LMFDB - Embedded newform 819.2.et.c.136.6

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			136.6
Character	$\chi$	$=$	819.136
Dual form			819.2.et.c.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +O(q^{10})$	\(q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +(-0.202846 - 0.351339i) q^{10} +(0.230214 - 0.859171i) q^{11} +(0.659853 + 3.54466i) q^{13} +(1.27033 - 0.871831i) q^{14} -2.08030 q^{16} +0.0460661 q^{17} +(-0.843398 + 0.225988i) q^{19} +(1.11765 + 0.299472i) q^{20} +(-0.258989 - 0.448581i) q^{22} -3.19116i q^{23} +(3.90981 + 2.25733i) q^{25} +(1.73131 + 1.18789i) q^{26} +(-0.803659 + 4.32017i) q^{28} +(-4.08244 + 7.07099i) q^{29} +(3.90039 - 1.04511i) q^{31} +(-3.87153 + 3.87153i) q^{32} +(0.0189689 - 0.0189689i) q^{34} +(0.794617 - 1.66311i) q^{35} +(-4.97904 - 4.97904i) q^{37} +(-0.254234 + 0.440346i) q^{38} +(1.28621 - 0.742594i) q^{40} +(8.56284 - 2.29441i) q^{41} +(1.29226 - 0.746085i) q^{43} +(1.42698 + 0.382359i) q^{44} +(-1.31404 - 1.31404i) q^{46} +(12.1286 + 3.24985i) q^{47} +(6.53173 + 2.51724i) q^{49} +(2.53947 - 0.680450i) q^{50} +(-5.88726 + 1.09594i) q^{52} +(-4.89224 + 8.47362i) q^{53} +(-0.536646 - 0.309833i) q^{55} +(3.19167 + 4.65051i) q^{56} +(1.23061 + 4.59270i) q^{58} +(-6.25586 + 6.25586i) q^{59} +(0.877507 + 0.506629i) q^{61} +(1.17573 - 2.03643i) q^{62} -0.972206i q^{64} +(2.50426 + 0.195103i) q^{65} +(2.42048 + 0.648566i) q^{67} +0.0765105i q^{68} +(-0.357623 - 1.01203i) q^{70} +(0.798336 + 0.213913i) q^{71} +(-4.09226 - 15.2725i) q^{73} -4.10048 q^{74} +(-0.375340 - 1.40079i) q^{76} +(1.01455 - 2.12342i) q^{77} +(-4.73655 - 8.20394i) q^{79} +(-0.375097 + 1.39988i) q^{80} +(2.58118 - 4.47074i) q^{82} +(3.50364 + 3.50364i) q^{83} +(0.00830614 - 0.0309989i) q^{85} +(0.224900 - 0.839337i) q^{86} +(1.64220 - 0.948127i) q^{88} +(3.69759 - 3.69759i) q^{89} +(0.00119323 + 9.53939i) q^{91} +5.30014 q^{92} +(6.33246 - 3.65605i) q^{94} +0.608289i q^{95} +(-0.288642 + 1.07723i) q^{97} +(3.72614 - 1.65306i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.411775	−	0.411775i	0.291169	−	0.291169i	−0.546373	−	0.837542i	$-0.683992\pi$
$2$	0.411775	−	0.411775i	0.291169	−	0.291169i	0.837542	+	0.546373i	$0.183992\pi$
$3$		0			0
$3$		0			0
$4$			1.66088i			0.830442i
$5$	0.180309	−	0.672922i	0.0806367	−	0.300940i	−0.913816	−	0.406129i	$-0.866878\pi$
$5$	0.180309	−	0.672922i	0.0806367	−	0.300940i	0.994452	+	0.105189i	$0.0335449\pi$
$6$		0			0
$7$	2.60113	+	0.483875i	0.983134	+	0.182887i
$7$	2.60113	+	0.483875i	0.983134	+	0.182887i
$8$	1.50746	+	1.50746i	0.532967	+	0.532967i
$9$		0			0
$10$	−0.202846	−	0.351339i	−0.0641454	−	0.111103i
$11$	0.230214	−	0.859171i	0.0694122	−	0.259050i	−0.922496	−	0.386007i	$-0.873854\pi$
$11$	0.230214	−	0.859171i	0.0694122	−	0.259050i	0.991908	+	0.126957i	$0.0405209\pi$
$12$		0			0
$13$	0.659853	+	3.54466i	0.183010	+	0.983111i
$13$	0.659853	+	3.54466i	0.183010	+	0.983111i
$14$	1.27033	−	0.871831i	0.339509	−	0.233007i
$15$		0			0
$16$	−2.08030			−0.520075
$17$	0.0460661			0.0111727			0.00558634	−	0.999984i	$-0.498222\pi$
$17$	0.0460661			0.0111727			0.00558634	+	0.999984i	$0.498222\pi$
$18$		0			0
$19$	−0.843398	+	0.225988i	−0.193489	+	0.0518452i	−0.354262	−	0.935146i	$-0.615268\pi$
$19$	−0.843398	+	0.225988i	−0.193489	+	0.0518452i	0.160773	+	0.986991i	$0.448601\pi$
$20$	1.11765	+	0.299472i	0.249913	+	0.0669640i
$21$		0			0
$22$	−0.258989	−	0.448581i	−0.0552165	−	0.0956379i
$23$		−	3.19116i		−	0.665403i	−0.943032	−	0.332701i	$-0.892040\pi$
$23$		−	3.19116i		−	0.665403i	0.943032	−	0.332701i	$-0.107960\pi$
$24$		0			0
$25$	3.90981	+	2.25733i	0.781963	+	0.451466i
$26$	1.73131	+	1.18789i	0.339538	+	0.232964i
$27$		0			0
$28$	−0.803659	+	4.32017i	−0.151877	+	0.816435i
$29$	−4.08244	+	7.07099i	−0.758090	+	1.31305i	0.185734	+	0.982600i	$0.440534\pi$
$29$	−4.08244	+	7.07099i	−0.758090	+	1.31305i	−0.943824	+	0.330450i	$0.892800\pi$
$30$		0			0
$31$	3.90039	−	1.04511i	0.700531	−	0.187707i	0.109063	−	0.994035i	$-0.465215\pi$
$31$	3.90039	−	1.04511i	0.700531	−	0.187707i	0.591468	+	0.806328i	$0.298548\pi$
$32$	−3.87153	+	3.87153i	−0.684397	+	0.684397i
$33$		0			0
$34$	0.0189689	−	0.0189689i	0.00325313	−	0.00325313i
$35$	0.794617	−	1.66311i	0.134315	−	0.281117i
$36$		0			0
$37$	−4.97904	−	4.97904i	−0.818549	−	0.818549i	0.167349	−	0.985898i	$-0.446479\pi$
$37$	−4.97904	−	4.97904i	−0.818549	−	0.818549i	−0.985898	+	0.167349i	$0.946479\pi$
$38$	−0.254234	+	0.440346i	−0.0412422	+	0.0714335i
$39$		0			0
$40$	1.28621	−	0.742594i	0.203368	−	0.117414i
$41$	8.56284	−	2.29441i	1.33729	−	0.358326i	0.481863	−	0.876247i	$-0.339960\pi$
$41$	8.56284	−	2.29441i	1.33729	−	0.358326i	0.855429	+	0.517921i	$0.173294\pi$
$42$		0			0
$43$	1.29226	−	0.746085i	0.197067	−	0.113777i	−0.398219	−	0.917290i	$-0.630372\pi$
$43$	1.29226	−	0.746085i	0.197067	−	0.113777i	0.595287	+	0.803513i	$0.297038\pi$
$44$	1.42698	+	0.382359i	0.215126	+	0.0576428i
$45$		0			0
$46$	−1.31404	−	1.31404i	−0.193744	−	0.193744i
$47$	12.1286	+	3.24985i	1.76914	+	0.474039i	0.988536	−	0.150987i	$-0.0482451\pi$
$47$	12.1286	+	3.24985i	1.76914	+	0.474039i	0.780604	+	0.625026i	$0.214912\pi$
$48$		0			0
$49$	6.53173	+	2.51724i	0.933104	+	0.359606i
$50$	2.53947	−	0.680450i	0.359136	−	0.0962301i
$51$		0			0
$52$	−5.88726	+	1.09594i	−0.816416	+	0.151979i
$53$	−4.89224	+	8.47362i	−0.672001	+	1.16394i	0.305334	+	0.952245i	$0.401232\pi$
$53$	−4.89224	+	8.47362i	−0.672001	+	1.16394i	−0.977336	+	0.211695i	$0.932102\pi$
$54$		0			0
$55$	−0.536646	−	0.309833i	−0.0723613	−	0.0417778i
$56$	3.19167	+	4.65051i	0.426505	+	0.621451i
$57$		0			0
$58$	1.23061	+	4.59270i	0.161587	+	0.603051i
$59$	−6.25586	+	6.25586i	−0.814444	+	0.814444i	−0.985297	−	0.170853i	$-0.945348\pi$
$59$	−6.25586	+	6.25586i	−0.814444	+	0.814444i	0.170853	+	0.985297i	$0.445348\pi$
$60$		0			0
$61$	0.877507	+	0.506629i	0.112353	+	0.0648672i	0.555124	−	0.831768i	$-0.312671\pi$
$61$	0.877507	+	0.506629i	0.112353	+	0.0648672i	−0.442770	+	0.896635i	$0.646004\pi$
$62$	1.17573	−	2.03643i	0.149318	−	0.258627i
$63$		0			0
$64$		−	0.972206i		−	0.121526i
$65$	2.50426	+	0.195103i	0.310615	+	0.0241996i
$66$		0			0
$67$	2.42048	+	0.648566i	0.295709	+	0.0792350i	0.403623	−	0.914925i	$-0.367751\pi$
$67$	2.42048	+	0.648566i	0.295709	+	0.0792350i	−0.107915	+	0.994160i	$0.534417\pi$
$68$			0.0765105i			0.00927826i
$69$		0			0
$70$	−0.357623	−	1.01203i	−0.0427442	−	0.120961i
$71$	0.798336	+	0.213913i	0.0947450	+	0.0253869i	0.305880	−	0.952070i	$-0.401049\pi$
$71$	0.798336	+	0.213913i	0.0947450	+	0.0253869i	−0.211135	+	0.977457i	$0.567716\pi$
$72$		0			0
$73$	−4.09226	−	15.2725i	−0.478963	−	1.78751i	−0.605830	−	0.795594i	$-0.707159\pi$
$73$	−4.09226	−	15.2725i	−0.478963	−	1.78751i	0.126867	−	0.991920i	$-0.459508\pi$
$74$	−4.10048			−0.476672
$75$		0			0
$76$	−0.375340	−	1.40079i	−0.0430544	−	0.160681i
$77$	1.01455	−	2.12342i	0.115618	−	0.241986i
$78$		0			0
$79$	−4.73655	−	8.20394i	−0.532903	−	0.923016i	−0.999262	−	0.0384199i	$-0.987768\pi$
$79$	−4.73655	−	8.20394i	−0.532903	−	0.923016i	0.466358	−	0.884596i	$-0.345566\pi$
$80$	−0.375097	+	1.39988i	−0.0419371	+	0.156511i
$81$		0			0
$82$	2.58118	−	4.47074i	0.285044	−	0.493711i
$83$	3.50364	+	3.50364i	0.384574	+	0.384574i	0.872747	−	0.488173i	$-0.162336\pi$
$83$	3.50364	+	3.50364i	0.384574	+	0.384574i	−0.488173	+	0.872747i	$0.662336\pi$
$84$		0			0
$85$	0.00830614	−	0.0309989i	0.000900927	−	0.00336231i
$86$	0.224900	−	0.839337i	0.0242516	−	0.0905081i
