LMFDB - Embedded newform 324.3.j.a.307.18

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			307.18
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.103865 + 1.99730i) q^{2} +(-3.97842 - 0.414901i) q^{4} +(-1.50670 + 8.54492i) q^{5} +(7.53806 + 8.98351i) q^{7} +(1.24190 - 7.90302i) q^{8} +O(q^{10})$	\(q+(-0.103865 + 1.99730i) q^{2} +(-3.97842 - 0.414901i) q^{4} +(-1.50670 + 8.54492i) q^{5} +(7.53806 + 8.98351i) q^{7} +(1.24190 - 7.90302i) q^{8} +(-16.9103 - 3.89685i) q^{10} +(2.27133 - 0.400497i) q^{11} +(-4.42594 + 1.61091i) q^{13} +(-18.7257 + 14.1227i) q^{14} +(15.6557 + 3.30130i) q^{16} +(-6.77412 + 11.7331i) q^{17} +(13.9009 - 8.02568i) q^{19} +(9.53958 - 33.3702i) q^{20} +(0.564001 + 4.57813i) q^{22} +(3.20904 - 3.82439i) q^{23} +(-47.2531 - 17.1987i) q^{25} +(-2.75777 - 9.00726i) q^{26} +(-26.2623 - 38.8678i) q^{28} +(-34.0967 - 12.4102i) q^{29} +(-0.283047 + 0.337322i) q^{31} +(-8.21978 + 30.9263i) q^{32} +(-22.7310 - 14.7486i) q^{34} +(-88.1209 + 50.8766i) q^{35} +(18.9267 - 32.7821i) q^{37} +(14.5859 + 28.5979i) q^{38} +(65.6594 + 22.5194i) q^{40} +(-2.35960 + 0.858824i) q^{41} +(-17.5866 + 3.10099i) q^{43} +(-9.20249 + 0.650970i) q^{44} +(7.30515 + 6.80665i) q^{46} +(-5.64102 - 6.72271i) q^{47} +(-15.3723 + 87.1809i) q^{49} +(39.2590 - 92.5924i) q^{50} +(18.2767 - 4.57256i) q^{52} +41.4639 q^{53} +20.0118i q^{55} +(80.3584 - 48.4168i) q^{56} +(28.3283 - 66.8123i) q^{58} +(-25.5867 - 4.51163i) q^{59} +(51.1770 - 42.9426i) q^{61} +(-0.644335 - 0.600365i) q^{62} +(-60.9154 - 19.6296i) q^{64} +(-7.09654 - 40.2465i) q^{65} +(32.3784 + 88.9589i) q^{67} +(31.8184 - 43.8687i) q^{68} +(-92.4633 - 181.288i) q^{70} +(100.208 + 57.8552i) q^{71} +(22.5335 + 39.0292i) q^{73} +(63.5098 + 41.2073i) q^{74} +(-58.6335 + 26.1621i) q^{76} +(20.7193 + 17.3856i) q^{77} +(-19.8334 + 54.4917i) q^{79} +(-51.7978 + 128.803i) q^{80} +(-1.47025 - 4.80203i) q^{82} +(22.8909 - 62.8923i) q^{83} +(-90.0519 - 75.5626i) q^{85} +(-4.36697 - 35.4478i) q^{86} +(-0.344363 - 18.4478i) q^{88} +(-54.3190 - 94.0833i) q^{89} +(-47.8347 - 27.6174i) q^{91} +(-14.3537 + 13.8836i) q^{92} +(14.0132 - 10.5686i) q^{94} +(47.6343 + 130.874i) q^{95} +(30.2853 + 171.757i) q^{97} +(-172.530 - 39.7583i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.103865	+	1.99730i	−0.0519327	+	0.998651i
$2$	−0.103865	+	1.99730i	−0.0519327	+	0.998651i
$3$		0			0
$3$		0			0
$4$	−3.97842	−	0.414901i	−0.994606	−	0.103725i
$5$	−1.50670	+	8.54492i	−0.301340	+	1.70898i	0.338912	+	0.940818i	$0.389941\pi$
$5$	−1.50670	+	8.54492i	−0.301340	+	1.70898i	−0.640252	+	0.768165i	$0.721170\pi$
$6$		0			0
$7$	7.53806	+	8.98351i	1.07687	+	1.28336i	0.956849	+	0.290587i	$0.0938505\pi$
$7$	7.53806	+	8.98351i	1.07687	+	1.28336i	0.120017	+	0.992772i	$0.461705\pi$
$8$	1.24190	−	7.90302i	0.155238	−	0.987877i
$9$		0			0
$10$	−16.9103	−	3.89685i	−1.69103	−	0.389685i
$11$	2.27133	−	0.400497i	0.206485	−	0.0364089i	−0.0694489	−	0.997586i	$-0.522124\pi$
$11$	2.27133	−	0.400497i	0.206485	−	0.0364089i	0.275934	+	0.961177i	$0.411013\pi$
$12$		0			0
$13$	−4.42594	+	1.61091i	−0.340457	+	0.123916i	−0.506590	−	0.862187i	$-0.669094\pi$
$13$	−4.42594	+	1.61091i	−0.340457	+	0.123916i	0.166133	+	0.986103i	$0.446872\pi$
$14$	−18.7257	+	14.1227i	−1.33755	+	1.00876i
$15$		0			0
$16$	15.6557	+	3.30130i	0.978482	+	0.206331i
$17$	−6.77412	+	11.7331i	−0.398478	+	0.690183i	−0.993538	−	0.113497i	$-0.963795\pi$
$17$	−6.77412	+	11.7331i	−0.398478	+	0.690183i	0.595061	+	0.803681i	$0.297128\pi$
$18$		0			0
$19$	13.9009	−	8.02568i	0.731626	−	0.422404i	−0.0873908	−	0.996174i	$-0.527853\pi$
$19$	13.9009	−	8.02568i	0.731626	−	0.422404i	0.819017	+	0.573770i	$0.194520\pi$
$20$	9.53958	−	33.3702i	0.476979	−	1.66851i
$21$		0			0
$22$	0.564001	+	4.57813i	0.0256364	+	0.208097i
$23$	3.20904	−	3.82439i	0.139524	−	0.166278i	−0.691758	−	0.722130i	$-0.743163\pi$
$23$	3.20904	−	3.82439i	0.139524	−	0.166278i	0.831281	+	0.555852i	$0.187608\pi$
$24$		0			0
$25$	−47.2531	−	17.1987i	−1.89013	−	0.687949i
$26$	−2.75777	−	9.00726i	−0.106068	−	0.346433i
$27$		0			0
$28$	−26.2623	−	38.8678i	−0.937940	−	1.38813i
$29$	−34.0967	−	12.4102i	−1.17575	−	0.427937i	−0.321049	−	0.947063i	$-0.604035\pi$
$29$	−34.0967	−	12.4102i	−1.17575	−	0.427937i	−0.854698	+	0.519126i	$0.826258\pi$
$30$		0			0
$31$	−0.283047	+	0.337322i	−0.00913054	+	0.0108813i	−0.770590	−	0.637331i	$-0.780039\pi$
$31$	−0.283047	+	0.337322i	−0.00913054	+	0.0108813i	0.761460	+	0.648212i	$0.224483\pi$
$32$	−8.21978	+	30.9263i	−0.256868	+	0.966446i
$33$		0			0
$34$	−22.7310	−	14.7486i	−0.668558	−	0.433783i
$35$	−88.1209	+	50.8766i	−2.51774	+	1.45362i
$36$		0			0
$37$	18.9267	−	32.7821i	0.511533	−	0.886002i	−0.488377	−	0.872633i	$-0.662411\pi$
$37$	18.9267	−	32.7821i	0.511533	−	0.886002i	0.999911	−	0.0133691i	$-0.00425565\pi$
$38$	14.5859	+	28.5979i	0.383839	+	0.752575i
$39$		0			0
$40$	65.6594	+	22.5194i	1.64149	+	0.562986i
$41$	−2.35960	+	0.858824i	−0.0575512	+	0.0209469i	−0.370635	−	0.928778i	$-0.620860\pi$
$41$	−2.35960	+	0.858824i	−0.0575512	+	0.0209469i	0.313084	+	0.949725i	$0.398638\pi$
$42$		0			0
$43$	−17.5866	+	3.10099i	−0.408990	+	0.0721160i	−0.374358	−	0.927284i	$-0.622137\pi$
$43$	−17.5866	+	3.10099i	−0.408990	+	0.0721160i	−0.0346317	+	0.999400i	$0.511026\pi$
$44$	−9.20249	+	0.650970i	−0.209148	+	0.0147948i
$45$		0			0
$46$	7.30515	+	6.80665i	0.158808	+	0.147971i
$47$	−5.64102	−	6.72271i	−0.120022	−	0.143036i	0.702688	−	0.711498i	$-0.251983\pi$
$47$	−5.64102	−	6.72271i	−0.120022	−	0.143036i	−0.822710	+	0.568462i	$0.807539\pi$
$48$		0			0
$49$	−15.3723	+	87.1809i	−0.313721	+	1.77920i
$50$	39.2590	−	92.5924i	0.785180	−	1.85185i
$51$		0			0
$52$	18.2767	−	4.57256i	0.351474	−	0.0879339i
$53$	41.4639			0.782338			0.391169	−	0.920319i	$-0.372071\pi$
$53$	41.4639			0.782338			0.391169	+	0.920319i	$0.372071\pi$
$54$		0			0
$55$			20.0118i			0.363851i
$56$	80.3584	−	48.4168i	1.43497	−	0.864585i
$57$		0			0
$58$	28.3283	−	66.8123i	0.488419	−	1.15194i
$59$	−25.5867	−	4.51163i	−0.433674	−	0.0764684i	−0.0474502	−	0.998874i	$-0.515110\pi$
$59$	−25.5867	−	4.51163i	−0.433674	−	0.0764684i	−0.386224	+	0.922405i	$0.626221\pi$
$60$		0			0
$61$	51.1770	−	42.9426i	0.838967	−	0.703977i	−0.118364	−	0.992970i	$-0.537765\pi$
$61$	51.1770	−	42.9426i	0.838967	−	0.703977i	0.957331	+	0.288993i	$0.0933206\pi$
$62$	−0.644335	−	0.600365i	−0.0103925	−	0.00968331i
$63$		0			0
$64$	−60.9154	−	19.6296i	−0.951802	−	0.306712i
$65$	−7.09654	−	40.2465i	−0.109178	−	0.619177i
$66$		0			0
$67$	32.3784	+	88.9589i	0.483260	+	1.32775i	0.906683	+	0.421813i	$0.138606\pi$
$67$	32.3784	+	88.9589i	0.483260	+	1.32775i	−0.423423	+	0.905932i	$0.639172\pi$
$68$	31.8184	−	43.8687i	0.467918	−	0.645128i
$69$		0			0
$70$	−92.4633	−	181.288i	−1.32090	−	2.58983i
$71$	100.208	+	57.8552i	1.41138	+	0.814862i	0.995519	−	0.0945652i	$-0.0301461\pi$
$71$	100.208	+	57.8552i	1.41138	+	0.814862i	0.415863	+	0.909427i	$0.363479\pi$
$72$		0			0
$73$	22.5335	+	39.0292i	0.308678	+	0.534646i	0.978073	−	0.208260i	$-0.0667801\pi$
$73$	22.5335	+	39.0292i	0.308678	+	0.534646i	−0.669395	+	0.742906i	$0.733447\pi$
$74$	63.5098	+	41.2073i	0.858241	+	0.556855i
$75$		0			0
$76$	−58.6335	+	26.1621i	−0.771494	+	0.344238i
$77$	20.7193	+	17.3856i	0.269082	+	0.225787i
$78$		0			0
$79$	−19.8334	+	54.4917i	−0.251055	+	0.689769i	0.748587	+	0.663036i	$0.230733\pi$
$79$	−19.8334	+	54.4917i	−0.251055	+	0.689769i	−0.999643	+	0.0267327i	$0.991490\pi$
$80$	−51.7978	+	128.803i	−0.647473	+	1.61003i
$81$		0			0
$82$	−1.47025	−	4.80203i	−0.0179299	−	0.0585614i
