LMFDB - Embedded newform 819.2.et.c.271.6

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			271.6
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.6

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.411775	+	0.411775i	0.291169	+	0.291169i	0.837542	−	0.546373i	$-0.183992\pi$
$2$	0.411775	+	0.411775i	0.291169	+	0.291169i	−0.546373	+	0.837542i	$0.683992\pi$
$3$		0			0
$3$		0			0
$4$		−	1.66088i		−	0.830442i
$5$	0.180309	+	0.672922i	0.0806367	+	0.300940i	0.994452	−	0.105189i	$-0.0335449\pi$
$5$	0.180309	+	0.672922i	0.0806367	+	0.300940i	−0.913816	+	0.406129i	$0.866878\pi$
$6$		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	0.991908	−	0.126957i	$-0.0405209\pi$
$11$	0.230214	+	0.859171i	0.0694122	+	0.259050i	−0.922496	+	0.386007i	$0.873854\pi$
$12$		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	0.160773	−	0.986991i	$-0.448601\pi$
$19$	−0.843398	−	0.225988i	−0.193489	−	0.0518452i	−0.354262	+	0.935146i	$0.615268\pi$
$20$	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	$0.107960\pi$
$23$			3.19116i			0.665403i	−0.943032	+	0.332701i	$0.892040\pi$
$24$		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	−0.943824	−	0.330450i	$-0.892800\pi$
$29$	−4.08244	−	7.07099i	−0.758090	−	1.31305i	0.185734	−	0.982600i	$-0.440534\pi$
$30$		0			0
$31$	3.90039	+	1.04511i	0.700531	+	0.187707i	0.591468	−	0.806328i	$-0.298548\pi$
$31$	3.90039	+	1.04511i	0.700531	+	0.187707i	0.109063	+	0.994035i	$0.465215\pi$
$32$	−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	−0.985898	−	0.167349i	$-0.946479\pi$
$37$	−4.97904	+	4.97904i	−0.818549	+	0.818549i	0.167349	+	0.985898i	$0.446479\pi$
$38$	−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	0.855429	−	0.517921i	$-0.173294\pi$
$41$	8.56284	+	2.29441i	1.33729	+	0.358326i	0.481863	+	0.876247i	$0.339960\pi$
$42$		0			0
$43$	1.29226	+	0.746085i	0.197067	+	0.113777i	0.595287	−	0.803513i	$-0.297038\pi$
$43$	1.29226	+	0.746085i	0.197067	+	0.113777i	−0.398219	+	0.917290i	$0.630372\pi$
$44$	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	0.780604	−	0.625026i	$-0.214912\pi$
$47$	12.1286	−	3.24985i	1.76914	−	0.474039i	0.988536	+	0.150987i	$0.0482451\pi$
$48$		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	−0.977336	−	0.211695i	$-0.932102\pi$
$53$	−4.89224	−	8.47362i	−0.672001	−	1.16394i	0.305334	−	0.952245i	$-0.401232\pi$
$54$		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	0.170853	−	0.985297i	$-0.445348\pi$
$59$	−6.25586	−	6.25586i	−0.814444	−	0.814444i	−0.985297	+	0.170853i	$0.945348\pi$
$60$		0			0
$61$	0.877507	−	0.506629i	0.112353	−	0.0648672i	−0.442770	−	0.896635i	$-0.646004\pi$
$61$	0.877507	−	0.506629i	0.112353	−	0.0648672i	0.555124	+	0.831768i	$0.312671\pi$
$62$	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	−0.107915	−	0.994160i	$-0.534417\pi$
$67$	2.42048	−	0.648566i	0.295709	−	0.0792350i	0.403623	+	0.914925i	$0.367751\pi$
$68$		−	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	−0.211135	−	0.977457i	$-0.567716\pi$
$71$	0.798336	−	0.213913i	0.0947450	−	0.0253869i	0.305880	+	0.952070i	$0.401049\pi$
$72$		0			0
$73$	−4.09226	+	15.2725i	−0.478963	+	1.78751i	0.126867	+	0.991920i	$0.459508\pi$
$73$	−4.09226	+	15.2725i	−0.478963	+	1.78751i	−0.605830	+	0.795594i	$0.707159\pi$
$74$	−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	0.466358	+	0.884596i	$0.345566\pi$
$79$	−4.73655	+	8.20394i	−0.532903	+	0.923016i	−0.999262	+	0.0384199i	$0.987768\pi$
$80$	−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	−0.488173	−	0.872747i	$-0.662336\pi$
