LMFDB - Embedded newform 27.7.d.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$1.07323 - 1.85889i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.7.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.21969 - 1.85889i) q^{2} +(-25.0891 + 43.4555i) q^{4} +(-136.563 - 78.8448i) q^{5} +(-256.037 - 443.470i) q^{7} +424.489i q^{8} +O(q^{10})$	\(q+(3.21969 - 1.85889i) q^{2} +(-25.0891 + 43.4555i) q^{4} +(-136.563 - 78.8448i) q^{5} +(-256.037 - 443.470i) q^{7} +424.489i q^{8} -586.255 q^{10} +(-1017.33 + 587.357i) q^{11} +(41.9925 - 72.7331i) q^{13} +(-1648.72 - 951.890i) q^{14} +(-816.622 - 1414.43i) q^{16} +2145.70i q^{17} +1526.08 q^{19} +(6852.48 - 3956.28i) q^{20} +(-2183.66 + 3782.22i) q^{22} +(715.392 + 413.032i) q^{23} +(4620.50 + 8002.94i) q^{25} -312.238i q^{26} +25695.0 q^{28} +(28915.7 - 16694.5i) q^{29} +(214.119 - 370.866i) q^{31} +(-28786.1 - 16619.7i) q^{32} +(3988.63 + 6908.50i) q^{34} +80748.9i q^{35} -88462.1 q^{37} +(4913.51 - 2836.81i) q^{38} +(33468.7 - 57969.6i) q^{40} +(-54327.1 - 31365.8i) q^{41} +(-27127.8 - 46986.7i) q^{43} -58945.0i q^{44} +3071.12 q^{46} +(-96604.4 + 55774.5i) q^{47} +(-72285.8 + 125203. i) q^{49} +(29753.2 + 17178.0i) q^{50} +(2107.10 + 3649.61i) q^{52} +40319.2i q^{53} +185240. q^{55} +(188248. - 108685. i) q^{56} +(62066.4 - 107502. i) q^{58} +(155365. + 89700.2i) q^{59} +(38796.6 + 67197.7i) q^{61} -1592.10i q^{62} -19048.9 q^{64} +(-11469.3 + 6621.78i) q^{65} +(-50705.9 + 87825.2i) q^{67} +(-93242.7 - 53833.7i) q^{68} +(150103. + 259986. i) q^{70} -600639. i q^{71} -29830.7 q^{73} +(-284820. + 164441. i) q^{74} +(-38287.9 + 66316.6i) q^{76} +(520950. + 300771. i) q^{77} +(-334535. - 579432. i) q^{79} +257545. i q^{80} -233222. q^{82} +(-776966. + 448581. i) q^{83} +(169178. - 293024. i) q^{85} +(-174686. - 100855. i) q^{86} +(-249327. - 431847. i) q^{88} -185663. i q^{89} -43006.6 q^{91} +(-35897.0 + 20725.2i) q^{92} +(-207357. + 359154. i) q^{94} +(-208406. - 120323. i) q^{95} +(679711. + 1.17729e6i) q^{97} +537485. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.21969	−	1.85889i	0.402461	−	0.232361i	−0.285084	−	0.958503i	$-0.592022\pi$
$2$	3.21969	−	1.85889i	0.402461	−	0.232361i	0.687545	+	0.726141i	$0.258688\pi$
$3$		0			0
$3$		0			0
$4$	−25.0891	+	43.4555i	−0.392017	+	0.678993i
$5$	−136.563	−	78.8448i	−1.09251	−	0.630758i	−0.158263	−	0.987397i	$-0.550589\pi$
$5$	−136.563	−	78.8448i	−1.09251	−	0.630758i	−0.934242	+	0.356639i	$0.883923\pi$
$6$		0			0
$7$	−256.037	−	443.470i	−0.746465	−	1.29291i	−0.949507	−	0.313745i	$-0.898416\pi$
$7$	−256.037	−	443.470i	−0.746465	−	1.29291i	0.203043	−	0.979170i	$-0.434917\pi$
$8$			424.489i			0.829080i
$9$		0			0
$10$	−586.255			−0.586255
$11$	−1017.33	+	587.357i	−0.764337	+	0.441290i	−0.830851	−	0.556495i	$-0.812146\pi$
$11$	−1017.33	+	587.357i	−0.764337	+	0.441290i	0.0665136	+	0.997786i	$0.478812\pi$
$12$		0			0
$13$	41.9925	−	72.7331i	0.0191136	−	0.0331056i	−0.856310	−	0.516461i	$-0.827249\pi$
$13$	41.9925	−	72.7331i	0.0191136	−	0.0331056i	0.875424	+	0.483356i	$0.160582\pi$
$14$	−1648.72	−	951.890i	−0.600846	−	0.346899i
$15$		0			0
$16$	−816.622	−	1414.43i	−0.199371	−	0.345320i
$17$			2145.70i			0.436740i	0.975866	+	0.218370i	$0.0700740\pi$
$17$			2145.70i			0.436740i	−0.975866	+	0.218370i	$0.929926\pi$
$18$		0			0
$19$	1526.08			0.222493			0.111247	−	0.993793i	$-0.464516\pi$
$19$	1526.08			0.222493			0.111247	+	0.993793i	$0.464516\pi$
$20$	6852.48	−	3956.28i	0.856560	−	0.494535i
$21$		0			0
$22$	−2183.66	+	3782.22i	−0.205077	+	0.355205i
$23$	715.392	+	413.032i	0.0587977	+	0.0339469i	0.529111	−	0.848553i	$-0.322526\pi$
$23$	715.392	+	413.032i	0.0587977	+	0.0339469i	−0.470313	+	0.882500i	$0.655859\pi$
$24$		0			0
$25$	4620.50	+	8002.94i	0.295712	+	0.512188i
$26$		−	312.238i		−	0.0177650i
$27$		0			0
$28$	25695.0			1.17051
$29$	28915.7	−	16694.5i	1.18560	−	0.684509i	0.228299	−	0.973591i	$-0.426683\pi$
$29$	28915.7	−	16694.5i	1.18560	−	0.684509i	0.957304	+	0.289082i	$0.0933502\pi$
$30$		0			0
$31$	214.119	−	370.866i	0.00718738	−	0.0124489i	−0.862409	−	0.506212i	$-0.831045\pi$
$31$	214.119	−	370.866i	0.00718738	−	0.0124489i	0.869597	+	0.493763i	$0.164379\pi$
$32$	−28786.1	−	16619.7i	−0.878482	−	0.507192i
$33$		0			0
$34$	3988.63	+	6908.50i	0.101481	+	0.175771i
$35$			80748.9i			1.88336i
$36$		0			0
$37$	−88462.1			−1.74643			−0.873216	−	0.487333i	$-0.837970\pi$
$37$	−88462.1			−1.74643			−0.873216	+	0.487333i	$0.837970\pi$
$38$	4913.51	−	2836.81i	0.0895449	−	0.0516988i
$39$		0			0
$40$	33468.7	−	57969.6i	0.522949	−	0.905774i
$41$	−54327.1	−	31365.8i	−0.788252	−	0.455097i	0.0510949	−	0.998694i	$-0.483729\pi$
$41$	−54327.1	−	31365.8i	−0.788252	−	0.455097i	−0.839347	+	0.543596i	$0.817062\pi$
$42$		0			0
$43$	−27127.8	−	46986.7i	−0.341200	−	0.590976i	0.643456	−	0.765483i	$-0.277500\pi$
$43$	−27127.8	−	46986.7i	−0.341200	−	0.590976i	−0.984656	+	0.174507i	$0.944167\pi$
$44$		−	58945.0i		−	0.691972i
$45$		0			0
$46$	3071.12			0.0315517
$47$	−96604.4	+	55774.5i	−0.930472	+	0.537208i	−0.886961	−	0.461845i	$-0.847188\pi$
$47$	−96604.4	+	55774.5i	−0.930472	+	0.537208i	−0.0435109	+	0.999053i	$0.513854\pi$
$48$		0			0
$49$	−72285.8	+	125203.i	−0.614419	+	1.06421i
$50$	29753.2	+	17178.0i	0.238025	+	0.137424i
$51$		0			0
$52$	2107.10	+	3649.61i	0.0149857	+	0.0259559i
$53$			40319.2i			0.270822i	0.990790	+	0.135411i	$0.0432355\pi$
$53$			40319.2i			0.270822i	−0.990790	+	0.135411i	$0.956765\pi$
$54$		0			0
$55$	185240.			1.11339
$56$	188248.	−	108685.i	1.07193	−	0.618879i
$57$		0			0
$58$	62066.4	−	107502.i	0.318106	−	0.550977i
$59$	155365.	+	89700.2i	0.756481	+	0.436754i	0.828031	−	0.560683i	$-0.189461\pi$
$59$	155365.	+	89700.2i	0.756481	+	0.436754i	−0.0715501	+	0.997437i	$0.522795\pi$
$60$		0			0
$61$	38796.6	+	67197.7i	0.170924	+	0.296050i	0.938743	−	0.344617i	$-0.111991\pi$
$61$	38796.6	+	67197.7i	0.170924	+	0.296050i	−0.767819	+	0.640667i	$0.778658\pi$
$62$		−	1592.10i		−	0.00668028i
$63$		0			0
$64$	−19048.9			−0.0726658
$65$	−11469.3	+	6621.78i	−0.0417633	+	0.0241121i
$66$		0			0
$67$	−50705.9	+	87825.2i	−0.168591	+	0.292008i	−0.937925	−	0.346839i	$-0.887255\pi$
$67$	−50705.9	+	87825.2i	−0.168591	+	0.292008i	0.769334	+	0.638847i	$0.220588\pi$
$68$	−93242.7	−	53833.7i	−0.296543	−	0.171209i
$69$		0			0
$70$	150103.	+	259986.i	0.437619	+	0.757978i
$71$		−	600639.i		−	1.67818i	−0.543993	−	0.839090i	$-0.683088\pi$
$71$		−	600639.i		−	1.67818i	0.543993	−	0.839090i	$-0.316912\pi$
$72$		0			0
$73$	−29830.7			−0.0766824			−0.0383412	−	0.999265i	$-0.512207\pi$
$73$	−29830.7			−0.0766824			−0.0383412	+	0.999265i	$0.512207\pi$
$74$	−284820.	+	164441.i	−0.702872	+	0.405803i
$75$		0			0
$76$	−38287.9	+	66316.6i	−0.0872210	+	0.151071i
$77$	520950.	+	300771.i	1.14110	+	0.658815i
$78$		0			0
$79$	−334535.	−	579432.i	−0.678516	−	1.17522i	−0.975428	−	0.220320i	$-0.929290\pi$
$79$	−334535.	−	579432.i	−0.678516	−	1.17522i	0.296911	−	0.954905i	$-0.404043\pi$
$80$			257545.i			0.503018i
$81$		0			0
$82$	−233222.			−0.422988
$83$	−776966.	+	448581.i	−1.35884	+	0.784526i	−0.989467	−	0.144757i	$-0.953760\pi$
$83$	−776966.	+	448581.i	−1.35884	+	0.784526i	−0.369371	+	0.929282i	$0.620427\pi$
$84$		0			0
$85$	169178.	−	293024.i	0.275477	−	0.477141i
$86$	−174686.	−	100855.i	−0.274640	−	0.158563i
