LMFDB - Embedded newform 225.2.h.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.1
Root			$-1.21700 + 0.720348i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.c.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655837 + 2.01846i) q^{2} +(-2.02602 - 1.47199i) q^{4} +(2.21700 - 0.291365i) q^{5} +4.35840 q^{7} +(0.865884 - 0.629102i) q^{8} +O(q^{10})$	\(q+(-0.655837 + 2.01846i) q^{2} +(-2.02602 - 1.47199i) q^{4} +(2.21700 - 0.291365i) q^{5} +4.35840 q^{7} +(0.865884 - 0.629102i) q^{8} +(-0.865884 + 4.66602i) q^{10} +(0.488218 - 1.50258i) q^{11} +(0.370184 + 1.13931i) q^{13} +(-2.85840 + 8.79726i) q^{14} +(-0.845805 - 2.60312i) q^{16} +(-0.907987 + 0.659691i) q^{17} +(-6.21218 + 4.51341i) q^{19} +(-4.92058 - 2.67310i) q^{20} +(2.71270 + 1.97090i) q^{22} +(0.717004 - 2.20671i) q^{23} +(4.83021 - 1.29192i) q^{25} -2.54243 q^{26} +(-8.83021 - 6.41552i) q^{28} +(-4.45307 - 3.23535i) q^{29} +(-3.88495 + 2.82258i) q^{31} +7.94959 q^{32} +(-0.736068 - 2.26538i) q^{34} +(9.66259 - 1.26989i) q^{35} +(-1.96915 - 6.06043i) q^{37} +(-5.03596 - 15.4991i) q^{38} +(1.73637 - 1.64701i) q^{40} +(2.30902 + 7.10642i) q^{41} -1.24998 q^{43} +(-3.20092 + 2.32561i) q^{44} +(3.98392 + 2.89449i) q^{46} +(3.33934 + 2.42617i) q^{47} +11.9957 q^{49} +(-0.560152 + 10.5969i) q^{50} +(0.927051 - 2.85317i) q^{52} +(3.03032 + 2.20166i) q^{53} +(0.644581 - 3.47347i) q^{55} +(3.77387 - 2.74188i) q^{56} +(9.45090 - 6.86648i) q^{58} +(-2.82940 - 8.70799i) q^{59} +(0.431351 - 1.32756i) q^{61} +(-3.14937 - 9.69276i) q^{62} +(-3.52202 + 10.8397i) q^{64} +(1.15265 + 2.41799i) q^{65} +(3.12499 - 2.27044i) q^{67} +2.81066 q^{68} +(-3.77387 + 20.3364i) q^{70} +(-8.57970 - 6.23352i) q^{71} +(1.54407 - 4.75216i) q^{73} +13.5242 q^{74} +19.2297 q^{76} +(2.12785 - 6.54885i) q^{77} +(-11.7737 - 8.55407i) q^{79} +(-2.63361 - 5.52469i) q^{80} -15.8584 q^{82} +(-7.06760 + 5.13491i) q^{83} +(-1.82080 + 1.72709i) q^{85} +(0.819784 - 2.52304i) q^{86} +(-0.522535 - 1.60820i) q^{88} +(3.10195 - 9.54683i) q^{89} +(1.61341 + 4.96556i) q^{91} +(-4.70092 + 3.41542i) q^{92} +(-7.08719 + 5.14914i) q^{94} +(-12.4574 + 11.8163i) q^{95} +(6.06760 + 4.40837i) q^{97} +(-7.86720 + 24.2128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7	$ 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7 - 16 * q^11 - 8 * q^13 + 8 * q^14 - 17 * q^16 + q^17 - 5 * q^19 + 10 * q^20 + 13 * q^22 - 7 * q^23 - 15 * q^25 - 6 * q^26 - 17 * q^28 - 5 * q^29 - 19 * q^31 - 24 * q^32 + 12 * q^34 + 10 * q^35 - q^37 + 10 * q^38 + 25 * q^40 + 14 * q^41 + 32 * q^43 + 3 * q^44 + 16 * q^46 + q^47 + 16 * q^49 - 10 * q^50 - 6 * q^52 + 3 * q^53 + 15 * q^55 + 15 * q^56 + 5 * q^58 - 30 * q^59 - 14 * q^61 + 17 * q^62 - 44 * q^64 - 25 * q^65 + 4 * q^67 + 22 * q^68 - 15 * q^70 - 21 * q^71 + 2 * q^73 + 38 * q^74 + 80 * q^76 + 37 * q^77 - 30 * q^79 + 50 * q^80 - 12 * q^82 - 2 * q^83 - 30 * q^85 + 34 * q^86 + 70 * q^88 + 21 * q^91 - 9 * q^92 - 33 * q^94 - 65 * q^95 - 6 * q^97 - 73 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−0.655837	+	2.01846i	−0.463747	+	1.42727i	0.396805	+	0.917903i	$0.370119\pi$
$2$	−0.655837	+	2.01846i	−0.463747	+	1.42727i	−0.860552	+	0.509363i	$0.829881\pi$
$3$		0			0
$3$		0			0
$4$	−2.02602	−	1.47199i	−1.01301	−	0.735995i
$5$	2.21700	−	0.291365i	0.991474	−	0.130303i
$5$	2.21700	−	0.291365i	0.991474	−	0.130303i
$6$		0			0
$7$	4.35840			1.64732			0.823660	−	0.567083i	$-0.191928\pi$
$7$	4.35840			1.64732			0.823660	+	0.567083i	$0.191928\pi$
$8$	0.865884	−	0.629102i	0.306136	−	0.222421i
$9$		0			0
$10$	−0.865884	+	4.66602i	−0.273817	+	1.47553i
$11$	0.488218	−	1.50258i	0.147203	−	0.453045i	−0.850085	−	0.526646i	$-0.823449\pi$
$11$	0.488218	−	1.50258i	0.147203	−	0.453045i	0.997288	+	0.0736014i	$0.0234493\pi$
$12$		0			0
$13$	0.370184	+	1.13931i	0.102670	+	0.315987i	0.989177	−	0.146729i	$-0.0468747\pi$
$13$	0.370184	+	1.13931i	0.102670	+	0.315987i	−0.886506	+	0.462717i	$0.846875\pi$
$14$	−2.85840	+	8.79726i	−0.763940	+	2.35117i
$15$		0			0
$16$	−0.845805	−	2.60312i	−0.211451	−	0.650780i
$17$	−0.907987	+	0.659691i	−0.220219	+	0.159999i	−0.692425	−	0.721490i	$-0.743458\pi$
$17$	−0.907987	+	0.659691i	−0.220219	+	0.159999i	0.472206	+	0.881488i	$0.343458\pi$
$18$		0			0
$19$	−6.21218	+	4.51341i	−1.42517	+	1.03545i	−0.434281	+	0.900777i	$0.642998\pi$
$19$	−6.21218	+	4.51341i	−1.42517	+	1.03545i	−0.990890	+	0.134670i	$0.957002\pi$
$20$	−4.92058	−	2.67310i	−1.10028	−	0.597722i
$21$		0			0
$22$	2.71270	+	1.97090i	0.578351	+	0.420196i
$23$	0.717004	−	2.20671i	0.149506	−	0.460131i	−0.848057	−	0.529905i	$-0.822228\pi$
$23$	0.717004	−	2.20671i	0.149506	−	0.460131i	0.997563	+	0.0697736i	$0.0222277\pi$
$24$		0			0
$25$	4.83021	−	1.29192i	0.966042	−	0.258383i
$26$	−2.54243			−0.498611
$27$		0			0
$28$	−8.83021	−	6.41552i	−1.66875	−	1.21242i
$29$	−4.45307	−	3.23535i	−0.826915	−	0.600789i	0.0917701	−	0.995780i	$-0.470748\pi$
$29$	−4.45307	−	3.23535i	−0.826915	−	0.600789i	−0.918685	+	0.394992i	$0.870748\pi$
$30$		0			0
$31$	−3.88495	+	2.82258i	−0.697757	+	0.506950i	−0.879201	−	0.476451i	$-0.841923\pi$
$31$	−3.88495	+	2.82258i	−0.697757	+	0.506950i	0.181444	+	0.983401i	$0.441923\pi$
$32$	7.94959			1.40530
$33$		0			0
$34$	−0.736068	−	2.26538i	−0.126235	−	0.388510i
$35$	9.66259	−	1.26989i	1.63328	−	0.214650i
$36$		0			0
$37$	−1.96915	−	6.06043i	−0.323727	−	0.996329i	−0.972012	−	0.234931i	$-0.924514\pi$
$37$	−1.96915	−	6.06043i	−0.323727	−	0.996329i	0.648285	−	0.761398i	$-0.275486\pi$
$38$	−5.03596	−	15.4991i	−0.816941	−	2.51428i
$39$		0			0
$40$	1.73637	−	1.64701i	0.274544	−	0.260415i
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	0.952686	+	0.303956i	$0.0983077\pi$
$41$	2.30902	+	7.10642i	0.360608	+	1.10984i	−0.592078	+	0.805881i	$0.701692\pi$
$42$		0			0
$43$	−1.24998			−0.190620			−0.0953102	−	0.995448i	$-0.530384\pi$
$43$	−1.24998			−0.190620			−0.0953102	+	0.995448i	$0.530384\pi$
$44$	−3.20092	+	2.32561i	−0.482557	+	0.350598i
$45$		0			0
$46$	3.98392	+	2.89449i	0.587397	+	0.426769i
$47$	3.33934	+	2.42617i	0.487092	+	0.353893i	0.804065	−	0.594541i	$-0.202666\pi$
$47$	3.33934	+	2.42617i	0.487092	+	0.353893i	−0.316973	+	0.948435i	$0.602666\pi$
$48$		0			0
$49$	11.9957			1.71367
$50$	−0.560152	+	10.5969i	−0.0792174	+	1.49862i
$51$		0			0
$52$	0.927051	−	2.85317i	0.128559	−	0.395663i
$53$	3.03032	+	2.20166i	0.416247	+	0.302421i	0.776126	−	0.630578i	$-0.217182\pi$
$53$	3.03032	+	2.20166i	0.416247	+	0.302421i	−0.359879	+	0.932999i	$0.617182\pi$
$54$		0			0
$55$	0.644581	−	3.47347i	0.0869153	−	0.468363i
$56$	3.77387	−	2.74188i	0.504305	−	0.366399i
$57$		0			0
$58$	9.45090	−	6.86648i	1.24096	−	0.901613i
$59$	−2.82940	−	8.70799i	−0.368356	−	1.13368i	−0.947853	−	0.318709i	$-0.896751\pi$
$59$	−2.82940	−	8.70799i	−0.368356	−	1.13368i	0.579496	−	0.814975i	$-0.303249\pi$
$60$		0			0
$61$	0.431351	−	1.32756i	0.0552288	−	0.169977i	−0.919637	−	0.392769i	$-0.871517\pi$
$61$	0.431351	−	1.32756i	0.0552288	−	0.169977i	0.974866	+	0.222792i	$0.0715172\pi$
$62$	−3.14937	−	9.69276i	−0.399970	−	1.23098i
$63$		0			0
$64$	−3.52202	+	10.8397i	−0.440253	+	1.35496i
$65$	1.15265	+	2.41799i	0.142969	+	0.299915i
$66$		0			0
$67$	3.12499	−	2.27044i	0.381778	−	0.277378i	−0.380300	−	0.924863i	$-0.624179\pi$
$67$	3.12499	−	2.27044i	0.381778	−	0.277378i	0.762078	+	0.647485i	$0.224179\pi$
$68$	2.81066			0.340843
$69$		0			0
$70$	−3.77387	+	20.3364i	−0.451064	+	2.43066i
$71$	−8.57970	−	6.23352i	−1.01822	−	0.739783i	−0.0523057	−	0.998631i	$-0.516657\pi$
$71$	−8.57970	−	6.23352i	−1.01822	−	0.739783i	−0.965918	+	0.258848i	$0.916657\pi$