$83$	3.50364	−	3.50364i	0.384574	−	0.384574i	0.872747	+	0.488173i	$0.162336\pi$
$84$		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	0.875380	−	0.483436i	$-0.160611\pi$
$89$	3.69759	+	3.69759i	0.391944	+	0.391944i	−0.483436	+	0.875380i	$0.660611\pi$
$90$		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	0.949723	−	0.313092i	$-0.101365\pi$
$97$	−0.288642	−	1.07723i	−0.0293071	−	0.109376i	−0.979030	+	0.203716i	$0.934698\pi$
$98$	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	0.231497	+	0.972836i	$0.425638\pi$
$101$	−7.30376	+	12.6505i	−0.726752	+	1.25877i	−0.958249	+	0.285935i	$0.907696\pi$
$102$		0			0
$103$	−6.34652	+	10.9925i	−0.625342	+	1.08312i	0.363133	+	0.931737i	$0.381707\pi$
$103$	−6.34652	+	10.9925i	−0.625342	+	1.08312i	−0.988475	+	0.151386i	$0.951626\pi$
$104$	−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	−0.910224	−	0.414117i	$-0.864090\pi$
$109$	0.888593	−	3.31627i	0.0851118	−	0.317641i	0.995335	+	0.0964758i	$0.0307570\pi$
$110$	−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	0.256498	+	0.966545i	$0.417431\pi$
$113$	−7.53468	+	13.0504i	−0.708803	+	1.22768i	−0.965301	+	0.261138i	$0.915902\pi$
$114$		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	−0.748321	−	0.663337i	$-0.769140\pi$
$127$	−6.17582	+	3.56561i	−0.548016	+	0.316397i	0.200306	+	0.979733i	$0.435806\pi$
$128$	−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	0.919231	−	0.393718i	$-0.128811\pi$
$131$	11.8790	+	6.85837i	1.03788	+	0.599219i	0.118646	+	0.992937i	$0.462145\pi$
$132$		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	−0.965556	−	0.260195i	$-0.916213\pi$
$137$	−8.25603	+	8.25603i	−0.705361	+	0.705361i	0.260195	+	0.965556i	$0.416213\pi$
$138$		0			0
$139$	−0.834941	−	0.482054i	−0.0708188	−	0.0408873i	0.464172	−	0.885745i	$-0.346352\pi$
$139$	−0.834941	−	0.482054i	−0.0708188	−	0.0408873i	−0.534991	+	0.844858i	$0.679685\pi$
$140$	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	−0.986159	−	0.165803i	$-0.946979\pi$
$149$	−0.600793	+	2.24219i	−0.0492189	+	0.183687i	0.936940	+	0.349490i	$0.113645\pi$
$150$		0			0
$151$	−13.1629	−	3.52700i	−1.07118	−	0.287023i	−0.320205	−	0.947348i	$-0.603752\pi$
$151$	−13.1629	−	3.52700i	−1.07118	−	0.287023i	−0.750980	+	0.660325i	$0.770418\pi$
$152$	−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	−0.340136	−	0.940376i	$-0.610473\pi$
$157$	3.81144	−	2.20054i	0.304186	−	0.175622i	0.644322	+	0.764754i	$0.277140\pi$
$158$	−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	0.247258	−	0.968950i	$-0.420470\pi$
$163$	−0.294730	−	0.0789727i	−0.0230850	−	0.00618562i	−0.270343	+	0.962764i	$0.587137\pi$
$164$	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	−0.969910	−	0.243465i	$-0.921716\pi$
$167$	−0.106108	+	0.396000i	−0.00821087	+	0.0306434i	0.961699	+	0.274108i	$0.0883826\pi$
$168$		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	0.902782	−	0.430098i	$-0.141521\pi$
$173$	1.03796	+	1.79781i	0.0789149	+	0.136685i	−0.823867	+	0.566783i	$0.808188\pi$
$174$		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	−0.00140439	−	0.999999i	$-0.500447\pi$
$179$	−11.6148	−	6.70581i	−0.868131	−	0.501216i	−0.866727	+	0.498783i	$0.833780\pi$
$180$		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	0.896503	+	0.443038i	$0.146099\pi$
$191$	11.4976	+	19.9143i	0.831934	+	1.44095i	−0.0645691	+	0.997913i	$0.520567\pi$
$192$		0			0
$193$	1.74638	+	6.51759i	0.125707	+	0.469146i	0.999864	−	0.0164980i	$-0.00525171\pi$
$193$	1.74638	+	6.51759i	0.125707	+	0.469146i	−0.874157	+	0.485644i	$0.838585\pi$
