LMFDB - Embedded newform 198.5.j.a.145.4

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			145.4
Root			$0.809017 + 3.49146i$ of defining polynomial
Character	$\chi$	$=$	198.145
Dual form			198.5.j.a.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68999 + 0.874032i) q^{2} +(6.47214 + 4.70228i) q^{4} +(10.0117 + 30.8128i) q^{5} +(50.5008 - 69.5083i) q^{7} +(13.3001 + 18.3060i) q^{8} +O(q^{10})$	\(q+(2.68999 + 0.874032i) q^{2} +(6.47214 + 4.70228i) q^{4} +(10.0117 + 30.8128i) q^{5} +(50.5008 - 69.5083i) q^{7} +(13.3001 + 18.3060i) q^{8} +91.6368i q^{10} +(44.2851 - 112.605i) q^{11} +(97.9585 + 31.8286i) q^{13} +(196.599 - 142.838i) q^{14} +(19.7771 + 60.8676i) q^{16} +(-121.020 + 39.3217i) q^{17} +(158.082 + 217.581i) q^{19} +(-80.0935 + 246.502i) q^{20} +(217.547 - 264.199i) q^{22} +446.426 q^{23} +(-343.559 + 249.610i) q^{25} +(235.689 + 171.238i) q^{26} +(653.696 - 212.399i) q^{28} +(-639.233 + 879.829i) q^{29} +(-155.334 + 478.068i) q^{31} +181.019i q^{32} -359.911 q^{34} +(2647.34 + 860.174i) q^{35} +(1568.75 + 1139.76i) q^{37} +(235.066 + 723.460i) q^{38} +(-430.902 + 593.086i) q^{40} +(-951.709 - 1309.92i) q^{41} -1441.78i q^{43} +(816.119 - 520.552i) q^{44} +(1200.88 + 390.191i) q^{46} +(2665.57 - 1936.65i) q^{47} +(-1539.13 - 4736.96i) q^{49} +(-1142.34 + 371.168i) q^{50} +(484.333 + 666.628i) q^{52} +(-906.672 + 2790.45i) q^{53} +(3913.04 + 237.186i) q^{55} +1944.08 q^{56} +(-2488.53 + 1808.02i) q^{58} +(1304.22 + 947.571i) q^{59} +(-3170.81 + 1030.26i) q^{61} +(-835.694 + 1150.23i) q^{62} +(-158.217 + 486.941i) q^{64} +3337.03i q^{65} -2147.45 q^{67} +(-968.159 - 314.574i) q^{68} +(6369.52 + 4627.73i) q^{70} +(-1044.65 - 3215.10i) q^{71} +(-4442.75 + 6114.92i) q^{73} +(3223.74 + 4437.10i) q^{74} +2151.56i q^{76} +(-5590.54 - 8764.81i) q^{77} +(-6155.63 - 2000.08i) q^{79} +(-1677.50 + 1218.77i) q^{80} +(-1415.18 - 4355.49i) q^{82} +(-3860.37 + 1254.31i) q^{83} +(-2423.22 - 3335.28i) q^{85} +(1260.16 - 3878.38i) q^{86} +(2650.33 - 686.968i) q^{88} +6032.84 q^{89} +(7159.34 - 5201.56i) q^{91} +(2889.33 + 2099.22i) q^{92} +(8863.05 - 2879.78i) q^{94} +(-5121.61 + 7049.29i) q^{95} +(4241.03 - 13052.6i) q^{97} -14087.7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

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

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
$5$	10.0117	+	30.8128i	0.400467	+	1.23251i	0.924621	+	0.380888i	$0.124382\pi$
$5$	10.0117	+	30.8128i	0.400467	+	1.23251i	−0.524154	+	0.851624i	$0.675618\pi$
$6$		0			0
$7$	50.5008	−	69.5083i	1.03063	−	1.41854i	0.126153	−	0.992011i	$-0.459737\pi$
$7$	50.5008	−	69.5083i	1.03063	−	1.41854i	0.904475	−	0.426527i	$-0.140263\pi$
$8$	13.3001	+	18.3060i	0.207813	+	0.286031i
$9$		0			0
$10$			91.6368i			0.916368i
$11$	44.2851	−	112.605i	0.365993	−	0.930618i
$11$	44.2851	−	112.605i	0.365993	−	0.930618i
$12$		0			0
$13$	97.9585	+	31.8286i	0.579636	+	0.188335i	0.584138	−	0.811655i	$-0.301433\pi$
$13$	97.9585	+	31.8286i	0.579636	+	0.188335i	−0.00450146	+	0.999990i	$0.501433\pi$
$14$	196.599	−	142.838i	1.00306	−	0.728764i
$15$		0			0
$16$	19.7771	+	60.8676i	0.0772542	+	0.237764i
$17$	−121.020	+	39.3217i	−0.418754	+	0.136061i	−0.510812	−	0.859692i	$-0.670655\pi$
$17$	−121.020	+	39.3217i	−0.418754	+	0.136061i	0.0920586	+	0.995754i	$0.470655\pi$
$18$		0			0
$19$	158.082	+	217.581i	0.437900	+	0.602717i	0.969744	−	0.244125i	$-0.0785008\pi$
$19$	158.082	+	217.581i	0.437900	+	0.602717i	−0.531844	+	0.846842i	$0.678501\pi$
$20$	−80.0935	+	246.502i	−0.200234	+	0.616256i
$21$		0			0
$22$	217.547	−	264.199i	0.449477	−	0.545867i
$23$	446.426			0.843905			0.421953	−	0.906618i	$-0.361345\pi$
$23$	446.426			0.843905			0.421953	+	0.906618i	$0.361345\pi$
$24$		0			0
$25$	−343.559	+	249.610i	−0.549694	+	0.399376i
$26$	235.689	+	171.238i	0.348652	+	0.253310i
$27$		0			0
$28$	653.696	−	212.399i	0.833796	−	0.270917i
$29$	−639.233	+	879.829i	−0.760087	+	1.04617i	0.237120	+	0.971480i	$0.423797\pi$
$29$	−639.233	+	879.829i	−0.760087	+	1.04617i	−0.997207	+	0.0746895i	$0.976203\pi$
$30$		0			0
$31$	−155.334	+	478.068i	−0.161638	+	0.497470i	−0.998773	−	0.0495264i	$-0.984229\pi$
$31$	−155.334	+	478.068i	−0.161638	+	0.497470i	0.837135	+	0.546996i	$0.184229\pi$
$32$			181.019i			0.176777i
$33$		0			0
$34$	−359.911			−0.311342
$35$	2647.34	+	860.174i	2.16110	+	0.702183i
$36$		0			0
$37$	1568.75	+	1139.76i	1.14591	+	0.832553i	0.987932	−	0.154890i	$-0.0495022\pi$
$37$	1568.75	+	1139.76i	1.14591	+	0.832553i	0.157979	+	0.987443i	$0.449502\pi$
$38$	235.066	+	723.460i	0.162788	+	0.501011i
$39$		0			0
$40$	−430.902	+	593.086i	−0.269314	+	0.370678i
$41$	−951.709	−	1309.92i	−0.566157	−	0.779248i	0.425936	−	0.904753i	$-0.359945\pi$
$41$	−951.709	−	1309.92i	−0.566157	−	0.779248i	−0.992093	+	0.125505i	$0.959945\pi$
$42$		0			0
$43$		−	1441.78i		−	0.779763i	−0.920865	−	0.389881i	$-0.872516\pi$
$43$		−	1441.78i		−	0.779763i	0.920865	−	0.389881i	$-0.127484\pi$
$44$	816.119	−	520.552i	0.421549	−	0.268880i
$45$		0			0
$46$	1200.88	+	390.191i	0.567525	+	0.184400i
$47$	2665.57	−	1936.65i	1.20668	−	0.876708i	0.211759	−	0.977322i	$-0.432081\pi$
$47$	2665.57	−	1936.65i	1.20668	−	0.876708i	0.994926	+	0.100614i	$0.0320808\pi$
$48$		0			0
$49$	−1539.13	−	4736.96i	−0.641038	−	1.97291i
$50$	−1142.34	+	371.168i	−0.456935	+	0.148467i
$51$		0			0
$52$	484.333	+	666.628i	0.179117	+	0.246534i
$53$	−906.672	+	2790.45i	−0.322774	+	0.993396i	0.649662	+	0.760223i	$0.274911\pi$
$53$	−906.672	+	2790.45i	−0.322774	+	0.993396i	−0.972435	+	0.233172i	$0.925089\pi$
$54$		0			0
$55$	3913.04	+	237.186i	1.29357	+	0.0784085i
$56$	1944.08			0.619924
$57$		0			0
$58$	−2488.53	+	1808.02i	−0.739754	+	0.537463i
$59$	1304.22	+	947.571i	0.374668	+	0.272212i	0.759144	−	0.650923i	$-0.225618\pi$
$59$	1304.22	+	947.571i	0.374668	+	0.272212i	−0.384476	+	0.923135i	$0.625618\pi$
$60$		0			0
$61$	−3170.81	+	1030.26i	−0.852138	+	0.276877i	−0.702341	−	0.711840i	$-0.747862\pi$
$61$	−3170.81	+	1030.26i	−0.852138	+	0.276877i	−0.149797	+	0.988717i	$0.547862\pi$
$62$	−835.694	+	1150.23i	−0.217402	+	0.299229i
$63$		0			0
$64$	−158.217	+	486.941i	−0.0386271	+	0.118882i
$65$			3337.03i			0.789830i
$66$		0			0
$67$	−2147.45			−0.478380			−0.239190	−	0.970973i	$-0.576882\pi$
$67$	−2147.45			−0.478380			−0.239190	+	0.970973i	$0.576882\pi$
$68$	−968.159	−	314.574i	−0.209377	−	0.0680307i
$69$		0			0
$70$	6369.52	+	4627.73i	1.29990	+	0.944434i
$71$	−1044.65	−	3215.10i	−0.207230	−	0.637789i	−0.999614	−	0.0277668i	$-0.991160\pi$
$71$	−1044.65	−	3215.10i	−0.207230	−	0.637789i	0.792384	−	0.610022i	$-0.208840\pi$
$72$		0			0
$73$	−4442.75	+	6114.92i	−0.833692	+	1.14748i	0.153532	+	0.988144i	$0.450935\pi$
$73$	−4442.75	+	6114.92i	−0.833692	+	1.14748i	−0.987224	+	0.159336i	$0.949065\pi$
$74$	3223.74	+	4437.10i	0.588704	+	0.810281i
$75$		0			0
$76$			2151.56i			0.372500i
$77$	−5590.54	−	8764.81i	−0.942914	−	1.47830i
$78$		0			0
$79$	−6155.63	−	2000.08i	−0.986320	−	0.320475i	−0.228934	−	0.973442i	$-0.573524\pi$
$79$	−6155.63	−	2000.08i	−0.986320	−	0.320475i	−0.757386	+	0.652967i	$0.773524\pi$
$80$	−1677.50	+	1218.77i	−0.262109	+	0.190434i
$81$		0			0
$82$	−1415.18	−	4355.49i	−0.210468	−	0.647753i
$83$	−3860.37	+	1254.31i	−0.560367	+	0.182074i	−0.575486	−	0.817811i	$-0.695187\pi$
