LMFDB - Embedded newform 324.3.j.a.307.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.23
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07434 + 1.68695i) q^{2} +(-1.69158 + 3.62471i) q^{4} +(0.755508 - 4.28470i) q^{5} +(6.44162 + 7.67682i) q^{7} +(-7.93204 + 1.04057i) q^{8} +O(q^{10})$	\(q+(1.07434 + 1.68695i) q^{2} +(-1.69158 + 3.62471i) q^{4} +(0.755508 - 4.28470i) q^{5} +(6.44162 + 7.67682i) q^{7} +(-7.93204 + 1.04057i) q^{8} +(8.03973 - 3.32873i) q^{10} +(16.5915 - 2.92553i) q^{11} +(7.70282 - 2.80360i) q^{13} +(-6.02990 + 19.1142i) q^{14} +(-10.2771 - 12.2630i) q^{16} +(-13.2638 + 22.9735i) q^{17} +(-10.2637 + 5.92574i) q^{19} +(14.2528 + 9.98641i) q^{20} +(22.7602 + 24.8460i) q^{22} +(-14.3578 + 17.1110i) q^{23} +(5.70448 + 2.07626i) q^{25} +(13.0050 + 9.98223i) q^{26} +(-38.7228 + 10.3631i) q^{28} +(29.1256 + 10.6009i) q^{29} +(-12.9259 + 15.4045i) q^{31} +(9.64589 - 30.5116i) q^{32} +(-53.0049 + 2.30613i) q^{34} +(37.7596 - 21.8005i) q^{35} +(20.1962 - 34.9808i) q^{37} +(-21.0231 - 10.9480i) q^{38} +(-1.53417 + 34.7725i) q^{40} +(34.1160 - 12.4172i) q^{41} +(-25.3466 + 4.46929i) q^{43} +(-17.4617 + 65.0882i) q^{44} +(-44.2905 - 5.83783i) q^{46} +(-12.9992 - 15.4919i) q^{47} +(-8.93040 + 50.6468i) q^{49} +(2.62602 + 11.8538i) q^{50} +(-2.86770 + 32.6630i) q^{52} -46.7045 q^{53} -73.2998i q^{55} +(-59.0835 - 54.1899i) q^{56} +(13.4078 + 60.5223i) q^{58} +(36.4280 + 6.42325i) q^{59} +(48.7491 - 40.9054i) q^{61} +(-39.8734 - 5.25563i) q^{62} +(61.8344 - 16.5078i) q^{64} +(-6.19303 - 35.1224i) q^{65} +(-25.9527 - 71.3043i) q^{67} +(-60.8357 - 86.9390i) q^{68} +(77.3429 + 40.2772i) q^{70} +(-17.4692 - 10.0858i) q^{71} +(-50.2648 - 87.0613i) q^{73} +(80.7083 - 3.51145i) q^{74} +(-4.11727 - 47.2268i) q^{76} +(129.335 + 108.525i) q^{77} +(29.7876 - 81.8406i) q^{79} +(-60.3076 + 34.7695i) q^{80} +(57.5993 + 44.2115i) q^{82} +(25.2237 - 69.3017i) q^{83} +(88.4137 + 74.1879i) q^{85} +(-34.7704 - 37.9569i) q^{86} +(-128.560 + 40.4701i) q^{88} +(37.6081 + 65.1392i) q^{89} +(71.1414 + 41.0735i) q^{91} +(-37.7350 - 80.9875i) q^{92} +(12.1684 - 38.5725i) q^{94} +(17.6357 + 48.4537i) q^{95} +(12.6145 + 71.5405i) q^{97} +(-95.0328 + 39.3469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	1.07434	+	1.68695i	0.537171	+	0.843474i
$2$	1.07434	+	1.68695i	0.537171	+	0.843474i
$3$		0			0
$3$		0			0
$4$	−1.69158	+	3.62471i	−0.422895	+	0.906179i
$5$	0.755508	−	4.28470i	0.151102	−	0.856939i	−0.811162	−	0.584821i	$-0.801165\pi$
$5$	0.755508	−	4.28470i	0.151102	−	0.856939i	0.962264	−	0.272118i	$-0.0877242\pi$
$6$		0			0
$7$	6.44162	+	7.67682i	0.920232	+	1.09669i	0.995038	+	0.0994912i	$0.0317215\pi$
$7$	6.44162	+	7.67682i	0.920232	+	1.09669i	−0.0748069	+	0.997198i	$0.523834\pi$
$8$	−7.93204	+	1.04057i	−0.991505	+	0.130072i
$9$		0			0
$10$	8.03973	−	3.32873i	0.803973	−	0.332873i
$11$	16.5915	−	2.92553i	1.50832	−	0.265957i	0.642489	−	0.766295i	$-0.277902\pi$
$11$	16.5915	−	2.92553i	1.50832	−	0.265957i	0.865830	+	0.500338i	$0.166791\pi$
$12$		0			0
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	−0.0283148	−	0.999599i	$-0.509014\pi$
$13$	7.70282	−	2.80360i	0.592525	−	0.215661i	0.620840	+	0.783938i	$0.286792\pi$
$14$	−6.02990	+	19.1142i	−0.430707	+	1.36530i
$15$		0			0
$16$	−10.2771	−	12.2630i	−0.642319	−	0.766437i
$17$	−13.2638	+	22.9735i	−0.780222	+	1.35138i	0.151590	+	0.988443i	$0.451561\pi$
$17$	−13.2638	+	22.9735i	−0.780222	+	1.35138i	−0.931812	+	0.362941i	$0.881773\pi$
$18$		0			0
$19$	−10.2637	+	5.92574i	−0.540194	+	0.311881i	−0.745158	−	0.666888i	$-0.767626\pi$
$19$	−10.2637	+	5.92574i	−0.540194	+	0.311881i	0.204964	+	0.978770i	$0.434292\pi$
$20$	14.2528	+	9.98641i	0.712640	+	0.499320i
$21$		0			0
$22$	22.7602	+	24.8460i	1.03455	+	1.12936i
$23$	−14.3578	+	17.1110i	−0.624252	+	0.743955i	−0.981795	−	0.189942i	$-0.939170\pi$
$23$	−14.3578	+	17.1110i	−0.624252	+	0.743955i	0.357543	+	0.933897i	$0.383615\pi$
$24$		0			0
$25$	5.70448	+	2.07626i	0.228179	+	0.0830505i
$26$	13.0050	+	9.98223i	0.500192	+	0.383932i
$27$		0			0
$28$	−38.7228	+	10.3631i	−1.38296	+	0.370110i
$29$	29.1256	+	10.6009i	1.00433	+	0.365547i	0.791254	−	0.611488i	$-0.209429\pi$
$29$	29.1256	+	10.6009i	1.00433	+	0.365547i	0.213078	+	0.977035i	$0.431651\pi$
$30$		0			0
$31$	−12.9259	+	15.4045i	−0.416965	+	0.496920i	−0.933115	−	0.359579i	$-0.882920\pi$
$31$	−12.9259	+	15.4045i	−0.416965	+	0.496920i	0.516150	+	0.856498i	$0.327365\pi$
$32$	9.64589	−	30.5116i	0.301434	−	0.953487i
$33$		0			0
$34$	−53.0049	+	2.30613i	−1.55897	+	0.0678275i
$35$	37.7596	−	21.8005i	1.07884	−	0.622871i
$36$		0			0
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	−0.452711	−	0.891657i	$-0.649543\pi$
$37$	20.1962	−	34.9808i	0.545842	−	0.945426i	0.998553	−	0.0537690i	$-0.0171235\pi$
$38$	−21.0231	−	10.9480i	−0.553240	−	0.288106i
$39$		0			0
$40$	−1.53417	+	34.7725i	−0.0383542	+	0.869313i
$41$	34.1160	−	12.4172i	0.832096	−	0.302858i	0.109377	−	0.994000i	$-0.465114\pi$
$41$	34.1160	−	12.4172i	0.832096	−	0.302858i	0.722719	+	0.691142i	$0.242892\pi$
$42$		0			0
$43$	−25.3466	+	4.46929i	−0.589456	+	0.103937i	−0.460417	−	0.887703i	$-0.652300\pi$
$43$	−25.3466	+	4.46929i	−0.589456	+	0.103937i	−0.129039	+	0.991640i	$0.541189\pi$
$44$	−17.4617	+	65.0882i	−0.396856	+	1.47928i
$45$		0			0
$46$	−44.2905	−	5.83783i	−0.962836	−	0.126909i
$47$	−12.9992	−	15.4919i	−0.276579	−	0.329614i	0.609817	−	0.792543i	$-0.291243\pi$
$47$	−12.9992	−	15.4919i	−0.276579	−	0.329614i	−0.886396	+	0.462928i	$0.846799\pi$
$48$		0			0
$49$	−8.93040	+	50.6468i	−0.182253	+	1.03361i
$50$	2.62602	+	11.8538i	0.0525204	+	0.237076i
$51$		0			0
$52$	−2.86770	+	32.6630i	−0.0551481	+	0.628135i
$53$	−46.7045			−0.881217			−0.440609	−	0.897699i	$-0.645237\pi$
$53$	−46.7045			−0.881217			−0.440609	+	0.897699i	$0.645237\pi$
$54$		0			0
$55$		−	73.2998i		−	1.33272i
$56$	−59.0835	−	54.1899i	−1.05506	−	0.967676i
$57$		0			0
$58$	13.4078	+	60.5223i	0.231169	+	1.04349i
$59$	36.4280	+	6.42325i	0.617424	+	0.108869i	0.473608	−	0.880736i	$-0.342951\pi$
$59$	36.4280	+	6.42325i	0.617424	+	0.108869i	0.143817	+	0.989604i	$0.454062\pi$
$60$		0			0
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	−0.148830	−	0.988863i	$-0.547551\pi$
$61$	48.7491	−	40.9054i	0.799166	−	0.670580i	0.947996	+	0.318283i	$0.103106\pi$
$62$	−39.8734	−	5.25563i	−0.643120	−	0.0847683i
$63$		0			0
$64$	61.8344	−	16.5078i	0.966163	−	0.257934i
$65$	−6.19303	−	35.1224i	−0.0952773	−	0.540344i
$66$		0			0
$67$	−25.9527	−	71.3043i	−0.387353	−	1.06424i	−0.968188	−	0.250223i	$-0.919496\pi$
$67$	−25.9527	−	71.3043i	−0.387353	−	1.06424i	0.580835	−	0.814021i	$-0.302726\pi$
$68$	−60.8357	−	86.9390i	−0.894643	−	1.27851i
$69$		0			0
$70$	77.3429	+	40.2772i	1.10490	+	0.575389i
$71$	−17.4692	−	10.0858i	−0.246045	−	0.142054i	0.371907	−	0.928270i	$-0.378704\pi$
$71$	−17.4692	−	10.0858i	−0.246045	−	0.142054i	−0.617952	+	0.786216i	$0.712037\pi$
$72$		0			0
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	−0.972304	−	0.233720i	$-0.924910\pi$
$73$	−50.2648	−	87.0613i	−0.688560	−	1.19262i	0.283744	−	0.958900i	$-0.408423\pi$
$74$	80.7083	−	3.51145i	1.09065	−	0.0474520i
$75$		0			0
$76$	−4.11727	−	47.2268i	−0.0541746	−	0.621405i
$77$	129.335	+	108.525i	1.67967	+	1.40941i
$78$		0			0
$79$	29.7876	−	81.8406i	0.377058	−	1.03596i	−0.595512	−	0.803346i	$-0.703051\pi$
$79$	29.7876	−	81.8406i	0.377058	−	1.03596i	0.972570	−	0.232611i	$-0.0747269\pi$
$80$	−60.3076	+	34.7695i	−0.753845	+	0.434619i
$81$		0			0
$82$	57.5993	+	44.2115i	0.702431	+	0.539165i
