LMFDB - Embedded newform 693.2.m.f.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.1
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.f.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.449894 - 1.38463i) q^{2} +(-0.0967635 + 0.0703028i) q^{4} +(-0.737640 + 2.27022i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-2.21480 - 1.60914i) q^{8} +O(q^{10})$	\(q+(-0.449894 - 1.38463i) q^{2} +(-0.0967635 + 0.0703028i) q^{4} +(-0.737640 + 2.27022i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-2.21480 - 1.60914i) q^{8} +3.47528 q^{10} +(3.30902 - 0.224514i) q^{11} +(-0.281754 - 0.867148i) q^{13} +(-1.17784 - 0.855749i) q^{14} +(-1.30557 + 4.01813i) q^{16} +(0.675706 - 2.07961i) q^{17} +(-0.575493 - 0.418120i) q^{19} +(-0.0882264 - 0.271533i) q^{20} +(-1.79958 - 4.48076i) q^{22} +7.80466 q^{23} +(-0.564716 - 0.410290i) q^{25} +(-1.07392 + 0.780249i) q^{26} +(-0.0369604 + 0.113752i) q^{28} +(7.17390 - 5.21214i) q^{29} +(-2.04763 - 6.30195i) q^{31} +0.675706 q^{32} -3.18348 q^{34} +(0.737640 + 2.27022i) q^{35} +(3.40233 - 2.47194i) q^{37} +(-0.320031 + 0.984955i) q^{38} +(5.28684 - 3.84112i) q^{40} +(-9.67390 - 7.02850i) q^{41} +7.51601 q^{43} +(-0.304408 + 0.254358i) q^{44} +(-3.51127 - 10.8066i) q^{46} +(5.07392 + 3.68642i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.314038 + 0.966510i) q^{50} +(0.0882264 + 0.0641003i) q^{52} +(2.02884 + 6.24411i) q^{53} +(-1.93117 + 7.67782i) q^{55} -2.73764 q^{56} +(-10.4444 - 7.58829i) q^{58} +(-7.78527 + 5.65633i) q^{59} +(-0.0193938 + 0.0596881i) q^{61} +(-7.80466 + 5.67042i) q^{62} +(2.30714 + 7.10065i) q^{64} +2.17645 q^{65} -11.3294 q^{67} +(0.0808187 + 0.248734i) q^{68} +(2.81156 - 2.04272i) q^{70} +(1.84466 - 5.67728i) q^{71} +(3.54920 - 2.57865i) q^{73} +(-4.95341 - 3.59886i) q^{74} +0.0850818 q^{76} +(2.54508 - 2.12663i) q^{77} +(-1.50097 - 4.61952i) q^{79} +(-8.15900 - 5.92786i) q^{80} +(-5.37965 + 16.5568i) q^{82} +(-3.10530 + 9.55713i) q^{83} +(4.22275 + 3.06801i) q^{85} +(-3.38141 - 10.4069i) q^{86} +(-7.69008 - 4.82743i) q^{88} +0.261535 q^{89} +(-0.737640 - 0.535927i) q^{91} +(-0.755207 + 0.548690i) q^{92} +(2.82160 - 8.68400i) q^{94} +(1.37373 - 0.998076i) q^{95} +(3.05453 + 9.40087i) q^{97} -1.45589 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.449894	−	1.38463i	−0.318123	−	0.979082i	−0.974450	−	0.224605i	$-0.927891\pi$
$2$	−0.449894	−	1.38463i	−0.318123	−	0.979082i	0.656327	−	0.754477i	$-0.272109\pi$
$3$		0			0
$3$		0			0
$4$	−0.0967635	+	0.0703028i	−0.0483818	+	0.0351514i
$5$	−0.737640	+	2.27022i	−0.329883	+	1.01527i	0.639305	+	0.768953i	$0.279222\pi$
$5$	−0.737640	+	2.27022i	−0.329883	+	1.01527i	−0.969188	+	0.246322i	$0.920778\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−2.21480	−	1.60914i	−0.783049	−	0.568919i
$9$		0			0
$10$	3.47528			1.09898
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	−0.281754	−	0.867148i	−0.0781444	−	0.240504i	0.904351	−	0.426789i	$-0.140355\pi$
$13$	−0.281754	−	0.867148i	−0.0781444	−	0.240504i	−0.982496	+	0.186285i	$0.940355\pi$
$14$	−1.17784	−	0.855749i	−0.314790	−	0.228708i
$15$		0			0
$16$	−1.30557	+	4.01813i	−0.326392	+	1.00453i
$17$	0.675706	−	2.07961i	0.163883	−	0.504379i	−0.835070	−	0.550144i	$-0.814573\pi$
$17$	0.675706	−	2.07961i	0.163883	−	0.504379i	0.998952	+	0.0457654i	$0.0145727\pi$
$18$		0			0
$19$	−0.575493	−	0.418120i	−0.132027	−	0.0959234i	0.519812	−	0.854281i	$-0.326002\pi$
$19$	−0.575493	−	0.418120i	−0.132027	−	0.0959234i	−0.651839	+	0.758358i	$0.726002\pi$
$20$	−0.0882264	−	0.271533i	−0.0197280	−	0.0607166i
$21$		0			0
$22$	−1.79958	−	4.48076i	−0.383671	−	0.955301i
$23$	7.80466			1.62738			0.813692	−	0.581296i	$-0.197454\pi$
$23$	7.80466			1.62738			0.813692	+	0.581296i	$0.197454\pi$
$24$		0			0
$25$	−0.564716	−	0.410290i	−0.112943	−	0.0820581i
$26$	−1.07392	+	0.780249i	−0.210613	+	0.153019i
$27$		0			0
$28$	−0.0369604	+	0.113752i	−0.00698486	+	0.0214972i
$29$	7.17390	−	5.21214i	1.33216	−	0.967870i	0.332465	−	0.943115i	$-0.392120\pi$
$29$	7.17390	−	5.21214i	1.33216	−	0.967870i	0.999694	−	0.0247547i	$-0.00788049\pi$
$30$		0			0
$31$	−2.04763	−	6.30195i	−0.367765	−	1.13186i	−0.948231	−	0.317580i	$-0.897130\pi$
$31$	−2.04763	−	6.30195i	−0.367765	−	1.13186i	0.580466	−	0.814284i	$-0.302870\pi$
$32$	0.675706			0.119449
$33$		0			0
$34$	−3.18348			−0.545963
$35$	0.737640	+	2.27022i	0.124684	+	0.383738i
$36$		0			0
$37$	3.40233	−	2.47194i	0.559340	−	0.406384i	−0.271877	−	0.962332i	$-0.587645\pi$
$37$	3.40233	−	2.47194i	0.559340	−	0.406384i	0.831217	+	0.555948i	$0.187645\pi$
$38$	−0.320031	+	0.984955i	−0.0519159	+	0.159781i
$39$		0			0
$40$	5.28684	−	3.84112i	0.835923	−	0.607334i
$41$	−9.67390	−	7.02850i	−1.51081	−	1.09767i	−0.965817	−	0.259225i	$-0.916533\pi$
$41$	−9.67390	−	7.02850i	−1.51081	−	1.09767i	−0.544992	−	0.838441i	$-0.683467\pi$
$42$		0			0
$43$	7.51601			1.14618			0.573091	−	0.819492i	$-0.305744\pi$
$43$	7.51601			1.14618			0.573091	+	0.819492i	$0.305744\pi$
$44$	−0.304408	+	0.254358i	−0.0458913	+	0.0383459i
$45$		0			0
$46$	−3.51127	−	10.8066i	−0.517708	−	1.59334i
$47$	5.07392	+	3.68642i	0.740107	+	0.537720i	0.892745	−	0.450563i	$-0.148777\pi$
$47$	5.07392	+	3.68642i	0.740107	+	0.537720i	−0.152637	+	0.988282i	$0.548777\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.314038	+	0.966510i	−0.0444117	+	0.136685i
$51$		0			0
$52$	0.0882264	+	0.0641003i	0.0122348	+	0.00888911i
$53$	2.02884	+	6.24411i	0.278682	+	0.857695i	0.988222	+	0.153030i	$0.0489030\pi$
$53$	2.02884	+	6.24411i	0.278682	+	0.857695i	−0.709540	+	0.704666i	$0.751097\pi$
$54$		0			0
$55$	−1.93117	+	7.67782i	−0.260399	+	1.03528i
$56$	−2.73764			−0.365833
$57$		0			0
$58$	−10.4444	−	7.58829i	−1.37141	−	0.996391i
$59$	−7.78527	+	5.65633i	−1.01356	+	0.736391i	−0.964952	−	0.262427i	$-0.915477\pi$
$59$	−7.78527	+	5.65633i	−1.01356	+	0.736391i	−0.0486038	+	0.998818i	$0.515477\pi$
$60$		0			0
$61$	−0.0193938	+	0.0596881i	−0.00248313	+	0.00764227i	−0.952290	−	0.305193i	$-0.901279\pi$
$61$	−0.0193938	+	0.0596881i	−0.00248313	+	0.00764227i	0.949807	+	0.312836i	$0.101279\pi$
$62$	−7.80466	+	5.67042i	−0.991193	+	0.720144i
$63$		0			0
$64$	2.30714	+	7.10065i	0.288393	+	0.887581i
$65$	2.17645			0.269956
$66$		0			0
$67$	−11.3294			−1.38410			−0.692052	−	0.721847i	$-0.743293\pi$
$67$	−11.3294			−1.38410			−0.692052	+	0.721847i	$0.743293\pi$
$68$	0.0808187	+	0.248734i	0.00980070	+	0.0301635i
$69$		0			0
$70$	2.81156	−	2.04272i	0.336046	−	0.244152i
$71$	1.84466	−	5.67728i	0.218921	−	0.673769i	−0.779931	−	0.625865i	$-0.784746\pi$
$71$	1.84466	−	5.67728i	0.218921	−	0.673769i	0.998852	−	0.0479037i	$-0.0152541\pi$
$72$		0			0
$73$	3.54920	−	2.57865i	0.415403	−	0.301808i	−0.360383	−	0.932805i	$-0.617354\pi$
$73$	3.54920	−	2.57865i	0.415403	−	0.301808i	0.775785	+	0.630997i	$0.217354\pi$
$74$	−4.95341	−	3.59886i	−0.575822	−	0.418359i
$75$		0			0
$76$	0.0850818			0.00975955
$77$	2.54508	−	2.12663i	0.290039	−	0.242352i
$78$		0			0
$79$	−1.50097	−	4.61952i	−0.168873	−	0.519736i	0.830428	−	0.557126i	$-0.188096\pi$
$79$	−1.50097	−	4.61952i	−0.168873	−	0.519736i	−0.999301	+	0.0373894i	$0.988096\pi$
$80$	−8.15900	−	5.92786i	−0.912204	−	0.662755i
$81$		0			0
$82$	−5.37965	+	16.5568i	−0.594083	+	1.82840i
$83$	−3.10530	+	9.55713i	−0.340851	+	1.04903i	0.622917	+	0.782288i	$0.285948\pi$
