LMFDB - Embedded newform 324.3.j.a.199.9

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			199.9
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37493 - 1.45244i) q^{2} +(-0.219153 + 3.99399i) q^{4} +(3.09520 - 1.12656i) q^{5} +(-9.81257 + 1.73022i) q^{7} +(6.10235 - 5.17314i) q^{8} +O(q^{10})$	\(q+(-1.37493 - 1.45244i) q^{2} +(-0.219153 + 3.99399i) q^{4} +(3.09520 - 1.12656i) q^{5} +(-9.81257 + 1.73022i) q^{7} +(6.10235 - 5.17314i) q^{8} +(-5.89194 - 2.94665i) q^{10} +(0.511212 - 1.40454i) q^{11} +(7.50220 + 6.29509i) q^{13} +(16.0046 + 11.8732i) q^{14} +(-15.9039 - 1.75059i) q^{16} +(-2.21325 + 3.83347i) q^{17} +(-15.6270 + 9.02228i) q^{19} +(3.82115 + 12.6091i) q^{20} +(-2.74289 + 1.18864i) q^{22} +(-31.4351 - 5.54285i) q^{23} +(-10.8400 + 9.09582i) q^{25} +(-1.17174 - 19.5518i) q^{26} +(-4.76004 - 39.5705i) q^{28} +(-17.2158 + 14.4458i) q^{29} +(42.5711 + 7.50643i) q^{31} +(19.3241 + 25.5064i) q^{32} +(8.61094 - 2.05612i) q^{34} +(-28.4227 + 16.4099i) q^{35} +(-35.6586 + 61.7625i) q^{37} +(34.5903 + 10.2923i) q^{38} +(13.0601 - 22.8866i) q^{40} +(2.00560 + 1.68290i) q^{41} +(-15.2234 + 41.8259i) q^{43} +(5.49770 + 2.34958i) q^{44} +(35.1703 + 53.2785i) q^{46} +(8.16324 - 1.43940i) q^{47} +(47.2480 - 17.1969i) q^{49} +(28.1153 + 3.23831i) q^{50} +(-26.7867 + 28.5841i) q^{52} +54.0794 q^{53} -4.92325i q^{55} +(-50.9290 + 61.3202i) q^{56} +(44.6521 + 5.14301i) q^{58} +(31.7936 + 87.3522i) q^{59} +(-14.4068 - 81.7051i) q^{61} +(-47.6295 - 72.1527i) q^{62} +(10.4772 - 63.1366i) q^{64} +(30.3126 + 11.0329i) q^{65} +(-45.3111 + 53.9997i) q^{67} +(-14.8258 - 9.67984i) q^{68} +(62.9134 + 18.7199i) q^{70} +(-95.6408 - 55.2183i) q^{71} +(-28.1437 - 48.7462i) q^{73} +(138.734 - 33.1270i) q^{74} +(-32.6102 - 64.3915i) q^{76} +(-2.58613 + 14.6667i) q^{77} +(68.8774 + 82.0848i) q^{79} +(-51.1981 + 12.4983i) q^{80} +(-0.313248 - 5.22688i) q^{82} +(-21.4079 - 25.5130i) q^{83} +(-2.53183 + 14.3587i) q^{85} +(81.6805 - 35.3965i) q^{86} +(-4.14631 - 11.2156i) q^{88} +(-9.14904 - 15.8466i) q^{89} +(-84.5078 - 48.7906i) q^{91} +(29.0272 - 124.337i) q^{92} +(-13.3145 - 9.87753i) q^{94} +(-38.2047 + 45.5306i) q^{95} +(-69.4916 - 25.2929i) q^{97} +(-89.9399 - 44.9804i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.37493	−	1.45244i	−0.687463	−	0.726219i
$2$	−1.37493	−	1.45244i	−0.687463	−	0.726219i
$3$		0			0
$3$		0			0
$4$	−0.219153	+	3.99399i	−0.0547882	+	0.998498i
$5$	3.09520	−	1.12656i	0.619040	−	0.225312i	−0.0134138	−	0.999910i	$-0.504270\pi$
$5$	3.09520	−	1.12656i	0.619040	−	0.225312i	0.632454	+	0.774598i	$0.282048\pi$
$6$		0			0
$7$	−9.81257	+	1.73022i	−1.40180	+	0.247175i	−0.822881	−	0.568213i	$-0.807635\pi$
$7$	−9.81257	+	1.73022i	−1.40180	+	0.247175i	−0.578915	+	0.815388i	$0.696524\pi$
$8$	6.10235	−	5.17314i	0.762793	−	0.646643i
$9$		0			0
$10$	−5.89194	−	2.94665i	−0.589194	−	0.294665i
$11$	0.511212	−	1.40454i	0.0464738	−	0.127686i	−0.914284	−	0.405073i	$-0.867246\pi$
$11$	0.511212	−	1.40454i	0.0464738	−	0.127686i	0.960758	+	0.277387i	$0.0894684\pi$
$12$		0			0
$13$	7.50220	+	6.29509i	0.577092	+	0.484238i	0.883991	−	0.467504i	$-0.154847\pi$
$13$	7.50220	+	6.29509i	0.577092	+	0.484238i	−0.306898	+	0.951742i	$0.599291\pi$
$14$	16.0046	+	11.8732i	1.14319	+	0.848088i
$15$		0			0
$16$	−15.9039	−	1.75059i	−0.993997	−	0.109412i
$17$	−2.21325	+	3.83347i	−0.130191	+	0.225498i	−0.923750	−	0.382995i	$-0.874893\pi$
$17$	−2.21325	+	3.83347i	−0.130191	+	0.225498i	0.793559	+	0.608494i	$0.208226\pi$
$18$		0			0
$19$	−15.6270	+	9.02228i	−0.822476	+	0.474857i	−0.851270	−	0.524729i	$-0.824167\pi$
$19$	−15.6270	+	9.02228i	−0.822476	+	0.474857i	0.0287936	+	0.999585i	$0.490833\pi$
$20$	3.82115	+	12.6091i	0.191058	+	0.630455i
$21$		0			0
$22$	−2.74289	+	1.18864i	−0.124677	+	0.0540291i
$23$	−31.4351	−	5.54285i	−1.36674	−	0.240993i	−0.558334	−	0.829616i	$-0.688559\pi$
$23$	−31.4351	−	5.54285i	−1.36674	−	0.240993i	−0.808408	+	0.588623i	$0.799670\pi$
$24$		0			0
$25$	−10.8400	+	9.09582i	−0.433599	+	0.363833i
$26$	−1.17174	−	19.5518i	−0.0450670	−	0.751991i
$27$		0			0
$28$	−4.76004	−	39.5705i	−0.170001	−	1.41323i
$29$	−17.2158	+	14.4458i	−0.593648	+	0.498130i	−0.889397	−	0.457136i	$-0.848875\pi$
$29$	−17.2158	+	14.4458i	−0.593648	+	0.498130i	0.295749	+	0.955266i	$0.404431\pi$
$30$		0			0
$31$	42.5711	+	7.50643i	1.37326	+	0.242143i	0.811111	−	0.584892i	$-0.198863\pi$
$31$	42.5711	+	7.50643i	1.37326	+	0.242143i	0.562150	+	0.827035i	$0.309974\pi$
$32$	19.3241	+	25.5064i	0.603879	+	0.797076i
$33$		0			0
$34$	8.61094	−	2.05612i	0.253263	−	0.0604742i
$35$	−28.4227	+	16.4099i	−0.812077	+	0.468853i
$36$		0			0
$37$	−35.6586	+	61.7625i	−0.963745	+	1.66926i	−0.250796	+	0.968040i	$0.580692\pi$
$37$	−35.6586	+	61.7625i	−0.963745	+	1.66926i	−0.712950	+	0.701215i	$0.752641\pi$
$38$	34.5903	+	10.2923i	0.910272	+	0.270851i
$39$		0			0
$40$	13.0601	−	22.8866i	0.326503	−	0.572165i
$41$	2.00560	+	1.68290i	0.0489172	+	0.0410464i	0.666918	−	0.745131i	$-0.267613\pi$
$41$	2.00560	+	1.68290i	0.0489172	+	0.0410464i	−0.618001	+	0.786177i	$0.712057\pi$
$42$		0			0
$43$	−15.2234	+	41.8259i	−0.354032	+	0.972695i	0.627029	+	0.778996i	$0.284271\pi$
$43$	−15.2234	+	41.8259i	−0.354032	+	0.972695i	−0.981061	+	0.193699i	$0.937951\pi$
$44$	5.49770	+	2.34958i	0.124948	+	0.0533997i
$45$		0			0
$46$	35.1703	+	53.2785i	0.764571	+	1.15823i
$47$	8.16324	−	1.43940i	0.173686	−	0.0306255i	−0.0861287	−	0.996284i	$-0.527450\pi$
$47$	8.16324	−	1.43940i	0.173686	−	0.0306255i	0.259815	+	0.965658i	$0.416339\pi$
$48$		0			0
$49$	47.2480	−	17.1969i	0.964245	−	0.350957i
$50$	28.1153	+	3.23831i	0.562306	+	0.0647662i
$51$		0			0
$52$	−26.7867	+	28.5841i	−0.515129	+	0.549695i
$53$	54.0794			1.02037			0.510183	−	0.860066i	$-0.329578\pi$
$53$	54.0794			1.02037			0.510183	+	0.860066i	$0.329578\pi$
$54$		0			0
$55$		−	4.92325i		−	0.0895137i
$56$	−50.9290	+	61.3202i	−0.909447	+	1.09500i
$57$		0			0
$58$	44.6521	+	5.14301i	0.769863	+	0.0886725i
$59$	31.7936	+	87.3522i	0.538875	+	1.48055i	0.848245	+	0.529604i	$0.177660\pi$
$59$	31.7936	+	87.3522i	0.538875	+	1.48055i	−0.309370	+	0.950942i	$0.600118\pi$
$60$		0			0
$61$	−14.4068	−	81.7051i	−0.236177	−	1.33943i	−0.840120	−	0.542400i	$-0.817516\pi$
$61$	−14.4068	−	81.7051i	−0.236177	−	1.33943i	0.603943	−	0.797028i	$-0.293595\pi$
$62$	−47.6295	−	72.1527i	−0.768218	−	1.16375i
$63$		0			0
$64$	10.4772	−	63.1366i	0.163707	−	0.986509i
$65$	30.3126	+	11.0329i	0.466348	+	0.169737i
$66$		0			0
$67$	−45.3111	+	53.9997i	−0.676285	+	0.805965i	−0.989625	−	0.143676i	$-0.954108\pi$
$67$	−45.3111	+	53.9997i	−0.676285	+	0.805965i	0.313340	+	0.949641i	$0.398552\pi$
$68$	−14.8258	−	9.67984i	−0.218027	−	0.142351i
$69$		0			0
$70$	62.9134	+	18.7199i	0.898763	+	0.267427i
$71$	−95.6408	−	55.2183i	−1.34705	−	0.777722i	−0.359223	−	0.933252i	$-0.616958\pi$
$71$	−95.6408	−	55.2183i	−1.34705	−	0.777722i	−0.987831	+	0.155530i	$0.950291\pi$
$72$		0			0
$73$	−28.1437	−	48.7462i	−0.385530	−	0.667757i	0.606313	−	0.795226i	$-0.292648\pi$
$73$	−28.1437	−	48.7462i	−0.385530	−	0.667757i	−0.991843	+	0.127469i	$0.959315\pi$
$74$	138.734	−	33.1270i	1.87478	−	0.447662i
$75$		0			0
$76$	−32.6102	−	64.3915i	−0.429082	−	0.847257i
$77$	−2.58613	+	14.6667i	−0.0335861	+	0.190476i
$78$		0			0
$79$	68.8774	+	82.0848i	0.871865	+	1.03905i	0.998888	+	0.0471488i	$0.0150135\pi$
$79$	68.8774	+	82.0848i	0.871865	+	1.03905i	−0.127023	+	0.991900i	$0.540542\pi$
$80$	−51.1981	+	12.4983i	−0.639976	+	0.156229i
$81$		0			0
$82$	−0.313248	−	5.22688i	−0.00382010	−	0.0637425i
