i	−0.682555	+	0.730835i	$0.739131\pi$
$608$	0.483757	+	0.492636i	0.0196190	+	0.0199790i
$609$	−1.27572	+	3.24741i	−0.0516949	+	0.131592i
$610$	7.64125	+	23.6637i	0.309385	+	0.958116i
$611$	2.54624	−	9.50271i	0.103010	−	0.384438i
$612$	8.37502	−	0.849462i	0.338540	−	0.0343375i
$613$	1.68609	+	6.29258i	0.0681006	+	0.254155i	0.991580	−	0.129492i	$-0.0413346\pi$
$613$	1.68609	+	6.29258i	0.0681006	+	0.254155i	−0.923480	+	0.383647i	$0.874668\pi$
$614$	45.7279	−	2.31311i	1.84543	−	0.0933497i
$615$			20.7246i			0.835695i
$616$	29.4445	+	6.66781i	1.18635	+	0.268654i
$617$		−	5.91905i		−	0.238292i	−0.992877	−	0.119146i	$-0.961984\pi$
$617$		−	5.91905i		−	0.238292i	0.992877	−	0.119146i	$-0.0380157\pi$
$618$	0.578054	+	11.4275i	0.0232527	+	0.459683i
$619$	2.78006	+	10.3753i	0.111740	+	0.417019i	0.999022	−	0.0442074i	$-0.0140763\pi$
$619$	2.78006	+	10.3753i	0.111740	+	0.417019i	−0.887282	+	0.461226i	$0.847410\pi$
$620$	2.03202	+	1.65777i	0.0816080	+	0.0665778i
$621$	−1.82964	+	6.82830i	−0.0734208	+	0.274010i
$622$	17.2835	−	5.58101i	0.693004	−	0.223778i
$623$	−6.43787	−	8.07818i	−0.257928	−	0.323645i
$624$	22.5970	+	7.52439i	0.904604	+	0.301217i
$625$	−15.5531	−	26.9387i	−0.622123	−	1.07755i
$626$	−1.97424	+	9.20569i	−0.0789064	+	0.367934i
$627$	0.475627	−	0.127444i	0.0189947	−	0.00508961i
$628$	−6.32841	−	16.6670i	−0.252531	−	0.665086i
$629$	−32.3578	+	32.3578i	−1.29019	+	1.29019i
$630$	−9.95711	−	3.34151i	−0.396701	−	0.133129i
$631$		−	16.9388i		−	0.674324i	−0.941447	−	0.337162i	$-0.890533\pi$
$631$		−	16.9388i		−	0.674324i	0.941447	−	0.337162i	$-0.109467\pi$
$632$	0.645299	−	5.83328i	0.0256686	−	0.232035i
$633$	−4.21588	−	2.43404i	−0.167566	−	0.0967443i
$634$	−0.329102	−	0.508796i	−0.0130703	−	0.0202069i
$635$	−59.2829	−	15.8848i	−2.35257	−	0.630369i
$636$	−17.9394	+	12.9343i	−0.711345	+	0.512880i
$637$	−36.8369	−	19.4992i	−1.45953	−	0.772588i
$638$	−2.31196	−	7.15976i	−0.0915314	−	0.283458i
$639$	−0.473622	−	0.820337i	−0.0187362	−	0.0324520i
$640$	24.4239	+	20.2983i	0.965438	+	0.802360i
$641$	−6.49512	+	11.2499i	−0.256542	+	0.444343i	−0.965313	−	0.261095i	$-0.915916\pi$
$641$	−6.49512	+	11.2499i	−0.256542	+	0.444343i	0.708771	+	0.705438i	$0.249250\pi$
$642$	−7.58166	+	8.38955i	−0.299224	+	0.331109i
$643$	17.4558	+	17.4558i	0.688391	+	0.688391i	0.961876	−	0.273486i	$-0.0881766\pi$
$643$	17.4558	+	17.4558i	0.688391	+	0.688391i	−0.273486	+	0.961876i	$0.588177\pi$
$644$	−26.7513	+	26.1461i	−1.05415	+	1.03030i
$645$	−1.26960	+	1.26960i	−0.0499904	+	0.0499904i
$646$	0.725590	−	0.0367034i	0.0285480	−	0.00144408i
$647$	−20.9068	−	12.0705i	−0.821931	−	0.474542i	0.0291508	−	0.999575i	$-0.490720\pi$
$647$	−20.9068	−	12.0705i	−0.821931	−	0.474542i	−0.851082	+	0.525033i	$0.824053\pi$
$648$	2.59014	−	1.13631i	0.101750	−	0.0446385i
$649$	12.1932	−	7.03973i	0.478624	−	0.276334i
$650$	−21.5823	−	11.0462i	−0.846528	−	0.433269i
$651$	1.22809	+	0.138774i	0.0481327	+	0.00543897i
$652$	40.1298	+	6.50565i	1.57160	+	0.254781i
$653$	4.26130	−	15.9034i	0.166758	−	0.622348i	−0.831052	−	0.556195i	$-0.812261\pi$
$653$	4.26130	−	15.9034i	0.166758	−	0.622348i	0.997809	−	0.0661532i	$-0.0210726\pi$
$654$	−5.85117	+	27.2835i	−0.228799	+	1.06687i
$655$	17.9723	−	31.1290i	0.702238	−	1.21631i
$656$	−5.92988	−	28.9312i	−0.231523	−	1.12957i
$657$	9.47019			0.369467
$658$	0.382933	−	6.17034i	0.0149283	−	0.240545i
$659$	−34.9342	−	34.9342i	−1.36084	−	1.36084i	−0.872843	−	0.488001i	$-0.837726\pi$
$659$	−34.9342	−	34.9342i	−1.36084	−	1.36084i	−0.488001	−	0.872843i	$-0.662274\pi$
$660$	21.1737	−	8.03958i	0.824186	−	0.312940i
