LMFDB - Embedded newform 225.2.h.d.46.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(46,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.46"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.3
Root			$-2.17386 - 1.57940i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.d.181.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.830342 - 2.55553i) q^{2} +(-4.22323 - 3.06835i) q^{4} +(1.34843 - 1.78375i) q^{5} +1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(-3.43876 - 4.92706i) q^{10} +(-0.333373 + 1.02602i) q^{11} +(0.827310 + 2.54620i) q^{13} +(1.40082 - 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(-3.18079 + 2.31098i) q^{17} +(0.952655 - 0.692144i) q^{19} +(-11.1679 + 3.39571i) q^{20} +(2.34520 + 1.70389i) q^{22} +(1.25552 - 3.86409i) q^{23} +(-1.36350 - 4.81050i) q^{25} +7.19384 q^{26} +(-7.12476 - 5.17644i) q^{28} +(4.81846 + 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} +17.1155 q^{32} +(3.26463 + 10.0475i) q^{34} +(2.27485 - 3.00925i) q^{35} +(-1.41587 - 4.35761i) q^{37} +(-0.977766 - 3.00925i) q^{38} +(-0.367227 + 19.3448i) q^{40} +(3.47998 + 10.7103i) q^{41} +2.58587 q^{43} +(4.55609 - 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.55155 - 1.12727i) q^{47} -4.15389 q^{49} +(-13.4255 - 0.509905i) q^{50} +(4.31872 - 13.2917i) q^{52} +(-2.06187 - 1.49803i) q^{53} +(1.38062 + 1.97816i) q^{55} +(-11.8097 + 8.58028i) q^{56} +(12.9474 - 9.40685i) q^{58} +(-0.412843 - 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-5.89800 - 18.1522i) q^{62} +(6.29470 - 19.3731i) q^{64} +(5.65734 + 1.95765i) q^{65} +(-10.0683 + 7.31502i) q^{67} +20.5241 q^{68} +(-5.80133 - 8.31216i) q^{70} +(-4.84181 - 3.51778i) q^{71} +(-1.01996 + 3.13911i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(-0.562414 + 1.73093i) q^{77} +(3.23934 + 2.35351i) q^{79} +(27.0693 + 9.36699i) q^{80} +30.2600 q^{82} +(7.17988 - 5.21649i) q^{83} +(-0.166861 + 8.78989i) q^{85} +(2.14716 - 6.60827i) q^{86} +(-2.88461 - 8.87792i) q^{88} +(-4.77234 + 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(-17.1587 + 12.4666i) q^{92} +(-4.16908 + 3.02901i) q^{94} +(0.0499753 - 2.63260i) q^{95} +(-8.71166 - 6.32939i) q^{97} +(-3.44915 + 10.6154i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29}+ \cdots + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.830342	−	2.55553i	0.587140	−	1.80703i	−0.00335992	−	0.999994i	$-0.501069\pi$
$2$	0.830342	−	2.55553i	0.587140	−	1.80703i	0.590500	−	0.807038i	$-0.298931\pi$
$3$		0			0
$3$		0			0
$4$	−4.22323	−	3.06835i	−2.11161	−	1.53418i
$5$	1.34843	−	1.78375i	0.603034	−	0.797715i
$5$	1.34843	−	1.78375i	0.603034	−	0.797715i
$6$		0			0
$7$	1.68704			0.637642			0.318821	−	0.947815i	$-0.396713\pi$
$7$	1.68704			0.637642			0.318821	+	0.947815i	$0.396713\pi$
$8$	−7.00026	+	5.08599i	−2.47497	+	1.79817i
$9$		0			0
$10$	−3.43876	−	4.92706i	−1.08743	−	1.55807i
$11$	−0.333373	+	1.02602i	−0.100516	+	0.309356i	−0.988652	−	0.150225i	$-0.952000\pi$
$11$	−0.333373	+	1.02602i	−0.100516	+	0.309356i	0.888136	+	0.459581i	$0.152000\pi$
$12$		0			0
$13$	0.827310	+	2.54620i	0.229455	+	0.706189i	0.997809	+	0.0661638i	$0.0210760\pi$
$13$	0.827310	+	2.54620i	0.229455	+	0.706189i	−0.768354	+	0.640025i	$0.778924\pi$
$14$	1.40082	−	4.31129i	0.374385	−	1.15224i
$15$		0			0
$16$	3.95852	+	12.1831i	0.989631	+	3.04577i
$17$	−3.18079	+	2.31098i	−0.771454	+	0.560494i	−0.902402	−	0.430895i	$-0.858198\pi$
$17$	−3.18079	+	2.31098i	−0.771454	+	0.560494i	0.130948	+	0.991389i	$0.458198\pi$
$18$		0			0
$19$	0.952655	−	0.692144i	0.218554	−	0.158789i	−0.473121	−	0.880997i	$-0.656873\pi$
$19$	0.952655	−	0.692144i	0.218554	−	0.158789i	0.691676	+	0.722208i	$0.256873\pi$
$20$	−11.1679	+	3.39571i	−2.49721	+	0.759305i
$21$		0			0
$22$	2.34520	+	1.70389i	0.499999	+	0.363270i
$23$	1.25552	−	3.86409i	0.261794	−	0.805719i	−0.730621	−	0.682783i	$-0.760769\pi$
$23$	1.25552	−	3.86409i	0.261794	−	0.805719i	0.992415	−	0.122935i	$-0.0392307\pi$
$24$		0			0
$25$	−1.36350	−	4.81050i	−0.272699	−	0.962099i
$26$	7.19384			1.41083
$27$		0			0
$28$	−7.12476	−	5.17644i	−1.34645	−	0.978256i
$29$	4.81846	+	3.50082i	0.894766	+	0.650086i	0.937116	−	0.349017i	$-0.113484\pi$
$29$	4.81846	+	3.50082i	0.894766	+	0.650086i	−0.0423500	+	0.999103i	$0.513484\pi$
$30$		0			0
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.0633776	−	0.997990i	$-0.479813\pi$
$31$	5.74653	−	4.17510i	1.03211	−	0.749870i	0.968729	+	0.248120i	$0.0798128\pi$
$32$	17.1155			3.02563
$33$		0			0
$34$	3.26463	+	10.0475i	0.559879	+	1.72313i
$35$	2.27485	−	3.00925i	0.384520	−	0.508657i
$36$		0			0
$37$	−1.41587	−	4.35761i	−0.232768	−	0.716387i	−0.997410	−	0.0719311i	$-0.977084\pi$
$37$	−1.41587	−	4.35761i	−0.232768	−	0.716387i	0.764641	−	0.644456i	$-0.222916\pi$
$38$	−0.977766	−	3.00925i	−0.158615	−	0.488165i
$39$		0			0
$40$	−0.367227	+	19.3448i	−0.0580637	+	3.05868i
$41$	3.47998	+	10.7103i	0.543481	+	1.67266i	0.724574	+	0.689197i	$0.242037\pi$
$41$	3.47998	+	10.7103i	0.543481	+	1.67266i	−0.181093	+	0.983466i	$0.557963\pi$
$42$		0			0
$43$	2.58587			0.394342			0.197171	−	0.980369i	$-0.436825\pi$
$43$	2.58587			0.394342			0.197171	+	0.980369i	$0.436825\pi$
$44$	4.55609	−	3.31019i	0.686857	−	0.499031i
$45$		0			0
$46$	−8.83229	−	6.41703i	−1.30225	−	0.946140i
$47$	−1.55155	−	1.12727i	−0.226317	−	0.164429i	0.468849	−	0.883278i	$-0.344669\pi$
$47$	−1.55155	−	1.12727i	−0.226317	−	0.164429i	−0.695166	+	0.718850i	$0.744669\pi$
$48$		0			0
$49$	−4.15389			−0.593413
$50$	−13.4255	−	0.509905i	−1.89866	−	0.0721114i
$51$		0			0
$52$	4.31872	−	13.2917i	0.598899	−	1.84322i
$53$	−2.06187	−	1.49803i	−0.283219	−	0.205771i	0.437101	−	0.899412i	$-0.356005\pi$
$53$	−2.06187	−	1.49803i	−0.283219	−	0.205771i	−0.720320	+	0.693642i	$0.756005\pi$
$54$		0			0
$55$	1.38062	+	1.97816i	0.186163	+	0.266735i
$56$	−11.8097	+	8.58028i	−1.57814	+	1.14659i
$57$		0			0
$58$	12.9474	−	9.40685i	1.70008	−	1.23518i
$59$	−0.412843	−	1.27060i	−0.0537476	−	0.165418i	0.920579	−	0.390555i	$-0.127717\pi$
$59$	−0.412843	−	1.27060i	−0.0537476	−	0.165418i	−0.974327	+	0.225137i	$0.927717\pi$
$60$		0			0
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	0.697379	+	0.716702i	$0.254349\pi$
$61$	−2.24997	+	6.92470i	−0.288079	+	0.886617i	−0.985459	+	0.169915i	$0.945651\pi$
$62$	−5.89800	−	18.1522i	−0.749047	−	2.30533i
$63$		0			0
$64$	6.29470	−	19.3731i	0.786838	−	2.42164i
$65$	5.65734	+	1.95765i	0.701706	+	0.242817i
$66$		0			0
$67$	−10.0683	+	7.31502i	−1.23003	+	0.893672i	−0.996893	−	0.0787711i	$-0.974900\pi$
$67$	−10.0683	+	7.31502i	−1.23003	+	0.893672i	−0.233141	+	0.972443i	$0.574900\pi$
$68$	20.5241			2.48891
$69$		0			0
$70$	−5.80133	−	8.31216i	−0.693392	−	0.993493i
$71$	−4.84181	−	3.51778i	−0.574617	−	0.417484i	0.262162	−	0.965024i	$-0.415564\pi$
$71$	−4.84181	−	3.51778i	−0.574617	−	0.417484i	−0.836779	+	0.547540i	$0.815564\pi$
$72$		0			0
$73$	−1.01996	+	3.13911i	−0.119377	+	0.367405i	−0.992835	−	0.119495i	$-0.961872\pi$
$73$	−1.01996	+	3.13911i	−0.119377	+	0.367405i	0.873458	+	0.486900i	$0.161872\pi$
$74$	−12.3117			−1.43120
$75$		0			0
$76$	−6.14702			−0.705112
$77$	−0.562414	+	1.73093i	−0.0640931	+	0.197258i
$78$		0			0
$79$	3.23934	+	2.35351i	0.364454	+	0.264791i	0.754907	−	0.655831i	$-0.227682\pi$
$79$	3.23934	+	2.35351i	0.364454	+	0.264791i	−0.390454	+	0.920623i	$0.627682\pi$
$80$	27.0693	+	9.36699i	3.02644	+	1.04726i
