LMFDB - Embedded newform 27.7.d.a.8.5

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			8.5
Root			$4.07727 + 7.06203i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.7.d.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.2318 + 7.06203i) q^{2} +(67.7447 + 117.337i) q^{4} +(103.839 - 59.9512i) q^{5} +(-128.891 + 223.245i) q^{7} +1009.72i q^{8} +O(q^{10})$	\(q+(12.2318 + 7.06203i) q^{2} +(67.7447 + 117.337i) q^{4} +(103.839 - 59.9512i) q^{5} +(-128.891 + 223.245i) q^{7} +1009.72i q^{8} +1693.51 q^{10} +(-518.417 - 299.308i) q^{11} +(-968.088 - 1676.78i) q^{13} +(-3153.13 + 1820.46i) q^{14} +(-2795.02 + 4841.12i) q^{16} -4874.12i q^{17} +7688.70 q^{19} +(14069.0 + 8122.75i) q^{20} +(-4227.45 - 7322.16i) q^{22} +(594.548 - 343.263i) q^{23} +(-624.198 + 1081.14i) q^{25} -27346.7i q^{26} -34926.6 q^{28} +(-29972.2 - 17304.5i) q^{29} +(-1387.88 - 2403.88i) q^{31} +(-12411.9 + 7166.00i) q^{32} +(34421.2 - 59619.2i) q^{34} +30908.6i q^{35} +17175.3 q^{37} +(94046.7 + 54297.9i) q^{38} +(60534.0 + 104848. i) q^{40} +(-71583.2 + 41328.6i) q^{41} +(-63212.6 + 109487. i) q^{43} -81106.2i q^{44} +9696.53 q^{46} +(72025.6 + 41584.0i) q^{47} +(25599.0 + 44338.7i) q^{49} +(-15270.1 + 8816.21i) q^{50} +(131166. - 227185. i) q^{52} +40017.8i q^{53} -71775.6 q^{55} +(-225415. - 130143. i) q^{56} +(-244410. - 423330. i) q^{58} +(57614.7 - 33263.9i) q^{59} +(-184662. + 319843. i) q^{61} -39205.0i q^{62} +155336. q^{64} +(-201050. - 116076. i) q^{65} +(-127954. - 221623. i) q^{67} +(571915. - 330195. i) q^{68} +(-218277. + 378068. i) q^{70} +269837. i q^{71} +551862. q^{73} +(210085. + 121292. i) q^{74} +(520869. + 902171. i) q^{76} +(133638. - 77156.0i) q^{77} +(355021. - 614915. i) q^{79} +670259. i q^{80} -1.16746e6 q^{82} +(-301612. - 174136. i) q^{83} +(-292209. - 506121. i) q^{85} +(-1.54641e6 + 892818. i) q^{86} +(302218. - 523456. i) q^{88} -836103. i q^{89} +499109. q^{91} +(80554.9 + 46508.4i) q^{92} +(587335. + 1.01729e6i) q^{94} +(798384. - 460947. i) q^{95} +(-47014.3 + 81431.2i) q^{97} +723123. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	12.2318	+	7.06203i	1.52898	+	0.882754i	0.999405	+	0.0344882i	$0.0109801\pi$
$2$	12.2318	+	7.06203i	1.52898	+	0.882754i	0.529570	+	0.848266i	$0.322353\pi$
$3$		0			0
$3$		0			0
$4$	67.7447	+	117.337i	1.05851	+	1.83339i
$5$	103.839	−	59.9512i	0.830709	−	0.479610i	−0.0233865	−	0.999726i	$-0.507445\pi$
$5$	103.839	−	59.9512i	0.830709	−	0.479610i	0.854095	+	0.520117i	$0.174112\pi$
$6$		0			0
$7$	−128.891	+	223.245i	−0.375774	+	0.650860i	−0.990443	−	0.137926i	$-0.955956\pi$
$7$	−128.891	+	223.245i	−0.375774	+	0.650860i	0.614668	+	0.788786i	$0.289290\pi$
$8$			1009.72i			1.97211i
$9$		0			0
$10$	1693.51			1.69351
$11$	−518.417	−	299.308i	−0.389495	−	0.224875i	0.292447	−	0.956282i	$-0.405531\pi$
$11$	−518.417	−	299.308i	−0.389495	−	0.224875i	−0.681941	+	0.731407i	$0.738864\pi$
$12$		0			0
$13$	−968.088	−	1676.78i	−0.440641	−	0.763212i	0.557096	−	0.830448i	$-0.311915\pi$
$13$	−968.088	−	1676.78i	−0.440641	−	0.763212i	−0.997737	+	0.0672356i	$0.978582\pi$
$14$	−3153.13	+	1820.46i	−1.14910	+	0.663432i
$15$		0			0
$16$	−2795.02	+	4841.12i	−0.682378	+	1.18191i
$17$		−	4874.12i		−	0.992085i	−0.868298	−	0.496043i	$-0.834786\pi$
$17$		−	4874.12i		−	0.992085i	0.868298	−	0.496043i	$-0.165214\pi$
$18$		0			0
$19$	7688.70			1.12097			0.560483	−	0.828166i	$-0.310616\pi$
$19$	7688.70			1.12097			0.560483	+	0.828166i	$0.310616\pi$
$20$	14069.0	+	8122.75i	1.75863	+	1.01534i
$21$		0			0
$22$	−4227.45	−	7322.16i	−0.397018	−	0.687656i
$23$	594.548	−	343.263i	0.0488656	−	0.0282126i	−0.475368	−	0.879787i	$-0.657685\pi$
$23$	594.548	−	343.263i	0.0488656	−	0.0282126i	0.524234	+	0.851574i	$0.324352\pi$
$24$		0			0
$25$	−624.198	+	1081.14i	−0.0399486	+	0.0691931i
$26$		−	27346.7i		−	1.55591i
$27$		0			0
$28$	−34926.6			−1.59104
$29$	−29972.2	−	17304.5i	−1.22892	−	0.709520i	−0.262119	−	0.965036i	$-0.584421\pi$
$29$	−29972.2	−	17304.5i	−1.22892	−	0.709520i	−0.966805	+	0.255516i	$0.917755\pi$
$30$		0			0
$31$	−1387.88	−	2403.88i	−0.0465872	−	0.0806915i	0.841791	−	0.539803i	$-0.181501\pi$
$31$	−1387.88	−	2403.88i	−0.0465872	−	0.0806915i	−0.888379	+	0.459111i	$0.848168\pi$
$32$	−12411.9	+	7166.00i	−0.378780	+	0.218689i
$33$		0			0
$34$	34421.2	−	59619.2i	0.875768	−	1.51687i
$35$			30908.6i			0.720900i
$36$		0			0
$37$	17175.3			0.339077			0.169539	−	0.985524i	$-0.445772\pi$
$37$	17175.3			0.339077			0.169539	+	0.985524i	$0.445772\pi$
$38$	94046.7	+	54297.9i	1.71393	+	0.989537i
$39$		0			0
$40$	60534.0	+	104848.i	0.945843	+	1.63825i
$41$	−71583.2	+	41328.6i	−1.03863	+	0.599652i	−0.919444	−	0.393221i	$-0.871361\pi$
$41$	−71583.2	+	41328.6i	−1.03863	+	0.599652i	−0.119183	+	0.992872i	$0.538027\pi$
$42$		0			0
$43$	−63212.6	+	109487.i	−0.795056	+	1.37708i	0.127747	+	0.991807i	$0.459225\pi$
$43$	−63212.6	+	109487.i	−0.795056	+	1.37708i	−0.922803	+	0.385271i	$0.874108\pi$
$44$		−	81106.2i		−	0.952129i
$45$		0			0
$46$	9696.53			0.0996191
$47$	72025.6	+	41584.0i	0.693734	+	0.400528i	0.805009	−	0.593262i	$-0.202160\pi$
$47$	72025.6	+	41584.0i	0.693734	+	0.400528i	−0.111275	+	0.993790i	$0.535494\pi$
$48$		0			0
$49$	25599.0	+	44338.7i	0.217588	+	0.376873i
$50$	−15270.1	+	8816.21i	−0.122161	+	0.0705297i
$51$		0			0
$52$	131166.	−	227185.i	0.932846	−	1.61574i
$53$			40017.8i			0.268798i	0.990927	+	0.134399i	$0.0429103\pi$
$53$			40017.8i			0.268798i	−0.990927	+	0.134399i	$0.957090\pi$
$54$		0			0
$55$	−71775.6			−0.431409
$56$	−225415.	−	130143.i	−1.28357	−	0.741068i
$57$		0			0
$58$	−244410.	−	423330.i	−1.25266	−	2.16968i
$59$	57614.7	−	33263.9i	0.280529	−	0.161963i	−0.353134	−	0.935573i	$-0.614884\pi$
$59$	57614.7	−	33263.9i	0.280529	−	0.161963i	0.633663	+	0.773609i	$0.281551\pi$
$60$		0			0
$61$	−184662.	+	319843.i	−0.813555	+	1.40912i	0.0968060	+	0.995303i	$0.469137\pi$
$61$	−184662.	+	319843.i	−0.813555	+	1.40912i	−0.910361	+	0.413815i	$0.864196\pi$
$62$		−	39205.0i		−	0.164500i
$63$		0			0
$64$	155336.			0.592561
$65$	−201050.	−	116076.i	−0.732088	−	0.422671i
$66$		0			0
$67$	−127954.	−	221623.i	−0.425432	−	0.736870i	0.571029	−	0.820930i	$-0.306545\pi$
$67$	−127954.	−	221623.i	−0.425432	−	0.736870i	−0.996461	+	0.0840603i	$0.973211\pi$
$68$	571915.	−	330195.i	1.81888	−	1.05013i
$69$		0			0
$70$	−218277.	+	378068.i	−0.636377	+	1.10224i
$71$			269837.i			0.753923i	0.926229	+	0.376961i	$0.123031\pi$
$71$			269837.i			0.753923i	−0.926229	+	0.376961i	$0.876969\pi$
$72$		0			0
$73$	551862.			1.41861			0.709303	−	0.704903i	$-0.249010\pi$
$73$	551862.			1.41861			0.709303	+	0.704903i	$0.249010\pi$
$74$	210085.	+	121292.i	0.518441	+	0.299322i
$75$		0			0
$76$	520869.	+	902171.i	1.18655	+	2.05517i
$77$	133638.	−	77156.0i	0.292724	−	0.169004i
$78$		0			0
$79$	355021.	−	614915.i	0.720068	−	1.24719i	−0.240905	−	0.970549i	$-0.577444\pi$
$79$	355021.	−	614915.i	0.720068	−	1.24719i	0.960972	−	0.276645i	$-0.0892226\pi$
$80$			670259.i			1.30910i
$81$		0			0
$82$	−1.16746e6			−2.11738
$83$	−301612.	−	174136.i	−0.527490	−	0.304547i	0.212503	−	0.977160i	$-0.431838\pi$
$83$	−301612.	−	174136.i	−0.527490	−	0.304547i	−0.739994	+	0.672614i	$0.765172\pi$
$84$		0			0
$85$	−292209.	−	506121.i	−0.475814	−	0.824134i