$72$		0			0
$73$	1.54407	−	4.75216i	0.180720	−	0.556198i	−0.819129	−	0.573610i	$-0.805543\pi$
$73$	1.54407	−	4.75216i	0.180720	−	0.556198i	0.999848	+	0.0174117i	$0.00554259\pi$
$74$	13.5242			1.57215
$75$		0			0
$76$	19.2297			2.20580
$77$	2.12785	−	6.54885i	0.242491	−	0.746310i
$78$		0			0
$79$	−11.7737	−	8.55407i	−1.32464	−	0.962408i	−0.999862	−	0.0166185i	$-0.994710\pi$
$79$	−11.7737	−	8.55407i	−1.32464	−	0.962408i	−0.324779	−	0.945790i	$-0.605290\pi$
$80$	−2.63361	−	5.52469i	−0.294447	−	0.617679i
$81$		0			0
$82$	−15.8584			−1.75126
$83$	−7.06760	+	5.13491i	−0.775770	+	0.563630i	−0.903706	−	0.428153i	$-0.859165\pi$
$83$	−7.06760	+	5.13491i	−0.775770	+	0.563630i	0.127937	+	0.991782i	$0.459165\pi$
$84$		0			0
$85$	−1.82080	+	1.72709i	−0.197493	+	0.187330i
$86$	0.819784	−	2.52304i	0.0883996	−	0.272066i
$87$		0			0
$88$	−0.522535	−	1.60820i	−0.0557025	−	0.171435i
$89$	3.10195	−	9.54683i	0.328806	−	1.01196i	−0.640887	−	0.767635i	$-0.721433\pi$
$89$	3.10195	−	9.54683i	0.328806	−	1.01196i	0.969693	−	0.244326i	$-0.0785668\pi$
$90$		0			0
$91$	1.61341	+	4.96556i	0.169131	+	0.520532i
$92$	−4.70092	+	3.41542i	−0.490105	+	0.356082i
$93$		0			0
$94$	−7.08719	+	5.14914i	−0.730988	+	0.531094i
$95$	−12.4574	+	11.8163i	−1.27810	+	1.21232i
$96$		0			0
$97$	6.06760	+	4.40837i	0.616071	+	0.447602i	0.851547	−	0.524278i	$-0.175665\pi$
$97$	6.06760	+	4.40837i	0.616071	+	0.447602i	−0.235476	+	0.971880i	$0.575665\pi$
$98$	−7.86720	+	24.2128i	−0.794707	+	2.44586i
$99$		0			0
$100$	−11.6878	−	4.49258i	−1.16878	−	0.449258i
$101$	6.51821			0.648586			0.324293	−	0.945957i	$-0.394874\pi$
$101$	6.51821			0.648586			0.324293	+	0.945957i	$0.394874\pi$
$102$		0			0
$103$	−6.51158	−	4.73094i	−0.641605	−	0.466153i	0.218796	−	0.975771i	$-0.429787\pi$
$103$	−6.51158	−	4.73094i	−0.641605	−	0.466153i	−0.860401	+	0.509617i	$0.829787\pi$
$104$	1.03728	+	0.753626i	0.101713	+	0.0738991i
$105$		0			0
$106$	−6.43135	+	4.67265i	−0.624668	+	0.453848i
$107$	−9.47745			−0.916220			−0.458110	−	0.888896i	$-0.651473\pi$
$107$	−9.47745			−0.916220			−0.458110	+	0.888896i	$0.651473\pi$
$108$		0			0
$109$	−3.60491	−	11.0948i	−0.345288	−	1.06269i	−0.961429	−	0.275052i	$-0.911305\pi$
$109$	−3.60491	−	11.0948i	−0.345288	−	1.06269i	0.616142	−	0.787635i	$-0.288695\pi$
$110$	6.58833	+	3.57909i	0.628172	+	0.341253i
$111$		0			0
$112$	−3.68636	−	11.3454i	−0.348328	−	1.07204i
$113$	4.61219	+	14.1949i	0.433879	+	1.33534i	0.894231	+	0.447605i	$0.147723\pi$
$113$	4.61219	+	14.1949i	0.433879	+	1.33534i	−0.460353	+	0.887736i	$0.652277\pi$
$114$		0			0
$115$	0.946641	−	5.10120i	0.0882747	−	0.475689i
$116$	4.25962	+	13.1098i	0.395496	+	1.21721i
$117$		0			0
$118$	19.4324			1.78889
$119$	−3.95737	+	2.87520i	−0.362772	+	0.263569i
$120$		0			0
$121$	6.87980	+	4.99847i	0.625436	+	0.454406i
$122$	2.39673	+	1.74133i	0.216990	+	0.157652i
$123$		0			0
$124$	12.0258			1.07995
$125$	10.3322	−	4.27154i	0.924138	−	0.382058i
$126$		0			0
$127$	−5.25195	+	16.1638i	−0.466035	+	1.43431i	0.391641	+	0.920118i	$0.371908\pi$
$127$	−5.25195	+	16.1638i	−0.466035	+	1.43431i	−0.857676	+	0.514190i	$0.828092\pi$
$128$	−6.70686	−	4.87282i	−0.592809	−	0.430701i
$129$		0			0
$130$	−5.63657	+	0.740776i	−0.494360	+	0.0649703i
$131$	−0.266063	+	0.193306i	−0.0232461	+	0.0168892i	−0.599348	−	0.800489i	$-0.704573\pi$
$131$	−0.266063	+	0.193306i	−0.0232461	+	0.0168892i	0.576102	+	0.817378i	$0.304573\pi$
$132$		0			0
$133$	−27.0752	+	19.6713i	−2.34771	+	1.70571i
$134$	2.53330	+	7.79670i	0.218844	+	0.673533i
$135$		0			0
$136$	−0.371199	+	1.14243i	−0.0318300	+	0.0979628i
$137$	−1.40995	−	4.33939i	−0.120461	−	0.370739i	0.872586	−	0.488460i	$-0.162441\pi$
$137$	−1.40995	−	4.33939i	−0.120461	−	0.370739i	−0.993047	+	0.117721i	$0.962441\pi$
$138$		0			0
$139$	−1.46289	+	4.50230i	−0.124080	+	0.381880i	−0.993732	−	0.111785i	$-0.964343\pi$
$139$	−1.46289	+	4.50230i	−0.124080	+	0.381880i	0.869652	+	0.493665i	$0.164343\pi$
$140$	−21.4459	−	11.6504i	−1.81251	−	0.984641i
$141$		0			0
$142$	18.2090	−	13.2296i	1.52806	−	1.11020i
$143$	1.89263			0.158270
$144$		0			0
$145$	−10.8151	−	5.87530i	−0.898149	−	0.487917i
$146$	8.57938	+	6.23328i	0.710035	+	0.515870i
$147$		0			0
$148$	−4.93135	+	15.1771i	−0.405355	+	1.24755i
$149$	−4.67644			−0.383109			−0.191555	−	0.981482i	$-0.561353\pi$
$149$	−4.67644			−0.383109			−0.191555	+	0.981482i	$0.561353\pi$
$150$		0			0
$151$	−6.54178			−0.532362			−0.266181	−	0.963923i	$-0.585762\pi$
$151$	−6.54178			−0.532362			−0.266181	+	0.963923i	$0.585762\pi$
$152$	−2.53963	+	7.81618i	−0.205991	+	0.633976i
$153$		0			0
$154$	11.8231	+	8.58995i	0.952729	+	0.692198i
$155$	−7.79054	+	7.38961i	−0.625751	+	0.593548i
$156$		0			0
$157$	3.99404			0.318759			0.159379	−	0.987217i	$-0.449051\pi$
$157$	3.99404			0.318759			0.159379	+	0.987217i	$0.449051\pi$
$158$	24.9877	−	18.1546i	1.98791	−	1.44430i
$159$		0			0
$160$	17.6243	−	2.31623i	1.39332	−	0.183114i
$161$	3.12499	−	9.61773i	0.246284	−	0.757984i
$162$		0			0
$163$	1.48372	+	4.56641i	0.116214	+	0.357669i	0.992198	−	0.124670i	$-0.0397873\pi$
$163$	1.48372	+	4.56641i	0.116214	+	0.357669i	−0.875985	+	0.482339i	$0.839787\pi$
$164$	5.78247	−	17.7966i	0.451535	−	1.38968i
$165$		0			0
$166$	−5.72941	−	17.6333i	−0.444689	−	1.36861i
$167$	19.1414	−	13.9070i	1.48120	−	1.07616i	0.504036	−	0.863682i	$-0.331848\pi$
$167$	19.1414	−	13.9070i	1.48120	−	1.07616i	0.977167	−	0.212474i	$-0.0681522\pi$
$168$		0			0
$169$	9.35623	−	6.79770i	0.719710	−	0.522900i
$170$	−2.29192	−	4.80790i	−0.175782	−	0.368749i
$171$		0			0
$172$	2.53249	+	1.83996i	0.193100	+	0.140296i
$173$	−4.48208	+	13.7944i	−0.340766	+	1.04877i	0.623046	+	0.782185i	$0.285895\pi$
$173$	−4.48208	+	13.7944i	−0.340766	+	1.04877i	−0.963812	+	0.266584i	$0.914105\pi$
$174$		0			0
$175$	21.0520	−	5.63069i	1.59138	−	0.425640i
$176$	−4.32433			−0.325959
$177$		0			0
$178$	17.2355	+	12.5223i	1.29186	+	0.938588i
$179$	0.644581	+	0.468315i	0.0481782	+	0.0350035i	0.611614	−	0.791157i	$-0.290521\pi$
$179$	0.644581	+	0.468315i	0.0481782	+	0.0350035i	−0.563436	+	0.826160i	$0.690521\pi$
$180$		0			0
$181$	11.5030	−	8.35741i	0.855010	−	0.621201i	−0.0715129	−	0.997440i	$-0.522783\pi$
$181$	11.5030	−	8.35741i	0.855010	−	0.621201i	0.926523	+	0.376239i	$0.122783\pi$
$182$	−11.0809			−0.821372
$183$		0			0
$184$	−0.767403	−	2.36182i	−0.0565737	−	0.174116i
$185$	−6.13142	−	12.8623i	−0.450791	−	0.945652i
$186$		0			0
$187$	0.547943	+	1.68640i	0.0400696	+	0.123321i
$188$	−3.19427	−	9.83094i	−0.232966	−	0.716995i
$189$		0			0
$190$	−15.6806	−	32.8942i	−1.13759	−	2.38640i
$191$	3.20441	+	9.86215i	0.231863	+	0.713600i	0.997522	+	0.0703540i	$0.0224129\pi$
$191$	3.20441	+	9.86215i	0.231863	+	0.713600i	−0.765659	+	0.643246i	$0.777587\pi$
$192$		0			0
$193$	4.34712			0.312913			0.156456	−	0.987685i	$-0.449993\pi$
$193$	4.34712			0.312913			0.156456	+	0.987685i	$0.449993\pi$
$194$	−12.8775	+	9.35603i	−0.924548	+	0.671724i
$195$		0			0
$196$	−24.3035	−	17.6575i	−1.73596	−	1.26125i
$197$	1.52087	+	1.10498i	0.108358	+	0.0787263i	0.640644	−	0.767838i	$-0.278667\pi$
$197$	1.52087	+	1.10498i	0.108358	+	0.0787263i	−0.532287	+	0.846564i	$0.678667\pi$
$198$		0			0
$199$	4.26028			0.302003			0.151002	−	0.988534i	$-0.451750\pi$
$199$	4.26028			0.302003			0.151002	+	0.988534i	$0.451750\pi$
$200$	3.36966	−	4.15735i	0.238271	−	0.293969i
$201$		0			0
$202$	−4.27489	+	13.1567i	−0.300780	+	0.925705i
$203$	−19.4083	−	14.1009i	−1.36219	−	0.989692i
$204$		0			0
$205$	7.18967	+	15.0822i	0.502148	+	1.05339i
$206$	13.8197	−	10.0406i	0.962867	−	0.699564i