$87$		0			0
$88$	−249327.	−	431847.i	−0.365865	−	0.633697i
$89$		−	185663.i		−	0.263364i	−0.991292	−	0.131682i	$-0.957962\pi$
$89$		−	185663.i		−	0.263364i	0.991292	−	0.131682i	$-0.0420377\pi$
$90$		0			0
$91$	−43006.6			−0.0570704
$92$	−35897.0	+	20725.2i	−0.0460994	+	0.0266155i
$93$		0			0
$94$	−207357.	+	359154.i	−0.249653	+	0.432411i
$95$	−208406.	−	120323.i	−0.243075	−	0.140339i
$96$		0			0
$97$	679711.	+	1.17729e6i	0.744748	+	1.28994i	0.950313	+	0.311297i	$0.100764\pi$
$97$	679711.	+	1.17729e6i	0.744748	+	1.28994i	−0.205565	+	0.978643i	$0.565903\pi$
$98$			537485.i			0.571069i
$99$		0			0
$100$	−463696.			−0.463696
$101$	945060.	−	545630.i	0.917265	−	0.529583i	0.0345038	−	0.999405i	$-0.489015\pi$
$101$	945060.	−	545630.i	0.917265	−	0.529583i	0.882762	+	0.469821i	$0.155682\pi$
$102$		0			0
$103$	519286.	−	899429.i	0.475220	−	0.823105i	−0.524377	−	0.851486i	$-0.675702\pi$
$103$	519286.	−	899429.i	0.475220	−	0.823105i	0.999597	+	0.0283810i	$0.00903516\pi$
$104$	30874.4	+	17825.3i	0.0274472	+	0.0158467i
$105$		0			0
$106$	74948.9	+	129815.i	0.0629285	+	0.108995i
$107$		−	1.11601e6i		−	0.910999i	−0.890236	−	0.455500i	$-0.849461\pi$
$107$		−	1.11601e6i		−	0.910999i	0.890236	−	0.455500i	$-0.150539\pi$
$108$		0			0
$109$	614582.			0.474570			0.237285	−	0.971440i	$-0.423743\pi$
$109$	614582.			0.474570			0.237285	+	0.971440i	$0.423743\pi$
$110$	596416.	−	344341.i	0.448096	−	0.258709i
$111$		0			0
$112$	−418171.	+	724294.i	−0.297646	+	0.515538i
$113$	−294828.	−	170219.i	−0.204331	−	0.117970i	0.394343	−	0.918963i	$-0.370972\pi$
$113$	−294828.	−	170219.i	−0.204331	−	0.117970i	−0.598674	+	0.800993i	$0.704305\pi$
$114$		0			0
$115$	−65130.8	−	112810.i	−0.0428245	−	0.0741743i
$116$			1.67540e6i			1.07335i
$117$		0			0
$118$	666971.			0.405939
$119$	951555.	−	549381.i	0.564668	−	0.326011i
$120$		0			0
$121$	−195803.	+	339141.i	−0.110526	+	0.191436i
$122$	249826.	+	144237.i	0.137581	+	0.0794324i
$123$		0			0
$124$	10744.1	+	18609.3i	0.00563515	+	0.00976036i
$125$			1.00669e6i			0.515425i
$126$		0			0
$127$	1.65204e6			0.806508			0.403254	−	0.915088i	$-0.367879\pi$
$127$	1.65204e6			0.806508			0.403254	+	0.915088i	$0.367879\pi$
$128$	1.78098e6	−	1.02825e6i	0.849237	−	0.490307i
$129$		0			0
$130$	−24618.3	+	42640.1i	−0.0112054	+	0.0194084i
$131$	−1.37330e6	−	792874.i	−0.610873	−	0.352688i	0.162434	−	0.986719i	$-0.448066\pi$
$131$	−1.37330e6	−	792874.i	−0.610873	−	0.352688i	−0.773307	+	0.634032i	$0.781399\pi$
$132$		0			0
$133$	−390734.	−	676771.i	−0.166083	−	0.287665i
$134$			377027.i			0.156696i
$135$		0			0
$136$	−910828.			−0.362093
$137$	−3.63165e6	+	2.09673e6i	−1.41235	+	0.815420i	−0.995609	−	0.0936061i	$-0.970161\pi$
$137$	−3.63165e6	+	2.09673e6i	−1.41235	+	0.815420i	−0.416739	+	0.909026i	$0.636827\pi$
$138$		0			0
$139$	−968640.	+	1.67773e6i	−0.360676	+	0.624710i	−0.988072	−	0.153990i	$-0.950787\pi$
$139$	−968640.	+	1.67773e6i	−0.360676	+	0.624710i	0.627396	+	0.778700i	$0.284121\pi$
$140$	−3.50898e6	−	2.02591e6i	−1.27878	−	0.738306i
$141$		0			0
$142$	−1.11652e6	−	1.93387e6i	−0.389944	−	0.675402i
$143$			98658.4i			0.0337385i
$144$		0			0
$145$	−5.26509e6			−1.72704
$146$	−96045.8	+	55452.0i	−0.0308617	+	0.0178180i
$147$		0			0
$148$	2.21943e6	−	3.84417e6i	0.684631	−	1.18581i
$149$	4.47398e6	+	2.58305e6i	1.35249	+	0.780862i	0.988598	−	0.150578i	$-0.0481135\pi$
$149$	4.47398e6	+	2.58305e6i	1.35249	+	0.780862i	0.363895	+	0.931440i	$0.381447\pi$
$150$		0			0
$151$	−1.07109e6	−	1.85518e6i	−0.311097	−	0.538835i	0.667503	−	0.744607i	$-0.267363\pi$
$151$	−1.07109e6	−	1.85518e6i	−0.311097	−	0.538835i	−0.978600	+	0.205772i	$0.934030\pi$
$152$			647804.i			0.184465i
$153$		0			0
$154$	2.23640e6			0.612332
$155$	−58481.6	+	33764.4i	−0.0157045	+	0.00906700i
$156$		0			0
$157$	−283047.	+	490251.i	−0.0731407	+	0.126683i	−0.900276	−	0.435319i	$-0.856636\pi$
$157$	−283047.	+	490251.i	−0.0731407	+	0.126683i	0.827136	+	0.562003i	$0.189969\pi$
$158$	−2.15420e6	−	1.24373e6i	−0.546153	−	0.315322i
$159$		0			0
$160$	2.62075e6	+	4.53927e6i	0.639831	+	1.10822i
$161$		−	423006.i		−	0.101361i
$162$		0			0
$163$	−479915.			−0.110816			−0.0554079	−	0.998464i	$-0.517646\pi$
$163$	−479915.			−0.110816			−0.0554079	+	0.998464i	$0.517646\pi$
$164$	2.72603e6	−	1.57388e6i	0.618016	−	0.356811i
$165$		0			0
$166$	−1.66773e6	+	2.88859e6i	−0.364587	+	0.631482i
$167$	49570.2	+	28619.4i	0.0106432	+	0.00614484i	0.505312	−	0.862937i	$-0.331377\pi$
$167$	49570.2	+	28619.4i	0.0106432	+	0.00614484i	−0.494669	+	0.869081i	$0.664711\pi$
$168$		0			0
$169$	2.40988e6	+	4.17403e6i	0.499269	+	0.864760i
$170$		−	1.25793e6i		−	0.256041i
$171$		0			0
$172$	2.72245e6			0.535025
$173$	238139.	−	137490.i	0.0459931	−	0.0265542i	−0.476827	−	0.878997i	$-0.658213\pi$
$173$	238139.	−	137490.i	0.0459931	−	0.0265542i	0.522820	+	0.852443i	$0.324880\pi$
$174$		0			0
$175$	2.36604e6	−	4.09810e6i	0.441477	−	0.764661i
$176$	1.66155e6	+	959298.i	0.304773	+	0.175961i
$177$		0			0
$178$	−345127.	−	597778.i	−0.0611955	−	0.105994i
$179$		−	4.58297e6i		−	0.799075i	−0.916717	−	0.399537i	$-0.869171\pi$
$179$		−	4.58297e6i		−	0.799075i	0.916717	−	0.399537i	$-0.130829\pi$
$180$		0			0
$181$	6.06092e6			1.02212			0.511061	−	0.859544i	$-0.329253\pi$
$181$	6.06092e6			1.02212			0.511061	+	0.859544i	$0.329253\pi$
$182$	−138468.	+	79944.5i	−0.0229686	+	0.0132609i
$183$		0			0
$184$	−175327.	+	303676.i	−0.0281447	+	0.0487480i
$185$	1.20807e7	+	6.97477e6i	1.90799	+	1.10158i
$186$		0			0
$187$	−1.26030e6	−	2.18290e6i	−0.192729	−	0.333817i
$188$		−	5.59732e6i		−	0.842378i
$189$		0			0
$190$	−894672.			−0.130438
$191$	−8.31484e6	+	4.80058e6i	−1.19331	+	0.688959i	−0.959056	−	0.283216i	$-0.908599\pi$
$191$	−8.31484e6	+	4.80058e6i	−1.19331	+	0.688959i	−0.234256	+	0.972175i	$0.575265\pi$
$192$		0			0
$193$	−4.59796e6	+	7.96390e6i	−0.639577	+	1.10778i	0.345948	+	0.938254i	$0.387557\pi$
$193$	−4.59796e6	+	7.96390e6i	−0.639577	+	1.10778i	−0.985526	+	0.169527i	$0.945776\pi$
$194$	4.37692e6	+	2.52702e6i	0.599464	+	0.346101i
$195$		0			0
$196$	−3.62717e6	−	6.28244e6i	−0.481725	−	0.834372i
$197$		−	602725.i		−	0.0788352i	−0.999223	−	0.0394176i	$-0.987450\pi$
$197$		−	602725.i		−	0.0788352i	0.999223	−	0.0394176i	$-0.0125503\pi$
$198$		0			0
$199$	−1.07119e7			−1.35927			−0.679636	−	0.733550i	$-0.737862\pi$
$199$	−1.07119e7			−1.35927			−0.679636	+	0.733550i	$0.737862\pi$
$200$	−3.39716e6	+	1.96135e6i	−0.424645	+	0.245169i
$201$		0			0
$202$	2.02853e6	−	3.51352e6i	0.246109	−	0.426274i
$203$	−1.48070e7	−	8.54882e6i	−1.77002	−	1.02192i
$204$		0			0
$205$	4.94605e6	+	8.56682e6i	0.574113	+	0.994393i
$206$		−	3.86118e6i		−	0.441691i
$207$		0			0
$208$	−137168.			−0.0152427
$209$	−1.55253e6	+	896355.i	−0.170060	+	0.0981841i
$210$		0			0
$211$	6.79448e6	−	1.17684e7i	0.723284	−	1.25276i	−0.236392	−	0.971658i	$-0.575965\pi$
$211$	6.79448e6	−	1.17684e7i	0.723284	−	1.25276i	0.959676	−	0.281107i	$-0.0907016\pi$
$212$	−1.75209e6	−	1.01157e6i	−0.183886	−	0.106167i
$213$		0			0
$214$	−2.07454e6	−	3.59322e6i	−0.211681	−	0.366642i
$215$			8.55555e6i			0.860860i
$216$		0			0
$217$	−219290.			−0.0214605
$218$	1.97876e6	−	1.14244e6i	0.190996	−	0.110272i
$219$		0			0
$220$	−4.64750e6	+	8.04971e6i	−0.436467	+	0.755984i
$221$	156064.	+	90103.4i	0.0144586	+	0.00834766i
