LMFDB - Embedded newform 990.2.n.j.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.2
Root			$-0.390899 + 1.20306i$ of defining polynomial
Character	$\chi$	$=$	990.361
Dual form			990.2.n.j.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(3.48828 + 2.53438i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(3.48828 + 2.53438i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000 q^{10} +(1.42705 + 2.99391i) q^{11} +(0.374078 - 1.15129i) q^{13} +(3.48828 - 2.53438i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.21437 + 6.81513i) q^{17} +(-2.19992 + 1.59833i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(3.28837 - 0.432036i) q^{22} -7.01787 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.979348 - 0.711538i) q^{26} +(-1.33240 - 4.10072i) q^{28} +(8.54782 + 6.21036i) q^{29} +(1.11908 - 3.44417i) q^{31} +1.00000 q^{32} +7.16586 q^{34} +(1.33240 - 4.10072i) q^{35} +(-1.71437 - 1.24556i) q^{37} +(0.840293 + 2.58616i) q^{38} +(0.809017 + 0.587785i) q^{40} +(2.22713 - 1.61811i) q^{41} +6.59251 q^{43} +(0.605270 - 3.26093i) q^{44} +(-2.16864 + 6.67439i) q^{46} +(4.64416 - 3.37418i) q^{47} +(3.58188 + 11.0239i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.979348 + 0.711538i) q^{52} +(1.81558 - 5.58779i) q^{53} +(2.40640 - 2.28238i) q^{55} -4.31175 q^{56} +(8.54782 - 6.21036i) q^{58} +(-4.77117 - 3.46646i) q^{59} +(-1.89879 - 5.84387i) q^{61} +(-2.92979 - 2.12861i) q^{62} +(0.309017 - 0.951057i) q^{64} -1.21054 q^{65} -1.63381 q^{67} +(2.21437 - 6.81513i) q^{68} +(-3.48828 - 2.53438i) q^{70} +(-2.29862 - 7.07443i) q^{71} +(5.98039 + 4.34501i) q^{73} +(-1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-2.60978 + 14.0603i) q^{77} +(2.16376 - 6.65938i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.850690 - 2.61815i) q^{82} +(0.492758 + 1.51655i) q^{83} +(5.79730 - 4.21198i) q^{85} +(2.03720 - 6.26985i) q^{86} +(-2.91429 - 1.58333i) q^{88} -1.24711 q^{89} +(4.22271 - 3.06798i) q^{91} +(5.67757 + 4.12500i) q^{92} +(-1.77391 - 5.45954i) q^{94} +(2.19992 + 1.59833i) q^{95} +(-2.13632 + 6.57491i) q^{97} +11.5912 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29} - 26 q^{31} + 8 q^{32} + 2 q^{34} - 4 q^{35} - 8 q^{37} + 3 q^{38} + 2 q^{40} + 15 q^{41} + 38 q^{43} - 7 q^{44} - 6 q^{46} - 6 q^{47} + 27 q^{49} - 2 q^{50} + 6 q^{52} + 4 q^{53} - 8 q^{55} - 6 q^{56} + 22 q^{58} - 39 q^{59} - 20 q^{61} + 14 q^{62} - 2 q^{64} + 14 q^{65} - 26 q^{67} + 12 q^{68} + q^{70} - 2 q^{71} + 8 q^{73} - 8 q^{74} + 8 q^{76} - 16 q^{77} + 14 q^{79} + 2 q^{80} - 15 q^{82} + 21 q^{83} + 13 q^{85} - 17 q^{86} - 7 q^{88} - 32 q^{89} + 53 q^{91} + 19 q^{92} + 9 q^{94} + 7 q^{95} - 31 q^{97} + 22 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	3.48828	+	2.53438i	1.31845	+	0.957907i	0.999950	+	0.00998336i	$0.00317786\pi$
$7$	3.48828	+	2.53438i	1.31845	+	0.957907i	0.318496	+	0.947924i	$0.396822\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	1.42705	+	2.99391i	0.430272	+	0.902699i
$11$	1.42705	+	2.99391i	0.430272	+	0.902699i
$12$		0			0
$13$	0.374078	−	1.15129i	0.103750	−	0.319311i	−0.885685	−	0.464287i	$-0.846311\pi$
$13$	0.374078	−	1.15129i	0.103750	−	0.319311i	0.989435	+	0.144976i	$0.0463105\pi$
$14$	3.48828	−	2.53438i	0.932282	−	0.677343i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.21437	+	6.81513i	0.537064	+	1.65291i	0.739147	+	0.673544i	$0.235229\pi$
$17$	2.21437	+	6.81513i	0.537064	+	1.65291i	−0.202083	+	0.979368i	$0.564771\pi$
$18$		0			0
$19$	−2.19992	+	1.59833i	−0.504695	+	0.366683i	−0.810808	−	0.585313i	$-0.800972\pi$
$19$	−2.19992	+	1.59833i	−0.504695	+	0.366683i	0.306112	+	0.951995i	$0.400972\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$		0			0
$22$	3.28837	−	0.432036i	0.701082	−	0.0921103i
$23$	−7.01787			−1.46333			−0.731663	−	0.681666i	$-0.761256\pi$
$23$	−7.01787			−1.46333			−0.731663	+	0.681666i	$0.761256\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−0.979348	−	0.711538i	−0.192066	−	0.139544i
$27$		0			0
$28$	−1.33240	−	4.10072i	−0.251801	−	0.774963i
$29$	8.54782	+	6.21036i	1.58729	+	1.15323i	0.907682	+	0.419659i	$0.137850\pi$
$29$	8.54782	+	6.21036i	1.58729	+	1.15323i	0.679609	+	0.733575i	$0.262150\pi$
$30$		0			0
$31$	1.11908	−	3.44417i	0.200993	−	0.618591i	−0.798862	−	0.601515i	$-0.794564\pi$
$31$	1.11908	−	3.44417i	0.200993	−	0.618591i	0.999854	−	0.0170766i	$-0.00543592\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	7.16586			1.22893
$35$	1.33240	−	4.10072i	0.225218	−	0.693148i
$36$		0			0
$37$	−1.71437	−	1.24556i	−0.281841	−	0.204769i	0.437879	−	0.899034i	$-0.355730\pi$
$37$	−1.71437	−	1.24556i	−0.281841	−	0.204769i	−0.719720	+	0.694265i	$0.755730\pi$
$38$	0.840293	+	2.58616i	0.136314	+	0.419530i
$39$		0			0
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	2.22713	−	1.61811i	0.347820	−	0.252706i	−0.400134	−	0.916457i	$-0.631036\pi$
$41$	2.22713	−	1.61811i	0.347820	−	0.252706i	0.747954	+	0.663751i	$0.231036\pi$
$42$		0			0
$43$	6.59251			1.00535			0.502674	−	0.864476i	$-0.332350\pi$
$43$	6.59251			1.00535			0.502674	+	0.864476i	$0.332350\pi$
$44$	0.605270	−	3.26093i	0.0912480	−	0.491603i
$45$		0			0
$46$	−2.16864	+	6.67439i	−0.319749	+	0.984085i
$47$	4.64416	−	3.37418i	0.677420	−	0.492175i	−0.195081	−	0.980787i	$-0.562497\pi$
$47$	4.64416	−	3.37418i	0.677420	−	0.492175i	0.872501	+	0.488613i	$0.162497\pi$
$48$		0			0
$49$	3.58188	+	11.0239i	0.511697	+	1.57484i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$		0			0
$52$	−0.979348	+	0.711538i	−0.135811	+	0.0986726i
$53$	1.81558	−	5.58779i	0.249390	−	0.767542i	−0.745494	−	0.666512i	$-0.767786\pi$
$53$	1.81558	−	5.58779i	0.249390	−	0.767542i	0.994883	−	0.101030i	$-0.0322137\pi$
$54$		0			0
$55$	2.40640	−	2.28238i	0.324479	−	0.307756i
$56$	−4.31175			−0.576182
$57$		0			0
$58$	8.54782	−	6.21036i	1.12238	−	0.815460i
$59$	−4.77117	−	3.46646i	−0.621154	−	0.451295i	0.232170	−	0.972675i	$-0.425417\pi$
$59$	−4.77117	−	3.46646i	−0.621154	−	0.451295i	−0.853324	+	0.521380i	$0.825417\pi$
$60$		0			0
$61$	−1.89879	−	5.84387i	−0.243115	−	0.748231i	−0.995941	−	0.0900109i	$-0.971310\pi$
$61$	−1.89879	−	5.84387i	−0.243115	−	0.748231i	0.752826	−	0.658220i	$-0.228690\pi$
$62$	−2.92979	−	2.12861i	−0.372083	−	0.270334i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.21054			−0.150149
$66$		0			0
$67$	−1.63381			−0.199602			−0.0998009	−	0.995007i	$-0.531821\pi$
$67$	−1.63381			−0.199602			−0.0998009	+	0.995007i	$0.531821\pi$
$68$	2.21437	−	6.81513i	0.268532	−	0.826456i
$69$		0			0
$70$	−3.48828	−	2.53438i	−0.416929	−	0.302917i
$71$	−2.29862	−	7.07443i	−0.272796	−	0.839580i	−0.989794	−	0.142505i	$-0.954484\pi$
$71$	−2.29862	−	7.07443i	−0.272796	−	0.839580i	0.716998	−	0.697075i	$-0.245516\pi$
$72$		0			0
$73$	5.98039	+	4.34501i	0.699952	+	0.508545i	0.879917	−	0.475128i	$-0.157598\pi$
$73$	5.98039	+	4.34501i	0.699952	+	0.508545i	−0.179965	+	0.983673i	$0.557598\pi$
$74$	−1.71437	+	1.24556i	−0.199292	+	0.144794i
$75$		0			0
$76$	2.71925			0.311919
$77$	−2.60978	+	14.0603i	−0.297412	+	1.60232i
$78$		0			0
$79$	2.16376	−	6.65938i	0.243443	−	0.749239i	−0.752446	−	0.658654i	$-0.771126\pi$
$79$	2.16376	−	6.65938i	0.243443	−	0.749239i	0.995889	−	0.0905854i	$-0.0288738\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$		0			0
$82$	−0.850690	−	2.61815i	−0.0939430	−	0.289127i
$83$	0.492758	+	1.51655i	0.0540872	+	0.166463i	0.974451	−	0.224600i	$-0.0721075\pi$
$83$	0.492758	+	1.51655i	0.0540872	+	0.166463i	−0.920364	+	0.391063i	$0.872107\pi$
$84$		0			0
$85$	5.79730	−	4.21198i	0.628805	−	0.456854i