$83$	25.2237	−	69.3017i	0.303900	−	0.834960i	−0.689912	−	0.723893i	$-0.742351\pi$
$83$	25.2237	−	69.3017i	0.303900	−	0.834960i	0.993813	−	0.111067i	$-0.0354268\pi$
$84$		0			0
$85$	88.4137	+	74.1879i	1.04016	+	0.872799i
$86$	−34.7704	−	37.9569i	−0.404307	−	0.441359i
$87$		0			0
$88$	−128.560	+	40.4701i	−1.46091	+	0.459888i
$89$	37.6081	+	65.1392i	0.422563	+	0.731901i	0.996189	−	0.0872163i	$-0.0277971\pi$
$89$	37.6081	+	65.1392i	0.422563	+	0.731901i	−0.573626	+	0.819117i	$0.694464\pi$
$90$		0			0
$91$	71.1414	+	41.0735i	0.781774	+	0.451357i
$92$	−37.7350	−	80.9875i	−0.410163	−	0.880299i
$93$		0			0
$94$	12.1684	−	38.5725i	0.129451	−	0.410346i
$95$	17.6357	+	48.4537i	0.185639	+	0.510039i
$96$		0			0
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	0.978182	+	0.207751i	$0.0666144\pi$
$97$	12.6145	+	71.5405i	0.130047	+	0.737531i	−0.848135	+	0.529780i	$0.822274\pi$
$98$	−95.0328	+	39.3469i	−0.969722	+	0.401499i
$99$		0			0
$100$	−17.1755	+	17.1650i	−0.171755	+	0.171650i
$101$	−40.3702	+	33.8746i	−0.399705	+	0.335392i	−0.820379	−	0.571820i	$-0.806238\pi$
$101$	−40.3702	+	33.8746i	−0.399705	+	0.335392i	0.420675	+	0.907211i	$0.361793\pi$
$102$		0			0
$103$	−42.8748	−	7.55998i	−0.416260	−	0.0733979i	−0.0384042	−	0.999262i	$-0.512227\pi$
$103$	−42.8748	−	7.55998i	−0.416260	−	0.0733979i	−0.377856	+	0.925864i	$0.623339\pi$
$104$	−58.1817	+	30.2536i	−0.559440	+	0.290900i
$105$		0			0
$106$	−50.1766	−	78.7880i	−0.473364	−	0.743283i
$107$		−	70.5658i		−	0.659493i	−0.944069	−	0.329747i	$-0.893037\pi$
$107$		−	70.5658i		−	0.659493i	0.944069	−	0.329747i	$-0.106963\pi$
$108$		0			0
$109$	−89.3232			−0.819479			−0.409739	−	0.912203i	$-0.634380\pi$
$109$	−89.3232			−0.819479			−0.409739	+	0.912203i	$0.634380\pi$
$110$	123.653	−	78.7490i	1.12412	−	0.715900i
$111$		0			0
$112$	27.9396	−	157.889i	0.249461	−	1.40972i
$113$	13.7107	−	77.7573i	0.121334	−	0.688118i	−0.862084	−	0.506765i	$-0.830841\pi$
$113$	13.7107	−	77.7573i	0.121334	−	0.688118i	0.983418	−	0.181353i	$-0.0580476\pi$
$114$		0			0
$115$	62.4678	+	74.4463i	0.543199	+	0.647359i
$116$	−87.6934	+	87.6399i	−0.755978	+	0.755516i
$117$		0			0
$118$	28.3005	+	68.3529i	0.239835	+	0.579262i
$119$	−261.804	+	46.1631i	−2.20003	+	0.387925i
$120$		0			0
$121$	153.017	−	55.6935i	1.26460	−	0.460277i
$122$	121.378	+	38.2909i	0.994905	+	0.313860i
$123$		0			0
$124$	−33.9717	−	72.9107i	−0.273965	−	0.587990i
$125$	67.5909	−	117.071i	0.540727	−	0.936567i
$126$		0			0
$127$	82.1426	−	47.4250i	0.646792	−	0.373425i	−0.140434	−	0.990090i	$-0.544850\pi$
$127$	82.1426	−	47.4250i	0.646792	−	0.373425i	0.787226	+	0.616665i	$0.211517\pi$
$128$	94.2790	+	86.5764i	0.736555	+	0.676378i
$129$		0			0
$130$	52.5962	−	48.1808i	0.404586	−	0.370621i
$131$	−7.26521	+	8.65835i	−0.0554597	+	0.0660942i	−0.793061	−	0.609142i	$-0.791514\pi$
$131$	−7.26521	+	8.65835i	−0.0554597	+	0.0660942i	0.737601	+	0.675236i	$0.235958\pi$
$132$		0			0
$133$	−111.606	−	40.6211i	−0.839140	−	0.305422i
$134$	92.4046	−	120.386i	0.689587	−	0.898403i
$135$		0			0
$136$	81.3031	−	196.029i	0.597817	−	1.44139i
$137$	−147.499	−	53.6854i	−1.07664	−	0.391864i	−0.257982	−	0.966150i	$-0.583058\pi$
$137$	−147.499	−	53.6854i	−1.07664	−	0.391864i	−0.818655	+	0.574286i	$0.805280\pi$
$138$		0			0
$139$	−113.198	+	134.904i	−0.814376	+	0.970535i	−0.999927	−	0.0120996i	$-0.996148\pi$
$139$	−113.198	+	134.904i	−0.814376	+	0.970535i	0.185551	+	0.982635i	$0.440593\pi$
$140$	15.1472	+	173.745i	0.108194	+	1.24103i
$141$		0			0
$142$	−1.75359	−	40.3052i	−0.0123493	−	0.283839i
$143$	119.599	−	69.0507i	0.836359	−	0.482872i
$144$		0			0
$145$	67.4261	−	116.785i	0.465008	−	0.805417i
$146$	92.8661	−	178.328i	0.636069	−	1.22142i
$147$		0			0
$148$	92.6319	+	132.378i	0.625891	+	0.894446i
$149$	92.5431	−	33.6829i	0.621094	−	0.226060i	−0.0122562	−	0.999925i	$-0.503901\pi$
$149$	92.5431	−	33.6829i	0.621094	−	0.226060i	0.633351	+	0.773865i	$0.281679\pi$
$150$		0			0
$151$	0.769516	−	0.135686i	0.00509613	−	0.000898586i	−0.171100	−	0.985254i	$-0.554732\pi$
$151$	0.769516	−	0.135686i	0.00509613	−	0.000898586i	0.176196	+	0.984355i	$0.443621\pi$
$152$	75.2458	−	57.6833i	0.495038	−	0.379496i
$153$		0			0
$154$	−44.1259	+	334.774i	−0.286532	+	2.17386i
$155$	56.2380	+	67.0219i	0.362826	+	0.432399i
$156$		0			0
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	0.713107	+	0.701055i	$0.247287\pi$
$157$	−30.8928	+	175.202i	−0.196769	+	1.11593i	−0.909876	+	0.414879i	$0.863824\pi$
$158$	170.063	−	37.6748i	1.07635	−	0.238448i
$159$		0			0
$160$	−123.445	−	64.3814i	−0.771533	−	0.402384i
$161$	−223.845			−1.39034
$162$		0			0
$163$		−	268.797i		−	1.64906i	−0.565818	−	0.824530i	$-0.691439\pi$
$163$		−	268.797i		−	1.64906i	0.565818	−	0.824530i	$-0.308561\pi$
$164$	−12.7011	+	144.665i	−0.0774458	+	0.882105i
$165$		0			0
$166$	144.007	−	31.9025i	0.867513	−	0.192184i
$167$	−21.3074	−	3.75708i	−0.127589	−	0.0224975i	0.109489	−	0.993988i	$-0.465079\pi$
$167$	−21.3074	−	3.75708i	−0.127589	−	0.0224975i	−0.237078	+	0.971491i	$0.576190\pi$
$168$		0			0
$169$	−77.9882	+	65.4399i	−0.461469	+	0.387218i
$170$	−30.1646	+	228.852i	−0.177439	+	1.34619i
$171$		0			0
$172$	26.6759	−	99.4344i	0.155093	−	0.578107i
$173$	20.3403	+	115.356i	0.117574	+	0.666796i	0.985443	+	0.170003i	$0.0543778\pi$
$173$	20.3403	+	115.356i	0.117574	+	0.666796i	−0.867869	+	0.496792i	$0.834511\pi$
$174$		0			0
$175$	20.8070	+	57.1668i	0.118897	+	0.326668i
$176$	−206.389	−	173.396i	−1.17266	−	0.985202i
$177$		0			0
$178$	−69.4824	+	133.425i	−0.390350	+	0.749577i
$179$	−17.3998	−	10.0458i	−0.0972054	−	0.0561216i	0.450609	−	0.892721i	$-0.351207\pi$
$179$	−17.3998	−	10.0458i	−0.0972054	−	0.0561216i	−0.547815	+	0.836600i	$0.684540\pi$
$180$		0			0
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	0.999219	+	0.0395201i	$0.0125829\pi$
$181$	96.6241	+	167.358i	0.533835	+	0.924629i	−0.465384	+	0.885109i	$0.654084\pi$
$182$	7.14133	+	164.139i	0.0392381	+	0.901861i
$183$		0			0
$184$	96.0814	−	150.665i	0.522181	−	0.818832i
$185$	−134.624	−	112.963i	−0.727695	−	0.610609i
$186$		0			0
$187$	−152.856	+	419.969i	−0.817413	+	2.24582i
$188$	78.1428	−	20.9127i	0.415653	−	0.111238i
$189$		0			0
$190$	−62.7921	+	81.8064i	−0.330485	+	0.430560i
$191$	87.6196	−	240.733i	0.458741	−	1.26038i	−0.467682	−	0.883897i	$-0.654911\pi$
$191$	87.6196	−	240.733i	0.458741	−	1.26038i	0.926423	−	0.376484i	$-0.122867\pi$
$192$		0			0
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.126087	−	0.992019i	$-0.540242\pi$
$193$	−217.111	−	182.178i	−1.12493	−	0.943928i	−0.998843	+	0.0480909i	$0.984686\pi$
$194$	−107.133	+	98.1390i	−0.552231	+	0.505871i
$195$		0			0
$196$	−168.474	−	118.043i	−0.859560	−	0.602262i
$197$	−142.022	−	245.990i	−0.720925	−	1.24868i	−0.960630	−	0.277832i	$-0.910384\pi$
$197$	−142.022	−	245.990i	−0.720925	−	1.24868i	0.239705	−	0.970846i	$-0.422949\pi$
$198$		0			0
$199$	118.652	+	68.5039i	0.596242	+	0.344241i	0.767562	−	0.640975i	$-0.221470\pi$
$199$	118.652	+	68.5039i	0.596242	+	0.344241i	−0.171320	+	0.985216i	$0.554803\pi$
$200$	−47.4087	−	10.5330i	−0.237043	−	0.0526652i
$201$		0			0
$202$	−100.516	−	31.7094i	−0.497604	−	0.156977i
$203$	106.235	+	291.879i	0.523326	+	1.43783i
$204$		0			0
$205$	−27.4290	−	155.558i	−0.133800	−	0.758818i
$206$	−33.3089	−	80.4495i	−0.161694	−	0.390532i
$207$		0			0
$208$	−113.543	−	65.6468i	−0.545881	−	0.315609i
$209$	−152.954	+	128.344i	−0.731838	+	0.614085i
$210$		0			0
$211$	−181.862	−	32.0671i	−0.861903	−	0.151977i	−0.274813	−	0.961498i	$-0.588616\pi$
$211$	−181.862	−	32.0671i	−0.861903	−	0.151977i	−0.587091	+	0.809521i	$0.699727\pi$