$194$	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	0.742470	+	0.669880i	$0.233654\pi$
$197$	−3.30495	+	12.3342i	−0.235468	+	0.878778i	−0.977937	+	0.208898i	$0.933012\pi$
$198$		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	0.921952	+	0.387305i	$0.126594\pi$
$211$	11.5683	+	20.0368i	0.796392	+	1.37939i	−0.125560	+	0.992086i	$0.540073\pi$
$212$	−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	−0.237670	−	0.971346i	$-0.576384\pi$
$223$	−13.8755	−	3.71792i	−0.929171	−	0.248971i	−0.691501	+	0.722375i	$0.743050\pi$
$224$	−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	−0.0346350	−	0.999400i	$-0.511027\pi$
$227$	14.5357	−	14.5357i	0.964765	−	0.964765i	0.999400	+	0.0346350i	$0.0110269\pi$
$228$		0			0
$229$	3.99397	−	1.07018i	0.263929	−	0.0707196i	−0.124428	−	0.992229i	$-0.539709\pi$
$229$	3.99397	−	1.07018i	0.263929	−	0.0707196i	0.388357	+	0.921509i	$0.373043\pi$
$230$	−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	0.555366	−	0.831606i	$-0.312578\pi$
$233$	1.72269	+	0.994594i	0.112857	+	0.0651580i	−0.442509	+	0.896764i	$0.645912\pi$
$234$		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	0.298805	−	0.954314i	$-0.403412\pi$
$239$	−10.1339	−	10.1339i	−0.655510	−	0.655510i	−0.954314	+	0.298805i	$0.903412\pi$
$240$		0			0
$241$	−19.5579	−	19.5579i	−1.25984	−	1.25984i	−0.951171	−	0.308664i	$-0.900118\pi$
$241$	−19.5579	−	19.5579i	−1.25984	−	1.25984i	−0.308664	−	0.951171i	$-0.599882\pi$
$242$	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	−0.715248	−	0.698871i	$-0.753686\pi$
$251$	3.92297	−	6.79478i	0.247616	−	0.428883i	0.962864	+	0.269988i	$0.0870197\pi$
$252$		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	−0.283211	−	0.959058i	$-0.591400\pi$
$263$	11.1731	−	19.3524i	0.688963	−	1.19332i	0.972174	−	0.234261i	$-0.0752671\pi$
$264$		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	$0.296012\pi$
$269$			26.2941i			1.60318i	−0.597874	+	0.801590i	$0.703988\pi$
$270$		0			0
$271$	0.167050	+	0.167050i	0.0101476	+	0.0101476i	0.712162	−	0.702015i	$-0.247716\pi$
$271$	0.167050	+	0.167050i	0.0101476	+	0.0101476i	−0.702015	+	0.712162i	$0.747716\pi$
$272$	−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	$-0.981947\pi$
$277$		−	1.88689i		−	0.113372i	0.998392	−	0.0566860i	$-0.0180534\pi$
$278$	−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	−0.990381	−	0.138370i	$-0.955814\pi$
$281$	−14.2823	+	14.2823i	−0.852011	+	0.852011i	0.138370	+	0.990381i	$0.455814\pi$
$282$		0			0
$283$	8.56272	−	14.8311i	0.509001	−	0.881615i	−0.490945	−	0.871191i	$-0.663348\pi$
$283$	8.56272	−	14.8311i	0.509001	−	0.881615i	0.999946	−	0.0104246i	$-0.00331831\pi$
$284$	−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	−0.257208	−	0.966356i	$-0.582802\pi$
$293$	0.0551536	−	0.0147783i	0.00322210	−	0.000863360i	0.260430	+	0.965493i	$0.416136\pi$
$294$		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	0.999937	+	0.0112203i	$0.00357162\pi$
$307$	17.7169	+	17.7169i	1.01116	+	1.01116i	0.0112203	+	0.999937i	$0.496428\pi$
$308$	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	0.998905	+	0.0467749i	$0.0148944\pi$
$311$	9.52232	+	16.4931i	0.539961	+	0.935240i	−0.458944	+	0.888465i	$0.651772\pi$
$312$		0			0
$313$	−2.59097	−	1.49590i	−0.146450	−	0.0845530i	0.424984	−	0.905201i	$-0.360280\pi$
$313$	−2.59097	−	1.49590i	−0.146450	−	0.0845530i	−0.571435	+	0.820648i	$0.693613\pi$
$314$	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	−0.277975	−	0.960588i	$-0.589663\pi$