$86$	−1.54641e6	+	892818.i	−2.43124	+	1.40368i
$87$		0			0
$88$	302218.	−	523456.i	0.443478	−	0.768126i
$89$		−	836103.i		−	1.18601i	−0.805197	−	0.593007i	$-0.797941\pi$
$89$		−	836103.i		−	1.18601i	0.805197	−	0.593007i	$-0.202059\pi$
$90$		0			0
$91$	499109.			0.662326
$92$	80554.9	+	46508.4i	0.103450	+	0.0597266i
$93$		0			0
$94$	587335.	+	1.01729e6i	0.707135	+	1.22479i
$95$	798384.	−	460947.i	0.931196	−	0.537626i
$96$		0			0
$97$	−47014.3	+	81431.2i	−0.0515128	+	0.0892227i	−0.890632	−	0.454725i	$-0.849738\pi$
$97$	−47014.3	+	81431.2i	−0.0515128	+	0.0892227i	0.839119	+	0.543948i	$0.183071\pi$
$98$			723123.i			0.768306i
$99$		0			0
$100$	−169144.			−0.169144
$101$	233315.	+	134704.i	0.226453	+	0.130743i	0.608935	−	0.793220i	$-0.291597\pi$
$101$	233315.	+	134704.i	0.226453	+	0.130743i	−0.382482	+	0.923963i	$0.624930\pi$
$102$		0			0
$103$	128429.	+	222446.i	0.117531	+	0.203569i	0.918789	−	0.394750i	$-0.129169\pi$
$103$	128429.	+	222446.i	0.117531	+	0.203569i	−0.801258	+	0.598319i	$0.795835\pi$
$104$	1.69308e6	−	977498.i	1.50514	−	0.868992i
$105$		0			0
$106$	−282607.	+	489490.i	−0.237282	+	0.410985i
$107$			983414.i			0.802759i	0.915912	+	0.401379i	$0.131469\pi$
$107$			983414.i			0.802759i	−0.915912	+	0.401379i	$0.868531\pi$
$108$		0			0
$109$	−1.19797e6			−0.925053			−0.462526	−	0.886606i	$-0.653057\pi$
$109$	−1.19797e6			−0.925053			−0.462526	+	0.886606i	$0.653057\pi$
$110$	−877945.	−	506882.i	−0.659613	−	0.380828i
$111$		0			0
$112$	−720503.	−	1.24795e6i	−0.512840	−	0.888264i
$113$	246875.	−	142533.i	0.171097	−	0.0987827i	−0.412006	−	0.911181i	$-0.635172\pi$
$113$	246875.	−	142533.i	0.171097	−	0.0987827i	0.583103	+	0.812398i	$0.301838\pi$
$114$		0			0
$115$	41158.0	−	71287.8i	0.0270621	−	0.0468729i
$116$		−	4.68914e6i		−	3.00414i
$117$		0			0
$118$	939643.			0.571896
$119$	1.08812e6	+	628227.i	0.645709	+	0.372800i
$120$		0			0
$121$	−706609.	−	1.22388e6i	−0.398863	−	0.690850i
$122$	−4.51749e6	+	2.60817e6i	−2.48781	+	1.43634i
$123$		0			0
$124$	188043.	−	325700.i	0.0986261	−	0.170825i
$125$			2.02316e6i			1.03586i
$126$		0			0
$127$	359846.			0.175673			0.0878365	−	0.996135i	$-0.472005\pi$
$127$	359846.			0.175673			0.0878365	+	0.996135i	$0.472005\pi$
$128$	2.69440e6	+	1.55561e6i	1.28479	+	0.741775i
$129$		0			0
$130$	−1.63947e6	−	2.83964e6i	−0.746230	−	1.29251i
$131$	1.24110e6	−	716547.i	0.552066	−	0.318736i	−0.197889	−	0.980225i	$-0.563408\pi$
$131$	1.24110e6	−	716547.i	0.552066	−	0.318736i	0.749955	+	0.661489i	$0.230075\pi$
$132$		0			0
$133$	−991001.	+	1.71646e6i	−0.421230	+	0.729591i
$134$		−	3.61447e6i		−	1.50221i
$135$		0			0
$136$	4.92149e6			1.95650
$137$	−3.36619e6	−	1.94347e6i	−1.30911	−	0.755816i	−0.327164	−	0.944968i	$-0.606093\pi$
$137$	−3.36619e6	−	1.94347e6i	−1.30911	−	0.755816i	−0.981948	+	0.189152i	$0.939426\pi$
$138$		0			0
$139$	2.53995e6	+	4.39933e6i	0.945760	+	1.63810i	0.754222	+	0.656620i	$0.228014\pi$
$139$	2.53995e6	+	4.39933e6i	0.945760	+	1.63810i	0.191538	+	0.981485i	$0.438652\pi$
$140$	−3.62673e6	+	2.09389e6i	−1.32169	+	0.763080i
$141$		0			0
$142$	−1.90560e6	+	3.30060e6i	−0.665529	+	1.15273i
$143$			1.15903e6i			0.396356i
$144$		0			0
$145$	−4.14970e6			−1.36117
$146$	6.75027e6	+	3.89727e6i	2.16902	+	1.25228i
$147$		0			0
$148$	1.16353e6	+	2.01530e6i	0.358917	+	0.621662i
$149$	842550.	−	486446.i	0.254705	−	0.147054i	−0.367212	−	0.930137i	$-0.619688\pi$
$149$	842550.	−	486446.i	0.254705	−	0.147054i	0.621917	+	0.783084i	$0.286354\pi$
$150$		0			0
$151$	3.13402e6	−	5.42828e6i	0.910271	−	1.57663i	0.0965886	−	0.995324i	$-0.469207\pi$
$151$	3.13402e6	−	5.42828e6i	0.910271	−	1.57663i	0.813682	−	0.581310i	$-0.197460\pi$
$152$			7.76344e6i			2.21067i
$153$		0			0
$154$	2.17951e6			0.596757
$155$	−288231.	−	166410.i	−0.0774008	−	0.0446874i
$156$		0			0
$157$	832183.	+	1.44138e6i	0.215040	+	0.372461i	0.953285	−	0.302072i	$-0.0976783\pi$
$157$	832183.	+	1.44138e6i	0.215040	+	0.372461i	−0.738245	+	0.674533i	$0.764345\pi$
$158$	8.68510e6	−	5.01435e6i	2.20193	−	1.27129i
$159$		0			0
$160$	−859221.	+	1.48822e6i	−0.209771	+	0.363334i
$161$			176973.i			0.0424062i
$162$		0			0
$163$	2.47297e6			0.571025			0.285513	−	0.958375i	$-0.407836\pi$
$163$	2.47297e6			0.571025			0.285513	+	0.958375i	$0.407836\pi$
$164$	−9.69876e6	−	5.59958e6i	−2.19879	−	1.26947i
$165$		0			0
$166$	−2.45951e6	−	4.25999e6i	−0.537680	−	0.931289i
$167$	−5.00452e6	+	2.88936e6i	−1.07452	+	0.620373i	−0.929412	−	0.369044i	$-0.879685\pi$
$167$	−5.00452e6	+	2.88936e6i	−1.07452	+	0.620373i	−0.145105	+	0.989416i	$0.546352\pi$
$168$		0			0
$169$	539017.	−	933604.i	0.111671	−	0.193421i
$170$		−	8.25437e6i		−	1.68011i
$171$		0			0
$172$	−1.71293e7			−3.36630
$173$	−6.80297e6	−	3.92770e6i	−1.31389	−	0.758577i	−0.331156	−	0.943576i	$-0.607438\pi$
$173$	−6.80297e6	−	3.92770e6i	−1.31389	−	0.758577i	−0.982739	+	0.184999i	$0.940772\pi$
$174$		0			0
$175$	−160906.	−	278698.i	−0.0300233	−	0.0520019i
$176$	2.89797e6	−	1.67315e6i	0.531565	−	0.306899i
$177$		0			0
$178$	5.90459e6	−	1.02270e7i	1.04696	−	1.81339i
$179$		−	1.71905e6i		−	0.299730i	−0.988706	−	0.149865i	$-0.952116\pi$
$179$		−	1.71905e6i		−	0.299730i	0.988706	−	0.149865i	$-0.0478839\pi$
$180$		0			0
$181$	−4.16259e6			−0.701985			−0.350993	−	0.936378i	$-0.614156\pi$
$181$	−4.16259e6			−0.701985			−0.350993	+	0.936378i	$0.614156\pi$
$182$	6.10501e6	+	3.52473e6i	1.01268	+	0.584671i
$183$		0			0
$184$	346599.	+	600327.i	0.0556383	+	0.0963684i
$185$	1.78346e6	−	1.02968e6i	0.281674	−	0.162625i
$186$		0			0
$187$	−1.45886e6	+	2.52683e6i	−0.223095	+	0.386412i
$188$			1.12684e7i			1.69585i
$189$		0			0
$190$	1.30209e7			1.89837
$191$	7.35905e6	+	4.24875e6i	1.05614	+	0.609763i	0.924362	−	0.381516i	$-0.124598\pi$
$191$	7.35905e6	+	4.24875e6i	1.05614	+	0.609763i	0.131778	+	0.991279i	$0.457931\pi$
$192$		0			0
$193$	1.99176e6	+	3.44984e6i	0.277055	+	0.479873i	0.970651	−	0.240490i	$-0.0773083\pi$
$193$	1.99176e6	+	3.44984e6i	0.277055	+	0.479873i	−0.693597	+	0.720364i	$0.743975\pi$
$194$	−1.15014e6	+	664033.i	−0.157523	+	0.0909462i
$195$		0			0
$196$	−3.46839e6	+	6.00742e6i	−0.460638	+	0.797848i
$197$		−	5.45308e6i		−	0.713252i	−0.934247	−	0.356626i	$-0.883927\pi$
$197$		−	5.45308e6i		−	0.713252i	0.934247	−	0.356626i	$-0.116073\pi$
$198$		0			0
$199$	3.95878e6			0.502345			0.251172	−	0.967942i	$-0.419184\pi$
$199$	3.95878e6			0.502345			0.251172	+	0.967942i	$0.419184\pi$
$200$	−1.09165e6	−	630265.i	−0.136456	−	0.0787831i
$201$		0			0
$202$	1.90257e6	+	3.29535e6i	0.230827	+	0.399805i
$203$	7.72627e6	−	4.46077e6i	0.923596	−	0.533238i
$204$		0			0
$205$	−4.95540e6	+	8.58300e6i	−0.575198	+	0.996272i
$206$			3.62788e6i			0.415003i
$207$		0			0
$208$	1.08233e7			1.20273
$209$	−3.98596e6	−	2.30129e6i	−0.436610	−	0.252077i
$210$		0			0
$211$	−4.70148e6	−	8.14320e6i	−0.500481	−	0.866858i	−1.00000		0.000555034i	$-0.999823\pi$
$211$	−4.70148e6	−	8.14320e6i	−0.500481	−	0.866858i	0.499519	−	0.866303i	$-0.333510\pi$
$212$	−4.69558e6	+	2.71099e6i	−0.492812	+	0.284525i
$213$		0			0
$214$	−6.94490e6	+	1.20289e7i	−0.708639	+	1.22740i
$215$			1.51587e7i			1.52527i
$216$		0			0
$217$	715538.			0.0700251
$218$	−1.46533e7	−	8.46010e6i	−1.41438	−	0.816594i
$219$		0			0
$220$	−4.86242e6	−	8.42195e6i	−0.456651	−	0.790942i