$661$	−7.55262	−	28.1868i	−0.293763	−	1.09634i	−0.942195	−	0.335065i	$-0.891242\pi$
$661$	−7.55262	−	28.1868i	−0.293763	−	1.09634i	0.648432	−	0.761273i	$-0.275425\pi$
$662$	7.16536	−	4.63473i	0.278489	−	0.180134i
$663$	21.7036	−	12.5306i	0.842900	−	0.486648i
$664$	−2.33554	−	15.2853i	−0.0906364	−	0.593184i
$665$	−0.843686	−	0.331436i	−0.0327167	−	0.0128525i
$666$	−7.00526	+	13.6870i	−0.271448	+	0.530361i
$667$	9.00461	+	2.41278i	0.348660	+	0.0934231i
$668$	−46.3584	+	4.70205i	−1.79366	+	0.181928i
$669$	−8.50733	+	2.27953i	−0.328912	+	0.0881318i
$670$	18.7123	−	20.7062i	0.722919	−	0.799952i
$671$	−25.2716			−0.975598
$672$	14.8561	+	1.81569i	0.573086	+	0.0700417i
$673$	−46.2436			−1.78256			−0.891280	−	0.453454i	$-0.850192\pi$
$673$	−46.2436			−1.78256			−0.891280	+	0.453454i	$0.850192\pi$
$674$	14.3106	−	15.8355i	0.551222	−	0.609960i
$675$	−2.78116	+	0.745209i	−0.107047	+	0.0286831i
$676$	44.6759	−	4.53139i	1.71830	−	0.174284i
$677$	−7.51860	−	2.01460i	−0.288963	−	0.0774275i	0.111426	−	0.993773i	$-0.464458\pi$
$677$	−7.51860	−	2.01460i	−0.288963	−	0.0774275i	−0.400389	+	0.916345i	$0.631125\pi$
$678$	6.80351	−	13.2928i	0.261287	−	0.510507i
$679$	1.66396	+	11.0638i	0.0638567	+	0.424590i
$680$	33.0335	−	5.04740i	1.26678	−	0.193559i
$681$	−12.9049	+	7.45063i	−0.494516	+	0.285509i
$682$	−2.23782	+	1.44748i	−0.0856905	+	0.0554268i
$683$	−6.36781	−	23.7650i	−0.243658	−	0.909342i	−0.974053	−	0.226318i	$-0.927331\pi$
$683$	−6.36781	−	23.7650i	−0.243658	−	0.909342i	0.730396	−	0.683024i	$-0.239336\pi$
$684$	0.228212	−	0.0866512i	0.00872589	−	0.00331319i
$685$	13.3433	+	13.3433i	0.509822	+	0.509822i
$686$	−25.1201	−	7.41484i	−0.959090	−	0.283100i
$687$	1.21778			0.0464613
$688$	1.40907	−	2.13561i	0.0537204	−	0.0814193i
$689$	−32.9209	+	57.0207i	−1.25419	+	2.17231i
$690$	−5.88444	+	27.4386i	−0.224017	+	1.04457i
$691$	9.14124	−	34.1156i	0.347749	−	1.29782i	−0.541618	−	0.840625i	$-0.682188\pi$
$691$	9.14124	−	34.1156i	0.347749	−	1.29782i	0.889368	−	0.457193i	$-0.151145\pi$
$692$	11.0241	+	1.78718i	0.419074	+	0.0679383i
$693$	6.34107	−	8.58606i	0.240877	−	0.326157i
$694$	−23.3419	−	11.9468i	−0.886048	−	0.453496i
$695$	33.7700	−	19.4971i	1.28097	−	0.739568i
$696$	−1.49847	−	3.41566i	−0.0567995	−	0.129470i
$697$	−26.9123	−	15.5378i	−1.01938	−	0.588538i
$698$	41.4045	−	2.09442i	1.56718	−	0.0792748i
$699$	−6.58159	+	6.58159i	−0.248938	+	0.248938i
$700$	−14.6704	−	4.11136i	−0.554490	−	0.155395i
$701$	10.4951	+	10.4951i	0.396393	+	0.396393i	0.876959	−	0.480566i	$-0.159569\pi$
$701$	10.4951	+	10.4951i	0.396393	+	0.396393i	−0.480566	+	0.876959i	$0.659569\pi$
$702$	5.64580	−	6.24741i	0.213087	−	0.235793i
$703$	−0.663497	+	1.14921i	−0.0250243	+	0.0433433i
$704$	−27.2579	+	17.2815i	−1.02732	+	0.651322i
$705$	−2.31896	−	4.01655i	−0.0873370	−	0.151272i
$706$	7.76749	+	24.0547i	0.292333	+	0.905309i
$707$	−39.4417	+	17.1931i	−1.48336	+	0.646614i
$708$	5.66171	−	4.08209i	0.212780	−	0.153415i
$709$	−21.0176	−	5.63166i	−0.789334	−	0.211501i	−0.158438	−	0.987369i	$-0.550646\pi$
$709$	−21.0176	−	5.63166i	−0.789334	−	0.211501i	−0.630896	+	0.775867i	$0.717313\pi$
$710$	−2.04225	−	3.15735i	−0.0766444	−	0.118493i
$711$	−1.79696	−	1.03748i	−0.0673914	−	0.0389084i
$712$	10.9760	+	1.21420i	0.411342	+	0.0455042i
$713$		−	3.30222i		−	0.123669i
$714$	11.8043	−	10.4248i	0.441766	−	0.390138i
$715$	47.6783	−	47.6783i	1.78307	−	1.78307i
$716$	−6.72271	−	17.7055i	−0.251240	−	0.661685i
$717$	14.4513	−	3.87222i	0.539695	−	0.144611i
$718$	−3.90126	+	18.1913i	−0.145594	+	0.678892i
$719$	−9.03014	−	15.6407i	−0.336767	−	0.583298i	0.647055	−	0.762443i	$-0.276000\pi$