$83$	−3860.37	+	1254.31i	−0.560367	+	0.182074i	0.0151193	+	0.999886i	$0.495187\pi$
$84$		0			0
$85$	−2423.22	−	3335.28i	−0.335394	−	0.461631i
$86$	1260.16	−	3878.38i	0.170384	−	0.524389i
$87$		0			0
$88$	2650.33	−	686.968i	0.342243	−	0.0887097i
$89$	6032.84			0.761626			0.380813	−	0.924652i	$-0.375644\pi$
$89$	6032.84			0.761626			0.380813	+	0.924652i	$0.375644\pi$
$90$		0			0
$91$	7159.34	−	5201.56i	0.864550	−	0.628132i
$92$	2889.33	+	2099.22i	0.341367	+	0.248018i
$93$		0			0
$94$	8863.05	−	2879.78i	1.00306	−	0.325914i
$95$	−5121.61	+	7049.29i	−0.567491	+	0.781085i
$96$		0			0
$97$	4241.03	−	13052.6i	0.450742	−	1.38724i	−0.425320	−	0.905043i	$-0.639839\pi$
$97$	4241.03	−	13052.6i	0.450742	−	1.38724i	0.876062	−	0.482198i	$-0.160161\pi$
$98$		−	14087.7i		−	1.46685i
$99$		0			0
$100$	−3397.30			−0.339730
$101$	−9144.05	−	2971.08i	−0.896388	−	0.291254i	−0.175643	−	0.984454i	$-0.556200\pi$
$101$	−9144.05	−	2971.08i	−0.896388	−	0.291254i	−0.720745	+	0.693200i	$0.756200\pi$
$102$		0			0
$103$	−893.689	−	649.303i	−0.0842387	−	0.0612030i	0.544869	−	0.838521i	$-0.316579\pi$
$103$	−893.689	−	649.303i	−0.0842387	−	0.0612030i	−0.629107	+	0.777318i	$0.716579\pi$
$104$	720.200	+	2216.55i	0.0665865	+	0.204932i
$105$		0			0
$106$	−4877.88	+	6713.83i	−0.434130	+	0.597528i
$107$	−5677.54	−	7814.47i	−0.495898	−	0.682546i	0.485564	−	0.874201i	$-0.338614\pi$
$107$	−5677.54	−	7814.47i	−0.495898	−	0.682546i	−0.981462	+	0.191656i	$0.938614\pi$
$108$		0			0
$109$		−	685.751i		−	0.0577183i	−0.999583	−	0.0288591i	$-0.990813\pi$
$109$		−	685.751i		−	0.0577183i	0.999583	−	0.0288591i	$-0.00918742\pi$
$110$	10318.7	+	4058.15i	0.852788	+	0.335384i
$111$		0			0
$112$	5229.57	+	1699.19i	0.416898	+	0.135458i
$113$	4633.79	−	3366.65i	0.362894	−	0.263658i	−0.391364	−	0.920236i	$-0.627997\pi$
$113$	4633.79	−	3366.65i	0.362894	−	0.263658i	0.754258	+	0.656578i	$0.227997\pi$
$114$		0			0
$115$	4469.47	+	13755.6i	0.337956	+	1.04012i
$116$	−8274.41	+	2688.52i	−0.614923	+	0.199801i
$117$		0			0
$118$	2680.14	+	3688.89i	0.192483	+	0.264930i
$119$	−3378.41	+	10397.7i	−0.238571	+	0.734247i
$120$		0			0
$121$	−10718.7	−	9973.43i	−0.732098	−	0.681199i
$122$	−9429.93			−0.633562
$123$		0			0
$124$	−3253.35	+	2363.70i	−0.211587	+	0.153727i
$125$	5251.04	+	3815.11i	0.336067	+	0.244167i
$126$		0			0
$127$	−29557.9	+	9603.94i	−1.83259	+	0.595446i	−0.833516	+	0.552495i	$0.813676\pi$
$127$	−29557.9	+	9603.94i	−1.83259	+	0.595446i	−0.999077	+	0.0429511i	$0.986324\pi$
$128$	−851.204	+	1171.58i	−0.0519534	+	0.0715077i
$129$		0			0
$130$	−2916.67	+	8976.60i	−0.172584	+	0.531160i
$131$		−	8729.96i		−	0.508709i	−0.967111	−	0.254355i	$-0.918137\pi$
$131$		−	8729.96i		−	0.508709i	0.967111	−	0.254355i	$-0.0818630\pi$
$132$		0			0
$133$	23106.9			1.30629
$134$	−5776.62	−	1876.94i	−0.321710	−	0.104530i
$135$		0			0
$136$	−2329.39	−	1692.40i	−0.125940	−	0.0915011i
$137$	−8160.42	−	25115.2i	−0.434782	−	1.33812i	−0.893310	−	0.449441i	$-0.851623\pi$
$137$	−8160.42	−	25115.2i	−0.434782	−	1.33812i	0.458528	−	0.888680i	$-0.348377\pi$
$138$		0			0
$139$	10425.4	−	14349.3i	0.539588	−	0.742679i	−0.448966	−	0.893549i	$-0.648208\pi$
$139$	10425.4	−	14349.3i	0.539588	−	0.742679i	0.988554	+	0.150870i	$0.0482076\pi$
$140$	13089.2	+	18015.7i	0.667816	+	0.919170i
$141$		0			0
$142$		−	9561.64i		−	0.474194i
$143$	7922.16	−	9621.06i	0.387411	−	0.470490i
$144$		0			0
$145$	−33509.8	−	10888.0i	−1.59381	−	0.517859i
$146$	−17295.6	+	12566.0i	−0.811390	+	0.589510i
$147$		0			0
$148$	4793.68	+	14753.4i	0.218849	+	0.673549i
$149$	−17975.7	+	5840.66i	−0.809679	+	0.263081i	−0.684462	−	0.729049i	$-0.739963\pi$
$149$	−17975.7	+	5840.66i	−0.809679	+	0.263081i	−0.125217	+	0.992129i	$0.539963\pi$
$150$		0			0
$151$	−264.180	−	363.612i	−0.0115863	−	0.0159472i	0.803185	−	0.595730i	$-0.203137\pi$
$151$	−264.180	−	363.612i	−0.0115863	−	0.0159472i	−0.814771	+	0.579783i	$0.803137\pi$
$152$	−1880.53	+	5787.68i	−0.0813942	+	0.250505i
$153$		0			0
$154$	−7377.78	−	28463.6i	−0.311089	−	1.20019i
$155$	−16285.8			−0.677868
$156$		0			0
$157$	28892.7	−	20991.8i	1.17217	−	0.851629i	0.180900	−	0.983502i	$-0.442099\pi$
$157$	28892.7	−	20991.8i	1.17217	−	0.851629i	0.991267	+	0.131873i	$0.0420990\pi$
$158$	−14810.5	−	10760.4i	−0.593273	−	0.431038i
$159$		0			0
$160$	−5577.71	+	1812.31i	−0.217879	+	0.0707933i
$161$	22544.8	−	31030.3i	0.869752	−	1.19711i
$162$		0			0
$163$	−7301.42	+	22471.5i	−0.274810	+	0.845777i	0.714460	+	0.699676i	$0.246672\pi$
$163$	−7301.42	+	22471.5i	−0.274810	+	0.845777i	−0.989270	+	0.146101i	$0.953328\pi$
$164$		−	12953.2i		−	0.481602i
$165$		0			0
$166$	−11480.7			−0.416631
$167$	616.899	+	200.443i	0.0221198	+	0.00718715i	0.320056	−	0.947399i	$-0.396298\pi$
$167$	616.899	+	200.443i	0.0221198	+	0.00718715i	−0.297936	+	0.954586i	$0.596298\pi$
$168$		0			0
$169$	−14523.5	−	10552.0i	−0.508509	−	0.369454i
$170$	−3603.32	−	11089.9i	−0.124682	−	0.383732i
$171$		0			0
$172$	6779.66	−	9331.40i	0.229166	−	0.315421i
$173$	13537.7	+	18633.0i	0.452326	+	0.622573i	0.972895	−	0.231246i	$-0.0742803\pi$
$173$	13537.7	+	18633.0i	0.452326	+	0.622573i	−0.520569	+	0.853819i	$0.674280\pi$
$174$		0			0
$175$			36485.7i			1.19137i
$176$	7729.81	+	468.537i	0.249542	+	0.0151258i
$177$		0			0
$178$	16228.3	+	5272.89i	0.512192	+	0.166421i
$179$	5194.85	−	3774.28i	0.162131	−	0.117795i	−0.503761	−	0.863843i	$-0.668051\pi$
$179$	5194.85	−	3774.28i	0.162131	−	0.117795i	0.665893	+	0.746048i	$0.268051\pi$
$180$		0			0
$181$	13260.0	+	40810.0i	0.404749	+	1.24569i	0.921105	+	0.389315i	$0.127288\pi$
$181$	13260.0	+	40810.0i	0.404749	+	1.24569i	−0.516356	+	0.856374i	$0.672712\pi$
$182$	23804.9	−	7734.68i	0.718660	−	0.233507i
$183$		0			0
$184$	5937.49	+	8172.26i	0.175375	+	0.241383i
$185$	−19413.5	+	59748.6i	−0.567231	+	1.74576i
$186$		0			0
$187$	−931.567	+	15368.8i	−0.0266398	+	0.439497i
$188$	26358.6			0.745772
$189$		0			0
$190$	−19938.4	+	14486.1i	−0.552310	+	0.401277i
$191$	−20652.0	−	15004.5i	−0.566102	−	0.411298i	0.267585	−	0.963534i	$-0.413774\pi$
$191$	−20652.0	−	15004.5i	−0.566102	−	0.411298i	−0.833687	+	0.552237i	$0.813774\pi$
$192$		0			0
$193$	40117.2	−	13034.9i	1.07700	−	0.349939i	0.283790	−	0.958886i	$-0.408408\pi$
$193$	40117.2	−	13034.9i	1.07700	−	0.349939i	0.793210	+	0.608948i	$0.208408\pi$
$194$	22816.7	−	31404.5i	0.606247	−	0.834427i
$195$		0			0
$196$	12313.1	−	37895.7i	0.320519	−	0.986456i
$197$			37597.4i			0.968781i	0.874852	+	0.484390i	$0.160959\pi$
$197$			37597.4i			0.968781i	−0.874852	+	0.484390i	$0.839041\pi$
$198$		0			0
$199$	−37450.3			−0.945690			−0.472845	−	0.881146i	$-0.656773\pi$
$199$	−37450.3			−0.945690			−0.472845	+	0.881146i	$0.656773\pi$
$200$	−9138.71	−	2969.35i	−0.228468	−	0.0742336i
$201$		0			0
$202$	−22000.6	−	15984.4i	−0.539178	−	0.391736i
$203$	28873.7	+	88864.1i	0.700665	+	2.15642i
$204$		0			0
$205$	30833.9	−	42439.3i	0.733705	−	1.00986i
$206$	−1836.51	−	2527.73i	−0.0432771	−	0.0595658i
$207$		0			0
$208$			6591.98i			0.152366i
$209$	31501.3	−	8165.16i	0.721167	−	0.186927i
$210$		0			0
$211$	−31716.5	−	10305.3i	−0.712394	−	0.231471i	−0.0696716	−	0.997570i	$-0.522195\pi$
$211$	−31716.5	−	10305.3i	−0.712394	−	0.231471i	−0.642722	+	0.766099i	$0.722195\pi$
$212$	−18989.6	+	13796.7i	−0.422516	+	0.306976i
$213$		0			0