$83$	−3.10530	+	9.55713i	−0.340851	+	1.04903i	−0.963768	+	0.266743i	$0.914052\pi$
$84$		0			0
$85$	4.22275	+	3.06801i	0.458021	+	0.332772i
$86$	−3.38141	−	10.4069i	−0.364626	−	1.12220i
$87$		0			0
$88$	−7.69008	−	4.82743i	−0.819765	−	0.514606i
$89$	0.261535			0.0277226			0.0138613	−	0.999904i	$-0.495588\pi$
$89$	0.261535			0.0277226			0.0138613	+	0.999904i	$0.495588\pi$
$90$		0			0
$91$	−0.737640	−	0.535927i	−0.0773257	−	0.0561804i
$92$	−0.755207	+	0.548690i	−0.0787358	+	0.0572049i
$93$		0			0
$94$	2.82160	−	8.68400i	0.291026	−	0.895687i
$95$	1.37373	−	0.998076i	0.140942	−	0.102400i
$96$		0			0
$97$	3.05453	+	9.40087i	0.310140	+	0.954513i	0.977709	+	0.209965i	$0.0673351\pi$
$97$	3.05453	+	9.40087i	0.310140	+	0.954513i	−0.667569	+	0.744548i	$0.732665\pi$
$98$	−1.45589			−0.147067
$99$		0			0
$100$	0.0834885			0.00834885
$101$	−3.07392	−	9.46056i	−0.305867	−	0.941360i	−0.979352	−	0.202160i	$-0.935204\pi$
$101$	−3.07392	−	9.46056i	−0.305867	−	0.941360i	0.673486	−	0.739200i	$-0.264796\pi$
$102$		0			0
$103$	0.532952	−	0.387212i	0.0525133	−	0.0381532i	−0.561219	−	0.827667i	$-0.689667\pi$
$103$	0.532952	−	0.387212i	0.0525133	−	0.0381532i	0.613732	+	0.789514i	$0.289667\pi$
$104$	−0.771340	+	2.37394i	−0.0756361	+	0.232784i
$105$		0			0
$106$	7.73303	−	5.61838i	0.751098	−	0.545705i
$107$	0.229023	+	0.166395i	0.0221405	+	0.0160860i	0.598800	−	0.800898i	$-0.295644\pi$
$107$	0.229023	+	0.166395i	0.0221405	+	0.0160860i	−0.576660	+	0.816984i	$0.695644\pi$
$108$		0			0
$109$	−8.97962			−0.860092			−0.430046	−	0.902807i	$-0.641503\pi$
$109$	−8.97962			−0.860092			−0.430046	+	0.902807i	$0.641503\pi$
$110$	11.4998	−	0.780249i	1.09646	−	0.0743938i
$111$		0			0
$112$	1.30557	+	4.01813i	0.123365	+	0.379677i
$113$	1.07549	+	0.781391i	0.101174	+	0.0735071i	0.637222	−	0.770680i	$-0.280083\pi$
$113$	1.07549	+	0.781391i	0.101174	+	0.0735071i	−0.536048	+	0.844187i	$0.680083\pi$
$114$		0			0
$115$	−5.75703	+	17.7183i	−0.536846	+	1.65224i
$116$	−0.327743	+	1.00869i	−0.0304302	+	0.0936545i
$117$		0			0
$118$	11.3345	+	8.23498i	1.04342	+	0.758091i
$119$	−0.675706	−	2.07961i	−0.0619418	−	0.190637i
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$	0.0913711			0.00827235
$123$		0			0
$124$	0.641181	+	0.465845i	0.0575798	+	0.0418341i
$125$	−8.30783	+	6.03599i	−0.743075	+	0.539875i
$126$		0			0
$127$	−6.74805	+	20.7684i	−0.598793	+	1.84290i	−0.0639336	+	0.997954i	$0.520365\pi$
$127$	−6.74805	+	20.7684i	−0.598793	+	1.84290i	−0.534859	+	0.844941i	$0.679635\pi$
$128$	9.88712	−	7.18341i	0.873906	−	0.634930i
$129$		0			0
$130$	−0.979173	−	3.01358i	−0.0858791	−	0.264309i
$131$	9.22227			0.805754			0.402877	−	0.915254i	$-0.368010\pi$
$131$	9.22227			0.805754			0.402877	+	0.915254i	$0.368010\pi$
$132$		0			0
$133$	−0.711349			−0.0616817
$134$	5.09702	+	15.6870i	0.440315	+	1.35515i
$135$		0			0
$136$	−4.84294	+	3.51860i	−0.415279	+	0.301718i
$137$	0.632711	−	1.94728i	0.0540561	−	0.166368i	−0.920384	−	0.391017i	$-0.872124\pi$
$137$	0.632711	−	1.94728i	0.0540561	−	0.166368i	0.974440	+	0.224649i	$0.0721235\pi$
$138$		0			0
$139$	10.3921	−	7.55033i	0.881450	−	0.640411i	−0.0521847	−	0.998637i	$-0.516618\pi$
$139$	10.3921	−	7.55033i	0.881450	−	0.640411i	0.933635	+	0.358227i	$0.116618\pi$
$140$	−0.230980	−	0.167817i	−0.0195214	−	0.0141831i
$141$		0			0
$142$	−8.69084			−0.729319
$143$	−1.12701	−	2.80615i	−0.0942457	−	0.234662i
$144$		0			0
$145$	6.54097	+	20.1310i	0.543198	+	1.67179i
$146$	−5.16724	−	3.75422i	−0.427643	−	0.310701i
$147$		0			0
$148$	−0.155437	+	0.478387i	−0.0127769	+	0.0393232i
$149$	−4.74190	+	14.5941i	−0.388472	+	1.19559i	0.545458	+	0.838138i	$0.316356\pi$
$149$	−4.74190	+	14.5941i	−0.388472	+	1.19559i	−0.933930	+	0.357456i	$0.883644\pi$
$150$		0			0
$151$	5.58979	+	4.06122i	0.454890	+	0.330497i	0.791524	−	0.611139i	$-0.209288\pi$
$151$	5.58979	+	4.06122i	0.454890	+	0.330497i	−0.336633	+	0.941636i	$0.609288\pi$
$152$	0.601785	+	1.85210i	0.0488112	+	0.150225i
$153$		0			0
$154$	−4.08961	−	2.56725i	−0.329550	−	0.206875i
$155$	15.8173			1.27047
$156$		0			0
$157$	7.55429	+	5.48851i	0.602898	+	0.438031i	0.846906	−	0.531742i	$-0.178462\pi$
$157$	7.55429	+	5.48851i	0.602898	+	0.438031i	−0.244008	+	0.969773i	$0.578462\pi$
$158$	−5.72105	+	4.15658i	−0.455142	+	0.330680i
$159$		0			0
$160$	−0.498428	+	1.53400i	−0.0394042	+	0.121274i
$161$	6.31411	−	4.58747i	0.497621	−	0.361543i
$162$		0			0
$163$	3.22333	+	9.92040i	0.252471	+	0.777026i	0.994317	+	0.106456i	$0.0339504\pi$
$163$	3.22333	+	9.92040i	0.252471	+	0.777026i	−0.741846	+	0.670570i	$0.766050\pi$
$164$	1.43020			0.111680
$165$		0			0
$166$	14.6302			1.13552
$167$	−0.417609	−	1.28527i	−0.0323156	−	0.0994571i	0.933598	−	0.358323i	$-0.116651\pi$
$167$	−0.417609	−	1.28527i	−0.0323156	−	0.0994571i	−0.965913	+	0.258866i	$0.916651\pi$
$168$		0			0
$169$	9.84466	−	7.15256i	0.757282	−	0.550197i
$170$	2.34827	−	7.22722i	0.180104	−	0.554303i
$171$		0			0
$172$	−0.727276	+	0.528397i	−0.0554543	+	0.0402899i
$173$	15.7641	+	11.4533i	1.19852	+	0.870776i	0.994138	−	0.108116i	$-0.0344817\pi$
$173$	15.7641	+	11.4533i	1.19852	+	0.870776i	0.204381	+	0.978891i	$0.434482\pi$
$174$		0			0
$175$	−0.698028			−0.0527659
$176$	−3.41802	+	13.5892i	−0.257643	+	1.02432i
$177$		0			0
$178$	−0.117663	−	0.362129i	−0.00881920	−	0.0271427i
$179$	−10.3992	−	7.55545i	−0.777272	−	0.564721i	0.126887	−	0.991917i	$-0.459501\pi$
$179$	−10.3992	−	7.55545i	−0.777272	−	0.564721i	−0.904159	+	0.427196i	$0.859501\pi$
$180$		0			0
$181$	4.44209	−	13.6714i	0.330178	−	1.01618i	−0.638871	−	0.769314i	$-0.720598\pi$
$181$	4.44209	−	13.6714i	0.330178	−	1.01618i	0.969049	−	0.246869i	$-0.0794019\pi$
$182$	−0.410201	+	1.26247i	−0.0304061	+	0.0935805i
$183$		0			0
$184$	−17.2857	−	12.5588i	−1.27432	−	0.925849i
$185$	3.10216	+	9.54745i	0.228075	+	0.701943i
$186$		0			0
$187$	1.76902	−	7.03316i	0.129364	−	0.514316i
$188$	−0.750136			−0.0547093
$189$		0			0
$190$	−2.00000	−	1.45309i	−0.145095	−	0.105418i
$191$	−19.3776	+	14.0786i	−1.40211	+	1.01870i	−0.407703	+	0.913115i	$0.633670\pi$
$191$	−19.3776	+	14.0786i	−1.40211	+	1.01870i	−0.994411	+	0.105581i	$0.966330\pi$
$192$		0			0
$193$	0.0431415	−	0.132776i	0.00310539	−	0.00955741i	−0.949492	−	0.313792i	$-0.898401\pi$
$193$	0.0431415	−	0.132776i	0.00310539	−	0.00955741i	0.952597	+	0.304234i	$0.0984006\pi$
$194$	11.6425	−	8.45878i	0.835884	−	0.607305i
$195$		0			0
$196$	0.0369604	+	0.113752i	0.00264003	+	0.00812517i
$197$	−14.6113			−1.04101			−0.520505	−	0.853859i	$-0.674256\pi$
$197$	−14.6113			−1.04101			−0.520505	+	0.853859i	$0.674256\pi$
$198$		0			0
$199$	−26.4702			−1.87642			−0.938210	−	0.346066i	$-0.887517\pi$
$199$	−26.4702			−1.87642			−0.938210	+	0.346066i	$0.887517\pi$
$200$	0.590516	+	1.81742i	0.0417558	+	0.128511i
$201$		0			0
$202$	−11.7164	+	8.51249i	−0.824366	+	0.598937i
$203$	2.74018	−	8.43342i	0.192323	−	0.591910i
$204$		0			0
$205$	23.0921	−	16.7774i	1.61282	−	1.17178i
$206$	−0.775918	−	0.563737i	−0.0540608	−	0.0392775i
$207$		0			0
$208$	3.85216			0.267099
$209$	−1.99819	−	1.25436i	−0.138218	−	0.0867659i
$210$		0			0
$211$	5.42690	+	16.7023i	0.373603	+	1.14983i	0.944416	+	0.328753i	$0.106628\pi$
$211$	5.42690	+	16.7023i	0.373603	+	1.14983i	−0.570812	+	0.821080i	$0.693372\pi$
$212$	−0.635296	−	0.461570i	−0.0436323	−	0.0317007i
$213$		0			0
