LMFDB - Embedded newform 429.2.n.b.313.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
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			313.1
Root			$-0.375422 + 1.15543i$ of defining polynomial
Character	$\chi$	$=$	429.313
Dual form			429.2.n.b.196.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.375422 - 1.15543i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.423959 - 0.308024i) q^{4} +(0.339998 - 1.04640i) q^{5} +(0.375422 - 1.15543i) q^{6} +(0.237146 - 0.172297i) q^{7} +(-2.48080 - 1.80240i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.375422 - 1.15543i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.423959 - 0.308024i) q^{4} +(0.339998 - 1.04640i) q^{5} +(0.375422 - 1.15543i) q^{6} +(0.237146 - 0.172297i) q^{7} +(-2.48080 - 1.80240i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.33669 q^{10} +(-0.323558 - 3.30080i) q^{11} +0.524042 q^{12} +(-0.309017 - 0.951057i) q^{13} +(-0.288107 - 0.209322i) q^{14} +(0.890125 - 0.646714i) q^{15} +(-0.827330 + 2.54626i) q^{16} +(0.568982 - 1.75115i) q^{17} +(0.982867 - 0.714095i) q^{18} +(0.351197 + 0.255159i) q^{19} +(-0.178173 - 0.548360i) q^{20} +0.293129 q^{21} +(-3.69238 + 1.61304i) q^{22} +2.58972 q^{23} +(-0.947580 - 2.91635i) q^{24} +(3.06572 + 2.22738i) q^{25} +(-0.982867 + 0.714095i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0474687 - 0.146094i) q^{28} +(0.749994 - 0.544902i) q^{29} +(-1.08140 - 0.785686i) q^{30} +(0.496795 + 1.52898i) q^{31} -2.88025 q^{32} +(1.67840 - 2.86059i) q^{33} -2.23694 q^{34} +(-0.0996632 - 0.306732i) q^{35} +(0.423959 + 0.308024i) q^{36} +(3.13476 - 2.27754i) q^{37} +(0.162972 - 0.501576i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-2.72951 + 1.98311i) q^{40} +(-2.66679 - 1.93754i) q^{41} +(-0.110047 - 0.338690i) q^{42} +0.832771 q^{43} +(-1.15390 - 1.29974i) q^{44} +1.10026 q^{45} +(-0.972237 - 2.99224i) q^{46} +(-1.39394 - 1.01276i) q^{47} +(-2.16598 + 1.57368i) q^{48} +(-2.13657 + 6.57568i) q^{49} +(1.42264 - 4.37843i) q^{50} +(1.48962 - 1.08227i) q^{51} +(-0.423959 - 0.308024i) q^{52} +(0.0466498 + 0.143573i) q^{53} +1.21489 q^{54} +(-3.56399 - 0.783693i) q^{55} -0.898861 q^{56} +(0.134145 + 0.412857i) q^{57} +(-0.911160 - 0.661997i) q^{58} +(3.09542 - 2.24895i) q^{59} +(0.178173 - 0.548360i) q^{60} +(-2.19191 + 6.74600i) q^{61} +(1.58012 - 1.14802i) q^{62} +(0.237146 + 0.172297i) q^{63} +(2.73597 + 8.42044i) q^{64} -1.10026 q^{65} +(-3.93532 - 0.865346i) q^{66} -2.04660 q^{67} +(-0.298171 - 0.917674i) q^{68} +(2.09513 + 1.52220i) q^{69} +(-0.316991 + 0.230307i) q^{70} +(-4.11762 + 12.6727i) q^{71} +(0.947580 - 2.91635i) q^{72} +(1.68800 - 1.22641i) q^{73} +(-3.80839 - 2.76696i) q^{74} +(1.17100 + 3.60397i) q^{75} +0.227488 q^{76} +(-0.645449 - 0.727026i) q^{77} -1.21489 q^{78} +(1.63172 + 5.02190i) q^{79} +(2.38313 + 1.73144i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.23752 + 3.80868i) q^{82} +(0.251130 - 0.772900i) q^{83} +(0.124275 - 0.0902908i) q^{84} +(-1.63896 - 1.19077i) q^{85} +(-0.312640 - 0.962208i) q^{86} +0.927043 q^{87} +(-5.14670 + 8.77181i) q^{88} +10.8989 q^{89} +(-0.413060 - 1.27127i) q^{90} +(-0.237146 - 0.172297i) q^{91} +(1.09793 - 0.797696i) q^{92} +(-0.496795 + 1.52898i) q^{93} +(-0.646855 + 1.99082i) q^{94} +(0.386406 - 0.280741i) q^{95} +(-2.33017 - 1.69297i) q^{96} +(2.30186 + 7.08439i) q^{97} +8.39984 q^{98} +(3.03927 - 1.32773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.375422	−	1.15543i	−0.265463	−	0.817012i	−0.991586	−	0.129447i	$-0.958680\pi$
$2$	−0.375422	−	1.15543i	−0.265463	−	0.817012i	0.726123	−	0.687565i	$-0.241320\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.423959	−	0.308024i	0.211979	−	0.154012i
$5$	0.339998	−	1.04640i	0.152052	−	0.467967i	−0.845799	−	0.533502i	$-0.820876\pi$
$5$	0.339998	−	1.04640i	0.152052	−	0.467967i	0.997850	+	0.0655357i	$0.0208756\pi$
$6$	0.375422	−	1.15543i	0.153265	−	0.471702i
$7$	0.237146	−	0.172297i	0.0896329	−	0.0651221i	−0.542066	−	0.840336i	$-0.682358\pi$
$7$	0.237146	−	0.172297i	0.0896329	−	0.0651221i	0.631699	+	0.775214i	$0.282358\pi$
$8$	−2.48080	−	1.80240i	−0.877094	−	0.637246i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.33669			−0.422698
$11$	−0.323558	−	3.30080i	−0.0975563	−	0.995230i
$11$	−0.323558	−	3.30080i	−0.0975563	−	0.995230i
$12$	0.524042			0.151278
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$	−0.288107	−	0.209322i	−0.0769998	−	0.0559436i
$15$	0.890125	−	0.646714i	0.229829	−	0.166981i
$16$	−0.827330	+	2.54626i	−0.206833	+	0.636565i
$17$	0.568982	−	1.75115i	0.137998	−	0.424716i	−0.858046	−	0.513573i	$-0.828322\pi$
$17$	0.568982	−	1.75115i	0.137998	−	0.424716i	0.996044	+	0.0888574i	$0.0283215\pi$
$18$	0.982867	−	0.714095i	0.231664	−	0.168314i
$19$	0.351197	+	0.255159i	0.0805701	+	0.0585376i	0.627341	−	0.778745i	$-0.284143\pi$
$19$	0.351197	+	0.255159i	0.0805701	+	0.0585376i	−0.546771	+	0.837282i	$0.684143\pi$
$20$	−0.178173	−	0.548360i	−0.0398407	−	0.122617i
$21$	0.293129			0.0639660
$22$	−3.69238	+	1.61304i	−0.787217	+	0.343902i
$23$	2.58972			0.539994			0.269997	−	0.962861i	$-0.412977\pi$
$23$	2.58972			0.539994			0.269997	+	0.962861i	$0.412977\pi$
$24$	−0.947580	−	2.91635i	−0.193424	−	0.595298i
$25$	3.06572	+	2.22738i	0.613144	+	0.445475i
$26$	−0.982867	+	0.714095i	−0.192756	+	0.140045i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.0474687	−	0.146094i	0.00897074	−	0.0276091i
$29$	0.749994	−	0.544902i	0.139270	−	0.101186i	−0.515969	−	0.856607i	$-0.672568\pi$
$29$	0.749994	−	0.544902i	0.139270	−	0.101186i	0.655239	+	0.755422i	$0.272568\pi$
$30$	−1.08140	−	0.785686i	−0.197437	−	0.143446i
$31$	0.496795	+	1.52898i	0.0892269	+	0.274612i	0.985706	−	0.168473i	$-0.0538837\pi$
$31$	0.496795	+	1.52898i	0.0892269	+	0.274612i	−0.896479	+	0.443086i	$0.853884\pi$
$32$	−2.88025			−0.509160
$33$	1.67840	−	2.86059i	0.292172	−	0.497965i
$34$	−2.23694			−0.383631
$35$	−0.0996632	−	0.306732i	−0.0168461	−	0.0518471i
$36$	0.423959	+	0.308024i	0.0706598	+	0.0513373i
$37$	3.13476	−	2.27754i	0.515352	−	0.374425i	−0.299498	−	0.954097i	$-0.596819\pi$
$37$	3.13476	−	2.27754i	0.515352	−	0.374425i	0.814850	+	0.579672i	$0.196819\pi$
$38$	0.162972	−	0.501576i	0.0264375	−	0.0813663i
$39$	0.309017	−	0.951057i	0.0494823	−	0.152291i
$40$	−2.72951	+	1.98311i	−0.431573	+	0.313556i
$41$	−2.66679	−	1.93754i	−0.416483	−	0.302592i	0.359738	−	0.933053i	$-0.382866\pi$
$41$	−2.66679	−	1.93754i	−0.416483	−	0.302592i	−0.776221	+	0.630461i	$0.782866\pi$
$42$	−0.110047	−	0.338690i	−0.0169806	−	0.0522610i
$43$	0.832771			0.126996			0.0634982	−	0.997982i	$-0.479774\pi$
$43$	0.832771			0.126996			0.0634982	+	0.997982i	$0.479774\pi$
$44$	−1.15390	−	1.29974i	−0.173957	−	0.195943i
$45$	1.10026			0.164016
$46$	−0.972237	−	2.99224i	−0.143349	−	0.441182i
$47$	−1.39394	−	1.01276i	−0.203328	−	0.147726i	0.481462	−	0.876467i	$-0.340106\pi$
$47$	−1.39394	−	1.01276i	−0.203328	−	0.147726i	−0.684790	+	0.728741i	$0.740106\pi$
$48$	−2.16598	+	1.57368i	−0.312632	+	0.227141i
$49$	−2.13657	+	6.57568i	−0.305224	+	0.939382i
$50$	1.42264	−	4.37843i	0.201191	−	0.619203i
$51$	1.48962	−	1.08227i	0.208588	−	0.151548i
$52$	−0.423959	−	0.308024i	−0.0587925	−	0.0427152i
$53$	0.0466498	+	0.143573i	0.00640784	+	0.0197213i	0.954209	−	0.299140i	$-0.0966997\pi$
$53$	0.0466498	+	0.143573i	0.00640784	+	0.0197213i	−0.947801	+	0.318861i	$0.896700\pi$
$54$	1.21489			0.165326
$55$	−3.56399	−	0.783693i	−0.480568	−	0.105673i
$56$	−0.898861			−0.120115
$57$	0.134145	+	0.412857i	0.0177680	+	0.0546842i
$58$	−0.911160	−	0.661997i	−0.119641	−	0.0869244i
$59$	3.09542	−	2.24895i	0.402989	−	0.292789i	−0.367768	−	0.929917i	$-0.619878\pi$
$59$	3.09542	−	2.24895i	0.402989	−	0.292789i	0.770757	+	0.637129i	$0.219878\pi$
$60$	0.178173	−	0.548360i	0.0230020	−	0.0707930i
$61$	−2.19191	+	6.74600i	−0.280645	+	0.863736i	0.707025	+	0.707188i	$0.250037\pi$
$61$	−2.19191	+	6.74600i	−0.280645	+	0.863736i	−0.987670	+	0.156548i	$0.949963\pi$
$62$	1.58012	−	1.14802i	0.200675	−	0.145799i
$63$	0.237146	+	0.172297i	0.0298776	+	0.0217074i
$64$	2.73597	+	8.42044i	0.341996	+	1.05256i
$65$	−1.10026			−0.136470
$66$	−3.93532	−	0.865346i	−0.484404	−	0.106517i
$67$	−2.04660			−0.250031			−0.125016	−	0.992155i	$-0.539898\pi$
$67$	−2.04660			−0.250031			−0.125016	+	0.992155i	$0.539898\pi$
$68$	−0.298171	−	0.917674i	−0.0361585	−	0.111284i
$69$	2.09513	+	1.52220i	0.252224	+	0.183251i
$70$	−0.316991	+	0.230307i	−0.0378877	+	0.0275270i
$71$	−4.11762	+	12.6727i	−0.488671	+	1.50398i	0.337921	+	0.941175i	$0.390276\pi$
$71$	−4.11762	+	12.6727i	−0.488671	+	1.50398i	−0.826592	+	0.562802i	$0.809724\pi$
$72$	0.947580	−	2.91635i	0.111673	−	0.343695i
$73$	1.68800	−	1.22641i	0.197566	−	0.143540i	−0.484604	−	0.874733i	$-0.661036\pi$
$73$	1.68800	−	1.22641i	0.197566	−	0.143540i	0.682170	+	0.731194i	$0.261036\pi$
$74$	−3.80839	−	2.76696i	−0.442717	−	0.321653i
$75$	1.17100	+	3.60397i	0.135216	+	0.416151i
$76$	0.227488			0.0260947