$221$	−8.17281e6	+	4.71857e6i	−0.757172	+	0.437153i
$222$		0			0
$223$	795234.	−	1.37739e6i	0.0717101	−	0.124205i	−0.827941	−	0.560816i	$-0.810488\pi$
$223$	795234.	−	1.37739e6i	0.0717101	−	0.124205i	0.899651	+	0.436610i	$0.143821\pi$
$224$		−	3.69452e6i		−	0.328711i
$225$		0			0
$226$	4.02630e6			0.348803
$227$	6.81870e6	+	3.93678e6i	0.582940	+	0.336561i	0.762301	−	0.647223i	$-0.224070\pi$
$227$	6.81870e6	+	3.93678e6i	0.582940	+	0.336561i	−0.179361	+	0.983783i	$0.557403\pi$
$228$		0			0
$229$	−1.97961e6	−	3.42878e6i	−0.164844	−	0.285518i	0.771756	−	0.635919i	$-0.219379\pi$
$229$	−1.97961e6	−	3.42878e6i	−0.164844	−	0.285518i	−0.936600	+	0.350401i	$0.886045\pi$
$230$	1.00687e6	−	581319.i	0.0827545	−	0.0477783i
$231$		0			0
$232$	1.74727e7	−	3.02636e7i	1.39925	−	2.42357i
$233$			2.89646e6i			0.228981i	0.993424	+	0.114491i	$0.0365236\pi$
$233$			2.89646e6i			0.228981i	−0.993424	+	0.114491i	$0.963476\pi$
$234$		0			0
$235$	9.97205e6			0.768388
$236$	7.80618e6	+	4.50690e6i	0.593885	+	0.342880i
$237$		0			0
$238$	8.87313e6	+	1.53687e7i	0.658182	+	1.14000i
$239$	−576101.	+	332612.i	−0.0421992	+	0.0243637i	−0.520951	−	0.853586i	$-0.674423\pi$
$239$	−576101.	+	332612.i	−0.0421992	+	0.0243637i	0.478752	+	0.877950i	$0.341089\pi$
$240$		0			0
$241$	−413009.	+	715353.i	−0.0295059	+	0.0511057i	−0.880401	−	0.474229i	$-0.842727\pi$
$241$	−413009.	+	715353.i	−0.0295059	+	0.0511057i	0.850895	+	0.525335i	$0.176060\pi$
$242$		−	1.99604e7i		−	1.40839i
$243$		0			0
$244$	−5.00393e7			−3.44462
$245$	5.31632e6	+	3.06938e6i	0.361504	+	0.208714i
$246$		0			0
$247$	−7.44334e6	−	1.28922e7i	−0.493943	−	0.855535i
$248$	2.42724e6	−	1.40137e6i	0.159132	−	0.0918751i
$249$		0			0
$250$	−1.42876e7	+	2.47469e7i	−0.914409	+	1.58380i
$251$		−	1.12048e7i		−	0.708568i	−0.935138	−	0.354284i	$-0.884725\pi$
$251$		−	1.12048e7i		−	0.708568i	0.935138	−	0.354284i	$-0.115275\pi$
$252$		0			0
$253$	−410965.			−0.0253772
$254$	4.40156e6	+	2.54124e6i	0.268600	+	0.155076i
$255$		0			0
$256$	1.70008e7	+	2.94463e7i	1.01333	+	1.75514i
$257$	6.71894e6	−	3.87918e6i	0.395823	−	0.228529i	−0.288857	−	0.957372i	$-0.593275\pi$
$257$	6.71894e6	−	3.87918e6i	0.395823	−	0.228529i	0.684680	+	0.728844i	$0.259942\pi$
$258$		0			0
$259$	−2.21373e6	+	3.83429e6i	−0.127416	+	0.220692i
$260$		−	3.14542e7i		−	1.78961i
$261$		0			0
$262$	2.02411e7			1.12546
$263$	1.56666e7	+	9.04514e6i	0.861209	+	0.497219i	0.864417	−	0.502776i	$-0.167688\pi$
$263$	1.56666e7	+	9.04514e6i	0.861209	+	0.497219i	−0.00320789	+	0.999995i	$0.501021\pi$
$264$		0			0
$265$	2.39912e6	+	4.15539e6i	0.128918	+	0.223293i
$266$	−2.42435e7	+	1.39970e7i	−1.28810	+	0.743685i
$267$		0			0
$268$	1.73364e7	−	3.00276e7i	0.900648	−	1.55997i
$269$		−	2.74843e7i		−	1.41198i	−0.708222	−	0.705990i	$-0.750502\pi$
$269$		−	2.74843e7i		−	1.41198i	0.708222	−	0.705990i	$-0.249498\pi$
$270$		0			0
$271$	3.70982e6			0.186400			0.0931999	−	0.995647i	$-0.470290\pi$
$271$	3.70982e6			0.186400			0.0931999	+	0.995647i	$0.470290\pi$
$272$	2.35962e7	+	1.36232e7i	1.17256	+	0.676977i
$273$		0			0
$274$	−2.74497e7	−	4.75443e7i	−1.33440	−	2.31125i
$275$	647190.	−	373655.i	0.0311196	−	0.0179669i
$276$		0			0
$277$	1.29022e7	−	2.23472e7i	0.607049	−	1.05144i	−0.384675	−	0.923052i	$-0.625687\pi$
$277$	1.29022e7	−	2.23472e7i	0.607049	−	1.05144i	0.991724	−	0.128387i	$-0.0409801\pi$
$278$			7.17489e7i			3.33950i
$279$		0			0
$280$	−3.12090e7			−1.42169
$281$	−1.85887e7	−	1.07322e7i	−0.837781	−	0.483693i	0.0187281	−	0.999825i	$-0.494038\pi$
$281$	−1.85887e7	−	1.07322e7i	−0.837781	−	0.483693i	−0.856509	+	0.516131i	$0.827372\pi$
$282$		0			0
$283$	4.29799e6	+	7.44434e6i	0.189630	+	0.328448i	0.945127	−	0.326704i	$-0.105938\pi$
$283$	4.29799e6	+	7.44434e6i	0.189630	+	0.328448i	−0.755497	+	0.655152i	$0.772605\pi$
$284$	−3.16620e7	+	1.82800e7i	−1.38224	+	0.798035i
$285$		0			0
$286$	−8.18509e6	+	1.41770e7i	−0.349885	+	0.606019i
$287$		−	2.13074e7i		−	0.901334i
$288$		0			0
$289$	380565.			0.0157665
$290$	−5.07583e7	−	2.93053e7i	−2.08120	−	1.20158i
$291$		0			0
$292$	3.73857e7	+	6.47540e7i	1.50161	+	2.60086i
$293$	2.62704e6	−	1.51672e6i	0.104439	−	0.0602980i	−0.446871	−	0.894599i	$-0.647462\pi$
$293$	2.62704e6	−	1.51672e6i	0.104439	−	0.0602980i	0.551310	+	0.834301i	$0.314128\pi$
$294$		0			0
$295$	3.98842e6	−	6.90815e6i	0.155359	−	0.269089i
$296$			1.73422e7i			0.668697i
$297$		0			0
$298$	1.37412e7			0.519249
$299$	−1.15115e6	−	664617.i	−0.0430644	−	0.0248632i
$300$		0			0
$301$	−1.62950e7	−	2.82238e7i	−0.597523	−	1.03494i
$302$	7.66693e7	−	4.42651e7i	2.78356	−	1.60709i
$303$		0			0
$304$	−2.14901e7	+	3.72219e7i	−0.764922	+	1.32488i
$305$			4.42827e7i			1.56076i
$306$		0			0
$307$	1.14414e7			0.395426			0.197713	−	0.980260i	$-0.436649\pi$
$307$	1.14414e7			0.395426			0.197713	+	0.980260i	$0.436649\pi$
$308$	1.81065e7	+	1.04538e7i	0.619703	+	0.357786i
$309$		0			0
$310$	−2.35039e6	−	4.07100e6i	−0.0788960	−	0.136652i
$311$	−2.38167e7	+	1.37506e7i	−0.791771	+	0.457129i	−0.840586	−	0.541679i	$-0.817789\pi$
$311$	−2.38167e7	+	1.37506e7i	−0.791771	+	0.457129i	0.0488146	+	0.998808i	$0.484456\pi$
$312$		0			0
$313$	−1.26080e7	+	2.18377e7i	−0.411163	+	0.712155i	−0.995017	−	0.0997035i	$-0.968211\pi$
$313$	−1.26080e7	+	2.18377e7i	−0.411163	+	0.712155i	0.583854	+	0.811858i	$0.301544\pi$
$314$			2.35076e7i			0.759311i
$315$		0			0
$316$	9.62032e7			3.04880
$317$	2.38960e7	+	1.37964e7i	0.750150	+	0.433099i	0.825748	−	0.564039i	$-0.190753\pi$
$317$	2.38960e7	+	1.37964e7i	0.750150	+	0.433099i	−0.0755979	+	0.997138i	$0.524087\pi$
$318$		0			0
$319$	1.03587e7	+	1.79419e7i	0.319106	+	0.552708i
$320$	1.61299e7	−	9.31260e6i	0.492245	−	0.284198i
$321$		0			0
$322$	−1.24979e6	+	2.16470e6i	−0.0374343	+	0.0648381i
$323$		−	3.74756e7i		−	1.11209i
$324$		0			0
$325$	2.41711e6			0.0704120
$326$	3.02488e7	+	1.74642e7i	0.873083	+	0.504075i
$327$		0			0
$328$	−4.17303e7	−	7.22790e7i	−1.18258	−	2.04829i
$329$	−1.85668e7	+	1.07196e7i	−0.521375	+	0.301016i
$330$		0			0
$331$	−2.48940e7	+	4.31176e7i	−0.686452	+	1.18897i	0.286527	+	0.958072i	$0.407499\pi$
$331$	−2.48940e7	+	4.31176e7i	−0.686452	+	1.18897i	−0.972978	+	0.230897i	$0.925834\pi$
$332$		−	4.71871e7i		−	1.28946i
$333$		0			0
$334$	−8.16191e7			−2.19055
$335$	−2.65732e7	−	1.53420e7i	−0.706820	−	0.408083i
$336$		0			0
$337$	1.25640e7	+	2.17615e7i	0.328275	+	0.568589i	0.982170	−	0.187997i	$-0.0601994\pi$
$337$	1.25640e7	+	2.17615e7i	0.328275	+	0.568589i	−0.653895	+	0.756586i	$0.726866\pi$
$338$	1.31863e7	−	7.61311e6i	0.341486	−	0.197157i
$339$		0			0
$340$	3.95912e7	−	6.85740e7i	1.00731	−	1.74471i
$341$			1.66162e6i			0.0419052i
$342$		0			0
$343$	−4.35255e7			−1.07860
$344$	−1.10552e8	−	6.38270e7i	−2.71575	−	1.56794i
$345$		0			0
$346$	−5.54751e7	−	9.60857e7i	−1.33927	−	2.31969i
$347$	−6.77305e7	+	3.91042e7i	−1.62105	+	0.935912i	−0.634408	+	0.772999i	$0.718756\pi$
$347$	−6.77305e7	+	3.91042e7i	−1.62105	+	0.935912i	−0.986640	+	0.162914i	$0.947911\pi$
$348$		0			0
$349$	1.64391e6	−	2.84733e6i	0.0386724	−	0.0669826i	−0.846041	−	0.533117i	$-0.821020\pi$
$349$	1.64391e6	−	2.84733e6i	0.0386724	−	0.0669826i	0.884714	+	0.466135i	$0.154354\pi$
$350$		−	4.54530e6i		−	0.106013i
$351$		0			0
$352$	8.57938e6			0.196711
