LMFDB - Embedded newform 231.2.j.f.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, 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("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	231.64
Dual form			231.2.j.f.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0501062 - 0.154211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.59676 + 1.16012i) q^{4} +(-1.35567 - 4.17234i) q^{5} +(-0.0501062 - 0.154211i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.521270 - 0.378725i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.0501062 - 0.154211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.59676 + 1.16012i) q^{4} +(-1.35567 - 4.17234i) q^{5} +(-0.0501062 - 0.154211i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.521270 - 0.378725i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.711349 q^{10} +(-3.30902 - 0.224514i) q^{11} +1.97371 q^{12} +(0.517822 - 1.59369i) q^{13} +(0.131180 - 0.0953077i) q^{14} +(-3.54920 - 2.57865i) q^{15} +(1.18753 + 3.65485i) q^{16} +(1.91177 + 5.88383i) q^{17} +(-0.131180 - 0.0953077i) q^{18} +(2.81156 - 2.04272i) q^{19} +(2.67571 - 8.23498i) q^{20} +1.00000 q^{21} +(-0.200425 + 0.499038i) q^{22} +0.568595 q^{23} +(0.199108 - 0.612790i) q^{24} +(-11.5255 + 8.37373i) q^{25} +(-0.219819 - 0.159708i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.609909 + 1.87711i) q^{28} +(7.17390 + 5.21214i) q^{29} +(-0.575493 + 0.418120i) q^{30} +(1.33943 - 4.12233i) q^{31} +1.91177 q^{32} +(-2.80902 + 1.76336i) q^{33} +1.00314 q^{34} +(1.35567 - 4.17234i) q^{35} +(1.59676 - 1.16012i) q^{36} +(-0.784298 - 0.569826i) q^{37} +(-0.174133 - 0.535927i) q^{38} +(-0.517822 - 1.59369i) q^{39} +(-2.28684 - 1.66149i) q^{40} +(-4.67390 + 3.39578i) q^{41} +(0.0501062 - 0.154211i) q^{42} -5.04388 q^{43} +(-5.02326 - 4.19734i) q^{44} -4.38705 q^{45} +(0.0284902 - 0.0876837i) q^{46} +(-3.78018 + 2.74646i) q^{47} +(3.10900 + 2.25882i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.713826 + 2.19693i) q^{50} +(5.00509 + 3.63641i) q^{51} +(2.67571 - 1.94401i) q^{52} +(-0.735096 + 2.26239i) q^{53} -0.162147 q^{54} +(3.54920 + 14.1107i) q^{55} +0.644326 q^{56} +(1.07392 - 3.30519i) q^{57} +(1.16323 - 0.845134i) q^{58} +(2.30490 + 1.67461i) q^{59} +(-2.67571 - 8.23498i) q^{60} +(2.87350 + 8.84371i) q^{61} +(-0.568595 - 0.413109i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-2.27928 + 7.01489i) q^{64} -7.35141 q^{65} +(0.131180 + 0.521537i) q^{66} -7.14275 q^{67} +(-3.77328 + 11.6130i) q^{68} +(0.460003 - 0.334212i) q^{69} +(-0.575493 - 0.418120i) q^{70} +(-0.245510 - 0.755602i) q^{71} +(-0.199108 - 0.612790i) q^{72} +(-1.93117 - 1.40308i) q^{73} +(-0.127172 + 0.0923956i) q^{74} +(-4.40233 + 13.5490i) q^{75} +6.85919 q^{76} +(-2.54508 - 2.12663i) q^{77} -0.271711 q^{78} +(-0.207232 + 0.637795i) q^{79} +(13.6394 - 9.90958i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.289476 + 0.890917i) q^{82} +(-2.86923 - 8.83059i) q^{83} +(1.59676 + 1.16012i) q^{84} +(21.9576 - 15.9531i) q^{85} +(-0.252730 + 0.777822i) q^{86} +8.86742 q^{87} +(-1.80992 + 1.13618i) q^{88} -12.2106 q^{89} +(-0.219819 + 0.676533i) q^{90} +(1.35567 - 0.984955i) q^{91} +(0.907912 + 0.659637i) q^{92} +(-1.33943 - 4.12233i) q^{93} +(0.234124 + 0.720561i) q^{94} +(-12.3345 - 8.96152i) q^{95} +(1.54666 - 1.12371i) q^{96} +(4.65368 - 14.3225i) q^{97} +0.162147 q^{98} +(-1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0501062	−	0.154211i	0.0354305	−	0.109044i	−0.931777	−	0.363031i	$-0.881742\pi$
$2$	0.0501062	−	0.154211i	0.0354305	−	0.109044i	0.967208	+	0.253987i	$0.0817420\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.59676	+	1.16012i	0.798382	+	0.580058i
$5$	−1.35567	−	4.17234i	−0.606276	−	1.86593i	−0.487770	−	0.872972i	$-0.662189\pi$
$5$	−1.35567	−	4.17234i	−0.606276	−	1.86593i	−0.118506	−	0.992953i	$-0.537811\pi$
$6$	−0.0501062	−	0.154211i	−0.0204558	−	0.0629564i
$7$	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
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.711349			−0.224948
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$	1.97371			0.569761
$13$	0.517822	−	1.59369i	0.143618	−	0.442010i	−0.853213	−	0.521563i	$-0.825349\pi$
$13$	0.517822	−	1.59369i	0.143618	−	0.442010i	0.996831	+	0.0795526i	$0.0253492\pi$
$14$	0.131180	−	0.0953077i	0.0350593	−	0.0254721i
$15$	−3.54920	−	2.57865i	−0.916400	−	0.665803i
$16$	1.18753	+	3.65485i	0.296884	+	0.913714i
$17$	1.91177	+	5.88383i	0.463673	+	1.42704i	0.860644	+	0.509208i	$0.170062\pi$
$17$	1.91177	+	5.88383i	0.463673	+	1.42704i	−0.396970	+	0.917831i	$0.629938\pi$
$18$	−0.131180	−	0.0953077i	−0.0309194	−	0.0224642i
$19$	2.81156	−	2.04272i	0.645016	−	0.468632i	−0.216554	−	0.976271i	$-0.569482\pi$
$19$	2.81156	−	2.04272i	0.645016	−	0.468632i	0.861570	+	0.507639i	$0.169482\pi$
$20$	2.67571	−	8.23498i	0.598306	−	1.84140i
$21$	1.00000			0.218218
$22$	−0.200425	+	0.499038i	−0.0427307	+	0.106395i
$23$	0.568595			0.118560			0.0592801	−	0.998241i	$-0.481119\pi$
$23$	0.568595			0.118560			0.0592801	+	0.998241i	$0.481119\pi$
$24$	0.199108	−	0.612790i	0.0406427	−	0.125085i
$25$	−11.5255	+	8.37373i	−2.30509	+	1.67475i
$26$	−0.219819	−	0.159708i	−0.0431100	−	0.0313213i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.609909	+	1.87711i	0.115262	+	0.354740i
$29$	7.17390	+	5.21214i	1.33216	+	0.967870i	0.999694	+	0.0247547i	$0.00788049\pi$
$29$	7.17390	+	5.21214i	1.33216	+	0.967870i	0.332465	+	0.943115i	$0.392120\pi$
$30$	−0.575493	+	0.418120i	−0.105070	+	0.0763380i
$31$	1.33943	−	4.12233i	0.240568	−	0.740392i	−0.755766	−	0.654842i	$-0.772735\pi$
$31$	1.33943	−	4.12233i	0.240568	−	0.740392i	0.996334	−	0.0855500i	$-0.0272647\pi$
$32$	1.91177			0.337957
$33$	−2.80902	+	1.76336i	−0.488987	+	0.306961i
$34$	1.00314			0.172038
$35$	1.35567	−	4.17234i	0.229151	−	0.705254i
$36$	1.59676	−	1.16012i	0.266127	−	0.193353i
$37$	−0.784298	−	0.569826i	−0.128938	−	0.0936787i	0.521447	−	0.853284i	$-0.325392\pi$
$37$	−0.784298	−	0.569826i	−0.128938	−	0.0936787i	−0.650385	+	0.759605i	$0.725392\pi$
$38$	−0.174133	−	0.535927i	−0.0282481	−	0.0869388i
$39$	−0.517822	−	1.59369i	−0.0829178	−	0.255195i
$40$	−2.28684	−	1.66149i	−0.361581	−	0.262704i
$41$	−4.67390	+	3.39578i	−0.729940	+	0.530332i	−0.889544	−	0.456849i	$-0.848978\pi$
$41$	−4.67390	+	3.39578i	−0.729940	+	0.530332i	0.159605	+	0.987181i	$0.448978\pi$
$42$	0.0501062	−	0.154211i	0.00773156	−	0.0237953i
$43$	−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
$45$	−4.38705			−0.653983
$46$	0.0284902	−	0.0876837i	0.00420065	−	0.0129283i
$47$	−3.78018	+	2.74646i	−0.551396	+	0.400613i	−0.828300	−	0.560285i	$-0.810692\pi$
$47$	−3.78018	+	2.74646i	−0.551396	+	0.400613i	0.276904	+	0.960898i	$0.410692\pi$
$48$	3.10900	+	2.25882i	0.448746	+	0.326033i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.713826	+	2.19693i	0.100950	+	0.310693i
$51$	5.00509	+	3.63641i	0.700853	+	0.509199i
$52$	2.67571	−	1.94401i	0.371054	−	0.269586i
$53$	−0.735096	+	2.26239i	−0.100973	+	0.310764i	−0.988764	−	0.149483i	$-0.952239\pi$
$53$	−0.735096	+	2.26239i	−0.100973	+	0.310764i	0.887791	+	0.460247i	$0.152239\pi$
$54$	−0.162147			−0.0220654
$55$	3.54920	+	14.1107i	0.478574	+	1.90269i
$56$	0.644326			0.0861016
$57$	1.07392	−	3.30519i	0.142244	−	0.437783i
$58$	1.16323	−	0.845134i	0.152739	−	0.110972i
$59$	2.30490	+	1.67461i	0.300072	+	0.218015i	0.727625	−	0.685975i	$-0.240624\pi$
$59$	2.30490	+	1.67461i	0.300072	+	0.218015i	−0.427553	+	0.903990i	$0.640624\pi$
$60$	−2.67571	−	8.23498i	−0.345432	−	1.06313i
$61$	2.87350	+	8.84371i	0.367913	+	1.13232i	0.948136	+	0.317864i	$0.102965\pi$
$61$	2.87350	+	8.84371i	0.367913	+	1.13232i	−0.580223	+	0.814458i	$0.697035\pi$
$62$	−0.568595	−	0.413109i	−0.0722117	−	0.0524648i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	−2.27928	+	7.01489i	−0.284910	+	0.876861i
$65$	−7.35141			−0.911830
$66$	0.131180	+	0.521537i	0.0161471	+	0.0641968i
$67$	−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
$69$	0.460003	−	0.334212i	0.0553779	−	0.0402344i
$70$	−0.575493	−	0.418120i	−0.0687846	−	0.0499749i
$71$	−0.245510	−	0.755602i	−0.0291367	−	0.0896734i	0.935431	−	0.353510i	$-0.115012\pi$
$71$	−0.245510	−	0.755602i	−0.0291367	−	0.0896734i	−0.964567	+	0.263837i	$0.915012\pi$
$72$	−0.199108	−	0.612790i	−0.0234651	−	0.0722180i
$73$	−1.93117	−	1.40308i	−0.226026	−	0.164218i	0.469009	−	0.883193i	$-0.344611\pi$
$73$	−1.93117	−	1.40308i	−0.226026	−	0.164218i	−0.695035	+	0.718976i	$0.744611\pi$
$74$	−0.127172	+	0.0923956i	−0.0147834	+	0.0107408i
$75$	−4.40233	+	13.5490i	−0.508337	+	1.56450i
$76$	6.85919			0.786803
$77$	−2.54508	−	2.12663i	−0.290039	−	0.242352i
$78$	−0.271711			−0.0307652