$83$	−21.4079	−	25.5130i	−0.257927	−	0.307385i	0.621505	−	0.783410i	$-0.286522\pi$
$83$	−21.4079	−	25.5130i	−0.257927	−	0.307385i	−0.879432	+	0.476025i	$0.842077\pi$
$84$		0			0
$85$	−2.53183	+	14.3587i	−0.0297863	+	0.168926i
$86$	81.6805	−	35.3965i	0.949774	−	0.411587i
$87$		0			0
$88$	−4.14631	−	11.2156i	−0.0471171	−	0.127450i
$89$	−9.14904	−	15.8466i	−0.102798	−	0.178052i	0.810038	−	0.586377i	$-0.199446\pi$
$89$	−9.14904	−	15.8466i	−0.102798	−	0.178052i	−0.912837	+	0.408325i	$0.866113\pi$
$90$		0			0
$91$	−84.5078	−	48.7906i	−0.928657	−	0.536160i
$92$	29.0272	−	124.337i	0.315513	−	1.35148i
$93$		0			0
$94$	−13.3145	−	9.87753i	−0.141644	−	0.105080i
$95$	−38.2047	+	45.5306i	−0.402155	+	0.479269i
$96$		0			0
$97$	−69.4916	−	25.2929i	−0.716409	−	0.260751i	−0.0420083	−	0.999117i	$-0.513376\pi$
$97$	−69.4916	−	25.2929i	−0.716409	−	0.260751i	−0.674400	+	0.738366i	$0.735598\pi$
$98$	−89.9399	−	44.9804i	−0.917755	−	0.458983i
$99$		0			0
$100$	−33.9530	−	45.2882i	−0.339530	−	0.452882i
$101$	−30.4311	−	172.583i	−0.301298	−	1.70874i	−0.640440	−	0.768008i	$-0.721248\pi$
$101$	−30.4311	−	172.583i	−0.301298	−	1.70874i	0.339142	−	0.940735i	$-0.389863\pi$
$102$		0			0
$103$	−14.0809	−	38.6869i	−0.136707	−	0.375601i	0.852381	−	0.522920i	$-0.175158\pi$
$103$	−14.0809	−	38.6869i	−0.136707	−	0.375601i	−0.989089	+	0.147320i	$0.952935\pi$
$104$	78.3464	−	0.395102i	0.753331	−	0.00379906i
$105$		0			0
$106$	−74.3553	−	78.5470i	−0.701465	−	0.741010i
$107$		−	37.2248i		−	0.347895i	−0.984755	−	0.173948i	$-0.944348\pi$
$107$		−	37.2248i		−	0.347895i	0.984755	−	0.173948i	$-0.0556524\pi$
$108$		0			0
$109$	30.9814			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$109$	30.9814			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$110$	−7.15072	+	6.76911i	−0.0650066	+	0.0615374i
$111$		0			0
$112$	159.088	−	10.3396i	1.42042	−	0.0923175i
$113$	−188.530	+	68.6193i	−1.66841	+	0.607250i	−0.991650	−	0.128957i	$-0.958837\pi$
$113$	−188.530	+	68.6193i	−1.66841	+	0.607250i	−0.676756	+	0.736207i	$0.736615\pi$
$114$		0			0
$115$	−103.542	+	18.2573i	−0.900367	+	0.158759i
$116$	−53.9234	−	71.9256i	−0.464857	−	0.620048i
$117$		0			0
$118$	83.1598	−	166.281i	0.704744	−	1.40916i
$119$	15.0850	−	41.4456i	0.126764	−	0.348283i
$120$		0			0
$121$	90.9800	+	76.3413i	0.751901	+	0.630920i
$122$	−98.8633	+	133.264i	−0.810355	+	1.09232i
$123$		0			0
$124$	−39.3102	+	168.384i	−0.317018	+	1.35793i
$125$	−64.4780	+	111.679i	−0.515824	+	0.893433i
$126$		0			0
$127$	26.0944	−	15.0656i	0.205467	−	0.118627i	−0.393736	−	0.919224i	$-0.628817\pi$
$127$	26.0944	−	15.0656i	0.205467	−	0.118627i	0.599203	+	0.800597i	$0.295484\pi$
$128$	−106.107	+	71.5906i	−0.828964	+	0.559302i
$129$		0			0
$130$	−25.6531	−	59.1967i	−0.197331	−	0.455359i
$131$	21.3011	+	3.75595i	0.162604	+	0.0286714i	0.254357	−	0.967110i	$-0.418136\pi$
$131$	21.3011	+	3.75595i	0.162604	+	0.0286714i	−0.0917536	+	0.995782i	$0.529247\pi$
$132$		0			0
$133$	137.731	−	115.570i	1.03557	−	0.868948i
$134$	140.731	−	8.43402i	1.05023	−	0.0629404i
$135$		0			0
$136$	6.32503	+	34.8426i	0.0465076	+	0.256196i
$137$	165.320	−	138.720i	1.20671	−	1.01255i	0.207302	−	0.978277i	$-0.433532\pi$
$137$	165.320	−	138.720i	1.20671	−	1.01255i	0.999412	−	0.0342764i	$-0.0109127\pi$
$138$		0			0
$139$	168.437	+	29.7001i	1.21178	+	0.213669i	0.742784	−	0.669531i	$-0.233505\pi$
$139$	168.437	+	29.7001i	1.21178	+	0.213669i	0.468996	+	0.883200i	$0.344616\pi$
$140$	−59.3119	−	117.116i	−0.423656	−	0.836545i
$141$		0			0
$142$	51.2980	+	214.833i	0.361254	+	1.51291i
$143$	12.6769	−	7.31903i	0.0886499	−	0.0511821i
$144$		0			0
$145$	−37.0123	+	64.1072i	−0.255257	+	0.442119i
$146$	−32.1054	+	107.899i	−0.219900	+	0.739037i
$147$		0			0
$148$	−238.864	−	155.955i	−1.61395	−	1.05375i
$149$	−159.712	−	134.014i	−1.07189	−	0.899422i	−0.0766671	−	0.997057i	$-0.524428\pi$
$149$	−159.712	−	134.014i	−1.07189	−	0.899422i	−0.995222	+	0.0976347i	$0.968872\pi$
$150$		0			0
$151$	29.9908	−	82.3989i	0.198614	−	0.545688i	−0.799903	−	0.600130i	$-0.795116\pi$
$151$	29.9908	−	82.3989i	0.198614	−	0.545688i	0.998517	+	0.0544415i	$0.0173379\pi$
$152$	−48.6881	+	135.898i	−0.320316	+	0.894065i
$153$		0			0
$154$	24.8582	−	16.4094i	0.161417	−	0.106555i
$155$	140.223	−	24.7250i	0.904662	−	0.159516i
$156$		0			0
$157$	58.4964	−	21.2910i	0.372589	−	0.135611i	−0.148937	−	0.988847i	$-0.547585\pi$
$157$	58.4964	−	21.2910i	0.372589	−	0.135611i	0.521526	+	0.853235i	$0.325363\pi$
$158$	24.5218	−	212.901i	0.155201	−	1.34747i
$159$		0			0
$160$	88.5467	+	57.1777i	0.553417	+	0.357361i
$161$	318.049			1.97546
$162$		0			0
$163$		−	78.7385i		−	0.483058i	−0.970394	−	0.241529i	$-0.922351\pi$
$163$		−	78.7385i		−	0.483058i	0.970394	−	0.241529i	$-0.0776489\pi$
$164$	−7.16103	+	7.64155i	−0.0436648	+	0.0465948i
$165$		0			0
$166$	−7.62169	+	66.1722i	−0.0459138	+	0.398628i
$167$	−35.1864	−	96.6740i	−0.210697	−	0.578886i	0.788656	−	0.614834i	$-0.210777\pi$
$167$	−35.1864	−	96.6740i	−0.210697	−	0.578886i	−0.999354	+	0.0359482i	$0.988555\pi$
$168$		0			0
$169$	−12.6917	−	71.9784i	−0.0750990	−	0.425908i
$170$	24.3362	−	16.0649i	0.143154	−	0.0944992i
$171$		0			0
$172$	−163.716	−	69.9683i	−0.951837	−	0.406792i
$173$	−116.323	−	42.3383i	−0.672390	−	0.244730i	−0.0168134	−	0.999859i	$-0.505352\pi$
$173$	−116.323	−	42.3383i	−0.672390	−	0.244730i	−0.655577	+	0.755129i	$0.727574\pi$
$174$		0			0
$175$	90.6303	−	108.009i	0.517887	−	0.617194i
$176$	−10.5891	+	21.4428i	−0.0601651	+	0.121834i
$177$		0			0
$178$	−10.4369	+	35.0763i	−0.0586345	+	0.197058i
$179$	142.292	+	82.1525i	0.794929	+	0.458952i	0.841695	−	0.539953i	$-0.181558\pi$
$179$	142.292	+	82.1525i	0.794929	+	0.458952i	−0.0467659	+	0.998906i	$0.514891\pi$
$180$		0			0
$181$	47.3831	+	82.0699i	0.261785	+	0.453425i	0.966716	−	0.255851i	$-0.0823555\pi$
$181$	47.3831	+	82.0699i	0.261785	+	0.453425i	−0.704931	+	0.709276i	$0.749022\pi$
$182$	45.3267	+	189.826i	0.249048	+	1.04300i
$183$		0			0
$184$	−220.501	+	128.794i	−1.19838	+	0.699965i
$185$	−40.7913	+	231.339i	−0.220493	+	1.25048i
$186$		0			0
$187$	4.25283	+	5.06832i	0.0227424	+	0.0271033i
$188$	3.95995	+	32.9194i	0.0210636	+	0.175103i
$189$		0			0
$190$	118.659	−	7.11126i	0.624521	−	0.0374277i
$191$	137.193	+	163.500i	0.718286	+	0.856020i	0.994463	−	0.105087i	$-0.0335120\pi$
$191$	137.193	+	163.500i	0.718286	+	0.856020i	−0.276177	+	0.961107i	$0.589068\pi$
$192$		0			0
$193$	−35.2575	+	199.955i	−0.182681	+	1.03604i	0.746217	+	0.665703i	$0.231868\pi$
$193$	−35.2575	+	199.955i	−0.182681	+	1.03604i	−0.928898	+	0.370335i	$0.879243\pi$
$194$	58.8096	+	135.708i	0.303142	+	0.699527i
$195$		0			0
$196$	58.3296	+	192.477i	0.297600	+	0.982025i
$197$	66.4342	+	115.067i	0.337230	+	0.584099i	0.983911	−	0.178662i	$-0.0571768\pi$
$197$	66.4342	+	115.067i	0.337230	+	0.584099i	−0.646681	+	0.762761i	$0.723843\pi$
$198$		0			0
$199$	85.4070	+	49.3097i	0.429181	+	0.247788i	0.698998	−	0.715124i	$-0.253630\pi$
$199$	85.4070	+	49.3097i	0.429181	+	0.247788i	−0.269817	+	0.962912i	$0.586963\pi$
$200$	−19.0953	+	111.583i	−0.0954766	+	0.557913i
$201$		0			0
$202$	−208.826	+	281.488i	−1.03379	+	1.39351i
$203$	143.937	−	171.537i	0.709049	−	0.845012i
$204$		0			0
$205$	8.10364	+	2.94948i	0.0395300	+	0.0143877i
$206$	−36.8301	+	73.6432i	−0.178787	+	0.357491i
$207$		0			0
$208$	−108.294	−	113.250i	−0.520646	−	0.544472i
$209$	4.68345	+	26.5611i	0.0224088	+	0.127087i
$210$		0			0
$211$	−68.4266	−	188.001i	−0.324297	−	0.890998i	−0.989526	−	0.144358i	$-0.953888\pi$
$211$	−68.4266	−	188.001i	−0.324297	−	0.890998i	0.665229	−	0.746640i	$-0.268334\pi$
