LMFDB - Embedded newform 819.2.et.c.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.3
Character	$\chi$	$=$	819.145
Dual form			819.2.et.c.514.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +O(q^{10})$	\(q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +(-0.466517 + 0.808031i) q^{10} +(-6.35142 + 1.70186i) q^{11} +(-3.43957 - 1.08136i) q^{13} +(-1.54138 + 2.11138i) q^{14} +0.904452 q^{16} -3.73354 q^{17} +(-0.325628 + 1.21526i) q^{19} +(0.250210 + 0.933796i) q^{20} +(3.24847 - 5.62651i) q^{22} +0.233411i q^{23} +(-3.55787 + 2.05414i) q^{25} +(3.15860 - 1.64759i) q^{26} +(0.417609 + 2.67619i) q^{28} +(2.32457 + 4.02628i) q^{29} +(-1.96967 + 7.35090i) q^{31} +(3.59324 - 3.59324i) q^{32} +(2.60848 - 2.60848i) q^{34} +(2.28473 - 1.01099i) q^{35} +(3.55684 + 3.55684i) q^{37} +(-0.621551 - 1.07656i) q^{38} +(-2.44328 - 1.41063i) q^{40} +(-2.49056 + 9.29490i) q^{41} +(-10.4062 - 6.00801i) q^{43} +(-1.74227 - 6.50224i) q^{44} +(-0.163075 - 0.163075i) q^{46} +(0.563747 + 2.10393i) q^{47} +(6.66720 - 2.13271i) q^{49} +(1.05060 - 3.92089i) q^{50} +(1.10703 - 3.52125i) q^{52} +(-2.04084 - 3.53484i) q^{53} +(-5.37742 + 3.10465i) q^{55} +(-6.38428 - 4.66074i) q^{56} +(-4.43709 - 1.18891i) q^{58} +(5.27715 - 5.27715i) q^{59} +(-2.12633 + 1.22764i) q^{61} +(-3.75966 - 6.51191i) q^{62} +6.82982i q^{64} +(-3.40165 - 0.145692i) q^{65} +(-2.63222 - 9.82360i) q^{67} -3.82220i q^{68} +(-0.889915 + 2.30259i) q^{70} +(-0.433350 - 1.61728i) q^{71} +(-7.85180 - 2.10388i) q^{73} -4.97005 q^{74} +(-1.24412 - 0.333360i) q^{76} +(-15.9091 + 7.03974i) q^{77} +(-0.942160 + 1.63187i) q^{79} +(0.824984 - 0.221054i) q^{80} +(-4.75393 - 8.23404i) q^{82} +(9.95023 + 9.95023i) q^{83} +(-3.40550 + 0.912500i) q^{85} +(11.4680 - 3.07283i) q^{86} +(17.0131 + 9.82254i) q^{88} +(2.88517 - 2.88517i) q^{89} +(-9.43255 - 1.42371i) q^{91} -0.238954 q^{92} +(-1.86380 - 1.07607i) q^{94} +1.18807i q^{95} +(2.41702 - 0.647638i) q^{97} +(-3.16807 + 6.14815i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.698661	+	0.698661i	−0.494028	+	0.494028i	−0.909573	−	0.415545i	$-0.863591\pi$
$2$	−0.698661	+	0.698661i	−0.494028	+	0.494028i	0.415545	+	0.909573i	$0.363591\pi$
$3$		0			0
$3$		0			0
$4$			1.02375i			0.511873i
$5$	0.912136	−	0.244406i	0.407920	−	0.109302i	−0.0490235	−	0.998798i	$-0.515611\pi$
$5$	0.912136	−	0.244406i	0.407920	−	0.109302i	0.456943	+	0.889496i	$0.348944\pi$
$6$		0			0
$7$	2.61412	−	0.407922i	0.988043	−	0.154180i
$7$	2.61412	−	0.407922i	0.988043	−	0.154180i
$8$	−2.11257	−	2.11257i	−0.746907	−	0.746907i
$9$		0			0
$10$	−0.466517	+	0.808031i	−0.147526	+	0.255522i
$11$	−6.35142	+	1.70186i	−1.91503	+	0.513130i	−0.923427	+	0.383774i	$0.874624\pi$
$11$	−6.35142	+	1.70186i	−1.91503	+	0.513130i	−0.991598	+	0.129356i	$0.958709\pi$
$12$		0			0
$13$	−3.43957	−	1.08136i	−0.953966	−	0.299914i
$13$	−3.43957	−	1.08136i	−0.953966	−	0.299914i
$14$	−1.54138	+	2.11138i	−0.411951	+	0.564290i
$15$		0			0
$16$	0.904452			0.226113
$17$	−3.73354			−0.905516			−0.452758	−	0.891633i	$-0.649560\pi$
$17$	−3.73354			−0.905516			−0.452758	+	0.891633i	$0.649560\pi$
$18$		0			0
$19$	−0.325628	+	1.21526i	−0.0747041	+	0.278800i	−0.993166	−	0.116710i	$-0.962765\pi$
$19$	−0.325628	+	1.21526i	−0.0747041	+	0.278800i	0.918462	+	0.395509i	$0.129432\pi$
$20$	0.250210	+	0.933796i	0.0559486	+	0.208803i
$21$		0			0
$22$	3.24847	−	5.62651i	0.692576	−	1.19958i
$23$			0.233411i			0.0486696i	0.999704	+	0.0243348i	$0.00774678\pi$
$23$			0.233411i			0.0486696i	−0.999704	+	0.0243348i	$0.992253\pi$
$24$		0			0
$25$	−3.55787	+	2.05414i	−0.711574	+	0.410827i
$26$	3.15860	−	1.64759i	0.619452	−	0.323120i
$27$		0			0
$28$	0.417609	+	2.67619i	0.0789207	+	0.505752i
$29$	2.32457	+	4.02628i	0.431662	+	0.747661i	0.997017	−	0.0771873i	$-0.0245939\pi$
$29$	2.32457	+	4.02628i	0.431662	+	0.747661i	−0.565354	+	0.824848i	$0.691261\pi$
$30$		0			0
$31$	−1.96967	+	7.35090i	−0.353763	+	1.32026i	0.528272	+	0.849075i	$0.322840\pi$
$31$	−1.96967	+	7.35090i	−0.353763	+	1.32026i	−0.882034	+	0.471185i	$0.843826\pi$
$32$	3.59324	−	3.59324i	0.635201	−	0.635201i
$33$		0			0
$34$	2.60848	−	2.60848i	0.447350	−	0.447350i
$35$	2.28473	−	1.01099i	0.386190	−	0.170888i
$36$		0			0
$37$	3.55684	+	3.55684i	0.584741	+	0.584741i	0.936202	−	0.351461i	$-0.114315\pi$
$37$	3.55684	+	3.55684i	0.584741	+	0.584741i	−0.351461	+	0.936202i	$0.614315\pi$
$38$	−0.621551	−	1.07656i	−0.100829	−	0.174641i
$39$		0			0
$40$	−2.44328	−	1.41063i	−0.386317	−	0.223040i
$41$	−2.49056	+	9.29490i	−0.388960	+	1.45162i	0.442868	+	0.896587i	$0.353961\pi$
$41$	−2.49056	+	9.29490i	−0.388960	+	1.45162i	−0.831828	+	0.555033i	$0.812706\pi$
$42$		0			0
$43$	−10.4062	−	6.00801i	−1.58693	−	0.916213i	−0.993809	−	0.111099i	$-0.964563\pi$
$43$	−10.4062	−	6.00801i	−1.58693	−	0.916213i	−0.593119	−	0.805115i	$-0.702104\pi$
$44$	−1.74227	−	6.50224i	−0.262657	−	0.980250i
$45$		0			0
$46$	−0.163075	−	0.163075i	−0.0240442	−	0.0240442i
$47$	0.563747	+	2.10393i	0.0822309	+	0.306890i	0.994775	−	0.102087i	$-0.0325521\pi$
$47$	0.563747	+	2.10393i	0.0822309	+	0.306890i	−0.912545	+	0.408977i	$0.865885\pi$
$48$		0			0
$49$	6.66720	−	2.13271i	0.952457	−	0.304673i
$50$	1.05060	−	3.92089i	0.148577	−	0.554497i
$51$		0			0
$52$	1.10703	−	3.52125i	0.153518	−	0.488309i
$53$	−2.04084	−	3.53484i	−0.280331	−	0.485548i	0.691135	−	0.722726i	$-0.257111\pi$
$53$	−2.04084	−	3.53484i	−0.280331	−	0.485548i	−0.971466	+	0.237178i	$0.923778\pi$
$54$		0			0
$55$	−5.37742	+	3.10465i	−0.725091	+	0.418631i
$56$	−6.38428	−	4.66074i	−0.853135	−	0.622818i
$57$		0			0
$58$	−4.43709	−	1.18891i	−0.582618	−	0.156112i
$59$	5.27715	−	5.27715i	0.687026	−	0.687026i	−0.274548	−	0.961573i	$-0.588528\pi$
$59$	5.27715	−	5.27715i	0.687026	−	0.687026i	0.961573	+	0.274548i	$0.0885281\pi$
$60$		0			0
$61$	−2.12633	+	1.22764i	−0.272248	+	0.157183i	−0.629909	−	0.776669i	$-0.716908\pi$
$61$	−2.12633	+	1.22764i	−0.272248	+	0.157183i	0.357661	+	0.933852i	$0.383574\pi$
$62$	−3.75966	−	6.51191i	−0.477477	−	0.827014i
$63$		0			0
$64$			6.82982i			0.853727i
$65$	−3.40165	−	0.145692i	−0.421923	−	0.0180708i
$66$		0			0
$67$	−2.63222	−	9.82360i	−0.321577	−	1.20014i	−0.917708	−	0.397256i	$-0.869963\pi$
$67$	−2.63222	−	9.82360i	−0.321577	−	1.20014i	0.596131	−	0.802888i	$-0.296704\pi$
$68$		−	3.82220i		−	0.463509i
$69$		0			0
$70$	−0.889915	+	2.30259i	−0.106365	+	0.275212i
$71$	−0.433350	−	1.61728i	−0.0514292	−	0.191936i	0.935432	−	0.353507i	$-0.115011\pi$
$71$	−0.433350	−	1.61728i	−0.0514292	−	0.191936i	−0.986861	+	0.161570i	$0.948344\pi$
$72$		0			0
$73$	−7.85180	−	2.10388i	−0.918984	−	0.246241i	−0.231833	−	0.972756i	$-0.574472\pi$
$73$	−7.85180	−	2.10388i	−0.918984	−	0.246241i	−0.687151	+	0.726515i	$0.741139\pi$
$74$	−4.97005			−0.577757
$75$		0			0
$76$	−1.24412	−	0.333360i	−0.142710	−	0.0382390i
$77$	−15.9091	+	7.03974i	−1.81301	+	0.802253i
$78$		0			0
$79$	−0.942160	+	1.63187i	−0.106001	+	0.183600i	−0.914147	−	0.405383i	$-0.867138\pi$
$79$	−0.942160	+	1.63187i	−0.106001	+	0.183600i	0.808146	+	0.588983i	$0.200471\pi$
$80$	0.824984	−	0.221054i	0.0922360	−	0.0247146i
$81$		0			0
$82$	−4.75393	−	8.23404i	−0.524983	−	0.909298i
$83$	9.95023	+	9.95023i	1.09218	+	1.09218i	0.995296	+	0.0968835i	$0.0308874\pi$
$83$	9.95023	+	9.95023i	1.09218	+	1.09218i	0.0968835	+	0.995296i	$0.469113\pi$
$84$		0			0
$85$	−3.40550	+	0.912500i	−0.369378	+	0.0989745i