$79$	−0.207232	+	0.637795i	−0.0233154	+	0.0717576i	−0.962037	−	0.272918i	$-0.912011\pi$
$79$	−0.207232	+	0.637795i	−0.0233154	+	0.0717576i	0.938722	+	0.344676i	$0.112011\pi$
$80$	13.6394	−	9.90958i	1.52493	−	1.10793i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.289476	+	0.890917i	0.0319673	+	0.0983853i
$83$	−2.86923	−	8.83059i	−0.314939	−	0.969283i	−0.975779	−	0.218757i	$-0.929800\pi$
$83$	−2.86923	−	8.83059i	−0.314939	−	0.969283i	0.660840	−	0.750527i	$-0.270200\pi$
$84$	1.59676	+	1.16012i	0.174221	+	0.126579i
$85$	21.9576	−	15.9531i	2.38164	−	1.73036i
$86$	−0.252730	+	0.777822i	−0.0272525	+	0.0838747i
$87$	8.86742			0.950688
$88$	−1.80992	+	1.13618i	−0.192938	+	0.121117i
$89$	−12.2106			−1.29432			−0.647161	−	0.762354i	$-0.724044\pi$
$89$	−12.2106			−1.29432			−0.647161	+	0.762354i	$0.724044\pi$
$90$	−0.219819	+	0.676533i	−0.0231709	+	0.0713128i
$91$	1.35567	−	0.984955i	0.142113	−	0.103251i
$92$	0.907912	+	0.659637i	0.0946564	+	0.0687719i
$93$	−1.33943	−	4.12233i	−0.138892	−	0.427465i
$94$	0.234124	+	0.720561i	0.0241481	+	0.0743202i
$95$	−12.3345	−	8.96152i	−1.26549	−	0.919432i
$96$	1.54666	−	1.12371i	0.157855	−	0.114688i
$97$	4.65368	−	14.3225i	0.472509	−	1.45423i	−0.376778	−	0.926304i	$-0.622968\pi$
$97$	4.65368	−	14.3225i	0.472509	−	1.45423i	0.849288	−	0.527931i	$-0.177032\pi$
$98$	0.162147			0.0163793
$99$	−1.23607	+	3.07768i	−0.124230	+	0.309319i
$100$	−28.1179			−2.81179
$101$	1.78018	−	5.47883i	0.177135	−	0.545164i	−0.822590	−	0.568635i	$-0.807472\pi$
$101$	1.78018	−	5.47883i	0.177135	−	0.545164i	0.999725	+	0.0234707i	$0.00747165\pi$
$102$	0.811561	−	0.589634i	0.0803565	−	0.0583824i
$103$	−6.24116	−	4.53447i	−0.614959	−	0.446794i	0.236198	−	0.971705i	$-0.424099\pi$
$103$	−6.24116	−	4.53447i	−0.614959	−	0.446794i	−0.851157	+	0.524911i	$0.824099\pi$
$104$	−0.333646	−	1.02686i	−0.0327167	−	0.100692i
$105$	−1.35567	−	4.17234i	−0.132300	−	0.407178i
$106$	0.312053	+	0.226720i	0.0303093	+	0.0220210i
$107$	13.3192	−	9.67696i	1.28762	−	0.935507i	0.287861	−	0.957672i	$-0.407056\pi$
$107$	13.3192	−	9.67696i	1.28762	−	0.935507i	0.999754	+	0.0221652i	$0.00705599\pi$
$108$	0.609909	−	1.87711i	0.0586886	−	0.180625i
$109$	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
$111$	−0.969445			−0.0920157
$112$	−1.18753	+	3.65485i	−0.112211	+	0.345351i
$113$	2.31156	−	1.67945i	0.217453	−	0.157989i	−0.473726	−	0.880672i	$-0.657091\pi$
$113$	2.31156	−	1.67945i	0.217453	−	0.157989i	0.691180	+	0.722683i	$0.257091\pi$
$114$	−0.455887	−	0.331221i	−0.0426977	−	0.0310217i
$115$	−0.770830	−	2.37237i	−0.0718803	−	0.221225i
$116$	5.40832	+	16.6451i	0.502150	+	1.54546i
$117$	−1.35567	−	0.984955i	−0.125332	−	0.0910591i
$118$	0.373733	−	0.271533i	0.0344049	−	0.0249966i
$119$	−1.91177	+	5.88383i	−0.175252	+	0.539370i
$120$	−2.82669			−0.258040
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$	1.50778			0.136508
$123$	−1.78527	+	5.49449i	−0.160972	+	0.495422i
$124$	6.92112	−	5.02849i	0.621535	−	0.451572i
$125$	32.8168	+	23.8428i	2.93522	+	2.13256i
$126$	−0.0501062	−	0.154211i	−0.00446382	−	0.0137382i
$127$	−4.96015	−	15.2658i	−0.440142	−	1.35462i	−0.887724	−	0.460375i	$-0.847715\pi$
$127$	−4.96015	−	15.2658i	−0.440142	−	1.35462i	0.447582	−	0.894243i	$-0.352285\pi$
$128$	4.06088	+	2.95040i	0.358935	+	0.260781i
$129$	−4.08058	+	2.96472i	−0.359275	+	0.261029i
$130$	−0.368352	+	1.13367i	−0.0323066	+	0.0994294i
$131$	0.750136			0.0655397			0.0327699	−	0.999463i	$-0.489567\pi$
$131$	0.750136			0.0655397			0.0327699	+	0.999463i	$0.489567\pi$
$132$	−6.53103	−	0.443125i	−0.568454	−	0.0385691i
$133$	3.47528			0.301345
$134$	−0.357897	+	1.10149i	−0.0309176	+	0.0951544i
$135$	−3.54920	+	2.57865i	−0.305467	+	0.221934i
$136$	3.22491	+	2.34303i	0.276533	+	0.200913i
$137$	−4.01977	−	12.3716i	−0.343432	−	1.05697i	−0.962418	−	0.271572i	$-0.912456\pi$
$137$	−4.01977	−	12.3716i	−0.343432	−	1.05697i	0.618986	−	0.785402i	$-0.287544\pi$
$138$	−0.0284902	−	0.0876837i	−0.00242524	−	0.00746413i
$139$	−3.15607	−	2.29302i	−0.267695	−	0.194492i	0.445838	−	0.895114i	$-0.352906\pi$
$139$	−3.15607	−	2.29302i	−0.267695	−	0.194492i	−0.713532	+	0.700622i	$0.752906\pi$
$140$	7.00509	−	5.08949i	0.592038	−	0.430141i
$141$	−1.44390	+	4.44387i	−0.121598	+	0.374241i
$142$	−0.128824			−0.0108107
$143$	−2.07129	+	5.15729i	−0.173210	+	0.431274i
$144$	3.84294			0.320245
$145$	12.0213	−	36.9979i	0.998318	−	3.07251i
$146$	−0.313133	+	0.227505i	−0.0259151	+	0.0188284i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	−0.591274	−	1.81975i	−0.0486024	−	0.149583i
$149$	5.73023	+	17.6358i	0.469439	+	1.44478i	0.853313	+	0.521399i	$0.174590\pi$
$149$	5.73023	+	17.6358i	0.469439	+	1.44478i	−0.383874	+	0.923385i	$0.625410\pi$
$150$	1.86882	+	1.35778i	0.152589	+	0.110862i
$151$	−16.8259	+	12.2247i	−1.36927	+	0.994832i	−0.371475	+	0.928443i	$0.621148\pi$
$151$	−16.8259	+	12.2247i	−1.36927	+	0.994832i	−0.997794	+	0.0663888i	$0.978852\pi$
$152$	0.691955	−	2.12962i	0.0561249	−	0.172735i
$153$	6.18663			0.500159
$154$	−0.455474	+	0.285923i	−0.0367032	+	0.0230403i
$155$	−19.0156			−1.52737
$156$	1.02203	−	3.14548i	0.0818278	−	0.251840i
$157$	−4.70019	+	3.41489i	−0.375116	+	0.272538i	−0.759329	−	0.650707i	$-0.774473\pi$
$157$	−4.70019	+	3.41489i	−0.375116	+	0.272538i	0.384213	+	0.923244i	$0.374473\pi$
$158$	0.0879715	+	0.0639150i	0.00699864	+	0.00508481i
$159$	0.735096	+	2.26239i	0.0582969	+	0.179419i
$160$	−2.59174	−	7.97656i	−0.204895	−	0.630603i
$161$	0.460003	+	0.334212i	0.0362533	+	0.0263396i
$162$	−0.131180	+	0.0953077i	−0.0103065	+	0.00748808i
$163$	−2.75120	+	8.46732i	−0.215491	+	0.663212i	0.783628	+	0.621230i	$0.213367\pi$
$163$	−2.75120	+	8.46732i	−0.215491	+	0.663212i	−0.999118	+	0.0419811i	$0.986633\pi$
$164$	−11.4026			−0.890394
$165$	11.1654	+	9.32963i	0.869227	+	0.726311i
$166$	−1.50554			−0.116853
$167$	−1.18154	+	3.63641i	−0.0914304	+	0.281394i	−0.986307	−	0.164920i	$-0.947263\pi$
$167$	−1.18154	+	3.63641i	−0.0914304	+	0.281394i	0.894877	+	0.446314i	$0.147263\pi$
$168$	0.521270	−	0.378725i	0.0402169	−	0.0292193i
$169$	8.24551	+	5.99071i	0.634270	+	0.460824i
$170$	−1.35994	−	4.18546i	−0.104302	−	0.321010i
$171$	−1.07392	−	3.30519i	−0.0821248	−	0.252754i
$172$	−8.05388	−	5.85148i	−0.614102	−	0.446171i
$173$	−1.41627	+	1.02898i	−0.107677	+	0.0782322i	−0.640321	−	0.768107i	$-0.721199\pi$
$173$	−1.41627	+	1.02898i	−0.107677	+	0.0782322i	0.532644	+	0.846340i	$0.321199\pi$
$174$	0.444313	−	1.36746i	0.0336833	−	0.103667i
$175$	−14.2462			−1.07691
$176$	−3.10900	−	12.3606i	−0.234350	−	0.931715i
$177$	2.84901			0.214145
$178$	−0.611827	+	1.88301i	−0.0458584	+	0.141138i
$179$	10.3992	−	7.55545i	0.777272	−	0.564721i	−0.126887	−	0.991917i	$-0.540499\pi$
$179$	10.3992	−	7.55545i	0.777272	−	0.564721i	0.904159	+	0.427196i	$0.140499\pi$
$180$	−7.00509	−	5.08949i	−0.522128	−	0.379349i
$181$	−6.82406	−	21.0023i	−0.507228	−	1.56109i	−0.796992	−	0.603990i	$-0.793577\pi$
$181$	−6.82406	−	21.0023i	−0.507228	−	1.56109i	0.289764	−	0.957098i	$-0.406423\pi$
$182$	−0.0839633	−	0.258413i	−0.00622377	−	0.0191548i
$183$	7.52291	+	5.46571i	0.556109	+	0.404037i
$184$	0.296392	−	0.215341i	0.0218503	−	0.0158752i
$185$	−1.31425	+	4.04485i	−0.0966257	+	0.297383i
$186$	−0.702822			−0.0515334
$187$	−5.00509	−	19.8989i	−0.366008	−	1.45515i
$188$	−9.22227			−0.672603
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	−2.00000	+	1.45309i	−0.145095	+	0.105418i
$191$	−11.9055	−	8.64983i	−0.861449	−	0.625879i	0.0668297	−	0.997764i	$-0.478712\pi$
$191$	−11.9055	−	8.64983i	−0.861449	−	0.625879i	−0.928279	+	0.371885i	$0.878712\pi$
$192$	2.27928	+	7.01489i	0.164493	+	0.506256i
$193$	2.63062	+	8.09622i	0.189356	+	0.582779i	0.999996	−	0.00276642i	$-0.000880579\pi$
$193$	2.63062	+	8.09622i	0.189356	+	0.582779i	−0.810640	+	0.585545i	$0.800881\pi$
$194$	−1.97552	−	1.43530i	−0.141834	−	0.103048i
$195$	−5.94742	+	4.32105i	−0.425903	+	0.309437i
$196$	−0.609909	+	1.87711i	−0.0435650	+	0.134079i
$197$	−4.72273			−0.336480			−0.168240	−	0.985746i	$-0.553808\pi$
$197$	−4.72273			−0.336480			−0.168240	+	0.985746i	$0.553808\pi$
$198$	0.412678	+	0.344827i	0.0293278	+	0.0245058i
$199$	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
$201$	−5.77861	+	4.19841i	−0.407592	+	0.296133i
$202$	−0.755699	−	0.549048i	−0.0531708	−	0.0386309i
$203$	2.74018	+	8.43342i	0.192323	+	0.591910i
$204$	3.77328	+	11.6130i	0.264183	+	0.813071i
$205$	20.5046	+	14.8975i	1.43211	+	1.04049i
$206$	−1.01199	+	0.735251i	−0.0705084	+	0.0512274i
$207$	0.175706	−	0.540766i	0.0122124	−	0.0375858i
$208$	6.43964			0.446509
$209$	−9.76212	+	6.12816i	−0.675260	+	0.423893i
$210$	−0.711349			−0.0490877