$77$	−0.645449	−	0.727026i	−0.0735557	−	0.0828523i
$78$	−1.21489			−0.137559
$79$	1.63172	+	5.02190i	0.183582	+	0.565008i	0.999921	−	0.0125651i	$-0.00399970\pi$
$79$	1.63172	+	5.02190i	0.183582	+	0.565008i	−0.816339	+	0.577573i	$0.804000\pi$
$80$	2.38313	+	1.73144i	0.266442	+	0.193581i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.23752	+	3.80868i	−0.136661	+	0.420598i
$83$	0.251130	−	0.772900i	0.0275651	−	0.0848368i	−0.936328	−	0.351128i	$-0.885798\pi$
$83$	0.251130	−	0.772900i	0.0275651	−	0.0848368i	0.963893	+	0.266291i	$0.0857982\pi$
$84$	0.124275	−	0.0902908i	0.0135595	−	0.00985153i
$85$	−1.63896	−	1.19077i	−0.177770	−	0.129157i
$86$	−0.312640	−	0.962208i	−0.0337129	−	0.103758i
$87$	0.927043			0.0993895
$88$	−5.14670	+	8.77181i	−0.548641	+	0.935078i
$89$	10.8989			1.15528			0.577641	−	0.816291i	$-0.303973\pi$
$89$	10.8989			1.15528			0.577641	+	0.816291i	$0.303973\pi$
$90$	−0.413060	−	1.27127i	−0.0435403	−	0.134003i
$91$	−0.237146	−	0.172297i	−0.0248597	−	0.0180616i
$92$	1.09793	−	0.797696i	0.114468	−	0.0831656i
$93$	−0.496795	+	1.52898i	−0.0515152	+	0.158547i
$94$	−0.646855	+	1.99082i	−0.0667180	+	0.205337i
$95$	0.386406	−	0.280741i	0.0396444	−	0.0288034i
$96$	−2.33017	−	1.69297i	−0.237822	−	0.172788i
$97$	2.30186	+	7.08439i	0.233718	+	0.719311i	0.997289	+	0.0735864i	$0.0234445\pi$
$97$	2.30186	+	7.08439i	0.233718	+	0.719311i	−0.763571	+	0.645724i	$0.776556\pi$
$98$	8.39984			0.848512
$99$	3.03927	−	1.32773i	0.305458	−	0.133442i
$100$	1.98582			0.198582
$101$	3.73090	+	11.4825i	0.371239	+	1.14256i	0.945981	+	0.324221i	$0.105102\pi$
$101$	3.73090	+	11.4825i	0.371239	+	1.14256i	−0.574742	+	0.818334i	$0.694898\pi$
$102$	−1.80972	−	1.31484i	−0.179189	−	0.130188i
$103$	7.88099	−	5.72587i	0.776537	−	0.564187i	−0.127401	−	0.991851i	$-0.540663\pi$
$103$	7.88099	−	5.72587i	0.776537	−	0.564187i	0.903938	+	0.427664i	$0.140663\pi$
$104$	−0.947580	+	2.91635i	−0.0929179	+	0.285972i
$105$	0.0996632	−	0.306732i	0.00972613	−	0.0299339i
$106$	0.148375	−	0.107801i	0.0144115	−	0.0104706i
$107$	−8.09080	−	5.87831i	−0.782167	−	0.568278i	0.123461	−	0.992349i	$-0.460601\pi$
$107$	−8.09080	−	5.87831i	−0.782167	−	0.568278i	−0.905629	+	0.424072i	$0.860601\pi$
$108$	0.161938	+	0.498393i	0.0155825	+	0.0479579i
$109$	15.1692			1.45295			0.726473	−	0.687195i	$-0.241158\pi$
$109$	15.1692			1.45295			0.726473	+	0.687195i	$0.241158\pi$
$110$	0.432496	+	4.41215i	0.0412369	+	0.420682i
$111$	3.87478			0.367778
$112$	0.242514	+	0.746383i	0.0229155	+	0.0705265i
$113$	8.76777	+	6.37016i	0.824803	+	0.599254i	0.918084	−	0.396385i	$-0.129736\pi$
$113$	8.76777	+	6.37016i	0.824803	+	0.599254i	−0.0932814	+	0.995640i	$0.529736\pi$
$114$	0.426666	−	0.309991i	0.0399609	−	0.0290333i
$115$	0.880499	−	2.70990i	0.0821069	−	0.252699i
$116$	0.150123	−	0.462032i	0.0139386	−	0.0428986i
$117$	0.809017	−	0.587785i	0.0747936	−	0.0543408i
$118$	−3.76059	−	2.73223i	−0.346191	−	0.251522i
$119$	−0.166785	−	0.513312i	−0.0152892	−	0.0470553i
$120$	−3.37386			−0.307990
$121$	−10.7906	+	2.13600i	−0.980966	+	0.194182i
$122$	8.61741			0.780184
$123$	−1.01862	−	3.13500i	−0.0918461	−	0.282673i
$124$	0.681582	+	0.495198i	0.0612079	+	0.0444701i
$125$	7.82370	−	5.68425i	0.699773	−	0.508415i
$126$	0.110047	−	0.338690i	0.00980377	−	0.0301729i
$127$	−1.94042	+	5.97199i	−0.172184	+	0.529929i	−0.999494	−	0.0318178i	$-0.989870\pi$
$127$	−1.94042	+	5.97199i	−0.172184	+	0.529929i	0.827309	+	0.561747i	$0.189870\pi$
$128$	4.04175	−	2.93650i	0.357243	−	0.259553i
$129$	0.673726	+	0.489491i	0.0593183	+	0.0430972i
$130$	0.413060	+	1.27127i	0.0362277	+	0.111498i
$131$	5.36606			0.468834			0.234417	−	0.972136i	$-0.424682\pi$
$131$	5.36606			0.468834			0.234417	+	0.972136i	$0.424682\pi$
$132$	−0.169558	−	1.72976i	−0.0147581	−	0.150556i
$133$	0.127248			0.0110338
$134$	0.768336	+	2.36470i	0.0663742	+	0.204279i
$135$	0.890125	+	0.646714i	0.0766098	+	0.0556603i
$136$	−4.56781	+	3.31871i	−0.391686	+	0.284577i
$137$	−4.84702	+	14.9176i	−0.414109	+	1.27450i	0.498937	+	0.866638i	$0.333724\pi$
$137$	−4.84702	+	14.9176i	−0.414109	+	1.27450i	−0.913046	+	0.407857i	$0.866276\pi$
$138$	0.972237	−	2.99224i	0.0827623	−	0.254716i
$139$	1.44148	−	1.04729i	0.122264	−	0.0888302i	−0.524973	−	0.851119i	$-0.675924\pi$
$139$	1.44148	−	1.04729i	0.122264	−	0.0888302i	0.647237	+	0.762289i	$0.275924\pi$
$140$	−0.136734	−	0.0993429i	−0.0115561	−	0.00839601i
$141$	−0.532439	−	1.63868i	−0.0448395	−	0.138002i
$142$	16.1883			1.35849
$143$	−3.03927	+	1.32773i	−0.254156	+	0.111030i
$144$	−2.67730			−0.223108
$145$	−0.315193	−	0.970063i	−0.0261753	−	0.0805593i
$146$	−2.05074	−	1.48995i	−0.169720	−	0.123309i
$147$	−5.59360	+	4.06399i	−0.461353	+	0.335192i
$148$	0.627473	−	1.93116i	0.0515780	−	0.158741i
$149$	−5.85767	+	18.0281i	−0.479879	+	1.47692i	0.359384	+	0.933190i	$0.382987\pi$
$149$	−5.85767	+	18.0281i	−0.479879	+	1.47692i	−0.839263	+	0.543726i	$0.817013\pi$
$150$	3.72451	−	2.70602i	0.304105	−	0.220945i
$151$	−13.7539	−	9.99278i	−1.11928	−	0.813201i	−0.135176	−	0.990822i	$-0.543160\pi$
$151$	−13.7539	−	9.99278i	−1.11928	−	0.813201i	−0.984099	+	0.177620i	$0.943160\pi$
$152$	−0.411348	−	1.26600i	−0.0333647	−	0.102686i
$153$	1.84127			0.148857
$154$	−0.597711	+	1.01871i	−0.0481650	+	0.0820901i
$155$	1.76884			0.142076
$156$	−0.161938	−	0.498393i	−0.0129654	−	0.0399034i
$157$	2.35292	+	1.70949i	0.187783	+	0.136432i	0.677705	−	0.735334i	$-0.262975\pi$
$157$	2.35292	+	1.70949i	0.187783	+	0.136432i	−0.489922	+	0.871766i	$0.662975\pi$
$158$	5.18987	−	3.77066i	0.412884	−	0.299978i
$159$	−0.0466498	+	0.143573i	−0.00369957	+	0.0113861i
$160$	−0.979277	+	3.01390i	−0.0774186	+	0.238270i
$161$	0.614143	−	0.446201i	0.0484012	−	0.0351656i
$162$	0.982867	+	0.714095i	0.0772213	+	0.0561046i
$163$	−4.04406	−	12.4463i	−0.316755	−	0.974871i	−0.975026	−	0.222090i	$-0.928712\pi$
$163$	−4.04406	−	12.4463i	−0.316755	−	0.974871i	0.658271	−	0.752781i	$-0.271288\pi$
$164$	−1.72742			−0.134889
$165$	−2.42268	−	2.72888i	−0.188606	−	0.212443i
$166$	−0.987311			−0.0766302
$167$	0.0949939	+	0.292361i	0.00735085	+	0.0226236i	0.954665	−	0.297683i	$-0.0962140\pi$
$167$	0.0949939	+	0.292361i	0.00735085	+	0.0226236i	−0.947314	+	0.320307i	$0.896214\pi$
$168$	−0.727194	−	0.528337i	−0.0561042	−	0.0407621i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−0.760553	+	2.34074i	−0.0583317	+	0.179527i
$171$	−0.134145	+	0.412857i	−0.0102583	+	0.0315719i
$172$	0.353061	−	0.256514i	0.0269206	−	0.0195590i
$173$	−13.9376	−	10.1263i	−1.05966	−	0.769887i	−0.0856328	−	0.996327i	$-0.527291\pi$
$173$	−13.9376	−	10.1263i	−1.05966	−	0.769887i	−0.974025	+	0.226440i	$0.927291\pi$
$174$	−0.348032	−	1.07113i	−0.0263843	−	0.0812024i
$175$	1.11079			0.0839682
$176$	8.67240	+	1.90699i	0.653707	+	0.143745i
$177$	3.82615			0.287591
$178$	−4.09169	−	12.5929i	−0.306685	−	0.943879i
$179$	4.32192	+	3.14006i	0.323035	+	0.234699i	0.737470	−	0.675380i	$-0.236021\pi$
$179$	4.32192	+	3.14006i	0.323035	+	0.234699i	−0.414434	+	0.910079i	$0.636021\pi$
$180$	0.466463	−	0.338905i	0.0347681	−	0.0252605i
$181$	4.52801	−	13.9358i	0.336564	−	1.03584i	−0.629382	−	0.777096i	$-0.716692\pi$
$181$	4.52801	−	13.9358i	0.336564	−	1.03584i	0.965946	−	0.258742i	$-0.0833080\pi$
$182$	−0.110047	+	0.338690i	−0.00815723	+	0.0251054i
$183$	−5.73849	+	4.16925i	−0.424201	+	0.308200i
$184$	−6.42457	−	4.66772i	−0.473626	−	0.344109i
$185$	−1.31742	−	4.05459i	−0.0968584	−	0.298099i
$186$	1.95313			0.143211
$187$	−5.96429	−	1.31150i	−0.436152	−	0.0959066i
$188$	−0.902929			−0.0658529
$189$	0.0905818	+	0.278782i	0.00658886	+	0.0202784i
$190$	−0.469441	−	0.341069i	−0.0340568	−	0.0247437i
$191$	−14.2108	+	10.3248i	−1.02826	+	0.747074i	−0.967960	−	0.251106i	$-0.919206\pi$
$191$	−14.2108	+	10.3248i	−1.02826	+	0.747074i	−0.0602999	+	0.998180i	$0.519206\pi$
$192$	−2.73597	+	8.42044i	−0.197451	+	0.607693i
$193$	5.19132	−	15.9772i	0.373679	−	1.15007i	−0.570686	−	0.821168i	$-0.693323\pi$
$193$	5.19132	−	15.9772i	0.373679	−	1.15007i	0.944365	−	0.328898i	$-0.106677\pi$
$194$	7.32134	−	5.31927i	0.525642	−	0.381901i
$195$	−0.890125	−	0.646714i	−0.0637432	−	0.0463121i
$196$	1.11965	+	3.44593i	0.0799750	+	0.246138i
$197$	−9.89782			−0.705191			−0.352595	−	0.935776i	$-0.614701\pi$
$197$	−9.89782			−0.705191			−0.352595	+	0.935776i	$0.614701\pi$
$198$	−2.67510	−	3.01320i	−0.190111	−	0.214139i
$199$	−16.2114			−1.14919			−0.574596	−	0.818437i	$-0.694841\pi$
$199$	−16.2114			−1.14919			−0.574596	+	0.818437i	$0.694841\pi$
$200$	−3.59080	−	11.0513i	−0.253908	−	0.781447i
$201$	−1.65573	−	1.20296i	−0.116786	−	0.0848502i
$202$	11.8666	−	8.62159i	0.834931	−	0.606613i
$203$	0.0839733	−	0.258443i	0.00589377	−	0.0181392i
$204$	0.298171	−	0.917674i	0.0208761	−	0.0642501i
$205$	−2.93415	+	2.13178i	−0.204930	+	0.148890i
$206$	−9.57454	−	6.95631i	−0.667090	−	0.484669i
$207$	0.800268	+	2.46297i	0.0556225	+	0.171188i
$208$	2.67730			0.185637
$209$	0.728599	−	1.24179i	0.0503983	−	0.0858965i
