LMFDB - Embedded newform 693.2.m.f.379.2

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			379.2
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.f.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0501062 - 0.154211i) q^{2} +(1.59676 - 1.16012i) q^{4} +(1.35567 - 4.17234i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-0.521270 - 0.378725i) q^{8} +O(q^{10})$	\(q+(-0.0501062 - 0.154211i) q^{2} +(1.59676 - 1.16012i) q^{4} +(1.35567 - 4.17234i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-0.521270 - 0.378725i) q^{8} -0.711349 q^{10} +(3.30902 - 0.224514i) q^{11} +(0.517822 + 1.59369i) q^{13} +(-0.131180 - 0.0953077i) q^{14} +(1.18753 - 3.65485i) q^{16} +(-1.91177 + 5.88383i) q^{17} +(2.81156 + 2.04272i) q^{19} +(-2.67571 - 8.23498i) q^{20} +(-0.200425 - 0.499038i) q^{22} -0.568595 q^{23} +(-11.5255 - 8.37373i) q^{25} +(0.219819 - 0.159708i) q^{26} +(0.609909 - 1.87711i) q^{28} +(-7.17390 + 5.21214i) q^{29} +(1.33943 + 4.12233i) q^{31} -1.91177 q^{32} +1.00314 q^{34} +(-1.35567 - 4.17234i) q^{35} +(-0.784298 + 0.569826i) q^{37} +(0.174133 - 0.535927i) q^{38} +(-2.28684 + 1.66149i) q^{40} +(4.67390 + 3.39578i) q^{41} -5.04388 q^{43} +(5.02326 - 4.19734i) q^{44} +(0.0284902 + 0.0876837i) q^{46} +(3.78018 + 2.74646i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.713826 + 2.19693i) q^{50} +(2.67571 + 1.94401i) q^{52} +(0.735096 + 2.26239i) q^{53} +(3.54920 - 14.1107i) q^{55} -0.644326 q^{56} +(1.16323 + 0.845134i) q^{58} +(-2.30490 + 1.67461i) q^{59} +(2.87350 - 8.84371i) q^{61} +(0.568595 - 0.413109i) q^{62} +(-2.27928 - 7.01489i) q^{64} +7.35141 q^{65} -7.14275 q^{67} +(3.77328 + 11.6130i) q^{68} +(-0.575493 + 0.418120i) q^{70} +(0.245510 - 0.755602i) q^{71} +(-1.93117 + 1.40308i) q^{73} +(0.127172 + 0.0923956i) q^{74} +6.85919 q^{76} +(2.54508 - 2.12663i) q^{77} +(-0.207232 - 0.637795i) q^{79} +(-13.6394 - 9.90958i) q^{80} +(0.289476 - 0.890917i) q^{82} +(2.86923 - 8.83059i) q^{83} +(21.9576 + 15.9531i) q^{85} +(0.252730 + 0.777822i) q^{86} +(-1.80992 - 1.13618i) q^{88} +12.2106 q^{89} +(1.35567 + 0.984955i) q^{91} +(-0.907912 + 0.659637i) q^{92} +(0.234124 - 0.720561i) q^{94} +(12.3345 - 8.96152i) q^{95} +(4.65368 + 14.3225i) q^{97} -0.162147 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.0501062	−	0.154211i	−0.0354305	−	0.109044i	0.931777	−	0.363031i	$-0.118258\pi$
$2$	−0.0501062	−	0.154211i	−0.0354305	−	0.109044i	−0.967208	+	0.253987i	$0.918258\pi$
$3$		0			0
$3$		0			0
$4$	1.59676	−	1.16012i	0.798382	−	0.580058i
$5$	1.35567	−	4.17234i	0.606276	−	1.86593i	0.118506	−	0.992953i	$-0.462189\pi$
$5$	1.35567	−	4.17234i	0.606276	−	1.86593i	0.487770	−	0.872972i	$-0.337811\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−0.521270	−	0.378725i	−0.184297	−	0.133900i
$9$		0			0
$10$	−0.711349			−0.224948
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	0.517822	+	1.59369i	0.143618	+	0.442010i	0.996831	−	0.0795526i	$-0.0253492\pi$
$13$	0.517822	+	1.59369i	0.143618	+	0.442010i	−0.853213	+	0.521563i	$0.825349\pi$
$14$	−0.131180	−	0.0953077i	−0.0350593	−	0.0254721i
$15$		0			0
$16$	1.18753	−	3.65485i	0.296884	−	0.913714i
$17$	−1.91177	+	5.88383i	−0.463673	+	1.42704i	0.396970	+	0.917831i	$0.370062\pi$
$17$	−1.91177	+	5.88383i	−0.463673	+	1.42704i	−0.860644	+	0.509208i	$0.829938\pi$
$18$		0			0
$19$	2.81156	+	2.04272i	0.645016	+	0.468632i	0.861570	−	0.507639i	$-0.169482\pi$
$19$	2.81156	+	2.04272i	0.645016	+	0.468632i	−0.216554	+	0.976271i	$0.569482\pi$
$20$	−2.67571	−	8.23498i	−0.598306	−	1.84140i
$21$		0			0
$22$	−0.200425	−	0.499038i	−0.0427307	−	0.106395i
$23$	−0.568595			−0.118560			−0.0592801	−	0.998241i	$-0.518881\pi$
$23$	−0.568595			−0.118560			−0.0592801	+	0.998241i	$0.518881\pi$
$24$		0			0
$25$	−11.5255	−	8.37373i	−2.30509	−	1.67475i
$26$	0.219819	−	0.159708i	0.0431100	−	0.0313213i
$27$		0			0
$28$	0.609909	−	1.87711i	0.115262	−	0.354740i
$29$	−7.17390	+	5.21214i	−1.33216	+	0.967870i	−0.332465	+	0.943115i	$0.607880\pi$
$29$	−7.17390	+	5.21214i	−1.33216	+	0.967870i	−0.999694	+	0.0247547i	$0.992120\pi$
$30$		0			0
$31$	1.33943	+	4.12233i	0.240568	+	0.740392i	0.996334	+	0.0855500i	$0.0272647\pi$
$31$	1.33943	+	4.12233i	0.240568	+	0.740392i	−0.755766	+	0.654842i	$0.772735\pi$
$32$	−1.91177			−0.337957
$33$		0			0
$34$	1.00314			0.172038
$35$	−1.35567	−	4.17234i	−0.229151	−	0.705254i
$36$		0			0
$37$	−0.784298	+	0.569826i	−0.128938	+	0.0936787i	−0.650385	−	0.759605i	$-0.725392\pi$
$37$	−0.784298	+	0.569826i	−0.128938	+	0.0936787i	0.521447	+	0.853284i	$0.325392\pi$
$38$	0.174133	−	0.535927i	0.0282481	−	0.0869388i
$39$		0			0
$40$	−2.28684	+	1.66149i	−0.361581	+	0.262704i
$41$	4.67390	+	3.39578i	0.729940	+	0.530332i	0.889544	−	0.456849i	$-0.151022\pi$
$41$	4.67390	+	3.39578i	0.729940	+	0.530332i	−0.159605	+	0.987181i	$0.551022\pi$
$42$		0			0
$43$	−5.04388			−0.769184			−0.384592	−	0.923087i	$-0.625658\pi$
$43$	−5.04388			−0.769184			−0.384592	+	0.923087i	$0.625658\pi$
$44$	5.02326	−	4.19734i	0.757284	−	0.632773i
$45$		0			0
$46$	0.0284902	+	0.0876837i	0.00420065	+	0.0129283i
$47$	3.78018	+	2.74646i	0.551396	+	0.400613i	0.828300	−	0.560285i	$-0.189308\pi$
$47$	3.78018	+	2.74646i	0.551396	+	0.400613i	−0.276904	+	0.960898i	$0.589308\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.713826	+	2.19693i	−0.100950	+	0.310693i
$51$		0			0
$52$	2.67571	+	1.94401i	0.371054	+	0.269586i
$53$	0.735096	+	2.26239i	0.100973	+	0.310764i	0.988764	−	0.149483i	$-0.0477609\pi$
$53$	0.735096	+	2.26239i	0.100973	+	0.310764i	−0.887791	+	0.460247i	$0.847761\pi$
$54$		0			0
$55$	3.54920	−	14.1107i	0.478574	−	1.90269i
$56$	−0.644326			−0.0861016
$57$		0			0
$58$	1.16323	+	0.845134i	0.152739	+	0.110972i
$59$	−2.30490	+	1.67461i	−0.300072	+	0.218015i	−0.727625	−	0.685975i	$-0.759376\pi$
$59$	−2.30490	+	1.67461i	−0.300072	+	0.218015i	0.427553	+	0.903990i	$0.359376\pi$
$60$		0			0
$61$	2.87350	−	8.84371i	0.367913	−	1.13232i	−0.580223	−	0.814458i	$-0.697035\pi$
$61$	2.87350	−	8.84371i	0.367913	−	1.13232i	0.948136	−	0.317864i	$-0.102965\pi$
$62$	0.568595	−	0.413109i	0.0722117	−	0.0524648i
$63$		0			0
$64$	−2.27928	−	7.01489i	−0.284910	−	0.876861i
$65$	7.35141			0.911830
$66$		0			0
$67$	−7.14275			−0.872626			−0.436313	−	0.899795i	$-0.643716\pi$
$67$	−7.14275			−0.872626			−0.436313	+	0.899795i	$0.643716\pi$
$68$	3.77328	+	11.6130i	0.457578	+	1.40828i
$69$		0			0
$70$	−0.575493	+	0.418120i	−0.0687846	+	0.0499749i
$71$	0.245510	−	0.755602i	0.0291367	−	0.0896734i	−0.935431	−	0.353510i	$-0.884988\pi$
$71$	0.245510	−	0.755602i	0.0291367	−	0.0896734i	0.964567	+	0.263837i	$0.0849880\pi$
$72$		0			0
$73$	−1.93117	+	1.40308i	−0.226026	+	0.164218i	−0.695035	−	0.718976i	$-0.744611\pi$
$73$	−1.93117	+	1.40308i	−0.226026	+	0.164218i	0.469009	+	0.883193i	$0.344611\pi$
$74$	0.127172	+	0.0923956i	0.0147834	+	0.0107408i
$75$		0			0
$76$	6.85919			0.786803
$77$	2.54508	−	2.12663i	0.290039	−	0.242352i
$78$		0			0
$79$	−0.207232	−	0.637795i	−0.0233154	−	0.0717576i	0.938722	−	0.344676i	$-0.112011\pi$
$79$	−0.207232	−	0.637795i	−0.0233154	−	0.0717576i	−0.962037	+	0.272918i	$0.912011\pi$
$80$	−13.6394	−	9.90958i	−1.52493	−	1.10793i
$81$		0			0
$82$	0.289476	−	0.890917i	0.0319673	−	0.0983853i
$83$	2.86923	−	8.83059i	0.314939	−	0.969283i	−0.660840	−	0.750527i	$-0.729800\pi$