$212$	−11.8517	+	215.993i	−0.0559041	+	1.01883i
$213$		0			0
$214$	−54.0667	+	51.1814i	−0.252648	+	0.239165i
$215$			146.610i			0.681905i
$216$		0			0
$217$	−430.720			−1.98488
$218$	−42.5971	−	44.9985i	−0.195400	−	0.206415i
$219$		0			0
$220$	19.6634	+	1.07895i	0.0893793	+	0.00490430i
$221$	−40.7363	+	14.8268i	−0.184327	+	0.0670896i
$222$		0			0
$223$	−128.275	+	22.6183i	−0.575223	+	0.101427i	−0.453689	−	0.891160i	$-0.649892\pi$
$223$	−128.275	+	22.6183i	−0.575223	+	0.101427i	−0.121534	+	0.992587i	$0.538781\pi$
$224$	−233.751	−	216.849i	−1.04353	−	0.968074i
$225$		0			0
$226$	358.880	+	179.482i	1.58797	+	0.794166i
$227$	16.5153	−	45.3753i	0.0727544	−	0.199891i	−0.897985	−	0.440026i	$-0.854969\pi$
$227$	16.5153	−	45.3753i	0.0727544	−	0.199891i	0.970740	+	0.240135i	$0.0771916\pi$
$228$		0			0
$229$	63.8786	+	53.6005i	0.278946	+	0.234063i	0.771517	−	0.636209i	$-0.219498\pi$
$229$	63.8786	+	53.6005i	0.278946	+	0.234063i	−0.492571	+	0.870272i	$0.663943\pi$
$230$	168.881	+	125.286i	0.734263	+	0.544723i
$231$		0			0
$232$	−30.3267	+	177.213i	−0.130719	+	0.763848i
$233$	−182.395	+	315.918i	−0.782812	+	1.35587i	0.147485	+	0.989064i	$0.452882\pi$
$233$	−182.395	+	315.918i	−0.782812	+	1.35587i	−0.930297	+	0.366807i	$0.880451\pi$
$234$		0			0
$235$	23.6453	−	13.6516i	0.100618	−	0.0580920i
$236$	−355.852	+	107.840i	−1.50785	+	0.456949i
$237$		0			0
$238$	−80.9379	+	35.0747i	−0.340075	+	0.147373i
$239$	0.406064	+	0.0716000i	0.00169901	+	0.000299582i	0.174498	−	0.984658i	$-0.444170\pi$
$239$	0.406064	+	0.0716000i	0.00169901	+	0.000299582i	−0.172799	+	0.984957i	$0.555281\pi$
$240$		0			0
$241$	−156.191	+	131.060i	−0.648095	+	0.543817i	−0.906492	−	0.422222i	$-0.861250\pi$
$241$	−156.191	+	131.060i	−0.648095	+	0.543817i	0.258397	+	0.966039i	$0.416806\pi$
$242$	−14.2098	−	237.106i	−0.0587184	−	0.979779i
$243$		0			0
$244$	329.487	−	39.6348i	1.35036	−	0.162438i
$245$	126.869	−	106.456i	0.517832	−	0.434513i
$246$		0			0
$247$	−174.033	−	30.6868i	−0.704588	−	0.124238i
$248$	298.615	−	174.419i	1.20409	−	0.703304i
$249$		0			0
$250$	250.860	−	59.9004i	1.00344	−	0.239601i
$251$	122.617	−	70.7932i	0.488515	−	0.282044i	−0.235443	−	0.971888i	$-0.575654\pi$
$251$	122.617	−	70.7932i	0.488515	−	0.282044i	0.723958	+	0.689844i	$0.242321\pi$
$252$		0			0
$253$	−23.8551	+	41.3183i	−0.0942891	+	0.163313i
$254$	−57.7597	−	17.1864i	−0.227400	−	0.0676629i
$255$		0			0
$256$	249.871	+	55.6826i	0.976058	+	0.217510i
$257$	185.148	+	155.357i	0.720419	+	0.604503i	0.927501	−	0.373820i	$-0.121952\pi$
$257$	185.148	+	155.357i	0.720419	+	0.604503i	−0.207082	+	0.978324i	$0.566397\pi$
$258$		0			0
$259$	243.040	−	667.746i	0.938377	−	2.57817i
$260$	−50.7084	+	118.651i	−0.195032	+	0.456348i
$261$		0			0
$262$	−23.8321	−	36.1027i	−0.0909623	−	0.137796i
$263$	−149.562	+	26.3718i	−0.568676	+	0.100273i	−0.450591	−	0.892731i	$-0.648787\pi$
$263$	−149.562	+	26.3718i	−0.568676	+	0.100273i	−0.118085	+	0.993003i	$0.537676\pi$
$264$		0			0
$265$	167.387	−	60.9238i	0.631648	−	0.229901i
$266$	−357.228	−	41.1454i	−1.34296	−	0.154682i
$267$		0			0
$268$	−205.744	−	192.806i	−0.767702	−	0.719427i
$269$	389.346			1.44738			0.723692	−	0.690123i	$-0.242444\pi$
$269$	389.346			1.44738			0.723692	+	0.690123i	$0.242444\pi$
$270$		0			0
$271$		−	21.9080i		−	0.0808415i	−0.999183	−	0.0404207i	$-0.987130\pi$
$271$		−	21.9080i		−	0.0808415i	0.999183	−	0.0404207i	$-0.0128698\pi$
$272$	41.9103	−	57.0928i	0.154082	−	0.209900i
$273$		0			0
$274$	−428.785	−	49.3872i	−1.56491	−	0.180245i
$275$	7.23394	+	19.8751i	0.0263053	+	0.0722731i
$276$		0			0
$277$	−30.1679	−	171.091i	−0.108909	−	0.617656i	−0.989587	−	0.143939i	$-0.954023\pi$
$277$	−30.1679	−	171.091i	−0.108909	−	0.617656i	0.880677	−	0.473717i	$-0.157088\pi$
$278$	−188.452	−	285.480i	−0.677883	−	1.02691i
$279$		0			0
$280$	−88.5546	+	247.173i	−0.316267	+	0.882761i
$281$	31.0959	+	11.3180i	0.110662	+	0.0402775i	0.396758	−	0.917923i	$-0.370135\pi$
$281$	31.0959	+	11.3180i	0.110662	+	0.0402775i	−0.286096	+	0.958201i	$0.592358\pi$
$282$		0			0
$283$	−272.974	+	325.317i	−0.964571	+	1.14953i	0.0241422	+	0.999709i	$0.492315\pi$
$283$	−272.974	+	325.317i	−0.964571	+	1.14953i	−0.988713	+	0.149822i	$0.952130\pi$
$284$	241.501	−	369.887i	0.850356	−	1.30242i
$285$		0			0
$286$	−28.0603	−	8.34933i	−0.0981130	−	0.0291935i
$287$	−22.5919	−	13.0435i	−0.0787175	−	0.0454476i
$288$		0			0
$289$	134.703	+	233.312i	0.466100	+	0.807310i
$290$	144.001	−	34.3846i	0.496555	−	0.118568i
$291$		0			0
$292$	200.860	−	101.723i	0.687876	−	0.348365i
$293$	52.8107	−	299.504i	0.180241	−	1.02220i	−0.751677	−	0.659531i	$-0.770755\pi$
$293$	52.8107	−	299.504i	0.180241	−	1.02220i	0.931919	−	0.362668i	$-0.118134\pi$
$294$		0			0
$295$	196.815	+	234.555i	0.667170	+	0.795103i
$296$	101.905	+	561.363i	0.344273	+	1.89650i
$297$		0			0
$298$	24.9448	+	416.230i	0.0837073	+	1.39675i
$299$	−200.939	−	239.470i	−0.672038	−	0.800904i
$300$		0			0
$301$	77.0125	−	436.759i	0.255855	−	1.45103i
$302$	−160.914	+	69.7328i	−0.532829	+	0.230903i
$303$		0			0
$304$	264.326	−	116.133i	0.869493	−	0.382017i
$305$	−136.638	−	236.664i	−0.447993	−	0.775946i
$306$		0			0
$307$	183.195	+	105.768i	0.596728	+	0.344521i	0.767753	−	0.640746i	$-0.221375\pi$
$307$	183.195	+	105.768i	0.596728	+	0.344521i	−0.171025	+	0.985267i	$0.554708\pi$
$308$	−58.0119	−	13.5432i	−0.188350	−	0.0439716i
$309$		0			0
$310$	−228.707	−	169.670i	−0.737766	−	0.547321i
$311$	71.2108	−	84.8657i	0.228974	−	0.272880i	−0.639309	−	0.768950i	$-0.720780\pi$
$311$	71.2108	−	84.8657i	0.228974	−	0.272880i	0.868283	+	0.496070i	$0.165224\pi$
$312$		0			0
$313$	−120.238	−	43.7630i	−0.384147	−	0.139818i	0.142726	−	0.989762i	$-0.454413\pi$
$313$	−120.238	−	43.7630i	−0.384147	−	0.139818i	−0.526873	+	0.849944i	$0.676635\pi$
$314$	−111.352	−	55.6889i	−0.354625	−	0.177353i
$315$		0			0
$316$	−342.941	+	257.106i	−1.08526	+	0.813628i
$317$	4.29263	+	24.3447i	0.0135414	+	0.0767973i	0.990830	−	0.135117i	$-0.0431412\pi$
$317$	4.29263	+	24.3447i	0.0135414	+	0.0767973i	−0.977288	+	0.211915i	$0.932030\pi$
$318$		0			0
$319$	11.4888	+	31.5652i	0.0360150	+	0.0989504i
$320$	−38.6981	−	207.224i	−0.120931	−	0.647574i
$321$		0			0
$322$	−437.294	−	461.947i	−1.35806	−	1.43462i
$323$		−	79.8744i		−	0.247289i
$324$		0			0
$325$	−138.583			−0.426408
$326$	−114.363	+	108.260i	−0.350806	+	0.332085i
$327$		0			0
$328$	20.9448	−	0.105625i	0.0638560	−	0.000322027i
$329$	−77.6119	+	28.2484i	−0.235902	+	0.0858615i
$330$		0			0
$331$	−51.7798	+	9.13017i	−0.156434	+	0.0275836i	−0.251317	−	0.967905i	$-0.580864\pi$
$331$	−51.7798	+	9.13017i	−0.156434	+	0.0275836i	0.0948824	+	0.995488i	$0.469752\pi$
$332$	106.590	−	79.9119i	0.321055	−	0.240699i
$333$		0			0
$334$	−92.0342	+	184.026i	−0.275551	+	0.550975i
$335$	−79.4131	+	218.186i	−0.237054	+	0.651300i
$336$		0			0
$337$	69.1763	+	58.0458i	0.205271	+	0.172243i	0.739628	−	0.673016i	$-0.235002\pi$
$337$	69.1763	+	58.0458i	0.205271	+	0.172243i	−0.534357	+	0.845259i	$0.679446\pi$
$338$	−87.0940	+	117.399i	−0.257674	+	0.347334i
$339$		0			0
$340$	−56.7938	−	13.2589i	−0.167041	−	0.0389967i
$341$	32.3059	−	55.9555i	0.0947388	−	0.164092i
$342$		0			0
$343$	−11.0476	+	6.37834i	−0.0322088	+	0.0185957i
$344$	123.473	+	333.989i	0.358933	+	0.970897i
$345$		0			0
$346$	98.4425	+	227.165i	0.284516	+	0.656545i
$347$	153.875	+	27.1323i	0.443444	+	0.0781912i	0.390912	−	0.920428i	$-0.372160\pi$
$347$	153.875	+	27.1323i	0.443444	+	0.0781912i	0.0525323	+	0.998619i	$0.483271\pi$
$348$		0			0
$349$	314.328	−	263.753i	0.900654	−	0.755738i	−0.0696643	−	0.997570i	$-0.522193\pi$