$214$	−8442.46	−	25983.2i	−0.184349	−	0.567369i
$215$	44425.3	−	14434.7i	0.961067	−	0.312269i
$216$		0			0
$217$	25385.3	+	34939.8i	0.539091	+	0.741995i
$218$	599.368	−	1844.67i	0.0126119	−	0.0388154i
$219$		0			0
$220$	24210.4	+	19935.3i	0.500215	+	0.411886i
$221$	−13106.5			−0.268350
$222$		0			0
$223$	24842.4	−	18049.1i	0.499556	−	0.362949i	−0.309291	−	0.950967i	$-0.600092\pi$
$223$	24842.4	−	18049.1i	0.499556	−	0.362949i	0.808848	+	0.588018i	$0.200092\pi$
$224$	12582.4	+	9141.62i	0.250764	+	0.182191i
$225$		0			0
$226$	15407.4	−	5006.18i	0.301657	−	0.0980143i
$227$	5431.00	−	7475.12i	0.105397	−	0.145066i	−0.753060	−	0.657951i	$-0.771423\pi$
$227$	5431.00	−	7475.12i	0.105397	−	0.145066i	0.858457	+	0.512885i	$0.171423\pi$
$228$		0			0
$229$	−23748.2	+	73089.5i	−0.452856	+	1.39375i	0.420778	+	0.907164i	$0.361757\pi$
$229$	−23748.2	+	73089.5i	−0.452856	+	1.39375i	−0.873634	+	0.486584i	$0.838243\pi$
$230$			40909.0i			0.773327i
$231$		0			0
$232$	−24608.0			−0.457193
$233$	10685.0	+	3471.75i	0.196816	+	0.0639495i	0.405766	−	0.913977i	$-0.367005\pi$
$233$	10685.0	+	3471.75i	0.196816	+	0.0639495i	−0.208950	+	0.977926i	$0.567005\pi$
$234$		0			0
$235$	86360.3	+	62744.4i	1.56379	+	1.13616i
$236$	3985.34	+	12265.6i	0.0715552	+	0.220224i
$237$		0			0
$238$	−18175.8	+	25016.8i	−0.320878	+	0.441650i
$239$	16277.0	+	22403.4i	0.284957	+	0.392210i	0.927368	−	0.374151i	$-0.122066\pi$
$239$	16277.0	+	22403.4i	0.284957	+	0.392210i	−0.642411	+	0.766360i	$0.722066\pi$
$240$		0			0
$241$		−	39221.5i		−	0.675289i	−0.941274	−	0.337644i	$-0.890370\pi$
$241$		−	39221.5i		−	0.675289i	0.941274	−	0.337644i	$-0.109630\pi$
$242$	−20116.0	−	36196.9i	−0.343488	−	0.618075i
$243$		0			0
$244$	−25366.5	−	8242.06i	−0.426069	−	0.138438i
$245$	130550.	−	94850.0i	2.17492	−	1.58017i
$246$		0			0
$247$	8560.15	+	26345.4i	0.140310	+	0.431828i
$248$	−10817.5	+	3514.80i	−0.175882	+	0.0571476i
$249$		0			0
$250$	10790.8	+	14852.2i	0.172652	+	0.237635i
$251$	25606.0	−	78807.1i	0.406438	−	1.25089i	−0.513251	−	0.858238i	$-0.671559\pi$
$251$	25606.0	−	78807.1i	0.406438	−	1.25089i	0.919689	−	0.392648i	$-0.128441\pi$
$252$		0			0
$253$	19770.0	−	50269.7i	0.308863	−	0.785353i
$254$	−87904.7			−1.36253
$255$		0			0
$256$	−3313.73	+	2407.57i	−0.0505636	+	0.0367366i
$257$	−4780.54	−	3473.26i	−0.0723786	−	0.0525861i	0.551008	−	0.834500i	$-0.314244\pi$
$257$	−4780.54	−	3473.26i	−0.0723786	−	0.0525861i	−0.623386	+	0.781914i	$0.714244\pi$
$258$		0			0
$259$	158446.	−	51482.3i	2.36201	−	0.767465i
$260$	−15691.7	+	21597.7i	−0.232125	+	0.319493i
$261$		0			0
$262$	7630.26	−	23483.5i	0.111157	−	0.342106i
$263$			107951.i			1.56069i	0.625351	+	0.780344i	$0.284956\pi$
$263$			107951.i			1.56069i	−0.625351	+	0.780344i	$0.715044\pi$
$264$		0			0
$265$	−95058.8			−1.35363
$266$	62157.5	+	20196.2i	0.878477	+	0.285435i
$267$		0			0
$268$	−13898.6	−	10097.9i	−0.193509	−	0.140592i
$269$	4826.05	+	14853.1i	0.0666941	+	0.205263i	0.978850	−	0.204581i	$-0.0655831\pi$
$269$	4826.05	+	14853.1i	0.0666941	+	0.205263i	−0.912156	+	0.409844i	$0.865583\pi$
$270$		0			0
$271$	−20136.9	+	27716.1i	−0.274192	+	0.377392i	−0.923799	−	0.382877i	$-0.874933\pi$
$271$	−20136.9	+	27716.1i	−0.274192	+	0.377392i	0.649608	+	0.760270i	$0.274933\pi$
$272$	−4786.84	−	6588.52i	−0.0647010	−	0.0890533i
$273$		0			0
$274$		−	74692.2i		−	0.994887i
$275$	12892.7	+	49740.4i	0.170482	+	0.657724i
$276$		0			0
$277$	68601.8	+	22290.1i	0.894079	+	0.290504i	0.719791	−	0.694191i	$-0.244238\pi$
$277$	68601.8	+	22290.1i	0.894079	+	0.290504i	0.174288	+	0.984695i	$0.444238\pi$
$278$	40585.9	−	29487.4i	0.525153	−	0.381546i
$279$		0			0
$280$	19463.5	+	59902.6i	0.248259	+	0.764063i
$281$	−96719.5	+	31426.1i	−1.22490	+	0.397995i	−0.848865	−	0.528610i	$-0.822713\pi$
$281$	−96719.5	+	31426.1i	−1.22490	+	0.397995i	−0.376037	+	0.926605i	$0.622713\pi$
$282$		0			0
$283$	−1793.34	−	2468.33i	−0.0223919	−	0.0308198i	0.797674	−	0.603089i	$-0.206063\pi$
$283$	−1793.34	−	2468.33i	−0.0223919	−	0.0308198i	−0.820066	+	0.572269i	$0.806063\pi$
$284$	8357.18	−	25720.8i	0.103615	−	0.318895i
$285$		0			0
$286$	29719.7	−	18956.4i	0.363339	−	0.231752i
$287$	−139112.			−1.68889
$288$		0			0
$289$	−54470.3	+	39575.0i	−0.652175	+	0.473833i
$290$	−80624.7	−	58577.3i	−0.958676	−	0.696519i
$291$		0			0
$292$	−57508.1	+	18685.5i	−0.674471	+	0.219149i
$293$	−6804.87	+	9366.10i	−0.0792656	+	0.109100i	−0.846809	−	0.531898i	$-0.821479\pi$
$293$	−6804.87	+	9366.10i	−0.0792656	+	0.109100i	0.767543	+	0.640997i	$0.221479\pi$
$294$		0			0
$295$	−16139.9	+	49673.4i	−0.185463	+	0.570795i
$296$			43876.5i			0.500781i
$297$		0			0
$298$	−53459.4			−0.601993
$299$	43731.2	+	14209.1i	0.489158	+	0.158937i
$300$		0			0
$301$	−100216.	−	72811.1i	−1.10612	−	0.803645i
$302$	−392.833	−	1209.02i	−0.00430720	−	0.0132562i
$303$		0			0
$304$	−10117.2	+	13925.2i	−0.109475	+	0.150679i
$305$	−63490.2	−	87386.8i	−0.682507	−	0.939391i
$306$		0			0
$307$			26745.6i			0.283776i	0.989883	+	0.141888i	$0.0453174\pi$
$307$			26745.6i			0.283776i	−0.989883	+	0.141888i	$0.954683\pi$
$308$	5031.91	−	83015.3i	0.0530434	−	0.875098i
$309$		0			0
$310$	−43808.6	−	14234.3i	−0.455865	−	0.148120i
$311$	−32169.2	+	23372.3i	−0.332598	+	0.241646i	−0.741532	−	0.670917i	$-0.765900\pi$
$311$	−32169.2	+	23372.3i	−0.332598	+	0.241646i	0.408934	+	0.912564i	$0.365900\pi$
$312$		0			0
$313$	−26400.8	−	81253.2i	−0.269481	−	0.829377i	−0.990627	−	0.136594i	$-0.956384\pi$
$313$	−26400.8	−	81253.2i	−0.269481	−	0.829377i	0.721146	−	0.692783i	$-0.243616\pi$
$314$	96068.8	−	31214.6i	0.974368	−	0.316591i
$315$		0			0
$316$	−30435.1	−	41890.3i	−0.304790	−	0.419507i
$317$	−7585.16	+	23344.7i	−0.0754825	+	0.232311i	−0.981678	−	0.190548i	$-0.938974\pi$
$317$	−7585.16	+	23344.7i	−0.0754825	+	0.232311i	0.906195	+	0.422859i	$0.138974\pi$
$318$		0			0
$319$	70764.4	+	110944.i	0.695398	+	1.09024i
$320$	−16588.0			−0.161992
$321$		0			0
$322$	87767.0	−	63766.5i	0.846486	−	0.615008i
$323$	−27686.7	−	20115.6i	−0.265379	−	0.192809i
$324$		0			0
$325$	−41599.3	+	13516.4i	−0.393839	+	0.127966i
$326$	−39281.5	+	54066.4i	−0.369618	+	0.508736i
$327$		0			0
$328$	11321.5	−	34843.9i	0.105234	−	0.323876i
$329$		−	283081.i		−	2.61529i
$330$		0			0
$331$	−88390.7			−0.806772			−0.403386	−	0.915030i	$-0.632167\pi$
$331$	−88390.7			−0.806772			−0.403386	+	0.915030i	$0.632167\pi$
$332$	−30883.0	−	10034.5i	−0.280184	−	0.0910372i
$333$		0			0
$334$	1484.26	+	1078.38i	0.0133051	+	0.00966670i
$335$	−21499.5	−	66168.8i	−0.191575	−	0.589608i
$336$		0			0
$337$	−59771.4	+	82268.3i	−0.526301	+	0.724391i	−0.986561	−	0.163393i	$-0.947756\pi$
$337$	−59771.4	+	82268.3i	−0.526301	+	0.724391i	0.460260	+	0.887784i	$0.347756\pi$
$338$	−29845.5	−	41078.7i	−0.261243	−	0.359570i
$339$		0			0
$340$		−	32981.1i		−	0.285304i
$341$	46953.8	+	38662.7i	0.403796	+	0.332493i
$342$		0			0
$343$	−210795.	−	68491.6i	−1.79173	−	0.582169i
$344$	26393.2	−	19175.8i	0.223036	−	0.162045i
$345$		0			0
$346$	20130.4	+	61955.0i	0.168151	+	0.517516i
$347$	−35079.8	+	11398.1i	−0.291338	+	0.0946616i	−0.451040	−	0.892504i	$-0.648947\pi$
$347$	−35079.8	+	11398.1i	−0.291338	+	0.0946616i	0.159702	+	0.987165i	$0.448947\pi$
$348$		0			0
$349$	−60796.7	−	83679.5i	−0.499148	−	0.687018i	0.482894	−	0.875679i	$-0.339585\pi$