$83$	2.86923	−	8.83059i	0.314939	−	0.969283i	0.975779	−	0.218757i	$-0.0702001\pi$
$84$		0			0
$85$	21.9576	+	15.9531i	2.38164	+	1.73036i
$86$	0.252730	+	0.777822i	0.0272525	+	0.0838747i
$87$		0			0
$88$	−1.80992	−	1.13618i	−0.192938	−	0.121117i
$89$	12.2106			1.29432			0.647161	−	0.762354i	$-0.275956\pi$
$89$	12.2106			1.29432			0.647161	+	0.762354i	$0.275956\pi$
$90$		0			0
$91$	1.35567	+	0.984955i	0.142113	+	0.103251i
$92$	−0.907912	+	0.659637i	−0.0946564	+	0.0687719i
$93$		0			0
$94$	0.234124	−	0.720561i	0.0241481	−	0.0743202i
$95$	12.3345	−	8.96152i	1.26549	−	0.919432i
$96$		0			0
$97$	4.65368	+	14.3225i	0.472509	+	1.45423i	0.849288	+	0.527931i	$0.177032\pi$
$97$	4.65368	+	14.3225i	0.472509	+	1.45423i	−0.376778	+	0.926304i	$0.622968\pi$
$98$	−0.162147			−0.0163793
$99$		0			0
$100$	−28.1179			−2.81179
$101$	−1.78018	−	5.47883i	−0.177135	−	0.545164i	0.822590	−	0.568635i	$-0.192528\pi$
$101$	−1.78018	−	5.47883i	−0.177135	−	0.545164i	−0.999725	+	0.0234707i	$0.992528\pi$
$102$		0			0
$103$	−6.24116	+	4.53447i	−0.614959	+	0.446794i	−0.851157	−	0.524911i	$-0.824099\pi$
$103$	−6.24116	+	4.53447i	−0.614959	+	0.446794i	0.236198	+	0.971705i	$0.424099\pi$
$104$	0.333646	−	1.02686i	0.0327167	−	0.100692i
$105$		0			0
$106$	0.312053	−	0.226720i	0.0303093	−	0.0220210i
$107$	−13.3192	−	9.67696i	−1.28762	−	0.935507i	−0.287861	−	0.957672i	$-0.592944\pi$
$107$	−13.3192	−	9.67696i	−1.28762	−	0.935507i	−0.999754	+	0.0221652i	$0.992944\pi$
$108$		0			0
$109$	9.74355			0.933263			0.466632	−	0.884452i	$-0.345467\pi$
$109$	9.74355			0.933263			0.466632	+	0.884452i	$0.345467\pi$
$110$	−2.35386	+	0.159708i	−0.224432	+	0.0152275i
$111$		0			0
$112$	−1.18753	−	3.65485i	−0.112211	−	0.345351i
$113$	−2.31156	−	1.67945i	−0.217453	−	0.157989i	0.473726	−	0.880672i	$-0.342909\pi$
$113$	−2.31156	−	1.67945i	−0.217453	−	0.157989i	−0.691180	+	0.722683i	$0.742909\pi$
$114$		0			0
$115$	−0.770830	+	2.37237i	−0.0718803	+	0.221225i
$116$	−5.40832	+	16.6451i	−0.502150	+	1.54546i
$117$		0			0
$118$	0.373733	+	0.271533i	0.0344049	+	0.0249966i
$119$	1.91177	+	5.88383i	0.175252	+	0.539370i
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$	−1.50778			−0.136508
$123$		0			0
$124$	6.92112	+	5.02849i	0.621535	+	0.451572i
$125$	−32.8168	+	23.8428i	−2.93522	+	2.13256i
$126$		0			0
$127$	−4.96015	+	15.2658i	−0.440142	+	1.35462i	0.447582	+	0.894243i	$0.352285\pi$
$127$	−4.96015	+	15.2658i	−0.440142	+	1.35462i	−0.887724	+	0.460375i	$0.847715\pi$
$128$	−4.06088	+	2.95040i	−0.358935	+	0.260781i
$129$		0			0
$130$	−0.368352	−	1.13367i	−0.0323066	−	0.0994294i
$131$	−0.750136			−0.0655397			−0.0327699	−	0.999463i	$-0.510433\pi$
$131$	−0.750136			−0.0655397			−0.0327699	+	0.999463i	$0.510433\pi$
$132$		0			0
$133$	3.47528			0.301345
$134$	0.357897	+	1.10149i	0.0309176	+	0.0951544i
$135$		0			0
$136$	3.22491	−	2.34303i	0.276533	−	0.200913i
$137$	4.01977	−	12.3716i	0.343432	−	1.05697i	−0.618986	−	0.785402i	$-0.712456\pi$
$137$	4.01977	−	12.3716i	0.343432	−	1.05697i	0.962418	−	0.271572i	$-0.0875436\pi$
$138$		0			0
$139$	−3.15607	+	2.29302i	−0.267695	+	0.194492i	−0.713532	−	0.700622i	$-0.752906\pi$
$139$	−3.15607	+	2.29302i	−0.267695	+	0.194492i	0.445838	+	0.895114i	$0.352906\pi$
$140$	−7.00509	−	5.08949i	−0.592038	−	0.430141i
$141$		0			0
$142$	−0.128824			−0.0108107
$143$	2.07129	+	5.15729i	0.173210	+	0.431274i
$144$		0			0
$145$	12.0213	+	36.9979i	0.998318	+	3.07251i
$146$	0.313133	+	0.227505i	0.0259151	+	0.0188284i
$147$		0			0
$148$	−0.591274	+	1.81975i	−0.0486024	+	0.149583i
$149$	−5.73023	+	17.6358i	−0.469439	+	1.44478i	0.383874	+	0.923385i	$0.374590\pi$
$149$	−5.73023	+	17.6358i	−0.469439	+	1.44478i	−0.853313	+	0.521399i	$0.825410\pi$
$150$		0			0
$151$	−16.8259	−	12.2247i	−1.36927	−	0.994832i	−0.997794	−	0.0663888i	$-0.978852\pi$
$151$	−16.8259	−	12.2247i	−1.36927	−	0.994832i	−0.371475	−	0.928443i	$-0.621148\pi$
$152$	−0.691955	−	2.12962i	−0.0561249	−	0.172735i
$153$		0			0
$154$	−0.455474	−	0.285923i	−0.0367032	−	0.0230403i
$155$	19.0156			1.52737
$156$		0			0
$157$	−4.70019	−	3.41489i	−0.375116	−	0.272538i	0.384213	−	0.923244i	$-0.374473\pi$
$157$	−4.70019	−	3.41489i	−0.375116	−	0.272538i	−0.759329	+	0.650707i	$0.774473\pi$
$158$	−0.0879715	+	0.0639150i	−0.00699864	+	0.00508481i
$159$		0			0
$160$	−2.59174	+	7.97656i	−0.204895	+	0.630603i
$161$	−0.460003	+	0.334212i	−0.0362533	+	0.0263396i
$162$		0			0
$163$	−2.75120	−	8.46732i	−0.215491	−	0.663212i	−0.999118	−	0.0419811i	$-0.986633\pi$
$163$	−2.75120	−	8.46732i	−0.215491	−	0.663212i	0.783628	−	0.621230i	$-0.213367\pi$
$164$	11.4026			0.890394
$165$		0			0
$166$	−1.50554			−0.116853
$167$	1.18154	+	3.63641i	0.0914304	+	0.281394i	0.986307	−	0.164920i	$-0.0527366\pi$
$167$	1.18154	+	3.63641i	0.0914304	+	0.281394i	−0.894877	+	0.446314i	$0.852737\pi$
$168$		0			0
$169$	8.24551	−	5.99071i	0.634270	−	0.460824i
$170$	1.35994	−	4.18546i	0.104302	−	0.321010i
$171$		0			0
$172$	−8.05388	+	5.85148i	−0.614102	+	0.446171i
$173$	1.41627	+	1.02898i	0.107677	+	0.0782322i	0.640321	−	0.768107i	$-0.278801\pi$
$173$	1.41627	+	1.02898i	0.107677	+	0.0782322i	−0.532644	+	0.846340i	$0.678801\pi$
$174$		0			0
$175$	−14.2462			−1.07691
$176$	3.10900	−	12.3606i	0.234350	−	0.931715i
$177$		0			0
$178$	−0.611827	−	1.88301i	−0.0458584	−	0.141138i
$179$	−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
$181$	−6.82406	+	21.0023i	−0.507228	+	1.56109i	0.289764	+	0.957098i	$0.406423\pi$
$181$	−6.82406	+	21.0023i	−0.507228	+	1.56109i	−0.796992	+	0.603990i	$0.793577\pi$
$182$	0.0839633	−	0.258413i	0.00622377	−	0.0191548i
$183$		0			0
$184$	0.296392	+	0.215341i	0.0218503	+	0.0158752i
$185$	1.31425	+	4.04485i	0.0966257	+	0.297383i
$186$		0			0
$187$	−5.00509	+	19.8989i	−0.366008	+	1.45515i
$188$	9.22227			0.672603
$189$		0			0
$190$	−2.00000	−	1.45309i	−0.145095	−	0.105418i
$191$	11.9055	−	8.64983i	0.861449	−	0.625879i	−0.0668297	−	0.997764i	$-0.521288\pi$
$191$	11.9055	−	8.64983i	0.861449	−	0.625879i	0.928279	+	0.371885i	$0.121288\pi$
$192$		0			0
$193$	2.63062	−	8.09622i	0.189356	−	0.582779i	−0.810640	−	0.585545i	$-0.800881\pi$
$193$	2.63062	−	8.09622i	0.189356	−	0.582779i	0.999996	+	0.00276642i	$0.000880579\pi$
$194$	1.97552	−	1.43530i	0.141834	−	0.103048i
$195$		0			0
$196$	−0.609909	−	1.87711i	−0.0435650	−	0.134079i
$197$	4.72273			0.336480			0.168240	−	0.985746i	$-0.446192\pi$
$197$	4.72273			0.336480			0.168240	+	0.985746i	$0.446192\pi$
$198$		0			0
$199$	16.7620			1.18822			0.594112	−	0.804382i	$-0.297504\pi$
$199$	16.7620			1.18822			0.594112	+	0.804382i	$0.297504\pi$
$200$	2.83654	+	8.72996i	0.200573	+	0.617301i
$201$		0			0
$202$	−0.755699	+	0.549048i	−0.0531708	+	0.0386309i
$203$	−2.74018	+	8.43342i	−0.192323	+	0.591910i
$204$		0			0
$205$	20.5046	−	14.8975i	1.43211	−	1.04049i
$206$	1.01199	+	0.735251i	0.0705084	+	0.0512274i
$207$		0			0
$208$	6.43964			0.446509
$209$	9.76212	+	6.12816i	0.675260	+	0.423893i
$210$		0			0
$211$	−3.13511	−	9.64887i	−0.215830	−	0.664256i	−0.999094	−	0.0425663i	$-0.986447\pi$
$211$	−3.13511	−	9.64887i	−0.215830	−	0.664256i	0.783264	−	0.621689i	$-0.213553\pi$
$212$	3.79842	+	2.75971i	0.260876	+	0.189538i
$213$		0			0
$214$	−0.824921	+	2.53884i	−0.0563904	+	0.173552i
$215$	−6.83785	+	21.0447i	−0.466338	+	1.43524i
$216$		0			0
