LMFDB - Embedded newform 819.2.do.e.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			667.4
Root			$0.655911 + 1.25291i$ of defining polynomial
Character	$\chi$	$=$	819.667
Dual form			819.2.do.e.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} +O(q^{10})$	\(q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} -0.485809 q^{10} -2.69424i q^{11} +(1.92153 - 3.05086i) q^{13} +(0.174889 + 0.445303i) q^{14} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} -0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(-2.19964 - 3.80989i) q^{23} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} +(-4.07019 - 3.24431i) q^{28} +(3.54280 - 6.13631i) q^{29} +(3.20369 - 1.84965i) q^{31} +(-1.83838 - 1.06139i) q^{32} +0.861613i q^{34} +(4.43058 - 5.55844i) q^{35} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(4.59027 + 2.65020i) q^{44} +(-0.688919 - 0.397748i) q^{46} +(-1.60118 - 0.924445i) q^{47} +(-6.68997 - 2.06016i) q^{49} +(0.347341 + 0.200538i) q^{50} +(3.30773 + 6.27476i) q^{52} +(-3.53622 - 6.12491i) q^{53} +(-3.61923 + 6.26869i) q^{55} +(-1.87688 - 0.282446i) q^{56} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} -0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-8.56910 + 4.51719i) q^{65} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(0.191271 - 1.27102i) q^{70} +(-2.89675 + 1.67244i) q^{71} +(-12.3112 + 7.10790i) q^{73} +(0.719148 - 1.24560i) q^{74} +(0.321025 + 0.185344i) q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(-1.25445 - 0.724258i) q^{86} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +(7.22539 + 6.22846i) q^{91} +8.65473 q^{92} -0.334323 q^{94} +(-0.253115 + 0.438407i) q^{95} +(0.390659 - 0.225547i) q^{97} +(-1.23390 + 0.282236i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.156598	−	0.0904119i	0.110731	−	0.0639308i	−0.443611	−	0.896219i	$-0.646303\pi$
$2$	0.156598	−	0.0904119i	0.110731	−	0.0639308i	0.554343	+	0.832288i	$0.312970\pi$
$3$		0			0
$3$		0			0
$4$	−0.983651	+	1.70373i	−0.491826	+	0.851867i
$5$	−2.32670	−	1.34332i	−1.04053	−	0.600751i	−0.120548	−	0.992708i	$-0.538465\pi$
$5$	−2.32670	−	1.34332i	−1.04053	−	0.600751i	−0.919984	+	0.391956i	$0.871799\pi$
$6$		0			0
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$8$			0.717383i			0.253633i
$9$		0			0
$10$	−0.485809			−0.153626
$11$		−	2.69424i		−	0.812345i	−0.913796	−	0.406172i	$-0.866863\pi$
$11$		−	2.69424i		−	0.812345i	0.913796	−	0.406172i	$-0.133137\pi$
$12$		0			0
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$13$	1.92153	−	3.05086i	0.532937	−	0.846155i
$14$	0.174889	+	0.445303i	0.0467409	+	0.119012i
$15$		0			0
$16$	−1.90244	−	3.29513i	−0.475611	−	0.823782i
$17$	−2.38247	+	4.12655i	−0.577833	+	1.00084i	0.417894	+	0.908496i	$0.362768\pi$
$17$	−2.38247	+	4.12655i	−0.577833	+	1.00084i	−0.995727	+	0.0923405i	$0.970565\pi$
$18$		0			0
$19$		−	0.188424i		−	0.0432275i	−0.999766	−	0.0216138i	$-0.993120\pi$
$19$		−	0.188424i		−	0.0432275i	0.999766	−	0.0216138i	$-0.00688041\pi$
$20$	4.57732	−	2.64272i	1.02352	−	0.590930i
$21$		0			0
$22$	−0.243592	−	0.421913i	−0.0519339	−	0.0899521i
$23$	−2.19964	−	3.80989i	−0.458657	−	0.794418i	0.540233	−	0.841516i	$-0.318336\pi$
$23$	−2.19964	−	3.80989i	−0.458657	−	0.794418i	−0.998890	+	0.0470977i	$0.985003\pi$
$24$		0			0
$25$	1.10902	+	1.92088i	0.221804	+	0.384177i
$26$	0.0250743	−	0.651487i	0.00491747	−	0.127767i
$27$		0			0
$28$	−4.07019	−	3.24431i	−0.769193	−	0.613117i
$29$	3.54280	−	6.13631i	0.657882	−	1.13948i	−0.323281	−	0.946303i	$-0.604786\pi$
$29$	3.54280	−	6.13631i	0.657882	−	1.13948i	0.981163	−	0.193182i	$-0.0618807\pi$
$30$		0			0
$31$	3.20369	−	1.84965i	0.575400	−	0.332207i	−0.183903	−	0.982944i	$-0.558873\pi$
$31$	3.20369	−	1.84965i	0.575400	−	0.332207i	0.759303	+	0.650737i	$0.225540\pi$
$32$	−1.83838	−	1.06139i	−0.324983	−	0.187629i
$33$		0			0
$34$			0.861613i			0.147765i
$35$	4.43058	−	5.55844i	0.748905	−	0.939548i
$36$		0			0
$37$	6.88848	−	3.97707i	1.13246	−	0.653826i	0.187907	−	0.982187i	$-0.439830\pi$
$37$	6.88848	−	3.97707i	1.13246	−	0.653826i	0.944552	+	0.328361i	$0.106496\pi$
$38$	−0.0170358	−	0.0295069i	−0.00276357	−	0.00478665i
$39$		0			0
$40$	0.963675	−	1.66913i	0.152370	−	0.263913i
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	0.0856594	−	0.996324i	$-0.472700\pi$
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	−0.820013	+	0.572345i	$0.806034\pi$
$42$		0			0
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	−0.991105	−	0.133084i	$-0.957512\pi$
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	0.380298	−	0.924864i	$-0.375821\pi$
$44$	4.59027	+	2.65020i	0.692010	+	0.399532i
$45$		0			0
$46$	−0.688919	−	0.397748i	−0.101576	−	0.0586447i
$47$	−1.60118	−	0.924445i	−0.233557	−	0.134844i	0.378655	−	0.925538i	$-0.376387\pi$
$47$	−1.60118	−	0.924445i	−0.233557	−	0.134844i	−0.612212	+	0.790694i	$0.709720\pi$
$48$		0			0
$49$	−6.68997	−	2.06016i	−0.955710	−	0.294308i
$50$	0.347341	+	0.200538i	0.0491215	+	0.0283603i
$51$		0			0
$52$	3.30773	+	6.27476i	0.458700	+	0.870152i
$53$	−3.53622	−	6.12491i	−0.485737	−	0.841321i	0.514128	−	0.857713i	$-0.328115\pi$
$53$	−3.53622	−	6.12491i	−0.485737	−	0.841321i	−0.999866	+	0.0163917i	$0.994782\pi$
$54$		0			0
$55$	−3.61923	+	6.26869i	−0.488017	+	0.845271i
$56$	−1.87688	−	0.282446i	−0.250809	−	0.0377434i
$57$		0			0
$58$		−	1.28125i		−	0.168236i
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	0.862544	−	0.505982i	$-0.168870\pi$
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	−0.00692130	+	0.999976i	$0.502203\pi$
$60$		0			0
$61$	−0.411564			−0.0526954			−0.0263477	−	0.999653i	$-0.508388\pi$
$61$	−0.411564			−0.0526954			−0.0263477	+	0.999653i	$0.508388\pi$
$62$	0.334461	−	0.579304i	0.0424766	−	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	−8.56910	+	4.51719i	−1.06287	+	0.560289i
$66$		0			0
$67$		−	11.4010i		−	1.39286i	−0.717626	−	0.696429i	$-0.754771\pi$
$67$		−	11.4010i		−	1.39286i	0.717626	−	0.696429i	$-0.245229\pi$
$68$	−4.68703	−	8.11818i	−0.568386	−	0.984474i
$69$		0			0
$70$	0.191271	−	1.27102i	0.0228613	−	0.151916i
$71$	−2.89675	+	1.67244i	−0.343781	+	0.198482i	−0.661943	−	0.749554i	$-0.730268\pi$
$71$	−2.89675	+	1.67244i	−0.343781	+	0.198482i	0.318162	+	0.948037i	$0.396935\pi$
$72$		0			0
$73$	−12.3112	+	7.10790i	−1.44092	+	0.831917i	−0.997911	−	0.0645994i	$-0.979423\pi$
$73$	−12.3112	+	7.10790i	−1.44092	+	0.831917i	−0.443011	+	0.896516i	$0.646090\pi$
$74$	0.719148	−	1.24560i	0.0835993	−	0.144798i
$75$		0			0
$76$	0.321025	+	0.185344i	0.0368241	+	0.0212604i
$77$	7.04893	+	1.06077i	0.803300	+	0.120886i
$78$		0			0
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	0.487384	+	0.873188i	$0.337951\pi$
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	−0.999895	+	0.0145069i	$0.995382\pi$
$80$			10.2224i			1.14290i
$81$		0			0
$82$	−0.981797			−0.108421
$83$			16.5866i			1.82061i	0.413934	+	0.910307i	$0.364155\pi$
$83$			16.5866i			1.82061i	−0.413934	+	0.910307i	$0.635845\pi$
$84$		0			0
$85$	11.0866	−	6.40083i	1.20251	−	0.694268i
$86$	−1.25445	−	0.724258i	−0.135271	−	0.0780988i
$87$		0			0
$88$	1.93280			0.206037
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	−0.204577	−	0.978851i	$-0.565582\pi$