$353$	5.41484e7	+	3.12626e7i	1.23101	+	0.710724i	0.967241	−	0.253861i	$-0.0817006\pi$
$353$	5.41484e7	+	3.12626e7i	1.23101	+	0.710724i	0.263770	+	0.964586i	$0.415034\pi$
$354$		0			0
$355$	1.61771e7	+	2.80195e7i	0.361589	+	0.626290i
$356$	9.81060e7	−	5.66415e7i	2.17443	−	1.25541i
$357$		0			0
$358$	1.21400e7	−	2.10271e7i	0.264588	−	0.458279i
$359$			2.74347e7i			0.592949i	0.955041	+	0.296475i	$0.0958110\pi$
$359$			2.74347e7i			0.592949i	−0.955041	+	0.296475i	$0.904189\pi$
$360$		0			0
$361$	1.20703e7			0.256564
$362$	−5.09160e7	−	2.93964e7i	−1.07332	−	0.619680i
$363$		0			0
$364$	3.38120e7	+	5.85641e7i	0.701078	+	1.21430i
$365$	5.73046e7	−	3.30848e7i	1.17845	−	0.680378i
$366$		0			0
$367$	2.15329e7	−	3.72960e7i	0.435616	−	0.754509i	−0.561730	−	0.827321i	$-0.689864\pi$
$367$	2.15329e7	−	3.72960e7i	0.435616	−	0.754509i	0.997346	+	0.0728120i	$0.0231973\pi$
$368$			3.83770e6i			0.0770066i
$369$		0			0
$370$	2.90865e7			0.574231
$371$	−8.93377e6	−	5.15791e6i	−0.174950	−	0.101007i
$372$		0			0
$373$	1.92734e7	+	3.33826e7i	0.371392	+	0.643270i	0.989780	−	0.142603i	$-0.0455472\pi$
$373$	1.92734e7	+	3.33826e7i	0.371392	+	0.643270i	−0.618388	+	0.785873i	$0.712214\pi$
$374$	−3.56891e7	+	2.06051e7i	−0.682214	+	0.393876i
$375$		0			0
$376$	−4.19882e7	+	7.27257e7i	−0.789884	+	1.36812i
$377$			6.70090e7i			1.25057i
$378$		0			0
$379$	−6.90700e7			−1.26874			−0.634369	−	0.773030i	$-0.718740\pi$
$379$	−6.90700e7			−1.26874			−0.634369	+	0.773030i	$0.718740\pi$
$380$	1.08173e8	+	6.24534e7i	1.97136	+	1.13817i
$381$		0			0
$382$	6.00096e7	+	1.03940e8i	1.07654	+	1.86463i
$383$	−1.05696e7	+	6.10238e6i	−0.188132	+	0.108618i	−0.591108	−	0.806592i	$-0.701309\pi$
$383$	−1.05696e7	+	6.10238e6i	−0.188132	+	0.108618i	0.402976	+	0.915211i	$0.367976\pi$
$384$		0			0
$385$	9.25120e6	−	1.60235e7i	0.162112	−	0.280787i
$386$			5.62636e7i			0.978285i
$387$		0			0
$388$	−1.27399e7			−0.218107
$389$	−4.23039e7	−	2.44242e7i	−0.718674	−	0.414926i	0.0955907	−	0.995421i	$-0.469526\pi$
$389$	−4.23039e7	−	2.44242e7i	−0.718674	−	0.414926i	−0.814264	+	0.580494i	$0.802859\pi$
$390$		0			0
$391$	−1.67310e6	−	2.89790e6i	−0.0279893	−	0.0484789i
$392$	−4.47697e7	+	2.58478e7i	−0.743235	+	0.429107i
$393$		0			0
$394$	3.85098e7	−	6.67010e7i	0.629626	−	1.09054i
$395$		−	8.51359e7i		−	1.38141i
$396$		0			0
$397$	−1.99924e7			−0.319516			−0.159758	−	0.987156i	$-0.551071\pi$
$397$	−1.99924e7			−0.319516			−0.159758	+	0.987156i	$0.551071\pi$
$398$	4.84230e7	+	2.79570e7i	0.768073	+	0.443447i
$399$		0			0
$400$	−3.48929e6	−	6.04362e6i	−0.0545201	−	0.0944316i
$401$	3.74023e7	−	2.15942e7i	0.580049	−	0.334892i	−0.181104	−	0.983464i	$-0.557967\pi$
$401$	3.74023e7	−	2.15942e7i	0.580049	−	0.334892i	0.761153	+	0.648572i	$0.224634\pi$
$402$		0			0
$403$	−2.68718e6	+	4.65433e6i	−0.0410565	+	0.0711119i
$404$			3.65020e7i			0.553570i
$405$		0			0
$406$	1.26008e8			1.88287
$407$	−8.90396e6	−	5.14071e6i	−0.132069	−	0.0762499i
$408$		0			0
$409$	1.84954e7	+	3.20349e7i	0.270329	+	0.468224i	0.968946	−	0.247272i	$-0.0795341\pi$
$409$	1.84954e7	+	3.20349e7i	0.270329	+	0.468224i	−0.698617	+	0.715496i	$0.746201\pi$
$410$	−1.21227e8	+	6.99904e7i	−1.75893	+	1.01552i
$411$		0			0
$412$	−1.74008e7	+	3.01390e7i	−0.248815	+	0.430960i
$413$			1.71496e7i			0.243447i
$414$		0			0
$415$	−4.17586e7			−0.584255
$416$	2.40316e7	+	1.38746e7i	0.333812	+	0.192727i
$417$		0			0
$418$	−3.25036e7	−	5.62979e7i	−0.445044	−	0.770839i
$419$	2.11639e7	−	1.22190e7i	0.287709	−	0.166109i	−0.349199	−	0.937049i	$-0.613546\pi$
$419$	2.11639e7	−	1.22190e7i	0.287709	−	0.166109i	0.636908	+	0.770939i	$0.280213\pi$
$420$		0			0
$421$	5.26175e7	−	9.11362e7i	0.705154	−	1.22136i	−0.261482	−	0.965208i	$-0.584211\pi$
$421$	5.26175e7	−	9.11362e7i	0.705154	−	1.22136i	0.966636	−	0.256154i	$-0.0824554\pi$
$422$		−	1.32808e8i		−	1.76721i
$423$		0			0
$424$	−4.04068e7			−0.530099
$425$	5.26961e6	+	3.04241e6i	0.0686454	+	0.0396325i
$426$		0			0
$427$	−4.76022e7	−	8.24495e7i	−0.611426	−	1.05902i
$428$	−1.15391e8	+	6.66210e7i	−1.47177	+	0.849728i
$429$		0			0
$430$	−1.07051e8	+	1.85418e8i	−1.34644	+	2.33210i
$431$		−	1.45082e8i		−	1.81210i	−0.423166	−	0.906052i	$-0.639081\pi$
$431$		−	1.45082e8i		−	1.81210i	0.423166	−	0.906052i	$-0.360919\pi$
$432$		0			0
$433$	1.53388e8			1.88941			0.944706	−	0.327920i	$-0.106347\pi$
$433$	1.53388e8			1.88941			0.944706	+	0.327920i	$0.106347\pi$
$434$	8.75232e6	+	5.05316e6i	0.107067	+	0.0618150i
$435$		0			0
$436$	−8.11561e7	−	1.40566e8i	−0.979178	−	1.69599i
$437$	4.57130e6	−	2.63924e6i	0.0547767	−	0.0316253i
$438$		0			0
$439$	−2.50547e6	+	4.33960e6i	−0.0296139	+	0.0512928i	−0.880453	−	0.474134i	$-0.842761\pi$
$439$	−2.50547e6	+	4.33960e6i	−0.0296139	+	0.0512928i	0.850839	+	0.525427i	$0.176094\pi$
$440$		−	7.24733e7i		−	0.850785i
$441$		0			0
$442$	−1.33291e8			−1.54360
$443$	5.63189e7	+	3.25157e7i	0.647803	+	0.374009i	0.787614	−	0.616169i	$-0.211316\pi$
$443$	5.63189e7	+	3.25157e7i	0.647803	+	0.374009i	−0.139811	+	0.990178i	$0.544650\pi$
$444$		0			0
$445$	−5.01254e7	−	8.68197e7i	−0.568824	−	0.985232i
$446$	1.94543e7	−	1.12319e7i	0.219286	−	0.126605i
$447$		0			0
$448$	−2.00214e7	+	3.46780e7i	−0.222669	+	0.385674i
$449$			7.25149e7i			0.801103i	0.916274	+	0.400551i	$0.131181\pi$
$449$			7.25149e7i			0.801103i	−0.916274	+	0.400551i	$0.868819\pi$
$450$		0			0
$451$	4.94800e7			0.539386
$452$	3.34489e7	+	1.93117e7i	0.362215	+	0.209125i
$453$		0			0
$454$	5.56033e7	+	9.63078e7i	0.594201	+	1.02919i
$455$	5.18268e7	−	2.99222e7i	0.550200	−	0.317658i
$456$		0			0
$457$	2.85809e7	−	4.95036e7i	0.299452	−	0.518667i	−0.676558	−	0.736389i	$-0.736529\pi$
$457$	2.85809e7	−	4.95036e7i	0.299452	−	0.518667i	0.976011	+	0.217722i	$0.0698627\pi$
$458$		−	5.59202e7i		−	0.582066i
$459$		0			0
$460$	1.11529e7			0.114582
$461$	−1.35879e8	−	7.84499e7i	−1.38692	−	0.800736i	−0.393950	−	0.919132i	$-0.628892\pi$
$461$	−1.35879e8	−	7.84499e7i	−1.38692	−	0.800736i	−0.992966	+	0.118396i	$0.962225\pi$
$462$		0			0
$463$	4.63223e7	+	8.02325e7i	0.466710	+	0.808365i	0.999277	−	0.0380229i	$-0.0121060\pi$
$463$	4.63223e7	+	8.02325e7i	0.466710	+	0.808365i	−0.532567	+	0.846388i	$0.678773\pi$
$464$	1.67546e8	−	9.67327e7i	1.67718	−	0.968321i
$465$		0			0
$466$	−2.04549e7	+	3.54289e7i	−0.202134	+	0.350107i
$467$			1.48541e8i			1.45846i	0.684269	+	0.729230i	$0.260122\pi$
$467$			1.48541e8i			1.45846i	−0.684269	+	0.729230i	$0.739878\pi$
$468$		0			0
$469$	6.59683e7			0.639465
$470$	1.21976e8	+	7.04229e7i	1.17485	+	0.678298i
$471$		0			0
$472$	3.35872e7	+	5.81748e7i	0.319410	+	0.553234i
$473$	6.55410e7	−	3.78401e7i	0.619340	−	0.357576i
$474$		0			0
$475$	−4.79927e6	+	8.31258e6i	−0.0447811	+	0.0775631i
$476$			1.70236e8i			1.57845i
$477$		0			0
$478$	−9.39567e6			−0.0860288
$479$	9.81933e7	+	5.66919e7i	0.893460	+	0.515839i	0.875073	−	0.483992i	$-0.160813\pi$
$479$	9.81933e7	+	5.66919e7i	0.893460	+	0.515839i	0.0183874	+	0.999831i	$0.494147\pi$
$480$		0			0
$481$	−1.66272e7	−	2.87991e7i	−0.149411	−	0.258788i
$482$	−1.01037e7	+	5.83337e6i	−0.0902275	+	0.0520929i
$483$		0			0
$484$	9.57380e7	−	1.65823e8i	0.844400	−	1.46254i
$485$			1.12743e7i			0.0988241i
$486$		0			0
$487$	−1.72741e8			−1.49558			−0.747789	−	0.663937i	$-0.768884\pi$
$487$	−1.72741e8			−1.49558			−0.747789	+	0.663937i	$0.768884\pi$