$86$	2.03720	−	6.26985i	0.219677	−	0.676095i
$87$		0			0
$88$	−2.91429	−	1.58333i	−0.310664	−	0.168783i
$89$	−1.24711			−0.132193			−0.0660967	−	0.997813i	$-0.521055\pi$
$89$	−1.24711			−0.132193			−0.0660967	+	0.997813i	$0.521055\pi$
$90$		0			0
$91$	4.22271	−	3.06798i	0.442660	−	0.321611i
$92$	5.67757	+	4.12500i	0.591928	+	0.430061i
$93$		0			0
$94$	−1.77391	−	5.45954i	−0.182965	−	0.563108i
$95$	2.19992	+	1.59833i	0.225707	+	0.163985i
$96$		0			0
$97$	−2.13632	+	6.57491i	−0.216910	+	0.667581i	0.782102	+	0.623150i	$0.214147\pi$
$97$	−2.13632	+	6.57491i	−0.216910	+	0.667581i	−0.999012	+	0.0444310i	$0.985853\pi$
$98$	11.5912			1.17089
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.00000	+	3.07768i	−0.0995037	+	0.306241i	−0.988401	−	0.151865i	$-0.951472\pi$
$101$	−1.00000	+	3.07768i	−0.0995037	+	0.306241i	0.888897	+	0.458106i	$0.151472\pi$
$102$		0			0
$103$	−4.67307	−	3.39518i	−0.460451	−	0.334537i	0.333257	−	0.942836i	$-0.391852\pi$
$103$	−4.67307	−	3.39518i	−0.460451	−	0.334537i	−0.793708	+	0.608299i	$0.791852\pi$
$104$	0.374078	+	1.15129i	0.0366813	+	0.112894i
$105$		0			0
$106$	−4.75326	−	3.45344i	−0.461677	−	0.335428i
$107$	0.138686	−	0.100761i	0.0134073	−	0.00974095i	−0.581061	−	0.813860i	$-0.697362\pi$
$107$	0.138686	−	0.100761i	0.0134073	−	0.00974095i	0.594469	+	0.804119i	$0.297362\pi$
$108$		0			0
$109$	−2.32753			−0.222937			−0.111468	−	0.993768i	$-0.535555\pi$
$109$	−2.32753			−0.222937			−0.111468	+	0.993768i	$0.535555\pi$
$110$	−1.42705	−	2.99391i	−0.136064	−	0.285459i
$111$		0			0
$112$	−1.33240	+	4.10072i	−0.125900	+	0.387482i
$113$	3.48555	−	2.53240i	0.327893	−	0.238228i	−0.411643	−	0.911345i	$-0.635045\pi$
$113$	3.48555	−	2.53240i	0.327893	−	0.238228i	0.739536	+	0.673117i	$0.235045\pi$
$114$		0			0
$115$	2.16864	+	6.67439i	0.202227	+	0.622390i
$116$	−3.26498	−	10.0486i	−0.303146	−	0.932986i
$117$		0			0
$118$	−4.77117	+	3.46646i	−0.439222	+	0.319114i
$119$	−9.54782	+	29.3852i	−0.875247	+	2.69373i
$120$		0			0
$121$	−6.92705	+	8.54494i	−0.629732	+	0.776813i
$122$	−6.14461			−0.556307
$123$		0			0
$124$	−2.92979	+	2.12861i	−0.263103	+	0.191155i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	3.34855	+	10.3058i	0.297136	+	0.914490i	0.982496	+	0.186285i	$0.0596449\pi$
$127$	3.34855	+	10.3058i	0.297136	+	0.914490i	−0.685360	+	0.728205i	$0.740355\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−0.374078	+	1.15129i	−0.0328088	+	0.100975i
$131$	−5.78518			−0.505454			−0.252727	−	0.967538i	$-0.581327\pi$
$131$	−5.78518			−0.505454			−0.252727	+	0.967538i	$0.581327\pi$
$132$		0			0
$133$	−11.7247			−1.01666
$134$	−0.504875	+	1.55385i	−0.0436146	+	0.134232i
$135$		0			0
$136$	−5.79730	−	4.21198i	−0.497114	−	0.361175i
$137$	−2.67310	−	8.22695i	−0.228378	−	0.702876i	−0.997931	−	0.0642926i	$-0.979521\pi$
$137$	−2.67310	−	8.22695i	−0.228378	−	0.702876i	0.769553	−	0.638583i	$-0.220479\pi$
$138$		0			0
$139$	−10.3135	−	7.49318i	−0.874777	−	0.635563i	0.0570872	−	0.998369i	$-0.481819\pi$
$139$	−10.3135	−	7.49318i	−0.874777	−	0.635563i	−0.931865	+	0.362806i	$0.881819\pi$
$140$	−3.48828	+	2.53438i	−0.294814	+	0.214195i
$141$		0			0
$142$	−7.43849			−0.624224
$143$	3.98070	−	0.522997i	0.332883	−	0.0437352i
$144$		0			0
$145$	3.26498	−	10.0486i	0.271142	−	0.834488i
$146$	5.98039	−	4.34501i	0.494941	−	0.359596i
$147$		0			0
$148$	0.654831	+	2.01536i	0.0538268	+	0.165662i
$149$	−2.04339	−	6.28892i	−0.167401	−	0.515208i	0.831804	−	0.555070i	$-0.187308\pi$
$149$	−2.04339	−	6.28892i	−0.167401	−	0.515208i	−0.999205	+	0.0398613i	$0.987308\pi$
$150$		0			0
$151$	−16.9064	+	12.2832i	−1.37582	+	0.999591i	−0.378562	+	0.925576i	$0.623581\pi$
$151$	−16.9064	+	12.2832i	−1.37582	+	0.999591i	−0.997257	+	0.0740153i	$0.976419\pi$
$152$	0.840293	−	2.58616i	0.0681568	−	0.209765i
$153$		0			0
$154$	12.5657	+	6.82692i	1.01257	+	0.550129i
$155$	−3.62142			−0.290879
$156$		0			0
$157$	16.3657	−	11.8904i	1.30613	−	0.948957i	0.306131	−	0.951989i	$-0.400965\pi$
$157$	16.3657	−	11.8904i	1.30613	−	0.948957i	0.999995	+	0.00303254i	$0.000965289\pi$
$158$	−5.66481	−	4.11573i	−0.450668	−	0.327430i
$159$		0			0
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	−24.4803	−	17.7860i	−1.92932	−	1.40173i
$162$		0			0
$163$	−2.49721	+	7.68564i	−0.195597	+	0.601986i	0.804372	+	0.594126i	$0.202502\pi$
$163$	−2.49721	+	7.68564i	−0.195597	+	0.601986i	−0.999969	+	0.00785979i	$0.997498\pi$
$164$	−2.75289			−0.214965
$165$		0			0
$166$	1.59460			0.123765
$167$	−5.33751	+	16.4272i	−0.413029	+	1.27117i	0.500973	+	0.865463i	$0.332975\pi$
$167$	−5.33751	+	16.4272i	−0.413029	+	1.27117i	−0.914002	+	0.405709i	$0.867025\pi$
$168$		0			0
$169$	9.33168	+	6.77986i	0.717822	+	0.521528i
$170$	−2.21437	−	6.81513i	−0.169835	−	0.522697i
$171$		0			0
$172$	−5.33345	−	3.87498i	−0.406672	−	0.295464i
$173$	11.6286	−	8.44868i	0.884107	−	0.642341i	−0.0502280	−	0.998738i	$-0.515995\pi$
$173$	11.6286	−	8.44868i	0.884107	−	0.642341i	0.934335	+	0.356397i	$0.115995\pi$
$174$		0			0
$175$	−4.31175			−0.325938
$176$	−2.40640	+	2.28238i	−0.181389	+	0.172041i
$177$		0			0
$178$	−0.385378	+	1.18607i	−0.0288853	+	0.0888999i
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.152953	−	0.988233i	$-0.451122\pi$
$179$	15.2533	−	11.0822i	1.14008	−	0.828320i	0.987131	+	0.159914i	$0.0511216\pi$
$180$		0			0
$181$	−4.04887	−	12.4611i	−0.300950	−	0.926228i	−0.981158	−	0.193209i	$-0.938110\pi$
$181$	−4.04887	−	12.4611i	−0.300950	−	0.926228i	0.680208	−	0.733019i	$-0.261890\pi$
$182$	−1.61293	−	4.96409i	−0.119558	−	0.367963i
$183$		0			0
$184$	5.67757	−	4.12500i	0.418556	−	0.304099i
$185$	−0.654831	+	2.01536i	−0.0481442	+	0.148173i
$186$		0			0
$187$	−17.2439	+	16.3552i	−1.26100	+	1.19601i
$188$	−5.74050			−0.418669
$189$		0			0
$190$	2.19992	−	1.59833i	0.159599	−	0.115955i
$191$	−9.11908	−	6.62540i	−0.659833	−	0.479397i	0.206773	−	0.978389i	$-0.433704\pi$
$191$	−9.11908	−	6.62540i	−0.659833	−	0.479397i	−0.866607	+	0.498992i	$0.833704\pi$
$192$		0			0
$193$	2.14590	+	6.60440i	0.154465	+	0.475395i	0.998106	−	0.0615126i	$-0.0195924\pi$
$193$	2.14590	+	6.60440i	0.154465	+	0.475395i	−0.843641	+	0.536907i	$0.819592\pi$
$194$	5.59295	+	4.06352i	0.401551	+	0.291744i
$195$		0			0
$196$	3.58188	−	11.0239i	0.255849	−	0.787421i
$197$	13.4389			0.957485			0.478743	−	0.877955i	$-0.341093\pi$
$197$	13.4389			0.957485			0.478743	+	0.877955i	$0.341093\pi$
$198$		0			0
$199$	−19.4427			−1.37825			−0.689127	−	0.724640i	$-0.742006\pi$
$199$	−19.4427			−1.37825			−0.689127	+	0.724640i	$0.742006\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$		0			0
$202$	2.61803	+	1.90211i	0.184204	+	0.133832i
$203$	14.0778	+	43.3269i	0.988066	+	3.04095i
$204$		0			0
$205$	−2.22713	−	1.61811i	−0.155550	−	0.113014i
$206$	−4.67307	+	3.39518i	−0.325588	+	0.236554i
$207$		0			0
$208$	1.21054			0.0839359
$209$	−7.92467	−	4.30546i	−0.548161	−	0.297815i
$210$		0			0
$211$	−0.728826	+	2.24309i	−0.0501744	+	0.154421i	−0.973004	−	0.230786i	$-0.925870\pi$
$211$	−0.728826	+	2.24309i	−0.0501744	+	0.154421i	0.922830	+	0.385207i	$0.125870\pi$
$212$	−4.75326	+	3.45344i	−0.326455	+	0.237184i
$213$		0			0
$214$	−0.0529733	−	0.163035i	−0.00362118	−	0.0111448i
$215$	−2.03720	−	6.26985i	−0.138936	−	0.427600i
$216$		0			0
$217$	12.6325	−	9.17806i	0.857551	−	0.623047i
$218$	−0.719246	+	2.21361i	−0.0487135	+	0.149925i
$219$		0			0
$220$	−3.28837	+	0.432036i	−0.221702	+	0.0291278i
$221$	8.67456			0.583514
$222$		0			0
$223$	11.8090	−	8.57978i	0.790792	−	0.574544i	−0.117406	−	0.993084i	$-0.537458\pi$