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	0.745421	+	0.666594i	$0.232248\pi$
$90$		0			0
$91$	7.22539	+	6.22846i	0.757427	+	0.652920i
$92$	8.65473			0.902318
$93$		0			0
$94$	−0.334323			−0.0344828
$95$	−0.253115	+	0.438407i	−0.0259690	+	0.0449796i
$96$		0			0
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	−0.480036	−	0.877249i	$-0.659376\pi$
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	0.519702	+	0.854348i	$0.326043\pi$
$98$	−1.23390	+	0.282236i	−0.124643	+	0.0285102i
$99$		0			0
$100$	−4.36356			−0.436356
$101$	−7.65680			−0.761880			−0.380940	−	0.924600i	$-0.624400\pi$
$101$	−7.65680			−0.761880			−0.380940	+	0.924600i	$0.624400\pi$
$102$		0			0
$103$	2.57870	−	4.46644i	0.254087	−	0.440091i	−0.710560	−	0.703636i	$-0.751558\pi$
$103$	2.57870	−	4.46644i	0.254087	−	0.440091i	0.964647	+	0.263545i	$0.0848918\pi$
$104$	2.18863	+	1.37847i	0.214613	+	0.135170i
$105$		0			0
$106$	−1.10753	−	0.639433i	−0.107573	−	0.0621072i
$107$	4.01644	+	6.95669i	0.388284	+	0.672528i	0.992219	−	0.124506i	$-0.0397345\pi$
$107$	4.01644	+	6.95669i	0.388284	+	0.672528i	−0.603935	+	0.797034i	$0.706401\pi$
$108$		0			0
$109$	−1.15490	+	0.666781i	−0.110619	+	0.0638660i	−0.554289	−	0.832324i	$-0.687010\pi$
$109$	−1.15490	+	0.666781i	−0.110619	+	0.0638660i	0.443670	+	0.896190i	$0.353676\pi$
$110$			1.30889i			0.124797i
$111$		0			0
$112$	9.37004	−	3.68000i	0.885386	−	0.347727i
$113$	−9.96917	−	17.2671i	−0.937821	−	1.62435i	−0.769525	−	0.638617i	$-0.779507\pi$
$113$	−9.96917	−	17.2671i	−0.937821	−	1.62435i	−0.168296	−	0.985736i	$-0.553827\pi$
$114$		0			0
$115$			11.8193i			1.10216i
$116$	6.96976	+	12.0720i	0.647126	+	1.12086i
$117$		0			0
$118$	1.37225			0.126326
$119$	−9.85825	−	7.85792i	−0.903704	−	0.720335i
$120$		0			0
$121$	3.74106			0.340096
$122$	−0.0644501	+	0.0372103i	−0.00583503	+	0.00336886i
$123$		0			0
$124$			7.27765i			0.653553i
$125$			7.47412i			0.668505i
$126$		0			0
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	−0.986858	−	0.161590i	$-0.948338\pi$
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	0.633370	+	0.773849i	$0.281671\pi$
$128$	4.80833	−	2.77609i	0.425000	−	0.245374i
$129$		0			0
$130$	−0.933496	+	1.48213i	−0.0818730	+	0.129992i
$131$	5.00897	−	8.67579i	0.437636	−	0.758007i	−0.559871	−	0.828580i	$-0.689149\pi$
$131$	5.00897	−	8.67579i	0.437636	−	0.758007i	0.997507	+	0.0705727i	$0.0224827\pi$
$132$		0			0
$133$	0.492974	+	0.0741860i	0.0427462	+	0.00643274i
$134$	−1.03079	−	1.78538i	−0.0890465	−	0.154233i
$135$		0			0
$136$	−2.96032	−	1.70914i	−0.253845	−	0.146558i
$137$	−4.38811	−	2.53348i	−0.374902	−	0.216450i	0.300696	−	0.953720i	$-0.402781\pi$
$137$	−4.38811	−	2.53348i	−0.374902	−	0.216450i	−0.675598	+	0.737270i	$0.736114\pi$
$138$		0			0
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	0.654398	−	0.756150i	$-0.272922\pi$
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	−0.982044	+	0.188650i	$0.939589\pi$
$140$	5.11195	+	13.0161i	0.432039	+	1.10006i
$141$		0			0
$142$	−0.302417	+	0.523802i	−0.0253783	+	0.0439565i
$143$	−8.21974	−	5.17707i	−0.687370	−	0.432928i
$144$		0			0
$145$	−16.4861	+	9.51824i	−1.36909	+	0.790447i
$146$	−1.28528	+	2.22617i	−0.106370	+	0.184239i
$147$		0			0
$148$			15.6482i			1.28627i
$149$			14.3185i			1.17301i	0.809944	+	0.586507i	$0.199498\pi$
$149$			14.3185i			1.17301i	−0.809944	+	0.586507i	$0.800502\pi$
$150$		0			0
$151$	−5.60534	+	3.23624i	−0.456156	+	0.263362i	−0.710427	−	0.703771i	$-0.751498\pi$
$151$	−5.60534	+	3.23624i	−0.456156	+	0.263362i	0.254271	+	0.967133i	$0.418165\pi$
$152$	0.135172			0.0109639
$153$		0			0
$154$	1.19975	−	0.471192i	0.0966789	−	0.0379698i
$155$	−9.93871			−0.798296
$156$		0			0
$157$	−7.95937	−	13.7860i	−0.635227	−	1.10025i	−0.986467	−	0.163960i	$-0.947573\pi$
$157$	−7.95937	−	13.7860i	−0.635227	−	1.10025i	0.351240	−	0.936285i	$-0.385760\pi$
$158$			1.64741i			0.131061i
$159$		0			0
$160$	2.85157	+	4.93907i	0.225437	+	0.390468i
$161$	10.8338	−	4.25489i	0.853826	−	0.335332i
$162$		0			0
$163$			4.78162i			0.374525i	0.982310	+	0.187263i	$0.0599616\pi$
$163$			4.78162i			0.374525i	−0.982310	+	0.187263i	$0.940038\pi$
$164$	9.25056	−	5.34081i	0.722348	−	0.417048i
$165$		0			0
$166$	1.49962	+	2.59743i	0.116393	+	0.201599i
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	0.588062	−	0.808816i	$-0.299891\pi$
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	−0.406424	+	0.913685i	$0.633224\pi$
$168$		0			0
$169$	−5.61544	−	11.7246i	−0.431957	−	0.901894i
$170$	1.15742	−	2.00472i	0.0887703	−	0.153755i
$171$		0			0
$172$	15.7594			1.20164
$173$	−0.899816			−0.0684118			−0.0342059	−	0.999415i	$-0.510890\pi$
$173$	−0.899816			−0.0684118			−0.0342059	+	0.999415i	$0.510890\pi$
$174$		0			0
$175$	−5.46223	+	2.14524i	−0.412906	+	0.162165i
$176$	−8.87787	+	5.12564i	−0.669195	+	0.386360i
$177$		0			0
$178$	0.532675	−	0.922620i	0.0399257	−	0.0691533i
$179$	−11.0558			−0.826351			−0.413175	−	0.910651i	$-0.635580\pi$
$179$	−11.0558			−0.826351			−0.413175	+	0.910651i	$0.635580\pi$
$180$		0			0
$181$	−3.52898			−0.262307			−0.131153	−	0.991362i	$-0.541868\pi$
$181$	−3.52898			−0.262307			−0.131153	+	0.991362i	$0.541868\pi$
$182$	1.69461	+	0.322103i	0.125613	+	0.0238759i
$183$		0			0
$184$	2.73315	−	1.57799i	0.201491	−	0.116331i
$185$	−21.3699			−1.57115
$186$		0			0
$187$	11.1179	+	6.41894i	0.813024	+	0.469400i
$188$	3.15002	−	1.81866i	0.229738	−	0.132640i
$189$		0			0
$190$			0.0915382i			0.00664088i
$191$	20.4004			1.47612			0.738059	−	0.674736i	$-0.235742\pi$
$191$	20.4004			1.47612			0.738059	+	0.674736i	$0.235742\pi$
$192$		0			0
$193$		−	17.2646i		−	1.24273i	−0.783521	−	0.621365i	$-0.786578\pi$
$193$		−	17.2646i		−	1.24273i	0.783521	−	0.621365i	$-0.213422\pi$
$194$	0.0407842	−	0.0706403i	0.00292814	−	0.00507168i
$195$		0			0
$196$	10.0906	−	9.37146i	0.720755	−	0.669390i
$197$	4.29264	+	2.47836i	0.305838	+	0.176576i	0.645063	−	0.764130i	$-0.276831\pi$
$197$	4.29264	+	2.47836i	0.305838	+	0.176576i	−0.339224	+	0.940705i	$0.610165\pi$
$198$		0			0
$199$	3.59097	−	6.21975i	0.254557	−	0.440906i	−0.710218	−	0.703982i	$-0.751404\pi$
$199$	3.59097	−	6.21975i	0.254557	−	0.440906i	0.964775	+	0.263076i	$0.0847369\pi$
$200$	−1.37801	+	0.795593i	−0.0974399	+	0.0562569i
$201$		0			0
$202$	−1.19904	+	0.692265i	−0.0843641	+	0.0487076i
$203$	14.6595	+	11.6850i	1.02890	+	0.820125i
$204$		0			0
$205$	7.29367	+	12.6330i	0.509412	+	0.882327i
$206$		−	0.932580i		−	0.0649759i
$207$		0			0
$208$	−13.7086	−	0.527611i	−0.950518	−	0.0365833i
$209$	−0.507661			−0.0351157
$210$		0			0
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	−0.386395	−	0.922333i	$-0.626280\pi$
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	0.991962	−	0.126539i	$-0.0403868\pi$
$212$	13.9136			0.955592
$213$		0			0
$214$	1.25793	+	0.726269i	0.0859906	+	0.0496467i
$215$			21.5218i			1.46777i
$216$		0			0
$217$	3.57788	+	9.11004i	0.242883	+	0.618430i
$218$	−0.120570	+	0.208833i	−0.00816602	+	0.0141440i
$219$		0			0
$220$	−7.12013	−	12.3324i	−0.480039	−	0.831452i
$221$	8.01153	+	15.1979i	0.538914	+	1.02232i
$222$		0			0
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	0.849733	−	0.527213i	$-0.176763\pi$
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	−0.0317129	+	0.999497i	$0.510096\pi$