$317$	−0.683930	+	0.183258i	−0.0384133	+	0.0102928i	0.239561	+	0.970881i	$0.422996\pi$
$318$		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	0.864970	+	0.501823i	$0.167337\pi$
$331$	−2.45661	+	9.16821i	−0.135028	+	0.503930i	−0.999998	+	0.00210683i	$0.999329\pi$
$332$	−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	$0.280907\pi$
$337$			28.3561i			1.54465i	−0.635226	+	0.772327i	$0.719093\pi$
$338$	−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	−0.999886	−	0.0150770i	$-0.995201\pi$
$349$	−2.36174	+	8.81412i	−0.126421	+	0.471809i	0.873465	+	0.486886i	$0.161867\pi$
$350$	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	0.943299	−	0.331945i	$-0.107705\pi$
$353$	−0.743912	−	2.77632i	−0.0395945	−	0.147769i	−0.982893	+	0.184177i	$0.941038\pi$
$354$		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	0.888657	−	0.458573i	$-0.151639\pi$
$359$	−2.08854	−	7.79454i	−0.110229	−	0.411380i	−0.998886	+	0.0471928i	$0.984972\pi$
$360$		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	0.461566	−	0.887106i	$-0.347288\pi$
$367$	−1.45417	−	0.839564i	−0.0759069	−	0.0438249i	−0.537473	+	0.843281i	$0.680621\pi$
$368$		−	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	0.893552	+	0.448960i	$0.148206\pi$
$373$	16.1379	+	27.9516i	0.835587	+	1.44728i	−0.0579649	+	0.998319i	$0.518461\pi$
$374$	−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	−0.678276	−	0.734808i	$-0.737272\pi$
$379$	5.38351	−	20.0915i	0.276532	−	1.03203i	0.954808	−	0.297224i	$-0.0960609\pi$
$380$	−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	0.874086	−	0.485772i	$-0.161461\pi$
$383$	27.1672	+	7.27943i	1.38818	+	0.371962i	0.514094	+	0.857734i	$0.328128\pi$
$384$		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	−0.247148	−	0.968978i	$-0.579493\pi$
$389$	9.23904	−	5.33416i	0.468438	−	0.270453i	0.715586	+	0.698525i	$0.246160\pi$
$390$		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	−0.979622	−	0.200852i	$-0.935629\pi$
$397$	−0.614054	+	2.29168i	−0.0308185	+	0.115016i	0.948803	+	0.315868i	$0.102296\pi$
$398$	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	−0.106278	+	0.994336i	$0.533893\pi$
$401$	−22.0398	+	22.0398i	−1.10061	+	1.10061i	−0.994336	+	0.106278i	$0.966107\pi$
$402$		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	−0.179144	−	0.983823i	$-0.557333\pi$
$409$	16.2736	−	16.2736i	0.804679	−	0.804679i	0.983823	+	0.179144i	$0.0573328\pi$
$410$	−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	−0.819498	−	0.573082i	$-0.805748\pi$
$419$	−15.0030	+	8.66198i	−0.732944	+	0.423166i	0.0865540	+	0.996247i	$0.472414\pi$
$420$		0			0
$421$	−28.4825	−	28.4825i	−1.38815	−	1.38815i	−0.829203	−	0.558947i	$-0.811206\pi$
$421$	−28.4825	−	28.4825i	−1.38815	−	1.38815i	−0.558947	−	0.829203i	$-0.688794\pi$
$422$	−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	0.638683	−	0.769470i	$-0.279479\pi$
$431$	32.7297	−	8.76990i	1.57653	−	0.422431i	0.937851	+	0.347039i	$0.112813\pi$
$432$		0			0
$433$	15.2303	−	26.3796i	0.731921	−	1.26772i	−0.224141	−	0.974557i	$-0.571958\pi$
$433$	15.2303	−	26.3796i	0.731921	−	1.26772i	0.956061	−	0.293167i	$-0.0947091\pi$
$434$	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	−0.0747467	−	0.997203i	$-0.523815\pi$
$443$	17.3901	−	30.1206i	0.826229	−	1.43107i	0.900976	−	0.433869i	$-0.142852\pi$
$444$		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	−0.717972	−	0.696072i	$-0.754930\pi$
$449$	−9.41298	−	35.1297i	−0.444226	−	1.65787i	0.273746	−	0.961802i	$-0.411737\pi$
$450$		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	0.998509	+	0.0545801i	$0.0173820\pi$