$211$	−3.13511	+	9.64887i	−0.215830	+	0.664256i	0.783264	+	0.621689i	$0.213553\pi$
$211$	−3.13511	+	9.64887i	−0.215830	+	0.664256i	−0.999094	+	0.0425663i	$0.986447\pi$
$212$	−3.79842	+	2.75971i	−0.260876	+	0.189538i
$213$	−0.642753	−	0.466988i	−0.0440407	−	0.0319975i
$214$	−0.824921	−	2.53884i	−0.0563904	−	0.173552i
$215$	6.83785	+	21.0447i	0.466338	+	1.43524i
$216$	−0.521270	−	0.378725i	−0.0354680	−	0.0257690i
$217$	3.50666	−	2.54774i	0.238048	−	0.172952i
$218$	0.488213	−	1.50256i	0.0330659	−	0.101767i
$219$	−2.38705			−0.161302
$220$	−10.7028	+	26.6489i	−0.721584	+	1.79667i
$221$	10.3670			0.697358
$222$	−0.0485753	+	0.149499i	−0.00326016	+	0.0100337i
$223$	4.94449	−	3.59238i	0.331107	−	0.240564i	−0.409793	−	0.912179i	$-0.634399\pi$
$223$	4.94449	−	3.59238i	0.331107	−	0.240564i	0.740900	+	0.671615i	$0.234399\pi$
$224$	1.54666	+	1.12371i	0.103340	+	0.0750812i
$225$	4.40233	+	13.5490i	0.293489	+	0.903266i
$226$	−0.143166	−	0.440619i	−0.00952325	−	0.0293096i
$227$	−11.4953	−	8.35181i	−0.762969	−	0.554329i	0.136851	−	0.990592i	$-0.456302\pi$
$227$	−11.4953	−	8.35181i	−0.762969	−	0.554329i	−0.899819	+	0.436262i	$0.856302\pi$
$228$	5.54920	−	4.03173i	0.367505	−	0.267008i
$229$	−0.842941	+	2.59431i	−0.0557031	+	0.171437i	−0.975037	−	0.222041i	$-0.928728\pi$
$229$	−0.842941	+	2.59431i	−0.0557031	+	0.171437i	0.919334	+	0.393478i	$0.128728\pi$
$230$	−0.404469			−0.0266699
$231$	−3.30902	−	0.224514i	−0.217717	−	0.0147719i
$232$	5.71351			0.375110
$233$	−5.49731	+	16.9190i	−0.360141	+	1.10840i	0.592828	+	0.805329i	$0.298012\pi$
$233$	−5.49731	+	16.9190i	−0.360141	+	1.10840i	−0.952968	+	0.303070i	$0.901988\pi$
$234$	−0.219819	+	0.159708i	−0.0143700	+	0.0104404i
$235$	16.5839	+	12.0489i	1.08181	+	0.785982i
$236$	1.73764	+	5.34791i	0.113111	+	0.348119i
$237$	0.207232	+	0.637795i	0.0134612	+	0.0414292i
$238$	0.811561	+	0.589634i	0.0526057	+	0.0382203i
$239$	−10.2792	+	7.46827i	−0.664906	+	0.483082i	−0.868316	−	0.496011i	$-0.834798\pi$
$239$	−10.2792	+	7.46827i	−0.664906	+	0.483082i	0.203410	+	0.979094i	$0.434798\pi$
$240$	5.20978	−	16.0340i	0.336290	−	1.03499i
$241$	−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
$243$	−1.00000			−0.0641500
$244$	−5.67144	+	17.4549i	−0.363077	+	1.11744i
$245$	3.54920	−	2.57865i	0.226750	−	0.164744i
$246$	0.757859	+	0.550617i	0.0483193	+	0.0351061i
$247$	−1.79958	−	5.53852i	−0.114504	−	0.352408i
$248$	−0.863026	−	2.65612i	−0.0548022	−	0.168664i
$249$	−7.51175	−	5.45760i	−0.476038	−	0.345862i
$250$	5.32115	−	3.86604i	0.336539	−	0.244510i
$251$	5.82475	−	17.9267i	0.367655	−	1.13153i	−0.580647	−	0.814155i	$-0.697200\pi$
$251$	5.82475	−	17.9267i	0.367655	−	1.13153i	0.948302	−	0.317370i	$-0.102800\pi$
$252$	1.97371			0.124332
$253$	−1.88149	−	0.127658i	−0.118288	−	0.00802576i
$254$	−2.60269			−0.163307
$255$	8.38705	−	25.8127i	0.525218	−	1.61645i
$256$	−11.2760	+	8.19248i	−0.704749	+	0.512030i
$257$	8.36076	+	6.07445i	0.521530	+	0.378914i	0.817180	−	0.576383i	$-0.195536\pi$
$257$	8.36076	+	6.07445i	0.521530	+	0.378914i	−0.295650	+	0.955296i	$0.595536\pi$
$258$	0.252730	+	0.777822i	0.0157343	+	0.0484251i
$259$	−0.299575	−	0.921997i	−0.0186147	−	0.0572901i
$260$	−11.7385	−	8.52849i	−0.727989	−	0.528915i
$261$	7.17390	−	5.21214i	0.444053	−	0.322623i
$262$	0.0375865	−	0.115679i	0.00232210	−	0.00714670i
$263$	−4.14979			−0.255887			−0.127943	−	0.991781i	$-0.540838\pi$
$263$	−4.14979			−0.255887			−0.127943	+	0.991781i	$0.540838\pi$
$264$	−0.796430	+	1.98303i	−0.0490169	+	0.122047i
$265$	10.4360			0.641079
$266$	0.174133	−	0.535927i	0.0106768	−	0.0328598i
$267$	−9.87858	+	7.17721i	−0.604560	+	0.439238i
$268$	−11.4053	−	8.28643i	−0.696689	−	0.506174i
$269$	−1.56433	−	4.81452i	−0.0953790	−	0.293546i	0.891973	−	0.452088i	$-0.149321\pi$
$269$	−1.56433	−	4.81452i	−0.0953790	−	0.293546i	−0.987352	+	0.158542i	$0.949321\pi$
$270$	0.219819	+	0.676533i	0.0133777	+	0.0411725i
$271$	21.2901	+	15.4682i	1.29328	+	0.939625i	0.999866	−	0.0163598i	$-0.00520772\pi$
$271$	21.2901	+	15.4682i	1.29328	+	0.939625i	0.293417	+	0.955985i	$0.405208\pi$
$272$	−19.2343	+	13.9745i	−1.16625	+	0.847329i
$273$	0.517822	−	1.59369i	0.0313400	−	0.0964545i
$274$	−2.10925			−0.127424
$275$	40.0179	−	25.1212i	2.41317	−	1.51487i
$276$	1.12224			0.0675510
$277$	7.97843	−	24.5551i	0.479377	−	1.47537i	−0.360585	−	0.932726i	$-0.617423\pi$
$277$	7.97843	−	24.5551i	0.479377	−	1.47537i	0.839962	−	0.542645i	$-0.182577\pi$
$278$	−0.511749	+	0.371807i	−0.0306926	+	0.0222995i
$279$	−3.50666	−	2.54774i	−0.209938	−	0.152529i
$280$	−0.873496	−	2.68834i	−0.0522014	−	0.160659i
$281$	−1.68057	−	5.17226i	−0.100254	−	0.308551i	0.888333	−	0.459200i	$-0.151864\pi$
$281$	−1.68057	−	5.17226i	−0.100254	−	0.308551i	−0.988587	+	0.150649i	$0.951864\pi$
$282$	0.612946	+	0.445331i	0.0365004	+	0.0265191i
$283$	−20.5360	+	14.9203i	−1.22074	+	0.886919i	−0.996161	−	0.0875371i	$-0.972100\pi$
$283$	−20.5360	+	14.9203i	−1.22074	+	0.886919i	−0.224578	+	0.974456i	$0.572100\pi$
$284$	0.484565	−	1.49134i	0.0287536	−	0.0884946i
$285$	−15.2462			−0.903110
$286$	0.691528	+	0.577828i	0.0408909	+	0.0341677i
$287$	−5.77725			−0.341020
$288$	0.590771	−	1.81820i	0.0348115	−	0.107139i
$289$	−17.2113	+	12.5048i	−1.01243	+	0.735575i
$290$	−5.10314	−	3.70765i	−0.299667	−	0.217721i
$291$	−4.65368	−	14.3225i	−0.272803	−	0.839602i
$292$	−1.45589	−	4.48076i	−0.0851993	−	0.262217i
$293$	−5.46412	−	3.96992i	−0.319217	−	0.231925i	0.416624	−	0.909079i	$-0.363213\pi$
$293$	−5.46412	−	3.96992i	−0.319217	−	0.231925i	−0.735841	+	0.677154i	$0.763213\pi$
$294$	0.131180	−	0.0953077i	0.00765056	−	0.00555846i
$295$	3.86233	−	11.8870i	0.224874	−	0.692090i
$296$	−0.624638			−0.0363064
$297$	0.809017	+	3.21644i	0.0469439	+	0.186637i
$298$	3.00676			0.174177
$299$	0.294431	−	0.906165i	0.0170274	−	0.0524049i
$300$	−22.7479	+	16.5273i	−1.31335	+	0.954204i
$301$	−4.08058	−	2.96472i	−0.235201	−	0.170883i
$302$	1.04210	+	3.20727i	0.0599664	+	0.184558i
$303$	−1.78018	−	5.47883i	−0.102269	−	0.314751i
$304$	10.8047	+	7.85005i	0.619690	+	0.450231i
$305$	33.0034	−	23.9784i	1.88977	−	1.37300i
$306$	0.309989	−	0.954047i	0.0177209	−	0.0545393i
$307$	−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
$309$	−7.71449			−0.438862
$310$	−0.952798	+	2.93241i	−0.0541153	+	0.166550i
$311$	9.90354	−	7.19534i	0.561578	−	0.408010i	−0.270458	−	0.962732i	$-0.587175\pi$
$311$	9.90354	−	7.19534i	0.561578	−	0.408010i	0.832036	+	0.554721i	$0.187175\pi$
$312$	−0.873496	−	0.634632i	−0.0494520	−	0.0359290i
$313$	0.976343	+	3.00487i	0.0551862	+	0.169846i	0.974851	−	0.222860i	$-0.0715392\pi$
$313$	0.976343	+	3.00487i	0.0551862	+	0.169846i	−0.919664	+	0.392705i	$0.871539\pi$
$314$	0.291105	+	0.895928i	0.0164280	+	0.0505602i
$315$	−3.54920	−	2.57865i	−0.199975	−	0.145290i
$316$	−1.07082	+	0.777994i	−0.0602382	+	0.0437656i
$317$	2.60614	−	8.02087i	0.146375	−	0.450497i	−0.850810	−	0.525473i	$-0.823888\pi$
$317$	2.60614	−	8.02087i	0.146375	−	0.450497i	0.997185	+	0.0749766i	$0.0238882\pi$
$318$	0.385719			0.0216301
$319$	−22.5683	−	18.8577i	−1.26358	−	1.05583i
$320$	32.3584			1.80889
$321$	5.08748	−	15.6577i	0.283955	−	0.873925i
$322$	0.0745882	−	0.0541915i	0.00415664	−	0.00301998i
$323$	17.3941	+	12.6375i	0.967833	+	0.703172i
$324$	−0.609909	−	1.87711i	−0.0338839	−	0.104284i
$325$	7.37701	+	22.7041i	0.409203	+	1.25940i
$326$	1.16790	+	0.848531i	0.0646842	+	0.0469958i
$327$	7.88270	−	5.72712i	0.435914	−	0.316710i
$328$	−1.15029	+	3.54024i	−0.0635144	+	0.195477i
$329$	−4.67256			−0.257607
$330$	1.99819	−	1.25436i	0.109997	−	0.0690503i
$331$	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
$333$	−0.784298	+	0.569826i	−0.0429792	+	0.0312262i
$334$	0.501572	+	0.364414i	0.0274448	+	0.0199398i
$335$	9.68325	+	29.8020i	0.529052	+	1.62826i
$336$	1.18753	+	3.65485i	0.0647853	+	0.199389i
$337$	24.1728	+	17.5626i	1.31678	+	0.956695i	0.999966	+	0.00820616i	$0.00261213\pi$
$337$	24.1728	+	17.5626i	1.31678	+	0.956695i	0.316811	+	0.948489i	$0.397388\pi$
$338$	1.33699	−	0.971377i	0.0727225	−	0.0528360i
$339$	0.882938	−	2.71740i	0.0479546	−	0.147589i
$340$	53.5686			2.90516
$341$	−5.35770	+	13.3401i	−0.290136	+	0.722408i
$342$	−0.563507			−0.0304710
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−2.62922	+	1.91024i	−0.141758	+	0.102993i
$345$	−2.01806	−	1.46621i	−0.108649	−	0.0789379i
$346$	0.0877165	+	0.269964i	0.00471567	+	0.0145133i
$347$	−9.01453	−	27.7439i	−0.483925	−	1.48937i	−0.833531	−	0.552472i	$-0.813685\pi$
$347$	−9.01453	−	27.7439i	−0.483925	−	1.48937i	0.349606	−	0.936897i	$-0.386315\pi$
$348$	14.1592	+	10.2872i	0.759012	+	0.551454i
$349$	−10.8347	+	7.87188i	−0.579969	+	0.421372i	−0.838713	−	0.544574i	$-0.816691\pi$