$214$	0.127360	−	0.391973i	0.00870613	−	0.0267947i
$215$	−5.54411	+	17.0630i	−0.378105	+	1.16369i
$216$		0			0
$217$	−5.36076	−	3.89482i	−0.363912	−	0.264398i
$218$	4.03988	+	12.4335i	0.273615	+	0.842100i
$219$		0			0
$220$	−0.352906	−	0.878699i	−0.0237929	−	0.0592419i
$221$	−1.99371			−0.134111
$222$		0			0
$223$	−18.2707	−	13.2745i	−1.22350	−	0.888924i	−0.227113	−	0.973868i	$-0.572929\pi$
$223$	−18.2707	−	13.2745i	−1.22350	−	0.888924i	−0.996386	+	0.0849449i	$0.972929\pi$
$224$	0.546657	−	0.397170i	0.0365251	−	0.0265370i
$225$		0			0
$226$	0.598081	−	1.84070i	0.0397838	−	0.122442i
$227$	17.7752	−	12.9145i	1.17978	−	0.857163i	0.187636	−	0.982239i	$-0.439917\pi$
$227$	17.7752	−	12.9145i	1.17978	−	0.857163i	0.992147	+	0.125076i	$0.0399174\pi$
$228$		0			0
$229$	7.22491	+	22.2360i	0.477435	+	1.46939i	0.842645	+	0.538469i	$0.180997\pi$
$229$	7.22491	+	22.2360i	0.477435	+	1.46939i	−0.365210	+	0.930925i	$0.619003\pi$
$230$	27.1234			1.78846
$231$		0			0
$232$	−24.2758			−1.59379
$233$	0.322351	+	0.992094i	0.0211179	+	0.0649942i	0.961060	−	0.276339i	$-0.0891214\pi$
$233$	0.322351	+	0.992094i	0.0211179	+	0.0649942i	−0.939942	+	0.341334i	$0.889121\pi$
$234$		0			0
$235$	−12.1117	+	8.79968i	−0.790082	+	0.574028i
$236$	0.355674	−	1.09465i	0.0231524	−	0.0712558i
$237$		0			0
$238$	−2.57549	+	1.87121i	−0.166944	+	0.121292i
$239$	−10.0431	−	7.29676i	−0.649636	−	0.471988i	0.213511	−	0.976941i	$-0.431510\pi$
$239$	−10.0431	−	7.29676i	−0.649636	−	0.471988i	−0.863147	+	0.504952i	$0.831510\pi$
$240$		0			0
$241$	9.42435			0.607076			0.303538	−	0.952819i	$-0.401832\pi$
$241$	9.42435			0.607076			0.303538	+	0.952819i	$0.401832\pi$
$242$	−6.96082	−	14.4229i	−0.447458	−	0.927138i
$243$		0			0
$244$	−0.00231962	−	0.00713907i	−0.000148499	−	0.000457032i
$245$	1.93117	+	1.40308i	0.123378	+	0.0896392i
$246$		0			0
$247$	−0.200425	+	0.616845i	−0.0127527	+	0.0392489i
$248$	−5.60567	+	17.2525i	−0.355961	+	1.09553i
$249$		0			0
$250$	12.0953	+	8.78772i	0.764971	+	0.555784i
$251$	0.949360	+	2.92183i	0.0599231	+	0.184424i	0.976537	−	0.215349i	$-0.0690889\pi$
$251$	0.949360	+	2.92183i	0.0599231	+	0.184424i	−0.916614	+	0.399773i	$0.869089\pi$
$252$		0			0
$253$	25.8258	−	1.75226i	1.62365	−	0.110163i
$254$	31.7924			1.99483
$255$		0			0
$256$	−2.31418	−	1.68135i	−0.144637	−	0.105085i
$257$	0.506660	−	0.368110i	0.0316046	−	0.0229621i	−0.571871	−	0.820344i	$-0.693782\pi$
$257$	0.506660	−	0.368110i	0.0316046	−	0.0229621i	0.603475	+	0.797382i	$0.293782\pi$
$258$		0			0
$259$	1.29958	−	3.99968i	0.0807517	−	0.248528i
$260$	−0.210601	+	0.153011i	−0.0130609	+	0.00948933i
$261$		0			0
$262$	−4.14904	−	12.7694i	−0.256329	−	0.788899i
$263$	−1.02517			−0.0632149			−0.0316074	−	0.999500i	$-0.510063\pi$
$263$	−1.02517			−0.0632149			−0.0316074	+	0.999500i	$0.510063\pi$
$264$		0			0
$265$	−15.6721			−0.962729
$266$	0.320031	+	0.984955i	0.0196224	+	0.0603915i
$267$		0			0
$268$	1.09627	−	0.796488i	0.0669654	−	0.0486532i
$269$	−9.89057	+	30.4400i	−0.603039	+	1.85596i	−0.0932899	+	0.995639i	$0.529738\pi$
$269$	−9.89057	+	30.4400i	−0.603039	+	1.85596i	−0.509749	+	0.860323i	$0.670262\pi$
$270$		0			0
$271$	−4.81798	+	3.50047i	−0.292672	+	0.212638i	−0.724426	−	0.689353i	$-0.757895\pi$
$271$	−4.81798	+	3.50047i	−0.292672	+	0.212638i	0.431754	+	0.901991i	$0.357895\pi$
$272$	7.47395	+	5.43014i	0.453175	+	0.329251i
$273$		0			0
$274$	−2.98092			−0.180084
$275$	−1.96077	−	1.23087i	−0.118239	−	0.0742243i
$276$		0			0
$277$	−0.394833	−	1.21517i	−0.0237232	−	0.0730126i	0.938494	−	0.345296i	$-0.112221\pi$
$277$	−0.394833	−	1.21517i	−0.0237232	−	0.0730126i	−0.962217	+	0.272283i	$0.912221\pi$
$278$	−15.1298	−	10.9924i	−0.907424	−	0.659282i
$279$		0			0
$280$	2.01939	−	6.21506i	0.120682	−	0.371421i
$281$	1.37516	−	4.23230i	0.0820351	−	0.252478i	−0.901624	−	0.432522i	$-0.857624\pi$
$281$	1.37516	−	4.23230i	0.0820351	−	0.252478i	0.983659	+	0.180044i	$0.0576239\pi$
$282$		0			0
$283$	−18.4427	−	13.3994i	−1.09630	−	0.796512i	−0.115852	−	0.993266i	$-0.536960\pi$
$283$	−18.4427	−	13.3994i	−1.09630	−	0.796512i	−0.980453	+	0.196755i	$0.936960\pi$
$284$	0.220633	+	0.679039i	0.0130922	+	0.0402935i
$285$		0			0
$286$	−3.37845	+	2.82297i	−0.199772	+	0.166926i
$287$	−11.9576			−0.705834
$288$		0			0
$289$	9.88510	+	7.18194i	0.581476	+	0.422467i
$290$	24.9313	−	18.1137i	1.46402	−	1.06367i
$291$		0			0
$292$	−0.162147	+	0.499038i	−0.00948895	+	0.0292040i
$293$	−6.79036	+	4.93348i	−0.396697	+	0.288217i	−0.768194	−	0.640217i	$-0.778844\pi$
$293$	−6.79036	+	4.93348i	−0.396697	+	0.288217i	0.371497	+	0.928434i	$0.378844\pi$
$294$		0			0
$295$	−7.09840	−	21.8466i	−0.413285	−	1.27196i
$296$	−11.5132			−0.669190
$297$		0			0
$298$	22.3408			1.29417
$299$	−2.19899	−	6.76780i	−0.127171	−	0.391392i
$300$		0			0
$301$	6.08058	−	4.41780i	0.350479	−	0.254638i
$302$	3.10848	−	9.56690i	0.178873	−	0.550514i
$303$		0			0
$304$	2.43140	−	1.76652i	0.139451	−	0.101317i
$305$	−0.121200	−	0.0880567i	−0.00693987	−	0.00504211i
$306$		0			0
$307$	11.0560			0.630999			0.315500	−	0.948926i	$-0.397828\pi$
$307$	11.0560			0.630999			0.315500	+	0.948926i	$0.397828\pi$
$308$	−0.0967635	+	0.384707i	−0.00551361	+	0.0219207i
$309$		0			0
$310$	−7.11609	−	21.9011i	−0.404166	−	1.24390i
$311$	−18.2768	−	13.2789i	−1.03638	−	0.752976i	−0.0668061	−	0.997766i	$-0.521281\pi$
$311$	−18.2768	−	13.2789i	−1.03638	−	0.752976i	−0.969576	+	0.244790i	$0.921281\pi$
$312$		0			0
$313$	0.787589	−	2.42395i	0.0445172	−	0.137010i	−0.926328	−	0.376719i	$-0.877052\pi$
$313$	0.787589	−	2.42395i	0.0445172	−	0.137010i	0.970845	+	0.239709i	$0.0770522\pi$
$314$	4.20093	−	12.9291i	0.237072	−	0.729634i
$315$		0			0
$316$	0.470004	+	0.341478i	0.0264398	+	0.0192096i
$317$	−9.68566	−	29.8094i	−0.544001	−	1.67426i	−0.723354	−	0.690477i	$-0.757401\pi$
$317$	−9.68566	−	29.8094i	−0.544001	−	1.67426i	0.179353	−	0.983785i	$-0.442599\pi$
$318$		0			0
$319$	22.5683	−	18.8577i	1.26358	−	1.05583i
$320$	−17.8219			−0.996274
$321$		0			0
$322$	−9.19262	−	6.67883i	−0.512285	−	0.372197i
$323$	−1.25839	+	0.914274i	−0.0700187	+	0.0508716i
$324$		0			0
$325$	−0.196672	+	0.605293i	−0.0109094	+	0.0335756i
$326$	12.2859	−	8.92626i	0.680455	−	0.494380i
$327$		0			0
$328$	10.1159	+	31.1334i	0.558555	+	1.71905i
$329$	6.27171			0.345771
$330$		0			0
$331$	−4.82789			−0.265365			−0.132682	−	0.991159i	$-0.542359\pi$
$331$	−4.82789			−0.265365			−0.132682	+	0.991159i	$0.542359\pi$
$332$	−0.371414	−	1.14309i	−0.0203840	−	0.0627354i
$333$		0			0
$334$	−1.59174	+	1.15647i	−0.0870963	+	0.0632791i
$335$	8.35701	−	25.7202i	0.456592	−	1.40525i
$336$		0			0
$337$	−17.0827	+	12.4113i	−0.930551	+	0.676085i	−0.946128	−	0.323794i	$-0.895042\pi$
$337$	−17.0827	+	12.4113i	−0.930551	+	0.676085i	0.0155765	+	0.999879i	$0.495042\pi$
$338$	−14.3327	−	10.4133i	−0.779597	−	0.566410i
$339$		0			0
$340$	−0.624297			−0.0338573
$341$	−8.19052	−	20.3936i	−0.443541	−	1.10437i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−16.6464	−	12.0943i	−0.897516	−	0.652084i
$345$		0			0
$346$	8.76639	−	26.9802i	0.471284	−	1.45046i
$347$	3.83957	−	11.8170i	0.206119	−	0.634369i	−0.793547	−	0.608510i	$-0.791768\pi$
$347$	3.83957	−	11.8170i	0.206119	−	0.634369i	0.999666	−	0.0258596i	$-0.00823228\pi$
$348$		0			0
$349$	−13.7276	−	9.97368i	−0.734821	−	0.533879i	0.156264	−	0.987715i	$-0.450055\pi$