$222$		0			0
$223$	−9.11942e6	−	1.57953e7i	−0.822342	−	1.42434i	−0.903934	−	0.427673i	$-0.859334\pi$
$223$	−9.11942e6	−	1.57953e7i	−0.822342	−	1.42434i	0.0815914	−	0.996666i	$-0.474000\pi$
$224$			1.70210e7i			1.51440i
$225$		0			0
$226$	−1.26567e6			−0.109647
$227$	6.46187e6	−	3.73076e6i	0.552434	−	0.318948i	−0.197669	−	0.980269i	$-0.563337\pi$
$227$	6.46187e6	−	3.73076e6i	0.552434	−	0.318948i	0.750103	+	0.661321i	$0.230004\pi$
$228$		0			0
$229$	−5.74845e6	+	9.95660e6i	−0.478679	+	0.829096i	−0.999701	−	0.0244471i	$-0.992217\pi$
$229$	−5.74845e6	+	9.95660e6i	−0.478679	+	0.829096i	0.521022	+	0.853543i	$0.325551\pi$
$230$	−419402.	−	242142.i	−0.0344705	−	0.0199015i
$231$		0			0
$232$	7.08662e6	+	1.22744e7i	0.567512	+	0.982960i
$233$		−	7.52864e6i		−	0.595181i	−0.954694	−	0.297590i	$-0.903817\pi$
$233$		−	7.52864e6i		−	0.595181i	0.954694	−	0.297590i	$-0.0961830\pi$
$234$		0			0
$235$	1.75901e7			1.35539
$236$	−7.79594e6	+	4.50099e6i	−0.593106	+	0.342430i
$237$		0			0
$238$	2.04248e6	−	3.53767e6i	0.151505	−	0.262414i
$239$	2.26772e6	+	1.30927e6i	0.166110	+	0.0959036i	0.580750	−	0.814082i	$-0.302759\pi$
$239$	2.26772e6	+	1.30927e6i	0.166110	+	0.0959036i	−0.414640	+	0.909985i	$0.636093\pi$
$240$		0			0
$241$	−4.71815e6	−	8.17207e6i	−0.337070	−	0.583823i	0.646810	−	0.762651i	$-0.276103\pi$
$241$	−4.71815e6	−	8.17207e6i	−0.337070	−	0.583823i	−0.983880	+	0.178828i	$0.942769\pi$
$242$			1.45591e6i			0.102728i
$243$		0			0
$244$	−3.89348e6			−0.268021
$245$	1.97432e7	−	1.13987e7i	1.34251	−	0.775100i
$246$		0			0
$247$	64083.9	−	110997.i	0.00425263	−	0.00736578i
$248$	157428.	+	90891.3i	0.0103211	+	0.00595892i
$249$		0			0
$250$	1.87133e6	+	3.24123e6i	0.119765	+	0.207439i
$251$		−	1.23436e7i		−	0.780583i	−0.920691	−	0.390291i	$-0.872374\pi$
$251$		−	1.23436e7i		−	0.780583i	0.920691	−	0.390291i	$-0.127626\pi$
$252$		0			0
$253$	−970389.			−0.0599217
$254$	5.31905e6	−	3.07095e6i	0.324588	−	0.187401i
$255$		0			0
$256$	4.43237e6	−	7.67708e6i	0.264190	−	0.457590i
$257$	−9.43973e6	−	5.45003e6i	−0.556109	−	0.321070i	0.195473	−	0.980709i	$-0.437376\pi$
$257$	−9.43973e6	−	5.45003e6i	−0.556109	−	0.321070i	−0.751582	+	0.659639i	$0.770709\pi$
$258$		0			0
$259$	2.26496e7	+	3.92303e7i	1.30365	+	2.25799i
$260$		−	664537.i		−	0.0378093i
$261$		0			0
$262$	−5.89546e6			−0.327804
$263$	1.17922e7	−	6.80823e6i	0.648228	−	0.374255i	−0.139549	−	0.990215i	$-0.544565\pi$
$263$	1.17922e7	−	6.80823e6i	0.648228	−	0.374255i	0.787777	+	0.615961i	$0.211232\pi$
$264$		0			0
$265$	3.17896e6	−	5.50611e6i	0.170823	−	0.295875i
$266$	−2.51608e6	−	1.45266e6i	−0.133684	−	0.0771826i
$267$		0			0
$268$	−2.54433e6	−	4.40691e6i	−0.132181	−	0.228944i
$269$			2.14498e7i			1.10196i	0.834518	+	0.550980i	$0.185746\pi$
$269$			2.14498e7i			1.10196i	−0.834518	+	0.550980i	$0.814254\pi$
$270$		0			0
$271$	9.52824e6			0.478746			0.239373	−	0.970928i	$-0.423058\pi$
$271$	9.52824e6			0.478746			0.239373	+	0.970928i	$0.423058\pi$
$272$	3.03495e6	−	1.75223e6i	0.150815	−	0.0870731i
$273$		0			0
$274$	−7.79519e6	+	1.35017e7i	−0.378944	+	0.656350i
$275$	−9.40117e6	−	5.42777e6i	−0.452047	−	0.260990i
$276$		0			0
$277$	−1.27186e7	−	2.20292e7i	−0.598410	−	1.03648i	−0.993056	−	0.117643i	$-0.962466\pi$
$277$	−1.27186e7	−	2.20292e7i	−0.598410	−	1.03648i	0.394646	−	0.918833i	$-0.370867\pi$
$278$			7.20238e6i			0.335229i
$279$		0			0
$280$	−3.42770e7			−1.56145
$281$	−7.37197e6	+	4.25621e6i	−0.332250	+	0.191824i	−0.656839	−	0.754030i	$-0.728107\pi$
$281$	−7.37197e6	+	4.25621e6i	−0.332250	+	0.191824i	0.324590	+	0.945855i	$0.394774\pi$
$282$		0			0
$283$	1.25889e7	−	2.18047e7i	0.555431	−	0.962035i	−0.442439	−	0.896799i	$-0.645887\pi$
$283$	1.25889e7	−	2.18047e7i	0.555431	−	0.962035i	0.997870	−	0.0652362i	$-0.0207801\pi$
$284$	2.61011e7	+	1.50695e7i	1.13947	+	0.657874i
$285$		0			0
$286$	183395.	+	317649.i	0.00783952	+	0.0135784i
$287$			3.21232e7i			1.35886i
$288$		0			0
$289$	1.95335e7			0.809258
$290$	−1.69520e7	+	9.78722e6i	−0.695066	+	0.401297i
$291$		0			0
$292$	748425.	−	1.29631e6i	0.0300608	−	0.0520667i
$293$	−3.17463e7	−	1.83287e7i	−1.26209	−	0.728668i	−0.288612	−	0.957446i	$-0.593194\pi$
$293$	−3.17463e7	−	1.83287e7i	−1.26209	−	0.728668i	−0.973479	+	0.228778i	$0.926527\pi$
$294$		0			0
$295$	−1.41448e7	−	2.44995e7i	−0.550973	−	0.954313i
$296$		−	3.75512e7i		−	1.44793i
$297$		0			0
$298$	1.92064e7			0.725768
$299$	60082.2	−	34688.4i	0.00224767	−	0.00129769i
$300$		0			0
$301$	−1.38915e7	+	2.40607e7i	−0.509388	+	0.882286i
$302$	−6.89716e6	−	3.98208e6i	−0.250409	−	0.144574i
$303$		0			0
$304$	−1.24623e6	−	2.15853e6i	−0.0443586	−	0.0768313i
$305$		−	1.22356e7i		−	0.431248i
$306$		0			0
$307$	−4.84834e7			−1.67563			−0.837814	−	0.545956i	$-0.816167\pi$
$307$	−4.84834e7			−1.67563			−0.837814	+	0.545956i	$0.816167\pi$
$308$	−2.61403e7	+	1.50921e7i	−0.894661	+	0.516533i
$309$		0			0
$310$	−125529.	+	217422.i	−0.00421364	+	0.00729824i
$311$	8.87684e6	+	5.12505e6i	0.295106	+	0.170379i	0.640242	−	0.768173i	$-0.278834\pi$
$311$	8.87684e6	+	5.12505e6i	0.295106	+	0.170379i	−0.345136	+	0.938553i	$0.612167\pi$
$312$		0			0
$313$	1.30917e6	+	2.26754e6i	0.0426935	+	0.0739474i	0.886583	−	0.462570i	$-0.153073\pi$
$313$	1.30917e6	+	2.26754e6i	0.0426935	+	0.0739474i	−0.843889	+	0.536518i	$0.819739\pi$
$314$			2.10461e6i			0.0679802i
$315$		0			0
$316$	3.35727e7			1.06396
$317$	1.91303e6	−	1.10449e6i	0.0600543	−	0.0346724i	−0.469672	−	0.882841i	$-0.655628\pi$
$317$	1.91303e6	−	1.10449e6i	0.0600543	−	0.0346724i	0.529727	+	0.848168i	$0.322295\pi$
$318$		0			0
$319$	−1.96113e7	+	3.39677e7i	−0.604134	+	1.04639i
$320$	2.60138e6	+	1.50191e6i	0.0793878	+	0.0458346i
$321$		0			0
$322$	−786322.	−	1.36195e6i	−0.0235523	−	0.0407937i
$323$			3.27452e6i			0.0971717i
$324$		0			0
$325$	776105.			0.0226084
$326$	−1.54518e6	+	892109.i	−0.0445991	+	0.0257493i
$327$		0			0
$328$	1.33144e7	−	2.30613e7i	0.377312	−	0.653524i
$329$	4.94687e7	+	2.85607e7i	1.38913	+	0.802014i
$330$		0			0
$331$	1.99612e6	+	3.45739e6i	0.0550432	+	0.0953375i	0.892234	−	0.451573i	$-0.149137\pi$
$331$	1.99612e6	+	3.45739e6i	0.0550432	+	0.0953375i	−0.837191	+	0.546911i	$0.815804\pi$
$332$		−	4.50180e7i		−	1.23019i
$333$		0			0
$334$	212801.			0.00571129
$335$	1.38491e7	−	7.99580e6i	0.368373	−	0.212680i
$336$		0			0
$337$	3.14357e7	−	5.44483e7i	0.821361	−	1.42264i	−0.0833082	−	0.996524i	$-0.526549\pi$
$337$	3.14357e7	−	5.44483e7i	0.821361	−	1.42264i	0.904669	−	0.426115i	$-0.140118\pi$
$338$	1.55181e7	+	8.95939e6i	0.401873	+	0.232022i
$339$		0			0
$340$	8.48901e6	+	1.47034e7i	0.215983	+	0.374094i
$341$			503058.i			0.0126869i
$342$		0			0
$343$	1.37864e7			0.341640
$344$	1.99454e7	−	1.15155e7i	0.489967	−	0.282882i
$345$		0			0
$346$	511157.	−	885350.i	0.0123403	−	0.0213740i
$347$	1.39265e7	+	8.04049e6i	0.333315	+	0.192439i	0.657312	−	0.753619i	$-0.271693\pi$
$347$	1.39265e7	+	8.04049e6i	0.333315	+	0.192439i	−0.323997	+	0.946058i	$0.605027\pi$
$348$		0			0
$349$	2.80328e7	+	4.85542e7i	0.659463	+	1.14222i	0.980755	+	0.195243i	$0.0625495\pi$
$349$	2.80328e7	+	4.85542e7i	0.659463	+	1.14222i	−0.321292	+	0.946980i	$0.604117\pi$
$350$		−	1.75928e7i		−	0.410329i
$351$		0			0
$352$	3.90467e7			0.895276
$353$	−6.34450e7	+	3.66300e7i	−1.44236	+	0.832746i	−0.998007	−	0.0631060i	$-0.979899\pi$