$349$	−10.8347	+	7.87188i	−0.579969	+	0.421372i	0.258744	+	0.965946i	$0.416691\pi$
$350$	−0.713826	+	2.19693i	−0.0381556	+	0.117431i
$351$	−1.67571			−0.0894425
$352$	−6.32609	−	0.429220i	−0.337182	−	0.0228775i
$353$	−21.3175			−1.13462			−0.567309	−	0.823505i	$-0.692015\pi$
$353$	−21.3175			−1.13462			−0.567309	+	0.823505i	$0.692015\pi$
$354$	0.142753	−	0.439350i	0.00758726	−	0.0233512i
$355$	−2.81979	+	2.04870i	−0.149659	+	0.108734i
$356$	−19.4974	−	14.1657i	−1.03336	−	0.750782i
$357$	1.91177	+	5.88383i	0.101182	+	0.311406i
$358$	−0.644071	−	1.98225i	−0.0340402	−	0.104765i
$359$	16.6847	+	12.1221i	0.880584	+	0.639782i	0.933406	−	0.358822i	$-0.116821\pi$
$359$	16.6847	+	12.1221i	0.880584	+	0.639782i	−0.0528216	+	0.998604i	$0.516821\pi$
$360$	−2.28684	+	1.66149i	−0.120527	+	0.0875681i
$361$	−2.13915	+	6.58362i	−0.112587	+	0.346506i
$362$	−3.58072			−0.188198
$363$	9.69098	−	5.20431i	0.508645	−	0.273155i
$364$	3.30735			0.173352
$365$	−3.23607	+	9.95959i	−0.169384	+	0.521309i
$366$	1.21982	−	0.886250i	0.0637610	−	0.0463250i
$367$	−26.5799	−	19.3114i	−1.38746	−	1.00805i	−0.996139	−	0.0877934i	$-0.972018\pi$
$367$	−26.5799	−	19.3114i	−1.38746	−	1.00805i	−0.391320	−	0.920255i	$-0.627982\pi$
$368$	0.675226	+	2.07813i	0.0351986	+	0.108330i
$369$	1.78527	+	5.49449i	0.0929374	+	0.286032i
$370$	0.557909	+	0.405345i	0.0290043	+	0.0210729i
$371$	−1.92451	+	1.39824i	−0.0999154	+	0.0725928i
$372$	2.64363	−	8.13627i	0.137066	−	0.421846i
$373$	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
$375$	40.5638			2.09470
$376$	−0.930342	+	2.86330i	−0.0479787	+	0.147663i
$377$	12.0213	−	8.73401i	0.619130	−	0.449825i
$378$	−0.131180	−	0.0953077i	−0.00674716	−	0.00490210i
$379$	−3.60724	−	11.1020i	−0.185292	−	0.570269i	0.814662	−	0.579937i	$-0.196923\pi$
$379$	−3.60724	−	11.1020i	−0.185292	−	0.570269i	−0.999953	+	0.00966747i	$0.996923\pi$
$380$	−9.29883	−	28.6188i	−0.477020	−	1.46812i
$381$	−12.9858	−	9.43477i	−0.665285	−	0.483358i
$382$	−1.93044	+	1.40255i	−0.0987698	+	0.0717604i
$383$	−4.74963	+	14.6178i	−0.242695	+	0.746937i	0.753313	+	0.657663i	$0.228455\pi$
$383$	−4.74963	+	14.6178i	−0.242695	+	0.746937i	−0.996007	+	0.0892743i	$0.971545\pi$
$384$	5.01953			0.256152
$385$	−5.42270	+	13.5020i	−0.276366	+	0.688124i
$386$	1.38034			0.0702573
$387$	−1.55864	+	4.79701i	−0.0792303	+	0.243846i
$388$	24.0466	−	17.4709i	1.22078	−	0.886951i
$389$	7.80236	+	5.66874i	0.395595	+	0.287417i	0.767744	−	0.640756i	$-0.221379\pi$
$389$	7.80236	+	5.66874i	0.395595	+	0.287417i	−0.372149	+	0.928173i	$0.621379\pi$
$390$	0.368352	+	1.13367i	0.0186522	+	0.0574056i
$391$	1.08703	+	3.34552i	0.0549732	+	0.169190i
$392$	0.521270	+	0.378725i	0.0263281	+	0.0191285i
$393$	0.606873	−	0.440919i	0.0306127	−	0.0222414i
$394$	−0.236638	+	0.728297i	−0.0119217	+	0.0366911i
$395$	2.94203			0.148030
$396$	−5.54418	+	3.48035i	−0.278606	+	0.174894i
$397$	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
$399$	2.81156	−	2.04272i	0.140754	−	0.102264i
$400$	−44.2916	−	32.1798i	−2.21458	−	1.60899i
$401$	−2.52051	−	7.75734i	−0.125868	−	0.387383i	0.868190	−	0.496232i	$-0.165283\pi$
$401$	−2.52051	−	7.75734i	−0.125868	−	0.387383i	−0.994058	+	0.108849i	$0.965283\pi$
$402$	0.357897	+	1.10149i	0.0178503	+	0.0549374i
$403$	−5.87613	−	4.26926i	−0.292711	−	0.212667i
$404$	9.19862	−	6.68319i	0.457648	−	0.332501i
$405$	−1.35567	+	4.17234i	−0.0673640	+	0.207325i
$406$	1.43783			0.0713582
$407$	2.46732	+	2.06165i	0.122301	+	0.102192i
$408$	3.98620			0.197347
$409$	−2.98884	+	9.19870i	−0.147789	+	0.454846i	−0.997359	−	0.0726287i	$-0.976861\pi$
$409$	−2.98884	+	9.19870i	−0.147789	+	0.454846i	0.849570	+	0.527475i	$0.176861\pi$
$410$	3.32477	−	2.41559i	0.164199	−	0.119297i
$411$	−10.5239	−	7.64605i	−0.519105	−	0.377152i
$412$	−4.70514	−	14.4809i	−0.231806	−	0.713425i
$413$	0.880394	+	2.70957i	0.0433213	+	0.133329i
$414$	−0.0745882	−	0.0541915i	−0.00366581	−	0.00266337i
$415$	−32.9544	+	23.9428i	−1.61767	+	1.17531i
$416$	0.989957	−	3.04678i	0.0485367	−	0.149380i
$417$	−3.90112			−0.191039
$418$	0.455887	+	1.81249i	0.0222982	+	0.0886516i
$419$	−18.9357			−0.925072			−0.462536	−	0.886601i	$-0.653060\pi$
$419$	−18.9357			−0.925072			−0.462536	+	0.886601i	$0.653060\pi$
$420$	2.67571	−	8.23498i	0.130561	−	0.401826i
$421$	10.5940	−	7.69703i	0.516322	−	0.375130i	−0.298894	−	0.954286i	$-0.596618\pi$
$421$	10.5940	−	7.69703i	0.516322	−	0.375130i	0.815217	+	0.579156i	$0.196618\pi$
$422$	1.33088	+	0.966937i	0.0647860	+	0.0470698i
$423$	1.44390	+	4.44387i	0.0702049	+	0.216068i
$424$	0.473641	+	1.45772i	0.0230021	+	0.0707931i
$425$	−71.3037	−	51.8052i	−3.45874	−	2.51292i
$426$	−0.104221	+	0.0757207i	−0.00504951	+	0.00366868i
$427$	−2.87350	+	8.84371i	−0.139058	+	0.427977i
$428$	32.4940			1.57066
$429$	1.35567	+	5.38981i	0.0654526	+	0.260222i
$430$	3.58795			0.173027
$431$	−5.03804	+	15.5055i	−0.242674	+	0.746873i	0.753336	+	0.657635i	$0.228443\pi$
$431$	−5.03804	+	15.5055i	−0.242674	+	0.746873i	−0.996010	+	0.0892381i	$0.971557\pi$
$432$	3.10900	−	2.25882i	0.149582	−	0.108678i
$433$	−9.45274	−	6.86782i	−0.454270	−	0.330046i	0.337009	−	0.941501i	$-0.390585\pi$
$433$	−9.45274	−	6.86782i	−0.454270	−	0.330046i	−0.791279	+	0.611455i	$0.790585\pi$
$434$	−0.217184	−	0.668424i	−0.0104252	−	0.0320854i
$435$	−12.0213	−	36.9979i	−0.576379	−	1.77391i
$436$	15.5582	+	11.3037i	0.745100	+	0.541347i
$437$	1.59864	−	1.16148i	0.0764733	−	0.0555611i
$438$	−0.119606	+	0.368110i	−0.00571501	+	0.0175890i
$439$	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
$441$	1.00000			0.0476190
$442$	0.519450	−	1.59870i	0.0247077	−	0.0760425i
$443$	10.1670	−	7.38676i	0.483049	−	0.350955i	−0.319456	−	0.947601i	$-0.603500\pi$
$443$	10.1670	−	7.38676i	0.483049	−	0.350955i	0.802505	+	0.596646i	$0.203500\pi$
$444$	−1.54797	−	1.12467i	−0.0734636	−	0.0533744i
$445$	16.5536	+	50.9467i	0.784716	+	2.41511i
$446$	−0.306236	−	0.942496i	−0.0145007	−	0.0446285i
$447$	15.0019	+	10.8995i	0.709568	+	0.515531i
$448$	−5.96722	+	4.33544i	−0.281925	+	0.204830i
$449$	−4.92451	+	15.1561i	−0.232402	+	0.715259i	0.765054	+	0.643967i	$0.222712\pi$
$449$	−4.92451	+	15.1561i	−0.232402	+	0.715259i	−0.997455	+	0.0712927i	$0.977288\pi$
$450$	2.30999			0.108894
$451$	16.2284	−	10.1874i	0.764166	−	0.479704i
$452$	5.63937			0.265254
$453$	−6.42690	+	19.7800i	−0.301962	+	0.929344i
$454$	−1.86393	+	1.35422i	−0.0874785	+	0.0635568i
$455$	−5.94742	−	4.32105i	−0.278819	−	0.202574i
$456$	−0.691955	−	2.12962i	−0.0324038	−	0.0997285i
$457$	−7.35290	−	22.6299i	−0.343954	−	1.05858i	−0.962141	−	0.272551i	$-0.912133\pi$
$457$	−7.35290	−	22.6299i	−0.343954	−	1.05858i	0.618187	−	0.786031i	$-0.287867\pi$
$458$	0.357834	+	0.259982i	0.0167205	+	0.0121482i
$459$	5.00509	−	3.63641i	0.233618	−	0.169733i
$460$	1.52139	−	4.68237i	0.0709353	−	0.218317i
$461$	−22.6035			−1.05275			−0.526375	−	0.850252i	$-0.676449\pi$
$461$	−22.6035			−1.05275			−0.526375	+	0.850252i	$0.676449\pi$
$462$	−0.200425	+	0.499038i	−0.00932461	+	0.0232173i
$463$	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
$465$	−15.3839	+	11.1771i	−0.713412	+	0.518324i
$466$	2.33365	+	1.69549i	0.108104	+	0.0785422i
$467$	−7.10896	−	21.8791i	−0.328963	−	1.01244i	−0.969620	−	0.244617i	$-0.921338\pi$
$467$	−7.10896	−	21.8791i	−0.328963	−	1.01244i	0.640657	−	0.767828i	$-0.278662\pi$
$468$	−1.02203	−	3.14548i	−0.0472433	−	0.145400i
$469$	−5.77861	−	4.19841i	−0.266831	−	0.193864i
$470$	2.68903	−	1.95369i	0.124036	−	0.0901171i
$471$	−1.79531	+	5.52540i	−0.0827236	+	0.254597i
$472$	1.83569			0.0844946
$473$	16.6903	+	1.13242i	0.767419	+	0.0520688i
$474$	0.108739			0.00499454
$475$	−15.2993	+	47.0865i	−0.701982	+	2.16048i
$476$	−9.87858	+	7.17721i	−0.452784	+	0.328967i
$477$	1.92451	+	1.39824i	0.0881171	+	0.0640208i
$478$	0.636639	+	1.95937i	0.0291192	+	0.0896197i
$479$	2.52554	+	7.77283i	0.115395	+	0.355150i	0.992029	−	0.126008i	$-0.0402165\pi$
$479$	2.52554	+	7.77283i	0.115395	+	0.355150i	−0.876634	+	0.481158i	$0.840217\pi$
$480$	−6.78527	−	4.92979i	−0.309704	−	0.225013i
$481$	−1.31425	+	0.954860i	−0.0599247	+	0.0435379i
$482$	−0.935003	+	2.87764i	−0.0425882	+	0.131073i
$483$	0.568595			0.0258720
$484$	15.6797	+	15.0169i	0.712713	+	0.682585i
$485$	−66.0673			−2.99996
$486$	−0.0501062	+	0.154211i	−0.00227287	+	0.00699516i
$487$	0.808395	−	0.587334i	0.0366319	−	0.0266146i	−0.569319	−	0.822117i	$-0.692793\pi$
$487$	0.808395	−	0.587334i	0.0366319	−	0.0266146i	0.605951	+	0.795502i	$0.292793\pi$
$488$	4.84720	+	3.52170i	0.219423	+	0.159420i
$489$	2.75120	+	8.46732i	0.124414	+	0.382905i
$490$	−0.219819	−	0.676533i	−0.00993040	−	0.0305626i
$491$	−19.6556	−	14.2806i	−0.887046	−	0.644476i	0.0480603	−	0.998844i	$-0.484696\pi$