$81$		0			0
$82$	30.2600			3.34166
$83$	7.17988	−	5.21649i	0.788094	−	0.572584i	−0.119303	−	0.992858i	$-0.538066\pi$
$83$	7.17988	−	5.21649i	0.788094	−	0.572584i	0.907397	+	0.420274i	$0.138066\pi$
$84$		0			0
$85$	−0.166861	+	8.78989i	−0.0180986	+	0.953398i
$86$	2.14716	−	6.60827i	0.231534	−	0.712588i
$87$		0			0
$88$	−2.88461	−	8.87792i	−0.307501	−	0.946389i
$89$	−4.77234	+	14.6877i	−0.505867	+	1.55690i	0.293442	+	0.955977i	$0.405199\pi$
$89$	−4.77234	+	14.6877i	−0.505867	+	1.55690i	−0.799309	+	0.600920i	$0.794801\pi$
$90$		0			0
$91$	1.39571	+	4.29555i	0.146310	+	0.450296i
$92$	−17.1587	+	12.4666i	−1.78892	+	1.29973i
$93$		0			0
$94$	−4.16908	+	3.02901i	−0.430008	+	0.312419i
$95$	0.0499753	−	2.63260i	0.00512736	−	0.270099i
$96$		0			0
$97$	−8.71166	−	6.32939i	−0.884535	−	0.642652i	0.0499122	−	0.998754i	$-0.484106\pi$
$97$	−8.71166	−	6.32939i	−0.884535	−	0.642652i	−0.934447	+	0.356101i	$0.884106\pi$
$98$	−3.44915	+	10.6154i	−0.348416	+	1.07232i
$99$		0			0
$100$	−9.00196	+	24.4995i	−0.900196	+	2.44995i
$101$	13.5654			1.34981			0.674905	−	0.737905i	$-0.264185\pi$
$101$	13.5654			1.34981			0.674905	+	0.737905i	$0.264185\pi$
$102$		0			0
$103$	−1.10757	−	0.804700i	−0.109133	−	0.0792894i	0.531880	−	0.846819i	$-0.321486\pi$
$103$	−1.10757	−	0.804700i	−0.109133	−	0.0792894i	−0.641013	+	0.767530i	$0.721486\pi$
$104$	−18.7413	−	13.6164i	−1.83774	−	1.33520i
$105$		0			0
$106$	−5.54032	+	4.02528i	−0.538124	+	0.390970i
$107$	−11.0115			−1.06452			−0.532262	−	0.846579i	$-0.678658\pi$
$107$	−11.0115			−1.06452			−0.532262	+	0.846579i	$0.678658\pi$
$108$		0			0
$109$	1.06577	+	3.28010i	0.102082	+	0.314176i	0.989035	−	0.147684i	$-0.0471820\pi$
$109$	1.06577	+	3.28010i	0.102082	+	0.314176i	−0.886952	+	0.461861i	$0.847182\pi$
$110$	6.20163	−	1.88568i	0.591303	−	0.179792i
$111$		0			0
$112$	6.67820	+	20.5534i	0.631030	+	1.94211i
$113$	−1.87015	−	5.75574i	−0.175929	−	0.541455i	0.823745	−	0.566960i	$-0.191881\pi$
$113$	−1.87015	−	5.75574i	−0.175929	−	0.541455i	−0.999675	+	0.0255053i	$0.991881\pi$
$114$		0			0
$115$	−5.19958	−	7.44997i	−0.484863	−	0.694713i
$116$	−9.60772	−	29.5695i	−0.892054	−	2.74546i
$117$		0			0
$118$	−3.58986			−0.330473
$119$	−5.36612	+	3.89872i	−0.491912	+	0.357395i
$120$		0			0
$121$	7.95761	+	5.78155i	0.723419	+	0.525595i
$122$	15.8280	+	11.4997i	1.43300	+	1.04114i
$123$		0			0
$124$	−37.0796			−3.32984
$125$	−10.4193	−	4.05447i	−0.931928	−	0.362643i
$126$		0			0
$127$	−6.25332	+	19.2457i	−0.554893	+	1.70778i	0.141334	+	0.989962i	$0.454861\pi$
$127$	−6.25332	+	19.2457i	−0.554893	+	1.70778i	−0.696227	+	0.717822i	$0.745139\pi$
$128$	−16.5882	−	12.0521i	−1.46621	−	1.06526i
$129$		0			0
$130$	9.70036	−	12.8320i	0.850778	−	1.12544i
$131$	−2.46759	+	1.79281i	−0.215595	+	0.156639i	−0.690341	−	0.723484i	$-0.742540\pi$
$131$	−2.46759	+	1.79281i	−0.215595	+	0.156639i	0.474747	+	0.880122i	$0.342540\pi$
$132$		0			0
$133$	1.60717	−	1.16768i	0.139359	−	0.101250i
$134$	10.3336	+	31.8037i	0.892691	+	2.74742i
$135$		0			0
$136$	10.5127	−	32.3549i	0.901460	−	2.77441i
$137$	6.33795	+	19.5062i	0.541487	+	1.66653i	0.729199	+	0.684302i	$0.239893\pi$
$137$	6.33795	+	19.5062i	0.541487	+	1.66653i	−0.187711	+	0.982224i	$0.560107\pi$
$138$		0			0
$139$	5.66068	−	17.4218i	0.480133	−	1.47770i	−0.358775	−	0.933424i	$-0.616806\pi$
$139$	5.66068	−	17.4218i	0.480133	−	1.47770i	0.838908	−	0.544273i	$-0.183194\pi$
$140$	−18.8407	+	5.72871i	−1.59233	+	0.484165i
$141$		0			0
$142$	−13.0101	+	9.45242i	−1.09179	+	0.793230i
$143$	−2.88825			−0.241527
$144$		0			0
$145$	12.7419	−	3.87432i	1.05816	−	0.321745i
$146$	7.17517	+	5.21306i	0.593821	+	0.431436i
$147$		0			0
$148$	−7.39114	+	22.7476i	−0.607548	+	1.86984i
$149$	−0.705938			−0.0578327			−0.0289163	−	0.999582i	$-0.509206\pi$
$149$	−0.705938			−0.0578327			−0.0289163	+	0.999582i	$0.509206\pi$
$150$		0			0
$151$	7.04538			0.573345			0.286673	−	0.958029i	$-0.407451\pi$
$151$	7.04538			0.573345			0.286673	+	0.958029i	$0.407451\pi$
$152$	−3.14860	+	9.69039i	−0.255385	+	0.785994i
$153$		0			0
$154$	3.95645	+	2.87453i	0.318820	+	0.231636i
$155$	0.301457	−	15.8802i	0.0242136	−	1.27552i
$156$		0			0
$157$	−5.12880			−0.409323			−0.204662	−	0.978833i	$-0.565609\pi$
$157$	−5.12880			−0.409323			−0.204662	+	0.978833i	$0.565609\pi$
$158$	8.70423	−	6.32399i	0.692471	−	0.503110i
$159$		0			0
$160$	23.0790	−	30.5298i	1.82456	−	2.41359i
$161$	2.11811	−	6.51888i	0.166931	−	0.513760i
$162$		0			0
$163$	−7.49715	−	23.0739i	−0.587222	−	1.80728i	−0.590157	−	0.807289i	$-0.700934\pi$
$163$	−7.49715	−	23.0739i	−0.587222	−	1.80728i	0.00293441	−	0.999996i	$-0.499066\pi$
$164$	18.1662	−	55.9097i	1.41854	−	4.36581i
$165$		0			0
$166$	−7.36913	−	22.6799i	−0.571955	−	1.76030i
$167$	3.68013	−	2.67377i	0.284777	−	0.206903i	−0.436221	−	0.899840i	$-0.643683\pi$
$167$	3.68013	−	2.67377i	0.284777	−	0.206903i	0.720998	+	0.692937i	$0.243683\pi$
$168$		0			0
$169$	4.71853	−	3.42821i	0.362964	−	0.263709i
$170$	22.3243	+	7.72503i	1.71219	+	0.592483i
$171$		0			0
$172$	−10.9207	−	7.93437i	−0.832697	−	0.604990i
$173$	0.827327	−	2.54625i	0.0629005	−	0.193588i	−0.914668	−	0.404206i	$-0.867548\pi$
$173$	0.827327	−	2.54625i	0.0629005	−	0.193588i	0.977568	+	0.210618i	$0.0675478\pi$
$174$		0			0
$175$	−2.30027	−	8.11551i	−0.173884	−	0.613475i
$176$	−13.8197			−1.04170
$177$		0			0
$178$	33.5723	+	24.3917i	2.51635	+	1.82823i
$179$	−12.6422	−	9.18511i	−0.944924	−	0.686528i	0.00467674	−	0.999989i	$-0.498511\pi$
$179$	−12.6422	−	9.18511i	−0.944924	−	0.686528i	−0.949601	+	0.313461i	$0.898511\pi$
$180$		0			0
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	−0.593867	−	0.804563i	$-0.702400\pi$
$181$	−0.164103	+	0.119228i	−0.0121977	+	0.00886215i	0.581670	+	0.813425i	$0.302400\pi$
$182$	12.1363			0.899603
$183$		0			0
$184$	10.8638	+	33.4352i	0.800887	+	2.46488i
$185$	−9.68207	−	3.35036i	−0.711840	−	0.246323i
$186$		0			0
$187$	−1.31071	−	4.03396i	−0.0958488	−	0.294992i
$188$	3.09369	+	9.52141i	0.225631	+	0.694420i
$189$		0			0
$190$	−6.68619	−	2.31367i	−0.485067	−	0.167851i
$191$	2.44734	+	7.53213i	0.177083	+	0.545006i	0.999722	−	0.0235578i	$-0.00749937\pi$
$191$	2.44734	+	7.53213i	0.177083	+	0.545006i	−0.822639	+	0.568563i	$0.807499\pi$
$192$		0			0
$193$	−16.4269			−1.18243			−0.591216	−	0.806513i	$-0.701352\pi$
$193$	−16.4269			−1.18243			−0.591216	+	0.806513i	$0.701352\pi$
$194$	−23.4086	+	17.0073i	−1.68064	+	1.22106i
$195$		0			0
$196$	17.5428	+	12.7456i	1.25306	+	0.910400i
$197$	−13.8640	−	10.0728i	−0.987770	−	0.717657i	−0.0283382	−	0.999598i	$-0.509022\pi$
$197$	−13.8640	−	10.0728i	−0.987770	−	0.717657i	−0.959432	+	0.281942i	$0.909022\pi$
$198$		0			0
$199$	−2.01848			−0.143086			−0.0715430	−	0.997438i	$-0.522792\pi$
$199$	−2.01848			−0.143086			−0.0715430	+	0.997438i	$0.522792\pi$
$200$	34.0110	+	26.7400i	2.40494	+	1.89081i
$201$		0			0
$202$	11.2639	−	34.6668i	0.792528	−	2.43915i
$203$	8.12895	+	5.90603i	0.570541	+	0.414522i
$204$		0			0
$205$	23.7969	+	8.23461i	1.66205	+	0.575130i
$206$	−2.97610	+	2.16226i	−0.207355	+	0.150652i
$207$		0			0
$208$	−27.7456	+	20.1584i	−1.92381	+	1.39773i
$209$	0.392562	+	1.20818i	0.0271541	+	0.0835717i
$210$		0			0
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	0.291018	+	0.956718i	$0.406006\pi$
$211$	−7.36119	+	22.6554i	−0.506765	+	1.55966i	−0.797783	+	0.602945i	$0.793994\pi$