$223$	11.8090	−	8.57978i	0.790792	−	0.574544i	0.908198	+	0.418540i	$0.137458\pi$
$224$	3.48828	+	2.53438i	0.233071	+	0.169336i
$225$		0			0
$226$	−1.33136	−	4.09750i	−0.0885607	−	0.272562i
$227$	2.41871	+	1.75730i	0.160536	+	0.116636i	0.665153	−	0.746707i	$-0.268366\pi$
$227$	2.41871	+	1.75730i	0.160536	+	0.116636i	−0.504617	+	0.863343i	$0.668366\pi$
$228$		0			0
$229$	0.487913	−	1.50164i	0.0322422	−	0.0992312i	−0.933640	−	0.358212i	$-0.883387\pi$
$229$	0.487913	−	1.50164i	0.0322422	−	0.0992312i	0.965883	+	0.258981i	$0.0833866\pi$
$230$	7.01787			0.462744
$231$		0			0
$232$	−10.5657			−0.693671
$233$	−0.156276	+	0.480967i	−0.0102380	+	0.0315092i	−0.956045	−	0.293220i	$-0.905273\pi$
$233$	−0.156276	+	0.480967i	−0.0102380	+	0.0315092i	0.945807	+	0.324729i	$0.105273\pi$
$234$		0			0
$235$	−4.64416	−	3.37418i	−0.302951	−	0.220107i
$236$	1.82243	+	5.60885i	0.118630	+	0.365105i
$237$		0			0
$238$	24.9965	+	18.1610i	1.62028	+	1.17721i
$239$	−13.5444	+	9.84061i	−0.876117	+	0.636536i	−0.932221	−	0.361889i	$-0.882132\pi$
$239$	−13.5444	+	9.84061i	−0.876117	+	0.636536i	0.0561044	+	0.998425i	$0.482132\pi$
$240$		0			0
$241$	−15.2947			−0.985217			−0.492609	−	0.870251i	$-0.663957\pi$
$241$	−15.2947			−0.985217			−0.492609	+	0.870251i	$0.663957\pi$
$242$	5.98614	+	9.22855i	0.384804	+	0.593234i
$243$		0			0
$244$	−1.89879	+	5.84387i	−0.121557	+	0.374115i
$245$	9.37749	−	6.81315i	0.599106	−	0.435276i
$246$		0			0
$247$	1.01721	+	3.13065i	0.0647235	+	0.199198i
$248$	1.11908	+	3.44417i	0.0710616	+	0.218705i
$249$		0			0
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	0.132071	−	0.406472i	0.00833623	−	0.0256563i	−0.946802	−	0.321817i	$-0.895706\pi$
$251$	0.132071	−	0.406472i	0.00833623	−	0.0256563i	0.955138	+	0.296161i	$0.0957064\pi$
$252$		0			0
$253$	−10.0149	−	21.0109i	−0.629628	−	1.32094i
$254$	10.8361			0.679920
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	14.4614	+	10.5068i	0.902076	+	0.655397i	0.938998	−	0.343921i	$-0.111755\pi$
$257$	14.4614	+	10.5068i	0.902076	+	0.655397i	−0.0369221	+	0.999318i	$0.511755\pi$
$258$		0			0
$259$	−2.82347	−	8.68975i	−0.175442	−	0.539955i
$260$	0.979348	+	0.711538i	0.0607366	+	0.0441277i
$261$		0			0
$262$	−1.78772	+	5.50203i	−0.110446	+	0.339917i
$263$	−14.4977			−0.893964			−0.446982	−	0.894543i	$-0.647501\pi$
$263$	−14.4977			−0.893964			−0.446982	+	0.894543i	$0.647501\pi$
$264$		0			0
$265$	−5.87535			−0.360920
$266$	−3.62314	+	11.1509i	−0.222149	+	0.683704i
$267$		0			0
$268$	1.32178	+	0.960330i	0.0807406	+	0.0586615i
$269$	−8.63326	−	26.5704i	−0.526379	−	1.62003i	−0.761573	−	0.648079i	$-0.775573\pi$
$269$	−8.63326	−	26.5704i	−0.526379	−	1.62003i	0.235194	−	0.971948i	$-0.424427\pi$
$270$		0			0
$271$	−8.40531	−	6.10681i	−0.510586	−	0.370962i	0.302460	−	0.953162i	$-0.402192\pi$
$271$	−8.40531	−	6.10681i	−0.510586	−	0.370962i	−0.813046	+	0.582200i	$0.802192\pi$
$272$	−5.79730	+	4.21198i	−0.351513	+	0.255389i
$273$		0			0
$274$	−8.65033			−0.522585
$275$	−2.91429	−	1.58333i	−0.175738	−	0.0954783i
$276$		0			0
$277$	−0.194167	+	0.597585i	−0.0116664	+	0.0359054i	−0.956720	−	0.291009i	$-0.906009\pi$
$277$	−0.194167	+	0.597585i	−0.0116664	+	0.0359054i	0.945054	+	0.326915i	$0.106009\pi$
$278$	−10.3135	+	7.49318i	−0.618561	+	0.449411i
$279$		0			0
$280$	1.33240	+	4.10072i	0.0796264	+	0.245065i
$281$	−9.30347	−	28.6331i	−0.554998	−	1.70811i	−0.695948	−	0.718092i	$-0.745016\pi$
$281$	−9.30347	−	28.6331i	−0.554998	−	1.70811i	0.140950	−	0.990017i	$-0.454984\pi$
$282$		0			0
$283$	13.0288	−	9.46599i	0.774482	−	0.562694i	−0.128836	−	0.991666i	$-0.541124\pi$
$283$	13.0288	−	9.46599i	0.774482	−	0.562694i	0.903318	+	0.428972i	$0.141124\pi$
$284$	−2.29862	+	7.07443i	−0.136398	+	0.419790i
$285$		0			0
$286$	0.732705	−	3.94749i	0.0433257	−	0.233420i
$287$	11.8698			0.700651
$288$		0			0
$289$	−27.7893	+	20.1901i	−1.63467	+	1.18765i
$290$	−8.54782	−	6.21036i	−0.501945	−	0.364685i
$291$		0			0
$292$	−2.28431	−	7.03037i	−0.133679	−	0.411422i
$293$	−3.21992	−	2.33941i	−0.188110	−	0.136670i	0.489745	−	0.871866i	$-0.337090\pi$
$293$	−3.21992	−	2.33941i	−0.188110	−	0.136670i	−0.677854	+	0.735196i	$0.737090\pi$
$294$		0			0
$295$	−1.82243	+	5.60885i	−0.106106	+	0.326560i
$296$	2.11908			0.123169
$297$		0			0
$298$	−6.61256			−0.383055
$299$	−2.62523	+	8.07962i	−0.151821	+	0.467256i
$300$		0			0
$301$	22.9965	+	16.7079i	1.32550	+	0.963030i
$302$	6.45765	+	19.8746i	0.371596	+	1.14366i
$303$		0			0
$304$	−2.19992	−	1.59833i	−0.126174	−	0.0916707i
$305$	−4.97109	+	3.61171i	−0.284644	+	0.206806i
$306$		0			0
$307$	17.6055			1.00480			0.502401	−	0.864635i	$-0.332450\pi$
$307$	17.6055			1.00480			0.502401	+	0.864635i	$0.332450\pi$
$308$	10.3758	−	9.84104i	0.591216	−	0.560746i
$309$		0			0
$310$	−1.11908	+	3.44417i	−0.0635594	+	0.195616i
$311$	−18.3117	+	13.3042i	−1.03836	+	0.754412i	−0.969964	−	0.243247i	$-0.921788\pi$
$311$	−18.3117	+	13.3042i	−1.03836	+	0.754412i	−0.0683942	+	0.997658i	$0.521788\pi$
$312$		0			0
$313$	−3.89659	−	11.9925i	−0.220248	−	0.677855i	−0.998739	−	0.0501989i	$-0.984014\pi$
$313$	−3.89659	−	11.9925i	−0.220248	−	0.677855i	0.778491	−	0.627656i	$-0.215986\pi$
$314$	−6.25115	−	19.2391i	−0.352773	−	1.08572i
$315$		0			0
$316$	−5.66481	+	4.11573i	−0.318670	+	0.231528i
$317$	−8.11722	+	24.9822i	−0.455908	+	1.40314i	0.414157	+	0.910205i	$0.364076\pi$
$317$	−8.11722	+	24.9822i	−0.455908	+	1.40314i	−0.870065	+	0.492936i	$0.835924\pi$
$318$		0			0
$319$	−6.39510	+	34.4539i	−0.358057	+	1.92905i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	−24.4803	+	17.7860i	−1.36423	+	0.991174i
$323$	−15.7643	−	11.4534i	−0.877148	−	0.637285i
$324$		0			0
$325$	0.374078	+	1.15129i	0.0207501	+	0.0638622i
$326$	6.53779	+	4.74999i	0.362095	+	0.263077i
$327$		0			0
$328$	−0.850690	+	2.61815i	−0.0469715	+	0.144563i
$329$	24.7516			1.36460
$330$		0			0
$331$	12.7406			0.700284			0.350142	−	0.936697i	$-0.386133\pi$
$331$	12.7406			0.700284			0.350142	+	0.936697i	$0.386133\pi$
$332$	0.492758	−	1.51655i	0.0270436	−	0.0832316i
$333$		0			0
$334$	13.9738	+	10.1525i	0.764611	+	0.555522i
$335$	0.504875	+	1.55385i	0.0275843	+	0.0848957i
$336$		0			0
$337$	15.4174	+	11.2014i	0.839841	+	0.610180i	0.922326	−	0.386412i	$-0.126286\pi$
$337$	15.4174	+	11.2014i	0.839841	+	0.610180i	−0.0824856	+	0.996592i	$0.526286\pi$
$338$	9.33168	−	6.77986i	0.507576	−	0.368776i
$339$		0			0
$340$	−7.16586			−0.388623
$341$	11.9085	−	1.56458i	0.644884	−	0.0847268i
$342$		0			0
$343$	−6.11736	+	18.8273i	−0.330306	+	1.01658i
$344$	−5.33345	+	3.87498i	−0.287560	+	0.208925i
$345$		0			0
$346$	−4.44173	−	13.6703i	−0.238789	−	0.734917i
$347$	−5.81663	−	17.9017i	−0.312253	−	0.961016i	−0.976870	−	0.213832i	$-0.931405\pi$
$347$	−5.81663	−	17.9017i	−0.312253	−	0.961016i	0.664617	−	0.747184i	$-0.268595\pi$
$348$		0			0
$349$	22.0200	−	15.9984i	1.17870	−	0.856377i	0.186677	−	0.982421i	$-0.440228\pi$
$349$	22.0200	−	15.9984i	1.17870	−	0.856377i	0.992025	+	0.126045i	$0.0402283\pi$
$350$	−1.33240	+	4.10072i	−0.0712200	+	0.219193i
$351$		0			0
$352$	1.42705	+	2.99391i	0.0760621	+	0.159576i
$353$	−25.6380			−1.36457			−0.682286	−	0.731085i	$-0.739014\pi$
$353$	−25.6380			−1.36457			−0.682286	+	0.731085i	$0.739014\pi$
$354$		0			0
$355$	−6.01787	+	4.37224i	−0.319395	+	0.232054i
$356$	1.00893	+	0.733033i	0.0534734	+	0.0388507i
$357$		0			0
$358$	−5.82624	−	17.9313i	−0.307926	−	0.947700i
$359$	7.82857	+	5.68779i	0.413176	+	0.300190i	0.774886	−	0.632100i	$-0.217807\pi$
$359$	7.82857	+	5.68779i	0.413176	+	0.300190i	−0.361710	+	0.932291i	$0.617807\pi$