$491$	−19.6556	−	14.2806i	−0.887046	−	0.644476i	−0.935106	+	0.354368i	$0.884696\pi$
$492$	−9.22491	+	6.70229i	−0.415891	+	0.302162i
$493$	−16.9525	+	52.1744i	−0.763502	+	2.34982i
$494$	−0.944272			−0.0424848
$495$	14.5168	+	0.984955i	0.652483	+	0.0442704i
$496$	16.6571			0.747927
$497$	0.245510	−	0.755602i	0.0110126	−	0.0338934i
$498$	−1.21801	+	0.884935i	−0.0545803	+	0.0396549i
$499$	33.2350	+	24.1466i	1.48780	+	1.08095i	0.974937	+	0.222482i	$0.0714160\pi$
$499$	33.2350	+	24.1466i	1.48780	+	1.08095i	0.512865	+	0.858469i	$0.328584\pi$
$500$	24.7402	+	76.1426i	1.10642	+	3.40520i
$501$	1.18154	+	3.63641i	0.0527874	+	0.162463i
$502$	−2.47265	−	1.79648i	−0.110360	−	0.0801809i
$503$	8.35469	−	6.07004i	0.372517	−	0.270650i	−0.385737	−	0.922609i	$-0.626053\pi$
$503$	8.35469	−	6.07004i	0.372517	−	0.270650i	0.758254	+	0.651959i	$0.226053\pi$
$504$	0.199108	−	0.612790i	0.00886896	−	0.0272958i
$505$	−25.2729			−1.12463
$506$	−0.113961	+	0.283750i	−0.00506617	+	0.0126142i
$507$	10.1920			0.452643
$508$	9.78989	−	30.1302i	0.434356	−	1.33681i
$509$	32.8546	−	23.8703i	1.45625	−	1.05803i	0.471935	−	0.881633i	$-0.343556\pi$
$509$	32.8546	−	23.8703i	1.45625	−	1.05803i	0.984319	−	0.176397i	$-0.0564442\pi$
$510$	−3.56036	−	2.58675i	−0.157655	−	0.114543i
$511$	−0.737640	−	2.27022i	−0.0326313	−	0.100429i
$512$	3.80061	+	11.6971i	0.167965	+	0.516943i
$513$	−2.81156	−	2.04272i	−0.124133	−	0.0901882i
$514$	1.35567	−	0.984955i	0.0597962	−	0.0434445i
$515$	−10.4583	+	32.1875i	−0.460850	+	1.41835i
$516$	−9.95514			−0.438251
$517$	13.1253	−	8.23939i	0.577250	−	0.362368i
$518$	−0.157193			−0.00690666
$519$	−0.540969	+	1.66493i	−0.0237459	+	0.0730823i
$520$	−3.83207	+	2.78416i	−0.168048	+	0.122094i
$521$	17.9719	+	13.0573i	0.787363	+	0.572053i	0.907180	−	0.420743i	$-0.138231\pi$
$521$	17.9719	+	13.0573i	0.787363	+	0.572053i	−0.119817	+	0.992796i	$0.538231\pi$
$522$	−0.444313	−	1.36746i	−0.0194471	−	0.0598519i
$523$	−7.00397	−	21.5560i	−0.306262	−	0.942578i	−0.979203	−	0.202882i	$-0.934969\pi$
$523$	−7.00397	−	21.5560i	−0.306262	−	0.942578i	0.672941	−	0.739696i	$-0.265031\pi$
$524$	1.19779	+	0.870246i	0.0523257	+	0.0380169i
$525$	−11.5255	+	8.37373i	−0.503012	+	0.365460i
$526$	−0.207930	+	0.639943i	−0.00906618	+	0.0279028i
$527$	26.8158			1.16811
$528$	−9.78061	−	8.17250i	−0.425646	−	0.355663i
$529$	−22.6767			−0.985943
$530$	0.522910	−	1.60935i	0.0227137	−	0.0699057i
$531$	2.30490	−	1.67461i	0.100024	−	0.0726718i
$532$	5.54920	+	4.03173i	0.240588	+	0.174798i
$533$	2.99159	+	9.20715i	0.129580	+	0.398806i
$534$	0.611827	+	1.88301i	0.0264764	+	0.0814859i
$535$	−58.4320	−	42.4533i	−2.52624	−	1.83542i
$536$	−3.72331	+	2.70514i	−0.160822	+	0.116844i
$537$	3.97214	−	12.2250i	0.171410	−	0.527547i
$538$	−0.820835			−0.0353887
$539$	−0.809017	−	3.21644i	−0.0348468	−	0.138542i
$540$	−8.65877			−0.372614
$541$	−1.93649	+	5.95991i	−0.0832563	+	0.256237i	−0.984016	−	0.178082i	$-0.943011\pi$
$541$	−1.93649	+	5.95991i	−0.0832563	+	0.256237i	0.900759	+	0.434319i	$0.143011\pi$
$542$	3.45213	−	2.50812i	0.148282	−	0.107733i
$543$	−17.8656	−	12.9801i	−0.766687	−	0.557031i
$544$	3.65488	+	11.2486i	0.156702	+	0.482278i
$545$	−13.2091	−	40.6534i	−0.565815	−	1.74140i
$546$	−0.219819	−	0.159708i	−0.00940738	−	0.00683486i
$547$	−27.5807	+	20.0386i	−1.17927	+	0.856787i	−0.992089	−	0.125539i	$-0.959934\pi$
$547$	−27.5807	+	20.0386i	−1.17927	+	0.856787i	−0.187178	+	0.982326i	$0.559934\pi$
$548$	7.93384	−	24.4179i	0.338917	−	1.04308i
$549$	9.29883			0.396864
$550$	−1.86882	−	7.42994i	−0.0796868	−	0.316814i
$551$	30.8168			1.31284
$552$	0.113212	−	0.348430i	0.00481861	−	0.0148301i
$553$	−0.542541	+	0.394179i	−0.0230712	+	0.0167622i
$554$	−3.38690	−	2.46072i	−0.143895	−	0.104546i
$555$	1.31425	+	4.04485i	0.0557869	+	0.171694i
$556$	−2.37933	−	7.32283i	−0.100906	−	0.310557i
$557$	21.3574	+	15.5170i	0.904941	+	0.657478i	0.939730	−	0.341916i	$-0.111076\pi$
$557$	21.3574	+	15.5170i	0.904941	+	0.657478i	−0.0347891	+	0.999395i	$0.511076\pi$
$558$	−0.568595	+	0.413109i	−0.0240706	+	0.0174883i
$559$	−2.61183	+	8.03838i	−0.110469	+	0.339987i
$560$	16.8592			0.712431
$561$	−15.7455	−	13.1567i	−0.664775	−	0.555474i
$562$	−0.881827			−0.0371976
$563$	−2.11715	+	6.51593i	−0.0892274	+	0.274614i	−0.985706	−	0.168473i	$-0.946116\pi$
$563$	−2.11715	+	6.51593i	−0.0892274	+	0.274614i	0.896479	+	0.443086i	$0.146116\pi$
$564$	−7.46097	+	5.42072i	−0.314164	+	0.228253i
$565$	−10.1409	−	7.36783i	−0.426633	−	0.309967i
$566$	1.27189	+	3.91448i	0.0534616	+	0.164538i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	−0.414143	−	0.300892i	−0.0173770	−	0.0126252i
$569$	−14.8866	+	10.8157i	−0.624079	+	0.453420i	−0.854344	−	0.519708i	$-0.826041\pi$
$569$	−14.8866	+	10.8157i	−0.624079	+	0.453420i	0.230265	+	0.973128i	$0.426041\pi$
$570$	−0.763932	+	2.35114i	−0.0319976	+	0.0984785i
$571$	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
$573$	−14.7160			−0.614768
$574$	−0.289476	+	0.890917i	−0.0120825	+	0.0371862i
$575$	−6.55332	+	4.76126i	−0.273292	+	0.198558i
$576$	5.96722	+	4.33544i	0.248634	+	0.180643i
$577$	−7.98337	−	24.5703i	−0.332352	−	1.02288i	−0.968012	−	0.250905i	$-0.919272\pi$
$577$	−7.98337	−	24.5703i	−0.332352	−	1.02288i	0.635659	−	0.771970i	$-0.280728\pi$
$578$	1.06598	+	3.28075i	0.0443389	+	0.136461i
$579$	6.88705	+	5.00374i	0.286216	+	0.207948i
$580$	62.1171	−	45.1307i	2.57927	−	1.87395i
$581$	2.86923	−	8.83059i	0.119036	−	0.366355i
$582$	−2.44187			−0.101219
$583$	2.94038	−	7.32126i	0.121778	−	0.303216i
$584$	−1.53804			−0.0636446
$585$	−2.27171	+	6.99161i	−0.0939237	+	0.289067i
$586$	−0.885992	+	0.643711i	−0.0366000	+	0.0265914i
$587$	3.02099	+	2.19488i	0.124689	+	0.0905922i	0.648382	−	0.761315i	$-0.275446\pi$
$587$	3.02099	+	2.19488i	0.124689	+	0.0905922i	−0.523693	+	0.851907i	$0.675446\pi$
$588$	0.609909	+	1.87711i	0.0251522	+	0.0774106i
$589$	−4.65488	−	14.3262i	−0.191801	−	0.590303i
$590$	−1.63959	−	1.19123i	−0.0675008	−	0.0490422i
$591$	−3.82077	+	2.77595i	−0.157165	+	0.114187i
$592$	1.15125	−	3.54318i	0.0473160	−	0.145624i
$593$	17.5647			0.721295			0.360648	−	0.932702i	$-0.382556\pi$
$593$	17.5647			0.721295			0.360648	+	0.932702i	$0.382556\pi$
$594$	0.536548	+	0.0364043i	0.0220148	+	0.00149369i
$595$	27.1411			1.11268
$596$	−11.3098	+	34.8080i	−0.463268	+	1.42579i
$597$	13.5607	−	9.85243i	0.555003	−	0.403233i
$598$	−0.124988	−	0.0908090i	−0.00511114	−	0.00371346i
$599$	3.49462	+	10.7553i	0.142786	+	0.439451i	0.996720	−	0.0809314i	$-0.0257895\pi$
$599$	3.49462	+	10.7553i	0.142786	+	0.439451i	−0.853933	+	0.520382i	$0.825789\pi$
$600$	2.83654	+	8.72996i	0.115801	+	0.356399i
$601$	23.4470	+	17.0353i	0.956424	+	0.694883i	0.952317	−	0.305109i	$-0.0986929\pi$
$601$	23.4470	+	17.0353i	0.956424	+	0.694883i	0.00410642	+	0.999992i	$0.498693\pi$
$602$	−0.661655	+	0.480720i	−0.0269670	+	0.0195927i
$603$	−2.20723	+	6.79316i	−0.0898854	+	0.276639i
$604$	−41.0490			−1.67026
$605$	−8.57632	−	47.4894i	−0.348677	−	1.93072i
$606$	−0.934096			−0.0379450
$607$	2.26926	−	6.98406i	0.0921063	−	0.283474i	−0.894382	−	0.447303i	$-0.852385\pi$
$607$	2.26926	−	6.98406i	0.0921063	−	0.283474i	0.986489	+	0.163829i	$0.0523845\pi$
$608$	5.37507	−	3.90522i	0.217988	−	0.158377i
$609$	7.17390	+	5.21214i	0.290701	+	0.211207i
$610$	−2.04406	−	6.29096i	−0.0827615	−	0.254714i
$611$	2.41955	+	7.44662i	0.0978846	+	0.301258i
$612$	9.87858	+	7.17721i	0.399318	+	0.290122i
$613$	−15.3337	+	11.1406i	−0.619323	+	0.449965i	−0.852685	−	0.522425i	$-0.825027\pi$
$613$	−15.3337	+	11.1406i	−0.619323	+	0.449965i	0.233362	+	0.972390i	$0.425027\pi$
$614$	−0.883853	+	2.72022i	−0.0356694	+	0.109779i
$615$	25.3451			1.02201
$616$	−2.13208	−	0.144660i	−0.0859041	−	0.00582852i
$617$	25.2571			1.01681			0.508407	−	0.861117i	$-0.330234\pi$
$617$	25.2571			1.01681			0.508407	+	0.861117i	$0.330234\pi$
$618$	−0.386544	+	1.18966i	−0.0155491	+	0.0478552i
$619$	12.5984	−	9.15329i	0.506373	−	0.367902i	−0.305073	−	0.952329i	$-0.598681\pi$
$619$	12.5984	−	9.15329i	0.506373	−	0.367902i	0.811446	+	0.584427i	$0.198681\pi$
$620$	−30.3633	−	22.0603i	−1.21942	−	0.885962i
$621$	−0.175706	−	0.540766i	−0.00705082	−	0.0217002i
$622$	−0.613373	−	1.88777i	−0.0245940	−	0.0756926i
$623$	−9.87858	−	7.17721i	−0.395777	−	0.287549i
$624$	5.20978	−	3.78512i	0.208558	−	0.151526i
$625$	32.9796	−	101.501i	1.31918	−	4.06003i
$626$	0.512306			0.0204759
$627$	−4.29568	+	10.6958i	−0.171553	+	0.427150i
$628$	−11.4668			−0.457573
$629$	1.85336	−	5.70405i	0.0738983	−	0.227436i
$630$	−0.575493	+	0.418120i	−0.0229282	+	0.0166583i
$631$	29.1383	+	21.1702i	1.15998	+	0.842773i	0.989775	−	0.142636i	$-0.0455579\pi$