$224$	3.50071	−	4.39185i	0.233901	−	0.293443i
$225$		0			0
$226$	−3.12230	−	1.80266i	−0.207693	−	0.119911i
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	0.415280	−	0.909694i	$-0.363684\pi$
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	−0.580178	+	0.814490i	$0.697017\pi$
$228$		0			0
$229$	−7.59860	−	4.38706i	−0.502130	−	0.289905i	0.227463	−	0.973787i	$-0.426957\pi$
$229$	−7.59860	−	4.38706i	−0.502130	−	0.289905i	−0.729593	+	0.683882i	$0.760290\pi$
$230$	1.06861	+	1.85088i	0.0704618	+	0.122043i
$231$		0			0
$232$	4.40208	+	2.54154i	0.289011	+	0.166861i
$233$	−2.55371	+	4.42316i	−0.167299	+	0.289771i	−0.937469	−	0.348068i	$-0.886838\pi$
$233$	−2.55371	+	4.42316i	−0.167299	+	0.289771i	0.770170	+	0.637839i	$0.220171\pi$
$234$		0			0
$235$	2.48365	+	4.30181i	0.162016	+	0.280619i
$236$	−12.9294	+	7.46481i	−0.841634	+	0.485918i
$237$		0			0
$238$	−2.25423	−	0.339232i	−0.146120	−	0.0219891i
$239$			2.49797i			0.161580i	0.996731	+	0.0807901i	$0.0257443\pi$
$239$			2.49797i			0.161580i	−0.996731	+	0.0807901i	$0.974256\pi$
$240$		0			0
$241$	6.91532	+	3.99256i	0.445455	+	0.257183i	0.705909	−	0.708303i	$-0.250539\pi$
$241$	6.91532	+	3.99256i	0.445455	+	0.257183i	−0.260454	+	0.965486i	$0.583872\pi$
$242$	0.585842	−	0.338236i	0.0376593	−	0.0217426i
$243$		0			0
$244$	0.404835	−	0.701195i	0.0259169	−	0.0448894i
$245$	12.7981	+	13.7802i	0.817641	+	0.880382i
$246$		0			0
$247$	−0.574856	−	0.362063i	−0.0365772	−	0.0230375i
$248$	1.32691	+	2.29827i	0.0842588	+	0.145941i
$249$		0			0
$250$	0.675749	+	1.17043i	0.0427381	+	0.0740246i
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	−0.921494	−	0.388393i	$-0.873030\pi$
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	0.124389	−	0.992234i	$-0.460303\pi$
$252$		0			0
$253$	−10.2648	+	5.92637i	−0.645341	+	0.372588i
$254$			1.44066i			0.0903952i
$255$		0			0
$256$	−6.72394	+	11.6462i	−0.420246	+	0.727888i
$257$	1.68682	+	2.92165i	0.105221	+	0.182248i	0.913828	−	0.406101i	$-0.133112\pi$
$257$	1.68682	+	2.92165i	0.105221	+	0.182248i	−0.808608	+	0.588348i	$0.799778\pi$
$258$		0			0
$259$	7.69305	+	19.5881i	0.478023	+	1.21715i
$260$	0.732915	−	19.0428i	0.0454535	−	1.18099i
$261$		0			0
$262$		−	1.81148i		−	0.111914i
$263$	0.158935			0.00980037			0.00490019	−	0.999988i	$-0.498440\pi$
$263$	0.158935			0.00980037			0.00490019	+	0.999988i	$0.498440\pi$
$264$		0			0
$265$			19.0011i			1.16723i
$266$	0.0839059	−	0.0329533i	0.00514460	−	0.00202050i
$267$		0			0
$268$	19.4243	+	11.2146i	1.18653	+	0.685043i
$269$	−11.6633	+	20.2014i	−0.711124	+	1.23170i	0.253311	+	0.967385i	$0.418480\pi$
$269$	−11.6633	+	20.2014i	−0.711124	+	1.23170i	−0.964435	+	0.264318i	$0.914853\pi$
$270$		0			0
$271$	10.2373	−	5.91049i	0.621870	−	0.359037i	−0.155727	−	0.987800i	$-0.549772\pi$
$271$	10.2373	−	5.91049i	0.621870	−	0.359037i	0.777597	+	0.628763i	$0.216439\pi$
$272$	18.1300			1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$	5.17532	−	2.98797i	0.312084	−	0.180182i
$276$		0			0
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	0.0819961	+	0.996633i	$0.473870\pi$
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	−0.904107	+	0.427306i	$0.859463\pi$
$278$	−1.20984	−	0.698503i	−0.0725615	−	0.0418934i
$279$		0			0
$280$	3.98753	+	3.17842i	0.238300	+	0.189947i
$281$		−	28.5383i		−	1.70245i	−0.524801	−	0.851225i	$-0.675860\pi$
$281$		−	28.5383i		−	1.70245i	0.524801	−	0.851225i	$-0.324140\pi$
$282$		0			0
$283$	−17.9721			−1.06833			−0.534165	−	0.845380i	$-0.679374\pi$
$283$	−17.9721			−1.06833			−0.534165	+	0.845380i	$0.679374\pi$
$284$		−	6.58040i		−	0.390475i
$285$		0			0
$286$	−1.75526	−	0.0675561i	−0.103791	−	0.00399468i
$287$	8.95400	−	11.2334i	0.528538	−	0.663084i
$288$		0			0
$289$	−2.85229	−	4.94032i	−0.167782	−	0.290607i
$290$	−1.72112	+	2.98107i	−0.101068	+	0.175055i
$291$		0			0
$292$		−	27.9668i		−	1.63663i
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476554\pi$
$294$		0			0
$295$	−10.1943	−	17.6570i	−0.593535	−	1.02803i
$296$	2.85308	+	4.94168i	0.165832	+	0.287229i
$297$		0			0
$298$	1.29456	+	2.24224i	0.0749918	+	0.129890i
$299$	−15.8501	−	0.610035i	−0.916636	−	0.0352792i
$300$		0			0
$301$	19.7273	−	7.74772i	1.13706	−	0.446571i
$302$	−0.585190	+	1.01358i	−0.0336739	+	0.0583249i
$303$		0			0
$304$	−0.620883	+	0.358467i	−0.0356101	+	0.0205595i
$305$	0.957586	+	0.552862i	0.0548312	+	0.0316568i
$306$		0			0
$307$		−	23.5161i		−	1.34214i	−0.741396	−	0.671068i	$-0.765836\pi$
$307$		−	23.5161i		−	1.34214i	0.741396	−	0.671068i	$-0.234164\pi$
$308$	−8.74096	+	10.9661i	−0.498062	+	0.624850i
$309$		0			0
$310$	−1.55638	+	0.898577i	−0.0883965	+	0.0510358i
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	0.841979	−	0.539510i	$-0.181391\pi$
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	−0.888219	+	0.459420i	$0.848057\pi$
$312$		0			0
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	−0.856012	−	0.516956i	$-0.827065\pi$
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	0.875703	+	0.482850i	$0.160398\pi$
$314$	−2.49284	−	1.43924i	−0.140679	−	0.0812212i
$315$		0			0
$316$	−8.96164	−	15.5220i	−0.504132	−	0.873182i
$317$	18.5579	+	10.7144i	1.04231	+	0.601780i	0.920488	−	0.390771i	$-0.127792\pi$
$317$	18.5579	+	10.7144i	1.04231	+	0.601780i	0.121826	+	0.992551i	$0.461125\pi$
$318$		0			0
$319$	−16.5327	−	9.54517i	−0.925654	−	0.534427i
$320$	−16.8126	−	9.70673i	−0.939850	−	0.542623i
$321$		0			0
$322$	1.31186	−	1.64581i	0.0731073	−	0.0917177i
$323$	0.777544	+	0.448915i	0.0432637	+	0.0249783i
$324$		0			0
$325$	7.99136	+	0.307569i	0.443281	+	0.0170609i
$326$	0.432315	+	0.748792i	0.0239437	+	0.0414717i
$327$		0			0
$328$	1.94754	−	3.37324i	0.107535	−	0.186256i
$329$	3.04903	−	3.82520i	0.168099	−	0.210890i
$330$		0			0
$331$			1.52046i			0.0835722i	0.999127	+	0.0417861i	$0.0133048\pi$
$331$			1.52046i			0.0835722i	−0.999127	+	0.0417861i	$0.986695\pi$
$332$	−28.2591	−	16.3154i	−1.55092	−	0.895425i
$333$		0			0
$334$	0.490108			0.0268175
$335$	−15.3152	+	26.5268i	−0.836761	+	1.44931i
$336$		0			0
$337$	−32.2304			−1.75570			−0.877850	−	0.478936i	$-0.841023\pi$
$337$	−32.2304			−1.75570			−0.877850	+	0.478936i	$0.841023\pi$
$338$	−1.93941	−	1.32835i	−0.105490	−	0.0722527i
$339$		0			0
$340$			25.1848i			1.36584i
$341$	−4.98341	−	8.63153i	−0.269867	−	0.467423i
$342$		0			0
$343$	8.02394	−	16.6918i	0.433252	−	0.901273i
$344$	4.97679	−	2.87335i	0.268331	−	0.154921i
$345$		0			0
$346$	−0.140909	+	0.0813541i	−0.00757534	+	0.00437362i
$347$	4.09215	−	7.08782i	0.219678	−	0.380494i	−0.735031	−	0.678033i	$-0.762833\pi$
$347$	4.09215	−	7.08782i	0.219678	−	0.380494i	0.954710	+	0.297539i	$0.0961659\pi$
$348$		0			0
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.100841	−	0.994903i	$-0.532153\pi$
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.912031	+	0.410120i	$0.865487\pi$
$350$	−0.661419	+	0.829791i	−0.0353543	+	0.0443542i
$351$		0			0
$352$	−2.85964	+	4.95304i	−0.152419	+	0.263998i
$353$			0.567179i			0.0301879i	0.999886	+	0.0150940i	$0.00480474\pi$
$353$			0.567179i			0.0301879i	−0.999886	+	0.0150940i	$0.995195\pi$
$354$		0			0
$355$	8.98650			0.476954
$356$			11.5907i			0.614303i
$357$		0			0
$358$	−1.73132	+	0.999577i	−0.0915030	+	0.0528293i