$488$	−3.22952e8	−	1.86456e8i	−2.77894	−	1.60442i
$489$		0			0
$490$	4.33521e7	+	7.50881e7i	0.368487	+	0.638238i
$491$	−1.40807e8	+	8.12949e7i	−1.18954	+	0.686782i	−0.958202	−	0.286092i	$-0.907644\pi$
$491$	−1.40807e8	+	8.12949e7i	−1.18954	+	0.686782i	−0.231339	+	0.972873i	$0.574311\pi$
$492$		0			0
$493$	−8.43440e7	+	1.46088e8i	−0.703904	+	1.21920i
$494$		−	2.10260e8i		−	1.74412i
$495$		0			0
$496$	1.55166e7			0.127160
$497$	−6.02398e7	−	3.47795e7i	−0.490698	−	0.283305i
$498$		0			0
$499$	−5.94818e7	−	1.03026e8i	−0.478721	−	0.829169i	0.520981	−	0.853568i	$-0.325566\pi$
$499$	−5.94818e7	−	1.03026e8i	−0.478721	−	0.829169i	−0.999702	+	0.0243990i	$0.992233\pi$
$500$	−2.37392e8	+	1.37058e8i	−1.89914	+	1.09647i
$501$		0			0
$502$	7.91285e7	−	1.37055e8i	0.625492	−	1.08338i
$503$		−	5.21107e7i		−	0.409471i	−0.978817	−	0.204736i	$-0.934367\pi$
$503$		−	5.21107e7i		−	0.409471i	0.978817	−	0.204736i	$-0.0656334\pi$
$504$		0			0
$505$	3.23028e7			0.250822
$506$	−5.02685e6	−	2.90225e6i	−0.0388011	−	0.0224018i
$507$		0			0
$508$	2.43776e7	+	4.22233e7i	0.185952	+	0.322078i
$509$	1.99506e8	−	1.15185e8i	1.51287	−	0.873458i	0.512987	−	0.858397i	$-0.328539\pi$
$509$	1.99506e8	−	1.15185e8i	1.51287	−	0.873458i	0.999887	−	0.0150611i	$-0.00479427\pi$
$510$		0			0
$511$	−7.11298e7	+	1.23200e8i	−0.533076	+	0.923314i
$512$			2.81123e8i			2.09453i
$513$		0			0
$514$	1.09580e8			0.806938
$515$	2.66718e7	+	1.53990e7i	0.195268	+	0.112738i
$516$		0			0
$517$	−2.48929e7	−	4.31157e7i	−0.180137	−	0.312007i
$518$	−5.41558e7	+	3.12669e7i	−0.389633	+	0.224955i
$519$		0			0
$520$	1.17204e8	−	2.03004e8i	0.833554	−	1.44376i
$521$			2.01324e8i			1.42358i	0.702392	+	0.711790i	$0.252115\pi$
$521$			2.01324e8i			1.42358i	−0.702392	+	0.711790i	$0.747885\pi$
$522$		0			0
$523$	1.15112e8			0.804669			0.402334	−	0.915493i	$-0.368199\pi$
$523$	1.15112e8			0.804669			0.402334	+	0.915493i	$0.368199\pi$
$524$	1.68155e8	+	9.70844e7i	1.16874	+	0.674770i
$525$		0			0
$526$	1.27754e8	+	2.21277e8i	0.877845	+	1.52047i
$527$	−1.17168e7	+	6.76469e6i	−0.0800528	+	0.0462185i
$528$		0			0
$529$	−7.37823e7	+	1.27795e8i	−0.498408	+	0.863268i
$530$			6.77706e7i			0.455212i
$531$		0			0
$532$	−2.68540e8			−1.78350
$533$	1.38598e8	+	8.00194e7i	0.915323	+	0.528462i
$534$		0			0
$535$	5.89569e7	+	1.02116e8i	0.385011	+	0.666859i
$536$	2.23777e8	−	1.29198e8i	1.45319	−	0.838998i
$537$		0			0
$538$	1.94095e8	−	3.36183e8i	1.24643	−	2.15888i
$539$		−	3.06480e7i		−	0.195720i
$540$		0			0
$541$	−1.95684e8			−1.23584			−0.617921	−	0.786241i	$-0.712025\pi$
$541$	−1.95684e8			−1.23584			−0.617921	+	0.786241i	$0.712025\pi$
$542$	4.53778e7	+	2.61989e7i	0.285001	+	0.164545i
$543$		0			0
$544$	3.49279e7	+	6.04969e7i	0.216958	+	0.375783i
$545$	−1.24396e8	+	7.18198e7i	−0.768449	+	0.443664i
$546$		0			0
$547$	1.66519e7	−	2.88419e7i	0.101742	−	0.176222i	−0.810660	−	0.585517i	$-0.800892\pi$
$547$	1.66519e7	−	2.88419e7i	0.101742	−	0.176222i	0.912402	+	0.409294i	$0.134225\pi$
$548$		−	5.26639e8i		−	3.20016i
$549$		0			0
$550$	1.05551e7			0.0634414
$551$	−2.30448e8	−	1.33049e8i	−1.37758	−	0.795347i
$552$		0			0
$553$	9.15178e7	+	1.58513e8i	0.541166	+	0.937326i
$554$	3.15634e8	−	1.82231e8i	1.85632	−	1.07175i
$555$		0			0
$556$	−3.44136e8	+	5.96062e8i	−2.00219	+	3.46790i
$557$			2.14530e7i			0.124143i	0.998072	+	0.0620716i	$0.0197707\pi$
$557$			2.14530e7i			0.124143i	−0.998072	+	0.0620716i	$0.980229\pi$
$558$		0			0
$559$	2.44781e8			1.40134
$560$	−1.49632e8	−	8.63901e7i	−0.852041	−	0.491926i
$561$		0			0
$562$	−1.51582e8	−	2.62548e8i	−0.853965	−	1.47911i
$563$	5.21863e7	−	3.01297e7i	0.292436	−	0.168838i	−0.346604	−	0.938012i	$-0.612665\pi$
$563$	5.21863e7	−	3.01297e7i	0.292436	−	0.168838i	0.639040	+	0.769174i	$0.279332\pi$
$564$		0			0
$565$	1.70901e7	−	2.96009e7i	0.0947543	−	0.164119i
$566$			1.21410e8i			0.669586i
$567$		0			0
$568$	−2.72460e8			−1.48682
$569$	−2.39117e8	−	1.38054e8i	−1.29800	−	0.749398i	−0.317938	−	0.948112i	$-0.602990\pi$
$569$	−2.39117e8	−	1.38054e8i	−1.29800	−	0.749398i	−0.980058	+	0.198714i	$0.936324\pi$
$570$		0			0
$571$	−1.49346e8	−	2.58675e8i	−0.802204	−	1.38946i	−0.918162	−	0.396205i	$-0.870327\pi$
$571$	−1.49346e8	−	2.58675e8i	−0.802204	−	1.38946i	0.115958	−	0.993254i	$-0.463006\pi$
$572$	−1.35997e8	+	7.85179e7i	−0.726677	+	0.419547i
$573$		0			0
$574$	1.50474e8	−	2.60628e8i	0.795656	−	1.37812i
$575$			857055.i			0.00450822i
$576$		0			0
$577$	9.68320e7			0.504071			0.252035	−	0.967718i	$-0.418900\pi$
$577$	9.68320e7			0.504071			0.252035	+	0.967718i	$0.418900\pi$
$578$	4.65499e6	+	2.68756e6i	0.0241066	+	0.0139179i
$579$		0			0
$580$	−2.81120e8	−	4.86914e8i	−1.44081	−	2.49556i
$581$	7.77499e7	−	4.48889e7i	0.396435	−	0.228882i
$582$		0			0
$583$	1.19777e7	−	2.07459e7i	0.0604458	−	0.104695i
$584$			5.57226e8i			2.79765i
$585$		0			0
$586$	4.28446e7			0.212913
$587$	8.25319e7	+	4.76498e7i	0.408044	+	0.235585i	0.689949	−	0.723858i	$-0.257633\pi$
$587$	8.25319e7	+	4.76498e7i	0.408044	+	0.235585i	−0.281905	+	0.959442i	$0.590966\pi$
$588$		0			0
$589$	−1.06710e7	−	1.84827e7i	−0.0522227	−	0.0904523i
$590$	9.75712e7	−	5.63328e7i	0.475079	−	0.274287i
$591$		0			0
$592$	−4.80052e7	+	8.31475e7i	−0.231379	+	0.400760i
$593$		−	5.27042e7i		−	0.252744i	−0.991983	−	0.126372i	$-0.959667\pi$
$593$		−	5.27042e7i		−	0.252744i	0.991983	−	0.126372i	$-0.0403333\pi$
$594$		0			0
$595$	1.50652e8			0.715194
$596$	1.14156e8	+	6.59083e7i	0.539215	+	0.311316i
$597$		0			0
$598$	−9.38709e6	−	1.62589e7i	−0.0438963	−	0.0760305i
$599$	−2.56013e8	+	1.47809e8i	−1.19119	+	0.687733i	−0.958576	−	0.284836i	$-0.908061\pi$
$599$	−2.56013e8	+	1.47809e8i	−1.19119	+	0.687733i	−0.232613	+	0.972569i	$0.574728\pi$
$600$		0			0
$601$	9.74992e7	−	1.68874e8i	0.449136	−	0.777926i	−0.549194	−	0.835695i	$-0.685065\pi$
$601$	9.74992e7	−	1.68874e8i	0.449136	−	0.777926i	0.998330	+	0.0577686i	$0.0183986\pi$
$602$		−	4.60303e8i		−	2.10986i
$603$		0			0
$604$	8.49252e8			3.85412
$605$	−1.46747e8	−	8.47242e7i	−0.662677	−	0.382597i
$606$		0			0
$607$	7.29203e7	+	1.26302e8i	0.326049	+	0.564733i	0.981724	−	0.190310i	$-0.0609493\pi$
$607$	7.29203e7	+	1.26302e8i	0.326049	+	0.564733i	−0.655675	+	0.755043i	$0.727616\pi$
$608$	−9.54313e7	+	5.50973e7i	−0.424600	+	0.245143i
$609$		0			0
$610$	−3.12726e8	+	5.41658e8i	−1.37776	+	2.38636i
$611$		−	1.61028e8i		−	0.705955i
$612$		0			0
$613$	−4.48295e8			−1.94618			−0.973089	−	0.230431i	$-0.925986\pi$
$613$	−4.48295e8			−1.94618			−0.973089	+	0.230431i	$0.925986\pi$
$614$	1.39949e8	+	8.07997e7i	0.604596	+	0.349064i
$615$		0			0
$616$	7.79060e7	+	1.34937e8i	0.333295	+	0.577284i
$617$	−1.11067e8	+	6.41247e7i	−0.472857	+	0.273004i	−0.717435	−	0.696625i	$-0.754684\pi$
$617$	−1.11067e8	+	6.41247e7i	−0.472857	+	0.273004i	0.244578	+	0.969630i	$0.421351\pi$
$618$		0			0
$619$	2.15337e6	−	3.72975e6i	0.00907919	−	0.0157256i	−0.861450	−	0.507842i	$-0.830443\pi$
$619$	2.15337e6	−	3.72975e6i	0.00907919	−	0.0157256i	0.870529	+	0.492117i	$0.163777\pi$
$620$		−	4.50936e7i		−	0.189208i
$621$		0			0
$622$	−3.88427e8			−1.61413
$623$	1.86656e8	+	1.07766e8i	0.771929	+	0.445673i
$624$		0			0
$625$	1.11538e8	+	1.93189e8i	0.456860	+	0.791304i
$626$	−3.08438e8	+	1.78077e8i	−1.25732	+	0.725912i
$627$		0			0