$217$	3.50666	+	2.54774i	0.238048	+	0.172952i
$218$	−0.488213	−	1.50256i	−0.0330659	−	0.101767i
$219$		0			0
$220$	−10.7028	−	26.6489i	−0.721584	−	1.79667i
$221$	−10.3670			−0.697358
$222$		0			0
$223$	4.94449	+	3.59238i	0.331107	+	0.240564i	0.740900	−	0.671615i	$-0.234399\pi$
$223$	4.94449	+	3.59238i	0.331107	+	0.240564i	−0.409793	+	0.912179i	$0.634399\pi$
$224$	−1.54666	+	1.12371i	−0.103340	+	0.0750812i
$225$		0			0
$226$	−0.143166	+	0.440619i	−0.00952325	+	0.0293096i
$227$	11.4953	−	8.35181i	0.762969	−	0.554329i	−0.136851	−	0.990592i	$-0.543698\pi$
$227$	11.4953	−	8.35181i	0.762969	−	0.554329i	0.899819	+	0.436262i	$0.143698\pi$
$228$		0			0
$229$	−0.842941	−	2.59431i	−0.0557031	−	0.171437i	0.919334	−	0.393478i	$-0.128728\pi$
$229$	−0.842941	−	2.59431i	−0.0557031	−	0.171437i	−0.975037	+	0.222041i	$0.928728\pi$
$230$	0.404469			0.0266699
$231$		0			0
$232$	5.71351			0.375110
$233$	5.49731	+	16.9190i	0.360141	+	1.10840i	0.952968	+	0.303070i	$0.0980115\pi$
$233$	5.49731	+	16.9190i	0.360141	+	1.10840i	−0.592828	+	0.805329i	$0.701988\pi$
$234$		0			0
$235$	16.5839	−	12.0489i	1.08181	−	0.785982i
$236$	−1.73764	+	5.34791i	−0.113111	+	0.348119i
$237$		0			0
$238$	0.811561	−	0.589634i	0.0526057	−	0.0382203i
$239$	10.2792	+	7.46827i	0.664906	+	0.483082i	0.868316	−	0.496011i	$-0.165202\pi$
$239$	10.2792	+	7.46827i	0.664906	+	0.483082i	−0.203410	+	0.979094i	$0.565202\pi$
$240$		0			0
$241$	−18.6604			−1.20202			−0.601012	−	0.799240i	$-0.705235\pi$
$241$	−18.6604			−1.20202			−0.601012	+	0.799240i	$0.705235\pi$
$242$	−0.775251	−	1.60633i	−0.0498350	−	0.103259i
$243$		0			0
$244$	−5.67144	−	17.4549i	−0.363077	−	1.11744i
$245$	−3.54920	−	2.57865i	−0.226750	−	0.164744i
$246$		0			0
$247$	−1.79958	+	5.53852i	−0.114504	+	0.352408i
$248$	0.863026	−	2.65612i	0.0548022	−	0.168664i
$249$		0			0
$250$	5.32115	+	3.86604i	0.336539	+	0.244510i
$251$	−5.82475	−	17.9267i	−0.367655	−	1.13153i	−0.948302	−	0.317370i	$-0.897200\pi$
$251$	−5.82475	−	17.9267i	−0.367655	−	1.13153i	0.580647	−	0.814155i	$-0.302800\pi$
$252$		0			0
$253$	−1.88149	+	0.127658i	−0.118288	+	0.00802576i
$254$	2.60269			0.163307
$255$		0			0
$256$	−11.2760	−	8.19248i	−0.704749	−	0.512030i
$257$	−8.36076	+	6.07445i	−0.521530	+	0.378914i	−0.817180	−	0.576383i	$-0.804464\pi$
$257$	−8.36076	+	6.07445i	−0.521530	+	0.378914i	0.295650	+	0.955296i	$0.404464\pi$
$258$		0			0
$259$	−0.299575	+	0.921997i	−0.0186147	+	0.0572901i
$260$	11.7385	−	8.52849i	0.727989	−	0.528915i
$261$		0			0
$262$	0.0375865	+	0.115679i	0.00232210	+	0.00714670i
$263$	4.14979			0.255887			0.127943	−	0.991781i	$-0.459162\pi$
$263$	4.14979			0.255887			0.127943	+	0.991781i	$0.459162\pi$
$264$		0			0
$265$	10.4360			0.641079
$266$	−0.174133	−	0.535927i	−0.0106768	−	0.0328598i
$267$		0			0
$268$	−11.4053	+	8.28643i	−0.696689	+	0.506174i
$269$	1.56433	−	4.81452i	0.0953790	−	0.293546i	−0.891973	−	0.452088i	$-0.850679\pi$
$269$	1.56433	−	4.81452i	0.0953790	−	0.293546i	0.987352	+	0.158542i	$0.0506792\pi$
$270$		0			0
$271$	21.2901	−	15.4682i	1.29328	−	0.939625i	0.293417	−	0.955985i	$-0.405208\pi$
$271$	21.2901	−	15.4682i	1.29328	−	0.939625i	0.999866	+	0.0163598i	$0.00520772\pi$
$272$	19.2343	+	13.9745i	1.16625	+	0.847329i
$273$		0			0
$274$	−2.10925			−0.127424
$275$	−40.0179	−	25.1212i	−2.41317	−	1.51487i
$276$		0			0
$277$	7.97843	+	24.5551i	0.479377	+	1.47537i	0.839962	+	0.542645i	$0.182577\pi$
$277$	7.97843	+	24.5551i	0.479377	+	1.47537i	−0.360585	+	0.932726i	$0.617423\pi$
$278$	0.511749	+	0.371807i	0.0306926	+	0.0222995i
$279$		0			0
$280$	−0.873496	+	2.68834i	−0.0522014	+	0.160659i
$281$	1.68057	−	5.17226i	0.100254	−	0.308551i	−0.888333	−	0.459200i	$-0.848136\pi$
$281$	1.68057	−	5.17226i	0.100254	−	0.308551i	0.988587	+	0.150649i	$0.0481362\pi$
$282$		0			0
$283$	−20.5360	−	14.9203i	−1.22074	−	0.886919i	−0.224578	−	0.974456i	$-0.572100\pi$
$283$	−20.5360	−	14.9203i	−1.22074	−	0.886919i	−0.996161	+	0.0875371i	$0.972100\pi$
$284$	−0.484565	−	1.49134i	−0.0287536	−	0.0884946i
$285$		0			0
$286$	0.691528	−	0.577828i	0.0408909	−	0.0341677i
$287$	5.77725			0.341020
$288$		0			0
$289$	−17.2113	−	12.5048i	−1.01243	−	0.735575i
$290$	5.10314	−	3.70765i	0.299667	−	0.217721i
$291$		0			0
$292$	−1.45589	+	4.48076i	−0.0851993	+	0.262217i
$293$	5.46412	−	3.96992i	0.319217	−	0.231925i	−0.416624	−	0.909079i	$-0.636787\pi$
$293$	5.46412	−	3.96992i	0.319217	−	0.231925i	0.735841	+	0.677154i	$0.236787\pi$
$294$		0			0
$295$	3.86233	+	11.8870i	0.224874	+	0.692090i
$296$	0.624638			0.0363064
$297$		0			0
$298$	3.00676			0.174177
$299$	−0.294431	−	0.906165i	−0.0170274	−	0.0524049i
$300$		0			0
$301$	−4.08058	+	2.96472i	−0.235201	+	0.170883i
$302$	−1.04210	+	3.20727i	−0.0599664	+	0.184558i
$303$		0			0
$304$	10.8047	−	7.85005i	0.619690	−	0.450231i
$305$	−33.0034	−	23.9784i	−1.88977	−	1.37300i
$306$		0			0
$307$	−17.6396			−1.00674			−0.503372	−	0.864070i	$-0.667908\pi$
$307$	−17.6396			−1.00674			−0.503372	+	0.864070i	$0.667908\pi$
$308$	1.59676	−	6.34832i	0.0909840	−	0.361729i
$309$		0			0
$310$	−0.952798	−	2.93241i	−0.0541153	−	0.166550i
$311$	−9.90354	−	7.19534i	−0.561578	−	0.408010i	0.270458	−	0.962732i	$-0.412825\pi$
$311$	−9.90354	−	7.19534i	−0.561578	−	0.408010i	−0.832036	+	0.554721i	$0.812825\pi$
$312$		0			0
$313$	0.976343	−	3.00487i	0.0551862	−	0.169846i	−0.919664	−	0.392705i	$-0.871539\pi$
$313$	0.976343	−	3.00487i	0.0551862	−	0.169846i	0.974851	+	0.222860i	$0.0715392\pi$
$314$	−0.291105	+	0.895928i	−0.0164280	+	0.0505602i
$315$		0			0
$316$	−1.07082	−	0.777994i	−0.0602382	−	0.0437656i
$317$	−2.60614	−	8.02087i	−0.146375	−	0.450497i	0.850810	−	0.525473i	$-0.176112\pi$
$317$	−2.60614	−	8.02087i	−0.146375	−	0.450497i	−0.997185	+	0.0749766i	$0.976112\pi$
$318$		0			0
$319$	−22.5683	+	18.8577i	−1.26358	+	1.05583i
$320$	−32.3584			−1.80889
$321$		0			0
$322$	0.0745882	+	0.0541915i	0.00415664	+	0.00301998i
$323$	−17.3941	+	12.6375i	−0.967833	+	0.703172i
$324$		0			0
$325$	7.37701	−	22.7041i	0.409203	−	1.25940i
$326$	−1.16790	+	0.848531i	−0.0646842	+	0.0469958i
$327$		0			0
$328$	−1.15029	−	3.54024i	−0.0635144	−	0.195477i
$329$	4.67256			0.257607
$330$		0			0
$331$	6.13284			0.337092			0.168546	−	0.985694i	$-0.446093\pi$
$331$	6.13284			0.337092			0.168546	+	0.985694i	$0.446093\pi$
$332$	−5.66303	−	17.4290i	−0.310799	−	0.956541i
$333$		0			0
$334$	0.501572	−	0.364414i	0.0274448	−	0.0199398i
$335$	−9.68325	+	29.8020i	−0.529052	+	1.62826i
$336$		0			0
$337$	24.1728	−	17.5626i	1.31678	−	0.956695i	0.316811	−	0.948489i	$-0.397388\pi$
$337$	24.1728	−	17.5626i	1.31678	−	0.956695i	0.999966	−	0.00820616i	$-0.00261213\pi$
$338$	−1.33699	−	0.971377i	−0.0727225	−	0.0528360i
$339$		0			0
$340$	53.5686			2.90516
$341$	5.35770	+	13.3401i	0.290136	+	0.722408i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	2.62922	+	1.91024i	0.141758	+	0.102993i
$345$		0			0
$346$	0.0877165	−	0.269964i	0.00471567	−	0.0145133i
$347$	9.01453	−	27.7439i	0.483925	−	1.48937i	−0.349606	−	0.936897i	$-0.613685\pi$
$347$	9.01453	−	27.7439i	0.483925	−	1.48937i	0.833531	−	0.552472i	$-0.186315\pi$
$348$		0			0
$349$	−10.8347	−	7.87188i	−0.579969	−	0.421372i	0.258744	−	0.965946i	$-0.416691\pi$
$349$	−10.8347	−	7.87188i	−0.579969	−	0.421372i	−0.838713	+	0.544574i	$0.816691\pi$
$350$	0.713826	+	2.19693i	0.0381556	+	0.117431i