$87$		0			0
$88$	1.64220	−	0.948127i	0.175060	−	0.101071i
$89$	3.69759	−	3.69759i	0.391944	−	0.391944i	−0.483436	−	0.875380i	$-0.660611\pi$
$89$	3.69759	−	3.69759i	0.391944	−	0.391944i	0.875380	+	0.483436i	$0.160611\pi$
$90$		0			0
$91$	0.00119323	+	9.53939i	0.000125084	+	1.00000i
$92$	5.30014			0.552578
$93$		0			0
$94$	6.33246	−	3.65605i	0.653143	−	0.377092i
$95$			0.608289i			0.0624092i
$96$		0			0
$97$	−0.288642	+	1.07723i	−0.0293071	+	0.109376i	−0.979030	−	0.203716i	$-0.934698\pi$
$97$	−0.288642	+	1.07723i	−0.0293071	+	0.109376i	0.949723	+	0.313092i	$0.101365\pi$
$98$	3.72614	−	1.65306i	0.376396	−	0.166985i
$99$		0			0
$100$	−3.74917	+	6.49375i	−0.374917	+	0.649375i
$101$	−7.30376	−	12.6505i	−0.726752	−	1.25877i	−0.958249	−	0.285935i	$-0.907696\pi$
$101$	−7.30376	−	12.6505i	−0.726752	−	1.25877i	0.231497	−	0.972836i	$-0.425638\pi$
$102$		0			0
$103$	−6.34652	−	10.9925i	−0.625342	−	1.08312i	−0.988475	−	0.151386i	$-0.951626\pi$
$103$	−6.34652	−	10.9925i	−0.625342	−	1.08312i	0.363133	−	0.931737i	$-0.381707\pi$
$104$	−4.34872	+	6.33812i	−0.426427	+	0.621504i
$105$		0			0
$106$	1.47472	+	5.50372i	0.143237	+	0.534569i
$107$	−11.7922			−1.14000			−0.569999	−	0.821645i	$-0.693056\pi$
$107$	−11.7922			−1.14000			−0.569999	+	0.821645i	$0.693056\pi$
$108$		0			0
$109$	0.888593	+	3.31627i	0.0851118	+	0.317641i	0.995335	−	0.0964758i	$-0.0307570\pi$
$109$	0.888593	+	3.31627i	0.0851118	+	0.317641i	−0.910224	+	0.414117i	$0.864090\pi$
$110$	−0.348558	+	0.0933959i	−0.0332337	+	0.00890495i
$111$		0			0
$112$	−5.41113	−	1.00661i	−0.511304	−	0.0951152i
$113$	−7.53468	−	13.0504i	−0.708803	−	1.22768i	−0.965301	−	0.261138i	$-0.915902\pi$
$113$	−7.53468	−	13.0504i	−0.708803	−	1.22768i	0.256498	−	0.966545i	$-0.417431\pi$
$114$		0			0
$115$	−2.14740	−	0.575395i	−0.200246	−	0.0536559i
$116$	−11.7441	−	6.78045i	−1.09041	−	0.629549i
$117$		0			0
$118$			5.15201i			0.474281i
$119$	0.119824	+	0.0222902i	0.0109842	+	0.00204334i
$120$		0			0
$121$	8.84110	+	5.10441i	0.803737	+	0.464038i
$122$	0.569952	−	0.152718i	0.0516010	−	0.0138265i
$123$		0			0
$124$	1.73580	+	6.47810i	0.155879	+	0.581750i
$125$	4.68705	−	4.68705i	0.419223	−	0.419223i
$126$		0			0
$127$	−6.17582	−	3.56561i	−0.548016	−	0.316397i	0.200306	−	0.979733i	$-0.435806\pi$
$127$	−6.17582	−	3.56561i	−0.548016	−	0.316397i	−0.748321	+	0.663337i	$0.769140\pi$
$128$	−8.14339	−	8.14339i	−0.719781	−	0.719781i
$129$		0			0
$130$	1.11153	−	0.950851i	0.0974874	−	0.0833951i
$131$	11.8790	−	6.85837i	1.03788	−	0.599219i	0.118646	−	0.992937i	$-0.462145\pi$
$131$	11.8790	−	6.85837i	1.03788	−	0.599219i	0.919231	+	0.393718i	$0.128811\pi$
$132$		0			0
$133$	−2.30314	+	0.179724i	−0.199707	+	0.0155841i
$134$	1.26376	−	0.729630i	0.109172	−	0.0630304i
$135$		0			0
$136$	0.0694428	+	0.0694428i	0.00595467	+	0.00595467i
$137$	−8.25603	−	8.25603i	−0.705361	−	0.705361i	0.260195	−	0.965556i	$-0.416213\pi$
$137$	−8.25603	−	8.25603i	−0.705361	−	0.705361i	−0.965556	+	0.260195i	$0.916213\pi$
$138$		0			0
$139$	−0.834941	+	0.482054i	−0.0708188	+	0.0408873i	−0.534991	−	0.844858i	$-0.679685\pi$
$139$	−0.834941	+	0.482054i	−0.0708188	+	0.0408873i	0.464172	+	0.885745i	$0.346352\pi$
$140$	2.76223	+	1.31977i	0.233451	+	0.111541i
$141$		0			0
$142$	0.416818	−	0.240650i	0.0349786	−	0.0201949i
$143$	3.19738	+	0.249103i	0.267378	+	0.0208311i
$144$		0			0
$145$	4.02213	+	4.02213i	0.334019	+	0.334019i
$146$	−7.97393	−	4.60375i	−0.659927	−	0.381009i
$147$		0			0
$148$	8.26961	−	8.26961i	0.679757	−	0.679757i
$149$	−0.600793	−	2.24219i	−0.0492189	−	0.183687i	0.936940	−	0.349490i	$-0.113645\pi$
$149$	−0.600793	−	2.24219i	−0.0492189	−	0.183687i	−0.986159	+	0.165803i	$0.946979\pi$
$150$		0			0
$151$	−13.1629	+	3.52700i	−1.07118	+	0.287023i	−0.750980	−	0.660325i	$-0.770418\pi$
$151$	−13.1629	+	3.52700i	−1.07118	+	0.287023i	−0.320205	+	0.947348i	$0.603752\pi$
$152$	−1.61206	−	0.930720i	−0.130755	−	0.0754914i
$153$		0			0
$154$	−0.456605	−	1.29214i	−0.0367943	−	0.104123i
$155$		−	2.81310i		−	0.225954i
$156$		0			0
$157$	3.81144	+	2.20054i	0.304186	+	0.175622i	0.644322	−	0.764754i	$-0.277140\pi$
$157$	3.81144	+	2.20054i	0.304186	+	0.175622i	−0.340136	+	0.940376i	$0.610473\pi$
$158$	−5.32857	−	1.42778i	−0.423918	−	0.113588i
$159$		0			0
$160$	1.90717	+	3.30331i	0.150775	+	0.261150i
$161$	1.54412	−	8.30061i	0.121694	−	0.654180i
$162$		0			0
$163$	−0.294730	+	0.0789727i	−0.0230850	+	0.00618562i	−0.270343	−	0.962764i	$-0.587137\pi$
$163$	−0.294730	+	0.0789727i	−0.0230850	+	0.00618562i	0.247258	+	0.968950i	$0.420470\pi$
$164$	3.81074	+	14.2219i	0.297569	+	1.11054i
$165$		0			0
$166$	2.88542			0.223952
$167$	−0.106108	−	0.396000i	−0.00821087	−	0.0306434i	0.961699	−	0.274108i	$-0.0883826\pi$
$167$	−0.106108	−	0.396000i	−0.00821087	−	0.0306434i	−0.969910	+	0.243465i	$0.921716\pi$
$168$		0			0
$169$	−12.1292	+	4.67791i	−0.933014	+	0.359839i
$170$	−0.00934431	−	0.0161848i	−0.000716676	−	0.00124132i
$171$		0			0
$172$	1.23916	+	2.14629i	0.0944851	+	0.163653i
$173$	1.03796	−	1.79781i	0.0789149	−	0.136685i	−0.823867	−	0.566783i	$-0.808188\pi$
$173$	1.03796	−	1.79781i	0.0789149	−	0.136685i	0.902782	+	0.430098i	$0.141521\pi$
$174$		0			0
$175$	9.07766	+	7.76347i	0.686207	+	0.586863i
$176$	−0.478915	+	1.78734i	−0.0360996	+	0.134725i
$177$		0			0
$178$		−	3.04514i		−	0.228243i
$179$	−11.6148	+	6.70581i	−0.868131	+	0.501216i	−0.866727	−	0.498783i	$-0.833780\pi$
$179$	−11.6148	+	6.70581i	−0.868131	+	0.501216i	−0.00140439	+	0.999999i	$0.500447\pi$
$180$		0			0
$181$	−2.32661			−0.172935			−0.0864677	−	0.996255i	$-0.527558\pi$
$181$	−2.32661			−0.172935			−0.0864677	+	0.996255i	$0.527558\pi$
$182$	3.92857	+	3.92759i	0.291205	+	0.291132i
$183$		0			0
$184$	4.81054	−	4.81054i	0.354638	−	0.354638i
$185$	−4.24827	+	2.45274i	−0.312339	+	0.180329i
$186$		0			0
$187$	0.0106051	−	0.0395787i	0.000775520	−	0.00289428i
$188$	−5.39762	+	20.1442i	−0.393662	+	1.46917i
$189$		0			0
$190$	0.250478	+	0.250478i	0.0181716	+	0.0181716i
$191$	11.4976	−	19.9143i	0.831934	−	1.44095i	−0.0645691	−	0.997913i	$-0.520567\pi$
$191$	11.4976	−	19.9143i	0.831934	−	1.44095i	0.896503	−	0.443038i	$-0.146099\pi$
$192$		0			0
$193$	1.74638	−	6.51759i	0.125707	−	0.469146i	−0.874157	−	0.485644i	$-0.838585\pi$
$193$	1.74638	−	6.51759i	0.125707	−	0.469146i	0.999864	+	0.0164980i	$0.00525171\pi$
$194$	0.324719	+	0.562430i	0.0233135	+	0.0403801i
$195$		0			0
$196$	−4.18084	+	10.8484i	−0.298632	+	0.774889i
$197$	−3.30495	−	12.3342i	−0.235468	−	0.878778i	−0.977937	−	0.208898i	$-0.933012\pi$
$197$	−3.30495	−	12.3342i	−0.235468	−	0.878778i	0.742470	−	0.669880i	$-0.233654\pi$
$198$		0			0
$199$	0.830455			0.0588694			0.0294347	−	0.999567i	$-0.490629\pi$
$199$	0.830455			0.0588694			0.0294347	+	0.999567i	$0.490629\pi$
$200$	2.49105	+	9.29672i	0.176144	+	0.657377i
$201$		0			0
$202$	−8.21665	−	2.20165i	−0.578122	−	0.154907i
$203$	−14.0404	+	16.4172i	−0.985444	+	1.15226i
$204$		0			0
$205$		−	6.17583i		−	0.431339i
$206$	−7.13977	−	1.91310i	−0.497451	−	0.133292i
$207$		0			0
$208$	−1.37269	−	7.37395i	−0.0951792	−	0.511292i
$209$			0.776649i			0.0537220i
$210$		0			0
$211$	11.5683	−	20.0368i	0.796392	−	1.37939i	−0.125560	−	0.992086i	$-0.540073\pi$
$211$	11.5683	−	20.0368i	0.796392	−	1.37939i	0.921952	−	0.387305i	$-0.126594\pi$
$212$	−14.0737	−	8.12545i	−0.966585	−	0.558058i
$213$		0			0
$214$	−4.85574	+	4.85574i	−0.331931	+	0.331931i
$215$	−0.269052	−	1.00411i	−0.0183492	−	0.0684801i
$216$		0			0