$210$	−0.391822			−0.0270383
$211$	−2.12679	−	6.54559i	−0.146414	−	0.450617i	0.850776	−	0.525529i	$-0.176133\pi$
$211$	−2.12679	−	6.54559i	−0.146414	−	0.450617i	−0.997190	+	0.0749117i	$0.976133\pi$
$212$	0.0640016	+	0.0464998i	0.00439564	+	0.00319362i
$213$	−10.7801	+	7.83218i	−0.738638	+	0.536652i
$214$	−3.75451	+	11.5552i	−0.256653	+	0.789897i
$215$	0.283140	−	0.871416i	0.0193100	−	0.0594301i
$216$	2.48080	−	1.80240i	0.168797	−	0.122638i
$217$	0.381251	+	0.276995i	0.0258810	+	0.0188036i
$218$	−5.69485	−	17.5270i	−0.385704	−	1.18707i
$219$	2.08649			0.140992
$220$	−1.75238	+	0.765540i	−0.118145	+	0.0516127i
$221$	−1.84127			−0.123857
$222$	−1.45468	−	4.47704i	−0.0976315	−	0.300479i
$223$	−3.78853	−	2.75253i	−0.253699	−	0.184323i	0.453666	−	0.891172i	$-0.350116\pi$
$223$	−3.78853	−	2.75253i	−0.253699	−	0.184323i	−0.707364	+	0.706849i	$0.750116\pi$
$224$	−0.683040	+	0.496257i	−0.0456375	+	0.0331576i
$225$	−1.17100	+	3.60397i	−0.0780667	+	0.240265i
$226$	4.06866	−	12.5220i	0.270643	−	0.832954i
$227$	−9.77762	+	7.10386i	−0.648963	+	0.471499i	−0.862918	−	0.505344i	$-0.831366\pi$
$227$	−9.77762	+	7.10386i	−0.648963	+	0.471499i	0.213955	+	0.976844i	$0.431366\pi$
$228$	0.184042	+	0.133714i	0.0121885	+	0.00885544i
$229$	−4.39525	−	13.5272i	−0.290446	−	0.893902i	−0.984713	−	0.174184i	$-0.944271\pi$
$229$	−4.39525	−	13.5272i	−0.290446	−	0.893902i	0.694267	−	0.719718i	$-0.255729\pi$
$230$	−3.46165			−0.228255
$231$	−0.0948441	−	0.967562i	−0.00624028	−	0.0636609i
$232$	−2.84272			−0.186634
$233$	−4.29512	−	13.2190i	−0.281383	−	0.866007i	−0.987460	−	0.157872i	$-0.949537\pi$
$233$	−4.29512	−	13.2190i	−0.281383	−	0.866007i	0.706077	−	0.708135i	$-0.250463\pi$
$234$	−0.982867	−	0.714095i	−0.0642520	−	0.0466818i
$235$	−1.53369	+	1.11429i	−0.100047	+	0.0726885i
$236$	0.619598	−	1.90693i	0.0403324	−	0.124130i
$237$	−1.63172	+	5.02190i	−0.105991	+	0.326208i
$238$	−0.530481	+	0.385417i	−0.0343860	+	0.0249829i
$239$	2.01551	+	1.46435i	0.130373	+	0.0947212i	0.651060	−	0.759026i	$-0.274324\pi$
$239$	2.01551	+	1.46435i	0.130373	+	0.0947212i	−0.520688	+	0.853747i	$0.674324\pi$
$240$	0.910274	+	2.80154i	0.0587580	+	0.180838i
$241$	6.14860			0.396066			0.198033	−	0.980195i	$-0.436545\pi$
$241$	6.14860			0.396066			0.198033	+	0.980195i	$0.436545\pi$
$242$	6.51903	+	11.6659i	0.419059	+	0.749912i
$243$	−1.00000			−0.0641500
$244$	1.14865	+	3.53518i	0.0735348	+	0.226317i
$245$	6.15439	+	4.47143i	0.393190	+	0.285669i
$246$	−3.23986	+	2.35389i	−0.206566	+	0.150079i
$247$	0.134145	−	0.412857i	0.00853546	−	0.0262694i
$248$	1.52339	−	4.68850i	0.0967352	−	0.297720i
$249$	0.657468	−	0.477678i	0.0416653	−	0.0302716i
$250$	−9.50494	−	6.90574i	−0.601145	−	0.436757i
$251$	−4.58627	−	14.1151i	−0.289483	−	0.890936i	−0.985019	−	0.172445i	$-0.944833\pi$
$251$	−4.58627	−	14.1151i	−0.289483	−	0.890936i	0.695537	−	0.718491i	$-0.255167\pi$
$252$	0.153612			0.00967664
$253$	−0.837924	−	8.54816i	−0.0526798	−	0.537418i
$254$	7.62869			0.478667
$255$	−0.626026	−	1.92671i	−0.0392033	−	0.120655i
$256$	9.41543	+	6.84071i	0.588464	+	0.427544i
$257$	18.3863	−	13.3584i	1.14690	−	0.833274i	0.158838	−	0.987305i	$-0.449225\pi$
$257$	18.3863	−	13.3584i	1.14690	−	0.833274i	0.988066	+	0.154030i	$0.0492254\pi$
$258$	0.312640	−	0.962208i	0.0194641	−	0.0599045i
$259$	0.350985	−	1.08022i	0.0218091	−	0.0671216i
$260$	−0.466463	+	0.338905i	−0.0289288	+	0.0210180i
$261$	0.749994	+	0.544902i	0.0464235	+	0.0337286i
$262$	−2.01453	−	6.20010i	−0.124458	−	0.383043i
$263$	−13.9364			−0.859358			−0.429679	−	0.902982i	$-0.641373\pi$
$263$	−13.9364			−0.859358			−0.429679	+	0.902982i	$0.641373\pi$
$264$	−9.31971	+	4.07138i	−0.573589	+	0.250576i
$265$	0.166096			0.0102032
$266$	−0.0477718	−	0.147026i	−0.00292907	−	0.00901476i
$267$	8.81740	+	6.40622i	0.539616	+	0.392054i
$268$	−0.867672	+	0.630401i	−0.0530015	+	0.0385078i
$269$	−8.22907	+	25.3265i	−0.501736	+	1.54418i	0.304455	+	0.952527i	$0.401526\pi$
$269$	−8.22907	+	25.3265i	−0.501736	+	1.54418i	−0.806190	+	0.591656i	$0.798474\pi$
$270$	0.413060	−	1.27127i	0.0251380	−	0.0773669i
$271$	19.9622	−	14.5034i	1.21262	−	0.881020i	0.217154	−	0.976137i	$-0.430323\pi$
$271$	19.9622	−	14.5034i	1.21262	−	0.881020i	0.995466	+	0.0951171i	$0.0303226\pi$
$272$	3.98814	+	2.89755i	0.241817	+	0.175690i
$273$	−0.0905818	−	0.278782i	−0.00548226	−	0.0168727i
$274$	19.0559			1.15121
$275$	6.36020	−	10.8400i	0.383534	−	0.653678i
$276$	1.35712			0.0816891
$277$	5.54792	+	17.0747i	0.333342	+	1.02592i	0.967533	+	0.252745i	$0.0813333\pi$
$277$	5.54792	+	17.0747i	0.333342	+	1.02592i	−0.634191	+	0.773176i	$0.718667\pi$
$278$	−1.75123	−	1.27235i	−0.105032	−	0.0763103i
$279$	−1.30063	+	0.944959i	−0.0778664	+	0.0565732i
$280$	−0.305610	+	0.940572i	−0.0182637	+	0.0562099i
$281$	−3.30860	+	10.1828i	−0.197374	+	0.607456i	0.802566	+	0.596563i	$0.203467\pi$
$281$	−3.30860	+	10.1828i	−0.197374	+	0.607456i	−0.999941	+	0.0108928i	$0.996533\pi$
$282$	−1.69349	+	1.23039i	−0.100846	+	0.0732688i
$283$	−20.4471	−	14.8557i	−1.21545	−	0.883077i	−0.219737	−	0.975559i	$-0.570520\pi$
$283$	−20.4471	−	14.8557i	−1.21545	−	0.883077i	−0.995714	+	0.0924821i	$0.970520\pi$
$284$	2.15780	+	6.64104i	0.128042	+	0.394073i
$285$	0.477624			0.0282920
$286$	2.67510	+	3.01320i	0.158182	+	0.178174i
$287$	−0.966251			−0.0570360
$288$	−0.890045	−	2.73928i	−0.0524464	−	0.161413i
$289$	11.0105	+	7.99961i	0.647677	+	0.470565i
$290$	−1.00251	+	0.728365i	−0.0588694	+	0.0427711i
$291$	−2.30186	+	7.08439i	−0.134937	+	0.415294i
$292$	0.337881	−	1.03989i	0.0197730	−	0.0608550i
$293$	15.9134	−	11.5617i	0.929670	−	0.675445i	−0.0162422	−	0.999868i	$-0.505170\pi$
$293$	15.9134	−	11.5617i	0.929670	−	0.675445i	0.945912	+	0.324423i	$0.105170\pi$
$294$	6.79562	+	4.93730i	0.396328	+	0.287949i
$295$	−1.30088	−	4.00370i	−0.0757402	−	0.233104i
$296$	−11.8818			−0.690613
$297$	3.23924	+	0.712283i	0.187960	+	0.0413309i
$298$	23.0292			1.33405
$299$	−0.800268	−	2.46297i	−0.0462807	−	0.142437i
$300$	1.60657	+	1.16724i	0.0927551	+	0.0673905i
$301$	0.197489	−	0.143484i	0.0113831	−	0.00827028i
$302$	−6.38245	+	19.6432i	−0.367269	+	1.13034i
$303$	−3.73090	+	11.4825i	−0.214335	+	0.659655i
$304$	−0.940258	+	0.683138i	−0.0539275	+	0.0391806i
$305$	6.31380	+	4.58724i	0.361527	+	0.262665i
$306$	−0.691251	−	2.12745i	−0.0395162	−	0.121618i
$307$	−5.00052			−0.285395			−0.142697	−	0.989766i	$-0.545578\pi$
$307$	−5.00052			−0.285395			−0.142697	+	0.989766i	$0.545578\pi$
$308$	−0.497585	−	0.109415i	−0.0283525	−	0.00623451i
$309$	9.74144			0.554171
$310$	−0.664060	−	2.04377i	−0.0377161	−	0.116078i
$311$	10.2338	+	7.43529i	0.580306	+	0.421617i	0.838834	−	0.544387i	$-0.183238\pi$
$311$	10.2338	+	7.43529i	0.580306	+	0.421617i	−0.258529	+	0.966004i	$0.583238\pi$
$312$	−2.48080	+	1.80240i	−0.140447	+	0.102041i
$313$	7.51653	−	23.1335i	0.424859	−	1.30758i	−0.478270	−	0.878213i	$-0.658736\pi$
$313$	7.51653	−	23.1335i	0.424859	−	1.30758i	0.903129	−	0.429369i	$-0.141264\pi$
$314$	1.09186	−	3.36041i	0.0616174	−	0.189639i
$315$	0.260922	−	0.189571i	0.0147013	−	0.0106811i
$316$	2.23865	+	1.62647i	0.125934	+	0.0914962i
$317$	−7.15074	−	22.0077i	−0.401625	−	1.23608i	−0.923680	−	0.383164i	$-0.874834\pi$
$317$	−7.15074	−	22.0077i	−0.401625	−	1.23608i	0.522055	−	0.852912i	$-0.325166\pi$
$318$	0.183402			0.0102847
$319$	−2.04128	−	2.29928i	−0.114290	−	0.128735i
$320$	9.74141			0.544562
$321$	−3.09041	−	9.51131i	−0.172490	−	0.530869i
$322$	−0.746116	−	0.542085i	−0.0415794	−	0.0302092i
$323$	0.646647	−	0.469816i	0.0359804	−	0.0261413i
$324$	−0.161938	+	0.498393i	−0.00899654	+	0.0276885i
$325$	1.17100	−	3.60397i	0.0649554	−	0.199912i
$326$	−12.8626	+	9.34524i	−0.712395	+	0.517585i
$327$	12.2721	+	8.91624i	0.678651	+	0.493069i
$328$	3.12354	+	9.61327i	0.172469	+	0.530804i
$329$	−0.505064			−0.0278451
$330$	−2.24350	+	3.82372i	−0.123501	+	0.210489i
$331$	−15.4745			−0.850553			−0.425277	−	0.905063i	$-0.639823\pi$
$331$	−15.4745			−0.850553			−0.425277	+	0.905063i	$0.639823\pi$
$332$	−0.131603	−	0.405032i	−0.00722264	−	0.0222290i
$333$	3.13476	+	2.27754i	0.171784	+	0.124808i
$334$	0.302140	−	0.219518i	0.0165324	−	0.0120115i
$335$	−0.695838	+	2.14157i	−0.0380177	+	0.117006i
$336$	−0.242514	+	0.746383i	−0.0132302	+	0.0407185i
$337$	23.5062	−	17.0782i	1.28046	−	0.930311i	0.280896	−	0.959738i	$-0.409368\pi$
$337$	23.5062	−	17.0782i	1.28046	−	0.930311i	0.999567	+	0.0294273i	$0.00936836\pi$
$338$	0.982867	+	0.714095i	0.0534609	+	0.0388416i
$339$	3.34899	+	10.3071i	0.181892	+	0.559807i
$340$	−1.06164			−0.0575753
$341$	4.88611	−	2.13453i	0.264598	−	0.115591i
$342$	0.527388			0.0285179
$343$	1.26036	+	3.87900i	0.0680532	+	0.209446i
$344$	−2.06594	−	1.50099i	−0.111388	−	0.0809280i
$345$	2.30518	−	1.67481i	0.124106	−	0.0901686i
$346$	−6.46771	+	19.9056i	−0.347706	+	1.07013i
$347$	−10.4286	+	32.0959i	−0.559837	+	1.72300i	0.122979	+	0.992409i	$0.460755\pi$
$347$	−10.4286	+	32.0959i	−0.559837	+	1.72300i	−0.682815	+	0.730591i	$0.739245\pi$
