LMFDB - Embedded newform 81.5.f.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, 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:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	81.17
Dual form			81.5.f.a.62.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940198 + 2.58317i) q^{2} +(6.46790 + 5.42721i) q^{4} +(-20.2618 - 3.57269i) q^{5} +(-3.42243 + 2.87176i) q^{7} +(-58.1912 + 33.5967i) q^{8} +O(q^{10})$	\(q+(-0.940198 + 2.58317i) q^{2} +(6.46790 + 5.42721i) q^{4} +(-20.2618 - 3.57269i) q^{5} +(-3.42243 + 2.87176i) q^{7} +(-58.1912 + 33.5967i) q^{8} +(28.2789 - 48.9806i) q^{10} +(-52.5310 + 9.26263i) q^{11} +(-137.982 + 50.2213i) q^{13} +(-4.20048 - 11.5407i) q^{14} +(-8.61636 - 48.8658i) q^{16} +(20.3466 + 11.7471i) q^{17} +(-332.362 - 575.668i) q^{19} +(-111.661 - 133.073i) q^{20} +(25.4626 - 144.405i) q^{22} +(-467.109 + 556.678i) q^{23} +(-189.533 - 68.9845i) q^{25} -403.649i q^{26} -37.7215 q^{28} +(239.097 - 656.913i) q^{29} +(660.190 + 553.965i) q^{31} +(-924.431 - 163.002i) q^{32} +(-49.4746 + 41.5141i) q^{34} +(79.6042 - 45.9595i) q^{35} +(-6.91875 + 11.9836i) q^{37} +(1799.54 - 317.307i) q^{38} +(1299.09 - 472.829i) q^{40} +(906.896 + 2491.68i) q^{41} +(585.265 + 3319.20i) q^{43} +(-390.036 - 225.187i) q^{44} +(-998.822 - 1730.01i) q^{46} +(1488.80 + 1774.28i) q^{47} +(-413.463 + 2344.87i) q^{49} +(356.398 - 424.738i) q^{50} +(-1165.02 - 424.031i) q^{52} -3687.20i q^{53} +1097.46 q^{55} +(102.673 - 282.093i) q^{56} +(1472.12 + 1235.26i) q^{58} +(716.683 + 126.370i) q^{59} +(-1985.92 + 1666.38i) q^{61} +(-2051.70 + 1184.55i) q^{62} +(1687.17 - 2922.26i) q^{64} +(2975.18 - 524.605i) q^{65} +(4902.93 - 1784.52i) q^{67} +(67.8456 + 186.404i) q^{68} +(43.8777 + 248.843i) q^{70} +(-3584.69 - 2069.62i) q^{71} +(1179.61 + 2043.14i) q^{73} +(-24.4508 - 29.1393i) q^{74} +(974.588 - 5527.16i) q^{76} +(153.183 - 182.557i) q^{77} +(-11379.3 - 4141.72i) q^{79} +1020.89i q^{80} -7289.09 q^{82} +(-411.586 + 1130.82i) q^{83} +(-370.288 - 310.709i) q^{85} +(-9124.34 - 1608.87i) q^{86} +(2745.65 - 2303.87i) q^{88} +(1335.39 - 770.989i) q^{89} +(328.010 - 568.129i) q^{91} +(-6042.42 + 1065.44i) q^{92} +(-5983.04 + 2177.65i) q^{94} +(4677.55 + 12851.5i) q^{95} +(620.366 + 3518.27i) q^{97} +(-5668.46 - 3272.69i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28} - 5016 q^{29} - 1671 q^{31} - 10224 q^{32} - 342 q^{34} + 2682 q^{35} - 3 q^{37} + 6564 q^{38} - 1113 q^{40} - 5754 q^{41} - 1266 q^{43} + 4545 q^{44} - 3 q^{46} + 9159 q^{47} + 5898 q^{49} + 34977 q^{50} + 2871 q^{52} - 12 q^{55} - 39243 q^{56} - 12291 q^{58} - 24762 q^{59} - 8358 q^{61} - 38304 q^{62} + 6141 q^{64} - 23727 q^{65} + 15996 q^{67} + 43533 q^{68} - 7251 q^{70} + 19773 q^{71} + 6108 q^{73} + 74847 q^{74} - 28614 q^{76} + 33909 q^{77} - 5658 q^{79} - 12 q^{82} - 18813 q^{83} + 24219 q^{85} - 96474 q^{86} + 36042 q^{88} - 110232 q^{89} - 6042 q^{91} - 73545 q^{92} + 2631 q^{94} + 65163 q^{95} - 3696 q^{97} + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.940198	+	2.58317i	−0.235049	+	0.645793i	0.764949	+	0.644091i	$0.222764\pi$
$2$	−0.940198	+	2.58317i	−0.235049	+	0.645793i	−0.999999	+	0.00170240i	$0.999458\pi$
$3$		0			0
$3$		0			0
$4$	6.46790	+	5.42721i	0.404244	+	0.339201i
$5$	−20.2618	−	3.57269i	−0.810470	−	0.142908i	−0.246969	−	0.969023i	$-0.579435\pi$
$5$	−20.2618	−	3.57269i	−0.810470	−	0.142908i	−0.563501	+	0.826116i	$0.690546\pi$
$6$		0			0
$7$	−3.42243	+	2.87176i	−0.0698454	+	0.0586073i	−0.677042	−	0.735944i	$-0.736738\pi$
$7$	−3.42243	+	2.87176i	−0.0698454	+	0.0586073i	0.607197	+	0.794552i	$0.292294\pi$
$8$	−58.1912	+	33.5967i	−0.909237	+	0.524948i
$9$		0			0
$10$	28.2789	−	48.9806i	0.282789	−	0.489806i
$11$	−52.5310	+	9.26263i	−0.434140	+	0.0765507i	−0.386448	−	0.922311i	$-0.626298\pi$
$11$	−52.5310	+	9.26263i	−0.434140	+	0.0765507i	−0.0476928	+	0.998862i	$0.515187\pi$
$12$		0			0
$13$	−137.982	+	50.2213i	−0.816462	+	0.297168i	−0.716290	−	0.697802i	$-0.754161\pi$
$13$	−137.982	+	50.2213i	−0.816462	+	0.297168i	−0.100171	+	0.994970i	$0.531939\pi$
$14$	−4.20048	−	11.5407i	−0.0214310	−	0.0588813i
$15$		0			0
$16$	−8.61636	−	48.8658i	−0.0336577	−	0.190882i
$17$	20.3466	+	11.7471i	0.0704034	+	0.0406474i	0.534788	−	0.844986i	$-0.320391\pi$
$17$	20.3466	+	11.7471i	0.0704034	+	0.0406474i	−0.464385	+	0.885633i	$0.653725\pi$
$18$		0			0
$19$	−332.362	−	575.668i	−0.920670	−	1.59465i	−0.798381	−	0.602153i	$-0.794310\pi$
$19$	−332.362	−	575.668i	−0.920670	−	1.59465i	−0.122289	−	0.992494i	$-0.539024\pi$
$20$	−111.661	−	133.073i	−0.279153	−	0.332682i
$21$		0			0
$22$	25.4626	−	144.405i	0.0526086	−	0.298358i
$23$	−467.109	+	556.678i	−0.883003	+	1.05232i	0.115256	+	0.993336i	$0.463231\pi$
$23$	−467.109	+	556.678i	−0.883003	+	1.05232i	−0.998259	+	0.0589860i	$0.981213\pi$
$24$		0			0
$25$	−189.533	−	68.9845i	−0.303253	−	0.110375i
$26$		−	403.649i		−	0.597114i
$27$		0			0
$28$	−37.7215			−0.0481142
$29$	239.097	−	656.913i	0.284301	−	0.781110i	−0.712536	−	0.701635i	$-0.752454\pi$
$29$	239.097	−	656.913i	0.284301	−	0.781110i	0.996837	−	0.0794743i	$-0.0253242\pi$
$30$		0			0
$31$	660.190	+	553.965i	0.686982	+	0.576446i	0.918037	−	0.396494i	$-0.129773\pi$
$31$	660.190	+	553.965i	0.686982	+	0.576446i	−0.231055	+	0.972941i	$0.574218\pi$
$32$	−924.431	−	163.002i	−0.902765	−	0.159182i
$33$		0			0
$34$	−49.4746	+	41.5141i	−0.0427981	+	0.0359119i
$35$	79.6042	−	45.9595i	0.0649831	−	0.0375180i
$36$		0			0
$37$	−6.91875	+	11.9836i	−0.00505387	+	0.00875357i	−0.868541	−	0.495617i	$-0.834942\pi$
$37$	−6.91875	+	11.9836i	−0.00505387	+	0.00875357i	0.863487	+	0.504370i	$0.168275\pi$
$38$	1799.54	−	317.307i	1.24622	−	0.219741i
$39$		0			0
$40$	1299.09	−	472.829i	0.811929	−	0.295518i
$41$	906.896	+	2491.68i	0.539498	+	1.48226i	0.847460	+	0.530860i	$0.178131\pi$
$41$	906.896	+	2491.68i	0.539498	+	1.48226i	−0.307962	+	0.951399i	$0.599647\pi$
$42$		0			0
$43$	585.265	+	3319.20i	0.316530	+	1.79513i	0.563506	+	0.826112i	$0.309452\pi$
$43$	585.265	+	3319.20i	0.316530	+	1.79513i	−0.246976	+	0.969022i	$0.579437\pi$
$44$	−390.036	−	225.187i	−0.201465	−	0.116316i
$45$		0			0
$46$	−998.822	−	1730.01i	−0.472033	−	0.817585i
$47$	1488.80	+	1774.28i	0.673970	+	0.803206i	0.989319	−	0.145770i	$-0.0465660\pi$
$47$	1488.80	+	1774.28i	0.673970	+	0.803206i	−0.315349	+	0.948976i	$0.602122\pi$
$48$		0			0
$49$	−413.463	+	2344.87i	−0.172205	+	0.976621i
$50$	356.398	−	424.738i	0.142559	−	0.169895i
$51$		0			0
$52$	−1165.02	−	424.031i	−0.430849	−	0.156816i
$53$		−	3687.20i		−	1.31264i	−0.754484	−	0.656319i	$-0.772113\pi$
$53$		−	3687.20i		−	1.31264i	0.754484	−	0.656319i	$-0.227887\pi$
$54$		0			0
$55$	1097.46			0.362797
$56$	102.673	−	282.093i	0.0327403	−	0.0899531i
$57$		0			0
$58$	1472.12	+	1235.26i	0.437611	+	0.367199i
$59$	716.683	+	126.370i	0.205884	+	0.0363029i	0.275639	−	0.961261i	$-0.411111\pi$
$59$	716.683	+	126.370i	0.205884	+	0.0363029i	−0.0697548	+	0.997564i	$0.522222\pi$
$60$		0			0
$61$	−1985.92	+	1666.38i	−0.533705	+	0.447832i	−0.869379	−	0.494147i	$-0.835481\pi$
$61$	−1985.92	+	1666.38i	−0.533705	+	0.447832i	0.335673	+	0.941978i	$0.391036\pi$
$62$	−2051.70	+	1184.55i	−0.533740	+	0.308155i
$63$		0			0
$64$	1687.17	−	2922.26i	0.411906	−	0.713443i
$65$	2975.18	−	524.605i	0.704185	−	0.124167i
$66$		0			0
$67$	4902.93	−	1784.52i	1.09221	−	0.397532i	0.267771	−	0.963483i	$-0.413713\pi$
$67$	4902.93	−	1784.52i	1.09221	−	0.397532i	0.824439	+	0.565951i	$0.191491\pi$
$68$	67.8456	+	186.404i	0.0146725	+	0.0403123i
$69$		0			0
$70$	43.8777	+	248.843i	0.00895462	+	0.0507842i
$71$	−3584.69	−	2069.62i	−0.711107	−	0.410558i	0.100364	−	0.994951i	$-0.467999\pi$