$360$		0			0
$361$	−3.58636	+	11.0377i	−0.188756	+	0.580930i
$362$	−13.1024			−0.688647
$363$		0			0
$364$	−5.21955			−0.273579
$365$	2.28431	−	7.03037i	0.119566	−	0.367987i
$366$		0			0
$367$	16.7495	+	12.1692i	0.874317	+	0.635229i	0.931742	−	0.363121i	$-0.118289\pi$
$367$	16.7495	+	12.1692i	0.874317	+	0.635229i	−0.0574247	+	0.998350i	$0.518289\pi$
$368$	−2.16864	−	6.67439i	−0.113048	−	0.347927i
$369$		0			0
$370$	1.71437	+	1.24556i	0.0891259	+	0.0647538i
$371$	20.4949	−	14.8904i	1.06404	−	0.773071i
$372$		0			0
$373$	−16.1463			−0.836021			−0.418011	−	0.908442i	$-0.637273\pi$
$373$	−16.1463			−0.836021			−0.418011	+	0.908442i	$0.637273\pi$
$374$	10.2260	+	21.4540i	0.528776	+	1.10936i
$375$		0			0
$376$	−1.77391	+	5.45954i	−0.0914825	+	0.281554i
$377$	10.3475	−	7.51789i	0.532923	−	0.387191i
$378$		0			0
$379$	−0.0709811	−	0.218457i	−0.00364605	−	0.0112214i	0.949217	−	0.314622i	$-0.101878\pi$
$379$	−0.0709811	−	0.218457i	−0.00364605	−	0.0112214i	−0.952863	+	0.303401i	$0.901878\pi$
$380$	−0.840293	−	2.58616i	−0.0431061	−	0.132667i
$381$		0			0
$382$	−9.11908	+	6.62540i	−0.466573	+	0.338985i
$383$	−4.02403	+	12.3847i	−0.205619	+	0.632829i	0.794069	+	0.607828i	$0.207959\pi$
$383$	−4.02403	+	12.3847i	−0.205619	+	0.632829i	−0.999687	+	0.0250010i	$0.992041\pi$
$384$		0			0
$385$	14.1786	−	1.86283i	0.722609	−	0.0949387i
$386$	6.94427			0.353454
$387$		0			0
$388$	5.59295	−	4.06352i	0.283939	−	0.206294i
$389$	23.9676	+	17.4135i	1.21521	+	0.882899i	0.995693	−	0.0927106i	$-0.0295532\pi$
$389$	23.9676	+	17.4135i	1.21521	+	0.882899i	0.219513	+	0.975610i	$0.429553\pi$
$390$		0			0
$391$	−15.5402	−	47.8277i	−0.785900	−	2.41875i
$392$	−9.37749	−	6.81315i	−0.473635	−	0.344116i
$393$		0			0
$394$	4.15286	−	12.7812i	0.209218	−	0.643908i
$395$	−7.00209			−0.352313
$396$		0			0
$397$	2.18665			0.109745			0.0548724	−	0.998493i	$-0.482525\pi$
$397$	2.18665			0.109745			0.0548724	+	0.998493i	$0.482525\pi$
$398$	−6.00812	+	18.4911i	−0.301160	+	0.926874i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	4.04638	+	12.4535i	0.202066	+	0.621896i	0.999821	+	0.0189143i	$0.00602098\pi$
$401$	4.04638	+	12.4535i	0.202066	+	0.621896i	−0.797755	+	0.602982i	$0.793979\pi$
$402$		0			0
$403$	−3.54663	−	2.57678i	−0.176670	−	0.128358i
$404$	2.61803	−	1.90211i	0.130252	−	0.0946337i
$405$		0			0
$406$	45.5566			2.26094
$407$	1.28262	−	6.91016i	0.0635769	−	0.342524i
$408$		0			0
$409$	9.40299	−	28.9394i	0.464948	−	1.43096i	−0.394100	−	0.919067i	$-0.628944\pi$
$409$	9.40299	−	28.9394i	0.464948	−	1.43096i	0.859048	−	0.511895i	$-0.171056\pi$
$410$	−2.22713	+	1.61811i	−0.109990	+	0.0799127i
$411$		0			0
$412$	1.78495	+	5.49352i	0.0879383	+	0.270646i
$413$	−7.85785	−	24.1840i	−0.386660	−	1.19002i
$414$		0			0
$415$	1.29006	−	0.937281i	0.0633264	−	0.0460093i
$416$	0.374078	−	1.15129i	0.0183407	−	0.0564468i
$417$		0			0
$418$	−6.54359	+	6.20634i	−0.320058	+	0.303562i
$419$	−26.7473			−1.30669			−0.653346	−	0.757059i	$-0.726635\pi$
$419$	−26.7473			−1.30669			−0.653346	+	0.757059i	$0.726635\pi$
$420$		0			0
$421$	24.5477	−	17.8350i	1.19638	−	0.869223i	0.202459	−	0.979291i	$-0.435107\pi$
$421$	24.5477	−	17.8350i	1.19638	−	0.869223i	0.993924	+	0.110068i	$0.0351068\pi$
$422$	1.90809	+	1.38631i	0.0928844	+	0.0674844i
$423$		0			0
$424$	1.81558	+	5.58779i	0.0881725	+	0.271367i
$425$	−5.79730	−	4.21198i	−0.281210	−	0.204311i
$426$		0			0
$427$	8.18710	−	25.1973i	0.396202	−	1.21938i
$428$	−0.171425			−0.00828615
$429$		0			0
$430$	−6.59251			−0.317919
$431$	3.65506	−	11.2491i	0.176058	−	0.541851i	−0.823622	−	0.567139i	$-0.808050\pi$
$431$	3.65506	−	11.2491i	0.176058	−	0.541851i	0.999680	+	0.0252880i	$0.00805028\pi$
$432$		0			0
$433$	−26.3685	−	19.1578i	−1.26719	−	0.920665i	−0.268100	−	0.963391i	$-0.586396\pi$
$433$	−26.3685	−	19.1578i	−1.26719	−	0.920665i	−0.999087	+	0.0427255i	$0.986396\pi$
$434$	−4.82519	−	14.8504i	−0.231617	−	0.712843i
$435$		0			0
$436$	1.88301	+	1.36809i	0.0901799	+	0.0655195i
$437$	15.4387	−	11.2169i	0.738534	−	0.536576i
$438$		0			0
$439$	5.09564			0.243202			0.121601	−	0.992579i	$-0.461197\pi$
$439$	5.09564			0.243202			0.121601	+	0.992579i	$0.461197\pi$
$440$	−0.605270	+	3.26093i	−0.0288551	+	0.155459i
$441$		0			0
$442$	2.68059	−	8.25000i	0.127503	−	0.392412i
$443$	19.9660	−	14.5061i	0.948612	−	0.689207i	−0.00186632	−	0.999998i	$-0.500594\pi$
$443$	19.9660	−	14.5061i	0.948612	−	0.689207i	0.950478	+	0.310791i	$0.100594\pi$
$444$		0			0
$445$	0.385378	+	1.18607i	0.0182687	+	0.0562252i
$446$	−4.51065	−	13.8824i	−0.213586	−	0.657349i
$447$		0			0
$448$	3.48828	−	2.53438i	0.164806	−	0.119738i
$449$	5.86154	−	18.0400i	0.276623	−	0.851359i	−0.712162	−	0.702015i	$-0.752284\pi$
$449$	5.86154	−	18.0400i	0.276623	−	0.851359i	0.988785	−	0.149344i	$-0.0477161\pi$
$450$		0			0
$451$	8.02271	+	4.35873i	0.377775	+	0.205245i
$452$	−4.30837			−0.202649
$453$		0			0
$454$	2.41871	−	1.75730i	0.113516	−	0.0824741i
$455$	−4.22271	−	3.06798i	−0.197964	−	0.143829i
$456$		0			0
$457$	−8.81134	−	27.1185i	−0.412177	−	1.26855i	−0.914752	−	0.404016i	$-0.867614\pi$
$457$	−8.81134	−	27.1185i	−0.412177	−	1.26855i	0.502575	−	0.864534i	$-0.332386\pi$
$458$	−1.27737	−	0.928065i	−0.0596877	−	0.0433656i
$459$		0			0
$460$	2.16864	−	6.67439i	0.101113	−	0.311195i
$461$	35.3117			1.64463			0.822315	−	0.569032i	$-0.192682\pi$
$461$	35.3117			1.64463			0.822315	+	0.569032i	$0.192682\pi$
$462$		0			0
$463$	3.89605			0.181065			0.0905323	−	0.995894i	$-0.471143\pi$
$463$	3.89605			0.181065			0.0905323	+	0.995894i	$0.471143\pi$
$464$	−3.26498	+	10.0486i	−0.151573	+	0.466493i
$465$		0			0
$466$	0.409135	+	0.297254i	0.0189528	+	0.0137700i
$467$	3.66272	+	11.2727i	0.169490	+	0.521638i	0.999339	−	0.0363506i	$-0.0115733\pi$
$467$	3.66272	+	11.2727i	0.169490	+	0.521638i	−0.829849	+	0.557989i	$0.811573\pi$
$468$		0			0
$469$	−5.69919	−	4.14070i	−0.263164	−	0.191200i
$470$	−4.64416	+	3.37418i	−0.214219	+	0.155639i
$471$		0			0
$472$	5.89750			0.271454
$473$	9.40784	+	19.7374i	0.432573	+	0.907527i
$474$		0			0
$475$	0.840293	−	2.58616i	0.0385553	−	0.118661i
$476$	24.9965	−	18.1610i	1.14571	−	0.832410i
$477$		0			0
$478$	5.17352	+	15.9224i	0.236631	+	0.728276i
$479$	−3.22158	−	9.91501i	−0.147198	−	0.453029i	0.850089	−	0.526639i	$-0.176548\pi$
$479$	−3.22158	−	9.91501i	−0.147198	−	0.453029i	−0.997287	+	0.0736102i	$0.976548\pi$
$480$		0			0
$481$	−2.07532	+	1.50781i	−0.0946263	+	0.0687500i
$482$	−4.72632	+	14.5461i	−0.215278	+	0.662557i
$483$		0			0
$484$	10.6267	−	2.84138i	0.483031	−	0.129154i
$485$	6.91327			0.313916
$486$		0			0
$487$	19.9030	−	14.4604i	0.901890	−	0.655261i	−0.0370611	−	0.999313i	$-0.511800\pi$
$487$	19.9030	−	14.4604i	0.901890	−	0.655261i	0.938951	+	0.344052i	$0.111800\pi$
$488$	4.97109	+	3.61171i	0.225031	+	0.163494i
$489$		0			0
$490$	−3.58188	−	11.0239i	−0.161813	−	0.498009i
$491$	−18.7305	−	13.6085i	−0.845296	−	0.614143i	0.0785493	−	0.996910i	$-0.474971\pi$
$491$	−18.7305	−	13.6085i	−0.845296	−	0.614143i	−0.923845	+	0.382767i	$0.874971\pi$
$492$		0			0
$493$	−23.3964	+	72.0066i	−1.05372	+	3.24301i
$494$	3.29176			0.148103
$495$		0			0
$496$	3.62142			0.162606
$497$	9.91108	−	30.5032i	0.444573	−	1.36825i
$498$		0			0
$499$	−18.3406	−	13.3253i	−0.821040	−	0.596520i	0.0959702	−	0.995384i	$-0.469405\pi$
$499$	−18.3406	−	13.3253i	−0.821040	−	0.596520i	−0.917010	+	0.398864i	$0.869405\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$		0			0
$502$	−0.345766	−	0.251213i	−0.0154323	−	0.0112122i