$83$	22.8909	−	62.8923i	0.275794	−	0.757738i	−0.722033	−	0.691858i	$-0.756792\pi$
$83$	22.8909	−	62.8923i	0.275794	−	0.757738i	0.997828	−	0.0658799i	$-0.0209854\pi$
$84$		0			0
$85$	−90.0519	−	75.5626i	−1.05943	−	0.888971i
$86$	−4.36697	−	35.4478i	−0.0507787	−	0.412183i
$87$		0			0
$88$	−0.344363	−	18.4478i	−0.00391322	−	0.209634i
$89$	−54.3190	−	94.0833i	−0.610326	−	1.05712i	−0.991185	−	0.132482i	$-0.957705\pi$
$89$	−54.3190	−	94.0833i	−0.610326	−	1.05712i	0.380860	−	0.924633i	$-0.375628\pi$
$90$		0			0
$91$	−47.8347	−	27.6174i	−0.525656	−	0.303487i
$92$	−14.3537	+	13.8836i	−0.156018	+	0.150909i
$93$		0			0
$94$	14.0132	−	10.5686i	0.149076	−	0.112432i
$95$	47.6343	+	130.874i	0.501414	+	1.37762i
$96$		0			0
$97$	30.2853	+	171.757i	0.312220	+	1.77069i	0.587403	+	0.809295i	$0.300150\pi$
$97$	30.2853	+	171.757i	0.312220	+	1.77069i	−0.275183	+	0.961392i	$0.588738\pi$
$98$	−172.530	−	39.7583i	−1.76051	−	0.405697i
$99$		0			0
$100$	180.857	+	88.0292i	1.80857	+	0.880292i
$101$	57.1968	−	47.9938i	0.566305	−	0.475186i	−0.314112	−	0.949386i	$-0.601707\pi$
$101$	57.1968	−	47.9938i	0.566305	−	0.475186i	0.880417	+	0.474200i	$0.157262\pi$
$102$		0			0
$103$	137.158	+	24.1847i	1.33163	+	0.234803i	0.793764	−	0.608226i	$-0.208119\pi$
$103$	137.158	+	24.1847i	1.33163	+	0.234803i	0.537868	+	0.843029i	$0.319230\pi$
$104$	7.23447	+	36.9789i	0.0695622	+	0.355566i
$105$		0			0
$106$	−4.30667	+	82.8160i	−0.0406289	+	0.781283i
$107$		−	28.1004i		−	0.262621i	−0.991341	−	0.131310i	$-0.958082\pi$
$107$		−	28.1004i		−	0.262621i	0.991341	−	0.131310i	$-0.0419185\pi$
$108$		0			0
$109$	12.7869			0.117311			0.0586555	−	0.998278i	$-0.481319\pi$
$109$	12.7869			0.117311			0.0586555	+	0.998278i	$0.481319\pi$
$110$	−39.9696	−	2.07853i	−0.363360	−	0.0188957i
$111$		0			0
$112$	88.3564	+	165.529i	0.788897	+	1.47793i
$113$	−36.5416	+	207.238i	−0.323377	+	1.83396i	0.197465	+	0.980310i	$0.436729\pi$
$113$	−36.5416	+	207.238i	−0.323377	+	1.83396i	−0.520842	+	0.853653i	$0.674382\pi$
$114$		0			0
$115$	27.8440	+	33.1832i	0.242122	+	0.288550i
$116$	130.502	+	63.5196i	1.12502	+	0.547583i
$117$		0			0
$118$	11.6687	−	50.6358i	0.0988870	−	0.429117i
$119$	−156.468	+	27.5896i	−1.31486	+	0.231845i
$120$		0			0
$121$	−108.704	+	39.5651i	−0.898382	+	0.326984i
$122$	80.4538	+	106.676i	0.659457	+	0.874394i
$123$		0			0
$124$	1.26603	−	1.22457i	0.0102100	−	0.00987559i
$125$	109.699	−	190.004i	0.877590	−	1.52003i
$126$		0			0
$127$	96.5648	−	55.7517i	0.760353	−	0.438990i	−0.0690695	−	0.997612i	$-0.522003\pi$
$127$	96.5648	−	55.7517i	0.760353	−	0.438990i	0.829422	+	0.558622i	$0.188670\pi$
$128$	45.5331	−	119.627i	0.355728	−	0.934590i
$129$		0			0
$130$	81.1214	−	9.99371i	0.624011	−	0.0768747i
$131$	10.1474	−	12.0932i	0.0774612	−	0.0923146i	−0.725922	−	0.687777i	$-0.758587\pi$
$131$	10.1474	−	12.0932i	0.0774612	−	0.0923146i	0.803383	+	0.595462i	$0.203031\pi$
$132$		0			0
$133$	176.885	+	64.3807i	1.32996	+	0.484066i
$134$	−181.041	+	55.4297i	−1.35105	+	0.413654i
$135$		0			0
$136$	84.3142	+	68.1074i	0.619958	+	0.500789i
$137$	−99.8901	−	36.3570i	−0.729125	−	0.265380i	−0.0493306	−	0.998783i	$-0.515709\pi$
$137$	−99.8901	−	36.3570i	−0.729125	−	0.265380i	−0.679794	+	0.733403i	$0.737931\pi$
$138$		0			0
$139$	−36.3183	+	43.2824i	−0.261283	+	0.311385i	−0.880697	−	0.473679i	$-0.842926\pi$
$139$	−36.3183	+	43.2824i	−0.261283	+	0.311385i	0.619415	+	0.785064i	$0.287370\pi$
$140$	371.691	−	165.847i	2.65494	−	1.18462i
$141$		0			0
$142$	−125.962	+	194.137i	−0.887059	+	1.36716i
$143$	−9.40763	+	5.43150i	−0.0657876	+	0.0379825i
$144$		0			0
$145$	157.417	−	272.655i	1.08564	−	1.88038i
$146$	−80.2935	+	40.9524i	−0.549955	+	0.280496i
$147$		0			0
$148$	−88.8999	+	122.568i	−0.600675	+	0.828164i
$149$	−110.073	+	40.0635i	−0.738748	+	0.268882i	−0.683863	−	0.729610i	$-0.739701\pi$
$149$	−110.073	+	40.0635i	−0.738748	+	0.268882i	−0.0548851	+	0.998493i	$0.517479\pi$
$150$		0			0
$151$	−244.777	+	43.1607i	−1.62104	+	0.285832i	−0.909152	−	0.416464i	$-0.863269\pi$
$151$	−244.777	+	43.1607i	−1.62104	+	0.285832i	−0.711884	+	0.702297i	$0.752158\pi$
$152$	−46.1636	−	119.826i	−0.303708	−	0.788330i
$153$		0			0
$154$	−36.8762	+	39.5770i	−0.239456	+	0.256993i
$155$	−2.45592	−	2.92685i	−0.0158446	−	0.0188829i
$156$		0			0
$157$	32.2061	−	182.650i	0.205134	−	1.16337i	−0.692094	−	0.721807i	$-0.743312\pi$
$157$	32.2061	−	182.650i	0.205134	−	1.16337i	0.897228	−	0.441567i	$-0.145577\pi$
$158$	−106.776	−	45.2730i	−0.675800	−	0.286538i
$159$		0			0
$160$	−251.878	−	116.834i	−1.57424	−	0.730212i
$161$	58.5464			0.363642
$162$		0			0
$163$		−	3.07052i		−	0.0188375i	−0.999956	−	0.00941877i	$-0.997002\pi$
$163$		−	3.07052i		−	0.0188375i	0.999956	−	0.00941877i	$-0.00299813\pi$
$164$	9.74381	−	2.43777i	0.0594135	−	0.0148644i
$165$		0			0
$166$	123.237	+	52.2524i	0.742393	+	0.314773i
$167$	90.6052	+	15.9761i	0.542546	+	0.0956655i	0.438203	−	0.898876i	$-0.355615\pi$
$167$	90.6052	+	15.9761i	0.542546	+	0.0956655i	0.104343	+	0.994541i	$0.466726\pi$
$168$		0			0
$169$	−112.468	+	94.3715i	−0.665489	+	0.558411i
$170$	160.274	−	172.013i	0.942791	−	1.01184i
$171$		0			0
$172$	71.2534	−	5.04036i	0.414264	−	0.0293044i
$173$	49.4146	+	280.244i	0.285633	+	1.61991i	0.703014	+	0.711176i	$0.251837\pi$
$173$	49.4146	+	280.244i	0.285633	+	1.61991i	−0.417381	+	0.908732i	$0.637052\pi$
$174$		0			0
$175$	−201.692	−	554.144i	−1.15253	−	3.16654i
$176$	36.8815	+	1.22829i	0.209554	+	0.00697891i
$177$		0			0
$178$	193.554	−	98.7194i	1.08738	−	0.554603i
$179$	37.3404	+	21.5585i	0.208606	+	0.120438i	0.600663	−	0.799502i	$-0.294903\pi$
$179$	37.3404	+	21.5585i	0.208606	+	0.120438i	−0.392058	+	0.919941i	$0.628237\pi$
$180$		0			0
$181$	−52.2292	−	90.4636i	−0.288559	−	0.499799i	0.684907	−	0.728630i	$-0.259843\pi$
$181$	−52.2292	−	90.4636i	−0.288559	−	0.499799i	−0.973466	+	0.228832i	$0.926509\pi$
$182$	60.1286	−	92.6718i	0.330377	−	0.509186i
$183$		0			0
$184$	−26.2389	−	30.1107i	−0.142603	−	0.163645i
$185$	251.603	+	211.120i	1.36002	+	1.14119i
$186$		0			0
$187$	−10.6872	+	29.3628i	−0.0571508	+	0.157021i
$188$	19.6531	+	29.0863i	0.104538	+	0.154714i
$189$		0			0
$190$	−266.343	+	81.5468i	−1.40180	+	0.429194i
$191$	86.7947	−	238.466i	0.454422	−	1.24852i	−0.475160	−	0.879900i	$-0.657610\pi$
$191$	86.7947	−	238.466i	0.454422	−	1.24852i	0.929582	−	0.368616i	$-0.120168\pi$
$192$		0			0
$193$	−0.204011	−	0.171186i	−0.00105705	−	0.000886973i	0.642259	−	0.766488i	$-0.277997\pi$
$193$	−0.204011	−	0.171186i	−0.00105705	−	0.000886973i	−0.643316	+	0.765601i	$0.722442\pi$
$194$	−346.195	+	42.6493i	−1.78451	+	0.219842i
$195$		0			0
$196$	97.3291	−	340.465i	0.496577	−	1.73706i
$197$	−25.6282	−	44.3894i	−0.130093	−	0.225327i	0.793620	−	0.608414i	$-0.208194\pi$
$197$	−25.6282	−	44.3894i	−0.130093	−	0.225327i	−0.923712	+	0.383087i	$0.874861\pi$
$198$		0			0
$199$	86.0717	+	49.6935i	0.432521	+	0.249716i	0.700420	−	0.713731i	$-0.252996\pi$
$199$	86.0717	+	49.6935i	0.432521	+	0.249716i	−0.267899	+	0.963447i	$0.586329\pi$
$200$	−194.606	+	352.083i	−0.973028	+	1.76042i
$201$		0			0
$202$	89.9173	+	119.224i	0.445135	+	0.590218i
$203$	−145.536	−	399.856i	−0.716925	−	1.96974i
$204$		0			0
$205$	−3.78337	−	21.4566i	−0.0184555	−	0.104666i
$206$	−62.5501	+	271.434i	−0.303641	+	1.31764i
$207$		0			0
$208$	−74.6094	+	10.6086i	−0.358699	+	0.0510029i
$209$	28.3593	−	23.7963i	0.135690	−	0.113858i
$210$		0			0
$211$	100.532	+	17.7265i	0.476456	+	0.0840120i	0.406719	−	0.913553i	$-0.366673\pi$
$211$	100.532	+	17.7265i	0.476456	+	0.0840120i	0.0697369	+	0.997565i	$0.477784\pi$