$359$	−28.0630	−	16.2022i	−1.48111	−	0.855118i	−0.481336	−	0.876536i	$-0.659848\pi$
$359$	−28.0630	−	16.2022i	−1.48111	−	0.855118i	−0.999771	+	0.0214184i	$0.993182\pi$
$360$		0			0
$361$	18.9645			0.998131
$362$	−0.552631	+	0.319061i	−0.0290456	+	0.0167695i
$363$		0			0
$364$	−17.7189	+	6.18351i	−0.928723	+	0.324104i
$365$	38.1928			1.99910
$366$		0			0
$367$	−7.86888			−0.410752			−0.205376	−	0.978683i	$-0.565842\pi$
$367$	−7.86888			−0.410752			−0.205376	+	0.978683i	$0.565842\pi$
$368$	−8.36939	+	14.4962i	−0.436285	+	0.755667i
$369$		0			0
$370$	−3.34648	+	1.93209i	−0.173975	+	0.100445i
$371$	17.4168	−	6.84030i	0.904237	−	0.355131i
$372$		0			0
$373$	−2.09163			−0.108300			−0.0541502	−	0.998533i	$-0.517245\pi$
$373$	−2.09163			−0.108300			−0.0541502	+	0.998533i	$0.517245\pi$
$374$	2.32139			0.120036
$375$		0			0
$376$	0.663180	−	1.14866i	0.0342009	−	0.0592377i
$377$	−11.9134	−	22.5997i	−0.613571	−	1.16394i
$378$		0			0
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	0.783404	−	0.621513i	$-0.213482\pi$
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	−0.146545	+	0.989204i	$0.546815\pi$
$380$	−0.497953	−	0.862480i	−0.0255444	−	0.0442443i
$381$		0			0
$382$	3.19466	−	1.84444i	0.163453	−	0.0943695i
$383$			25.1873i			1.28701i	0.765441	+	0.643507i	$0.222521\pi$
$383$			25.1873i			1.28701i	−0.765441	+	0.643507i	$0.777479\pi$
$384$		0			0
$385$	−14.9758	−	11.9371i	−0.763237	−	0.608369i
$386$	−1.56092	−	2.70359i	−0.0794488	−	0.137609i
$387$		0			0
$388$			0.887438i			0.0450528i
$389$	−14.0512	−	24.3373i	−0.712422	−	1.23395i	−0.963946	−	0.266099i	$-0.914265\pi$
$389$	−14.0512	−	24.3373i	−0.712422	−	1.23395i	0.251524	−	0.967851i	$-0.419068\pi$
$390$		0			0
$391$	20.9623			1.06011
$392$	1.47792	−	4.79927i	0.0746463	−	0.242400i
$393$		0			0
$394$	0.896292			0.0451546
$395$	21.1976	−	12.2384i	1.06657	−	0.615783i
$396$		0			0
$397$			21.7765i			1.09293i	0.837482	+	0.546465i	$0.184027\pi$
$397$			21.7765i			1.09293i	−0.837482	+	0.546465i	$0.815973\pi$
$398$		−	1.29867i		−	0.0650963i
$399$		0			0
$400$	4.21970	−	7.30874i	0.210985	−	0.365437i
$401$	17.7786	−	10.2645i	0.887821	−	0.512584i	0.0145918	−	0.999894i	$-0.495355\pi$
$401$	17.7786	−	10.2645i	0.887821	−	0.512584i	0.873229	+	0.487310i	$0.162022\pi$
$402$		0			0
$403$	0.512971	−	13.3282i	0.0255529	−	0.663923i
$404$	7.53162	−	13.0451i	0.374712	−	0.649020i
$405$		0			0
$406$	3.35211	+	0.504448i	0.166363	+	0.0250354i
$407$	−10.7152	−	18.5592i	−0.531132	−	0.919947i
$408$		0			0
$409$	5.42879	+	3.13431i	0.268436	+	0.154982i	0.628177	−	0.778071i	$-0.283801\pi$
$409$	5.42879	+	3.13431i	0.268436	+	0.154982i	−0.359741	+	0.933052i	$0.617135\pi$
$410$	2.28435	+	1.31887i	0.112816	+	0.0651343i
$411$		0			0
$412$	5.07308	+	8.78683i	0.249933	+	0.432896i
$413$	−12.5149	+	15.7008i	−0.615820	+	0.772584i
$414$		0			0
$415$	22.2811	−	38.5920i	1.09374	−	1.89441i
$416$	−6.77065	+	3.56914i	−0.331958	+	0.174991i
$417$		0			0
$418$	−0.0794987	+	0.0458986i	−0.00388841	+	0.00224497i
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	−0.0599424	−	0.998202i	$-0.519092\pi$
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	0.894439	−	0.447189i	$-0.147575\pi$
$420$		0			0
$421$		−	11.5233i		−	0.561613i	−0.959764	−	0.280806i	$-0.909398\pi$
$421$		−	11.5233i		−	0.561613i	0.959764	−	0.280806i	$-0.0906019\pi$
$422$		−	3.18118i		−	0.154858i
$423$		0			0
$424$	4.39391	−	2.53682i	0.213387	−	0.123199i
$425$	−10.5688			−0.512664
$426$		0			0
$427$	0.162040	−	1.07677i	0.00784165	−	0.0521086i
$428$	−15.8031			−0.763873
$429$		0			0
$430$	1.94582	+	3.37026i	0.0938359	+	0.162529i
$431$			8.77001i			0.422436i	0.977439	+	0.211218i	$0.0677431\pi$
$431$			8.77001i			0.422436i	−0.977439	+	0.211218i	$0.932257\pi$
$432$		0			0
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	0.999337	+	0.0364046i	$0.0115905\pi$
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	−0.468141	+	0.883654i	$0.655076\pi$
$434$	1.38394	+	1.10313i	0.0664315	+	0.0529519i
$435$		0			0
$436$		−	2.62352i		−	0.125644i
$437$	−0.717877	+	0.414467i	−0.0343407	+	0.0198266i
$438$		0			0
$439$	−5.18547	−	8.98150i	−0.247489	−	0.428664i	0.715339	−	0.698777i	$-0.246272\pi$
$439$	−5.18547	−	8.98150i	−0.247489	−	0.428664i	−0.962828	+	0.270114i	$0.912939\pi$
$440$	−4.49705	−	2.59637i	−0.214389	−	0.123777i
$441$		0			0
$442$	2.62866	+	1.65562i	0.125032	+	0.0787496i
$443$	17.9068	−	31.0156i	0.850780	−	1.47359i	−0.0297257	−	0.999558i	$-0.509463\pi$
$443$	17.9068	−	31.0156i	0.850780	−	1.47359i	0.880506	−	0.474036i	$-0.157203\pi$
$444$		0			0
$445$	−15.8287			−0.750354
$446$	2.55059			0.120774
$447$		0			0
$448$	−2.84497	+	18.9051i	−0.134412	+	0.893183i
$449$	19.7023	−	11.3751i	0.929809	−	0.536825i	0.0430575	−	0.999073i	$-0.486290\pi$
$449$	19.7023	−	11.3751i	0.929809	−	0.536825i	0.886751	+	0.462247i	$0.152957\pi$
$450$		0			0
$451$	−7.31430	+	12.6687i	−0.344417	+	0.596548i
$452$	39.2248			1.84498
$453$		0			0
$454$	−0.518742			−0.0243458
$455$	−8.44449	−	24.1978i	−0.395884	−	1.13441i
$456$		0			0
$457$	−27.1215	+	15.6586i	−1.26869	+	0.732478i	−0.974740	−	0.223344i	$-0.928303\pi$
$457$	−27.1215	+	15.6586i	−1.26869	+	0.732478i	−0.293949	+	0.955821i	$0.594969\pi$
$458$	−1.58657			−0.0741354
$459$		0			0
$460$	−20.1370	−	11.6261i	−0.938891	−	0.542069i
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	−0.320765	−	0.947159i	$-0.603940\pi$
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	0.659881	+	0.751370i	$0.270607\pi$
$462$		0			0
$463$			10.0392i			0.466563i	0.972409	+	0.233281i	$0.0749463\pi$
$463$			10.0392i			0.466563i	−0.972409	+	0.233281i	$0.925054\pi$
$464$	−26.9599			−1.25158
$465$		0			0
$466$			0.923545i			0.0427824i
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	−0.381594	−	0.924330i	$-0.624625\pi$
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	0.991290	−	0.131695i	$-0.0420418\pi$
$468$		0			0
$469$	29.8284	+	4.48878i	1.37735	+	0.207273i
$470$	0.777869	+	0.449103i	0.0358804	+	0.0207156i
$471$		0			0
$472$	−2.72206	+	4.71475i	−0.125293	+	0.217014i
$473$	−18.6911	+	10.7913i	−0.859418	+	0.496185i
$474$		0			0
$475$	0.361941	−	0.208967i	0.0166070	−	0.00958806i
$476$	23.0849	−	9.06638i	1.05809	−	0.415557i
$477$		0			0
$478$	0.225846	+	0.391177i	0.0103300	+	0.0178920i
$479$			8.58414i			0.392220i	0.980582	+	0.196110i	$0.0628309\pi$
$479$			8.58414i			0.392220i	−0.980582	+	0.196110i	$0.937169\pi$
$480$		0			0
$481$	1.10297	−	28.6578i	0.0502913	−	1.30668i
$482$	1.44390			0.0657678
$483$		0			0
$484$	−3.67990	+	6.37377i	−0.167268	+	0.289717i
$485$	−1.21193			−0.0550308
$486$		0			0
$487$	18.4084	+	10.6281i	0.834166	+	0.481606i	0.855277	−	0.518171i	$-0.173387\pi$
$487$	18.4084	+	10.6281i	0.834166	+	0.481606i	−0.0211110	+	0.999777i	$0.506720\pi$
$488$		−	0.295249i		−	0.0133653i
$489$		0			0
$490$	3.25005	+	1.00084i	0.146822	+	0.0452135i
$491$	11.2268	−	19.4453i	0.506657	−	0.877556i	−0.493313	−	0.869852i	$-0.664214\pi$
$491$	11.2268	−	19.4453i	0.506657	−	0.877556i	0.999970	−	0.00770409i	$-0.00245231\pi$
$492$		0			0
$493$	16.8812	+	29.2391i	0.760292	+	1.31686i
$494$	−0.122756	−	0.00472460i	−0.00552306	−	0.000212570i
$495$		0			0
$496$	−12.1897	−	7.03772i	−0.547333	−	0.316003i
$497$	−3.23509	−	8.23722i	−0.145114	−	0.369490i