$86$	11.4680	−	3.07283i	1.23662	−	0.331352i
$87$		0			0
$88$	17.0131	+	9.82254i	1.81361	+	1.04709i
$89$	2.88517	−	2.88517i	0.305827	−	0.305827i	−0.537461	−	0.843288i	$-0.680617\pi$
$89$	2.88517	−	2.88517i	0.305827	−	0.305827i	0.843288	+	0.537461i	$0.180617\pi$
$90$		0			0
$91$	−9.43255	−	1.42371i	−0.988800	−	0.149246i
$92$	−0.238954			−0.0249127
$93$		0			0
$94$	−1.86380	−	1.07607i	−0.192237	−	0.110988i
$95$			1.18807i			0.121893i
$96$		0			0
$97$	2.41702	−	0.647638i	0.245411	−	0.0657576i	−0.134017	−	0.990979i	$-0.542788\pi$
$97$	2.41702	−	0.647638i	0.245411	−	0.0657576i	0.379428	+	0.925221i	$0.376121\pi$
$98$	−3.16807	+	6.14815i	−0.320023	+	0.621057i
$99$		0			0
$100$	−2.10291	−	3.64235i	−0.210291	−	0.364235i
$101$	−1.20221	+	2.08228i	−0.119624	+	0.207195i	−0.919619	−	0.392812i	$-0.871502\pi$
$101$	−1.20221	+	2.08228i	−0.119624	+	0.207195i	0.799995	+	0.600007i	$0.204836\pi$
$102$		0			0
$103$	1.45067	−	2.51263i	0.142938	−	0.247577i	−0.785663	−	0.618654i	$-0.787678\pi$
$103$	1.45067	−	2.51263i	0.142938	−	0.247577i	0.928602	+	0.371077i	$0.121012\pi$
$104$	4.98191	+	9.55080i	0.488516	+	0.936533i
$105$		0			0
$106$	3.89551	+	1.04380i	0.378366	+	0.101383i
$107$	11.0841			1.07154			0.535770	−	0.844364i	$-0.320021\pi$
$107$	11.0841			1.07154			0.535770	+	0.844364i	$0.320021\pi$
$108$		0			0
$109$	7.01612	+	1.87996i	0.672023	+	0.180068i	0.578666	−	0.815565i	$-0.303574\pi$
$109$	7.01612	+	1.87996i	0.672023	+	0.180068i	0.0933569	+	0.995633i	$0.470240\pi$
$110$	1.58789	−	5.92609i	0.151399	−	0.565031i
$111$		0			0
$112$	2.36434	−	0.368946i	0.223409	−	0.0348621i
$113$	0.604359	−	1.04678i	0.0568533	−	0.0984728i	−0.836198	−	0.548428i	$-0.815227\pi$
$113$	0.604359	−	1.04678i	0.0568533	−	0.0984728i	0.893051	+	0.449955i	$0.148560\pi$
$114$		0			0
$115$	0.0570472	+	0.212903i	0.00531968	+	0.0198533i
$116$	−4.12188	+	2.37977i	−0.382707	+	0.220956i
$117$		0			0
$118$			7.37387i			0.678820i
$119$	−9.75990	+	1.52299i	−0.894689	+	0.139613i
$120$		0			0
$121$	27.9179	−	16.1184i	2.53799	−	1.46531i
$122$	0.627881	−	2.34328i	0.0568457	−	0.212151i
$123$		0			0
$124$	−7.52545	−	2.01644i	−0.675806	−	0.181082i
$125$	−6.08187	+	6.08187i	−0.543979	+	0.543979i
$126$		0			0
$127$	−8.44594	+	4.87627i	−0.749456	+	0.432699i	−0.825497	−	0.564406i	$-0.809105\pi$
$127$	−8.44594	+	4.87627i	−0.749456	+	0.432699i	0.0760413	+	0.997105i	$0.475772\pi$
$128$	2.41475	+	2.41475i	0.213436	+	0.213436i
$129$		0			0
$130$	2.47839	−	2.27481i	0.217369	−	0.199514i
$131$	−14.7264	−	8.50232i	−1.28666	−	0.742851i	−0.308599	−	0.951192i	$-0.599860\pi$
$131$	−14.7264	−	8.50232i	−1.28666	−	0.742851i	−0.978056	+	0.208341i	$0.933194\pi$
$132$		0			0
$133$	−0.355497	+	3.30966i	−0.0308255	+	0.286984i
$134$	8.70239	+	5.02433i	0.751772	+	0.434036i
$135$		0			0
$136$	7.88737	+	7.88737i	0.676337	+	0.676337i
$137$	3.39152	+	3.39152i	0.289757	+	0.289757i	0.836984	−	0.547227i	$-0.184317\pi$
$137$	3.39152	+	3.39152i	0.289757	+	0.289757i	−0.547227	+	0.836984i	$0.684317\pi$
$138$		0			0
$139$	−6.97771	−	4.02859i	−0.591842	−	0.341700i	0.173984	−	0.984749i	$-0.444336\pi$
$139$	−6.97771	−	4.02859i	−0.591842	−	0.341700i	−0.765826	+	0.643048i	$0.777669\pi$
$140$	1.03499	+	2.33898i	0.0874729	+	0.197680i
$141$		0			0
$142$	1.43270	+	0.827168i	0.120229	+	0.0694144i
$143$	23.6865	+	1.01448i	1.98076	+	0.0848355i
$144$		0			0
$145$	3.10437	+	3.10437i	0.257804	+	0.257804i
$146$	6.95565	−	4.01584i	0.575653	−	0.332354i
$147$		0			0
$148$	−3.64130	+	3.64130i	−0.299313	+	0.299313i
$149$	14.8614	+	3.98209i	1.21749	+	0.326225i	0.809697	−	0.586849i	$-0.199632\pi$
$149$	14.8614	+	3.98209i	1.21749	+	0.326225i	0.407793	+	0.913074i	$0.366298\pi$
$150$		0			0
$151$	−6.32512	+	23.6057i	−0.514731	+	1.92100i	−0.155142	+	0.987892i	$0.549584\pi$
$151$	−6.32512	+	23.6057i	−0.514731	+	1.92100i	−0.359589	+	0.933111i	$0.617083\pi$
$152$	3.25524	−	1.87941i	0.264035	−	0.152440i
$153$		0			0
$154$	6.19669	−	16.0335i	0.499343	−	1.29201i
$155$			7.18642i			0.577227i
$156$		0			0
$157$	8.18219	−	4.72399i	0.653010	−	0.377015i	−0.136599	−	0.990626i	$-0.543617\pi$
$157$	8.18219	−	4.72399i	0.653010	−	0.377015i	0.789608	+	0.613611i	$0.210284\pi$
$158$	−0.481873	−	1.79837i	−0.0383357	−	0.143071i
$159$		0			0
$160$	2.39932	−	4.15574i	0.189683	−	0.328540i
$161$	0.0952137	+	0.610164i	0.00750389	+	0.0480877i
$162$		0			0
$163$	4.87434	−	18.1913i	0.381788	−	1.42485i	−0.461380	−	0.887203i	$-0.652646\pi$
$163$	4.87434	−	18.1913i	0.381788	−	1.42485i	0.843168	−	0.537650i	$-0.180688\pi$
$164$	−9.51562	−	2.54970i	−0.743045	−	0.199098i
$165$		0			0
$166$	−13.9037			−1.07913
$167$	−22.1608	−	5.93797i	−1.71486	−	0.459494i	−0.738249	−	0.674528i	$-0.764347\pi$
$167$	−22.1608	−	5.93797i	−1.71486	−	0.459494i	−0.976606	+	0.215034i	$0.931014\pi$
$168$		0			0
$169$	10.6613	+	7.43881i	0.820103	+	0.572216i
$170$	1.74176	−	3.01682i	0.133587	−	0.231379i
$171$		0			0
$172$	6.15068	−	10.6533i	0.468985	−	0.812306i
$173$	−4.29402	−	7.43747i	−0.326469	−	0.565460i	0.655340	−	0.755334i	$-0.272525\pi$
$173$	−4.29402	−	7.43747i	−0.326469	−	0.565460i	−0.981808	+	0.189874i	$0.939192\pi$
$174$		0			0
$175$	−8.46275	+	6.82108i	−0.639724	+	0.515625i
$176$	−5.74456	+	1.53925i	−0.433012	+	0.116025i
$177$		0			0
$178$			4.03150i			0.302174i
$179$	−11.8098	−	6.81837i	−0.882703	−	0.509629i	−0.0111545	−	0.999938i	$-0.503551\pi$
$179$	−11.8098	−	6.81837i	−0.882703	−	0.509629i	−0.871549	+	0.490309i	$0.836884\pi$
$180$		0			0
$181$	11.2556			0.836622			0.418311	−	0.908304i	$-0.362622\pi$
$181$	11.2556			0.836622			0.418311	+	0.908304i	$0.362622\pi$
$182$	7.58485	−	5.59546i	0.562226	−	0.414763i
$183$		0			0
$184$	0.493099	−	0.493099i	0.0363517	−	0.0363517i
$185$	4.11364	+	2.37501i	0.302441	+	0.174614i
$186$		0			0
$187$	23.7133	−	6.35395i	1.73409	−	0.464647i
$188$	−2.15389	+	0.577134i	−0.157089	+	0.0420918i
$189$		0			0
$190$	−0.830056	−	0.830056i	−0.0602186	−	0.0602186i
$191$	5.69836	+	9.86984i	0.412319	+	0.714157i	0.995143	−	0.0984414i	$-0.0313857\pi$
$191$	5.69836	+	9.86984i	0.412319	+	0.714157i	−0.582824	+	0.812598i	$0.698052\pi$
$192$		0			0
$193$	2.39856	−	0.642692i	0.172652	−	0.0462620i	−0.171457	−	0.985192i	$-0.554848\pi$
$193$	2.39856	−	0.642692i	0.172652	−	0.0462620i	0.344109	+	0.938930i	$0.388181\pi$
$194$	−1.23620	+	2.14115i	−0.0887537	+	0.153726i
$195$		0			0
$196$	2.18336	+	6.82552i	0.155954	+	0.487537i
$197$	14.0826	+	3.77342i	1.00334	+	0.268845i	0.722846	−	0.691009i	$-0.242834\pi$
$197$	14.0826	+	3.77342i	1.00334	+	0.268845i	0.280498	+	0.959854i	$0.409500\pi$
$198$		0			0
$199$	5.22960			0.370716			0.185358	−	0.982671i	$-0.440655\pi$
$199$	5.22960			0.370716			0.185358	+	0.982671i	$0.440655\pi$
$200$	11.8558	+	3.17674i	0.838330	+	0.224630i
$201$		0			0
$202$	−0.614874	−	2.29474i	−0.0432624	−	0.161457i
$203$	7.71911	+	9.57691i	0.541775	+	0.672167i
$204$		0			0
$205$			9.08693i			0.634658i
$206$	0.741951	+	2.76900i	0.0516942	+	0.192925i
$207$		0			0
$208$	−3.11093	−	0.978035i	−0.215704	−	0.0678146i
$209$		−	8.27280i		−	0.572241i
$210$		0			0
$211$	5.55565	+	9.62266i	0.382466	+	0.662451i	0.991414	−	0.130759i	$-0.0417414\pi$
$211$	5.55565	+	9.62266i	0.382466	+	0.662451i	−0.608948	+	0.793210i	$0.708408\pi$
$212$	3.61878	−	2.08930i	0.248539	−	0.143494i
$213$		0			0
$214$	−7.74402	+	7.74402i	−0.529370	+	0.529370i
$215$	−10.9603	−	2.93679i	−0.747483	−	0.200288i