$207$		0			0
$208$	2.65265	−	1.92727i	0.183928	−	0.133632i
$209$	3.74887	+	11.5378i	0.259314	+	0.798088i
$210$		0			0
$211$	−2.87284	+	8.84170i	−0.197775	+	0.608687i	0.802158	+	0.597111i	$0.203685\pi$
$211$	−2.87284	+	8.84170i	−0.197775	+	0.608687i	−0.999933	+	0.0115762i	$0.996315\pi$
$212$	−2.89868	−	8.92120i	−0.199082	−	0.612711i
$213$		0			0
$214$	6.21566	−	19.1298i	0.424894	−	1.30769i
$215$	−2.77121	+	0.364201i	−0.188995	+	0.0248383i
$216$		0			0
$217$	−16.9322	+	12.3019i	−1.14943	+	0.835110i
$218$	24.7586			1.67686
$219$		0			0
$220$	−6.41886	+	6.08852i	−0.432759	+	0.410488i
$221$	−1.08771	−	0.790270i	−0.0731675	−	0.0531593i
$222$		0			0
$223$	−1.04991	+	3.23129i	−0.0703072	+	0.216383i	−0.980036	−	0.198819i	$-0.936289\pi$
$223$	−1.04991	+	3.23129i	−0.0703072	+	0.216383i	0.909729	+	0.415203i	$0.136289\pi$
$224$	34.6475			2.31498
$225$		0			0
$226$	−31.6766			−2.10710
$227$	−8.28083	+	25.4858i	−0.549618	+	1.69155i	0.160132	+	0.987096i	$0.448808\pi$
$227$	−8.28083	+	25.4858i	−0.549618	+	1.69155i	−0.709750	+	0.704454i	$0.751192\pi$
$228$		0			0
$229$	0.956255	+	0.694760i	0.0631911	+	0.0459110i	0.618932	−	0.785444i	$-0.287565\pi$
$229$	0.956255	+	0.694760i	0.0631911	+	0.0459110i	−0.555741	+	0.831355i	$0.687565\pi$
$230$	9.67572	+	5.25631i	0.637998	+	0.346591i
$231$		0			0
$232$	−5.89121			−0.386777
$233$	5.73984	−	4.17024i	0.376030	−	0.273201i	−0.383677	−	0.923467i	$-0.625342\pi$
$233$	5.73984	−	4.17024i	0.376030	−	0.273201i	0.759707	+	0.650266i	$0.225342\pi$
$234$		0			0
$235$	8.11023	+	4.40586i	0.529053	+	0.287407i
$236$	−7.08566	+	21.8074i	−0.461237	+	1.41954i
$237$		0			0
$238$	−3.20808	−	9.87345i	−0.207949	−	0.640001i
$239$	−0.0132236	+	0.0406981i	−0.000855365	+	0.00263254i	−0.951483	−	0.307700i	$-0.900441\pi$
$239$	−0.0132236	+	0.0406981i	−0.000855365	+	0.00263254i	0.950628	+	0.310333i	$0.100441\pi$
$240$		0			0
$241$	−3.63746	−	11.1950i	−0.234310	−	0.721131i	−0.997212	−	0.0746174i	$-0.976226\pi$
$241$	−3.63746	−	11.1950i	−0.234310	−	0.721131i	0.762903	−	0.646513i	$-0.223774\pi$
$242$	−14.6012	+	10.6084i	−0.938602	+	0.681934i
$243$		0			0
$244$	−2.82808	+	2.05472i	−0.181049	+	0.131540i
$245$	26.5944	−	3.49512i	1.69906	−	0.223295i
$246$		0			0
$247$	−7.44182	−	5.40680i	−0.473511	−	0.344026i
$248$	−1.58823	+	4.88806i	−0.100852	+	0.310392i
$249$		0			0
$250$	1.84570	+	23.6565i	0.116733	+	1.49617i
$251$	−17.4764			−1.10310			−0.551550	−	0.834142i	$-0.685964\pi$
$251$	−17.4764			−1.10310			−0.551550	+	0.834142i	$0.685964\pi$
$252$		0			0
$253$	−2.96571	−	2.15471i	−0.186452	−	0.135466i
$254$	−29.1816	−	21.2017i	−1.83102	−	1.33031i
$255$		0			0
$256$	−4.20735	+	3.05682i	−0.262960	+	0.191051i
$257$	−15.4671			−0.964814			−0.482407	−	0.875947i	$-0.660237\pi$
$257$	−15.4671			−0.964814			−0.482407	+	0.875947i	$0.660237\pi$
$258$		0			0
$259$	−8.58236	−	26.4138i	−0.533282	−	1.64127i
$260$	1.22396	−	6.59560i	0.0759068	−	0.409042i
$261$		0			0
$262$	−0.215687	−	0.663815i	−0.0133252	−	0.0410106i
$263$	−0.447331	−	1.37674i	−0.0275836	−	0.0848936i	0.936317	−	0.351156i	$-0.114211\pi$
$263$	−0.447331	−	1.37674i	−0.0275836	−	0.0848936i	−0.963901	+	0.266262i	$0.914211\pi$
$264$		0			0
$265$	7.35972	+	3.99815i	0.452104	+	0.245604i
$266$	−21.9487	−	67.5513i	−1.34576	−	4.14183i
$267$		0			0
$268$	−9.67336			−0.590895
$269$	−7.04344	+	5.11736i	−0.429446	+	0.312011i	−0.781427	−	0.623996i	$-0.785508\pi$
$269$	−7.04344	+	5.11736i	−0.429446	+	0.312011i	0.351981	+	0.936007i	$0.385508\pi$
$270$		0			0
$271$	23.1652	+	16.8305i	1.40719	+	1.02238i	0.993724	+	0.111860i	$0.0356807\pi$
$271$	23.1652	+	16.8305i	1.40719	+	1.02238i	0.413462	+	0.910521i	$0.364319\pi$
$272$	2.48524	+	1.80563i	0.150690	+	0.109482i
$273$		0			0
$274$	9.68359			0.585007
$275$	0.416988	−	7.88852i	0.0251453	−	0.475695i
$276$		0			0
$277$	1.63844	−	5.04259i	0.0984442	−	0.302980i	−0.889692	−	0.456562i	$-0.849081\pi$
$277$	1.63844	−	5.04259i	0.0984442	−	0.302980i	0.988136	+	0.153582i	$0.0490808\pi$
$278$	−8.12830	−	5.90555i	−0.487503	−	0.354192i
$279$		0			0
$280$	7.56780	−	7.17833i	0.452262	−	0.428987i
$281$	−19.4837	+	14.1557i	−1.16230	+	0.844461i	−0.990067	−	0.140595i	$-0.955098\pi$
$281$	−19.4837	+	14.1557i	−1.16230	+	0.844461i	−0.172234	+	0.985056i	$0.555098\pi$
$282$		0			0
$283$	21.9359	−	15.9374i	1.30396	−	0.947380i	0.303970	−	0.952682i	$-0.401688\pi$
$283$	21.9359	−	15.9374i	1.30396	−	0.947380i	0.999986	+	0.00530192i	$0.00168766\pi$
$284$	8.20698	+	25.2585i	0.486995	+	1.49882i
$285$		0			0
$286$	−1.24126	+	3.82020i	−0.0733971	+	0.225893i
$287$	10.0636	+	30.9726i	0.594037	+	1.82826i
$288$		0			0
$289$	−4.86404	+	14.9700i	−0.286120	+	0.880587i
$290$	18.9520	−	17.9767i	1.11290	−	1.05563i
$291$		0			0
$292$	−10.1234	+	7.35512i	−0.592430	+	0.430426i
$293$	20.3016			1.18603			0.593017	−	0.805190i	$-0.297937\pi$
$293$	20.3016			1.18603			0.593017	+	0.805190i	$0.297937\pi$
$294$		0			0
$295$	−8.81000	−	18.4813i	−0.512938	−	1.07602i
$296$	−5.51769	−	4.00883i	−0.320709	−	0.233009i
$297$		0			0
$298$	3.06698	−	9.43921i	0.177666	−	0.546799i
$299$	2.77955			0.160745
$300$		0			0
$301$	−5.44792			−0.314013
$302$	4.29034	−	13.2043i	0.246881	−	0.759823i
$303$		0			0
$304$	17.0032	+	12.3536i	0.975203	+	0.708527i
$305$	0.569501	−	3.06889i	0.0326095	−	0.175724i
$306$		0			0
$307$	−2.51330			−0.143442			−0.0717208	−	0.997425i	$-0.522849\pi$
$307$	−2.51330			−0.143442			−0.0717208	+	0.997425i	$0.522849\pi$
$308$	−13.9509	+	10.1359i	−0.794927	+	0.577548i
$309$		0			0
$310$	−9.80630	−	20.5713i	−0.556960	−	1.16837i
$311$	−1.49075	+	4.58806i	−0.0845327	+	0.260165i	−0.984385	−	0.176030i	$-0.943674\pi$
$311$	−1.49075	+	4.58806i	−0.0845327	+	0.260165i	0.899852	+	0.436195i	$0.143674\pi$
$312$		0			0
$313$	−1.85043	−	5.69504i	−0.104592	−	0.321903i	0.885042	−	0.465511i	$-0.154129\pi$
$313$	−1.85043	−	5.69504i	−0.104592	−	0.321903i	−0.989635	+	0.143608i	$0.954129\pi$
$314$	−2.61944	+	8.06180i	−0.147823	+	0.454954i
$315$		0			0
$316$	11.2622	+	34.6615i	0.633548	+	1.94986i
$317$	14.0389	−	10.1999i	0.788506	−	0.572883i	−0.119014	−	0.992893i	$-0.537973\pi$
$317$	14.0389	−	10.1999i	0.788506	−	0.572883i	0.907520	+	0.420010i	$0.137973\pi$
$318$		0			0
$319$	−7.03543	+	5.11154i	−0.393909	+	0.286191i
$320$	−4.65003	+	25.0578i	−0.259945	+	1.40077i
$321$		0			0
$322$	17.3635	+	12.6153i	0.967631	+	0.703025i
$323$	2.66312	−	8.19624i	0.148180	−	0.456051i
$324$		0			0
$325$	3.25996	+	5.02486i	0.180830	+	0.278729i
$326$	−10.1902			−0.564383
$327$		0			0
$328$	6.47000	+	4.70073i	0.357246	+	0.259555i
$329$	14.5542	+	10.5742i	0.802398	+	0.582976i
$330$		0			0
$331$	−16.4518	+	11.9529i	−0.904270	+	0.656991i	−0.939559	−	0.342386i	$-0.888765\pi$
$331$	−16.4518	+	11.9529i	−0.904270	+	0.656991i	0.0352890	+	0.999377i	$0.488765\pi$
$332$	21.8776			1.20069
$333$		0			0
$334$	15.5171	+	47.7568i	0.849059	+	2.61314i
$335$	6.26659	−	5.94409i	0.342380	−	0.324760i
$336$		0			0
$337$	10.5860	+	32.5805i	0.576658	+	1.77477i	0.630463	+	0.776219i	$0.282865\pi$
$337$	10.5860	+	32.5805i	0.576658	+	1.77477i	−0.0538048	+	0.998551i	$0.517135\pi$
$338$	7.58472	+	23.3434i	0.412554	+	1.26971i
$339$		0			0
$340$	6.23124	−	0.818929i	0.337937	−	0.0444127i
$341$	2.34445	+	7.21548i	0.126959	+	0.390740i
$342$		0			0
$343$	21.7731			1.17564
$344$	−1.08234	+	0.786366i	−0.0583558	+	0.0423980i
$345$		0			0
$346$	−24.9039	−	18.0938i	−1.33884	−	0.972727i
$347$	−0.0399344	−	0.0290140i	−0.00214379	−	0.00155756i	0.586713	−	0.809795i	$-0.300422\pi$
$347$	−0.0399344	−	0.0290140i	−0.00214379	−	0.00155756i	−0.588857	+	0.808238i	$0.700422\pi$