$212$	4.11123	+	12.6531i	0.282361	+	0.869017i
$213$		0			0
$214$	−9.14333	+	28.1403i	−0.625025	+	1.92363i
$215$	3.48686	−	4.61254i	0.237802	−	0.314572i
$216$		0			0
$217$	9.69463	−	7.04356i	0.658115	−	0.478148i
$218$	9.26733			0.627663
$219$		0			0
$220$	0.239008	−	12.5905i	0.0161139	−	0.848849i
$221$	−8.51571	−	6.18702i	−0.572828	−	0.416184i
$222$		0			0
$223$	4.05158	−	12.4695i	0.271314	−	0.835017i	−0.718858	−	0.695157i	$-0.755335\pi$
$223$	4.05158	−	12.4695i	0.271314	−	0.835017i	0.990171	−	0.139860i	$-0.0446653\pi$
$224$	28.8746			1.92927
$225$		0			0
$226$	−16.2618			−1.08172
$227$	8.12118	−	24.9944i	0.539022	−	1.65894i	−0.195774	−	0.980649i	$-0.562722\pi$
$227$	8.12118	−	24.9944i	0.539022	−	1.65894i	0.734795	−	0.678289i	$-0.237278\pi$
$228$		0			0
$229$	−1.61484	−	1.17325i	−0.106711	−	0.0775304i	0.533150	−	0.846021i	$-0.321008\pi$
$229$	−1.61484	−	1.17325i	−0.106711	−	0.0775304i	−0.639861	+	0.768490i	$0.721008\pi$
$230$	−23.3560	+	7.10166i	−1.54005	+	0.468269i
$231$		0			0
$232$	−51.5357			−3.38348
$233$	−0.425178	+	0.308910i	−0.0278543	+	0.0202373i	−0.601625	−	0.798778i	$-0.705480\pi$
$233$	−0.425178	+	0.308910i	−0.0278543	+	0.0202373i	0.573771	+	0.819016i	$0.305480\pi$
$234$		0			0
$235$	−4.10291	+	1.24753i	−0.267644	+	0.0813801i
$236$	−2.15512	+	6.63278i	−0.140286	+	0.431757i
$237$		0			0
$238$	5.50757	+	16.9505i	0.357002	+	1.09874i
$239$	2.16612	−	6.66663i	0.140115	−	0.431229i	−0.856236	−	0.516585i	$-0.827203\pi$
$239$	2.16612	−	6.66663i	0.140115	−	0.431229i	0.996350	+	0.0853565i	$0.0272029\pi$
$240$		0			0
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	0.971454	−	0.237228i	$-0.0762388\pi$
$241$	0.715542	+	2.20221i	0.0460921	+	0.141857i	−0.925362	+	0.379085i	$0.876239\pi$
$242$	21.3824	−	15.5353i	1.37452	−	0.998644i
$243$		0			0
$244$	30.7496	−	22.3409i	1.96854	−	1.43023i
$245$	−5.60121	+	7.40948i	−0.357848	+	0.473374i
$246$		0			0
$247$	2.55048	+	1.85303i	0.162283	+	0.117906i
$248$	−18.9927	+	58.4536i	−1.20604	+	3.71180i
$249$		0			0
$250$	−19.0129	+	23.2602i	−1.20248	+	1.47110i
$251$	6.17885			0.390005			0.195003	−	0.980803i	$-0.437528\pi$
$251$	6.17885			0.390005			0.195003	+	0.980803i	$0.437528\pi$
$252$		0			0
$253$	3.54607	+	2.57637i	0.222939	+	0.161975i
$254$	43.9907	+	31.9611i	2.76022	+	2.00542i
$255$		0			0
$256$	−11.6138	+	8.43794i	−0.725864	+	0.527371i
$257$	−13.2239			−0.824882			−0.412441	−	0.910984i	$-0.635324\pi$
$257$	−13.2239			−0.824882			−0.412441	+	0.910984i	$0.635324\pi$
$258$		0			0
$259$	−2.38864	−	7.35148i	−0.148423	−	0.456799i
$260$	−17.8855	−	25.6263i	−1.10921	−	1.58928i
$261$		0			0
$262$	2.53264	+	7.79465i	0.156467	+	0.481555i
$263$	2.15583	+	6.63498i	0.132934	+	0.409130i	0.995263	−	0.0972190i	$-0.0309947\pi$
$263$	2.15583	+	6.63498i	0.132934	+	0.409130i	−0.862329	+	0.506349i	$0.830995\pi$
$264$		0			0
$265$	−5.45239	+	1.65786i	−0.334937	+	0.101841i
$266$	−1.64953	−	5.07674i	−0.101139	−	0.311275i
$267$		0			0
$268$	64.9656			3.96841
$269$	19.1898	−	13.9422i	1.17002	−	0.850070i	0.179010	−	0.983847i	$-0.442711\pi$
$269$	19.1898	−	13.9422i	1.17002	−	0.850070i	0.991011	+	0.133777i	$0.0427107\pi$
$270$		0			0
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.990966	−	0.134114i	$-0.957181\pi$
$271$	−23.4542	−	17.0405i	−1.42474	−	1.03514i	−0.433775	−	0.901021i	$-0.642819\pi$
$272$	−40.7460	−	29.6037i	−2.47059	−	1.79499i
$273$		0			0
$274$	55.1113			3.32940
$275$	5.39020	+	0.204721i	0.325041	+	0.0123451i
$276$		0			0
$277$	−2.65343	+	8.16641i	−0.159429	+	0.490672i	−0.998583	−	0.0532223i	$-0.983051\pi$
$277$	−2.65343	+	8.16641i	−0.159429	+	0.490672i	0.839154	+	0.543894i	$0.183051\pi$
$278$	−39.8216	−	28.9321i	−2.38834	−	1.73523i
$279$		0			0
$280$	−0.619527	+	32.6354i	−0.0370238	+	1.95034i
$281$	13.8877	−	10.0900i	0.828471	−	0.601919i	−0.0906557	−	0.995882i	$-0.528896\pi$
$281$	13.8877	−	10.0900i	0.828471	−	0.601919i	0.919126	+	0.393963i	$0.128896\pi$
$282$		0			0
$283$	7.78278	−	5.65452i	0.462638	−	0.336126i	−0.331927	−	0.943305i	$-0.607699\pi$
$283$	7.78278	−	5.65452i	0.462638	−	0.336126i	0.794565	+	0.607179i	$0.207699\pi$
$284$	9.65426	+	29.7128i	0.572875	+	1.76313i
$285$		0			0
$286$	−2.39823	+	7.38100i	−0.141810	+	0.436447i
$287$	5.87087	+	18.0687i	0.346546	+	1.06656i
$288$		0			0
$289$	−0.476498	+	1.46651i	−0.0280293	+	0.0862654i
$290$	0.679209	−	35.7793i	0.0398845	−	2.10104i
$291$		0			0
$292$	13.9394	−	10.1276i	0.815742	−	0.592671i
$293$	−16.8202			−0.982649			−0.491324	−	0.870977i	$-0.663487\pi$
$293$	−16.8202			−0.982649			−0.491324	+	0.870977i	$0.663487\pi$
$294$		0			0
$295$	−2.82312	−	0.976903i	−0.164368	−	0.0568775i
$296$	32.0743	+	23.3033i	1.86428	+	1.35448i
$297$		0			0
$298$	−0.586170	+	1.80404i	−0.0339559	+	0.104505i
$299$	10.8775			0.629059
$300$		0			0
$301$	4.36247			0.251449
$302$	5.85008	−	18.0047i	0.336634	−	1.03605i
$303$		0			0
$304$	12.2036	+	8.86641i	0.699922	+	0.508523i
$305$	9.31799	+	13.3508i	0.533546	+	0.764466i
$306$		0			0
$307$	11.3212			0.646134			0.323067	−	0.946376i	$-0.395286\pi$
$307$	11.3212			0.646134			0.323067	+	0.946376i	$0.395286\pi$
$308$	7.68632	−	5.58444i	0.437969	−	0.318203i
$309$		0			0
$310$	−40.3319	−	13.9563i	−2.29070	−	0.792667i
$311$	−5.73642	+	17.6549i	−0.325283	+	1.00112i	0.646030	+	0.763312i	$0.276428\pi$
$311$	−5.73642	+	17.6549i	−0.325283	+	1.00112i	−0.971313	+	0.237805i	$0.923572\pi$
$312$		0			0
$313$	−2.99731	−	9.22478i	−0.169418	−	0.521416i	0.829916	−	0.557888i	$-0.188388\pi$
$313$	−2.99731	−	9.22478i	−0.169418	−	0.521416i	−0.999335	+	0.0364720i	$0.988388\pi$
$314$	−4.25866	+	13.1068i	−0.240330	+	0.739660i
$315$		0			0
$316$	−6.45903	−	19.8789i	−0.363349	−	1.11827i
$317$	6.04859	−	4.39456i	0.339723	−	0.246823i	−0.404822	−	0.914395i	$-0.632667\pi$
$317$	6.04859	−	4.39456i	0.339723	−	0.246823i	0.744545	+	0.667573i	$0.232667\pi$
$318$		0			0
$319$	−5.19825	+	3.77675i	−0.291046	+	0.211457i
$320$	−26.0688	−	37.3514i	−1.45729	−	2.08800i
$321$		0			0
$322$	−14.9004	−	10.8258i	−0.830369	−	0.603298i
$323$	−1.43066	+	4.40313i	−0.0796042	+	0.244997i
$324$		0			0
$325$	11.1205	−	7.45150i	0.616852	−	0.413335i
$326$	−65.1911			−3.61060
$327$		0			0
$328$	−78.8331	−	57.2756i	−4.35283	−	3.16252i
$329$	−2.61753	−	1.90175i	−0.144309	−	0.104847i
$330$		0			0
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.138439	−	0.990371i	$-0.455791\pi$
$331$	20.4333	−	14.8457i	1.12312	−	0.815993i	0.984679	+	0.174378i	$0.0557914\pi$
$332$	−46.3283			−2.54259
$333$		0			0
$334$	−3.77714	−	11.6248i	−0.206676	−	0.636083i
$335$	−0.528171	+	27.8230i	−0.0288571	+	1.52013i
$336$		0			0
$337$	−4.02464	−	12.3866i	−0.219236	−	0.674739i	−0.998826	−	0.0484485i	$-0.984572\pi$
$337$	−4.02464	−	12.3866i	−0.219236	−	0.674739i	0.779590	−	0.626291i	$-0.215428\pi$
$338$	−4.84291	−	14.9049i	−0.263419	−	0.810721i
$339$		0			0
$340$	27.6752	−	36.6097i	1.50090	−	1.98544i
$341$	2.36798	+	7.28790i	0.128233	+	0.394662i
$342$		0			0
$343$	−18.8171			−1.01603
$344$	−18.1018	+	13.1517i	−0.975983	+	0.709093i
$345$		0			0
$346$	−5.82005	−	4.22852i	−0.312888	−	0.227326i
$347$	−4.85531	−	3.52759i	−0.260647	−	0.189371i	0.449785	−	0.893137i	$-0.351500\pi$
$347$	−4.85531	−	3.52759i	−0.260647	−	0.189371i	−0.710432	+	0.703766i	$0.751500\pi$
$348$		0			0
$349$	−22.7183			−1.21608			−0.608042	−	0.793905i	$-0.708045\pi$
$349$	−22.7183			−1.21608			−0.608042	+	0.793905i	$0.708045\pi$