$212$	−164.961	−	17.2034i	−0.778119	−	0.0811482i
$213$		0			0
$214$	56.1250	+	2.91866i	0.262267	+	0.0136386i
$215$		−	154.948i		−	0.720688i
$216$		0			0
$217$	−5.16396			−0.0237970
$218$	−1.32811	+	25.5393i	−0.00609227	+	0.117153i
$219$		0			0
$220$	8.30291	−	79.6154i	0.0377405	−	0.361888i
$221$	11.0809	−	62.8426i	0.0501396	−	0.284356i
$222$		0			0
$223$	−211.508	−	252.065i	−0.948464	−	1.13034i	−0.991349	−	0.131256i	$-0.958099\pi$
$223$	−211.508	−	252.065i	−0.948464	−	1.13034i	0.0428842	−	0.999080i	$-0.486345\pi$
$224$	−339.788	+	159.282i	−1.51691	+	0.711079i
$225$		0			0
$226$	−410.121	−	94.5095i	−1.81469	−	0.418183i
$227$	339.879	−	59.9299i	1.49727	−	0.264008i	0.635812	−	0.771844i	$-0.280665\pi$
$227$	339.879	−	59.9299i	1.49727	−	0.264008i	0.861454	+	0.507836i	$0.169554\pi$
$228$		0			0
$229$	−273.587	+	99.5776i	−1.19470	+	0.434837i	−0.861373	−	0.507973i	$-0.830395\pi$
$229$	−273.587	+	99.5776i	−1.19470	+	0.434837i	−0.333331	+	0.942810i	$0.608173\pi$
$230$	−69.1689	+	52.1663i	−0.300734	+	0.226810i
$231$		0			0
$232$	−140.422	+	254.054i	−0.605269	+	1.09506i
$233$	−49.5426	+	85.8104i	−0.212629	+	0.368285i	−0.952537	−	0.304424i	$-0.901536\pi$
$233$	−49.5426	+	85.8104i	−0.212629	+	0.368285i	0.739907	+	0.672709i	$0.234869\pi$
$234$		0			0
$235$	65.9443	−	38.0730i	0.280614	−	0.162013i
$236$	99.9231	+	28.5652i	0.423403	+	0.121039i
$237$		0			0
$238$	−38.8531	−	315.380i	−0.163248	−	1.32513i
$239$	−74.1713	+	88.3940i	−0.310340	+	0.369849i	−0.898559	−	0.438853i	$-0.855385\pi$
$239$	−74.1713	+	88.3940i	−0.310340	+	0.369849i	0.588219	+	0.808702i	$0.299829\pi$
$240$		0			0
$241$	109.908	+	40.0034i	0.456051	+	0.165989i	0.559823	−	0.828612i	$-0.310869\pi$
$241$	109.908	+	40.0034i	0.456051	+	0.165989i	−0.103772	+	0.994601i	$0.533091\pi$
$242$	−67.7328	−	221.225i	−0.279888	−	0.914151i
$243$		0			0
$244$	−221.421	+	149.610i	−0.907462	+	0.613158i
$245$	−721.792	−	262.711i	−2.94609	−	1.07229i
$246$		0			0
$247$	−48.5959	+	57.9143i	−0.196745	+	0.234471i
$248$	2.31434	+	2.65584i	0.00933203	+	0.0107090i
$249$		0			0
$250$	368.101	+	238.836i	1.47240	+	0.955345i
$251$	127.608	−	73.6744i	0.508397	−	0.293523i	−0.223777	−	0.974640i	$-0.571839\pi$
$251$	127.608	−	73.6744i	0.508397	−	0.293523i	0.732175	+	0.681117i	$0.238505\pi$
$252$		0			0
$253$	5.75715	−	9.97168i	0.0227555	−	0.0394138i
$254$	101.323	+	198.660i	0.398910	+	0.782125i
$255$		0			0
$256$	234.203	+	103.369i	0.914855	+	0.403783i
$257$	294.633	−	107.238i	1.14643	−	0.417267i	0.302199	−	0.953245i	$-0.402279\pi$
$257$	294.633	−	107.238i	1.14643	−	0.417267i	0.844232	+	0.535978i	$0.180057\pi$
$258$		0			0
$259$	437.169	−	77.0847i	1.68791	−	0.297624i
$260$	11.5347	+	163.062i	0.0443644	+	0.627161i
$261$		0			0
$262$	23.0998	+	21.5235i	0.0881673	+	0.0821508i
$263$	131.924	+	157.221i	0.501613	+	0.597799i	0.956131	−	0.292938i	$-0.0946330\pi$
$263$	131.924	+	157.221i	0.501613	+	0.597799i	−0.454518	+	0.890737i	$0.650189\pi$
$264$		0			0
$265$	−62.4737	+	354.306i	−0.235750	+	1.33700i
$266$	−146.960	+	346.605i	−0.552481	+	1.30303i
$267$		0			0
$268$	−91.9059	−	367.350i	−0.342932	−	1.37071i
$269$	270.423			1.00529			0.502645	−	0.864493i	$-0.332360\pi$
$269$	270.423			1.00529			0.502645	+	0.864493i	$0.332360\pi$
$270$		0			0
$271$			232.697i			0.858661i	0.903148	+	0.429330i	$0.141250\pi$
$271$			232.697i			0.858661i	−0.903148	+	0.429330i	$0.858750\pi$
$272$	−144.788	+	161.327i	−0.532310	+	0.593114i
$273$		0			0
$274$	82.9911	−	195.734i	0.302887	−	0.714359i
$275$	−114.216	−	20.1393i	−0.415330	−	0.0732338i
$276$		0			0
$277$	−57.6704	+	48.3912i	−0.208196	+	0.174698i	−0.740923	−	0.671590i	$-0.765612\pi$
$277$	−57.6704	+	48.3912i	−0.208196	+	0.174698i	0.532727	+	0.846287i	$0.321167\pi$
$278$	−82.6759	−	77.0341i	−0.297395	−	0.277101i
$279$		0			0
$280$	292.641	+	759.605i	1.04515	+	2.71287i
$281$	−24.3783	−	138.256i	−0.0867556	−	0.492015i	−0.996964	−	0.0778647i	$-0.975190\pi$
$281$	−24.3783	−	138.256i	−0.0867556	−	0.492015i	0.910208	−	0.414151i	$-0.135921\pi$
$282$		0			0
$283$	−48.0225	−	131.941i	−0.169691	−	0.466221i	0.825474	−	0.564440i	$-0.190908\pi$
$283$	−48.0225	−	131.941i	−0.169691	−	0.466221i	−0.995165	+	0.0982185i	$0.968686\pi$
$284$	−374.666	−	271.749i	−1.31925	−	0.956862i
$285$		0			0
$286$	−9.87121	−	19.3540i	−0.0345147	−	0.0676714i
$287$	−25.5021	−	14.7236i	−0.0888573	−	0.0513018i
$288$		0			0
$289$	52.7226	+	91.3183i	0.182431	+	0.315980i
$290$	528.223	+	342.729i	1.82146	+	1.18182i
$291$		0			0
$292$	−73.4546	−	164.624i	−0.251557	−	0.563780i
$293$	−255.034	−	213.999i	−0.870422	−	0.730371i	0.0937648	−	0.995594i	$-0.470110\pi$
$293$	−255.034	−	213.999i	−0.870422	−	0.730371i	−0.964187	+	0.265223i	$0.914554\pi$
$294$		0			0
$295$	77.1031	−	211.839i	0.261366	−	0.718098i
$296$	−235.572	−	190.290i	−0.795851	−	0.642873i
$297$		0			0
$298$	−68.5860	−	224.011i	−0.230154	−	0.751715i
$299$	−8.04230	+	22.0960i	−0.0268973	+	0.0738997i
$300$		0			0
$301$	−160.426	−	134.614i	−0.532978	−	0.447221i
$302$	−60.7811	−	493.375i	−0.201262	−	1.63369i
$303$		0			0
$304$	244.124	−	79.7568i	0.803038	−	0.262358i
$305$	289.832	+	502.005i	0.950270	+	1.64592i
$306$		0			0
$307$	−176.337	−	101.808i	−0.574387	−	0.331622i	0.184513	−	0.982830i	$-0.440929\pi$
$307$	−176.337	−	101.808i	−0.574387	−	0.331622i	−0.758900	+	0.651208i	$0.774263\pi$
$308$	−75.2169	−	77.7636i	−0.244211	−	0.252479i
$309$		0			0
$310$	6.10089	−	4.60121i	0.0196803	−	0.0148426i
$311$	63.2509	+	173.780i	0.203379	+	0.558779i	0.998887	−	0.0471636i	$-0.0150182\pi$
$311$	63.2509	+	173.780i	0.203379	+	0.558779i	−0.795508	+	0.605943i	$0.792796\pi$
$312$		0			0
$313$	−19.2606	−	109.232i	−0.0615355	−	0.348985i	−0.999994	−	0.00359201i	$-0.998857\pi$
$313$	−19.2606	−	109.232i	−0.0615355	−	0.348985i	0.938458	−	0.345393i	$-0.112254\pi$
$314$	361.462	+	83.2963i	1.15115	+	0.265275i
$315$		0			0
$316$	101.514	−	208.562i	0.321248	−	0.660008i
$317$	−104.031	+	87.2920i	−0.328172	+	0.275369i	−0.791955	−	0.610580i	$-0.790936\pi$
$317$	−104.031	+	87.2920i	−0.328172	+	0.275369i	0.463783	+	0.885949i	$0.346492\pi$
$318$		0			0
$319$	−82.4151	−	14.5320i	−0.258355	−	0.0455549i
$320$	259.514	−	490.941i	0.810981	−	1.53419i
$321$		0			0
$322$	−6.08094	+	116.935i	−0.0188849	+	0.363152i
$323$			217.468i			0.673275i
$324$		0			0
$325$	236.845			0.728755
$326$	6.13275	+	0.318920i	0.0188121	+	0.000978284i
$327$		0			0
$328$	3.85691	+	19.7145i	0.0117589	+	0.0601053i
$329$	17.8712	−	101.352i	0.0543196	−	0.308062i
$330$		0			0
$331$	114.419	+	136.359i	0.345677	+	0.411962i	0.910670	−	0.413133i	$-0.135566\pi$
$331$	114.419	+	136.359i	0.345677	+	0.411962i	−0.564993	+	0.825095i	$0.691121\pi$
$332$	−117.164	+	240.715i	−0.352903	+	0.725044i
$333$		0			0
$334$	−41.3199	+	179.307i	−0.123712	+	0.536846i
$335$	−808.931	+	142.636i	−2.41472	+	0.425780i
$336$		0			0
$337$	547.261	−	199.187i	1.62392	−	0.591059i	0.639797	−	0.768544i	$-0.279019\pi$
$337$	547.261	−	199.187i	1.62392	−	0.591059i	0.984123	+	0.177486i	$0.0567963\pi$
$338$	−176.807	−	234.434i	−0.523097	−	0.693590i
$339$		0			0
$340$	326.914	+	337.983i	0.961511	+	0.994066i
$341$	−0.507797	+	0.879530i	−0.00148914	+	0.00257927i
$342$		0			0
$343$	−401.424	+	231.762i	−1.17033	+	0.675692i
$344$	2.66635	+	142.838i	0.00775101	+	0.415227i
$345$		0			0
$346$	−564.864	+	69.5881i	−1.63255	+	0.201122i
$347$	−174.936	+	208.480i	−0.504138	+	0.600808i	−0.956754	−	0.290897i	$-0.906046\pi$
$347$	−174.936	+	208.480i	−0.504138	+	0.600808i	0.452616	+	0.891705i	$0.350491\pi$
$348$		0			0
$349$	239.597	+	87.2061i	0.686524	+	0.249874i	0.661646	−	0.749816i	$-0.269858\pi$