$457$	22.5125	+	22.5125i	1.05309	+	1.05309i	0.0545801	+	0.998509i	$0.482618\pi$
$458$	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	0.985264	+	0.171042i	$0.0547133\pi$
$461$	4.67038	+	17.4301i	0.217521	+	0.811800i	−0.767743	+	0.640758i	$0.778620\pi$
$462$		0			0
$463$	16.2446	−	16.2446i	0.754951	−	0.754951i	−0.220448	−	0.975399i	$-0.570752\pi$
$463$	16.2446	−	16.2446i	0.754951	−	0.754951i	0.975399	+	0.220448i	$0.0707518\pi$
$464$	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	0.00232895	−	0.999997i	$-0.499259\pi$
$467$	18.7401	−	32.4588i	0.867188	−	1.50201i	0.864859	−	0.502016i	$-0.167408\pi$
$468$		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	−0.794765	−	0.606918i	$-0.792406\pi$
$479$	−25.8166	+	6.91755i	−1.17959	+	0.316071i	−0.384828	+	0.922988i	$0.625739\pi$
$480$		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	0.188064	−	0.982157i	$-0.439779\pi$
$487$	−17.5241	−	17.5241i	−0.794093	−	0.794093i	−0.982157	+	0.188064i	$0.939779\pi$
$488$	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	−0.701127	−	0.713036i	$-0.747319\pi$
$491$	−9.62086	+	5.55460i	−0.434183	+	0.250676i	0.266944	+	0.963712i	$0.413986\pi$
$492$		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	−0.262837	−	0.964840i	$-0.584658\pi$
$499$	−0.179598	+	0.0481231i	−0.00803990	+	0.00215428i	0.254797	+	0.966995i	$0.417991\pi$
$500$	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	0.489064	−	0.872248i	$-0.337338\pi$
$503$	−0.488766	−	0.282189i	−0.0217930	−	0.0125822i	−0.510857	+	0.859666i	$0.670672\pi$
$504$		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	−0.967625	−	0.252390i	$-0.918783\pi$
$509$	−16.1364	+	16.1364i	−0.715235	+	0.715235i	0.252390	+	0.967625i	$0.418783\pi$
$510$		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	−0.879311	−	0.476249i	$-0.841996\pi$
$521$	−20.6918	+	11.9464i	−0.906523	+	0.523381i	−0.0272119	+	0.999630i	$0.508663\pi$
$522$		0			0
$523$		−	32.7387i		−	1.43156i	−0.698324	−	0.715782i	$-0.746071\pi$
$523$		−	32.7387i		−	1.43156i	0.698324	−	0.715782i	$-0.253929\pi$
$524$	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	−0.991870	−	0.127254i	$-0.959384\pi$
$541$	−4.57076	−	17.0583i	−0.196512	−	0.733394i	0.795358	−	0.606140i	$-0.207283\pi$
$542$			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	−0.813959	−	0.580922i	$-0.802692\pi$
$557$	−9.42880	−	35.1888i	−0.399511	−	1.49100i	0.414448	−	0.910073i	$-0.363975\pi$
$558$		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	$-0.815389\pi$
$569$		−	26.1438i		−	1.09600i	0.836477	−	0.548002i	$-0.184611\pi$
$570$		0			0
$571$	20.3089	−	11.7254i	0.849902	−	0.490691i	−0.0107157	−	0.999943i	$-0.503411\pi$
$571$	20.3089	−	11.7254i	0.849902	−	0.490691i	0.860618	+	0.509251i	$0.170078\pi$
$572$	−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	0.570331	−	0.821415i	$-0.306815\pi$
$577$	15.6987	+	4.20645i	0.653544	+	0.175117i	0.0832134	+	0.996532i	$0.473482\pi$
$578$	−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	−0.304991	−	0.952355i	$-0.598653\pi$
$587$	−25.3256	−	6.78596i	−1.04530	−	0.280087i	−0.740307	+	0.672269i	$0.765320\pi$
$588$		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	−0.456690	−	0.889626i	$-0.650965\pi$
$593$	−9.92038	+	2.65816i	−0.407381	+	0.109157i	0.0493084	+	0.998784i	$0.484298\pi$
$594$		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	0.601825	−	0.798628i	$-0.294440\pi$
$599$	−9.56265	−	16.5630i	−0.390719	−	0.676746i	−0.992545	+	0.121882i	$0.961107\pi$
$600$		0			0