$217$	10.6511	−	0.831155i	0.723045	−	0.0564225i
$218$	1.73146	+	0.999657i	0.117269	+	0.0677053i
$219$		0			0
$220$	0.514596	−	0.891307i	0.0346941	−	0.0600919i
$221$	0.0303969	+	0.163289i	0.00204472	+	0.0109840i
$222$		0			0
$223$	−13.8755	+	3.71792i	−0.929171	+	0.248971i	−0.691501	−	0.722375i	$-0.743050\pi$
$223$	−13.8755	+	3.71792i	−0.929171	+	0.248971i	−0.237670	+	0.971346i	$0.576384\pi$
$224$	−11.9437	+	8.19701i	−0.798021	+	0.547686i
$225$		0			0
$226$	−8.47643	−	2.27125i	−0.563844	−	0.151081i
$227$	14.5357	+	14.5357i	0.964765	+	0.964765i	0.999400	−	0.0346350i	$-0.0110269\pi$
$227$	14.5357	+	14.5357i	0.964765	+	0.964765i	−0.0346350	+	0.999400i	$0.511027\pi$
$228$		0			0
$229$	3.99397	+	1.07018i	0.263929	+	0.0707196i	0.388357	−	0.921509i	$-0.373043\pi$
$229$	3.99397	+	1.07018i	0.263929	+	0.0707196i	−0.124428	+	0.992229i	$0.539709\pi$
$230$	−1.12118	+	0.647313i	−0.0739283	+	0.0426826i
$231$		0			0
$232$	−16.8133	+	4.50512i	−1.10385	+	0.295775i
$233$	1.72269	−	0.994594i	0.112857	−	0.0651580i	−0.442509	−	0.896764i	$-0.645912\pi$
$233$	1.72269	−	0.994594i	0.112857	−	0.0651580i	0.555366	+	0.831606i	$0.312578\pi$
$234$		0			0
$235$	4.37380	−	7.57564i	0.285315	−	0.494180i
$236$	−10.3903	−	10.3903i	−0.676348	−	0.676348i
$237$		0			0
$238$	0.0585190	−	0.0401619i	0.00379322	−	0.00260331i
$239$	−10.1339	+	10.1339i	−0.655510	+	0.655510i	−0.954314	−	0.298805i	$-0.903412\pi$
$239$	−10.1339	+	10.1339i	−0.655510	+	0.655510i	0.298805	+	0.954314i	$0.403412\pi$
$240$		0			0
$241$	−19.5579	+	19.5579i	−1.25984	+	1.25984i	−0.308664	+	0.951171i	$0.599882\pi$
$241$	−19.5579	+	19.5579i	−1.25984	+	1.25984i	−0.951171	+	0.308664i	$0.900118\pi$
$242$	5.74241	−	1.53867i	0.369136	−	0.0989097i
$243$		0			0
$244$	−0.841452	+	1.45744i	−0.0538684	+	0.0933029i
$245$	2.87164	−	3.94147i	0.183462	−	0.251811i
$246$		0			0
$247$	−1.35757	−	2.84044i	−0.0863800	−	0.180733i
$248$	7.45513	+	4.30422i	0.473401	+	0.273318i
$249$		0			0
$250$		−	3.86002i		−	0.244129i
$251$	3.92297	+	6.79478i	0.247616	+	0.428883i	0.962864	−	0.269988i	$-0.0870197\pi$
$251$	3.92297	+	6.79478i	0.247616	+	0.428883i	−0.715248	+	0.698871i	$0.753686\pi$
$252$		0			0
$253$	−2.74175	−	0.734651i	−0.172373	−	0.0461871i
$254$	−4.01127	+	1.07482i	−0.251690	+	0.0674401i
$255$		0			0
$256$	−4.76207			−0.297629
$257$	0.363807			0.0226936			0.0113468	−	0.999936i	$-0.496388\pi$
$257$	0.363807			0.0226936			0.0113468	+	0.999936i	$0.496388\pi$
$258$		0			0
$259$	−10.5419	−	15.3604i	−0.655041	−	0.954446i
$260$	−0.324044	+	4.15928i	−0.0200964	+	0.257948i
$261$		0			0
$262$	2.06739	−	7.71559i	0.127724	−	0.476671i
$263$	11.1731	+	19.3524i	0.688963	+	1.19332i	0.972174	+	0.234261i	$0.0752671\pi$
$263$	11.1731	+	19.3524i	0.688963	+	1.19332i	−0.283211	+	0.959058i	$0.591400\pi$
$264$		0			0
$265$	4.81997	+	4.81997i	0.296088	+	0.296088i
$266$	−0.874367	+	1.02238i	−0.0536109	+	0.0626861i
$267$		0			0
$268$	−1.07719	+	4.02014i	−0.0658000	+	0.245569i
$269$		−	26.2941i		−	1.60318i	−0.597874	−	0.801590i	$-0.703988\pi$
$269$		−	26.2941i		−	1.60318i	0.597874	−	0.801590i	$-0.296012\pi$
$270$		0			0
$271$	0.167050	−	0.167050i	0.0101476	−	0.0101476i	−0.702015	−	0.712162i	$-0.747716\pi$
$271$	0.167050	−	0.167050i	0.0101476	−	0.0101476i	0.712162	+	0.702015i	$0.247716\pi$
$272$	−0.0958314			−0.00581063
$273$		0			0
$274$	−6.79925			−0.410758
$275$	2.83953	−	2.83953i	0.171230	−	0.171230i
$276$		0			0
$277$			1.88689i			0.113372i	0.998392	+	0.0566860i	$0.0180534\pi$
$277$			1.88689i			0.113372i	−0.998392	+	0.0566860i	$0.981947\pi$
$278$	−0.145310	+	0.542305i	−0.00871513	+	0.0325253i
$279$		0			0
$280$	3.70492	−	1.30922i	0.221411	−	0.0782407i
$281$	−14.2823	−	14.2823i	−0.852011	−	0.852011i	0.138370	−	0.990381i	$-0.455814\pi$
$281$	−14.2823	−	14.2823i	−0.852011	−	0.852011i	−0.990381	+	0.138370i	$0.955814\pi$
$282$		0			0
$283$	8.56272	+	14.8311i	0.509001	+	0.881615i	0.999946	+	0.0104246i	$0.00331831\pi$
$283$	8.56272	+	14.8311i	0.509001	+	0.881615i	−0.490945	+	0.871191i	$0.663348\pi$
$284$	−0.355285	+	1.32594i	−0.0210823	+	0.0786802i
$285$		0			0
$286$	1.41917	−	1.21402i	0.0839174	−	0.0717867i
$287$	23.3833	−	1.82470i	1.38027	−	0.107709i
$288$		0			0
$289$	−16.9979			−0.999875
$290$	3.31242			0.194512
$291$		0			0
$292$	25.3659	−	6.79677i	1.48443	−	0.397751i
$293$	0.0551536	+	0.0147783i	0.00322210	+	0.000863360i	0.260430	−	0.965493i	$-0.416136\pi$
$293$	0.0551536	+	0.0147783i	0.00322210	+	0.000863360i	−0.257208	+	0.966356i	$0.582802\pi$
$294$		0			0
$295$	3.08172	+	5.33770i	0.179425	+	0.310773i
$296$		−	15.0114i		−	0.872519i
$297$		0			0
$298$	−1.17067	−	0.675886i	−0.0678150	−	0.0391530i
$299$	11.3116	−	2.10570i	0.654165	−	0.121776i
$300$		0			0
$301$	3.72234	−	1.31537i	0.214552	−	0.0758168i
$302$	−3.96783	+	6.87249i	−0.228323	+	0.395467i
$303$		0			0
$304$	1.75452	−	0.470123i	0.100629	−	0.0269634i
$305$	0.499145	−	0.499145i	0.0285809	−	0.0285809i
$306$		0			0
$307$	17.7169	−	17.7169i	1.01116	−	1.01116i	0.0112203	−	0.999937i	$-0.496428\pi$
$307$	17.7169	−	17.7169i	1.01116	−	1.01116i	0.999937	−	0.0112203i	$-0.00357162\pi$
$308$	3.52675	+	1.68505i	0.200955	+	0.0960144i
$309$		0			0
$310$	−1.15836	−	1.15836i	−0.0657907	−	0.0657907i
$311$	9.52232	−	16.4931i	0.539961	−	0.935240i	−0.458944	−	0.888465i	$-0.651772\pi$
$311$	9.52232	−	16.4931i	0.539961	−	0.935240i	0.998905	−	0.0467749i	$-0.0148944\pi$
$312$		0			0
$313$	−2.59097	+	1.49590i	−0.146450	+	0.0845530i	−0.571435	−	0.820648i	$-0.693613\pi$
$313$	−2.59097	+	1.49590i	−0.146450	+	0.0845530i	0.424984	+	0.905201i	$0.360280\pi$
$314$	2.47558	−	0.663329i	0.139705	−	0.0374338i
$315$		0			0
$316$	13.6258	−	7.86686i	0.766511	−	0.442545i
$317$	−0.683930	−	0.183258i	−0.0384133	−	0.0102928i	0.239561	−	0.970881i	$-0.422996\pi$
$317$	−0.683930	−	0.183258i	−0.0384133	−	0.0102928i	−0.277975	+	0.960588i	$0.589663\pi$
$318$		0			0
$319$	5.13536	+	5.13536i	0.287525	+	0.287525i
$320$	−0.654219	−	0.175298i	−0.0365720	−	0.00979943i
$321$		0			0
$322$	−2.78215	−	4.05381i	−0.155043	−	0.225910i
$323$	−0.0388521	+	0.0104104i	−0.00216179	+	0.000579249i
$324$		0			0
$325$	−5.42156	+	15.3485i	−0.300734	+	0.851379i
$326$	−0.0888434	+	0.153881i	−0.00492058	+	0.00852269i
$327$		0			0
$328$	16.3669	+	9.44941i	0.903708	+	0.521756i
$329$	29.9755	+	14.3220i	1.65261	+	0.789598i
$330$		0			0
$331$	−2.45661	−	9.16821i	−0.135028	−	0.503930i	−0.999998	−	0.00210683i	$-0.999329\pi$
$331$	−2.45661	−	9.16821i	−0.135028	−	0.503930i	0.864970	−	0.501823i	$-0.167337\pi$
$332$	−5.81913	+	5.81913i	−0.319366	+	0.319366i
$333$		0			0
$334$	−0.206755	−	0.119370i	−0.0113131	−	0.00653164i
$335$	0.872869	−	1.51185i	0.0476899	−	0.0826014i
$336$		0			0
$337$		−	28.3561i		−	1.54465i	−0.635226	−	0.772327i	$-0.719093\pi$
$337$		−	28.3561i		−	1.54465i	0.635226	−	0.772327i	$-0.280907\pi$
$338$	−3.06825	+	6.92073i	−0.166891	+	0.376438i
$339$		0			0
$340$	0.0514856	+	0.0137955i	0.00279220	+	0.000748167i
$341$		−	3.59170i		−	0.194502i
$342$		0			0
$343$	15.7718	+	9.70820i	0.851599	+	0.524194i
$344$	3.07272	+	0.823332i	0.165670	+	0.0443911i
$345$		0			0
$346$	−0.312884	−	1.16770i	−0.0168207	−	0.0627758i
$347$	22.3797			1.20140			0.600702	−	0.799473i	$-0.294888\pi$
$347$	22.3797			1.20140			0.600702	+	0.799473i	$0.294888\pi$
$348$		0			0
$349$	−2.36174	−	8.81412i	−0.126421	−	0.471809i	0.873465	−	0.486886i	$-0.161867\pi$
$349$	−2.36174	−	8.81412i	−0.126421	−	0.471809i	−0.999886	+	0.0150770i	$0.995201\pi$
$350$	6.93475	−	0.541150i	0.370678	−	0.0289257i