$498$		0			0
$499$	33.6694	+	19.4390i	1.50725	+	0.870210i	0.999964	+	0.00843082i	$0.00268365\pi$
$499$	33.6694	+	19.4390i	1.50725	+	0.870210i	0.507284	+	0.861779i	$0.330650\pi$
$500$	−12.7339	−	7.35193i	−0.569478	−	0.328788i
$501$		0			0
$502$	−3.95520	−	2.28354i	−0.176529	−	0.101919i
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	0.920422	−	0.390927i	$-0.127846\pi$
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	−0.798764	+	0.601645i	$0.794512\pi$
$504$		0			0
$505$	17.8151	+	10.2855i	0.792760	+	0.457700i
$506$	−1.07163	+	1.85612i	−0.0476397	+	0.0825144i
$507$		0			0
$508$	−7.83697	−	13.5740i	−0.347709	−	0.602250i
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	−0.694271	−	0.719713i	$-0.744273\pi$
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	0.276154	+	0.961113i	$0.410940\pi$
$510$		0			0
$511$	−13.7492	−	35.0083i	−0.608229	−	1.54868i
$512$			13.5360i			0.598214i
$513$		0			0
$514$	0.528304	+	0.305017i	0.0233025	+	0.0134537i
$515$	−11.9997	+	6.92804i	−0.528771	+	0.305286i
$516$		0			0
$517$	−2.49068	+	4.31398i	−0.109540	+	0.189729i
$518$	2.97572	+	2.37192i	0.130745	+	0.104216i
$519$		0			0
$520$	−3.24056	−	6.14733i	−0.142108	−	0.269578i
$521$	13.9480	+	24.1587i	0.611074	+	1.05841i	0.991060	+	0.133419i	$0.0425957\pi$
$521$	13.9480	+	24.1587i	0.611074	+	1.05841i	−0.379985	+	0.924993i	$0.624071\pi$
$522$		0			0
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	0.623242	−	0.782029i	$-0.285815\pi$
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	−0.988878	+	0.148729i	$0.952482\pi$
$524$	9.85416	+	17.0679i	0.430481	+	0.745615i
$525$		0			0
$526$	0.0248890	−	0.0143696i	0.00108521	−	0.000626546i
$527$			17.6269i			0.767842i
$528$		0			0
$529$	1.82314	−	3.15777i	0.0792668	−	0.137294i
$530$	1.71793	+	2.97554i	0.0746219	+	0.129249i
$531$		0			0
$532$	−0.611307	+	0.766923i	−0.0265035	+	0.0332503i
$533$	−17.3178	+	9.12904i	−0.750116	+	0.395423i
$534$		0			0
$535$		−	21.5815i		−	0.933049i
$536$	8.17890			0.353275
$537$		0			0
$538$			4.21800i			0.181851i
$539$	−5.55057	+	18.0244i	−0.239080	+	0.776366i
$540$		0			0
$541$	−9.66528	−	5.58025i	−0.415543	−	0.239914i	0.277626	−	0.960689i	$-0.410453\pi$
$541$	−9.66528	−	5.58025i	−0.415543	−	0.239914i	−0.693169	+	0.720776i	$0.743786\pi$
$542$	1.06876	−	1.85114i	0.0459070	−	0.0795133i
$543$		0			0
$544$	8.75976	−	5.05745i	0.375572	−	0.216836i
$545$	3.58280			0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$	8.63275	−	4.98412i	0.368773	−	0.212911i
$549$		0			0
$550$	0.540297	−	0.935821i	0.0230383	−	0.0399036i
$551$	−1.15623	−	0.667551i	−0.0492571	−	0.0284386i
$552$		0			0
$553$	−18.8491	−	15.0244i	−0.801543	−	0.638903i
$554$			4.94830i			0.210233i
$555$		0			0
$556$	15.1990			0.644579
$557$			33.0776i			1.40154i	0.713386	+	0.700772i	$0.247161\pi$
$557$			33.0776i			1.40154i	−0.713386	+	0.700772i	$0.752839\pi$
$558$		0			0
$559$	−28.8615	−	1.11081i	−1.22071	−	0.0469823i
$560$	−26.7447	−	4.02472i	−1.13017	−	0.170076i
$561$		0			0
$562$	−2.58020	−	4.46903i	−0.108839	−	0.188515i
$563$	−8.89836	+	15.4124i	−0.375021	+	0.649556i	−0.990330	−	0.138730i	$-0.955698\pi$
$563$	−8.89836	+	15.4124i	−0.375021	+	0.649556i	0.615309	+	0.788286i	$0.289031\pi$
$564$		0			0
$565$			53.5672i			2.25359i
$566$	−2.81439	+	1.62489i	−0.118298	+	0.0682992i
$567$		0			0
$568$	−1.19978	−	2.07808i	−0.0503417	−	0.0871943i
$569$	4.11047	+	7.11954i	0.172320	+	0.298467i	0.939231	−	0.343287i	$-0.111540\pi$
$569$	4.11047	+	7.11954i	0.172320	+	0.298467i	−0.766911	+	0.641754i	$0.778207\pi$
$570$		0			0
$571$	−12.8776	−	22.3047i	−0.538912	−	0.933424i	−0.998963	−	0.0455309i	$-0.985502\pi$
$571$	−12.8776	−	22.3047i	−0.538912	−	0.933424i	0.460051	−	0.887893i	$-0.347831\pi$
$572$	16.9057	−	8.91183i	0.706863	−	0.372622i
$573$		0			0
$574$	0.386550	−	2.56867i	0.0161343	−	0.107214i
$575$	4.87891	−	8.45051i	0.203464	−	0.352411i
$576$		0			0
$577$	0.666314	−	0.384697i	0.0277390	−	0.0160151i	−0.486066	−	0.873922i	$-0.661569\pi$
$577$	0.666314	−	0.384697i	0.0277390	−	0.0160151i	0.513805	+	0.857907i	$0.328235\pi$
$578$	−0.893326	−	0.515762i	−0.0371575	−	0.0214529i
$579$		0			0
$580$		−	37.4505i		−	1.55505i
$581$	−43.3954	−	6.53042i	−1.80034	−	0.270928i
$582$		0			0
$583$	−16.5020	+	9.52743i	−0.683443	+	0.394586i
$584$	−5.09908	−	8.83187i	−0.211002	−	0.365465i
$585$		0			0
$586$	−1.34615	+	2.33159i	−0.0556088	+	0.0963173i
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	0.700307	−	0.713841i	$-0.253046\pi$
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	−0.268051	+	0.963405i	$0.586380\pi$
$588$		0			0
$589$	−0.348520	−	0.603654i	−0.0143605	−	0.0248731i
$590$	−3.19281	−	1.84337i	−0.131446	−	0.0758904i
$591$		0			0
$592$	−26.2099	−	15.1323i	−1.07722	−	0.621933i
$593$	−13.8115	−	7.97406i	−0.567170	−	0.327456i	0.188848	−	0.982006i	$-0.439525\pi$
$593$	−13.8115	−	7.97406i	−0.567170	−	0.327456i	−0.756018	+	0.654551i	$0.772858\pi$
$594$		0			0
$595$	12.3815	+	31.5258i	0.507591	+	1.29243i
$596$	−24.3949	−	14.0844i	−0.999253	−	0.576919i
$597$		0			0
$598$	−2.53725	+	1.33751i	−0.103756	+	0.0546948i
$599$	−3.55511	−	6.15763i	−0.145258	−	0.251594i	0.784211	−	0.620494i	$-0.213068\pi$
$599$	−3.55511	−	6.15763i	−0.145258	−	0.251594i	−0.929469	+	0.368900i	$0.879734\pi$
$600$		0			0
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	−0.996329	−	0.0856011i	$-0.972719\pi$
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	0.572297	+	0.820046i	$0.306052\pi$
$602$	2.38877	−	2.99686i	0.0973590	−	0.122143i
$603$		0			0
$604$		−	12.7333i		−	0.518112i
$605$	−8.70432	−	5.02544i	−0.353881	−	0.204313i
$606$		0			0
$607$	−7.71405			−0.313104			−0.156552	−	0.987670i	$-0.550038\pi$
$607$	−7.71405			−0.313104			−0.156552	+	0.987670i	$0.550038\pi$
$608$	−0.199992	+	0.346396i	−0.00811074	+	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	−5.89707	+	3.10864i	−0.238570	+	0.125762i
$612$		0			0
$613$		−	20.4378i		−	0.825476i	−0.910850	−	0.412738i	$-0.864572\pi$
$613$		−	20.4378i		−	0.825476i	0.910850	−	0.412738i	$-0.135428\pi$
$614$	−2.12614	−	3.68257i	−0.0858038	−	0.148617i
$615$		0			0
$616$	−0.760978	+	5.05678i	−0.0306607	+	0.203743i
$617$	3.98209	−	2.29906i	0.160313	−	0.0925567i	−0.417697	−	0.908586i	$-0.637163\pi$
$617$	3.98209	−	2.29906i	0.160313	−	0.0925567i	0.578010	+	0.816030i	$0.303829\pi$
$618$		0			0
$619$	8.70599	−	5.02641i	0.349923	−	0.202028i	−0.314728	−	0.949182i	$-0.601913\pi$
$619$	8.70599	−	5.02641i	0.349923	−	0.202028i	0.664651	+	0.747154i	$0.268580\pi$
$620$	9.77623	−	16.9329i	0.392623	−	0.680042i
$621$		0			0
$622$	−0.255396	−	0.147453i	−0.0102404	−	0.00591232i
$623$	5.69827	+	14.5090i	0.228296	+	0.581290i
$624$		0			0
$625$	15.5853	−	26.9944i	0.623410	−	1.07978i
$626$		−	0.125986i		−	0.00503541i
$627$		0			0
$628$	31.3170			1.24968
$629$			37.9009i			1.51121i
$630$		0			0
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	−0.620116	−	0.784510i	$-0.712914\pi$
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	0.369348	+	0.929291i	$0.379581\pi$
$632$	−5.66015	−	3.26789i	−0.225149	−	0.129990i
$633$		0			0
$634$	3.87483			0.153889
$635$	18.5373	−	10.7025i	0.735631	−	0.424717i
$636$		0			0
$637$	−19.1402	+	16.4515i	−0.758364	+	0.651831i
$638$	−3.45199			−0.136665