$719$	−9.03014	−	15.6407i	−0.336767	−	0.583298i	−0.983823	+	0.179145i	$0.942667\pi$
$720$	10.0410	−	5.02450i	0.374208	−	0.187252i
$721$	13.3412	+	16.7404i	0.496853	+	0.623446i
$722$	−25.5500	+	8.25034i	−0.950871	+	0.307046i
$723$	2.80975	−	10.4861i	0.104496	−	0.389983i
$724$	−23.4148	−	19.1024i	−0.870205	−	0.709934i
$725$	0.982721	+	3.66756i	0.0364973	+	0.136210i
$726$	0.376923	+	7.45138i	0.0139889	+	0.276547i
$727$		−	33.1802i		−	1.23059i	−0.788298	−	0.615294i	$-0.789037\pi$
$727$		−	33.1802i		−	1.23059i	0.788298	−	0.615294i	$-0.210963\pi$
$728$	42.5552	−	13.2059i	1.57720	−	0.489443i
$729$		−	1.00000i		−	0.0370370i
$730$	37.5458	−	1.89923i	1.38963	−	0.0702936i
$731$	−0.696808	−	2.60052i	−0.0257724	−	0.0961837i
$732$	−12.4644	+	1.26424i	−0.460696	+	0.0467275i
$733$	12.6878	−	47.3517i	0.468636	−	1.74897i	−0.175907	−	0.984407i	$-0.556286\pi$
$733$	12.6878	−	47.3517i	0.468636	−	1.74897i	0.644543	−	0.764568i	$-0.277048\pi$
$734$	7.44579	+	23.0584i	0.274829	+	0.851101i
$735$	−18.7798	+	5.77955i	−0.692703	+	0.213182i
$736$	0.363634	−	39.9877i	0.0134037	−	1.47396i
$737$	14.1815	+	24.5631i	0.522382	+	0.904792i
$738$	−10.2092	−	2.18945i	−0.375807	−	0.0805949i
$739$	0.794640	−	0.212923i	0.0292313	−	0.00783251i	−0.244174	−	0.969731i	$-0.578517\pi$
$739$	0.794640	−	0.212923i	0.0292313	−	0.00783251i	0.273405	+	0.961899i	$0.411850\pi$
$740$	−25.0284	+	55.6689i	−0.920062	+	2.04643i
$741$	0.513880	−	0.513880i	0.0188779	−	0.0188779i
$742$	−13.1637	+	39.2255i	−0.483254	+	1.44001i
$743$			53.5264i			1.96369i	0.189673	+	0.981847i	$0.439257\pi$
$743$			53.5264i			1.96369i	−0.189673	+	0.981847i	$0.560743\pi$
$744$	−1.03132	+	0.825870i	−0.0378100	+	0.0302779i
$745$	46.1931	+	26.6696i	1.69238	+	0.977099i
$746$	31.4261	−	20.3272i	1.15059	−	0.744231i
$747$	−5.28061	−	1.41493i	−0.193207	−	0.0517697i
$748$	−5.43461	+	33.5231i	−0.198709	+	1.22573i
$749$	−2.37538	+	21.0212i	−0.0867944	+	0.768097i
$750$	8.01136	−	2.58695i	0.292534	−	0.0944621i
$751$	20.2705	+	35.1096i	0.739682	+	1.28117i	0.952639	+	0.304104i	$0.0983572\pi$
$751$	20.2705	+	35.1096i	0.739682	+	1.28117i	−0.212957	+	0.977062i	$0.568309\pi$
$752$	4.38648	+	4.94353i	0.159958	+	0.180272i
$753$	13.6301	−	23.6080i	0.496707	−	0.860322i
$754$	−8.23857	−	7.44522i	−0.300031	−	0.271139i
$755$	−17.4438	−	17.4438i	−0.634845	−	0.634845i
$756$	2.69800	−	4.55201i	0.0981253	−	0.165555i
$757$	9.66498	−	9.66498i	0.351280	−	0.351280i	−0.509306	−	0.860586i	$-0.670098\pi$
$757$	9.66498	−	9.66498i	0.351280	−	0.351280i	0.860586	+	0.509306i	$0.170098\pi$
$758$	−0.973213	−	19.2394i	−0.0353487	−	0.698808i
$759$	−24.6984	−	14.2596i	−0.896495	−	0.517592i
$760$	0.887398	−	0.389307i	0.0321893	−	0.0141217i
$761$	4.82572	−	2.78613i	0.174932	−	0.100997i	−0.409977	−	0.912096i	$-0.634463\pi$
$761$	4.82572	−	2.78613i	0.174932	−	0.100997i	0.584909	+	0.811099i	$0.301130\pi$
$762$	14.0881	−	27.5255i	0.510357	−	0.997144i
$763$	20.8603	+	47.8544i	0.755193	+	1.73244i
$764$	5.85355	−	4.22041i	0.211774	−	0.152689i
$765$	3.05786	−	11.4121i	0.110557	−	0.412605i
$766$	−23.1975	−	4.97490i	−0.838160	−	0.179750i
$767$	10.3899	−	17.9958i	0.375157	−	0.649791i
$768$	−12.5795	+	9.88715i	−0.453924	+	0.356772i
$769$	−17.2011			−0.620288			−0.310144	−	0.950690i	$-0.600377\pi$
$769$	−17.2011			−0.620288			−0.310144	+	0.950690i	$0.600377\pi$
$770$	23.4181	−	35.3123i	0.843930	−	1.27257i
$771$	−12.9211	−	12.9211i	−0.465341	−	0.465341i
$772$	9.32171	+	4.19099i	0.335496	+	0.150837i
$773$	−6.68892	−	24.9634i	−0.240584	−	0.897870i	−0.975552	−	0.219769i	$-0.929470\pi$
$773$	−6.68892	−	24.9634i	−0.240584	−	0.897870i	0.734968	−	0.678101i	$-0.237197\pi$