$351$		0			0
$352$	−6.32609	+	0.429220i	−0.337182	+	0.0228775i
$353$	21.3175			1.13462			0.567309	−	0.823505i	$-0.307985\pi$
$353$	21.3175			1.13462			0.567309	+	0.823505i	$0.307985\pi$
$354$		0			0
$355$	−2.81979	−	2.04870i	−0.149659	−	0.108734i
$356$	19.4974	−	14.1657i	1.03336	−	0.750782i
$357$		0			0
$358$	−0.644071	+	1.98225i	−0.0340402	+	0.104765i
$359$	−16.6847	+	12.1221i	−0.880584	+	0.639782i	−0.933406	−	0.358822i	$-0.883179\pi$
$359$	−16.6847	+	12.1221i	−0.880584	+	0.639782i	0.0528216	+	0.998604i	$0.483179\pi$
$360$		0			0
$361$	−2.13915	−	6.58362i	−0.112587	−	0.346506i
$362$	3.58072			0.188198
$363$		0			0
$364$	3.30735			0.173352
$365$	3.23607	+	9.95959i	0.169384	+	0.521309i
$366$		0			0
$367$	−26.5799	+	19.3114i	−1.38746	+	1.00805i	−0.391320	+	0.920255i	$0.627982\pi$
$367$	−26.5799	+	19.3114i	−1.38746	+	1.00805i	−0.996139	+	0.0877934i	$0.972018\pi$
$368$	−0.675226	+	2.07813i	−0.0351986	+	0.108330i
$369$		0			0
$370$	0.557909	−	0.405345i	0.0290043	−	0.0210729i
$371$	1.92451	+	1.39824i	0.0999154	+	0.0725928i
$372$		0			0
$373$	26.0979			1.35130			0.675650	−	0.737223i	$-0.263863\pi$
$373$	26.0979			1.35130			0.675650	+	0.737223i	$0.263863\pi$
$374$	3.31942	−	0.225220i	0.171643	−	0.0116458i
$375$		0			0
$376$	−0.930342	−	2.86330i	−0.0479787	−	0.147663i
$377$	−12.0213	−	8.73401i	−0.619130	−	0.449825i
$378$		0			0
$379$	−3.60724	+	11.1020i	−0.185292	+	0.570269i	−0.999953	−	0.00966747i	$-0.996923\pi$
$379$	−3.60724	+	11.1020i	−0.185292	+	0.570269i	0.814662	+	0.579937i	$0.196923\pi$
$380$	9.29883	−	28.6188i	0.477020	−	1.46812i
$381$		0			0
$382$	−1.93044	−	1.40255i	−0.0987698	−	0.0717604i
$383$	4.74963	+	14.6178i	0.242695	+	0.746937i	0.996007	+	0.0892743i	$0.0284548\pi$
$383$	4.74963	+	14.6178i	0.242695	+	0.746937i	−0.753313	+	0.657663i	$0.771545\pi$
$384$		0			0
$385$	−5.42270	−	13.5020i	−0.276366	−	0.688124i
$386$	−1.38034			−0.0702573
$387$		0			0
$388$	24.0466	+	17.4709i	1.22078	+	0.886951i
$389$	−7.80236	+	5.66874i	−0.395595	+	0.287417i	−0.767744	−	0.640756i	$-0.778621\pi$
$389$	−7.80236	+	5.66874i	−0.395595	+	0.287417i	0.372149	+	0.928173i	$0.378621\pi$
$390$		0			0
$391$	1.08703	−	3.34552i	0.0549732	−	0.169190i
$392$	−0.521270	+	0.378725i	−0.0263281	+	0.0191285i
$393$		0			0
$394$	−0.236638	−	0.728297i	−0.0119217	−	0.0366911i
$395$	−2.94203			−0.148030
$396$		0			0
$397$	20.2855			1.01810			0.509050	−	0.860737i	$-0.329997\pi$
$397$	20.2855			1.01810			0.509050	+	0.860737i	$0.329997\pi$
$398$	−0.839879	−	2.58488i	−0.0420993	−	0.129568i
$399$		0			0
$400$	−44.2916	+	32.1798i	−2.21458	+	1.60899i
$401$	2.52051	−	7.75734i	0.125868	−	0.387383i	−0.868190	−	0.496232i	$-0.834717\pi$
$401$	2.52051	−	7.75734i	0.125868	−	0.387383i	0.994058	+	0.108849i	$0.0347165\pi$
$402$		0			0
$403$	−5.87613	+	4.26926i	−0.292711	+	0.212667i
$404$	−9.19862	−	6.68319i	−0.457648	−	0.332501i
$405$		0			0
$406$	1.43783			0.0713582
$407$	−2.46732	+	2.06165i	−0.122301	+	0.102192i
$408$		0			0
$409$	−2.98884	−	9.19870i	−0.147789	−	0.454846i	0.849570	−	0.527475i	$-0.176861\pi$
$409$	−2.98884	−	9.19870i	−0.147789	−	0.454846i	−0.997359	+	0.0726287i	$0.976861\pi$
$410$	−3.32477	−	2.41559i	−0.164199	−	0.119297i
$411$		0			0
$412$	−4.70514	+	14.4809i	−0.231806	+	0.713425i
$413$	−0.880394	+	2.70957i	−0.0433213	+	0.133329i
$414$		0			0
$415$	−32.9544	−	23.9428i	−1.61767	−	1.17531i
$416$	−0.989957	−	3.04678i	−0.0485367	−	0.149380i
$417$		0			0
$418$	0.455887	−	1.81249i	0.0222982	−	0.0886516i
$419$	18.9357			0.925072			0.462536	−	0.886601i	$-0.346940\pi$
$419$	18.9357			0.925072			0.462536	+	0.886601i	$0.346940\pi$
$420$		0			0
$421$	10.5940	+	7.69703i	0.516322	+	0.375130i	0.815217	−	0.579156i	$-0.196618\pi$
$421$	10.5940	+	7.69703i	0.516322	+	0.375130i	−0.298894	+	0.954286i	$0.596618\pi$
$422$	−1.33088	+	0.966937i	−0.0647860	+	0.0470698i
$423$		0			0
$424$	0.473641	−	1.45772i	0.0230021	−	0.0707931i
$425$	71.3037	−	51.8052i	3.45874	−	2.51292i
$426$		0			0
$427$	−2.87350	−	8.84371i	−0.139058	−	0.427977i
$428$	−32.4940			−1.57066
$429$		0			0
$430$	3.58795			0.173027
$431$	5.03804	+	15.5055i	0.242674	+	0.746873i	0.996010	+	0.0892381i	$0.0284432\pi$
$431$	5.03804	+	15.5055i	0.242674	+	0.746873i	−0.753336	+	0.657635i	$0.771557\pi$
$432$		0			0
$433$	−9.45274	+	6.86782i	−0.454270	+	0.330046i	−0.791279	−	0.611455i	$-0.790585\pi$
$433$	−9.45274	+	6.86782i	−0.454270	+	0.330046i	0.337009	+	0.941501i	$0.390585\pi$
$434$	0.217184	−	0.668424i	0.0104252	−	0.0320854i
$435$		0			0
$436$	15.5582	−	11.3037i	0.745100	−	0.541347i
$437$	−1.59864	−	1.16148i	−0.0764733	−	0.0555611i
$438$		0			0
$439$	11.7172			0.559230			0.279615	−	0.960112i	$-0.409793\pi$
$439$	11.7172			0.559230			0.279615	+	0.960112i	$0.409793\pi$
$440$	−7.19417	+	6.01132i	−0.342969	+	0.286578i
$441$		0			0
$442$	0.519450	+	1.59870i	0.0247077	+	0.0760425i
$443$	−10.1670	−	7.38676i	−0.483049	−	0.350955i	0.319456	−	0.947601i	$-0.396500\pi$
$443$	−10.1670	−	7.38676i	−0.483049	−	0.350955i	−0.802505	+	0.596646i	$0.796500\pi$
$444$		0			0
$445$	16.5536	−	50.9467i	0.784716	−	2.41511i
$446$	0.306236	−	0.942496i	0.0145007	−	0.0446285i
$447$		0			0
$448$	−5.96722	−	4.33544i	−0.281925	−	0.204830i
$449$	4.92451	+	15.1561i	0.232402	+	0.715259i	0.997455	+	0.0712927i	$0.0227124\pi$
$449$	4.92451	+	15.1561i	0.232402	+	0.715259i	−0.765054	+	0.643967i	$0.777288\pi$
$450$		0			0
$451$	16.2284	+	10.1874i	0.764166	+	0.479704i
$452$	−5.63937			−0.265254
$453$		0			0
$454$	−1.86393	−	1.35422i	−0.0874785	−	0.0635568i
$455$	5.94742	−	4.32105i	0.278819	−	0.202574i
$456$		0			0
$457$	−7.35290	+	22.6299i	−0.343954	+	1.05858i	0.618187	+	0.786031i	$0.287867\pi$
$457$	−7.35290	+	22.6299i	−0.343954	+	1.05858i	−0.962141	+	0.272551i	$0.912133\pi$
$458$	−0.357834	+	0.259982i	−0.0167205	+	0.0121482i
$459$		0			0
$460$	1.52139	+	4.68237i	0.0709353	+	0.218317i
$461$	22.6035			1.05275			0.526375	−	0.850252i	$-0.323551\pi$
$461$	22.6035			1.05275			0.526375	+	0.850252i	$0.323551\pi$
$462$		0			0
$463$	3.03759			0.141169			0.0705843	−	0.997506i	$-0.477514\pi$
$463$	3.03759			0.141169			0.0705843	+	0.997506i	$0.477514\pi$
$464$	10.5304	+	32.4091i	0.488860	+	1.50456i
$465$		0			0
$466$	2.33365	−	1.69549i	0.108104	−	0.0785422i
$467$	7.10896	−	21.8791i	0.328963	−	1.01244i	−0.640657	−	0.767828i	$-0.721338\pi$
$467$	7.10896	−	21.8791i	0.328963	−	1.01244i	0.969620	−	0.244617i	$-0.0786623\pi$
$468$		0			0
$469$	−5.77861	+	4.19841i	−0.266831	+	0.193864i
$470$	−2.68903	−	1.95369i	−0.124036	−	0.0901171i
$471$		0			0
$472$	1.83569			0.0844946
$473$	−16.6903	+	1.13242i	−0.767419	+	0.0520688i
$474$		0			0
$475$	−15.2993	−	47.0865i	−0.701982	−	2.16048i
$476$	9.87858	+	7.17721i	0.452784	+	0.328967i
$477$		0			0
$478$	0.636639	−	1.95937i	0.0291192	−	0.0896197i
$479$	−2.52554	+	7.77283i	−0.115395	+	0.355150i	−0.992029	−	0.126008i	$-0.959783\pi$
$479$	−2.52554	+	7.77283i	−0.115395	+	0.355150i	0.876634	+	0.481158i	$0.159783\pi$
$480$		0			0
$481$	−1.31425	−	0.954860i	−0.0599247	−	0.0435379i
$482$	0.935003	+	2.87764i	0.0425882	+	0.131073i
$483$		0			0
$484$	15.6797	−	15.0169i	0.712713	−	0.682585i
$485$	66.0673			2.99996
$486$		0			0
$487$	0.808395	+	0.587334i	0.0366319	+	0.0266146i	0.605951	−	0.795502i	$-0.292793\pi$
$487$	0.808395	+	0.587334i	0.0366319	+	0.0266146i	−0.569319	+	0.822117i	$0.692793\pi$