$212$	79.0044	−	169.291i	0.372662	−	0.798540i
$213$		0			0
$214$	119.041	−	75.8117i	0.556265	−	0.354260i
$215$			111.979i			0.520833i
$216$		0			0
$217$	−201.522			−0.928671
$218$	−95.9636	−	150.684i	−0.440200	−	0.691209i
$219$		0			0
$220$	265.691	+	123.993i	1.20769	+	0.563602i
$221$	−37.7599	+	214.147i	−0.170859	+	0.968992i
$222$		0			0
$223$	140.359	+	167.273i	0.629413	+	0.750105i	0.982658	−	0.185426i	$-0.0593664\pi$
$223$	140.359	+	167.273i	0.629413	+	0.750105i	−0.353245	+	0.935531i	$0.614922\pi$
$224$	296.367	−	122.494i	1.32307	−	0.546849i
$225$		0			0
$226$	145.902	−	60.4087i	0.645586	−	0.267295i
$227$	−298.580	+	52.6476i	−1.31533	+	0.231928i	−0.786916	−	0.617060i	$-0.788324\pi$
$227$	−298.580	+	52.6476i	−1.31533	+	0.231928i	−0.528412	+	0.848988i	$0.677212\pi$
$228$		0			0
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.887660	−	0.460499i	$-0.847671\pi$
$229$	−291.207	+	105.991i	−1.27164	+	0.462841i	−0.383985	+	0.923340i	$0.625448\pi$
$230$	−58.4751	+	185.361i	−0.254240	+	0.805916i
$231$		0			0
$232$	−242.056	−	53.7790i	−1.04335	−	0.231806i
$233$	21.7586	−	37.6870i	0.0933845	−	0.161747i	−0.815549	−	0.578688i	$-0.803565\pi$
$233$	21.7586	−	37.6870i	0.0933845	−	0.161747i	0.908933	+	0.416942i	$0.136898\pi$
$234$		0			0
$235$	−76.1989	+	43.9935i	−0.324251	+	0.187206i
$236$	−84.9034	+	121.176i	−0.359760	+	0.513457i
$237$		0			0
$238$	−359.142	−	392.054i	−1.50900	−	1.64729i
$239$	−214.161	+	255.227i	−0.896069	+	1.06789i	0.101260	+	0.994860i	$0.467713\pi$
$239$	−214.161	+	255.227i	−0.896069	+	1.06789i	−0.997329	+	0.0730337i	$0.976732\pi$
$240$		0			0
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.913684	−	0.406426i	$-0.133225\pi$
$241$	325.919	+	118.625i	1.35236	+	0.492219i	0.438677	+	0.898645i	$0.355447\pi$
$242$	258.344	+	198.297i	1.06754	+	0.819409i
$243$		0			0
$244$	65.8073	+	245.896i	0.269702	+	1.00777i
$245$	210.259	+	76.5281i	0.858201	+	0.312360i
$246$		0			0
$247$	−62.4460	+	74.4202i	−0.252818	+	0.301296i
$248$	86.4993	−	135.640i	0.348788	−	0.546934i
$249$		0			0
$250$	270.108	−	11.7518i	1.08043	−	0.0470073i
$251$	−12.1468	+	7.01295i	−0.0483935	+	0.0279400i	−0.524002	−	0.851717i	$-0.675561\pi$
$251$	−12.1468	+	7.01295i	−0.0483935	+	0.0279400i	0.475608	+	0.879657i	$0.342228\pi$
$252$		0			0
$253$	−188.159	+	325.901i	−0.743711	+	1.28815i
$254$	168.253	+	87.6195i	0.662412	+	0.344958i
$255$		0			0
$256$	−44.7620	+	252.056i	−0.174851	+	0.984595i
$257$	159.478	−	58.0452i	0.620537	−	0.225857i	−0.0125705	−	0.999921i	$-0.504001\pi$
$257$	159.478	−	58.0452i	0.620537	−	0.225857i	0.633107	+	0.774064i	$0.281779\pi$
$258$		0			0
$259$	398.637	−	70.2905i	1.53914	−	0.271392i
$260$	137.785	+	36.9644i	0.529941	+	0.142171i
$261$		0			0
$262$	−22.4115	−	2.95401i	−0.0855400	−	0.0112749i
$263$	208.683	+	248.699i	0.793473	+	0.945624i	0.999458	−	0.0329313i	$-0.0104843\pi$
$263$	208.683	+	248.699i	0.793473	+	0.945624i	−0.205985	+	0.978555i	$0.566040\pi$
$264$		0			0
$265$	−35.2856	+	200.115i	−0.133153	+	0.755150i
$266$	−51.3769	−	231.914i	−0.193146	−	0.871857i
$267$		0			0
$268$	302.359	+	26.5460i	1.12820	+	0.0990524i
$269$	281.085			1.04493			0.522463	−	0.852662i	$-0.325013\pi$
$269$	281.085			1.04493			0.522463	+	0.852662i	$0.325013\pi$
$270$		0			0
$271$			270.921i			0.999709i	0.866109	+	0.499855i	$0.166613\pi$
$271$			270.921i			0.999709i	−0.866109	+	0.499855i	$0.833387\pi$
$272$	418.037	−	73.4480i	1.53690	−	0.270029i
$273$		0			0
$274$	−67.9003	−	306.500i	−0.247811	−	1.11861i
$275$	100.720	+	17.7597i	0.366255	+	0.0645807i
$276$		0			0
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	−0.484763	−	0.874646i	$-0.661094\pi$
$277$	80.9996	−	67.9667i	0.292417	−	0.245367i	0.777180	+	0.629279i	$0.216650\pi$
$278$	−349.190	−	46.0260i	−1.25608	−	0.165561i
$279$		0			0
$280$	−276.825	+	212.214i	−0.988661	+	0.757907i
$281$	−14.7191	−	83.4761i	−0.0523811	−	0.297068i	0.947351	−	0.320196i	$-0.103749\pi$
$281$	−14.7191	−	83.4761i	−0.0523811	−	0.297068i	−0.999733	+	0.0231277i	$0.992638\pi$
$282$		0			0
$283$	−110.305	−	303.060i	−0.389770	−	1.07088i	−0.967105	−	0.254376i	$-0.918130\pi$
$283$	−110.305	−	303.060i	−0.389770	−	1.07088i	0.577336	−	0.816507i	$-0.304092\pi$
$284$	66.1088	−	46.2598i	0.232777	−	0.162887i
$285$		0			0
$286$	244.976	+	127.574i	0.856558	+	0.446062i
$287$	315.087	+	181.915i	1.09786	+	0.633851i
$288$		0			0
$289$	−207.355	−	359.150i	−0.717493	−	1.24273i
$290$	269.449	−	11.7232i	0.929136	−	0.0404248i
$291$		0			0
$292$	400.599	−	34.9246i	1.37192	−	0.119605i
$293$	−157.814	−	132.422i	−0.538615	−	0.451952i	0.332449	−	0.943121i	$-0.392125\pi$
$293$	−157.814	−	132.422i	−0.538615	−	0.451952i	−0.871064	+	0.491170i	$0.836570\pi$
$294$		0			0
$295$	55.0433	−	151.230i	0.186588	−	0.512645i
$296$	−123.797	+	298.484i	−0.418232	+	1.00839i
$297$		0			0
$298$	156.244	+	119.928i	0.524309	+	0.402444i
$299$	−62.6233	+	172.056i	−0.209443	+	0.575439i
$300$		0			0
$301$	−197.583	−	165.792i	−0.656423	−	0.550804i
$302$	1.05562	+	1.15236i	0.00349543	+	0.00381576i
$303$		0			0
$304$	178.148	+	64.9640i	0.586014	+	0.213697i
$305$	−138.437	−	239.780i	−0.453891	−	0.786163i
$306$		0			0
$307$	−194.400	−	112.237i	−0.633225	−	0.365593i	0.148775	−	0.988871i	$-0.452467\pi$
$307$	−194.400	−	112.237i	−0.633225	−	0.365593i	−0.782000	+	0.623278i	$0.785800\pi$
$308$	−612.152	+	285.224i	−1.98751	+	0.926051i
$309$		0			0
$310$	−52.6435	+	166.875i	−0.169818	+	0.538306i
$311$	−76.8272	−	211.081i	−0.247033	−	0.678717i	−0.999791	−	0.0204207i	$-0.993499\pi$
$311$	−76.8272	−	211.081i	−0.247033	−	0.678717i	0.752759	−	0.658297i	$-0.228723\pi$
$312$		0			0
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	−0.868912	−	0.494966i	$-0.835181\pi$
$313$	−69.3890	−	393.525i	−0.221690	−	1.25727i	0.647222	−	0.762301i	$-0.275931\pi$
$314$	−328.745	+	136.112i	−1.04696	+	0.433478i
$315$		0			0
$316$	246.261	+	246.411i	0.779307	+	0.779783i
$317$	−11.8267	+	9.92380i	−0.0373083	+	0.0313054i	−0.661251	−	0.750165i	$-0.729974\pi$
$317$	−11.8267	+	9.92380i	−0.0373083	+	0.0313054i	0.623943	+	0.781470i	$0.285530\pi$
$318$		0			0
$319$	514.251	+	90.6763i	1.61207	+	0.284252i
$320$	−24.0144	−	277.413i	−0.0750449	−	0.866917i
$321$		0			0
$322$	−240.486	−	377.615i	−0.746852	−	1.17272i
$323$		−	314.391i		−	0.973346i
$324$		0			0
$325$	49.7616			0.153113
$326$	453.446	−	288.780i	1.39094	−	0.885827i
$327$		0			0
$328$	−257.688	+	133.994i	−0.785634	+	0.408518i
$329$	35.1923	−	199.585i	0.106967	−	0.606643i
$330$		0			0
$331$	−178.560	−	212.799i	−0.539455	−	0.642898i	0.425610	−	0.904907i	$-0.360059\pi$
$331$	−178.560	−	212.799i	−0.539455	−	0.642898i	−0.965065	+	0.262009i	$0.915615\pi$
$332$	208.531	+	208.658i	0.628105	+	0.628488i
$333$		0			0
$334$	−16.5535	−	39.9809i	−0.0495613	−	0.119703i
$335$	−325.125	+	57.3283i	−0.970522	+	0.171129i
$336$		0			0
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.586850	−	0.809696i	$-0.300368\pi$
$337$	524.664	−	190.962i	1.55687	−	0.566653i	0.970015	+	0.243043i	$0.0781457\pi$
$338$	−194.180	−	61.2572i	−0.574496	−	0.181234i
$339$		0			0
$340$	−418.469	+	194.980i	−1.23079	+	0.573470i
$341$	−169.394	+	293.399i	−0.496757	+	0.860408i
$342$		0			0
$343$	−21.0731	+	12.1666i	−0.0614376	+	0.0354710i
$344$	196.400	−	61.8256i	0.570929	−	0.179726i
$345$		0			0
$346$	−172.746	+	158.244i	−0.499267	+	0.457354i
$347$	288.093	−	343.336i	0.830241	−	0.989442i	−0.169752	−	0.985487i	$-0.554297\pi$
$347$	288.093	−	343.336i	0.830241	−	0.989442i	0.999992	−	0.00395526i	$-0.00125900\pi$
$348$		0			0