$353$	−6.34450e7	+	3.66300e7i	−1.44236	+	0.832746i	−0.444352	+	0.895852i	$0.646566\pi$
$354$		0			0
$355$	−4.73572e7	+	8.20251e7i	−1.05853	+	1.83342i
$356$	8.06809e6	+	4.65811e6i	0.178822	+	0.103243i
$357$		0			0
$358$	−8.51923e6	−	1.47557e7i	−0.185674	−	0.321597i
$359$		−	1.88510e7i		−	0.407429i	−0.979030	−	0.203714i	$-0.934699\pi$
$359$		−	1.88510e7i		−	0.407429i	0.979030	−	0.203714i	$-0.0653014\pi$
$360$		0			0
$361$	−4.47170e7			−0.950497
$362$	1.95143e7	−	1.12666e7i	0.411365	−	0.237502i
$363$		0			0
$364$	1.07899e6	−	1.86887e6i	0.0223725	−	0.0387504i
$365$	4.07378e6	+	2.35200e6i	0.0837759	+	0.0483680i
$366$		0			0
$367$	1.98982e7	+	3.44647e7i	0.402546	+	0.697230i	0.994032	−	0.109085i	$-0.0347920\pi$
$367$	1.98982e7	+	3.44647e7i	0.402546	+	0.697230i	−0.591486	+	0.806315i	$0.701459\pi$
$368$		−	1.34916e6i		−	0.0270720i
$369$		0			0
$370$	5.18613e7			1.02385
$371$	1.78803e7	−	1.03232e7i	0.350150	−	0.202159i
$372$		0			0
$373$	4.50225e7	−	7.79812e7i	0.867566	−	1.50267i	0.00309003	−	0.999995i	$-0.499016\pi$
$373$	4.50225e7	−	7.79812e7i	0.867566	−	1.50267i	0.864476	−	0.502674i	$-0.167650\pi$
$374$	−8.11552e6	−	4.68550e6i	−0.155132	−	0.0895656i
$375$		0			0
$376$	−2.36757e7	−	4.10075e7i	−0.445388	−	0.771435i
$377$		−	2.80417e6i		−	0.0523336i
$378$		0			0
$379$	−4.91004e7			−0.901920			−0.450960	−	0.892544i	$-0.648918\pi$
$379$	−4.91004e7			−0.901920			−0.450960	+	0.892544i	$0.648918\pi$
$380$	1.04574e7	−	6.03761e6i	0.190579	−	0.110031i
$381$		0			0
$382$	−1.78475e7	+	3.09128e7i	−0.320175	+	0.554559i
$383$	−3.85644e7	−	2.22652e7i	−0.686420	−	0.396305i	0.115849	−	0.993267i	$-0.463041\pi$
$383$	−3.85644e7	−	2.22652e7i	−0.686420	−	0.396305i	−0.802270	+	0.596962i	$0.796374\pi$
$384$		0			0
$385$	−4.74284e7	−	8.21485e7i	−0.831106	−	1.43952i
$386$			3.41884e7i			0.594452i
$387$		0			0
$388$	−6.82133e7			−1.16781
$389$	−4.19123e7	+	2.41981e7i	−0.712021	+	0.411086i	−0.811809	−	0.583923i	$-0.801517\pi$
$389$	−4.19123e7	+	2.41981e7i	−0.712021	+	0.411086i	0.0997877	+	0.995009i	$0.468184\pi$
$390$		0			0
$391$	−886244.	+	1.53502e6i	−0.0148260	+	0.0256793i
$392$	−5.31472e7	−	3.06845e7i	−0.882311	−	0.509403i
$393$		0			0
$394$	−1.12040e6	−	1.94059e6i	−0.0183182	−	0.0317281i
$395$			1.05505e8i			1.71192i
$396$		0			0
$397$	−9.73090e6			−0.155518			−0.0777592	−	0.996972i	$-0.524777\pi$
$397$	−9.73090e6			−0.155518			−0.0777592	+	0.996972i	$0.524777\pi$
$398$	−3.44889e7	+	1.99122e7i	−0.547054	+	0.315842i
$399$		0			0
$400$	7.54640e6	−	1.30708e7i	0.117913	−	0.204231i
$401$	−5.52279e7	−	3.18858e7i	−0.856496	−	0.494498i	0.00634154	−	0.999980i	$-0.497981\pi$
$401$	−5.52279e7	−	3.18858e7i	−0.856496	−	0.494498i	−0.862837	+	0.505482i	$0.831315\pi$
$402$		0			0
$403$	−17982.8	−	31147.1i	−0.000274753	−	0.000475886i
$404$			5.47574e7i			0.830422i
$405$		0			0
$406$	−6.35653e7			−0.949821
$407$	8.99954e7	−	5.19588e7i	1.33486	−	0.770684i
$408$		0			0
$409$	−3.52598e6	+	6.10717e6i	−0.0515359	+	0.0892627i	−0.890643	−	0.454704i	$-0.849745\pi$
$409$	−3.52598e6	+	6.10717e6i	−0.0515359	+	0.0892627i	0.839107	+	0.543967i	$0.183078\pi$
$410$	3.18495e7	+	1.83883e7i	0.462117	+	0.266803i
$411$		0			0
$412$	2.60568e7	+	4.51317e7i	0.372588	+	0.645342i
$413$		−	9.18664e7i		−	1.30409i
$414$		0			0
$415$	1.41473e8			1.97938
$416$	−2.41760e6	+	1.39580e6i	−0.0335818	+	0.0193885i
$417$		0			0
$418$	−3.33245e6	+	5.77197e6i	−0.0456283	+	0.0790306i
$419$	7.82055e6	+	4.51519e6i	0.106315	+	0.0613811i	0.552215	−	0.833702i	$-0.313783\pi$
$419$	7.82055e6	+	4.51519e6i	0.106315	+	0.0613811i	−0.445900	+	0.895083i	$0.647116\pi$
$420$		0			0
$421$	1.94239e7	+	3.36432e7i	0.260309	+	0.450869i	0.966324	−	0.257328i	$-0.0828421\pi$
$421$	1.94239e7	+	3.36432e7i	0.260309	+	0.450869i	−0.706015	+	0.708197i	$0.749509\pi$
$422$		−	5.05208e7i		−	0.672253i
$423$		0			0
$424$	−1.71150e7			−0.224533
$425$	−1.71719e7	+	9.91423e6i	−0.223693	+	0.129149i
$426$		0			0
$427$	1.98668e7	−	3.44102e7i	0.255178	−	0.441982i
$428$	4.84969e7	+	2.79997e7i	0.618562	+	0.357127i
$429$		0			0
$430$	1.59038e7	+	2.75462e7i	0.200030	+	0.346463i
$431$			7.01340e7i			0.875985i	0.898979	+	0.437992i	$0.144310\pi$
$431$			7.01340e7i			0.875985i	−0.898979	+	0.437992i	$0.855690\pi$
$432$		0			0
$433$	2.80606e6			0.0345647			0.0172824	−	0.999851i	$-0.494499\pi$
$433$	2.80606e6			0.0345647			0.0172824	+	0.999851i	$0.494499\pi$
$434$	−706047.	+	407636.i	−0.00863703	+	0.00498659i
$435$		0			0
$436$	−1.54193e7	+	2.67070e7i	−0.186039	+	0.322229i
$437$	1.09175e6	+	630320.i	0.0130821	+	0.00755295i
$438$		0			0
$439$	−1.08412e7	−	1.87774e7i	−0.128139	−	0.221944i	0.794816	−	0.606850i	$-0.207567\pi$
$439$	−1.08412e7	−	1.87774e7i	−0.128139	−	0.221944i	−0.922956	+	0.384906i	$0.874234\pi$
$440$			7.86324e7i			0.923089i
$441$		0			0
$442$	669969.			0.00775869
$443$	9.39202e7	−	5.42248e7i	1.08031	−	0.623716i	0.149329	−	0.988788i	$-0.452289\pi$
$443$	9.39202e7	−	5.42248e7i	1.08031	−	0.623716i	0.930980	+	0.365071i	$0.118955\pi$
$444$		0			0
$445$	−1.46386e7	+	2.53547e7i	−0.166119	+	0.287726i
$446$	−5.87234e7	−	3.39040e7i	−0.661922	−	0.382161i
$447$		0			0
$448$	4.87723e6	+	8.44761e6i	0.0542425	+	0.0939507i
$449$		−	1.61714e8i		−	1.78652i	−0.449536	−	0.893262i	$-0.648411\pi$
$449$		−	1.61714e8i		−	1.78652i	0.449536	−	0.893262i	$-0.351589\pi$
$450$		0			0
$451$	7.36917e7			0.803320
$452$	1.47939e7	−	8.54127e6i	0.160202	−	0.0924926i
$453$		0			0
$454$	1.38701e7	−	2.40238e7i	0.148222	−	0.256728i
$455$	5.87312e6	+	3.39084e6i	0.0623497	+	0.0359976i
$456$		0			0
$457$	−2.13188e7	−	3.69252e7i	−0.223364	−	0.386878i	0.732463	−	0.680806i	$-0.238371\pi$
$457$	−2.13188e7	−	3.69252e7i	−0.223364	−	0.386878i	−0.955827	+	0.293929i	$0.905037\pi$
$458$			4.27429e7i			0.444905i
$459$		0			0
$460$	6.53628e6			0.0671517
$461$	1.03509e8	−	5.97611e7i	1.05652	−	0.609980i	0.132050	−	0.991243i	$-0.457844\pi$
$461$	1.03509e8	−	5.97611e7i	1.05652	−	0.609980i	0.924467	+	0.381263i	$0.124511\pi$
$462$		0			0
$463$	−3.26876e7	+	5.66165e7i	−0.329336	+	0.570427i	−0.982380	−	0.186893i	$-0.940158\pi$
$463$	−3.26876e7	+	5.66165e7i	−0.329336	+	0.570427i	0.653044	+	0.757320i	$0.273492\pi$
$464$	−4.72264e7	−	2.72662e7i	−0.472749	−	0.272942i
$465$		0			0
$466$	−1.39949e7	−	2.42399e7i	−0.138297	−	0.239537i
$467$			1.69569e8i			1.66493i	0.554076	+	0.832466i	$0.313072\pi$
$467$			1.69569e8i			1.66493i	−0.554076	+	0.832466i	$0.686928\pi$
$468$		0			0
$469$	5.19305e7			0.503389
$470$	5.66348e7	−	3.26981e7i	0.545494	−	0.314941i
$471$		0			0
$472$	−3.80767e7	+	6.59508e7i	−0.362104	+	0.627183i
$473$	5.51960e7	+	3.18674e7i	0.521584	+	0.301137i
$474$		0			0
$475$	7.05126e6	+	1.22131e7i	0.0657939	+	0.113958i
$476$			5.51338e7i			0.511207i
$477$		0			0
$478$	9.73514e6			0.0891371
$479$	−8.82328e7	+	5.09413e7i	−0.802830	+	0.463514i	−0.844460	−	0.535619i	$-0.820078\pi$
$479$	−8.82328e7	+	5.09413e7i	−0.802830	+	0.463514i	0.0416296	+	0.999133i	$0.486745\pi$
$480$		0			0
$481$	−3.71474e6	+	6.43412e6i	−0.0333805	+	0.0578168i
$482$	−3.03820e7	−	1.75410e7i	−0.271316	−	0.156644i
$483$		0			0
$484$	−9.82504e6	−	1.70175e7i	−0.0866559	−	0.150092i
$485$		−	2.14367e8i		−	1.87902i
$486$		0			0
$487$	−9.64697e7			−0.835226			−0.417613	−	0.908625i	$-0.637133\pi$
$487$	−9.64697e7			−0.835226			−0.417613	+	0.908625i	$0.637133\pi$