$349$	239.597	+	87.2061i	0.686524	+	0.249874i	0.0248779	+	0.999690i	$0.492080\pi$
$350$	1127.74	−	345.283i	3.22212	−	0.986523i
$351$		0			0
$352$	−6.28397	+	73.5359i	−0.0178522	+	0.208909i
$353$	216.192	+	78.6876i	0.612443	+	0.222911i	0.629572	−	0.776942i	$-0.283230\pi$
$353$	216.192	+	78.6876i	0.612443	+	0.222911i	−0.0171289	+	0.999853i	$0.505453\pi$
$354$		0			0
$355$	−645.351	+	769.100i	−1.81789	+	2.16648i
$356$	177.069	+	396.840i	0.497384	+	1.11472i
$357$		0			0
$358$	−46.9372	+	72.3408i	−0.131109	+	0.202069i
$359$	513.681	−	296.574i	1.43087	−	0.826112i	0.433680	−	0.901067i	$-0.357215\pi$
$359$	513.681	−	296.574i	1.43087	−	0.826112i	0.997187	+	0.0749550i	$0.0238813\pi$
$360$		0			0
$361$	−51.6768	+	89.5068i	−0.143149	+	0.247941i
$362$	186.108	−	94.9214i	0.514110	−	0.262214i
$363$		0			0
$364$	178.848	+	129.720i	0.491341	+	0.356374i
$365$	−367.452	+	133.742i	−1.00672	+	0.366415i
$366$		0			0
$367$	328.288	−	57.8861i	0.894519	−	0.157728i	0.292553	−	0.956249i	$-0.405495\pi$
$367$	328.288	−	57.8861i	0.894519	−	0.157728i	0.601966	+	0.798522i	$0.294384\pi$
$368$	62.8654	−	49.2795i	0.170830	−	0.133912i
$369$		0			0
$370$	−447.803	+	480.599i	−1.21028	+	1.29892i
$371$	312.558	+	372.492i	0.842473	+	1.00402i
$372$		0			0
$373$	10.8367	−	61.4578i	0.0290527	−	0.164766i	−0.966829	−	0.255423i	$-0.917785\pi$
$373$	10.8367	−	61.4578i	0.0290527	−	0.164766i	0.995882	+	0.0906564i	$0.0288965\pi$
$374$	−57.5364	−	24.3953i	−0.153841	−	0.0652282i
$375$		0			0
$376$	−60.1353	+	36.2322i	−0.159934	+	0.0963621i
$377$	170.902			0.453320
$378$		0			0
$379$		−	341.891i		−	0.902088i	−0.892502	−	0.451044i	$-0.851052\pi$
$379$		−	341.891i		−	0.902088i	0.892502	−	0.451044i	$-0.148948\pi$
$380$	−135.210	−	540.437i	−0.355815	−	1.42220i
$381$		0			0
$382$	467.274	+	198.124i	1.22323	+	0.518648i
$383$	−173.175	−	30.5355i	−0.452155	−	0.0797272i	−0.0570670	−	0.998370i	$-0.518175\pi$
$383$	−173.175	−	30.5355i	−0.452155	−	0.0797272i	−0.395088	+	0.918643i	$0.629286\pi$
$384$		0			0
$385$	−179.776	+	150.850i	−0.466951	+	0.391818i
$386$	0.363099	−	0.389692i	0.000940672	−	0.00100956i
$387$		0			0
$388$	−49.2259	−	695.886i	−0.126871	−	1.79352i
$389$	−18.0397	−	102.308i	−0.0463746	−	0.263003i	0.952801	−	0.303595i	$-0.0981869\pi$
$389$	−18.0397	−	102.308i	−0.0463746	−	0.263003i	−0.999176	+	0.0405915i	$0.987076\pi$
$390$		0			0
$391$	23.1336	+	63.5590i	0.0591651	+	0.162555i
$392$	669.901	+	229.758i	1.70893	+	0.586117i
$393$		0			0
$394$	91.3209	−	46.5768i	0.231779	−	0.118215i
$395$	−435.744	−	251.577i	−1.10315	−	0.636904i
$396$		0			0
$397$	−309.052	−	535.294i	−0.778469	−	1.34835i	−0.932824	−	0.360333i	$-0.882663\pi$
$397$	−309.052	−	535.294i	−0.778469	−	1.34835i	0.154354	−	0.988016i	$-0.450670\pi$
$398$	−108.193	+	166.750i	−0.271841	+	0.418969i
$399$		0			0
$400$	−683.003	−	425.255i	−1.70751	−	1.06314i
$401$	157.870	+	132.468i	0.393690	+	0.330345i	0.818048	−	0.575149i	$-0.195056\pi$
$401$	157.870	+	132.468i	0.393690	+	0.330345i	−0.424359	+	0.905494i	$0.639500\pi$
$402$		0			0
$403$	0.709353	−	1.94893i	0.00176018	−	0.00483606i
$404$	−247.466	+	167.209i	−0.612539	+	0.413883i
$405$		0			0
$406$	813.749	−	249.148i	2.00431	−	0.613664i
$407$	29.8598	−	82.0391i	0.0733656	−	0.201570i
$408$		0			0
$409$	−197.638	−	165.838i	−0.483222	−	0.405472i	0.368368	−	0.929680i	$-0.379917\pi$
$409$	−197.638	−	165.838i	−0.483222	−	0.405472i	−0.851590	+	0.524208i	$0.824361\pi$
$410$	43.2482	−	5.32794i	0.105483	−	0.0129950i
$411$		0			0
$412$	−535.639	−	153.124i	−1.30009	−	0.371660i
$413$	−152.344	−	263.868i	−0.368872	−	0.638905i
$414$		0			0
$415$	502.919	+	290.361i	1.21185	+	0.699664i
$416$	−13.4392	−	150.119i	−0.0323058	−	0.360864i
$417$		0			0
$418$	44.5828	+	59.1137i	0.106657	+	0.141420i
$419$	41.7733	+	114.771i	0.0996975	+	0.273917i	0.979507	−	0.201410i	$-0.0645522\pi$
$419$	41.7733	+	114.771i	0.0996975	+	0.273917i	−0.879810	+	0.475326i	$0.842330\pi$
$420$		0			0
$421$	−19.2591	−	109.224i	−0.0457461	−	0.259439i	0.953354	−	0.301855i	$-0.0976058\pi$
$421$	−19.2591	−	109.224i	−0.0457461	−	0.259439i	−0.999100	+	0.0424156i	$0.986495\pi$
$422$	−45.8470	+	198.952i	−0.108642	+	0.471450i
$423$		0			0
$424$	51.4942	−	327.690i	0.121449	−	0.772854i
$425$	521.893	−	437.920i	1.22798	−	1.03040i
$426$		0			0
$427$	771.550	+	136.045i	1.80691	+	0.318607i
$428$	−11.6589	+	111.795i	−0.0272404	+	0.261204i
$429$		0			0
$430$	309.478	+	16.0937i	0.719716	+	0.0374273i
$431$			697.944i			1.61936i	0.586872	+	0.809679i	$0.300359\pi$
$431$			697.944i			1.61936i	−0.586872	+	0.809679i	$0.699641\pi$
$432$		0			0
$433$	−599.940			−1.38554			−0.692772	−	0.721157i	$-0.743611\pi$
$433$	−599.940			−1.38554			−0.692772	+	0.721157i	$0.743611\pi$
$434$	0.536356	−	10.3140i	0.00123584	−	0.0237649i
$435$		0			0
$436$	−50.8717	−	5.30529i	−0.116678	−	0.0121681i
$437$	13.9152	−	78.9172i	0.0318426	−	0.180589i
$438$		0			0
$439$	501.455	+	597.611i	1.14227	+	1.36130i	0.922615	+	0.385722i	$0.126048\pi$
$439$	501.455	+	597.611i	1.14227	+	1.36130i	0.219652	+	0.975578i	$0.429508\pi$
$440$	158.153	+	24.8527i	0.359440	+	0.0564834i
$441$		0			0
$442$	124.365	+	28.6590i	0.281368	+	0.0648393i
$443$	682.883	−	120.411i	1.54150	−	0.271807i	0.662656	−	0.748924i	$-0.269429\pi$
$443$	682.883	−	120.411i	1.54150	−	0.271807i	0.878840	+	0.477117i	$0.158318\pi$
$444$		0			0
$445$	885.776	−	322.396i	1.99051	−	0.724485i
$446$	525.418	−	396.263i	1.17807	−	0.888483i
$447$		0			0
$448$	−282.841	−	695.202i	−0.631342	−	1.55179i
$449$	263.993	−	457.250i	0.587959	−	1.01837i	−0.406541	−	0.913633i	$-0.633265\pi$
$449$	263.993	−	457.250i	0.587959	−	1.01837i	0.994499	−	0.104742i	$-0.0334016\pi$
$450$		0			0
$451$	−5.01548	+	2.89569i	−0.0111208	+	0.00642060i
$452$	231.361	−	809.319i	0.511861	−	1.79053i
$453$		0			0
$454$	84.3964	+	685.066i	0.185895	+	1.50896i
$455$	308.060	−	367.132i	0.677056	−	0.806884i
$456$		0			0
$457$	125.330	+	45.6162i	0.274244	+	0.0998167i	0.475481	−	0.879726i	$-0.342274\pi$
$457$	125.330	+	45.6162i	0.274244	+	0.0998167i	−0.201237	+	0.979543i	$0.564496\pi$
$458$	−170.470	−	556.779i	−0.372206	−	1.21567i
$459$		0			0
$460$	−97.0076	−	143.569i	−0.210886	−	0.312107i
$461$	497.956	+	181.241i	1.08017	+	0.393148i	0.819969	−	0.572408i	$-0.193991\pi$
$461$	497.956	+	181.241i	1.08017	+	0.393148i	0.260196	+	0.965556i	$0.416213\pi$
$462$		0			0
$463$	314.968	−	375.364i	0.680277	−	0.810722i	−0.309867	−	0.950780i	$-0.600284\pi$
$463$	314.968	−	375.364i	0.680277	−	0.810722i	0.990143	+	0.140058i	$0.0447289\pi$
$464$	−492.838	−	306.853i	−1.06215	−	0.661322i
$465$		0			0
$466$	−166.243	−	107.864i	−0.356745	−	0.231468i
$467$	−168.249	+	97.1384i	−0.360276	+	0.208005i	−0.669202	−	0.743081i	$-0.733364\pi$
$467$	−168.249	+	97.1384i	−0.360276	+	0.208005i	0.308926	+	0.951086i	$0.400030\pi$
$468$		0			0
$469$	−555.093	+	961.449i	−1.18357	+	2.05000i
$470$	69.1939	+	135.665i	0.147221	+	0.288649i
$471$		0			0
$472$	−67.4318	+	196.610i	−0.142864	+	0.416546i
$473$	−38.7030	+	14.0867i	−0.0818246	+	0.0297817i
$474$		0			0
$475$	−794.892	+	140.161i	−1.67346	+	0.295076i
$476$	633.944	−	44.8442i	1.33182	−	0.0942106i
$477$		0			0
$478$	−168.846	−	157.324i	−0.353233	−	0.329129i
$479$	13.8081	+	16.4559i	0.0288270	+	0.0343547i	0.780265	−	0.625449i	$-0.215084\pi$
$479$	13.8081	+	16.4559i	0.0288270	+	0.0343547i	−0.751438	+	0.659803i	$0.770640\pi$
$480$		0			0
$481$	−30.9596	+	175.581i	−0.0643652	+	0.365033i
$482$	−91.3144	+	215.365i	−0.189449	+	0.446815i
$483$		0			0
$484$	448.887	−	112.305i	0.927453	−	0.232036i
$485$	−1513.28			−3.12016