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.920294	−	0.391228i	$-0.127950\pi$
$349$	479.457	+	174.508i	1.37380	+	0.500023i	0.453509	+	0.891252i	$0.350172\pi$
$350$	−74.0836	+	96.5170i	−0.211667	+	0.275763i
$351$		0			0
$352$	70.7773	−	534.452i	0.201072	−	1.51833i
$353$	194.831	+	70.9126i	0.551928	+	0.200885i	0.602903	−	0.797814i	$-0.294011\pi$
$353$	194.831	+	70.9126i	0.551928	+	0.200885i	−0.0509748	+	0.998700i	$0.516233\pi$
$354$		0			0
$355$	−56.4128	+	67.2302i	−0.158909	+	0.189381i
$356$	−299.728	+	26.1305i	−0.841933	+	0.0734004i
$357$		0			0
$358$	−1.74663	−	40.1451i	−0.00487885	−	0.112137i
$359$	52.8592	−	30.5183i	0.147240	−	0.0850091i	−0.424570	−	0.905395i	$-0.639575\pi$
$359$	52.8592	−	30.5183i	0.147240	−	0.0850091i	0.571810	+	0.820386i	$0.306241\pi$
$360$		0			0
$361$	−110.271	+	190.995i	−0.305460	+	0.529073i
$362$	−178.517	+	342.799i	−0.493140	+	0.946959i
$363$		0			0
$364$	−269.221	+	188.388i	−0.739618	+	0.517550i
$365$	−411.007	+	149.594i	−1.12605	+	0.409847i
$366$		0			0
$367$	−258.395	+	45.5620i	−0.704073	+	0.124147i	−0.514211	−	0.857664i	$-0.671915\pi$
$367$	−258.395	+	45.5620i	−0.704073	+	0.124147i	−0.189862	+	0.981811i	$0.560804\pi$
$368$	357.388	+	0.218360i	0.971164	+	0.000593369i
$369$		0			0
$370$	45.9302	−	348.463i	0.124136	−	0.941793i
$371$	−300.853	−	358.542i	−0.810924	−	0.966421i
$372$		0			0
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	0.530893	+	0.847439i	$0.321857\pi$
$373$	−96.1685	+	545.399i	−0.257824	+	1.46219i	−0.788717	+	0.614756i	$0.789254\pi$
$374$	−872.685	+	193.330i	−2.33338	+	0.516925i
$375$		0			0
$376$	119.231	+	109.355i	0.317103	+	0.290839i
$377$	254.070			0.673926
$378$		0			0
$379$		−	61.8712i		−	0.163249i	−0.996663	−	0.0816243i	$-0.973989\pi$
$379$		−	61.8712i		−	0.163249i	0.996663	−	0.0816243i	$-0.0260107\pi$
$380$	−205.463	−	18.0389i	−0.540693	−	0.0474709i
$381$		0			0
$382$	500.237	−	110.820i	1.30952	−	0.290104i
$383$	−356.264	−	62.8189i	−0.930193	−	0.164018i	−0.312034	−	0.950071i	$-0.601010\pi$
$383$	−356.264	−	62.8189i	−0.930193	−	0.164018i	−0.618159	+	0.786053i	$0.712121\pi$
$384$		0			0
$385$	562.710	−	472.170i	1.46158	−	1.22641i
$386$	74.0730	−	561.977i	0.191899	−	1.45590i
$387$		0			0
$388$	−280.652	−	75.2925i	−0.723331	−	0.194053i
$389$	51.9683	+	294.727i	0.133595	+	0.757653i	0.975828	+	0.218540i	$0.0701294\pi$
$389$	51.9683	+	294.727i	0.133595	+	0.757653i	−0.842233	+	0.539113i	$0.818759\pi$
$390$		0			0
$391$	−202.661	−	556.805i	−0.518313	−	1.42405i
$392$	18.1345	−	411.025i	0.0462614	−	1.04853i
$393$		0			0
$394$	262.391	−	503.861i	0.665967	−	1.27883i
$395$	−328.158	−	189.462i	−0.830778	−	0.479650i
$396$		0			0
$397$	197.081	+	341.354i	0.496425	+	0.859833i	0.999991	−	0.00412318i	$-0.00131245\pi$
$397$	197.081	+	341.354i	0.496425	+	0.859833i	−0.503567	+	0.863956i	$0.667979\pi$
$398$	11.9106	+	273.757i	0.0299261	+	0.687831i
$399$		0			0
$400$	−33.1644	−	91.2920i	−0.0829111	−	0.228230i
$401$	33.5438	+	28.1466i	0.0836503	+	0.0701909i	0.683654	−	0.729806i	$-0.260390\pi$
$401$	33.5438	+	28.1466i	0.0836503	+	0.0701909i	−0.600004	+	0.799997i	$0.704834\pi$
$402$		0			0
$403$	−56.3780	+	154.897i	−0.139896	+	0.384360i
$404$	−54.4963	−	203.632i	−0.134892	−	0.504039i
$405$		0			0
$406$	−378.251	+	492.791i	−0.931654	+	1.21377i
$407$	232.747	−	639.468i	0.571861	−	1.57117i
$408$		0			0
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	0.165033	−	0.986288i	$-0.447227\pi$
$409$	−318.044	−	266.870i	−0.777613	−	0.652495i	−0.942646	+	0.333793i	$0.891671\pi$
$410$	232.950	−	213.393i	0.568170	−	0.520472i
$411$		0			0
$412$	99.9290	−	142.621i	0.242546	−	0.346166i
$413$	185.346	+	321.028i	0.448778	+	0.777307i
$414$		0			0
$415$	−277.880	−	160.434i	−0.669590	−	0.386588i
$416$	−11.2416	−	262.069i	−0.0270232	−	0.629972i
$417$		0			0
$418$	−380.834	−	120.140i	−0.911086	−	0.287417i
$419$	−21.7249	−	59.6886i	−0.0518493	−	0.142455i	0.911065	−	0.412264i	$-0.135262\pi$
$419$	−21.7249	−	59.6886i	−0.0518493	−	0.142455i	−0.962914	+	0.269809i	$0.913039\pi$
$420$		0			0
$421$	108.764	+	616.830i	0.258346	+	1.46515i	0.787335	+	0.616525i	$0.211460\pi$
$421$	108.764	+	616.830i	0.258346	+	1.46515i	−0.528989	+	0.848629i	$0.677429\pi$
$422$	−141.286	−	341.242i	−0.334801	−	0.808630i
$423$		0			0
$424$	370.462	−	48.5995i	0.873731	−	0.114622i
$425$	−123.362	+	103.513i	−0.290264	+	0.243560i
$426$		0			0
$427$	628.047	+	110.742i	1.47084	+	0.259348i
$428$	255.781	+	119.368i	0.597619	+	0.278896i
$429$		0			0
$430$	−188.903	+	120.304i	−0.439309	+	0.279776i
$431$		−	127.048i		−	0.294775i	−0.989079	−	0.147388i	$-0.952914\pi$
$431$		−	127.048i		−	0.294775i	0.989079	−	0.147388i	$-0.0470865\pi$
$432$		0			0
$433$	587.542			1.35691			0.678454	−	0.734642i	$-0.262650\pi$
$433$	587.542			1.35691			0.678454	+	0.734642i	$0.262650\pi$
$434$	−216.503	−	339.956i	−0.498855	−	0.783309i
$435$		0			0
$436$	151.097	−	323.771i	0.346554	−	0.742594i
$437$	45.9688	−	260.702i	0.105192	−	0.596573i
$438$		0			0
$439$	−277.190	−	330.342i	−0.631412	−	0.752488i	0.351576	−	0.936159i	$-0.385646\pi$
$439$	−277.190	−	330.342i	−0.631412	−	0.752488i	−0.982988	+	0.183672i	$0.941202\pi$
$440$	76.2740	+	581.417i	0.173350	+	1.32140i
$441$		0			0
$442$	−401.822	+	166.368i	−0.909100	+	0.376399i
$443$	774.476	−	136.561i	1.74825	−	0.308264i	0.794145	−	0.607729i	$-0.207919\pi$
$443$	774.476	−	136.561i	1.74825	−	0.308264i	0.954107	+	0.299465i	$0.0968081\pi$
$444$		0			0
$445$	307.515	−	111.926i	0.691045	−	0.251520i
$446$	−131.388	+	416.487i	−0.294592	+	0.933828i
$447$		0			0
$448$	525.041	+	368.355i	1.17197	+	0.822221i
$449$	242.525	−	420.066i	0.540145	−	0.935559i	−0.458750	−	0.888566i	$-0.651703\pi$
$449$	242.525	−	420.066i	0.540145	−	0.935559i	0.998895	−	0.0469939i	$-0.0149641\pi$
$450$		0			0
$451$	529.708	−	305.827i	1.17452	−	0.678109i
$452$	258.655	+	181.230i	0.572246	+	0.400952i
$453$		0			0
$454$	−409.590	−	447.126i	−0.902181	−	0.984860i
$455$	229.735	−	273.788i	0.504913	−	0.601732i
$456$		0			0
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.999746	−	0.0225304i	$-0.992828\pi$
$457$	−813.496	−	296.088i	−1.78008	−	0.647896i	−0.780332	−	0.625365i	$-0.784950\pi$
$458$	−491.656	−	377.380i	−1.07348	−	0.823974i
$459$		0			0
$460$	−375.516	+	100.496i	−0.816339	+	0.218470i
$461$	652.111	+	237.349i	1.41456	+	0.514857i	0.932464	−	0.361263i	$-0.117654\pi$
$461$	652.111	+	237.349i	1.41456	+	0.514857i	0.482094	+	0.876120i	$0.339876\pi$
$462$		0			0
$463$	−438.512	+	522.598i	−0.947111	+	1.12872i	0.0444414	+	0.999012i	$0.485849\pi$
$463$	−438.512	+	522.598i	−0.947111	+	1.12872i	−0.991552	+	0.129710i	$0.958595\pi$
$464$	−169.329	−	466.113i	−0.364933	−	1.00455i
$465$		0			0
$466$	86.9521	−	3.78310i	0.186592	−	0.00811825i
$467$	−388.222	+	224.140i	−0.831310	+	0.479957i	−0.854301	−	0.519779i	$-0.826014\pi$
$467$	−388.222	+	224.140i	−0.831310	+	0.479957i	0.0229910	+	0.999736i	$0.492681\pi$
$468$		0			0
$469$	380.214	−	658.549i	0.810690	−	1.40416i
$470$	−156.078	−	81.2796i	−0.332082	−	0.172935i
$471$		0			0
$472$	−295.632	−	13.0433i	−0.626340	−	0.0276342i
$473$	−407.463	+	148.305i	−0.861445	+	0.313540i
$474$		0			0
$475$	−70.8524	+	12.4932i	−0.149163	+	0.0263015i
$476$	275.534	−	1027.05i	0.578854	−	2.15767i
$477$		0			0
$478$	−660.635	−	87.0770i	−1.38208	−	0.182169i
$479$	370.059	+	441.020i	0.772567	+	0.920709i	0.998572	−	0.0534168i	$-0.0170112\pi$
$479$	370.059	+	441.020i	0.772567	+	0.920709i	−0.226006	+	0.974126i	$0.572567\pi$
$480$		0			0
$481$	57.4954	−	326.073i	0.119533	−	0.677905i
$482$	150.034	+	677.251i	0.311275	+	1.40509i
$483$		0			0
$484$	−56.9669	+	648.851i	−0.117700	+	1.34060i