$349$	314.328	−	263.753i	0.900654	−	0.755738i	0.970318	+	0.241832i	$0.0777484\pi$
$350$	−281.486	+	16.8695i	−0.804247	+	0.0481987i
$351$		0			0
$352$	45.7036	−	14.1024i	0.129840	−	0.0400636i
$353$	−299.202	+	251.060i	−0.847597	+	0.711219i	−0.959259	−	0.282528i	$-0.908827\pi$
$353$	−299.202	+	251.060i	−0.847597	+	0.711219i	0.111662	+	0.993746i	$0.464383\pi$
$354$		0			0
$355$	−358.234	−	63.1664i	−1.00911	−	0.177934i
$356$	65.2962	−	33.0684i	0.183416	−	0.0928887i
$357$		0			0
$358$	−76.3201	−	319.624i	−0.213185	−	0.892806i
$359$	288.076	−	166.321i	0.802441	−	0.463290i	−0.0418827	−	0.999123i	$-0.513336\pi$
$359$	288.076	−	166.321i	0.802441	−	0.463290i	0.844324	+	0.535833i	$0.180002\pi$
$360$		0			0
$361$	−17.6970	+	30.6521i	−0.0490222	+	0.0849089i
$362$	54.0532	−	181.661i	0.149318	−	0.501826i
$363$		0			0
$364$	213.389	−	326.831i	0.586235	−	0.897887i
$365$	−142.026	−	119.174i	−0.389112	−	0.326504i
$366$		0			0
$367$	37.8093	−	103.880i	0.103023	−	0.283052i	−0.877463	−	0.479645i	$-0.840765\pi$
$367$	37.8093	−	103.880i	0.103023	−	0.283052i	0.980485	+	0.196593i	$0.0629877\pi$
$368$	490.238	+	143.183i	1.33217	+	0.389084i
$369$		0			0
$370$	392.090	−	258.827i	1.05970	−	0.699533i
$371$	−530.659	+	93.5694i	−1.43035	+	0.252209i
$372$		0			0
$373$	136.487	−	49.6773i	0.365918	−	0.133183i	−0.152516	−	0.988301i	$-0.548738\pi$
$373$	136.487	−	49.6773i	0.365918	−	0.133183i	0.518434	+	0.855118i	$0.326515\pi$
$374$	1.51410	−	13.1455i	0.00404839	−	0.0351485i
$375$		0			0
$376$	42.3687	−	51.0133i	0.112683	−	0.135674i
$377$	−220.094			−0.583803
$378$		0			0
$379$			383.589i			1.01211i	0.862502	+	0.506054i	$0.168896\pi$
$379$			383.589i			1.01211i	−0.862502	+	0.506054i	$0.831104\pi$
$380$	−173.476	−	162.567i	−0.456516	−	0.427809i
$381$		0			0
$382$	48.8435	−	424.064i	0.127863	−	1.11012i
$383$	−95.1799	−	261.505i	−0.248511	−	0.682779i	−0.999741	−	0.0227390i	$-0.992761\pi$
$383$	−95.1799	−	261.505i	−0.248511	−	0.682779i	0.751230	−	0.660040i	$-0.229461\pi$
$384$		0			0
$385$	8.51832	+	48.3098i	0.0221255	+	0.125480i
$386$	338.899	−	223.715i	0.877977	−	0.579571i
$387$		0			0
$388$	116.249	−	272.006i	0.299611	−	0.701047i
$389$	−431.452	−	157.036i	−1.10913	−	0.403691i	−0.278456	−	0.960449i	$-0.589823\pi$
$389$	−431.452	−	157.036i	−1.10913	−	0.403691i	−0.830675	+	0.556758i	$0.812045\pi$
$390$		0			0
$391$	90.8221	−	108.238i	0.232282	−	0.276822i
$392$	199.362	−	349.362i	0.508576	−	0.891229i
$393$		0			0
$394$	75.7862	−	254.701i	0.192351	−	0.646449i
$395$	305.663	+	176.475i	0.773830	+	0.446771i
$396$		0			0
$397$	23.8466	+	41.3035i	0.0600670	+	0.104039i	0.894495	−	0.447078i	$-0.147535\pi$
$397$	23.8466	+	41.3035i	0.0600670	+	0.104039i	−0.834428	+	0.551117i	$0.814202\pi$
$398$	−45.8090	−	191.846i	−0.115098	−	0.482024i
$399$		0			0
$400$	188.321	−	125.683i	0.470804	−	0.314208i
$401$	−17.2725	+	97.9571i	−0.0430735	+	0.244282i	−0.998741	−	0.0501664i	$-0.984025\pi$
$401$	−17.2725	+	97.9571i	−0.0430735	+	0.244282i	0.955667	+	0.294448i	$0.0951359\pi$
$402$		0			0
$403$	272.123	+	324.304i	0.675244	+	0.804724i
$404$	695.964	−	83.7193i	1.72268	−	0.207226i
$405$		0			0
$406$	−447.050	+	26.7918i	−1.10111	+	0.0659897i
$407$	68.5189	+	81.6577i	0.168351	+	0.200633i
$408$		0			0
$409$	−41.3507	+	234.511i	−0.101102	+	0.573377i	0.891604	+	0.452816i	$0.149581\pi$
$409$	−41.3507	+	234.511i	−0.101102	+	0.573377i	−0.992706	+	0.120561i	$0.961531\pi$
$410$	−6.85797	−	15.8254i	−0.0167268	−	0.0385984i
$411$		0			0
$412$	157.601	−	47.7605i	0.382526	−	0.115924i
$413$	−463.116	−	802.140i	−1.12135	−	1.94223i
$414$		0			0
$415$	−95.0039	−	54.8505i	−0.228925	−	0.132170i
$416$	−15.5918	+	313.002i	−0.0374803	+	0.752408i
$417$		0			0
$418$	32.1390	−	43.3220i	0.0768876	−	0.103641i
$419$	−371.181	+	442.356i	−0.885872	+	1.05574i	0.112200	+	0.993686i	$0.464210\pi$
$419$	−371.181	+	442.356i	−0.885872	+	1.05574i	−0.998073	+	0.0620560i	$0.980234\pi$
$420$		0			0
$421$	123.109	+	44.8078i	0.292419	+	0.106432i	0.484064	−	0.875032i	$-0.339160\pi$
$421$	123.109	+	44.8078i	0.292419	+	0.106432i	−0.191645	+	0.981464i	$0.561382\pi$
$422$	−178.978	+	357.872i	−0.424117	+	0.848039i
$423$		0			0
$424$	330.011	−	279.761i	0.778329	−	0.659813i
$425$	−10.8769	−	61.6861i	−0.0255928	−	0.145144i
$426$		0			0
$427$	282.736	+	776.810i	0.662145	+	1.81923i
$428$	148.676	+	8.15792i	0.347373	+	0.0190606i
$429$		0			0
$430$	212.941	−	201.577i	0.495213	−	0.468785i
$431$			307.551i			0.713576i	0.934185	+	0.356788i	$0.116128\pi$
$431$			307.551i			0.713576i	−0.934185	+	0.356788i	$0.883872\pi$
$432$		0			0
$433$	506.142			1.16892			0.584460	−	0.811423i	$-0.301307\pi$
$433$	506.142			1.16892			0.584460	+	0.811423i	$0.301307\pi$
$434$	592.208	+	625.594i	1.36454	+	1.44146i
$435$		0			0
$436$	−6.78965	+	123.739i	−0.0155726	+	0.283806i
$437$	541.246	−	196.997i	1.23855	−	0.450795i
$438$		0			0
$439$	−754.597	+	133.056i	−1.71890	+	0.303088i	−0.944232	−	0.329281i	$-0.893194\pi$
$439$	−754.597	+	133.056i	−1.71890	+	0.303088i	−0.774667	+	0.632370i	$0.782082\pi$
$440$	−25.4687	−	30.0434i	−0.0578834	−	0.0682804i
$441$		0			0
$442$	77.5445	+	38.7812i	0.175440	+	0.0877403i
$443$	−124.615	+	342.378i	−0.281299	+	0.772863i	0.715909	+	0.698193i	$0.246012\pi$
$443$	−124.615	+	342.378i	−0.281299	+	0.772863i	−0.997208	+	0.0746693i	$0.976210\pi$
$444$		0			0
$445$	−46.1703	−	38.7415i	−0.103753	−	0.0870595i
$446$	209.220	+	155.213i	0.469103	+	0.348010i
$447$		0			0
$448$	6.43163	+	637.660i	0.0143563	+	1.42335i
$449$	−118.549	+	205.332i	−0.264028	+	0.457310i	−0.967308	−	0.253603i	$-0.918384\pi$
$449$	−118.549	+	205.332i	−0.264028	+	0.457310i	0.703281	+	0.710912i	$0.251718\pi$
$450$		0			0
$451$	3.38899	−	1.95664i	0.00751440	−	0.00433844i
$452$	−232.748	−	768.025i	−0.514929	−	1.69917i
$453$		0			0
$454$	−88.6121	+	38.4003i	−0.195181	+	0.0845822i
$455$	−316.534	−	55.8135i	−0.695680	−	0.122667i
$456$		0			0
$457$	−442.073	+	370.943i	−0.967336	+	0.811692i	−0.982131	−	0.188199i	$-0.939735\pi$
$457$	−442.073	+	370.943i	−0.967336	+	0.811692i	0.0147946	+	0.999891i	$0.495291\pi$
$458$	−9.97697	−	166.476i	−0.0217838	−	0.363486i
$459$		0			0
$460$	−50.2279	−	417.548i	−0.109191	−	0.907713i
$461$	166.429	−	139.651i	0.361018	−	0.302930i	−0.444178	−	0.895938i	$-0.646504\pi$
$461$	166.429	−	139.651i	0.361018	−	0.302930i	0.805196	+	0.593008i	$0.202060\pi$
$462$		0			0
$463$	−0.639575	−	0.112774i	−0.00138137	−	0.000243573i	0.172957	−	0.984929i	$-0.444668\pi$
$463$	−0.639575	−	0.112774i	−0.00138137	−	0.000243573i	−0.174339	+	0.984686i	$0.555779\pi$
$464$	299.088	−	199.607i	0.644586	−	0.430187i
$465$		0			0
$466$	709.631	−	169.446i	1.52281	−	0.363618i
$467$	−756.889	+	436.990i	−1.62075	+	0.935738i	−0.634026	+	0.773312i	$0.718599\pi$
$467$	−756.889	+	436.990i	−1.62075	+	0.935738i	−0.986721	+	0.162426i	$0.948068\pi$
$468$		0			0
$469$	351.187	−	608.274i	0.748800	−	1.29696i
$470$	−52.3387	−	15.5734i	−0.111359	−	0.0331348i
$471$		0			0
$472$	645.901	+	368.581i	1.36843	+	0.780891i
$473$	50.9639	+	42.7638i	0.107746	+	0.0904096i
$474$		0			0
$475$	87.3318	−	239.942i	0.183856	−	0.505141i
$476$	162.228	+	69.3322i	0.340814	+	0.145656i
$477$		0			0
$478$	−0.454313	−	0.688227i	−0.000950446	−	0.00143981i
$479$	459.413	−	81.0069i	0.959108	−	0.169117i	0.327885	−	0.944718i	$-0.393664\pi$
$479$	459.413	−	81.0069i	0.959108	−	0.169117i	0.631223	+	0.775601i	$0.282553\pi$
$480$		0			0
$481$	−656.318	+	238.880i	−1.36449	+	0.496633i
$482$	405.107	+	46.6601i	0.840472	+	0.0968052i
$483$		0			0
$484$	−324.845	+	346.643i	−0.671167	+	0.716204i
$485$	−243.585			−0.502236
$486$		0			0
