LMFDB - Embedded newform 198.5.j.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,5,Mod(19,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("198.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	198.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.4672526906$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			127.3
Root			$0.809017 + 5.77971i$ of defining polynomial
Character	$\chi$	$=$	198.127
Dual form			198.5.j.a.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68999 - 0.874032i) q^{2} +(6.47214 - 4.70228i) q^{4} +(-13.3838 + 41.1910i) q^{5} +(-7.80030 - 10.7362i) q^{7} +(13.3001 - 18.3060i) q^{8} +O(q^{10})$	\(q+(2.68999 - 0.874032i) q^{2} +(6.47214 - 4.70228i) q^{4} +(-13.3838 + 41.1910i) q^{5} +(-7.80030 - 10.7362i) q^{7} +(13.3001 - 18.3060i) q^{8} +122.501i q^{10} +(-90.5882 - 80.2170i) q^{11} +(-170.407 + 55.3685i) q^{13} +(-30.3665 - 22.0626i) q^{14} +(19.7771 - 60.8676i) q^{16} +(-167.901 - 54.5543i) q^{17} +(213.240 - 293.500i) q^{19} +(107.070 + 329.528i) q^{20} +(-313.794 - 136.606i) q^{22} -564.946 q^{23} +(-1011.94 - 735.215i) q^{25} +(-409.999 + 297.882i) q^{26} +(-100.969 - 32.8069i) q^{28} +(-505.658 - 695.978i) q^{29} +(276.141 + 849.875i) q^{31} -181.019i q^{32} -499.334 q^{34} +(546.632 - 177.611i) q^{35} +(-164.418 + 119.457i) q^{37} +(317.087 - 975.892i) q^{38} +(576.036 + 792.845i) q^{40} +(-1540.12 + 2119.80i) q^{41} +2603.62i q^{43} +(-963.502 - 93.2040i) q^{44} +(-1519.70 + 493.780i) q^{46} +(1250.87 + 908.812i) q^{47} +(687.529 - 2116.00i) q^{49} +(-3364.70 - 1093.26i) q^{50} +(-842.537 + 1159.65i) q^{52} +(454.551 + 1398.97i) q^{53} +(4516.63 - 2657.81i) q^{55} -300.281 q^{56} +(-1968.52 - 1430.22i) q^{58} +(-3977.33 + 2889.70i) q^{59} +(-1508.75 - 490.221i) q^{61} +(1485.64 + 2044.80i) q^{62} +(-158.217 - 486.941i) q^{64} -7760.26i q^{65} -3004.99 q^{67} +(-1343.21 + 436.434i) q^{68} +(1315.20 - 955.547i) q^{70} +(2625.89 - 8081.67i) q^{71} +(2674.58 + 3681.24i) q^{73} +(-337.875 + 465.045i) q^{74} -2902.29i q^{76} +(-154.610 + 1598.29i) q^{77} +(2009.88 - 653.050i) q^{79} +(2242.51 + 1629.28i) q^{80} +(-2290.15 + 7048.37i) q^{82} +(8994.67 + 2922.55i) q^{83} +(4494.29 - 6185.86i) q^{85} +(2275.65 + 7003.72i) q^{86} +(-2673.28 + 591.414i) q^{88} -14557.2 q^{89} +(1923.67 + 1397.63i) q^{91} +(-3656.40 + 2656.53i) q^{92} +(4159.17 + 1351.40i) q^{94} +(9235.60 + 12711.7i) q^{95} +(2097.12 + 6454.28i) q^{97} -6292.94i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 30 q^{5} + 150 q^{7}+O(q^{10}) $ 16 * q + 32 * q^4 - 30 * q^5 + 150 * q^7	$ 16 q + 32 q^{4} - 30 q^{5} + 150 q^{7} + 30 q^{11} - 510 q^{13} + 96 q^{14} - 256 q^{16} - 1770 q^{17} + 1020 q^{19} + 240 q^{20} + 240 q^{22} + 2424 q^{23} - 858 q^{25} - 480 q^{26} + 1600 q^{28} - 4890 q^{29} + 602 q^{31} - 3904 q^{34} + 8670 q^{35} - 4518 q^{37} + 4800 q^{38} - 1280 q^{40} - 1290 q^{41} - 720 q^{44} + 4480 q^{46} - 642 q^{47} + 9534 q^{49} - 6720 q^{50} + 4000 q^{52} - 2598 q^{53} + 2582 q^{55} + 3072 q^{56} - 6496 q^{58} - 6660 q^{59} - 27410 q^{61} + 19680 q^{62} + 2048 q^{64} + 21524 q^{67} - 14160 q^{68} + 34400 q^{70} + 5562 q^{71} - 7790 q^{73} - 5760 q^{74} + 1110 q^{77} - 2770 q^{79} + 3840 q^{80} - 17472 q^{82} + 36900 q^{83} - 24750 q^{85} - 624 q^{86} - 5760 q^{88} - 46596 q^{89} + 32370 q^{91} - 14112 q^{92} + 58880 q^{94} - 74250 q^{95} - 3732 q^{97}+O(q^{100}) $ 16 * q + 32 * q^4 - 30 * q^5 + 150 * q^7 + 30 * q^11 - 510 * q^13 + 96 * q^14 - 256 * q^16 - 1770 * q^17 + 1020 * q^19 + 240 * q^20 + 240 * q^22 + 2424 * q^23 - 858 * q^25 - 480 * q^26 + 1600 * q^28 - 4890 * q^29 + 602 * q^31 - 3904 * q^34 + 8670 * q^35 - 4518 * q^37 + 4800 * q^38 - 1280 * q^40 - 1290 * q^41 - 720 * q^44 + 4480 * q^46 - 642 * q^47 + 9534 * q^49 - 6720 * q^50 + 4000 * q^52 - 2598 * q^53 + 2582 * q^55 + 3072 * q^56 - 6496 * q^58 - 6660 * q^59 - 27410 * q^61 + 19680 * q^62 + 2048 * q^64 + 21524 * q^67 - 14160 * q^68 + 34400 * q^70 + 5562 * q^71 - 7790 * q^73 - 5760 * q^74 + 1110 * q^77 - 2770 * q^79 + 3840 * q^80 - 17472 * q^82 + 36900 * q^83 - 24750 * q^85 - 624 * q^86 - 5760 * q^88 - 46596 * q^89 + 32370 * q^91 - 14112 * q^92 + 58880 * q^94 - 74250 * q^95 - 3732 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	2.68999	−	0.874032i	0.672499	−	0.218508i
$2$	2.68999	−	0.874032i	0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	6.47214	−	4.70228i	0.404508	−	0.293893i
$5$	−13.3838	+	41.1910i	−0.535350	+	1.64764i	0.207540	+	0.978226i	$0.433454\pi$
$5$	−13.3838	+	41.1910i	−0.535350	+	1.64764i	−0.742891	+	0.669413i	$0.766546\pi$
$6$		0			0
$7$	−7.80030	−	10.7362i	−0.159190	−	0.219106i	0.721970	−	0.691924i	$-0.243237\pi$
$7$	−7.80030	−	10.7362i	−0.159190	−	0.219106i	−0.881160	+	0.472818i	$0.843237\pi$
$8$	13.3001	−	18.3060i	0.207813	−	0.286031i
$9$		0			0
$10$			122.501i			1.22501i
$11$	−90.5882	−	80.2170i	−0.748663	−	0.662951i
$11$	−90.5882	−	80.2170i	−0.748663	−	0.662951i
$12$		0			0
$13$	−170.407	+	55.3685i	−1.00832	+	0.327624i	−0.766187	−	0.642618i	$-0.777848\pi$
$13$	−170.407	+	55.3685i	−1.00832	+	0.327624i	−0.242137	+	0.970242i	$0.577848\pi$
$14$	−30.3665	−	22.0626i	−0.154931	−	0.112564i
$15$		0			0
$16$	19.7771	−	60.8676i	0.0772542	−	0.237764i
$17$	−167.901	−	54.5543i	−0.580972	−	0.188769i	0.00376408	−	0.999993i	$-0.498802\pi$
$17$	−167.901	−	54.5543i	−0.580972	−	0.188769i	−0.584736	+	0.811224i	$0.698802\pi$
$18$		0			0
$19$	213.240	−	293.500i	0.590693	−	0.813019i	−0.404123	−	0.914704i	$-0.632423\pi$
$19$	213.240	−	293.500i	0.590693	−	0.813019i	0.994817	+	0.101685i	$0.0324234\pi$
$20$	107.070	+	329.528i	0.267675	+	0.823820i
$21$		0			0
$22$	−313.794	−	136.606i	−0.648335	−	0.282244i
$23$	−564.946			−1.06795			−0.533975	−	0.845500i	$-0.679302\pi$
$23$	−564.946			−1.06795			−0.533975	+	0.845500i	$0.679302\pi$
$24$		0			0
$25$	−1011.94	−	735.215i	−1.61910	−	1.17634i
$26$	−409.999	+	297.882i	−0.606508	+	0.440654i
$27$		0			0
$28$	−100.969	−	32.8069i	−0.128787	−	0.0418455i
$29$	−505.658	−	695.978i	−0.601258	−	0.827560i	0.394565	−	0.918868i	$-0.370895\pi$
$29$	−505.658	−	695.978i	−0.601258	−	0.827560i	−0.995823	+	0.0913079i	$0.970895\pi$
$30$		0			0
$31$	276.141	+	849.875i	0.287348	+	0.884365i	0.985685	+	0.168596i	$0.0539234\pi$
$31$	276.141	+	849.875i	0.287348	+	0.884365i	−0.698338	+	0.715769i	$0.746077\pi$
$32$		−	181.019i		−	0.176777i
$33$		0			0
$34$	−499.334			−0.431950
$35$	546.632	−	177.611i	0.446230	−	0.144989i
$36$		0			0
$37$	−164.418	+	119.457i	−0.120101	+	0.0872585i	−0.646214	−	0.763156i	$-0.723649\pi$
$37$	−164.418	+	119.457i	−0.120101	+	0.0872585i	0.526113	+	0.850415i	$0.323649\pi$
$38$	317.087	−	975.892i	0.219589	−	0.675826i
$39$		0			0
$40$	576.036	+	792.845i	0.360022	+	0.495528i
$41$	−1540.12	+	2119.80i	−0.916196	+	1.26103i	0.0488107	+	0.998808i	$0.484457\pi$
$41$	−1540.12	+	2119.80i	−0.916196	+	1.26103i	−0.965006	+	0.262227i	$0.915543\pi$
$42$		0			0
$43$			2603.62i			1.40812i	0.710140	+	0.704061i	$0.248632\pi$
$43$			2603.62i			1.40812i	−0.710140	+	0.704061i	$0.751368\pi$
$44$	−963.502	−	93.2040i	−0.497677	−	0.0481425i
$45$		0			0
$46$	−1519.70	+	493.780i	−0.718195	+	0.233356i
$47$	1250.87	+	908.812i	0.566262	+	0.411413i	0.833745	−	0.552149i	$-0.186192\pi$
$47$	1250.87	+	908.812i	0.566262	+	0.411413i	−0.267484	+	0.963562i	$0.586192\pi$
$48$		0			0
$49$	687.529	−	2116.00i	0.286351	−	0.881298i
$50$	−3364.70	−	1093.26i	−1.34588	−	0.437303i
$51$		0			0
$52$	−842.537	+	1159.65i	−0.311589	+	0.428866i
$53$	454.551	+	1398.97i	0.161820	+	0.498030i	0.998788	−	0.0492218i	$-0.0156741\pi$
$53$	454.551	+	1398.97i	0.161820	+	0.498030i	−0.836968	+	0.547251i	$0.815674\pi$
$54$		0			0
$55$	4516.63	−	2657.81i	1.49310	−	0.878616i
$56$	−300.281			−0.0957528
$57$		0			0
$58$	−1968.52	−	1430.22i	−0.585173	−	0.425153i