$774$	−0.491296	−	0.759551i	−0.0176593	−	0.0273015i
$775$	1.16480	−	0.672495i	0.0418407	−	0.0241567i
$776$	−9.63793	−	7.08303i	−0.345982	−	0.254266i
$777$	4.27804	+	28.4451i	0.153474	+	1.02046i
$778$	−19.6761	−	10.0706i	−0.705421	−	0.361048i
$779$	−0.870441	−	0.233234i	−0.0311868	−	0.00835647i
$780$	21.1306	−	25.9009i	0.756597	−	0.927402i
$781$	3.69126	−	0.989070i	0.132084	−	0.0353917i
$782$	−31.2193	−	28.2130i	−1.11640	−	1.00889i
$783$	−1.31872			−0.0471272
$784$	24.5626	−	13.4416i	0.877237	−	0.480057i
$785$	−25.0216			−0.893061
$786$	13.4359	+	12.1421i	0.479244	+	0.433094i
$787$	30.4259	−	8.15258i	1.08456	−	0.290608i	0.328100	−	0.944643i	$-0.393592\pi$
$787$	30.4259	−	8.15258i	1.08456	−	0.290608i	0.756465	+	0.654035i	$0.226925\pi$
$788$	−2.91431	−	2.37756i	−0.103818	−	0.0846972i
$789$	3.20654	+	0.859189i	0.114156	+	0.0305879i
$790$	−7.33237	−	3.75284i	−0.260874	−	0.133520i
$791$	−4.15483	−	27.6259i	−0.147729	−	0.982264i
$792$	1.72352	+	11.2798i	0.0612425	+	0.400812i
$793$	−32.3011	+	18.6490i	−1.14705	+	0.662247i
$794$	−1.06626	−	1.64846i	−0.0378403	−	0.0585015i
$795$	8.03373	+	29.9823i	0.284927	+	1.06336i
$796$	16.7961	−	37.3583i	0.595322	−	1.32413i
$797$	34.4032	+	34.4032i	1.21862	+	1.21862i	0.968114	+	0.250511i	$0.0805986\pi$
$797$	34.4032	+	34.4032i	1.21862	+	1.21862i	0.250511	+	0.968114i	$0.419401\pi$
$798$	0.252402	−	0.380598i	0.00893493	−	0.0134730i
$799$	6.95437			0.246028
$800$	14.1789	−	8.01519i	0.501301	−	0.283380i
$801$	1.95213	−	3.38120i	0.0689753	−	0.119469i
$802$	18.1234	+	3.88671i	0.639959	+	0.137244i
$803$	−9.88836	+	36.9039i	−0.348953	+	1.30231i
$804$	8.22335	+	11.4055i	0.290015	+	0.402240i
$805$	20.9789	+	48.1264i	0.739409	+	1.69623i
$806$	−1.79213	+	3.50150i	−0.0631251	+	0.123335i
$807$	−14.6545	+	8.46079i	−0.515864	+	0.297834i
$808$	16.7179	−	42.8512i	0.588133	−	1.50750i
$809$	−24.6954	−	14.2579i	−0.868245	−	0.501282i	−0.00148058	−	0.999999i	$-0.500471\pi$
$809$	−24.6954	−	14.2579i	−0.868245	−	0.501282i	−0.866765	+	0.498717i	$0.833805\pi$
$810$	−0.200548	−	3.96463i	−0.00704654	−	0.139303i
$811$	7.72704	−	7.72704i	0.271333	−	0.271333i	−0.558304	−	0.829637i	$-0.688548\pi$
$811$	7.72704	−	7.72704i	0.271333	−	0.271333i	0.829637	+	0.558304i	$0.188548\pi$
$812$	−6.00282	−	3.55790i	−0.210658	−	0.124858i
$813$	11.3546	+	11.3546i	0.398223	+	0.398223i
$814$	−46.0216	−	41.5898i	−1.61305	−	1.45772i
$815$	28.5287	−	49.4132i	0.999318	−	1.73087i
$816$	−1.00341	+	16.8060i	−0.0351264	+	0.588329i
$817$	−0.0390356	−	0.0676117i	−0.00136568	−	0.00236543i
$818$	3.00188	−	0.969337i	0.104958	−	0.0338921i
$819$	1.76886	−	15.6537i	0.0618090	−	0.546985i
$820$	−40.9150	−	6.63294i	−1.42881	−	0.231632i
$821$	13.8872	+	3.72105i	0.484665	+	0.129866i	0.492874	−	0.870101i	$-0.335946\pi$
$821$	13.8872	+	3.72105i	0.484665	+	0.129866i	−0.00820877	+	0.999966i	$0.502613\pi$
$822$	−7.98278	+	5.16346i	−0.278431	+	0.180096i
$823$	−28.1602	−	16.2583i	−0.981602	−	0.566728i	−0.0788485	−	0.996887i	$-0.525124\pi$
$823$	−28.1602	−	16.2583i	−0.981602	−	0.566728i	−0.902753	+	0.430159i	$0.858458\pi$
$824$	−22.7455	−	2.51620i	−0.792379	−	0.0876559i
$825$		−	11.6159i		−	0.404412i
$826$	4.15448	−	12.3796i	0.144553	−	0.430742i
$827$	−0.756749	+	0.756749i	−0.0263147	+	0.0263147i	−0.720142	−	0.693827i	$-0.755923\pi$
$827$	−0.756749	+	0.756749i	−0.0263147	+	0.0263147i	0.693827	+	0.720142i	$0.255923\pi$
$828$	−12.8950	−	5.79753i	−0.448133	−	0.201478i
$829$	53.7061	−	14.3905i	1.86529	−	0.499803i	0.865292	−	0.501268i	$-0.167133\pi$
$829$	53.7061	−	14.3905i	1.86529	−	0.499803i	0.999999	+	0.00146456i	$0.000466185\pi$