$488$	−4.84720	+	3.52170i	−0.219423	+	0.159420i
$489$		0			0
$490$	−0.219819	+	0.676533i	−0.00993040	+	0.0305626i
$491$	19.6556	−	14.2806i	0.887046	−	0.644476i	−0.0480603	−	0.998844i	$-0.515304\pi$
$491$	19.6556	−	14.2806i	0.887046	−	0.644476i	0.935106	+	0.354368i	$0.115304\pi$
$492$		0			0
$493$	−16.9525	−	52.1744i	−0.763502	−	2.34982i
$494$	0.944272			0.0424848
$495$		0			0
$496$	16.6571			0.747927
$497$	−0.245510	−	0.755602i	−0.0110126	−	0.0338934i
$498$		0			0
$499$	33.2350	−	24.1466i	1.48780	−	1.08095i	0.512865	−	0.858469i	$-0.328584\pi$
$499$	33.2350	−	24.1466i	1.48780	−	1.08095i	0.974937	−	0.222482i	$-0.0714160\pi$
$500$	−24.7402	+	76.1426i	−1.10642	+	3.40520i
$501$		0			0
$502$	−2.47265	+	1.79648i	−0.110360	+	0.0801809i
$503$	−8.35469	−	6.07004i	−0.372517	−	0.270650i	0.385737	−	0.922609i	$-0.373947\pi$
$503$	−8.35469	−	6.07004i	−0.372517	−	0.270650i	−0.758254	+	0.651959i	$0.773947\pi$
$504$		0			0
$505$	−25.2729			−1.12463
$506$	0.113961	+	0.283750i	0.00506617	+	0.0126142i
$507$		0			0
$508$	9.78989	+	30.1302i	0.434356	+	1.33681i
$509$	−32.8546	−	23.8703i	−1.45625	−	1.05803i	−0.984319	−	0.176397i	$-0.943556\pi$
$509$	−32.8546	−	23.8703i	−1.45625	−	1.05803i	−0.471935	−	0.881633i	$-0.656444\pi$
$510$		0			0
$511$	−0.737640	+	2.27022i	−0.0326313	+	0.100429i
$512$	−3.80061	+	11.6971i	−0.167965	+	0.516943i
$513$		0			0
$514$	1.35567	+	0.984955i	0.0597962	+	0.0434445i
$515$	10.4583	+	32.1875i	0.460850	+	1.41835i
$516$		0			0
$517$	13.1253	+	8.23939i	0.577250	+	0.362368i
$518$	0.157193			0.00690666
$519$		0			0
$520$	−3.83207	−	2.78416i	−0.168048	−	0.122094i
$521$	−17.9719	+	13.0573i	−0.787363	+	0.572053i	−0.907180	−	0.420743i	$-0.861769\pi$
$521$	−17.9719	+	13.0573i	−0.787363	+	0.572053i	0.119817	+	0.992796i	$0.461769\pi$
$522$		0			0
$523$	−7.00397	+	21.5560i	−0.306262	+	0.942578i	0.672941	+	0.739696i	$0.265031\pi$
$523$	−7.00397	+	21.5560i	−0.306262	+	0.942578i	−0.979203	+	0.202882i	$0.934969\pi$
$524$	−1.19779	+	0.870246i	−0.0523257	+	0.0380169i
$525$		0			0
$526$	−0.207930	−	0.639943i	−0.00906618	−	0.0279028i
$527$	−26.8158			−1.16811
$528$		0			0
$529$	−22.6767			−0.985943
$530$	−0.522910	−	1.60935i	−0.0227137	−	0.0699057i
$531$		0			0
$532$	5.54920	−	4.03173i	0.240588	−	0.174798i
$533$	−2.99159	+	9.20715i	−0.129580	+	0.398806i
$534$		0			0
$535$	−58.4320	+	42.4533i	−2.52624	+	1.83542i
$536$	3.72331	+	2.70514i	0.160822	+	0.116844i
$537$		0			0
$538$	−0.820835			−0.0353887
$539$	0.809017	−	3.21644i	0.0348468	−	0.138542i
$540$		0			0
$541$	−1.93649	−	5.95991i	−0.0832563	−	0.256237i	0.900759	−	0.434319i	$-0.143011\pi$
$541$	−1.93649	−	5.95991i	−0.0832563	−	0.256237i	−0.984016	+	0.178082i	$0.943011\pi$
$542$	−3.45213	−	2.50812i	−0.148282	−	0.107733i
$543$		0			0
$544$	3.65488	−	11.2486i	0.156702	−	0.482278i
$545$	13.2091	−	40.6534i	0.565815	−	1.74140i
$546$		0			0
$547$	−27.5807	−	20.0386i	−1.17927	−	0.856787i	−0.187178	−	0.982326i	$-0.559934\pi$
$547$	−27.5807	−	20.0386i	−1.17927	−	0.856787i	−0.992089	+	0.125539i	$0.959934\pi$
$548$	−7.93384	−	24.4179i	−0.338917	−	1.04308i
$549$		0			0
$550$	−1.86882	+	7.42994i	−0.0796868	+	0.316814i
$551$	−30.8168			−1.31284
$552$		0			0
$553$	−0.542541	−	0.394179i	−0.0230712	−	0.0167622i
$554$	3.38690	−	2.46072i	0.143895	−	0.104546i
$555$		0			0
$556$	−2.37933	+	7.32283i	−0.100906	+	0.310557i
$557$	−21.3574	+	15.5170i	−0.904941	+	0.657478i	−0.939730	−	0.341916i	$-0.888924\pi$
$557$	−21.3574	+	15.5170i	−0.904941	+	0.657478i	0.0347891	+	0.999395i	$0.488924\pi$
$558$		0			0
$559$	−2.61183	−	8.03838i	−0.110469	−	0.339987i
$560$	−16.8592			−0.712431
$561$		0			0
$562$	−0.881827			−0.0371976
$563$	2.11715	+	6.51593i	0.0892274	+	0.274614i	0.985706	−	0.168473i	$-0.0538835\pi$
$563$	2.11715	+	6.51593i	0.0892274	+	0.274614i	−0.896479	+	0.443086i	$0.853884\pi$
$564$		0			0
$565$	−10.1409	+	7.36783i	−0.426633	+	0.309967i
$566$	−1.27189	+	3.91448i	−0.0534616	+	0.164538i
$567$		0			0
$568$	−0.414143	+	0.300892i	−0.0173770	+	0.0126252i
$569$	14.8866	+	10.8157i	0.624079	+	0.453420i	0.854344	−	0.519708i	$-0.173959\pi$
$569$	14.8866	+	10.8157i	0.624079	+	0.453420i	−0.230265	+	0.973128i	$0.573959\pi$
$570$		0			0
$571$	0.336889			0.0140984			0.00704918	−	0.999975i	$-0.497756\pi$
$571$	0.336889			0.0140984			0.00704918	+	0.999975i	$0.497756\pi$
$572$	9.29041	+	5.83204i	0.388452	+	0.243850i
$573$		0			0
$574$	−0.289476	−	0.890917i	−0.0120825	−	0.0371862i
$575$	6.55332	+	4.76126i	0.273292	+	0.198558i
$576$		0			0
$577$	−7.98337	+	24.5703i	−0.332352	+	1.02288i	0.635659	+	0.771970i	$0.280728\pi$
$577$	−7.98337	+	24.5703i	−0.332352	+	1.02288i	−0.968012	+	0.250905i	$0.919272\pi$
$578$	−1.06598	+	3.28075i	−0.0443389	+	0.136461i
$579$		0			0
$580$	62.1171	+	45.1307i	2.57927	+	1.87395i
$581$	−2.86923	−	8.83059i	−0.119036	−	0.366355i
$582$		0			0
$583$	2.94038	+	7.32126i	0.121778	+	0.303216i
$584$	1.53804			0.0636446
$585$		0			0
$586$	−0.885992	−	0.643711i	−0.0366000	−	0.0265914i
$587$	−3.02099	+	2.19488i	−0.124689	+	0.0905922i	−0.648382	−	0.761315i	$-0.724554\pi$
$587$	−3.02099	+	2.19488i	−0.124689	+	0.0905922i	0.523693	+	0.851907i	$0.324554\pi$
$588$		0			0
$589$	−4.65488	+	14.3262i	−0.191801	+	0.590303i
$590$	1.63959	−	1.19123i	0.0675008	−	0.0490422i
$591$		0			0
$592$	1.15125	+	3.54318i	0.0473160	+	0.145624i
$593$	−17.5647			−0.721295			−0.360648	−	0.932702i	$-0.617444\pi$
$593$	−17.5647			−0.721295			−0.360648	+	0.932702i	$0.617444\pi$
$594$		0			0
$595$	27.1411			1.11268
$596$	11.3098	+	34.8080i	0.463268	+	1.42579i
$597$		0			0
$598$	−0.124988	+	0.0908090i	−0.00511114	+	0.00371346i
$599$	−3.49462	+	10.7553i	−0.142786	+	0.439451i	−0.996720	−	0.0809314i	$-0.974211\pi$
$599$	−3.49462	+	10.7553i	−0.142786	+	0.439451i	0.853933	+	0.520382i	$0.174211\pi$
$600$		0			0
$601$	23.4470	−	17.0353i	0.956424	−	0.694883i	0.00410642	−	0.999992i	$-0.498693\pi$
$601$	23.4470	−	17.0353i	0.956424	−	0.694883i	0.952317	+	0.305109i	$0.0986929\pi$
$602$	0.661655	+	0.480720i	0.0269670	+	0.0195927i
$603$		0			0
$604$	−41.0490			−1.67026
$605$	8.57632	−	47.4894i	0.348677	−	1.93072i
$606$		0			0
$607$	2.26926	+	6.98406i	0.0921063	+	0.283474i	0.986489	−	0.163829i	$-0.0523845\pi$
$607$	2.26926	+	6.98406i	0.0921063	+	0.283474i	−0.894382	+	0.447303i	$0.852385\pi$
$608$	−5.37507	−	3.90522i	−0.217988	−	0.158377i
$609$		0			0
$610$	−2.04406	+	6.29096i	−0.0827615	+	0.254714i
$611$	−2.41955	+	7.44662i	−0.0978846	+	0.301258i
$612$		0			0
$613$	−15.3337	−	11.1406i	−0.619323	−	0.449965i	0.233362	−	0.972390i	$-0.425027\pi$
$613$	−15.3337	−	11.1406i	−0.619323	−	0.449965i	−0.852685	+	0.522425i	$0.825027\pi$
$614$	0.883853	+	2.72022i	0.0356694	+	0.109779i
$615$		0			0
$616$	−2.13208	+	0.144660i	−0.0859041	+	0.00582852i
$617$	−25.2571			−1.01681			−0.508407	−	0.861117i	$-0.669766\pi$
$617$	−25.2571			−1.01681			−0.508407	+	0.861117i	$0.669766\pi$
$618$		0			0
$619$	12.5984	+	9.15329i	0.506373	+	0.367902i	0.811446	−	0.584427i	$-0.198681\pi$
$619$	12.5984	+	9.15329i	0.506373	+	0.367902i	−0.305073	+	0.952329i	$0.598681\pi$
$620$	30.3633	−	22.0603i	1.21942	−	0.885962i
$621$		0			0
$622$	−0.613373	+	1.88777i	−0.0245940	+	0.0756926i
$623$	9.87858	−	7.17721i	0.395777	−	0.287549i
$624$		0			0
$625$	32.9796	+	101.501i	1.31918	+	4.06003i
$626$	−0.512306			−0.0204759
$627$		0			0
$628$	−11.4668			−0.457573