$350$	−22.6494	−	0.860231i	−1.21066	−	0.0459813i
$351$		0			0
$352$	−5.70586	+	17.5608i	−0.304123	+	0.935996i
$353$	−3.92772	−	2.85366i	−0.209052	−	0.151885i	0.478333	−	0.878179i	$-0.341241\pi$
$353$	−3.92772	−	2.85366i	−0.209052	−	0.151885i	−0.687385	+	0.726294i	$0.741241\pi$
$354$		0			0
$355$	−12.8036	+	3.89309i	−0.679547	+	0.206624i
$356$	65.2218	−	47.3864i	3.45675	−	2.51148i
$357$		0			0
$358$	−33.9702	+	24.6808i	−1.79538	+	1.30442i
$359$	−8.92780	−	27.4769i	−0.471191	−	1.45018i	−0.851026	−	0.525123i	$-0.824019\pi$
$359$	−8.92780	−	27.4769i	−0.471191	−	1.45018i	0.379835	−	0.925054i	$-0.375981\pi$
$360$		0			0
$361$	−5.44284	+	16.7513i	−0.286465	+	0.881649i
$362$	0.168429	+	0.518371i	0.00885242	+	0.0272450i
$363$		0			0
$364$	7.28587	−	22.4236i	0.381883	−	1.17532i
$365$	4.22403	+	6.05220i	0.221096	+	0.316787i
$366$		0			0
$367$	11.8998	−	8.64570i	0.621163	−	0.451302i	−0.232164	−	0.972677i	$-0.574581\pi$
$367$	11.8998	−	8.64570i	0.621163	−	0.451302i	0.853328	+	0.521375i	$0.174581\pi$
$368$	52.0465			2.71311
$369$		0			0
$370$	−16.6014	+	21.9609i	−0.863064	+	1.14169i
$371$	−3.47846	−	2.52725i	−0.180592	−	0.131208i
$372$		0			0
$373$	−10.2096	+	31.4220i	−0.528635	+	1.62697i	0.228378	+	0.973572i	$0.426658\pi$
$373$	−10.2096	+	31.4220i	−0.528635	+	1.62697i	−0.757013	+	0.653399i	$0.773342\pi$
$374$	−11.3972			−0.589337
$375$		0			0
$376$	16.5945			0.855797
$377$	−4.92742	+	15.1650i	−0.253775	+	0.781039i
$378$		0			0
$379$	12.2612	+	8.90826i	0.629814	+	0.457587i	0.856336	−	0.516419i	$-0.172735\pi$
$379$	12.2612	+	8.90826i	0.629814	+	0.457587i	−0.226522	+	0.974006i	$0.572735\pi$
$380$	−8.28880	+	10.9647i	−0.425207	+	0.562478i
$381$		0			0
$382$	21.2807			1.08882
$383$	−6.47870	+	4.70705i	−0.331046	+	0.240519i	−0.740874	−	0.671644i	$-0.765589\pi$
$383$	−6.47870	+	4.70705i	−0.331046	+	0.240519i	0.409828	+	0.912163i	$0.365589\pi$
$384$		0			0
$385$	2.32917	+	3.33724i	0.118706	+	0.170081i
$386$	−13.6399	+	41.9793i	−0.694253	+	2.13669i
$387$		0			0
$388$	17.3705	+	53.4609i	0.881854	+	2.71407i
$389$	−0.332078	+	1.02203i	−0.0168370	+	0.0518191i	−0.959122	−	0.282993i	$-0.908673\pi$
$389$	−0.332078	+	1.02203i	−0.0168370	+	0.0518191i	0.942285	+	0.334812i	$0.108673\pi$
$390$		0			0
$391$	4.93629	+	15.1923i	0.249639	+	0.768309i
$392$	29.0783	−	21.1266i	1.46868	−	1.06706i
$393$		0			0
$394$	−37.2532	+	27.0660i	−1.87679	+	1.36357i
$395$	8.56607	−	2.60461i	0.431006	−	0.131052i
$396$		0			0
$397$	19.5894	+	14.2326i	0.983166	+	0.714312i	0.958414	−	0.285382i	$-0.0921205\pi$
$397$	19.5894	+	14.2326i	0.983166	+	0.714312i	0.0247517	+	0.999694i	$0.492120\pi$
$398$	−1.67603	+	5.15828i	−0.0840116	+	0.258561i
$399$		0			0
$400$	53.2093	−	35.6540i	2.66046	−	1.78270i
$401$	1.99317			0.0995340			0.0497670	−	0.998761i	$-0.484152\pi$
$401$	1.99317			0.0995340			0.0497670	+	0.998761i	$0.484152\pi$
$402$		0			0
$403$	15.3848	+	11.1777i	0.766371	+	0.556801i
$404$	−57.2899	−	41.6235i	−2.85028	−	2.07085i
$405$		0			0
$406$	21.8428	−	15.8698i	1.08404	−	0.787603i
$407$	4.94300			0.245015
$408$		0			0
$409$	2.05953	+	6.33858i	0.101837	+	0.313423i	0.988975	−	0.148082i	$-0.0473098\pi$
$409$	2.05953	+	6.33858i	0.101837	+	0.313423i	−0.887138	+	0.461504i	$0.847310\pi$
$410$	40.8033	−	53.9761i	2.01513	−	2.66569i
$411$		0			0
$412$	2.20843	+	6.79686i	0.108802	+	0.334857i
$413$	−0.696484	−	2.14356i	−0.0342717	−	0.105477i
$414$		0			0
$415$	0.376649	−	19.8411i	0.0184890	−	0.973962i
$416$	14.1599	+	43.5796i	0.694245	+	2.13667i
$417$		0			0
$418$	3.41351			0.166960
$419$	17.2758	−	12.5516i	0.843977	−	0.613185i	−0.0795021	−	0.996835i	$-0.525333\pi$
$419$	17.2758	−	12.5516i	0.843977	−	0.613185i	0.923479	+	0.383650i	$0.125333\pi$
$420$		0			0
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	0.0527243	−	0.998609i	$-0.483210\pi$
$421$	−18.0708	−	13.1292i	−0.880717	−	0.639878i	−0.933441	+	0.358731i	$0.883210\pi$
$422$	51.7842	+	37.6235i	2.52082	+	1.83148i
$423$		0			0
$424$	22.0526			1.07097
$425$	15.4539	+	12.1502i	0.749626	+	0.589369i
$426$		0			0
$427$	−3.79580	+	11.6823i	−0.183692	+	0.565344i
$428$	46.5042	+	33.7873i	2.24786	+	1.63317i
$429$		0			0
$430$	−8.89219	−	12.7407i	−0.428819	−	0.614413i
$431$	−24.6046	+	17.8763i	−1.18516	+	0.861070i	−0.992744	−	0.120244i	$-0.961632\pi$
$431$	−24.6046	+	17.8763i	−1.18516	+	0.861070i	−0.192416	+	0.981313i	$0.561632\pi$
$432$		0			0
$433$	−0.466511	+	0.338940i	−0.0224191	+	0.0162884i	−0.598938	−	0.800795i	$-0.704411\pi$
$433$	−0.466511	+	0.338940i	−0.0224191	+	0.0162884i	0.576519	+	0.817084i	$0.304411\pi$
$434$	−9.95017	−	30.6235i	−0.477624	−	1.46997i
$435$		0			0
$436$	5.56352	−	17.1227i	0.266444	−	0.820031i
$437$	−1.47843	−	4.55015i	−0.0707230	−	0.217663i
$438$		0			0
$439$	3.95681	−	12.1778i	0.188848	−	0.581215i	−0.811145	−	0.584845i	$-0.801155\pi$
$439$	3.95681	−	12.1778i	0.188848	−	0.581215i	0.999993	+	0.00363006i	$0.00115549\pi$
$440$	−19.7256	−	6.82580i	−0.940383	−	0.325407i
$441$		0			0
$442$	−22.8821	+	16.6248i	−1.08839	+	0.790761i
$443$	−14.3147			−0.680110			−0.340055	−	0.940405i	$-0.610446\pi$
$443$	−14.3147			−0.680110			−0.340055	+	0.940405i	$0.610446\pi$
$444$		0			0
$445$	19.7640	+	28.3180i	0.936906	+	1.34240i
$446$	−28.5019	−	20.7078i	−1.34960	−	0.980545i
$447$		0			0
$448$	10.6194	−	32.6833i	0.501721	−	1.54414i
$449$	11.9663			0.564724			0.282362	−	0.959308i	$-0.408882\pi$
$449$	11.9663			0.564724			0.282362	+	0.959308i	$0.408882\pi$
$450$		0			0
$451$	−12.1490			−0.572076
$452$	−9.76257	+	30.0461i	−0.459193	+	1.41325i
$453$		0			0
$454$	−57.1306	−	41.5078i	−2.68127	−	1.94806i
$455$	9.54417	+	3.30264i	0.447438	+	0.154830i
$456$		0			0
$457$	−8.22154			−0.384587			−0.192294	−	0.981337i	$-0.561593\pi$
$457$	−8.22154			−0.384587			−0.192294	+	0.981337i	$0.561593\pi$
$458$	−4.33913	+	3.15257i	−0.202754	+	0.147310i
$459$		0			0
$460$	−0.900131	+	47.4171i	−0.0419688	+	2.21083i
$461$	−0.393120	+	1.20990i	−0.0183094	+	0.0563506i	−0.959794	−	0.280706i	$-0.909431\pi$
$461$	−0.393120	+	1.20990i	−0.0183094	+	0.0563506i	0.941484	+	0.337057i	$0.109431\pi$
$462$		0			0
$463$	10.0976	+	31.0771i	0.469273	+	1.44428i	0.853527	+	0.521048i	$0.174459\pi$
$463$	10.0976	+	31.0771i	0.469273	+	1.44428i	−0.384254	+	0.923227i	$0.625541\pi$
$464$	−23.5768	+	72.5618i	−1.09452	+	3.36860i
$465$		0			0
$466$	0.436385	+	1.34305i	0.0202151	+	0.0622158i
$467$	11.6779	−	8.48450i	0.540389	−	0.392616i	−0.283840	−	0.958872i	$-0.591609\pi$
$467$	11.6779	−	8.48450i	0.540389	−	0.392616i	0.824230	+	0.566256i	$0.191609\pi$
$468$		0			0
$469$	−16.9856	+	12.3407i	−0.784321	+	0.569843i
$470$	−0.218706	+	11.5210i	−0.0100881	+	0.531423i
$471$		0			0
$472$	9.35227	+	6.79482i	0.430473	+	0.312757i
$473$	−0.862060	+	2.65315i	−0.0396375	+	0.121992i
$474$		0			0
$475$	−4.62850	−	3.63901i	−0.212370	−	0.166969i
$476$	34.6250			1.58703
$477$		0			0
$478$	−15.2382	−	11.0712i	−0.696977	−	0.506383i
$479$	−13.6415	−	9.91113i	−0.623296	−	0.452851i	0.230775	−	0.973007i	$-0.425874\pi$
$479$	−13.6415	−	9.91113i	−0.623296	−	0.452851i	−0.854071	+	0.520156i	$0.825874\pi$
$480$		0			0
$481$	9.92398	−	7.21020i	0.452495	−	0.328757i
$482$	6.22196			0.283403
$483$		0			0
$484$	−15.8670	−	48.8336i	−0.721227	−	2.21971i
$485$	−23.0371	+	7.00467i	−1.04606	+	0.318066i
$486$		0			0
$487$	12.3061	+	37.8744i	0.557644	+	1.71625i	0.688856	+	0.724898i	$0.258113\pi$