$348$	0.393028	−	0.285552i	0.0210685	−	0.0153072i
$349$	17.1134	+	12.4336i	0.916062	+	0.665558i	0.942541	−	0.334092i	$-0.108429\pi$
$349$	17.1134	+	12.4336i	0.916062	+	0.665558i	−0.0264788	+	0.999649i	$0.508429\pi$
$350$	−0.417016	−	1.28344i	−0.0222905	−	0.0686030i
$351$	1.00000			0.0533761
$352$	0.931925	+	9.50713i	0.0496718	+	0.506732i
$353$	−13.7037			−0.729373			−0.364687	−	0.931130i	$-0.618824\pi$
$353$	−13.7037			−0.729373			−0.364687	+	0.931130i	$0.618824\pi$
$354$	−1.43642	−	4.42084i	−0.0763448	−	0.234965i
$355$	11.8608	+	8.61739i	0.629507	+	0.457364i
$356$	4.62069	−	3.35713i	0.244896	−	0.177927i
$357$	0.166785	−	0.513312i	0.00882721	−	0.0271674i
$358$	2.00557	−	6.17252i	0.105998	−	0.326228i
$359$	−5.66286	+	4.11431i	−0.298874	+	0.217145i	−0.727108	−	0.686523i	$-0.759136\pi$
$359$	−5.66286	+	4.11431i	−0.298874	+	0.217145i	0.428234	+	0.903668i	$0.359136\pi$
$360$	−2.72951	−	1.98311i	−0.143858	−	0.104519i
$361$	−5.81309	−	17.8909i	−0.305952	−	0.941624i
$362$	−17.8017			−0.935637
$363$	−9.98531	−	4.61451i	−0.524093	−	0.242199i
$364$	−0.153612			−0.00805145
$365$	−0.709400	−	2.18331i	−0.0371317	−	0.114280i
$366$	6.97163	+	5.06519i	0.364413	+	0.264762i
$367$	−20.3047	+	14.7522i	−1.05990	+	0.770061i	−0.974069	−	0.226249i	$-0.927354\pi$
$367$	−20.3047	+	14.7522i	−1.05990	+	0.770061i	−0.0858282	+	0.996310i	$0.527354\pi$
$368$	−2.14255	+	6.59410i	−0.111688	+	0.343741i
$369$	1.01862	−	3.13500i	0.0530274	−	0.163202i
$370$	−4.19021	+	3.04436i	−0.217838	+	0.158269i
$371$	0.0358000	+	0.0260102i	0.00185865	+	0.00135038i
$372$	0.260341	+	0.801247i	0.0134981	+	0.0415427i
$373$	27.2972			1.41339			0.706697	−	0.707516i	$-0.250184\pi$
$373$	27.2972			1.41339			0.706697	+	0.707516i	$0.250184\pi$
$374$	0.723777	+	7.38369i	0.0374256	+	0.381801i
$375$	9.67063			0.499389
$376$	1.63269	+	5.02490i	0.0841995	+	0.259140i
$377$	−0.749994	−	0.544902i	−0.0386267	−	0.0280639i
$378$	0.288107	−	0.209322i	0.0148186	−	0.0107664i
$379$	7.31992	−	22.5284i	0.375999	−	1.15721i	−0.566803	−	0.823853i	$-0.691820\pi$
$379$	7.31992	−	22.5284i	0.375999	−	1.15721i	0.942802	−	0.333353i	$-0.108180\pi$
$380$	0.0773455	−	0.238045i	0.00396774	−	0.0122114i
$381$	−5.08008	+	3.69090i	−0.260260	+	0.189090i
$382$	17.2646	+	12.5435i	0.883334	+	0.641779i
$383$	−1.87898	−	5.78290i	−0.0960113	−	0.295492i	0.891505	−	0.453012i	$-0.149650\pi$
$383$	−1.87898	−	5.78290i	−0.0960113	−	0.295492i	−0.987516	+	0.157519i	$0.949650\pi$
$384$	4.99587			0.254945
$385$	−0.980214	+	0.428214i	−0.0499564	+	0.0218238i
$386$	−20.4095			−1.03882
$387$	0.257340	+	0.792013i	0.0130814	+	0.0402603i
$388$	3.15805	+	2.29446i	0.160326	+	0.116484i
$389$	0.804947	−	0.584828i	0.0408124	−	0.0296520i	−0.567192	−	0.823586i	$-0.691970\pi$
$389$	0.804947	−	0.584828i	0.0408124	−	0.0296520i	0.608004	+	0.793934i	$0.291970\pi$
$390$	−0.413060	+	1.27127i	−0.0209161	+	0.0643731i
$391$	1.47351	−	4.53498i	0.0745184	−	0.229344i
$392$	17.1524	−	12.4620i	0.866328	−	0.629424i
$393$	4.34123	+	3.15409i	0.218986	+	0.159103i
$394$	3.71586	+	11.4362i	0.187202	+	0.576149i
$395$	5.80973			0.292319
$396$	0.879552	−	1.49907i	0.0441992	−	0.0753310i
$397$	−14.8992			−0.747768			−0.373884	−	0.927476i	$-0.621974\pi$
$397$	−14.8992			−0.747768			−0.373884	+	0.927476i	$0.621974\pi$
$398$	6.08609	+	18.7311i	0.305068	+	0.938904i
$399$	0.102946	+	0.0747947i	0.00515375	+	0.00374442i
$400$	−8.20784	+	5.96335i	−0.410392	+	0.298167i
$401$	−3.61036	+	11.1115i	−0.180293	+	0.554884i	−0.999836	−	0.0181341i	$-0.994227\pi$
$401$	−3.61036	+	11.1115i	−0.180293	+	0.554884i	0.819543	+	0.573018i	$0.194227\pi$
$402$	−0.768336	+	2.36470i	−0.0383211	+	0.117940i
$403$	1.30063	−	0.944959i	0.0647888	−	0.0470718i
$404$	5.11865	+	3.71891i	0.254662	+	0.185023i
$405$	0.339998	+	1.04640i	0.0168946	+	0.0519963i
$406$	−0.330138			−0.0163845
$407$	−8.53199	−	9.61033i	−0.422915	−	0.476366i
$408$	−5.64612			−0.279525
$409$	−1.73548	−	5.34125i	−0.0858138	−	0.264108i	0.898937	−	0.438078i	$-0.144340\pi$
$409$	−1.73548	−	5.34125i	−0.0858138	−	0.264108i	−0.984751	+	0.173970i	$0.944340\pi$
$410$	3.56467	+	2.58988i	0.176046	+	0.127905i
$411$	−12.6897	+	9.21958i	−0.625935	+	0.454768i
$412$	1.57751	−	4.85507i	0.0777182	−	0.239192i
$413$	0.346579	−	1.06666i	0.0170541	−	0.0524870i
$414$	2.54535	−	1.84931i	0.125097	−	0.0908884i
$415$	−0.723383	−	0.525568i	−0.0355095	−	0.0257991i
$416$	0.890045	+	2.73928i	0.0436380	+	0.134304i
$417$	1.78176			0.0872532
$418$	−1.70833	−	0.375649i	−0.0835573	−	0.0183736i
$419$	13.4323			0.656210			0.328105	−	0.944641i	$-0.393590\pi$
$419$	13.4323			0.656210			0.328105	+	0.944641i	$0.393590\pi$
$420$	−0.0522277	−	0.160740i	−0.00254845	−	0.00784332i
$421$	16.7457	+	12.1664i	0.816133	+	0.592955i	0.915602	−	0.402085i	$-0.131714\pi$
$421$	16.7457	+	12.1664i	0.816133	+	0.592955i	−0.0994691	+	0.995041i	$0.531714\pi$
$422$	−6.76453	+	4.91472i	−0.329292	+	0.239245i
$423$	0.532439	−	1.63868i	0.0258881	−	0.0796753i
$424$	0.143048	−	0.440258i	0.00694704	−	0.0213808i
$425$	5.64480	−	4.10119i	0.273813	−	0.198937i
$426$	13.0966	+	9.51524i	0.634532	+	0.461015i
$427$	0.642511	+	1.97745i	0.0310933	+	0.0956954i
$428$	−5.24083			−0.253325
$429$	−3.23924	−	0.712283i	−0.156392	−	0.0343894i
$430$	−1.11316			−0.0536812
$431$	8.85521	+	27.2535i	0.426541	+	1.31276i	0.901511	+	0.432755i	$0.142459\pi$
$431$	8.85521	+	27.2535i	0.426541	+	1.31276i	−0.474971	+	0.880002i	$0.657541\pi$
$432$	−2.16598	−	1.57368i	−0.104211	−	0.0757135i
$433$	0.333459	−	0.242272i	0.0160250	−	0.0116428i	−0.579744	−	0.814799i	$-0.696847\pi$
$433$	0.333459	−	0.242272i	0.0160250	−	0.0116428i	0.595769	+	0.803156i	$0.296847\pi$
$434$	0.176918	−	0.544498i	0.00849235	−	0.0261368i
$435$	0.315193	−	0.970063i	0.0151123	−	0.0465110i
$436$	6.43112	−	4.67248i	0.307995	−	0.223771i
$437$	0.909502	+	0.660792i	0.0435074	+	0.0316100i
$438$	−0.783312	−	2.41079i	−0.0374281	−	0.115192i
$439$	−23.8114			−1.13645			−0.568227	−	0.822872i	$-0.692371\pi$
$439$	−23.8114			−1.13645			−0.568227	+	0.822872i	$0.692371\pi$
$440$	7.42900	+	8.36793i	0.354163	+	0.398925i
$441$	−6.91408			−0.329242
$442$	0.691251	+	2.12745i	0.0328795	+	0.101193i
$443$	−25.7528	−	18.7105i	−1.22355	−	0.888962i	−0.227162	−	0.973857i	$-0.572945\pi$
$443$	−25.7528	−	18.7105i	−1.22355	−	0.888962i	−0.996390	+	0.0848946i	$0.972945\pi$
$444$	1.64275	−	1.19353i	0.0779613	−	0.0566422i
$445$	3.70560	−	11.4047i	0.175662	−	0.540633i
$446$	−1.75806	+	5.41074i	−0.0832463	+	0.256206i
$447$	−15.3356	+	11.1420i	−0.725348	+	0.526996i
$448$	2.09964	+	1.52548i	0.0991987	+	0.0720721i
$449$	−8.74049	−	26.9005i	−0.412489	−	1.26951i	−0.914478	−	0.404637i	$-0.867398\pi$
$449$	−8.74049	−	26.9005i	−0.412489	−	1.26951i	0.501988	−	0.864874i	$-0.332602\pi$
$450$	4.60375			0.217023
$451$	−5.53257	+	9.42945i	−0.260518	+	0.444016i
$452$	5.67934			0.267134
$453$	−5.25352	−	16.1687i	−0.246832	−	0.759670i
$454$	11.8787	+	8.63040i	0.557497	+	0.405045i
$455$	−0.260922	+	0.189571i	−0.0122322	+	0.00888721i
$456$	0.411348	−	1.26600i	0.0192631	−	0.0592858i
$457$	−9.88606	+	30.4262i	−0.462450	+	1.42328i	0.399711	+	0.916641i	$0.369111\pi$
$457$	−9.88606	+	30.4262i	−0.462450	+	1.42328i	−0.862161	+	0.506635i	$0.830889\pi$
$458$	−13.9796	+	10.1568i	−0.653226	+	0.474596i
$459$	1.48962	+	1.08227i	0.0695293	+	0.0505160i
$460$	−0.461418	−	1.42010i	−0.0215137	−	0.0662125i
$461$	−28.2620			−1.31629			−0.658147	−	0.752890i	$-0.728659\pi$
$461$	−28.2620			−1.31629			−0.658147	+	0.752890i	$0.728659\pi$
$462$	−1.08234	+	0.472829i	−0.0503551	+	0.0219980i
$463$	−27.9220			−1.29764			−0.648822	−	0.760940i	$-0.724738\pi$
$463$	−27.9220			−1.29764			−0.648822	+	0.760940i	$0.724738\pi$
$464$	0.766971	+	2.36049i	0.0356057	+	0.109583i
$465$	1.43102	+	1.03970i	0.0663619	+	0.0482148i
$466$	−13.6612	+	9.92542i	−0.632841	+	0.459786i
$467$	6.40931	−	19.7258i	0.296587	−	0.912802i	−0.686096	−	0.727511i	$-0.740677\pi$
$467$	6.40931	−	19.7258i	0.296587	−	0.912802i	0.982684	−	0.185291i	$-0.0593229\pi$
$468$	0.161938	−	0.498393i	0.00748558	−	0.0230382i
$469$	−0.485343	+	0.352622i	−0.0224110	+	0.0162826i
$470$	1.86327	+	1.35375i	0.0859463	+	0.0624436i
$471$	0.898734	+	2.76602i	0.0414115	+	0.127451i
$472$	−11.7326			−0.540038
$473$	−0.269449	−	2.74882i	−0.0123893	−	0.126391i
$474$	6.41504			0.294652
$475$	0.508335	+	1.56450i	0.0233240	+	0.0717840i
$476$	−0.228823	−	0.166249i	−0.0104881	−	0.00762002i
$477$	−0.122131	+	0.0887331i	−0.00559198	+	0.00406281i
$478$	0.935291	−	2.87853i	0.0427792	−	0.131661i
$479$	−10.8649	+	33.4388i	−0.496431	+	1.52786i	0.318283	+	0.947996i	$0.396894\pi$
$479$	−10.8649	+	33.4388i	−0.496431	+	1.52786i	−0.814715	+	0.579862i	$0.803106\pi$
$480$	−2.56378	+	1.86269i	−0.117020	+	0.0850200i
$481$	−3.13476	−	2.27754i	−0.142933	−	0.103847i
$482$	−2.30832	−	7.10427i	−0.105141	−	0.323591i
$483$	0.759122			0.0345413
$484$	−3.91684	+	4.22935i	−0.178038	+	0.192243i
$485$	8.19577			0.372151
$486$	0.375422	+	1.15543i	0.0170295	+	0.0524113i