$351$		0			0
$352$	2.43503	+	4.21759i	0.129787	+	0.224798i
$353$	−0.743912	+	2.77632i	−0.0395945	+	0.147769i	−0.982893	−	0.184177i	$-0.941038\pi$
$353$	−0.743912	+	2.77632i	−0.0395945	+	0.147769i	0.943299	+	0.331945i	$0.107705\pi$
$354$		0			0
$355$	0.287894	−	0.498648i	0.0152798	−	0.0264655i
$356$	6.14126	+	6.14126i	0.325486	+	0.325486i
$357$		0			0
$358$	−2.02140	+	7.54396i	−0.106834	+	0.398711i
$359$	−2.08854	+	7.79454i	−0.110229	+	0.411380i	−0.998886	−	0.0471928i	$-0.984972\pi$
$359$	−2.08854	+	7.79454i	−0.110229	+	0.411380i	0.888657	+	0.458573i	$0.151639\pi$
$360$		0			0
$361$	−15.7942	+	9.11880i	−0.831275	+	0.479937i
$362$	−0.958038	+	0.958038i	−0.0503534	+	0.0503534i
$363$		0			0
$364$	−15.8438	+	0.00198181i	−0.830442	+	0.000103875i
$365$	−11.0151			−0.576557
$366$		0			0
$367$	−1.45417	+	0.839564i	−0.0759069	+	0.0438249i	−0.537473	−	0.843281i	$-0.680621\pi$
$367$	−1.45417	+	0.839564i	−0.0759069	+	0.0438249i	0.461566	+	0.887106i	$0.347288\pi$
$368$			6.63857i			0.346060i
$369$		0			0
$370$	−0.739354	+	2.75931i	−0.0384372	+	0.143450i
$371$	−16.8255	+	19.6737i	−0.873537	+	1.02141i
$372$		0			0
$373$	16.1379	−	27.9516i	0.835587	−	1.44728i	−0.0579649	−	0.998319i	$-0.518461\pi$
$373$	16.1379	−	27.9516i	0.835587	−	1.44728i	0.893552	−	0.448960i	$-0.148206\pi$
$374$	−0.0119306	−	0.0206644i	−0.000616916	−	0.00106853i
$375$		0			0
$376$	13.3844	+	23.1824i	0.690246	+	1.19554i
$377$	−27.7580	−	9.80502i	−1.42961	−	0.504984i
$378$		0			0
$379$	5.38351	+	20.0915i	0.276532	+	1.03203i	0.954808	+	0.297224i	$0.0960609\pi$
$379$	5.38351	+	20.0915i	0.276532	+	1.03203i	−0.678276	+	0.734808i	$0.737272\pi$
$380$	−1.01030			−0.0518272
$381$		0			0
$382$	−3.46582	−	12.9346i	−0.177327	−	0.661793i
$383$	27.1672	−	7.27943i	1.38818	−	0.371962i	0.514094	−	0.857734i	$-0.328128\pi$
$383$	27.1672	−	7.27943i	1.38818	−	0.371962i	0.874086	+	0.485772i	$0.161461\pi$
$384$		0			0
$385$	−1.24596	−	1.06558i	−0.0635002	−	0.0543072i
$386$	−1.96466	−	3.40289i	−0.0999986	−	0.173203i
$387$		0			0
$388$	−1.78915	−	0.479401i	−0.0908302	−	0.0243379i
$389$	9.23904	+	5.33416i	0.468438	+	0.270453i	0.715586	−	0.698525i	$-0.246160\pi$
$389$	9.23904	+	5.33416i	0.468438	+	0.270453i	−0.247148	+	0.968978i	$0.579493\pi$
$390$		0			0
$391$		−	0.147004i		−	0.00743433i
$392$	6.05168	+	13.6409i	0.305656	+	0.688972i
$393$		0			0
$394$	−6.43981	−	3.71803i	−0.324433	−	0.187312i
$395$	−6.37466	+	1.70809i	−0.320744	+	0.0859431i
$396$		0			0
$397$	−0.614054	−	2.29168i	−0.0308185	−	0.115016i	0.948803	−	0.315868i	$-0.102296\pi$
$397$	−0.614054	−	2.29168i	−0.0308185	−	0.115016i	−0.979622	+	0.200852i	$0.935629\pi$
$398$	0.341960	−	0.341960i	0.0171409	−	0.0171409i
$399$		0			0
$400$	−8.13359	−	4.69593i	−0.406679	−	0.234797i
$401$	−22.0398	−	22.0398i	−1.10061	−	1.10061i	−0.994336	−	0.106278i	$-0.966107\pi$
$401$	−22.0398	−	22.0398i	−1.10061	−	1.10061i	−0.106278	−	0.994336i	$-0.533893\pi$
$402$		0			0
$403$	6.27823	+	13.1359i	0.312741	+	0.654347i
$404$	21.0110	−	12.1307i	1.04534	−	0.603525i
$405$		0			0
$406$	0.978682	+	12.5416i	0.0485712	+	0.622432i
$407$	−5.42410	+	3.13160i	−0.268862	+	0.155228i
$408$		0			0
$409$	16.2736	+	16.2736i	0.804679	+	0.804679i	0.983823	−	0.179144i	$-0.0573328\pi$
$409$	16.2736	+	16.2736i	0.804679	+	0.804679i	−0.179144	+	0.983823i	$0.557333\pi$
$410$	−2.54305	−	2.54305i	−0.125592	−	0.125592i
$411$		0			0
$412$	18.2573	−	10.5408i	0.899471	−	0.519310i
$413$	−19.2994	+	13.2452i	−0.949659	+	0.651756i
$414$		0			0
$415$	2.98941	−	1.72594i	0.146745	−	0.0847230i
$416$	−16.2779	−	11.1686i	−0.798090	−	0.547586i
$417$		0			0
$418$	0.319804	+	0.319804i	0.0156421	+	0.0156421i
$419$	−15.0030	−	8.66198i	−0.732944	−	0.423166i	0.0865540	−	0.996247i	$-0.472414\pi$
$419$	−15.0030	−	8.66198i	−0.732944	−	0.423166i	−0.819498	+	0.573082i	$0.805748\pi$
$420$		0			0
$421$	−28.4825	+	28.4825i	−1.38815	+	1.38815i	−0.558947	+	0.829203i	$0.688794\pi$
$421$	−28.4825	+	28.4825i	−1.38815	+	1.38815i	−0.829203	+	0.558947i	$0.811206\pi$
$422$	−3.48714	−	13.0142i	−0.169751	−	0.633520i
$423$		0			0
$424$	−20.1485	+	5.39877i	−0.978497	+	0.262187i
$425$	0.180110	+	0.103987i	0.00873662	+	0.00504409i
$426$		0			0
$427$	2.03736	+	1.74241i	0.0985949	+	0.0843211i
$428$		−	19.5855i		−	0.946702i
$429$		0			0
$430$	−0.524258	−	0.302680i	−0.0252819	−	0.0145965i
$431$	32.7297	+	8.76990i	1.57653	+	0.422431i	0.937851	−	0.347039i	$-0.112813\pi$
$431$	32.7297	+	8.76990i	1.57653	+	0.422431i	0.638683	+	0.769470i	$0.279479\pi$
$432$		0			0
$433$	15.2303	+	26.3796i	0.731921	+	1.26772i	0.956061	+	0.293167i	$0.0947091\pi$
$433$	15.2303	+	26.3796i	0.731921	+	1.26772i	−0.224141	+	0.974557i	$0.571958\pi$
$434$	4.04361	−	4.72811i	0.194099	−	0.226956i
$435$		0			0
$436$	−5.50794	+	1.47585i	−0.263783	+	0.0706804i
$437$	0.721163	+	2.69142i	0.0344979	+	0.128748i
$438$		0			0
$439$	−2.72571			−0.130091			−0.0650455	−	0.997882i	$-0.520719\pi$
$439$	−2.72571			−0.130091			−0.0650455	+	0.997882i	$0.520719\pi$
$440$	−0.341912	−	1.27603i	−0.0163000	−	0.0608324i
$441$		0			0
$442$	0.0797547	+	0.0547214i	0.00379355	+	0.00260283i
$443$	17.3901	+	30.1206i	0.826229	+	1.43107i	0.900976	+	0.433869i	$0.142852\pi$
$443$	17.3901	+	30.1206i	0.826229	+	1.43107i	−0.0747467	+	0.997203i	$0.523815\pi$
$444$		0			0
$445$	−1.82148	−	3.15490i	−0.0863465	−	0.149557i
$446$	−4.18262	+	7.24452i	−0.198053	+	0.343038i
$447$		0			0
$448$	0.470426	−	2.52883i	0.0222255	−	0.119476i
$449$	−9.41298	+	35.1297i	−0.444226	+	1.65787i	0.273746	+	0.961802i	$0.411737\pi$
$449$	−9.41298	+	35.1297i	−0.444226	+	1.65787i	−0.717972	+	0.696072i	$0.754930\pi$
$450$		0			0
$451$		−	7.88516i		−	0.371298i
$452$	21.6753	−	12.5142i	1.01952	−	0.588620i
$453$		0			0
$454$	11.9708			0.561818
$455$	6.41949	+	1.71924i	0.300950	+	0.0805990i
$456$		0			0
$457$	22.5125	−	22.5125i	1.05309	−	1.05309i	0.0545801	−	0.998509i	$-0.482618\pi$
$457$	22.5125	−	22.5125i	1.05309	−	1.05309i	0.998509	−	0.0545801i	$-0.0173820\pi$
$458$	2.08529	−	1.20394i	0.0974392	−	0.0562566i
$459$		0			0
$460$	0.955664	−	3.56659i	0.0445581	−	0.166293i
$461$	4.67038	−	17.4301i	0.217521	−	0.811800i	−0.767743	−	0.640758i	$-0.778620\pi$
$461$	4.67038	−	17.4301i	0.217521	−	0.811800i	0.985264	−	0.171042i	$-0.0547133\pi$
$462$		0			0
$463$	16.2446	+	16.2446i	0.754951	+	0.754951i	0.975399	−	0.220448i	$-0.0707518\pi$
$463$	16.2446	+	16.2446i	0.754951	+	0.754951i	−0.220448	+	0.975399i	$0.570752\pi$
$464$	8.49270	−	14.7098i	0.394264	−	0.682885i
$465$		0			0
$466$	0.299810	−	1.11891i	0.0138884	−	0.0518323i
$467$	18.7401	+	32.4588i	0.867188	+	1.50201i	0.864859	+	0.502016i	$0.167408\pi$
$467$	18.7401	+	32.4588i	0.867188	+	1.50201i	0.00232895	+	0.999997i	$0.499259\pi$
$468$		0			0
$469$	5.98216	+	2.85821i	0.276230	+	0.131980i
$470$	−1.31844	−	4.92047i	−0.0608149	−	0.226964i
$471$		0			0
$472$	−18.8609			−0.868144
$473$	−0.343519	−	1.28203i	−0.0157950	−	0.0589478i
$474$		0			0
$475$	−3.80766	−	1.02026i	−0.174707	−	0.0468127i
$476$	−0.0370215	+	0.199013i	−0.00169688	+	0.00912177i
$477$		0			0
$478$			8.34579i			0.381728i
$479$	−25.8166	−	6.91755i	−1.17959	−	0.316071i	−0.384828	−	0.922988i	$-0.625739\pi$
$479$	−25.8166	−	6.91755i	−1.17959	−	0.316071i	−0.794765	+	0.606918i	$0.792406\pi$
$480$		0			0
$481$	14.3636	−	20.9344i	0.654922	−	0.954528i
$482$			16.1069i			0.733649i
$483$		0			0
$484$	−8.47784	+	14.6840i	−0.385356	+	0.667456i
$485$	0.672845	+	0.388467i	0.0305523	+	0.0176394i
$486$		0			0