$830$	−21.2194	−	4.55068i	−0.736537	−	0.157956i
$831$	7.19095	+	12.4551i	0.249451	+	0.432062i
$832$	−22.0871	+	42.2034i	−0.765731	+	1.46314i
$833$	6.57464	−	28.7200i	0.227798	−	0.995090i
$834$	6.03693	+	18.6954i	0.209042	+	0.647369i
$835$	−16.9262	+	63.1696i	−0.585757	+	2.18607i
$836$	0.0993775	+	0.979783i	0.00343704	+	0.0338865i
$837$	0.120902	+	0.451212i	0.00417898	+	0.0155962i
$838$	−6.13433	+	0.310301i	−0.211907	+	0.0107192i
$839$		−	28.4483i		−	0.982145i	−0.871119	−	0.491073i	$-0.836605\pi$
$839$		−	28.4483i		−	0.982145i	0.871119	−	0.491073i	$-0.163395\pi$
$840$	9.78368	−	18.5881i	0.337569	−	0.641351i
$841$		−	27.2610i		−	0.940034i
$842$	1.79058	+	35.3979i	0.0617074	+	1.21989i
$843$	3.72913	+	13.9173i	0.128438	+	0.479338i
$844$	6.15464	−	7.54407i	0.211851	−	0.259678i
$845$	16.3119	−	60.8769i	0.561147	−	2.09423i
$846$	2.22360	−	0.718023i	0.0764490	−	0.0246862i
$847$	8.69920	+	10.9157i	0.298908	+	0.375067i
$848$	−19.7937	−	39.5562i	−0.679720	−	1.35836i
$849$	−1.44563	−	2.50390i	−0.0496139	−	0.0859337i
$850$	3.59380	−	16.7576i	0.123266	−	0.574780i
$851$	74.2384	−	19.8921i	2.54486	−	0.681893i
$852$	1.77111	−	0.672486i	0.0606774	−	0.0230390i
$853$	7.54163	−	7.54163i	0.258221	−	0.258221i	−0.566110	−	0.824330i	$-0.691552\pi$
$853$	7.54163	−	7.54163i	0.258221	−	0.258221i	0.824330	+	0.566110i	$0.191552\pi$
$854$	−17.5682	+	15.5150i	−0.601170	+	0.530913i
$855$		−	0.342607i		−	0.0117169i
$856$	−14.1363	−	17.6530i	−0.483170	−	0.603367i
$857$	19.0661	+	11.0078i	0.651285	+	0.376020i	0.788948	−	0.614460i	$-0.210626\pi$
$857$	19.0661	+	11.0078i	0.651285	+	0.376020i	−0.137663	+	0.990479i	$0.543959\pi$
$858$	18.4501	+	28.5241i	0.629875	+	0.973796i
$859$	−13.2707	−	3.55588i	−0.452791	−	0.121325i	0.0252138	−	0.999682i	$-0.491973\pi$
$859$	−13.2707	−	3.55588i	−0.452791	−	0.121325i	−0.478005	+	0.878357i	$0.658640\pi$
$860$	−2.10014	−	2.91281i	−0.0716140	−	0.0993260i
$861$	−17.9067	+	7.80573i	−0.610257	+	0.266018i
$862$	4.14410	+	12.8336i	0.141148	+	0.437114i
$863$	9.00925	+	15.6045i	0.306679	+	0.531183i	0.977634	−	0.210315i	$-0.0674490\pi$
$863$	9.00925	+	15.6045i	0.306679	+	0.531183i	−0.670955	+	0.741498i	$0.734116\pi$
$864$	1.41435	+	5.47719i	0.0481173	+	0.186338i
$865$	7.83718	−	13.5744i	0.266472	−	0.461543i
$866$	−12.7412	+	14.0988i	−0.432962	+	0.479098i
$867$	0.506023	+	0.506023i	0.0171854	+	0.0171854i
$868$	−0.667024	+	2.38012i	−0.0226403	+	0.0807864i
$869$	5.91920	−	5.91920i	0.200795	−	0.200795i
$870$	−5.22824	+	0.264467i	−0.177254	+	0.00896625i
$871$	36.2524	+	20.9303i	1.22837	+	0.709198i
$872$	−51.9911	−	20.2837i	−1.76064	−	0.686892i
$873$	−3.66221	+	2.11438i	−0.123947	+	0.0715609i
$874$	−1.08621	−	0.555943i	−0.0367417	−	0.0188051i
$875$	9.35670	−	12.6693i	0.316314	−	0.428302i
$876$	−3.03095	+	18.6963i	−0.102406	+	0.631689i
$877$	−12.7599	+	47.6205i	−0.430871	+	1.60803i	0.319889	+	0.947455i	$0.396354\pi$
$877$	−12.7599	+	47.6205i	−0.430871	+	1.60803i	−0.750759	+	0.660576i	$0.770312\pi$
$878$	−3.97665	+	18.5428i	−0.134205	+	0.625788i
$879$	−1.55814	+	2.69879i	−0.0525549	+	0.0910278i
$880$	9.09526	+	44.3748i	0.306601	+	1.49587i
$881$	10.0345			0.338069			0.169035	−	0.985610i	$-0.445935\pi$
$881$	10.0345			0.338069			0.169035	+	0.985610i	$0.445935\pi$
$882$	−0.863095	−	9.86180i	−0.0290619	−	0.332064i
$883$	−0.809865	−	0.809865i	−0.0272541	−	0.0272541i	0.693348	−	0.720603i	$-0.256135\pi$
$883$	−0.809865	−	0.809865i	−0.0272541	−	0.0272541i	−0.720603	+	0.693348i	$0.756135\pi$
$884$	17.7919	+	46.8583i	0.598408	+	1.57602i
$885$	−2.53546	−	9.46245i	−0.0852284	−	0.318077i