$487$	−28.6420	−	20.8096i	−1.29789	−	0.942975i	−0.297961	−	0.954578i	$-0.596307\pi$
$487$	−28.6420	−	20.8096i	−1.29789	−	0.942975i	−0.999933	+	0.0116029i	$0.996307\pi$
$488$	17.5967	−	12.7847i	0.796565	−	0.578738i
$489$	4.04406	−	12.4463i	0.182878	−	0.562842i
$490$	2.85593	−	8.78964i	0.129018	−	0.397075i
$491$	34.2971	−	24.9183i	1.54781	−	1.12455i	0.602612	−	0.798034i	$-0.294127\pi$
$491$	34.2971	−	24.9183i	1.54781	−	1.12455i	0.945193	−	0.326512i	$-0.105873\pi$
$492$	−1.39751	−	1.01535i	−0.0630046	−	0.0457755i
$493$	−0.527471	−	1.62339i	−0.0237561	−	0.0731138i
$494$	−0.527388			−0.0237283
$495$	−0.355996	−	3.63173i	−0.0160008	−	0.163234i
$496$	−4.30419			−0.193264
$497$	1.20699	+	3.71474i	0.0541411	+	0.166629i
$498$	−0.798751	−	0.580327i	−0.0357929	−	0.0260051i
$499$	−21.7947	+	15.8348i	−0.975664	+	0.708861i	−0.956735	−	0.290960i	$-0.906025\pi$
$499$	−21.7947	+	15.8348i	−0.975664	+	0.708861i	−0.0189283	+	0.999821i	$0.506025\pi$
$500$	1.56604	−	4.81978i	0.0700354	−	0.215547i
$501$	−0.0949939	+	0.292361i	−0.00424402	+	0.0130617i
$502$	−14.5872	+	10.5982i	−0.651058	+	0.473021i
$503$	−5.82044	−	4.22880i	−0.259520	−	0.188553i	0.450415	−	0.892819i	$-0.351276\pi$
$503$	−5.82044	−	4.22880i	−0.259520	−	0.188553i	−0.709936	+	0.704267i	$0.751276\pi$
$504$	−0.277763	−	0.854867i	−0.0123726	−	0.0380788i
$505$	13.2839			0.591125
$506$	−9.56222	+	4.17733i	−0.425093	+	0.185705i
$507$	−1.00000			−0.0444116
$508$	1.01686	+	3.12957i	0.0451159	+	0.138852i
$509$	26.9684	+	19.5937i	1.19535	+	0.868476i	0.993820	−	0.111005i	$-0.0354071\pi$
$509$	26.9684	+	19.5937i	1.19535	+	0.868476i	0.201535	+	0.979481i	$0.435407\pi$
$510$	−1.99115	+	1.44666i	−0.0881697	+	0.0640591i
$511$	0.188998	−	0.581675i	0.00836077	−	0.0257318i
$512$	7.45682	−	22.9497i	0.329548	−	1.01424i
$513$	−0.351197	+	0.255159i	−0.0155057	+	0.0112656i
$514$	−22.3373	−	16.2290i	−0.985256	−	0.715830i
$515$	−3.31207	−	10.1935i	−0.145947	−	0.449179i
$516$	0.436407			0.0192117
$517$	−2.89190	+	4.92882i	−0.127186	+	0.216769i
$518$	−1.37989			−0.0606287
$519$	−5.32370	−	16.3847i	−0.233684	−	0.719207i
$520$	2.72951	+	1.98311i	0.119697	+	0.0869649i
$521$	1.83621	−	1.33409i	0.0804459	−	0.0584474i	−0.546835	−	0.837240i	$-0.684168\pi$
$521$	1.83621	−	1.33409i	0.0804459	−	0.0584474i	0.627281	+	0.778793i	$0.284168\pi$
$522$	0.348032	−	1.07113i	0.0152330	−	0.0468822i
$523$	0.742081	−	2.28389i	0.0324489	−	0.0998675i	−0.933520	−	0.358525i	$-0.883280\pi$
$523$	0.742081	−	2.28389i	0.0324489	−	0.0998675i	0.965969	+	0.258657i	$0.0832799\pi$
$524$	2.27499	−	1.65287i	0.0993832	−	0.0722061i
$525$	0.898651	+	0.652909i	0.0392204	+	0.0284953i
$526$	5.23205	+	16.1026i	0.228128	+	0.702106i
$527$	2.96013			0.128945
$528$	5.89521	+	6.64030i	0.256556	+	0.288982i
$529$	−16.2933			−0.708406
$530$	−0.0623562	−	0.191913i	−0.00270858	−	0.00833616i
$531$	3.09542	+	2.24895i	0.134330	+	0.0975962i
$532$	0.0539480	−	0.0391955i	0.00233894	−	0.00169934i
$533$	−1.01862	+	3.13500i	−0.0441215	+	0.135792i
$534$	4.09169	−	12.5929i	0.177065	−	0.544949i
$535$	−8.90195	+	6.46764i	−0.384865	+	0.279621i
$536$	5.07719	+	3.68879i	0.219301	+	0.159332i
$537$	1.65083	+	5.08072i	0.0712384	+	0.219249i
$538$	32.3523			1.39481
$539$	22.3963	+	4.92478i	0.964678	+	0.212125i
$540$	0.576580			0.0248120
$541$	9.18175	+	28.2585i	0.394754	+	1.21493i	0.929153	+	0.369696i	$0.120538\pi$
$541$	9.18175	+	28.2585i	0.394754	+	1.21493i	−0.534399	+	0.845233i	$0.679462\pi$
$542$	−24.2519	−	17.6201i	−1.04171	−	0.756847i
$543$	11.8545	−	8.61278i	0.508724	−	0.369610i
$544$	−1.63881	+	5.04374i	−0.0702634	+	0.216248i
$545$	5.15750	−	15.8731i	0.220923	−	0.679931i
$546$	−0.288107	+	0.209322i	−0.0123298	+	0.00895815i
$547$	22.5142	+	16.3575i	0.962637	+	0.699397i	0.953762	−	0.300564i	$-0.0971748\pi$
$547$	22.5142	+	16.3575i	0.962637	+	0.699397i	0.00887561	+	0.999961i	$0.497175\pi$
$548$	2.54004	+	7.81744i	0.108505	+	0.333944i
$549$	−7.09316			−0.302729
$550$	−14.9126	−	3.27917i	−0.635877	−	0.139824i
$551$	0.402433			0.0171442
$552$	−2.45397	−	7.55254i	−0.104448	−	0.321457i
$553$	1.25221	+	0.909787i	0.0532496	+	0.0386881i
$554$	17.6458	−	12.8204i	0.749700	−	0.544689i
$555$	1.31742	−	4.05459i	0.0559212	−	0.172108i
$556$	0.288535	−	0.888018i	0.0122366	−	0.0376604i
$557$	4.92110	−	3.57539i	0.208514	−	0.151494i	−0.478627	−	0.878018i	$-0.658865\pi$
$557$	4.92110	−	3.57539i	0.208514	−	0.151494i	0.687141	+	0.726524i	$0.258865\pi$
$558$	1.58012	+	1.14802i	0.0668917	+	0.0485996i
$559$	−0.257340	−	0.792013i	−0.0108843	−	0.0334986i
$560$	0.863473			0.0364884
$561$	−4.05433	−	4.56675i	−0.171174	−	0.192808i
$562$	13.0076			0.548694
$563$	1.22526	+	3.77095i	0.0516384	+	0.158927i	0.973550	−	0.228473i	$-0.0733733\pi$
$563$	1.22526	+	3.77095i	0.0516384	+	0.158927i	−0.921912	+	0.387400i	$0.873373\pi$
$564$	−0.730485	−	0.530728i	−0.0307590	−	0.0223477i
$565$	9.64679	−	7.00880i	0.405843	−	0.294863i
$566$	−9.48839	+	29.2023i	−0.398827	+	1.22746i
$567$	−0.0905818	+	0.278782i	−0.00380408	+	0.0117078i
$568$	33.0564	−	24.0169i	1.38701	−	1.00772i
$569$	7.73091	+	5.61684i	0.324097	+	0.235470i	0.737922	−	0.674887i	$-0.235807\pi$
$569$	7.73091	+	5.61684i	0.324097	+	0.235470i	−0.413825	+	0.910356i	$0.635807\pi$
$570$	−0.179311	−	0.551861i	−0.00751049	−	0.0231149i
$571$	5.48522			0.229549			0.114775	−	0.993392i	$-0.463385\pi$
$571$	5.48522			0.229549			0.114775	+	0.993392i	$0.463385\pi$
$572$	−0.879552	+	1.49907i	−0.0367759	+	0.0626792i
$573$	−17.5656			−0.733811
$574$	0.362752	+	1.11643i	0.0151410	+	0.0465991i
$575$	7.93936	+	5.76828i	0.331094	+	0.240554i
$576$	−7.16286	+	5.20412i	−0.298452	+	0.216838i
$577$	−0.940301	+	2.89395i	−0.0391453	+	0.120477i	−0.968720	−	0.248158i	$-0.920175\pi$
$577$	−0.940301	+	2.89395i	−0.0391453	+	0.120477i	0.929574	+	0.368635i	$0.120175\pi$
$578$	5.10939	−	15.7251i	0.212523	−	0.654078i
$579$	13.5910	−	9.87447i	0.564824	−	0.410369i
$580$	−0.432431	−	0.314180i	−0.0179557	−	0.0130456i
$581$	−0.0736136	−	0.226559i	−0.00305401	−	0.00939927i
$582$	9.04968			0.375121
$583$	0.458813	−	0.200436i	0.0190021	−	0.00830121i
$584$	−6.39807			−0.264754
$585$	−0.339998	−	1.04640i	−0.0140572	−	0.0432635i
$586$	−19.3330	−	14.0463i	−0.798639	−	0.580246i
$587$	5.24121	−	3.80796i	0.216328	−	0.157171i	−0.474344	−	0.880339i	$-0.657315\pi$
$587$	5.24121	−	3.80796i	0.216328	−	0.157171i	0.690672	+	0.723168i	$0.257315\pi$
$588$	−1.11965	+	3.44593i	−0.0461736	+	0.142108i
$589$	−0.215660	+	0.663734i	−0.00888612	+	0.0273487i
$590$	−4.13761	+	3.00615i	−0.170343	+	0.123761i
$591$	−8.00751	−	5.81779i	−0.329385	−	0.239312i
$592$	3.20572	+	9.86620i	0.131754	+	0.405498i
$593$	20.5458			0.843713			0.421857	−	0.906663i	$-0.361379\pi$
$593$	20.5458			0.843713			0.421857	+	0.906663i	$0.361379\pi$
$594$	−0.393087	−	4.01012i	−0.0161285	−	0.164537i
$595$	−0.593839			−0.0243450
$596$	3.06966	+	9.44745i	0.125738	+	0.386983i
$597$	−13.1153	−	9.52879i	−0.536772	−	0.389988i
$598$	−2.54535	+	1.84931i	−0.104087	+	0.0756237i
$599$	1.77572	−	5.46510i	0.0725539	−	0.223298i	−0.908203	−	0.418529i	$-0.862546\pi$
$599$	1.77572	−	5.46510i	0.0725539	−	0.223298i	0.980757	+	0.195231i	$0.0625457\pi$
$600$	3.59080	−	11.0513i	0.146594	−	0.451169i
$601$	6.44160	−	4.68010i	0.262758	−	0.190905i	−0.448604	−	0.893731i	$-0.648079\pi$
$601$	6.44160	−	4.68010i	0.262758	−	0.190905i	0.711362	+	0.702826i	$0.248079\pi$
$602$	−0.239927	−	0.174317i	−0.00977870	−	0.00710464i
$603$	−0.632433	−	1.94643i	−0.0257547	−	0.0792647i
$604$	−8.90910			−0.362506
$605$	−1.43366	+	12.0176i	−0.0582867	+	0.488585i
$606$	14.6679			0.595844
$607$	−2.95743	−	9.10203i	−0.120038	−	0.369440i	0.872926	−	0.487852i	$-0.162220\pi$
$607$	−2.95743	−	9.10203i	−0.120038	−	0.369440i	−0.992965	+	0.118412i	$0.962220\pi$
$608$	−1.01153	−	0.734922i	−0.0410231	−	0.0298050i
$609$	0.219845	−	0.159727i	0.00890857	−	0.00647245i
$610$	2.92990	−	9.01730i	0.118628	−	0.365100i
$611$	−0.532439	+	1.63868i	−0.0215402	+	0.0662939i
$612$	0.780621	−	0.567154i	0.0315547	−	0.0229258i
$613$	24.1419	+	17.5401i	0.975083	+	0.708439i	0.956604	−	0.291390i	$-0.0941178\pi$
$613$	24.1419	+	17.5401i	0.975083	+	0.708439i	0.0184785	+	0.999829i	$0.494118\pi$
$614$	1.87730	+	5.77774i	0.0757618	+	0.233171i
$615$	−3.62681			−0.146247
$616$	0.290833	+	2.96696i	0.0117180	+	0.119542i
$617$	−11.4293			−0.460128			−0.230064	−	0.973176i	$-0.573893\pi$
$617$	−11.4293			−0.460128			−0.230064	+	0.973176i	$0.573893\pi$
$618$	−3.65715	−	11.2555i	−0.147112	−	0.452764i
$619$	−38.1411	−	27.7112i	−1.53302	−	1.11381i	−0.954529	−	0.298119i	$-0.903641\pi$
$619$	−38.1411	−	27.7112i	−1.53302	−	1.11381i	−0.578493	−	0.815687i	$-0.696359\pi$
$620$	0.749914	−	0.544844i	0.0301173	−	0.0218815i
$621$	−0.800268	+	2.46297i	−0.0321136	+	0.0988356i
$622$	4.74896	−	14.6158i	0.190416	−	0.586040i
$623$	2.58464	−	1.87785i	0.103551	−	0.0752344i
$624$	2.16598	+	1.57368i	0.0867085	+	0.0629974i
$625$	2.56701	+	7.90046i	0.102681	+	0.316018i
$626$	−29.5510			−1.18109
$627$	1.31936	−	0.576370i	0.0526900	−	0.0230180i