$59$	−3977.33	+	2889.70i	−1.14258	+	0.830135i	−0.987477	−	0.157762i	$-0.949572\pi$
$59$	−3977.33	+	2889.70i	−1.14258	+	0.830135i	−0.155106	+	0.987898i	$0.549572\pi$
$60$		0			0
$61$	−1508.75	−	490.221i	−0.405468	−	0.131745i	0.0991805	−	0.995069i	$-0.468378\pi$
$61$	−1508.75	−	490.221i	−0.405468	−	0.131745i	−0.504648	+	0.863325i	$0.668378\pi$
$62$	1485.64	+	2044.80i	0.386482	+	0.531946i
$63$		0			0
$64$	−158.217	−	486.941i	−0.0386271	−	0.118882i
$65$		−	7760.26i		−	1.83675i
$66$		0			0
$67$	−3004.99			−0.669413			−0.334706	−	0.942323i	$-0.608637\pi$
$67$	−3004.99			−0.669413			−0.334706	+	0.942323i	$0.608637\pi$
$68$	−1343.21	+	436.434i	−0.290486	+	0.0943846i
$69$		0			0
$70$	1315.20	−	955.547i	0.268408	−	0.195010i
$71$	2625.89	−	8081.67i	0.520907	−	1.60319i	−0.251362	−	0.967893i	$-0.580879\pi$
$71$	2625.89	−	8081.67i	0.520907	−	1.60319i	0.772270	−	0.635295i	$-0.219121\pi$
$72$		0			0
$73$	2674.58	+	3681.24i	0.501891	+	0.690793i	0.982526	−	0.186127i	$-0.0595937\pi$
$73$	2674.58	+	3681.24i	0.501891	+	0.690793i	−0.480635	+	0.876921i	$0.659594\pi$
$74$	−337.875	+	465.045i	−0.0617011	+	0.0849243i
$75$		0			0
$76$		−	2902.29i		−	0.502474i
$77$	−154.610	+	1598.29i	−0.0260769	+	0.269572i
$78$		0			0
$79$	2009.88	−	653.050i	0.322045	−	0.104639i	−0.143533	−	0.989645i	$-0.545846\pi$
$79$	2009.88	−	653.050i	0.322045	−	0.104639i	0.465578	+	0.885007i	$0.345846\pi$
$80$	2242.51	+	1629.28i	0.350391	+	0.254574i
$81$		0			0
$82$	−2290.15	+	7048.37i	−0.340594	+	1.04824i
$83$	8994.67	+	2922.55i	1.30566	+	0.424234i	0.877546	−	0.479493i	$-0.159179\pi$
$83$	8994.67	+	2922.55i	1.30566	+	0.424234i	0.428111	+	0.903726i	$0.359179\pi$
$84$		0			0
$85$	4494.29	−	6185.86i	0.622047	−	0.856174i
$86$	2275.65	+	7003.72i	0.307686	+	0.946960i
$87$		0			0
$88$	−2673.28	+	591.414i	−0.345207	+	0.0763706i
$89$	−14557.2			−1.83779			−0.918896	−	0.394499i	$-0.870918\pi$
$89$	−14557.2			−1.83779			−0.918896	+	0.394499i	$0.870918\pi$
$90$		0			0
$91$	1923.67	+	1397.63i	0.232299	+	0.168775i
$92$	−3656.40	+	2656.53i	−0.431995	+	0.313863i
$93$		0			0
$94$	4159.17	+	1351.40i	0.470707	+	0.152942i
$95$	9235.60	+	12711.7i	1.02333	+	1.40850i
$96$		0			0
$97$	2097.12	+	6454.28i	0.222885	+	0.685969i	0.998499	+	0.0547624i	$0.0174401\pi$
$97$	2097.12	+	6454.28i	0.222885	+	0.685969i	−0.775614	+	0.631207i	$0.782560\pi$
$98$		−	6292.94i		−	0.655241i
$99$		0			0
$100$	−10006.6			−1.00066
$101$	12997.2	−	4223.06i	1.27411	−	0.413985i	0.407611	−	0.913156i	$-0.366362\pi$
$101$	12997.2	−	4223.06i	1.27411	−	0.413985i	0.866504	+	0.499171i	$0.166362\pi$
$102$		0			0
$103$	−995.164	+	723.029i	−0.0938038	+	0.0681524i	−0.633699	−	0.773580i	$-0.718464\pi$
$103$	−995.164	+	723.029i	−0.0938038	+	0.0681524i	0.539895	+	0.841733i	$0.318464\pi$
$104$	−1252.85	+	3855.86i	−0.115833	+	0.356496i
$105$		0			0
$106$	2445.48	+	3365.92i	0.217647	+	0.299565i
$107$	4974.60	−	6846.95i	0.434501	−	0.598040i	−0.534478	−	0.845182i	$-0.679492\pi$
$107$	4974.60	−	6846.95i	0.434501	−	0.598040i	0.968979	+	0.247143i	$0.0794917\pi$
$108$		0			0
$109$		−	7648.65i		−	0.643771i	−0.946779	−	0.321886i	$-0.895683\pi$
$109$		−	7648.65i		−	0.643771i	0.946779	−	0.321886i	$-0.104317\pi$
$110$	9826.69	−	11097.2i	0.812123	−	0.917122i
$111$		0			0
$112$	−807.754	+	262.455i	−0.0643936	+	0.0209228i
$113$	−7345.60	−	5336.89i	−0.575269	−	0.417957i	0.261747	−	0.965137i	$-0.415702\pi$
$113$	−7345.60	−	5336.89i	−0.575269	−	0.417957i	−0.837015	+	0.547180i	$0.815702\pi$
$114$		0			0
$115$	7561.10	−	23270.7i	0.571728	−	1.75960i
$116$	−6545.37	−	2126.72i	−0.486428	−	0.158050i
$117$		0			0
$118$	−8173.31	+	11249.6i	−0.586994	+	0.807928i
$119$	723.972	+	2228.16i	0.0511243	+	0.157345i
$120$		0			0
$121$	1771.46	+	14533.4i	0.120993	+	0.992653i
$122$	−4486.99			−0.301464
$123$		0			0
$124$	5783.57	+	4202.01i	0.376143	+	0.273284i
$125$	21928.3	−	15931.8i	1.40341	−	1.01964i
$126$		0			0
$127$	−6550.78	−	2128.48i	−0.406149	−	0.131966i	0.0988156	−	0.995106i	$-0.468495\pi$
$127$	−6550.78	−	2128.48i	−0.406149	−	0.131966i	−0.504965	+	0.863140i	$0.668495\pi$
$128$	−851.204	−	1171.58i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	−6782.72	−	20875.1i	−0.401344	−	1.23521i
$131$		−	1471.01i		−	0.0857182i	−0.999081	−	0.0428591i	$-0.986353\pi$
$131$		−	1471.01i		−	0.0857182i	0.999081	−	0.0428591i	$-0.0136467\pi$
$132$		0			0
$133$	−4814.41			−0.272170
$134$	−8083.41	+	2626.46i	−0.450179	+	0.146272i
$135$		0			0
$136$	−3231.76	+	2348.01i	−0.174728	+	0.126947i
$137$	−5600.55	+	17236.7i	−0.298394	+	0.918361i	0.683667	+	0.729794i	$0.260384\pi$
$137$	−5600.55	+	17236.7i	−0.298394	+	0.918361i	−0.982060	+	0.188567i	$0.939616\pi$
$138$		0			0
$139$	5984.50	+	8236.96i	0.309741	+	0.426322i	0.935300	−	0.353855i	$-0.115129\pi$
$139$	5984.50	+	8236.96i	0.309741	+	0.426322i	−0.625559	+	0.780176i	$0.715129\pi$
$140$	2702.70	−	3719.94i	0.137893	−	0.189793i
$141$		0			0
$142$		−	24034.8i		−	1.19196i
$143$	19878.3	+	8653.78i	0.972094	+	0.423189i
$144$		0			0
$145$	35435.6	−	11513.7i	1.68540	−	0.547621i
$146$	10412.1	+	7564.84i	0.488465	+	0.354890i
$147$		0			0
$148$	−502.418	+	1546.28i	−0.0229373	+	0.0705936i
$149$	25251.0	+	8204.56i	1.13738	+	0.369558i	0.816377	−	0.577519i	$-0.195979\pi$
$149$	25251.0	+	8204.56i	1.13738	+	0.369558i	0.321006	+	0.947077i	$0.395979\pi$
$150$		0			0
$151$	−11161.2	+	15362.0i	−0.489503	+	0.673744i	−0.980296	−	0.197533i	$-0.936707\pi$
$151$	−11161.2	+	15362.0i	−0.489503	+	0.673744i	0.490793	+	0.871276i	$0.336707\pi$
$152$	−2536.69	−	7807.14i	−0.109795	−	0.337913i
$153$		0			0
$154$	981.057	+	4434.52i	0.0413669	+	0.186984i
$155$	−38703.0			−1.61095
$156$		0			0
$157$	2755.25	+	2001.81i	0.111779	+	0.0812124i	0.642271	−	0.766478i	$-0.277993\pi$
$157$	2755.25	+	2001.81i	0.111779	+	0.0812124i	−0.530491	+	0.847690i	$0.677993\pi$
$158$	4835.78	−	3513.40i	0.193710	−	0.140739i
$159$		0			0
$160$	7456.36	+	2422.72i	0.291264	+	0.0946375i
$161$	4406.74	+	6065.36i	0.170007	+	0.233994i
$162$		0			0
$163$	2632.77	+	8102.84i	0.0990918	+	0.304973i	0.988298	−	0.152533i	$-0.0487429\pi$
$163$	2632.77	+	8102.84i	0.0990918	+	0.304973i	−0.889207	+	0.457506i	$0.848743\pi$
$164$			20961.7i			0.779362i
$165$		0			0
$166$	26750.0			0.970751
$167$	−12611.3	+	4097.65i	−0.452196	+	0.146927i	−0.526255	−	0.850327i	$-0.676404\pi$
$167$	−12611.3	+	4097.65i	−0.452196	+	0.146927i	0.0740598	+	0.997254i	$0.476404\pi$
$168$		0			0
$169$	2866.45	−	2082.59i	0.100362	−	0.0729174i
$170$	6682.97	−	20568.1i	0.231245	−	0.711698i
$171$		0			0
$172$	12242.9	+	16851.0i	0.413837	+	0.569597i
$173$	12984.4	−	17871.4i	0.433839	−	0.597128i	−0.534990	−	0.844858i	$-0.679685\pi$
$173$	12984.4	−	17871.4i	0.433839	−	0.597128i	0.968829	+	0.247730i	$0.0796847\pi$
$174$		0			0
$175$			16599.2i			0.542016i
$176$	−6674.19	+	3927.43i	−0.215463	+	0.126790i
$177$		0			0
$178$	−39158.7	+	12723.4i	−1.23591	+	0.401572i
$179$	−6760.86	−	4912.05i	−0.211006	−	0.153305i	0.477263	−	0.878761i	$-0.341629\pi$
$179$	−6760.86	−	4912.05i	−0.211006	−	0.153305i	−0.688269	+	0.725456i	$0.741629\pi$
$180$		0			0
$181$	3111.80	−	9577.13i	0.0949848	−	0.292333i	−0.892265	−	0.451512i	$-0.850885\pi$
$181$	3111.80	−	9577.13i	0.0949848	−	0.292333i	0.987250	+	0.159179i	$0.0508847\pi$
$182$	6396.23	+	2078.26i	0.193100	+	0.0627419i
$183$		0			0
$184$	−7513.81	+	10341.9i	−0.221934	+	0.305466i
$185$	−2720.01	−	8371.34i	−0.0794744	−	0.244597i
$186$		0			0
$187$	10833.7	+	18410.5i	0.309808	+	0.526480i
$188$	12369.3			0.349969
$189$		0			0
$190$	35954.1	+	26122.2i	0.995960	+	0.723607i
$191$	−28569.5	+	20757.0i	−0.783134	+	0.568980i	−0.905918	−	0.423453i	$-0.860818\pi$
$191$	−28569.5	+	20757.0i	−0.783134	+	0.568980i	0.122784	+	0.992433i	$0.460818\pi$
$192$		0			0
$193$	−7441.19	−	2417.79i	−0.199769	−	0.0649088i	0.207424	−	0.978251i	$-0.433492\pi$