$349$	−13.7276	−	9.97368i	−0.734821	−	0.533879i	−0.891085	+	0.453836i	$0.850055\pi$
$350$	0.314038	+	0.966510i	0.0167861	+	0.0516622i
$351$		0			0
$352$	2.23592	−	0.151705i	0.119175	−	0.00808592i
$353$	4.57101			0.243291			0.121645	−	0.992574i	$-0.461183\pi$
$353$	4.57101			0.243291			0.121645	+	0.992574i	$0.461183\pi$
$354$		0			0
$355$	11.5280	+	8.37558i	0.611843	+	0.444530i
$356$	−0.0253070	+	0.0183866i	−0.00134127	+	0.000974489i
$357$		0			0
$358$	−5.78298	+	17.7982i	−0.305640	+	0.940663i
$359$	−25.0580	+	18.2057i	−1.32251	+	0.960858i	−0.322611	+	0.946532i	$0.604560\pi$
$359$	−25.0580	+	18.2057i	−1.32251	+	0.960858i	−0.999897	+	0.0143267i	$0.995440\pi$
$360$		0			0
$361$	−5.71496	−	17.5888i	−0.300787	−	0.925728i
$362$	−20.9282			−1.09996
$363$		0			0
$364$	0.109054			0.00571598
$365$	3.23607	+	9.95959i	0.169384	+	0.521309i
$366$		0			0
$367$	−11.9267	+	8.66525i	−0.622568	+	0.452322i	−0.853818	−	0.520572i	$-0.825719\pi$
$367$	−11.9267	+	8.66525i	−0.622568	+	0.452322i	0.231250	+	0.972894i	$0.425719\pi$
$368$	−10.1895	+	31.3601i	−0.531165	+	1.63476i
$369$		0			0
$370$	11.8241	−	8.59068i	0.614703	−	0.446608i
$371$	5.31156	+	3.85908i	0.275763	+	0.200353i
$372$		0			0
$373$	−12.5701			−0.650853			−0.325427	−	0.945567i	$-0.605508\pi$
$373$	−12.5701			−0.650853			−0.325427	+	0.945567i	$0.605508\pi$
$374$	−10.5342	+	0.714737i	−0.544711	+	0.0369582i
$375$		0			0
$376$	−5.30573	−	16.3293i	−0.273622	−	0.842122i
$377$	−6.54097	−	4.75229i	−0.336877	−	0.244755i
$378$		0			0
$379$	4.95477	−	15.2492i	0.254509	−	0.783299i	−0.739417	−	0.673248i	$-0.764899\pi$
$379$	4.95477	−	15.2492i	0.254509	−	0.783299i	0.993926	−	0.110051i	$-0.0351014\pi$
$380$	−0.0627598	+	0.193155i	−0.00321951	+	0.00990862i
$381$		0			0
$382$	28.2116	+	20.4969i	1.44343	+	1.04871i
$383$	0.868408	+	2.67268i	0.0443736	+	0.136568i	0.970789	−	0.239936i	$-0.0771263\pi$
$383$	0.868408	+	2.67268i	0.0443736	+	0.136568i	−0.926415	+	0.376503i	$0.877126\pi$
$384$		0			0
$385$	2.95056	+	7.34660i	0.150375	+	0.374417i
$386$	−0.203254			−0.0103454
$387$		0			0
$388$	−0.956474	−	0.694919i	−0.0485576	−	0.0352792i
$389$	−16.6698	+	12.1113i	−0.845191	+	0.614067i	−0.923816	−	0.382837i	$-0.874947\pi$
$389$	−16.6698	+	12.1113i	−0.845191	+	0.614067i	0.0786246	+	0.996904i	$0.474947\pi$
$390$		0			0
$391$	5.27365	−	16.2306i	0.266700	−	0.820819i
$392$	−2.21480	+	1.60914i	−0.111864	+	0.0812741i
$393$		0			0
$394$	6.57352	+	20.2312i	0.331169	+	1.01923i
$395$	11.5945			0.583383
$396$		0			0
$397$	28.6588			1.43834			0.719171	−	0.694833i	$-0.244522\pi$
$397$	28.6588			1.43834			0.719171	+	0.694833i	$0.244522\pi$
$398$	11.9088	+	36.6514i	0.596932	+	1.83717i
$399$		0			0
$400$	2.38587	−	1.73344i	0.119294	−	0.0866719i
$401$	6.89590	−	21.2234i	0.344365	−	1.05985i	−0.617558	−	0.786525i	$-0.711878\pi$
$401$	6.89590	−	21.2234i	0.344365	−	1.05985i	0.961923	−	0.273320i	$-0.0881219\pi$
$402$		0			0
$403$	−4.88780	+	3.55120i	−0.243479	+	0.176898i
$404$	0.962547	+	0.699332i	0.0478885	+	0.0347930i
$405$		0			0
$406$	−12.9100			−0.640711
$407$	10.7034	−	8.94356i	0.530547	−	0.443316i
$408$		0			0
$409$	5.07901	+	15.6316i	0.251141	+	0.772932i	0.994566	+	0.104112i	$0.0332002\pi$
$409$	5.07901	+	15.6316i	0.251141	+	0.772932i	−0.743425	+	0.668820i	$0.766800\pi$
$410$	−33.6195	−	24.4260i	−1.66035	−	1.20631i
$411$		0			0
$412$	−0.0243482	+	0.0749361i	−0.00119955	+	0.00369184i
$413$	−2.97371	+	9.15213i	−0.146327	+	0.450347i
$414$		0			0
$415$	−19.4062	−	14.0995i	−0.952614	−	0.692115i
$416$	−0.190382	−	0.585937i	−0.00933427	−	0.0287279i
$417$		0			0
$418$	−0.837853	+	3.33108i	−0.0409807	+	0.162929i
$419$	12.7725			0.623975			0.311988	−	0.950086i	$-0.399005\pi$
$419$	12.7725			0.623975			0.311988	+	0.950086i	$0.399005\pi$
$420$		0			0
$421$	−8.73995	−	6.34994i	−0.425959	−	0.309477i	0.354072	−	0.935218i	$-0.384797\pi$
$421$	−8.73995	−	6.34994i	−0.425959	−	0.309477i	−0.780031	+	0.625741i	$0.784797\pi$
$422$	20.6850	−	15.0285i	1.00693	−	0.731577i
$423$		0			0
$424$	5.55422	−	17.0941i	0.269737	−	0.830165i
$425$	−1.23482	+	0.897153i	−0.0598978	+	0.0435183i
$426$		0			0
$427$	0.0193938	+	0.0596881i	0.000938533	+	0.00288851i
$428$	−0.0338592			−0.00163664
$429$		0			0
$430$	26.1202			1.25963
$431$	−8.51018	−	26.1916i	−0.409921	−	1.26161i	−0.916716	−	0.399540i	$-0.869170\pi$
$431$	−8.51018	−	26.1916i	−0.409921	−	1.26161i	0.506795	−	0.862067i	$-0.330830\pi$
$432$		0			0
$433$	−12.3456	+	8.96963i	−0.593293	+	0.431053i	−0.843492	−	0.537142i	$-0.819504\pi$
$433$	−12.3456	+	8.96963i	−0.593293	+	0.431053i	0.250199	+	0.968194i	$0.419504\pi$
$434$	−2.98112	+	9.17493i	−0.143098	+	0.440411i
$435$		0			0
$436$	0.868900	−	0.631293i	0.0416128	−	0.0302334i
$437$	−4.49153	−	3.26329i	−0.214859	−	0.156104i
$438$		0			0
$439$	−28.5500			−1.36262			−0.681308	−	0.731997i	$-0.738589\pi$
$439$	−28.5500			−1.36262			−0.681308	+	0.731997i	$0.738589\pi$
$440$	16.6319	−	13.8973i	0.792893	−	0.662527i
$441$		0			0
$442$	0.896958	+	2.76055i	0.0426639	+	0.131306i
$443$	9.16700	+	6.66021i	0.435537	+	0.316436i	0.783859	−	0.620939i	$-0.213248\pi$
$443$	9.16700	+	6.66021i	0.435537	+	0.316436i	−0.348322	+	0.937375i	$0.613248\pi$
$444$		0			0
$445$	−0.192919	+	0.593742i	−0.00914521	+	0.0281461i
$446$	−10.1603	+	31.2703i	−0.481106	+	1.48069i
$447$		0			0
$448$	6.04017	+	4.38844i	0.285371	+	0.207334i
$449$	8.31156	+	25.5804i	0.392247	+	1.20721i	0.931085	+	0.364802i	$0.118863\pi$
$449$	8.31156	+	25.5804i	0.392247	+	1.20721i	−0.538838	+	0.842409i	$0.681137\pi$
$450$		0			0
$451$	−33.5891	−	21.0855i	−1.58165	−	0.992877i
$452$	−0.159003			−0.00747885
$453$		0			0
$454$	−25.8787	−	18.8020i	−1.21455	−	0.882421i
$455$	1.76079	−	1.27929i	0.0825470	−	0.0599739i
$456$		0			0
$457$	−8.95205	+	27.5516i	−0.418759	+	1.28881i	0.490086	+	0.871674i	$0.336966\pi$
$457$	−8.95205	+	27.5516i	−0.418759	+	1.28881i	−0.908845	+	0.417134i	$0.863034\pi$
$458$	27.5382	−	20.0077i	1.28677	−	0.934896i
$459$		0			0
$460$	−0.688578	−	2.11922i	−0.0321051	−	0.0988093i
$461$	41.9375			1.95322			0.976612	−	0.215008i	$-0.0689778\pi$
$461$	41.9375			1.95322			0.976612	+	0.215008i	$0.0689778\pi$
$462$		0			0
$463$	−1.14904			−0.0534005			−0.0267003	−	0.999643i	$-0.508500\pi$
$463$	−1.14904			−0.0534005			−0.0267003	+	0.999643i	$0.508500\pi$
$464$	11.5770	+	35.6304i	0.537450	+	1.65410i
$465$		0			0
$466$	1.22866	−	0.892674i	0.0569166	−	0.0413523i
$467$	−9.14340	+	28.1405i	−0.423106	+	1.30219i	0.481690	+	0.876342i	$0.340023\pi$
$467$	−9.14340	+	28.1405i	−0.423106	+	1.30219i	−0.904796	+	0.425845i	$0.859977\pi$
$468$		0			0
$469$	−9.16566	+	6.65924i	−0.423231	+	0.307495i
$470$	17.6333	+	12.8113i	0.813363	+	0.590943i
$471$		0			0
$472$	26.3446			1.21261
$473$	24.8706	−	1.68745i	1.14355	−	0.0775890i
$474$		0			0
$475$	0.153440	+	0.472239i	0.00704029	+	0.0216678i
$476$	0.211586	+	0.153726i	0.00969803	+	0.00704603i
$477$		0			0
$478$	−5.58498	+	17.1888i	−0.255451	+	0.786197i
$479$	3.14358	−	9.67494i	0.143634	−	0.442059i	−0.853199	−	0.521586i	$-0.825341\pi$
$479$	3.14358	−	9.67494i	0.143634	−	0.442059i	0.996833	+	0.0795262i	$0.0253407\pi$
$480$		0			0
$481$	−3.10216	−	2.25385i	−0.141446	−	0.102767i
$482$	−4.23995	−	13.0492i	−0.193125	−	0.594377i
$483$		0			0
$484$	−0.950185	+	0.910019i	−0.0431902	+	0.0413645i
$485$	−23.5952			−1.07140
$486$		0			0