$486$		0			0
$487$			669.554i			1.37485i	0.726254	+	0.687427i	$0.241260\pi$
$487$			669.554i			1.37485i	−0.726254	+	0.687427i	$0.758740\pi$
$488$	−275.819	−	457.783i	−0.565203	−	0.938080i
$489$		0			0
$490$	599.682	−	1414.35i	1.22384	−	2.88643i
$491$	−571.962	−	100.852i	−1.16489	−	0.205402i	−0.442424	−	0.896806i	$-0.645881\pi$
$491$	−571.962	−	100.852i	−1.16489	−	0.205402i	−0.722468	+	0.691404i	$0.756993\pi$
$492$		0			0
$493$	376.585	−	315.992i	0.763864	−	0.640958i
$494$	−110.625	−	103.076i	−0.223937	−	0.208656i
$495$		0			0
$496$	−5.54490	+	4.34659i	−0.0111792	+	0.00876329i
$497$	235.632	+	1336.34i	0.474109	+	2.68881i
$498$		0			0
$499$	−164.520	−	452.016i	−0.329700	−	0.905844i	−0.988187	−	0.153252i	$-0.951025\pi$
$499$	−164.520	−	452.016i	−0.329700	−	0.905844i	0.658487	−	0.752592i	$-0.271197\pi$
$500$	−515.261	+	710.402i	−1.03052	+	1.42080i
$501$		0			0
$502$	133.896	+	262.523i	0.266725	+	0.522955i
$503$	−373.012	−	215.359i	−0.741575	−	0.428148i	0.0810668	−	0.996709i	$-0.474167\pi$
$503$	−373.012	−	215.359i	−0.741575	−	0.428148i	−0.822642	+	0.568560i	$0.807501\pi$
$504$		0			0
$505$	323.925	+	561.054i	0.641435	+	1.11100i
$506$	19.3185	+	12.5345i	0.0381788	+	0.0247717i
$507$		0			0
$508$	−407.307	+	181.739i	−0.801786	+	0.357754i
$509$	−444.761	−	373.199i	−0.873793	−	0.733200i	0.0911001	−	0.995842i	$-0.470962\pi$
$509$	−444.761	−	373.199i	−0.873793	−	0.733200i	−0.964893	+	0.262642i	$0.915406\pi$
$510$		0			0
$511$	−180.760	+	496.634i	−0.353738	+	0.971887i
$512$	−230.784	+	457.037i	−0.450749	+	0.892651i
$513$		0			0
$514$	183.584	+	599.609i	0.357167	+	1.16655i
$515$	−413.312	+	1135.57i	−0.802548	+	2.20498i
$516$		0			0
$517$	−15.5051	−	13.0103i	−0.0299905	−	0.0251650i
$518$	108.555	+	881.164i	0.209565	+	1.70109i
$519$		0			0
$520$	−326.882	+	6.10188i	−0.628619	+	0.0117344i
$521$	−193.570	−	335.273i	−0.371535	−	0.643517i	0.618267	−	0.785968i	$-0.287835\pi$
$521$	−193.570	−	335.273i	−0.371535	−	0.643517i	−0.989802	+	0.142451i	$0.954502\pi$
$522$		0			0
$523$	142.838	+	82.4674i	0.273112	+	0.157681i	0.630301	−	0.776351i	$-0.282931\pi$
$523$	142.838	+	82.4674i	0.273112	+	0.157681i	−0.357189	+	0.934032i	$0.616265\pi$
$524$	−45.3882	+	43.9018i	−0.0866187	+	0.0837820i
$525$		0			0
$526$	−327.720	+	247.163i	−0.623043	+	0.469891i
$527$	−2.04045	−	5.60608i	−0.00387181	−	0.0106377i
$528$		0			0
$529$	87.5319	+	496.418i	0.165467	+	0.938408i
$530$	−701.167	−	161.579i	−1.32296	−	0.304866i
$531$		0			0
$532$	−677.010	−	329.523i	−1.27258	−	0.619405i
$533$	9.05997	−	7.60221i	0.0169981	−	0.0142631i
$534$		0			0
$535$	240.116	+	42.3389i	0.448815	+	0.0791382i
$536$	743.255	−	145.409i	1.38667	−	0.271285i
$537$		0			0
$538$	−28.0876	+	540.116i	−0.0522074	+	1.00393i
$539$			204.173i			0.378800i
$540$		0			0
$541$	543.641			1.00488			0.502441	−	0.864612i	$-0.332436\pi$
$541$	543.641			1.00488			0.502441	+	0.864612i	$0.332436\pi$
$542$	−464.766	−	24.1692i	−0.857502	−	0.0445926i
$543$		0			0
$544$	−307.180	−	305.942i	−0.564669	−	0.562393i
$545$	−19.2660	+	109.263i	−0.0353504	+	0.200482i
$546$		0			0
$547$	−557.244	−	664.097i	−1.01873	−	1.21407i	−0.976623	−	0.214958i	$-0.931038\pi$
$547$	−557.244	−	664.097i	−1.01873	−	1.21407i	−0.0421038	−	0.999113i	$-0.513406\pi$
$548$	382.321	+	186.088i	0.697666	+	0.339577i
$549$		0			0
$550$	52.0873	−	226.031i	0.0947042	−	0.410966i
$551$	−573.574	+	101.137i	−1.04097	+	0.183551i
$552$		0			0
$553$	−639.032	+	232.589i	−1.15557	+	0.420594i
$554$	−90.6619	−	120.211i	−0.163650	−	0.216988i
$555$		0			0
$556$	162.447	−	157.127i	0.292172	−	0.282603i
$557$	−251.191	+	435.076i	−0.450972	+	0.781106i	−0.998447	−	0.0557163i	$-0.982256\pi$
$557$	−251.191	+	435.076i	−0.450972	+	0.781106i	0.547475	+	0.836822i	$0.315589\pi$
$558$		0			0
$559$	72.8417	−	42.0552i	0.130307	−	0.0752329i
$560$	−1547.56	+	505.596i	−2.76349	+	0.902850i
$561$		0			0
$562$	278.672	−	34.3308i	0.495857	−	0.0610868i
$563$	34.7389	−	41.4002i	0.0617032	−	0.0735351i	−0.734310	−	0.678814i	$-0.762494\pi$
$563$	34.7389	−	41.4002i	0.0617032	−	0.0735351i	0.796013	+	0.605279i	$0.206939\pi$
$564$		0			0
$565$	−1715.77	−	624.490i	−3.03677	−	1.10529i
$566$	268.513	−	82.2113i	0.474405	−	0.145250i
$567$		0			0
$568$	581.679	−	720.096i	1.02408	−	1.26777i
$569$	−216.377	−	78.7548i	−0.380276	−	0.138409i	0.144808	−	0.989460i	$-0.453744\pi$
$569$	−216.377	−	78.7548i	−0.380276	−	0.138409i	−0.525083	+	0.851051i	$0.675966\pi$
$570$		0			0
$571$	−305.971	+	364.642i	−0.535850	+	0.638602i	−0.964252	−	0.264987i	$-0.914632\pi$
$571$	−305.971	+	364.642i	−0.535850	+	0.638602i	0.428402	+	0.903588i	$0.359077\pi$
$572$	39.6811	−	17.7056i	0.0693725	−	0.0309538i
$573$		0			0
$574$	32.0563	−	49.4060i	0.0558472	−	0.0860732i
$575$	−217.412	+	125.523i	−0.378108	+	0.218301i
$576$		0			0
$577$	−146.058	+	252.980i	−0.253133	+	0.438440i	−0.964387	−	0.264496i	$-0.914795\pi$
$577$	−146.058	+	252.980i	−0.253133	+	0.438440i	0.711253	+	0.702936i	$0.248128\pi$
$578$	−187.866	+	95.8182i	−0.325028	+	0.165775i
$579$		0			0
$580$	−739.397	+	1019.42i	−1.27482	+	1.75763i
$581$	737.546	−	268.445i	1.26944	−	0.462039i
$582$		0			0
$583$	94.1784	−	16.6062i	0.161541	−	0.0284840i
$584$	336.433	−	129.612i	0.576083	−	0.221939i
$585$		0			0
$586$	453.909	−	487.152i	0.774589	−	0.831318i
$587$	−536.993	−	639.963i	−0.914809	−	1.09023i	−0.995620	−	0.0934972i	$-0.970195\pi$
$587$	−536.993	−	639.963i	−0.914809	−	1.09023i	0.0808107	−	0.996729i	$-0.474249\pi$
$588$		0			0
$589$	−1.22736	+	6.96072i	−0.00208381	+	0.0118179i
$590$	415.098	+	176.001i	0.703556	+	0.298306i
$591$		0			0
$592$	404.535	−	450.744i	0.683336	−	0.761391i
$593$	253.977			0.428292			0.214146	−	0.976802i	$-0.431303\pi$
$593$	253.977			0.428292			0.214146	+	0.976802i	$0.431303\pi$
$594$		0			0
$595$		−	1378.58i		−	2.31694i
$596$	454.541	−	113.720i	0.762653	−	0.190805i
$597$		0			0
$598$	−43.2971	−	18.3579i	−0.0724032	−	0.0306988i
$599$	1092.94	+	192.715i	1.82460	+	0.321727i	0.977698	−	0.210015i	$-0.0673512\pi$
$599$	1092.94	+	192.715i	1.82460	+	0.321727i	0.846907	+	0.531742i	$0.178462\pi$
$600$		0			0
$601$	303.355	−	254.545i	0.504750	−	0.423536i	−0.354527	−	0.935046i	$-0.615358\pi$
$601$	303.355	−	254.545i	0.504750	−	0.423536i	0.859277	+	0.511510i	$0.170914\pi$
$602$	285.527	−	306.438i	0.474297	−	0.509033i
$603$		0			0
$604$	991.732	−	70.1536i	1.64194	−	0.116148i
$605$	−174.296	−	988.481i	−0.288092	−	1.63385i
$606$		0			0
$607$	−185.277	−	509.044i	−0.305234	−	0.838622i	−0.993569	−	0.113230i	$-0.963880\pi$
$607$	−185.277	−	509.044i	−0.305234	−	0.838622i	0.688335	−	0.725393i	$-0.258342\pi$
$608$	133.942	+	495.872i	0.220300	+	0.815580i
$609$		0			0
$610$	−1032.76	+	526.742i	−1.69305	+	0.863511i
$611$	35.7965	+	20.6671i	0.0585868	+	0.0338251i
$612$		0			0
$613$	−343.368	−	594.730i	−0.560143	−	0.970196i	−0.997483	−	0.0709000i	$-0.977413\pi$
$613$	−343.368	−	594.730i	−0.560143	−	0.970196i	0.437341	−	0.899296i	$-0.355920\pi$
$614$	221.657	−	341.623i	0.361004	−	0.556390i
$615$		0			0
$616$	163.130	−	142.154i	0.264821	−	0.230769i
$617$	−657.785	−	551.947i	−1.06610	−	0.894566i	−0.0714083	−	0.997447i	$-0.522749\pi$
$617$	−657.785	−	551.947i	−1.06610	−	0.894566i	−0.994694	+	0.102881i	$0.967194\pi$
$618$		0			0
$619$	80.2415	−	220.462i	0.129631	−	0.356158i	−0.857849	−	0.513901i	$-0.828200\pi$
$619$	80.2415	−	220.462i	0.129631	−	0.356158i	0.987480	+	0.157743i	$0.0504219\pi$
$620$	8.55634	+	12.6632i	0.0138005	+	0.0204246i
$621$		0			0
$622$	−353.661	+	108.281i	−0.568587	+	0.174086i
$623$	435.738	−	1197.18i	0.699419	−	1.92164i
$624$		0			0