$487$	−17.5241	+	17.5241i	−0.794093	+	0.794093i	−0.982157	−	0.188064i	$-0.939779\pi$
$487$	−17.5241	+	17.5241i	−0.794093	+	0.794093i	0.188064	+	0.982157i	$0.439779\pi$
$488$	0.559083	+	2.08653i	0.0253085	+	0.0944527i
$489$		0			0
$490$	−0.440529	−	2.80546i	−0.0199011	−	0.126738i
$491$	−9.62086	−	5.55460i	−0.434183	−	0.250676i	0.266944	−	0.963712i	$-0.413986\pi$
$491$	−9.62086	−	5.55460i	−0.434183	−	0.250676i	−0.701127	+	0.713036i	$0.747319\pi$
$492$		0			0
$493$	−0.188062	+	0.325733i	−0.00846989	+	0.0146703i
$494$	−1.72863	−	0.610608i	−0.0777748	−	0.0274726i
$495$		0			0
$496$	−8.11399	+	2.17414i	−0.364329	+	0.0976216i
$497$	1.97307	+	0.942711i	0.0885041	+	0.0422863i
$498$		0			0
$499$	−0.179598	−	0.0481231i	−0.00803990	−	0.00215428i	0.254797	−	0.966995i	$-0.417991\pi$
$499$	−0.179598	−	0.0481231i	−0.00803990	−	0.00215428i	−0.262837	+	0.964840i	$0.584658\pi$
$500$	7.78465	+	7.78465i	0.348140	+	0.348140i
$501$		0			0
$502$	4.41330	+	1.18254i	0.196975	+	0.0527793i
$503$	−0.488766	+	0.282189i	−0.0217930	+	0.0125822i	−0.510857	−	0.859666i	$-0.670672\pi$
$503$	−0.488766	+	0.282189i	−0.0217930	+	0.0125822i	0.489064	+	0.872248i	$0.337338\pi$
$504$		0			0
$505$	−9.82973	+	2.63387i	−0.437417	+	0.117206i
$506$	−1.43149	+	0.826474i	−0.0636377	+	0.0367412i
$507$		0			0
$508$	5.92207	−	10.2573i	0.262749	−	0.455095i
$509$	−16.1364	−	16.1364i	−0.715235	−	0.715235i	0.252390	−	0.967625i	$-0.418783\pi$
$509$	−16.1364	−	16.1364i	−0.715235	−	0.715235i	−0.967625	+	0.252390i	$0.918783\pi$
$510$		0			0
$511$	−3.25450	−	41.7059i	−0.143971	−	1.84496i
$512$	14.3259	−	14.3259i	0.633121	−	0.633121i
$513$		0			0
$514$	0.149806	−	0.149806i	0.00660767	−	0.00660767i
$515$	−8.54144	+	2.28867i	−0.376381	+	0.100851i
$516$		0			0
$517$	5.58436	−	9.67239i	0.245600	−	0.425391i
$518$	−10.6659	−	1.98412i	−0.468632	−	0.0871772i
$519$		0			0
$520$	3.48095	+	4.06917i	0.152650	+	0.178445i
$521$	−20.6918	−	11.9464i	−0.906523	−	0.523381i	−0.0272119	−	0.999630i	$-0.508663\pi$
$521$	−20.6918	−	11.9464i	−0.906523	−	0.523381i	−0.879311	+	0.476249i	$0.841996\pi$
$522$		0			0
$523$			32.7387i			1.43156i	0.698324	+	0.715782i	$0.253929\pi$
$523$			32.7387i			1.43156i	−0.698324	+	0.715782i	$0.746071\pi$
$524$	11.3910	+	19.7297i	0.497616	+	0.861897i
$525$		0			0
$526$	12.5696	+	3.36802i	0.548061	+	0.146853i
$527$	0.179676	−	0.0481440i	0.00782680	−	0.00209719i
$528$		0			0
$529$	12.8165			0.557239
$530$	3.96948			0.172423
$531$		0			0
$532$	−0.298501	−	3.82524i	−0.0129417	−	0.165845i
$533$	13.7831	+	28.8384i	0.597013	+	1.24913i
$534$		0			0
$535$	−2.12625	+	7.93526i	−0.0919256	+	0.343071i
$536$	2.67109	+	4.62646i	0.115373	+	0.199833i
$537$		0			0
$538$	−10.8272	−	10.8272i	−0.466796	−	0.466796i
$539$	3.66644	−	5.03237i	0.157925	−	0.216760i
$540$		0			0
$541$	−4.57076	+	17.0583i	−0.196512	+	0.733394i	0.795358	+	0.606140i	$0.207283\pi$
$541$	−4.57076	+	17.0583i	−0.196512	+	0.733394i	−0.991870	+	0.127254i	$0.959384\pi$
$542$		−	0.137574i		−	0.00590931i
$543$		0			0
$544$	−0.178346	+	0.178346i	−0.00764654	+	0.00764654i
$545$	2.39182			0.102454
$546$		0			0
$547$	24.8672			1.06324			0.531621	−	0.846982i	$-0.321583\pi$
$547$	24.8672			1.06324			0.531621	+	0.846982i	$0.321583\pi$
$548$	13.7123	−	13.7123i	0.585761	−	0.585761i
$549$		0			0
$550$		−	2.33849i		−	0.0997136i
$551$	1.84516	−	6.88624i	0.0786066	−	0.293364i
$552$		0			0
$553$	−8.35069	−	23.6314i	−0.355107	−	1.00491i
$554$	0.776972	+	0.776972i	0.0330104	+	0.0330104i
$555$		0			0
$556$	−0.800635	−	1.38674i	−0.0339545	−	0.0588109i
$557$	−9.42880	+	35.1888i	−0.399511	+	1.49100i	0.414448	+	0.910073i	$0.363975\pi$
$557$	−9.42880	+	35.1888i	−0.399511	+	1.49100i	−0.813959	+	0.580922i	$0.802692\pi$
$558$		0			0
$559$	3.49732	+	4.08830i	0.147921	+	0.172917i
$560$	−1.65304	+	3.45977i	−0.0698538	+	0.146202i
$561$		0			0
$562$	−11.7622			−0.496157
$563$	39.9539			1.68386			0.841928	−	0.539590i	$-0.181421\pi$
$563$	39.9539			1.68386			0.841928	+	0.539590i	$0.181421\pi$
$564$		0			0
$565$	−10.1405	+	2.71714i	−0.426614	+	0.114311i
$566$	9.63296	+	2.58114i	0.404904	+	0.108494i
$567$		0			0
$568$	0.880992	+	1.52592i	0.0369656	+	0.0640263i
$569$			26.1438i			1.09600i	0.836477	+	0.548002i	$0.184611\pi$
$569$			26.1438i			1.09600i	−0.836477	+	0.548002i	$0.815389\pi$
$570$		0			0
$571$	20.3089	+	11.7254i	0.849902	+	0.490691i	0.860618	−	0.509251i	$-0.170078\pi$
$571$	20.3089	+	11.7254i	0.849902	+	0.490691i	−0.0107157	+	0.999943i	$0.503411\pi$
$572$	−0.413732	+	5.31047i	−0.0172990	+	0.222042i
$573$		0			0
$574$	8.87726	−	10.3800i	0.370530	−	0.433253i
$575$	7.20351	−	12.4768i	0.300407	−	0.520320i
$576$		0			0
$577$	15.6987	−	4.20645i	0.653544	−	0.175117i	0.0832134	−	0.996532i	$-0.473482\pi$
$577$	15.6987	−	4.20645i	0.653544	−	0.175117i	0.570331	+	0.821415i	$0.306815\pi$
$578$	−6.99929	+	6.99929i	−0.291132	+	0.291132i
$579$		0			0
$580$	−6.68028	+	6.68028i	−0.277384	+	0.277384i
$581$	7.41809	+	10.8087i	0.307754	+	0.448422i
$582$		0			0
$583$	6.15402	+	6.15402i	0.254874	+	0.254874i
$584$	16.8538	−	29.1916i	0.697415	−	1.20796i
$585$		0			0
$586$	0.0287962	−	0.0166255i	0.00118956	−	0.000686792i
$587$	−25.3256	+	6.78596i	−1.04530	+	0.280087i	−0.740307	−	0.672269i	$-0.765320\pi$
$587$	−25.3256	+	6.78596i	−1.04530	+	0.280087i	−0.304991	+	0.952355i	$0.598653\pi$
$588$		0			0
$589$	−3.05340	+	1.76288i	−0.125813	+	0.0726383i
$590$	3.46690	+	0.928954i	0.142730	+	0.0382444i
$591$		0			0
$592$	10.3579	+	10.3579i	0.425707	+	0.425707i
$593$	−9.92038	−	2.65816i	−0.407381	−	0.109157i	0.0493084	−	0.998784i	$-0.484298\pi$
$593$	−9.92038	−	2.65816i	−0.407381	−	0.109157i	−0.456690	+	0.889626i	$0.650965\pi$
$594$		0			0
$595$	0.0366049	−	0.0766130i	0.00150066	−	0.00314083i
$596$	3.72402	−	0.997848i	0.152542	−	0.0408734i
$597$		0			0
$598$	3.79074	−	5.52489i	0.155015	−	0.225929i
$599$	−9.56265	+	16.5630i	−0.390719	+	0.676746i	−0.992545	−	0.121882i	$-0.961107\pi$
$599$	−9.56265	+	16.5630i	−0.390719	+	0.676746i	0.601825	+	0.798628i	$0.294440\pi$
$600$		0			0
$601$	−38.9868	−	22.5091i	−1.59031	−	0.918164i	−0.993254	−	0.115961i	$-0.963005\pi$
$601$	−38.9868	−	22.5091i	−1.59031	−	0.918164i	−0.597052	−	0.802202i	$-0.703661\pi$
$602$	0.991127	−	2.07440i	0.0403953	−	0.0845463i
$603$		0			0
$604$	−5.85793	−	21.8621i	−0.238356	−	0.889556i
$605$	5.02900	−	5.02900i	0.204458	−	0.204458i
$606$		0			0
$607$	−41.0361	−	23.6922i	−1.66561	−	0.961638i	−0.969964	−	0.243248i	$-0.921787\pi$
$607$	−41.0361	−	23.6922i	−1.66561	−	0.961638i	−0.695641	−	0.718389i	$-0.744880\pi$
$608$	2.39032	−	4.14016i	0.0969404	−	0.167906i
$609$		0			0
$610$		−	0.411070i		−	0.0166437i
$611$	−3.51650	+	45.1362i	−0.142262	+	1.82601i
$612$		0			0
$613$	−38.9499	−	10.4366i	−1.57317	−	0.421531i	−0.636369	−	0.771385i	$-0.719564\pi$
$613$	−38.9499	−	10.4366i	−1.57317	−	0.421531i	−0.936804	+	0.349854i	$0.886231\pi$
$614$		−	14.5907i		−	0.588834i
$615$		0			0
$616$	4.73036	−	1.67158i	0.190591	−	0.0673498i
$617$	12.1180	+	3.24702i	0.487854	+	0.130720i	0.494357	−	0.869259i	$-0.335404\pi$
$617$	12.1180	+	3.24702i	0.487854	+	0.130720i	−0.00650361	+	0.999979i	$0.502070\pi$
$618$		0			0
$619$	−2.16855	−	8.09314i	−0.0871614	−	0.325291i	0.908553	−	0.417769i	$-0.137188\pi$
$619$	−2.16855	−	8.09314i	−0.0871614	−	0.325291i	−0.995715	+	0.0924781i	$0.970521\pi$
$620$	4.67224			0.187642
$621$		0			0
$622$	−2.87041	−	10.7125i	−0.115093	−	0.429532i
$623$	11.4071	−	7.82873i	0.457014	−	0.313651i
$624$		0			0
$625$	8.97776	+	15.5499i	0.359110	+	0.621997i