$349$	−60796.7	−	83679.5i	−0.499148	−	0.687018i	−0.982042	+	0.188660i	$0.939585\pi$
$350$	−31889.7	+	98146.3i	−0.260324	+	0.801194i
$351$		0			0
$352$	20383.6	+	8016.47i	0.164512	+	0.0646990i
$353$	−50438.5			−0.404774			−0.202387	−	0.979306i	$-0.564870\pi$
$353$	−50438.5			−0.404774			−0.202387	+	0.979306i	$0.564870\pi$
$354$		0			0
$355$	88607.4	−	64377.0i	0.703094	−	0.510827i
$356$	39045.3	+	28368.1i	0.308084	+	0.223836i
$357$		0			0
$358$	17273.0	−	5612.33i	0.134772	−	0.0437902i
$359$	−51281.0	+	70582.2i	−0.397894	+	0.547654i	−0.960214	−	0.279266i	$-0.909909\pi$
$359$	−51281.0	+	70582.2i	−0.397894	+	0.547654i	0.562320	+	0.826920i	$0.309909\pi$
$360$		0			0
$361$	17919.8	−	55151.5i	0.137505	−	0.423197i
$362$			121368.i			0.926165i
$363$		0			0
$364$	70795.4			0.534321
$365$	−232897.	−	75672.8i	−1.74815	−	0.568008i
$366$		0			0
$367$	41866.7	+	30417.9i	0.310840	+	0.225838i	0.732257	−	0.681029i	$-0.238467\pi$
$367$	41866.7	+	30417.9i	0.310840	+	0.225838i	−0.421417	+	0.906867i	$0.638467\pi$
$368$	8829.00	+	27172.9i	0.0651953	+	0.200650i
$369$		0			0
$370$	−104444.	+	143755.i	−0.762924	+	1.05008i
$371$	148172.	+	203941.i	1.07651	+	1.48169i
$372$		0			0
$373$		−	180034.i		−	1.29401i	−0.762487	−	0.647003i	$-0.776022\pi$
$373$		−	180034.i		−	1.29401i	0.762487	−	0.647003i	$-0.223978\pi$
$374$	−15938.7	+	40527.7i	−0.113949	+	0.289740i
$375$		0			0
$376$	70904.4	+	23038.2i	0.501531	+	0.162957i
$377$	−90622.1	+	65840.8i	−0.637604	+	0.463247i
$378$		0			0
$379$	57325.3	+	176429.i	0.399087	+	1.22826i	0.925732	+	0.378179i	$0.123450\pi$
$379$	57325.3	+	176429.i	0.399087	+	1.22826i	−0.526645	+	0.850085i	$0.676550\pi$
$380$	−66295.5	+	21540.7i	−0.459110	+	0.149174i
$381$		0			0
$382$	−42439.3	−	58412.6i	−0.290831	−	0.400295i
$383$	1955.49	−	6018.39i	0.0133309	−	0.0410283i	−0.944170	−	0.329459i	$-0.893134\pi$
$383$	1955.49	−	6018.39i	0.0133309	−	0.0410283i	0.957501	+	0.288431i	$0.0931336\pi$
$384$		0			0
$385$	214098.	−	260011.i	1.44441	−	1.75416i
$386$	119308.			0.800746
$387$		0			0
$388$	88825.3	−	64535.4i	0.590029	−	0.428681i
$389$	89160.2	+	64778.7i	0.589212	+	0.428088i	0.842034	−	0.539425i	$-0.181358\pi$
$389$	89160.2	+	64778.7i	0.589212	+	0.428088i	−0.252821	+	0.967513i	$0.581358\pi$
$390$		0			0
$391$	−54026.4	+	17554.2i	−0.353388	+	0.114823i
$392$	66244.1	−	91177.2i	0.431097	−	0.593354i
$393$		0			0
$394$	−32861.3	+	101137.i	−0.211686	+	0.651503i
$395$		−	209696.i		−	1.34399i
$396$		0			0
$397$	−205760.			−1.30551			−0.652755	−	0.757569i	$-0.726387\pi$
$397$	−205760.			−1.30551			−0.652755	+	0.757569i	$0.726387\pi$
$398$	−100741.	−	32732.7i	−0.635975	−	0.206641i
$399$		0			0
$400$	−21987.8	−	15975.0i	−0.137424	−	0.0998440i
$401$	−40707.1	−	125284.i	−0.253152	−	0.779122i	−0.994188	−	0.107657i	$-0.965665\pi$
$401$	−40707.1	−	125284.i	−0.253152	−	0.779122i	0.741036	−	0.671465i	$-0.234335\pi$
$402$		0			0
$403$	−30432.5	+	41886.8i	−0.187382	+	0.257909i
$404$	−45210.7	−	62227.2i	−0.276999	−	0.381257i
$405$		0			0
$406$			264280.i			1.60329i
$407$	197815.	−	126174.i	1.19418	−	0.761696i
$408$		0			0
$409$	75524.9	+	24539.5i	0.451485	+	0.146696i	0.525928	−	0.850529i	$-0.323718\pi$
$409$	75524.9	+	24539.5i	0.451485	+	0.146696i	−0.0744433	+	0.997225i	$0.523718\pi$
$410$	120036.	−	87211.6i	0.714077	−	0.518808i
$411$		0			0
$412$	−2730.87	−	8404.75i	−0.0160882	−	0.0495143i
$413$	131728.	−	42801.1i	0.772287	−	0.250931i
$414$		0			0
$415$	−77297.6	−	106391.i	−0.448817	−	0.617744i
$416$	−5761.60	+	17732.4i	−0.0332933	+	0.102466i
$417$		0			0
$418$	91874.9	+	5568.93i	0.525829	+	0.0318727i
$419$	−281150.			−1.60144			−0.800718	−	0.599041i	$-0.795549\pi$
$419$	−281150.			−1.60144			−0.800718	+	0.599041i	$0.795549\pi$
$420$		0			0
$421$	268282.	−	194918.i	1.51366	−	1.09974i	0.549136	−	0.835733i	$-0.314957\pi$
$421$	268282.	−	194918.i	1.51366	−	1.09974i	0.964522	−	0.264004i	$-0.0850433\pi$
$422$	−76310.0	−	55442.5i	−0.428506	−	0.311328i
$423$		0			0
$424$	−63140.6	+	20515.6i	−0.351218	+	0.114118i
$425$	31762.3	−	43717.1i	0.175847	−	0.242032i
$426$		0			0
$427$	−88516.7	+	272426.i	−0.485478	+	1.49415i
$428$		−	77273.7i		−	0.421836i
$429$		0			0
$430$	132120.			0.714549
$431$	118641.	+	38548.8i	0.638675	+	0.207518i	0.610414	−	0.792083i	$-0.291003\pi$
$431$	118641.	+	38548.8i	0.638675	+	0.207518i	0.0282608	+	0.999601i	$0.491003\pi$
$432$		0			0
$433$	−20821.9	−	15128.0i	−0.111057	−	0.0806874i	0.530871	−	0.847453i	$-0.321865\pi$
$433$	−20821.9	−	15128.0i	−0.111057	−	0.0806874i	−0.641927	+	0.766765i	$0.721865\pi$
$434$	37747.7	+	116175.i	0.200406	+	0.616787i
$435$		0			0
$436$	3224.59	−	4438.27i	0.0169630	−	0.0233475i
$437$	70571.8	+	97133.7i	0.369546	+	0.508636i
$438$		0			0
$439$		−	123861.i		−	0.642693i	−0.946962	−	0.321347i	$-0.895865\pi$
$439$		−	123861.i		−	0.642693i	0.946962	−	0.321347i	$-0.104135\pi$
$440$	47701.7	+	74786.5i	0.246393	+	0.386294i
$441$		0			0
$442$	−35256.4	−	11455.5i	−0.180465	−	0.0586366i
$443$	−59932.0	+	43543.2i	−0.305388	+	0.221877i	−0.729915	−	0.683538i	$-0.760440\pi$
$443$	−59932.0	+	43543.2i	−0.305388	+	0.221877i	0.424527	+	0.905415i	$0.360440\pi$
$444$		0			0
$445$	60398.9	+	185889.i	0.305006	+	0.938713i
$446$	82601.5	−	26838.9i	0.415258	−	0.134926i
$447$		0			0
$448$	25856.4	+	35588.3i	0.128828	+	0.177317i
$449$	−71324.2	+	219513.i	−0.353789	+	1.08885i	0.602920	+	0.797802i	$0.294004\pi$
$449$	−71324.2	+	219513.i	−0.353789	+	1.08885i	−0.956708	+	0.291048i	$0.905996\pi$
$450$		0			0
$451$	−189649.	+	49157.2i	−0.932391	+	0.241676i
$452$	45821.4			0.224281
$453$		0			0
$454$	21142.8	−	15361.2i	0.102577	−	0.0745268i
$455$	231952.	+	168523.i	1.12040	+	0.814021i
$456$		0			0
$457$	120027.	−	38999.1i	0.574706	−	0.186733i	−0.00722142	−	0.999974i	$-0.502299\pi$
$457$	120027.	−	38999.1i	0.574706	−	0.186733i	0.581928	+	0.813241i	$0.302299\pi$
$458$	−127765.	+	175854.i	−0.609090	+	0.838341i
$459$		0			0
$460$	−35755.8	+	110045.i	−0.168978	+	0.520062i
$461$		−	65227.4i		−	0.306922i	−0.988155	−	0.153461i	$-0.950958\pi$
$461$		−	65227.4i		−	0.306922i	0.988155	−	0.153461i	$-0.0490420\pi$
$462$		0			0
$463$	308377.			1.43853			0.719267	−	0.694733i	$-0.244478\pi$
$463$	308377.			1.43853			0.719267	+	0.694733i	$0.244478\pi$
$464$	−66195.3	−	21508.1i	−0.307462	−	0.0999003i
$465$		0			0
$466$	25708.0	+	18678.0i	0.118385	+	0.0860119i
$467$	115280.	+	354796.i	0.528592	+	1.62684i	0.757102	+	0.653297i	$0.226615\pi$
$467$	115280.	+	354796.i	0.528592	+	1.62684i	−0.228510	+	0.973542i	$0.573385\pi$
$468$		0			0
$469$	−108448.	+	149265.i	−0.493031	+	0.678599i
$470$	177468.	+	244264.i	0.803386	+	1.10577i
$471$		0			0
$472$			36477.8i			0.163736i
$473$	−162351.	−	63849.5i	−0.725661	−	0.285388i
$474$		0			0
$475$	−108621.	−	35293.0i	−0.481422	−	0.156423i
$476$	−70758.3	+	51408.9i	−0.312294	+	0.226895i
$477$		0			0
$478$	24203.8	+	74491.7i	0.105932	+	0.326026i
$479$	243681.	−	79176.8i	1.06207	−	0.345086i	0.274673	−	0.961538i	$-0.411431\pi$
$479$	243681.	−	79176.8i	1.06207	−	0.345086i	0.787392	+	0.616452i	$0.211431\pi$
$480$		0			0
$481$	117395.	+	161581.i	0.507412	+	0.698393i
$482$	34280.8	−	105505.i	0.147556	−	0.454131i
$483$		0			0
$484$	−22474.7	−	114952.i	−0.0959408	−	0.490709i
$485$	444645.			1.89030
$486$		0			0
$487$	−181763.	+	132058.i	−0.766385	+	0.556811i	−0.900862	−	0.434105i	$-0.857065\pi$