$488$	−2.85247e7	+	1.64687e7i	−0.245449	+	0.141710i
$489$		0			0
$490$	4.23779e7	−	7.34007e7i	0.360206	−	0.623896i
$491$	−3.82447e7	−	2.20806e7i	−0.323092	−	0.186537i	0.329678	−	0.944093i	$-0.393060\pi$
$491$	−3.82447e7	−	2.20806e7i	−0.323092	−	0.186537i	−0.652770	+	0.757556i	$0.726393\pi$
$492$		0			0
$493$	3.58214e7	+	6.20445e7i	0.298952	+	0.517801i
$494$		−	476500.i		−	0.00395259i
$495$		0			0
$496$	−699418.			−0.00573181
$497$	−2.66365e8	+	1.53786e8i	−2.16974	+	1.25270i
$498$		0			0
$499$	8.31738e7	−	1.44061e8i	0.669399	−	1.15943i	−0.308674	−	0.951168i	$-0.599885\pi$
$499$	8.31738e7	−	1.44061e8i	0.669399	−	1.15943i	0.978073	−	0.208264i	$-0.0667814\pi$
$500$	−4.37462e7	−	2.52569e7i	−0.349970	−	0.202055i
$501$		0			0
$502$	−2.29453e7	−	3.97424e7i	−0.181377	−	0.314154i
$503$		−	1.18279e8i		−	0.929400i	−0.885468	−	0.464700i	$-0.846162\pi$
$503$		−	1.18279e8i		−	0.929400i	0.885468	−	0.464700i	$-0.153838\pi$
$504$		0			0
$505$	−1.72080e8			−1.33616
$506$	−3.12435e6	+	1.80385e6i	−0.0241162	+	0.0139235i
$507$		0			0
$508$	−4.14480e7	+	7.17901e7i	−0.316164	+	0.547613i
$509$	1.81504e8	+	1.04791e8i	1.37636	+	0.794644i	0.991720	−	0.128422i	$-0.0409911\pi$
$509$	1.81504e8	+	1.04791e8i	1.37636	+	0.794644i	0.384643	+	0.923065i	$0.374324\pi$
$510$		0			0
$511$	7.63778e6	+	1.32290e7i	0.0572407	+	0.0991437i
$512$			9.86587e7i			0.735065i
$513$		0			0
$514$	−4.05240e7			−0.298417
$515$	−1.41831e8	+	8.18859e7i	−1.03836	+	0.599498i
$516$		0			0
$517$	6.55192e7	−	1.13483e8i	0.474129	−	0.821216i
$518$	1.45849e8	+	8.42062e7i	1.04934	+	0.605836i
$519$		0			0
$520$	−2.81087e6	−	4.86857e6i	−0.0199908	−	0.0346251i
$521$			4.92211e7i			0.348047i	0.984741	+	0.174024i	$0.0556769\pi$
$521$			4.92211e7i			0.348047i	−0.984741	+	0.174024i	$0.944323\pi$
$522$		0			0
$523$	−1.23826e8			−0.865581			−0.432790	−	0.901495i	$-0.642471\pi$
$523$	−1.23826e8			−0.865581			−0.432790	+	0.901495i	$0.642471\pi$
$524$	6.89095e7	−	3.97849e7i	0.478945	−	0.276519i
$525$		0			0
$526$	2.53115e7	−	4.38408e7i	0.173924	−	0.301246i
$527$	795768.	+	459437.i	0.00543694	+	0.00313902i
$528$		0			0
$529$	−7.36768e7	−	1.27612e8i	−0.497695	−	0.862033i
$530$		−	2.36373e7i		−	0.158771i
$531$		0			0
$532$	3.92126e7			0.260430
$533$	−4.56266e6	+	2.63425e6i	−0.0301326	+	0.0173971i
$534$		0			0
$535$	−8.79918e7	+	1.52406e8i	−0.574620	+	0.995271i
$536$	−3.72809e7	−	2.15241e7i	−0.242098	−	0.139775i
$537$		0			0
$538$	3.98728e7	+	6.90616e7i	0.256053	+	0.443496i
$539$		−	1.69830e8i		−	1.08455i
$540$		0			0
$541$	3.06104e8			1.93320			0.966602	−	0.256282i	$-0.0824977\pi$
$541$	3.06104e8			1.93320			0.966602	+	0.256282i	$0.0824977\pi$
$542$	3.06780e7	−	1.77119e7i	0.192677	−	0.111242i
$543$		0			0
$544$	3.56609e7	−	6.17665e7i	0.221511	−	0.383668i
$545$	−8.39292e7	−	4.84566e7i	−0.518470	−	0.299339i
$546$		0			0
$547$	6.54341e7	+	1.13335e8i	0.399800	+	0.692473i	0.993701	−	0.112065i	$-0.0357464\pi$
$547$	6.54341e7	+	1.13335e8i	0.399800	+	0.692473i	−0.593901	+	0.804538i	$0.702413\pi$
$548$		−	2.10420e8i		−	1.27863i
$549$		0			0
$550$	−4.03585e7			−0.242575
$551$	4.41277e7	−	2.54771e7i	0.263789	−	0.152298i
$552$		0			0
$553$	−1.71307e8	+	2.96712e8i	−1.01298	+	1.75453i
$554$	−8.18996e7	−	4.72848e7i	−0.481673	−	0.278094i
$555$		0			0
$556$	−4.86045e7	−	8.41855e7i	−0.282782	−	0.489793i
$557$			1.61787e8i			0.936219i	0.883670	+	0.468110i	$0.155065\pi$
$557$			1.61787e8i			0.936219i	−0.883670	+	0.468110i	$0.844935\pi$
$558$		0			0
$559$	−4.55666e6			−0.0260862
$560$	1.14214e8	−	6.59413e7i	0.650360	−	0.375486i
$561$		0			0
$562$	−1.58236e7	+	2.74073e7i	−0.0891451	+	0.154404i
$563$	1.40583e8	+	8.11654e7i	0.787783	+	0.454827i	0.839181	−	0.543852i	$-0.183035\pi$
$563$	1.40583e8	+	8.11654e7i	0.787783	+	0.454827i	−0.0513986	+	0.998678i	$0.516368\pi$
$564$		0			0
$565$	2.68418e7	+	4.64913e7i	0.148821	+	0.257766i
$566$		−	9.36059e7i		−	0.516242i
$567$		0			0
$568$	2.54965e8			1.39134
$569$	−1.28707e8	+	7.43091e7i	−0.698660	+	0.403371i	−0.806848	−	0.590759i	$-0.798828\pi$
$569$	−1.28707e8	+	7.43091e7i	−0.698660	+	0.403371i	0.108188	+	0.994130i	$0.465495\pi$
$570$		0			0
$571$	7.48580e7	−	1.29658e8i	0.402096	−	0.696451i	−0.591883	−	0.806024i	$-0.701615\pi$
$571$	7.48580e7	−	1.29658e8i	0.402096	−	0.696451i	0.993979	+	0.109573i	$0.0349484\pi$
$572$	−4.28725e6	−	2.47525e6i	−0.0229082	−	0.0132261i
$573$		0			0
$574$	5.97136e7	+	1.03427e8i	0.315746	+	0.546887i
$575$			7.63365e6i			0.0401540i
$576$		0			0
$577$	4.00807e7			0.208645			0.104322	−	0.994544i	$-0.466733\pi$
$577$	4.00807e7			0.208645			0.104322	+	0.994544i	$0.466733\pi$
$578$	6.28919e7	−	3.63107e7i	0.325695	−	0.188040i
$579$		0			0
$580$	1.32096e8	−	2.28797e8i	0.677027	−	1.17265i
$581$	3.97865e8	+	2.29707e8i	2.02865	+	1.17124i
$582$		0			0
$583$	−2.36818e7	−	4.10180e7i	−0.119511	−	0.206999i
$584$		−	1.26628e7i		−	0.0635758i
$585$		0			0
$586$	−1.36284e8			−0.677257
$587$	3.36136e8	−	1.94068e8i	1.66189	−	0.959490i	0.690072	−	0.723741i	$-0.257579\pi$
$587$	3.36136e8	−	1.94068e8i	1.66189	−	0.959490i	0.971814	−	0.235749i	$-0.0757544\pi$
$588$		0			0
$589$	326763.	−	565971.i	0.00159914	−	0.00276980i
$590$	−9.10836e7	−	5.25872e7i	−0.443491	−	0.256049i
$591$		0			0
$592$	7.22400e7	+	1.25123e8i	0.348187	+	0.603078i
$593$			3.03816e8i			1.45695i	0.685070	+	0.728477i	$0.259772\pi$
$593$			3.03816e8i			1.45695i	−0.685070	+	0.728477i	$0.740228\pi$
$594$		0			0
$595$	−1.73263e8			−0.822537
$596$	−2.24496e8	+	1.29613e8i	−1.06040	+	0.612222i
$597$		0			0
$598$	128964.	−	223372.i	0.000603066	−	0.00104454i
$599$	−2.98889e8	−	1.72564e8i	−1.39069	−	0.802913i	−0.397295	−	0.917691i	$-0.630051\pi$
$599$	−2.98889e8	−	1.72564e8i	−1.39069	−	0.802913i	−0.993391	+	0.114777i	$0.963385\pi$
$600$		0			0
$601$	−1.91457e7	−	3.31613e7i	−0.0881957	−	0.152759i	0.818553	−	0.574431i	$-0.194777\pi$
$601$	−1.91457e7	−	3.31613e7i	−0.0881957	−	0.152759i	−0.906748	+	0.421672i	$0.861443\pi$
$602$			1.03291e8i			0.473448i
$603$		0			0
$604$	1.07491e8			0.487820
$605$	5.34790e7	−	3.08761e7i	0.241500	−	0.139430i
$606$		0			0
$607$	−1.07899e8	+	1.86887e8i	−0.482450	+	0.835629i	−0.999797	−	0.0201473i	$-0.993586\pi$
$607$	−1.07899e8	+	1.86887e8i	−0.482450	+	0.835629i	0.517347	+	0.855776i	$0.326920\pi$
$608$	−4.39299e7	−	2.53629e7i	−0.195456	−	0.112847i
$609$		0			0
$610$	−2.27447e7	−	3.93950e7i	−0.100205	−	0.173561i
$611$			9.36845e6i			0.0410718i
$612$		0			0
$613$	−1.84396e8			−0.800518			−0.400259	−	0.916402i	$-0.631080\pi$
$613$	−1.84396e8			−0.800518			−0.400259	+	0.916402i	$0.631080\pi$
$614$	−1.56101e8	+	9.01252e7i	−0.674375	+	0.389351i
$615$		0			0
$616$	−1.27674e8	+	2.21138e8i	−0.546211	+	0.946064i
$617$	−3.02301e8	−	1.74533e8i	−1.28702	−	0.743059i	−0.308895	−	0.951096i	$-0.599959\pi$
$617$	−3.02301e8	−	1.74533e8i	−1.28702	−	0.743059i	−0.978121	+	0.208037i	$0.933292\pi$
$618$		0			0
$619$	−2.13354e8	−	3.69540e8i	−0.899558	−	1.55808i	−0.828061	−	0.560638i	$-0.810556\pi$
$619$	−2.13354e8	−	3.69540e8i	−0.899558	−	1.55808i	−0.0714968	−	0.997441i	$-0.522778\pi$
$620$		−	3.38847e6i		−	0.0142177i
$621$		0			0
$622$	3.81076e7			0.158358
$623$	−8.23360e7	+	4.75367e7i	−0.340507	+	0.196592i
$624$		0			0
$625$	1.51568e8	−	2.62523e8i	0.620821	−	1.07529i
$626$	8.43023e6	+	4.86720e6i	0.0343650	+	0.0198406i
$627$		0			0