$487$			209.497i			0.430178i	0.976594	+	0.215089i	$0.0690042\pi$
$487$			209.497i			0.430178i	−0.976594	+	0.215089i	$0.930996\pi$
$488$	−510.587	−	424.064i	−1.04629	−	0.868984i
$489$		0			0
$490$	−329.055	−	37.9005i	−0.671542	−	0.0773479i
$491$	−244.348	−	671.341i	−0.497654	−	1.36729i	−0.893536	−	0.448992i	$-0.851783\pi$
$491$	−244.348	−	671.341i	−0.497654	−	1.36729i	0.395882	−	0.918302i	$-0.370439\pi$
$492$		0			0
$493$	−17.2745	−	97.9684i	−0.0350395	−	0.198719i
$494$	194.712	+	294.965i	0.394155	+	0.597094i
$495$		0			0
$496$	−663.908	−	193.906i	−1.33852	−	0.390940i
$497$	1034.02	+	376.353i	2.08053	+	0.757250i
$498$		0			0
$499$	389.541	−	464.236i	0.780642	−	0.930333i	−0.218320	−	0.975877i	$-0.570058\pi$
$499$	389.541	−	464.236i	0.780642	−	0.930333i	0.998962	+	0.0455438i	$0.0145021\pi$
$500$	−431.915	−	281.999i	−0.863830	−	0.563999i
$501$		0			0
$502$	−271.413	−	80.7587i	−0.540663	−	0.160874i
$503$	−679.865	−	392.520i	−1.35162	−	0.780358i	−0.363143	−	0.931733i	$-0.618296\pi$
$503$	−679.865	−	392.520i	−1.35162	−	0.780358i	−0.988476	+	0.151376i	$0.951630\pi$
$504$		0			0
$505$	−288.616	−	499.897i	−0.571516	−	0.989895i
$506$	92.8113	−	22.1615i	0.183422	−	0.0437975i
$507$		0			0
$508$	54.4532	+	107.522i	0.107191	+	0.211658i
$509$	−48.3318	+	274.104i	−0.0949545	+	0.538514i	0.899807	+	0.436289i	$0.143707\pi$
$509$	−48.3318	+	274.104i	−0.0949545	+	0.538514i	−0.994761	+	0.102225i	$0.967404\pi$
$510$		0			0
$511$	360.504	+	429.631i	0.705486	+	0.840766i
$512$	−262.679	−	439.481i	−0.513044	−	0.858362i
$513$		0			0
$514$	−28.9176	−	482.521i	−0.0562599	−	0.938756i
$515$	−87.1662	−	103.881i	−0.169255	−	0.201710i
$516$		0			0
$517$	2.15145	−	12.2015i	0.00416140	−	0.0236005i
$518$	−1304.02	+	565.102i	−2.51742	+	1.09093i
$519$		0			0
$520$	242.053	−	89.4850i	0.465486	−	0.172086i
$521$	377.300	+	653.504i	0.724185	+	1.25433i	0.959309	+	0.282360i	$0.0911172\pi$
$521$	377.300	+	653.504i	0.724185	+	1.25433i	−0.235123	+	0.971966i	$0.575549\pi$
$522$		0			0
$523$	141.132	+	81.4826i	0.269851	+	0.155798i	0.628820	−	0.777551i	$-0.283538\pi$
$523$	141.132	+	81.4826i	0.269851	+	0.155798i	−0.358969	+	0.933349i	$0.616872\pi$
$524$	−19.6694	+	84.2532i	−0.0375371	+	0.160789i
$525$		0			0
$526$	243.940	+	180.970i	0.463764	+	0.344049i
$527$	−122.996	+	146.581i	−0.233390	+	0.278143i
$528$		0			0
$529$	460.342	+	167.551i	0.870212	+	0.316731i
$530$	−318.633	−	159.353i	−0.601194	−	0.300666i
$531$		0			0
$532$	431.402	+	575.424i	0.810905	+	1.08162i
$533$	4.45242	+	25.2509i	0.00835351	+	0.0473751i
$534$		0			0
$535$	−41.9360	−	115.218i	−0.0783851	−	0.215361i
$536$	2.84389	+	563.925i	0.00530576	+	1.05210i
$537$		0			0
$538$	−535.323	−	565.501i	−0.995023	−	1.05112i
$539$		−	75.1531i		−	0.139431i
$540$		0			0
$541$	737.486			1.36319			0.681595	−	0.731729i	$-0.261286\pi$
$541$	737.486			1.36319			0.681595	+	0.731729i	$0.261286\pi$
$542$	−31.8201	+	30.1220i	−0.0587086	+	0.0555756i
$543$		0			0
$544$	−140.547	+	17.6263i	−0.258359	+	0.0324012i
$545$	95.8936	−	34.9024i	0.175952	−	0.0640411i
$546$		0			0
$547$	−869.124	+	153.250i	−1.58889	+	0.280165i	−0.897065	−	0.441899i	$-0.854305\pi$
$547$	−869.124	+	153.250i	−1.58889	+	0.280165i	−0.691827	+	0.722063i	$0.743194\pi$
$548$	517.816	+	690.687i	0.944919	+	1.26038i
$549$		0			0
$550$	18.9212	−	37.8337i	0.0344022	−	0.0687885i
$551$	138.698	−	381.070i	0.251721	−	0.691598i
$552$		0			0
$553$	−817.889	−	686.290i	−1.47900	−	1.24103i
$554$	−207.020	+	279.054i	−0.373682	+	0.503708i
$555$		0			0
$556$	−155.535	+	666.229i	−0.279740	+	1.19825i
$557$	60.6879	−	105.114i	0.108955	−	0.188715i	−0.806392	−	0.591381i	$-0.798583\pi$
$557$	60.6879	−	105.114i	0.108955	−	0.188715i	0.915347	+	0.402666i	$0.131916\pi$
$558$		0			0
$559$	−377.507	+	217.954i	−0.675325	+	0.389899i
$560$	480.760	−	211.225i	0.858500	−	0.377187i
$561$		0			0
$562$	−26.3159	−	60.7263i	−0.0468255	−	0.108054i
$563$	455.146	+	80.2545i	0.808430	+	0.142548i	0.562562	−	0.826755i	$-0.309816\pi$
$563$	455.146	+	80.2545i	0.808430	+	0.142548i	0.245868	+	0.969303i	$0.420927\pi$
$564$		0			0
$565$	−506.234	+	424.781i	−0.895990	+	0.751825i
$566$	847.822	−	50.8101i	1.49792	−	0.0897706i
$567$		0			0
$568$	−869.285	+	157.803i	−1.53043	+	0.277821i
$569$	−684.076	+	574.008i	−1.20224	+	1.00880i	−0.202680	+	0.979245i	$0.564965\pi$
$569$	−684.076	+	574.008i	−1.20224	+	1.00880i	−0.999563	+	0.0295562i	$0.990591\pi$
$570$		0			0
$571$	−508.791	−	89.7136i	−0.891052	−	0.157117i	−0.290664	−	0.956825i	$-0.593876\pi$
$571$	−508.791	−	89.7136i	−0.891052	−	0.157117i	−0.600388	+	0.799709i	$0.704987\pi$
$572$	26.4540	+	52.2356i	0.0462482	+	0.0913209i
$573$		0			0
$574$	12.1174	+	50.7472i	0.0211105	+	0.0884097i
$575$	391.172	−	225.843i	0.680299	−	0.392771i
$576$		0			0
$577$	−395.771	+	685.495i	−0.685911	+	1.18803i	0.287238	+	0.957859i	$0.407263\pi$
$577$	−395.771	+	685.495i	−0.685911	+	1.18803i	−0.973150	+	0.230174i	$0.926071\pi$
$578$	153.665	−	516.435i	0.265857	−	0.893487i
$579$		0			0
$580$	−247.932	−	161.876i	−0.427470	−	0.279097i
$581$	254.210	+	213.308i	0.437539	+	0.367139i
$582$		0			0
$583$	27.6460	−	75.9569i	0.0474203	−	0.130286i
$584$	−423.913	−	151.875i	−0.725879	−	0.260060i
$585$		0			0
$586$	−507.622	+	335.092i	−0.866249	+	0.571830i
$587$	81.2525	−	14.3270i	0.138420	−	0.0244072i	−0.104009	−	0.994576i	$-0.533167\pi$
$587$	81.2525	−	14.3270i	0.138420	−	0.0244072i	0.242429	+	0.970169i	$0.422056\pi$
$588$		0			0
$589$	−732.985	+	266.785i	−1.24446	+	0.452946i
$590$	70.0705	−	608.358i	0.118764	−	1.03112i
$591$		0			0
$592$	675.233	−	919.843i	1.14060	−	1.55379i
$593$	222.673			0.375503			0.187751	−	0.982217i	$-0.439880\pi$
$593$	222.673			0.375503			0.187751	+	0.982217i	$0.439880\pi$
$594$		0			0
$595$		−	145.277i		−	0.244163i
$596$	570.252	−	608.517i	0.956798	−	1.02100i
$597$		0			0
$598$	−71.5387	+	621.106i	−0.119630	+	1.03864i
$599$	299.957	+	824.125i	0.500763	+	1.37583i	0.890532	+	0.454921i	$0.150333\pi$
$599$	299.957	+	824.125i	0.500763	+	1.37583i	−0.389769	+	0.920913i	$0.627445\pi$
$600$		0			0
$601$	185.751	+	1053.45i	0.309070	+	1.75282i	0.603701	+	0.797211i	$0.293692\pi$
$601$	185.751	+	1053.45i	0.309070	+	1.75282i	−0.294632	+	0.955611i	$0.595197\pi$
$602$	−740.252	+	488.656i	−1.22966	+	0.811722i
$603$		0			0
$604$	322.528	+	137.841i	0.533987	+	0.228213i
$605$	367.605	+	133.797i	0.607611	+	0.221152i
$606$		0			0
$607$	248.589	−	296.257i	0.409538	−	0.488068i	−0.521366	−	0.853333i	$-0.674577\pi$
$607$	248.589	−	296.257i	0.409538	−	0.488068i	0.930904	+	0.365265i	$0.119022\pi$
$608$	−532.105	−	224.242i	−0.875173	−	0.368820i
$609$		0			0
$610$	−155.872	+	523.853i	−0.255528	+	0.858776i
$611$	70.3034	+	40.5897i	0.115063	+	0.0664316i
$612$		0			0
$613$	−415.861	−	720.293i	−0.678403	−	1.17503i	−0.975462	−	0.220169i	$-0.929339\pi$
$613$	−415.861	−	720.293i	−0.678403	−	1.17503i	0.297058	−	0.954859i	$-0.403994\pi$
$614$	−98.2590	−	411.503i	−0.160031	−	0.670201i
$615$		0			0
$616$	60.0914	+	102.880i	0.0975509	+	0.167012i
$617$	139.903	−	793.430i	0.226747	−	1.28595i	−0.632569	−	0.774504i	$-0.718000\pi$
$617$	139.903	−	793.430i	0.226747	−	1.28595i	0.859317	−	0.511444i	$-0.170889\pi$
$618$		0			0
$619$	187.623	+	223.600i	0.303106	+	0.361228i	0.896001	−	0.444052i	$-0.146459\pi$
$619$	187.623	+	223.600i	0.303106	+	0.361228i	−0.592895	+	0.805280i	$0.702015\pi$
$620$	68.0214	+	565.466i	0.109712	+	0.912043i
$621$		0			0
$622$	−221.172	+	13.2549i	−0.355582	+	0.0213101i
$623$	117.194	+	139.666i	0.188112	+	0.224183i
$624$		0			0
$625$	−12.3284	+	69.9178i	−0.0197254	+	0.111868i