$487$	−181763.	+	132058.i	−0.766385	+	0.556811i	0.134477	+	0.990917i	$0.457065\pi$
$488$	−61031.8	−	44342.2i	−0.256281	−	0.186199i
$489$		0			0
$490$	434080.	−	141041.i	1.80791	−	0.587427i
$491$	−58960.8	+	81152.6i	−0.244568	+	0.336620i	−0.913600	−	0.406615i	$-0.866709\pi$
$491$	−58960.8	+	81152.6i	−0.244568	+	0.336620i	0.669031	+	0.743234i	$0.266709\pi$
$492$		0			0
$493$	42763.5	−	131612.i	0.175946	−	0.541506i
$494$			78350.9i			0.321063i
$495$		0			0
$496$	−32170.9			−0.130768
$497$	−276231.	−	89753.0i	−1.11831	−	0.363359i
$498$		0			0
$499$	−208468.	−	151461.i	−0.837217	−	0.608274i	0.0843746	−	0.996434i	$-0.473111\pi$
$499$	−208468.	−	151461.i	−0.837217	−	0.608274i	−0.921592	+	0.388160i	$0.873111\pi$
$500$	16045.8	+	49383.8i	0.0641831	+	0.197535i
$501$		0			0
$502$	137760.	−	189610.i	0.546657	−	0.752409i
$503$	−238719.	−	328568.i	−0.943518	−	1.29864i	−0.954347	−	0.298700i	$-0.903447\pi$
$503$	−238719.	−	328568.i	−0.943518	−	1.29864i	0.0108292	−	0.999941i	$-0.496553\pi$
$504$		0			0
$505$		−	311499.i		−	1.22145i
$506$	97118.6	−	117945.i	0.379316	−	0.460660i
$507$		0			0
$508$	−236463.	−	76831.6i	−0.916297	−	0.297723i
$509$	263060.	−	191124.i	1.01536	−	0.737700i	0.0500314	−	0.998748i	$-0.484068\pi$
$509$	263060.	−	191124.i	1.01536	−	0.737700i	0.965326	+	0.261047i	$0.0840679\pi$
$510$		0			0
$511$	200676.	+	617616.i	0.768516	+	2.36525i
$512$	−11018.2	+	3580.04i	−0.0420312	+	0.0136568i
$513$		0			0
$514$	−9823.87	−	13521.4i	−0.0371840	−	0.0511794i
$515$	11059.5	−	34037.7i	0.0416986	−	0.128335i
$516$		0			0
$517$	−100031.	−	385920.i	−0.374242	−	1.44383i
$518$	471217.			1.75615
$519$		0			0
$520$	−61087.6	+	44382.7i	−0.225916	+	0.164137i
$521$	322750.	+	234492.i	1.18903	+	0.863878i	0.993161	−	0.116753i	$-0.0372486\pi$
$521$	322750.	+	234492.i	1.18903	+	0.863878i	0.195865	+	0.980631i	$0.437249\pi$
$522$		0			0
$523$	295038.	−	95863.6i	1.07863	−	0.350470i	0.284790	−	0.958590i	$-0.408076\pi$
$523$	295038.	−	95863.6i	1.07863	−	0.350470i	0.793845	+	0.608120i	$0.208076\pi$
$524$	41050.7	−	56501.5i	0.149506	−	0.205777i
$525$		0			0
$526$	−94352.8	+	290388.i	−0.341023	+	1.04956i
$527$		−	63963.8i		−	0.230310i
$528$		0			0
$529$	−80545.0			−0.287824
$530$	−255708.	−	83084.4i	−0.910315	−	0.295779i
$531$		0			0
$532$	149551.	+	108655.i	0.528405	+	0.383909i
$533$	−51535.2	−	158609.i	−0.181405	−	0.558307i
$534$		0			0
$535$	183944.	−	253177.i	0.642654	−	0.884538i
$536$	−28561.2	−	39311.1i	−0.0994137	−	0.136831i
$537$		0			0
$538$			44172.8i			0.152613i
$539$	−601565.	−	36463.4i	−2.07064	−	0.125510i
$540$		0			0
$541$	−356881.	−	115958.i	−1.21935	−	0.396191i	−0.372505	−	0.928030i	$-0.621501\pi$
$541$	−356881.	−	115958.i	−1.21935	−	0.396191i	−0.846845	+	0.531839i	$0.821501\pi$
$542$	−78392.9	+	56955.8i	−0.266857	+	0.193883i
$543$		0			0
$544$	−7117.99	−	21906.9i	−0.0240525	−	0.0740259i
$545$	21129.9	−	6865.52i	0.0711384	−	0.0231143i
$546$		0			0
$547$	−129542.	−	178299.i	−0.432947	−	0.595901i	0.535679	−	0.844422i	$-0.320056\pi$
$547$	−129542.	−	178299.i	−0.432947	−	0.595901i	−0.968627	+	0.248521i	$0.920056\pi$
$548$	65283.3	−	200921.i	0.217391	−	0.669060i
$549$		0			0
$550$	−8793.30	+	145070.i	−0.0290688	+	0.479570i
$551$	−292485.			−0.963386
$552$		0			0
$553$	−449886.	+	326862.i	−1.47114	+	1.06884i
$554$	165056.	+	119920.i	0.537789	+	0.390727i
$555$		0			0
$556$	134949.	−	43847.5i	0.436536	−	0.141839i
$557$	−252579.	+	347646.i	−0.814118	+	1.12054i	0.176557	+	0.984290i	$0.443504\pi$
$557$	−252579.	+	347646.i	−0.814118	+	1.12054i	−0.990675	+	0.136247i	$0.956496\pi$
$558$		0			0
$559$	45889.9	−	141235.i	0.146857	−	0.451979i
$560$			178149.i			0.568078i
$561$		0			0
$562$	−287642.			−0.910710
$563$	438495.	+	142476.i	1.38340	+	0.449494i	0.903786	−	0.427984i	$-0.140776\pi$
$563$	438495.	+	142476.i	1.38340	+	0.449494i	0.479615	+	0.877479i	$0.340776\pi$
$564$		0			0
$565$	150128.	+	109074.i	0.470288	+	0.341685i
$566$	−2666.69	−	8207.23i	−0.00832414	−	0.0256191i
$567$		0			0
$568$	44961.5	−	61884.2i	0.139362	−	0.191815i
$569$	98286.5	+	135280.i	0.303577	+	0.417838i	0.933365	−	0.358929i	$-0.116858\pi$
$569$	98286.5	+	135280.i	0.303577	+	0.417838i	−0.629788	+	0.776767i	$0.716858\pi$
$570$		0			0
$571$		−	317894.i		−	0.975012i	−0.873119	−	0.487506i	$-0.837907\pi$
$571$		−	317894.i		−	0.975012i	0.873119	−	0.487506i	$-0.162093\pi$
$572$	96514.2	−	25016.5i	0.294985	−	0.0764602i
$573$		0			0
$574$	−374211.	−	121588.i	−1.13578	−	0.369036i
$575$	−153374.	+	111432.i	−0.463890	+	0.337036i
$576$		0			0
$577$	93148.0	+	286680.i	0.279783	+	0.861084i	0.987914	+	0.155003i	$0.0495388\pi$
$577$	93148.0	+	286680.i	0.279783	+	0.861084i	−0.708131	+	0.706081i	$0.750461\pi$
$578$	−181115.	+	58847.7i	−0.542123	+	0.176146i
$579$		0			0
$580$	−165681.	−	228041.i	−0.492513	−	0.677886i
$581$	−107767.	+	331671.i	−0.319251	+	0.982553i
$582$		0			0
$583$	274066.	+	225671.i	0.806339	+	0.663955i
$584$	−171028.			−0.501467
$585$		0			0
$586$	−26491.3	+	19247.1i	−0.0771452	+	0.0560492i
$587$	−371096.	−	269617.i	−1.07699	−	0.782477i	−0.0998318	−	0.995004i	$-0.531830\pi$
$587$	−371096.	−	269617.i	−1.07699	−	0.782477i	−0.977155	+	0.212528i	$0.931830\pi$
$588$		0			0
$589$	−128574.	+	41776.2i	−0.370615	+	0.120420i
$590$	−86832.3	+	119514.i	−0.249447	+	0.343334i
$591$		0			0
$592$	−38349.4	+	118027.i	−0.109425	+	0.336775i
$593$		−	32457.6i		−	0.0923011i	−0.998934	−	0.0461506i	$-0.985305\pi$
$593$		−	32457.6i		−	0.0923011i	0.998934	−	0.0461506i	$-0.0146954\pi$
$594$		0			0
$595$	−354205.			−1.00051
$596$	−143806.	−	46725.2i	−0.404840	−	0.131540i
$597$		0			0
$598$	105217.	+	76445.0i	0.294229	+	0.213770i
$599$	213563.	+	657279.i	0.595213	+	1.83188i	0.553664	+	0.832740i	$0.313229\pi$
$599$	213563.	+	657279.i	0.595213	+	1.83188i	0.0415485	+	0.999136i	$0.486771\pi$
$600$		0			0
$601$	−50232.0	+	69138.5i	−0.139070	+	0.191413i	−0.872871	−	0.487951i	$-0.837744\pi$
$601$	−50232.0	+	69138.5i	−0.139070	+	0.191413i	0.733801	+	0.679364i	$0.237744\pi$
$602$	−205941.	−	283453.i	−0.568263	−	0.782147i
$603$		0			0
$604$		−	3595.60i		−	0.00985592i
$605$	199998.	−	430123.i	0.546404	−	1.17512i
$606$		0			0
$607$	126369.	+	41059.7i	0.342975	+	0.111439i	0.475439	−	0.879748i	$-0.342289\pi$
$607$	126369.	+	41059.7i	0.342975	+	0.111439i	−0.132465	+	0.991188i	$0.542289\pi$
$608$	−39386.3	+	28615.9i	−0.106546	+	0.0774104i
$609$		0			0
$610$	−94409.5	−	290562.i	−0.253721	−	0.780872i
$611$	322756.	−	104870.i	0.864553	−	0.280910i
$612$		0			0
$613$	387238.	+	532987.i	1.03052	+	1.41839i	0.904556	+	0.426355i	$0.140203\pi$
$613$	387238.	+	532987.i	1.03052	+	1.41839i	0.125965	+	0.992035i	$0.459797\pi$
$614$	−23376.5	+	71945.6i	−0.0620074	+	0.190839i
$615$		0			0
$616$	86093.9	−	218913.i	0.226888	−	0.576912i
$617$	−116511.			−0.306053			−0.153026	−	0.988222i	$-0.548902\pi$
$617$	−116511.			−0.306053			−0.153026	+	0.988222i	$0.548902\pi$
$618$		0			0
$619$	102297.	−	74322.9i	0.266981	−	0.193973i	−0.446238	−	0.894914i	$-0.647237\pi$
$619$	102297.	−	74322.9i	0.266981	−	0.193973i	0.713219	+	0.700941i	$0.247237\pi$
$620$	−105404.	−	76580.3i	−0.274203	−	0.199220i
$621$		0			0
$622$	−106963.	+	34754.4i	−0.276473	+	0.0898315i
$623$	304663.	−	419333.i	0.784953	−	1.08039i
$624$		0			0
$625$	−147000.	+	452418.i	−0.376319	+	1.15819i
$626$		−	241646.i		−	0.616638i