$487$	12.3061	+	37.8744i	0.557644	+	1.71625i	−0.131212	+	0.991354i	$0.541887\pi$
$488$	−19.4686	−	59.9181i	−0.881301	−	2.71236i
$489$		0			0
$490$	14.2842	+	20.4665i	0.645295	+	0.924580i
$491$	−4.33411	−	13.3390i	−0.195596	−	0.601981i	−0.999969	−	0.00785739i	$-0.997499\pi$
$491$	−4.33411	−	13.3390i	−0.195596	−	0.601981i	0.804374	−	0.594124i	$-0.202501\pi$
$492$		0			0
$493$	−23.4168			−1.05464
$494$	6.85324	−	4.97917i	0.308342	−	0.224024i
$495$		0			0
$496$	73.6133	+	53.4832i	3.30534	+	2.40147i
$497$	−8.16834	−	5.93464i	−0.366400	−	0.266205i
$498$		0			0
$499$	15.2315			0.681857			0.340929	−	0.940089i	$-0.389259\pi$
$499$	15.2315			0.681857			0.340929	+	0.940089i	$0.389259\pi$
$500$	31.5624	+	49.0930i	1.41151	+	2.19550i
$501$		0			0
$502$	5.13055	−	15.7902i	0.228988	−	0.704752i
$503$	19.2004	+	13.9499i	0.856104	+	0.621996i	0.926822	−	0.375501i	$-0.122529\pi$
$503$	19.2004	+	13.9499i	0.856104	+	0.621996i	−0.0707185	+	0.997496i	$0.522529\pi$
$504$		0			0
$505$	18.2920	−	24.1973i	0.813982	−	1.07676i
$506$	9.52843	−	6.92281i	0.423590	−	0.307756i
$507$		0			0
$508$	85.4620	−	62.0918i	3.79176	−	2.75488i
$509$	3.86570	+	11.8974i	0.171344	+	0.527343i	0.999448	−	0.0332320i	$-0.0105800\pi$
$509$	3.86570	+	11.8974i	0.171344	+	0.527343i	−0.828103	+	0.560575i	$0.810580\pi$
$510$		0			0
$511$	−1.72071	+	5.29581i	−0.0761198	+	0.234273i
$512$	−0.752345	−	2.31548i	−0.0332493	−	0.102331i
$513$		0			0
$514$	−10.9803	+	33.7940i	−0.484321	+	1.49059i
$515$	−2.92886	+	0.890552i	−0.129061	+	0.0392424i
$516$		0			0
$517$	1.67384	−	1.21612i	0.0736154	−	0.0534847i
$518$	−20.7703			−0.912595
$519$		0			0
$520$	−49.5594	+	15.0691i	−2.17333	+	0.660823i
$521$	−22.6232	−	16.4367i	−0.991141	−	0.720106i	−0.0309702	−	0.999520i	$-0.509860\pi$
$521$	−22.6232	−	16.4367i	−0.991141	−	0.720106i	−0.960171	+	0.279414i	$0.909860\pi$
$522$		0			0
$523$	4.85196	−	14.9328i	0.212162	−	0.652966i	−0.787181	−	0.616722i	$-0.788460\pi$
$523$	4.85196	−	14.9328i	0.212162	−	0.652966i	0.999343	−	0.0362446i	$-0.0115395\pi$
$524$	15.9222			0.695564
$525$		0			0
$526$	18.7460			0.817362
$527$	−8.62993	+	26.5602i	−0.375926	+	1.15698i
$528$		0			0
$529$	5.25252	+	3.81618i	0.228370	+	0.165921i
$530$	−0.290640	+	15.3103i	−0.0126246	+	0.665038i
$531$		0			0
$532$	−10.3703			−0.449609
$533$	−24.3915	+	17.7214i	−1.05651	+	0.767601i
$534$		0			0
$535$	−14.8482	+	19.6418i	−0.641945	+	0.849187i
$536$	33.2764	−	102.414i	1.43732	−	4.42362i
$537$		0			0
$538$	−19.6956	−	60.6168i	−0.849137	−	2.61338i
$539$	1.38479	−	4.26196i	0.0596473	−	0.183576i
$540$		0			0
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	−0.974261	−	0.225425i	$-0.927623\pi$
$541$	−7.40971	−	22.8048i	−0.318569	−	0.980453i	0.655692	−	0.755028i	$-0.272377\pi$
$542$	−63.0224	+	45.7885i	−2.70705	+	1.96678i
$543$		0			0
$544$	−54.4409	+	39.5536i	−2.33413	+	1.69585i
$545$	7.28796	+	2.52191i	0.312182	+	0.108027i
$546$		0			0
$547$	4.55219	+	3.30736i	0.194637	+	0.141412i	0.680836	−	0.732436i	$-0.261617\pi$
$547$	4.55219	+	3.30736i	0.194637	+	0.141412i	−0.486198	+	0.873848i	$0.661617\pi$
$548$	33.0853	−	101.826i	1.41333	−	4.34980i
$549$		0			0
$550$	4.99888	−	13.6048i	0.213153	−	0.580112i
$551$	7.01341			0.298781
$552$		0			0
$553$	5.46490	+	3.97048i	0.232391	+	0.168842i
$554$	18.6663	+	13.5618i	0.793053	+	0.576187i
$555$		0			0
$556$	−77.3626	+	56.2072i	−3.28090	+	2.38372i
$557$	42.4247			1.79759			0.898796	−	0.438366i	$-0.144443\pi$
$557$	42.4247			1.79759			0.898796	+	0.438366i	$0.144443\pi$
$558$		0			0
$559$	2.13932	+	6.58414i	0.0904835	+	0.278480i
$560$	45.6670	+	15.8025i	1.92978	+	0.667778i
$561$		0			0
$562$	−14.2538	−	43.8686i	−0.601259	−	1.85048i
$563$	−1.78796	−	5.50279i	−0.0753537	−	0.231915i	0.906284	−	0.422669i	$-0.138907\pi$
$563$	−1.78796	−	5.50279i	−0.0753537	−	0.231915i	−0.981638	+	0.190754i	$0.938907\pi$
$564$		0			0
$565$	−12.7885	−	4.42531i	−0.538018	−	0.186174i
$566$	−7.98793	−	24.5843i	−0.335758	−	1.03336i
$567$		0			0
$568$	51.7853			2.17286
$569$	−17.8029	+	12.9346i	−0.746336	+	0.542245i	−0.894689	−	0.446690i	$-0.852603\pi$
$569$	−17.8029	+	12.9346i	−0.746336	+	0.542245i	0.148353	+	0.988934i	$0.452603\pi$
$570$		0			0
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.151210	−	0.988502i	$-0.548317\pi$
$571$	−27.1946	−	19.7580i	−1.13806	−	0.826847i	−0.986847	+	0.161654i	$0.948317\pi$
$572$	12.1977	+	8.86216i	0.510012	+	0.370546i
$573$		0			0
$574$	51.0499			2.13078
$575$	−20.3001	−	0.771002i	−0.846572	−	0.0321530i
$576$		0			0
$577$	12.4333	−	38.2658i	0.517605	−	1.59303i	−0.260886	−	0.965370i	$-0.584015\pi$
$577$	12.4333	−	38.2658i	0.517605	−	1.59303i	0.778491	−	0.627656i	$-0.215985\pi$
$578$	3.35205	+	2.43541i	0.139427	+	0.101300i
$579$		0			0
$580$	−65.6998	−	22.7346i	−2.72803	−	0.944002i
$581$	12.1128	−	8.80043i	0.502522	−	0.365103i
$582$		0			0
$583$	2.22438	−	1.61611i	0.0921243	−	0.0669323i
$584$	−8.82549	−	27.1621i	−0.365201	−	1.12397i
$585$		0			0
$586$	−13.9665	+	42.9846i	−0.576952	+	1.77568i
$587$	0.872353	+	2.68483i	0.0360059	+	0.110815i	0.967444	−	0.253085i	$-0.0814452\pi$
$587$	0.872353	+	2.68483i	0.0360059	+	0.110815i	−0.931438	+	0.363899i	$0.881445\pi$
$588$		0			0
$589$	2.58469	−	7.95485i	0.106500	−	0.327774i
$590$	−4.84066	+	6.40339i	−0.199287	+	0.263623i
$591$		0			0
$592$	47.4844	−	34.4994i	1.95160	−	1.41792i
$593$	24.6805			1.01351			0.506754	−	0.862091i	$-0.330845\pi$
$593$	24.6805			1.01351			0.506754	+	0.862091i	$0.330845\pi$
$594$		0			0
$595$	−0.281501	+	14.8289i	−0.0115404	+	0.607927i
$596$	2.98134	+	2.16607i	0.122120	+	0.0887256i
$597$		0			0
$598$	9.03200	−	27.7976i	0.369346	−	1.13673i
$599$	7.71547			0.315245			0.157623	−	0.987499i	$-0.449617\pi$
$599$	7.71547			0.315245			0.157623	+	0.987499i	$0.449617\pi$
$600$		0			0
$601$	22.6506			0.923938			0.461969	−	0.886896i	$-0.347143\pi$
$601$	22.6506			0.923938			0.461969	+	0.886896i	$0.347143\pi$
$602$	3.62234	−	11.1484i	0.147636	−	0.454376i
$603$		0			0
$604$	−29.7543	−	21.6177i	−1.21068	−	0.879613i
$605$	21.0431	−	6.39837i	0.855522	−	0.260131i
$606$		0			0
$607$	−24.6423			−1.00020			−0.500099	−	0.865968i	$-0.666703\pi$
$607$	−24.6423			−1.00020			−0.500099	+	0.865968i	$0.666703\pi$
$608$	16.3052	−	11.8464i	0.661264	−	0.480436i
$609$		0			0
$610$	41.8555	−	12.7266i	1.69468	−	0.515286i
$611$	1.58663	−	4.88315i	0.0641883	−	0.197551i
$612$		0			0
$613$	−12.9180	−	39.7574i	−0.521751	−	1.60579i	−0.770652	−	0.637256i	$-0.780069\pi$
$613$	−12.9180	−	39.7574i	−0.521751	−	1.60579i	0.248901	−	0.968529i	$-0.419931\pi$
$614$	9.40045	−	28.9316i	0.379371	−	1.16758i
$615$		0			0
$616$	−4.86646	−	14.9774i	−0.196075	−	0.603458i
$617$	12.8949	−	9.36871i	0.519130	−	0.377170i	−0.297146	−	0.954832i	$-0.596035\pi$
$617$	12.8949	−	9.36871i	0.519130	−	0.377170i	0.816276	+	0.577662i	$0.196035\pi$
$618$		0			0
$619$	38.1613	−	27.7258i	1.53383	−	1.11440i	0.579775	−	0.814777i	$-0.303141\pi$
$619$	38.1613	−	27.7258i	1.53383	−	1.11440i	0.954059	−	0.299619i	$-0.0968595\pi$
$620$	−49.9990	+	66.1405i	−2.00801	+	2.65627i
$621$		0			0
$622$	40.3544	+	29.3192i	1.61806	+	1.17559i
$623$	−8.05113	+	24.7788i	−0.322562	+	0.992743i
$624$		0			0
$625$	−21.2818	+	13.1182i	−0.851270	+	0.524727i
$626$	−26.0630			−1.04169
$627$		0			0
$628$	21.6601	+	15.7370i	0.864332	+	0.627974i
$629$	14.5739	+	10.5886i	0.581101	+	0.422195i
$630$		0			0
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.970735	−	0.240153i	$-0.922802\pi$