$628$	−1.42028e7	−	2.45999e7i	−0.0573447	−	0.0993240i
$629$		−	1.89813e8i		−	0.762737i
$630$		0			0
$631$	2.07920e8			0.827575			0.413788	−	0.910373i	$-0.364206\pi$
$631$	2.07920e8			0.827575			0.413788	+	0.910373i	$0.364206\pi$
$632$	2.45962e8	−	1.42006e8i	0.974356	−	0.562544i
$633$		0			0
$634$	4.10625e6	−	7.11223e6i	0.0161130	−	0.0279086i
$635$	−2.25607e8	−	1.30254e8i	−0.881114	−	0.508711i
$636$		0			0
$637$	6.07092e6	+	1.05151e7i	0.0234875	+	0.0406815i
$638$			1.45821e8i			0.561509i
$639$		0			0
$640$	−3.24288e8			−1.23706
$641$	−2.68002e7	+	1.54731e7i	−0.101757	+	0.0587494i	−0.550015	−	0.835155i	$-0.685378\pi$
$641$	−2.68002e7	+	1.54731e7i	−0.101757	+	0.0587494i	0.448258	+	0.893904i	$0.352045\pi$
$642$		0			0
$643$	7.40144e7	−	1.28197e8i	0.278409	−	0.482219i	−0.692580	−	0.721341i	$-0.743526\pi$
$643$	7.40144e7	−	1.28197e8i	0.278409	−	0.482219i	0.970990	+	0.239122i	$0.0768596\pi$
$644$	1.83820e7	+	1.06128e7i	0.0688231	+	0.0397350i
$645$		0			0
$646$	6.08697e6	+	1.05429e7i	0.0225789	+	0.0391078i
$647$			2.27002e8i			0.838140i	0.907954	+	0.419070i	$0.137644\pi$
$647$			2.27002e8i			0.838140i	−0.907954	+	0.419070i	$0.862356\pi$
$648$		0			0
$649$	−2.10744e8			−0.770942
$650$	2.49882e6	−	1.44269e6i	0.00909902	−	0.00525332i
$651$		0			0
$652$	1.20406e7	−	2.08550e7i	0.0434416	−	0.0752431i
$653$	2.05681e8	+	1.18750e8i	0.738678	+	0.426476i	0.821589	−	0.570081i	$-0.193088\pi$
$653$	2.05681e8	+	1.18750e8i	0.738678	+	0.426476i	−0.0829103	+	0.996557i	$0.526422\pi$
$654$		0			0
$655$	1.25028e8	+	2.16555e8i	0.444921	+	0.770626i
$656$			1.02456e8i			0.362932i
$657$		0			0
$658$	2.12365e8			0.745427
$659$	−1.74878e8	+	1.00966e8i	−0.611054	+	0.352792i	−0.773378	−	0.633945i	$-0.781434\pi$
$659$	−1.74878e8	+	1.00966e8i	−0.611054	+	0.352792i	0.162324	+	0.986738i	$0.448101\pi$
$660$		0			0
$661$	−2.84813e8	+	4.93311e8i	−0.986178	+	1.70811i	−0.349599	+	0.936900i	$0.613682\pi$
$661$	−2.84813e8	+	4.93311e8i	−0.986178	+	1.70811i	−0.636579	+	0.771211i	$0.719651\pi$
$662$	1.28538e7	+	7.42114e6i	0.0443055	+	0.0255798i
$663$		0			0
$664$	−1.90418e8	−	3.29813e8i	−0.650434	−	1.12659i
$665$			1.23229e8i			0.419034i
$666$		0			0
$667$	2.75814e7			0.0929477
$668$	−2.48734e6	+	1.43607e6i	−0.00834460	+	0.00481776i
$669$		0			0
$670$	2.97266e7	−	5.14880e7i	0.0988373	−	0.171191i
$671$	−7.89381e7	−	4.55749e7i	−0.261288	−	0.150855i
$672$		0			0
$673$	1.59298e8	+	2.75911e8i	0.522593	+	0.905158i	0.999654	+	0.0262880i	$0.00836871\pi$
$673$	1.59298e8	+	2.75911e8i	0.522593	+	0.905158i	−0.477061	+	0.878870i	$0.658298\pi$
$674$		−	2.33742e8i		−	0.763409i
$675$		0			0
$676$	−2.41846e8			−0.782887
$677$	4.13152e8	−	2.38533e8i	1.33151	−	0.768747i	0.345978	−	0.938243i	$-0.387547\pi$
$677$	4.13152e8	−	2.38533e8i	1.33151	−	0.768747i	0.985531	+	0.169496i	$0.0542140\pi$
$678$		0			0
$679$	3.48063e8	−	6.02863e8i	1.11186	−	1.92579i
$680$	1.24386e8	+	7.18140e7i	0.395588	+	0.228393i
$681$		0			0
$682$	935130.	+	1.61969e6i	0.00294794	+	0.00510598i
$683$			1.52482e8i			0.478583i	0.970948	+	0.239292i	$0.0769152\pi$
$683$			1.52482e8i			0.478583i	−0.970948	+	0.239292i	$0.923085\pi$
$684$		0			0
$685$	6.61266e8			2.05733
$686$	4.43879e7	−	2.56274e7i	0.137497	−	0.0793838i
$687$		0			0
$688$	−4.43063e7	+	7.67408e7i	−0.136051	+	0.235647i
$689$	2.93254e6	+	1.69310e6i	0.00896574	+	0.00517637i
$690$		0			0
$691$	1.29564e8	+	2.24412e8i	0.392691	+	0.680162i	0.992804	−	0.119754i	$-0.0382107\pi$
$691$	1.29564e8	+	2.24412e8i	0.392691	+	0.680162i	−0.600112	+	0.799916i	$0.704877\pi$
$692$			1.37980e7i			0.0416387i
$693$		0			0
$694$	5.97855e7			0.178862
$695$	2.64561e8	−	1.52744e8i	0.788082	−	0.454999i
$696$		0			0
$697$	6.73017e7	−	1.16570e8i	0.198759	−	0.344261i
$698$	1.80514e8	+	1.04220e8i	0.530816	+	0.306467i
$699$		0			0
$700$	1.18724e8	+	2.05635e8i	0.346133	+	0.599519i
$701$		−	4.77529e8i		−	1.38626i	−0.720811	−	0.693132i	$-0.756230\pi$
$701$		−	4.77529e8i		−	1.38626i	0.720811	−	0.693132i	$-0.243770\pi$
$702$		0			0
$703$	−1.35000e8			−0.388569
$704$	1.93791e7	−	1.11885e7i	0.0555412	−	0.0320667i
$705$		0			0
$706$	−1.36182e8	+	2.35874e8i	−0.386996	+	0.670296i
$707$	−4.83941e8	−	2.79404e8i	−1.36941	−	0.790631i
$708$		0			0
$709$	2.40026e8	+	4.15738e8i	0.673473	+	1.16649i	0.976913	+	0.213639i	$0.0685317\pi$
$709$	2.40026e8	+	4.15738e8i	0.673473	+	1.16649i	−0.303439	+	0.952851i	$0.598135\pi$
$710$			3.52127e8i			0.983841i
$711$		0			0
$712$	7.88120e7			0.218349
$713$	306358.	−	176876.i	0.000845203	−	0.000487978i
$714$		0			0
$715$	7.77870e6	−	1.34731e7i	0.0212808	−	0.0368595i
$716$	1.99155e8	+	1.14982e8i	0.542566	+	0.313251i
$717$		0			0
$718$	−3.50420e7	−	6.06945e7i	−0.0946706	−	0.163974i
$719$		−	3.27626e8i		−	0.881439i	−0.897645	−	0.440719i	$-0.854723\pi$
$719$		−	3.27626e8i		−	0.881439i	0.897645	−	0.440719i	$-0.145277\pi$
$720$		0			0
$721$	−5.31826e8			−1.41894
$722$	−1.43975e8	+	8.31239e7i	−0.382538	+	0.220859i
$723$		0			0
$724$	−1.52063e8	+	2.63380e8i	−0.400689	+	0.694014i
$725$	2.67210e8	+	1.54274e8i	0.701195	+	0.404835i
$726$		0			0
$727$	−1.87797e8	−	3.25274e8i	−0.488748	−	0.846537i	0.511168	−	0.859481i	$-0.329213\pi$
$727$	−1.87797e8	−	3.25274e8i	−0.488748	−	0.846537i	−0.999916	+	0.0129440i	$0.995880\pi$
$728$		−	1.82558e7i		−	0.0473159i
$729$		0			0
$730$	1.74884e7			0.0449554
$731$	1.00820e8	−	5.82083e7i	0.258103	−	0.149016i
$732$		0			0
$733$	−2.12651e7	+	3.68323e7i	−0.0539953	+	0.0935226i	−0.891760	−	0.452509i	$-0.850529\pi$
$733$	−2.12651e7	+	3.68323e7i	−0.0539953	+	0.0935226i	0.837764	+	0.546032i	$0.183862\pi$
$734$	1.28132e8	+	7.39771e7i	0.324019	+	0.187072i
$735$		0			0
$736$	−1.37289e7	−	2.37791e7i	−0.0344352	−	0.0596435i
$737$		−	1.19130e8i		−	0.297590i
$738$		0			0
$739$	3.17495e8			0.786689			0.393344	−	0.919391i	$-0.371318\pi$
$739$	3.17495e8			0.786689			0.393344	+	0.919391i	$0.371318\pi$
$740$	−6.06185e8	+	3.49981e8i	−1.49593	+	0.863673i
$741$		0			0
$742$	3.83794e7	−	6.64751e7i	0.0939478	−	0.162722i
$743$	−2.09597e7	−	1.21011e7i	−0.0510998	−	0.0295025i	0.474232	−	0.880400i	$-0.342726\pi$
$743$	−2.09597e7	−	1.21011e7i	−0.0510998	−	0.0295025i	−0.525332	+	0.850897i	$0.676059\pi$
$744$		0			0
$745$	−4.07320e8	−	7.05500e8i	−0.985070	−	1.70619i
$746$		−	3.34767e8i		−	0.806355i
$747$		0			0
$748$	1.26478e8			0.302212
$749$	−4.94918e8	+	2.85741e8i	−1.17784	+	0.680029i
$750$		0			0
$751$	1.32536e8	−	2.29559e8i	0.312906	−	0.541969i	−0.666084	−	0.745877i	$-0.732031\pi$
$751$	1.32536e8	−	2.29559e8i	0.312906	−	0.541969i	0.978990	+	0.203908i	$0.0653642\pi$
$752$	1.57778e8	+	9.10934e7i	0.371017	+	0.214207i
$753$		0			0
$754$	−5.21264e6	−	9.02856e6i	−0.0121603	−	0.0210622i
$755$			3.37800e8i			0.784907i
$756$		0			0
$757$	−1.59361e8			−0.367363			−0.183681	−	0.982986i	$-0.558801\pi$
$757$	−1.59361e8			−0.367363			−0.183681	+	0.982986i	$0.558801\pi$
$758$	−1.58088e8	+	9.12723e7i	−0.362988	+	0.209571i
$759$		0			0
$760$	5.10760e7	−	8.84662e7i	0.116353	−	0.201529i
$761$	5.37523e8	+	3.10339e8i	1.21967	+	0.704178i	0.964848	−	0.262810i	$-0.0846492\pi$
$761$	5.37523e8	+	3.10339e8i	1.21967	+	0.704178i	0.254824	+	0.966987i	$0.417983\pi$
$762$		0			0
$763$	−1.57356e8	−	2.72548e8i	−0.354250	−	0.613578i
$764$		−	4.81768e8i		−	1.08033i
$765$		0			0
$766$	−1.65554e8			−0.368343
$767$	1.30483e7	−	7.53346e6i	0.0289181	−	0.0166959i