$628$	−1.12752e8	+	1.95292e8i	−0.455245	+	0.788508i
$629$		−	8.37143e7i		−	0.336394i
$630$		0			0
$631$	2.51870e6			0.0100251			0.00501255	−	0.999987i	$-0.498404\pi$
$631$	2.51870e6			0.0100251			0.00501255	+	0.999987i	$0.498404\pi$
$632$	6.20892e8	+	3.58472e8i	2.45960	+	1.42005i
$633$		0			0
$634$	1.94861e8	+	3.37509e8i	0.764641	+	1.32440i
$635$	3.73659e7	−	2.15732e7i	0.145933	−	0.0842545i
$636$		0			0
$637$	4.95641e7	−	8.58475e7i	0.191756	−	0.332131i
$638$			2.92615e8i			1.12677i
$639$		0			0
$640$	3.73044e8			1.42305
$641$	1.94736e8	+	1.12431e8i	0.739387	+	0.426885i	0.821846	−	0.569709i	$-0.192944\pi$
$641$	1.94736e8	+	1.12431e8i	0.739387	+	0.426885i	−0.0824597	+	0.996594i	$0.526278\pi$
$642$		0			0
$643$	1.85392e8	+	3.21108e8i	0.697360	+	1.20786i	0.969378	+	0.245572i	$0.0789756\pi$
$643$	1.85392e8	+	3.21108e8i	0.697360	+	1.20786i	−0.272018	+	0.962292i	$0.587691\pi$
$644$	−2.07655e7	+	1.19890e7i	−0.0777473	+	0.0448874i
$645$		0			0
$646$	2.64654e8	−	4.58394e8i	0.981705	−	1.70036i
$647$		−	1.34128e8i		−	0.495230i	−0.968858	−	0.247615i	$-0.920353\pi$
$647$		−	1.34128e8i		−	0.495230i	0.968858	−	0.247615i	$-0.0796468\pi$
$648$		0			0
$649$	−3.98246e7			−0.145686
$650$	2.95656e7	+	1.70697e7i	0.107658	+	0.0621565i
$651$		0			0
$652$	1.67530e8	+	2.90171e8i	0.604436	+	1.04691i
$653$	1.53586e8	−	8.86727e7i	0.551583	−	0.318457i	−0.198177	−	0.980166i	$-0.563502\pi$
$653$	1.53586e8	−	8.86727e7i	0.551583	−	0.318457i	0.749760	+	0.661710i	$0.230169\pi$
$654$		0			0
$655$	8.59157e7	−	1.48810e8i	0.305738	−	0.529553i
$656$		−	4.62057e8i		−	1.63676i
$657$		0			0
$658$	−3.02808e8			−1.06289
$659$	1.53754e8	+	8.87701e7i	0.537243	+	0.310177i	0.743961	−	0.668223i	$-0.232945\pi$
$659$	1.53754e8	+	8.87701e7i	0.537243	+	0.310177i	−0.206718	+	0.978401i	$0.566278\pi$
$660$		0			0
$661$	−2.74792e8	−	4.75953e8i	−0.951479	−	1.64801i	−0.742228	−	0.670148i	$-0.766231\pi$
$661$	−2.74792e8	−	4.75953e8i	−0.951479	−	1.64801i	−0.209251	−	0.977862i	$-0.567103\pi$
$662$	−6.08996e8	+	3.51604e8i	−2.09914	+	1.21194i
$663$		0			0
$664$	1.75828e8	−	3.04544e8i	0.600600	−	1.04027i
$665$			2.37647e8i			0.808104i
$666$		0			0
$667$	−2.37599e7			−0.0800695
$668$	−6.78059e8	−	3.91478e8i	−2.27477	−	1.31334i
$669$		0			0
$670$	−2.16692e8	−	3.75321e8i	−0.720474	−	1.24790i
$671$	1.91463e8	−	1.10541e8i	0.633751	−	0.365896i
$672$		0			0
$673$	−1.22468e8	+	2.12121e8i	−0.401770	+	0.695886i	−0.993940	−	0.109927i	$-0.964938\pi$
$673$	−1.22468e8	+	2.12121e8i	−0.401770	+	0.695886i	0.592170	+	0.805813i	$0.298272\pi$
$674$			3.54909e8i			1.15914i
$675$		0			0
$676$	1.46062e8			0.472821
$677$	−4.25927e8	−	2.45909e8i	−1.37268	−	0.792518i	−0.381416	−	0.924404i	$-0.624563\pi$
$677$	−4.25927e8	−	2.45909e8i	−1.37268	−	0.792518i	−0.991265	+	0.131886i	$0.957897\pi$
$678$		0			0
$679$	−1.21194e7	−	2.09914e7i	−0.0387143	−	0.0670552i
$680$	5.11041e8	−	2.95050e8i	1.62528	−	0.938357i
$681$		0			0
$682$	−1.17344e7	+	2.03246e7i	−0.0369920	+	0.0640720i
$683$			5.92974e8i			1.86112i	0.366143	+	0.930559i	$0.380678\pi$
$683$			5.92974e8i			1.86112i	−0.366143	+	0.930559i	$0.619322\pi$
$684$		0			0
$685$	−4.66054e8			−1.44999
$686$	−5.32396e8	−	3.07379e8i	−1.64916	−	0.952142i
$687$		0			0
$688$	−3.53361e8	−	6.12038e8i	−1.08506	−	1.87937i
$689$	6.71009e7	−	3.87407e7i	0.205150	−	0.118443i
$690$		0			0
$691$	1.74226e8	−	3.01769e8i	0.528056	−	0.914620i	−0.471409	−	0.881915i	$-0.656254\pi$
$691$	1.74226e8	−	3.01769e8i	0.528056	−	0.914620i	0.999465	−	0.0327051i	$-0.0104122\pi$
$692$		−	1.06432e9i		−	3.21185i
$693$		0			0
$694$	−1.10462e9			−3.30472
$695$	5.27490e8	+	3.04546e8i	1.57130	+	0.907192i
$696$		0			0
$697$	2.01440e8	+	3.48905e8i	0.594906	+	1.03041i
$698$	4.02159e7	−	2.32187e7i	0.118258	−	0.0682765i
$699$		0			0
$700$	2.18011e7	−	3.77606e7i	0.0635600	−	0.110089i
$701$		−	5.37432e8i		−	1.56016i	−0.625679	−	0.780080i	$-0.715178\pi$
$701$		−	5.37432e8i		−	1.56016i	0.625679	−	0.780080i	$-0.284822\pi$
$702$		0			0
$703$	1.32056e8			0.380094
$704$	−8.05290e7	−	4.64934e7i	−0.230799	−	0.133252i
$705$		0			0
$706$	4.41555e8	+	7.64796e8i	1.25479	+	2.17336i
$707$	−6.01441e7	+	3.47242e7i	−0.170190	+	0.0982594i
$708$		0			0
$709$	−7.46671e7	+	1.29327e8i	−0.209503	+	0.362870i	−0.951558	−	0.307469i	$-0.900518\pi$
$709$	−7.46671e7	+	1.29327e8i	−0.209503	+	0.362870i	0.742055	+	0.670339i	$0.233851\pi$
$710$			4.56972e8i			1.27678i
$711$		0			0
$712$	8.44230e8			2.33895
$713$	−1.65032e6	−	952815.i	−0.00455303	−	0.00262869i
$714$		0			0
$715$	6.94851e7	+	1.20352e8i	0.190096	+	0.329256i
$716$	2.01709e8	−	1.16457e8i	0.549522	−	0.317267i
$717$		0			0
$718$	−1.93745e8	+	3.35576e8i	−0.523429	+	0.906605i
$719$		−	7.89635e7i		−	0.212442i	−0.994343	−	0.106221i	$-0.966125\pi$
$719$		−	7.89635e7i		−	0.212442i	0.994343	−	0.106221i	$-0.0338751\pi$
$720$		0			0
$721$	−6.62132e7			−0.176660
$722$	1.47641e8	+	8.52407e7i	0.392280	+	0.226483i
$723$		0			0
$724$	−2.81993e8	−	4.88427e8i	−0.743059	−	1.28702i
$725$	3.74172e7	−	2.16028e7i	0.0981877	−	0.0566887i
$726$		0			0
$727$	−4.83494e7	+	8.37436e7i	−0.125831	+	0.217946i	−0.922057	−	0.387053i	$-0.873493\pi$
$727$	−4.83494e7	+	8.37436e7i	−0.125831	+	0.217946i	0.796226	+	0.604999i	$0.206826\pi$
$728$			5.03961e8i			1.30618i
$729$		0			0
$730$	9.34585e8			2.40243
$731$	5.33654e8	+	3.08105e8i	1.36618	+	0.788764i
$732$		0			0
$733$	−6.61563e7	−	1.14586e8i	−0.167981	−	0.290951i	0.769729	−	0.638371i	$-0.220391\pi$
$733$	−6.61563e7	−	1.14586e8i	−0.167981	−	0.290951i	−0.937710	+	0.347420i	$0.887058\pi$
$734$	5.26771e8	−	3.04132e8i	1.33209	−	0.769083i
$735$		0			0
$736$	−4.91964e6	+	8.52107e6i	−0.0123396	+	0.0213728i
$737$			1.53191e8i			0.382676i
$738$		0			0
$739$	−2.72581e7			−0.0675401			−0.0337700	−	0.999430i	$-0.510751\pi$
$739$	−2.72581e7			−0.0675401			−0.0337700	+	0.999430i	$0.510751\pi$
$740$	2.41639e8	+	1.39511e8i	0.596311	+	0.344280i
$741$		0			0
$742$	−7.28507e7	−	1.26181e8i	−0.178329	−	0.308875i
$743$	−1.77637e7	+	1.02559e7i	−0.0433078	+	0.0250038i	−0.521498	−	0.853253i	$-0.674626\pi$
$743$	−1.77637e7	+	1.02559e7i	−0.0433078	+	0.0250038i	0.478190	+	0.878257i	$0.341293\pi$
$744$		0			0
$745$	5.83261e7	−	1.01024e8i	0.141057	−	0.244318i
$746$			5.44439e8i			1.31139i
$747$		0			0
$748$	−3.95321e8			−0.944594
$749$	−2.19542e8	−	1.26753e8i	−0.522483	−	0.301656i
$750$		0			0
$751$	−3.15842e8	−	5.47054e8i	−0.745676	−	1.29155i	−0.949878	−	0.312620i	$-0.898793\pi$
$751$	−3.15842e8	−	5.47054e8i	−0.745676	−	1.29155i	0.204202	−	0.978929i	$-0.434540\pi$
$752$	−4.02626e8	+	2.32456e8i	−0.946778	+	0.546622i
$753$		0			0
$754$	−4.73220e8	+	8.19641e8i	−1.10395	+	1.91210i
$755$		−	7.51553e8i		−	1.74630i
$756$		0			0
$757$	6.20833e8			1.43116			0.715578	−	0.698533i	$-0.246163\pi$
$757$	6.20833e8			1.43116			0.715578	+	0.698533i	$0.246163\pi$
$758$	−8.44851e8	−	4.87775e8i	−1.93987	−	1.11998i
$759$		0			0
$760$	4.65428e8	+	8.06144e8i	1.06026	+	1.83642i
$761$	−7.24053e8	+	4.18032e8i	−1.64292	+	0.948540i	−0.663130	+	0.748504i	$0.730772\pi$
$761$	−7.24053e8	+	4.18032e8i	−1.64292	+	0.948540i	−0.979789	+	0.200035i	$0.935894\pi$
$762$		0			0
$763$	1.54407e8	−	2.67441e8i	0.347611	−	0.602080i
$764$			1.15132e9i			2.58176i
$765$		0			0
$766$	−1.72381e8			−0.383533
$767$	−1.11552e8	−	6.44047e7i	−0.247225	−	0.142735i