$485$	316.060			0.651670
$486$		0			0
$487$			109.976i			0.225824i	0.993605	+	0.112912i	$0.0360178\pi$
$487$			109.976i			0.225824i	−0.993605	+	0.112912i	$0.963982\pi$
$488$	−344.115	+	375.190i	−0.705153	+	0.768832i
$489$		0			0
$490$	96.7914	+	436.913i	0.197533	+	0.891660i
$491$	382.906	+	67.5166i	0.779849	+	0.137508i	0.549381	−	0.835572i	$-0.314863\pi$
$491$	382.906	+	67.5166i	0.779849	+	0.137508i	0.230467	+	0.973080i	$0.425975\pi$
$492$		0			0
$493$	−629.855	+	528.511i	−1.27760	+	1.07203i
$494$	−192.631	−	25.3903i	−0.389942	−	0.0513974i
$495$		0			0
$496$	321.746	+	0.196583i	0.648682	+	0.000396337i
$497$	−35.1026	−	199.077i	−0.0706290	−	0.400557i
$498$		0			0
$499$	36.1272	+	99.2586i	0.0723992	+	0.198915i	0.970614	−	0.240642i	$-0.0773578\pi$
$499$	36.1272	+	99.2586i	0.0723992	+	0.198915i	−0.898215	+	0.439557i	$0.855136\pi$
$500$	310.013	+	443.032i	0.620026	+	0.886065i
$501$		0			0
$502$	−24.8803	−	12.9567i	−0.0495623	−	0.0258101i
$503$	417.548	+	241.072i	0.830116	+	0.479268i	0.853892	−	0.520449i	$-0.174236\pi$
$503$	417.548	+	241.072i	0.830116	+	0.479268i	−0.0237762	+	0.999717i	$0.507569\pi$
$504$		0			0
$505$	114.642	+	198.566i	0.227015	+	0.393201i
$506$	−751.924	+	32.7147i	−1.48602	+	0.0646535i
$507$		0			0
$508$	32.9514	+	377.967i	0.0648650	+	0.744029i
$509$	466.979	+	391.842i	0.917443	+	0.769826i	0.973520	−	0.228600i	$-0.0734148\pi$
$509$	466.979	+	391.842i	0.917443	+	0.769826i	−0.0560770	+	0.998426i	$0.517859\pi$
$510$		0			0
$511$	344.567	−	946.690i	0.674299	−	1.85262i
$512$	−473.295	+	195.283i	−0.924405	+	0.381413i
$513$		0			0
$514$	269.253	+	206.670i	0.523839	+	0.402083i
$515$	−64.7845	+	177.994i	−0.125795	+	0.345619i
$516$		0			0
$517$	−260.999	−	219.004i	−0.504833	−	0.423605i
$518$	546.849	+	596.964i	1.05569	+	1.15244i
$519$		0			0
$520$	85.6708	+	272.148i	0.164752	+	0.523361i
$521$	96.1278	+	166.498i	0.184506	+	0.319575i	0.943410	−	0.331628i	$-0.107598\pi$
$521$	96.1278	+	166.498i	0.184506	+	0.319575i	−0.758904	+	0.651203i	$0.774265\pi$
$522$		0			0
$523$	−261.108	−	150.751i	−0.499250	−	0.288242i	0.229154	−	0.973390i	$-0.426404\pi$
$523$	−261.108	−	150.751i	−0.499250	−	0.288242i	−0.728404	+	0.685148i	$0.759738\pi$
$524$	−19.0943	−	40.9806i	−0.0364396	−	0.0782073i
$525$		0			0
$526$	−195.345	+	619.225i	−0.371378	+	1.17723i
$527$	−182.449	−	501.276i	−0.346204	−	0.951188i
$528$		0			0
$529$	5.22135	+	29.6117i	0.00987022	+	0.0559768i
$530$	−375.492	+	155.467i	−0.708475	+	0.293333i
$531$		0			0
$532$	336.030	−	335.825i	0.631635	−	0.631250i
$533$	227.976	−	191.295i	0.427723	−	0.358902i
$534$		0			0
$535$	−302.353	−	53.3130i	−0.565146	−	0.0996504i
$536$	280.055	+	538.583i	0.522490	+	1.00482i
$537$		0			0
$538$	301.982	+	474.176i	0.561304	+	0.881368i
$539$			866.433i			1.60748i
$540$		0			0
$541$	−53.7516			−0.0993561			−0.0496780	−	0.998765i	$-0.515820\pi$
$541$	−53.7516			−0.0993561			−0.0496780	+	0.998765i	$0.515820\pi$
$542$	−457.030	+	291.062i	−0.843228	+	0.537014i
$543$		0			0
$544$	573.018	+	626.299i	1.05334	+	1.15128i
$545$	−67.4844	+	382.723i	−0.123825	+	0.702244i
$546$		0			0
$547$	309.469	+	368.810i	0.565756	+	0.674242i	0.970754	−	0.240076i	$-0.0771723\pi$
$547$	309.469	+	368.810i	0.565756	+	0.674242i	−0.404998	+	0.914318i	$0.632728\pi$
$548$	444.101	−	443.830i	0.810403	−	0.809908i
$549$		0			0
$550$	78.2482	+	188.990i	0.142269	+	0.343617i
$551$	−361.754	+	63.7870i	−0.656541	+	0.115766i
$552$		0			0
$553$	820.156	−	298.512i	1.48310	−	0.539806i
$554$	201.677	+	63.6225i	0.364039	+	0.114842i
$555$		0			0
$556$	−297.506	−	638.513i	−0.535083	−	1.14840i
$557$	−220.981	+	382.751i	−0.396735	+	0.687165i	−0.993321	−	0.115384i	$-0.963190\pi$
$557$	−220.981	+	382.751i	−0.396735	+	0.687165i	0.596586	+	0.802549i	$0.296523\pi$
$558$		0			0
$559$	−182.710	+	105.488i	−0.326852	+	0.188708i
$560$	−655.398	−	238.999i	−1.17035	−	0.426784i
$561$		0			0
$562$	125.006	−	114.512i	0.222431	−	0.203758i
$563$	−539.434	+	642.872i	−0.958142	+	1.14187i	0.0316719	+	0.999498i	$0.489917\pi$
$563$	−539.434	+	642.872i	−0.958142	+	1.14187i	−0.989813	+	0.142370i	$0.954528\pi$
$564$		0			0
$565$	−322.808	−	117.492i	−0.571341	−	0.207951i
$566$	392.741	−	511.668i	0.693889	−	0.904008i
$567$		0			0
$568$	149.061	+	61.8232i	0.262432	+	0.108844i
$569$	−1001.95	−	364.680i	−1.76090	−	0.640914i	−0.760927	−	0.648838i	$-0.775255\pi$
$569$	−1001.95	−	364.680i	−1.76090	−	0.640914i	−0.999969	+	0.00792419i	$0.997478\pi$
$570$		0			0
$571$	421.903	−	502.804i	0.738884	−	0.880567i	−0.257435	−	0.966296i	$-0.582877\pi$
$571$	421.903	−	502.804i	0.738884	−	0.880567i	0.996319	+	0.0857285i	$0.0273218\pi$
$572$	47.9772	+	550.319i	0.0838763	+	0.962095i
$573$		0			0
$574$	31.6291	+	726.974i	0.0551030	+	1.26650i
$575$	−117.431	+	67.7987i	−0.204227	+	0.117911i
$576$		0			0
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	−0.949862	−	0.312670i	$-0.898777\pi$
$577$	−117.795	+	204.027i	−0.204151	+	0.353600i	0.745711	+	0.666270i	$0.232110\pi$
$578$	383.097	−	735.647i	0.662797	−	1.27275i
$579$		0			0
$580$	309.257	+	441.952i	0.533202	+	0.761987i
$581$	694.498	−	252.777i	1.19535	−	0.435072i
$582$		0			0
$583$	−774.898	+	136.635i	−1.32916	+	0.234366i
$584$	489.296	+	638.269i	0.837836	+	1.09293i
$585$		0			0
$586$	53.8423	−	408.490i	0.0918810	−	0.697083i
$587$	294.660	+	351.162i	0.501976	+	0.598232i	0.956221	−	0.292645i	$-0.0945354\pi$
$587$	294.660	+	351.162i	0.501976	+	0.598232i	−0.454245	+	0.890877i	$0.650091\pi$
$588$		0			0
$589$	41.3844	−	234.703i	0.0702622	−	0.398477i
$590$	314.253	−	69.6178i	0.532632	−	0.117996i
$591$		0			0
$592$	−636.527	+	111.836i	−1.07521	+	0.188912i
$593$	−530.547			−0.894683			−0.447342	−	0.894363i	$-0.647629\pi$
$593$	−530.547			−0.894683			−0.447342	+	0.894363i	$0.647629\pi$
$594$		0			0
$595$			1156.63i			1.94391i
$596$	−34.4531	+	392.420i	−0.0578071	+	0.658422i
$597$		0			0
$598$	−357.529	+	79.2049i	−0.597874	+	0.132450i
$599$	367.257	+	64.7574i	0.613118	+	0.108109i	0.471579	−	0.881824i	$-0.343684\pi$
$599$	367.257	+	64.7574i	0.613118	+	0.108109i	0.141538	+	0.989933i	$0.454795\pi$
$600$		0			0
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	−0.877759	−	0.479102i	$-0.840962\pi$
$601$	−335.573	+	281.579i	−0.558358	+	0.468518i	0.319402	+	0.947619i	$0.396518\pi$
$602$	67.4105	−	511.430i	0.111978	−	0.849551i
$603$		0			0
$604$	−0.809874	+	3.01880i	−0.00134085	+	0.00499801i
$605$	−123.024	−	697.706i	−0.203346	−	1.15323i
$606$		0			0
$607$	56.8614	+	156.226i	0.0936762	+	0.257373i	0.977677	−	0.210111i	$-0.0673826\pi$
$607$	56.8614	+	156.226i	0.0936762	+	0.257373i	−0.884001	+	0.467484i	$0.845160\pi$
$608$	81.8014	+	370.320i	0.134542	+	0.609080i
$609$		0			0
$610$	255.767	−	491.141i	0.419290	−	0.805149i
$611$	−143.564	−	82.8865i	−0.234965	−	0.135657i
$612$		0			0
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	0.777320	−	0.629106i	$-0.216579\pi$
$613$	−95.7272	−	165.804i	−0.156162	−	0.270480i	−0.933481	+	0.358626i	$0.883245\pi$
$614$	−19.5143	−	448.524i	−0.0317823	−	0.730495i
$615$		0			0
$616$	−1138.82	−	726.241i	−1.84873	−	1.17896i
$617$	−216.274	−	181.476i	−0.350526	−	0.294126i	0.450475	−	0.892789i	$-0.351255\pi$
$617$	−216.274	−	181.476i	−0.350526	−	0.294126i	−0.801001	+	0.598663i	$0.795699\pi$
$618$		0			0
$619$	−22.1636	+	60.8940i	−0.0358055	+	0.0983748i	−0.956307	−	0.292364i	$-0.905558\pi$
$619$	−22.1636	+	60.8940i	−0.0358055	+	0.0983748i	0.920502	+	0.390739i	$0.127780\pi$
$620$	−338.066	+	90.4739i	−0.545268	+	0.145926i
$621$		0			0
$622$	273.544	−	356.377i	0.439781	−	0.572953i