$71$	−3584.69	−	2069.62i	−0.711107	−	0.410558i	−0.811471	+	0.584393i	$0.801333\pi$
$72$		0			0
$73$	1179.61	+	2043.14i	0.221357	+	0.383401i	0.955220	−	0.295896i	$-0.0956182\pi$
$73$	1179.61	+	2043.14i	0.221357	+	0.383401i	−0.733863	+	0.679297i	$0.762285\pi$
$74$	−24.4508	−	29.1393i	−0.00446508	−	0.00532128i
$75$		0			0
$76$	974.588	−	5527.16i	0.168731	−	0.956919i
$77$	153.183	−	182.557i	0.0258363	−	0.0307905i
$78$		0			0
$79$	−11379.3	−	4141.72i	−1.82331	−	0.663630i	−0.994579	−	0.103982i	$-0.966842\pi$
$79$	−11379.3	−	4141.72i	−1.82331	−	0.663630i	−0.828730	−	0.559648i	$-0.810936\pi$
$80$			1020.89i			0.159514i
$81$		0			0
$82$	−7289.09			−1.08404
$83$	−411.586	+	1130.82i	−0.0597454	+	0.164149i	−0.965974	−	0.258639i	$-0.916726\pi$
$83$	−411.586	+	1130.82i	−0.0597454	+	0.164149i	0.906229	+	0.422788i	$0.138948\pi$
$84$		0			0
$85$	−370.288	−	310.709i	−0.0512510	−	0.0430047i
$86$	−9124.34	−	1608.87i	−1.23369	−	0.217532i
$87$		0			0
$88$	2745.65	−	2303.87i	0.354551	−	0.297504i
$89$	1335.39	−	770.989i	0.168589	−	0.0973347i	−0.413331	−	0.910581i	$-0.635635\pi$
$89$	1335.39	−	770.989i	0.168589	−	0.0973347i	0.581920	+	0.813246i	$0.302302\pi$
$90$		0			0
$91$	328.010	−	568.129i	0.0396099	−	0.0686064i
$92$	−6042.42	+	1065.44i	−0.713897	+	0.125879i
$93$		0			0
$94$	−5983.04	+	2177.65i	−0.677121	+	0.246452i
$95$	4677.55	+	12851.5i	0.518288	+	1.42398i
$96$		0			0
$97$	620.366	+	3518.27i	0.0659333	+	0.373926i	0.999864	+	0.0164729i	$0.00524374\pi$
$97$	620.366	+	3518.27i	0.0659333	+	0.373926i	−0.933931	+	0.357453i	$0.883645\pi$
$98$	−5668.46	−	3272.69i	−0.590218	−	0.340763i
$99$		0			0
$100$	−851.490	−	1474.82i	−0.0851490	−	0.147482i
$101$	−196.802	−	234.540i	−0.0192924	−	0.0229918i	0.756312	−	0.654211i	$-0.226999\pi$
$101$	−196.802	−	234.540i	−0.0192924	−	0.0229918i	−0.775604	+	0.631219i	$0.782555\pi$
$102$		0			0
$103$	324.540	−	1840.56i	0.0305910	−	0.173490i	−0.965684	−	0.259718i	$-0.916370\pi$
$103$	324.540	−	1840.56i	0.0305910	−	0.173490i	0.996275	+	0.0862281i	$0.0274814\pi$
$104$	6342.06	−	7558.18i	0.586359	−	0.698796i
$105$		0			0
$106$	9524.67	+	3466.70i	0.847693	+	0.308535i
$107$			6251.50i			0.546030i	0.962010	+	0.273015i	$0.0880209\pi$
$107$			6251.50i			0.546030i	−0.962010	+	0.273015i	$0.911979\pi$
$108$		0			0
$109$	5358.48			0.451013			0.225506	−	0.974242i	$-0.427596\pi$
$109$	5358.48			0.451013			0.225506	+	0.974242i	$0.427596\pi$
$110$	−1031.83	+	2834.93i	−0.0852754	+	0.234292i
$111$		0			0
$112$	169.820	+	142.496i	0.0135379	+	0.0113597i
$113$	−11270.7	−	1987.32i	−0.882658	−	0.155636i	−0.286094	−	0.958202i	$-0.592357\pi$
$113$	−11270.7	−	1987.32i	−0.882658	−	0.155636i	−0.596564	+	0.802565i	$0.703468\pi$
$114$		0			0
$115$	11453.3	−	9610.44i	0.866032	−	0.726687i
$116$	5111.66	−	2951.22i	0.379880	−	0.219324i
$117$		0			0
$118$	−1000.26	+	1732.50i	−0.0718371	+	0.124426i
$119$	−103.369	+	18.2268i	−0.00729959	+	0.00128711i
$120$		0			0
$121$	−11084.3	+	4034.37i	−0.757075	+	0.275553i
$122$	−2437.40	−	6696.70i	−0.163760	−	0.449926i
$123$		0			0
$124$	1263.56	+	7165.98i	0.0821772	+	0.466050i
$125$	14730.0	+	8504.37i	0.942720	+	0.544280i
$126$		0			0
$127$	5996.21	+	10385.7i	0.371766	+	0.643917i	0.989837	−	0.142205i	$-0.0454191\pi$
$127$	5996.21	+	10385.7i	0.371766	+	0.643917i	−0.618072	+	0.786122i	$0.712086\pi$
$128$	−3691.64	−	4399.53i	−0.225320	−	0.268526i
$129$		0			0
$130$	−1442.12	+	8178.64i	−0.0853323	+	0.483943i
$131$	18982.4	−	22622.4i	1.10614	−	1.31824i	0.162708	−	0.986674i	$-0.447977\pi$
$131$	18982.4	−	22622.4i	1.10614	−	1.31824i	0.943431	−	0.331570i	$-0.107578\pi$
$132$		0			0
$133$	2790.66	+	1015.72i	0.157763	+	0.0574209i
$134$			14342.9i			0.798782i
$135$		0			0
$136$	−1578.65			−0.0853511
$137$	4555.34	−	12515.7i	0.242705	−	0.666828i	−0.757202	−	0.653181i	$-0.773434\pi$
$137$	4555.34	−	12515.7i	0.242705	−	0.666828i	0.999907	−	0.0136462i	$-0.00434385\pi$
$138$		0			0
$139$	−12832.9	−	10768.1i	−0.664194	−	0.557325i	0.247146	−	0.968978i	$-0.420507\pi$
$139$	−12832.9	−	10768.1i	−0.664194	−	0.557325i	−0.911341	+	0.411653i	$0.864952\pi$
$140$	764.305	+	134.768i	0.0389951	+	0.00687589i
$141$		0			0
$142$	8716.51	−	7314.02i	0.432281	−	0.362726i
$143$	6783.15	−	3916.25i	0.331711	−	0.191513i
$144$		0			0
$145$	−7191.47	+	12456.0i	−0.342044	+	0.592437i
$146$	−6386.86	+	1126.18i	−0.299628	+	0.0528324i
$147$		0			0
$148$	−109.788	+	39.9594i	−0.00501221	+	0.00182430i
$149$	10767.4	+	29583.3i	0.484998	+	1.33252i	0.905159	+	0.425072i	$0.139751\pi$
$149$	10767.4	+	29583.3i	0.484998	+	1.33252i	−0.420161	+	0.907449i	$0.638027\pi$
$150$		0			0
$151$	−4885.35	−	27706.2i	−0.214260	−	1.21513i	−0.882186	−	0.470902i	$-0.843929\pi$
$151$	−4885.35	−	27706.2i	−0.214260	−	1.21513i	0.667926	−	0.744228i	$-0.267182\pi$
$152$	38681.1	+	22332.5i	1.67421	+	0.966608i
$153$		0			0
$154$	327.553	+	567.339i	0.0138115	+	0.0239222i
$155$	−11397.5	−	13583.0i	−0.474400	−	0.565368i
$156$		0			0
$157$	−5071.13	+	28759.8i	−0.205734	+	1.16677i	0.690547	+	0.723287i	$0.257370\pi$
$157$	−5071.13	+	28759.8i	−0.205734	+	1.16677i	−0.896281	+	0.443487i	$0.853741\pi$
$158$	21397.5	−	25500.6i	0.857136	−	1.02149i
$159$		0			0
$160$	18148.2	+	6605.42i	0.708916	+	0.258024i
$161$		−	3246.61i		−	0.125250i
$162$		0			0
$163$	39397.1			1.48282			0.741410	−	0.671052i	$-0.234157\pi$
$163$	39397.1			1.48282			0.741410	+	0.671052i	$0.234157\pi$
$164$	−7657.15	+	21037.8i	−0.284695	+	0.782192i
$165$		0			0
$166$	−2534.14	−	2126.39i	−0.0919632	−	0.0771663i
$167$	−39262.9	−	6923.11i	−1.40783	−	0.248238i	−0.582472	−	0.812850i	$-0.697915\pi$
$167$	−39262.9	−	6923.11i	−1.40783	−	0.248238i	−0.825356	+	0.564612i	$0.809026\pi$
$168$		0			0
$169$	−5362.15	+	4499.37i	−0.187744	+	0.157536i
$170$	1150.76	−	664.391i	0.0398187	−	0.0229893i
$171$		0			0
$172$	−14228.6	+	24644.6i	−0.480955	+	0.833039i
$173$	−29475.3	+	5197.29i	−0.984841	+	0.173654i	−0.642803	−	0.766032i	$-0.722228\pi$
$173$	−29475.3	+	5197.29i	−0.984841	+	0.173654i	−0.342038	+	0.939686i	$0.611117\pi$
$174$		0			0
$175$	846.771	−	308.199i	0.0276497	−	0.0100637i
$176$	905.252	+	2487.16i	0.0292243	+	0.0802931i
$177$		0			0
$178$	736.064	+	4174.43i	0.0232314	+	0.131752i
$179$	−44449.0	−	25662.6i	−1.38725	−	0.800931i	−0.394248	−	0.919004i	$-0.628995\pi$
$179$	−44449.0	−	25662.6i	−1.38725	−	0.800931i	−0.993005	+	0.118073i	$0.962328\pi$
$180$		0			0
$181$	−534.462	−	925.715i	−0.0163140	−	0.0282566i	0.857753	−	0.514062i	$-0.171860\pi$
$181$	−534.462	−	925.715i	−0.0163140	−	0.0282566i	−0.874067	+	0.485805i	$0.838526\pi$
$182$	1159.18	+	1381.46i	0.0349952	+	0.0417057i
$183$		0			0
$184$	8479.05	−	48087.1i	0.250444	−	1.42034i
$185$	183.000	−	218.091i	0.00534697	−	0.00637227i
$186$		0			0
$187$	−1177.63	−	428.624i	−0.0336765	−	0.0122573i
$188$			19555.9i			0.553302i
$189$		0			0
$190$	−37595.4			−1.04142
$191$	−1453.05	+	3992.22i	−0.0398303	+	0.109433i	−0.958013	−	0.286723i	$-0.907434\pi$
$191$	−1453.05	+	3992.22i	−0.0398303	+	0.109433i	0.918183	+	0.396156i	$0.129656\pi$
$192$		0			0
$193$	−13748.6	−	11536.5i	−0.369101	−	0.309712i	0.439305	−	0.898338i	$-0.355225\pi$
$193$	−13748.6	−	11536.5i	−0.369101	−	0.309712i	−0.808406	+	0.588626i	$0.799669\pi$
$194$	−9671.57	−	1705.36i	−0.256977	−	0.0453119i
$195$		0			0
$196$	−15400.3	+	12922.4i	−0.400883	+	0.336381i
$197$	−43964.1	+	25382.7i	−1.13283	+	0.654042i	−0.944646	−	0.328091i	$-0.893595\pi$
$197$	−43964.1	+	25382.7i	−1.13283	+	0.654042i	−0.188187	+	0.982133i	$0.560261\pi$
$198$		0			0
$199$	11453.9	−	19838.8i	0.289233	−	0.500967i	−0.684394	−	0.729113i	$-0.739933\pi$
$199$	11453.9	−	19838.8i	0.289233	−	0.500967i	0.973627	+	0.228146i	$0.0732664\pi$