$768$		0			0
$769$	−1.67140e8	+	2.89495e8i	−0.367538	+	0.636594i	−0.989180	−	0.146707i	$-0.953132\pi$
$769$	−1.67140e8	+	2.89495e8i	−0.367538	+	0.636594i	0.621642	+	0.783301i	$0.286466\pi$
$770$	−3.05410e8	−	1.76328e8i	−0.668976	−	0.386234i
$771$		0			0
$772$	−2.30717e8	−	3.99613e8i	−0.501450	−	0.868537i
$773$			2.54632e7i			0.0551283i	0.999620	+	0.0275641i	$0.00877505\pi$
$773$			2.54632e7i			0.0551283i	−0.999620	+	0.0275641i	$0.991225\pi$
$774$		0			0
$775$	3.95735e6			0.00850158
$776$	−4.99748e8	+	2.88530e8i	−1.06946	+	0.617455i
$777$		0			0
$778$	−8.99632e7	+	1.55821e8i	−0.191041	+	0.330892i
$779$	−8.29075e7	−	4.78667e7i	−0.175381	−	0.101256i
$780$		0			0
$781$	3.52790e8	+	6.11049e8i	0.740564	+	1.28269i
$782$			6.58972e6i			0.0137799i
$783$		0			0
$784$	2.36121e8			0.489988
$785$	7.73075e7	−	4.46335e7i	0.159813	−	0.0922682i
$786$		0			0
$787$	−2.21510e8	+	3.83667e8i	−0.454433	+	0.787101i	−0.998655	−	0.0518397i	$-0.983491\pi$
$787$	−2.21510e8	+	3.83667e8i	−0.454433	+	0.787101i	0.544222	+	0.838941i	$0.316825\pi$
$788$	2.61917e7	+	1.51218e7i	0.0535285	+	0.0309047i
$789$		0			0
$790$	1.96123e8	+	3.39695e8i	0.397784	+	0.688981i
$791$			1.74330e8i			0.352243i
$792$		0			0
$793$	6.51666e6			0.0130679
$794$	−3.13305e7	+	1.80887e7i	−0.0625901	+	0.0361364i
$795$		0			0
$796$	2.68751e8	−	4.65490e8i	0.532857	−	0.922936i
$797$	−3.96495e8	−	2.28917e8i	−0.783183	−	0.452171i	0.0543744	−	0.998521i	$-0.482684\pi$
$797$	−3.96495e8	−	2.28917e8i	−0.783183	−	0.452171i	−0.837557	+	0.546350i	$0.816017\pi$
$798$		0			0
$799$	−1.19676e8	−	2.07284e8i	−0.234620	−	0.406374i
$800$		−	3.07165e8i		−	0.599931i
$801$		0			0
$802$	−2.37089e8			−0.459609
$803$	3.03478e7	−	1.75213e7i	0.0586112	−	0.0338392i
$804$		0			0
$805$	−3.33518e7	+	5.77671e7i	−0.0639340	+	0.110737i
$806$	−115798.	−	66856.1i	−0.000221155	−	0.000127684i
$807$		0			0
$808$	2.31614e8	+	4.01167e8i	0.439067	+	0.760487i
$809$			5.57473e8i			1.05288i	0.850213	+	0.526439i	$0.176473\pi$
$809$			5.57473e8i			1.05288i	−0.850213	+	0.526439i	$0.823527\pi$
$810$		0			0
$811$	1.46646e8			0.274921			0.137460	−	0.990507i	$-0.456106\pi$
$811$	1.46646e8			0.274921			0.137460	+	0.990507i	$0.456106\pi$
$812$	7.42987e8	−	4.28964e8i	1.38776	−	0.801222i
$813$		0			0
$814$	1.93171e8	−	3.34583e8i	0.358154	−	0.620341i
$815$	6.55387e7	+	3.78388e7i	0.121067	+	0.0698980i
$816$		0			0
$817$	−4.13992e7	−	7.17056e7i	−0.0759147	−	0.131488i
$818$			2.62176e7i			0.0478997i
$819$		0			0
$820$	−4.96367e8			−0.900247
$821$	3.31338e8	−	1.91298e8i	0.598744	−	0.345685i	−0.169803	−	0.985478i	$-0.554313\pi$
$821$	3.31338e8	−	1.91298e8i	0.598744	−	0.345685i	0.768547	+	0.639793i	$0.220980\pi$
$822$		0			0
$823$	5.88425e7	−	1.01918e8i	0.105558	−	0.182832i	−0.808408	−	0.588623i	$-0.799670\pi$
$823$	5.88425e7	−	1.01918e8i	0.105558	−	0.182832i	0.913966	+	0.405790i	$0.133004\pi$
$824$	3.81798e8	+	2.20431e8i	0.682420	+	0.393995i
$825$		0			0
$826$	−1.70769e8	−	2.95781e8i	−0.303019	−	0.524845i
$827$			3.49222e8i			0.617426i	0.951155	+	0.308713i	$0.0998983\pi$
$827$			3.49222e8i			0.617426i	−0.951155	+	0.308713i	$0.900102\pi$
$828$		0			0
$829$	1.09403e8			0.192028			0.0960141	−	0.995380i	$-0.469391\pi$
$829$	1.09403e8			0.192028			0.0960141	+	0.995380i	$0.469391\pi$
$830$	4.55500e8	−	2.62983e8i	0.796626	−	0.459932i
$831$		0			0
$832$	−799911.	+	1.38549e6i	−0.00138890	+	0.00240565i
$833$	−2.68648e8	−	1.55104e8i	−0.464781	−	0.268342i
$834$		0			0
$835$	−4.51297e6	−	7.81670e6i	−0.00775182	−	0.0134265i
$836$		−	8.99548e7i		−	0.153959i
$837$		0			0
$838$	3.35730e7			0.0570503
$839$	−1.95149e8	+	1.12669e8i	−0.330431	+	0.190774i	−0.656032	−	0.754733i	$-0.727766\pi$
$839$	−1.95149e8	+	1.12669e8i	−0.330431	+	0.190774i	0.325602	+	0.945507i	$0.394433\pi$
$840$		0			0
$841$	2.60000e8	−	4.50333e8i	0.437104	−	0.757086i
$842$	1.25078e8	+	7.22137e7i	0.209529	+	0.120972i
$843$		0			0
$844$	3.40934e8	+	5.90515e8i	0.567079	+	0.982209i
$845$		−	7.60025e8i		−	1.25967i
$846$		0			0
$847$	2.00532e8			0.330014
$848$	5.70287e7	−	3.29255e7i	0.0935202	−	0.0539939i
$849$		0			0
$850$	−3.68589e7	+	6.38415e7i	−0.0600186	+	0.103955i
$851$	−6.32850e7	−	3.65376e7i	−0.102686	−	0.0592859i
$852$		0			0
$853$	2.90477e8	+	5.03121e8i	0.468021	+	0.810636i	0.999332	−	0.0365409i	$-0.0116339\pi$
$853$	2.90477e8	+	5.03121e8i	0.468021	+	0.810636i	−0.531311	+	0.847177i	$0.678301\pi$
$854$		−	1.47720e8i		−	0.237174i
$855$		0			0
$856$	4.73735e8			0.755291
$857$	−1.62249e8	+	9.36743e7i	−0.257774	+	0.148826i	−0.623319	−	0.781968i	$-0.714216\pi$
$857$	−1.62249e8	+	9.36743e7i	−0.257774	+	0.148826i	0.365545	+	0.930794i	$0.380883\pi$
$858$		0			0
$859$	−4.97153e8	+	8.61094e8i	−0.784351	+	1.35854i	0.145036	+	0.989426i	$0.453670\pi$
$859$	−4.97153e8	+	8.61094e8i	−0.784351	+	1.35854i	−0.929386	+	0.369109i	$0.879663\pi$
$860$	−3.71786e8	−	2.14651e8i	−0.584517	−	0.337471i
$861$		0			0
$862$	1.30371e8	+	2.25810e8i	0.203545	+	0.352550i
$863$		−	1.10380e8i		−	0.171734i	−0.996307	−	0.0858670i	$-0.972634\pi$
$863$		−	1.10380e8i		−	0.171734i	0.996307	−	0.0858670i	$-0.0273660\pi$
$864$		0			0
$865$	−4.33614e7			−0.0669970
$866$	9.03464e6	−	5.21615e6i	0.0139110	−	0.00803150i
$867$		0			0
$868$	5.50179e6	−	9.52937e6i	0.00841288	−	0.0145715i
$869$	6.80667e8	+	3.92983e8i	1.03723	+	0.598845i
$870$		0			0
$871$	4.25854e6	+	7.37600e6i	0.00644475	+	0.0111626i
$872$			2.60883e8i			0.393456i
$873$		0			0
$874$	4.68678e6			0.00702005
$875$	4.46437e8	−	2.57750e8i	0.666401	−	0.384747i
$876$		0			0
$877$	−2.19844e7	+	3.80781e7i	−0.0325923	+	0.0564516i	−0.881861	−	0.471509i	$-0.843710\pi$
$877$	−2.19844e7	+	3.80781e7i	−0.0325923	+	0.0564516i	0.849269	+	0.527960i	$0.177043\pi$
$878$	−6.98104e7	−	4.03050e7i	−0.103142	−	0.0595492i
$879$		0			0
$880$	−1.51271e8	−	2.62009e8i	−0.221977	−	0.384476i
$881$			9.61247e8i			1.40575i	0.711315	+	0.702873i	$0.248100\pi$
$881$			9.61247e8i			1.40575i	−0.711315	+	0.702873i	$0.751900\pi$
$882$		0			0
$883$	−2.46127e8			−0.357502			−0.178751	−	0.983894i	$-0.557206\pi$
$883$	−2.46127e8			−0.357502			−0.178751	+	0.983894i	$0.557206\pi$
$884$	−7.83099e6	+	4.52122e6i	−0.0113360	+	0.00654484i
$885$		0			0
$886$	2.01596e8	−	3.49174e8i	0.289855	−	0.502043i
$887$	5.00314e7	+	2.88856e7i	0.0716922	+	0.0413915i	0.535418	−	0.844587i	$-0.320154\pi$
$887$	5.00314e7	+	2.88856e7i	0.0716922	+	0.0413915i	−0.463725	+	0.885979i	$0.653488\pi$
$888$		0			0
$889$	−4.22983e8	−	7.32628e8i	−0.602030	−	1.04275i
$890$			1.08846e8i			0.154398i
$891$		0			0
$892$	9.15191e8			1.28949
$893$	−1.47426e8	+	8.51164e7i	−0.207024	+	0.119525i
$894$		0			0
$895$	−3.61343e8	+	6.25864e8i	−0.504023	+	0.872994i
$896$	−9.11995e8	−	5.26540e8i	−1.26785	−	0.731994i
$897$		0			0
$898$	−3.00609e8	−	5.20670e8i	−0.415119	−	0.719007i
$899$		−	1.42984e7i		−	0.0196793i
$900$		0			0
$901$	−8.65130e7			−0.118279
$902$	2.37264e8	−	1.36985e8i	0.323305	−	0.186660i
$903$		0			0
$904$	7.22561e7	−	1.25151e8i	0.0978068	−	0.169406i
$905$	−8.27699e8	−	4.77872e8i	−1.11667	−	0.644712i
$906$		0			0
$907$	2.43210e8	+	4.21252e8i	0.325957	+	0.564574i	0.981706	−	0.190406i	$-0.0609803\pi$
$907$	2.43210e8	+	4.21252e8i	0.325957	+	0.564574i	−0.655749	+	0.754979i	$0.727647\pi$
$908$			3.74405e8i			0.500131i
$909$		0			0
$910$	2.52128e7			0.0334578