$623$	−257.805	+	708.313i	−0.413812	+	1.13694i
$624$		0			0
$625$	−334.289	−	280.502i	−0.534862	−	0.448803i
$626$	589.308	−	539.835i	0.941386	−	0.862357i
$627$		0			0
$628$	−582.798	−	408.345i	−0.928023	−	0.650231i
$629$	535.754	+	927.954i	0.851756	+	1.47528i
$630$		0			0
$631$	310.209	+	179.099i	0.491615	+	0.283834i	0.725244	−	0.688492i	$-0.241727\pi$
$631$	310.209	+	179.099i	0.491615	+	0.283834i	−0.233629	+	0.972326i	$0.575060\pi$
$632$	−151.115	+	680.159i	−0.239105	+	1.07620i
$633$		0			0
$634$	−29.4469	−	9.28951i	−0.0464462	−	0.0146522i
$635$	−141.143	−	387.786i	−0.222272	−	0.610686i
$636$		0			0
$637$	73.2040	+	415.161i	0.114920	+	0.651744i
$638$	399.515	+	964.932i	0.626199	+	1.51243i
$639$		0			0
$640$	442.182	−	338.548i	0.690909	−	0.528981i
$641$	575.070	−	482.541i	0.897146	−	0.752795i	−0.0724847	−	0.997370i	$-0.523093\pi$
$641$	575.070	−	482.541i	0.897146	−	0.752795i	0.969630	+	0.244575i	$0.0786484\pi$
$642$		0			0
$643$	899.318	+	158.574i	1.39863	+	0.246616i	0.821580	−	0.570093i	$-0.193093\pi$
$643$	899.318	+	158.574i	1.39863	+	0.246616i	0.577049	+	0.816709i	$0.304204\pi$
$644$	378.652	−	811.376i	0.587970	−	1.25990i
$645$		0			0
$646$	530.361	−	337.763i	0.820992	−	0.522853i
$647$		−	457.889i		−	0.707710i	−0.935300	−	0.353855i	$-0.884871\pi$
$647$		−	457.889i		−	0.707710i	0.935300	−	0.353855i	$-0.115129\pi$
$648$		0			0
$649$	623.187			0.960227
$650$	53.4610	+	83.9452i	0.0822477	+	0.129147i
$651$		0			0
$652$	974.312	+	454.692i	1.49434	+	0.697380i
$653$	−44.8800	+	254.527i	−0.0687289	+	0.389781i	0.930967	+	0.365104i	$0.118967\pi$
$653$	−44.8800	+	254.527i	−0.0687289	+	0.389781i	−0.999695	+	0.0246765i	$0.992144\pi$
$654$		0			0
$655$	31.6095	+	37.6707i	0.0482587	+	0.0575125i
$656$	−502.885	−	290.751i	−0.766593	−	0.443218i
$657$		0			0
$658$	374.499	−	155.055i	0.569147	−	0.235646i
$659$	773.092	−	136.317i	1.17313	−	0.206854i	0.447078	−	0.894495i	$-0.352465\pi$
$659$	773.092	−	136.317i	1.17313	−	0.206854i	0.726051	+	0.687640i	$0.241353\pi$
$660$		0			0
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.415337	−	0.909668i	$-0.363664\pi$
$661$	871.348	−	317.145i	1.31823	−	0.479795i	0.902890	+	0.429872i	$0.141441\pi$
$662$	167.147	−	529.840i	0.252488	−	0.800362i
$663$		0			0
$664$	−127.962	+	575.950i	−0.192714	+	0.867395i
$665$	−258.368	+	447.507i	−0.388524	+	0.672943i
$666$		0			0
$667$	−599.571	+	346.162i	−0.898907	+	0.518984i
$668$	49.6616	−	70.8780i	0.0743437	−	0.106105i
$669$		0			0
$670$	−446.005	−	486.878i	−0.665679	−	0.726684i
$671$	689.152	−	821.299i	1.02705	−	1.22399i
$672$		0			0
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.00240244	−	0.999997i	$-0.500765\pi$
$673$	−435.450	−	158.491i	−0.647029	−	0.235499i	−0.644626	+	0.764498i	$0.722987\pi$
$674$	885.811	+	679.921i	1.31426	+	1.00879i
$675$		0			0
$676$	−105.278	−	393.382i	−0.155736	−	0.581926i
$677$	−1255.40	−	456.930i	−1.85436	−	0.674933i	−0.982806	−	0.184642i	$-0.940887\pi$
$677$	−1255.40	−	456.930i	−1.85436	−	0.674933i	−0.871559	−	0.490291i	$-0.836890\pi$
$678$		0			0
$679$	−467.946	+	557.676i	−0.689169	+	0.821320i
$680$	−778.499	−	496.460i	−1.14485	−	0.730088i
$681$		0			0
$682$	−676.936	+	29.4521i	−0.992575	+	0.0431848i
$683$	−608.347	+	351.229i	−0.890698	+	0.514245i	−0.874171	−	0.485619i	$-0.838594\pi$
$683$	−608.347	+	351.229i	−0.890698	+	0.514245i	−0.0165271	+	0.999863i	$0.505261\pi$
$684$		0			0
$685$	−341.462	+	591.430i	−0.498485	+	0.863402i
$686$	−43.1641	−	22.4782i	−0.0629214	−	0.0327670i
$687$		0			0
$688$	315.297	+	264.894i	0.458280	+	0.385020i
$689$	−359.757	+	130.941i	−0.522143	+	0.190045i
$690$		0			0
$691$	57.8084	−	10.1932i	0.0836590	−	0.0147513i	−0.131662	−	0.991295i	$-0.542031\pi$
$691$	57.8084	−	10.1932i	0.0836590	−	0.0147513i	0.215321	+	0.976543i	$0.430920\pi$
$692$	−452.539	−	121.406i	−0.653957	−	0.175442i
$693$		0			0
$694$	888.701	+	117.138i	1.28055	+	0.168786i
$695$	492.502	+	586.941i	0.708636	+	0.844520i
$696$		0			0
$697$	−167.240	+	948.463i	−0.239942	+	1.36078i
$698$	220.715	+	996.300i	0.316210	+	1.42736i
$699$		0			0
$700$	−242.410	−	21.2828i	−0.346300	−	0.0304040i
$701$	50.6411			0.0722413			0.0361206	−	0.999347i	$-0.488500\pi$
$701$	50.6411			0.0722413			0.0361206	+	0.999347i	$0.488500\pi$
$702$		0			0
$703$			478.709i			0.680951i
$704$	977.632	−	454.787i	1.38868	−	0.646004i
$705$		0			0
$706$	89.6889	+	404.853i	0.127038	+	0.573447i
$707$	−520.099	−	91.7074i	−0.735641	−	0.129713i
$708$		0			0
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	−0.939267	−	0.343186i	$-0.888494\pi$
$709$	−541.957	+	454.756i	−0.764397	+	0.641405i	0.174870	+	0.984591i	$0.444049\pi$
$710$	−174.020	−	22.9373i	−0.245099	−	0.0323060i
$711$		0			0
$712$	−366.091	−	477.552i	−0.514173	−	0.670719i
$713$	−77.9982	−	442.350i	−0.109394	−	0.620406i
$714$		0			0
$715$	−205.503	−	564.615i	−0.287417	−	0.789672i
$716$	65.8461	−	46.0760i	0.0919639	−	0.0643519i
$717$		0			0
$718$	108.272	+	56.3836i	0.150796	+	0.0785287i
$719$	−1042.00	−	601.598i	−1.44923	−	0.836715i	−0.450798	−	0.892626i	$-0.648860\pi$
$719$	−1042.00	−	601.598i	−1.44923	−	0.836715i	−0.998436	+	0.0559107i	$0.982194\pi$
$720$		0			0
$721$	−218.147	−	377.841i	−0.302561	−	0.524051i
$722$	−440.668	+	19.1725i	−0.610343	+	0.0265548i
$723$		0			0
$724$	−770.072	+	67.1355i	−1.06364	+	0.0927286i
$725$	144.136	+	120.945i	0.198809	+	0.166821i
$726$		0			0
$727$	74.9737	−	205.989i	0.103128	−	0.283341i	−0.877388	−	0.479781i	$-0.840716\pi$
$727$	74.9737	−	205.989i	0.103128	−	0.283341i	0.980516	+	0.196441i	$0.0629383\pi$
$728$	−607.036	−	251.769i	−0.833841	−	0.345836i
$729$		0			0
$730$	−693.919	−	532.631i	−0.950574	−	0.729632i
$731$	233.516	−	641.581i	0.319448	−	0.877676i
$732$		0			0
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	0.655439	−	0.755248i	$-0.272484\pi$
$733$	18.6768	+	15.6717i	0.0254799	+	0.0213802i	−0.629959	+	0.776629i	$0.716928\pi$
$734$	−354.465	−	386.949i	−0.482922	−	0.527179i
$735$		0			0
$736$	383.589	+	603.130i	0.521180	+	0.819470i
$737$	−639.196	−	1107.12i	−0.867295	−	1.50220i
$738$		0			0
$739$	−223.668	−	129.135i	−0.302664	−	0.174743i	0.340975	−	0.940072i	$-0.389243\pi$
$739$	−223.668	−	129.135i	−0.302664	−	0.174743i	−0.643639	+	0.765329i	$0.722576\pi$
$740$	637.184	−	296.887i	0.861059	−	0.401198i
$741$		0			0
$742$	281.623	−	892.720i	0.379546	−	1.20313i
$743$	118.080	+	324.422i	0.158923	+	0.436638i	0.993441	−	0.114342i	$-0.0364761\pi$
$743$	118.080	+	324.422i	0.158923	+	0.436638i	−0.834518	+	0.550980i	$0.814254\pi$
$744$		0			0
$745$	−74.4041	−	421.967i	−0.0998713	−	0.566398i
$746$	−1023.38	+	423.713i	−1.37182	+	0.567980i
$747$		0			0
$748$	−1263.70	−	1264.47i	−1.68944	−	1.69047i
$749$	541.721	−	454.558i	0.723259	−	0.606886i
$750$		0			0
$751$	461.870	+	81.4402i	0.615007	+	0.108442i	0.472470	−	0.881347i	$-0.343363\pi$
$751$	461.870	+	81.4402i	0.615007	+	0.108442i	0.142538	+	0.989789i	$0.454474\pi$
$752$	−56.3822	+	318.621i	−0.0749763	+	0.423698i
$753$		0			0
$754$	272.958	+	428.603i	0.362013	+	0.568439i
$755$		−	3.39966i		−	0.00450285i
$756$		0			0
$757$	−653.653			−0.863479			−0.431739	−	0.901998i	$-0.642100\pi$
$757$	−653.653			−0.863479			−0.431739	+	0.901998i	$0.642100\pi$
$758$	104.373	−	66.4708i	0.137696	−	0.0876923i
$759$		0			0
$760$	−190.307	−	365.985i	−0.250404	−	0.481560i
$761$	−114.654	+	650.234i	−0.150662	+	0.854446i	0.811983	+	0.583681i	$0.198388\pi$
$761$	−114.654	+	650.234i	−0.150662	+	0.854446i	−0.962645	+	0.270766i	$0.912723\pi$
$762$		0			0
$763$	−575.386	−	685.719i	−0.754110	−	0.898714i
$764$	724.372	+	724.815i	0.948131	+	0.948710i