$193$	−7441.19	−	2417.79i	−0.199769	−	0.0649088i	−0.407192	+	0.913342i	$0.633492\pi$
$194$	11282.5	+	15529.0i	0.299780	+	0.412611i
$195$		0			0
$196$	−5500.23	−	16928.0i	−0.143175	−	0.440649i
$197$		−	1473.23i		−	0.0379610i	−0.999820	−	0.0189805i	$-0.993958\pi$
$197$		−	1473.23i		−	0.0379610i	0.999820	−	0.0189805i	$-0.00604205\pi$
$198$		0			0
$199$	−26096.6			−0.658987			−0.329494	−	0.944158i	$-0.606878\pi$
$199$	−26096.6			−0.658987			−0.329494	+	0.944158i	$0.606878\pi$
$200$	−26917.6	+	8746.07i	−0.672941	+	0.218652i
$201$		0			0
$202$	31271.4	−	22720.0i	0.766381	−	0.556809i
$203$	−3527.87	+	10857.7i	−0.0856093	+	0.263478i
$204$		0			0
$205$	−66704.0	−	91810.1i	−1.58725	−	2.18466i
$206$	−2045.04	+	2814.75i	−0.0481910	+	0.0663293i
$207$		0			0
$208$			11467.3i			0.265054i
$209$	−42860.8	+	9482.15i	−0.981222	+	0.217077i
$210$		0			0
$211$	−68859.0	+	22373.6i	−1.54666	+	0.502541i	−0.953205	−	0.302323i	$-0.902238\pi$
$211$	−68859.0	+	22373.6i	−1.54666	+	0.502541i	−0.593458	+	0.804865i	$0.702238\pi$
$212$	9520.25	+	6916.86i	0.211825	+	0.153900i
$213$		0			0
$214$	7397.20	−	22766.2i	0.161525	−	0.497123i
$215$	−107246.	−	34846.2i	−2.32008	−	0.753839i
$216$		0			0
$217$	6970.43	−	9593.98i	0.148027	−	0.203741i
$218$	−6685.16	−	20574.8i	−0.140669	−	0.432935i
$219$		0			0
$220$	16734.5	−	38440.2i	0.345753	−	0.794219i
$221$	31632.0			0.647653
$222$		0			0
$223$	−22887.6	−	16628.8i	−0.460246	−	0.334388i	0.333382	−	0.942792i	$-0.391810\pi$
$223$	−22887.6	−	16628.8i	−0.460246	−	0.334388i	−0.793628	+	0.608404i	$0.791810\pi$
$224$	−1943.46	+	1412.01i	−0.0387328	+	0.0281410i
$225$		0			0
$226$	−24424.2	−	7935.92i	−0.478194	−	0.155375i
$227$	−42352.4	−	58293.1i	−0.821913	−	1.13127i	−0.989375	−	0.145388i	$-0.953557\pi$
$227$	−42352.4	−	58293.1i	−0.821913	−	1.13127i	0.167461	−	0.985879i	$-0.446443\pi$
$228$		0			0
$229$	2762.09	+	8500.84i	0.0526704	+	0.162103i	0.973932	−	0.226841i	$-0.0728399\pi$
$229$	2762.09	+	8500.84i	0.0526704	+	0.162103i	−0.921261	+	0.388944i	$0.872840\pi$
$230$		−	69206.6i		−	1.30825i
$231$		0			0
$232$	−19465.8			−0.361657
$233$	−46046.9	+	14961.6i	−0.848182	+	0.275591i	−0.700684	−	0.713472i	$-0.747122\pi$
$233$	−46046.9	+	14961.6i	−0.848182	+	0.275591i	−0.147497	+	0.989062i	$0.547122\pi$
$234$		0			0
$235$	−54176.2	+	39361.3i	−0.981009	+	0.712745i
$236$	−12153.6	+	37405.1i	−0.218214	+	0.671594i
$237$		0			0
$238$	3894.96	+	5360.95i	0.0687621	+	0.0946429i
$239$	31831.6	−	43812.5i	0.557266	−	0.767011i	−0.433709	−	0.901053i	$-0.642796\pi$
$239$	31831.6	−	43812.5i	0.557266	−	0.767011i	0.990976	+	0.134041i	$0.0427955\pi$
$240$		0			0
$241$			54166.9i			0.932610i	0.884624	+	0.466305i	$0.154415\pi$
$241$			54166.9i			0.932610i	−0.884624	+	0.466305i	$0.845585\pi$
$242$	17467.9	+	37546.5i	0.298270	+	0.641120i
$243$		0			0
$244$	−12070.0	+	3921.77i	−0.202734	+	0.0658723i
$245$	77958.2	+	56640.0i	1.29876	+	0.943606i
$246$		0			0
$247$	−20086.9	+	61821.2i	−0.329245	+	1.01331i
$248$	19230.5	+	6248.36i	0.312670	+	0.101593i
$249$		0			0
$250$	45062.0	−	62022.5i	0.720992	−	0.992360i
$251$	−4416.42	−	13592.3i	−0.0701008	−	0.215748i	0.909868	−	0.414897i	$-0.136182\pi$
$251$	−4416.42	−	13592.3i	−0.0701008	−	0.215748i	−0.979969	+	0.199149i	$0.936182\pi$
$252$		0			0
$253$	51177.4	+	45318.2i	0.799535	+	0.707998i
$254$	−19481.9			−0.301970
$255$		0			0
$256$	−3313.73	−	2407.57i	−0.0505636	−	0.0367366i
$257$	−31133.7	+	22619.9i	−0.471372	+	0.342472i	−0.797976	−	0.602689i	$-0.794096\pi$
$257$	−31133.7	+	22619.9i	−0.471372	+	0.342472i	0.326604	+	0.945161i	$0.394096\pi$
$258$		0			0
$259$	2565.02	+	833.427i	0.0382377	+	0.0124242i
$260$	−36490.9	−	50225.5i	−0.539807	−	0.742980i
$261$		0			0
$262$	−1285.71	−	3957.01i	−0.0187301	−	0.0576454i
$263$			130054.i			1.88024i	0.340841	+	0.940121i	$0.389288\pi$
$263$			130054.i			1.88024i	−0.340841	+	0.940121i	$0.610712\pi$
$264$		0			0
$265$	−63708.4			−0.907203
$266$	−12950.7	+	4207.95i	−0.183034	+	0.0594713i
$267$		0			0
$268$	−19448.7	+	14130.3i	−0.270783	+	0.196735i
$269$	21831.7	−	67190.9i	0.301705	−	0.928552i	−0.679182	−	0.733970i	$-0.737665\pi$
$269$	21831.7	−	67190.9i	0.301705	−	0.928552i	0.980886	−	0.194582i	$-0.0623349\pi$
$270$		0			0
$271$	46867.1	+	64507.0i	0.638160	+	0.878352i	0.998516	−	0.0544632i	$-0.0173448\pi$
$271$	46867.1	+	64507.0i	0.638160	+	0.878352i	−0.360356	+	0.932815i	$0.617345\pi$
$272$	−6641.18	+	9140.80i	−0.0897651	+	0.123551i
$273$		0			0
$274$			51261.7i			0.682798i
$275$	32692.8	+	147776.i	0.432301	+	1.95407i
$276$		0			0
$277$	42143.0	−	13693.1i	0.549245	−	0.178461i	−0.0212312	−	0.999775i	$-0.506759\pi$
$277$	42143.0	−	13693.1i	0.549245	−	0.178461i	0.570476	+	0.821314i	$0.306759\pi$
$278$	23297.7	+	16926.7i	0.301455	+	0.219020i
$279$		0			0
$280$	4018.89	−	12368.9i	0.0512613	−	0.157766i
$281$	−74439.7	−	24186.9i	−0.942740	−	0.306315i	−0.202978	−	0.979183i	$-0.565062\pi$
$281$	−74439.7	−	24186.9i	−0.942740	−	0.306315i	−0.739762	+	0.672868i	$0.765062\pi$
$282$		0			0
$283$	52782.1	−	72648.4i	0.659043	−	0.907095i	−0.340406	−	0.940279i	$-0.610564\pi$
$283$	52782.1	−	72648.4i	0.659043	−	0.907095i	0.999449	+	0.0331832i	$0.0105645\pi$
$284$	−21007.2	−	64653.4i	−0.260454	−	0.801594i
$285$		0			0
$286$	61036.3	+	5904.32i	0.746202	+	0.0721835i
$287$	34772.0			0.422149
$288$		0			0
$289$	−42355.4	−	30773.0i	−0.507123	−	0.368446i
$290$	85258.2	−	61943.7i	1.01377	−	0.736549i
$291$		0			0
$292$	34620.4	+	11248.9i	0.406038	+	0.131930i
$293$	−12058.9	−	16597.6i	−0.140466	−	0.193335i	0.732988	−	0.680242i	$-0.238125\pi$
$293$	−12058.9	−	16597.6i	−0.140466	−	0.193335i	−0.873454	+	0.486907i	$0.838125\pi$
$294$		0			0
$295$	−65798.0	−	202505.i	−0.756081	−	2.32698i
$296$			4598.62i			0.0524861i
$297$		0			0
$298$	75096.2			0.845640
$299$	96270.5	−	31280.2i	1.07684	−	0.349886i
$300$		0			0
$301$	27952.9	−	20309.0i	0.308528	−	0.224159i
$302$	−16596.6	+	51079.0i	−0.181972	+	0.560052i
$303$		0			0
$304$	−13647.4	−	18784.0i	−0.147673	−	0.203255i
$305$	40385.4	−	55585.7i	0.434135	−	0.597535i
$306$		0			0
$307$			133825.i			1.41991i	0.704248	+	0.709954i	$0.251284\pi$
$307$			133825.i			1.41991i	−0.704248	+	0.709954i	$0.748716\pi$
$308$	6514.95	+	11071.4i	0.0686768	+	0.116708i
$309$		0			0
$310$	−104111.	+	33827.6i	−1.08336	+	0.352005i
$311$	34207.5	+	24853.2i	0.353672	+	0.256958i	0.750408	−	0.660975i	$-0.229857\pi$
$311$	34207.5	+	24853.2i	0.353672	+	0.256958i	−0.396736	+	0.917933i	$0.629857\pi$
$312$		0			0
$313$	53394.1	−	164330.i	0.545011	−	1.67737i	−0.175954	−	0.984398i	$-0.556301\pi$
$313$	53394.1	−	164330.i	0.545011	−	1.67737i	0.720965	−	0.692972i	$-0.243699\pi$
$314$	9161.25	+	2976.67i	0.0929170	+	0.0301906i
$315$		0			0
$316$	9937.41	−	13677.7i	0.0995174	−	0.136974i
$317$	−26059.8	−	80203.7i	−0.259329	−	0.798134i	−0.992946	−	0.118570i	$-0.962169\pi$
$317$	−26059.8	−	80203.7i	−0.259329	−	0.798134i	0.733616	−	0.679564i	$-0.237831\pi$
$318$		0			0
$319$	−10022.6	+	103610.i	−0.0984920	+	1.01817i
$320$	22175.1			0.216554
$321$		0			0
$322$	17155.4	+	12464.2i	0.165459	+	0.120213i
$323$	−51814.9	+	37645.7i	−0.496649	+	0.360837i
$324$		0			0
$325$	213149.	+	69256.1i	2.01797	+	0.655679i
$326$	14164.3	+	19495.5i	0.133278	+	0.183442i
$327$		0			0
$328$	18321.2	+	56386.9i	0.170297	+	0.524120i
$329$		−	20518.6i		−	0.189564i
$330$		0			0
$331$	−130067.			−1.18717			−0.593583	−	0.804773i	$-0.702287\pi$
$331$	−130067.			−1.18717			−0.593583	+	0.804773i	$0.702287\pi$
$332$	71957.4	−	23380.4i	0.652828	−	0.212117i
$333$		0			0
$334$	−30342.8	+	22045.3i	−0.271996	+	0.197617i
$335$	40218.1	−	123779.i	0.358370	−	1.10295i
$336$		0			0
$337$	−48084.9	−	66183.1i	−0.423398	−	0.582757i	0.543024	−	0.839717i	$-0.317279\pi$
$337$	−48084.9	−	66183.1i	−0.423398	−	0.582757i	−0.966422	+	0.256960i	$0.917279\pi$