$768$		0			0
$769$	−6.70941e7	−	1.16210e8i	−0.147538	−	0.255544i	0.782779	−	0.622300i	$-0.213802\pi$
$769$	−6.70941e7	−	1.16210e8i	−0.147538	−	0.255544i	−0.930317	+	0.366756i	$0.880468\pi$
$770$	2.26318e8	−	1.30665e8i	0.495731	−	0.286211i
$771$		0			0
$772$	−2.69863e8	+	4.67416e8i	−0.586531	+	1.01590i
$773$		−	5.46031e8i		−	1.18217i	−0.806611	−	0.591083i	$-0.798701\pi$
$773$		−	5.46031e8i		−	1.18217i	0.806611	−	0.591083i	$-0.201299\pi$
$774$		0			0
$775$	3.46525e6			0.00744439
$776$	−8.22227e7	−	4.74713e7i	−0.175957	−	0.101589i
$777$		0			0
$778$	−3.44969e8	−	5.97503e8i	−0.732556	−	1.26882i
$779$	−5.50382e8	+	3.17763e8i	−1.16427	+	0.672189i
$780$		0			0
$781$	8.07646e7	−	1.39888e8i	0.169538	−	0.293649i
$782$		−	4.72620e7i		−	0.0988307i
$783$		0			0
$784$	−2.86198e8			−0.593908
$785$	1.72826e8	+	9.97809e7i	0.357272	+	0.206271i
$786$		0			0
$787$	1.03958e8	+	1.80060e8i	0.213272	+	0.369397i	0.952736	−	0.303798i	$-0.0982548\pi$
$787$	1.03958e8	+	1.80060e8i	0.213272	+	0.369397i	−0.739465	+	0.673195i	$0.764921\pi$
$788$	6.39849e8	−	3.69417e8i	1.30767	−	0.754984i
$789$		0			0
$790$	6.01233e8	−	1.04137e9i	1.21944	−	2.11214i
$791$			7.34847e7i			0.148480i
$792$		0			0
$793$	7.15074e8			1.43394
$794$	−2.44543e8	−	1.41187e8i	−0.488533	−	0.282055i
$795$		0			0
$796$	2.68186e8	+	4.64512e8i	0.531737	+	0.920996i
$797$	6.08306e8	−	3.51206e8i	1.20157	−	0.693724i	0.240662	−	0.970609i	$-0.422635\pi$
$797$	6.08306e8	−	3.51206e8i	1.20157	−	0.693724i	0.960903	+	0.276885i	$0.0893021\pi$
$798$		0			0
$799$	2.02685e8	−	3.51061e8i	0.397358	−	0.688244i
$800$		−	1.78920e7i		−	0.0349453i
$801$		0			0
$802$	6.09996e8			1.18251
$803$	−2.86095e8	−	1.65177e8i	−0.552540	−	0.319009i
$804$		0			0
$805$	1.06098e7	+	1.83766e7i	0.0203385	+	0.0352272i
$806$	−6.57381e7	+	3.79539e7i	−0.125549	+	0.0724855i
$807$		0			0
$808$	−1.36014e8	+	2.35583e8i	−0.257839	+	0.446590i
$809$			8.20042e8i			1.54878i	0.632707	+	0.774392i	$0.281944\pi$
$809$			8.20042e8i			1.54878i	−0.632707	+	0.774392i	$0.718056\pi$
$810$		0			0
$811$	−6.91041e8			−1.29551			−0.647756	−	0.761848i	$-0.724292\pi$
$811$	−6.91041e8			−1.29551			−0.647756	+	0.761848i	$0.724292\pi$
$812$	1.04683e9	+	6.04386e8i	1.95527	+	1.12888i
$813$		0			0
$814$	−7.26077e7	−	1.25760e8i	−0.134620	−	0.233169i
$815$	2.56789e8	−	1.48257e8i	0.474356	−	0.273869i
$816$		0			0
$817$	−4.86023e8	+	8.41816e8i	−0.891231	+	1.54366i
$818$			5.22459e8i			0.954537i
$819$		0			0
$820$	−1.34281e9			−2.43541
$821$	−6.01769e8	−	3.47432e8i	−1.08743	−	0.627827i	−0.154538	−	0.987987i	$-0.549389\pi$
$821$	−6.01769e8	−	3.47432e8i	−1.08743	−	0.627827i	−0.932891	+	0.360160i	$0.882722\pi$
$822$		0			0
$823$	−7.18960e7	−	1.24528e8i	−0.128975	−	0.223391i	0.794305	−	0.607519i	$-0.207835\pi$
$823$	−7.18960e7	−	1.24528e8i	−0.128975	−	0.223391i	−0.923280	+	0.384128i	$0.874502\pi$
$824$	−2.24608e8	+	1.29677e8i	−0.401461	+	0.231784i
$825$		0			0
$826$	−1.21111e8	+	2.09770e8i	−0.214904	+	0.372224i
$827$		−	6.36987e8i		−	1.12620i	−0.826390	−	0.563098i	$-0.809609\pi$
$827$		−	6.36987e8i		−	1.12620i	0.826390	−	0.563098i	$-0.190391\pi$
$828$		0			0
$829$	9.52328e7			0.167156			0.0835782	−	0.996501i	$-0.473365\pi$
$829$	9.52328e7			0.167156			0.0835782	+	0.996501i	$0.473365\pi$
$830$	−5.10784e8	−	2.94901e8i	−0.893311	−	0.515753i
$831$		0			0
$832$	−1.50379e8	−	2.60464e8i	−0.261106	−	0.452250i
$833$	2.16112e8	−	1.24772e8i	0.373890	−	0.215866i
$834$		0			0
$835$	−3.46442e8	+	6.00055e8i	−0.595074	+	1.03070i
$836$		−	6.23601e8i		−	1.06730i
$837$		0			0
$838$	3.45164e8			0.586534
$839$	2.46672e8	+	1.42416e8i	0.417671	+	0.241143i	0.694081	−	0.719897i	$-0.255811\pi$
$839$	2.46672e8	+	1.42416e8i	0.417671	+	0.241143i	−0.276409	+	0.961040i	$0.589144\pi$
$840$		0			0
$841$	3.01478e8	+	5.22175e8i	0.506836	+	0.877866i
$842$	1.28721e9	−	7.43173e8i	2.15633	−	1.24496i
$843$		0			0
$844$	6.37000e8	−	1.10332e9i	1.05953	−	1.83516i
$845$		−	1.29259e8i		−	0.214235i
$846$		0			0
$847$	3.64301e8			0.599529
$848$	−1.93731e8	−	1.11851e8i	−0.317695	−	0.183422i
$849$		0			0
$850$	4.29712e7	+	7.44283e7i	0.0699715	+	0.121194i
$851$	1.02115e7	−	5.89563e6i	0.0165692	−	0.00956625i
$852$		0			0
$853$	4.56817e7	−	7.91230e7i	0.0736029	−	0.127484i	−0.826875	−	0.562386i	$-0.809884\pi$
$853$	4.56817e7	−	7.91230e7i	0.0736029	−	0.127484i	0.900478	+	0.434902i	$0.143217\pi$
$854$		−	1.34467e9i		−	2.15895i
$855$		0			0
$856$	−9.92973e8			−1.58313
$857$	4.56487e8	+	2.63553e8i	0.725247	+	0.418721i	0.816681	−	0.577090i	$-0.195812\pi$
$857$	4.56487e8	+	2.63553e8i	0.725247	+	0.418721i	−0.0914341	+	0.995811i	$0.529145\pi$
$858$		0			0
$859$	1.81645e8	+	3.14618e8i	0.286578	+	0.496368i	0.972991	−	0.230845i	$-0.0741489\pi$
$859$	1.81645e8	+	3.14618e8i	0.286578	+	0.496368i	−0.686413	+	0.727212i	$0.740816\pi$
$860$	−1.77868e9	+	1.02692e9i	−2.79642	+	1.61451i
$861$		0			0
$862$	1.02458e9	−	1.77462e9i	1.59964	−	2.77066i
$863$			9.96932e8i			1.55108i	0.631300	+	0.775538i	$0.282522\pi$
$863$			9.96932e8i			1.55108i	−0.631300	+	0.775538i	$0.717478\pi$
$864$		0			0
$865$	−9.41881e8			−1.45528
$866$	1.87621e9	+	1.08323e9i	2.88886	+	1.66789i
$867$		0			0
$868$	4.84739e7	+	8.39593e7i	0.0741223	+	0.128384i
$869$	−3.68099e8	+	2.12522e8i	−0.560925	+	0.323850i
$870$		0			0
$871$	−2.47742e8	+	4.29101e8i	−0.374925	+	0.649390i
$872$		−	1.20961e9i		−	1.82430i
$873$		0			0
$874$	7.45537e7			0.111670
$875$	−4.51661e8	−	2.60766e8i	−0.674199	−	0.389249i
$876$		0			0
$877$	−4.01845e8	−	6.96015e8i	−0.595744	−	1.03186i	−0.993441	−	0.114342i	$-0.963524\pi$
$877$	−4.01845e8	−	6.96015e8i	−0.595744	−	1.03186i	0.397698	−	0.917517i	$-0.369809\pi$
$878$	−6.12928e7	+	3.53874e7i	−0.0905578	+	0.0522836i
$879$		0			0
$880$	2.00614e8	−	3.47474e8i	0.294384	−	0.509888i
$881$			1.05052e8i			0.153630i	0.997045	+	0.0768151i	$0.0244751\pi$
$881$			1.05052e8i			0.153630i	−0.997045	+	0.0768151i	$0.975525\pi$
$882$		0			0
$883$	−8.90921e7			−0.129407			−0.0647034	−	0.997905i	$-0.520610\pi$
$883$	−8.90921e7			−0.129407			−0.0647034	+	0.997905i	$0.520610\pi$
$884$	−1.10733e9	−	6.39316e8i	−1.60295	−	0.925463i
$885$		0			0
$886$	4.59254e8	+	7.95452e8i	0.660316	+	1.14370i
$887$	−8.98422e8	+	5.18704e8i	−1.28739	+	0.743274i	−0.978188	−	0.207722i	$-0.933395\pi$
$887$	−8.98422e8	+	5.18704e8i	−1.28739	+	0.743274i	−0.309201	+	0.950997i	$0.600062\pi$
$888$		0			0
$889$	−4.63807e7	+	8.03337e7i	−0.0660134	+	0.114339i
$890$		−	1.41595e9i		−	2.00853i
$891$		0			0
$892$	2.15491e8			0.303623
$893$	5.53783e8	+	3.19727e8i	0.777652	+	0.448978i
$894$		0			0
$895$	−1.03059e8	−	1.78504e8i	−0.143753	−	0.248988i
$896$	−6.94566e8	+	4.01008e8i	−0.965582	+	0.557479i
$897$		0			0
$898$	−5.12103e8	+	8.86988e8i	−0.707177	+	1.22487i
$899$			9.60662e7i			0.132218i
$900$		0			0
$901$	1.95051e8			0.266670
$902$	6.05229e8	+	3.49429e8i	0.824708	+	0.476145i
$903$		0			0
$904$	1.43919e8	+	2.49274e8i	0.194810	+	0.337421i
$905$	−4.32238e8	+	2.49552e8i	−0.583145	+	0.336679i
$906$		0			0
$907$	−2.83227e8	+	4.90564e8i	−0.379589	+	0.657467i	−0.991002	−	0.133844i	$-0.957268\pi$
$907$	−2.83227e8	+	4.90564e8i	−0.379589	+	0.657467i	0.611414	+	0.791311i	$0.290601\pi$
$908$			1.06678e9i			1.42501i
$909$		0			0
$910$	8.45247e8			1.12166