$216$		0			0
$217$	−2.15034	+	20.0196i	−0.145975	+	1.35902i
$218$	−6.21535	+	3.58843i	−0.420956	+	0.243039i
$219$		0			0
$220$	−3.17838	−	5.50511i	−0.214286	−	0.371154i
$221$	12.8418	+	4.03729i	0.863832	+	0.271577i
$222$		0			0
$223$	−7.12168	+	26.5785i	−0.476903	+	1.77983i	0.137137	+	0.990552i	$0.456210\pi$
$223$	−7.12168	+	26.5785i	−0.476903	+	1.77983i	−0.614040	+	0.789275i	$0.710457\pi$
$224$	7.92738	−	10.8589i	0.529671	−	0.725541i
$225$		0			0
$226$	0.309102	+	1.15359i	0.0205612	+	0.0767354i
$227$	8.30155	+	8.30155i	0.550993	+	0.550993i	0.926727	−	0.375734i	$-0.122610\pi$
$227$	8.30155	+	8.30155i	0.550993	+	0.550993i	−0.375734	+	0.926727i	$0.622610\pi$
$228$		0			0
$229$	−3.62802	−	13.5399i	−0.239746	−	0.894745i	−0.975952	−	0.217987i	$-0.930051\pi$
$229$	−3.62802	−	13.5399i	−0.239746	−	0.894745i	0.736206	−	0.676758i	$-0.236616\pi$
$230$	−0.188604	−	0.108890i	−0.0124362	−	0.00718002i
$231$		0			0
$232$	3.59498	−	13.4166i	0.236022	−	0.880845i
$233$	5.26788	+	3.04141i	0.345110	+	0.199249i	0.662529	−	0.749036i	$-0.269483\pi$
$233$	5.26788	+	3.04141i	0.345110	+	0.199249i	−0.317419	+	0.948285i	$0.602816\pi$
$234$		0			0
$235$	1.02843	+	1.78129i	0.0670872	+	0.116199i
$236$	5.40246	+	5.40246i	0.351670	+	0.351670i
$237$		0			0
$238$	5.75481	−	7.88292i	0.373029	−	0.510974i
$239$	3.72605	−	3.72605i	0.241018	−	0.241018i	−0.576253	−	0.817271i	$-0.695486\pi$
$239$	3.72605	−	3.72605i	0.241018	−	0.241018i	0.817271	+	0.576253i	$0.195486\pi$
$240$		0			0
$241$	−18.9861	+	18.9861i	−1.22300	+	1.22300i	−0.256439	+	0.966560i	$0.582549\pi$
$241$	−18.9861	+	18.9861i	−1.22300	+	1.22300i	−0.966560	+	0.256439i	$0.917451\pi$
$242$	−8.24386	+	30.7665i	−0.529935	+	1.97775i
$243$		0			0
$244$	−1.25679	−	2.17682i	−0.0804576	−	0.139357i
$245$	5.56015	−	3.57483i	0.355225	−	0.228387i
$246$		0			0
$247$	2.43415	−	3.82785i	0.154881	−	0.243561i
$248$	19.6904	−	11.3682i	1.25034	−	0.721884i
$249$		0			0
$250$		−	8.49833i		−	0.537481i
$251$	6.48321	−	11.2292i	0.409217	−	0.708784i	−0.585586	−	0.810611i	$-0.699135\pi$
$251$	6.48321	−	11.2292i	0.409217	−	0.708784i	0.994802	+	0.101827i	$0.0324687\pi$
$252$		0			0
$253$	−0.397233	−	1.48249i	−0.0249738	−	0.0932036i
$254$	2.49399	−	9.30771i	0.156487	−	0.584017i
$255$		0			0
$256$	−17.0338			−1.06461
$257$	−18.5733			−1.15857			−0.579284	−	0.815126i	$-0.696668\pi$
$257$	−18.5733			−1.15857			−0.579284	+	0.815126i	$0.696668\pi$
$258$		0			0
$259$	10.7489	+	7.84708i	0.667905	+	0.487594i
$260$	0.149151	−	3.48243i	0.00924996	−	0.215971i
$261$		0			0
$262$	16.2290	−	4.34855i	1.00263	−	0.268655i
$263$	−4.33110	+	7.50169i	−0.267067	+	0.462574i	−0.968103	−	0.250552i	$-0.919388\pi$
$263$	−4.33110	+	7.50169i	−0.267067	+	0.462574i	0.701036	+	0.713126i	$0.252721\pi$
$264$		0			0
$265$	−2.72546	−	2.72546i	−0.167424	−	0.167424i
$266$	−2.06396	−	2.56070i	−0.126549	−	0.157007i
$267$		0			0
$268$	10.0569	−	2.69473i	0.614321	−	0.164607i
$269$		−	7.28972i		−	0.444462i	−0.974994	−	0.222231i	$-0.928666\pi$
$269$		−	7.28972i		−	0.444462i	0.974994	−	0.222231i	$-0.0713339\pi$
$270$		0			0
$271$	−16.6156	+	16.6156i	−1.00933	+	1.00933i	−0.00937188	+	0.999956i	$0.502983\pi$
$271$	−16.6156	+	16.6156i	−1.00933	+	1.00933i	−0.999956	+	0.00937188i	$0.997017\pi$
$272$	−3.37681			−0.204749
$273$		0			0
$274$	−4.73904			−0.286296
$275$	19.1017	−	19.1017i	1.15187	−	1.15187i
$276$		0			0
$277$		−	2.45156i		−	0.147300i	−0.997284	−	0.0736499i	$-0.976535\pi$
$277$		−	2.45156i		−	0.147300i	0.997284	−	0.0736499i	$-0.0234647\pi$
$278$	7.68967	−	2.06044i	0.461196	−	0.123577i
$279$		0			0
$280$	−6.96244	−	2.69088i	−0.416086	−	0.160811i
$281$	9.26224	+	9.26224i	0.552539	+	0.552539i	0.927173	−	0.374634i	$-0.122232\pi$
$281$	9.26224	+	9.26224i	0.552539	+	0.552539i	−0.374634	+	0.927173i	$0.622232\pi$
$282$		0			0
$283$	0.287880	−	0.498622i	0.0171127	−	0.0296400i	−0.857342	−	0.514747i	$-0.827886\pi$
$283$	0.287880	−	0.498622i	0.0171127	−	0.0296400i	0.874455	+	0.485107i	$0.161219\pi$
$284$	1.65569	−	0.443640i	0.0982470	−	0.0263252i
$285$		0			0
$286$	−17.2576	+	15.8400i	−1.02046	+	0.936642i
$287$	−2.71902	+	25.3139i	−0.160498	+	1.49423i
$288$		0			0
$289$	−3.06068			−0.180040
$290$	−4.33781			−0.254725
$291$		0			0
$292$	2.15384	−	8.03825i	0.126044	−	0.470403i
$293$	4.53613	+	16.9291i	0.265004	+	0.989007i	0.962248	+	0.272174i	$0.0877425\pi$
$293$	4.53613	+	16.9291i	0.265004	+	0.989007i	−0.697245	+	0.716833i	$0.745591\pi$
$294$		0			0
$295$	3.52371	−	6.10324i	0.205158	−	0.355345i
$296$		−	15.0282i		−	0.873495i
$297$		0			0
$298$	−13.1652	+	7.60092i	−0.762638	+	0.440310i
$299$	0.252401	−	0.802836i	0.0145967	−	0.0464292i
$300$		0			0
$301$	−29.6538	−	11.4607i	−1.70921	−	0.660585i
$302$	−12.0732	−	20.9115i	−0.694737	−	1.20332i
$303$		0			0
$304$	−0.294515	+	1.09914i	−0.0168916	+	0.0630402i
$305$	−1.63946	+	1.63946i	−0.0938752	+	0.0938752i
$306$		0			0
$307$	−10.3888	+	10.3888i	−0.592923	+	0.592923i	−0.938420	−	0.345497i	$-0.887710\pi$
$307$	−10.3888	+	10.3888i	−0.592923	+	0.592923i	0.345497	+	0.938420i	$0.387710\pi$
$308$	−7.20691	−	16.2869i	−0.410652	−	0.928032i
$309$		0			0
$310$	−5.02087	−	5.02087i	−0.285166	−	0.285166i
$311$	−6.38744	−	11.0634i	−0.362199	−	0.627346i	0.626124	−	0.779724i	$-0.284640\pi$
$311$	−6.38744	−	11.0634i	−0.362199	−	0.627346i	−0.988322	+	0.152377i	$0.951307\pi$
$312$		0			0
$313$	12.3070	+	7.10546i	0.695633	+	0.401624i	0.805719	−	0.592298i	$-0.201779\pi$
$313$	12.3070	+	7.10546i	0.695633	+	0.401624i	−0.110086	+	0.993922i	$0.535112\pi$
$314$	−2.41611	+	9.01704i	−0.136349	+	0.508861i
$315$		0			0
$316$	−1.67062	−	0.964532i	−0.0939797	−	0.0542592i
$317$	4.84186	+	18.0701i	0.271946	+	1.01492i	0.957860	+	0.287234i	$0.0927358\pi$
$317$	4.84186	+	18.0701i	0.271946	+	1.01492i	−0.685914	+	0.727682i	$0.740598\pi$
$318$		0			0
$319$	−21.6165	−	21.6165i	−1.21029	−	1.21029i
$320$	1.66925	+	6.22973i	0.0933139	+	0.348252i
$321$		0			0
$322$	−0.492820	−	0.359776i	−0.0274638	−	0.0200495i
$323$	1.21574	−	4.53722i	0.0676458	−	0.252458i
$324$		0			0
$325$	14.4588	−	3.21803i	0.802030	−	0.178504i
$326$	9.30403	+	16.1151i	0.515303	+	0.892531i
$327$		0			0
$328$	24.8976	−	14.3747i	1.37474	−	0.793708i
$329$	2.33194	+	5.26996i	0.128564	+	0.290542i
$330$		0			0
$331$	3.81375	+	1.02189i	0.209623	+	0.0561682i	0.362102	−	0.932138i	$-0.382059\pi$
$331$	3.81375	+	1.02189i	0.209623	+	0.0561682i	−0.152480	+	0.988307i	$0.548726\pi$
$332$	−10.1865	+	10.1865i	−0.559057	+	0.559057i
$333$		0			0
$334$	19.6315	−	11.3343i	1.07419	−	0.620183i
$335$	−4.80190	−	8.31713i	−0.262356	−	0.454413i
$336$		0			0
$337$		−	15.1443i		−	0.824962i	−0.910966	−	0.412481i	$-0.864662\pi$
$337$		−	15.1443i		−	0.824962i	0.910966	−	0.412481i	$-0.135338\pi$
$338$	−12.6459	+	2.25145i	−0.687844	+	0.122463i
$339$		0			0
$340$	−0.934168	−	3.48636i	−0.0506624	−	0.189075i
$341$		−	50.0407i		−	2.70986i
$342$		0			0
$343$	16.5588	−	8.29486i	0.894094	−	0.447880i
$344$	9.29146	+	34.6762i	0.500962	+	1.86961i
$345$		0			0
$346$	8.19633	+	2.19620i	0.440638	+	0.118069i
$347$	−6.79449			−0.364747			−0.182374	−	0.983229i	$-0.558378\pi$
$347$	−6.79449			−0.364747			−0.182374	+	0.983229i	$0.558378\pi$
$348$		0			0
$349$	0.378000	+	0.101285i	0.0202339	+	0.00542165i	0.268922	−	0.963162i	$-0.413333\pi$
$349$	0.378000	+	0.101285i	0.0202339	+	0.00542165i	−0.248688	+	0.968584i	$0.579999\pi$
$350$	1.14697	−	10.6782i	0.0613081	−	0.570775i