$601$	−38.9868	+	22.5091i	−1.59031	+	0.918164i	−0.597052	+	0.802202i	$0.703661\pi$
$601$	−38.9868	+	22.5091i	−1.59031	+	0.918164i	−0.993254	+	0.115961i	$0.963005\pi$
$602$	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	−0.695641	+	0.718389i	$0.744880\pi$
$607$	−41.0361	+	23.6922i	−1.66561	+	0.961638i	−0.969964	+	0.243248i	$0.921787\pi$
$608$	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	−0.936804	−	0.349854i	$-0.886231\pi$
$613$	−38.9499	+	10.4366i	−1.57317	+	0.421531i	−0.636369	+	0.771385i	$0.719564\pi$
$614$			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	−0.00650361	−	0.999979i	$-0.502070\pi$
$617$	12.1180	−	3.24702i	0.487854	−	0.130720i	0.494357	+	0.869259i	$0.335404\pi$
$618$		0			0
$619$	−2.16855	+	8.09314i	−0.0871614	+	0.325291i	−0.995715	−	0.0924781i	$-0.970521\pi$
$619$	−2.16855	+	8.09314i	−0.0871614	+	0.325291i	0.908553	+	0.417769i	$0.137188\pi$
$620$	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	0.999814	+	0.0192694i	$0.00613403\pi$
$631$	3.60680	+	13.4608i	0.143584	+	0.535864i	−0.856230	+	0.516595i	$0.827199\pi$
$632$	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	$0.402798\pi$
$641$			48.2934i			1.90747i	−0.300644	+	0.953736i	$0.597202\pi$
$642$		0			0
$643$	4.25643	+	15.8852i	0.167857	+	0.626451i	0.997658	+	0.0683924i	$0.0217870\pi$
$643$	4.25643	+	15.8852i	0.167857	+	0.626451i	−0.829801	+	0.558059i	$0.811546\pi$
$644$	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	−0.692010	−	0.721888i	$-0.743275\pi$
$647$	7.10098	−	12.2993i	0.279168	−	0.483533i	0.971178	+	0.238354i	$0.0766080\pi$
$648$		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	−0.999525	−	0.0308117i	$-0.990191\pi$
$659$	−12.1444	+	21.0347i	−0.473079	+	0.819397i	0.526446	+	0.850208i	$0.323524\pi$
$660$		0			0
$661$	23.2228	−	6.22253i	0.903262	−	0.242028i	0.222845	−	0.974854i	$-0.428466\pi$
$661$	23.2228	−	6.22253i	0.903262	−	0.242028i	0.680416	+	0.732826i	$0.261799\pi$
$662$	−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	−0.807567	−	0.589776i	$-0.799216\pi$
$673$	−18.1748	+	10.4933i	−0.700589	+	0.404485i	0.106978	+	0.994261i	$0.465883\pi$
$674$	−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	−0.985052	−	0.172256i	$-0.944894\pi$
$677$	−42.3269	−	24.4375i	−1.62676	−	0.939208i	−0.641705	−	0.766952i	$-0.721772\pi$
$678$		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	−0.108553	+	0.994091i	$0.534622\pi$
$683$	−28.8168	+	28.8168i	−1.10264	+	1.10264i	−0.994091	+	0.108553i	$0.965378\pi$
$684$		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	−0.662325	−	0.749217i	$-0.730430\pi$
$691$	2.28413	−	2.28413i	0.0868923	−	0.0868923i	0.749217	+	0.662325i	$0.230430\pi$
$692$	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	$-0.950990\pi$
$701$		−	8.12097i		−	0.306725i	0.988170	−	0.153362i	$-0.0490102\pi$
$702$		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	0.497554	−	0.867433i	$-0.334232\pi$
$709$	13.1733	+	3.52976i	0.494732	+	0.132563i	−0.00282213	+	0.999996i	$0.500898\pi$
$710$	−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	0.999635	+	0.0270000i	$0.00859542\pi$
$719$	14.0292	+	24.2993i	0.523200	+	0.906210i	−0.476435	+	0.879210i	$0.658071\pi$
$720$		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	0.913436	−	0.406982i	$-0.133419\pi$
$733$	−2.19607	−	8.19585i	−0.0811138	−	0.302721i	−0.994550	+	0.104261i	$0.966752\pi$
$734$	−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	0.987777	+	0.155871i	$0.0498183\pi$
$739$	5.71616	+	21.3330i	0.210272	+	0.784747i	−0.777505	+	0.628877i	$0.783515\pi$