$348$		0			0
$349$	−7.47437			−0.400094			−0.200047	−	0.979786i	$-0.564109\pi$
$349$	−7.47437			−0.400094			−0.200047	+	0.979786i	$0.564109\pi$
$350$	−2.44137	+	46.1854i	−0.130497	+	2.46871i
$351$		0			0
$352$	3.88113	−	11.9449i	0.206865	−	0.636665i
$353$	−15.0194	−	10.9122i	−0.799401	−	0.580799i	0.111337	−	0.993783i	$-0.464487\pi$
$353$	−15.0194	−	10.9122i	−0.799401	−	0.580799i	−0.910738	+	0.412984i	$0.864487\pi$
$354$		0			0
$355$	−20.8375	−	11.3199i	−1.10594	−	0.600798i
$356$	−20.3375	+	14.7760i	−1.07788	+	0.783128i
$357$		0			0
$358$	−1.36802	+	0.993921i	−0.0723019	+	0.0525304i
$359$	−3.27695	−	10.0854i	−0.172951	−	0.532289i	0.826583	−	0.562815i	$-0.190282\pi$
$359$	−3.27695	−	10.0854i	−0.172951	−	0.532289i	−0.999534	+	0.0305264i	$0.990282\pi$
$360$		0			0
$361$	12.3490	−	38.0062i	0.649945	−	2.00032i
$362$	9.32500	+	28.6994i	0.490111	+	1.50841i
$363$		0			0
$364$	4.04046	−	12.4353i	0.211778	−	0.651785i
$365$	2.03859	−	10.9854i	0.106705	−	0.575004i
$366$		0			0
$367$	9.39886	−	6.82867i	0.490617	−	0.356454i	−0.314805	−	0.949156i	$-0.601939\pi$
$367$	9.39886	−	6.82867i	0.490617	−	0.356454i	0.805421	+	0.592703i	$0.201939\pi$
$368$	−6.35078			−0.331057
$369$		0			0
$370$	29.9832	−	3.94048i	1.55875	−	0.204856i
$371$	13.2074	+	9.59570i	0.685692	+	0.498184i
$372$		0			0
$373$	−7.14671	+	21.9953i	−0.370043	+	1.13887i	0.576720	+	0.816942i	$0.304332\pi$
$373$	−7.14671	+	21.9953i	−0.370043	+	1.13887i	−0.946763	+	0.321932i	$0.895668\pi$
$374$	−3.76328			−0.194595
$375$		0			0
$376$	4.41779			0.227830
$377$	2.03760	−	6.27109i	0.104942	−	0.322978i
$378$		0			0
$379$	−20.1374	−	14.6307i	−1.03439	−	0.751527i	−0.0652058	−	0.997872i	$-0.520770\pi$
$379$	−20.1374	−	14.6307i	−1.03439	−	0.751527i	−0.969182	+	0.246345i	$0.920770\pi$
$380$	42.6323	−	5.60287i	2.18699	−	0.287421i
$381$		0			0
$382$	−22.0079			−1.12602
$383$	−12.7195	+	9.24123i	−0.649934	+	0.472205i	−0.863249	−	0.504779i	$-0.831574\pi$
$383$	−12.7195	+	9.24123i	−0.649934	+	0.472205i	0.213315	+	0.976984i	$0.431574\pi$
$384$		0			0
$385$	2.80934	−	15.1388i	0.143177	−	0.771545i
$386$	−2.85100	+	8.77449i	−0.145112	+	0.446610i
$387$		0			0
$388$	−5.80400	−	17.8629i	−0.294654	−	0.906851i
$389$	2.62860	−	8.09000i	0.133275	−	0.410179i	−0.862042	−	0.506836i	$-0.830815\pi$
$389$	2.62860	−	8.09000i	0.133275	−	0.410179i	0.995318	+	0.0966568i	$0.0308149\pi$
$390$		0			0
$391$	0.804717	+	2.47667i	0.0406963	+	0.125250i
$392$	10.3869	−	7.54649i	0.524615	−	0.381155i
$393$		0			0
$394$	−3.22779	+	2.34513i	−0.162614	+	0.118146i
$395$	−28.5946	−	15.5340i	−1.43875	−	0.781599i
$396$		0			0
$397$	−21.2407	−	15.4322i	−1.06604	−	0.774522i	−0.0908420	−	0.995865i	$-0.528956\pi$
$397$	−21.2407	−	15.4322i	−1.06604	−	0.774522i	−0.975196	+	0.221343i	$0.928956\pi$
$398$	−2.79405	+	8.59921i	−0.140053	+	0.431039i
$399$		0			0
$400$	−7.44843	−	11.4809i	−0.372422	−	0.574046i
$401$	25.2815			1.26250			0.631250	−	0.775579i	$-0.282542\pi$
$401$	25.2815			1.26250			0.631250	+	0.775579i	$0.282542\pi$
$402$		0			0
$403$	−4.65393	−	3.38128i	−0.231829	−	0.168434i
$404$	−13.2060	−	9.59475i	−0.657025	−	0.477356i
$405$		0			0
$406$	41.1908	−	29.9269i	2.04427	−	1.48525i
$407$	−10.0677			−0.499035
$408$		0			0
$409$	10.4427	+	32.1392i	0.516357	+	1.58918i	0.780800	+	0.624781i	$0.214812\pi$
$409$	10.4427	+	32.1392i	0.516357	+	1.58918i	−0.264443	+	0.964401i	$0.585188\pi$
$410$	−35.1581	+	4.62058i	−1.73633	+	0.228194i
$411$		0			0
$412$	6.22870	+	19.1700i	0.306866	+	0.944437i
$413$	−12.3317	−	37.9529i	−0.606801	−	1.86754i
$414$		0			0
$415$	−14.1728	+	13.4434i	−0.695713	+	0.659909i
$416$	2.94281	+	9.05703i	0.144283	+	0.444057i
$417$		0			0
$418$	−25.7473			−1.25934
$419$	6.41819	−	4.66309i	0.313549	−	0.227807i	−0.419869	−	0.907585i	$-0.637924\pi$
$419$	6.41819	−	4.66309i	0.313549	−	0.227807i	0.733418	+	0.679778i	$0.237924\pi$
$420$		0			0
$421$	−6.05788	−	4.40131i	−0.295243	−	0.214507i	0.430296	−	0.902688i	$-0.358409\pi$
$421$	−6.05788	−	4.40131i	−0.295243	−	0.214507i	−0.725539	+	0.688181i	$0.758409\pi$
$422$	−15.9625	−	11.5974i	−0.777042	−	0.564554i
$423$		0			0
$424$	4.00897			0.194693
$425$	−3.53350	+	4.35949i	−0.171400	+	0.211466i
$426$		0			0
$427$	1.88000	−	5.78604i	0.0909795	−	0.280006i
$428$	19.2015	+	13.9507i	0.928140	+	0.674333i
$429$		0			0
$430$	1.08234	−	5.83244i	0.0521950	−	0.281265i
$431$	18.8882	−	13.7231i	0.909811	−	0.661016i	−0.0311564	−	0.999515i	$-0.509919\pi$
$431$	18.8882	−	13.7231i	0.909811	−	0.661016i	0.940967	+	0.338498i	$0.109919\pi$
$432$		0			0
$433$	2.71569	−	1.97306i	0.130508	−	0.0948193i	−0.520616	−	0.853791i	$-0.674298\pi$
$433$	2.71569	−	1.97306i	0.130508	−	0.0948193i	0.651124	+	0.758971i	$0.274298\pi$
$434$	−13.7262	−	42.2449i	−0.658879	−	2.02782i
$435$		0			0
$436$	−9.02778	+	27.7846i	−0.432352	+	1.33064i
$437$	5.50564	+	16.9446i	0.263370	+	0.810571i
$438$		0			0
$439$	−2.93072	+	9.01984i	−0.139876	+	0.430493i	−0.996317	−	0.0857520i	$-0.972671\pi$
$439$	−2.93072	+	9.01984i	−0.139876	+	0.430493i	0.856441	+	0.516245i	$0.172671\pi$
$440$	−1.62704	−	3.41313i	−0.0775659	−	0.162715i
$441$		0			0
$442$	2.30849	−	1.67722i	0.109804	−	0.0797771i
$443$	−9.65446			−0.458697			−0.229349	−	0.973344i	$-0.573660\pi$
$443$	−9.65446			−0.458697			−0.229349	+	0.973344i	$0.573660\pi$
$444$		0			0
$445$	4.09542	−	22.0692i	0.194142	−	1.04618i
$446$	−5.83366	−	4.23840i	−0.276232	−	0.200694i
$447$		0			0
$448$	−15.3504	+	47.2437i	−0.725238	+	2.23205i
$449$	−31.5260			−1.48780			−0.743902	−	0.668289i	$-0.767027\pi$
$449$	−31.5260			−1.48780			−0.743902	+	0.668289i	$0.767027\pi$
$450$		0			0
$451$	11.8053			0.555888
$452$	11.5503	−	35.5482i	0.543281	−	1.67205i
$453$		0			0
$454$	−46.0111	−	33.4290i	−2.15941	−	1.56890i
$455$	5.02373	+	10.5386i	0.235516	+	0.494056i
$456$		0			0
$457$	−9.94467			−0.465192			−0.232596	−	0.972573i	$-0.574722\pi$
$457$	−9.94467			−0.465192			−0.232596	+	0.972573i	$0.574722\pi$
$458$	−2.02949	+	1.47451i	−0.0948319	+	0.0688994i
$459$		0			0
$460$	−9.42683	+	8.94169i	−0.439528	+	0.416908i
$461$	7.31863	−	22.5244i	0.340863	−	1.04907i	−0.622899	−	0.782302i	$-0.714045\pi$
$461$	7.31863	−	22.5244i	0.340863	−	1.04907i	0.963762	−	0.266765i	$-0.0859548\pi$
$462$		0			0
$463$	8.54443	+	26.2971i	0.397094	+	1.22213i	0.927319	+	0.374272i	$0.122107\pi$
$463$	8.54443	+	26.2971i	0.397094	+	1.22213i	−0.530226	+	0.847857i	$0.677893\pi$
$464$	−4.65556	+	14.3284i	−0.216129	+	0.665177i
$465$		0			0
$466$	4.65306	+	14.3206i	0.215549	+	0.663391i
$467$	3.52602	−	2.56180i	0.163165	−	0.118546i	−0.503207	−	0.864166i	$-0.667847\pi$
$467$	3.52602	−	2.56180i	0.163165	−	0.118546i	0.666371	+	0.745620i	$0.267847\pi$
$468$		0			0
$469$	13.6200	−	9.89548i	0.628912	−	0.456931i
$470$	−14.2120	+	13.4806i	−0.655553	+	0.621815i
$471$		0			0
$472$	−7.92814	−	5.76013i	−0.364922	−	0.265132i
$473$	−0.610263	+	1.87820i	−0.0280599	+	0.0863596i
$474$		0			0
$475$	−24.1752	+	29.8264i	−1.10923	+	1.36853i
$476$	12.2500			0.561477
$477$		0			0
$478$	−0.0734750	−	0.0533827i	−0.00336067	−	0.00244167i
$479$	10.3670	+	7.53204i	0.473679	+	0.344148i	0.798873	−	0.601499i	$-0.205430\pi$
$479$	10.3670	+	7.53204i	0.473679	+	0.344148i	−0.325195	+	0.945647i	$0.605430\pi$
$480$		0			0
$481$	6.17575	−	4.48695i	0.281590	−	0.204587i
$482$	24.9822			1.13791
$483$		0			0
$484$	−6.58092	−	20.2540i	−0.299133	−	0.920636i
$485$	14.7363	+	8.00548i	0.669142	+	0.363510i
$486$		0			0
$487$	−2.13904	−	6.58330i	−0.0969293	−	0.298318i	0.890822	−	0.454352i	$-0.150129\pi$
$487$	−2.13904	−	6.58330i	−0.0969293	−	0.298318i	−0.987752	+	0.156034i	$0.950129\pi$