$631$	29.1383	+	21.1702i	1.15998	+	0.842773i	0.170202	+	0.985409i	$0.445558\pi$
$632$	0.133525	+	0.410948i	0.00531134	+	0.0163466i
$633$	3.13511	+	9.64887i	0.124609	+	0.383508i
$634$	−1.10632	−	0.803791i	−0.0439377	−	0.0319226i
$635$	−56.9696	+	41.3908i	−2.26077	+	1.64254i
$636$	−1.45087	+	4.46530i	−0.0575306	+	0.177061i
$637$	1.67571			0.0663939
$638$	−4.03888	+	2.53540i	−0.159901	+	0.100378i
$639$	−0.794487			−0.0314294
$640$	6.80484	−	20.9432i	0.268985	−	0.827851i
$641$	21.6339	−	15.7179i	0.854487	−	0.620821i	−0.0718924	−	0.997412i	$-0.522904\pi$
$641$	21.6339	−	15.7179i	0.854487	−	0.620821i	0.926380	+	0.376591i	$0.122904\pi$
$642$	−2.15967	−	1.56909i	−0.0852354	−	0.0619271i
$643$	2.26004	+	6.95569i	0.0891273	+	0.274306i	0.985679	−	0.168634i	$-0.0539356\pi$
$643$	2.26004	+	6.95569i	0.0891273	+	0.274306i	−0.896551	+	0.442940i	$0.853936\pi$
$644$	0.346792	+	1.06731i	0.0136655	+	0.0420581i
$645$	17.9017	+	13.0064i	0.704880	+	0.512125i
$646$	2.82040	−	2.04914i	0.110967	−	0.0806224i
$647$	−10.8224	+	33.3080i	−0.425474	+	1.30947i	0.477067	+	0.878867i	$0.341700\pi$
$647$	−10.8224	+	33.3080i	−0.425474	+	1.30947i	−0.902540	+	0.430606i	$0.858300\pi$
$648$	−0.644326			−0.0253115
$649$	−7.25098	−	6.05879i	−0.284626	−	0.237828i
$650$	3.87086			0.151828
$651$	1.33943	−	4.12233i	0.0524962	−	0.161567i
$652$	−14.2161	+	10.3286i	−0.556745	+	0.404499i
$653$	3.27764	+	2.38134i	0.128264	+	0.0931891i	0.650067	−	0.759877i	$-0.274741\pi$
$653$	3.27764	+	2.38134i	0.128264	+	0.0931891i	−0.521804	+	0.853066i	$0.674741\pi$
$654$	−0.488213	−	1.50256i	−0.0190906	−	0.0587549i
$655$	−1.01694	−	3.12982i	−0.0397352	−	0.122292i
$656$	−17.9615	−	13.0498i	−0.701279	−	0.509509i
$657$	−1.93117	+	1.40308i	−0.0753420	+	0.0547392i
$658$	−0.234124	+	0.720561i	−0.00912712	+	0.0280904i
$659$	28.6360			1.11550			0.557750	−	0.830009i	$-0.311665\pi$
$659$	28.6360			1.11550			0.557750	+	0.830009i	$0.311665\pi$
$660$	7.00509	+	27.8504i	0.272673	+	1.08408i
$661$	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
$663$	8.38705	−	6.09355i	0.325726	−	0.236654i
$664$	−4.84001	−	3.51648i	−0.187829	−	0.136466i
$665$	−4.71135	−	14.5000i	−0.182698	−	0.562287i
$666$	0.0485753	+	0.149499i	0.00188225	+	0.00579298i
$667$	4.07904	+	2.96360i	0.157941	+	0.114751i
$668$	−6.10530	+	4.43576i	−0.236221	+	0.171625i
$669$	1.88863	−	5.81259i	0.0730185	−	0.224728i
$670$	5.08099			0.196296
$671$	−7.52291	−	29.9091i	−0.290419	−	1.15463i
$672$	1.91177			0.0737483
$673$	0.0157313	−	0.0484159i	0.000606396	−	0.00186630i	−0.950753	−	0.309950i	$-0.899688\pi$
$673$	0.0157313	−	0.0484159i	0.000606396	−	0.00186630i	0.951359	+	0.308084i	$0.0996877\pi$
$674$	3.91956	−	2.84772i	0.150976	−	0.109690i
$675$	11.5255	+	8.37373i	0.443615	+	0.322305i
$676$	6.21620	+	19.1315i	0.239085	+	0.735827i
$677$	12.0961	+	37.2279i	0.464890	+	1.43079i	0.859121	+	0.511773i	$0.171011\pi$
$677$	12.0961	+	37.2279i	0.464890	+	1.43079i	−0.394230	+	0.919012i	$0.628989\pi$
$678$	−0.374813	−	0.272318i	−0.0143946	−	0.0104583i
$679$	12.1835	−	8.85182i	0.467559	−	0.339702i
$680$	5.40399	−	16.6318i	0.207234	−	0.637800i
$681$	−14.2090			−0.544488
$682$	1.78874	+	1.49464i	0.0684945	+	0.0572328i
$683$	15.4140			0.589800			0.294900	−	0.955528i	$-0.404714\pi$
$683$	15.4140			0.589800			0.294900	+	0.955528i	$0.404714\pi$
$684$	2.11961	−	6.52348i	0.0810452	−	0.249431i
$685$	−46.1688	+	33.5436i	−1.76402	+	1.28164i
$686$	0.131180	+	0.0953077i	0.00500847	+	0.00363887i
$687$	0.842941	+	2.59431i	0.0321602	+	0.0989789i
$688$	−5.98977	−	18.4346i	−0.228358	−	0.702814i
$689$	3.22491	+	2.34303i	0.122859	+	0.0892624i
$690$	−0.327223	+	0.237741i	−0.0124572	+	0.00905065i
$691$	−11.8275	+	36.4013i	−0.449939	+	1.38477i	0.427036	+	0.904235i	$0.359558\pi$
$691$	−11.8275	+	36.4013i	−0.449939	+	1.38477i	−0.876975	+	0.480536i	$0.840442\pi$
$692$	−3.45520			−0.131347
$693$	−2.80902	+	1.76336i	−0.106706	+	0.0669843i
$694$	−4.73010			−0.179552
$695$	−5.28865	+	16.2768i	−0.200610	+	0.617414i
$696$	4.62233	−	3.35832i	0.175209	−	0.127297i
$697$	−28.9157	−	21.0085i	−1.09526	−	0.795752i
$698$	0.671045	+	2.06526i	0.0253994	+	0.0781714i
$699$	5.49731	+	16.9190i	0.207927	+	0.639935i
$700$	−22.7479	−	16.5273i	−0.859789	−	0.624673i
$701$	1.12351	−	0.816275i	0.0424342	−	0.0308303i	−0.566366	−	0.824154i	$-0.691651\pi$
$701$	1.12351	−	0.816275i	0.0424342	−	0.0308303i	0.608800	+	0.793324i	$0.291651\pi$
$702$	−0.0839633	+	0.258413i	−0.00316899	+	0.00975315i
$703$	−3.36909			−0.127068
$704$	9.11711	−	22.7007i	0.343614	−	0.855564i
$705$	20.4988			0.772029
$706$	−1.06814	+	3.28740i	−0.0402000	+	0.123723i
$707$	4.66057	−	3.38611i	0.175279	−	0.127348i
$708$	4.54920	+	3.30519i	0.170969	+	0.124217i
$709$	−3.96659	−	12.2079i	−0.148968	−	0.458477i	0.848532	−	0.529145i	$-0.177487\pi$
$709$	−3.96659	−	12.2079i	−0.148968	−	0.458477i	−0.997500	+	0.0706674i	$0.977487\pi$
$710$	0.174643	+	0.537496i	0.00655424	+	0.0201719i
$711$	0.542541	+	0.394179i	0.0203469	+	0.0147829i
$712$	−6.36503	+	4.62446i	−0.238539	+	0.173309i
$713$	0.761591	−	2.34394i	0.0285218	−	0.0877811i
$714$	1.00314			0.0375417
$715$	24.3259	+	1.65049i	0.909739	+	0.0617250i
$716$	25.3702			0.948131
$717$	−3.92630	+	12.0839i	−0.146630	+	0.451282i
$718$	2.70538	−	1.96557i	0.100964	−	0.0733545i
$719$	17.3983	+	12.6406i	0.648849	+	0.471416i	0.862879	−	0.505411i	$-0.168659\pi$
$719$	17.3983	+	12.6406i	0.648849	+	0.471416i	−0.214030	+	0.976827i	$0.568659\pi$
$720$	−5.20978	−	16.0340i	−0.194157	−	0.597553i
$721$	−2.38391	−	7.33692i	−0.0887814	−	0.273241i
$722$	0.908083	+	0.659761i	0.0337953	+	0.0245537i
$723$	−15.0966	+	10.9683i	−0.561448	+	0.407916i
$724$	13.4687	−	41.4524i	0.500560	−	1.54057i
$725$	−126.327			−4.69168
$726$	−0.316984	−	1.75523i	−0.0117644	−	0.0651426i
$727$	−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
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	1.37373	+	0.998076i	0.0508441	+	0.0369404i
$731$	−9.64275	−	29.6773i	−0.356650	−	1.09766i
$732$	5.67144	+	17.4549i	0.209623	+	0.645152i
$733$	−33.5342	−	24.3640i	−1.23861	−	0.899906i	−0.241109	−	0.970498i	$-0.577511\pi$
$733$	−33.5342	−	24.3640i	−1.23861	−	0.899906i	−0.997505	+	0.0705923i	$0.977511\pi$
$734$	−4.30985	+	3.13129i	−0.159080	+	0.115578i
$735$	1.35567	−	4.17234i	0.0500048	−	0.153899i
$736$	1.08703			0.0400683
$737$	23.6355	+	1.60365i	0.870625	+	0.0590711i
$738$	0.936765			0.0344828
$739$	13.1668	−	40.5231i	0.484347	−	1.49067i	−0.348576	−	0.937280i	$-0.613335\pi$
$739$	13.1668	−	40.5231i	0.484347	−	1.49067i	0.832924	−	0.553388i	$-0.186665\pi$
$740$	−6.79105	+	4.93399i	−0.249644	+	0.181377i
$741$	−4.71135	−	3.42300i	−0.173076	−	0.125747i
$742$	0.119194	+	0.366841i	0.00437574	+	0.0134671i
$743$	−9.40891	−	28.9576i	−0.345179	−	1.06235i	−0.961488	−	0.274848i	$-0.911372\pi$
$743$	−9.40891	−	28.9576i	−0.345179	−	1.06235i	0.616308	−	0.787505i	$-0.288628\pi$
$744$	−2.25943	−	1.64157i	−0.0828348	−	0.0601830i
$745$	65.8143	−	47.8169i	2.41125	−	1.75188i
$746$	1.30767	−	4.02459i	0.0478772	−	0.147351i
$747$	−9.28503			−0.339722
$748$	15.0931	−	37.5804i	0.551860	−	1.37407i
$749$	16.4634			0.601561
$750$	2.03250	−	6.25539i	0.0742163	−	0.228414i
$751$	−7.33483	+	5.32907i	−0.267652	+	0.194460i	−0.713514	−	0.700641i	$-0.752897\pi$
$751$	−7.33483	+	5.32907i	−0.267652	+	0.194460i	0.445862	+	0.895102i	$0.352897\pi$
$752$	−14.5270	−	10.5545i	−0.529746	−	0.384883i
$753$	−5.82475	−	17.9267i	−0.212266	−	0.653286i
$754$	−0.744538	−	2.29145i	−0.0271145	−	0.0834498i
$755$	73.8159	+	53.6304i	2.68644	+	1.95181i
$756$	1.59676	−	1.16012i	0.0580737	−	0.0421930i
$757$	2.41984	−	7.44750i	0.0879505	−	0.270684i	−0.897402	−	0.441214i	$-0.854548\pi$
$757$	2.41984	−	7.44750i	0.0879505	−	0.270684i	0.985352	+	0.170530i	$0.0545480\pi$
$758$	−1.89279			−0.0687493
$759$	−1.59719	+	1.00264i	−0.0579745	+	0.0363934i
$760$	−9.82355			−0.356338
$761$	8.18844	−	25.2014i	0.296831	−	0.913551i	−0.685770	−	0.727819i	$-0.740534\pi$
$761$	8.18844	−	25.2014i	0.296831	−	0.913551i	0.982600	−	0.185732i	$-0.0594657\pi$
$762$	−2.10562	+	1.52982i	−0.0762785	+	0.0554196i
$763$	7.88270	+	5.72712i	0.285373	+	0.207336i
$764$	−8.97540	−	27.6235i	−0.324719	−	0.999381i
$765$	−8.38705	−	25.8127i	−0.303235	−	0.933260i
$766$	2.01625	+	1.46489i	0.0728500	+	0.0529287i
$767$	3.86233	−	2.80615i	0.139461	−	0.101324i
$768$	−4.30704	+	13.2557i	−0.155417	+	0.478324i
$769$	−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
$771$	10.3345			0.372187
$772$	−5.19208	+	15.9796i	−0.186867	+	0.575117i
$773$	−27.6333	+	20.0768i	−0.993901	+	0.722111i	−0.960772	−	0.277340i	$-0.910547\pi$
$773$	−27.6333	+	20.0768i	−0.993901	+	0.722111i	−0.0331288	+	0.999451i	$0.510547\pi$