$886$	−28.5060	+	18.4384i	−0.957679	+	0.619451i
$887$	13.2417	−	7.64511i	0.444614	−	0.256698i	−0.260939	−	0.965355i	$-0.584032\pi$
$887$	13.2417	−	7.64511i	0.444614	−	0.256698i	0.705553	+	0.708658i	$0.250699\pi$
$888$	−24.7792	−	18.2105i	−0.831535	−	0.611105i
$889$	−8.60343	−	57.2051i	−0.288550	−	1.91860i
$890$	7.06140	−	13.7967i	0.236699	−	0.462466i
$891$	3.89684	+	1.04416i	0.130549	+	0.0349806i
$892$	−1.77752	−	17.5250i	−0.0595159	−	0.586779i
$893$	0.194794	−	0.0521950i	0.00651855	−	0.00174664i
$894$	−18.0179	+	19.9379i	−0.602610	+	0.666824i
$895$	−26.5807			−0.888494
$896$	−8.33930	+	28.7481i	−0.278596	+	0.960408i
$897$	−42.0913			−1.40539
$898$	−4.53798	+	5.02154i	−0.151434	+	0.167571i
$899$	0.595022	−	0.159436i	0.0198451	−	0.00531748i
$900$	−0.581095	−	5.72914i	−0.0193698	−	0.190971i
$901$	−44.9573	−	12.0463i	−1.49774	−	0.401319i
$902$	19.1920	−	37.4977i	0.639024	−	1.24854i
$903$	−1.57515	−	0.618789i	−0.0524179	−	0.0205920i
$904$	24.0655	+	17.6860i	0.800408	+	0.588229i
$905$	−36.7296	+	21.2058i	−1.22093	+	0.704905i
$906$	10.4359	−	6.75022i	0.346711	−	0.224261i
$907$	5.08829	+	18.9898i	0.168954	+	0.630545i	0.997503	+	0.0706279i	$0.0225003\pi$
$907$	5.08829	+	18.9898i	0.168954	+	0.630545i	−0.828549	+	0.559917i	$0.810833\pi$
$908$	−10.5790	−	27.8617i	−0.351076	−	0.924624i
$909$	−11.4992	−	11.4992i	−0.381405	−	0.381405i
$910$	3.87356	−	62.4160i	0.128407	−	2.06907i
$911$	4.13047			0.136848			0.0684242	−	0.997656i	$-0.478203\pi$
$911$	4.13047			0.136848			0.0684242	+	0.997656i	$0.478203\pi$
$912$	0.0980294	+	0.478274i	0.00324608	+	0.0158372i
$913$	11.0276	−	19.1003i	0.364959	−	0.632127i
$914$	0.645887	−	3.01172i	0.0213641	−	0.0996188i
$915$	−4.55095	+	16.9844i	−0.150450	+	0.561486i
$916$	−0.389754	+	2.40418i	−0.0128778	+	0.0794363i
$917$	33.6656	+	3.80418i	1.11173	+	0.125625i
$918$	5.29872	+	2.71198i	0.174884	+	0.0895087i
$919$	−11.3524	+	6.55428i	−0.374480	+	0.216206i	−0.675414	−	0.737439i	$-0.736035\pi$
$919$	−11.3524	+	6.55428i	−0.374480	+	0.216206i	0.300934	+	0.953645i	$0.402702\pi$
$920$	−52.2867	−	20.3990i	−1.72384	−	0.672535i
$921$	28.0383	+	16.1879i	0.923894	+	0.533411i
$922$	−34.2181	+	1.73090i	−1.12691	+	0.0570041i
$923$	3.98814	−	3.98814i	0.131271	−	0.131271i
$924$	14.9213	+	15.2667i	0.490876	+	0.502237i
$925$	22.1352	+	22.1352i	0.727800	+	0.727800i
$926$	31.8459	−	35.2394i	1.04652	−	1.15804i
$927$	−4.04541	+	7.00686i	−0.132869	+	0.230135i
$928$	7.22287	−	1.86514i	0.237102	−	0.0612261i
$929$	1.33927	+	2.31969i	0.0439401	+	0.0761066i	0.887159	−	0.461464i	$-0.152676\pi$
$929$	1.33927	+	2.31969i	0.0439401	+	0.0761066i	−0.843219	+	0.537570i	$0.819342\pi$
$930$	0.569822	+	1.76464i	0.0186852	+	0.0578650i
$931$	−0.0313960	−	0.853803i	−0.00102896	−	0.0279823i
$932$	−10.8871	−	15.1000i	−0.356618	−	0.494617i
$933$	12.4050	+	3.32391i	0.406122	+	0.108820i
$934$	−2.98398	−	4.61327i	−0.0976387	−	0.150951i
$935$	41.2782	+	23.8320i	1.34994	+	0.779390i
$936$	10.5268	+	13.1456i	0.344081	+	0.429677i
$937$			4.68365i			0.153008i	0.997069	+	0.0765041i	$0.0243758\pi$
$937$			4.68365i			0.153008i	−0.997069	+	0.0765041i	$0.975624\pi$
$938$	24.9387	+	8.36916i	0.814276	+	0.273263i
$939$	−4.70751	+	4.70751i	−0.153624	+	0.153624i
$940$	8.67176	−	3.29264i	0.282842	−	0.107394i
$941$	−47.2809	+	12.6689i	−1.54131	+	0.412994i	−0.926690	−	0.375827i	$-0.877359\pi$
$941$	−47.2809	+	12.6689i	−1.54131	+	0.412994i	−0.614624	+	0.788820i	$0.710692\pi$
$942$	2.64342	−	12.3260i	0.0861273	−	0.401604i
$943$	26.0965	+	45.2004i	0.849817	+	1.47193i
$944$	6.24693	+	12.4840i	0.203320	+	0.406319i
$945$	−4.62856	−	5.80787i	−0.150567	−	0.188930i