$488$	−0.461671	−	1.42088i	−0.0208989	−	0.0643201i
$489$		0			0
$490$	−10.3869	+	55.9720i	−0.469230	+	2.52856i
$491$	−8.28665	−	25.5037i	−0.373971	−	1.15096i	−0.944170	−	0.329458i	$-0.893134\pi$
$491$	−8.28665	−	25.5037i	−0.373971	−	1.15096i	0.570199	−	0.821507i	$-0.306866\pi$
$492$		0			0
$493$	6.17766			0.278228
$494$	15.7940	−	11.4750i	0.710606	−	0.516286i
$495$		0			0
$496$	10.6334	+	7.72564i	0.477455	+	0.346891i
$497$	−37.3938	−	27.1682i	−1.67734	−	1.21866i
$498$		0			0
$499$	2.75460			0.123313			0.0616565	−	0.998097i	$-0.480362\pi$
$499$	2.75460			0.123313			0.0616565	+	0.998097i	$0.480362\pi$
$500$	−27.2209	−	6.55464i	−1.21735	−	0.293132i
$501$		0			0
$502$	11.4617	−	35.2754i	0.511559	−	1.57442i
$503$	12.7098	+	9.23422i	0.566702	+	0.411733i	0.833906	−	0.551907i	$-0.186100\pi$
$503$	12.7098	+	9.23422i	0.566702	+	0.411733i	−0.267203	+	0.963640i	$0.586100\pi$
$504$		0			0
$505$	14.4509	−	1.89918i	0.643057	−	0.0845125i
$506$	6.29422	−	4.57302i	0.279812	−	0.203295i
$507$		0			0
$508$	34.4336	−	25.0175i	1.52774	−	1.10997i
$509$	12.6970	+	39.0774i	0.562785	+	1.73207i	0.674442	+	0.738328i	$0.264384\pi$
$509$	12.6970	+	39.0774i	0.562785	+	1.73207i	−0.111657	+	0.993747i	$0.535616\pi$
$510$		0			0
$511$	6.72968	−	20.7118i	0.297703	−	0.916237i
$512$	−8.53432	−	26.2659i	−0.377167	−	1.16080i
$513$		0			0
$514$	10.1439	−	31.2198i	0.447430	−	1.37705i
$515$	−15.8146	−	8.59126i	−0.696876	−	0.378576i
$516$		0			0
$517$	5.27584	−	3.83312i	0.232031	−	0.168580i
$518$	58.9438			2.58984
$519$		0			0
$520$	2.51923	+	1.36856i	0.110475	+	0.0600155i
$521$	29.2630	+	21.2608i	1.28203	+	0.931452i	0.999612	−	0.0278383i	$-0.00886235\pi$
$521$	29.2630	+	21.2608i	1.28203	+	0.931452i	0.282421	+	0.959290i	$0.408862\pi$
$522$		0			0
$523$	8.66761	−	26.6761i	0.379008	−	1.16647i	−0.561727	−	0.827323i	$-0.689863\pi$
$523$	8.66761	−	26.6761i	0.379008	−	1.16647i	0.940735	−	0.339144i	$-0.110137\pi$
$524$	0.823595			0.0359789
$525$		0			0
$526$	3.07228			0.133958
$527$	1.66545	−	5.12573i	0.0725482	−	0.223280i
$528$		0			0
$529$	14.2519	+	10.3546i	0.619648	+	0.450201i
$530$	−12.8969	+	12.2332i	−0.560205	+	0.531374i
$531$		0			0
$532$	83.8108			3.63366
$533$	−7.24165	+	5.26137i	−0.313671	+	0.227895i
$534$		0			0
$535$	−21.0115	+	2.76140i	−0.908408	+	0.119386i
$536$	1.27754	−	3.93187i	0.0551815	−	0.169831i
$537$		0			0
$538$	−5.70983	−	17.5731i	−0.246168	−	0.757628i
$539$	5.85650	−	18.0244i	0.252257	−	0.776368i
$540$		0			0
$541$	1.06865	+	3.28896i	0.0459448	+	0.141404i	0.971397	−	0.237460i	$-0.0763149\pi$
$541$	1.06865	+	3.28896i	0.0459448	+	0.141404i	−0.925452	+	0.378864i	$0.876315\pi$
$542$	−49.1643	+	35.7200i	−2.11179	+	1.53430i
$543$		0			0
$544$	−7.21812	+	5.24427i	−0.309474	+	0.224846i
$545$	−11.2247	−	23.5468i	−0.480815	−	1.00863i
$546$		0			0
$547$	−11.2967	−	8.20751i	−0.483011	−	0.350928i	0.319479	−	0.947593i	$-0.396492\pi$
$547$	−11.2967	−	8.20751i	−0.483011	−	0.350928i	−0.802490	+	0.596665i	$0.796492\pi$
$548$	−3.53095	+	10.8671i	−0.150835	+	0.464221i
$549$		0			0
$550$	15.6492	+	6.01525i	0.667283	+	0.256491i
$551$	42.2657			1.80058
$552$		0			0
$553$	−51.3144	−	37.2821i	−2.18211	−	1.58540i
$554$	9.10372	+	6.61424i	0.386780	+	0.281012i
$555$		0			0
$556$	9.59118	−	6.96840i	0.406757	−	0.295526i
$557$	6.59585			0.279475			0.139738	−	0.990189i	$-0.455374\pi$
$557$	6.59585			0.279475			0.139738	+	0.990189i	$0.455374\pi$
$558$		0			0
$559$	−0.462723	−	1.42411i	−0.0195711	−	0.0602336i
$560$	−11.4783	−	24.0788i	−0.485048	−	1.01752i
$561$		0			0
$562$	−15.7947	−	48.6110i	−0.666257	−	2.05053i
$563$	4.95100	+	15.2376i	0.208660	+	0.642189i	0.999543	+	0.0302222i	$0.00962148\pi$
$563$	4.95100	+	15.2376i	0.208660	+	0.642189i	−0.790883	+	0.611967i	$0.790379\pi$
$564$		0			0
$565$	14.3611	+	30.1263i	0.604178	+	1.26742i
$566$	17.7826	+	54.7291i	0.747457	+	2.30044i
$567$		0			0
$568$	−11.3505			−0.476258
$569$	18.6813	−	13.5728i	0.783162	−	0.569001i	−0.122764	−	0.992436i	$-0.539176\pi$
$569$	18.6813	−	13.5728i	0.783162	−	0.569001i	0.905926	+	0.423435i	$0.139176\pi$
$570$		0			0
$571$	27.5148	+	19.9907i	1.15146	+	0.836583i	0.988674	−	0.150078i	$-0.0479526\pi$
$571$	27.5148	+	19.9907i	1.15146	+	0.836583i	0.162784	+	0.986662i	$0.447953\pi$
$572$	−3.83451	−	2.78594i	−0.160329	−	0.116486i
$573$		0			0
$574$	−69.1171			−2.88489
$575$	0.612394	−	11.5852i	0.0255386	−	0.483136i
$576$		0			0
$577$	−1.99850	+	6.15074i	−0.0831985	+	0.256059i	−0.983999	−	0.178175i	$-0.942981\pi$
$577$	−1.99850	+	6.15074i	−0.0831985	+	0.256059i	0.900800	+	0.434233i	$0.142981\pi$
$578$	−27.0263	−	19.6357i	−1.12414	−	0.816739i
$579$		0			0
$580$	13.2633	+	27.8233i	0.550729	+	1.15530i
$581$	−30.8034	+	22.3800i	−1.27794	+	0.928479i
$582$		0			0
$583$	4.78762	−	3.47841i	0.198283	−	0.144061i
$584$	−1.65261	−	5.08620i	−0.0683853	−	0.210468i
$585$		0			0
$586$	−13.3146	+	40.9780i	−0.550019	+	1.69279i
$587$	−11.8975	−	36.6168i	−0.491063	−	1.51134i	−0.823003	−	0.568037i	$-0.807703\pi$
$587$	−11.8975	−	36.6168i	−0.491063	−	1.51134i	0.331940	−	0.943301i	$-0.392297\pi$
$588$		0			0
$589$	11.3945	−	35.0687i	0.469503	−	1.44498i
$590$	43.0816	−	5.66192i	1.77364	−	0.233097i
$591$		0			0
$592$	−14.1105	+	10.2519i	−0.579939	+	0.421350i
$593$	−4.93069			−0.202479			−0.101240	−	0.994862i	$-0.532281\pi$
$593$	−4.93069			−0.202479			−0.101240	+	0.994862i	$0.532281\pi$
$594$		0			0
$595$	−7.93577	+	7.52737i	−0.325335	+	0.308592i
$596$	9.47457	+	6.88368i	0.388093	+	0.281966i
$597$		0			0
$598$	−1.82293	+	5.61040i	−0.0745452	+	0.229426i
$599$	35.0268			1.43116			0.715578	−	0.698533i	$-0.246164\pi$
$599$	35.0268			1.43116			0.715578	+	0.698533i	$0.246164\pi$
$600$		0			0
$601$	−4.90570			−0.200108			−0.100054	−	0.994982i	$-0.531901\pi$
$601$	−4.90570			−0.200108			−0.100054	+	0.994982i	$0.531901\pi$
$602$	3.57295	−	10.9964i	0.145623	−	0.448180i
$603$		0			0
$604$	13.2538	+	9.62943i	0.539289	+	0.391816i
$605$	16.7089	+	9.07708i	0.679314	+	0.369036i
$606$		0			0
$607$	48.6955			1.97649			0.988244	−	0.152884i	$-0.0488562\pi$
$607$	48.6955			1.97649			0.988244	+	0.152884i	$0.0488562\pi$
$608$	−49.3842	+	35.8798i	−2.00280	+	1.45512i
$609$		0			0
$610$	5.82092	+	3.16220i	0.235682	+	0.128034i
$611$	−1.52799	+	4.70266i	−0.0618158	+	0.190249i
$612$		0			0
$613$	5.31938	+	16.3714i	0.214848	+	0.661234i	0.999164	+	0.0408728i	$0.0130138\pi$
$613$	5.31938	+	16.3714i	0.214848	+	0.661234i	−0.784317	+	0.620361i	$0.786986\pi$
$614$	1.64832	−	5.07299i	0.0665206	−	0.204729i
$615$		0			0
$616$	−2.27742	−	7.00918i	−0.0917598	−	0.282408i
$617$	−25.5723	+	18.5794i	−1.02950	+	0.747978i	−0.968209	−	0.250141i	$-0.919523\pi$
$617$	−25.5723	+	18.5794i	−1.02950	+	0.747978i	−0.0612947	+	0.998120i	$0.519523\pi$
$618$		0			0
$619$	18.4615	−	13.4130i	0.742029	−	0.539116i	−0.151317	−	0.988485i	$-0.548351\pi$
$619$	18.4615	−	13.4130i	0.742029	−	0.539116i	0.893346	+	0.449370i	$0.148351\pi$
$620$	26.6612	−	3.50390i	1.07074	−	0.140720i
$621$		0			0
$622$	−8.28312	−	6.01804i	−0.332123	−	0.241301i
$623$	13.5196	−	41.6089i	0.541649	−	1.66703i
$624$		0			0
$625$	21.6619	−	12.4805i	0.866476	−	0.499219i
$626$	12.7088			0.507945
$627$		0			0
$628$	−8.09200	−	5.87918i	−0.322906	−	0.234605i
$629$	5.78598	+	4.20376i	0.230702	+	0.167615i
$630$		0			0
$631$	−30.7830	+	22.3652i	−1.22545	+	0.890344i	−0.996541	−	0.0831027i	$-0.973517\pi$
$631$	−30.7830	+	22.3652i	−1.22545	+	0.890344i	−0.228913	+	0.973447i	$0.573517\pi$
$632$	−15.5760			−0.619581
$633$		0			0
$634$	11.3808	+	35.0265i	0.451989	+	1.39108i
$635$	−6.93401	+	37.3655i	−0.275168	+	1.48281i