$774$	0.661655	+	0.480720i	0.0237827	+	0.0172791i
$775$	19.0818	+	58.7277i	0.685438	+	2.10956i
$776$	−2.99848	−	9.22838i	−0.107639	−	0.331280i
$777$	−0.784298	−	0.569826i	−0.0281365	−	0.0204424i
$778$	1.26513	−	0.919171i	0.0453571	−	0.0329539i
$779$	−6.20431	+	19.0949i	−0.222293	+	0.684146i
$780$	−14.5095			−0.519525
$781$	0.642753	+	2.55542i	0.0229995	+	0.0914401i
$782$	0.570383			0.0203969
$783$	2.74018	−	8.43342i	0.0979262	−	0.301386i
$784$	−3.10900	+	2.25882i	−0.111036	+	0.0806723i
$785$	20.6200	+	14.9813i	0.735959	+	0.534705i
$786$	−0.0375865	−	0.115679i	−0.00134067	−	0.00412615i
$787$	3.63104	+	11.1752i	0.129433	+	0.398353i	0.994683	−	0.102988i	$-0.0328404\pi$
$787$	3.63104	+	11.1752i	0.129433	+	0.398353i	−0.865250	+	0.501341i	$0.832840\pi$
$788$	−7.54108	−	5.47891i	−0.268640	−	0.195178i
$789$	−3.35725	+	2.43918i	−0.119521	+	0.0868372i
$790$	0.147414	−	0.453695i	0.00524477	−	0.0161417i
$791$	2.85725			0.101592
$792$	0.521270	+	2.07244i	0.0185225	+	0.0736408i
$793$	15.5821			0.553337
$794$	1.01643	−	3.12825i	0.0360718	−	0.111017i
$795$	8.44292	−	6.13414i	0.299439	−	0.217555i
$796$	26.7649	+	19.4458i	0.948656	+	0.689239i
$797$	4.72880	+	14.5537i	0.167503	+	0.515520i	0.999212	−	0.0396911i	$-0.0126374\pi$
$797$	4.72880	+	14.5537i	0.167503	+	0.515520i	−0.831709	+	0.555211i	$0.812637\pi$
$798$	−0.174133	−	0.535927i	−0.00616425	−	0.0189716i
$799$	−23.3866	−	16.9913i	−0.827358	−	0.601111i
$800$	−22.0341	+	16.0087i	−0.779022	+	0.565992i
$801$	−3.77328	+	11.6130i	−0.133322	+	0.410324i
$802$	−1.32256			−0.0467013
$803$	6.07526	+	5.07637i	0.214391	+	0.179141i
$804$	−14.0977			−0.497188
$805$	0.770830	−	2.37237i	0.0271682	−	0.0836151i
$806$	−0.952798	+	0.692248i	−0.0335609	+	0.0243834i
$807$	−4.09547	−	2.97554i	−0.144168	−	0.104744i
$808$	−1.14702	−	3.53015i	−0.0403519	−	0.124190i
$809$	5.63373	+	17.3388i	0.198071	+	0.609601i	0.999927	+	0.0120833i	$0.00384631\pi$
$809$	5.63373	+	17.3388i	0.198071	+	0.609601i	−0.801856	+	0.597518i	$0.796154\pi$
$810$	0.575493	+	0.418120i	0.0202208	+	0.0146912i
$811$	−5.04254	+	3.66362i	−0.177068	+	0.128647i	−0.672789	−	0.739835i	$-0.734904\pi$
$811$	−5.04254	+	3.66362i	−0.177068	+	0.128647i	0.495721	+	0.868482i	$0.334904\pi$
$812$	−5.40832	+	16.6451i	−0.189795	+	0.584129i
$813$	26.3160			0.922944
$814$	0.441557	−	0.277187i	0.0154766	−	0.00971539i
$815$	39.0582			1.36815
$816$	−7.34683	+	22.6112i	−0.257191	+	0.791551i
$817$	−14.1812	+	10.3032i	−0.496136	+	0.360464i
$818$	1.26878	+	0.921825i	0.0443619	+	0.0322308i
$819$	−0.517822	−	1.59369i	−0.0180941	−	0.0556881i
$820$	15.4582	+	47.5755i	0.539825	+	1.66141i
$821$	23.9791	+	17.4219i	0.836878	+	0.608027i	0.921497	−	0.388386i	$-0.126967\pi$
$821$	23.9791	+	17.4219i	0.836878	+	0.608027i	−0.0846188	+	0.996413i	$0.526967\pi$
$822$	−1.70642	+	1.23979i	−0.0595182	+	0.0432425i
$823$	−6.09698	+	18.7646i	−0.212527	+	0.654092i	0.786793	+	0.617217i	$0.211740\pi$
$823$	−6.09698	+	18.7646i	−0.212527	+	0.654092i	−0.999320	+	0.0368743i	$0.988260\pi$
$824$	−4.97065			−0.173161
$825$	17.6093	−	43.8454i	0.613078	−	1.52650i
$826$	0.461960			0.0160736
$827$	12.7225	−	39.1560i	0.442406	−	1.36159i	−0.442897	−	0.896572i	$-0.646049\pi$
$827$	12.7225	−	39.1560i	0.442406	−	1.36159i	0.885303	−	0.465014i	$-0.153951\pi$
$828$	0.907912	−	0.659637i	0.0315521	−	0.0229240i
$829$	−18.4424	−	13.3992i	−0.640532	−	0.465374i	0.219501	−	0.975612i	$-0.429557\pi$
$829$	−18.4424	−	13.3992i	−0.640532	−	0.465374i	−0.860033	+	0.510238i	$0.829557\pi$
$830$	2.04102	+	6.28163i	0.0708450	+	0.218038i
$831$	−7.97843	−	24.5551i	−0.276769	−	0.851806i
$832$	9.99931	+	7.26492i	0.346664	+	0.251866i
$833$	−5.00509	+	3.63641i	−0.173416	+	0.125994i
$834$	−0.195471	+	0.601597i	−0.00676859	+	0.0208316i
$835$	16.7741			0.580492
$836$	−22.6972	−	1.53998i	−0.784998	−	0.0532615i
$837$	−4.33447			−0.149821
$838$	−0.948799	+	2.92010i	−0.0327757	+	0.100873i
$839$	38.2442	−	27.7861i	1.32034	−	0.959281i	0.320409	−	0.947279i	$-0.396180\pi$
$839$	38.2442	−	27.7861i	1.32034	−	0.959281i	0.999928	−	0.0120017i	$-0.00382036\pi$
$840$	−2.28684	−	1.66149i	−0.0789035	−	0.0573268i
$841$	15.3369	+	47.2021i	0.528858	+	1.62766i
$842$	−0.656139	−	2.01939i	−0.0226121	−	0.0695928i
$843$	−4.39979	−	3.19663i	−0.151537	−	0.110098i
$844$	−16.1998	+	11.7699i	−0.557622	+	0.405136i
$845$	13.8170	−	42.5245i	0.475321	−	1.46289i
$846$	0.757643			0.0260483
$847$	7.94427	+	7.60845i	0.272968	+	0.261430i
$848$	−9.14167			−0.313926
$849$	−7.84406	+	24.1415i	−0.269207	+	0.828535i
$850$	−11.5617	+	8.40006i	−0.396563	+	0.288120i
$851$	−0.445948	−	0.324000i	−0.0152869	−	0.0111066i
$852$	−0.484565	−	1.49134i	−0.0166009	−	0.0510924i
$853$	3.35434	+	10.3236i	0.114850	+	0.353473i	0.991916	−	0.126898i	$-0.0405020\pi$
$853$	3.35434	+	10.3236i	0.114850	+	0.353473i	−0.877065	+	0.480371i	$0.840502\pi$
$854$	1.21982	+	0.886250i	0.0417413	+	0.0303269i
$855$	−12.3345	+	8.96152i	−0.421830	+	0.306477i
$856$	3.27799	−	10.0886i	0.112040	−	0.344822i
$857$	28.5431			0.975014			0.487507	−	0.873119i	$-0.337906\pi$
$857$	28.5431			0.975014			0.487507	+	0.873119i	$0.337906\pi$
$858$	0.899096	+	0.0610029i	0.0306946	+	0.00208261i
$859$	−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
$861$	−4.67390	+	3.39578i	−0.159286	+	0.115728i
$862$	2.13868	+	1.55384i	0.0728438	+	0.0529241i
$863$	−13.9537	−	42.9451i	−0.474990	−	1.46187i	−0.845972	−	0.533228i	$-0.820979\pi$
$863$	−13.9537	−	42.9451i	−0.474990	−	1.46187i	0.370982	−	0.928640i	$-0.379021\pi$
$864$	−0.590771	−	1.81820i	−0.0200984	−	0.0618566i
$865$	6.21327	+	4.51421i	0.211258	+	0.153488i
$866$	−1.53274	+	1.11360i	−0.0520845	+	0.0378416i
$867$	−6.57415	+	20.2331i	−0.223270	+	0.687153i
$868$	8.55498			0.290375
$869$	0.828929	−	2.06395i	0.0281195	−	0.0700146i
$870$	−6.30783			−0.213855
$871$	−3.69867	+	11.3833i	−0.125325	+	0.385710i
$872$	5.07903	−	3.69013i	0.171998	−	0.124964i
$873$	−12.1835	−	8.85182i	−0.412348	−	0.299589i
$874$	−0.0990113	−	0.304726i	−0.00334911	−	0.0103075i
$875$	12.5349	+	38.5784i	0.423757	+	1.30419i
$876$	−3.81156	−	2.76926i	−0.128781	−	0.0935647i
$877$	−28.1956	+	20.4853i	−0.952097	+	0.691739i	−0.951302	−	0.308261i	$-0.900253\pi$
$877$	−28.1956	+	20.4853i	−0.952097	+	0.691739i	−0.000795243		1.00000i	$0.500253\pi$
$878$	0.587103	−	1.80692i	0.0198138	−	0.0609805i
$879$	−6.75402			−0.227808
$880$	−47.3578	+	29.7287i	−1.59643	+	1.00216i
$881$	−35.3563			−1.19118			−0.595592	−	0.803287i	$-0.703083\pi$
$881$	−35.3563			−1.19118			−0.595592	+	0.803287i	$0.703083\pi$
$882$	0.0501062	−	0.154211i	0.00168716	−	0.00519256i
$883$	20.1340	−	14.6282i	0.677565	−	0.492279i	−0.194984	−	0.980806i	$-0.562466\pi$
$883$	20.1340	−	14.6282i	0.677565	−	0.492279i	0.872549	+	0.488527i	$0.162466\pi$
$884$	16.5536	+	12.0269i	0.556758	+	0.404508i
$885$	−3.86233	−	11.8870i	−0.129831	−	0.399579i
$886$	−0.629690	−	1.93799i	−0.0211549	−	0.0651080i
$887$	40.1036	+	29.1370i	1.34655	+	0.978324i	0.999176	+	0.0405971i	$0.0129260\pi$
$887$	40.1036	+	29.1370i	1.34655	+	0.978324i	0.347372	+	0.937727i	$0.387074\pi$
$888$	−0.505343	+	0.367153i	−0.0169582	+	0.0123209i
$889$	4.96015	−	15.2658i	0.166358	−	0.511998i
$890$	8.68599			0.291155
$891$	2.54508	+	2.12663i	0.0852636	+	0.0712447i
$892$	12.0628			0.403891
$893$	−5.01796	+	15.4437i	−0.167920	+	0.516804i
$894$	2.43252	−	1.76733i	0.0813557	−	0.0591084i
$895$	−45.6218	−	33.1462i	−1.52497	−	1.10795i
$896$	1.55112	+	4.77385i	0.0518193	+	0.159483i
$897$	−0.294431	−	0.906165i	−0.00983076	−	0.0302560i
$898$	2.09049	+	1.51883i	0.0697605	+	0.0506839i
$899$	31.0950	−	22.5919i	1.03708	−	0.753481i
$900$	−8.68892	+	26.7417i	−0.289631	+	0.891391i
$901$	−14.7169			−0.490291
$902$	−0.757859	−	3.01305i	−0.0252340	−	0.100324i
$903$	−5.04388			−0.167850
$904$	0.568899	−	1.75089i	0.0189213	−	0.0582338i
$905$	−78.3774	+	56.9445i	−2.60535	+	1.89290i
$906$	2.72827	+	1.98220i	0.0906405	+	0.0658542i
$907$	−0.441357	−	1.35836i	−0.0146550	−	0.0451035i	0.943462	−	0.331482i	$-0.107549\pi$
$907$	−0.441357	−	1.35836i	−0.0146550	−	0.0451035i	−0.958117	+	0.286378i	$0.907549\pi$
$908$	−8.66617	−	26.6717i	−0.287597	−	0.885133i
$909$	−4.66057	−	3.38611i	−0.154582	−	0.112310i
$910$	−0.964357	+	0.700646i	−0.0319681	+	0.0232262i
$911$	16.7402	−	51.5211i	0.554628	−	1.70697i	−0.142294	−	0.989824i	$-0.545448\pi$
$911$	16.7402	−	51.5211i	0.554628	−	1.70697i	0.696922	−	0.717147i	$-0.254552\pi$
$912$	13.3553			0.442238
$913$	7.51175	+	29.8648i	0.248603	+	0.988379i
$914$	−3.85821			−0.127618
$915$	12.6062	−	38.7978i	0.416748	−	1.28262i
$916$	−4.35567	+	3.16458i	−0.143916	+	0.104561i
$917$	0.606873	+	0.440919i	0.0200407	+	0.0145604i
$918$	−0.309989	−	0.954047i	−0.0102312	−	0.0314883i