$628$	1.52410			0.0608184
$629$	−2.20468	−	6.78531i	−0.0879064	−	0.270548i
$630$	−0.316991	−	0.230307i	−0.0126292	−	0.00917567i
$631$	−27.1748	+	19.7436i	−1.08181	+	0.785981i	−0.977998	−	0.208616i	$-0.933104\pi$
$631$	−27.1748	+	19.7436i	−1.08181	+	0.785981i	−0.103813	+	0.994597i	$0.533104\pi$
$632$	5.00355	−	15.3993i	0.199030	−	0.612553i
$633$	2.12679	−	6.54559i	0.0845324	−	0.260164i
$634$	−22.7438	+	16.5243i	−0.903272	+	0.656266i
$635$	5.58939	+	4.06093i	0.221808	+	0.161153i
$636$	0.0244464	+	0.0752383i	0.000969363	+	0.00298339i
$637$	6.91408			0.273946
$638$	−1.89031	+	3.22176i	−0.0748380	+	0.127551i
$639$	−13.3249			−0.527125
$640$	−1.69859	−	5.22771i	−0.0671425	−	0.206643i
$641$	27.2496	+	19.7980i	1.07630	+	0.781975i	0.977033	−	0.213086i	$-0.0683516\pi$
$641$	27.2496	+	19.7980i	1.07630	+	0.781975i	0.0992627	+	0.995061i	$0.468352\pi$
$642$	−9.82944	+	7.14150i	−0.387937	+	0.281853i
$643$	13.5591	−	41.7307i	0.534720	−	1.64570i	−0.209535	−	0.977801i	$-0.567195\pi$
$643$	13.5591	−	41.7307i	0.534720	−	1.64570i	0.744254	−	0.667896i	$-0.232805\pi$
$644$	0.122931	−	0.378341i	0.00484414	−	0.0149087i
$645$	0.741271	−	0.538565i	0.0291875	−	0.0212060i
$646$	−0.785605	−	0.570775i	−0.0309092	−	0.0224569i
$647$	−9.01054	−	27.7316i	−0.354241	−	1.09024i	−0.956448	−	0.291902i	$-0.905712\pi$
$647$	−9.01054	−	27.7316i	−0.354241	−	1.09024i	0.602208	−	0.798340i	$-0.294288\pi$
$648$	3.06643			0.120461
$649$	−8.42490	−	9.48970i	−0.330706	−	0.372503i
$650$	−4.60375			−0.180574
$651$	0.145625	+	0.448187i	0.00570749	+	0.0175658i
$652$	−5.54828	−	4.03106i	−0.217287	−	0.157868i
$653$	22.5436	−	16.3789i	0.882200	−	0.640956i	−0.0516324	−	0.998666i	$-0.516442\pi$
$653$	22.5436	−	16.3789i	0.882200	−	0.640956i	0.933833	+	0.357710i	$0.116442\pi$
$654$	5.69485	−	17.5270i	0.222686	−	0.685358i
$655$	1.82445	−	5.61507i	0.0712870	−	0.219399i
$656$	7.13979	−	5.18736i	0.278762	−	0.202532i
$657$	1.68800	+	1.22641i	0.0658552	+	0.0478466i
$658$	0.189612	+	0.583566i	0.00739185	+	0.0227498i
$659$	2.09110			0.0814577			0.0407288	−	0.999170i	$-0.487032\pi$
$659$	2.09110			0.0814577			0.0407288	+	0.999170i	$0.487032\pi$
$660$	−1.86768	−	0.410688i	−0.0726993	−	0.0159860i
$661$	−30.7967			−1.19785			−0.598926	−	0.800804i	$-0.704406\pi$
$661$	−30.7967			−1.19785			−0.598926	+	0.800804i	$0.704406\pi$
$662$	5.80945	+	17.8796i	0.225791	+	0.694912i
$663$	−1.48962	−	1.08227i	−0.0578519	−	0.0420318i
$664$	−2.01608	+	1.46477i	−0.0782392	+	0.0568441i
$665$	0.0432641	−	0.133153i	0.00167771	−	0.00516346i
$666$	1.45468	−	4.47704i	0.0563676	−	0.173482i
$667$	1.94227	−	1.41115i	0.0752052	−	0.0546398i
$668$	0.130328	+	0.0946887i	0.00504253	+	0.00366362i
$669$	−1.44709	−	4.45369i	−0.0559477	−	0.172189i
$670$	2.73566			0.105688
$671$	22.9764	+	5.05234i	0.886995	+	0.195043i
$672$	−0.844284			−0.0325689
$673$	−4.28893	−	13.2000i	−0.165326	−	0.508821i	0.833734	−	0.552166i	$-0.186199\pi$
$673$	−4.28893	−	13.2000i	−0.165326	−	0.508821i	−0.999060	+	0.0433450i	$0.986199\pi$
$674$	−28.5574	−	20.7482i	−1.09999	−	0.799190i
$675$	−3.06572	+	2.22738i	−0.118000	+	0.0857317i
$676$	−0.161938	+	0.498393i	−0.00622838	+	0.0191690i
$677$	5.55141	−	17.0855i	0.213358	−	0.656649i	−0.785908	−	0.618344i	$-0.787804\pi$
$677$	5.55141	−	17.0855i	0.213358	−	0.656649i	0.999266	−	0.0383054i	$-0.0121960\pi$
$678$	10.6519	−	7.73905i	0.409083	−	0.297216i
$679$	1.76650	+	1.28343i	0.0677919	+	0.0492537i
$680$	1.91967	+	5.90813i	0.0736159	+	0.226566i
$681$	−12.0858			−0.463129
$682$	−4.30065	−	4.84421i	−0.164681	−	0.185494i
$683$	9.13938			0.349709			0.174854	−	0.984594i	$-0.444055\pi$
$683$	9.13938			0.349709			0.174854	+	0.984594i	$0.444055\pi$
$684$	0.0702977	+	0.216354i	0.00268790	+	0.00827251i
$685$	13.9619	+	10.1439i	0.533455	+	0.387578i
$686$	4.00874	−	2.91252i	0.153054	−	0.111201i
$687$	4.39525	−	13.5272i	0.167689	−	0.516094i
$688$	−0.688977	+	2.12045i	−0.0262670	+	0.0808415i
$689$	0.122131	−	0.0887331i	0.00465281	−	0.00338046i
$690$	−2.80054	−	2.03471i	−0.106615	−	0.0774600i
$691$	2.97021	+	9.14138i	0.112992	+	0.347755i	0.991523	−	0.129931i	$-0.0414757\pi$
$691$	2.97021	+	9.14138i	0.112992	+	0.347755i	−0.878531	+	0.477686i	$0.841476\pi$
$692$	−9.02811			−0.343197
$693$	0.491988	−	0.838522i	0.0186891	−	0.0318528i
$694$	40.9997			1.55633
$695$	−0.605795	−	1.86444i	−0.0229791	−	0.0707224i
$696$	−2.29981	−	1.67091i	−0.0871739	−	0.0633356i
$697$	−4.91027	+	3.56752i	−0.185990	+	0.135129i
$698$	7.94144	−	24.4412i	0.300588	−	0.925115i
$699$	4.29512	−	13.2190i	0.162456	−	0.499989i
$700$	0.470931	−	0.342151i	0.0177995	−	0.0129321i
$701$	−14.1365	−	10.2708i	−0.533929	−	0.387922i	0.287896	−	0.957662i	$-0.407044\pi$
$701$	−14.1365	−	10.2708i	−0.533929	−	0.387922i	−0.821825	+	0.569739i	$0.807044\pi$
$702$	−0.375422	−	1.15543i	−0.0141694	−	0.0436089i
$703$	1.68206			0.0634399
$704$	26.9090	−	11.7554i	1.01417	−	0.443048i
$705$	−1.89575			−0.0713981
$706$	5.14466	+	15.8336i	0.193622	+	0.595907i
$707$	2.86318	+	2.08022i	0.107681	+	0.0782347i
$708$	1.62213	−	1.17855i	0.0609633	−	0.0442924i
$709$	−8.73186	+	26.8739i	−0.327932	+	1.00927i	0.642168	+	0.766564i	$0.278035\pi$
$709$	−8.73186	+	26.8739i	−0.327932	+	1.00927i	−0.970100	+	0.242707i	$0.921965\pi$
$710$	5.50398	−	16.9395i	0.206561	−	0.635728i
$711$	−4.27189	+	3.10371i	−0.160208	+	0.116398i
$712$	−27.0380	−	19.6442i	−1.01329	−	0.736199i
$713$	1.28656	+	3.95962i	0.0481820	+	0.148289i
$714$	−0.655711			−0.0245394
$715$	0.355996	+	3.63173i	0.0133135	+	0.135819i
$716$	2.79953			0.104623
$717$	0.769857	+	2.36937i	0.0287508	+	0.0884859i
$718$	6.87976	+	4.99844i	0.256750	+	0.186540i
$719$	1.34976	−	0.980656i	0.0503375	−	0.0365723i	−0.562332	−	0.826912i	$-0.690096\pi$
$719$	1.34976	−	0.980656i	0.0503375	−	0.0365723i	0.612669	+	0.790339i	$0.290096\pi$
$720$	−0.910274	+	2.80154i	−0.0339239	+	0.104407i
$721$	0.882398	−	2.71574i	0.0328622	−	0.101139i
$722$	−18.4893	+	13.4332i	−0.688099	+	0.499933i
$723$	4.97432	+	3.61406i	0.184997	+	0.134408i
$724$	−2.37287	−	7.30293i	−0.0881868	−	0.271411i
$725$	3.51297			0.130469
$726$	−1.58304	+	13.2697i	−0.0587520	+	0.492485i
$727$	−3.96788			−0.147160			−0.0735802	−	0.997289i	$-0.523443\pi$
$727$	−3.96788			−0.147160			−0.0735802	+	0.997289i	$0.523443\pi$
$728$	0.277763	+	0.854867i	0.0102946	+	0.0316835i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−2.25633	+	1.63932i	−0.0835107	+	0.0606741i
$731$	0.473832	−	1.45831i	0.0175253	−	0.0539374i
$732$	−1.14865	+	3.53518i	−0.0424553	+	0.130664i
$733$	−21.3196	+	15.4896i	−0.787458	+	0.572122i	−0.907208	−	0.420682i	$-0.861791\pi$
$733$	−21.3196	+	15.4896i	−0.787458	+	0.572122i	0.119750	+	0.992804i	$0.461791\pi$
$734$	24.6680	+	17.9224i	0.910513	+	0.661526i
$735$	2.35077	+	7.23492i	0.0867094	+	0.266864i
$736$	−7.45903			−0.274944
$737$	0.662191	+	6.75541i	0.0243921	+	0.248839i
$738$	−4.00468			−0.147414
$739$	0.0348869	+	0.107371i	0.00128333	+	0.00394970i	0.951696	−	0.307041i	$-0.0993390\pi$
$739$	0.0348869	+	0.107371i	0.00128333	+	0.00394970i	−0.950413	+	0.310991i	$0.899339\pi$
$740$	−1.80744	−	1.31318i	−0.0664429	−	0.0482736i
$741$	0.351197	−	0.255159i	0.0129015	−	0.00937352i
$742$	0.0166129	−	0.0511292i	0.000609878	−	0.00187701i
$743$	−8.68556	+	26.7314i	−0.318642	+	0.980680i	0.655587	+	0.755120i	$0.272421\pi$
$743$	−8.68556	+	26.7314i	−0.318642	+	0.980680i	−0.974229	+	0.225560i	$0.927579\pi$
$744$	3.98828	−	2.89766i	0.146217	−	0.106233i
$745$	16.8731	+	12.2590i	0.618181	+	0.449135i
$746$	−10.2480	−	31.5400i	−0.375204	−	1.15476i
$747$	0.812675			0.0297342
$748$	−2.93259	+	1.28112i	−0.107226	+	0.0468425i
$749$	−2.93152			−0.107115
$750$	−3.63056	−	11.1737i	−0.132569	−	0.408007i
$751$	−6.70723	−	4.87309i	−0.244750	−	0.177822i	0.458647	−	0.888619i	$-0.348334\pi$
$751$	−6.70723	−	4.87309i	−0.244750	−	0.177822i	−0.703397	+	0.710797i	$0.748334\pi$
$752$	3.73200	−	2.71146i	0.136092	−	0.0988767i
$753$	4.58627	−	14.1151i	0.167133	−	0.514382i
$754$	−0.348032	+	1.07113i	−0.0126746	+	0.0390084i
$755$	−15.1328	+	10.9946i	−0.550739	+	0.400135i
$756$	0.124275	+	0.0902908i	0.00451982	+	0.00328384i
$757$	10.7801	+	33.1778i	0.391810	+	1.20587i	0.931418	+	0.363950i	$0.118572\pi$
$757$	10.7801	+	33.1778i	0.391810	+	1.20587i	−0.539609	+	0.841916i	$0.681428\pi$
$758$	−28.7780			−1.04527
$759$	4.34659	−	7.40813i	0.157771	−	0.268898i
$760$	−1.46460			−0.0531268
$761$	0.659597	+	2.03003i	0.0239104	+	0.0735886i	0.962300	−	0.271991i	$-0.0876822\pi$
$761$	0.659597	+	2.03003i	0.0239104	+	0.0735886i	−0.938389	+	0.345580i	$0.887682\pi$
$762$	6.17174	+	4.48403i	0.223579	+	0.162439i
$763$	3.59732	−	2.61361i	0.130232	−	0.0946190i
$764$	−2.84453	+	8.75455i	−0.102911	+	0.316729i
$765$	0.626026	−	1.92671i	0.0226340	−	0.0696603i
$766$	−5.97632	+	4.34205i	−0.215933	+	0.156885i
$767$	−3.09542	−	2.24895i	−0.111769	−	0.0812050i
$768$	3.59637	+	11.0685i	0.129773	+	0.399400i
$769$	−44.3782			−1.60032			−0.800160	−	0.599787i	$-0.795252\pi$