$338$	5890.47	−	8107.53i	0.0515604	−	0.0709668i
$339$		0			0
$340$		−	61169.1i		−	0.529145i
$341$	43159.3	−	99139.9i	0.371164	−	0.852589i
$342$		0			0
$343$	−58384.0	+	18970.1i	−0.496256	+	0.161243i
$344$	47661.7	+	34628.3i	0.402766	+	0.292627i
$345$		0			0
$346$	19307.6	−	59422.8i	0.161279	−	0.496365i
$347$	219762.	+	71404.9i	1.82513	+	0.593019i	0.999589	+	0.0286715i	$0.00912768\pi$
$347$	219762.	+	71404.9i	1.82513	+	0.593019i	0.825537	+	0.564348i	$0.190872\pi$
$348$		0			0
$349$	−7604.61	+	10466.9i	−0.0624347	+	0.0859340i	−0.839093	−	0.543989i	$-0.816913\pi$
$349$	−7604.61	+	10466.9i	−0.0624347	+	0.0859340i	0.776658	+	0.629923i	$0.216913\pi$
$350$	14508.3	+	44651.9i	0.118435	+	0.364505i
$351$		0			0
$352$	−14520.8	+	16398.2i	−0.117194	+	0.132346i
$353$	−59097.3			−0.474262			−0.237131	−	0.971478i	$-0.576207\pi$
$353$	−59097.3			−0.474262			−0.237131	+	0.971478i	$0.576207\pi$
$354$		0			0
$355$	297748.	+	216326.i	2.36261	+	1.71654i
$356$	−94215.9	+	68451.8i	−0.743403	+	0.540114i
$357$		0			0
$358$	−22480.0	−	7304.18i	−0.175400	−	0.0569909i
$359$	32828.5	+	45184.6i	0.254720	+	0.350591i	0.917157	−	0.398526i	$-0.130478\pi$
$359$	32828.5	+	45184.6i	0.254720	+	0.350591i	−0.662438	+	0.749117i	$0.730478\pi$
$360$		0			0
$361$	−399.455	−	1229.40i	−0.00306517	−	0.00943361i
$362$		−	28482.2i		−	0.217349i
$363$		0			0
$364$	19022.3			0.143569
$365$	−187430.	+	60899.6i	−1.40687	+	0.457118i
$366$		0			0
$367$	128062.	−	93042.3i	0.950796	−	0.690793i	−0.000199318	−	1.00000i	$-0.500063\pi$
$367$	128062.	−	93042.3i	0.950796	−	0.690793i	0.950995	+	0.309207i	$0.100063\pi$
$368$	−11173.0	+	34386.9i	−0.0825037	+	0.253920i
$369$		0			0
$370$	−14633.6	−	20141.5i	−0.106893	−	0.147125i
$371$	11473.9	−	15792.5i	0.0833612	−	0.114737i
$372$		0			0
$373$		−	133744.i		−	0.961297i	−0.876913	−	0.480649i	$-0.840401\pi$
$373$		−	133744.i		−	0.961297i	0.876913	−	0.480649i	$-0.159599\pi$
$374$	45233.8	+	40055.1i	0.323385	+	0.286362i
$375$		0			0
$376$	33273.4	−	10811.2i	0.235354	−	0.0764710i
$377$	124703.	+	90601.8i	0.877391	+	0.637462i
$378$		0			0
$379$	−16655.2	+	51259.4i	−0.115950	+	0.356858i	−0.992144	−	0.125101i	$-0.960075\pi$
$379$	−16655.2	+	51259.4i	−0.115950	+	0.356858i	0.876194	+	0.481959i	$0.160075\pi$
$380$	119548.	+	38843.5i	0.827895	+	0.269000i
$381$		0			0
$382$	−58709.6	+	80806.8i	−0.402330	+	0.553759i
$383$	−15091.9	−	46448.1i	−0.102884	−	0.316643i	0.886344	−	0.463027i	$-0.153237\pi$
$383$	−15091.9	−	46448.1i	−0.102884	−	0.316643i	−0.989228	+	0.146383i	$0.953237\pi$
$384$		0			0
$385$	−63765.9	−	27759.7i	−0.430196	−	0.187281i
$386$	−22130.0			−0.148527
$387$		0			0
$388$	43922.7	+	31911.7i	0.291760	+	0.211976i
$389$	221746.	−	161108.i	1.46540	−	1.06468i	0.483491	−	0.875349i	$-0.339369\pi$
$389$	221746.	−	161108.i	1.46540	−	1.06468i	0.981914	−	0.189329i	$-0.0606313\pi$
$390$		0			0
$391$	94854.8	+	30820.2i	0.620449	+	0.201596i
$392$	−29591.2	−	40728.7i	−0.192571	−	0.265051i
$393$		0			0
$394$	−1287.65	−	3962.98i	−0.00829479	−	0.0255287i
$395$			91529.3i			0.586632i
$396$		0			0
$397$	49313.3			0.312884			0.156442	−	0.987687i	$-0.449998\pi$
$397$	49313.3			0.312884			0.156442	+	0.987687i	$0.449998\pi$
$398$	−70199.6	+	22809.2i	−0.443168	+	0.143994i
$399$		0			0
$400$	−64763.9	+	47053.7i	−0.404775	+	0.294086i
$401$	−2341.63	+	7206.79i	−0.0145623	+	0.0448181i	−0.958074	−	0.286522i	$-0.907501\pi$
$401$	−2341.63	+	7206.79i	−0.0145623	+	0.0448181i	0.943511	+	0.331340i	$0.107501\pi$
$402$		0			0
$403$	−94112.6	−	129535.i	−0.579479	−	0.797584i
$404$	64261.9	−	88448.9i	0.393723	−	0.541913i
$405$		0			0
$406$			32290.6i			0.195895i
$407$	24476.8	+	2367.76i	0.147763	+	0.0142938i
$408$		0			0
$409$	−13724.0	+	4459.20i	−0.0820417	+	0.0266570i	−0.349750	−	0.936843i	$-0.613734\pi$
$409$	−13724.0	+	4459.20i	−0.0820417	+	0.0266570i	0.267709	+	0.963500i	$0.413734\pi$
$410$	−259678.	−	188667.i	−1.54478	−	1.12235i
$411$		0			0
$412$	−3040.95	+	9359.09i	−0.0179149	+	0.0551365i
$413$	62048.8	+	20160.9i	0.363775	+	0.118198i
$414$		0			0
$415$	−240765.	+	331385.i	−1.39797	+	1.92414i
$416$	10022.8	+	30846.9i	0.0579163	+	0.178248i
$417$		0			0
$418$	−107007.	+	62968.6i	−0.612437	+	0.360389i
$419$	−229500.			−1.30724			−0.653619	−	0.756824i	$-0.726750\pi$
$419$	−229500.			−1.30724			−0.653619	+	0.756824i	$0.726750\pi$
$420$		0			0
$421$	−9854.14	−	7159.45i	−0.0555974	−	0.0403939i	0.559639	−	0.828736i	$-0.310940\pi$
$421$	−9854.14	−	7159.45i	−0.0555974	−	0.0403939i	−0.615237	+	0.788342i	$0.710940\pi$
$422$	−165675.	+	120370.i	−0.930320	+	0.675917i
$423$		0			0
$424$	31655.0	+	10285.3i	0.176080	+	0.0572119i
$425$	129796.	+	178649.i	0.718593	+	0.989058i
$426$		0			0
$427$	6505.56	+	20022.1i	0.0356803	+	0.109813i
$428$		−	67706.4i		−	0.369609i
$429$		0			0
$430$	−318947.			−1.72497
$431$	40180.7	−	13055.5i	0.216303	−	0.0702813i	−0.198861	−	0.980028i	$-0.563724\pi$
$431$	40180.7	−	13055.5i	0.216303	−	0.0702813i	0.415164	+	0.909747i	$0.363724\pi$
$432$		0			0
$433$	−53631.9	+	38965.8i	−0.286053	+	0.207830i	−0.721553	−	0.692359i	$-0.756572\pi$
$433$	−53631.9	+	38965.8i	−0.286053	+	0.207830i	0.435500	+	0.900189i	$0.356572\pi$
$434$	10365.0	−	31900.1i	0.0550287	−	0.169361i
$435$		0			0
$436$	−35966.1	−	49503.1i	−0.189200	−	0.260411i
$437$	−120469.	+	165812.i	−0.630831	+	0.868264i
$438$		0			0
$439$		−	212489.i		−	1.10257i	−0.834316	−	0.551287i	$-0.814137\pi$
$439$		−	212489.i		−	1.10257i	0.834316	−	0.551287i	$-0.185863\pi$
$440$	11417.6	−	118030.i	0.0589753	−	0.609661i
$441$		0			0
$442$	85090.0	−	27647.4i	0.435546	−	0.141517i
$443$	−289268.	−	210166.i	−1.47399	−	1.07091i	−0.979434	−	0.201766i	$-0.935332\pi$
$443$	−289268.	−	210166.i	−1.47399	−	1.07091i	−0.494553	−	0.869148i	$-0.664668\pi$
$444$		0			0
$445$	194829.	−	599624.i	0.983863	−	3.02802i
$446$	−76101.5	−	24726.9i	−0.382581	−	0.124308i
$447$		0			0
$448$	−3993.75	+	5496.93i	−0.0198987	+	0.0273882i
$449$	−11170.1	−	34378.0i	−0.0554069	−	0.170525i	0.919523	−	0.393035i	$-0.128575\pi$
$449$	−11170.1	−	34378.0i	−0.0554069	−	0.170525i	−0.974930	+	0.222510i	$0.928575\pi$
$450$		0			0
$451$	309561.	−	68484.7i	1.52193	−	0.336698i
$452$	−72637.3			−0.355536
$453$		0			0
$454$	−164878.	−	119791.i	−0.799926	−	0.581181i
$455$	−83315.6	+	60532.3i	−0.402442	+	0.292391i
$456$		0			0
$457$	23357.6	+	7589.34i	0.111840	+	0.0363389i	0.364402	−	0.931242i	$-0.381273\pi$
$457$	23357.6	+	7589.34i	0.111840	+	0.0363389i	−0.252563	+	0.967581i	$0.581273\pi$
$458$	14860.0	+	20453.1i	0.0708416	+	0.0975051i
$459$		0			0
$460$	−60488.8	−	186165.i	−0.285864	−	0.879798i
$461$		−	41038.8i		−	0.193105i	−0.995328	−	0.0965523i	$-0.969218\pi$
$461$		−	41038.8i		−	0.193105i	0.995328	−	0.0965523i	$-0.0307815\pi$
$462$		0			0
$463$	−263948.			−1.23128			−0.615640	−	0.788027i	$-0.711103\pi$
$463$	−263948.			−1.23128			−0.615640	+	0.788027i	$0.711103\pi$
$464$	−52363.0	+	17013.8i	−0.243214	+	0.0790250i
$465$		0			0
$466$	−110789.	+	80493.0i	−0.510182	+	0.370669i
$467$	7002.66	−	21552.0i	0.0321092	−	0.0988219i	−0.933718	−	0.358011i	$-0.883455\pi$
$467$	7002.66	−	21552.0i	0.0321092	−	0.0988219i	0.965827	+	0.259189i	$0.0834552\pi$
$468$		0			0
$469$	23439.8	+	32262.2i	0.106564	+	0.146672i
$470$	−111331.	+	153234.i	−0.503987	+	0.693678i
$471$		0			0
$472$			111242.i			0.499327i
$473$	208854.	−	235857.i	0.933515	−	1.05421i
$474$		0			0
$475$	−431571.	+	140226.i	−1.91278	+	0.621500i
$476$	15163.1	+	11016.6i	0.0669226	+	0.0486221i
$477$		0			0
$478$	47333.4	−	145677.i	0.207163	−	0.637581i
$479$	−63206.4	−	20537.0i	−0.275480	−	0.0895089i	0.168019	−	0.985784i	$-0.446263\pi$
$479$	−63206.4	−	20537.0i	−0.275480	−	0.0895089i	−0.443499	+	0.896275i	$0.646263\pi$
$480$		0			0
$481$	21403.8	−	29459.9i	0.0925127	−	0.127333i
$482$	47343.6	+	145709.i	0.203783	+	0.627179i
$483$		0			0