$351$		0			0
$352$	−16.7070	+	28.9374i	−0.890486	+	1.54237i
$353$	−19.2883	+	5.16829i	−1.02661	+	0.275081i	−0.732556	−	0.680707i	$-0.761673\pi$
$353$	−19.2883	+	5.16829i	−1.02661	+	0.275081i	−0.294059	+	0.955787i	$0.595006\pi$
$354$		0			0
$355$	−0.790548	−	1.36927i	−0.0419579	−	0.0726733i
$356$	2.95368	+	2.95368i	0.156545	+	0.156545i
$357$		0			0
$358$	13.0147	−	3.48729i	0.687851	−	0.184309i
$359$	−26.7736	+	7.17397i	−1.41306	+	0.378628i	−0.883016	−	0.469344i	$-0.844491\pi$
$359$	−26.7736	+	7.17397i	−1.41306	+	0.378628i	−0.530042	+	0.847971i	$0.677824\pi$
$360$		0			0
$361$	15.0837	+	8.70856i	0.793877	+	0.458345i
$362$	−7.86384	+	7.86384i	−0.413314	+	0.413314i
$363$		0			0
$364$	1.45752	−	9.65654i	0.0763948	−	0.506140i
$365$	−7.67612			−0.401786
$366$		0			0
$367$	−5.78423	−	3.33953i	−0.301934	−	0.174322i	0.341377	−	0.939926i	$-0.389107\pi$
$367$	−5.78423	−	3.33953i	−0.301934	−	0.174322i	−0.643312	+	0.765605i	$0.722440\pi$
$368$			0.211109i			0.0110048i
$369$		0			0
$370$	−4.53337	+	1.21471i	−0.235678	+	0.0631499i
$371$	−6.77694	−	8.40798i	−0.351841	−	0.436520i
$372$		0			0
$373$	−0.503050	−	0.871308i	−0.0260469	−	0.0451146i	0.852708	−	0.522388i	$-0.174959\pi$
$373$	−0.503050	−	0.871308i	−0.0260469	−	0.0451146i	−0.878755	+	0.477273i	$0.841625\pi$
$374$	−12.1283	+	21.0068i	−0.627138	+	1.08624i
$375$		0			0
$376$	3.25375	−	5.63567i	0.167800	−	0.290637i
$377$	−3.64170	−	16.3624i	−0.187557	−	0.842705i
$378$		0			0
$379$	−20.6414	−	5.53086i	−1.06028	−	0.284101i	−0.313786	−	0.949494i	$-0.601597\pi$
$379$	−20.6414	−	5.53086i	−1.06028	−	0.284101i	−0.746493	+	0.665393i	$0.768264\pi$
$380$	−1.21628			−0.0623938
$381$		0			0
$382$	−10.8769	−	2.91445i	−0.556510	−	0.149116i
$383$	5.91371	−	22.0703i	0.302177	−	1.12774i	−0.633172	−	0.774011i	$-0.718247\pi$
$383$	5.91371	−	22.0703i	0.302177	−	1.12774i	0.935349	−	0.353727i	$-0.115086\pi$
$384$		0			0
$385$	−12.7907	+	10.3095i	−0.651876	+	0.525420i
$386$	−1.22676	+	2.12480i	−0.0624402	+	0.108150i
$387$		0			0
$388$	0.663016	+	2.47441i	0.0336596	+	0.125619i
$389$	−17.3058	+	9.99148i	−0.877437	+	0.506588i	−0.869812	−	0.493383i	$-0.835760\pi$
$389$	−17.3058	+	9.99148i	−0.877437	+	0.506588i	−0.00762436	+	0.999971i	$0.502427\pi$
$390$		0			0
$391$		−	0.871451i		−	0.0440712i
$392$	−18.5905	−	9.57943i	−0.938960	−	0.483834i
$393$		0			0
$394$	−12.4753	+	7.20262i	−0.628497	+	0.362863i
$395$	−0.460539	+	1.71876i	−0.0231723	+	0.0864800i
$396$		0			0
$397$	24.1600	+	6.47366i	1.21256	+	0.324904i	0.807765	−	0.589505i	$-0.200677\pi$
$397$	24.1600	+	6.47366i	1.21256	+	0.324904i	0.404793	+	0.914408i	$0.367344\pi$
$398$	−3.65372	+	3.65372i	−0.183144	+	0.183144i
$399$		0			0
$400$	−3.21792	+	1.85787i	−0.160896	+	0.0928934i
$401$	−0.994403	−	0.994403i	−0.0496581	−	0.0496581i	0.681842	−	0.731500i	$-0.261179\pi$
$401$	−0.994403	−	0.994403i	−0.0496581	−	0.0496581i	−0.731500	+	0.681842i	$0.761179\pi$
$402$		0			0
$403$	14.7238	−	23.1540i	0.733443	−	1.15339i
$404$	−2.13173	−	1.23075i	−0.106057	−	0.0612322i
$405$		0			0
$406$	−12.0840	−	1.29797i	−0.599721	−	0.0644173i
$407$	−28.6442	−	16.5378i	−1.41984	−	0.819746i
$408$		0			0
$409$	1.96094	+	1.96094i	0.0969623	+	0.0969623i	0.753924	−	0.656962i	$-0.228159\pi$
$409$	1.96094	+	1.96094i	0.0969623	+	0.0969623i	−0.656962	+	0.753924i	$0.728159\pi$
$410$	−6.34868	−	6.34868i	−0.313539	−	0.313539i
$411$		0			0
$412$	2.57229	+	1.48511i	0.126728	+	0.0731663i
$413$	11.6424	−	15.9477i	0.572885	−	0.784737i
$414$		0			0
$415$	11.5079	+	6.64407i	0.564899	+	0.326144i
$416$	−16.2448	+	8.47364i	−0.796466	+	0.415454i
$417$		0			0
$418$	5.77988	+	5.77988i	0.282703	+	0.282703i
$419$	−16.7456	+	9.66807i	−0.818075	+	0.472316i	−0.849752	−	0.527182i	$-0.823249\pi$
$419$	−16.7456	+	9.66807i	−0.818075	+	0.472316i	0.0316770	+	0.999498i	$0.489915\pi$
$420$		0			0
$421$	2.40433	−	2.40433i	0.117180	−	0.117180i	−0.646085	−	0.763265i	$-0.723595\pi$
$421$	2.40433	−	2.40433i	0.117180	−	0.117180i	0.763265	+	0.646085i	$0.223595\pi$
$422$	−10.6045	−	2.84146i	−0.516218	−	0.138320i
$423$		0			0
$424$	−3.15618	+	11.7790i	−0.153278	+	0.572041i
$425$	13.2834	−	7.66920i	0.644342	−	0.372011i
$426$		0			0
$427$	−5.05769	+	4.07656i	−0.244759	+	0.197279i
$428$			11.3473i			0.548492i
$429$		0			0
$430$	9.70932	−	5.60568i	0.468225	−	0.270330i
$431$	0.179529	+	0.670011i	0.00864760	+	0.0322733i	0.970115	−	0.242646i	$-0.0780154\pi$
$431$	0.179529	+	0.670011i	0.00864760	+	0.0322733i	−0.961467	+	0.274920i	$0.911349\pi$
$432$		0			0
$433$	10.5144	−	18.2115i	0.505290	−	0.875188i	−0.494691	−	0.869069i	$-0.664719\pi$
$433$	10.5144	−	18.2115i	0.505290	−	0.875188i	0.999981	−	0.00611893i	$-0.00194773\pi$
$434$	−12.4845	−	15.4892i	−0.599277	−	0.743508i
$435$		0			0
$436$	−1.92461	+	7.18273i	−0.0921719	+	0.343990i
$437$	−0.283655	−	0.0760052i	−0.0135691	−	0.00363582i
$438$		0			0
$439$	−22.8237			−1.08932			−0.544659	−	0.838658i	$-0.683341\pi$
$439$	−22.8237			−1.08932			−0.544659	+	0.838658i	$0.683341\pi$
$440$	17.9190	+	4.80138i	0.854255	+	0.228897i
$441$		0			0
$442$	−11.7927	+	6.15136i	−0.560924	+	0.292590i
$443$	8.38733	−	14.5273i	0.398494	−	0.690212i	−0.595046	−	0.803691i	$-0.702866\pi$
$443$	8.38733	−	14.5273i	0.398494	−	0.690212i	0.993540	+	0.113480i	$0.0361997\pi$
$444$		0			0
$445$	1.92651	−	3.33682i	0.0913254	−	0.158180i
$446$	−13.5937	−	23.5450i	−0.643681	−	1.11489i
$447$		0			0
$448$	2.78604	+	17.8539i	0.131628	+	0.843519i
$449$	−14.8030	+	3.96646i	−0.698599	+	0.187189i	−0.590603	−	0.806962i	$-0.701110\pi$
$449$	−14.8030	+	3.96646i	−0.698599	+	0.187189i	−0.107996	+	0.994151i	$0.534443\pi$
$450$		0			0
$451$		−	63.2744i		−	2.97948i
$452$	1.07164	+	0.618710i	0.0504055	+	0.0291017i
$453$		0			0
$454$	−11.5999			−0.544412
$455$	−8.95174	+	1.00675i	−0.419664	+	0.0471974i
$456$		0			0
$457$	−9.84760	+	9.84760i	−0.460651	+	0.460651i	−0.898869	−	0.438218i	$-0.855610\pi$
$457$	−9.84760	+	9.84760i	−0.460651	+	0.460651i	0.438218	+	0.898869i	$0.355610\pi$
$458$	11.9946	+	6.92507i	0.560470	+	0.323587i
$459$		0			0
$460$	−0.217959	+	0.0584018i	−0.0101624	+	0.00272300i
$461$	−15.2937	+	4.09793i	−0.712298	+	0.190860i	−0.596733	−	0.802440i	$-0.703535\pi$
$461$	−15.2937	+	4.09793i	−0.712298	+	0.190860i	−0.115565	+	0.993300i	$0.536868\pi$
$462$		0			0
$463$	26.2699	+	26.2699i	1.22086	+	1.22086i	0.967325	+	0.253538i	$0.0815943\pi$
$463$	26.2699	+	26.2699i	1.22086	+	1.22086i	0.253538	+	0.967325i	$0.418406\pi$
$464$	2.10246	+	3.64157i	0.0976044	+	0.169056i
$465$		0			0
$466$	−5.80537	+	1.55555i	−0.268929	+	0.0720592i
$467$	−16.6813	+	28.8928i	−0.771917	+	1.33700i	0.164595	+	0.986361i	$0.447368\pi$
$467$	−16.6813	+	28.8928i	−0.771917	+	1.33700i	−0.936511	+	0.350637i	$0.885965\pi$
$468$		0			0
$469$	−10.8882	−	24.6063i	−0.502771	−	1.13621i
$470$	−1.96304	−	0.525995i	−0.0905483	−	0.0242623i
$471$		0			0
$472$	−22.2967			−1.02629
$473$	76.3188	+	20.4496i	3.50914	+	0.940272i
$474$		0			0
$475$	−1.33777	−	4.99262i	−0.0613810	−	0.229077i
$476$	−1.55916	−	9.99166i	−0.0714639	−	0.457967i
$477$		0			0
$478$			5.20650i			0.238140i
$479$	1.37572	+	5.13427i	0.0628584	+	0.234591i	0.990207	−	0.139608i	$-0.0445844\pi$
$479$	1.37572	+	5.13427i	0.0628584	+	0.234591i	−0.927348	+	0.374199i	$0.877918\pi$
$480$		0			0
$481$	−8.38781	−	16.0802i	−0.382451	−	0.733196i
$482$		−	26.5296i		−	1.20839i
$483$		0			0
$484$	16.5012	+	28.5809i	0.750054	+	1.29913i