$740$	−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	−0.704377	−	0.709826i	$-0.748774\pi$
$743$	7.10193	−	26.5048i	0.260544	−	0.972365i	0.964921	−	0.262539i	$-0.0845598\pi$
$744$		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	$0.0471165\pi$
$751$			8.08325i			0.294962i	−0.989065	+	0.147481i	$0.952883\pi$
$752$	−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	−0.997958	−	0.0638779i	$-0.979653\pi$
$757$	−15.2508	−	26.4151i	−0.554299	−	0.960074i	0.443659	−	0.896196i	$-0.353680\pi$
$758$	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	−0.867912	−	0.496718i	$-0.834538\pi$
$761$	3.64361	−	13.5982i	0.132081	−	0.492933i	0.999993	+	0.00378550i	$0.00120496\pi$
$762$		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	0.196480	−	0.980508i	$-0.437049\pi$
$769$	−3.42800	−	0.918529i	−0.123617	−	0.0331230i	−0.320097	+	0.947385i	$0.603715\pi$
$770$	−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	0.290072	−	0.957005i	$-0.406321\pi$
$773$	34.6723	−	34.6723i	1.24708	−	1.24708i	0.957005	−	0.290072i	$-0.0936793\pi$
$774$		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	0.205146	−	0.978731i	$-0.434233\pi$
$787$	−21.7018	−	21.7018i	−0.773585	−	0.773585i	−0.978731	+	0.205146i	$0.934233\pi$
$788$	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	−0.986678	−	0.162684i	$-0.947985\pi$
$797$	−9.95011	+	17.2341i	−0.352451	+	0.610463i	0.634227	+	0.773147i	$0.281318\pi$
$798$		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	−0.894421	−	0.447226i	$-0.852412\pi$
$809$	−1.70377	+	2.95102i	−0.0599015	+	0.103752i	0.834520	+	0.550978i	$0.185745\pi$
$810$		0			0
$811$	6.11425	−	6.11425i	0.214700	−	0.214700i	−0.591560	−	0.806261i	$-0.701488\pi$
$811$	6.11425	−	6.11425i	0.214700	−	0.214700i	0.806261	+	0.591560i	$0.201488\pi$
$812$	−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	0.496590	−	0.867985i	$-0.334585\pi$
$821$	−10.6416	−	10.6416i	−0.371395	−	0.371395i	−0.867985	+	0.496590i	$0.834585\pi$
$822$		0			0
$823$		−	46.4521i		−	1.61922i	−0.586970	−	0.809608i	$-0.699680\pi$
$823$		−	46.4521i		−	1.61922i	0.586970	−	0.809608i	$-0.300320\pi$
$824$	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	−0.0790236	+	0.996873i	$0.525180\pi$
$827$	−30.9402	+	30.9402i	−1.07590	+	1.07590i	−0.996873	+	0.0790236i	$0.974820\pi$
$828$		0			0
$829$	−16.3432	+	28.3073i	−0.567623	+	0.983152i	0.429177	+	0.903220i	$0.358804\pi$
$829$	−16.3432	+	28.3073i	−0.567623	+	0.983152i	−0.996800	+	0.0799317i	$0.974530\pi$
$830$	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	−0.667389	−	0.744710i	$-0.732588\pi$
$839$	−25.2872	+	6.77567i	−0.873010	+	0.233922i	−0.205621	+	0.978632i	$0.565921\pi$
$840$		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	0.0841944	−	0.996449i	$-0.473168\pi$
$853$	−26.6435	−	26.6435i	−0.912255	−	0.912255i	−0.996449	+	0.0841944i	$0.973168\pi$
$854$	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	0.999830	−	0.0184467i	$-0.00587210\pi$
$857$	14.1671	+	24.5382i	0.483940	+	0.838208i	−0.515890	+	0.856655i	$0.672539\pi$
$858$		0			0
$859$	−10.1518	−	5.86113i	−0.346374	−	0.199979i	0.316713	−	0.948521i	$-0.397421\pi$
$859$	−10.1518	−	5.86113i	−0.346374	−	0.199979i	−0.663087	+	0.748542i	$0.730754\pi$
$860$	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	0.530174	−	0.847889i	$-0.322127\pi$
$863$	41.5172	−	11.1245i	1.41326	−	0.378682i	0.883088	+	0.469207i	$0.155460\pi$
$864$		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	−0.719117	−	0.694889i	$-0.755454\pi$
$877$	7.43615	−	27.7521i	0.251101	−	0.937122i	0.970218	−	0.242233i	$-0.0778798\pi$