$625$	495.256	+	415.569i	0.792410	+	0.664911i
$626$	220.171	−	27.1238i	0.351710	−	0.0433287i
$627$		0			0
$628$	−203.911	+	713.296i	−0.324699	+	1.13582i
$629$	256.424	+	444.139i	0.407669	+	0.706104i
$630$		0			0
$631$	−124.225	−	71.7213i	−0.196870	−	0.113663i	0.398325	−	0.917244i	$-0.369592\pi$
$631$	−124.225	−	71.7213i	−0.196870	−	0.113663i	−0.595195	+	0.803582i	$0.702925\pi$
$632$	406.018	+	224.417i	0.642434	+	0.355090i
$633$		0			0
$634$	−163.543	−	216.847i	−0.257955	−	0.342030i
$635$	330.900	+	909.139i	0.521102	+	1.43172i
$636$		0			0
$637$	−72.4036	−	410.621i	−0.113663	−	0.644617i
$638$	37.5849	−	163.098i	0.0589105	−	0.255640i
$639$		0			0
$640$	953.602	+	569.319i	1.49000	+	0.889561i
$641$	−334.138	+	280.375i	−0.521276	+	0.437403i	−0.865076	−	0.501640i	$-0.832730\pi$
$641$	−334.138	+	280.375i	−0.521276	+	0.437403i	0.343800	+	0.939043i	$0.388286\pi$
$642$		0			0
$643$	1138.09	+	200.676i	1.76997	+	0.312094i	0.961164	−	0.275978i	$-0.0890017\pi$
$643$	1138.09	+	200.676i	1.76997	+	0.312094i	0.808809	+	0.588072i	$0.200113\pi$
$644$	−232.922	−	24.2910i	−0.361681	−	0.0377189i
$645$		0			0
$646$	−434.349	−	22.5874i	−0.672366	−	0.0349650i
$647$		−	935.380i		−	1.44572i	−0.690995	−	0.722859i	$-0.742827\pi$
$647$		−	935.380i		−	1.44572i	0.690995	−	0.722859i	$-0.257173\pi$
$648$		0			0
$649$	−59.9229			−0.0923312
$650$	−24.6000	+	473.052i	−0.0378462	+	0.727772i
$651$		0			0
$652$	−1.27396	+	12.2158i	−0.00195393	+	0.0187359i
$653$	140.779	−	798.399i	0.215588	−	1.22266i	−0.664294	−	0.747471i	$-0.731268\pi$
$653$	140.779	−	798.399i	0.215588	−	1.22266i	0.879882	−	0.475191i	$-0.157621\pi$
$654$		0			0
$655$	88.0464	+	104.930i	0.134422	+	0.160198i
$656$	−39.7765	+	5.65575i	−0.0606348	+	0.00862157i
$657$		0			0
$658$	200.575	+	46.2211i	0.304825	+	0.0702448i
$659$	−209.650	+	36.9669i	−0.318133	+	0.0560954i	−0.330435	−	0.943829i	$-0.607195\pi$
$659$	−209.650	+	36.9669i	−0.318133	+	0.0560954i	0.0123016	+	0.999924i	$0.496084\pi$
$660$		0			0
$661$	−88.9075	+	32.3597i	−0.134505	+	0.0489556i	−0.408395	−	0.912805i	$-0.633912\pi$
$661$	−88.9075	+	32.3597i	−0.134505	+	0.0489556i	0.273891	+	0.961761i	$0.411689\pi$
$662$	−284.235	+	214.366i	−0.429358	+	0.323816i
$663$		0			0
$664$	−468.610	−	259.013i	−0.705738	−	0.390080i
$665$	−816.640	+	1414.46i	−1.22803	+	2.12701i
$666$		0			0
$667$	−156.879	+	90.5741i	−0.235201	+	0.135793i
$668$	−353.837	−	101.152i	−0.529697	−	0.151425i
$669$		0			0
$670$	−200.868	−	1630.49i	−0.299803	−	2.43357i
$671$	99.0416	−	118.033i	0.147603	−	0.175906i
$672$		0			0
$673$	−635.081	−	231.150i	−0.943656	−	0.343463i	−0.176048	−	0.984382i	$-0.556331\pi$
$673$	−635.081	−	231.150i	−0.943656	−	0.343463i	−0.767609	+	0.640919i	$0.778553\pi$
$674$	340.994	+	1113.73i	0.505926	+	1.65242i
$675$		0			0
$676$	486.598	−	328.787i	0.719820	−	0.486371i
$677$	916.610	+	333.619i	1.35393	+	0.492790i	0.914172	−	0.405327i	$-0.132842\pi$
$677$	916.610	+	333.619i	1.35393	+	0.492790i	0.439757	+	0.898117i	$0.355065\pi$
$678$		0			0
$679$	−1314.68	+	1566.78i	−1.93621	+	2.30748i
$680$	−709.008	+	617.841i	−1.04266	+	0.908589i
$681$		0			0
$682$	−1.70394	−	1.10558i	−0.00249845	−	0.00162108i
$683$	193.748	−	111.861i	0.283672	−	0.163778i	−0.351412	−	0.936221i	$-0.614299\pi$
$683$	193.748	−	111.861i	0.283672	−	0.163778i	0.635085	+	0.772442i	$0.280965\pi$
$684$		0			0
$685$	461.172	−	798.774i	0.673244	−	1.16609i
$686$	−421.205	−	825.837i	−0.614001	−	1.20384i
$687$		0			0
$688$	−285.568	−	9.51043i	−0.415069	−	0.0138233i
$689$	−183.517	+	66.7948i	−0.266353	+	0.0969445i
$690$		0			0
$691$	204.026	−	35.9752i	0.295262	−	0.0520626i	−0.0240551	−	0.999711i	$-0.507658\pi$
$691$	204.026	−	35.9752i	0.295262	−	0.0520626i	0.319317	+	0.947648i	$0.396547\pi$
$692$	−80.3186	−	1135.43i	−0.116067	−	1.64080i
$693$		0			0
$694$	−398.228	−	371.053i	−0.573816	−	0.534659i
$695$	−315.124	−	375.550i	−0.453416	−	0.540360i
$696$		0			0
$697$	5.90752	−	33.5032i	0.00847565	−	0.0480678i
$698$	−199.063	+	469.489i	−0.285190	+	0.672621i
$699$		0			0
$700$	572.501	+	2288.30i	0.817859	+	3.26900i
$701$	318.924			0.454955			0.227478	−	0.973783i	$-0.426952\pi$
$701$	318.924			0.454955			0.227478	+	0.973783i	$0.426952\pi$
$702$		0			0
$703$		−	607.600i		−	0.864296i
$704$	−146.221	−	20.1888i	−0.207700	−	0.0286773i
$705$		0			0
$706$	−179.618	+	423.628i	−0.254416	+	0.600040i
$707$	862.306	+	152.048i	1.21967	+	0.215060i
$708$		0			0
$709$	469.253	−	393.750i	0.661852	−	0.555360i	−0.248789	−	0.968558i	$-0.580033\pi$
$709$	469.253	−	393.750i	0.661852	−	0.555360i	0.910641	+	0.413198i	$0.135588\pi$
$710$	−1469.09	−	1368.84i	−2.06915	−	1.92795i
$711$		0			0
$712$	−811.000	+	312.442i	−1.13905	+	0.438823i
$713$	0.381741	+	2.16496i	0.000535401	+	0.00303641i
$714$		0			0
$715$	−32.2372	−	88.5710i	−0.0450870	−	0.123876i
$716$	−139.611	−	101.261i	−0.194988	−	0.141426i
$717$		0			0
$718$	538.994	+	1056.78i	0.750688	+	1.47184i
$719$	983.957	+	568.088i	1.36851	+	0.790108i	0.990737	−	0.135792i	$-0.0433577\pi$
$719$	983.957	+	568.088i	1.36851	+	0.790108i	0.377770	+	0.925900i	$0.376691\pi$
$720$		0			0
$721$	816.643	+	1414.47i	1.13265	+	1.96181i
$722$	−173.405	−	112.511i	−0.240173	−	0.155832i
$723$		0			0
$724$	170.256	+	381.572i	0.235161	+	0.527034i
$725$	1397.73	+	1172.84i	1.92791	+	1.61771i
$726$		0			0
$727$	393.913	−	1082.27i	0.541834	−	1.48868i	−0.302653	−	0.953101i	$-0.597872\pi$
$727$	393.913	−	1082.27i	0.541834	−	1.48868i	0.844487	−	0.535576i	$-0.179905\pi$
$728$	−277.666	+	343.740i	−0.381410	+	0.472171i
$729$		0			0
$730$	−228.957	−	747.804i	−0.313639	−	1.02439i
$731$	82.7492	−	227.352i	0.113200	−	0.311015i
$732$		0			0
$733$	405.935	+	340.620i	0.553800	+	0.464693i	0.876225	−	0.481902i	$-0.160054\pi$
$733$	405.935	+	340.620i	0.553800	+	0.464693i	−0.322426	+	0.946595i	$0.604498\pi$
$734$	81.5182	+	661.703i	0.111060	+	0.901503i
$735$		0			0
$736$	91.8965	+	130.679i	0.124859	+	0.177554i
$737$	109.170	+	189.088i	0.148127	+	0.256564i
$738$		0			0
$739$	−1010.52	−	583.424i	−1.36742	−	0.789478i	−0.376819	−	0.926287i	$-0.622982\pi$
$739$	−1010.52	−	583.424i	−1.36742	−	0.789478i	−0.990597	+	0.136809i	$0.956315\pi$
$740$	−913.390	−	944.315i	−1.23431	−	1.27610i
$741$		0			0
$742$	−776.442	+	585.583i	−1.04642	+	0.789195i
$743$	−297.963	−	818.648i	−0.401028	−	1.10181i	−0.961778	−	0.273829i	$-0.911710\pi$
$743$	−297.963	−	818.648i	−0.401028	−	1.10181i	0.560751	−	0.827985i	$-0.310513\pi$
$744$		0			0
$745$	−176.491	−	1000.93i	−0.236901	−	1.34353i
$746$	121.624	+	28.0274i	0.163035	+	0.0375703i
$747$		0			0
$748$	54.7009	−	112.384i	0.0731295	−	0.150246i
$749$	252.441	−	211.823i	0.337037	−	0.282807i
$750$		0			0
$751$	925.603	+	163.209i	1.23249	+	0.217322i	0.751696	−	0.659510i	$-0.229236\pi$
$751$	925.603	+	163.209i	1.23249	+	0.217322i	0.480798	+	0.876832i	$0.340347\pi$
$752$	−66.1205	−	123.872i	−0.0879263	−	0.164723i
$753$		0			0
$754$	−17.7508	+	341.342i	−0.0235421	+	0.452708i
$755$		−	2156.62i		−	2.85646i
$756$		0			0
$757$	1407.53			1.85935			0.929677	−	0.368376i	$-0.120086\pi$
$757$	1407.53			1.85935			0.929677	+	0.368376i	$0.120086\pi$
$758$	682.860	+	35.5107i	0.900871	+	0.0468478i
$759$		0			0
$760$	1093.46	−	213.922i	1.43876	−	0.281476i
$761$	40.6037	−	230.275i	0.0533558	−	0.302596i	−0.946438	−	0.322884i	$-0.895347\pi$
$761$	40.6037	−	230.275i	0.0533558	−	0.302596i	0.999794	+	0.0202889i	$0.00645859\pi$
$762$		0			0
$763$	96.3883	+	114.871i	0.126328	+	0.150552i
$764$	−444.246	+	912.709i	−0.581474	+	1.19465i
$765$		0			0
$766$	78.9755	−	342.712i	0.103101	−	0.447405i
$767$	120.513	−	21.2498i	0.157123	−	0.0277050i