$487$	−35.4609	−	25.7638i	−1.60689	−	1.16747i	−0.872324	−	0.488929i	$-0.837388\pi$
$487$	−35.4609	−	25.7638i	−1.60689	−	1.16747i	−0.734562	−	0.678542i	$-0.762612\pi$
$488$	0.139000	−	0.100990i	0.00629224	−	0.00457158i
$489$		0			0
$490$	1.07392	−	3.30519i	0.0485148	−	0.149313i
$491$	15.4690	−	11.2389i	0.698106	−	0.507204i	−0.181209	−	0.983445i	$-0.558001\pi$
$491$	15.4690	−	11.2389i	0.698106	−	0.507204i	0.879315	+	0.476241i	$0.158001\pi$
$492$		0			0
$493$	−5.99177	−	18.4408i	−0.269856	−	0.830530i
$494$	0.944272			0.0424848
$495$		0			0
$496$	27.9954			1.25703
$497$	−1.84466	−	5.67728i	−0.0827443	−	0.254661i
$498$		0			0
$499$	−16.5825	+	12.0479i	−0.742335	+	0.539338i	−0.893441	−	0.449180i	$-0.851716\pi$
$499$	−16.5825	+	12.0479i	−0.742335	+	0.539338i	0.151107	+	0.988517i	$0.451716\pi$
$500$	0.379548	−	1.16813i	0.0169739	−	0.0522403i
$501$		0			0
$502$	3.61854	−	2.62903i	0.161504	−	0.117339i
$503$	15.3547	+	11.1558i	0.684632	+	0.497414i	0.874891	−	0.484320i	$-0.160933\pi$
$503$	15.3547	+	11.1558i	0.684632	+	0.497414i	−0.190259	+	0.981734i	$0.560933\pi$
$504$		0			0
$505$	23.7450			1.05664
$506$	−14.0451	−	34.9708i	−0.624380	−	1.55464i
$507$		0			0
$508$	−0.807110	−	2.48403i	−0.0358097	−	0.110211i
$509$	19.0562	+	13.8451i	0.844652	+	0.613675i	0.923666	−	0.383198i	$-0.125177\pi$
$509$	19.0562	+	13.8451i	0.844652	+	0.613675i	−0.0790145	+	0.996873i	$0.525177\pi$
$510$		0			0
$511$	1.35567	−	4.17234i	0.0599715	−	0.184573i
$512$	6.26617	−	19.2853i	0.276928	−	0.852298i
$513$		0			0
$514$	−0.737640	−	0.535927i	−0.0325359	−	0.0236387i
$515$	0.485932	+	1.49554i	0.0214127	+	0.0659015i
$516$		0			0
$517$	17.6173	+	11.0593i	0.774810	+	0.486386i
$518$	−6.12275			−0.269018
$519$		0			0
$520$	−4.82040	−	3.50223i	−0.211389	−	0.153583i
$521$	−4.11827	+	2.99210i	−0.180425	+	0.131086i	−0.674332	−	0.738428i	$-0.735568\pi$
$521$	−4.11827	+	2.99210i	−0.180425	+	0.131086i	0.493907	+	0.869515i	$0.335568\pi$
$522$		0			0
$523$	7.03841	−	21.6620i	0.307768	−	0.947213i	−0.670861	−	0.741583i	$-0.734075\pi$
$523$	7.03841	−	21.6620i	0.307768	−	0.947213i	0.978630	−	0.205631i	$-0.0659245\pi$
$524$	−0.892380	+	0.648352i	−0.0389838	+	0.0283234i
$525$		0			0
$526$	0.461219	+	1.41949i	0.0201101	+	0.0618925i
$527$	−14.4892			−0.631159
$528$		0			0
$529$	37.9128			1.64838
$530$	7.05077	+	21.7001i	0.306266	+	0.942590i
$531$		0			0
$532$	0.0688326	−	0.0500098i	0.00298427	−	0.00216820i
$533$	−3.36909	+	10.3690i	−0.145932	+	0.449131i
$534$		0			0
$535$	−0.546691	+	0.397194i	−0.0236355	+	0.0171722i
$536$	25.0923	+	18.2306i	1.08382	+	0.787443i
$537$		0			0
$538$	46.5979			2.00898
$539$	0.809017	−	3.21644i	0.0348468	−	0.138542i
$540$		0			0
$541$	−3.53564	−	10.8816i	−0.152009	−	0.467836i	0.845836	−	0.533442i	$-0.179102\pi$
$541$	−3.53564	−	10.8816i	−0.152009	−	0.467836i	−0.997846	+	0.0656062i	$0.979102\pi$
$542$	7.01444	+	5.09629i	0.301296	+	0.218904i
$543$		0			0
$544$	0.456578	−	1.40520i	0.0195756	−	0.0602476i
$545$	6.62373	−	20.3857i	0.283729	−	0.873229i
$546$		0			0
$547$	−3.07176	−	2.23176i	−0.131339	−	0.0954234i	0.520176	−	0.854059i	$-0.325866\pi$
$547$	−3.07176	−	2.23176i	−0.131339	−	0.0954234i	−0.651515	+	0.758636i	$0.725866\pi$
$548$	0.0756762	+	0.232907i	0.00323273	+	0.00994931i
$549$		0			0
$550$	−0.822163	+	3.26871i	−0.0350571	+	0.139378i
$551$	−6.30783			−0.268723
$552$		0			0
$553$	−3.92960	−	2.85502i	−0.167103	−	0.121408i
$554$	−1.50493	+	1.09340i	−0.0639384	+	0.0464539i
$555$		0			0
$556$	−0.474771	+	1.46119i	−0.0201348	+	0.0619684i
$557$	−2.82296	+	2.05100i	−0.119613	+	0.0869037i	−0.645983	−	0.763352i	$-0.723552\pi$
$557$	−2.82296	+	2.05100i	−0.119613	+	0.0869037i	0.526371	+	0.850255i	$0.323552\pi$
$558$		0			0
$559$	−2.11766	−	6.51750i	−0.0895676	−	0.275661i
$560$	−10.0851			−0.426172
$561$		0			0
$562$	−6.47885			−0.273294
$563$	8.70251	+	26.7836i	0.366767	+	1.12879i	0.948867	+	0.315676i	$0.102231\pi$
$563$	8.70251	+	26.7836i	0.366767	+	1.12879i	−0.582100	+	0.813117i	$0.697769\pi$
$564$		0			0
$565$	−2.56726	+	1.86522i	−0.108005	+	0.0784706i
$566$	−10.2560	+	31.5646i	−0.431091	+	1.32676i
$567$		0			0
$568$	−13.2211	+	9.60570i	−0.554746	+	0.403046i
$569$	17.4741	+	12.6957i	0.732552	+	0.532230i	0.890370	−	0.455238i	$-0.150446\pi$
$569$	17.4741	+	12.6957i	0.732552	+	0.532230i	−0.157818	+	0.987468i	$0.550446\pi$
$570$		0			0
$571$	14.4959			0.606636			0.303318	−	0.952889i	$-0.401906\pi$
$571$	14.4959			0.606636			0.303318	+	0.952889i	$0.401906\pi$
$572$	0.306334	+	0.192301i	0.0128085	+	0.00804050i
$573$		0			0
$574$	5.37965	+	16.5568i	0.224542	+	0.691070i
$575$	−4.40742	−	3.20218i	−0.183802	−	0.133540i
$576$		0			0
$577$	1.56697	−	4.82263i	0.0652337	−	0.200769i	−0.913127	−	0.407675i	$-0.866340\pi$
$577$	1.56697	−	4.82263i	0.0652337	−	0.200769i	0.978361	+	0.206906i	$0.0663396\pi$
$578$	5.49710	−	16.9183i	0.228649	−	0.703709i
$579$		0			0
$580$	−2.04820	−	1.48810i	−0.0850467	−	0.0617900i
$581$	3.10530	+	9.55713i	0.128830	+	0.396497i
$582$		0			0
$583$	8.11534	+	20.2064i	0.336103	+	0.836863i
$584$	−12.0102			−0.496985
$585$		0			0
$586$	9.88599	+	7.18259i	0.408387	+	0.296710i
$587$	−35.1036	+	25.5043i	−1.44888	+	1.05267i	−0.462791	+	0.886468i	$0.653152\pi$
$587$	−35.1036	+	25.5043i	−1.44888	+	1.05267i	−0.986091	+	0.166207i	$0.946848\pi$
$588$		0			0
$589$	−1.45658	+	4.48289i	−0.0600173	+	0.184714i
$590$	−27.0560	+	19.6573i	−1.11388	+	0.809280i
$591$		0			0
$592$	5.49058	+	16.8983i	0.225662	+	0.694515i
$593$	31.4532			1.29163			0.645815	−	0.763494i	$-0.276518\pi$
$593$	31.4532			1.29163			0.645815	+	0.763494i	$0.276518\pi$
$594$		0			0
$595$	5.21960			0.213983
$596$	−0.567162	−	1.74554i	−0.0232318	−	0.0715003i
$597$		0			0
$598$	−8.38159	+	6.08958i	−0.342749	+	0.249022i
$599$	6.85530	−	21.0984i	0.280100	−	0.862059i	−0.707725	−	0.706488i	$-0.750278\pi$
$599$	6.85530	−	21.0984i	0.280100	−	0.862059i	0.987825	−	0.155571i	$-0.0497216\pi$
$600$		0			0
$601$	−26.0651	+	18.9374i	−1.06322	+	0.772471i	−0.974681	−	0.223602i	$-0.928219\pi$
$601$	−26.0651	+	18.9374i	−1.06322	+	0.772471i	−0.0885351	+	0.996073i	$0.528219\pi$
$602$	−8.85264	−	6.43182i	−0.360807	−	0.262141i
$603$		0			0
$604$	−0.826403			−0.0336258
$605$	−4.66649	+	25.8396i	−0.189720	+	1.05053i
$606$		0			0
$607$	9.34878	+	28.7726i	0.379455	+	1.16784i	0.940423	+	0.340006i	$0.110429\pi$
$607$	9.34878	+	28.7726i	0.379455	+	1.16784i	−0.560968	+	0.827837i	$0.689571\pi$
$608$	−0.388864	−	0.282526i	−0.0157705	−	0.0114579i
$609$		0			0
$610$	−0.0673990	+	0.207433i	−0.00272891	+	0.00839871i
$611$	1.76708	−	5.43850i	0.0714883	−	0.220018i
$612$		0			0
$613$	3.38945	+	2.46258i	0.136899	+	0.0994627i	0.654127	−	0.756385i	$-0.273036\pi$
$613$	3.38945	+	2.46258i	0.136899	+	0.0994627i	−0.517228	+	0.855847i	$0.673036\pi$
$614$	−4.97402	−	15.3085i	−0.200735	−	0.617800i
$615$		0			0
$616$	−9.05890	+	0.614639i	−0.364993	+	0.0247645i
$617$	31.1457			1.25388			0.626939	−	0.779068i	$-0.284307\pi$
$617$	31.1457			1.25388			0.626939	+	0.779068i	$0.284307\pi$
$618$		0			0
$619$	38.7065	+	28.1219i	1.55575	+	1.13032i	0.939391	+	0.342849i	$0.111392\pi$
$619$	38.7065	+	28.1219i	1.55575	+	1.13032i	0.616356	+	0.787468i	$0.288608\pi$
$620$	−1.53053	+	1.11200i	−0.0614677	+	0.0446589i
$621$		0			0
$622$	−10.1637	+	31.2807i	−0.407528	+	1.25424i
$623$	0.211586	−	0.153726i	0.00847701	−	0.00615891i
$624$		0			0