$911$	−7.72892e8	−	4.46229e8i	−1.02227	−	0.590205i	−0.107506	−	0.994204i	$-0.534286\pi$
$911$	−7.72892e8	−	4.46229e8i	−1.02227	−	0.590205i	−0.914759	+	0.403999i	$0.867620\pi$
$912$		0			0
$913$	1.04241e8	+	1.80550e8i	0.136970	+	0.237239i
$914$	6.99193e8	−	4.03679e8i	0.915711	−	0.528686i
$915$		0			0
$916$	2.68216e8	−	4.64563e8i	0.348978	−	0.604447i
$917$			3.69424e8i			0.479090i
$918$		0			0
$919$	2.10427e8			0.271116			0.135558	−	0.990769i	$-0.456717\pi$
$919$	2.10427e8			0.271116			0.135558	+	0.990769i	$0.456717\pi$
$920$	7.19807e7	+	4.15581e7i	0.0924385	+	0.0533694i
$921$		0			0
$922$	−1.10803e9	−	1.91917e9i	−1.41371	−	2.44861i
$923$	4.52457e8	−	2.61226e8i	0.575403	−	0.332209i
$924$		0			0
$925$	−1.07208e7	+	1.85689e7i	−0.0135457	+	0.0234618i
$926$			1.30852e9i			1.64796i
$927$		0			0
$928$	4.96016e8			0.620657
$929$	7.86889e8	+	4.54310e8i	0.981445	+	0.566638i	0.902706	−	0.430257i	$-0.141577\pi$
$929$	7.86889e8	+	4.54310e8i	0.981445	+	0.566638i	0.0787392	+	0.996895i	$0.474911\pi$
$930$		0			0
$931$	1.96823e8	+	3.40907e8i	0.243908	+	0.422462i
$932$	−3.39863e8	+	1.96220e8i	−0.419813	+	0.242379i
$933$		0			0
$934$	−1.04900e9	+	1.81692e9i	−1.28746	+	2.22995i
$935$			3.49843e8i			0.427994i
$936$		0			0
$937$	1.34303e9			1.63255			0.816275	−	0.577663i	$-0.196035\pi$
$937$	1.34303e9			1.63255			0.816275	+	0.577663i	$0.196035\pi$
$938$	8.06912e8	+	4.65871e8i	0.977727	+	0.564491i
$939$		0			0
$940$	6.75553e8	+	1.17009e9i	0.813347	+	1.40876i
$941$	8.97969e8	−	5.18443e8i	1.07769	−	0.622202i	0.147415	−	0.989075i	$-0.452905\pi$
$941$	8.97969e8	−	5.18443e8i	1.07769	−	0.622202i	0.930271	+	0.366872i	$0.119571\pi$
$942$		0			0
$943$	−2.83731e7	+	4.91437e7i	−0.0338354	+	0.0586047i
$944$			3.71893e8i			0.442081i
$945$		0			0
$946$	1.06891e9			1.26261
$947$	−2.00750e8	−	1.15903e8i	−0.236377	−	0.136472i	0.377133	−	0.926159i	$-0.376910\pi$
$947$	−2.00750e8	−	1.15903e8i	−0.236377	−	0.136472i	−0.613510	+	0.789687i	$0.710243\pi$
$948$		0			0
$949$	−5.34251e8	−	9.25350e8i	−0.625096	−	1.08270i
$950$	−1.17407e8	+	6.77852e7i	−0.136938	+	0.0790613i
$951$		0			0
$952$	−6.34334e8	+	1.09870e9i	−0.735202	+	1.27341i
$953$		−	2.56619e8i		−	0.296490i	−0.988951	−	0.148245i	$-0.952638\pi$
$953$		−	2.56619e8i		−	0.296490i	0.988951	−	0.148245i	$-0.0473625\pi$
$954$		0			0
$955$	1.01887e9			1.16979
$956$	−7.80555e7	−	4.50654e7i	−0.0893367	−	0.0515785i
$957$		0			0
$958$	8.00720e8	+	1.38689e9i	0.910719	+	1.57741i
$959$	8.67739e8	−	5.00990e8i	0.983860	−	0.568032i
$960$		0			0
$961$	4.39899e8	−	7.61928e8i	0.495659	−	0.858507i
$962$		−	4.69687e8i		−	0.527574i
$963$		0			0
$964$	−1.11917e8			−0.124929
$965$	4.13644e8	+	2.38817e8i	0.460304	+	0.265757i
$966$		0			0
$967$	1.62366e8	+	2.81225e8i	0.179562	+	0.311010i	0.941731	−	0.336368i	$-0.109199\pi$
$967$	1.62366e8	+	2.81225e8i	0.179562	+	0.311010i	−0.762169	+	0.647379i	$0.775865\pi$
$968$	1.23578e9	−	7.13478e8i	1.36243	−	0.786601i
$969$		0			0
$970$	−7.96192e7	+	1.37905e8i	−0.0872374	+	0.151100i
$971$		−	1.01485e9i		−	1.10852i	−0.832342	−	0.554262i	$-0.813001\pi$
$971$		−	1.01485e9i		−	1.10852i	0.832342	−	0.554262i	$-0.186999\pi$
$972$		0			0
$973$	−1.30950e9			−1.42157
$974$	−2.11293e9	−	1.21990e9i	−2.28670	−	1.32023i
$975$		0			0
$976$	−1.03226e9	−	1.78794e9i	−1.11030	−	1.92310i
$977$	−3.71703e8	+	2.14603e8i	−0.398578	+	0.230119i	−0.685870	−	0.727724i	$-0.740578\pi$
$977$	−3.71703e8	+	2.14603e8i	−0.398578	+	0.230119i	0.287292	+	0.957843i	$0.407245\pi$
$978$		0			0
$979$	−2.50253e8	+	4.33450e8i	−0.266705	+	0.461946i
$980$			8.31736e8i			0.883705i
$981$		0			0
$982$	−2.29643e9			−2.42504
$983$	−1.36423e9	−	7.87641e8i	−1.43624	−	0.829216i	−0.438658	−	0.898654i	$-0.644546\pi$
$983$	−1.36423e9	−	7.87641e8i	−1.43624	−	0.829216i	−0.997586	+	0.0694381i	$0.977879\pi$
$984$		0			0
$985$	−3.26919e8	−	5.66240e8i	−0.342083	−	0.592505i
$986$	−2.06336e9	+	1.19128e9i	−2.15250	+	1.24275i
$987$		0			0
$988$	1.00849e9	−	1.74676e9i	1.04569	−	1.81118i
$989$			8.67940e7i			0.0897224i
$990$		0			0
$991$	−1.55480e9			−1.59755			−0.798774	−	0.601631i	$-0.794518\pi$
$991$	−1.55480e9			−1.59755			−0.798774	+	0.601631i	$0.794518\pi$
$992$	3.44524e7	+	1.98911e7i	0.0352927	+	0.0203762i
$993$		0			0
$994$	−4.91228e8	−	8.50831e8i	−0.500177	−	0.866332i
$995$	4.11074e8	−	2.37334e8i	0.417302	−	0.240930i
$996$		0			0
$997$	5.50335e8	−	9.53207e8i	0.555317	−	0.961838i	−0.442561	−	0.896738i	$-0.645930\pi$
$997$	5.50335e8	−	9.53207e8i	0.555317	−	0.961838i	0.997879	−	0.0650998i	$-0.0207366\pi$
$998$		−	1.68025e9i		−	1.69037i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.d.a.8.5		10
3.2	odd	2		9.7.d.a.2.1	✓	10
4.3	odd	2		432.7.q.a.305.4		10
9.2	odd	6		81.7.b.a.80.10		10
9.4	even	3		9.7.d.a.5.1	yes	10
9.5	odd	6	inner	27.7.d.a.17.5		10
9.7	even	3		81.7.b.a.80.1		10
12.11	even	2		144.7.q.a.65.2		10
36.23	even	6		432.7.q.a.17.4		10
36.31	odd	6		144.7.q.a.113.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.1	✓	10	3.2	odd	2
9.7.d.a.5.1	yes	10	9.4	even	3
27.7.d.a.8.5		10	1.1	even	1	trivial
27.7.d.a.17.5		10	9.5	odd	6	inner
81.7.b.a.80.1		10	9.7	even	3
81.7.b.a.80.10		10	9.2	odd	6
144.7.q.a.65.2		10	12.11	even	2
144.7.q.a.113.2		10	36.31	odd	6
432.7.q.a.17.4		10	36.23	even	6
432.7.q.a.305.4		10	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(12.2318 + 7.06203i) q^{2} +(67.7447 + 117.337i) q^{4} +(103.839 - 59.9512i) q^{5} +(-128.891 + 223.245i) q^{7} +1009.72i q^{8} +O(q^{10})\)	\(q+(12.2318 + 7.06203i) q^{2} +(67.7447 + 117.337i) q^{4} +(103.839 - 59.9512i) q^{5} +(-128.891 + 223.245i) q^{7} +1009.72i q^{8} +1693.51 q^{10} +(-518.417 - 299.308i) q^{11} +(-968.088 - 1676.78i) q^{13} +(-3153.13 + 1820.46i) q^{14} +(-2795.02 + 4841.12i) q^{16} -4874.12i q^{17} +7688.70 q^{19} +(14069.0 + 8122.75i) q^{20} +(-4227.45 - 7322.16i) q^{22} +(594.548 - 343.263i) q^{23} +(-624.198 + 1081.14i) q^{25} -27346.7i q^{26} -34926.6 q^{28} +(-29972.2 - 17304.5i) q^{29} +(-1387.88 - 2403.88i) q^{31} +(-12411.9 + 7166.00i) q^{32} +(34421.2 - 59619.2i) q^{34} +30908.6i q^{35} +17175.3 q^{37} +(94046.7 + 54297.9i) q^{38} +(60534.0 + 104848. i) q^{40} +(-71583.2 + 41328.6i) q^{41} +(-63212.6 + 109487. i) q^{43} -81106.2i q^{44} +9696.53 q^{46} +(72025.6 + 41584.0i) q^{47} +(25599.0 + 44338.7i) q^{49} +(-15270.1 + 8816.21i) q^{50} +(131166. - 227185. i) q^{52} +40017.8i q^{53} -71775.6 q^{55} +(-225415. - 130143. i) q^{56} +(-244410. - 423330. i) q^{58} +(57614.7 - 33263.9i) q^{59} +(-184662. + 319843. i) q^{61} -39205.0i q^{62} +155336. q^{64} +(-201050. - 116076. i) q^{65} +(-127954. - 221623. i) q^{67} +(571915. - 330195. i) q^{68} +(-218277. + 378068. i) q^{70} +269837. i q^{71} +551862. q^{73} +(210085. + 121292. i) q^{74} +(520869. + 902171. i) q^{76} +(133638. - 77156.0i) q^{77} +(355021. - 614915. i) q^{79} +670259. i q^{80} -1.16746e6 q^{82} +(-301612. - 174136. i) q^{83} +(-292209. - 506121. i) q^{85} +(-1.54641e6 + 892818. i) q^{86} +(302218. - 523456. i) q^{88} -836103. i q^{89} +499109. q^{91} +(80554.9 + 46508.4i) q^{92} +(587335. + 1.01729e6i) q^{94} +(798384. - 460947. i) q^{95} +(-47014.3 + 81431.2i) q^{97} +723123. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) \) 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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