$765$		0			0
$766$	−276.777	−	668.487i	−0.361328	−	0.872699i
$767$	298.607	−	52.6525i	0.389318	−	0.0686473i
$768$		0			0
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.987662	−	0.156602i	$-0.949946\pi$
$769$	−1263.92	+	460.030i	−1.64359	+	0.598219i	−0.655931	+	0.754821i	$0.727724\pi$
$770$	1401.07	+	441.990i	1.81957	+	0.574013i
$771$		0			0
$772$	1027.61	−	478.798i	1.33109	−	0.620205i
$773$	116.766	−	202.245i	0.151056	−	0.261637i	−0.780560	−	0.625081i	$-0.785066\pi$
$773$	116.766	−	202.245i	0.151056	−	0.261637i	0.931616	+	0.363444i	$0.118399\pi$
$774$		0			0
$775$	−105.720	+	61.0372i	−0.136412	+	0.0787577i
$776$	−174.502	−	554.336i	−0.224874	−	0.714350i
$777$		0			0
$778$	−441.357	+	404.305i	−0.567297	+	0.519673i
$779$	−276.574	+	329.609i	−0.355038	+	0.423117i
$780$		0			0
$781$	−319.346	−	116.233i	−0.408894	−	0.148825i
$782$	721.574	−	940.077i	0.922729	−	1.20214i
$783$		0			0
$784$	712.860	−	410.989i	0.909260	−	0.524221i
$785$	727.346	+	264.732i	0.926556	+	0.337239i
$786$		0			0
$787$	393.189	−	468.584i	0.499604	−	0.595405i	−0.456029	−	0.889965i	$-0.650729\pi$
$787$	393.189	−	468.584i	0.499604	−	0.595405i	0.955633	+	0.294560i	$0.0951730\pi$
$788$	1131.88	−	98.6786i	1.43640	−	0.125227i
$789$		0			0
$790$	−32.9412	−	757.131i	−0.0416977	−	0.958394i
$791$	685.248	−	395.628i	0.866306	−	0.500162i
$792$		0			0
$793$	260.824	−	451.760i	0.328908	−	0.569685i
$794$	−364.114	+	699.195i	−0.458582	+	0.880599i
$795$		0			0
$796$	−449.017	+	314.201i	−0.564091	+	0.394724i
$797$	−494.327	+	179.920i	−0.620234	+	0.225747i	−0.632975	−	0.774172i	$-0.718167\pi$
$797$	−494.327	+	179.920i	−0.620234	+	0.225747i	0.0127409	+	0.999919i	$0.495944\pi$
$798$		0			0
$799$	528.321	−	93.1573i	0.661228	−	0.116592i
$800$	118.375	−	154.025i	0.147969	−	0.192532i
$801$		0			0
$802$	−11.4443	+	86.8255i	−0.0142697	+	0.108261i
$803$	−1088.67	−	1297.43i	−1.35575	−	1.61572i
$804$		0			0
$805$	−169.117	+	959.109i	−0.210083	+	1.19144i
$806$	−321.873	+	71.3059i	−0.399346	+	0.0884688i
$807$		0			0
$808$	284.969	−	310.703i	0.352684	−	0.384533i
$809$	−544.887			−0.673531			−0.336766	−	0.941588i	$-0.609333\pi$
$809$	−544.887			−0.673531			−0.336766	+	0.941588i	$0.609333\pi$
$810$		0			0
$811$		−	770.624i		−	0.950214i	−0.879928	−	0.475107i	$-0.842409\pi$
$811$		−	770.624i		−	0.950214i	0.879928	−	0.475107i	$-0.157591\pi$
$812$	−1237.68	−	108.664i	−1.52424	−	0.133823i
$813$		0			0
$814$	1328.80	−	294.375i	1.63243	−	0.361640i
$815$	−1151.71	−	203.078i	−1.41315	−	0.249176i
$816$		0			0
$817$	233.666	−	196.069i	0.286005	−	0.239986i
$818$	108.509	−	823.233i	0.132651	−	1.00640i
$819$		0			0
$820$	610.251	+	163.716i	0.744208	+	0.199654i
$821$	−11.4448	−	64.9068i	−0.0139401	−	0.0790582i	0.977044	−	0.213037i	$-0.0683356\pi$
$821$	−11.4448	−	64.9068i	−0.0139401	−	0.0790582i	−0.990984	+	0.133979i	$0.957224\pi$
$822$		0			0
$823$	408.452	+	1122.21i	0.496297	+	1.36356i	0.894828	+	0.446410i	$0.147298\pi$
$823$	408.452	+	1122.21i	0.496297	+	1.36356i	−0.398531	+	0.917155i	$0.630480\pi$
$824$	347.951	+	15.3516i	0.422271	+	0.0186306i
$825$		0			0
$826$	−342.433	+	657.562i	−0.414567	+	0.796079i
$827$	−956.879	−	552.455i	−1.15705	−	0.668022i	−0.206454	−	0.978456i	$-0.566192\pi$
$827$	−956.879	−	552.455i	−1.15705	−	0.668022i	−0.950595	+	0.310434i	$0.899526\pi$
$828$		0			0
$829$	281.510	+	487.590i	0.339578	+	0.588167i	0.984353	−	0.176205i	$-0.0563823\pi$
$829$	281.510	+	487.590i	0.339578	+	0.588167i	−0.644775	+	0.764372i	$0.723049\pi$
$830$	−27.8942	−	641.129i	−0.0336075	−	0.772445i
$831$		0			0
$832$	430.018	−	300.515i	0.516849	−	0.361196i
$833$	−1045.09	−	876.931i	−1.25460	−	1.05274i
$834$		0			0
$835$	−32.1959	+	88.4574i	−0.0385579	+	0.105937i
$836$	−206.475	−	771.519i	−0.246980	−	0.922869i
$837$		0			0
$838$	77.3515	−	100.775i	0.0923049	−	0.120256i
$839$	−341.688	+	938.779i	−0.407256	+	1.11893i	0.551371	+	0.834260i	$0.314105\pi$
$839$	−341.688	+	938.779i	−0.407256	+	1.11893i	−0.958627	+	0.284666i	$0.908117\pi$
$840$		0			0
$841$	91.6803	+	76.9289i	0.109013	+	0.0914731i
$842$	−923.710	+	846.165i	−1.09704	+	1.00495i
$843$		0			0
$844$	423.868	−	604.952i	0.502213	−	0.716768i
$845$	221.469	+	383.596i	0.262094	+	0.453960i
$846$		0			0
$847$	1413.22	+	815.925i	1.66850	+	0.963312i
$848$	479.987	+	572.737i	0.566023	+	0.675397i
$849$		0			0
$850$	−307.154	−	96.8969i	−0.361358	−	0.113996i
$851$	308.582	+	847.823i	0.362611	+	0.996266i
$852$		0			0
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	0.995442	−	0.0953710i	$-0.0304037\pi$
$853$	23.3839	+	132.617i	0.0274137	+	0.155471i	−0.968028	+	0.250842i	$0.919293\pi$
$854$	487.922	+	1178.46i	0.571337	+	1.37993i
$855$		0			0
$856$	73.4290	+	559.730i	0.0857815	+	0.653891i
$857$	−219.310	+	184.023i	−0.255904	+	0.214729i	−0.761710	−	0.647918i	$-0.775640\pi$
$857$	−219.310	+	184.023i	−0.255904	+	0.214729i	0.505806	+	0.862647i	$0.331195\pi$
$858$		0			0
$859$	1032.05	+	181.978i	1.20145	+	0.211848i	0.738326	−	0.674444i	$-0.235617\pi$
$859$	1032.05	+	181.978i	1.20145	+	0.211848i	0.463126	+	0.886292i	$0.346728\pi$
$860$	−405.892	−	189.422i	−0.471968	−	0.220258i
$861$		0			0
$862$	214.323	−	136.493i	0.248635	−	0.158345i
$863$			1607.61i			1.86282i	0.363973	+	0.931409i	$0.381420\pi$
$863$			1607.61i			1.86282i	−0.363973	+	0.931409i	$0.618580\pi$
$864$		0			0
$865$	509.631			0.589169
$866$	631.220	+	991.151i	0.728892	+	1.14452i
$867$		0			0
$868$	340.890	−	730.458i	0.392730	−	0.841542i
$869$	254.793	−	1445.00i	0.293203	−	1.66283i
$870$		0			0
$871$	−399.817	−	476.484i	−0.459032	−	0.547054i
$872$	708.515	−	92.9475i	0.812517	−	0.106591i
$873$		0			0
$874$	489.177	−	202.536i	0.559699	−	0.231735i
$875$	1334.13	−	235.243i	1.52472	−	0.268849i
$876$		0			0
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.308929	−	0.951085i	$-0.400030\pi$
$877$	1014.63	−	369.294i	1.15693	−	0.421087i	0.847999	+	0.529998i	$0.177807\pi$
$878$	259.473	−	822.505i	0.295527	−	0.936794i
$879$		0			0
$880$	−898.875	+	753.310i	−1.02145	+	0.856035i
$881$	−152.141	+	263.516i	−0.172691	+	0.299110i	−0.939360	−	0.342933i	$-0.888580\pi$
$881$	−152.141	+	263.516i	−0.172691	+	0.299110i	0.766668	+	0.642043i	$0.221913\pi$
$882$		0			0
$883$	−960.150	+	554.343i	−1.08737	+	0.627795i	−0.932876	−	0.360198i	$-0.882709\pi$
$883$	−960.150	+	554.343i	−1.08737	+	0.627795i	−0.154497	+	0.987993i	$0.549376\pi$
$884$	−712.349	−	499.116i	−0.805824	−	0.564611i
$885$		0			0
$886$	1062.42	+	1159.79i	1.19912	+	1.30901i
$887$	−215.519	+	256.845i	−0.242975	+	0.289566i	−0.873725	−	0.486419i	$-0.838303\pi$
$887$	−215.519	+	256.845i	−0.242975	+	0.289566i	0.630750	+	0.775986i	$0.282747\pi$
$888$		0			0
$889$	893.205	+	325.100i	1.00473	+	0.365692i
$890$	519.190	+	398.514i	0.583359	+	0.447769i
$891$		0			0
$892$	−843.747	+	225.805i	−0.945905	+	0.253145i
$893$	225.221	+	81.9736i	0.252207	+	0.0917958i
$894$		0			0
$895$	−56.1887	+	66.9631i	−0.0627807	+	0.0748191i
$896$	−57.3224	+	1281.46i	−0.0639759	+	1.43020i
$897$		0			0
$898$	969.184	−	42.1672i	1.07927	−	0.0469568i
$899$	−539.776	+	311.640i	−0.600419	+	0.346652i
$900$		0			0
$901$	619.478	−	1072.97i	0.687545	−	1.19086i
$902$	1085.00	+	565.027i	1.20288	+	0.626415i
$903$		0			0
$904$	−27.8416	+	631.041i	−0.0307982	+	0.698054i
$905$	790.078	−	287.565i	0.873014	−	0.317751i
$906$		0			0
$907$	−187.688	+	33.0945i	−0.206933	+	0.0364878i	−0.276154	−	0.961114i	$-0.589060\pi$
$907$	−187.688	+	33.0945i	−0.206933	+	0.0364878i	0.0692208	+	0.997601i	$0.477949\pi$
$908$	314.239	−	1171.32i	0.346078	−	1.29000i
$909$		0			0
$910$	708.680	+	93.4096i	0.778769	+	0.102648i