$485$	2.04636	−	1.18147i	0.0929205	−	0.0536477i
$486$		0			0
$487$	9.83431	−	9.83431i	0.445635	−	0.445635i	−0.448265	−	0.893900i	$-0.647958\pi$
$487$	9.83431	−	9.83431i	0.445635	−	0.445635i	0.893900	+	0.448265i	$0.147958\pi$
$488$	7.08549	+	1.89855i	0.320745	+	0.0859434i
$489$		0			0
$490$	−1.38706	+	6.38225i	−0.0626611	+	0.288321i
$491$	6.73956	−	3.89109i	0.304152	−	0.175602i	−0.340155	−	0.940370i	$-0.610479\pi$
$491$	6.73956	−	3.89109i	0.304152	−	0.175602i	0.644307	+	0.764767i	$0.277146\pi$
$492$		0			0
$493$	−8.67888	−	15.0323i	−0.390877	−	0.677019i
$494$	0.973727	+	4.37502i	0.0438101	+	0.196841i
$495$		0			0
$496$	−1.78147	+	6.64854i	−0.0799904	+	0.298528i
$497$	−1.79255	−	4.05099i	−0.0804070	−	0.181712i
$498$		0			0
$499$	−3.34017	−	12.4657i	−0.149527	−	0.558041i	−0.999512	−	0.0312347i	$-0.990056\pi$
$499$	−3.34017	−	12.4657i	−0.149527	−	0.558041i	0.849985	−	0.526806i	$-0.176611\pi$
$500$	−6.22629	−	6.22629i	−0.278448	−	0.278448i
$501$		0			0
$502$	3.31587	+	12.3750i	0.147995	+	0.552323i
$503$	0.631010	+	0.364314i	0.0281354	+	0.0162440i	0.514002	−	0.857789i	$-0.328162\pi$
$503$	0.631010	+	0.364314i	0.0281354	+	0.0162440i	−0.485866	+	0.874033i	$0.661496\pi$
$504$		0			0
$505$	−0.587653	+	2.19315i	−0.0261502	+	0.0975939i
$506$	1.31329	+	0.758229i	0.0583829	+	0.0337074i
$507$		0			0
$508$	−4.99206	−	8.64650i	−0.221487	−	0.383626i
$509$	10.5628	+	10.5628i	0.468188	+	0.468188i	0.901327	−	0.433139i	$-0.142594\pi$
$509$	10.5628	+	10.5628i	0.468188	+	0.468188i	−0.433139	+	0.901327i	$0.642594\pi$
$510$		0			0
$511$	−21.3837	−	2.29687i	−0.945961	−	0.101608i
$512$	7.07136	−	7.07136i	0.312513	−	0.312513i
$513$		0			0
$514$	12.9764	−	12.9764i	0.572365	−	0.572365i
$515$	0.709104	−	2.64641i	0.0312469	−	0.116615i
$516$		0			0
$517$	−7.16119	−	12.4035i	−0.314949	−	0.545507i
$518$	−12.9923	+	2.02740i	−0.570849	+	0.0890787i
$519$		0			0
$520$	6.87845	+	7.49402i	0.301640	+	0.328635i
$521$	−26.7816	+	15.4624i	−1.17332	+	0.677419i	−0.954461	−	0.298336i	$-0.903568\pi$
$521$	−26.7816	+	15.4624i	−1.17332	+	0.677419i	−0.218864	+	0.975755i	$0.570235\pi$
$522$		0			0
$523$		−	19.8628i		−	0.868538i	−0.900783	−	0.434269i	$-0.857007\pi$
$523$		−	19.8628i		−	0.868538i	0.900783	−	0.434269i	$-0.142993\pi$
$524$	8.70421	−	15.0761i	0.380245	−	0.658604i
$525$		0			0
$526$	−2.21517	−	8.26711i	−0.0965858	−	0.360463i
$527$	7.35383	−	27.4449i	0.320338	−	1.19552i
$528$		0			0
$529$	22.9455			0.997631
$530$	3.80835			0.165424
$531$		0			0
$532$	−3.38825	−	0.363939i	−0.146899	−	0.0157787i
$533$	18.6176	−	29.2773i	0.806417	−	1.26814i
$534$		0			0
$535$	10.1102	−	2.70902i	0.437102	−	0.117121i
$536$	−15.1923	+	26.3138i	−0.656207	+	1.13658i
$537$		0			0
$538$	5.09304	+	5.09304i	0.219577	+	0.219577i
$539$	−38.7166	+	24.8924i	−1.66764	+	1.07219i
$540$		0			0
$541$	9.59205	−	2.57018i	0.412395	−	0.110501i	−0.0466559	−	0.998911i	$-0.514856\pi$
$541$	9.59205	−	2.57018i	0.412395	−	0.110501i	0.459050	+	0.888410i	$0.348190\pi$
$542$		−	23.2174i		−	0.997272i
$543$		0			0
$544$	−13.4155	+	13.4155i	−0.575185	+	0.575185i
$545$	6.85914			0.293813
$546$		0			0
$547$	−5.37266			−0.229718			−0.114859	−	0.993382i	$-0.536642\pi$
$547$	−5.37266			−0.229718			−0.114859	+	0.993382i	$0.536642\pi$
$548$	−3.47205	+	3.47205i	−0.148319	+	0.148319i
$549$		0			0
$550$			26.6912i			1.13812i
$551$	−5.64992	+	1.51389i	−0.240694	+	0.0644939i
$552$		0			0
$553$	−1.79724	+	4.65022i	−0.0764264	+	0.197748i
$554$	1.71281	+	1.71281i	0.0727702	+	0.0727702i
$555$		0			0
$556$	4.12425	−	7.14341i	0.174907	−	0.302948i
$557$	12.4110	−	3.32551i	0.525869	−	0.140906i	0.0138891	−	0.999904i	$-0.495579\pi$
$557$	12.4110	−	3.32551i	0.525869	−	0.140906i	0.511980	+	0.858997i	$0.328912\pi$
$558$		0			0
$559$	29.2960	+	31.9178i	1.23909	+	1.34998i
$560$	2.06643	−	0.914389i	0.0873226	−	0.0386400i
$561$		0			0
$562$	−12.9423			−0.545939
$563$	−6.31884			−0.266307			−0.133154	−	0.991095i	$-0.542510\pi$
$563$	−6.31884			−0.266307			−0.133154	+	0.991095i	$0.542510\pi$
$564$		0			0
$565$	0.295418	−	1.10252i	0.0124283	−	0.0463832i
$566$	0.147238	+	0.549498i	0.00618886	+	0.0230971i
$567$		0			0
$568$	−2.50115	+	4.33211i	−0.104946	+	0.181771i
$569$			5.11436i			0.214405i	0.994237	+	0.107203i	$0.0341893\pi$
$569$			5.11436i			0.214405i	−0.994237	+	0.107203i	$0.965811\pi$
$570$		0			0
$571$	−24.2776	+	14.0167i	−1.01599	+	0.586580i	−0.912939	−	0.408097i	$-0.866193\pi$
$571$	−24.2776	+	14.0167i	−1.01599	+	0.586580i	−0.103047	+	0.994676i	$0.532859\pi$
$572$	−1.03857	+	24.2490i	−0.0434250	+	1.01390i
$573$		0			0
$574$	−15.7862	−	19.5855i	−0.658902	−	0.817483i
$575$	−0.479459	−	0.830447i	−0.0199948	−	0.0346320i
$576$		0			0
$577$	−5.18104	+	19.3359i	−0.215689	+	0.804964i	0.770233	+	0.637762i	$0.220140\pi$
$577$	−5.18104	+	19.3359i	−0.215689	+	0.804964i	−0.985923	+	0.167202i	$0.946527\pi$
$578$	2.13838	−	2.13838i	0.0889449	−	0.0889449i
$579$		0			0
$580$	−3.17809	+	3.17809i	−0.131963	+	0.131963i
$581$	30.0700	+	21.9521i	1.24751	+	0.910727i
$582$		0			0
$583$	18.9780	+	18.9780i	0.785990	+	0.785990i
$584$	12.1429	+	21.0321i	0.502477	+	0.870315i
$585$		0			0
$586$	−14.9969	−	8.65846i	−0.619516	−	0.357678i
$587$	−1.06109	+	3.96003i	−0.0437957	+	0.163448i	−0.984360	−	0.176167i	$-0.943630\pi$
$587$	−1.06109	+	3.96003i	−0.0437957	+	0.163448i	0.940565	+	0.339615i	$0.110297\pi$
$588$		0			0
$589$	−8.29187	−	4.78731i	−0.341661	−	0.197258i
$590$	1.80222	+	6.72598i	0.0741962	+	0.276904i
$591$		0			0
$592$	3.21699	+	3.21699i	0.132218	+	0.132218i
$593$	4.49553	+	16.7775i	0.184609	+	0.688971i	0.994714	+	0.102686i	$0.0327435\pi$
$593$	4.49553	+	16.7775i	0.184609	+	0.688971i	−0.810105	+	0.586285i	$0.800590\pi$
$594$		0			0
$595$	−8.53013	+	3.77456i	−0.349701	+	0.154742i
$596$	−4.07665	+	15.2143i	−0.166986	+	0.623200i
$597$		0			0
$598$	0.384567	+	0.737253i	0.0157261	+	0.0301485i
$599$	7.18140	+	12.4386i	0.293424	+	0.508226i	0.974617	−	0.223878i	$-0.0718718\pi$
$599$	7.18140	+	12.4386i	0.293424	+	0.508226i	−0.681193	+	0.732104i	$0.738539\pi$
$600$		0			0
$601$	7.65598	−	4.42018i	0.312294	−	0.180303i	−0.335659	−	0.941984i	$-0.608959\pi$
$601$	7.65598	−	4.42018i	0.312294	−	0.180303i	0.647952	+	0.761681i	$0.275626\pi$
$602$	28.7251	−	12.7108i	1.17075	−	0.518052i
$603$		0			0
$604$	−24.1662	−	6.47532i	−0.983310	−	0.263477i
$605$	21.5255	−	21.5255i	0.875137	−	0.875137i
$606$		0			0
$607$	−23.5526	+	13.5981i	−0.955971	+	0.551930i	−0.894931	−	0.446205i	$-0.852775\pi$
$607$	−23.5526	+	13.5981i	−0.955971	+	0.551930i	−0.0610406	+	0.998135i	$0.519442\pi$
$608$	3.19666	+	5.53678i	0.129642	+	0.224546i
$609$		0			0
$610$		−	2.29085i		−	0.0927539i
$611$	0.336052	−	7.84624i	0.0135952	−	0.317425i
$612$		0			0
$613$	11.4723	+	42.8151i	0.463361	+	1.72929i	0.662267	+	0.749268i	$0.269594\pi$
$613$	11.4723	+	42.8151i	0.463361	+	1.72929i	−0.198906	+	0.980019i	$0.563739\pi$
$614$		−	14.5166i		−	0.585841i
$615$		0			0
$616$	48.4811	+	18.7372i	1.95336	+	0.754944i
$617$	7.15534	+	26.7041i	0.288063	+	1.07507i	0.946572	+	0.322493i	$0.104521\pi$
$617$	7.15534	+	26.7041i	0.288063	+	1.07507i	−0.658509	+	0.752573i	$0.728812\pi$
$618$		0			0
$619$	−38.0315	−	10.1905i	−1.52861	−	0.409591i	−0.606047	−	0.795429i	$-0.707246\pi$
$619$	−38.0315	−	10.1905i	−1.52861	−	0.409591i	−0.922567	+	0.385838i	$0.873912\pi$
$620$	−7.35707			−0.295467
$621$		0			0
$622$	12.1922	+	3.26689i	0.488863	+	0.130990i