$627$		0			0
$628$	285707.			0.724439
$629$	−234668.	−	76248.1i	−0.593133	−	0.192720i
$630$		0			0
$631$	387143.	+	281276.i	0.972328	+	0.706437i	0.955981	−	0.293429i	$-0.0947965\pi$
$631$	387143.	+	281276.i	0.972328	+	0.706437i	0.0163467	+	0.999866i	$0.494796\pi$
$632$	−45256.7	−	139286.i	−0.113305	−	0.348717i
$633$		0			0
$634$	−40808.1	+	56167.5i	−0.101524	+	0.139735i
$635$	−591849.	−	814610.i	−1.46779	−	2.02024i
$636$		0			0
$637$		−	513014.i		−	1.26430i
$638$	93387.1	+	360289.i	0.229428	+	0.885135i
$639$		0			0
$640$	−44621.7	−	14498.5i	−0.108940	−	0.0353966i
$641$	562038.	−	408345.i	1.36789	−	0.993827i	0.369986	−	0.929037i	$-0.379362\pi$
$641$	562038.	−	408345.i	1.36789	−	0.993827i	0.997899	−	0.0647894i	$-0.0206376\pi$
$642$		0			0
$643$	74090.8	+	228028.i	0.179202	+	0.551526i	0.999800	−	0.0199785i	$-0.00635978\pi$
$643$	74090.8	+	228028.i	0.179202	+	0.551526i	−0.820599	+	0.571505i	$0.806360\pi$
$644$	291827.	−	94820.2i	0.703644	−	0.228628i
$645$		0			0
$646$	−56895.4	−	78309.8i	−0.136336	−	0.187651i
$647$	126061.	−	387977.i	0.301143	−	0.926824i	−0.679945	−	0.733263i	$-0.737996\pi$
$647$	126061.	−	387977.i	0.301143	−	0.926824i	0.981088	−	0.193561i	$-0.0620036\pi$
$648$		0			0
$649$	164459.	−	104898.i	0.390451	−	0.249045i
$650$	−123716.			−0.292818
$651$		0			0
$652$	−152923.	+	111105.i	−0.359731	+	0.261360i
$653$	−293149.	−	212985.i	−0.687483	−	0.499486i	0.188349	−	0.982102i	$-0.439686\pi$
$653$	−293149.	−	212985.i	−0.687483	−	0.499486i	−0.875832	+	0.482617i	$0.839686\pi$
$654$		0			0
$655$	268994.	−	87401.6i	0.626990	−	0.203721i
$656$	60909.4	−	83834.6i	0.141539	−	0.194812i
$657$		0			0
$658$	247422.	−	761487.i	0.571461	−	1.75878i
$659$			56157.5i			0.129311i	0.997908	+	0.0646557i	$0.0205949\pi$
$659$			56157.5i			0.129311i	−0.997908	+	0.0646557i	$0.979405\pi$
$660$		0			0
$661$	−43617.9			−0.0998301			−0.0499150	−	0.998753i	$-0.515895\pi$
$661$	−43617.9			−0.0998301			−0.0499150	+	0.998753i	$0.515895\pi$
$662$	−237770.	−	77256.3i	−0.542553	−	0.176286i
$663$		0			0
$664$	−74304.5	−	53985.4i	−0.168531	−	0.122445i
$665$	231339.	+	711989.i	0.523126	+	1.61002i
$666$		0			0
$667$	−285370.	+	392778.i	−0.641441	+	0.882868i
$668$	3050.12	+	4198.12i	0.00683539	+	0.00940811i
$669$		0			0
$670$		−	196785.i		−	0.438372i
$671$	−24407.7	+	402673.i	−0.0542103	+	0.894350i
$672$		0			0
$673$	2428.77	+	789.155i	0.00536237	+	0.00174234i	0.311697	−	0.950182i	$-0.399103\pi$
$673$	2428.77	+	789.155i	0.00536237	+	0.00174234i	−0.306335	+	0.951924i	$0.599103\pi$
$674$	−232690.	+	169059.i	−0.512222	+	0.372151i
$675$		0			0
$676$	−44380.0	−	136587.i	−0.0971166	−	0.298894i
$677$	−460823.	+	149731.i	−1.00544	+	0.326688i	−0.765038	−	0.643985i	$-0.777280\pi$
$677$	−460823.	+	149731.i	−1.00544	+	0.326688i	−0.240404	+	0.970673i	$0.577280\pi$
$678$		0			0
$679$	−693086.	−	953951.i	−1.50331	−	2.06912i
$680$	28826.5	−	88718.9i	0.0623411	−	0.191866i
$681$		0			0
$682$	92513.0	+	145041.i	0.198900	+	0.311834i
$683$	498694.			1.06904			0.534519	−	0.845157i	$-0.320493\pi$
$683$	498694.			1.06904			0.534519	+	0.845157i	$0.320493\pi$
$684$		0			0
$685$	692169.	−	502891.i	1.47513	−	1.07175i
$686$	−507175.	−	368484.i	−1.07773	−	0.783016i
$687$		0			0
$688$	87757.8	−	28514.2i	0.185400	−	0.0602400i
$689$	−177632.	+	244490.i	−0.374183	+	0.515018i
$690$		0			0
$691$	44449.9	−	136803.i	0.0930924	−	0.286509i	−0.893659	−	0.448746i	$-0.851871\pi$
$691$	44449.9	−	136803.i	0.0930924	−	0.286509i	0.986752	+	0.162237i	$0.0518709\pi$
$692$			184253.i			0.384771i
$693$		0			0
$694$	−104327.			−0.216609
$695$	546517.	+	177574.i	1.13145	+	0.367630i
$696$		0			0
$697$	166684.	+	121103.i	0.343106	+	0.249281i
$698$	−90404.2	−	278236.i	−0.185557	−	0.571087i
$699$		0			0
$700$	−171566.	+	236140.i	−0.350135	+	0.481919i
$701$	−271424.	−	373582.i	−0.552346	−	0.760240i	0.437982	−	0.898984i	$-0.355693\pi$
$701$	−271424.	−	373582.i	−0.552346	−	0.760240i	−0.990328	+	0.138744i	$0.955693\pi$
$702$		0			0
$703$			521506.i			1.05523i
$704$	47825.2	+	39380.2i	0.0964965	+	0.0794571i
$705$		0			0
$706$	−135679.	−	44084.8i	−0.272210	−	0.0884464i
$707$	−668297.	+	485546.i	−1.33700	+	0.971385i
$708$		0			0
$709$	88470.5	+	272284.i	0.175997	+	0.541664i	0.999678	−	0.0253903i	$-0.00808286\pi$
$709$	88470.5	+	272284.i	0.175997	+	0.541664i	−0.823680	+	0.567055i	$0.808083\pi$
$710$	294621.	−	95728.1i	0.584449	−	0.189899i
$711$		0			0
$712$	80237.1	+	110437.i	0.158276	+	0.217848i
$713$	−69345.0	+	213422.i	−0.136407	+	0.419817i
$714$		0			0
$715$	375766.	+	147781.i	0.735030	+	0.289072i
$716$	51369.5			0.100203
$717$		0			0
$718$	−199637.	+	145044.i	−0.387250	+	0.281354i
$719$	58393.7	+	42425.5i	0.112956	+	0.0820672i	0.642829	−	0.766010i	$-0.277761\pi$
$719$	58393.7	+	42425.5i	0.112956	+	0.0820672i	−0.529873	+	0.848077i	$0.677761\pi$
$720$		0			0
$721$	−90263.9	+	29328.5i	−0.173638	+	0.0564183i
$722$	96408.4	−	132695.i	0.184944	−	0.254554i
$723$		0			0
$724$	−106080.	+	326480.i	−0.202374	+	0.622844i
$725$		−	461832.i		−	0.878634i
$726$		0			0
$727$	−620396.			−1.17382			−0.586908	−	0.809653i	$-0.699655\pi$
$727$	−620396.			−1.17382			−0.586908	+	0.809653i	$0.699655\pi$
$728$	190439.	+	61877.5i	0.359330	+	0.116753i
$729$		0			0
$730$	−560351.	−	407119.i	−1.05151	−	0.763969i
$731$	56693.3	+	174484.i	0.106096	+	0.326529i
$732$		0			0
$733$	28232.2	−	38858.3i	0.0525456	−	0.0723229i	−0.781936	−	0.623359i	$-0.785767\pi$
$733$	28232.2	−	38858.3i	0.0525456	−	0.0723229i	0.834481	+	0.551036i	$0.185767\pi$
$734$	86034.9	+	118417.i	0.159692	+	0.219797i
$735$		0			0
$736$			80811.7i			0.149183i
$737$	−95099.9	+	241813.i	−0.175083	+	0.445188i
$738$		0			0
$739$	41233.3	+	13397.5i	0.0755021	+	0.0245321i	0.346525	−	0.938041i	$-0.387362\pi$
$739$	41233.3	+	13397.5i	0.0755021	+	0.0245321i	−0.271022	+	0.962573i	$0.587362\pi$
$740$	−406601.	+	295413.i	−0.742515	+	0.539469i
$741$		0			0
$742$	220330.	+	678107.i	0.400190	+	1.23166i
$743$	−311459.	+	101199.i	−0.564187	+	0.183315i	−0.577204	−	0.816600i	$-0.695856\pi$
$743$	−311459.	+	101199.i	−0.564187	+	0.183315i	0.0130172	+	0.999915i	$0.495856\pi$
$744$		0			0
$745$	−359934.	−	495406.i	−0.648500	−	0.892584i
$746$	157355.	−	484290.i	0.282751	−	0.870217i
$747$		0			0
$748$	−78297.5	+	95088.3i	−0.139941	+	0.169951i
$749$	−829891.			−1.47930
$750$		0			0
$751$	157605.	−	114507.i	0.279441	−	0.203026i	−0.439232	−	0.898374i	$-0.644749\pi$
$751$	157605.	−	114507.i	0.279441	−	0.203026i	0.718674	+	0.695347i	$0.244749\pi$
$752$	170596.	+	123945.i	0.301671	+	0.219177i
$753$		0			0
$754$	−301320.	+	97904.7i	−0.530011	+	0.172211i
$755$	8559.03	−	11780.5i	0.0150152	−	0.0206666i
$756$		0			0
$757$	118949.	−	366087.i	0.207572	−	0.638841i	−0.792026	−	0.610487i	$-0.790974\pi$
$757$	118949.	−	366087.i	0.207572	−	0.638841i	0.999598	−	0.0283533i	$-0.00902635\pi$
$758$			524698.i			0.913210i
$759$		0			0
$760$	−197162.			−0.341347
$761$	263860.	+	85733.3i	0.455622	+	0.148040i	0.527832	−	0.849349i	$-0.323005\pi$
$761$	263860.	+	85733.3i	0.455622	+	0.148040i	−0.0722100	+	0.997389i	$0.523005\pi$
$762$		0			0
$763$	−47665.4	−	34630.9i	−0.0818755	−	0.0594861i
$764$	−63106.8	−	194223.i	−0.108116	−	0.332747i
$765$		0			0
$766$	10520.5	−	14480.3i	0.0179300	−	0.0246785i
$767$	97599.5	+	134334.i	0.165904	+	0.228347i