$636$		0			0
$637$	4.44060	+	13.6668i	0.175943	+	0.541497i
$638$	−5.70334	−	17.5531i	−0.225797	−	0.694933i
$639$		0			0
$640$	−16.2889	−	8.84892i	−0.643876	−	0.349784i
$641$	−8.19229	−	25.2133i	−0.323576	−	0.995864i	−0.972079	−	0.234652i	$-0.924605\pi$
$641$	−8.19229	−	25.2133i	−0.323576	−	0.995864i	0.648504	−	0.761212i	$-0.275395\pi$
$642$		0			0
$643$	−36.0014			−1.41976			−0.709879	−	0.704324i	$-0.751250\pi$
$643$	−36.0014			−1.41976			−0.709879	+	0.704324i	$0.751250\pi$
$644$	−20.4885	+	14.8858i	−0.807360	+	0.586582i
$645$		0			0
$646$	14.7972	+	10.7508i	0.582188	+	0.422984i
$647$	33.8040	+	24.5600i	1.32897	+	0.965554i	0.999773	+	0.0212924i	$0.00677811\pi$
$647$	33.8040	+	24.5600i	1.32897	+	0.965554i	0.329197	+	0.944261i	$0.393222\pi$
$648$		0			0
$649$	−14.4658			−0.567833
$650$	−12.2805	+	3.28460i	−0.481679	+	0.128833i
$651$		0			0
$652$	3.71567	−	11.4357i	0.145517	−	0.447855i
$653$	17.3456	+	12.6023i	0.678787	+	0.493168i	0.872955	−	0.487801i	$-0.162201\pi$
$653$	17.3456	+	12.6023i	0.678787	+	0.493168i	−0.194168	+	0.980968i	$0.562201\pi$
$654$		0			0
$655$	−0.533541	+	0.506082i	−0.0208472	+	0.0197743i
$656$	16.5459	−	12.0213i	0.646009	−	0.469353i
$657$		0			0
$658$	−30.8888	+	22.4420i	−1.20417	+	0.874882i
$659$	5.20135	+	16.0081i	0.202616	+	0.623587i	0.999803	+	0.0198549i	$0.00632042\pi$
$659$	5.20135	+	16.0081i	0.202616	+	0.623587i	−0.797187	+	0.603732i	$0.793680\pi$
$660$		0			0
$661$	0.629918	−	1.93869i	0.0245010	−	0.0754062i	−0.938058	−	0.346477i	$-0.887378\pi$
$661$	0.629918	−	1.93869i	0.0245010	−	0.0754062i	0.962559	+	0.271071i	$0.0873778\pi$
$662$	−13.3368	−	41.0463i	−0.518348	−	1.59531i
$663$		0			0
$664$	−2.88934	+	8.89248i	−0.112128	+	0.345095i
$665$	−54.2942	+	51.5000i	−2.10544	+	1.99709i
$666$		0			0
$667$	−10.3323	+	7.50689i	−0.400070	+	0.290668i
$668$	−59.2518			−2.29252
$669$		0			0
$670$	7.88803	+	16.5472i	0.304741	+	0.639274i
$671$	−1.78417	−	1.29628i	−0.0688772	−	0.0500422i
$672$		0			0
$673$	10.9323	−	33.6461i	0.421409	−	1.29696i	−0.484983	−	0.874524i	$-0.661174\pi$
$673$	10.9323	−	33.6461i	0.421409	−	1.29696i	0.906391	−	0.422439i	$-0.138826\pi$
$674$	−72.7050			−2.80049
$675$		0			0
$676$	−28.9621			−1.11393
$677$	−13.7257	+	42.2434i	−0.527522	+	1.62354i	0.231753	+	0.972775i	$0.425554\pi$
$677$	−13.7257	+	42.2434i	−0.527522	+	1.62354i	−0.759275	+	0.650770i	$0.774446\pi$
$678$		0			0
$679$	26.4450	+	19.2134i	1.01487	+	0.737344i
$680$	−0.490084	+	2.64093i	−0.0187939	+	0.101275i
$681$		0			0
$682$	−16.1017			−0.616567
$683$	34.3793	−	24.9780i	1.31549	−	0.955758i	0.315512	−	0.948922i	$-0.397824\pi$
$683$	34.3793	−	24.9780i	1.31549	−	0.955758i	0.999977	−	0.00683639i	$-0.00217611\pi$
$684$		0			0
$685$	−4.39022	−	9.20964i	−0.167742	−	0.351882i
$686$	−14.2796	+	43.9481i	−0.545198	+	1.67795i
$687$		0			0
$688$	1.05724	+	3.25385i	0.0403069	+	0.124052i
$689$	−1.38659	+	4.26749i	−0.0528249	+	0.162578i
$690$		0			0
$691$	8.67746	+	26.7065i	0.330106	+	1.01596i	0.969083	+	0.246736i	$0.0793580\pi$
$691$	8.67746	+	26.7065i	0.330106	+	1.01596i	−0.638977	+	0.769226i	$0.720642\pi$
$692$	29.3860	−	21.3502i	1.11709	−	0.811612i
$693$		0			0
$694$	0.0847541	−	0.0615775i	0.00321722	−	0.00233745i
$695$	−1.93141	+	10.4079i	−0.0732626	+	0.394793i
$696$		0			0
$697$	−6.78460	−	4.92930i	−0.256985	−	0.186711i
$698$	4.90197	−	15.0867i	0.185542	−	0.571040i
$699$		0			0
$700$	−50.9401	−	19.5804i	−1.92536	−	0.740071i
$701$	−46.4314			−1.75369			−0.876845	−	0.480772i	$-0.840356\pi$
$701$	−46.4314			−1.75369			−0.876845	+	0.480772i	$0.840356\pi$
$702$		0			0
$703$	39.5860	+	28.7609i	1.49301	+	1.08474i
$704$	14.5680	+	10.5842i	0.549051	+	0.398909i
$705$		0			0
$706$	31.8762	−	23.1594i	1.19967	−	0.871615i
$707$	28.4090			1.06843
$708$		0			0
$709$	15.0285	+	46.2529i	0.564406	+	1.73706i	0.669710	+	0.742622i	$0.266418\pi$
$709$	15.0285	+	46.2529i	0.564406	+	1.73706i	−0.105305	+	0.994440i	$0.533582\pi$
$710$	36.5148	−	34.6356i	1.37037	−	1.29985i
$711$		0			0
$712$	−3.31999	−	10.2179i	−0.124422	−	0.382932i
$713$	3.44310	+	10.5968i	0.128945	+	0.396852i
$714$		0			0
$715$	4.19597	−	0.551448i	0.156920	−	0.0206230i
$716$	−0.616579	−	1.89763i	−0.0230426	−	0.0709179i
$717$		0			0
$718$	22.5062			0.839923
$719$	−17.1475	+	12.4584i	−0.639493	+	0.464619i	−0.859676	−	0.510840i	$-0.829334\pi$
$719$	−17.1475	+	12.4584i	−0.639493	+	0.464619i	0.220183	+	0.975459i	$0.429334\pi$
$720$		0			0
$721$	−28.3801	−	20.6193i	−1.05693	−	0.767904i
$722$	68.6150	+	49.8517i	2.55359	+	1.85529i
$723$		0			0
$724$	−35.6073			−1.32333
$725$	−25.6891	−	9.87441i	−0.954068	−	0.366726i
$726$		0			0
$727$	4.19988	−	12.9259i	0.155765	−	0.479396i	−0.842473	−	0.538739i	$-0.818901\pi$
$727$	4.19988	−	12.9259i	0.155765	−	0.479396i	0.998238	+	0.0593437i	$0.0189008\pi$
$728$	4.52087	+	3.28460i	0.167555	+	0.121736i
$729$		0			0
$730$	20.8367	+	11.3195i	0.771200	+	0.418953i
$731$	1.13497	−	0.824602i	0.0419783	−	0.0304990i
$732$		0			0
$733$	−15.0907	+	10.9640i	−0.557386	+	0.404965i	−0.830501	−	0.557017i	$-0.811946\pi$
$733$	−15.0907	+	10.9640i	−0.557386	+	0.404965i	0.273115	+	0.961981i	$0.411946\pi$
$734$	7.61927	+	23.4497i	0.281233	+	0.865545i
$735$		0			0
$736$	5.69988	−	17.5424i	0.210101	−	0.646623i
$737$	−1.88584	−	5.80402i	−0.0694658	−	0.213794i
$738$		0			0
$739$	8.17202	−	25.1509i	0.300613	−	0.925191i	−0.680665	−	0.732594i	$-0.738309\pi$
$739$	8.17202	−	25.1509i	0.300613	−	0.925191i	0.981278	−	0.192596i	$-0.0616907\pi$
$740$	−6.51073	+	35.0846i	−0.239339	+	1.28974i
$741$		0			0
$742$	−28.0304	+	20.3653i	−1.02903	+	0.747633i
$743$	29.0191			1.06461			0.532304	−	0.846553i	$-0.321326\pi$
$743$	29.0191			1.06461			0.532304	+	0.846553i	$0.321326\pi$
$744$		0			0
$745$	−10.3677	+	1.36255i	−0.379843	+	0.0499201i
$746$	−39.7096	−	28.8507i	−1.45387	−	1.05630i
$747$		0			0
$748$	1.37221	−	4.22324i	0.0501731	−	0.154417i
$749$	−41.3065			−1.50931
$750$		0			0
$751$	15.9489			0.581985			0.290992	−	0.956725i	$-0.406015\pi$
$751$	15.9489			0.581985			0.290992	+	0.956725i	$0.406015\pi$
$752$	3.49119	−	10.7448i	0.127310	−	0.391821i
$753$		0			0
$754$	11.3216	+	8.22563i	0.412309	+	0.299560i
$755$	−14.5031	+	1.90605i	−0.527824	+	0.0693682i
$756$		0			0
$757$	−16.4183			−0.596734			−0.298367	−	0.954451i	$-0.596442\pi$
$757$	−16.4183			−0.596734			−0.298367	+	0.954451i	$0.596442\pi$
$758$	42.7382	−	31.0512i	1.55232	−	1.12783i
$759$		0			0
$760$	−3.35301	+	18.0685i	−0.121626	+	0.655412i
$761$	15.2257	−	46.8600i	0.551932	−	1.69867i	−0.151978	−	0.988384i	$-0.548564\pi$
$761$	15.2257	−	46.8600i	0.551932	−	1.69867i	0.703910	−	0.710289i	$-0.251436\pi$
$762$		0			0
$763$	−15.7117	−	48.3555i	−0.568800	−	1.75059i
$764$	8.02480	−	24.6978i	0.290327	−	0.893534i
$765$		0			0
$766$	−10.3111	−	31.7345i	−0.372557	−	1.14661i
$767$	8.87369	−	6.44711i	0.320410	−	0.232792i
$768$		0			0
$769$	−39.9845	+	29.0504i	−1.44188	+	1.04759i	−0.454232	+	0.890884i	$0.650086\pi$
$769$	−39.9845	+	29.0504i	−1.44188	+	1.04759i	−0.987646	+	0.156702i	$0.949914\pi$
$770$	28.7146	+	15.5991i	1.03480	+	0.562154i
$771$		0			0
$772$	−8.80736	−	6.39892i	−0.316984	−	0.230302i
$773$	−8.00613	+	24.6403i	−0.287960	+	0.886251i	0.697535	+	0.716550i	$0.254280\pi$
$773$	−8.00613	+	24.6403i	−0.287960	+	0.886251i	−0.985496	+	0.169701i	$0.945720\pi$
$774$		0			0
$775$	−15.1186	+	18.6527i	−0.543076	+	0.670024i
$776$	8.02715			0.288158
$777$		0			0
$778$	14.6054	+	10.6114i	0.523629	+	0.380439i
$779$	−46.4182	−	33.7248i	−1.66311	−	1.20832i
$780$		0			0
$781$	−13.5551	+	9.84838i	−0.485041	+	0.352403i
$782$	−5.52681			−0.197638
$783$		0			0