$623$	6.36523	−	8.71908i	0.255018	−	0.349322i
$624$		0			0
$625$	6.20963	−	10.7554i	0.248385	−	0.430216i
$626$	−13.5627	+	3.63412i	−0.542076	+	0.145249i
$627$		0			0
$628$	4.83616	+	8.37648i	0.192984	+	0.334258i
$629$	−13.2796	−	13.2796i	−0.529493	−	0.529493i
$630$		0			0
$631$	7.08811	−	1.89925i	0.282173	−	0.0756081i	−0.114957	−	0.993371i	$-0.536673\pi$
$631$	7.08811	−	1.89925i	0.282173	−	0.0756081i	0.397130	+	0.917762i	$0.370006\pi$
$632$	5.43782	−	1.45706i	0.216305	−	0.0579588i
$633$		0			0
$634$	−16.0077	−	9.24203i	−0.635746	−	0.367048i
$635$	−6.51206	+	6.51206i	−0.258423	+	0.258423i
$636$		0			0
$637$	−25.2385	+	0.126001i	−0.999988	+	0.00499235i
$638$	30.2052			1.19583
$639$		0			0
$640$	2.79277	+	1.61240i	0.110394	+	0.0637359i
$641$		−	33.6134i		−	1.32765i	−0.747887	−	0.663826i	$-0.768932\pi$
$641$		−	33.6134i		−	1.32765i	0.747887	−	0.663826i	$-0.231068\pi$
$642$		0			0
$643$	22.8004	−	6.10935i	0.899160	−	0.240929i	0.220504	−	0.975386i	$-0.429230\pi$
$643$	22.8004	−	6.10935i	0.899160	−	0.240929i	0.678655	+	0.734457i	$0.262563\pi$
$644$	−0.624653	+	0.0974747i	−0.0246148	+	0.00384104i
$645$		0			0
$646$	2.32058	+	4.01937i	0.0913022	+	0.158140i
$647$	−0.513809	+	0.889943i	−0.0201999	+	0.0349873i	−0.875949	−	0.482404i	$-0.839764\pi$
$647$	−0.513809	+	0.889943i	−0.0201999	+	0.0349873i	0.855749	+	0.517392i	$0.173097\pi$
$648$		0			0
$649$	−24.5364	+	42.4983i	−0.963139	+	1.66821i
$650$	−7.85349	+	12.3501i	−0.308039	+	0.484411i
$651$		0			0
$652$	18.6233	+	4.99009i	0.729343	+	0.195427i
$653$	−22.4684			−0.879256			−0.439628	−	0.898180i	$-0.644890\pi$
$653$	−22.4684			−0.879256			−0.439628	+	0.898180i	$0.644890\pi$
$654$		0			0
$655$	−15.5105	−	4.15604i	−0.606047	−	0.162390i
$656$	−2.25259	+	8.40679i	−0.0879490	+	0.328230i
$657$		0			0
$658$	−5.31115	−	2.05268i	−0.207050	−	0.0800217i
$659$	15.3326	−	26.5569i	0.597275	−	1.03451i	−0.395947	−	0.918273i	$-0.629584\pi$
$659$	15.3326	−	26.5569i	0.597275	−	1.03451i	0.993222	−	0.116237i	$-0.0370831\pi$
$660$		0			0
$661$	8.93857	+	33.3592i	0.347670	+	1.29752i	0.889462	+	0.457010i	$0.151079\pi$
$661$	8.93857	+	33.3592i	0.347670	+	1.29752i	−0.541792	+	0.840513i	$0.682254\pi$
$662$	−3.37847	+	1.95056i	−0.131308	+	0.0758107i
$663$		0			0
$664$		−	42.0412i		−	1.63151i
$665$	0.484639	+	3.10575i	0.0187935	+	0.120436i
$666$		0			0
$667$	−0.939779	+	0.542582i	−0.0363884	+	0.0210088i
$668$	6.07898	−	22.6870i	0.235203	−	0.877788i
$669$		0			0
$670$	9.16575	+	2.45595i	0.354104	+	0.0948818i
$671$	11.4159	−	11.4159i	0.440708	−	0.440708i
$672$		0			0
$673$	27.9964	−	16.1637i	1.07918	−	0.623066i	0.148506	−	0.988912i	$-0.452554\pi$
$673$	27.9964	−	16.1637i	1.07918	−	0.623066i	0.930675	+	0.365846i	$0.119220\pi$
$674$	10.5807	+	10.5807i	0.407554	+	0.407554i
$675$		0			0
$676$	−7.61545	+	10.9145i	−0.292902	+	0.419788i
$677$	25.7232	+	14.8513i	0.988623	+	0.570782i	0.904862	−	0.425704i	$-0.139974\pi$
$677$	25.7232	+	14.8513i	0.988623	+	0.570782i	0.0837606	+	0.996486i	$0.473307\pi$
$678$		0			0
$679$	6.05417	−	2.67895i	0.232338	−	0.102809i
$680$	9.12208	+	5.26664i	0.349816	+	0.201966i
$681$		0			0
$682$	34.9615	+	34.9615i	1.33875	+	1.33875i
$683$	−13.2049	−	13.2049i	−0.505271	−	0.505271i	0.407800	−	0.913071i	$-0.366296\pi$
$683$	−13.2049	−	13.2049i	−0.505271	−	0.505271i	−0.913071	+	0.407800i	$0.866296\pi$
$684$		0			0
$685$	3.92244	+	2.26462i	0.149869	+	0.0865267i
$686$	−5.77373	+	17.3643i	−0.220442	+	0.662972i
$687$		0			0
$688$	−9.41190	−	5.43396i	−0.358825	−	0.207168i
$689$	3.19720	+	14.3652i	0.121804	+	0.547271i
$690$		0			0
$691$	7.85320	+	7.85320i	0.298750	+	0.298750i	0.840524	−	0.541774i	$-0.182247\pi$
$691$	7.85320	+	7.85320i	0.298750	+	0.298750i	−0.541774	+	0.840524i	$0.682247\pi$
$692$	7.61408	−	4.39599i	0.289444	−	0.167110i
$693$		0			0
$694$	4.74704	−	4.74704i	0.180195	−	0.180195i
$695$	−7.34924	−	1.96922i	−0.278772	−	0.0746969i
$696$		0			0
$697$	9.29861	−	34.7029i	0.352210	−	1.31447i
$698$	−0.334858	+	0.193330i	−0.0126746	+	0.00731766i
$699$		0			0
$700$	−6.98306	−	8.66371i	−0.263935	−	0.327457i
$701$			9.68156i			0.365668i	0.983144	+	0.182834i	$0.0585270\pi$
$701$			9.68156i			0.365668i	−0.983144	+	0.182834i	$0.941473\pi$
$702$		0			0
$703$	−5.48069	+	3.16428i	−0.206708	+	0.119343i
$704$	−11.6234	−	43.3790i	−0.438073	−	1.63491i
$705$		0			0
$706$	9.86512	−	17.0869i	0.371279	−	0.643074i
$707$	−2.29329	+	5.93373i	−0.0862482	+	0.223161i
$708$		0			0
$709$	−0.391304	+	1.46036i	−0.0146957	+	0.0548452i	−0.972884	−	0.231292i	$-0.925705\pi$
$709$	−0.391304	+	1.46036i	−0.0146957	+	0.0548452i	0.958189	+	0.286137i	$0.0923713\pi$
$710$	1.50898	+	0.404330i	0.0566310	+	0.0151742i
$711$		0			0
$712$	−12.1902			−0.456849
$713$	−1.71578	−	0.459743i	−0.0642566	−	0.0172175i
$714$		0			0
$715$	21.8533	−	4.86378i	0.817266	−	0.181895i
$716$	6.98028	−	12.0902i	0.260865	−	0.451832i
$717$		0			0
$718$	13.6935	−	23.7179i	0.511037	−	0.885142i
$719$	−13.8587	−	24.0039i	−0.516842	−	0.895196i	−0.999809	−	0.0195576i	$-0.993774\pi$
$719$	−13.8587	−	24.0039i	−0.516842	−	0.895196i	0.482967	−	0.875639i	$-0.339559\pi$
$720$		0			0
$721$	2.76725	−	7.16006i	0.103058	−	0.266655i
$722$	−16.6227	+	4.45404i	−0.618632	+	0.165762i
$723$		0			0
$724$			11.5229i			0.428244i
$725$	−16.5410	−	9.54997i	−0.614319	−	0.354677i
$726$		0			0
$727$	−29.0510			−1.07744			−0.538721	−	0.842484i	$-0.681092\pi$
$727$	−29.0510			−1.07744			−0.538721	+	0.842484i	$0.681092\pi$
$728$	16.9193	+	22.9347i	0.627069	+	0.850015i
$729$		0			0
$730$	5.36300	−	5.36300i	0.198494	−	0.198494i
$731$	38.8519	+	22.4312i	1.43699	+	0.829646i
$732$		0			0
$733$	32.8045	−	8.78993i	1.21166	−	0.324663i	0.404247	−	0.914650i	$-0.367534\pi$
$733$	32.8045	−	8.78993i	1.21166	−	0.324663i	0.807413	+	0.589986i	$0.200867\pi$
$734$	6.37441	−	1.70802i	0.235284	−	0.0630441i
$735$		0			0
$736$	0.838703	+	0.838703i	0.0309150	+	0.0309150i
$737$	33.4367	+	57.9141i	1.23166	+	2.13329i
$738$		0			0
$739$	−13.2974	+	3.56302i	−0.489152	+	0.131068i	−0.494961	−	0.868915i	$-0.664818\pi$
$739$	−13.2974	+	3.56302i	−0.489152	+	0.131068i	0.00580900	+	0.999983i	$0.498151\pi$
$740$	−2.43141	+	4.21132i	−0.0893803	+	0.154811i
$741$		0			0
$742$	10.6091	+	1.13955i	0.389472	+	0.0418340i
$743$	30.3940	+	8.14404i	1.11505	+	0.298776i	0.768878	−	0.639396i	$-0.220816\pi$
$743$	30.3940	+	8.14404i	1.11505	+	0.298776i	0.346169	+	0.938172i	$0.387482\pi$
$744$		0			0
$745$	14.5288			0.532295
$746$	0.960210	+	0.257288i	0.0351558	+	0.00941997i
$747$		0			0
$748$	6.50483	+	24.2764i	0.237840	+	0.887632i
$749$	28.9751	−	4.52145i	1.05873	−	0.165210i
$750$		0			0
$751$		−	26.5309i		−	0.968127i	−0.875033	−	0.484064i	$-0.839160\pi$
$751$		−	26.5309i		−	0.968127i	0.875033	−	0.484064i	$-0.160840\pi$
$752$	0.509882	+	1.90291i	0.0185935	+	0.0693918i
$753$		0			0
$754$	13.9761	+	8.88743i	0.508978	+	0.323661i
$755$			23.0775i			0.839876i
$756$		0			0
$757$	7.38184	+	12.7857i	0.268298	+	0.464705i	0.968422	−	0.249315i	$-0.0802056\pi$
$757$	7.38184	+	12.7857i	0.268298	+	0.464705i	−0.700125	+	0.714021i	$0.746872\pi$
$758$	18.2856	−	10.5572i	0.664161	−	0.383454i
$759$		0			0
$760$	2.50988	−	2.50988i	0.0910429	−	0.0910429i
$761$	−31.6870	−	8.49051i	−1.14865	−	0.307781i	−0.366228	−	0.930525i	$-0.619351\pi$
$761$	−31.6870	−	8.49051i	−1.14865	−	0.307781i	−0.782425	+	0.622744i	$0.786018\pi$
$762$		0			0