$625$	−8.65337	−	26.6323i	−0.346135	−	1.06529i
$626$	−3.71061			−0.148306
$627$		0			0
$628$	−1.11684			−0.0445667
$629$	−2.84169	−	8.74582i	−0.113306	−	0.348719i
$630$		0			0
$631$	−3.24975	+	2.36108i	−0.129371	+	0.0939932i	−0.650589	−	0.759430i	$-0.725478\pi$
$631$	−3.24975	+	2.36108i	−0.129371	+	0.0939932i	0.521218	+	0.853423i	$0.325478\pi$
$632$	−4.10912	+	12.6466i	−0.163452	+	0.503054i
$633$		0			0
$634$	−36.9175	+	26.8221i	−1.46618	+	1.06524i
$635$	−42.1712	−	30.6392i	−1.67351	−	1.21588i
$636$		0			0
$637$	−0.911774			−0.0361258
$638$	−36.2643	−	22.7649i	−1.43572	−	0.901269i
$639$		0			0
$640$	9.01482	+	27.7447i	0.356342	+	1.09671i
$641$	22.3978	+	16.2730i	0.884661	+	0.642744i	0.934480	−	0.356015i	$-0.115865\pi$
$641$	22.3978	+	16.2730i	0.884661	+	0.642744i	−0.0498197	+	0.998758i	$0.515865\pi$
$642$		0			0
$643$	−1.31577	+	4.04952i	−0.0518888	+	0.159697i	−0.973643	−	0.228077i	$-0.926756\pi$
$643$	−1.31577	+	4.04952i	−0.0518888	+	0.159697i	0.921754	+	0.387775i	$0.126756\pi$
$644$	−0.288463	+	0.887799i	−0.0113670	+	0.0349842i
$645$		0			0
$646$	1.83207	+	1.33108i	0.0720820	+	0.0523706i
$647$	−1.62080	−	4.98832i	−0.0637203	−	0.196111i	0.914128	−	0.405426i	$-0.132877\pi$
$647$	−1.62080	−	4.98832i	−0.0637203	−	0.196111i	−0.977848	+	0.209315i	$0.932877\pi$
$648$		0			0
$649$	−24.4917	+	20.4648i	−0.961382	+	0.803313i
$650$	0.926589			0.0363438
$651$		0			0
$652$	−1.00933	−	0.733324i	−0.0395286	−	0.0287192i
$653$	−7.95843	+	5.78214i	−0.311437	+	0.226273i	−0.732513	−	0.680753i	$-0.761653\pi$
$653$	−7.95843	+	5.78214i	−0.311437	+	0.226273i	0.421076	+	0.907026i	$0.361653\pi$
$654$		0			0
$655$	−6.80272	+	20.9366i	−0.265804	+	0.818061i
$656$	40.8713	−	29.6947i	1.59576	−	1.15939i
$657$		0			0
$658$	−2.82160	−	8.68400i	−0.109998	−	0.338538i
$659$	−50.5575			−1.96944			−0.984720	−	0.174145i	$-0.944284\pi$
$659$	−50.5575			−1.96944			−0.984720	+	0.174145i	$0.944284\pi$
$660$		0			0
$661$	22.9751			0.893629			0.446814	−	0.894627i	$-0.352558\pi$
$661$	22.9751			0.893629			0.446814	+	0.894627i	$0.352558\pi$
$662$	2.17204	+	6.68485i	0.0844187	+	0.259814i
$663$		0			0
$664$	22.2564	−	16.1702i	0.863717	−	0.627527i
$665$	0.524719	−	1.61492i	0.0203477	−	0.0626239i
$666$		0			0
$667$	55.9898	−	40.6790i	2.16794	−	1.57510i
$668$	0.130767	+	0.0950080i	0.00505954	+	0.00367597i
$669$		0			0
$670$	−39.3728			−1.52110
$671$	−0.0507737	+	0.201863i	−0.00196010	+	0.00779284i
$672$		0			0
$673$	−6.75838	−	20.8001i	−0.260516	−	0.801787i	−0.992693	−	0.120671i	$-0.961495\pi$
$673$	−6.75838	−	20.8001i	−0.260516	−	0.801787i	0.732176	−	0.681115i	$-0.238505\pi$
$674$	24.8704	+	18.0694i	0.957972	+	0.696008i
$675$		0			0
$676$	−0.449759	+	1.38421i	−0.0172984	+	0.0532390i
$677$	4.53378	−	13.9535i	0.174247	−	0.536278i	−0.825351	−	0.564620i	$-0.809023\pi$
$677$	4.53378	−	13.9535i	0.174247	−	0.536278i	0.999598	+	0.0283421i	$0.00902278\pi$
$678$		0			0
$679$	7.99686	+	5.81006i	0.306891	+	0.222969i
$680$	−4.41567	−	13.5900i	−0.169333	−	0.521154i
$681$		0			0
$682$	−24.5527	+	20.5158i	−0.940171	+	0.785589i
$683$	9.70579			0.371382			0.185691	−	0.982608i	$-0.440548\pi$
$683$	9.70579			0.371382			0.185691	+	0.982608i	$0.440548\pi$
$684$		0			0
$685$	3.95406	+	2.87279i	0.151077	+	0.109764i
$686$	−1.17784	+	0.855749i	−0.0449700	+	0.0326726i
$687$		0			0
$688$	−9.81266	+	30.2003i	−0.374104	+	1.15137i
$689$	4.84294	−	3.51860i	0.184501	−	0.134048i
$690$		0			0
$691$	−13.4987	−	41.5449i	−0.513516	−	1.58044i	−0.785965	−	0.618271i	$-0.787834\pi$
$691$	−13.4987	−	41.5449i	−0.513516	−	1.58044i	0.272449	−	0.962170i	$-0.412166\pi$
$692$	−2.33058			−0.0885955
$693$		0			0
$694$	−18.0896			−0.686670
$695$	9.47528	+	29.1619i	0.359418	+	1.10617i
$696$		0			0
$697$	−21.1532	+	15.3687i	−0.801235	+	0.582132i
$698$	−7.63391	+	23.4948i	−0.288948	+	0.889289i
$699$		0			0
$700$	0.0675436	−	0.0490733i	0.00255291	−	0.00185480i
$701$	−16.7650	−	12.1805i	−0.633207	−	0.460052i	0.224303	−	0.974519i	$-0.427989\pi$
$701$	−16.7650	−	12.1805i	−0.633207	−	0.460052i	−0.857510	+	0.514468i	$0.827989\pi$
$702$		0			0
$703$	−2.99159			−0.112830
$704$	9.22856	+	22.9782i	0.347814	+	0.866023i
$705$		0			0
$706$	−2.05647	−	6.32917i	−0.0773963	−	0.238201i
$707$	−8.04763	−	5.84694i	−0.302662	−	0.219897i
$708$		0			0
$709$	−5.94324	+	18.2914i	−0.223203	+	0.686949i	0.775266	+	0.631635i	$0.217616\pi$
$709$	−5.94324	+	18.2914i	−0.223203	+	0.686949i	−0.998469	+	0.0553137i	$0.982384\pi$
$710$	6.41071	−	19.7301i	0.240590	−	0.740459i
$711$		0			0
$712$	−0.579246	−	0.420847i	−0.0217082	−	0.0157719i
$713$	−15.9811	−	49.1846i	−0.598495	−	1.84198i
$714$		0			0
$715$	7.20192	−	0.488644i	0.269337	−	0.0182743i
$716$	1.53743			0.0574565
$717$		0			0
$718$	36.4815	+	26.5054i	1.36148	+	0.989172i
$719$	−4.34430	+	3.15632i	−0.162015	+	0.117711i	−0.665839	−	0.746096i	$-0.731926\pi$
$719$	−4.34430	+	3.15632i	−0.162015	+	0.117711i	0.503824	+	0.863806i	$0.331926\pi$
$720$		0			0
$721$	0.203570	−	0.626523i	0.00758133	−	0.0233329i
$722$	−21.7829	+	15.8262i	−0.810676	+	0.588990i
$723$		0			0
$724$	0.531302	+	1.63518i	0.0197457	+	0.0607710i
$725$	−6.18971			−0.229880
$726$		0			0
$727$	8.19052			0.303769			0.151885	−	0.988398i	$-0.451466\pi$
$727$	8.19052			0.303769			0.151885	+	0.988398i	$0.451466\pi$
$728$	0.771340	+	2.37394i	0.0285878	+	0.0879841i
$729$		0			0
$730$	12.3345	−	8.96152i	0.456519	−	0.331681i
$731$	5.07861	−	15.6304i	0.187839	−	0.578110i
$732$		0			0
$733$	−19.6806	+	14.2988i	−0.726919	+	0.528137i	−0.888587	−	0.458708i	$-0.848312\pi$
$733$	−19.6806	+	14.2988i	−0.726919	+	0.528137i	0.161668	+	0.986845i	$0.448312\pi$
$734$	17.3639	+	12.6156i	0.640914	+	0.465651i
$735$		0			0
$736$	5.27365			0.194389
$737$	−37.4891	+	2.54360i	−1.38093	+	0.0936949i
$738$		0			0
$739$	−5.86182	−	18.0408i	−0.215630	−	0.663642i	−0.999108	−	0.0422224i	$-0.986556\pi$
$739$	−5.86182	−	18.0408i	−0.215630	−	0.663642i	0.783478	−	0.621420i	$-0.213444\pi$
$740$	−0.971389	−	0.705755i	−0.0357090	−	0.0259441i
$741$		0			0
$742$	2.95376	−	9.09072i	0.108436	−	0.333731i
$743$	5.22228	−	16.0725i	0.191587	−	0.589644i	−0.808413	−	0.588616i	$-0.799673\pi$
$743$	5.22228	−	16.0725i	0.191587	−	0.589644i	0.999999	−	0.00102754i	$-0.000327077\pi$
$744$		0			0
$745$	−29.6340	−	21.5304i	−1.08571	−	0.788811i
$746$	5.65519	+	17.4049i	0.207051	+	0.637238i
$747$		0			0
$748$	0.323275	+	0.804921i	0.0118201	+	0.0294308i
$749$	0.283088			0.0103438
$750$		0			0
$751$	18.2791	+	13.2805i	0.667014	+	0.484614i	0.869024	−	0.494769i	$-0.164747\pi$
$751$	18.2791	+	13.2805i	0.667014	+	0.484614i	−0.202010	+	0.979383i	$0.564747\pi$
$752$	−21.4368	+	15.5748i	−0.781721	+	0.567954i
$753$		0			0
$754$	−3.63743	+	11.1949i	−0.132467	+	0.407692i
$755$	−13.3431	+	9.69435i	−0.485606	+	0.352813i
$756$		0			0
$757$	1.19820	+	3.68767i	0.0435492	+	0.134031i	0.970467	−	0.241234i	$-0.0775520\pi$
$757$	1.19820	+	3.68767i	0.0435492	+	0.134031i	−0.926918	+	0.375264i	$0.877552\pi$
$758$	−23.3436			−0.847879
$759$		0			0
$760$	−4.64859			−0.168622
$761$	−11.5755	−	35.6257i	−0.419611	−	1.29143i	−0.908061	−	0.418839i	$-0.862437\pi$
$761$	−11.5755	−	35.6257i	−0.419611	−	1.29143i	0.488449	−	0.872592i	$-0.337563\pi$
$762$		0			0
$763$	−7.26467	+	5.27809i	−0.262999	+	0.191080i
$764$	0.885276	−	2.72460i	0.0320282	−	0.0985726i
$765$		0			0
$766$	3.30999	−	2.40485i	0.119595	−	0.0868907i