$769$	−44.3782			−1.60032			−0.800160	+	0.599787i	$0.795252\pi$
$770$	0.862765	+	0.971808i	0.0310919	+	0.0350215i
$771$	22.7267			0.818481
$772$	−2.72047	−	8.37273i	−0.0979117	−	0.301341i
$773$	−16.8434	−	12.2375i	−0.605815	−	0.440151i	0.242123	−	0.970246i	$-0.422156\pi$
$773$	−16.8434	−	12.2375i	−0.605815	−	0.440151i	−0.847938	+	0.530095i	$0.822156\pi$
$774$	0.818503	−	0.594677i	0.0294205	−	0.0213752i
$775$	−1.88257	+	5.79396i	−0.0676240	+	0.208125i
$776$	7.05849	−	21.7238i	0.253385	−	0.779839i
$777$	0.918890	−	0.667613i	0.0329650	−	0.0239505i
$778$	−0.977922	−	0.710502i	−0.0350602	−	0.0254727i
$779$	−0.442188	−	1.36091i	−0.0158430	−	0.0487598i
$780$	−0.576580			−0.0206449
$781$	43.1625	+	9.49110i	1.54448	+	0.339618i
$782$	−5.79304			−0.207159
$783$	0.286472	+	0.881671i	0.0102377	+	0.0315083i
$784$	−14.9757	−	10.8805i	−0.534848	−	0.388590i
$785$	2.58881	−	1.88088i	0.0923985	−	0.0671315i
$786$	2.01453	−	6.20010i	0.0718560	−	0.221150i
$787$	−4.95349	+	15.2453i	−0.176573	+	0.543435i	−0.999702	−	0.0244192i	$-0.992226\pi$
$787$	−4.95349	+	15.2453i	−0.176573	+	0.543435i	0.823129	+	0.567854i	$0.192226\pi$
$788$	−4.19627	+	3.04877i	−0.149486	+	0.108608i
$789$	−11.2748	−	8.19164i	−0.401394	−	0.291630i
$790$	−2.18110	−	6.71273i	−0.0776000	−	0.238828i
$791$	3.17680			0.112954
$792$	−9.93290	−	2.18417i	−0.352950	−	0.0776111i
$793$	7.09316			0.251885
$794$	5.59347	+	17.2149i	0.198505	+	0.610935i
$795$	0.134375	+	0.0976291i	0.00476579	+	0.00346255i
$796$	−6.87294	+	4.99349i	−0.243605	+	0.176989i
$797$	7.63984	−	23.5130i	0.270617	−	0.832873i	−0.719729	−	0.694255i	$-0.755734\pi$
$797$	7.63984	−	23.5130i	0.270617	−	0.832873i	0.990346	−	0.138618i	$-0.0442660\pi$
$798$	0.0477718	−	0.147026i	0.00169110	−	0.00520468i
$799$	−2.56662	+	1.86476i	−0.0908005	+	0.0659705i
$800$	−8.83003	−	6.41539i	−0.312189	−	0.226818i
$801$	3.36795	+	10.3655i	0.119001	+	0.366246i
$802$	14.1940			0.501208
$803$	−4.59429	−	5.17495i	−0.162129	−	0.182620i
$804$	−1.07250			−0.0378242
$805$	−0.258100	−	0.794349i	−0.00909682	−	0.0279971i
$806$	−1.58012	−	1.14802i	−0.0556572	−	0.0404373i
$807$	−21.5440	+	15.6526i	−0.758385	+	0.550999i
$808$	11.4406	−	35.2104i	0.402478	−	1.23870i
$809$	5.13051	−	15.7901i	0.180379	−	0.555150i	−0.819459	−	0.573138i	$-0.805726\pi$
$809$	5.13051	−	15.7901i	0.180379	−	0.555150i	0.999838	+	0.0179876i	$0.00572594\pi$
$810$	1.08140	−	0.785686i	0.0379967	−	0.0276062i
$811$	32.5622	+	23.6578i	1.14341	+	0.830739i	0.987591	−	0.157046i	$-0.0501971\pi$
$811$	32.5622	+	23.6578i	1.14341	+	0.830739i	0.155823	+	0.987785i	$0.450197\pi$
$812$	−0.0440055	−	0.135435i	−0.00154429	−	0.00475284i
$813$	24.6747			0.865379
$814$	−7.90096	+	13.4660i	−0.276928	+	0.471984i
$815$	−14.3989			−0.504370
$816$	1.52333	+	4.68834i	0.0533274	+	0.164125i
$817$	0.292467	+	0.212489i	0.0102321	+	0.00743407i
$818$	−5.51990	+	4.01044i	−0.192999	+	0.140222i
$819$	0.0905818	−	0.278782i	0.00316519	−	0.00974144i
$820$	−0.587317	+	1.80758i	−0.0205100	+	0.0631233i
$821$	−33.6986	+	24.4835i	−1.17609	+	0.854480i	−0.991725	−	0.128378i	$-0.959023\pi$
$821$	−33.6986	+	24.4835i	−1.17609	+	0.854480i	−0.184365	+	0.982858i	$0.559023\pi$
$822$	15.4165	+	11.2008i	0.537714	+	0.390672i
$823$	−3.19074	−	9.82009i	−0.111222	−	0.342307i	0.879918	−	0.475125i	$-0.157597\pi$
$823$	−3.19074	−	9.82009i	−0.111222	−	0.342307i	−0.991140	+	0.132818i	$0.957597\pi$
$824$	−29.8715			−1.04062
$825$	11.5171	−	5.03134i	0.400974	−	0.175169i
$826$	−1.36257			−0.0474097
$827$	−1.89950	−	5.84606i	−0.0660520	−	0.203287i	0.912583	−	0.408891i	$-0.134084\pi$
$827$	−1.89950	−	5.84606i	−0.0660520	−	0.203287i	−0.978635	+	0.205603i	$0.934084\pi$
$828$	1.09793	+	0.797696i	0.0381559	+	0.0277219i
$829$	−33.9470	+	24.6639i	−1.17903	+	0.856614i	−0.992062	−	0.125752i	$-0.959866\pi$
$829$	−33.9470	+	24.6639i	−1.17903	+	0.856614i	−0.186967	+	0.982366i	$0.559866\pi$
$830$	−0.335683	+	1.03313i	−0.0116517	+	0.0358604i
$831$	−5.54792	+	17.0747i	−0.192455	+	0.592316i
$832$	7.16286	−	5.20412i	0.248327	−	0.180420i
$833$	10.2993	+	7.48289i	0.356850	+	0.259267i
$834$	−0.668912	−	2.05870i	−0.0231625	−	0.0712869i
$835$	0.338226			0.0117048
$836$	−0.0736055	−	0.750894i	−0.00254570	−	0.0259702i
$837$	−1.60766			−0.0555689
$838$	−5.04277	−	15.5201i	−0.174200	−	0.536132i
$839$	−0.157655	−	0.114543i	−0.00544287	−	0.00395447i	0.585060	−	0.810990i	$-0.301071\pi$
$839$	−0.157655	−	0.114543i	−0.00544287	−	0.00395447i	−0.590503	+	0.807035i	$0.701071\pi$
$840$	−0.800099	+	0.581306i	−0.0276060	+	0.0200570i
$841$	−8.69592	+	26.7633i	−0.299859	+	0.922872i
$842$	7.77077	−	23.9160i	0.267798	−	0.824198i
$843$	−8.66202	+	6.29332i	−0.298336	+	0.216754i
$844$	−2.91787	−	2.11996i	−0.100437	−	0.0729720i
$845$	0.339998	+	1.04640i	0.0116963	+	0.0359974i
$846$	−2.09327			−0.0719680
$847$	−2.19093	+	2.36574i	−0.0752813	+	0.0812876i
$848$	−0.404169			−0.0138792
$849$	−7.81008	−	24.0370i	−0.268041	−	0.824946i
$850$	−6.85782	−	4.98250i	−0.235221	−	0.170898i
$851$	8.11816	−	5.89819i	0.278287	−	0.202187i
$852$	−2.15780	+	6.64104i	−0.0739252	+	0.227518i
$853$	3.04620	−	9.37523i	0.104300	−	0.321002i	−0.885266	−	0.465086i	$-0.846024\pi$
$853$	3.04620	−	9.37523i	0.104300	−	0.321002i	0.989565	+	0.144084i	$0.0460235\pi$
$854$	2.04359	−	1.48475i	0.0699301	−	0.0508072i
$855$	0.386406	+	0.280741i	0.0132148	+	0.00960113i
$856$	9.47654	+	29.1658i	0.323902	+	0.996866i
$857$	−54.3048			−1.85502			−0.927508	−	0.373804i	$-0.878053\pi$
$857$	−54.3048			−1.85502			−0.927508	+	0.373804i	$0.878053\pi$
$858$	0.393087	+	4.01012i	0.0134198	+	0.136903i
$859$	30.5300			1.04167			0.520835	−	0.853658i	$-0.325621\pi$
$859$	30.5300			1.04167			0.520835	+	0.853658i	$0.325621\pi$
$860$	−0.148377	−	0.456658i	−0.00505962	−	0.0155719i
$861$	−0.781713	−	0.567948i	−0.0266407	−	0.0193556i
$862$	28.1651	−	20.4631i	0.959307	−	0.696977i
$863$	−11.5664	+	35.5977i	−0.393724	+	1.21176i	0.536226	+	0.844074i	$0.319849\pi$
$863$	−11.5664	+	35.5977i	−0.393724	+	1.21176i	−0.929950	+	0.367685i	$0.880151\pi$
$864$	0.890045	−	2.73928i	0.0302799	−	0.0931921i
$865$	−15.3349	+	11.1415i	−0.521404	+	0.378822i
$866$	−0.405116	−	0.294334i	−0.0137664	−	0.0100019i
$867$	4.20564	+	12.9436i	0.142831	+	0.439589i
$868$	0.246956			0.00838222
$869$	16.0484	−	7.01085i	0.544404	−	0.237827i
$870$	−1.23917			−0.0420118
$871$	0.632433	+	1.94643i	0.0214292	+	0.0659522i
$872$	−37.6317	−	27.3411i	−1.27437	−	0.925885i
$873$	−6.02634	+	4.37839i	−0.203961	+	0.148186i
$874$	0.422051	−	1.29894i	0.0142761	−	0.0439373i
$875$	0.875983	−	2.69600i	0.0296136	−	0.0911414i
$876$	0.884584	−	0.642688i	0.0298873	−	0.0217144i
$877$	34.4343	+	25.0180i	1.16277	+	0.844798i	0.990125	−	0.140187i	$-0.0447703\pi$
$877$	34.4343	+	25.0180i	1.16277	+	0.844798i	0.172640	+	0.984985i	$0.444770\pi$
$878$	8.93931	+	27.5124i	0.301687	+	0.928497i
$879$	19.6700			0.663453
$880$	4.94408	−	8.42647i	0.166665	−	0.284056i
$881$	21.9666			0.740075			0.370038	−	0.929017i	$-0.379345\pi$
$881$	21.9666			0.740075			0.370038	+	0.929017i	$0.379345\pi$
$882$	2.59569	+	7.98873i	0.0874016	+	0.268994i
$883$	15.5157	+	11.2728i	0.522146	+	0.379361i	0.817412	−	0.576054i	$-0.195408\pi$
$883$	15.5157	+	11.2728i	0.522146	+	0.379361i	−0.295266	+	0.955415i	$0.595408\pi$
$884$	−0.780621	+	0.567154i	−0.0262551	+	0.0190755i
$885$	1.30088	−	4.00370i	0.0437286	−	0.134583i
$886$	−11.9505	+	36.7798i	−0.401485	+	1.23564i
$887$	8.74505	−	6.35365i	0.293630	−	0.213335i	−0.431211	−	0.902251i	$-0.641913\pi$
$887$	8.74505	−	6.35365i	0.293630	−	0.213335i	0.724841	+	0.688917i	$0.241913\pi$
$888$	−9.61254	−	6.98392i	−0.322576	−	0.234365i
$889$	0.568793	+	1.75056i	0.0190767	+	0.0587121i
$890$	−14.5685			−0.488336
$891$	2.20193	+	2.48022i	0.0737674	+	0.0830907i
$892$	−2.45403			−0.0821669
$893$	−0.231134	−	0.711356i	−0.00773459	−	0.0238046i
$894$	18.6310	+	13.5362i	0.623115	+	0.452720i
$895$	4.75521	−	3.45486i	0.158949	−	0.115483i
$896$	0.452536	−	1.39276i	0.0151182	−	0.0465289i
$897$	0.800268	−	2.46297i	0.0267202	−	0.0822362i
$898$	−27.8002	+	20.1980i	−0.927705	+	0.674017i
$899$	1.20574	+	0.876019i	0.0402135	+	0.0292169i
$900$	0.613653	+	1.88863i	0.0204551	+	0.0629544i
$901$	0.277961			0.00926021
$902$	12.9721	+	2.85247i	0.431924	+	0.0949768i
$903$	0.244109			0.00812345
$904$	−10.2695	−	31.6061i	−0.341557	−	1.05120i
$905$	−13.0430	−	9.47626i	−0.433562	−	0.315002i
$906$	−16.7095	+	12.1401i	−0.555135	+	0.403329i
$907$	4.06015	−	12.4959i	0.134815	−	0.414918i	−0.860746	−	0.509035i	$-0.830003\pi$
$907$	4.06015	−	12.4959i	0.134815	−	0.414918i	0.995561	+	0.0941163i	$0.0300025\pi$
$908$	−1.95715	+	6.02348i	−0.0649502	+	0.199896i
$909$	−9.76763	+	7.09660i	−0.323972	+	0.235379i
$910$	0.316991	+	0.230307i	0.0105082	+	0.00763462i
$911$	2.41370	+	7.42860i	0.0799694	+	0.246120i	0.983046	−	0.183359i	$-0.0586971\pi$
$911$	2.41370	+	7.42860i	0.0799694	+	0.246120i	−0.903077	+	0.429479i	$0.858697\pi$
$912$	−1.16222			−0.0384851
$913$	−2.63245	−	0.578855i	−0.0871213	−	0.0191573i
$914$	38.8667			1.28560