$768$		0			0
$769$			927410.i			1.56826i	0.620595	+	0.784131i	$0.286891\pi$
$769$			927410.i			1.56826i	−0.620595	+	0.784131i	$0.713109\pi$
$770$	803179.	−	512299.i	1.35466	−	0.864056i
$771$		0			0
$772$	320938.	+	104279.i	0.538500	+	0.174969i
$773$	82488.3	−	59931.2i	0.138049	−	0.100298i	−0.516618	−	0.856216i	$-0.672809\pi$
$773$	82488.3	−	59931.2i	0.138049	−	0.100298i	0.654666	+	0.755918i	$0.272809\pi$
$774$		0			0
$775$	−65964.4	−	203017.i	−0.109826	−	0.338010i
$776$	295345.	−	95963.6i	0.490464	−	0.159361i
$777$		0			0
$778$	183222.	+	252183.i	0.302704	+	0.416636i
$779$	134565.	−	414148.i	0.221746	−	0.682465i
$780$		0			0
$781$	−408297.	−	24748.6i	−0.669383	−	0.0405741i
$782$	−160674.			−0.262743
$783$		0			0
$784$	257888.	−	187367.i	0.419565	−	0.304832i
$785$	936081.	+	680103.i	1.51906	+	1.10366i
$786$		0			0
$787$	−746565.	+	242574.i	−1.20536	+	0.391646i	−0.841732	−	0.539896i	$-0.818463\pi$
$787$	−746565.	+	242574.i	−1.20536	+	0.391646i	−0.363632	+	0.931543i	$0.618463\pi$
$788$	−176794.	+	243336.i	−0.284717	+	0.391880i
$789$		0			0
$790$	183281.	−	564082.i	0.293673	−	0.903832i
$791$		−	492105.i		−	0.786512i
$792$		0			0
$793$	−343399.			−0.546076
$794$	−553494.	−	179841.i	−0.877954	−	0.285264i
$795$		0			0
$796$	−242383.	−	176102.i	−0.382540	−	0.277931i
$797$	−146626.	−	451268.i	−0.230831	−	0.710424i	−0.997647	−	0.0685576i	$-0.978160\pi$
$797$	−146626.	−	451268.i	−0.230831	−	0.710424i	0.766816	−	0.641867i	$-0.221840\pi$
$798$		0			0
$799$	−246434.	+	339187.i	−0.386018	+	0.531308i
$800$	−45184.2	−	62190.8i	−0.0706004	−	0.0971731i
$801$		0			0
$802$		−	372591.i		−	0.579274i
$803$	491821.	+	771074.i	0.762739	+	1.19582i
$804$		0			0
$805$	1.18184e6	+	384004.i	1.82376	+	0.592576i
$806$	−118474.	+	86076.2i	−0.182369	+	0.132499i
$807$		0			0
$808$	−67227.9	−	206906.i	−0.102974	−	0.316921i
$809$	−325525.	+	105770.i	−0.497379	+	0.161608i	−0.546955	−	0.837162i	$-0.684213\pi$
$809$	−325525.	+	105770.i	−0.497379	+	0.161608i	0.0495756	+	0.998770i	$0.484213\pi$
$810$		0			0
$811$	267565.	+	368272.i	0.406807	+	0.559922i	0.962436	−	0.271509i	$-0.0875226\pi$
$811$	267565.	+	368272.i	0.406807	+	0.559922i	−0.555629	+	0.831430i	$0.687523\pi$
$812$	−230990.	+	710913.i	−0.350332	+	1.07821i
$813$		0			0
$814$	642402.	−	166511.i	0.969523	−	0.251301i
$815$	−765508.			−1.15248
$816$		0			0
$817$	313704.	−	227919.i	0.469976	−	0.341458i
$818$	181713.	+	132022.i	0.271569	+	0.197306i
$819$		0			0
$820$	399123.	−	129683.i	0.593580	−	0.192866i
$821$	233166.	−	320925.i	0.345923	−	0.476122i	−0.600237	−	0.799822i	$-0.704927\pi$
$821$	233166.	−	320925.i	0.345923	−	0.476122i	0.946160	+	0.323701i	$0.104927\pi$
$822$		0			0
$823$	300791.	−	925738.i	0.444083	−	1.36675i	−0.439402	−	0.898290i	$-0.644810\pi$
$823$	300791.	−	925738.i	0.444083	−	1.36675i	0.883486	−	0.468458i	$-0.155190\pi$
$824$		−	24995.6i		−	0.0368137i
$825$		0			0
$826$	391758.			0.574192
$827$	−136766.	−	44438.1i	−0.199972	−	0.0649748i	0.207319	−	0.978273i	$-0.433526\pi$
$827$	−136766.	−	44438.1i	−0.199972	−	0.0649748i	−0.407290	+	0.913299i	$0.633526\pi$
$828$		0			0
$829$	289762.	+	210524.i	0.421631	+	0.306333i	0.778294	−	0.627901i	$-0.216086\pi$
$829$	289762.	+	210524.i	0.421631	+	0.306333i	−0.356663	+	0.934233i	$0.616086\pi$
$830$	−114941.	−	353752.i	−0.166847	−	0.513502i
$831$		0			0
$832$	−30997.3	+	42664.2i	−0.0447793	+	0.0616335i
$833$	372531.	+	512745.i	0.536874	+	0.738944i
$834$		0			0
$835$			21015.1i			0.0301411i
$836$	242276.	+	95282.0i	0.346655	+	0.136332i
$837$		0			0
$838$	−756291.	−	245734.i	−1.07696	−	0.349927i
$839$	1.09425e6	−	795018.i	1.55451	−	1.12941i	0.614166	−	0.789177i	$-0.289493\pi$
$839$	1.09425e6	−	795018.i	1.55451	−	1.12941i	0.940340	−	0.340237i	$-0.110507\pi$
$840$		0			0
$841$	−146918.	−	452167.i	−0.207722	−	0.639304i
$842$	892043.	−	289842.i	1.25823	−	0.408825i
$843$		0			0
$844$	−156815.	−	215837.i	−0.220142	−	0.302999i
$845$	179730.	−	553153.i	0.251714	−	0.774698i
$846$		0			0
$847$	−1.23454e6	+	241370.i	−1.72083	+	0.336447i
$848$	−187779.			−0.261129
$849$		0			0
$850$	123651.	−	89837.4i	0.171143	−	0.124342i
$851$	700331.	+	508820.i	0.967040	+	0.702596i
$852$		0			0
$853$	691608.	−	224717.i	0.950521	−	0.308843i	0.207594	−	0.978215i	$-0.433437\pi$
$853$	691608.	−	224717.i	0.950521	−	0.308843i	0.742927	+	0.669372i	$0.233437\pi$
$854$	−476219.	+	655459.i	−0.652966	+	0.898731i
$855$		0			0
$856$	67539.7	−	207866.i	0.0921746	−	0.283684i
$857$		−	269066.i		−	0.366351i	−0.983080	−	0.183175i	$-0.941362\pi$
$857$		−	269066.i		−	0.366351i	0.983080	−	0.183175i	$-0.0586376\pi$
$858$		0			0
$859$	919865.			1.24663			0.623315	−	0.781971i	$-0.285785\pi$
$859$	919865.			1.24663			0.623315	+	0.781971i	$0.285785\pi$
$860$	355402.	+	115477.i	0.480533	+	0.156135i
$861$		0			0
$862$	285450.	+	207392.i	0.384163	+	0.279111i
$863$	89869.0	+	276588.i	0.120667	+	0.371374i	0.993087	−	0.117383i	$-0.0374504\pi$
$863$	89869.0	+	276588.i	0.120667	+	0.371374i	−0.872420	+	0.488757i	$0.837450\pi$
$864$		0			0
$865$	−438600.	+	603681.i	−0.586187	+	0.806817i
$866$	−42788.4	−	58893.2i	−0.0570546	−	0.0785289i
$867$		0			0
$868$			345504.i			0.458578i
$869$	−497822.	+	604579.i	−0.659226	+	0.800596i
$870$		0			0
$871$	−210361.	−	68350.3i	−0.277286	−	0.0900957i
$872$	12553.3	−	9120.53i	0.0165092	−	0.0119946i
$873$		0			0
$874$	104940.	+	322971.i	0.137378	+	0.422806i
$875$	530364.	−	172326.i	0.692720	−	0.225078i
$876$		0			0
$877$	6751.69	+	9292.90i	0.00877835	+	0.0120824i	0.813384	−	0.581728i	$-0.197623\pi$
$877$	6751.69	+	9292.90i	0.00877835	+	0.0120824i	−0.804605	+	0.593810i	$0.797623\pi$
$878$	108258.	−	333184.i	0.140434	−	0.432210i
$879$		0			0
$880$	62951.5	+	242868.i	0.0812907	+	0.313621i
$881$	742939.			0.957197			0.478599	−	0.878034i	$-0.341145\pi$
$881$	742939.			0.957197			0.478599	+	0.878034i	$0.341145\pi$
$882$		0			0
$883$	945222.	−	686744.i	1.21231	−	0.880792i	0.216868	−	0.976201i	$-0.430416\pi$
$883$	945222.	−	686744.i	1.21231	−	0.880792i	0.995438	+	0.0954091i	$0.0304159\pi$
$884$	−84826.9	−	61630.4i	−0.108550	−	0.0788661i
$885$		0			0
$886$	−199275.	+	64748.4i	−0.253855	+	0.0824824i
$887$	382008.	−	525789.i	0.485540	−	0.668289i	−0.494018	−	0.869452i	$-0.664472\pi$
$887$	382008.	−	525789.i	0.485540	−	0.668289i	0.979558	+	0.201163i	$0.0644722\pi$
$888$		0			0
$889$	−825143.	+	2.53953e6i	−1.04406	+	3.21329i
$890$			552830.i			0.697929i
$891$		0			0
$892$	245656.			0.308743
$893$	842755.	+	273828.i	1.05681	+	0.343379i
$894$		0			0
$895$	168305.	+	122281.i	0.210113	+	0.152656i
$896$	38448.3	+	118332.i	0.0478917	+	0.147396i
$897$		0			0
$898$	−383723.	+	528150.i	−0.475845	+	0.654944i
$899$	−321324.	−	442264.i	−0.397579	−	0.547221i
$900$		0			0
$901$		−	373351.i		−	0.459905i
$902$	−553120.	−	33527.0i	−0.679840	−	0.0412080i
$903$		0			0
$904$	123259.	+	40049.4i	0.150828	+	0.0490071i
$905$	−1.12472e6	+	817154.i	−1.37324	+	0.997715i
$906$		0			0
$907$	−68802.5	−	211752.i	−0.0836354	−	0.257403i	0.900490	−	0.434876i	$-0.143208\pi$
$907$	−68802.5	−	211752.i	−0.0836354	−	0.257403i	−0.984126	+	0.177473i	$0.943208\pi$
$908$	70300.3	−	22841.9i	0.0852679	−	0.0277052i
$909$		0			0
$910$	476654.	+	656058.i	0.575600	+	0.792245i
$911$	−376111.	+	1.15755e6i	−0.453189	+	1.39477i	0.420060	+	0.907496i	$0.362009\pi$