$626$	101.755	+	234.809i	0.162548	+	0.375094i
$627$		0			0
$628$	72.2163	+	238.300i	0.114994	+	0.379459i
$629$	−157.843	−	273.392i	−0.250943	−	0.434646i
$630$		0			0
$631$	−598.496	−	345.542i	−0.948488	−	0.547610i	−0.0558770	−	0.998438i	$-0.517795\pi$
$631$	−598.496	−	345.542i	−0.948488	−	0.547610i	−0.892611	+	0.450828i	$0.851129\pi$
$632$	844.950	+	144.598i	1.33695	+	0.228794i
$633$		0			0
$634$	29.4572	−	39.7070i	0.0464624	−	0.0626294i
$635$	63.7950	−	76.0280i	0.100465	−	0.119729i
$636$		0			0
$637$	462.720	+	168.416i	0.726405	+	0.264390i
$638$	30.0502	−	60.0865i	0.0471007	−	0.0941795i
$639$		0			0
$640$	−247.773	+	341.124i	−0.387145	+	0.533006i
$641$	136.341	+	773.228i	0.212700	+	1.20628i	0.884853	+	0.465871i	$0.154259\pi$
$641$	136.341	+	773.228i	0.212700	+	1.20628i	−0.672153	+	0.740413i	$0.734630\pi$
$642$		0			0
$643$	112.920	+	310.245i	0.175614	+	0.482496i	0.996004	−	0.0893087i	$-0.0284658\pi$
$643$	112.920	+	310.245i	0.175614	+	0.482496i	−0.820390	+	0.571805i	$0.806244\pi$
$644$	−69.7014	+	1270.29i	−0.108232	+	1.97249i
$645$		0			0
$646$	−116.013	+	109.821i	−0.179586	+	0.170002i
$647$		−	629.667i		−	0.973210i	−0.873622	−	0.486605i	$-0.838235\pi$
$647$		−	629.667i		−	0.973210i	0.873622	−	0.486605i	$-0.161765\pi$
$648$		0			0
$649$	138.943			0.214088
$650$	190.541	+	201.283i	0.293140	+	0.309666i
$651$		0			0
$652$	314.481	+	17.2558i	0.482333	+	0.0264659i
$653$	−327.426	+	119.173i	−0.501418	+	0.182501i	−0.580332	−	0.814380i	$-0.697077\pi$
$653$	−327.426	+	119.173i	−0.501418	+	0.182501i	0.0789137	+	0.996881i	$0.474855\pi$
$654$		0			0
$655$	70.1624	−	12.3715i	0.107118	−	0.0188878i
$656$	−28.9509	−	30.2758i	−0.0441325	−	0.0461521i
$657$		0			0
$658$	147.740	+	73.8870i	0.224529	+	0.112290i
$659$	298.779	−	820.890i	0.453383	−	1.24566i	−0.476946	−	0.878933i	$-0.658256\pi$
$659$	298.779	−	820.890i	0.453383	−	1.24566i	0.930329	−	0.366727i	$-0.119522\pi$
$660$		0			0
$661$	449.891	+	377.504i	0.680622	+	0.571110i	0.916188	−	0.400749i	$-0.131250\pi$
$661$	449.891	+	377.504i	0.680622	+	0.571110i	−0.235566	+	0.971858i	$0.575694\pi$
$662$	84.4544	+	62.6536i	0.127575	+	0.0946429i
$663$		0			0
$664$	−262.621	−	44.9428i	−0.395514	−	0.0676849i
$665$	296.108	−	512.875i	0.445276	−	0.771241i
$666$		0			0
$667$	621.250	−	358.679i	0.931410	−	0.537750i
$668$	393.826	−	119.348i	0.589560	−	0.178665i
$669$		0			0
$670$	426.088	−	184.647i	0.635953	−	0.275592i
$671$	−122.123	−	21.5336i	−0.182002	−	0.0320918i
$672$		0			0
$673$	610.053	−	511.895i	0.906468	−	0.760617i	−0.0649756	−	0.997887i	$-0.520697\pi$
$673$	610.053	−	511.895i	0.906468	−	0.760617i	0.971444	+	0.237270i	$0.0762525\pi$
$674$	−10.8044	−	180.283i	−0.0160303	−	0.267482i
$675$		0			0
$676$	290.263	−	34.9164i	0.429383	−	0.0516515i
$677$	−37.5532	+	31.5108i	−0.0554699	+	0.0465448i	−0.670101	−	0.742270i	$-0.733749\pi$
$677$	−37.5532	+	31.5108i	−0.0554699	+	0.0465448i	0.614631	+	0.788815i	$0.289305\pi$
$678$		0			0
$679$	725.654	+	127.952i	1.06871	+	0.188442i
$680$	58.8296	+	100.719i	0.0865141	+	0.148117i
$681$		0			0
$682$	−125.690	+	30.0124i	−0.184297	+	0.0440064i
$683$	−694.858	+	401.177i	−1.01736	+	0.587374i	−0.913339	−	0.407201i	$-0.866505\pi$
$683$	−694.858	+	401.177i	−1.01736	+	0.587374i	−0.104023	+	0.994575i	$0.533172\pi$
$684$		0			0
$685$	355.422	−	615.609i	0.518864	−	0.898699i
$686$	24.4538	+	7.27622i	0.0356469	+	0.0106067i
$687$		0			0
$688$	315.332	−	638.547i	0.458331	−	0.928120i
$689$	405.715	+	340.435i	0.588846	+	0.494100i
$690$		0			0
$691$	240.011	−	659.425i	0.347339	−	0.954306i	−0.635866	−	0.771800i	$-0.719357\pi$
$691$	240.011	−	659.425i	0.347339	−	0.954306i	0.983205	−	0.182506i	$-0.0584209\pi$
$692$	194.591	−	455.316i	0.281201	−	0.657972i
$693$		0			0
$694$	−172.159	−	260.799i	−0.248068	−	0.375791i
$695$	554.807	−	97.8274i	0.798283	−	0.140759i
$696$		0			0
$697$	−10.8903	+	3.96373i	−0.0156245	+	0.00568685i
$698$	−815.263	−	93.9016i	−1.16800	−	0.134530i
$699$		0			0
$700$	411.525	+	385.647i	0.587893	+	0.550924i
$701$	−1238.63			−1.76695			−0.883473	−	0.468482i	$-0.844801\pi$
$701$	−1238.63			−1.76695			−0.883473	+	0.468482i	$0.844801\pi$
$702$		0			0
$703$		−	1286.89i		−	1.83056i
$704$	−83.3219	−	46.9919i	−0.118355	−	0.0667498i
$705$		0			0
$706$	776.030	+	89.3828i	1.09919	+	0.126605i
$707$	597.214	+	1640.83i	0.844716	+	2.32084i
$708$		0			0
$709$	199.491	+	1131.37i	0.281370	+	1.59573i	0.717971	+	0.696073i	$0.245071\pi$
$709$	199.491	+	1131.37i	0.281370	+	1.59573i	−0.436601	+	0.899655i	$0.643818\pi$
$710$	400.801	+	607.162i	0.564508	+	0.855158i
$711$		0			0
$712$	−137.807	−	49.3722i	−0.193550	−	0.0693429i
$713$	−1296.62	−	471.930i	−1.81854	−	0.661894i
$714$		0			0
$715$	30.9923	−	36.9352i	0.0433459	−	0.0516577i
$716$	−359.300	+	550.310i	−0.501816	+	0.768590i
$717$		0			0
$718$	−637.655	−	189.734i	−0.888099	−	0.264253i
$719$	73.9087	+	42.6712i	0.102794	+	0.0593480i	0.550516	−	0.834825i	$-0.314431\pi$
$719$	73.9087	+	42.6712i	0.102794	+	0.0593480i	−0.447722	+	0.894173i	$0.647765\pi$
$720$		0			0
$721$	205.106	+	355.255i	0.284475	+	0.492725i
$722$	68.8524	−	16.4406i	0.0953634	−	0.0227709i
$723$		0			0
$724$	−338.171	+	171.262i	−0.467087	+	0.236549i
$725$	55.2227	−	313.184i	0.0761693	−	0.431977i
$726$		0			0
$727$	683.362	+	814.399i	0.939975	+	1.12022i	0.992579	+	0.121603i	$0.0388034\pi$
$727$	683.362	+	814.399i	0.939975	+	1.12022i	−0.0526041	+	0.998615i	$0.516752\pi$
$728$	−768.096	+	139.434i	−1.05508	+	0.191530i
$729$		0			0
$730$	22.1825	+	370.139i	0.0303870	+	0.507040i
$731$	−126.645	−	150.930i	−0.173249	−	0.206470i
$732$		0			0
$733$	89.9972	−	510.399i	0.122779	−	0.696315i	−0.859823	−	0.510592i	$-0.829426\pi$
$733$	89.9972	−	510.399i	0.122779	−	0.696315i	0.982602	−	0.185723i	$-0.0594627\pi$
$734$	−202.865	+	87.9120i	−0.276382	+	0.119771i
$735$		0			0
$736$	−466.077	−	908.907i	−0.633257	−	1.23493i
$737$	52.6813	+	91.2466i	0.0714807	+	0.123808i
$738$		0			0
$739$	360.111	+	207.910i	0.487295	+	0.281340i	0.723452	−	0.690375i	$-0.242554\pi$
$739$	360.111	+	207.910i	0.487295	+	0.281340i	−0.236157	+	0.971715i	$0.575888\pi$
$740$	−915.026	−	213.619i	−1.23652	−	0.288674i
$741$		0			0
$742$	865.520	+	642.098i	1.16647	+	0.865361i
$743$	69.2890	−	82.5754i	0.0932557	−	0.111138i	−0.717398	−	0.696663i	$-0.754667\pi$
$743$	69.2890	−	82.5754i	0.0932557	−	0.111138i	0.810654	+	0.585525i	$0.199112\pi$
$744$		0			0
$745$	−645.314	−	234.875i	−0.866194	−	0.315269i
$746$	−259.813	−	129.937i	−0.348275	−	0.174178i
$747$		0			0
$748$	−21.1749	+	15.8750i	−0.0283086	+	0.0212233i
$749$	64.4072	+	365.271i	0.0859909	+	0.487678i
$750$		0			0
$751$	−346.070	−	950.819i	−0.460812	−	1.26607i	−0.924876	−	0.380269i	$-0.875831\pi$
$751$	−346.070	−	950.819i	−0.460812	−	1.26607i	0.464064	−	0.885802i	$-0.346391\pi$
$752$	−132.348	+	8.60165i	−0.175994	+	0.0114384i
$753$		0			0
$754$	302.613	+	319.673i	0.401343	+	0.423969i
$755$		−	288.828i		−	0.382553i
$756$		0			0
$757$	629.345			0.831367			0.415683	−	0.909509i	$-0.363542\pi$
$757$	629.345			0.831367			0.415683	+	0.909509i	$0.363542\pi$
$758$	557.139	−	527.406i	0.735012	−	0.695787i
$759$		0			0
$760$	2.39786	+	475.482i	0.00315508	+	0.625634i
$761$	1180.91	−	429.816i	1.55179	−	0.564804i	0.582951	−	0.812507i	$-0.301898\pi$
$761$	1180.91	−	429.816i	1.55179	−	0.564804i	0.968836	+	0.247703i	$0.0796758\pi$
$762$		0			0
$763$	−304.007	+	53.6046i	−0.398436	+	0.0702551i
$764$	−683.083	+	512.115i	−0.894088	+	0.670308i
$765$		0			0
$766$	−248.954	+	497.792i	−0.325005	+	0.649860i
$767$	−311.368	+	855.477i	−0.405956	+	1.11536i
$768$		0			0