$878$	−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	0.969770	+	0.244021i	$0.0784665\pi$
$881$	20.6648	+	35.7924i	0.696213	+	1.20588i	−0.273557	+	0.961856i	$0.588200\pi$
$882$		0			0
$883$		−	14.7746i		−	0.497205i	−0.968606	−	0.248603i	$-0.920029\pi$
$883$		−	14.7746i		−	0.497205i	0.968606	−	0.248603i	$-0.0799713\pi$
$884$	−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	$0.0868575\pi$
$887$			16.0526i			0.538994i	−0.963001	+	0.269497i	$0.913143\pi$
$888$		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	0.705901	−	0.708310i	$-0.250542\pi$
$907$	13.4150	+	7.74514i	0.445437	+	0.257173i	−0.260464	+	0.965484i	$0.583876\pi$
$908$	−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	−0.995580	−	0.0939198i	$-0.970060\pi$
$919$	−17.5562	−	30.4083i	−0.579127	−	1.00308i	0.416453	−	0.909157i	$-0.363273\pi$
$920$	−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	0.145942	−	0.989293i	$-0.453379\pi$
$929$	−6.77606	−	1.81564i	−0.222315	−	0.0595692i	−0.368257	+	0.929724i	$0.620045\pi$
$930$		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	$0.229140\pi$
$937$			40.3619i			1.31857i	−0.751894	+	0.659284i	$0.770860\pi$
$938$	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	−0.204834	−	0.978797i	$-0.565665\pi$
$941$	−26.7377	−	7.16434i	−0.871624	−	0.233551i	−0.666790	+	0.745246i	$0.732332\pi$
$942$		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	−0.790651	−	0.612267i	$-0.790258\pi$
$947$	−5.48950	+	5.48950i	−0.178385	+	0.178385i	0.612267	+	0.790651i	$0.290258\pi$
$948$		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	0.157459	−	0.987526i	$-0.449670\pi$
$953$	−19.1100	−	11.0332i	−0.619034	−	0.357400i	−0.776493	+	0.630126i	$0.783003\pi$
$954$		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	−0.954607	−	0.297868i	$-0.903724\pi$
$967$	−38.9477	−	38.9477i	−1.25248	−	1.25248i	−0.297868	−	0.954607i	$-0.596276\pi$
$968$	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	−0.810183	−	0.586177i	$-0.800632\pi$
$971$	−22.0504	+	12.7308i	−0.707630	+	0.408551i	0.102553	+	0.994728i	$0.467299\pi$
$972$		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	0.258395	−	0.966039i	$-0.416806\pi$
$977$	30.1690	−	8.08375i	0.965191	−	0.258622i	0.706796	+	0.707417i	$0.250140\pi$
$978$		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	−0.514125	−	0.857715i	$-0.671883\pi$
$983$	11.2863	−	42.1212i	0.359978	−	1.34346i	0.874103	−	0.485741i	$-0.161450\pi$
$984$		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	−0.727561	−	0.686043i	$-0.759346\pi$
$991$	7.25148	−	12.5599i	0.230351	−	0.398979i	0.957911	+	0.287064i	$0.0926793\pi$
$992$	−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	$0.282376\pi$
$997$			48.9575i			1.55050i	−0.631655	+	0.775249i	$0.717624\pi$
$998$	−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.271.6		36
3.2	odd	2		273.2.bt.a.271.4	yes	36
7.3	odd	6		819.2.gh.c.388.4		36
13.6	odd	12		819.2.gh.c.19.4		36
21.17	even	6		273.2.cg.a.115.6	yes	36
39.32	even	12		273.2.cg.a.19.6	yes	36
91.45	even	12	inner	819.2.et.c.136.6		36
273.227	odd	12		273.2.bt.a.136.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.4	✓	36	273.227	odd	12
273.2.bt.a.271.4	yes	36	3.2	odd	2
273.2.cg.a.19.6	yes	36	39.32	even	12
273.2.cg.a.115.6	yes	36	21.17	even	6
819.2.et.c.136.6		36	91.45	even	12	inner
819.2.et.c.271.6		36	1.1	even	1	trivial
819.2.gh.c.19.4		36	13.6	odd	12
819.2.gh.c.388.4		36	7.3	odd	6

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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