$503$	17.5238	−	12.7318i	0.781347	−	0.567682i	−0.124036	−	0.992278i	$-0.539584\pi$
$503$	17.5238	−	12.7318i	0.781347	−	0.567682i	0.905383	+	0.424596i	$0.139584\pi$
$504$		0			0
$505$	3.23607			0.144003
$506$	−23.0773	+	3.03197i	−1.02591	+	0.134787i
$507$		0			0
$508$	3.34855	−	10.3058i	0.148568	−	0.457245i
$509$	−12.4590	+	9.05200i	−0.552236	+	0.401223i	−0.828609	−	0.559828i	$-0.810867\pi$
$509$	−12.4590	+	9.05200i	−0.552236	+	0.401223i	0.276373	+	0.961050i	$0.410867\pi$
$510$		0			0
$511$	9.84937	+	30.3132i	0.435710	+	1.34098i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	14.4614	−	10.5068i	0.637864	−	0.463436i
$515$	−1.78495	+	5.49352i	−0.0786544	+	0.242073i
$516$		0			0
$517$	16.7295	+	9.08909i	0.735760	+	0.399738i
$518$	−9.13695			−0.401454
$519$		0			0
$520$	0.979348	−	0.711538i	0.0429473	−	0.0312030i
$521$	23.3132	+	16.9380i	1.02137	+	0.742069i	0.966563	−	0.256428i	$-0.0825458\pi$
$521$	23.3132	+	16.9380i	1.02137	+	0.742069i	0.0548065	+	0.998497i	$0.482546\pi$
$522$		0			0
$523$	11.0884	+	34.1267i	0.484863	+	1.49226i	0.832179	+	0.554507i	$0.187093\pi$
$523$	11.0884	+	34.1267i	0.484863	+	1.49226i	−0.347316	+	0.937748i	$0.612907\pi$
$524$	4.68031	+	3.40044i	0.204460	+	0.148549i
$525$		0			0
$526$	−4.48002	+	13.7881i	−0.195338	+	0.601190i
$527$	25.9505			1.13042
$528$		0			0
$529$	26.2505			1.14132
$530$	−1.81558	+	5.58779i	−0.0788639	+	0.242718i
$531$		0			0
$532$	9.48550	+	6.89162i	0.411248	+	0.298789i
$533$	−1.02979	−	3.16938i	−0.0446054	−	0.137281i
$534$		0			0
$535$	−0.138686	−	0.100761i	−0.00599591	−	0.00435629i
$536$	1.32178	−	0.960330i	0.0570922	−	0.0414799i
$537$		0			0
$538$	−27.9378			−1.20448
$539$	−27.8931	+	26.4555i	−1.20144	+	1.13952i
$540$		0			0
$541$	2.17819	−	6.70378i	0.0936477	−	0.288218i	−0.893251	−	0.449558i	$-0.851582\pi$
$541$	2.17819	−	6.70378i	0.0936477	−	0.288218i	0.986899	+	0.161340i	$0.0515816\pi$
$542$	−8.40531	+	6.10681i	−0.361039	+	0.262310i
$543$		0			0
$544$	2.21437	+	6.81513i	0.0949404	+	0.292196i
$545$	0.719246	+	2.21361i	0.0308091	+	0.0948207i
$546$		0			0
$547$	−12.2661	+	8.91181i	−0.524459	+	0.381041i	−0.818281	−	0.574819i	$-0.805073\pi$
$547$	−12.2661	+	8.91181i	−0.524459	+	0.381041i	0.293822	+	0.955860i	$0.405073\pi$
$548$	−2.67310	+	8.22695i	−0.114189	+	0.351438i
$549$		0			0
$550$	−2.40640	+	2.28238i	−0.102609	+	0.0973209i
$551$	−28.7307			−1.22397
$552$		0			0
$553$	24.4253	−	17.7460i	1.03867	−	0.754636i
$554$	0.508336	+	0.369328i	0.0215971	+	0.0156912i
$555$		0			0
$556$	3.93940	+	12.1242i	0.167068	+	0.514181i
$557$	−9.32902	−	6.77793i	−0.395283	−	0.287190i	0.372334	−	0.928099i	$-0.378558\pi$
$557$	−9.32902	−	6.77793i	−0.395283	−	0.287190i	−0.767617	+	0.640909i	$0.778558\pi$
$558$		0			0
$559$	2.46611	−	7.58991i	0.104305	−	0.321019i
$560$	4.31175			0.182205
$561$		0			0
$562$	−30.1066			−1.26997
$563$	10.5443	−	32.4519i	0.444388	−	1.36769i	−0.438766	−	0.898601i	$-0.644584\pi$
$563$	10.5443	−	32.4519i	0.444388	−	1.36769i	0.883154	−	0.469084i	$-0.155416\pi$
$564$		0			0
$565$	−3.48555	−	2.53240i	−0.146638	−	0.106539i
$566$	−4.97656	−	15.3163i	−0.209181	−	0.643792i
$567$		0			0
$568$	6.01787	+	4.37224i	0.252504	+	0.183455i
$569$	−6.45701	+	4.69129i	−0.270692	+	0.196669i	−0.714847	−	0.699281i	$-0.753504\pi$
$569$	−6.45701	+	4.69129i	−0.270692	+	0.196669i	0.444155	+	0.895950i	$0.353504\pi$
$570$		0			0
$571$	−3.62605			−0.151746			−0.0758728	−	0.997118i	$-0.524174\pi$
$571$	−3.62605			−0.151746			−0.0758728	+	0.997118i	$0.524174\pi$
$572$	−3.52786	−	1.91668i	−0.147507	−	0.0801406i
$573$		0			0
$574$	3.66796	−	11.2888i	0.153098	−	0.471187i
$575$	5.67757	−	4.12500i	0.236771	−	0.172024i
$576$		0			0
$577$	−1.13103	−	3.48094i	−0.0470852	−	0.144913i	0.924750	−	0.380576i	$-0.124274\pi$
$577$	−1.13103	−	3.48094i	−0.0470852	−	0.144913i	−0.971835	+	0.235662i	$0.924274\pi$
$578$	10.6146	+	32.6683i	0.441508	+	1.35882i
$579$		0			0
$580$	−8.54782	+	6.21036i	−0.354929	+	0.257871i
$581$	−2.12465	+	6.53900i	−0.0881453	+	0.271283i
$582$		0			0
$583$	19.3203	−	2.53836i	0.800165	−	0.105128i
$584$	−7.39217			−0.305890
$585$		0			0
$586$	−3.21992	+	2.33941i	−0.133014	+	0.0966402i
$587$	−14.4242	−	10.4798i	−0.595350	−	0.432547i	0.248875	−	0.968536i	$-0.419939\pi$
$587$	−14.4242	−	10.4798i	−0.595350	−	0.432547i	−0.844225	+	0.535988i	$0.819939\pi$
$588$		0			0
$589$	3.04305	+	9.36555i	0.125387	+	0.385901i
$590$	4.77117	+	3.46646i	0.196426	+	0.142712i
$591$		0			0
$592$	0.654831	−	2.01536i	0.0269134	−	0.0828309i
$593$	−23.0006			−0.944523			−0.472262	−	0.881458i	$-0.656562\pi$
$593$	−23.0006			−0.944523			−0.472262	+	0.881458i	$0.656562\pi$
$594$		0			0
$595$	30.8974			1.26667
$596$	−2.04339	+	6.28892i	−0.0837007	+	0.257604i
$597$		0			0
$598$	6.87293	+	4.99348i	0.281055	+	0.204199i
$599$	−1.03235	−	3.17725i	−0.0421807	−	0.129819i	0.927749	−	0.373206i	$-0.121742\pi$
$599$	−1.03235	−	3.17725i	−0.0421807	−	0.129819i	−0.969929	+	0.243387i	$0.921742\pi$
$600$		0			0
$601$	−28.2605	−	20.5324i	−1.15277	−	0.837535i	−0.163921	−	0.986473i	$-0.552414\pi$
$601$	−28.2605	−	20.5324i	−1.15277	−	0.837535i	−0.988846	+	0.148939i	$0.952414\pi$
$602$	22.9965	−	16.7079i	0.937268	−	0.680965i
$603$		0			0
$604$	20.8974			0.850303
$605$	10.2673	+	3.94749i	0.417425	+	0.160488i
$606$		0			0
$607$	3.89620	−	11.9913i	0.158142	−	0.486711i	−0.840324	−	0.542085i	$-0.817635\pi$
$607$	3.89620	−	11.9913i	0.158142	−	0.486711i	0.998466	+	0.0553739i	$0.0176351\pi$
$608$	−2.19992	+	1.59833i	−0.0892184	+	0.0648210i
$609$		0			0
$610$	1.89879	+	5.84387i	0.0768797	+	0.236611i
$611$	−2.14739	−	6.60899i	−0.0868742	−	0.267371i
$612$		0			0
$613$	−6.92760	+	5.03320i	−0.279803	+	0.203289i	−0.718832	−	0.695184i	$-0.755323\pi$
$613$	−6.92760	+	5.03320i	−0.279803	+	0.203289i	0.439028	+	0.898473i	$0.355323\pi$
$614$	5.44041	−	16.7439i	0.219557	−	0.675727i
$615$		0			0
$616$	−6.15309	−	12.9090i	−0.247915	−	0.520119i
$617$	−1.77165			−0.0713241			−0.0356620	−	0.999364i	$-0.511354\pi$
$617$	−1.77165			−0.0713241			−0.0356620	+	0.999364i	$0.511354\pi$
$618$		0			0
$619$	15.6706	−	11.3854i	0.629855	−	0.457616i	−0.226495	−	0.974012i	$-0.572727\pi$
$619$	15.6706	−	11.3854i	0.629855	−	0.457616i	0.856350	+	0.516396i	$0.172727\pi$
$620$	2.92979	+	2.12861i	0.117663	+	0.0854872i
$621$		0			0
$622$	6.99443	+	21.5266i	0.280451	+	0.863140i
$623$	−4.35027	−	3.16066i	−0.174290	−	0.126629i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−12.6096			−0.503982
$627$		0			0
$628$	−20.2291			−0.807231
$629$	4.69243	−	14.4418i	0.187099	−	0.575833i
$630$		0			0
$631$	−22.1727	−	16.1094i	−0.882680	−	0.641305i	0.0512788	−	0.998684i	$-0.483670\pi$
$631$	−22.1727	−	16.1094i	−0.882680	−	0.641305i	−0.933959	+	0.357379i	$0.883670\pi$
$632$	2.16376	+	6.65938i	0.0860699	+	0.264896i
$633$		0			0
$634$	21.2511	+	15.4399i	0.843991	+	0.613195i
$635$	8.76662	−	6.36932i	0.347893	−	0.252759i
$636$		0			0
$637$	14.0316			0.555954
$638$	30.7915	+	16.7290i	1.21905	+	0.662306i
$639$		0			0
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−19.3094	+	14.0291i	−0.762676	+	0.554117i	−0.899730	−	0.436447i	$-0.856237\pi$
$641$	−19.3094	+	14.0291i	−0.762676	+	0.554117i	0.137054	+	0.990564i	$0.456237\pi$
$642$		0			0
$643$	3.85766	+	11.8726i	0.152131	+	0.468211i	0.997859	−	0.0654032i	$-0.0208334\pi$
$643$	3.85766	+	11.8726i	0.152131	+	0.468211i	−0.845728	+	0.533614i	$0.820833\pi$
$644$	9.35064	+	28.7783i	0.368467	+	1.13402i
$645$		0			0
$646$	−15.7643	+	11.4534i	−0.620237	+	0.450629i
$647$	−2.18034	+	6.71040i	−0.0857180	+	0.263813i	−0.984724	−	0.174124i	$-0.944291\pi$