$767$	7.09840	+	5.15729i	0.256308	+	0.186219i
$768$		0			0
$769$	−20.6137			−0.743349			−0.371674	−	0.928363i	$-0.621216\pi$
$769$	−20.6137			−0.743349			−0.371674	+	0.928363i	$0.621216\pi$
$770$	8.84488	−	7.39063i	0.318748	−	0.266340i
$771$		0			0
$772$	0.00515999	+	0.0158808i	0.000185712	+	0.000571563i
$773$	7.31097	+	5.31173i	0.262957	+	0.191050i	0.711450	−	0.702737i	$-0.248039\pi$
$773$	7.31097	+	5.31173i	0.262957	+	0.191050i	−0.448492	+	0.893787i	$0.648039\pi$
$774$		0			0
$775$	−1.42930	+	4.39894i	−0.0513420	+	0.158015i
$776$	8.36220	−	25.7362i	0.300185	−	0.923875i
$777$		0			0
$778$	24.2693	+	17.6327i	0.870097	+	0.632162i
$779$	2.62850	+	8.08970i	0.0941759	+	0.289844i
$780$		0			0
$781$	4.82938	−	19.2004i	0.172809	−	0.687043i
$782$	−24.8460			−0.888492
$783$		0			0
$784$	3.41802	+	2.48334i	0.122072	+	0.0886906i
$785$	−18.0325	+	13.1014i	−0.643607	+	0.467608i
$786$		0			0
$787$	−10.3392	+	31.8209i	−0.368554	+	1.13429i	0.579171	+	0.815206i	$0.303376\pi$
$787$	−10.3392	+	31.8209i	−0.368554	+	1.13429i	−0.947725	+	0.319087i	$0.896624\pi$
$788$	1.41384	−	1.02721i	0.0503659	−	0.0365930i
$789$		0			0
$790$	−5.21630	−	16.0541i	−0.185588	−	0.571180i
$791$	1.32938			0.0472674
$792$		0			0
$793$	0.0572227			0.00203204
$794$	−12.8934	−	39.6818i	−0.457570	−	1.40825i
$795$		0			0
$796$	2.56135	−	1.86093i	0.0907845	−	0.0659588i
$797$	−0.236759	+	0.728670i	−0.00838644	+	0.0258108i	−0.955162	−	0.296083i	$-0.904319\pi$
$797$	−0.236759	+	0.728670i	−0.00838644	+	0.0258108i	0.946776	+	0.321894i	$0.104319\pi$
$798$		0			0
$799$	11.0948	−	8.06083i	0.392505	−	0.285172i
$800$	−0.381582	−	0.277235i	−0.0134910	−	0.00980175i
$801$		0			0
$802$	−32.4890			−1.14723
$803$	11.1654	−	9.32963i	0.394019	−	0.329235i
$804$		0			0
$805$	5.75703	+	17.7183i	0.202909	+	0.624489i
$806$	7.11609	+	5.17014i	0.250653	+	0.182110i
$807$		0			0
$808$	−8.41529	+	25.8996i	−0.296049	+	0.911145i
$809$	3.16159	−	9.73039i	0.111156	−	0.342102i	−0.879970	−	0.475029i	$-0.842438\pi$
$809$	3.16159	−	9.73039i	0.111156	−	0.342102i	0.991126	+	0.132927i	$0.0424375\pi$
$810$		0			0
$811$	−8.42960	−	6.12446i	−0.296003	−	0.215059i	0.429864	−	0.902894i	$-0.358561\pi$
$811$	−8.42960	−	6.12446i	−0.296003	−	0.215059i	−0.725867	+	0.687835i	$0.758561\pi$
$812$	0.327743	+	1.00869i	0.0115015	+	0.0353981i
$813$		0			0
$814$	−17.1989	−	10.7966i	−0.602822	−	0.378420i
$815$	−24.8992			−0.872181
$816$		0			0
$817$	−4.32541	−	3.14260i	−0.151327	−	0.109946i
$818$	19.3590	−	14.0651i	0.676870	−	0.491775i
$819$		0			0
$820$	−1.05498	+	3.24688i	−0.0368414	+	0.113386i
$821$	22.4513	−	16.3118i	0.783555	−	0.569286i	−0.122489	−	0.992470i	$-0.539088\pi$
$821$	22.4513	−	16.3118i	0.783555	−	0.569286i	0.906044	+	0.423184i	$0.139088\pi$
$822$		0			0
$823$	−5.79157	−	17.8246i	−0.201881	−	0.621327i	−0.999827	−	0.0185975i	$-0.994080\pi$
$823$	−5.79157	−	17.8246i	−0.201881	−	0.621327i	0.797946	−	0.602729i	$-0.205920\pi$
$824$	−1.80346			−0.0628266
$825$		0			0
$826$	14.0102			0.487476
$827$	17.1947	+	52.9198i	0.597918	+	1.84020i	0.539631	+	0.841901i	$0.318564\pi$
$827$	17.1947	+	52.9198i	0.597918	+	1.84020i	0.0582861	+	0.998300i	$0.481436\pi$
$828$		0			0
$829$	30.3867	−	22.0772i	1.05537	−	0.766774i	0.0821472	−	0.996620i	$-0.473822\pi$
$829$	30.3867	−	22.0772i	1.05537	−	0.766774i	0.973227	+	0.229846i	$0.0738222\pi$
$830$	−10.7918	+	33.2137i	−0.374589	+	1.15286i
$831$		0			0
$832$	5.50727	−	4.00127i	0.190930	−	0.138719i
$833$	−1.76902	−	1.28527i	−0.0612929	−	0.0445319i
$834$		0			0
$835$	3.22589			0.111637
$836$	0.281537	−	0.0191021i	0.00973716	−	0.000660658i
$837$		0			0
$838$	−5.74625	−	17.6851i	−0.198501	−	0.610923i
$839$	−36.1509	−	26.2652i	−1.24807	−	0.906774i	−0.249960	−	0.968256i	$-0.580417\pi$
$839$	−36.1509	−	26.2652i	−1.24807	−	0.906774i	−0.998108	+	0.0614819i	$0.980417\pi$
$840$		0			0
$841$	15.3369	−	47.2021i	0.528858	−	1.62766i
$842$	−4.86028	+	14.9584i	−0.167496	+	0.515500i
$843$		0			0
$844$	−1.69934	−	1.23465i	−0.0584939	−	0.0424983i
$845$	8.97610	+	27.6256i	0.308787	+	0.950349i
$846$		0			0
$847$	7.94427	−	7.60845i	0.272968	−	0.261430i
$848$	−27.7384			−0.952541
$849$		0			0
$850$	1.79777	+	1.30615i	0.0616628	+	0.0448007i
$851$	26.5541	−	19.2926i	0.910261	−	0.661343i
$852$		0			0
$853$	17.2080	−	52.9607i	0.589190	−	1.81334i	0.00743815	−	0.999972i	$-0.497632\pi$
$853$	17.2080	−	52.9607i	0.589190	−	1.81334i	0.581751	−	0.813367i	$-0.302368\pi$
$854$	0.0739208	−	0.0537066i	0.00252952	−	0.00183780i
$855$		0			0
$856$	−0.239486	−	0.737063i	−0.00818548	−	0.0251923i
$857$	37.5988			1.28435			0.642176	−	0.766557i	$-0.278032\pi$
$857$	37.5988			1.28435			0.642176	+	0.766557i	$0.278032\pi$
$858$		0			0
$859$	44.1084			1.50496			0.752479	−	0.658616i	$-0.228858\pi$
$859$	44.1084			1.50496			0.752479	+	0.658616i	$0.228858\pi$
$860$	−0.663111	−	2.04085i	−0.0226119	−	0.0695923i
$861$		0			0
$862$	−32.4371	+	23.5669i	−1.10481	+	0.802692i
$863$	1.39382	−	4.28973i	0.0474461	−	0.146024i	−0.924527	−	0.381117i	$-0.875539\pi$
$863$	1.39382	−	4.28973i	0.0474461	−	0.146024i	0.971973	+	0.235093i	$0.0755395\pi$
$864$		0			0
$865$	−37.6297	+	27.3396i	−1.27945	+	0.929573i
$866$	17.9738	+	13.0588i	0.610776	+	0.443755i
$867$		0			0
$868$	0.792543			0.0269007
$869$	−6.00389	−	14.9491i	−0.203668	−	0.507112i
$870$		0			0
$871$	3.19209	+	9.82425i	0.108160	+	0.332882i
$872$	19.8880	+	14.4495i	0.673494	+	0.489322i
$873$		0			0
$874$	−2.49774	+	7.68724i	−0.0844872	+	0.260025i
$875$	−3.17331	+	9.76644i	−0.107277	+	0.330166i
$876$		0			0
$877$	29.1956	+	21.2118i	0.985865	+	0.716273i	0.959012	−	0.283367i	$-0.0914513\pi$
$877$	29.1956	+	21.2118i	0.985865	+	0.716273i	0.0268532	+	0.999639i	$0.491451\pi$
$878$	12.8445	+	39.5312i	0.433479	+	1.33411i
$879$		0			0
$880$	−28.3292	−	17.7836i	−0.954976	−	0.599485i
$881$	12.8240			0.432052			0.216026	−	0.976388i	$-0.430690\pi$
$881$	12.8240			0.432052			0.216026	+	0.976388i	$0.430690\pi$
$882$		0			0
$883$	7.57416	+	5.50295i	0.254891	+	0.185189i	0.707892	−	0.706321i	$-0.249647\pi$
$883$	7.57416	+	5.50295i	0.254891	+	0.185189i	−0.453001	+	0.891510i	$0.649647\pi$
$884$	0.192919	−	0.140164i	0.00648855	−	0.00471421i
$885$		0			0
$886$	5.09776	−	15.6893i	0.171263	−	0.527092i
$887$	−8.02099	+	5.82759i	−0.269318	+	0.195671i	−0.714245	−	0.699896i	$-0.753230\pi$
$887$	−8.02099	+	5.82759i	−0.269318	+	0.195671i	0.444927	+	0.895567i	$0.353230\pi$
$888$		0			0
$889$	6.74805	+	20.7684i	0.226322	+	0.696549i
$890$	0.908906			0.0304666
$891$		0			0
$892$	2.70117			0.0904419
$893$	−1.37864	−	4.24302i	−0.0461344	−	0.141987i
$894$		0			0
$895$	24.8234	−	18.0353i	0.829756	−	0.602853i
$896$	3.77654	−	11.6230i	0.126165	−	0.388297i
$897$		0			0
$898$	31.6800	−	23.0169i	1.05718	−	0.768083i
$899$	−47.5361	−	34.5370i	−1.58542	−	1.15187i
$900$		0			0
$901$	14.3562			0.478275
$902$	−14.0841	+	55.9947i	−0.468949	+	1.86442i
$903$		0			0
$904$	−1.12463	−	3.46125i	−0.0374046	−	0.115119i
$905$	27.7604	+	20.1691i	0.922785	+	0.670443i
$906$		0			0
$907$	−4.32258	+	13.3035i	−0.143529	+	0.441736i	−0.996819	−	0.0797004i	$-0.974604\pi$
$907$	−4.32258	+	13.3035i	−0.143529	+	0.441736i	0.853290	+	0.521436i	$0.174604\pi$
$908$	−0.812071	+	2.49930i	−0.0269495	+	0.0829421i
$909$		0			0
$910$	−2.56351	−	1.86250i	−0.0849794	−	0.0617412i
$911$	8.37955	+	25.7896i	0.277627	+	0.854447i	0.988512	+	0.151140i	$0.0482944\pi$