$639$		0			0
$640$	−14.9167			−0.589635
$641$	−1.92516	+	3.33448i	−0.0760394	+	0.131704i	−0.901538	−	0.432700i	$-0.857561\pi$
$641$	−1.92516	+	3.33448i	−0.0760394	+	0.131704i	0.825498	+	0.564404i	$0.190894\pi$
$642$		0			0
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	−0.450065	−	0.892996i	$-0.648599\pi$
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	0.548325	+	0.836265i	$0.315266\pi$
$644$	−3.40752	+	22.6433i	−0.134275	+	0.892271i
$645$		0			0
$646$	0.162349			0.00638754
$647$	37.1001			1.45856			0.729278	−	0.684218i	$-0.239856\pi$
$647$	37.1001			1.45856			0.729278	+	0.684218i	$0.239856\pi$
$648$		0			0
$649$	10.2231	−	17.7070i	0.401293	−	0.695061i
$650$	1.27924	−	0.674349i	0.0501758	−	0.0264501i
$651$		0			0
$652$	−8.14661	−	4.70345i	−0.319046	−	0.184201i
$653$	10.0475	+	17.4028i	0.393189	+	0.681023i	0.992868	−	0.119218i	$-0.0380386\pi$
$653$	10.0475	+	17.4028i	0.393189	+	0.681023i	−0.599679	+	0.800240i	$0.704705\pi$
$654$		0			0
$655$	−23.3087	+	13.4573i	−0.910748	+	0.525820i
$656$			20.6589i			0.806596i
$657$		0			0
$658$	0.131629	−	0.874687i	0.00513142	−	0.0340988i
$659$	4.95529	+	8.58281i	0.193031	+	0.334339i	0.946253	−	0.323427i	$-0.104835\pi$
$659$	4.95529	+	8.58281i	0.193031	+	0.334339i	−0.753223	+	0.657766i	$0.771502\pi$
$660$		0			0
$661$			47.2266i			1.83690i	0.395537	+	0.918450i	$0.370558\pi$
$661$			47.2266i			1.83690i	−0.395537	+	0.918450i	$0.629442\pi$
$662$	0.137468	+	0.238102i	0.00534284	+	0.00925408i
$663$		0			0
$664$	−11.8989			−0.461768
$665$	−1.04735	−	0.834830i	−0.0406143	−	0.0323733i
$666$		0			0
$667$	−31.1716			−1.20697
$668$	−4.61783	+	2.66611i	−0.178669	+	0.103155i
$669$		0			0
$670$			5.53872i			0.213979i
$671$			1.10885i			0.0428068i
$672$		0			0
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	−0.791639	−	0.610990i	$-0.790772\pi$
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	0.924952	+	0.380084i	$0.124105\pi$
$674$	−5.04721	+	2.91401i	−0.194411	+	0.112243i
$675$		0			0
$676$	25.4993	+	1.96573i	0.980742	+	0.0756050i
$677$	−6.16453	+	10.6773i	−0.236922	+	0.410361i	−0.959830	−	0.280584i	$-0.909472\pi$
$677$	−6.16453	+	10.6773i	−0.236922	+	0.410361i	0.722908	+	0.690945i	$0.242805\pi$
$678$		0			0
$679$	0.436287	+	1.11088i	0.0167432	+	0.0426316i
$680$	4.59185	+	7.95331i	0.176089	+	0.304996i
$681$		0			0
$682$	−1.56078	−	0.901120i	−0.0597655	−	0.0345057i
$683$	−21.2491	−	12.2682i	−0.813076	−	0.469430i	0.0349470	−	0.999389i	$-0.488874\pi$
$683$	−21.2491	−	12.2682i	−0.813076	−	0.469430i	−0.848023	+	0.529960i	$0.822207\pi$
$684$		0			0
$685$	6.80655	+	11.7893i	0.260065	+	0.450446i
$686$	−0.252606	−	3.33936i	−0.00964453	−	0.127497i
$687$		0			0
$688$	−15.2398	+	26.3961i	−0.581012	+	1.00634i
$689$	−25.4812	−	0.980713i	−0.970756	−	0.0373622i
$690$		0			0
$691$	−7.88703	+	4.55358i	−0.300037	+	0.173226i	−0.642459	−	0.766320i	$-0.722086\pi$
$691$	−7.88703	+	4.55358i	−0.300037	+	0.173226i	0.342423	+	0.939546i	$0.388753\pi$
$692$	0.885106	−	1.53305i	0.0336467	−	0.0582777i
$693$		0			0
$694$		−	1.47992i		−	0.0561769i
$695$			20.7564i			0.787336i
$696$		0			0
$697$	22.4055	−	12.9358i	0.848667	−	0.489978i
$698$	−3.95087			−0.149542
$699$		0			0
$700$	1.71801	−	11.4164i	0.0649347	−	0.431498i
$701$	−0.286950			−0.0108380			−0.00541898	−	0.999985i	$-0.501725\pi$
$701$	−0.286950			−0.0108380			−0.00541898	+	0.999985i	$0.501725\pi$
$702$		0			0
$703$	−0.749377	−	1.29796i	−0.0282633	−	0.0489534i
$704$		−	19.4684i		−	0.733742i
$705$		0			0
$706$	0.0512797	+	0.0888191i	0.00192994	+	0.00334275i
$707$	3.01461	−	20.0324i	0.113376	−	0.753397i
$708$		0			0
$709$		−	18.5848i		−	0.697967i	−0.937129	−	0.348984i	$-0.886527\pi$
$709$		−	18.5848i		−	0.697967i	0.937129	−	0.348984i	$-0.113473\pi$
$710$	1.40727	−	0.812486i	0.0528138	−	0.0304921i
$711$		0			0
$712$	2.11328	+	3.66031i	0.0791986	+	0.137176i
$713$	−14.0940	−	8.13715i	−0.527823	−	0.304739i
$714$		0			0
$715$	12.1704	+	23.0872i	0.455148	+	0.863414i
$716$	10.8751	−	18.8362i	0.406421	−	0.703941i
$717$		0			0
$718$	−5.85947			−0.218674
$719$	41.6949			1.55496			0.777479	−	0.628909i	$-0.216498\pi$
$719$	41.6949			1.55496			0.777479	+	0.628909i	$0.216498\pi$
$720$		0			0
$721$	10.6702	+	8.50514i	0.397380	+	0.316748i
$722$	2.96980	−	1.71462i	0.110525	−	0.0638114i
$723$		0			0
$724$	3.47128	−	6.01244i	0.129009	−	0.223451i
$725$	15.7162			0.583684
$726$		0			0
$727$	32.7039			1.21292			0.606461	−	0.795113i	$-0.292589\pi$
$727$	32.7039			1.21292			0.606461	+	0.795113i	$0.292589\pi$
$728$	−4.46819	+	5.18337i	−0.165602	+	0.192108i
$729$		0			0
$730$	5.98091	−	3.45308i	0.221363	−	0.127804i
$731$	38.1702			1.41178
$732$		0			0
$733$	−8.60423	−	4.96765i	−0.317804	−	0.183484i	0.332609	−	0.943065i	$-0.392071\pi$
$733$	−8.60423	−	4.96765i	−0.317804	−	0.183484i	−0.650413	+	0.759580i	$0.725404\pi$
$734$	−1.23225	+	0.711440i	−0.0454832	+	0.0262597i
$735$		0			0
$736$			9.33871i			0.344230i
$737$	−30.7171			−1.13148
$738$		0			0
$739$		−	10.4022i		−	0.382649i	−0.981527	−	0.191325i	$-0.938722\pi$
$739$		−	10.4022i		−	0.382649i	0.981527	−	0.191325i	$-0.0612784\pi$
$740$	21.0205	−	36.4086i	0.772730	−	1.33841i
$741$		0			0
$742$	2.10900	−	2.64587i	0.0774237	−	0.0971328i
$743$	1.47972	+	0.854317i	0.0542857	+	0.0313419i	0.526897	−	0.849929i	$-0.323355\pi$
$743$	1.47972	+	0.854317i	0.0542857	+	0.0313419i	−0.472612	+	0.881271i	$0.656689\pi$
$744$		0			0
$745$	19.2343	−	33.3148i	0.704690	−	1.22056i
$746$	−0.327545	+	0.189108i	−0.0119923	+	0.00692374i
$747$		0			0
$748$	−21.8723	+	12.6280i	−0.799732	+	0.461726i
$749$	−19.7821	+	7.76923i	−0.722821	+	0.283881i
$750$		0			0
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	0.998477	+	0.0551673i	$0.0175692\pi$
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	−0.451462	+	0.892290i	$0.649097\pi$
$752$			7.03481i			0.256533i
$753$		0			0
$754$	−3.90890	−	2.46195i	−0.142354	−	0.0896590i
$755$	17.3893			0.632860
$756$		0			0
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	−0.932232	−	0.361861i	$-0.882141\pi$
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	0.779497	+	0.626406i	$0.215475\pi$
$758$	2.58874			0.0940271
$759$		0			0
$760$	−0.314506	−	0.181580i	−0.0114083	−	0.00658660i
$761$			51.0590i			1.85089i	0.378885	+	0.925444i	$0.376308\pi$
$761$			51.0590i			1.85089i	−0.378885	+	0.925444i	$0.623692\pi$
$762$		0			0
$763$	−1.28979	−	3.28407i	−0.0466935	−	0.118891i
$764$	−20.0668	+	34.7568i	−0.725993	+	1.25746i
$765$		0			0
$766$	2.27723	+	3.94429i	0.0822798	+	0.142513i
$767$	24.2049	−	12.7596i	0.873988	−	0.460722i
$768$		0			0
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	0.488960	−	0.872306i	$-0.337376\pi$
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	−0.510959	+	0.859605i	$0.670710\pi$
$770$	−3.42443	−	0.515331i	−0.123408	−	0.0185712i
$771$		0			0
$772$	29.4142	+	16.9823i	1.05864	+	0.611206i
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	0.519575	−	0.854425i	$-0.326090\pi$
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	−0.480166	+	0.877178i	$0.659423\pi$
$774$		0			0
$775$	7.10593	+	4.10261i	0.255253	+	0.147370i
$776$	0.161803	+	0.280252i	0.00580840	+	0.0100604i
$777$		0			0
$778$	−4.40076	−	2.54078i	−0.157775	−	0.0910914i
$779$	−0.511533	+	0.886001i	−0.0183276	+	0.0317443i