$768$		0			0
$769$	352.803	−	128.410i	0.458781	−	0.166983i	−0.102282	−	0.994755i	$-0.532615\pi$
$769$	352.803	−	128.410i	0.458781	−	0.166983i	0.561064	+	0.827773i	$0.310392\pi$
$770$	−282.620	−	374.735i	−0.367039	−	0.486669i
$771$		0			0
$772$	0.740619	+	0.765694i	0.000959351	+	0.000991832i
$773$	−82.5621	+	143.002i	−0.106807	+	0.184996i	−0.914475	−	0.404642i	$-0.867396\pi$
$773$	−82.5621	+	143.002i	−0.106807	+	0.184996i	0.807668	+	0.589638i	$0.200729\pi$
$774$		0			0
$775$	19.1763	−	11.0715i	0.0247437	−	0.0142858i
$776$	1395.01	−	26.0405i	1.79769	−	0.0335573i
$777$		0			0
$778$	206.214	−	25.4044i	0.265057	−	0.0326535i
$779$	−25.9079	+	30.8758i	−0.0332579	+	0.0396352i
$780$		0			0
$781$	250.777	+	91.2753i	0.321097	+	0.116870i
$782$	−129.349	+	39.6031i	−0.165408	+	0.0506434i
$783$		0			0
$784$	−528.476	+	1314.13i	−0.674076	+	1.67619i
$785$	1512.20	+	550.397i	1.92637	+	0.701142i
$786$		0			0
$787$	681.597	−	812.295i	0.866070	−	1.03214i	−0.133088	−	0.991104i	$-0.542489\pi$
$787$	681.597	−	812.295i	0.866070	−	1.03214i	0.999158	−	0.0410374i	$-0.0130663\pi$
$788$	83.5428	+	187.233i	0.106019	+	0.237605i
$789$		0			0
$790$	547.734	−	844.183i	0.693334	−	1.06859i
$791$	−2137.18	+	1233.90i	−2.70187	+	1.55992i
$792$		0			0
$793$	−157.330	+	272.503i	−0.198398	+	0.343636i
$794$	1101.24	−	561.672i	1.38696	−	0.707396i
$795$		0			0
$796$	−321.812	−	233.413i	−0.404286	−	0.293233i
$797$	−649.352	+	236.345i	−0.814745	+	0.296543i	−0.715583	−	0.698528i	$-0.753839\pi$
$797$	−649.352	+	236.345i	−0.814745	+	0.296543i	−0.0991628	+	0.995071i	$0.531616\pi$
$798$		0			0
$799$	117.091	−	20.6464i	0.146547	−	0.0258402i
$800$	920.303	−	1319.99i	1.15038	−	1.64999i
$801$		0			0
$802$	−280.976	+	301.554i	−0.350344	+	0.376003i
$803$	66.8122	+	79.6236i	0.0832032	+	0.0991577i
$804$		0			0
$805$	−88.2118	+	500.274i	−0.109580	+	0.621459i
$806$	3.81892	+	1.61922i	0.00473812	+	0.00200895i
$807$		0			0
$808$	−308.263	−	511.631i	−0.381514	−	0.633207i
$809$	−10.7246			−0.0132566			−0.00662832	−	0.999978i	$-0.502110\pi$
$809$	−10.7246			−0.0132566			−0.00662832	+	0.999978i	$0.502110\pi$
$810$		0			0
$811$			1400.90i			1.72738i	0.504026	+	0.863688i	$0.331852\pi$
$811$			1400.90i			1.72738i	−0.504026	+	0.863688i	$0.668148\pi$
$812$	413.102	+	1651.18i	0.508747	+	2.03347i
$813$		0			0
$814$	160.755	+	68.1600i	0.197488	+	0.0837347i
$815$	26.2373	+	4.62635i	0.0321930	+	0.00567650i
$816$		0			0
$817$	−219.581	+	184.251i	−0.268766	+	0.225521i
$818$	351.756	−	377.518i	0.430020	−	0.461513i
$819$		0			0
$820$	6.14951	+	86.9331i	0.00749940	+	0.106016i
$821$	−142.689	−	809.228i	−0.173799	−	0.985661i	−0.939521	−	0.342490i	$-0.888730\pi$
$821$	−142.689	−	809.228i	−0.173799	−	0.985661i	0.765723	−	0.643171i	$-0.222381\pi$
$822$		0			0
$823$	−321.791	−	884.112i	−0.390997	−	1.07426i	−0.966547	−	0.256489i	$-0.917434\pi$
$823$	−321.791	−	884.112i	−0.390997	−	1.07426i	0.575550	−	0.817767i	$-0.304788\pi$
$824$	361.469	−	1053.93i	0.438676	−	1.27904i
$825$		0			0
$826$	542.847	−	276.870i	0.657199	−	0.335194i
$827$	876.335	+	505.952i	1.05965	+	0.611792i	0.925337	−	0.379146i	$-0.123782\pi$
$827$	876.335	+	505.952i	1.05965	+	0.611792i	0.134318	+	0.990938i	$0.457116\pi$
$828$		0			0
$829$	−460.400	−	797.436i	−0.555368	−	0.961925i	−0.997875	−	0.0651600i	$-0.979244\pi$
$829$	−460.400	−	797.436i	−0.555368	−	0.961925i	0.442507	−	0.896765i	$-0.354089\pi$
$830$	−632.173	+	974.323i	−0.761655	+	1.17388i
$831$		0			0
$832$	301.229	−	11.2500i	0.362055	−	0.0135216i
$833$	−918.770	−	770.939i	−1.10296	−	0.925497i
$834$		0			0
$835$	−273.030	+	750.143i	−0.326982	+	0.898375i
$836$	−122.698	+	82.9054i	−0.146768	+	0.0991691i
$837$		0			0
$838$	−233.571	+	71.5130i	−0.278725	+	0.0853377i
$839$	−139.473	+	383.198i	−0.166237	+	0.456732i	−0.994640	−	0.103401i	$-0.967028\pi$
$839$	−139.473	+	383.198i	−0.166237	+	0.456732i	0.828403	+	0.560133i	$0.189250\pi$
$840$		0			0
$841$	364.326	+	305.706i	0.433206	+	0.363503i
$842$	220.153	−	27.1217i	0.261465	−	0.0322110i
$843$		0			0
$844$	−392.605	−	112.235i	−0.465171	−	0.132979i
$845$	−636.942	−	1103.22i	−0.753777	−	1.30558i
$846$		0			0
$847$	−1174.85	−	678.302i	−1.38708	−	0.800828i
$848$	649.148	+	136.885i	0.765504	+	0.161421i
$849$		0			0
$850$	820.452	+	1087.86i	0.965238	+	1.27984i
$851$	−64.6347	−	177.582i	−0.0759514	−	0.208675i
$852$		0			0
$853$	−199.253	−	1130.02i	−0.233591	−	1.32476i	−0.845561	−	0.533879i	$-0.820734\pi$
$853$	−199.253	−	1130.02i	−0.233591	−	1.32476i	0.611970	−	0.790881i	$-0.290377\pi$
$854$	−351.860	+	1526.89i	−0.412015	+	1.78792i
$855$		0			0
$856$	−222.078	−	34.8980i	−0.259437	−	0.0407687i
$857$	−248.410	+	208.441i	−0.289861	+	0.243222i	−0.776109	−	0.630599i	$-0.782809\pi$
$857$	−248.410	+	208.441i	−0.289861	+	0.243222i	0.486249	+	0.873821i	$0.338365\pi$
$858$		0			0
$859$	−978.617	−	172.557i	−1.13925	−	0.200881i	−0.427974	−	0.903791i	$-0.640772\pi$
$859$	−978.617	−	172.557i	−1.13925	−	0.200881i	−0.711278	+	0.702910i	$0.751883\pi$
$860$	−64.2880	+	616.449i	−0.0747535	+	0.716801i
$861$		0			0
$862$	−1394.00	−	72.4922i	−1.61717	−	0.0840976i
$863$			1635.75i			1.89543i	0.319121	+	0.947714i	$0.396613\pi$
$863$			1635.75i			1.89543i	−0.319121	+	0.947714i	$0.603387\pi$
$864$		0			0
$865$	−2469.11			−2.85447
$866$	62.3130	−	1198.26i	0.0719550	−	1.38367i
$867$		0			0
$868$	20.5444	+	2.14253i	0.0236687	+	0.00246835i
$869$	−23.2244	+	131.712i	−0.0267254	+	0.151567i
$870$		0			0
$871$	−286.610	−	341.568i	−0.329059	−	0.392157i
$872$	15.8801	−	101.055i	0.0182111	−	0.115889i
$873$		0			0
$874$	156.176	+	35.9897i	0.178691	+	0.0411781i
$875$	2533.82	−	446.780i	2.89579	−	0.510606i
$876$		0			0
$877$	1496.49	−	544.677i	1.70637	−	0.621068i	0.709845	−	0.704358i	$-0.248765\pi$
$877$	1496.49	−	544.677i	1.70637	−	0.621068i	0.996525	+	0.0832905i	$0.0265429\pi$
$878$	−1245.69	+	939.486i	−1.41878	+	1.07003i
$879$		0			0
$880$	−66.0650	+	313.299i	−0.0750738	+	0.356021i
$881$	418.502	−	724.867i	0.475031	−	0.822777i	−0.524560	−	0.851373i	$-0.675770\pi$
$881$	418.502	−	724.867i	0.475031	−	0.822777i	0.999591	+	0.0285961i	$0.00910366\pi$
$882$		0			0
$883$	951.790	−	549.516i	1.07791	−	0.622329i	0.147575	−	0.989051i	$-0.452853\pi$
$883$	951.790	−	549.516i	1.07791	−	0.622329i	0.930331	+	0.366722i	$0.119520\pi$
$884$	−70.1578	+	245.417i	−0.0793640	+	0.277621i
$885$		0			0
$886$	169.568	+	1376.43i	0.191387	+	1.55353i
$887$	607.213	−	723.649i	0.684570	−	0.815838i	−0.306118	−	0.951994i	$-0.599030\pi$
$887$	607.213	−	723.649i	0.684570	−	0.815838i	0.990688	+	0.136155i	$0.0434746\pi$
$888$		0			0
$889$	1228.76	+	447.231i	1.38218	+	0.503072i
$890$	551.921	+	1802.65i	0.620135	+	2.02545i
$891$		0			0
$892$	736.885	+	1090.58i	0.826104	+	1.22262i
$893$	−132.370	−	48.1786i	−0.148230	−	0.0539514i
$894$		0			0
$895$	−240.476	+	286.588i	−0.268688	+	0.320210i
$896$	1417.91	−	492.712i	1.58248	−	0.549902i
$897$		0			0
$898$	885.846	+	574.767i	0.986466	+	0.640052i
$899$	13.8372	−	7.98889i	0.0153917	−	0.00888642i
$900$		0			0
$901$	−280.882	+	486.501i	−0.311744	+	0.539957i
$902$	−5.26263	−	10.3182i	−0.00583440	−	0.0114392i
$903$		0			0
$904$	1592.42	+	546.158i	1.76153	+	0.604157i
$905$	851.697	−	309.992i	0.941102	−	0.342533i
$906$		0			0
$907$	−1707.97	+	301.161i	−1.88310	+	0.332041i	−0.992449	−	0.122655i	$-0.960859\pi$
$907$	−1707.97	+	301.161i	−1.88310	+	0.332041i	−0.890647	+	0.454696i	$0.849748\pi$
$908$	−1377.05	+	97.4103i	−1.51657	+	0.107280i
$909$		0			0
$910$	701.277	+	653.422i	0.770634	+	0.718046i
$911$	242.902	+	289.479i	0.266632	+	0.317760i	0.882703	−	0.469931i	$-0.155721\pi$