$200$	13346.8	−	2353.41i	0.333671	−	0.0588351i
$201$		0			0
$202$	790.889	−	287.860i	0.0193826	−	0.00705470i
$203$	1068.20	+	2934.86i	0.0259216	+	0.0712190i
$204$		0			0
$205$	−9473.31	−	53725.8i	−0.225421	−	1.27842i
$206$	4449.35	+	2568.83i	0.104848	+	0.0605342i
$207$		0			0
$208$	3643.01	+	6309.88i	0.0842042	+	0.145846i
$209$	22791.5	+	27161.8i	0.521771	+	0.621823i
$210$		0			0
$211$	3951.94	−	22412.5i	0.0887657	−	0.503415i	−0.907715	−	0.419588i	$-0.862175\pi$
$211$	3951.94	−	22412.5i	0.0887657	−	0.503415i	0.996480	−	0.0838271i	$-0.0267143\pi$
$212$	20011.2	−	23848.4i	0.445248	−	0.530626i
$213$		0			0
$214$	−16148.7	−	5877.65i	−0.352623	−	0.128344i
$215$		−	69343.8i		−	1.50014i
$216$		0			0
$217$	−3850.30			−0.0817665
$218$	−5038.03	+	13841.9i	−0.106010	+	0.291261i
$219$		0			0
$220$	7098.28	+	5956.16i	0.146659	+	0.123061i
$221$	−3397.42	−	599.056i	−0.0695607	−	0.0122654i
$222$		0			0
$223$	−32204.7	+	27022.9i	−0.647604	+	0.543404i	−0.906343	−	0.422543i	$-0.861137\pi$
$223$	−32204.7	+	27022.9i	−0.647604	+	0.543404i	0.258739	+	0.965947i	$0.416693\pi$
$224$	3631.90	−	2096.88i	0.0723832	−	0.0417905i
$225$		0			0
$226$	15730.2	−	27245.6i	0.307977	−	0.533432i
$227$	49345.9	−	8701.01i	0.957634	−	0.168857i	0.327075	−	0.944998i	$-0.393937\pi$
$227$	49345.9	−	8701.01i	0.957634	−	0.168857i	0.630558	+	0.776142i	$0.282826\pi$
$228$		0			0
$229$	−8081.42	+	2941.40i	−0.154105	+	0.0560896i	−0.417921	−	0.908483i	$-0.637241\pi$
$229$	−8081.42	+	2941.40i	−0.154105	+	0.0560896i	0.263816	+	0.964573i	$0.415019\pi$
$230$	14057.1	+	38621.5i	0.265729	+	0.730085i
$231$		0			0
$232$	8156.78	+	46259.4i	0.151545	+	0.859457i
$233$	−27557.0	−	15910.1i	−0.507599	−	0.293062i	0.224247	−	0.974532i	$-0.428008\pi$
$233$	−27557.0	−	15910.1i	−0.507599	−	0.293062i	−0.731846	+	0.681470i	$0.761341\pi$
$234$		0			0
$235$	−23826.7	−	41269.1i	−0.431448	−	0.747290i
$236$	3949.59	+	4706.94i	0.0709134	+	0.0845113i
$237$		0			0
$238$	50.1047	−	284.158i	0.000884555	−	0.00501656i
$239$	−82.7880	+	98.6629i	−0.00144934	+	0.00172726i	−0.766769	−	0.641924i	$-0.778137\pi$
$239$	−82.7880	+	98.6629i	−0.00144934	+	0.00172726i	0.765319	+	0.643651i	$0.222581\pi$
$240$		0			0
$241$	9610.04	+	3497.77i	0.165459	+	0.0602222i	0.423422	−	0.905933i	$-0.360829\pi$
$241$	9610.04	+	3497.77i	0.165459	+	0.0602222i	−0.257962	+	0.966155i	$0.583051\pi$
$242$		−	32425.8i		−	0.553682i
$243$		0			0
$244$	−21888.5			−0.367652
$245$	16755.0	−	46033.9i	0.279133	−	0.766913i
$246$		0			0
$247$	74770.8	+	62740.1i	1.22557	+	1.02837i
$248$	−57028.6	−	10055.7i	−0.927234	−	0.163496i
$249$		0			0
$250$	−35817.4	+	30054.3i	−0.573078	+	0.480869i
$251$	8750.76	−	5052.25i	0.138899	−	0.0801932i	−0.428940	−	0.903333i	$-0.641113\pi$
$251$	8750.76	−	5052.25i	0.138899	−	0.0801932i	0.567839	+	0.823140i	$0.307780\pi$
$252$		0			0
$253$	19381.4	−	33569.5i	0.302791	−	0.524450i
$254$	−32465.8	+	5724.59i	−0.503221	+	0.0887314i
$255$		0			0
$256$	65569.0	−	23865.2i	1.00050	−	0.364154i
$257$	37147.6	+	102062.i	0.562425	+	1.54525i	0.816071	+	0.577952i	$0.196148\pi$
$257$	37147.6	+	102062.i	0.562425	+	1.54525i	−0.253646	+	0.967297i	$0.581630\pi$
$258$		0			0
$259$	−10.7351	−	60.8821i	−0.000160033	−	0.000907590i
$260$	22090.3	+	12753.9i	0.326780	+	0.188667i
$261$		0			0
$262$	40590.3	+	70304.4i	0.591316	+	1.02419i
$263$	4024.19	+	4795.84i	0.0581790	+	0.0693351i	0.794349	−	0.607462i	$-0.207812\pi$
$263$	4024.19	+	4795.84i	0.0581790	+	0.0693351i	−0.736170	+	0.676797i	$0.763368\pi$
$264$		0			0
$265$	−13173.2	+	74709.1i	−0.187586	+	1.06385i
$266$	−5247.55	+	6253.78i	−0.0741640	+	0.0883852i
$267$		0			0
$268$	41396.7	+	15067.2i	0.576363	+	0.209779i
$269$			53634.0i			0.741200i	0.928793	+	0.370600i	$0.120848\pi$
$269$			53634.0i			0.741200i	−0.928793	+	0.370600i	$0.879152\pi$
$270$		0			0
$271$	33888.1			0.461433			0.230717	−	0.973021i	$-0.425893\pi$
$271$	33888.1			0.461433			0.230717	+	0.973021i	$0.425893\pi$
$272$	398.718	−	1095.47i	0.00538925	−	0.0148068i
$273$		0			0
$274$	28047.3	+	23534.4i	0.373585	+	0.313475i
$275$	10595.4	+	1868.25i	0.140104	+	0.0247041i
$276$		0			0
$277$	−18203.4	+	15274.5i	−0.237243	+	0.199071i	−0.753656	−	0.657269i	$-0.771711\pi$
$277$	−18203.4	+	15274.5i	−0.237243	+	0.199071i	0.516413	+	0.856340i	$0.327267\pi$
$278$	39881.3	−	23025.5i	0.516035	−	0.297933i
$279$		0			0
$280$	−3088.18	+	5348.88i	−0.0393900	+	0.0682255i
$281$	127567.	−	22493.4i	1.61557	−	0.284868i	0.708453	−	0.705758i	$-0.249393\pi$
$281$	127567.	−	22493.4i	1.61557	−	0.284868i	0.907112	+	0.420890i	$0.138282\pi$
$282$		0			0
$283$	9301.61	−	3385.51i	0.116141	−	0.0422719i	−0.283296	−	0.959033i	$-0.591428\pi$
$283$	9301.61	−	3385.51i	0.116141	−	0.0422719i	0.399437	+	0.916761i	$0.369206\pi$
$284$	−11953.1	−	32841.0i	−0.148199	−	0.407173i
$285$		0			0
$286$	3738.85	+	21204.1i	0.0457095	+	0.259231i
$287$	−10259.3	−	5923.19i	−0.124553	−	0.0719105i
$288$		0			0
$289$	−41484.5	−	71853.3i	−0.496696	−	0.860302i
$290$	−25414.6	−	30287.9i	−0.302195	−	0.360142i
$291$		0			0
$292$	−3458.98	+	19616.9i	−0.0405679	+	0.230072i
$293$	−81305.1	+	96895.6i	−0.947071	+	1.12868i	0.0444870	+	0.999010i	$0.485835\pi$
$293$	−81305.1	+	96895.6i	−0.947071	+	1.12868i	−0.991558	+	0.129665i	$0.958610\pi$
$294$		0			0
$295$	−14069.8	−	5120.97i	−0.161675	−	0.0588449i
$296$		−	929.789i		−	0.0106121i
$297$		0			0
$298$	−86542.3			−0.974532
$299$	36495.4	−	100270.i	0.408222	−	1.12158i
$300$		0			0
$301$	−11535.0	−	9678.98i	−0.127316	−	0.106831i
$302$	76163.0	+	13429.6i	0.835084	+	0.147248i
$303$		0			0
$304$	−25266.7	+	21201.3i	−0.273402	+	0.229412i
$305$	46191.6	−	26668.7i	0.496551	−	0.286684i
$306$		0			0
$307$	12178.0	−	21092.9i	0.129211	−	0.223799i	−0.794160	−	0.607708i	$-0.792089\pi$
$307$	12178.0	−	21092.9i	0.129211	−	0.223799i	0.923371	+	0.383909i	$0.125422\pi$
$308$	1981.55	−	349.401i	0.0208883	−	0.00368318i
$309$		0			0
$310$	45803.0	−	16670.9i	0.476618	−	0.173475i
$311$	−35810.3	−	98388.1i	−0.370244	−	1.01724i	−0.975267	−	0.221029i	$-0.929059\pi$
$311$	−35810.3	−	98388.1i	−0.370244	−	1.01724i	0.605024	−	0.796208i	$-0.293164\pi$
$312$		0			0
$313$	4791.37	+	27173.2i	0.0489070	+	0.277365i	0.999448	−	0.0332350i	$-0.0105810\pi$
$313$	4791.37	+	27173.2i	0.0489070	+	0.277365i	−0.950541	+	0.310600i	$0.899470\pi$
$314$	−69523.7	−	40139.5i	−0.705137	−	0.407111i
$315$		0			0
$316$	−51122.0	−	88546.0i	−0.511958	−	0.886737i
$317$	100817.	+	120149.i	1.00326	+	1.19564i	0.980625	+	0.195896i	$0.0627616\pi$
$317$	100817.	+	120149.i	1.00326	+	1.19564i	0.0226365	+	0.999744i	$0.492794\pi$
$318$		0			0
$319$	−6475.25	+	36723.0i	−0.0636319	+	0.360875i
$320$	−44625.3	+	53182.4i	−0.435794	+	0.519359i
$321$		0			0
$322$	8386.56	+	3052.46i	0.0808858	+	0.0294400i
$323$		−	15617.2i		−	0.149691i
$324$		0			0
$325$	29616.7			0.280395
$326$	−37041.0	+	101769.i	−0.348536	+	0.957595i
$327$		0			0
$328$	−136485.	−	114525.i	−1.26864	−	1.06452i
$329$	−10190.6	−	1796.88i	−0.0941474	−	0.0166007i
$330$		0			0
$331$	83652.1	−	70192.4i	0.763521	−	0.640670i	−0.175520	−	0.984476i	$-0.556161\pi$
$331$	83652.1	−	70192.4i	0.763521	−	0.640670i	0.939041	+	0.343806i	$0.111716\pi$
$332$	−8799.31	+	5080.29i	−0.0798312	+	0.0460906i
$333$		0			0
$334$	54798.5	−	94913.8i	0.491220	−	0.850818i
$335$	−105718.	+	18640.9i	−0.942014	+	0.166103i
$336$		0			0
$337$	−117385.	+	42724.5i	−1.03360	+	0.376198i	−0.802449	−	0.596720i	$-0.796470\pi$
$337$	−117385.	+	42724.5i	−1.03360	+	0.376198i	−0.231147	+	0.972919i	$0.574248\pi$
$338$	−6581.18	−	18081.7i	−0.0576064	−	0.158272i
$339$		0			0
$340$	−708.706	−	4019.27i	−0.00613067	−	0.0347688i
$341$	−39811.6	−	22985.2i	−0.342374	−	0.197670i
$342$		0			0