$784$	−10.1460	−	31.2262i	−0.362357	−	1.11522i
$785$	8.85479	−	1.16372i	0.316041	−	0.0415351i
$786$		0			0
$787$	9.49160	+	29.2122i	0.338339	+	1.04130i	0.965054	+	0.262052i	$0.0843992\pi$
$787$	9.49160	+	29.2122i	0.338339	+	1.04130i	−0.626715	+	0.779249i	$0.715601\pi$
$788$	−1.45480	−	4.47741i	−0.0518251	−	0.159501i
$789$		0			0
$790$	50.1081	−	47.5293i	1.78277	−	1.69102i
$791$	20.1018	+	61.8670i	0.714737	+	2.19974i
$792$		0			0
$793$	1.67218			0.0593808
$794$	45.0798	−	32.7524i	1.59982	−	1.16234i
$795$		0			0
$796$	−8.63142	−	6.27109i	−0.305933	−	0.222273i
$797$	−27.2753	−	19.8166i	−0.966140	−	0.701942i	−0.0115713	−	0.999933i	$-0.503683\pi$
$797$	−27.2753	−	19.8166i	−0.966140	−	0.701942i	−0.954569	+	0.297991i	$0.903683\pi$
$798$		0			0
$799$	−4.63260			−0.163890
$800$	38.3982	−	10.2702i	1.35758	−	0.363106i
$801$		0			0
$802$	−16.5806	+	51.0298i	−0.585480	+	1.80192i
$803$	−6.38665	−	4.64018i	−0.225380	−	0.163748i
$804$		0			0
$805$	4.12584	−	22.2331i	0.145417	−	0.783613i
$806$	9.87720	−	7.17621i	0.347910	−	0.252771i
$807$		0			0
$808$	5.64402	−	4.10062i	0.198556	−	0.144259i
$809$	0.285227	+	0.877838i	0.0100280	+	0.0308632i	0.955945	−	0.293545i	$-0.0948350\pi$
$809$	0.285227	+	0.877838i	0.0100280	+	0.0308632i	−0.945917	+	0.324408i	$0.894835\pi$
$810$		0			0
$811$	8.27593	−	25.4707i	0.290607	−	0.894397i	−0.694055	−	0.719922i	$-0.744177\pi$
$811$	8.27593	−	25.4707i	0.290607	−	0.894397i	0.984662	−	0.174474i	$-0.0558226\pi$
$812$	18.5651	+	57.1376i	0.651508	+	2.00514i
$813$		0			0
$814$	6.60274	−	20.3212i	0.231426	−	0.712256i
$815$	4.61990	+	9.69145i	0.161828	+	0.339477i
$816$		0			0
$817$	7.76511	−	5.64168i	0.271667	−	0.197377i
$818$	−71.7204			−2.50765
$819$		0			0
$820$	7.63444	−	41.1400i	0.266606	−	1.43667i
$821$	−29.8114	−	21.6592i	−1.04042	−	0.755912i	−0.0700559	−	0.997543i	$-0.522318\pi$
$821$	−29.8114	−	21.6592i	−1.04042	−	0.755912i	−0.970368	+	0.241631i	$0.922318\pi$
$822$		0			0
$823$	6.31204	−	19.4265i	0.220024	−	0.677164i	−0.778735	−	0.627353i	$-0.784138\pi$
$823$	6.31204	−	19.4265i	0.220024	−	0.677164i	0.998759	−	0.0498106i	$-0.0158618\pi$
$824$	−8.61452			−0.300101
$825$		0			0
$826$	84.6940			2.94688
$827$	−1.33810	+	4.11824i	−0.0465302	+	0.143205i	−0.971622	−	0.236537i	$-0.923987\pi$
$827$	−1.33810	+	4.11824i	−0.0465302	+	0.143205i	0.925092	+	0.379743i	$0.123987\pi$
$828$		0			0
$829$	0.497018	+	0.361104i	0.0172621	+	0.0125417i	0.596383	−	0.802700i	$-0.296604\pi$
$829$	0.497018	+	0.361104i	0.0172621	+	0.0125417i	−0.579121	+	0.815242i	$0.696604\pi$
$830$	−17.8399	−	37.4238i	−0.619231	−	1.29900i
$831$		0			0
$832$	−13.6535			−0.473351
$833$	−10.8919	+	7.91343i	−0.377382	+	0.274184i
$834$		0			0
$835$	38.3844	−	36.4090i	1.32835	−	1.25999i
$836$	9.38828	−	28.8942i	0.324701	−	0.999325i
$837$		0			0
$838$	5.20297	+	16.0131i	0.179733	+	0.553163i
$839$	−1.66863	+	5.13553i	−0.0576077	+	0.177298i	−0.975720	−	0.219023i	$-0.929713\pi$
$839$	−1.66863	+	5.13553i	−0.0576077	+	0.177298i	0.918112	+	0.396321i	$0.129713\pi$
$840$		0			0
$841$	0.400892	+	1.23382i	0.0138239	+	0.0425455i
$842$	12.8568	−	9.34105i	0.443076	−	0.321914i
$843$		0			0
$844$	18.8353	−	13.6847i	0.648339	−	0.471046i
$845$	18.7622	−	17.7966i	0.645439	−	0.612222i
$846$		0			0
$847$	29.9849	+	21.7853i	1.03029	+	0.748552i
$848$	3.16812	−	9.75046i	0.108794	−	0.334832i
$849$		0			0
$850$	−6.48205	−	9.99135i	−0.222333	−	0.342700i
$851$	−14.7855			−0.506841
$852$		0			0
$853$	32.1936	+	23.3900i	1.10229	+	0.800860i	0.981432	−	0.191810i	$-0.0614358\pi$
$853$	32.1936	+	23.3900i	1.10229	+	0.800860i	0.120857	+	0.992670i	$0.461436\pi$
$854$	10.4459	+	7.58940i	0.357452	+	0.259704i
$855$		0			0
$856$	−8.20637	+	5.96228i	−0.280488	+	0.203787i
$857$	42.8643			1.46422			0.732109	−	0.681188i	$-0.238536\pi$
$857$	42.8643			1.46422			0.732109	+	0.681188i	$0.238536\pi$
$858$		0			0
$859$	−1.41064	−	4.34152i	−0.0481306	−	0.148131i	0.924103	−	0.382144i	$-0.124814\pi$
$859$	−1.41064	−	4.34152i	−0.0481306	−	0.148131i	−0.972233	+	0.234013i	$0.924814\pi$
$860$	6.15064	+	3.34132i	0.209735	+	0.113938i
$861$		0			0
$862$	15.3119	+	47.1251i	0.521524	+	1.60509i
$863$	11.6275	+	35.7857i	0.395804	+	1.21816i	0.928334	+	0.371747i	$0.121241\pi$
$863$	11.6275	+	35.7857i	0.395804	+	1.21816i	−0.532530	+	0.846411i	$0.678759\pi$
$864$		0			0
$865$	−5.91756	+	31.8882i	−0.201203	+	1.08423i
$866$	2.20150	+	6.77551i	0.0748099	+	0.230241i
$867$		0			0
$868$	52.4133			1.77902
$869$	−18.6013	+	13.5146i	−0.631006	+	0.458452i
$870$		0			0
$871$	3.74355	+	2.71985i	0.126845	+	0.0921586i
$872$	−10.1012	−	7.33894i	−0.342069	−	0.248528i
$873$		0			0
$874$	−37.8128			−1.27904
$875$	45.0318	−	18.6171i	1.52235	−	0.629373i
$876$		0			0
$877$	16.1938	−	49.8393i	0.546825	−	1.68295i	−0.169787	−	0.985481i	$-0.554308\pi$
$877$	16.1938	−	49.8393i	0.546825	−	1.68295i	0.716612	−	0.697472i	$-0.245692\pi$
$878$	−16.2841	−	11.8311i	−0.549562	−	0.399280i
$879$		0			0
$880$	−9.58706	+	1.25996i	−0.323180	+	0.0424733i
$881$	−6.42180	+	4.66571i	−0.216356	+	0.157192i	−0.690685	−	0.723156i	$-0.742691\pi$
$881$	−6.42180	+	4.66571i	−0.216356	+	0.157192i	0.474329	+	0.880348i	$0.342691\pi$
$882$		0			0
$883$	−25.6393	+	18.6280i	−0.862831	+	0.626883i	−0.928654	−	0.370948i	$-0.879033\pi$
$883$	−25.6393	+	18.6280i	−0.862831	+	0.626883i	0.0658227	+	0.997831i	$0.479033\pi$
$884$	1.04046	+	3.20221i	0.0349945	+	0.107702i
$885$		0			0
$886$	6.33175	−	19.4871i	0.212719	−	0.654683i
$887$	−0.871749	−	2.68297i	−0.0292705	−	0.0900853i	0.935354	−	0.353713i	$-0.115081\pi$
$887$	−0.871749	−	2.68297i	−0.0292705	−	0.0900853i	−0.964625	+	0.263628i	$0.915081\pi$
$888$		0			0
$889$	−22.8901	+	70.4485i	−0.767709	+	2.36277i
$890$	41.8598	+	22.7402i	1.40314	+	0.762254i
$891$		0			0
$892$	6.88357	−	5.00121i	0.230479	−	0.167453i
$893$	−31.6949			−1.06063
$894$		0			0
$895$	1.56549	+	0.850448i	0.0523285	+	0.0284274i
$896$	−29.2312	−	21.2377i	−0.976546	−	0.709502i
$897$		0			0
$898$	20.6759	−	63.6340i	0.689965	−	2.12349i
$899$	26.4320			0.881556
$900$		0			0
$901$	−4.20390			−0.140052
$902$	−7.74233	+	23.8285i	−0.257792	+	0.793401i
$903$		0			0
$904$	12.9236	+	9.38958i	0.429834	+	0.312293i
$905$	23.0671	−	21.8800i	0.766776	−	0.727315i
$906$		0			0
$907$	−44.1799			−1.46697			−0.733485	−	0.679705i	$-0.762108\pi$
$907$	−44.1799			−1.46697			−0.733485	+	0.679705i	$0.762108\pi$
$908$	54.2919	−	39.4454i	1.80174	−	1.30904i
$909$		0			0
$910$	−24.5664	+	3.22860i	−0.814370	+	0.107027i
$911$	10.6691	−	32.8362i	0.353484	−	1.08791i	−0.603400	−	0.797439i	$-0.706188\pi$
$911$	10.6691	−	32.8362i	0.353484	−	1.08791i	0.956883	−	0.290472i	$-0.0938124\pi$
$912$		0			0
$913$	4.26509	+	13.1266i	0.141154	+	0.434426i
$914$	6.52209	−	20.0729i	0.215731	−	0.663953i
$915$		0			0
$916$	−0.914713	−	2.81520i	−0.0302230	−	0.0930167i
$917$	−1.15961	+	0.842506i	−0.0382937	+	0.0278220i
$918$		0			0
$919$	0.429648	−	0.312158i	0.0141728	−	0.0102971i	−0.580676	−	0.814135i	$-0.697212\pi$
$919$	0.429648	−	0.312158i	0.0141728	−	0.0102971i	0.594849	+	0.803837i	$0.297212\pi$
$920$	−2.38949	−	5.01258i	−0.0787792	−	0.165260i
$921$		0			0
$922$	40.6648	+	29.5447i	1.33922	+	0.973003i
$923$	3.92584	−	12.0825i	0.129220	−	0.397700i
$924$		0			0
$925$	−17.3410	−	26.7292i	−0.570169	−	0.878850i
$926$	−58.6833			−1.92845
$927$		0			0
$928$	−35.4001	−	25.7197i	−1.16206	−	0.844289i
$929$	37.3735	+	27.1534i	1.22618	+	0.890874i	0.996598	−	0.0824143i	$-0.0262631\pi$
$929$	37.3735	+	27.1534i	1.22618	+	0.890874i	0.229585	+	0.973289i	$0.426263\pi$
$930$		0			0
$931$	−74.5192	+	54.1414i	−2.44227	+	1.77441i