$629$	−1.85336	−	5.70405i	−0.0738983	−	0.227436i
$630$		0			0
$631$	29.1383	−	21.1702i	1.15998	−	0.842773i	0.170202	−	0.985409i	$-0.445558\pi$
$631$	29.1383	−	21.1702i	1.15998	−	0.842773i	0.989775	+	0.142636i	$0.0455579\pi$
$632$	−0.133525	+	0.410948i	−0.00531134	+	0.0163466i
$633$		0			0
$634$	−1.10632	+	0.803791i	−0.0439377	+	0.0319226i
$635$	56.9696	+	41.3908i	2.26077	+	1.64254i
$636$		0			0
$637$	1.67571			0.0663939
$638$	4.03888	+	2.53540i	0.159901	+	0.100378i
$639$		0			0
$640$	6.80484	+	20.9432i	0.268985	+	0.827851i
$641$	−21.6339	−	15.7179i	−0.854487	−	0.620821i	0.0718924	−	0.997412i	$-0.477096\pi$
$641$	−21.6339	−	15.7179i	−0.854487	−	0.620821i	−0.926380	+	0.376591i	$0.877096\pi$
$642$		0			0
$643$	2.26004	−	6.95569i	0.0891273	−	0.274306i	−0.896551	−	0.442940i	$-0.853936\pi$
$643$	2.26004	−	6.95569i	0.0891273	−	0.274306i	0.985679	+	0.168634i	$0.0539356\pi$
$644$	−0.346792	+	1.06731i	−0.0136655	+	0.0420581i
$645$		0			0
$646$	2.82040	+	2.04914i	0.110967	+	0.0806224i
$647$	10.8224	+	33.3080i	0.425474	+	1.30947i	0.902540	+	0.430606i	$0.141700\pi$
$647$	10.8224	+	33.3080i	0.425474	+	1.30947i	−0.477067	+	0.878867i	$0.658300\pi$
$648$		0			0
$649$	−7.25098	+	6.05879i	−0.284626	+	0.237828i
$650$	−3.87086			−0.151828
$651$		0			0
$652$	−14.2161	−	10.3286i	−0.556745	−	0.404499i
$653$	−3.27764	+	2.38134i	−0.128264	+	0.0931891i	−0.650067	−	0.759877i	$-0.725259\pi$
$653$	−3.27764	+	2.38134i	−0.128264	+	0.0931891i	0.521804	+	0.853066i	$0.325259\pi$
$654$		0			0
$655$	−1.01694	+	3.12982i	−0.0397352	+	0.122292i
$656$	17.9615	−	13.0498i	0.701279	−	0.509509i
$657$		0			0
$658$	−0.234124	−	0.720561i	−0.00912712	−	0.0280904i
$659$	−28.6360			−1.11550			−0.557750	−	0.830009i	$-0.688335\pi$
$659$	−28.6360			−1.11550			−0.557750	+	0.830009i	$0.688335\pi$
$660$		0			0
$661$	45.2741			1.76096			0.880479	−	0.474085i	$-0.157221\pi$
$661$	45.2741			1.76096			0.880479	+	0.474085i	$0.157221\pi$
$662$	−0.307294	−	0.945753i	−0.0119433	−	0.0367577i
$663$		0			0
$664$	−4.84001	+	3.51648i	−0.187829	+	0.136466i
$665$	4.71135	−	14.5000i	0.182698	−	0.562287i
$666$		0			0
$667$	4.07904	−	2.96360i	0.157941	−	0.114751i
$668$	6.10530	+	4.43576i	0.236221	+	0.171625i
$669$		0			0
$670$	5.08099			0.196296
$671$	7.52291	−	29.9091i	0.290419	−	1.15463i
$672$		0			0
$673$	0.0157313	+	0.0484159i	0.000606396	+	0.00186630i	0.951359	−	0.308084i	$-0.0996877\pi$
$673$	0.0157313	+	0.0484159i	0.000606396	+	0.00186630i	−0.950753	+	0.309950i	$0.899688\pi$
$674$	−3.91956	−	2.84772i	−0.150976	−	0.109690i
$675$		0			0
$676$	6.21620	−	19.1315i	0.239085	−	0.735827i
$677$	−12.0961	+	37.2279i	−0.464890	+	1.43079i	0.394230	+	0.919012i	$0.371011\pi$
$677$	−12.0961	+	37.2279i	−0.464890	+	1.43079i	−0.859121	+	0.511773i	$0.828989\pi$
$678$		0			0
$679$	12.1835	+	8.85182i	0.467559	+	0.339702i
$680$	−5.40399	−	16.6318i	−0.207234	−	0.637800i
$681$		0			0
$682$	1.78874	−	1.49464i	0.0684945	−	0.0572328i
$683$	−15.4140			−0.589800			−0.294900	−	0.955528i	$-0.595286\pi$
$683$	−15.4140			−0.589800			−0.294900	+	0.955528i	$0.595286\pi$
$684$		0			0
$685$	−46.1688	−	33.5436i	−1.76402	−	1.28164i
$686$	−0.131180	+	0.0953077i	−0.00500847	+	0.00363887i
$687$		0			0
$688$	−5.98977	+	18.4346i	−0.228358	+	0.702814i
$689$	−3.22491	+	2.34303i	−0.122859	+	0.0892624i
$690$		0			0
$691$	−11.8275	−	36.4013i	−0.449939	−	1.38477i	−0.876975	−	0.480536i	$-0.840442\pi$
$691$	−11.8275	−	36.4013i	−0.449939	−	1.38477i	0.427036	−	0.904235i	$-0.359558\pi$
$692$	3.45520			0.131347
$693$		0			0
$694$	−4.73010			−0.179552
$695$	5.28865	+	16.2768i	0.200610	+	0.617414i
$696$		0			0
$697$	−28.9157	+	21.0085i	−1.09526	+	0.795752i
$698$	−0.671045	+	2.06526i	−0.0253994	+	0.0781714i
$699$		0			0
$700$	−22.7479	+	16.5273i	−0.859789	+	0.624673i
$701$	−1.12351	−	0.816275i	−0.0424342	−	0.0308303i	0.566366	−	0.824154i	$-0.308349\pi$
$701$	−1.12351	−	0.816275i	−0.0424342	−	0.0308303i	−0.608800	+	0.793324i	$0.708349\pi$
$702$		0			0
$703$	−3.36909			−0.127068
$704$	−9.11711	−	22.7007i	−0.343614	−	0.855564i
$705$		0			0
$706$	−1.06814	−	3.28740i	−0.0402000	−	0.123723i
$707$	−4.66057	−	3.38611i	−0.175279	−	0.127348i
$708$		0			0
$709$	−3.96659	+	12.2079i	−0.148968	+	0.458477i	−0.997500	−	0.0706674i	$-0.977487\pi$
$709$	−3.96659	+	12.2079i	−0.148968	+	0.458477i	0.848532	+	0.529145i	$0.177487\pi$
$710$	−0.174643	+	0.537496i	−0.00655424	+	0.0201719i
$711$		0			0
$712$	−6.36503	−	4.62446i	−0.238539	−	0.173309i
$713$	−0.761591	−	2.34394i	−0.0285218	−	0.0877811i
$714$		0			0
$715$	24.3259	−	1.65049i	0.909739	−	0.0617250i
$716$	−25.3702			−0.948131
$717$		0			0
$718$	2.70538	+	1.96557i	0.100964	+	0.0733545i
$719$	−17.3983	+	12.6406i	−0.648849	+	0.471416i	−0.862879	−	0.505411i	$-0.831341\pi$
$719$	−17.3983	+	12.6406i	−0.648849	+	0.471416i	0.214030	+	0.976827i	$0.431341\pi$
$720$		0			0
$721$	−2.38391	+	7.33692i	−0.0887814	+	0.273241i
$722$	−0.908083	+	0.659761i	−0.0337953	+	0.0245537i
$723$		0			0
$724$	13.4687	+	41.4524i	0.500560	+	1.54057i
$725$	126.327			4.69168
$726$		0			0
$727$	−5.35770			−0.198706			−0.0993531	−	0.995052i	$-0.531677\pi$
$727$	−5.35770			−0.198706			−0.0993531	+	0.995052i	$0.531677\pi$
$728$	−0.333646	−	1.02686i	−0.0123657	−	0.0380578i
$729$		0			0
$730$	1.37373	−	0.998076i	0.0508441	−	0.0369404i
$731$	9.64275	−	29.6773i	0.356650	−	1.09766i
$732$		0			0
$733$	−33.5342	+	24.3640i	−1.23861	+	0.899906i	−0.997505	−	0.0705923i	$-0.977511\pi$
$733$	−33.5342	+	24.3640i	−1.23861	+	0.899906i	−0.241109	+	0.970498i	$0.577511\pi$
$734$	4.30985	+	3.13129i	0.159080	+	0.115578i
$735$		0			0
$736$	1.08703			0.0400683
$737$	−23.6355	+	1.60365i	−0.870625	+	0.0590711i
$738$		0			0
$739$	13.1668	+	40.5231i	0.484347	+	1.49067i	0.832924	+	0.553388i	$0.186665\pi$
$739$	13.1668	+	40.5231i	0.484347	+	1.49067i	−0.348576	+	0.937280i	$0.613335\pi$
$740$	6.79105	+	4.93399i	0.249644	+	0.181377i
$741$		0			0
$742$	0.119194	−	0.366841i	0.00437574	−	0.0134671i
$743$	9.40891	−	28.9576i	0.345179	−	1.06235i	−0.616308	−	0.787505i	$-0.711372\pi$
$743$	9.40891	−	28.9576i	0.345179	−	1.06235i	0.961488	−	0.274848i	$-0.0886275\pi$
$744$		0			0
$745$	65.8143	+	47.8169i	2.41125	+	1.75188i
$746$	−1.30767	−	4.02459i	−0.0478772	−	0.147351i
$747$		0			0
$748$	15.0931	+	37.5804i	0.551860	+	1.37407i
$749$	−16.4634			−0.601561
$750$		0			0
$751$	−7.33483	−	5.32907i	−0.267652	−	0.194460i	0.445862	−	0.895102i	$-0.352897\pi$
$751$	−7.33483	−	5.32907i	−0.267652	−	0.194460i	−0.713514	+	0.700641i	$0.752897\pi$
$752$	14.5270	−	10.5545i	0.529746	−	0.384883i
$753$		0			0
$754$	−0.744538	+	2.29145i	−0.0271145	+	0.0834498i
$755$	−73.8159	+	53.6304i	−2.68644	+	1.95181i
$756$		0			0
$757$	2.41984	+	7.44750i	0.0879505	+	0.270684i	0.985352	−	0.170530i	$-0.0545480\pi$
$757$	2.41984	+	7.44750i	0.0879505	+	0.270684i	−0.897402	+	0.441214i	$0.854548\pi$
$758$	1.89279			0.0687493
$759$		0			0
$760$	−9.82355			−0.356338
$761$	−8.18844	−	25.2014i	−0.296831	−	0.913551i	−0.982600	−	0.185732i	$-0.940534\pi$
$761$	−8.18844	−	25.2014i	−0.296831	−	0.913551i	0.685770	−	0.727819i	$-0.259466\pi$
$762$		0			0
$763$	7.88270	−	5.72712i	0.285373	−	0.207336i
$764$	8.97540	−	27.6235i	0.324719	−	0.999381i
$765$		0			0
$766$	2.01625	−	1.46489i	0.0728500	−	0.0529287i
$767$	−3.86233	−	2.80615i	−0.139461	−	0.101324i
$768$		0			0