$626$	−0.450922	+	1.68287i	−0.0180225	+	0.0672608i
$627$		0			0
$628$	−3.65484	+	6.33036i	−0.145844	+	0.252609i
$629$	−0.229365	−	0.229365i	−0.00914538	−	0.00914538i
$630$		0			0
$631$	3.60680	−	13.4608i	0.143584	−	0.535864i	−0.856230	−	0.516595i	$-0.827199\pi$
$631$	3.60680	−	13.4608i	0.143584	−	0.535864i	0.999814	−	0.0192694i	$-0.00613403\pi$
$632$	5.22695	−	19.5073i	0.207917	−	0.775957i
$633$		0			0
$634$	−0.357086	+	0.206164i	−0.0141817	+	0.00818781i
$635$	−3.51294	+	3.51294i	−0.139407	+	0.139407i
$636$		0			0
$637$	−4.61277	+	24.8138i	−0.182764	+	0.983157i
$638$	4.22922			0.167436
$639$		0			0
$640$	−6.94820	+	4.01155i	−0.274652	+	0.158570i
$641$		−	48.2934i		−	1.90747i	−0.300644	−	0.953736i	$-0.597202\pi$
$641$		−	48.2934i		−	1.90747i	0.300644	−	0.953736i	$-0.402798\pi$
$642$		0			0
$643$	4.25643	−	15.8852i	0.167857	−	0.626451i	−0.829801	−	0.558059i	$-0.811546\pi$
$643$	4.25643	−	15.8852i	0.167857	−	0.626451i	0.997658	−	0.0683924i	$-0.0217870\pi$
$644$	13.7864	+	2.56461i	0.543258	+	0.101060i
$645$		0			0
$646$	−0.0117116	+	0.0202850i	−0.000460785	+	0.000798104i
$647$	7.10098	+	12.2993i	0.279168	+	0.483533i	0.971178	−	0.238354i	$-0.0766080\pi$
$647$	7.10098	+	12.2993i	0.279168	+	0.483533i	−0.692010	+	0.721888i	$0.743275\pi$
$648$		0			0
$649$	3.93467	+	6.81505i	0.154449	+	0.267514i
$650$	4.08764	+	8.55256i	0.160330	+	0.335459i
$651$		0			0
$652$	−0.131164	−	0.489512i	−0.00513680	−	0.0191708i
$653$	9.98626			0.390793			0.195396	−	0.980724i	$-0.437401\pi$
$653$	9.98626			0.390793			0.195396	+	0.980724i	$0.437401\pi$
$654$		0			0
$655$	−2.47325	−	9.23031i	−0.0966380	−	0.360658i
$656$	−17.8133	+	4.77306i	−0.695492	+	0.186357i
$657$		0			0
$658$	18.2406	−	6.44573i	0.711093	−	0.251281i
$659$	−12.1444	−	21.0347i	−0.473079	−	0.819397i	0.526446	−	0.850208i	$-0.323524\pi$
$659$	−12.1444	−	21.0347i	−0.473079	−	0.819397i	−0.999525	+	0.0308117i	$0.990191\pi$
$660$		0			0
$661$	23.2228	+	6.22253i	0.903262	+	0.242028i	0.680416	−	0.732826i	$-0.261799\pi$
$661$	23.2228	+	6.22253i	0.903262	+	0.242028i	0.222845	+	0.974854i	$0.428466\pi$
$662$	−4.78681	−	2.76366i	−0.186044	−	0.107413i
$663$		0			0
$664$			10.5632i			0.409931i
$665$	−0.294336	+	1.58224i	−0.0114139	+	0.0613566i
$666$		0			0
$667$	22.5647	+	13.0277i	0.873707	+	0.504435i
$668$	0.657709	−	0.176233i	0.0254475	−	0.00681865i
$669$		0			0
$670$	−0.263118	−	0.981968i	−0.0101651	−	0.0379367i
$671$	0.637296	−	0.637296i	0.0246025	−	0.0246025i
$672$		0			0
$673$	−18.1748	−	10.4933i	−0.700589	−	0.404485i	0.106978	−	0.994261i	$-0.465883\pi$
$673$	−18.1748	−	10.4933i	−0.700589	−	0.404485i	−0.807567	+	0.589776i	$0.799216\pi$
$674$	−11.6763	−	11.6763i	−0.449754	−	0.449754i
$675$		0			0
$676$	−7.76946	−	20.1452i	−0.298825	−	0.774814i
$677$	−42.3269	+	24.4375i	−1.62676	+	0.939208i	−0.641705	+	0.766952i	$0.721772\pi$
$677$	−42.3269	+	24.4375i	−1.62676	+	0.939208i	−0.985052	+	0.172256i	$0.944894\pi$
$678$		0			0
$679$	−1.27204	+	2.66234i	−0.0488163	+	0.102171i
$680$	0.0592508	−	0.0342084i	0.00227216	−	0.00131183i
$681$		0			0
$682$	−1.47897	−	1.47897i	−0.0566328	−	0.0566328i
$683$	−28.8168	−	28.8168i	−1.10264	−	1.10264i	−0.994091	−	0.108553i	$-0.965378\pi$
$683$	−28.8168	−	28.8168i	−1.10264	−	1.10264i	−0.108553	−	0.994091i	$-0.534622\pi$
$684$		0			0
$685$	−7.04431	+	4.06703i	−0.269149	+	0.155393i
$686$	10.4920	−	2.49685i	0.400588	−	0.0953302i
$687$		0			0
$688$	−2.68828	+	1.55208i	−0.102490	+	0.0591726i
$689$	−33.2642	−	11.7500i	−1.26727	−	0.447639i
$690$		0			0
$691$	2.28413	+	2.28413i	0.0868923	+	0.0868923i	0.749217	−	0.662325i	$-0.230430\pi$
$691$	2.28413	+	2.28413i	0.0868923	+	0.0868923i	−0.662325	+	0.749217i	$0.730430\pi$
$692$	2.98595	+	1.72394i	0.113509	+	0.0655342i
$693$		0			0
$694$	9.21538	−	9.21538i	0.349811	−	0.349811i
$695$	0.173837	+	0.648769i	0.00659402	+	0.0246092i
$696$		0			0
$697$	0.394457	−	0.105694i	0.0149411	−	0.00400346i
$698$	−4.60193	−	2.65693i	−0.174186	−	0.100566i
$699$		0			0
$700$	−12.8942	+	15.0769i	−0.487356	+	0.569855i
$701$			8.12097i			0.306725i	0.988170	+	0.153362i	$0.0490102\pi$
$701$			8.12097i			0.306725i	−0.988170	+	0.153362i	$0.950990\pi$
$702$		0			0
$703$	5.32452	+	3.07411i	0.200818	+	0.115942i
$704$	−0.835292	−	0.223816i	−0.0314812	−	0.00843537i
$705$		0			0
$706$	0.836893	+	1.44954i	0.0314969	+	0.0545542i
$707$	−12.8768	−	36.4396i	−0.484281	−	1.37045i
$708$		0			0
$709$	13.1733	−	3.52976i	0.494732	−	0.132563i	−0.00282213	−	0.999996i	$-0.500898\pi$
$709$	13.1733	−	3.52976i	0.494732	−	0.132563i	0.497554	+	0.867433i	$0.334232\pi$
$710$	−0.0867828	−	0.323878i	−0.00325690	−	0.0121549i
$711$		0			0
$712$	11.1479			0.417786
$713$	−3.33510	−	12.4468i	−0.124901	−	0.466135i
$714$		0			0
$715$	0.744143	−	2.10667i	0.0278294	−	0.0787850i
$716$	−11.1376	−	19.2908i	−0.416230	−	0.720932i
$717$		0			0
$718$	2.34958	+	4.06960i	0.0876857	+	0.151876i
$719$	14.0292	−	24.2993i	0.523200	−	0.906210i	−0.476435	−	0.879210i	$-0.658071\pi$
$719$	14.0292	−	24.2993i	0.523200	−	0.906210i	0.999635	−	0.0270000i	$-0.00859542\pi$
$720$		0			0
$721$	−11.1891	−	31.6638i	−0.416705	−	1.17922i
$722$	−2.74877	+	10.2586i	−0.102299	+	0.381784i
$723$		0			0
$724$		−	3.86423i		−	0.143613i
$725$	−31.9231	+	18.4308i	−1.18560	+	0.684504i
$726$		0			0
$727$	−21.2410			−0.787785			−0.393893	−	0.919156i	$-0.628872\pi$
$727$	−21.2410			−0.787785			−0.393893	+	0.919156i	$0.628872\pi$
$728$	−14.3784	+	14.3820i	−0.532900	+	0.533034i
$729$		0			0
$730$	−4.53574	+	4.53574i	−0.167875	+	0.167875i
$731$	0.0595293	−	0.0343692i	0.00220177	−	0.00127119i
$732$		0			0
$733$	−2.19607	+	8.19585i	−0.0811138	+	0.302721i	−0.994550	−	0.104261i	$-0.966752\pi$
$733$	−2.19607	+	8.19585i	−0.0811138	+	0.302721i	0.913436	+	0.406982i	$0.133419\pi$
$734$	−0.253078	+	0.944500i	−0.00934128	+	0.0348621i
$735$		0			0
$736$	12.3547	+	12.3547i	0.455399	+	0.455399i
$737$	1.11446	−	1.93030i	0.0410516	−	0.0711035i
$738$		0			0
$739$	5.71616	−	21.3330i	0.210272	−	0.784747i	−0.777505	−	0.628877i	$-0.783515\pi$
$739$	5.71616	−	21.3330i	0.210272	−	0.784747i	0.987777	−	0.155871i	$-0.0498183\pi$
$740$	−4.07372	−	7.05589i	−0.149753	−	0.259380i
$741$		0			0
$742$	1.17282	+	15.0295i	0.0430555	+	0.551749i
$743$	7.10193	+	26.5048i	0.260544	+	0.972365i	0.964921	+	0.262539i	$0.0845598\pi$
$743$	7.10193	+	26.5048i	0.260544	+	0.972365i	−0.704377	+	0.709826i	$0.748774\pi$
$744$		0			0
$745$	−1.61715			−0.0592478
$746$	−4.86459	−	18.1549i	−0.178105	−	0.664699i
$747$		0			0
$748$	0.0657356	+	0.0176138i	0.00240353	+	0.000644024i
$749$	−30.6731	−	5.70596i	−1.12077	−	0.208491i
$750$		0			0
$751$		−	8.08325i		−	0.294962i	−0.989065	−	0.147481i	$-0.952883\pi$
$751$		−	8.08325i		−	0.294962i	0.989065	−	0.147481i	$-0.0471165\pi$
$752$	−25.2312	−	6.76067i	−0.920086	−	0.246536i
$753$		0			0
$754$	−15.4675	+	7.39259i	−0.563294	+	0.269222i
$755$			9.49358i			0.345507i
$756$		0			0
$757$	−15.2508	+	26.4151i	−0.554299	+	0.960074i	0.443659	+	0.896196i	$0.353680\pi$
$757$	−15.2508	+	26.4151i	−0.554299	+	0.960074i	−0.997958	+	0.0638779i	$0.979653\pi$
$758$	10.4900	+	6.05638i	0.381013	+	0.219978i
$759$		0			0
$760$	−0.916971	+	0.916971i	−0.0332620	+	0.0332620i
$761$	3.64361	+	13.5982i	0.132081	+	0.492933i	0.999993	−	0.00378550i	$-0.00120496\pi$
$761$	3.64361	+	13.5982i	0.132081	+	0.492933i	−0.867912	+	0.496718i	$0.834538\pi$
$762$		0			0
$763$	0.706683	+	9.05602i	0.0255836	+	0.327850i
$764$	33.0754	+	19.0961i	1.19663	+	0.690872i
$765$		0			0
$766$	8.18928	−	14.1843i	0.295891	−	0.512498i