$915$	2.41166	+	7.42232i	0.0797269	+	0.245374i
$916$	−6.03010	−	4.38113i	−0.199240	−	0.144756i
$917$	1.27254	−	0.924555i	0.0420230	−	0.0305315i
$918$	0.691251	−	2.12745i	0.0228147	−	0.0702164i
$919$	−14.5141	+	44.6699i	−0.478777	+	1.47352i	0.362019	+	0.932171i	$0.382088\pi$
$919$	−14.5141	+	44.6699i	−0.478777	+	1.47352i	−0.840796	+	0.541353i	$0.817912\pi$
$920$	−7.06867	+	5.13569i	−0.233047	+	0.169319i
$921$	−4.04550	−	2.93923i	−0.133304	−	0.0968509i
$922$	10.6102	+	32.6548i	0.349427	+	1.07543i
$923$	13.3249			0.438594
$924$	−0.338242	−	0.380992i	−0.0111274	−	0.0125337i
$925$	14.6832			0.482782
$926$	10.4825	+	32.2619i	0.344477	+	1.06019i
$927$	7.88099	+	5.72587i	0.258846	+	0.188062i
$928$	−2.16017	+	1.56945i	−0.0709109	+	0.0515198i
$929$	11.3544	−	34.9453i	0.372527	−	1.14652i	−0.572606	−	0.819831i	$-0.694067\pi$
$929$	11.3544	−	34.9453i	0.372527	−	1.14652i	0.945132	−	0.326688i	$-0.105933\pi$
$930$	0.664060	−	2.04377i	0.0217754	−	0.0670178i
$931$	−2.42820	+	1.76419i	−0.0795811	+	0.0578191i
$932$	−5.89273	−	4.28132i	−0.193023	−	0.140239i
$933$	3.90896	+	12.0306i	0.127974	+	0.393863i
$934$	−25.1980			−0.824503
$935$	−3.40021	+	5.79516i	−0.111199	+	0.189522i
$936$	−3.06643			−0.100230
$937$	8.90160	+	27.3963i	0.290803	+	0.894999i	0.984599	+	0.174828i	$0.0559368\pi$
$937$	8.90160	+	27.3963i	0.290803	+	0.894999i	−0.693796	+	0.720171i	$0.744063\pi$
$938$	0.589638	+	0.428397i	0.0192524	+	0.0139877i
$939$	19.6785	−	14.2973i	0.642184	−	0.466574i
$940$	−0.306994	+	0.944829i	−0.0100130	+	0.0308169i
$941$	−2.42044	+	7.44936i	−0.0789042	+	0.242842i	−0.982726	−	0.185067i	$-0.940750\pi$
$941$	−2.42044	+	7.44936i	−0.0789042	+	0.242842i	0.903822	+	0.427909i	$0.140750\pi$
$942$	2.85853	−	2.07685i	0.0931361	−	0.0676673i
$943$	−6.90624	−	5.01768i	−0.224898	−	0.163398i
$944$	3.16549	+	9.74237i	0.103028	+	0.317087i
$945$	0.322517			0.0104915
$946$	−3.07490	+	1.34329i	−0.0999738	+	0.0436743i
$947$	15.1344			0.491802			0.245901	−	0.969295i	$-0.420916\pi$
$947$	15.1344			0.491802			0.245901	+	0.969295i	$0.420916\pi$
$948$	0.855087	+	2.63169i	0.0277719	+	0.0854732i
$949$	−1.68800	−	1.22641i	−0.0547949	−	0.0398108i
$950$	1.61682	−	1.17469i	0.0524567	−	0.0381120i
$951$	7.15074	−	22.0077i	0.231879	−	0.713649i
$952$	−0.511436	+	1.57404i	−0.0165757	+	0.0510149i
$953$	3.10223	−	2.25390i	0.100491	−	0.0730109i	−0.536405	−	0.843961i	$-0.680218\pi$
$953$	3.10223	−	2.25390i	0.100491	−	0.0730109i	0.636896	+	0.770950i	$0.280218\pi$
$954$	0.148375	+	0.107801i	0.00480383	+	0.00349019i
$955$	5.97224	+	18.3807i	0.193257	+	0.594785i
$956$	1.30555			0.0422245
$957$	−0.299952	−	3.05999i	−0.00969607	−	0.0989154i
$958$	42.7151			1.38006
$959$	1.42080	+	4.37278i	0.0458801	+	0.141204i
$960$	7.88097	+	5.72586i	0.254357	+	0.184801i
$961$	22.9886	−	16.7022i	0.741567	−	0.538780i
$962$	−1.45468	+	4.47704i	−0.0469007	+	0.144345i
$963$	3.09041	−	9.51131i	0.0995871	−	0.306498i
$964$	2.60675	−	1.89392i	0.0839578	−	0.0609989i
$965$	−14.9536	−	10.8644i	−0.481374	−	0.349739i
$966$	−0.284991	−	0.877112i	−0.00916944	−	0.0282206i
$967$	20.1852			0.649112			0.324556	−	0.945866i	$-0.394785\pi$
$967$	20.1852			0.649112			0.324556	+	0.945866i	$0.394785\pi$
$968$	30.6193	+	14.1501i	0.984141	+	0.454801i
$969$	0.799299			0.0256772
$970$	−3.07687	−	9.46963i	−0.0987923	−	0.304051i
$971$	31.3414	+	22.7709i	1.00579	+	0.730752i	0.963323	−	0.268346i	$-0.0864770\pi$
$971$	31.3414	+	22.7709i	1.00579	+	0.730752i	0.0424710	+	0.999098i	$0.486477\pi$
$972$	−0.423959	+	0.308024i	−0.0135985	+	0.00987987i
$973$	0.161395	−	0.496723i	0.00517409	−	0.0159242i
$974$	−13.2912	+	40.9062i	−0.425879	+	1.31072i
$975$	3.06572	−	2.22738i	0.0981816	−	0.0713331i
$976$	−15.3636	−	11.1623i	−0.491778	−	0.357298i
$977$	13.5230	+	41.6195i	0.432639	+	1.33153i	0.895486	+	0.445089i	$0.146828\pi$
$977$	13.5230	+	41.6195i	0.432639	+	1.33153i	−0.462847	+	0.886438i	$0.653172\pi$
$978$	−15.8991			−0.508396
$979$	−3.52642	−	35.9752i	−0.112705	−	1.14977i
$980$	3.98652			0.127345
$981$	4.68754	+	14.4268i	0.149662	+	0.460612i
$982$	−41.6672	−	30.2730i	−1.32965	−	0.966049i
$983$	−8.66083	+	6.29246i	−0.276238	+	0.200698i	−0.717275	−	0.696790i	$-0.754611\pi$
$983$	−8.66083	+	6.29246i	−0.276238	+	0.200698i	0.441037	+	0.897489i	$0.354611\pi$
$984$	−3.12354	+	9.61327i	−0.0995748	+	0.306460i
$985$	−3.36524	+	10.3571i	−0.107225	+	0.330006i
$986$	−1.67769	+	1.21891i	−0.0534285	+	0.0388181i
$987$	−0.408605	−	0.296869i	−0.0130061	−	0.00944945i
$988$	−0.0702977	−	0.216354i	−0.00223647	−	0.00688314i
$989$	2.15665			0.0685773
$990$	−4.06256	+	1.77476i	−0.129117	+	0.0564055i
$991$	23.4821			0.745935			0.372967	−	0.927844i	$-0.378340\pi$
$991$	23.4821			0.745935			0.372967	+	0.927844i	$0.378340\pi$
$992$	−1.43089	−	4.40383i	−0.0454308	−	0.139822i
$993$	−12.5191	−	9.09566i	−0.397282	−	0.288642i
$994$	3.83899	−	2.78919i	0.121765	−	0.0884678i
$995$	−5.51182	+	16.9636i	−0.174736	+	0.537784i
$996$	0.131603	−	0.405032i	0.00417000	−	0.0128339i
$997$	2.47208	−	1.79607i	0.0782915	−	0.0568821i	−0.547951	−	0.836510i	$-0.684592\pi$
$997$	2.47208	−	1.79607i	0.0782915	−	0.0568821i	0.626243	+	0.779628i	$0.284592\pi$
$998$	26.4781	+	19.2375i	0.838151	+	0.608952i
$999$	1.19737	+	3.68514i	0.0378832	+	0.116593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.313.1	yes	20
11.3	even	5		4719.2.a.bn.1.3		10
11.8	odd	10		4719.2.a.bi.1.8		10
11.9	even	5	inner	429.2.n.b.196.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.196.1	✓	20	11.9	even	5	inner
429.2.n.b.313.1	yes	20	1.1	even	1	trivial
4719.2.a.bi.1.8		10	11.8	odd	10
4719.2.a.bn.1.3		10	11.3	even	5

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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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.375422 - 1.15543i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.423959 - 0.308024i) q^{4} +(0.339998 - 1.04640i) q^{5} +(0.375422 - 1.15543i) q^{6} +(0.237146 - 0.172297i) q^{7} +(-2.48080 - 1.80240i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.375422 - 1.15543i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.423959 - 0.308024i) q^{4} +(0.339998 - 1.04640i) q^{5} +(0.375422 - 1.15543i) q^{6} +(0.237146 - 0.172297i) q^{7} +(-2.48080 - 1.80240i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.33669 q^{10} +(-0.323558 - 3.30080i) q^{11} +0.524042 q^{12} +(-0.309017 - 0.951057i) q^{13} +(-0.288107 - 0.209322i) q^{14} +(0.890125 - 0.646714i) q^{15} +(-0.827330 + 2.54626i) q^{16} +(0.568982 - 1.75115i) q^{17} +(0.982867 - 0.714095i) q^{18} +(0.351197 + 0.255159i) q^{19} +(-0.178173 - 0.548360i) q^{20} +0.293129 q^{21} +(-3.69238 + 1.61304i) q^{22} +2.58972 q^{23} +(-0.947580 - 2.91635i) q^{24} +(3.06572 + 2.22738i) q^{25} +(-0.982867 + 0.714095i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.0474687 - 0.146094i) q^{28} +(0.749994 - 0.544902i) q^{29} +(-1.08140 - 0.785686i) q^{30} +(0.496795 + 1.52898i) q^{31} -2.88025 q^{32} +(1.67840 - 2.86059i) q^{33} -2.23694 q^{34} +(-0.0996632 - 0.306732i) q^{35} +(0.423959 + 0.308024i) q^{36} +(3.13476 - 2.27754i) q^{37} +(0.162972 - 0.501576i) q^{38} +(0.309017 - 0.951057i) q^{39} +(-2.72951 + 1.98311i) q^{40} +(-2.66679 - 1.93754i) q^{41} +(-0.110047 - 0.338690i) q^{42} +0.832771 q^{43} +(-1.15390 - 1.29974i) q^{44} +1.10026 q^{45} +(-0.972237 - 2.99224i) q^{46} +(-1.39394 - 1.01276i) q^{47} +(-2.16598 + 1.57368i) q^{48} +(-2.13657 + 6.57568i) q^{49} +(1.42264 - 4.37843i) q^{50} +(1.48962 - 1.08227i) q^{51} +(-0.423959 - 0.308024i) q^{52} +(0.0466498 + 0.143573i) q^{53} +1.21489 q^{54} +(-3.56399 - 0.783693i) q^{55} -0.898861 q^{56} +(0.134145 + 0.412857i) q^{57} +(-0.911160 - 0.661997i) q^{58} +(3.09542 - 2.24895i) q^{59} +(0.178173 - 0.548360i) q^{60} +(-2.19191 + 6.74600i) q^{61} +(1.58012 - 1.14802i) q^{62} +(0.237146 + 0.172297i) q^{63} +(2.73597 + 8.42044i) q^{64} -1.10026 q^{65} +(-3.93532 - 0.865346i) q^{66} -2.04660 q^{67} +(-0.298171 - 0.917674i) q^{68} +(2.09513 + 1.52220i) q^{69} +(-0.316991 + 0.230307i) q^{70} +(-4.11762 + 12.6727i) q^{71} +(0.947580 - 2.91635i) q^{72} +(1.68800 - 1.22641i) q^{73} +(-3.80839 - 2.76696i) q^{74} +(1.17100 + 3.60397i) q^{75} +0.227488 q^{76} +(-0.645449 - 0.727026i) q^{77} -1.21489 q^{78} +(1.63172 + 5.02190i) q^{79} +(2.38313 + 1.73144i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.23752 + 3.80868i) q^{82} +(0.251130 - 0.772900i) q^{83} +(0.124275 - 0.0902908i) q^{84} +(-1.63896 - 1.19077i) q^{85} +(-0.312640 - 0.962208i) q^{86} +0.927043 q^{87} +(-5.14670 + 8.77181i) q^{88} +10.8989 q^{89} +(-0.413060 - 1.27127i) q^{90} +(-0.237146 - 0.172297i) q^{91} +(1.09793 - 0.797696i) q^{92} +(-0.496795 + 1.52898i) q^{93} +(-0.646855 + 1.99082i) q^{94} +(0.386406 - 0.280741i) q^{95} +(-2.33017 - 1.69297i) q^{96} +(2.30186 + 7.08439i) q^{97} +8.39984 q^{98} +(3.03927 - 1.32773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

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