$769$	−26.3995			−0.951989			−0.475995	−	0.879448i	$-0.657912\pi$
$769$	−26.3995			−0.951989			−0.475995	+	0.879448i	$0.657912\pi$
$770$	−1.81044	+	1.51277i	−0.0652438	+	0.0545166i
$771$		0			0
$772$	−5.19208	−	15.9796i	−0.186867	−	0.575117i
$773$	27.6333	+	20.0768i	0.993901	+	0.722111i	0.960772	−	0.277340i	$-0.0894528\pi$
$773$	27.6333	+	20.0768i	0.993901	+	0.722111i	0.0331288	+	0.999451i	$0.489453\pi$
$774$		0			0
$775$	19.0818	−	58.7277i	0.685438	−	2.10956i
$776$	2.99848	−	9.22838i	0.107639	−	0.331280i
$777$		0			0
$778$	1.26513	+	0.919171i	0.0453571	+	0.0329539i
$779$	6.20431	+	19.0949i	0.222293	+	0.684146i
$780$		0			0
$781$	0.642753	−	2.55542i	0.0229995	−	0.0914401i
$782$	−0.570383			−0.0203969
$783$		0			0
$784$	−3.10900	−	2.25882i	−0.111036	−	0.0806723i
$785$	−20.6200	+	14.9813i	−0.735959	+	0.534705i
$786$		0			0
$787$	3.63104	−	11.1752i	0.129433	−	0.398353i	−0.865250	−	0.501341i	$-0.832840\pi$
$787$	3.63104	−	11.1752i	0.129433	−	0.398353i	0.994683	+	0.102988i	$0.0328404\pi$
$788$	7.54108	−	5.47891i	0.268640	−	0.195178i
$789$		0			0
$790$	0.147414	+	0.453695i	0.00524477	+	0.0161417i
$791$	−2.85725			−0.101592
$792$		0			0
$793$	15.5821			0.553337
$794$	−1.01643	−	3.12825i	−0.0360718	−	0.111017i
$795$		0			0
$796$	26.7649	−	19.4458i	0.948656	−	0.689239i
$797$	−4.72880	+	14.5537i	−0.167503	+	0.515520i	−0.999212	−	0.0396911i	$-0.987363\pi$
$797$	−4.72880	+	14.5537i	−0.167503	+	0.515520i	0.831709	+	0.555211i	$0.187363\pi$
$798$		0			0
$799$	−23.3866	+	16.9913i	−0.827358	+	0.601111i
$800$	22.0341	+	16.0087i	0.779022	+	0.565992i
$801$		0			0
$802$	−1.32256			−0.0467013
$803$	−6.07526	+	5.07637i	−0.214391	+	0.179141i
$804$		0			0
$805$	0.770830	+	2.37237i	0.0271682	+	0.0836151i
$806$	0.952798	+	0.692248i	0.0335609	+	0.0243834i
$807$		0			0
$808$	−1.14702	+	3.53015i	−0.0403519	+	0.124190i
$809$	−5.63373	+	17.3388i	−0.198071	+	0.609601i	0.801856	+	0.597518i	$0.203846\pi$
$809$	−5.63373	+	17.3388i	−0.198071	+	0.609601i	−0.999927	+	0.0120833i	$0.996154\pi$
$810$		0			0
$811$	−5.04254	−	3.66362i	−0.177068	−	0.128647i	0.495721	−	0.868482i	$-0.334904\pi$
$811$	−5.04254	−	3.66362i	−0.177068	−	0.128647i	−0.672789	+	0.739835i	$0.734904\pi$
$812$	5.40832	+	16.6451i	0.189795	+	0.584129i
$813$		0			0
$814$	0.441557	+	0.277187i	0.0154766	+	0.00971539i
$815$	−39.0582			−1.36815
$816$		0			0
$817$	−14.1812	−	10.3032i	−0.496136	−	0.360464i
$818$	−1.26878	+	0.921825i	−0.0443619	+	0.0322308i
$819$		0			0
$820$	15.4582	−	47.5755i	0.539825	−	1.66141i
$821$	−23.9791	+	17.4219i	−0.836878	+	0.608027i	−0.921497	−	0.388386i	$-0.873033\pi$
$821$	−23.9791	+	17.4219i	−0.836878	+	0.608027i	0.0846188	+	0.996413i	$0.473033\pi$
$822$		0			0
$823$	−6.09698	−	18.7646i	−0.212527	−	0.654092i	−0.999320	−	0.0368743i	$-0.988260\pi$
$823$	−6.09698	−	18.7646i	−0.212527	−	0.654092i	0.786793	−	0.617217i	$-0.211740\pi$
$824$	4.97065			0.173161
$825$		0			0
$826$	0.461960			0.0160736
$827$	−12.7225	−	39.1560i	−0.442406	−	1.36159i	−0.885303	−	0.465014i	$-0.846049\pi$
$827$	−12.7225	−	39.1560i	−0.442406	−	1.36159i	0.442897	−	0.896572i	$-0.353951\pi$
$828$		0			0
$829$	−18.4424	+	13.3992i	−0.640532	+	0.465374i	−0.860033	−	0.510238i	$-0.829557\pi$
$829$	−18.4424	+	13.3992i	−0.640532	+	0.465374i	0.219501	+	0.975612i	$0.429557\pi$
$830$	−2.04102	+	6.28163i	−0.0708450	+	0.218038i
$831$		0			0
$832$	9.99931	−	7.26492i	0.346664	−	0.251866i
$833$	5.00509	+	3.63641i	0.173416	+	0.125994i
$834$		0			0
$835$	16.7741			0.580492
$836$	22.6972	−	1.53998i	0.784998	−	0.0532615i
$837$		0			0
$838$	−0.948799	−	2.92010i	−0.0327757	−	0.100873i
$839$	−38.2442	−	27.7861i	−1.32034	−	0.959281i	−0.999928	−	0.0120017i	$-0.996180\pi$
$839$	−38.2442	−	27.7861i	−1.32034	−	0.959281i	−0.320409	−	0.947279i	$-0.603820\pi$
$840$		0			0
$841$	15.3369	−	47.2021i	0.528858	−	1.62766i
$842$	0.656139	−	2.01939i	0.0226121	−	0.0695928i
$843$		0			0
$844$	−16.1998	−	11.7699i	−0.557622	−	0.405136i
$845$	−13.8170	−	42.5245i	−0.475321	−	1.46289i
$846$		0			0
$847$	7.94427	−	7.60845i	0.272968	−	0.261430i
$848$	9.14167			0.313926
$849$		0			0
$850$	−11.5617	−	8.40006i	−0.396563	−	0.288120i
$851$	0.445948	−	0.324000i	0.0152869	−	0.0111066i
$852$		0			0
$853$	3.35434	−	10.3236i	0.114850	−	0.353473i	−0.877065	−	0.480371i	$-0.840502\pi$
$853$	3.35434	−	10.3236i	0.114850	−	0.353473i	0.991916	+	0.126898i	$0.0405020\pi$
$854$	−1.21982	+	0.886250i	−0.0417413	+	0.0303269i
$855$		0			0
$856$	3.27799	+	10.0886i	0.112040	+	0.344822i
$857$	−28.5431			−0.975014			−0.487507	−	0.873119i	$-0.662094\pi$
$857$	−28.5431			−0.975014			−0.487507	+	0.873119i	$0.662094\pi$
$858$		0			0
$859$	−36.8034			−1.25572			−0.627858	−	0.778328i	$-0.716068\pi$
$859$	−36.8034			−1.25572			−0.627858	+	0.778328i	$0.716068\pi$
$860$	13.4959	+	41.5362i	0.460207	+	1.41637i
$861$		0			0
$862$	2.13868	−	1.55384i	0.0728438	−	0.0529241i
$863$	13.9537	−	42.9451i	0.474990	−	1.46187i	−0.370982	−	0.928640i	$-0.620979\pi$
$863$	13.9537	−	42.9451i	0.474990	−	1.46187i	0.845972	−	0.533228i	$-0.179021\pi$
$864$		0			0
$865$	6.21327	−	4.51421i	0.211258	−	0.153488i
$866$	1.53274	+	1.11360i	0.0520845	+	0.0378416i
$867$		0			0
$868$	8.55498			0.290375
$869$	−0.828929	−	2.06395i	−0.0281195	−	0.0700146i
$870$		0			0
$871$	−3.69867	−	11.3833i	−0.125325	−	0.385710i
$872$	−5.07903	−	3.69013i	−0.171998	−	0.124964i
$873$		0			0
$874$	−0.0990113	+	0.304726i	−0.00334911	+	0.0103075i
$875$	−12.5349	+	38.5784i	−0.423757	+	1.30419i
$876$		0			0
$877$	−28.1956	−	20.4853i	−0.952097	−	0.691739i	−0.000795243	−	1.00000i	$-0.500253\pi$
$877$	−28.1956	−	20.4853i	−0.952097	−	0.691739i	−0.951302	+	0.308261i	$0.900253\pi$
$878$	−0.587103	−	1.80692i	−0.0198138	−	0.0609805i
$879$		0			0
$880$	−47.3578	−	29.7287i	−1.59643	−	1.00216i
$881$	35.3563			1.19118			0.595592	−	0.803287i	$-0.296917\pi$
$881$	35.3563			1.19118			0.595592	+	0.803287i	$0.296917\pi$
$882$		0			0
$883$	20.1340	+	14.6282i	0.677565	+	0.492279i	0.872549	−	0.488527i	$-0.162466\pi$
$883$	20.1340	+	14.6282i	0.677565	+	0.492279i	−0.194984	+	0.980806i	$0.562466\pi$
$884$	−16.5536	+	12.0269i	−0.556758	+	0.404508i
$885$		0			0
$886$	−0.629690	+	1.93799i	−0.0211549	+	0.0651080i
$887$	−40.1036	+	29.1370i	−1.34655	+	0.978324i	−0.347372	+	0.937727i	$0.612926\pi$
$887$	−40.1036	+	29.1370i	−1.34655	+	0.978324i	−0.999176	+	0.0405971i	$0.987074\pi$
$888$		0			0
$889$	4.96015	+	15.2658i	0.166358	+	0.511998i
$890$	−8.68599			−0.291155
$891$		0			0
$892$	12.0628			0.403891
$893$	5.01796	+	15.4437i	0.167920	+	0.516804i
$894$		0			0
$895$	−45.6218	+	33.1462i	−1.52497	+	1.10795i
$896$	−1.55112	+	4.77385i	−0.0518193	+	0.159483i
$897$		0			0
$898$	2.09049	−	1.51883i	0.0697605	−	0.0506839i
$899$	−31.0950	−	22.5919i	−1.03708	−	0.753481i
$900$		0			0
$901$	−14.7169			−0.490291
$902$	0.757859	−	3.01305i	0.0252340	−	0.100324i
$903$		0			0
$904$	0.568899	+	1.75089i	0.0189213	+	0.0582338i
$905$	78.3774	+	56.9445i	2.60535	+	1.89290i
$906$		0			0
$907$	−0.441357	+	1.35836i	−0.0146550	+	0.0451035i	−0.958117	−	0.286378i	$-0.907549\pi$
$907$	−0.441357	+	1.35836i	−0.0146550	+	0.0451035i	0.943462	+	0.331482i	$0.107549\pi$
$908$	8.66617	−	26.6717i	0.287597	−	0.885133i
$909$		0			0
$910$	−0.964357	−	0.700646i	−0.0319681	−	0.0232262i
$911$	−16.7402	−	51.5211i	−0.554628	−	1.70697i	−0.696922	−	0.717147i	$-0.745448\pi$