$647$	−2.18034	+	6.71040i	−0.0857180	+	0.263813i	0.899006	+	0.437937i	$0.144291\pi$
$648$		0			0
$649$	3.56958	−	19.2313i	0.140118	−	0.754895i
$650$	1.21054			0.0474813
$651$		0			0
$652$	6.53779	−	4.74999i	0.256040	−	0.186024i
$653$	2.16526	+	1.57315i	0.0847331	+	0.0615622i	0.629345	−	0.777126i	$-0.283323\pi$
$653$	2.16526	+	1.57315i	0.0847331	+	0.0615622i	−0.544612	+	0.838688i	$0.683323\pi$
$654$		0			0
$655$	1.78772	+	5.50203i	0.0698520	+	0.214982i
$656$	2.22713	+	1.61811i	0.0869550	+	0.0631765i
$657$		0			0
$658$	7.64866	−	23.5402i	0.298176	−	0.917691i
$659$	36.5069			1.42211			0.711053	−	0.703138i	$-0.248219\pi$
$659$	36.5069			1.42211			0.711053	+	0.703138i	$0.248219\pi$
$660$		0			0
$661$	40.3521			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$661$	40.3521			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$662$	3.93705	−	12.1170i	0.153018	−	0.470940i
$663$		0			0
$664$	−1.29006	−	0.937281i	−0.0500639	−	0.0363735i
$665$	3.62314	+	11.1509i	0.140499	+	0.432412i
$666$		0			0
$667$	−59.9875	−	43.5834i	−2.32272	−	1.68756i
$668$	13.9738	−	10.1525i	0.540662	−	0.392814i
$669$		0			0
$670$	1.63381			0.0631196
$671$	14.7864	−	14.0243i	0.570822	−	0.541402i
$672$		0			0
$673$	3.94257	−	12.1340i	0.151975	−	0.467731i	−0.845867	−	0.533394i	$-0.820916\pi$
$673$	3.94257	−	12.1340i	0.151975	−	0.467731i	0.997842	+	0.0656634i	$0.0209163\pi$
$674$	15.4174	−	11.2014i	0.593857	−	0.431462i
$675$		0			0
$676$	−3.56438	−	10.9700i	−0.137092	−	0.421925i
$677$	3.85703	+	11.8707i	0.148238	+	0.456228i	0.997413	−	0.0718823i	$-0.0229006\pi$
$677$	3.85703	+	11.8707i	0.148238	+	0.456228i	−0.849175	+	0.528111i	$0.822901\pi$
$678$		0			0
$679$	−24.1154	+	17.5209i	−0.925466	+	0.672390i
$680$	−2.21437	+	6.81513i	−0.0849173	+	0.261348i
$681$		0			0
$682$	2.19194	−	11.8092i	0.0839336	−	0.452197i
$683$	−5.10260			−0.195246			−0.0976228	−	0.995223i	$-0.531124\pi$
$683$	−5.10260			−0.195246			−0.0976228	+	0.995223i	$0.531124\pi$
$684$		0			0
$685$	−6.99826	+	5.08453i	−0.267390	+	0.194270i
$686$	16.0155	+	11.6359i	0.611473	+	0.444261i
$687$		0			0
$688$	2.03720	+	6.26985i	0.0776674	+	0.239036i
$689$	−5.75401	−	4.18054i	−0.219210	−	0.159266i
$690$		0			0
$691$	3.68372	−	11.3373i	0.140135	−	0.431292i	−0.856218	−	0.516615i	$-0.827192\pi$
$691$	3.68372	−	11.3373i	0.140135	−	0.431292i	0.996353	+	0.0853223i	$0.0271920\pi$
$692$	−14.3738			−0.546408
$693$		0			0
$694$	−18.8230			−0.714511
$695$	−3.93940	+	12.1242i	−0.149430	+	0.459898i
$696$		0			0
$697$	15.9593	+	11.5951i	0.604502	+	0.439197i
$698$	−8.41088	−	25.8860i	−0.318356	−	0.979800i
$699$		0			0
$700$	3.48828	+	2.53438i	0.131845	+	0.0957907i
$701$	−9.19138	+	6.67793i	−0.347154	+	0.252222i	−0.747674	−	0.664066i	$-0.768829\pi$
$701$	−9.19138	+	6.67793i	−0.347154	+	0.252222i	0.400520	+	0.916288i	$0.368829\pi$
$702$		0			0
$703$	5.76230			0.217329
$704$	3.28837	−	0.432036i	0.123935	−	0.0162830i
$705$		0			0
$706$	−7.92257	+	24.3832i	−0.298170	+	0.917673i
$707$	−11.2883	+	8.20144i	−0.424541	+	0.308447i
$708$		0			0
$709$	3.75791	+	11.5656i	0.141131	+	0.434357i	0.996493	−	0.0836737i	$-0.0266653\pi$
$709$	3.75791	+	11.5656i	0.141131	+	0.434357i	−0.855362	+	0.518031i	$0.826665\pi$
$710$	2.29862	+	7.07443i	0.0862657	+	0.265499i
$711$		0			0
$712$	1.00893	−	0.733033i	0.0378114	−	0.0274716i
$713$	−7.85355	+	24.1707i	−0.294118	+	0.905201i
$714$		0			0
$715$	−1.72750	−	3.62426i	−0.0646050	−	0.135539i
$716$	−18.8541			−0.704611
$717$		0			0
$718$	7.82857	−	5.68779i	0.292160	−	0.212267i
$719$	−27.9662	−	20.3186i	−1.04296	−	0.757756i	−0.0721003	−	0.997397i	$-0.522970\pi$
$719$	−27.9662	−	20.3186i	−1.04296	−	0.757756i	−0.970862	+	0.239641i	$0.922970\pi$
$720$		0			0
$721$	−7.69628	−	23.6867i	−0.286624	−	0.882139i
$722$	9.38921	+	6.82166i	0.349430	+	0.253876i
$723$		0			0
$724$	−4.04887	+	12.4611i	−0.150475	+	0.463114i
$725$	−10.5657			−0.392400
$726$		0			0
$727$	46.4273			1.72189			0.860947	−	0.508695i	$-0.169872\pi$
$727$	46.4273			1.72189			0.860947	+	0.508695i	$0.169872\pi$
$728$	−1.61293	+	4.96409i	−0.0597792	+	0.183981i
$729$		0			0
$730$	−5.98039	−	4.34501i	−0.221344	−	0.160816i
$731$	14.5983	+	44.9288i	0.539936	+	1.66175i
$732$		0			0
$733$	−11.8252	−	8.59151i	−0.436773	−	0.317334i	0.347578	−	0.937651i	$-0.387004\pi$
$733$	−11.8252	−	8.59151i	−0.436773	−	0.317334i	−0.784352	+	0.620317i	$0.787004\pi$
$734$	16.7495	−	12.1692i	0.618236	−	0.449174i
$735$		0			0
$736$	−7.01787			−0.258682
$737$	−2.33153	−	4.89149i	−0.0858830	−	0.180180i
$738$		0			0
$739$	−12.8330	+	39.4959i	−0.472070	+	1.45288i	0.377800	+	0.925887i	$0.376681\pi$
$739$	−12.8330	+	39.4959i	−0.472070	+	1.45288i	−0.849869	+	0.526994i	$0.823319\pi$
$740$	1.71437	−	1.24556i	0.0630215	−	0.0457878i
$741$		0			0
$742$	−7.82835	−	24.0932i	−0.287388	−	0.884488i
$743$	12.3655	+	38.0571i	0.453646	+	1.39618i	0.872717	+	0.488226i	$0.162356\pi$
$743$	12.3655	+	38.0571i	0.453646	+	1.39618i	−0.419071	+	0.907953i	$0.637644\pi$
$744$		0			0
$745$	−5.34967	+	3.88677i	−0.195997	+	0.142400i
$746$	−4.98947	+	15.3560i	−0.182677	+	0.562223i
$747$		0			0
$748$	23.5639	−	3.09590i	0.861583	−	0.113197i
$749$	0.739143			0.0270077
$750$		0			0
$751$	−11.5210	+	8.37050i	−0.420407	+	0.305444i	−0.777802	−	0.628510i	$-0.783665\pi$
$751$	−11.5210	+	8.37050i	−0.420407	+	0.305444i	0.357394	+	0.933954i	$0.383665\pi$
$752$	4.64416	+	3.37418i	0.169355	+	0.123044i
$753$		0			0
$754$	−3.95239	−	12.1642i	−0.143937	−	0.442994i
$755$	16.9064	+	12.2832i	0.615285	+	0.447031i
$756$		0			0
$757$	−9.20948	+	28.3439i	−0.334724	+	1.03017i	0.632134	+	0.774859i	$0.282179\pi$
$757$	−9.20948	+	28.3439i	−0.334724	+	1.03017i	−0.966858	+	0.255316i	$0.917821\pi$
$758$	−0.229700			−0.00834306
$759$		0			0
$760$	−2.71925			−0.0986374
$761$	4.10031	−	12.6195i	0.148636	−	0.457455i	−0.848825	−	0.528675i	$-0.822689\pi$
$761$	4.10031	−	12.6195i	0.148636	−	0.457455i	0.997461	+	0.0712199i	$0.0226892\pi$
$762$		0			0
$763$	−8.11908	−	5.89886i	−0.293930	−	0.213553i
$764$	3.48318	+	10.7201i	0.126017	+	0.387840i
$765$		0			0
$766$	10.5351	+	7.65417i	0.380647	+	0.276556i
$767$	−5.77570	+	4.19629i	−0.208548	+	0.151519i
$768$		0			0
$769$	−46.3160			−1.67020			−0.835099	−	0.550099i	$-0.814590\pi$
$769$	−46.3160			−1.67020			−0.835099	+	0.550099i	$0.814590\pi$
$770$	2.60978	−	14.0603i	0.0940498	−	0.506699i
$771$		0			0
$772$	2.14590	−	6.60440i	0.0772326	−	0.237697i
$773$	41.3802	−	30.0645i	1.48834	−	1.08134i	0.513596	−	0.858032i	$-0.328313\pi$
$773$	41.3802	−	30.0645i	1.48834	−	1.08134i	0.974747	−	0.223312i	$-0.0716868\pi$
$774$		0			0
$775$	1.11908	+	3.44417i	0.0401985	+	0.123718i
$776$	−2.13632	−	6.57491i	−0.0766894	−	0.236026i
$777$		0			0
$778$	23.9676	−	17.4135i	0.859280	−	0.624304i
$779$	−2.31323	+	7.11940i	−0.0828802	+	0.255079i
$780$		0			0
$781$	17.9000	−	16.9774i	0.640512	−	0.607501i
$782$	−50.2890			−1.79833
$783$		0			0
$784$	−9.37749	+	6.81315i	−0.334910	+	0.243327i
$785$	−16.3657	−	11.8904i	−0.584118	−	0.424386i
$786$		0			0
$787$	10.7231	+	33.0022i	0.382236	+	1.17640i	0.938465	+	0.345374i	$0.112248\pi$
$787$	10.7231	+	33.0022i	0.382236	+	1.17640i	−0.556229	+	0.831029i	$0.687752\pi$
$788$	−10.8723	−	7.89922i	−0.387311	−	0.281398i
$789$		0			0
$790$	−2.16376	+	6.65938i	−0.0769833	+	0.236930i
$791$	18.5766			0.660509
$792$		0			0
$793$	−7.43830			−0.264142
$794$	0.675711	−	2.07963i	0.0239801	−	0.0738032i
$795$		0			0
$796$	15.7295	+	11.4281i	0.557516	+	0.405059i
$797$	−13.8054	−	42.4885i	−0.489011	−	1.50502i	−0.826086	−	0.563544i	$-0.809438\pi$