$911$	−4.19276e6	+	2.42069e6i	−0.00554556	+	0.00320173i	−0.502770	−	0.864420i	$-0.667686\pi$
$911$	−4.19276e6	+	2.42069e6i	−0.00554556	+	0.00320173i	0.497225	+	0.867622i	$0.334352\pi$
$912$		0			0
$913$	5.26955e8	−	9.12713e8i	0.692407	−	1.19928i
$914$	−1.37280e8	−	7.92584e7i	−0.179791	−	0.103802i
$915$		0			0
$916$	−2.88446e8	−	4.99604e8i	−0.375300	−	0.650039i
$917$			8.12022e8i			1.05308i
$918$		0			0
$919$	−1.39831e9			−1.80159			−0.900796	−	0.434242i	$-0.857016\pi$
$919$	−1.39831e9			−1.80159			−0.900796	+	0.434242i	$0.857016\pi$
$920$	4.78865e7	−	2.76473e7i	0.0614964	−	0.0355050i
$921$		0			0
$922$	2.22179e8	−	3.84825e8i	0.283472	−	0.490987i
$923$	−4.36863e7	−	2.52223e7i	−0.0555572	−	0.0320760i
$924$		0			0
$925$	−4.08739e8	−	7.07957e8i	−0.516441	−	0.894502i
$926$			2.43050e8i			0.306100i
$927$		0			0
$928$	−1.10983e9			−1.38871
$929$	−6.44786e8	+	3.72267e8i	−0.804208	+	0.464310i	−0.844940	−	0.534860i	$-0.820364\pi$
$929$	−6.44786e8	+	3.72267e8i	−0.804208	+	0.464310i	0.0407324	+	0.999170i	$0.487031\pi$
$930$		0			0
$931$	−1.10314e8	+	1.91069e8i	−0.136704	+	0.236778i
$932$	3.27161e8	+	1.88887e8i	0.404123	+	0.233321i
$933$		0			0
$934$	3.15211e8	+	5.45961e8i	0.386866	+	0.670071i
$935$			3.97471e8i			0.486262i
$936$		0			0
$937$	−7.62738e8			−0.927164			−0.463582	−	0.886054i	$-0.653436\pi$
$937$	−7.62738e8			−0.927164			−0.463582	+	0.886054i	$0.653436\pi$
$938$	1.67200e8	−	9.65330e7i	0.202595	−	0.116968i
$939$		0			0
$940$	−4.41320e8	+	7.64388e8i	−0.531337	+	0.920302i
$941$	−9.93617e8	−	5.73665e8i	−1.19248	−	0.688477i	−0.233609	−	0.972331i	$-0.575054\pi$
$941$	−9.93617e8	−	5.73665e8i	−1.19248	−	0.688477i	−0.958868	+	0.283854i	$0.908387\pi$
$942$		0			0
$943$	−2.59101e7	−	4.48776e7i	−0.0308983	−	0.0535174i
$944$		−	2.93004e8i		−	0.348304i
$945$		0			0
$946$	2.36952e8			0.279890
$947$	−4.42601e8	+	2.55536e8i	−0.521149	+	0.300886i	−0.737405	−	0.675451i	$-0.763949\pi$
$947$	−4.42601e8	+	2.55536e8i	−0.521149	+	0.300886i	0.216255	+	0.976337i	$0.430616\pi$
$948$		0			0
$949$	−1.25267e6	+	2.16968e6i	−0.00146567	+	0.00253862i
$950$	4.54057e7	+	2.62150e7i	0.0529590	+	0.0305759i
$951$		0			0
$952$	2.33206e8	+	4.03925e8i	0.270289	+	0.468155i
$953$		−	1.34950e9i		−	1.55917i	−0.626298	−	0.779584i	$-0.715431\pi$
$953$		−	1.34950e9i		−	1.55917i	0.626298	−	0.779584i	$-0.284569\pi$
$954$		0			0
$955$	1.51400e9			1.73827
$956$	−1.13790e8	+	6.56966e7i	−0.130236	+	0.0751916i
$957$		0			0
$958$	−1.89388e8	+	3.28030e8i	−0.215405	+	0.373093i
$959$	1.85968e9	+	1.07368e9i	2.10854	+	1.21736i
$960$		0			0
$961$	4.43660e8	+	7.68442e8i	0.499897	+	0.865846i
$962$			2.76212e7i			0.0310254i
$963$		0			0
$964$	4.73496e8			0.528549
$965$	1.25582e9	−	7.25050e8i	1.39748	−	0.806837i
$966$		0			0
$967$	2.63074e8	−	4.55657e8i	0.290936	−	0.503916i	−0.683095	−	0.730329i	$-0.739367\pi$
$967$	2.63074e8	−	4.55657e8i	0.290936	−	0.503916i	0.974031	+	0.226413i	$0.0726999\pi$
$968$	−1.43962e8	−	8.31163e7i	−0.158716	−	0.0916347i
$969$		0			0
$970$	−3.98484e8	−	6.90195e8i	−0.436612	−	0.756234i
$971$		−	1.39252e9i		−	1.52105i	−0.649309	−	0.760525i	$-0.724942\pi$
$971$		−	1.39252e9i		−	1.52105i	0.649309	−	0.760525i	$-0.275058\pi$
$972$		0			0
$973$	9.92032e8			1.07693
$974$	−3.10603e8	+	1.79326e8i	−0.336146	+	0.194074i
$975$		0			0
$976$	6.33643e7	−	1.09750e8i	0.0681546	−	0.118047i
$977$	−1.10387e9	−	6.37317e8i	−1.18368	−	0.683396i	−0.226814	−	0.973938i	$-0.572831\pi$
$977$	−1.10387e9	−	6.37317e8i	−1.18368	−	0.683396i	−0.956862	+	0.290543i	$0.906164\pi$
$978$		0			0
$979$	1.09051e8	+	1.88881e8i	0.116220	+	0.201299i
$980$			1.14393e9i			1.21541i
$981$		0			0
$982$	−1.64181e8			−0.173376
$983$	−1.28604e8	+	7.42493e7i	−0.135392	+	0.0781685i	−0.566166	−	0.824291i	$-0.691574\pi$
$983$	−1.28604e8	+	7.42493e7i	−0.135392	+	0.0781685i	0.430774	+	0.902460i	$0.358241\pi$
$984$		0			0
$985$	−4.75217e7	+	8.23100e7i	−0.0497260	+	0.0861279i
$986$	2.30668e8	+	1.33176e8i	0.240634	+	0.138930i
$987$		0			0
$988$	3.21561e6	+	5.56960e6i	0.00333421	+	0.00577502i
$989$		−	4.48186e7i		−	0.0463307i
$990$		0			0
$991$	5.81534e8			0.597522			0.298761	−	0.954328i	$-0.403427\pi$
$991$	5.81534e8			0.597522			0.298761	+	0.954328i	$0.403427\pi$
$992$	−1.23273e7	+	7.11718e6i	−0.0126280	+	0.00729077i
$993$		0			0
$994$	−5.71742e8	+	9.90287e8i	−0.582158	+	1.00833i
$995$	1.46285e9	+	8.44576e8i	1.48501	+	0.857372i
$996$		0			0
$997$	−4.58130e8	−	7.93504e8i	−0.462278	−	0.800688i	0.536796	−	0.843712i	$-0.319634\pi$
$997$	−4.58130e8	−	7.93504e8i	−0.462278	−	0.800688i	−0.999074	+	0.0430235i	$0.986301\pi$
$998$		−	6.18443e8i		−	0.622169i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.d.a.17.3		10
3.2	odd	2		9.7.d.a.5.3	yes	10
4.3	odd	2		432.7.q.a.17.1		10
9.2	odd	6	inner	27.7.d.a.8.3		10
9.4	even	3		81.7.b.a.80.6		10
9.5	odd	6		81.7.b.a.80.5		10
9.7	even	3		9.7.d.a.2.3	✓	10
12.11	even	2		144.7.q.a.113.1		10
36.7	odd	6		144.7.q.a.65.1		10
36.11	even	6		432.7.q.a.305.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.3	✓	10	9.7	even	3
9.7.d.a.5.3	yes	10	3.2	odd	2
27.7.d.a.8.3		10	9.2	odd	6	inner
27.7.d.a.17.3		10	1.1	even	1	trivial
81.7.b.a.80.5		10	9.5	odd	6
81.7.b.a.80.6		10	9.4	even	3
144.7.q.a.65.1		10	36.7	odd	6
144.7.q.a.113.1		10	12.11	even	2
432.7.q.a.17.1		10	4.3	odd	2
432.7.q.a.305.1		10	36.11	even	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.21969 - 1.85889i) q^{2} +(-25.0891 + 43.4555i) q^{4} +(-136.563 - 78.8448i) q^{5} +(-256.037 - 443.470i) q^{7} +424.489i q^{8} +O(q^{10})\)	\(q+(3.21969 - 1.85889i) q^{2} +(-25.0891 + 43.4555i) q^{4} +(-136.563 - 78.8448i) q^{5} +(-256.037 - 443.470i) q^{7} +424.489i q^{8} -586.255 q^{10} +(-1017.33 + 587.357i) q^{11} +(41.9925 - 72.7331i) q^{13} +(-1648.72 - 951.890i) q^{14} +(-816.622 - 1414.43i) q^{16} +2145.70i q^{17} +1526.08 q^{19} +(6852.48 - 3956.28i) q^{20} +(-2183.66 + 3782.22i) q^{22} +(715.392 + 413.032i) q^{23} +(4620.50 + 8002.94i) q^{25} -312.238i q^{26} +25695.0 q^{28} +(28915.7 - 16694.5i) q^{29} +(214.119 - 370.866i) q^{31} +(-28786.1 - 16619.7i) q^{32} +(3988.63 + 6908.50i) q^{34} +80748.9i q^{35} -88462.1 q^{37} +(4913.51 - 2836.81i) q^{38} +(33468.7 - 57969.6i) q^{40} +(-54327.1 - 31365.8i) q^{41} +(-27127.8 - 46986.7i) q^{43} -58945.0i q^{44} +3071.12 q^{46} +(-96604.4 + 55774.5i) q^{47} +(-72285.8 + 125203. i) q^{49} +(29753.2 + 17178.0i) q^{50} +(2107.10 + 3649.61i) q^{52} +40319.2i q^{53} +185240. q^{55} +(188248. - 108685. i) q^{56} +(62066.4 - 107502. i) q^{58} +(155365. + 89700.2i) q^{59} +(38796.6 + 67197.7i) q^{61} -1592.10i q^{62} -19048.9 q^{64} +(-11469.3 + 6621.78i) q^{65} +(-50705.9 + 87825.2i) q^{67} +(-93242.7 - 53833.7i) q^{68} +(150103. + 259986. i) q^{70} -600639. i q^{71} -29830.7 q^{73} +(-284820. + 164441. i) q^{74} +(-38287.9 + 66316.6i) q^{76} +(520950. + 300771. i) q^{77} +(-334535. - 579432. i) q^{79} +257545. i q^{80} -233222. q^{82} +(-776966. + 448581. i) q^{83} +(169178. - 293024. i) q^{85} +(-174686. - 100855. i) q^{86} +(-249327. - 431847. i) q^{88} -185663. i q^{89} -43006.6 q^{91} +(-35897.0 + 20725.2i) q^{92} +(-207357. + 359154. i) q^{94} +(-208406. - 120323. i) q^{95} +(679711. + 1.17729e6i) q^{97} +537485. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Introduction

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