$932$	−17.7676			−0.581997
$933$		0			0
$934$	2.85840	+	8.79726i	0.0935298	+	0.287855i
$935$	1.70615	+	3.57909i	0.0557971	+	0.117049i
$936$		0			0
$937$	−9.30820	−	28.6477i	−0.304086	−	0.935880i	−0.980017	−	0.198915i	$-0.936258\pi$
$937$	−9.30820	−	28.6477i	−0.304086	−	0.935880i	0.675931	−	0.736965i	$-0.263742\pi$
$938$	11.0412	+	33.9812i	0.360506	+	1.10952i
$939$		0			0
$940$	−9.94610	−	20.8645i	−0.324406	−	0.680526i
$941$	−17.6382	−	54.2847i	−0.574988	−	1.76963i	−0.636220	−	0.771508i	$-0.719503\pi$
$941$	−17.6382	−	54.2847i	−0.574988	−	1.76963i	0.0612315	−	0.998124i	$-0.480497\pi$
$942$		0			0
$943$	17.3374			0.564583
$944$	−20.2748	+	14.7305i	−0.659890	+	0.479438i
$945$		0			0
$946$	−3.39083	−	2.46358i	−0.110245	−	0.0800980i
$947$	−33.2708	−	24.1727i	−1.08116	−	0.785506i	−0.103273	−	0.994653i	$-0.532931\pi$
$947$	−33.2708	−	24.1727i	−1.08116	−	0.785506i	−0.977884	+	0.209147i	$0.932931\pi$
$948$		0			0
$949$	5.98576			0.194306
$950$	−44.3483	−	68.3579i	−1.43885	−	2.21782i
$951$		0			0
$952$	−1.61783	+	4.97918i	−0.0524343	+	0.161376i
$953$	28.1654	+	20.4633i	0.912366	+	0.662873i	0.941612	−	0.336700i	$-0.109311\pi$
$953$	28.1654	+	20.4633i	0.912366	+	0.662873i	−0.0292462	+	0.999572i	$0.509311\pi$
$954$		0			0
$955$	9.97767	+	20.9308i	0.322870	+	0.677304i
$956$	0.0866986	−	0.0629902i	0.00280403	−	0.00203725i
$957$		0			0
$958$	−22.0022	+	15.9855i	−0.710857	+	0.516468i
$959$	−6.14515	−	18.9128i	−0.198437	−	0.610727i
$960$		0			0
$961$	−2.45366	+	7.55160i	−0.0791504	+	0.243600i
$962$	5.00643	+	15.4082i	0.161414	+	0.496781i
$963$		0			0
$964$	−9.10930	+	28.0355i	−0.293391	+	0.902964i
$965$	9.63759	−	1.26660i	0.310245	−	0.0407733i
$966$		0			0
$967$	30.1519	−	21.9066i	0.969618	−	0.704469i	0.0142537	−	0.999898i	$-0.495463\pi$
$967$	30.1519	−	21.9066i	0.969618	−	0.704469i	0.955365	+	0.295430i	$0.0954628\pi$
$968$	9.10165			0.292538
$969$		0			0
$970$	−25.8234	+	24.4944i	−0.829138	+	0.786468i
$971$	−21.0419	−	15.2879i	−0.675267	−	0.490611i	0.196517	−	0.980500i	$-0.437037\pi$
$971$	−21.0419	−	15.2879i	−0.675267	−	0.490611i	−0.871784	+	0.489890i	$0.837037\pi$
$972$		0			0
$973$	−6.37585	+	19.6228i	−0.204400	+	0.629079i
$974$	14.6910			0.470729
$975$		0			0
$976$	−3.82064			−0.122296
$977$	−0.141709	+	0.436134i	−0.00453366	+	0.0139532i	−0.953298	−	0.302032i	$-0.902335\pi$
$977$	−0.141709	+	0.436134i	−0.00453366	+	0.0139532i	0.948764	+	0.315985i	$0.102335\pi$
$978$		0			0
$979$	−12.8304	−	9.32186i	−0.410063	−	0.297928i
$980$	−59.0257	−	32.0656i	−1.88551	−	1.02430i
$981$		0			0
$982$	56.9128			1.81616
$983$	7.23718	−	5.25812i	0.230830	−	0.167708i	−0.466358	−	0.884596i	$-0.654434\pi$
$983$	7.23718	−	5.25812i	0.230830	−	0.167708i	0.697188	+	0.716888i	$0.254434\pi$
$984$		0			0
$985$	3.69373	+	2.00661i	0.117692	+	0.0639359i
$986$	−4.05154	+	12.4694i	−0.129027	+	0.397105i
$987$		0			0
$988$	7.11852	+	21.9086i	0.226470	+	0.697004i
$989$	−0.896242	+	2.75835i	−0.0284988	+	0.0877104i
$990$		0			0
$991$	−17.4699	−	53.7667i	−0.554949	−	1.70796i	−0.696079	−	0.717965i	$-0.745074\pi$
$991$	−17.4699	−	53.7667i	−0.554949	−	1.70796i	0.141130	−	0.989991i	$-0.454926\pi$
$992$	−30.8837	+	22.4383i	−0.980559	+	0.712418i
$993$		0			0
$994$	79.3621	−	57.6599i	2.51721	−	1.82886i
$995$	9.44506	−	1.24130i	0.299429	−	0.0393518i
$996$		0			0
$997$	−32.0463	−	23.2830i	−1.01492	−	0.737380i	−0.0496816	−	0.998765i	$-0.515821\pi$
$997$	−32.0463	−	23.2830i	−1.01492	−	0.737380i	−0.965235	+	0.261385i	$0.915821\pi$
$998$	−1.80657	+	5.56005i	−0.0571860	+	0.176000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.c.46.1		8
3.2	odd	2		75.2.g.b.46.2	yes	8
15.2	even	4		375.2.i.b.274.4		16
15.8	even	4		375.2.i.b.274.1		16
15.14	odd	2		375.2.g.b.226.1		8
25.6	even	5	inner	225.2.h.c.181.1		8
25.9	even	10		5625.2.a.n.1.3		4
25.16	even	5		5625.2.a.i.1.2		4
75.8	even	20		375.2.i.b.349.4		16
75.17	even	20		375.2.i.b.349.1		16
75.38	even	20		1875.2.b.c.1249.2		8
75.41	odd	10		1875.2.a.h.1.3		4
75.44	odd	10		375.2.g.b.151.1		8
75.56	odd	10		75.2.g.b.31.2	✓	8
75.59	odd	10		1875.2.a.e.1.2		4
75.62	even	20		1875.2.b.c.1249.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.2	✓	8	75.56	odd	10
75.2.g.b.46.2	yes	8	3.2	odd	2
225.2.h.c.46.1		8	1.1	even	1	trivial
225.2.h.c.181.1		8	25.6	even	5	inner
375.2.g.b.151.1		8	75.44	odd	10
375.2.g.b.226.1		8	15.14	odd	2
375.2.i.b.274.1		16	15.8	even	4
375.2.i.b.274.4		16	15.2	even	4
375.2.i.b.349.1		16	75.17	even	20
375.2.i.b.349.4		16	75.8	even	20
1875.2.a.e.1.2		4	75.59	odd	10
1875.2.a.h.1.3		4	75.41	odd	10
1875.2.b.c.1249.2		8	75.38	even	20
1875.2.b.c.1249.7		8	75.62	even	20
5625.2.a.i.1.2		4	25.16	even	5
5625.2.a.n.1.3		4	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.655837 + 2.01846i) q^{2} +(-2.02602 - 1.47199i) q^{4} +(2.21700 - 0.291365i) q^{5} +4.35840 q^{7} +(0.865884 - 0.629102i) q^{8} +O(q^{10})\)	\(q+(-0.655837 + 2.01846i) q^{2} +(-2.02602 - 1.47199i) q^{4} +(2.21700 - 0.291365i) q^{5} +4.35840 q^{7} +(0.865884 - 0.629102i) q^{8} +(-0.865884 + 4.66602i) q^{10} +(0.488218 - 1.50258i) q^{11} +(0.370184 + 1.13931i) q^{13} +(-2.85840 + 8.79726i) q^{14} +(-0.845805 - 2.60312i) q^{16} +(-0.907987 + 0.659691i) q^{17} +(-6.21218 + 4.51341i) q^{19} +(-4.92058 - 2.67310i) q^{20} +(2.71270 + 1.97090i) q^{22} +(0.717004 - 2.20671i) q^{23} +(4.83021 - 1.29192i) q^{25} -2.54243 q^{26} +(-8.83021 - 6.41552i) q^{28} +(-4.45307 - 3.23535i) q^{29} +(-3.88495 + 2.82258i) q^{31} +7.94959 q^{32} +(-0.736068 - 2.26538i) q^{34} +(9.66259 - 1.26989i) q^{35} +(-1.96915 - 6.06043i) q^{37} +(-5.03596 - 15.4991i) q^{38} +(1.73637 - 1.64701i) q^{40} +(2.30902 + 7.10642i) q^{41} -1.24998 q^{43} +(-3.20092 + 2.32561i) q^{44} +(3.98392 + 2.89449i) q^{46} +(3.33934 + 2.42617i) q^{47} +11.9957 q^{49} +(-0.560152 + 10.5969i) q^{50} +(0.927051 - 2.85317i) q^{52} +(3.03032 + 2.20166i) q^{53} +(0.644581 - 3.47347i) q^{55} +(3.77387 - 2.74188i) q^{56} +(9.45090 - 6.86648i) q^{58} +(-2.82940 - 8.70799i) q^{59} +(0.431351 - 1.32756i) q^{61} +(-3.14937 - 9.69276i) q^{62} +(-3.52202 + 10.8397i) q^{64} +(1.15265 + 2.41799i) q^{65} +(3.12499 - 2.27044i) q^{67} +2.81066 q^{68} +(-3.77387 + 20.3364i) q^{70} +(-8.57970 - 6.23352i) q^{71} +(1.54407 - 4.75216i) q^{73} +13.5242 q^{74} +19.2297 q^{76} +(2.12785 - 6.54885i) q^{77} +(-11.7737 - 8.55407i) q^{79} +(-2.63361 - 5.52469i) q^{80} -15.8584 q^{82} +(-7.06760 + 5.13491i) q^{83} +(-1.82080 + 1.72709i) q^{85} +(0.819784 - 2.52304i) q^{86} +(-0.522535 - 1.60820i) q^{88} +(3.10195 - 9.54683i) q^{89} +(1.61341 + 4.96556i) q^{91} +(-4.70092 + 3.41542i) q^{92} +(-7.08719 + 5.14914i) q^{94} +(-12.4574 + 11.8163i) q^{95} +(6.06760 + 4.40837i) q^{97} +(-7.86720 + 24.2128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7	\( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^4 + 5 * q^5 + 4 * q^7 - 16 * q^11 - 8 * q^13 + 8 * q^14 - 17 * q^16 + q^17 - 5 * q^19 + 10 * q^20 + 13 * q^22 - 7 * q^23 - 15 * q^25 - 6 * q^26 - 17 * q^28 - 5 * q^29 - 19 * q^31 - 24 * q^32 + 12 * q^34 + 10 * q^35 - q^37 + 10 * q^38 + 25 * q^40 + 14 * q^41 + 32 * q^43 + 3 * q^44 + 16 * q^46 + q^47 + 16 * q^49 - 10 * q^50 - 6 * q^52 + 3 * q^53 + 15 * q^55 + 15 * q^56 + 5 * q^58 - 30 * q^59 - 14 * q^61 + 17 * q^62 - 44 * q^64 - 25 * q^65 + 4 * q^67 + 22 * q^68 - 15 * q^70 - 21 * q^71 + 2 * q^73 + 38 * q^74 + 80 * q^76 + 37 * q^77 - 30 * q^79 + 50 * q^80 - 12 * q^82 - 2 * q^83 - 30 * q^85 + 34 * q^86 + 70 * q^88 + 21 * q^91 - 9 * q^92 - 33 * q^94 - 65 * q^95 - 6 * q^97 - 73 * q^98

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