$343$	−10682.3	−	18502.2i	−0.0907977	−	0.157266i
$344$	−145571.	−	173485.i	−1.23015	−	1.46604i
$345$		0			0
$346$	14287.1	−	81026.3i	0.119342	−	0.676821i
$347$	4265.94	−	5083.95i	0.0354288	−	0.0422224i	−0.748039	−	0.663655i	$-0.769004\pi$
$347$	4265.94	−	5083.95i	0.0354288	−	0.0422224i	0.783468	+	0.621432i	$0.213449\pi$
$348$		0			0
$349$	−32603.4	−	11866.7i	−0.267678	−	0.0974267i	0.204695	−	0.978826i	$-0.434380\pi$
$349$	−32603.4	−	11866.7i	−0.267678	−	0.0974267i	−0.472372	+	0.881399i	$0.656602\pi$
$350$			2477.12i			0.0202214i
$351$		0			0
$352$	50071.1			0.404112
$353$	3406.82	−	9360.15i	0.0273401	−	0.0751162i	−0.925272	−	0.379305i	$-0.876163\pi$
$353$	3406.82	−	9360.15i	0.0273401	−	0.0751162i	0.952612	+	0.304189i	$0.0983854\pi$
$354$		0			0
$355$	65238.0	+	54741.1i	0.517659	+	0.434367i
$356$	12821.5	+	2260.78i	0.101167	+	0.0178385i
$357$		0			0
$358$	108082.	−	90691.4i	0.843309	−	0.707620i
$359$	−117460.	+	67815.5i	−0.911383	+	0.526187i	−0.880876	−	0.473347i	$-0.843046\pi$
$359$	−117460.	+	67815.5i	−0.911383	+	0.526187i	−0.0305071	+	0.999535i	$0.509712\pi$
$360$		0			0
$361$	−155768.	+	269799.i	−1.19527	+	2.07026i
$362$	2893.78	−	510.252i	0.0220825	−	0.00389374i
$363$		0			0
$364$	5204.89	−	1894.43i	0.0392834	−	0.0142980i
$365$	−16601.4	−	45612.1i	−0.124612	−	0.342369i
$366$		0			0
$367$	9228.99	+	52340.2i	0.0685208	+	0.388601i	0.999710	+	0.0240654i	$0.00766100\pi$
$367$	9228.99	+	52340.2i	0.0685208	+	0.388601i	−0.931190	+	0.364535i	$0.881228\pi$
$368$	31227.3	+	18029.1i	0.230589	+	0.133131i
$369$		0			0
$370$	391.310	+	677.769i	0.00285836	+	0.00495083i
$371$	10588.7	+	12619.2i	0.0769301	+	0.0916818i
$372$		0			0
$373$	20141.6	−	114229.i	0.144769	−	0.821028i	−0.822783	−	0.568356i	$-0.807580\pi$
$373$	20141.6	−	114229.i	0.144769	−	0.821028i	0.967552	−	0.252672i	$-0.0813093\pi$
$374$	2214.42	−	2639.04i	0.0158313	−	0.0188670i
$375$		0			0
$376$	−146245.	−	53228.8i	−1.03444	−	0.376505i
$377$			102650.i			0.722231i
$378$		0			0
$379$	96083.1			0.668912			0.334456	−	0.942411i	$-0.391448\pi$
$379$	96083.1			0.668912			0.334456	+	0.942411i	$0.391448\pi$
$380$	−39493.7	+	108508.i	−0.273502	+	0.751441i
$381$		0			0
$382$	−8946.44	−	7506.95i	−0.0613089	−	0.0514443i
$383$	77310.8	+	13632.0i	0.527039	+	0.0929311i	0.430835	−	0.902431i	$-0.358219\pi$
$383$	77310.8	+	13632.0i	0.527039	+	0.0929311i	0.0962033	+	0.995362i	$0.469330\pi$
$384$		0			0
$385$	−3755.98	+	3151.64i	−0.0253397	+	0.0212626i
$386$	42727.2	−	24668.5i	0.286767	−	0.165565i
$387$		0			0
$388$	−15081.9	+	26122.7i	−0.100183	+	0.173522i
$389$	−198289.	+	34963.8i	−1.31039	+	0.231057i	−0.784836	−	0.619704i	$-0.787253\pi$
$389$	−198289.	+	34963.8i	−1.31039	+	0.231057i	−0.525553	+	0.850761i	$0.676142\pi$
$390$		0			0
$391$	−16043.4	+	5839.32i	−0.104941	+	0.0381952i
$392$	−54719.8	−	150342.i	−0.356101	−	0.978378i
$393$		0			0
$394$	−24232.9	−	137432.i	−0.156104	−	0.885308i
$395$	215767.	+	124573.i	1.38290	+	0.798418i
$396$		0			0
$397$	135773.	+	235165.i	0.861453	+	1.49208i	0.870526	+	0.492122i	$0.163779\pi$
$397$	135773.	+	235165.i	0.861453	+	1.49208i	−0.00907265	+	0.999959i	$0.502888\pi$
$398$	40478.0	+	48239.8i	0.255537	+	0.304537i
$399$		0			0
$400$	−1737.90	+	9856.10i	−0.0108619	+	0.0616006i
$401$	54180.2	−	64569.4i	0.336939	−	0.401549i	−0.570796	−	0.821092i	$-0.693365\pi$
$401$	54180.2	−	64569.4i	0.336939	−	0.401549i	0.907735	+	0.419543i	$0.137810\pi$
$402$		0			0
$403$	−118915.	−	43281.6i	−0.732196	−	0.266497i
$404$		−	2585.07i		−	0.0158383i
$405$		0			0
$406$	−8585.58			−0.0520856
$407$	252.449	−	693.598i	0.00152400	−	0.00418715i
$408$		0			0
$409$	−15527.6	−	13029.2i	−0.0928236	−	0.0778882i	0.595195	−	0.803581i	$-0.297075\pi$
$409$	−15527.6	−	13029.2i	−0.0928236	−	0.0778882i	−0.688019	+	0.725693i	$0.741519\pi$
$410$	147690.	+	26041.7i	0.878583	+	0.154918i
$411$		0			0
$412$	12088.2	−	10143.2i	0.0712142	−	0.0597558i
$413$	−2815.70	+	1625.64i	−0.0165077	+	0.00953071i
$414$		0			0
$415$	12379.5	−	21442.0i	0.0718800	−	0.124500i
$416$	135741.	−	23934.8i	0.784376	−	0.138307i
$417$		0			0
$418$	−91592.3	+	33336.9i	−0.524211	+	0.190797i
$419$	−75483.4	−	207389.i	−0.429955	−	1.18129i	−0.945840	−	0.324634i	$-0.894759\pi$
$419$	−75483.4	−	207389.i	−0.429955	−	1.18129i	0.515884	−	0.856658i	$-0.327463\pi$
$420$		0			0
$421$	14696.9	+	83350.0i	0.0829202	+	0.470264i	0.997786	+	0.0665059i	$0.0211851\pi$
$421$	14696.9	+	83350.0i	0.0829202	+	0.470264i	−0.914866	+	0.403758i	$0.867704\pi$
$422$	54179.9	+	31280.8i	0.304238	+	0.175652i
$423$		0			0
$424$	123878.	+	214563.i	0.689067	+	1.19350i
$425$	−3045.99	−	3630.07i	−0.0168636	−	0.0200973i
$426$		0			0
$427$	2011.21	−	11406.1i	0.0110307	−	0.0625580i
$428$	−33928.2	+	40434.1i	−0.185214	+	0.220729i
$429$		0			0
$430$	179127.	+	65196.9i	0.968778	+	0.352606i
$431$			29925.1i			0.161095i	0.996751	+	0.0805473i	$0.0256668\pi$
$431$			29925.1i			0.161095i	−0.996751	+	0.0805473i	$0.974333\pi$
$432$		0			0
$433$	−3195.13			−0.0170417			−0.00852084	−	0.999964i	$-0.502712\pi$
$433$	−3195.13			−0.0170417			−0.00852084	+	0.999964i	$0.502712\pi$
$434$	3620.05	−	9946.00i	0.0192192	−	0.0528042i
$435$		0			0
$436$	34658.1	+	29081.6i	0.182319	+	0.152984i
$437$	475711.	+	83880.6i	2.49104	+	0.439237i
$438$		0			0
$439$	135548.	−	113738.i	0.703336	−	0.590169i	−0.219384	−	0.975639i	$-0.570405\pi$
$439$	135548.	−	113738.i	0.703336	−	0.590169i	0.922721	+	0.385469i	$0.125960\pi$
$440$	−63862.6	+	36871.1i	−0.329869	+	0.190450i
$441$		0			0
$442$	4741.71	−	8212.88i	0.0242712	−	0.0420389i
$443$	−202076.	+	35631.4i	−1.02969	+	0.181562i	−0.662874	−	0.748731i	$-0.730663\pi$
$443$	−202076.	+	35631.4i	−1.02969	+	0.181562i	−0.366817	+	0.930293i	$0.619552\pi$
$444$		0			0
$445$	−29811.9	+	10850.6i	−0.150546	+	0.0547943i
$446$	−39526.1	−	108597.i	−0.198708	−	0.545945i
$447$		0			0
$448$	2617.81	+	14846.4i	0.0130432	+	0.0739714i
$449$	−79625.9	−	45972.0i	−0.394968	−	0.228035i	0.289343	−	0.957226i	$-0.406563\pi$
$449$	−79625.9	−	45972.0i	−0.394968	−	0.228035i	−0.684310	+	0.729191i	$0.739897\pi$
$450$		0			0
$451$	−70719.6	−	122490.i	−0.347686	−	0.602209i
$452$	−62111.9	−	74022.1i	−0.304017	−	0.362313i
$453$		0			0
$454$	−23918.7	+	135650.i	−0.116045	+	0.658123i
$455$	−8675.80	+	10339.4i	−0.0419070	+	0.0499429i
$456$		0			0
$457$	154652.	+	56288.6i	0.740494	+	0.269518i	0.684600	−	0.728919i	$-0.259977\pi$
$457$	154652.	+	56288.6i	0.740494	+	0.269518i	0.0558943	+	0.998437i	$0.482199\pi$
$458$		−	23641.2i		−	0.112704i
$459$		0			0
$460$	126237.			0.596581
$461$	−26192.6	+	71963.7i	−0.123247	+	0.338619i	−0.985938	−	0.167113i	$-0.946555\pi$
$461$	−26192.6	+	71963.7i	−0.123247	+	0.338619i	0.862690	+	0.505732i	$0.168778\pi$
$462$		0			0
$463$	−216642.	−	181785.i	−1.01061	−	0.847999i	−0.0221872	−	0.999754i	$-0.507063\pi$
$463$	−216642.	−	181785.i	−1.01061	−	0.847999i	−0.988418	+	0.151755i	$0.951507\pi$
$464$	−34160.7	−	6023.46i	−0.158669	−	0.0279776i
$465$		0			0
$466$	67007.5	−	56226.0i	0.308569	−	0.258920i
$467$	271326.	−	156650.i	1.24411	−	0.718284i	0.274178	−	0.961679i	$-0.411594\pi$
$467$	271326.	−	156650.i	1.24411	−	0.718284i	0.969927	+	0.243395i	$0.0782610\pi$
$468$		0			0
$469$	−11655.2	+	20187.4i	−0.0529876	+	0.0917773i
$470$	129007.	−	22747.4i	0.584006	−	0.102976i
$471$		0			0
$472$	−45950.2	+	16724.5i	−0.206255	+	0.0750706i
$473$	−61489.1	−	168940.i	−0.274837	−	0.755109i
$474$		0			0
$475$	23281.5	+	132036.i	0.103187	+	0.585202i
$476$	−767.504	−	443.119i	−0.00338740	−	0.00195572i
$477$		0			0
$478$	−177.026	−	306.618i	−0.000774786	−	0.00134197i
$479$	67891.4	+	80909.8i	0.295899	+	0.352639i	0.893426	−	0.449210i	$-0.148294\pi$