$946$	3.47284	−	1.12142i	0.112912	−	0.0364604i
$947$	5.37444	−	20.0577i	0.174646	−	0.651787i	−0.821966	−	0.569537i	$-0.807123\pi$
$947$	5.37444	−	20.0577i	0.174646	−	0.651787i	0.996612	−	0.0822504i	$-0.0262107\pi$
$948$	2.62334	−	3.21557i	0.0852020	−	0.104437i
$949$	14.5942	+	54.4661i	0.473746	+	1.76805i
$950$	−0.0251079	−	0.496358i	−0.000814608	−	0.0161040i
$951$		−	0.428475i		−	0.0138943i
$952$	16.8029	+	26.6409i	0.544585	+	0.863437i
$953$		−	28.5365i		−	0.924389i	−0.886779	−	0.462194i	$-0.847062\pi$
$953$		−	28.5365i		−	0.924389i	0.886779	−	0.462194i	$-0.152938\pi$
$954$	−15.6185	+	0.790048i	−0.505666	+	0.0255788i
$955$	−2.62137	−	9.78307i	−0.0848254	−	0.316573i
$956$	3.01946	+	29.7695i	0.0976564	+	0.962814i
$957$	1.37695	−	5.13884i	0.0445104	−	0.166115i
$958$	−4.62654	−	14.3276i	−0.149477	−	0.462905i
$959$	−6.50339	+	16.5547i	−0.210005	+	0.534578i
$960$	6.70584	+	21.4314i	0.216430	+	0.691695i
$961$	15.3909	+	26.6578i	0.496480	+	0.859929i
$962$	−89.5139	−	19.1970i	−2.88605	−	0.618936i
$963$	−7.72337	+	2.06947i	−0.248882	+	0.0666877i
$964$	19.8027	+	8.90319i	0.637803	+	0.286752i
$965$	10.1431	−	10.1431i	0.326518	−	0.326518i
$966$	−25.9241	+	5.25019i	−0.834096	+	0.168922i
$967$			41.6338i			1.33885i	0.742879	+	0.669426i	$0.233460\pi$
$967$			41.6338i			1.33885i	−0.742879	+	0.669426i	$0.766540\pi$
$968$	−14.8313	−	1.64070i	−0.476697	−	0.0527341i
$969$	0.444899	+	0.256863i	0.0142922	+	0.00825162i
$970$	−14.0953	+	9.11718i	−0.452572	+	0.292735i
$971$	−42.4563	−	11.3761i	−1.36249	−	0.365078i	−0.497759	−	0.867316i	$-0.665843\pi$
$971$	−42.4563	−	11.3761i	−1.36249	−	0.365078i	−0.864729	+	0.502238i	$0.832510\pi$
$972$	1.97423	+	0.320052i	0.0633233	+	0.0102657i
$973$	29.5653	+	21.8349i	0.947820	+	0.699995i
$974$	50.6976	−	16.3708i	1.62446	−	0.524554i
$975$	−8.57187	−	14.8469i	−0.274520	−	0.475482i
$976$	1.49336	−	25.0121i	0.0478012	−	0.800618i
$977$	−24.1014	+	41.7449i	−0.771073	+	1.33554i	0.165903	+	0.986142i	$0.446946\pi$
$977$	−24.1014	+	41.7449i	−0.771073	+	1.33554i	−0.936975	+	0.349395i	$0.886387\pi$
$978$	21.3278	+	19.2740i	0.681987	+	0.616314i
$979$	11.1377	+	11.1377i	0.355961	+	0.355961i
$980$	−5.39962	−	38.9253i	−0.172484	−	1.24342i
$981$	−13.9519	+	13.9519i	−0.445451	+	0.445451i
$982$	2.45412	+	48.5156i	0.0783143	+	1.54819i
$983$	5.80178	+	3.34966i	0.185048	+	0.106838i	0.589662	−	0.807650i	$-0.299261\pi$
$983$	5.80178	+	3.34966i	0.185048	+	0.106838i	−0.404614	+	0.914488i	$0.632594\pi$
$984$	7.58996	−	19.4546i	0.241959	−	0.620190i
$985$	−4.57151	+	2.63937i	−0.145661	+	0.0840972i
$986$	3.57634	−	6.98752i	0.113894	−	0.222528i
$987$	2.59701	−	3.51645i	0.0826637	−	0.111930i
$988$	0.850047	+	1.17898i	0.0270436	+	0.0375085i
$989$	−1.17032	+	4.36768i	−0.0372139	+	0.138884i
$990$	15.6590	+	3.35819i	0.497674	+	0.106730i
$991$	−30.1009	+	52.1363i	−0.956186	+	1.65616i	−0.224557	+	0.974461i	$0.572094\pi$
$991$	−30.1009	+	52.1363i	−0.956186	+	1.65616i	−0.731629	+	0.681703i	$0.761240\pi$
$992$	−1.30038	−	2.30038i	−0.0412870	−	0.0730371i
$993$	6.03420			0.191489
$994$	1.95885	−	2.95376i	0.0621310	−	0.0936875i
$995$	−40.6502	−	40.6502i	−1.28870	−	1.28870i
$996$	4.48347	−	9.97226i	0.142064	−	0.315983i
$997$	11.0995	+	41.4241i	0.351526	+	1.31191i	0.884800	+	0.465971i	$0.154295\pi$
$997$	11.0995	+	41.4241i	0.351526	+	1.31191i	−0.533274	+	0.845943i	$0.679038\pi$
$998$	7.74412	+	11.9725i	0.245136	+	0.378983i
$999$	−9.41557	+	5.43608i	−0.297896	+	0.171990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.10	yes	120
7.2	even	3	inner	336.2.bq.b.205.29	yes	120
16.5	even	4	inner	336.2.bq.b.277.29	yes	120