$484$	79805.5	+	85732.5i	0.340676	+	0.365978i
$485$	−293926.			−1.24955
$486$		0			0
$487$	329613.	+	239478.i	1.38978	+	1.00973i	0.995890	+	0.0905764i	$0.0288709\pi$
$487$	329613.	+	239478.i	1.38978	+	1.00973i	0.393890	+	0.919158i	$0.371129\pi$
$488$	−29040.4	+	21099.1i	−0.121945	+	0.0885980i
$489$		0			0
$490$	259212.	+	84223.2i	1.07960	+	0.350784i
$491$	−20767.7	−	28584.3i	−0.0861442	−	0.118567i	0.763770	−	0.645489i	$-0.223346\pi$
$491$	−20767.7	−	28584.3i	−0.0861442	−	0.118567i	−0.849914	+	0.526921i	$0.823346\pi$
$492$		0			0
$493$	46931.8	+	144441.i	0.193096	+	0.594288i
$494$			183855.i			0.753394i
$495$		0			0
$496$	57191.1			0.232469
$497$	−107249.	+	34847.4i	−0.434191	+	0.141077i
$498$		0			0
$499$	−24801.7	+	18019.5i	−0.0996046	+	0.0723670i	−0.636473	−	0.771299i	$-0.719607\pi$
$499$	−24801.7	+	18019.5i	−0.0996046	+	0.0723670i	0.536868	+	0.843666i	$0.319607\pi$
$500$	67006.8	−	206226.i	0.268027	−	0.824903i
$501$		0			0
$502$	−23760.3	−	32703.2i	−0.0942854	−	0.129773i
$503$	−164396.	+	226272.i	−0.649764	+	0.894323i	−0.999089	−	0.0426785i	$-0.986411\pi$
$503$	−164396.	+	226272.i	−0.649764	+	0.894323i	0.349325	+	0.937002i	$0.386411\pi$
$504$		0			0
$505$			591890.i			2.32091i
$506$	177277.	+	77175.1i	0.692389	+	0.301423i
$507$		0			0
$508$	−52406.3	+	17027.8i	−0.203075	+	0.0659830i
$509$	122810.	+	89227.0i	0.474024	+	0.344398i	0.799007	−	0.601321i	$-0.205359\pi$
$509$	122810.	+	89227.0i	0.474024	+	0.344398i	−0.324984	+	0.945720i	$0.605359\pi$
$510$		0			0
$511$	18660.0	−	57429.5i	0.0714611	−	0.219935i
$512$	−11018.2	−	3580.04i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	−63978.8	+	88059.3i	−0.242164	+	0.333311i
$515$	−16463.2	−	50668.6i	−0.0620727	−	0.191040i
$516$		0			0
$517$	−40412.1	−	182669.i	−0.151193	−	0.683414i
$518$	7628.34			0.0284296
$519$		0			0
$520$	−142059.	−	103212.i	−0.525366	−	0.381701i
$521$	−1689.60	+	1227.57i	−0.00622455	+	0.00452240i	−0.590893	−	0.806750i	$-0.701225\pi$
$521$	−1689.60	+	1227.57i	−0.00622455	+	0.00452240i	0.584669	+	0.811272i	$0.301225\pi$
$522$		0			0
$523$	−290679.	−	94447.4i	−1.06270	−	0.345292i	−0.275060	−	0.961427i	$-0.588698\pi$
$523$	−290679.	−	94447.4i	−1.06270	−	0.345292i	−0.787641	+	0.616135i	$0.788698\pi$
$524$	−6917.11	−	9520.58i	−0.0251920	−	0.0346737i
$525$		0			0
$526$	113672.	+	349846.i	0.410848	+	1.26446i
$527$		−	157759.i		−	0.568033i
$528$		0			0
$529$	39322.4			0.140517
$530$	−171375.	+	55683.2i	−0.610093	+	0.198231i
$531$		0			0
$532$	−31159.5	+	22638.7i	−0.110095	+	0.0799887i
$533$	145077.	−	446503.i	0.510676	−	1.57170i
$534$		0			0
$535$	215454.	+	296547.i	0.752743	+	1.03606i
$536$	−39966.6	+	55009.3i	−0.139113	+	0.191473i
$537$		0			0
$538$		−	199825.i		−	0.690375i
$539$	−232021.	+	136533.i	−0.798637	+	0.469959i
$540$		0			0
$541$	−120348.	+	39103.4i	−0.411192	+	0.133604i	−0.507306	−	0.861766i	$-0.669359\pi$
$541$	−120348.	+	39103.4i	−0.411192	+	0.133604i	0.0961142	+	0.995370i	$0.469359\pi$
$542$	182453.	+	132560.i	0.621088	+	0.451247i
$543$		0			0
$544$	−9875.38	+	30393.3i	−0.0333700	+	0.102702i
$545$	315055.	+	102368.i	1.06070	+	0.344643i
$546$		0			0
$547$	208238.	−	286615.i	0.695961	−	0.957908i	−0.304025	−	0.952664i	$-0.598331\pi$
$547$	208238.	−	286615.i	0.695961	−	0.957908i	0.999986	−	0.00524442i	$-0.00166936\pi$
$548$	44804.4	+	137894.i	0.149197	+	0.459180i
$549$		0			0
$550$	217105.	+	368943.i	0.717701	+	1.21965i
$551$	−312096.			−1.02798
$552$		0			0
$553$	−22689.0	−	16484.5i	−0.0741932	−	0.0539045i
$554$	101396.	−	73668.7i	0.330372	−	0.240029i
$555$		0			0
$556$	77465.1	+	25169.9i	0.250586	+	0.0814202i
$557$	−18181.9	−	25025.2i	−0.0586042	−	0.0806618i	0.778709	−	0.627385i	$-0.215875\pi$
$557$	−18181.9	−	25025.2i	−0.0586042	−	0.0806618i	−0.837313	+	0.546724i	$0.815875\pi$
$558$		0			0
$559$	−144158.	−	443674.i	−0.461335	−	1.41984i
$560$		−	36784.8i		−	0.117298i
$561$		0			0
$562$	−221383.			−0.700924
$563$	338262.	−	109908.i	1.06718	−	0.346747i	0.277789	−	0.960642i	$-0.410398\pi$
$563$	338262.	−	109908.i	1.06718	−	0.346747i	0.789387	+	0.613896i	$0.210398\pi$
$564$		0			0
$565$	318144.	−	231145.i	0.996613	−	0.724082i
$566$	78486.6	−	241557.i	0.244998	−	0.754027i
$567$		0			0
$568$	−113018.	−	155556.i	−0.350309	−	0.482160i
$569$	−257141.	+	353925.i	−0.794232	+	1.09317i	0.199337	+	0.979931i	$0.436121\pi$
$569$	−257141.	+	353925.i	−0.794232	+	1.09317i	−0.993568	+	0.113235i	$0.963879\pi$
$570$		0			0
$571$			1830.95i			0.00561570i	0.999996	+	0.00280785i	$0.000893767\pi$
$571$			1830.95i			0.00561570i	−0.999996	+	0.00280785i	$0.999106\pi$
$572$	169348.	−	37465.1i	0.517592	−	0.114508i
$573$		0			0
$574$	93536.5	−	30391.9i	0.283895	−	0.0922430i
$575$	571689.	+	415356.i	1.72912	+	1.25628i
$576$		0			0
$577$	71653.2	−	220526.i	0.215221	−	0.662381i	−0.783917	−	0.620865i	$-0.786781\pi$
$577$	71653.2	−	220526.i	0.215221	−	0.662381i	0.999138	−	0.0415155i	$-0.0132186\pi$
$578$	−140832.	−	45759.2i	−0.421548	−	0.136969i
$579$		0			0
$580$	175203.	−	241147.i	0.520818	−	0.716845i
$581$	−38784.1	−	119365.i	−0.114895	−	0.353611i
$582$		0			0
$583$	71043.8	−	163193.i	0.209021	−	0.480135i
$584$	102961.			0.301888
$585$		0			0
$586$	−46945.2	−	34107.7i	−0.136709	−	0.0993247i
$587$	41941.6	−	30472.3i	0.121722	−	0.0884361i	−0.525259	−	0.850943i	$-0.676031\pi$
$587$	41941.6	−	30472.3i	0.121722	−	0.0884361i	0.646981	+	0.762506i	$0.276031\pi$
$588$		0			0
$589$	308323.	+	100180.i	0.888740	+	0.288769i
$590$	−353992.	−	487229.i	−1.01693	−	1.39968i
$591$		0			0
$592$	4019.34	+	12370.3i	0.0114686	+	0.0352968i
$593$			94653.9i			0.269171i	0.990902	+	0.134586i	$0.0429704\pi$
$593$			94653.9i			0.269171i	−0.990902	+	0.134586i	$0.957030\pi$
$594$		0			0
$595$	−101469.			−0.286616
$596$	202008.	−	65636.5i	0.568692	−	0.184779i
$597$		0			0
$598$	231627.	−	168287.i	0.647720	−	0.470596i
$599$	−35391.5	+	108924.i	−0.0986382	+	0.303577i	−0.988185	−	0.153267i	$-0.951020\pi$
$599$	−35391.5	+	108924.i	−0.0986382	+	0.303577i	0.889547	+	0.456844i	$0.151020\pi$
$600$		0			0
$601$	−190529.	−	262240.i	−0.527486	−	0.726023i	0.459258	−	0.888303i	$-0.348115\pi$
$601$	−190529.	−	262240.i	−0.527486	−	0.726023i	−0.986745	+	0.162280i	$0.948115\pi$
$602$	57442.5	−	79062.8i	0.158504	−	0.218162i
$603$		0			0
$604$			151908.i			0.416397i
$605$	−622355.	−	121544.i	−1.70031	−	0.332064i
$606$		0			0
$607$	−666226.	+	216470.i	−1.80819	+	0.587517i	−0.999999	−	0.00140328i	$-0.999553\pi$
$607$	−666226.	+	216470.i	−1.80819	+	0.587517i	−0.808191	+	0.588920i	$0.799553\pi$
$608$	−53129.2	−	38600.6i	−0.143723	−	0.104421i
$609$		0			0
$610$	60052.8	−	184823.i	0.161389	−	0.496704i
$611$	−263477.	−	85608.7i	−0.705764	−	0.229317i
$612$		0			0
$613$	−351341.	+	483580.i	−0.934992	+	1.28691i	0.0228878	+	0.999738i	$0.492714\pi$
$613$	−351341.	+	483580.i	−0.934992	+	1.28691i	−0.957880	+	0.287168i	$0.907286\pi$
$614$	116967.	+	359988.i	0.310261	+	0.954886i
$615$		0			0
$616$	27201.9	+	24087.6i	0.0716866	+	0.0634794i
$617$	704195.			1.84979			0.924896	−	0.380221i	$-0.124152\pi$
$617$	704195.			1.84979			0.924896	+	0.380221i	$0.124152\pi$
$618$		0			0
$619$	−31537.5	−	22913.3i	−0.0823087	−	0.0598008i	0.545870	−	0.837870i	$-0.316199\pi$
$619$	−31537.5	−	22913.3i	−0.0823087	−	0.0598008i	−0.628179	+	0.778069i	$0.716199\pi$
$620$	−250491.	+	181992.i	−0.651641	+	0.473445i
$621$		0			0
$622$	113740.	+	36956.5i	0.293991	+	0.0955235i
$623$	113550.	+	156288.i	0.292558	+	0.402671i
$624$		0			0
$625$	121186.	+	372973.i	0.310237	+	0.954811i
$626$		−	488716.i		−	1.24712i
$627$		0			0
$628$	27245.4			0.0690834
$629$	34122.9	−	11087.2i	0.0862471	−	0.0280234i
$630$		0			0
$631$	15476.7	−	11244.5i	0.0388706	−	0.0282411i	−0.568180	−	0.822904i	$-0.692352\pi$
$631$	15476.7	−	11244.5i	0.0388706	−	0.0282411i	0.607051	+	0.794663i	$0.292352\pi$