$479$	67891.4	+	80909.8i	0.295899	+	0.352639i	−0.597527	+	0.801849i	$0.703850\pi$
$480$		0			0
$481$	352.829	−	2000.99i	0.00152502	−	0.00864880i
$482$	−18070.7	+	21535.8i	−0.0777822	+	0.0926972i
$483$		0			0
$484$	−93587.7	−	34063.2i	−0.399511	−	0.145410i
$485$		−	73502.7i		−	0.312478i
$486$		0			0
$487$	−202757.			−0.854907			−0.427453	−	0.904037i	$-0.640589\pi$
$487$	−202757.			−0.854907			−0.427453	+	0.904037i	$0.640589\pi$
$488$	59577.9	−	163689.i	0.250176	−	0.687353i
$489$		0			0
$490$	103161.	+	86562.0i	0.429657	+	0.360525i
$491$	−177302.	−	31263.1i	−0.735445	−	0.129679i	−0.206634	−	0.978418i	$-0.566251\pi$
$491$	−177302.	−	31263.1i	−0.735445	−	0.129679i	−0.528811	+	0.848740i	$0.677362\pi$
$492$		0			0
$493$	12581.6	−	10557.2i	0.0517658	−	0.0434367i
$494$	−232368.	+	134158.i	−0.952187	+	0.549745i
$495$		0			0
$496$	21381.5	−	37033.9i	0.0869111	−	0.150534i
$497$	18211.8	−	3211.23i	0.0737292	−	0.0130004i
$498$		0			0
$499$	210354.	−	76562.7i	0.844793	−	0.307480i	0.116878	−	0.993146i	$-0.462711\pi$
$499$	210354.	−	76562.7i	0.844793	−	0.307480i	0.727916	+	0.685667i	$0.240489\pi$
$500$	49117.2	+	134948.i	0.196469	+	0.539793i
$501$		0			0
$502$	4823.40	+	27354.8i	0.0191402	+	0.108549i
$503$	249553.	+	144079.i	0.986339	+	0.569463i	0.904178	−	0.427156i	$-0.140485\pi$
$503$	249553.	+	144079.i	0.986339	+	0.569463i	0.0821609	+	0.996619i	$0.473818\pi$
$504$		0			0
$505$	3149.62	+	5455.30i	0.0123502	+	0.0213912i
$506$	68493.5	+	81627.4i	0.267515	+	0.318812i
$507$		0			0
$508$	−17582.7	+	99716.7i	−0.0681333	+	0.386403i
$509$	−273689.	+	326170.i	−1.05638	+	1.25895i	−0.0916295	+	0.995793i	$0.529208\pi$
$509$	−273689.	+	326170.i	−1.05638	+	1.25895i	−0.964754	+	0.263155i	$0.915237\pi$
$510$		0			0
$511$	−9904.54	−	3604.96i	−0.0379308	−	0.0138057i
$512$			99923.4i			0.381177i
$513$		0			0
$514$	−298570.			−1.13011
$515$	−13151.5	+	36133.4i	−0.0495862	+	0.136237i
$516$		0			0
$517$	−94642.6	−	79414.6i	−0.354083	−	0.297111i
$518$	167.362	+	29.5104i	0.000623731	+	0.000109981i
$519$		0			0
$520$	−155504.	+	130484.i	−0.575090	+	0.482558i
$521$	−132765.	+	76652.0i	−0.489112	+	0.282389i	−0.724206	−	0.689584i	$-0.757794\pi$
$521$	−132765.	+	76652.0i	−0.489112	+	0.282389i	0.235094	+	0.971973i	$0.424460\pi$
$522$		0			0
$523$	165253.	−	286227.i	0.604153	−	1.04642i	−0.388032	−	0.921646i	$-0.626845\pi$
$523$	165253.	−	286227.i	0.604153	−	1.04642i	0.992185	−	0.124778i	$-0.0398217\pi$
$524$	245553.	−	43297.6i	0.894299	−	0.157689i
$525$		0			0
$526$	−16172.0	+	5886.13i	−0.0584511	+	0.0212745i
$527$	6925.12	+	19026.6i	0.0249348	+	0.0685078i
$528$		0			0
$529$	−43106.4	−	244469.i	−0.154039	−	0.873599i
$530$	−180601.	−	104270.i	−0.642938	−	0.371200i
$531$		0			0
$532$	12537.2	+	21715.1i	0.0442973	+	0.0767252i
$533$	−250271.	−	298261.i	−0.880959	−	1.04989i
$534$		0			0
$535$	22334.7	−	126666.i	0.0780320	−	0.442541i
$536$	−225353.	+	268566.i	−0.784394	+	0.934805i
$537$		0			0
$538$	−138546.	−	50426.6i	−0.478662	−	0.174219i
$539$		−	127008.i		−	0.437173i
$540$		0			0
$541$	−61881.3			−0.211429			−0.105715	−	0.994397i	$-0.533713\pi$
$541$	−61881.3			−0.211429			−0.105715	+	0.994397i	$0.533713\pi$
$542$	−31861.5	+	87538.8i	−0.108460	+	0.297990i
$543$		0			0
$544$	−16894.2	−	14175.9i	−0.0570874	−	0.0479020i
$545$	−108572.	−	19144.2i	−0.365532	−	0.0644532i
$546$		0			0
$547$	−148113.	+	124281.i	−0.495015	+	0.415367i	−0.855819	−	0.517275i	$-0.826947\pi$
$547$	−148113.	+	124281.i	−0.495015	+	0.415367i	0.360805	+	0.932641i	$0.382502\pi$
$548$	97388.8	−	56227.4i	0.324301	−	0.187235i
$549$		0			0
$550$	−14787.7	+	25613.1i	−0.0488851	+	0.0846714i
$551$	−457630.	+	80692.6i	−1.50734	+	0.265785i
$552$		0			0
$553$	50838.7	−	18503.8i	0.166243	−	0.0605076i
$554$	−22341.8	−	61383.6i	−0.0727946	−	0.200001i
$555$		0			0
$556$	−24561.2	−	139294.i	−0.0794513	−	0.450591i
$557$	−173114.	−	99947.1i	−0.557983	−	0.322151i	0.194353	−	0.980932i	$-0.437739\pi$
$557$	−173114.	−	99947.1i	−0.557983	−	0.322151i	−0.752335	+	0.658780i	$0.771073\pi$
$558$		0			0
$559$	−247451.	−	428597.i	−0.791891	−	1.37159i
$560$	−2931.75	−	3493.92i	−0.00934869	−	0.0111413i
$561$		0			0
$562$	−61833.5	+	350675.i	−0.195772	+	1.11028i
$563$	−115906.	+	138131.i	−0.365669	+	0.435787i	−0.917237	−	0.398343i	$-0.869585\pi$
$563$	−115906.	+	138131.i	−0.365669	+	0.435787i	0.551568	+	0.834130i	$0.314030\pi$
$564$		0			0
$565$	221263.	+	80533.2i	0.693126	+	0.252277i
$566$			27210.7i			0.0849390i
$567$		0			0
$568$	278130.			0.862086
$569$	166889.	−	458524.i	0.515470	−	1.41624i	−0.359992	−	0.932955i	$-0.617221\pi$
$569$	166889.	−	458524.i	0.515470	−	1.41624i	0.875462	−	0.483287i	$-0.160557\pi$
$570$		0			0
$571$	375368.	+	314972.i	1.15129	+	0.966049i	0.999749	−	0.0224018i	$-0.00713130\pi$
$571$	375368.	+	314972.i	1.15129	+	0.966049i	0.151543	+	0.988451i	$0.451576\pi$
$572$	65127.1	+	11483.7i	0.199053	+	0.0350985i
$573$		0			0
$574$	24946.4	−	20932.5i	0.0757153	−	0.0635327i
$575$	126935.	−	73285.9i	0.383924	−	0.221659i
$576$		0			0
$577$	−7129.98	+	12349.5i	−0.0214159	+	0.0370935i	−0.876535	−	0.481339i	$-0.840151\pi$
$577$	−7129.98	+	12349.5i	−0.0214159	+	0.0370935i	0.855119	+	0.518432i	$0.173484\pi$
$578$	224613.	−	39605.3i	0.672325	−	0.118549i
$579$		0			0
$580$	−114115.	+	41534.5i	−0.339224	+	0.123468i
$581$	−1838.82	−	5052.13i	−0.00544739	−	0.0149666i
$582$		0			0
$583$	34153.2	+	193692.i	0.100483	+	0.569869i
$584$	−137286.	−	79262.0i	−0.402532	−	0.232402i
$585$		0			0
$586$	−173855.	−	301126.i	−0.506282	−	0.876906i
$587$	154803.	+	184486.i	0.449264	+	0.535412i	0.942377	−	0.334553i	$-0.108585\pi$
$587$	154803.	+	184486.i	0.449264	+	0.535412i	−0.493113	+	0.869965i	$0.664141\pi$
$588$		0			0
$589$	99477.8	−	564167.i	0.286745	−	1.62621i
$590$	26456.7	−	31529.9i	0.0760032	−	0.0905771i
$591$		0			0
$592$	645.204	+	234.835i	0.00184100	+	0.000670069i
$593$		−	183216.i		−	0.521018i	−0.965471	−	0.260509i	$-0.916110\pi$
$593$		−	183216.i		−	0.521018i	0.965471	−	0.260509i	$-0.0838904\pi$
$594$		0			0
$595$	2159.56			0.00610003
$596$	−90912.2	+	249779.i	−0.255935	+	0.703176i
$597$		0			0
$598$	224703.	+	188548.i	0.628357	+	0.527254i
$599$	41314.9	+	7284.93i	0.115147	+	0.0203035i	0.230925	−	0.972972i	$-0.425825\pi$
$599$	41314.9	+	7284.93i	0.115147	+	0.0203035i	−0.115778	+	0.993275i	$0.536936\pi$
$600$		0			0
$601$	−327235.	+	274583.i	−0.905964	+	0.760194i	−0.971347	−	0.237666i	$-0.923618\pi$
$601$	−327235.	+	274583.i	−0.905964	+	0.760194i	0.0653827	+	0.997860i	$0.479173\pi$
$602$	35847.6	−	20696.6i	0.0989162	−	0.0571093i
$603$		0			0
$604$	118769.	−	205715.i	0.325560	−	0.563886i
$605$	239002.	−	42142.4i	0.652965	−	0.115135i
$606$		0			0
$607$	281906.	−	102605.i	0.765115	−	0.278479i	0.0701630	−	0.997536i	$-0.477648\pi$
$607$	281906.	−	102605.i	0.765115	−	0.278479i	0.694951	+	0.719057i	$0.255426\pi$
$608$	213411.	+	586341.i	0.577310	+	1.58615i
$609$		0			0
$610$	25460.7	+	144395.i	0.0684244	+	0.388054i
$611$	−294534.	−	170049.i	−0.788957	−	0.455505i
$612$		0			0
$613$	−31507.3	−	54572.2i	−0.0838475	−	0.145228i	0.821052	−	0.570853i	$-0.193388\pi$
$613$	−31507.3	−	54572.2i	−0.0838475	−	0.145228i	−0.904900	+	0.425625i	$0.860054\pi$
$614$	43036.8	+	51289.3i	0.114157	+	0.136047i
$615$		0			0
$616$	−2780.62	+	15769.7i	−0.00732790	+	0.0415586i
$617$	416190.	−	495996.i	1.09325	−	1.30289i	0.143585	−	0.989638i	$-0.454137\pi$
$617$	416190.	−	495996.i	1.09325	−	1.30289i	0.949670	−	0.313252i	$-0.101419\pi$
$618$		0			0
$619$	−167117.	−	60825.7i	−0.436154	−	0.158747i	0.114605	−	0.993411i	$-0.463440\pi$
$619$	−167117.	−	60825.7i	−0.436154	−	0.158747i	−0.550760	+	0.834664i	$0.685662\pi$
$620$		−	149710.i		−	0.389463i
$621$		0			0
$622$	287822.			0.743950