$797$	−13.8054	−	42.4885i	−0.489011	−	1.50502i	0.337075	−	0.941478i	$-0.390562\pi$
$798$		0			0
$799$	33.2794	+	24.1789i	1.17734	+	0.855387i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$		0			0
$802$	13.0944			0.462378
$803$	−4.47426	+	24.1053i	−0.157893	+	0.850659i
$804$		0			0
$805$	−9.35064	+	28.7783i	−0.329567	+	1.01430i
$806$	−3.54663	+	2.57678i	−0.124925	+	0.0907630i
$807$		0			0
$808$	−1.00000	−	3.07768i	−0.0351799	−	0.108273i
$809$	4.04819	+	12.4590i	0.142327	+	0.438037i	0.996658	−	0.0816929i	$-0.0260327\pi$
$809$	4.04819	+	12.4590i	0.142327	+	0.438037i	−0.854331	+	0.519730i	$0.826033\pi$
$810$		0			0
$811$	6.33646	−	4.60371i	0.222503	−	0.161658i	−0.470949	−	0.882160i	$-0.656089\pi$
$811$	6.33646	−	4.60371i	0.222503	−	0.161658i	0.693453	+	0.720502i	$0.256089\pi$
$812$	14.0778	−	43.3269i	0.494033	−	1.52048i
$813$		0			0
$814$	−6.17561	−	3.35520i	−0.216455	−	0.117600i
$815$	8.08116			0.283071
$816$		0			0
$817$	−14.5030	+	10.5370i	−0.507394	+	0.368644i
$818$	−24.6173	−	17.8855i	−0.860725	−	0.625353i
$819$		0			0
$820$	0.850690	+	2.61815i	0.0297074	+	0.0914299i
$821$	−19.4432	−	14.1263i	−0.678573	−	0.493012i	0.194311	−	0.980940i	$-0.437753\pi$
$821$	−19.4432	−	14.1263i	−0.678573	−	0.493012i	−0.872884	+	0.487928i	$0.837753\pi$
$822$		0			0
$823$	3.73052	−	11.4813i	0.130038	−	0.400215i	−0.864748	−	0.502207i	$-0.832522\pi$
$823$	3.73052	−	11.4813i	0.130038	−	0.400215i	0.994785	+	0.101992i	$0.0325216\pi$
$824$	5.77623			0.201224
$825$		0			0
$826$	−25.4285			−0.884772
$827$	−10.8899	+	33.5158i	−0.378680	+	1.16546i	0.562282	+	0.826946i	$0.309924\pi$
$827$	−10.8899	+	33.5158i	−0.378680	+	1.16546i	−0.940962	+	0.338512i	$0.890076\pi$
$828$		0			0
$829$	−19.6457	−	14.2734i	−0.682322	−	0.495736i	0.191805	−	0.981433i	$-0.438566\pi$
$829$	−19.6457	−	14.2734i	−0.682322	−	0.495736i	−0.874127	+	0.485697i	$0.838566\pi$
$830$	−0.492758	−	1.51655i	−0.0171039	−	0.0526403i
$831$		0			0
$832$	−0.979348	−	0.711538i	−0.0339528	−	0.0246681i
$833$	−67.1977	+	48.8220i	−2.32826	+	1.69158i
$834$		0			0
$835$	17.2725			0.597741
$836$	3.88050	+	8.14119i	0.134210	+	0.281569i
$837$		0			0
$838$	−8.26538	+	25.4382i	−0.285523	+	0.878748i
$839$	12.3220	−	8.95243i	0.425401	−	0.309072i	−0.354406	−	0.935092i	$-0.615317\pi$
$839$	12.3220	−	8.95243i	0.425401	−	0.309072i	0.779807	+	0.626019i	$0.215317\pi$
$840$		0			0
$841$	25.5352	+	78.5894i	0.880525	+	2.70998i
$842$	−9.37640	−	28.8576i	−0.323132	−	0.994498i
$843$		0			0
$844$	1.90809	−	1.38631i	0.0656792	−	0.0477187i
$845$	3.56438	−	10.9700i	0.122619	−	0.377381i
$846$		0			0
$847$	−45.8197	+	12.2513i	−1.57438	+	0.420961i
$848$	5.87535			0.201760
$849$		0			0
$850$	−5.79730	+	4.21198i	−0.198846	+	0.144470i
$851$	12.0312	+	8.74120i	0.412425	+	0.299644i
$852$		0			0
$853$	−2.13420	−	6.56839i	−0.0730736	−	0.224897i	0.907849	−	0.419298i	$-0.137724\pi$
$853$	−2.13420	−	6.56839i	−0.0730736	−	0.224897i	−0.980922	+	0.194401i	$0.937724\pi$
$854$	−21.4341	−	15.5728i	−0.733460	−	0.532890i
$855$		0			0
$856$	−0.0529733	+	0.163035i	−0.00181059	+	0.00557242i
$857$	1.68576			0.0575845			0.0287922	−	0.999585i	$-0.490834\pi$
$857$	1.68576			0.0575845			0.0287922	+	0.999585i	$0.490834\pi$
$858$		0			0
$859$	−52.7330			−1.79923			−0.899613	−	0.436688i	$-0.856151\pi$
$859$	−52.7330			−1.79923			−0.899613	+	0.436688i	$0.856151\pi$
$860$	−2.03720	+	6.26985i	−0.0694678	+	0.213800i
$861$		0			0
$862$	−9.56907	−	6.95234i	−0.325924	−	0.236798i
$863$	−9.11412	−	28.0504i	−0.310248	−	0.954846i	−0.977666	−	0.210163i	$-0.932601\pi$
$863$	−9.11412	−	28.0504i	−0.310248	−	0.954846i	0.667418	−	0.744683i	$-0.267399\pi$
$864$		0			0
$865$	−11.6286	−	8.44868i	−0.395385	−	0.287264i
$866$	−26.3685	+	19.1578i	−0.896037	+	0.651009i
$867$		0			0
$868$	−15.6147			−0.529996
$869$	23.0254	−	3.02515i	0.781084	−	0.102621i
$870$		0			0
$871$	−0.611172	+	1.88099i	−0.0207088	+	0.0637351i
$872$	1.88301	−	1.36809i	0.0637668	−	0.0463293i
$873$		0			0
$874$	−5.89707	−	18.1493i	−0.199471	−	0.613909i
$875$	1.33240	+	4.10072i	0.0450435	+	0.138630i
$876$		0			0
$877$	22.6710	−	16.4715i	0.765547	−	0.556202i	−0.135060	−	0.990837i	$-0.543123\pi$
$877$	22.6710	−	16.4715i	0.765547	−	0.556202i	0.900607	+	0.434635i	$0.143123\pi$
$878$	1.57464	−	4.84624i	0.0531415	−	0.163553i
$879$		0			0
$880$	2.91429	+	1.58333i	0.0982406	+	0.0533740i
$881$	28.1345			0.947875			0.473937	−	0.880559i	$-0.342832\pi$
$881$	28.1345			0.947875			0.473937	+	0.880559i	$0.342832\pi$
$882$		0			0
$883$	−32.7842	+	23.8191i	−1.10328	+	0.801578i	−0.981592	−	0.190991i	$-0.938830\pi$
$883$	−32.7842	+	23.8191i	−1.10328	+	0.801578i	−0.121686	+	0.992569i	$0.538830\pi$
$884$	−7.01787	−	5.09878i	−0.236036	−	0.171490i
$885$		0			0
$886$	−7.62632	−	23.4714i	−0.256211	−	0.788537i
$887$	11.5317	+	8.37825i	0.387196	+	0.281314i	0.764305	−	0.644854i	$-0.223082\pi$
$887$	11.5317	+	8.37825i	0.387196	+	0.281314i	−0.377110	+	0.926169i	$0.623082\pi$
$888$		0			0
$889$	−14.4381	+	44.4360i	−0.484239	+	1.49033i
$890$	1.24711			0.0418032
$891$		0			0
$892$	−14.5968			−0.488737
$893$	−4.82370	+	14.8458i	−0.161419	+	0.496796i
$894$		0			0
$895$	−15.2533	−	11.0822i	−0.509861	−	0.370436i
$896$	−1.33240	−	4.10072i	−0.0445125	−	0.136995i
$897$		0			0
$898$	−15.3457	−	11.1493i	−0.512093	−	0.372057i
$899$	30.9552	−	22.4903i	1.03241	−	0.750093i
$900$		0			0
$901$	42.1019			1.40262
$902$	6.62455	−	6.28313i	0.220573	−	0.209205i
$903$		0			0
$904$	−1.33136	+	4.09750i	−0.0442804	+	0.136281i
$905$	−10.6001	+	7.70140i	−0.352358	+	0.256003i
$906$		0			0
$907$	−13.3997	−	41.2401i	−0.444931	−	1.36936i	−0.882560	−	0.470200i	$-0.844182\pi$
$907$	−13.3997	−	41.2401i	−0.444931	−	1.36936i	0.437629	−	0.899156i	$-0.355818\pi$
$908$	−0.923867	−	2.84337i	−0.0306596	−	0.0943605i
$909$		0			0
$910$	−4.22271	+	3.06798i	−0.139981	+	0.101702i
$911$	−7.33435	+	22.5728i	−0.242998	+	0.747871i	0.752961	+	0.658065i	$0.228625\pi$
$911$	−7.33435	+	22.5728i	−0.242998	+	0.747871i	−0.995959	+	0.0898061i	$0.971375\pi$
$912$		0			0
$913$	−3.83724	+	3.63947i	−0.126994	+	0.120449i
$914$	−28.5141			−0.943162
$915$		0			0
$916$	−1.27737	+	0.928065i	−0.0422055	+	0.0306641i
$917$	−20.1803	−	14.6619i	−0.666414	−	0.484178i
$918$		0			0
$919$	−4.34410	−	13.3698i	−0.143299	−	0.441028i	0.853490	−	0.521110i	$-0.174482\pi$
$919$	−4.34410	−	13.3698i	−0.143299	−	0.441028i	−0.996788	+	0.0800817i	$0.974482\pi$
$920$	−5.67757	−	4.12500i	−0.187184	−	0.135997i
$921$		0			0
$922$	10.9119	−	33.5834i	0.359365	−	1.10601i
$923$	−9.00460			−0.296390
$924$		0			0
$925$	2.11908			0.0696749
$926$	1.20394	−	3.70536i	0.0395641	−	0.121766i
$927$		0			0
$928$	8.54782	+	6.21036i	0.280596	+	0.203865i
$929$	17.2507	+	53.0922i	0.565977	+	1.74190i	0.665030	+	0.746816i	$0.268419\pi$
$929$	17.2507	+	53.0922i	0.565977	+	1.74190i	−0.0990531	+	0.995082i	$0.531581\pi$
$930$		0			0
$931$	−25.4997	−	18.5266i	−0.835719	−	0.607185i
$932$	0.409135	−	0.297254i	0.0134017	−	0.00973688i
$933$		0			0
$934$	11.8528			0.387836
$935$	20.8834	+	11.3459i	0.682959	+	0.371051i
$936$		0			0
$937$	−3.84000	+	11.8183i	−0.125447	+	0.386088i	−0.993982	−	0.109540i	$-0.965062\pi$
$937$	−3.84000	+	11.8183i	−0.125447	+	0.386088i	0.868535	+	0.495628i	$0.165062\pi$
$938$	−5.69919	+	4.14070i	−0.186085	+	0.135199i
$939$		0			0
$940$	1.77391	+	5.45954i	0.0578586	+	0.178070i
$941$	4.50996	+	13.8802i	0.147020	+	0.452483i	0.997265	−	0.0739049i	$-0.0235461\pi$
$941$	4.50996	+	13.8802i	0.147020	+	0.452483i	−0.850245	+	0.526387i	$0.823546\pi$
$942$		0			0
$943$	−15.6297	+	11.3557i	−0.508974	+	0.369791i