$632$	14776.8	−	45478.4i	0.0369954	−	0.113860i
$633$		0			0
$634$	−140201.	−	192970.i	−0.348797	−	0.480078i
$635$	175348.	−	241346.i	0.434864	−	0.598540i
$636$		0			0
$637$			398647.i			0.982449i
$638$	63597.4	+	287470.i	0.156242	+	0.706238i
$639$		0			0
$640$	59650.9	−	19381.8i	0.145632	−	0.0473187i
$641$	−277946.	−	201939.i	−0.676462	−	0.491479i	0.195720	−	0.980660i	$-0.437296\pi$
$641$	−277946.	−	201939.i	−0.676462	−	0.491479i	−0.872182	+	0.489181i	$0.837296\pi$
$642$		0			0
$643$	−22016.3	+	67759.1i	−0.0532503	+	0.163887i	−0.974145	−	0.225924i	$-0.927460\pi$
$643$	−22016.3	+	67759.1i	−0.0532503	+	0.163887i	0.920895	+	0.389812i	$0.127460\pi$
$644$	57042.1	+	18534.1i	0.137538	+	0.0446889i
$645$		0			0
$646$	−106478.	+	146555.i	−0.255150	+	0.351184i
$647$	−42270.7	−	130096.i	−0.100979	−	0.310781i	0.887787	−	0.460255i	$-0.152242\pi$
$647$	−42270.7	−	130096.i	−0.100979	−	0.310781i	−0.988766	+	0.149474i	$0.952242\pi$
$648$		0			0
$649$	592103.	+	57276.8i	1.40575	+	0.135984i
$650$	633900.			1.50036
$651$		0			0
$652$	55141.5	+	40062.6i	0.129713	+	0.0942419i
$653$	439262.	−	319143.i	1.03014	−	0.748443i	0.0618056	−	0.998088i	$-0.480314\pi$
$653$	439262.	−	319143.i	1.03014	−	0.748443i	0.968337	+	0.249646i	$0.0803141\pi$
$654$		0			0
$655$	60592.4	+	19687.7i	0.141233	+	0.0458893i
$656$	98568.0	+	135667.i	0.229049	+	0.315259i
$657$		0			0
$658$	−17933.9	−	55194.9i	−0.0414213	−	0.127482i
$659$			702060.i			1.61660i	0.588768	+	0.808302i	$0.299613\pi$
$659$			702060.i			1.61660i	−0.588768	+	0.808302i	$0.700387\pi$
$660$		0			0
$661$	−226372.			−0.518108			−0.259054	−	0.965863i	$-0.583411\pi$
$661$	−226372.			−0.518108			−0.259054	+	0.965863i	$0.583411\pi$
$662$	−349879.	+	113683.i	−0.798367	+	0.259405i
$663$		0			0
$664$	173130.	−	125786.i	0.392677	−	0.285296i
$665$	64434.9	−	198310.i	0.145706	−	0.448438i
$666$		0			0
$667$	285669.	+	393190.i	0.642113	+	0.883793i
$668$	−62353.6	+	85822.4i	−0.139736	+	0.192330i
$669$		0			0
$670$		−	368116.i		−	0.820039i
$671$	97350.6	+	165435.i	0.216219	+	0.367437i
$672$		0			0
$673$	−41554.0	+	13501.7i	−0.0917450	+	0.0298097i	−0.354530	−	0.935045i	$-0.615359\pi$
$673$	−41554.0	+	13501.7i	−0.0917450	+	0.0298097i	0.262785	+	0.964854i	$0.415359\pi$
$674$	−187194.	−	136005.i	−0.412072	−	0.299388i
$675$		0			0
$676$	8759.08	−	26957.7i	0.0191675	−	0.0589914i
$677$	488471.	+	158714.i	1.06577	+	0.346288i	0.788837	−	0.614602i	$-0.210683\pi$
$677$	488471.	+	158714.i	1.06577	+	0.346288i	0.276929	+	0.960891i	$0.410683\pi$
$678$		0			0
$679$	52936.2	−	72860.5i	0.114819	−	0.158035i
$680$	−53463.8	−	164545.i	−0.115622	−	0.355849i
$681$		0			0
$682$	29446.8	−	304408.i	0.0633096	−	0.654467i
$683$	289751.			0.621131			0.310566	−	0.950552i	$-0.399482\pi$
$683$	289751.			0.621131			0.310566	+	0.950552i	$0.399482\pi$
$684$		0			0
$685$	−635041.	−	461384.i	−1.35338	−	0.983290i
$686$	−140472.	+	102059.i	−0.298499	+	0.216872i
$687$		0			0
$688$	158476.	+	51492.0i	0.334801	+	0.108783i
$689$	−154917.	−	213225.i	−0.326333	−	0.449159i
$690$		0			0
$691$	−148192.	−	456087.i	−0.310361	−	0.955194i	−0.977622	−	0.210370i	$-0.932533\pi$
$691$	−148192.	−	456087.i	−0.310361	−	0.955194i	0.667261	−	0.744824i	$-0.267467\pi$
$692$		−	176723.i		−	0.369045i
$693$		0			0
$694$	653568.			1.35697
$695$	−419384.	+	136266.i	−0.868245	+	0.282110i
$696$		0			0
$697$	374232.	−	271896.i	0.770328	−	0.559676i
$698$	−11308.0	+	34802.4i	−0.0232100	+	0.0714330i
$699$		0			0
$700$	78054.3	+	107433.i	0.159294	+	0.219250i
$701$	−397842.	+	547582.i	−0.809607	+	1.11433i	0.181777	+	0.983340i	$0.441815\pi$
$701$	−397842.	+	547582.i	−0.809607	+	1.11433i	−0.991384	+	0.130989i	$0.958185\pi$
$702$		0			0
$703$			73729.8i			0.149188i
$704$	−24728.4	+	56802.8i	−0.0498942	+	0.114610i
$705$		0			0
$706$	−158971.	+	51653.0i	−0.318941	+	0.103630i
$707$	−146722.	−	106600.i	−0.293533	−	0.213264i
$708$		0			0
$709$	−69762.5	+	214707.i	−0.138781	+	0.427124i	−0.996159	−	0.0875635i	$-0.972092\pi$
$709$	−69762.5	+	214707.i	−0.138781	+	0.427124i	0.857378	+	0.514687i	$0.172092\pi$
$710$	990016.	+	321676.i	1.96393	+	0.638119i
$711$		0			0
$712$	−193611.	+	266483.i	−0.381918	+	0.525665i
$713$	−156005.	−	480133.i	−0.306873	−	0.944457i
$714$		0			0
$715$	−622505.	+	702988.i	−1.21767	+	1.37511i
$716$	−66855.0			−0.130409
$717$		0			0
$718$	127801.	+	92853.1i	0.247906	+	0.180114i
$719$	752504.	−	546726.i	1.45563	−	1.05758i	0.471155	−	0.882050i	$-0.343837\pi$
$719$	752504.	−	546726.i	1.45563	−	1.05758i	0.984475	−	0.175527i	$-0.0561629\pi$
$720$		0			0
$721$	15525.2	+	5044.43i	0.0298652	+	0.00970379i
$722$	−2149.07	−	2957.93i	−0.00412264	−	0.00567432i
$723$		0			0
$724$	−24894.4	−	76617.0i	−0.0474924	−	0.146167i
$725$			1.07605e6i			2.04719i
$726$		0			0
$727$	141940.			0.268556			0.134278	−	0.990944i	$-0.457128\pi$
$727$	141940.			0.268556			0.134278	+	0.990944i	$0.457128\pi$
$728$	51169.9	−	16626.1i	0.0965498	−	0.0313709i
$729$		0			0
$730$	−450957.	+	327639.i	−0.846231	+	0.614823i
$731$	142039.	−	437150.i	0.265810	−	0.818079i
$732$		0			0
$733$	−599214.	−	824747.i	−1.11525	−	1.53502i	−0.813441	−	0.581648i	$-0.802408\pi$
$733$	−599214.	−	824747.i	−1.11525	−	1.53502i	−0.301813	−	0.953367i	$-0.597592\pi$
$734$	263163.	−	362213.i	0.488465	−	0.672314i
$735$		0			0
$736$			102266.i			0.188789i
$737$	272217.	+	241052.i	0.501165	+	0.443787i
$738$		0			0
$739$	902735.	−	293316.i	1.65299	−	0.537091i	0.673609	−	0.739088i	$-0.264743\pi$
$739$	902735.	−	293316.i	1.65299	−	0.537091i	0.979386	+	0.201997i	$0.0647432\pi$
$740$	−56968.7	−	41390.2i	−0.104033	−	0.0755847i
$741$		0			0
$742$	17061.6	−	52510.3i	0.0309894	−	0.0953755i
$743$	−432128.	−	140407.i	−0.782771	−	0.254338i	−0.109748	−	0.993959i	$-0.535004\pi$
$743$	−432128.	−	140407.i	−0.782771	−	0.254338i	−0.673023	+	0.739622i	$0.735004\pi$
$744$		0			0
$745$	−675908.	+	930308.i	−1.21780	+	1.67615i
$746$	−116897.	−	359771.i	−0.210051	−	0.646471i
$747$		0			0
$748$	156688.	+	68212.2i	0.280048	+	0.121916i
$749$	−112314.			−0.200202
$750$		0			0
$751$	337489.	+	245200.i	0.598383	+	0.434751i	0.845305	−	0.534285i	$-0.179419\pi$
$751$	337489.	+	245200.i	0.598383	+	0.434751i	−0.246921	+	0.969036i	$0.579419\pi$
$752$	80055.8	−	58164.0i	0.141565	−	0.102853i
$753$		0			0
$754$	414638.	+	134724.i	0.729335	+	0.236975i
$755$	−483399.	−	665341.i	−0.848031	−	1.16721i
$756$		0			0
$757$	−344073.	−	1.05895e6i	−0.600425	−	1.84792i	−0.525620	−	0.850719i	$-0.676167\pi$
$757$	−344073.	−	1.05895e6i	−0.600425	−	1.84792i	−0.0748048	−	0.997198i	$-0.523833\pi$
$758$			152445.i			0.265322i
$759$		0			0
$760$	355534.			0.615537
$761$	−230550.	+	74910.2i	−0.398103	+	0.129352i	−0.501225	−	0.865317i	$-0.667117\pi$
$761$	−230550.	+	74910.2i	−0.398103	+	0.129352i	0.103121	+	0.994669i	$0.467117\pi$
$762$		0			0
$763$	−82117.3	+	59661.7i	−0.141054	+	0.102482i
$764$	−87300.7	+	268684.i	−0.149565	+	0.460315i
$765$		0			0
$766$	−81194.3	−	111754.i	−0.138378	−	0.190461i
$767$	517766.	−	712643.i	0.880121	−	1.21138i
$768$		0			0
$769$			502205.i			0.849235i	0.905373	+	0.424618i	$0.139591\pi$
$769$			502205.i			0.849235i	−0.905373	+	0.424618i	$0.860409\pi$
$770$	−195793.	−	18939.9i	−0.330229	−	0.0319445i
$771$		0			0
$772$	−59529.5	+	19342.3i	−0.0998844	+	0.0324544i
$773$	−514266.	−	373636.i	−0.860654	−	0.625302i	0.0674085	−	0.997725i	$-0.478527\pi$
$773$	−514266.	−	373636.i	−0.860654	−	0.625302i	−0.928063	+	0.372423i	$0.878527\pi$
$774$		0			0
$775$	345403.	−	1.06304e6i	0.575073	−	1.76989i
$776$	146044.	+	47452.5i	0.242527	+	0.0788017i
$777$		0			0
$778$	455683.	−	627194.i	0.752841	−	1.03620i
$779$	293745.	+	904053.i	0.484055	+	1.48977i
$780$		0			0
$781$	−886163.	+	521463.i	−1.45282	+	0.854912i
$782$	282097.			0.461301
$783$		0			0
$784$	−115198.	−	83696.5i	−0.187419	−	0.136168i