112.37	even	12	inner	336.2.bq.b.37.10	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.10	✓	120	112.37	even	12	inner
336.2.bq.b.109.10	yes	120	1.1	even	1	trivial
336.2.bq.b.205.29	yes	120	7.2	even	3	inner
336.2.bq.b.277.29	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)

\(f(q)\)	\(=\)	\(q+(-0.948203 + 1.04924i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.201821 - 1.98979i) q^{4} +(-2.71136 - 0.726506i) q^{5} +(0.644330 - 1.25890i) q^{6} +(-0.393486 - 2.61633i) q^{7} +(2.27914 + 1.67497i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.948203 + 1.04924i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.201821 - 1.98979i) q^{4} +(-2.71136 - 0.726506i) q^{5} +(0.644330 - 1.25890i) q^{6} +(-0.393486 - 2.61633i) q^{7} +(2.27914 + 1.67497i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.33320 - 2.15600i) q^{10} +(1.04416 + 3.89684i) q^{11} +(0.709940 + 1.86976i) q^{12} +(4.21026 + 4.21026i) q^{13} +(3.11827 + 2.06795i) q^{14} +2.80700 q^{15} +(-3.91854 + 0.803162i) q^{16} +(-2.10450 + 3.64510i) q^{17} +(-0.296547 + 1.38277i) q^{18} +(-0.0315900 + 0.117895i) q^{19} +(-0.898387 + 5.54166i) q^{20} +(1.05723 + 2.42534i) q^{21} +(-5.07881 - 2.59943i) q^{22} +(6.12209 - 3.53459i) q^{23} +(-2.63499 - 1.02801i) q^{24} +(2.49352 + 1.43963i) q^{25} +(-8.40977 + 0.425402i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-5.12653 + 1.31098i) q^{28} +(0.932475 + 0.932475i) q^{29} +(-2.66161 + 2.94523i) q^{30} +(0.233565 - 0.404546i) q^{31} +(2.87286 - 4.87306i) q^{32} +(-2.01716 - 3.49382i) q^{33} +(-1.82910 - 5.66442i) q^{34} +(-0.833897 + 7.37967i) q^{35} +(-1.16968 - 1.62230i) q^{36} +(10.5017 + 2.81392i) q^{37} +(-0.0937472 - 0.144934i) q^{38} +(-5.15649 - 2.97710i) q^{39} +(-4.96269 - 6.19724i) q^{40} +7.38316i q^{41} +(-3.54724 - 1.19042i) q^{42} +(-0.452297 + 0.452297i) q^{43} +(7.54317 - 2.86412i) q^{44} +(-2.71136 + 0.726506i) q^{45} +(-2.09634 + 9.77507i) q^{46} +(-0.826133 - 1.43090i) q^{47} +(3.57714 - 1.78999i) q^{48} +(-6.69034 + 2.05897i) q^{49} +(-3.87489 + 1.25124i) q^{50} +(1.08937 - 4.06558i) q^{51} +(7.52782 - 9.22725i) q^{52} +(2.86203 + 10.6812i) q^{53} +(-0.0714456 - 1.41241i) q^{54} -11.3243i q^{55} +(3.48545 - 6.62205i) q^{56} -0.122054i q^{57} +(-1.86257 + 0.0942167i) q^{58} +(-0.903261 - 3.37102i) q^{59} +(-0.566511 - 5.58535i) q^{60} +(-1.62128 + 6.05071i) q^{61} +(0.203000 + 0.628658i) q^{62} +(-1.64893 - 2.06906i) q^{63} +(2.38897 + 7.63497i) q^{64} +(-8.35674 - 14.4743i) q^{65} +(5.57853 + 1.19636i) q^{66} +(6.79088 - 1.81961i) q^{67} +(7.67771 + 3.45185i) q^{68} +(-4.99866 + 4.99866i) q^{69} +(-6.95236 - 7.87239i) q^{70} -0.947244i q^{71} +(2.81128 + 0.310994i) q^{72} +(8.20143 + 4.73510i) q^{73} +(-12.9102 + 8.35067i) q^{74} +(-2.78116 - 0.745209i) q^{75} +(0.240963 + 0.0390637i) q^{76} +(9.78456 - 4.26521i) q^{77} +(8.01311 - 2.58751i) q^{78} +(-1.03748 - 1.79696i) q^{79} +(11.2081 + 0.669181i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-7.74673 - 7.00074i) q^{82} +(-3.86567 - 3.86567i) q^{83} +(4.61254 - 2.59316i) q^{84} +(8.35422 - 8.35422i) q^{85} +(-0.0456998 - 0.903438i) q^{86} +(-1.14204 - 0.659359i) q^{87} +(-4.14731 + 10.6304i) q^{88} +(3.38120 - 1.95213i) q^{89} +(1.80864 - 3.53375i) q^{90} +(9.35874 - 12.6721i) q^{91} +(-8.26866 - 11.4683i) q^{92} +(-0.120902 + 0.451212i) q^{93} +(2.28471 + 0.489974i) q^{94} +(0.171303 - 0.296706i) q^{95} +(-1.51373 + 5.45056i) q^{96} -4.22876 q^{97} +(4.18344 - 8.97212i) q^{98} +(2.85269 + 2.85269i) 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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