$767$	−26.3028	−	18.0469i	−0.949741	−	0.651637i
$768$		0			0
$769$	−3.42800	+	0.918529i	−0.123617	+	0.0331230i	−0.320097	−	0.947385i	$-0.603715\pi$
$769$	−3.42800	+	0.918529i	−0.123617	+	0.0331230i	0.196480	+	0.980508i	$0.437049\pi$
$770$	−0.951837	+	0.0742762i	−0.0343018	+	0.00267673i
$771$		0			0
$772$	10.8250	+	2.90054i	0.389599	+	0.104393i
$773$	34.6723	+	34.6723i	1.24708	+	1.24708i	0.957005	+	0.290072i	$0.0936793\pi$
$773$	34.6723	+	34.6723i	1.24708	+	1.24708i	0.290072	+	0.957005i	$0.406321\pi$
$774$		0			0
$775$	17.6090	+	4.71831i	0.632532	+	0.169487i
$776$	−2.05899	+	1.18876i	−0.0739134	+	0.0426739i
$777$		0			0
$778$	6.00087	−	1.60793i	0.215142	−	0.0576471i
$779$	−6.70338	+	3.87020i	−0.240173	+	0.138664i
$780$		0			0
$781$	0.367577	−	0.636661i	0.0131529	−	0.0227815i
$782$	−0.0605326	−	0.0605326i	−0.00216464	−	0.00216464i
$783$		0			0
$784$	−13.5880	−	5.23662i	−0.485285	−	0.187022i
$785$	2.16803	−	2.16803i	0.0773802	−	0.0773802i
$786$		0			0
$787$	−21.7018	+	21.7018i	−0.773585	+	0.773585i	−0.978731	−	0.205146i	$-0.934233\pi$
$787$	−21.7018	+	21.7018i	−0.773585	+	0.773585i	0.205146	+	0.978731i	$0.434233\pi$
$788$	20.4857	−	5.48913i	0.729774	−	0.195542i
$789$		0			0
$790$	−1.92158	+	3.32827i	−0.0683666	+	0.118414i
$791$	−13.2839	−	37.5917i	−0.472320	−	1.33661i
$792$		0			0
$793$	−1.21680	+	3.44476i	−0.0432098	+	0.122327i
$794$	−1.19651	−	0.690804i	−0.0424624	−	0.0245157i
$795$		0			0
$796$			1.37929i			0.0488876i
$797$	−9.95011	−	17.2341i	−0.352451	−	0.610463i	0.634227	−	0.773147i	$-0.281318\pi$
$797$	−9.95011	−	17.2341i	−0.352451	−	0.610463i	−0.986678	+	0.162684i	$0.947985\pi$
$798$		0			0
$799$	0.558718	+	0.149708i	0.0197660	+	0.00529629i
$800$	−23.8763	+	6.39764i	−0.844155	+	0.226191i
$801$		0			0
$802$	−18.1508			−0.640929
$803$	−14.0638			−0.496301
$804$		0			0
$805$	−5.30725	−	2.53575i	−0.187056	−	0.0893734i
$806$	7.99426	+	2.82383i	0.281586	+	0.0994650i
$807$		0			0
$808$	8.05997	−	30.0802i	0.283549	−	1.05822i
$809$	−1.70377	−	2.95102i	−0.0599015	−	0.103752i	0.834520	−	0.550978i	$-0.185745\pi$
$809$	−1.70377	−	2.95102i	−0.0599015	−	0.103752i	−0.894421	+	0.447226i	$0.852412\pi$
$810$		0			0
$811$	6.11425	+	6.11425i	0.214700	+	0.214700i	0.806261	−	0.591560i	$-0.201488\pi$
$811$	6.11425	+	6.11425i	0.214700	+	0.214700i	−0.591560	+	0.806261i	$0.701488\pi$
$812$	−27.2670	−	23.3195i	−0.956884	−	0.818354i
$813$		0			0
$814$	−0.943990	+	3.52302i	−0.0330868	+	0.123482i
$815$			0.212570i			0.00744600i
$816$		0			0
$817$	−0.921281	+	0.921281i	−0.0322316	+	0.0322316i
$818$	13.4021			0.468594
$819$		0			0
$820$	10.2573			0.358202
$821$	−10.6416	+	10.6416i	−0.371395	+	0.371395i	−0.867985	−	0.496590i	$-0.834585\pi$
$821$	−10.6416	+	10.6416i	−0.371395	+	0.371395i	0.496590	+	0.867985i	$0.334585\pi$
$822$		0			0
$823$			46.4521i			1.61922i	0.586970	+	0.809608i	$0.300320\pi$
$823$			46.4521i			1.61922i	−0.586970	+	0.809608i	$0.699680\pi$
$824$	7.00362	−	26.1379i	0.243983	−	0.910556i
$825$		0			0
$826$	−2.49293	+	13.4010i	−0.0867400	+	0.466282i
$827$	−30.9402	−	30.9402i	−1.07590	−	1.07590i	−0.996873	−	0.0790236i	$-0.974820\pi$
$827$	−30.9402	−	30.9402i	−1.07590	−	1.07590i	−0.0790236	−	0.996873i	$-0.525180\pi$
$828$		0			0
$829$	−16.3432	−	28.3073i	−0.567623	−	0.983152i	−0.996800	−	0.0799317i	$-0.974530\pi$
$829$	−16.3432	−	28.3073i	−0.567623	−	0.983152i	0.429177	−	0.903220i	$-0.358804\pi$
$830$	0.520267	−	1.94166i	0.0180587	−	0.0673961i
$831$		0			0
$832$	3.44614	−	0.641513i	0.119473	−	0.0222405i
$833$	0.300891	+	0.115959i	0.0104253	+	0.00401776i
$834$		0			0
$835$	−0.285609			−0.00988392
$836$	−1.28992			−0.0446130
$837$		0			0
$838$	−9.74464	+	2.61107i	−0.336623	+	0.0901978i
$839$	−25.2872	−	6.77567i	−0.873010	−	0.233922i	−0.205621	−	0.978632i	$-0.565921\pi$
$839$	−25.2872	−	6.77567i	−0.873010	−	0.233922i	−0.667389	+	0.744710i	$0.732588\pi$
$840$		0			0
$841$	−18.8326	−	32.6190i	−0.649399	−	1.12479i
$842$			23.4567i			0.808371i
$843$		0			0
$844$	33.2788	+	19.2135i	1.14550	+	0.661357i
$845$	0.960868	+	9.00547i	0.0330549	+	0.309798i
$846$		0			0
$847$	20.5269	+	17.5552i	0.705314	+	0.603204i
$848$	10.1773	−	17.6277i	0.349491	−	0.605337i
$849$		0			0
$850$	0.116984	−	0.0313457i	0.00401251	−	0.00107515i
$851$	−15.8889	+	15.8889i	−0.544665	+	0.544665i
$852$		0			0
$853$	−26.6435	+	26.6435i	−0.912255	+	0.912255i	−0.996449	−	0.0841944i	$-0.973168\pi$
$853$	−26.6435	+	26.6435i	−0.912255	+	0.912255i	0.0841944	+	0.996449i	$0.473168\pi$
$854$	1.55641	−	0.121454i	0.0532594	−	0.00415608i
$855$		0			0
$856$	−17.7763	−	17.7763i	−0.607581	−	0.607581i
$857$	14.1671	−	24.5382i	0.483940	−	0.838208i	−0.515890	−	0.856655i	$-0.672539\pi$
$857$	14.1671	−	24.5382i	0.483940	−	0.838208i	0.999830	+	0.0184467i	$0.00587210\pi$
$858$		0			0
$859$	−10.1518	+	5.86113i	−0.346374	+	0.199979i	−0.663087	−	0.748542i	$-0.730754\pi$
$859$	−10.1518	+	5.86113i	−0.346374	+	0.199979i	0.316713	+	0.948521i	$0.397421\pi$
$860$	1.66772	−	0.446864i	0.0568687	−	0.0152379i
$861$		0			0
$862$	17.0885	−	9.86603i	0.582036	−	0.336038i
$863$	41.5172	+	11.1245i	1.41326	+	0.378682i	0.883088	−	0.469207i	$-0.155460\pi$
$863$	41.5172	+	11.1245i	1.41326	+	0.378682i	0.530174	+	0.847889i	$0.322127\pi$
$864$		0			0
$865$	−1.02263	−	1.02263i	−0.0347704	−	0.0347704i
$866$	17.1339	+	4.59101i	0.582233	+	0.156009i
$867$		0			0
$868$	1.38045	+	17.6903i	0.0468556	+	0.600447i
$869$	−8.13902	+	2.18084i	−0.276097	+	0.0739800i
$870$		0			0
$871$	−0.701781	+	9.00774i	−0.0237789	+	0.305215i
$872$	−3.65963	+	6.33866i	−0.123931	+	0.214654i
$873$		0			0
$874$	1.40521	+	0.811301i	0.0475321	+	0.0274427i
$875$	14.4596	−	9.92367i	0.488823	−	0.335481i
$876$		0			0
$877$	7.43615	+	27.7521i	0.251101	+	0.937122i	0.970218	+	0.242233i	$0.0778798\pi$
$877$	7.43615	+	27.7521i	0.251101	+	0.937122i	−0.719117	+	0.694889i	$0.755454\pi$
$878$	−1.12238	+	1.12238i	−0.0378784	+	0.0378784i
$879$		0			0
$880$	1.11639	+	0.644545i	0.0376333	+	0.0217276i
$881$	20.6648	−	35.7924i	0.696213	−	1.20588i	−0.273557	−	0.961856i	$-0.588200\pi$
$881$	20.6648	−	35.7924i	0.696213	−	1.20588i	0.969770	−	0.244021i	$-0.0784665\pi$
$882$		0			0
$883$			14.7746i			0.497205i	0.968606	+	0.248603i	$0.0799713\pi$
$883$			14.7746i			0.497205i	−0.968606	+	0.248603i	$0.920029\pi$
$884$	−0.271203	+	0.0504857i	−0.00912156	+	0.00169802i
$885$		0			0
$886$	19.5637	+	5.24207i	0.657255	+	0.176111i
$887$		−	16.0526i		−	0.538994i	−0.963001	−	0.269497i	$-0.913143\pi$
$887$		−	16.0526i		−	0.538994i	0.963001	−	0.269497i	$-0.0868575\pi$
$888$		0			0
$889$	−14.3388	−	12.2629i	−0.480908	−	0.411286i
$890$	−2.04915	−	0.549067i	−0.0686875	−	0.0184048i
$891$		0			0
$892$	−6.17504	−	23.0456i	−0.206756	−	0.771622i
$893$	−10.9637			−0.366885
$894$		0			0
$895$	2.41824	+	9.02498i	0.0808327	+	0.301672i
$896$	−17.2416	−	25.1224i	−0.576002	−	0.839280i
$897$		0			0
$898$	10.5895	+	18.3415i	0.353376	+	0.612065i
$899$	−8.53316	+	31.8462i	−0.284597	+	1.06213i
$900$		0			0
$901$	−0.225367	+	0.390347i	−0.00750805	+	0.0130043i
$902$	−3.24691	−	3.24691i	−0.108110	−	0.108110i
$903$		0			0
$904$	8.31479	−	31.0312i	0.276546	−	1.03208i
$905$	−0.419509	+	1.56563i	−0.0139449	+	0.0520432i
$906$		0			0
$907$	13.4150	−	7.74514i	0.445437	−	0.257173i	−0.260464	−	0.965484i	$-0.583876\pi$
$907$	13.4150	−	7.74514i	0.445437	−	0.257173i	0.705901	+	0.708310i	$0.250542\pi$
$908$	−24.1420	+	24.1420i	−0.801181	+	0.801181i
$909$		0			0
$910$	3.35132	−	1.93544i	0.111095	−	0.0641593i