$623$	−2356.19	+	6473.57i	−0.00607063	+	0.0166789i
$624$		0			0
$625$	−171504.	−	143909.i	−0.439050	−	0.368407i
$626$	−74697.9	−	13171.3i	−0.190616	−	0.0336108i
$627$		0			0
$628$	−188885.	+	158494.i	−0.478937	+	0.401876i
$629$	−281.546	+	162.551i	−0.000711619	+	0.000410854i
$630$		0			0
$631$	−196507.	+	340360.i	−0.493536	+	0.854830i	−0.999972	−	0.00744748i	$-0.997629\pi$
$631$	−196507.	+	340360.i	−0.493536	+	0.854830i	0.506436	+	0.862278i	$0.330963\pi$
$632$	801321.	−	141295.i	2.00619	−	0.353746i
$633$		0			0
$634$	−405152.	+	147463.i	−1.00795	+	0.366865i
$635$	−84388.7	−	231856.i	−0.209284	−	0.575004i
$636$		0			0
$637$	−60711.9	−	344314.i	−0.149622	−	0.848547i
$638$	−88773.7	−	51253.5i	−0.218094	−	0.125916i
$639$		0			0
$640$	59080.9	+	102331.i	0.144241	+	0.249832i
$641$	480838.	+	573041.i	1.17026	+	1.39466i	0.902231	+	0.431254i	$0.141929\pi$
$641$	480838.	+	573041.i	1.17026	+	1.39466i	0.268032	+	0.963410i	$0.413627\pi$
$642$		0			0
$643$	−54652.7	+	309951.i	−0.132187	+	0.749671i	0.844590	+	0.535414i	$0.179844\pi$
$643$	−54652.7	+	309951.i	−0.132187	+	0.749671i	−0.976777	+	0.214258i	$0.931267\pi$
$644$	17620.1	−	20998.8i	0.0424850	−	0.0506316i
$645$		0			0
$646$	40341.8	+	14683.2i	0.0966697	+	0.0351849i
$647$			550784.i			1.31575i	0.753128	+	0.657874i	$0.228544\pi$
$647$			550784.i			1.31575i	−0.753128	+	0.657874i	$0.771456\pi$
$648$		0			0
$649$	−38818.6			−0.0921616
$650$	−27845.6	+	76505.0i	−0.0659066	+	0.181077i
$651$		0			0
$652$	254816.	+	213816.i	0.599421	+	0.502974i
$653$	−228046.	−	40210.6i	−0.534805	−	0.0943006i	−0.100278	−	0.994959i	$-0.531973\pi$
$653$	−228046.	−	40210.6i	−0.534805	−	0.0943006i	−0.434527	+	0.900659i	$0.643084\pi$
$654$		0			0
$655$	−465440.	+	390551.i	−1.08488	+	0.910322i
$656$	113944.	−	65785.4i	0.264778	−	0.152870i
$657$		0			0
$658$	14222.8	−	24634.7i	0.0328499	−	0.0568978i
$659$	−394686.	+	69593.8i	−0.908826	+	0.160251i	−0.608470	−	0.793577i	$-0.708217\pi$
$659$	−394686.	+	69593.8i	−0.908826	+	0.160251i	−0.300356	+	0.953827i	$0.597105\pi$
$660$		0			0
$661$	699174.	−	254479.i	1.60023	−	0.582436i	0.620756	−	0.784004i	$-0.286826\pi$
$661$	699174.	−	254479.i	1.60023	−	0.582436i	0.979475	+	0.201567i	$0.0646035\pi$
$662$	102670.	+	282083.i	0.234275	+	0.643666i
$663$		0			0
$664$	−14041.2	−	79631.8i	−0.0318471	−	0.180614i
$665$	−52914.8	−	30550.4i	−0.119656	−	0.0690834i
$666$		0			0
$667$	254005.	+	439950.i	0.570940	+	0.988898i
$668$	−216376.	−	257866.i	−0.484904	−	0.577886i
$669$		0			0
$670$	51242.9	−	290613.i	0.114152	−	0.647389i
$671$	88887.1	−	105932.i	0.197421	−	0.235277i
$672$		0			0
$673$	728273.	+	265070.i	1.60792	+	0.585234i	0.981027	−	0.193873i	$-0.0621049\pi$
$673$	728273.	+	265070.i	1.60792	+	0.585234i	0.626891	+	0.779107i	$0.284327\pi$
$674$		−	343394.i		−	0.755915i
$675$		0			0
$676$	−59100.9			−0.129330
$677$	60203.6	−	165408.i	0.131355	−	0.360894i	−0.856527	−	0.516102i	$-0.827383\pi$
$677$	60203.6	−	165408.i	0.131355	−	0.360894i	0.987882	+	0.155208i	$0.0496048\pi$
$678$		0			0
$679$	−12226.8	−	10259.5i	−0.0265199	−	0.0222529i
$680$	31986.3	+	5640.05i	0.0691746	+	0.0121973i
$681$		0			0
$682$	96805.6	−	81229.5i	0.208129	−	0.174641i
$683$	18413.3	−	10630.9i	0.0394721	−	0.0227893i	−0.480134	−	0.877195i	$-0.659412\pi$
$683$	18413.3	−	10630.9i	0.0394721	−	0.0227893i	0.519606	+	0.854406i	$0.326079\pi$
$684$		0			0
$685$	−137014.	+	237315.i	−0.292000	+	0.505759i
$686$	57837.9	−	10198.4i	0.122903	−	0.0216712i
$687$		0			0
$688$	157153.	−	57198.9i	0.332005	−	0.120840i
$689$	185176.	+	508767.i	0.390074	+	1.07172i
$690$		0			0
$691$	112676.	+	639019.i	0.235981	+	1.33831i	0.840539	+	0.541752i	$0.182239\pi$
$691$	112676.	+	639019.i	0.235981	+	1.33831i	−0.604558	+	0.796561i	$0.706650\pi$
$692$	−218850.	−	126353.i	−0.457020	−	0.263860i
$693$		0			0
$694$	9121.90	+	15799.6i	0.0189394	+	0.0328040i
$695$	221546.	+	264028.i	0.458663	+	0.546614i
$696$		0			0
$697$	−10817.7	+	61350.5i	−0.0222675	+	0.126285i
$698$	61307.3	−	73063.2i	0.125835	−	0.149964i
$699$		0			0
$700$	7149.49	+	2602.20i	0.0145908	+	0.00531062i
$701$		−	485207.i		−	0.987396i	−0.869633	−	0.493698i	$-0.835645\pi$
$701$		−	485207.i		−	0.987396i	0.869633	−	0.493698i	$-0.164355\pi$
$702$		0			0
$703$	9198.12			0.0186118
$704$	−61560.8	+	169137.i	−0.124211	+	0.341266i
$705$		0			0
$706$	20975.8	+	17600.8i	0.0420832	+	0.0353120i
$707$	1347.08	+	237.527i	0.00269498	+	0.000475197i
$708$		0			0
$709$	312797.	−	262468.i	0.622258	−	0.522136i	−0.276254	−	0.961085i	$-0.589093\pi$
$709$	312797.	−	262468.i	0.622258	−	0.522136i	0.898512	+	0.438948i	$0.144649\pi$
$710$	−202742.	+	117053.i	−0.402187	+	0.232203i
$711$		0			0
$712$	−51805.3	+	89729.5i	−0.102191	+	0.177001i
$713$	−616761.	+	108752.i	−1.21321	+	0.213922i
$714$		0			0
$715$	−151430.	+	55116.0i	−0.296210	+	0.107812i
$716$	−148215.	−	407217.i	−0.289112	−	0.794329i
$717$		0			0
$718$	−64743.6	−	367179.i	−0.125588	−	0.712245i
$719$	800012.	+	461887.i	1.54753	+	0.893466i	0.998330	+	0.0577735i	$0.0184001\pi$
$719$	800012.	+	461887.i	1.54753	+	0.893466i	0.549198	+	0.835692i	$0.314933\pi$
$720$		0			0
$721$	4174.92	+	7231.17i	0.00803114	+	0.0139103i
$722$	−550484.	−	656041.i	−1.05601	−	1.25851i
$723$		0			0
$724$	1567.21	−	8888.07i	0.00298985	−	0.0169563i
$725$	−90633.7	+	108013.i	−0.172430	+	0.205494i
$726$		0			0
$727$	−676309.	−	246156.i	−1.27961	−	0.465738i	−0.389304	−	0.921109i	$-0.627284\pi$
$727$	−676309.	−	246156.i	−1.27961	−	0.465738i	−0.890302	+	0.455371i	$0.849507\pi$
$728$			44080.2i			0.0831726i
$729$		0			0
$730$	133432.			0.250389
$731$	−27082.9	+	74409.6i	−0.0506827	+	0.139250i
$732$		0			0
$733$	−455658.	−	382342.i	−0.848068	−	0.711613i	0.111295	−	0.993787i	$-0.464500\pi$
$733$	−455658.	−	382342.i	−0.848068	−	0.711613i	−0.959363	+	0.282174i	$0.908944\pi$
$734$	−143881.	−	25370.1i	−0.267061	−	0.0470901i
$735$		0			0
$736$	522549.	−	438471.i	0.964654	−	0.809441i
$737$	−241026.	+	139157.i	−0.443741	+	0.256194i
$738$		0			0
$739$	172228.	−	298308.i	0.315367	−	0.546231i	−0.664149	−	0.747600i	$-0.731206\pi$
$739$	172228.	−	298308.i	0.315367	−	0.546231i	0.979515	+	0.201369i	$0.0645392\pi$
$740$	2367.25	−	417.410i	0.00432296	−	0.000762254i
$741$		0			0
$742$	−42553.0	+	15488.0i	−0.0772898	+	0.0281312i
$743$	27503.9	+	75566.4i	0.0498215	+	0.136883i	0.962108	−	0.272670i	$-0.0879067\pi$
$743$	27503.9	+	75566.4i	0.0498215	+	0.136883i	−0.912286	+	0.409553i	$0.865685\pi$
$744$		0			0
$745$	−112475.	−	637879.i	−0.202649	−	1.14928i
$746$	276136.	+	159427.i	0.496186	+	0.286473i
$747$		0			0
$748$	−5290.59	−	9163.57i	−0.00945586	−	0.0163780i
$749$	−17952.8	−	21395.3i	−0.0320013	−	0.0381377i
$750$		0			0
$751$	−95468.4	+	541428.i	−0.169270	+	0.959977i	0.775282	+	0.631615i	$0.217608\pi$
$751$	−95468.4	+	541428.i	−0.169270	+	0.959977i	−0.944552	+	0.328362i	$0.893503\pi$
$752$	73873.7	−	88039.2i	0.130633	−	0.155683i
$753$		0			0
$754$	−265163.	−	96511.3i	−0.466412	−	0.169760i
$755$			578829.i			1.01545i
$756$		0			0
$757$	−351011.			−0.612532			−0.306266	−	0.951946i	$-0.599080\pi$
$757$	−351011.			−0.612532			−0.306266	+	0.951946i	$0.599080\pi$
$758$	−90337.2	+	248199.i	−0.157227	+	0.431979i
$759$		0			0
$760$	−703959.	−	590692.i	−1.21877	−	1.02267i
$761$	−720904.	−	127115.i	−1.24482	−	0.219496i	−0.487842	−	0.872932i	$-0.662216\pi$
$761$	−720904.	−	127115.i	−1.24482	−	0.219496i	−0.756982	+	0.653436i	$0.773327\pi$
$762$		0			0
$763$	−18339.0	+	15388.3i	−0.0315012	+	0.0264326i
$764$	−31064.8	+	17935.3i	−0.0532209	+	0.0307271i
$765$		0			0
$766$	−107901.	+	186890.i	−0.183894	+	0.318515i
$767$	−105236.	+	18555.9i	−0.178885	+	0.0315422i
$768$		0			0