$631$	−26.1825	+	19.0227i	−1.04231	+	0.757282i	−0.0715741	+	0.997435i	$0.522802\pi$
$632$	−34.6462			−1.37815
$633$		0			0
$634$	−6.20802	−	19.1063i	−0.246552	−	0.758809i
$635$	25.8974	+	37.1058i	1.02771	+	1.47250i
$636$		0			0
$637$	−3.43656	−	10.5766i	−0.136161	−	0.419061i
$638$	5.33526	+	16.4203i	0.211225	+	0.650084i
$639$		0			0
$640$	−43.8658	+	13.3379i	−1.73395	+	0.527226i
$641$	−5.56360	−	17.1230i	−0.219749	−	0.676317i	−0.998782	−	0.0493350i	$-0.984290\pi$
$641$	−5.56360	−	17.1230i	−0.219749	−	0.676317i	0.779033	−	0.626982i	$-0.215710\pi$
$642$		0			0
$643$	21.8891			0.863224			0.431612	−	0.902059i	$-0.357945\pi$
$643$	21.8891			0.863224			0.431612	+	0.902059i	$0.357945\pi$
$644$	−28.9475	+	21.0316i	−1.14069	+	0.828761i
$645$		0			0
$646$	10.0644	+	7.31220i	0.395978	+	0.287695i
$647$	15.3926	+	11.1834i	0.605147	+	0.439665i	0.847702	−	0.530473i	$-0.177985\pi$
$647$	15.3926	+	11.1834i	0.605147	+	0.439665i	−0.242555	+	0.970138i	$0.577985\pi$
$648$		0			0
$649$	1.44129			0.0565755
$650$	−9.80876	−	34.6059i	−0.384731	−	1.35736i
$651$		0			0
$652$	−39.1366	+	120.450i	−1.53271	+	4.71719i
$653$	−1.87669	−	1.36349i	−0.0734405	−	0.0533576i	0.550459	−	0.834862i	$-0.314453\pi$
$653$	−1.87669	−	1.36349i	−0.0734405	−	0.0533576i	−0.623900	+	0.781504i	$0.714453\pi$
$654$		0			0
$655$	−0.129447	+	6.81903i	−0.00505793	+	0.266442i
$656$	−116.709	+	84.7937i	−4.55670	+	3.31064i
$657$		0			0
$658$	−7.03341	+	5.11007i	−0.274191	+	0.199211i
$659$	−2.22239	−	6.83980i	−0.0865719	−	0.266441i	0.898394	−	0.439191i	$-0.144735\pi$
$659$	−2.22239	−	6.83980i	−0.0865719	−	0.266441i	−0.984966	+	0.172750i	$0.944735\pi$
$660$		0			0
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	−0.262358	−	0.964971i	$-0.584500\pi$
$661$	13.2943	−	40.9158i	0.517090	−	1.59144i	0.779447	−	0.626468i	$-0.215500\pi$
$662$	−20.9719	−	64.5450i	−0.815098	−	2.50861i
$663$		0			0
$664$	−23.7300	+	73.0336i	−0.920904	+	2.83425i
$665$	0.0843105	−	4.44131i	0.00326942	−	0.172226i
$666$		0			0
$667$	19.5772	−	14.2236i	0.758031	−	0.550742i
$668$	−23.7461			−0.918765
$669$		0			0
$670$	70.6639	+	24.4523i	2.72998	+	0.944676i
$671$	−6.35478	−	4.61702i	−0.245324	−	0.178238i
$672$		0			0
$673$	−9.20966	+	28.3444i	−0.355006	+	1.09260i	0.600999	+	0.799250i	$0.294769\pi$
$673$	−9.20966	+	28.3444i	−0.355006	+	1.09260i	−0.956006	+	0.293348i	$0.905231\pi$
$674$	−34.9961			−1.34800
$675$		0			0
$676$	−30.4464			−1.17102
$677$	8.26144	−	25.4261i	0.317513	−	0.977204i	−0.657195	−	0.753721i	$-0.728257\pi$
$677$	8.26144	−	25.4261i	0.317513	−	0.977204i	0.974708	−	0.223483i	$-0.0717428\pi$
$678$		0			0
$679$	−14.6969	−	10.6780i	−0.564017	−	0.409782i
$680$	−43.5372	−	62.3802i	−1.66958	−	2.39217i
$681$		0			0
$682$	20.5907			0.788457
$683$	23.0529	−	16.7489i	0.882096	−	0.640880i	−0.0517093	−	0.998662i	$-0.516467\pi$
$683$	23.0529	−	16.7489i	0.882096	−	0.640880i	0.933805	+	0.357782i	$0.116467\pi$
$684$		0			0
$685$	43.3403	+	14.9974i	1.65595	+	0.573020i
$686$	−15.6246	+	48.0876i	−0.596550	+	1.83599i
$687$		0			0
$688$	10.2362	+	31.5039i	0.390253	+	1.20107i
$689$	2.10849	−	6.48926i	0.0803270	−	0.247221i
$690$		0			0
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	0.918965	+	0.394340i	$0.129027\pi$
$691$	10.7065	+	32.9512i	0.407294	+	1.25352i	−0.511671	+	0.859182i	$0.670973\pi$
$692$	−11.3068	+	8.21486i	−0.429820	+	0.312282i
$693$		0			0
$694$	−13.0464	+	9.47878i	−0.495235	+	0.359810i
$695$	−23.4430	−	33.5892i	−0.889245	−	1.27411i
$696$		0			0
$697$	−35.8203	−	26.0249i	−1.35679	−	0.985765i
$698$	−18.8640	+	58.0574i	−0.714012	+	2.19750i
$699$		0			0
$700$	−15.1867	+	41.3317i	−0.574003	+	1.56219i
$701$	−0.973305			−0.0367612			−0.0183806	−	0.999831i	$-0.505851\pi$
$701$	−0.973305			−0.0367612			−0.0183806	+	0.999831i	$0.505851\pi$
$702$		0			0
$703$	−4.36494	−	3.17131i	−0.164627	−	0.119608i
$704$	17.7786	+	12.9169i	0.670058	+	0.486826i
$705$		0			0
$706$	−10.5540	+	7.66790i	−0.397204	+	0.288585i
$707$	22.8854			0.860696
$708$		0			0
$709$	−3.49938	−	10.7700i	−0.131422	−	0.404475i	0.863594	−	0.504187i	$-0.168208\pi$
$709$	−3.49938	−	10.7700i	−0.131422	−	0.404475i	−0.995016	+	0.0997119i	$0.968208\pi$
$710$	−0.682499	+	35.9527i	−0.0256137	+	1.34928i
$711$		0			0
$712$	−41.2941	−	127.090i	−1.54756	−	4.76290i
$713$	−8.91808	−	27.4470i	−0.333985	−	1.02790i
$714$		0			0
$715$	−3.89459	+	5.15190i	−0.145649	+	0.192670i
$716$	25.2078	+	77.5816i	0.942060	+	2.89936i
$717$		0			0
$718$	−77.6312			−2.89717
$719$	−24.8627	+	18.0638i	−0.927224	+	0.673667i	−0.945311	−	0.326169i	$-0.894242\pi$
$719$	−24.8627	+	18.0638i	−0.927224	+	0.673667i	0.0180878	+	0.999836i	$0.494242\pi$
$720$		0			0
$721$	−1.86852	−	1.35756i	−0.0695875	−	0.0505583i
$722$	38.2891	+	27.8186i	1.42497	+	1.03530i
$723$		0			0
$724$	1.05888			0.0393529
$725$	10.2707	−	27.9526i	0.381445	−	1.03813i
$726$		0			0
$727$	−2.02973	+	6.24688i	−0.0752787	+	0.231684i	−0.981615	−	0.190874i	$-0.938868\pi$
$727$	−2.02973	+	6.24688i	−0.0752787	+	0.231684i	0.906336	+	0.422558i	$0.138868\pi$
$728$	−31.6174	−	22.9714i	−1.17182	−	0.851377i
$729$		0			0
$730$	18.9740	−	5.76924i	0.702258	−	0.213529i
$731$	−8.22510	+	5.97589i	−0.304216	+	0.221026i
$732$		0			0
$733$	25.8300	−	18.7666i	0.954051	−	0.693159i	0.00228977	−	0.999997i	$-0.499271\pi$
$733$	25.8300	−	18.7666i	0.954051	−	0.693159i	0.951762	+	0.306838i	$0.0992711\pi$
$734$	−12.2134	−	37.5891i	−0.450806	−	1.38744i
$735$		0			0
$736$	21.4889	−	66.1360i	0.792091	−	2.43781i
$737$	−4.14885	−	12.7688i	−0.152825	−	0.470346i
$738$		0			0
$739$	−4.73017	+	14.5580i	−0.174002	+	0.535524i	−0.999586	−	0.0287550i	$-0.990846\pi$
$739$	−4.73017	+	14.5580i	−0.174002	+	0.535524i	0.825584	+	0.564279i	$0.190846\pi$
$740$	30.6095	+	43.8574i	1.12523	+	1.61223i
$741$		0			0
$742$	−9.34676	+	6.79082i	−0.343130	+	0.249299i
$743$	−16.5455			−0.606995			−0.303498	−	0.952832i	$-0.598154\pi$
$743$	−16.5455			−0.606995			−0.303498	+	0.952832i	$0.598154\pi$
$744$		0			0
$745$	−0.951905	+	1.25921i	−0.0348751	+	0.0461340i
$746$	71.8225	+	52.1821i	2.62961	+	1.91052i
$747$		0			0
$748$	−6.84217	+	21.0580i	−0.250175	+	0.769959i
$749$	−18.5769			−0.678786
$750$		0			0
$751$	46.0279			1.67958			0.839791	−	0.542911i	$-0.182678\pi$
$751$	46.0279			1.67958			0.839791	+	0.542911i	$0.182678\pi$
$752$	7.59174	−	23.3650i	0.276842	−	0.852033i
$753$		0			0
$754$	34.6632	+	25.1843i	1.26236	+	0.917159i
$755$	9.50018	−	12.5672i	0.345747	−	0.457366i
$756$		0			0
$757$	−26.5282			−0.964184			−0.482092	−	0.876121i	$-0.660123\pi$
$757$	−26.5282			−0.964184			−0.482092	+	0.876121i	$0.660123\pi$
$758$	32.9463	−	23.9369i	1.19666	−	0.869427i
$759$		0			0
$760$	13.0395	+	18.6831i	0.472994	+	0.677706i
$761$	8.78353	−	27.0329i	0.318403	−	0.979943i	−0.655928	−	0.754823i	$-0.727723\pi$
$761$	8.78353	−	27.0329i	0.318403	−	0.979943i	0.974331	−	0.225120i	$-0.0722774\pi$
$762$		0			0
$763$	1.79800	+	5.53366i	0.0650918	+	0.200332i
$764$	12.7756	−	39.3192i	0.462204	−	1.42252i
$765$		0			0
$766$	6.64947	+	20.4650i	0.240255	+	0.739429i
$767$	2.89365	−	2.10236i	0.104484	−	0.0759119i
$768$		0			0
$769$	7.24841	−	5.26628i	0.261384	−	0.189907i	−0.449373	−	0.893344i	$-0.648353\pi$
$769$	7.24841	−	5.26628i	0.261384	−	0.189907i	0.710757	+	0.703438i	$0.248353\pi$
$770$	10.4624	−	3.18121i	0.377039	−	0.114643i
$771$		0			0
$772$	69.3744	+	50.4034i	2.49684	+	1.81406i