$769$	−560.371	−	470.207i	−0.728700	−	0.611452i	0.201077	−	0.979576i	$-0.435556\pi$
$769$	−560.371	−	470.207i	−0.728700	−	0.611452i	−0.929777	+	0.368123i	$0.880000\pi$
$770$	58.4549	−	78.7948i	0.0759155	−	0.102331i
$771$		0			0
$772$	−790.893	−	184.639i	−1.02447	−	0.239170i
$773$	267.621	−	463.532i	0.346210	−	0.599654i	−0.639363	−	0.768905i	$-0.720802\pi$
$773$	267.621	−	463.532i	0.346210	−	0.599654i	0.985573	+	0.169252i	$0.0541351\pi$
$774$		0			0
$775$	−529.747	+	305.849i	−0.683544	+	0.394644i
$776$	−554.906	+	205.144i	−0.715085	+	0.264361i
$777$		0			0
$778$	365.130	+	842.570i	0.469319	+	1.08299i
$779$	−46.5253	−	8.20366i	−0.0597243	−	0.0105310i
$780$		0			0
$781$	−126.449	+	106.103i	−0.161907	+	0.135856i
$782$	−282.082	+	16.9052i	−0.360719	+	0.0216180i
$783$		0			0
$784$	−781.534	+	190.786i	−0.996855	+	0.243350i
$785$	157.073	−	131.800i	0.200093	−	0.167898i
$786$		0			0
$787$	789.624	+	139.232i	1.00333	+	0.176915i	0.651096	−	0.758996i	$-0.274310\pi$
$787$	789.624	+	139.232i	1.00333	+	0.176915i	0.352238	+	0.935910i	$0.385421\pi$
$788$	−474.138	+	240.120i	−0.601698	+	0.304721i
$789$		0			0
$790$	−163.946	−	686.596i	−0.207526	−	0.869109i
$791$	1731.24	−	999.530i	2.18867	−	1.26363i
$792$		0			0
$793$	406.258	−	703.660i	0.512306	−	0.887340i
$794$	27.2035	−	91.4250i	0.0342613	−	0.115145i
$795$		0			0
$796$	−215.660	+	330.308i	−0.270930	+	0.414960i
$797$	−737.833	−	619.115i	−0.925763	−	0.776807i	0.0492893	−	0.998785i	$-0.484304\pi$
$797$	−737.833	−	619.115i	−0.925763	−	0.776807i	−0.975052	+	0.221978i	$0.928749\pi$
$798$		0			0
$799$	−12.5494	+	34.4793i	−0.0157064	+	0.0431531i
$800$	−441.475	−	100.720i	−0.551844	−	0.125900i
$801$		0			0
$802$	166.025	−	109.597i	0.207014	−	0.136654i
$803$	−82.8535	+	14.6093i	−0.103180	+	0.0181934i
$804$		0			0
$805$	984.426	−	358.302i	1.22289	−	0.445096i
$806$	96.8817	−	841.136i	0.120201	−	1.04359i
$807$		0			0
$808$	−1078.50	−	895.737i	−1.33477	−	1.10859i
$809$	−1009.30			−1.24759			−0.623796	−	0.781587i	$-0.714410\pi$
$809$	−1009.30			−1.24759			−0.623796	+	0.781587i	$0.714410\pi$
$810$		0			0
$811$		−	703.838i		−	0.867864i	−0.900946	−	0.433932i	$-0.857126\pi$
$811$		−	703.838i		−	0.867864i	0.900946	−	0.433932i	$-0.142874\pi$
$812$	653.575	+	612.476i	0.804895	+	0.754281i
$813$		0			0
$814$	24.3942	−	211.793i	0.0299683	−	0.260188i
$815$	−88.7038	−	243.712i	−0.108839	−	0.299033i
$816$		0			0
$817$	−139.468	−	790.964i	−0.170708	−	0.968133i
$818$	397.467	−	262.376i	0.485901	−	0.320754i
$819$		0			0
$820$	−13.5562	+	31.7195i	−0.0165319	+	0.0386823i
$821$	25.2468	+	9.18908i	0.0307513	+	0.0111925i	0.357350	−	0.933971i	$-0.383680\pi$
$821$	25.2468	+	9.18908i	0.0307513	+	0.0111925i	−0.326599	+	0.945163i	$0.605903\pi$
$822$		0			0
$823$	−32.2359	+	38.4172i	−0.0391688	+	0.0466795i	−0.785273	−	0.619149i	$-0.787478\pi$
$823$	−32.2359	+	38.4172i	−0.0391688	+	0.0466795i	0.746104	+	0.665829i	$0.231922\pi$
$824$	−286.059	−	163.238i	−0.347159	−	0.198105i
$825$		0			0
$826$	−528.308	+	1775.53i	−0.639599	+	2.14955i
$827$	−74.9392	−	43.2662i	−0.0906157	−	0.0523170i	0.454007	−	0.890998i	$-0.349994\pi$
$827$	−74.9392	−	43.2662i	−0.0906157	−	0.0523170i	−0.544623	+	0.838681i	$0.683327\pi$
$828$		0			0
$829$	205.168	+	355.361i	0.247488	+	0.428662i	0.962828	−	0.270114i	$-0.0870615\pi$
$829$	205.168	+	355.361i	0.247488	+	0.428662i	−0.715340	+	0.698777i	$0.753728\pi$
$830$	50.9564	+	213.403i	0.0613932	+	0.257112i
$831$		0			0
$832$	476.053	−	407.708i	0.572179	−	0.490034i
$833$	−38.6482	+	219.185i	−0.0463964	+	0.263127i
$834$		0			0
$835$	−217.818	−	259.586i	−0.260860	−	0.310881i
$836$	−107.111	+	12.8847i	−0.128124	+	0.0154123i
$837$		0			0
$838$	1152.84	−	69.0900i	1.37570	−	0.0824463i
$839$	564.691	+	672.972i	0.673052	+	0.802112i	0.989196	−	0.146599i	$-0.0468327\pi$
$839$	564.691	+	672.972i	0.673052	+	0.802112i	−0.316144	+	0.948711i	$0.602388\pi$
$840$		0			0
$841$	−58.3347	+	330.832i	−0.0693635	+	0.393380i
$842$	−104.185	−	240.415i	−0.123735	−	0.285528i
$843$		0			0
$844$	765.868	−	232.094i	0.907427	−	0.274993i
$845$	−120.372	−	208.490i	−0.142452	−	0.246733i
$846$		0			0
$847$	−1024.84	−	591.689i	−1.20996	−	0.698570i
$848$	−860.076	−	94.6709i	−1.01424	−	0.111640i
$849$		0			0
$850$	−74.6402	+	100.612i	−0.0878121	+	0.118367i
$851$	1463.27	−	1743.86i	1.71947	−	2.04918i
$852$		0			0
$853$	−332.142	−	120.890i	−0.389381	−	0.141723i	0.139908	−	0.990164i	$-0.455319\pi$
$853$	−332.142	−	120.890i	−0.389381	−	0.141723i	−0.529289	+	0.848441i	$0.677541\pi$
$854$	739.528	−	1478.71i	0.865958	−	1.73151i
$855$		0			0
$856$	−192.569	−	227.159i	−0.224964	−	0.265372i
$857$	63.4321	+	359.741i	0.0740165	+	0.419768i	0.999191	+	0.0402255i	$0.0128076\pi$
$857$	63.4321	+	359.741i	0.0740165	+	0.419768i	−0.925174	+	0.379543i	$0.876081\pi$
$858$		0			0
$859$	−175.372	−	481.832i	−0.204159	−	0.560922i	0.794784	−	0.606892i	$-0.207584\pi$
$859$	−175.372	−	481.832i	−0.204159	−	0.560922i	−0.998943	+	0.0459708i	$0.985362\pi$
$860$	−585.558	−	32.1299i	−0.680881	−	0.0373604i
$861$		0			0
$862$	446.699	−	422.860i	0.518212	−	0.490557i
$863$			298.152i			0.345483i	0.984967	+	0.172742i	$0.0552626\pi$
$863$			298.152i			0.345483i	−0.984967	+	0.172742i	$0.944737\pi$
$864$		0			0
$865$	−407.741			−0.471377
$866$	−695.908	−	735.140i	−0.803589	−	0.848891i
$867$		0			0
$868$	94.3935	−	1720.29i	0.108748	−	1.98190i
$869$	150.503	−	54.7785i	0.173191	−	0.0630362i
$870$		0			0
$871$	−679.866	+	119.879i	−0.780558	+	0.137633i
$872$	189.059	−	160.271i	0.216811	−	0.183797i
$873$		0			0
$874$	−1030.30	−	515.269i	−1.17883	−	0.589553i
$875$	439.465	−	1207.42i	0.502246	−	1.37991i
$876$		0			0
$877$	−149.799	−	125.696i	−0.170809	−	0.143326i	0.553376	−	0.832932i	$-0.313339\pi$
$877$	−149.799	−	125.696i	−0.170809	−	0.143326i	−0.724185	+	0.689606i	$0.757784\pi$
$878$	1230.77	+	913.063i	1.40179	+	1.03993i
$879$		0			0
$880$	−8.61860	+	78.2992i	−0.00979386	+	0.0889763i
$881$	255.802	−	443.061i	0.290354	−	0.502907i	−0.683540	−	0.729913i	$-0.739560\pi$
$881$	255.802	−	443.061i	0.290354	−	0.502907i	0.973893	+	0.227006i	$0.0728937\pi$
$882$		0			0
$883$	935.627	−	540.184i	1.05960	−	0.611760i	0.134278	−	0.990944i	$-0.457128\pi$
$883$	935.627	−	540.184i	1.05960	−	0.611760i	0.925322	+	0.379183i	$0.123795\pi$
$884$	−50.2907	−	165.950i	−0.0568899	−	0.187726i
$885$		0			0
$886$	668.620	−	289.749i	0.754650	−	0.327030i
$887$	−690.686	−	121.787i	−0.778677	−	0.137302i	−0.229837	−	0.973229i	$-0.573819\pi$
$887$	−690.686	−	121.787i	−0.778677	−	0.137302i	−0.548840	+	0.835927i	$0.684930\pi$
$888$		0			0
$889$	−229.986	+	192.981i	−0.258702	+	0.217077i
$890$	7.21118	+	120.326i	0.00810245	+	0.135198i
$891$		0			0
$892$	−62.2255	−	517.285i	−0.0697596	−	0.579916i
$893$	−114.581	+	96.1446i	−0.128310	+	0.107665i
$894$		0			0
$895$	532.973	+	93.9776i	0.595501	+	0.105003i
$896$	917.319	−	886.078i	1.02379	−	0.988926i
$897$		0			0
$898$	461.228	−	110.132i	0.513617	−	0.122642i
$899$	−841.332	+	485.743i	−0.935853	+	0.540315i
$900$		0			0
$901$	−119.692	+	207.312i	−0.132843	+	0.230091i
$902$	−7.50151	−	2.23207i	−0.00831653	−	0.00247458i
$903$		0			0
$904$	−795.498	+	1394.03i	−0.879975	+	1.54207i
$905$	239.117	+	200.643i	0.264218	+	0.221705i
$906$		0			0
$907$	167.768	−	460.939i	0.184970	−	0.508202i	−0.812200	−	0.583379i	$-0.801730\pi$
$907$	167.768	−	460.939i	0.184970	−	0.508202i	0.997170	+	0.0751776i	$0.0239524\pi$
$908$	177.609	+	75.9059i	0.195605	+	0.0835968i
$909$		0			0
$910$	354.146	+	536.486i	0.389171	+	0.589545i
$911$	550.236	−	97.0215i	0.603992	−	0.106500i	0.136714	−	0.990611i	$-0.456346\pi$
$911$	550.236	−	97.0215i	0.603992	−	0.106500i	0.467278	+	0.884111i	$0.345235\pi$