$769$	−865052.	+	314853.i	−1.46282	+	0.532421i	−0.946139	−	0.323759i	$-0.895053\pi$
$769$	−865052.	+	314853.i	−1.46282	+	0.532421i	−0.516676	+	0.856181i	$0.672831\pi$
$770$	−4609.87	−	12665.5i	−0.00777513	−	0.0213620i
$771$		0			0
$772$	−26313.9	−	149234.i	−0.0441521	−	0.250399i
$773$	−58538.1	−	33797.0i	−0.0979669	−	0.0565612i	0.450216	−	0.892920i	$-0.351347\pi$
$773$	−58538.1	−	33797.0i	−0.0979669	−	0.0565612i	−0.548183	+	0.836358i	$0.684680\pi$
$774$		0			0
$775$	−86913.0	−	150538.i	−0.144704	−	0.250635i
$776$	−154302.	−	183890.i	−0.256241	−	0.305376i
$777$		0			0
$778$	96113.8	−	545089.i	0.158791	−	0.900550i
$779$	1.13296e6	−	1.35021e6i	1.86698	−	2.22498i
$780$		0			0
$781$	207477.	+	75515.6i	0.340149	+	0.123804i
$782$		−	46933.0i		−	0.0767476i
$783$		0			0
$784$	118146.			0.192215
$785$	205500.	−	564607.i	0.333482	−	0.916235i
$786$		0			0
$787$	35564.6	+	29842.2i	0.0574207	+	0.0481817i	0.671046	−	0.741415i	$-0.265845\pi$
$787$	35564.6	+	29842.2i	0.0574207	+	0.0481817i	−0.613626	+	0.789597i	$0.710290\pi$
$788$	−422113.	−	74429.9i	−0.679792	−	0.119866i
$789$		0			0
$790$	−524658.	+	440240.i	−0.840663	+	0.705400i
$791$	44280.1	−	25565.1i	0.0707711	−	0.0408597i
$792$		0			0
$793$	190333.	−	329666.i	0.302669	−	0.524237i
$794$	−735126.	+	129623.i	−1.16606	+	0.205608i
$795$		0			0
$796$	181752.	−	66152.4i	0.286849	−	0.104405i
$797$	232558.	+	638948.i	0.366113	+	1.00589i	0.976826	+	0.214034i	$0.0686605\pi$
$797$	232558.	+	638948.i	0.366113	+	1.00589i	−0.610714	+	0.791852i	$0.709117\pi$
$798$		0			0
$799$	9449.30	+	53589.6i	0.0148015	+	0.0839435i
$800$	163966.	+	94665.8i	0.256197	+	0.147915i
$801$		0			0
$802$	115854.	+	200665.i	0.180120	+	0.311977i
$803$	−80891.0	−	96402.1i	−0.125449	−	0.149505i
$804$		0			0
$805$	−11599.1	+	65782.0i	−0.0178992	+	0.101512i
$806$	223608.	−	266485.i	0.344204	−	0.410207i
$807$		0			0
$808$	19331.9	+	7036.24i	0.0296109	+	0.0107775i
$809$			801127.i			1.22406i	0.790833	+	0.612032i	$0.209648\pi$
$809$			801127.i			1.22406i	−0.790833	+	0.612032i	$0.790352\pi$
$810$		0			0
$811$	−992087.			−1.50837			−0.754186	−	0.656661i	$-0.771968\pi$
$811$	−992087.			−1.50837			−0.754186	+	0.656661i	$0.771968\pi$
$812$	−9019.10	+	24779.8i	−0.0136789	+	0.0375825i
$813$		0			0
$814$	1554.33	+	1304.24i	0.00234582	+	0.00196838i
$815$	−798253.	−	140754.i	−1.20178	−	0.211907i
$816$		0			0
$817$	1.71624e6	−	1.44009e6i	2.57118	−	2.15748i
$818$	48255.8	−	27860.5i	0.0721178	−	0.0416372i
$819$		0			0
$820$	230309.	−	398907.i	0.342518	−	0.593258i
$821$	51642.7	−	9105.99i	0.0766165	−	0.0135096i	−0.135209	−	0.990817i	$-0.543170\pi$
$821$	51642.7	−	9105.99i	0.0766165	−	0.0135096i	0.211825	+	0.977308i	$0.432059\pi$
$822$		0			0
$823$	−539451.	+	196344.i	−0.796438	+	0.289880i	−0.708010	−	0.706203i	$-0.750407\pi$
$823$	−539451.	+	196344.i	−0.796438	+	0.289880i	−0.0884284	+	0.996083i	$0.528184\pi$
$824$	42951.3	+	118008.i	0.0632589	+	0.173802i
$825$		0			0
$826$	−1552.01	−	8801.86i	−0.00227475	−	0.0129007i
$827$	488790.	+	282203.i	0.714680	+	0.412621i	0.812791	−	0.582555i	$-0.197947\pi$
$827$	488790.	+	282203.i	0.714680	+	0.412621i	−0.0981116	+	0.995175i	$0.531280\pi$
$828$		0			0
$829$	547234.	+	947838.i	0.796277	+	1.37919i	0.922025	+	0.387130i	$0.126534\pi$
$829$	547234.	+	947838.i	0.796277	+	1.37919i	−0.125748	+	0.992062i	$0.540133\pi$
$830$	43749.1	+	52138.2i	0.0635058	+	0.0756832i
$831$		0			0
$832$	−86039.0	+	487951.i	−0.124294	+	0.704904i
$833$	−35957.9	+	42853.0i	−0.0518209	+	0.0617577i
$834$		0			0
$835$	770802.	+	280549.i	1.10553	+	0.402379i
$836$			299374.i			0.428353i
$837$		0			0
$838$	606691.			0.863932
$839$	−372998.	+	1.02480e6i	−0.529887	+	1.45585i	0.329317	+	0.944219i	$0.393181\pi$
$839$	−372998.	+	1.02480e6i	−0.529887	+	1.45585i	−0.859204	+	0.511633i	$0.829041\pi$
$840$		0			0
$841$	167441.	+	140500.i	0.236739	+	0.198648i
$842$	−229126.	−	40401.0i	−0.323184	−	0.0569860i
$843$		0			0
$844$	147198.	−	123514.i	0.206642	−	0.173393i
$845$	124721.	−	72007.9i	0.174674	−	0.100848i
$846$		0			0
$847$	26349.6	−	45638.8i	0.0367288	−	0.0636162i
$848$	−180178.	+	31770.3i	−0.250559	+	0.0441803i
$849$		0			0
$850$	12240.9	−	4455.33i	0.0169425	−	0.00616655i
$851$	−3439.22	−	9449.17i	−0.00474898	−	0.0130477i
$852$		0			0
$853$	215844.	+	1.22411e6i	0.296649	+	1.68238i	0.660426	+	0.750891i	$0.270376\pi$
$853$	215844.	+	1.22411e6i	0.296649	+	1.68238i	−0.363777	+	0.931486i	$0.618513\pi$
$854$	27573.1	+	15919.3i	0.0378068	+	0.0218278i
$855$		0			0
$856$	−210030.	−	363782.i	−0.286638	−	0.496471i
$857$	−465252.	−	554466.i	−0.633471	−	0.754942i	0.349853	−	0.936805i	$-0.386232\pi$
$857$	−465252.	−	554466.i	−0.633471	−	0.754942i	−0.983324	+	0.181863i	$0.941787\pi$
$858$		0			0
$859$	11097.1	−	62934.5i	0.0150391	−	0.0852909i	−0.976364	−	0.216131i	$-0.930656\pi$
$859$	11097.1	−	62934.5i	0.0150391	−	0.0852909i	0.991404	+	0.130840i	$0.0417674\pi$
$860$	376344.	−	448509.i	0.508848	−	0.606421i
$861$		0			0
$862$	−77301.6	−	28135.5i	−0.104034	−	0.0378652i
$863$		−	735396.i		−	0.987415i	−0.869628	−	0.493708i	$-0.835641\pi$
$863$		−	735396.i		−	0.987415i	0.869628	−	0.493708i	$-0.164359\pi$
$864$		0			0
$865$	615790.			0.823001
$866$	3004.05	−	8253.57i	0.00400564	−	0.0110054i
$867$		0			0
$868$	−24903.4	−	20896.4i	−0.0330536	−	0.0277353i
$869$	636128.	+	112166.i	0.842374	+	0.148533i
$870$		0			0
$871$	−586895.	+	492464.i	−0.773614	+	0.649139i
$872$	−311816.	+	180027.i	−0.410078	+	0.236758i
$873$		0			0
$874$	−663941.	+	1.14998e6i	−0.869173	+	1.50545i
$875$	−74834.8	+	13195.4i	−0.0977434	+	0.0172348i
$876$		0			0
$877$	−1.24600e6	+	453506.i	−1.62001	+	0.589635i	−0.983384	−	0.181537i	$-0.941893\pi$
$877$	−1.24600e6	+	453506.i	−1.62001	+	0.589635i	−0.636626	+	0.771173i	$0.719670\pi$
$878$	166363.	+	457079.i	0.215808	+	0.592929i
$879$		0			0
$880$	−9456.13	−	53628.4i	−0.0122109	−	0.0692515i
$881$	−191232.	−	110408.i	−0.246382	−	0.142249i	0.371724	−	0.928343i	$-0.378767\pi$
$881$	−191232.	−	110408.i	−0.246382	−	0.142249i	−0.618107	+	0.786094i	$0.712100\pi$
$882$		0			0
$883$	80437.2	+	139321.i	0.103166	+	0.178688i	0.912987	−	0.407988i	$-0.133769\pi$
$883$	80437.2	+	139321.i	0.103166	+	0.178688i	−0.809822	+	0.586676i	$0.800436\pi$
$884$	−18722.9	−	22313.1i	−0.0239591	−	0.0285533i
$885$		0			0
$886$	97949.1	−	555497.i	0.124777	−	0.707643i
$887$	−194665.	+	231993.i	−0.247424	+	0.294868i	−0.875435	−	0.483336i	$-0.839425\pi$
$887$	−194665.	+	231993.i	−0.247424	+	0.294868i	0.628011	+	0.778205i	$0.283869\pi$
$888$		0			0
$889$	−50346.9	−	18324.8i	−0.0637044	−	0.0231865i
$890$		−	87211.0i		−	0.110101i
$891$		0			0
$892$	−354956.			−0.446113
$893$	526577.	−	1.44676e6i	0.660326	−	1.81423i
$894$		0			0
$895$	808929.	+	678772.i	1.00987	+	0.847380i
$896$	25268.7	+	4455.56i	0.0314751	+	0.00554991i
$897$		0			0
$898$	193618.	−	162465.i	0.240100	−	0.201468i
$899$	521756.	−	301236.i	0.645577	−	0.372724i
$900$		0			0
$901$	43313.9	−	75021.9i	0.0533553	−	0.0924141i
$902$	382903.	−	67516.2i	0.470626	−	0.0829840i
$903$		0			0
$904$	722621.	−	263012.i	0.884247	−	0.321839i
$905$	7521.83	+	20666.1i	0.00918389	+	0.0252325i
$906$		0			0
$907$	−99716.3	−	565519.i	−0.121214	−	0.687437i	−0.983485	−	0.180990i	$-0.942070\pi$
$907$	−99716.3	−	565519.i	−0.121214	−	0.687437i	0.862271	−	0.506447i	$-0.169041\pi$
$908$	366387.	+	211533.i	0.444394	+	0.256571i
$909$		0			0
$910$	−18551.5	−	32132.2i	−0.0224025	−	0.0388023i
$911$	905349.	+	1.07895e6i	1.09089	+	1.30007i	0.950758	+	0.309933i	$0.100307\pi$
$911$	905349.	+	1.07895e6i	1.09089	+	1.30007i	0.140127	+	0.990134i	$0.455249\pi$
$912$		0			0
$913$	11146.6	−	63215.6i	0.0133722	−	0.0758373i
$914$	−290806.	+	346569.i	−0.348106	+	0.414856i