$773$	−7.13959	+	21.9734i	−0.256793	+	0.790329i	0.736678	+	0.676244i	$0.236393\pi$
$773$	−7.13959	+	21.9734i	−0.256793	+	0.790329i	−0.993471	+	0.114085i	$0.963607\pi$
$774$		0			0
$775$	−27.9197	−	21.9509i	−1.00290	−	0.788501i
$776$	93.1752			3.34479
$777$		0			0
$778$	2.33609	+	1.69727i	0.0837530	+	0.0608501i
$779$	10.7283	+	7.79455i	0.384380	+	0.279269i
$780$		0			0
$781$	5.22343	−	3.79504i	0.186909	−	0.135797i
$782$	42.9232			1.53493
$783$		0			0
$784$	−16.4433	−	50.6072i	−0.587260	−	1.80740i
$785$	−6.91581	+	9.14848i	−0.246836	+	0.326523i
$786$		0			0
$787$	−0.628511	−	1.93436i	−0.0224040	−	0.0689524i	0.939229	−	0.343290i	$-0.111541\pi$
$787$	−0.628511	−	1.93436i	−0.0224040	−	0.0689524i	−0.961633	+	0.274338i	$0.911541\pi$
$788$	27.6440	+	85.0794i	0.984776	+	3.03083i
$789$		0			0
$790$	0.456615	−	24.0536i	0.0162456	−	0.855788i
$791$	−3.15503	−	9.71018i	−0.112180	−	0.345254i
$792$		0			0
$793$	−19.4931			−0.692220
$794$	52.6376	−	38.2435i	1.86804	−	1.35721i
$795$		0			0
$796$	8.52449	+	6.19340i	0.302142	+	0.219519i
$797$	−9.86379	−	7.16646i	−0.349393	−	0.253849i	0.399221	−	0.916855i	$-0.369281\pi$
$797$	−9.86379	−	7.16646i	−0.349393	−	0.253849i	−0.748614	+	0.663006i	$0.769281\pi$
$798$		0			0
$799$	7.54024			0.266754
$800$	−23.3370	−	82.3343i	−0.825086	−	2.91096i
$801$		0			0
$802$	1.65501	−	5.09359i	0.0584404	−	0.179861i
$803$	−2.88075	−	2.09299i	−0.101659	−	0.0738599i
$804$		0			0
$805$	−8.77191	−	12.5684i	−0.309169	−	0.442978i
$806$	41.3396	−	30.0350i	1.45612	−	1.05794i
$807$		0			0
$808$	−94.9616	+	68.9936i	−3.34074	+	2.42719i
$809$	−2.72972	−	8.40121i	−0.0959718	−	0.295371i	0.891534	−	0.452954i	$-0.149630\pi$
$809$	−2.72972	−	8.40121i	−0.0959718	−	0.295371i	−0.987506	+	0.157583i	$0.949630\pi$
$810$		0			0
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	−0.997737	−	0.0672381i	$-0.978581\pi$
$811$	−4.30102	+	13.2372i	−0.151029	+	0.464820i	0.846708	+	0.532058i	$0.178581\pi$
$812$	−16.2086	−	49.8850i	−0.568811	−	1.75062i
$813$		0			0
$814$	4.10438	−	12.6320i	0.143858	−	0.442750i
$815$	−51.2673	−	17.7404i	−1.79581	−	0.621419i
$816$		0			0
$817$	2.46344	−	1.78980i	0.0861850	−	0.0626170i
$818$	17.9085			0.626158
$819$		0			0
$820$	−75.2330	−	107.794i	−2.62725	−	3.76433i
$821$	−23.8603	−	17.3355i	−0.832731	−	0.605015i	0.0875994	−	0.996156i	$-0.472080\pi$
$821$	−23.8603	−	17.3355i	−0.832731	−	0.605015i	−0.920331	+	0.391141i	$0.872080\pi$
$822$		0			0
$823$	−12.9682	+	39.9121i	−0.452044	+	1.39125i	0.422527	+	0.906350i	$0.361143\pi$
$823$	−12.9682	+	39.9121i	−0.452044	+	1.39125i	−0.874571	+	0.484898i	$0.838857\pi$
$824$	11.8460			0.412675
$825$		0			0
$826$	−6.05624			−0.210724
$827$	−11.5781	+	35.6336i	−0.402609	+	1.23910i	0.520266	+	0.854004i	$0.325833\pi$
$827$	−11.5781	+	35.6336i	−0.402609	+	1.23910i	−0.922875	+	0.385099i	$0.874167\pi$
$828$		0			0
$829$	7.73108	+	5.61696i	0.268512	+	0.195085i	0.713891	−	0.700257i	$-0.246931\pi$
$829$	7.73108	+	5.61696i	0.268512	+	0.195085i	−0.445379	+	0.895342i	$0.646931\pi$
$830$	−50.3918	−	17.4374i	−1.74913	−	0.605263i
$831$		0			0
$832$	54.5355			1.89068
$833$	13.2126	−	9.59954i	0.457791	−	0.332604i
$834$		0			0
$835$	0.193056	−	10.1698i	0.00668099	−	0.351941i
$836$	2.04925	−	6.30695i	0.0708748	−	0.218130i
$837$		0			0
$838$	−17.7311	−	54.5708i	−0.612512	−	1.88512i
$839$	−16.9128	+	52.0522i	−0.583895	+	1.79704i	0.0197702	+	0.999805i	$0.493707\pi$
$839$	−16.9128	+	52.0522i	−0.583895	+	1.79704i	−0.603665	+	0.797238i	$0.706293\pi$
$840$		0			0
$841$	2.00037	+	6.15651i	0.0689783	+	0.212294i
$842$	−48.5570	+	35.2787i	−1.67338	+	1.21579i
$843$		0			0
$844$	100.603	−	73.0922i	3.46289	−	2.51594i
$845$	0.247529	−	13.0394i	0.00851527	−	0.448567i
$846$		0			0
$847$	13.4248	+	9.75371i	0.461283	+	0.335141i
$848$	10.0887	−	31.0499i	0.346448	−	1.06626i
$849$		0			0
$850$	43.8821	−	29.4042i	1.50514	−	1.00856i
$851$	−18.6159			−0.638144
$852$		0			0
$853$	12.3834	+	8.99706i	0.423999	+	0.308053i	0.779245	−	0.626720i	$-0.215603\pi$
$853$	12.3834	+	8.99706i	0.423999	+	0.308053i	−0.355246	+	0.934773i	$0.615603\pi$
$854$	26.7026	+	19.4005i	0.913743	+	0.663873i
$855$		0			0
$856$	77.0836	−	56.0045i	2.63466	−	1.91419i
$857$	8.66910			0.296131			0.148065	−	0.988978i	$-0.452695\pi$
$857$	8.66910			0.296131			0.148065	+	0.988978i	$0.452695\pi$
$858$		0			0
$859$	−9.39653	−	28.9195i	−0.320605	−	0.986722i	−0.973385	−	0.229174i	$-0.926397\pi$
$859$	−9.39653	−	28.9195i	−0.320605	−	0.986722i	0.652780	−	0.757547i	$-0.273603\pi$
$860$	−28.8787	+	8.78088i	−0.984755	+	0.299425i
$861$		0			0
$862$	25.2531	+	77.7211i	0.860125	+	2.64719i
$863$	5.57545	+	17.1595i	0.189791	+	0.584115i	0.999998	−	0.00202803i	$-0.000645543\pi$
$863$	5.57545	+	17.1595i	0.189791	+	0.584115i	−0.810207	+	0.586143i	$0.800646\pi$
$864$		0			0
$865$	−3.42627	−	4.90917i	−0.116497	−	0.166917i
$866$	0.478808	+	1.47362i	0.0162706	+	0.0500756i
$867$		0			0
$868$	−62.5548			−2.12325
$869$	−3.49465	+	2.53901i	−0.118548	+	0.0861301i
$870$		0			0
$871$	−26.9551	−	19.5840i	−0.913338	−	0.663579i
$872$	−24.1432	−	17.5411i	−0.817591	−	0.594015i
$873$		0			0
$874$	−12.8556			−0.434848
$875$	−17.5778	−	6.84006i	−0.594237	−	0.231236i
$876$		0			0
$877$	6.89285	−	21.2140i	0.232755	−	0.716346i	−0.764656	−	0.644438i	$-0.777091\pi$
$877$	6.89285	−	21.2140i	0.232755	−	0.716346i	0.997411	−	0.0719076i	$-0.0229087\pi$
$878$	−27.8352	−	20.2235i	−0.939393	−	0.682509i
$879$		0			0
$880$	−18.6349	+	24.6508i	−0.628181	+	0.830980i
$881$	6.27761	−	4.56095i	0.211498	−	0.153662i	−0.476993	−	0.878907i	$-0.658273\pi$
$881$	6.27761	−	4.56095i	0.211498	−	0.153662i	0.688491	+	0.725245i	$0.258273\pi$
$882$		0			0
$883$	16.1421	−	11.7279i	0.543224	−	0.394675i	−0.282057	−	0.959398i	$-0.591017\pi$
$883$	16.1421	−	11.7279i	0.543224	−	0.394675i	0.825281	+	0.564722i	$0.191017\pi$
$884$	16.9798	+	52.2584i	0.571092	+	1.75764i
$885$		0			0
$886$	−11.8861	+	36.5816i	−0.399320	+	1.22898i
$887$	−2.65844	−	8.18183i	−0.0892616	−	0.274719i	0.896454	−	0.443137i	$-0.146134\pi$
$887$	−2.65844	−	8.18183i	−0.0892616	−	0.274719i	−0.985716	+	0.168418i	$0.946134\pi$
$888$		0			0
$889$	−10.5496	+	32.4684i	−0.353823	+	1.08895i
$890$	88.7783	−	26.9940i	2.97585	−	0.904841i
$891$		0			0
$892$	−55.3715	+	40.2297i	−1.85397	+	1.34699i
$893$	−2.25832			−0.0755719
$894$		0			0
$895$	−33.4310	+	10.1651i	−1.11748	+	0.339781i
$896$	−27.9851	−	20.3323i	−0.934916	−	0.679256i
$897$		0			0
$898$	9.93611	−	30.5802i	0.331572	−	1.02047i
$899$	42.3057			1.41097
$900$		0			0
$901$	10.0203			0.333824
$902$	−10.0879	+	31.0472i	−0.335889	+	1.03376i
$903$		0			0
$904$	42.3652	+	30.7801i	1.40905	+	1.02373i
$905$	−0.00860869	+	0.453488i	−0.000286163	+	0.0150745i
$906$		0			0
$907$	6.26125			0.207902			0.103951	−	0.994582i	$-0.466852\pi$
$907$	6.26125			0.207902			0.103951	+	0.994582i	$0.466852\pi$
$908$	−110.989	+	80.6385i	−3.68331	+	2.67608i
$909$		0			0
$910$	16.3649	−	21.6481i	0.542491	−	0.717627i
$911$	−0.279838	+	0.861253i	−0.00927145	+	0.0285346i	−0.955585	−	0.294715i	$-0.904775\pi$
$911$	−0.279838	+	0.861253i	−0.00927145	+	0.0285346i	0.946314	+	0.323250i	$0.104775\pi$
$912$		0			0
$913$	2.95862	+	9.10571i	0.0979162	+	0.301355i
$914$	−6.82669	+	21.0104i	−0.225807	+	0.694962i
$915$		0			0
$916$	3.21988	+	9.90978i	0.106388	+	0.327428i
$917$	−4.16293	+	3.02455i	−0.137472	+	0.0998794i
$918$		0			0