$912$		0			0
$913$	−46.7781	+	17.0258i	−0.0512356	+	0.0186482i
$914$	1146.59	+	132.064i	1.25447	+	0.144490i
$915$		0			0
$916$	−228.079	+	243.384i	−0.248995	+	0.265703i
$917$	−215.517			−0.235024
$918$		0			0
$919$			1707.28i			1.85776i	0.370387	+	0.928878i	$0.379225\pi$
$919$			1707.28i			1.85776i	−0.370387	+	0.928878i	$0.620775\pi$
$920$	−537.403	+	647.051i	−0.584133	+	0.703316i
$921$		0			0
$922$	−431.662	−	49.7187i	−0.468180	−	0.0539248i
$923$	−369.913	−	1016.33i	−0.400772	−	1.10111i
$924$		0			0
$925$	−175.242	−	993.847i	−0.189451	−	1.07443i
$926$	0.715571	+	1.08400i	0.000772755	+	0.00117063i
$927$		0			0
$928$	−701.140	−	159.961i	−0.755539	−	0.172372i
$929$	174.849	+	63.6397i	0.188212	+	0.0685035i	0.434407	−	0.900717i	$-0.356958\pi$
$929$	174.849	+	63.6397i	0.188212	+	0.0685035i	−0.246195	+	0.969220i	$0.579180\pi$
$930$		0			0
$931$	−583.192	+	695.021i	−0.626414	+	0.746532i
$932$	−1221.80	−	797.720i	−1.31095	−	0.855922i
$933$		0			0
$934$	1675.37	+	498.505i	1.79375	+	0.533731i
$935$	18.8731	+	10.8964i	0.0201852	+	0.0116539i
$936$		0			0
$937$	480.527	+	832.297i	0.512836	+	0.888257i	0.999889	+	0.0148853i	$0.00473831\pi$
$937$	480.527	+	832.297i	0.512836	+	0.888257i	−0.487054	+	0.873372i	$0.661928\pi$
$938$	−1366.34	+	326.255i	−1.45665	+	0.347819i
$939$		0			0
$940$	49.3425	+	97.4310i	0.0524921	+	0.103650i
$941$	2.75395	−	15.6184i	0.00292662	−	0.0165977i	−0.983309	−	0.181941i	$-0.941762\pi$
$941$	2.75395	−	15.6184i	0.00292662	−	0.0165977i	0.986236	+	0.165343i	$0.0528732\pi$
$942$		0			0
$943$	−53.7182	−	64.0189i	−0.0569652	−	0.0678885i
$944$	−352.726	−	1444.90i	−0.373650	−	1.53062i
$945$		0			0
$946$	−7.95987	−	132.819i	−0.00841424	−	0.140401i
$947$	−277.085	−	330.217i	−0.292592	−	0.348698i	0.599644	−	0.800267i	$-0.295309\pi$
$947$	−277.085	−	330.217i	−0.292592	−	0.348698i	−0.892236	+	0.451569i	$0.850864\pi$
$948$		0			0
$949$	95.7228	−	542.871i	0.100867	−	0.572045i
$950$	−468.576	+	203.059i	−0.493238	+	0.213746i
$951$		0			0
$952$	−122.350	−	330.952i	−0.128519	−	0.347639i
$953$	212.724	+	368.449i	0.223215	+	0.386620i	0.955782	−	0.294075i	$-0.0950115\pi$
$953$	212.724	+	368.449i	0.223215	+	0.386620i	−0.732567	+	0.680694i	$0.761678\pi$
$954$		0			0
$955$	608.832	+	351.509i	0.637520	+	0.368072i
$956$	−0.374960	+	1.60612i	−0.000392217	+	0.00168005i
$957$		0			0
$958$	−749.317	−	555.890i	−0.782168	−	0.580261i
$959$	−1382.20	+	1647.24i	−1.44129	+	1.71766i
$960$		0			0
$961$	852.907	+	310.433i	0.887520	+	0.323031i
$962$	1249.35	+	624.819i	1.29870	+	0.649500i
$963$		0			0
$964$	−489.222	−	652.548i	−0.507492	−	0.676917i
$965$	116.133	+	658.622i	0.120345	+	0.682510i
$966$		0			0
$967$	25.4541	+	69.9345i	0.0263227	+	0.0723211i	0.952158	−	0.305606i	$-0.0988591\pi$
$967$	25.4541	+	69.9345i	0.0263227	+	0.0723211i	−0.925835	+	0.377927i	$0.876637\pi$
$968$	950.115	−	4.79145i	0.981524	−	0.00494984i
$969$		0			0
$970$	334.911	+	353.792i	0.345269	+	0.364734i
$971$			316.171i			0.325614i	0.986658	+	0.162807i	$0.0520547\pi$
$971$			316.171i			0.325614i	−0.986658	+	0.162807i	$0.947945\pi$
$972$		0			0
$973$	−1704.19			−1.75148
$974$	304.281	−	288.043i	0.312404	−	0.295732i
$975$		0			0
$976$	86.0931	+	1324.65i	0.0882101	+	1.35723i
$977$	−2.19559	+	0.799131i	−0.00224728	+	0.000817944i	−0.343144	−	0.939283i	$-0.611492\pi$
$977$	−2.19559	+	0.799131i	−0.00224728	+	0.000817944i	0.340896	+	0.940101i	$0.389270\pi$
$978$		0			0
$979$	−26.9343	+	4.74925i	−0.0275121	+	0.00485112i
$980$	397.379	+	530.043i	0.405489	+	0.540860i
$981$		0			0
$982$	−639.121	+	1277.95i	−0.650836	+	1.30137i
$983$	−225.214	+	618.771i	−0.229109	+	0.629472i	−0.999972	−	0.00752963i	$-0.997603\pi$
$983$	−225.214	+	618.771i	−0.229109	+	0.629472i	0.770863	+	0.637001i	$0.219825\pi$
$984$		0			0
$985$	335.258	+	281.315i	0.340363	+	0.285599i
$986$	−118.542	+	159.789i	−0.120225	+	0.162058i
$987$		0			0
$988$	160.703	−	688.362i	0.162654	−	0.696723i
$989$	710.382	−	1230.42i	0.718283	−	1.24410i
$990$		0			0
$991$	−591.557	+	341.536i	−0.596929	+	0.344637i	−0.767833	−	0.640650i	$-0.778665\pi$
$991$	−591.557	+	341.536i	−0.596929	+	0.344637i	0.170903	+	0.985288i	$0.445331\pi$
$992$	631.187	+	1230.89i	0.636278	+	1.24082i
$993$		0			0
$994$	−875.075	−	2019.31i	−0.880357	−	2.03150i
$995$	319.902	+	56.4074i	0.321510	+	0.0566909i
$996$		0			0
$997$	−212.486	+	178.297i	−0.213126	+	0.178834i	−0.743101	−	0.669180i	$-0.766646\pi$
$997$	−212.486	+	178.297i	−0.213126	+	0.178834i	0.529975	+	0.848013i	$0.322201\pi$
$998$	−1209.86	+	72.5075i	−1.21229	+	0.0726528i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.9		204
3.2	odd	2		108.3.j.a.103.26	yes	204
4.3	odd	2	inner	324.3.j.a.199.24		204
12.11	even	2		108.3.j.a.103.11	yes	204
27.11	odd	18		108.3.j.a.43.11	✓	204
27.16	even	9	inner	324.3.j.a.127.24		204
108.11	even	18		108.3.j.a.43.26	yes	204
108.43	odd	18	inner	324.3.j.a.127.9		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.11	✓	204	27.11	odd	18
108.3.j.a.43.26	yes	204	108.11	even	18
108.3.j.a.103.11	yes	204	12.11	even	2
108.3.j.a.103.26	yes	204	3.2	odd	2
324.3.j.a.127.9		204	108.43	odd	18	inner
324.3.j.a.127.24		204	27.16	even	9	inner
324.3.j.a.199.9		204	1.1	even	1	trivial
324.3.j.a.199.24		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)

\(f(q)\)	\(=\)	\(q+(-1.37493 - 1.45244i) q^{2} +(-0.219153 + 3.99399i) q^{4} +(3.09520 - 1.12656i) q^{5} +(-9.81257 + 1.73022i) q^{7} +(6.10235 - 5.17314i) q^{8} +O(q^{10})\)	\(q+(-1.37493 - 1.45244i) q^{2} +(-0.219153 + 3.99399i) q^{4} +(3.09520 - 1.12656i) q^{5} +(-9.81257 + 1.73022i) q^{7} +(6.10235 - 5.17314i) q^{8} +(-5.89194 - 2.94665i) q^{10} +(0.511212 - 1.40454i) q^{11} +(7.50220 + 6.29509i) q^{13} +(16.0046 + 11.8732i) q^{14} +(-15.9039 - 1.75059i) q^{16} +(-2.21325 + 3.83347i) q^{17} +(-15.6270 + 9.02228i) q^{19} +(3.82115 + 12.6091i) q^{20} +(-2.74289 + 1.18864i) q^{22} +(-31.4351 - 5.54285i) q^{23} +(-10.8400 + 9.09582i) q^{25} +(-1.17174 - 19.5518i) q^{26} +(-4.76004 - 39.5705i) q^{28} +(-17.2158 + 14.4458i) q^{29} +(42.5711 + 7.50643i) q^{31} +(19.3241 + 25.5064i) q^{32} +(8.61094 - 2.05612i) q^{34} +(-28.4227 + 16.4099i) q^{35} +(-35.6586 + 61.7625i) q^{37} +(34.5903 + 10.2923i) q^{38} +(13.0601 - 22.8866i) q^{40} +(2.00560 + 1.68290i) q^{41} +(-15.2234 + 41.8259i) q^{43} +(5.49770 + 2.34958i) q^{44} +(35.1703 + 53.2785i) q^{46} +(8.16324 - 1.43940i) q^{47} +(47.2480 - 17.1969i) q^{49} +(28.1153 + 3.23831i) q^{50} +(-26.7867 + 28.5841i) q^{52} +54.0794 q^{53} -4.92325i q^{55} +(-50.9290 + 61.3202i) q^{56} +(44.6521 + 5.14301i) q^{58} +(31.7936 + 87.3522i) q^{59} +(-14.4068 - 81.7051i) q^{61} +(-47.6295 - 72.1527i) q^{62} +(10.4772 - 63.1366i) q^{64} +(30.3126 + 11.0329i) q^{65} +(-45.3111 + 53.9997i) q^{67} +(-14.8258 - 9.67984i) q^{68} +(62.9134 + 18.7199i) q^{70} +(-95.6408 - 55.2183i) q^{71} +(-28.1437 - 48.7462i) q^{73} +(138.734 - 33.1270i) q^{74} +(-32.6102 - 64.3915i) q^{76} +(-2.58613 + 14.6667i) q^{77} +(68.8774 + 82.0848i) q^{79} +(-51.1981 + 12.4983i) q^{80} +(-0.313248 - 5.22688i) q^{82} +(-21.4079 - 25.5130i) q^{83} +(-2.53183 + 14.3587i) q^{85} +(81.6805 - 35.3965i) q^{86} +(-4.14631 - 11.2156i) q^{88} +(-9.14904 - 15.8466i) q^{89} +(-84.5078 - 48.7906i) q^{91} +(29.0272 - 124.337i) q^{92} +(-13.3145 - 9.87753i) q^{94} +(-38.2047 + 45.5306i) q^{95} +(-69.4916 - 25.2929i) q^{97} +(-89.9399 - 44.9804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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

Introduction

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