$785$	−119332.	+	86699.7i	−0.193650	+	0.140695i
$786$		0			0
$787$	573732.	+	186417.i	0.926317	+	0.300979i	0.733056	−	0.680168i	$-0.238093\pi$
$787$	573732.	+	186417.i	0.926317	+	0.300979i	0.193262	+	0.981147i	$0.438093\pi$
$788$	−6927.54	−	9534.94i	−0.0111565	−	0.0153556i
$789$		0			0
$790$	79999.5	+	246213.i	0.128184	+	0.394509i
$791$			120493.i			0.192579i
$792$		0			0
$793$	284243.			0.452006
$794$	132652.	−	43101.4i	0.210414	−	0.0683676i
$795$		0			0
$796$	−168900.	+	122713.i	−0.266566	+	0.193671i
$797$	−268673.	+	826889.i	−0.422967	+	1.30176i	0.481960	+	0.876193i	$0.339925\pi$
$797$	−268673.	+	826889.i	−0.422967	+	1.30176i	−0.904927	+	0.425566i	$0.860075\pi$
$798$		0			0
$799$	−160443.	−	220831.i	−0.251320	−	0.345912i
$800$	−133088.	+	183180.i	−0.207950	+	0.286219i
$801$		0			0
$802$			21432.9i			0.0333221i
$803$	53012.8	−	548023.i	0.0822147	−	0.849900i
$804$		0			0
$805$	−308817.	+	100341.i	−0.476551	+	0.154841i
$806$	−366380.	−	266191.i	−0.563977	−	0.409753i
$807$		0			0
$808$	95557.0	−	294094.i	0.146366	−	0.450468i
$809$	−344281.	−	111864.i	−0.526036	−	0.170920i	0.0339467	−	0.999424i	$-0.489192\pi$
$809$	−344281.	−	111864.i	−0.526036	−	0.170920i	−0.559983	+	0.828504i	$0.689192\pi$
$810$		0			0
$811$	332769.	−	458018.i	0.505943	−	0.696371i	−0.477285	−	0.878748i	$-0.658379\pi$
$811$	332769.	−	458018.i	0.505943	−	0.696371i	0.983229	+	0.182377i	$0.0583792\pi$
$812$	28223.0	+	86861.4i	0.0428046	+	0.131739i
$813$		0			0
$814$	67912.1	−	15024.3i	0.102494	−	0.0226749i
$815$	−369000.			−0.555535
$816$		0			0
$817$	764162.	+	555196.i	1.14483	+	0.831768i
$818$	−33020.0	+	23990.4i	−0.0493481	+	0.0358535i
$819$		0			0
$820$	−863434.	−	280547.i	−1.28411	−	0.417232i
$821$	−426408.	−	586901.i	−0.632615	−	0.870720i	0.365580	−	0.930780i	$-0.380871\pi$
$821$	−426408.	−	586901.i	−0.632615	−	0.870720i	−0.998195	+	0.0600604i	$0.980871\pi$
$822$		0			0
$823$	291256.	+	896394.i	0.430007	+	1.32343i	0.898118	+	0.439756i	$0.144935\pi$
$823$	291256.	+	896394.i	0.430007	+	1.32343i	−0.468110	+	0.883670i	$0.655065\pi$
$824$			27833.8i			0.0409938i
$825$		0			0
$826$	184532.			0.270465
$827$	−303169.	+	98505.6i	−0.443276	+	0.144029i	−0.522146	−	0.852856i	$-0.674869\pi$
$827$	−303169.	+	98505.6i	−0.443276	+	0.144029i	0.0788708	+	0.996885i	$0.474869\pi$
$828$		0			0
$829$	−793128.	+	576241.i	−1.15408	+	0.838485i	−0.989017	−	0.147799i	$-0.952781\pi$
$829$	−793128.	+	576241.i	−1.15408	+	0.838485i	−0.165058	+	0.986284i	$0.552781\pi$
$830$	−358016.	+	1.10186e6i	−0.519692	+	1.59945i
$831$		0			0
$832$	53922.4	+	74217.8i	0.0778973	+	0.107216i
$833$	−230873.	+	317770.i	−0.332724	+	0.457955i
$834$		0			0
$835$		−	574313.i		−	0.823713i
$836$	−232813.	+	262913.i	−0.333115	+	0.376184i
$837$		0			0
$838$	−617354.	+	200590.i	−0.879116	+	0.285642i
$839$	423441.	+	307648.i	0.601546	+	0.437048i	0.846427	−	0.532505i	$-0.178749\pi$
$839$	423441.	+	307648.i	0.601546	+	0.437048i	−0.244882	+	0.969553i	$0.578749\pi$
$840$		0			0
$841$	−10133.9	+	31188.9i	−0.0143280	+	0.0440969i
$842$	−32765.2	−	10646.1i	−0.0462156	−	0.0150163i
$843$		0			0
$844$	−340458.	+	468600.i	−0.477945	+	0.657835i
$845$	47420.3	+	145945.i	0.0664127	+	0.204397i
$846$		0			0
$847$	142216.	−	132384.i	0.198235	−	0.184531i
$848$	94141.4			0.130915
$849$		0			0
$850$	505295.	+	367118.i	0.699370	+	0.508122i
$851$	92887.4	−	67486.7i	0.128262	−	0.0931877i
$852$		0			0
$853$	328116.	+	106611.i	0.450951	+	0.146523i	0.525683	−	0.850681i	$-0.323810\pi$
$853$	328116.	+	106611.i	0.450951	+	0.146523i	−0.0747314	+	0.997204i	$0.523810\pi$
$854$	34999.8	+	48173.2i	0.0479900	+	0.0660525i
$855$		0			0
$856$	−59177.6	−	182130.i	−0.0807625	−	0.248561i
$857$			652071.i			0.887837i	0.896067	+	0.443919i	$0.146412\pi$
$857$			652071.i			0.887837i	−0.896067	+	0.443919i	$0.853588\pi$
$858$		0			0
$859$	−559418.			−0.758142			−0.379071	−	0.925368i	$-0.623756\pi$
$859$	−559418.			−0.758142			−0.379071	+	0.925368i	$0.623756\pi$
$860$	−857964.	+	278770.i	−1.16004	+	0.376919i
$861$		0			0
$862$	96675.0	−	70238.5i	0.130107	−	0.0945281i
$863$	116919.	−	359840.i	0.156987	−	0.483157i	−0.841370	−	0.540460i	$-0.818250\pi$
$863$	116919.	−	359840.i	0.156987	−	0.483157i	0.998357	+	0.0573033i	$0.0182502\pi$
$864$		0			0
$865$	562363.	+	774026.i	0.751596	+	1.03448i
$866$	−110212.	+	151694.i	−0.146958	+	0.202270i
$867$		0			0
$868$		−	94870.5i		−	0.125919i
$869$	−234457.	−	102068.i	−0.310474	−	0.135161i
$870$		0			0
$871$	512071.	−	166382.i	0.674985	−	0.219316i
$872$	−140016.	−	101727.i	−0.184138	−	0.133784i
$873$		0			0
$874$	−179137.	+	551326.i	−0.234510	+	0.721748i
$875$	−342094.	−	111153.i	−0.446817	−	0.145180i
$876$		0			0
$877$	133607.	−	183894.i	0.173712	−	0.239094i	−0.713280	−	0.700880i	$-0.752791\pi$
$877$	133607.	−	183894.i	0.173712	−	0.239094i	0.886992	+	0.461785i	$0.152791\pi$
$878$	−185722.	−	571594.i	−0.240921	−	0.741479i
$879$		0			0
$880$	−72449.0	−	327480.i	−0.0935550	−	0.422883i
$881$	−721351.			−0.929383			−0.464692	−	0.885473i	$-0.653835\pi$
$881$	−721351.			−0.929383			−0.464692	+	0.885473i	$0.653835\pi$
$882$		0			0
$883$	−173179.	−	125822.i	−0.222113	−	0.161374i	0.471165	−	0.882045i	$-0.343834\pi$
$883$	−173179.	−	125822.i	−0.222113	−	0.161374i	−0.693277	+	0.720671i	$0.743834\pi$
$884$	204727.	−	148743.i	0.261981	−	0.190340i
$885$		0			0
$886$	−961822.	−	312515.i	−1.22526	−	0.398110i
$887$	720290.	+	991394.i	0.915504	+	1.26008i	0.965252	+	0.261322i	$0.0841583\pi$
$887$	720290.	+	991394.i	0.915504	+	1.26008i	−0.0497477	+	0.998762i	$0.515842\pi$
$888$		0			0
$889$	28246.3	+	86933.2i	0.0357403	+	0.109997i
$890$		−	1.78327e6i		−	2.25132i
$891$		0			0
$892$	−226325.			−0.284448
$893$	533473.	−	173336.i	0.668974	−	0.217363i
$894$		0			0
$895$	292818.	−	212745.i	0.365554	−	0.265591i
$896$	−5938.68	+	18277.4i	−0.00739731	+	0.0227666i
$897$		0			0
$898$	−60094.9	−	82713.6i	−0.0745221	−	0.102571i
$899$	451861.	−	621934.i	0.559095	−	0.769528i
$900$		0			0
$901$		−	259685.i		−	0.319888i
$902$	772860.	−	454790.i	0.949922	−	0.558982i
$903$		0			0
$904$	−195394.	+	63487.4i	−0.239097	+	0.0776874i
$905$	352844.	+	256356.i	0.430810	+	0.313001i
$906$		0			0
$907$	−313569.	+	965067.i	−0.381170	+	1.17312i	0.558050	+	0.829807i	$0.311550\pi$
$907$	−313569.	+	965067.i	−0.381170	+	1.17312i	−0.939221	+	0.343314i	$0.888450\pi$
$908$	−548221.	−	178128.i	−0.664942	−	0.216053i
$909$		0			0
$910$	−171211.	+	235652.i	−0.206752	+	0.284570i
$911$	−369150.	−	1.13613e6i	−0.444802	−	1.36896i	−0.882701	−	0.469935i	$-0.844277\pi$
$911$	−369150.	−	1.13613e6i	−0.444802	−	1.36896i	0.437899	−	0.899024i	$-0.355723\pi$
$912$		0			0
$913$	−580373.	−	986274.i	−0.696251	−	1.18319i
$914$	69465.1			0.0831523
$915$		0			0
$916$	57850.0	+	42030.5i	0.0689465	+	0.0500926i
$917$	−15793.0	+	11474.3i	−0.0187814	+	0.0136455i
$918$		0			0
$919$	−1.42102e6	−	461717.i	−1.68255	−	0.546695i	−0.697150	−	0.716925i	$-0.745549\pi$
$919$	−1.42102e6	−	461717.i	−1.68255	−	0.546695i	−0.985404	+	0.170230i	$0.945549\pi$
$920$	−325429.	−	447914.i	−0.384486	−	0.529199i
$921$		0			0
$922$	−35869.2	−	110394.i	−0.0421949	−	0.129863i
$923$			1.52256e6i			1.78719i
$924$		0			0
$925$	254207.			0.297101
$926$	−710020.	+	230699.i	−0.828034	+	0.269045i
$927$		0			0
$928$	−125985.	+	91533.8i	−0.146293	+	0.106288i
$929$	147042.	−	452547.i	0.170376	−	0.524364i	−0.829016	−	0.559225i	$-0.811099\pi$
$929$	147042.	−	452547.i	0.170376	−	0.524364i	0.999392	+	0.0348610i	$0.0110989\pi$
$930$		0			0
$931$	−474436.	−	653005.i	−0.547367	−	0.753385i
$932$	−227669.	+	313359.i	−0.262103	+	0.360753i
$933$		0			0
$934$		−	64095.2i		−	0.0734737i
$935$	−903341.	+	199848.i	−1.03330	+	0.228600i
$936$		0			0
$937$	869952.	−	282665.i	0.990869	−	0.321953i	0.231658	−	0.972797i	$-0.425585\pi$
$937$	869952.	−	282665.i	0.990869	−	0.321953i	0.759211	+	0.650845i	$0.225585\pi$