$763$	19.1078	+	2.05241i	0.691750	+	0.0743023i
$764$	−10.1042	+	5.83367i	−0.365558	+	0.211055i
$765$		0			0
$766$	11.2880	+	19.5513i	0.407850	+	0.706418i
$767$	−23.8576	+	12.4447i	−0.861448	+	0.449350i
$768$		0			0
$769$	−1.79577	+	6.70191i	−0.0647572	+	0.241677i	−0.990716	−	0.135947i	$-0.956592\pi$
$769$	−1.79577	+	6.70191i	−0.0647572	+	0.241677i	0.925959	+	0.377624i	$0.123259\pi$
$770$	1.73355	−	16.1392i	0.0624727	−	0.581617i
$771$		0			0
$772$	0.657953	+	2.45551i	0.0236802	+	0.0883759i
$773$	−0.711465	−	0.711465i	−0.0255896	−	0.0255896i	0.694196	−	0.719786i	$-0.255760\pi$
$773$	−0.711465	−	0.711465i	−0.0255896	−	0.0255896i	−0.719786	+	0.694196i	$0.755760\pi$
$774$		0			0
$775$	−8.09193	−	30.1995i	−0.290671	−	1.08480i
$776$	−6.47431	−	3.73794i	−0.232414	−	0.134184i
$777$		0			0
$778$	5.11020	−	19.0715i	0.183209	−	0.683747i
$779$	−10.4847	−	6.05336i	−0.375654	−	0.216884i
$780$		0			0
$781$	5.50477	+	9.53455i	0.196976	+	0.341173i
$782$	0.608848	+	0.608848i	0.0217724	+	0.0217724i
$783$		0			0
$784$	6.03016	−	1.92894i	0.215363	−	0.0688906i
$785$	6.30870	−	6.30870i	0.225167	−	0.225167i
$786$		0			0
$787$	−28.0302	+	28.0302i	−0.999170	+	0.999170i	−1.00000		0.000830028i	$-0.999736\pi$
$787$	−28.0302	+	28.0302i	−0.999170	+	0.999170i	0.000830028		1.00000i	$0.499736\pi$
$788$	−3.86303	+	14.4170i	−0.137615	+	0.513585i
$789$		0			0
$790$	−0.879067	−	1.52259i	−0.0312758	−	0.0541713i
$791$	1.15286	−	2.98293i	0.0409909	−	0.106061i
$792$		0			0
$793$	8.64117	−	1.92323i	0.306857	−	0.0682958i
$794$	−21.4026	+	12.3568i	−0.759549	+	0.438526i
$795$		0			0
$796$			5.35378i			0.189760i
$797$	18.4889	−	32.0238i	0.654912	−	1.13434i	−0.327004	−	0.945023i	$-0.606039\pi$
$797$	18.4889	−	32.0238i	0.654912	−	1.13434i	0.981916	−	0.189318i	$-0.0606276\pi$
$798$		0			0
$799$	−2.10477	−	7.85511i	−0.0744614	−	0.277894i
$800$	−5.40327	+	20.1653i	−0.191034	+	0.712950i
$801$		0			0
$802$	1.38950			0.0490650
$803$	53.4506			1.88623
$804$		0			0
$805$	0.235976	+	0.533282i	0.00831706	+	0.0187957i
$806$	5.88991	+	26.4637i	0.207463	+	0.932145i
$807$		0			0
$808$	6.93872	−	1.85922i	0.244103	−	0.0654072i
$809$	9.84541	−	17.0528i	0.346146	−	0.599543i	−0.639415	−	0.768862i	$-0.720823\pi$
$809$	9.84541	−	17.0528i	0.346146	−	0.599543i	0.985561	+	0.169319i	$0.0541567\pi$
$810$		0			0
$811$	−25.0100	−	25.0100i	−0.878220	−	0.878220i	0.115131	−	0.993350i	$-0.463271\pi$
$811$	−25.0100	−	25.0100i	−0.878220	−	0.878220i	−0.993350	+	0.115131i	$0.963271\pi$
$812$	−9.80432	+	7.90240i	−0.344064	+	0.277320i
$813$		0			0
$814$	31.5669	−	8.45832i	1.10642	−	0.296464i
$815$		−	17.7843i		−	0.622956i
$816$		0			0
$817$	10.6898	−	10.6898i	0.373990	−	0.373990i
$818$	−2.74007			−0.0958042
$819$		0			0
$820$	−9.30270			−0.324865
$821$	4.39077	−	4.39077i	0.153239	−	0.153239i	−0.626324	−	0.779563i	$-0.715441\pi$
$821$	4.39077	−	4.39077i	0.153239	−	0.153239i	0.779563	+	0.626324i	$0.215441\pi$
$822$		0			0
$823$		−	2.52297i		−	0.0879451i	−0.999033	−	0.0439726i	$-0.985999\pi$
$823$		−	2.52297i		−	0.0879451i	0.999033	−	0.0439726i	$-0.0140014\pi$
$824$	−8.37275	+	2.24347i	−0.291679	+	0.0781550i
$825$		0			0
$826$	3.00797	+	19.2761i	0.104661	+	0.670703i
$827$	−36.7114	−	36.7114i	−1.27658	−	1.27658i	−0.942569	−	0.334011i	$-0.891598\pi$
$827$	−36.7114	−	36.7114i	−1.27658	−	1.27658i	−0.334011	−	0.942569i	$-0.608402\pi$
$828$		0			0
$829$	13.1165	−	22.7185i	0.455555	−	0.789045i	−0.543164	−	0.839626i	$-0.682774\pi$
$829$	13.1165	−	22.7185i	0.455555	−	0.789045i	0.998720	+	0.0505811i	$0.0161073\pi$
$830$	−12.6820	+	3.39814i	−0.440200	+	0.117951i
$831$		0			0
$832$	7.38547	−	23.4917i	0.256045	−	0.814427i
$833$	−24.8922	+	7.96257i	−0.862465	+	0.275887i
$834$		0			0
$835$	−21.6650			−0.749747
$836$	8.46924			0.292915
$837$		0			0
$838$	4.94478	−	18.4542i	0.170815	−	0.637489i
$839$	−9.29570	−	34.6920i	−0.320923	−	1.19770i	−0.918347	−	0.395776i	$-0.870476\pi$
$839$	−9.29570	−	34.6920i	−0.320923	−	1.19770i	0.597424	−	0.801926i	$-0.296191\pi$
$840$		0			0
$841$	3.69273	−	6.39600i	0.127336	−	0.220552i
$842$			3.35962i			0.115780i
$843$		0			0
$844$	−9.85116	+	5.68757i	−0.339091	+	0.195774i
$845$	11.5427	+	4.17951i	0.397080	+	0.143780i
$846$		0			0
$847$	66.4057	−	53.5238i	2.28173	−	1.83910i
$848$	−1.84584	−	3.19709i	−0.0633865	−	0.109789i
$849$		0			0
$850$	−3.92245	+	14.6388i	−0.134539	+	0.502106i
$851$	−0.830208	+	0.830208i	−0.0284591	+	0.0284591i
$852$		0			0
$853$	0.749751	−	0.749751i	0.0256710	−	0.0256710i	−0.694155	−	0.719826i	$-0.744222\pi$
$853$	0.749751	−	0.749751i	0.0256710	−	0.0256710i	0.719826	+	0.694155i	$0.244222\pi$
$854$	0.685475	−	6.38174i	0.0234565	−	0.218379i
$855$		0			0
$856$	−23.4160	−	23.4160i	−0.800341	−	0.800341i
$857$	1.48116	+	2.56544i	0.0505953	+	0.0876336i	0.890214	−	0.455543i	$-0.150555\pi$
$857$	1.48116	+	2.56544i	0.0505953	+	0.0876336i	−0.839619	+	0.543176i	$0.817221\pi$
$858$		0			0
$859$	20.5020	+	11.8368i	0.699518	+	0.403867i	0.807168	−	0.590322i	$-0.200999\pi$
$859$	20.5020	+	11.8368i	0.699518	+	0.403867i	−0.107650	+	0.994189i	$0.534333\pi$
$860$	3.00653	−	11.2205i	0.102522	−	0.382616i
$861$		0			0
$862$	−0.593540	−	0.342681i	−0.0202161	−	0.0116717i
$863$	−5.04247	−	18.8188i	−0.171648	−	0.640598i	−0.997098	−	0.0761238i	$-0.975746\pi$
$863$	−5.04247	−	18.8188i	−0.171648	−	0.640598i	0.825451	−	0.564474i	$-0.190921\pi$
$864$		0			0
$865$	−5.73450	−	5.73450i	−0.194979	−	0.194979i
$866$	5.37764	+	20.0696i	0.182740	+	0.681994i
$867$		0			0
$868$	−20.4950	−	2.20140i	−0.695644	−	0.0747205i
$869$	3.20684	−	11.9681i	0.108785	−	0.405990i
$870$		0			0
$871$	−1.56908	+	36.6354i	−0.0531663	+	1.24134i
$872$	−10.8505	−	18.7936i	−0.367445	−	0.636433i
$873$		0			0
$874$	0.251281	−	0.145077i	0.00849970	−	0.00490730i
$875$	−13.4178	+	18.3796i	−0.453604	+	0.621345i
$876$		0			0
$877$	−33.2379	−	8.90606i	−1.12236	−	0.300736i	−0.350523	−	0.936554i	$-0.613996\pi$
$877$	−33.2379	−	8.90606i	−1.12236	−	0.300736i	−0.771839	+	0.635818i	$0.780663\pi$
$878$	15.9460	−	15.9460i	0.538153	−	0.538153i
$879$		0			0
$880$	−4.86362	+	2.80801i	−0.163952	+	0.0946580i
$881$	16.0850	+	27.8600i	0.541918	+	0.938629i	0.998794	+	0.0490986i	$0.0156348\pi$
$881$	16.0850	+	27.8600i	0.541918	+	0.938629i	−0.456876	+	0.889530i	$0.651032\pi$
$882$		0			0
$883$			24.5604i			0.826522i	0.910613	+	0.413261i	$0.135610\pi$
$883$			24.5604i			0.826522i	−0.910613	+	0.413261i	$0.864390\pi$
$884$	−4.13316	+	13.1467i	−0.139013	+	0.442172i
$885$		0			0
$886$	4.28974	+	16.0095i	0.144117	+	0.537851i
$887$			21.8838i			0.734786i	0.930066	+	0.367393i	$0.119750\pi$
$887$			21.8838i			0.734786i	−0.930066	+	0.367393i	$0.880250\pi$
$888$		0			0
$889$	−20.0895	+	16.1924i	−0.673781	+	0.543076i
$890$	0.985325	+	3.67728i	0.0330282	+	0.123263i
$891$		0			0
$892$	−27.2096	−	7.29080i	−0.911045	−	0.244114i
$893$	−2.74039			−0.0917038
$894$		0			0
$895$	−12.4386	−	3.33290i	−0.415775	−	0.111407i
$896$	7.29748	+	5.32742i	0.243792	+	0.177976i
$897$		0			0
$898$	7.57109	−	13.1135i	0.252651	−	0.437604i
$899$	−34.1754	+	9.15727i	−1.13981	+	0.305412i
$900$		0			0
$901$	7.61956	+	13.1975i	0.253844	+	0.439671i
$902$	44.2074	+	44.2074i	1.47194	+	1.47194i
$903$		0			0
$904$	−3.48815	+	0.934647i	−0.116014	+	0.0310859i
$905$	10.2666	−	2.75094i	0.341275	−	0.0914442i
$906$		0			0
$907$	−1.35415	−	0.781820i	−0.0449639	−	0.0259599i	0.477350	−	0.878713i	$-0.341598\pi$