$780$		0			0
$781$	4.50596	+	7.80456i	0.161236	+	0.279269i
$782$	3.28265	−	1.89524i	0.117387	−	0.0677737i
$783$		0			0
$784$	5.93881	+	25.9637i	0.212100	+	0.927273i
$785$			42.7679i			1.52645i
$786$		0			0
$787$	37.9292	+	21.8984i	1.35203	+	0.780595i	0.988534	−	0.151000i	$-0.0482494\pi$
$787$	37.9292	+	21.8984i	1.35203	+	0.780595i	0.363497	+	0.931595i	$0.381583\pi$
$788$	−8.44493	+	4.87568i	−0.300838	+	0.173689i
$789$		0			0
$790$	2.21300	−	3.83303i	0.0787351	−	0.136373i
$791$	49.1009	−	19.2839i	1.74583	−	0.685657i
$792$		0			0
$793$	−0.790833	+	1.25562i	−0.0280833	+	0.0445884i
$794$	1.96885	+	3.41015i	0.0698719	+	0.121022i
$795$		0			0
$796$	7.06453	+	12.2361i	0.250396	+	0.433698i
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	0.719033	−	0.694976i	$-0.244585\pi$
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	−0.961383	+	0.275213i	$0.911252\pi$
$798$		0			0
$799$	7.62954	−	4.40492i	0.269914	−	0.155835i
$800$		−	4.70842i		−	0.166468i
$801$		0			0
$802$	1.85606	−	3.21479i	0.0655398	−	0.113518i
$803$	19.1504	+	33.1695i	0.675803	+	1.17053i
$804$		0			0
$805$	−30.9228	−	4.65347i	−1.08988	−	0.164013i
$806$	−1.12469	−	2.13354i	−0.0396157	−	0.0751508i
$807$		0			0
$808$		−	5.49285i		−	0.193238i
$809$	−9.11375			−0.320422			−0.160211	−	0.987083i	$-0.551218\pi$
$809$	−9.11375			−0.320422			−0.160211	+	0.987083i	$0.551218\pi$
$810$		0			0
$811$			2.31899i			0.0814309i	0.999171	+	0.0407154i	$0.0129637\pi$
$811$			2.31899i			0.0814309i	−0.999171	+	0.0407154i	$0.987036\pi$
$812$	−34.3280	+	13.4820i	−1.20468	+	0.473125i
$813$		0			0
$814$	−3.35595	−	1.93756i	−0.117626	−	0.0679114i
$815$	6.42325	−	11.1254i	0.224997	−	0.389706i
$816$		0			0
$817$	−1.30718	+	0.754702i	−0.0457325	+	0.0264037i
$818$	1.13352			0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$	−8.78557	+	5.07235i	−0.306619	+	0.177026i	−0.645412	−	0.763834i	$-0.723314\pi$
$821$	−8.78557	+	5.07235i	−0.306619	+	0.177026i	0.338794	+	0.940861i	$0.389981\pi$
$822$		0			0
$823$	−13.4089	+	23.2249i	−0.467405	+	0.809570i	−0.999306	−	0.0372366i	$-0.988144\pi$
$823$	−13.4089	+	23.2249i	−0.467405	+	0.809570i	0.531901	+	0.846806i	$0.321478\pi$
$824$	3.20414	+	1.84991i	0.111622	+	0.0644448i
$825$		0			0
$826$	−0.540278	+	3.59021i	−0.0187987	+	0.124919i
$827$			33.6015i			1.16844i	0.811596	+	0.584219i	$0.198599\pi$
$827$			33.6015i			1.16844i	−0.811596	+	0.584219i	$0.801401\pi$
$828$		0			0
$829$	−11.8666			−0.412142			−0.206071	−	0.978537i	$-0.566068\pi$
$829$	−11.8666			−0.412142			−0.206071	+	0.978537i	$0.566068\pi$
$830$		−	8.05791i		−	0.279694i
$831$		0			0
$832$	13.8848	−	22.0452i	0.481370	−	0.764281i
$833$	24.4400	−	22.6983i	0.846796	−	0.786448i
$834$		0			0
$835$	−3.64096	−	6.30633i	−0.126001	−	0.218240i
$836$	0.499362	−	0.864920i	0.0172708	−	0.0299139i
$837$		0			0
$838$		−	6.17756i		−	0.213400i
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.116600	−	0.993179i	$-0.462801\pi$
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.918418	+	0.395611i	$0.129467\pi$
$840$		0			0
$841$	−10.6029	−	18.3648i	−0.365617	−	0.633267i
$842$	−1.04185	−	1.80453i	−0.0359044	−	0.0621882i
$843$		0			0
$844$	17.3051	+	29.9733i	0.595666	+	1.03172i
$845$	−2.68450	+	34.8230i	−0.0923494	+	1.19795i
$846$		0			0
$847$	−1.47292	+	9.78770i	−0.0506101	+	0.336309i
$848$	−13.4549	+	23.3046i	−0.462044	+	0.800283i
$849$		0			0
$850$	−1.65506	+	0.955548i	−0.0567680	+	0.0327750i
$851$	−30.3044	−	17.4963i	−1.03882	−	0.599764i
$852$		0			0
$853$			29.1897i			0.999436i	0.866188	+	0.499718i	$0.166563\pi$
$853$			29.1897i			0.999436i	−0.866188	+	0.499718i	$0.833437\pi$
$854$	−0.0719778	−	0.183271i	−0.00246303	−	0.00627139i
$855$		0			0
$856$	−4.99061	+	2.88133i	−0.170575	+	0.0984817i
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	0.997084	−	0.0763112i	$-0.0243142\pi$
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	−0.564629	+	0.825345i	$0.690981\pi$
$858$		0			0
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	−0.998052	−	0.0623818i	$-0.980130\pi$
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	0.553050	+	0.833148i	$0.313464\pi$
$860$	−36.6674	−	21.1699i	−1.25035	−	0.721888i
$861$		0			0
$862$	0.792913	+	1.37337i	0.0270067	+	0.0467770i
$863$	31.2061	+	18.0169i	1.06227	+	0.613302i	0.926059	−	0.377378i	$-0.123174\pi$
$863$	31.2061	+	18.0169i	1.06227	+	0.613302i	0.136210	+	0.990680i	$0.456508\pi$
$864$		0			0
$865$	2.09360	+	1.20874i	0.0711846	+	0.0410985i
$866$	3.46190	+	1.99873i	0.117640	+	0.0679196i
$867$		0			0
$868$	−19.0405	−	2.86534i	−0.646276	−	0.0972559i
$869$	21.2576	+	12.2731i	0.721114	+	0.416335i
$870$		0			0
$871$	−34.7829	−	21.9074i	−1.17857	−	0.742305i
$872$	−0.478337	−	0.828504i	−0.0161985	−	0.0280567i
$873$		0			0
$874$	−0.0749454	+	0.129809i	−0.00253507	+	0.00439086i
$875$	−19.5545	−	2.94269i	−0.661062	−	0.0994811i
$876$		0			0
$877$		−	9.12168i		−	0.308017i	−0.988070	−	0.154009i	$-0.950782\pi$
$877$		−	9.12168i		−	0.308017i	0.988070	−	0.154009i	$-0.0492184\pi$
$878$	−1.62407	−	0.937657i	−0.0548097	−	0.0316444i
$879$		0			0
$880$	27.5415			0.928425
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	−0.954670	−	0.297667i	$-0.903791\pi$
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	0.735122	+	0.677935i	$0.237125\pi$
$882$		0			0
$883$	−2.13222			−0.0717548			−0.0358774	−	0.999356i	$-0.511423\pi$
$883$	−2.13222			−0.0717548			−0.0358774	+	0.999356i	$0.511423\pi$
$884$	−33.7737	−	1.29987i	−1.13593	−	0.0437194i
$885$		0			0
$886$		−	6.47597i		−	0.217564i
$887$	−23.5857	−	40.8517i	−0.791932	−	1.37167i	−0.924769	−	0.380528i	$-0.875742\pi$
$887$	−23.5857	−	40.8517i	−0.791932	−	1.37167i	0.132838	−	0.991138i	$-0.457591\pi$
$888$		0			0
$889$	−16.4835	−	13.1389i	−0.552839	−	0.440663i
$890$	−2.47875	+	1.43111i	−0.0830878	+	0.0479708i
$891$		0			0
$892$	−24.0319	+	13.8748i	−0.804647	+	0.464563i
$893$	−0.174188	+	0.301702i	−0.00582898	+	0.0100961i
$894$		0			0
$895$	25.7236	+	14.8515i	0.859844	+	0.496431i
$896$	5.36994	+	13.6730i	0.179397	+	0.456782i
$897$		0			0
$898$	2.05689	−	3.56264i	0.0686394	−	0.118887i
$899$		−	26.2118i		−	0.874213i
$900$		0			0
$901$	33.6997			1.12270
$902$			2.64520i			0.0880755i
$903$		0			0
$904$	12.3871	−	7.15171i	0.411990	−	0.237862i
$905$	8.21087	+	4.74055i	0.272939	+	0.157581i
$906$		0			0
$907$	−16.0431			−0.532702			−0.266351	−	0.963876i	$-0.585818\pi$
$907$	−16.0431			−0.532702			−0.266351	+	0.963876i	$0.585818\pi$
$908$	4.88763	−	2.82187i	0.162202	−	0.0936471i
$909$		0			0
$910$	−3.51016	−	3.02584i	−0.116361	−	0.100306i
$911$	24.4319			0.809466			0.404733	−	0.914435i	$-0.367364\pi$
$911$	24.4319			0.809466			0.404733	+	0.914435i	$0.367364\pi$
$912$		0			0
$913$	44.6883			1.47897
$914$	−2.83144	+	4.90420i	−0.0936558	+	0.162217i
$915$		0			0
$916$	14.9488	−	8.63067i	0.493921	−	0.285165i
$917$	20.7263	+	16.5207i	0.684442	+	0.545563i
$918$		0			0
$919$	15.9160			0.525020			0.262510	−	0.964929i	$-0.415450\pi$
$919$	15.9160			0.525020			0.262510	+	0.964929i	$0.415450\pi$
$920$	−8.47897			−0.279543
$921$		0			0
$922$	0.760140	−	1.31660i	0.0250339	−	0.0433600i
$923$	−0.463824	+	12.0512i	−0.0152670	+	0.396671i
$924$		0			0
$925$	15.2790	+	8.82131i	0.502369	+	0.290043i
$926$	0.907665	+	1.57212i	0.0298277	+	0.0516632i