$911$	242.902	+	289.479i	0.266632	+	0.317760i	−0.616071	+	0.787691i	$0.711277\pi$
$912$		0			0
$913$	26.8047	−	152.017i	0.0293589	−	0.166503i
$914$	−104.127	+	245.583i	−0.113924	+	0.268690i
$915$		0			0
$916$	1129.76	−	282.650i	1.23336	−	0.308570i
$917$	185.131			0.201888
$918$		0			0
$919$		−	577.379i		−	0.628268i	−0.949379	−	0.314134i	$-0.898286\pi$
$919$		−	577.379i		−	0.628268i	0.949379	−	0.314134i	$-0.101714\pi$
$920$	296.827	−	178.842i	0.322638	−	0.194393i
$921$		0			0
$922$	−413.714	+	975.744i	−0.448713	+	1.05829i
$923$	−536.715	−	94.6374i	−0.581490	−	0.102532i
$924$		0			0
$925$	−1458.16	+	1223.54i	−1.57639	+	1.32275i
$926$	717.001	+	668.074i	0.774300	+	0.721462i
$927$		0			0
$928$	664.068	−	952.474i	0.715590	−	1.02637i
$929$	−58.9907	−	334.553i	−0.0634991	−	0.360121i	−0.999956	−	0.00933976i	$-0.997027\pi$
$929$	−58.9907	−	334.553i	−0.0634991	−	0.360121i	0.936457	−	0.350782i	$-0.114084\pi$
$930$		0			0
$931$	485.997	+	1335.27i	0.522016	+	1.43423i
$932$	232.704	−	320.835i	0.249683	−	0.344243i
$933$		0			0
$934$	−176.539	−	346.133i	−0.189014	−	0.370592i
$935$	−234.801	−	135.562i	−0.251124	−	0.144986i
$936$		0			0
$937$	583.029	+	1009.84i	0.622230	+	1.07773i	0.989070	+	0.147449i	$0.0471063\pi$
$937$	583.029	+	1009.84i	0.622230	+	1.07773i	−0.366840	+	0.930284i	$0.619560\pi$
$938$	−1862.65	−	1208.55i	−1.98577	−	1.28843i
$939$		0			0
$940$	−278.151	+	124.110i	−0.295905	+	0.132032i
$941$	−398.127	−	334.068i	−0.423089	−	0.355014i	0.406248	−	0.913763i	$-0.366837\pi$
$941$	−398.127	−	334.068i	−0.423089	−	0.355014i	−0.829337	+	0.558749i	$0.811282\pi$
$942$		0			0
$943$	−4.28758	+	11.7800i	−0.00454675	+	0.0124921i
$944$	−385.685	−	155.102i	−0.408564	−	0.164303i
$945$		0			0
$946$	−24.1156	−	78.7647i	−0.0254921	−	0.0832608i
$947$	−456.322	+	1253.73i	−0.481861	+	1.32390i	0.426036	+	0.904706i	$0.359910\pi$
$947$	−456.322	+	1253.73i	−0.481861	+	1.32390i	−0.907896	+	0.419195i	$0.862312\pi$
$948$		0			0
$949$	−162.605	−	136.441i	−0.171343	−	0.143774i
$950$	−197.382	−	1602.20i	−0.207770	−	1.68652i
$951$		0			0
$952$	23.7226	+	1270.84i	0.0249187	+	1.33491i
$953$	−8.15378	−	14.1228i	−0.00855591	−	0.0148193i	0.861716	−	0.507391i	$-0.169390\pi$
$953$	−8.15378	−	14.1228i	−0.00855591	−	0.0148193i	−0.870272	+	0.492572i	$0.836057\pi$
$954$		0			0
$955$	1906.90	+	1100.95i	1.99676	+	1.15283i
$956$	331.760	−	320.895i	0.347029	−	0.335664i
$957$		0			0
$958$	−34.3016	+	25.8698i	−0.0358054	+	0.0270040i
$959$	−426.364	−	1171.43i	−0.444592	−	1.22151i
$960$		0			0
$961$	166.842	+	946.209i	0.173613	+	0.984609i
$962$	−347.472	−	80.0725i	−0.361198	−	0.0832355i
$963$		0			0
$964$	−420.664	−	204.751i	−0.436374	−	0.212398i
$965$	1.77015	−	1.48533i	0.00183436	−	0.00153921i
$966$		0			0
$967$	−817.785	−	144.198i	−0.845693	−	0.149118i	−0.266020	−	0.963968i	$-0.585709\pi$
$967$	−817.785	−	144.198i	−0.845693	−	0.149118i	−0.579673	+	0.814849i	$0.696820\pi$
$968$	177.684	+	908.228i	0.183558	+	0.938252i
$969$		0			0
$970$	157.177	−	3022.47i	0.162038	−	3.11595i
$971$		−	308.493i		−	0.317706i	−0.987302	−	0.158853i	$-0.949220\pi$
$971$		−	308.493i		−	0.317706i	0.987302	−	0.158853i	$-0.0507796\pi$
$972$		0			0
$973$	−662.598			−0.680984
$974$	−1337.30	−	69.5434i	−1.37300	−	0.0713998i
$975$		0			0
$976$	942.979	−	503.346i	0.966167	−	0.515723i
$977$	−98.4489	+	558.332i	−0.100767	+	0.571476i	0.892060	+	0.451916i	$0.149259\pi$
$977$	−98.4489	+	558.332i	−0.100767	+	0.571476i	−0.992827	+	0.119560i	$0.961852\pi$
$978$		0			0
$979$	−161.057	−	191.940i	−0.164511	−	0.196057i
$980$	2762.59	+	1344.65i	2.81897	+	1.37209i
$981$		0			0
$982$	260.840	−	1131.91i	0.265621	−	1.15265i
$983$	−36.2725	+	6.39583i	−0.0368998	+	0.00650644i	−0.192068	−	0.981382i	$-0.561519\pi$
$983$	−36.2725	+	6.39583i	−0.0368998	+	0.00650644i	0.155168	+	0.987888i	$0.450408\pi$
$984$		0			0
$985$	417.918	−	152.110i	0.424282	−	0.154426i
$986$	592.017	+	784.974i	0.600423	+	0.796120i
$987$		0			0
$988$	217.364	−	210.245i	0.220004	−	0.212799i
$989$	−44.5767	+	77.2091i	−0.0450725	+	0.0780678i
$990$		0			0
$991$	−988.565	+	570.748i	−0.997543	+	0.575932i	−0.907520	−	0.420008i	$-0.862027\pi$
$991$	−988.565	+	570.748i	−0.997543	+	0.575932i	−0.0900228	+	0.995940i	$0.528694\pi$
$992$	−8.10553	−	11.5263i	−0.00817090	−	0.0116192i
$993$		0			0
$994$	−2693.54	+	331.829i	−2.70980	+	0.333832i
$995$	−554.311	+	660.602i	−0.557097	+	0.663922i
$996$		0			0
$997$	1263.46	+	459.861i	1.26726	+	0.461245i	0.886199	−	0.463306i	$-0.153337\pi$
$997$	1263.46	+	459.861i	1.26726	+	0.461245i	0.381060	+	0.924550i	$0.375559\pi$
$998$	919.900	−	281.648i	0.921744	−	0.282212i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.18		204
3.2	odd	2		108.3.j.a.31.17	yes	204
4.3	odd	2	inner	324.3.j.a.307.25		204
12.11	even	2		108.3.j.a.31.10	yes	204
27.7	even	9	inner	324.3.j.a.19.25		204
27.20	odd	18		108.3.j.a.7.10	✓	204
108.7	odd	18	inner	324.3.j.a.19.18		204
108.47	even	18		108.3.j.a.7.17	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.10	✓	204	27.20	odd	18
108.3.j.a.7.17	yes	204	108.47	even	18
108.3.j.a.31.10	yes	204	12.11	even	2
108.3.j.a.31.17	yes	204	3.2	odd	2
324.3.j.a.19.18		204	108.7	odd	18	inner
324.3.j.a.19.25		204	27.7	even	9	inner
324.3.j.a.307.18		204	1.1	even	1	trivial
324.3.j.a.307.25		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)

\(f(q)\)	\(=\)	\(q+(-0.103865 + 1.99730i) q^{2} +(-3.97842 - 0.414901i) q^{4} +(-1.50670 + 8.54492i) q^{5} +(7.53806 + 8.98351i) q^{7} +(1.24190 - 7.90302i) q^{8} +O(q^{10})\)	\(q+(-0.103865 + 1.99730i) q^{2} +(-3.97842 - 0.414901i) q^{4} +(-1.50670 + 8.54492i) q^{5} +(7.53806 + 8.98351i) q^{7} +(1.24190 - 7.90302i) q^{8} +(-16.9103 - 3.89685i) q^{10} +(2.27133 - 0.400497i) q^{11} +(-4.42594 + 1.61091i) q^{13} +(-18.7257 + 14.1227i) q^{14} +(15.6557 + 3.30130i) q^{16} +(-6.77412 + 11.7331i) q^{17} +(13.9009 - 8.02568i) q^{19} +(9.53958 - 33.3702i) q^{20} +(0.564001 + 4.57813i) q^{22} +(3.20904 - 3.82439i) q^{23} +(-47.2531 - 17.1987i) q^{25} +(-2.75777 - 9.00726i) q^{26} +(-26.2623 - 38.8678i) q^{28} +(-34.0967 - 12.4102i) q^{29} +(-0.283047 + 0.337322i) q^{31} +(-8.21978 + 30.9263i) q^{32} +(-22.7310 - 14.7486i) q^{34} +(-88.1209 + 50.8766i) q^{35} +(18.9267 - 32.7821i) q^{37} +(14.5859 + 28.5979i) q^{38} +(65.6594 + 22.5194i) q^{40} +(-2.35960 + 0.858824i) q^{41} +(-17.5866 + 3.10099i) q^{43} +(-9.20249 + 0.650970i) q^{44} +(7.30515 + 6.80665i) q^{46} +(-5.64102 - 6.72271i) q^{47} +(-15.3723 + 87.1809i) q^{49} +(39.2590 - 92.5924i) q^{50} +(18.2767 - 4.57256i) q^{52} +41.4639 q^{53} +20.0118i q^{55} +(80.3584 - 48.4168i) q^{56} +(28.3283 - 66.8123i) q^{58} +(-25.5867 - 4.51163i) q^{59} +(51.1770 - 42.9426i) q^{61} +(-0.644335 - 0.600365i) q^{62} +(-60.9154 - 19.6296i) q^{64} +(-7.09654 - 40.2465i) q^{65} +(32.3784 + 88.9589i) q^{67} +(31.8184 - 43.8687i) q^{68} +(-92.4633 - 181.288i) q^{70} +(100.208 + 57.8552i) q^{71} +(22.5335 + 39.0292i) q^{73} +(63.5098 + 41.2073i) q^{74} +(-58.6335 + 26.1621i) q^{76} +(20.7193 + 17.3856i) q^{77} +(-19.8334 + 54.4917i) q^{79} +(-51.7978 + 128.803i) q^{80} +(-1.47025 - 4.80203i) q^{82} +(22.8909 - 62.8923i) q^{83} +(-90.0519 - 75.5626i) q^{85} +(-4.36697 - 35.4478i) q^{86} +(-0.344363 - 18.4478i) q^{88} +(-54.3190 - 94.0833i) q^{89} +(-47.8347 - 27.6174i) q^{91} +(-14.3537 + 13.8836i) q^{92} +(14.0132 - 10.5686i) q^{94} +(47.6343 + 130.874i) q^{95} +(30.2853 + 171.757i) q^{97} +(-172.530 - 39.7583i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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