$911$	−358.732	−	427.520i	−0.393778	−	0.469287i	0.532334	−	0.846534i	$-0.321315\pi$
$911$	−358.732	−	427.520i	−0.393778	−	0.469287i	−0.926112	+	0.377248i	$0.876871\pi$
$912$		0			0
$913$	215.756	−	1223.61i	0.236315	−	1.34021i
$914$	−374.487	−	1690.42i	−0.409723	−	1.84948i
$915$		0			0
$916$	108.414	−	1234.83i	0.118356	−	1.34807i
$917$	−113.268			−0.123521
$918$		0			0
$919$		−	1133.08i		−	1.23295i	−0.787376	−	0.616473i	$-0.788561\pi$
$919$		−	1133.08i		−	1.23295i	0.787376	−	0.616473i	$-0.211439\pi$
$920$	−572.964	−	525.508i	−0.622787	−	0.571205i
$921$		0			0
$922$	300.195	+	1355.07i	0.325591	+	1.46971i
$923$	−162.839	−	28.7128i	−0.176423	−	0.0311082i
$924$		0			0
$925$	187.838	−	157.615i	0.203068	−	0.170394i
$926$	−1352.71	−	178.298i	−1.46081	−	0.192546i
$927$		0			0
$928$	604.392	−	786.414i	0.651284	−	0.847429i
$929$	2.83827	+	16.0966i	0.00305519	+	0.0173269i	0.986297	−	0.164978i	$-0.0527553\pi$
$929$	2.83827	+	16.0966i	0.00305519	+	0.0173269i	−0.983242	+	0.182305i	$0.941644\pi$
$930$		0			0
$931$	−208.461	−	572.742i	−0.223911	−	0.615190i
$932$	99.7981	+	142.619i	0.107080	+	0.153025i
$933$		0			0
$934$	−795.195	−	414.107i	−0.851386	−	0.443369i
$935$	1683.96	+	972.232i	1.80102	+	1.03982i
$936$		0			0
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	0.733374	−	0.679825i	$-0.237944\pi$
$937$	−208.069	−	360.386i	−0.222059	−	0.384617i	−0.955433	+	0.295208i	$0.904611\pi$
$938$	1519.42	−	66.1067i	1.61985	−	0.0704762i
$939$		0			0
$940$	−30.5672	−	350.618i	−0.0325183	−	0.372998i
$941$	248.379	+	208.415i	0.263952	+	0.221482i	0.765153	−	0.643849i	$-0.222664\pi$
$941$	248.379	+	208.415i	0.263952	+	0.221482i	−0.501200	+	0.865331i	$0.667108\pi$
$942$		0			0
$943$	−277.360	+	762.040i	−0.294125	+	0.808102i
$944$	−295.607	−	512.729i	−0.313143	−	0.543145i
$945$		0			0
$946$	−687.937	−	528.040i	−0.727206	−	0.558181i
$947$	−505.822	+	1389.74i	−0.534131	+	1.46751i	0.319980	+	0.947424i	$0.396324\pi$
$947$	−505.822	+	1389.74i	−0.534131	+	1.46751i	−0.854112	+	0.520090i	$0.825899\pi$
$948$		0			0
$949$	−631.266	−	529.695i	−0.665191	−	0.558161i
$950$	−97.1951	−	106.102i	−0.102311	−	0.111687i
$951$		0			0
$952$	2028.60	−	638.594i	2.13088	−	0.670792i
$953$	711.138	+	1231.73i	0.746210	+	1.29247i	0.949627	+	0.313382i	$0.101462\pi$
$953$	711.138	+	1231.73i	0.746210	+	1.29247i	−0.203417	+	0.979092i	$0.565205\pi$
$954$		0			0
$955$	−965.270	−	557.299i	−1.01075	−	0.583559i
$956$	−562.854	−	1208.01i	−0.588759	−	1.26361i
$957$		0			0
$958$	−346.407	+	1098.08i	−0.361594	+	1.14622i
$959$	−538.002	−	1478.15i	−0.561003	−	1.54134i
$960$		0			0
$961$	96.6563	+	548.165i	0.100579	+	0.570411i
$962$	611.837	−	253.322i	0.636005	−	0.263328i
$963$		0			0
$964$	−981.299	+	980.699i	−1.01794	+	1.01732i
$965$	−944.607	+	792.620i	−0.978868	+	0.821368i
$966$		0			0
$967$	−1199.62	−	211.526i	−1.24056	−	0.218745i	−0.485405	−	0.874289i	$-0.661328\pi$
$967$	−1199.62	−	211.526i	−1.24056	−	0.218745i	−0.755156	+	0.655545i	$0.772439\pi$
$968$	−1155.78	+	600.988i	−1.19399	+	0.620855i
$969$		0			0
$970$	339.556	+	533.176i	0.350058	+	0.549666i
$971$		−	203.866i		−	0.209955i	−0.994475	−	0.104977i	$-0.966523\pi$
$971$		−	203.866i		−	0.209955i	0.994475	−	0.104977i	$-0.0334770\pi$
$972$		0			0
$973$	−1764.82			−1.81379
$974$	−185.524	+	118.152i	−0.190476	+	0.121306i
$975$		0			0
$976$	−1002.62	−	177.421i	−1.02728	−	0.181784i
$977$	65.5958	−	372.012i	0.0671400	−	0.380770i	−0.932660	−	0.360757i	$-0.882518\pi$
$977$	65.5958	−	372.012i	0.0671400	−	0.380770i	0.999800	−	0.0200126i	$-0.00637062\pi$
$978$		0			0
$979$	814.542	+	970.733i	0.832014	+	0.991556i
$980$	−633.063	+	632.676i	−0.645983	+	0.645588i
$981$		0			0
$982$	297.475	+	718.478i	0.302927	+	0.731647i
$983$	−215.781	+	38.0481i	−0.219513	+	0.0387061i	−0.282323	−	0.959319i	$-0.591105\pi$
$983$	−215.781	+	38.0481i	−0.219513	+	0.0387061i	0.0628098	+	0.998026i	$0.479994\pi$
$984$		0			0
$985$	−1161.29	+	422.675i	−1.17897	+	0.429112i
$986$	−1568.25	−	494.730i	−1.59052	−	0.501755i
$987$		0			0
$988$	−164.120	−	352.237i	−0.166113	−	0.356515i
$989$	287.448	−	497.874i	0.290645	−	0.503412i
$990$		0			0
$991$	1357.24	−	783.603i	1.36957	−	0.790720i	0.378694	−	0.925522i	$-0.376373\pi$
$991$	1357.24	−	783.603i	1.36957	−	0.790720i	0.990873	+	0.134802i	$0.0430400\pi$
$992$	345.334	+	542.980i	0.348119	+	0.547359i
$993$		0			0
$994$	298.120	−	273.093i	0.299919	−	0.274741i
$995$	383.161	−	456.633i	0.385086	−	0.458928i
$996$		0			0
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	0.409695	−	0.912223i	$-0.365635\pi$
$997$	136.762	+	49.7773i	0.137174	+	0.0499271i	−0.272521	+	0.962150i	$0.587857\pi$
$998$	−128.631	+	167.582i	−0.128889	+	0.167918i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.23		204
3.2	odd	2		108.3.j.a.31.12	yes	204
4.3	odd	2	inner	324.3.j.a.307.31		204
12.11	even	2		108.3.j.a.31.4	yes	204
27.7	even	9	inner	324.3.j.a.19.31		204
27.20	odd	18		108.3.j.a.7.4	✓	204
108.7	odd	18	inner	324.3.j.a.19.23		204
108.47	even	18		108.3.j.a.7.12	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.4	✓	204	27.20	odd	18
108.3.j.a.7.12	yes	204	108.47	even	18
108.3.j.a.31.4	yes	204	12.11	even	2
108.3.j.a.31.12	yes	204	3.2	odd	2
324.3.j.a.19.23		204	108.7	odd	18	inner
324.3.j.a.19.31		204	27.7	even	9	inner
324.3.j.a.307.23		204	1.1	even	1	trivial
324.3.j.a.307.31		204	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07434 + 1.68695i) q^{2} +(-1.69158 + 3.62471i) q^{4} +(0.755508 - 4.28470i) q^{5} +(6.44162 + 7.67682i) q^{7} +(-7.93204 + 1.04057i) q^{8} +O(q^{10})\)	\(q+(1.07434 + 1.68695i) q^{2} +(-1.69158 + 3.62471i) q^{4} +(0.755508 - 4.28470i) q^{5} +(6.44162 + 7.67682i) q^{7} +(-7.93204 + 1.04057i) q^{8} +(8.03973 - 3.32873i) q^{10} +(16.5915 - 2.92553i) q^{11} +(7.70282 - 2.80360i) q^{13} +(-6.02990 + 19.1142i) q^{14} +(-10.2771 - 12.2630i) q^{16} +(-13.2638 + 22.9735i) q^{17} +(-10.2637 + 5.92574i) q^{19} +(14.2528 + 9.98641i) q^{20} +(22.7602 + 24.8460i) q^{22} +(-14.3578 + 17.1110i) q^{23} +(5.70448 + 2.07626i) q^{25} +(13.0050 + 9.98223i) q^{26} +(-38.7228 + 10.3631i) q^{28} +(29.1256 + 10.6009i) q^{29} +(-12.9259 + 15.4045i) q^{31} +(9.64589 - 30.5116i) q^{32} +(-53.0049 + 2.30613i) q^{34} +(37.7596 - 21.8005i) q^{35} +(20.1962 - 34.9808i) q^{37} +(-21.0231 - 10.9480i) q^{38} +(-1.53417 + 34.7725i) q^{40} +(34.1160 - 12.4172i) q^{41} +(-25.3466 + 4.46929i) q^{43} +(-17.4617 + 65.0882i) q^{44} +(-44.2905 - 5.83783i) q^{46} +(-12.9992 - 15.4919i) q^{47} +(-8.93040 + 50.6468i) q^{49} +(2.62602 + 11.8538i) q^{50} +(-2.86770 + 32.6630i) q^{52} -46.7045 q^{53} -73.2998i q^{55} +(-59.0835 - 54.1899i) q^{56} +(13.4078 + 60.5223i) q^{58} +(36.4280 + 6.42325i) q^{59} +(48.7491 - 40.9054i) q^{61} +(-39.8734 - 5.25563i) q^{62} +(61.8344 - 16.5078i) q^{64} +(-6.19303 - 35.1224i) q^{65} +(-25.9527 - 71.3043i) q^{67} +(-60.8357 - 86.9390i) q^{68} +(77.3429 + 40.2772i) q^{70} +(-17.4692 - 10.0858i) q^{71} +(-50.2648 - 87.0613i) q^{73} +(80.7083 - 3.51145i) q^{74} +(-4.11727 - 47.2268i) q^{76} +(129.335 + 108.525i) q^{77} +(29.7876 - 81.8406i) q^{79} +(-60.3076 + 34.7695i) q^{80} +(57.5993 + 44.2115i) q^{82} +(25.2237 - 69.3017i) q^{83} +(88.4137 + 74.1879i) q^{85} +(-34.7704 - 37.9569i) q^{86} +(-128.560 + 40.4701i) q^{88} +(37.6081 + 65.1392i) q^{89} +(71.1414 + 41.0735i) q^{91} +(-37.7350 - 80.9875i) q^{92} +(12.1684 - 38.5725i) q^{94} +(17.6357 + 48.4537i) q^{95} +(12.6145 + 71.5405i) q^{97} +(-95.0328 + 39.3469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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