$938$	91251.2	+	66297.9i	0.103713	+	0.0753519i
$939$		0			0
$940$	−165548.	+	509504.i	−0.187356	+	0.576623i
$941$	−790180.	−	256745.i	−0.892374	−	0.289950i	−0.173288	−	0.984871i	$-0.555439\pi$
$941$	−790180.	−	256745.i	−0.892374	−	0.289950i	−0.719086	+	0.694921i	$0.755439\pi$
$942$		0			0
$943$	870087.	−	1.19757e6i	0.978451	−	1.34672i
$944$	97229.2	+	299241.i	0.109107	+	0.335797i
$945$		0			0
$946$	355670.	−	817000.i	0.397434	−	0.912935i
$947$	322279.			0.359362			0.179681	−	0.983725i	$-0.442494\pi$
$947$	322279.			0.359362			0.179681	+	0.983725i	$0.442494\pi$
$948$		0			0
$949$	−659590.	−	479220.i	−0.732389	−	0.532112i
$950$	−1.03836e6	+	754414.i	−1.15054	+	0.835916i
$951$		0			0
$952$	50417.4	+	16381.6i	0.0556297	+	0.0180752i
$953$	182953.	+	251813.i	0.201444	+	0.277263i	0.897772	−	0.440459i	$-0.145184\pi$
$953$	182953.	+	251813.i	0.201444	+	0.277263i	−0.696329	+	0.717723i	$0.745184\pi$
$954$		0			0
$955$	−472632.	−	1.45461e6i	−0.518223	−	1.59493i
$956$		−	433241.i		−	0.474039i
$957$		0			0
$958$	−187975.			−0.204818
$959$	228743.	−	74323.0i	0.248720	−	0.0808139i
$960$		0			0
$961$	101111.	−	73461.5i	0.109484	−	0.0795450i
$962$	31827.3	−	97954.5i	0.0343914	−	0.105846i
$963$		0			0
$964$	254708.	+	350576.i	0.274087	+	0.377248i
$965$	199182.	−	274151.i	0.213893	−	0.294398i
$966$		0			0
$967$			852868.i			0.912072i	0.889961	+	0.456036i	$0.150731\pi$
$967$			852868.i			0.912072i	−0.889961	+	0.456036i	$0.849269\pi$
$968$	289609.	+	160867.i	0.309073	+	0.171679i
$969$		0			0
$970$	−790659.	+	256901.i	−0.840322	+	0.273037i
$971$	372880.	+	270914.i	0.395486	+	0.287337i	0.767700	−	0.640810i	$-0.221401\pi$
$971$	372880.	+	270914.i	0.395486	+	0.287337i	−0.372214	+	0.928147i	$0.621401\pi$
$972$		0			0
$973$	41752.7	−	128502.i	0.0441021	−	0.135732i
$974$	1.09597e6	+	356101.i	1.15526	+	0.375367i
$975$		0			0
$976$	−59677.2	+	82138.6i	−0.0626482	+	0.0862279i
$977$	252268.	+	776402.i	0.264285	+	0.813387i	0.991857	+	0.127355i	$0.0406489\pi$
$977$	252268.	+	776402.i	0.264285	+	0.813387i	−0.727572	+	0.686032i	$0.759351\pi$
$978$		0			0
$979$	1.31871e6	+	1.16773e6i	1.37589	+	1.21837i
$980$	770893.			0.802679
$981$		0			0
$982$	−80848.7	−	58740.0i	−0.0838397	−	0.0609131i
$983$	−1.31752e6	+	957232.i	−1.36348	+	0.990627i	−0.365267	+	0.930903i	$0.619022\pi$
$983$	−1.31752e6	+	957232.i	−1.36348	+	0.990627i	−0.998215	+	0.0597245i	$0.980978\pi$
$984$		0			0
$985$	60683.8	+	19717.4i	0.0625461	+	0.0203225i
$986$	252492.	+	347526.i	0.259713	+	0.357465i
$987$		0			0
$988$	160695.	+	494569.i	0.164623	+	0.506656i
$989$		−	1.47090e6i		−	1.50380i
$990$		0			0
$991$	−552727.			−0.562812			−0.281406	−	0.959589i	$-0.590801\pi$
$991$	−552727.			−0.562812			−0.281406	+	0.959589i	$0.590801\pi$
$992$	153844.	−	49986.9i	0.156335	−	0.0507964i
$993$		0			0
$994$	−258042.	+	187478.i	−0.261166	+	0.189749i
$995$	349270.	−	1.07494e6i	0.352789	−	1.08577i
$996$		0			0
$997$	701494.	+	965524.i	0.705722	+	0.971344i	0.999879	+	0.0155861i	$0.00496143\pi$
$997$	701494.	+	965524.i	0.705722	+	0.971344i	−0.294156	+	0.955757i	$0.595039\pi$
$998$	−50966.7	+	70149.7i	−0.0511712	+	0.0704311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.5.j.a.127.3		16
3.2	odd	2		22.5.d.a.17.1	yes	16
11.2	odd	10	inner	198.5.j.a.145.3		16
12.11	even	2		176.5.n.c.17.3		16
33.2	even	10		22.5.d.a.13.1	✓	16
33.8	even	10		242.5.b.e.241.5		16
33.14	odd	10		242.5.b.e.241.13		16
132.35	odd	10		176.5.n.c.145.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.1	✓	16	33.2	even	10
22.5.d.a.17.1	yes	16	3.2	odd	2
176.5.n.c.17.3		16	12.11	even	2
176.5.n.c.145.3		16	132.35	odd	10
198.5.j.a.127.3		16	1.1	even	1	trivial
198.5.j.a.145.3		16	11.2	odd	10	inner
242.5.b.e.241.5		16	33.8	even	10
242.5.b.e.241.13		16	33.14	odd	10

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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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	198.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.68999 - 0.874032i) q^{2} +(6.47214 - 4.70228i) q^{4} +(-13.3838 + 41.1910i) q^{5} +(-7.80030 - 10.7362i) q^{7} +(13.3001 - 18.3060i) q^{8} +O(q^{10})\)	\(q+(2.68999 - 0.874032i) q^{2} +(6.47214 - 4.70228i) q^{4} +(-13.3838 + 41.1910i) q^{5} +(-7.80030 - 10.7362i) q^{7} +(13.3001 - 18.3060i) q^{8} +122.501i q^{10} +(-90.5882 - 80.2170i) q^{11} +(-170.407 + 55.3685i) q^{13} +(-30.3665 - 22.0626i) q^{14} +(19.7771 - 60.8676i) q^{16} +(-167.901 - 54.5543i) q^{17} +(213.240 - 293.500i) q^{19} +(107.070 + 329.528i) q^{20} +(-313.794 - 136.606i) q^{22} -564.946 q^{23} +(-1011.94 - 735.215i) q^{25} +(-409.999 + 297.882i) q^{26} +(-100.969 - 32.8069i) q^{28} +(-505.658 - 695.978i) q^{29} +(276.141 + 849.875i) q^{31} -181.019i q^{32} -499.334 q^{34} +(546.632 - 177.611i) q^{35} +(-164.418 + 119.457i) q^{37} +(317.087 - 975.892i) q^{38} +(576.036 + 792.845i) q^{40} +(-1540.12 + 2119.80i) q^{41} +2603.62i q^{43} +(-963.502 - 93.2040i) q^{44} +(-1519.70 + 493.780i) q^{46} +(1250.87 + 908.812i) q^{47} +(687.529 - 2116.00i) q^{49} +(-3364.70 - 1093.26i) q^{50} +(-842.537 + 1159.65i) q^{52} +(454.551 + 1398.97i) q^{53} +(4516.63 - 2657.81i) q^{55} -300.281 q^{56} +(-1968.52 - 1430.22i) q^{58} +(-3977.33 + 2889.70i) q^{59} +(-1508.75 - 490.221i) q^{61} +(1485.64 + 2044.80i) q^{62} +(-158.217 - 486.941i) q^{64} -7760.26i q^{65} -3004.99 q^{67} +(-1343.21 + 436.434i) q^{68} +(1315.20 - 955.547i) q^{70} +(2625.89 - 8081.67i) q^{71} +(2674.58 + 3681.24i) q^{73} +(-337.875 + 465.045i) q^{74} -2902.29i q^{76} +(-154.610 + 1598.29i) q^{77} +(2009.88 - 653.050i) q^{79} +(2242.51 + 1629.28i) q^{80} +(-2290.15 + 7048.37i) q^{82} +(8994.67 + 2922.55i) q^{83} +(4494.29 - 6185.86i) q^{85} +(2275.65 + 7003.72i) q^{86} +(-2673.28 + 591.414i) q^{88} -14557.2 q^{89} +(1923.67 + 1397.63i) q^{91} +(-3656.40 + 2656.53i) q^{92} +(4159.17 + 1351.40i) q^{94} +(9235.60 + 12711.7i) q^{95} +(2097.12 + 6454.28i) q^{97} -6292.94i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 30 q^{5} + 150 q^{7}+O(q^{10}) \) 16 * q + 32 * q^4 - 30 * q^5 + 150 * q^7	\( 16 q + 32 q^{4} - 30 q^{5} + 150 q^{7} + 30 q^{11} - 510 q^{13} + 96 q^{14} - 256 q^{16} - 1770 q^{17} + 1020 q^{19} + 240 q^{20} + 240 q^{22} + 2424 q^{23} - 858 q^{25} - 480 q^{26} + 1600 q^{28} - 4890 q^{29} + 602 q^{31} - 3904 q^{34} + 8670 q^{35} - 4518 q^{37} + 4800 q^{38} - 1280 q^{40} - 1290 q^{41} - 720 q^{44} + 4480 q^{46} - 642 q^{47} + 9534 q^{49} - 6720 q^{50} + 4000 q^{52} - 2598 q^{53} + 2582 q^{55} + 3072 q^{56} - 6496 q^{58} - 6660 q^{59} - 27410 q^{61} + 19680 q^{62} + 2048 q^{64} + 21524 q^{67} - 14160 q^{68} + 34400 q^{70} + 5562 q^{71} - 7790 q^{73} - 5760 q^{74} + 1110 q^{77} - 2770 q^{79} + 3840 q^{80} - 17472 q^{82} + 36900 q^{83} - 24750 q^{85} - 624 q^{86} - 5760 q^{88} - 46596 q^{89} + 32370 q^{91} - 14112 q^{92} + 58880 q^{94} - 74250 q^{95} - 3732 q^{97}+O(q^{100}) \) 16 * q + 32 * q^4 - 30 * q^5 + 150 * q^7 + 30 * q^11 - 510 * q^13 + 96 * q^14 - 256 * q^16 - 1770 * q^17 + 1020 * q^19 + 240 * q^20 + 240 * q^22 + 2424 * q^23 - 858 * q^25 - 480 * q^26 + 1600 * q^28 - 4890 * q^29 + 602 * q^31 - 3904 * q^34 + 8670 * q^35 - 4518 * q^37 + 4800 * q^38 - 1280 * q^40 - 1290 * q^41 - 720 * q^44 + 4480 * q^46 - 642 * q^47 + 9534 * q^49 - 6720 * q^50 + 4000 * q^52 - 2598 * q^53 + 2582 * q^55 + 3072 * q^56 - 6496 * q^58 - 6660 * q^59 - 27410 * q^61 + 19680 * q^62 + 2048 * q^64 + 21524 * q^67 - 14160 * q^68 + 34400 * q^70 + 5562 * q^71 - 7790 * q^73 - 5760 * q^74 + 1110 * q^77 - 2770 * q^79 + 3840 * q^80 - 17472 * q^82 + 36900 * q^83 - 24750 * q^85 - 624 * q^86 - 5760 * q^88 - 46596 * q^89 + 32370 * q^91 - 14112 * q^92 + 58880 * q^94 - 74250 * q^95 - 3732 * q^97

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