$911$	8.37955	+	25.7896i	0.277627	+	0.854447i	−0.710886	+	0.703308i	$0.751706\pi$
$912$		0			0
$913$	−8.12978	+	32.3219i	−0.269057	+	1.06970i
$914$	42.1762			1.39507
$915$		0			0
$916$	−2.26236	−	1.64370i	−0.0747505	−	0.0543094i
$917$	7.46097	−	5.42072i	0.246383	−	0.179008i
$918$		0			0
$919$	1.36858	−	4.21204i	0.0451452	−	0.138943i	−0.925943	−	0.377663i	$-0.876728\pi$
$919$	1.36858	−	4.21204i	0.0451452	−	0.138943i	0.971088	+	0.238720i	$0.0767279\pi$
$920$	41.2620	−	29.9786i	1.36037	−	0.988366i
$921$		0			0
$922$	−18.8674	−	58.0680i	−0.621365	−	1.91237i
$923$	−5.44278			−0.179151
$924$		0			0
$925$	−2.93556			−0.0965208
$926$	0.516947	+	1.59100i	0.0169879	+	0.0522835i
$927$		0			0
$928$	4.84744	−	3.52187i	0.159125	−	0.115611i
$929$	17.5442	−	53.9956i	0.575608	−	1.77154i	−0.0584913	−	0.998288i	$-0.518629\pi$
$929$	17.5442	−	53.9956i	0.575608	−	1.77154i	0.634099	−	0.773252i	$-0.281371\pi$
$930$		0			0
$931$	−0.575493	+	0.418120i	−0.0188610	+	0.0137033i
$932$	−0.100939	−	0.0733364i	−0.00330636	−	0.00240221i
$933$		0			0
$934$	43.0777			1.40955
$935$	14.6620	+	9.20402i	0.479497	+	0.301004i
$936$		0			0
$937$	−0.883162	−	2.71809i	−0.0288517	−	0.0887963i	0.935594	−	0.353078i	$-0.114865\pi$
$937$	−0.883162	−	2.71809i	−0.0288517	−	0.0887963i	−0.964445	+	0.264282i	$0.914865\pi$
$938$	13.3442	+	9.69511i	0.435703	+	0.316556i
$939$		0			0
$940$	0.553331	−	1.70298i	0.0180477	−	0.0555450i
$941$	−7.49416	+	23.0647i	−0.244303	+	0.751887i	0.751448	+	0.659793i	$0.229356\pi$
$941$	−7.49416	+	23.0647i	−0.244303	+	0.751887i	−0.995750	+	0.0920938i	$0.970644\pi$
$942$		0			0
$943$	−75.5015	−	54.8550i	−2.45867	−	1.78633i
$944$	−12.5636	−	38.6669i	−0.408912	−	1.25850i
$945$		0			0
$946$	−13.5256	−	33.6774i	−0.439756	−	1.09495i
$947$	45.0901			1.46523			0.732616	−	0.680642i	$-0.238299\pi$
$947$	45.0901			1.46523			0.732616	+	0.680642i	$0.238299\pi$
$948$		0			0
$949$	−3.23607	−	2.35114i	−0.105047	−	0.0763213i
$950$	0.584844	−	0.424914i	0.0189749	−	0.0137860i
$951$		0			0
$952$	−1.84984	+	5.69322i	−0.0599536	+	0.184518i
$953$	−30.5081	+	22.1654i	−0.988255	+	0.718009i	−0.959538	−	0.281578i	$-0.909142\pi$
$953$	−30.5081	+	22.1654i	−0.988255	+	0.718009i	−0.0287166	+	0.999588i	$0.509142\pi$
$954$		0			0
$955$	−17.6680	−	54.3765i	−0.571722	−	1.75958i
$956$	1.48479			0.0480216
$957$		0			0
$958$	−14.8105			−0.478505
$959$	−0.632711	−	1.94728i	−0.0204313	−	0.0628811i
$960$		0			0
$961$	−10.4423	+	7.58679i	−0.336849	+	0.244735i
$962$	−1.72511	+	5.30933i	−0.0556197	+	0.171180i
$963$		0			0
$964$	−0.911933	+	0.662558i	−0.0293714	+	0.0213396i
$965$	0.269608	+	0.195882i	0.00867898	+	0.00630565i
$966$		0			0
$967$	−60.7131			−1.95240			−0.976201	−	0.216870i	$-0.930415\pi$
$967$	−60.7131			−1.95240			−0.976201	+	0.216870i	$0.930415\pi$
$968$	−26.5304	−	14.2475i	−0.852720	−	0.457933i
$969$		0			0
$970$	10.6153	+	32.6707i	0.340838	+	1.04899i
$971$	−23.8546	−	17.3314i	−0.765530	−	0.556190i	0.135071	−	0.990836i	$-0.456874\pi$
$971$	−23.8546	−	17.3314i	−0.765530	−	0.556190i	−0.900602	+	0.434646i	$0.856874\pi$
$972$		0			0
$973$	3.96945	−	12.2167i	0.127255	−	0.391649i
$974$	−19.7198	+	60.6912i	−0.631862	+	1.94467i
$975$		0			0
$976$	−0.214514	−	0.155854i	−0.00686643	−	0.00498875i
$977$	−1.40608	−	4.32746i	−0.0449844	−	0.138448i	0.926042	−	0.377421i	$-0.123189\pi$
$977$	−1.40608	−	4.32746i	−0.0449844	−	0.138448i	−0.971026	+	0.238973i	$0.923189\pi$
$978$		0			0
$979$	0.865423	−	0.0587182i	0.0276590	−	0.00187664i
$980$	−0.285507			−0.00912018
$981$		0			0
$982$	−22.5211	−	16.3625i	−0.718677	−	0.522150i
$983$	−29.9123	+	21.7325i	−0.954053	+	0.693160i	−0.951762	−	0.306837i	$-0.900729\pi$
$983$	−29.9123	+	21.7325i	−0.954053	+	0.693160i	−0.00229090	+	0.999997i	$0.500729\pi$
$984$		0			0
$985$	10.7779	−	33.1708i	0.343411	−	1.05691i
$986$	−22.8380	+	16.5928i	−0.727310	+	0.528421i
$987$		0			0
$988$	−0.0239721	−	0.0737785i	−0.000762654	−	0.00234721i
$989$	58.6599			1.86528
$990$		0			0
$991$	30.5701			0.971090			0.485545	−	0.874212i	$-0.338621\pi$
$991$	30.5701			0.971090			0.485545	+	0.874212i	$0.338621\pi$
$992$	−1.38359	−	4.25827i	−0.0439292	−	0.135200i
$993$		0			0
$994$	−7.03103	+	5.10835i	−0.223011	+	0.162027i
$995$	19.5255	−	60.0932i	0.618999	−	1.90508i
$996$		0			0
$997$	2.14749	−	1.56024i	0.0680117	−	0.0494134i	−0.553260	−	0.833009i	$-0.686616\pi$
$997$	2.14749	−	1.56024i	0.0680117	−	0.0494134i	0.621272	+	0.783595i	$0.286616\pi$
$998$	24.1422	+	17.5404i	0.764210	+	0.555231i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.f.379.1		8
3.2	odd	2		231.2.j.f.148.2	yes	8
11.3	even	5		7623.2.a.ci.1.2		4
11.8	odd	10		7623.2.a.cl.1.3		4
11.9	even	5	inner	693.2.m.f.64.1		8
33.8	even	10		2541.2.a.bm.1.2		4
33.14	odd	10		2541.2.a.bn.1.3		4
33.20	odd	10		231.2.j.f.64.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.64.2	✓	8	33.20	odd	10
231.2.j.f.148.2	yes	8	3.2	odd	2
693.2.m.f.64.1		8	11.9	even	5	inner
693.2.m.f.379.1		8	1.1	even	1	trivial
2541.2.a.bm.1.2		4	33.8	even	10
2541.2.a.bn.1.3		4	33.14	odd	10
7623.2.a.ci.1.2		4	11.3	even	5
7623.2.a.cl.1.3		4	11.8	odd	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.449894 - 1.38463i) q^{2} +(-0.0967635 + 0.0703028i) q^{4} +(-0.737640 + 2.27022i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-2.21480 - 1.60914i) q^{8} +O(q^{10})\)	\(q+(-0.449894 - 1.38463i) q^{2} +(-0.0967635 + 0.0703028i) q^{4} +(-0.737640 + 2.27022i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-2.21480 - 1.60914i) q^{8} +3.47528 q^{10} +(3.30902 - 0.224514i) q^{11} +(-0.281754 - 0.867148i) q^{13} +(-1.17784 - 0.855749i) q^{14} +(-1.30557 + 4.01813i) q^{16} +(0.675706 - 2.07961i) q^{17} +(-0.575493 - 0.418120i) q^{19} +(-0.0882264 - 0.271533i) q^{20} +(-1.79958 - 4.48076i) q^{22} +7.80466 q^{23} +(-0.564716 - 0.410290i) q^{25} +(-1.07392 + 0.780249i) q^{26} +(-0.0369604 + 0.113752i) q^{28} +(7.17390 - 5.21214i) q^{29} +(-2.04763 - 6.30195i) q^{31} +0.675706 q^{32} -3.18348 q^{34} +(0.737640 + 2.27022i) q^{35} +(3.40233 - 2.47194i) q^{37} +(-0.320031 + 0.984955i) q^{38} +(5.28684 - 3.84112i) q^{40} +(-9.67390 - 7.02850i) q^{41} +7.51601 q^{43} +(-0.304408 + 0.254358i) q^{44} +(-3.51127 - 10.8066i) q^{46} +(5.07392 + 3.68642i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.314038 + 0.966510i) q^{50} +(0.0882264 + 0.0641003i) q^{52} +(2.02884 + 6.24411i) q^{53} +(-1.93117 + 7.67782i) q^{55} -2.73764 q^{56} +(-10.4444 - 7.58829i) q^{58} +(-7.78527 + 5.65633i) q^{59} +(-0.0193938 + 0.0596881i) q^{61} +(-7.80466 + 5.67042i) q^{62} +(2.30714 + 7.10065i) q^{64} +2.17645 q^{65} -11.3294 q^{67} +(0.0808187 + 0.248734i) q^{68} +(2.81156 - 2.04272i) q^{70} +(1.84466 - 5.67728i) q^{71} +(3.54920 - 2.57865i) q^{73} +(-4.95341 - 3.59886i) q^{74} +0.0850818 q^{76} +(2.54508 - 2.12663i) q^{77} +(-1.50097 - 4.61952i) q^{79} +(-8.15900 - 5.92786i) q^{80} +(-5.37965 + 16.5568i) q^{82} +(-3.10530 + 9.55713i) q^{83} +(4.22275 + 3.06801i) q^{85} +(-3.38141 - 10.4069i) q^{86} +(-7.69008 - 4.82743i) q^{88} +0.261535 q^{89} +(-0.737640 - 0.535927i) q^{91} +(-0.755207 + 0.548690i) q^{92} +(2.82160 - 8.68400i) q^{94} +(1.37373 - 0.998076i) q^{95} +(3.05453 + 9.40087i) q^{97} -1.45589 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

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