$911$	−376111.	+	1.15755e6i	−0.453189	+	1.39477i	−0.873249	+	0.487275i	$0.837991\pi$
$912$		0			0
$913$	−29715.7	+	490243.i	−0.0356488	+	0.588125i
$914$	356958.			0.427292
$915$		0			0
$916$	−497389.	+	361375.i	−0.592796	+	0.430692i
$917$	−606805.	−	440870.i	−0.721623	−	0.524290i
$918$		0			0
$919$	1.58795e6	−	515957.i	1.88021	−	0.610917i	0.893343	−	0.449375i	$-0.148353\pi$
$919$	1.58795e6	−	515957.i	1.88021	−	0.610917i	0.986866	−	0.161542i	$-0.0516469\pi$
$920$	−192366.	+	264769.i	−0.227275	+	0.312818i
$921$		0			0
$922$	57010.8	−	175461.i	0.0670650	−	0.206405i
$923$		−	348196.i		−	0.408714i
$924$		0			0
$925$	−823455.			−0.962402
$926$	829533.	+	269532.i	0.967412	+	0.314331i
$927$		0			0
$928$	−159266.	−	115714.i	−0.184938	−	0.134366i
$929$	95030.8	+	292475.i	0.110112	+	0.338888i	0.990896	−	0.134629i	$-0.0429842\pi$
$929$	95030.8	+	292475.i	0.110112	+	0.338888i	−0.880785	+	0.473517i	$0.842984\pi$
$930$		0			0
$931$	787364.	−	1.08371e6i	0.908398	−	1.25030i
$932$	52829.3	+	72713.3i	0.0608196	+	0.0837110i
$933$		0			0
$934$			1.05516e6i			1.20955i
$935$	−482881.	+	125163.i	−0.552354	+	0.143170i
$936$		0			0
$937$	−1.12048e6	−	364066.i	−1.27622	−	0.414668i	−0.408971	−	0.912547i	$-0.634112\pi$
$937$	−1.12048e6	−	364066.i	−1.27622	−	0.414668i	−0.867247	+	0.497879i	$0.834112\pi$
$938$	−422186.	+	306736.i	−0.479842	+	0.348626i
$939$		0			0
$940$	263894.	+	812181.i	0.298657	+	0.919173i
$941$	40929.6	−	13298.8i	0.0462230	−	0.0150187i	−0.285814	−	0.958285i	$-0.592264\pi$
$941$	40929.6	−	13298.8i	0.0462230	−	0.0150187i	0.332037	+	0.943266i	$0.392264\pi$
$942$		0			0
$943$	−424868.	−	584780.i	−0.477783	−	0.657611i
$944$	−31882.7	+	98124.9i	−0.0357776	+	0.110112i
$945$		0			0
$946$	−380918.	−	313655.i	−0.425646	−	0.350485i
$947$	137993.			0.153871			0.0769354	−	0.997036i	$-0.475486\pi$
$947$	137993.			0.153871			0.0769354	+	0.997036i	$0.475486\pi$
$948$		0			0
$949$	−629834.	+	457601.i	−0.699349	+	0.508107i
$950$	−261342.	−	189876.i	−0.289576	−	0.210389i
$951$		0			0
$952$	−235272.	+	76444.6i	−0.259595	+	0.0843477i
$953$	813768.	−	1.12006e6i	0.896014	−	1.23326i	−0.0757081	−	0.997130i	$-0.524122\pi$
$953$	813768.	−	1.12006e6i	0.896014	−	1.23326i	0.971722	−	0.236127i	$-0.0758783\pi$
$954$		0			0
$955$	255571.	−	786566.i	0.280223	−	0.862439i
$956$			221537.i			0.242399i
$957$		0			0
$958$	724704.			0.789641
$959$	−2.15782e6	−	701119.i	−2.34627	−	0.762350i
$960$		0			0
$961$	542723.	+	394312.i	0.587668	+	0.426966i
$962$	174566.	+	537259.i	0.188629	+	0.580542i
$963$		0			0
$964$	184430.	−	253847.i	0.198462	−	0.273160i
$965$	803281.	+	1.10562e6i	0.862607	+	1.18728i
$966$		0			0
$967$		−	1.79906e6i		−	1.92394i	−0.273150	−	0.961972i	$-0.588065\pi$
$967$		−	1.79906e6i		−	1.92394i	0.273150	−	0.961972i	$-0.411935\pi$
$968$	40014.5	−	328863.i	0.0427038	−	0.350965i
$969$		0			0
$970$	1.19609e6	+	388634.i	1.27122	+	0.413045i
$971$	1.07308e6	−	779641.i	1.13814	−	0.826907i	0.151280	−	0.988491i	$-0.451660\pi$
$971$	1.07308e6	−	779641.i	1.13814	−	0.826907i	0.986859	+	0.161584i	$0.0516604\pi$
$972$		0			0
$973$	−470906.	−	1.44930e6i	−0.497404	−	1.53085i
$974$	−604364.	+	196370.i	−0.637061	+	0.206994i
$975$		0			0
$976$	−125419.	−	172624.i	−0.131663	−	0.181218i
$977$	−422787.	+	1.30120e6i	−0.442927	+	1.36319i	0.441814	+	0.897107i	$0.354335\pi$
$977$	−422787.	+	1.30120e6i	−0.442927	+	1.36319i	−0.884741	+	0.466083i	$0.845665\pi$
$978$		0			0
$979$	267165.	−	679326.i	0.278750	−	0.708782i
$980$	1.29095e6			1.34418
$981$		0			0
$982$	−229534.	+	166766.i	−0.238026	+	0.172936i
$983$	−728116.	−	529007.i	−0.753518	−	0.547463i	0.143397	−	0.989665i	$-0.454197\pi$
$983$	−728116.	−	529007.i	−0.753518	−	0.547463i	−0.896915	+	0.442202i	$0.854197\pi$
$984$		0			0
$985$	−1.15848e6	+	376413.i	−1.19403	+	0.387965i
$986$	230067.	−	316660.i	0.236647	−	0.325716i
$987$		0			0
$988$	−68481.2	+	210763.i	−0.0701548	+	0.215914i
$989$		−	643648.i		−	0.658046i
$990$		0			0
$991$	846524.			0.861969			0.430985	−	0.902359i	$-0.358166\pi$
$991$	846524.			0.861969			0.430985	+	0.902359i	$0.358166\pi$
$992$	−86539.6	−	28118.4i	−0.0879411	−	0.0285738i
$993$		0			0
$994$	−664614.	−	482870.i	−0.672662	−	0.488717i
$995$	−374940.	−	1.15395e6i	−0.378718	−	1.16557i
$996$		0			0
$997$	816248.	−	1.12347e6i	0.821167	−	1.13024i	−0.168336	−	0.985730i	$-0.553839\pi$
$997$	816248.	−	1.12347e6i	0.821167	−	1.13024i	0.989503	−	0.144510i	$-0.0461607\pi$
$998$	−428396.	−	589636.i	−0.430115	−	0.592002i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.5.j.a.145.4		16
3.2	odd	2		22.5.d.a.13.2	✓	16
11.6	odd	10	inner	198.5.j.a.127.4		16
12.11	even	2		176.5.n.c.145.2		16
33.17	even	10		22.5.d.a.17.2	yes	16
33.26	odd	10		242.5.b.e.241.3		16
33.29	even	10		242.5.b.e.241.11		16
132.83	odd	10		176.5.n.c.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.13.2	✓	16	3.2	odd	2
22.5.d.a.17.2	yes	16	33.17	even	10
176.5.n.c.17.2		16	132.83	odd	10
176.5.n.c.145.2		16	12.11	even	2
198.5.j.a.127.4		16	11.6	odd	10	inner
198.5.j.a.145.4		16	1.1	even	1	trivial
242.5.b.e.241.3		16	33.26	odd	10
242.5.b.e.241.11		16	33.29	even	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)

\(f(q)\)	\(=\)	\(q+(2.68999 + 0.874032i) q^{2} +(6.47214 + 4.70228i) q^{4} +(10.0117 + 30.8128i) q^{5} +(50.5008 - 69.5083i) q^{7} +(13.3001 + 18.3060i) q^{8} +O(q^{10})\)	\(q+(2.68999 + 0.874032i) q^{2} +(6.47214 + 4.70228i) q^{4} +(10.0117 + 30.8128i) q^{5} +(50.5008 - 69.5083i) q^{7} +(13.3001 + 18.3060i) q^{8} +91.6368i q^{10} +(44.2851 - 112.605i) q^{11} +(97.9585 + 31.8286i) q^{13} +(196.599 - 142.838i) q^{14} +(19.7771 + 60.8676i) q^{16} +(-121.020 + 39.3217i) q^{17} +(158.082 + 217.581i) q^{19} +(-80.0935 + 246.502i) q^{20} +(217.547 - 264.199i) q^{22} +446.426 q^{23} +(-343.559 + 249.610i) q^{25} +(235.689 + 171.238i) q^{26} +(653.696 - 212.399i) q^{28} +(-639.233 + 879.829i) q^{29} +(-155.334 + 478.068i) q^{31} +181.019i q^{32} -359.911 q^{34} +(2647.34 + 860.174i) q^{35} +(1568.75 + 1139.76i) q^{37} +(235.066 + 723.460i) q^{38} +(-430.902 + 593.086i) q^{40} +(-951.709 - 1309.92i) q^{41} -1441.78i q^{43} +(816.119 - 520.552i) q^{44} +(1200.88 + 390.191i) q^{46} +(2665.57 - 1936.65i) q^{47} +(-1539.13 - 4736.96i) q^{49} +(-1142.34 + 371.168i) q^{50} +(484.333 + 666.628i) q^{52} +(-906.672 + 2790.45i) q^{53} +(3913.04 + 237.186i) q^{55} +1944.08 q^{56} +(-2488.53 + 1808.02i) q^{58} +(1304.22 + 947.571i) q^{59} +(-3170.81 + 1030.26i) q^{61} +(-835.694 + 1150.23i) q^{62} +(-158.217 + 486.941i) q^{64} +3337.03i q^{65} -2147.45 q^{67} +(-968.159 - 314.574i) q^{68} +(6369.52 + 4627.73i) q^{70} +(-1044.65 - 3215.10i) q^{71} +(-4442.75 + 6114.92i) q^{73} +(3223.74 + 4437.10i) q^{74} +2151.56i q^{76} +(-5590.54 - 8764.81i) q^{77} +(-6155.63 - 2000.08i) q^{79} +(-1677.50 + 1218.77i) q^{80} +(-1415.18 - 4355.49i) q^{82} +(-3860.37 + 1254.31i) q^{83} +(-2423.22 - 3335.28i) q^{85} +(1260.16 - 3878.38i) q^{86} +(2650.33 - 686.968i) q^{88} +6032.84 q^{89} +(7159.34 - 5201.56i) q^{91} +(2889.33 + 2099.22i) q^{92} +(8863.05 - 2879.78i) q^{94} +(-5121.61 + 7049.29i) q^{95} +(4241.03 - 13052.6i) q^{97} -14087.7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 30 q^{5} + 150 q^{7}+O(q^{10}) \) 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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