$915$		0			0
$916$	−68233.4	−	24834.9i	−0.0813217	−	0.0295987i
$917$			131936.i			0.156901i
$918$		0			0
$919$	236611.			0.280158			0.140079	−	0.990140i	$-0.455264\pi$
$919$	236611.			0.280158			0.140079	+	0.990140i	$0.455264\pi$
$920$	−343601.	+	944035.i	−0.405955	+	1.11535i
$921$		0			0
$922$	−161268.	−	135320.i	−0.189709	−	0.159185i
$923$	598562.	+	105543.i	0.702596	+	0.123887i
$924$		0			0
$925$	2138.02	−	1794.01i	0.00249878	−	0.00209673i
$926$	673268.	−	388711.i	0.785174	−	0.453320i
$927$		0			0
$928$	−328107.	+	568298.i	−0.380995	+	0.659903i
$929$	1.24657e6	−	219804.i	1.44439	−	0.254685i	0.604138	−	0.796880i	$-0.293518\pi$
$929$	1.24657e6	−	219804.i	1.44439	−	0.254685i	0.840253	+	0.542195i	$0.182407\pi$
$930$		0			0
$931$	1.48728e6	−	541327.i	1.71591	−	0.624540i
$932$	−91888.9	−	252463.i	−0.105787	−	0.290647i
$933$		0			0
$934$	149554.	+	848163.i	0.171437	+	0.972267i
$935$	22329.6	+	12892.0i	0.0255422	+	0.0147468i
$936$		0			0
$937$	−50419.0	−	87328.3i	−0.0574269	−	0.0994663i	0.835883	−	0.548908i	$-0.184956\pi$
$937$	−50419.0	−	87328.3i	−0.0574269	−	0.0994663i	−0.893310	+	0.449442i	$0.851623\pi$
$938$	−41189.4	−	49087.6i	−0.0468144	−	0.0557912i
$939$		0			0
$940$	69867.3	−	396237.i	0.0790712	−	0.448435i
$941$	143674.	−	171223.i	0.162255	−	0.193368i	−0.678791	−	0.734331i	$-0.737496\pi$
$941$	143674.	−	171223.i	0.162255	−	0.193368i	0.841046	+	0.540964i	$0.181940\pi$
$942$		0			0
$943$	−1.81068e6	−	659034.i	−2.03619	−	0.741113i
$944$		−	36110.1i		−	0.0405215i
$945$		0			0
$946$	494213.			0.552245
$947$	44077.8	−	121103.i	0.0491496	−	0.135037i	−0.912689	−	0.408655i	$-0.865998\pi$
$947$	44077.8	−	121103.i	0.0491496	−	0.135037i	0.961839	+	0.273617i	$0.0882202\pi$
$948$		0			0
$949$	−265374.	−	222676.i	−0.294664	−	0.247252i
$950$	−362961.	−	63999.9i	−0.402173	−	0.0709140i
$951$		0			0
$952$	5402.83	−	4533.51i	0.00596139	−	0.00500220i
$953$	−297153.	+	171561.i	−0.327185	+	0.188901i	−0.654591	−	0.755983i	$-0.727159\pi$
$953$	−297153.	+	171561.i	−0.327185	+	0.188901i	0.327405	+	0.944884i	$0.393826\pi$
$954$		0			0
$955$	43704.3	−	75698.0i	0.0479201	−	0.0830000i
$956$	−1070.93	+	188.834i	−0.00117178	+	0.000206616i
$957$		0			0
$958$	−272835.	+	99304.0i	−0.297283	+	0.108202i
$959$	20351.7	+	55915.8i	0.0221291	+	0.0607991i
$960$		0			0
$961$	−31394.4	−	178047.i	−0.0339943	−	0.192791i
$962$	4837.18	+	2792.75i	0.00522688	+	0.00301774i
$963$		0			0
$964$	43173.6	+	74778.9i	0.0464584	+	0.0804684i
$965$	237355.	+	282869.i	0.254885	+	0.303760i
$966$		0			0
$967$	−91152.7	+	516952.i	−0.0974802	+	0.552838i	0.896479	+	0.443086i	$0.146117\pi$
$967$	−91152.7	+	516952.i	−0.0974802	+	0.552838i	−0.993959	+	0.109751i	$0.964995\pi$
$968$	509469.	−	607161.i	0.543710	−	0.647968i
$969$		0			0
$970$	189870.	+	69107.1i	0.201796	+	0.0734479i
$971$		−	720017.i		−	0.763668i	−0.924231	−	0.381834i	$-0.875293\pi$
$971$		−	720017.i		−	0.763668i	0.924231	−	0.381834i	$-0.124707\pi$
$972$		0			0
$973$	74842.9			0.0790542
$974$	190632.	−	523757.i	0.200945	−	0.552093i
$975$		0			0
$976$	98540.5	+	82685.3i	0.103446	+	0.0868018i
$977$	−140510.	−	24775.6i	−0.147203	−	0.0259559i	0.0995610	−	0.995031i	$-0.468256\pi$
$977$	−140510.	−	24775.6i	−0.147203	−	0.0259559i	−0.246764	+	0.969076i	$0.579367\pi$
$978$		0			0
$979$	−63008.0	+	52870.0i	−0.0657401	+	0.0551625i
$980$	358206.	−	206810.i	0.372975	−	0.215337i
$981$		0			0
$982$	247457.	−	428608.i	0.256612	−	0.444464i
$983$	−619056.	+	109156.i	−0.640654	+	0.112965i	−0.484532	−	0.874773i	$-0.661010\pi$
$983$	−619056.	+	109156.i	−0.640654	+	0.112965i	−0.156121	+	0.987738i	$0.549899\pi$
$984$		0			0
$985$	981475.	−	357228.i	1.01160	−	0.368191i
$986$	15442.0	+	42426.4i	0.0158836	+	0.0436398i
$987$		0			0
$988$	143106.	+	811594.i	0.146603	+	0.831428i
$989$	−2.12111e6	−	1.22462e6i	−2.16856	−	1.25202i
$990$		0			0
$991$	−308014.	−	533496.i	−0.313634	−	0.543230i	0.665512	−	0.746387i	$-0.268213\pi$
$991$	−308014.	−	533496.i	−0.313634	−	0.543230i	−0.979146	+	0.203157i	$0.934880\pi$
$992$	−520002.	−	619715.i	−0.528423	−	0.629751i
$993$		0			0
$994$	−8827.52	+	50063.4i	−0.00893441	+	0.0506696i
$995$	−302954.	+	361047.i	−0.306007	+	0.364685i
$996$		0			0
$997$	−784154.	−	285409.i	−0.788880	−	0.287129i	−0.0840098	−	0.996465i	$-0.526773\pi$
$997$	−784154.	−	285409.i	−0.788880	−	0.287129i	−0.704871	+	0.709336i	$0.748995\pi$
$998$			615366.i			0.617835i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.17.4		66
3.2	odd	2		27.5.f.a.23.8	yes	66
27.7	even	9		27.5.f.a.20.8	✓	66
27.20	odd	18	inner	81.5.f.a.62.4		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.20.8	✓	66	27.7	even	9
27.5.f.a.23.8	yes	66	3.2	odd	2
81.5.f.a.17.4		66	1.1	even	1	trivial
81.5.f.a.62.4		66	27.20	odd	18	inner

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.940198 + 2.58317i) q^{2} +(6.46790 + 5.42721i) q^{4} +(-20.2618 - 3.57269i) q^{5} +(-3.42243 + 2.87176i) q^{7} +(-58.1912 + 33.5967i) q^{8} +O(q^{10})\)	\(q+(-0.940198 + 2.58317i) q^{2} +(6.46790 + 5.42721i) q^{4} +(-20.2618 - 3.57269i) q^{5} +(-3.42243 + 2.87176i) q^{7} +(-58.1912 + 33.5967i) q^{8} +(28.2789 - 48.9806i) q^{10} +(-52.5310 + 9.26263i) q^{11} +(-137.982 + 50.2213i) q^{13} +(-4.20048 - 11.5407i) q^{14} +(-8.61636 - 48.8658i) q^{16} +(20.3466 + 11.7471i) q^{17} +(-332.362 - 575.668i) q^{19} +(-111.661 - 133.073i) q^{20} +(25.4626 - 144.405i) q^{22} +(-467.109 + 556.678i) q^{23} +(-189.533 - 68.9845i) q^{25} -403.649i q^{26} -37.7215 q^{28} +(239.097 - 656.913i) q^{29} +(660.190 + 553.965i) q^{31} +(-924.431 - 163.002i) q^{32} +(-49.4746 + 41.5141i) q^{34} +(79.6042 - 45.9595i) q^{35} +(-6.91875 + 11.9836i) q^{37} +(1799.54 - 317.307i) q^{38} +(1299.09 - 472.829i) q^{40} +(906.896 + 2491.68i) q^{41} +(585.265 + 3319.20i) q^{43} +(-390.036 - 225.187i) q^{44} +(-998.822 - 1730.01i) q^{46} +(1488.80 + 1774.28i) q^{47} +(-413.463 + 2344.87i) q^{49} +(356.398 - 424.738i) q^{50} +(-1165.02 - 424.031i) q^{52} -3687.20i q^{53} +1097.46 q^{55} +(102.673 - 282.093i) q^{56} +(1472.12 + 1235.26i) q^{58} +(716.683 + 126.370i) q^{59} +(-1985.92 + 1666.38i) q^{61} +(-2051.70 + 1184.55i) q^{62} +(1687.17 - 2922.26i) q^{64} +(2975.18 - 524.605i) q^{65} +(4902.93 - 1784.52i) q^{67} +(67.8456 + 186.404i) q^{68} +(43.8777 + 248.843i) q^{70} +(-3584.69 - 2069.62i) q^{71} +(1179.61 + 2043.14i) q^{73} +(-24.4508 - 29.1393i) q^{74} +(974.588 - 5527.16i) q^{76} +(153.183 - 182.557i) q^{77} +(-11379.3 - 4141.72i) q^{79} +1020.89i q^{80} -7289.09 q^{82} +(-411.586 + 1130.82i) q^{83} +(-370.288 - 310.709i) q^{85} +(-9124.34 - 1608.87i) q^{86} +(2745.65 - 2303.87i) q^{88} +(1335.39 - 770.989i) q^{89} +(328.010 - 568.129i) q^{91} +(-6042.42 + 1065.44i) q^{92} +(-5983.04 + 2177.65i) q^{94} +(4677.55 + 12851.5i) q^{95} +(620.366 + 3518.27i) q^{97} +(-5668.46 - 3272.69i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28} - 5016 q^{29} - 1671 q^{31} - 10224 q^{32} - 342 q^{34} + 2682 q^{35} - 3 q^{37} + 6564 q^{38} - 1113 q^{40} - 5754 q^{41} - 1266 q^{43} + 4545 q^{44} - 3 q^{46} + 9159 q^{47} + 5898 q^{49} + 34977 q^{50} + 2871 q^{52} - 12 q^{55} - 39243 q^{56} - 12291 q^{58} - 24762 q^{59} - 8358 q^{61} - 38304 q^{62} + 6141 q^{64} - 23727 q^{65} + 15996 q^{67} + 43533 q^{68} - 7251 q^{70} + 19773 q^{71} + 6108 q^{73} + 74847 q^{74} - 28614 q^{76} + 33909 q^{77} - 5658 q^{79} - 12 q^{82} - 18813 q^{83} + 24219 q^{85} - 96474 q^{86} + 36042 q^{88} - 110232 q^{89} - 6042 q^{91} - 73545 q^{92} + 2631 q^{94} + 65163 q^{95} - 3696 q^{97} + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Introduction

L-functions

Modular forms

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