$907$	−1.35415	−	0.781820i	−0.0449639	−	0.0259599i	−0.522313	+	0.852754i	$0.674931\pi$
$908$	−8.49867	+	8.49867i	−0.282038	+	0.282038i
$909$		0			0
$910$	5.55085	−	6.95761i	0.184009	−	0.230643i
$911$	−27.1812			−0.900555			−0.450277	−	0.892889i	$-0.648675\pi$
$911$	−27.1812			−0.900555			−0.450277	+	0.892889i	$0.648675\pi$
$912$		0			0
$913$	−80.1319	−	46.2642i	−2.65198	−	1.53112i
$914$		−	13.7603i		−	0.455149i
$915$		0			0
$916$	13.8615	−	3.71417i	0.457996	−	0.122720i
$917$	−41.9649	−	16.2188i	−1.38580	−	0.535592i
$918$		0			0
$919$	26.0917	+	45.1922i	0.860687	+	1.49075i	0.871267	+	0.490810i	$0.163299\pi$
$919$	26.0917	+	45.1922i	0.860687	+	1.49075i	−0.0105794	+	0.999944i	$0.503368\pi$
$920$	0.329257	−	0.570290i	0.0108553	−	0.0188019i
$921$		0			0
$922$	7.82204	−	13.5482i	0.257605	−	0.446185i
$923$	−0.258322	+	6.03137i	−0.00850276	+	0.198525i
$924$		0			0
$925$	−19.9610	−	5.34854i	−0.656314	−	0.175859i
$926$	−36.7074			−1.20628
$927$		0			0
$928$	22.8201	+	6.11463i	0.749107	+	0.200723i
$929$	7.07456	−	26.4026i	0.232109	−	0.866241i	−0.747322	−	0.664462i	$-0.768661\pi$
$929$	7.07456	−	26.4026i	0.232109	−	0.866241i	0.979431	−	0.201780i	$-0.0646725\pi$
$930$		0			0
$931$	0.420773	+	8.79685i	0.0137903	+	0.288305i
$932$	−3.11363	+	5.39297i	−0.101990	+	0.176653i
$933$		0			0
$934$	−8.53172	−	31.8408i	−0.279166	−	1.04186i
$935$	20.0768	−	11.5913i	0.656582	−	0.379078i
$936$		0			0
$937$		−	33.8356i		−	1.10536i	−0.833393	−	0.552680i	$-0.813605\pi$
$937$		−	33.8356i		−	1.10536i	0.833393	−	0.552680i	$-0.186395\pi$
$938$	24.7986	+	9.58428i	0.809703	+	0.312938i
$939$		0			0
$940$	−1.82359	+	1.05285i	−0.0594789	+	0.0343401i
$941$	13.4242	−	50.0997i	0.437615	−	1.63320i	−0.297114	−	0.954842i	$-0.596024\pi$
$941$	13.4242	−	50.0997i	0.437615	−	1.63320i	0.734729	−	0.678360i	$-0.237309\pi$
$942$		0			0
$943$	−2.16954	−	0.581325i	−0.0706498	−	0.0189306i
$944$	4.77293	−	4.77293i	0.155346	−	0.155346i
$945$		0			0
$946$	−67.6083	+	39.0337i	−2.19814	+	1.26909i
$947$	22.9502	+	22.9502i	0.745782	+	0.745782i	0.973684	−	0.227902i	$-0.0731866\pi$
$947$	22.9502	+	22.9502i	0.745782	+	0.745782i	−0.227902	+	0.973684i	$0.573187\pi$
$948$		0			0
$949$	24.7318	+	15.7271i	0.802828	+	0.510522i
$950$	4.42279	+	2.55350i	0.143494	+	0.0828465i
$951$		0			0
$952$	23.8359	+	17.4011i	0.772527	+	0.563972i
$953$	4.71317	+	2.72115i	0.152675	+	0.0881468i	0.574391	−	0.818581i	$-0.305239\pi$
$953$	4.71317	+	2.72115i	0.152675	+	0.0881468i	−0.421716	+	0.906728i	$0.638572\pi$
$954$		0			0
$955$	7.60993	+	7.60993i	0.246252	+	0.246252i
$956$	3.81453	+	3.81453i	0.123371	+	0.123371i
$957$		0			0
$958$	−4.54827	−	2.62595i	−0.146948	−	0.0848405i
$959$	10.2493	+	7.48235i	0.330967	+	0.241618i
$960$		0			0
$961$	−23.3093	−	13.4576i	−0.751914	−	0.434118i
$962$	17.0949	+	5.37440i	0.551161	+	0.173278i
$963$		0			0
$964$	−19.4369	−	19.4369i	−0.626020	−	0.626020i
$965$	2.03073	−	1.17245i	0.0653717	−	0.0377423i
$966$		0			0
$967$	17.2286	−	17.2286i	0.554035	−	0.554035i	−0.373568	−	0.927603i	$-0.621866\pi$
$967$	17.2286	−	17.2286i	0.554035	−	0.554035i	0.927603	+	0.373568i	$0.121866\pi$
$968$	−93.0301	−	24.9273i	−2.99010	−	0.801195i
$969$		0			0
$970$	−0.604268	+	2.25516i	−0.0194019	+	0.0724088i
$971$	−32.7698	+	18.9196i	−1.05163	+	0.607160i	−0.923106	−	0.384546i	$-0.874358\pi$
$971$	−32.7698	+	18.9196i	−1.05163	+	0.607160i	−0.128526	+	0.991706i	$0.541025\pi$
$972$		0			0
$973$	−19.8839	−	7.68482i	−0.637449	−	0.246364i
$974$			13.7417i			0.440312i
$975$		0			0
$976$	−1.92316	+	1.11034i	−0.0615589	+	0.0355411i
$977$	−15.3858	−	57.4206i	−0.492236	−	1.83705i	−0.544992	−	0.838442i	$-0.683467\pi$
$977$	−15.3858	−	57.4206i	−0.492236	−	1.83705i	0.0527558	−	0.998607i	$-0.483200\pi$
$978$		0			0
$979$	−13.4148	+	23.2350i	−0.428737	+	0.742595i
$980$	3.65972	+	5.69218i	0.116905	+	0.181830i
$981$		0			0
$982$	−1.99012	+	7.42721i	−0.0635072	+	0.237012i
$983$	−9.83824	−	2.63615i	−0.313791	−	0.0840800i	0.0984864	−	0.995138i	$-0.468600\pi$
$983$	−9.83824	−	2.63615i	−0.313791	−	0.0840800i	−0.412277	+	0.911058i	$0.635267\pi$
$984$		0			0
$985$	13.7675			0.438669
$986$	16.5660	+	4.43886i	0.527570	+	0.141362i
$987$		0			0
$988$	3.91875	+	2.49195i	0.124672	+	0.0792795i
$989$	1.40234	−	2.42892i	0.0445918	−	0.0772352i
$990$		0			0
$991$	25.9169	−	44.8894i	0.823277	−	1.42596i	−0.0799520	−	0.996799i	$-0.525477\pi$
$991$	25.9169	−	44.8894i	0.823277	−	1.42596i	0.903229	−	0.429159i	$-0.141190\pi$
$992$	19.3361	+	33.4910i	0.613920	+	1.06334i
$993$		0			0
$994$	4.08266	+	1.57788i	0.129494	+	0.0500474i
$995$	4.77011	−	1.27815i	0.151223	−	0.0405200i
$996$		0			0
$997$			43.9684i			1.39249i	0.717802	+	0.696247i	$0.245148\pi$
$997$			43.9684i			1.39249i	−0.717802	+	0.696247i	$0.754852\pi$
$998$	11.0429	+	6.37564i	0.349558	+	0.201817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.145.3		36
3.2	odd	2		273.2.bt.a.145.7	✓	36
7.3	odd	6		819.2.gh.c.262.3		36
13.7	odd	12		819.2.gh.c.397.3		36
21.17	even	6		273.2.cg.a.262.7	yes	36
39.20	even	12		273.2.cg.a.124.7	yes	36
91.59	even	12	inner	819.2.et.c.514.3		36
273.59	odd	12		273.2.bt.a.241.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.7	✓	36	3.2	odd	2
273.2.bt.a.241.7	yes	36	273.59	odd	12
273.2.cg.a.124.7	yes	36	39.20	even	12
273.2.cg.a.262.7	yes	36	21.17	even	6
819.2.et.c.145.3		36	1.1	even	1	trivial
819.2.et.c.514.3		36	91.59	even	12	inner
819.2.gh.c.262.3		36	7.3	odd	6
819.2.gh.c.397.3		36	13.7	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +O(q^{10})\)	\(q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +(-0.466517 + 0.808031i) q^{10} +(-6.35142 + 1.70186i) q^{11} +(-3.43957 - 1.08136i) q^{13} +(-1.54138 + 2.11138i) q^{14} +0.904452 q^{16} -3.73354 q^{17} +(-0.325628 + 1.21526i) q^{19} +(0.250210 + 0.933796i) q^{20} +(3.24847 - 5.62651i) q^{22} +0.233411i q^{23} +(-3.55787 + 2.05414i) q^{25} +(3.15860 - 1.64759i) q^{26} +(0.417609 + 2.67619i) q^{28} +(2.32457 + 4.02628i) q^{29} +(-1.96967 + 7.35090i) q^{31} +(3.59324 - 3.59324i) q^{32} +(2.60848 - 2.60848i) q^{34} +(2.28473 - 1.01099i) q^{35} +(3.55684 + 3.55684i) q^{37} +(-0.621551 - 1.07656i) q^{38} +(-2.44328 - 1.41063i) q^{40} +(-2.49056 + 9.29490i) q^{41} +(-10.4062 - 6.00801i) q^{43} +(-1.74227 - 6.50224i) q^{44} +(-0.163075 - 0.163075i) q^{46} +(0.563747 + 2.10393i) q^{47} +(6.66720 - 2.13271i) q^{49} +(1.05060 - 3.92089i) q^{50} +(1.10703 - 3.52125i) q^{52} +(-2.04084 - 3.53484i) q^{53} +(-5.37742 + 3.10465i) q^{55} +(-6.38428 - 4.66074i) q^{56} +(-4.43709 - 1.18891i) q^{58} +(5.27715 - 5.27715i) q^{59} +(-2.12633 + 1.22764i) q^{61} +(-3.75966 - 6.51191i) q^{62} +6.82982i q^{64} +(-3.40165 - 0.145692i) q^{65} +(-2.63222 - 9.82360i) q^{67} -3.82220i q^{68} +(-0.889915 + 2.30259i) q^{70} +(-0.433350 - 1.61728i) q^{71} +(-7.85180 - 2.10388i) q^{73} -4.97005 q^{74} +(-1.24412 - 0.333360i) q^{76} +(-15.9091 + 7.03974i) q^{77} +(-0.942160 + 1.63187i) q^{79} +(0.824984 - 0.221054i) q^{80} +(-4.75393 - 8.23404i) q^{82} +(9.95023 + 9.95023i) q^{83} +(-3.40550 + 0.912500i) q^{85} +(11.4680 - 3.07283i) q^{86} +(17.0131 + 9.82254i) q^{88} +(2.88517 - 2.88517i) q^{89} +(-9.43255 - 1.42371i) q^{91} -0.238954 q^{92} +(-1.86380 - 1.07607i) q^{94} +1.18807i q^{95} +(2.41702 - 0.647638i) q^{97} +(-3.16807 + 6.14815i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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