$944$	1.82243	−	5.60885i	0.0593149	−	0.182553i
$945$		0			0
$946$	21.6786	−	2.84820i	0.704831	−	0.0926029i
$947$	−38.1184			−1.23868			−0.619340	−	0.785123i	$-0.712600\pi$
$947$	−38.1184			−1.23868			−0.619340	+	0.785123i	$0.712600\pi$
$948$		0			0
$949$	7.23951	−	5.25981i	0.235004	−	0.170741i
$950$	−2.19992	−	1.59833i	−0.0713747	−	0.0518568i
$951$		0			0
$952$	−9.54782	−	29.3852i	−0.309447	−	0.952379i
$953$	0.381518	+	0.277189i	0.0123586	+	0.00897903i	0.593947	−	0.804504i	$-0.297569\pi$
$953$	0.381518	+	0.277189i	0.0123586	+	0.00897903i	−0.581589	+	0.813483i	$0.697569\pi$
$954$		0			0
$955$	−3.48318	+	10.7201i	−0.112713	+	0.346895i
$956$	16.7418			0.541470
$957$		0			0
$958$	−10.4253			−0.336825
$959$	11.5257	−	35.4726i	0.372185	−	1.14547i
$960$		0			0
$961$	14.4695	+	10.5127i	0.466760	+	0.339121i
$962$	0.792700	+	2.43968i	0.0255577	+	0.0786585i
$963$		0			0
$964$	12.3737	+	8.98999i	0.398529	+	0.289548i
$965$	5.61803	−	4.08174i	0.180851	−	0.131396i
$966$		0			0
$967$	−29.1678			−0.937975			−0.468987	−	0.883205i	$-0.655381\pi$
$967$	−29.1678			−0.937975			−0.468987	+	0.883205i	$0.655381\pi$
$968$	0.581513	−	10.9846i	0.0186906	−	0.353059i
$969$		0			0
$970$	2.13632	−	6.57491i	0.0685931	−	0.211108i
$971$	−12.8033	+	9.30216i	−0.410878	+	0.298520i	−0.773957	−	0.633238i	$-0.781725\pi$
$971$	−12.8033	+	9.30216i	−0.410878	+	0.298520i	0.363079	+	0.931758i	$0.381725\pi$
$972$		0			0
$973$	−16.9857	−	52.2766i	−0.544537	−	1.67591i
$974$	−7.60226	−	23.3973i	−0.243592	−	0.749699i
$975$		0			0
$976$	4.97109	−	3.61171i	0.159121	−	0.115608i
$977$	−12.9305	+	39.7961i	−0.413684	+	1.27319i	0.499738	+	0.866176i	$0.333429\pi$
$977$	−12.9305	+	39.7961i	−0.413684	+	1.27319i	−0.913423	+	0.407013i	$0.866571\pi$
$978$		0			0
$979$	−1.77969	−	3.73374i	−0.0568791	−	0.119331i
$980$	−11.5912			−0.370268
$981$		0			0
$982$	−18.7305	+	13.6085i	−0.597714	+	0.434265i
$983$	4.12492	+	2.99693i	0.131565	+	0.0955872i	0.651621	−	0.758545i	$-0.274089\pi$
$983$	4.12492	+	2.99693i	0.131565	+	0.0955872i	−0.520057	+	0.854132i	$0.674089\pi$
$984$		0			0
$985$	−4.15286	−	12.7812i	−0.132321	−	0.407243i
$986$	61.2524	+	44.5025i	1.95068	+	1.41725i
$987$		0			0
$988$	1.01721	−	3.13065i	0.0323617	−	0.0995992i
$989$	−46.2653			−1.47115
$990$		0			0
$991$	−14.8133			−0.470560			−0.235280	−	0.971928i	$-0.575601\pi$
$991$	−14.8133			−0.470560			−0.235280	+	0.971928i	$0.575601\pi$
$992$	1.11908	−	3.44417i	0.0355308	−	0.109353i
$993$		0			0
$994$	−25.9476	−	18.8520i	−0.823007	−	0.597949i
$995$	6.00812	+	18.4911i	0.190470	+	0.586207i
$996$		0			0
$997$	46.9861	+	34.1374i	1.48807	+	1.08114i	0.974844	+	0.222886i	$0.0715478\pi$
$997$	46.9861	+	34.1374i	1.48807	+	1.08114i	0.513221	+	0.858257i	$0.328452\pi$
$998$	−18.3406	+	13.3253i	−0.580563	+	0.421804i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.j.361.2		8
3.2	odd	2		110.2.g.c.31.2	✓	8
11.5	even	5	inner	990.2.n.j.181.2		8
12.11	even	2		880.2.bo.g.801.1		8
15.2	even	4		550.2.ba.f.449.1		16
15.8	even	4		550.2.ba.f.449.4		16
15.14	odd	2		550.2.h.l.251.1		8
33.5	odd	10		110.2.g.c.71.2	yes	8
33.26	odd	10		1210.2.a.u.1.2		4
33.29	even	10		1210.2.a.v.1.2		4
132.59	even	10		9680.2.a.cj.1.3		4
132.71	even	10		880.2.bo.g.401.1		8
132.95	odd	10		9680.2.a.ci.1.3		4
165.29	even	10		6050.2.a.cy.1.3		4
165.38	even	20		550.2.ba.f.49.1		16
165.59	odd	10		6050.2.a.dh.1.3		4
165.104	odd	10		550.2.h.l.401.1		8
165.137	even	20		550.2.ba.f.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.2	✓	8	3.2	odd	2
110.2.g.c.71.2	yes	8	33.5	odd	10
550.2.h.l.251.1		8	15.14	odd	2
550.2.h.l.401.1		8	165.104	odd	10
550.2.ba.f.49.1		16	165.38	even	20
550.2.ba.f.49.4		16	165.137	even	20
550.2.ba.f.449.1		16	15.2	even	4
550.2.ba.f.449.4		16	15.8	even	4
880.2.bo.g.401.1		8	132.71	even	10
880.2.bo.g.801.1		8	12.11	even	2
990.2.n.j.181.2		8	11.5	even	5	inner
990.2.n.j.361.2		8	1.1	even	1	trivial
1210.2.a.u.1.2		4	33.26	odd	10
1210.2.a.v.1.2		4	33.29	even	10
6050.2.a.cy.1.3		4	165.29	even	10
6050.2.a.dh.1.3		4	165.59	odd	10
9680.2.a.ci.1.3		4	132.95	odd	10
9680.2.a.cj.1.3		4	132.59	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(3.48828 + 2.53438i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(3.48828 + 2.53438i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000 q^{10} +(1.42705 + 2.99391i) q^{11} +(0.374078 - 1.15129i) q^{13} +(3.48828 - 2.53438i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.21437 + 6.81513i) q^{17} +(-2.19992 + 1.59833i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(3.28837 - 0.432036i) q^{22} -7.01787 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.979348 - 0.711538i) q^{26} +(-1.33240 - 4.10072i) q^{28} +(8.54782 + 6.21036i) q^{29} +(1.11908 - 3.44417i) q^{31} +1.00000 q^{32} +7.16586 q^{34} +(1.33240 - 4.10072i) q^{35} +(-1.71437 - 1.24556i) q^{37} +(0.840293 + 2.58616i) q^{38} +(0.809017 + 0.587785i) q^{40} +(2.22713 - 1.61811i) q^{41} +6.59251 q^{43} +(0.605270 - 3.26093i) q^{44} +(-2.16864 + 6.67439i) q^{46} +(4.64416 - 3.37418i) q^{47} +(3.58188 + 11.0239i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.979348 + 0.711538i) q^{52} +(1.81558 - 5.58779i) q^{53} +(2.40640 - 2.28238i) q^{55} -4.31175 q^{56} +(8.54782 - 6.21036i) q^{58} +(-4.77117 - 3.46646i) q^{59} +(-1.89879 - 5.84387i) q^{61} +(-2.92979 - 2.12861i) q^{62} +(0.309017 - 0.951057i) q^{64} -1.21054 q^{65} -1.63381 q^{67} +(2.21437 - 6.81513i) q^{68} +(-3.48828 - 2.53438i) q^{70} +(-2.29862 - 7.07443i) q^{71} +(5.98039 + 4.34501i) q^{73} +(-1.71437 + 1.24556i) q^{74} +2.71925 q^{76} +(-2.60978 + 14.0603i) q^{77} +(2.16376 - 6.65938i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.850690 - 2.61815i) q^{82} +(0.492758 + 1.51655i) q^{83} +(5.79730 - 4.21198i) q^{85} +(2.03720 - 6.26985i) q^{86} +(-2.91429 - 1.58333i) q^{88} -1.24711 q^{89} +(4.22271 - 3.06798i) q^{91} +(5.67757 + 4.12500i) q^{92} +(-1.77391 - 5.45954i) q^{94} +(2.19992 + 1.59833i) q^{95} +(-2.13632 + 6.57491i) q^{97} +11.5912 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - q^{7} - 2 q^{8} - 8 q^{10} - 2 q^{11} + q^{13} - q^{14} - 2 q^{16} + 12 q^{17} - 7 q^{19} + 2 q^{20} + 8 q^{22} - 26 q^{23} - 2 q^{25} + 6 q^{26} + 4 q^{28} + 22 q^{29} - 26 q^{31} + 8 q^{32} + 2 q^{34} - 4 q^{35} - 8 q^{37} + 3 q^{38} + 2 q^{40} + 15 q^{41} + 38 q^{43} - 7 q^{44} - 6 q^{46} - 6 q^{47} + 27 q^{49} - 2 q^{50} + 6 q^{52} + 4 q^{53} - 8 q^{55} - 6 q^{56} + 22 q^{58} - 39 q^{59} - 20 q^{61} + 14 q^{62} - 2 q^{64} + 14 q^{65} - 26 q^{67} + 12 q^{68} + q^{70} - 2 q^{71} + 8 q^{73} - 8 q^{74} + 8 q^{76} - 16 q^{77} + 14 q^{79} + 2 q^{80} - 15 q^{82} + 21 q^{83} + 13 q^{85} - 17 q^{86} - 7 q^{88} - 32 q^{89} + 53 q^{91} + 19 q^{92} + 9 q^{94} + 7 q^{95} - 31 q^{97} + 22 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - q^7 - 2 * q^8 - 8 * q^10 - 2 * q^11 + q^13 - q^14 - 2 * q^16 + 12 * q^17 - 7 * q^19 + 2 * q^20 + 8 * q^22 - 26 * q^23 - 2 * q^25 + 6 * q^26 + 4 * q^28 + 22 * q^29 - 26 * q^31 + 8 * q^32 + 2 * q^34 - 4 * q^35 - 8 * q^37 + 3 * q^38 + 2 * q^40 + 15 * q^41 + 38 * q^43 - 7 * q^44 - 6 * q^46 - 6 * q^47 + 27 * q^49 - 2 * q^50 + 6 * q^52 + 4 * q^53 - 8 * q^55 - 6 * q^56 + 22 * q^58 - 39 * q^59 - 20 * q^61 + 14 * q^62 - 2 * q^64 + 14 * q^65 - 26 * q^67 + 12 * q^68 + q^70 - 2 * q^71 + 8 * q^73 - 8 * q^74 + 8 * q^76 - 16 * q^77 + 14 * q^79 + 2 * q^80 - 15 * q^82 + 21 * q^83 + 13 * q^85 - 17 * q^86 - 7 * q^88 - 32 * q^89 + 53 * q^91 + 19 * q^92 + 9 * q^94 + 7 * q^95 - 31 * q^97 + 22 * q^98

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