$927$		0			0
$928$	−13.0260	+	7.52059i	−0.427601	+	0.246875i
$929$		−	47.3235i		−	1.55263i	−0.630342	−	0.776317i	$-0.717086\pi$
$929$		−	47.3235i		−	1.55263i	0.630342	−	0.776317i	$-0.282914\pi$
$930$		0			0
$931$	−0.388184	+	1.26055i	−0.0127222	+	0.0413130i
$932$	−5.02393	−	8.70170i	−0.164564	−	0.285034i
$933$		0			0
$934$		−	4.76494i		−	0.155914i
$935$	−17.2454	−	29.8699i	−0.563985	−	0.976850i
$936$		0			0
$937$	−29.7044			−0.970401			−0.485200	−	0.874403i	$-0.661253\pi$
$937$	−29.7044			−0.970401			−0.485200	+	0.874403i	$0.661253\pi$
$938$	5.07691	−	1.99391i	0.165767	−	0.0651035i
$939$		0			0
$940$	−9.77219			−0.318734
$941$	35.0068	−	20.2112i	1.14119	−	0.658866i	0.194465	−	0.980909i	$-0.437703\pi$
$941$	35.0068	−	20.2112i	1.14119	−	0.658866i	0.946725	+	0.322043i	$0.104370\pi$
$942$		0			0
$943$			23.8863i			0.777844i
$944$		−	28.8748i		−	0.939795i
$945$		0			0
$946$	−1.95133	+	3.37980i	−0.0634431	+	0.109887i
$947$	−39.7703	+	22.9614i	−1.29236	+	0.746146i	−0.979072	−	0.203512i	$-0.934764\pi$
$947$	−39.7703	+	22.9614i	−1.29236	+	0.746146i	−0.313290	+	0.949658i	$0.601431\pi$
$948$		0			0
$949$	−1.97126	+	51.2179i	−0.0639898	+	1.66260i
$950$	0.0377862	−	0.0654476i	0.00122595	−	0.00212340i
$951$		0			0
$952$	5.63714	−	7.07214i	0.182701	−	0.229209i
$953$	−6.19465	−	10.7294i	−0.200664	−	0.347561i	0.748078	−	0.663610i	$-0.230977\pi$
$953$	−6.19465	−	10.7294i	−0.200664	−	0.347561i	−0.948743	+	0.316050i	$0.897643\pi$
$954$		0			0
$955$	−47.4655	−	27.4042i	−1.53595	−	0.886780i
$956$	−4.25587	−	2.45713i	−0.137645	−	0.0794693i
$957$		0			0
$958$	0.776108	+	1.34426i	0.0250749	+	0.0434310i
$959$	8.35600	−	10.4831i	0.269829	−	0.338517i
$960$		0			0
$961$	−8.65757	+	14.9953i	−0.279276	+	0.483721i
$962$	−2.41828	−	4.58748i	−0.0779686	−	0.147906i
$963$		0			0
$964$	−13.6045	+	7.85457i	−0.438172	+	0.252979i
$965$	−23.1918	+	40.1694i	−0.746572	+	1.29310i
$966$		0			0
$967$		−	9.44932i		−	0.303870i	−0.988391	−	0.151935i	$-0.951450\pi$
$967$		−	9.44932i		−	0.303870i	0.988391	−	0.151935i	$-0.0485504\pi$
$968$			2.68377i			0.0862596i
$969$		0			0
$970$	−0.189785	+	0.109573i	−0.00609364	+	0.00351816i
$971$	20.9763			0.673163			0.336581	−	0.941654i	$-0.390729\pi$
$971$	20.9763			0.673163			0.336581	+	0.941654i	$0.390729\pi$
$972$		0			0
$973$	19.0258	−	7.47220i	0.609939	−	0.239548i
$974$	3.84363			0.123158
$975$		0			0
$976$	0.782977	+	1.35616i	0.0250625	+	0.0434095i
$977$			13.1843i			0.421802i	0.977507	+	0.210901i	$0.0676398\pi$
$977$			13.1843i			0.421802i	−0.977507	+	0.210901i	$0.932360\pi$
$978$		0			0
$979$	−7.93676	−	13.7469i	−0.253660	−	0.439352i
$980$	−36.0666	+	8.24971i	−1.15211	+	0.263527i
$981$		0			0
$982$		−	4.06013i		−	0.129564i
$983$	−20.2294	+	11.6794i	−0.645216	+	0.372516i	−0.786621	−	0.617436i	$-0.788171\pi$
$983$	−20.2294	+	11.6794i	−0.645216	+	0.372516i	0.141405	+	0.989952i	$0.454838\pi$
$984$		0			0
$985$	−6.65846	−	11.5328i	−0.212156	−	0.367465i
$986$	5.28713	+	3.05252i	0.168376	+	0.0972122i
$987$		0			0
$988$	1.18232	−	0.623257i	0.0376145	−	0.0198285i
$989$	−17.6206	+	30.5197i	−0.560302	+	0.970471i
$990$		0			0
$991$	39.4929			1.25453			0.627267	−	0.778804i	$-0.284173\pi$
$991$	39.4929			1.25453			0.627267	+	0.778804i	$0.284173\pi$
$992$	−7.85281			−0.249327
$993$		0			0
$994$	−1.25135	−	0.997441i	−0.0396905	−	0.0316369i
$995$	−16.7102	+	9.64766i	−0.529750	+	0.305851i
$996$		0			0
$997$	25.7396	−	44.5822i	0.815180	−	1.41193i	−0.0940184	−	0.995570i	$-0.529971\pi$
$997$	25.7396	−	44.5822i	0.815180	−	1.41193i	0.909199	−	0.416363i	$-0.136695\pi$
$998$	7.03007			0.222533
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.667.4		12
3.2	odd	2		91.2.u.b.30.3	yes	12
7.4	even	3		819.2.bm.f.550.4		12
13.10	even	6		819.2.bm.f.478.3		12
21.2	odd	6		637.2.q.g.589.4		12
21.5	even	6		637.2.q.i.589.4		12
21.11	odd	6		91.2.k.b.4.3	✓	12
21.17	even	6		637.2.k.i.459.3		12
21.20	even	2		637.2.u.g.30.3		12
39.20	even	12		1183.2.e.j.170.6		24
39.23	odd	6		91.2.k.b.23.4	yes	12
39.32	even	12		1183.2.e.j.170.7		24
91.88	even	6	inner	819.2.do.e.361.4		12
273.23	odd	6		637.2.q.g.491.4		12
273.32	even	12		1183.2.e.j.508.7		24
273.62	even	6		637.2.k.i.569.4		12
273.101	even	6		637.2.u.g.361.3		12
273.110	odd	12		8281.2.a.co.1.6		12
273.137	even	12		1183.2.e.j.508.6		24
273.149	even	12		8281.2.a.cp.1.6		12
273.179	odd	6		91.2.u.b.88.3	yes	12
273.215	odd	12		8281.2.a.co.1.7		12
273.254	even	12		8281.2.a.cp.1.7		12
273.257	even	6		637.2.q.i.491.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	21.11	odd	6
91.2.k.b.23.4	yes	12	39.23	odd	6
91.2.u.b.30.3	yes	12	3.2	odd	2
91.2.u.b.88.3	yes	12	273.179	odd	6
637.2.k.i.459.3		12	21.17	even	6
637.2.k.i.569.4		12	273.62	even	6
637.2.q.g.491.4		12	273.23	odd	6
637.2.q.g.589.4		12	21.2	odd	6
637.2.q.i.491.4		12	273.257	even	6
637.2.q.i.589.4		12	21.5	even	6
637.2.u.g.30.3		12	21.20	even	2
637.2.u.g.361.3		12	273.101	even	6
819.2.bm.f.478.3		12	13.10	even	6
819.2.bm.f.550.4		12	7.4	even	3
819.2.do.e.361.4		12	91.88	even	6	inner
819.2.do.e.667.4		12	1.1	even	1	trivial
1183.2.e.j.170.6		24	39.20	even	12
1183.2.e.j.170.7		24	39.32	even	12
1183.2.e.j.508.6		24	273.137	even	12
1183.2.e.j.508.7		24	273.32	even	12
8281.2.a.co.1.6		12	273.110	odd	12
8281.2.a.co.1.7		12	273.215	odd	12
8281.2.a.cp.1.6		12	273.149	even	12
8281.2.a.cp.1.7		12	273.254	even	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.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} +O(q^{10})\)	\(q+(0.156598 - 0.0904119i) q^{2} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.393717 + 2.61629i) q^{7} +0.717383i q^{8} -0.485809 q^{10} -2.69424i q^{11} +(1.92153 - 3.05086i) q^{13} +(0.174889 + 0.445303i) q^{14} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} -0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(-2.19964 - 3.80989i) q^{23} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} +(-4.07019 - 3.24431i) q^{28} +(3.54280 - 6.13631i) q^{29} +(3.20369 - 1.84965i) q^{31} +(-1.83838 - 1.06139i) q^{32} +0.861613i q^{34} +(4.43058 - 5.55844i) q^{35} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(0.963675 - 1.66913i) q^{40} +(-4.70215 - 2.71479i) q^{41} +(-4.00533 - 6.93743i) q^{43} +(4.59027 + 2.65020i) q^{44} +(-0.688919 - 0.397748i) q^{46} +(-1.60118 - 0.924445i) q^{47} +(-6.68997 - 2.06016i) q^{49} +(0.347341 + 0.200538i) q^{50} +(3.30773 + 6.27476i) q^{52} +(-3.53622 - 6.12491i) q^{53} +(-3.61923 + 6.26869i) q^{55} +(-1.87688 - 0.282446i) q^{56} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} -0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(-8.56910 + 4.51719i) q^{65} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(0.191271 - 1.27102i) q^{70} +(-2.89675 + 1.67244i) q^{71} +(-12.3112 + 7.10790i) q^{73} +(0.719148 - 1.24560i) q^{74} +(0.321025 + 0.185344i) q^{76} +(7.04893 + 1.06077i) q^{77} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(-1.25445 - 0.724258i) q^{86} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +(7.22539 + 6.22846i) q^{91} +8.65473 q^{92} -0.334323 q^{94} +(-0.253115 + 0.438407i) q^{95} +(0.390659 - 0.225547i) q^{97} +(-1.23390 + 0.282236i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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