$919$	−35.5913	+	25.8586i	−1.17405	+	0.852997i	−0.991488	−	0.130198i	$-0.958439\pi$
$919$	−35.5913	+	25.8586i	−1.17405	+	0.852997i	−0.182561	+	0.983194i	$0.558439\pi$
$920$	74.2889	+	25.7067i	2.44923	+	0.847526i
$921$		0			0
$922$	2.76551	+	2.00926i	0.0910771	+	0.0661714i
$923$	4.95129	−	15.2385i	0.162974	−	0.501582i
$924$		0			0
$925$	−19.0317	+	12.7526i	−0.625760	+	0.419304i
$926$	87.8029			2.88538
$927$		0			0
$928$	82.4707	+	59.9184i	2.70723	+	1.96692i
$929$	−29.7271	−	21.5980i	−0.975313	−	0.708606i	−0.0186568	−	0.999826i	$-0.505939\pi$
$929$	−29.7271	−	21.5980i	−0.975313	−	0.708606i	−0.956656	+	0.291220i	$0.905939\pi$
$930$		0			0
$931$	−3.95722	+	2.87509i	−0.129693	+	0.0942273i
$932$	2.74347			0.0898652
$933$		0			0
$934$	−11.9857	−	36.8883i	−0.392185	−	1.20702i
$935$	−8.96295	−	3.10152i	−0.293120	−	0.101430i
$936$		0			0
$937$	7.61696	+	23.4426i	0.248835	+	0.765836i	0.994982	+	0.100055i	$0.0319017\pi$
$937$	7.61696	+	23.4426i	0.248835	+	0.765836i	−0.746147	+	0.665782i	$0.768098\pi$
$938$	17.4333	+	53.6542i	0.569217	+	1.75187i
$939$		0			0
$940$	21.1554	+	7.32055i	0.690012	+	0.238770i
$941$	18.2777	+	56.2530i	0.595836	+	1.83379i	0.550520	+	0.834822i	$0.314429\pi$
$941$	18.2777	+	56.2530i	0.595836	+	1.83379i	0.0453159	+	0.998973i	$0.485571\pi$
$942$		0			0
$943$	45.7546			1.48998
$944$	13.8456	−	10.0594i	0.450635	−	0.327406i
$945$		0			0
$946$	6.06439	+	4.40604i	0.197170	+	0.143253i
$947$	−24.3482	−	17.6900i	−0.791210	−	0.574848i	0.117112	−	0.993119i	$-0.462636\pi$
$947$	−24.3482	−	17.6900i	−0.791210	−	0.574848i	−0.908322	+	0.418271i	$0.862636\pi$
$948$		0			0
$949$	−8.83661			−0.286849
$950$	−13.1428	+	8.80664i	−0.426410	+	0.285725i
$951$		0			0
$952$	17.7354	−	54.5841i	0.574809	−	1.76908i
$953$	−16.6975	−	12.1315i	−0.540886	−	0.392977i	0.283528	−	0.958964i	$-0.408495\pi$
$953$	−16.6975	−	12.1315i	−0.540886	−	0.392977i	−0.824414	+	0.565987i	$0.808495\pi$
$954$		0			0
$955$	16.7355	+	5.79109i	0.541547	+	0.187395i
$956$	−29.6036	+	21.5083i	−0.957449	+	0.695628i
$957$		0			0
$958$	−36.6553	+	26.6316i	−1.18428	+	0.860429i
$959$	10.6924	+	32.9078i	0.345275	+	1.06265i
$960$		0			0
$961$	6.01162	−	18.5019i	0.193923	−	0.596834i
$962$	−10.1856	−	31.3480i	−0.328396	−	1.01070i
$963$		0			0
$964$	3.73527	−	11.4960i	0.120305	−	0.370260i
$965$	−22.1504	+	29.3013i	−0.713047	+	0.943244i
$966$		0			0
$967$	18.2850	−	13.2849i	0.588007	−	0.427212i	−0.253595	−	0.967311i	$-0.581613\pi$
$967$	18.2850	−	13.2849i	0.588007	−	0.427212i	0.841602	+	0.540098i	$0.181613\pi$
$968$	−85.1103			−2.73555
$969$		0			0
$970$	−1.22799	+	64.6881i	−0.0394284	+	2.07701i
$971$	19.5281	+	14.1880i	0.626687	+	0.455315i	0.855251	−	0.518214i	$-0.173403\pi$
$971$	19.5281	+	14.1880i	0.626687	+	0.455315i	−0.228564	+	0.973529i	$0.573403\pi$
$972$		0			0
$973$	9.54981	−	29.3913i	0.306153	−	0.942242i
$974$	107.007			3.42874
$975$		0			0
$976$	−93.2708			−2.98553
$977$	−7.12302	+	21.9224i	−0.227886	+	0.701360i	0.770100	+	0.637923i	$0.220206\pi$
$977$	−7.12302	+	21.9224i	−0.227886	+	0.701360i	−0.997986	+	0.0634371i	$0.979794\pi$
$978$		0			0
$979$	−13.4789	−	9.79299i	−0.430787	−	0.312985i
$980$	46.3901	−	14.1054i	1.48188	−	0.450581i
$981$		0			0
$982$	−37.6870			−1.20264
$983$	24.1664	−	17.5579i	0.770787	−	0.560010i	−0.131413	−	0.991328i	$-0.541951\pi$
$983$	24.1664	−	17.5579i	0.770787	−	0.560010i	0.902200	+	0.431318i	$0.141951\pi$
$984$		0			0
$985$	−36.6619	+	11.1474i	−1.16814	+	0.355187i
$986$	−19.4440	+	59.8424i	−0.619222	+	1.90577i
$987$		0			0
$988$	−5.08550	−	15.6515i	−0.161791	−	0.497942i
$989$	3.24661	−	9.99204i	0.103236	−	0.317728i
$990$		0			0
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	0.998923	−	0.0464072i	$-0.0147772\pi$
$991$	5.14700	+	15.8408i	0.163500	+	0.503201i	−0.835423	+	0.549608i	$0.814777\pi$
$992$	98.3550	−	71.4591i	3.12277	−	2.26883i
$993$		0			0
$994$	−21.9487	+	15.9466i	−0.696169	+	0.505797i
$995$	−2.72177	+	3.60045i	−0.0862858	+	0.114142i
$996$		0			0
$997$	−10.1074	−	7.34343i	−0.320103	−	0.232569i	0.416116	−	0.909311i	$-0.363391\pi$
$997$	−10.1074	−	7.34343i	−0.320103	−	0.232569i	−0.736220	+	0.676743i	$0.763391\pi$
$998$	12.6474	−	38.9246i	0.400346	−	1.23214i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.46.3		12
3.2	odd	2		75.2.g.c.46.1	yes	12
15.2	even	4		375.2.i.d.274.1		24
15.8	even	4		375.2.i.d.274.6		24
15.14	odd	2		375.2.g.c.226.3		12
25.6	even	5	inner	225.2.h.d.181.3		12
25.9	even	10		5625.2.a.q.1.1		6
25.16	even	5		5625.2.a.p.1.6		6
75.8	even	20		375.2.i.d.349.1		24
75.17	even	20		375.2.i.d.349.6		24
75.38	even	20		1875.2.b.f.1249.12		12
75.41	odd	10		1875.2.a.j.1.1		6
75.44	odd	10		375.2.g.c.151.3		12
75.56	odd	10		75.2.g.c.31.1	✓	12
75.59	odd	10		1875.2.a.k.1.6		6
75.62	even	20		1875.2.b.f.1249.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.1	✓	12	75.56	odd	10
75.2.g.c.46.1	yes	12	3.2	odd	2
225.2.h.d.46.3		12	1.1	even	1	trivial
225.2.h.d.181.3		12	25.6	even	5	inner
375.2.g.c.151.3		12	75.44	odd	10
375.2.g.c.226.3		12	15.14	odd	2
375.2.i.d.274.1		24	15.2	even	4
375.2.i.d.274.6		24	15.8	even	4
375.2.i.d.349.1		24	75.8	even	20
375.2.i.d.349.6		24	75.17	even	20
1875.2.a.j.1.1		6	75.41	odd	10
1875.2.a.k.1.6		6	75.59	odd	10
1875.2.b.f.1249.1		12	75.62	even	20
1875.2.b.f.1249.12		12	75.38	even	20
5625.2.a.p.1.6		6	25.16	even	5
5625.2.a.q.1.1		6	25.9	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.830342 - 2.55553i) q^{2} +(-4.22323 - 3.06835i) q^{4} +(1.34843 - 1.78375i) q^{5} +1.68704 q^{7} +(-7.00026 + 5.08599i) q^{8} +(-3.43876 - 4.92706i) q^{10} +(-0.333373 + 1.02602i) q^{11} +(0.827310 + 2.54620i) q^{13} +(1.40082 - 4.31129i) q^{14} +(3.95852 + 12.1831i) q^{16} +(-3.18079 + 2.31098i) q^{17} +(0.952655 - 0.692144i) q^{19} +(-11.1679 + 3.39571i) q^{20} +(2.34520 + 1.70389i) q^{22} +(1.25552 - 3.86409i) q^{23} +(-1.36350 - 4.81050i) q^{25} +7.19384 q^{26} +(-7.12476 - 5.17644i) q^{28} +(4.81846 + 3.50082i) q^{29} +(5.74653 - 4.17510i) q^{31} +17.1155 q^{32} +(3.26463 + 10.0475i) q^{34} +(2.27485 - 3.00925i) q^{35} +(-1.41587 - 4.35761i) q^{37} +(-0.977766 - 3.00925i) q^{38} +(-0.367227 + 19.3448i) q^{40} +(3.47998 + 10.7103i) q^{41} +2.58587 q^{43} +(4.55609 - 3.31019i) q^{44} +(-8.83229 - 6.41703i) q^{46} +(-1.55155 - 1.12727i) q^{47} -4.15389 q^{49} +(-13.4255 - 0.509905i) q^{50} +(4.31872 - 13.2917i) q^{52} +(-2.06187 - 1.49803i) q^{53} +(1.38062 + 1.97816i) q^{55} +(-11.8097 + 8.58028i) q^{56} +(12.9474 - 9.40685i) q^{58} +(-0.412843 - 1.27060i) q^{59} +(-2.24997 + 6.92470i) q^{61} +(-5.89800 - 18.1522i) q^{62} +(6.29470 - 19.3731i) q^{64} +(5.65734 + 1.95765i) q^{65} +(-10.0683 + 7.31502i) q^{67} +20.5241 q^{68} +(-5.80133 - 8.31216i) q^{70} +(-4.84181 - 3.51778i) q^{71} +(-1.01996 + 3.13911i) q^{73} -12.3117 q^{74} -6.14702 q^{76} +(-0.562414 + 1.73093i) q^{77} +(3.23934 + 2.35351i) q^{79} +(27.0693 + 9.36699i) q^{80} +30.2600 q^{82} +(7.17988 - 5.21649i) q^{83} +(-0.166861 + 8.78989i) q^{85} +(2.14716 - 6.60827i) q^{86} +(-2.88461 - 8.87792i) q^{88} +(-4.77234 + 14.6877i) q^{89} +(1.39571 + 4.29555i) q^{91} +(-17.1587 + 12.4666i) q^{92} +(-4.16908 + 3.02901i) q^{94} +(0.0499753 - 2.63260i) q^{95} +(-8.71166 - 6.32939i) q^{97} +(-3.44915 + 10.6154i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29}+ \cdots + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

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