$919$	−7.07678	−	21.7801i	−0.233441	−	0.718459i	−0.997324	−	0.0731040i	$-0.976710\pi$
$919$	−7.07678	−	21.7801i	−0.233441	−	0.718459i	0.763883	−	0.645355i	$-0.223290\pi$
$920$	−1.30029	−	0.944714i	−0.0428692	−	0.0311463i
$921$	−14.2707	+	10.3683i	−0.470236	+	0.341647i
$922$	−1.13258	+	3.48571i	−0.0372994	+	0.114796i
$923$	−1.33133			−0.0438211
$924$	−5.02326	−	4.19734i	−0.165253	−	0.138082i
$925$	13.8110			0.454101
$926$	0.152202	−	0.468430i	0.00500167	−	0.0153936i
$927$	−6.24116	+	4.53447i	−0.204986	+	0.148931i
$928$	13.7149	+	9.96443i	0.450212	+	0.327099i
$929$	−4.49019	−	13.8194i	−0.147319	−	0.453400i	0.849983	−	0.526810i	$-0.176612\pi$
$929$	−4.49019	−	13.8194i	−0.147319	−	0.453400i	−0.997302	+	0.0734098i	$0.976612\pi$
$930$	0.952798	+	2.93241i	0.0312435	+	0.0961576i
$931$	2.81156	+	2.04272i	0.0921452	+	0.0669474i
$932$	−28.4059	+	20.6381i	−0.930466	+	0.676023i
$933$	3.78282	−	11.6423i	0.123844	−	0.381152i
$934$	−3.73021			−0.122056
$935$	−76.2397	+	47.8594i	−2.49331	+	1.56517i
$936$	−1.07970			−0.0352911
$937$	9.46675	−	29.1357i	0.309265	−	0.951821i	−0.668786	−	0.743455i	$-0.733186\pi$
$937$	9.46675	−	29.1357i	0.309265	−	0.951821i	0.978051	−	0.208366i	$-0.0668144\pi$
$938$	−0.936985	+	0.680760i	−0.0305937	+	0.0222276i
$939$	2.55610	+	1.85711i	0.0834151	+	0.0606047i
$940$	12.5024	+	38.4784i	0.407783	+	1.25503i
$941$	6.50584	+	20.0229i	0.212084	+	0.652728i	0.999348	+	0.0361114i	$0.0114971\pi$
$941$	6.50584	+	20.0229i	0.212084	+	0.652728i	−0.787264	+	0.616617i	$0.788503\pi$
$942$	0.762122	+	0.553714i	0.0248313	+	0.0180410i
$943$	−2.65755	+	1.93083i	−0.0865419	+	0.0628764i
$944$	−3.38330	+	10.4127i	−0.110117	+	0.338905i
$945$	−4.38705			−0.142711
$946$	1.01092	−	2.51708i	0.0328678	−	0.0818375i
$947$	0.729464			0.0237044			0.0118522	−	0.999930i	$-0.496227\pi$
$947$	0.729464			0.0237044			0.0118522	+	0.999930i	$0.496227\pi$
$948$	−0.409016	+	1.25882i	−0.0132842	+	0.0408846i
$949$	−3.23607	+	2.35114i	−0.105047	+	0.0763213i
$950$	6.49467	+	4.71866i	0.210715	+	0.153093i
$951$	−2.60614	−	8.02087i	−0.0845098	−	0.260095i
$952$	1.23180	+	3.79111i	0.0399230	+	0.122870i
$953$	−31.5638	−	22.9325i	−1.02245	−	0.742856i	−0.0556689	−	0.998449i	$-0.517729\pi$
$953$	−31.5638	−	22.9325i	−1.02245	−	0.742856i	−0.966784	+	0.255594i	$0.917729\pi$
$954$	0.312053	−	0.226720i	0.0101031	−	0.00734033i
$955$	−19.9501	+	61.3999i	−0.645569	+	1.98686i
$956$	−25.0775			−0.811065
$957$	−29.3425	−	1.99086i	−0.948507	−	0.0643554i
$958$	1.32520			0.0428153
$959$	4.01977	−	12.3716i	0.129805	−	0.399499i
$960$	26.1785	−	19.0198i	0.844908	−	0.613862i
$961$	9.88001	+	7.17825i	0.318710	+	0.231556i
$962$	0.0813978	+	0.250517i	0.00262437	+	0.00807698i
$963$	−5.08748	−	15.6577i	−0.163942	−	0.504561i
$964$	−29.7963	−	21.6483i	−0.959673	−	0.697243i
$965$	30.2139	−	21.9517i	0.972619	−	0.706649i
$966$	0.0284902	−	0.0876837i	0.000916656	−	0.00282118i
$967$	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
$969$	21.5003			0.690688
$970$	−3.31039	+	10.1883i	−0.106290	+	0.327127i
$971$	−28.0562	+	20.3840i	−0.900367	+	0.654155i	−0.938560	−	0.345116i	$-0.887840\pi$
$971$	−28.0562	+	20.3840i	−0.900367	+	0.654155i	0.0381935	+	0.999270i	$0.487840\pi$
$972$	−1.59676	−	1.16012i	−0.0512162	−	0.0372108i
$973$	−1.20551	−	3.71019i	−0.0386470	−	0.118943i
$974$	−0.0500677	−	0.154093i	−0.00160427	−	0.00493745i
$975$	19.3133	+	14.0319i	0.618520	+	0.449381i
$976$	−28.9101	+	21.0044i	−0.925390	+	0.672335i
$977$	−7.76676	+	23.9036i	−0.248481	+	0.764745i	0.746564	+	0.665314i	$0.231702\pi$
$977$	−7.76676	+	23.9036i	−0.248481	+	0.764745i	−0.995044	+	0.0994308i	$0.968298\pi$
$978$	1.44361			0.0461615
$979$	40.4051	+	2.74145i	1.29135	+	0.0876171i
$980$	8.65877			0.276594
$981$	3.01092	−	9.26667i	0.0961314	−	0.295862i
$982$	−3.18710	+	2.31557i	−0.101705	+	0.0738927i
$983$	−24.5860	−	17.8628i	−0.784172	−	0.569734i	0.122056	−	0.992523i	$-0.461051\pi$
$983$	−24.5860	−	17.8628i	−0.784172	−	0.569734i	−0.906228	+	0.422789i	$0.861051\pi$
$984$	1.15029	+	3.54024i	0.0366701	+	0.112859i
$985$	6.40248	+	19.7048i	0.204000	+	0.627847i
$986$	7.19646	+	5.22853i	0.229182	+	0.166510i
$987$	−3.78018	+	2.74646i	−0.120324	+	0.0874209i
$988$	3.55184	−	10.9314i	0.112999	−	0.347775i
$989$	−2.86792			−0.0911947
$990$	0.879275	−	2.18931i	0.0279452	−	0.0695807i
$991$	−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
$993$	4.96158	−	3.60480i	0.157451	−	0.114395i
$994$	−0.104221	−	0.0757207i	−0.00330568	−	0.00240172i
$995$	−22.7238	−	69.9365i	−0.720392	−	2.21714i
$996$	−5.66303	−	17.4290i	−0.179440	−	0.552259i
$997$	37.1230	+	26.9715i	1.17570	+	0.854194i	0.991680	−	0.128728i	$-0.0410896\pi$
$997$	37.1230	+	26.9715i	1.17570	+	0.854194i	0.184018	+	0.982923i	$0.441090\pi$
$998$	5.38896	−	3.91531i	0.170585	−	0.123937i
$999$	−0.299575	+	0.921997i	−0.00947813	+	0.0291707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.f.64.1	✓	8
3.2	odd	2		693.2.m.f.64.2		8
11.4	even	5		2541.2.a.bn.1.2		4
11.5	even	5	inner	231.2.j.f.148.1	yes	8
11.7	odd	10		2541.2.a.bm.1.3		4
33.5	odd	10		693.2.m.f.379.2		8
33.26	odd	10		7623.2.a.ci.1.3		4
33.29	even	10		7623.2.a.cl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.64.1	✓	8	1.1	even	1	trivial
231.2.j.f.148.1	yes	8	11.5	even	5	inner
693.2.m.f.64.2		8	3.2	odd	2
693.2.m.f.379.2		8	33.5	odd	10
2541.2.a.bm.1.3		4	11.7	odd	10
2541.2.a.bn.1.2		4	11.4	even	5
7623.2.a.ci.1.3		4	33.26	odd	10
7623.2.a.cl.1.2		4	33.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0501062 - 0.154211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.59676 + 1.16012i) q^{4} +(-1.35567 - 4.17234i) q^{5} +(-0.0501062 - 0.154211i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.521270 - 0.378725i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.0501062 - 0.154211i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.59676 + 1.16012i) q^{4} +(-1.35567 - 4.17234i) q^{5} +(-0.0501062 - 0.154211i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.521270 - 0.378725i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.711349 q^{10} +(-3.30902 - 0.224514i) q^{11} +1.97371 q^{12} +(0.517822 - 1.59369i) q^{13} +(0.131180 - 0.0953077i) q^{14} +(-3.54920 - 2.57865i) q^{15} +(1.18753 + 3.65485i) q^{16} +(1.91177 + 5.88383i) q^{17} +(-0.131180 - 0.0953077i) q^{18} +(2.81156 - 2.04272i) q^{19} +(2.67571 - 8.23498i) q^{20} +1.00000 q^{21} +(-0.200425 + 0.499038i) q^{22} +0.568595 q^{23} +(0.199108 - 0.612790i) q^{24} +(-11.5255 + 8.37373i) q^{25} +(-0.219819 - 0.159708i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.609909 + 1.87711i) q^{28} +(7.17390 + 5.21214i) q^{29} +(-0.575493 + 0.418120i) q^{30} +(1.33943 - 4.12233i) q^{31} +1.91177 q^{32} +(-2.80902 + 1.76336i) q^{33} +1.00314 q^{34} +(1.35567 - 4.17234i) q^{35} +(1.59676 - 1.16012i) q^{36} +(-0.784298 - 0.569826i) q^{37} +(-0.174133 - 0.535927i) q^{38} +(-0.517822 - 1.59369i) q^{39} +(-2.28684 - 1.66149i) q^{40} +(-4.67390 + 3.39578i) q^{41} +(0.0501062 - 0.154211i) q^{42} -5.04388 q^{43} +(-5.02326 - 4.19734i) q^{44} -4.38705 q^{45} +(0.0284902 - 0.0876837i) q^{46} +(-3.78018 + 2.74646i) q^{47} +(3.10900 + 2.25882i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.713826 + 2.19693i) q^{50} +(5.00509 + 3.63641i) q^{51} +(2.67571 - 1.94401i) q^{52} +(-0.735096 + 2.26239i) q^{53} -0.162147 q^{54} +(3.54920 + 14.1107i) q^{55} +0.644326 q^{56} +(1.07392 - 3.30519i) q^{57} +(1.16323 - 0.845134i) q^{58} +(2.30490 + 1.67461i) q^{59} +(-2.67571 - 8.23498i) q^{60} +(2.87350 + 8.84371i) q^{61} +(-0.568595 - 0.413109i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-2.27928 + 7.01489i) q^{64} -7.35141 q^{65} +(0.131180 + 0.521537i) q^{66} -7.14275 q^{67} +(-3.77328 + 11.6130i) q^{68} +(0.460003 - 0.334212i) q^{69} +(-0.575493 - 0.418120i) q^{70} +(-0.245510 - 0.755602i) q^{71} +(-0.199108 - 0.612790i) q^{72} +(-1.93117 - 1.40308i) q^{73} +(-0.127172 + 0.0923956i) q^{74} +(-4.40233 + 13.5490i) q^{75} +6.85919 q^{76} +(-2.54508 - 2.12663i) q^{77} -0.271711 q^{78} +(-0.207232 + 0.637795i) q^{79} +(13.6394 - 9.90958i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.289476 + 0.890917i) q^{82} +(-2.86923 - 8.83059i) q^{83} +(1.59676 + 1.16012i) q^{84} +(21.9576 - 15.9531i) q^{85} +(-0.252730 + 0.777822i) q^{86} +8.86742 q^{87} +(-1.80992 + 1.13618i) q^{88} -12.2106 q^{89} +(-0.219819 + 0.676533i) q^{90} +(1.35567 - 0.984955i) q^{91} +(0.907912 + 0.659637i) q^{92} +(-1.33943 - 4.12233i) q^{93} +(0.234124 + 0.720561i) q^{94} +(-12.3345 - 8.96152i) q^{95} +(1.54666 - 1.12371i) q^{96} +(4.65368 - 14.3225i) q^{97} +0.162147 q^{98} +(-1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

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