$911$	28.0514			0.929383			0.464691	−	0.885473i	$-0.346165\pi$
$911$	28.0514			0.929383			0.464691	+	0.885473i	$0.346165\pi$
$912$		0			0
$913$	3.81681	−	2.20364i	0.126318	−	0.0729298i
$914$		−	18.5401i		−	0.613253i
$915$		0			0
$916$	−1.77745	+	6.63353i	−0.0587285	+	0.219178i
$917$	34.2175	−	12.0915i	1.12996	−	0.399298i
$918$		0			0
$919$	−17.5562	+	30.4083i	−0.579127	+	1.00308i	0.416453	+	0.909157i	$0.363273\pi$
$919$	−17.5562	+	30.4083i	−0.579127	+	1.00308i	−0.995580	+	0.0939198i	$0.970060\pi$
$920$	−2.36974	−	4.10451i	−0.0781279	−	0.135322i
$921$		0			0
$922$	−5.25412	−	9.10041i	−0.173035	−	0.299706i
$923$	−0.231465	+	2.97098i	−0.00761877	+	0.0977909i
$924$		0			0
$925$	−8.22777	−	30.7065i	−0.270527	−	1.00962i
$926$	13.3782			0.439636
$927$		0			0
$928$	−11.5703	−	43.1808i	−0.379813	−	1.41748i
$929$	−6.77606	+	1.81564i	−0.222315	+	0.0595692i	−0.368257	−	0.929724i	$-0.620045\pi$
$929$	−6.77606	+	1.81564i	−0.222315	+	0.0595692i	0.145942	+	0.989293i	$0.453379\pi$
$930$		0			0
$931$	−6.07772	−	0.646944i	−0.199189	−	0.0212027i
$932$	1.65190	+	2.86118i	0.0541099	+	0.0937211i
$933$		0			0
$934$	21.0824	+	5.64901i	0.689837	+	0.184841i
$935$	−0.0247212	−	0.0142728i	−0.000808470	−	0.000466770i
$936$		0			0
$937$		−	40.3619i		−	1.31857i	−0.751894	−	0.659284i	$-0.770860\pi$
$937$		−	40.3619i		−	1.31857i	0.751894	−	0.659284i	$-0.229140\pi$
$938$	3.64024	−	1.28636i	0.118858	−	0.0420012i
$939$		0			0
$940$	12.5822	+	7.26437i	0.410388	+	0.236937i
$941$	−26.7377	+	7.16434i	−0.871624	+	0.233551i	−0.666790	−	0.745246i	$-0.732332\pi$
$941$	−26.7377	+	7.16434i	−0.871624	+	0.233551i	−0.204834	+	0.978797i	$0.565665\pi$
$942$		0			0
$943$	−7.32182	−	27.3254i	−0.238431	−	0.889838i
$944$	13.0141	−	13.0141i	0.423572	−	0.423572i
$945$		0			0
$946$	−0.669360	−	0.386455i	−0.0217628	−	0.0125647i
$947$	−5.48950	−	5.48950i	−0.178385	−	0.178385i	0.612267	−	0.790651i	$-0.290258\pi$
$947$	−5.48950	−	5.48950i	−0.178385	−	0.178385i	−0.790651	+	0.612267i	$0.790258\pi$
$948$		0			0
$949$	51.4356	−	24.5833i	1.66967	−	0.798007i
$950$	−1.98801	+	1.14778i	−0.0644997	+	0.0372389i
$951$		0			0
$952$	0.147028	+	0.214231i	0.00476520	+	0.00694327i
$953$	−19.1100	+	11.0332i	−0.619034	+	0.357400i	−0.776493	−	0.630126i	$-0.783003\pi$
$953$	−19.1100	+	11.0332i	−0.619034	+	0.357400i	0.157459	+	0.987526i	$0.449670\pi$
$954$		0			0
$955$	−11.3277	−	11.3277i	−0.366556	−	0.366556i
$956$	−16.8313	−	16.8313i	−0.544362	−	0.544362i
$957$		0			0
$958$	−13.4791	+	7.78217i	−0.435490	+	0.251430i
$959$	−17.4801	−	25.4699i	−0.564462	−	0.822466i
$960$		0			0
$961$	−12.7260	+	7.34735i	−0.410516	+	0.237011i
$962$	−2.70572	−	14.5348i	−0.0872359	−	0.468621i
$963$		0			0
$964$	−32.4834	−	32.4834i	−1.04622	−	1.04622i
$965$	−4.07094	−	2.35036i	−0.131048	−	0.0756608i
$966$		0			0
$967$	−38.9477	+	38.9477i	−1.25248	+	1.25248i	−0.297868	+	0.954607i	$0.596276\pi$
$967$	−38.9477	+	38.9477i	−1.25248	+	1.25248i	−0.954607	+	0.297868i	$0.903724\pi$
$968$	5.63290	+	21.0223i	0.181048	+	0.675682i
$969$		0			0
$970$	0.437021	−	0.117100i	0.0140319	−	0.00375984i
$971$	−22.0504	−	12.7308i	−0.707630	−	0.408551i	0.102553	−	0.994728i	$-0.467299\pi$
$971$	−22.0504	−	12.7308i	−0.707630	−	0.408551i	−0.810183	+	0.586177i	$0.800632\pi$
$972$		0			0
$973$	−2.40504	+	0.849876i	−0.0771021	+	0.0272458i
$974$			14.4320i			0.462430i
$975$		0			0
$976$	−1.82548	−	1.05394i	−0.0584322	−	0.0337358i
$977$	30.1690	+	8.08375i	0.965191	+	0.258622i	0.706796	−	0.707417i	$-0.250140\pi$
$977$	30.1690	+	8.08375i	0.965191	+	0.258622i	0.258395	+	0.966039i	$0.416806\pi$
$978$		0			0
$979$	−2.32562	−	4.02810i	−0.0743273	−	0.128739i
$980$	6.54632	+	4.76945i	0.209114	+	0.152355i
$981$		0			0
$982$	−6.24887	+	1.67438i	−0.199409	+	0.0534316i
$983$	11.2863	+	42.1212i	0.359978	+	1.34346i	0.874103	+	0.485741i	$0.161450\pi$
$983$	11.2863	+	42.1212i	0.359978	+	1.34346i	−0.514125	+	0.857715i	$0.671883\pi$
$984$		0			0
$985$	−8.89589			−0.283447
$986$	0.0566894	+	0.211568i	0.00180536	+	0.00673769i
$987$		0			0
$988$	4.71764	−	2.25476i	0.150088	−	0.0717336i
$989$	−2.38088	−	4.12380i	−0.0757075	−	0.131129i
$990$		0			0
$991$	7.25148	+	12.5599i	0.230351	+	0.398979i	0.957911	−	0.287064i	$-0.0926793\pi$
$991$	7.25148	+	12.5599i	0.230351	+	0.398979i	−0.727561	+	0.686043i	$0.759346\pi$
$992$	−11.0543	+	19.1467i	−0.350975	+	0.607907i
$993$		0			0
$994$	1.20064	−	0.424274i	0.0380821	−	0.0134572i
$995$	0.149738	−	0.558832i	0.00474703	−	0.0177162i
$996$		0			0
$997$		−	48.9575i		−	1.55050i	−0.631655	−	0.775249i	$-0.717624\pi$
$997$		−	48.9575i		−	1.55050i	0.631655	−	0.775249i	$-0.282376\pi$
$998$	−0.0937696	+	0.0541379i	−0.00296823	+	0.00171371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.136.6		36
3.2	odd	2		273.2.bt.a.136.4	✓	36
7.5	odd	6		819.2.gh.c.19.4		36
13.11	odd	12		819.2.gh.c.388.4		36
21.5	even	6		273.2.cg.a.19.6	yes	36
39.11	even	12		273.2.cg.a.115.6	yes	36
91.89	even	12	inner	819.2.et.c.271.6		36
273.89	odd	12		273.2.bt.a.271.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.4	✓	36	3.2	odd	2
273.2.bt.a.271.4	yes	36	273.89	odd	12
273.2.cg.a.19.6	yes	36	21.5	even	6
273.2.cg.a.115.6	yes	36	39.11	even	12
819.2.et.c.136.6		36	1.1	even	1	trivial
819.2.et.c.271.6		36	91.89	even	12	inner
819.2.gh.c.19.4		36	7.5	odd	6
819.2.gh.c.388.4		36	13.11	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)

\(f(q)\)	\(=\)	\(q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +O(q^{10})\)	\(q+(0.411775 - 0.411775i) q^{2} +1.66088i q^{4} +(0.180309 - 0.672922i) q^{5} +(2.60113 + 0.483875i) q^{7} +(1.50746 + 1.50746i) q^{8} +(-0.202846 - 0.351339i) q^{10} +(0.230214 - 0.859171i) q^{11} +(0.659853 + 3.54466i) q^{13} +(1.27033 - 0.871831i) q^{14} -2.08030 q^{16} +0.0460661 q^{17} +(-0.843398 + 0.225988i) q^{19} +(1.11765 + 0.299472i) q^{20} +(-0.258989 - 0.448581i) q^{22} -3.19116i q^{23} +(3.90981 + 2.25733i) q^{25} +(1.73131 + 1.18789i) q^{26} +(-0.803659 + 4.32017i) q^{28} +(-4.08244 + 7.07099i) q^{29} +(3.90039 - 1.04511i) q^{31} +(-3.87153 + 3.87153i) q^{32} +(0.0189689 - 0.0189689i) q^{34} +(0.794617 - 1.66311i) q^{35} +(-4.97904 - 4.97904i) q^{37} +(-0.254234 + 0.440346i) q^{38} +(1.28621 - 0.742594i) q^{40} +(8.56284 - 2.29441i) q^{41} +(1.29226 - 0.746085i) q^{43} +(1.42698 + 0.382359i) q^{44} +(-1.31404 - 1.31404i) q^{46} +(12.1286 + 3.24985i) q^{47} +(6.53173 + 2.51724i) q^{49} +(2.53947 - 0.680450i) q^{50} +(-5.88726 + 1.09594i) q^{52} +(-4.89224 + 8.47362i) q^{53} +(-0.536646 - 0.309833i) q^{55} +(3.19167 + 4.65051i) q^{56} +(1.23061 + 4.59270i) q^{58} +(-6.25586 + 6.25586i) q^{59} +(0.877507 + 0.506629i) q^{61} +(1.17573 - 2.03643i) q^{62} -0.972206i q^{64} +(2.50426 + 0.195103i) q^{65} +(2.42048 + 0.648566i) q^{67} +0.0765105i q^{68} +(-0.357623 - 1.01203i) q^{70} +(0.798336 + 0.213913i) q^{71} +(-4.09226 - 15.2725i) q^{73} -4.10048 q^{74} +(-0.375340 - 1.40079i) q^{76} +(1.01455 - 2.12342i) q^{77} +(-4.73655 - 8.20394i) q^{79} +(-0.375097 + 1.39988i) q^{80} +(2.58118 - 4.47074i) q^{82} +(3.50364 + 3.50364i) q^{83} +(0.00830614 - 0.0309989i) q^{85} +(0.224900 - 0.839337i) q^{86} +(1.64220 - 0.948127i) q^{88} +(3.69759 - 3.69759i) q^{89} +(0.00119323 + 9.53939i) q^{91} +5.30014 q^{92} +(6.33246 - 3.65605i) q^{94} +0.608289i q^{95} +(-0.288642 + 1.07723i) q^{97} +(3.72614 - 1.65306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 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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