$911$	−16.7402	−	51.5211i	−0.554628	−	1.70697i	0.142294	−	0.989824i	$-0.454552\pi$
$912$		0			0
$913$	7.51175	−	29.8648i	0.248603	−	0.988379i
$914$	3.85821			0.127618
$915$		0			0
$916$	−4.35567	−	3.16458i	−0.143916	−	0.104561i
$917$	−0.606873	+	0.440919i	−0.0200407	+	0.0145604i
$918$		0			0
$919$	−7.07678	+	21.7801i	−0.233441	+	0.718459i	0.763883	+	0.645355i	$0.223290\pi$
$919$	−7.07678	+	21.7801i	−0.233441	+	0.718459i	−0.997324	+	0.0731040i	$0.976710\pi$
$920$	1.30029	−	0.944714i	0.0428692	−	0.0311463i
$921$		0			0
$922$	−1.13258	−	3.48571i	−0.0372994	−	0.114796i
$923$	1.33133			0.0438211
$924$		0			0
$925$	13.8110			0.454101
$926$	−0.152202	−	0.468430i	−0.00500167	−	0.0153936i
$927$		0			0
$928$	13.7149	−	9.96443i	0.450212	−	0.327099i
$929$	4.49019	−	13.8194i	0.147319	−	0.453400i	−0.849983	−	0.526810i	$-0.823388\pi$
$929$	4.49019	−	13.8194i	0.147319	−	0.453400i	0.997302	+	0.0734098i	$0.0233881\pi$
$930$		0			0
$931$	2.81156	−	2.04272i	0.0921452	−	0.0669474i
$932$	28.4059	+	20.6381i	0.930466	+	0.676023i
$933$		0			0
$934$	−3.73021			−0.122056
$935$	76.2397	+	47.8594i	2.49331	+	1.56517i
$936$		0			0
$937$	9.46675	+	29.1357i	0.309265	+	0.951821i	0.978051	+	0.208366i	$0.0668144\pi$
$937$	9.46675	+	29.1357i	0.309265	+	0.951821i	−0.668786	+	0.743455i	$0.733186\pi$
$938$	0.936985	+	0.680760i	0.0305937	+	0.0222276i
$939$		0			0
$940$	12.5024	−	38.4784i	0.407783	−	1.25503i
$941$	−6.50584	+	20.0229i	−0.212084	+	0.652728i	0.787264	+	0.616617i	$0.211497\pi$
$941$	−6.50584	+	20.0229i	−0.212084	+	0.652728i	−0.999348	+	0.0361114i	$0.988503\pi$
$942$		0			0
$943$	−2.65755	−	1.93083i	−0.0865419	−	0.0628764i
$944$	3.38330	+	10.4127i	0.110117	+	0.338905i
$945$		0			0
$946$	1.01092	+	2.51708i	0.0328678	+	0.0818375i
$947$	−0.729464			−0.0237044			−0.0118522	−	0.999930i	$-0.503773\pi$
$947$	−0.729464			−0.0237044			−0.0118522	+	0.999930i	$0.503773\pi$
$948$		0			0
$949$	−3.23607	−	2.35114i	−0.105047	−	0.0763213i
$950$	−6.49467	+	4.71866i	−0.210715	+	0.153093i
$951$		0			0
$952$	1.23180	−	3.79111i	0.0399230	−	0.122870i
$953$	31.5638	−	22.9325i	1.02245	−	0.742856i	0.0556689	−	0.998449i	$-0.482271\pi$
$953$	31.5638	−	22.9325i	1.02245	−	0.742856i	0.966784	+	0.255594i	$0.0822709\pi$
$954$		0			0
$955$	−19.9501	−	61.3999i	−0.645569	−	1.98686i
$956$	25.0775			0.811065
$957$		0			0
$958$	1.32520			0.0428153
$959$	−4.01977	−	12.3716i	−0.129805	−	0.399499i
$960$		0			0
$961$	9.88001	−	7.17825i	0.318710	−	0.231556i
$962$	−0.0813978	+	0.250517i	−0.00262437	+	0.00807698i
$963$		0			0
$964$	−29.7963	+	21.6483i	−0.959673	+	0.697243i
$965$	−30.2139	−	21.9517i	−0.972619	−	0.706649i
$966$		0			0
$967$	2.46386			0.0792324			0.0396162	−	0.999215i	$-0.487386\pi$
$967$	2.46386			0.0792324			0.0396162	+	0.999215i	$0.487386\pi$
$968$	−6.24415	−	3.35327i	−0.200695	−	0.107778i
$969$		0			0
$970$	−3.31039	−	10.1883i	−0.106290	−	0.327127i
$971$	28.0562	+	20.3840i	0.900367	+	0.654155i	0.938560	−	0.345116i	$-0.112160\pi$
$971$	28.0562	+	20.3840i	0.900367	+	0.654155i	−0.0381935	+	0.999270i	$0.512160\pi$
$972$		0			0
$973$	−1.20551	+	3.71019i	−0.0386470	+	0.118943i
$974$	0.0500677	−	0.154093i	0.00160427	−	0.00493745i
$975$		0			0
$976$	−28.9101	−	21.0044i	−0.925390	−	0.672335i
$977$	7.76676	+	23.9036i	0.248481	+	0.764745i	0.995044	+	0.0994308i	$0.0317022\pi$
$977$	7.76676	+	23.9036i	0.248481	+	0.764745i	−0.746564	+	0.665314i	$0.768298\pi$
$978$		0			0
$979$	40.4051	−	2.74145i	1.29135	−	0.0876171i
$980$	−8.65877			−0.276594
$981$		0			0
$982$	−3.18710	−	2.31557i	−0.101705	−	0.0738927i
$983$	24.5860	−	17.8628i	0.784172	−	0.569734i	−0.122056	−	0.992523i	$-0.538949\pi$
$983$	24.5860	−	17.8628i	0.784172	−	0.569734i	0.906228	+	0.422789i	$0.138949\pi$
$984$		0			0
$985$	6.40248	−	19.7048i	0.204000	−	0.627847i
$986$	−7.19646	+	5.22853i	−0.229182	+	0.166510i
$987$		0			0
$988$	3.55184	+	10.9314i	0.112999	+	0.347775i
$989$	2.86792			0.0911947
$990$		0			0
$991$	−8.09793			−0.257239			−0.128620	−	0.991694i	$-0.541055\pi$
$991$	−8.09793			−0.257239			−0.128620	+	0.991694i	$0.541055\pi$
$992$	−2.56068	−	7.88096i	−0.0813016	−	0.250221i
$993$		0			0
$994$	−0.104221	+	0.0757207i	−0.00330568	+	0.00240172i
$995$	22.7238	−	69.9365i	0.720392	−	2.21714i
$996$		0			0
$997$	37.1230	−	26.9715i	1.17570	−	0.854194i	0.184018	−	0.982923i	$-0.441090\pi$
$997$	37.1230	−	26.9715i	1.17570	−	0.854194i	0.991680	+	0.128728i	$0.0410896\pi$
$998$	−5.38896	−	3.91531i	−0.170585	−	0.123937i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.f.379.2		8
3.2	odd	2		231.2.j.f.148.1	yes	8
11.3	even	5		7623.2.a.ci.1.3		4
11.8	odd	10		7623.2.a.cl.1.2		4
11.9	even	5	inner	693.2.m.f.64.2		8
33.8	even	10		2541.2.a.bm.1.3		4
33.14	odd	10		2541.2.a.bn.1.2		4
33.20	odd	10		231.2.j.f.64.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.64.1	✓	8	33.20	odd	10
231.2.j.f.148.1	yes	8	3.2	odd	2
693.2.m.f.64.2		8	11.9	even	5	inner
693.2.m.f.379.2		8	1.1	even	1	trivial
2541.2.a.bm.1.3		4	33.8	even	10
2541.2.a.bn.1.2		4	33.14	odd	10
7623.2.a.ci.1.3		4	11.3	even	5
7623.2.a.cl.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.0501062 - 0.154211i) q^{2} +(1.59676 - 1.16012i) q^{4} +(1.35567 - 4.17234i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-0.521270 - 0.378725i) q^{8} +O(q^{10})\)	\(q+(-0.0501062 - 0.154211i) q^{2} +(1.59676 - 1.16012i) q^{4} +(1.35567 - 4.17234i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-0.521270 - 0.378725i) q^{8} -0.711349 q^{10} +(3.30902 - 0.224514i) q^{11} +(0.517822 + 1.59369i) q^{13} +(-0.131180 - 0.0953077i) q^{14} +(1.18753 - 3.65485i) q^{16} +(-1.91177 + 5.88383i) q^{17} +(2.81156 + 2.04272i) q^{19} +(-2.67571 - 8.23498i) q^{20} +(-0.200425 - 0.499038i) q^{22} -0.568595 q^{23} +(-11.5255 - 8.37373i) q^{25} +(0.219819 - 0.159708i) q^{26} +(0.609909 - 1.87711i) q^{28} +(-7.17390 + 5.21214i) q^{29} +(1.33943 + 4.12233i) q^{31} -1.91177 q^{32} +1.00314 q^{34} +(-1.35567 - 4.17234i) q^{35} +(-0.784298 + 0.569826i) q^{37} +(0.174133 - 0.535927i) q^{38} +(-2.28684 + 1.66149i) q^{40} +(4.67390 + 3.39578i) q^{41} -5.04388 q^{43} +(5.02326 - 4.19734i) q^{44} +(0.0284902 + 0.0876837i) q^{46} +(3.78018 + 2.74646i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.713826 + 2.19693i) q^{50} +(2.67571 + 1.94401i) q^{52} +(0.735096 + 2.26239i) q^{53} +(3.54920 - 14.1107i) q^{55} -0.644326 q^{56} +(1.16323 + 0.845134i) q^{58} +(-2.30490 + 1.67461i) q^{59} +(2.87350 - 8.84371i) q^{61} +(0.568595 - 0.413109i) q^{62} +(-2.27928 - 7.01489i) q^{64} +7.35141 q^{65} -7.14275 q^{67} +(3.77328 + 11.6130i) q^{68} +(-0.575493 + 0.418120i) q^{70} +(0.245510 - 0.755602i) q^{71} +(-1.93117 + 1.40308i) q^{73} +(0.127172 + 0.0923956i) q^{74} +6.85919 q^{76} +(2.54508 - 2.12663i) q^{77} +(-0.207232 - 0.637795i) q^{79} +(-13.6394 - 9.90958i) q^{80} +(0.289476 - 0.890917i) q^{82} +(2.86923 - 8.83059i) q^{83} +(21.9576 + 15.9531i) q^{85} +(0.252730 + 0.777822i) q^{86} +(-1.80992 - 1.13618i) q^{88} +12.2106 q^{89} +(1.35567 + 0.984955i) q^{91} +(-0.907912 + 0.659637i) q^{92} +(0.234124 - 0.720561i) q^{94} +(12.3345 - 8.96152i) q^{95} +(4.65368 + 14.3225i) q^{97} -0.162147 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 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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